1
1
1
2
0
1
1
1
2
2
1
1
1
1
2
0
2
2
1
1
0
1
1
1
1
1
2
1
1
2
2
1
1
0
1
1
1
0
1
1
0
0
2
1
0
1
1
2
1
2
2
2
1
0
1
1
0
1
1
1
1
1
2
2
1
3
0
0
0
1
1
1
1
2
2
3
1
0
1
1
0
1
0
1
1
2
1
1
0
1
2
1
1
1
1
0
2
1
1
1
1
1
1
2
1
1
1
1
2
2
1
2
2
1
2
0
1
1
0
2
0
1
1
1
0
1
0
1
2
1
2
2
1
1
2
1
2
1
2
1
2
2
2
2
2
1
2
1
1
1
1
1
1
1
1
1
2
2
1
2
1
1
2
1
1
1
2
1
1
1
1
1
0
1
0
1
1
1
1
1
1
0
1
0
1
2
2
0
1
1
0
0
1
1
2
1
1
0
1
1
1
2
0
1
1
1
1
0
1
1
1
1
2
1
0
1
1
1
1
1
1
1
1
1
2
1
1
1
2
0
0
1
1
1
1
1
1
1
0
1
2
1
1
2
1
2
0
1
1
1
1
1
1
1
1
0
1
1
2
0
1
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
0
1
2
1
1
1
1
1
1
1
1
1
1
1
0
0
0
1
1
1
1
2
2
1
2
1
1
2
2
1
1
1
0
1
1
1
1
1
1
2
2
1
0
1
2
1
1
0
2
1
1
1
2
0
2
1
2
2
1
1
1
1
1
2
2
1
1
2
0
1
1
2
2
1
1
0
1
1
1
2
1
1
0
1
0
1
1
1
1
1
2
1
0
2
2
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
2
1
0
0
0
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
0
0
1
1
1
1
1
0
1
1
1
1
1
2
2
1
0
1
0
2
1
1
1
1
2
1
2
1
2
0
1
1
1
2
1
2
1
1
1
2
2
2
1
1
1
1
2
1
2
1
0
1
1
2
1
1
1
1
2
2
2
1
0
1
1
1
1
1
2
1
0
1
1
1
1
2
1
0
1
1
2
2
2
1
1
2
1
1
1
1
1
1
2
1
0
1
1
2
1
1
1
1
2
2
1
2
1
1
0
2
2
0
1
1
1
2
1
1
1
4
1
1
2
1
2
1
2
1
1
1
1
0
2
1
2
1
1
1
0
2
0
1
1
2
1
1
3
1
1
0
1
1
1
1
1
2
2
2
1
1
1
2
2
1
2
1
0
0
0
1
2
1
1
1
2
1
1
1
1
1
0
2
1
1
1
1
1
1
1
1
2
1
1
1
1
0
1
0
1
0
1
2
1
1
1
1
1
1
2
1
2
2
2
1
1
0
2
1
1
2
1
1
1
0
1
1
1
0
2
1
1
1
2
2
2
2
1
1
1
0
2
1
2
2
1
2
2
1
1
1
1
1
1
1
0
1
0
2
1
2
1
1
1
1
1
0
1
1
2
1
2
1
2
1
2
0
2
1
1
0
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
0
1
2
1
2
0
1
2
0
2
2
1
2
2
1
1
1
2
1
2
1
1
1
1
0
1
1
2
1
1
0
0
2
1
2
2
2
2
2
1
1
1
1
2
1
1
1
1
2
0
1
2
2
0
1
2
0
1
1
1
2
2
2
2
2
0
1
1
2
1
1
0
2
2
1
1
1
2
1
1
1
0
0
2
2
1
2
2
2
1
1
2
1
2
2
1
2
1
2
2
1
1
1
1
1
2
1
2
0
2
2
2
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
2
3
1
1
2
1
0
1
1
0
0
1
0
1
1
3
1
0
1
1
1
2
0
1
1
1
1
0
1
2
2
1
1
2
2
1
1
0
2
1
1
1
2
1
0
2
2
2
2
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
1
1
1
2
1
1
2
1
1
2
0
1
2
1
0
1
1
2
1
2
1
1
1
2
2
1
1
1
1
1
0
0
1
1
1
1
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
1
2
1
1
1
1
0
1
2
0
1
1
1
2
1
0
2
2
1
1
1
2
0
1
1
1
1
1
0
1
1
2
1
1
1
1
2
0
2
2
0
1
2
1
1
0
0
2
2
1
2
1
2
1
1
1
1
2
2
0
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
0
2
1
1
1
1
1
2
2
2
1
1
3
2
1
1
1
0
2
1
0
2
2
1
1
1
2
1
0
1
1
1
1
2
1
3
1
2
2
0
0
2
0
1
1
0
1
2
1
1
0
1
1
0
1
0
1
0
2
1
1
2
0
1
1
1
1
1
2
2
0
1
1
2
2
1
0
2
2
1
1
1
1
1
2
2
1
3
1
0
1
1
1
1
0
0
1
0
2
1
0
1
2
1
1
1
2
1
1
0
1
2
2
1
0
1
1
2
2
2
1
2
2
1
2
1
2
2
2
1
2
1
1
1
1
2
2
1
2
1
0
1
1
1
1
1
1
2
2
0
0
0
2
1
2
1
1
1
1
2
1
1
1
1
2
1
0
0
1
1
1
1
1
1
1
1
1
1
1
0
0
2
2
1
0
1
1
1
1
1
1
1
1
1
0
2
0
1
1
1
0
1
1
1
2
0
1
1
1
1
1
1
2
1
0
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
0
1
0
1
2
1
1
1
1
2
1
1
2
0
1
1
2
1
1
1
1
2
1
1
0
1
1
1
2
0
1
1
1
2
1
1
1
1
1
0
0
1
0
2
0
2
1
0
1
1
2
1
1
1
1
0
2
1
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
2
2
1
1
1
1
1
2
1
0
1
1
0
1
1
1
2
1
1
2
1
1
1
1
1
1
1
3
1
1
1
1
2
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
2
1
1
0
2
1
1
2
1
2
2
1
1
1
1
1
1
1
1
3
1
1
2
1
1
1
2
2
1
2
1
2
1
2
1
1
1
2
0
0
0
1
1
1
1
1
2
1
2
2
2
2
1
1
1
1
1
2
0
1
1
1
2
1
1
2
2
2
0
0
0
1
1
0
1
1
1
1
0
1
0
0
1
0
1
2
1
0
0
1
0
1
1
1
1
2
1
0
1
1
2
1
1
1
1
1
2
0
1
0
2
0
1
0
1
2
1
1
0
1
1
1
2
1
1
1
1
1
1
0
1
1
1
1
0
1
1
1
2
1
3
2
1
1
1
1
1
1
1
2
1
0
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
0
2
1
0
1
1
1
2
1
1
2
2
1
2
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
2
0
0
2
1
1
0
1
2
2
1
1
1
1
0
1
2
1
1
2
1
1
2
0
1
2
1
1
2
2
2
1
2
1
1
1
1
1
1
1
2
1
1
2
1
0
0
1
1
2
1
2
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
0
1
2
2
1
0
1
1
1
1
1
2
1
2
2
1
1
2
1
2
2
1
2
1
2
2
1
2
1
1
1
0
2
1
2
2
0
0
1
1
1
2
1
2
1
1
1
1
1
0
1
1
1
1
2
1
1
2
1
0
1
1
1
1
1
1
1
1
1
1
0
1
2
1
1
1
1
2
0
0
1
0
1
1
1
1
1
1
1
2
1
2
1
4
1
1
0
2
1
1
1
2
1
1
1
1
2
1
1
2
0
2
1
1
0
1
1
2
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
2
0
1
1
1
1
2
1
2
1
2
0
2
0
1
2
2
1
1
2
1
1
1
1
0
1
1
1
0
1
1
2
1
1
0
2
1
2
1
1
2
1
1
1
1
2
1
1
1
1
1
0
1
1
1
2
1
2
2
0
1
1
1
0
0
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
0
0
1
2
1
0
0
1
0
1
2
1
0
3
1
2
2
1
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
0
2
1
1
1
1
1
1
2
1
2
2
1
2
1
1
1
1
0
1
1
1
2
1
2
2
1
2
1
2
0
1
1
2
2
1
1
1
1
1
1
1
2
1
0
1
1
2
1
2
1
1
1
2
4
1
1
1
2
0
1
1
1
1
1
1
1
0
1
2
1
1
1
1
1
2
1
1
2
0
1
1
2
1
2
2
1
1
0
0
1
1
1
1
0
2
2
2
1
0
1
1
1
1
1
1
2
2
1
2
1
2
1
1
2
1
1
1
1
0
0
2
1
1
1
2
0
1
2
1
2
1
1
1
1
1
1
1
1
1
1
0
2
1
1
0
2
2
0
1
2
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
2
2
1
2
1
2
2
2
1
1
1
1
1
2
1
1
2
1
2
2
1
1
2
1
1
1
1
2
1
1
0
1
2
1
1
1
1
1
2
1
2
1
2
0
1
1
2
1
1
0
1
1
2
1
1
2
2
2
1
1
1
0
1
2
1
2
1
2
0
0
1
1
1
0
0
1
2
0
1
1
1
1
1
1
1
1
1
1
2
1
1
3
1
1
1
1
1
1
2
1
1
2
1
1
1
2
1
2
1
0
0
1
1
1
2
1
0
1
1
2
1
1
0
1
1
2
1
1
0
1
1
0
1
1
1
1
2
2
2
1
1
2
2
0
4
1
2
1
1
1
0
1
1
1
1
2
0
1
2
1
1
2
1
1
1
2
1
0
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
0
0
1
2
2
2
1
2
1
1
0
1
2
2
0
2
2
2
0
1
1
0
1
1
2
2
2
1
0
1
1
1
1
1
1
0
1
1
2
3
1
1
0
1
1
0
2
0
2
1
1
0
1
2
2
1
1
2
1
2
1
0
2
1
2
1
0
1
0
1
1
0
0
2
1
2
1
1
2
1
1
1
1
1
1
1
2
1
2
0
1
2
1
1
2
0
1
0
1
1
1
1
1
1
1
2
1
1
2
0
1
2
2
1
2
2
0
2
0
1
1
1
1
0
1
1
1
0
1
1
2
2
1
1
1
2
2
2
0
0
1
1
1
1
2
1
1
2
2
2
1
1
1
1
1
1
0
1
0
2
1
2
1
1
0
1
1
1
2
2
0
1
1
1
2
1
1
2
1
2
2
1
0
2
1
0
2
1
1
2
1
2
1
2
1
2
1
1
1
1
1
2
0
2
2
1
0
1
2
0
1
1
1
0
2
1
0
2
1
1
0
1
1
1
1
2
0
1
2
1
0
1
1
1
1
1
1
2
1
0
1
3
0
1
1
2
2
1
1
2
1
2
2
1
0
0
1
2
1
1
3
1
2
1
2
2
1
0
1
1
2
1
0
3
1
1
0
1
1
1
1
1
1
1
0
1
1
1
0
1
1
1
1
1
1
0
0
0
1
1
1
0
1
1
1
2
2
2
2
0
2
1
1
1
1
2
2
1
0
1
0
1
2
1
0
2
0
1
1
1
1
1
3
2
2
1
1
2
2
2
2
0
2
0
1
2
0
1
1
1
1
1
1
1
0
1
1
2
1
2
2
1
2
1
2
1
1
1
1
1
2
2
2
1
1
2
1
2
2
1
0
1
1
2
1
2
1
1
1
1
1
0
1
1
1
1
0
1
2
2
1
2
1
3
0
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
2
2
2
1
2
0
2
1
1
1
2
1
1
1
2
2
2
2
1
2
0
0
1
1
1
2
1
2
1
1
0
1
1
1
2
1
0
2
1
1
1
1
2
1
2
1
2
1
2
2
1
2
1
1
1
2
2
1
1
1
1
0
3
1
1
2
2
0
1
1
1
0
1
1
1
2
1
1
1
1
1
2
0
1
1
1
1
3
2
0
1
1
0
1
1
1
1
1
2
1
0
1
1
2
2
1
2
2
2
2
1
2
2
1
1
1
2
0
1
1
0
0
1
1
1
1
1
2
1
1
1
1
0
1
1
0
0
0
1
1
0
1
2
1
1
1
1
2
2
1
0
0
0
1
2
0
0
1
1
1
1
1
2
0
1
1
1
2
1
1
2
1
1
1
2
2
1
0
0
1
1
1
1
1
0
1
0
1
1
1
1
4
1
1
2
1
2
2
2
1
0
1
1
1
0
1
2
0
0
1
2
1
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
0
2
1
1
1
1
1
1
1
2
2
2
1
2
2
1
1
1
0
1
1
2
1
1
0
2
0
1
2
1
1
1
1
1
0
2
2
1
1
1
1
1
1
4
1
1
1
1
2
2
2
1
1
1
1
1
1
2
0
2
2
1
2
1
2
1
1
1
2
1
1
1
0
1
2
0
2
0
1
1
1
1
1
1
2
1
2
1
1
0
1
1
1
1
1
1
2
1
1
0
1
1
1
2
1
1
1
1
0
2
1
2
1
2
2
1
2
2
2
0
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
2
0
2
1
3
1
1
1
1
0
2
2
0
0
2
0
1
1
1
1
1
1
1
1
0
0
2
2
1
1
2
0
1
1
1
1
1
1
1
1
1
0
1
1
1
0
2
1
1
1
1
2
1
2
1
2
1
1
1
2
1
2
2
2
2
1
0
2
1
1
1
1
1
1
1
1
1
1
1
0
2
0
1
0
0
1
1
2
1
1
1
1
1
2
0
2
1
1
2
2
0
1
1
1
1
0
2
1
2
0
1
1
1
2
2
2
0
2
2
1
2
1
2
2
1
1
1
2
1
3
1
1
1
1
0
2
0
0
2
1
1
1
1
2
1
1
1
2
2
1
0
1
0
1
0
1
2
2
1
1
0
1
1
1
0
2
0
2
1
1
1
1
2
1
1
1
2
2
1
1
2
2
1
2
2
0
2
1
2
2
1
1
1
1
2
1
1
2
2
0
1
1
1
1
2
2
2
1
2
2
1
1
1
1
2
1
2
2
0
1
1
0
1
1
2
0
2
0
1
1
2
1
2
1
0
2
1
1
1
1
1
2
0
2
1
2
2
1
0
1
2
2
1
0
1
1
1
2
1
0
0
1
2
0
2
0
1
1
2
0
1
1
2
1
1
1
0
2
2
2
2
1
1
2
1
1
1
2
1
1
1
1
1
2
2
2
2
1
1
0
2
2
1
2
1
2
2
2
1
0
1
0
0
1
2
1
1
1
2
1
1
1
1
1
1
2
1
2
2
2
1
1
1
1
1
2
0
2
0
1
2
0
2
2
2
2
2
2
1
1
1
1
1
1
1
1
1
2
1
2
0
1
1
1
1
1
2
0
1
1
1
1
1
1
1
2
1
1
1
0
1
2
1
1
0
2
1
0
2
0
2
2
2
1
2
1
2
2
2
2
0
2
1
1
1
1
1
2
2
1
2
1
1
2
2
2
2
0
1
1
2
2
2
1
0
2
1
1
1
1
1
0
2
1
0
0
1
1
3
1
1
1
0
1
1
1
1
1
1
2
2
0
0
2
1
1
1
0
1
2
1
2
1
2
1
2
1
2
1
1
1
1
1
2
1
2
2
1
1
1
1
2
1
1
1
1
1
2
1
2
2
1
1
1
1
1
1
0
1
1
2
0
1
1
1
1
1
1
0
1
1
1
1
2
0
1
1
1
1
0
2
1
1
0
1
1
1
1
2
1
1
2
2
1
1
0
1
1
1
1
2
1
1
1
1
2
1
2
0
2
1
1
1
1
2
1
1
2
2
1
1
1
0
1
2
1
1
1
2
1
2
1
2
2
2
2
2
1
1
0
1
1
1
1
1
1
1
1
2
1
2
1
2
0
0
1
1
2
1
1
1
1
1
1
2
2
1
1
1
2
2
0
1
1
2
0
1
1
2
1
1
1
1
0
1
1
1
1
1
0
1
0
2
2
2
2
1
1
1
1
1
1
1
0
1
1
2
3
1
2
2
1
1
1
1
0
1
0
1
1
2
1
1
2
1
1
1
1
0
1
2
2
2
0
1
0
1
2
1
0
1
1
0
1
1
2
1
1
1
4
1
0
1
0
2
2
1
1
1
2
1
1
1
0
0
1
1
1
2
2
1
2
1
2
0
0
1
1
1
1
1
1
1
1
1
2
1
1
1
0
1
2
0
1
0
1
0
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
2
0
1
2
1
1
1
1
4
0
1
1
3
1
1
1
1
1
1
0
2
2
2
1
2
1
1
1
2
0
0
1
1
2
1
2
1
0
3
1
2
0
2
2
2
1
1
1
1
2
2
1
1
1
1
1
1
2
2
2
1
1
1
1
0
1
2
1
1
1
1
1
2
1
1
2
1
1
1
0
1
1
1
2
1
2
1
1
2
0
1
1
2
2
0
1
1
1
0
1
1
0
2
1
1
1
1
1
2
0
0
2
2
2
1
1
2
1
1
1
1
1
2
1
2
1
1
1
0
1
2
1
1
1
2
1
0
2
1
2
1
1
1
1
2
0
1
1
1
2
1
1
1
0
1
1
1
2
1
1
0
2
1
1
2
1
1
1
2
1
2
3
1
1
2
2
1
1
1
1
1
0
0
2
1
1
1
2
2
1
0
2
2
1
1
2
0
2
2
1
2
1
0
0
1
1
1
1
1
1
0
1
1
1
2
1
1
1
1
1
2
1
1
2
1
1
1
1
0
1
2
2
1
1
2
1
2
1
1
1
1
0
0
0
1
1
2
1
2
1
2
1
2
1
1
1
0
0
2
1
1
0
1
1
1
1
1
2
1
1
1
0
2
1
1
1
1
2
0
1
2
1
1
2
1
2
0
1
1
0
0
2
1
1
2
0
1
0
2
1
1
1
2
1
2
2
2
2
1
1
1
1
1
2
1
1
1
2
2
0
0
2
2
2
2
2
2
2
2
2
1
2
1
1
1
1
2
1
0
0
1
2
1
2
1
1
2
1
2
1
1
1
0
2
1
1
1
1
1
2
1
1
1
1
2
1
1
1
0
1
0
0
1
1
1
1
2
1
0
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
1
1
2
2
1
2
1
2
1
1
1
1
2
2
1
0
0
1
1
2
1
0
2
0
1
2
2
0
1
1
1
1
1
0
1
2
1
2
2
1
2
1
2
1
1
1
1
0
1
1
1
1
0
2
1
2
1
1
1
1
1
1
1
2
1
1
1
2
1
0
1
2
2
1
2
2
1
1
1
1
1
0
1
1
2
2
1
1
0
0
2
2
1
0
1
1
1
0
0
2
2
1
1
1
2
1
1
1
1
1
2
1
2
0
2
2
1
1
2
1
0
2
2
1
1
2
1
1
1
2
2
2
0
1
1
0
1
2
1
1
1
2
2
0
1
3
1
2
1
1
2
2
1
1
1
2
1
1
1
1
1
0
1
1
1
1
2
1
2
2
1
0
1
2
0
2
1
1
1
2
0
1
1
1
1
0
1
0
1
2
1
1
2
0
1
1
2
1
0
1
1
1
2
1
0
1
2
0
1
3
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
2
1
0
1
0
1
2
1
2
1
2
0
0
2
1
1
1
1
1
2
2
1
2
2
1
2
1
2
1
1
0
1
1
1
1
0
1
2
1
1
1
1
1
2
1
2
1
1
1
2
0
0
1
1
1
1
2
1
1
2
2
1
1
0
1
2
1
1
1
2
2
1
0
1
1
2
1
1
1
2
1
1
1
2
0
2
2
1
2
1
1
2
2
2
0
3
2
2
1
2
1
1
1
2
0
0
2
0
2
1
2
1
1
2
1
0
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
2
2
1
1
0
1
2
2
1
1
0
2
1
1
1
0
1
1
0
1
1
2
1
1
1
2
1
1
1
1
2
2
2
1
0
1
0
1
2
1
1
0
0
2
2
2
0
1
0
0
1
2
1
0
1
2
1
1
1
1
1
3
1
2
2
1
2
2
1
1
1
0
0
2
0
1
1
2
1
0
1
2
2
1
1
0
1
0
1
1
2
3
2
0
0
1
1
2
2
1
2
2
1
1
1
1
1
1
1
1
0
2
1
2
1
2
1
1
1
2
1
1
2
1
0
2
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
2
1
1
0
1
2
1
1
0
1
1
2
2
2
1
2
1
1
2
1
1
1
1
1
1
1
2
2
1
2
2
2
1
1
1
2
1
1
1
1
1
3
2
2
3
2
1
1
1
2
1
1
2
2
2
1
1
2
1
1
1
1
2
1
2
0
2
1
1
2
2
1
2
1
3
1
0
2
2
1
2
1
1
1
2
2
1
0
2
2
1
2
1
2
2
0
1
1
2
1
1
1
1
2
1
1
1
1
1
0
2
1
1
1
2
1
1
1
2
1
0
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
0
1
1
1
1
0
1
1
2
2
1
0
0
1
0
0
0
1
1
1
1
2
2
1
1
1
2
2
1
1
0
1
1
2
1
2
1
2
1
1
2
1
2
1
2
1
2
1
0
1
1
1
1
2
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
2
0
1
1
0
2
1
1
1
2
0
1
0
2
2
1
1
2
1
0
1
1
1
2
1
0
1
2
2
1
2
2
1
2
0
1
2
2
1
1
2
2
0
2
0
1
2
1
0
1
2
1
2
2
0
0
1
1
1
1
2
1
1
2
1
2
1
1
1
1
1
1
2
1
1
0
1
1
1
0
1
1
1
2
1
1
1
2
2
2
1
1
1
0
2
2
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
0
1
1
2
1
1
2
1
1
1
1
2
0
1
2
2
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
2
0
1
1
1
0
1
1
1
1
1
1
1
0
1
2
1
1
1
2
2
2
1
1
0
1
1
1
2
1
0
1
1
1
1
2
1
1
2
1
2
1
1
1
1
1
2
0
0
1
2
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
0
1
1
1
2
1
2
2
2
0
0
2
1
1
2
1
1
1
1
2
2
0
1
1
2
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
2
1
1
2
1
0
2
2
0
2
1
2
1
1
2
2
0
0
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
2
1
1
2
1
0
2
1
1
1
1
2
1
1
1
1
0
1
1
1
1
0
1
1
1
2
1
1
2
1
1
1
2
1
2
2
2
1
1
2
3
1
2
2
0
0
2
0
1
2
2
3
0
0
2
0
1
2
2
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
0
2
2
1
1
1
1
0
1
1
2
1
2
1
2
1
1
2
0
1
1
1
1
1
1
1
1
1
1
0
1
1
0
1
2
1
2
2
1
2
1
2
1
1
2
0
1
1
1
1
2
2
2
1
1
1
2
2
1
1
0
2
1
1
1
1
1
0
1
2
2
1
2
2
1
1
1
0
2
1
1
1
2
0
0
2
0
1
2
1
1
1
2
2
2
1
2
1
1
1
1
1
1
1
1
1
2
0
2
1
2
2
1
1
1
2
0
1
1
1
2
1
2
3
2
1
1
1
1
1
2
2
1
0
1
2
0
1
2
3
0
2
2
1
1
2
0
1
1
2
1
2
0
1
2
1
1
2
2
2
1
1
1
2
2
1
1
1
2
0
0
0
1
1
1
2
1
2
1
1
2
1
1
2
0
0
2
2
1
1
0
2
1
0
2
0
1
1
1
1
1
1
1
0
1
1
1
1
1
2
0
2
1
1
1
1
0
1
1
0
1
0
2
2
1
0
1
1
1
1
1
2
2
0
1
1
1
2
2
2
1
1
1
1
2
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
2
0
1
2
2
1
1
1
1
2
0
1
2
1
0
2
2
1
1
0
1
1
2
1
1
0
1
0
2
2
0
1
1
1
1
0
2
1
1
1
1
1
0
1
2
1
1
2
1
1
1
0
2
1
1
2
1
1
2
1
1
1
1
1
1
0
0
1
1
1
2
1
2
1
2
2
1
2
1
2
0
2
1
2
1
2
1
0
2
1
1
1
0
2
1
1
1
1
1
2
1
1
1
1
2
0
1
1
1
1
2
1
2
0
2
1
1
2
2
0
1
0
0
0
0
2
1
1
2
2
1
1
2
1
1
1
1
0
2
2
2
1
0
1
2
1
2
1
1
1
0
1
1
2
1
1
2
2
2
0
1
1
1
1
1
2
2
1
0
1
1
1
1
0
1
1
1
1
2
1
1
0
1
1
0
2
1
1
2
1
1
1
1
1
1
1
1
2
2
1
1
1
0
1
1
1
2
1
3
2
5
1
1
1
1
1
0
1
1
2
1
2
1
0
3
1
0
1
1
1
0
1
2
1
1
2
2
1
2
2
1
2
1
1
0
1
2
2
1
1
1
2
0
2
2
1
1
1
2
0
2
2
1
2
1
1
2
1
1
1
1
3
5
1
1
2
2
0
1
1
2
1
2
1
1
1
1
1
1
0
1
0
1
0
0
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
1
0
1
1
2
2
1
1
0
1
1
1
0
1
0
1
1
1
1
1
1
2
1
2
1
0
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
0
1
1
1
0
1
2
1
0
2
0
1
2
2
1
2
1
1
2
1
0
1
2
1
1
1
1
1
2
1
1
1
1
1
2
0
1
0
1
1
2
1
1
1
1
1
1
2
1
0
2
1
1
1
2
0
0
1
2
1
1
1
1
2
2
1
1
2
1
1
2
0
0
2
3
3
1
1
3
0
2
1
2
1
1
1
1
1
1
1
0
1
1
1
1
0
0
2
1
1
1
1
1
1
1
1
1
1
0
2
1
1
2
1
1
1
1
2
2
2
2
1
2
0
2
0
0
1
1
1
2
1
2
2
1
0
2
2
2
1
0
1
1
0
2
2
2
0
3
1
2
1
1
1
1
1
1
1
1
0
2
1
1
1
2
2
1
1
1
2
1
1
1
2
2
1
1
1
1
1
2
1
0
1
1
2
2
0
1
1
2
1
1
1
0
1
0
1
1
1
2
1
1
2
1
1
1
1
1
1
0
2
2
1
2
1
2
2
2
1
1
1
2
3
2
1
1
1
2
0
2
1
1
2
1
1
2
1
2
1
1
0
1
1
2
1
2
1
1
2
2
1
1
1
1
0
2
1
0
2
1
2
1
1
1
0
1
1
1
1
2
2
1
1
1
2
1
2
1
0
2
1
2
0
1
1
2
1
0
1
1
2
0
1
1
1
1
1
0
1
1
1
1
1
1
3
1
1
1
2
2
1
1
2
1
0
1
2
0
1
1
1
1
2
1
0
2
2
1
1
1
1
1
1
2
1
0
2
1
1
1
1
2
0
1
1
2
1
1
2
1
1
1
1
1
2
1
0
2
1
1
1
0
1
1
2
1
0
1
1
1
1
1
1
1
0
1
1
0
2
1
1
1
2
1
1
1
2
2
1
1
0
0
2
0
1
1
1
1
1
1
1
1
2
2
1
2
1
1
0
1
2
0
1
2
1
0
1
2
2
2
1
1
1
0
0
2
0
1
1
1
2
1
2
1
1
0
1
0
2
1
1
2
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
0
1
0
1
1
2
1
1
1
0
1
2
1
2
2
2
2
1
0
1
1
1
1
1
1
1
1
3
0
1
1
2
2
2
2
2
1
2
1
1
2
0
0
0
0
0
1
2
1
1
1
1
1
1
1
1
2
1
2
1
1
0
2
2
0
2
2
0
1
1
1
1
1
2
1
2
1
2
1
2
2
1
1
0
2
1
1
2
0
0
0
1
0
0
1
1
1
1
0
1
1
1
1
0
1
2
1
1
2
1
1
1
1
0
2
1
1
2
2
1
1
1
2
1
2
1
1
1
1
1
2
1
0
1
1
1
1
2
2
1
1
1
1
0
1
1
2
2
1
1
1
1
1
2
1
2
0
1
1
1
2
2
1
1
0
1
1
0
1
1
1
1
2
1
1
2
1
2
1
0
0
1
0
0
1
1
1
0
1
1
1
0
1
2
1
1
1
1
2
1
2
0
2
1
1
1
1
0
2
2
1
1
0
1
0
1
1
1
1
1
1
0
1
0
1
1
1
1
2
2
1
2
0
1
1
1
1
1
0
1
1
1
1
2
1
2
1
1
0
2
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
0
1
1
2
1
2
1
1
2
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
0
2
1
1
1
1
2
1
1
1
1
2
0
1
1
2
0
1
1
1
1
0
2
1
1
0
0
1
1
2
0
1
0
1
1
2
1
1
1
1
1
2
1
2
2
1
1
2
1
2
1
1
1
2
1
1
1
1
2
1
2
1
2
2
2
2
1
1
1
1
1
1
1
1
1
2
1
1
0
2
1
1
1
1
1
1
2
1
2
1
3
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
0
1
1
1
2
2
1
1
1
1
1
2
1
1
1
1
2
1
2
1
2
2
2
1
2
1
2
1
1
1
1
1
0
1
2
0
1
1
1
2
2
0
0
1
3
2
1
1
1
1
1
0
0
4
2
1
1
1
1
1
2
1
1
2
2
1
1
0
0
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
2
1
1
2
1
1
2
1
1
1
1
2
1
1
2
2
0
1
2
1
1
2
2
2
2
2
1
2
1
2
1
2
0
1
2
2
0
1
2
1
2
1
0
1
1
1
2
0
1
1
0
1
1
2
1
2
1
1
1
1
1
1
2
0
2
0
1
1
1
2
1
1
1
1
2
1
2
2
1
1
1
2
1
0
1
1
2
1
1
1
2
2
1
1
2
1
1
1
0
0
0
1
1
0
2
2
1
0
0
1
1
0
1
2
0
1
1
2
1
2
2
1
1
1
1
1
2
2
2
2
1
1
1
1
1
2
0
1
2
1
1
2
1
1
1
1
1
1
1
1
2
0
1
0
1
1
1
2
1
1
1
2
1
1
0
1
1
1
1
1
1
2
2
2
1
1
0
0
1
1
0
2
2
2
1
1
2
2
1
1
1
2
2
2
2
1
1
0
1
1
1
0
1
0
0
2
1
1
1
2
1
1
1
2
1
1
1
1
1
0
3
2
1
1
1
1
1
0
2
1
2
1
0
1
2
2
2
2
1
1
0
0
2
1
1
0
2
2
1
1
1
1
2
2
1
2
1
2
2
1
2
1
1
1
2
1
1
1
2
1
1
1
1
1
0
1
1
0
1
1
2
2
1
2
1
1
1
2
2
1
2
1
1
0
1
1
1
1
1
1
2
1
1
1
1
2
0
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
2
1
0
1
2
1
1
2
2
0
2
2
1
0
1
1
1
2
2
2
1
2
1
1
1
1
2
0
1
1
1
2
2
1
0
0
1
1
2
0
1
2
1
1
0
0
2
1
0
2
2
1
0
1
1
1
1
1
2
1
1
1
1
1
0
1
1
0
2
1
1
2
2
0
1
2
1
2
1
1
1
1
0
1
0
2
1
1
2
1
1
1
1
1
1
1
0
2
1
2
1
1
2
1
2
1
2
1
2
1
2
2
2
2
0
2
2
0
2
0
1
1
2
3
1
1
1
0
2
1
1
1
2
2
0
0
2
2
1
1
1
1
2
1
1
1
1
0
1
2
1
1
1
0
0
1
0
1
2
1
2
1
1
1
1
1
0
1
2
1
0
2
2
1
1
1
1
1
1
2
1
1
1
0
1
1
1
0
2
1
2
1
1
0
2
1
0
1
1
2
0
1
1
1
1
1
1
2
1
1
2
1
1
0
0
2
2
2
2
2
1
2
0
1
1
0
1
1
1
0
1
0
1
1
2
1
2
2
2
1
0
2
0
1
0
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
0
1
1
1
1
1
2
1
0
0
2
2
0
1
1
2
0
1
0
1
2
1
0
1
1
1
1
2
1
1
1
1
1
1
1
0
1
2
1
1
1
1
1
1
1
1
1
2
1
2
2
1
2
2
0
2
2
1
1
1
1
1
0
1
2
0
1
2
0
2
2
1
2
1
1
2
1
0
1
1
1
0
1
0
2
1
1
1
1
1
1
1
1
0
2
1
0
1
2
2
2
1
2
1
1
1
1
1
1
1
2
1
0
1
0
1
1
1
1
2
1
2
1
1
1
2
1
1
2
2
2
0
2
1
0
1
1
1
0
1
1
2
1
1
2
2
1
1
1
1
1
1
0
2
1
2
1
2
2
1
1
1
0
2
1
1
1
1
1
2
1
1
1
2
2
0
2
1
1
3
1
0
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
2
0
0
1
1
1
1
1
1
1
2
2
1
2
2
0
1
0
1
1
1
1
1
2
1
1
2
1
2
1
1
2
1
0
1
1
1
1
2
1
0
2
1
1
1
2
1
1
2
2
2
1
1
0
1
2
0
1
3
0
1
0
1
2
1
1
1
1
0
2
1
1
2
2
1
0
0
1
1
1
0
1
1
2
0
1
1
1
0
1
0
1
2
2
1
0
0
1
1
0
1
2
1
1
0
1
2
1
1
1
1
1
2
1
1
1
2
1
1
0
1
0
1
1
2
1
2
2
1
1
1
1
0
1
1
1
2
1
1
2
2
1
1
2
2
2
1
1
2
2
2
2
1
1
1
1
2
2
1
1
1
2
1
1
1
0
1
1
2
2
1
0
2
1
1
0
0
2
1
2
0
1
1
2
1
1
2
1
2
1
1
2
1
0
1
1
1
1
1
1
2
2
1
0
1
2
1
1
1
2
0
1
1
2
0
2
1
1
2
1
1
1
1
2
1
1
2
1
2
2
1
1
2
2
2
0
1
0
1
2
1
2
1
1
1
1
1
1
1
1
0
1
2
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
1
1
0
1
1
1
1
2
0
1
1
2
1
2
1
1
2
1
1
1
1
1
1
2
2
1
0
1
0
1
2
1
1
1
1
2
1
0
2
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
0
1
2
0
2
1
1
1
2
0
0
1
2
2
1
1
2
1
0
0
2
1
1
1
2
1
2
1
2
1
1
1
0
0
1
1
1
1
1
1
2
2
0
1
1
1
1
2
2
4
1
2
2
0
0
1
1
0
2
1
1
1
1
1
2
1
2
1
1
1
1
2
1
0
1
1
1
1
1
2
2
1
2
1
1
2
1
2
2
1
1
0
1
1
0
2
1
1
1
2
1
1
1
2
1
2
0
2
1
2
1
1
1
2
2
1
1
2
1
2
1
1
2
1
1
2
2
1
0
1
2
1
1
1
2
2
1
1
2
1
1
2
1
2
1
2
2
1
0
2
1
2
1
0
2
1
0
2
2
0
2
0
2
1
1
1
2
1
2
0
2
2
1
2
1
0
2
1
1
1
1
2
1
2
1
1
2
1
1
0
1
1
1
1
2
1
1
1
2
1
1
0
2
1
1
0
2
0
2
1
0
2
1
1
2
0
1
1
2
2
1
1
1
2
1
1
1
2
1
2
1
1
2
2
1
1
2
1
2
1
1
1
2
2
1
1
1
2
0
1
1
1
2
1
0
0
1
0
2
1
1
2
1
1
0
1
0
2
2
1
0
1
2
0
1
1
1
2
1
1
2
2
1
1
1
1
1
1
0
3
1
2
0
2
1
1
0
0
0
0
1
2
1
1
0
2
1
1
1
3
2
1
1
1
1
0
1
1
1
2
0
2
2
0
0
1
2
0
2
1
1
2
2
2
1
1
1
2
2
2
2
1
2
1
1
1
2
1
0
2
2
1
1
2
2
1
1
1
1
1
1
1
1
2
1
1
2
0
1
1
0
1
1
2
0
2
1
1
1
2
0
2
2
2
2
1
2
2
1
1
1
2
1
1
1
2
1
1
0
1
0
1
1
1
1
0
1
1
2
1
2
0
1
1
1
1
1
1
2
2
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
0
1
1
1
2
1
2
1
1
1
1
1
3
1
1
2
2
1
0
2
0
0
2
2
1
1
0
2
1
1
0
3
2
1
1
1
2
1
0
2
0
2
2
0
2
2
3
2
1
2
2
1
2
1
1
2
2
1
1
1
1
0
1
1
1
0
2
1
0
0
1
2
2
2
2
1
2
2
1
1
1
0
2
0
2
2
1
1
2
1
1
1
1
0
1
2
1
1
0
1
1
1
1
1
1
2
1
1
1
1
1
0
1
1
0
2
2
0
2
1
1
1
2
0
1
1
2
2
2
2
2
1
0
1
2
1
1
1
2
1
1
0
0
2
1
2
1
1
0
2
2
1
1
1
1
1
2
1
1
2
1
2
1
2
2
0
2
2
1
1
1
2
1
2
1
1
1
2
1
2
2
1
1
1
1
2
2
1
1
2
1
1
1
1
1
2
2
2
1
2
2
1
0
1
0
2
1
1
1
1
1
3
1
1
1
1
1
2
2
1
2
1
1
1
0
1
2
1
1
1
1
1
1
1
0
1
1
0
1
2
2
0
1
0
1
1
0
1
1
1
1
2
0
2
2
1
1
2
1
1
1
2
1
1
0
0
1
1
2
1
1
2
1
1
1
0
0
2
2
2
0
2
1
1
2
2
1
1
1
1
1
2
1
1
2
2
1
2
1
1
1
2
1
1
1
2
1
1
1
2
2
1
1
1
1
1
2
2
2
2
1
0
1
1
1
1
1
0
1
1
1
2
1
1
4
1
1
1
1
1
1
1
1
1
2
1
2
1
2
1
2
0
1
1
1
1
0
1
1
1
2
1
1
1
0
2
1
0
1
2
1
1
1
1
1
2
1
2
2
1
1
1
2
0
1
1
2
2
2
2
1
2
0
0
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
2
0
0
1
1
0
2
2
1
2
1
1
0
1
0
1
0
1
1
1
1
1
1
2
2
1
1
2
0
1
1
2
1
0
1
0
2
2
0
1
2
0
0
1
1
1
1
1
1
1
2
2
2
1
2
0
2
0
1
0
1
1
2
1
1
1
1
1
2
0
1
1
1
2
1
2
1
2
2
2
1
2
0
1
1
0
1
1
1
1
0
1
2
1
1
1
0
1
1
1
1
1
2
2
2
1
1
1
2
2
1
2
1
1
1
0
1
1
1
1
1
1
1
0
0
1
1
1
1
1
1
1
1
1
1
2
1
0
1
1
2
1
1
0
0
0
2
1
1
1
1
2
1
1
1
2
1
1
2
1
1
2
2
1
1
0
1
2
1
1
2
2
2
0
2
1
2
1
1
1
1
2
0
2
1
2
0
1
1
1
1
1
1
2
1
0
2
1
1
1
1
2
2
2
1
1
2
1
1
1
2
0
0
1
1
2
2
2
0
1
1
1
0
2
1
1
2
2
2
2
2
1
2
2
2
2
2
1
2
1
1
1
0
1
1
1
0
1
1
0
1
1
1
0
2
1
1
0
1
1
2
0
1
0
1
1
2
1
2
1
1
0
1
2
2
1
1
1
1
1
2
1
1
1
1
2
0
1
0
2
1
2
1
0
1
1
1
1
1
1
1
2
1
2
0
0
1
2
1
0
1
1
2
1
2
2
0
1
2
2
1
0
1
1
3
1
2
1
1
1
1
1
1
0
2
1
1
2
1
1
1
1
1
1
1
2
0
1
1
1
1
0
1
2
1
1
2
2
2
1
2
1
0
1
1
2
1
1
2
1
2
1
1
1
0
2
1
1
2
2
2
1
1
0
2
1
1
1
1
1
1
1
2
1
1
2
0
1
1
2
0
1
1
1
0
1
1
2
2
2
1
2
1
0
2
2
2
1
1
0
0
1
2
0
1
2
2
0
1
1
1
2
0
2
1
1
2
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
2
2
1
2
0
1
1
2
2
1
1
1
1
1
2
2
0
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
0
2
1
1
1
0
1
1
1
2
1
1
0
0
1
1
1
1
1
0
1
0
1
1
1
2
2
1
1
3
1
1
2
1
2
2
1
2
2
1
1
1
2
1
0
1
1
2
1
2
2
1
1
1
1
1
1
1
1
1
0
1
1
2
1
1
1
1
2
1
1
2
1
1
2
1
1
0
2
2
1
1
1
1
1
1
0
1
2
1
1
2
0
1
1
1
3
0
2
1
0
1
1
2
0
2
1
0
1
0
1
2
1
1
1
2
1
1
2
1
2
2
2
1
1
2
0
0
1
1
1
1
2
1
1
0
1
1
2
1
2
1
1
1
1
1
2
1
1
2
1
1
0
1
1
1
1
1
2
2
1
1
1
2
2
1
1
1
1
1
2
1
1
1
0
2
1
1
1
1
1
1
1
2
1
2
1
1
2
2
1
1
1
0
1
1
1
1
1
1
1
1
0
2
1
2
2
1
1
2
1
0
1
1
1
1
0
1
1
1
1
2
0
1
1
2
1
1
0
2
2
2
2
2
1
1
1
1
1
0
1
1
1
0
1
0
3
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
0
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
0
0
1
1
2
1
0
1
1
1
1
1
2
2
1
1
1
2
5
1
1
0
2
1
1
2
1
1
2
1
1
1
0
1
2
1
1
1
1
1
1
2
1
1
1
2
2
0
2
1
1
3
2
2
2
1
1
1
1
1
2
1
1
2
2
1
1
2
1
1
1
0
0
2
2
2
2
1
1
1
1
1
2
1
0
1
2
0
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
0
1
1
2
1
1
1
1
0
1
2
2
1
1
0
1
1
1
1
2
2
1
1
1
2
2
1
1
0
0
1
0
1
1
2
2
1
2
0
1
1
1
1
2
2
2
1
1
1
1
1
2
2
1
0
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
0
1
0
1
2
1
2
1
2
2
2
1
1
1
1
0
1
2
1
1
1
2
1
1
2
2
1
1
2
1
1
2
1
1
2
2
1
2
0
2
0
1
2
1
1
0
2
1
2
1
2
1
1
0
1
1
0
1
1
1
1
2
1
1
2
0
1
1
1
1
0
1
1
1
2
1
1
1
0
0
1
1
1
0
2
1
2
0
1
2
2
1
1
1
1
1
1
1
1
0
1
1
1
1
2
1
1
0
2
2
1
2
1
2
2
0
0
0
1
1
0
0
4
0
1
1
1
1
0
1
1
1
0
1
2
1
1
2
0
1
0
1
2
1
1
1
1
1
2
2
1
1
1
1
1
1
2
2
1
1
1
1
2
2
1
1
2
1
0
1
1
0
2
1
1
2
3
1
2
1
1
1
2
1
2
3
1
1
1
1
1
1
1
2
1
1
0
1
1
1
0
1
2
2
0
1
2
0
2
1
2
2
1
1
0
2
1
0
0
0
2
2
0
1
1
1
1
1
0
2
1
2
1
0
1
1
1
1
2
1
1
1
2
1
1
2
1
2
2
1
0
2
1
2
2
3
1
2
2
2
2
2
2
1
1
0
2
1
2
1
1
2
1
1
1
1
0
1
1
2
2
2
1
2
1
1
1
1
2
1
0
1
1
0
1
1
1
0
1
1
2
1
1
1
0
1
1
2
1
1
1
1
1
2
0
1
2
0
2
1
2
1
1
1
1
2
1
2
1
2
2
1
1
1
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
1
1
0
1
1
1
1
2
1
2
0
0
1
1
2
1
0
1
2
0
2
0
2
1
1
0
1
0
1
1
1
1
2
1
2
2
1
2
1
1
0
2
1
1
2
0
2
2
1
2
0
2
0
1
1
1
1
0
2
1
1
1
1
2
1
1
2
2
2
0
1
1
1
2
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
2
1
2
0
1
2
1
1
1
2
0
1
0
2
1
1
1
1
2
2
2
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
2
2
0
1
2
1
0
1
1
1
2
0
1
1
1
1
0
2
1
1
1
1
1
1
1
2
1
1
2
0
0
1
0
1
1
0
2
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
0
1
2
0
1
1
1
0
1
1
0
2
1
1
1
1
1
1
0
2
1
1
2
1
2
1
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
0
1
1
1
1
1
1
2
1
2
1
1
1
2
0
1
1
1
1
2
1
1
2
1
2
2
1
1
2
1
1
1
0
2
1
0
0
2
2
1
1
1
2
2
2
2
1
1
1
1
2
1
1
2
2
1
1
2
0
1
0
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
2
1
0
1
2
2
1
2
1
0
2
2
2
1
0
1
1
2
1
2
1
1
1
1
1
1
0
1
1
1
1
2
1
1
2
1
1
1
1
0
0
1
1
1
1
0
1
1
1
1
1
1
1
0
2
1
2
1
1
1
1
1
1
1
1
1
2
1
0
1
1
2
1
1
1
1
0
2
1
2
0
0
1
2
2
0
1
1
2
1
0
1
1
2
1
1
0
1
2
1
1
1
1
0
1
1
1
1
1
0
1
0
2
1
1
2
1
1
1
2
1
1
1
1
1
1
0
2
2
1
1
2
1
1
1
1
1
1
1
0
0
1
1
2
1
2
1
1
1
2
1
0
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
2
1
1
1
2
2
1
2
2
1
2
2
1
0
1
1
1
1
1
1
2
0
0
1
0
0
1
0
1
1
1
2
1
1
0
2
2
1
2
1
1
0
0
0
1
1
1
1
2
2
2
0
1
1
1
1
2
1
2
1
1
1
2
1
2
0
1
2
0
2
1
1
2
2
1
2
2
0
2
1
2
1
2
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
2
1
2
2
1
0
1
2
1
1
1
0
1
1
1
1
0
4
1
1
1
2
1
1
1
1
1
1
0
1
1
1
1
1
1
1
2
1
0
0
1
1
2
1
1
0
0
1
1
2
2
1
2
1
2
1
2
1
1
0
1
1
2
1
1
1
1
1
1
1
1
1
2
2
2
2
2
2
1
0
2
2
1
0
1
1
1
2
1
1
1
0
1
2
2
1
0
3
1
1
1
0
0
1
2
1
1
1
1
2
2
2
2
2
1
1
1
2
1
0
1
1
2
1
1
0
2
1
2
1
2
1
2
1
1
1
1
1
2
1
0
0
2
0
2
2
1
2
2
1
1
1
1
1
1
1
2
2
1
1
1
3
1
1
1
0
2
1
1
1
2
1
1
1
2
1
2
1
1
2
1
2
2
1
2
1
1
0
0
1
1
2
2
1
1
1
1
1
1
1
1
2
1
0
2
1
1
1
1
0
1
0
2
1
0
1
1
1
1
2
1
2
1
2
2
1
1
2
1
1
1
2
1
1
2
2
1
2
1
1
1
0
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
2
1
2
0
1
1
1
1
1
0
2
2
1
2
1
2
1
2
1
1
1
1
1
1
2
1
1
2
1
1
2
1
1
2
2
2
2
1
2
1
1
1
1
1
1
2
0
1
2
1
1
0
1
1
2
2
1
0
2
1
1
1
1
1
1
1
2
1
0
1
1
1
1
1
1
1
1
2
1
2
0
2
1
1
1
1
1
1
2
1
1
1
1
2
2
1
1
1
0
2
0
2
1
1
1
1
1
2
1
0
1
2
1
0
1
1
0
2
2
1
1
2
1
2
1
3
1
5
1
2
2
1
1
2
2
1
1
1
1
1
1
2
1
2
1
2
1
2
2
2
1
2
2
1
1
1
1
1
0
0
1
1
0
1
2
0
1
0
1
2
2
0
0
2
2
1
0
2
2
1
2
1
0
1
1
2
2
0
2
2
1
2
2
1
1
1
2
1
1
2
0
1
0
1
1
1
1
2
2
1
1
1
1
1
1
1
1
0
0
1
1
1
1
1
1
2
1
1
2
1
1
1
0
1
0
1
0
1
1
1
1
2
2
2
3
1
1
0
1
1
2
0
1
0
1
1
1
1
2
0
1
1
1
1
2
2
2
1
1
1
2
1
1
1
2
2
0
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
0
1
2
1
1
1
1
1
2
0
2
2
2
1
2
1
0
0
1
1
1
1
1
1
1
1
1
1
2
1
2
0
1
2
1
0
1
1
1
1
1
2
1
1
0
1
1
1
1
1
2
0
1
1
1
0
1
1
0
1
1
1
1
1
1
1
1
1
3
1
0
2
1
1
2
2
2
0
2
2
2
1
2
2
0
1
1
1
0
2
1
2
1
2
0
1
2
1
1
2
1
2
1
1
1
2
2
1
1
2
1
1
0
1
1
1
1
1
3
1
2
1
1
1
1
1
2
1
1
1
0
1
1
1
2
1
1
1
0
2
1
1
2
1
1
1
0
1
1
2
0
1
2
2
2
1
2
1
1
1
0
1
2
2
1
1
1
1
1
1
1
2
0
0
1
2
5
0
1
1
2
1
2
2
1
1
1
1
1
1
0
1
1
2
1
2
1
2
1
2
0
2
1
0
1
0
0
1
1
2
0
2
1
1
0
1
1
1
1
1
2
1
1
1
2
1
0
2
2
2
1
2
1
2
2
1
2
1
0
1
1
2
1
0
1
1
1
1
2
1
1
1
0
1
1
0
2
1
1
1
1
1
0
0
0
2
1
0
1
1
1
1
2
1
1
1
2
2
2
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
2
1
1
1
0
1
2
2
1
1
1
1
1
1
2
2
1
2
0
1
1
1
1
2
1
1
0
1
2
1
1
2
1
2
0
0
0
1
1
1
2
1
1
1
1
1
1
1
2
2
2
2
1
0
0
2
2
1
2
0
2
1
1
1
2
2
2
2
0
1
1
3
0
1
1
1
1
2
2
2
1
2
1
1
1
1
1
1
2
1
1
2
2
0
1
2
1
1
1
0
0
1
1
1
1
2
1
0
1
1
2
2
3
1
0
1
1
1
1
0
1
1
1
2
1
1
0
1
0
1
1
1
2
1
1
1
0
1
2
1
1
1
1
2
1
0
1
1
2
2
4
1
1
2
1
1
2
1
1
1
2
2
2
2
1
2
2
1
0
1
2
2
1
1
1
1
2
2
1
2
2
1
1
1
1
2
1
1
1
0
1
1
2
1
1
1
2
0
1
2
1
1
0
1
1
1
2
1
1
2
2
1
1
1
2
1
1
2
1
2
2
1
1
1
2
0
0
1
1
1
2
1
1
2
1
1
0
2
1
1
2
2
1
1
1
1
1
2
2
0
1
1
1
1
2
0
1
1
1
0
2
1
2
2
1
1
1
1
1
1
2
2
2
1
2
1
1
1
2
2
2
1
1
2
1
1
1
2
1
2
0
2
0
1
1
2
1
0
2
1
0
1
1
1
1
2
1
0
1
0
1
1
2
1
1
1
0
2
1
1
1
2
1
1
0
0
1
1
1
2
2
2
1
2
1
1
1
0
1
1
1
0
0
2
1
1
1
1
1
1
1
1
1
1
0
1
1
1
2
1
2
1
1
1
1
1
1
1
1
2
1
0
2
1
1
1
1
1
1
2
1
2
2
1
0
0
1
2
1
0
1
2
0
2
2
1
2
0
2
2
2
1
2
0
1
2
1
1
1
2
2
0
0
0
1
1
0
1
2
1
1
1
0
1
2
1
1
1
1
1
1
2
1
0
1
0
2
1
1
1
0
0
2
1
1
1
0
0
2
3
1
1
1
2
2
0
1
2
1
0
2
0
1
1
1
2
1
1
2
1
1
2
1
2
1
1
1
2
1
2
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
2
2
1
0
2
1
2
1
1
2
1
2
2
2
1
1
1
1
2
1
2
1
1
1
1
1
1
0
1
2
2
0
1
1
1
1
1
1
1
1
1
1
0
2
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
0
0
1
1
1
1
1
2
1
0
2
0
1
1
1
2
1
1
1
1
2
1
1
1
2
1
2
1
0
1
2
1
4
1
1
1
1
1
1
3
1
1
1
1
0
2
0
1
0
2
1
0
0
1
1
1
1
1
1
1
1
1
1
1
2
0
2
1
1
1
2
2
1
2
1
2
1
1
1
1
0
0
2
1
1
2
1
1
1
1
2
1
1
0
1
1
2
0
1
1
1
1
1
1
2
1
1
1
0
0
0
2
1
1
2
2
2
1
1
2
2
1
2
0
1
1
0
1
2
1
1
1
1
1
2
1
1
1
3
2
1
1
1
0
1
1
1
0
2
1
1
1
2
1
2
2
2
0
1
2
2
2
1
0
1
2
1
2
2
2
1
1
3
1
1
2
1
2
2
1
1
1
1
2
1
2
1
1
1
2
2
0
2
1
1
1
1
0
0
2
1
1
1
3
1
1
1
2
2
2
1
2
1
0
0
1
1
1
0
2
1
1
2
1
1
2
1
2
1
1
1
1
0
1
2
1
1
1
1
2
1
0
1
1
1
1
1
2
1
1
2
2
2
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
2
0
1
1
1
1
2
1
1
1
1
2
1
0
1
1
1
2
1
1
2
1
1
1
1
1
0
2
1
1
1
2
1
1
1
1
0
1
1
1
2
2
1
1
2
1
1
1
1
1
2
1
1
0
1
1
0
1
2
1
2
0
1
1
1
1
1
2
3
1
1
2
2
2
3
1
1
1
0
1
1
1
1
0
1
1
2
0
1
1
1
0
1
1
2
2
3
0
0
1
1
1
2
1
1
1
2
0
0
1
1
2
1
1
1
1
2
0
1
2
1
0
1
1
2
1
0
1
1
1
2
1
1
2
2
0
1
1
1
1
1
1
2
0
1
1
0
1
2
2
1
1
1
1
2
2
1
1
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
3
1
1
2
1
1
1
0
1
2
2
2
1
2
1
1
0
1
1
0
1
1
0
0
1
1
2
1
1
0
2
1
2
0
1
0
2
1
1
0
0
1
2
1
2
0
1
1
1
1
1
1
0
2
0
1
1
1
2
2
0
2
1
1
2
2
2
2
1
1
0
2
1
1
2
1
0
1
2
1
1
2
0
1
2
1
2
2
2
1
0
0
2
1
1
2
1
2
1
1
2
2
2
2
1
2
1
1
1
1
1
1
1
1
1
2
0
1
2
2
2
0
0
1
1
2
1
0
1
2
1
2
2
1
1
1
2
1
1
1
1
3
1
1
1
1
2
1
1
1
1
1
2
1
2
5
1
2
2
2
1
2
1
1
1
1
1
1
2
2
1
1
2
2
1
2
3
1
1
1
1
2
1
1
1
2
1
2
1
1
0
1
1
0
1
1
1
1
1
1
0
1
2
0
0
2
1
1
2
0
2
1
0
1
2
0
1
1
2
1
1
1
1
1
2
1
0
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
1
1
1
2
2
2
1
1
1
0
1
1
1
2
0
1
1
1
2
2
1
0
1
2
0
1
1
1
0
1
1
1
1
2
1
1
2
2
2
0
1
1
2
1
1
1
1
1
1
1
1
1
0
1
1
2
1
1
1
0
1
1
0
2
1
1
2
0
1
1
0
1
1
1
0
2
0
2
1
1
2
1
0
1
1
2
1
1
1
1
2
1
1
2
2
0
0
1
1
1
0
1
1
2
1
0
1
2
1
1
1
1
0
2
0
2
1
1
2
1
1
2
1
0
0
2
1
1
2
1
1
2
0
1
1
1
1
2
1
1
1
1
2
1
0
1
1
2
2
1
1
1
0
2
1
1
2
0
0
1
1
0
1
2
1
1
1
0
1
1
1
1
1
2
2
1
2
1
1
2
0
1
0
1
1
1
2
1
1
2
1
0
1
1
0
2
1
1
1
1
2
1
2
1
0
1
2
1
1
0
2
0
2
2
2
0
1
1
1
0
1
1
1
1
0
2
1
1
2
2
1
2
2
2
2
1
2
1
2
1
1
1
0
0
2
1
1
2
1
1
1
2
2
2
2
1
1
1
1
3
1
1
1
2
1
0
2
1
2
1
1
2
0
1
2
3
2
1
2
1
0
1
1
1
1
2
2
2
1
2
1
1
1
2
1
1
1
1
1
1
2
2
2
2
0
1
2
1
1
1
1
2
1
1
0
1
2
1
0
2
1
1
1
1
1
2
1
1
1
0
1
1
2
1
2
1
0
1
1
0
1
1
1
1
2
1
2
1
1
2
1
2
2
1
2
2
1
2
1
2
2
1
1
2
0
1
0
1
1
0
1
1
1
1
1
1
2
0
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
0
2
1
2
1
1
1
2
2
1
1
1
1
2
1
1
1
1
2
1
2
2
1
0
1
1
2
1
2
1
2
0
1
0
0
1
1
1
1
2
1
0
0
0
1
0
1
0
1
0
2
2
1
1
1
2
0
2
1
2
2
2
1
1
1
1
1
1
1
1
2
1
2
1
1
1
2
2
0
0
1
1
1
2
1
1
2
0
1
3
1
2
2
1
2
1
1
1
2
2
2
2
1
2
1
1
1
1
1
1
0
1
0
1
0
1
1
2
1
0
1
2
0
1
0
1
1
1
1
1
1
2
0
1
2
1
0
1
1
1
1
1
2
2
1
1
1
0
2
2
2
1
1
0
1
2
1
2
2
2
0
1
1
2
1
0
1
1
1
1
2
1
0
2
1
2
2
2
2
1
1
2
1
1
1
1
2
0
0
1
1
1
1
1
3
0
1
1
0
1
1
1
1
1
0
1
1
1
1
1
2
1
1
1
1
2
1
1
0
2
1
1
1
0
0
2
2
2
0
3
2
0
1
1
2
2
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
0
2
1
1
1
1
2
0
1
1
2
1
1
2
2
2
0
1
1
1
1
1
0
2
1
1
2
2
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
0
1
1
1
1
1
2
0
0
1
2
1
1
1
0
1
1
1
1
0
1
0
1
1
1
1
1
1
1
1
1
0
2
1
2
1
0
1
1
1
1
0
2
1
1
1
1
1
2
1
1
1
0
0
2
1
0
1
3
1
1
1
1
2
1
1
2
1
0
1
2
1
1
2
1
0
1
2
2
1
2
2
0
1
2
0
1
2
1
2
2
1
0
0
0
1
1
1
0
1
1
1
2
1
1
0
2
1
2
1
1
0
1
1
1
1
2
1
1
2
2
2
2
1
2
1
1
1
2
1
2
2
1
2
1
2
2
1
2
0
2
2
1
1
1
2
0
1
1
2
2
1
1
1
1
1
1
1
1
1
2
1
1
1
0
2
2
1
2
1
0
0
1
1
1
2
1
1
2
0
1
0
2
1
1
2
1
2
1
1
1
1
2
2
1
1
0
0
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
0
1
1
1
0
2
1
1
0
2
2
1
0
1
2
2
0
1
2
1
2
2
1
2
0
2
2
1
1
0
2
1
1
1
2
0
2
1
1
2
1
2
1
1
0
1
0
1
2
2
1
2
1
2
0
1
1
1
2
0
1
0
2
2
1
1
1
1
0
1
1
2
1
1
2
1
1
1
2
1
0
1
1
1
1
1
2
0
2
2
0
1
1
1
1
2
1
1
5
1
1
1
1
2
0
2
1
1
1
2
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
0
1
1
0
1
2
1
2
0
1
1
2
1
1
2
1
1
0
1
1
1
2
2
1
1
2
0
2
0
1
1
1
1
0
1
2
1
1
2
0
1
2
1
2
1
1
1
1
1
2
2
1
2
2
1
1
1
1
1
0
1
2
2
1
1
1
0
2
2
0
1
1
1
0
1
2
1
0
1
1
1
1
1
1
2
1
1
1
0
1
1
1
1
1
2
2
1
1
1
2
0
1
0
0
1
2
1
1
1
1
2
1
2
1
2
2
2
0
0
0
1
1
1
1
1
1
2
1
2
1
2
1
1
0
2
1
1
2
1
1
0
1
2
1
1
2
1
1
1
2
1
1
1
1
2
2
1
1
1
1
1
1
2
1
2
2
1
1
1
2
1
1
2
1
1
2
1
1
1
0
1
1
1
2
2
0
2
1
0
1
2
0
1
2
2
1
2
2
1
1
1
2
2
1
1
2
1
1
1
1
1
1
0
2
1
2
2
1
1
1
1
2
0
2
1
1
2
1
2
1
1
1
1
1
2
0
2
2
1
0
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
0
1
1
2
1
1
1
1
1
0
2
1
1
0
1
1
2
1
0
2
0
1
1
1
2
2
0
1
1
2
1
1
2
2
1
1
1
1
1
2
2
1
1
1
1
2
1
0
2
1
0
1
0
1
2
1
2
2
1
1
1
1
2
0
1
1
0
1
1
2
1
1
1
1
1
1
2
2
2
1
1
1
0
2
1
1
1
1
0
2
2
1
0
0
1
2
1
0
1
1
0
2
2
1
1
1
1
1
0
1
1
1
1
1
1
0
1
0
1
1
1
1
1
2
2
0
2
0
2
1
1
1
1
2
1
1
1
2
0
0
0
1
2
1
2
1
0
0
1
0
0
1
2
1
1
2
1
0
1
1
1
1
1
2
0
1
1
2
1
2
2
1
2
1
1
1
1
1
2
2
1
1
1
1
1
0
1
1
1
1
1
2
0
1
1
2
1
1
2
2
2
1
1
1
0
2
2
1
1
1
1
2
1
1
1
2
0
1
2
1
0
2
2
1
1
0
1
2
1
1
1
1
2
2
2
1
1
0
0
1
1
0
1
1
1
2
2
2
1
1
1
1
2
1
1
1
2
2
1
0
1
1
2
1
1
1
1
1
2
0
1
1
0
1
1
1
2
1
2
1
1
1
1
1
1
2
1
0
2
0
1
0
1
2
2
1
0
2
1
1
1
1
1
1
1
0
1
1
0
1
1
1
2
0
0
2
0
1
1
1
0
2
2
1
2
2
1
1
1
1
0
2
1
1
2
1
0
1
1
1
1
2
2
1
1
2
1
1
2
0
0
1
2
1
2
0
3
2
1
2
2
2
1
2
1
2
0
1
1
1
1
1
1
1
2
1
2
0
2
1
2
1
0
1
0
2
1
1
1
1
2
2
0
3
1
1
1
2
2
2
0
1
0
0
0
1
2
2
1
0
2
1
0
1
1
0
1
1
1
2
1
1
2
2
2
2
0
1
1
1
1
2
2
1
2
2
1
1
1
2
2
1
2
1
2
1
0
2
2
1
1
1
0
2
0
2
0
1
1
1
1
1
0
1
2
1
1
1
2
1
1
1
1
1
0
0
0
1
1
1
1
1
2
0
0
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
0
2
2
1
2
1
0
1
1
0
1
1
1
1
2
1
1
2
0
1
1
1
1
1
2
1
0
1
2
1
1
1
1
1
1
1
2
0
0
1
1
2
1
1
1
1
1
2
1
1
2
1
0
2
1
2
1
1
1
2
1
2
1
1
1
1
2
2
1
2
1
2
1
1
1
0
1
1
2
1
2
1
1
1
1
2
2
1
1
0
1
1
2
2
2
1
1
1
1
1
1
2
0
1
1
1
1
2
1
1
2
1
2
2
2
0
2
0
1
2
0
2
1
1
1
2
2
2
1
1
2
1
2
2
0
1
1
1
1
1
0
1
0
1
0
2
1
0
2
2
2
1
1
1
0
2
1
0
0
2
1
1
1
1
0
1
1
1
1
2
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
0
1
1
2
1
2
1
1
2
1
1
2
1
1
1
0
1
1
0
2
1
1
1
0
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
0
1
2
2
1
1
1
1
0
1
2
2
1
1
1
1
0
2
0
0
1
1
1
1
2
0
0
1
2
0
1
1
1
1
1
1
1
2
0
1
1
1
2
0
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
1
1
0
1
1
1
1
1
1
2
0
0
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
2
1
1
1
1
0
0
1
1
1
1
1
1
0
1
2
1
1
2
2
2
1
2
0
0
2
1
3
1
2
1
1
2
1
2
2
0
0
1
1
1
1
1
2
1
1
1
2
2
0
2
1
1
2
1
0
1
1
2
0
1
2
0
1
1
0
0
1
2
2
1
2
2
2
1
1
0
1
1
2
1
1
1
1
2
1
1
1
2
1
1
1
2
2
1
1
1
2
1
1
1
2
1
0
1
1
2
2
2
1
1
1
0
1
1
1
1
2
1
1
2
0
2
2
2
0
1
0
0
2
2
1
1
1
0
1
1
1
0
1
1
1
1
1
1
2
3
1
1
2
1
0
1
1
2
2
1
1
2
2
0
2
1
1
2
0
1
1
1
1
1
1
1
0
2
0
2
1
1
2
1
2
0
1
1
1
2
2
0
1
0
1
2
1
1
2
1
1
2
1
1
1
0
1
1
0
2
1
1
0
2
1
1
1
1
2
1
2
1
2
2
1
0
0
2
1
1
1
1
1
2
0
1
1
0
2
1
1
2
1
1
1
1
2
0
1
1
1
0
1
1
1
1
1
1
1
1
0
2
1
2
2
0
1
2
1
1
2
1
1
1
1
1
0
1
0
1
1
0
2
2
2
1
1
1
1
2
1
0
1
2
1
2
2
2
1
1
0
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
0
1
1
2
1
1
1
2
1
1
1
1
0
1
1
1
1
2
1
0
1
3
1
1
2
2
1
1
1
1
2
1
0
1
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
2
1
1
1
2
0
2
1
1
2
2
1
1
1
1
0
1
2
2
1
2
1
1
2
2
1
1
0
2
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
2
2
0
1
0
0
1
1
2
1
1
1
1
1
1
1
2
1
1
2
0
0
1
1
2
1
1
1
1
0
1
1
1
1
1
1
1
1
1
2
1
1
2
2
1
1
3
1
1
0
2
1
1
0
2
1
1
1
2
1
1
1
0
0
1
1
1
1
0
1
1
1
1
2
2
1
1
1
1
2
2
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
1
2
1
0
2
1
1
1
1
2
1
2
1
2
0
0
1
1
1
0
1
1
2
1
1
1
1
0
1
1
1
1
2
1
2
2
1
2
1
2
0
1
1
1
1
1
1
1
2
2
2
2
0
2
1
1
1
2
2
1
1
1
2
2
2
1
2
1
1
0
1
1
2
2
1
2
1
1
1
2
2
1
2
1
1
1
2
1
1
1
2
2
1
2
2
2
1
1
2
2
2
1
2
1
2
1
1
1
1
2
1
2
1
1
2
1
1
2
1
2
1
1
1
1
2
1
1
2
1
2
1
0
0
1
1
0
0
2
2
2
1
1
1
0
2
1
0
0
1
0
1
1
1
1
1
1
0
2
1
1
1
1
2
2
1
1
2
1
2
1
1
0
1
1
0
2
2
1
1
2
2
1
2
1
0
0
1
2
1
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
0
3
0
0
1
1
1
1
0
0
1
2
1
1
1
1
0
2
1
0
1
2
2
2
1
2
1
1
1
1
1
1
2
2
1
2
1
1
1
0
1
1
1
1
0
1
1
2
2
2
1
0
0
1
1
1
2
0
1
1
1
2
1
1
1
1
1
2
1
2
1
2
1
0
1
1
0
2
1
1
2
1
1
1
1
0
1
1
1
0
0
0
2
0
1
1
1
1
1
2
2
1
1
2
4
2
0
1
1
1
1
1
2
1
2
0
1
1
1
0
1
1
0
1
0
2
1
0
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
0
0
1
0
2
2
1
2
0
0
1
1
1
1
0
1
1
1
2
2
1
0
0
0
0
1
1
1
2
2
1
2
0
2
1
1
1
1
0
2
0
2
1
1
1
2
4
2
1
2
1
1
1
2
0
2
2
2
2
1
1
1
2
1
2
1
1
2
0
1
1
1
2
1
0
2
1
1
1
1
1
2
1
0
1
1
1
1
1
1
1
1
2
0
1
2
2
0
1
0
1
1
1
1
0
2
1
2
1
0
1
1
1
0
1
1
1
1
1
1
1
2
1
1
2
1
0
2
1
2
0
1
1
1
2
1
1
1
1
1
2
1
1
1
2
2
2
1
1
1
1
3
1
0
0
1
2
1
1
1
1
0
2
1
1
1
1
1
2
1
1
1
1
2
2
2
2
1
1
1
1
1
0
1
0
1
2
2
0
2
1
1
1
2
2
1
1
2
1
1
1
1
2
1
0
1
1
1
2
1
1
1
1
2
2
0
0
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
0
1
1
2
1
1
1
1
1
2
1
0
1
1
0
1
1
1
1
0
1
2
1
1
0
1
0
2
2
1
1
1
1
2
1
1
0
2
1
1
1
2
0
2
1
1
1
2
2
1
2
0
2
0
1
1
1
2
1
1
1
1
1
0
0
2
0
1
1
2
1
1
1
2
1
1
0
2
1
2
1
1
1
1
2
1
1
1
1
1
2
1
1
0
0
1
2
1
0
2
1
1
1
1
1
1
2
3
1
1
1
2
0
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
2
0
2
0
0
1
1
1
1
2
1
1
2
1
0
1
1
0
1
1
1
1
2
2
1
2
2
1
1
2
1
1
0
1
2
1
2
2
1
2
1
1
1
1
1
2
2
0
1
1
0
2
1
0
2
0
1
0
0
0
1
2
1
2
1
1
0
1
2
1
1
1
1
1
2
1
2
2
1
1
0
1
1
2
2
1
3
1
2
0
2
1
1
0
1
1
1
1
2
1
1
1
1
1
1
2
1
1
0
2
0
2
1
1
1
2
1
1
1
1
2
2
1
1
2
1
1
0
2
1
2
2
1
0
1
1
1
1
2
1
1
1
0
1
1
1
1
1
0
1
1
1
2
0
1
1
2
0
1
1
1
1
1
1
2
1
2
1
0
1
2
2
1
0
0
1
1
2
1
1
0
0
2
1
2
1
2
1
1
2
1
1
1
2
2
2
1
2
1
2
1
1
1
1
2
2
1
0
0
1
1
1
3
1
2
1
0
2
1
1
2
1
1
1
1
1
2
1
1
2
1
2
1
1
0
0
1
1
1
1
1
1
1
0
1
1
1
2
1
1
0
2
1
1
1
0
0
1
2
1
2
1
1
2
1
2
1
1
2
1
1
1
2
1
1
2
1
1
1
0
1
1
1
1
1
2
1
2
1
1
0
2
1
2
2
1
1
1
2
1
1
1
1
1
1
0
2
1
0
2
1
1
2
1
2
1
2
1
2
1
1
2
1
1
1
1
1
1
1
0
1
1
2
1
0
1
0
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
3
1
1
2
2
1
2
1
1
1
2
2
0
1
2
1
1
2
2
1
2
2
1
2
1
1
1
1
0
0
1
2
2
2
2
2
1
1
3
2
0
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
2
1
2
2
2
2
2
2
1
0
1
1
0
2
1
0
0
2
1
1
3
1
1
2
3
0
0
1
1
2
2
2
1
1
1
1
2
1
1
1
2
1
2
0
1
1
1
1
2
1
2
2
1
2
2
1
1
1
2
1
0
1
2
1
1
1
0
1
0
1
0
1
1
1
4
1
1
2
1
1
2
1
1
1
2
0
2
1
1
0
2
1
1
1
0
1
1
1
0
1
2
0
0
1
2
1
1
1
1
0
1
1
0
1
1
1
1
1
2
1
2
1
2
1
1
2
1
1
0
1
1
2
2
1
1
0
0
1
1
1
1
0
1
1
1
1
1
3
2
2
1
2
0
2
2
2
1
1
2
2
2
1
1
1
1
1
1
1
1
1
2
1
0
2
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
2
1
1
1
1
1
0
1
1
0
2
1
1
0
2
1
0
0
1
1
1
0
1
1
1
1
1
2
1
1
0
0
1
1
1
1
1
1
0
0
2
1
2
1
1
0
2
1
1
2
2
1
2
1
1
1
0
1
1
1
0
1
2
1
1
1
1
1
1
1
1
1
2
1
0
2
1
0
2
2
1
1
1
1
1
1
2
1
2
1
0
0
1
1
2
1
1
2
0
3
2
1
1
1
1
2
1
1
2
2
1
1
1
0
2
1
3
1
2
1
1
0
2
2
1
1
1
2
2
1
1
2
2
1
1
1
1
0
0
2
0
2
0
1
1
1
1
1
1
1
1
1
2
2
0
1
0
2
1
2
2
2
1
1
1
2
2
2
1
2
2
1
2
0
1
1
1
1
2
2
2
1
2
2
1
0
2
1
1
1
1
0
2
1
0
1
1
1
0
1
2
1
1
1
1
0
1
1
1
1
1
1
2
1
1
2
1
1
1
1
0
1
1
1
2
1
1
1
2
3
1
1
1
2
1
1
0
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
0
2
1
1
1
1
2
1
1
1
2
1
1
1
2
2
2
1
1
1
2
2
1
1
2
2
1
1
0
0
1
1
0
2
1
2
1
0
2
1
0
1
1
2
1
1
1
1
1
0
1
3
2
2
1
2
2
0
1
1
1
1
1
1
1
1
1
0
0
1
1
1
0
2
1
1
2
2
1
2
2
1
2
1
1
2
0
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
0
2
2
1
1
1
1
1
1
1
1
1
0
1
1
2
1
1
2
2
1
1
1
1
1
1
0
2
0
1
1
1
1
1
1
1
2
1
1
0
1
2
1
1
1
2
2
2
1
2
0
1
0
1
1
1
0
1
0
2
1
1
1
2
2
2
0
2
1
2
1
1
0
1
1
2
1
1
2
0
2
1
1
0
1
2
2
2
2
1
1
1
2
1
2
0
1
2
1
0
1
1
1
1
2
1
1
2
1
2
1
1
0
2
1
1
2
0
1
0
1
2
2
1
1
1
1
1
3
1
1
0
1
2
2
2
1
2
2
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
0
2
1
2
1
1
1
1
0
1
1
2
1
1
2
2
0
1
2
1
2
1
1
1
1
0
1
2
2
1
2
1
1
2
1
1
1
1
1
1
2
1
2
1
0
2
2
2
1
0
2
1
2
1
1
1
1
1
0
1
1
2
1
1
0
1
2
2
1
1
1
1
2
1
1
1
2
1
1
1
1
1
2
0
0
2
1
2
1
1
1
1
0
1
1
1
1
1
1
1
2
2
2
1
1
1
1
2
1
1
1
0
1
2
1
2
1
0
1
2
2
1
1
2
1
2
2
1
2
2
1
0
1
1
1
2
2
2
0
1
2
2
1
1
1
1
1
1
1
1
2
1
1
1
1
0
2
1
2
2
1
0
1
1
2
1
2
1
2
2
1
1
1
2
2
1
2
1
2
1
1
0
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
1
1
0
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
0
1
2
2
2
1
0
1
1
1
0
0
2
2
1
1
1
1
1
1
2
1
3
1
1
1
2
1
2
1
2
1
1
0
1
2
1
2
2
2
0
2
2
1
1
1
1
0
2
1
1
1
0
1
2
1
1
1
1
1
1
2
0
1
1
1
1
2
1
1
2
1
1
1
1
1
2
2
3
1
2
1
2
1
2
2
2
1
1
1
1
0
1
1
0
2
1
1
0
1
1
2
1
2
1
1
1
1
2
1
2
1
1
0
1
1
1
0
2
1
1
2
1
1
2
2
0
2
2
1
2
2
0
1
0
1
2
0
1
1
1
2
1
1
2
1
2
2
2
1
1
2
1
1
1
1
1
1
1
2
1
1
2
1
0
1
2
1
2
1
1
1
1
1
1
3
2
1
0
1
1
2
0
1
1
1
0
2
1
2
1
0
1
1
1
2
2
0
2
0
1
1
2
0
1
1
1
2
1
2
2
2
1
1
0
1
1
0
1
1
1
0
1
2
1
1
1
1
2
1
2
2
1
0
2
0
2
2
1
1
1
1
2
0
2
2
1
0
1
0
1
1
1
0
0
1
0
1
2
1
1
2
1
1
1
1
2
1
2
1
1
2
2
1
1
1
1
2
2
0
1
1
1
1
2
1
0
2
2
1
1
1
2
1
0
1
0
1
1
1
1
1
2
2
1
1
1
1
1
1
0
1
1
2
2
1
2
0
2
1
1
1
1
1
0
0
1
1
1
2
1
1
1
1
0
1
2
2
1
0
1
2
1
1
0
1
2
1
1
0
1
2
1
1
0
0
1
1
1
1
1
1
1
1
1
2
1
1
1
0
1
1
2
1
0
1
1
2
1
1
1
0
2
2
1
2
1
2
1
2
2
1
1
1
1
1
1
0
1
1
1
1
2
1
1
2
2
1
1
0
0
1
1
3
1
1
2
0
1
1
1
1
2
1
2
1
2
1
1
1
2
0
2
2
2
1
2
2
2
1
0
1
1
2
1
1
0
2
1
1
2
1
1
2
2
1
1
1
2
1
1
1
1
1
0
4
1
2
1
1
1
1
1
2
1
1
2
1
1
2
0
1
2
4
2
1
0
1
1
1
1
1
2
0
1
2
1
1
2
1
1
2
1
1
1
1
0
1
1
0
2
2
0
0
1
1
0
1
1
1
1
0
0
1
0
2
2
2
1
1
1
1
1
1
1
1
1
1
2
0
2
2
1
1
0
1
1
2
1
1
1
2
1
1
1
1
2
0
1
1
1
1
2
0
2
1
1
1
0
2
2
1
1
1
1
1
0
1
1
1
2
2
1
1
1
0
2
2
1
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
2
1
2
0
1
1
0
1
0
1
2
2
0
1
1
0
1
1
1
0
1
1
0
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
2
1
1
0
2
1
1
1
2
2
0
0
2
2
1
0
1
0
2
1
1
1
1
1
1
1
1
1
2
1
0
1
0
1
0
1
2
2
1
1
2
1
1
2
0
0
1
2
1
1
1
1
2
2
2
0
2
1
2
1
0
2
2
1
2
1
1
1
3
2
1
2
1
2
1
1
2
1
1
1
1
2
1
2
1
1
2
0
2
1
1
1
2
2
2
0
0
1
2
1
1
1
0
2
2
1
0
1
1
1
1
1
1
1
0
1
1
1
1
1
1
2
2
1
2
1
0
0
1
3
1
0
1
2
2
1
0
2
0
1
2
1
2
0
1
0
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
0
1
0
2
1
1
1
1
2
2
0
1
1
1
2
1
1
1
0
1
2
1
1
0
1
2
1
2
1
1
1
0
1
1
1
1
1
1
2
2
1
1
1
0
1
1
3
0
2
1
0
1
1
1
2
2
0
1
1
1
2
1
0
2
2
0
1
1
1
1
2
1
1
2
1
1
2
1
1
2
1
3
1
1
1
1
1
1
2
2
2
1
1
1
2
0
2
0
1
2
0
0
1
2
2
1
3
1
0
1
1
0
1
1
1
2
0
2
0
1
1
0
1
2
1
2
1
1
1
2
1
1
2
1
0
2
1
2
0
0
2
2
1
0
1
1
2
1
0
1
2
2
2
1
1
1
1
1
1
2
1
2
1
1
2
2
1
0
0
1
0
1
0
2
1
1
1
1
1
1
1
0
1
1
1
2
2
2
1
1
1
1
1
1
2
0
2
1
1
1
1
1
1
1
1
1
0
2
0
0
2
2
2
1
2
1
1
0
2
1
2
1
1
0
2
1
1
1
1
0
2
1
2
1
1
1
2
1
3
3
1
0
2
1
1
1
0
1
1
2
1
0
2
2
2
1
1
2
1
0
0
2
2
1
1
1
0
1
1
2
1
2
2
1
1
1
1
1
0
2
0
2
1
0
2
1
2
1
0
1
2
1
1
1
1
1
1
0
1
1
1
2
1
1
1
1
2
2
1
2
1
2
1
2
0
1
1
2
3
2
1
2
1
1
1
2
1
1
1
2
0
1
0
0
0
1
2
2
1
1
1
2
2
2
1
0
2
1
1
1
1
2
2
0
2
1
1
2
1
1
1
1
1
1
1
2
1
1
2
0
1
2
1
2
1
1
0
1
2
0
2
1
1
1
1
1
0
1
1
4
1
1
1
2
2
1
0
1
1
1
1
0
1
0
0
0
1
2
1
2
1
1
1
1
1
0
1
2
0
2
1
1
6
1
2
2
1
1
1
2
2
1
2
1
1
1
1
2
1
1
1
1
1
2
2
1
1
1
0
0
1
1
1
1
2
1
1
1
1
1
0
1
1
0
1
1
1
1
0
1
1
1
0
2
2
2
4
1
1
2
1
1
1
1
2
4
0
1
2
2
1
1
1
1
1
2
2
2
2
2
1
1
1
1
0
1
0
0
0
1
1
1
1
2
0
1
2
1
2
1
1
1
1
1
2
1
2
0
1
1
1
2
0
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
0
1
1
1
2
1
2
1
2
1
2
1
1
1
0
1
1
2
2
1
1
2
1
1
2
2
1
1
2
1
1
2
1
2
1
1
2
1
2
2
1
1
1
2
2
0
1
1
1
0
0
1
0
1
1
2
0
1
1
1
2
1
0
1
2
2
1
1
2
1
1
1
1
1
0
1
2
1
1
2
1
1
1
2
1
2
1
1
1
1
2
2
2
1
1
0
1
1
2
1
1
0
2
0
1
1
1
1
1
1
1
0
1
1
1
2
2
1
2
0
0
1
2
1
1
1
1
0
1
2
1
2
1
0
1
0
1
2
0
2
1
1
1
1
1
1
2
1
1
1
1
0
1
2
0
0
1
1
1
2
1
2
2
1
1
1
1
1
2
1
1
2
1
2
1
1
0
2
1
1
1
1
1
1
1
1
0
2
1
1
0
1
0
2
1
2
2
1
2
2
1
2
1
1
1
1
1
2
1
1
2
1
0
2
1
1
1
1
2
1
2
1
3
1
2
2
1
1
2
1
2
0
1
1
1
1
0
1
1
2
1
1
2
1
1
2
1
1
0
1
1
2
1
1
4
1
1
1
0
1
1
1
1
1
1
1
1
1
2
1
1
2
2
1
1
1
2
1
2
1
2
1
2
0
2
0
0
1
1
1
2
1
0
1
2
2
2
2
1
1
2
2
1
1
1
0
1
1
1
2
0
2
1
1
0
1
1
1
1
1
1
2
0
1
2
1
2
1
1
2
0
1
2
1
1
1
2
1
1
2
1
1
1
1
2
0
0
1
2
2
1
0
1
1
1
1
1
1
2
1
2
1
2
0
1
1
2
1
1
2
2
2
1
0
1
1
1
1
1
1
1
1
2
2
1
1
1
2
3
0
1
1
1
2
0
1
1
0
1
1
1
1
2
2
1
1
1
1
2
2
1
2
0
1
1
1
2
1
1
2
2
1
0
1
2
2
2
1
1
1
1
2
1
1
2
1
1
0
1
1
1
1
1
2
1
1
2
1
2
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
1
1
0
1
1
2
1
2
2
1
1
1
1
1
1
1
2
0
2
2
1
1
0
1
1
1
0
1
1
2
1
0
3
1
1
1
1
1
1
0
2
1
0
2
1
1
1
1
1
1
2
1
2
1
2
0
1
0
1
2
0
1
0
2
1
0
2
1
0
1
1
2
4
0
2
2
1
1
1
1
1
2
1
1
0
0
1
1
1
0
1
1
1
1
2
1
0
1
2
1
1
2
2
2
1
1
1
1
2
1
2
1
2
2
0
0
2
1
0
1
1
1
0
0
0
1
1
2
1
1
1
1
2
1
1
2
1
0
1
2
0
1
1
1
2
0
1
1
1
1
2
0
1
2
1
2
1
1
1
0
2
2
1
1
0
1
2
1
1
0
2
2
1
0
1
1
2
2
2
0
1
0
1
1
1
1
2
1
2
1
1
0
2
1
1
1
1
0
0
1
0
1
1
1
1
1
2
0
2
1
1
1
1
2
1
0
2
1
0
0
2
1
2
1
1
0
2
1
0
1
2
0
2
1
1
0
0
2
2
1
0
2
0
1
2
2
2
2
0
2
1
2
1
1
2
0
1
2
2
1
1
1
1
2
1
1
2
1
1
1
0
1
1
1
1
2
2
2
2
2
2
1
2
2
1
0
2
1
1
1
2
1
0
0
1
2
1
1
1
0
2
1
1
1
1
2
1
0
1
2
2
1
1
1
1
1
0
2
1
1
1
1
1
1
1
2
2
1
1
2
1
1
0
1
1
2
1
0
2
1
0
0
1
2
0
2
1
2
1
1
1
1
1
1
1
1
1
1
3
2
0
1
1
1
1
2
1
2
1
2
1
2
3
1
1
1
1
1
0
1
0
1
1
1
0
1
1
1
0
1
1
1
2
1
1
1
1
2
3
2
1
2
2
1
0
2
1
0
1
2
1
2
1
2
1
1
1
0
1
0
1
2
1
1
2
2
1
1
1
1
1
0
2
1
0
1
2
1
1
1
1
1
2
1
2
1
2
1
1
2
1
2
1
1
0
2
1
1
2
1
1
2
1
2
2
0
1
1
1
1
1
1
2
1
1
1
2
2
1
1
0
1
1
1
1
1
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
1
1
0
0
2
1
0
2
2
1
2
1
0
1
0
1
1
2
1
2
1
2
1
2
0
2
0
1
1
1
0
2
1
1
1
2
2
2
1
2
1
1
2
1
2
1
2
3
1
1
2
1
1
2
1
0
1
0
1
2
1
1
1
2
1
1
1
1
0
1
2
1
1
1
0
1
1
1
2
1
1
2
1
2
1
1
1
2
1
2
1
1
1
2
1
1
0
2
1
1
0
1
2
2
1
1
0
1
1
2
1
1
1
1
0
1
1
1
0
1
1
1
2
1
2
0
1
1
1
1
0
1
1
0
2
0
1
1
1
2
1
1
1
0
1
2
1
1
1
1
1
1
1
2
1
0
1
1
2
1
0
1
2
1
1
1
1
1
1
2
0
1
2
2
2
1
0
1
1
1
1
0
1
2
0
1
1
2
2
0
1
0
1
1
2
1
1
1
1
1
1
2
1
1
0
1
2
1
2
1
1
1
2
0
1
1
1
1
0
1
1
1
0
1
1
1
1
2
2
1
1
1
1
1
2
2
2
1
0
1
1
1
0
1
1
0
1
0
2
2
1
2
1
1
2
1
2
2
2
1
1
1
1
1
1
0
1
1
1
1
0
1
2
2
2
0
2
1
1
0
1
1
1
1
1
0
1
0
0
1
1
1
1
2
0
1
2
2
2
1
1
2
2
1
1
1
2
1
1
1
1
1
2
2
2
2
1
1
1
1
1
2
1
1
1
2
2
2
0
2
2
1
3
1
1
1
1
1
0
1
1
1
1
1
0
0
1
2
1
2
0
1
1
1
1
1
1
1
1
1
1
1
1
0
2
1
0
1
1
1
1
2
2
1
0
1
2
1
1
2
0
0
2
1
0
1
2
1
1
2
1
1
2
2
1
1
1
0
2
1
1
1
1
1
1
2
1
0
1
0
1
1
2
1
2
1
1
1
0
1
2
1
1
0
1
1
1
0
1
1
1
2
1
1
2
1
0
2
1
1
1
1
0
1
2
0
1
1
1
1
1
0
1
1
1
1
2
1
0
2
2
0
1
2
1
2
0
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
1
1
1
2
0
1
0
2
2
1
1
1
1
1
1
1
2
2
0
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
0
0
1
1
1
1
0
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
0
2
2
2
2
2
2
2
2
2
2
2
1
1
0
1
1
2
1
1
1
2
1
2
1
1
1
2
0
1
1
1
2
1
2
1
3
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
2
0
1
0
0
2
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
0
1
2
0
2
1
2
1
1
2
2
1
1
0
1
2
1
2
1
1
1
1
1
1
1
1
2
2
1
1
1
1
2
2
1
1
2
2
1
1
1
2
2
1
1
1
1
1
2
2
1
1
2
1
2
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
2
1
2
2
1
1
0
2
1
1
0
2
2
1
1
2
1
1
2
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
2
1
1
2
2
0
1
1
1
2
2
1
0
2
1
1
1
1
2
2
1
1
0
1
2
0
2
1
1
1
1
1
1
1
2
3
1
2
1
2
0
2
1
2
2
1
1
1
1
2
2
1
1
0
2
1
1
1
1
0
1
2
1
0
0
1
1
1
1
1
1
1
1
2
0
2
2
2
0
1
1
1
1
1
0
2
1
1
1
1
1
1
1
2
0
1
1
1
1
2
1
1
2
1
0
2
1
2
1
1
0
2
1
1
0
0
1
1
2
2
1
0
0
1
2
2
1
1
0
0
1
1
2
1
1
1
1
1
1
2
1
2
2
1
1
2
1
2
1
0
1
1
2
1
2
2
2
2
1
2
2
2
2
0
2
2
2
1
2
2
1
1
1
1
1
0
1
2
1
1
1
1
1
0
0
1
1
2
0
1
1
1
2
1
1
0
0
0
1
2
2
1
2
2
1
0
1
1
2
1
1
0
1
1
2
1
1
2
0
2
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
2
0
1
1
2
0
1
1
1
0
1
1
2
1
1
1
0
1
0
1
1
2
1
1
2
2
1
1
5
1
1
2
1
1
1
1
2
1
0
1
2
2
1
2
1
1
1
1
1
2
2
1
1
1
1
1
2
1
2
1
1
1
0
1
1
1
1
1
1
1
1
0
0
1
1
1
1
1
1
1
1
0
2
1
1
2
2
1
2
1
1
1
1
1
1
1
0
1
1
1
2
2
1
2
2
1
1
2
1
0
2
1
2
1
2
1
0
1
1
1
2
2
1
1
0
0
0
0
1
2
2
1
1
1
1
1
1
0
2
1
2
1
1
4
2
2
1
2
1
2
0
2
2
1
1
1
1
1
2
0
1
2
2
0
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
0
1
1
2
2
2
4
2
1
2
2
1
1
2
1
0
1
1
2
1
1
1
1
1
1
1
0
1
0
1
1
1
2
0
2
1
2
2
1
1
0
1
1
1
1
0
1
1
1
1
1
1
0
2
1
2
1
1
2
0
1
1
0
1
0
1
1
1
1
1
1
1
1
1
0
0
0
1
1
1
1
2
1
0
2
1
1
1
2
1
1
2
2
0
2
1
1
1
1
1
3
0
1
0
0
1
1
2
2
1
1
2
2
1
1
2
1
1
1
2
2
2
0
1
2
1
1
1
1
1
1
1
1
1
2
1
0
2
0
0
1
1
2
1
2
1
1
1
0
1
1
0
2
1
1
0
1
1
1
2
1
1
1
0
1
2
1
0
0
1
2
1
1
1
1
1
1
2
2
1
1
2
2
1
1
3
1
0
1
2
1
2
1
1
2
1
1
1
1
1
1
2
0
0
1
1
2
1
1
2
1
1
1
1
2
0
2
1
1
1
1
1
2
2
1
2
1
0
1
1
1
0
1
1
1
1
2
1
1
2
1
2
2
1
2
1
2
1
1
2
2
1
1
0
2
0
1
1
2
1
1
1
1
2
2
0
1
1
0
2
1
0
1
0
0
2
2
2
2
0
1
2
2
1
2
1
1
1
1
2
2
2
1
0
2
2
1
0
1
1
1
2
1
1
1
1
1
1
2
0
1
1
0
1
1
1
1
1
1
0
1
1
1
1
2
2
1
2
2
1
1
2
1
2
1
0
2
2
0
1
1
0
1
1
1
1
1
1
1
1
0
1
1
0
1
1
1
2
1
2
1
1
0
1
1
2
1
0
2
0
2
1
2
1
1
1
1
1
1
2
2
1
3
2
1
1
0
1
1
1
0
1
1
1
1
1
1
2
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
2
1
1
1
2
2
1
0
1
1
1
1
1
1
2
1
2
2
1
1
0
1
2
1
1
0
2
2
2
1
1
1
3
0
2
2
1
1
0
1
1
1
0
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
2
2
1
2
1
1
1
0
1
2
1
1
1
2
1
1
1
2
1
2
1
1
0
1
2
1
1
1
1
1
1
1
0
2
2
2
1
1
1
2
2
1
1
1
1
1
2
0
2
2
1
1
0
1
2
1
0
1
0
1
0
1
2
1
0
1
2
1
1
1
0
2
1
1
1
1
2
1
1
1
1
4
1
0
2
1
0
2
3
2
1
2
0
2
1
2
1
1
1
1
1
2
0
0
1
2
0
0
2
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
0
1
1
1
1
1
1
0
1
0
1
1
0
2
0
1
1
1
1
2
1
2
2
2
1
1
1
1
2
1
1
2
1
1
3
1
2
0
1
0
1
0
2
1
1
1
1
2
2
0
1
1
2
2
1
2
1
2
0
1
1
1
1
2
1
1
1
1
2
2
1
1
0
0
1
1
1
1
2
1
1
2
1
1
1
1
2
2
2
2
2
1
0
2
1
0
1
2
1
1
1
0
1
2
0
1
1
1
1
1
2
2
1
2
0
1
1
1
0
0
1
2
2
0
1
0
1
1
0
1
1
1
2
2
1
1
2
1
0
1
0
0
1
2
2
1
1
1
1
1
1
1
2
2
1
2
1
1
2
1
0
1
2
1
2
2
1
1
1
2
2
2
1
0
1
1
2
1
1
1
2
0
1
2
1
1
2
1
1
1
1
1
1
1
1
0
1
1
2
2
2
2
2
1
1
0
1
2
0
1
1
2
0
1
1
2
1
1
2
1
1
0
1
1
1
1
0
1
1
2
2
2
0
1
1
2
1
1
1
2
1
1
1
0
2
1
1
1
0
0
1
1
1
1
1
1
1
1
0
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
1
1
0
1
2
1
1
1
2
2
1
1
1
2
0
0
1
1
1
0
1
1
0
1
1
2
1
0
2
0
1
1
1
0
2
2
2
0
1
2
1
2
2
2
2
1
1
3
1
1
1
1
0
0
1
1
2
1
1
0
1
0
1
2
1
1
0
2
1
2
0
2
1
2
2
1
1
2
0
0
0
1
1
1
1
1
1
0
0
1
1
2
1
2
2
1
2
1
2
1
1
1
1
0
1
2
0
1
0
2
2
1
1
2
1
1
1
0
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
1
2
1
2
1
1
1
0
1
2
2
1
2
2
1
1
0
1
2
2
0
0
2
0
2
1
1
0
2
0
2
2
2
1
2
1
0
0
3
2
2
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
2
1
2
0
1
1
0
1
1
1
2
2
1
1
1
0
0
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
2
0
1
0
1
1
0
1
2
2
1
2
1
1
0
1
0
1
1
2
1
1
1
0
2
1
1
1
1
1
2
1
0
1
1
0
2
1
2
1
1
0
2
1
2
2
2
2
2
1
1
2
2
1
1
1
2
1
2
1
2
1
2
1
1
0
1
2
1
1
1
2
1
1
1
1
1
1
1
0
1
1
1
0
1
1
0
3
1
2
1
2
1
1
0
1
1
1
1
1
1
1
1
1
1
1
2
0
2
0
0
1
1
0
2
1
1
1
2
1
1
2
1
1
0
0
1
2
1
1
1
1
1
1
0
1
1
1
2
1
1
2
0
1
1
1
1
1
2
1
2
1
1
2
2
1
1
1
1
2
1
2
0
1
0
1
1
2
1
1
0
1
2
1
1
2
1
1
2
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
0
2
2
1
1
0
1
1
1
2
0
2
1
1
2
2
2
1
2
1
2
1
1
1
2
0
1
1
2
1
1
0
1
1
2
2
1
2
1
2
2
1
1
2
1
1
2
2
1
1
1
1
2
1
1
2
1
0
1
1
0
2
2
1
2
2
1
1
1
1
1
2
1
1
2
1
1
2
0
1
2
2
2
1
1
2
1
1
1
1
2
2
1
0
1
2
0
2
1
0
1
1
2
1
4
2
1
1
1
2
1
1
2
1
2
0
0
2
1
1
1
1
1
2
0
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
0
0
2
1
1
2
1
1
0
1
1
1
2
1
1
1
2
2
0
2
0
1
1
1
0
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
2
2
1
2
2
2
0
2
0
1
2
1
1
2
1
2
1
0
2
1
1
2
1
1
2
1
1
0
1
1
1
1
2
1
0
1
2
1
1
2
0
0
2
1
1
1
2
2
1
2
1
1
1
1
1
1
2
2
0
1
2
2
2
2
1
2
2
2
2
1
2
1
0
1
1
2
1
1
1
1
1
1
2
1
1
0
1
1
1
1
1
1
0
1
1
1
2
2
2
0
1
0
1
0
2
1
2
0
1
2
2
1
2
1
2
1
1
1
1
1
1
0
0
0
1
1
0
0
2
1
1
2
2
1
1
1
1
1
1
1
1
1
0
1
2
1
2
1
1
0
0
1
1
0
2
0
1
0
1
1
1
1
1
1
0
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
2
1
1
1
2
2
2
3
2
1
2
0
2
1
2
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
2
0
1
1
0
2
1
0
1
0
1
1
1
2
1
1
1
1
0
2
0
2
1
2
0
1
1
0
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
2
0
1
0
1
1
1
2
1
0
1
0
0
1
0
1
1
2
2
0
1
1
1
1
1
1
1
0
2
1
2
1
2
1
1
1
1
0
1
1
1
0
1
1
1
1
1
1
0
0
1
1
2
1
2
2
0
1
1
1
1
2
0
0
1
1
1
1
1
1
1
1
1
2
0
1
1
1
2
1
2
2
1
1
1
2
1
0
3
1
0
2
1
1
1
2
2
1
1
1
0
1
1
1
1
3
0
1
1
1
1
2
1
1
1
1
1
1
1
1
1
0
2
2
2
1
1
1
2
1
2
1
1
2
1
1
1
1
1
1
1
0
2
1
2
1
1
2
1
2
2
2
1
1
1
2
2
1
2
1
1
2
1
2
1
4
1
1
2
2
1
1
1
1
1
2
1
0
1
0
1
3
1
1
1
2
1
1
1
1
2
1
2
1
2
1
1
2
1
2
2
1
2
1
2
1
1
1
1
2
2
2
1
0
1
1
1
1
0
1
1
1
0
1
1
1
1
0
1
2
2
1
1
1
2
1
1
2
2
2
1
1
1
2
1
1
2
1
0
1
0
1
2
1
1
1
1
1
1
2
1
1
2
2
1
2
0
1
2
0
1
1
1
2
1
2
1
0
1
2
1
1
1
2
1
1
0
0
1
1
2
2
2
1
1
1
1
0
2
0
1
0
0
1
1
1
2
1
1
1
2
1
1
1
1
1
2
0
1
1
1
3
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
0
1
2
1
1
2
2
2
2
2
1
1
1
2
2
1
0
1
1
1
2
0
0
0
1
2
1
1
1
2
1
2
1
1
2
1
0
1
0
1
1
0
0
2
1
2
1
1
1
1
2
1
0
1
1
1
2
1
0
1
2
1
1
1
1
2
1
2
1
1
2
1
1
1
1
1
2
0
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
0
2
1
2
2
2
1
1
0
2
2
1
2
0
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
2
2
1
3
2
2
1
1
1
2
1
1
1
0
1
1
1
1
2
1
1
0
1
1
1
1
2
2
1
0
2
1
1
1
1
1
2
2
1
1
2
1
1
1
2
1
1
0
2
1
1
1
1
1
1
2
1
3
2
1
1
1
0
1
2
2
1
2
1
1
0
1
0
3
1
1
1
1
1
1
2
2
2
1
0
1
2
2
1
1
1
2
2
1
1
1
0
1
2
0
2
1
1
2
1
2
1
2
2
1
2
2
2
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
0
2
1
2
2
1
1
2
0
0
1
1
1
1
1
1
1
2
1
1
2
1
2
2
2
1
1
0
1
1
1
0
1
1
2
1
1
1
0
1
1
2
1
1
1
1
1
1
0
1
1
1
4
1
4
2
2
3
1
2
1
1
2
0
2
1
2
1
1
1
1
1
1
1
1
2
1
0
1
2
1
1
0
1
0
1
2
0
1
1
1
1
2
1
2
1
2
2
2
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
2
0
2
1
1
2
1
1
1
1
1
2
3
2
1
2
1
0
1
1
1
1
0
1
0
0
1
2
2
1
1
2
1
0
2
1
1
1
1
2
1
1
1
1
1
1
3
0
1
1
1
1
1
2
2
2
1
0
0
1
1
2
2
1
1
2
1
0
2
1
1
0
1
1
0
1
0
1
2
1
1
1
1
1
1
0
2
1
0
2
2
1
1
2
1
0
1
1
1
0
2
0
1
2
2
2
2
1
1
0
1
0
1
1
0
2
2
2
2
1
1
2
1
1
1
1
1
2
3
1
1
2
1
1
1
0
0
2
2
1
2
2
1
1
2
1
2
1
2
1
2
1
1
1
1
2
1
1
1
1
3
1
1
2
2
1
2
1
1
2
2
1
1
1
0
1
0
1
2
2
0
1
1
1
1
1
0
2
0
0
1
2
1
1
1
2
1
1
2
1
1
2
1
1
2
2
2
1
1
1
1
2
2
1
1
0
1
1
1
1
0
0
1
1
1
1
1
2
1
1
1
0
0
0
1
1
1
1
1
1
2
0
1
0
1
1
1
1
2
1
1
2
1
1
2
0
2
2
1
1
1
1
2
0
1
1
1
1
1
1
2
1
1
0
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
0
0
1
2
1
1
1
1
1
1
1
0
1
2
1
0
1
0
1
0
0
0
0
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
0
2
2
1
1
1
1
0
1
2
1
1
0
0
1
1
1
2
1
0
1
1
2
1
1
1
1
2
1
0
2
1
1
1
1
2
1
2
0
1
1
1
1
1
1
1
0
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
0
2
2
2
0
1
0
0
2
2
2
2
1
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
2
1
1
2
1
1
1
2
0
0
1
2
1
1
1
1
1
1
1
2
1
1
1
1
0
1
1
2
0
1
2
1
1
2
0
2
2
1
1
1
2
2
2
0
1
2
1
0
2
1
2
0
1
0
1
2
2
1
2
0
2
1
1
1
2
2
2
3
0
0
1
1
1
1
1
2
1
0
2
2
0
1
1
1
1
1
1
0
1
2
2
1
1
1
2
2
1
0
2
2
1
1
0
2
1
1
0
1
1
1
1
2
1
1
1
2
1
2
1
0
1
1
1
2
1
2
1
1
1
2
1
1
1
2
1
1
2
0
1
1
2
1
1
1
1
2
1
2
2
0
1
1
1
2
2
1
1
1
1
1
1
2
2
2
1
2
1
1
1
0
1
1
1
2
1
1
1
2
1
0
1
1
2
2
1
1
2
1
1
1
1
0
1
3
1
1
0
2
2
2
1
1
1
1
0
1
1
0
0
1
1
0
1
1
1
0
0
1
1
1
1
2
2
1
0
1
1
1
1
1
1
2
1
1
2
1
2
1
1
0
0
1
1
1
2
1
1
1
2
2
2
2
1
1
2
0
1
2
1
0
1
1
2
1
1
1
1
1
1
2
1
2
1
1
0
1
2
2
1
1
2
2
0
1
2
2
0
2
1
0
1
1
1
2
1
1
1
2
0
1
1
2
1
0
1
1
2
1
1
1
1
1
2
1
2
1
1
1
2
2
1
1
1
1
2
0
1
2
2
1
1
2
2
2
1
2
1
2
1
1
0
0
1
1
1
1
2
2
1
1
1
2
1
1
1
2
1
1
2
1
1
2
1
1
1
1
1
1
0
2
1
1
2
1
1
1
1
2
2
1
2
1
0
2
1
2
0
1
2
2
2
2
1
1
1
1
2
1
1
3
2
1
2
3
1
2
2
1
1
2
2
1
1
0
2
1
1
2
2
1
1
1
2
1
1
1
0
2
0
1
1
2
1
2
1
2
2
2
2
1
2
1
1
1
1
1
2
2
1
1
1
1
0
0
0
1
2
1
1
2
1
1
2
2
0
2
2
1
1
1
1
0
1
2
1
0
2
1
2
1
1
1
2
1
2
2
2
2
2
0
1
1
2
6
1
2
0
1
0
2
1
1
0
2
1
2
2
1
2
1
2
2
2
1
2
1
2
1
1
0
2
1
2
0
1
1
1
1
1
1
0
0
0
1
2
2
1
2
1
2
0
0
1
0
0
1
2
1
2
0
1
1
1
1
2
0
1
2
1
0
1
1
2
1
1
1
1
1
0
1
2
1
1
0
5
1
1
1
1
1
1
2
1
1
1
1
1
1
1
0
1
2
1
2
0
2
1
1
0
1
0
2
1
1
1
1
1
1
0
1
1
2
2
2
1
1
1
1
0
0
1
1
2
1
0
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
0
1
2
1
1
1
1
1
0
2
1
2
2
1
1
1
2
1
2
1
1
0
1
1
0
1
1
0
1
1
1
7
2
0
1
2
1
1
0
1
1
1
0
0
0
2
1
1
0
2
1
1
1
1
2
2
2
2
0
1
2
2
2
0
1
1
1
2
1
1
1
2
1
0
1
2
1
1
1
1
1
2
1
0
1
2
2
2
1
0
1
1
1
0
0
1
1
2
1
2
1
2
2
1
1
1
1
1
1
2
1
1
1
1
2
1
0
1
1
1
2
1
1
1
1
1
3
1
2
2
1
2
1
2
1
2
1
1
1
2
1
1
0
0
0
1
2
0
1
1
2
0
1
1
2
0
2
2
1
1
1
2
1
1
1
1
2
1
1
1
2
2
1
2
1
1
1
1
1
1
1
2
2
1
1
1
1
2
2
1
1
1
1
2
2
2
1
1
1
1
1
2
2
1
2
1
0
0
0
2
1
2
1
1
1
1
1
1
0
1
2
2
1
1
1
2
1
1
2
2
2
2
1
1
1
1
1
2
0
1
1
1
2
1
1
1
2
2
0
0
2
0
1
2
1
1
1
1
1
1
0
2
1
2
1
2
2
0
2
1
1
0
0
1
1
2
2
1
2
1
1
1
2
0
0
1
0
1
2
1
1
2
1
1
3
1
0
1
2
1
2
1
0
1
2
1
2
2
2
1
1
1
1
0
1
1
0
1
2
1
1
0
0
1
1
1
1
0
2
1
1
1
1
1
1
2
0
1
1
1
2
3
2
0
1
3
1
1
2
1
1
1
1
2
1
1
1
0
0
2
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
1
1
2
2
0
1
1
2
1
1
2
0
0
1
1
1
0
1
1
2
1
1
0
0
1
1
1
0
2
1
1
1
1
1
2
1
2
1
0
1
1
2
1
2
1
1
1
2
1
0
1
1
1
2
0
0
0
1
1
1
0
1
2
2
1
1
2
1
0
1
0
1
0
1
3
2
2
0
1
1
1
1
1
1
0
1
2
1
2
2
1
1
2
1
1
2
1
1
2
1
2
1
1
1
2
1
2
2
0
1
1
2
1
1
0
0
2
1
1
1
1
1
0
1
1
2
2
2
1
1
2
1
1
0
2
1
1
0
1
2
1
1
2
0
1
1
2
0
2
2
1
1
1
1
1
1
1
2
1
1
2
1
3
2
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
2
0
1
1
1
1
0
1
2
1
3
2
1
2
1
3
1
1
2
0
1
1
2
2
1
1
0
1
2
1
2
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
1
0
2
1
1
0
2
3
0
1
1
2
2
1
1
2
2
1
1
1
0
1
1
2
1
0
1
1
2
2
2
2
1
1
1
2
1
1
1
1
1
1
5
1
1
2
0
0
1
1
1
0
1
2
2
1
0
0
1
1
0
1
1
1
2
2
1
1
1
1
1
2
0
1
1
1
2
0
1
0
1
1
1
2
1
2
1
1
1
1
2
1
2
1
1
1
2
2
0
1
1
1
0
1
1
1
1
1
2
1
1
1
2
1
1
0
1
2
1
1
1
0
1
0
1
1
1
2
2
3
2
1
1
2
1
1
1
1
3
2
1
2
1
1
1
1
1
0
2
1
1
1
1
1
1
1
2
2
2
1
2
2
1
1
1
1
1
2
0
2
1
0
1
2
1
2
1
2
1
1
2
2
1
1
1
1
0
2
1
1
1
1
1
1
1
1
1
2
2
1
3
0
1
2
2
1
0
2
1
2
1
0
0
2
0
0
2
2
1
1
1
1
2
1
1
1
2
0
2
1
1
0
2
1
2
1
1
1
1
1
1
2
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
1
0
2
1
2
2
1
1
1
1
1
2
1
0
0
1
2
2
1
1
2
0
2
2
2
1
2
1
2
1
0
0
1
1
1
2
1
2
1
1
0
1
0
1
2
1
1
1
1
3
1
1
1
1
2
1
1
1
0
1
2
2
1
1
1
1
1
1
1
1
1
1
0
2
1
1
0
1
1
1
1
2
0
2
2
2
1
2
2
1
1
2
1
1
2
2
2
1
0
2
1
1
1
1
2
1
1
0
1
0
3
1
1
1
2
2
1
1
0
2
1
0
2
1
1
1
2
1
1
1
1
2
1
2
1
0
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
0
1
1
1
1
1
1
2
2
1
1
2
1
1
0
0
1
1
1
1
2
1
2
0
1
1
0
1
2
2
1
1
0
1
2
2
0
1
1
1
2
1
3
0
0
1
1
2
0
2
1
2
1
1
1
0
2
1
2
1
0
0
1
1
2
1
2
0
1
1
2
1
1
1
1
1
1
2
0
1
1
1
2
0
0
2
1
1
2
1
2
1
1
1
1
1
1
1
1
2
1
0
1
0
2
1
1
1
2
0
1
2
2
1
1
1
2
1
2
5
1
2
2
1
1
2
2
0
1
1
1
1
1
1
1
2
1
2
0
1
1
1
1
2
1
1
1
2
1
1
0
2
1
2
0
1
1
0
2
2
2
1
2
0
1
1
1
1
3
0
2
1
1
0
1
2
1
2
1
2
1
1
2
1
0
2
1
1
1
2
0
1
1
1
2
1
1
0
2
1
1
2
1
1
2
0
1
2
1
2
2
1
1
2
2
0
2
2
1
2
2
1
1
1
0
2
2
1
1
2
1
1
1
2
1
2
0
2
2
1
1
1
0
2
1
1
7
1
2
2
0
1
1
1
1
1
0
1
2
2
1
2
1
1
1
1
2
2
1
2
1
2
0
1
2
2
2
1
1
2
1
1
1
0
1
1
1
2
1
1
1
1
1
0
0
1
2
1
1
2
1
1
2
1
1
2
2
2
1
1
1
0
1
1
2
1
1
1
1
1
1
0
1
2
2
2
2
1
1
0
0
1
1
1
2
1
1
2
0
1
1
1
2
2
1
1
0
1
1
2
1
1
0
2
2
1
1
6
1
2
0
1
0
1
1
1
1
0
1
1
2
1
1
2
1
3
1
2
1
2
1
1
1
1
1
0
2
1
1
1
1
1
1
0
1
1
2
2
1
2
1
1
1
2
1
2
2
1
0
1
1
0
2
2
0
2
1
1
3
2
2
0
2
1
1
1
1
1
1
1
1
1
1
2
1
2
0
2
2
2
2
1
2
2
0
1
1
1
2
2
2
1
1
2
1
1
0
0
1
2
2
2
2
1
2
1
1
1
1
1
2
1
2
1
1
0
2
1
1
1
0
1
0
1
2
1
1
1
1
1
1
1
2
1
0
2
2
1
1
1
1
2
2
1
1
1
2
2
1
2
0
1
1
1
1
1
1
0
2
1
1
1
1
2
1
2
0
2
2
1
1
0
0
1
2
2
1
1
0
1
1
1
0
1
1
1
2
1
1
1
2
1
1
1
1
1
0
1
0
1
1
1
1
1
1
2
0
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
0
1
1
2
0
2
2
1
1
0
2
2
2
1
1
2
1
2
1
1
2
1
1
1
1
1
1
0
0
1
1
2
0
1
1
2
0
0
1
1
2
1
2
0
1
2
2
0
1
1
2
1
2
1
1
1
2
1
0
1
1
1
1
2
1
2
0
2
0
1
1
0
1
1
0
1
1
2
1
1
1
2
0
1
2
2
1
1
2
1
1
1
2
1
1
1
2
1
1
0
2
1
2
2
1
1
2
1
1
1
2
1
1
1
1
1
1
2
1
2
1
2
1
2
1
2
2
1
1
1
2
1
1
0
1
1
1
0
1
1
1
1
2
1
2
1
1
1
1
1
0
1
1
2
1
1
1
1
1
1
1
1
0
1
1
1
1
2
1
1
2
0
2
2
2
1
0
1
2
1
2
1
1
2
1
1
2
1
2
1
1
2
1
1
3
1
0
1
1
1
1
1
0
1
1
1
1
3
1
0
1
1
1
0
1
2
1
1
1
1
2
1
0
2
1
1
1
0
1
2
0
1
1
1
2
2
2
2
0
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
0
2
2
2
1
1
1
1
2
0
2
1
1
1
1
1
0
2
1
1
2
1
2
1
2
1
0
1
1
1
1
1
0
2
1
1
1
1
1
1
2
2
0
1
1
2
1
1
1
1
2
2
0
1
0
1
1
0
1
2
2
1
1
2
0
1
1
0
0
1
1
1
2
2
1
1
1
2
1
1
1
0
2
1
1
1
2
1
0
1
0
1
1
2
2
0
1
1
1
1
1
1
1
2
0
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
2
3
1
1
1
1
1
1
1
2
1
2
2
1
2
0
0
1
2
1
2
1
1
2
2
2
1
1
2
0
1
2
1
2
1
0
2
1
2
1
1
2
0
1
1
1
2
2
1
1
1
2
1
1
1
1
0
0
1
0
1
2
2
0
1
1
2
1
2
1
0
1
2
1
1
2
1
1
1
2
1
0
0
1
1
1
1
2
1
1
2
0
1
2
2
2
1
0
2
1
1
2
2
1
0
1
0
0
0
0
1
1
2
1
1
1
2
1
0
2
2
2
1
2
1
1
1
2
1
1
1
2
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
2
0
1
2
2
2
1
2
1
2
0
1
2
1
1
1
1
2
1
2
1
0
1
1
2
0
0
0
1
1
1
1
1
1
2
1
0
1
1
1
0
0
2
1
1
1
1
2
1
1
1
0
1
2
0
1
0
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
0
1
2
1
1
1
0
1
1
1
1
2
2
1
0
2
1
1
1
2
0
1
1
1
0
0
1
1
2
1
0
1
1
1
1
0
1
2
2
1
1
2
1
2
2
2
1
1
1
1
0
0
2
1
0
1
1
1
1
1
2
1
2
2
2
0
1
1
1
0
2
1
2
2
1
1
1
1
1
1
1
0
1
1
1
2
2
1
1
0
1
1
2
1
1
1
2
1
1
0
1
1
1
1
0
1
1
1
1
0
1
2
0
1
2
1
2
2
1
1
0
2
1
2
1
1
1
2
1
1
1
2
1
2
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
2
1
2
1
0
1
2
1
2
1
3
1
1
2
2
0
2
2
1
2
0
2
1
1
1
1
2
0
1
2
1
1
1
2
1
1
1
2
0
1
0
1
1
1
0
1
2
1
3
2
2
1
1
2
1
1
2
2
1
1
1
1
1
0
1
2
2
1
0
2
1
1
2
1
1
1
2
1
2
1
1
2
1
0
1
0
3
1
1
2
1
0
0
2
1
0
1
1
1
2
1
1
2
1
2
1
1
1
1
2
1
1
2
1
0
2
0
0
1
2
0
1
1
1
1
1
1
1
1
0
1
1
1
2
1
1
1
1
0
2
2
1
1
1
2
1
1
1
1
1
2
2
1
1
1
1
2
1
2
1
1
1
1
2
2
1
2
2
0
1
2
1
1
2
1
2
1
1
1
1
2
1
1
0
1
2
2
2
0
1
0
1
2
1
0
1
1
1
2
0
2
1
2
0
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
0
1
1
2
0
1
1
1
1
1
3
1
1
1
2
0
0
1
1
1
0
2
1
1
1
0
1
2
1
0
1
1
1
0
1
1
1
1
1
1
0
0
2
0
1
0
1
0
1
1
1
1
2
1
1
2
1
1
0
2
1
0
1
1
1
2
1
0
1
0
1
1
2
1
1
1
2
0
1
1
0
2
0
2
2
1
2
1
1
2
1
1
2
1
1
1
1
2
1
2
0
1
0
2
2
2
2
1
1
2
1
1
2
1
0
2
1
1
1
0
2
1
2
1
1
0
1
1
1
1
1
1
1
0
1
1
0
1
1
1
0
2
2
1
0
1
2
1
2
0
0
1
0
2
2
1
2
2
1
1
0
0
0
1
1
1
2
1
2
0
0
1
2
1
1
0
1
0
2
1
2
2
0
3
1
2
1
2
2
1
0
2
1
0
2
1
1
2
2
1
1
0
2
0
1
0
1
1
1
1
0
1
0
1
1
1
1
2
1
1
2
0
0
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
2
0
1
1
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
2
1
0
0
1
1
2
1
1
2
2
1
2
2
1
2
2
1
1
1
2
1
0
2
2
1
2
2
1
2
2
1
2
0
1
1
1
2
1
1
1
2
2
1
2
2
1
2
2
1
2
1
0
1
1
1
2
2
1
0
1
2
2
1
2
2
1
0
1
1
1
1
2
2
1
2
1
1
1
1
1
1
3
1
1
1
1
2
1
1
1
2
1
1
2
1
2
1
1
1
1
0
1
1
2
1
1
1
2
2
1
2
1
1
1
2
2
2
2
1
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
0
2
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
0
2
1
1
1
2
1
2
1
0
2
0
1
1
1
2
1
1
1
1
2
1
2
1
1
1
1
3
1
1
0
2
2
1
1
0
2
2
1
1
1
1
2
2
1
1
0
1
1
1
1
2
1
0
0
1
1
0
0
1
2
1
2
1
1
1
1
0
1
2
1
2
1
2
1
1
1
2
1
1
1
1
2
0
2
1
1
2
1
2
0
1
1
1
2
2
1
2
2
2
1
1
1
1
2
1
1
1
1
0
0
1
2
1
2
1
2
2
3
1
0
1
1
1
1
0
1
1
1
1
2
2
1
1
1
0
1
1
1
1
1
1
1
2
2
1
1
1
0
1
1
2
2
1
1
2
1
1
1
1
1
0
0
1
2
2
1
2
2
2
1
1
1
1
1
2
0
1
1
1
2
1
1
2
1
2
2
1
0
1
1
2
2
1
1
1
2
2
2
2
1
0
1
1
1
1
0
2
1
1
1
1
2
1
1
2
2
1
0
1
1
0
1
2
1
0
2
2
1
1
1
2
1
1
1
1
1
1
2
0
2
1
2
1
1
1
1
2
1
1
1
1
0
0
0
1
0
0
1
1
1
2
1
0
1
2
2
0
0
0
1
0
1
1
2
1
2
1
1
1
2
1
1
2
1
1
1
1
1
2
0
2
0
2
1
1
1
1
1
0
2
0
1
1
2
2
2
1
2
1
1
1
0
0
0
1
2
1
2
2
1
2
2
2
2
1
1
1
1
0
0
1
1
2
1
1
1
1
0
1
1
1
2
0
0
1
1
1
2
0
2
1
2
2
1
1
2
2
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
2
1
1
1
0
2
1
2
1
1
1
1
1
2
0
1
1
2
2
1
2
2
1
1
1
2
2
2
2
1
1
2
2
1
1
1
1
2
1
1
1
2
1
1
2
2
0
0
2
1
1
1
1
1
2
1
2
1
1
3
1
2
1
1
1
2
0
1
1
1
4
0
1
2
2
2
1
1
1
1
1
1
1
0
2
1
1
2
1
2
1
1
1
1
0
1
1
1
2
2
2
0
1
2
2
2
2
1
1
1
1
2
1
2
1
1
1
2
2
0
1
1
1
1
1
0
1
1
1
1
2
1
2
1
2
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
3
1
1
2
2
1
2
1
2
1
0
2
1
1
1
0
2
2
2
1
1
1
1
1
1
2
1
1
2
1
2
1
1
2
2
1
2
1
1
1
1
1
2
1
1
2
0
1
1
1
2
1
1
1
1
1
0
1
2
1
2
1
0
1
1
1
1
2
1
0
1
1
2
2
1
2
1
1
0
1
1
0
1
1
1
2
0
1
0
0
2
1
2
1
1
0
1
2
2
2
2
2
1
1
2
1
2
2
2
2
1
1
1
2
1
1
2
1
1
1
1
1
1
2
2
1
1
2
1
0
1
1
1
2
1
2
1
2
1
1
1
2
2
1
1
0
1
1
1
1
0
1
2
1
2
0
2
2
1
1
1
2
0
2
1
1
0
1
1
1
2
1
1
1
1
0
1
1
0
2
0
0
1
1
0
1
1
2
1
1
2
1
1
1
0
1
1
1
2
2
2
1
1
2
1
1
1
0
1
2
1
1
2
1
1
0
0
1
1
1
1
1
0
1
1
1
1
1
1
1
2
1
1
2
0
0
2
0
2
1
2
0
2
0
1
1
1
2
0
1
1
2
2
1
1
1
1
1
3
2
2
1
1
2
1
0
1
0
1
2
1
1
1
1
1
2
1
1
1
0
1
0
2
0
2
1
1
1
1
0
1
1
1
2
1
1
1
1
0
2
1
1
1
1
2
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
2
1
0
1
0
0
1
0
1
1
2
1
1
1
1
1
1
2
0
1
1
1
1
1
2
0
0
1
1
2
0
1
1
1
1
1
1
2
1
2
0
2
1
0
1
1
1
2
1
0
1
1
1
2
0
1
1
1
1
2
1
1
1
2
2
1
2
0
2
2
2
1
1
0
2
1
2
2
1
1
2
2
1
1
2
2
1
1
1
2
0
1
2
1
2
0
2
1
1
1
1
1
1
2
0
0
1
0
2
1
1
1
1
1
2
0
1
1
1
0
2
0
1
2
1
1
1
0
0
1
0
2
1
1
1
1
2
2
0
1
2
0
1
2
1
1
2
2
1
1
0
1
2
1
1
1
1
1
1
1
1
2
2
2
1
1
1
2
0
1
2
2
2
3
1
1
2
1
2
1
1
1
0
0
2
1
1
1
1
2
1
1
0
0
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
0
0
0
0
2
1
1
1
1
1
1
2
2
2
2
1
2
1
1
2
0
1
1
1
2
1
0
1
2
1
1
2
2
1
1
2
1
2
1
1
1
0
1
2
0
2
1
1
2
2
0
0
1
1
1
1
0
0
1
2
1
3
1
1
1
2
2
2
1
2
1
1
1
0
1
2
2
1
0
1
0
0
1
2
1
1
1
0
2
2
1
1
1
1
1
1
1
1
2
0
2
1
0
1
1
2
1
1
0
1
1
1
3
2
1
1
1
1
2
0
1
1
2
0
1
2
0
1
1
0
2
1
1
0
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
2
2
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
2
1
0
2
0
1
1
1
0
0
1
1
1
1
1
3
1
1
1
1
1
0
2
2
1
1
1
2
2
1
1
2
1
1
1
2
1
0
1
0
0
2
1
0
2
1
0
1
1
2
1
1
2
1
1
2
1
1
1
0
2
0
2
1
0
0
1
0
1
1
0
1
0
1
1
1
1
1
1
0
1
1
2
0
1
1
1
1
2
2
1
2
1
1
1
2
1
1
2
1
1
2
2
1
4
1
1
1
1
0
1
2
1
1
1
0
1
0
0
1
2
2
1
1
0
1
1
2
0
2
2
1
0
1
1
1
2
2
2
1
0
1
1
1
1
1
2
1
1
0
0
2
1
1
0
1
1
1
1
0
1
0
2
2
1
2
1
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
2
2
2
1
2
2
1
1
1
1
1
1
1
2
1
1
2
0
2
2
2
1
1
0
0
1
2
2
1
1
1
1
2
2
1
1
1
2
1
1
1
0
1
1
2
0
1
2
1
1
1
1
0
0
1
2
1
2
1
1
1
2
1
1
2
0
1
2
2
1
1
2
1
1
2
2
1
1
1
1
1
1
2
2
1
1
1
0
1
2
0
1
1
2
1
1
2
1
1
0
1
1
1
2
2
1
1
1
1
1
2
1
0
1
1
2
2
0
1
1
2
0
1
1
1
1
1
1
1
2
0
1
1
2
0
2
2
1
1
1
2
1
1
1
1
0
0
1
1
1
1
1
1
1
1
1
1
0
1
2
0
1
1
0
1
1
1
2
1
2
1
2
2
1
0
2
2
2
1
0
1
1
0
1
1
2
1
1
1
1
1
2
0
1
2
0
2
1
1
1
2
1
1
0
2
1
1
0
1
2
1
1
2
1
1
2
1
1
1
2
2
1
1
1
1
2
1
0
1
1
0
1
2
1
0
1
1
1
1
1
0
2
0
2
1
1
1
1
1
1
2
0
2
2
2
1
0
1
1
2
1
1
0
1
1
1
1
1
1
1
0
2
2
1
1
1
1
1
1
2
1
1
1
2
1
0
1
1
1
1
1
2
1
1
2
2
1
2
1
1
2
1
2
0
1
1
2
1
1
1
1
2
1
0
0
1
1
2
2
1
2
1
2
1
2
1
0
1
1
2
1
4
1
2
1
0
1
2
1
1
1
1
1
2
1
1
2
1
1
1
2
1
2
1
2
1
2
1
1
1
1
1
0
1
1
1
0
0
1
1
1
2
3
1
1
0
0
0
1
0
2
1
0
0
1
2
1
0
1
1
1
1
0
1
1
0
2
1
1
1
1
0
1
0
1
2
1
1
1
2
1
3
1
1
0
1
3
2
2
1
1
1
1
1
2
1
1
2
0
1
1
1
2
2
1
1
1
0
0
1
1
1
1
1
2
1
2
1
1
2
2
1
1
1
2
1
2
1
1
0
0
1
1
1
1
2
1
2
2
0
1
2
2
1
1
2
2
1
2
1
2
1
1
1
2
1
2
1
1
0
1
1
2
1
1
2
1
1
2
1
2
1
1
2
1
1
1
1
1
2
1
1
2
2
0
1
2
1
1
1
1
2
1
1
1
2
2
1
1
1
0
1
1
2
2
2
2
1
1
1
2
2
2
2
2
1
1
1
1
2
2
2
1
2
2
1
1
0
1
1
1
0
2
1
2
2
1
0
1
1
2
1
1
1
2
2
1
1
2
2
1
1
1
0
1
1
2
2
1
2
2
1
1
1
1
1
1
2
1
1
1
1
0
0
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
0
1
0
1
2
1
1
1
1
1
1
2
1
0
2
1
4
1
2
1
1
1
0
2
1
2
1
1
1
1
1
0
0
1
1
1
1
2
1
1
3
1
1
1
1
1
1
1
2
1
1
2
2
1
2
1
1
1
1
1
1
1
0
1
2
1
1
1
0
1
1
1
1
1
2
1
1
1
1
2
4
2
1
1
1
2
1
1
2
0
1
2
1
1
1
1
2
3
1
2
1
1
2
0
1
1
1
2
1
0
1
2
1
1
1
2
2
0
1
2
0
1
1
1
1
1
1
1
1
2
1
0
2
1
1
0
1
1
2
0
1
1
1
2
1
2
1
1
2
1
1
2
1
0
1
1
1
0
1
2
1
1
1
1
2
1
1
2
1
2
1
1
1
0
1
1
0
2
2
1
2
2
1
1
1
1
1
2
1
1
1
0
2
1
0
2
1
1
1
1
0
2
1
1
1
1
1
1
1
1
1
1
0
1
2
2
2
0
0
0
2
1
2
0
2
2
1
1
1
1
0
2
1
1
1
1
1
1
1
1
1
1
2
0
0
0
2
1
2
1
1
1
1
1
2
1
1
1
0
2
1
1
1
0
0
1
1
1
1
2
2
2
1
1
1
1
1
2
1
1
1
2
0
1
1
1
1
1
2
1
2
0
0
0
2
1
1
1
2
0
0
0
2
2
1
1
1
1
1
2
1
1
2
5
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
0
2
1
0
1
1
0
1
2
0
2
1
2
2
1
1
1
2
2
1
1
2
1
1
0
2
2
1
0
2
1
1
1
3
1
2
2
2
1
1
1
2
0
1
0
2
1
1
1
1
1
1
2
1
0
2
1
2
2
2
1
1
1
0
2
1
2
1
1
1
2
1
2
0
2
2
1
2
1
1
2
1
0
1
2
1
2
0
2
0
2
0
2
0
1
0
2
1
1
1
2
2
1
1
2
2
2
1
1
2
1
0
1
2
2
1
1
2
1
2
1
1
2
1
1
1
2
1
0
2
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
2
1
0
0
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
2
1
1
1
0
2
1
1
1
0
1
1
2
0
2
2
1
1
2
1
1
1
2
2
1
1
1
1
1
0
1
1
1
1
1
1
2
1
1
2
1
0
2
1
1
1
1
1
2
1
2
1
0
1
1
2
2
1
2
1
1
1
1
1
1
2
1
2
2
2
1
1
1
1
1
2
0
1
2
2
1
1
1
1
1
2
2
2
1
2
1
1
1
1
1
1
1
2
2
2
2
1
2
3
1
1
1
1
2
0
2
1
2
2
1
2
1
1
2
0
2
2
1
1
1
0
1
1
2
2
1
1
0
2
2
1
1
1
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
0
1
2
1
1
2
2
2
0
1
1
0
3
1
1
1
0
2
0
0
0
1
1
2
2
1
2
1
0
1
1
0
1
0
2
1
2
1
2
1
1
2
1
1
1
2
1
1
2
0
1
0
1
3
0
1
3
1
1
0
1
2
1
1
1
1
2
1
0
1
1
2
1
1
2
1
0
1
1
2
1
2
1
2
0
1
1
1
1
1
0
1
1
0
0
1
2
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
1
2
1
0
1
2
3
2
0
2
1
1
1
1
2
1
0
2
0
1
1
1
1
0
1
1
0
1
2
1
2
1
0
2
2
1
1
1
1
1
2
2
1
0
1
2
1
1
2
0
0
3
0
0
2
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
0
2
2
2
2
1
1
1
2
1
1
2
2
1
2
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
0
2
1
1
2
1
0
1
1
1
1
2
0
1
2
1
0
2
1
2
1
2
1
1
1
1
2
1
1
1
2
1
0
0
1
2
1
2
1
1
2
1
0
1
2
2
2
1
2
1
1
1
1
2
1
0
1
2
1
0
2
1
2
1
1
1
0
2
1
1
1
1
2
1
2
0
0
1
1
2
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
2
1
0
2
0
1
1
1
1
0
2
1
2
2
1
1
1
1
1
2
0
1
0
2
1
0
0
1
0
1
1
2
1
1
1
1
1
1
0
2
0
1
1
2
1
2
1
2
1
0
1
1
1
1
2
0
1
1
2
1
2
1
2
2
0
2
1
1
2
1
1
2
1
1
1
1
0
1
2
1
2
2
1
1
1
1
1
0
1
1
1
2
2
1
1
1
1
1
1
2
1
1
1
2
1
0
0
1
1
1
1
1
0
1
1
1
2
1
1
1
2
0
2
1
1
1
1
3
1
1
2
0
1
1
0
0
1
2
1
2
1
2
1
1
1
2
1
2
1
1
1
1
1
2
1
2
0
1
1
1
2
1
1
1
1
1
1
0
1
1
1
1
1
2
0
0
0
1
1
1
2
0
1
1
1
2
1
1
2
2
1
2
1
1
1
1
1
1
1
1
0
1
0
2
2
2
3
1
0
0
2
1
1
1
1
2
1
2
2
2
1
1
0
2
1
1
0
1
1
1
2
1
1
1
1
1
1
1
1
2
1
2
2
2
1
2
1
1
1
2
0
1
1
0
2
2
1
1
2
0
0
1
1
2
1
1
2
2
2
1
0
1
2
1
1
1
1
2
2
1
0
1
2
1
1
0
1
0
1
0
1
1
1
1
2
0
1
1
1
2
2
0
0
1
1
1
1
1
1
2
1
2
2
0
1
2
1
1
1
1
2
2
0
2
2
2
1
2
2
2
0
1
2
1
1
1
1
1
2
0
1
1
1
1
1
1
2
1
0
1
2
0
1
1
2
0
1
1
2
1
1
2
1
1
1
1
2
1
2
2
1
1
1
1
0
2
2
3
1
1
0
1
1
1
1
1
1
1
2
1
1
1
1
1
1
0
1
2
2
1
1
1
1
1
2
2
0
2
2
1
1
1
1
0
0
1
1
1
0
0
2
1
1
2
2
2
1
1
0
1
0
1
0
1
2
2
2
1
1
2
1
0
1
0
0
0
1
0
1
2
1
1
1
1
1
2
1
2
1
1
2
0
1
1
1
0
1
1
1
1
1
1
2
2
1
1
2
0
1
1
2
1
1
1
2
1
1
1
1
1
0
1
1
1
1
0
2
1
0
1
1
0
1
2
1
1
2
2
1
0
1
2
2
1
1
1
1
0
1
2
1
0
1
2
1
0
0
1
0
1
1
0
1
1
1
2
1
1
1
2
1
2
0
1
1
1
1
1
2
2
1
1
2
2
1
1
1
1
1
1
0
1
2
1
1
2
2
1
2
1
0
2
2
1
1
2
1
2
1
2
1
1
1
1
0
1
1
1
0
0
1
0
0
2
0
1
1
1
2
0
1
2
1
1
2
0
0
2
2
1
1
1
0
1
0
0
1
1
1
0
0
2
1
2
1
1
2
3
2
0
0
1
1
2
1
1
2
2
1
0
1
1
1
2
1
2
2
1
1
1
1
3
1
0
2
0
1
1
1
1
1
1
1
1
1
1
2
0
2
2
1
2
2
1
0
1
1
2
1
1
1
2
2
1
1
2
2
1
0
1
0
1
1
1
1
0
1
1
1
2
2
1
0
2
1
2
0
0
2
2
1
0
0
2
1
2
1
1
1
1
1
2
2
1
2
1
2
1
2
1
2
1
0
1
0
1
1
0
1
1
0
2
2
1
1
2
0
1
1
1
1
1
1
2
2
0
1
1
1
1
0
1
2
1
2
1
0
1
0
2
0
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
1
2
2
1
1
2
2
1
1
1
1
1
1
0
1
1
2
0
2
1
1
2
2
0
0
1
0
0
1
1
1
1
1
1
1
2
1
2
0
2
1
1
1
1
2
0
1
1
2
1
1
0
1
2
1
1
1
1
1
1
1
1
1
2
1
0
2
1
1
1
2
1
1
2
2
1
1
1
2
1
1
2
1
1
2
0
1
2
0
1
1
1
1
1
2
1
1
1
1
0
2
2
2
2
0
0
2
2
2
1
1
1
2
1
1
1
1
0
1
2
1
1
2
1
1
1
1
1
2
1
1
1
4
2
2
1
1
3
1
1
1
1
1
0
1
2
2
1
1
1
1
1
1
1
0
1
1
2
1
2
1
1
1
1
1
2
1
1
2
3
1
1
1
0
1
1
0
2
2
2
1
1
0
1
2
1
1
0
0
1
1
2
2
1
1
0
2
2
1
1
1
0
1
1
3
1
1
1
2
1
1
0
1
1
2
1
1
2
1
1
1
1
1
2
0
0
2
1
1
2
1
2
1
1
1
2
2
1
1
2
1
1
1
0
2
1
1
1
1
1
2
1
2
1
2
0
1
0
1
1
1
1
1
1
1
4
0
1
0
2
2
3
1
1
2
1
1
1
2
2
2
1
2
1
1
2
1
1
0
1
2
2
1
0
1
1
0
1
1
0
2
1
1
1
2
1
3
2
0
0
2
2
1
1
1
1
2
2
2
2
2
1
2
1
0
0
0
1
2
0
1
2
2
1
1
1
2
1
0
1
1
1
0
0
0
2
2
2
1
4
1
1
1
1
0
2
0
1
1
1
2
0
0
1
2
2
2
1
1
1
1
1
0
1
1
0
0
2
1
2
1
1
1
2
2
1
2
1
2
1
1
0
2
0
3
2
1
1
1
2
2
1
1
2
2
2
1
1
2
1
1
2
1
0
2
1
1
2
2
4
2
2
1
1
1
1
1
2
0
1
2
1
1
1
1
1
1
1
1
0
2
1
0
1
1
1
1
2
1
1
1
2
1
2
2
0
1
1
1
1
1
1
1
2
2
1
2
0
1
1
2
2
1
1
2
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
2
1
1
0
2
1
1
2
1
1
2
2
1
1
2
1
1
0
0
2
1
1
1
1
0
2
1
1
1
2
2
0
1
1
1
1
1
1
0
1
0
1
1
2
1
1
1
1
2
0
1
1
1
0
2
1
1
1
1
1
1
2
1
1
1
1
1
2
0
2
1
1
1
0
2
1
1
1
1
2
1
1
1
1
2
0
1
1
2
1
1
1
1
1
2
1
1
0
2
1
1
2
0
1
0
1
1
0
2
1
2
1
1
0
1
1
2
2
1
2
1
1
1
0
1
1
1
1
2
2
1
2
1
1
1
1
1
2
2
0
1
1
2
1
0
1
2
1
1
1
0
2
1
1
2
2
1
1
1
2
1
1
0
2
1
1
2
1
0
1
2
1
1
1
1
2
2
1
1
0
2
3
1
1
2
2
1
2
1
2
1
0
2
0
1
0
2
2
1
1
1
1
2
1
1
1
2
2
1
2
2
1
1
2
2
1
1
1
0
1
1
2
1
1
1
0
1
1
2
1
1
1
1
2
1
1
1
1
2
2
0
2
1
1
2
1
1
1
1
2
1
1
1
1
2
0
0
1
1
1
1
1
1
1
1
1
0
7
0
0
2
2
2
1
1
1
1
2
0
1
1
1
1
1
2
0
1
1
1
0
2
2
1
2
2
1
0
1
1
2
2
0
2
2
1
1
0
1
1
1
2
2
2
1
1
1
1
0
1
1
1
1
1
1
2
1
2
1
2
0
1
1
0
2
1
1
2
1
1
1
1
1
2
0
3
1
1
1
1
0
1
0
1
1
0
2
2
0
1
1
0
1
2
1
1
1
1
1
0
1
1
0
1
1
1
1
1
2
1
1
2
1
1
1
0
0
2
1
0
2
1
1
1
2
2
2
1
1
3
2
2
2
0
1
1
1
1
1
1
1
1
2
1
2
1
1
2
0
1
0
1
1
2
1
1
1
1
1
2
2
1
2
1
2
1
1
1
2
1
0
1
1
2
2
0
1
0
1
1
2
2
1
2
2
2
2
2
1
1
0
1
0
1
1
0
2
1
0
1
1
2
1
1
1
2
1
1
1
1
1
1
0
1
0
1
2
1
1
2
2
2
1
1
1
1
1
0
0
1
1
1
1
1
1
1
2
1
2
1
1
2
1
0
2
1
0
1
1
1
1
1
3
1
1
1
1
2
1
2
1
1
2
1
2
1
1
1
2
1
1
1
2
1
1
1
2
1
1
0
2
1
1
0
2
1
0
2
0
1
0
1
1
2
1
0
0
2
1
1
1
1
0
2
1
1
2
2
1
2
1
1
1
1
2
2
2
2
1
2
1
1
1
1
0
2
1
1
1
1
1
0
2
1
1
2
0
1
1
1
1
3
2
1
2
1
1
1
1
1
1
1
1
2
0
1
2
1
0
1
2
1
1
1
0
2
0
2
0
2
1
1
1
1
1
2
2
1
1
0
1
2
1
1
1
0
2
2
2
1
0
1
1
1
2
1
1
2
1
1
0
1
2
2
2
2
1
1
0
1
1
0
1
2
1
1
2
1
1
2
1
1
0
2
1
0
1
1
1
1
1
2
2
1
1
1
1
2
2
0
1
1
2
1
1
0
1
1
1
1
2
1
1
1
0
2
1
2
1
1
3
0
2
1
2
1
1
0
1
1
0
1
1
2
2
1
1
2
2
1
1
1
2
2
2
1
2
1
1
2
2
1
1
1
1
2
1
0
0
1
1
0
1
1
1
2
2
1
1
2
0
2
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
0
1
1
0
1
2
2
1
2
2
2
2
1
1
2
2
2
1
0
1
1
1
2
1
1
0
1
1
1
0
1
2
1
2
0
1
0
2
1
1
1
2
1
2
1
1
1
1
1
1
2
0
1
0
1
1
1
1
1
2
1
1
1
1
1
1
2
1
2
2
1
2
0
1
1
2
0
1
0
2
1
1
1
1
2
1
0
1
2
1
1
0
2
2
1
0
1
1
2
1
1
1
1
1
1
1
0
1
1
0
1
1
1
1
1
1
1
1
0
1
1
2
2
2
2
1
1
2
2
1
1
1
1
1
2
1
1
1
1
1
2
2
1
2
1
1
1
1
1
2
1
1
1
1
2
0
2
1
1
2
1
1
1
1
1
1
2
1
1
0
0
0
1
0
2
1
0
1
1
1
2
0
1
2
1
0
2
2
1
1
1
1
1
1
0
1
1
0
1
1
1
0
2
2
2
0
1
3
1
2
1
2
2
2
1
0
2
0
1
2
2
2
2
0
2
1
1
1
1
1
1
0
1
2
1
1
1
1
2
2
2
1
2
1
0
2
2
2
0
0
1
1
2
2
1
1
2
1
0
1
1
1
2
0
1
2
1
2
1
1
1
1
1
1
2
0
1
0
1
2
1
1
2
1
1
1
2
1
0
2
1
1
1
2
1
1
0
2
2
1
1
1
2
2
1
1
1
2
0
1
1
3
1
0
1
1
1
0
0
1
1
1
0
0
1
2
2
2
0
0
1
1
2
2
2
1
1
1
2
1
2
1
2
1
1
2
1
2
0
2
1
1
2
1
1
1
1
2
1
2
1
1
1
2
0
1
1
2
1
1
1
0
1
1
1
1
1
1
0
1
1
1
2
1
1
2
2
1
0
1
1
2
1
2
1
1
2
1
1
1
2
1
1
2
1
1
2
1
1
1
1
1
0
0
1
0
0
1
1
1
2
1
1
0
1
1
2
1
1
1
1
2
1
1
0
1
1
1
1
1
2
1
2
1
2
1
2
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
0
1
2
0
1
0
1
1
2
1
0
2
2
1
2
2
1
2
0
0
1
1
1
2
0
2
0
2
1
0
3
1
1
1
1
2
2
2
2
1
2
2
1
1
1
1
1
0
1
2
1
1
1
2
1
2
1
1
1
2
2
1
1
1
1
1
1
2
0
0
0
1
2
3
1
0
2
2
1
1
1
1
1
2
1
2
2
0
1
1
2
2
1
1
1
2
1
1
1
1
1
1
1
1
0
2
2
1
2
0
1
0
2
1
1
1
1
0
1
2
1
1
1
1
1
1
2
0
0
1
1
1
1
0
2
1
1
1
1
2
0
0
1
1
1
2
1
1
0
1
2
0
1
1
1
2
1
1
1
0
1
1
1
2
1
1
1
1
1
1
2
2
0
0
0
2
1
1
1
1
2
0
1
2
0
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
2
0
2
1
1
1
1
1
2
1
2
1
0
2
0
0
1
2
1
0
0
1
0
1
2
2
1
0
1
1
2
1
2
1
1
2
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
0
1
0
1
0
1
2
1
1
1
1
2
2
1
1
1
1
2
1
1
2
1
1
2
1
1
2
2
1
0
1
1
2
2
1
1
2
1
1
1
1
2
0
0
0
0
1
1
0
1
2
1
2
1
1
1
1
2
2
0
2
1
1
2
1
1
2
1
1
2
2
1
1
0
1
1
0
2
1
2
1
2
2
2
1
2
1
1
0
2
1
1
1
0
1
1
1
0
1
0
0
2
1
1
1
1
1
0
1
1
1
1
1
1
2
1
2
1
1
1
1
2
1
2
1
1
1
0
0
1
1
2
0
2
1
2
1
1
1
1
1
1
0
1
0
1
2
1
1
2
0
1
0
1
1
2
1
1
1
1
2
1
1
1
0
1
1
1
0
2
2
1
2
1
1
1
1
2
1
1
1
0
1
1
2
1
1
0
0
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
0
1
1
1
2
2
1
2
2
1
2
0
2
1
1
2
1
1
1
1
1
0
3
1
0
2
1
2
2
1
0
1
1
1
1
2
1
1
1
1
2
1
1
2
1
0
1
0
1
2
0
1
0
2
2
2
1
1
0
0
1
1
1
0
2
1
0
1
1
1
1
1
2
1
1
1
1
1
2
1
0
2
2
1
1
2
2
2
1
1
1
1
1
1
1
0
1
2
1
1
1
1
0
1
0
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
1
0
1
1
1
2
1
1
0
1
1
2
1
1
1
1
1
1
1
1
1
1
3
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
2
2
2
2
2
1
1
2
1
1
1
1
1
1
0
1
0
1
1
1
1
1
1
0
1
0
1
1
1
1
1
1
1
0
1
1
1
1
2
1
2
1
1
1
1
1
1
1
0
0
1
2
0
2
2
1
1
1
2
1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
0
2
1
1
1
1
0
1
2
1
2
1
2
1
2
1
1
2
1
1
1
1
1
1
0
1
1
1
1
1
1
1
2
1
1
2
2
1
1
1
2
0
1
1
2
0
2
1
1
1
2
0
1
2
2
2
1
1
2
0
1
1
1
2
1
2
1
1
1
1
1
2
1
1
2
1
1
0
2
1
0
1
1
1
1
2
1
0
1
1
1
1
2
1
2
1
0
2
1
1
1
0
2
2
4
2
2
0
2
1
1
1
1
1
1
1
2
2
2
2
1
1
1
1
1
1
1
1
1
0
2
2
0
1
1
1
1
1
2
1
2
2
1
2
2
1
0
1
2
1
1
1
2
1
0
1
1
2
2
1
2
1
2
1
2
1
2
1
1
2
1
1
1
1
1
1
2
1
1
0
1
0
2
2
2
1
1
0
1
1
2
2
1
2
1
1
2
1
2
2
1
1
2
1
0
1
1
2
1
2
0
1
1
1
1
1
0
1
1
1
1
1
1
2
1
0
2
1
1
1
0
1
0
1
1
1
2
1
1
1
2
2
1
1
1
0
1
1
1
1
2
1
1
2
0
1
2
1
2
0
1
1
1
1
2
1
2
1
1
1
1
1
2
0
3
1
2
0
2
2
0
1
1
1
1
2
1
1
1
1
1
1
1
1
1
0
2
1
2
0
1
1
2
0
1
2
2
1
1
2
1
1
2
1
2
1
1
2
0
1
1
2
2
1
1
2
1
1
1
2
2
1
2
2
1
1
1
1
1
1
1
2
1
1
2
2
1
1
1
1
2
1
0
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
2
2
1
0
1
1
1
1
1
1
1
1
1
1
2
2
0
2
2
2
1
2
1
1
2
1
2
1
1
1
3
2
1
1
0
1
1
1
1
1
0
1
1
1
1
1
1
1
2
2
2
1
1
1
1
2
1
2
2
1
2
3
1
1
2
5
0
0
2
1
0
1
1
1
2
1
1
2
1
1
1
2
1
1
1
1
1
0
1
1
1
2
1
1
1
1
2
0
1
1
0
2
1
1
2
1
1
1
1
1
0
2
2
3
2
2
1
1
1
1
1
2
2
1
1
1
2
1
2
2
1
1
2
2
2
1
2
1
1
1
2
2
1
1
1
2
1
2
2
0
2
1
1
1
1
1
1
1
2
2
1
1
1
2
2
1
1
0
1
2
1
1
0
1
1
1
1
2
2
1
1
1
2
2
1
1
1
2
2
1
1
1
1
2
2
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
0
0
1
1
1
1
1
1
2
1
1
1
1
0
1
1
1
1
0
1
1
2
1
2
1
1
6
1
0
0
2
1
1
1
0
1
2
2
1
1
1
2
1
1
1
1
0
1
0
1
1
1
1
2
1
1
0
1
1
1
1
1
2
2
1
2
2
1
0
1
1
1
1
2
1
2
0
1
2
1
1
2
1
1
0
1
3
1
2
2
1
1
1
1
1
1
1
1
2
2
1
2
1
2
1
1
2
1
0
1
1
2
0
1
1
2
1
1
0
1
1
2
1
3
3
0
1
0
2
1
1
1
0
2
1
1
0
1
1
2
2
1
1
2
1
1
0
1
1
1
1
1
2
1
0
2
1
1
1
0
1
1
1
1
1
1
1
1
1
2
2
1
1
1
2
1
1
1
2
1
1
0
0
1
1
1
1
1
0
2
3
2
1
1
2
1
1
1
1
2
2
0
1
1
1
2
1
1
1
2
1
1
0
1
2
0
2
2
1
2
1
1
1
2
0
1
1
1
1
1
2
2
0
1
1
2
1
1
1
2
2
2
2
1
1
0
1
1
0
2
2
1
1
0
0
1
1
1
2
1
2
1
1
0
2
2
1
0
2
1
1
1
1
0
1
1
2
1
0
0
1
1
1
1
1
1
1
1
1
1
2
1
0
1
1
2
2
1
1
1
1
2
2
1
2
1
1
1
2
1
0
2
1
1
0
1
1
1
3
2
0
2
1
1
2
1
1
1
1
1
1
1
2
2
0
1
1
1
1
1
1
1
2
1
1
1
3
1
0
1
1
1
2
1
0
1
1
0
2
2
1
0
2
1
1
0
0
2
1
1
2
1
2
0
2
1
1
2
2
0
0
0
1
2
1
2
1
2
1
0
2
1
1
1
1
1
0
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
0
2
2
0
1
2
1
2
1
1
2
1
0
2
1
1
1
1
1
0
1
2
1
1
1
2
0
2
1
1
1
2
2
1
2
2
2
2
1
1
2
0
1
0
1
1
2
1
2
1
1
2
1
1
0
2
1
1
2
1
1
0
1
2
2
2
2
1
2
2
1
1
1
1
0
1
1
1
1
0
2
1
1
1
0
1
1
1
0
1
1
2
1
1
0
1
1
2
1
2
2
1
0
2
1
1
1
2
2
1
2
1
1
0
1
1
2
1
1
0
1
1
1
1
1
1
2
0
0
1
2
1
1
2
1
2
1
2
1
1
2
1
1
1
0
2
2
1
1
0
1
1
1
1
0
2
1
1
0
1
1
2
1
1
0
2
0
1
1
0
1
2
1
1
2
2
1
2
1
1
1
1
0
1
1
2
1
0
1
1
1
1
2
1
2
0
1
1
1
0
1
2
2
1
0
1
1
2
1
1
1
1
0
1
1
2
1
2
1
1
2
1
2
0
1
1
2
0
2
1
0
1
0
0
0
1
2
1
2
1
1
1
1
2
1
2
2
2
2
1
2
1
0
0
1
1
2
1
1
1
1
2
1
2
1
1
2
1
2
1
1
1
1
2
1
2
0
2
1
0
1
1
1
1
2
2
0
1
2
1
2
1
0
1
2
1
2
2
1
2
1
1
0
1
1
1
0
1
1
1
1
1
1
2
2
0
1
0
1
1
1
1
1
0
1
1
1
0
1
1
0
8
1
1
1
1
1
1
1
1
2
2
2
1
1
2
1
1
1
1
0
1
1
2
1
1
1
1
1
1
2
1
1
1
2
2
1
2
1
1
1
1
1
0
1
1
1
1
1
0
2
0
1
1
1
1
1
1
2
1
2
1
2
0
1
2
2
0
2
2
1
2
2
1
1
1
1
1
1
1
2
3
2
0
1
1
1
0
1
2
2
1
1
2
1
1
1
2
2
2
1
1
1
1
1
0
2
0
1
0
1
1
1
2
1
1
2
1
2
1
1
2
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
0
1
1
1
0
0
1
2
1
1
1
0
2
1
1
1
1
3
1
1
1
3
1
1
1
2
1
1
2
1
0
2
0
1
2
1
1
1
3
2
2
1
2
0
0
1
0
1
1
2
2
1
0
2
2
1
0
2
2
1
2
1
1
1
2
1
1
2
1
1
1
1
1
0
1
0
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
0
1
2
1
2
1
2
2
1
1
1
1
2
0
1
1
0
2
2
1
2
1
1
1
2
2
2
1
0
1
0
1
1
1
2
1
2
1
2
2
1
1
0
1
1
0
2
2
1
1
1
0
1
1
2
2
1
2
1
0
0
1
2
1
0
1
1
1
2
2
1
2
1
1
2
1
1
0
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
0
2
1
0
1
3
2
2
1
1
1
1
1
2
2
1
1
1
1
0
2
1
0
1
1
1
1
1
1
1
2
1
0
1
2
1
1
1
1
1
2
1
1
1
0
1
1
1
1
1
1
2
2
2
2
0
2
2
1
1
1
2
1
1
2
2
2
2
2
0
1
2
1
1
1
1
1
2
0
1
0
2
2
1
2
2
1
1
0
1
1
2
1
2
1
1
1
2
1
1
2
2
1
0
1
0
1
1
2
1
1
0
1
1
2
0
2
5
1
2
1
2
1
1
0
1
1
1
1
1
0
1
1
2
1
2
2
3
1
0
2
1
0
1
1
0
2
1
1
1
1
1
2
1
1
1
0
1
0
1
1
0
0
3
2
1
1
1
1
3
2
2
1
1
1
1
1
1
1
0
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
2
1
2
0
0
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
2
0
2
0
1
1
2
1
1
1
2
1
1
2
2
1
0
2
1
2
1
1
2
1
1
1
2
1
2
0
1
0
2
1
2
1
1
1
2
2
2
1
2
1
2
1
1
2
1
1
1
1
2
1
1
2
2
1
1
1
2
1
1
1
2
2
2
0
1
1
0
1
1
2
0
1
1
1
1
1
0
1
1
1
2
1
1
1
0
0
1
1
2
0
1
2
1
1
1
2
1
0
1
1
2
1
1
1
2
2
1
2
1
2
2
1
1
1
2
2
2
0
2
0
2
0
1
2
1
1
1
1
2
1
2
1
0
2
1
1
0
1
1
1
1
0
1
2
1
1
1
1
1
1
1
1
1
1
2
0
1
2
0
2
2
0
2
1
0
0
1
1
1
1
2
2
1
1
0
0
1
2
1
1
1
1
1
0
1
2
1
1
0
2
1
1
1
1
1
1
2
1
1
1
2
1
1
2
2
2
1
1
1
2
1
1
2
1
1
1
1
2
1
1
1
2
0
1
1
1
1
1
1
1
1
1
1
1
1
2
1
0
2
2
2
1
1
2
1
1
1
0
1
2
2
1
1
2
2
1
1
1
1
1
0
2
0
2
1
2
1
1
0
2
0
1
2
1
2
1
1
2
2
1
1
1
1
1
0
2
2
1
1
1
2
2
1
1
1
0
2
2
1
1
1
1
2
1
1
2
1
1
0
1
1
1
2
1
2
1
0
1
0
2
2
2
0
0
1
0
1
2
1
0
2
0
1
2
1
1
1
1
1
2
2
1
0
1
1
2
0
2
1
1
1
1
1
1
1
1
1
2
0
0
2
1
1
1
1
1
1
1
1
0
2
1
2
1
2
1
2
2
0
0
1
0
2
1
2
1
1
1
1
1
1
0
1
1
1
2
2
0
1
1
1
1
1
1
0
1
0
2
0
1
0
2
0
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
2
2
1
1
1
2
2
2
0
2
0
3
0
0
1
1
2
1
1
1
1
1
2
2
1
1
1
2
1
1
2
0
1
1
1
1
2
1
2
2
1
1
2
1
1
1
1
1
0
2
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
2
2
2
1
0
1
1
0
1
2
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
0
2
2
1
1
1
2
2
1
1
1
0
1
2
1
0
1
2
2
2
2
2
2
1
0
1
2
1
2
1
1
2
1
1
2
1
1
1
1
1
0
1
1
1
1
1
1
1
2
2
1
2
1
1
1
1
1
2
2
1
2
1
1
2
1
0
1
0
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
2
1
1
1
2
1
1
0
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
2
1
1
0
1
0
1
1
0
2
1
0
2
1
2
0
1
2
0
1
1
0
1
0
1
1
1
1
1
1
0
2
1
0
2
1
1
1
2
1
1
1
1
3
1
1
1
2
1
1
2
1
1
0
1
1
1
1
0
2
2
1
2
1
1
1
1
2
1
3
1
1
1
1
1
1
1
1
1
0
0
2
1
0
1
2
1
1
1
1
2
1
2
1
2
2
1
2
1
1
1
2
2
1
2
0
1
1
1
1
1
2
2
0
2
1
1
2
1
1
2
1
1
2
2
1
1
2
1
1
1
0
0
1
1
1
2
0
1
1
1
1
2
2
1
2
0
1
1
1
1
1
1
1
1
2
1
1
0
1
1
1
2
1
3
1
1
2
1
2
1
1
1
1
1
1
1
2
1
0
2
0
2
1
1
2
0
1
2
1
1
1
1
1
1
2
0
1
1
1
2
2
1
1
1
2
2
2
2
2
2
1
1
1
1
1
1
2
1
1
1
2
1
0
2
1
1
1
1
0
1
1
1
1
1
1
0
2
2
2
2
2
1
1
1
1
2
1
1
2
2
1
0
2
1
1
0
1
2
2
0
1
1
2
2
1
1
1
1
2
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
0
1
2
2
1
1
1
0
2
2
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
0
1
1
2
1
1
1
2
1
1
1
2
1
2
2
1
1
1
1
2
2
1
1
2
1
1
2
0
1
0
1
2
2
0
2
0
2
2
1
1
1
2
1
2
1
1
1
2
2
1
0
1
0
2
2
1
1
1
2
1
1
1
2
1
1
2
1
1
2
0
1
0
3
1
1
1
1
1
2
1
1
0
1
2
1
2
2
0
2
1
2
1
1
2
1
1
0
1
2
2
3
1
1
1
2
1
2
1
2
1
0
1
1
1
1
1
1
2
2
1
1
0
1
3
0
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
0
2
2
2
1
3
1
2
1
1
2
0
1
1
1
1
1
1
1
0
0
1
2
0
2
1
1
1
1
2
0
1
1
1
0
1
1
1
1
1
0
1
1
1
0
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
0
1
0
1
2
1
1
1
2
2
1
1
0
2
1
1
1
2
0
2
1
1
1
0
1
2
1
2
0
1
1
2
1
1
2
2
1
0
0
0
2
2
2
2
0
1
1
3
1
1
2
2
1
1
1
0
1
1
1
0
2
2
2
1
1
0
2
1
2
1
1
0
0
1
1
1
2
1
1
1
1
0
1
1
1
1
0
2
1
2
2
2
1
1
1
1
1
0
1
1
1
1
1
1
1
1
2
0
1
1
1
2
0
1
1
1
1
0
1
0
1
2
1
0
1
1
1
1
1
0
1
0
0
2
2
2
2
2
1
0
2
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
1
2
1
2
1
1
1
1
1
2
1
2
1
2
1
1
1
1
1
1
0
2
1
1
1
1
1
2
1
1
2
1
2
1
2
1
1
0
1
1
2
2
2
2
1
2
1
1
0
1
0
1
2
1
1
1
1
1
1
1
0
1
0
1
0
1
2
1
1
1
1
2
1
1
2
1
2
0
1
0
0
1
1
0
1
2
2
1
1
1
1
1
2
1
1
1
0
1
2
2
1
2
1
1
0
1
2
2
1
2
1
2
1
1
0
2
1
1
0
1
0
1
1
1
4
1
1
0
1
2
2
0
2
1
1
1
2
1
1
1
0
0
1
0
1
1
1
0
1
0
1
2
1
0
2
1
0
1
2
0
2
2
2
1
1
1
2
1
1
0
1
1
1
2
1
1
1
2
1
1
1
2
1
2
1
1
1
2
1
2
2
2
2
1
2
0
1
1
1
1
1
2
1
1
2
0
1
2
2
1
2
0
2
1
2
2
1
2
2
1
1
1
1
1
1
1
2
1
0
1
2
2
2
1
1
1
1
1
0
1
0
1
1
2
1
1
1
1
1
0
1
1
1
1
2
1
1
1
2
2
0
1
1
1
1
0
1
2
1
0
1
1
1
1
2
1
2
1
2
0
1
2
0
2
2
1
0
1
2
2
1
1
1
2
1
1
2
0
1
0
0
2
2
1
1
1
0
2
1
1
1
0
1
2
1
2
1
2
1
2
0
1
3
2
1
1
2
1
0
1
2
2
1
2
2
0
1
1
1
1
2
0
2
1
2
2
2
2
2
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
2
1
0
2
1
1
2
1
0
1
2
2
1
1
1
2
0
1
1
1
1
1
1
0
1
1
1
1
0
1
2
1
1
1
2
0
1
1
1
1
1
1
1
2
1
0
1
0
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
0
2
1
0
3
0
2
0
1
1
2
2
0
1
0
1
1
1
1
0
1
2
2
1
0
1
0
2
1
1
2
0
2
1
1
1
1
2
1
1
0
1
1
1
1
0
1
1
1
1
1
1
1
2
2
0
2
1
1
1
2
0
1
0
1
1
1
1
1
1
2
2
2
2
0
1
1
1
2
0
1
1
1
2
2
1
1
1
1
2
1
1
1
2
0
2
1
3
2
0
0
1
2
1
2
0
0
1
0
3
1
2
1
1
2
1
1
2
1
1
1
2
2
1
2
1
1
0
2
1
2
1
2
2
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
2
1
1
1
1
1
2
2
0
2
1
1
1
2
1
2
0
0
1
1
1
0
2
1
1
1
2
2
2
1
2
1
1
1
1
1
1
0
1
1
0
1
1
1
1
1
1
1
2
2
1
1
1
0
2
2
1
1
0
1
1
2
2
2
1
1
0
1
1
1
3
2
1
1
1
2
1
0
1
1
1
1
2
2
2
1
1
1
0
1
1
0
2
0
2
1
2
1
2
0
1
1
0
1
2
0
2
1
1
0
2
2
0
1
1
1
1
0
0
2
2
1
0
1
1
1
2
1
1
1
1
0
1
1
1
1
2
1
2
0
0
2
0
2
1
1
1
1
1
2
2
1
1
2
1
1
1
2
1
1
2
1
2
1
1
1
2
1
0
1
0
0
2
1
0
1
1
2
1
0
1
1
2
2
2
1
1
2
1
1
1
2
1
2
2
1
1
0
1
1
1
1
2
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
1
2
2
2
1
1
1
2
1
1
2
1
1
2
2
2
1
1
0
1
2
1
1
2
0
1
0
1
1
2
0
1
1
2
0
1
1
1
1
1
2
1
2
1
2
1
1
1
0
1
2
3
1
1
2
2
1
1
1
2
1
1
1
0
2
1
1
1
1
1
1
1
1
1
2
1
0
1
1
1
2
2
1
1
1
1
1
1
1
1
0
1
0
1
1
2
1
1
0
1
1
1
1
1
1
1
1
2
1
2
0
1
2
2
1
1
0
1
2
1
0
1
1
1
1
1
1
2
1
1
1
0
2
1
1
1
1
1
2
1
2
1
1
2
2
2
1
1
2
2
1
1
2
1
2
1
2
1
1
0
1
1
1
1
0
1
1
2
2
0
2
2
2
1
1
1
1
2
1
1
1
1
2
2
1
1
2
1
1
1
0
1
2
1
1
1
0
2
1
1
2
1
2
2
1
2
2
1
0
1
2
2
1
1
1
1
2
0
1
1
1
1
2
0
2
1
1
1
0
1
0
1
1
0
1
1
1
1
0
1
1
1
1
1
1
0
1
1
1
2
0
1
1
1
1
1
1
1
1
1
1
2
2
1
2
1
2
1
2
1
1
1
1
1
1
1
2
1
0
1
2
2
1
1
1
1
2
1
1
1
1
2
1
2
1
2
1
1
2
0
1
0
1
1
1
1
1
2
2
2
1
1
1
1
0
1
1
1
2
2
0
1
1
1
1
0
2
1
2
2
2
1
2
2
1
1
2
1
0
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
2
0
0
0
2
1
1
1
0
0
2
1
2
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
2
2
0
1
2
1
1
1
2
1
1
1
1
2
1
1
1
0
1
2
1
2
1
1
1
1
1
2
2
1
1
2
1
1
1
1
2
2
1
2
2
2
0
2
1
1
0
1
2
2
2
1
2
1
1
1
1
1
0
0
1
1
1
2
1
0
2
1
2
1
1
0
1
1
1
1
1
1
1
1
1
1
0
2
1
2
2
1
0
2
2
1
1
1
1
2
0
1
1
1
1
1
2
0
1
1
1
2
2
1
0
0
0
1
0
1
1
2
1
1
0
1
2
1
1
2
0
1
1
0
1
2
2
2
1
1
2
1
2
1
1
2
1
2
2
2
1
1
0
0
1
1
1
2
1
1
1
2
1
2
1
2
1
1
0
0
1
1
0
1
1
2
1
1
1
1
2
2
0
2
2
1
0
1
1
0
0
0
0
1
1
2
1
2
1
0
2
1
1
2
1
1
0
1
1
2
1
0
1
2
1
1
2
1
0
2
1
1
1
1
1
2
2
1
2
1
2
2
1
0
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
2
1
2
1
1
2
1
1
1
0
0
2
1
1
2
1
2
1
1
2
2
2
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
2
2
1
1
1
1
1
2
1
0
1
2
1
0
0
1
0
1
1
2
1
1
1
2
1
1
1
1
0
1
0
2
2
2
1
1
1
2
0
2
1
1
1
0
2
1
0
0
0
0
1
1
1
2
1
1
1
2
2
1
1
1
1
2
1
2
1
1
0
1
0
1
2
2
0
1
0
1
1
1
1
1
1
2
1
1
1
1
2
2
0
0
1
2
0
2
2
2
2
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
2
2
1
1
2
1
2
3
1
1
1
1
1
2
1
3
1
0
1
0
0
1
1
2
1
2
2
1
2
1
1
1
2
2
2
0
1
2
2
1
1
1
1
2
0
1
1
1
0
1
1
0
2
1
1
2
2
1
0
1
1
2
2
0
1
2
1
1
1
1
2
2
0
1
1
1
3
1
1
1
1
2
1
2
2
1
2
2
2
1
2
2
1
1
3
2
1
1
2
1
1
0
1
1
1
1
1
1
0
2
1
2
1
1
2
1
2
0
1
1
1
2
1
1
2
2
1
1
1
1
1
1
1
2
2
1
1
1
0
1
0
1
0
0
0
1
1
1
0
1
1
1
2
1
2
0
1
1
1
1
2
1
1
2
0
0
0
1
1
0
1
2
2
1
2
1
2
1
1
1
2
2
0
1
1
0
1
1
1
1
0
1
2
0
1
1
1
1
2
1
1
1
2
2
1
1
1
2
1
2
1
1
1
1
2
1
2
2
2
2
1
1
2
1
1
0
1
1
0
2
1
1
0
2
1
1
1
1
0
1
1
1
2
2
1
0
1
2
1
1
1
0
1
1
0
1
1
0
2
0
1
2
3
1
2
0
2
1
1
2
1
1
1
2
1
1
2
1
0
2
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
2
2
1
1
0
0
0
1
1
1
1
1
2
1
1
2
1
1
2
0
0
1
1
1
2
1
0
1
1
1
0
1
1
1
1
2
2
1
0
1
1
2
1
1
1
2
2
1
2
1
2
2
1
2
1
1
1
1
1
2
0
1
0
2
1
0
2
1
1
1
1
0
0
1
0
2
1
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
1
2
2
0
0
1
1
1
2
2
0
2
1
2
1
1
3
0
1
2
1
2
2
1
1
1
1
1
0
1
2
0
0
1
1
0
2
2
1
1
1
2
1
1
1
1
1
1
2
1
1
2
2
2
2
1
1
1
2
1
2
1
1
2
1
1
2
2
0
0
2
1
1
1
2
2
1
0
1
1
1
3
2
2
2
1
1
1
1
0
1
1
2
1
1
1
2
1
0
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
0
2
1
1
1
1
1
1
2
0
1
0
1
1
2
1
2
2
1
1
0
1
1
2
1
1
1
1
1
1
2
1
2
0
1
1
2
2
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
2
1
2
1
1
1
0
1
1
1
1
1
1
2
2
2
1
1
2
1
2
1
2
2
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
2
0
0
0
3
2
2
1
2
0
1
1
1
2
2
1
1
1
1
2
2
2
1
1
2
1
0
2
1
2
2
1
1
1
2
0
1
0
1
1
2
2
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
2
2
2
1
1
1
2
1
2
1
1
1
0
2
2
1
2
1
0
1
2
1
2
1
1
1
1
1
2
1
2
1
1
2
1
2
2
1
0
1
0
2
1
2
2
2
1
1
0
0
1
2
1
2
0
1
1
1
1
1
0
2
2
1
1
2
1
1
2
1
1
1
2
0
2
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
2
2
2
2
1
1
0
0
1
1
1
1
1
1
1
1
1
0
2
0
1
1
1
1
2
2
1
0
2
1
1
1
1
0
1
1
1
1
2
2
2
1
0
1
0
0
1
2
1
1
2
1
1
0
1
2
2
2
1
1
1
1
1
1
1
2
1
2
1
1
0
1
1
1
2
1
1
1
1
1
2
0
2
2
1
1
1
1
2
2
1
2
0
1
1
1
0
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
0
1
1
2
1
2
1
1
1
2
1
1
2
1
1
1
1
1
1
0
0
2
1
0
1
2
1
3
1
1
0
1
1
1
1
1
1
2
2
0
1
1
1
1
2
0
1
1
1
1
1
0
1
2
1
2
2
1
1
1
2
1
1
1
0
1
1
0
0
2
2
1
1
2
1
1
1
2
2
1
2
1
1
2
1
1
1
1
0
1
1
1
1
1
1
2
1
1
2
0
1
1
2
1
1
0
1
2
1
1
0
1
1
1
1
1
2
1
1
1
1
0
0
1
1
1
1
2
1
2
1
1
1
0
0
1
2
1
1
2
1
1
4
2
1
1
1
0
0
2
0
0
2
1
1
2
0
2
2
1
1
0
0
1
2
1
2
0
1
1
1
1
2
1
0
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
0
1
1
2
1
0
0
1
3
1
2
1
1
2
0
1
1
2
1
2
1
1
0
2
0
1
2
1
1
0
2
1
1
1
0
2
1
0
1
1
2
2
1
1
1
1
1
1
1
2
2
1
2
2
1
1
1
1
1
2
2
2
1
2
2
1
1
1
1
1
1
2
2
2
2
1
1
0
1
1
1
1
1
1
2
1
1
1
2
2
1
1
1
2
1
1
1
2
1
1
1
2
2
0
2
1
0
2
1
0
0
1
1
1
1
1
2
1
0
1
1
0
1
1
1
0
0
2
1
1
1
2
1
1
2
2
1
2
0
1
1
1
1
1
1
2
2
1
2
2
0
1
2
1
0
1
1
2
1
1
1
0
2
1
1
1
1
0
2
1
2
2
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
1
1
2
0
2
1
1
2
1
0
1
1
1
1
1
1
1
0
1
1
2
2
1
1
1
2
2
1
1
1
1
1
1
1
0
1
1
2
1
0
0
1
1
0
2
2
1
0
1
1
1
1
1
0
1
2
1
2
1
2
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
0
2
1
0
2
2
1
1
1
0
1
0
1
2
1
2
1
1
0
0
1
1
2
1
2
1
2
1
2
1
1
1
2
1
2
1
1
2
2
1
1
1
0
1
2
1
1
2
1
1
1
1
1
1
1
1
0
2
1
2
0
1
2
1
0
1
1
2
1
1
1
1
2
1
1
2
0
2
0
1
2
1
1
1
1
2
2
1
0
1
1
1
2
1
3
2
1
0
2
1
0
0
1
1
1
1
1
2
2
1
0
1
1
1
1
1
2
1
1
1
1
1
1
2
2
2
1
0
1
1
1
0
1
2
1
2
1
1
1
1
2
2
2
2
1
2
1
1
1
1
1
1
1
2
2
2
1
2
2
0
1
2
2
2
0
1
2
2
1
2
0
2
2
2
1
1
1
1
2
1
2
2
1
0
1
1
1
1
1
0
1
1
2
1
1
1
1
1
1
1
2
2
1
0
2
1
0
0
2
1
2
1
1
1
1
0
0
1
1
1
0
1
1
1
1
0
1
1
0
1
2
1
1
0
1
1
2
1
2
1
2
1
1
1
1
1
1
1
0
1
2
1
1
1
1
0
1
2
1
2
0
1
1
1
1
2
1
1
1
0
1
1
1
1
1
2
1
1
3
2
1
2
1
1
1
2
1
2
2
2
1
1
2
1
1
1
1
1
1
3
1
1
1
0
2
1
2
2
2
1
2
1
2
1
1
1
0
2
2
2
1
1
1
1
0
1
1
2
1
1
1
1
2
1
1
1
2
3
1
2
1
0
2
1
1
1
2
1
1
2
1
1
1
0
1
1
1
1
0
2
1
3
1
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
0
2
1
2
2
1
1
2
0
1
0
2
2
1
1
2
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
0
1
2
1
1
1
2
2
1
2
2
1
1
1
1
2
2
1
1
2
1
1
1
0
1
1
1
2
1
1
2
0
2
0
1
2
2
2
2
0
1
1
1
1
2
1
1
2
1
2
2
1
1
2
1
1
2
0
0
1
1
0
1
1
1
1
1
1
2
1
2
1
0
1
1
2
1
1
1
2
0
2
2
2
1
2
1
0
1
2
1
1
1
0
1
1
2
1
2
0
2
0
2
2
1
1
1
1
1
2
1
0
2
2
1
1
2
1
1
2
0
1
1
0
1
0
1
2
2
0
1
1
1
0
2
1
1
2
1
2
2
1
1
1
1
2
1
1
1
1
1
2
1
1
1
0
2
1
1
1
2
1
1
1
2
2
1
1
2
2
1
1
0
1
1
0
1
3
0
1
1
1
1
0
0
2
1
1
0
1
2
1
1
0
2
1
2
1
0
1
1
1
2
0
1
2
1
2
1
2
1
1
2
1
1
2
1
1
0
1
1
4
1
1
2
1
0
1
0
2
1
0
1
1
0
1
1
1
1
0
0
1
2
2
1
1
1
1
2
1
1
2
1
1
0
2
1
1
2
1
0
1
1
0
1
1
1
1
1
1
1
2
2
1
3
3
1
1
1
2
2
2
0
2
1
2
2
1
1
1
2
2
1
1
1
1
0
0
1
0
1
1
0
0
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
0
1
1
2
1
1
1
2
0
1
0
1
1
1
1
1
1
1
2
2
1
1
1
0
1
1
0
1
1
2
1
2
1
0
1
2
1
2
1
2
1
2
1
1
0
2
1
1
2
1
2
1
1
0
2
1
1
1
0
2
1
2
0
0
1
1
1
2
2
0
2
1
1
2
1
1
2
1
1
1
1
0
1
1
0
0
1
2
1
1
1
1
2
2
0
1
2
1
1
0
1
1
0
1
1
1
2
0
2
1
0
2
1
1
2
2
1
1
2
1
1
2
2
1
1
1
1
1
2
0
1
1
1
1
1
1
1
1
1
1
1
1
0
2
2
2
1
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
2
0
1
2
1
1
2
0
1
2
1
1
1
1
1
1
1
2
0
1
1
2
1
1
1
1
1
1
1
1
2
2
1
2
2
1
1
2
2
2
1
1
2
2
1
1
2
1
1
2
1
2
1
1
1
2
1
1
1
0
1
1
2
0
2
1
2
2
1
1
1
0
2
1
1
1
0
0
1
1
0
1
2
1
2
2
0
0
1
1
0
1
0
0
1
2
0
2
1
1
1
1
2
1
2
2
0
1
2
2
2
1
1
2
2
1
1
1
1
1
2
1
2
2
1
1
1
1
1
1
1
0
1
2
1
1
1
1
2
1
1
0
1
1
2
2
1
1
1
4
1
1
1
1
1
2
2
2
1
1
2
1
0
2
2
1
1
1
0
1
1
1
1
3
2
1
2
1
2
1
1
2
1
1
1
1
2
1
1
1
1
0
0
2
2
1
2
0
1
0
2
1
1
1
1
1
0
1
2
1
1
1
2
1
2
2
2
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
3
1
2
1
1
1
2
2
1
2
1
2
0
1
1
2
1
1
0
1
0
1
1
2
1
1
1
1
1
1
2
1
0
1
1
2
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
0
1
1
2
1
1
1
1
2
1
2
0
2
0
0
1
1
0
1
2
1
2
1
0
1
1
1
1
2
1
1
1
1
1
1
3
1
1
2
0
2
1
2
1
1
2
1
0
0
1
0
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
2
1
0
2
1
1
2
0
1
1
1
1
1
2
1
1
2
1
0
1
1
1
0
1
2
2
1
1
1
2
2
2
2
1
1
2
2
2
2
2
0
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
2
1
2
2
1
1
1
0
1
2
1
2
0
2
1
2
1
1
2
1
1
1
1
0
1
1
2
1
1
1
1
2
1
2
2
1
2
1
1
1
1
1
2
1
0
0
2
2
2
1
2
1
1
2
1
1
1
0
1
2
2
1
0
0
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
2
2
1
0
0
2
2
1
1
1
1
0
2
1
1
1
1
2
1
2
0
1
2
1
1
2
1
1
1
1
1
2
0
2
0
2
1
0
1
1
0
0
1
1
1
1
1
1
1
1
0
2
1
2
0
1
1
2
1
1
2
2
1
1
1
2
1
1
0
2
1
0
1
1
2
1
1
1
2
2
2
2
2
0
1
1
2
1
1
1
1
2
1
1
1
1
1
1
2
0
1
1
1
2
1
2
2
0
0
1
2
1
0
1
1
2
0
2
1
0
2
1
1
1
2
1
2
2
2
1
1
2
2
1
1
2
0
1
0
1
2
1
0
0
2
2
1
1
1
2
1
0
1
1
2
2
2
1
1
1
1
1
1
1
1
0
1
1
1
1
1
2
1
2
2
0
2
2
1
1
2
2
1
2
2
0
1
2
0
2
0
1
1
1
1
3
2
2
1
1
1
2
1
1
0
1
0
1
2
0
1
0
1
1
1
1
2
2
1
1
2
2
1
1
1
1
1
1
0
1
2
1
1
2
1
1
1
1
1
2
2
1
0
2
3
3
1
2
0
0
0
1
1
2
1
0
1
2
2
1
2
0
1
1
1
1
0
1
0
1
1
1
0
2
1
2
2
1
1
2
0
1
1
2
0
1
1
1
1
1
2
0
1
2
1
1
2
2
2
2
1
0
1
1
1
0
2
1
2
1
0
2
1
0
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
0
1
1
1
1
2
2
1
1
1
2
1
0
1
1
1
1
2
1
0
1
1
1
1
2
1
1
1
1
1
1
1
1
1
0
2
1
1
1
1
1
0
1
1
1
1
1
0
1
2
1
2
0
0
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
0
2
1
0
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
2
0
1
1
1
1
2
1
1
1
1
0
1
1
2
0
2
1
1
1
1
0
2
1
1
2
2
1
1
0
1
1
0
3
2
2
1
1
1
1
0
1
1
2
0
1
2
3
2
2
1
2
1
1
2
1
2
0
1
1
2
2
1
2
2
1
2
2
2
1
0
1
1
0
1
0
1
1
1
1
0
1
1
1
1
2
2
2
1
1
1
1
2
1
1
1
0
1
1
1
2
2
1
2
1
1
2
1
0
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
2
2
2
1
1
1
0
2
1
2
2
1
2
1
2
1
2
1
1
2
1
1
0
1
3
1
1
2
1
1
2
1
2
1
2
1
0
2
2
0
1
0
2
0
2
2
1
2
1
2
2
1
2
2
1
1
1
1
1
1
2
0
0
1
1
1
1
0
1
1
0
2
1
2
0
2
0
1
1
0
1
1
2
2
0
1
1
1
2
2
1
0
2
2
1
1
1
1
2
1
0
1
1
1
1
1
0
1
2
1
1
1
2
1
0
2
0
3
1
0
1
1
3
1
2
1
1
1
1
2
2
2
1
0
1
2
1
1
1
2
2
0
2
2
0
1
1
1
2
2
1
1
0
2
0
1
1
0
1
1
0
1
1
0
1
3
1
0
2
1
2
0
1
1
1
1
1
2
1
1
2
0
2
1
1
1
0
1
1
2
2
0
1
2
1
2
1
1
1
2
1
1
1
2
0
1
1
1
1
0
0
1
1
1
2
2
1
1
1
1
0
2
1
1
1
1
1
2
1
5
1
1
1
1
1
1
1
1
1
2
0
2
1
1
1
2
1
2
1
3
2
2
1
0
1
0
2
1
1
1
1
0
1
2
1
1
0
1
2
1
2
1
0
1
1
2
0
2
1
0
1
0
1
3
2
1
0
2
1
0
1
1
0
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
2
2
1
0
1
1
1
1
1
1
1
2
1
2
1
1
2
2
1
1
1
1
0
1
1
2
2
1
1
1
2
1
1
0
1
1
1
1
1
1
1
2
1
1
2
0
1
1
1
1
1
1
1
2
0
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
0
1
0
1
2
2
1
0
1
1
2
1
2
2
1
2
1
2
2
1
1
1
2
1
1
0
1
2
0
1
1
0
0
1
1
1
2
2
1
0
1
1
1
2
1
1
1
2
2
1
1
1
1
2
1
1
0
2
1
1
2
1
2
1
0
2
2
1
1
2
2
1
1
1
1
1
3
0
1
0
2
2
2
1
0
1
1
2
1
1
0
0
1
1
1
2
0
1
2
2
2
1
1
1
1
1
1
1
1
2
1
0
1
2
1
2
1
1
2
1
2
1
2
0
2
1
1
1
1
1
2
1
2
1
2
1
0
1
1
1
2
1
2
0
3
1
0
2
0
2
2
2
1
1
9
1
1
0
1
2
1
1
1
2
2
2
1
1
1
1
2
2
1
2
2
1
1
2
1
1
2
4
1
1
1
2
1
2
2
0
1
1
0
1
1
2
1
1
1
1
2
2
2
1
2
0
2
4
1
0
1
1
1
1
2
1
1
1
1
2
1
1
1
1
0
1
1
1
1
1
1
2
2
2
1
2
1
1
2
1
0
1
1
2
1
1
1
1
1
2
2
2
1
1
2
0
0
1
1
1
1
2
1
1
1
0
2
2
1
1
1
1
0
0
2
1
1
0
1
1
1
0
1
2
1
1
1
1
1
1
1
1
0
1
1
1
1
0
2
2
0
1
1
1
1
0
0
2
2
1
0
2
1
2
1
1
1
2
2
1
2
1
1
2
2
2
1
2
1
1
1
2
1
1
1
2
2
2
0
1
1
1
1
0
1
1
2
1
1
0
1
1
2
1
1
1
2
0
1
1
2
1
0
1
2
1
1
1
0
2
1
1
1
2
2
1
2
2
1
0
1
1
1
0
1
1
1
1
1
2
0
2
1
1
1
0
1
1
1
0
2
2
2
0
2
1
2
1
1
2
1
2
2
0
1
2
2
2
1
0
0
0
2
1
1
2
0
1
1
1
2
1
1
2
0
1
2
1
1
0
1
1
0
0
0
1
2
1
0
2
1
1
1
1
1
1
0
1
1
1
2
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
1
1
2
2
1
1
1
0
1
1
1
1
1
1
1
0
0
1
2
2
2
1
2
1
1
0
2
1
1
2
2
0
0
1
1
2
1
2
1
1
1
1
2
1
1
1
2
1
1
1
2
0
1
2
1
0
0
0
0
2
2
1
2
1
0
2
1
2
1
1
2
2
1
0
1
1
1
2
1
1
1
2
1
0
1
2
1
1
0
2
1
2
2
1
2
1
2
2
2
2
1
1
1
2
1
1
1
1
2
1
0
1
2
1
2
1
0
1
1
1
2
1
2
1
2
2
4
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
2
1
2
1
2
2
1
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
0
1
1
0
1
1
2
2
1
1
1
1
1
1
1
1
0
2
2
1
1
1
1
2
1
0
0
0
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
0
2
1
1
1
1
0
0
1
1
1
1
1
2
2
1
1
1
1
2
2
1
2
0
1
2
1
0
2
2
1
1
0
2
2
2
1
1
1
4
1
1
1
1
2
2
2
1
1
2
0
1
1
2
0
1
1
1
2
1
1
1
1
1
1
1
2
1
1
2
0
1
2
1
1
2
2
2
2
2
1
4
1
1
2
1
1
1
1
1
1
0
1
2
1
0
1
0
1
2
1
1
1
1
1
1
1
2
3
1
1
0
1
1
2
1
1
1
1
1
1
0
1
1
1
1
3
1
1
1
1
0
2
3
2
1
1
2
2
1
2
0
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
0
1
1
2
1
1
1
1
1
2
1
1
1
1
0
1
2
2
1
1
2
0
1
2
2
1
0
2
2
1
2
2
1
1
2
2
1
1
1
2
1
1
1
2
1
1
2
1
2
1
1
1
2
0
1
1
1
1
1
1
2
2
1
1
1
1
2
1
1
2
1
0
0
1
1
1
1
1
1
1
1
0
0
1
1
2
2
1
1
1
1
1
2
1
1
0
1
0
2
1
1
1
1
1
1
2
2
1
1
1
1
2
1
0
1
1
1
2
0
1
1
1
1
0
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
2
1
0
1
1
2
1
2
1
1
1
1
1
2
1
2
1
1
1
2
1
1
0
2
1
1
1
1
1
1
2
2
1
1
2
1
1
0
2
1
0
2
0
0
2
1
0
2
1
1
1
2
1
1
1
1
1
1
0
1
2
2
1
2
1
2
1
1
1
2
1
2
1
1
1
0
1
2
1
0
1
1
2
1
1
1
1
1
0
0
0
1
0
0
1
1
1
1
1
1
1
1
0
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
2
2
1
1
1
1
1
1
2
2
1
1
1
1
2
2
1
3
1
1
1
1
1
0
2
1
1
1
2
0
0
0
1
1
1
1
1
1
1
0
1
1
1
1
2
1
2
2
1
1
2
1
1
1
1
0
1
1
1
2
1
0
1
2
1
1
1
1
1
1
2
2
1
1
1
1
0
1
1
1
1
1
1
1
1
6
2
2
0
2
2
1
1
1
0
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
2
1
2
2
1
0
1
2
1
1
0
1
0
1
2
0
2
1
0
2
1
1
3
1
2
1
1
1
1
1
1
2
2
1
1
0
1
1
1
2
1
1
1
1
2
0
0
1
2
1
1
1
1
2
1
1
1
1
0
1
1
1
1
0
0
2
1
1
2
1
1
1
1
1
0
1
1
2
2
1
1
1
1
1
0
2
1
0
2
2
1
2
0
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
2
1
0
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
2
1
1
1
0
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
3
1
2
1
1
1
2
1
2
1
1
0
1
1
2
1
1
1
2
1
2
1
0
1
1
1
1
2
1
1
1
1
3
2
2
1
1
1
1
1
1
0
0
1
1
1
2
1
1
1
1
1
2
1
1
2
1
0
1
0
1
1
2
1
1
1
2
2
0
1
1
2
1
2
1
1
1
0
1
0
1
1
1
1
1
1
2
2
2
1
1
2
0
1
1
0
1
2
1
2
1
1
2
1
2
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
2
1
0
1
1
1
1
2
2
1
0
1
1
1
1
2
0
1
2
2
1
1
1
1
1
1
2
2
1
2
0
1
1
1
1
2
2
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
0
0
0
1
1
1
1
2
2
2
1
1
1
0
0
2
1
1
2
2
1
2
0
1
1
1
1
1
1
1
1
2
2
2
1
1
3
0
1
2
1
1
1
2
2
0
0
1
1
2
1
1
2
2
1
2
0
1
2
1
1
0
0
1
2
1
0
2
2
1
2
1
2
1
1
1
1
0
2
1
1
1
1
1
0
1
2
1
1
2
1
1
1
2
0
2
1
1
1
2
1
1
1
1
1
1
2
0
2
1
1
0
2
1
1
1
1
0
2
1
1
1
0
1
2
1
2
1
1
1
1
1
1
1
2
2
2
2
1
2
2
1
2
2
1
1
1
1
0
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
0
2
1
1
0
0
2
2
1
1
2
1
1
1
1
0
3
2
2
2
2
0
1
2
2
1
2
1
1
0
2
1
1
0
1
1
0
0
1
1
1
2
1
2
2
2
1
1
1
1
1
0
2
1
2
1
2
1
2
2
2
2
2
1
1
1
1
1
2
1
2
2
1
1
1
2
1
1
2
0
1
0
1
2
1
1
1
2
2
1
1
1
0
1
1
1
1
1
1
0
1
1
1
2
0
1
1
1
1
1
1
1
0
1
0
0
0
1
2
1
2
1
1
0
0
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
1
2
1
1
2
1
2
1
1
1
1
2
2
1
1
2
1
2
0
1
1
1
1
0
1
2
1
0
1
0
1
1
0
1
0
0
2
1
2
2
1
2
2
1
0
1
1
2
2
1
1
2
0
1
2
1
2
2
2
1
1
2
2
0
1
1
1
1
1
1
1
2
1
1
2
2
2
0
1
1
1
1
2
1
2
1
1
0
2
1
1
1
1
1
2
1
2
1
0
3
1
2
2
2
1
0
2
2
1
1
0
2
1
0
1
1
2
1
2
1
0
1
0
0
1
1
2
0
1
1
2
2
1
2
1
1
1
2
2
2
1
1
1
1
0
1
1
1
0
1
1
2
2
1
1
1
1
1
1
2
1
3
2
2
2
1
1
2
2
1
2
2
0
1
1
1
1
2
1
0
2
1
1
2
1
0
2
0
1
1
1
1
2
1
1
1
2
1
1
0
0
2
1
1
1
1
2
2
1
1
2
1
1
1
2
1
1
1
1
2
2
1
1
1
0
0
1
1
2
1
1
0
1
1
2
2
0
1
1
0
1
1
2
0
2
2
1
2
1
0
0
1
1
1
0
2
2
1
0
1
0
1
1
1
1
0
0
1
1
1
1
1
1
0
0
0
2
1
0
1
1
1
1
1
2
1
1
2
1
1
1
2
2
1
1
1
2
1
1
2
1
1
2
2
0
0
1
2
0
1
1
1
1
1
1
0
1
0
0
0
1
2
1
2
2
1
1
1
2
1
0
2
0
1
2
0
2
2
1
1
1
2
1
2
1
1
1
1
1
1
1
1
2
1
2
0
1
2
2
1
1
2
1
1
1
1
2
2
0
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
2
2
1
0
1
1
1
1
1
1
1
0
1
1
1
1
1
0
1
2
2
1
0
2
1
2
2
1
1
1
2
1
1
1
1
0
2
2
1
2
1
2
2
1
1
2
2
3
1
2
1
0
1
1
2
1
1
1
1
0
1
0
1
1
2
0
2
0
0
1
1
0
2
1
1
0
2
2
2
1
1
1
1
2
2
2
1
2
2
1
0
1
2
2
1
1
1
1
1
1
2
1
2
1
0
2
1
1
2
3
1
1
1
1
1
1
2
1
0
1
0
1
2
2
1
2
1
1
2
1
1
1
1
2
0
1
2
1
2
2
0
2
0
1
1
1
0
1
1
2
2
1
2
2
2
2
1
1
0
1
0
2
1
0
0
1
1
2
1
1
1
0
0
1
1
2
1
0
1
1
0
1
1
1
1
1
2
1
1
1
1
0
1
0
1
1
0
2
0
1
1
1
2
1
0
2
1
1
1
1
2
1
1
0
0
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
2
0
1
0
1
1
0
1
1
1
1
1
1
1
1
1
0
2
1
0
1
0
1
1
1
1
2
1
1
2
2
2
1
1
2
1
0
1
0
0
1
1
1
2
1
1
0
1
1
1
1
1
1
1
0
1
2
1
1
3
1
1
1
1
2
1
1
1
1
0
3
1
1
1
0
1
2
0
1
1
2
1
2
2
1
1
1
1
1
1
1
2
1
1
0
1
0
2
1
1
2
1
1
2
0
2
2
1
1
2
0
1
1
1
2
1
1
2
2
1
0
1
1
2
1
1
2
2
0
0
1
1
1
1
2
1
1
0
1
2
0
1
1
1
1
1
1
2
1
2
0
1
2
2
2
1
1
1
2
0
2
1
1
0
0
2
1
1
1
1
1
1
1
1
1
1
1
0
1
2
2
2
1
1
2
1
1
1
0
1
2
2
1
1
1
1
1
2
1
2
0
1
1
2
1
0
1
0
1
1
1
1
1
0
1
1
2
0
1
1
1
2
1
1
1
1
0
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
2
1
1
2
2
2
1
0
2
1
2
1
3
1
2
1
1
1
1
1
0
1
1
2
1
2
2
2
1
1
2
1
1
0
1
1
2
1
2
1
1
2
1
2
2
1
1
1
2
1
2
0
1
1
1
2
1
2
2
2
1
2
0
1
2
0
1
2
1
1
1
1
0
2
1
1
0
2
1
1
1
2
1
2
2
2
1
1
1
1
1
0
2
2
1
2
2
2
1
1
0
1
1
0
1
1
1
2
2
2
1
1
1
2
1
1
1
1
2
1
1
1
1
1
2
1
1
0
1
1
1
2
1
1
1
1
1
0
0
0
1
2
1
1
2
1
1
3
1
1
0
2
1
1
1
3
1
0
0
1
2
1
2
1
1
1
1
1
1
2
1
1
2
0
1
1
0
2
1
1
1
2
1
2
1
1
1
2
2
0
1
1
1
2
1
2
1
2
2
1
0
1
2
1
0
1
1
1
2
1
1
1
2
1
0
0
1
1
1
1
1
1
1
2
1
1
0
1
1
1
1
2
0
2
2
1
0
1
1
1
0
0
1
1
1
1
1
1
1
1
2
0
2
1
1
2
2
1
1
2
1
1
1
2
2
1
1
1
2
2
1
2
0
1
2
1
2
1
1
1
1
1
1
1
2
1
1
2
1
2
2
1
1
1
2
2
1
1
1
1
2
1
2
2
2
1
2
1
1
1
2
1
2
1
1
1
1
1
0
1
1
1
2
1
2
2
1
1
1
2
2
1
2
2
1
1
1
2
1
2
2
2
1
1
1
1
1
2
2
2
1
2
1
1
1
0
1
0
1
2
1
0
0
1
1
1
1
1
0
2
1
1
0
2
1
1
1
1
1
1
0
1
1
1
2
1
0
1
1
2
1
2
0
1
0
2
1
2
1
1
1
1
2
2
1
1
2
1
1
0
1
1
1
2
1
2
1
1
2
1
0
2
0
1
0
1
1
1
1
1
2
2
2
1
2
1
1
1
1
1
1
1
1
4
1
0
1
1
1
1
1
1
2
1
1
1
1
1
1
2
0
1
1
2
2
2
1
1
2
2
1
2
1
2
0
2
1
2
1
1
1
1
2
2
0
1
1
1
2
2
0
1
1
1
1
1
2
1
0
2
0
2
2
1
0
1
1
1
1
1
0
1
1
0
1
1
2
1
1
1
1
1
1
1
0
1
2
1
1
0
2
1
1
3
1
2
1
0
1
1
1
1
0
2
1
2
1
1
1
2
2
1
0
0
0
1
1
2
1
1
1
1
1
1
1
1
1
0
1
1
1
0
1
1
0
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
0
2
2
1
2
1
0
1
2
0
1
2
1
0
2
2
1
2
2
2
1
0
1
1
1
1
2
1
1
1
2
2
1
2
2
2
1
1
1
1
1
2
1
2
1
1
2
2
1
2
2
1
1
2
0
2
0
1
2
2
1
2
1
1
1
0
1
1
1
0
1
2
1
0
2
1
0
1
2
0
1
1
1
1
0
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
0
1
1
1
2
2
2
1
1
0
1
1
1
2
2
2
2
2
1
1
2
2
1
1
1
1
1
2
1
1
2
1
2
1
2
2
1
1
2
2
0
2
1
0
1
0
2
1
1
1
0
1
2
1
1
2
1
1
1
0
1
2
2
0
2
1
1
1
1
1
1
1
1
0
1
0
1
2
1
1
1
2
1
1
0
1
1
1
1
1
0
0
0
1
2
1
0
0
2
0
1
1
2
1
1
1
1
0
1
1
1
4
0
1
1
2
2
0
2
1
1
0
1
1
1
0
1
0
1
1
1
2
1
1
0
1
1
2
1
1
2
1
0
2
1
1
1
1
1
0
0
2
1
2
1
0
1
1
1
1
2
1
1
1
1
0
1
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
2
1
0
1
1
1
1
1
3
1
1
1
1
2
2
1
2
2
2
1
0
1
1
1
2
1
0
1
0
1
1
0
1
1
1
1
2
1
1
0
1
1
2
0
2
1
2
2
1
1
2
0
2
1
1
2
2
1
1
1
1
1
1
2
1
2
2
1
2
1
0
2
0
1
1
1
1
2
0
1
1
2
0
2
2
0
2
2
1
1
1
2
1
0
1
1
2
2
1
1
2
2
0
1
1
1
2
1
0
1
1
1
1
1
1
1
1
1
1
2
1
1
2
2
2
2
1
2
2
1
1
1
2
1
1
2
1
3
1
1
2
1
1
0
2
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
0
1
2
1
1
2
2
1
1
1
1
1
0
1
1
1
1
2
1
1
2
1
1
2
2
2
1
1
2
0
2
2
1
2
1
1
0
1
2
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
0
2
1
1
1
1
1
1
1
1
1
1
3
1
1
1
0
1
2
1
1
0
2
1
1
1
2
1
2
1
1
1
2
1
0
1
1
1
2
1
1
1
2
1
0
2
2
1
1
1
1
2
1
0
0
1
3
1
0
1
1
0
0
2
1
1
2
1
1
2
2
1
1
1
1
0
1
1
1
0
1
1
1
1
1
2
1
1
1
1
2
1
1
1
0
1
1
2
1
1
1
2
1
1
2
0
1
1
1
1
2
1
1
1
1
2
1
1
1
1
0
1
0
1
0
1
1
1
1
2
3
2
1
1
1
1
2
1
0
2
1
1
0
1
2
1
1
0
0
1
2
1
1
1
1
0
1
1
1
2
1
0
0
1
0
0
2
1
1
1
2
1
1
2
1
2
1
1
2
2
1
2
1
0
0
0
1
2
2
2
1
1
2
1
1
2
1
0
2
2
1
2
2
1
1
1
2
2
1
1
1
2
1
0
1
1
1
1
2
2
1
1
3
1
1
1
1
0
2
1
2
0
2
1
2
1
1
1
1
1
2
0
1
1
1
2
1
1
1
1
0
0
2
1
1
2
0
1
2
1
1
1
1
0
1
2
4
1
0
1
2
1
1
1
2
1
2
1
2
2
1
1
0
2
0
1
1
1
1
1
1
2
1
1
1
1
1
1
1
0
2
1
0
2
1
0
0
1
2
2
2
1
2
1
0
2
2
2
1
1
1
2
2
1
0
1
2
1
1
1
1
1
1
2
2
1
0
2
1
1
2
1
2
1
0
1
2
1
1
1
1
0
0
2
2
1
2
1
1
1
2
2
1
2
1
2
0
0
2
0
1
1
2
1
1
1
1
1
2
0
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
2
1
2
1
2
1
1
1
1
2
1
2
0
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
2
2
1
1
1
0
2
1
1
0
0
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
0
2
1
1
1
1
2
1
1
1
2
2
1
1
0
2
1
1
1
1
2
2
2
1
2
1
2
2
1
1
2
1
1
1
1
1
1
2
0
1
0
1
2
2
2
1
0
2
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
0
0
2
1
1
2
2
0
2
2
3
2
1
1
2
1
1
0
1
2
0
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
0
1
1
1
2
2
1
1
1
1
2
0
1
0
1
1
1
2
1
0
1
1
1
2
1
1
1
1
0
1
1
1
2
2
2
1
1
1
1
1
2
2
0
1
1
1
2
1
0
1
2
1
1
1
1
1
1
2
2
1
1
0
1
1
1
1
1
1
1
2
1
2
1
0
0
2
1
2
1
0
1
1
0
0
0
1
1
0
1
1
2
0
2
1
1
1
2
1
2
1
2
1
1
1
1
1
1
1
2
1
0
1
1
1
1
2
1
1
1
0
2
2
1
1
1
1
2
1
0
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
0
2
1
1
1
1
2
1
2
1
2
2
1
1
2
2
1
1
1
2
2
0
2
1
3
1
1
1
2
1
1
0
1
1
1
1
2
2
1
2
1
2
1
1
1
1
1
2
1
1
0
2
2
1
2
1
2
1
0
2
2
1
1
1
1
1
1
1
5
2
1
2
1
2
1
1
1
1
1
1
0
2
1
1
0
1
2
0
1
0
1
1
1
1
1
1
1
1
0
2
1
0
1
1
0
1
1
1
1
1
1
2
0
1
1
2
1
1
1
1
2
0
1
0
1
2
1
1
1
0
1
2
1
1
1
1
1
2
0
2
1
2
0
1
0
1
1
2
1
2
1
1
1
1
1
1
2
2
1
1
1
0
1
2
1
1
1
0
1
1
1
0
1
2
1
1
2
2
1
2
1
2
1
2
2
1
2
1
1
1
1
1
1
2
1
1
2
2
1
2
1
1
1
2
0
1
1
0
3
2
1
1
1
0
1
1
1
1
2
1
1
0
1
0
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
0
2
2
2
0
1
1
1
2
1
2
1
2
1
1
1
2
1
2
1
1
2
1
1
1
1
2
1
0
2
1
2
2
1
1
1
1
1
1
1
1
1
2
1
2
2
1
2
3
2
0
1
2
1
1
1
1
1
1
0
1
1
0
2
1
1
2
1
1
1
2
0
1
1
1
0
1
0
1
2
1
1
1
1
1
1
3
1
1
1
2
2
2
2
2
1
1
2
1
2
0
1
1
1
2
1
1
1
1
1
1
2
1
0
1
0
0
1
1
2
1
1
1
2
1
1
1
2
1
0
0
1
0
1
1
1
1
1
1
2
1
1
1
1
1
2
2
2
2
1
0
1
1
2
1
1
1
1
0
1
2
2
1
1
0
1
2
2
2
1
2
2
2
2
1
2
2
0
2
1
2
0
1
2
1
0
1
1
1
1
1
1
1
2
1
1
0
0
2
1
1
1
1
0
1
0
1
2
1
1
0
1
2
0
2
1
1
1
1
1
4
2
1
1
2
1
1
1
1
1
1
1
2
1
3
2
1
0
2
1
1
1
0
1
1
2
1
2
1
0
1
2
1
2
0
1
1
1
1
2
1
0
1
2
0
2
0
1
1
2
2
1
1
2
1
1
1
1
1
1
0
1
2
1
1
0
1
1
1
1
1
1
1
2
2
1
2
1
1
1
1
1
2
1
4
0
1
2
1
1
1
2
1
1
1
1
1
1
2
1
1
2
2
2
1
1
1
2
2
1
1
1
1
0
2
1
1
2
1
0
1
1
1
2
2
2
1
1
0
2
1
1
1
1
0
1
0
1
1
2
1
1
1
1
0
2
1
1
1
1
1
2
2
2
2
1
1
1
2
0
1
1
2
1
1
2
2
2
1
2
1
1
1
1
2
2
1
2
1
1
2
1
0
1
1
1
2
1
0
1
0
0
0
1
2
1
0
2
1
1
1
0
1
1
1
4
1
1
2
1
0
1
1
2
2
1
1
1
1
1
1
2
1
1
1
0
0
1
1
0
1
1
2
0
1
1
0
0
1
2
2
1
2
1
2
1
1
1
2
0
1
2
1
1
2
2
1
2
1
1
1
2
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
0
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
2
2
2
2
1
0
1
0
1
2
1
1
0
1
2
1
1
1
1
2
1
1
1
2
1
1
1
1
1
2
1
2
0
1
1
2
2
1
0
2
1
2
1
1
1
1
1
1
1
1
2
1
2
0
2
2
1
2
0
1
1
1
2
2
2
2
2
1
3
2
1
0
1
2
1
1
1
1
1
1
1
0
2
2
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
2
1
2
0
1
2
1
2
1
2
1
2
1
1
2
2
0
1
2
1
1
2
1
1
1
2
1
1
2
1
0
1
1
2
1
1
1
2
1
0
0
2
2
1
2
1
2
1
1
1
1
2
2
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
1
0
2
2
2
1
0
1
1
1
1
1
0
1
1
1
1
0
1
2
2
1
1
1
2
2
1
1
2
1
2
2
2
1
1
1
2
3
1
1
2
1
2
2
1
0
1
1
0
1
1
2
1
1
1
1
2
1
1
1
2
1
1
0
3
2
1
1
1
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
2
1
2
1
1
0
2
1
1
0
1
3
2
1
2
1
2
1
2
4
1
0
2
1
0
1
1
1
2
1
2
0
1
1
1
3
1
1
0
2
1
1
1
0
1
1
2
1
0
2
0
1
0
1
2
0
1
1
2
1
1
1
1
2
1
1
1
1
2
2
1
2
1
0
0
1
2
0
1
1
1
1
2
2
1
1
1
1
2
1
1
2
2
2
1
0
1
1
0
1
0
1
1
1
3
2
2
1
3
3
1
1
1
1
1
3
1
1
1
2
1
1
1
1
1
1
1
2
1
1
2
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
0
0
1
2
0
0
1
1
1
0
2
1
1
1
3
2
1
0
0
1
0
1
1
0
2
2
1
0
1
2
2
1
1
0
4
1
1
1
1
2
2
0
1
1
1
1
2
2
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
0
1
1
0
1
2
1
0
1
1
1
1
1
0
1
2
1
1
2
0
0
2
1
0
1
0
1
2
2
1
0
1
2
1
0
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
0
1
1
1
0
1
1
2
2
2
0
1
2
1
2
1
0
1
1
1
1
1
0
1
1
2
2
3
1
2
1
2
0
1
0
1
1
1
0
1
2
1
2
1
2
1
1
1
1
1
2
0
0
0
1
2
1
0
2
1
1
2
1
1
1
0
1
1
0
1
2
1
2
0
1
1
1
1
1
3
2
1
2
1
2
1
1
1
2
1
1
1
1
1
1
2
1
2
2
2
1
1
2
1
1
2
1
2
2
2
2
1
0
1
1
1
2
1
1
1
2
2
2
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
0
1
1
1
2
1
1
1
1
0
1
1
1
1
2
2
2
1
2
1
0
2
1
2
1
1
1
2
1
1
1
1
2
2
1
1
1
8
1
2
1
1
1
0
2
1
1
2
2
0
0
1
1
1
2
1
1
1
1
1
0
2
1
1
1
1
1
2
1
2
2
2
1
1
2
1
2
2
1
2
1
1
2
1
2
1
1
0
1
1
0
0
2
1
2
1
1
1
1
1
1
2
2
2
1
1
1
0
2
1
1
2
1
1
1
1
1
1
1
1
2
2
1
0
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
0
1
2
1
1
1
1
1
2
0
2
1
1
0
1
2
2
2
1
1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
0
1
1
2
1
1
2
2
0
1
0
1
1
2
1
1
2
1
1
1
2
2
1
1
1
0
1
1
2
0
1
1
2
2
1
1
1
1
1
1
0
1
0
2
1
1
1
0
1
0
1
0
2
1
3
2
1
1
1
1
2
1
1
1
2
1
1
1
0
1
2
1
1
1
2
1
1
1
2
1
0
1
2
0
1
1
1
1
2
2
1
1
1
2
2
1
2
2
1
0
1
1
0
1
1
0
1
0
2
1
1
2
2
1
1
2
2
2
2
1
1
1
0
2
1
1
1
1
2
1
0
2
1
1
1
1
0
1
1
2
2
1
1
1
1
1
1
2
1
0
1
1
0
2
2
0
1
1
1
1
2
1
1
1
1
0
1
1
1
1
2
2
1
2
2
1
2
1
1
2
2
1
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
1
0
1
1
0
1
1
1
1
1
0
1
1
1
2
0
1
1
2
0
1
1
1
1
1
0
1
0
1
2
0
1
1
2
1
2
1
1
1
2
1
1
2
1
1
3
1
1
1
0
2
2
1
2
1
2
1
1
0
2
0
2
1
0
1
1
2
1
1
0
2
1
0
1
1
2
2
1
1
0
1
1
1
1
2
2
1
0
1
1
0
1
2
1
1
6
1
1
1
2
1
0
2
2
0
1
1
1
2
1
1
2
2
1
1
1
1
1
1
1
1
1
2
0
1
0
1
2
1
2
2
2
2
0
2
1
2
1
2
2
2
1
2
1
1
0
2
1
1
1
2
1
0
1
2
1
0
1
1
1
1
1
1
1
1
2
2
1
1
1
0
1
1
1
2
1
1
1
2
2
1
2
1
1
1
0
1
1
1
1
0
2
1
2
1
1
1
1
2
0
2
1
1
0
1
1
2
1
1
2
1
2
1
1
1
1
1
2
2
2
1
0
1
1
2
2
2
2
1
1
1
0
1
1
1
1
2
1
1
0
1
2
0
1
1
1
1
1
0
0
1
1
1
1
1
1
0
2
2
0
0
2
1
1
1
1
1
1
1
1
0
1
0
1
0
2
1
1
1
0
0
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
0
1
1
1
1
1
2
1
1
0
1
2
0
2
2
2
1
2
2
1
2
1
0
2
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
2
0
0
0
1
1
1
0
1
1
1
1
2
1
1
2
1
1
2
1
1
1
0
1
1
1
1
1
2
2
0
2
1
1
1
2
1
1
1
0
2
0
1
0
1
1
1
1
1
0
1
1
1
1
1
1
2
2
0
1
2
2
0
0
1
2
1
1
1
1
1
0
1
1
1
2
1
0
1
2
1
0
1
2
2
0
2
2
2
1
2
1
1
2
1
0
1
1
1
0
1
1
3
1
2
1
1
2
1
1
1
0
2
1
2
2
0
2
1
1
2
1
1
2
1
2
0
1
1
2
1
1
1
1
1
1
1
1
1
1
0
2
1
2
1
1
2
1
1
2
2
1
1
2
1
1
1
1
1
1
1
2
1
7
1
1
2
1
3
1
1
2
2
2
1
2
1
1
1
1
2
1
1
2
1
1
2
1
1
1
2
0
2
1
1
1
0
2
1
0
1
0
1
2
1
1
1
2
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
2
1
1
1
0
2
1
1
2
1
1
1
1
1
2
1
2
2
1
0
1
1
2
3
2
1
1
1
2
2
1
1
0
1
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
1
1
2
0
2
2
1
1
1
1
1
2
2
2
1
2
1
1
1
1
1
2
1
1
1
2
3
1
0
1
1
2
1
1
0
0
1
1
1
1
1
2
1
1
1
2
0
0
1
1
2
1
2
1
0
1
1
1
1
1
1
2
2
2
2
1
1
1
2
1
1
1
1
1
0
1
1
1
2
2
2
1
1
2
1
1
0
0
1
0
2
1
1
1
0
0
2
0
1
1
0
1
2
1
1
1
1
1
0
1
1
1
1
1
2
2
1
1
2
1
2
1
1
2
2
1
2
0
1
2
2
1
2
2
1
1
1
2
1
1
2
1
1
2
1
1
1
0
0
0
2
1
2
1
1
2
2
1
2
1
1
1
0
2
1
1
2
1
1
1
1
2
2
2
1
1
0
1
0
1
0
2
1
1
1
1
1
1
0
1
1
1
1
0
1
1
1
2
2
1
1
1
1
1
2
1
2
2
1
1
1
2
1
1
1
0
0
2
2
1
2
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
0
0
2
2
1
1
2
1
1
2
1
1
2
0
1
1
0
1
2
0
1
2
0
1
1
1
1
2
2
1
1
1
0
2
1
1
2
0
0
0
3
1
2
1
1
1
2
2
1
1
1
2
1
2
1
0
1
1
1
1
1
1
2
2
1
1
1
1
2
1
1
0
2
1
0
2
2
1
1
1
1
1
1
1
0
1
0
1
1
1
2
1
1
2
0
0
1
2
0
1
1
2
2
1
1
1
2
1
1
1
1
2
1
1
2
1
2
0
2
1
2
2
2
1
2
1
1
2
0
2
0
0
2
1
1
0
0
1
2
1
0
0
1
1
1
0
0
1
1
0
1
0
1
0
1
1
1
1
1
1
0
1
1
1
0
1
1
2
2
1
2
2
0
1
1
0
1
1
2
1
2
1
1
1
2
0
0
2
1
2
1
1
1
0
1
2
1
0
1
1
1
2
1
2
1
1
0
0
1
2
1
1
1
1
2
2
1
1
1
2
1
1
1
1
1
1
0
1
2
1
2
2
2
1
2
1
0
1
1
4
2
0
1
1
1
1
1
2
1
2
0
1
1
2
2
1
1
0
1
1
1
1
1
2
1
2
0
2
1
2
1
0
1
2
1
0
3
1
0
2
0
1
1
1
2
1
1
1
1
2
2
2
2
1
1
1
2
1
1
2
1
0
2
1
1
1
2
0
1
2
1
1
1
0
2
1
1
1
2
0
2
1
2
1
1
1
1
2
1
1
2
2
0
1
0
1
1
1
0
1
0
2
1
2
1
1
1
2
2
1
2
2
0
1
1
0
1
0
1
1
0
1
0
1
1
1
2
1
1
0
2
1
2
1
1
2
2
2
1
2
1
2
1
1
1
2
1
1
1
2
0
0
2
1
1
2
0
0
1
0
1
1
1
3
1
1
1
1
1
1
2
2
0
2
1
5
1
2
1
1
1
2
1
1
1
2
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
2
1
0
2
0
1
2
1
1
1
1
2
1
2
1
2
1
2
1
1
0
2
1
0
1
1
1
1
1
1
1
1
2
1
0
1
1
1
2
1
0
0
1
1
1
1
0
0
2
0
1
0
1
1
1
1
1
0
1
1
0
2
1
1
1
1
2
1
1
3
0
1
0
1
1
2
1
2
1
0
0
2
2
2
1
1
1
1
1
1
1
1
1
1
2
0
1
1
1
1
1
0
2
2
1
1
1
1
2
1
2
1
1
2
1
1
1
1
2
1
1
1
0
1
2
1
2
1
1
1
1
2
2
0
1
1
1
1
2
1
1
1
0
2
2
2
2
2
2
2
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
2
0
1
2
1
1
1
1
2
1
2
2
2
2
1
2
1
1
1
0
2
1
0
1
1
2
3
1
2
1
1
1
2
1
1
1
1
0
1
1
3
1
2
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
2
1
1
2
1
0
2
0
2
2
3
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
0
1
1
1
1
1
0
1
1
0
2
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
2
0
1
2
1
1
1
1
1
1
2
0
1
0
1
1
2
1
0
1
1
1
1
2
1
2
1
2
1
1
1
1
1
0
0
2
2
2
1
1
1
1
1
1
1
1
2
1
1
1
3
1
1
0
1
1
2
0
1
2
1
1
1
1
2
1
2
2
1
1
1
1
1
1
1
0
2
1
0
1
1
1
1
2
1
2
2
0
1
1
1
1
2
1
1
2
1
1
1
2
1
2
2
1
1
1
1
2
1
1
1
2
1
1
2
2
1
1
1
0
1
2
1
1
1
1
1
2
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
0
1
2
0
0
2
1
2
1
0
0
2
1
1
1
1
1
2
1
2
2
0
1
0
1
0
1
1
2
2
1
1
0
2
1
1
1
1
2
1
1
1
1
1
1
2
1
1
2
0
1
2
1
1
1
1
1
1
1
2
2
1
2
0
1
2
1
1
0
2
1
0
2
2
2
1
2
0
2
2
2
1
2
2
1
1
2
2
1
1
1
1
1
2
2
1
2
2
1
1
1
1
2
1
2
2
0
2
0
0
2
1
0
1
1
1
1
2
1
1
1
1
1
2
1
1
2
1
1
1
1
2
2
2
1
2
2
1
2
1
1
1
1
1
2
1
1
2
2
2
2
0
1
1
1
1
2
1
2
1
1
1
1
1
1
1
0
0
0
1
1
2
5
1
2
1
1
0
0
1
1
0
1
1
0
0
1
2
1
1
3
1
2
1
2
1
0
2
1
0
2
1
1
1
1
1
1
2
2
2
2
1
2
1
0
0
2
1
2
1
0
1
0
1
2
0
1
1
1
2
1
1
1
2
0
2
2
1
1
0
0
1
2
2
1
1
2
2
1
1
1
1
2
1
2
1
2
1
2
1
1
1
1
0
1
2
1
1
2
1
1
2
2
1
2
1
1
2
1
0
1
2
2
2
1
1
1
1
2
2
1
2
2
2
0
2
3
1
1
2
0
1
2
1
1
0
1
0
1
1
2
2
1
1
1
1
1
1
2
1
2
1
1
1
2
1
2
0
1
1
2
1
3
1
1
2
2
2
1
1
1
2
1
1
1
2
1
1
1
0
0
1
2
1
0
1
1
1
2
1
1
2
1
1
1
2
1
0
1
1
1
2
1
1
1
1
1
1
1
1
0
2
1
1
1
1
1
1
1
0
1
1
1
1
2
2
1
2
2
1
1
1
2
1
1
1
2
1
1
2
0
2
2
1
1
2
2
1
2
1
2
2
2
1
1
0
1
1
2
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
0
1
0
2
1
1
0
3
0
1
0
1
1
1
1
2
2
1
1
1
1
1
1
2
1
0
1
0
0
1
2
1
0
2
1
2
1
1
1
1
1
0
0
1
1
2
2
1
1
2
0
1
2
1
1
1
0
1
2
1
0
1
1
2
0
0
2
2
1
1
2
0
0
1
1
2
2
1
0
1
1
0
2
1
1
2
2
0
1
0
2
1
1
2
2
2
1
1
0
1
1
1
1
1
3
5
1
1
0
1
1
2
1
1
1
2
1
0
1
1
2
1
2
1
1
2
1
2
1
1
1
1
0
0
1
0
3
1
1
1
1
1
0
1
2
1
2
1
0
1
1
1
1
1
2
1
1
1
1
1
0
2
1
1
0
2
2
1
2
2
2
1
4
2
0
1
1
1
1
1
1
0
1
2
1
1
2
0
2
1
1
1
1
1
0
2
1
1
1
1
1
1
1
1
1
2
1
1
2
2
1
1
1
1
0
1
1
2
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
2
2
1
1
2
1
1
1
1
0
1
1
1
0
1
1
2
0
1
2
1
2
3
1
0
0
2
2
1
1
1
2
3
2
1
1
1
2
1
2
2
1
2
0
2
2
2
0
2
1
2
1
0
1
0
0
2
1
0
0
1
0
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
0
1
0
0
1
1
1
1
1
1
0
0
1
1
2
1
1
1
1
0
0
2
2
1
1
1
2
2
1
2
2
1
1
2
1
1
1
1
0
0
1
1
1
1
0
2
1
1
1
1
1
2
1
1
1
1
2
1
1
0
1
1
1
0
1
0
0
2
2
1
1
2
3
0
1
0
1
2
1
1
1
1
1
1
1
1
1
2
1
0
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
2
1
0
1
1
1
1
0
1
2
2
2
2
1
1
2
1
1
2
2
2
2
0
2
1
2
2
1
1
2
1
2
2
1
0
0
0
1
1
2
1
0
2
2
1
1
1
2
0
1
2
1
1
1
1
2
2
1
1
1
1
2
1
0
2
2
2
1
1
2
0
1
1
1
1
0
2
0
2
1
0
1
1
1
1
2
0
2
0
3
1
1
0
2
1
1
1
0
1
1
0
1
1
1
1
1
1
1
1
2
0
1
2
1
1
2
1
1
1
2
2
2
1
1
2
1
1
1
2
1
1
2
1
1
2
2
1
1
1
1
1
1
1
1
0
2
1
1
1
2
1
0
1
1
1
2
1
0
1
1
1
2
2
1
1
1
2
2
2
2
1
2
1
2
0
0
1
1
1
2
1
1
1
2
1
1
1
1
1
2
1
1
3
1
0
1
1
0
1
0
1
1
0
2
1
0
2
1
1
2
1
1
0
1
2
1
1
1
2
0
2
2
1
2
1
1
0
0
2
1
2
2
2
1
0
2
1
1
1
2
1
1
1
0
2
1
1
1
2
1
1
2
2
2
1
2
1
0
1
2
0
1
2
1
2
1
1
0
0
1
2
1
1
2
2
1
1
2
0
1
1
0
1
1
1
0
1
2
2
1
1
2
1
1
2
1
0
0
1
0
1
2
1
2
1
1
0
0
1
1
2
1
1
1
1
1
3
2
1
1
2
2
0
1
0
0
0
1
2
2
1
1
1
1
1
1
1
0
1
1
1
1
0
1
2
2
0
1
1
2
1
2
1
2
1
2
2
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
2
2
2
1
1
1
1
2
0
2
3
1
1
1
2
0
1
2
2
1
1
2
1
2
2
1
1
2
2
0
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
2
2
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
2
2
1
2
2
2
0
1
1
1
1
2
2
0
1
1
2
1
1
2
1
2
1
0
1
3
0
1
2
1
2
1
1
1
0
1
1
1
0
1
1
2
1
4
2
1
1
0
1
2
2
1
1
0
1
1
1
1
1
0
1
1
0
0
1
1
1
1
0
1
1
1
2
2
1
1
2
0
0
1
1
1
1
1
1
0
2
1
2
2
1
1
0
2
1
2
1
0
1
2
0
1
1
2
1
0
2
1
0
3
1
1
2
1
1
1
2
0
1
1
1
0
1
1
1
1
1
2
1
0
2
1
0
1
1
1
2
1
1
2
1
1
2
2
1
2
0
1
1
1
1
2
2
0
1
2
1
1
1
1
1
1
1
2
2
1
1
1
1
2
1
2
2
1
0
2
1
1
2
0
2
1
1
1
2
1
2
0
2
1
1
0
1
1
2
2
2
1
1
1
2
1
1
1
1
2
0
2
1
2
1
0
1
1
1
1
1
1
0
2
2
0
2
1
1
1
1
0
1
1
1
1
1
1
1
2
2
2
2
1
1
1
1
1
2
2
1
1
1
2
1
2
1
0
2
2
1
1
1
1
1
1
1
0
1
1
2
1
1
2
1
1
1
1
1
1
1
1
0
1
1
1
1
2
1
2
1
1
0
1
2
2
0
0
2
1
1
2
1
1
0
1
1
1
1
1
1
0
1
1
1
1
1
1
2
1
1
1
1
1
1
0
1
2
1
2
2
1
1
1
1
1
0
2
1
1
2
2
1
1
1
1
0
2
1
1
1
2
1
1
3
2
1
1
1
1
2
1
0
2
1
1
0
1
1
1
0
2
2
1
1
1
1
1
1
1
1
0
1
0
2
1
1
1
2
2
1
1
0
1
2
2
0
1
1
1
1
1
1
0
1
1
1
2
1
1
1
1
1
1
1
2
0
1
0
1
0
1
1
1
2
2
1
0
2
2
2
1
2
1
2
1
1
0
1
0
1
1
1
1
1
1
1
0
1
1
1
2
1
1
1
2
1
0
1
1
2
1
1
0
1
1
2
2
1
2
1
1
1
1
1
0
1
1
1
0
2
1
1
0
1
1
2
1
1
1
2
2
1
1
0
0
2
1
1
1
1
1
2
0
1
1
1
2
0
0
0
1
1
0
0
2
2
2
1
0
2
3
0
1
1
1
2
2
1
1
2
1
1
2
2
0
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
0
1
1
1
1
2
1
2
1
0
1
1
2
1
1
1
1
1
1
1
1
1
2
1
2
1
2
1
0
2
1
2
1
1
1
1
2
1
1
2
0
2
1
1
1
0
2
1
1
0
0
2
0
1
2
1
2
1
1
1
1
1
1
2
1
0
2
1
1
1
1
0
1
2
2
1
1
0
1
2
2
1
1
1
1
2
2
1
2
1
1
0
1
1
2
2
0
1
1
2
0
1
1
1
1
2
1
2
1
1
0
1
1
1
2
0
2
2
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
2
2
1
2
1
1
1
1
1
0
0
2
0
1
2
1
2
1
2
1
2
2
1
2
2
2
1
1
1
0
1
1
1
1
2
1
1
0
1
1
1
2
2
1
0
0
1
1
1
1
1
2
0
1
1
1
1
2
0
1
1
1
1
1
1
0
1
0
2
1
1
1
1
2
1
0
1
2
1
1
1
1
1
1
1
2
0
0
0
2
2
1
1
1
1
2
0
1
2
1
2
1
3
1
1
2
0
1
1
2
1
1
1
1
1
0
2
1
0
1
2
2
1
1
2
2
1
1
2
1
1
1
2
1
2
2
0
2
1
1
1
1
2
1
2
2
1
2
1
1
1
1
1
1
1
2
2
0
0
1
2
1
1
1
1
1
0
2
1
1
2
1
1
1
1
1
1
0
0
1
1
1
1
1
1
0
0
1
2
1
1
1
1
1
3
1
1
1
2
2
1
1
1
2
1
1
2
0
2
0
1
1
1
1
1
2
2
1
0
1
1
2
2
1
2
1
1
1
1
1
1
1
1
2
0
1
2
2
1
1
1
1
1
1
1
1
2
0
1
1
1
0
1
1
1
2
1
2
1
2
2
1
1
1
2
2
2
1
1
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
0
1
1
0
1
1
1
2
1
1
1
1
1
2
1
2
0
0
0
2
1
0
2
2
2
1
2
0
1
2
1
2
2
1
1
1
2
1
2
1
2
2
1
1
2
2
1
3
1
0
1
1
2
1
0
1
1
2
1
1
0
1
2
1
2
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
2
1
2
1
0
2
0
1
1
0
1
2
1
2
2
2
0
1
2
1
1
1
1
0
1
1
2
1
1
0
2
1
1
2
1
2
1
3
1
1
1
1
1
1
0
1
0
2
1
2
2
1
1
1
2
2
1
2
0
1
1
2
1
1
1
1
1
1
1
1
1
1
0
2
2
2
0
1
2
1
2
2
1
1
0
2
0
2
1
2
0
2
2
2
1
2
1
1
1
1
1
2
2
1
1
2
1
2
1
1
1
1
1
0
1
2
1
1
1
1
2
2
1
0
1
2
0
1
2
1
1
0
1
1
1
0
1
1
2
1
2
2
0
1
2
2
2
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
2
2
0
1
1
1
1
1
1
1
1
2
2
1
1
1
1
2
2
2
0
0
1
1
2
3
1
2
1
1
2
0
1
1
1
2
1
2
2
2
1
1
1
1
1
1
0
0
2
0
2
2
2
1
1
1
0
2
2
1
1
1
0
1
1
2
2
1
2
0
2
2
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
0
2
1
3
1
1
1
0
1
1
0
0
1
0
1
1
1
2
1
2
1
0
1
1
2
1
2
1
0
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
0
2
1
1
1
3
1
2
2
1
2
1
1
1
1
1
1
1
2
2
1
1
2
0
1
0
1
0
1
1
2
1
1
1
2
0
2
1
1
2
2
0
0
1
1
2
1
1
1
1
0
1
2
1
1
1
1
1
1
1
1
2
1
2
2
1
1
1
2
1
1
1
2
2
1
1
1
2
1
1
2
1
1
2
2
2
1
2
1
1
1
0
1
1
1
1
2
2
0
1
0
1
1
2
1
2
1
1
2
0
1
1
1
1
1
0
1
1
1
2
2
2
1
1
0
1
1
2
1
1
1
2
1
2
1
1
1
1
0
2
2
2
1
2
2
4
2
1
2
2
2
2
1
1
0
0
2
2
1
2
0
2
1
1
0
1
1
1
1
0
2
0
2
0
1
1
2
1
0
2
2
0
1
2
1
2
2
0
1
1
0
2
1
2
1
2
2
1
2
1
2
1
1
2
2
1
1
2
0
1
2
1
2
2
1
1
2
2
0
2
2
1
1
1
1
2
2
1
0
2
2
1
2
1
1
1
1
0
2
0
0
1
2
1
0
1
1
2
1
1
1
1
0
1
1
1
1
1
2
0
0
1
2
0
1
1
2
1
1
1
1
2
0
1
2
0
2
2
1
2
1
0
1
0
1
2
2
1
1
1
2
1
2
1
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
2
2
1
2
1
2
2
2
0
1
1
0
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
0
2
1
1
1
1
1
1
1
1
0
2
1
2
2
2
1
0
1
1
2
1
1
1
1
0
1
1
2
1
1
1
1
1
1
0
2
1
1
1
1
1
2
2
1
1
1
2
1
1
1
1
0
1
2
2
1
0
1
1
1
0
2
1
1
1
2
1
2
2
1
1
0
1
2
1
1
1
1
1
1
1
1
2
2
2
1
0
1
1
1
0
0
2
1
1
0
1
2
1
2
1
1
1
1
1
2
1
0
0
2
1
2
1
0
1
1
0
2
1
0
1
1
1
2
2
0
1
2
2
2
1
0
1
1
1
0
1
1
2
2
1
2
2
0
1
0
2
1
1
2
1
2
0
1
1
0
2
1
2
1
1
1
0
2
1
1
2
1
0
2
1
0
1
2
1
1
1
1
2
0
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
2
2
1
2
1
1
2
1
1
0
1
0
0
1
1
1
1
2
1
0
2
2
1
1
1
2
1
1
1
2
1
1
1
0
1
2
2
1
1
1
1
1
1
2
2
1
1
2
1
1
2
2
2
2
2
2
1
2
2
1
2
1
3
1
1
1
1
1
0
1
1
0
2
1
1
2
1
0
1
1
1
0
2
1
2
1
1
1
1
2
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
2
2
2
1
1
1
0
2
1
1
2
1
1
2
1
2
1
2
1
2
2
1
1
1
2
1
2
1
1
1
1
0
1
1
2
1
1
0
2
1
1
2
0
1
2
0
0
0
2
1
1
1
0
2
0
1
2
1
2
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
1
2
0
2
1
1
1
0
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
3
1
1
3
1
1
1
1
2
1
2
1
1
0
1
1
1
1
1
1
2
1
2
1
0
0
2
2
0
2
2
1
2
2
1
1
2
1
1
1
1
1
1
0
1
1
0
1
2
2
1
1
0
2
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
2
1
2
1
1
2
1
1
1
1
1
0
1
1
1
0
2
2
2
1
1
1
1
2
0
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
0
0
2
2
0
2
2
2
1
1
1
1
1
1
1
0
0
2
1
1
0
2
2
1
2
2
2
1
1
1
2
1
1
1
1
1
2
1
1
0
1
1
1
1
1
2
2
0
1
1
1
1
2
1
2
1
2
2
2
1
1
0
1
1
1
1
2
2
2
2
2
2
1
2
1
1
2
1
2
1
2
1
0
1
1
2
2
1
0
0
0
2
1
1
1
1
1
1
0
2
2
0
2
2
1
1
1
2
2
2
1
0
1
2
2
2
2
1
1
1
2
1
2
0
1
0
2
0
1
1
0
2
1
2
2
2
1
0
1
1
1
2
1
1
1
1
2
1
1
1
2
1
2
0
2
1
3
2
1
2
0
2
1
1
2
0
2
1
2
1
2
2
1
1
0
1
2
2
2
1
1
1
1
1
1
2
1
1
0
1
1
1
2
1
1
1
2
2
2
2
1
1
1
2
1
2
1
2
1
1
1
1
1
1
0
0
2
1
1
1
0
1
1
1
1
1
1
1
2
1
1
2
2
2
2
1
0
1
1
2
1
1
1
2
1
1
0
0
2
1
1
1
1
1
0
1
0
1
1
1
1
0
1
1
2
1
1
1
1
2
0
1
1
1
1
0
1
1
1
1
2
2
2
1
0
1
1
1
1
1
1
1
2
1
1
0
1
0
1
2
1
1
2
1
2
1
1
2
2
0
2
2
1
1
2
0
0
1
1
1
2
1
1
2
0
0
0
1
1
2
1
0
1
1
2
0
1
1
1
1
2
2
1
0
1
1
1
2
1
1
1
1
1
2
1
1
1
2
0
1
1
1
1
1
2
0
0
0
0
1
1
1
2
2
2
1
1
1
1
1
1
2
1
1
1
1
2
2
2
2
1
1
1
2
2
1
2
1
1
0
1
0
1
1
1
0
2
1
0
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
0
1
2
1
2
2
1
3
0
1
1
1
1
1
2
1
1
1
1
1
1
0
1
1
2
1
1
0
1
2
1
1
1
2
1
1
1
2
0
3
2
1
2
1
1
1
1
1
2
2
2
1
2
2
2
2
1
1
2
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
2
0
1
1
1
2
1
1
1
1
1
1
1
2
0
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
0
1
2
2
1
2
1
2
2
3
2
1
1
1
2
0
0
0
2
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
1
1
0
1
2
0
1
1
2
1
1
0
1
2
2
1
1
0
0
0
1
1
0
1
2
0
1
2
2
1
2
0
1
2
1
1
1
1
1
0
1
1
1
2
2
2
1
2
0
0
1
0
2
1
2
1
1
1
0
2
2
2
2
1
2
1
1
1
1
1
2
1
1
2
1
2
1
1
0
3
2
2
1
1
1
1
1
2
1
0
1
2
2
1
2
0
1
2
1
2
2
2
1
1
0
2
1
1
1
1
2
2
1
2
2
2
2
2
1
1
0
2
1
1
0
1
1
1
0
1
0
1
2
0
2
2
0
2
1
1
1
0
2
1
3
1
2
1
2
0
1
1
1
2
2
2
2
0
1
1
0
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
2
1
1
0
1
1
2
2
2
1
0
1
1
1
0
1
2
1
2
1
1
1
2
1
1
1
1
1
2
1
2
1
1
2
1
2
1
1
1
1
2
1
2
1
2
1
1
2
1
1
0
1
1
2
1
1
2
0
2
2
1
2
1
2
1
1
1
2
1
1
2
1
1
2
2
2
1
1
1
2
5
2
2
2
1
1
1
0
1
1
1
1
1
1
2
1
1
1
2
2
2
1
0
1
2
1
1
2
2
2
2
0
1
1
1
1
0
1
1
2
1
4
1
2
1
0
1
2
2
1
1
1
1
1
1
1
1
1
1
2
2
1
2
1
2
1
0
1
0
2
1
2
1
2
1
1
1
1
1
1
1
1
1
2
1
2
2
0
0
1
1
1
0
1
1
2
1
0
1
0
1
1
2
0
2
2
1
1
1
1
1
1
1
0
1
1
1
1
1
1
2
2
2
0
0
2
1
1
1
1
1
1
2
1
1
0
1
1
1
1
2
2
2
1
1
1
1
1
2
3
1
2
0
1
2
1
2
1
0
2
1
0
1
1
2
1
2
1
1
1
2
1
1
2
2
1
0
2
3
1
1
1
1
1
1
1
2
2
1
1
2
0
2
1
1
1
0
1
0
1
0
1
2
1
1
0
1
0
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
2
2
0
1
0
0
1
1
1
1
1
4
0
2
1
2
1
2
0
1
1
1
0
0
1
1
1
3
1
0
1
0
1
1
2
1
2
1
1
1
2
1
1
1
1
2
0
1
1
2
1
0
1
0
2
2
0
0
1
1
2
0
1
1
1
1
0
1
1
2
1
1
2
0
1
1
3
1
2
1
1
1
1
2
2
2
0
1
1
2
2
1
2
2
2
0
0
3
2
2
0
1
1
2
1
1
1
1
2
1
2
0
1
1
2
1
2
1
1
2
1
2
1
1
2
2
1
2
2
1
2
1
0
1
0
1
2
2
2
0
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
2
1
2
2
0
1
1
1
1
2
1
1
1
1
0
2
1
1
2
2
1
1
1
2
2
2
1
1
1
0
2
0
1
3
2
1
1
0
2
2
1
2
1
2
1
1
3
2
1
0
2
1
2
1
0
1
0
1
2
0
2
2
1
0
2
2
1
1
1
1
1
2
1
2
1
2
1
0
1
0
2
0
2
1
2
1
1
0
1
1
1
2
1
1
1
2
2
2
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
0
1
1
1
2
2
2
0
0
1
0
0
0
1
1
2
1
1
4
1
1
1
1
1
1
1
1
1
2
2
1
1
0
1
1
1
2
1
1
2
1
2
1
0
0
1
2
1
1
1
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
0
2
1
0
2
2
2
1
1
1
1
1
2
1
2
1
1
0
1
1
1
1
2
1
1
1
0
1
0
0
1
1
0
0
2
1
1
2
1
1
1
2
1
1
2
1
1
0
1
1
1
1
1
1
1
1
1
2
1
2
2
1
1
1
2
0
2
1
1
2
0
1
2
2
1
1
1
1
0
1
1
1
1
1
0
1
2
2
1
1
2
2
0
2
1
1
1
1
2
1
0
1
0
0
2
0
1
1
0
2
0
2
2
2
1
1
2
1
2
1
2
1
0
0
1
1
2
0
2
1
1
0
1
1
0
1
0
2
2
1
1
1
1
0
1
1
2
2
1
1
1
1
1
2
1
0
2
1
2
1
2
1
2
1
2
1
1
1
1
1
2
1
1
1
0
2
2
1
2
2
1
2
2
1
2
1
1
1
1
2
1
1
1
1
0
2
1
1
2
1
2
1
1
0
1
1
1
1
1
1
2
0
1
0
1
1
1
1
2
0
1
0
1
1
1
1
1
2
2
1
1
1
2
1
1
0
2
1
2
1
2
2
0
1
1
0
2
1
1
1
2
1
1
2
1
1
2
1
1
1
2
2
1
0
1
2
1
0
0
1
0
0
2
1
1
0
1
1
1
1
1
2
1
1
2
1
1
1
1
1
0
1
1
2
0
1
0
1
1
1
2
1
1
2
1
1
2
2
2
1
1
2
1
1
2
1
1
1
1
2
1
1
1
2
0
2
1
1
1
2
2
0
1
1
1
2
1
2
1
0
2
0
1
2
1
2
1
1
0
0
2
1
1
1
1
1
2
2
1
2
2
1
1
1
1
1
1
1
0
2
1
2
0
1
1
1
1
0
1
1
1
1
2
1
1
1
2
2
2
1
1
1
1
2
2
0
1
1
2
1
1
1
2
1
1
2
2
1
1
1
1
1
0
1
1
1
1
1
0
2
0
2
1
2
0
1
0
0
0
0
0
1
2
1
2
2
1
2
1
1
1
1
2
1
2
1
1
1
2
1
1
1
0
1
1
1
1
0
0
1
1
2
2
2
1
1
2
1
2
0
1
1
1
2
1
1
2
0
2
1
1
2
2
2
1
2
1
1
2
1
1
1
0
1
1
2
1
2
2
1
1
2
0
2
1
1
2
2
1
2
1
1
1
2
1
0
1
2
2
2
1
0
0
1
1
1
1
1
2
0
1
1
0
2
1
0
2
1
2
1
1
2
2
0
1
2
1
1
1
2
2
0
1
2
1
1
1
1
1
1
0
1
2
0
1
1
1
1
1
1
0
1
1
1
1
2
1
1
1
1
1
1
2
0
1
0
4
2
2
1
1
1
1
1
2
1
1
1
1
2
1
1
0
2
2
2
2
0
2
2
2
2
2
1
1
0
1
1
2
1
1
1
1
2
1
1
1
2
1
1
2
2
2
2
0
2
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
0
2
1
2
2
2
1
2
1
2
1
0
1
1
1
0
1
1
2
1
2
1
2
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
0
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
0
0
1
1
1
1
1
1
0
0
1
2
2
1
1
2
2
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
0
1
1
1
2
2
1
2
2
1
1
2
0
1
1
2
1
2
1
1
1
2
2
0
1
1
1
1
0
2
2
1
2
0
1
2
0
0
2
1
1
1
2
2
1
1
2
1
1
2
2
2
2
2
1
1
1
1
2
1
0
1
1
0
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
2
3
1
1
2
0
1
1
1
2
1
3
2
2
1
1
1
1
1
2
1
1
1
1
0
1
1
1
1
2
1
1
2
1
0
0
2
0
2
2
2
1
2
1
0
0
2
1
2
2
1
1
2
2
1
1
1
1
1
0
2
1
1
0
1
1
2
1
1
1
2
1
2
0
1
1
1
1
1
1
2
2
1
2
2
2
2
2
1
2
1
1
1
1
1
1
1
0
2
1
1
2
1
1
1
2
2
1
2
1
2
1
1
1
1
2
1
1
0
2
1
1
1
2
1
1
0
1
1
1
1
1
1
1
0
1
0
0
2
2
1
1
2
1
1
0
1
2
0
1
2
0
1
1
1
1
1
1
1
1
2
2
1
1
1
2
1
1
1
1
1
2
1
0
1
0
2
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
0
1
2
0
1
0
0
1
2
1
1
0
1
2
0
0
2
1
0
2
1
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
0
1
3
1
1
0
1
1
1
1
1
2
2
1
1
1
1
1
1
0
1
2
1
2
1
0
1
1
1
1
1
0
2
1
1
0
1
1
2
1
1
2
2
2
0
1
1
1
1
2
2
0
2
0
1
1
1
2
1
2
0
1
2
1
1
2
2
1
1
1
1
1
1
2
1
2
2
1
0
1
1
2
1
1
2
2
1
2
1
1
1
1
1
1
2
2
1
2
1
2
2
2
2
2
0
1
0
2
1
2
1
2
1
1
1
1
1
0
1
0
2
0
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
0
1
1
1
2
1
1
2
1
2
2
1
1
1
1
1
2
1
0
2
0
2
2
2
0
1
1
1
2
1
0
0
1
2
2
1
2
0
1
1
2
1
1
1
1
1
1
1
2
2
0
0
0
1
0
2
1
2
2
0
2
1
1
1
2
2
2
2
1
1
2
1
1
1
1
1
2
1
1
2
2
1
1
1
1
2
2
1
2
2
1
2
1
2
1
1
2
2
1
1
1
2
1
2
2
0
0
1
1
0
1
1
1
0
1
2
1
2
1
1
1
2
1
0
1
1
1
2
1
1
2
1
1
2
0
1
1
1
0
0
2
2
2
1
1
1
2
1
2
2
1
1
1
0
2
2
2
2
2
1
1
2
2
1
1
1
2
1
1
1
1
1
1
2
1
2
1
2
2
1
1
1
1
1
1
1
1
2
2
1
1
1
0
1
1
1
0
1
1
2
1
2
1
2
1
1
0
2
1
1
2
1
1
2
1
2
1
1
0
1
0
2
0
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
2
1
1
1
1
2
0
1
2
1
0
2
1
1
1
1
0
1
1
2
1
1
0
1
2
1
1
1
1
1
2
1
1
2
1
0
1
5
1
1
1
2
1
1
1
1
1
0
1
2
1
2
1
0
1
1
2
1
2
2
0
1
2
2
1
2
2
1
1
2
2
2
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
0
0
1
1
1
1
1
1
2
1
2
1
1
1
0
1
0
1
2
2
1
0
1
1
1
5
1
0
1
0
1
0
2
1
1
1
1
1
1
1
1
1
2
1
2
2
1
1
2
2
0
1
2
1
1
1
2
0
1
1
0
1
1
1
1
1
2
1
2
1
1
1
2
0
1
1
1
0
0
1
2
2
1
0
1
1
1
1
0
1
1
2
1
1
1
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
0
1
1
1
1
2
0
1
1
1
1
1
1
2
2
0
1
1
0
2
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
2
1
0
1
1
0
1
1
2
1
0
1
0
2
2
2
1
1
1
1
2
2
2
1
1
1
2
1
0
1
2
1
3
1
1
2
1
1
2
1
1
1
1
1
2
1
1
0
2
1
1
1
1
2
1
0
1
1
2
2
1
1
1
1
1
2
0
1
1
0
1
1
1
0
1
0
2
1
1
1
1
1
2
1
0
0
1
1
2
1
1
1
1
0
1
1
1
1
2
1
1
1
1
1
1
2
1
1
2
0
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
0
1
1
1
2
2
2
1
1
2
0
2
1
2
1
0
1
2
0
0
1
2
2
1
0
1
1
1
2
1
2
1
1
1
2
1
1
2
0
0
1
1
1
2
1
1
2
1
2
0
1
1
1
1
1
1
1
1
2
2
1
1
0
2
1
2
2
1
1
1
2
2
1
0
1
1
1
2
1
1
2
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
1
0
0
1
2
2
2
1
1
2
2
1
2
1
2
1
1
1
1
1
2
1
1
1
1
1
1
2
0
0
1
2
1
2
1
2
1
2
0
1
1
1
2
2
1
2
1
1
1
1
2
1
1
2
1
2
2
0
1
2
0
0
1
0
1
1
2
1
1
1
1
2
1
1
2
1
0
2
1
1
2
1
1
1
1
2
1
1
0
2
2
1
1
1
1
2
1
1
2
1
1
1
0
2
1
1
0
1
0
0
1
2
0
1
1
1
0
1
1
2
1
1
2
1
1
0
1
2
0
0
2
1
1
2
1
1
1
0
1
2
1
2
1
1
0
2
1
1
1
2
0
1
1
0
1
2
1
2
3
1
1
2
0
1
2
1
1
0
2
1
0
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
0
1
0
1
0
1
2
1
1
1
1
0
1
2
1
1
1
1
1
1
2
1
1
0
0
1
2
2
1
2
1
1
1
1
1
1
1
2
1
1
1
2
1
2
2
1
1
0
2
1
1
2
1
1
1
2
2
0
1
0
3
1
2
1
1
1
1
2
1
2
2
2
2
2
0
1
0
2
1
2
2
0
2
1
0
1
2
0
1
1
0
2
1
2
1
0
2
1
1
2
1
1
1
0
2
2
0
1
0
1
0
1
1
1
2
2
1
1
1
2
2
2
1
1
1
1
1
1
1
0
1
1
2
1
0
2
2
1
2
2
1
1
1
1
1
1
1
0
1
1
2
1
1
2
1
1
1
2
2
1
1
2
1
1
1
1
2
1
1
2
2
2
2
1
1
1
2
3
1
1
0
1
1
1
2
1
2
2
1
2
1
1
1
1
2
2
1
2
1
1
0
1
1
2
1
1
1
1
0
1
2
0
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
2
2
1
2
1
2
0
0
1
1
2
2
1
1
2
1
1
1
2
1
1
2
2
1
2
0
1
1
1
1
1
1
0
1
1
2
1
1
1
2
2
2
1
2
1
1
1
1
1
2
2
2
4
0
2
2
2
1
1
2
1
3
2
1
2
2
1
2
1
1
0
2
1
1
1
1
0
2
0
1
1
1
2
2
0
1
0
2
2
1
1
2
1
2
1
2
2
1
0
1
2
1
1
1
2
0
0
2
2
1
1
0
1
0
1
0
1
1
1
1
1
2
2
1
1
2
1
1
1
1
0
0
2
1
1
0
2
1
0
1
2
0
2
1
0
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
0
1
0
2
0
1
1
1
1
2
1
2
3
1
2
1
2
1
2
0
2
2
0
1
2
2
1
1
0
2
2
2
1
1
1
0
2
2
2
1
1
1
1
1
2
1
1
2
2
0
2
1
1
1
0
2
2
1
2
2
0
1
1
1
1
1
1
1
0
2
1
1
1
3
2
1
1
2
2
1
0
1
0
3
2
1
2
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
0
1
1
1
2
1
2
2
2
1
1
2
0
1
0
1
1
2
1
1
1
2
0
1
2
1
2
0
1
2
1
0
2
2
1
2
0
1
2
0
2
1
2
0
1
1
0
0
1
2
1
2
0
1
0
1
2
2
0
1
1
1
2
1
1
2
2
1
1
2
1
0
0
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
2
1
1
1
4
1
2
1
1
1
1
1
1
1
2
1
1
2
1
2
1
2
1
0
2
0
1
1
1
1
2
3
1
1
1
1
1
1
0
2
2
1
0
1
2
1
0
2
1
1
1
2
2
1
2
2
0
1
1
1
1
1
1
0
2
1
1
1
1
2
0
0
1
2
2
1
1
0
1
2
1
1
2
2
1
1
2
0
1
2
1
0
2
1
1
1
2
2
2
1
1
0
1
1
2
1
1
1
1
2
1
2
1
1
2
2
1
2
0
1
0
1
1
1
1
2
1
2
0
2
1
1
1
2
1
1
0
1
1
1
2
1
2
1
2
2
0
1
1
1
0
2
2
2
1
2
1
2
1
1
2
1
3
2
1
1
0
2
2
2
1
1
2
1
1
1
1
1
5
2
1
1
1
1
2
1
1
2
1
1
1
2
1
2
2
1
0
2
1
1
1
1
1
1
2
1
2
1
0
1
1
0
1
1
0
2
1
0
1
1
2
1
2
1
1
1
1
0
0
0
1
1
1
0
1
1
2
1
2
1
0
1
1
1
0
1
2
1
1
1
1
1
2
1
2
0
1
2
0
2
1
1
0
1
1
2
0
0
2
1
1
2
1
2
0
1
1
0
1
0
0
0
1
0
1
1
2
0
1
1
1
1
2
1
2
2
1
1
1
0
1
2
1
1
1
1
1
0
0
1
2
1
0
1
2
2
1
1
1
1
2
1
1
2
2
0
2
1
1
1
0
1
0
2
1
1
1
1
2
1
2
1
2
1
1
2
1
2
1
1
1
2
2
1
1
0
0
2
2
2
0
1
1
2
0
2
0
1
1
1
1
1
1
2
2
1
0
1
1
1
2
2
1
1
2
1
1
1
1
0
1
2
1
1
0
1
2
2
2
1
1
0
2
1
0
1
1
2
2
2
1
2
2
1
1
1
1
1
2
2
1
2
1
2
2
0
2
1
1
2
2
2
0
1
0
1
2
1
1
2
1
1
1
1
2
1
1
2
1
2
1
2
2
1
1
2
1
2
2
1
1
2
1
0
1
1
1
1
1
0
2
1
1
2
1
3
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
2
1
1
2
1
1
2
2
1
2
1
2
1
2
1
2
1
3
1
1
1
1
2
2
1
2
1
2
2
1
0
2
1
1
1
1
1
1
1
1
0
2
1
1
2
1
1
2
1
1
1
1
2
2
2
1
1
2
1
1
1
2
1
1
2
2
2
1
1
2
0
2
1
1
1
1
0
1
0
2
1
1
1
1
1
2
1
0
2
2
1
0
1
2
1
2
1
0
1
1
1
0
2
2
1
2
1
1
0
0
1
1
2
1
0
2
0
1
2
1
0
1
1
1
1
2
1
1
1
0
2
0
1
0
2
2
0
1
1
1
1
0
1
2
3
2
1
1
1
1
2
0
1
2
1
2
1
0
1
1
0
1
1
1
2
2
1
2
1
1
0
1
1
2
0
0
1
1
1
2
0
1
2
1
1
1
1
2
3
1
1
1
1
1
2
2
1
2
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
1
0
1
1
1
1
2
1
2
1
2
1
1
1
1
1
2
1
1
1
1
2
3
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
0
2
0
1
2
1
0
1
1
2
1
1
2
1
2
2
0
1
1
2
1
1
1
1
1
2
1
2
2
1
2
0
1
0
2
1
1
1
1
1
2
0
1
2
1
1
1
1
1
1
2
1
1
0
1
2
1
1
1
1
2
0
1
1
1
2
0
1
1
2
2
1
2
1
0
1
2
2
1
2
2
1
1
0
1
1
1
0
1
1
1
1
2
1
1
2
2
2
2
2
0
2
1
1
2
1
2
2
1
1
1
1
0
2
1
1
2
1
2
1
1
1
1
1
0
2
0
1
0
0
2
1
1
0
1
1
1
1
2
1
1
1
2
1
3
0
1
1
1
0
2
1
2
0
2
2
1
2
2
0
1
1
1
1
1
1
1
1
1
1
1
0
1
1
2
1
1
0
1
1
1
0
2
0
1
1
0
1
1
2
1
1
0
1
2
1
2
1
2
1
2
1
1
2
2
1
1
2
0
0
2
1
0
0
1
0
1
1
1
1
1
1
2
1
1
1
2
1
1
3
1
1
0
1
1
0
0
2
2
1
3
1
1
1
1
1
1
1
1
1
1
1
2
2
1
0
2
0
2
1
1
1
1
2
1
1
1
1
1
2
2
2
2
2
1
0
1
1
2
0
2
1
2
1
1
2
1
1
1
2
1
1
1
2
1
0
1
2
1
2
1
1
0
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
2
0
0
1
1
0
1
1
1
2
1
1
1
2
0
1
1
1
2
2
1
1
1
2
2
1
0
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
2
1
1
1
2
2
2
0
1
0
1
1
2
2
0
1
1
1
1
0
1
1
1
1
2
2
1
1
0
1
0
1
2
2
1
1
1
0
1
1
1
1
2
1
1
2
1
1
2
1
2
2
1
1
1
1
0
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
2
1
1
1
2
2
2
1
2
1
1
1
0
1
1
1
1
2
1
1
1
1
1
1
1
1
2
2
2
2
2
1
1
1
1
1
2
1
0
2
1
2
2
2
2
1
2
0
1
1
1
1
1
2
1
1
1
0
1
1
1
1
2
2
1
2
2
1
1
1
0
0
1
2
2
1
2
1
2
1
1
1
0
2
1
2
1
1
2
1
1
2
1
1
1
1
1
1
1
1
2
2
0
1
2
0
2
1
1
0
1
1
1
0
1
1
1
0
1
2
0
1
1
1
2
1
1
0
5
1
1
1
2
2
1
0
0
2
1
1
2
1
2
2
1
0
1
1
0
1
1
0
1
1
1
1
2
0
1
2
2
2
1
2
1
1
1
1
0
1
2
1
1
2
0
0
0
2
1
1
1
1
0
2
1
1
1
1
1
1
1
1
1
1
0
2
1
1
0
1
2
1
1
0
0
2
0
1
2
2
1
1
1
1
2
0
2
1
1
1
2
1
1
2
1
2
1
0
2
2
1
2
1
1
1
1
1
1
2
1
1
2
1
0
1
2
1
1
0
2
1
2
1
0
2
1
2
1
0
1
2
1
2
2
1
1
1
1
1
2
1
1
2
0
1
2
2
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
2
1
1
1
1
1
2
2
2
1
1
2
1
1
1
1
2
1
0
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
0
1
1
1
0
0
0
2
2
1
2
1
1
0
1
1
2
2
1
2
1
1
2
2
1
1
2
0
1
2
1
2
0
1
2
0
0
1
1
1
1
1
1
1
1
2
1
0
2
1
1
2
1
1
1
1
0
1
0
1
1
1
2
1
0
2
2
1
1
2
1
1
0
1
2
1
1
1
0
0
1
1
1
1
1
0
0
1
0
1
1
3
2
1
1
2
0
1
1
1
2
1
1
1
1
2
4
1
1
2
2
2
1
1
1
2
1
1
1
1
1
1
1
1
0
1
2
4
0
2
1
1
1
3
1
2
2
1
1
2
1
1
1
2
1
1
1
2
0
2
2
0
1
1
1
2
2
1
1
1
1
1
1
2
1
0
1
1
0
1
1
1
1
1
2
1
2
0
2
1
1
2
1
2
1
2
1
1
1
0
2
2
2
0
2
1
2
1
1
0
2
1
1
2
2
1
1
1
1
0
1
0
0
2
2
1
1
1
1
4
1
1
1
1
2
1
2
0
0
1
2
1
1
1
1
2
1
1
2
1
0
1
0
2
0
2
1
1
1
2
1
2
1
2
1
1
1
2
0
0
0
1
2
2
2
1
1
1
1
0
1
1
2
1
1
2
3
0
1
1
1
1
1
1
1
2
1
1
2
2
2
0
1
1
0
1
1
0
1
1
0
1
1
0
2
1
1
1
1
1
1
1
1
1
2
0
1
2
2
0
2
1
1
1
2
1
2
1
2
1
1
3
1
2
2
1
2
2
1
2
1
1
1
0
1
1
1
1
1
2
1
1
0
2
1
2
1
1
0
2
1
2
2
0
1
0
1
1
1
1
1
2
1
1
0
2
2
1
0
1
0
1
2
2
2
2
1
1
2
2
1
1
2
1
1
0
2
1
0
1
0
1
1
1
1
0
1
2
1
1
1
2
1
1
1
1
1
1
2
2
0
2
1
1
1
1
2
1
1
2
1
1
1
1
2
1
0
1
0
1
1
2
0
1
1
2
1
1
1
2
1
1
1
2
2
2
1
1
1
0
5
2
1
1
1
0
1
1
1
2
1
1
1
2
1
1
1
1
1
2
2
2
1
2
1
3
1
1
1
1
2
0
1
1
1
2
1
2
1
1
1
1
1
0
1
2
1
0
1
1
1
2
1
1
0
0
1
1
0
0
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
0
1
2
2
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
0
2
1
1
1
1
1
1
2
2
1
0
0
1
1
1
1
0
1
1
0
1
1
0
1
1
1
1
1
1
1
2
1
2
1
2
1
1
2
1
1
1
2
1
1
2
2
1
1
1
1
1
0
1
1
1
2
1
1
0
1
1
0
1
1
1
1
1
1
1
2
2
0
1
2
0
0
0
1
0
2
0
2
3
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
2
1
1
3
2
1
1
0
2
1
1
1
1
2
2
1
1
0
1
0
2
2
1
0
1
1
1
1
0
1
1
1
1
1
1
2
2
1
2
1
1
2
1
1
2
2
1
2
1
1
1
1
1
1
0
2
1
1
1
1
0
1
2
1
1
2
1
1
1
1
1
0
1
2
1
0
2
1
1
1
0
0
1
0
1
1
1
1
1
2
1
1
2
1
0
1
2
2
1
1
1
1
0
1
1
2
2
2
0
1
1
0
0
1
1
1
1
1
1
2
1
0
1
2
2
1
1
1
2
2
1
2
1
1
1
1
1
2
1
1
2
2
1
2
2
2
1
1
1
2
2
1
2
2
0
2
0
2
2
1
2
2
1
2
0
2
0
1
1
0
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
2
2
2
1
1
1
2
0
1
1
1
2
1
1
1
1
2
2
1
0
1
1
1
1
0
1
1
1
1
1
2
1
0
0
0
2
0
1
2
0
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
0
1
1
2
0
0
1
2
2
1
0
1
1
0
1
2
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
2
2
0
2
1
1
1
1
1
1
2
1
1
1
0
1
1
1
1
1
1
1
2
1
0
1
1
1
2
2
2
0
2
1
1
2
1
1
2
2
1
1
1
1
2
1
2
0
0
0
2
1
2
1
1
3
1
2
1
1
2
1
2
1
0
2
1
1
2
2
1
0
1
2
0
1
1
1
2
1
2
0
1
1
1
2
2
1
1
1
1
1
2
2
1
1
0
1
1
1
2
1
1
2
2
2
1
2
1
1
1
1
0
1
2
1
1
2
0
2
2
1
1
1
0
1
2
1
1
1
1
1
1
1
0
1
2
1
1
2
1
1
1
1
1
1
1
1
1
0
2
1
2
1
1
1
1
0
1
2
1
2
1
1
1
0
2
1
0
1
2
0
2
0
1
0
1
2
1
2
1
2
1
2
2
1
1
1
1
2
4
0
1
1
1
1
1
2
1
2
1
1
2
1
2
2
1
1
1
1
1
1
1
0
1
1
1
1
1
0
1
2
1
1
2
2
1
1
0
4
2
1
2
0
2
2
1
1
0
1
1
1
1
1
0
0
1
2
2
1
1
1
2
1
1
2
0
2
1
1
2
1
2
0
1
1
1
1
1
2
1
2
1
1
2
1
2
1
1
1
0
1
1
0
2
1
2
1
1
1
1
1
1
2
1
1
0
4
1
1
1
2
0
2
1
1
1
2
1
1
1
1
2
1
1
1
1
0
2
1
2
1
1
2
4
1
1
1
2
1
2
1
1
2
1
1
1
1
1
2
2
1
1
1
1
1
1
0
1
0
1
1
1
1
1
1
1
0
2
1
1
1
1
1
2
1
2
1
2
2
0
1
1
1
2
4
2
0
1
1
1
1
1
2
1
1
1
1
1
2
0
1
1
1
2
1
2
0
2
2
2
1
2
2
1
1
1
2
0
1
1
1
2
2
2
2
1
2
1
1
1
1
2
1
1
1
1
0
1
1
0
2
2
2
1
1
1
2
1
0
1
1
1
1
2
2
2
2
2
2
1
0
2
1
0
1
1
1
1
2
1
2
0
1
0
2
1
1
1
1
2
1
1
1
2
2
1
2
2
2
2
1
1
2
1
1
2
0
1
1
2
1
1
2
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
0
0
2
1
1
1
1
2
1
2
1
1
1
1
2
0
2
2
0
1
2
0
0
1
2
1
1
1
1
1
1
1
0
0
2
1
1
2
0
1
1
2
0
1
1
1
0
1
1
1
0
1
1
2
1
1
1
2
0
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
0
1
0
2
0
1
2
1
1
2
1
1
1
2
1
1
0
1
0
1
2
1
2
1
2
2
1
1
2
0
1
1
1
1
2
1
2
1
1
1
0
1
1
2
1
2
1
2
1
1
2
2
1
0
2
1
1
1
1
2
1
1
1
1
1
0
1
1
2
1
1
1
0
2
2
1
1
0
1
1
2
1
1
1
0
2
0
2
2
1
1
2
0
0
2
2
1
1
2
1
2
1
2
2
2
2
0
0
1
1
1
1
2
1
2
1
2
1
2
0
1
0
0
1
1
1
1
1
1
1
1
1
0
1
1
2
1
1
1
1
0
1
1
1
1
0
1
1
2
1
2
2
0
2
1
1
1
1
1
0
0
1
1
1
2
0
1
2
1
2
0
1
1
2
2
2
1
1
1
1
1
1
1
0
1
1
2
1
2
2
2
1
1
1
1
2
1
2
2
1
1
2
1
1
1
1
0
1
2
1
1
2
1
2
1
2
1
1
2
1
0
1
0
1
2
1
0
2
0
2
2
1
2
2
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
2
2
1
1
1
2
1
1
1
2
1
0
1
1
1
0
2
0
1
1
1
1
1
1
1
2
2
1
0
1
1
3
1
2
1
1
1
1
2
1
1
1
1
1
1
0
1
2
2
2
1
1
1
2
1
1
2
1
3
2
1
2
0
1
1
3
1
1
0
1
2
1
1
1
2
1
1
1
0
1
1
2
2
0
0
2
1
1
1
1
1
1
0
1
1
2
2
0
2
1
1
1
2
1
1
1
1
2
1
1
2
1
0
2
1
2
1
1
1
1
0
1
2
2
1
1
1
1
2
1
1
1
1
2
2
0
1
0
2
2
2
2
2
2
1
1
1
1
1
0
1
0
0
1
1
1
0
1
2
1
1
1
0
1
1
1
2
2
1
0
1
0
1
0
2
2
1
1
0
0
1
1
0
1
1
2
1
1
1
1
2
1
1
2
0
1
0
1
1
2
1
2
2
1
1
2
1
1
1
0
1
1
1
1
2
1
1
1
2
1
1
2
1
2
0
0
1
1
1
1
1
1
2
2
2
1
2
1
1
2
0
1
0
2
1
1
0
2
1
1
1
2
1
1
2
1
1
1
0
2
1
1
2
2
1
1
1
1
1
0
2
0
2
1
1
2
0
1
2
0
2
2
2
2
1
1
1
2
1
1
1
1
2
1
2
2
2
1
2
2
0
2
1
2
1
0
1
0
1
2
2
1
1
1
1
1
1
0
1
1
1
1
1
1
4
1
1
1
1
1
2
1
1
1
1
1
2
0
1
1
1
1
0
1
1
2
0
0
0
0
1
1
0
1
1
1
1
2
2
2
1
1
2
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
0
1
1
1
2
1
2
2
1
1
1
0
1
1
1
2
1
2
1
1
1
2
0
1
1
2
1
1
2
1
1
1
1
1
1
0
0
2
1
1
2
1
1
1
1
1
1
1
1
0
1
1
2
1
0
2
1
0
0
2
2
1
1
1
1
2
1
1
0
1
2
2
2
2
1
1
1
2
1
2
2
2
2
2
2
1
2
2
2
1
1
2
1
1
1
1
0
2
1
0
1
1
2
2
1
2
1
1
1
1
2
2
2
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
0
1
2
1
1
2
2
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
0
2
0
1
1
1
1
1
1
2
1
2
0
0
0
2
1
1
1
1
1
2
1
1
2
1
2
0
1
1
2
1
1
2
1
1
1
1
2
1
1
2
0
0
1
1
0
1
1
2
1
0
1
0
2
1
2
1
1
1
2
1
1
1
2
1
2
0
1
0
1
1
1
0
2
0
1
1
1
1
1
2
1
1
0
0
1
1
1
2
2
1
1
1
1
2
2
2
2
1
2
2
1
2
1
1
2
1
1
1
2
1
1
2
1
5
2
2
2
1
0
1
1
0
1
1
1
2
1
1
0
1
1
2
2
1
2
2
1
2
1
0
0
1
1
1
2
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
2
1
1
1
2
2
2
1
1
0
1
1
0
1
1
0
1
1
1
0
1
1
0
1
1
1
0
1
1
2
1
1
1
0
2
0
0
0
1
1
1
1
1
2
1
3
1
1
1
1
2
1
2
0
0
1
2
1
1
0
1
1
1
2
2
0
1
1
0
0
1
0
1
1
1
1
2
1
0
1
1
0
1
3
1
2
2
1
0
1
1
1
1
0
1
1
1
1
1
1
0
1
1
2
2
0
1
1
1
2
2
1
0
1
1
2
1
1
0
1
1
2
1
1
2
1
2
1
1
0
1
2
1
1
1
0
1
2
1
1
1
1
1
2
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
2
1
1
0
2
1
1
1
2
1
1
0
1
1
0
2
2
1
2
1
1
1
1
1
1
2
2
1
1
0
1
2
2
1
1
0
1
0
2
1
2
1
2
1
0
1
0
1
2
1
0
1
1
1
0
2
1
1
0
2
1
2
1
1
1
1
1
2
1
1
0
2
2
1
2
1
0
1
0
1
1
2
3
1
1
1
2
1
0
2
0
2
2
1
2
1
2
1
2
1
2
1
1
1
1
0
1
1
2
2
1
1
1
1
3
1
1
1
1
1
2
1
1
1
1
1
1
0
1
1
1
1
1
1
2
1
1
2
1
1
0
1
1
1
1
2
1
1
1
1
2
2
1
2
2
1
2
1
2
2
1
1
1
2
0
1
2
1
1
1
1
1
0
0
1
1
1
2
0
2
2
0
1
1
2
0
1
1
1
1
1
1
1
1
1
0
2
1
3
2
2
2
2
1
1
2
2
2
1
1
0
2
1
1
0
1
0
1
0
1
0
1
1
1
1
1
2
1
2
2
1
2
1
2
2
1
0
1
1
1
1
1
2
1
1
2
2
0
2
0
1
2
1
1
2
1
0
1
1
1
2
1
2
2
2
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
2
2
2
1
1
2
1
1
1
1
1
0
2
1
1
1
1
1
1
0
0
2
1
1
1
2
1
1
1
2
1
2
1
1
2
1
1
0
2
1
1
2
1
1
2
1
0
2
1
0
1
2
1
1
2
1
1
2
1
1
1
1
2
0
1
1
1
2
1
2
2
1
1
2
2
2
1
2
2
0
1
1
1
1
1
0
0
2
1
0
0
1
0
1
1
1
1
2
1
2
0
1
1
1
2
1
2
2
2
2
1
2
1
1
1
2
2
1
2
1
2
2
0
1
1
1
2
1
1
2
1
2
1
2
1
0
1
2
1
1
0
1
2
1
1
1
2
0
2
1
2
2
2
1
1
1
1
1
0
1
2
2
1
2
1
1
2
1
1
1
2
0
0
1
1
1
1
1
2
1
0
1
0
1
2
1
1
2
2
1
1
4
2
0
1
1
1
1
2
1
0
0
1
2
2
1
2
1
2
1
1
1
1
2
2
1
1
2
2
2
2
0
1
1
1
0
1
1
1
2
0
1
2
2
1
1
1
1
1
2
2
1
1
1
1
1
0
1
2
2
2
1
1
2
1
2
1
1
1
1
1
1
1
1
2
2
1
1
1
1
0
1
1
1
2
1
1
1
0
1
1
0
1
1
2
1
1
1
1
1
1
1
1
0
2
2
2
1
1
1
1
1
1
1
1
1
0
1
0
1
2
1
1
3
1
0
1
0
1
1
1
0
1
0
1
0
1
2
1
1
0
1
2
1
1
2
1
1
2
1
1
2
1
0
1
1
0
1
1
0
1
1
1
2
2
2
1
2
2
1
2
1
1
2
1
1
0
1
2
1
1
2
1
2
2
1
1
1
2
1
1
1
1
2
0
1
0
2
0
1
1
1
1
1
0
1
1
0
2
2
2
2
2
0
0
2
1
2
1
1
1
2
1
0
2
1
1
2
1
0
1
1
1
2
2
0
1
1
1
1
1
1
1
1
2
0
1
1
0
2
2
2
2
2
1
0
1
1
2
2
2
1
1
1
1
0
2
2
2
0
1
2
1
0
1
1
1
1
1
1
1
0
1
1
0
1
1
1
1
0
1
2
1
0
2
2
1
1
0
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
2
1
2
1
1
1
0
1
1
1
1
2
1
1
1
0
1
1
2
1
2
2
1
1
1
0
2
1
1
1
2
2
0
2
0
1
1
0
2
1
2
1
1
0
1
2
2
0
1
1
1
1
0
1
1
1
1
1
2
1
2
0
1
0
1
0
1
1
1
1
1
2
1
0
1
1
1
0
1
1
2
0
0
0
1
1
1
0
1
1
2
0
1
1
1
2
1
2
1
1
1
1
1
2
1
2
1
1
1
2
1
1
0
1
1
1
2
1
0
2
1
2
1
0
1
2
1
1
1
1
1
1
1
1
0
1
0
1
1
0
2
0
1
1
1
1
1
1
1
2
0
1
1
1
1
1
1
2
2
0
1
2
1
1
1
1
1
1
1
1
1
1
0
1
2
1
1
1
2
2
2
1
0
0
1
2
1
1
1
1
2
2
0
1
2
2
1
1
0
1
0
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
0
1
2
1
0
0
0
2
1
1
1
0
0
1
1
2
1
1
1
2
2
0
0
1
1
2
1
2
1
1
1
1
1
2
2
2
2
1
1
1
2
1
1
1
1
1
2
0
1
1
2
1
1
0
2
1
1
1
2
1
1
0
2
2
1
1
2
2
1
2
1
1
1
1
0
1
2
2
1
1
0
1
1
1
1
1
1
1
1
0
2
1
2
1
1
1
2
1
0
1
1
0
0
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
0
3
1
0
1
0
2
2
1
1
1
0
1
2
2
1
1
1
3
1
1
1
1
1
2
1
2
1
1
1
1
1
1
2
0
2
2
1
0
1
1
2
2
1
0
2
0
0
1
2
1
1
1
2
2
1
1
1
1
2
0
1
2
2
1
1
1
2
1
0
1
1
1
1
0
1
0
1
2
1
2
2
1
1
1
2
2
1
1
2
0
1
1
1
1
0
1
2
2
2
1
1
2
2
0
1
2
1
2
2
0
1
1
1
1
1
1
1
2
2
1
0
1
0
0
2
1
1
0
1
1
0
1
1
1
1
1
3
1
0
2
1
2
1
1
1
2
0
1
1
0
1
1
2
1
2
1
1
2
0
1
1
1
1
0
1
0
1
1
2
1
0
0
2
1
1
1
0
1
2
1
1
1
2
2
2
1
1
1
1
1
1
2
0
1
1
1
2
1
2
2
1
1
1
2
2
1
1
2
0
1
1
1
1
1
1
2
0
1
1
1
1
2
0
1
2
1
1
0
1
1
1
1
1
1
2
1
1
1
2
2
1
0
1
1
2
1
2
1
1
1
1
1
2
1
1
2
1
0
2
1
1
0
1
0
1
1
2
2
1
1
2
1
2
0
1
1
2
1
1
2
0
1
2
1
1
0
1
1
1
1
1
1
2
2
1
1
2
2
2
0
2
3
1
0
2
1
1
1
2
0
2
1
1
1
2
2
3
1
1
1
0
1
1
1
1
2
2
2
1
2
2
0
1
1
1
2
1
2
1
1
1
2
2
1
1
1
1
2
1
2
2
0
1
1
1
2
1
1
1
1
1
1
2
1
1
0
0
2
1
1
2
2
0
1
1
1
1
1
0
2
2
1
1
1
1
0
1
0
0
1
1
1
1
1
1
1
2
1
1
2
2
2
1
0
1
2
0
2
1
1
2
1
4
1
0
0
0
1
0
0
2
1
0
0
1
0
2
2
1
1
1
0
1
1
0
1
1
1
1
2
1
1
1
0
1
1
1
1
1
1
1
0
1
2
1
0
0
1
1
2
0
2
0
1
2
2
1
1
1
1
0
1
1
0
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
0
1
1
2
1
0
0
2
1
1
1
0
1
1
1
2
1
2
1
2
1
2
1
1
1
2
1
0
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
2
0
0
1
1
1
1
2
1
0
1
1
1
1
1
2
1
2
0
2
1
2
1
0
1
2
1
1
1
0
1
0
1
2
2
1
1
1
1
1
1
1
1
1
2
1
1
0
1
1
2
2
1
1
1
1
0
1
1
1
0
1
2
2
1
1
2
1
1
0
1
1
2
1
2
0
1
1
0
1
1
1
1
1
2
0
1
2
1
1
1
1
1
1
1
2
0
1
1
1
2
1
1
0
1
1
1
2
2
1
2
1
2
1
2
1
1
1
1
2
1
2
2
1
0
2
1
0
1
0
1
0
1
2
1
2
1
1
0
2
1
0
2
1
1
2
1
1
1
2
0
1
2
2
1
1
2
2
1
1
1
1
2
1
2
1
1
2
1
1
2
1
2
1
2
1
1
1
0
2
2
1
1
1
0
2
1
0
0
2
1
2
1
1
2
1
1
0
2
1
1
1
1
0
1
1
1
1
0
1
1
1
0
1
0
2
1
1
1
1
1
1
1
0
2
1
1
0
2
1
0
1
1
1
1
1
2
0
0
0
1
0
2
2
1
1
0
0
2
1
1
1
1
1
1
0
1
0
1
1
1
1
1
1
0
2
1
1
1
2
1
1
0
2
1
2
1
2
1
2
1
2
1
1
2
0
2
1
2
1
1
2
0
2
1
0
1
2
1
1
1
2
1
1
2
0
1
1
2
2
1
1
1
2
1
2
2
0
2
2
1
1
2
1
1
2
1
2
0
1
1
1
2
2
0
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
2
1
1
1
2
1
2
2
1
0
1
1
0
1
1
0
1
1
1
1
3
1
2
1
2
1
2
2
1
1
3
1
2
1
1
1
2
1
1
2
2
1
1
1
1
1
1
2
1
1
1
2
1
0
1
2
1
1
1
1
1
2
2
1
1
0
2
2
1
1
1
3
1
1
1
1
1
1
1
1
0
1
2
1
2
1
0
1
1
2
2
2
0
0
2
0
1
1
1
1
1
1
0
2
2
0
0
1
2
0
2
1
1
2
2
1
2
2
1
1
2
1
2
1
1
1
1
1
2
1
1
1
1
0
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
0
0
1
1
1
0
1
2
2
1
0
2
1
1
1
1
1
1
1
1
2
2
1
0
0
0
1
1
1
1
1
1
2
1
2
1
0
2
1
2
2
2
0
2
1
2
2
1
1
1
2
1
2
1
1
0
0
1
1
1
1
0
1
0
1
1
2
1
1
2
1
1
1
2
1
1
1
0
0
1
1
1
2
1
2
2
1
2
0
1
4
1
1
1
1
1
1
1
2
1
1
1
1
2
2
1
1
1
2
2
0
1
0
1
2
1
1
1
1
1
2
1
1
1
0
1
2
1
2
2
2
1
1
1
0
0
1
2
1
1
1
0
0
2
2
1
1
1
2
1
1
2
2
1
1
1
1
1
1
2
1
0
1
1
2
1
0
1
1
2
1
1
1
1
1
1
0
1
1
1
1
1
1
0
1
1
2
1
1
1
0
1
1
1
1
2
1
1
1
1
1
1
2
0
0
1
0
0
2
2
1
1
2
0
0
0
1
1
1
1
1
1
0
3
2
1
1
1
1
2
2
1
2
1
1
0
1
3
0
2
2
2
1
0
0
0
1
0
1
1
2
1
1
1
0
2
1
1
2
2
1
0
1
1
1
0
2
2
2
1
2
0
0
1
1
2
1
2
1
1
1
1
2
1
2
2
0
1
1
2
2
1
1
0
0
1
1
1
2
1
1
1
0
1
1
1
1
1
1
1
1
1
0
1
1
0
1
1
1
1
0
1
1
1
2
0
1
1
2
1
1
1
1
1
1
2
1
2
1
1
1
2
1
0
1
1
1
1
2
2
1
1
1
1
1
2
2
0
0
1
1
1
1
1
2
1
0
0
1
0
4
1
0
1
0
1
1
1
2
0
2
2
2
0
0
1
1
1
1
1
2
1
1
1
2
1
0
1
0
1
1
2
1
2
1
1
0
0
2
0
1
2
1
2
0
1
1
1
1
1
1
2
1
0
1
1
2
1
0
1
2
1
1
1
2
2
2
1
2
1
1
2
0
1
1
1
1
2
2
1
1
1
3
1
1
0
0
2
1
2
0
2
1
1
1
1
0
1
1
1
1
1
0
0
1
1
1
1
1
2
1
2
2
1
0
1
1
1
1
1
0
1
0
1
2
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
0
1
0
0
0
0
1
1
1
1
1
0
1
1
1
1
1
2
1
1
1
1
1
1
2
2
2
2
2
1
2
1
1
0
1
2
1
0
1
2
1
0
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
2
1
1
2
1
2
1
1
1
1
2
1
2
1
1
1
0
2
2
1
1
1
1
2
1
2
0
1
1
2
1
1
1
1
1
2
2
1
1
1
2
1
0
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
2
1
1
1
1
1
2
0
0
1
2
1
2
1
0
2
2
1
3
1
1
1
1
2
1
1
1
2
1
2
1
0
2
1
2
0
2
1
1
0
1
1
2
1
2
1
2
2
0
1
1
1
2
1
2
1
2
1
1
0
1
1
1
1
1
1
0
1
0
1
0
1
1
3
1
1
1
2
1
1
2
0
1
1
1
2
1
1
1
1
2
1
1
1
2
1
2
1
1
2
0
1
1
1
2
1
1
2
1
1
0
2
0
2
2
1
1
1
1
1
2
2
1
1
2
1
1
2
1
1
1
2
1
1
2
1
1
2
1
1
2
1
1
2
1
2
1
1
1
2
1
0
2
1
0
0
1
0
1
1
2
1
1
1
1
0
2
0
1
1
2
0
1
1
0
2
2
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
0
1
1
1
2
2
1
1
1
2
0
1
1
3
1
1
1
1
0
2
1
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
2
1
2
0
1
2
1
2
1
2
2
1
1
2
1
1
2
2
2
1
2
0
1
2
1
1
0
1
0
1
1
2
2
1
1
0
1
1
0
2
0
1
1
1
1
1
1
2
2
2
2
2
0
2
1
1
1
1
1
1
2
1
1
1
0
2
1
1
2
2
1
2
1
1
1
1
1
0
2
2
1
1
1
1
1
1
0
1
2
2
1
0
0
1
1
2
1
1
1
0
2
1
2
1
5
1
1
2
2
1
0
0
1
2
1
1
1
1
0
2
1
0
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
2
1
1
3
1
0
2
2
2
1
2
1
2
2
1
1
1
1
2
1
1
1
1
2
1
1
0
0
1
2
1
1
1
1
2
1
1
2
1
2
1
1
1
4
1
1
1
1
2
1
1
2
2
1
1
2
1
2
2
1
1
1
2
1
1
2
1
1
0
0
1
2
0
2
2
2
0
2
2
1
2
1
2
0
1
2
1
1
1
2
1
1
1
0
0
2
0
2
2
1
1
0
1
2
2
1
1
2
1
2
2
1
1
2
2
1
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
0
0
1
1
1
1
0
0
1
1
1
2
3
1
1
1
0
2
1
2
0
1
1
0
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
1
2
1
1
0
1
1
2
0
1
1
0
0
1
1
1
0
1
2
1
1
0
0
1
2
1
2
1
1
1
1
2
1
2
2
0
2
1
1
1
1
1
2
2
1
1
2
0
1
2
0
1
0
0
1
2
2
1
1
1
1
0
1
1
1
1
1
0
1
2
1
1
1
0
1
1
1
1
0
1
1
1
1
2
1
2
1
1
2
1
1
3
0
1
2
0
1
2
1
1
0
1
1
1
1
1
0
1
2
1
0
2
0
0
1
2
1
3
1
2
2
0
2
1
1
1
0
1
1
0
2
1
1
6
1
0
1
1
2
1
1
1
1
1
2
1
1
0
0
2
2
0
2
1
1
2
2
1
1
2
0
0
2
0
1
1
1
1
1
2
2
1
0
1
1
1
2
2
1
1
0
4
1
2
2
1
1
1
1
1
2
2
1
1
1
2
1
2
1
0
1
2
1
1
1
1
1
2
1
1
0
1
1
0
1
1
0
1
1
0
2
1
2
2
1
1
2
1
1
1
0
1
0
0
2
2
1
2
1
1
1
1
2
1
1
1
2
1
1
2
2
1
1
0
2
2
1
2
1
1
2
1
2
2
2
1
1
0
1
1
2
1
0
1
2
1
1
0
2
1
0
3
1
2
0
2
2
1
1
1
1
1
1
1
1
0
1
1
1
1
2
1
1
1
1
1
0
1
2
2
0
2
1
0
1
1
1
1
0
2
2
2
0
2
1
2
1
1
1
1
1
1
0
1
1
1
2
0
1
1
1
2
2
1
2
1
1
0
0
1
1
1
1
0
2
1
0
1
1
1
2
1
1
0
0
1
0
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
2
2
1
0
2
1
0
1
2
1
0
2
1
1
2
1
2
1
2
1
1
1
9
0
1
0
2
1
0
1
2
1
1
1
1
2
1
1
1
1
2
1
1
0
1
1
2
0
1
1
2
1
2
1
2
1
1
2
2
1
1
1
1
0
1
1
1
2
1
2
4
1
1
1
0
1
1
1
2
1
1
1
1
1
0
1
2
0
1
1
0
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
0
1
2
0
0
1
1
1
1
0
1
1
1
1
2
2
1
0
2
1
2
2
1
1
1
2
1
0
1
0
1
0
2
0
2
2
2
1
1
1
1
1
0
1
2
0
2
1
1
1
2
1
1
1
1
1
0
2
2
1
1
2
1
1
1
1
1
2
1
1
2
2
1
1
1
2
2
1
1
2
1
1
2
1
1
1
1
1
1
1
2
0
1
2
1
0
2
1
1
0
2
1
2
2
1
1
0
1
0
2
1
1
1
2
1
1
0
0
1
2
1
0
0
0
1
2
1
1
2
1
1
1
1
2
1
1
2
1
2
1
2
0
1
1
1
1
1
2
0
2
1
1
1
0
1
1
0
1
1
2
0
1
1
1
1
0
1
1
2
1
2
0
1
2
1
1
1
2
2
2
1
1
0
2
1
1
2
1
1
1
1
1
2
2
1
1
1
2
2
1
1
1
1
1
0
1
2
2
2
2
1
1
1
1
1
2
1
1
2
0
2
1
2
1
1
0
2
2
1
1
1
0
1
1
2
1
1
0
0
2
1
1
1
0
1
2
1
1
1
2
1
1
1
2
2
1
1
2
1
2
1
2
1
1
1
1
1
2
0
1
1
0
1
2
1
1
1
2
0
1
1
1
0
2
2
1
1
2
3
1
2
2
2
1
2
2
0
1
1
0
2
3
0
0
2
1
0
2
1
1
1
3
1
0
1
1
1
1
1
1
2
0
2
1
2
1
2
1
0
1
2
0
2
1
1
1
1
2
2
2
1
0
2
1
2
1
2
0
1
2
1
1
2
2
1
1
0
1
1
1
1
1
0
0
1
2
1
0
0
1
1
2
1
1
1
1
2
2
1
0
2
2
0
1
1
1
2
0
1
1
0
2
2
1
2
2
1
1
2
1
2
2
1
2
1
1
2
0
1
1
1
2
1
0
1
1
1
1
1
2
0
1
1
1
2
0
2
1
2
2
0
2
1
2
1
1
1
1
0
1
1
1
1
1
1
1
2
2
1
1
1
2
1
0
1
1
1
2
2
2
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
0
0
2
1
0
2
0
2
1
1
1
1
1
1
1
1
0
2
2
1
0
1
0
2
0
1
1
1
1
1
1
1
1
2
1
1
1
0
1
1
1
1
1
1
1
2
2
1
2
1
1
0
1
3
0
1
1
1
1
1
2
1
1
1
1
1
1
2
0
0
1
1
1
1
1
2
1
1
2
1
1
1
2
2
1
1
2
2
1
2
1
1
3
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
0
1
1
2
0
1
1
1
1
2
2
2
1
2
1
1
1
1
0
2
0
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
0
1
1
1
1
1
1
0
0
1
1
1
1
0
0
2
1
1
1
1
3
2
2
1
2
2
0
1
0
1
1
0
1
0
2
0
1
1
0
1
1
1
2
0
1
1
2
2
2
5
1
1
1
1
2
3
1
0
2
1
0
0
1
1
0
1
3
1
1
1
1
2
0
1
0
0
1
0
2
1
2
1
1
0
2
1
1
2
2
1
1
0
1
1
2
2
1
2
1
1
1
1
1
2
2
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
0
0
0
1
2
2
0
2
1
1
1
1
0
1
1
2
0
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
3
1
2
1
2
1
1
1
1
1
2
1
2
1
1
0
1
2
2
1
0
1
2
1
2
1
2
2
2
1
1
0
1
1
1
1
1
1
2
1
1
0
0
2
2
1
1
1
0
1
3
1
1
1
0
1
2
1
1
2
1
0
0
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
0
1
2
2
2
1
2
2
1
0
0
2
1
1
2
0
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
0
1
2
1
2
2
1
1
2
1
1
1
1
1
1
1
2
1
1
0
0
0
2
1
0
1
1
0
2
1
3
2
1
0
1
1
2
3
1
1
1
1
0
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
1
1
2
1
2
1
2
2
1
1
1
2
1
2
2
1
0
2
1
0
0
1
2
2
2
1
0
1
2
1
0
0
1
1
1
1
0
1
1
1
0
1
1
0
1
1
1
1
2
1
1
0
1
1
0
1
0
2
1
1
2
1
1
1
1
2
0
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
0
2
2
2
0
1
1
1
1
1
1
1
2
2
0
1
1
1
1
1
1
1
1
2
2
2
2
0
2
1
1
1
1
2
1
2
1
1
1
0
1
1
0
0
0
0
3
1
2
1
2
2
2
1
1
1
1
1
1
1
1
1
1
0
1
0
1
1
1
0
2
1
1
2
2
1
1
2
2
0
1
2
1
1
1
1
1
1
0
1
1
2
1
0
1
1
1
1
1
2
2
2
1
1
0
1
1
2
1
1
1
1
1
1
1
0
2
2
1
0
1
1
1
1
2
1
1
0
1
1
1
2
1
0
1
1
1
1
1
1
1
1
1
0
1
2
1
1
1
1
1
1
1
2
1
1
0
2
0
1
1
0
1
1
1
1
1
0
0
1
0
2
2
1
1
1
1
2
2
1
1
0
1
0
1
1
1
2
1
1
2
1
1
1
1
1
2
2
2
0
1
2
2
1
0
0
1
1
0
1
1
0
1
1
2
2
1
1
2
2
1
1
0
2
2
0
2
0
0
1
1
1
1
2
1
1
1
2
1
1
0
1
0
0
1
1
1
1
1
1
1
1
2
1
1
1
1
1
0
1
1
1
2
1
1
0
0
1
2
1
1
1
1
1
1
0
1
1
1
1
1
1
2
1
0
1
1
0
1
0
0
2
1
2
1
1
0
0
1
1
1
1
1
2
2
1
0
1
1
2
1
1
2
2
2
2
1
1
1
1
2
1
1
2
1
1
1
2
2
1
1
2
0
1
1
2
2
1
1
0
1
1
2
1
0
0
2
1
0
2
1
2
1
1
2
1
0
1
3
2
1
2
1
1
2
1
0
1
1
1
2
1
1
1
1
1
1
0
1
3
1
0
2
2
1
3
1
2
1
2
1
2
2
2
2
1
1
2
1
0
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
0
2
2
1
2
2
2
0
1
0
2
2
1
1
2
1
1
0
2
2
0
1
1
1
1
1
1
2
1
2
2
2
1
1
2
1
1
0
1
0
1
1
2
2
2
0
0
2
1
1
1
1
1
2
1
1
0
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
0
1
1
1
1
2
2
1
1
1
1
0
1
0
2
1
4
2
1
1
0
2
1
2
1
1
1
2
1
1
2
1
1
1
1
2
1
2
1
0
1
2
0
1
2
2
1
2
1
2
1
1
1
2
1
1
1
2
1
2
0
1
2
0
1
1
1
1
1
1
2
2
2
2
1
0
1
0
1
1
1
2
2
0
2
1
1
2
2
0
1
1
1
2
1
1
1
1
1
2
1
0
1
1
2
1
2
1
2
1
2
2
2
1
3
1
1
1
1
1
2
2
2
0
1
0
1
2
0
1
1
1
1
2
2
1
2
0
1
0
2
2
1
2
1
0
1
1
2
2
1
1
1
2
1
1
1
2
1
2
1
1
1
0
2
1
1
1
1
1
0
1
1
2
1
2
1
1
0
1
0
1
2
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
2
1
2
1
2
0
1
1
1
1
1
1
2
1
3
1
2
2
3
1
2
1
1
1
2
1
1
2
1
2
1
2
0
2
2
1
0
1
1
0
1
1
2
1
2
1
1
0
2
1
1
0
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
0
0
1
1
2
2
1
2
1
1
2
2
1
2
1
1
2
2
1
1
1
1
0
2
1
1
2
1
1
0
1
1
1
2
2
0
2
2
1
2
1
1
2
2
2
0
1
0
0
0
0
1
1
1
1
1
2
2
0
1
1
2
1
1
2
0
1
1
2
1
1
1
1
2
1
2
1
0
2
0
1
1
2
1
1
2
2
1
2
1
0
1
1
1
2
1
2
1
2
0
1
2
1
1
1
2
0
1
1
1
1
0
2
1
1
1
1
1
1
0
1
1
0
2
1
1
2
2
2
1
1
1
1
1
0
2
2
2
1
1
1
1
1
1
1
2
2
1
1
0
1
2
2
2
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
0
2
1
2
2
1
1
0
1
1
1
1
1
0
1
1
1
0
1
1
1
1
1
1
1
1
1
2
3
1
1
2
2
1
1
0
0
2
0
1
1
0
1
1
1
1
1
1
2
1
1
1
1
2
1
0
1
1
2
1
2
1
1
1
2
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
2
2
1
2
1
1
1
1
0
1
1
1
2
1
2
2
1
2
2
0
1
1
1
0
1
1
0
1
1
1
1
1
2
0
2
1
2
2
2
0
1
1
0
2
3
2
1
2
1
1
1
4
1
2
0
1
1
0
2
2
2
1
1
1
1
0
1
3
1
1
1
1
1
1
2
1
2
2
1
0
2
3
1
2
2
0
1
1
1
1
1
1
2
1
1
1
1
0
1
2
2
1
1
0
1
1
1
1
2
1
1
1
2
1
1
2
1
0
1
1
1
2
1
0
1
1
0
2
2
2
0
1
2
1
2
2
1
3
3
1
1
1
1
1
1
1
0
1
1
1
2
2
2
3
2
1
0
2
1
1
1
2
2
2
1
1
2
1
2
1
1
1
1
2
1
1
1
0
2
2
1
1
0
2
1
2
1
0
2
1
1
1
2
1
2
1
0
1
2
1
1
1
2
1
1
1
1
0
2
1
2
2
2
1
0
1
0
1
2
2
1
1
2
1
1
1
1
1
0
1
1
1
2
1
1
1
0
1
0
0
2
2
1
1
2
2
2
1
1
2
2
1
1
1
2
0
2
2
1
2
0
0
1
2
1
2
0
0
1
2
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
2
1
2
1
1
1
2
2
2
0
1
1
0
1
1
0
1
1
1
2
1
1
1
2
1
2
1
1
1
1
0
2
1
1
0
1
2
2
0
0
0
1
1
0
1
0
3
1
1
1
0
1
1
1
1
1
1
0
1
1
1
1
2
1
1
2
2
1
1
2
6
1
1
3
1
2
1
2
2
2
1
1
1
1
1
0
1
0
0
1
2
1
2
2
1
1
0
2
1
1
1
1
2
0
1
1
1
2
2
2
1
1
1
2
2
1
1
1
1
2
1
1
0
1
1
1
2
2
2
2
1
1
2
1
1
2
1
1
1
0
0
3
1
2
0
0
2
1
1
2
0
1
1
1
1
1
1
1
2
1
2
1
1
0
2
1
2
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
2
0
1
2
1
1
2
1
0
1
2
0
2
1
2
1
2
2
1
1
1
1
1
0
2
1
1
2
1
1
1
0
1
0
2
2
1
1
1
1
1
2
1
2
0
0
1
1
1
1
1
2
0
2
1
2
2
2
1
0
1
2
1
1
1
2
0
1
2
1
1
1
2
1
1
2
1
2
2
2
1
1
1
1
1
2
2
1
2
0
1
1
1
1
1
2
1
1
1
2
0
1
2
1
1
1
2
1
2
1
2
1
1
2
1
1
1
1
1
2
1
0
0
2
0
1
1
1
1
1
1
1
1
0
2
1
1
2
1
1
1
1
1
1
1
2
0
3
1
1
0
0
1
1
1
1
1
1
2
1
1
0
2
2
1
1
1
2
1
1
1
1
2
2
1
2
0
1
1
1
0
3
1
0
1
0
1
1
1
1
1
2
1
1
2
2
2
1
1
2
2
1
1
1
2
2
1
2
0
1
5
1
1
2
0
3
0
2
1
1
1
1
1
1
1
0
2
1
2
2
2
1
2
1
1
1
1
2
1
2
1
1
1
2
0
1
1
1
1
0
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
2
0
1
2
2
1
1
2
1
1
1
1
1
1
1
1
0
1
0
0
1
1
1
2
1
2
1
1
1
1
1
1
1
2
2
1
1
0
1
2
1
1
0
2
1
1
1
2
1
1
1
1
0
0
1
2
0
1
0
1
1
2
1
2
0
2
2
1
2
2
2
1
1
1
1
1
1
1
1
1
0
1
1
1
2
1
1
3
0
1
0
1
1
1
2
1
1
0
1
0
0
1
2
1
1
1
1
2
1
1
0
1
2
1
1
2
1
1
2
1
1
2
0
1
2
2
1
0
1
1
1
0
1
0
2
2
1
1
1
1
2
1
1
2
1
2
2
1
0
2
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
0
1
1
0
1
2
0
1
0
1
1
1
1
1
0
1
1
1
1
2
2
2
1
2
1
1
1
2
2
2
1
2
2
0
2
1
1
4
1
2
2
1
1
0
1
1
1
2
1
1
1
2
2
1
0
1
1
2
1
2
2
1
2
0
1
1
3
1
1
1
1
1
1
1
0
2
2
1
1
1
2
2
2
2
2
2
1
1
2
0
1
1
2
2
1
0
1
0
2
1
2
1
1
2
1
1
1
1
1
2
2
1
2
2
1
0
2
1
2
1
2
1
1
0
2
1
1
2
1
1
3
1
1
1
1
2
1
1
1
0
1
2
2
1
2
1
1
1
1
0
0
1
2
2
1
0
1
1
2
0
1
1
2
1
2
0
2
1
0
0
0
0
1
1
0
0
1
1
1
0
1
1
1
1
1
1
2
1
0
1
0
1
2
2
1
1
1
2
1
2
0
1
1
1
2
1
0
2
0
1
1
1
1
1
1
1
2
1
1
2
2
1
1
1
0
2
1
1
1
1
2
2
0
2
2
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
0
1
1
1
2
1
1
2
1
1
1
0
1
1
1
2
1
1
1
1
0
1
0
1
1
1
1
1
1
1
2
2
1
2
1
2
2
2
1
1
1
1
1
2
2
0
1
2
1
2
1
1
1
0
1
1
1
0
1
2
0
0
1
1
1
2
1
1
2
2
0
0
1
1
2
2
1
2
1
0
1
1
1
1
2
1
0
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
2
1
1
1
1
2
0
2
2
1
1
1
1
1
1
3
2
1
1
0
1
1
2
1
1
1
2
1
0
1
2
2
2
1
1
1
1
1
2
3
1
1
2
2
2
2
1
1
0
0
1
1
1
1
1
1
2
1
2
1
0
2
1
1
1
1
1
1
2
1
1
1
2
1
1
2
2
2
1
2
1
1
1
1
1
2
1
1
1
1
0
0
2
1
1
0
0
1
1
0
1
0
1
1
1
1
1
2
1
1
2
2
2
1
1
2
2
2
0
1
2
0
0
2
2
1
1
1
1
0
0
1
1
1
2
1
0
2
2
2
2
0
1
1
2
1
1
1
2
2
1
1
1
0
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
0
2
2
0
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
0
1
1
1
2
1
1
2
1
0
2
2
0
1
2
1
1
0
2
2
2
2
2
1
1
1
1
2
1
1
1
2
1
0
0
1
1
2
1
2
1
0
1
1
1
1
1
2
0
1
1
1
1
1
0
1
0
1
0
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
2
2
1
2
0
2
1
2
1
2
1
1
2
1
0
1
1
1
1
1
1
1
3
1
1
2
1
0
1
1
1
2
1
2
1
3
1
2
1
1
0
1
1
0
0
2
1
1
1
1
1
1
2
1
0
1
1
1
1
1
1
0
1
1
1
2
1
1
0
1
2
2
1
2
1
1
0
1
2
1
2
0
1
1
1
2
2
1
2
1
0
1
1
1
1
1
2
2
1
1
1
1
2
2
1
1
1
1
2
1
4
2
1
2
2
2
2
2
0
1
2
1
1
1
1
1
1
0
1
1
1
1
1
0
2
0
2
1
2
2
2
1
2
1
2
0
1
1
1
2
1
1
1
0
1
1
1
1
1
1
2
1
1
1
1
1
2
1
0
2
2
1
0
0
1
0
2
1
1
1
2
0
3
1
1
2
2
3
1
0
2
0
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
2
1
1
2
2
1
2
1
0
0
1
1
2
1
1
1
0
1
3
1
1
1
1
1
1
1
2
0
0
1
0
2
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
0
1
2
1
1
2
2
2
1
2
1
1
1
1
2
2
1
1
0
1
2
1
0
1
1
3
1
1
2
1
1
2
1
1
1
1
0
1
0
2
1
2
1
2
1
1
1
2
2
1
3
1
2
1
2
2
1
1
1
2
4
2
0
0
1
1
0
2
1
2
1
1
1
1
0
0
1
1
1
1
1
1
1
1
1
2
2
0
2
1
1
1
1
1
0
0
1
2
2
1
1
1
0
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
0
2
1
1
1
1
1
1
1
1
1
1
2
1
2
2
2
0
1
2
2
1
1
2
1
2
1
2
0
0
2
2
1
2
1
1
1
1
1
0
2
1
0
1
1
5
1
1
1
2
2
2
1
2
1
1
2
1
2
1
1
2
1
1
1
1
1
2
2
1
2
1
1
1
2
2
2
1
1
1
1
2
1
1
2
1
2
1
0
2
1
1
1
1
1
2
1
1
6
1
1
2
1
1
1
2
1
1
1
0
1
1
1
1
2
0
1
1
1
0
1
1
0
1
0
1
1
2
1
2
1
1
1
1
2
1
0
0
1
0
1
1
1
1
1
1
0
1
2
1
1
1
2
1
2
1
0
1
1
1
1
1
2
2
1
2
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
2
1
0
2
1
1
0
0
2
1
0
2
2
0
2
1
1
1
1
1
2
2
0
2
1
1
1
1
2
2
0
1
0
1
2
1
1
2
1
1
2
1
0
2
2
2
1
1
1
1
1
1
0
2
1
2
2
1
2
2
1
1
1
2
1
1
1
1
1
1
0
2
1
0
1
1
2
2
1
1
1
1
2
1
0
1
2
1
1
0
0
1
1
2
0
2
1
2
1
0
1
1
0
1
1
1
1
1
1
1
0
2
0
0
0
2
1
1
2
2
2
2
1
1
1
1
2
1
2
1
1
1
2
1
2
1
2
2
2
1
0
1
0
1
1
2
1
1
2
1
1
4
1
2
1
2
2
1
2
1
0
1
1
1
1
1
1
1
2
0
2
1
1
1
1
1
2
0
2
1
1
2
2
0
1
1
0
2
1
0
1
2
1
0
1
2
2
1
1
2
1
1
0
1
2
0
1
0
1
1
1
1
1
1
2
1
2
0
1
1
0
1
2
1
1
2
1
2
1
1
1
1
0
0
1
1
1
2
2
0
1
1
1
0
3
1
1
2
1
1
1
2
1
0
2
2
1
1
1
2
2
1
1
1
1
0
1
1
1
1
0
1
1
1
1
1
0
1
2
1
1
1
1
1
0
1
1
1
0
1
1
1
1
0
2
1
2
2
1
0
1
2
1
1
1
2
1
2
1
1
1
2
1
0
1
1
0
1
2
1
2
2
2
1
2
1
1
1
1
0
1
2
2
2
1
0
1
2
2
2
2
1
2
1
1
1
1
2
1
2
1
2
2
2
1
1
2
1
2
1
1
2
1
1
1
1
2
2
2
1
1
1
1
2
0
2
1
0
1
2
2
1
1
0
1
1
1
1
1
2
1
1
2
2
1
1
1
0
1
1
2
1
2
2
1
1
1
1
1
2
1
2
1
1
0
1
0
1
2
1
1
1
1
2
1
1
1
2
2
1
2
1
2
0
0
2
0
2
1
0
1
1
2
1
1
1
2
2
1
2
1
1
1
2
2
1
1
1
0
1
1
1
2
1
1
1
0
1
1
1
2
2
1
1
2
1
2
1
1
2
1
0
1
2
1
1
1
2
1
0
1
1
2
1
0
1
2
0
2
1
0
2
2
1
2
1
1
2
1
1
0
2
1
1
0
2
1
2
2
2
1
2
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
0
1
2
1
2
1
1
0
1
1
2
1
1
2
0
1
1
1
0
1
0
0
1
1
1
0
1
1
1
2
1
0
2
1
1
1
0
1
0
0
2
1
1
1
1
1
1
0
1
1
2
0
1
1
1
0
1
1
1
1
1
1
1
2
1
1
0
2
1
1
1
1
3
2
2
1
2
0
1
0
1
2
1
1
1
0
2
1
1
1
1
1
1
1
3
1
2
1
1
0
0
2
1
0
0
2
1
2
1
1
1
1
1
2
1
2
1
1
2
2
1
2
2
1
0
1
0
1
1
0
3
1
2
1
1
2
1
1
2
1
1
2
2
2
2
0
0
1
2
2
2
1
0
1
2
2
2
1
0
1
1
2
1
1
2
2
1
2
2
2
0
1
0
1
1
1
2
1
1
1
1
0
1
1
2
1
1
2
2
1
1
1
0
1
1
1
1
1
1
1
0
1
0
1
1
2
2
1
1
2
2
2
1
1
2
2
3
2
1
1
2
1
2
2
1
1
1
0
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
0
1
0
2
1
1
1
2
1
1
1
0
2
1
4
1
0
2
2
1
0
2
1
1
2
1
1
1
0
1
2
0
1
1
2
1
1
1
0
2
2
1
2
2
2
2
2
1
1
1
1
1
1
1
2
1
1
1
2
2
2
1
1
1
2
0
1
2
2
1
0
1
1
1
1
2
2
0
2
1
2
2
2
1
2
2
0
1
2
1
1
2
1
0
1
2
2
1
1
1
2
1
2
1
1
2
1
1
1
2
2
1
2
1
2
1
1
1
1
1
1
1
2
1
2
2
1
1
1
0
1
1
1
2
1
1
1
1
1
2
1
1
2
1
2
1
2
0
2
0
2
2
1
1
1
0
1
0
1
0
1
0
0
1
0
0
1
2
2
2
1
2
0
0
2
1
2
2
1
1
1
1
0
1
2
0
2
1
1
1
1
2
1
1
1
2
2
1
2
1
1
0
1
2
1
2
1
1
1
2
0
2
2
1
1
1
1
1
1
1
0
1
1
1
2
2
0
2
1
1
0
2
2
1
1
1
2
1
1
1
1
0
2
1
1
0
1
1
1
1
2
1
2
2
2
1
0
0
1
2
1
0
1
0
0
2
2
2
1
0
1
2
2
1
1
1
1
0
1
1
1
0
2
2
1
2
2
2
1
1
2
2
0
1
1
0
1
1
1
1
1
1
0
1
2
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
0
3
1
2
1
1
1
1
0
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
2
1
1
2
1
1
1
1
1
1
0
2
1
1
1
1
1
2
1
1
1
0
1
2
2
1
2
2
0
1
1
2
1
1
2
1
2
1
2
2
1
2
2
2
1
1
2
1
1
1
2
2
1
1
0
1
1
1
0
2
1
2
1
1
2
1
1
2
1
1
2
1
1
2
2
2
0
1
2
1
1
2
1
0
1
2
1
1
1
2
2
1
1
2
1
0
1
2
2
2
1
1
1
1
1
2
1
2
1
2
1
0
2
1
1
1
1
1
3
1
1
1
1
1
2
1
0
1
2
1
1
3
1
0
1
2
2
2
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
0
2
1
1
1
0
1
1
2
1
1
1
2
0
2
2
1
1
1
2
1
1
1
0
1
0
2
1
1
1
2
0
1
2
1
1
1
1
1
1
2
1
1
0
1
1
1
1
1
1
2
1
1
1
1
2
1
2
1
1
1
1
2
1
1
2
2
1
1
2
0
1
1
1
1
1
1
1
1
1
1
2
0
0
2
1
1
1
1
1
0
1
1
2
1
1
1
1
0
1
0
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
0
1
1
2
0
1
1
1
2
2
2
1
1
2
2
2
1
2
1
2
1
1
1
1
3
1
1
1
1
1
1
1
0
1
2
1
1
2
2
0
2
1
1
1
1
1
2
1
0
1
1
1
1
1
1
1
3
1
1
1
2
1
1
1
1
1
2
0
1
2
0
1
1
2
2
1
2
1
2
1
1
0
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
0
2
1
1
1
1
1
2
1
1
1
1
1
2
0
1
1
2
2
1
1
2
0
0
2
2
2
1
1
2
2
0
1
1
1
1
0
1
1
1
0
0
1
1
1
2
1
2
1
0
0
1
1
1
1
1
0
2
2
2
1
1
1
0
1
0
2
1
1
1
2
2
1
1
1
2
1
2
1
1
1
1
1
0
2
2
1
0
1
1
1
1
0
1
0
1
1
1
0
2
1
0
1
2
2
2
1
2
1
1
0
1
2
1
1
2
1
2
1
1
2
2
1
2
1
1
2
1
1
1
1
0
2
0
2
1
1
1
1
1
1
0
1
1
0
0
1
0
1
1
0
2
1
1
2
0
1
1
1
1
2
1
2
2
1
2
1
2
2
1
1
0
1
1
2
2
0
1
1
1
1
1
0
1
1
0
0
1
2
3
1
1
1
1
2
2
2
1
1
2
0
1
2
2
1
0
1
1
2
1
1
1
1
1
0
1
1
2
1
0
2
2
2
0
1
1
1
2
2
1
0
1
0
1
2
0
1
2
1
0
1
2
2
1
1
1
2
2
2
2
1
0
2
2
0
2
2
1
2
0
0
2
0
1
1
1
1
3
1
1
0
2
1
1
1
2
1
1
1
0
0
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
2
1
2
2
1
2
1
0
1
1
1
1
0
0
1
1
1
1
1
0
1
1
1
1
1
1
1
1
2
2
1
1
1
2
2
0
1
2
2
0
1
2
1
1
1
2
2
1
1
0
2
2
2
1
2
1
1
3
2
2
1
1
2
1
2
1
2
0
1
1
1
1
1
1
2
2
1
1
1
1
1
2
2
0
1
1
1
2
1
0
2
2
1
0
0
1
1
1
2
1
2
2
1
1
2
2
1
1
1
1
0
1
1
1
1
2
2
2
0
1
1
0
1
2
2
2
1
1
1
2
1
1
2
1
2
1
2
2
2
1
0
1
2
2
2
1
1
1
1
2
0
1
1
2
1
2
1
2
1
2
0
1
0
0
1
2
1
1
0
2
0
2
2
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
2
1
1
1
2
1
1
1
0
1
2
1
1
1
2
1
1
1
1
0
2
1
2
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
0
1
1
1
1
1
1
2
2
2
1
2
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
0
1
2
2
1
1
1
1
1
1
1
1
2
3
0
1
0
1
0
1
1
1
1
0
1
2
1
1
2
0
1
1
1
0
2
0
1
2
1
2
1
1
0
0
1
0
1
2
1
2
1
2
2
1
1
0
2
2
0
1
0
0
1
2
1
2
3
0
1
1
0
2
1
1
1
2
2
1
1
2
1
1
1
1
1
1
2
1
1
0
0
2
0
3
1
2
0
1
2
1
2
1
2
2
2
1
1
0
1
0
2
2
2
1
2
1
0
1
2
0
2
1
1
1
1
1
2
0
2
2
1
1
2
2
1
2
1
2
2
2
1
2
0
0
1
2
1
1
1
1
2
2
1
1
2
0
1
2
0
1
1
1
0
1
1
1
1
1
2
1
0
1
2
2
1
1
2
2
2
1
1
1
2
2
0
1
1
1
1
2
1
1
1
2
1
2
1
1
2
2
1
3
0
1
2
2
1
1
1
2
1
1
0
1
2
1
1
1
1
2
2
2
2
1
0
0
2
1
1
1
1
1
1
0
3
1
1
1
1
2
1
2
0
1
0
1
1
2
1
1
2
1
1
1
1
1
1
2
1
2
0
1
2
0
1
1
2
1
1
2
1
2
0
1
1
1
2
0
0
1
1
1
2
1
2
1
2
2
0
2
0
0
1
1
2
0
1
1
2
0
2
0
2
1
0
0
1
1
1
1
1
1
2
1
1
2
1
3
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
1
0
2
1
1
1
1
2
0
1
2
1
1
2
0
2
2
1
1
1
2
0
1
1
1
0
2
1
1
0
0
1
1
1
1
2
1
2
2
1
1
1
2
2
1
1
2
1
2
2
0
1
2
1
2
0
1
1
1
1
0
0
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
2
1
1
1
1
1
1
2
1
2
1
1
3
1
2
2
2
0
0
1
1
1
2
1
2
0
0
1
0
1
1
2
1
0
2
2
1
1
0
1
1
13
0
2
0
1
1
2
2
2
0
1
1
1
1
1
2
1
1
2
1
1
0
1
1
0
0
1
0
1
2
1
0
1
0
1
1
0
1
2
1
0
1
2
2
0
1
1
1
1
2
1
1
2
1
1
1
1
0
2
1
1
2
0
2
1
1
1
2
1
1
1
2
0
2
2
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
0
1
1
2
1
0
1
1
2
1
1
0
1
1
1
1
1
1
1
0
1
2
0
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
2
1
2
0
2
1
1
1
2
1
1
0
1
1
1
1
1
1
1
1
2
2
2
1
0
2
1
2
1
1
2
1
1
1
0
2
2
1
1
1
1
2
2
2
1
1
2
0
1
1
0
0
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
1
1
2
1
1
1
1
0
1
1
1
1
1
2
0
1
1
1
1
1
1
2
1
0
1
0
1
1
1
1
2
2
1
2
1
1
1
1
1
0
2
1
1
2
1
1
2
0
2
2
1
2
1
1
1
3
1
1
2
2
2
1
1
1
1
1
2
1
1
0
1
2
1
1
0
1
2
2
1
1
1
2
1
2
2
2
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
3
1
2
2
1
1
1
1
2
1
1
2
1
0
2
1
1
1
2
1
1
1
1
2
1
2
0
1
1
1
1
2
1
1
1
1
1
1
2
2
1
2
1
1
1
2
0
1
1
1
1
1
1
2
2
1
1
1
2
1
0
1
1
2
1
1
1
0
1
2
2
1
1
0
2
2
0
1
2
1
2
2
0
1
0
2
1
1
2
2
2
2
1
1
1
0
2
2
2
2
1
2
0
1
2
2
1
1
2
1
1
1
1
1
2
2
2
0
1
2
1
0
1
1
2
0
1
1
1
1
1
2
1
2
0
1
1
1
1
2
1
1
2
1
2
1
2
2
2
1
1
0
1
1
1
3
1
1
1
1
1
1
1
1
2
1
2
1
2
1
0
1
0
0
0
2
2
1
2
0
0
1
1
0
1
1
1
1
1
0
1
1
2
1
2
1
1
2
1
1
1
3
1
1
1
2
1
1
1
1
1
2
1
2
0
1
0
1
2
0
1
2
2
1
2
1
0
1
2
1
2
1
1
2
1
2
1
1
0
0
1
1
0
1
2
1
2
1
1
1
1
1
2
0
1
2
1
2
2
2
1
1
1
2
2
2
1
1
2
2
1
1
1
1
2
2
0
2
1
1
2
1
0
1
2
1
2
2
2
1
2
1
2
1
2
2
1
1
1
1
1
2
0
1
1
2
2
1
1
2
1
1
2
1
2
1
1
1
1
1
0
1
1
1
1
0
1
1
0
1
2
1
1
2
1
1
1
2
0
2
1
2
2
1
1
1
2
1
1
1
1
1
1
1
1
1
0
1
1
1
1
2
1
1
1
2
1
2
1
2
0
2
1
1
0
1
0
2
1
2
2
1
1
1
2
2
1
0
2
1
1
1
1
1
1
0
0
2
1
2
2
1
1
2
2
1
1
1
1
1
0
1
1
1
1
1
1
2
2
2
1
1
1
2
1
1
2
1
1
0
2
2
1
2
0
2
0
1
1
2
2
1
1
2
1
1
1
1
2
1
1
0
1
1
0
2
0
2
1
2
2
0
0
0
2
2
1
1
0
1
1
1
1
1
1
2
1
1
0
2
2
0
2
0
0
1
2
1
2
1
0
2
0
1
1
1
2
2
1
1
1
1
2
1
1
1
1
2
1
0
2
2
1
1
2
0
1
1
1
0
1
1
2
2
1
1
1
2
2
2
1
1
2
1
1
1
1
1
1
1
1
2
2
1
0
1
1
1
2
2
2
1
1
1
1
2
1
2
2
1
1
1
2
0
1
1
2
0
2
0
1
1
2
1
1
1
1
1
1
1
1
1
1
0
1
1
0
1
2
2
1
2
0
1
1
0
2
1
1
1
2
1
1
1
2
1
2
2
1
0
1
1
1
1
1
1
0
1
2
0
1
1
1
1
2
2
2
2
1
2
4
1
1
2
1
1
0
1
2
1
1
2
1
0
2
1
1
1
0
0
1
2
1
1
1
1
0
2
0
1
1
1
1
1
2
1
1
0
1
0
1
1
1
1
2
2
1
1
2
0
2
2
0
1
1
1
2
1
1
2
1
0
2
1
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
2
2
1
2
1
1
1
1
0
2
2
1
2
1
2
1
2
1
0
2
0
1
1
1
2
2
0
2
2
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
2
2
1
0
1
1
1
2
1
1
2
1
1
1
1
1
1
1
0
1
1
2
2
1
1
0
1
1
1
1
2
2
1
1
1
1
2
0
1
1
1
2
1
2
0
1
1
1
1
2
0
1
1
0
1
1
0
1
0
1
1
1
1
2
1
3
1
0
2
1
1
1
1
1
1
2
3
1
1
2
1
2
1
0
0
1
0
1
2
2
2
1
1
2
1
1
2
1
2
1
1
2
1
0
1
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
0
1
1
1
2
0
1
2
1
2
2
1
2
1
2
0
0
1
0
2
1
2
2
0
1
0
1
0
2
1
1
2
2
1
1
1
1
1
1
2
1
1
1
0
1
0
1
2
1
2
2
1
2
1
2
1
1
0
1
1
1
2
2
1
1
0
1
1
2
1
1
1
1
2
2
2
2
2
0
1
2
2
1
1
1
1
2
2
2
1
1
1
1
1
2
2
0
1
1
1
2
1
1
2
1
1
3
0
0
1
0
1
1
1
1
1
0
1
1
1
0
1
1
2
1
0
1
1
1
2
2
1
1
1
1
1
1
1
3
1
2
2
1
2
1
0
0
2
1
1
1
0
1
1
1
1
1
2
1
2
2
1
1
2
1
1
1
0
2
1
0
1
1
1
1
1
0
1
1
1
1
1
2
1
2
1
2
0
1
0
2
1
1
1
1
2
1
2
0
1
1
2
1
1
2
1
1
1
1
2
2
0
1
1
1
2
2
0
1
1
2
1
1
2
1
1
1
1
1
2
0
1
1
1
2
1
1
1
1
1
1
2
0
1
1
1
1
2
1
0
1
2
3
1
1
2
1
1
1
1
0
2
2
1
3
1
1
2
1
0
1
1
0
1
1
1
1
1
0
2
1
1
2
1
1
1
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
0
1
2
2
2
1
1
1
1
2
2
0
1
1
0
1
1
1
1
1
1
0
1
1
1
2
1
1
1
1
1
1
1
2
1
1
0
2
2
1
1
2
1
2
1
1
1
1
1
1
1
1
2
0
0
3
2
1
1
1
2
2
2
1
2
1
1
2
0
1
0
0
1
2
1
1
1
1
1
1
2
1
1
0
0
1
1
1
1
0
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
0
1
1
1
1
2
0
1
0
1
1
1
0
1
1
0
1
1
2
0
7
1
1
0
2
1
1
0
1
1
2
1
1
1
1
0
0
1
2
2
0
2
1
1
2
1
1
0
2
1
1
1
2
1
2
1
2
1
1
1
2
1
0
2
2
2
1
1
1
1
2
0
0
2
1
1
1
2
1
0
0
0
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
0
2
1
2
2
1
1
0
0
1
1
1
1
2
2
2
2
1
2
1
1
0
1
1
2
1
2
1
2
0
2
1
2
0
1
1
2
2
1
2
2
1
1
1
1
1
0
2
2
1
1
1
2
2
1
1
2
2
1
2
1
2
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
0
1
0
0
1
1
0
1
1
2
1
1
1
1
1
3
2
0
2
1
1
1
1
2
1
2
2
1
1
0
0
1
1
2
1
1
1
2
0
3
2
2
1
1
2
2
0
2
1
0
1
1
1
2
1
2
1
1
1
0
1
1
1
2
0
2
2
2
1
0
2
2
2
1
1
1
1
2
2
2
2
1
2
2
2
1
2
1
1
2
1
1
0
1
1
1
0
2
1
2
1
2
1
1
1
0
1
0
0
0
2
1
1
1
2
2
1
1
1
0
1
1
1
0
0
2
1
0
1
1
1
2
1
1
2
2
1
1
2
0
1
1
1
1
0
1
1
2
2
1
2
1
2
2
1
2
1
1
2
1
1
1
2
1
1
1
2
2
1
1
2
2
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
2
2
2
2
2
1
1
1
2
1
0
0
1
2
1
2
1
2
0
2
1
1
1
0
1
1
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
1
1
1
2
2
2
2
1
1
1
1
1
1
1
2
1
1
2
2
1
1
2
1
1
1
2
2
1
1
1
0
1
2
1
1
2
1
1
0
2
1
1
1
1
1
1
1
1
3
1
0
1
2
2
2
1
1
1
1
1
1
0
1
1
2
1
1
0
1
2
1
2
2
1
1
1
2
1
2
0
1
1
2
3
2
1
1
1
1
2
2
2
1
1
1
1
2
0
2
0
2
1
1
0
1
1
1
1
2
1
1
1
1
1
0
2
3
1
0
1
1
2
1
0
1
0
1
1
2
2
1
1
1
3
1
2
2
1
0
1
2
1
2
1
1
1
1
1
0
1
1
2
1
0
1
1
2
2
1
1
2
1
1
2
1
1
1
1
1
1
1
1
0
0
1
1
0
1
2
1
1
1
1
1
2
1
3
1
1
2
1
1
2
2
2
0
1
1
0
1
1
1
1
2
1
2
2
2
1
1
2
1
2
1
1
2
1
1
0
0
0
0
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
0
1
0
1
1
0
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
2
0
1
1
1
1
2
2
1
1
1
2
1
1
2
1
1
2
1
2
1
1
0
2
0
1
1
1
0
1
1
1
0
0
0
1
2
1
1
2
2
2
1
1
1
0
1
2
1
1
1
2
2
1
0
1
1
1
2
1
1
0
1
1
2
1
1
2
1
2
1
1
0
1
1
0
1
1
0
0
2
0
1
1
0
1
1
0
2
2
1
1
1
1
2
2
2
1
1
1
1
0
1
0
3
2
2
1
1
0
1
1
1
1
1
0
1
1
1
1
1
2
1
0
1
2
0
1
1
1
1
1
2
2
1
1
1
1
2
1
1
2
2
1
1
2
2
1
2
1
1
2
1
1
1
1
1
1
1
2
1
0
1
2
1
1
1
2
1
0
2
0
2
1
1
0
1
1
1
2
1
1
0
1
1
1
1
2
1
0
2
1
1
0
1
0
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
1
1
2
0
1
1
2
1
1
2
1
1
2
1
1
1
2
2
1
1
1
1
1
0
2
2
2
2
1
1
1
1
1
1
1
2
2
1
1
1
0
2
1
2
1
1
2
0
2
0
1
2
1
1
1
2
1
1
1
0
1
2
1
2
1
0
1
1
1
1
2
2
0
1
2
1
1
1
1
1
1
1
2
1
0
1
1
1
1
1
0
1
2
1
1
1
2
1
0
2
1
2
1
1
2
1
1
1
2
1
1
2
1
1
2
1
0
1
1
1
1
2
1
1
1
1
1
2
1
0
1
1
2
1
2
0
1
1
2
1
2
2
1
1
2
1
1
1
1
2
1
1
1
1
2
2
1
1
2
1
2
1
3
1
1
1
0
0
1
1
1
1
1
2
1
1
1
1
1
1
2
0
2
1
1
1
2
1
1
3
1
2
0
2
2
1
0
1
1
2
1
1
1
0
1
1
1
1
2
2
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
0
1
1
1
1
1
1
0
1
1
1
2
2
2
2
1
2
1
1
2
1
1
0
1
2
1
1
2
0
0
2
2
1
0
1
2
1
1
2
1
2
1
1
1
1
0
0
0
2
2
0
1
1
2
2
2
1
2
1
2
1
1
1
2
1
2
1
1
2
2
1
2
3
2
0
1
1
2
1
1
0
1
1
2
0
0
1
1
3
2
1
1
0
2
2
0
1
1
0
1
0
1
1
2
2
2
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
2
1
0
1
3
1
1
1
1
1
2
1
1
2
2
2
2
2
1
2
1
0
1
1
1
1
1
1
2
1
1
1
1
1
1
0
0
2
2
1
1
2
1
1
2
1
1
1
1
1
0
2
1
0
1
1
1
1
0
1
2
1
1
1
0
2
1
1
0
2
2
2
1
2
0
1
1
2
1
1
1
2
1
2
2
2
1
1
1
2
1
2
1
1
0
1
1
0
1
1
0
1
1
1
0
1
1
1
2
1
1
1
1
1
0
3
2
1
2
1
1
1
0
2
1
1
1
1
1
1
0
2
1
0
1
0
1
1
1
2
1
2
0
2
1
1
1
1
1
0
2
0
0
1
0
1
1
1
2
2
2
1
1
1
2
1
1
2
3
0
2
1
2
1
2
2
1
2
0
2
1
1
1
2
2
1
2
2
1
1
1
0
1
1
1
1
1
2
0
1
2
1
1
2
1
1
0
1
2
1
1
1
1
2
1
1
1
1
0
1
1
1
1
0
2
1
2
1
0
1
1
1
2
1
1
1
0
1
1
1
1
0
1
2
1
0
2
1
1
1
0
2
1
2
1
0
1
0
0
1
1
2
1
1
1
0
2
1
1
2
2
1
1
2
1
2
1
1
4
0
2
2
2
1
1
1
1
1
1
1
4
1
1
1
1
1
1
1
2
1
0
5
1
1
1
2
0
0
2
1
0
2
1
1
1
1
2
1
1
1
2
2
1
0
1
2
1
1
1
2
2
1
0
1
1
1
1
1
0
1
1
2
1
2
1
1
1
1
2
1
2
1
1
0
2
1
1
0
2
1
2
2
2
1
2
2
2
2
1
1
1
1
3
1
1
2
1
1
1
1
2
1
0
1
0
1
0
2
1
1
1
2
1
1
2
2
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
2
2
1
1
1
0
1
2
1
2
1
2
2
1
2
1
1
1
1
1
2
2
1
1
1
2
2
1
1
2
1
2
1
1
1
1
2
1
0
1
1
1
2
0
1
0
1
1
2
1
2
1
1
1
1
0
1
1
1
2
1
2
1
1
1
1
1
1
1
0
2
1
1
1
1
2
0
2
0
1
1
1
1
1
2
1
1
1
1
1
1
0
2
1
0
1
1
1
0
1
1
2
1
2
1
2
1
2
1
2
1
1
1
2
1
1
1
1
0
2
2
1
1
2
1
1
2
1
1
2
2
1
1
1
1
2
1
1
1
2
1
0
2
2
1
1
2
2
1
0
1
2
1
1
2
2
0
2
2
2
0
2
0
1
2
1
2
1
2
1
1
2
2
1
1
2
2
1
1
2
1
1
1
2
2
0
0
2
1
1
1
1
1
1
2
1
2
1
2
1
1
1
1
3
1
1
1
1
1
2
1
0
1
1
1
2
1
1
1
2
0
2
1
1
2
1
1
1
2
1
1
1
1
1
0
0
1
1
0
2
1
0
2
1
1
1
1
2
1
2
2
0
1
1
1
1
1
1
0
1
1
1
2
1
0
0
1
2
2
2
0
1
2
1
1
1
1
1
2
2
1
1
2
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
0
0
1
1
1
1
1
1
2
1
1
1
1
0
1
2
1
1
1
1
1
2
1
1
1
0
2
0
1
1
2
2
1
1
1
1
1
0
1
0
0
1
2
0
0
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
0
1
1
2
1
1
0
2
0
1
0
1
1
1
2
0
2
1
1
1
1
1
1
2
1
1
2
2
1
1
0
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
0
2
1
1
1
1
1
1
2
1
0
2
2
2
1
2
0
1
2
2
1
2
1
2
2
1
0
0
1
0
2
1
2
1
1
2
1
2
2
1
2
1
1
1
1
1
2
1
1
0
0
1
2
1
1
1
1
2
1
0
0
0
2
1
1
1
1
1
1
1
1
1
0
1
0
2
2
2
1
0
1
2
0
2
2
2
2
0
1
1
1
1
2
1
1
0
2
0
2
1
2
2
1
0
1
2
1
2
0
1
1
1
1
2
1
1
1
2
0
1
1
1
1
2
1
2
1
1
1
1
0
0
1
2
1
2
0
1
1
2
1
2
1
2
1
2
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
0
2
2
2
1
4
1
2
1
1
2
2
1
3
2
1
1
1
1
2
1
2
0
2
2
1
1
2
2
1
1
2
2
0
0
1
1
1
0
1
1
0
2
1
1
1
1
1
1
1
2
1
1
2
1
0
2
2
1
1
2
1
1
0
2
1
2
2
2
0
1
2
2
0
1
1
0
1
1
1
1
0
1
0
0
1
2
1
1
1
1
1
0
2
1
1
1
1
0
1
1
1
1
1
2
1
1
2
1
0
0
1
1
1
1
1
1
1
2
2
1
1
1
1
2
2
1
1
2
2
1
1
1
1
2
2
2
0
1
1
2
2
1
1
2
1
1
2
0
1
2
2
1
0
1
1
1
1
2
1
0
2
1
1
1
1
0
1
1
2
1
2
0
2
1
1
1
2
1
1
0
2
1
1
1
1
1
3
1
1
0
1
1
0
1
2
1
1
2
2
2
1
2
0
1
1
1
2
0
1
1
2
1
1
0
1
1
0
1
2
1
0
2
0
1
1
0
2
2
1
0
2
0
1
2
0
1
1
2
1
2
1
1
1
0
1
1
1
1
2
1
1
1
1
1
0
1
0
1
1
2
2
3
1
2
1
1
2
0
1
1
1
2
1
1
1
2
2
0
1
1
2
0
2
1
1
1
2
0
0
1
2
1
2
2
1
1
2
1
1
1
1
1
1
2
1
2
1
2
0
2
3
1
1
2
2
1
0
0
2
2
0
1
0
2
1
2
0
2
2
2
1
1
1
1
2
2
1
0
1
2
1
1
2
2
1
2
2
1
1
2
1
0
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
2
1
2
1
1
0
1
1
1
1
1
2
1
1
0
2
1
2
1
2
1
2
2
1
0
1
1
1
1
2
0
0
1
0
1
0
1
1
1
1
1
1
1
2
1
2
1
2
1
0
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
0
1
1
1
1
1
1
2
1
0
1
2
1
1
1
2
2
1
2
1
1
0
0
1
1
2
1
1
1
1
2
1
2
1
1
1
2
1
0
0
2
1
0
1
2
2
1
0
1
2
1
1
1
2
1
1
1
1
1
2
1
2
2
1
1
1
1
2
1
1
1
0
1
1
0
1
1
1
2
1
2
1
1
2
1
1
0
1
1
1
1
1
1
1
2
2
2
1
1
1
2
2
1
2
1
0
2
2
0
1
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
0
2
1
2
0
1
1
1
1
1
1
2
1
1
1
1
0
1
0
1
1
1
1
1
1
1
1
2
0
1
1
1
2
1
1
2
1
1
1
0
1
0
1
1
2
1
1
1
0
1
0
1
1
0
1
2
0
1
1
0
1
2
1
1
1
1
1
4
2
1
1
1
1
1
0
1
2
1
1
1
1
1
2
0
2
2
2
1
1
1
5
1
1
0
2
1
1
1
1
0
1
2
1
1
1
2
2
2
0
2
1
1
1
1
1
2
1
6
0
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
0
1
2
1
2
1
2
0
0
2
1
2
1
1
1
0
0
2
1
2
0
1
0
1
1
0
2
1
1
1
1
1
0
1
1
1
1
1
0
1
1
1
1
2
1
1
1
1
1
1
1
0
2
0
1
1
1
2
1
1
1
2
1
0
1
1
2
2
1
1
1
2
1
1
1
1
0
1
1
1
0
1
2
1
1
2
2
1
2
1
1
1
1
2
1
1
0
2
1
1
1
0
1
2
2
0
1
0
1
1
2
0
1
1
2
1
0
0
0
1
1
1
1
1
1
1
2
1
2
1
2
1
1
1
1
1
2
2
1
0
1
2
1
2
0
1
2
1
1
0
1
1
1
0
1
1
0
1
1
2
2
1
2
2
1
1
2
2
1
1
2
1
1
0
1
1
0
1
1
1
1
1
0
1
0
1
0
1
1
1
0
1
1
2
0
1
2
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
2
2
1
1
2
0
1
2
1
2
1
1
1
2
2
0
2
1
0
1
1
2
2
2
1
1
2
1
1
2
1
1
1
2
1
1
1
2
0
2
0
2
1
1
1
1
1
0
1
1
0
0
1
1
1
1
2
1
1
1
1
2
1
1
2
1
0
0
1
0
1
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
0
1
1
2
1
2
1
2
0
1
1
1
1
1
1
2
0
1
2
2
0
1
1
2
2
1
2
1
1
1
2
1
1
1
0
1
2
1
1
0
2
1
2
1
2
1
2
0
1
1
2
2
0
1
1
0
1
1
1
1
0
1
2
1
1
1
1
1
2
1
1
2
1
2
1
2
2
1
1
2
2
2
1
1
2
1
1
1
1
0
1
1
1
1
2
1
0
0
1
1
2
1
2
0
2
1
2
1
0
1
1
2
2
0
2
2
1
0
1
2
1
1
1
1
2
1
1
1
1
1
2
1
2
0
1
0
1
1
1
1
1
2
1
0
1
1
2
0
1
2
2
0
2
2
1
1
1
0
1
2
2
1
2
1
1
1
1
1
1
0
0
1
1
3
1
0
2
1
1
2
1
1
0
1
2
2
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
0
1
1
2
1
2
2
1
0
2
0
0
2
1
1
1
0
2
0
2
1
1
0
1
2
1
2
2
1
2
0
1
1
1
1
0
1
1
1
2
2
2
1
1
3
1
1
2
1
1
0
1
1
1
0
2
1
2
1
2
0
1
2
1
1
1
2
2
2
1
1
1
1
2
1
1
1
2
2
1
1
1
1
2
2
2
2
1
1
1
1
2
0
1
1
2
2
1
2
1
0
0
1
1
2
1
3
1
1
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
2
2
1
0
2
1
0
1
1
1
0
1
2
1
1
3
1
2
1
1
0
1
1
1
1
2
1
2
1
1
1
2
2
1
1
1
1
0
1
1
1
1
2
1
0
2
1
1
2
0
1
1
1
2
1
1
1
0
1
1
2
1
2
1
1
0
1
2
1
2
1
1
2
1
1
0
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
0
1
1
0
0
1
1
1
1
0
0
2
2
1
2
1
1
2
2
1
1
1
1
1
1
1
2
1
0
1
1
1
2
1
2
2
1
2
3
1
1
2
1
1
2
1
1
1
0
0
1
2
2
2
1
1
2
2
1
1
0
1
1
1
1
2
1
1
1
1
1
2
1
0
1
1
1
2
1
2
1
1
1
1
2
2
1
2
0
2
1
1
0
1
1
1
1
1
1
1
1
0
2
1
2
1
1
1
0
1
2
1
1
0
1
1
2
1
0
1
2
1
0
1
0
2
1
1
1
1
2
1
1
1
1
0
1
2
1
1
2
1
2
0
2
1
1
2
1
2
1
2
1
1
2
0
1
1
0
2
1
2
1
2
1
2
1
0
1
0
1
0
1
1
1
0
0
2
1
1
1
2
2
1
2
1
1
1
2
1
0
0
2
0
1
0
2
2
2
1
1
0
1
1
2
1
2
1
1
1
1
1
1
0
1
1
1
0
1
2
0
1
2
0
1
0
1
1
1
2
2
2
1
1
1
2
2
1
1
2
1
0
1
0
2
1
0
2
2
1
1
2
2
1
2
2
1
1
1
1
1
1
0
1
2
1
1
2
1
1
0
2
0
0
2
1
1
1
2
1
1
1
2
1
0
0
0
2
1
1
1
1
0
1
1
1
1
1
1
0
2
1
1
2
1
1
2
1
1
1
2
1
1
0
2
1
1
1
1
1
1
2
1
2
2
1
1
0
1
1
1
1
2
1
2
1
1
1
2
1
1
1
2
2
1
0
1
0
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
0
1
2
1
1
2
1
1
1
1
2
1
2
1
1
0
1
1
2
0
1
1
2
1
2
1
1
1
1
1
1
2
1
2
2
1
1
0
2
1
1
1
1
1
0
2
0
2
1
1
1
1
1
1
1
1
2
1
1
1
0
0
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
2
1
1
1
1
2
1
1
1
0
1
1
2
0
1
1
1
0
1
1
2
1
2
2
2
0
1
1
1
0
2
1
1
1
1
1
3
1
1
2
1
2
2
1
0
2
0
1
1
2
1
3
1
1
1
1
1
2
3
1
2
1
2
1
0
1
1
2
1
2
1
1
1
2
1
1
1
2
2
2
2
2
2
1
1
1
1
1
1
2
1
2
1
1
0
1
1
1
2
0
1
1
1
1
0
1
2
1
2
1
1
2
1
2
1
1
2
1
0
2
1
1
2
2
1
2
2
2
2
2
1
0
1
2
1
1
1
2
1
1
0
1
1
0
1
1
1
1
1
2
2
1
1
1
1
1
1
1
3
1
1
2
1
1
0
3
1
0
1
0
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
0
1
2
1
0
1
2
1
1
1
1
2
1
1
2
2
1
1
0
1
1
1
1
1
1
1
1
2
1
0
2
2
2
1
1
0
2
0
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
0
2
0
1
1
1
0
1
2
1
0
2
1
0
1
1
0
1
2
2
1
0
1
2
1
0
2
0
2
0
2
0
1
1
2
1
2
2
1
1
1
0
1
1
2
1
1
1
1
1
1
0
2
2
1
2
2
1
1
1
1
1
3
1
1
1
2
1
1
2
1
1
1
1
1
2
2
2
2
1
2
2
0
1
2
2
2
1
0
1
0
1
1
1
0
1
2
2
2
2
0
2
2
1
1
2
1
0
0
1
2
0
2
1
2
1
1
2
2
1
2
1
1
1
0
1
0
2
1
0
1
1
1
1
1
1
1
1
1
2
1
2
1
2
1
1
2
1
1
0
1
1
1
2
1
1
1
1
1
2
2
1
2
1
2
1
1
0
0
1
2
0
1
1
1
1
1
2
1
1
1
2
2
0
1
0
0
1
1
1
1
0
1
1
1
0
1
1
1
1
1
2
2
0
2
1
1
1
1
2
2
1
1
1
2
2
2
1
1
1
2
0
2
1
1
2
1
1
2
2
0
1
2
2
3
1
2
2
1
1
1
0
1
1
1
1
0
1
1
1
1
1
2
0
1
1
1
2
1
2
1
1
2
0
0
0
1
2
1
2
1
0
1
0
1
1
1
1
1
1
0
1
1
2
1
1
1
0
2
0
1
2
1
1
1
1
2
2
2
2
0
1
1
0
1
0
2
2
2
1
2
1
0
1
1
0
1
2
2
1
1
1
2
0
1
1
1
1
2
1
1
3
1
1
1
2
1
1
2
2
1
1
1
3
2
1
1
2
1
1
2
1
0
2
1
1
2
1
2
2
2
2
2
1
1
2
1
2
2
1
0
1
1
5
1
0
1
1
1
0
1
1
2
1
2
1
1
2
1
1
1
2
2
1
0
1
2
1
2
1
1
1
2
1
1
2
1
1
1
1
1
2
2
1
2
1
2
0
0
0
1
1
2
1
1
0
0
1
2
2
1
1
0
0
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
0
0
1
1
2
1
1
0
1
2
2
0
1
2
1
1
1
3
1
1
0
2
0
1
1
1
2
1
1
2
1
1
1
1
1
2
1
1
1
2
2
1
2
2
2
1
1
2
1
0
0
2
2
1
2
1
2
1
1
0
1
1
1
2
1
1
1
2
1
2
2
0
2
2
2
2
1
2
1
1
2
1
1
0
1
1
1
1
0
2
1
0
2
2
1
1
2
1
1
1
1
2
2
1
2
2
1
2
0
2
1
1
0
1
1
2
0
0
1
1
1
2
0
2
1
2
1
1
1
1
0
1
2
1
1
1
0
5
2
1
1
1
0
1
2
1
1
2
1
0
1
1
2
1
1
2
1
0
0
1
1
1
1
2
1
0
2
1
1
1
0
1
1
1
0
1
1
2
2
2
1
2
1
0
1
1
1
1
2
1
2
1
2
2
1
2
1
1
1
1
2
3
1
1
1
1
1
2
1
0
1
1
1
0
2
1
1
1
1
1
2
2
2
1
2
1
2
2
0
1
2
2
1
2
2
1
1
0
0
1
0
1
1
1
1
0
1
0
1
1
1
1
1
2
0
1
1
1
1
1
2
2
1
1
1
2
1
1
1
0
0
2
2
1
1
1
1
1
0
1
2
2
1
1
0
0
2
1
2
0
1
1
1
1
1
1
2
1
2
1
1
1
1
1
0
2
1
0
1
1
0
1
1
1
2
0
2
2
2
1
2
1
1
1
1
1
1
0
2
1
1
0
1
0
1
1
0
0
0
0
1
1
0
1
1
1
1
1
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
0
0
1
2
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
1
0
1
1
0
1
1
2
1
1
1
2
1
2
2
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
0
2
2
0
1
0
0
1
0
2
1
1
1
1
2
2
1
2
1
2
1
0
0
2
1
1
2
2
0
2
0
2
2
1
1
1
1
2
1
1
2
1
0
1
1
0
1
0
2
1
2
1
1
1
1
1
1
2
0
0
1
1
1
1
1
1
0
0
1
1
2
1
1
0
2
2
1
2
2
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
1
1
1
2
2
1
1
0
2
1
1
2
1
2
1
2
1
1
2
1
1
0
1
0
1
1
0
2
2
1
1
1
2
1
1
0
2
1
1
1
2
2
1
1
1
1
0
0
2
1
2
0
1
1
1
1
2
0
0
0
1
1
2
0
2
1
1
2
0
0
1
1
0
1
1
1
1
2
2
0
1
2
0
1
1
1
0
1
1
1
2
1
1
1
2
1
1
1
0
1
1
1
2
2
1
1
0
1
2
0
1
1
1
1
1
2
1
2
1
2
1
1
2
1
1
1
1
1
0
2
1
1
1
0
1
1
1
1
2
1
2
1
1
2
0
1
1
1
1
1
2
1
2
1
1
1
1
2
2
1
0
2
1
1
2
1
2
1
1
2
1
1
1
1
2
2
2
2
1
1
0
1
1
1
1
2
2
1
0
2
2
1
2
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
2
2
1
1
2
2
1
1
0
1
1
1
1
0
1
2
2
1
2
1
1
1
2
1
1
1
2
2
1
1
2
1
0
1
1
1
2
1
2
0
2
0
1
2
1
1
2
1
0
1
2
2
0
1
2
2
2
2
1
1
1
0
2
2
0
1
1
1
0
1
1
2
0
1
0
2
2
1
0
1
1
1
1
1
1
2
1
2
0
1
1
1
1
1
0
1
1
1
0
1
1
0
0
1
1
1
1
1
3
0
1
2
1
1
2
1
1
2
2
1
1
1
1
1
2
2
0
1
1
1
1
1
1
0
1
1
2
1
2
1
0
1
1
1
1
2
2
1
1
1
0
2
1
2
1
2
1
2
2
1
2
2
1
1
1
1
2
1
1
2
2
2
1
1
1
1
1
1
1
2
2
1
2
1
1
0
0
1
0
1
2
2
2
2
1
1
1
0
2
1
1
1
2
1
0
2
1
2
2
2
1
1
1
2
0
1
1
2
0
1
0
1
1
1
2
1
1
1
0
1
2
1
2
1
2
1
1
0
2
1
1
1
1
1
1
2
1
2
0
1
2
0
0
1
1
1
1
1
1
1
1
2
2
2
0
1
0
1
1
1
1
3
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
0
2
1
2
1
1
1
1
2
2
1
2
1
0
1
1
1
0
0
2
1
1
1
1
1
1
1
1
1
4
0
0
1
1
1
1
1
1
0
2
1
1
0
0
0
1
0
1
2
1
1
1
2
1
1
2
1
1
1
2
1
2
0
0
2
1
2
2
1
0
2
2
1
1
1
1
2
1
2
2
1
1
1
1
1
0
4
1
1
1
1
1
1
1
1
2
2
0
1
1
0
1
0
1
1
0
1
0
1
0
1
0
1
2
1
1
1
2
1
2
1
0
2
2
1
0
2
3
1
1
1
1
1
1
2
1
1
2
3
1
1
1
2
2
1
1
1
2
2
1
2
1
1
1
1
2
0
1
2
1
1
2
1
1
1
0
2
2
1
0
2
1
1
2
1
2
0
0
1
0
1
1
1
1
1
2
1
1
2
1
2
1
1
2
1
1
2
1
1
1
1
1
2
1
0
2
0
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
2
2
1
0
0
2
2
1
0
0
2
0
1
2
1
1
2
1
1
2
1
1
2
1
1
0
2
1
1
0
1
1
0
1
1
1
2
0
1
1
2
1
2
1
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
2
2
1
2
1
0
1
1
1
1
1
2
1
1
1
1
2
2
1
1
1
1
1
1
1
0
2
1
0
2
0
2
2
2
1
2
1
1
0
1
1
0
1
1
1
1
0
0
1
2
2
2
1
1
0
0
0
0
1
1
1
1
1
2
1
1
1
1
2
1
1
0
0
1
2
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
0
1
0
1
1
1
1
0
1
2
1
1
1
0
1
2
0
1
1
0
1
2
1
1
1
1
1
3
1
1
1
2
1
0
2
1
1
2
1
2
1
1
0
2
0
2
1
1
2
1
2
1
1
2
1
1
1
2
2
1
1
2
0
0
1
1
1
1
1
2
2
1
0
1
1
1
1
1
1
1
1
1
2
1
0
1
1
0
1
1
1
2
1
2
1
1
2
1
1
1
1
2
1
1
2
1
2
1
0
2
1
2
0
1
2
2
2
1
1
1
1
0
2
1
2
2
1
2
1
2
1
1
1
2
1
1
1
2
0
1
2
2
2
0
1
1
1
2
2
1
2
1
2
1
1
1
1
1
1
1
2
1
1
0
2
1
2
1
1
0
1
1
1
1
0
2
2
0
1
1
1
2
1
1
2
1
2
2
1
1
0
1
1
2
0
1
1
1
1
1
1
3
1
2
1
1
1
2
2
1
1
1
1
1
2
1
2
1
2
0
0
1
1
1
1
0
0
1
1
0
1
0
1
1
1
0
0
1
2
1
1
1
1
0
1
2
1
2
1
1
0
1
0
0
2
2
1
1
0
1
2
1
0
0
1
1
1
1
0
1
1
1
0
2
1
2
1
1
1
2
2
1
1
1
0
1
0
1
1
2
2
2
1
0
1
1
0
1
1
2
1
2
1
1
2
1
1
2
0
1
1
0
2
1
2
1
2
1
3
1
2
1
1
2
1
1
1
0
2
1
1
2
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
1
2
2
1
1
1
1
1
0
0
1
1
2
2
1
1
2
0
0
1
2
2
1
9
1
2
2
1
0
1
1
1
1
1
1
0
1
2
1
0
1
0
1
1
1
2
1
1
0
2
2
1
1
2
1
1
2
1
2
1
1
1
2
2
0
0
1
1
2
1
2
1
1
2
2
0
1
1
2
1
1
0
1
1
1
2
1
0
2
2
0
2
1
2
3
1
1
1
1
2
0
1
2
1
2
1
2
1
0
1
0
1
0
1
1
2
2
0
2
1
1
1
2
2
2
2
0
1
1
0
1
1
0
1
0
1
1
1
1
1
1
1
1
1
1
2
2
1
2
2
1
2
2
1
2
3
2
1
1
1
1
1
1
2
1
0
2
1
2
1
1
1
2
2
1
2
1
1
2
2
0
2
1
1
0
0
0
1
1
1
1
1
1
2
2
1
1
1
1
1
2
2
1
1
0
2
2
0
1
1
0
0
1
1
0
1
2
2
0
2
1
1
1
0
1
2
1
1
1
2
1
1
0
1
0
2
1
1
2
2
1
1
0
0
1
1
2
1
0
1
0
1
0
1
1
0
2
2
2
1
2
2
2
0
1
1
1
1
2
1
0
0
0
2
1
1
1
1
2
2
1
1
2
2
1
2
2
0
1
0
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
2
2
0
2
1
1
1
1
2
1
1
2
1
2
1
1
1
2
0
1
1
1
2
1
1
1
1
1
1
1
2
1
0
1
1
2
1
1
1
0
1
0
1
1
1
0
1
1
2
2
0
2
1
1
1
1
1
2
2
0
1
1
0
1
1
0
0
1
2
2
1
1
2
1
0
1
1
2
0
3
0
1
2
2
1
2
1
1
1
0
1
1
2
2
0
3
1
1
2
1
1
0
1
1
1
1
1
2
1
1
2
2
1
1
2
1
1
1
2
2
0
1
1
1
1
1
0
0
1
0
1
1
2
1
2
1
0
1
1
1
1
1
2
0
1
1
0
0
1
1
1
0
0
0
1
2
2
1
1
2
1
0
1
1
1
2
1
1
1
1
1
1
1
2
2
1
2
1
2
2
1
0
0
0
2
1
1
1
1
2
1
1
1
2
0
2
1
1
1
1
1
1
1
2
1
2
2
0
1
1
1
1
1
1
1
0
1
1
1
1
1
1
2
0
2
2
2
2
2
1
1
1
2
1
0
1
1
2
1
0
2
1
1
1
2
1
1
2
1
0
1
0
1
1
1
1
1
1
3
1
2
1
1
1
0
1
2
1
1
0
1
2
2
0
1
2
1
1
2
1
2
2
1
0
3
1
1
1
2
2
1
1
0
1
2
1
1
2
0
1
1
2
1
2
1
2
0
2
2
2
1
1
2
2
2
1
1
0
1
1
1
2
2
1
2
1
0
0
1
1
1
1
1
1
1
1
1
1
2
1
1
2
2
0
1
1
2
1
2
2
1
1
0
2
0
1
2
1
0
0
1
1
2
2
1
2
2
1
1
2
0
1
1
0
0
2
2
1
1
2
2
1
1
2
0
1
2
1
0
0
1
1
2
2
2
2
0
1
0
1
1
1
0
0
1
1
2
2
1
0
1
1
0
2
3
2
2
2
1
1
0
0
1
0
2
2
1
2
1
2
1
1
0
1
2
1
1
1
2
1
1
1
1
2
2
1
1
1
1
1
0
1
2
0
2
3
1
0
1
0
2
1
1
1
1
1
1
1
0
0
1
0
1
1
1
1
2
1
1
2
0
1
1
0
1
2
1
1
2
2
1
1
1
1
1
1
1
2
2
1
1
1
2
1
1
0
1
1
1
2
0
0
2
1
1
0
1
0
1
2
0
1
1
1
1
2
1
1
2
1
1
1
1
1
1
0
2
1
1
2
0
1
0
1
2
1
1
1
1
1
2
1
0
1
0
1
0
1
1
1
2
1
1
0
1
1
0
1
1
1
1
2
1
1
1
2
2
1
1
0
0
1
1
2
1
1
0
2
0
1
1
1
1
1
0
2
1
1
2
1
2
2
2
1
1
1
2
1
1
1
1
0
1
1
2
1
1
1
1
0
2
1
1
2
1
2
1
1
1
2
2
2
2
2
0
0
1
1
1
1
1
2
2
2
0
1
0
1
1
2
0
2
2
2
1
1
2
0
1
1
1
1
1
0
1
1
1
1
2
1
1
1
1
2
1
2
2
1
2
1
1
2
0
1
2
2
1
0
0
2
1
1
1
2
1
1
0
2
1
1
1
0
2
0
0
0
2
0
1
2
1
2
1
1
0
1
2
1
1
2
1
1
1
1
1
1
1
0
0
0
1
1
1
2
0
1
1
1
2
1
2
1
2
2
0
1
1
1
0
1
2
0
0
2
0
0
2
2
1
1
1
1
0
0
1
1
1
2
1
2
1
1
1
2
1
1
1
2
0
0
0
1
2
1
0
1
1
1
1
2
2
1
0
1
0
2
1
1
0
0
1
1
1
1
2
1
1
1
2
2
1
0
1
2
2
1
2
0
0
1
1
2
1
2
1
1
1
1
1
1
2
1
0
1
1
1
1
2
0
1
1
2
1
2
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
0
1
1
1
2
1
1
1
1
1
1
0
2
1
1
0
1
1
1
1
1
1
1
1
1
2
1
0
1
1
0
2
1
0
1
1
1
0
0
0
1
0
2
0
1
1
1
2
0
1
1
2
2
1
2
2
2
1
1
2
2
0
1
1
1
1
2
0
1
1
1
1
0
1
1
2
0
1
1
0
3
1
2
0
1
1
2
2
1
1
1
1
1
1
1
1
1
0
1
1
1
2
2
1
1
1
0
1
1
1
2
1
1
1
0
1
1
1
0
0
1
1
1
1
1
2
1
1
1
1
1
1
2
2
1
2
0
1
1
1
2
1
1
1
1
1
2
1
1
2
1
0
2
0
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
2
3
1
4
1
1
2
2
1
1
1
2
1
2
2
2
1
2
1
1
2
1
2
1
0
2
1
1
1
2
1
1
1
2
2
1
2
1
0
1
1
1
1
1
1
2
1
2
1
1
0
2
2
2
1
2
2
1
0
2
1
1
1
1
1
1
0
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
2
2
0
0
2
1
2
2
1
1
2
1
2
1
1
1
2
2
1
1
2
1
1
1
2
1
0
1
1
2
1
2
1
1
1
2
0
2
2
2
2
1
1
2
1
1
1
2
2
1
1
1
1
1
1
1
0
1
2
2
1
2
1
1
1
2
1
2
0
2
1
1
1
2
2
2
0
2
1
1
2
0
1
1
1
2
2
1
1
1
1
0
1
0
1
1
1
1
1
0
1
2
2
1
2
1
1
1
1
1
2
1
1
1
0
2
1
0
1
1
1
1
2
1
1
1
0
2
2
1
2
1
2
0
1
2
2
1
0
0
1
2
1
1
1
1
1
1
1
1
1
1
2
0
2
2
1
0
1
2
1
1
1
0
1
1
2
1
1
1
1
2
1
1
2
0
1
1
1
2
1
1
1
0
1
2
2
1
2
0
0
2
0
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
0
1
1
1
1
2
1
0
1
1
1
1
1
1
1
1
3
2
2
1
1
2
1
1
0
1
2
1
2
1
1
1
1
1
1
1
0
2
1
1
2
1
2
1
2
1
1
1
2
2
1
1
2
1
2
1
1
1
1
1
1
0
2
1
1
1
1
0
1
1
1
2
0
0
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
2
2
0
0
1
1
2
2
3
1
1
2
1
1
1
2
1
2
1
1
2
1
2
2
2
1
2
2
1
2
2
2
1
1
0
0
0
1
2
1
1
2
2
1
1
1
0
1
0
2
1
0
0
1
1
2
1
1
1
1
1
0
0
1
1
1
1
1
1
0
1
1
1
1
2
2
2
1
1
0
1
1
0
1
1
1
1
0
2
1
0
0
1
2
2
1
0
1
0
2
1
1
2
1
1
1
1
2
1
2
2
1
2
1
2
1
0
0
2
1
1
1
2
1
1
1
3
1
1
2
1
1
0
1
2
1
1
0
2
1
0
1
1
0
1
2
0
1
2
0
1
1
2
1
1
0
1
2
1
2
1
1
1
2
1
1
1
1
0
2
2
1
1
1
0
2
1
1
2
1
1
1
1
2
1
1
1
0
1
1
1
1
1
1
1
1
2
0
1
1
1
2
1
1
1
1
1
1
1
2
1
0
1
2
1
1
1
1
2
2
1
0
1
1
1
1
0
1
1
1
1
1
2
1
1
1
1
1
1
0
1
1
1
1
1
2
1
0
1
1
0
2
1
1
1
2
1
2
1
1
2
1
1
0
2
1
1
1
1
1
2
1
2
0
2
1
3
1
1
1
0
1
1
2
0
1
1
1
1
2
1
1
1
0
0
1
1
1
1
2
1
2
1
0
1
1
1
1
1
0
2
1
1
0
2
1
1
1
1
1
1
1
2
0
1
0
1
1
1
1
0
1
1
2
0
0
0
0
1
2
1
1
1
2
1
1
1
2
1
1
1
1
1
2
0
1
1
2
1
1
2
2
1
1
0
1
2
1
1
1
1
2
1
2
1
1
1
2
1
1
1
1
2
1
2
1
1
2
1
1
1
2
2
0
1
1
1
0
1
1
1
1
2
2
2
1
2
0
1
1
1
2
0
2
2
1
0
1
1
1
1
2
2
1
1
3
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
0
1
0
1
0
1
1
1
2
2
1
0
1
1
2
1
1
1
2
2
2
1
2
0
2
2
1
1
1
1
2
0
1
1
1
1
3
2
0
1
1
2
0
2
2
2
1
2
1
1
2
1
1
1
1
0
1
1
1
1
2
2
1
0
0
1
1
2
1
0
1
1
1
1
2
2
1
0
0
1
1
1
2
0
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
0
1
1
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
0
1
0
1
1
1
0
1
1
2
2
1
1
1
3
1
2
1
1
1
2
2
3
1
0
1
2
1
1
1
2
2
1
1
1
2
2
2
1
1
0
0
1
1
0
1
2
1
1
1
2
1
1
0
2
1
0
1
1
1
0
2
2
1
1
1
1
2
2
2
2
1
2
1
1
1
2
2
1
1
1
1
2
2
2
1
1
1
1
1
1
1
2
0
1
0
1
1
1
1
2
1
2
1
1
2
1
1
2
2
2
1
2
1
1
1
2
2
1
1
1
1
1
0
1
1
1
2
1
1
2
1
1
1
1
0
1
1
1
1
1
1
1
2
0
1
2
1
2
1
2
1
2
1
1
0
1
1
1
2
1
1
1
1
1
0
1
0
1
1
1
0
2
1
1
1
1
1
2
1
1
1
1
2
0
1
1
2
1
1
2
2
1
1
1
1
1
1
0
2
1
2
0
1
2
1
1
1
0
1
2
1
1
1
2
1
1
2
1
1
1
1
1
1
0
1
2
1
1
2
2
1
2
1
1
2
1
0
0
1
1
0
2
0
1
2
1
1
1
1
2
1
2
1
2
1
1
2
0
1
2
0
2
0
1
1
2
1
0
1
2
2
2
1
2
1
0
1
1
2
1
0
1
1
1
1
1
1
1
0
1
1
2
1
1
1
0
1
2
1
1
2
1
1
1
0
2
0
1
2
1
2
0
1
1
1
2
1
1
0
1
1
2
2
1
2
0
1
1
0
1
0
2
2
1
1
1
1
2
1
2
2
1
2
1
1
1
1
2
1
1
2
1
1
2
1
1
0
1
2
1
1
2
1
1
1
0
1
2
1
0
1
1
1
2
1
1
1
0
1
2
1
2
1
1
1
1
1
1
1
1
0
3
1
1
2
1
1
1
2
0
2
1
1
1
1
2
1
2
1
1
1
1
1
1
2
0
1
0
2
1
2
2
1
2
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
0
1
1
0
2
0
1
1
1
1
2
2
0
2
1
0
1
2
2
2
1
2
1
2
1
1
1
2
1
0
1
1
2
0
1
1
1
1
1
1
1
1
2
1
2
2
2
1
0
2
1
2
2
1
1
1
1
0
1
1
1
1
1
1
2
1
1
2
1
1
1
1
2
0
2
1
1
1
1
1
1
2
0
2
2
2
2
1
1
0
1
2
1
1
1
0
1
1
1
1
2
0
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
2
1
2
1
2
1
1
2
1
2
2
1
1
1
1
2
2
2
1
0
1
0
1
1
1
2
1
1
1
0
0
2
1
1
0
2
2
1
2
1
1
0
0
2
0
1
1
1
1
1
1
2
1
1
2
2
2
2
1
2
1
1
0
1
1
1
0
2
1
2
1
2
1
2
1
1
1
2
1
1
1
1
0
1
2
1
0
0
1
0
1
1
1
2
1
1
2
1
1
2
1
0
1
0
1
1
1
1
3
0
1
0
1
1
1
2
1
1
0
1
1
1
1
1
2
1
1
2
2
1
1
0
1
1
1
1
1
1
1
1
1
1
1
0
1
2
0
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
0
1
1
2
1
1
1
0
1
2
2
2
2
1
0
1
1
1
2
1
2
1
1
1
1
1
0
1
2
1
1
1
0
1
1
2
1
1
1
1
0
1
0
2
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
0
2
1
2
2
1
1
1
1
1
1
0
0
0
1
2
1
1
1
1
0
1
1
0
2
1
0
1
2
1
2
1
1
2
1
1
1
1
1
0
1
2
1
1
1
2
1
1
1
2
1
1
2
2
0
2
1
1
1
1
1
2
1
1
1
1
1
1
0
0
0
1
1
1
0
1
2
2
0
2
0
2
2
1
1
1
1
1
1
0
1
2
0
2
2
1
1
1
1
1
2
2
1
1
2
1
2
1
0
2
1
5
2
1
1
2
1
1
0
0
0
1
0
1
1
0
3
0
1
2
1
1
2
1
1
1
0
1
1
2
1
1
2
2
1
1
1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
0
2
1
0
2
1
0
1
2
1
2
2
2
0
1
1
2
1
1
1
0
1
1
2
2
1
0
2
1
1
2
2
1
1
0
1
1
1
1
1
0
2
1
2
1
2
2
1
1
1
1
1
0
1
1
0
1
1
1
1
1
2
1
1
2
2
1
2
1
1
1
0
2
1
1
1
1
0
2
1
1
2
2
2
1
1
1
0
2
2
1
0
1
1
1
1
1
2
1
2
0
1
2
0
0
1
1
1
1
1
2
1
2
0
1
1
1
2
1
2
2
1
1
1
2
1
1
2
2
1
2
1
2
2
1
1
1
1
1
1
1
0
0
1
2
2
0
0
0
1
1
2
1
2
2
1
0
1
2
2
2
2
2
1
1
1
2
1
2
0
2
1
1
1
0
1
2
1
1
1
1
1
1
1
1
1
1
0
0
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
2
1
2
1
2
1
1
1
1
0
0
1
1
2
1
1
1
1
0
2
2
1
1
1
1
2
2
1
1
1
1
2
1
1
2
1
1
1
1
0
2
1
2
0
2
1
0
1
1
1
2
2
1
1
1
2
0
1
2
1
1
1
1
2
1
1
2
0
2
1
1
0
1
0
1
1
1
0
2
1
1
2
1
1
0
1
2
2
1
1
1
0
1
2
2
1
2
0
2
1
1
2
2
1
2
1
1
1
0
1
1
1
1
1
0
2
1
1
0
1
2
1
1
1
1
2
2
2
0
1
1
2
1
1
1
1
1
1
2
1
2
0
1
1
2
1
2
1
2
1
1
2
1
1
1
1
1
0
2
1
1
1
0
1
2
2
1
1
2
0
1
0
1
1
1
2
2
2
1
1
0
0
1
2
1
2
1
0
2
1
2
2
1
1
2
2
1
1
2
1
2
2
2
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
2
1
0
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
2
2
1
1
0
0
1
0
0
2
2
1
1
1
2
1
1
1
1
1
1
1
0
2
0
1
1
1
0
1
1
0
1
1
1
1
1
1
1
1
2
1
2
2
1
1
2
1
2
1
0
1
1
2
1
2
1
2
2
1
2
2
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
2
2
1
1
1
0
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
2
2
1
2
1
0
2
1
1
1
2
0
1
2
1
1
1
1
1
1
1
1
2
0
2
1
1
2
1
1
1
1
1
1
2
2
1
0
1
1
1
2
2
0
2
2
1
1
1
1
1
2
1
1
2
1
2
0
1
1
1
1
2
1
1
2
2
1
1
2
2
0
1
1
2
2
0
1
1
2
1
1
2
1
2
1
1
2
1
2
1
1
2
1
1
1
2
1
1
1
0
2
1
2
1
2
1
2
2
1
2
1
1
1
1
1
1
1
1
1
2
1
0
1
2
0
2
0
0
1
2
0
0
1
1
1
1
1
1
1
1
1
2
0
1
1
0
0
2
1
1
1
1
0
0
1
1
2
2
2
1
1
1
1
2
1
1
2
2
0
1
1
2
1
1
1
1
1
1
0
2
1
2
2
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
0
1
1
2
1
2
2
1
2
1
1
1
0
2
1
1
1
2
1
1
2
1
1
1
2
1
2
2
0
1
2
2
1
1
2
2
1
1
1
1
2
1
0
1
1
1
2
2
1
2
1
2
2
2
2
2
1
1
0
2
2
1
1
1
0
1
0
2
1
1
1
1
1
0
2
0
0
1
2
1
1
2
2
1
0
1
1
1
1
0
1
1
0
1
1
2
0
0
2
2
1
1
0
1
0
2
1
1
1
2
2
1
2
2
1
1
1
1
1
1
1
1
2
1
1
3
1
0
1
2
2
1
1
1
2
1
1
1
2
2
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
0
1
3
2
1
1
2
2
1
2
1
2
1
1
2
1
1
1
1
1
1
0
1
2
1
2
2
2
1
1
1
2
1
1
2
1
0
1
1
1
1
1
0
2
2
1
2
1
2
2
1
2
1
1
2
0
1
1
1
1
1
2
1
1
1
1
0
1
2
1
0
1
1
0
1
1
1
1
2
0
0
0
2
0
0
0
2
1
1
1
2
2
1
2
0
1
2
1
1
1
2
1
0
1
1
0
1
1
1
1
0
1
2
2
2
1
1
2
1
1
2
1
1
1
1
1
1
2
1
2
1
1
2
1
1
2
1
1
1
1
1
1
0
0
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
2
1
2
0
2
1
0
1
1
2
0
2
1
1
1
2
0
2
1
1
2
2
2
2
2
1
1
2
1
1
1
2
0
2
2
0
2
0
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
2
0
1
2
2
1
1
2
1
2
2
2
1
0
1
1
1
0
0
1
1
1
1
1
1
2
1
1
1
2
2
1
1
2
1
1
0
2
2
2
2
2
1
2
2
1
1
2
1
0
2
2
1
1
2
1
1
2
2
1
1
2
1
1
2
2
1
1
0
1
0
1
1
2
2
1
1
2
0
1
1
1
1
2
1
1
2
1
2
1
1
1
2
2
0
1
1
1
1
1
2
0
1
1
1
1
1
1
1
1
1
1
0
2
2
1
2
1
1
0
1
2
1
0
1
2
0
0
1
2
1
1
0
2
1
1
2
1
2
1
1
0
0
1
1
1
2
1
1
1
2
2
0
2
2
1
0
0
1
1
1
2
1
1
1
1
1
1
2
1
1
2
1
1
2
2
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
2
1
1
1
1
2
1
2
2
0
1
0
1
1
0
2
1
1
2
1
1
0
2
1
0
1
1
1
2
2
1
1
1
1
2
1
1
1
1
0
1
2
1
0
0
2
1
2
2
2
1
1
1
1
1
1
1
1
3
0
1
1
2
1
1
2
2
1
1
2
1
2
1
1
1
1
1
1
1
2
1
2
0
1
1
2
2
0
1
2
1
1
2
1
0
1
1
3
2
0
1
1
1
1
1
1
1
1
1
0
2
1
1
1
0
1
1
1
2
1
1
1
1
2
1
2
3
2
1
2
1
2
2
2
1
0
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
0
2
2
1
1
1
2
1
2
1
2
1
1
0
1
1
1
0
1
1
1
1
0
1
0
2
1
1
1
1
0
1
1
0
1
2
1
1
2
4
1
1
1
1
1
2
0
0
3
1
2
0
2
2
1
1
2
1
1
1
1
1
1
1
0
1
1
0
0
1
0
1
1
2
1
1
2
2
1
0
1
1
1
1
1
1
2
2
1
1
1
0
2
2
2
2
0
0
1
2
1
1
1
1
1
1
1
2
1
1
1
0
1
1
0
2
3
1
2
2
1
1
1
1
1
1
1
2
0
1
1
1
1
0
1
1
1
2
1
2
1
2
2
1
1
0
2
1
0
2
1
2
1
1
0
1
2
1
2
2
1
2
2
0
1
1
2
2
0
1
0
1
1
1
2
2
1
1
1
2
1
1
0
1
1
2
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
3
1
1
1
0
1
2
2
1
2
2
2
2
1
1
2
0
1
1
2
0
2
1
1
1
1
1
1
1
1
2
1
2
1
2
2
2
1
1
1
1
2
1
1
0
1
0
1
1
2
1
1
1
1
1
1
0
2
0
1
0
0
2
2
1
1
0
1
0
1
2
1
2
1
2
1
2
2
1
0
1
1
1
1
1
1
1
1
2
1
2
1
1
0
1
1
1
1
1
1
2
1
1
1
0
1
1
1
1
1
0
1
2
1
1
2
0
1
1
0
1
0
2
1
2
1
1
1
1
2
1
1
0
1
1
1
2
2
1
2
1
2
0
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
0
2
1
1
2
0
1
1
1
2
1
1
1
1
1
2
2
2
1
2
1
1
1
1
0
1
2
2
2
1
1
1
1
3
1
1
1
1
1
2
1
2
2
2
2
2
1
1
2
1
2
1
1
1
1
1
2
1
1
1
0
2
1
0
1
1
2
1
2
1
1
2
2
1
1
1
0
2
1
1
1
1
0
1
1
1
0
1
1
1
0
5
1
1
1
1
1
0
1
1
2
1
1
1
1
2
1
2
1
2
2
2
1
1
1
1
1
1
2
1
1
0
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
0
2
0
2
1
1
2
1
1
2
0
1
1
2
1
1
1
0
0
1
1
2
1
1
1
2
1
0
0
1
1
1
0
1
1
2
1
1
2
1
2
2
0
1
1
1
2
1
0
1
2
1
1
1
2
1
2
2
1
1
1
2
1
1
0
1
2
0
1
1
1
1
1
0
0
1
1
1
1
1
2
1
2
0
0
1
1
2
0
2
1
1
3
1
0
1
0
1
2
2
1
1
2
1
1
1
1
1
1
2
1
0
1
2
1
2
1
2
1
2
2
2
1
1
1
2
0
0
1
1
1
1
1
0
0
1
0
1
1
1
1
2
0
1
1
0
1
1
1
1
2
2
2
0
2
1
0
1
1
1
2
1
1
1
2
1
2
2
1
0
1
1
2
2
2
1
1
1
2
1
1
2
3
1
2
1
1
1
2
2
1
1
1
2
2
1
1
1
1
2
2
0
1
1
2
2
1
1
1
1
0
0
1
2
2
1
2
0
1
1
1
0
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
2
1
1
2
2
0
1
2
1
1
0
1
1
2
2
2
1
0
1
2
1
1
1
2
1
1
0
1
1
2
1
2
1
0
2
1
1
2
1
1
2
1
2
2
1
1
2
0
2
1
1
1
2
1
1
0
1
1
1
1
1
1
2
1
2
3
1
1
1
1
2
1
1
1
2
1
0
2
3
1
0
1
0
1
1
1
1
2
1
1
2
1
1
0
0
2
1
2
2
1
1
0
0
2
1
1
2
2
1
1
1
0
1
1
1
1
2
0
0
1
1
0
0
1
1
1
2
0
1
1
1
1
2
0
1
1
2
3
1
1
2
2
1
1
1
1
1
2
1
0
1
2
0
4
2
1
0
1
0
2
1
1
1
2
0
2
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
0
2
1
1
2
0
2
2
2
0
1
2
1
2
2
2
2
2
1
1
2
2
0
1
0
1
1
1
1
1
0
2
1
1
1
2
1
3
0
1
1
1
1
2
1
2
1
2
0
1
1
1
1
1
1
2
2
1
2
2
1
1
2
1
1
1
0
1
1
1
2
1
1
2
1
1
0
1
1
1
2
1
1
0
1
0
0
0
1
1
0
1
1
1
1
1
2
1
0
1
1
2
0
1
2
1
1
1
1
0
1
1
1
1
1
2
1
1
1
2
1
1
1
1
0
2
1
2
1
1
2
2
2
2
1
1
1
1
1
1
1
2
0
2
1
0
1
2
2
1
3
1
1
0
1
1
1
1
2
0
1
0
1
0
1
0
2
1
2
1
1
1
2
1
2
1
1
2
1
2
1
1
0
2
2
1
2
1
1
1
1
1
0
1
1
2
1
0
1
2
1
1
1
2
1
1
1
1
1
2
2
2
1
1
2
0
2
2
1
1
1
2
2
2
1
0
0
2
1
1
1
1
1
1
2
3
1
1
1
1
0
1
1
2
2
2
1
1
1
4
1
2
1
1
0
1
1
1
1
1
1
1
1
2
1
1
0
2
1
2
1
1
0
1
1
1
1
1
1
1
1
1
1
2
0
2
2
0
1
1
1
1
2
0
0
1
0
2
1
0
2
1
1
2
0
1
1
0
2
2
1
1
2
2
1
2
2
1
1
0
2
2
2
0
1
1
0
1
0
1
2
0
1
0
1
1
1
1
1
1
0
1
2
1
2
1
0
1
0
0
0
2
1
1
2
1
1
1
2
1
0
1
1
1
1
2
1
2
1
0
2
1
1
1
1
2
1
1
2
1
2
0
2
2
1
1
1
1
1
1
1
1
2
1
1
0
1
1
1
0
1
2
1
2
1
2
0
2
1
2
2
1
1
2
2
1
1
1
0
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
0
2
0
2
1
1
1
1
2
1
1
1
1
1
0
1
1
1
0
1
1
2
2
2
1
1
1
1
1
1
1
1
1
2
2
1
2
1
1
1
1
0
1
1
2
1
1
1
1
2
0
1
2
1
2
1
2
0
1
2
1
1
1
1
1
1
1
1
2
2
1
1
0
1
2
4
1
0
2
2
1
1
2
1
1
1
1
1
1
0
0
1
1
1
2
2
1
1
1
2
1
0
0
2
1
0
1
2
1
3
0
2
1
1
1
2
1
1
2
1
2
2
2
1
0
1
1
2
0
0
1
1
1
2
1
2
1
0
2
1
1
1
1
2
0
0
2
1
0
1
1
1
2
1
1
2
1
1
2
2
1
1
2
1
1
2
2
1
2
3
1
1
1
3
1
0
1
1
1
0
1
1
1
2
0
0
2
0
2
1
1
0
2
2
1
2
1
1
2
1
1
1
1
1
2
2
1
1
0
1
1
2
0
2
1
1
2
1
1
1
1
2
2
0
1
1
1
1
1
2
1
1
1
2
2
1
1
1
2
2
1
0
1
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
0
1
2
1
1
1
2
3
1
1
0
1
0
0
1
1
2
0
1
1
1
0
1
1
2
1
2
1
1
2
1
1
1
1
1
1
1
0
0
0
0
1
1
2
1
2
0
1
2
2
2
1
1
1
2
1
2
1
1
2
1
1
1
1
2
1
1
2
2
0
1
1
1
1
2
2
1
1
1
0
1
1
1
2
2
0
1
1
1
1
0
0
0
1
1
0
0
1
1
1
2
1
1
1
1
1
0
1
1
1
0
2
2
1
1
0
1
0
1
1
0
0
2
2
2
1
1
2
1
1
1
1
1
2
2
1
2
1
0
1
1
0
0
1
0
0
1
1
1
0
2
2
1
2
2
0
1
1
2
1
1
3
2
0
1
1
2
1
1
1
1
2
1
2
2
1
1
1
1
1
1
2
2
1
2
1
0
1
2
0
0
1
2
1
1
2
1
1
1
1
1
1
1
1
2
0
1
1
0
1
1
1
1
1
0
2
1
1
2
1
2
1
1
1
2
0
2
1
1
1
0
1
1
2
2
1
0
1
1
2
2
1
1
1
2
0
0
0
2
1
1
0
1
1
1
1
1
0
1
2
1
1
2
1
2
2
0
0
1
1
1
1
1
2
1
0
2
0
0
1
0
1
1
0
1
1
2
1
2
1
1
2
0
1
1
1
2
1
1
0
1
2
0
1
2
2
2
2
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
0
1
1
2
0
2
0
2
1
2
1
2
2
1
0
2
2
1
1
1
1
1
1
1
1
2
0
1
2
0
1
1
2
1
2
1
0
1
1
1
1
1
2
0
1
1
1
1
1
1
1
1
2
2
1
2
2
1
1
1
1
2
0
1
1
1
1
1
1
0
1
1
0
1
1
1
1
1
2
2
1
1
2
1
0
1
2
1
1
0
0
0
2
0
1
1
2
1
1
1
1
0
1
1
1
1
1
1
1
0
1
0
0
0
2
1
1
2
1
2
1
2
0
1
2
1
1
1
1
1
2
0
1
1
0
1
1
2
1
2
1
1
1
1
1
1
1
2
0
2
2
2
1
1
2
1
1
2
1
0
0
2
0
2
1
2
1
2
1
1
1
0
2
1
2
1
1
0
1
1
1
1
2
1
2
2
2
2
0
2
2
2
1
1
1
1
1
1
1
2
2
1
1
1
0
2
1
2
2
0
0
1
2
2
1
2
0
2
1
1
2
0
1
1
1
2
2
1
0
1
1
1
0
1
1
1
1
2
1
1
1
2
1
0
2
2
2
1
0
0
1
0
1
1
1
0
0
1
2
1
1
2
1
2
1
1
1
2
1
1
0
1
1
0
1
1
0
1
2
1
2
0
0
0
2
1
1
1
1
1
1
2
2
0
1
2
0
2
0
1
2
2
1
1
2
2
1
1
2
2
1
2
1
2
1
1
1
1
2
1
2
2
2
1
4
1
1
0
2
1
1
0
2
2
1
1
1
1
1
2
0
2
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
0
1
1
1
2
1
1
1
1
2
2
0
1
1
1
1
1
0
1
1
2
1
1
1
1
0
2
0
0
3
1
1
2
2
2
1
2
1
1
2
2
1
2
0
1
1
2
1
1
2
1
0
0
1
2
0
2
1
1
2
2
1
1
0
2
1
1
1
1
1
2
1
1
1
0
1
1
1
1
1
1
3
2
2
1
2
1
2
2
0
2
2
1
1
1
1
0
0
1
1
1
2
1
1
0
1
1
1
2
1
0
2
2
1
0
1
0
1
2
1
1
2
0
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
2
0
1
1
2
0
1
1
1
1
1
1
1
2
1
1
0
1
1
2
1
1
0
2
1
2
2
1
3
0
0
1
1
1
2
1
1
1
2
1
1
1
1
1
2
1
2
2
1
2
2
0
1
2
1
2
1
1
1
2
1
1
0
2
1
2
1
1
1
0
2
1
1
2
2
1
2
1
1
1
2
0
1
1
1
1
1
2
0
1
2
2
1
1
0
2
1
2
2
1
1
2
0
1
0
2
0
0
1
1
1
1
1
2
1
1
1
2
1
2
2
0
0
2
1
0
1
2
1
2
2
2
1
0
0
1
3
2
1
2
1
1
1
0
0
1
1
1
1
1
1
2
1
1
0
1
2
2
0
1
1
2
0
1
1
1
2
1
1
0
1
1
1
0
2
1
1
2
2
3
1
1
1
1
2
2
0
1
2
2
1
2
1
2
2
1
2
0
1
1
0
1
1
0
2
1
1
2
1
2
1
2
2
1
2
1
0
2
2
1
2
1
1
1
4
1
1
1
1
1
0
2
0
0
0
2
0
0
1
0
1
1
2
1
2
1
1
1
1
0
2
1
2
2
1
2
0
1
1
2
1
1
2
2
2
1
0
1
2
2
0
1
1
1
1
1
1
2
1
1
0
1
0
0
1
2
1
1
2
0
1
1
1
1
1
0
1
1
1
2
0
1
1
2
1
3
0
0
1
1
1
2
1
2
1
2
2
1
1
2
1
1
2
1
0
2
1
0
1
2
2
1
1
2
2
2
1
1
0
1
2
1
1
2
1
0
1
1
2
2
1
2
1
0
2
2
2
1
1
1
1
0
4
1
1
1
1
0
0
0
1
1
1
1
1
1
1
0
1
1
1
1
1
2
2
0
1
2
2
1
0
1
2
1
2
2
1
1
1
2
2
1
1
1
2
1
0
1
2
1
1
1
0
1
2
1
1
0
1
0
1
1
0
2
2
1
1
1
0
1
1
1
1
1
0
0
1
1
1
1
2
2
2
0
1
2
2
2
2
1
2
0
1
1
0
1
1
2
2
1
2
1
1
1
2
2
1
0
0
1
1
1
1
1
1
1
2
2
1
2
2
1
2
1
0
1
0
2
1
1
1
1
1
1
1
2
0
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
0
0
1
1
1
1
2
1
1
1
2
2
1
2
1
1
2
1
1
1
2
2
2
1
2
2
2
1
2
2
1
1
1
2
2
1
1
2
1
1
1
1
2
0
1
2
2
3
1
1
1
1
2
1
1
1
1
1
1
1
1
1
0
1
1
0
2
1
1
1
1
1
2
1
2
1
1
0
1
2
2
1
2
2
1
1
2
1
1
2
1
1
1
2
1
1
2
1
1
2
1
1
0
1
1
1
0
1
2
1
1
1
1
2
1
3
2
2
1
1
1
2
2
0
2
1
1
2
1
0
1
2
2
1
2
1
1
0
0
1
2
2
1
1
1
1
1
1
1
1
2
2
2
2
0
1
1
1
1
1
1
1
0
0
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
2
2
1
2
2
1
0
2
1
1
1
0
1
1
1
2
1
1
0
1
1
0
0
2
1
0
1
0
2
0
1
2
1
1
1
1
2
0
1
1
1
1
1
1
0
1
1
1
1
1
1
2
1
1
1
1
2
2
1
0
1
1
0
1
1
1
1
2
2
1
1
1
2
0
2
2
0
1
2
1
2
1
1
0
1
2
1
2
3
6
1
0
1
1
0
1
2
0
2
1
0
1
1
2
1
0
1
0
1
1
1
1
1
1
0
1
0
1
1
2
2
1
1
0
2
1
2
2
2
1
1
1
2
1
0
1
2
1
1
1
0
1
3
1
1
0
2
1
1
0
0
2
1
2
1
1
2
1
2
1
0
1
2
1
1
1
2
1
1
1
1
1
2
1
1
1
1
0
1
1
2
1
2
1
1
1
1
1
1
0
1
1
0
1
2
2
2
2
1
2
2
2
0
1
2
2
2
1
1
2
1
1
1
1
0
0
4
1
2
0
1
1
0
1
1
1
1
1
1
2
1
2
2
1
1
1
1
0
1
1
1
1
2
2
1
2
2
1
2
1
1
1
1
1
2
1
1
1
2
0
0
1
2
2
1
3
2
2
1
2
1
2
2
2
2
1
1
0
0
2
1
1
1
1
2
1
1
1
1
0
2
1
1
2
2
1
0
2
2
1
2
1
1
0
1
2
4
0
1
1
1
1
3
1
2
0
1
1
1
1
1
2
1
2
2
1
2
1
1
0
2
0
1
2
1
0
1
2
1
1
1
1
2
1
1
1
1
2
0
2
1
1
1
0
0
2
1
1
1
1
1
2
1
0
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
0
1
2
1
1
2
1
2
0
0
2
2
1
6
1
0
0
0
1
1
1
2
2
2
0
1
2
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
0
1
1
0
2
1
2
1
0
1
1
1
2
2
1
1
1
1
1
2
2
1
0
2
1
0
1
1
2
2
2
2
1
0
1
2
1
1
1
1
2
0
0
1
1
2
1
0
1
0
2
1
2
1
1
1
1
0
1
1
1
1
1
1
1
1
1
2
0
0
1
1
1
1
0
0
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
2
2
0
2
0
1
1
0
1
1
1
1
1
0
2
1
2
1
1
1
1
2
1
1
1
2
2
2
2
0
1
1
1
2
1
1
1
1
1
1
1
1
1
1
0
2
1
1
2
1
1
1
2
2
1
1
1
2
2
2
1
1
1
0
1
1
2
1
1
2
1
2
3
1
2
1
2
1
1
1
0
0
1
1
1
1
3
1
1
1
0
1
2
1
0
1
0
1
1
2
2
2
1
1
1
0
1
1
1
1
1
2
1
2
2
1
0
2
2
1
1
0
0
2
2
1
1
1
2
2
0
1
1
1
1
1
1
0
1
2
2
1
1
1
1
1
1
1
2
0
0
1
0
1
0
1
2
1
1
2
1
2
2
1
0
2
1
1
1
2
2
1
0
1
1
2
2
1
1
1
0
2
0
1
1
1
1
1
1
1
0
1
1
1
1
2
1
2
1
1
2
0
1
1
0
1
1
1
1
0
1
1
1
1
1
1
2
2
1
2
0
1
1
1
2
1
1
1
1
0
1
0
1
1
2
2
2
1
1
1
1
2
1
2
3
1
2
2
0
1
2
1
1
2
1
1
2
4
2
1
1
1
2
1
2
1
1
1
1
1
2
2
2
1
1
0
1
0
1
1
2
0
1
1
0
0
0
1
1
1
1
1
2
0
1
6
1
1
2
1
1
1
3
1
1
0
2
2
1
1
2
0
1
2
2
1
1
0
1
1
0
1
1
2
1
1
1
1
1
2
1
2
1
1
2
0
2
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
0
1
0
1
1
1
1
1
2
2
1
1
0
1
1
1
2
1
1
1
1
1
1
0
1
1
1
1
1
1
0
2
1
1
1
3
1
0
1
2
1
1
2
1
1
2
1
1
0
2
1
1
2
2
1
0
1
2
2
1
1
1
2
1
1
1
1
1
1
1
2
2
1
0
1
1
2
1
1
2
1
1
2
1
1
1
2
1
2
0
1
1
1
2
1
1
2
1
1
2
1
1
1
1
0
1
0
1
1
2
1
1
2
0
2
2
1
1
2
2
0
2
2
1
0
0
1
1
1
1
1
0
2
2
2
2
1
1
0
1
1
1
2
2
0
1
1
1
1
1
1
1
1
1
1
2
1
1
0
0
1
1
2
1
2
0
2
1
1
1
1
1
2
1
1
2
1
0
1
1
1
0
0
1
1
1
0
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
0
1
2
1
2
1
1
1
1
2
1
1
2
1
1
1
0
1
2
2
2
2
2
2
1
0
2
1
1
1
2
1
1
2
1
2
1
0
1
1
1
2
1
1
1
1
2
1
1
2
1
2
0
2
0
1
1
1
1
2
2
1
1
1
1
1
1
2
1
2
1
2
1
1
2
1
1
2
1
0
1
0
1
2
1
0
2
2
0
1
2
1
1
1
2
1
0
2
2
1
2
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
0
2
1
1
1
1
0
0
1
2
1
2
1
1
1
3
1
2
2
1
1
2
2
1
1
2
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
2
2
2
1
1
1
2
1
1
1
2
1
2
1
2
1
1
1
1
1
1
1
1
1
2
1
0
1
1
1
1
2
0
1
1
0
1
1
1
0
1
1
1
1
1
2
1
1
1
1
1
0
2
0
1
2
1
1
1
1
1
1
1
1
2
1
1
1
0
1
2
2
1
1
1
1
2
1
1
1
1
0
1
2
0
0
0
0
2
1
2
1
1
0
1
1
0
3
2
1
1
0
2
1
2
1
1
1
2
1
1
1
2
1
0
2
1
1
1
1
2
0
1
1
1
1
2
1
1
1
1
1
3
0
2
1
2
0
2
1
0
2
1
0
1
1
1
1
2
1
1
0
1
1
1
0
1
1
1
2
2
1
2
1
2
1
1
0
1
2
1
1
1
1
1
1
0
2
2
0
1
2
1
1
1
2
0
2
0
1
2
2
1
1
1
0
0
2
2
1
1
2
1
1
1
2
1
1
0
1
1
1
1
1
0
1
1
1
2
1
2
2
0
1
2
1
1
2
1
0
2
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
2
0
1
1
1
2
1
2
1
1
1
2
1
0
1
1
1
1
1
1
1
1
1
1
2
2
1
0
1
2
2
1
2
1
1
1
1
1
1
1
3
1
1
1
2
1
1
1
2
1
1
1
1
1
2
1
0
1
1
1
2
1
1
1
1
0
2
1
1
2
0
1
1
1
2
1
2
0
0
1
2
0
1
0
2
2
1
1
2
2
2
0
0
1
1
1
1
2
2
1
2
1
1
2
1
1
1
2
2
0
1
1
2
1
1
1
1
2
1
1
1
1
0
2
1
1
1
1
1
1
0
1
1
0
2
1
2
1
2
1
1
2
1
1
1
1
1
2
0
1
1
1
3
2
1
2
1
1
1
1
0
0
0
1
1
1
1
0
2
0
1
1
2
0
1
0
1
1
1
2
2
2
1
0
0
2
1
0
2
1
1
2
1
0
2
1
2
2
1
1
2
1
1
0
1
1
0
1
2
1
0
2
2
1
1
1
1
1
0
1
1
2
1
1
2
0
1
2
2
2
1
2
0
1
2
1
1
0
1
1
1
2
1
0
0
2
1
1
1
1
0
1
1
1
2
0
2
1
1
1
1
2
2
2
1
2
1
1
2
1
1
1
1
2
2
1
2
1
1
1
2
1
0
2
1
2
1
1
1
2
2
1
1
2
1
0
1
1
1
2
1
2
1
2
0
1
2
2
2
1
1
2
1
2
2
1
1
1
1
1
0
2
1
1
2
1
1
1
2
2
1
1
0
1
1
2
1
0
1
2
1
1
0
2
1
1
1
2
1
2
2
2
1
1
1
1
2
3
1
0
0
1
1
2
1
1
0
1
2
1
1
2
1
1
0
2
1
2
4
0
0
2
2
1
1
1
1
1
1
2
2
1
2
1
2
1
1
2
1
1
0
1
1
1
1
1
1
2
1
2
0
1
2
2
1
1
1
1
1
0
1
1
0
1
1
0
1
1
1
1
0
1
0
1
1
1
1
1
1
1
1
1
0
1
2
2
2
1
1
1
1
2
1
1
0
1
2
1
1
1
2
1
1
1
0
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
4
1
1
1
1
1
0
0
2
1
0
2
2
2
2
2
2
1
1
0
0
1
1
1
0
1
1
1
1
2
1
1
0
2
1
1
0
2
0
1
2
2
1
2
1
1
0
1
2
1
3
1
0
1
1
1
1
1
1
1
2
2
2
2
0
1
0
0
2
2
1
2
0
1
1
1
1
1
1
1
2
2
0
0
2
1
1
1
2
1
2
1
2
2
1
2
0
1
1
2
2
2
2
1
2
1
1
1
1
0
1
0
0
1
1
1
1
1
0
2
1
1
2
0
1
2
1
0
1
2
2
1
1
2
1
1
0
1
1
2
2
1
1
1
2
0
1
0
0
1
2
1
2
2
1
0
2
1
1
1
2
2
2
3
1
2
1
1
2
2
1
1
1
1
1
1
1
1
0
1
2
1
1
1
1
1
2
1
0
1
1
1
2
1
1
1
1
1
1
2
2
2
1
2
1
1
2
0
1
1
2
2
2
2
2
1
2
1
1
1
2
1
0
1
1
1
1
1
1
1
1
0
2
1
1
2
0
0
1
1
1
1
1
1
0
2
1
1
1
1
1
1
2
1
1
1
1
2
1
2
1
1
0
2
2
1
1
2
1
1
2
1
1
2
1
1
1
1
1
0
1
1
2
2
1
0
1
0
1
2
2
1
1
2
0
1
1
1
2
1
1
2
2
1
1
1
1
1
2
1
0
2
1
2
1
0
2
2
2
1
1
1
1
1
1
1
0
1
2
1
1
1
1
1
1
1
2
1
1
1
2
1
0
1
1
1
1
2
1
1
0
2
1
2
1
2
1
1
1
2
2
0
1
1
1
0
1
2
0
1
0
1
1
1
0
2
2
1
1
1
1
1
1
0
1
2
0
1
1
2
1
1
2
1
2
1
1
1
1
2
1
1
2
1
1
2
0
2
1
2
2
2
1
1
1
2
2
1
1
1
1
1
0
1
1
1
2
1
1
1
1
2
1
1
1
1
0
1
0
2
0
1
0
0
1
2
2
2
2
2
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
0
1
1
2
1
1
2
2
2
0
2
2
1
2
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
2
1
1
2
1
1
0
1
1
2
1
1
1
2
1
2
0
0
1
2
0
1
1
1
1
2
1
1
1
1
2
1
1
1
2
2
1
0
1
2
1
1
2
1
1
1
1
0
1
1
1
2
0
2
2
1
1
1
1
6
1
2
1
1
2
2
1
2
1
2
2
1
1
2
2
1
1
3
2
1
0
1
1
1
1
2
1
1
2
1
1
0
1
1
1
0
2
1
1
1
1
1
1
0
1
0
2
0
2
1
2
1
1
0
1
1
1
1
1
1
1
2
2
1
2
2
1
1
2
1
1
2
2
2
1
1
0
2
1
1
1
2
1
1
1
2
1
1
2
1
1
2
2
2
1
1
2
1
2
1
2
1
0
1
1
1
2
1
1
1
1
1
2
2
1
1
2
2
1
2
1
1
1
1
2
1
0
1
0
1
1
2
2
2
1
2
1
0
1
2
2
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
0
1
1
2
2
1
1
1
1
1
0
1
1
1
1
2
1
2
2
2
5
2
1
2
1
2
0
1
1
1
1
1
2
2
1
1
1
2
1
1
2
1
1
1
2
1
1
1
1
1
2
0
1
1
2
1
2
1
1
1
2
1
1
2
2
0
0
2
0
3
2
0
1
1
1
1
1
3
1
1
1
5
2
1
1
2
2
1
0
1
1
1
1
1
2
1
1
2
0
1
1
0
3
1
1
2
1
2
2
1
1
1
2
2
1
0
1
1
2
1
0
1
1
1
1
0
1
1
2
1
2
1
1
0
1
1
0
1
2
1
0
1
1
1
1
0
2
2
1
1
1
2
1
1
1
2
1
0
1
2
1
2
1
0
1
1
2
2
2
1
2
2
1
0
1
0
4
0
1
1
2
2
1
1
1
1
0
1
1
1
2
2
2
2
1
2
1
1
1
0
1
2
2
2
1
0
2
2
0
2
1
2
1
2
0
0
1
3
0
1
1
1
1
2
2
1
1
1
0
0
2
1
1
1
2
1
1
1
1
1
1
2
2
0
0
1
2
1
0
1
1
1
1
1
0
1
1
1
0
1
2
1
2
1
1
2
2
1
0
1
0
1
1
1
3
1
0
0
2
1
1
1
1
1
2
2
1
1
1
1
1
2
0
0
2
1
1
1
2
0
1
2
2
1
0
1
2
1
1
2
0
2
2
1
1
2
1
2
0
2
1
2
1
2
1
1
1
2
2
0
1
0
1
1
1
2
1
2
2
1
1
2
1
1
1
1
2
1
2
1
2
1
2
2
1
2
1
0
2
1
1
0
2
1
2
2
1
0
1
2
3
0
1
0
2
0
2
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
2
1
1
0
1
2
0
2
0
1
2
1
1
2
2
1
0
1
1
1
2
1
1
1
1
2
0
2
1
2
0
2
0
0
1
1
2
1
1
1
1
1
2
1
2
2
1
1
1
1
1
0
0
1
1
2
2
2
1
2
1
1
1
0
0
1
2
0
1
1
1
1
2
0
2
2
3
1
1
1
1
2
1
1
1
1
2
2
1
1
2
1
2
2
2
2
0
1
1
1
2
2
1
2
1
1
2
1
2
1
2
1
1
1
2
0
2
1
0
1
1
2
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
0
2
0
1
2
2
0
1
1
0
2
1
1
1
2
1
1
2
1
1
1
1
1
2
1
2
1
2
0
2
1
2
1
0
1
1
1
1
1
1
0
1
1
0
2
2
1
1
0
2
2
2
1
1
1
1
1
2
1
0
2
2
0
0
2
0
2
0
1
1
1
0
1
1
1
0
1
2
0
1
1
1
0
1
1
1
1
2
1
1
1
1
0
1
1
2
1
1
0
1
1
2
1
0
2
1
2
1
1
1
2
0
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
2
1
2
1
1
0
1
2
1
1
0
2
1
1
1
1
0
1
1
2
1
1
1
0
0
1
1
1
2
1
1
2
1
1
1
2
2
0
1
2
1
1
0
1
2
1
1
2
1
1
0
1
1
2
1
2
0
2
2
2
1
2
1
2
1
1
0
2
1
0
1
0
2
1
2
0
1
1
1
1
2
1
0
0
1
1
2
1
2
1
2
1
0
2
0
0
0
0
1
1
1
2
1
0
1
2
2
1
1
1
1
1
1
2
1
2
1
0
1
2
2
2
0
1
1
1
1
1
0
1
1
1
1
0
1
3
1
2
2
1
1
1
1
0
2
2
1
1
1
1
1
1
1
2
0
2
1
1
2
1
2
2
2
0
1
0
1
1
1
0
2
0
1
2
0
1
1
1
1
1
1
1
1
2
1
1
1
2
0
1
1
2
3
2
1
1
1
1
0
1
1
1
0
2
1
1
0
1
1
0
1
1
0
2
1
2
2
1
1
0
1
1
2
0
1
1
1
1
2
1
2
1
1
1
3
1
1
2
2
1
1
1
0
1
1
1
1
2
2
1
1
1
0
2
1
1
0
1
1
1
0
1
2
1
1
0
1
1
2
2
1
1
1
1
1
1
1
1
2
1
2
0
1
2
1
0
1
2
2
1
2
1
0
1
1
2
1
1
1
1
2
1
2
0
2
1
1
1
1
1
2
1
1
0
1
2
2
2
2
1
2
1
1
1
2
1
2
2
2
2
1
1
1
1
1
2
1
2
1
1
0
1
1
1
1
1
1
1
0
1
2
1
2
1
1
2
2
0
1
2
2
1
1
1
1
1
0
2
0
1
2
1
2
1
1
1
2
0
1
1
1
1
1
0
2
2
2
2
1
1
1
0
2
1
1
2
1
2
1
1
1
2
1
0
2
1
1
1
1
1
1
1
1
1
0
1
1
1
2
1
0
0
2
2
1
1
1
2
1
2
1
1
1
1
1
1
1
2
2
1
1
1
0
1
1
1
2
1
1
2
1
1
1
1
2
2
1
1
1
2
1
1
1
1
0
1
2
2
2
1
1
1
2
1
1
1
0
1
2
1
1
0
2
2
1
1
0
1
1
2
0
0
1
1
2
1
1
1
1
2
3
1
1
0
1
2
2
0
1
1
1
1
1
2
1
1
2
2
2
1
1
2
2
0
2
2
2
2
0
2
1
1
1
1
2
1
2
1
0
2
1
1
0
1
0
1
1
1
1
1
1
0
1
0
2
1
1
1
2
2
2
1
0
1
1
3
0
0
1
2
1
1
1
0
2
2
2
1
1
2
0
1
1
0
2
1
1
1
1
2
0
1
2
1
1
1
0
1
0
1
1
2
1
1
1
1
1
1
1
1
2
1
0
2
1
1
2
2
1
2
1
0
0
1
1
1
1
2
1
0
1
2
1
1
1
1
1
1
0
1
0
2
2
1
1
0
2
2
0
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
0
1
1
2
1
1
1
1
1
2
2
2
1
1
2
1
1
2
2
1
2
1
2
1
2
1
2
3
1
1
0
2
2
2
1
1
0
1
1
1
1
0
1
0
0
1
1
1
2
1
0
2
1
2
1
2
1
1
2
1
1
0
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
2
1
1
2
2
5
2
1
1
1
2
1
2
0
0
1
2
0
0
1
2
2
1
2
0
1
1
1
2
1
1
2
0
1
0
0
2
2
1
1
1
2
1
1
2
1
1
2
1
2
1
3
1
1
1
1
1
2
1
2
1
1
2
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
0
1
1
1
1
1
1
0
1
0
2
1
1
1
1
1
1
2
1
1
0
1
1
1
1
1
2
1
2
1
0
1
2
1
1
1
2
2
0
1
2
6
1
1
1
1
1
1
1
1
1
2
2
2
2
1
0
1
1
2
1
2
1
1
0
1
1
1
2
2
2
1
1
2
0
1
1
1
1
1
1
1
0
1
1
2
0
1
0
1
1
2
1
1
2
2
1
1
0
1
1
1
3
2
2
2
2
0
1
2
1
1
2
2
1
2
1
2
2
2
2
1
1
1
1
2
2
2
4
2
1
1
1
1
1
1
1
2
1
2
2
1
2
1
2
2
1
2
1
1
1
2
0
1
1
1
1
1
0
1
0
2
2
1
0
2
1
1
1
1
1
1
1
0
1
2
0
1
1
0
1
1
1
0
2
0
0
1
2
1
0
1
1
2
1
0
0
2
1
1
2
0
1
1
1
2
1
0
1
1
2
0
2
2
0
1
2
0
2
1
0
2
1
0
1
1
1
1
1
1
1
0
1
1
1
2
1
0
1
2
1
1
1
1
1
2
1
1
2
2
1
1
2
1
1
1
2
0
1
1
1
1
1
1
1
3
1
0
0
1
2
2
1
0
2
1
2
2
0
1
1
1
2
0
0
1
1
1
0
2
2
1
1
1
1
1
2
0
1
0
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
1
1
2
0
1
0
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
0
1
1
2
1
0
2
0
1
1
2
1
1
1
1
1
2
2
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
1
0
1
1
1
0
1
1
2
1
0
1
2
1
1
1
1
1
1
2
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
2
2
1
2
1
0
1
2
1
1
2
1
1
1
2
2
1
0
2
2
0
0
1
1
1
1
2
0
1
1
1
2
1
2
1
1
0
1
1
1
1
0
2
1
1
1
1
0
2
1
1
2
1
0
1
1
1
0
1
0
1
1
2
0
1
1
1
1
1
1
0
0
1
0
0
1
1
1
0
1
1
1
1
1
0
1
2
1
0
1
1
1
1
2
1
1
0
1
1
1
2
1
1
1
1
2
2
1
2
2
2
0
1
2
2
0
1
1
1
1
1
2
2
2
1
1
2
2
2
2
2
1
1
2
1
1
1
1
2
1
0
0
1
1
1
2
2
2
1
2
2
1
1
0
1
1
1
2
1
2
2
2
2
2
1
1
1
1
1
0
2
2
2
2
1
2
0
1
1
2
2
2
1
1
2
1
1
1
1
1
2
2
2
1
1
1
1
1
1
0
2
2
1
1
2
1
1
1
1
1
1
0
0
2
0
1
0
1
2
2
1
1
1
1
2
2
1
2
2
1
1
1
1
2
0
1
1
1
1
1
2
1
0
2
1
0
1
1
1
1
1
1
2
2
1
1
1
1
1
2
1
0
2
2
1
1
1
1
1
1
1
0
1
1
1
2
2
1
2
1
2
2
1
2
2
2
1
2
1
1
2
1
1
0
0
1
1
1
1
2
1
2
2
1
1
0
2
1
1
1
0
2
2
1
1
2
2
1
1
1
0
1
1
2
1
0
2
2
2
1
2
1
1
2
1
2
1
2
0
2
2
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
0
0
1
1
1
1
1
1
1
2
2
1
0
1
0
1
2
2
1
2
1
1
1
1
1
1
0
1
1
0
1
1
1
0
1
2
1
1
1
0
1
1
1
1
1
1
2
2
1
2
1
1
1
2
1
0
2
0
1
1
1
0
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
1
0
1
2
1
1
1
1
0
1
1
1
0
1
0
1
1
1
1
1
1
2
1
1
1
1
1
1
1
0
1
0
1
2
1
2
1
1
1
1
1
2
1
1
1
2
2
2
1
1
2
0
2
1
1
1
0
1
1
2
2
1
2
1
1
2
0
1
1
1
2
2
1
2
0
1
1
1
1
2
0
1
0
0
2
1
1
2
2
2
1
2
1
1
0
1
1
1
1
0
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
0
1
1
2
0
1
0
1
1
1
1
1
1
2
1
2
1
1
2
2
1
0
1
1
2
2
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
0
2
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
0
1
1
0
2
2
1
0
1
1
1
1
3
1
1
2
1
2
1
2
1
2
2
1
1
2
1
1
1
2
0
1
1
2
1
1
0
2
1
1
0
1
1
1
1
0
2
0
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
1
2
2
2
2
0
2
2
1
2
1
2
1
2
1
1
1
1
1
1
2
2
0
1
1
1
2
1
2
1
1
1
2
0
1
1
1
1
1
1
1
2
1
1
2
2
1
0
1
1
0
2
2
1
0
1
2
1
1
2
0
0
1
1
1
1
1
2
1
1
1
2
2
1
1
0
2
1
0
1
1
1
0
3
2
1
1
2
1
2
1
2
2
2
2
1
1
0
1
2
1
1
0
1
1
1
1
1
1
1
1
1
0
2
0
0
2
1
1
1
0
0
2
0
1
1
2
1
0
1
2
0
1
1
0
1
1
1
1
0
1
1
1
1
2
2
2
2
0
1
1
2
2
2
1
1
1
2
1
2
1
2
1
1
1
1
2
2
1
2
2
0
1
1
2
2
1
2
1
2
1
1
1
1
1
1
1
1
2
2
0
0
1
1
1
1
1
1
1
1
1
1
2
1
0
0
2
2
1
0
1
1
2
1
0
1
1
1
2
0
1
1
0
1
1
1
1
2
0
2
0
2
0
0
2
1
2
0
1
1
1
1
1
0
2
2
2
2
2
2
1
2
1
1
2
1
2
2
2
2
2
1
1
1
1
1
2
2
2
1
2
2
1
1
0
0
0
1
1
1
0
2
2
2
1
1
1
1
1
1
1
1
1
2
1
0
0
0
1
1
1
1
0
2
0
2
2
1
1
1
1
1
1
2
1
0
2
1
1
1
1
1
1
0
1
1
2
1
3
1
1
1
1
0
1
1
1
1
0
2
1
1
1
2
2
0
2
1
2
2
1
1
1
1
1
0
2
1
1
2
1
2
2
1
2
2
2
1
2
1
2
1
1
1
1
1
1
0
1
1
1
1
1
2
1
1
0
1
1
1
1
1
1
2
1
0
1
2
1
2
1
1
1
1
2
2
1
0
1
2
1
0
2
1
2
2
1
2
2
2
2
1
1
1
1
2
1
1
1
2
0
1
2
2
2
1
1
0
2
1
1
1
1
1
0
1
2
1
1
2
1
2
1
1
0
1
1
2
1
0
1
2
1
1
2
1
1
1
1
1
1
2
2
2
1
2
2
0
1
1
1
1
2
0
1
1
2
2
0
1
1
2
1
1
0
0
1
1
2
1
2
2
1
2
1
1
1
2
1
2
2
2
1
1
1
1
1
0
1
0
1
1
2
0
2
2
1
1
1
2
1
1
2
2
2
1
2
1
1
0
1
0
2
1
1
1
1
0
1
1
1
2
2
1
1
1
1
2
2
1
1
0
0
0
1
6
2
2
0
1
2
1
1
0
1
2
2
1
1
1
2
2
1
2
2
1
1
1
1
2
1
1
2
1
1
2
0
6
1
1
2
1
2
2
2
0
2
1
2
2
2
2
1
2
1
0
2
1
0
0
1
1
2
1
0
2
0
1
1
0
1
1
1
1
3
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
0
2
1
0
0
1
1
2
1
1
0
2
2
2
1
2
2
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
0
1
2
1
1
1
1
2
1
1
1
2
2
1
1
1
1
2
1
1
1
2
0
0
1
2
1
1
2
1
2
1
2
0
1
1
2
2
1
1
2
1
1
2
1
0
0
1
2
0
1
1
3
1
1
2
1
2
1
0
1
2
1
1
1
1
1
1
0
1
1
1
1
1
2
0
1
2
1
1
1
2
1
1
0
1
2
0
1
2
2
0
1
2
2
1
1
1
0
1
1
1
1
2
1
1
1
1
2
0
1
2
1
0
2
0
1
2
1
0
1
1
1
1
1
0
1
1
1
2
2
1
1
2
1
1
1
0
2
1
2
0
1
2
1
0
1
3
1
2
2
1
1
1
0
2
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
1
0
0
1
1
1
1
1
2
1
1
0
1
0
1
2
1
2
4
1
1
1
1
1
0
1
1
0
0
1
1
1
1
1
1
1
0
1
1
1
1
1
2
2
2
1
2
1
1
1
2
1
2
0
2
1
1
1
0
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
2
2
1
0
2
1
2
1
2
0
1
1
1
1
1
1
1
2
2
1
1
1
2
1
1
1
1
1
2
0
2
0
0
1
0
0
1
1
0
2
0
1
1
2
1
2
1
1
1
0
1
1
2
1
1
1
0
1
0
1
1
0
1
1
1
1
1
1
2
2
1
2
1
2
1
0
1
1
2
1
1
1
1
2
1
2
1
1
1
0
1
1
1
1
0
1
1
2
1
1
2
2
1
2
1
1
1
2
1
0
1
0
1
1
1
1
1
1
1
1
1
2
2
1
1
5
0
0
1
1
1
1
1
1
0
2
1
1
1
2
1
1
1
0
1
2
1
1
0
0
1
0
1
0
0
2
1
1
1
1
1
0
1
2
1
1
2
1
2
1
1
0
1
1
2
0
1
1
1
1
1
1
1
1
1
0
1
1
2
2
1
0
1
0
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
0
1
1
2
1
1
1
1
2
1
1
1
1
0
2
0
1
2
1
1
1
1
1
1
2
1
2
1
1
2
2
1
1
1
1
2
1
2
1
2
1
1
1
1
1
1
1
0
1
0
2
1
1
1
2
1
2
1
1
1
1
2
1
2
2
0
1
1
1
1
1
1
0
2
2
0
0
1
2
1
2
1
1
2
2
2
2
1
1
2
0
2
1
2
1
0
1
1
1
1
1
1
1
1
1
1
1
2
2
1
0
1
1
1
1
2
4
2
0
1
0
1
0
2
0
1
2
1
1
1
1
1
2
0
2
0
1
1
1
1
0
2
1
2
1
0
1
2
0
1
1
1
2
0
1
0
2
2
1
2
1
1
2
0
2
1
0
1
1
2
2
1
0
1
2
1
0
2
1
1
2
1
1
1
1
2
3
2
2
2
2
1
1
1
1
1
2
1
1
2
1
2
1
1
2
2
1
1
1
0
1
1
1
2
1
0
2
2
1
1
1
0
2
1
1
1
2
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
2
1
1
1
2
1
2
1
2
1
0
1
1
1
1
1
1
2
1
2
1
1
1
1
0
2
1
1
1
1
2
1
2
1
2
1
1
1
1
2
2
2
1
1
2
1
2
2
1
1
1
1
1
1
1
1
2
0
1
2
2
1
2
0
1
2
1
0
2
1
2
1
2
1
1
2
2
2
1
1
4
1
0
1
1
1
1
1
0
2
0
1
1
2
1
1
1
2
1
2
0
1
2
0
2
1
1
1
2
1
1
2
1
1
1
1
4
0
1
1
2
2
1
1
2
0
2
2
1
1
1
1
1
0
1
1
2
1
1
1
1
1
1
3
1
1
1
2
2
2
1
2
2
1
3
1
2
2
1
2
1
2
1
2
1
1
1
2
0
1
1
2
2
2
0
1
2
1
1
2
2
2
1
1
2
1
1
0
1
1
2
2
2
1
1
1
1
2
2
2
1
1
1
1
2
2
1
1
1
2
2
1
2
2
1
2
2
2
2
1
0
0
1
1
1
2
1
1
0
1
2
1
1
1
0
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
2
0
1
1
1
2
1
0
1
0
0
1
1
1
0
1
2
1
1
1
1
0
1
1
2
2
2
0
1
2
2
0
0
2
2
1
1
1
1
1
2
1
0
1
1
1
1
0
2
1
2
1
0
1
1
0
1
1
0
2
2
1
1
1
1
1
2
1
1
0
0
2
1
1
1
2
2
1
2
1
1
1
1
1
0
1
1
1
0
1
1
1
2
1
1
1
1
2
1
1
1
2
1
1
1
2
2
0
0
1
2
1
1
2
2
0
1
1
2
1
0
1
1
2
0
1
2
1
1
1
0
1
0
1
1
1
1
1
1
1
1
2
1
0
0
1
1
2
1
2
1
1
1
2
2
1
0
2
1
1
0
0
1
2
1
1
1
1
0
1
2
1
2
2
0
1
0
1
2
1
1
1
1
1
2
2
1
1
1
2
2
1
2
1
1
1
2
1
0
1
1
2
2
2
1
1
1
2
1
1
1
1
0
1
1
2
1
1
1
1
1
2
1
1
2
0
1
2
1
0
1
1
2
1
0
0
2
1
1
1
1
1
1
2
2
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
2
1
1
1
2
1
1
1
2
0
1
0
1
0
1
1
1
1
2
0
2
0
2
1
2
0
2
1
1
2
0
1
1
1
1
1
1
1
1
1
2
2
1
2
0
1
1
1
1
2
2
1
2
1
0
1
0
2
2
1
1
1
0
1
1
1
1
1
1
1
2
1
1
0
1
1
1
1
2
1
1
1
1
1
2
1
2
0
0
1
1
2
1
2
1
0
2
1
1
2
2
1
1
2
1
2
2
1
1
2
1
1
2
2
1
2
2
2
1
0
0
1
1
1
1
1
2
1
1
1
1
1
0
0
0
0
1
1
2
2
1
1
1
1
1
2
0
1
1
0
1
1
1
1
1
2
1
1
2
1
3
2
1
2
0
1
1
1
1
1
2
1
1
0
0
1
1
1
1
1
2
1
1
1
2
1
2
1
1
2
1
0
0
1
1
1
1
1
1
1
2
2
1
2
2
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
0
0
0
1
2
2
2
2
2
1
1
0
0
1
1
1
1
2
0
0
2
1
1
2
0
1
2
2
2
1
1
2
0
2
2
1
0
1
2
1
2
0
1
2
1
1
1
1
1
1
0
2
1
1
0
1
1
1
1
0
1
0
1
0
1
2
1
1
0
1
2
1
0
2
2
2
1
1
1
1
2
1
1
2
0
1
0
1
1
2
1
2
1
2
2
2
1
2
1
1
2
0
1
0
1
1
1
1
0
1
1
1
1
2
0
1
2
1
0
1
1
1
1
2
1
1
1
0
2
1
2
1
0
2
0
1
1
2
1
1
1
1
1
1
1
1
0
1
1
2
1
0
2
0
1
1
2
2
0
1
2
1
2
2
1
2
1
2
1
1
1
0
0
2
1
2
1
1
1
1
2
1
1
1
0
1
0
0
1
1
1
0
1
2
1
1
0
1
1
1
0
1
0
1
0
1
0
2
2
2
2
1
1
1
1
1
2
1
2
2
1
1
2
1
2
2
0
1
2
1
1
1
0
2
1
1
0
0
2
1
2
1
2
2
1
2
0
2
1
1
2
1
1
2
1
1
2
1
1
1
1
1
1
0
1
2
1
1
2
2
1
1
1
1
1
0
2
3
2
1
1
1
1
0
1
1
2
1
1
1
0
1
1
1
0
1
1
2
1
0
2
1
1
1
1
1
1
0
2
2
2
2
1
1
1
2
1
0
2
2
1
1
1
1
0
1
1
2
2
1
0
1
1
1
1
1
2
1
0
2
2
1
2
1
1
1
1
0
1
3
1
2
2
2
0
0
1
1
1
2
0
1
1
1
2
1
1
1
0
1
1
0
2
2
1
0
1
1
1
2
1
1
2
2
2
1
1
1
1
1
1
2
2
1
1
0
0
1
1
1
1
1
0
1
0
0
1
2
1
1
1
1
1
2
2
1
2
1
1
2
0
1
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
0
2
1
2
1
1
2
2
1
2
1
1
1
2
1
2
1
0
0
1
1
1
0
2
1
1
1
1
1
1
1
1
1
0
1
0
1
1
1
2
2
0
1
1
2
1
1
1
2
1
1
1
2
2
0
0
2
0
1
1
1
1
0
1
2
2
1
1
2
2
0
2
1
1
2
0
1
0
1
2
0
1
1
1
0
1
1
3
1
1
1
2
1
0
1
2
2
2
1
1
2
1
1
1
1
2
1
1
1
2
2
0
2
2
1
1
2
2
1
1
1
2
1
1
0
2
2
2
1
2
1
1
1
2
1
1
1
0
1
1
2
0
1
1
2
2
1
0
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
0
2
1
1
1
1
1
0
0
1
0
2
1
1
1
1
1
1
1
1
1
0
2
0
0
0
2
1
1
1
1
2
1
1
1
2
2
2
2
2
2
1
2
1
1
1
2
1
0
1
1
2
1
1
1
2
2
2
1
2
2
2
2
1
0
1
1
2
1
1
0
2
1
1
0
1
1
1
1
1
0
0
1
1
1
1
2
1
1
2
3
2
1
1
1
1
1
1
1
1
1
0
1
0
1
1
1
1
1
1
1
1
1
2
2
1
1
1
0
2
1
3
2
2
1
1
0
1
2
2
1
1
0
2
1
1
2
1
2
0
2
1
1
2
1
1
1
0
2
2
1
1
1
1
1
1
1
1
1
1
2
1
0
2
2
2
1
2
1
1
1
0
2
2
1
1
2
0
2
1
1
1
2
1
1
2
2
1
1
2
1
2
1
1
0
2
0
2
1
2
1
1
2
0
1
2
0
1
1
2
1
1
2
1
2
1
0
1
1
1
2
1
2
1
1
0
1
1
1
0
0
0
1
2
1
2
1
1
1
2
1
1
1
1
1
2
1
0
2
0
2
1
1
1
1
0
1
2
1
1
1
0
1
1
1
1
0
1
2
0
2
2
1
1
1
1
2
0
1
2
1
2
1
2
1
2
1
1
2
2
1
1
2
2
1
1
2
1
1
2
1
1
2
1
1
2
1
1
0
2
3
1
1
1
1
2
1
1
1
1
2
1
1
2
1
0
1
2
2
2
1
0
2
1
1
2
1
1
2
2
2
2
0
1
1
1
1
2
2
1
1
1
1
0
1
0
1
1
0
2
0
0
2
1
0
1
1
1
1
1
1
1
1
0
1
1
1
0
0
0
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
2
2
2
1
2
2
2
1
0
1
1
1
1
2
1
1
1
1
2
1
2
2
1
2
1
2
1
0
1
1
1
1
1
2
0
1
1
1
2
1
2
0
1
1
1
1
2
1
1
1
1
2
0
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
2
2
2
1
1
1
1
1
2
1
1
0
1
1
1
1
1
2
1
1
0
1
1
1
1
1
1
1
2
1
1
1
1
0
1
1
1
2
1
2
2
1
1
2
1
1
1
1
2
2
1
2
1
1
1
1
1
1
2
1
2
1
1
0
2
1
1
2
2
1
1
1
1
1
2
1
2
2
2
1
1
1
1
0
1
1
1
2
2
3
1
1
3
1
1
0
2
1
0
1
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
2
1
0
2
2
1
1
1
0
2
1
2
1
2
2
2
1
1
2
1
2
2
1
1
1
2
2
2
2
1
0
0
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
2
2
0
1
1
1
1
1
1
1
1
1
0
1
2
1
2
2
2
1
2
1
1
1
1
2
1
1
2
0
1
1
1
1
2
1
1
1
2
1
1
2
1
1
1
1
1
1
1
2
2
1
3
0
1
2
2
0
0
2
2
1
1
1
1
1
1
1
1
1
1
0
1
1
0
1
2
5
1
0
2
0
0
1
2
0
1
1
2
2
1
1
2
1
1
2
2
3
1
1
2
1
1
1
1
1
2
1
1
1
2
0
1
0
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
2
2
1
2
2
1
0
2
1
2
1
0
0
1
2
0
1
2
1
2
2
2
1
1
0
2
1
1
1
1
1
2
0
1
1
1
1
1
2
1
2
2
0
1
2
1
1
2
1
2
1
2
1
2
2
1
1
2
1
1
1
0
1
1
0
1
1
0
0
2
1
1
1
1
1
1
1
2
1
1
1
1
1
0
1
1
1
0
2
0
1
1
1
2
2
1
1
1
0
1
2
1
1
1
2
1
1
1
1
2
2
1
1
2
2
2
0
1
2
1
2
1
1
2
1
2
1
2
1
1
2
1
1
2
2
1
1
1
0
1
1
0
2
1
1
1
1
1
1
0
1
0
1
1
1
1
1
1
0
1
2
0
1
1
2
1
0
2
2
2
2
1
0
1
1
1
1
1
1
2
2
1
2
1
1
0
1
1
2
0
1
2
1
1
0
1
1
1
1
1
1
1
2
1
2
0
1
1
1
2
2
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
2
0
1
2
1
1
2
1
1
1
1
0
0
1
2
2
1
0
1
1
2
0
1
1
1
2
1
1
1
2
2
2
1
1
1
2
0
2
2
1
2
2
1
1
2
2
1
1
1
1
1
1
1
0
1
1
0
1
1
2
0
1
1
1
1
0
1
1
1
1
2
1
2
0
1
2
1
1
2
1
1
0
1
2
2
2
1
1
1
2
1
1
2
0
2
1
1
0
0
0
1
1
1
1
1
1
0
1
0
2
1
1
1
1
2
2
1
0
1
2
2
1
0
2
1
1
1
1
1
1
1
2
1
1
1
2
0
2
0
1
1
3
2
1
0
1
1
2
2
0
1
2
1
0
1
2
1
1
1
1
2
1
1
1
1
1
2
1
1
2
1
2
1
1
1
1
1
2
1
2
2
1
1
2
2
1
1
2
1
0
2
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
0
1
2
1
1
1
2
1
2
2
1
1
1
1
0
1
1
1
3
0
1
1
1
0
2
2
1
1
1
1
1
0
1
0
1
2
1
1
1
1
1
2
1
2
1
0
2
1
2
0
1
1
1
2
1
1
2
0
1
2
1
2
0
2
1
1
1
0
1
0
1
2
2
0
1
1
1
0
1
1
0
1
1
1
2
1
1
2
2
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
0
1
2
2
3
1
1
2
0
1
2
1
2
1
2
2
1
1
1
1
1
1
1
1
2
0
1
1
2
2
1
2
2
2
1
0
1
2
1
1
1
2
1
1
1
3
2
2
2
1
1
2
0
1
2
1
1
0
1
1
1
1
1
1
2
1
2
1
1
0
2
1
1
1
2
2
1
1
1
1
2
1
1
1
2
2
0
2
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
1
1
0
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
0
1
2
2
1
2
1
1
1
2
1
1
1
2
2
0
1
2
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
2
2
1
2
1
1
1
0
2
1
0
1
1
2
2
2
1
1
1
1
0
1
2
1
2
2
1
1
1
1
1
1
1
2
0
1
1
1
1
1
1
2
1
1
1
1
1
2
2
2
2
0
1
1
1
1
1
2
1
1
2
1
1
2
1
1
1
2
2
1
1
0
2
1
1
1
2
1
1
0
1
0
1
1
2
1
1
2
1
1
2
1
2
1
2
2
1
1
1
1
1
1
2
1
1
0
2
2
1
0
1
1
1
2
1
1
0
1
1
1
1
1
2
1
0
1
1
1
1
1
1
0
2
0
0
2
1
0
0
1
1
1
0
2
2
1
1
1
2
1
1
1
1
2
0
1
0
1
1
1
1
1
1
1
2
1
0
2
1
2
1
2
2
0
1
0
2
2
2
1
1
1
2
1
2
2
2
2
1
1
2
1
0
2
2
1
2
1
1
1
1
0
1
1
2
1
1
1
2
1
2
1
2
1
1
1
0
1
2
2
0
1
1
2
1
2
1
1
1
1
1
2
1
1
1
0
1
1
1
2
0
2
2
1
0
1
2
2
2
1
1
1
1
2
1
0
1
1
1
1
2
1
1
1
2
2
2
2
1
2
1
2
2
1
1
2
1
1
1
1
1
0
1
1
1
1
2
0
2
1
0
2
2
1
2
1
1
2
1
2
1
2
1
1
1
0
2
1
1
1
1
2
2
2
1
1
1
1
0
0
1
1
0
2
2
1
2
1
1
0
0
0
1
1
2
1
1
1
1
2
1
0
1
2
2
1
1
0
1
1
1
2
2
1
2
2
0
0
1
1
1
1
1
1
2
1
2
1
0
2
1
1
0
1
1
1
1
1
1
2
0
1
1
0
1
0
2
0
1
1
1
1
0
1
0
2
1
1
1
0
1
2
1
1
2
1
1
1
2
1
1
2
2
1
2
1
0
2
0
1
2
1
1
1
2
1
1
0
1
1
1
1
1
1
1
2
1
1
0
1
2
2
1
1
2
1
1
1
3
0
1
1
2
1
0
1
0
2
1
2
2
1
2
1
1
1
1
2
1
1
0
2
0
1
2
1
1
2
2
1
2
0
1
1
1
1
1
1
2
1
1
2
0
2
2
0
0
1
1
2
1
1
2
2
1
2
0
1
2
1
2
2
2
1
1
1
1
0
1
2
1
1
1
1
2
0
2
0
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
2
1
2
1
1
2
1
1
2
1
1
2
1
2
0
1
1
1
1
1
1
2
2
2
1
2
1
2
1
1
0
1
1
1
1
1
2
2
1
1
1
2
1
2
2
1
1
1
2
2
0
1
2
2
1
0
2
0
1
2
1
1
1
2
1
2
2
0
1
1
2
1
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
2
2
2
2
1
0
2
0
2
1
1
2
0
1
1
1
2
1
0
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
2
0
1
2
1
1
0
0
2
1
1
0
1
2
1
1
1
1
2
1
1
2
3
1
0
2
2
1
1
2
2
2
1
1
1
1
4
0
1
1
1
3
1
1
1
1
0
1
0
1
1
1
1
0
1
2
1
2
1
1
2
1
0
2
2
1
0
1
1
1
0
1
1
2
2
1
1
0
2
1
1
0
1
1
2
1
1
0
0
1
1
1
1
2
1
2
2
1
1
1
1
2
1
1
2
2
1
2
1
1
1
1
2
1
2
1
2
1
1
1
1
1
2
1
1
1
1
1
0
1
1
2
3
2
2
1
1
1
1
1
2
0
1
2
1
1
1
2
1
0
2
1
0
1
2
1
1
2
1
1
2
1
2
0
1
1
1
1
1
1
0
1
1
1
1
1
2
1
1
2
2
1
1
1
1
2
2
1
1
1
1
1
2
1
2
0
2
0
1
1
2
1
1
1
1
1
0
1
0
2
2
1
1
1
2
1
1
1
2
2
1
2
1
1
2
2
1
1
1
1
0
1
1
0
0
0
0
1
1
1
2
1
1
0
1
0
2
2
1
0
1
1
0
1
2
1
2
2
1
0
1
1
1
2
1
0
0
1
1
1
1
1
2
1
1
2
0
1
1
1
1
1
1
1
1
2
1
1
2
1
0
1
2
1
2
1
1
0
1
1
0
1
1
1
2
2
2
0
2
1
1
1
1
0
1
3
1
2
1
1
1
3
1
1
2
1
2
1
0
1
2
1
1
1
1
2
1
1
1
1
1
1
2
1
1
0
2
1
1
2
1
1
2
1
2
1
1
1
1
2
1
2
1
1
0
1
1
1
1
2
0
1
1
1
1
1
1
0
1
1
1
0
1
2
1
2
1
1
1
0
2
1
1
1
1
1
1
1
1
0
2
1
0
1
1
2
1
0
1
1
1
1
0
1
1
1
1
1
1
1
2
1
1
2
2
0
0
2
1
3
1
1
1
2
0
1
0
1
1
1
2
0
2
1
1
0
1
2
1
1
1
1
1
1
0
1
1
1
1
2
1
1
1
1
1
1
0
4
2
0
1
1
2
2
1
0
1
2
2
3
1
1
2
1
0
1
0
1
1
1
1
1
0
1
0
1
2
1
1
1
1
2
0
1
2
1
1
0
2
1
1
1
0
2
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
2
0
2
1
0
1
2
0
0
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
3
1
1
1
1
1
0
1
0
1
1
1
2
1
1
1
0
0
1
0
1
2
1
1
1
0
1
1
1
1
2
2
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
0
2
1
0
1
1
1
2
0
1
1
1
2
2
0
1
1
2
2
1
2
0
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
2
2
1
1
1
2
1
1
1
2
2
1
1
1
0
1
2
1
1
1
1
2
1
1
1
1
2
2
0
1
2
1
0
2
1
1
1
0
1
2
2
1
1
0
2
1
0
0
2
1
2
1
0
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
1
2
0
1
2
1
2
1
1
3
1
1
1
1
0
2
1
1
0
0
1
1
2
2
1
2
2
1
1
1
1
0
1
1
1
0
1
0
1
1
1
1
2
1
2
2
1
1
2
2
1
1
1
0
2
1
1
1
2
2
1
1
2
1
2
1
2
1
1
1
2
0
0
1
2
1
1
1
0
1
1
2
2
2
0
1
1
1
2
1
1
2
1
1
1
1
1
3
1
1
1
2
1
0
1
1
1
1
2
2
2
2
1
2
1
1
1
1
1
1
2
1
1
1
1
2
0
1
1
1
2
2
2
1
2
1
1
1
1
1
0
1
2
1
1
1
1
2
1
2
2
1
2
1
0
1
0
1
2
0
1
2
1
1
1
2
1
2
0
1
0
1
1
1
1
1
1
1
1
2
0
0
1
1
2
1
1
1
2
2
2
1
2
2
2
1
1
0
0
1
1
1
1
1
1
1
1
0
1
0
2
0
1
1
1
1
0
1
2
2
1
1
2
1
1
2
2
1
1
1
1
1
0
2
1
1
1
1
2
3
0
0
2
1
0
2
0
1
1
1
0
1
2
0
2
2
0
1
1
1
1
1
2
1
1
2
1
1
1
1
0
1
2
1
1
1
1
1
1
1
1
1
2
1
2
0
1
1
0
1
1
1
0
2
1
2
1
0
1
2
1
1
2
1
0
2
0
1
2
1
0
1
1
0
1
2
0
1
0
1
2
1
1
1
1
1
1
2
0
1
0
1
1
1
1
1
1
0
1
1
1
2
2
1
1
1
1
1
2
1
1
1
2
1
0
2
2
2
1
0
2
1
1
2
1
1
1
1
1
2
0
1
1
2
0
2
2
1
1
2
1
1
1
1
1
0
0
1
2
1
1
2
1
0
1
1
1
1
0
1
1
1
1
1
2
2
1
1
2
2
1
1
2
1
2
1
1
1
2
1
1
2
0
0
1
1
1
2
1
1
1
2
1
1
1
1
2
0
1
2
1
2
2
0
1
1
1
1
2
1
1
2
2
0
2
0
1
1
2
1
1
1
0
0
1
0
1
1
1
2
2
1
1
2
1
1
2
0
1
1
2
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
2
2
1
2
3
1
1
1
1
0
1
1
2
1
1
2
0
2
1
1
1
1
2
1
2
1
2
0
2
1
1
2
1
1
1
2
1
2
1
1
1
2
2
1
1
1
0
0
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
0
2
0
1
1
1
1
1
2
1
1
0
2
1
1
1
1
1
1
2
1
1
2
1
1
0
2
2
1
2
2
1
1
2
2
2
1
2
2
1
2
2
1
2
1
1
1
2
1
2
1
0
1
0
1
1
2
2
1
1
1
1
1
0
1
1
1
2
2
0
2
1
1
1
1
1
2
1
1
1
1
0
1
2
2
1
1
1
2
1
3
1
1
1
0
1
1
1
2
1
1
0
0
0
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
0
1
2
1
1
2
2
1
1
0
2
1
1
2
1
1
1
1
1
1
1
2
2
1
2
2
2
1
3
1
1
1
0
2
1
1
1
1
1
1
1
2
0
1
2
1
1
1
0
1
1
1
1
1
2
1
2
1
1
1
2
1
2
1
1
1
1
2
1
0
0
1
2
1
1
1
0
0
2
1
2
1
0
1
2
1
2
2
3
1
2
2
2
1
0
1
1
1
0
1
2
1
1
1
1
2
2
1
2
1
1
1
2
2
1
1
2
1
1
1
1
1
1
0
1
1
2
2
2
1
1
1
0
1
2
1
1
0
1
2
2
1
1
2
1
1
1
1
2
1
0
2
1
0
1
1
1
1
2
0
1
1
2
1
1
1
2
1
1
2
1
1
2
2
1
1
2
1
1
2
0
1
0
2
1
2
2
1
1
0
1
1
1
1
2
1
1
1
1
1
1
1
1
0
1
1
2
1
1
1
1
0
1
1
1
0
0
1
1
2
1
1
2
2
1
1
1
1
1
1
1
0
1
0
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
2
2
2
1
0
2
1
1
2
1
1
2
1
1
2
0
1
1
1
0
2
2
2
1
1
1
2
1
0
0
1
2
0
1
1
0
2
1
2
1
1
1
1
0
2
1
2
2
1
0
1
2
1
0
0
1
1
2
1
1
1
2
2
1
2
1
1
1
2
2
1
2
1
1
2
1
1
0
2
1
1
1
1
1
0
2
2
1
1
1
1
1
1
2
1
1
1
2
2
2
0
1
1
0
1
1
2
1
1
2
3
2
1
2
1
1
3
1
2
1
1
1
1
1
1
0
0
2
2
2
1
1
1
1
1
2
1
2
1
0
0
1
1
1
1
1
1
0
0
1
2
1
1
0
2
1
2
1
1
2
2
3
1
1
0
0
1
2
1
2
1
1
0
1
1
0
1
1
1
1
1
1
1
2
1
1
1
0
1
2
2
1
1
2
1
1
1
1
1
1
2
1
1
0
1
1
2
2
2
1
1
2
1
1
2
1
1
1
1
1
0
1
0
1
1
0
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
0
1
1
1
1
1
2
2
2
2
1
1
0
0
0
0
1
1
1
1
1
2
1
1
2
1
2
1
2
2
1
1
1
2
1
2
1
1
1
1
1
2
1
1
2
1
0
1
1
1
1
2
1
1
1
2
2
2
0
1
1
1
1
1
1
0
2
1
2
2
1
1
2
2
1
1
1
1
0
1
0
2
1
0
1
2
1
1
1
1
2
1
1
1
1
2
1
2
1
2
2
1
1
1
2
1
1
1
2
1
2
1
1
2
1
0
2
1
1
2
2
0
0
1
2
1
1
0
2
1
2
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
0
1
1
1
1
1
1
1
1
2
1
1
0
1
1
1
2
2
1
1
8
1
1
2
2
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
2
1
0
1
2
0
1
1
1
2
1
1
1
1
2
2
1
1
1
1
1
1
2
2
1
0
1
2
1
1
2
1
1
2
0
1
2
1
0
1
1
1
1
1
1
1
2
0
0
2
1
1
1
1
0
1
1
1
0
0
1
1
1
1
2
1
1
1
2
2
1
1
1
2
1
1
2
2
1
1
1
1
0
0
1
1
1
0
2
1
1
1
1
2
2
1
1
1
1
1
2
1
2
1
0
1
1
2
1
1
1
2
1
1
1
1
2
0
0
2
1
0
1
1
1
1
1
2
1
2
1
1
1
1
1
2
0
1
1
1
1
1
1
1
1
1
1
2
2
2
2
2
2
2
2
1
2
2
1
0
1
1
1
2
1
0
1
1
0
0
0
1
1
0
1
1
1
1
1
1
1
1
1
2
0
1
1
1
2
1
1
1
1
1
2
1
1
0
1
2
1
1
2
1
1
1
2
1
2
1
2
1
0
2
1
1
1
1
1
1
1
0
1
0
1
0
1
1
2
1
1
2
0
1
2
1
0
2
1
1
2
1
0
0
1
2
1
1
2
2
1
2
1
1
1
0
1
1
1
0
1
1
1
1
2
1
0
1
1
2
1
1
1
1
1
2
1
2
2
1
2
1
1
1
0
2
0
1
2
2
1
1
1
1
0
1
1
2
1
1
1
1
2
0
0
1
1
1
1
1
0
2
1
1
2
1
1
2
1
1
1
0
0
2
1
1
1
2
0
1
2
1
1
1
1
1
0
2
1
1
2
2
1
1
1
2
1
0
2
1
1
2
1
1
1
0
1
2
1
1
3
2
1
2
0
0
1
3
1
1
1
1
2
1
1
1
2
1
1
2
0
1
1
1
2
0
2
2
1
1
1
1
1
1
2
2
2
2
1
1
0
2
1
2
1
1
1
1
1
1
1
0
1
0
1
1
0
0
1
1
1
1
1
1
2
1
1
1
0
1
1
1
2
1
0
0
1
1
1
1
1
1
1
1
0
0
2
1
2
1
0
2
1
1
1
1
0
1
0
1
1
2
0
1
1
1
2
1
0
1
1
2
2
1
2
1
1
1
2
1
1
1
0
1
1
1
2
1
2
2
2
2
1
1
1
1
1
1
0
2
1
1
2
1
1
2
0
1
1
2
1
2
1
2
0
2
1
2
2
1
0
1
3
2
1
1
1
2
1
1
1
2
2
0
1
1
1
2
2
1
1
2
1
2
0
2
1
2
0
1
1
2
1
1
1
2
1
1
1
1
1
1
4
2
1
1
3
2
1
2
1
0
1
1
0
0
0
2
2
2
1
1
2
2
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
2
1
2
1
1
2
1
0
1
1
1
1
0
1
1
1
2
1
0
2
1
1
2
1
1
0
1
2
0
2
1
1
1
1
1
1
0
1
2
1
1
1
0
1
1
1
1
0
1
2
0
1
0
2
0
2
1
0
1
3
1
1
1
1
1
2
1
1
0
1
0
1
1
1
0
2
1
1
1
1
1
1
0
1
2
1
2
1
0
1
0
1
1
1
2
2
1
1
2
2
1
1
0
1
1
2
0
1
1
1
3
1
1
2
1
1
1
2
1
1
2
1
2
2
2
2
0
1
1
1
2
1
1
0
2
1
1
1
0
1
1
0
0
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
0
2
1
1
1
1
0
1
0
1
0
2
1
1
1
0
1
2
2
1
1
1
1
1
0
1
1
1
1
0
1
3
0
1
1
2
2
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
2
1
1
0
2
1
2
1
1
1
1
2
2
1
1
0
2
2
1
0
1
1
2
0
1
1
1
0
0
2
1
2
1
0
2
1
2
1
2
0
1
1
3
1
1
2
1
1
0
1
0
2
0
2
0
1
1
1
2
2
1
0
1
0
1
0
2
0
1
1
1
1
1
1
1
2
1
1
0
0
2
2
1
0
1
2
0
1
2
1
1
1
2
0
2
1
1
1
1
1
1
0
1
0
1
2
2
1
1
2
0
2
1
2
1
0
1
2
1
1
1
2
1
1
1
1
1
1
2
1
2
1
2
0
1
0
1
1
0
2
1
1
1
1
1
1
1
1
1
2
0
1
0
2
1
2
1
1
2
1
1
1
1
1
0
1
1
2
1
0
1
1
1
0
1
1
0
2
1
0
2
1
2
1
2
1
2
1
2
1
2
1
1
2
2
1
1
0
2
0
1
1
0
2
1
2
1
1
2
1
0
1
1
1
1
1
1
1
0
2
1
2
2
1
1
1
1
2
1
0
1
1
1
2
2
1
2
2
1
1
2
0
1
1
1
1
2
1
1
0
1
1
1
1
2
0
2
1
1
1
1
1
0
2
1
2
1
2
1
2
2
0
1
1
1
2
2
0
1
1
1
1
2
1
1
1
0
1
0
1
1
1
1
1
1
1
1
1
1
2
1
0
2
1
1
0
2
0
1
0
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
1
2
2
0
0
1
0
2
1
1
1
1
1
2
1
1
2
2
0
1
1
2
1
2
1
1
0
2
1
0
1
0
1
1
1
2
1
0
1
0
1
2
2
1
2
0
1
1
1
2
1
2
1
0
1
1
2
2
1
2
1
1
1
2
1
0
1
1
1
0
1
1
1
3
1
0
0
2
1
0
1
1
1
1
2
2
1
1
1
1
0
0
2
2
1
1
1
2
1
1
1
2
1
1
2
0
1
2
0
1
2
2
2
0
1
1
1
2
1
2
2
1
1
2
0
1
0
1
0
1
1
0
1
2
0
1
1
0
1
2
2
0
1
1
1
1
2
0
0
2
0
2
1
2
2
1
2
1
2
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
2
2
1
1
1
0
1
1
1
1
2
0
2
1
1
0
1
1
1
0
1
1
1
2
1
1
2
1
2
1
1
2
0
1
1
1
2
1
1
1
1
2
1
1
2
1
2
0
1
1
0
1
1
0
1
2
1
0
1
1
2
1
1
1
2
0
1
1
2
2
1
2
1
1
0
1
2
1
1
1
1
1
1
2
1
0
2
0
1
2
1
2
2
3
1
1
1
0
2
1
2
1
1
1
0
2
1
1
2
1
1
1
2
2
1
0
2
2
1
2
1
1
1
1
1
1
2
1
2
2
2
1
1
1
1
1
1
2
2
1
1
0
2
1
0
1
1
2
1
0
2
0
2
1
1
1
1
1
1
1
1
2
1
1
0
2
1
1
1
1
1
0
0
2
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
0
1
1
1
1
1
1
1
2
2
2
1
2
2
2
1
2
1
1
1
0
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
0
1
1
2
1
2
1
2
1
2
1
1
1
1
1
1
1
2
2
2
1
1
2
1
1
0
1
1
1
0
1
0
1
0
1
1
2
2
1
0
2
1
1
1
0
1
2
2
1
2
0
1
0
0
1
1
1
1
2
1
1
1
0
1
2
1
1
1
2
1
1
0
1
2
2
2
1
1
1
1
2
0
0
1
1
1
2
1
1
1
0
1
1
2
2
0
1
1
2
1
1
2
1
2
0
1
1
1
2
1
1
1
1
1
0
1
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
2
1
1
2
2
1
1
1
1
2
2
2
2
1
2
1
1
1
1
2
1
2
1
1
1
2
1
2
1
1
1
1
1
1
0
1
1
2
1
1
2
0
2
1
1
2
1
2
1
1
2
0
0
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
0
1
1
1
2
1
1
1
0
2
2
0
2
1
2
1
1
2
1
1
1
2
2
1
1
2
1
1
1
2
2
0
1
2
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
2
1
2
2
2
1
3
1
1
1
1
1
2
0
2
2
2
1
1
2
1
1
1
1
1
1
1
1
1
0
1
1
2
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
0
1
2
1
2
2
1
1
2
1
2
1
1
0
2
1
0
0
2
2
1
1
2
1
1
1
1
2
0
1
1
2
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
0
1
1
2
2
0
1
1
1
2
1
1
1
1
1
1
1
2
1
1
0
1
1
1
1
1
2
3
2
1
2
0
0
1
1
1
1
1
1
1
2
2
1
1
1
0
1
1
0
0
0
2
1
1
2
1
1
1
0
2
1
2
1
1
1
1
1
2
1
1
1
2
0
2
2
0
1
1
1
2
1
2
2
1
1
1
1
2
0
2
1
1
1
1
1
1
1
1
1
1
1
0
1
0
0
1
2
1
0
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
2
1
1
1
2
1
0
2
1
1
0
1
2
1
1
2
2
1
2
2
2
2
1
2
2
1
2
0
1
1
1
1
1
2
1
1
2
2
1
1
0
1
1
1
0
1
2
1
0
2
2
1
1
2
1
2
1
2
1
2
1
1
2
1
2
0
2
2
2
1
1
0
0
1
2
2
0
2
0
1
1
1
2
1
1
1
2
2
2
1
1
0
1
1
1
2
2
1
1
1
1
2
1
1
1
0
1
1
2
1
1
1
1
0
3
1
2
2
1
2
1
0
2
2
1
0
1
1
1
0
1
1
1
1
0
1
2
1
1
1
1
1
1
2
2
1
2
2
2
1
1
1
0
2
0
1
1
1
1
1
0
1
2
0
1
1
1
1
1
2
1
1
2
1
0
2
0
1
2
0
2
0
2
1
1
0
2
1
0
0
1
1
0
2
2
1
2
1
1
1
0
1
0
1
0
1
2
1
1
2
0
1
2
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
0
1
1
1
0
1
1
1
1
1
2
2
2
1
1
2
2
1
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
2
2
1
2
1
1
1
2
1
1
1
0
2
1
1
1
2
1
1
1
1
1
1
0
2
0
2
1
1
2
2
1
1
1
1
1
1
2
0
1
2
1
1
1
1
1
0
1
1
2
1
1
1
1
1
1
0
2
1
1
1
1
1
1
1
3
1
1
1
2
0
2
2
2
0
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
0
1
0
1
0
2
2
1
2
1
2
1
1
1
1
1
1
2
1
2
1
2
1
1
1
2
2
1
1
1
1
2
1
1
1
1
0
1
2
2
2
1
2
1
1
0
1
1
1
2
1
2
1
0
3
1
0
2
1
0
0
1
1
1
1
1
0
0
0
1
1
2
1
2
2
2
0
2
1
1
2
1
2
1
1
0
1
0
0
2
0
1
1
2
2
1
1
1
1
0
1
2
1
0
1
1
1
2
2
0
1
1
0
1
2
1
0
0
1
1
1
1
2
1
2
1
2
0
1
2
1
2
2
1
1
2
2
1
1
1
1
2
4
1
0
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
0
2
1
1
1
2
1
1
0
2
1
1
1
1
2
2
0
1
2
2
1
1
0
1
1
1
1
0
2
1
1
1
1
2
2
1
2
1
0
2
1
1
1
1
1
0
0
1
0
1
1
0
2
0
2
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
2
1
1
0
2
2
0
1
1
2
1
1
1
0
0
2
1
1
1
1
2
2
2
1
1
2
2
1
1
1
1
1
2
1
1
1
2
2
2
1
0
0
2
2
1
0
2
1
2
0
2
1
1
0
2
2
0
2
1
2
1
1
2
2
1
1
1
1
1
1
1
1
1
0
1
1
0
1
2
1
2
2
0
1
1
1
1
1
1
0
1
2
0
1
1
0
1
1
2
1
1
2
1
1
1
2
0
1
0
1
2
1
1
1
0
0
1
2
1
0
2
1
1
0
1
1
1
1
1
1
1
2
1
2
2
0
2
1
2
1
0
1
1
1
1
3
2
1
1
2
2
1
1
1
2
1
2
2
2
1
1
2
0
2
0
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
0
1
1
1
1
1
1
1
0
1
2
2
1
1
2
0
1
1
0
0
2
1
1
2
1
1
1
1
2
0
1
1
0
2
1
1
0
1
1
1
1
1
2
1
1
1
1
2
1
2
1
2
0
1
2
1
0
1
2
0
0
1
1
1
1
2
1
0
2
1
2
1
2
1
2
2
2
1
1
1
1
1
1
2
0
0
2
1
1
0
1
1
1
1
1
0
2
1
1
0
1
0
1
1
1
1
1
1
1
1
0
2
1
2
1
1
0
1
1
1
1
0
2
2
2
1
0
2
1
1
1
0
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
0
2
1
2
1
1
0
2
1
1
1
1
2
2
1
1
1
2
2
0
1
2
1
1
1
2
2
2
2
2
2
1
0
0
2
0
2
2
2
1
2
2
1
2
0
1
2
0
1
1
1
1
1
2
0
2
2
1
2
1
1
1
1
1
1
1
1
1
1
0
2
1
1
1
1
2
0
1
1
2
1
1
2
1
1
2
2
2
1
1
1
0
0
1
1
3
2
0
1
1
1
1
1
1
1
1
2
0
1
1
1
1
2
1
1
1
2
1
1
2
1
2
3
1
2
1
2
1
1
1
1
2
1
1
2
1
2
1
1
0
2
1
2
1
1
1
2
2
1
1
3
2
1
0
2
0
1
2
2
1
2
1
1
1
2
2
1
1
1
1
1
2
1
1
1
1
1
0
2
1
1
1
0
2
1
1
1
1
0
1
2
1
1
2
0
1
1
2
0
2
0
1
1
1
2
2
2
1
2
0
1
1
1
2
1
2
1
2
1
2
1
2
1
2
2
2
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
3
1
1
1
2
2
1
2
1
1
2
2
0
2
0
1
2
1
2
0
2
0
1
0
1
2
1
0
1
1
1
1
1
1
1
2
1
1
1
1
1
1
0
1
0
1
1
2
2
1
1
1
2
2
1
3
2
1
1
1
0
1
1
5
1
1
1
1
0
1
0
2
1
1
1
1
1
2
2
2
1
1
1
2
1
2
1
1
1
1
1
2
2
1
2
1
0
1
2
2
1
0
1
0
1
0
2
2
1
2
1
0
0
1
1
2
1
1
1
1
2
2
2
2
1
1
0
2
0
1
1
3
1
1
2
2
1
0
0
1
0
1
1
1
0
2
2
1
1
0
1
1
0
0
1
1
1
2
1
2
1
1
1
2
1
2
2
0
2
1
1
2
1
0
0
1
1
2
1
1
1
1
2
2
1
2
1
2
2
2
2
0
0
1
1
1
2
1
2
2
1
1
1
1
0
2
2
2
2
1
1
1
2
1
0
1
1
2
1
0
1
0
1
2
1
1
1
2
2
1
2
1
2
2
1
1
2
0
1
1
1
1
2
1
1
1
2
1
2
2
1
1
2
2
2
0
0
1
2
2
2
1
2
1
0
1
0
1
2
2
1
1
3
0
1
1
2
1
0
1
1
1
1
0
0
1
0
2
2
1
1
1
1
1
2
2
1
2
0
0
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
0
1
0
2
1
1
1
1
0
1
1
1
2
1
2
1
1
1
2
1
2
1
1
2
1
1
2
5
1
1
0
0
2
2
2
1
2
1
1
1
0
0
1
1
1
1
0
2
1
1
2
1
1
1
1
0
0
2
1
1
1
0
1
1
1
2
1
2
1
0
1
1
1
1
1
2
1
0
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
0
2
1
1
2
1
1
1
1
2
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
0
1
2
2
2
2
2
2
2
0
1
2
2
2
3
1
1
1
1
1
1
2
2
2
1
1
2
1
1
2
3
2
1
2
2
1
2
1
1
1
1
0
1
0
2
0
2
1
2
1
1
1
1
1
1
1
0
1
1
1
1
2
2
0
1
0
0
0
1
1
2
2
1
2
0
1
0
1
2
1
2
1
2
1
1
1
1
0
1
1
1
2
1
1
1
2
1
1
1
1
0
2
1
1
1
1
2
2
1
1
2
2
1
0
1
2
2
2
2
1
0
1
1
2
2
2
1
1
1
1
2
1
4
2
1
1
0
1
1
1
2
1
1
2
1
2
0
1
1
2
1
1
2
0
1
1
2
1
2
1
1
1
1
0
1
1
2
0
1
1
1
1
1
2
3
1
1
1
2
1
2
1
1
1
1
2
2
1
1
1
1
3
1
1
0
1
1
1
1
1
1
1
1
2
1
2
1
2
1
2
1
1
2
1
1
2
1
2
0
1
1
1
2
0
1
1
1
0
2
2
1
1
1
1
0
2
1
1
1
1
1
1
1
2
0
0
2
2
1
1
1
1
1
0
1
2
2
1
1
1
1
0
0
1
1
1
1
1
1
1
1
2
0
1
1
2
0
1
1
0
1
2
1
1
1
1
2
1
1
2
1
1
1
1
2
1
2
2
1
1
1
1
1
2
1
2
1
1
0
1
2
1
1
1
1
1
0
1
0
1
1
0
0
0
1
0
1
1
2
1
1
1
2
2
1
1
1
2
2
2
1
2
2
1
1
0
1
1
1
1
2
1
2
1
1
1
0
0
1
1
0
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
0
1
0
1
1
1
1
1
1
1
1
0
1
1
1
2
2
1
1
1
2
2
1
1
2
0
1
2
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
2
2
1
1
2
2
1
1
1
1
1
2
1
1
1
0
1
1
1
1
1
1
1
1
2
2
1
1
1
1
2
1
0
1
1
1
1
1
2
1
1
1
2
0
1
1
1
1
1
1
1
2
0
2
1
1
1
1
1
2
1
1
1
2
0
1
1
1
1
0
1
1
2
0
1
2
1
1
1
1
1
1
2
0
1
2
2
1
1
2
2
1
1
1
2
0
1
1
1
0
2
1
1
1
1
1
0
1
0
1
2
1
1
0
2
2
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
0
1
1
1
1
0
2
1
1
1
1
1
0
0
1
0
2
1
2
2
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
0
2
1
2
0
2
2
1
1
2
1
0
1
1
1
1
1
2
1
1
2
1
2
1
2
2
2
1
1
3
2
2
1
2
2
1
2
0
1
2
1
2
1
1
1
0
2
1
2
2
1
2
1
0
1
1
1
1
2
1
0
1
0
0
1
1
2
1
1
1
2
1
1
1
1
1
1
1
0
0
1
0
1
0
2
1
1
1
1
2
1
1
2
1
1
1
2
1
0
1
2
2
2
1
2
0
1
1
1
2
1
1
2
1
0
1
1
1
2
2
1
0
1
0
1
1
1
2
1
1
1
1
2
0
2
1
1
2
1
2
0
1
0
2
2
1
1
1
1
1
2
0
1
1
0
2
0
1
2
2
1
0
1
1
2
1
1
2
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
2
0
2
0
2
2
1
0
0
1
2
1
0
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
2
0
0
2
2
1
2
1
2
1
2
2
1
1
1
3
0
0
1
1
1
0
1
2
1
1
1
1
2
2
2
0
2
1
1
2
1
2
1
2
1
2
2
1
3
1
1
2
2
0
1
1
2
2
0
2
1
1
2
0
1
1
1
1
0
2
2
1
2
0
1
2
2
1
2
2
2
1
1
1
2
0
1
1
1
1
1
1
1
1
2
1
1
0
1
1
1
2
2
2
1
2
2
1
2
1
1
1
1
2
1
1
1
2
1
1
2
1
2
3
2
2
1
1
1
2
1
2
1
2
1
1
2
1
1
0
1
0
1
1
1
2
1
2
1
1
2
1
1
1
1
2
2
1
1
1
1
2
1
1
0
2
1
1
1
0
1
1
2
1
1
1
1
2
1
0
2
2
1
2
2
0
2
1
1
1
2
1
2
2
0
1
1
1
1
2
1
1
1
1
1
2
2
1
1
2
0
1
2
0
1
1
1
1
1
1
2
0
1
1
1
1
2
1
2
0
1
1
1
1
0
1
2
0
1
2
0
2
2
2
2
0
1
1
1
1
0
1
1
2
1
1
1
0
1
1
1
1
1
1
1
1
1
2
2
2
2
1
2
1
1
0
1
2
1
1
2
1
1
1
1
0
1
1
1
2
1
0
1
1
1
2
2
1
2
1
1
1
1
1
1
2
2
1
2
2
1
0
1
2
1
1
1
1
1
1
1
1
0
2
2
1
1
2
1
2
1
2
2
1
1
1
2
0
1
0
2
0
1
1
1
1
1
1
1
0
1
2
1
1
2
1
2
1
2
1
1
1
0
1
1
1
2
1
2
2
1
0
2
1
1
1
1
2
0
1
1
0
2
1
1
1
2
1
1
1
1
1
1
0
0
1
2
2
0
1
1
1
1
1
2
2
2
1
1
1
1
2
1
1
1
2
1
1
2
1
0
1
1
1
1
2
1
1
1
1
1
1
1
0
2
0
0
1
1
1
2
0
2
1
1
0
1
2
2
2
1
1
0
0
1
2
1
1
1
1
0
1
2
1
0
2
2
1
1
0
2
1
0
0
2
1
2
1
2
0
2
1
1
2
1
1
2
1
2
1
1
2
1
1
1
1
2
1
1
1
2
1
2
1
1
2
1
1
1
0
1
2
1
2
1
1
2
2
2
1
0
1
1
0
1
2
2
1
1
1
1
1
2
1
1
1
2
1
1
0
2
1
2
1
1
1
1
1
1
1
1
1
0
2
1
2
1
2
0
1
1
1
1
0
1
2
1
0
1
1
2
0
1
2
3
1
1
1
0
2
2
0
1
1
1
0
2
1
0
1
1
3
2
1
2
1
1
0
2
1
1
0
1
1
2
1
1
1
1
0
2
0
1
1
1
1
1
2
1
1
1
1
2
1
1
2
2
1
2
1
1
1
2
2
1
1
1
2
0
0
2
1
1
1
1
2
1
1
1
1
2
0
2
2
2
1
1
1
1
2
2
1
1
1
2
1
1
1
2
1
1
1
2
1
1
1
2
2
0
1
1
1
1
1
0
1
0
1
1
1
1
0
0
1
1
2
1
1
1
1
2
2
1
1
2
2
1
1
1
1
1
2
1
1
1
3
1
0
1
1
1
1
1
1
1
1
2
1
1
0
1
0
1
1
2
2
1
0
1
1
3
1
2
1
1
1
1
2
0
1
1
1
0
1
1
1
0
1
2
1
2
2
1
2
0
2
2
1
1
1
0
0
2
0
2
2
2
0
2
1
1
1
1
1
1
2
1
0
1
2
1
2
1
1
0
0
1
2
0
1
1
1
1
1
1
0
1
2
0
1
1
1
1
1
2
2
1
2
1
1
1
2
2
1
1
1
1
1
1
2
0
1
1
1
1
2
2
1
1
1
1
1
1
1
2
2
1
1
2
2
1
1
2
1
0
1
1
0
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
0
1
1
1
1
1
0
1
1
0
2
2
1
1
1
1
2
0
2
2
1
1
0
0
2
1
1
1
3
1
1
2
1
1
2
1
1
0
2
1
2
1
0
1
2
1
2
1
2
2
1
1
2
2
1
1
2
1
1
1
2
1
0
2
2
1
1
1
0
0
1
1
1
2
1
2
1
1
1
2
1
1
0
1
1
2
1
1
1
1
1
2
2
1
1
2
2
0
1
3
1
1
2
1
1
2
1
0
0
1
1
0
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
1
0
0
1
2
1
1
1
1
2
0
0
1
1
1
2
2
0
2
2
2
1
2
1
2
0
1
1
1
1
1
1
1
2
1
0
1
0
1
0
1
1
0
1
3
1
2
2
1
2
1
2
0
1
1
1
1
0
2
1
1
1
1
2
0
1
1
1
1
1
1
0
2
1
1
1
2
1
2
1
0
1
0
1
1
1
1
1
1
1
1
1
1
1
0
1
2
1
2
1
1
2
2
1
0
1
0
2
1
1
1
1
1
1
1
1
1
1
0
1
2
2
1
0
1
1
0
2
1
1
0
1
2
1
1
1
2
2
1
1
1
1
1
0
2
0
1
0
1
1
1
1
1
1
1
1
1
0
1
1
1
1
2
1
1
1
1
2
1
1
2
0
1
1
1
1
2
2
2
1
2
0
2
1
1
1
2
1
2
1
2
1
1
2
1
2
0
1
1
1
1
0
1
1
1
0
1
2
1
1
1
2
0
1
1
1
0
1
1
0
1
1
1
1
2
1
2
1
2
1
1
0
1
1
1
1
1
0
2
2
0
0
1
1
0
2
1
1
1
1
1
2
1
1
2
0
2
1
1
1
1
1
1
1
1
0
2
2
7
1
1
1
1
1
1
2
1
1
1
1
0
0
1
0
2
1
1
1
1
1
1
2
1
0
2
1
0
2
1
2
1
1
1
1
2
0
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
1
2
1
1
2
0
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
0
1
2
2
1
1
1
1
1
0
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
0
2
0
1
1
1
1
2
1
0
1
1
1
1
1
1
2
2
1
1
2
1
2
2
1
1
2
1
1
2
2
2
1
2
1
2
1
1
2
2
1
0
0
1
2
1
2
1
2
1
2
0
1
1
1
1
1
1
1
0
1
1
1
1
1
1
2
0
2
1
1
1
2
2
1
2
1
1
1
0
2
0
1
1
2
1
1
2
1
1
1
1
1
2
1
1
1
3
2
1
2
0
0
1
1
2
1
1
0
1
2
1
1
2
1
4
1
2
1
2
1
1
1
1
0
1
2
1
1
1
1
1
2
0
1
1
1
1
1
0
1
1
0
1
1
1
1
2
2
1
0
1
1
1
2
0
1
2
1
1
2
2
1
2
1
1
2
1
2
1
1
0
2
1
2
1
2
1
1
2
1
1
0
1
1
2
2
1
0
1
1
1
0
2
2
1
0
1
1
1
2
1
1
1
1
1
2
1
0
1
2
1
2
1
1
1
1
1
1
0
1
1
1
1
2
0
1
1
1
2
2
3
2
1
1
0
1
0
1
1
1
2
2
1
2
1
1
0
0
1
1
1
1
0
1
2
1
1
1
1
2
1
1
0
1
1
1
1
2
2
2
2
2
0
1
1
1
1
1
2
2
1
1
1
1
1
2
1
0
1
2
0
1
2
0
1
0
1
1
2
2
1
1
2
1
1
1
1
1
0
0
2
1
1
1
2
1
2
1
1
0
0
2
2
2
1
1
0
0
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
0
2
2
1
1
1
1
2
0
1
2
0
2
1
2
1
0
1
1
2
1
2
1
1
1
2
2
0
2
2
1
2
1
2
1
1
2
1
1
0
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
2
2
1
0
2
2
1
1
0
2
2
1
0
1
2
1
1
2
0
1
1
1
0
0
2
1
0
1
1
1
1
1
1
1
2
1
2
1
2
1
1
2
1
1
0
0
1
1
1
1
1
1
1
0
2
1
2
0
1
1
2
1
1
1
1
1
1
0
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
2
1
1
0
1
1
2
0
1
2
2
1
1
0
1
1
1
1
0
1
2
1
1
1
2
1
1
2
1
2
1
1
1
2
1
1
2
1
1
0
1
0
2
1
1
1
1
2
1
1
0
0
2
1
2
2
1
1
2
1
1
1
2
1
1
1
1
2
0
2
1
1
1
2
1
1
1
0
1
1
1
1
2
1
2
2
0
1
0
1
2
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
2
0
2
2
1
2
2
0
1
0
0
2
1
1
2
1
2
1
1
1
1
1
1
1
1
1
2
0
1
0
1
2
2
0
1
1
1
1
2
1
2
0
0
1
1
1
1
0
1
1
1
1
2
1
0
1
1
0
1
1
1
0
2
2
1
2
1
1
1
1
2
0
0
1
1
1
1
1
1
1
2
1
1
0
2
2
1
1
1
1
1
1
0
1
0
1
1
1
1
1
1
2
0
2
2
1
1
0
1
2
2
1
2
1
1
0
0
1
0
1
2
1
1
2
2
1
1
1
2
0
1
1
1
0
2
2
1
0
0
2
0
1
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
1
1
2
1
0
1
1
1
1
2
1
0
1
1
1
2
1
1
2
1
1
2
1
1
2
0
2
1
1
1
2
2
1
2
1
2
2
0
1
1
1
2
1
1
1
2
1
2
1
1
1
2
1
0
1
1
2
2
1
1
1
1
1
2
1
1
2
1
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
2
2
0
1
2
1
1
1
2
1
2
1
0
1
1
1
0
1
1
1
1
1
1
2
0
1
1
1
1
1
1
2
1
2
0
2
1
1
0
1
2
1
2
1
1
0
1
1
3
0
1
0
1
2
1
2
1
1
1
2
0
1
1
1
2
2
1
1
2
1
2
1
1
2
0
2
0
1
1
0
1
0
1
2
2
1
1
1
1
1
1
2
2
1
1
0
1
0
1
3
1
2
1
0
1
0
0
1
1
1
1
1
0
1
1
1
2
1
0
2
1
0
1
2
2
0
1
2
1
2
1
1
2
1
1
1
1
3
1
1
0
1
1
0
1
1
1
0
1
1
1
1
0
1
1
0
2
1
1
0
2
1
1
2
1
1
2
0
2
1
0
1
1
1
0
1
1
2
2
1
0
1
1
1
0
0
1
1
2
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
0
1
2
1
0
0
2
2
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
0
2
0
2
1
2
1
1
2
1
2
0
1
2
0
0
1
1
1
2
0
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
0
2
0
2
1
2
0
1
2
1
1
0
2
1
2
2
1
2
1
1
1
2
1
0
1
0
2
1
0
1
2
1
1
1
1
1
1
1
1
0
2
1
1
1
1
1
2
1
2
1
1
1
1
1
0
1
1
2
2
1
1
2
1
2
2
1
1
0
1
0
1
1
1
1
1
2
2
2
0
2
1
1
1
1
2
1
1
0
1
1
1
0
2
2
0
2
1
0
1
1
1
1
0
1
1
1
1
1
1
0
1
1
0
2
1
0
2
2
1
0
1
1
1
3
1
1
2
0
6
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
0
2
1
0
1
0
2
1
1
1
1
1
1
1
1
1
2
1
0
1
2
1
1
1
1
2
0
2
1
1
1
1
2
1
2
1
1
1
2
0
0
1
2
2
1
1
1
2
2
0
1
1
1
1
1
1
1
0
0
1
1
1
0
1
1
2
2
1
1
2
2
1
2
2
1
2
1
1
1
1
0
0
2
1
2
1
1
1
2
2
1
1
2
0
2
1
1
1
0
2
1
2
2
1
2
2
1
2
0
1
2
0
2
2
1
2
0
2
1
2
2
1
0
1
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
0
1
1
1
1
1
0
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
2
2
1
0
1
1
2
1
1
1
2
1
1
2
1
2
1
1
1
2
1
1
0
2
2
2
0
1
1
1
1
1
2
0
1
0
1
1
1
1
1
0
0
0
1
1
1
1
1
0
1
0
0
1
1
1
1
0
1
2
1
1
1
1
2
1
2
0
2
2
2
1
0
0
0
1
1
2
1
1
2
1
1
1
1
1
2
2
1
1
2
1
2
1
1
2
2
1
0
1
1
2
1
1
2
0
1
2
0
1
1
1
1
1
2
2
1
1
1
2
2
1
1
1
2
1
1
1
2
1
2
1
2
2
1
0
0
2
1
1
2
1
2
1
2
1
2
2
2
1
1
1
1
1
1
1
2
2
1
1
1
0
1
1
2
0
1
2
2
1
1
2
1
2
1
1
1
1
2
1
0
2
2
1
0
1
0
0
1
1
1
1
1
0
1
2
1
1
1
1
1
2
1
1
0
1
1
1
1
1
0
0
1
2
1
2
2
1
1
2
1
1
0
1
1
1
1
2
1
3
1
0
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
0
2
1
1
1
1
1
2
2
2
2
2
1
0
1
1
0
2
1
1
1
1
1
2
1
1
2
2
1
1
1
2
1
0
0
2
0
0
1
2
1
1
2
1
1
1
2
1
0
2
2
1
1
1
1
1
1
1
2
1
1
2
1
1
2
2
1
1
1
1
2
2
1
0
1
2
1
1
2
2
2
2
1
1
1
2
1
2
2
2
1
1
1
0
1
0
0
1
1
1
1
0
1
1
1
1
1
2
1
2
1
2
1
1
1
1
1
1
1
0
2
2
1
1
1
1
1
2
1
1
1
1
1
1
2
2
1
0
2
0
1
1
1
1
1
2
1
1
1
1
2
2
1
2
2
0
0
1
1
0
0
0
2
1
1
1
0
2
1
1
2
1
1
1
1
1
2
1
2
1
2
2
1
1
2
0
0
2
0
0
1
0
1
1
0
1
1
1
1
1
1
2
1
2
1
2
2
2
1
2
2
1
0
1
1
2
0
2
1
1
1
1
0
1
2
2
1
1
0
1
2
1
1
1
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
2
0
1
1
1
0
2
1
2
1
2
1
1
1
0
1
1
1
1
2
1
1
1
1
1
2
2
3
1
1
2
2
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
0
2
0
0
1
0
1
1
1
2
1
1
2
1
1
1
2
1
1
0
1
2
0
1
2
2
2
1
1
1
2
0
1
1
2
0
1
1
1
2
1
1
1
2
1
1
1
2
1
2
1
1
1
1
0
1
0
1
0
1
1
2
1
1
2
1
2
0
0
0
0
2
1
1
1
2
1
1
1
0
0
1
1
1
1
0
1
1
0
2
1
0
1
2
2
1
1
2
1
1
1
2
1
2
1
1
1
1
0
1
2
1
0
0
0
1
2
1
1
2
2
1
0
1
1
1
0
1
1
1
2
1
0
0
2
1
1
1
1
2
0
2
1
2
1
1
1
2
1
2
2
1
1
1
1
1
2
1
1
0
1
1
1
1
1
1
1
2
0
1
2
2
1
1
2
2
1
0
2
1
2
1
2
1
1
1
1
0
2
1
1
1
1
1
1
0
1
1
2
1
1
2
1
0
1
2
1
1
1
2
2
1
0
1
1
1
2
1
2
1
1
0
0
1
1
2
2
1
1
1
1
2
2
1
1
1
2
2
1
1
2
2
1
2
2
1
2
2
1
1
1
1
1
2
3
1
4
2
1
2
1
1
1
2
1
1
2
1
2
1
1
2
2
0
2
0
1
1
1
2
1
1
0
2
2
1
1
1
0
2
2
1
2
0
0
1
1
1
2
1
2
2
1
0
1
2
1
2
1
1
2
2
1
1
1
1
1
1
1
1
2
2
1
2
2
1
1
2
1
1
1
1
0
0
1
1
1
2
2
1
2
1
1
1
0
2
1
0
1
1
1
2
2
1
1
1
1
1
2
1
1
2
1
1
1
2
1
1
2
1
1
2
2
1
1
0
1
1
0
1
1
0
1
1
2
4
1
2
2
2
1
2
1
0
0
1
1
0
2
0
2
1
1
0
2
1
1
1
1
1
1
2
2
2
1
2
1
1
0
1
1
1
2
2
1
0
1
1
1
1
2
1
1
1
1
1
1
0
3
1
1
1
1
1
1
1
3
2
2
1
2
1
0
1
1
1
2
2
1
1
1
2
1
0
1
2
1
1
1
1
1
0
0
0
1
2
1
1
0
1
1
0
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
3
2
1
1
2
1
1
1
1
0
1
1
1
2
1
2
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
0
1
1
2
1
0
1
2
2
1
2
1
1
2
2
1
0
2
0
1
2
1
1
1
2
2
1
2
1
0
1
1
1
2
1
1
1
2
1
1
2
1
2
4
1
2
1
1
2
2
1
2
2
1
2
2
1
1
1
2
1
1
0
1
2
0
1
1
1
1
1
1
1
2
2
1
2
1
1
2
1
2
1
1
1
1
2
2
2
1
2
1
1
1
1
1
1
0
2
1
2
0
2
2
1
0
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
0
1
1
1
2
2
0
1
1
1
1
1
1
0
1
2
0
2
1
1
2
2
1
1
0
1
1
1
0
2
0
1
1
0
1
1
2
1
2
1
1
1
1
2
2
1
3
1
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
2
2
1
0
1
1
1
0
1
1
1
1
1
1
1
0
0
1
0
2
1
2
1
1
1
1
0
1
1
1
2
2
1
1
2
1
1
2
1
1
1
1
1
1
1
1
0
0
1
2
2
1
1
1
1
2
3
2
2
1
0
2
0
2
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
2
1
1
2
1
1
2
2
1
0
1
1
2
2
1
1
0
1
1
1
0
1
1
1
1
2
1
0
1
2
0
2
1
1
2
1
2
1
1
1
0
1
0
1
2
1
1
1
1
1
3
2
1
0
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
2
2
1
1
3
1
1
1
1
1
1
1
1
1
0
1
1
2
1
1
2
2
0
1
1
1
2
2
1
0
1
1
0
2
2
1
4
2
2
2
1
1
1
2
2
2
2
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
3
0
2
0
1
2
1
0
1
1
1
1
1
2
0
2
1
2
0
1
2
1
2
1
1
1
1
2
1
0
1
1
2
2
2
3
0
1
2
0
1
1
1
1
1
1
1
2
2
2
2
0
2
1
0
0
1
1
1
1
1
0
2
0
1
1
0
1
2
1
1
0
1
2
1
1
2
0
1
2
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
2
1
1
0
2
2
1
1
1
1
2
1
1
1
1
2
1
2
1
0
0
2
1
0
1
1
1
2
1
0
1
2
1
0
1
1
1
1
2
1
1
1
1
1
2
2
0
0
1
2
1
1
2
1
1
1
0
1
2
1
0
2
1
2
1
0
1
1
2
1
1
0
0
1
1
2
0
0
1
2
2
0
2
2
1
0
0
0
1
1
1
0
1
2
2
0
1
1
0
2
1
0
2
1
2
0
0
1
1
1
1
0
2
0
2
1
1
2
1
1
1
2
2
1
1
1
2
1
2
1
2
1
1
1
2
1
1
1
1
2
2
2
1
1
1
2
1
1
2
1
0
2
1
1
1
2
1
1
1
1
1
1
2
2
2
1
1
1
0
0
1
0
1
1
1
1
1
0
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
0
2
1
1
1
2
1
0
1
2
1
1
2
1
2
1
1
2
2
1
2
2
2
0
0
1
2
0
1
1
1
1
2
1
2
1
1
1
1
2
0
2
2
0
2
1
2
0
1
1
1
0
1
2
1
1
2
1
2
2
2
1
1
1
1
2
1
1
0
2
1
0
1
1
0
1
0
2
1
1
0
1
1
1
2
2
2
1
1
2
1
2
1
2
1
1
1
1
1
0
0
1
2
0
1
1
1
1
1
1
2
2
2
1
1
1
0
1
1
1
2
1
1
0
1
1
1
1
1
2
1
2
1
2
1
1
0
2
1
1
1
2
0
2
2
2
2
1
2
1
1
2
1
1
0
1
1
1
2
1
1
1
2
1
0
2
1
1
1
1
1
2
1
1
0
2
1
2
2
2
1
2
1
2
2
1
1
1
1
0
2
1
1
1
1
1
2
1
1
0
1
2
2
2
1
1
2
0
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
0
0
1
2
1
1
0
1
1
0
1
1
1
1
2
1
1
0
0
1
1
2
2
1
1
1
2
3
1
1
2
1
1
2
1
0
0
0
2
0
1
2
2
1
1
1
1
2
1
1
2
2
1
1
1
1
1
0
0
2
1
1
0
1
1
1
1
0
1
0
2
1
2
1
2
1
1
1
0
1
2
1
2
2
1
0
1
2
1
1
0
0
2
1
1
2
1
1
1
1
0
1
0
2
1
1
1
0
1
1
0
1
2
0
2
0
1
0
1
1
2
1
1
2
1
1
0
1
0
1
1
1
1
2
1
0
1
2
0
1
1
1
1
2
1
1
1
2
1
1
1
1
1
2
1
0
1
1
1
0
2
1
1
1
1
2
1
1
2
1
1
1
2
1
1
2
2
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
0
1
1
0
1
1
1
2
1
1
1
2
2
2
2
1
1
1
0
0
1
1
1
2
1
1
1
2
2
1
1
1
0
0
1
1
1
2
1
2
2
1
0
1
1
1
1
1
0
1
1
2
2
1
1
1
1
1
2
2
2
1
2
0
1
1
1
1
1
1
2
2
1
1
2
1
0
0
2
1
1
1
1
1
1
2
2
0
2
1
1
1
2
0
1
2
0
0
2
1
2
2
0
2
1
1
1
1
2
1
3
2
0
1
2
3
1
2
2
2
1
1
0
2
1
1
1
1
2
2
2
1
0
1
2
2
1
2
1
1
1
0
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
2
1
1
0
1
1
1
2
1
2
1
1
1
0
1
2
2
1
1
2
2
0
2
1
2
2
1
1
2
1
1
1
3
2
1
2
0
0
1
2
1
1
1
1
2
1
1
1
5
1
1
2
2
0
1
1
0
1
1
1
1
2
1
2
0
0
1
1
2
1
2
1
1
2
1
2
1
1
2
1
2
2
2
1
2
1
2
1
1
1
1
1
2
2
1
1
2
0
2
1
1
1
1
2
1
0
2
1
1
2
1
2
2
0
1
0
1
2
0
1
1
1
1
1
2
2
1
2
1
1
1
2
2
2
1
2
1
1
1
0
1
1
1
1
2
1
1
0
2
2
1
1
1
0
1
1
1
0
1
0
1
1
1
2
2
2
0
1
2
0
1
1
1
2
1
0
2
1
1
1
1
0
1
2
1
1
2
2
2
1
0
2
0
1
0
2
2
0
2
1
1
1
1
1
0
1
1
1
1
1
2
1
1
1
1
2
2
1
1
1
1
0
1
0
2
2
2
3
2
0
1
0
1
1
2
1
1
1
0
1
1
1
3
2
1
1
2
1
1
2
1
1
1
1
1
1
2
0
1
2
1
2
2
2
1
2
2
1
1
0
3
1
2
2
3
1
1
2
2
1
2
2
2
1
1
2
1
1
1
1
1
1
2
0
1
0
2
1
2
2
0
1
1
2
1
1
2
2
1
1
1
1
1
1
0
1
1
1
0
2
1
1
1
1
1
0
1
1
0
2
2
0
2
1
1
1
1
1
2
1
2
1
1
1
2
1
1
0
2
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
0
3
2
0
1
1
1
1
0
1
2
1
2
2
1
2
1
2
2
1
1
1
2
1
1
1
2
0
1
1
1
1
2
2
0
1
1
1
0
1
1
2
0
1
4
1
2
1
1
1
1
1
0
2
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
2
0
1
2
1
0
2
1
0
2
2
1
2
1
2
2
1
1
1
1
2
1
2
1
2
1
1
1
1
1
1
1
0
1
2
1
2
2
1
2
1
2
1
0
1
1
1
1
1
2
1
1
1
2
1
1
1
2
2
1
1
0
1
2
1
2
1
1
2
1
0
0
2
1
1
1
1
0
2
2
1
1
1
1
2
1
1
1
2
2
1
1
2
1
1
1
1
0
1
1
1
1
1
2
1
1
1
1
1
0
2
2
1
0
2
1
1
0
1
1
2
0
0
1
1
2
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
0
1
1
1
1
2
1
1
2
2
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
0
1
1
2
1
1
0
1
1
2
1
0
1
1
1
1
1
1
2
1
0
0
1
1
2
2
1
2
0
1
2
1
2
1
0
2
1
1
2
2
2
4
2
1
2
2
1
1
1
2
1
1
1
1
1
1
1
1
0
1
1
1
1
1
2
1
0
2
1
1
0
1
2
1
1
2
2
0
2
1
1
2
2
1
2
2
1
2
1
1
1
1
2
1
1
2
1
2
2
2
1
0
0
1
1
2
2
1
2
1
0
1
1
1
1
2
1
1
2
1
0
1
2
1
0
2
2
1
2
1
1
1
2
1
0
1
1
2
1
0
0
1
1
1
1
1
1
2
0
1
1
1
0
1
1
1
1
2
1
2
1
1
1
2
2
1
2
2
2
1
1
1
1
2
2
1
1
1
2
1
0
1
2
1
1
1
1
2
2
2
2
1
0
0
0
1
2
0
1
2
1
2
1
1
0
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
0
1
0
1
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
2
1
2
1
1
0
1
0
1
1
1
1
1
2
1
2
2
1
1
1
1
2
1
2
2
1
1
1
1
1
1
1
0
1
0
1
2
1
1
2
1
1
1
1
1
2
2
2
2
2
1
0
1
1
1
2
2
2
1
1
2
2
1
1
0
0
0
1
1
2
1
2
2
0
2
1
2
2
1
2
1
1
1
1
2
1
1
1
1
1
2
2
1
0
0
1
2
1
1
2
3
1
0
0
2
1
0
1
2
1
1
1
2
2
1
2
2
1
2
0
0
1
1
2
1
1
1
1
2
0
2
1
1
1
1
1
1
1
0
0
1
2
1
1
1
0
1
1
3
1
1
2
4
1
0
0
1
1
1
1
0
2
0
2
1
1
1
2
1
0
1
1
1
1
1
2
2
1
2
1
0
1
2
0
2
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
2
1
1
1
1
2
1
2
1
0
1
1
1
2
1
1
2
1
1
1
2
1
1
1
2
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
2
1
1
0
1
2
1
2
2
2
2
1
1
2
0
1
1
2
1
1
1
1
1
1
0
1
2
2
2
1
2
1
2
1
0
2
1
1
2
1
2
2
1
1
1
2
0
1
1
1
2
1
1
1
2
1
1
2
2
1
1
2
2
1
1
1
1
1
2
1
0
1
0
1
1
2
2
1
0
2
2
2
1
1
1
1
1
0
1
0
2
2
0
1
2
1
1
1
1
2
1
2
2
0
0
1
2
2
1
2
0
1
1
1
0
3
1
2
1
0
0
2
2
1
1
1
2
1
0
2
1
2
1
0
1
1
1
1
0
1
2
1
1
1
0
1
1
1
2
1
1
1
2
2
1
0
1
1
1
1
2
2
1
1
1
2
2
2
2
1
1
1
2
0
1
1
2
2
1
1
1
1
1
1
1
1
0
1
1
1
0
2
1
2
1
1
1
0
0
2
4
2
0
1
2
0
1
2
2
1
1
1
2
2
1
1
0
1
4
1
2
3
2
0
1
1
1
1
1
0
1
1
1
2
0
0
1
0
1
1
2
0
1
1
1
0
1
1
1
1
1
1
1
1
1
0
1
1
1
1
0
1
1
2
1
2
0
2
1
1
1
1
1
2
1
1
1
1
2
1
2
1
1
1
1
2
1
1
1
1
3
2
1
1
3
2
1
1
1
0
1
2
2
2
1
1
1
1
2
1
1
1
1
1
1
1
1
0
1
1
0
0
2
0
1
1
1
1
1
1
2
1
1
2
1
1
2
1
2
1
0
1
2
2
1
1
1
0
1
1
1
0
1
0
1
1
1
1
2
1
2
1
2
1
1
1
1
1
1
0
1
2
1
1
2
1
1
2
2
2
1
0
1
1
1
0
1
2
1
1
1
2
0
1
1
1
2
1
2
2
1
1
0
2
2
1
0
1
1
0
2
2
1
2
1
2
0
1
1
1
2
2
1
1
1
1
1
2
1
1
1
0
1
2
1
1
2
0
1
1
1
2
2
1
2
2
2
1
1
2
2
1
2
0
1
1
2
2
1
1
1
1
1
1
2
0
1
2
1
2
1
2
0
1
1
1
1
1
1
2
2
1
1
2
1
1
1
1
1
1
2
1
1
3
1
1
0
2
1
1
1
1
1
1
1
0
0
1
0
1
1
1
1
1
5
1
2
2
1
1
1
1
1
2
1
1
2
0
3
2
1
1
1
1
1
1
1
0
1
1
1
1
1
2
1
0
1
0
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
0
1
2
1
1
1
2
2
1
2
1
1
2
2
1
1
2
2
1
1
1
2
1
3
1
1
1
1
0
1
1
1
1
0
1
1
1
1
0
1
1
1
1
2
2
1
2
1
2
2
2
1
1
1
0
1
1
1
2
2
2
1
1
1
1
1
2
1
2
0
1
0
1
1
1
1
1
2
1
1
1
1
1
2
0
1
1
1
1
1
2
1
1
1
0
1
2
0
3
1
1
2
2
1
0
1
1
1
1
1
1
1
2
2
1
0
1
1
2
0
1
2
2
1
1
2
1
1
2
1
1
0
0
1
1
2
1
1
2
1
1
1
1
1
0
0
2
1
1
1
0
1
1
1
1
1
1
2
2
1
0
1
1
1
2
0
1
1
1
0
1
1
1
1
2
1
0
1
2
2
1
1
0
1
1
1
1
1
1
1
1
2
1
1
0
1
1
1
2
1
2
1
2
1
0
2
1
0
1
2
2
1
1
2
1
0
0
1
0
1
1
2
2
0
1
0
1
1
1
1
2
1
2
2
0
1
1
2
1
1
0
0
2
0
2
1
2
2
2
0
1
1
2
2
0
1
1
0
0
0
1
2
2
2
1
0
1
1
1
2
2
2
2
0
0
1
0
1
0
1
1
1
1
1
1
1
1
0
2
1
1
1
1
1
1
1
0
2
1
1
2
2
1
2
1
1
1
0
2
2
2
1
1
1
0
2
3
1
2
1
2
1
2
2
1
1
2
2
1
1
1
1
1
2
2
1
1
0
1
2
2
2
1
0
2
1
1
0
1
1
1
2
0
1
1
1
1
2
1
1
1
2
1
1
1
1
1
0
1
2
3
2
2
1
1
1
1
1
1
1
1
1
0
0
1
2
1
0
2
1
1
2
1
1
1
1
1
0
1
0
1
1
1
2
1
2
0
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
2
1
2
1
2
1
2
2
1
1
2
0
2
1
1
0
0
1
0
1
1
1
1
1
1
0
2
1
2
1
2
1
1
1
1
2
2
1
1
1
2
1
1
1
1
2
1
2
2
1
1
2
1
0
1
1
2
1
1
2
2
2
1
0
1
1
1
0
1
1
2
1
1
1
1
0
0
1
0
1
2
1
1
2
2
1
0
2
1
1
1
0
1
1
1
2
1
1
2
1
0
1
1
1
0
1
1
0
2
1
1
1
2
1
1
2
0
1
1
1
1
1
1
1
1
0
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
2
1
2
2
1
1
2
0
1
1
1
0
0
1
0
0
1
1
1
1
1
1
1
0
1
1
1
2
1
1
1
2
2
1
3
1
1
1
1
2
2
0
1
0
2
1
2
2
1
1
1
1
1
2
1
2
1
1
2
1
2
1
2
1
1
1
1
2
2
1
1
1
1
1
1
1
0
1
2
1
1
0
1
1
0
1
2
1
1
1
1
2
1
1
0
0
0
2
1
1
1
1
2
1
2
1
1
1
2
2
1
1
1
0
1
1
1
2
0
1
1
2
1
1
1
1
1
0
1
1
2
1
1
2
1
1
1
0
1
3
1
1
1
1
1
1
2
1
1
1
0
1
1
1
2
1
1
21
1
1
2
1
1
0
1
1
2
1
2
1
1
1
1
1
0
1
1
2
1
1
1
1
1
1
1
0
2
1
1
1
1
2
0
1
2
2
1
1
1
2
1
1
1
1
1
1
1
2
1
2
2
1
1
1
2
1
0
1
1
1
1
0
1
1
1
0
1
2
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
2
1
1
1
3
1
2
1
1
0
1
1
0
1
2
0
1
1
0
1
1
1
1
1
1
1
0
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
0
2
1
1
1
1
1
1
0
1
1
1
1
0
1
1
1
1
1
1
1
1
1
2
1
1
1
1
0
1
2
2
2
1
1
1
1
2
1
2
0
1
1
2
1
2
3
2
1
2
1
0
1
2
1
1
2
1
1
1
0
2
0
2
0
1
2
2
2
2
1
1
0
1
1
1
1
0
1
0
1
1
1
1
1
1
2
1
1
1
1
1
0
3
1
2
2
1
1
1
1
1
2
1
2
2
1
1
2
2
2
2
1
0
2
1
1
0
1
1
1
1
2
1
1
1
4
1
2
2
0
2
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
0
1
1
2
1
1
0
1
1
1
1
0
1
0
1
1
1
1
1
1
2
1
2
2
2
1
2
1
0
1
2
1
1
1
1
1
2
2
2
2
1
1
2
1
2
1
1
1
1
1
1
1
1
0
1
2
2
2
2
0
2
1
2
2
2
2
1
2
2
1
1
1
1
2
2
1
5
0
1
1
2
1
1
1
1
0
2
2
2
2
1
2
1
2
1
1
1
2
1
1
2
2
1
1
1
2
1
3
1
0
0
2
1
2
1
1
1
1
2
2
1
1
1
1
2
2
1
2
0
0
1
1
1
1
2
2
1
3
1
2
1
1
1
1
1
1
2
1
2
2
1
1
1
1
0
1
1
1
2
2
0
2
1
2
2
2
1
2
1
1
0
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
0
1
2
2
2
2
2
2
1
1
2
1
1
1
1
2
1
1
1
2
1
1
2
1
1
1
1
1
4
0
1
0
2
1
1
1
1
1
1
1
2
1
0
2
2
2
1
0
0
2
1
1
1
2
1
1
1
1
1
1
0
2
1
1
2
2
0
1
1
1
1
3
1
1
1
1
1
2
1
2
1
1
1
0
1
1
2
2
1
2
2
1
2
2
1
1
1
1
0
1
0
1
1
2
1
1
2
0
1
2
1
2
2
2
1
1
1
1
0
1
1
1
2
1
1
1
0
1
2
1
0
1
2
1
1
1
1
1
1
2
2
2
1
1
1
0
2
2
2
0
1
1
2
0
2
0
1
0
0
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
0
0
0
1
0
1
2
2
1
2
2
1
1
2
1
1
1
1
2
1
1
1
1
2
2
1
0
1
1
1
1
2
1
2
1
1
1
2
1
1
2
1
0
1
1
1
1
1
1
0
0
1
1
1
1
2
1
1
2
2
2
2
2
2
1
1
1
1
0
0
0
1
1
0
1
6
1
1
1
2
0
1
2
2
1
2
0
2
1
0
1
1
1
0
0
1
2
3
2
1
0
1
0
0
2
1
1
1
0
0
2
2
1
1
0
1
2
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
2
0
1
0
1
1
0
1
1
0
2
1
1
2
2
0
0
2
1
1
1
0
2
1
2
1
0
1
1
1
0
1
1
2
1
1
2
1
0
1
1
0
1
1
1
2
2
1
1
0
1
0
1
2
1
2
0
2
0
1
1
1
1
1
2
2
2
1
1
2
1
1
0
1
1
1
1
1
0
0
1
2
1
0
1
2
2
1
2
2
0
1
1
2
1
0
0
1
1
2
0
1
1
0
1
1
1
2
0
0
1
2
1
0
3
2
1
0
1
1
1
0
1
1
1
0
1
0
2
1
1
1
0
1
2
1
2
0
1
1
1
1
1
1
1
1
0
1
2
2
2
1
1
0
1
0
1
1
2
1
0
1
0
2
0
2
1
0
1
1
2
3
1
1
2
0
1
1
1
0
2
1
2
1
2
2
2
2
2
1
0
1
1
1
1
1
1
1
1
1
1
3
2
1
1
2
2
0
2
1
1
2
2
1
1
1
1
2
0
0
1
1
0
1
2
1
2
1
1
1
0
2
0
2
1
1
1
0
0
1
1
2
0
1
1
2
0
0
2
1
1
0
1
2
1
1
0
2
1
0
1
0
1
1
2
1
0
1
1
2
1
2
0
1
2
1
1
2
1
1
2
1
2
2
1
1
1
0
1
1
1
0
1
1
1
2
1
1
2
1
2
1
1
1
1
1
1
0
2
0
2
2
0
1
1
2
2
0
1
1
2
2
1
0
1
2
1
0
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
0
0
1
1
1
1
1
1
1
2
0
2
2
0
4
1
2
1
1
1
2
1
1
2
1
1
1
1
1
0
2
0
1
1
2
2
1
1
0
1
1
1
1
1
0
0
1
2
1
2
0
1
0
1
2
1
1
1
0
2
1
1
0
1
1
1
2
1
1
1
2
1
1
1
1
2
0
1
1
2
2
1
2
1
0
0
1
0
1
2
1
1
2
1
1
1
2
0
1
1
1
2
1
1
0
0
1
1
2
1
1
1
1
2
1
0
2
2
1
2
2
1
0
2
1
2
0
0
1
2
2
1
0
1
1
1
2
1
2
2
1
0
1
2
2
1
1
1
0
2
2
1
1
1
1
1
1
0
1
3
1
2
2
1
3
1
1
2
3
1
1
1
0
1
1
1
1
1
1
1
2
2
1
2
1
2
1
1
1
1
2
1
2
2
1
1
1
1
1
0
1
0
1
1
1
1
0
2
2
1
1
1
1
2
1
1
1
0
2
1
2
1
1
1
1
1
2
1
1
1
2
2
1
2
0
1
2
1
2
2
3
2
1
1
2
0
1
2
1
0
1
0
0
1
1
1
1
1
0
1
1
3
2
1
2
1
1
2
1
1
2
1
1
1
1
0
1
1
1
1
0
0
2
1
1
2
3
1
1
0
1
1
1
2
1
2
1
1
1
2
1
2
1
2
0
1
2
0
2
0
2
2
1
2
1
0
2
2
1
1
0
1
1
0
1
0
2
1
2
1
1
2
1
1
1
2
2
1
0
1
1
1
2
1
2
1
1
1
1
1
1
0
2
2
2
1
2
1
0
1
1
0
2
0
1
1
1
1
1
1
1
2
2
1
1
1
0
1
2
2
1
2
1
0
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
0
1
1
1
1
2
2
2
2
1
1
3
1
2
1
1
1
0
2
2
1
1
1
2
0
0
1
0
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
0
0
2
2
1
2
2
0
1
2
1
1
2
0
1
2
0
1
1
0
1
1
1
2
1
1
0
1
2
2
0
0
1
1
1
1
1
1
2
2
1
1
0
1
0
1
1
2
1
1
2
1
2
1
2
0
1
2
2
2
1
2
1
1
2
2
1
2
2
2
0
0
1
0
2
0
1
2
2
1
1
1
1
1
1
1
1
0
1
2
1
1
1
1
1
1
1
1
1
1
2
0
2
1
2
1
1
2
1
1
1
1
1
1
1
1
1
0
0
0
0
2
1
1
1
1
1
1
0
1
1
1
1
1
2
1
2
1
1
1
2
1
0
1
0
1
2
1
2
1
1
1
2
1
1
0
2
0
2
1
0
2
1
2
1
2
1
0
1
2
1
1
2
0
1
1
0
1
1
1
2
1
1
2
1
1
1
0
1
2
1
3
3
1
1
2
0
0
2
2
1
2
2
1
1
1
0
1
2
2
2
1
1
1
1
0
0
1
1
1
1
1
1
1
0
1
1
0
2
1
1
1
0
1
1
1
1
0
1
1
1
2
1
2
1
1
2
1
0
2
1
1
1
2
2
1
1
0
1
1
1
2
3
1
0
2
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
2
0
1
1
1
0
1
1
1
2
1
1
2
1
0
0
2
1
0
0
1
1
1
2
1
1
1
0
2
0
1
2
2
1
1
1
2
0
1
1
2
1
2
2
1
1
1
1
1
1
1
0
1
1
1
1
1
2
2
2
1
1
1
2
2
1
1
1
1
0
2
1
1
1
0
1
1
0
2
1
1
1
0
1
2
1
0
1
1
1
4
0
1
2
0
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
0
2
1
1
2
1
1
2
1
1
0
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
2
1
2
1
1
1
1
2
2
1
1
2
2
1
1
0
1
1
2
2
2
0
2
1
1
3
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
2
2
0
2
2
1
1
1
2
2
1
1
2
2
0
1
2
0
2
1
1
1
0
1
1
0
1
2
1
2
2
0
0
1
1
1
1
1
2
2
2
1
2
1
1
1
0
2
2
1
0
2
2
0
1
1
0
1
2
1
1
0
2
1
2
2
2
2
1
2
2
1
1
2
1
1
2
1
1
2
2
0
2
2
2
0
1
1
1
2
1
1
2
1
1
2
1
2
1
2
1
1
0
2
1
3
1
2
0
1
1
4
2
1
1
1
0
1
1
1
1
1
1
1
1
2
1
2
0
2
1
2
2
0
1
1
2
1
2
2
1
2
2
1
2
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
2
2
1
2
2
1
2
2
1
0
1
1
0
1
1
2
2
1
1
2
0
1
1
1
1
2
1
0
1
2
1
1
1
1
0
1
1
2
0
1
0
1
1
1
1
1
3
1
1
1
0
1
1
0
1
0
0
1
1
2
0
1
1
1
0
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
2
2
1
1
1
0
1
1
1
2
1
1
1
2
2
2
2
1
2
1
1
1
2
2
1
2
1
2
1
1
2
2
0
1
0
1
1
2
0
1
2
0
2
1
2
1
1
2
2
0
1
1
1
1
1
1
1
2
1
1
1
1
2
2
0
1
1
0
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
2
1
2
1
1
2
1
0
2
1
1
0
1
1
1
2
0
2
1
0
1
1
1
0
1
1
1
2
1
1
1
1
1
2
1
2
2
1
2
1
1
1
0
1
1
2
1
1
2
2
1
2
1
1
2
2
1
2
1
2
1
0
2
2
2
2
2
1
0
1
1
1
1
1
1
2
1
1
2
0
1
2
2
2
2
1
2
2
1
1
1
1
1
1
2
2
0
1
2
2
1
2
1
2
2
1
1
2
1
1
0
2
2
1
0
2
1
1
0
0
1
1
1
1
2
1
0
2
1
2
1
0
2
0
1
1
0
3
1
1
1
2
1
1
1
1
1
0
1
1
2
2
2
1
1
1
2
1
1
1
0
1
1
2
2
1
2
1
1
2
1
3
1
1
0
2
2
1
0
1
1
1
1
2
1
1
1
2
1
1
1
2
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
0
1
0
2
1
1
1
1
1
0
0
1
0
1
1
1
1
1
1
0
0
0
1
2
2
1
1
1
2
0
0
1
1
2
1
0
2
2
1
2
1
2
1
2
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
0
0
2
1
2
2
1
1
2
1
1
1
1
2
1
2
1
1
1
1
2
0
1
1
2
2
0
2
1
0
2
1
1
2
1
1
1
2
1
1
2
2
1
2
2
0
1
1
1
1
1
1
1
2
2
1
2
1
2
2
0
0
1
2
1
1
1
1
1
2
1
1
0
1
2
1
1
2
1
1
1
1
1
0
1
1
0
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
0
2
1
1
2
1
2
0
2
1
1
0
1
2
1
2
0
1
1
0
1
2
1
1
1
2
1
1
1
2
1
2
0
2
1
1
0
1
1
1
0
1
1
2
1
2
1
2
2
1
2
0
1
1
0
2
2
1
2
1
1
2
1
0
1
1
1
2
1
1
1
2
1
0
1
1
1
0
1
2
1
0
1
1
1
1
1
1
2
1
1
1
2
1
0
2
0
2
0
2
2
0
2
1
1
1
0
2
1
2
1
0
0
1
1
1
2
2
1
1
2
1
1
1
2
1
2
6
1
1
1
0
1
2
1
2
1
1
1
1
0
1
1
1
1
1
1
1
1
1
2
2
1
1
2
0
1
1
2
0
2
1
0
1
1
1
1
1
1
1
1
0
1
2
2
2
1
2
1
2
2
1
1
2
1
1
1
2
1
1
0
1
1
2
2
1
0
1
0
0
0
2
1
1
2
1
0
1
1
2
2
2
1
2
1
1
1
2
1
1
2
1
2
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
2
1
2
1
1
1
1
4
1
1
2
1
0
2
0
0
1
2
1
1
0
1
1
2
1
1
1
1
1
1
2
1
2
0
1
1
1
2
1
1
2
2
2
2
1
1
1
1
2
1
1
1
1
1
1
0
1
1
1
2
0
1
1
1
1
0
1
2
2
1
1
2
1
1
2
1
1
1
1
0
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
2
1
1
1
1
1
1
1
2
1
1
2
0
0
1
0
2
2
1
2
1
2
1
2
1
1
2
2
2
0
0
1
2
2
2
1
2
0
2
1
0
2
1
2
2
2
1
1
0
1
2
1
1
2
2
1
1
1
1
1
1
2
1
2
2
2
1
1
1
0
1
2
2
1
1
1
1
2
2
2
1
2
1
2
2
2
2
0
1
1
2
1
1
0
0
2
0
2
2
0
1
1
1
2
0
0
1
2
2
1
1
0
2
1
1
0
1
1
1
1
1
2
1
1
1
1
1
1
2
1
0
2
1
1
2
0
2
2
2
1
1
2
1
1
1
1
2
2
0
2
0
1
1
1
1
1
1
1
1
2
1
2
2
1
2
1
1
1
1
1
1
0
2
1
1
1
2
2
1
2
2
2
2
0
1
1
1
0
1
0
1
1
0
1
1
1
1
0
1
0
1
2
1
1
0
2
1
1
0
2
1
2
2
1
1
1
1
2
0
1
0
1
1
1
1
1
1
1
2
1
1
0
2
0
2
1
0
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
0
1
0
2
0
1
1
1
1
1
1
6
1
2
1
2
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
0
2
0
1
1
1
1
1
2
1
2
1
2
2
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
2
1
0
3
1
2
0
1
1
1
2
1
2
1
1
1
2
1
2
3
1
0
2
2
1
0
1
2
1
1
0
2
2
1
1
1
1
2
1
1
1
1
0
1
1
1
2
0
1
1
1
2
1
2
1
1
1
2
1
2
1
2
1
0
1
2
2
1
1
0
0
1
2
0
2
2
2
1
0
1
2
1
1
1
1
2
1
1
2
0
1
2
1
1
2
1
0
2
1
1
2
0
1
2
1
1
2
2
0
1
1
1
1
1
1
1
2
0
1
1
1
1
1
1
1
1
0
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
0
2
1
1
1
1
2
2
2
1
2
1
1
1
2
1
1
2
1
0
2
0
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
2
1
2
0
1
2
1
1
2
1
1
2
1
2
1
0
0
1
1
2
2
2
1
1
1
1
1
2
1
1
0
1
2
1
2
0
1
2
1
2
1
1
1
1
1
2
2
1
1
1
2
2
1
1
1
2
2
1
1
3
2
1
1
1
1
1
1
1
1
2
1
0
2
2
1
1
2
1
1
2
1
2
2
1
1
1
1
1
1
2
2
0
1
2
2
1
1
1
1
1
0
1
1
2
1
0
1
1
1
1
2
2
1
1
1
1
1
0
2
1
1
0
1
2
1
2
0
1
1
1
2
1
1
1
1
0
1
1
1
0
2
1
0
1
2
1
1
1
2
0
1
0
2
2
1
1
1
1
1
0
1
2
1
1
1
1
2
2
1
1
1
1
1
0
1
2
1
1
1
2
0
1
2
0
2
1
2
0
1
1
2
2
1
1
2
1
0
1
2
2
1
0
1
1
1
0
2
1
2
2
2
1
1
1
1
1
1
0
0
1
2
1
1
0
1
1
1
2
2
1
2
1
2
2
2
1
1
1
1
1
0
1
2
1
1
2
0
1
0
1
1
1
1
1
1
2
2
1
1
2
2
1
1
2
0
1
2
1
0
1
1
1
1
1
1
1
2
2
1
1
2
2
1
2
0
2
2
1
1
1
0
1
1
1
1
1
0
2
2
1
1
2
2
2
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
0
0
2
1
0
1
2
1
1
2
1
1
1
0
1
1
2
1
2
2
1
2
1
1
2
2
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
2
0
2
1
1
2
1
1
1
1
1
2
2
2
1
1
3
1
1
1
1
2
1
1
0
1
2
1
1
2
1
1
2
1
2
2
1
2
0
1
1
2
0
0
3
0
1
0
2
0
1
1
2
1
0
2
1
0
2
1
0
2
2
0
2
0
0
0
2
1
0
2
1
0
1
0
1
2
0
1
0
1
1
2
1
2
0
0
1
1
1
0
1
1
0
1
1
0
1
1
2
1
2
2
2
1
1
1
0
0
2
1
2
2
0
2
1
1
1
0
2
1
0
2
2
1
1
1
1
1
1
1
2
1
2
0
1
1
1
2
2
1
2
2
2
1
0
1
1
1
1
1
2
1
0
2
2
1
1
2
1
2
0
1
3
1
2
1
1
1
1
2
1
1
2
1
0
0
1
2
1
1
1
1
2
2
1
1
1
0
1
1
0
0
0
1
1
1
1
0
2
1
2
0
0
1
0
1
1
1
0
1
1
1
2
1
1
1
1
1
3
1
1
1
1
1
2
1
1
1
1
2
1
1
2
2
1
1
1
1
0
2
1
1
1
2
2
1
2
1
2
0
1
0
2
1
1
2
1
2
0
1
2
0
0
0
1
1
1
2
2
1
0
1
2
1
1
1
2
2
1
1
2
2
1
2
1
2
1
2
1
0
1
1
2
1
2
1
1
0
2
0
1
2
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
0
1
1
2
1
0
1
1
0
1
1
2
2
1
2
1
1
0
2
1
2
1
2
1
2
1
1
1
2
2
2
2
1
1
1
0
1
1
0
1
1
1
1
1
2
2
0
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
2
0
1
1
2
1
0
1
1
1
1
1
1
1
1
2
1
2
1
1
0
1
1
0
1
1
0
1
1
1
1
1
1
1
2
0
5
0
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
2
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
0
1
1
2
0
2
2
0
2
1
1
2
2
1
1
1
2
2
1
1
1
1
2
1
2
2
2
0
2
1
1
0
1
1
1
1
2
1
0
0
2
1
2
0
0
1
0
1
1
2
1
1
1
2
0
1
2
1
2
2
1
0
2
1
1
1
2
2
2
0
0
2
2
1
1
2
0
1
1
2
2
2
2
2
1
2
1
1
1
1
1
2
1
1
2
2
1
1
1
1
1
0
0
1
1
2
1
0
1
1
1
1
1
2
1
1
1
1
1
1
0
1
2
2
1
1
1
1
1
2
0
1
1
1
2
1
1
1
1
2
2
2
0
2
1
2
1
1
1
1
1
1
1
0
1
2
1
1
2
1
1
2
1
2
1
2
0
1
2
2
2
0
1
1
1
1
1
1
3
1
1
0
1
2
2
2
1
1
1
2
0
1
1
1
1
1
1
2
1
1
2
0
1
2
1
1
0
2
1
2
1
1
2
1
1
1
1
1
1
1
1
2
2
1
1
1
1
2
1
1
2
1
2
2
2
2
0
2
1
2
2
1
0
1
1
0
1
2
2
1
2
1
1
1
2
1
2
2
1
2
2
1
1
1
1
0
1
0
1
1
0
0
1
1
2
2
1
1
1
3
2
0
1
1
1
3
0
1
1
1
1
1
2
2
1
1
1
2
2
0
1
1
0
2
1
2
0
1
3
2
1
1
1
1
2
1
1
1
0
1
2
1
1
1
0
1
0
1
2
1
0
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
2
1
1
0
0
1
2
1
0
1
1
2
2
2
1
1
1
1
1
1
0
2
1
1
1
1
2
1
2
1
1
1
1
1
1
0
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
0
1
2
2
1
2
1
0
1
1
2
1
1
1
0
1
1
1
1
2
1
1
2
0
1
1
1
1
2
1
1
0
1
0
2
1
1
1
1
1
2
2
1
1
1
1
0
2
0
0
2
1
0
1
2
0
1
2
1
1
0
1
1
1
1
1
1
2
0
1
5
3
1
1
1
1
1
1
1
1
1
1
1
2
0
1
1
1
1
1
1
2
1
0
1
1
1
2
1
1
2
2
1
1
1
2
2
0
2
1
2
1
2
0
2
0
1
0
0
1
2
1
1
2
1
1
1
1
1
2
0
2
1
1
1
1
1
2
2
0
0
1
1
1
1
1
2
2
1
2
1
2
1
1
0
1
2
2
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
0
1
1
0
1
1
0
2
1
1
1
0
0
1
2
3
1
1
1
1
1
1
1
0
1
2
1
3
1
1
1
1
1
0
1
1
1
1
1
0
1
2
2
1
1
1
2
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
0
1
1
2
1
2
2
1
1
1
1
1
2
2
1
1
1
1
2
1
2
1
1
2
1
1
2
1
2
1
1
1
2
1
1
1
1
1
2
2
0
1
1
1
2
1
1
0
2
2
2
1
1
2
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
0
1
0
1
1
1
1
1
1
1
1
0
1
0
1
0
1
1
2
0
1
1
1
1
2
1
1
0
2
1
1
1
2
1
1
1
1
1
2
1
1
1
1
0
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
2
2
2
2
1
1
1
1
1
0
1
1
1
1
2
1
0
2
2
1
1
1
2
0
2
1
2
2
2
2
1
1
2
2
2
1
1
1
0
1
2
1
1
1
1
1
1
0
1
1
1
0
1
1
0
1
2
2
1
1
1
2
1
1
1
0
2
1
0
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
0
2
1
1
1
1
2
1
2
2
2
1
1
1
2
1
2
2
2
2
1
2
0
2
1
3
2
1
1
1
1
1
2
2
1
1
1
1
1
1
0
1
1
1
2
1
2
2
1
0
1
1
1
1
1
1
0
1
1
1
1
1
2
2
1
1
2
2
1
1
2
1
0
2
1
1
1
1
1
1
2
2
1
0
1
2
1
2
1
0
1
1
1
0
1
1
1
0
1
1
2
2
2
1
1
1
2
2
1
0
1
1
2
2
1
1
1
1
1
2
2
0
0
1
1
1
2
1
0
1
2
2
1
1
1
1
0
1
0
1
1
0
1
1
1
2
2
2
1
2
1
1
0
1
2
1
1
2
1
0
2
2
2
1
0
2
1
2
2
1
1
1
1
1
2
1
0
1
1
1
1
2
1
1
2
1
1
1
2
0
1
2
1
2
1
1
1
2
1
1
1
0
1
1
2
1
1
2
2
1
1
2
1
2
1
1
2
1
1
1
2
0
0
0
1
1
1
1
1
1
1
0
0
1
1
2
2
1
2
1
1
1
2
1
2
1
2
2
1
1
1
1
2
1
2
1
0
1
1
1
1
0
2
0
0
1
2
1
0
1
1
2
1
1
1
1
1
1
2
1
1
2
2
2
1
1
2
1
2
1
2
1
0
0
2
1
1
1
1
3
2
2
1
1
1
1
2
2
1
2
1
2
1
1
1
1
0
0
1
1
1
2
1
1
1
1
1
0
1
4
1
1
2
0
2
0
1
1
1
1
1
2
2
2
1
0
2
2
1
1
1
2
1
1
2
2
1
1
1
1
1
0
0
1
1
1
1
2
1
2
0
1
1
2
1
1
1
1
0
0
1
2
1
2
2
2
2
1
2
1
2
1
0
1
2
1
2
1
1
0
0
2
1
1
1
2
2
1
2
2
1
1
0
2
2
2
1
2
1
1
1
0
2
1
1
2
1
2
1
2
1
2
1
2
2
1
1
1
1
1
0
1
0
1
1
1
1
1
1
0
2
1
0
3
1
2
4
1
1
0
1
1
2
1
2
1
0
1
1
1
1
2
1
2
2
2
1
1
2
1
1
1
2
2
1
2
0
0
1
1
2
2
1
1
2
1
1
1
2
1
1
0
1
2
2
2
0
0
1
1
2
1
3
1
1
0
1
2
1
0
1
1
2
2
1
1
1
1
1
1
1
1
1
2
1
2
1
0
2
1
2
2
0
1
1
0
2
0
1
1
1
2
1
1
1
1
1
1
0
2
0
0
0
2
0
2
1
1
0
1
2
0
1
1
0
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
0
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
0
0
0
1
2
2
1
1
1
2
2
1
1
1
2
0
1
1
1
1
1
1
2
1
1
0
1
2
2
0
1
1
1
0
1
1
1
2
1
1
2
1
1
1
1
1
3
1
1
0
2
1
2
1
1
0
1
1
1
1
1
1
1
2
1
1
0
2
1
1
1
1
0
1
1
1
2
1
2
1
1
2
1
0
1
0
0
1
2
1
1
1
2
1
1
0
1
1
2
1
2
1
1
1
1
1
1
2
0
1
2
1
2
1
1
2
2
0
1
2
1
1
1
2
0
2
1
0
1
1
0
1
1
2
1
0
2
1
1
1
0
2
1
0
2
1
2
0
0
0
1
2
2
1
1
1
2
1
1
1
0
1
1
1
1
1
1
2
1
2
1
1
1
2
2
0
1
1
2
0
1
1
1
1
1
2
2
1
1
0
1
2
1
1
0
2
2
1
0
1
1
1
1
2
1
1
2
1
1
1
1
0
1
2
1
2
0
1
1
2
1
3
1
0
1
2
0
1
1
0
1
1
0
1
1
1
1
1
2
1
0
1
1
1
1
0
1
1
1
1
1
1
1
0
0
1
2
1
1
1
0
1
0
1
1
1
1
0
2
1
2
1
1
1
2
2
1
1
1
1
1
0
1
1
1
2
2
2
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
2
0
2
1
1
1
1
2
2
1
1
1
2
1
1
0
1
0
1
1
2
2
1
0
0
0
2
1
1
1
0
2
1
1
1
1
1
1
0
1
2
2
1
1
0
1
1
1
1
2
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
0
2
0
1
1
1
1
0
1
2
1
2
1
1
1
2
1
2
2
1
1
0
1
0
1
0
1
2
1
1
1
2
1
1
1
2
2
1
1
1
0
1
1
2
1
1
1
1
2
1
1
1
0
1
2
1
2
1
0
1
1
1
1
2
1
1
2
1
1
1
2
1
1
1
1
1
1
2
1
1
0
1
1
1
1
1
0
1
1
2
1
0
1
1
1
1
1
0
2
2
1
1
1
0
1
1
1
1
2
0
1
2
1
2
1
1
0
0
2
1
2
2
0
2
1
2
1
2
0
2
1
1
1
1
1
1
0
2
1
1
2
1
1
1
1
1
0
2
2
1
1
0
2
2
2
3
0
0
2
1
1
1
1
1
0
1
1
1
1
1
1
2
2
1
2
2
1
2
0
1
1
1
1
1
0
1
1
1
1
1
1
2
0
1
1
0
1
2
1
1
0
1
1
0
0
2
1
1
1
1
2
2
0
1
1
1
1
1
1
0
0
0
1
0
2
1
1
2
1
2
1
1
1
2
1
1
2
2
0
1
1
1
0
1
1
1
1
2
2
2
1
2
1
2
2
0
2
1
3
1
2
2
1
2
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
0
1
1
2
0
1
1
1
1
1
1
1
1
1
1
1
0
1
2
0
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
0
1
1
2
1
1
1
1
1
1
1
0
1
2
2
2
0
2
2
0
0
1
1
1
2
2
2
3
2
1
1
0
2
2
1
1
1
0
1
2
1
2
0
1
2
0
1
1
2
2
1
2
1
1
1
2
2
0
2
2
1
1
1
2
1
1
2
1
1
2
0
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
1
1
2
0
2
1
2
2
1
1
1
1
2
2
1
0
1
1
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
1
0
1
1
2
1
2
0
2
1
1
2
1
0
1
2
1
0
1
1
1
1
1
2
1
1
1
0
2
2
1
1
1
1
1
2
1
1
2
1
1
1
1
0
3
1
0
1
2
2
1
1
1
1
2
1
1
3
1
1
1
2
1
2
1
0
1
0
1
1
1
1
2
0
2
0
1
1
1
2
2
1
2
2
1
1
1
1
0
2
1
2
2
1
0
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
2
0
1
2
1
2
1
1
2
1
2
1
1
1
0
1
1
1
1
3
3
3
1
0
2
0
1
1
1
1
0
1
1
1
1
1
0
1
0
0
1
1
2
1
1
2
1
2
1
1
0
1
0
2
2
1
1
1
1
2
2
1
2
1
1
1
1
1
2
1
0
1
1
1
0
2
1
2
1
1
2
1
1
0
1
1
1
1
1
1
0
1
2
1
1
1
1
0
1
1
0
1
1
1
1
1
2
1
1
1
1
1
0
1
1
1
1
1
1
1
2
2
1
1
1
2
1
2
1
1
1
2
2
0
1
1
1
1
1
1
1
1
1
1
2
1
2
1
0
2
1
1
1
1
1
2
1
1
2
0
1
2
1
2
2
1
1
2
1
2
1
0
1
1
1
1
2
1
1
1
2
2
1
1
1
2
2
1
2
0
1
0
1
1
1
1
2
1
1
1
2
1
1
1
0
1
2
1
1
0
2
1
1
1
1
0
1
1
1
1
1
2
0
1
1
1
2
1
1
1
1
1
1
1
0
4
2
1
1
2
2
1
1
1
2
1
1
2
1
1
1
0
1
1
1
2
2
1
1
1
1
1
2
2
1
1
2
0
1
2
2
1
2
2
1
1
2
0
2
2
1
1
0
1
1
1
1
2
1
1
0
0
2
0
1
0
1
2
2
0
1
0
0
0
1
1
2
1
1
1
1
2
0
2
2
1
1
2
1
1
1
1
1
0
1
1
2
0
1
2
1
1
1
2
1
2
1
0
1
2
2
1
1
3
2
1
1
2
0
1
0
2
0
1
2
1
1
1
1
1
0
2
2
1
2
0
0
0
1
2
1
2
2
1
0
0
1
0
2
1
1
1
1
0
1
1
1
0
2
1
0
1
1
1
1
1
1
1
1
2
0
2
1
1
1
1
1
1
1
1
1
2
1
2
1
2
1
2
1
2
1
2
1
2
0
1
2
1
1
1
0
2
1
2
1
2
1
1
2
0
2
1
1
1
3
2
1
2
2
1
2
2
2
1
2
1
1
2
1
1
1
1
1
1
1
2
1
2
2
1
1
2
1
1
1
1
0
1
2
1
1
1
2
1
2
1
1
1
1
0
0
1
0
1
1
2
1
2
1
1
1
3
1
1
1
1
1
1
2
1
0
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
2
2
1
0
2
2
1
0
2
0
2
1
0
2
1
1
2
2
1
1
1
0
2
0
1
0
2
1
2
2
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
2
2
0
1
1
2
1
1
1
0
1
1
1
1
0
2
1
1
1
2
1
1
1
1
2
1
2
2
1
1
1
1
1
1
0
1
1
2
1
2
1
1
0
3
1
1
2
2
1
1
1
0
1
1
0
1
1
1
2
1
2
0
1
1
2
2
1
2
2
1
2
1
1
2
1
1
0
0
1
1
1
2
1
1
0
1
1
2
1
0
1
1
2
2
0
1
2
2
1
1
1
2
0
1
1
0
1
0
1
1
2
1
1
2
1
1
2
1
1
1
1
1
0
1
2
1
1
2
0
1
2
1
0
0
0
2
1
1
2
2
1
1
0
2
1
1
1
1
1
2
2
0
1
2
1
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
0
1
2
1
2
2
2
1
2
1
1
1
1
0
2
1
0
1
1
1
2
2
2
1
0
1
0
1
1
1
0
2
1
1
1
1
0
0
1
1
1
1
2
0
1
1
1
0
1
1
0
2
0
2
0
1
1
1
3
1
2
1
2
1
1
2
0
2
1
1
1
1
1
2
1
0
2
1
1
1
1
1
1
1
2
2
1
1
1
2
2
0
0
1
1
0
2
2
2
2
0
0
1
1
2
1
2
1
1
2
1
2
0
2
1
2
1
1
1
2
1
2
1
2
2
1
1
0
1
1
1
1
1
2
1
1
1
1
1
2
1
0
2
1
1
1
1
2
1
1
1
1
1
1
2
0
0
0
1
1
1
1
0
1
2
2
1
2
1
1
1
1
1
1
1
1
2
0
2
1
2
1
2
1
2
1
2
2
2
1
2
1
0
1
0
1
0
2
0
1
1
1
1
1
1
1
1
2
1
1
2
1
0
1
2
1
1
1
2
1
2
1
1
1
2
2
1
2
2
2
2
1
2
2
1
1
2
1
0
1
1
2
0
1
2
1
2
1
2
1
1
1
1
1
0
0
1
2
1
1
1
0
2
1
0
2
0
1
1
0
2
1
1
1
2
2
1
2
1
1
2
1
2
2
0
1
2
3
3
1
0
1
2
1
1
1
1
1
1
1
2
2
0
1
1
2
1
1
2
1
1
1
1
1
1
1
1
0
1
1
1
0
2
1
1
1
1
1
2
1
2
1
1
1
2
2
1
1
2
1
1
2
1
2
1
1
2
1
1
1
1
2
1
0
1
1
1
1
0
1
1
1
1
1
2
1
1
1
0
1
2
1
1
1
2
1
1
0
0
2
1
1
3
2
1
2
1
2
1
1
1
0
1
2
0
1
0
1
1
1
1
1
1
1
1
1
2
1
0
0
1
1
1
0
1
1
2
2
1
1
0
1
1
1
1
0
0
1
2
1
1
2
1
1
1
2
1
1
2
2
2
0
2
2
1
0
0
1
0
2
2
1
0
0
0
1
2
2
1
1
1
0
1
1
1
1
0
1
1
2
2
0
1
1
1
0
1
1
1
2
2
2
1
1
1
2
2
1
2
2
2
1
1
1
1
2
2
2
1
2
2
2
1
2
1
1
1
1
0
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
2
1
2
1
1
2
1
2
1
1
1
1
2
1
0
1
0
2
1
2
1
2
1
0
1
1
1
1
1
2
0
1
1
2
1
1
1
1
1
1
0
2
2
2
1
1
1
1
2
1
1
2
2
1
1
0
1
2
2
1
2
1
1
2
1
2
1
1
2
1
4
2
2
2
1
2
1
1
1
1
2
2
1
2
1
2
1
1
1
1
1
2
0
0
2
1
1
0
1
1
2
2
0
0
1
1
1
1
0
0
0
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
0
1
1
0
2
1
0
2
1
0
2
1
1
1
1
0
2
1
1
1
1
1
1
1
1
0
2
1
0
0
1
1
1
1
2
1
1
1
0
1
0
1
2
2
2
1
3
2
1
1
1
1
1
1
1
1
1
0
1
2
2
1
1
1
2
0
2
1
2
1
1
0
1
1
1
1
1
1
3
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
2
2
2
1
2
1
1
1
1
1
1
0
1
1
2
2
2
1
0
1
1
1
1
1
2
0
1
2
1
2
2
0
1
1
1
1
1
1
1
1
1
2
2
1
1
2
2
2
1
1
2
1
1
0
3
1
1
1
1
0
0
0
1
0
0
2
2
1
1
2
0
1
1
2
1
1
1
2
1
2
2
1
1
1
1
0
2
1
0
1
1
1
1
1
1
1
0
0
1
2
1
2
1
1
0
1
1
1
0
1
1
2
0
1
2
1
1
1
1
1
0
2
1
2
1
1
1
2
1
1
2
0
0
1
0
0
0
2
3
1
1
2
2
1
1
1
1
2
1
0
1
1
1
2
1
0
2
1
2
1
1
1
1
2
1
1
1
1
1
1
2
1
1
0
1
2
1
0
1
1
1
1
1
1
2
1
2
2
1
1
1
2
2
1
0
1
1
1
1
2
1
4
0
1
1
0
1
2
1
0
1
2
1
1
2
1
1
1
2
0
2
1
1
2
1
1
0
1
1
1
1
1
0
1
0
1
0
3
0
2
2
1
1
1
0
1
1
2
1
1
1
1
2
0
2
1
1
1
1
1
2
2
1
1
1
1
1
1
0
2
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
2
1
1
1
2
2
1
0
2
2
5
2
1
2
1
1
1
1
2
0
2
0
0
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
2
1
1
2
2
2
1
2
1
1
1
1
1
1
1
2
1
1
1
0
1
1
1
1
2
1
1
1
1
0
2
1
1
1
1
1
0
1
1
1
0
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
0
2
3
2
1
1
1
2
2
0
2
1
2
1
1
1
0
1
0
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
0
1
1
2
1
1
0
2
1
1
1
1
1
0
1
1
1
2
0
2
1
0
1
1
2
1
1
1
2
1
2
1
2
1
1
1
2
1
2
1
1
1
1
1
2
0
1
0
1
1
2
2
1
1
1
2
0
2
2
1
1
0
1
1
1
2
1
2
1
0
0
0
2
1
2
1
3
2
1
1
2
1
1
0
1
1
2
0
1
2
2
2
2
0
1
1
2
1
1
2
1
0
1
1
1
1
0
1
1
1
0
2
1
2
2
1
1
2
0
1
1
2
1
2
1
1
0
2
1
1
2
1
1
1
2
0
1
1
1
2
2
2
1
1
1
1
0
1
1
1
2
1
1
0
2
2
2
2
1
2
1
0
1
1
2
1
1
2
1
1
0
1
1
0
1
2
1
1
1
1
0
1
0
2
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
0
1
2
2
1
2
0
0
0
2
1
1
0
1
1
1
2
2
1
1
1
0
1
0
1
1
2
0
1
2
1
2
1
1
1
1
0
0
2
1
0
1
1
2
2
1
2
1
2
2
1
2
1
1
1
2
2
1
1
1
0
1
0
2
1
2
1
1
1
1
1
0
1
2
1
1
1
2
1
0
1
2
1
2
1
1
2
1
2
1
1
1
0
1
2
0
1
1
2
1
2
0
1
2
2
1
1
1
2
2
1
1
1
1
0
1
1
0
1
1
2
2
1
1
0
1
1
1
2
1
1
1
2
2
1
1
1
0
1
1
1
1
2
2
1
1
1
1
2
1
2
1
1
2
1
1
0
1
2
1
2
2
1
1
2
1
1
2
1
2
1
2
1
1
0
2
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
2
0
1
1
2
1
0
1
1
1
3
2
1
1
1
2
1
1
1
2
1
0
1
2
1
2
0
0
0
1
1
1
1
2
1
1
1
1
1
2
1
1
1
2
0
1
1
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
1
0
1
0
1
0
2
0
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
0
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
2
1
1
2
0
1
3
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
0
1
1
1
2
2
0
2
1
1
1
1
1
1
0
1
1
0
2
1
1
2
2
1
2
0
1
2
1
2
1
1
1
1
1
1
0
2
1
1
1
3
1
1
0
1
1
1
1
1
2
1
1
0
1
1
1
0
2
2
1
1
1
1
1
1
1
1
2
1
1
1
1
2
2
0
1
1
1
1
2
1
1
2
0
2
0
1
1
2
2
1
0
1
1
3
2
1
1
1
1
1
1
2
2
1
1
2
1
1
1
1
2
1
1
1
2
0
1
1
2
1
1
1
1
1
0
1
0
2
1
2
1
0
2
1
1
1
0
0
1
2
1
1
0
0
2
1
1
1
1
1
0
0
1
1
1
1
2
0
2
1
1
1
1
3
1
0
1
1
2
0
1
1
1
1
1
1
0
1
1
2
1
1
1
1
1
1
1
1
1
1
1
0
1
2
2
3
2
1
0
1
1
2
1
1
0
1
1
1
1
0
2
1
1
0
2
1
0
1
1
2
1
1
1
1
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
0
1
1
1
1
1
0
1
1
1
1
1
0
1
0
1
0
2
1
1
1
2
2
2
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
2
1
2
2
1
1
1
1
0
1
1
1
1
1
1
1
2
2
1
0
1
2
0
2
2
2
1
1
1
2
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
0
1
1
1
2
2
1
2
2
1
1
2
0
1
0
1
0
2
0
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
2
0
1
1
2
2
1
1
1
0
1
1
1
2
0
0
1
1
0
1
1
1
2
1
1
2
2
1
0
1
5
1
1
2
1
1
1
1
0
1
1
1
0
0
1
2
1
0
2
1
2
1
2
1
2
0
1
1
1
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
0
1
1
2
0
2
1
1
1
1
1
0
2
1
1
1
1
1
0
1
1
2
2
0
1
1
1
1
1
0
2
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
2
1
2
2
1
1
1
0
2
1
0
0
1
2
1
1
1
1
1
1
1
2
1
2
1
2
1
1
1
1
2
0
1
2
1
1
2
0
1
1
1
1
1
2
1
1
0
2
0
1
1
2
0
1
1
0
1
1
0
1
2
1
2
1
1
1
1
0
2
0
0
1
2
0
0
1
2
2
1
1
2
0
1
1
1
1
1
1
1
0
1
1
1
2
1
1
1
1
1
1
1
1
2
2
1
2
1
1
1
2
2
2
1
0
2
1
2
2
2
1
0
2
1
2
1
1
1
1
2
2
1
1
2
2
1
1
2
1
0
1
2
1
1
1
2
1
1
1
1
2
1
0
2
1
2
1
1
1
1
2
2
2
1
1
2
1
1
1
1
1
2
2
2
1
0
0
2
1
0
1
1
1
2
0
2
1
1
1
0
2
1
1
2
1
1
1
2
2
1
2
1
1
1
1
1
2
2
2
1
2
1
1
1
0
2
1
0
1
0
2
0
1
1
1
1
1
1
1
2
0
1
2
1
1
2
1
1
0
1
1
1
2
2
1
1
2
1
0
1
2
1
1
1
1
2
2
0
2
1
0
1
1
2
1
1
1
2
1
2
1
2
1
2
1
1
1
1
0
1
2
1
1
1
2
1
1
1
2
1
1
2
1
1
0
1
2
1
1
1
2
1
1
2
2
2
1
1
1
1
3
1
1
1
1
1
1
1
2
1
2
2
2
1
2
0
1
1
2
2
1
1
2
1
1
0
2
1
1
2
0
2
1
1
1
0
2
1
1
2
1
2
2
2
1
0
1
1
1
3
0
1
1
1
2
0
2
2
1
2
2
2
1
2
1
1
2
1
1
1
2
1
1
1
0
0
1
1
1
2
1
1
2
1
1
1
1
1
2
1
1
0
1
2
1
0
2
1
1
2
0
1
1
1
1
1
1
1
2
1
1
1
2
1
2
0
1
1
1
1
2
1
1
1
1
1
1
2
2
0
2
1
1
2
1
3
1
1
1
2
1
1
1
0
1
1
2
3
2
1
1
2
1
1
2
3
1
1
1
2
1
2
0
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
2
1
1
1
2
2
0
1
0
1
2
1
1
1
1
1
2
1
2
0
2
1
1
2
2
2
1
2
1
1
1
2
2
1
2
2
1
1
0
1
1
0
1
1
1
2
2
2
2
1
0
0
1
2
2
0
2
2
0
2
1
2
2
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
1
0
1
1
0
1
2
0
1
0
1
1
1
1
1
1
1
1
1
2
1
0
2
0
1
2
1
2
1
0
2
0
1
2
2
2
1
1
2
1
1
3
1
2
1
1
1
2
2
2
1
1
2
1
0
0
2
1
1
1
0
1
1
1
1
1
2
0
0
2
1
1
0
0
1
1
2
1
2
1
2
1
2
1
2
1
1
2
2
1
0
1
1
0
2
2
1
1
1
1
1
1
1
0
1
1
1
1
2
2
1
4
1
1
1
1
1
1
1
1
1
2
0
1
1
1
2
1
1
1
0
0
1
1
5
1
1
1
1
0
2
2
1
2
1
0
2
2
2
0
1
1
1
1
0
1
1
2
1
1
2
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
2
1
1
1
0
1
0
1
2
0
1
0
1
1
0
1
2
1
2
2
1
0
1
1
1
1
2
0
1
1
1
1
2
1
1
1
1
0
1
1
1
1
0
1
1
1
2
1
1
1
2
2
1
1
1
2
1
2
1
2
2
2
1
2
2
2
1
1
1
1
0
1
1
1
1
0
0
1
2
2
1
2
1
0
0
0
2
1
1
0
1
1
2
0
2
1
2
1
1
1
1
1
3
1
2
2
1
1
1
2
1
1
0
2
1
1
1
2
1
0
2
2
2
1
1
0
1
3
0
1
0
2
0
1
1
1
1
1
1
3
1
1
0
2
1
1
1
1
1
1
1
0
1
1
0
0
1
1
0
2
2
0
0
1
2
2
0
2
1
2
1
1
0
1
2
2
1
1
1
0
1
2
1
1
2
0
2
1
2
1
0
1
1
2
1
1
1
2
1
1
2
1
2
1
2
2
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
2
0
1
2
1
2
0
1
1
2
2
1
1
1
0
1
1
1
0
1
2
1
2
1
1
1
0
1
1
0
1
2
1
0
2
2
0
0
1
1
1
1
1
2
1
2
2
2
2
1
1
0
1
1
2
1
1
1
2
1
2
1
2
2
2
1
1
1
1
2
1
2
1
1
2
1
1
1
2
1
1
1
1
1
0
0
2
1
1
1
2
1
1
1
1
0
1
1
0
1
0
1
1
1
1
0
1
1
2
1
1
1
1
0
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
0
0
1
1
1
1
2
2
1
1
1
0
1
2
1
2
2
2
1
0
1
2
1
1
2
1
1
2
2
1
2
1
1
2
1
2
2
1
1
1
1
4
1
1
2
1
0
1
0
2
1
0
1
1
1
2
2
2
0
1
1
1
1
1
1
1
2
1
2
1
1
0
1
2
2
1
1
1
1
0
2
1
1
1
2
1
1
0
1
0
1
1
1
0
2
2
1
2
2
2
1
1
1
2
1
1
2
1
1
2
2
1
2
2
1
1
2
1
1
0
2
1
1
0
2
0
1
1
2
1
2
2
1
1
1
1
2
2
1
1
1
2
1
1
1
1
0
1
0
2
2
2
2
0
1
1
2
0
2
0
1
1
1
1
1
0
1
1
1
2
0
1
1
0
1
0
1
4
0
1
0
0
1
1
1
1
0
1
1
2
1
0
1
1
2
1
1
2
1
0
2
1
1
2
1
1
1
3
1
2
2
1
1
2
1
0
1
1
0
1
2
1
1
1
2
2
1
1
1
1
2
1
1
1
1
2
1
2
1
0
1
1
2
1
2
1
2
1
0
1
2
1
1
0
0
0
1
2
0
0
1
0
2
1
1
2
2
1
0
0
1
1
1
1
1
1
0
0
2
1
1
1
1
1
0
0
1
2
1
1
0
2
2
1
2
2
1
1
1
1
0
1
0
0
0
1
1
2
0
2
2
1
2
1
1
2
1
1
1
2
2
1
1
3
0
0
1
2
2
2
1
2
2
2
1
1
1
1
1
1
1
1
1
1
2
1
3
2
2
2
1
1
2
1
1
0
1
0
1
1
1
1
1
0
1
1
1
1
2
1
2
2
2
1
1
1
1
2
1
1
1
1
2
2
0
1
1
1
1
2
1
2
1
2
1
1
2
0
1
1
2
1
1
1
0
0
2
0
1
2
1
1
1
1
2
1
0
0
1
2
1
0
2
1
0
0
1
1
0
2
2
2
1
2
0
1
2
2
1
1
1
2
1
1
1
1
1
2
1
1
2
2
2
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
0
2
2
0
1
1
2
1
2
1
2
3
1
0
1
1
1
2
0
1
1
2
1
0
1
1
1
0
2
1
1
1
0
0
2
1
2
1
0
1
1
1
2
1
1
1
0
1
1
1
2
1
2
2
1
2
0
1
2
2
1
2
1
0
0
1
2
1
1
1
1
0
1
2
2
1
1
1
0
1
1
2
0
1
0
0
1
1
2
2
1
2
2
0
2
1
2
0
1
2
1
1
1
1
1
2
1
1
0
1
1
1
0
1
1
0
1
1
2
2
0
1
1
1
1
1
2
1
2
2
2
1
1
1
0
1
1
1
1
1
0
1
2
1
1
1
1
1
1
1
0
0
1
2
1
1
1
2
1
1
1
1
1
1
1
1
0
1
2
2
2
1
3
1
2
1
2
1
1
1
1
2
1
2
2
2
1
2
2
1
1
2
2
1
2
2
1
1
2
2
0
2
1
2
2
2
2
1
1
2
0
2
1
1
2
2
0
2
1
2
2
0
1
2
1
2
2
0
0
2
5
2
1
0
1
1
1
1
2
1
1
1
2
0
1
2
1
1
1
1
2
1
1
1
1
0
2
1
0
1
1
2
1
1
1
1
1
1
1
1
1
1
0
2
1
1
2
1
2
1
1
1
2
0
1
1
1
2
2
1
2
2
1
1
1
2
1
1
2
1
1
2
0
1
1
1
2
1
1
1
2
1
0
0
0
1
1
1
1
1
1
0
1
1
0
1
1
1
1
2
1
2
1
1
1
1
1
0
2
1
2
1
1
1
1
1
2
1
2
2
1
1
1
0
1
1
1
2
1
0
2
1
1
1
2
1
1
1
1
1
1
1
2
2
1
0
1
1
1
2
2
0
2
2
0
2
2
2
1
2
2
0
0
0
2
2
2
1
2
1
0
0
1
1
2
1
0
1
1
1
1
1
1
2
2
1
2
1
1
1
0
3
2
1
2
2
1
1
0
1
1
1
0
2
0
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
2
2
1
1
2
1
1
1
2
1
2
1
2
2
1
2
1
2
1
1
1
1
1
1
2
1
1
1
2
0
2
0
1
2
1
0
0
1
0
2
1
1
2
2
2
1
2
1
1
2
1
1
1
1
1
0
1
2
1
2
2
2
1
1
2
0
2
1
2
1
1
1
2
2
2
1
1
2
1
2
1
1
1
0
2
0
1
2
1
0
2
2
0
0
2
0
1
1
1
2
2
1
1
1
1
0
1
1
1
1
0
0
1
1
1
1
2
2
1
2
2
1
1
1
1
0
1
1
2
1
2
2
1
1
1
2
1
1
1
1
1
2
2
1
0
2
1
1
1
2
2
1
1
1
2
1
1
0
1
0
2
1
1
2
1
0
3
1
0
2
1
1
1
0
1
1
2
1
1
2
1
0
1
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
2
1
1
1
2
0
1
1
1
1
2
1
1
1
1
1
1
1
2
2
2
0
2
1
2
1
2
0
1
0
2
1
2
1
2
1
1
1
2
1
1
1
1
1
1
1
2
0
0
1
1
1
1
0
1
1
2
1
0
1
1
2
2
2
2
1
2
1
2
2
1
1
1
2
1
1
1
1
2
1
1
1
1
0
1
1
0
2
1
1
1
2
2
1
1
2
0
1
2
0
1
0
2
2
1
1
1
1
1
2
1
1
2
1
0
1
1
2
1
2
1
4
1
1
1
1
1
1
2
1
1
1
2
1
0
0
2
1
0
1
2
0
0
0
1
1
1
1
1
1
0
2
2
1
0
1
1
0
1
0
2
0
2
1
1
1
2
1
0
1
2
1
2
1
1
1
0
1
1
2
2
2
1
0
0
0
2
1
1
1
1
1
1
2
2
2
2
0
1
2
1
2
1
1
1
1
2
2
1
1
1
2
2
1
1
2
2
1
1
2
1
0
2
1
6
1
2
2
1
0
2
2
0
1
1
1
1
1
2
1
1
1
2
1
2
2
0
1
2
1
1
1
2
2
1
1
2
2
1
0
1
0
1
0
2
1
1
0
1
2
0
2
1
1
1
0
1
1
0
1
1
2
2
1
2
2
0
1
2
2
2
1
0
1
2
2
1
1
2
2
1
1
2
1
1
1
1
1
2
1
1
1
0
1
1
1
1
1
1
1
2
1
1
2
1
1
0
2
2
1
0
1
0
1
1
2
2
1
0
1
2
0
1
2
1
1
1
1
1
0
1
1
3
1
1
2
1
1
1
1
0
0
0
2
2
1
2
1
1
2
2
2
1
0
1
2
1
1
1
1
0
2
1
1
1
1
1
0
1
0
1
2
0
1
1
1
2
1
1
1
1
2
2
1
2
0
1
0
0
0
1
1
1
2
1
1
1
1
2
2
1
0
1
1
2
1
0
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
2
2
1
1
2
1
2
1
0
2
1
1
1
1
0
1
1
1
1
1
1
2
1
0
1
2
2
1
1
1
0
1
1
1
2
1
0
1
0
1
1
1
1
0
3
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
2
2
2
1
1
1
2
2
1
2
2
2
1
1
1
2
1
2
2
1
1
1
2
1
0
4
1
1
0
1
1
1
1
1
1
1
2
2
2
0
1
1
1
2
2
1
1
2
1
2
0
1
2
2
1
1
1
2
1
2
2
2
1
2
1
2
2
1
1
1
1
2
1
1
2
1
2
2
1
1
1
1
1
1
2
1
2
1
1
2
1
0
1
1
0
0
1
2
1
1
3
1
2
0
1
2
2
0
2
1
1
1
1
1
1
1
2
2
1
1
1
1
2
1
2
1
1
1
0
2
1
2
2
1
1
2
1
0
2
0
2
1
1
2
0
0
1
1
3
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
1
2
1
2
0
1
1
2
1
1
2
0
2
2
2
2
1
1
1
1
1
0
2
0
1
2
1
0
1
1
0
2
1
1
2
1
0
1
1
0
1
2
1
0
1
1
1
2
1
1
1
1
2
1
1
0
0
1
2
1
1
1
0
1
1
1
1
2
0
0
1
1
1
2
1
1
1
0
1
1
1
0
2
1
2
1
1
1
1
0
1
2
2
2
1
0
1
2
1
1
1
0
2
2
2
1
1
2
1
1
2
2
1
1
1
2
1
1
1
2
2
1
1
1
2
2
1
0
2
1
1
1
1
0
1
1
2
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
2
4
1
1
1
2
1
1
1
2
1
0
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
2
2
1
1
0
2
1
1
1
1
1
2
1
2
2
2
1
1
1
1
0
0
1
3
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
0
1
0
1
1
1
1
1
1
2
0
1
1
2
1
0
2
1
1
0
1
2
2
2
1
0
0
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
2
1
0
1
1
1
1
1
0
2
0
1
1
0
2
0
2
1
1
2
0
1
2
0
1
2
1
0
1
1
0
2
0
2
1
2
0
1
1
1
1
0
1
2
1
0
1
1
2
1
1
1
0
0
1
2
1
1
1
1
1
1
1
1
1
1
1
0
2
2
1
1
1
1
2
2
1
1
3
1
2
1
2
1
2
2
2
1
1
2
2
2
1
0
2
2
1
1
1
2
2
1
2
2
2
2
1
1
0
0
2
1
2
1
1
2
1
2
1
2
1
2
1
2
2
2
2
1
0
1
1
2
1
1
1
1
2
0
2
2
1
1
2
1
2
1
1
1
2
2
1
0
2
1
2
2
1
1
1
1
2
1
1
1
1
1
1
1
0
0
1
0
1
1
1
1
1
1
1
1
1
1
1
1
2
0
1
1
1
1
2
0
1
1
1
1
0
2
1
1
1
1
1
1
1
1
2
2
1
1
1
1
2
1
0
2
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
0
2
1
1
2
1
1
1
1
1
1
1
0
1
1
1
0
2
1
2
1
2
2
1
2
0
0
1
1
1
0
1
2
1
2
1
0
1
1
2
1
0
2
2
1
1
1
1
1
2
2
2
1
1
1
2
1
0
1
1
1
2
2
1
1
0
1
1
0
1
1
1
0
1
1
1
2
1
1
2
1
0
1
1
1
1
1
1
2
1
1
0
1
1
2
1
1
1
1
2
1
0
1
0
1
1
2
1
1
1
1
2
1
2
1
2
1
1
2
1
0
2
1
1
1
1
1
1
0
0
2
0
1
1
1
1
1
2
1
2
2
1
0
2
2
2
1
1
2
1
1
2
1
2
1
1
1
0
1
1
2
2
1
1
2
1
2
1
1
1
1
2
1
2
1
2
1
1
0
2
1
2
1
0
0
1
1
1
1
3
1
1
1
2
1
1
0
1
1
1
1
1
0
2
1
1
2
2
2
2
1
2
1
0
1
1
1
2
1
0
0
4
1
1
1
1
2
2
1
0
1
1
2
0
0
2
0
1
1
2
1
1
1
1
1
0
0
0
1
1
2
1
1
2
1
2
1
2
1
2
2
2
1
1
1
2
1
1
1
1
0
1
1
1
1
2
1
0
2
2
1
2
1
2
2
2
1
1
1
1
0
1
2
2
1
1
1
2
1
1
2
1
1
1
1
0
1
1
2
2
2
1
0
1
1
0
1
1
1
2
1
2
0
1
1
1
1
1
2
2
0
1
2
1
1
1
1
3
1
2
2
1
1
1
1
2
1
1
2
1
1
1
1
0
1
1
1
2
1
2
2
1
1
0
0
1
0
1
2
2
1
0
1
1
1
3
1
1
1
2
1
1
1
1
1
1
1
0
1
1
2
2
2
0
1
1
0
0
2
0
1
1
2
1
1
2
0
2
1
0
2
1
1
1
1
0
1
1
2
2
1
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
0
1
2
1
1
0
1
1
2
2
1
1
2
1
1
2
1
1
2
0
3
1
1
1
2
0
1
1
1
2
1
0
1
1
2
1
1
1
1
1
2
1
1
1
1
0
1
2
0
1
1
1
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
0
1
0
1
1
1
2
1
0
0
1
1
1
1
1
1
1
2
1
0
1
1
2
1
1
1
1
1
1
1
2
2
1
1
2
2
1
1
2
2
1
2
0
1
2
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
0
2
1
0
1
1
0
0
1
1
1
2
1
1
2
2
1
1
1
2
1
1
0
1
0
1
1
1
2
1
1
2
2
2
2
2
1
2
1
1
1
1
1
2
2
1
1
0
2
1
1
0
0
1
1
1
1
2
1
2
2
0
1
2
1
1
1
0
1
1
1
1
1
1
1
1
2
1
1
0
1
1
1
1
1
1
2
1
1
2
1
1
2
1
1
2
0
1
1
2
1
1
0
0
1
0
1
2
1
1
2
1
0
2
1
1
2
1
0
1
2
1
2
2
1
0
1
1
3
1
0
1
0
1
2
2
0
1
1
1
1
0
1
2
0
2
2
0
1
1
2
1
2
1
0
1
2
1
0
1
0
0
1
2
1
1
1
1
1
1
1
0
1
2
0
1
1
0
2
1
1
1
1
1
1
0
1
1
0
1
1
2
2
2
1
1
3
1
2
1
1
1
1
0
2
1
2
1
1
1
2
0
1
0
1
2
1
1
1
1
1
3
1
1
2
2
1
2
0
0
1
1
1
2
1
2
1
1
1
1
2
2
1
1
0
0
2
1
1
1
1
1
2
2
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
0
1
0
1
0
1
1
1
1
1
2
1
1
1
2
1
2
2
2
1
0
1
2
2
2
1
1
1
2
1
1
0
0
2
1
1
1
2
2
1
1
2
1
1
1
2
3
2
1
2
2
1
1
1
2
1
1
1
1
2
1
0
1
1
2
1
2
2
2
1
1
1
2
2
1
1
1
2
1
2
0
1
0
1
1
1
2
1
1
1
1
0
1
1
2
0
0
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
0
2
1
2
1
2
2
2
2
2
1
0
2
1
0
1
0
2
1
1
1
1
2
1
1
2
2
0
1
1
2
0
1
2
0
2
2
2
1
2
1
0
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
2
1
0
0
1
1
2
2
1
1
1
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
0
0
0
1
0
1
1
2
1
2
1
2
1
1
1
2
0
1
1
2
1
1
1
1
2
1
0
2
2
1
2
0
1
1
0
0
2
1
1
1
2
1
1
0
1
2
1
1
1
1
1
2
2
1
2
1
2
1
2
3
0
2
0
2
0
2
1
1
1
1
2
1
1
1
1
2
1
2
2
1
1
0
1
1
1
1
2
1
1
1
1
0
0
1
2
0
2
1
1
1
1
1
0
1
1
0
1
1
1
1
2
0
0
1
0
1
0
1
2
1
2
1
2
1
2
1
1
2
2
1
1
2
1
1
2
0
2
1
0
1
1
1
1
1
1
1
2
1
2
0
0
0
1
0
2
1
2
2
1
1
2
1
1
1
0
1
0
2
1
1
1
1
1
1
1
1
1
1
2
0
2
2
1
1
1
0
1
0
0
1
1
1
1
1
0
0
1
2
1
1
2
1
1
2
2
1
1
1
1
0
1
1
2
1
2
2
2
2
1
1
0
1
1
1
2
1
1
2
0
1
1
1
2
2
2
1
2
1
1
1
1
0
1
1
1
2
2
1
1
1
1
1
1
2
2
1
1
1
1
2
1
0
0
2
1
1
2
1
2
2
1
1
1
2
2
1
1
1
1
1
0
2
1
0
1
1
2
2
1
1
0
1
1
1
2
1
1
0
0
2
1
1
1
1
0
2
2
1
2
0
1
2
2
1
1
2
1
1
1
0
0
1
1
2
0
1
1
1
0
2
1
0
1
0
2
2
2
0
2
0
0
1
0
2
1
0
0
1
1
1
2
2
1
0
2
1
2
1
1
2
0
1
2
1
1
2
1
1
1
0
1
1
1
1
2
1
1
2
1
1
0
1
1
1
2
1
2
1
0
1
2
2
1
1
0
3
1
1
0
1
1
1
2
0
1
1
2
2
1
1
1
0
2
1
2
2
1
1
0
2
1
2
2
2
1
1
1
1
0
1
1
2
1
1
2
1
2
1
2
2
0
1
1
1
2
1
1
1
1
2
1
0
0
1
1
1
2
1
2
1
2
0
1
2
2
1
2
2
1
1
2
1
1
2
2
1
2
1
1
1
1
2
1
1
1
1
1
1
0
1
1
1
1
1
0
2
1
1
1
2
1
1
0
0
2
2
1
1
2
1
1
0
1
1
1
1
0
0
2
2
1
1
1
2
1
0
2
2
1
2
3
1
1
1
2
1
1
1
2
1
1
0
1
1
1
1
1
2
1
1
1
2
2
1
1
0
1
2
1
0
1
0
0
1
0
1
1
2
1
0
1
2
1
2
2
1
1
2
1
2
1
2
0
1
2
1
0
1
1
2
1
1
2
0
0
2
1
1
2
1
2
2
1
1
2
1
1
2
1
0
1
1
1
0
2
1
2
1
0
1
1
2
2
1
1
2
2
2
2
1
1
1
1
1
1
1
2
0
1
1
2
2
1
2
2
2
1
2
2
1
1
1
1
1
1
2
1
1
1
1
0
1
1
1
1
1
1
0
2
1
0
1
0
1
1
1
2
2
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
2
1
2
0
1
1
1
1
1
1
1
1
1
0
1
2
1
1
0
1
2
2
0
2
1
1
1
1
1
0
2
1
1
1
0
0
2
1
2
1
1
1
0
1
2
0
1
1
0
1
1
1
0
1
1
0
1
1
1
1
2
2
1
1
0
0
2
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
0
1
2
1
3
1
0
2
1
2
1
2
2
2
2
2
2
0
1
1
1
1
2
2
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
0
1
1
1
2
1
1
2
2
1
0
1
1
1
1
2
1
1
1
1
1
1
2
2
2
1
0
2
0
0
1
1
2
2
2
1
1
1
2
1
1
2
1
2
1
1
1
1
1
2
2
2
1
1
1
1
0
2
0
2
1
1
0
1
2
1
1
0
0
1
1
1
1
1
2
1
1
1
1
1
2
2
1
1
2
1
1
0
1
1
1
1
1
1
2
0
1
1
1
2
1
2
1
2
1
1
1
1
1
1
1
2
2
1
2
0
0
0
1
1
1
1
1
2
1
1
1
1
0
1
1
1
2
2
3
2
1
1
2
3
0
0
1
2
0
2
1
1
2
1
0
1
0
2
1
0
0
2
0
1
1
0
2
1
1
0
1
2
2
1
1
2
1
1
2
1
2
1
2
2
1
1
1
0
1
1
1
1
0
1
1
1
1
1
1
2
0
2
1
1
2
2
0
2
2
1
2
1
1
1
0
1
1
1
2
1
1
1
1
2
1
1
1
0
1
1
0
1
1
0
1
2
2
1
0
1
2
1
1
0
2
2
1
0
1
1
2
0
1
2
1
1
1
1
2
2
1
1
1
2
1
1
1
2
1
1
2
2
2
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
0
1
1
2
1
1
1
1
1
1
1
1
1
0
2
2
0
0
0
1
2
1
1
2
1
1
1
0
2
2
0
2
1
1
1
2
2
1
2
2
1
1
2
0
1
0
1
1
1
1
1
0
0
2
1
1
1
0
1
1
1
1
1
2
1
2
1
1
1
0
1
2
1
2
1
0
1
1
2
0
1
1
0
1
1
1
1
1
2
2
1
2
1
0
1
0
2
2
1
1
1
1
1
2
1
1
2
1
1
2
1
2
0
1
1
0
1
1
1
1
1
0
1
0
1
0
1
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
0
2
0
2
1
1
1
2
1
1
2
1
1
2
2
1
1
1
2
1
1
0
1
0
0
0
1
1
0
1
2
1
1
0
2
2
2
2
2
1
1
1
1
1
1
2
2
2
1
1
1
2
2
1
1
2
1
1
2
0
1
2
1
1
1
0
1
2
2
1
1
1
1
0
2
1
2
2
1
2
1
1
1
0
1
1
2
1
1
1
1
1
2
1
1
1
1
0
1
1
2
1
0
1
2
2
2
1
1
1
1
1
1
1
1
1
2
1
1
1
0
1
2
0
1
2
2
2
1
0
0
2
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
3
2
0
1
2
1
0
0
1
1
0
0
1
1
1
1
2
0
1
0
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
0
2
2
1
1
1
2
1
1
2
1
2
2
1
1
1
1
3
0
1
2
2
1
1
0
2
2
1
1
1
1
1
2
2
1
1
1
1
2
0
1
1
2
1
1
1
1
1
2
2
1
2
0
1
2
0
1
1
1
2
1
1
1
0
0
2
1
1
1
2
2
1
2
2
3
2
2
1
1
1
1
1
1
1
2
2
0
2
2
1
1
0
2
1
1
1
2
3
1
1
2
1
1
1
2
1
1
2
2
1
1
2
1
1
2
1
2
1
2
2
2
0
1
1
0
1
2
1
1
1
1
1
1
2
1
1
1
0
1
1
1
2
1
1
0
1
2
1
1
2
2
2
1
2
0
0
1
2
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
1
2
2
1
3
2
2
0
2
1
2
2
0
0
1
1
2
1
1
2
0
1
2
2
1
1
1
0
1
2
1
1
2
1
0
1
2
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
0
1
1
1
1
1
2
1
1
2
0
1
0
2
1
2
0
1
1
1
1
1
0
1
2
2
2
1
1
2
1
0
1
2
0
2
1
1
0
2
0
1
2
1
0
2
2
1
2
2
1
1
2
1
1
1
1
2
1
2
1
0
1
1
0
1
0
1
0
1
2
2
1
1
1
1
1
2
2
1
2
1
0
0
0
1
1
2
1
2
1
1
2
2
2
1
2
1
1
1
1
1
1
1
1
0
0
1
1
1
2
1
4
0
1
2
1
0
2
2
1
2
0
0
1
1
2
0
1
1
0
2
2
2
0
1
1
2
1
2
1
1
2
1
1
1
0
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
0
2
1
2
2
2
1
1
1
1
1
1
1
1
2
1
0
0
1
1
1
2
2
1
1
1
1
0
1
1
2
0
2
0
2
2
1
1
1
1
2
1
1
2
2
2
1
0
0
2
1
1
2
1
1
1
2
2
0
0
1
1
0
0
1
2
0
1
2
0
1
1
1
0
1
1
1
2
2
0
1
1
2
2
1
2
1
1
1
1
1
1
1
0
2
2
1
2
1
1
0
1
0
1
2
1
1
2
1
2
1
1
2
1
1
1
0
0
1
2
1
1
1
1
1
1
1
2
0
1
1
0
1
1
2
1
0
1
1
1
2
1
2
1
1
1
1
1
1
2
1
2
1
0
1
1
2
1
1
1
2
1
0
0
2
1
1
1
1
1
1
1
1
1
1
1
2
1
0
2
1
0
1
1
1
2
1
1
0
1
1
1
0
1
3
0
0
1
1
1
2
1
2
1
1
1
1
1
1
1
1
2
1
2
2
1
1
1
2
1
1
2
2
2
1
0
1
2
2
1
1
0
1
2
2
1
1
1
0
1
1
1
0
2
2
1
1
2
1
1
2
2
1
1
1
1
1
1
2
2
2
0
1
2
1
1
0
1
1
2
0
1
2
1
1
1
1
0
1
2
1
0
2
2
2
1
1
1
2
0
1
1
1
1
0
1
2
1
0
1
1
1
2
1
2
1
2
1
1
2
2
0
0
0
1
1
1
2
1
1
1
1
0
2
2
2
0
2
1
1
0
0
1
1
2
1
2
2
1
1
2
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
1
0
1
0
1
0
1
1
2
1
1
1
0
1
2
1
1
0
1
1
1
2
2
2
0
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
0
2
2
1
0
1
2
1
1
2
1
1
1
1
2
2
2
0
1
1
0
1
2
1
0
1
2
0
1
2
0
2
1
2
2
1
1
1
1
1
1
0
2
1
2
1
1
1
2
1
1
2
1
2
1
1
2
1
0
2
1
0
1
1
1
1
1
1
0
1
2
1
1
2
1
2
0
1
1
1
1
1
0
1
1
2
1
2
1
1
1
1
0
0
1
1
1
0
1
2
2
2
1
1
1
1
2
0
2
1
2
1
1
2
1
1
1
0
2
2
1
1
1
1
1
1
1
0
1
1
1
2
2
0
1
0
0
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
2
0
1
0
1
0
1
0
1
1
2
1
1
4
0
1
1
0
2
1
2
0
1
1
1
1
1
1
1
2
1
1
0
2
1
1
2
2
0
1
1
1
0
0
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
0
2
1
1
1
4
1
2
1
2
1
3
2
1
1
1
1
2
3
1
1
2
0
1
2
1
1
0
2
1
2
1
2
1
0
1
0
1
0
1
2
1
1
1
2
1
1
2
1
0
0
1
1
1
1
0
1
1
2
2
2
1
1
1
1
1
0
1
2
2
1
1
1
1
1
0
1
2
1
1
1
1
1
0
1
2
1
1
2
1
2
1
1
1
1
1
0
1
1
0
2
2
1
2
1
2
0
1
2
1
2
1
2
2
1
1
1
2
1
1
1
1
1
1
1
2
1
0
0
0
1
1
1
1
1
1
1
1
2
2
0
2
2
1
1
1
1
0
0
1
1
1
1
1
2
1
1
0
1
0
1
0
1
1
1
1
2
1
1
1
0
2
0
2
1
1
1
2
1
0
2
1
1
2
1
2
0
2
1
1
2
1
0
1
0
0
0
2
1
1
1
1
2
1
1
1
1
2
1
2
1
1
1
1
2
1
1
1
0
1
0
1
1
1
1
1
2
1
2
1
2
1
2
2
1
1
1
1
2
2
1
2
1
1
1
1
1
1
1
2
2
1
1
1
1
2
0
1
0
1
1
1
1
1
1
1
0
0
1
1
1
0
1
0
1
1
4
1
1
1
1
1
1
2
1
2
1
1
1
2
0
1
1
2
1
2
2
1
1
3
1
1
2
2
2
1
2
1
0
1
2
1
2
2
0
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
2
2
1
1
2
1
0
1
0
1
1
1
0
0
1
2
1
1
1
1
1
0
1
2
1
2
1
1
2
1
1
1
1
2
2
0
2
1
1
2
2
1
2
1
4
0
2
0
1
2
1
1
1
1
2
1
2
0
1
1
1
1
1
2
0
1
2
1
1
1
1
1
2
1
1
1
1
2
2
0
2
3
2
1
0
1
1
0
2
1
1
1
1
2
1
2
1
2
1
4
0
1
1
1
2
1
1
1
1
1
1
2
1
0
1
1
1
2
1
1
1
1
0
0
0
1
1
1
1
2
2
2
1
1
1
1
0
0
1
1
1
0
0
0
2
2
0
1
1
1
1
1
2
1
1
1
1
1
0
2
1
1
1
2
2
1
0
2
1
1
2
0
1
2
0
2
2
1
1
2
2
1
2
2
2
1
1
1
1
2
1
2
1
1
1
1
2
1
2
0
2
2
1
1
2
0
2
1
1
1
1
1
2
1
1
0
2
0
1
1
1
1
2
0
2
1
2
2
1
1
1
1
1
1
1
2
2
1
2
0
1
0
0
1
2
2
1
2
2
2
1
2
1
1
1
2
2
2
1
1
0
1
1
2
1
1
2
1
1
0
2
0
1
2
1
1
0
2
1
1
1
1
1
0
1
1
1
1
1
1
1
2
2
4
1
0
1
1
1
2
1
1
1
1
1
1
2
1
1
0
1
2
1
1
1
1
1
1
0
1
1
0
2
1
2
1
0
1
0
2
1
1
1
1
1
2
1
2
1
1
1
1
1
0
1
0
1
1
1
1
0
1
2
1
1
0
2
2
0
0
1
2
0
1
1
1
1
2
0
0
1
2
1
1
1
2
1
1
1
0
1
2
1
2
1
0
1
1
1
1
0
0
1
1
0
2
1
1
1
1
1
2
2
2
0
1
1
1
1
1
1
1
1
1
1
2
2
2
1
2
1
0
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
0
1
1
1
1
1
0
1
1
1
2
1
1
1
2
1
1
1
0
3
0
2
0
1
1
1
1
1
2
1
1
1
2
2
1
1
0
1
1
1
1
1
0
2
2
2
1
2
2
2
1
1
2
2
0
2
2
1
0
2
1
1
1
2
1
1
0
1
2
0
2
2
1
2
2
1
2
2
2
1
2
2
1
1
2
0
2
0
0
1
2
1
1
1
1
1
1
2
2
1
1
2
1
1
1
0
1
1
2
1
0
1
2
1
1
1
2
1
1
1
1
1
0
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
0
1
2
1
1
1
2
2
1
1
2
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
0
2
0
2
2
2
1
2
2
1
1
1
2
2
1
1
1
0
2
1
2
2
1
0
2
1
1
1
2
1
2
1
1
1
2
1
1
2
1
1
1
2
2
1
1
1
1
2
2
2
2
0
1
2
1
1
2
1
2
1
1
1
1
1
1
0
1
0
1
1
1
2
1
0
1
0
1
0
2
1
1
1
2
1
0
1
1
1
2
2
0
1
1
1
1
2
1
1
0
1
1
1
1
0
2
2
1
1
1
1
0
1
1
0
0
2
1
1
1
2
1
1
2
1
0
2
1
0
1
1
0
1
1
2
1
2
1
2
1
0
2
1
0
1
1
1
2
1
0
0
1
1
1
1
2
0
0
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
0
1
1
2
1
0
0
1
1
0
1
1
1
2
1
1
2
1
1
2
1
1
2
1
1
1
1
2
1
2
1
2
2
1
2
0
1
1
2
1
1
2
0
1
1
0
1
1
1
1
0
1
1
2
1
1
1
2
2
1
1
1
0
0
1
2
1
2
2
2
2
1
2
1
2
2
1
1
2
2
2
1
1
1
1
2
2
0
1
1
1
1
1
1
1
1
1
0
1
0
1
0
0
1
1
1
1
0
2
1
2
0
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
0
1
1
0
1
0
1
1
1
2
1
1
1
2
1
2
0
2
0
1
0
2
0
1
1
1
1
1
0
1
1
0
1
1
2
1
1
1
2
1
1
0
1
1
0
1
0
2
1
2
2
1
2
1
0
1
1
2
1
1
1
1
0
2
1
1
1
2
2
1
0
0
2
0
1
0
2
0
1
1
1
1
1
0
1
0
0
2
1
1
2
0
1
1
1
2
1
0
1
1
2
2
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
1
0
2
1
1
1
1
1
1
2
0
0
2
0
2
1
1
2
1
1
2
1
1
1
1
1
0
2
1
0
2
1
1
1
1
2
2
1
0
2
1
2
1
1
0
2
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
2
0
1
2
2
2
1
1
1
1
1
2
1
0
1
1
2
1
2
2
1
1
2
1
2
1
0
1
2
1
2
2
2
2
1
1
0
1
1
3
1
0
1
1
2
2
0
2
1
1
1
1
2
1
1
1
0
1
1
2
1
2
1
1
1
1
1
1
1
2
1
2
0
1
1
1
1
1
1
1
2
1
2
0
1
0
1
2
1
1
1
2
2
0
1
0
1
1
1
2
2
0
1
1
1
1
2
2
1
1
1
1
1
0
1
0
1
0
1
1
0
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
2
0
2
2
1
2
0
1
1
1
1
0
1
2
1
0
2
1
1
2
0
1
2
2
2
0
1
0
2
1
2
1
1
1
0
1
1
0
3
1
1
1
0
1
1
2
1
1
1
2
1
1
1
1
1
2
1
1
2
1
1
2
1
1
0
2
2
1
1
1
1
1
0
1
0
1
1
1
1
1
0
1
2
1
1
1
2
1
2
1
2
1
1
1
2
0
0
1
1
1
1
1
1
1
2
2
1
2
1
1
0
1
1
2
0
2
2
1
1
1
1
2
0
1
0
2
1
2
1
0
1
2
2
1
2
1
1
2
0
0
2
1
2
1
1
1
0
4
2
1
1
2
2
2
1
1
1
0
1
1
1
1
2
0
1
2
2
0
1
2
1
1
1
1
1
1
1
1
2
1
1
1
0
1
1
1
0
0
1
1
0
1
1
2
0
0
1
3
1
1
1
1
1
1
2
1
1
2
1
1
2
1
2
1
0
1
2
2
1
1
1
0
1
1
0
1
0
1
2
1
3
1
2
0
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
2
1
2
1
2
1
1
1
1
0
2
1
1
1
0
2
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
2
1
1
0
2
0
1
1
1
2
1
1
1
0
1
2
0
1
2
1
2
2
0
0
1
1
1
1
1
1
0
1
1
1
0
2
1
1
2
1
1
1
1
1
2
0
1
1
1
1
1
1
1
1
1
1
1
1
2
0
1
1
0
0
1
1
2
1
0
1
1
2
1
1
0
1
2
2
1
0
2
2
1
1
1
2
1
1
1
1
0
2
2
1
1
1
1
0
1
1
2
1
1
1
2
1
1
1
2
2
1
2
0
2
1
1
2
1
0
0
0
2
1
2
2
2
1
1
2
1
1
1
1
0
1
1
2
0
0
2
2
1
2
1
1
1
1
2
1
1
1
1
2
2
1
1
0
2
1
1
1
2
1
1
0
1
2
1
1
1
0
0
1
2
2
1
2
2
1
0
2
1
1
1
0
1
2
1
1
1
2
0
0
1
2
1
0
1
1
1
1
2
1
1
2
1
0
1
0
1
2
1
1
0
1
1
0
1
1
1
2
1
1
1
2
1
2
1
0
1
1
1
3
1
1
1
1
2
1
2
1
2
1
1
2
1
1
0
2
1
1
1
2
1
1
1
1
1
0
2
2
1
2
1
2
1
1
1
1
1
1
0
2
1
1
2
0
1
2
2
1
1
1
0
1
2
1
1
0
1
2
2
1
1
1
1
2
1
2
3
1
1
1
1
0
2
2
1
1
1
1
1
1
1
2
1
2
1
0
1
0
0
1
0
1
1
2
1
1
1
1
1
1
1
1
0
1
1
1
1
1
0
1
1
1
1
0
1
1
2
1
1
1
2
0
1
1
1
1
1
2
1
1
1
1
0
1
1
1
2
2
1
0
0
1
2
1
1
1
1
1
2
2
2
2
1
2
1
2
1
2
1
2
1
1
1
1
1
2
1
1
2
1
3
1
1
2
1
2
2
1
2
1
0
1
1
1
2
1
0
0
2
1
1
1
2
2
2
0
0
2
1
1
1
1
2
1
1
1
1
0
1
1
2
1
1
1
1
0
1
2
1
2
2
2
2
1
1
1
1
1
2
1
2
1
1
2
2
1
1
2
0
1
0
2
1
1
2
1
1
1
1
2
2
1
1
1
2
1
1
1
2
1
2
1
2
1
1
0
0
2
2
1
0
1
1
1
1
1
2
0
1
1
2
3
1
2
1
1
2
0
2
0
1
1
1
1
1
0
1
2
2
2
1
2
0
1
2
0
1
1
1
2
1
2
1
1
2
1
1
1
1
1
1
2
1
1
0
1
1
0
1
1
1
1
1
2
1
2
1
1
3
2
0
1
2
0
2
2
2
1
1
1
2
1
2
1
2
2
1
2
1
1
1
1
1
2
1
1
1
1
1
1
0
1
0
1
1
1
1
0
1
1
1
0
1
0
1
2
1
0
1
0
2
1
1
2
2
2
2
1
2
0
1
2
1
1
2
1
0
1
1
1
2
1
1
2
1
1
2
2
3
2
2
2
1
1
1
2
1
1
1
2
1
0
2
1
1
1
2
1
1
2
2
2
1
2
2
1
1
1
1
2
1
1
1
1
1
0
0
0
2
2
2
2
1
2
1
1
1
2
2
0
0
1
2
1
0
1
1
2
1
2
1
1
1
1
1
1
0
1
1
1
1
2
2
1
1
0
2
1
1
1
2
0
2
1
2
1
1
2
1
2
2
1
1
1
1
0
2
1
1
1
0
1
0
0
1
0
1
1
2
1
1
2
2
1
1
1
1
2
2
1
1
1
1
2
0
1
1
0
1
1
1
1
1
1
2
1
1
2
2
1
2
1
1
1
1
2
4
3
2
1
1
2
1
1
2
1
1
1
0
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
1
1
2
1
1
2
1
1
1
2
2
1
1
1
3
2
1
1
1
2
1
2
1
1
2
0
1
2
2
1
1
1
1
1
1
2
1
1
2
1
1
1
2
1
2
1
2
2
1
2
1
0
2
1
0
1
1
1
1
2
2
1
1
2
1
1
1
2
1
2
1
2
1
1
1
1
2
1
1
1
0
1
1
1
2
2
1
2
0
2
1
1
1
2
2
2
1
0
1
2
1
0
2
2
1
1
1
1
1
1
0
1
1
0
0
1
1
1
2
1
1
1
1
2
1
0
1
0
1
1
2
1
2
2
2
1
1
2
1
0
1
1
1
2
1
1
1
1
0
0
2
2
1
2
1
1
1
1
1
1
0
1
2
0
1
1
1
1
1
2
0
1
1
1
1
1
1
1
1
1
1
2
0
2
1
1
1
2
1
1
1
2
1
2
2
1
1
0
2
1
1
1
2
0
1
2
0
1
1
0
0
1
2
0
2
1
1
1
1
2
1
1
1
0
2
2
2
1
0
2
0
2
1
2
0
1
2
1
1
2
0
1
0
1
2
1
2
1
1
1
1
2
2
1
2
1
1
1
2
1
2
2
1
3
2
1
2
1
1
1
1
1
0
2
1
1
1
0
2
2
2
1
1
0
0
1
0
2
0
2
2
1
1
1
1
1
1
1
1
0
1
2
2
2
2
2
0
0
1
1
0
1
1
0
2
1
1
1
1
0
0
1
0
1
2
1
0
2
1
2
2
2
1
1
2
1
0
1
2
1
1
2
1
1
1
2
1
2
0
1
0
0
1
1
2
0
2
1
1
2
1
1
2
1
0
2
1
1
1
0
2
2
1
0
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
0
2
2
0
1
0
1
2
1
2
1
1
1
1
1
2
1
2
1
0
1
1
2
2
1
1
1
1
1
1
2
1
1
2
2
1
2
2
2
1
2
1
2
2
1
1
1
1
2
1
1
1
1
2
1
2
2
1
1
1
0
1
2
1
1
1
1
2
1
1
1
0
0
0
1
1
2
2
0
1
1
2
1
1
1
1
1
2
1
0
2
1
1
2
2
1
0
2
0
1
2
2
2
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
0
2
2
1
0
0
2
1
1
1
2
1
2
2
1
2
2
1
0
2
2
0
1
1
1
0
4
1
2
0
1
0
1
1
1
1
1
1
2
1
1
2
2
3
1
2
2
1
1
2
2
2
2
1
1
2
1
1
0
1
1
2
1
1
1
1
1
2
1
1
2
1
2
1
2
1
1
1
1
2
1
2
1
1
2
3
1
1
2
2
1
1
1
2
1
2
1
2
1
1
1
1
2
1
2
1
1
1
2
1
2
2
2
0
0
2
1
1
0
2
1
1
1
1
2
1
0
2
1
2
2
1
1
1
1
1
1
1
1
1
0
1
1
2
2
2
1
1
1
1
0
1
1
2
1
1
3
2
2
1
2
1
1
2
1
1
2
1
1
1
1
1
1
2
1
1
2
1
2
2
1
1
1
1
0
2
2
2
0
1
2
2
2
0
1
1
0
1
0
1
0
1
2
1
2
1
1
1
2
1
1
1
1
1
2
1
1
0
2
2
1
1
2
0
1
1
0
1
2
1
1
1
0
1
1
1
1
1
2
1
1
1
1
1
0
2
1
1
2
2
0
1
1
1
1
1
2
1
1
1
0
1
2
1
1
1
2
0
2
1
1
1
4
2
0
2
1
1
0
0
1
2
1
2
2
2
1
1
1
1
0
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
2
1
0
1
1
1
2
2
1
2
2
1
1
0
1
1
1
1
1
2
1
1
2
1
1
2
1
1
1
0
1
1
1
1
0
1
1
1
0
2
2
2
2
2
2
3
1
2
1
2
2
2
0
2
1
0
1
2
1
1
1
1
0
1
0
2
0
1
2
1
1
2
1
0
1
1
2
0
2
2
1
2
2
1
0
0
1
1
2
0
1
1
2
2
1
1
1
2
1
1
1
1
1
0
1
2
1
1
1
1
1
1
1
3
1
1
1
0
0
2
2
2
2
1
1
1
1
1
1
1
0
2
0
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
1
2
1
0
1
1
1
2
2
1
1
1
2
2
1
1
2
0
1
2
1
1
0
1
1
1
1
2
1
1
2
0
1
1
0
1
1
2
1
1
1
0
1
1
1
1
2
2
2
1
1
1
1
2
1
0
1
2
2
2
2
0
1
1
1
1
2
1
1
1
1
2
1
2
1
1
1
0
2
2
1
1
1
2
0
1
1
0
1
1
2
1
1
1
1
2
1
2
2
0
1
2
1
2
1
1
1
0
1
1
1
2
1
2
1
1
1
2
1
2
2
1
1
1
2
1
1
0
2
0
0
0
1
2
1
1
1
0
0
2
1
1
1
1
1
0
0
1
2
1
1
0
1
1
1
2
1
1
2
1
2
1
2
2
0
1
1
1
1
1
1
1
1
1
2
1
2
1
2
2
1
1
1
1
2
2
1
2
1
2
1
2
2
0
1
1
1
1
1
2
1
1
2
2
1
1
0
1
1
0
1
1
1
1
1
1
2
0
2
1
2
1
2
2
1
1
2
1
0
1
0
1
1
1
1
1
2
0
1
1
1
3
0
2
2
2
1
1
1
1
1
0
2
1
1
0
2
0
2
2
0
1
1
1
3
1
1
1
0
1
1
1
1
1
0
0
2
1
0
1
1
0
0
1
1
1
1
1
1
0
1
0
1
1
2
2
2
1
1
1
2
0
0
1
2
0
1
2
1
1
1
2
0
1
1
2
2
1
1
1
2
2
1
1
1
1
2
2
1
1
0
0
1
1
1
1
3
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
2
0
1
1
2
1
1
1
1
2
1
2
2
3
1
1
1
2
1
0
2
1
1
1
1
1
1
2
2
2
1
0
1
0
1
2
1
2
1
2
1
0
0
1
1
1
2
2
0
2
2
1
2
1
1
2
1
1
1
1
0
0
2
2
1
1
1
0
2
0
1
1
2
0
1
1
0
2
1
1
1
2
1
0
2
1
0
1
3
2
1
2
2
0
1
1
1
0
1
1
1
2
2
2
1
0
1
0
2
2
1
0
3
2
1
1
0
2
1
2
1
0
1
2
1
1
1
1
1
0
2
1
1
1
1
1
1
1
1
1
1
0
2
1
1
2
1
1
1
1
1
1
1
2
1
2
1
0
1
1
0
2
1
2
2
1
2
0
1
0
1
1
1
1
1
1
1
1
0
1
2
2
0
1
0
0
1
2
2
1
2
1
1
1
1
2
2
1
1
0
0
1
2
1
2
3
1
0
1
1
2
1
0
1
2
1
2
0
2
1
1
1
1
0
0
0
1
1
2
2
1
2
1
2
2
1
0
1
1
1
1
1
1
1
0
1
2
2
1
1
1
1
1
1
1
0
2
1
2
0
1
1
1
1
2
2
1
1
1
1
0
1
1
1
1
0
1
2
1
2
2
0
2
0
2
1
2
1
1
2
1
1
0
1
1
1
0
1
1
0
2
1
1
1
1
1
2
1
0
2
1
2
2
0
2
1
1
1
1
2
2
1
1
2
1
0
1
2
1
2
0
2
1
2
4
2
0
2
1
1
1
1
1
1
2
0
4
1
2
1
0
2
2
1
2
0
1
1
1
1
0
1
2
2
1
1
2
1
2
1
1
1
1
1
1
0
2
1
2
2
2
1
1
1
1
1
1
1
1
0
1
1
0
2
2
2
0
1
2
1
1
2
1
1
2
1
1
2
2
0
0
1
1
1
1
1
1
3
2
2
1
1
1
1
2
1
1
1
1
1
1
0
1
2
1
0
1
1
2
1
1
1
2
1
2
1
1
1
1
1
0
2
1
0
1
1
0
1
1
2
2
1
0
1
2
2
1
1
0
1
2
1
1
1
2
0
2
1
1
1
1
2
1
0
1
1
1
0
1
2
2
2
1
1
2
2
1
1
1
1
1
1
1
1
0
1
1
0
2
1
2
1
0
3
2
1
1
1
0
1
0
1
2
2
1
2
1
1
2
2
1
0
2
1
2
1
1
1
1
2
0
1
0
1
1
2
1
1
1
1
0
2
2
1
1
1
0
1
2
1
2
2
1
2
2
1
2
1
2
2
1
1
1
1
1
2
1
0
1
1
1
1
1
1
1
1
2
2
1
0
1
1
2
2
2
1
1
2
1
1
1
1
1
1
0
1
2
1
1
1
1
2
2
1
2
1
1
2
2
2
1
0
0
1
2
0
1
1
1
1
1
1
1
1
1
1
0
2
0
2
2
1
1
1
1
2
2
1
0
1
1
2
2
1
1
1
2
1
1
0
0
1
1
2
1
1
2
1
1
1
2
2
1
2
2
1
1
0
1
1
1
1
2
1
2
1
1
2
1
1
2
1
2
2
1
1
1
2
1
1
1
0
1
2
0
1
1
1
2
1
2
2
1
1
1
1
2
0
1
1
1
1
1
0
1
1
0
1
0
1
2
1
2
1
0
1
1
1
2
1
0
1
1
0
1
1
1
2
2
1
1
1
1
2
1
1
1
0
1
1
1
2
1
2
2
2
1
1
1
1
1
1
0
0
1
1
2
2
2
2
1
1
1
2
1
1
1
1
0
1
1
1
1
1
1
0
2
1
1
1
0
3
1
0
1
0
1
2
0
0
3
1
2
1
1
1
1
0
1
1
1
2
1
1
2
1
1
1
1
1
0
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
0
2
0
1
2
1
2
0
1
2
1
1
1
0
1
1
2
1
1
1
1
1
1
1
1
0
1
1
1
1
0
1
0
1
1
1
1
1
1
2
1
2
2
1
1
0
2
1
0
1
1
0
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
2
2
1
1
1
1
2
2
1
1
1
1
0
1
1
2
0
1
1
2
1
1
0
2
2
1
2
2
2
2
2
1
1
1
0
1
0
1
2
0
2
2
1
1
1
1
0
2
2
0
1
1
1
0
1
2
1
1
1
0
1
2
2
1
0
1
2
1
0
1
1
2
1
1
1
1
1
2
0
1
2
1
1
1
1
1
1
0
1
1
2
1
1
2
1
1
1
1
1
0
1
1
2
1
1
1
2
0
2
0
1
1
0
0
2
2
1
2
2
1
2
0
1
1
1
0
2
1
1
1
0
1
1
1
1
2
2
2
1
2
2
0
1
1
1
1
2
2
2
1
1
2
2
0
0
2
1
1
2
1
1
1
1
2
1
1
1
1
1
1
0
2
2
2
1
2
1
1
0
2
2
1
1
1
1
1
0
2
1
0
1
1
1
0
0
2
1
1
1
1
1
2
0
1
1
1
0
1
2
1
1
1
0
1
1
1
1
1
2
1
1
1
0
0
1
0
1
1
0
1
1
1
1
1
1
1
0
1
1
1
2
1
2
1
0
1
2
1
1
1
1
2
1
1
2
2
2
1
1
1
2
1
1
1
1
1
1
1
1
1
0
1
0
1
1
1
2
1
1
1
1
1
2
0
1
1
2
1
1
2
1
0
2
1
2
1
2
1
2
1
0
1
1
1
1
2
2
1
1
1
0
1
1
1
1
1
0
1
1
2
1
1
1
1
1
1
2
1
0
1
0
1
1
1
2
2
1
2
1
1
1
1
2
1
1
1
2
1
1
1
1
2
0
2
0
1
2
1
2
1
1
2
1
1
1
0
1
1
0
1
1
1
1
1
1
2
1
1
2
0
0
1
1
2
2
2
1
1
1
1
1
0
1
1
1
1
1
1
2
0
0
2
2
1
2
1
1
1
0
0
1
1
2
1
3
1
1
1
1
1
0
1
2
2
2
1
1
2
2
0
1
1
2
1
1
1
1
1
0
1
1
0
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
2
2
1
2
0
0
1
0
1
2
2
1
1
1
1
2
1
1
1
0
1
1
0
0
1
1
2
2
1
2
1
1
2
1
1
2
1
2
1
1
2
1
1
2
1
1
2
2
1
0
1
1
1
1
1
1
2
1
2
0
1
1
2
2
1
1
0
2
0
1
2
1
1
0
1
2
1
1
2
1
1
0
1
1
1
1
1
1
1
1
6
1
1
2
1
1
1
1
1
2
1
1
2
2
1
2
1
0
2
1
2
2
1
0
1
1
1
2
1
1
1
2
0
1
0
1
1
1
1
1
1
1
2
2
1
1
0
0
1
1
2
1
1
1
0
2
1
2
1
1
1
2
0
2
0
1
1
1
0
2
0
0
1
2
1
2
1
2
1
2
2
1
1
1
1
1
1
1
2
2
1
1
1
1
0
0
0
1
1
1
2
2
2
1
1
1
0
1
1
1
1
1
2
0
2
1
1
1
1
1
1
1
1
1
0
1
1
0
1
1
1
2
1
1
1
2
0
2
2
3
2
2
0
1
1
1
2
1
0
0
0
1
1
1
0
1
3
1
1
1
0
1
1
2
1
1
1
1
2
1
1
1
2
0
1
0
1
2
0
1
2
1
2
2
1
1
2
1
0
2
2
0
1
0
1
2
2
2
2
2
2
1
2
1
2
1
1
1
1
1
1
0
2
0
1
1
1
1
0
1
2
2
1
1
0
2
2
2
1
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
0
1
2
1
1
1
1
2
1
1
2
1
0
1
1
1
0
0
1
2
1
1
1
1
2
1
2
2
2
1
1
1
1
1
2
1
2
1
1
2
2
2
1
1
1
1
0
1
0
1
2
1
1
1
1
1
0
4
1
2
1
1
2
2
1
1
1
1
1
1
1
1
2
2
3
1
1
2
1
1
1
2
1
2
1
2
2
1
1
1
2
2
1
0
1
0
1
1
0
1
0
0
1
1
1
0
1
1
1
0
1
2
2
1
1
1
0
1
1
0
1
1
1
1
2
2
1
1
1
2
0
1
0
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
2
1
0
1
1
1
1
1
1
2
0
0
1
1
0
0
1
2
1
2
1
1
1
1
1
0
2
1
1
2
2
0
2
1
2
2
1
2
0
1
1
1
1
1
0
1
1
1
0
0
1
0
1
1
1
2
1
1
1
1
2
1
1
1
1
0
1
2
2
1
1
0
1
1
1
1
0
1
2
2
2
1
2
2
2
1
2
1
2
2
1
1
1
1
1
1
2
2
1
1
1
0
1
2
1
2
0
2
1
2
1
1
2
0
0
0
1
0
0
1
2
1
2
1
1
2
1
2
1
1
2
1
2
0
1
2
3
0
2
1
1
1
1
1
1
1
1
0
1
1
1
1
0
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
2
1
2
1
0
2
1
0
1
1
1
2
0
1
2
1
1
0
1
2
2
2
1
1
1
1
0
2
1
1
1
1
1
2
1
0
1
2
1
1
1
0
2
0
2
1
1
0
2
2
1
2
1
0
2
0
2
1
2
1
2
2
0
1
1
1
1
2
2
2
1
0
3
1
1
1
2
2
2
1
2
1
1
1
0
1
1
1
2
1
1
1
0
2
1
2
1
0
1
1
1
1
1
0
1
1
1
1
0
1
0
1
2
2
1
1
1
2
2
1
1
2
1
1
1
2
0
1
2
2
2
1
2
1
1
0
1
2
1
1
1
2
2
0
2
1
1
0
1
1
1
2
1
1
0
1
1
1
2
1
2
1
1
1
1
1
1
1
0
2
1
1
1
1
0
1
0
0
2
2
1
1
0
1
1
1
2
1
1
1
1
1
2
1
2
2
2
2
0
1
2
1
1
1
1
1
0
1
1
0
1
2
2
1
1
2
1
1
2
1
2
1
2
1
1
0
0
1
1
1
2
1
1
0
1
1
1
2
0
2
2
2
1
2
1
1
2
0
1
1
1
1
2
1
1
1
1
1
2
1
0
0
2
2
0
3
2
2
1
1
2
2
1
2
0
1
1
1
2
1
2
2
1
1
2
0
2
2
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
0
2
2
2
1
1
1
1
2
1
1
0
2
2
1
1
1
2
2
1
2
1
0
1
1
1
1
1
1
2
2
2
1
1
2
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
2
2
0
2
1
1
2
1
2
1
1
1
1
2
1
1
2
2
1
1
0
1
1
1
2
1
1
1
2
1
1
2
2
1
1
2
1
2
2
2
0
1
1
1
2
1
1
1
0
2
0
1
1
1
1
1
1
1
1
1
1
1
0
2
1
1
1
2
1
1
2
1
2
0
2
1
2
1
1
1
2
1
1
0
0
0
1
1
0
1
2
1
1
2
1
1
1
0
0
1
1
1
1
2
2
1
0
2
1
1
1
2
1
1
2
0
2
1
2
1
2
2
2
0
1
1
1
0
1
1
0
1
1
1
1
1
1
1
2
1
1
2
2
1
2
2
1
1
0
1
2
0
2
1
1
1
1
0
1
1
1
1
0
0
2
1
1
1
2
2
2
1
1
1
0
3
2
1
1
1
2
1
0
1
0
1
1
1
1
2
0
1
1
1
1
1
1
1
2
1
1
1
1
2
2
1
1
1
2
2
2
1
0
2
1
1
2
0
2
1
2
1
1
1
1
2
1
1
1
2
2
1
1
2
1
1
1
2
1
2
0
1
1
1
1
0
1
1
1
2
1
1
1
1
2
1
1
1
2
1
1
1
2
1
2
1
0
1
2
1
1
0
1
1
1
1
0
1
1
2
2
1
0
2
2
1
1
2
1
1
1
1
1
2
1
0
1
1
2
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
2
0
1
1
0
1
1
1
1
1
1
2
2
0
1
1
1
0
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
0
1
1
1
0
1
2
1
1
1
0
1
1
2
1
2
1
0
1
1
2
1
0
1
2
1
1
1
2
1
1
1
1
0
2
1
1
1
2
0
1
2
1
2
2
0
1
2
0
1
1
1
0
1
1
1
1
1
0
1
1
1
0
1
3
2
1
1
1
1
1
1
0
2
1
2
2
1
1
2
1
1
1
1
1
2
1
1
0
1
0
2
0
1
1
2
1
1
1
1
1
1
1
0
2
0
2
1
1
2
2
0
1
1
1
2
1
1
1
2
1
2
2
0
2
1
1
0
2
2
2
1
1
1
1
2
1
1
1
2
1
1
1
0
1
2
2
3
1
1
1
2
2
0
2
2
1
1
1
2
1
0
1
1
3
2
1
2
2
1
2
1
0
1
2
1
2
1
2
2
1
1
0
1
0
1
2
0
1
1
1
1
2
1
0
1
1
1
2
1
2
1
1
1
1
1
0
2
1
1
0
2
1
1
1
1
2
1
2
1
2
2
1
1
1
2
1
2
1
0
2
1
0
0
2
2
1
2
1
1
1
1
2
2
1
0
1
1
1
2
2
1
2
4
2
1
2
1
2
2
2
1
2
1
1
0
0
1
1
0
2
1
1
1
1
0
3
1
2
1
1
2
1
1
1
0
2
1
2
1
0
3
1
1
1
2
2
1
0
1
0
1
1
0
1
0
2
1
2
1
1
1
1
0
2
0
1
1
1
1
1
1
1
2
2
1
1
1
2
3
1
1
1
1
1
1
1
1
1
2
1
2
1
2
1
1
2
2
1
3
2
2
1
1
2
1
2
2
1
2
1
1
0
0
1
2
2
1
0
2
1
2
1
0
2
1
1
2
1
2
1
1
2
1
1
2
2
1
1
1
2
2
1
2
1
2
2
2
2
1
2
1
0
1
2
1
1
1
2
1
1
1
2
1
1
1
2
1
0
1
2
1
2
2
2
0
1
0
1
1
1
1
2
1
2
2
2
1
1
1
1
0
1
0
1
1
2
1
1
1
1
2
0
1
0
2
1
0
1
0
1
1
1
2
2
1
1
1
0
0
2
1
1
1
1
0
1
2
1
1
2
2
1
0
2
2
1
0
0
1
1
1
1
2
1
1
1
1
2
1
0
2
2
0
0
0
1
0
1
2
1
1
2
2
2
2
1
2
2
0
1
1
1
1
2
0
2
1
0
0
1
2
1
1
1
2
1
1
2
3
1
1
0
2
0
1
0
1
1
1
2
1
1
2
1
1
1
2
0
1
1
1
1
2
1
2
2
1
0
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
2
1
0
1
1
1
1
1
1
1
0
1
1
0
2
1
1
1
2
0
1
0
1
0
1
1
2
2
1
1
1
2
2
1
1
1
1
2
2
1
1
0
1
1
0
1
2
1
2
1
2
2
1
2
2
1
1
1
2
0
0
1
0
2
1
1
1
1
0
1
1
1
1
2
0
0
2
2
1
2
2
1
1
1
1
1
1
2
1
1
1
2
1
1
2
1
1
1
1
2
1
2
0
1
1
2
0
1
2
0
1
2
1
2
1
1
0
1
2
0
2
2
1
2
0
1
1
0
2
0
1
1
1
0
2
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
0
2
1
2
0
1
2
2
1
1
1
1
1
1
1
1
0
1
1
1
1
2
2
0
1
1
1
2
2
0
0
1
4
0
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
2
3
1
1
2
1
2
1
1
2
1
1
1
1
1
1
1
0
1
2
2
1
1
1
0
1
2
1
1
1
1
2
1
1
2
3
1
0
1
1
1
1
1
1
0
1
1
1
1
0
1
2
0
1
1
1
2
1
1
1
1
0
1
1
2
2
1
2
2
1
2
1
2
2
1
1
2
2
1
2
2
1
1
2
2
1
1
1
0
0
1
2
2
1
2
2
2
0
1
1
1
1
1
1
1
1
0
2
1
1
0
2
1
1
1
1
1
1
1
1
2
2
0
1
2
0
1
1
1
2
2
1
0
1
1
2
1
0
2
1
2
1
1
0
2
1
0
2
14
1
1
1
1
1
1
2
1
1
2
2
1
2
1
2
1
0
1
1
1
1
2
0
1
2
0
0
2
0
2
1
1
1
2
2
1
1
1
0
2
2
1
2
1
1
1
1
1
0
1
2
1
2
1
1
1
2
2
1
1
1
1
1
2
0
1
2
1
1
1
1
1
1
1
1
2
2
1
2
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
1
1
2
1
2
1
0
1
1
0
1
0
1
1
1
2
1
1
2
0
2
0
1
1
1
1
0
2
0
2
2
1
1
1
1
1
2
1
2
2
1
1
1
0
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
4
2
1
1
1
1
1
1
1
1
1
2
0
1
0
1
1
1
1
2
1
1
1
1
2
2
1
1
1
2
1
0
1
2
1
1
1
1
1
2
2
2
1
2
2
2
1
1
2
2
1
1
1
1
1
0
1
1
1
0
1
1
2
0
2
1
0
1
1
2
0
1
0
1
1
2
0
1
1
2
1
1
2
0
1
0
1
2
0
1
1
1
0
1
2
1
0
2
2
1
1
2
1
2
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
0
0
2
2
1
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
1
1
2
2
1
1
1
0
2
1
1
2
1
1
2
1
1
1
2
1
2
0
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
2
1
1
2
1
1
2
1
1
1
1
2
1
1
1
0
1
1
1
1
1
1
0
2
1
1
1
1
0
2
2
0
1
2
0
1
2
2
2
1
2
1
0
1
1
0
1
1
0
2
1
1
0
0
2
2
2
2
1
2
1
1
2
2
1
1
2
0
1
2
1
0
2
2
1
2
0
2
2
1
1
1
1
1
2
1
1
1
2
1
1
2
2
0
2
2
1
1
2
1
1
0
1
0
1
0
2
1
1
1
0
1
1
0
1
1
0
0
1
2
1
1
2
1
0
1
2
1
1
1
2
0
1
1
2
1
1
1
1
1
1
1
0
1
1
1
1
2
0
1
1
0
2
1
1
1
1
1
1
2
1
1
0
1
2
2
1
1
1
1
1
1
1
6
2
1
0
1
2
1
1
1
1
2
1
1
1
2
0
1
1
1
1
2
1
0
2
1
1
2
0
1
0
1
1
1
1
2
3
1
1
2
1
1
1
0
1
1
0
1
1
0
2
2
1
2
1
1
1
2
0
1
1
2
1
1
0
1
2
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
2
2
2
1
1
1
1
1
0
1
1
1
1
1
2
1
0
2
2
1
1
1
2
2
0
2
0
1
0
1
1
0
1
1
1
1
2
1
1
2
0
2
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
0
0
1
0
1
1
0
1
2
1
2
1
1
1
1
2
1
1
1
2
1
1
0
1
2
1
0
2
1
1
2
1
1
1
2
2
1
1
1
1
0
1
1
1
0
2
2
1
1
1
2
1
2
1
2
2
1
1
1
0
2
0
1
1
1
1
1
1
1
0
1
1
1
1
0
2
2
1
2
2
1
0
0
1
2
1
1
0
1
1
1
2
2
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
2
0
2
1
0
1
0
2
1
1
1
1
1
1
0
2
1
1
2
4
2
1
1
1
2
1
2
1
1
1
1
0
1
1
1
1
1
1
0
1
0
0
1
2
1
1
1
1
2
1
1
1
1
0
1
1
2
0
2
1
1
1
1
1
0
1
1
1
1
0
0
1
1
1
2
1
0
2
2
2
2
1
1
1
1
0
1
2
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
0
1
1
1
1
0
1
1
2
2
1
1
2
1
1
1
1
1
2
1
1
1
2
1
2
3
1
2
1
1
0
1
1
1
1
2
1
1
1
1
1
1
2
1
1
0
1
2
1
1
1
1
1
1
1
1
2
1
2
1
2
0
0
1
2
0
1
2
0
1
1
0
1
2
1
3
1
1
1
1
1
2
2
1
1
1
1
2
0
1
1
1
1
0
1
2
2
1
1
1
2
2
1
2
1
1
1
0
0
1
1
2
1
1
0
1
1
1
1
0
1
1
2
1
0
1
0
2
1
1
1
1
1
1
2
1
2
1
1
0
1
2
1
0
1
1
2
0
1
1
1
1
2
1
1
1
1
1
2
2
0
1
1
1
1
1
1
0
1
0
1
2
2
1
2
1
1
1
1
1
3
1
1
1
1
1
0
1
1
1
0
2
2
0
2
1
1
1
1
2
1
1
2
1
1
2
0
1
1
0
2
0
2
1
1
2
0
1
1
1
1
1
2
1
1
0
1
0
1
1
2
1
1
1
1
1
0
1
2
1
1
0
1
1
1
1
2
2
1
0
2
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
0
1
1
2
2
2
0
1
1
2
2
2
1
1
1
1
1
1
4
2
1
0
1
1
0
0
2
0
1
1
1
2
1
1
1
2
2
1
1
1
2
1
1
1
1
1
1
0
1
0
2
1
1
1
1
1
1
2
1
1
0
0
2
1
2
1
0
1
0
2
0
1
2
2
1
2
2
1
1
1
2
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
2
0
1
1
1
1
1
1
1
2
0
0
1
1
2
1
1
0
2
1
1
2
2
1
1
1
1
1
1
1
1
1
2
0
2
1
1
1
1
1
0
3
0
1
0
0
0
1
1
1
1
2
2
1
1
0
2
1
3
1
1
1
2
1
1
2
1
1
2
1
1
0
2
1
1
2
1
2
0
1
1
1
2
1
2
2
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
2
1
2
1
0
1
2
1
1
0
1
1
1
1
1
1
1
3
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
1
1
2
1
0
2
1
1
1
2
0
2
1
1
1
1
1
1
2
1
1
2
2
0
1
2
1
1
0
1
2
1
1
1
1
0
1
1
1
1
1
2
2
1
0
1
1
1
1
2
1
1
1
2
1
2
1
0
0
1
1
2
1
0
0
2
1
2
1
1
0
1
1
2
1
1
1
1
2
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
2
1
0
2
0
0
1
1
2
1
3
2
1
1
2
1
1
2
2
1
1
2
2
1
1
1
0
2
1
2
1
2
1
1
1
1
1
1
2
2
0
2
1
3
1
1
1
0
1
1
1
1
2
1
2
0
2
1
2
2
2
1
1
1
1
1
0
1
2
1
1
1
2
1
1
1
2
2
2
2
2
1
3
2
1
1
1
2
0
1
2
2
1
1
2
2
2
1
2
2
1
1
0
1
1
1
2
1
1
1
2
2
2
0
1
1
1
1
1
1
2
1
2
1
2
1
1
1
2
0
1
1
0
0
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
2
1
1
1
0
1
2
1
1
1
2
1
2
2
1
1
0
1
1
1
0
2
0
1
1
1
1
2
2
2
0
1
0
2
1
1
0
1
1
2
2
0
2
2
1
1
1
2
1
1
1
2
2
1
1
2
1
3
1
1
1
2
2
1
2
1
0
1
1
1
1
0
1
0
1
1
1
2
2
1
2
1
1
1
1
0
1
1
1
2
1
1
1
1
3
0
1
2
1
1
2
2
2
1
3
1
1
1
1
1
2
2
3
2
1
0
1
0
0
0
1
1
1
0
1
1
0
2
3
2
2
2
1
1
1
2
1
1
1
0
1
2
1
0
2
1
1
1
1
1
1
1
1
2
1
1
1
2
1
2
0
0
1
1
1
1
2
1
1
1
1
2
1
2
2
1
1
1
1
1
0
1
1
0
0
1
1
2
1
1
2
2
1
1
1
0
0
1
1
2
0
1
0
1
0
0
2
1
1
1
1
2
1
1
2
0
1
1
1
1
2
1
1
0
1
0
1
1
0
1
2
1
1
2
1
2
2
2
1
1
1
1
2
1
1
2
2
2
0
0
2
1
2
2
1
0
1
1
1
1
1
2
1
1
1
0
1
1
1
0
0
0
0
0
1
1
1
2
1
2
0
0
1
1
1
2
1
1
2
1
2
2
1
1
1
1
1
2
0
2
1
0
1
1
0
2
1
1
2
0
2
1
0
1
1
2
1
2
1
1
1
2
0
1
1
1
1
3
1
2
1
1
2
1
1
1
1
0
2
1
1
1
2
0
1
1
1
2
1
1
0
1
1
2
2
1
0
1
1
2
2
1
2
0
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
0
1
1
1
2
0
1
2
1
0
4
1
2
0
1
0
1
1
1
1
1
1
2
2
1
0
1
2
2
1
1
1
1
1
1
1
1
2
1
1
1
2
0
1
1
1
1
1
2
1
1
1
1
2
1
0
0
1
1
2
2
1
1
1
1
0
1
1
2
0
1
1
1
2
1
1
2
3
1
2
1
1
1
0
1
2
1
2
1
1
1
2
2
1
1
2
1
1
1
1
0
0
1
1
1
1
0
1
4
1
1
1
2
2
2
1
2
2
2
1
1
1
1
2
0
2
2
1
2
1
0
2
1
2
1
2
2
0
2
0
1
2
1
0
1
1
0
2
1
0
0
1
1
1
2
0
1
0
1
1
1
1
1
0
2
1
1
0
0
2
1
2
1
1
1
2
1
2
1
1
1
1
2
1
2
1
2
0
1
1
1
0
1
2
1
1
1
1
1
1
1
0
1
1
2
2
2
1
0
1
2
1
1
2
2
2
1
1
0
1
0
1
1
1
1
0
0
1
1
0
0
1
1
2
1
0
1
1
1
1
0
1
1
1
1
1
1
0
2
1
1
1
0
1
2
1
2
1
1
0
2
1
2
1
2
2
1
1
1
1
1
2
3
1
1
1
2
4
2
1
1
2
2
2
2
2
2
1
1
2
1
0
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
0
1
1
1
1
1
2
1
2
1
1
1
1
0
1
0
2
1
2
1
1
1
2
1
1
1
0
0
1
1
1
1
1
1
1
1
1
0
1
0
2
1
0
1
1
2
2
1
1
1
1
0
1
0
1
1
1
1
2
0
1
0
1
1
2
1
1
2
1
1
1
2
1
1
1
1
0
1
1
1
1
1
0
1
1
2
1
2
1
2
1
2
1
1
1
0
1
1
1
1
0
1
1
2
1
0
1
1
2
1
1
1
1
1
2
1
2
1
1
2
2
2
2
2
2
1
1
1
1
2
1
1
0
1
2
2
2
1
1
2
1
1
2
1
1
2
1
1
1
0
1
1
1
1
2
1
1
1
1
2
1
0
1
1
0
2
2
2
2
0
1
0
1
2
2
0
1
1
1
2
1
1
1
1
1
0
1
1
1
1
1
1
1
1
0
1
0
1
1
1
2
1
2
1
2
2
1
1
1
0
2
0
0
2
1
1
1
1
1
2
1
0
1
1
1
1
1
2
1
2
1
1
3
1
2
2
1
1
2
0
0
1
1
1
0
1
1
1
1
1
2
2
0
2
2
1
1
1
1
1
0
1
1
2
1
2
1
0
2
2
0
2
2
0
2
1
2
1
0
2
1
1
1
1
2
2
1
1
2
1
2
1
1
0
1
1
1
1
2
0
2
1
1
1
1
2
1
1
1
1
2
2
0
1
1
1
1
0
2
2
2
0
1
2
1
1
1
2
0
2
1
1
1
1
0
0
1
1
1
1
1
2
2
1
1
1
2
1
0
1
2
0
1
1
1
2
0
1
1
1
1
1
1
2
1
1
1
1
2
1
0
1
5
2
0
0
1
2
1
2
0
1
1
2
2
1
1
1
1
2
2
2
2
0
2
2
1
0
0
2
1
2
1
1
2
0
0
1
1
1
2
2
0
1
2
1
2
1
1
0
1
2
1
0
1
1
0
2
1
2
2
1
2
1
1
1
2
2
2
2
1
2
2
1
2
1
1
1
1
2
1
1
0
1
2
1
1
2
1
0
1
1
1
1
2
1
1
2
0
1
1
2
1
1
1
1
1
1
2
2
1
1
2
2
1
2
0
0
1
1
1
2
1
1
0
1
1
1
2
1
1
0
2
1
1
0
1
0
2
2
2
2
0
1
1
2
2
1
1
1
1
1
2
1
1
1
2
1
1
2
2
1
0
2
2
1
1
1
2
0
1
2
1
2
0
2
2
1
1
2
1
2
1
1
2
1
1
2
2
0
2
2
1
1
1
1
1
0
2
1
1
1
1
0
1
1
1
2
2
1
1
2
1
2
1
1
1
1
1
1
2
2
1
1
1
3
2
1
0
1
1
1
1
1
2
2
2
1
2
2
2
2
0
2
1
2
1
2
1
2
0
2
0
2
0
2
2
1
1
0
2
1
1
2
1
1
1
1
2
2
2
2
1
2
2
1
1
0
1
1
1
2
1
1
0
1
1
1
1
1
2
2
1
0
1
1
1
1
2
2
1
2
0
0
1
1
1
1
1
1
2
2
2
2
0
1
0
2
2
0
1
1
0
1
2
2
1
2
2
2
1
2
1
1
2
0
1
1
2
2
1
1
1
0
2
1
1
1
1
0
1
1
2
1
2
1
0
1
2
1
2
1
1
1
1
1
2
2
1
2
1
1
1
1
1
2
1
2
1
1
1
1
2
2
1
0
1
1
0
1
0
1
0
1
2
2
2
1
1
1
1
2
1
1
1
2
2
1
1
1
0
2
1
3
2
0
1
1
1
1
1
2
1
2
1
1
2
1
2
0
1
0
1
2
2
1
1
1
0
1
2
1
2
2
2
1
1
1
1
0
1
2
2
1
1
2
1
1
2
1
2
1
1
5
2
2
1
0
1
1
1
2
1
2
0
2
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
2
2
2
0
1
1
1
2
2
1
1
2
2
2
1
0
0
2
3
1
2
2
1
2
1
0
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
0
2
1
1
1
1
2
0
1
1
1
1
2
2
2
1
1
1
1
2
1
1
1
0
1
1
2
2
1
1
1
1
2
2
2
1
2
1
1
1
0
0
1
1
1
1
1
2
1
1
1
2
1
1
1
2
2
1
1
1
1
1
2
1
2
1
1
1
2
1
1
1
1
1
2
3
2
1
2
1
2
1
1
1
0
1
0
2
2
1
2
1
1
1
2
1
2
1
0
2
0
1
1
1
1
0
1
1
1
1
1
1
1
2
0
1
2
2
1
0
0
2
1
1
1
2
1
1
1
1
1
1
1
2
2
1
2
1
0
0
2
1
2
2
0
2
2
1
1
1
2
1
0
2
1
2
0
2
1
2
1
2
0
1
1
2
1
1
1
1
1
2
1
2
1
1
1
2
2
1
2
1
0
0
1
0
2
1
1
1
1
1
2
0
0
1
1
1
1
1
2
2
1
1
1
2
1
1
1
1
2
1
0
0
2
0
1
1
2
1
1
1
2
1
1
1
0
1
0
1
1
2
1
1
1
1
0
1
0
0
2
1
0
1
1
1
1
1
0
1
2
1
2
1
0
1
1
0
1
1
1
1
2
1
1
1
1
1
1
2
2
2
1
2
0
1
2
1
2
1
1
2
1
1
2
1
1
2
1
1
1
2
2
1
1
1
1
0
0
1
2
1
0
1
1
1
1
1
1
0
1
2
1
1
1
0
2
1
1
1
1
1
0
1
1
1
2
1
2
1
2
0
1
2
2
1
1
0
1
0
0
1
0
0
2
1
1
1
2
2
1
0
1
1
1
0
2
2
1
2
2
1
0
1
1
1
1
1
0
1
1
1
1
1
0
2
0
2
0
1
1
0
1
2
0
1
1
2
1
1
1
1
1
2
0
0
2
0
0
1
1
1
2
2
2
2
1
1
1
1
1
1
3
1
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
1
0
0
1
1
2
1
1
0
0
1
1
0
1
1
1
1
0
1
1
2
1
0
2
1
2
1
2
0
1
1
2
0
1
2
2
0
2
2
2
1
2
1
0
1
0
1
1
2
0
2
2
1
0
2
2
1
1
2
1
1
1
1
0
1
1
1
1
1
1
1
2
2
0
1
1
2
2
1
0
1
1
1
2
1
2
1
1
1
1
1
1
1
0
2
0
1
1
1
2
1
1
1
1
1
2
2
1
1
2
1
2
2
2
2
2
1
1
0
1
1
0
1
0
2
1
2
1
2
1
0
1
1
1
1
2
1
1
1
1
0
1
1
2
2
0
1
1
1
1
1
2
0
2
1
0
2
2
2
1
2
1
0
1
1
1
1
1
2
1
1
2
2
1
1
1
1
2
1
1
1
1
1
0
1
1
1
1
1
1
1
2
1
0
2
1
0
1
1
2
2
0
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
2
1
1
1
1
1
1
1
1
1
1
2
2
1
2
1
2
0
1
1
1
1
2
1
1
1
3
1
2
1
1
1
1
1
2
1
1
1
2
1
1
2
2
1
1
0
0
0
1
1
2
1
1
2
2
2
1
0
1
1
2
1
2
1
1
0
1
1
1
1
1
1
2
3
1
0
1
1
1
1
1
1
1
0
1
1
1
1
2
1
1
1
2
2
0
1
1
2
0
0
1
1
1
2
1
1
1
0
2
1
1
1
2
1
2
0
2
1
2
1
1
2
1
1
0
1
0
1
1
1
1
1
0
2
0
2
2
1
1
1
1
1
0
2
1
2
1
1
0
1
0
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
0
2
2
2
1
2
1
2
2
2
2
1
2
1
2
1
1
1
0
2
0
0
1
0
2
1
1
2
1
1
2
1
1
2
1
2
1
1
2
1
2
1
1
0
1
1
2
2
2
1
1
1
1
0
0
1
1
1
2
2
1
2
2
1
1
2
1
1
2
2
1
2
0
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
2
1
2
1
1
1
0
2
1
2
0
1
1
2
1
2
1
2
1
2
2
1
1
2
0
2
1
2
1
1
1
1
2
0
1
1
2
1
1
1
0
1
1
2
2
0
1
1
2
1
1
0
1
1
1
2
1
2
0
1
1
1
0
0
1
1
1
2
1
1
2
1
1
0
1
0
1
1
0
0
1
1
1
0
0
1
1
2
1
1
0
1
1
1
1
2
1
1
2
1
2
1
1
2
0
1
1
2
2
2
1
1
1
1
1
1
2
1
1
1
2
1
2
0
2
2
0
1
0
1
1
0
2
2
2
1
1
1
2
0
1
1
0
1
1
2
2
1
1
0
2
1
1
1
2
2
2
1
2
0
1
2
2
1
1
1
1
2
1
2
2
0
2
1
1
1
0
0
1
1
1
1
1
1
1
1
1
2
1
1
1
1
0
1
2
2
2
0
1
0
2
1
1
2
1
1
1
2
2
1
3
1
0
2
2
2
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
0
1
2
0
2
1
0
0
1
2
2
0
0
1
1
2
1
1
2
2
1
1
2
1
0
2
1
1
1
1
1
1
1
1
0
0
1
1
2
1
1
2
1
2
1
2
1
1
2
2
1
1
1
0
1
2
2
1
0
1
5
0
1
0
0
1
1
1
1
2
1
2
2
1
2
2
1
0
1
1
0
1
1
2
1
1
1
1
1
2
2
1
1
2
1
2
2
1
2
1
1
2
1
2
1
2
0
1
0
1
1
1
1
1
0
2
0
1
0
0
2
1
1
1
1
2
1
2
1
1
1
2
1
1
1
1
2
1
0
1
0
0
1
1
0
3
2
1
0
2
1
1
1
2
1
2
2
1
1
1
1
1
2
0
1
1
2
1
2
1
1
1
1
0
1
1
1
2
2
0
2
1
1
0
1
1
0
0
1
0
1
1
0
1
0
1
1
2
1
1
0
1
2
0
1
1
1
0
1
1
0
1
2
1
2
0
2
1
2
2
2
2
0
2
0
2
1
1
1
1
1
2
2
0
1
0
2
1
1
1
1
0
1
1
3
1
1
1
0
2
1
1
2
1
2
2
1
1
1
1
2
2
2
1
1
1
1
0
0
1
1
1
1
2
0
1
1
2
0
1
2
0
1
0
1
1
0
2
1
0
1
0
2
1
0
1
1
1
2
1
2
2
1
0
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
0
2
2
2
1
2
1
1
1
1
1
1
0
1
0
2
0
1
1
2
1
1
1
1
1
2
1
2
1
1
1
2
1
1
2
1
1
2
1
1
0
2
1
0
0
1
1
1
2
1
2
1
1
0
1
2
0
1
1
1
2
1
0
1
1
1
1
2
0
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
1
1
2
2
1
2
0
1
1
1
1
1
1
0
1
2
1
1
1
1
1
2
2
1
1
1
2
2
1
0
1
1
1
0
1
2
1
2
0
1
2
1
1
1
1
2
2
1
2
1
1
1
1
2
2
2
2
2
2
0
1
1
1
0
1
0
1
2
2
2
1
1
2
1
1
2
1
0
1
1
2
2
1
1
2
1
0
2
1
1
2
3
2
1
1
1
2
0
2
1
1
0
1
1
1
0
1
1
1
1
0
1
1
1
1
1
1
1
1
2
1
1
2
0
1
2
0
1
2
1
1
0
2
2
1
0
1
1
1
0
2
2
2
1
1
0
1
1
1
1
1
1
1
1
1
0
1
1
2
2
1
1
2
0
1
1
2
1
1
1
1
1
1
1
1
1
0
2
2
2
1
1
1
1
1
0
2
1
0
1
2
1
2
1
2
1
1
1
1
2
3
0
0
1
1
1
1
1
1
1
1
2
1
1
0
1
1
2
1
1
1
1
1
1
0
1
0
1
0
1
2
1
1
1
1
1
1
2
0
0
2
1
2
1
0
1
1
1
1
2
1
0
1
1
1
1
2
1
2
1
1
1
2
1
2
2
1
1
3
1
2
0
1
0
0
2
1
1
2
3
1
1
2
2
1
1
1
0
1
2
3
1
1
1
0
1
1
0
1
0
2
2
1
0
0
2
1
1
2
1
1
1
0
0
3
2
1
1
0
1
2
0
0
2
1
1
2
2
2
1
2
0
1
1
1
2
1
2
2
2
1
1
1
1
2
2
1
2
1
2
1
1
1
1
2
1
1
2
1
1
1
1
2
1
1
1
1
1
2
0
1
1
2
1
2
2
1
1
2
2
1
1
2
1
1
1
1
1
0
1
0
1
1
2
2
2
1
1
1
1
2
1
1
2
2
1
1
2
1
2
1
2
3
5
0
0
2
1
1
1
0
1
0
1
1
1
1
2
1
1
1
2
1
2
1
1
0
1
1
1
1
1
0
1
1
1
0
1
1
1
1
0
1
1
1
2
1
1
1
2
1
2
1
0
1
0
2
2
2
2
1
1
2
1
1
2
2
3
0
1
1
1
1
2
1
1
2
1
1
1
2
1
1
1
1
1
0
0
1
1
2
0
1
1
1
1
2
1
1
2
1
2
4
1
1
2
1
2
2
0
1
2
1
1
1
1
1
1
2
2
1
1
1
1
0
1
2
2
1
2
1
0
2
1
1
1
1
1
0
2
2
1
1
2
1
2
2
1
0
2
1
1
2
1
2
1
1
1
1
2
1
1
2
1
1
1
2
2
1
1
0
2
0
0
1
0
0
1
1
1
1
1
2
1
1
0
0
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
0
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
1
1
0
1
2
0
1
1
0
1
1
2
2
1
1
2
2
1
1
0
4
0
0
1
1
1
1
1
1
1
1
1
2
0
1
2
2
1
1
2
2
1
0
1
1
0
1
2
1
1
1
1
1
1
2
1
1
1
0
1
2
2
2
1
1
1
1
0
0
0
1
1
1
1
1
0
1
2
1
2
1
1
1
2
1
2
1
1
1
2
1
0
1
1
1
2
1
2
2
0
1
1
1
1
1
0
2
1
1
1
1
1
1
1
1
1
2
0
1
1
1
1
0
1
1
1
1
1
1
1
2
1
1
1
0
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
0
1
1
1
1
1
1
1
4
0
2
3
0
1
1
2
1
2
1
1
2
1
3
1
0
2
2
1
1
0
1
1
1
4
1
2
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
2
2
0
1
2
1
1
1
0
1
2
0
1
1
3
1
2
2
2
1
2
2
1
0
1
2
2
2
2
1
1
1
1
0
3
2
2
1
1
1
2
1
1
1
2
1
1
2
0
1
1
1
2
2
1
1
1
1
2
1
1
2
2
0
1
1
2
1
1
1
1
2
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
2
0
2
2
2
1
0
1
1
2
1
1
2
1
1
1
1
1
1
2
2
1
1
2
1
1
0
1
2
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
2
1
2
0
1
0
3
0
1
2
1
1
2
1
1
2
0
2
1
1
1
0
2
1
0
1
0
1
0
1
2
1
1
2
1
2
1
1
2
1
1
1
1
2
1
1
1
2
2
2
1
1
1
3
2
2
1
1
1
1
0
1
2
2
1
1
2
1
0
0
1
2
2
1
1
3
0
2
1
2
1
0
1
2
0
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
0
2
1
1
1
0
3
1
2
1
0
1
2
1
1
2
0
1
1
2
0
1
1
1
0
1
2
1
1
1
2
3
1
1
1
1
1
1
0
1
1
2
1
1
2
1
1
1
1
2
1
2
1
2
0
0
0
1
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
1
1
0
1
2
0
2
1
1
2
2
2
0
1
1
1
1
2
1
0
0
2
1
1
1
2
1
2
1
0
1
2
2
1
1
2
1
2
2
1
1
1
0
1
1
2
1
1
1
0
0
2
2
1
2
1
1
2
2
1
1
1
0
1
1
1
1
1
0
1
1
0
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
2
1
2
2
1
0
0
2
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
2
1
0
0
2
1
1
1
1
0
1
1
1
2
1
1
1
0
1
1
2
2
1
1
1
0
1
1
2
1
1
2
1
2
3
1
2
1
1
0
0
0
1
1
2
1
1
1
0
1
0
1
1
2
1
1
3
2
1
1
1
1
1
0
1
2
1
1
1
0
1
2
1
0
1
1
1
1
0
1
1
1
2
2
1
2
0
1
1
0
1
1
0
1
2
0
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
1
0
2
1
2
1
1
2
0
0
1
1
1
0
2
1
1
1
1
1
1
2
2
1
1
2
1
0
2
1
2
1
1
0
2
1
2
1
1
1
1
2
1
1
2
1
1
1
2
1
2
1
0
2
2
1
1
1
1
1
2
1
0
1
2
1
2
1
1
1
1
1
0
1
0
1
1
1
1
2
0
1
1
1
2
1
1
1
0
2
2
2
2
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
2
0
1
0
1
0
1
3
2
1
2
2
1
1
1
0
1
1
0
2
2
1
1
2
2
0
1
1
2
0
2
2
1
1
2
1
0
2
1
0
3
1
1
2
1
1
1
2
1
1
1
1
1
1
2
2
0
1
1
1
2
2
1
2
1
1
1
1
1
1
0
2
1
1
0
1
2
1
2
2
1
2
4
0
1
1
2
0
1
2
1
2
1
2
1
1
1
1
1
1
1
0
2
1
1
1
2
1
0
1
2
0
0
1
1
1
1
2
1
1
0
2
2
0
0
1
2
1
1
1
1
1
1
2
2
3
1
2
1
1
1
2
1
1
1
1
1
2
2
1
1
1
1
0
2
0
1
0
1
1
1
0
0
0
2
0
1
1
1
1
1
2
1
2
2
1
1
1
1
1
2
2
2
1
2
1
1
1
0
2
1
2
1
2
1
2
1
2
1
1
2
1
1
1
1
2
2
1
1
1
0
2
0
0
2
0
1
1
1
2
0
2
3
1
1
2
1
0
1
1
1
0
1
2
1
1
1
1
2
2
0
1
2
2
1
1
2
1
2
1
1
1
1
2
0
1
1
1
0
1
2
1
2
1
1
0
0
2
1
1
1
1
2
1
2
2
2
1
2
1
1
2
0
1
1
0
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
2
2
1
2
1
2
2
0
2
1
1
2
1
0
2
2
2
2
2
1
1
1
1
1
1
0
0
0
2
1
1
1
2
1
2
2
0
2
0
2
1
0
2
1
1
1
1
0
1
1
2
2
1
2
1
1
2
0
2
2
1
0
1
1
1
2
4
1
1
0
2
2
0
1
1
1
0
1
1
1
2
0
2
2
1
1
1
1
1
0
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
0
0
1
2
2
0
1
1
1
2
1
1
1
1
2
2
1
1
1
2
2
0
1
1
1
2
1
1
0
0
1
1
1
1
2
0
1
1
2
2
0
1
1
1
0
2
1
2
1
2
1
0
1
2
1
1
2
2
1
1
0
1
2
1
1
1
2
1
0
2
0
1
1
2
1
1
1
2
1
1
2
1
1
2
0
1
1
2
1
1
1
1
1
1
1
2
2
0
1
1
2
5
1
0
0
1
2
0
0
2
2
1
1
1
1
1
1
1
1
1
2
2
2
2
2
2
1
1
0
1
0
1
1
1
1
1
1
1
1
0
1
1
1
1
1
2
1
2
2
1
0
0
1
2
1
2
1
2
2
1
1
0
1
2
1
0
1
0
1
1
1
1
1
2
2
2
1
1
1
1
1
0
1
1
0
2
2
1
2
2
1
1
1
2
2
2
1
1
1
1
2
1
1
2
1
0
1
2
1
2
1
2
2
2
1
1
1
1
1
3
2
0
1
1
1
1
1
2
2
0
1
1
2
3
2
1
1
1
0
1
1
0
1
2
1
1
2
1
2
1
2
1
2
1
1
2
1
2
1
1
1
1
1
0
1
2
0
0
1
1
1
1
1
1
1
1
2
1
1
2
2
2
1
0
2
1
0
1
1
1
1
2
1
1
1
1
0
2
2
1
1
1
2
0
1
2
1
1
1
3
1
1
1
1
2
1
2
1
0
1
1
1
0
1
1
1
1
2
1
1
1
1
1
1
2
1
1
2
2
2
0
2
1
0
1
1
2
1
1
0
0
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
0
2
1
1
2
1
2
0
0
1
2
0
0
1
1
1
1
1
0
1
1
2
1
1
1
1
1
0
1
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
2
1
0
1
1
1
1
1
1
1
0
1
1
1
1
2
1
1
1
2
1
0
2
1
0
2
2
2
2
2
2
1
2
1
2
2
1
1
1
1
3
1
0
1
2
1
1
2
1
1
1
1
1
2
1
2
1
0
1
2
2
1
1
2
1
1
1
2
1
1
0
1
1
1
2
0
2
0
0
0
1
1
1
1
1
2
1
0
1
1
1
1
1
0
4
1
1
1
0
2
1
2
1
1
1
1
1
1
2
1
1
0
1
1
2
1
0
0
2
1
1
1
1
2
1
1
2
1
1
1
1
1
1
0
1
2
2
1
1
1
1
0
2
1
1
1
1
1
2
1
0
0
2
0
2
1
1
1
1
1
0
2
0
1
1
2
1
0
2
1
1
2
3
0
1
1
1
1
1
2
2
0
1
1
1
3
1
1
1
1
0
2
0
1
1
1
1
2
1
1
1
2
1
1
0
1
1
1
1
2
0
1
1
2
0
1
1
1
2
1
1
1
0
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
0
0
2
1
1
1
1
1
1
0
1
1
0
1
0
0
1
1
0
2
1
2
2
1
0
2
1
1
1
0
1
1
2
1
1
1
1
1
2
1
1
0
1
3
1
2
2
2
1
1
2
1
1
2
1
1
1
2
1
2
2
1
2
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
2
0
2
1
2
1
1
1
1
2
0
1
0
0
2
2
0
2
1
2
2
2
1
1
1
1
0
1
0
1
1
1
2
0
2
2
2
1
1
2
1
1
1
1
2
1
1
1
1
0
0
1
0
1
2
1
1
1
1
1
0
0
0
1
1
0
0
2
1
0
1
0
2
2
2
1
1
1
1
2
1
1
1
1
1
2
1
1
2
1
2
2
1
1
0
1
0
2
1
2
1
1
1
2
2
1
1
2
1
1
1
0
1
2
1
1
1
0
2
2
1
0
0
2
1
1
1
0
1
2
1
1
1
2
1
1
0
0
2
1
2
1
1
0
1
2
1
0
1
2
0
1
1
1
1
2
0
0
1
1
0
0
1
2
1
1
0
1
2
3
0
1
1
1
2
0
2
2
1
1
0
2
2
1
2
1
2
2
2
1
1
2
0
1
1
1
1
1
2
1
0
1
0
2
0
1
1
2
0
1
0
2
1
2
2
1
1
3
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
2
2
2
1
1
1
1
1
1
2
0
1
1
2
1
0
2
0
1
1
1
1
2
1
1
1
1
1
1
1
0
0
1
1
1
2
1
1
2
2
2
2
2
1
1
1
2
1
1
1
1
2
0
1
1
2
0
0
2
2
1
1
1
2
2
1
0
2
2
1
1
1
1
1
0
1
2
1
1
0
1
3
3
2
2
0
3
1
1
2
1
0
2
0
0
1
0
1
1
1
2
1
2
0
0
2
1
1
1
0
2
2
0
1
2
2
1
1
1
1
1
1
0
2
2
1
1
2
1
1
1
1
1
1
1
2
1
1
2
2
1
2
1
1
2
1
1
0
1
2
3
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
0
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
0
1
2
2
1
2
1
1
2
1
2
0
1
1
2
2
1
1
1
1
1
0
1
1
0
2
1
1
1
2
1
1
2
1
1
2
1
2
2
2
0
1
1
2
1
1
2
1
1
1
1
0
1
0
2
1
0
1
1
0
1
1
0
1
2
0
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
2
2
1
1
1
0
1
1
1
2
1
2
1
2
1
1
0
0
0
0
1
1
1
1
2
1
1
1
1
2
2
2
0
1
1
0
2
1
1
0
1
2
1
2
0
1
1
1
2
2
1
1
1
1
2
1
2
1
1
1
1
1
1
2
1
2
1
2
0
2
1
1
1
0
2
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
0
1
0
2
1
1
1
3
2
2
2
1
1
0
1
1
1
0
2
2
1
1
1
1
1
1
1
2
1
1
2
1
1
2
0
1
1
2
1
2
2
1
2
1
0
1
0
1
0
1
1
1
2
1
0
2
1
1
0
1
0
1
1
1
1
2
1
1
1
1
1
1
1
1
0
3
1
2
0
2
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
0
2
1
2
1
1
2
2
1
1
1
1
1
1
1
2
2
0
1
1
1
1
1
0
1
1
1
1
2
0
0
0
1
1
1
1
1
2
2
2
1
1
1
0
2
1
2
0
1
2
2
1
0
1
2
2
2
0
2
1
1
1
1
0
0
0
1
1
1
0
0
2
1
1
1
1
2
1
2
1
1
1
2
1
0
0
2
2
2
0
1
2
0
1
1
2
1
1
1
1
1
2
0
1
1
2
1
1
2
1
1
0
0
0
2
1
1
1
2
1
0
0
1
1
1
1
1
2
1
1
1
2
2
2
1
0
0
1
2
1
1
1
1
0
2
1
1
1
0
1
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
1
0
2
2
1
1
1
2
2
1
1
1
2
1
1
0
1
1
1
2
1
1
1
1
1
1
1
1
1
1
0
0
0
1
1
0
0
1
2
1
1
1
1
2
1
2
2
1
0
1
2
1
1
1
1
1
1
1
1
1
2
2
1
1
1
2
0
0
1
1
1
1
1
0
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
0
1
1
1
1
1
1
1
1
2
2
2
2
2
1
1
2
1
1
2
1
1
2
2
0
2
1
2
1
1
0
1
1
1
1
1
1
0
1
1
2
2
2
1
1
1
0
1
2
1
1
1
1
0
2
1
2
2
1
1
2
2
2
1
1
1
0
1
1
1
0
1
0
1
1
2
1
1
1
0
2
1
1
2
1
2
1
1
1
1
1
2
2
2
1
1
1
1
1
0
0
1
1
2
1
1
1
1
0
1
1
1
1
2
0
1
2
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
0
2
2
2
1
1
0
1
1
2
1
1
1
1
2
1
1
1
2
1
1
1
3
1
1
1
1
0
1
2
1
1
1
2
2
1
2
1
1
2
1
2
1
1
2
2
2
1
1
1
1
2
1
1
1
2
2
1
1
1
0
0
0
1
1
2
1
2
1
2
1
1
2
1
2
1
0
1
1
1
1
1
1
1
2
2
0
1
2
1
2
2
1
0
1
1
1
0
2
1
1
0
1
1
2
1
1
2
1
2
1
2
1
0
1
1
1
1
1
1
1
1
0
1
2
1
1
2
0
2
1
1
2
0
1
2
0
1
2
1
2
1
0
1
1
2
1
1
1
1
2
1
2
2
1
1
1
2
2
2
1
1
1
2
1
0
1
1
2
2
1
1
2
1
0
0
1
1
2
2
1
2
1
1
1
2
0
1
2
1
2
2
0
2
1
1
2
2
1
1
1
0
2
1
1
1
1
2
1
1
1
1
1
1
2
1
1
2
1
1
0
1
2
1
2
1
1
1
1
1
1
1
1
2
1
0
1
1
1
1
1
0
1
2
1
1
1
0
1
1
2
1
1
1
1
1
0
2
0
1
1
2
1
1
2
0
1
1
2
1
2
1
2
0
2
1
2
1
1
2
1
1
2
1
1
2
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
1
2
2
1
1
1
0
1
1
1
1
1
1
1
2
1
2
2
1
1
1
2
1
0
1
1
2
2
0
2
1
1
1
2
1
1
1
0
1
1
1
0
1
2
1
1
1
2
2
1
2
1
2
0
1
1
1
0
2
1
1
1
1
0
1
1
0
1
0
1
2
1
2
1
2
2
1
2
1
0
1
2
1
1
1
1
1
2
1
1
0
1
1
1
2
1
1
0
0
2
1
1
1
0
1
1
2
1
2
1
1
1
1
1
0
1
1
1
0
1
1
6
1
1
1
1
1
2
1
2
0
1
3
0
2
1
1
1
1
2
1
1
2
1
1
1
0
0
1
2
1
1
2
1
0
1
1
1
1
1
1
2
2
2
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
2
1
2
2
2
1
1
1
1
0
2
1
0
1
1
2
1
1
1
2
0
1
2
2
2
1
0
1
1
2
1
2
1
1
1
2
1
1
1
1
1
2
1
2
1
1
3
1
2
1
2
1
1
2
1
0
1
1
2
1
1
1
0
0
2
1
0
2
1
2
0
2
1
1
1
2
2
0
2
1
0
2
1
2
1
0
1
1
1
1
0
0
1
2
0
1
1
1
0
2
1
1
1
2
1
2
0
1
2
1
1
2
1
1
1
1
2
1
1
1
0
1
0
1
1
2
1
2
1
1
1
2
1
1
1
0
0
2
2
1
0
1
1
0
1
2
2
1
1
0
0
1
0
1
1
1
1
1
1
2
2
1
1
0
0
1
1
1
1
1
2
0
2
2
2
2
1
1
2
1
1
2
2
0
1
1
1
1
1
1
1
0
1
2
1
2
2
1
2
2
1
2
1
1
1
2
1
0
1
1
1
0
2
1
1
1
1
1
1
1
2
2
1
1
0
2
2
0
2
2
0
1
1
0
3
2
2
1
2
1
0
1
1
2
1
1
1
1
1
1
1
2
1
2
2
1
1
0
2
1
1
2
1
1
2
2
2
1
1
1
1
0
2
0
2
2
1
1
2
1
2
1
1
1
1
1
2
2
2
2
0
2
1
1
0
1
0
2
2
1
2
2
2
1
1
2
1
1
1
1
1
1
2
1
0
1
1
2
1
1
0
2
1
1
1
2
1
1
2
2
1
0
1
1
2
1
1
2
1
1
1
1
0
1
1
1
1
1
1
1
1
2
1
0
0
1
2
1
1
1
1
1
2
1
1
2
1
1
0
0
4
2
1
1
2
0
1
1
1
1
0
1
1
1
1
2
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
0
1
1
2
1
2
1
1
1
0
2
2
2
0
0
1
1
1
1
2
1
2
2
1
1
1
2
1
1
2
1
0
2
3
0
1
1
0
1
2
1
1
1
1
2
0
1
1
1
0
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
0
1
2
0
2
1
2
1
2
2
1
1
1
2
1
1
1
1
1
2
1
0
2
1
1
2
1
0
2
2
2
2
1
1
1
1
1
1
1
2
0
1
2
2
2
1
1
0
1
2
1
1
0
1
2
2
1
1
1
0
0
1
1
2
0
2
2
1
2
0
2
2
3
2
1
1
1
1
2
2
1
1
0
0
2
1
0
1
2
2
1
0
1
2
0
1
2
1
1
0
1
1
2
1
1
1
1
2
1
1
1
2
1
2
0
2
2
1
1
1
1
2
2
1
1
1
1
2
1
2
1
2
1
1
1
1
1
2
2
1
1
0
1
1
1
2
2
0
1
2
1
1
1
2
2
2
1
1
1
2
1
2
1
2
1
1
1
1
1
1
1
0
1
2
2
2
1
2
1
2
0
2
0
2
1
2
0
0
2
0
1
2
1
0
1
2
2
1
2
2
0
2
1
1
2
1
1
1
2
1
2
2
2
1
1
2
1
2
1
0
1
0
1
0
1
1
1
0
1
1
1
1
1
2
2
0
1
0
1
1
2
0
1
2
1
1
1
0
1
1
2
1
2
0
2
0
1
0
2
2
1
1
2
1
2
1
2
1
2
1
0
1
1
1
2
1
2
1
1
2
1
1
1
1
1
2
2
1
0
1
1
0
1
2
1
1
1
1
0
1
2
0
0
1
1
0
0
1
1
1
0
2
2
1
1
2
1
1
1
1
2
1
2
0
1
1
1
1
1
0
1
1
1
1
0
1
1
3
1
2
2
1
1
1
0
0
1
1
1
1
1
1
2
1
1
2
1
1
1
1
2
1
1
1
2
1
1
2
1
1
1
1
2
2
2
0
1
2
2
1
0
1
1
1
2
1
1
2
1
1
1
2
2
2
1
2
1
1
1
2
1
2
1
1
1
1
1
0
2
0
1
1
2
2
1
2
1
1
1
1
1
0
1
1
0
1
1
1
1
0
2
1
1
1
2
1
2
0
1
2
1
1
2
1
0
0
2
1
1
1
2
1
1
1
1
1
1
2
2
2
2
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
0
1
0
2
1
2
1
2
0
1
2
1
2
3
2
1
1
1
1
2
1
2
1
1
1
2
1
1
2
1
2
1
1
1
0
0
2
2
2
1
0
1
1
2
1
1
1
2
2
1
0
2
2
0
1
1
0
2
1
1
1
1
2
1
2
1
1
1
2
2
1
1
1
0
1
1
1
2
1
0
1
2
1
0
1
2
2
0
1
0
1
1
2
0
1
1
1
0
2
0
0
1
2
3
1
1
2
1
1
0
1
1
2
1
1
1
0
2
1
2
1
1
0
1
1
2
1
1
1
2
1
1
0
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
0
2
1
1
1
2
1
2
2
2
2
0
1
1
1
1
2
1
2
0
1
1
1
1
1
1
2
2
2
2
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
2
2
1
2
1
2
1
1
0
2
2
1
1
0
2
2
1
1
0
1
1
2
0
0
1
1
1
1
1
1
1
0
1
1
1
1
2
1
1
1
1
1
1
0
3
1
1
1
0
1
1
2
2
1
2
1
2
1
2
1
2
2
2
1
2
1
0
2
1
1
1
1
2
1
1
2
1
1
2
1
2
1
2
2
1
1
0
2
1
2
1
0
1
0
2
0
1
1
2
1
2
1
2
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
2
1
0
2
2
1
0
2
1
1
2
2
0
2
2
1
1
1
1
2
1
0
1
0
2
1
1
1
1
1
2
1
1
1
1
0
0
1
0
0
1
1
2
1
1
2
0
1
1
2
1
0
2
2
2
1
0
0
2
1
1
0
0
0
1
1
1
1
1
1
2
2
1
2
2
1
2
2
1
1
1
1
1
1
2
1
1
1
2
1
2
2
1
0
1
1
1
1
0
1
2
2
2
1
0
1
0
2
1
1
1
1
1
0
1
1
1
2
2
2
3
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
1
0
1
1
1
2
1
2
1
0
1
1
1
2
1
2
1
1
2
0
1
2
1
1
1
0
1
1
1
1
2
2
2
1
1
1
0
2
1
1
1
1
0
1
0
2
1
1
1
0
2
2
1
1
0
1
2
1
0
1
2
2
1
1
2
1
1
1
0
2
1
2
0
1
2
1
1
1
1
1
2
2
1
1
2
1
1
2
0
1
0
3
1
1
1
2
1
1
1
0
1
1
1
2
1
1
0
1
1
1
2
1
1
1
2
3
1
1
0
0
3
1
0
2
1
1
1
2
2
2
1
1
0
1
2
1
0
2
1
1
1
2
2
1
0
1
0
1
2
1
2
1
1
0
1
1
0
1
1
1
1
2
1
1
1
1
1
2
0
1
1
1
1
2
0
1
1
1
2
1
0
1
0
1
2
2
1
0
1
1
1
1
1
0
2
1
1
1
1
1
2
2
1
1
0
1
1
1
1
0
2
0
1
1
1
1
1
2
1
1
0
1
1
1
2
1
1
1
1
2
2
2
0
1
1
1
1
2
1
1
1
1
1
2
0
0
1
2
1
1
2
1
1
2
1
1
2
1
1
2
2
1
2
1
0
1
1
1
0
2
2
2
1
1
3
1
2
1
1
1
1
0
1
1
0
1
2
2
2
1
2
0
1
1
2
1
2
0
1
1
1
1
1
1
2
0
1
2
2
1
1
1
1
1
1
1
1
1
2
1
1
1
0
1
1
1
1
2
2
1
1
1
1
0
0
1
2
0
1
1
2
2
1
1
1
1
2
1
2
2
2
1
1
1
1
1
1
0
2
1
2
2
1
1
0
1
1
1
1
1
2
0
2
1
2
1
1
2
0
2
2
1
1
1
2
0
1
1
1
1
1
1
1
2
2
1
1
1
2
1
1
2
0
1
2
1
1
1
1
1
1
1
1
0
1
1
0
1
1
1
1
2
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
0
1
1
1
1
1
1
2
1
2
2
2
0
0
1
1
2
1
1
1
2
1
1
1
1
2
0
1
2
1
1
2
1
1
1
0
1
0
2
1
1
1
2
1
2
2
1
0
1
2
1
2
0
2
1
1
1
1
1
2
0
2
1
2
1
1
0
0
1
1
2
1
1
0
1
1
1
1
1
1
0
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
0
0
1
1
1
2
1
1
0
2
1
0
0
1
2
2
0
2
1
1
1
1
2
1
1
0
1
1
2
2
1
1
2
1
2
2
1
1
1
1
1
2
1
2
1
1
1
1
1
0
1
0
1
1
2
2
1
2
2
1
1
0
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
2
1
3
1
1
1
1
1
2
1
0
0
1
2
1
2
1
0
1
1
1
2
1
2
2
1
2
2
2
2
1
0
0
2
1
2
0
1
1
1
2
2
2
2
2
1
1
2
1
2
2
2
2
2
1
1
2
1
2
0
1
0
1
1
3
1
2
1
2
1
1
2
2
1
1
1
0
3
2
1
2
0
1
1
1
2
1
1
1
1
0
1
1
3
4
0
2
1
2
0
2
0
0
1
1
1
1
1
2
1
2
1
0
1
1
1
1
1
2
1
1
1
0
1
1
1
1
1
1
0
1
1
2
2
1
1
1
1
1
1
1
0
1
2
1
1
1
1
1
1
1
1
3
1
2
1
0
1
1
1
1
2
1
1
1
1
1
1
2
1
2
3
1
1
1
2
1
0
1
1
1
1
2
1
2
0
1
1
2
1
1
0
2
1
2
1
2
1
2
1
2
2
2
0
2
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
0
0
1
1
2
1
1
2
2
1
0
2
2
2
2
1
1
2
2
1
1
0
1
1
1
1
1
0
1
1
2
1
2
1
1
2
2
0
2
1
1
1
1
1
1
2
1
1
1
1
1
0
2
1
1
1
1
2
1
2
2
1
1
2
2
2
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
2
1
1
0
1
1
1
1
1
1
1
1
1
1
0
1
2
1
2
2
1
1
0
1
2
3
2
1
1
2
0
1
2
0
1
0
2
1
2
2
2
1
2
1
0
1
0
0
2
1
2
2
1
1
2
1
1
1
1
0
1
1
1
2
2
1
1
1
1
0
2
1
1
1
1
1
1
1
1
0
1
1
0
1
1
2
1
1
1
2
0
1
2
1
1
1
1
1
1
1
1
0
0
0
1
2
2
0
1
2
1
0
1
3
1
2
2
1
2
2
2
2
1
1
0
1
0
2
1
1
1
1
1
1
1
1
2
2
2
2
1
1
1
2
1
2
2
1
2
0
0
1
1
2
1
0
1
0
2
2
0
2
3
1
1
1
0
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
0
1
1
2
2
2
0
1
1
0
1
1
1
1
1
1
1
1
2
1
1
1
2
1
2
0
2
2
0
1
1
1
2
0
2
2
1
1
2
2
1
1
1
1
1
2
0
2
2
1
1
0
2
0
1
1
0
2
1
1
1
1
1
1
1
1
1
2
1
2
1
0
1
0
1
1
1
1
1
0
1
1
1
1
2
0
1
1
0
1
1
1
1
0
1
2
1
1
1
2
2
2
1
0
0
1
1
0
2
1
1
1
1
1
2
1
2
1
1
2
2
0
2
1
2
1
2
1
1
0
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
0
2
1
1
1
2
2
1
1
3
1
1
1
0
1
2
2
2
0
1
1
0
0
2
1
1
1
1
2
1
2
1
1
2
2
1
1
4
1
1
1
1
1
1
1
1
0
0
2
1
0
2
1
1
2
2
1
2
0
1
1
2
2
1
2
1
2
1
1
1
1
1
2
0
1
1
1
2
0
2
1
1
2
1
2
1
1
1
1
1
1
1
1
2
2
1
1
1
1
2
0
1
2
2
2
1
2
1
1
1
1
1
1
1
0
2
1
1
2
1
0
0
1
1
1
1
1
1
2
1
0
1
0
1
0
2
1
0
1
1
1
1
0
1
1
2
1
0
2
0
1
2
1
1
2
2
3
1
0
1
1
2
0
2
1
1
1
1
2
2
2
2
1
2
2
1
3
1
0
2
1
1
1
1
2
1
1
1
1
1
2
0
0
1
2
1
3
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
0
1
1
2
1
1
1
2
1
0
2
3
1
1
1
0
2
1
1
1
0
1
1
1
1
1
2
2
2
2
0
1
2
1
0
2
1
2
2
1
1
0
1
0
2
1
1
1
2
2
1
1
1
1
1
1
2
2
2
1
0
0
2
1
1
1
2
1
1
0
0
1
2
1
1
1
1
1
2
1
1
2
0
1
1
1
1
1
0
1
1
0
1
2
1
1
1
2
2
1
1
0
1
1
1
1
1
2
2
0
1
2
0
1
0
0
1
1
2
1
1
1
1
1
1
2
2
1
1
0
1
2
3
1
1
1
2
0
1
1
2
1
1
0
2
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
0
1
1
1
1
1
1
2
0
2
2
1
0
1
1
2
1
2
0
1
1
2
2
2
1
1
1
2
2
1
2
1
1
0
1
3
1
1
2
3
1
2
1
1
1
1
0
1
1
1
2
2
2
1
1
0
1
2
1
1
1
1
1
1
2
1
0
2
1
1
1
2
2
1
2
1
1
1
0
1
0
1
2
1
1
2
1
2
2
1
1
1
1
1
1
1
1
0
2
1
1
1
1
0
1
1
1
2
2
0
1
1
1
1
2
1
2
0
1
0
1
0
1
0
1
1
2
1
1
1
1
2
1
2
2
0
1
1
0
1
2
2
1
1
2
1
2
1
1
1
2
2
0
1
1
1
0
2
2
1
2
0
0
2
1
0
0
0
1
1
1
0
1
0
2
1
1
2
1
1
1
1
2
1
1
1
0
1
1
1
2
1
1
0
1
1
3
1
1
1
1
1
2
1
1
2
2
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
1
1
1
1
4
1
1
1
2
1
2
1
1
1
2
1
2
1
1
2
1
2
1
1
2
1
0
1
1
1
2
1
1
2
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
0
1
0
2
1
1
1
2
0
1
1
1
2
1
0
1
0
0
1
1
0
2
1
2
2
1
1
1
1
1
1
0
2
1
2
2
2
1
2
2
2
2
2
1
1
1
1
1
0
1
2
1
2
2
0
1
1
2
1
1
2
0
2
1
1
1
0
1
1
2
1
0
1
1
1
1
1
1
2
2
1
1
1
1
0
1
1
1
1
2
1
1
1
2
0
1
0
1
1
2
2
2
1
1
1
2
1
1
2
2
1
1
0
1
1
1
2
0
1
1
1
2
2
0
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
2
2
1
0
1
1
1
1
1
2
1
2
1
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
0
1
1
1
1
3
1
2
1
1
2
0
1
2
2
1
2
0
1
1
0
1
1
0
2
1
2
1
1
1
0
2
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
0
0
1
2
2
0
2
0
0
2
1
1
2
1
1
2
2
1
0
2
2
1
1
1
1
1
1
2
0
0
1
1
2
1
1
1
2
1
1
1
1
1
1
1
0
2
1
2
1
1
1
1
2
2
3
2
1
1
2
1
2
1
1
2
0
1
0
1
1
2
1
1
0
1
2
2
1
2
0
1
1
1
0
0
2
2
2
1
2
2
0
1
1
0
1
2
2
1
4
2
1
1
0
1
1
1
1
2
1
1
1
2
1
1
1
2
1
2
1
1
1
1
2
0
2
1
2
2
1
1
1
2
1
2
2
1
0
2
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
2
2
0
1
1
1
2
1
1
2
2
1
1
1
2
1
0
2
2
0
1
1
2
2
1
2
2
1
1
1
0
2
1
1
1
2
1
1
1
1
1
2
1
1
2
4
1
0
1
1
1
0
2
2
1
0
2
1
0
1
1
2
1
1
1
1
0
1
2
2
1
1
1
1
1
1
2
2
2
2
1
1
1
1
3
1
0
1
1
1
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
2
1
1
1
1
2
1
2
2
2
1
2
1
1
1
1
1
1
1
1
1
0
2
1
1
2
2
0
0
1
1
1
1
2
1
1
1
2
1
2
2
1
1
2
1
2
2
1
1
2
1
1
1
0
1
1
1
2
0
1
1
1
0
1
1
2
1
2
2
2
1
1
1
1
2
0
2
1
1
2
0
1
0
2
2
0
1
1
1
1
1
0
0
1
2
1
1
1
1
1
1
1
2
0
2
1
1
1
2
2
1
1
1
0
2
1
2
0
2
1
0
2
0
0
2
1
1
2
2
1
1
1
3
2
2
1
2
1
1
1
1
0
1
1
2
2
1
1
1
1
2
0
1
1
1
2
2
2
1
1
1
2
1
1
0
0
1
2
2
2
1
1
2
2
1
2
0
1
1
2
1
1
1
1
1
1
2
1
2
1
2
2
2
1
2
1
1
1
3
1
0
0
1
2
2
2
2
0
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
2
1
1
2
1
0
1
1
1
1
1
0
1
1
1
0
2
1
1
2
1
1
0
1
1
2
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
0
1
2
3
1
1
2
2
0
1
2
1
2
1
0
2
0
2
2
1
1
1
1
1
2
1
1
2
1
1
1
0
1
1
2
1
0
1
1
1
1
1
0
1
0
1
0
1
1
1
1
1
1
0
2
1
0
1
2
1
1
1
2
1
2
1
0
2
1
1
1
0
1
1
1
2
0
2
0
2
1
2
1
1
1
0
1
0
0
2
2
2
0
1
1
2
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
2
1
2
1
1
2
1
1
0
2
1
0
1
2
1
1
2
1
2
1
1
0
2
1
2
2
1
2
1
1
1
1
2
2
1
1
1
1
1
2
0
1
2
1
0
1
1
2
1
1
1
1
1
2
2
2
2
1
1
0
1
2
1
3
1
2
0
1
0
1
0
0
1
2
1
1
0
3
1
1
0
1
2
1
0
2
2
0
1
1
1
0
1
1
1
2
1
2
0
2
1
1
1
1
1
2
2
0
2
2
1
1
1
2
1
2
1
1
1
1
1
2
2
1
1
1
2
1
0
2
1
1
1
0
1
1
2
1
1
0
1
2
1
1
2
1
2
2
1
2
1
1
1
1
1
1
2
1
2
2
1
1
1
2
1
2
2
1
1
0
0
1
1
2
2
1
2
0
1
1
2
1
0
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
0
0
2
1
0
1
1
1
1
1
1
1
2
0
2
1
1
2
1
0
1
1
1
1
2
2
0
1
1
0
2
0
1
1
1
2
2
2
2
1
1
1
1
2
1
1
2
3
1
1
0
2
1
0
1
2
2
2
2
1
1
2
0
1
1
2
1
2
1
1
1
0
1
0
0
1
0
1
0
0
1
1
1
0
0
1
1
1
1
1
1
1
1
0
0
1
2
1
2
2
1
1
1
0
0
1
1
1
1
2
1
0
0
1
1
1
1
0
1
0
1
0
2
1
2
1
1
1
1
0
1
1
0
0
2
1
1
0
2
1
1
3
1
0
2
2
2
0
1
1
1
0
2
1
1
0
0
2
0
1
0
1
2
1
1
1
0
3
1
1
1
2
1
2
1
0
1
1
2
1
0
2
2
1
1
1
1
1
0
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
2
0
0
2
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
1
2
2
1
2
2
1
1
1
2
2
1
0
2
1
1
2
2
2
1
1
1
0
2
2
1
2
1
1
1
1
1
1
1
2
0
1
1
1
1
0
1
2
0
2
1
2
1
2
1
1
1
1
1
0
1
1
2
1
2
2
0
1
0
1
1
0
1
1
2
2
1
1
2
1
1
0
0
1
0
2
0
1
2
1
1
1
1
1
1
1
1
1
1
0
0
1
1
2
2
1
2
0
2
1
1
1
2
2
1
0
1
1
1
2
1
1
2
2
2
1
1
2
1
1
1
0
1
1
1
0
0
1
1
1
1
0
1
1
1
1
2
1
1
0
1
1
2
2
1
1
1
2
0
2
1
1
1
2
2
1
0
0
1
0
0
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
0
1
0
1
2
1
0
0
1
1
2
1
1
2
1
1
1
1
2
1
1
1
1
1
2
1
2
1
1
0
1
1
2
1
1
1
0
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
0
2
1
1
2
2
0
1
1
1
1
2
1
2
1
1
1
0
2
1
0
1
1
1
1
0
0
1
1
1
1
1
1
2
1
1
1
1
1
2
1
2
1
1
1
2
2
2
1
1
1
2
1
1
1
0
1
3
2
1
2
2
1
0
1
1
1
1
1
2
0
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
0
1
0
1
1
1
1
0
1
1
1
0
1
0
1
1
1
2
1
1
1
0
1
1
1
1
1
1
0
2
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
2
2
1
2
2
2
2
1
1
1
2
2
2
0
1
2
1
0
1
0
0
1
1
1
1
1
2
0
2
1
2
5
0
1
1
1
0
0
0
1
1
0
2
1
0
2
1
0
0
1
2
1
1
0
1
1
1
1
0
1
0
1
0
0
2
0
2
1
1
2
1
1
1
1
2
1
1
1
0
2
1
2
2
0
1
0
1
1
2
1
1
1
1
1
1
0
2
1
2
1
1
1
1
2
1
1
2
2
2
1
0
1
1
2
1
1
1
2
1
1
1
2
1
0
1
2
2
1
1
2
1
2
1
0
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
0
0
2
1
0
1
0
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
1
0
1
1
2
1
1
1
1
1
0
1
2
1
1
0
2
2
1
2
1
2
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
0
1
1
1
0
0
1
1
1
1
0
1
2
2
2
1
1
2
2
0
1
1
1
0
0
0
2
1
2
1
1
1
1
1
1
1
2
1
2
0
1
1
1
2
0
0
2
2
1
2
2
0
1
1
1
1
0
1
1
1
1
1
1
1
0
1
1
2
1
1
1
1
1
1
0
1
1
2
1
1
2
2
1
1
1
1
2
2
2
1
1
1
2
1
1
0
1
1
2
1
2
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
2
0
1
1
0
1
1
2
1
2
1
1
0
0
2
0
1
3
0
0
0
2
0
1
1
1
2
0
1
2
0
1
2
2
2
1
1
1
0
2
1
0
2
0
1
1
2
1
1
1
1
1
2
1
1
1
1
1
0
1
1
1
1
1
2
2
1
1
1
2
1
1
2
1
2
1
1
0
2
1
2
1
2
1
0
1
0
1
2
1
1
2
1
1
2
0
0
0
0
1
0
2
2
0
2
3
2
1
1
2
1
2
1
1
2
1
0
2
2
0
1
1
1
2
0
1
0
2
1
0
2
0
0
0
2
2
1
2
0
1
1
1
1
2
1
1
2
0
1
1
2
2
2
2
0
1
1
1
2
2
1
0
2
1
0
1
0
1
1
2
2
2
1
2
2
1
2
1
2
1
1
1
2
1
1
2
2
1
2
2
1
2
2
1
1
0
1
1
0
2
2
1
2
1
2
3
1
2
1
0
1
1
1
1
1
1
0
1
1
1
2
1
1
1
1
2
2
1
2
2
1
2
1
0
1
2
0
2
1
0
1
2
1
0
1
2
2
1
1
0
2
1
3
1
1
1
2
1
2
1
2
1
2
2
1
2
2
1
1
2
1
1
1
1
1
1
1
2
1
1
2
2
1
1
1
2
2
1
1
1
2
0
2
1
1
1
1
0
1
2
2
1
1
1
2
2
0
1
1
2
1
1
1
1
2
2
2
1
0
2
2
1
1
1
1
0
1
1
1
1
1
1
1
0
2
2
1
1
2
2
1
1
2
2
1
1
1
2
2
2
1
1
2
0
2
2
1
2
1
0
1
1
0
1
1
1
2
1
2
2
0
1
0
1
1
2
1
1
2
1
1
1
1
0
1
0
1
1
1
1
1
0
1
0
1
2
0
0
1
1
2
0
1
1
1
1
1
0
1
1
1
2
2
2
0
2
1
1
1
1
1
2
1
2
2
1
0
0
1
1
2
1
0
0
1
2
0
1
1
1
1
1
0
2
2
2
1
2
2
1
2
0
2
2
1
0
0
0
2
1
2
1
1
1
1
2
1
1
2
1
2
2
0
1
2
1
2
2
1
1
1
1
1
2
2
2
1
1
1
2
1
1
2
1
2
1
1
1
1
2
2
1
1
1
1
2
2
1
2
1
1
1
2
1
2
1
1
1
2
2
2
1
1
1
1
1
1
2
1
1
1
1
2
0
1
1
1
1
2
1
2
1
1
2
1
2
0
1
2
0
1
1
2
0
1
2
2
2
1
1
1
1
1
1
1
2
1
1
2
2
2
1
1
1
2
1
2
1
1
1
1
0
0
1
1
2
1
1
1
2
1
2
1
1
2
1
2
1
1
1
2
1
2
1
0
2
2
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
2
1
2
1
1
1
2
0
0
1
2
1
1
1
1
0
0
1
1
2
1
0
1
1
1
1
1
1
2
2
1
1
2
2
1
0
1
0
1
2
1
2
2
1
0
1
2
1
1
1
1
1
0
2
1
1
1
2
2
1
1
2
1
1
1
2
0
1
2
1
0
0
1
1
1
1
0
1
1
0
1
1
1
1
1
1
1
1
0
1
1
1
2
2
1
1
1
2
2
1
1
1
1
1
2
1
1
1
1
1
1
1
0
0
0
1
2
0
2
1
1
1
1
8
1
0
0
2
2
2
2
1
1
2
1
1
2
0
1
2
2
1
1
0
1
2
1
1
1
1
2
1
1
1
1
1
2
2
1
0
1
1
2
1
2
2
0
1
1
2
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
1
2
1
2
1
1
1
1
1
1
0
2
1
1
1
2
0
1
1
1
1
2
1
1
1
1
1
2
1
0
0
1
0
2
2
2
2
2
2
1
1
2
2
2
2
1
3
1
1
0
1
1
1
2
2
1
1
2
1
1
0
1
2
2
2
0
1
2
1
1
1
1
2
2
1
1
1
2
2
1
1
2
0
0
2
1
2
1
1
0
1
1
1
2
2
1
1
2
1
0
0
2
0
2
1
1
1
1
1
1
2
2
2
0
1
0
1
1
0
0
1
1
1
1
1
1
1
1
0
1
1
1
2
0
1
1
1
1
0
1
2
1
2
0
1
1
1
1
1
2
1
1
2
1
0
1
2
2
1
1
1
2
1
2
0
1
0
1
2
2
1
1
1
2
2
1
2
1
1
1
2
1
1
1
1
2
1
1
1
1
0
0
2
2
1
1
2
0
1
1
2
0
1
1
0
1
2
1
1
1
1
1
2
1
1
2
1
1
1
0
2
2
2
1
2
0
2
1
1
1
1
0
2
2
0
0
0
1
1
2
1
2
0
2
0
1
0
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
2
1
2
0
2
1
1
1
1
1
0
1
1
2
0
2
1
1
1
1
2
2
2
1
2
1
1
0
1
1
1
1
2
2
1
0
1
1
1
1
1
2
1
3
2
1
1
0
1
1
1
2
1
1
1
2
2
4
2
2
2
1
1
2
0
1
2
2
1
1
1
1
0
2
2
1
1
2
2
1
2
0
1
1
2
1
1
1
2
0
2
2
1
0
1
1
1
1
0
2
1
1
1
2
1
2
1
1
0
0
1
1
0
1
1
1
1
1
0
1
2
0
0
1
2
1
1
2
0
1
1
1
2
1
1
0
2
2
1
0
2
1
0
1
2
3
0
1
0
0
1
2
1
0
0
2
1
1
1
1
1
1
2
2
1
2
1
3
1
0
1
1
1
1
0
1
2
2
1
0
2
2
2
1
0
1
0
0
0
2
2
0
1
2
1
1
1
0
2
2
1
1
2
2
1
1
1
0
0
2
1
0
0
1
1
0
2
1
1
1
2
1
1
1
1
1
0
1
1
0
2
1
1
1
1
0
2
0
3
0
2
0
1
1
1
0
2
2
1
1
1
1
1
1
1
1
1
3
0
2
1
1
0
2
1
1
1
1
1
2
2
1
2
0
0
1
2
1
1
1
1
1
2
1
1
0
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
2
0
1
1
1
1
2
1
0
2
1
2
1
2
1
0
2
1
0
1
1
1
2
1
2
1
2
2
1
1
1
1
2
2
1
1
2
0
1
1
2
2
1
1
1
2
1
1
1
2
1
1
2
1
1
1
0
1
1
1
0
0
0
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
0
1
1
0
1
1
1
1
1
2
2
1
1
1
0
0
0
2
1
1
1
1
2
2
0
0
0
2
2
1
2
1
0
1
2
2
1
1
0
0
1
1
1
1
1
0
2
1
1
2
1
1
2
1
2
1
1
0
0
1
1
1
1
1
2
1
1
2
1
1
1
1
2
1
2
1
1
1
1
2
1
1
1
2
0
1
1
1
1
1
1
1
0
0
1
1
2
2
1
1
2
1
2
1
1
2
0
1
2
2
0
1
2
1
1
1
0
2
1
1
1
1
2
1
2
1
1
1
0
1
1
1
2
1
0
1
1
1
1
2
1
1
2
2
1
1
2
2
1
1
1
1
1
1
1
0
0
1
1
2
1
2
1
2
1
0
1
1
1
2
1
2
1
1
1
1
0
1
1
1
1
0
1
0
1
2
1
1
1
2
1
1
2
1
1
1
0
1
1
2
2
0
1
2
2
1
1
1
1
2
2
1
2
2
2
1
0
1
0
1
2
2
1
2
0
0
2
1
0
1
1
1
0
1
2
1
2
0
1
1
2
2
2
2
1
1
1
0
1
1
1
3
0
1
1
1
2
2
1
1
1
2
1
1
1
2
0
1
1
1
1
1
2
1
2
1
0
1
1
2
2
1
1
1
1
1
2
0
1
3
2
1
2
1
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
2
1
2
1
1
1
0
0
0
1
0
1
3
2
3
2
1
1
1
2
1
2
0
1
2
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
2
2
1
1
1
2
2
0
2
1
1
1
2
0
1
1
0
0
1
1
0
2
1
0
1
2
1
1
1
0
2
2
1
1
1
2
0
2
1
1
1
1
2
1
1
1
2
2
1
2
1
0
1
2
1
1
1
2
0
2
2
1
2
1
1
2
0
2
2
2
2
2
1
0
1
0
1
1
1
1
0
1
1
1
1
1
2
1
2
0
2
1
1
1
0
1
2
2
1
1
1
2
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
0
0
2
3
1
1
2
1
1
1
2
1
0
2
2
1
1
1
1
1
1
1
1
0
1
1
2
2
1
1
2
1
1
1
1
0
0
1
2
1
2
1
1
0
1
1
2
2
0
2
2
2
1
1
1
2
1
1
1
0
1
1
1
2
1
1
1
2
1
2
1
2
1
1
2
1
2
1
2
2
1
1
1
1
1
2
1
1
1
2
2
0
1
1
1
1
1
2
2
0
2
1
1
1
1
1
1
2
1
1
2
2
2
2
0
1
2
1
1
1
2
0
1
1
0
0
1
2
3
1
0
2
0
1
2
2
2
1
1
2
1
1
0
1
1
1
2
1
1
1
3
0
2
1
1
0
2
1
2
2
1
3
1
1
0
1
2
0
1
1
0
1
1
1
0
1
1
0
1
1
2
0
0
2
1
1
1
1
1
2
1
2
1
0
2
1
2
1
1
1
2
1
1
1
2
2
1
1
1
2
0
1
1
0
3
1
2
1
1
2
1
0
1
1
1
1
1
2
0
1
2
1
2
1
1
2
1
1
2
2
1
1
2
2
0
2
0
0
1
1
1
1
3
2
1
1
1
1
2
1
2
1
1
3
2
2
1
1
1
1
2
1
2
1
1
1
0
2
1
0
1
0
1
1
2
0
1
2
1
1
2
1
2
1
0
1
1
1
2
3
1
1
2
1
2
0
2
1
1
1
1
1
0
2
1
2
2
2
1
1
2
1
1
1
1
1
2
1
1
0
0
0
1
1
2
1
1
2
1
1
1
0
2
2
1
2
1
1
0
1
0
1
2
2
2
0
1
1
2
2
1
2
1
2
1
1
2
1
1
1
0
1
1
1
2
0
2
1
1
1
1
2
1
1
1
2
1
1
0
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
0
0
1
1
1
1
2
1
2
0
0
1
2
1
1
1
1
1
1
1
2
1
1
1
1
0
0
1
1
2
1
2
1
1
1
2
1
1
0
1
2
1
1
1
1
1
1
0
2
1
1
1
2
1
1
2
0
1
1
1
1
0
0
2
1
1
0
2
1
1
1
1
1
1
1
0
2
1
2
0
0
1
3
2
1
2
0
1
2
1
1
1
1
2
1
1
1
2
1
2
1
2
2
1
1
1
1
1
1
1
1
0
1
1
2
1
2
1
1
1
2
0
2
1
1
1
1
1
1
2
1
0
1
1
2
1
0
0
2
1
1
1
2
0
1
1
1
1
1
1
0
1
2
1
1
1
1
1
2
1
0
2
0
2
1
2
1
1
2
2
1
0
1
2
1
0
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
2
2
1
1
2
0
1
1
1
1
1
2
1
1
0
1
1
1
1
1
1
1
1
1
0
1
1
1
1
2
1
1
0
2
2
1
1
2
2
1
0
1
2
1
2
2
1
1
0
1
1
1
1
1
2
2
1
1
0
0
1
1
2
2
1
1
1
1
1
1
1
1
1
1
0
0
2
1
2
1
1
1
1
1
2
1
0
1
0
1
1
1
1
2
1
2
1
2
1
0
0
0
2
1
1
1
2
1
0
0
1
2
0
1
1
1
1
1
1
1
1
2
1
0
2
1
1
1
0
1
1
1
1
2
1
0
0
1
1
1
2
1
1
1
0
1
1
1
2
2
0
1
0
1
1
1
1
1
2
0
2
2
2
2
1
1
1
2
1
1
1
1
2
0
2
1
1
1
1
0
1
1
1
1
1
1
1
0
1
2
1
2
1
1
1
0
1
1
2
2
1
0
2
1
1
1
1
1
1
2
0
1
2
1
1
0
1
1
1
1
1
1
0
2
1
1
1
1
1
1
1
0
0
1
0
1
1
1
1
1
1
1
1
1
1
2
2
1
0
2
1
2
1
1
1
1
2
0
1
2
2
2
1
1
1
1
2
0
1
1
1
0
1
1
1
1
0
1
1
1
1
2
2
0
1
1
1
0
2
1
1
1
2
2
1
0
0
2
1
1
2
2
1
1
1
2
1
2
3
2
2
1
1
2
2
1
0
2
1
1
1
2
1
2
1
2
1
0
1
0
1
1
1
1
0
2
2
1
2
1
1
1
1
1
2
1
1
1
2
1
0
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
2
2
2
1
1
1
2
1
1
2
1
2
2
1
1
1
2
1
2
1
1
1
2
1
0
1
1
2
1
1
2
2
0
1
1
0
0
0
1
1
0
0
1
1
2
2
1
2
1
2
0
2
1
1
0
1
2
1
0
2
1
0
2
1
1
1
1
2
1
1
1
2
1
2
2
1
1
2
2
3
0
0
1
1
2
1
1
1
1
0
0
1
1
1
1
1
1
2
1
1
2
3
2
1
1
1
2
1
1
2
1
1
1
1
2
1
1
1
1
0
1
2
1
1
1
2
2
1
2
1
2
0
2
1
1
2
1
1
2
0
2
1
1
1
0
1
2
1
1
0
2
1
1
1
2
2
2
1
1
4
1
2
1
1
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
4
0
1
2
1
2
1
2
1
2
1
1
2
1
2
1
2
2
1
0
0
1
2
1
1
0
1
1
1
1
2
2
1
1
1
1
2
1
1
2
1
1
2
1
2
1
1
1
1
2
2
1
1
1
0
2
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
0
1
1
1
1
2
2
1
2
0
2
2
1
1
1
1
1
0
1
1
1
1
1
1
2
1
1
2
1
2
0
2
1
1
1
2
1
2
2
1
1
1
1
1
0
2
1
1
0
0
1
1
1
2
0
2
1
2
0
1
1
0
0
0
1
1
1
1
1
0
0
1
0
1
1
1
0
3
0
0
1
1
1
1
1
1
1
1
1
2
0
1
1
1
2
1
0
2
1
1
0
1
1
0
2
1
2
1
2
2
1
1
0
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
0
2
1
1
2
0
1
2
1
0
0
0
3
1
2
1
2
1
2
1
2
0
2
1
1
0
0
1
2
1
1
2
2
2
1
1
1
1
1
1
1
0
1
1
0
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
2
1
2
1
1
1
2
1
1
2
1
1
1
1
1
1
2
2
0
1
0
0
1
0
2
0
1
2
1
1
1
2
2
1
1
1
0
1
1
1
1
2
2
2
2
1
2
2
1
0
1
2
2
1
2
1
1
1
2
1
1
0
1
1
1
0
1
2
1
0
1
1
1
2
2
1
1
2
0
1
2
2
1
1
1
2
0
1
1
2
2
2
1
1
1
1
0
2
1
1
1
1
1
0
1
1
1
1
1
2
1
2
1
1
0
0
0
2
2
1
1
2
1
1
2
1
1
2
0
2
2
1
1
2
2
1
0
1
2
2
1
0
2
0
2
1
2
1
1
1
1
1
1
2
1
0
1
1
1
0
1
2
1
1
0
1
2
4
0
0
2
1
0
2
1
1
1
0
1
2
0
0
1
2
1
1
1
1
1
1
1
0
1
2
2
1
1
1
2
1
2
1
3
1
2
1
1
2
1
1
1
1
1
1
2
0
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
0
2
2
2
1
1
1
2
0
1
1
1
1
1
0
1
1
1
0
1
1
0
1
1
1
2
1
1
2
2
0
0
1
2
0
1
1
1
1
1
1
2
1
1
1
0
1
1
0
2
1
2
1
2
0
2
1
0
1
2
1
1
2
2
1
2
2
0
1
1
0
1
1
1
0
1
1
1
0
1
0
0
1
1
1
1
1
0
0
1
1
1
2
2
2
0
2
1
2
3
1
2
1
1
1
2
1
1
2
1
1
1
2
1
2
1
1
2
1
0
1
0
2
3
1
2
1
1
1
2
1
2
1
1
1
1
1
1
2
1
0
1
0
1
1
0
0
0
1
1
2
1
1
1
1
1
1
0
1
0
1
3
1
1
1
1
2
0
0
1
1
0
1
2
2
1
1
1
1
1
2
1
2
1
1
1
1
1
2
2
1
1
1
1
0
1
2
1
2
1
1
2
1
2
1
0
1
1
2
0
0
2
1
1
1
0
1
1
2
0
1
1
1
1
1
1
1
2
1
1
2
1
1
1
0
1
1
2
1
1
1
2
1
0
1
2
3
1
0
1
0
1
2
2
1
0
1
2
1
2
1
2
1
1
0
2
1
1
2
0
2
2
1
1
1
1
2
1
2
2
1
2
2
1
2
0
1
1
1
1
2
1
1
1
1
2
0
1
1
0
1
2
1
2
1
0
0
1
2
1
2
1
2
1
2
1
1
2
1
0
1
0
0
1
1
1
0
3
1
1
2
1
1
1
1
1
2
1
1
1
0
0
1
0
1
1
2
1
2
2
0
0
2
0
1
1
2
2
1
1
1
1
2
2
0
0
1
1
1
1
0
3
1
1
1
1
0
2
1
1
1
2
1
1
2
2
0
1
1
1
1
1
1
1
1
0
1
1
1
2
2
1
2
2
2
2
2
2
1
1
1
2
1
1
1
2
0
1
0
1
1
1
1
3
1
1
1
1
1
1
1
0
1
1
2
2
1
1
1
2
1
2
2
1
2
2
1
1
1
1
0
2
0
1
0
1
1
1
2
1
1
1
2
2
2
0
2
2
1
0
1
0
3
2
1
2
1
0
2
1
1
1
1
1
2
2
2
2
1
1
1
1
1
0
0
0
2
1
1
1
1
0
1
2
0
2
2
0
1
0
1
1
1
0
2
1
2
1
1
2
1
1
2
1
1
1
0
1
2
0
1
2
2
1
2
2
2
0
2
0
1
1
0
1
1
1
2
1
2
2
1
1
1
1
1
2
1
2
1
1
2
2
1
1
1
1
2
2
1
2
1
1
0
2
1
2
1
1
1
0
1
1
1
1
1
2
1
2
2
1
1
1
1
2
2
1
0
1
2
1
1
1
1
1
2
2
2
1
2
1
1
2
0
1
1
0
2
0
1
1
3
1
1
1
1
2
0
1
2
0
1
1
1
2
1
0
1
1
1
1
1
1
0
1
1
0
1
1
0
0
0
2
2
1
2
0
1
1
1
1
1
2
0
1
0
2
1
1
1
1
1
1
0
2
2
1
1
1
1
1
1
0
2
0
0
0
1
0
1
1
2
2
1
1
1
1
1
2
2
2
1
2
2
1
1
1
1
2
2
1
1
1
1
0
1
2
1
1
1
1
1
1
0
2
1
1
1
0
1
1
2
1
1
1
1
0
2
0
1
1
1
1
2
2
2
1
1
2
1
1
1
0
1
2
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
0
1
1
1
1
0
1
1
1
2
1
0
1
2
1
2
2
1
0
2
1
1
0
2
0
1
1
1
2
1
1
1
1
1
0
0
1
1
1
1
2
1
1
1
1
1
0
0
0
0
1
0
0
0
2
0
2
0
1
0
1
2
1
1
1
2
1
0
1
1
0
2
1
0
1
1
0
0
1
0
1
1
1
1
2
1
1
1
1
1
2
2
2
2
2
1
0
1
1
2
1
1
1
1
1
0
1
2
1
4
1
1
1
2
0
2
1
2
1
0
1
2
1
2
1
2
1
2
1
1
1
2
1
1
1
2
2
1
0
2
1
1
2
1
2
1
1
1
0
2
1
1
0
1
1
0
1
0
1
1
0
0
2
2
1
1
0
1
1
1
1
2
2
2
0
1
2
1
0
2
2
1
4
1
1
1
1
1
0
2
1
2
1
1
0
2
1
2
1
1
1
0
0
2
1
1
1
1
1
1
1
1
1
1
2
2
0
1
1
1
0
0
1
1
2
2
1
2
2
2
1
3
1
1
2
2
1
1
1
2
1
1
1
2
2
1
1
2
1
2
2
2
2
1
2
0
1
1
2
1
2
1
0
2
1
1
0
1
2
2
1
2
1
0
2
1
0
1
1
2
1
2
0
1
2
1
2
2
1
1
2
2
0
1
1
1
1
1
1
1
2
1
1
1
1
1
2
0
1
1
1
1
1
0
1
2
2
0
1
0
1
1
2
1
1
3
2
1
2
1
1
4
1
1
1
1
1
1
1
1
2
0
2
1
1
1
1
0
0
1
1
1
1
1
0
0
2
2
1
1
1
1
1
1
2
2
1
1
1
0
2
1
1
2
1
1
0
2
1
2
2
1
2
1
1
1
1
1
0
1
1
1
0
0
1
1
1
1
2
1
1
1
1
2
2
1
0
1
1
1
1
1
2
1
1
1
1
1
0
0
1
1
2
0
1
1
0
1
1
1
1
0
1
0
1
1
1
1
1
1
2
1
1
1
2
0
1
1
1
2
1
1
0
1
1
1
1
0
1
1
1
1
2
0
0
0
1
1
1
1
2
2
1
1
2
1
1
1
2
2
2
1
1
1
1
2
1
0
1
2
2
2
2
1
1
1
1
1
1
1
2
2
1
1
2
2
2
1
1
1
1
1
2
1
0
2
1
1
1
1
1
1
1
1
1
2
2
1
1
2
2
1
1
1
2
1
1
1
1
1
2
1
2
0
1
1
1
0
1
1
1
0
2
1
1
1
1
1
1
1
1
0
2
2
1
1
0
0
1
1
2
1
1
0
2
1
1
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
2
1
1
0
0
2
0
1
1
0
1
2
1
1
2
1
1
1
1
1
2
2
1
2
1
1
1
3
1
0
1
1
1
1
1
1
1
1
1
1
0
1
2
2
1
2
1
1
1
4
1
1
2
1
1
0
1
1
1
0
2
0
1
2
1
1
1
1
1
1
1
0
0
1
1
2
1
1
1
1
1
2
1
1
1
1
1
0
0
1
1
2
2
1
1
1
2
2
1
1
1
2
1
1
2
1
2
1
0
0
2
1
2
2
1
1
1
1
1
1
1
1
1
0
2
1
2
0
1
1
1
2
1
1
0
1
0
1
3
1
2
2
1
1
2
1
1
1
1
2
1
2
1
0
2
1
1
2
2
2
2
1
2
1
1
2
0
1
1
0
1
1
1
1
1
1
2
1
1
1
1
1
1
1
0
2
1
2
1
2
1
0
1
0
1
1
1
1
1
1
2
1
2
1
1
2
1
0
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
2
0
1
1
2
1
2
1
1
1
2
1
1
1
0
1
2
1
1
1
2
1
0
0
0
2
1
1
1
1
1
2
2
1
0
0
0
1
2
1
1
2
2
0
1
0
0
1
2
2
0
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
2
1
0
1
2
1
1
0
2
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
1
1
1
2
1
1
0
1
2
1
1
0
4
1
1
2
2
0
1
2
0
2
1
1
2
1
2
2
2
0
1
2
1
1
1
2
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
0
2
0
1
1
2
0
2
1
1
1
0
1
1
2
2
0
2
1
1
1
0
1
1
1
1
1
1
2
1
1
1
1
1
1
0
1
1
1
2
1
2
1
1
1
0
1
2
1
1
2
1
1
1
1
2
0
1
1
2
2
1
1
1
2
1
1
2
0
1
0
1
2
1
2
2
1
1
0
1
2
1
1
2
0
0
0
2
2
1
1
0
1
1
0
0
1
0
0
2
1
1
2
1
1
1
1
0
1
2
1
1
1
2
1
1
0
0
1
2
1
1
1
1
1
1
1
2
2
1
2
1
1
2
0
2
4
0
2
1
1
1
1
1
1
1
0
1
2
1
1
1
1
1
1
0
2
2
1
2
1
1
1
1
2
1
1
1
2
1
2
1
1
2
1
2
1
1
2
2
1
1
1
1
1
1
2
2
1
1
1
1
1
2
1
2
1
1
1
1
1
2
2
1
2
1
1
1
1
2
0
1
0
0
1
1
1
1
1
0
1
0
1
2
1
2
1
0
2
1
2
0
1
1
2
1
1
2
2
2
0
1
1
2
2
2
2
0
1
1
1
2
1
1
0
1
1
1
2
1
1
2
1
0
1
1
1
2
1
1
1
2
1
2
0
3
2
2
1
1
0
0
1
2
0
3
1
0
2
2
1
2
1
1
2
1
1
2
2
1
1
0
1
2
2
2
2
0
1
0
12
1
2
2
2
1
1
0
1
2
1
1
2
0
1
2
1
1
0
2
1
1
1
1
0
1
1
1
1
2
1
2
1
1
2
1
0
1
1
1
1
1
2
1
1
1
2
0
2
1
1
2
1
1
1
1
1
2
2
1
1
1
0
1
2
1
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
2
1
1
0
2
1
1
1
1
2
1
1
2
1
2
1
0
2
1
1
1
1
2
1
1
0
2
1
0
0
1
1
1
2
2
0
1
2
2
1
1
2
1
0
1
1
1
2
1
1
1
1
1
0
2
2
1
1
2
1
1
1
1
1
0
1
1
1
0
2
1
1
1
1
1
2
1
2
1
1
2
3
0
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
0
2
1
1
2
1
1
2
2
2
1
2
2
2
1
1
1
1
1
2
0
1
1
1
1
2
1
1
1
1
1
2
0
1
1
2
0
1
1
1
0
1
0
2
0
1
1
1
1
1
1
1
0
1
1
0
2
1
1
2
0
1
2
1
1
0
1
1
2
0
0
2
0
1
2
2
2
1
1
1
1
1
1
1
2
1
2
1
1
1
0
2
2
0
1
1
0
1
1
0
1
0
2
1
2
1
0
1
1
1
1
1
1
0
0
1
1
1
1
1
0
1
1
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
0
1
2
1
0
1
2
2
2
2
1
2
1
2
1
1
1
2
1
1
1
1
1
0
1
0
0
2
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
2
2
1
0
1
1
2
1
1
2
1
0
1
1
1
1
0
2
1
1
2
1
1
2
0
2
0
2
1
2
1
1
0
1
1
1
2
1
1
0
2
1
2
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
0
1
2
1
1
2
1
2
1
1
1
2
1
1
0
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
0
1
1
1
1
1
0
2
1
1
2
2
1
0
1
1
0
0
1
2
0
1
2
0
1
2
1
1
1
1
2
0
1
2
1
1
0
1
1
1
1
2
1
0
1
2
1
0
1
0
1
1
1
1
0
1
1
2
2
2
1
2
1
1
2
2
0
2
2
1
1
0
1
1
1
1
1
1
1
1
0
2
1
1
1
2
1
1
1
2
0
1
0
1
2
2
0
2
1
2
2
2
2
1
1
1
1
1
1
2
1
1
2
0
1
2
0
1
0
0
2
1
1
2
0
0
1
0
2
1
1
1
1
1
3
1
1
1
1
2
1
1
1
2
1
1
1
2
2
2
2
1
1
1
1
1
1
1
0
1
1
1
2
1
1
1
1
2
0
2
1
2
1
1
0
1
1
1
0
2
0
1
2
0
1
2
0
1
0
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
2
1
2
1
1
1
1
0
1
0
1
1
2
1
1
2
2
1
2
1
0
1
1
1
1
0
1
2
2
3
2
0
1
1
1
1
1
1
2
3
0
2
1
2
2
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
1
2
1
2
0
2
2
1
1
1
0
1
0
1
2
1
1
2
1
1
1
2
1
2
0
2
0
1
3
1
2
1
2
0
1
2
1
0
1
1
1
2
1
2
0
0
1
2
1
1
1
1
1
0
1
1
2
1
2
0
1
1
1
0
2
1
1
0
1
0
1
1
1
2
2
1
1
2
2
1
2
1
1
1
0
1
0
2
0
1
2
0
1
1
2
2
1
1
1
1
1
1
0
1
2
2
1
2
1
1
1
0
4
2
1
1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
1
4
1
1
2
1
2
2
1
2
2
2
0
1
1
0
2
2
0
1
1
1
0
2
0
1
1
1
0
1
1
0
1
0
2
1
1
1
1
1
1
2
1
2
2
1
2
2
2
1
0
2
1
1
1
1
1
1
0
1
1
1
2
1
1
0
1
1
1
1
1
1
1
9
1
1
1
2
2
1
1
1
0
0
1
1
2
1
1
0
1
0
1
0
1
1
2
2
1
0
0
1
1
0
0
1
1
2
2
1
1
1
2
2
1
0
0
4
1
1
1
2
1
1
2
1
1
1
1
1
2
1
0
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
0
0
2
1
2
2
1
2
2
2
1
2
2
0
0
2
1
1
1
2
1
1
1
1
1
1
0
1
0
2
0
1
1
0
1
1
2
1
0
0
1
1
1
1
1
1
1
0
2
2
2
2
1
1
1
1
1
2
0
2
1
1
1
1
0
0
1
1
1
1
1
2
0
1
1
2
0
0
1
2
2
1
1
2
1
1
1
3
2
0
0
1
2
1
1
0
2
0
1
1
1
2
1
1
1
1
2
0
2
1
1
2
1
0
1
1
1
0
1
0
0
1
1
1
1
0
1
2
1
0
1
1
1
1
1
1
2
1
1
0
1
1
1
1
1
2
1
0
0
0
1
2
1
2
2
2
1
1
0
1
1
1
0
0
2
1
2
2
1
2
1
1
0
1
2
2
1
1
2
2
1
1
1
1
1
0
1
0
0
2
2
0
1
1
1
1
2
1
1
2
1
2
1
1
1
2
1
1
1
2
1
1
2
1
2
2
0
1
1
2
1
2
1
2
1
2
1
1
1
1
1
2
2
2
2
2
1
1
1
1
2
1
1
2
0
1
2
2
1
1
2
1
2
1
2
1
1
1
1
0
2
1
1
1
2
3
1
2
1
0
1
1
0
1
2
1
1
2
1
2
2
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
0
1
0
2
1
1
0
2
1
1
1
1
1
2
1
1
1
1
0
1
0
1
2
2
1
1
1
2
1
1
0
1
0
0
2
1
1
1
1
1
2
1
0
2
0
2
1
1
1
0
2
2
2
1
2
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
1
1
2
1
2
1
2
0
1
1
1
1
1
1
2
1
1
1
2
1
1
1
2
0
1
0
2
1
1
1
1
1
1
1
2
1
2
0
0
1
2
1
1
6
1
0
2
1
1
1
2
0
1
1
1
2
2
2
2
1
1
1
0
2
1
2
1
1
1
1
1
0
2
2
1
1
2
0
2
1
0
2
2
1
1
1
0
1
2
1
2
2
1
1
1
2
2
2
0
2
1
1
0
1
1
1
1
1
3
2
2
1
2
1
1
2
1
0
1
0
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
0
0
1
1
1
2
1
1
1
2
2
1
0
1
1
0
2
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
0
0
2
2
2
0
0
2
1
1
1
0
2
0
1
0
2
2
1
0
0
1
1
2
2
1
1
2
1
0
2
1
1
1
1
1
2
1
1
1
2
1
1
2
1
1
2
0
1
2
1
1
2
1
0
1
1
0
2
0
1
1
1
2
1
1
1
0
2
2
1
1
0
2
1
1
1
1
2
1
1
1
1
1
1
1
0
1
1
2
0
2
1
0
0
2
2
1
2
1
1
0
1
2
1
0
1
1
1
1
0
1
2
1
1
0
1
1
1
1
2
2
3
1
1
1
1
2
0
1
1
2
2
2
1
1
1
2
1
1
2
2
1
2
2
2
2
2
1
1
1
1
2
2
1
1
1
1
0
2
2
1
1
1
2
2
0
1
1
1
1
0
1
1
2
1
2
2
1
2
1
1
1
1
1
0
2
1
2
1
1
0
2
0
1
0
2
1
1
2
2
1
2
1
2
2
2
2
1
2
1
1
2
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
0
1
1
1
1
1
1
1
0
1
2
1
1
2
1
1
0
1
1
1
2
3
1
1
1
1
2
0
1
1
1
1
1
1
2
1
1
1
1
1
2
0
1
1
1
1
0
1
1
1
0
1
2
1
1
2
1
2
1
2
2
0
2
1
2
1
1
2
2
1
1
1
1
1
1
2
1
0
0
1
1
0
1
1
0
1
0
2
1
1
2
2
1
2
2
1
2
1
1
1
2
1
1
1
1
1
1
2
1
2
2
1
2
1
2
1
1
1
0
1
1
1
2
1
1
2
1
1
1
2
1
0
1
1
1
1
1
2
1
1
1
1
0
1
2
2
0
1
0
1
1
1
0
1
0
0
1
1
1
1
1
1
2
1
0
1
1
1
1
2
2
2
1
1
1
1
1
1
1
0
1
2
0
1
2
1
0
1
1
1
0
1
1
2
3
1
2
0
1
1
1
0
1
1
1
1
1
1
2
2
1
2
0
1
1
1
2
0
0
1
1
1
1
0
1
1
1
1
1
1
1
0
1
2
0
1
2
0
1
1
1
1
1
1
1
1
2
1
2
1
1
2
1
1
2
0
1
2
1
2
1
1
1
2
1
1
0
0
2
2
0
1
0
1
2
2
1
0
0
1
1
2
2
1
1
2
1
0
2
2
2
1
0
2
1
1
1
0
2
2
1
1
2
0
0
2
1
1
1
0
0
0
1
0
0
2
1
1
2
1
1
0
1
1
1
0
0
0
0
1
0
1
2
1
1
1
2
1
2
0
1
2
0
1
1
2
1
2
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
2
0
1
2
1
1
1
0
2
2
2
1
1
2
1
1
1
1
0
1
1
2
2
2
1
2
1
1
1
1
1
1
1
1
2
1
2
0
1
0
0
1
1
1
2
0
1
2
1
1
1
2
1
1
2
1
1
2
2
1
2
1
0
1
1
1
2
2
1
1
1
1
0
2
0
1
1
1
1
0
1
1
2
2
1
1
0
2
1
1
1
1
1
1
1
1
2
2
1
1
1
1
0
2
1
1
2
2
2
2
2
1
1
3
1
0
1
2
1
2
1
0
2
2
0
1
1
1
1
2
1
1
1
2
1
2
1
0
1
1
0
2
1
0
1
2
0
0
2
1
1
1
1
1
1
2
2
1
1
2
2
1
0
0
2
1
1
1
2
2
1
1
0
2
1
2
0
2
1
1
0
2
1
1
2
2
2
1
1
1
0
1
1
0
2
1
2
1
2
2
1
0
0
1
0
0
2
1
2
1
1
2
0
1
1
1
1
1
1
1
1
1
1
3
1
1
1
1
2
1
1
1
0
2
2
1
2
1
1
2
1
2
1
2
1
1
0
1
2
2
2
2
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
0
1
2
2
1
1
2
2
1
2
2
2
2
2
1
2
1
1
2
1
2
1
2
1
1
2
1
1
1
2
1
1
1
0
1
1
1
1
1
1
1
2
1
2
2
1
1
0
1
1
1
1
1
0
1
1
2
1
1
2
1
1
1
1
2
1
1
2
1
1
1
2
1
0
2
0
1
1
0
2
0
1
0
1
1
1
0
1
1
2
0
1
1
0
2
2
1
2
2
1
1
0
2
1
0
2
1
1
2
1
1
2
0
1
2
2
1
2
1
0
2
1
0
1
2
2
1
1
1
2
0
1
1
1
1
1
0
1
1
1
2
1
1
0
0
1
1
1
1
1
2
1
1
1
1
1
0
2
2
0
1
1
0
1
1
1
1
0
2
1
1
2
1
2
1
1
0
1
0
1
2
1
1
1
2
0
2
1
1
0
1
1
2
1
1
1
1
2
1
1
2
1
0
2
1
1
2
1
0
1
1
2
1
0
0
1
1
1
0
1
1
1
1
1
1
1
1
1
1
2
1
0
3
1
2
2
2
1
0
2
1
1
2
1
1
0
1
2
2
0
1
2
1
1
2
1
1
0
2
0
0
1
2
1
2
0
1
1
1
1
1
1
1
2
1
2
1
1
0
1
1
2
1
1
0
1
2
2
1
0
4
2
1
2
2
1
1
1
2
2
1
2
2
1
1
2
1
1
1
1
2
1
1
0
2
1
2
2
1
2
1
1
1
1
1
0
1
2
0
1
1
0
2
2
1
1
2
1
1
1
0
1
2
1
1
2
2
0
1
0
1
1
0
1
2
2
2
1
2
2
0
0
1
1
0
1
2
2
1
2
1
2
1
1
1
1
2
2
2
2
2
1
0
1
0
1
1
2
2
1
1
0
1
2
1
1
2
1
2
2
2
2
2
0
1
1
1
1
1
0
1
1
1
1
2
1
1
1
1
1
1
0
0
0
2
2
1
1
1
2
1
0
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
2
1
1
2
1
1
1
2
2
0
1
1
1
2
2
1
2
0
2
1
1
1
1
1
2
1
1
0
1
1
2
1
1
0
1
1
1
1
2
0
1
1
1
1
1
0
1
1
1
1
1
2
1
1
2
1
4
2
1
2
2
1
1
1
1
0
2
1
0
2
2
0
0
1
1
1
2
1
2
1
1
1
1
1
1
1
1
2
0
1
1
1
1
0
1
1
0
0
1
1
2
1
1
1
1
1
0
2
1
1
2
0
1
1
0
1
1
0
1
1
0
1
2
1
2
2
2
2
1
1
1
0
1
0
1
2
2
2
2
0
2
2
2
1
2
1
1
0
1
1
1
1
2
1
2
1
1
0
1
1
0
1
1
1
2
1
0
1
0
2
2
2
1
1
1
1
1
2
1
1
1
1
1
1
1
0
1
1
1
0
2
1
1
2
1
2
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
0
2
1
0
1
2
2
2
1
1
2
0
1
2
0
1
1
1
1
0
2
2
1
0
2
2
1
2
1
2
1
1
1
2
1
1
1
1
1
2
1
1
0
1
2
2
2
2
2
2
1
2
1
0
0
1
0
2
1
2
1
1
0
1
2
1
1
1
1
0
1
2
1
3
1
1
1
1
1
1
2
0
2
1
2
1
2
2
1
1
1
2
1
1
1
1
0
3
0
1
0
1
1
1
1
1
1
2
1
2
1
1
0
1
1
1
2
1
1
2
1
2
1
1
2
1
1
2
1
2
1
1
1
1
0
2
1
2
1
1
2
2
1
2
2
1
1
1
1
2
1
1
1
0
1
1
1
1
1
1
1
1
1
2
1
0
1
2
2
3
1
1
0
1
1
2
2
2
1
1
0
0
2
1
0
2
0
1
0
2
1
1
1
0
2
1
1
1
1
1
1
1
1
1
1
1
2
0
1
1
1
1
1
2
1
2
1
2
2
2
2
1
2
2
1
0
1
1
1
1
1
0
0
1
1
2
1
0
1
0
1
2
1
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
0
0
0
1
1
1
1
0
2
1
0
2
1
0
0
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
0
1
2
1
1
1
2
2
1
2
1
1
1
1
1
1
1
2
1
1
0
1
1
1
1
0
1
1
0
1
1
2
2
1
1
2
1
2
1
2
1
1
2
1
1
0
2
1
2
1
1
0
0
2
1
1
2
0
2
0
1
1
0
0
1
1
0
4
1
1
0
1
1
1
0
0
1
0
1
2
1
1
0
2
1
1
1
1
2
1
1
2
2
0
1
0
1
1
1
1
1
1
0
1
1
1
1
1
0
1
1
1
2
2
1
1
0
1
2
0
1
1
1
1
0
0
1
1
1
2
2
1
2
0
1
1
1
0
1
2
1
1
1
1
2
1
1
1
0
1
1
2
1
1
2
1
1
2
1
2
2
1
2
1
1
1
1
1
1
2
1
2
2
2
1
1
2
1
2
1
0
0
0
1
1
2
0
1
1
1
2
2
1
1
1
2
1
1
0
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
0
0
1
2
1
1
0
1
2
0
2
1
1
1
1
0
2
1
1
1
1
2
0
1
0
1
2
1
2
0
1
1
1
1
1
1
1
1
1
2
0
2
1
1
1
1
0
1
1
1
2
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
2
2
2
1
2
1
1
1
1
0
1
2
0
2
1
2
1
1
1
1
1
1
0
1
2
1
1
1
1
2
0
1
1
1
0
1
1
1
1
1
2
1
1
1
1
2
2
1
1
1
2
1
0
2
0
1
2
2
2
1
0
1
2
2
1
0
2
1
1
1
2
1
1
2
1
1
1
2
1
2
1
1
1
1
0
1
1
2
1
1
1
1
1
1
2
3
1
1
0
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
0
1
1
1
1
2
1
2
1
2
2
1
1
1
2
3
1
2
0
1
1
1
2
1
2
1
1
1
1
1
2
1
0
0
1
1
1
1
2
1
1
0
2
1
2
0
2
1
1
1
1
0
1
1
1
1
1
3
1
1
1
2
1
2
0
1
1
1
2
1
0
1
0
1
2
2
2
1
1
1
1
2
1
2
1
1
1
1
1
1
3
1
2
1
0
2
1
1
1
1
1
2
1
1
2
2
1
2
2
1
1
1
1
2
1
1
1
1
1
1
2
2
1
2
1
1
1
2
2
2
1
1
1
2
1
1
1
0
2
1
2
2
1
1
1
1
1
2
2
0
1
0
1
1
1
1
1
0
1
2
1
1
1
1
1
2
1
1
2
1
2
2
1
1
2
0
1
1
1
1
0
1
1
1
1
1
0
1
0
1
2
0
1
0
2
1
1
1
1
1
0
1
0
1
1
2
1
1
2
1
1
1
0
1
2
0
1
1
2
2
1
2
1
1
2
2
1
1
1
1
1
2
2
0
1
2
1
1
1
1
0
0
1
1
2
1
0
2
3
1
2
1
1
1
0
2
0
0
1
2
0
0
1
1
1
1
2
1
2
1
1
1
1
0
1
1
2
1
1
1
2
1
1
1
1
1
1
0
2
0
2
1
1
0
2
1
1
1
2
1
1
3
2
1
1
0
0
1
1
1
2
2
1
1
1
1
1
1
2
0
1
1
1
1
1
2
1
1
1
2
2
2
2
1
1
1
0
1
0
1
1
0
2
2
1
2
1
1
0
1
1
1
1
2
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
3
2
1
2
1
1
2
1
1
1
0
1
1
2
0
0
1
1
1
2
2
1
1
0
2
1
1
1
1
2
1
1
1
1
1
1
2
1
1
0
1
2
1
1
1
2
1
1
1
2
0
1
0
2
1
1
2
1
2
2
1
1
0
1
0
1
2
0
1
1
1
1
3
1
2
1
2
2
1
1
1
2
1
2
5
1
1
1
1
1
1
0
1
2
1
1
1
0
2
2
1
1
1
1
1
2
1
2
0
1
0
6
2
1
1
1
2
2
2
2
2
1
1
1
1
1
1
1
2
0
1
2
2
1
0
1
1
1
0
1
1
1
1
1
1
0
2
1
2
0
1
2
1
1
2
1
2
1
1
1
2
2
1
0
1
1
2
1
1
2
1
0
1
0
2
1
1
1
2
1
1
1
2
1
1
2
1
2
2
1
0
0
1
1
0
1
1
2
0
0
1
1
3
3
1
1
0
0
1
1
2
2
1
1
0
2
2
0
2
1
2
1
1
1
0
1
0
1
1
0
1
1
0
1
1
1
1
1
0
2
1
1
1
1
0
1
2
2
2
1
1
1
2
1
1
2
1
1
1
2
1
1
1
1
0
2
1
2
1
1
0
2
1
1
2
0
1
2
2
2
1
2
2
0
1
1
1
1
1
2
1
2
1
2
2
1
1
1
0
1
1
0
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
0
2
1
1
0
0
2
2
0
1
1
2
2
2
1
1
1
2
2
1
2
1
1
2
1
1
2
2
0
1
2
1
1
1
2
0
1
0
1
1
0
1
2
1
1
2
1
1
1
1
2
2
1
2
1
1
2
2
0
1
1
1
2
2
1
2
1
1
0
2
1
2
0
1
1
1
1
1
1
2
1
2
2
1
1
1
1
0
1
0
1
2
2
1
1
1
1
1
1
1
1
1
1
0
2
1
1
1
1
1
1
0
1
2
2
1
1
2
1
1
1
1
2
1
1
2
1
1
1
2
2
2
2
1
1
0
2
2
1
1
2
2
1
1
1
0
2
1
1
2
2
2
0
1
2
0
1
1
2
0
2
1
2
1
1
1
1
1
1
1
2
2
1
1
1
2
1
1
2
0
1
1
1
1
2
0
1
2
2
1
1
2
1
1
1
1
0
2
1
1
1
0
1
2
1
1
1
1
0
1
1
1
2
2
0
2
0
1
1
2
1
0
1
1
2
2
1
1
0
1
1
1
0
0
1
1
2
2
2
1
1
0
1
0
1
0
3
2
2
1
1
1
1
1
1
1
2
2
1
1
2
1
1
2
2
1
0
1
1
1
1
1
1
1
0
1
1
1
0
2
2
2
2
1
1
2
2
0
0
2
1
1
0
1
1
1
0
1
1
1
2
2
2
1
2
2
1
1
0
1
1
2
2
1
1
1
2
2
2
0
2
0
0
2
1
1
2
1
1
1
0
0
1
2
1
1
1
2
1
1
2
1
1
2
1
1
2
0
1
1
1
1
2
1
1
1
1
0
1
1
1
2
1
1
1
0
1
2
1
1
0
1
1
1
1
1
0
1
1
1
1
1
1
1
1
2
2
0
1
1
2
1
1
1
1
1
1
2
1
2
2
2
2
1
1
1
1
1
2
0
1
2
2
2
0
1
3
1
1
2
2
1
2
1
2
1
0
1
2
2
1
0
1
1
1
1
1
1
2
1
0
1
0
2
1
1
1
1
1
0
1
0
1
1
2
1
1
1
2
1
1
1
0
1
2
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
0
1
0
1
1
1
1
1
2
1
1
3
1
1
2
2
0
1
0
2
1
1
1
1
0
1
1
1
1
1
2
1
1
1
1
1
1
1
0
2
2
2
0
1
1
2
0
2
1
1
1
1
1
1
0
2
1
1
0
1
0
1
0
1
0
1
1
1
1
1
1
2
1
1
1
1
1
1
1
0
1
1
0
1
1
0
2
1
0
1
1
1
1
2
1
2
0
1
1
2
1
1
2
1
1
1
2
1
2
1
2
1
1
0
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
2
0
1
0
1
1
1
1
1
0
2
1
1
1
1
1
0
0
1
1
1
1
0
1
2
2
1
1
1
1
1
0
0
2
1
1
1
1
2
1
1
1
0
2
1
0
1
1
1
1
1
1
1
1
1
1
1
1
0
2
1
1
1
2
2
0
1
1
1
1
2
2
1
1
1
1
1
1
2
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
0
1
1
0
0
1
2
1
1
0
2
0
2
1
0
1
1
2
1
2
1
0
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
2
1
2
0
1
2
2
0
1
1
0
1
2
1
1
1
1
1
2
1
0
0
1
1
1
0
1
1
1
1
1
1
1
0
2
2
1
1
2
1
1
0
1
1
1
1
1
1
1
1
1
0
1
2
2
2
0
1
0
1
1
1
2
0
1
1
2
1
1
1
1
1
2
2
2
1
1
1
0
1
1
2
2
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
2
1
1
2
1
1
2
1
1
1
2
0
2
1
1
1
2
2
1
1
0
0
1
1
1
0
2
1
2
2
1
2
2
1
1
1
2
2
1
1
2
1
1
1
1
1
1
2
2
1
2
1
2
1
1
2
0
2
2
1
2
2
1
1
0
1
1
1
1
1
1
0
1
1
1
1
1
2
1
0
2
1
1
0
1
1
2
1
0
1
1
1
1
0
1
1
1
2
1
0
2
0
1
2
1
2
1
2
1
0
1
1
1
1
2
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
2
2
1
1
1
0
1
1
2
1
1
1
1
0
2
1
0
3
1
2
1
2
2
1
1
1
1
2
0
0
1
1
1
1
1
2
0
1
1
1
1
1
0
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
0
1
1
1
2
0
1
2
1
1
1
0
1
1
2
1
2
1
3
1
1
1
1
1
1
2
1
0
0
0
1
0
1
1
2
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
2
0
1
1
2
2
1
1
1
1
1
1
2
1
0
1
0
2
0
1
1
0
1
1
0
2
0
1
2
1
1
2
2
1
0
1
2
0
0
0
2
1
1
1
2
1
2
1
0
2
2
1
0
2
1
1
0
1
1
1
1
2
1
1
1
2
1
0
1
2
1
1
2
1
1
1
1
0
1
1
2
1
1
1
1
0
0
2
1
1
1
1
1
1
1
2
1
1
0
1
2
0
1
1
1
2
2
2
2
1
1
1
1
1
1
1
1
2
0
2
1
1
1
2
2
0
2
1
1
0
1
1
1
1
2
2
2
2
1
1
2
2
1
1
1
2
1
1
2
2
1
1
1
0
1
0
1
1
2
1
1
1
0
0
1
1
0
0
2
1
2
1
1
0
1
1
1
1
1
2
2
1
2
0
1
1
1
1
1
0
1
1
1
1
0
1
1
2
1
1
1
1
1
0
1
1
1
2
2
1
1
1
1
1
2
1
2
0
1
2
1
1
1
1
2
1
1
1
0
0
1
1
1
2
1
1
2
2
1
0
1
2
1
2
1
1
1
1
1
2
1
1
1
1
1
0
1
1
1
1
3
1
2
1
1
0
1
1
1
1
2
0
1
0
1
1
1
2
2
1
1
1
0
1
2
1
2
1
1
2
1
2
1
1
0
2
1
0
2
2
1
1
0
1
1
0
1
2
1
2
2
2
0
2
1
1
1
2
1
0
2
1
1
1
1
2
1
2
1
0
1
0
1
1
1
1
0
1
1
1
1
0
1
2
1
1
0
1
1
2
1
1
2
1
2
1
0
1
1
2
1
0
1
1
1
1
1
1
1
1
1
2
1
0
1
1
0
0
1
2
2
1
1
3
1
1
2
2
1
2
1
1
1
2
1
1
1
2
1
0
1
0
2
2
1
2
1
0
0
2
2
1
1
1
2
1
1
1
0
1
2
1
1
1
1
2
1
2
0
2
1
0
1
1
2
1
1
0
1
2
1
2
1
2
1
1
0
0
0
2
1
1
1
1
1
1
2
1
1
1
2
1
1
0
1
1
1
1
1
1
2
1
1
1
1
1
2
2
1
1
1
2
0
2
1
1
1
2
0
2
2
1
1
1
2
1
3
2
2
1
0
1
1
1
2
1
1
1
2
1
2
0
2
2
1
1
2
2
2
2
1
1
1
2
1
1
1
1
2
1
2
0
1
1
1
1
1
1
1
1
1
2
1
1
1
1
0
0
1
1
2
1
1
1
0
2
1
1
1
1
1
2
1
4
1
2
2
1
1
1
2
1
1
1
2
2
1
1
1
2
2
1
0
1
2
1
2
1
0
1
1
1
2
1
2
2
1
2
1
2
1
2
1
2
1
2
2
2
1
1
1
2
2
1
2
1
2
1
2
1
1
0
2
1
2
0
1
0
4
1
1
2
2
1
1
2
2
2
2
1
2
1
2
1
0
1
1
1
2
2
2
0
1
1
1
1
1
0
2
0
1
1
2
2
0
2
0
1
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
2
1
1
1
2
2
1
1
1
1
1
2
0
1
0
0
2
1
1
1
1
1
1
1
1
1
2
1
0
2
1
1
0
1
1
1
0
2
1
0
1
0
1
1
2
1
0
1
1
1
1
2
1
1
1
1
1
0
2
1
2
1
1
2
1
1
1
2
2
1
2
1
1
1
1
1
1
2
1
2
1
2
0
0
2
2
1
2
2
2
1
2
1
1
2
2
1
2
1
2
2
1
1
0
2
1
1
1
1
2
1
2
1
2
2
1
0
2
1
1
1
1
1
1
1
1
1
0
2
2
1
2
1
1
1
1
1
1
1
2
1
1
2
0
1
1
0
1
1
1
2
1
1
1
1
0
1
0
0
1
1
2
1
1
1
0
1
0
1
2
1
1
2
1
2
1
1
2
1
2
1
1
1
1
2
1
1
0
1
1
1
1
1
1
1
2
1
1
2
1
1
0
0
1
2
1
1
1
1
2
2
1
1
1
1
1
2
1
1
2
1
1
0
0
1
1
2
1
2
0
1
2
2
1
2
2
2
1
2
1
0
1
1
2
2
1
1
0
0
0
2
1
2
1
1
2
1
1
2
2
1
0
0
2
1
2
1
1
1
1
1
1
0
1
1
1
1
1
1
1
0
1
1
1
1
1
1
2
1
1
0
0
1
0
1
1
2
1
2
1
1
0
1
2
2
1
1
1
2
1
1
1
1
2
0
1
2
2
2
1
1
2
1
1
2
1
1
2
1
0
2
2
1
1
2
1
1
0
1
1
2
2
1
1
1
2
2
1
1
1
1
1
1
1
1
1
0
1
1
1
1
2
2
1
0
0
1
1
1
2
2
1
0
1
1
1
0
2
1
2
2
1
1
1
0
0
2
1
1
1
2
0
1
1
0
2
2
1
1
1
1
0
2
1
2
1
2
1
2
2
1
1
1
1
0
2
2
1
1
1
1
2
1
0
1
1
1
1
1
1
2
2
1
0
0
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
0
1
1
0
1
2
1
1
1
1
1
1
2
1
1
2
1
2
2
1
2
1
1
2
2
0
1
1
0
0
1
1
1
1
2
1
0
0
0
1
1
1
1
1
2
2
1
1
0
1
1
0
1
1
1
2
1
1
0
2
0
0
1
1
1
1
2
0
1
0
2
1
2
1
2
1
1
2
1
2
2
1
2
0
2
1
1
1
1
1
1
0
1
1
1
1
1
1
2
1
0
0
0
1
1
1
2
1
1
2
1
1
1
0
0
1
0
2
2
1
2
0
2
2
1
0
2
2
1
0
1
2
1
1
2
0
1
2
1
1
1
2
2
1
0
1
2
2
2
1
1
1
0
2
1
0
2
1
2
2
1
2
0
1
1
2
0
0
2
2
1
1
0
1
1
1
0
2
1
1
0
1
2
1
0
1
1
0
2
2
0
1
1
0
1
1
1
2
2
1
2
2
1
1
1
1
2
1
1
0
1
1
1
2
1
1
0
2
2
1
2
2
2
1
1
2
1
1
2
2
1
1
1
1
1
0
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
2
0
2
1
2
2
1
2
2
2
1
1
1
1
1
1
1
1
0
0
2
2
1
0
0
2
1
1
3
1
0
1
1
1
1
2
0
1
1
1
1
2
1
1
1
0
0
0
1
0
2
1
1
1
2
1
1
1
1
2
0
2
1
1
1
1
1
1
0
1
2
1
1
0
0
1
1
1
1
2
1
2
1
1
2
0
2
1
1
1
1
2
1
2
1
0
0
1
1
2
2
2
1
1
0
1
1
1
1
0
1
1
1
1
2
1
1
1
1
1
2
2
1
1
2
0
1
1
1
1
1
2
1
0
1
2
1
0
1
2
1
1
2
1
2
2
1
0
1
2
1
0
3
1
2
2
2
2
1
0
1
1
1
1
1
1
1
2
2
0
1
1
0
1
2
1
2
1
2
1
2
2
2
1
2
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
0
1
1
0
1
2
2
0
1
1
2
0
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
0
1
1
1
1
2
1
1
0
1
1
0
1
2
2
2
0
1
2
1
1
1
2
1
1
1
1
1
1
0
2
2
1
1
2
1
2
1
2
1
2
1
1
2
0
0
1
0
1
2
1
2
2
1
1
1
1
1
2
1
0
0
0
1
1
1
1
1
0
2
0
2
1
1
1
1
1
2
0
1
2
1
1
0
2
1
2
1
0
1
2
0
1
2
1
1
1
2
1
1
1
2
1
0
2
2
1
1
1
1
1
2
1
1
2
0
1
1
1
1
1
2
1
2
1
0
0
2
2
1
0
1
1
1
2
1
1
1
2
1
2
1
1
2
1
1
0
1
1
0
2
1
1
0
1
1
1
1
0
2
0
1
1
1
1
0
1
1
0
1
0
1
2
2
1
1
2
2
1
1
1
1
2
1
1
1
2
2
2
0
1
0
1
1
0
0
1
1
1
1
1
1
0
1
0
1
1
0
1
1
2
1
1
1
1
1
2
0
2
0
0
2
1
1
1
1
2
1
1
1
0
1
1
2
1
1
2
0
2
1
1
2
1
1
1
2
2
4
2
1
2
1
2
1
1
1
0
1
1
2
2
5
1
2
2
0
2
1
1
2
1
2
1
1
1
1
1
5
2
1
1
1
1
1
1
2
1
2
0
1
1
1
2
1
3
1
2
1
0
1
1
1
0
0
1
1
0
1
2
1
1
1
1
1
1
2
0
2
1
1
2
2
1
1
2
1
0
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
2
2
1
1
1
2
2
1
1
1
2
1
1
0
1
1
1
2
0
1
1
1
1
1
0
1
1
1
1
1
1
2
1
1
1
1
2
1
0
1
0
2
1
1
2
2
0
0
1
0
2
2
1
2
3
1
0
1
0
1
1
1
1
1
2
2
1
1
1
1
2
2
1
1
1
1
1
0
2
1
1
0
1
1
2
1
2
0
2
1
0
2
0
2
1
2
2
1
1
1
0
0
2
1
1
2
1
2
2
1
2
1
1
2
0
2
1
1
0
1
0
1
1
0
1
1
2
1
1
1
0
1
1
2
1
1
1
1
3
1
1
1
1
0
1
1
1
1
1
1
0
2
1
1
1
2
2
1
0
0
2
1
2
1
1
1
1
1
2
1
1
0
1
1
1
1
2
1
1
1
1
1
0
1
2
1
1
0
1
1
0
1
1
2
1
2
1
1
2
0
1
1
1
1
0
1
0
1
2
1
1
1
1
1
2
1
0
2
1
1
2
1
2
1
1
2
2
1
1
2
1
1
1
2
1
1
2
2
1
1
1
2
1
2
2
2
1
1
0
2
1
2
0
1
0
2
2
1
1
1
1
1
1
1
1
1
2
1
0
1
1
1
0
1
1
1
6
0
1
1
1
1
2
1
1
1
2
1
2
1
0
1
1
2
2
0
0
0
1
1
1
2
2
1
2
1
1
2
1
2
0
1
1
1
1
2
0
2
1
1
1
1
1
2
1
1
2
0
1
2
0
0
1
1
2
1
1
2
1
1
2
2
1
1
0
2
1
1
1
1
0
1
0
2
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
0
1
1
2
1
1
1
1
1
1
1
1
2
1
2
1
1
1
0
1
1
1
2
1
1
1
1
1
2
2
1
1
2
1
1
0
1
1
0
1
1
1
1
1
1
0
1
1
2
2
1
1
3
1
2
1
1
1
1
2
1
1
2
2
1
2
2
2
2
1
1
1
0
1
1
1
1
1
2
2
1
1
1
1
2
2
1
1
1
1
1
1
0
2
1
2
1
1
1
1
0
2
1
1
1
2
2
2
1
0
1
1
2
1
2
1
1
2
0
1
2
0
1
1
2
1
1
1
1
1
1
2
1
0
1
1
1
1
1
1
0
1
1
1
0
0
1
1
1
1
2
0
1
2
0
1
0
1
1
1
0
1
0
2
1
1
2
1
0
0
1
0
0
1
2
2
0
1
2
1
1
0
2
2
1
1
2
2
0
1
1
1
2
1
1
1
0
1
0
2
0
0
1
1
0
0
1
1
1
2
1
2
1
1
0
0
1
2
0
1
2
1
1
1
0
2
1
0
1
0
1
2
0
1
1
1
0
0
0
1
1
1
0
1
1
2
1
0
1
2
1
2
1
0
1
1
2
0
1
1
2
1
1
1
1
1
0
0
1
0
1
1
2
2
1
1
1
2
2
2
2
2
1
1
1
1
1
1
1
0
1
1
1
1
1
2
1
0
1
1
1
0
1
1
1
2
1
2
2
1
2
1
0
2
2
0
1
1
1
2
1
2
1
1
1
2
1
1
1
2
1
1
1
1
2
1
0
1
1
1
0
1
2
1
1
1
1
1
1
2
1
1
1
1
0
1
2
1
1
1
0
1
1
1
1
1
1
1
1
2
0
1
1
0
1
1
1
1
0
1
1
1
2
1
1
1
0
0
2
1
1
1
1
1
2
0
0
1
2
2
2
0
1
2
2
2
1
2
1
1
1
1
1
2
1
2
1
2
2
2
1
2
1
2
0
1
1
1
1
1
2
2
1
1
1
2
2
2
1
2
1
1
1
1
0
1
1
1
1
1
0
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
2
2
1
1
2
1
1
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
2
1
1
1
0
1
1
2
1
2
1
0
2
2
1
1
2
2
2
1
1
1
1
0
0
1
1
2
1
2
0
2
0
1
0
1
0
1
1
1
1
0
1
1
0
1
1
1
1
2
1
1
1
1
1
0
1
0
1
2
1
1
1
1
2
2
2
1
1
1
2
1
0
1
1
0
2
1
0
2
0
1
0
2
0
1
1
1
1
2
1
0
1
0
1
1
2
2
1
1
1
1
1
0
1
2
1
1
2
2
1
1
0
2
1
1
1
0
2
1
1
1
1
1
1
1
1
2
0
1
0
1
2
2
1
1
1
0
1
1
2
1
2
2
2
1
0
2
2
2
0
0
1
1
1
1
2
1
0
1
1
1
1
1
1
1
2
0
2
1
0
2
1
2
1
1
1
1
2
1
1
1
0
1
1
2
2
0
1
1
1
1
1
1
0
2
2
2
2
1
1
1
1
1
2
1
1
2
1
1
2
2
2
1
1
1
2
1
1
1
0
1
2
1
1
2
1
1
1
1
2
0
1
0
1
2
0
1
1
1
2
2
0
1
1
1
1
2
0
0
1
2
3
1
1
0
1
0
2
1
1
2
1
1
0
2
1
2
2
2
1
1
2
1
1
1
0
1
2
0
1
1
1
1
1
0
2
1
1
1
0
2
0
1
1
1
2
0
2
2
1
1
2
2
1
1
1
1
2
2
2
2
2
1
1
1
1
1
0
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
2
2
2
1
1
0
1
2
1
2
0
1
1
2
1
2
2
0
1
1
0
1
2
0
2
1
1
1
1
2
1
0
1
1
2
1
1
2
1
1
2
2
1
2
1
2
2
1
0
1
2
1
0
1
2
2
1
1
1
1
2
0
2
1
2
1
2
2
1
1
0
1
2
1
1
1
1
1
1
2
1
1
2
1
1
0
2
2
1
1
2
1
2
1
2
2
1
1
2
1
0
2
1
1
1
2
2
1
1
1
2
0
1
1
2
1
1
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
1
1
0
0
2
2
2
2
1
1
2
1
1
1
0
1
3
2
0
2
1
0
0
2
2
1
1
1
1
1
2
1
1
2
0
2
1
1
1
1
0
2
1
1
1
3
1
2
2
1
1
1
0
1
1
0
1
2
1
1
0
1
1
1
0
0
2
2
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
0
2
0
1
1
1
1
2
2
1
1
1
2
1
1
2
0
1
2
1
1
1
1
1
1
1
0
1
1
2
1
1
1
0
1
2
1
1
1
1
2
1
0
0
2
1
1
2
0
0
2
2
1
1
0
1
1
1
1
1
1
2
1
1
1
0
1
1
1
1
1
1
1
1
2
2
1
2
1
1
1
2
2
1
1
1
1
1
1
0
2
1
2
2
0
2
1
2
1
0
1
1
1
1
1
2
1
2
1
1
2
2
1
1
1
2
1
2
1
1
1
1
1
3
1
1
1
1
0
1
1
1
1
1
2
2
0
1
1
2
1
2
1
2
2
1
2
2
0
1
1
0
1
1
2
1
1
1
1
1
0
1
2
1
1
0
1
1
1
2
2
2
1
2
1
1
1
1
1
1
2
2
2
2
0
0
1
2
2
1
1
1
1
0
3
1
2
1
1
0
1
1
2
2
2
1
0
1
2
1
1
1
4
1
2
0
2
2
1
1
1
2
0
1
2
1
1
0
1
1
1
2
0
1
0
1
1
1
2
1
1
2
1
2
1
1
1
1
1
1
0
2
0
1
1
1
1
1
1
1
2
2
0
1
1
2
0
1
1
1
2
1
1
2
1
2
0
0
1
1
0
0
1
1
2
1
0
1
2
2
1
1
1
1
0
1
1
2
2
1
2
0
1
1
2
0
1
1
0
1
2
1
0
2
2
1
1
2
0
0
1
0
1
1
0
1
2
2
2
1
1
0
2
2
0
1
0
2
2
1
2
0
2
1
1
1
1
1
2
1
1
2
2
2
1
2
2
1
1
2
2
1
0
0
2
1
1
1
1
0
1
1
1
1
2
1
1
1
1
3
2
0
0
1
0
1
1
2
1
0
1
1
1
0
1
2
1
1
1
1
1
1
1
1
0
3
1
1
1
1
1
1
1
1
0
1
1
3
1
0
1
1
1
1
0
1
1
2
2
1
1
1
1
1
0
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
0
2
0
2
2
2
2
1
1
1
2
0
2
1
0
1
1
1
1
1
1
0
0
2
1
1
1
2
1
1
1
1
1
1
1
1
0
1
2
1
2
1
2
1
2
1
1
0
2
1
0
2
0
2
1
2
1
1
2
1
2
0
2
2
1
1
1
2
0
2
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
2
2
2
1
1
2
1
1
1
1
2
1
2
1
1
0
2
2
3
1
1
1
1
1
2
0
2
2
1
1
1
2
1
1
1
0
0
1
1
0
1
1
2
1
1
1
2
1
0
1
1
1
2
1
1
0
2
1
1
1
2
2
1
1
2
2
1
1
1
1
1
1
2
0
1
1
1
1
2
1
0
1
1
1
1
1
1
1
1
1
2
1
2
1
2
1
0
2
1
2
1
1
1
1
1
2
1
1
2
1
1
0
1
1
1
2
1
1
1
1
1
1
0
1
0
1
2
1
1
1
1
2
1
2
1
2
1
0
1
0
2
0
1
1
2
1
1
0
2
2
2
2
1
2
1
1
1
1
0
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
2
1
1
2
1
1
2
2
1
1
2
1
0
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
2
2
1
1
2
1
2
1
1
1
0
1
1
1
1
1
1
1
2
1
1
1
1
1
2
2
2
2
2
0
2
1
1
2
1
2
1
2
1
2
1
2
1
0
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
2
1
2
1
2
1
2
1
2
2
1
1
1
2
1
1
2
2
2
1
1
0
1
1
2
1
1
2
1
1
1
1
0
1
1
1
0
1
1
2
2
2
1
2
2
0
1
1
1
1
1
1
0
0
1
1
1
0
2
1
0
1
0
1
1
1
0
4
1
2
1
2
1
1
1
1
0
2
1
0
1
1
1
1
1
2
1
1
1
1
1
1
0
1
1
1
0
2
1
2
2
1
2
1
1
0
2
1
1
1
1
1
1
0
1
0
1
2
2
1
1
0
1
1
1
1
1
1
1
2
2
0
1
1
1
2
2
1
1
2
0
1
2
2
1
1
1
1
2
0
1
1
2
1
1
2
1
0
1
1
1
1
2
1
2
0
0
1
2
1
1
1
2
0
1
1
1
2
0
1
2
1
1
1
1
2
2
0
0
1
1
1
1
1
2
2
1
2
2
0
0
2
1
2
0
1
4
0
2
2
2
1
1
0
1
2
2
0
2
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
0
2
1
1
1
1
1
1
1
1
1
1
1
1
1
0
2
1
2
1
1
1
0
1
0
1
1
2
2
2
1
1
0
1
1
0
1
1
1
2
2
2
1
1
2
1
2
2
1
0
1
1
1
1
1
2
2
2
2
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
0
2
1
2
2
1
2
1
1
0
0
2
0
2
1
1
2
1
2
1
1
1
1
0
2
1
0
0
2
0
3
1
1
1
1
1
1
2
0
0
1
1
1
1
0
1
0
1
1
1
2
2
1
1
1
0
1
1
1
2
5
1
1
1
1
2
1
2
1
0
1
0
2
1
1
1
0
1
2
2
2
1
1
1
1
1
1
2
1
1
0
1
1
2
1
1
1
1
2
0
1
1
2
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
1
2
0
1
1
1
2
2
1
1
1
1
0
1
2
1
1
2
1
0
1
3
1
0
2
2
1
0
2
1
1
0
1
1
1
1
1
1
1
1
1
2
2
1
1
1
0
1
0
2
1
0
2
1
2
1
1
2
1
1
2
0
1
1
2
2
1
0
1
1
1
1
1
1
1
1
1
1
1
2
1
2
0
1
2
1
1
1
1
1
1
2
2
1
2
2
1
2
0
1
1
2
1
1
1
1
2
1
0
1
0
2
2
1
0
1
1
2
1
1
1
1
1
1
2
1
0
1
0
2
1
0
3
1
2
1
1
2
1
0
1
0
1
1
1
1
1
2
1
1
2
1
1
0
2
0
1
2
1
2
1
1
1
0
2
0
1
1
1
1
1
2
0
1
1
1
1
1
2
1
1
0
1
1
1
2
1
1
2
2
1
3
1
1
2
2
1
2
2
1
1
2
2
1
1
1
1
1
1
2
1
2
1
2
1
1
1
2
1
0
0
2
2
2
2
1
2
2
2
1
2
0
1
2
1
1
1
1
2
2
1
2
1
0
2
0
1
2
2
1
1
0
2
1
1
2
2
1
1
1
1
2
1
1
0
0
2
2
2
2
1
0
1
1
2
2
2
1
1
1
1
5
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
0
1
1
0
1
1
1
1
1
1
2
0
1
1
1
1
1
2
3
1
1
1
2
1
2
1
1
2
2
1
1
2
1
1
2
0
1
1
1
1
0
0
2
1
2
1
2
1
1
1
2
0
0
1
1
0
1
1
1
0
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
1
0
2
1
1
0
2
1
1
0
1
2
2
1
1
1
1
1
1
1
2
1
1
1
0
2
1
2
0
1
1
1
1
1
2
1
1
1
0
2
1
1
1
1
0
1
1
1
0
0
1
1
1
2
1
2
1
2
1
1
1
1
2
1
1
2
1
2
2
1
1
0
1
1
1
0
2
1
1
1
1
0
1
2
1
1
0
1
1
1
2
1
1
0
0
2
1
2
1
2
1
1
2
1
2
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
2
1
1
1
1
1
1
1
2
2
1
2
2
1
1
1
0
1
1
0
1
2
2
2
1
1
2
1
0
1
2
1
1
0
1
2
2
2
2
1
2
1
1
1
0
1
1
1
1
1
1
2
1
1
1
2
2
1
1
2
0
2
1
1
2
0
1
1
1
2
2
0
1
2
1
1
1
1
1
1
1
0
1
1
2
1
1
1
1
1
1
2
1
1
0
2
2
2
1
1
1
2
2
1
2
1
1
1
1
1
0
2
1
3
1
1
1
1
1
2
2
2
2
1
0
1
2
1
1
1
1
1
2
1
1
2
2
1
1
2
1
1
1
1
0
1
1
1
1
2
1
1
2
2
0
1
1
1
0
2
1
1
2
1
2
2
2
1
2
2
1
1
1
1
2
1
0
1
1
1
2
1
0
2
2
2
2
1
2
2
2
1
1
1
1
1
2
1
0
1
2
1
2
1
1
0
1
0
2
1
1
1
1
2
1
2
2
2
1
1
1
0
1
0
1
1
2
0
1
1
1
1
1
2
1
1
1
2
1
0
1
0
1
0
1
1
0
0
1
2
1
1
1
1
2
1
0
1
2
2
1
2
2
1
2
1
0
1
1
1
0
1
0
0
2
1
1
1
1
1
1
2
1
2
2
0
2
1
1
1
1
0
1
0
0
1
2
1
0
0
2
2
1
2
1
2
1
2
0
2
1
0
1
0
1
1
1
2
1
1
1
1
0
1
2
1
1
0
0
1
0
2
1
2
1
1
1
1
2
2
1
0
2
1
1
2
1
1
2
1
2
2
1
1
1
2
1
1
0
1
1
1
0
2
2
2
2
1
1
1
1
1
1
1
1
1
1
2
0
2
1
1
0
2
2
2
2
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
0
1
1
1
0
2
1
2
1
2
1
1
2
1
1
1
0
1
2
1
1
1
1
2
1
1
1
2
2
0
1
1
0
2
2
0
2
1
1
0
0
1
1
1
1
2
0
1
1
1
1
0
0
2
1
2
1
2
1
2
2
1
1
1
1
2
1
1
2
1
1
2
2
2
1
1
0
2
1
1
1
2
1
1
1
1
1
1
2
2
1
1
2
1
1
1
0
2
2
1
0
2
1
1
0
2
2
2
0
1
3
1
1
1
2
1
1
0
1
0
1
0
1
0
1
1
1
1
2
1
1
2
1
2
1
1
2
3
1
1
1
1
0
1
1
1
2
1
2
6
2
2
1
1
1
1
3
1
0
0
2
1
1
0
1
1
1
0
1
2
1
1
2
1
1
2
2
1
2
1
2
1
1
0
1
2
2
1
1
2
0
0
1
1
2
1
1
2
2
1
1
1
2
1
0
1
2
1
1
1
1
1
0
1
2
1
1
1
2
2
2
1
0
0
1
0
2
2
1
2
1
0
1
1
1
2
0
1
1
2
1
1
2
0
1
1
1
1
2
0
1
1
1
1
1
0
0
1
1
1
0
2
0
1
1
1
1
2
1
1
1
1
1
1
1
1
0
1
0
1
0
1
0
2
1
1
1
1
2
2
1
0
0
1
1
2
1
3
1
1
1
1
1
0
0
1
0
2
1
2
1
1
1
1
1
0
1
2
0
1
1
2
1
1
2
2
1
1
1
1
0
1
1
1
2
1
2
1
2
1
2
2
2
1
2
1
1
1
4
1
1
0
0
1
0
1
1
1
0
1
1
0
1
1
2
2
2
0
1
1
2
1
0
1
1
0
0
0
2
2
2
2
1
2
2
1
1
0
1
2
1
1
1
1
1
1
2
1
2
1
1
2
1
0
1
1
1
1
1
1
2
1
2
1
2
2
0
1
2
1
2
1
2
1
1
2
0
0
1
1
0
0
1
0
2
0
1
2
2
0
2
1
2
1
1
1
2
0
1
1
1
1
1
1
1
0
1
1
2
2
1
2
1
2
1
2
3
0
1
1
1
1
2
5
2
1
1
1
1
3
1
1
1
2
1
1
0
2
1
2
0
2
1
2
1
1
1
2
1
1
1
0
1
0
0
0
1
1
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
2
1
0
2
1
1
1
1
1
1
1
1
1
2
0
1
1
1
1
1
2
2
0
1
2
1
2
0
1
0
1
1
1
2
1
2
0
2
0
1
1
2
2
2
0
2
1
2
3
1
3
2
2
2
2
0
1
1
2
1
1
2
1
1
0
1
1
0
2
1
1
1
1
1
0
0
1
2
2
1
1
1
2
1
1
1
2
0
1
2
3
1
1
2
2
1
0
1
2
1
0
2
1
1
2
1
1
0
1
1
1
2
2
2
1
1
0
1
3
1
1
1
1
0
1
2
1
1
1
2
1
0
2
1
1
2
1
0
1
2
2
1
2
0
1
1
2
1
1
1
1
0
1
1
3
1
2
1
2
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
2
1
2
2
1
1
2
1
1
2
1
1
1
1
1
1
1
2
2
1
1
3
1
2
2
1
1
2
0
1
1
1
0
2
1
2
1
1
0
2
1
1
1
2
1
2
0
1
1
2
2
2
1
1
1
1
1
1
1
1
2
2
0
2
1
2
1
1
1
1
1
1
0
2
1
2
1
2
1
1
1
2
1
1
0
2
2
2
1
2
2
3
2
0
0
1
1
1
1
1
1
2
0
2
1
1
1
2
0
1
1
1
1
2
1
2
2
1
1
2
1
0
0
0
1
1
1
2
1
1
1
2
1
1
0
1
1
0
1
1
1
2
1
1
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
0
2
1
2
1
1
2
0
2
0
1
0
1
1
2
2
1
2
2
2
1
1
1
1
0
3
2
0
1
1
1
2
0
2
1
1
3
1
1
2
2
1
1
0
1
1
1
1
1
1
1
0
1
1
1
1
0
1
2
2
1
0
2
1
4
1
2
0
1
0
1
0
0
1
1
2
1
2
2
2
2
2
2
1
2
1
2
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
0
1
1
1
1
1
1
1
2
1
1
1
1
1
1
0
2
1
2
1
1
1
1
2
1
1
1
1
1
1
2
3
1
1
2
2
2
1
0
0
1
0
2
1
1
2
1
1
1
0
0
4
1
2
1
1
1
0
0
1
1
1
1
1
1
0
2
1
2
1
2
2
1
1
1
2
0
1
2
0
1
1
2
2
2
2
0
1
1
1
1
1
2
2
1
2
0
1
1
1
1
1
2
1
2
0
1
1
1
1
2
0
2
1
2
1
1
1
1
0
1
2
2
1
2
1
2
1
1
1
0
2
1
2
1
1
1
0
1
2
2
2
1
1
1
2
1
0
1
1
2
4
0
2
1
2
1
1
0
1
2
1
0
1
1
2
1
1
0
1
1
1
1
1
2
2
0
0
2
0
2
0
1
2
0
0
2
2
0
0
1
1
1
0
1
2
1
2
1
1
1
2
1
2
2
1
2
1
2
1
1
2
0
1
1
1
0
2
1
1
2
1
2
2
1
2
1
1
1
1
1
1
1
1
0
1
1
2
2
1
1
0
1
1
1
1
0
2
1
2
2
2
2
1
0
2
0
1
2
1
1
1
1
1
0
1
1
1
2
2
2
1
2
2
1
0
0
1
2
2
2
2
2
2
2
1
2
1
1
1
1
1
1
0
1
0
2
1
2
0
0
0
1
1
2
1
0
1
2
1
1
1
1
0
1
1
2
1
1
1
1
1
2
1
2
0
1
0
2
1
1
1
2
2
1
1
0
1
1
1
0
1
0
1
0
2
1
0
2
1
0
0
1
0
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
1
2
0
1
1
1
1
2
0
1
1
1
0
1
1
1
1
1
1
0
1
0
2
2
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
1
1
0
2
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
0
1
1
2
1
1
1
1
1
1
1
2
0
1
1
2
1
2
1
1
2
0
2
1
2
1
1
0
1
1
1
1
2
1
2
2
0
1
1
2
1
1
1
0
0
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
0
2
2
1
1
1
1
2
0
1
0
1
1
2
1
0
1
1
1
2
1
1
0
1
1
1
1
1
0
1
2
1
0
1
1
0
1
1
1
2
1
2
1
0
2
1
1
1
1
1
2
0
2
0
1
2
0
2
1
0
1
1
2
1
1
2
1
3
1
2
0
2
2
1
1
1
0
1
2
1
1
0
2
2
1
4
1
2
0
2
2
1
1
3
1
1
2
1
2
1
1
2
2
2
2
1
1
1
1
1
2
0
1
1
2
2
1
2
1
1
1
2
1
1
1
1
1
2
0
2
2
1
1
1
1
0
1
1
1
2
1
1
0
1
1
1
1
1
0
1
1
0
1
1
1
1
1
0
1
0
1
1
1
1
1
2
1
1
1
0
1
1
1
1
2
1
0
1
1
2
2
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
2
1
0
1
1
0
0
1
2
1
2
1
1
1
0
1
1
1
2
2
2
1
1
1
2
1
1
2
2
1
1
1
1
2
1
2
2
1
2
1
1
1
1
0
1
1
1
2
1
1
1
1
1
0
1
2
1
1
1
0
1
1
1
1
1
0
1
1
1
1
1
0
1
2
2
0
0
1
1
1
3
1
1
0
2
1
1
1
1
1
2
0
1
1
0
1
1
2
1
1
1
0
1
1
2
1
1
1
2
1
1
1
2
2
1
1
2
1
1
1
1
2
1
1
0
1
1
1
1
0
3
0
1
1
1
1
2
0
2
1
1
1
2
2
1
0
1
2
2
2
1
2
2
1
1
1
2
0
1
2
1
2
1
1
1
1
1
1
1
1
1
0
1
2
1
0
1
1
0
2
1
0
1
2
1
1
1
1
1
2
1
1
1
1
0
2
1
1
1
1
2
1
2
2
1
2
1
1
1
1
1
2
0
2
1
1
0
1
2
1
1
2
1
0
1
1
0
1
2
1
1
1
2
1
0
2
1
1
1
1
1
3
1
1
2
2
1
1
1
1
2
2
2
0
2
2
2
0
1
1
1
0
2
1
1
1
2
2
1
1
0
1
2
1
2
1
0
1
1
1
1
1
2
1
1
1
2
1
1
2
1
1
1
0
2
1
2
1
2
1
1
2
2
1
2
1
2
0
1
2
1
1
1
1
1
1
1
2
2
2
1
2
2
0
2
1
1
2
0
1
1
1
0
0
1
2
1
1
0
1
2
0
2
1
0
1
2
1
1
2
1
0
2
2
0
2
1
2
0
1
1
0
0
1
2
1
1
1
2
2
1
1
1
1
1
2
1
2
1
1
1
1
2
1
0
2
0
2
2
1
0
3
1
2
2
2
0
1
1
1
2
0
1
1
2
2
2
1
1
2
1
0
2
1
2
1
1
0
1
1
1
1
1
1
1
1
1
1
2
1
0
2
1
2
1
1
1
1
2
1
1
1
2
2
2
1
2
1
1
2
1
1
2
1
1
2
1
1
1
2
1
1
2
1
2
1
0
2
1
2
0
2
2
1
1
1
1
2
2
2
1
2
1
1
1
2
1
1
1
1
1
1
1
0
1
2
1
1
1
1
1
1
0
2
1
2
1
1
2
2
1
1
1
2
0
1
1
1
1
0
2
1
1
0
1
1
0
1
1
1
1
1
1
1
1
1
1
2
1
1
2
0
2
0
2
1
1
1
1
2
1
1
2
1
1
1
1
2
1
1
0
1
1
2
1
1
0
2
2
1
2
1
1
2
2
1
0
1
1
2
1
1
1
1
1
1
1
1
1
2
0
0
1
2
1
2
1
1
1
1
1
1
1
2
1
1
0
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
0
1
0
1
3
2
1
1
1
0
1
1
1
3
1
0
2
1
1
1
1
1
2
1
1
2
0
2
1
1
2
1
0
1
6
1
2
1
1
1
2
1
1
0
0
2
1
2
1
1
1
0
1
1
2
1
2
1
1
1
2
2
2
2
1
1
2
1
2
2
1
1
1
1
2
2
0
0
2
2
1
0
2
2
0
1
2
2
1
1
1
1
3
0
1
2
1
1
1
2
1
2
1
1
2
2
1
1
2
2
0
1
1
1
1
0
1
1
0
2
0
1
1
1
2
1
1
2
1
1
1
0
1
1
2
0
1
1
1
1
2
2
2
2
1
0
2
1
0
1
2
1
0
1
2
2
1
1
0
0
1
1
2
1
0
2
1
1
2
4
0
1
1
1
0
1
2
0
1
1
1
0
1
1
2
1
1
2
1
0
1
1
0
0
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
2
1
2
2
2
1
1
1
1
1
1
0
1
1
2
2
1
1
1
2
1
2
1
1
1
1
2
4
0
1
1
2
1
1
1
1
1
4
2
2
1
2
1
0
1
2
0
1
1
0
2
1
2
2
1
1
1
1
1
1
0
1
2
2
1
0
2
1
2
0
1
0
1
2
1
2
1
1
2
2
1
1
1
1
1
1
0
1
2
1
1
3
0
1
2
1
1
1
1
1
1
1
1
2
1
2
1
1
0
1
2
1
1
1
2
1
2
1
1
1
1
1
0
1
1
1
2
0
3
1
0
2
2
4
0
2
0
3
2
1
1
1
1
1
0
1
1
1
1
2
1
1
1
2
1
0
1
1
1
1
1
1
0
1
1
0
2
1
2
1
1
1
0
0
1
1
1
0
0
1
1
2
2
1
0
1
1
1
1
1
0
1
1
2
3
1
1
1
1
2
1
0
1
1
0
1
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
1
0
1
1
1
2
2
1
2
0
1
1
1
1
1
2
1
1
1
0
1
1
1
2
1
1
1
1
2
1
2
2
0
2
1
1
2
0
0
0
2
1
1
1
1
1
1
1
1
2
1
2
0
1
0
1
1
1
1
1
1
1
2
2
2
1
1
0
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
0
0
2
1
0
0
2
0
2
1
2
2
1
2
0
1
1
2
1
0
2
1
1
0
1
1
1
0
1
2
1
2
2
0
4
1
1
2
2
1
1
2
2
2
1
1
1
1
3
1
1
0
1
1
1
0
0
2
2
1
1
1
2
0
1
1
2
1
1
1
1
1
0
1
1
1
1
1
2
1
0
1
2
1
0
1
1
0
1
2
2
1
1
2
0
1
1
1
1
0
1
0
1
1
1
1
1
1
1
1
1
1
1
1
2
1
0
1
1
0
1
1
1
0
2
2
1
1
1
1
1
1
1
2
0
1
1
1
1
0
1
2
2
3
2
2
1
1
1
1
1
1
2
2
1
0
2
2
1
1
1
1
1
0
2
1
2
1
1
1
1
2
2
2
1
1
1
1
1
3
1
1
2
1
1
1
1
0
0
1
1
1
2
1
1
1
1
1
1
0
1
1
1
1
1
0
0
1
1
0
1
1
0
1
1
1
2
0
0
1
1
0
0
1
1
2
1
2
2
2
1
2
1
0
0
1
1
2
1
1
1
2
0
1
2
0
1
1
1
1
1
1
2
2
2
2
0
2
1
1
0
2
1
1
0
1
1
0
1
1
1
1
1
1
1
3
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
0
1
0
0
2
1
1
1
1
1
2
0
2
2
1
1
2
1
1
1
1
1
1
2
2
2
2
1
1
1
1
2
2
0
1
0
1
1
1
2
1
1
2
1
2
1
2
1
1
1
1
0
1
0
2
1
1
2
1
0
1
0
1
1
2
2
1
1
1
1
2
0
1
1
1
2
1
0
1
1
1
0
1
0
0
1
1
1
1
1
1
1
0
1
1
1
1
1
2
2
1
1
0
1
2
1
2
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
2
0
2
2
2
1
1
1
2
0
1
1
2
0
2
1
1
1
1
2
1
2
2
1
2
1
1
1
0
0
0
1
2
1
2
0
1
1
1
1
1
2
1
1
2
2
0
2
1
2
0
1
1
1
1
0
2
1
2
1
1
2
0
2
1
0
1
1
1
1
2
1
2
1
1
1
1
1
1
2
2
1
1
2
1
1
1
2
1
1
2
2
1
0
0
0
0
1
1
0
1
1
1
1
2
1
1
1
1
2
1
1
0
1
1
1
2
2
0
2
0
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
2
1
0
0
2
1
1
2
2
0
0
2
1
1
1
1
1
1
1
1
1
1
1
0
2
0
0
0
1
1
1
1
2
0
2
1
1
1
2
2
0
1
2
2
3
2
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
0
2
1
1
0
1
2
2
2
1
1
1
1
0
1
0
1
1
1
1
2
1
2
1
1
1
1
2
0
1
1
1
1
1
2
0
0
1
1
0
2
1
1
1
2
2
1
1
0
1
1
0
1
2
3
2
1
1
2
0
1
2
1
1
1
2
1
0
1
0
1
1
1
1
0
2
1
2
2
2
1
0
3
2
1
1
1
2
1
0
2
1
2
1
1
1
1
2
0
2
0
1
1
0
1
1
0
1
0
1
2
1
2
1
1
2
0
1
2
1
2
1
1
1
2
1
1
1
1
2
1
1
1
0
1
2
2
1
1
1
1
1
0
2
2
0
1
2
1
2
1
2
1
1
0
0
2
1
2
2
2
1
2
2
1
1
3
1
1
2
1
0
0
1
1
0
0
2
1
1
2
2
1
1
2
0
1
1
2
2
2
0
1
1
2
1
1
1
1
1
2
2
2
1
1
1
1
1
1
0
0
2
2
0
0
2
1
1
1
1
0
0
1
2
1
0
1
0
1
2
2
1
1
2
1
2
1
1
1
1
0
1
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
0
1
1
0
2
1
1
0
2
1
0
2
1
1
1
1
1
2
1
2
1
2
1
2
2
1
2
1
1
1
2
1
1
1
2
1
2
1
1
1
1
0
0
2
1
1
1
1
0
1
1
2
0
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
2
1
2
0
2
1
2
1
1
2
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
0
1
0
1
1
2
1
1
1
1
1
0
1
1
1
1
1
1
1
1
0
2
1
1
2
1
2
1
0
1
1
1
1
1
1
1
2
1
1
2
1
1
2
2
1
2
2
1
0
1
2
1
1
1
1
1
0
1
1
1
0
1
1
1
2
2
1
1
1
1
0
1
1
1
0
2
1
1
1
1
2
2
0
1
1
2
1
1
2
1
1
2
1
1
1
1
1
0
1
0
2
1
2
1
1
0
1
2
1
1
1
1
1
1
2
1
1
1
2
0
2
1
1
0
2
2
1
3
2
0
2
1
0
1
1
1
1
1
1
0
0
1
1
1
1
2
1
2
1
2
2
0
1
2
1
1
2
1
2
1
1
1
1
2
2
1
0
1
0
0
1
0
1
0
1
2
1
1
1
1
1
1
3
1
2
1
1
1
1
0
2
1
1
1
1
2
1
1
1
1
1
2
1
1
2
2
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
2
1
1
0
1
0
1
0
1
1
2
1
2
1
1
1
0
2
1
2
2
1
1
2
1
1
0
0
1
2
1
1
2
1
1
1
1
1
1
1
0
0
2
1
2
2
1
1
1
1
2
1
2
2
1
1
2
0
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
0
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
2
1
1
2
0
1
2
1
1
1
0
2
2
1
1
2
1
1
0
2
1
1
1
1
1
1
1
0
1
1
1
2
1
1
1
1
0
0
1
0
1
0
1
0
1
0
1
0
1
2
1
1
2
2
1
0
2
1
0
2
2
1
1
1
2
2
1
1
2
1
1
2
1
1
1
2
2
1
2
1
1
1
2
1
0
2
0
0
2
1
1
1
1
0
2
2
2
1
1
1
0
2
1
2
0
0
2
1
1
1
1
0
2
0
2
1
1
1
1
1
1
1
2
0
1
2
2
1
2
0
0
2
1
1
1
1
2
0
1
1
2
2
1
2
1
0
1
1
1
0
1
1
2
0
0
2
1
2
2
0
0
1
1
2
2
1
0
2
0
1
0
0
2
2
1
1
1
1
1
0
1
1
1
1
1
2
1
0
2
1
1
2
1
1
1
1
1
1
2
0
2
1
1
2
2
1
1
1
1
1
2
0
2
1
1
1
2
1
0
2
1
0
0
1
1
2
0
2
1
1
1
2
1
2
0
2
1
1
2
1
0
2
1
1
1
2
1
1
0
1
2
2
1
1
2
1
2
2
1
2
1
1
1
2
0
1
1
1
1
1
2
1
1
2
1
1
1
1
1
2
0
0
2
2
1
0
2
1
1
0
1
1
1
1
1
1
1
1
1
0
1
2
1
2
1
1
1
1
1
1
3
1
1
0
1
2
1
0
1
1
1
0
1
1
1
0
1
1
2
1
1
2
1
2
2
2
1
1
2
2
1
1
2
0
1
2
2
1
2
2
0
2
0
1
1
1
1
0
1
0
1
2
2
1
1
2
1
1
1
1
0
1
1
1
1
1
0
0
2
1
1
2
2
1
1
2
1
1
1
2
2
1
2
2
0
1
2
2
2
2
1
0
1
1
1
1
1
1
1
0
2
2
1
2
1
0
1
2
1
1
2
2
1
1
0
2
1
2
2
1
2
0
0
2
1
1
1
1
2
2
2
1
1
1
2
1
1
1
1
1
1
1
0
1
1
2
2
1
1
1
1
1
1
1
2
0
2
0
1
1
1
0
1
1
2
0
1
1
0
1
1
2
1
0
0
1
1
1
1
1
0
1
2
1
1
1
1
1
0
2
2
1
1
2
1
2
2
2
1
1
0
1
1
2
2
0
1
0
1
2
1
0
1
1
2
2
1
1
2
1
2
1
1
1
2
1
1
0
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
2
0
1
1
1
1
0
1
2
1
1
1
1
0
0
1
2
0
2
2
1
2
0
1
1
1
2
2
1
2
0
1
0
0
1
2
2
1
0
2
1
1
1
2
0
0
1
1
1
1
1
1
1
0
1
1
0
2
2
1
1
1
1
1
1
2
0
1
1
2
0
2
0
0
1
1
2
1
1
1
2
1
2
2
2
1
1
0
1
0
2
1
2
1
1
0
0
1
2
1
1
1
2
1
1
2
1
2
1
0
1
0
1
1
1
2
1
1
2
1
0
1
1
2
1
0
1
2
2
0
0
2
1
1
1
1
0
1
0
1
2
2
0
1
1
2
0
2
1
2
1
1
2
2
1
0
2
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
2
1
2
2
1
1
2
2
1
1
2
1
1
1
1
1
1
2
2
1
0
2
1
1
0
1
1
1
2
0
2
1
0
1
0
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
2
1
0
0
0
2
1
1
2
1
0
1
1
1
1
1
2
0
1
2
1
1
2
1
1
1
2
2
1
1
1
2
1
0
1
1
2
1
2
0
1
1
2
1
1
2
1
1
1
2
2
2
1
0
1
0
0
1
1
2
0
2
1
1
1
1
2
1
1
2
1
0
0
2
1
0
1
2
0
0
1
2
1
2
1
1
1
2
2
2
1
0
1
1
1
1
2
1
1
1
1
1
1
2
1
1
2
2
2
1
1
1
1
0
1
1
0
1
1
1
1
2
1
1
1
0
2
1
1
2
2
0
1
1
2
1
1
1
1
2
2
2
1
2
1
2
1
1
2
1
1
1
2
1
1
1
0
0
3
1
2
1
0
1
1
1
1
2
0
1
2
1
1
2
1
0
1
1
1
1
2
1
3
1
0
1
1
1
1
1
2
1
0
1
1
1
1
0
0
1
0
1
1
1
2
1
1
0
1
0
2
1
1
2
0
1
0
1
2
1
2
1
0
1
2
2
0
1
1
1
1
2
0
1
0
1
1
2
2
1
2
0
1
1
2
2
1
2
0
0
0
2
1
1
1
1
1
2
2
1
1
2
1
1
2
1
2
2
1
2
0
1
2
1
1
1
1
2
1
1
2
2
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
0
0
1
1
0
1
1
1
1
2
2
1
1
1
2
1
1
1
1
1
0
1
2
1
1
2
1
1
1
2
0
2
2
1
1
3
1
0
1
1
1
0
1
0
0
2
1
1
2
1
0
0
1
1
1
1
0
0
1
2
1
1
1
2
1
0
0
2
2
1
0
1
2
2
0
0
1
0
1
0
1
2
0
1
1
2
2
0
1
0
2
1
2
1
1
1
1
1
1
2
1
1
1
0
1
1
1
1
1
1
1
0
1
1
0
0
1
2
2
1
1
0
1
2
1
2
2
2
0
2
5
1
1
1
1
1
1
1
2
1
0
1
2
1
2
1
1
2
0
2
1
1
3
2
1
2
1
1
1
2
1
0
0
1
1
1
0
1
1
1
1
0
1
2
1
2
1
2
2
1
1
1
2
2
0
1
1
2
2
3
1
0
1
1
0
2
1
1
1
1
1
0
1
0
1
1
0
0
1
0
0
0
0
3
1
1
1
1
1
2
1
0
1
1
2
1
1
2
1
2
2
0
1
2
1
1
1
1
1
2
2
1
1
2
1
2
2
2
1
1
1
1
2
1
1
1
1
0
1
1
1
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
1
1
1
2
1
2
2
0
1
1
2
1
1
2
0
2
0
1
2
1
0
1
1
1
1
2
1
1
2
2
1
1
1
1
1
2
1
0
1
1
1
1
1
1
1
0
2
0
1
1
1
1
1
2
0
1
1
1
1
1
0
1
0
1
2
2
1
2
1
2
0
2
0
1
1
1
1
2
2
2
1
0
2
2
1
1
3
1
1
1
1
0
1
1
1
1
1
2
1
0
1
1
1
1
2
1
1
1
1
1
1
1
0
1
1
1
1
1
1
0
1
1
1
1
1
1
1
2
1
1
2
2
0
0
1
1
0
1
1
2
1
1
1
1
1
1
0
2
1
1
1
1
1
2
2
2
1
1
0
0
0
2
1
1
1
2
1
1
1
1
1
1
1
1
2
0
2
0
2
2
1
2
0
0
1
1
0
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
2
2
1
1
0
1
0
1
1
1
1
1
1
0
1
1
2
2
1
1
2
2
1
2
1
1
1
0
2
2
1
0
0
1
1
1
1
1
2
1
1
1
0
1
1
1
1
1
0
2
0
0
1
1
1
2
1
2
1
2
1
1
0
1
1
1
0
0
2
1
1
2
1
1
0
2
2
1
0
1
1
2
1
1
1
0
1
1
3
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
2
1
2
0
2
2
1
1
1
1
1
1
1
2
1
0
2
1
1
1
1
0
1
1
2
1
0
1
1
2
2
2
1
1
2
1
1
0
2
0
2
1
1
0
0
2
2
1
2
1
1
1
1
1
2
2
1
1
1
1
1
2
0
1
2
1
1
0
2
1
2
2
1
2
1
1
2
2
1
1
1
0
2
2
1
1
1
2
0
1
0
2
2
1
0
1
1
0
0
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
2
1
1
2
1
0
0
0
1
1
1
0
2
1
2
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
2
0
1
2
2
2
1
2
1
1
1
2
3
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
2
2
0
1
1
1
1
1
1
1
0
2
2
1
0
2
1
1
1
2
2
0
2
1
1
1
1
1
1
1
2
1
1
2
1
2
2
1
0
1
1
2
1
2
1
1
1
2
1
1
1
2
1
1
1
1
1
1
0
2
1
0
2
1
1
1
2
1
1
0
1
2
1
2
1
1
2
1
0
1
1
3
2
1
1
1
1
0
2
1
2
1
2
1
2
2
1
1
1
0
2
1
1
2
1
1
1
1
1
1
1
1
1
0
2
1
1
1
2
1
2
0
1
1
1
1
1
1
2
1
1
2
2
1
2
1
0
1
0
2
1
1
1
1
1
2
2
1
2
0
1
2
0
2
1
0
1
0
2
2
1
2
2
2
1
1
3
2
1
0
1
1
0
2
0
1
1
2
1
1
1
0
1
1
0
2
0
1
1
1
1
1
1
0
2
1
1
2
2
1
0
0
1
2
1
2
0
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
0
1
1
1
1
2
1
2
1
1
1
2
1
2
2
2
1
2
2
1
0
2
0
1
2
1
1
1
0
2
1
1
1
2
1
2
1
1
1
2
1
1
0
1
2
1
1
2
2
1
2
1
2
2
1
2
1
1
2
1
1
1
1
2
1
2
1
2
1
2
0
1
1
0
0
1
1
1
1
0
0
1
1
1
0
1
2
1
1
2
1
1
1
1
1
1
0
2
1
1
1
1
2
1
2
1
1
1
2
2
2
1
2
2
2
1
2
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
0
1
0
1
1
1
2
1
2
2
1
1
1
2
0
1
1
1
1
2
1
2
2
2
0
0
2
2
0
1
1
1
2
1
1
1
1
2
2
0
1
1
1
1
1
1
2
2
2
1
1
1
2
1
2
0
2
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
2
0
1
1
1
2
2
1
1
1
1
2
1
1
0
2
1
2
1
0
1
2
1
1
0
1
1
1
2
1
1
1
2
1
2
0
2
1
0
0
0
1
1
0
2
1
1
0
1
1
1
1
1
2
2
2
1
1
1
1
2
1
2
1
1
1
1
1
1
2
1
0
0
1
0
1
2
1
2
1
1
1
1
1
2
1
2
2
1
0
1
1
1
1
2
1
2
2
1
1
1
2
1
1
1
2
2
2
1
1
1
1
1
1
1
1
0
1
2
1
2
1
1
1
1
0
1
1
2
1
1
0
2
0
1
1
1
2
1
2
0
2
1
1
1
1
1
2
1
1
1
1
1
2
2
2
1
1
1
2
2
1
0
0
1
2
0
1
1
2
0
1
1
1
1
0
1
0
2
1
1
2
1
1
2
1
1
1
0
1
1
1
2
1
2
1
1
2
0
2
1
2
2
2
2
2
2
1
1
1
0
1
1
1
1
1
2
2
1
2
0
2
2
2
1
1
0
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
1
1
1
1
0
1
0
0
2
1
1
1
0
2
1
0
0
1
2
0
1
2
2
1
1
2
1
1
2
1
1
1
1
2
2
4
2
2
1
0
1
0
1
1
1
2
2
1
1
2
1
0
2
1
1
1
1
1
1
1
0
1
1
2
1
1
2
1
2
1
2
1
0
2
1
0
1
1
1
0
1
2
1
1
1
1
1
1
1
2
1
1
1
2
2
2
1
1
2
2
0
0
2
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
0
1
1
1
1
1
1
2
2
0
1
1
0
2
2
1
0
1
2
1
1
0
1
2
1
3
1
1
2
1
1
2
2
1
1
1
1
1
2
1
1
2
2
1
2
2
0
1
1
1
1
0
1
1
1
2
2
2
1
1
1
0
1
2
2
1
0
2
1
1
1
2
2
0
1
1
1
1
1
0
1
0
1
1
1
1
1
2
2
1
0
0
1
1
2
0
2
1
1
2
1
0
1
1
0
1
1
1
2
1
1
0
1
2
2
1
1
1
1
1
1
1
0
0
0
1
1
1
0
1
1
1
1
2
1
1
0
1
0
1
1
1
1
1
1
2
1
0
1
2
1
1
2
1
0
2
1
3
1
1
1
1
1
1
1
1
1
0
1
0
1
1
0
1
2
2
1
2
2
1
2
1
1
1
3
0
0
2
1
2
1
2
2
1
0
1
1
0
1
0
2
0
1
1
1
2
1
1
1
1
0
1
2
2
1
1
1
2
2
1
1
2
2
1
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
0
2
1
1
1
0
2
2
2
2
1
1
1
1
1
1
1
1
1
1
2
1
0
2
1
1
1
0
1
2
0
1
1
1
2
1
1
0
2
1
2
1
1
1
1
1
0
2
1
1
1
1
1
0
1
1
1
3
1
3
1
1
1
1
0
2
1
1
1
2
1
2
1
2
1
2
1
1
1
1
2
2
2
1
0
2
1
1
2
1
2
1
2
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
0
1
0
0
1
1
1
2
0
2
1
2
2
2
2
1
1
1
1
1
0
1
1
1
0
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
0
0
0
1
1
0
1
0
1
1
1
3
1
1
1
2
0
2
1
2
1
1
1
1
1
1
0
2
0
1
2
2
1
2
1
1
0
0
1
1
1
2
2
1
2
0
2
1
0
0
1
1
1
1
0
1
1
1
1
2
1
0
0
2
1
1
1
2
1
2
2
1
2
2
1
1
2
1
1
1
0
2
2
2
0
0
2
1
1
1
1
1
1
0
2
1
0
2
1
1
1
1
1
1
1
1
2
0
1
1
1
1
1
1
1
0
1
1
1
1
2
2
1
2
3
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
0
1
1
1
1
1
1
1
2
0
1
1
1
2
1
2
2
2
2
1
2
1
2
1
2
1
1
1
0
2
1
2
2
1
0
2
2
0
1
1
1
1
2
2
1
1
0
1
1
1
1
1
1
1
0
0
2
1
1
1
0
3
1
1
2
1
0
1
1
2
1
1
1
1
3
2
1
1
1
1
0
0
0
0
1
0
1
2
1
1
1
2
1
2
1
2
2
0
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
0
1
1
0
1
2
2
1
1
2
0
0
0
2
2
1
1
0
2
1
1
1
1
1
2
2
0
1
2
2
1
2
1
2
1
2
2
1
1
0
0
2
1
1
1
2
1
1
2
2
2
2
1
2
1
1
1
2
1
1
1
1
1
1
1
0
2
1
1
2
0
1
1
2
1
1
1
1
1
2
1
1
1
0
1
1
0
1
1
1
1
1
1
2
0
1
1
1
1
0
1
1
2
1
2
1
1
1
1
1
1
2
1
1
0
2
1
0
1
1
1
1
1
2
1
1
1
1
2
0
1
0
1
0
1
0
2
1
1
2
1
1
0
2
1
1
1
1
2
1
1
2
1
1
0
1
0
2
1
1
1
2
1
1
2
0
0
1
1
2
2
2
1
1
1
1
1
1
0
2
1
1
0
1
1
1
2
0
0
1
1
2
2
0
1
1
0
1
0
1
2
1
2
0
1
1
2
0
1
0
1
1
1
1
1
2
0
1
1
1
1
0
1
1
0
2
2
2
1
2
1
1
2
2
1
1
2
1
0
1
1
1
2
2
1
1
2
1
1
1
2
2
2
1
2
1
1
2
1
2
1
1
2
1
2
2
2
1
2
2
2
1
2
2
1
1
1
1
1
3
1
1
1
1
2
1
2
2
0
2
1
1
0
1
1
0
1
4
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
2
1
2
1
1
1
2
1
0
0
0
1
0
1
2
1
1
2
2
1
0
1
2
1
0
2
2
1
1
2
0
1
0
1
0
1
1
2
2
1
2
2
2
0
0
1
1
1
1
2
1
0
2
1
0
1
2
2
1
1
1
0
1
0
1
1
2
1
1
1
0
1
1
1
1
0
1
1
1
2
1
1
1
1
0
0
1
1
1
1
1
0
0
1
2
2
0
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
0
1
2
1
1
1
1
1
2
1
1
1
2
2
2
2
1
1
0
2
1
2
1
1
1
1
1
2
1
2
1
1
2
0
1
2
2
1
0
0
2
0
1
2
1
1
1
2
1
1
2
1
2
2
1
1
1
1
1
2
2
2
1
2
1
1
1
1
2
2
2
1
1
0
1
1
2
1
1
1
2
0
1
1
1
2
2
1
1
2
1
0
1
2
1
1
2
1
1
2
1
0
0
1
1
1
1
1
1
1
2
1
2
2
1
1
0
1
1
2
1
0
2
2
1
0
0
1
1
0
1
2
2
1
2
1
1
2
2
1
1
2
1
1
2
1
2
1
1
1
1
1
2
1
0
1
1
1
0
1
2
3
1
1
1
2
1
0
1
2
1
2
0
1
1
1
1
1
2
0
2
1
1
2
1
1
1
0
2
1
1
1
1
1
1
0
2
2
1
0
1
0
1
1
2
2
1
1
2
1
0
1
1
1
1
1
0
1
1
2
1
1
1
1
1
2
1
1
2
2
1
1
0
1
1
3
1
2
2
1
1
1
1
2
0
1
1
2
1
1
1
1
1
0
1
1
0
1
1
2
1
1
2
1
1
1
0
2
0
1
1
1
1
2
1
1
1
0
0
0
1
2
1
1
0
1
3
1
0
1
2
0
1
2
0
1
2
1
2
1
3
1
1
1
0
1
2
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
3
1
0
2
1
0
1
0
2
2
2
1
1
2
3
2
1
1
2
1
1
2
1
0
2
1
0
1
1
2
2
1
1
1
2
0
0
1
1
1
1
1
1
1
3
1
1
2
0
2
1
2
2
2
1
1
1
0
2
0
1
2
2
1
1
1
2
1
0
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
0
1
1
1
1
2
0
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
2
1
1
1
1
1
1
0
1
1
1
1
2
1
2
1
1
1
1
2
1
1
0
2
1
1
2
1
1
0
1
1
1
1
2
1
1
1
1
1
1
1
0
3
1
1
0
1
0
2
1
1
1
2
1
1
2
1
2
0
0
1
1
0
1
1
1
1
1
2
0
0
0
1
1
3
2
1
1
1
0
1
1
0
1
0
1
1
2
2
0
2
1
2
2
2
2
1
1
0
0
2
1
1
0
0
2
1
1
1
1
2
1
2
2
1
1
0
1
2
1
2
1
2
1
1
1
2
1
1
1
1
1
2
2
1
1
1
0
1
1
1
1
1
1
1
1
2
0
1
0
1
0
2
0
0
1
1
0
1
1
1
1
1
1
1
2
1
2
2
0
1
1
1
2
1
1
1
2
2
1
1
2
1
1
1
1
1
1
2
1
1
1
2
2
2
0
2
1
2
0
2
2
1
1
1
1
2
1
1
2
1
1
1
1
2
2
1
2
1
1
1
1
0
0
0
2
1
1
1
2
1
1
2
2
1
1
1
1
2
0
1
0
1
1
2
0
1
1
1
2
1
1
1
1
1
1
1
1
2
2
0
1
1
1
1
1
2
2
1
1
0
1
2
2
1
1
0
1
2
2
2
1
1
2
2
2
2
1
2
1
1
1
1
0
2
1
2
0
1
0
1
1
1
1
0
2
1
1
1
1
1
1
1
1
2
0
0
0
2
2
1
2
1
1
0
2
1
2
1
2
1
1
2
2
1
0
1
1
1
1
1
1
1
1
0
0
1
1
2
3
2
2
1
1
1
2
2
2
0
2
2
2
2
2
1
2
1
1
2
1
1
0
1
1
1
2
2
0
0
0
1
1
1
2
1
2
0
1
1
1
1
1
2
1
1
1
1
1
2
2
0
1
1
1
1
1
1
1
2
1
1
1
1
0
1
1
1
1
1
1
2
1
0
1
2
1
0
2
1
1
2
1
2
1
2
1
1
2
1
1
0
1
1
1
1
1
1
1
1
1
2
2
0
0
0
1
1
1
1
1
1
1
1
0
2
0
2
2
1
1
2
1
2
1
0
1
2
2
1
1
0
1
1
2
1
1
1
1
1
1
0
1
2
1
0
1
0
1
2
2
0
1
1
1
2
0
2
1
2
1
1
2
1
1
1
1
1
2
1
1
2
1
1
1
2
2
1
0
2
1
4
1
1
0
2
0
1
0
2
1
1
1
1
1
2
2
2
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
1
0
1
1
1
1
5
0
0
2
2
2
2
1
1
2
0
2
1
1
1
0
1
2
1
1
1
0
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
1
1
1
0
1
1
2
1
1
1
1
1
2
1
2
0
1
3
0
1
1
0
2
2
2
1
2
1
1
1
0
1
1
1
0
2
1
0
1
1
2
2
2
1
1
1
1
1
2
1
1
1
2
1
2
2
1
1
1
2
1
1
1
1
2
1
1
1
2
1
2
1
1
3
2
1
1
1
1
1
1
2
1
1
1
1
0
1
1
2
1
1
0
0
0
1
0
1
2
1
0
1
1
1
2
1
1
1
1
1
0
1
1
1
1
1
1
1
1
2
1
2
1
0
2
1
2
1
2
1
2
1
0
1
1
1
0
2
0
1
1
1
2
2
1
1
0
0
1
0
1
1
1
1
1
1
1
1
2
1
1
0
0
1
1
2
4
0
1
1
1
2
0
1
0
1
1
1
2
1
1
2
1
0
1
2
2
1
1
1
1
2
1
1
0
1
0
1
0
1
1
1
0
1
1
3
1
1
1
1
1
2
2
1
2
1
1
0
1
1
2
1
1
1
1
1
1
0
1
0
2
2
1
0
2
2
0
1
1
1
2
2
2
0
0
2
1
0
1
1
0
2
1
1
1
2
1
2
3
1
2
1
1
1
1
2
1
2
0
0
1
1
1
2
2
1
1
1
2
2
1
1
1
2
1
2
1
1
1
1
1
0
1
1
0
2
1
1
1
2
1
0
2
2
1
2
2
1
0
2
1
0
2
1
1
1
1
1
1
2
1
3
2
0
1
2
0
1
0
1
1
1
2
1
2
0
0
1
2
1
1
2
1
0
2
1
1
1
2
2
1
1
2
1
2
2
3
1
3
1
1
1
1
1
1
2
1
2
2
2
0
1
2
1
2
2
1
1
1
1
1
0
0
1
1
1
1
0
1
2
2
1
1
1
2
2
2
1
0
1
1
0
2
1
1
1
2
1
1
1
0
1
2
1
2
1
1
1
0
1
2
1
2
1
1
1
0
0
1
1
1
1
1
2
1
1
2
1
2
1
1
0
1
1
3
1
2
1
3
1
1
1
1
1
1
0
1
1
1
2
1
1
1
2
0
1
2
2
1
1
3
2
1
1
1
1
1
1
1
1
0
2
0
1
1
1
1
1
1
1
4
1
2
1
0
1
1
2
1
1
1
3
1
1
0
1
2
1
1
1
1
0
1
0
1
2
0
2
1
1
2
0
1
1
1
1
1
1
2
1
2
2
1
0
2
2
1
2
1
1
1
1
0
1
1
1
2
1
2
2
1
1
2
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
2
2
1
1
1
0
1
2
1
1
2
0
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
2
2
1
1
1
2
1
1
1
0
1
2
1
0
2
2
2
1
1
1
0
1
1
0
2
1
0
1
2
1
2
0
2
2
2
1
1
1
1
2
2
1
1
1
2
1
1
1
2
2
1
0
1
2
1
2
1
1
0
1
2
2
1
1
1
1
2
1
1
1
2
2
1
1
2
1
1
1
2
0
2
2
0
1
1
2
0
2
1
2
0
2
0
2
1
1
2
0
2
1
2
1
1
1
1
0
1
3
1
0
2
1
1
2
1
0
1
0
2
2
1
2
1
1
1
1
1
1
1
2
2
1
1
0
1
2
1
2
1
2
1
2
1
0
1
2
2
3
3
1
1
1
1
0
2
1
1
1
1
0
2
1
1
1
1
1
1
1
2
1
2
1
0
1
0
0
1
0
1
0
1
0
2
1
0
1
1
2
0
1
1
2
1
2
1
1
1
0
1
1
1
2
1
1
1
1
2
2
1
1
1
2
1
2
1
1
1
1
2
1
1
1
2
1
1
1
1
0
2
1
1
2
0
2
1
1
1
1
1
2
1
1
0
1
1
1
0
0
1
1
1
2
0
1
2
1
1
2
2
2
2
1
0
2
1
1
1
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
0
2
0
1
1
1
1
1
1
3
2
1
1
0
1
1
1
1
2
0
1
1
2
2
2
1
2
1
1
1
0
0
1
1
2
2
2
1
0
0
1
0
1
1
2
1
0
0
1
0
1
2
1
1
2
1
2
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
2
1
1
2
2
2
0
1
2
1
2
2
0
1
0
1
1
0
1
1
1
1
2
0
0
2
1
1
2
2
1
1
2
1
0
1
1
1
2
2
1
2
2
1
1
2
0
1
0
1
1
1
1
1
1
1
5
1
1
2
1
1
0
2
1
2
1
1
2
2
2
2
2
1
3
0
1
1
2
1
1
1
1
2
2
2
2
1
1
2
1
1
1
1
1
2
2
1
1
0
2
1
1
1
2
1
2
1
1
1
0
0
1
1
1
2
1
1
2
2
0
1
2
1
1
0
1
1
1
1
1
1
4
1
0
1
2
0
1
1
2
2
1
1
2
1
2
0
2
2
2
1
1
2
1
1
1
1
0
1
1
1
1
1
1
1
0
1
0
2
1
0
2
1
2
1
1
0
1
1
1
0
1
1
2
2
2
2
2
1
1
1
2
1
1
4
1
1
1
1
1
1
2
1
1
1
1
1
1
0
0
1
2
1
1
1
1
1
0
2
1
1
1
1
2
1
1
1
1
1
2
2
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
0
1
1
1
2
1
2
1
1
2
2
1
2
1
1
1
0
1
2
0
1
2
1
1
1
1
1
2
1
2
2
2
1
1
2
1
1
2
1
2
1
1
1
2
1
2
2
2
1
1
0
1
1
2
1
1
1
1
1
2
2
1
0
2
1
2
2
0
1
1
1
1
1
2
1
1
1
1
2
0
1
1
1
0
2
1
2
0
1
2
2
1
2
1
1
1
2
1
2
0
1
2
1
2
1
1
1
2
1
1
1
1
2
1
0
2
1
1
1
1
1
2
1
1
2
1
1
2
0
0
1
0
0
1
1
1
0
1
1
1
1
1
1
2
1
1
1
1
1
1
1
0
0
1
1
1
1
1
2
1
1
1
2
2
2
2
1
2
2
1
1
1
1
0
0
1
0
1
2
2
1
1
2
1
0
1
1
1
0
2
1
2
1
1
2
0
2
1
1
1
2
1
2
2
1
0
1
1
0
1
1
1
1
2
1
2
0
1
0
1
1
1
2
2
1
1
2
1
2
1
1
0
2
2
2
0
0
1
1
1
1
1
1
1
0
1
1
1
1
0
1
2
1
2
1
1
0
1
2
1
0
2
1
2
2
2
0
1
1
1
1
1
2
2
3
0
1
2
1
0
0
1
0
1
0
1
1
0
1
2
2
0
1
2
1
1
1
1
2
2
1
1
1
0
1
1
1
0
1
1
1
1
0
1
2
1
1
1
2
2
2
1
1
2
2
1
2
1
1
0
2
2
1
0
2
1
1
2
2
1
2
2
1
1
2
2
1
1
1
2
1
0
1
1
1
1
1
2
2
1
1
2
2
0
1
1
0
1
1
1
1
2
1
1
1
0
1
1
1
2
0
1
0
2
3
0
1
1
1
0
1
0
1
1
1
0
2
1
1
2
0
1
1
0
1
2
1
1
2
1
0
1
1
2
0
2
1
1
1
1
1
0
1
1
1
0
1
2
1
1
2
1
2
2
2
1
1
2
1
1
1
2
2
1
1
1
2
1
1
2
2
1
2
2
2
1
2
1
0
1
1
1
2
1
1
1
1
2
1
2
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
1
1
0
1
1
0
2
1
0
1
2
1
1
2
1
1
2
2
3
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
0
2
0
2
1
1
1
1
1
2
1
2
1
2
1
1
2
1
2
1
1
1
2
1
1
0
1
0
1
1
1
1
1
0
0
1
1
0
1
1
1
0
3
0
2
0
1
3
1
1
1
2
1
0
1
1
2
2
2
0
0
1
1
1
1
2
1
1
2
2
2
1
1
1
2
1
2
1
1
1
1
2
1
0
2
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
0
1
2
1
2
1
1
0
0
1
2
1
1
2
2
1
1
1
2
1
1
1
1
1
3
0
2
1
1
1
0
1
0
1
1
1
0
1
2
1
3
1
1
2
2
2
1
1
2
2
1
2
1
1
1
1
1
1
2
2
1
1
0
1
1
2
1
1
2
1
1
1
1
2
1
1
0
1
2
1
1
1
1
1
0
1
1
1
2
1
1
1
1
2
2
0
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
2
2
2
1
1
2
1
1
1
2
2
1
1
2
2
0
0
0
2
1
1
1
1
2
1
1
1
1
1
1
0
2
1
1
2
1
1
0
1
2
1
1
2
2
1
2
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
0
2
0
0
1
1
2
1
1
0
0
0
1
1
2
1
2
2
1
0
2
2
1
2
1
2
1
2
1
0
1
2
0
1
1
1
1
1
1
1
0
1
0
1
1
1
1
1
1
1
2
2
1
0
1
2
1
2
1
1
0
1
1
2
1
1
1
2
1
1
1
2
2
2
0
1
1
1
0
1
2
1
1
1
2
1
1
1
1
0
2
1
2
1
1
2
1
1
1
1
2
0
2
1
1
0
1
1
1
1
1
2
2
1
1
1
1
0
2
1
1
1
0
0
1
1
2
1
2
0
1
2
1
0
1
2
0
2
1
0
1
1
4
2
1
2
2
1
1
1
2
1
1
1
1
1
2
2
0
1
1
1
2
0
1
1
1
2
1
0
0
2
3
1
1
1
2
1
1
1
1
1
2
2
1
1
2
2
1
2
1
1
1
1
1
2
0
2
1
2
1
2
1
1
1
0
1
1
1
1
0
1
1
2
1
0
0
1
2
1
1
0
1
1
1
1
2
0
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
2
0
2
1
1
1
1
1
1
1
1
3
1
1
1
1
1
1
2
2
1
1
0
1
2
1
1
1
1
1
1
1
1
2
1
1
2
0
0
1
1
2
1
1
1
1
2
1
1
0
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
2
2
1
1
0
2
1
1
0
1
1
1
1
0
0
0
2
1
0
2
2
1
1
2
1
1
1
1
1
2
1
0
0
2
2
0
1
2
2
2
2
2
1
0
2
1
0
2
2
1
0
2
1
1
2
1
2
1
1
2
1
0
2
1
0
2
1
1
2
1
1
1
2
1
2
1
2
1
2
2
0
2
2
1
1
2
1
2
1
1
1
0
1
0
2
1
1
1
1
1
0
2
2
1
1
1
0
1
1
0
1
0
0
0
0
2
2
1
2
2
1
2
1
1
1
1
1
2
2
2
1
2
1
1
2
0
1
0
1
2
0
1
1
1
0
2
0
1
2
1
1
2
1
0
0
2
1
1
2
1
1
2
1
2
1
1
1
2
2
1
1
1
1
2
0
1
1
2
1
0
2
1
1
1
1
0
0
1
2
1
2
0
1
1
1
0
2
0
1
2
2
1
2
0
1
2
1
0
1
1
1
2
1
2
2
0
3
1
1
0
2
1
1
1
1
0
1
2
1
1
2
1
1
1
2
1
1
2
1
2
2
1
1
1
1
1
1
1
1
2
0
1
1
1
1
1
2
1
1
0
1
1
1
1
1
2
1
2
1
0
0
1
2
1
0
2
1
1
1
2
1
1
2
1
2
1
1
1
1
1
0
1
2
2
2
1
1
1
2
1
1
1
1
1
1
2
1
0
0
2
0
2
1
1
2
1
1
0
1
0
0
2
2
2
2
1
1
2
1
2
1
1
3
2
1
0
2
2
1
1
1
1
0
1
1
1
1
2
1
1
2
0
2
1
1
1
2
1
0
1
2
1
1
1
2
1
1
1
2
0
0
0
1
1
0
1
2
2
1
2
1
2
1
2
1
2
1
1
0
0
2
0
0
2
4
0
2
1
1
1
0
2
1
1
1
1
1
1
2
2
1
1
1
1
0
0
1
1
2
3
2
1
1
1
2
2
1
0
1
1
1
0
1
1
1
1
1
1
2
0
1
5
1
1
1
2
1
0
2
1
1
0
1
1
2
0
1
1
1
2
1
1
2
1
1
0
2
1
1
2
1
2
1
2
2
2
1
2
1
2
2
0
1
0
2
1
1
2
1
0
1
0
2
1
1
1
1
0
0
2
1
1
2
1
1
1
1
1
2
0
1
2
2
1
2
1
2
2
2
0
1
2
0
1
1
2
2
1
2
2
2
2
1
0
1
1
1
2
2
2
1
2
1
1
1
1
2
1
1
0
1
2
1
1
1
1
3
1
1
1
1
1
1
1
0
0
1
0
1
0
1
1
1
1
0
0
1
1
1
0
1
1
1
2
1
2
2
2
2
0
1
1
2
1
1
1
1
1
1
1
2
2
1
1
1
2
2
1
1
1
1
3
1
1
1
0
1
0
0
0
2
2
1
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
0
1
1
2
1
0
1
2
1
1
2
0
1
1
1
1
2
1
1
1
1
1
2
3
1
1
1
1
2
0
1
1
1
2
2
1
0
1
2
1
1
1
1
2
1
1
1
1
1
1
0
0
1
2
2
0
2
1
0
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
2
2
1
2
2
1
1
1
2
1
1
1
1
1
1
1
1
3
0
1
1
3
1
1
2
1
2
2
0
0
0
1
1
1
2
2
1
1
1
2
1
1
1
2
1
1
1
1
1
2
2
1
1
1
1
0
1
1
1
0
1
1
1
2
1
0
1
0
3
2
2
1
1
1
1
2
1
1
1
2
1
1
2
1
2
0
2
1
2
1
2
1
2
1
1
1
2
1
1
1
1
1
0
0
1
1
2
2
1
1
2
2
1
1
0
1
2
1
1
2
1
2
2
1
1
1
1
1
1
2
2
1
2
0
2
1
1
2
1
1
0
2
1
1
1
1
1
1
1
1
1
2
1
2
0
1
0
2
1
1
1
1
2
2
0
1
2
2
1
2
1
0
1
1
2
1
0
1
0
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
0
0
1
0
1
1
1
2
1
1
1
1
0
1
1
1
1
2
1
1
2
0
1
1
1
1
0
2
1
1
0
1
1
2
1
1
0
1
1
1
1
1
1
1
1
2
1
2
1
1
3
1
1
0
2
2
1
1
1
1
1
0
2
1
3
1
0
2
1
1
2
0
2
2
2
1
1
2
1
1
1
1
1
2
1
1
2
2
2
1
1
1
1
1
2
0
2
1
1
1
0
2
1
1
0
2
2
1
1
1
2
2
1
1
0
1
1
0
1
1
2
1
1
2
1
1
0
2
1
2
0
1
2
0
1
1
1
1
1
1
1
1
1
2
2
2
1
1
2
0
2
1
1
1
0
1
0
1
1
1
1
2
1
1
1
1
1
1
2
1
1
2
1
0
1
2
1
1
1
1
0
1
1
2
1
1
2
1
1
1
0
2
0
1
2
0
1
2
1
1
1
1
1
2
1
1
1
2
0
1
2
2
2
2
2
3
0
1
2
1
2
2
1
0
1
1
1
2
1
2
2
1
1
1
2
1
1
0
1
2
1
1
0
2
2
2
1
1
1
1
1
2
1
1
1
1
1
0
1
1
0
2
1
1
1
1
1
0
2
1
1
2
1
1
1
1
1
1
1
2
1
2
2
1
1
1
0
1
1
2
0
0
0
1
2
1
1
2
1
1
1
2
2
1
1
1
1
0
2
1
1
1
0
2
2
1
2
0
2
2
1
1
2
1
1
2
1
1
1
0
2
0
1
2
1
2
2
2
1
1
1
1
1
1
1
1
1
2
1
0
1
1
1
1
1
2
2
2
2
1
2
1
1
0
1
1
1
1
1
1
2
1
2
1
2
1
0
1
1
0
1
1
1
1
1
1
2
1
1
1
1
1
0
1
2
1
0
0
0
1
1
2
1
1
1
1
1
1
2
1
1
0
1
1
1
2
2
0
0
2
2
1
0
2
1
1
2
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
0
2
2
2
2
1
0
2
1
1
1
0
0
1
1
1
2
1
1
0
1
1
0
1
1
2
2
1
1
4
1
2
2
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
3
0
2
2
1
1
1
1
2
1
2
1
2
2
2
1
2
1
0
1
2
2
1
1
2
2
0
1
2
1
1
1
1
2
1
1
1
1
2
1
2
1
0
1
1
1
1
1
1
1
2
1
1
2
0
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
1
1
1
2
2
1
1
1
1
1
2
1
1
2
0
1
1
1
1
1
1
2
1
1
1
1
0
1
1
1
2
0
1
0
2
2
0
1
2
1
2
1
2
1
1
1
0
1
1
1
1
0
1
1
2
1
1
1
2
1
1
2
1
1
1
1
1
2
0
2
1
1
1
1
1
1
0
2
2
2
1
2
2
1
2
3
1
2
1
1
1
1
2
2
1
1
0
1
2
0
0
1
0
1
0
2
1
1
3
1
2
1
2
1
1
2
1
2
2
0
1
1
1
1
1
2
1
2
0
1
1
1
2
2
0
1
1
1
1
2
2
1
1
1
3
1
1
1
1
1
1
1
2
0
0
2
0
1
1
1
1
1
2
1
0
1
1
2
2
2
1
1
1
2
1
1
2
1
1
0
1
0
1
2
1
1
1
2
1
0
1
0
1
2
1
1
2
1
1
0
0
1
1
1
1
1
0
1
2
1
1
2
1
1
0
1
1
0
0
1
2
1
1
1
1
1
1
0
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
0
1
1
0
2
2
0
2
1
2
1
2
1
0
2
1
1
2
2
0
1
1
2
2
1
2
1
1
1
2
1
1
1
0
1
1
2
1
1
1
0
1
1
1
1
1
1
2
0
1
0
2
3
1
1
1
1
2
1
1
2
1
2
1
1
1
1
2
0
1
1
1
2
2
1
1
1
1
2
1
0
2
1
1
1
2
2
1
0
2
1
1
0
2
1
0
1
1
0
3
1
0
2
2
1
2
0
2
1
2
0
2
1
0
2
1
0
1
1
1
0
1
2
1
1
2
3
1
1
1
1
2
1
2
2
1
1
1
0
2
1
1
1
1
2
1
1
1
1
3
1
1
1
1
2
2
0
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
0
1
1
1
2
1
2
2
1
1
1
1
1
0
0
2
2
0
2
0
0
2
1
1
0
0
2
1
2
2
1
0
1
1
2
1
1
2
1
1
1
1
2
1
0
1
1
1
1
2
1
1
1
1
0
1
1
1
2
1
1
0
1
1
1
1
1
1
1
2
2
2
1
2
1
1
1
1
2
2
1
2
1
1
1
1
2
2
1
1
1
1
1
1
1
0
1
2
1
3
1
1
0
2
2
2
1
1
1
1
1
1
0
1
0
1
1
1
1
1
2
0
1
2
2
0
1
0
3
2
0
0
0
1
1
2
1
2
1
1
1
2
2
1
2
2
1
1
2
1
1
1
2
1
1
0
1
1
1
2
1
2
1
2
1
2
2
1
1
1
1
1
1
2
1
0
1
2
1
1
2
1
2
1
1
2
0
1
0
1
0
1
1
2
1
4
2
1
2
1
1
1
1
2
2
1
2
1
2
1
1
1
1
1
0
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
2
2
1
3
1
1
1
2
3
1
2
1
0
1
1
0
1
1
2
2
2
2
1
1
1
2
1
1
2
1
1
0
2
2
1
1
1
2
1
1
1
0
1
2
1
1
1
2
1
1
2
1
1
1
2
4
2
1
0
1
1
1
1
1
1
1
1
2
5
1
1
2
1
1
0
1
1
1
1
0
3
1
1
1
1
1
0
1
1
1
1
1
1
3
1
1
0
3
2
1
1
0
1
1
2
2
2
1
1
0
1
1
1
1
1
1
0
1
1
1
1
1
0
2
2
1
1
1
1
2
1
0
2
1
0
1
1
1
1
2
2
0
0
0
2
2
2
1
2
1
1
1
1
1
0
1
1
1
2
1
1
1
2
1
1
2
1
1
2
2
2
1
1
2
1
1
2
2
1
2
0
1
1
1
1
2
2
1
3
1
1
1
1
1
1
1
1
0
1
1
1
0
2
2
1
1
2
2
1
0
1
0
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
0
2
2
1
1
1
2
0
1
2
1
1
1
1
1
2
2
1
1
1
2
1
1
2
1
2
1
0
1
1
1
1
1
1
2
0
1
1
1
2
2
2
0
0
0
1
1
2
0
1
0
1
1
1
0
1
1
1
0
2
2
1
2
2
0
1
1
1
2
0
1
1
1
2
1
1
1
1
1
1
1
0
1
1
1
1
2
0
2
1
1
1
1
2
0
0
1
1
1
2
1
1
0
1
1
1
2
0
1
2
1
1
1
1
1
1
0
2
1
1
1
2
0
1
1
1
1
2
1
0
1
1
1
2
1
1
2
0
2
2
2
0
1
2
1
1
2
2
1
1
1
1
1
2
0
1
1
1
0
0
2
1
2
1
1
2
1
1
1
1
1
0
0
0
1
0
2
1
2
2
1
1
1
2
0
1
1
1
1
2
2
2
1
0
0
0
2
2
2
1
2
1
1
1
2
3
2
2
2
1
0
1
2
2
1
1
1
1
2
0
2
1
1
1
0
1
2
1
0
1
2
0
1
2
2
1
1
2
1
1
1
0
1
1
1
1
1
1
1
0
1
1
0
2
1
1
2
1
0
0
2
0
2
0
1
1
1
2
1
2
1
1
1
1
1
2
2
0
2
1
1
1
1
2
2
0
2
1
1
1
0
1
2
1
1
1
2
1
1
1
0
0
1
3
1
1
2
2
1
1
1
1
0
0
2
0
1
0
2
2
1
2
1
2
1
2
2
1
1
1
1
2
1
1
1
2
2
2
1
2
2
1
1
2
2
2
2
1
1
0
2
0
1
2
0
2
1
1
1
0
1
1
1
1
0
1
1
1
1
2
1
2
1
1
1
1
0
1
1
1
0
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
0
1
1
1
2
1
1
1
1
1
1
2
1
0
2
1
2
1
1
1
1
1
2
0
1
2
1
2
2
1
1
1
2
1
1
1
1
1
2
1
0
1
1
1
1
1
2
1
1
0
1
1
2
2
1
1
2
1
1
2
1
2
1
1
1
1
2
1
1
1
1
1
3
1
2
2
1
1
1
1
1
2
0
1
1
2
1
2
1
1
1
0
2
1
2
2
1
2
1
1
1
1
2
0
1
2
2
1
2
1
1
0
1
2
0
1
1
2
2
2
1
1
1
2
1
1
1
1
1
1
0
1
1
1
1
1
1
1
2
2
1
1
1
1
2
1
1
1
0
1
2
1
1
2
2
0
1
2
2
1
2
2
0
1
1
2
1
1
0
2
2
1
2
0
2
0
0
1
1
0
1
1
1
1
2
1
1
1
0
1
2
2
1
1
1
2
0
2
1
1
1
2
0
1
2
1
2
1
1
2
1
1
1
1
1
1
1
2
2
0
2
1
0
1
1
1
1
1
2
1
1
2
0
1
1
1
1
1
2
1
2
2
1
0
1
2
1
1
2
1
3
0
1
1
1
1
0
1
1
1
1
1
1
2
2
1
2
1
2
1
2
1
1
0
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
2
1
1
0
2
1
1
1
1
1
2
2
1
1
2
0
1
1
2
1
2
2
1
2
1
2
0
1
1
1
1
1
1
1
2
2
1
2
2
2
2
1
1
0
1
1
2
1
1
1
1
0
2
2
1
1
1
1
2
2
1
1
0
1
2
2
1
0
1
2
1
6
1
0
1
1
1
0
1
1
1
1
1
2
1
1
1
1
0
1
1
1
1
1
1
1
2
2
2
1
2
2
1
0
1
1
1
1
2
1
1
1
1
1
1
1
0
1
1
1
1
1
0
2
2
1
1
2
1
0
1
1
2
1
0
1
1
2
2
1
1
1
1
0
1
2
1
1
1
1
0
1
0
1
1
1
1
2
0
2
1
2
1
2
2
1
0
2
2
1
1
1
2
1
2
1
1
1
1
1
0
2
1
1
1
1
1
2
0
1
2
1
1
1
1
2
2
0
0
2
1
1
1
2
1
2
1
1
1
1
1
2
1
1
2
1
1
2
2
1
1
2
2
1
1
2
1
1
2
1
1
2
1
1
2
1
0
1
1
1
2
0
2
2
2
1
1
1
1
1
1
0
2
1
0
1
0
1
1
1
1
2
1
1
1
1
0
2
2
1
0
1
2
2
0
1
1
1
1
1
2
1
2
1
1
2
1
2
2
1
1
1
1
0
2
1
1
2
1
1
2
1
1
0
1
1
1
1
1
1
1
2
1
2
1
1
1
1
2
2
1
1
1
2
1
2
2
0
0
1
4
2
1
0
1
1
1
1
1
1
2
0
1
2
1
0
1
1
1
2
1
0
1
1
1
1
1
1
1
2
2
1
1
1
1
1
4
2
1
0
1
1
2
3
1
1
2
0
1
1
0
1
1
1
1
2
2
1
1
2
2
2
2
2
0
2
2
2
2
0
0
2
1
1
1
1
1
0
1
0
0
1
1
0
1
1
0
1
1
1
2
1
2
1
1
1
1
1
1
1
1
0
1
1
0
2
1
5
1
1
1
1
1
2
1
2
1
1
1
0
1
1
1
1
1
2
1
0
1
1
0
1
2
2
1
2
1
0
1
1
2
1
1
1
1
2
1
1
2
2
1
1
1
1
1
2
1
2
1
0
0
1
1
1
1
2
2
1
2
1
2
2
0
1
1
1
1
1
1
1
2
2
0
1
1
2
0
2
1
2
2
1
1
1
2
1
0
1
2
1
1
1
2
1
2
2
1
0
1
1
2
1
1
1
1
1
1
2
0
1
1
1
0
1
1
1
1
2
0
1
1
2
2
0
2
2
1
0
1
1
1
1
2
2
2
2
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
0
1
0
0
2
1
0
1
1
2
0
1
2
0
0
1
1
1
2
1
1
1
1
2
1
1
1
1
1
0
1
1
1
2
2
1
1
2
1
1
1
1
2
2
2
2
1
2
1
2
1
0
2
0
1
2
1
1
2
1
2
1
1
1
0
2
1
2
2
0
1
1
1
1
2
1
1
2
1
2
1
1
0
1
0
0
2
2
2
0
1
1
2
1
2
1
1
0
0
1
0
1
2
1
1
0
0
1
2
1
1
1
1
0
1
0
2
0
2
1
0
1
1
1
2
1
1
0
1
1
1
2
1
0
1
0
1
0
1
1
1
1
1
1
1
3
2
1
2
2
1
2
2
2
1
2
1
2
2
2
1
1
3
2
1
1
1
1
0
1
1
2
1
2
1
2
1
1
2
1
0
1
2
1
2
1
1
1
1
2
1
1
2
1
2
1
1
3
2
1
2
1
1
0
0
0
1
2
2
1
1
1
1
1
1
1
1
1
0
1
0
1
2
0
0
2
1
1
1
1
2
1
0
2
1
2
1
1
1
2
1
1
2
2
1
1
1
1
2
2
1
1
1
1
2
1
2
1
2
1
1
2
1
1
2
1
1
1
2
1
0
2
0
1
1
1
1
0
2
2
1
1
1
1
1
1
1
1
2
2
2
2
1
1
1
0
0
2
1
2
1
1
0
1
1
0
1
1
2
0
1
1
0
1
0
2
1
1
2
2
1
1
2
2
1
1
1
1
1
1
1
2
2
2
0
1
2
1
2
1
0
0
1
1
1
2
1
0
1
1
0
2
1
2
0
2
1
0
0
1
1
1
1
2
2
1
1
2
1
2
1
0
1
1
2
1
2
1
2
1
0
1
1
2
3
1
1
1
1
1
1
1
2
1
2
2
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
0
1
1
1
0
2
1
1
0
0
2
1
1
1
1
1
0
1
2
1
1
1
1
0
1
2
2
0
0
1
2
0
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
0
0
0
1
1
1
1
1
1
1
1
2
1
0
0
1
1
1
0
1
3
2
1
2
1
1
1
0
1
1
0
1
0
0
1
1
0
1
1
0
2
2
2
1
0
2
2
1
1
1
1
2
1
1
1
1
1
1
2
0
1
1
1
1
1
1
1
1
0
0
2
2
1
2
2
0
1
1
1
1
2
0
2
0
1
0
1
1
0
2
1
1
2
1
2
1
1
1
1
1
2
1
2
1
1
1
2
1
1
2
1
0
1
1
2
2
1
1
1
1
2
1
1
1
2
1
1
0
2
1
0
2
2
1
2
0
1
1
1
1
0
1
2
1
1
0
1
1
1
0
1
2
1
1
1
3
2
1
1
1
2
2
1
1
0
2
1
2
1
2
2
0
1
0
1
1
1
1
2
1
1
0
1
1
0
1
0
1
0
2
1
3
1
1
1
1
1
1
1
0
0
1
1
2
2
1
2
2
1
1
1
1
1
1
2
2
1
1
1
1
0
2
1
2
1
1
2
1
1
1
1
2
2
1
1
1
1
1
1
2
1
1
1
0
1
1
0
2
2
1
2
2
1
1
1
1
2
1
1
2
4
1
1
1
1
1
1
1
1
1
1
1
1
2
2
0
1
1
0
1
1
1
1
2
2
2
1
2
1
1
1
1
0
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
2
0
0
2
0
1
0
2
1
2
0
0
1
1
0
1
1
2
0
2
1
2
0
1
1
0
1
1
2
2
1
1
2
1
1
2
1
0
1
1
0
1
2
1
1
1
1
1
2
1
2
2
2
0
0
1
1
2
1
1
1
1
1
1
1
1
2
1
0
1
1
1
1
2
1
1
2
1
2
1
0
1
1
2
0
1
2
1
1
1
1
2
0
0
1
1
1
1
0
1
2
1
2
2
1
1
1
2
2
2
1
0
2
0
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
0
2
2
1
1
2
2
1
1
1
1
1
1
2
2
1
2
3
2
1
1
1
1
0
1
1
1
1
2
1
1
2
0
1
1
1
2
2
1
1
1
1
0
1
2
1
1
2
2
2
1
2
2
1
1
0
1
2
1
1
1
2
1
1
2
1
1
1
2
1
0
2
1
2
1
0
0
0
1
2
1
1
1
1
2
1
2
1
2
0
2
2
2
2
2
0
1
0
2
1
1
1
2
1
1
0
1
1
1
2
2
1
1
1
0
0
0
1
0
2
1
1
1
2
2
2
1
2
0
1
1
2
1
2
1
0
1
2
1
0
1
1
1
1
0
1
2
1
1
1
0
1
0
1
1
2
0
2
0
2
1
1
2
2
2
2
5
1
1
2
1
1
2
1
2
1
1
2
1
1
2
1
1
1
1
1
2
2
2
1
1
1
2
1
1
1
2
2
2
0
1
2
1
2
2
1
1
2
1
2
1
0
2
2
1
2
1
1
1
3
0
2
1
1
1
0
2
1
0
2
1
1
1
1
0
0
1
1
2
0
1
1
0
2
1
2
2
1
1
1
1
1
2
1
2
2
0
1
2
1
1
2
2
2
1
2
2
1
1
2
1
1
2
2
2
2
1
1
1
1
1
1
1
0
1
1
2
1
1
2
0
0
1
1
1
1
0
0
1
1
2
0
1
2
1
1
2
2
1
1
1
1
1
1
3
1
2
0
1
1
2
1
1
1
1
2
2
1
2
0
1
2
0
1
2
1
0
2
1
1
2
0
0
0
1
1
0
2
2
2
2
1
1
1
1
1
0
2
1
1
2
1
2
0
2
2
1
2
1
0
2
1
2
2
1
1
1
1
1
0
2
2
2
1
1
1
1
1
2
1
2
1
1
1
0
0
2
0
1
2
1
2
0
1
1
1
1
2
1
2
2
1
2
1
1
1
1
1
1
1
1
1
2
1
0
0
1
1
1
2
2
1
1
1
1
1
1
1
2
0
2
1
0
0
1
0
1
1
2
2
1
1
2
1
2
1
1
2
1
2
0
0
1
1
2
2
1
2
1
0
1
1
0
2
2
1
1
2
1
2
1
1
0
1
2
1
1
1
1
1
1
0
1
1
1
1
1
2
1
2
1
1
2
1
0
1
1
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
0
1
2
1
1
1
2
2
1
2
1
2
1
2
1
2
1
0
1
1
1
0
2
1
1
0
2
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
2
2
1
0
2
1
1
2
0
0
0
1
1
1
0
0
2
2
1
3
1
1
1
1
1
1
2
2
2
2
1
1
2
1
1
1
0
1
1
2
1
1
0
2
0
1
1
0
2
0
1
1
3
1
0
1
1
2
1
1
1
1
1
1
1
1
2
1
2
0
2
2
2
1
1
2
1
0
1
1
2
2
3
1
0
1
1
1
1
0
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
2
2
1
2
1
0
1
2
1
1
2
1
0
1
1
1
1
2
2
2
1
1
1
2
1
0
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
1
2
1
1
2
1
1
0
1
1
1
1
0
1
1
2
2
2
1
1
0
1
1
1
1
1
1
1
2
1
1
2
0
1
1
1
2
1
0
1
1
1
1
1
1
2
3
0
2
0
2
1
2
2
1
1
2
2
1
2
1
1
0
1
1
1
2
1
1
2
0
1
2
1
1
1
0
2
1
2
1
1
1
0
2
1
1
2
2
2
1
1
0
1
1
1
1
1
1
1
2
1
1
2
2
0
1
1
1
1
2
1
1
2
1
1
2
2
1
1
1
0
2
1
2
1
1
2
0
1
1
1
0
2
2
2
0
1
1
1
1
0
1
2
1
3
1
1
1
0
1
1
1
1
2
1
0
2
1
1
2
2
1
0
1
0
1
1
1
1
1
2
0
1
0
0
2
0
2
1
1
2
1
0
2
1
1
1
2
1
2
0
2
2
1
2
1
1
2
0
1
1
1
1
1
1
1
0
1
2
1
1
1
1
1
2
2
0
1
1
2
0
1
2
2
1
0
1
2
1
1
1
0
1
1
2
2
1
1
2
1
1
1
2
3
2
1
0
1
1
1
1
2
1
1
1
2
1
1
1
0
1
1
0
2
2
1
0
1
1
2
1
1
2
1
1
1
0
1
1
1
0
1
1
0
1
1
1
2
1
0
1
1
1
1
1
1
1
0
1
2
0
1
2
1
2
1
0
1
1
0
1
2
1
1
2
1
1
0
1
2
1
1
1
1
1
1
2
1
0
1
1
0
1
2
1
1
1
1
2
0
1
1
1
2
1
0
1
1
1
1
1
1
2
1
0
0
2
1
1
1
1
2
1
1
1
2
0
1
2
2
2
2
1
2
1
2
1
1
2
2
1
1
1
2
1
2
2
1
0
2
1
0
1
2
0
1
1
2
1
1
1
1
1
1
1
1
1
1
1
0
0
0
1
1
1
2
0
2
1
1
2
1
2
0
2
1
1
1
2
1
1
1
0
0
1
1
1
1
1
1
1
1
1
1
1
1
0
2
1
1
0
2
1
1
1
2
1
1
1
0
1
1
1
1
1
1
0
1
1
1
2
2
2
2
1
1
1
1
1
1
1
2
1
2
2
0
1
2
2
2
1
1
1
1
0
1
2
1
0
1
1
0
2
1
1
2
1
0
0
2
1
1
1
1
2
1
2
1
2
1
2
1
3
1
0
1
1
2
1
1
2
1
0
2
1
1
2
1
1
1
1
2
2
1
1
1
1
1
2
1
2
1
2
1
2
0
2
1
2
1
1
1
1
1
2
2
2
2
2
1
1
1
1
1
1
1
1
1
2
1
1
0
1
1
1
3
1
1
1
1
1
2
1
2
1
1
2
1
1
2
0
1
1
1
1
2
1
1
2
1
1
2
2
1
1
1
0
1
2
0
1
2
1
1
2
1
2
0
1
1
2
2
0
0
2
1
1
1
1
0
0
2
0
2
0
0
1
2
1
2
2
1
1
0
2
0
0
1
2
1
2
2
1
2
0
2
1
1
1
0
2
1
1
0
2
1
1
1
1
1
0
1
0
1
1
1
2
1
1
0
1
1
0
1
2
1
1
1
1
1
2
2
1
1
0
2
2
2
1
1
2
2
1
0
1
1
1
0
1
2
1
1
2
1
2
1
0
2
2
1
2
1
4
2
1
1
2
0
2
2
1
1
0
1
1
2
2
1
2
1
1
1
0
1
2
1
2
2
1
1
0
1
2
1
1
1
1
1
0
0
0
0
2
1
2
2
1
1
2
2
2
1
0
0
2
0
1
0
1
1
1
1
0
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
0
2
1
1
1
1
1
1
1
1
1
2
2
1
0
1
1
4
1
1
1
1
0
0
1
1
1
1
2
1
2
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
2
0
1
1
1
2
1
0
1
1
0
1
1
1
1
0
1
2
1
1
1
2
0
1
2
0
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
2
3
1
0
1
1
1
0
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
2
2
1
2
1
1
1
0
2
1
2
0
0
2
1
0
0
0
1
1
1
2
1
2
1
2
2
1
1
2
1
1
1
1
1
1
1
1
3
1
0
2
1
0
1
1
1
2
2
2
2
1
2
1
0
1
2
1
0
0
2
1
1
2
0
2
1
0
1
0
1
1
0
2
2
1
2
2
2
1
1
2
2
1
1
0
2
1
1
1
1
2
2
2
1
1
1
1
1
1
2
2
2
0
1
1
1
1
1
0
2
0
2
1
1
1
1
1
1
1
0
1
2
2
1
1
1
2
1
0
2
1
1
1
1
2
1
2
1
0
1
0
1
2
0
1
1
1
1
1
2
1
2
1
2
1
1
2
1
0
1
1
1
1
1
1
1
2
0
1
0
1
1
1
1
2
1
1
2
1
1
2
0
1
2
1
1
0
1
0
1
1
0
2
2
1
1
1
1
0
2
1
1
2
1
1
1
1
1
2
1
1
2
2
1
1
1
1
2
1
1
2
2
1
1
0
1
2
1
1
1
1
1
2
1
0
1
1
0
1
0
1
1
0
1
1
1
2
0
2
1
1
1
1
1
2
1
1
1
1
2
1
1
0
1
2
0
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
0
1
0
2
1
1
2
2
2
2
1
1
2
1
1
1
1
0
2
1
1
1
1
1
1
1
1
1
1
0
2
2
1
1
4
2
1
1
1
1
1
2
1
1
2
2
2
2
2
3
1
2
0
1
2
1
1
2
1
2
0
2
0
1
1
1
1
2
0
2
1
1
1
1
2
0
1
0
2
1
2
1
1
1
1
3
1
1
2
1
1
1
2
1
0
2
0
1
1
0
1
1
1
2
1
1
1
0
2
2
2
0
1
1
1
1
1
2
2
1
2
2
1
1
2
1
2
0
1
2
1
1
1
1
2
0
2
1
1
1
1
2
1
0
2
1
0
1
1
0
1
1
1
1
2
1
1
2
1
2
0
2
4
1
2
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
2
1
2
1
3
1
1
1
1
1
1
0
1
1
2
2
2
2
0
0
0
2
2
1
2
1
2
2
0
1
1
1
1
1
1
0
0
2
2
2
2
1
1
0
1
0
2
1
1
1
2
2
1
1
1
1
1
1
2
1
2
0
2
1
1
2
0
1
1
2
1
1
1
2
1
2
1
2
1
1
1
1
1
2
2
1
1
1
1
0
2
1
2
1
0
2
1
1
1
1
2
1
0
1
4
1
0
2
0
1
2
1
2
2
2
1
1
1
2
1
1
2
0
1
1
2
0
1
1
2
2
0
2
1
2
1
1
1
0
1
2
0
1
0
1
1
1
1
1
2
2
1
0
1
0
1
1
1
2
0
0
1
1
2
0
1
1
2
0
2
0
1
1
2
2
1
2
1
3
2
0
1
1
2
1
1
1
1
1
1
1
2
1
2
0
0
1
1
1
1
0
1
1
1
1
0
1
1
2
1
2
1
1
0
1
0
1
1
1
2
1
1
1
1
1
0
1
1
1
1
0
1
1
2
2
1
1
2
1
2
2
2
2
1
1
1
1
0
1
2
2
0
1
1
2
0
1
0
1
1
2
1
2
1
2
1
0
0
1
1
1
1
1
1
1
1
4
1
1
1
1
1
1
2
1
0
1
1
0
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
0
1
1
0
2
2
1
1
1
0
1
0
1
1
1
1
1
1
1
1
1
1
0
1
1
2
1
1
0
1
2
1
1
0
1
1
0
1
1
1
1
0
1
2
2
1
1
1
2
1
0
1
0
1
0
1
0
1
0
2
2
2
1
1
1
1
1
1
2
0
2
1
1
1
1
0
0
1
2
1
1
1
1
2
2
2
2
1
1
1
1
1
1
1
2
2
0
2
2
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
2
1
1
0
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
0
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
2
1
1
2
1
1
1
0
1
1
1
0
1
0
1
1
1
1
1
1
1
0
0
1
1
2
0
1
1
0
2
0
1
1
2
0
1
2
1
1
0
2
1
1
1
0
1
1
2
2
2
2
1
2
1
1
1
1
1
1
0
0
0
1
1
1
1
0
0
0
1
1
1
0
1
1
1
2
2
2
1
1
0
0
0
0
1
0
1
1
1
0
1
1
1
2
2
2
2
1
1
1
1
2
1
1
1
2
1
4
1
1
2
2
1
1
1
2
2
1
0
2
1
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
2
1
0
0
1
1
1
1
2
1
0
1
1
1
1
0
0
1
1
0
1
1
1
1
1
2
1
1
0
1
0
1
1
2
2
1
1
0
0
0
2
1
1
1
2
1
1
1
1
0
0
1
0
1
0
1
1
1
1
2
1
2
2
2
1
2
0
1
1
1
1
2
1
1
0
2
2
0
0
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
1
2
1
2
2
1
1
1
2
1
1
1
0
1
1
1
2
0
1
2
2
1
1
1
1
1
2
0
1
1
1
1
2
1
2
1
2
2
1
1
0
1
0
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
0
1
1
2
1
1
2
2
0
1
1
1
2
2
1
0
1
0
1
1
2
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
0
0
1
2
1
0
1
1
1
1
0
2
1
1
1
1
2
2
1
1
1
1
2
1
2
1
1
1
2
0
1
1
2
2
1
1
2
0
1
1
2
1
2
2
2
2
1
1
2
0
1
0
1
2
1
2
2
1
0
2
1
1
1
1
0
0
1
1
1
1
1
1
1
0
1
0
1
0
0
1
1
1
1
1
1
1
2
0
1
1
1
1
1
1
0
2
1
1
0
1
1
0
1
1
2
1
2
2
0
6
1
0
2
1
1
1
1
1
1
2
1
1
1
1
0
1
2
2
1
2
2
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
0
2
2
2
1
0
2
1
2
1
0
1
2
1
1
1
2
0
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
2
2
2
2
1
1
1
2
2
1
1
1
2
2
1
2
2
1
2
1
1
0
2
0
0
2
1
1
1
2
1
1
2
1
1
2
1
1
0
2
4
1
1
1
0
0
1
1
1
2
0
1
1
2
1
2
2
1
1
1
1
2
5
2
2
2
1
2
0
1
2
1
1
2
1
2
0
0
1
1
2
1
1
1
0
2
1
2
1
1
1
1
2
1
1
1
1
1
0
1
3
1
1
1
0
1
1
1
1
1
0
1
1
2
1
2
1
1
1
2
1
0
2
0
2
1
1
2
0
1
2
1
2
2
1
1
1
2
1
0
0
2
1
1
1
0
2
1
1
1
1
2
1
2
2
2
1
1
2
0
0
1
1
2
1
1
1
0
2
1
1
2
2
1
1
1
1
1
0
0
2
0
1
0
1
1
1
0
1
1
1
1
1
2
2
2
1
1
1
0
1
0
1
0
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
0
0
1
1
2
1
0
1
1
0
1
1
1
1
1
0
2
1
1
2
1
1
1
1
2
1
1
2
2
1
2
2
1
1
1
1
1
0
1
1
1
0
0
1
2
2
1
1
1
1
1
0
1
1
0
3
1
2
1
2
1
1
1
1
2
2
2
1
0
1
1
1
1
1
1
2
1
1
1
0
2
2
1
2
1
2
0
2
0
1
0
1
1
1
1
0
1
0
1
1
1
0
1
0
1
1
1
2
2
0
0
2
2
2
1
1
1
1
2
2
1
1
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
2
1
1
2
1
2
1
1
1
1
2
0
1
1
1
2
1
1
0
1
2
2
1
0
1
1
2
1
0
2
1
2
1
1
1
0
1
1
1
1
0
1
0
1
1
1
1
2
2
2
2
1
0
1
2
0
2
2
1
2
1
2
2
1
1
2
0
1
1
1
0
1
0
1
1
1
1
2
1
2
1
2
1
2
1
0
0
1
2
1
1
1
1
1
2
1
1
1
1
2
2
1
0
1
0
1
1
2
2
1
2
2
1
0
2
1
1
2
2
2
2
1
1
1
1
2
1
1
1
0
2
1
2
1
2
1
1
2
1
2
1
1
1
1
1
0
1
1
2
1
0
1
1
2
2
2
1
2
1
1
1
0
0
1
2
1
1
1
1
2
1
1
1
0
1
1
1
2
2
1
2
2
1
0
0
1
0
0
1
1
0
1
2
0
2
0
1
0
1
2
1
0
0
1
1
2
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
2
1
1
2
0
2
2
1
2
1
2
3
2
2
1
1
1
2
2
1
0
0
1
1
1
1
2
1
1
1
0
2
0
1
1
1
2
2
1
1
2
0
0
2
1
1
1
1
2
1
1
1
0
1
1
1
2
1
2
1
1
1
0
1
1
0
0
1
0
1
1
1
1
1
1
2
1
2
1
1
1
2
1
2
0
1
0
2
1
1
1
1
1
2
2
2
1
1
1
0
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
2
1
2
2
2
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
0
1
0
1
0
1
2
1
2
1
1
2
1
1
1
1
1
1
1
1
0
1
1
1
2
1
1
1
1
2
1
1
2
2
2
2
1
2
2
0
3
1
0
1
2
0
1
0
0
1
1
0
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
0
1
1
1
1
1
0
2
1
1
1
1
1
2
0
2
1
0
0
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
0
1
1
2
2
2
2
1
1
3
2
1
1
0
1
2
1
1
1
2
1
1
2
1
1
2
2
1
0
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
2
1
1
1
1
0
1
1
1
1
2
1
2
2
2
2
2
2
1
1
1
1
2
1
1
1
1
1
2
1
1
2
1
2
1
2
0
2
2
1
2
1
1
0
2
0
1
0
1
1
1
0
0
1
2
2
1
1
1
0
2
2
1
2
0
2
0
1
2
1
1
1
1
1
2
1
1
1
1
1
0
2
1
0
2
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
2
1
1
1
1
1
1
1
2
3
0
0
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
0
0
2
1
1
1
1
2
1
1
2
1
2
1
2
1
2
0
0
1
1
0
0
1
1
1
1
0
1
0
0
2
1
2
2
0
0
2
0
2
1
2
1
1
2
1
1
1
0
1
1
1
1
2
0
1
1
2
0
1
1
2
2
2
1
0
0
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
0
1
2
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
2
0
0
2
1
1
1
1
2
1
1
1
1
1
1
0
1
2
1
0
2
0
1
1
1
2
1
1
3
0
1
0
2
0
1
1
1
2
0
1
1
2
0
2
2
2
0
2
2
1
1
1
2
1
1
1
2
1
1
1
0
1
1
1
0
2
1
1
1
1
1
2
2
2
1
2
2
0
1
1
1
1
1
1
0
1
0
2
1
0
2
1
0
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
0
1
1
1
2
1
1
1
1
2
1
1
1
0
2
0
1
0
1
2
1
1
1
2
2
1
1
1
1
1
1
2
1
1
0
2
1
1
1
1
2
1
0
1
0
2
1
1
0
1
1
0
1
1
2
1
1
1
1
1
1
0
2
1
1
0
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
2
0
2
1
1
1
1
2
1
1
2
1
1
1
2
2
0
1
1
2
1
0
1
0
1
1
1
1
0
1
2
1
1
2
1
0
2
1
1
1
1
1
1
2
1
1
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
2
1
1
0
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
2
0
0
2
1
1
2
1
1
1
1
1
1
2
2
1
1
2
2
1
0
1
1
1
1
1
1
1
1
1
1
0
2
0
1
1
0
1
1
1
2
1
2
0
2
1
1
1
1
1
1
0
0
2
1
1
1
1
2
1
1
1
1
2
0
1
1
1
1
0
0
0
1
1
1
2
2
1
1
2
0
2
2
2
0
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
0
2
2
0
0
1
2
1
1
2
2
0
1
1
1
1
1
2
1
2
2
1
2
1
1
1
1
1
0
2
2
2
1
1
2
1
1
1
1
0
1
0
1
2
1
1
1
1
1
1
1
1
1
2
1
1
2
2
1
0
1
0
1
2
2
1
1
1
1
2
2
1
1
1
1
0
1
1
1
1
1
0
1
1
1
3
1
2
1
2
1
0
1
2
0
1
1
1
1
1
0
1
0
1
2
1
0
2
0
2
1
1
0
1
2
1
2
1
1
2
1
0
2
1
1
1
0
1
2
1
2
2
0
1
1
0
2
1
2
2
0
1
2
1
2
0
1
1
2
2
2
1
1
1
2
2
1
0
0
0
2
1
0
1
2
1
1
2
1
1
1
1
1
0
2
2
1
2
2
1
0
1
1
1
2
1
2
1
1
0
1
1
2
2
2
0
1
1
1
2
1
1
1
1
2
1
2
2
0
1
1
1
0
2
1
1
2
0
1
2
1
1
1
1
1
1
1
2
1
2
2
1
2
1
2
1
1
3
2
0
1
2
1
0
1
2
2
2
0
2
1
1
1
1
1
1
1
1
1
1
1
1
0
2
0
1
1
1
0
4
1
1
0
1
2
1
2
1
1
1
0
1
2
0
1
2
2
1
1
2
2
0
2
0
1
1
1
1
1
1
6
1
2
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
0
1
0
1
0
1
2
1
1
1
1
1
1
2
2
1
0
1
1
2
0
1
2
1
0
1
2
2
0
1
1
2
0
1
1
1
2
2
1
1
1
1
2
1
1
0
0
1
1
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
0
2
1
1
0
1
1
0
2
2
2
1
1
1
1
2
2
1
1
1
2
1
0
1
2
0
1
1
1
1
0
1
0
2
1
1
1
0
0
1
2
1
2
1
1
1
3
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
2
1
0
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
0
0
2
1
1
1
1
2
1
1
1
1
2
2
1
0
0
0
1
1
2
1
0
1
0
1
2
1
1
1
1
1
2
1
2
1
1
2
2
0
0
1
1
1
2
0
0
2
1
0
0
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
0
1
0
1
1
1
1
1
0
3
2
1
2
2
2
1
1
1
2
2
2
1
1
1
1
1
2
2
2
2
0
1
1
1
2
2
1
2
1
2
1
1
1
2
0
2
1
1
1
1
0
2
1
1
2
2
1
2
2
0
1
1
2
1
0
1
1
0
1
1
2
2
2
1
1
2
1
1
1
2
1
0
2
1
2
2
1
1
2
1
1
1
1
1
0
1
1
3
0
2
1
1
1
1
2
1
2
0
1
0
2
1
2
0
1
1
2
1
1
2
0
1
0
1
1
1
1
2
1
0
0
1
1
0
1
1
1
2
1
2
1
1
3
1
1
1
1
0
1
2
1
2
2
2
4
1
1
1
1
1
1
0
1
0
2
1
2
2
1
1
1
1
0
1
1
0
2
1
0
1
2
1
1
1
1
1
1
1
0
1
2
0
2
1
2
1
0
1
3
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
2
0
2
1
1
2
2
1
1
1
2
2
1
2
2
2
1
1
0
2
1
0
2
0
1
2
2
1
0
1
1
1
1
2
1
1
1
2
1
0
2
1
1
2
1
1
1
2
1
1
0
1
2
1
0
2
0
1
0
1
1
1
1
1
1
1
1
2
1
1
0
2
2
1
1
1
0
1
1
2
2
1
1
1
2
0
1
2
0
1
1
0
1
1
1
1
1
1
1
0
1
1
1
2
1
1
1
1
0
0
1
2
0
1
2
1
2
1
1
1
1
1
1
0
1
1
1
1
2
0
2
0
1
1
1
2
2
1
1
2
2
2
1
1
2
1
2
0
1
1
1
1
2
1
1
1
2
2
1
0
1
1
2
1
1
2
1
0
2
1
2
2
1
2
1
1
2
2
2
0
1
2
1
1
3
0
1
1
1
1
2
4
1
1
2
2
1
0
1
1
2
2
1
1
2
0
0
2
0
1
1
1
1
2
1
0
1
0
1
2
0
1
1
2
0
1
0
1
2
2
2
0
1
1
2
1
1
1
1
1
1
0
2
0
1
2
1
2
0
1
1
1
2
0
0
1
1
1
1
1
2
1
1
2
2
2
0
0
1
2
2
1
2
2
1
1
2
1
1
1
1
3
1
1
0
1
1
1
1
1
1
1
2
2
1
1
1
0
2
2
1
2
1
2
2
1
1
1
2
1
1
2
1
1
0
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
0
1
1
1
1
1
1
1
1
2
1
2
2
0
0
1
2
1
1
0
1
2
1
1
0
2
2
2
1
1
1
2
2
1
1
1
1
1
1
1
1
0
1
1
2
2
2
2
1
1
0
1
0
2
2
0
2
0
2
1
1
1
0
1
1
1
0
1
1
1
0
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
2
1
1
1
2
1
1
2
1
1
1
0
1
0
2
2
1
1
1
0
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
2
0
1
2
1
1
1
1
1
2
0
1
1
1
2
2
1
1
1
1
2
1
1
1
0
3
1
1
1
2
1
0
1
1
1
2
1
1
1
1
1
1
1
2
1
1
0
2
2
0
1
2
0
0
2
1
1
1
1
2
0
1
0
1
1
2
1
1
0
2
0
1
2
0
1
1
1
0
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
0
0
1
1
2
1
1
1
0
2
1
1
2
0
1
0
1
1
2
2
1
1
1
0
1
1
2
1
2
2
1
1
1
0
1
1
1
1
1
1
2
1
1
0
3
1
0
1
2
2
1
1
1
1
1
1
1
1
2
2
0
1
1
1
2
2
1
1
1
2
1
1
0
1
2
2
1
1
1
1
2
1
1
1
2
1
2
1
1
0
1
1
1
1
1
1
1
2
0
1
2
2
2
1
1
1
1
1
2
1
2
2
0
1
2
1
0
2
2
1
1
1
1
2
1
1
2
1
1
2
3
2
2
1
0
0
1
2
2
1
2
1
2
2
2
1
2
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
2
0
0
2
1
1
1
2
2
2
1
1
0
1
1
0
1
1
1
2
1
1
1
1
1
2
1
0
1
1
1
1
1
2
0
0
1
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
2
1
1
1
1
1
2
1
1
2
0
1
2
1
2
1
2
1
1
1
3
1
0
1
1
0
1
0
0
0
1
1
1
0
1
1
2
1
1
2
1
2
1
0
0
2
1
1
1
0
1
1
2
1
1
1
4
0
0
1
1
2
2
1
1
1
2
1
2
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
0
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
2
1
0
0
1
2
1
1
1
2
1
1
2
2
2
0
1
0
2
2
1
2
1
1
1
1
1
0
2
2
1
1
1
1
1
1
1
1
2
0
2
1
0
1
2
0
1
2
1
2
1
1
2
0
2
0
1
1
1
1
1
2
1
1
1
2
2
2
2
1
2
1
0
6
3
0
1
1
1
1
2
1
1
1
1
2
1
1
1
0
1
2
4
0
2
1
1
1
2
2
1
1
1
2
2
2
1
2
2
1
1
1
2
1
1
1
2
0
1
2
0
1
2
1
2
2
1
1
0
2
1
2
2
1
1
1
2
1
1
1
2
1
0
1
1
1
1
2
1
2
1
2
2
1
1
3
1
1
2
2
2
2
2
1
1
1
2
0
1
2
2
0
2
1
0
1
2
1
1
1
2
1
2
1
0
1
2
1
1
1
1
1
2
1
1
2
1
2
2
1
2
2
0
2
1
2
2
2
1
1
1
2
2
1
0
1
2
1
1
1
0
2
1
2
2
2
1
0
2
1
1
1
1
1
1
2
1
1
0
1
1
1
1
1
2
2
2
1
1
1
0
1
2
2
1
1
1
1
0
2
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
2
1
0
2
2
0
1
1
1
2
1
1
2
1
0
1
1
1
1
2
1
1
2
1
0
2
1
2
1
1
1
1
1
2
3
2
1
1
1
1
1
0
1
0
0
2
2
2
0
2
1
2
2
1
2
0
1
2
1
2
1
2
2
1
2
2
1
1
0
1
1
1
0
1
1
2
1
1
1
2
2
0
1
2
1
2
1
1
1
2
1
1
1
2
1
2
1
1
0
2
2
2
1
1
1
1
2
1
2
1
2
1
1
2
1
2
2
1
1
0
1
1
0
2
1
2
1
2
1
1
1
1
1
1
2
0
1
1
1
1
1
1
2
2
0
1
1
1
1
0
0
2
2
2
2
2
2
0
0
2
1
2
1
1
0
1
0
1
1
0
1
1
2
1
1
1
1
0
2
1
2
2
0
1
1
1
2
2
1
1
1
0
1
2
1
1
0
1
0
0
1
1
0
1
1
1
1
2
2
1
2
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
0
1
1
0
1
1
2
1
2
2
1
0
1
1
0
0
0
1
1
2
0
2
1
1
1
1
2
1
1
1
1
2
1
2
2
1
2
1
1
2
1
2
1
1
1
1
3
1
1
0
1
1
0
2
2
0
1
1
2
1
1
0
1
1
1
1
1
1
2
2
1
1
2
2
1
2
1
2
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
0
2
2
1
1
2
1
0
2
1
1
2
1
2
1
1
1
1
1
2
2
0
2
2
1
0
1
1
1
1
2
2
2
0
1
2
1
0
1
2
1
2
2
1
1
1
2
1
1
1
1
1
2
2
1
1
1
1
2
1
1
2
0
0
2
1
1
0
2
2
0
1
1
0
0
1
0
1
1
1
1
1
2
2
1
2
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
2
1
1
2
2
2
2
2
1
1
0
1
1
1
1
1
2
2
1
0
1
2
2
1
1
1
1
1
1
0
1
0
1
1
1
1
2
1
0
1
1
1
1
0
2
1
1
1
1
1
0
1
1
0
1
1
1
1
2
1
2
1
1
2
1
2
1
1
0
1
1
1
2
0
1
1
0
1
2
1
2
1
2
1
2
3
1
1
1
1
1
1
1
2
2
2
2
2
1
1
1
2
2
0
2
0
2
1
0
1
1
1
2
2
1
1
1
2
1
0
1
1
1
1
0
1
1
2
1
1
0
1
1
0
0
0
2
2
1
0
1
0
2
2
1
1
2
2
1
1
1
1
2
0
0
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
0
0
1
1
0
0
1
0
1
1
0
1
1
0
2
1
2
2
1
2
2
2
1
1
3
0
2
1
1
1
3
2
1
2
1
1
2
1
2
1
1
1
1
1
2
1
1
1
2
2
1
0
2
1
1
0
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
2
1
0
1
1
1
1
1
0
1
2
1
1
0
2
1
2
1
1
1
2
2
1
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
2
0
0
2
0
1
1
1
1
0
2
1
1
1
1
2
2
1
0
2
0
1
1
2
1
1
2
2
2
1
2
1
1
1
1
1
1
1
0
2
1
2
1
2
2
0
1
1
0
0
2
0
1
1
1
1
1
1
1
1
2
1
0
1
2
1
1
1
2
2
0
1
1
2
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
2
2
1
0
1
0
1
1
1
1
0
2
1
0
2
1
1
1
2
2
2
1
2
0
1
2
2
1
1
0
2
2
1
2
2
1
2
2
2
2
2
1
2
1
2
2
1
1
1
1
1
1
0
1
0
0
0
0
2
1
0
1
1
0
1
1
1
2
2
1
1
1
0
1
2
1
1
1
1
2
1
1
0
1
2
1
1
2
1
1
1
1
1
1
2
0
2
2
1
1
1
2
2
1
2
1
1
1
1
1
2
1
1
0
1
0
1
1
0
1
0
0
0
1
0
2
1
1
2
1
1
1
1
2
1
1
1
2
2
1
1
1
2
2
1
0
0
1
2
1
1
1
1
2
1
2
2
2
2
1
0
2
0
2
1
1
2
0
1
2
2
1
1
1
2
1
1
0
1
1
2
0
2
1
1
2
1
0
1
2
2
1
2
1
1
1
0
0
2
1
0
2
1
1
1
1
1
1
1
2
0
0
1
1
2
2
1
0
0
1
1
2
2
1
1
1
0
1
1
1
1
2
2
2
2
2
2
1
2
1
2
2
1
2
1
1
1
1
1
1
2
2
1
2
1
1
1
1
2
0
1
1
1
2
1
1
0
0
1
1
1
1
1
0
2
1
0
1
1
2
1
1
0
0
1
0
1
1
1
0
2
1
3
1
1
1
3
1
2
2
1
1
0
1
2
1
1
0
1
2
0
1
1
1
1
2
2
1
1
0
1
1
1
1
1
2
1
1
1
1
1
1
2
1
2
2
1
0
1
1
1
2
0
1
1
1
2
1
1
1
1
2
0
2
1
2
1
1
2
2
1
1
1
0
1
2
2
1
1
1
1
1
2
2
2
2
1
0
2
2
1
0
1
2
2
1
1
2
2
2
2
1
3
0
1
1
0
1
1
1
1
1
1
1
1
1
1
0
2
1
1
2
1
1
1
1
1
2
2
2
1
1
1
0
1
1
1
0
1
1
1
1
1
1
0
1
0
0
1
0
2
2
0
0
0
2
1
1
1
1
2
1
1
1
2
1
0
1
2
2
1
1
1
2
1
1
2
0
1
2
0
1
1
1
1
1
1
2
2
0
1
2
1
2
1
2
1
0
2
1
1
1
1
0
2
2
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
0
1
0
1
2
2
1
2
2
0
1
0
1
1
1
0
1
0
0
2
1
1
0
2
1
2
1
1
2
2
1
1
1
0
2
2
1
1
2
1
1
2
1
2
1
0
2
1
0
2
0
2
2
1
2
2
1
1
1
1
1
2
2
1
0
2
1
1
1
0
2
1
1
2
0
1
0
1
0
2
1
1
1
2
1
0
2
1
2
0
1
1
1
0
0
2
1
1
2
1
1
1
1
1
1
0
1
1
2
1
1
1
1
0
1
1
2
2
1
2
1
1
1
0
3
1
1
1
0
1
1
0
2
1
1
1
1
2
3
1
1
0
1
2
1
1
1
0
1
1
0
1
1
1
2
1
1
1
0
1
1
1
1
1
1
1
0
1
1
1
1
2
1
2
1
1
1
0
2
1
1
2
1
1
0
2
2
0
0
1
2
0
3
1
1
2
1
1
1
1
0
2
1
0
1
0
2
1
1
2
1
1
1
2
0
1
0
2
2
1
0
2
2
1
1
1
1
2
1
0
1
1
1
1
1
2
0
1
1
2
1
1
1
1
2
2
1
2
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
2
2
1
1
2
2
1
1
1
1
1
1
1
1
0
1
1
3
1
1
1
1
2
1
1
2
2
0
1
1
1
1
1
1
1
1
2
2
2
1
0
2
0
2
1
2
2
1
1
2
0
0
1
1
1
1
1
2
1
0
1
2
0
0
1
1
1
1
2
1
2
4
2
1
1
1
3
2
0
1
1
1
1
2
1
1
1
1
1
1
1
0
1
0
1
0
2
0
0
1
2
0
2
1
2
1
1
2
1
2
1
2
1
1
2
1
1
1
1
2
1
1
2
2
1
2
2
1
3
1
1
1
1
1
2
2
1
3
1
2
2
1
1
1
1
1
0
2
0
1
1
1
1
2
1
2
1
1
0
0
1
1
1
2
1
0
0
1
1
2
1
1
1
1
2
1
2
2
2
1
2
3
2
0
1
0
1
2
2
0
1
2
2
1
2
1
2
1
2
1
1
1
1
0
2
2
1
1
1
1
0
1
1
2
1
1
2
1
1
1
1
2
1
2
2
2
1
1
2
2
1
0
2
1
1
1
2
1
1
1
1
1
2
1
0
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
0
1
1
1
0
2
1
0
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
2
2
2
1
2
1
2
1
1
1
1
0
1
1
2
2
2
1
1
1
1
1
1
1
0
1
0
2
2
1
1
2
1
1
1
1
2
1
1
2
0
2
0
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
0
1
1
0
1
1
1
1
3
0
1
1
1
1
2
2
1
1
0
1
1
2
1
1
2
1
1
1
1
1
1
1
1
2
2
0
2
0
1
2
1
1
0
1
1
2
1
0
0
1
1
0
0
2
1
0
1
1
1
1
1
2
0
0
1
1
1
1
0
1
2
0
1
3
2
1
1
1
1
1
1
1
0
1
1
1
0
1
1
1
2
2
2
2
1
2
0
2
2
2
2
1
2
2
1
1
1
2
1
1
1
2
1
2
1
1
1
2
2
0
1
0
2
2
1
0
2
1
2
1
1
0
2
2
1
1
2
1
1
1
1
1
2
2
0
0
1
2
2
1
1
1
1
0
1
1
2
2
1
1
1
0
1
1
1
1
1
1
1
0
2
2
1
1
1
2
1
0
0
1
0
1
2
1
2
1
2
1
0
1
2
1
2
1
0
0
1
1
1
1
2
1
1
1
1
1
1
0
2
1
1
1
0
1
1
1
1
2
1
1
1
2
1
2
2
1
0
2
1
2
1
1
1
1
2
2
2
1
2
0
1
1
2
1
1
2
2
2
0
1
1
1
1
2
1
2
1
0
2
1
1
1
1
2
2
1
1
1
1
1
1
1
1
2
1
2
1
1
0
0
1
1
0
0
1
1
1
2
1
2
1
3
1
1
0
1
1
1
1
1
1
1
0
1
0
1
1
1
1
2
1
2
2
0
1
1
1
1
1
0
1
2
2
1
1
1
2
1
1
1
1
1
2
2
1
1
2
2
1
1
1
1
1
0
2
2
1
1
1
2
2
0
0
1
1
1
2
1
1
2
1
1
2
2
1
1
1
1
0
1
1
1
1
2
2
2
1
0
1
1
2
1
1
1
0
1
0
1
1
0
2
0
0
1
2
1
1
1
1
1
1
1
1
1
0
1
1
0
2
1
0
1
1
1
1
2
1
2
1
1
2
0
1
1
1
2
1
1
1
1
1
0
1
1
1
0
1
2
1
0
1
1
1
2
0
1
1
1
1
1
0
0
0
1
0
1
2
1
1
1
1
1
0
2
1
0
1
0
1
2
2
1
1
1
0
1
1
2
1
2
4
1
1
0
0
2
0
1
1
1
2
1
1
1
1
1
2
1
1
1
0
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
2
2
1
1
1
0
0
0
2
1
1
2
2
1
1
0
1
2
1
1
1
1
1
1
1
2
1
1
1
0
1
1
2
0
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
0
1
2
1
1
1
1
1
1
2
1
1
2
1
1
1
1
2
2
1
1
2
1
1
1
2
1
1
2
1
1
2
5
1
1
0
1
1
0
2
1
2
2
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
0
1
1
2
2
2
1
2
1
1
1
1
2
1
1
2
1
1
0
2
1
2
1
1
1
2
1
2
2
0
1
2
2
3
0
0
1
0
2
2
2
2
2
1
1
1
0
2
1
1
0
1
1
2
1
0
2
1
2
1
2
1
2
1
2
1
2
2
0
2
0
1
0
1
1
1
1
2
1
2
1
1
1
1
2
0
1
1
1
1
1
1
2
4
1
1
0
1
1
1
1
1
0
2
1
1
2
2
0
2
1
1
2
1
1
1
1
2
2
2
2
0
1
1
1
1
1
1
1
2
1
1
1
1
1
3
1
1
2
2
0
1
1
1
1
2
1
1
1
1
1
2
3
2
0
1
1
1
1
2
2
2
1
1
0
2
1
1
1
2
1
2
1
1
2
1
1
1
0
2
2
1
0
1
1
2
1
1
2
0
1
2
1
1
2
1
1
0
1
2
1
1
1
1
1
1
2
2
0
0
2
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
2
1
0
1
1
1
1
1
1
2
2
1
1
1
2
1
0
2
2
1
2
1
2
2
2
1
1
0
2
1
0
1
1
2
1
1
0
1
1
2
1
1
1
1
0
1
1
2
0
1
0
1
1
1
2
1
1
1
0
2
1
1
1
0
0
1
1
0
2
0
1
1
1
2
1
2
2
1
1
2
1
1
1
2
2
1
0
2
1
1
1
2
1
1
2
2
2
1
1
2
1
1
2
1
1
2
0
1
2
0
1
0
1
4
0
1
0
2
1
2
2
1
3
0
2
1
1
1
0
1
2
1
1
1
1
2
1
2
1
2
1
1
2
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
2
2
1
0
1
1
1
0
2
2
1
2
1
0
1
1
1
1
2
2
1
1
1
1
2
1
1
2
2
0
0
1
1
1
1
2
2
1
1
1
2
1
0
1
2
2
0
1
2
2
1
1
1
0
2
0
2
0
1
2
1
1
1
1
1
1
0
0
2
1
1
1
1
1
2
1
1
2
1
0
1
1
1
1
1
0
1
1
2
1
2
1
1
1
1
0
1
2
1
2
2
1
0
1
0
0
2
1
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
2
0
0
1
1
1
2
1
1
1
0
1
2
1
2
2
0
1
2
1
1
1
2
2
1
1
1
2
1
1
1
1
1
0
0
1
1
2
2
2
1
2
1
2
2
0
1
2
2
1
1
1
0
0
1
1
0
1
1
2
0
1
1
1
2
1
1
1
1
1
0
1
0
1
1
2
2
1
1
1
1
1
1
2
2
1
0
0
0
1
1
1
1
1
1
1
1
2
0
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
1
2
1
1
1
2
0
1
0
1
2
0
1
1
2
1
1
1
1
2
1
1
2
1
0
1
1
1
2
1
0
1
1
0
1
1
2
2
1
0
0
2
1
1
2
2
2
0
1
2
2
1
2
1
2
0
1
0
0
2
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
0
1
1
0
0
2
0
3
1
2
1
0
1
0
1
0
0
0
1
1
0
1
1
0
1
1
1
1
1
2
1
0
2
0
1
1
1
1
2
1
1
1
0
1
2
2
0
2
1
1
1
2
1
0
0
1
1
1
1
1
2
1
1
0
0
2
1
2
2
1
0
3
0
1
1
2
1
0
1
1
0
1
1
2
2
1
0
2
1
1
2
1
0
2
0
1
1
1
0
1
1
2
1
1
0
2
3
1
1
1
2
2
0
1
1
1
1
1
1
2
1
1
2
0
1
0
1
1
2
1
1
2
2
2
1
1
1
0
0
0
2
1
1
1
0
2
2
1
1
1
2
1
1
1
1
1
1
1
2
1
0
0
1
1
1
1
1
0
2
1
2
1
1
2
1
1
0
1
0
1
1
1
0
1
1
2
1
1
2
0
0
0
1
2
0
1
0
1
0
1
1
1
2
1
1
1
1
2
1
0
1
2
1
2
1
1
2
2
1
1
1
1
2
1
0
0
1
2
1
2
1
1
1
1
0
1
1
1
1
1
1
2
1
0
1
1
2
0
2
1
2
2
2
2
1
2
1
0
0
0
2
0
1
0
1
1
1
1
0
1
1
2
0
1
1
1
1
0
1
0
1
2
2
2
0
1
1
2
0
1
1
2
1
2
0
2
1
2
1
2
2
1
1
0
2
2
1
1
2
1
2
2
1
2
2
2
1
1
0
1
1
0
2
1
1
2
1
1
0
1
0
2
1
0
2
1
0
2
0
0
0
2
0
2
1
1
0
1
1
2
1
2
1
2
1
2
1
1
2
1
2
1
2
2
0
1
1
2
2
2
1
1
1
1
0
1
2
2
1
0
1
2
2
2
1
2
1
0
1
1
0
2
1
2
1
0
1
1
0
2
0
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
2
2
1
1
1
0
1
1
2
2
1
1
1
1
1
2
1
0
1
0
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
0
0
2
2
2
2
2
1
1
1
1
1
1
2
1
1
2
1
1
1
1
2
1
1
2
1
1
1
0
2
1
2
1
1
2
1
2
1
2
1
1
2
2
1
2
1
1
1
1
0
2
1
1
1
1
1
1
1
2
0
0
1
1
1
2
2
2
1
1
1
1
1
1
1
1
2
1
2
1
1
1
0
1
0
1
1
1
1
0
2
1
0
1
1
2
0
2
0
2
1
2
2
1
1
2
1
1
1
2
0
1
0
1
0
2
1
0
0
1
1
1
1
1
0
1
0
0
2
1
0
1
1
1
1
1
1
2
1
1
0
2
2
1
1
0
1
0
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
2
2
3
2
0
0
1
0
2
0
1
0
1
1
2
1
0
2
1
1
1
2
1
2
2
1
2
1
2
1
2
0
1
2
1
1
2
1
0
1
0
0
1
0
0
2
1
2
1
1
1
1
3
1
1
2
2
1
2
1
1
1
0
1
0
1
2
1
2
1
1
1
1
1
0
1
1
1
1
1
0
1
2
1
0
0
1
1
1
2
1
1
0
1
1
0
2
2
1
1
1
1
1
0
1
1
1
1
1
2
2
2
0
1
0
1
1
1
1
1
1
1
0
1
1
1
1
2
1
1
1
1
1
0
2
2
1
1
1
1
1
0
1
1
1
2
1
1
2
1
2
1
2
0
1
1
1
2
1
0
1
2
1
1
1
2
1
1
2
1
1
0
1
1
1
2
1
1
1
2
2
1
0
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
0
1
2
2
1
1
1
1
2
1
1
1
1
1
1
1
2
2
0
1
1
1
1
0
2
1
2
1
0
1
1
1
1
1
2
1
1
1
4
1
0
1
2
0
0
2
1
1
0
1
1
2
1
2
1
1
1
1
1
2
1
2
1
1
1
0
2
1
1
1
1
1
1
1
2
1
2
2
2
2
2
1
0
2
1
1
1
0
1
1
1
1
2
1
1
2
2
0
2
2
2
1
1
2
0
0
1
2
1
1
1
1
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
2
0
2
2
1
1
1
1
1
2
1
0
0
1
1
0
1
1
1
1
1
1
1
0
2
1
1
2
2
0
2
1
1
0
2
1
1
0
1
2
1
2
2
2
1
2
1
1
1
0
1
1
1
2
2
1
0
2
1
1
1
2
1
1
2
1
2
2
2
1
1
2
1
2
1
2
2
1
0
2
1
1
2
1
1
0
1
1
1
2
2
0
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
0
1
0
1
1
1
1
0
0
1
1
0
1
1
2
1
2
1
1
1
2
2
3
1
1
1
1
1
1
1
0
1
1
2
1
1
1
1
0
1
2
1
1
2
1
2
1
1
1
1
2
1
0
0
1
1
2
1
0
1
2
1
2
1
2
1
2
1
1
1
1
0
1
1
2
0
1
1
1
1
2
1
0
2
1
1
1
1
1
1
0
0
1
1
2
0
1
2
2
0
1
1
1
1
1
1
2
2
1
2
1
1
1
1
1
2
1
1
1
1
2
1
0
1
1
1
1
0
1
1
0
0
3
2
1
1
1
2
1
1
1
1
1
1
1
1
1
2
0
0
2
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
2
2
1
1
2
1
0
1
2
1
1
2
0
1
1
1
2
2
0
1
1
2
2
1
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
0
2
1
0
0
1
0
0
1
2
2
0
2
1
3
1
2
2
2
2
2
1
1
1
2
1
0
2
2
1
1
1
2
1
1
1
2
1
2
1
2
1
1
1
0
1
2
1
2
2
1
2
1
1
2
2
1
1
1
1
1
1
1
1
0
2
0
1
1
1
0
1
2
1
2
1
1
1
1
2
1
2
1
1
0
0
1
1
0
1
0
1
2
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
0
1
1
1
2
2
2
1
0
1
2
0
1
1
1
1
1
1
0
0
1
2
2
2
1
2
2
0
0
2
2
2
0
1
1
1
2
1
1
0
1
1
2
2
1
1
1
2
0
2
1
1
2
1
1
2
0
1
1
1
0
1
1
2
2
1
1
1
1
1
2
1
1
1
3
1
1
2
2
1
1
1
2
0
1
1
1
2
1
1
1
1
2
0
1
1
1
1
1
1
1
2
1
1
0
1
1
1
2
2
2
2
2
1
1
1
2
2
1
1
0
0
1
2
1
1
1
1
1
2
1
0
2
2
2
1
2
2
1
1
1
1
2
1
2
1
0
1
0
2
1
1
1
2
1
1
0
1
2
1
2
1
1
1
1
2
2
1
0
1
1
1
2
0
0
2
0
2
1
2
0
1
1
1
2
1
1
1
1
3
1
1
1
1
0
0
1
2
1
2
1
1
1
2
1
1
1
1
2
0
2
2
1
2
2
1
1
2
0
1
1
1
2
2
2
1
1
1
1
2
1
2
1
1
1
1
2
0
1
1
1
1
1
1
2
2
2
1
0
1
2
1
1
1
1
2
1
1
2
2
1
1
2
1
2
1
1
1
0
2
2
1
1
1
1
1
2
1
2
0
1
1
2
1
1
2
1
2
2
1
1
1
1
1
2
1
2
2
2
1
1
0
1
1
1
0
2
1
3
2
2
0
1
1
1
1
1
0
2
2
1
1
1
1
1
2
1
1
1
1
1
2
1
2
2
2
0
2
2
1
1
1
1
2
1
1
1
1
2
1
1
2
2
1
2
1
1
1
0
2
2
0
2
1
0
1
1
1
2
2
1
2
1
1
2
2
1
1
2
1
1
1
0
2
1
2
2
0
0
1
1
1
2
2
2
1
1
1
0
1
1
1
1
1
1
1
1
2
1
2
2
1
2
1
2
2
0
2
2
1
1
2
1
2
1
1
1
1
3
1
1
2
2
1
1
1
2
2
6
1
1
1
1
1
1
1
0
1
2
2
1
1
0
1
1
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
0
1
2
1
0
2
2
1
1
1
1
1
0
1
2
1
0
1
0
2
0
1
1
1
0
0
2
1
2
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
0
2
2
1
1
1
1
0
0
2
1
1
1
2
0
1
1
1
0
2
1
1
1
0
1
2
1
2
1
2
2
0
0
2
1
2
1
1
2
1
1
1
0
2
1
2
2
2
1
1
1
1
1
1
1
0
0
2
0
0
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
2
0
2
0
1
1
0
0
1
2
1
0
1
1
2
1
2
2
1
1
2
1
1
1
1
1
1
1
1
0
2
2
2
0
1
2
1
1
1
2
1
2
1
0
1
2
2
0
2
1
2
1
1
0
2
1
2
0
1
1
1
1
2
1
1
2
1
3
1
0
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
2
1
2
1
1
2
2
1
2
1
1
1
2
1
1
2
2
1
0
2
1
0
1
1
2
1
1
1
2
1
2
2
2
1
1
1
1
1
1
2
1
2
1
0
1
1
0
1
1
1
1
1
1
2
1
1
2
1
1
2
1
1
1
2
1
1
2
2
2
0
1
1
1
0
1
1
1
2
1
1
2
1
1
1
2
2
2
1
2
1
1
2
1
2
1
1
1
1
2
2
1
2
0
1
1
2
2
1
1
2
1
1
1
2
1
1
1
1
0
2
1
1
2
1
2
1
2
0
2
2
2
2
1
2
1
2
0
0
1
1
1
1
1
0
1
2
1
0
1
2
1
1
1
1
0
1
1
0
1
1
2
1
1
1
1
0
1
1
1
1
1
2
1
1
1
0
1
2
0
1
2
1
1
0
1
1
0
2
2
1
1
0
1
0
0
2
2
2
0
2
0
2
0
2
2
1
1
1
1
1
0
1
2
1
1
1
0
1
1
1
2
1
0
2
2
2
1
2
1
2
1
0
2
0
0
0
2
2
1
1
2
1
2
2
1
1
1
1
2
2
1
1
2
1
2
1
1
1
1
1
1
1
1
0
1
1
2
1
2
1
1
2
1
0
0
1
1
1
1
2
2
2
2
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
1
2
0
1
1
1
1
1
3
0
1
1
2
1
0
0
2
1
1
2
1
1
1
0
0
1
0
2
2
2
1
1
1
1
3
1
1
0
0
2
1
1
1
1
1
1
0
1
2
1
1
2
1
1
1
2
1
1
1
3
2
2
2
1
2
2
0
1
1
1
1
1
1
1
1
1
1
1
0
0
1
0
2
1
2
1
2
1
1
2
1
1
0
2
1
1
1
0
1
2
1
2
1
1
0
2
2
1
1
1
2
1
1
1
2
1
1
0
1
2
2
0
1
1
2
0
2
1
2
0
2
2
2
0
1
1
1
1
0
1
1
1
0
1
1
1
1
1
2
0
1
2
2
1
1
1
0
1
2
0
1
1
0
1
1
1
2
1
2
1
1
1
1
1
2
0
1
2
2
2
1
1
2
1
0
1
0
2
1
1
0
1
1
1
2
1
1
1
1
2
1
0
2
1
1
1
1
1
1
1
2
1
2
1
2
1
0
1
1
0
1
1
1
1
1
1
1
2
1
2
1
2
1
1
1
1
1
1
1
0
2
2
1
1
5
1
1
0
2
0
1
0
1
2
0
1
1
1
1
1
1
2
1
1
1
1
1
1
1
0
0
2
1
2
2
1
1
1
1
2
1
1
2
2
1
1
2
1
2
2
1
1
2
1
2
1
1
1
2
1
2
2
1
1
1
2
1
1
1
1
1
0
0
1
2
2
2
1
1
1
1
0
2
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
1
0
2
2
1
1
1
1
1
2
2
0
0
1
1
1
0
1
1
1
1
1
0
1
1
1
1
2
2
1
1
2
1
2
1
2
2
1
1
1
0
1
2
2
0
2
2
1
0
1
1
1
2
0
1
1
2
2
1
1
1
1
0
1
1
1
0
1
1
2
1
1
0
0
1
1
1
1
1
1
1
2
2
1
1
1
1
3
0
2
2
1
1
1
1
2
0
1
1
1
0
1
1
1
1
0
1
2
1
2
1
1
2
1
1
2
2
1
2
1
0
0
1
1
1
1
1
0
0
0
2
1
1
1
2
2
2
2
1
1
0
1
0
2
1
1
1
1
1
1
2
1
1
1
1
1
0
0
1
0
2
1
2
1
1
1
2
2
2
0
2
1
1
1
2
2
1
2
1
2
3
2
2
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
2
2
2
2
1
1
2
2
1
2
2
0
1
1
1
1
1
1
2
0
2
8
1
0
1
2
1
1
1
2
0
0
1
1
1
2
1
1
2
1
1
1
1
1
2
0
4
2
2
0
1
1
0
2
0
1
1
1
2
1
1
2
2
1
0
2
2
2
0
1
1
2
1
1
2
1
1
1
1
1
0
1
1
1
0
0
1
0
1
1
1
2
1
2
2
1
0
0
1
0
1
1
0
0
1
1
2
2
1
1
0
1
1
1
2
1
2
0
2
1
2
1
1
1
2
0
0
2
0
1
2
1
1
1
1
1
2
1
1
1
1
4
1
1
2
1
2
1
0
2
1
1
2
1
2
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
2
2
0
1
2
2
1
1
1
1
0
2
2
1
1
0
2
2
1
1
1
0
1
1
1
1
1
1
1
1
1
0
1
1
0
1
2
2
1
0
0
1
1
2
1
1
2
1
1
1
1
0
2
2
1
1
2
1
2
1
1
1
0
2
1
2
1
1
1
1
2
2
0
2
1
0
0
1
1
1
0
2
1
1
1
1
1
1
1
2
0
0
1
1
1
2
1
1
1
3
1
1
2
1
2
1
1
2
0
2
2
1
2
2
0
2
2
1
2
1
1
1
1
1
1
1
0
2
0
1
1
1
0
2
1
1
1
0
2
1
2
1
1
1
0
1
1
2
2
3
2
0
1
2
1
1
2
1
0
1
2
1
0
2
0
1
1
1
1
1
2
1
1
1
1
1
2
1
2
2
1
1
2
1
2
2
2
2
0
1
2
1
1
1
0
0
1
1
0
2
1
0
0
1
1
2
1
1
1
2
2
1
1
1
1
0
1
1
2
1
1
1
0
0
1
0
1
1
2
1
0
1
1
2
2
1
1
2
2
1
2
1
2
1
0
1
1
1
2
0
2
1
1
0
2
2
2
1
1
2
1
1
1
1
2
1
0
1
1
4
1
2
1
1
1
1
1
1
2
0
2
2
1
1
2
1
1
1
2
1
2
1
2
1
2
1
1
2
1
1
1
1
1
2
1
2
2
1
1
0
1
1
0
1
2
0
1
1
2
1
2
1
1
2
2
1
1
1
1
2
1
2
2
2
0
1
1
1
2
0
2
2
1
2
2
1
2
1
1
1
0
2
1
2
1
2
1
2
0
2
1
0
1
2
0
1
1
2
1
2
1
2
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
2
2
1
2
1
0
1
1
1
2
2
1
2
1
1
1
2
1
1
1
2
0
0
1
2
1
2
1
2
1
2
2
0
0
2
1
2
2
0
1
2
1
1
0
2
1
1
2
0
2
2
1
2
1
1
2
0
1
1
2
1
2
1
1
1
1
0
1
1
1
1
1
2
2
1
2
2
1
1
1
2
1
2
2
1
2
1
1
3
0
0
2
2
2
0
1
1
1
2
1
0
0
0
2
1
1
1
1
1
1
1
2
1
1
1
1
2
2
1
0
1
1
1
0
0
1
2
2
0
1
1
1
1
1
1
1
2
2
1
2
2
0
2
2
2
0
2
1
2
2
1
1
0
0
0
1
1
0
1
2
0
1
1
1
1
1
2
0
0
2
1
1
1
1
1
0
0
0
2
1
1
0
1
2
2
1
1
1
1
1
1
1
1
1
1
1
0
1
2
1
1
1
1
1
2
1
1
2
1
2
1
1
1
1
1
1
0
1
1
0
2
1
1
2
1
1
0
1
1
2
1
2
1
1
1
1
1
2
0
2
1
1
1
1
1
1
1
0
0
1
1
1
1
2
2
1
1
1
1
2
1
2
1
2
1
1
0
2
1
1
1
1
1
0
2
0
1
2
1
2
1
1
1
1
1
1
1
0
1
2
2
1
1
1
1
1
1
0
1
2
1
1
0
1
1
0
1
0
1
1
2
1
0
1
2
1
1
1
1
1
1
1
1
1
1
1
1
0
2
1
2
2
2
1
1
0
2
1
1
1
1
0
1
1
0
2
2
1
1
1
1
1
1
1
2
2
1
1
2
2
0
0
1
1
1
1
2
2
2
1
2
1
1
2
1
0
1
0
1
2
1
1
1
1
2
2
0
1
1
0
1
0
2
1
2
2
1
2
1
1
2
2
1
1
1
1
1
2
0
1
1
1
2
1
1
1
0
1
1
1
1
1
1
1
2
1
0
0
1
1
1
2
2
1
2
2
0
2
1
1
2
1
1
1
2
0
1
3
1
1
0
2
1
1
1
0
1
1
1
1
2
1
1
1
1
2
1
2
1
1
0
1
1
2
1
1
0
2
1
1
1
1
2
1
1
1
1
1
1
2
0
1
1
2
1
0
1
1
0
1
1
0
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
0
0
1
2
1
2
1
0
1
1
0
1
2
1
1
0
1
2
1
2
2
1
0
0
1
0
2
2
1
1
1
2
1
0
1
2
1
1
1
0
1
1
2
0
0
2
1
1
1
2
1
1
1
1
1
2
2
1
0
1
1
1
2
1
1
1
0
1
1
0
0
0
1
1
1
2
2
1
1
1
2
1
1
2
1
2
1
1
1
1
1
1
2
1
2
1
2
1
1
2
2
0
2
1
1
1
1
1
2
1
1
1
2
1
0
2
1
1
2
1
1
1
1
1
1
1
0
2
1
1
1
1
1
0
1
1
2
1
1
1
1
1
0
1
1
1
1
1
2
1
2
1
1
2
1
1
2
2
1
1
1
2
2
2
2
1
2
1
1
1
2
2
1
1
2
1
2
1
1
1
1
1
1
1
1
2
3
1
0
1
1
1
1
0
1
0
1
1
1
0
1
2
1
0
1
1
1
0
3
2
1
1
1
1
0
1
2
2
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
0
1
1
2
1
1
1
2
3
1
2
1
1
0
2
1
1
1
1
1
1
1
0
1
0
0
1
0
1
2
0
0
1
1
2
1
0
2
2
2
1
0
0
2
0
1
2
1
1
1
1
1
0
2
1
1
1
2
1
1
2
1
1
1
2
1
1
2
0
0
1
1
0
1
1
1
2
0
2
1
1
0
1
1
2
0
1
1
1
1
2
2
1
1
2
2
1
1
0
1
1
1
1
2
0
0
0
1
1
1
0
2
1
2
1
1
1
1
0
0
1
2
2
1
1
2
1
1
2
1
2
1
1
1
1
1
2
2
2
2
1
0
0
2
0
0
1
1
2
1
0
1
2
1
1
2
1
1
0
0
1
1
2
1
1
2
2
2
1
2
1
1
1
1
1
2
0
1
1
2
1
1
0
1
2
0
1
1
1
1
1
1
2
2
0
1
2
2
1
2
1
0
1
1
1
1
2
1
1
1
0
2
1
1
2
1
0
1
2
1
0
1
1
1
1
0
2
1
0
1
1
1
1
2
0
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
0
1
1
0
1
2
2
0
2
1
1
2
2
0
2
2
1
1
1
1
1
1
1
1
1
1
2
0
2
1
1
1
1
1
1
1
1
1
2
2
2
0
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
0
1
2
1
1
1
1
1
0
1
1
3
1
1
2
1
2
1
1
2
2
2
2
1
1
2
1
2
0
0
2
2
0
2
1
0
1
0
2
1
2
1
0
0
1
2
1
2
1
1
2
1
1
0
0
1
1
1
1
2
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
0
0
1
1
1
2
2
1
2
1
2
1
1
0
1
1
1
0
2
0
1
0
2
0
2
1
1
2
1
0
2
1
1
1
1
1
2
1
2
2
1
1
2
0
1
0
1
1
0
1
1
0
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
2
0
1
2
1
1
1
1
0
2
2
1
1
1
1
1
2
1
1
2
1
0
2
1
2
1
1
2
2
1
1
2
1
1
1
1
2
1
1
2
1
0
2
1
2
1
1
2
1
1
1
1
1
1
2
0
1
1
2
1
1
2
2
2
1
1
2
2
1
2
0
1
1
1
0
1
1
1
2
2
0
1
0
1
0
1
1
1
1
3
0
2
1
0
1
1
1
1
1
1
2
2
1
1
1
0
2
1
2
1
1
2
1
1
1
2
1
1
2
0
0
1
1
2
2
1
2
1
2
1
1
1
1
1
0
1
2
1
1
1
0
0
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
0
2
0
1
2
1
1
2
2
1
1
2
1
1
1
0
1
1
1
2
0
2
1
2
1
1
1
2
2
1
1
0
1
2
1
1
2
1
3
2
1
1
1
0
1
1
2
1
1
3
1
1
1
2
0
1
1
1
2
1
2
1
0
2
0
2
1
2
1
1
2
0
0
1
1
1
1
1
2
0
1
1
0
2
2
1
1
0
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
0
1
1
1
1
2
1
2
1
1
1
1
0
1
2
1
1
1
1
1
1
1
1
1
2
1
2
1
2
2
2
2
1
1
1
1
2
2
2
0
1
1
1
1
0
1
1
1
1
1
1
1
2
1
1
2
1
1
1
2
0
1
1
1
1
1
1
0
1
2
2
1
2
1
1
0
1
2
2
1
1
1
2
1
2
2
1
1
0
1
1
2
1
2
1
2
2
2
1
2
1
1
1
1
1
1
1
1
2
2
2
1
0
1
1
2
1
0
2
1
0
1
2
1
1
1
1
0
1
2
1
0
0
1
1
1
1
1
2
0
2
2
1
2
1
1
0
1
1
1
1
1
1
0
1
0
1
2
2
2
0
1
0
2
2
0
1
2
1
1
1
2
1
2
1
2
1
0
2
1
1
1
1
0
1
1
0
2
1
1
0
0
0
1
2
1
0
2
1
2
1
2
2
1
1
1
1
1
2
1
1
3
0
1
1
1
1
2
2
2
2
0
2
2
1
1
2
1
4
1
0
1
1
1
1
2
2
1
1
1
1
1
1
2
0
1
1
1
1
1
2
2
1
1
1
1
2
0
0
1
1
0
1
1
1
0
0
0
1
1
1
1
1
1
2
1
1
2
1
2
2
1
1
1
1
1
1
1
2
1
1
0
1
2
1
2
2
1
1
2
1
1
0
1
1
1
1
1
1
0
0
2
1
2
1
1
1
1
1
0
2
1
0
1
2
2
1
0
2
1
1
1
2
2
1
1
1
1
1
1
2
1
1
2
1
0
1
2
1
1
1
1
1
2
1
0
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
0
2
1
1
2
0
1
2
0
1
1
1
1
0
1
1
2
1
1
0
1
1
1
1
2
2
2
2
0
1
0
1
2
1
1
2
1
0
2
0
2
2
0
1
0
2
1
0
0
2
1
1
1
1
0
1
2
1
1
2
1
1
1
1
1
2
1
1
2
2
1
0
1
1
0
0
2
1
2
1
1
2
1
1
1
0
2
2
1
1
1
1
0
1
1
1
1
1
2
0
1
1
2
1
1
1
1
1
1
2
0
1
2
0
2
1
0
3
1
1
1
1
1
2
1
1
1
2
0
1
0
1
1
2
2
2
1
1
1
2
1
2
2
1
2
1
2
0
1
2
1
2
2
0
3
1
1
0
1
1
0
1
0
1
2
1
1
1
0
0
2
1
1
0
2
1
1
0
1
1
1
1
1
1
2
1
0
2
1
1
1
1
1
1
1
1
2
1
2
1
0
1
1
1
1
1
0
0
1
2
1
2
2
1
1
0
1
1
2
2
1
1
1
2
2
1
0
0
1
2
1
0
1
2
0
1
1
1
2
1
1
0
1
0
0
1
1
0
1
1
2
2
1
2
1
2
1
1
0
1
1
1
0
2
2
1
2
2
2
2
1
0
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
0
1
1
1
1
2
1
0
1
1
2
2
1
1
1
1
2
1
1
0
1
2
1
1
1
1
1
0
0
1
1
1
2
0
1
1
1
1
1
0
1
2
2
1
1
1
0
1
1
2
1
1
1
1
0
2
2
1
1
1
2
2
0
1
0
1
2
0
1
0
1
2
2
1
2
1
1
1
1
1
1
1
2
2
0
1
2
1
1
2
1
1
1
1
2
1
2
1
2
1
0
1
1
1
1
0
1
1
1
0
0
1
1
1
2
2
0
1
2
1
1
2
1
1
1
1
0
2
0
2
2
1
1
2
1
1
1
2
1
1
1
1
1
2
1
2
0
2
1
1
2
0
0
2
2
1
1
1
1
1
1
1
2
1
1
1
2
1
1
2
0
2
1
1
1
0
1
2
2
1
2
1
0
1
1
1
1
0
1
2
1
1
1
1
2
1
2
2
2
1
1
0
1
1
1
0
1
1
1
0
1
2
1
2
2
0
1
1
1
1
1
1
1
0
2
2
1
2
2
2
2
1
0
1
2
1
2
1
1
1
0
1
1
1
2
2
1
1
1
1
1
2
1
1
1
2
1
1
0
1
2
0
0
1
2
1
0
2
1
1
2
2
1
1
1
0
1
1
1
1
1
2
2
1
1
1
0
1
1
0
2
1
2
1
0
1
2
0
1
1
1
0
1
1
1
2
1
2
0
1
1
0
1
1
1
1
1
1
2
0
1
1
2
2
1
2
1
1
1
1
2
0
1
1
1
1
0
1
2
2
1
1
2
1
1
2
1
1
0
1
1
0
2
1
1
2
1
0
1
2
0
1
1
1
1
1
0
0
2
2
0
1
2
1
1
2
1
2
1
0
2
1
2
1
1
1
1
1
2
1
1
1
0
1
2
1
1
2
1
2
0
0
1
1
1
1
1
2
1
1
2
1
2
1
1
1
0
2
2
1
1
1
1
2
1
1
2
1
1
1
0
1
1
1
1
1
2
1
0
2
1
1
1
1
1
1
1
1
2
1
0
2
2
1
2
2
1
1
1
0
0
1
2
1
1
0
1
1
2
1
1
1
2
2
1
0
2
2
1
1
1
1
2
2
1
2
0
1
0
0
1
1
1
0
2
1
1
1
2
2
1
1
1
2
0
1
1
1
2
1
0
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
2
2
2
2
2
1
0
1
0
1
1
0
1
1
1
1
0
1
1
1
1
1
1
2
2
1
1
2
0
1
1
2
2
2
1
1
0
2
1
1
1
1
2
1
1
1
1
2
0
2
1
1
1
2
1
1
2
1
1
0
1
0
2
1
2
1
1
1
1
1
1
1
1
1
3
0
2
2
1
1
1
1
0
2
2
1
0
1
1
2
1
1
1
0
1
2
2
1
1
2
0
0
2
1
1
1
1
1
1
1
0
2
2
2
2
0
1
0
1
2
2
1
1
0
2
2
2
2
0
1
0
1
1
0
0
1
2
1
2
3
2
1
2
0
0
2
1
1
1
0
2
0
2
1
1
0
1
1
1
2
1
1
1
2
2
2
1
2
2
0
1
1
2
2
1
1
1
1
0
1
1
1
0
1
2
2
2
0
1
0
1
2
1
0
1
1
1
1
1
0
2
1
1
2
1
1
2
1
2
1
1
2
1
1
2
1
1
1
1
1
0
1
1
1
1
1
1
1
3
0
0
1
1
2
1
1
1
1
1
1
2
2
1
0
1
0
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
0
1
2
1
2
3
0
1
2
2
1
2
1
0
2
1
2
1
1
0
0
1
0
2
0
1
3
1
1
0
1
0
1
2
1
1
2
2
1
1
2
0
2
1
2
2
2
1
1
2
2
1
2
0
2
1
1
5
2
2
1
0
2
1
1
1
1
1
1
0
2
1
1
1
1
2
2
1
0
1
2
2
0
1
1
1
1
0
1
2
1
1
2
1
1
1
1
1
1
2
0
1
1
2
1
2
1
2
1
1
0
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
0
1
0
2
1
1
1
1
1
0
1
2
0
1
1
1
1
0
1
1
1
2
1
1
0
2
1
0
0
1
1
1
1
1
1
1
0
1
1
2
0
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
0
2
1
2
2
1
1
2
1
1
0
2
1
0
0
1
1
1
2
1
1
2
1
1
1
0
1
1
1
2
1
1
1
1
0
1
1
2
2
2
1
1
1
1
2
1
2
0
1
1
1
0
2
0
0
0
1
2
1
1
2
2
2
1
1
2
1
1
2
2
0
2
1
2
1
1
2
2
1
1
1
1
2
2
0
0
3
1
1
1
1
2
2
2
1
1
1
1
1
2
1
0
1
0
2
1
1
2
2
0
1
2
1
1
2
1
1
1
0
1
1
1
1
0
1
2
2
2
1
0
2
1
1
1
1
1
1
1
0
1
2
0
2
1
1
1
1
1
1
1
1
1
0
1
2
1
1
2
1
1
1
1
0
1
1
1
1
2
1
0
0
0
1
1
1
2
2
2
1
0
1
2
1
1
1
2
1
0
1
1
1
2
2
1
2
0
0
1
1
1
1
1
1
2
3
1
0
1
0
1
2
1
1
1
1
2
1
1
1
2
2
1
1
0
1
1
1
2
1
1
1
1
1
2
1
1
0
1
0
1
2
2
2
1
1
2
1
1
1
0
1
1
0
1
2
1
1
1
2
2
1
1
3
2
1
1
1
0
2
2
2
1
1
2
2
1
1
1
1
1
2
1
2
2
2
1
1
1
1
2
1
1
2
2
0
1
1
0
1
0
2
1
1
1
2
1
0
2
2
2
1
0
1
1
1
2
0
2
1
1
0
1
1
1
0
0
0
2
1
2
1
2
1
1
1
2
1
2
2
2
1
2
1
1
2
0
1
1
2
1
1
0
2
2
1
2
1
1
1
1
2
1
1
1
1
2
1
0
1
2
2
1
2
2
1
0
1
2
0
0
0
0
1
0
1
1
1
2
2
1
2
1
1
1
1
1
2
1
0
0
2
1
1
2
1
1
1
1
2
0
2
1
1
0
0
1
2
2
1
1
2
1
2
2
2
1
1
1
2
2
1
1
2
1
2
1
1
1
2
0
1
1
0
2
1
0
1
1
1
0
1
1
1
1
1
1
3
1
0
1
1
1
1
1
0
1
1
2
0
1
1
1
2
1
1
1
0
1
1
1
0
2
2
0
2
1
0
2
1
2
1
1
0
1
1
0
2
2
2
0
1
1
1
1
0
2
1
1
0
2
2
2
1
0
0
0
1
1
1
2
1
2
0
1
1
2
0
2
1
2
1
1
2
1
2
1
0
1
0
1
1
1
2
2
2
2
1
2
1
0
2
0
1
1
1
1
2
0
1
2
1
1
1
1
1
2
2
0
2
1
1
1
1
1
2
1
1
2
1
0
1
1
2
1
2
1
1
2
1
1
1
2
2
1
2
1
1
1
1
1
1
1
2
2
1
1
2
2
1
1
0
1
0
0
2
1
2
2
2
2
1
1
1
0
2
1
1
1
0
2
2
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
2
2
1
2
1
1
0
1
2
1
2
1
1
1
2
2
1
1
0
1
1
2
2
0
0
1
1
1
1
1
1
1
1
1
5
1
2
1
1
1
1
1
2
2
1
2
1
2
1
1
2
1
0
1
1
1
1
1
2
1
2
2
2
2
1
2
2
1
2
1
2
2
1
1
1
1
2
0
1
1
1
2
2
0
0
2
1
1
1
0
1
0
0
2
1
0
1
1
2
2
1
1
1
1
2
0
0
2
1
2
2
2
2
1
1
1
0
1
1
1
2
0
1
1
1
1
1
1
2
1
1
1
1
1
0
2
1
1
1
0
1
1
1
0
1
1
1
1
1
2
0
1
1
0
2
2
1
2
2
1
1
1
1
1
1
0
1
2
1
1
1
2
1
0
1
1
1
0
2
1
1
1
1
2
1
2
2
1
1
1
2
1
1
1
1
1
2
1
1
1
3
2
1
1
1
0
1
1
3
1
1
2
2
1
1
1
1
2
1
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
2
1
1
1
0
2
1
1
1
1
1
2
1
1
0
1
1
2
3
1
1
1
1
2
1
1
1
2
1
0
0
1
2
1
1
1
1
1
1
1
1
1
0
0
1
1
1
0
2
1
1
1
1
1
2
0
1
1
2
2
1
1
1
0
0
1
1
1
1
1
1
1
1
1
2
1
1
1
0
2
1
0
0
1
1
1
1
1
0
2
2
2
1
2
1
1
1
0
4
1
2
0
1
1
0
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
0
1
1
1
2
1
1
1
2
2
2
0
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
0
2
2
1
1
2
2
1
1
1
2
0
1
1
2
1
0
2
1
1
2
2
2
0
2
1
0
2
0
1
1
0
2
1
0
2
1
1
2
2
0
1
1
2
1
2
2
1
0
1
2
2
1
1
1
1
1
0
1
2
1
1
1
1
1
3
1
1
1
1
2
2
1
3
1
1
1
0
6
1
0
2
0
1
1
1
2
1
0
0
1
1
1
0
0
2
1
0
1
2
1
4
1
2
0
1
1
1
2
1
1
1
0
2
0
1
1
2
1
1
2
0
0
1
2
1
1
0
1
1
1
1
2
1
1
1
2
3
2
1
1
1
2
1
2
1
1
0
1
1
0
0
0
1
1
0
2
1
1
1
1
2
0
2
1
1
1
0
0
2
2
0
2
2
1
2
2
0
2
2
1
2
2
2
0
2
1
3
1
0
1
2
1
1
1
2
1
1
0
1
2
2
1
1
1
1
0
1
1
2
1
1
1
1
1
1
2
1
1
2
1
2
1
1
1
0
1
2
2
1
1
1
1
1
3
1
1
2
1
2
2
2
2
1
1
1
2
2
0
1
1
1
2
1
2
1
2
1
2
1
1
0
2
2
0
1
1
0
2
0
2
1
2
1
1
2
2
2
1
1
2
1
1
2
0
1
4
1
2
1
2
1
1
1
1
1
2
1
2
1
1
2
2
1
2
1
1
1
1
0
1
2
1
2
1
1
1
1
0
0
2
1
2
1
1
2
1
0
1
2
1
1
2
1
1
1
3
2
2
1
2
1
1
1
0
2
1
1
1
2
1
1
1
2
1
1
0
1
1
2
0
2
1
1
2
2
1
0
0
0
1
1
2
2
1
2
2
2
1
2
1
0
1
1
1
2
1
1
1
2
0
0
1
2
2
2
2
1
1
1
1
1
1
1
0
1
1
1
1
1
2
1
2
2
1
0
1
1
1
1
1
1
1
1
1
1
1
1
2
0
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
0
2
2
2
1
2
1
1
2
1
1
1
2
2
0
1
2
1
2
1
1
1
0
1
1
2
0
1
1
1
1
1
2
1
2
0
2
1
2
1
1
1
1
2
2
1
1
2
2
1
1
0
2
1
1
1
1
1
2
1
0
2
1
2
1
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
0
2
1
0
1
1
0
1
1
2
1
1
2
1
2
1
1
2
1
2
1
1
1
2
1
2
0
0
1
2
2
1
1
2
1
2
1
2
2
2
2
1
2
2
0
0
1
1
1
1
1
0
1
2
2
1
1
1
1
1
0
1
1
1
2
1
0
2
2
2
0
1
2
1
1
1
2
2
2
2
1
1
1
1
1
2
0
1
2
2
1
2
2
1
0
1
0
0
1
1
1
1
1
2
1
1
1
2
1
2
2
1
1
3
0
0
1
1
2
2
0
1
2
0
1
1
1
0
1
2
0
1
1
3
2
0
1
3
1
1
1
1
0
2
1
1
1
1
1
1
2
0
2
1
1
1
1
2
1
2
0
1
2
1
2
1
2
0
2
1
0
1
1
0
1
0
2
1
2
2
0
0
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
0
1
1
1
1
1
1
1
2
1
1
2
1
1
0
1
1
1
0
1
2
1
1
1
3
0
0
2
1
2
1
1
1
1
2
1
1
2
0
1
1
0
1
2
2
1
0
4
1
1
2
1
2
1
1
1
2
1
2
2
0
0
0
1
1
2
2
2
2
2
1
1
2
1
0
1
0
0
1
1
1
2
1
1
1
1
1
1
2
0
1
1
1
2
1
1
1
2
1
2
1
1
1
2
0
1
0
1
1
1
1
1
2
1
1
2
0
2
1
1
0
2
1
1
0
2
2
1
1
1
1
1
0
0
1
0
0
2
1
0
2
1
2
2
1
0
1
2
1
0
0
1
1
0
1
1
1
1
0
2
0
1
2
2
1
1
0
1
1
1
1
1
1
1
1
1
2
0
2
1
1
1
1
1
1
0
1
1
1
0
2
1
1
1
1
2
1
1
2
1
1
2
1
1
2
1
1
1
2
2
2
1
1
1
2
0
2
1
1
1
1
1
1
1
1
2
1
2
1
1
1
0
2
1
1
1
1
0
0
1
1
1
1
1
1
2
0
1
2
0
1
1
1
1
1
2
0
1
1
1
2
1
1
1
2
1
2
1
1
0
1
0
0
0
1
1
2
2
1
2
1
1
1
1
2
1
1
2
1
0
1
2
2
1
0
2
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
0
1
1
1
2
1
1
0
0
1
1
0
2
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
3
1
0
1
1
1
2
2
1
1
0
1
1
1
1
2
1
2
1
2
1
0
1
0
1
1
1
0
1
1
1
1
2
2
2
1
0
1
2
1
1
2
1
1
2
0
1
2
2
1
1
2
1
2
2
2
1
0
2
2
1
1
1
1
2
1
1
2
1
1
1
2
1
1
1
2
0
1
0
1
0
1
0
2
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
0
0
2
1
2
1
1
0
2
1
2
1
1
1
2
1
2
1
1
2
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
2
0
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
0
1
1
1
1
0
1
2
1
0
1
1
2
2
1
2
0
1
1
3
2
2
0
1
1
1
0
1
0
1
2
2
2
2
1
1
2
2
1
2
1
2
2
0
2
1
0
2
2
1
2
3
1
2
1
1
1
1
1
1
2
1
1
1
1
1
0
1
0
2
0
2
0
2
1
1
1
4
1
1
2
1
2
1
1
1
2
1
4
2
0
1
1
0
1
2
2
1
0
2
1
0
0
1
1
1
1
0
1
1
0
1
2
1
1
1
1
1
1
1
1
0
2
0
2
1
1
1
1
1
0
1
1
2
1
1
2
2
1
1
2
2
1
1
0
1
1
1
1
1
1
1
2
1
0
1
1
1
1
0
1
1
0
1
2
1
1
2
0
2
1
1
2
0
1
0
1
1
1
2
2
1
0
1
1
0
1
1
2
1
1
0
2
1
1
2
1
1
1
1
2
0
2
1
1
2
1
1
1
3
1
0
2
2
1
1
0
1
1
1
2
1
1
2
2
1
0
0
1
1
2
1
1
1
2
1
1
1
1
1
0
1
1
1
2
2
2
0
1
1
1
2
1
2
1
1
1
1
1
2
0
2
1
1
1
1
1
1
1
2
1
2
1
1
1
0
2
2
1
1
1
0
2
2
2
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
2
1
1
1
2
2
1
0
2
1
1
2
1
1
1
2
1
1
1
1
0
1
1
2
0
1
2
2
1
1
1
2
1
1
1
1
0
0
1
1
1
1
1
1
1
0
2
1
2
2
1
1
0
1
1
1
0
1
0
1
2
2
1
1
1
2
1
1
2
2
1
1
1
1
1
1
2
2
1
0
2
2
1
1
0
2
1
2
1
2
1
2
2
1
2
0
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
0
1
2
0
1
0
2
0
1
2
1
2
2
2
2
1
1
1
1
1
0
1
1
0
1
1
1
2
2
1
1
1
2
3
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
0
1
2
2
1
2
2
2
1
1
3
0
2
1
1
1
1
1
1
1
1
2
1
1
0
1
2
1
1
1
1
1
2
1
1
2
1
1
2
1
1
2
2
2
2
1
1
1
1
2
2
0
2
1
2
0
1
1
2
3
1
0
2
2
1
3
0
1
1
1
0
0
1
2
1
1
1
1
1
1
0
1
1
2
1
1
2
1
1
1
1
0
2
2
1
1
1
2
2
1
1
2
1
1
1
3
1
1
1
1
1
2
2
0
1
0
1
2
1
1
1
2
1
1
1
1
0
2
1
1
1
1
1
5
2
1
1
1
1
1
1
1
1
0
1
3
2
1
0
1
1
0
1
1
0
1
1
1
2
1
1
2
2
1
1
2
1
0
1
1
0
0
1
2
2
1
0
1
1
1
2
0
2
1
1
3
3
2
1
2
0
1
1
1
2
0
1
1
0
1
0
0
2
1
1
1
1
2
2
1
1
1
1
0
1
1
1
1
1
1
1
1
1
2
4
1
1
1
2
0
1
1
2
1
0
1
0
1
2
2
2
1
2
2
1
1
2
1
1
2
1
1
0
1
1
1
1
1
0
2
1
1
1
1
1
2
1
2
1
1
1
2
2
1
1
0
1
0
1
2
3
2
1
2
0
2
1
2
1
1
1
1
1
1
1
1
0
1
1
1
0
2
2
1
1
1
2
1
1
1
1
1
0
0
1
2
1
0
0
1
2
2
1
0
2
2
1
1
1
1
2
1
1
2
1
1
2
2
0
1
2
1
1
2
1
1
1
1
1
1
1
1
0
1
1
1
1
0
1
1
0
2
1
0
0
1
1
1
1
1
2
1
2
1
1
0
1
0
1
1
0
1
1
2
1
2
2
0
0
1
1
1
1
1
1
1
0
1
1
2
1
0
0
1
1
0
1
1
1
1
1
0
2
1
1
1
1
1
2
1
1
1
0
2
2
1
2
2
2
1
2
1
2
1
1
1
1
0
1
0
1
2
1
0
0
1
1
1
1
1
1
2
2
1
0
0
1
2
1
1
2
1
0
1
2
0
0
2
0
0
2
1
0
1
1
1
2
2
1
1
1
0
1
1
1
2
1
0
1
1
1
1
1
1
2
1
0
2
0
1
1
0
1
0
1
1
1
2
2
1
2
1
0
1
1
2
2
0
2
2
2
2
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
0
1
2
1
1
1
1
1
1
2
1
1
0
2
2
2
1
1
1
1
1
1
2
1
1
2
2
2
1
2
1
1
2
1
1
1
2
0
2
1
1
1
1
0
1
1
2
1
2
2
1
0
2
1
1
1
1
0
1
1
1
0
1
1
0
1
2
1
1
1
0
0
1
1
1
6
1
1
1
1
1
1
2
2
0
1
2
1
1
1
1
1
1
0
2
0
1
1
1
1
1
2
1
2
1
2
1
0
1
2
1
2
1
2
1
1
1
1
2
2
1
1
1
1
1
1
0
1
2
1
0
1
0
0
0
1
1
2
1
0
0
1
1
1
1
1
1
1
2
0
2
1
1
1
1
1
3
2
1
2
2
1
2
2
1
0
0
1
2
0
1
1
0
1
1
2
1
1
2
2
0
2
1
0
2
1
1
2
1
1
1
1
2
1
1
1
1
1
1
2
0
1
2
1
2
1
1
1
1
1
1
0
2
0
1
0
1
1
1
2
2
1
1
1
0
0
1
1
2
1
1
0
1
2
2
2
1
1
2
2
1
2
1
1
1
1
1
2
2
1
1
2
1
1
1
1
2
2
2
1
1
2
1
1
0
1
1
1
1
1
1
1
1
2
2
1
0
1
2
1
2
2
1
1
0
1
0
1
2
1
1
1
1
0
1
1
1
1
1
2
1
1
1
1
2
1
0
1
1
2
1
0
1
1
1
1
1
1
1
0
2
0
1
2
0
1
1
2
0
1
1
2
0
2
1
1
2
2
2
2
1
2
2
1
0
2
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
2
2
1
1
2
1
1
1
2
0
1
0
1
0
1
1
2
1
2
2
1
0
0
2
1
1
1
1
1
2
1
0
2
0
1
1
1
2
1
2
1
1
1
1
1
0
1
1
1
2
1
1
2
0
0
2
1
2
1
0
3
2
1
1
1
0
1
2
1
1
1
2
1
1
0
1
2
1
1
2
1
0
1
1
1
1
0
1
0
1
1
1
2
2
1
0
2
1
1
1
2
2
1
1
1
1
0
1
0
1
2
1
0
1
1
1
2
1
1
2
1
2
2
1
1
1
1
1
1
1
0
2
2
1
1
1
2
1
1
1
0
2
2
1
1
1
2
2
2
0
0
1
2
2
1
2
1
2
1
1
1
3
2
1
2
1
1
1
2
1
2
1
0
1
2
1
1
1
0
1
2
2
2
1
1
0
1
1
0
1
1
2
1
2
0
1
0
0
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
0
1
0
1
0
1
1
2
1
1
2
1
1
1
2
2
1
1
2
1
1
2
2
1
1
1
2
2
2
1
0
1
1
1
0
1
0
0
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
0
1
0
1
0
2
1
0
1
1
1
1
1
0
1
1
1
1
1
2
1
1
1
2
1
0
0
1
0
1
1
2
1
1
0
1
1
2
2
2
2
2
1
2
0
1
1
1
2
2
1
1
2
0
2
1
1
0
2
2
2
0
2
0
1
0
1
1
1
1
1
2
2
1
2
2
1
2
2
1
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
2
0
1
1
1
1
1
2
1
1
0
2
2
1
0
1
0
1
0
2
2
2
2
0
2
0
2
2
1
1
2
0
1
2
1
1
0
1
0
0
2
1
2
1
1
1
1
1
2
1
1
0
1
1
1
1
1
2
1
0
1
1
1
1
2
2
1
2
1
0
1
0
1
2
1
0
0
2
1
2
2
1
0
2
1
1
0
1
1
1
1
2
0
1
1
1
1
2
2
1
2
1
1
2
1
2
0
1
2
1
1
1
0
1
1
1
1
1
2
1
1
2
2
1
1
2
1
2
2
2
0
2
1
2
1
1
1
1
1
0
1
1
2
2
2
2
1
1
0
1
1
0
2
1
1
1
2
1
1
1
0
1
2
2
2
0
1
1
1
1
1
2
2
2
1
0
0
3
2
1
0
1
0
2
1
1
1
0
1
1
1
2
1
2
1
1
2
1
0
1
2
2
2
2
1
1
1
1
1
2
2
1
2
1
1
0
0
1
1
1
2
1
1
1
1
2
0
1
0
1
1
0
1
1
2
0
1
1
2
1
1
0
1
0
2
0
1
1
1
1
1
1
1
1
1
1
1
0
1
2
2
1
1
1
0
1
1
0
2
1
1
0
1
1
2
1
1
1
0
1
2
1
1
0
1
2
1
0
2
1
0
1
1
2
1
0
1
1
1
1
1
1
1
2
0
2
1
1
1
1
1
1
0
0
0
2
1
2
1
1
1
1
1
1
2
1
1
2
2
2
0
1
2
1
2
1
1
2
1
1
1
2
2
2
1
0
2
1
0
1
1
1
1
1
1
2
2
1
1
1
0
0
1
0
1
2
1
1
0
1
0
2
1
1
1
1
0
2
1
2
1
2
0
1
2
1
1
1
1
1
2
1
1
0
2
2
1
1
0
2
1
0
1
1
2
1
0
1
2
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
0
1
0
1
1
1
1
1
1
1
1
0
0
1
2
1
1
2
2
1
1
2
2
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
0
0
0
2
2
1
2
1
1
2
2
1
1
2
0
0
1
0
2
2
1
1
1
1
1
2
1
0
2
1
1
2
1
0
2
2
1
0
1
1
1
1
2
1
1
1
1
1
1
0
1
1
1
2
1
1
2
1
1
2
2
0
1
2
0
2
1
2
1
1
1
2
1
1
1
0
2
1
2
0
1
1
1
1
1
4
1
1
1
1
1
1
1
1
1
1
0
1
1
0
1
2
1
1
2
2
1
1
0
2
1
0
2
1
2
2
1
2
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
0
1
2
2
0
2
1
1
1
1
1
2
1
0
1
2
0
1
2
1
2
1
1
3
1
1
2
2
2
1
1
1
1
0
1
1
2
2
1
1
1
1
1
2
0
1
1
1
1
1
1
1
1
1
1
1
2
2
2
2
1
1
1
1
2
0
1
4
1
1
1
2
2
1
1
1
2
2
1
1
1
1
1
1
1
0
1
0
2
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
0
1
1
1
1
1
0
1
1
2
1
1
1
0
2
2
1
2
1
1
0
1
1
0
1
1
2
1
2
1
1
2
1
1
1
2
0
0
1
2
1
1
2
0
2
1
1
1
1
2
1
1
1
1
0
2
1
1
1
1
0
2
2
0
1
1
1
2
1
0
1
1
2
1
1
1
1
1
0
2
0
1
1
0
1
2
1
1
2
1
1
1
0
2
1
0
2
1
1
1
1
1
2
1
0
1
2
2
1
2
0
1
1
2
1
0
1
1
1
0
4
1
1
1
1
2
0
2
2
2
1
0
2
1
1
1
0
1
0
2
0
1
1
2
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
0
1
1
0
2
1
1
0
1
1
2
1
1
0
1
1
4
1
0
1
1
0
2
1
1
1
1
1
1
1
0
2
1
1
0
2
0
1
0
1
1
2
1
1
0
1
1
2
0
1
2
2
1
1
1
1
2
0
1
1
1
1
0
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
2
2
1
2
3
1
1
1
1
1
1
1
1
1
0
1
1
1
1
0
1
1
1
0
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
2
1
1
2
2
1
2
2
1
2
2
1
1
1
2
0
2
1
1
2
2
1
2
1
2
1
1
1
1
2
2
0
2
1
0
0
1
2
2
2
2
2
1
2
0
1
1
1
2
1
1
2
1
0
2
1
2
1
2
0
1
1
0
1
0
0
1
1
0
1
0
2
1
1
1
1
1
2
1
1
1
1
2
1
0
2
1
1
2
1
1
0
1
2
2
2
1
2
0
1
2
1
1
2
1
2
2
1
0
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
0
1
2
1
2
1
1
1
2
3
1
2
2
2
1
0
1
1
1
1
2
1
2
1
2
1
0
1
1
1
0
0
1
2
1
1
2
2
1
1
2
2
1
0
1
1
1
1
1
2
0
1
1
1
2
1
1
1
1
0
2
1
0
1
1
1
2
1
2
1
1
1
1
2
2
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
0
1
2
1
1
1
1
1
2
2
1
2
1
1
0
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
0
1
1
1
2
1
1
2
1
2
1
2
1
0
1
1
0
0
1
1
1
1
2
1
1
1
1
2
1
0
2
2
1
1
0
0
1
2
1
1
1
2
0
1
1
1
1
2
2
1
2
1
2
0
1
1
2
1
1
1
1
0
1
1
1
1
1
1
1
1
2
1
1
2
0
1
2
0
1
2
2
2
0
2
2
1
2
2
2
1
1
1
1
1
1
2
1
1
1
1
1
2
2
2
1
2
1
1
1
0
1
1
0
2
1
0
0
1
1
1
2
2
1
1
2
1
2
1
1
2
0
1
1
1
1
1
0
0
1
0
2
1
0
0
0
0
2
1
0
1
1
3
1
1
1
1
0
1
1
2
1
0
0
2
1
1
2
1
1
1
1
2
1
1
0
1
2
1
1
1
1
0
1
1
1
1
1
0
1
1
1
1
1
2
1
1
2
1
1
1
1
0
1
1
2
1
1
0
1
1
1
2
1
2
1
1
1
2
2
2
2
2
2
2
2
1
2
2
2
1
1
0
0
2
2
2
0
1
1
2
1
0
1
1
1
1
0
1
1
3
1
1
1
1
1
2
1
1
0
2
1
0
1
0
1
1
1
1
0
2
2
2
1
1
1
2
1
1
0
2
1
1
1
1
1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
1
0
1
1
2
1
2
1
1
1
1
1
1
1
2
2
2
0
2
2
1
2
1
2
1
0
2
0
5
1
1
0
1
1
1
1
2
1
2
1
1
1
1
1
0
1
2
1
1
1
1
0
1
1
2
0
1
1
1
1
1
1
1
1
2
1
1
1
1
0
1
1
1
0
1
1
1
2
1
1
1
1
0
1
2
1
2
1
0
2
2
1
1
0
1
0
2
0
1
2
2
0
1
1
1
1
2
1
1
1
1
1
2
1
1
0
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
0
2
1
1
1
1
2
1
0
1
0
1
1
1
0
1
1
0
0
1
2
1
1
1
1
2
1
1
1
2
1
1
2
1
1
2
0
0
1
0
2
1
1
1
1
1
2
1
1
0
1
1
2
1
0
0
2
1
1
1
1
1
2
1
2
1
1
2
2
0
1
2
1
1
1
1
1
1
2
0
2
1
1
2
2
1
1
2
2
0
2
1
0
2
1
1
2
2
1
0
1
1
0
0
0
1
1
1
1
0
1
1
1
2
1
2
1
1
1
2
1
2
1
2
1
1
1
2
2
0
1
0
2
2
2
1
1
0
1
2
2
1
1
1
1
2
2
1
0
1
2
1
1
2
1
1
1
2
1
1
2
2
0
1
1
1
2
1
2
1
0
2
1
2
1
0
1
1
1
1
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
0
1
2
1
1
1
1
1
2
1
2
2
1
2
2
1
1
2
1
5
1
2
2
1
1
1
0
1
1
1
1
2
1
1
2
1
2
2
1
2
1
2
1
2
1
1
2
0
1
2
1
1
1
1
1
1
1
1
1
1
0
2
1
1
0
2
1
1
0
2
1
0
0
1
0
2
1
1
1
1
2
2
2
0
2
0
1
2
1
0
1
0
1
0
2
2
1
0
1
1
1
2
1
2
1
2
1
1
0
1
1
1
1
2
1
1
1
2
2
1
1
1
3
1
1
0
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
0
1
2
0
2
1
2
1
2
1
0
0
2
1
2
1
1
2
0
1
2
1
1
2
2
2
1
1
0
2
1
1
2
2
1
2
0
1
2
1
1
2
1
1
1
1
2
1
1
1
2
1
0
1
1
2
1
1
1
2
2
1
1
1
0
2
1
2
1
1
1
1
2
2
1
1
1
2
1
1
1
1
1
0
0
1
1
2
2
1
1
1
1
0
1
1
2
1
1
1
2
2
2
1
1
0
1
1
2
1
0
2
2
2
2
0
2
0
2
1
2
2
1
1
1
2
1
0
1
2
1
1
1
0
1
0
1
1
1
0
1
1
0
1
2
1
2
1
1
0
1
1
2
1
2
0
1
1
1
2
1
2
1
2
1
1
1
0
1
2
0
1
2
1
1
3
1
1
1
1
1
0
2
2
2
1
1
1
2
2
1
2
1
1
1
1
1
2
1
0
1
2
1
1
1
2
1
2
0
1
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
0
1
1
1
1
2
1
1
1
4
0
1
0
1
0
2
1
1
1
1
0
0
2
0
2
1
2
2
2
2
1
1
1
2
1
1
1
0
1
1
1
1
1
1
1
2
2
2
1
0
1
1
0
2
0
1
0
1
2
1
2
2
1
1
0
2
1
0
0
1
1
1
2
0
0
1
2
1
2
1
1
0
1
1
1
2
0
2
2
2
0
1
1
2
2
1
2
1
2
1
1
2
0
1
1
1
1
1
1
1
2
1
0
1
1
0
2
1
0
1
1
1
0
1
1
2
4
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
2
1
1
1
1
1
1
2
2
1
2
1
1
2
1
1
2
2
1
1
2
0
1
1
0
2
1
1
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
0
1
0
1
1
0
0
1
0
2
2
1
2
1
1
1
1
2
2
2
1
1
2
0
1
1
1
1
0
1
1
0
2
1
1
2
1
1
1
1
2
0
2
1
2
2
1
2
2
1
1
2
1
0
1
1
1
1
2
1
1
1
1
2
1
2
1
2
1
1
2
1
2
1
2
1
1
1
2
2
1
1
2
2
1
1
1
1
1
1
0
2
0
2
1
2
1
1
1
1
0
2
1
1
1
0
1
0
2
2
2
2
1
2
1
2
1
2
2
1
3
1
2
2
2
1
1
1
1
2
2
0
2
1
1
2
1
0
1
0
1
2
1
1
2
1
2
1
2
2
2
1
1
1
1
2
0
1
1
1
0
2
1
2
2
2
2
1
1
1
1
1
1
1
1
0
1
1
1
0
1
1
1
1
1
1
1
1
1
2
1
1
2
2
1
1
1
1
0
1
1
0
1
1
1
1
0
0
0
1
2
1
0
2
1
0
2
1
1
1
1
2
1
1
1
1
1
2
1
1
1
2
2
2
4
2
1
1
1
1
2
1
1
0
2
1
2
2
1
1
2
1
1
1
2
3
2
2
1
0
1
1
1
1
1
1
1
1
1
0
1
2
1
1
1
2
1
1
2
1
2
2
1
1
1
1
1
1
0
1
1
1
2
2
2
1
1
2
1
1
0
1
1
2
3
1
0
1
2
0
1
1
1
2
1
2
0
1
0
2
2
2
2
2
2
0
2
1
2
1
2
0
1
0
2
1
1
0
1
1
1
1
1
2
2
1
1
0
1
0
1
2
2
0
1
2
1
1
2
1
1
2
0
1
1
0
1
0
1
1
1
2
1
1
3
1
1
1
2
2
1
1
2
1
1
0
1
1
0
1
1
2
2
1
0
1
2
1
1
1
1
1
0
1
2
1
1
2
1
1
2
1
1
1
2
0
2
1
1
1
1
1
1
1
2
2
1
1
0
1
0
1
2
1
2
1
2
0
1
1
0
1
2
1
0
1
1
2
1
1
1
2
2
1
1
1
1
2
0
1
1
2
1
1
1
1
1
1
2
2
0
0
1
1
1
1
1
1
0
1
2
1
2
2
1
1
1
2
1
0
1
1
1
1
1
2
2
1
2
1
4
1
2
1
2
1
1
2
0
1
2
1
4
0
2
2
1
1
2
1
0
1
2
1
2
0
1
2
1
1
1
1
1
2
2
1
1
1
2
0
2
2
2
0
2
1
1
1
0
1
1
1
2
1
1
1
1
1
1
1
1
1
0
1
0
2
2
2
1
2
0
1
1
1
1
1
1
1
1
1
2
1
2
0
1
1
1
5
1
1
3
0
1
1
1
1
2
1
2
0
1
0
2
1
2
1
1
1
1
1
2
1
1
0
1
2
1
1
2
1
0
1
1
0
2
1
1
1
1
0
1
1
0
2
0
2
1
1
2
1
2
1
1
1
0
2
1
1
1
0
1
1
1
1
2
1
1
1
2
1
2
1
1
2
1
2
2
2
2
1
1
1
1
1
1
2
0
2
2
2
2
1
1
0
1
2
2
1
2
1
1
1
1
2
1
1
1
1
1
0
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
2
2
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
2
1
2
0
1
1
1
1
2
1
2
2
0
1
1
2
2
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
0
1
0
2
1
1
0
1
1
1
1
0
1
1
1
1
0
1
2
1
1
1
1
1
1
1
1
0
2
2
1
1
2
1
1
1
1
0
1
2
2
2
1
0
2
2
1
1
1
1
2
1
1
2
1
1
1
1
2
1
2
2
1
1
0
1
1
1
0
2
1
1
2
2
1
1
2
1
2
2
1
1
1
1
1
2
2
2
2
1
2
2
2
1
1
2
1
2
3
0
1
1
1
1
1
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
0
1
0
2
1
0
2
1
2
0
2
1
2
0
2
0
1
1
1
1
2
1
2
2
1
2
2
1
1
2
1
1
2
2
1
1
1
2
1
2
2
1
1
0
1
1
1
1
1
1
2
0
2
1
1
1
1
2
0
1
1
1
1
1
1
2
0
1
1
2
1
1
1
0
2
2
2
2
0
1
2
1
2
1
1
0
2
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
0
1
0
1
1
1
0
1
3
2
1
1
2
0
2
1
2
2
1
1
1
1
0
2
1
2
2
2
2
2
1
2
3
2
2
2
1
1
2
1
1
2
2
1
1
0
1
2
1
1
3
1
2
0
0
1
2
1
1
0
2
1
2
1
1
1
0
2
0
1
1
1
1
1
1
1
1
1
1
1
0
0
1
1
1
1
1
0
1
1
1
0
1
2
1
2
1
1
0
1
1
1
2
2
1
1
1
2
2
1
1
1
2
2
1
1
1
2
1
1
1
1
3
1
1
2
1
0
1
1
2
2
0
1
1
2
2
1
2
0
1
1
1
1
1
1
2
4
1
2
1
1
2
1
1
2
0
1
1
1
3
0
1
1
1
1
1
1
1
0
1
1
1
0
1
1
1
1
1
1
1
1
2
1
1
0
1
2
1
1
0
1
2
1
1
1
1
1
1
2
1
2
2
1
3
0
1
4
1
0
1
1
0
1
1
1
2
1
2
1
2
0
0
1
1
1
2
2
1
1
1
1
1
1
2
2
2
1
1
2
1
1
1
0
2
2
1
1
1
1
2
1
1
2
1
2
1
1
2
1
0
1
0
2
1
1
2
1
1
1
1
1
2
2
2
1
1
0
1
1
2
1
1
2
1
1
1
1
1
2
2
1
1
2
0
1
2
1
1
1
1
1
2
1
1
0
1
1
1
1
2
1
2
1
1
2
1
1
1
1
1
2
2
0
2
1
1
1
1
1
0
0
0
1
1
1
2
1
1
2
0
2
0
1
1
1
2
2
1
1
1
2
1
2
1
1
2
1
1
1
1
1
0
1
2
0
0
0
1
2
1
2
1
2
2
2
2
2
1
2
0
1
2
1
2
0
1
1
2
1
0
1
1
1
2
2
2
0
1
1
2
1
4
1
1
1
1
1
2
1
1
1
1
1
1
2
2
1
0
1
0
1
1
1
1
2
1
0
1
1
1
1
0
1
0
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
0
2
1
1
1
1
1
2
0
1
1
1
0
0
1
1
1
1
0
1
1
2
2
1
1
1
2
2
0
1
1
1
1
1
1
2
1
0
1
1
1
2
1
2
2
1
1
1
1
1
2
2
0
2
2
0
1
0
1
2
1
1
2
2
1
3
1
1
0
0
1
1
1
1
2
2
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
3
1
2
2
1
1
2
1
0
0
2
2
1
1
1
2
1
1
2
2
1
1
1
2
1
2
2
1
0
1
2
1
2
2
2
2
2
1
1
2
1
2
1
0
1
1
2
1
1
1
2
2
2
1
1
1
1
1
1
2
2
2
1
0
2
1
2
1
1
1
1
1
2
1
0
1
1
1
1
1
1
0
1
0
1
2
2
1
1
2
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
0
1
2
1
1
1
2
1
0
1
2
2
1
2
1
2
2
0
1
1
2
2
2
1
1
1
1
1
0
1
1
1
1
1
2
2
2
1
2
1
2
1
1
2
1
1
1
1
0
1
2
1
1
2
1
2
1
1
2
1
2
1
2
2
1
0
1
2
0
2
1
1
1
2
0
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
3
1
2
1
1
2
1
1
2
2
2
1
1
1
1
1
1
2
1
0
1
1
1
2
0
1
2
2
1
2
1
1
2
1
2
2
1
1
2
1
2
1
2
0
2
2
1
1
1
1
1
1
1
1
1
0
1
1
2
0
0
1
1
1
1
2
1
2
1
0
1
2
0
1
0
1
2
2
1
1
1
1
2
1
0
1
1
1
1
1
1
2
0
1
2
1
1
2
1
1
1
0
0
0
1
1
1
0
2
2
1
1
2
1
2
1
2
1
2
0
1
2
1
0
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
0
1
1
1
1
1
0
1
1
1
1
1
1
2
0
2
1
1
2
0
2
0
1
2
2
1
1
2
1
1
1
1
2
1
1
1
0
1
1
1
1
1
2
2
1
1
0
1
1
1
2
1
1
1
1
2
2
1
1
2
1
1
2
1
2
2
1
1
1
1
1
2
2
2
0
1
1
0
2
0
1
1
1
1
1
2
1
1
1
1
2
2
1
1
1
1
1
0
1
0
1
2
1
1
1
1
1
2
1
1
1
1
0
1
1
1
1
1
1
1
2
1
1
2
1
2
2
1
2
2
0
1
1
1
1
2
0
1
2
2
1
0
2
0
1
1
2
2
1
1
2
2
2
1
1
0
1
1
0
2
2
0
2
2
0
0
2
1
2
2
1
2
1
1
1
0
1
1
0
1
0
1
0
1
2
3
1
1
2
1
2
1
1
2
1
2
1
1
2
1
2
1
2
2
1
2
0
1
1
1
1
0
2
1
1
1
0
2
0
1
1
1
0
1
2
1
2
0
1
1
0
1
2
1
1
2
2
2
1
0
1
0
1
1
1
2
1
0
2
1
2
2
1
1
1
2
2
1
2
1
1
2
1
1
0
0
0
1
1
1
1
1
1
1
1
0
2
2
2
0
1
2
2
1
1
1
0
2
1
1
1
2
1
1
2
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
0
1
2
1
1
1
1
1
1
1
1
0
1
0
1
2
1
0
1
1
0
1
1
1
2
2
1
1
2
1
1
0
1
2
0
1
2
1
0
1
2
2
1
1
2
1
2
1
0
1
1
1
2
1
1
2
1
0
1
1
1
1
0
1
1
2
2
1
2
0
1
1
2
1
2
1
0
2
1
2
1
2
2
1
2
1
2
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
2
1
2
1
2
2
2
1
1
1
1
1
0
2
1
1
2
0
1
1
1
1
1
2
2
0
2
1
0
2
2
1
2
1
1
2
0
0
2
1
1
1
2
1
1
2
0
2
2
0
2
1
1
1
0
1
1
1
2
0
1
1
1
1
2
2
2
1
2
1
1
1
0
1
1
2
1
2
0
2
1
1
1
1
1
1
1
2
1
2
2
2
1
1
1
1
2
1
2
2
1
1
1
1
2
1
1
5
2
1
1
1
1
1
2
2
1
1
0
1
2
1
0
2
2
2
2
1
1
2
0
2
1
1
1
1
2
2
1
2
1
1
1
1
1
1
2
2
1
2
1
1
0
2
0
1
1
1
2
0
1
1
1
1
1
4
2
1
1
1
1
2
1
0
0
1
1
0
2
1
1
1
3
1
3
1
0
0
1
1
2
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
2
0
0
0
3
3
1
0
1
1
1
1
1
1
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
0
2
1
0
2
1
1
1
0
0
1
1
0
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
0
2
0
1
1
1
2
1
1
1
1
1
0
2
1
1
0
1
1
0
2
1
1
2
2
0
2
1
0
1
0
0
1
1
1
0
2
2
2
2
2
1
2
1
1
2
2
0
1
1
0
1
1
1
1
1
2
0
1
2
2
1
0
0
1
0
1
1
1
1
1
1
1
1
2
1
3
1
2
0
2
0
1
1
1
1
1
2
1
2
2
0
1
1
2
1
0
2
1
2
1
1
1
2
1
1
2
1
1
0
1
1
1
1
1
1
1
1
1
1
2
0
2
1
2
0
2
1
1
0
0
0
1
2
1
2
1
0
1
1
1
0
2
1
2
1
2
0
1
2
1
2
2
2
1
2
2
1
2
1
2
2
1
2
0
2
1
0
1
1
1
1
2
1
2
1
0
1
2
1
0
1
1
1
1
1
0
1
2
2
2
2
0
1
1
2
1
0
1
0
1
1
1
1
1
1
3
0
0
2
2
2
1
1
2
1
1
0
2
1
1
1
2
1
1
1
1
0
1
2
1
1
2
2
1
1
0
1
0
1
1
2
1
2
2
0
0
1
1
1
1
2
1
1
1
2
1
1
2
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
2
1
1
0
1
2
0
0
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
2
0
1
1
2
2
1
1
1
1
2
0
2
1
1
1
2
1
1
1
1
1
1
2
1
2
2
1
0
1
1
1
1
2
1
0
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
1
1
0
2
1
0
2
1
1
2
1
1
0
1
2
1
1
1
2
1
0
1
1
0
2
1
1
2
2
1
1
1
0
2
0
0
1
1
1
2
0
2
1
1
0
1
2
1
1
1
2
2
2
1
1
2
0
2
2
1
1
1
2
2
3
1
2
1
2
1
1
0
1
1
1
0
2
1
1
1
2
1
2
2
1
1
2
2
2
1
1
1
1
2
2
2
2
0
0
1
1
1
1
2
1
1
2
0
1
2
2
1
2
0
1
1
1
2
2
0
2
2
1
0
2
1
2
2
1
1
0
2
2
2
0
1
1
1
1
1
1
0
1
0
1
2
1
0
1
0
1
2
1
0
2
0
2
1
1
1
1
1
2
1
2
0
2
1
1
1
1
1
1
2
2
1
3
1
1
1
0
1
0
2
1
1
1
1
2
0
2
0
1
1
2
2
1
1
0
2
1
1
1
2
1
0
1
1
1
1
1
1
1
0
1
1
1
2
2
1
1
0
0
2
1
1
1
0
1
3
2
0
1
1
1
2
2
2
1
1
0
0
1
1
1
1
2
1
2
1
2
1
1
2
1
1
1
1
2
1
0
1
1
1
1
1
2
1
1
1
0
2
1
1
1
2
2
2
1
1
2
0
0
2
1
1
1
1
1
1
2
1
1
1
1
2
2
1
2
1
1
1
1
1
0
1
1
1
1
2
2
0
2
0
1
2
2
1
1
2
1
2
0
2
0
1
0
2
1
1
1
1
1
2
1
1
0
1
0
0
1
2
1
1
1
1
2
1
0
1
1
4
1
3
0
0
0
1
0
1
2
1
2
1
1
2
1
1
2
2
0
1
2
2
2
1
1
1
1
1
1
1
1
1
2
1
1
2
0
2
1
1
2
2
1
1
2
1
1
1
1
2
1
0
1
1
2
0
0
0
2
1
2
1
1
2
2
1
1
2
1
0
1
1
1
1
1
2
1
1
2
0
0
1
1
2
1
2
1
1
2
1
1
0
1
1
1
1
2
2
1
1
2
1
1
2
1
0
1
1
1
1
1
1
1
0
1
0
1
1
1
1
0
0
0
1
2
2
1
1
1
2
0
1
1
2
1
0
1
1
1
2
2
1
1
1
1
0
2
1
1
2
1
2
1
2
1
0
0
1
0
2
1
2
2
2
2
1
1
0
1
1
2
1
2
2
2
1
2
0
1
1
1
2
1
1
2
1
2
2
2
0
1
2
2
1
0
0
1
1
1
2
0
1
1
1
2
2
1
2
1
0
1
1
2
1
1
2
0
1
2
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
0
0
2
2
1
1
1
2
1
1
1
1
2
0
0
1
0
0
2
1
1
2
2
2
1
0
1
1
0
0
1
2
1
1
2
0
1
1
1
0
0
2
1
1
1
1
1
2
2
1
1
0
0
1
1
2
1
2
2
0
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
0
1
1
0
1
2
2
2
2
1
1
2
1
0
2
0
1
1
2
0
1
1
1
1
1
2
2
0
2
0
2
1
2
1
0
1
1
1
1
1
1
2
0
1
1
1
1
0
1
2
1
1
1
2
1
0
1
2
1
1
0
1
2
1
1
1
2
1
1
1
1
1
2
1
1
2
2
0
1
0
1
1
1
3
1
1
2
0
2
1
0
0
0
1
1
1
2
0
0
1
2
2
1
2
1
1
1
1
0
2
1
0
1
1
0
1
1
1
1
1
1
2
1
2
1
1
1
2
1
2
1
1
1
0
0
1
2
1
1
0
2
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
1
2
2
0
2
2
2
1
2
1
1
2
0
1
0
0
1
2
0
1
1
0
1
1
1
1
1
1
0
1
1
1
0
1
2
1
2
1
0
1
2
2
2
1
1
0
1
0
2
1
0
1
1
2
1
0
1
1
1
1
1
1
1
2
1
0
1
2
0
1
2
1
2
1
1
2
2
1
1
1
1
0
1
1
0
2
1
0
0
2
1
2
1
1
1
1
1
2
2
2
2
1
1
1
1
2
1
1
0
1
1
0
1
1
1
1
2
2
2
2
1
2
0
2
0
1
2
2
0
1
1
0
1
2
1
1
2
1
1
1
2
1
0
1
0
2
1
1
1
1
2
2
2
1
2
2
1
2
1
1
2
1
0
2
2
1
1
1
1
1
1
2
1
1
1
0
2
1
1
1
1
2
0
1
1
2
1
1
1
1
2
1
0
2
2
1
1
1
1
1
0
2
2
2
1
1
2
1
2
2
2
1
1
1
1
2
0
1
1
0
1
1
1
2
2
1
0
0
2
1
1
1
1
3
1
3
1
2
1
0
1
1
0
1
0
1
2
0
1
1
1
1
1
1
1
2
1
2
1
1
1
0
2
0
0
2
0
1
2
2
1
1
1
1
2
1
2
1
0
2
2
1
1
1
1
3
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
0
1
1
2
1
2
2
1
1
2
1
2
0
1
2
1
1
1
2
0
0
1
1
2
1
0
2
0
1
2
2
2
1
1
1
0
1
1
1
2
1
1
0
1
0
2
1
2
1
2
2
1
1
1
1
1
3
1
2
0
1
0
0
1
1
1
1
2
1
2
2
1
1
2
1
2
2
1
1
1
1
1
2
1
1
1
1
1
2
1
2
0
1
2
1
1
1
2
2
1
1
2
1
2
2
1
2
0
0
1
1
1
0
0
2
1
2
1
1
1
3
1
0
2
1
2
1
1
1
2
1
1
1
1
0
0
1
0
2
2
1
1
1
1
2
2
2
1
1
1
2
1
1
2
2
1
2
2
2
1
2
1
1
1
1
1
1
1
2
2
2
1
1
1
2
1
1
1
2
2
0
2
0
2
2
1
1
1
2
1
1
1
1
1
0
1
1
0
0
1
1
2
1
1
0
2
1
1
1
1
2
1
2
2
0
1
1
1
2
2
1
1
0
2
1
1
1
1
2
1
2
2
0
1
1
1
1
1
1
0
2
2
1
2
2
1
2
0
1
2
0
2
2
1
0
0
1
2
1
2
1
0
2
1
0
1
2
1
0
0
1
2
1
1
1
1
2
2
1
2
1
1
2
1
1
1
1
1
1
1
2
1
2
1
0
1
1
2
1
1
2
0
1
1
0
1
1
1
2
1
2
1
3
1
1
1
1
0
0
2
1
1
2
1
2
1
1
2
1
1
1
1
1
2
1
2
1
1
2
1
1
2
0
1
2
0
2
1
1
2
2
1
2
1
3
0
0
1
2
1
2
2
1
1
1
1
1
2
1
1
0
1
1
1
1
0
1
2
2
1
0
2
2
2
1
2
2
0
0
1
1
1
1
1
2
1
1
1
0
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
0
2
1
1
1
1
1
2
2
1
1
2
2
1
2
1
2
0
1
2
1
0
2
2
2
1
2
1
1
1
1
2
1
1
1
2
1
2
1
0
2
1
0
2
1
1
0
2
2
2
1
1
1
1
1
1
1
1
2
1
1
0
2
1
2
1
0
2
2
0
1
1
2
1
2
1
1
1
0
1
2
1
1
1
1
2
1
1
2
1
2
1
1
1
0
1
1
0
0
1
1
2
0
1
1
2
1
1
1
0
1
1
2
1
2
2
1
1
2
1
0
2
2
2
1
2
3
2
1
2
1
1
0
2
0
1
1
1
1
1
1
1
0
1
2
0
1
1
1
1
2
1
2
1
1
1
1
1
2
1
2
2
1
1
1
1
2
1
1
1
2
0
1
1
1
1
2
2
2
2
1
1
0
0
1
2
2
1
1
1
1
1
1
0
2
1
2
1
1
2
2
1
0
2
1
2
1
1
2
1
2
1
1
2
1
2
1
1
2
2
2
1
2
1
1
3
1
2
0
0
1
2
1
1
1
0
3
1
2
0
1
2
1
1
1
1
1
1
2
1
1
2
2
1
2
2
1
1
1
2
1
1
1
2
0
2
1
1
0
1
1
0
2
2
0
1
2
1
1
1
0
1
1
1
2
1
1
1
2
0
1
2
2
1
1
0
1
0
1
0
1
0
1
1
1
0
0
1
2
1
1
1
0
1
1
0
1
2
2
1
2
1
1
1
1
2
2
1
1
2
0
2
1
1
0
2
1
2
1
2
1
2
1
2
2
1
1
1
2
2
1
2
1
1
2
1
1
2
1
0
2
2
1
0
1
5
1
1
1
1
2
0
1
1
2
2
1
1
2
1
1
1
1
0
1
1
1
1
0
1
1
1
1
1
2
2
1
2
2
2
1
2
1
1
2
1
2
1
2
1
1
1
2
0
1
1
2
1
1
2
1
2
1
2
1
1
2
1
0
1
1
1
2
1
1
1
1
2
1
2
0
1
2
0
2
1
2
1
0
1
1
2
1
2
2
2
2
0
1
1
1
1
2
1
1
1
2
3
1
1
0
0
1
2
1
0
4
0
1
1
0
1
0
2
0
1
1
1
1
1
2
2
1
1
2
1
2
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
0
2
2
1
1
1
1
1
0
1
2
2
3
1
1
1
2
0
1
1
1
1
0
1
1
1
1
1
1
0
1
1
1
1
1
1
0
1
3
1
0
2
1
0
1
1
2
1
1
1
1
2
2
1
1
1
1
1
1
1
1
2
0
0
2
1
1
2
5
1
2
1
0
1
1
1
2
0
1
2
1
2
2
1
1
1
1
1
2
1
0
2
1
1
1
2
2
0
1
2
0
1
1
0
2
1
2
1
0
2
2
1
1
1
2
1
2
2
1
1
2
1
2
1
0
1
2
1
1
0
0
2
0
1
0
2
2
2
0
1
1
1
2
1
1
0
2
2
1
1
1
1
1
2
2
2
2
1
0
1
1
2
1
2
1
0
2
1
1
2
1
1
1
1
2
2
1
1
1
2
0
1
1
1
1
1
0
2
1
0
1
2
1
2
1
0
1
1
2
2
1
1
1
1
1
1
2
1
1
1
0
1
1
2
1
1
2
2
1
1
0
1
2
2
2
0
1
1
1
0
1
1
1
0
1
2
1
2
1
1
1
0
1
2
0
0
0
2
1
1
1
1
1
1
1
2
1
1
2
0
2
2
1
1
1
1
1
2
1
1
0
2
1
1
1
1
1
1
0
1
0
1
1
2
1
2
2
0
1
1
1
2
0
1
2
0
1
2
0
0
1
1
1
1
1
1
1
2
1
1
0
0
2
0
1
2
2
1
1
2
0
2
1
1
2
1
2
2
1
2
0
1
2
0
1
0
1
2
2
0
0
2
2
1
1
1
1
1
1
1
1
2
2
2
1
1
1
2
2
0
1
1
1
1
1
0
0
1
1
1
2
2
1
1
0
1
1
1
2
1
1
0
1
1
1
1
2
1
2
1
1
1
1
1
2
1
2
1
1
1
2
1
2
1
1
1
2
1
1
1
1
1
2
1
0
0
0
2
2
2
1
1
1
1
0
1
1
1
2
1
1
1
0
1
1
2
1
1
1
1
1
2
2
2
1
1
2
1
1
2
2
1
1
1
1
0
1
1
0
2
1
2
1
1
0
1
0
1
1
1
0
1
0
1
2
1
1
1
1
1
2
2
2
2
1
2
2
2
1
2
1
0
2
1
2
1
0
1
1
2
1
1
1
1
0
1
2
1
2
0
2
1
1
2
1
2
0
1
1
2
1
0
1
2
2
1
1
0
2
1
1
2
2
1
0
0
1
1
2
1
1
1
2
0
2
0
1
1
1
1
1
1
1
1
2
2
2
2
1
2
1
0
0
1
1
2
1
1
2
0
2
2
0
1
1
1
1
0
1
1
1
1
1
2
1
2
1
1
2
2
1
1
3
1
1
2
3
2
2
1
2
1
1
1
1
0
1
2
2
0
1
2
1
1
0
1
1
1
1
0
1
1
1
1
2
2
1
2
1
1
2
1
1
1
0
0
1
1
2
1
2
1
2
1
2
1
2
2
1
1
1
2
1
2
2
1
1
2
1
1
1
1
1
1
1
2
1
1
0
2
0
2
1
0
1
1
1
1
0
0
1
0
1
0
1
1
1
2
2
1
1
1
0
0
0
1
1
1
1
1
1
2
2
0
2
2
2
1
1
1
1
0
1
2
1
2
1
2
1
1
0
1
1
2
1
0
2
2
1
1
2
1
2
1
1
0
1
1
2
1
1
1
1
1
0
0
2
1
1
0
1
2
1
1
1
1
0
1
1
2
3
1
1
0
0
1
1
1
1
2
2
2
0
0
1
1
1
2
1
1
1
2
1
0
1
1
1
1
0
1
1
1
1
0
2
1
1
2
2
0
1
1
2
1
2
1
1
1
0
2
2
1
1
1
1
1
1
1
0
2
2
2
1
0
1
2
3
2
1
1
1
2
0
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
2
2
1
1
0
1
0
1
1
1
0
1
1
1
1
0
1
1
1
1
1
1
2
1
1
1
0
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
0
1
1
2
1
2
0
1
1
1
1
2
2
2
1
1
1
1
1
0
0
2
1
1
0
1
2
1
1
1
1
1
2
1
1
1
1
1
2
2
1
0
1
1
2
2
0
2
1
1
1
2
0
1
1
1
1
0
1
1
0
1
0
2
1
1
0
1
1
1
1
0
2
2
0
1
1
0
2
1
0
1
1
1
2
0
2
0
1
1
1
1
1
1
2
2
2
2
2
1
1
1
2
1
1
2
1
1
1
1
2
1
1
0
1
2
1
1
1
2
1
1
1
2
2
1
0
1
1
0
1
1
1
1
2
2
1
1
1
0
1
1
1
1
1
1
2
2
1
1
1
2
1
0
1
0
1
2
1
1
2
2
0
0
2
1
1
1
1
2
1
1
1
1
1
2
1
2
1
1
2
1
1
1
2
2
2
2
2
1
1
0
0
1
1
1
1
1
1
2
1
1
1
1
0
1
1
2
1
2
1
2
2
1
0
1
1
0
1
2
2
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
0
1
1
2
1
0
1
2
0
1
1
2
2
1
1
0
2
0
1
1
1
1
2
1
1
2
0
1
1
1
0
1
1
2
1
1
1
1
1
0
1
2
1
2
1
1
0
0
1
1
2
0
1
1
1
1
2
1
2
2
1
3
1
2
2
2
0
1
0
3
0
1
2
1
1
1
1
1
2
1
1
1
1
1
0
3
2
0
1
2
1
1
1
1
1
2
0
1
1
0
1
1
2
1
1
1
2
2
0
1
1
1
1
1
0
2
1
2
1
2
1
1
1
1
1
1
1
1
1
0
1
1
1
0
2
2
0
1
2
1
1
1
1
1
2
1
0
2
1
1
1
2
0
1
2
2
1
1
1
0
1
1
1
1
1
1
1
1
1
2
1
2
0
2
1
1
1
2
1
2
2
1
1
1
2
1
1
0
1
1
2
2
1
1
0
2
0
0
1
1
1
1
1
1
0
0
1
0
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
1
1
2
0
1
1
0
2
0
1
1
1
2
1
1
1
1
2
1
0
1
2
1
1
2
2
1
0
1
2
1
0
2
1
1
1
1
2
1
1
1
1
2
0
2
1
1
1
1
0
1
1
0
1
2
1
1
2
0
0
0
0
2
1
2
1
2
0
2
2
1
1
1
1
2
1
1
0
1
1
1
1
1
2
2
1
0
1
0
0
2
1
1
0
1
1
1
1
1
0
2
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
2
2
1
1
2
2
1
1
2
1
1
1
2
2
0
0
0
1
0
1
1
2
1
1
1
1
2
1
1
1
2
3
1
1
1
1
1
2
2
2
1
2
1
1
0
1
1
2
1
1
2
1
1
1
1
1
1
2
2
1
0
0
2
0
1
1
2
1
1
1
2
1
1
2
1
0
1
1
0
1
0
0
2
2
1
2
2
1
2
2
1
1
1
0
0
2
1
1
1
1
2
1
1
2
1
1
1
2
0
2
1
0
1
1
1
0
2
1
0
1
2
0
0
1
1
0
1
1
1
2
1
1
1
0
2
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
2
1
1
1
0
0
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
1
2
1
1
2
1
1
2
1
1
1
0
0
1
2
1
1
1
2
1
1
2
1
1
1
1
2
2
2
1
1
1
1
1
1
1
3
1
1
0
2
1
2
3
0
1
2
1
1
1
1
1
1
0
1
2
2
0
1
1
0
2
2
1
1
0
1
1
1
1
2
2
2
1
2
2
1
2
2
2
0
1
1
1
2
1
2
1
0
1
2
2
1
1
0
2
2
0
1
1
1
1
1
1
2
2
1
1
1
1
0
1
1
1
2
1
1
1
1
1
1
2
0
2
1
2
1
1
1
1
1
0
1
1
0
1
1
1
0
0
1
1
1
2
1
0
1
0
2
1
1
2
1
2
1
2
0
1
1
2
1
3
2
2
1
1
1
1
2
1
0
1
0
2
1
1
1
2
0
0
2
2
0
1
1
2
1
2
1
1
0
2
1
2
1
2
1
0
1
1
1
0
0
0
0
0
2
2
2
2
1
0
1
2
1
1
2
1
1
1
3
1
1
1
1
1
1
1
0
1
1
1
1
2
1
1
1
2
1
1
1
2
1
2
1
2
1
1
1
1
2
2
1
2
1
0
0
2
1
1
1
2
1
1
2
1
1
4
1
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
3
1
1
0
2
2
1
1
1
1
1
2
1
0
1
0
2
1
0
1
1
2
2
1
2
1
0
2
2
2
1
1
1
1
1
1
1
1
1
2
2
1
1
1
2
2
1
0
1
2
1
1
1
1
1
1
1
1
2
1
1
0
1
1
1
2
2
2
1
2
1
1
1
1
2
1
1
1
0
0
1
1
1
2
1
2
2
1
0
1
2
1
2
1
1
1
1
1
2
1
0
1
1
1
1
1
0
2
1
0
2
1
2
1
2
1
1
0
2
1
0
2
1
1
3
2
2
1
2
1
1
2
0
1
2
1
1
2
1
2
1
1
1
1
2
2
2
2
2
2
1
1
1
1
1
0
2
1
1
1
1
2
0
1
2
1
1
1
1
2
1
0
2
1
2
2
2
1
0
0
1
1
1
1
1
1
1
1
1
1
2
0
1
1
1
2
2
3
0
1
2
1
2
1
0
1
2
1
1
1
1
2
1
1
1
1
2
1
2
1
2
1
1
1
1
2
1
1
0
2
2
1
0
0
1
1
2
2
1
0
1
1
1
0
2
1
2
2
1
2
2
0
2
0
2
1
1
2
2
2
2
1
1
1
1
1
1
2
1
1
0
1
1
2
1
1
2
1
2
2
2
1
3
1
1
2
1
2
1
1
1
1
1
1
2
1
1
0
2
1
0
1
0
1
1
1
0
1
2
0
1
0
1
2
2
1
1
1
0
0
1
1
1
2
1
1
0
0
2
2
2
1
0
1
3
1
1
1
2
1
2
1
2
2
2
1
1
2
1
1
1
1
1
1
1
2
1
1
2
0
1
1
0
1
0
1
2
1
1
0
1
1
1
0
1
2
2
1
1
2
2
2
1
1
2
1
1
2
1
1
2
1
2
1
1
2
1
1
0
2
1
1
1
1
1
1
1
2
2
1
1
1
2
1
2
1
1
0
1
1
2
2
1
1
2
1
2
1
1
1
1
1
1
0
1
2
1
2
1
1
0
1
1
2
1
1
1
1
0
1
2
0
1
1
2
1
2
2
1
0
1
1
2
1
5
1
0
1
2
1
2
2
1
2
1
1
4
2
1
2
0
1
1
1
1
1
2
0
1
1
1
2
1
0
2
1
1
1
1
2
2
1
1
1
1
2
2
1
2
2
1
0
1
1
2
1
2
1
2
1
0
0
1
0
2
2
1
1
1
2
2
1
2
2
1
1
1
1
1
1
2
1
0
1
2
2
1
0
2
1
2
0
2
0
1
1
1
2
1
2
1
1
2
1
1
1
2
1
2
2
1
1
1
2
1
1
2
1
1
1
2
0
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
1
2
1
2
1
1
0
1
2
2
1
1
0
1
1
0
0
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
2
2
2
1
1
1
0
1
1
1
1
0
1
1
1
0
1
2
1
1
0
0
1
1
0
1
2
1
1
2
2
1
2
2
1
3
0
3
1
1
2
1
1
1
2
1
0
1
1
2
1
0
1
0
1
1
1
1
2
1
2
1
1
1
2
1
2
1
1
1
1
1
1
1
2
2
2
1
0
2
0
1
1
2
1
1
1
1
1
1
1
0
1
0
1
2
1
0
1
1
0
1
0
1
2
1
2
2
1
0
0
1
2
1
1
0
2
1
1
0
1
2
1
1
2
0
2
1
0
1
0
1
1
1
0
1
1
1
1
1
1
2
2
1
2
2
1
1
1
0
1
0
1
1
1
2
0
2
1
1
1
1
1
1
1
1
2
0
1
1
2
1
1
1
1
1
0
1
1
1
2
2
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
2
1
2
2
1
2
2
1
1
2
2
1
1
2
1
1
1
1
1
1
2
0
1
2
1
1
1
1
1
2
1
2
1
2
1
2
1
1
1
2
0
1
1
1
1
1
1
1
1
2
1
2
2
1
1
0
0
1
1
2
1
1
1
1
2
1
1
2
1
2
1
2
1
2
2
1
1
1
2
1
2
1
1
2
2
2
1
2
1
2
1
2
1
1
1
1
1
1
0
1
1
1
1
1
1
1
2
1
1
2
1
1
0
1
1
1
2
1
1
1
1
1
1
1
0
1
2
2
1
1
0
1
1
1
0
2
1
2
0
1
0
1
1
1
0
1
2
1
2
2
2
1
1
1
1
1
1
1
0
1
0
1
2
0
2
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
2
2
0
1
0
1
2
2
2
2
0
0
1
1
0
2
1
1
2
0
2
0
2
1
1
0
1
1
1
1
1
1
2
1
2
1
1
1
1
0
2
1
1
2
1
1
1
2
2
1
2
2
2
1
1
1
2
2
2
1
2
1
1
1
1
1
1
1
1
0
1
1
2
1
1
1
2
2
2
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
2
2
2
2
1
1
1
0
0
1
2
2
1
1
2
0
2
1
1
0
1
1
2
1
1
0
1
0
2
1
0
1
1
0
0
1
0
1
1
1
2
1
1
0
0
2
2
2
2
0
1
2
1
1
2
2
0
1
2
0
0
1
1
1
1
1
0
1
0
1
1
2
0
1
1
1
2
1
2
1
1
0
1
1
1
1
1
2
0
1
1
1
0
1
1
1
0
0
1
1
1
1
1
1
3
2
2
1
1
1
2
1
1
2
1
1
1
1
2
2
1
1
1
2
0
2
1
1
2
1
1
1
1
1
0
1
1
1
1
1
2
2
2
2
1
1
1
0
1
2
1
0
2
1
1
1
1
2
0
2
1
2
2
0
1
2
1
2
1
1
1
0
1
0
1
1
1
0
0
2
2
1
0
0
2
1
1
1
1
1
2
2
2
0
2
1
2
0
1
1
2
1
1
1
1
1
0
1
0
1
1
1
1
0
0
2
1
1
0
1
1
2
1
2
1
1
1
2
1
1
2
1
2
1
0
1
1
1
2
2
0
3
0
2
2
2
2
2
1
2
1
1
1
0
1
1
1
2
2
2
1
1
2
0
1
1
1
1
0
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
0
1
2
2
0
1
0
2
1
1
0
1
1
1
2
1
2
2
2
2
1
2
1
1
1
3
1
1
1
1
1
2
2
1
2
1
1
2
2
1
2
0
1
1
0
1
1
2
1
0
1
1
2
2
2
1
1
1
0
2
2
2
1
0
1
0
1
0
2
2
3
1
2
0
2
1
1
1
1
2
0
1
1
1
1
0
0
1
1
2
1
1
0
1
1
1
1
2
2
2
1
1
1
1
2
1
2
0
2
1
0
1
0
1
1
1
1
2
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
2
0
2
2
0
2
1
0
1
1
2
2
1
1
1
1
2
1
0
1
1
0
1
2
2
2
2
0
1
2
1
2
1
2
1
1
1
1
1
1
2
1
0
0
0
1
1
1
2
1
2
2
1
1
1
2
2
1
1
1
1
2
1
2
1
0
0
0
1
1
2
1
0
2
1
2
1
0
1
1
1
1
2
1
2
2
1
1
2
1
1
1
1
1
2
1
0
1
1
0
1
0
0
1
0
1
1
1
1
1
2
0
2
1
2
1
1
2
1
1
1
2
2
1
1
1
2
0
2
2
1
2
1
1
1
2
2
1
1
2
1
2
0
1
1
1
1
1
1
1
1
2
2
1
1
1
2
1
1
2
1
2
2
1
2
2
1
0
3
1
1
2
2
1
1
0
1
1
2
1
1
0
1
0
2
1
1
2
2
2
2
1
1
0
1
2
1
0
1
1
2
1
1
0
1
1
2
1
1
1
0
2
1
1
3
1
1
2
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
0
1
1
1
2
1
1
1
2
2
1
1
1
1
2
1
1
2
1
2
1
0
1
1
2
3
1
0
1
2
2
1
1
0
2
2
2
1
1
2
2
1
2
0
0
2
0
0
1
1
2
0
1
1
0
1
1
3
1
1
2
1
1
0
1
1
1
1
2
1
1
1
1
1
0
2
2
1
3
2
1
1
1
0
1
1
1
3
1
1
2
0
2
2
0
1
1
1
2
1
1
1
0
1
1
2
1
1
1
1
2
2
2
1
2
1
1
1
1
0
2
1
1
1
1
1
3
2
1
2
0
1
1
2
2
1
2
1
2
1
1
1
0
1
1
1
0
0
1
1
1
2
1
1
1
2
1
1
2
1
1
1
1
0
2
4
2
1
1
2
1
2
2
0
1
0
1
2
0
1
0
1
0
1
1
1
1
0
1
0
2
1
2
1
1
1
2
1
2
1
0
1
0
2
2
1
2
1
2
5
0
0
2
1
1
2
1
0
0
2
1
2
2
1
2
1
1
2
1
1
1
0
0
1
0
1
1
1
2
1
1
1
0
1
1
2
0
1
2
1
2
1
1
1
1
1
0
1
1
1
1
2
1
1
1
1
2
2
2
1
1
1
2
1
1
2
2
2
1
1
0
2
1
1
0
1
2
1
1
1
0
1
2
3
1
1
0
2
1
0
1
2
1
1
1
2
1
1
1
0
1
1
1
1
2
2
2
1
0
0
1
2
2
0
2
0
1
1
1
1
0
2
0
2
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
2
1
2
1
1
1
1
1
2
1
2
1
1
2
0
0
2
0
1
1
1
0
2
0
1
1
1
1
0
1
0
0
1
1
0
1
0
1
1
2
1
1
0
1
1
0
0
2
1
0
2
1
1
0
2
1
1
1
0
1
2
2
0
1
1
1
1
1
0
0
0
1
1
1
1
2
1
1
1
1
1
1
1
1
2
0
1
1
1
1
1
1
2
1
1
0
1
1
2
2
1
1
1
1
1
2
2
1
1
2
5
1
2
1
1
1
0
1
1
1
1
1
0
0
0
2
1
1
1
1
1
1
1
0
1
4
1
1
1
1
1
1
1
2
1
1
2
1
1
1
2
0
2
2
1
1
1
1
2
0
2
2
2
1
2
1
1
1
1
0
1
1
2
1
1
1
1
0
1
2
2
2
2
2
0
2
1
2
0
1
0
0
1
1
2
0
2
0
1
1
1
0
1
1
2
1
2
1
2
1
0
2
2
1
2
1
2
2
2
1
1
1
0
0
1
1
1
2
1
1
4
1
2
1
1
1
1
2
1
0
1
0
1
1
2
1
1
1
1
2
1
2
1
2
1
2
1
1
2
1
1
0
2
1
1
1
1
1
2
2
1
2
1
1
1
2
2
2
1
1
0
2
1
1
2
2
2
1
0
1
0
1
0
1
0
1
2
2
1
1
2
1
1
1
1
2
2
1
0
2
2
1
2
0
1
3
1
3
2
1
1
2
1
1
1
1
1
0
2
1
2
2
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
0
2
1
1
0
2
1
1
0
0
1
2
2
1
1
0
1
1
1
1
2
1
2
1
2
1
1
0
1
0
1
0
1
1
1
1
1
1
1
1
0
1
1
1
1
1
0
0
2
2
0
0
1
1
1
1
0
2
2
1
1
1
1
1
2
0
0
2
1
1
1
1
2
1
1
1
2
1
1
1
1
1
2
2
2
2
1
2
1
2
1
1
1
2
2
1
0
1
1
1
0
2
1
1
1
0
1
1
1
2
1
0
2
1
1
2
2
2
2
1
1
0
2
0
1
1
0
2
1
0
1
1
1
1
0
1
1
2
1
1
1
1
1
2
1
1
0
2
1
1
0
1
1
2
2
1
1
1
1
2
1
2
1
2
1
0
2
1
2
2
0
1
1
1
1
0
1
2
1
2
1
2
2
1
1
1
1
0
2
1
1
1
1
2
2
1
1
1
2
1
1
1
2
1
2
2
2
1
1
0
1
1
2
1
1
2
1
1
2
1
1
1
2
2
1
1
0
1
0
1
2
1
1
1
0
0
0
1
1
1
1
2
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
2
1
1
0
1
1
2
1
1
0
1
2
1
1
1
2
2
1
1
0
1
0
2
1
2
2
1
0
0
1
1
1
1
2
1
1
2
1
1
0
0
1
1
0
1
1
2
2
1
2
1
2
2
1
2
2
1
2
0
1
2
0
1
1
1
1
1
2
0
0
2
1
2
2
1
1
2
1
2
0
2
1
1
0
1
0
0
0
0
1
1
1
2
1
1
2
2
1
2
2
1
1
0
2
2
2
1
1
1
1
0
1
1
1
1
1
2
1
1
1
1
1
1
1
2
0
1
0
0
1
1
1
1
2
2
1
1
2
1
0
1
1
0
1
2
1
1
1
1
1
1
2
2
2
2
1
2
1
2
1
1
1
1
1
1
0
0
1
1
1
2
1
2
1
2
0
1
1
1
1
1
2
1
2
1
1
2
0
0
1
1
0
1
0
1
1
1
1
1
0
1
1
2
1
1
1
1
0
2
1
1
1
1
1
2
0
1
1
1
1
1
2
1
1
1
1
1
2
2
1
2
1
1
0
1
1
1
2
2
1
1
1
1
1
1
2
2
2
1
2
3
1
1
2
3
2
2
1
1
2
1
1
1
1
0
1
1
1
1
1
1
1
2
1
1
2
1
1
2
1
2
2
1
1
1
1
1
0
2
1
2
1
1
1
0
1
1
1
2
1
1
1
2
2
2
0
1
1
1
1
2
1
1
0
2
0
1
0
2
1
2
2
1
1
2
0
1
1
0
0
1
2
1
1
2
1
1
2
0
1
2
2
1
2
1
1
1
0
2
1
0
0
1
1
2
2
1
2
1
0
2
0
1
1
1
2
1
1
2
1
0
0
1
1
0
1
1
0
1
1
1
1
1
1
0
1
1
1
1
1
0
1
1
2
0
1
2
1
1
0
1
1
0
2
1
1
2
1
0
1
1
0
2
1
1
2
1
1
1
1
1
0
1
2
2
0
2
1
1
0
1
1
1
1
1
1
2
1
1
1
0
1
2
1
2
2
1
1
1
2
1
1
2
2
0
1
2
1
1
0
2
2
0
1
1
1
1
1
0
0
0
1
0
2
1
1
1
0
1
1
2
1
1
2
0
1
1
1
1
1
2
1
1
1
0
0
2
1
1
0
1
2
1
1
1
2
1
1
2
2
1
1
1
0
1
2
1
0
1
1
1
2
1
1
2
1
2
2
2
0
2
1
1
2
1
2
0
0
0
1
2
0
1
2
1
0
1
1
1
2
1
1
1
1
2
1
1
0
1
1
1
1
0
1
1
1
1
1
1
1
1
2
1
2
2
1
0
2
0
0
2
2
1
1
2
1
1
2
1
1
0
1
2
2
0
1
1
1
0
0
1
2
2
1
1
1
1
1
1
2
0
1
1
2
1
2
1
2
1
1
1
2
2
2
0
3
1
1
2
2
1
0
0
2
1
2
2
0
2
1
1
1
1
1
1
1
2
1
1
1
1
0
1
1
2
1
1
1
0
2
2
1
2
2
1
2
1
2
2
0
1
1
3
1
1
1
2
2
1
1
2
2
1
2
1
1
1
0
2
1
0
2
2
2
1
0
2
2
2
0
0
2
1
0
1
2
1
0
1
1
0
1
0
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
0
1
1
1
2
2
0
1
1
1
2
1
1
0
1
2
2
1
1
1
1
2
1
1
1
0
2
2
1
1
1
1
1
2
2
2
1
1
1
2
1
1
1
1
2
2
0
1
1
1
2
1
0
0
2
2
2
0
1
1
2
1
0
0
2
1
1
1
1
1
1
1
1
0
1
1
0
2
2
0
2
1
1
1
1
1
2
0
1
2
1
1
1
1
1
1
1
1
2
2
0
1
0
0
1
2
1
2
2
0
1
2
1
1
1
1
1
1
1
1
2
0
1
2
1
2
1
1
1
2
1
1
1
2
1
1
1
1
2
1
2
2
0
2
1
1
1
0
0
1
1
1
0
2
1
1
1
1
2
0
1
1
1
0
1
2
1
1
1
0
1
0
1
1
1
1
1
2
0
1
1
1
2
1
1
2
2
1
0
0
1
1
1
1
1
1
2
1
1
0
1
1
1
1
0
0
1
2
1
1
1
0
0
1
1
1
1
1
0
0
1
1
1
1
2
2
1
1
0
1
1
0
1
2
1
1
1
1
1
2
2
1
2
1
2
2
1
1
1
0
0
1
0
2
0
0
2
2
1
1
0
1
1
2
1
1
2
2
1
2
1
1
0
2
0
1
1
1
4
1
0
2
1
1
2
1
2
2
1
1
0
2
2
1
1
2
2
1
2
1
1
1
2
1
0
0
1
1
1
1
1
1
1
2
1
1
1
0
0
0
2
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
0
1
2
2
1
0
1
1
2
1
2
1
0
1
2
0
1
0
1
1
1
2
2
1
1
0
2
1
1
1
1
2
1
1
1
1
0
1
1
1
2
1
2
1
1
2
1
1
0
1
1
1
0
1
1
1
2
1
1
0
1
0
2
2
2
1
1
1
4
2
2
1
0
2
0
1
2
2
1
1
2
0
1
0
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
2
2
1
0
0
1
2
2
1
1
1
1
0
0
2
1
0
2
1
0
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
2
1
1
0
2
2
0
0
1
2
1
1
2
1
1
2
2
3
2
1
1
0
1
1
2
1
0
0
0
1
2
2
1
0
1
0
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
0
2
2
2
2
1
2
1
1
1
0
1
1
1
1
1
1
0
1
1
2
1
1
0
1
1
1
0
1
2
1
0
1
1
0
0
1
1
1
1
1
1
0
0
0
1
1
2
1
2
1
1
0
1
1
2
1
0
1
1
2
2
1
2
2
2
2
1
0
0
1
1
1
1
1
1
1
1
0
1
1
2
1
1
1
1
0
2
1
1
2
2
1
0
1
1
0
1
2
1
1
1
2
1
2
2
1
1
1
2
1
1
1
3
1
1
0
1
1
0
1
1
1
2
1
1
1
1
0
2
1
1
2
2
1
1
1
1
2
2
1
2
0
2
1
1
2
1
0
1
1
1
1
2
1
2
2
1
1
1
1
1
2
1
2
2
1
2
2
1
1
1
2
2
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
3
2
1
2
2
1
1
2
0
1
2
1
1
2
0
2
1
2
0
0
1
1
1
2
1
1
2
2
0
0
2
2
0
2
1
1
2
2
1
1
2
2
1
1
2
0
0
1
1
1
1
0
1
2
2
2
0
1
1
2
1
1
2
2
1
2
1
1
1
1
2
1
1
1
1
0
2
1
1
1
2
0
1
2
2
2
2
1
1
1
1
1
2
1
1
1
1
1
1
0
1
1
1
2
1
2
1
1
1
0
1
0
1
1
2
2
1
1
0
2
1
2
0
0
1
0
1
0
1
2
1
1
1
2
2
2
0
1
0
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
0
2
2
2
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
3
2
2
2
1
2
2
1
0
0
1
2
3
0
1
1
1
1
1
1
0
1
1
1
2
2
1
1
0
2
0
2
1
1
1
1
2
1
1
1
0
1
2
2
0
1
2
2
1
1
1
1
1
1
2
1
1
2
1
0
1
1
1
1
0
1
2
0
1
0
1
2
1
2
2
0
2
1
1
1
2
1
2
1
2
1
0
2
1
2
1
1
5
1
1
2
2
2
1
2
1
1
1
2
1
2
1
1
1
2
2
1
1
2
1
1
0
2
2
0
1
0
0
2
0
2
1
1
2
1
1
1
0
1
1
2
1
1
0
2
0
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
0
1
1
2
1
1
1
2
1
1
2
1
1
1
2
2
1
0
1
1
1
1
1
2
1
1
1
1
1
3
2
2
2
1
2
0
1
0
0
2
2
1
1
1
1
0
1
1
1
0
0
2
1
1
1
1
0
0
1
1
2
1
1
2
0
0
0
0
2
1
1
1
0
3
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
2
2
1
3
1
1
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
0
0
2
1
1
1
2
1
2
0
1
1
0
0
1
2
1
1
1
2
1
2
1
0
1
1
2
1
1
1
2
1
1
2
1
2
1
1
0
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
2
0
1
1
2
1
2
2
2
2
1
2
1
2
1
2
0
1
1
1
1
1
2
1
1
2
2
1
0
2
2
1
1
2
1
0
1
0
1
1
0
2
1
1
1
1
1
1
1
1
2
0
0
1
2
2
1
2
1
1
0
2
2
2
1
1
1
2
2
1
1
1
1
2
1
4
1
1
2
1
1
1
1
0
1
0
1
1
2
1
0
1
1
1
1
0
0
1
1
0
1
1
1
1
1
2
2
2
1
2
0
1
2
0
1
1
0
1
2
1
1
1
1
1
0
1
1
1
1
1
2
1
1
0
0
2
1
2
1
2
2
1
1
1
1
1
1
0
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
0
1
2
1
0
1
2
1
1
2
1
2
1
1
0
0
0
0
2
2
1
1
1
1
2
2
2
1
1
1
2
1
1
1
1
2
1
1
0
1
0
1
1
1
1
1
1
2
1
0
0
2
1
2
1
1
2
2
0
1
1
2
2
1
0
1
1
1
0
0
0
0
2
1
1
1
2
0
2
1
1
0
2
1
1
1
1
1
1
1
1
0
1
1
2
1
1
2
2
1
1
0
1
0
1
1
1
1
2
2
2
1
1
1
1
0
2
2
1
1
1
1
2
1
0
1
0
1
2
2
0
2
2
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
2
1
1
0
0
1
1
1
1
2
1
1
1
1
1
1
0
2
2
1
1
1
1
1
2
1
2
1
1
1
1
0
1
2
1
4
1
2
0
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
2
0
1
2
1
2
2
2
0
0
0
0
1
3
2
1
2
1
1
1
1
1
1
1
2
2
2
1
1
2
1
2
0
1
1
1
1
2
0
2
1
1
2
1
1
2
0
1
0
1
1
1
1
2
1
1
0
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
0
1
2
1
0
2
0
1
1
1
1
1
1
1
1
3
2
2
2
1
2
2
1
1
0
1
1
1
2
1
0
1
1
0
0
2
1
3
1
1
1
2
1
1
0
1
2
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
0
0
2
1
1
0
1
1
1
1
1
2
1
1
0
2
1
1
1
2
0
1
1
1
0
1
1
1
2
1
2
2
2
0
1
1
2
1
1
2
1
1
2
1
0
1
0
0
1
1
2
1
2
0
1
2
1
0
1
2
1
0
0
0
1
2
1
1
2
1
0
2
1
1
1
1
0
2
2
0
0
0
1
2
1
1
0
2
1
1
2
1
1
0
1
0
2
1
1
1
1
1
1
1
1
0
1
1
2
2
1
0
2
1
1
2
2
1
2
1
1
1
2
1
1
1
2
2
2
1
2
0
1
0
0
1
1
1
3
1
0
2
1
2
1
1
1
2
2
1
1
1
1
2
1
1
1
1
2
0
1
1
1
0
1
1
1
0
1
2
0
1
0
2
2
2
1
1
1
1
1
1
1
1
1
1
0
0
1
1
1
2
2
2
0
1
2
1
0
2
1
2
1
2
1
0
1
0
2
2
4
1
1
1
3
0
0
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
2
0
1
0
2
1
1
1
2
2
2
1
2
1
1
0
2
1
1
1
1
2
1
1
1
1
1
2
1
1
2
1
0
2
2
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
0
1
0
0
1
1
1
2
2
1
1
1
1
2
0
1
1
0
1
2
2
1
1
1
2
1
1
0
0
2
2
3
2
0
2
1
2
0
1
1
0
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
2
0
1
1
0
1
2
2
1
2
1
1
1
1
1
1
1
0
2
0
1
1
0
1
1
1
2
1
2
1
3
2
2
1
1
1
1
2
1
2
1
1
1
2
1
1
2
1
1
2
1
1
1
2
2
0
1
0
1
1
1
1
1
2
2
1
2
0
2
1
2
2
1
1
0
2
1
1
2
2
0
1
2
1
1
1
1
0
1
2
0
1
2
1
2
2
2
1
0
1
2
0
1
1
1
2
1
0
3
2
2
1
2
1
1
1
0
1
1
1
2
1
0
1
0
1
2
0
1
2
1
2
1
2
2
2
0
0
1
1
1
1
1
1
2
1
1
1
0
1
1
0
1
1
2
1
2
1
1
2
2
1
1
1
1
2
2
1
1
2
0
2
2
1
0
2
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
3
1
1
2
3
1
2
1
2
0
1
2
1
1
1
2
1
2
1
1
1
2
1
1
1
2
1
0
0
2
2
1
1
0
0
2
1
1
1
1
2
1
2
1
1
2
2
0
0
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
0
2
0
1
1
3
1
1
1
2
1
1
1
2
1
1
1
0
1
1
1
1
2
1
1
1
1
1
1
2
1
2
2
1
0
0
1
2
1
1
1
1
1
1
0
2
2
1
1
1
0
1
2
1
0
0
1
2
2
1
1
2
0
0
2
1
1
0
2
2
2
0
1
1
1
0
1
1
0
1
0
1
1
1
2
2
2
1
2
0
1
1
1
1
1
1
2
1
0
1
2
0
1
0
0
2
1
2
1
2
1
0
2
2
2
1
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
2
0
2
2
1
0
1
2
1
0
1
1
0
3
1
2
1
0
1
1
1
0
1
1
1
2
2
2
0
2
1
1
1
0
1
1
0
0
2
1
1
1
2
2
2
1
1
0
1
1
1
1
1
2
1
1
1
0
1
1
2
1
1
1
1
1
0
5
1
2
1
2
2
1
1
1
1
1
2
0
1
1
1
1
1
2
1
1
0
0
1
1
2
2
2
2
1
1
2
1
2
2
1
1
2
2
1
2
1
1
1
1
1
1
1
1
0
2
1
0
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
0
0
2
0
2
1
1
0
1
2
0
1
1
2
1
0
1
1
0
1
2
0
2
1
2
3
1
0
1
1
2
2
1
2
0
1
1
0
1
2
1
1
1
1
1
2
0
2
2
1
1
2
0
1
2
1
2
0
1
1
1
1
1
1
0
0
0
1
1
1
1
2
1
2
0
2
2
0
0
1
1
1
1
1
0
1
1
1
2
1
1
2
1
1
1
1
3
1
2
1
1
1
1
1
1
0
0
2
1
3
2
0
1
0
2
2
1
4
1
2
1
2
0
1
1
1
3
2
1
1
2
0
1
1
1
1
1
2
1
0
1
1
0
1
1
1
1
1
0
2
1
0
1
1
2
2
1
1
0
1
1
1
1
1
1
1
1
1
1
1
0
1
2
1
1
1
2
1
1
1
0
2
1
2
4
1
2
1
1
1
1
2
1
2
1
2
1
1
2
1
1
1
2
1
1
1
2
2
1
3
2
0
2
1
1
2
1
2
2
2
1
1
1
1
1
5
1
1
2
1
1
1
1
2
2
5
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
2
1
1
1
2
1
1
0
2
0
1
1
1
1
2
1
1
2
2
2
1
1
2
0
1
1
2
1
0
0
1
2
1
1
0
2
1
1
2
2
0
1
1
2
1
1
1
1
1
1
1
1
2
0
1
1
1
1
2
1
2
1
1
1
2
0
2
0
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
0
1
1
0
0
2
1
1
1
2
2
1
1
0
1
1
2
1
2
1
1
2
1
1
0
1
1
1
2
1
1
2
0
0
2
0
1
2
1
0
1
1
2
1
1
2
1
1
0
1
1
2
1
2
1
1
1
1
2
0
2
2
2
2
0
2
1
1
0
0
1
1
1
0
2
2
1
1
1
1
1
2
0
1
2
0
0
1
1
1
1
1
1
1
2
1
2
1
2
0
2
0
0
1
1
1
0
1
2
1
1
1
1
1
0
1
1
0
1
1
1
1
2
1
2
1
2
1
1
1
1
0
1
1
2
2
0
2
1
1
0
0
1
0
1
1
1
2
2
0
1
1
1
1
0
4
1
1
1
1
2
1
1
1
2
2
1
2
2
2
0
1
2
1
2
2
1
1
0
2
2
0
0
1
1
1
1
0
1
2
2
1
1
2
1
1
1
2
1
1
2
2
2
0
1
1
1
2
1
2
1
0
0
1
2
1
1
1
1
0
0
1
1
1
1
1
1
1
1
1
1
2
1
1
1
0
1
1
2
2
1
1
2
0
2
0
2
1
2
1
2
1
1
1
1
2
1
0
1
0
0
1
1
1
1
1
1
1
0
1
1
0
1
1
2
1
1
2
1
1
2
0
2
2
2
0
1
1
2
2
2
1
1
2
1
1
1
1
2
2
1
1
1
1
2
1
0
1
0
1
2
0
1
2
2
2
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
0
1
2
1
1
3
1
1
2
1
2
0
1
1
1
1
1
1
1
1
1
0
2
2
1
1
1
0
1
1
0
1
0
1
1
2
1
0
1
2
1
1
0
2
1
2
1
1
2
1
0
2
0
1
1
1
1
0
1
1
2
1
1
1
1
2
1
1
1
1
1
2
1
2
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
0
1
1
2
1
2
1
2
0
1
1
1
1
2
0
1
2
2
1
1
2
1
1
0
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
3
1
1
1
0
1
5
1
1
2
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
0
1
0
2
1
2
1
2
2
1
2
1
1
1
1
1
1
0
1
1
1
1
1
2
2
1
2
1
1
1
2
1
1
2
1
2
2
1
2
0
1
1
1
1
2
1
1
1
0
3
2
1
1
1
0
1
0
2
1
2
0
0
1
5
0
2
1
1
1
0
1
1
0
1
2
1
2
2
1
2
1
0
2
2
1
2
1
1
2
0
0
1
2
1
1
1
0
1
1
1
0
0
2
2
2
1
1
2
1
1
1
1
1
0
0
1
1
0
1
0
1
0
1
1
2
1
1
2
1
1
1
0
1
1
2
0
1
2
1
2
2
1
2
1
0
2
1
1
0
0
1
2
2
1
1
1
1
1
1
1
1
0
0
1
2
0
2
1
2
1
2
1
3
1
1
1
1
1
1
1
2
1
0
2
1
1
1
2
2
2
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
0
1
0
2
2
2
1
1
1
2
1
1
2
2
1
2
1
0
0
1
2
1
0
2
1
1
1
2
1
2
0
1
0
2
1
1
1
1
1
1
0
1
2
1
1
2
1
1
1
1
1
1
1
1
1
0
1
2
1
0
0
1
1
1
1
2
1
2
1
1
2
2
1
1
2
0
1
1
2
0
1
2
2
1
0
2
1
2
1
1
2
0
1
2
2
2
1
1
2
2
1
1
1
1
2
2
1
1
2
2
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
2
2
0
1
2
2
2
1
1
0
0
1
1
1
1
2
1
1
0
1
1
1
2
1
0
1
1
2
2
1
0
1
1
2
2
2
2
2
0
1
2
1
3
1
2
2
1
2
1
0
1
0
1
0
1
2
1
2
1
1
1
2
1
1
0
1
1
1
1
3
0
1
1
1
1
1
2
2
1
1
1
2
5
2
1
1
1
1
1
1
2
0
2
0
1
0
2
2
0
2
1
1
1
1
2
1
0
1
1
2
1
1
2
1
1
1
2
0
2
1
1
1
1
1
0
0
1
0
1
1
1
2
1
2
1
2
0
0
1
0
1
2
1
0
1
1
0
1
1
1
1
2
2
2
1
1
1
1
1
0
2
2
3
2
2
0
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
0
1
1
2
1
1
1
1
1
1
2
0
1
1
0
1
2
2
2
2
1
1
2
1
1
1
0
2
0
1
1
1
2
1
1
4
1
1
2
1
2
2
1
1
2
0
1
1
2
1
1
1
0
1
1
1
1
1
1
1
1
2
1
0
2
2
1
1
1
1
1
1
1
2
2
1
2
2
1
1
1
1
1
1
2
0
1
1
2
2
0
1
1
1
1
0
2
1
2
1
2
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
0
1
1
1
0
1
1
0
1
1
1
1
2
1
2
1
1
1
1
1
1
0
0
1
0
1
1
1
0
1
1
1
2
2
1
2
1
1
2
1
2
1
1
1
1
1
0
1
2
2
1
1
1
2
0
1
2
2
1
2
2
1
2
1
1
2
2
1
1
1
2
2
1
0
1
1
1
1
2
2
1
1
1
1
2
2
1
1
2
2
1
1
1
1
1
1
2
2
2
2
1
1
1
0
0
1
2
0
1
2
0
2
3
1
0
1
2
2
1
1
1
2
1
1
2
2
2
1
1
0
2
2
1
1
1
0
0
0
1
2
2
1
0
1
0
1
2
1
1
0
1
1
1
1
2
1
1
1
2
2
1
2
0
1
2
2
1
1
1
1
1
1
1
0
0
1
2
1
1
1
1
1
1
1
2
1
0
2
0
1
2
1
2
1
0
2
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
2
1
2
1
1
1
1
1
0
1
1
1
0
2
0
2
2
1
2
1
1
0
1
2
1
1
0
0
0
1
1
2
1
2
1
1
1
1
1
1
1
1
2
2
1
1
1
2
1
2
1
0
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
0
2
2
1
1
1
2
2
1
2
2
1
2
2
1
0
2
2
0
1
1
0
1
1
2
1
2
0
2
2
1
2
2
2
0
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
3
2
2
1
1
1
1
1
1
2
1
1
1
1
2
1
0
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
0
1
1
1
1
2
2
2
1
1
0
1
0
0
2
0
1
2
1
1
1
3
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
0
1
2
1
1
0
2
2
0
1
1
2
1
1
2
1
1
3
1
0
1
1
1
0
1
2
1
1
2
1
1
1
1
0
1
1
1
1
1
2
0
0
1
1
2
1
1
2
1
1
2
2
1
1
2
1
0
1
1
1
1
1
1
0
2
2
1
1
2
1
1
2
1
0
2
1
2
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
0
1
2
2
1
0
1
1
0
1
1
2
1
1
0
1
2
1
1
1
1
1
2
1
1
0
1
1
2
1
1
2
1
1
1
1
0
0
1
1
1
0
1
1
2
2
1
1
2
1
2
2
2
1
2
1
1
1
1
2
0
1
0
1
1
0
2
2
2
1
1
2
1
1
2
1
1
2
1
1
1
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
0
0
1
1
1
1
2
2
1
1
2
0
1
2
1
0
0
1
1
2
1
1
2
1
1
1
2
1
1
2
0
2
1
1
0
1
2
1
0
2
2
2
1
1
1
1
2
4
1
1
1
1
2
1
2
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
0
0
1
1
1
2
1
1
0
1
1
1
1
1
1
0
2
1
1
1
2
2
1
1
1
1
0
1
2
1
1
1
0
1
2
1
2
1
1
1
2
2
2
1
4
2
1
1
0
1
1
1
0
1
1
1
2
1
2
2
2
1
2
1
2
2
1
1
1
0
1
1
1
1
2
2
1
2
1
2
2
2
2
0
1
1
0
1
1
1
1
0
1
1
1
0
1
1
0
1
1
2
1
2
1
2
0
2
2
2
0
1
1
1
1
0
2
1
1
1
1
1
2
1
1
1
2
1
1
2
1
2
1
2
1
1
2
2
1
1
2
1
1
0
2
0
2
1
1
2
1
1
1
1
2
1
1
1
1
1
0
1
0
2
1
2
1
1
2
1
0
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
0
1
1
1
2
1
0
1
1
2
1
1
2
0
1
1
1
2
1
1
0
1
1
2
2
0
1
2
1
1
0
1
0
1
0
1
2
1
2
1
2
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
0
1
2
2
1
1
1
1
0
0
1
2
1
1
1
1
0
1
2
1
1
0
2
1
2
2
2
1
1
2
1
2
1
1
0
3
1
2
0
1
2
1
1
0
0
1
2
1
1
1
2
2
1
1
0
1
2
2
2
2
1
1
2
2
0
1
2
0
1
1
1
1
1
1
1
0
1
1
1
2
2
1
2
2
1
1
0
1
1
1
1
2
0
1
2
2
1
0
2
3
0
1
1
1
1
1
1
1
2
1
1
0
1
1
1
1
2
1
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
0
1
0
2
1
2
1
1
0
2
2
0
0
1
2
1
1
0
1
1
0
1
1
1
1
1
1
1
0
1
2
1
2
2
2
1
1
2
1
2
0
1
1
1
1
2
1
2
1
2
0
2
1
0
2
1
2
0
2
2
1
1
1
1
1
0
1
1
0
2
2
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
0
2
2
2
1
1
0
2
1
0
3
1
1
3
2
1
1
2
2
2
1
1
1
1
1
1
1
1
1
2
1
2
2
1
2
0
0
3
1
1
2
2
1
2
1
2
2
2
1
1
1
1
1
1
1
1
1
1
1
2
0
1
1
2
1
1
1
2
1
1
1
1
2
0
0
1
1
1
1
2
1
3
1
1
1
2
0
1
1
0
1
0
1
2
1
1
2
1
3
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
2
1
2
1
1
0
2
1
1
2
2
2
1
1
1
1
1
1
1
2
1
0
2
2
1
1
2
1
1
1
0
0
0
1
1
1
1
1
2
2
1
1
1
3
1
1
2
2
1
2
1
1
1
2
0
2
1
0
2
2
2
2
1
1
1
1
1
2
1
2
2
1
1
2
0
1
2
1
0
1
2
0
1
1
0
2
1
1
1
1
2
1
1
1
2
3
1
1
2
1
1
1
2
1
2
2
0
1
2
1
0
0
0
1
1
2
1
1
1
2
0
1
1
1
1
2
1
1
1
1
1
3
1
1
2
2
1
0
1
1
1
1
1
1
2
1
2
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
3
1
1
1
1
0
0
1
1
2
2
0
1
1
2
2
1
0
1
1
0
1
2
2
0
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
0
2
2
1
0
1
2
1
1
2
2
1
2
0
1
2
3
1
1
1
2
1
2
1
1
1
1
1
0
1
1
2
1
2
3
2
2
2
1
2
1
1
1
1
1
1
1
0
2
1
1
1
0
1
1
1
1
2
1
2
0
1
1
1
0
1
2
2
0
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
1
1
2
1
1
2
2
2
1
1
2
2
1
1
2
2
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
2
2
1
2
1
1
0
0
1
0
1
2
1
1
1
2
1
1
1
1
2
2
1
1
1
2
1
1
2
1
1
1
1
1
2
0
1
1
2
1
1
0
1
1
2
1
0
1
1
1
1
0
1
2
1
2
2
1
1
1
1
2
1
2
2
1
2
1
2
2
2
0
1
2
2
2
1
1
2
2
0
2
2
1
2
1
2
2
1
1
2
2
0
2
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
0
1
2
0
2
1
1
2
0
1
1
1
1
1
1
2
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
1
0
1
1
1
1
1
1
2
3
1
2
1
1
1
1
1
1
1
0
1
1
2
1
2
1
0
1
1
2
0
1
2
1
2
1
1
1
2
2
1
1
0
1
1
2
2
1
2
1
1
1
1
2
1
1
0
1
1
2
0
2
1
1
1
1
1
1
2
1
2
0
2
1
2
1
1
1
1
1
1
0
1
1
1
1
1
1
2
1
2
2
2
1
1
1
2
1
0
0
2
2
2
1
1
1
1
0
1
0
1
1
1
1
1
2
1
1
1
2
0
1
1
0
0
1
1
1
2
1
1
0
1
2
1
1
1
1
1
2
2
2
2
1
2
1
0
0
1
2
3
1
0
1
0
1
1
0
1
1
1
1
1
2
1
1
1
1
2
2
1
2
1
1
1
2
1
2
0
1
2
1
1
0
1
1
0
1
1
2
2
2
1
0
2
0
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
0
1
2
0
1
2
0
1
1
2
1
2
2
0
1
2
2
2
0
1
1
1
1
1
2
2
1
0
1
0
1
1
1
1
1
1
2
2
1
2
1
1
0
1
2
2
2
1
2
2
2
1
0
1
1
1
0
0
1
1
0
0
2
1
2
1
1
1
1
2
2
1
1
2
1
1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
2
1
1
2
1
3
1
2
2
2
1
0
1
2
1
2
2
0
1
3
2
0
1
2
1
1
1
1
0
1
1
0
2
2
1
2
1
1
1
0
1
1
1
1
1
0
1
1
1
1
1
1
2
2
1
0
1
1
2
1
2
2
1
2
1
1
1
2
0
1
1
1
2
1
1
1
1
1
1
1
0
1
1
1
1
2
2
2
1
2
1
1
1
1
0
1
1
2
0
0
2
1
1
1
1
2
1
1
1
2
1
0
1
1
2
2
1
2
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
2
2
1
1
0
2
2
2
2
3
1
1
1
1
2
1
1
1
1
2
0
2
2
1
1
2
1
0
0
1
1
1
1
1
2
2
1
1
2
1
1
1
2
1
2
1
2
1
0
1
1
1
1
1
1
1
1
1
1
1
0
2
1
0
1
2
1
2
0
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
0
1
0
1
1
0
1
1
0
1
1
1
1
1
1
1
1
1
2
2
1
1
0
2
2
4
2
2
0
1
3
1
1
1
2
0
2
0
1
1
1
2
2
1
2
1
0
2
2
1
2
2
2
1
1
1
1
0
1
0
0
1
1
1
1
2
0
1
1
1
1
1
1
1
1
1
2
1
3
1
0
1
2
0
2
1
0
1
1
2
1
1
1
0
1
1
1
1
2
2
2
1
0
2
2
1
1
1
1
1
1
0
0
1
1
1
1
1
1
1
0
1
0
1
1
1
1
1
0
2
2
1
1
1
1
2
1
0
1
2
1
1
1
1
2
1
2
1
2
1
0
1
1
1
2
1
2
1
1
1
2
2
0
1
1
1
2
1
1
1
1
1
0
1
1
1
2
2
2
2
2
1
1
1
2
1
2
2
1
1
2
1
2
2
0
2
1
1
1
1
2
1
1
0
0
1
2
1
1
1
1
1
1
2
1
0
1
1
1
1
0
1
1
2
2
0
2
2
1
1
2
2
1
1
2
2
2
1
2
1
1
0
1
0
2
1
2
0
1
2
0
1
1
1
1
1
1
1
2
0
1
0
1
2
2
0
1
2
1
1
2
2
1
1
1
1
1
1
2
2
1
2
1
1
0
1
0
2
1
2
1
1
1
1
1
1
2
0
1
1
1
1
1
1
1
1
1
2
1
0
2
1
1
2
2
1
1
3
1
0
1
1
2
1
0
1
2
2
1
1
1
1
2
1
1
1
0
1
1
1
1
2
1
0
1
2
2
1
1
1
1
2
1
1
1
1
1
2
1
1
2
1
2
1
1
1
2
2
0
3
2
2
1
2
1
1
1
2
1
2
1
1
2
2
1
1
1
1
1
1
1
0
1
0
0
1
0
1
0
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
3
1
2
0
1
2
0
1
0
1
0
0
1
0
1
2
1
1
2
2
2
1
2
2
2
1
0
1
1
1
1
2
1
0
1
0
1
1
1
1
1
1
2
1
1
2
1
1
1
2
1
1
1
2
1
2
2
1
1
2
1
1
1
1
2
1
1
2
1
1
2
1
1
2
1
2
2
2
1
2
1
1
2
1
2
1
1
0
1
0
1
1
1
1
1
1
2
1
0
2
2
2
2
1
1
2
1
2
1
1
3
1
1
2
1
1
1
3
1
3
1
0
1
2
0
0
2
2
0
0
2
2
2
1
1
1
1
1
1
1
2
2
0
1
2
1
1
2
1
1
1
1
2
1
2
1
1
0
1
1
0
1
0
0
0
1
1
0
0
1
1
1
1
1
1
0
2
0
2
0
0
1
1
1
1
1
2
1
2
1
1
1
1
1
2
1
2
2
0
2
0
1
1
1
1
1
2
2
1
2
1
2
1
1
2
0
2
0
2
0
0
2
2
2
2
1
0
0
2
2
1
0
1
1
1
1
1
2
0
1
2
1
1
1
2
1
0
1
0
1
2
2
2
1
0
1
1
0
1
2
1
1
1
0
1
1
3
1
1
1
1
2
0
1
1
4
1
2
1
2
0
1
3
1
2
1
0
2
1
1
2
1
0
1
1
1
1
1
0
1
1
0
1
2
0
1
1
0
1
1
0
1
1
1
0
0
1
1
0
0
0
1
1
2
1
1
1
1
1
2
1
2
2
1
2
1
1
1
0
0
1
2
1
1
1
1
2
2
2
1
1
1
1
2
1
1
1
1
1
3
2
1
1
1
1
1
2
2
1
2
1
0
1
1
1
2
1
2
2
3
2
2
0
0
1
0
1
1
2
2
1
2
1
1
1
1
2
2
0
1
2
1
2
1
0
1
1
1
2
2
1
1
1
1
1
2
1
1
1
2
2
2
2
2
1
1
1
1
1
2
1
0
0
0
2
2
1
0
2
1
1
2
1
1
1
2
2
1
1
1
2
1
1
0
1
1
2
1
0
1
0
1
2
2
1
0
0
2
1
1
1
0
1
1
1
2
2
1
2
2
0
1
1
2
2
2
2
0
1
2
2
1
0
2
1
2
0
1
1
1
1
1
0
1
1
2
1
2
0
1
1
1
0
1
1
1
1
1
1
2
0
1
2
2
1
1
0
1
1
1
1
1
2
1
1
1
2
0
1
1
2
1
2
2
0
2
2
2
1
1
1
1
1
2
1
1
2
1
0
2
2
1
1
1
2
1
0
1
1
1
0
1
2
1
1
1
1
2
1
2
1
1
1
0
0
1
2
1
0
1
0
2
1
1
1
0
1
1
1
1
2
1
0
0
2
1
2
1
2
1
2
4
1
1
1
2
1
1
0
2
1
1
1
2
1
2
1
2
2
1
1
1
2
1
2
1
2
0
1
1
1
2
1
0
2
1
2
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
2
1
1
2
0
1
1
1
1
0
1
1
1
0
1
1
2
1
1
0
1
2
1
1
1
2
2
1
1
2
2
0
1
1
1
2
1
1
1
0
1
1
2
1
1
0
2
1
0
2
2
2
1
2
1
2
1
1
2
1
1
0
0
2
1
1
1
1
1
1
1
1
1
1
2
0
1
1
1
1
2
2
1
2
1
2
2
2
1
1
2
1
2
2
1
2
1
2
1
0
1
1
2
1
2
1
1
2
1
2
1
0
2
1
1
1
2
1
1
2
1
1
1
1
0
2
2
2
2
1
1
1
0
2
1
1
1
1
1
0
1
1
2
1
0
1
1
1
1
2
1
1
1
1
1
2
1
1
2
1
0
0
0
1
1
2
1
0
0
1
2
2
1
1
1
1
1
2
1
1
1
1
2
1
0
2
2
1
1
2
1
1
2
3
1
1
0
1
2
1
1
2
2
0
1
1
0
1
2
1
1
1
0
2
1
1
1
2
2
0
1
1
1
1
1
1
1
2
1
2
1
1
1
1
2
1
0
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
0
2
2
1
1
2
1
2
1
0
3
0
2
2
1
1
1
1
2
1
1
1
0
2
1
1
2
1
1
0
2
1
1
1
1
2
2
0
1
2
2
2
1
0
1
1
1
0
1
1
0
1
1
1
2
0
2
2
1
1
1
1
1
1
0
3
1
1
0
1
1
1
1
1
0
1
2
1
1
1
1
0
2
1
1
1
1
1
0
2
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
2
1
1
3
1
2
1
0
1
1
1
1
0
1
2
2
1
1
1
2
1
2
2
1
2
1
1
2
2
1
1
2
2
0
1
1
2
1
0
1
2
2
0
1
1
1
2
1
2
0
2
1
1
0
1
1
2
1
1
1
1
0
1
2
1
1
1
2
1
1
0
2
1
1
1
2
1
2
1
1
2
0
1
0
1
1
2
0
1
2
1
2
2
1
0
1
1
1
1
0
2
0
1
1
1
1
1
1
1
0
1
1
1
1
2
1
2
0
0
1
0
1
1
2
1
2
0
0
2
1
1
1
1
2
1
1
1
2
1
1
5
2
1
1
1
2
1
1
1
1
1
1
2
0
2
1
0
0
1
1
2
2
0
1
1
2
2
0
1
2
2
1
1
1
1
0
1
1
1
1
1
2
1
0
1
0
2
2
1
0
2
0
2
1
2
0
0
2
1
1
1
1
1
1
2
1
2
1
1
1
0
0
1
0
0
2
1
1
1
1
1
1
2
0
1
1
1
2
1
0
1
1
1
1
1
1
0
1
2
1
1
2
2
0
1
1
2
1
1
1
2
1
1
1
2
0
1
1
0
1
1
2
1
0
0
1
2
3
2
0
1
1
2
1
1
2
1
0
1
0
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
2
1
2
0
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
1
1
0
2
1
1
1
3
2
1
1
1
2
1
1
1
2
1
1
1
0
0
1
2
2
1
1
0
2
1
2
1
1
1
0
1
1
0
1
1
0
2
1
1
0
1
1
1
1
2
1
1
2
1
0
2
1
2
2
1
1
2
0
1
1
1
2
0
0
1
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
2
1
1
0
0
1
1
0
1
0
0
2
1
1
1
2
2
2
2
1
1
0
0
1
2
1
2
1
2
1
1
0
1
1
1
2
1
2
2
1
2
2
0
0
1
2
1
1
2
1
1
2
0
1
1
2
1
1
1
8
2
0
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
2
0
2
2
2
1
2
1
1
0
2
1
0
1
1
1
1
1
1
1
0
1
2
1
2
3
1
1
2
0
1
0
0
0
1
1
1
1
1
1
2
1
1
0
2
1
1
1
1
1
2
1
1
1
1
2
0
1
0
1
1
2
3
2
1
1
0
1
0
1
2
2
2
1
0
1
1
0
1
1
0
1
0
1
0
1
1
2
2
2
1
1
0
1
2
2
0
1
1
2
1
2
0
0
1
1
0
1
0
0
2
2
1
0
1
2
1
1
2
1
0
0
2
2
1
2
1
0
1
1
1
2
2
2
1
1
2
1
1
1
2
2
1
1
1
2
0
1
2
1
2
1
1
1
2
2
2
1
1
1
1
1
1
1
1
1
1
2
1
0
2
1
2
0
1
2
1
1
1
2
1
1
1
1
2
2
2
1
1
1
2
1
1
2
1
1
1
1
2
1
2
1
1
0
1
2
0
1
2
1
2
1
1
1
1
1
1
0
2
1
1
2
1
2
1
1
1
1
1
1
1
1
0
2
1
1
2
2
1
0
1
1
2
1
1
1
0
1
1
1
0
1
1
2
1
1
2
0
1
1
1
1
1
0
1
0
1
1
2
2
0
2
1
2
1
1
0
2
1
1
2
1
1
2
2
1
1
1
2
0
2
2
1
0
1
1
2
1
1
1
1
2
2
1
2
2
1
2
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
0
1
1
1
0
1
1
1
0
1
0
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
2
2
0
1
1
2
1
1
1
1
1
2
1
1
2
1
0
2
0
2
1
2
1
0
2
1
2
1
2
1
1
2
2
1
1
1
1
1
0
2
2
1
1
1
1
1
0
1
2
2
0
0
1
1
1
1
2
2
2
2
1
1
2
1
0
0
1
2
1
2
1
1
2
0
1
2
1
2
1
0
1
1
2
1
2
1
1
1
1
2
1
2
1
1
1
4
1
0
0
1
1
1
2
1
1
2
1
0
2
1
1
1
1
1
2
1
1
2
3
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
0
2
1
0
0
1
2
1
1
0
1
1
2
1
1
0
0
1
1
2
2
2
2
1
1
0
1
1
1
2
1
1
0
1
3
2
1
1
1
1
0
1
1
1
0
1
2
1
2
1
1
2
2
2
1
1
1
2
0
3
1
1
1
1
1
2
0
1
1
1
1
0
1
2
1
1
2
1
1
2
1
1
1
2
1
0
1
2
1
1
2
2
1
1
0
1
0
1
1
1
1
1
0
2
1
1
1
2
1
1
2
2
1
1
2
1
1
1
2
1
2
1
2
0
1
0
1
1
2
1
1
1
1
1
0
1
0
2
1
1
2
1
2
2
1
1
1
1
1
1
2
1
1
1
1
2
1
0
1
2
0
2
0
1
1
0
2
1
1
2
2
2
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
0
1
1
1
1
1
1
0
2
3
1
1
1
0
0
1
0
1
1
1
1
1
1
1
1
1
1
2
0
1
2
0
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
2
2
0
1
1
1
2
1
2
1
1
1
1
1
1
2
1
0
1
1
1
1
0
1
1
1
2
2
2
2
1
1
3
2
0
1
1
0
2
1
2
0
2
1
2
1
2
1
1
1
1
1
2
1
1
1
2
2
1
2
2
1
0
1
2
0
1
1
2
0
0
1
1
1
1
2
2
1
3
1
0
1
1
1
2
2
1
2
1
2
2
3
1
1
1
1
2
2
1
1
1
1
1
1
2
1
1
2
0
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
0
0
0
1
1
1
1
2
1
1
2
0
2
2
1
1
1
1
0
1
2
2
2
2
2
0
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
0
1
1
2
1
0
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
0
1
2
2
1
1
1
0
2
1
2
2
1
1
1
2
2
0
1
1
3
0
1
1
1
0
2
1
1
1
1
1
1
1
0
1
2
2
1
2
1
1
1
1
2
2
1
1
0
2
1
0
2
2
2
2
2
2
2
1
2
1
1
1
1
1
1
1
2
3
1
1
0
1
1
1
2
1
0
1
0
0
0
1
1
2
1
2
2
2
1
1
1
0
0
2
1
1
1
1
1
0
2
1
1
0
2
5
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
2
1
1
0
2
1
1
1
1
2
1
2
1
1
1
2
1
2
2
1
1
1
1
1
1
2
1
2
1
1
2
1
0
0
1
0
1
1
1
1
1
2
0
1
1
1
2
2
2
2
2
2
1
0
1
2
0
1
1
2
2
1
0
2
1
1
1
1
0
1
1
0
2
0
1
2
0
1
1
1
2
1
2
1
1
0
1
1
0
1
1
2
1
1
1
0
0
0
2
1
1
1
0
1
1
2
2
1
1
1
0
1
2
1
1
2
1
1
1
1
0
1
2
0
2
1
2
0
1
2
2
1
1
1
2
1
1
2
2
0
1
0
1
1
1
1
1
1
1
1
0
1
0
2
2
1
1
1
2
0
2
1
1
1
1
0
1
1
2
1
1
2
1
1
0
1
1
2
1
0
0
0
1
2
1
1
1
1
0
1
2
2
1
1
1
1
1
0
1
1
1
2
1
1
2
2
0
1
2
1
1
2
1
2
2
1
2
1
1
1
1
1
1
0
0
2
1
1
1
1
1
1
1
1
2
1
1
0
2
2
2
2
1
1
1
1
1
1
1
2
1
0
2
1
1
2
1
1
1
2
1
2
1
2
1
1
1
1
1
1
0
0
2
1
1
2
1
2
1
1
2
1
1
1
1
0
0
1
1
1
1
1
1
1
1
1
1
1
2
0
2
2
0
2
1
1
2
1
1
1
1
1
2
2
0
1
1
2
1
1
1
1
1
1
1
2
0
1
2
2
2
1
2
1
1
1
2
2
1
2
1
1
1
1
1
1
1
0
0
1
1
3
2
0
1
1
1
0
2
1
2
1
1
1
2
1
1
2
1
1
1
1
2
1
1
1
1
1
0
1
1
1
1
1
2
1
2
2
1
1
1
1
2
0
1
1
1
1
0
1
1
1
1
1
1
1
1
2
1
2
0
1
0
1
2
1
1
1
2
1
1
1
2
0
2
2
1
1
2
1
0
2
1
1
0
0
1
0
2
1
1
1
2
1
1
1
1
0
1
0
2
1
1
1
2
1
2
2
1
2
1
1
1
2
1
1
1
1
1
2
0
1
2
1
1
0
1
1
1
1
1
0
1
0
2
1
1
0
2
0
2
1
1
1
1
1
2
1
1
0
1
1
2
1
1
1
3
1
1
0
1
1
1
1
0
1
0
2
0
0
1
2
1
1
1
1
1
1
1
0
1
0
1
1
1
1
1
2
0
2
1
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
2
2
1
2
1
1
0
2
1
2
2
2
2
2
1
1
2
2
0
2
2
1
2
0
2
1
1
1
1
2
1
1
1
1
1
1
1
0
2
1
1
2
1
2
1
1
1
1
0
2
1
0
1
1
1
1
1
2
1
2
2
1
0
1
1
1
0
1
0
1
1
1
1
1
0
2
0
1
0
0
1
1
1
1
2
2
2
0
1
1
1
2
1
1
2
1
2
1
1
2
2
1
2
2
2
2
2
2
1
2
2
2
1
1
2
1
0
0
1
1
0
1
1
2
3
1
1
1
0
2
0
2
1
1
1
0
1
2
1
0
1
0
1
0
1
2
1
1
1
1
2
1
1
0
2
1
1
1
0
1
2
1
1
1
1
1
0
2
1
1
2
1
2
2
2
1
2
1
1
2
1
2
2
1
1
2
1
1
2
1
1
1
2
1
0
1
0
1
2
2
1
1
0
2
1
1
2
1
2
1
2
0
1
1
0
1
0
1
1
1
1
1
2
0
2
2
1
1
1
1
2
1
2
2
2
1
0
2
1
1
1
1
1
1
2
1
2
1
1
0
1
1
1
1
1
2
1
0
1
1
1
1
1
1
1
1
1
1
2
1
2
1
0
2
2
1
0
1
1
1
0
2
1
2
1
1
2
1
2
1
0
1
2
1
1
1
2
0
0
2
1
2
1
1
1
2
1
2
1
1
1
1
2
1
1
2
1
1
1
1
2
1
2
1
2
1
1
1
2
1
2
1
0
0
2
2
1
1
1
1
1
2
1
1
1
1
1
0
1
1
1
1
2
2
2
1
1
0
1
2
1
1
1
2
1
1
1
2
1
1
0
2
1
1
2
0
2
1
2
1
1
0
2
1
1
2
0
1
1
1
1
0
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
0
1
0
1
2
2
1
1
0
2
1
0
2
1
2
2
0
2
1
2
1
1
1
0
1
1
1
1
0
2
1
1
2
1
2
1
2
2
1
1
1
2
1
2
1
1
1
2
2
1
2
1
1
2
1
3
1
2
1
1
0
2
1
1
2
2
1
0
2
1
1
1
1
2
2
2
0
1
1
1
1
1
1
0
1
2
1
2
2
1
1
1
1
1
1
1
2
1
2
1
1
0
1
2
1
1
1
1
1
1
1
2
0
3
1
1
1
1
0
1
1
2
1
0
0
2
1
1
1
1
1
2
1
1
2
1
0
2
2
2
1
2
1
1
1
1
1
1
1
1
0
1
1
1
2
1
2
2
1
2
1
1
1
1
1
2
1
1
0
1
1
2
2
1
1
1
1
1
1
1
1
2
1
2
1
1
1
2
0
1
1
1
1
1
1
2
2
1
1
1
0
1
0
0
1
1
2
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
2
2
1
1
1
1
1
2
1
0
4
1
1
2
1
1
1
1
1
0
2
2
1
1
1
3
1
1
1
0
1
1
2
2
1
1
1
0
1
0
1
1
1
1
1
1
1
2
1
1
1
0
1
2
1
1
1
1
2
1
0
1
2
1
0
1
1
1
1
0
5
1
1
1
2
1
1
1
2
1
1
1
1
1
0
1
2
1
1
2
2
2
1
1
1
1
2
1
2
1
2
1
1
1
1
0
1
0
1
4
1
2
1
1
1
1
1
2
2
1
0
1
2
1
2
1
1
0
1
2
2
2
1
2
3
0
1
2
0
0
0
0
1
1
1
2
1
1
1
2
2
2
2
1
1
1
1
1
2
2
2
1
1
0
2
1
2
1
1
1
1
1
1
1
2
2
1
2
2
1
2
2
1
1
1
0
1
1
0
0
1
0
2
2
1
1
1
1
2
2
3
2
1
2
0
2
0
0
2
1
1
2
1
0
1
0
1
2
1
0
1
1
0
1
2
1
1
1
1
1
1
0
0
1
1
1
1
1
1
1
2
1
0
1
2
1
1
0
1
2
1
1
1
1
1
2
2
1
1
1
1
2
1
1
0
2
0
0
2
1
1
1
0
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
0
2
2
1
1
1
2
2
2
2
2
2
1
0
0
1
1
2
1
1
2
0
1
1
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
1
2
2
2
1
2
1
2
1
2
1
1
2
1
1
1
1
1
0
1
2
2
1
1
2
1
1
0
1
1
1
2
1
1
1
1
1
2
1
0
0
0
1
1
0
2
2
2
1
1
2
1
1
2
1
1
1
1
1
0
1
2
0
1
4
1
0
1
0
1
2
0
2
0
1
1
0
2
1
1
1
1
1
1
1
0
1
0
4
2
1
1
1
2
2
1
2
1
2
2
0
2
0
2
1
1
1
1
2
1
0
1
1
2
1
1
2
1
1
1
1
2
1
1
4
1
2
1
2
2
0
1
1
1
0
1
0
1
2
0
1
2
2
2
1
2
1
2
1
1
1
1
1
2
2
2
1
1
1
2
1
1
2
2
2
1
1
0
1
1
1
1
0
1
1
1
1
1
2
1
2
2
2
1
1
1
1
0
1
3
2
1
1
1
2
1
0
2
1
1
2
1
1
1
1
1
2
2
1
1
1
1
2
1
1
3
2
2
0
2
1
2
1
1
1
2
2
0
2
2
1
2
1
2
2
1
1
1
1
1
1
0
2
1
1
1
0
2
0
2
1
2
1
1
1
1
2
1
1
0
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
0
2
0
1
1
0
1
0
1
1
2
2
1
1
1
1
1
2
2
1
1
1
2
0
2
0
1
1
1
2
0
0
0
2
2
2
1
0
2
1
1
1
1
0
1
0
1
1
0
1
1
1
1
1
1
1
1
0
2
1
1
2
0
1
1
1
1
1
2
1
1
0
1
1
2
1
1
1
0
0
0
1
2
1
1
2
2
2
1
1
0
1
1
1
0
1
3
0
1
1
2
1
1
1
2
2
1
2
2
1
2
1
1
1
2
1
0
1
1
1
2
1
0
2
1
1
2
2
1
1
1
0
2
1
1
2
0
2
1
1
1
0
1
1
2
2
2
2
2
1
1
1
2
1
1
2
1
1
0
1
2
1
0
0
1
1
2
1
2
1
1
0
2
1
1
0
1
0
1
1
1
2
1
2
0
0
1
2
1
2
2
0
1
0
1
0
1
1
1
1
1
1
1
2
1
2
2
1
1
2
2
1
0
1
1
0
1
1
2
1
1
2
1
0
0
1
1
1
1
1
1
1
0
2
1
1
1
1
1
1
2
1
1
0
1
1
2
1
2
1
0
1
1
1
0
1
1
1
1
1
1
2
1
1
2
1
1
1
1
2
1
2
1
2
1
1
1
1
0
3
1
1
1
1
0
1
1
1
1
1
1
2
1
2
1
4
1
1
2
1
1
1
1
0
2
1
1
2
1
1
0
1
0
1
1
2
2
1
1
1
1
2
1
0
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
0
0
1
1
0
1
1
1
1
0
2
0
2
1
1
1
0
2
1
2
0
1
1
2
0
2
1
1
1
1
1
3
2
1
2
1
2
1
2
0
1
0
2
1
1
1
0
2
1
0
1
1
1
1
1
1
1
1
0
1
1
1
1
2
2
1
2
2
0
1
1
1
1
2
1
1
1
2
1
1
2
2
1
1
1
2
2
1
1
1
1
1
1
1
1
2
1
2
1
2
1
2
1
1
2
1
1
2
0
1
2
1
2
2
1
2
1
2
1
1
2
1
1
1
1
0
1
1
0
0
1
1
1
2
0
1
1
1
2
2
1
2
0
2
1
1
1
0
1
1
1
1
1
1
1
2
1
1
2
2
2
2
1
0
1
1
1
1
2
2
0
1
2
1
2
1
2
1
1
1
1
0
2
1
0
2
1
1
1
1
2
1
1
2
1
1
1
0
1
0
2
2
2
1
2
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
1
2
0
1
1
1
1
1
1
1
2
0
1
1
1
1
1
2
1
0
1
1
0
2
1
1
1
2
2
1
1
2
1
2
0
1
2
1
1
1
0
1
1
1
2
2
1
2
1
2
2
1
1
1
2
1
1
2
1
2
1
1
2
1
1
2
0
2
0
1
2
2
3
1
0
1
1
1
1
1
0
1
0
2
1
1
2
2
1
1
1
2
1
1
1
1
1
0
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
2
1
1
1
0
2
1
1
1
1
1
2
2
1
1
2
1
0
2
2
1
1
1
2
1
1
0
1
1
1
1
2
2
1
2
1
1
0
1
1
2
1
1
0
1
1
1
0
1
1
1
1
1
0
1
1
1
0
2
0
1
2
2
2
1
1
2
2
0
1
1
1
1
1
1
1
2
2
1
1
1
1
2
1
1
0
2
0
2
0
1
2
2
0
0
1
1
1
0
1
0
1
1
1
1
0
1
1
1
1
0
1
2
2
2
2
1
1
0
1
1
1
2
2
2
0
1
0
0
2
1
1
1
0
1
1
5
2
0
1
0
2
1
2
1
1
2
1
2
1
1
1
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
0
3
1
1
2
1
2
1
2
2
1
1
1
1
2
2
1
2
1
1
2
1
1
0
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
0
2
1
1
2
1
2
0
0
0
2
2
1
2
1
1
0
1
1
1
1
2
2
2
1
1
2
1
1
1
2
0
1
1
1
0
1
1
1
2
1
1
1
0
1
0
1
1
0
2
2
2
1
2
0
1
1
1
1
2
2
1
2
2
1
1
2
1
2
1
1
0
2
1
1
1
2
2
1
1
1
1
2
2
2
1
1
1
1
2
1
1
1
2
0
0
2
1
1
2
3
1
1
1
1
0
2
1
1
1
1
1
1
1
2
2
1
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
2
2
0
1
2
1
2
2
1
1
1
1
1
1
2
1
2
1
1
2
2
1
1
1
1
1
0
0
0
2
1
2
1
2
1
1
1
2
1
1
2
1
2
1
2
1
1
1
2
3
1
2
1
1
0
0
1
1
2
1
2
1
0
2
0
1
1
1
1
1
2
1
2
1
1
2
0
1
1
1
1
1
2
2
2
1
2
2
1
1
2
1
2
1
1
1
4
1
1
1
1
0
1
1
1
0
1
1
2
1
1
1
2
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
1
4
1
1
1
2
1
1
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
1
2
1
2
2
1
1
1
1
2
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
2
0
0
1
2
0
1
1
1
1
2
0
1
1
0
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
2
1
2
1
0
1
0
2
2
1
2
2
1
1
1
2
1
2
2
2
2
1
1
1
1
2
1
3
2
1
1
1
1
1
2
2
1
0
1
2
1
2
2
1
1
1
1
2
2
1
0
0
2
1
1
1
2
1
2
1
0
1
0
1
2
1
1
1
2
2
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
2
0
1
1
1
1
1
0
0
1
1
2
1
1
1
1
1
1
0
1
1
2
1
1
1
1
2
0
1
1
2
1
1
1
2
0
1
1
1
1
0
0
1
4
1
0
2
2
1
1
1
1
2
1
1
1
1
1
1
2
2
2
2
2
1
2
2
1
2
0
1
1
2
1
1
1
1
1
2
2
1
1
1
1
0
1
2
1
1
2
2
1
1
3
1
1
2
1
1
0
1
1
2
1
1
2
1
1
0
2
1
1
1
1
2
2
0
1
1
2
2
1
2
1
1
2
1
2
0
1
2
2
0
2
2
2
1
1
1
2
0
2
1
1
1
2
1
1
0
1
1
0
2
2
2
1
2
0
2
1
2
2
1
1
1
1
1
1
1
1
1
2
1
0
2
2
1
1
1
2
1
2
1
1
1
0
2
1
2
2
4
1
1
2
2
1
2
3
2
2
2
1
2
2
2
0
1
1
2
1
1
2
1
2
1
2
1
0
1
2
1
1
1
2
4
2
1
1
1
1
1
2
1
1
1
0
2
1
1
2
1
1
1
1
1
1
1
1
2
1
2
1
0
0
1
1
0
2
1
1
2
3
1
2
1
1
2
1
1
1
1
0
1
1
0
2
1
1
1
1
1
2
2
2
1
2
1
2
1
1
2
0
1
1
1
1
1
2
1
1
1
1
1
1
2
0
0
1
2
1
0
2
2
2
2
1
0
2
1
1
2
0
1
2
2
1
2
0
0
1
1
1
2
1
0
1
0
2
0
1
2
0
1
0
1
1
1
1
2
1
1
1
1
2
3
1
1
1
1
1
2
0
0
1
0
0
1
1
1
0
1
0
1
2
1
0
1
1
0
1
2
1
1
1
1
1
1
1
1
1
1
0
0
2
0
1
0
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
0
1
2
1
1
1
1
2
1
2
2
1
2
2
1
1
1
1
1
1
1
2
2
2
1
2
1
1
0
1
2
2
0
2
1
2
0
2
1
1
2
1
0
0
1
2
1
0
2
2
1
1
0
1
1
2
1
2
1
1
1
0
1
2
1
1
1
1
1
1
1
1
2
0
1
0
0
1
2
1
2
1
1
1
1
1
0
0
1
1
1
1
1
1
0
1
1
2
1
1
2
1
1
2
2
2
1
0
1
1
1
0
1
1
1
1
3
1
1
1
1
1
1
1
0
1
1
2
1
2
1
1
0
1
2
1
1
1
1
1
1
1
0
1
1
0
1
2
2
1
1
2
1
1
1
2
1
0
1
1
2
2
1
1
0
2
2
1
1
1
1
0
1
2
2
1
1
1
1
2
1
1
1
1
1
0
2
1
2
1
1
1
2
1
1
2
0
1
1
2
1
2
0
1
1
1
2
1
0
1
0
2
0
0
1
1
1
1
2
2
1
1
1
1
2
1
2
0
2
0
1
0
1
1
0
1
2
1
1
1
2
2
1
1
2
1
1
1
1
1
2
1
2
1
2
1
1
1
1
1
1
1
1
1
0
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
2
2
1
1
1
1
0
2
1
2
2
2
1
0
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
0
1
1
1
0
2
1
1
2
1
1
1
0
2
1
1
1
1
2
2
1
1
1
0
1
0
1
2
1
0
0
1
1
1
1
0
1
1
1
0
1
0
1
1
1
1
1
1
1
1
1
2
1
2
0
1
1
1
2
1
2
1
1
1
2
1
2
1
0
1
1
1
1
1
1
1
0
1
1
1
1
2
1
1
1
1
1
0
2
2
1
2
1
2
2
1
0
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
0
1
1
2
1
0
2
1
1
1
2
2
1
1
2
1
1
2
0
1
1
1
1
1
1
2
1
1
1
0
1
0
1
0
2
0
1
2
0
1
2
2
1
1
1
2
1
1
2
1
2
0
1
0
1
1
2
1
1
0
1
1
1
1
1
1
2
2
0
1
1
1
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
2
2
0
1
0
2
1
1
1
1
2
1
1
2
2
1
1
1
0
2
1
1
2
1
1
2
1
1
0
2
0
1
2
1
2
1
1
1
1
1
1
1
1
1
0
1
1
1
2
2
1
2
0
2
2
1
0
2
1
1
1
2
1
1
1
1
2
1
2
1
1
0
1
0
1
2
1
1
2
2
1
2
2
0
1
1
1
1
1
2
1
0
2
1
1
1
2
1
1
1
1
1
1
2
1
1
2
1
0
0
1
1
2
2
0
1
0
1
2
1
1
2
2
1
0
1
1
1
0
1
1
1
1
1
1
0
0
3
1
1
2
1
1
1
1
1
2
2
1
1
1
0
1
2
2
1
0
2
1
1
1
1
1
1
2
1
0
2
2
1
1
1
1
1
1
1
1
2
1
0
1
1
2
2
1
1
1
1
1
1
1
2
2
0
1
1
1
2
1
1
1
1
1
1
1
0
1
1
2
1
1
1
1
2
2
2
1
1
1
1
2
0
2
1
1
1
0
0
1
1
2
2
1
1
1
1
1
0
1
1
1
1
1
2
2
1
1
1
0
1
0
1
0
0
0
1
2
1
1
1
2
1
1
2
1
0
2
2
0
2
0
1
1
2
1
1
1
1
2
1
1
2
1
0
1
1
2
1
2
1
1
1
2
1
1
0
1
1
2
2
1
1
1
2
2
1
2
1
1
2
0
1
0
2
1
2
1
1
1
1
0
2
1
2
1
1
2
2
1
1
1
2
2
1
1
1
1
2
2
1
0
1
1
1
1
2
1
1
2
1
1
1
1
0
1
1
1
1
1
1
1
1
2
0
0
1
1
0
1
2
1
2
1
2
1
1
1
0
2
1
2
0
0
1
1
0
1
1
2
2
1
0
1
2
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
1
1
1
2
2
1
0
1
1
1
1
1
2
1
1
0
0
2
1
1
1
1
2
0
0
2
2
1
2
1
2
1
1
1
1
1
1
1
2
1
0
1
2
2
1
1
2
2
2
1
2
2
1
1
2
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
2
1
2
2
1
0
0
1
1
1
2
0
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
0
1
2
1
2
0
1
1
3
2
1
1
1
1
1
2
1
0
0
1
1
1
1
2
1
1
1
1
0
1
0
0
1
0
2
2
2
1
1
2
0
1
1
1
2
1
1
1
2
2
2
0
1
1
1
1
0
2
1
2
2
1
1
1
2
1
0
1
2
2
0
1
1
1
2
1
2
1
1
2
0
1
2
1
0
1
1
2
1
2
1
0
1
2
1
2
1
1
1
1
1
1
1
1
0
2
1
1
1
2
1
1
2
1
1
1
1
1
1
0
1
2
1
2
0
0
1
2
1
1
2
0
1
1
1
0
0
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
0
0
1
1
1
0
1
1
1
2
2
2
1
1
0
1
1
0
2
2
0
1
1
1
1
1
1
1
2
1
1
2
0
1
1
2
1
0
0
1
1
1
2
2
1
0
1
1
1
2
1
2
1
2
1
2
1
0
0
1
0
1
1
1
1
2
0
1
1
1
2
1
1
1
1
1
2
1
2
0
1
1
1
1
1
1
1
1
1
1
1
0
1
1
2
1
1
2
2
0
2
1
2
2
2
0
1
1
0
2
0
1
1
1
1
1
1
0
2
1
1
2
0
1
2
1
1
1
1
0
0
0
1
1
1
2
1
2
0
1
1
1
1
1
2
1
2
2
1
1
1
1
0
1
1
1
2
2
1
2
2
1
2
1
1
1
2
1
0
2
2
1
1
2
1
2
2
2
2
2
2
1
0
1
2
1
1
1
2
2
2
1
2
2
1
0
1
1
0
1
2
1
1
2
2
1
1
1
2
1
1
1
2
2
1
2
1
1
1
2
0
0
1
1
0
1
1
0
1
1
0
0
2
0
1
1
1
1
1
1
2
1
1
2
1
1
1
2
1
2
2
2
1
0
1
1
1
1
0
2
1
1
2
2
1
1
2
1
1
1
1
2
1
2
2
2
1
0
1
2
1
1
0
0
0
2
1
1
1
1
2
2
0
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
0
0
1
2
1
0
1
2
1
1
1
0
1
1
0
1
1
1
0
1
1
2
0
2
1
1
2
2
1
1
1
1
1
1
1
2
2
2
2
1
2
2
1
1
2
1
1
1
2
2
2
1
1
1
2
1
2
1
1
2
0
2
1
1
1
0
2
1
1
1
1
1
0
4
2
1
1
1
1
0
1
1
1
1
2
0
0
1
2
2
0
1
1
2
2
1
1
1
2
0
1
1
1
1
0
1
1
1
1
1
1
1
1
0
0
2
1
7
0
1
1
1
1
1
1
1
2
0
1
1
2
0
2
1
1
2
1
1
1
0
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
2
1
2
1
1
1
1
0
0
1
1
0
1
1
2
1
2
2
2
1
1
1
1
1
1
1
0
2
1
1
0
0
1
1
2
1
2
1
0
1
2
2
1
2
1
1
1
1
0
0
0
1
1
0
1
1
1
1
1
1
1
1
1
0
1
1
2
2
2
1
2
1
2
1
1
2
1
1
1
1
2
1
1
1
2
0
1
1
1
1
1
0
1
1
2
1
2
1
1
1
0
1
0
1
2
2
1
1
2
0
2
1
2
1
2
2
1
2
2
0
1
2
0
0
1
0
1
1
0
1
1
1
1
1
1
1
2
2
1
1
1
0
0
2
2
2
1
1
1
1
1
1
2
2
1
1
2
1
2
1
2
1
1
2
1
2
1
1
1
1
0
1
0
1
0
1
1
2
0
0
2
1
0
1
1
1
1
1
1
2
1
2
1
1
1
1
1
0
0
1
1
0
0
1
1
2
0
1
0
2
1
0
2
1
1
1
1
2
1
2
1
2
2
2
2
0
2
0
1
2
3
0
1
1
1
1
1
1
1
2
1
2
2
1
1
1
0
0
1
0
2
1
2
1
1
2
1
2
1
1
1
2
1
2
2
0
1
2
1
1
1
2
1
3
2
1
1
1
1
2
1
2
1
1
2
2
2
1
1
2
0
1
2
0
0
0
2
2
1
1
1
0
1
1
2
1
1
1
1
2
0
1
1
2
1
1
1
0
1
1
1
1
2
2
2
1
2
0
1
2
2
1
1
1
0
2
1
1
0
1
0
0
0
1
1
2
1
1
1
1
3
1
1
1
2
1
1
1
1
1
1
2
0
2
1
1
1
1
1
1
1
1
1
2
1
1
2
2
1
1
1
1
1
2
1
1
1
1
1
1
0
1
0
1
1
1
1
1
1
1
0
2
1
2
1
1
1
1
0
2
1
3
1
1
0
1
1
2
1
2
2
1
0
0
1
2
2
1
2
1
1
1
0
1
0
0
2
1
2
1
1
2
1
1
0
2
1
2
2
2
1
0
2
2
1
1
2
1
1
0
2
1
2
1
1
1
2
0
1
1
4
2
1
1
0
2
1
2
2
1
1
1
1
1
1
0
1
1
0
1
2
1
1
1
1
1
2
1
1
0
1
2
0
1
1
0
2
2
1
1
1
1
1
1
2
1
1
1
2
0
2
0
1
2
1
1
1
1
1
2
2
2
1
2
1
0
1
1
0
1
4
1
1
2
1
2
1
2
1
1
1
1
1
2
2
1
2
1
1
2
1
2
1
1
2
1
1
1
1
2
0
2
1
2
1
1
1
1
0
2
1
2
1
0
1
1
0
1
1
1
1
1
1
1
2
1
1
2
2
1
1
1
1
1
0
2
2
1
0
1
1
1
1
2
1
0
1
0
1
1
2
1
0
1
1
1
1
1
1
1
1
1
2
1
2
1
1
0
2
2
1
1
1
1
2
1
1
1
1
2
2
1
2
1
1
2
1
2
1
2
2
1
1
2
1
1
0
1
1
2
2
2
1
2
1
0
1
1
0
1
1
0
1
1
0
1
1
1
1
1
0
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
2
2
2
1
1
1
1
0
1
1
0
1
2
1
1
1
2
1
1
2
0
0
1
0
2
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
0
2
1
1
0
1
2
2
2
1
1
2
1
0
1
1
0
1
1
1
1
0
1
1
1
1
1
1
0
0
1
1
2
1
1
0
1
2
1
1
1
0
1
1
2
2
2
1
1
2
1
1
0
0
1
0
1
2
1
1
1
1
1
1
1
2
1
2
1
0
0
1
1
1
2
1
0
3
2
2
0
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
0
1
1
0
2
2
2
1
1
2
1
1
2
0
1
0
0
1
1
1
1
2
2
1
0
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
0
2
1
1
0
2
1
1
1
1
1
2
1
1
1
1
1
2
2
2
2
2
0
1
1
1
2
2
1
1
0
1
2
0
2
1
1
2
1
1
1
0
0
1
1
2
1
1
1
1
1
1
1
1
0
2
1
1
1
2
0
0
1
1
1
1
1
1
1
2
1
2
1
0
1
0
2
1
1
0
1
1
1
1
0
1
1
1
1
1
0
0
2
0
2
0
1
2
0
1
2
0
2
1
1
0
0
1
1
1
1
1
1
1
1
1
2
1
2
1
2
2
1
2
1
1
2
1
1
1
2
2
1
1
2
2
1
2
2
1
1
1
0
1
1
1
0
1
1
0
1
1
1
2
1
1
1
1
1
0
0
1
3
2
0
2
1
2
1
1
1
1
0
1
1
1
1
0
0
0
1
1
1
1
1
1
2
1
1
1
2
2
1
2
0
2
2
1
1
2
1
0
2
1
3
2
2
1
1
1
1
1
1
1
2
1
0
1
0
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
2
2
2
2
2
1
1
1
1
1
0
1
1
1
1
0
1
2
0
1
1
2
1
1
2
1
1
1
1
1
1
2
1
0
1
2
1
1
1
1
2
1
1
2
2
2
1
1
2
1
0
1
2
1
1
1
1
2
2
2
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
0
2
1
1
0
0
2
2
0
1
1
1
1
0
1
1
2
1
0
1
1
1
1
2
1
0
0
1
1
1
1
1
0
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
0
1
2
1
1
0
1
1
0
2
1
1
0
1
1
1
1
2
1
1
1
1
1
1
1
1
1
0
1
2
1
0
0
1
1
2
1
1
2
1
2
1
1
2
1
2
1
0
0
1
1
1
2
2
2
1
2
0
0
1
1
1
1
2
1
1
1
1
0
2
1
1
1
2
1
1
3
1
2
1
2
0
1
1
1
1
1
1
1
1
1
1
2
2
1
0
1
1
1
1
1
1
1
2
1
0
2
2
1
1
1
0
1
0
1
1
1
1
1
1
1
1
1
1
2
1
2
2
2
2
0
2
1
1
2
1
0
1
2
0
2
2
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
1
1
0
1
1
2
1
2
1
2
1
2
1
2
1
1
0
1
1
0
1
1
2
1
1
2
2
1
0
1
1
1
0
1
1
2
2
1
1
1
1
1
1
0
2
1
1
1
1
2
1
0
1
2
1
2
1
1
0
0
1
1
0
0
2
1
2
1
2
1
1
1
1
1
1
1
1
1
0
0
1
1
1
2
3
1
0
1
2
2
1
2
1
2
1
1
1
2
2
0
2
1
2
2
2
1
0
2
1
2
2
1
1
2
1
1
2
1
1
0
1
2
1
2
2
1
1
0
1
1
1
0
1
1
1
2
2
1
2
2
1
1
1
1
2
1
0
2
1
1
1
1
0
1
1
1
1
0
1
2
1
2
1
2
1
2
2
0
1
1
1
2
1
2
2
1
1
1
0
2
2
0
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
0
1
1
2
2
1
1
1
2
1
1
2
1
1
2
1
0
1
1
2
1
2
2
1
2
1
1
0
2
1
1
2
2
0
2
1
1
2
0
2
1
1
0
1
2
1
1
2
1
1
2
1
2
1
2
0
1
1
2
1
1
2
1
2
2
1
1
0
2
1
1
1
1
2
2
2
2
1
2
1
1
2
1
1
2
2
1
1
1
7
1
0
1
2
0
1
1
1
2
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
2
0
2
0
1
1
1
1
1
1
2
1
1
0
1
0
1
2
1
1
1
2
0
1
2
1
2
1
2
2
0
2
0
1
1
1
1
0
1
0
1
1
1
0
1
2
2
2
1
1
1
1
2
1
2
1
2
1
1
1
2
2
1
1
0
1
1
2
2
0
2
1
1
1
1
1
0
0
1
1
0
2
1
1
1
1
1
0
1
2
1
1
1
1
1
1
1
1
2
0
0
2
2
1
1
0
1
1
1
1
2
1
2
1
1
1
2
1
2
2
2
2
1
1
3
1
2
3
1
2
0
1
1
0
1
2
0
1
2
0
1
1
1
2
1
1
1
1
1
2
1
1
0
0
1
1
1
2
0
1
1
0
1
2
3
1
1
1
1
1
1
0
1
1
1
0
1
1
1
0
1
0
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
2
2
2
1
1
0
1
2
2
1
1
1
0
1
1
1
1
0
1
1
2
2
2
2
1
1
0
2
1
0
1
2
1
0
1
1
1
1
1
2
0
2
2
1
1
1
1
2
2
2
1
1
2
2
1
1
2
1
1
0
1
2
2
2
1
2
2
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
0
1
1
2
1
2
1
0
1
2
2
1
1
1
0
2
1
1
1
1
1
2
0
0
1
1
2
1
2
1
1
1
1
1
2
1
1
1
1
1
0
1
1
1
1
0
2
1
1
2
0
1
0
0
1
0
1
2
0
2
1
4
0
2
1
1
0
1
1
1
1
0
0
2
1
2
1
1
1
1
2
2
1
1
1
0
1
1
2
1
1
2
1
1
1
1
2
1
1
1
2
2
1
1
1
2
0
2
1
2
2
1
0
2
2
1
1
0
2
0
1
1
2
1
1
0
2
1
1
1
1
1
2
1
2
1
1
2
1
1
0
1
2
2
2
1
1
0
1
0
1
0
1
1
1
2
2
1
0
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
0
2
2
0
1
1
1
2
2
2
1
0
2
1
1
1
1
0
1
0
2
3
1
3
0
1
0
1
1
1
2
1
2
1
0
1
1
0
1
2
1
1
1
2
2
2
2
1
2
0
2
1
1
1
2
1
1
2
3
1
2
0
1
2
1
1
1
1
1
1
1
1
1
2
1
1
0
1
2
1
1
1
2
1
1
1
1
2
1
2
0
1
1
1
2
1
2
2
1
1
2
1
0
2
1
1
1
1
1
1
1
1
2
1
0
1
1
0
1
1
1
1
1
1
1
1
2
1
2
1
1
0
1
1
1
1
1
2
0
1
1
1
2
1
1
0
2
2
2
2
0
1
2
1
1
1
0
1
2
2
1
1
1
1
1
1
2
1
1
2
1
1
0
1
2
0
1
1
0
1
1
1
2
0
1
2
2
2
0
1
2
2
2
1
0
1
2
1
1
1
2
1
1
2
2
2
1
1
2
1
2
2
0
0
1
2
1
1
2
1
1
1
1
1
1
1
2
2
1
0
0
1
0
1
2
1
1
1
1
2
1
1
1
2
1
1
1
1
1
2
0
2
2
1
1
1
1
1
0
1
1
2
1
2
0
2
0
2
1
1
1
1
2
1
2
1
0
1
1
2
1
1
1
0
1
1
1
2
2
1
1
1
2
1
1
2
1
0
2
1
2
1
0
1
1
1
1
1
0
1
2
2
2
1
2
1
1
1
0
1
2
1
1
1
0
1
1
1
1
1
1
0
2
1
2
3
2
1
2
1
2
1
1
1
2
2
1
0
1
1
2
2
0
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
0
1
0
1
1
0
1
1
1
0
2
1
0
2
1
1
1
1
1
1
1
0
1
2
1
1
1
2
1
2
1
2
1
1
0
1
1
2
1
1
0
0
1
1
1
1
2
1
2
0
1
1
2
1
1
1
0
2
2
2
1
2
0
2
1
2
0
0
1
0
1
1
1
1
1
1
1
1
1
2
1
1
0
0
1
1
1
2
1
2
2
2
1
1
1
2
1
1
2
1
1
1
1
1
1
0
1
1
2
1
2
2
1
1
1
1
1
1
2
1
0
0
2
1
0
1
2
1
1
1
2
1
1
1
1
1
1
0
1
1
1
2
1
1
1
2
2
1
0
1
1
1
1
1
2
1
1
1
0
2
1
1
0
1
1
2
2
1
1
1
2
2
2
1
1
1
1
2
2
1
1
1
0
1
0
1
2
2
1
2
1
1
1
2
1
1
2
1
2
1
0
2
1
1
0
1
1
1
1
1
1
2
1
1
1
1
2
1
2
1
1
0
0
0
1
1
2
0
0
2
2
2
1
1
1
1
1
1
1
2
2
1
1
0
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
0
1
0
0
2
1
1
1
1
1
1
1
1
0
2
1
1
1
1
2
1
2
1
1
2
1
4
1
1
1
2
1
1
0
1
1
2
2
1
1
1
1
2
0
1
1
0
0
2
1
1
1
1
1
1
2
1
1
2
0
1
1
1
1
1
1
2
1
2
2
1
1
1
1
0
1
1
1
2
2
1
2
2
1
1
2
1
2
1
0
1
1
1
1
1
0
2
1
2
1
1
1
1
2
1
0
1
1
2
2
1
1
1
1
1
0
2
2
1
0
0
1
2
2
1
1
2
1
0
1
2
1
1
1
1
0
2
1
1
0
2
2
1
2
1
1
1
2
1
0
0
2
2
1
1
1
1
1
0
1
2
1
0
2
2
1
1
1
1
1
1
2
2
1
2
0
4
1
1
0
2
0
1
1
1
2
1
1
1
2
0
1
1
0
1
1
1
2
0
1
2
1
1
0
0
1
2
1
0
1
1
1
1
2
1
1
1
1
0
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
2
1
0
1
1
2
2
0
1
1
1
1
1
1
0
1
1
1
1
0
2
1
1
2
1
2
1
0
0
1
1
1
2
1
0
1
2
1
1
2
1
1
1
2
1
2
0
0
1
1
0
1
1
1
2
1
1
2
2
0
0
1
1
2
1
3
2
0
1
1
1
1
0
1
1
2
1
1
1
1
1
1
0
1
1
1
1
1
1
0
0
1
0
2
1
1
1
2
1
1
1
1
1
1
1
2
1
2
0
2
2
1
1
0
1
0
0
1
1
2
1
1
1
1
2
1
1
1
0
2
0
1
0
0
1
1
1
2
2
2
2
2
1
2
1
1
1
1
1
1
2
1
1
1
1
0
2
1
1
2
1
1
2
2
1
2
1
0
1
1
0
1
1
0
1
1
0
1
1
1
1
1
2
1
2
2
0
2
1
1
1
1
1
0
0
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
0
1
1
1
1
0
1
1
2
1
2
1
1
1
1
1
1
1
0
1
1
1
1
1
0
1
1
0
1
1
2
2
1
1
1
0
1
1
1
1
2
1
2
1
0
1
2
0
1
1
1
1
1
1
1
0
2
1
1
1
2
1
1
1
0
2
0
1
1
1
2
2
1
1
2
1
1
1
2
1
2
1
1
1
1
0
0
0
2
0
0
1
2
1
2
1
1
1
0
1
1
1
1
1
1
2
1
1
2
1
2
2
1
2
2
1
2
2
0
0
1
2
2
1
2
1
1
1
2
1
1
1
1
2
1
1
1
1
1
2
1
0
2
1
0
1
2
2
1
1
0
0
1
0
0
1
0
1
1
1
0
0
2
0
1
2
1
1
2
1
0
2
1
0
1
1
1
1
1
1
1
1
2
1
1
2
1
1
0
1
1
2
1
2
1
0
2
1
0
0
1
1
0
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
0
1
2
1
1
0
0
1
2
0
2
0
1
0
1
1
1
1
0
1
3
2
2
0
2
0
2
2
1
1
1
2
1
1
3
2
1
1
2
1
0
1
2
1
0
1
0
2
3
1
1
0
1
1
1
2
3
1
1
1
1
1
1
2
1
2
2
1
2
1
0
2
2
2
1
0
0
2
0
1
2
1
1
1
1
1
1
1
0
1
1
1
1
1
2
2
1
1
2
1
0
2
1
1
1
1
1
2
0
2
2
1
2
1
1
1
2
1
1
2
1
1
1
1
0
2
1
2
1
1
2
1
1
1
1
0
1
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
2
2
0
2
0
1
1
2
1
1
1
0
1
1
1
1
2
1
1
0
0
2
0
1
2
0
1
0
1
2
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
0
1
1
0
1
0
2
1
2
1
1
2
1
2
1
0
1
1
0
1
1
1
1
1
1
1
0
1
1
0
1
1
1
1
2
1
1
1
1
1
2
1
1
0
2
2
1
1
1
2
2
2
2
1
2
1
2
1
1
1
0
1
1
1
2
0
0
2
1
1
1
2
0
2
2
1
2
1
1
2
1
2
1
1
1
0
1
1
1
1
1
1
1
1
1
1
2
0
2
2
2
2
1
1
0
1
0
2
2
0
1
1
1
2
1
0
1
1
1
1
0
1
1
1
2
1
1
0
0
0
1
2
1
1
2
1
2
2
2
1
1
0
1
1
1
1
2
1
2
1
1
0
2
1
1
2
2
2
0
1
2
1
0
1
1
1
1
0
1
1
1
0
1
1
1
1
1
1
2
1
2
2
1
1
0
1
2
1
2
1
1
1
1
1
1
2
2
2
1
1
1
2
1
2
0
1
1
1
2
1
2
1
1
1
0
0
2
1
1
1
1
2
1
1
2
1
3
2
2
2
1
1
1
0
2
1
1
3
1
2
1
2
1
2
1
1
1
1
1
1
0
1
1
0
1
0
2
2
1
2
1
1
1
2
2
1
2
1
2
0
0
2
1
2
1
1
2
1
2
1
1
1
1
2
1
1
1
1
2
2
1
0
1
2
2
2
1
2
0
1
1
1
1
3
2
0
1
1
1
2
1
0
0
1
1
0
2
0
1
2
1
2
2
0
2
0
1
2
0
1
0
0
1
1
1
0
1
2
2
2
1
2
1
2
0
2
1
1
0
2
1
1
2
1
0
1
1
1
2
1
1
1
1
1
2
2
2
2
0
1
1
1
2
2
1
1
2
1
2
1
0
1
1
0
2
1
0
0
1
1
1
1
0
1
1
1
2
0
2
2
2
1
0
1
1
2
1
1
0
1
1
0
1
1
1
2
1
1
2
1
2
1
2
1
1
1
2
1
2
1
1
0
2
1
0
1
0
1
0
1
2
2
0
0
1
2
0
2
1
0
2
0
2
2
2
1
1
1
1
2
0
1
1
2
1
1
2
1
1
1
1
1
1
2
0
1
2
0
2
1
1
1
2
2
1
1
1
1
1
1
1
1
0
1
2
1
1
1
2
1
1
1
1
2
1
1
1
1
0
1
1
1
2
2
1
1
1
1
1
2
1
0
1
2
2
0
1
1
2
3
1
0
1
1
1
2
0
1
1
2
1
0
2
0
1
2
2
2
1
1
1
0
1
2
0
2
1
1
1
1
2
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
2
0
0
2
2
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
0
0
2
1
1
1
1
1
1
1
1
0
1
1
1
1
1
0
1
1
0
1
1
1
1
1
1
0
1
1
0
1
0
1
2
1
2
1
0
2
1
2
1
2
1
1
1
2
2
1
2
1
0
2
1
1
1
1
2
1
1
0
1
2
1
1
1
1
0
0
1
1
0
1
1
1
1
1
0
0
2
2
0
1
2
2
1
1
1
2
2
1
2
2
1
2
1
2
1
1
2
1
1
1
1
2
2
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
2
2
1
1
1
2
1
2
1
2
1
2
2
1
2
1
2
1
1
1
1
1
1
1
2
2
0
1
1
2
1
2
2
1
1
1
0
2
0
1
1
2
1
1
2
1
2
1
1
1
1
2
1
1
1
0
1
2
0
2
0
2
1
1
1
1
1
1
1
1
1
1
2
0
1
1
1
1
1
1
1
1
0
0
1
2
1
1
1
0
1
2
2
1
1
1
0
1
1
1
1
1
0
0
0
1
1
0
2
0
2
1
2
1
1
3
2
1
1
2
1
0
1
2
2
2
1
1
1
0
0
1
1
1
1
1
1
1
1
0
1
1
2
2
1
1
1
1
1
1
1
2
2
1
1
1
2
1
2
1
1
1
2
2
0
1
1
2
1
0
1
1
1
1
1
2
3
1
1
1
1
2
1
1
2
3
1
1
1
1
1
0
1
2
0
1
1
1
1
1
2
0
1
1
1
2
1
2
1
1
1
1
1
1
2
0
1
1
2
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
0
1
1
1
1
0
1
1
0
1
1
1
1
1
1
0
1
1
1
1
2
1
0
1
1
1
1
1
1
2
1
1
2
1
1
1
1
2
2
2
1
0
1
1
1
2
0
1
0
2
1
0
2
1
2
2
3
2
1
1
1
1
1
1
0
1
0
1
1
1
1
2
1
1
2
1
2
1
0
2
1
2
2
0
1
1
0
1
1
1
1
0
1
2
1
2
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
2
1
1
0
1
1
1
2
1
1
1
1
2
1
1
1
2
2
0
0
0
0
1
2
1
2
2
2
1
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
0
1
2
1
1
1
1
1
1
1
1
1
1
0
2
1
1
2
1
1
1
1
2
1
2
1
2
1
2
1
1
1
0
1
1
0
2
1
2
1
1
1
1
2
2
1
1
0
0
1
1
1
2
1
1
1
1
3
2
1
1
0
1
1
1
1
1
1
1
2
1
1
2
2
1
1
1
1
1
2
1
0
1
0
1
1
2
2
1
1
1
2
0
1
1
3
1
0
0
2
2
2
1
1
1
0
2
1
2
1
1
1
1
0
1
2
1
1
0
0
0
0
1
1
1
0
1
1
2
0
1
1
1
1
2
3
1
1
1
1
2
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
3
1
1
2
2
1
2
1
2
2
1
1
2
0
2
1
1
2
1
1
1
0
1
1
2
2
1
1
2
1
1
1
0
1
2
1
1
1
1
2
1
1
2
2
2
0
0
2
2
0
1
1
0
0
1
1
1
1
2
2
0
1
1
1
0
1
1
1
1
1
1
0
1
1
0
1
1
2
1
1
0
1
1
0
1
0
2
1
1
1
1
1
0
1
1
2
0
2
1
1
1
1
2
2
2
0
0
1
0
0
1
0
1
2
0
2
2
1
1
1
2
2
2
2
3
1
1
1
1
1
2
0
2
2
1
1
0
1
1
1
1
1
1
0
2
2
1
0
1
2
1
1
1
1
2
1
2
1
1
1
2
3
1
0
0
1
2
2
1
0
0
1
1
3
1
1
2
1
1
2
1
2
1
1
1
2
1
0
1
2
1
1
1
1
1
1
1
1
1
0
2
1
1
0
1
1
2
2
1
2
1
2
2
2
1
2
2
1
2
2
2
1
2
1
1
1
2
2
1
1
2
2
1
2
1
1
1
1
2
1
1
1
2
1
1
1
1
1
0
0
2
2
1
2
1
2
1
1
3
2
1
2
1
1
1
2
0
1
1
0
2
0
1
1
1
1
2
0
0
1
2
1
1
1
2
0
0
1
1
2
1
1
1
1
2
2
2
2
0
1
0
1
1
2
1
0
1
1
2
0
1
1
1
1
0
1
0
2
0
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
2
0
1
1
1
1
0
0
0
1
1
2
0
1
2
1
1
1
2
0
1
1
1
0
1
2
2
1
0
1
2
2
2
0
1
1
2
1
1
2
0
1
2
1
2
1
1
1
1
1
2
2
2
1
1
0
1
2
1
2
1
0
1
1
1
0
1
2
0
2
1
1
1
2
0
2
0
2
1
1
1
2
1
1
1
0
1
1
1
2
2
1
1
1
2
1
1
0
1
1
2
1
2
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
0
0
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
0
2
1
1
2
0
1
1
0
1
1
1
1
2
1
1
2
1
0
1
1
0
2
1
1
1
1
2
1
1
2
1
1
1
2
2
1
1
1
1
1
2
1
1
1
2
0
1
1
2
0
2
1
0
2
1
1
1
2
2
0
1
1
2
3
0
2
1
2
2
1
2
0
1
1
0
1
2
1
0
1
0
2
1
1
1
1
2
1
2
1
1
1
1
2
1
1
2
3
1
0
2
1
1
1
1
1
0
1
2
1
2
1
1
2
1
0
2
1
2
2
1
1
1
2
1
1
1
1
1
2
1
0
2
2
1
1
1
1
1
1
1
2
2
1
1
2
2
0
0
1
0
2
2
1
1
1
2
1
2
1
1
1
1
2
1
2
1
2
2
1
1
1
1
0
1
2
1
1
1
1
1
2
1
0
2
1
1
1
2
1
0
2
1
2
1
1
0
2
1
1
1
1
1
1
1
1
0
1
2
1
2
1
1
2
0
1
1
1
1
2
2
2
0
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
2
2
2
1
1
1
1
2
1
2
0
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
1
2
2
3
2
0
2
2
1
2
1
1
1
0
2
1
1
1
2
1
1
2
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
2
2
2
1
1
1
1
1
0
0
2
1
1
1
2
1
2
1
2
2
1
1
2
0
2
1
0
2
1
1
1
1
1
0
2
1
1
0
2
1
1
1
1
1
1
2
0
1
1
1
0
1
1
0
0
1
0
1
2
1
1
1
1
2
1
1
1
1
1
2
1
0
1
1
0
1
1
2
1
1
1
1
1
2
1
2
1
2
2
1
1
1
1
2
2
1
2
1
0
1
0
1
1
0
2
1
0
1
1
1
1
1
1
0
0
2
1
2
1
1
0
1
2
1
2
0
2
1
2
1
2
0
1
1
2
1
0
1
2
2
1
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
2
1
3
1
1
1
1
2
2
1
1
0
1
1
1
1
2
0
1
0
1
1
1
1
2
3
2
1
0
2
1
1
1
2
2
2
2
1
1
0
2
1
0
1
1
1
1
1
2
2
1
1
2
1
1
1
1
1
0
1
1
1
0
0
0
1
2
1
1
1
1
2
0
1
1
1
2
1
2
1
1
2
1
2
1
1
1
1
1
2
1
1
1
1
1
0
1
1
1
1
0
1
1
1
1
1
1
1
0
1
0
1
1
1
2
1
2
2
1
1
0
1
2
1
1
1
1
1
1
3
2
2
1
1
1
1
2
2
1
2
2
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
1
2
1
2
0
0
2
1
1
1
1
1
0
1
1
1
0
0
1
1
0
0
1
1
1
1
1
2
1
1
1
1
1
2
0
1
1
1
1
1
1
2
1
2
0
2
2
1
1
2
2
1
0
2
1
0
2
0
1
0
1
1
1
1
2
1
0
1
0
1
1
1
1
1
2
0
2
2
2
1
0
1
1
1
2
0
2
1
0
1
1
1
1
1
1
2
0
1
2
0
2
2
2
1
1
1
1
1
1
0
2
1
1
0
1
1
1
2
2
2
1
1
1
1
1
1
1
1
1
0
0
2
0
1
1
2
1
2
1
2
0
1
2
1
0
1
2
0
1
0
2
0
1
1
1
2
2
1
1
1
0
2
1
0
1
2
1
1
1
1
1
1
1
1
2
1
1
0
2
2
1
0
1
0
0
1
2
1
1
1
1
2
1
1
1
1
0
1
1
1
1
1
0
1
2
1
2
1
0
2
1
1
1
1
0
1
2
1
1
1
1
2
1
1
1
1
1
1
2
1
1
0
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
0
1
1
2
2
2
1
2
1
1
2
1
0
1
1
0
2
2
1
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
1
2
1
1
1
0
0
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
2
1
1
1
3
1
1
1
2
2
2
1
3
1
1
1
2
2
1
0
2
2
2
1
1
1
2
0
2
1
0
1
2
2
0
0
1
1
1
0
1
1
0
1
1
1
1
1
1
1
1
2
1
1
0
1
1
0
0
0
1
1
1
1
0
2
1
1
1
2
0
1
1
2
2
2
2
1
1
1
2
1
1
2
1
0
1
0
0
1
1
1
0
1
2
1
2
1
1
1
1
1
1
0
2
1
1
0
2
0
1
0
1
1
1
2
1
1
1
0
1
0
1
2
0
1
2
2
1
1
1
1
2
1
1
2
2
2
2
1
1
1
1
0
1
2
1
1
1
0
2
1
1
0
1
1
2
1
2
2
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
0
1
1
3
1
1
1
2
3
1
1
1
2
0
1
0
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
0
1
0
1
1
2
2
0
2
1
2
1
1
1
2
0
1
1
2
1
1
1
1
1
2
1
1
1
2
2
0
1
1
2
1
1
0
1
1
1
1
1
2
2
1
0
2
2
1
2
1
1
3
1
2
1
2
0
1
1
1
0
1
2
2
0
1
1
1
1
1
2
1
2
1
1
1
1
2
2
2
1
2
0
1
2
1
1
2
2
1
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
0
1
1
1
1
1
1
0
2
1
2
1
1
1
1
1
2
1
0
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
0
1
1
1
1
1
1
2
1
1
1
1
2
1
2
1
0
2
1
0
1
0
2
1
0
2
1
2
2
1
1
1
0
1
1
0
1
1
2
1
1
1
2
1
1
1
1
0
1
1
2
2
1
2
0
1
1
1
1
2
1
1
2
1
0
1
1
2
2
3
1
1
3
2
1
1
1
2
1
1
1
2
1
0
1
1
1
1
0
2
2
0
1
2
1
1
11
1
1
1
1
2
1
0
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
1
2
1
1
1
1
2
1
0
2
1
1
1
2
1
2
2
0
1
1
1
1
2
1
1
1
1
0
0
1
1
2
2
1
1
0
1
1
1
0
1
2
1
0
2
0
2
0
1
1
2
2
1
1
1
1
1
1
1
1
1
0
2
1
1
2
1
1
2
1
1
1
1
2
1
2
1
2
1
1
1
1
0
2
1
2
1
2
1
1
2
1
1
2
1
1
2
2
1
0
3
1
1
1
1
1
1
1
2
1
2
1
1
1
2
1
2
2
1
2
2
2
2
2
2
1
1
0
0
1
0
0
1
1
2
2
1
0
1
1
1
1
1
1
0
2
1
1
1
1
2
1
2
2
1
2
1
1
1
0
2
0
1
1
1
0
1
2
0
2
1
1
1
1
2
1
2
3
1
1
1
1
3
1
1
2
1
0
1
2
1
1
2
1
2
1
1
2
2
1
2
1
1
1
1
0
2
1
2
1
1
1
1
2
2
1
1
0
0
1
2
1
1
1
2
1
2
1
1
2
1
1
1
1
1
1
0
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
0
1
1
2
1
1
1
2
2
1
1
0
0
2
1
1
2
1
1
1
1
1
2
2
0
2
1
2
1
1
1
1
2
2
1
0
1
0
1
2
1
2
1
0
1
0
1
0
1
2
1
0
1
2
0
1
2
1
1
1
1
1
2
1
0
2
1
1
1
1
2
1
2
1
0
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
0
1
1
1
1
2
1
0
0
0
1
1
1
0
0
1
1
2
1
1
1
2
1
1
2
2
1
1
1
1
1
1
1
1
2
1
1
1
0
2
2
2
1
1
1
1
0
1
1
1
1
1
1
1
0
1
2
2
1
1
1
1
1
2
2
2
1
0
2
1
1
1
1
0
0
2
1
1
1
0
1
1
2
0
2
1
0
1
1
0
2
2
2
2
2
1
1
1
1
1
1
0
0
2
0
2
1
2
2
1
1
0
1
1
0
1
1
1
1
1
1
1
1
1
1
0
1
1
1
2
1
1
2
1
1
2
2
1
2
1
1
2
1
1
2
1
2
0
2
1
1
1
1
1
1
1
2
2
1
0
1
1
2
1
2
1
1
1
2
0
2
2
1
1
1
0
2
0
2
1
1
1
1
1
1
1
2
2
2
1
1
1
2
2
1
1
2
1
1
2
0
2
2
2
1
1
1
2
1
2
1
1
0
2
0
2
1
1
2
1
1
1
1
2
0
2
2
1
2
2
2
1
1
1
1
1
1
0
0
1
1
1
1
1
2
1
2
2
2
1
2
1
1
1
0
1
1
1
0
1
1
1
2
2
1
1
1
0
2
1
1
0
2
1
1
0
3
0
0
2
2
2
1
1
0
1
2
1
0
0
2
1
0
1
2
1
2
1
2
2
1
1
1
1
1
2
2
1
2
1
2
0
1
1
1
1
0
2
2
1
0
2
2
2
0
2
1
2
1
1
2
2
1
1
1
2
1
1
1
1
0
1
1
2
1
1
1
1
1
1
2
2
2
1
2
1
1
2
1
2
2
1
1
1
2
2
0
1
2
0
1
1
0
1
1
1
0
0
1
0
2
2
1
1
1
1
1
1
1
0
0
2
1
3
1
2
0
1
1
2
2
1
2
2
1
0
1
2
2
1
0
1
1
2
0
1
2
1
1
1
1
0
1
1
1
1
2
0
2
2
2
1
1
1
1
2
2
2
1
2
1
2
1
1
2
1
1
1
1
2
1
1
0
1
1
1
1
1
0
2
0
1
1
1
2
0
0
1
0
1
2
1
0
1
1
1
1
0
0
1
0
0
2
2
0
1
1
2
1
1
1
1
0
1
0
1
2
2
1
1
1
0
1
1
2
1
1
1
2
1
1
1
0
0
2
1
0
1
0
1
0
1
2
2
2
1
0
2
0
0
1
1
1
1
1
1
1
1
1
2
2
0
2
2
0
1
1
2
1
2
1
0
1
1
1
1
1
1
0
0
1
1
0
1
1
2
1
1
1
1
1
1
0
2
2
0
0
2
1
1
1
2
1
2
1
1
1
1
2
1
1
1
1
1
2
0
1
0
2
1
2
1
1
0
2
1
1
1
1
1
1
1
2
1
0
1
1
1
1
1
0
0
1
1
0
1
1
0
2
0
2
0
1
2
1
1
1
1
1
0
1
0
1
1
0
2
2
1
0
1
1
1
2
1
1
3
2
2
2
1
1
1
1
1
1
0
1
2
1
2
1
1
1
2
1
2
1
1
0
0
1
2
0
2
2
1
1
1
1
1
1
2
1
1
1
1
2
2
1
2
1
2
1
1
1
2
1
2
1
1
1
2
2
1
2
1
1
2
1
2
2
1
1
1
1
1
1
1
2
2
1
2
1
1
1
0
2
1
2
1
1
1
1
1
1
1
1
1
0
0
1
0
1
1
0
3
1
1
0
0
2
1
0
2
1
4
1
0
1
2
2
1
1
1
1
1
0
2
1
1
1
1
0
1
1
2
1
0
1
1
1
1
0
1
2
1
1
2
1
1
0
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
1
1
1
2
1
1
1
2
1
3
2
0
1
2
1
0
0
2
1
0
1
1
1
2
1
1
1
1
0
0
1
1
1
1
2
1
1
1
2
1
1
1
1
3
0
2
1
1
0
2
1
1
0
1
1
2
2
1
1
1
1
0
2
2
2
2
2
1
1
2
0
1
1
1
2
1
1
2
1
1
0
1
1
1
2
0
1
1
2
1
2
1
1
1
2
2
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
2
1
1
1
1
0
2
0
1
1
1
1
2
1
1
1
1
1
1
1
0
2
1
1
1
1
2
1
1
1
1
2
1
2
1
1
0
1
2
1
1
1
1
2
1
1
2
1
1
1
1
0
1
1
1
0
1
1
3
2
1
2
1
1
1
1
1
2
1
2
2
0
1
1
2
1
1
1
2
1
2
1
1
1
1
2
1
1
1
1
0
1
1
1
1
1
2
1
0
0
1
0
1
2
1
0
0
2
1
0
0
0
0
1
0
0
1
1
0
0
1
1
0
3
1
1
1
1
0
2
2
1
2
0
1
1
1
1
0
1
1
2
1
2
0
1
0
2
0
1
2
1
1
1
1
1
1
0
1
1
2
1
1
1
1
1
1
2
1
0
1
1
2
1
2
0
0
0
1
1
1
2
0
1
1
1
2
0
1
1
1
1
2
2
1
1
1
1
1
1
2
0
0
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
0
1
1
0
1
2
0
0
1
1
0
1
2
1
0
1
1
2
2
1
1
1
1
1
2
1
1
1
2
2
0
1
0
1
1
1
1
2
2
0
3
1
0
1
1
1
1
1
1
1
1
2
2
1
1
0
0
1
1
1
1
0
1
1
2
2
1
2
2
0
1
0
2
1
1
2
1
1
2
2
1
2
2
2
1
1
0
1
1
2
2
0
2
1
1
1
0
2
1
1
1
2
1
1
1
1
1
1
0
1
2
1
1
1
1
1
1
2
2
1
2
1
3
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
2
2
1
1
1
2
0
1
1
1
2
1
1
2
1
1
1
2
2
0
2
2
1
1
1
1
1
1
0
0
1
1
2
1
2
1
1
2
1
1
1
1
1
1
1
1
0
2
2
2
1
1
1
0
1
0
1
2
1
0
1
0
1
0
1
1
1
0
1
0
1
0
2
2
0
1
1
0
1
2
1
1
1
3
1
1
0
1
1
1
2
1
0
1
1
1
1
1
1
1
0
2
1
1
1
1
2
2
2
2
0
1
1
1
2
1
1
2
0
1
1
0
0
1
3
1
1
1
1
1
2
1
1
1
1
1
2
1
2
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
0
1
0
2
2
2
1
1
1
1
1
1
1
1
1
2
1
1
2
2
1
1
1
2
2
1
1
2
1
1
1
1
1
1
0
1
1
2
1
0
2
1
0
2
1
0
1
1
2
0
2
2
2
2
2
0
1
2
2
2
2
1
0
1
2
1
1
1
2
1
2
1
1
1
2
2
1
1
1
2
0
1
2
1
2
1
1
0
1
1
1
1
1
1
2
2
0
0
1
1
1
0
2
1
1
1
2
1
1
1
2
2
2
1
2
1
0
1
2
2
0
2
2
1
2
1
2
2
2
2
1
1
1
2
1
2
1
2
1
2
1
0
2
1
2
1
1
1
2
1
2
0
1
1
1
1
1
0
2
1
2
1
1
2
0
2
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
2
0
1
1
1
1
1
1
0
2
2
2
2
1
2
1
1
2
1
2
1
1
1
1
0
2
1
1
1
2
1
1
1
1
2
1
1
2
3
1
1
2
1
1
1
1
2
0
1
1
1
1
1
2
1
1
1
2
2
1
1
2
0
2
1
1
2
1
2
1
1
2
0
1
1
2
1
1
2
1
1
1
1
1
1
0
2
0
2
2
1
1
1
1
2
1
1
1
1
1
1
2
1
1
0
1
1
0
2
1
1
0
0
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
0
1
4
0
2
1
2
1
0
2
1
3
2
1
1
0
1
1
1
2
1
2
0
1
0
2
0
1
1
1
1
1
0
1
1
1
0
2
0
1
2
0
1
1
0
1
1
2
1
1
2
1
2
1
1
1
2
0
1
2
1
1
1
1
1
1
3
2
1
0
1
1
2
2
1
1
2
1
1
1
2
2
1
2
1
1
1
2
1
1
2
1
1
1
1
2
1
1
1
2
1
1
1
1
0
2
0
2
1
2
1
1
1
1
1
1
0
1
0
2
0
1
1
1
2
2
1
2
1
0
1
1
0
1
1
1
1
0
0
2
1
1
1
1
1
1
1
2
1
2
2
0
1
3
1
1
1
2
2
1
1
1
2
0
1
0
2
1
2
2
2
1
2
1
1
0
0
1
2
0
2
2
1
0
3
1
2
1
1
1
3
1
1
1
1
2
1
1
1
1
1
1
1
1
1
0
1
2
1
1
1
1
1
2
1
1
2
1
1
0
1
2
2
1
1
1
1
1
2
1
1
1
2
1
1
1
2
2
1
1
1
0
1
1
1
2
1
1
1
2
2
2
1
1
2
1
2
1
1
1
2
1
1
0
2
1
1
1
1
1
1
1
1
2
0
1
1
0
1
1
1
2
1
2
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
1
2
2
0
1
1
1
1
1
1
1
1
1
2
1
2
2
1
2
2
1
0
1
1
1
1
2
0
1
1
2
2
1
1
2
1
1
1
2
1
2
1
1
1
0
1
2
0
1
2
1
1
2
2
1
1
0
0
2
2
0
0
0
1
2
1
2
1
1
1
1
1
0
1
2
0
1
1
1
1
2
1
1
1
2
1
0
1
2
1
2
1
1
2
0
1
1
1
1
1
1
2
2
1
2
0
2
2
1
2
1
0
2
1
3
1
2
1
0
1
0
1
0
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
2
2
1
2
1
1
1
1
0
2
2
2
1
2
1
1
1
2
2
1
1
0
1
1
1
2
0
1
0
2
1
1
1
0
1
0
2
0
1
2
1
1
1
2
1
1
2
1
1
2
1
1
1
1
0
2
2
0
1
2
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
0
2
1
1
1
1
0
1
2
1
1
2
1
2
1
1
1
1
1
1
1
2
1
0
1
1
1
1
1
0
0
1
1
0
1
1
2
1
1
1
1
2
1
2
2
2
1
0
2
1
1
2
1
1
0
2
0
2
2
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
2
0
2
1
1
2
2
1
0
1
2
1
1
2
1
1
1
2
1
1
2
1
2
0
2
2
2
1
1
1
2
1
1
2
1
2
1
1
0
1
1
1
3
2
2
1
0
1
0
2
1
1
2
2
0
2
2
2
2
1
2
1
1
1
1
2
0
1
1
2
1
2
1
1
1
1
2
1
3
1
2
1
0
0
0
1
2
1
2
0
1
1
1
2
2
3
1
1
1
1
2
1
1
1
1
1
2
1
1
2
1
1
1
1
0
1
1
2
1
2
2
2
1
1
0
1
1
2
1
2
1
1
2
2
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
2
1
0
1
2
1
0
1
1
2
0
2
1
1
1
0
1
1
1
2
1
0
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
0
1
1
1
0
1
1
2
2
0
1
1
1
0
1
1
1
1
1
2
2
1
1
2
2
0
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
5
1
2
0
1
1
1
1
2
1
1
0
0
1
1
1
1
1
2
1
0
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
2
1
2
1
1
1
0
0
2
1
2
0
1
1
1
1
2
1
0
2
1
1
1
1
1
1
1
2
2
2
1
0
1
2
2
1
1
1
0
1
2
1
0
1
1
1
1
2
2
2
1
0
1
1
1
2
1
1
1
2
1
1
2
1
1
1
1
1
1
0
1
2
1
0
0
1
1
1
1
0
1
1
0
2
1
1
1
2
1
2
2
1
1
1
1
2
2
0
1
0
1
1
1
2
1
0
2
0
2
1
1
1
2
2
2
0
2
2
1
1
2
1
2
1
1
1
2
2
2
1
1
2
1
1
1
2
1
0
2
1
1
2
1
1
1
2
1
2
0
1
0
1
1
2
0
1
2
1
1
2
2
1
2
2
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
2
1
2
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
2
2
2
2
1
1
2
2
2
1
2
1
2
1
1
1
1
1
1
0
1
1
2
2
2
1
2
1
2
2
2
0
2
1
2
2
1
1
1
1
1
1
0
0
2
2
3
2
2
0
0
1
1
1
1
1
2
1
1
1
1
2
2
2
1
0
1
1
1
1
1
1
1
1
2
1
1
0
0
0
3
0
1
1
1
1
1
0
1
2
1
1
2
2
1
1
0
2
1
0
1
1
1
1
1
2
0
1
1
2
0
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
2
2
0
1
1
1
1
1
0
1
2
2
1
0
2
1
0
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
0
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
2
1
2
3
2
2
0
1
0
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
2
1
0
2
1
1
2
1
0
1
1
2
1
1
2
0
1
2
1
1
1
1
1
1
0
1
1
2
2
1
1
0
1
1
2
6
3
1
1
1
1
0
1
1
1
1
0
1
1
0
2
1
2
1
1
0
2
2
1
1
1
1
0
1
2
1
1
1
1
1
1
1
1
1
1
0
2
1
2
1
1
1
1
2
2
1
1
0
1
1
1
2
1
2
2
0
1
2
2
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
0
1
1
2
2
1
2
1
2
1
2
1
1
1
1
1
0
1
0
1
1
2
2
2
1
0
0
1
2
1
2
2
1
2
1
1
2
1
1
1
0
1
0
1
1
0
2
1
0
1
1
1
0
1
1
2
3
1
0
2
2
2
1
2
0
0
1
0
1
2
1
1
1
1
1
2
1
1
1
2
0
1
1
2
2
1
2
2
1
2
2
1
1
2
1
1
0
2
0
1
0
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
0
1
2
1
1
2
0
1
1
1
1
0
1
1
1
2
2
1
1
1
2
2
1
1
1
2
1
1
1
1
2
1
0
1
2
0
1
1
1
1
1
1
0
0
0
1
1
0
1
2
2
1
2
1
1
1
1
2
2
1
1
2
2
2
1
0
0
1
0
1
1
3
2
1
1
0
2
1
0
1
1
2
2
1
2
2
2
1
1
2
1
2
1
1
1
1
2
2
2
1
1
0
1
1
2
0
1
1
1
2
1
0
2
0
2
1
1
1
0
0
0
1
1
1
0
0
2
1
1
1
1
2
2
1
1
0
0
1
1
1
0
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
2
1
2
2
1
0
2
2
1
1
1
2
1
1
1
2
1
0
1
1
1
2
1
0
1
1
2
0
1
2
1
2
2
0
1
1
2
2
1
1
1
2
2
2
1
0
2
2
1
1
1
0
2
1
1
0
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
0
1
1
1
1
2
2
2
2
2
3
1
2
2
2
1
2
0
1
2
1
2
0
1
1
2
1
2
4
2
1
1
2
1
1
1
1
0
1
2
1
2
0
1
1
1
0
2
0
0
0
1
1
1
1
1
1
1
1
2
1
1
0
1
2
2
1
1
0
1
1
2
1
1
2
0
2
1
1
1
0
0
1
1
0
0
1
2
1
2
1
1
0
1
1
2
1
2
2
1
2
0
1
1
1
2
2
1
2
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
2
2
1
1
3
1
1
1
2
0
1
2
1
1
2
2
2
1
0
1
1
1
1
0
1
1
0
1
2
1
1
2
0
0
1
0
1
1
2
1
1
1
1
2
1
2
1
2
2
2
2
1
1
2
1
2
2
0
1
1
0
1
1
1
1
1
1
1
2
2
2
1
2
2
1
1
1
2
2
2
2
0
1
0
2
2
1
1
2
1
1
1
1
2
1
1
1
2
3
1
1
0
2
1
1
0
1
1
1
0
1
1
1
1
1
1
2
1
1
0
2
1
2
1
0
1
2
2
1
1
1
2
2
1
2
0
0
1
1
1
0
2
2
1
1
2
1
1
1
2
0
1
2
1
1
1
1
2
1
2
2
1
2
2
2
1
1
1
1
2
2
1
2
0
1
1
2
2
1
1
0
1
0
1
8
2
1
1
1
1
1
2
0
2
1
0
1
2
1
1
1
2
1
1
1
1
1
2
2
1
2
1
1
2
2
1
2
2
2
2
0
1
1
1
1
2
2
1
1
1
2
2
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
0
0
0
2
1
0
2
1
1
0
0
1
2
1
1
1
2
1
1
2
1
2
1
0
1
0
1
1
1
0
1
2
2
1
2
1
0
1
1
2
1
1
2
1
0
1
2
2
1
1
0
2
1
0
1
1
1
1
1
2
1
1
1
2
0
1
1
1
2
2
0
2
1
1
1
2
1
1
1
1
1
1
1
0
1
1
1
1
2
1
2
1
2
1
1
2
2
1
0
1
1
2
2
0
1
0
1
2
1
1
1
1
0
2
2
0
1
2
2
0
1
1
1
1
2
1
2
1
1
0
1
2
1
0
1
1
1
2
2
1
2
1
2
1
2
0
2
1
1
1
1
2
1
1
2
0
1
0
1
1
0
2
1
0
0
2
1
2
1
2
0
1
1
1
2
1
1
1
0
1
1
1
2
1
1
1
0
1
0
1
2
1
1
1
1
1
2
0
1
2
0
0
0
2
1
1
1
1
1
1
1
1
1
1
2
1
1
0
2
1
2
2
2
2
2
1
1
2
2
4
2
1
2
1
1
0
1
1
1
1
1
2
1
2
1
1
1
1
1
1
2
1
0
1
1
3
2
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
0
1
1
1
1
1
0
1
2
1
1
2
2
1
3
1
0
1
1
1
1
1
1
3
0
0
1
1
1
1
1
0
1
1
1
1
1
2
2
1
1
2
1
1
1
2
1
2
2
1
2
0
1
0
1
1
2
1
2
1
2
2
1
1
1
1
2
2
1
0
1
1
0
3
1
1
1
1
1
0
2
1
2
2
1
2
1
1
2
1
1
1
2
1
0
1
1
2
1
1
1
1
1
1
1
1
0
2
2
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
1
2
2
1
2
1
0
0
1
0
2
1
2
1
1
1
2
2
1
1
1
2
2
2
1
1
2
0
0
2
0
1
2
1
0
1
1
3
1
1
2
1
2
1
2
2
2
1
0
1
1
2
1
0
2
2
1
1
1
1
0
1
2
2
1
2
1
1
2
0
2
2
1
0
1
1
2
0
0
0
1
1
1
2
2
1
2
2
2
1
0
1
1
1
2
1
1
1
1
2
1
1
1
1
0
0
1
2
0
0
1
1
1
1
0
1
0
2
1
1
1
0
1
1
1
1
2
1
1
1
2
2
1
0
0
2
2
1
1
1
1
2
2
1
1
1
1
1
1
0
2
1
2
1
0
2
1
1
0
1
2
1
1
2
0
1
0
2
1
1
1
1
1
0
1
2
1
0
1
1
1
1
2
2
2
2
2
1
1
2
2
1
0
2
1
1
1
1
2
0
1
0
1
1
1
1
1
1
0
2
2
0
1
1
1
1
1
2
0
1
2
0
1
1
1
1
2
1
2
2
0
1
2
2
1
1
0
1
2
1
1
2
1
1
0
1
1
2
2
1
0
1
1
1
0
2
1
1
2
1
3
0
1
3
2
0
1
1
1
2
1
2
2
1
2
1
1
1
1
0
1
1
0
1
0
1
1
1
1
2
2
1
1
1
2
1
1
1
1
2
1
1
2
1
2
0
1
1
1
1
2
1
2
2
2
1
2
0
1
2
2
4
1
0
2
0
1
1
2
1
1
1
1
1
2
2
2
0
0
1
2
1
1
2
2
2
0
1
1
1
0
2
1
2
0
2
1
1
2
1
1
2
1
1
1
0
2
1
2
1
0
0
1
1
0
1
1
1
2
0
1
1
1
1
0
2
1
1
1
0
0
1
1
1
1
2
2
1
2
1
0
1
1
1
0
0
0
1
1
1
1
1
1
2
1
2
1
1
2
1
1
2
1
1
1
0
2
1
1
2
1
2
2
1
0
1
1
0
1
1
1
1
1
2
1
1
2
1
1
2
1
2
1
0
1
2
1
2
1
2
0
0
1
1
0
2
1
2
2
2
1
1
1
2
2
1
2
2
1
1
1
1
1
0
1
1
2
2
1
1
0
1
1
1
1
2
1
1
1
1
1
1
1
0
1
2
1
2
2
1
1
2
1
0
1
2
0
2
1
2
1
2
0
2
2
1
1
1
1
2
1
1
2
0
1
0
2
1
2
1
0
1
1
1
1
2
1
2
1
1
1
2
1
2
0
2
1
1
1
1
2
1
2
1
0
1
1
2
1
0
1
2
3
1
2
2
2
1
1
0
1
1
1
2
2
2
1
2
1
0
1
1
1
1
1
2
2
1
1
1
1
2
0
1
2
1
1
2
1
1
1
1
1
0
0
0
0
1
0
0
1
1
1
2
0
0
1
1
2
2
0
2
2
2
1
1
0
0
1
1
2
0
1
1
1
1
2
1
1
2
1
1
1
1
1
1
0
1
1
1
2
1
0
0
1
1
1
1
1
0
2
2
0
1
2
2
0
0
1
1
2
1
1
2
0
2
1
1
1
1
1
1
2
1
1
1
1
0
2
1
1
2
2
1
1
1
1
1
0
1
0
0
1
0
1
1
2
2
1
1
2
0
1
1
2
2
1
1
1
1
2
1
1
2
1
1
1
1
2
2
1
1
0
2
1
1
1
1
1
1
1
2
1
2
2
1
1
2
1
1
1
1
0
1
0
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
2
1
1
0
2
2
1
2
2
1
1
1
1
0
0
2
1
0
2
1
1
1
1
2
1
1
0
2
1
1
1
1
1
1
2
2
1
2
2
1
0
2
2
2
0
1
0
1
1
1
1
2
1
2
2
0
0
0
1
1
2
1
1
2
2
1
1
1
2
1
2
1
0
1
1
2
2
1
1
1
2
1
1
0
0
2
1
2
1
1
1
2
1
1
0
1
1
1
1
2
1
1
1
1
2
1
1
1
2
0
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
0
2
2
2
1
2
2
1
1
1
1
2
1
1
1
1
2
2
1
1
1
2
1
0
2
1
1
0
1
0
2
1
0
2
1
1
1
2
2
1
1
1
1
1
0
1
1
1
1
2
2
2
0
2
2
0
2
2
1
1
1
0
1
1
0
1
0
1
1
2
0
2
2
3
2
2
1
2
0
1
2
0
1
1
2
2
2
0
1
1
2
1
2
1
1
2
1
1
1
1
0
1
1
2
1
0
2
1
2
1
1
1
1
2
1
1
1
1
2
1
0
1
1
1
1
1
2
2
1
2
2
1
1
0
2
1
1
1
1
1
1
0
0
1
1
1
1
1
2
1
1
2
1
1
1
0
2
0
1
1
0
1
2
1
2
1
1
1
1
0
1
2
1
1
4
1
0
1
1
1
0
1
1
1
1
1
1
1
1
2
1
1
1
2
0
2
1
0
1
1
1
1
0
1
0
1
2
1
0
1
1
0
1
1
2
2
2
2
1
1
1
0
1
1
2
1
2
1
3
2
2
2
2
1
2
2
1
1
0
1
1
0
1
1
1
1
1
2
2
1
0
0
2
0
1
1
0
1
1
0
1
1
2
2
2
1
0
2
1
1
1
2
2
0
1
1
1
2
1
2
1
1
0
0
1
1
2
1
1
0
2
1
2
1
1
1
1
0
1
1
1
2
1
2
1
1
0
1
1
1
1
2
2
1
2
2
1
2
1
2
0
1
1
2
1
1
1
1
1
1
1
2
0
2
1
1
1
1
1
1
1
2
0
0
1
1
0
1
2
1
1
0
1
1
0
1
2
0
1
1
1
2
1
2
2
1
2
2
1
2
1
2
2
1
1
0
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
0
2
0
1
1
1
2
1
1
1
0
1
2
1
2
1
1
1
1
12
1
0
3
1
1
2
2
1
1
1
1
2
2
1
2
1
1
1
1
0
1
0
1
1
1
1
1
1
1
1
1
0
1
1
1
1
2
0
1
1
2
0
1
1
1
2
1
2
1
2
2
1
2
1
1
1
6
1
1
1
0
1
2
2
2
2
1
2
1
2
0
2
1
1
1
1
2
1
1
1
1
1
0
2
0
0
1
1
2
2
1
2
1
0
0
1
0
1
1
2
1
1
0
0
1
1
1
1
1
0
2
0
2
1
2
2
0
0
1
1
1
0
1
2
1
2
1
1
2
1
1
0
1
1
1
1
0
2
1
1
0
1
1
0
1
1
1
1
1
1
2
1
1
1
1
0
2
0
0
1
0
2
1
2
1
0
0
0
1
0
1
1
1
2
1
1
0
1
1
1
1
1
1
1
0
2
1
1
1
2
1
1
0
1
2
0
2
1
1
2
2
2
2
2
0
1
1
1
0
1
0
1
2
2
1
1
1
1
2
1
0
2
2
1
1
1
1
2
2
1
0
1
2
1
1
1
1
1
1
2
1
2
1
1
0
1
1
2
1
1
1
1
1
0
1
1
0
1
1
1
1
1
0
2
2
1
1
2
1
1
0
0
2
2
2
0
1
0
1
1
2
0
1
1
0
1
2
0
1
2
1
1
1
2
1
1
1
2
1
0
2
0
1
0
1
1
1
1
1
1
1
1
1
2
1
0
2
2
0
1
1
1
0
1
1
2
1
1
2
1
0
2
2
1
1
0
2
1
1
1
1
1
1
2
0
1
1
0
2
1
1
2
1
1
0
2
1
1
2
1
2
1
1
1
1
0
1
1
2
1
1
2
1
1
1
0
0
1
1
2
2
1
1
0
1
1
1
0
1
2
0
2
2
0
1
1
1
1
1
1
1
0
2
0
1
1
1
1
1
0
1
1
2
2
1
2
1
1
1
0
2
1
0
1
2
1
0
1
1
0
1
2
1
2
1
0
1
1
1
1
1
1
2
1
1
1
2
1
1
1
0
0
1
1
1
1
2
2
1
2
1
2
1
1
2
1
1
1
2
1
1
0
2
1
1
1
2
1
0
2
1
1
2
2
2
1
1
0
2
2
2
0
1
1
0
2
0
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
2
2
1
2
1
1
1
1
1
2
1
2
1
2
2
1
1
0
1
2
1
0
1
2
1
1
1
2
1
1
1
2
1
0
1
1
1
1
1
1
0
0
1
1
1
2
2
2
1
2
0
1
0
0
2
1
2
1
2
1
2
0
1
2
2
2
1
1
0
0
1
2
1
0
1
1
1
1
1
0
2
1
0
1
1
1
1
2
1
1
2
2
2
1
2
1
1
1
2
2
0
2
1
1
1
1
0
1
1
0
2
1
1
2
1
1
1
1
0
1
1
1
1
1
1
2
1
1
1
2
1
1
1
2
0
1
1
2
1
0
1
1
2
1
2
1
2
2
2
2
1
0
1
2
2
1
2
1
0
2
1
1
0
1
0
1
1
1
2
2
2
1
0
1
1
0
1
1
1
1
2
2
1
1
1
1
2
1
1
2
1
1
1
0
1
1
0
1
0
2
0
1
1
2
1
1
2
1
1
2
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
0
0
1
2
0
0
1
1
1
2
2
2
1
1
2
0
1
1
1
1
1
1
1
1
2
0
1
1
1
2
1
0
1
1
1
1
2
0
1
1
2
0
0
1
0
0
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
3
1
0
0
1
1
0
1
1
1
2
2
7
1
1
2
1
1
1
1
1
2
1
1
2
2
1
1
2
0
1
1
2
0
0
1
1
1
1
0
1
1
1
1
1
2
2
1
1
1
2
1
1
1
2
1
1
2
2
2
2
0
1
0
1
0
2
1
1
1
1
1
1
1
1
2
0
0
2
1
2
2
2
1
1
0
2
1
1
2
0
1
1
1
1
1
2
1
2
1
1
2
0
2
0
1
0
2
1
1
1
0
0
1
2
1
1
1
2
2
1
2
0
1
1
1
0
1
1
1
1
1
1
0
2
2
0
0
1
1
1
0
1
0
2
1
0
0
2
2
1
1
1
1
0
2
1
1
1
1
1
0
2
1
2
1
2
1
0
1
1
1
1
1
2
0
2
2
1
1
1
0
1
2
1
2
1
1
2
1
0
1
2
1
1
2
1
2
0
1
0
1
1
2
2
2
2
0
1
0
0
2
1
2
1
1
1
1
0
1
1
1
2
1
1
0
2
0
1
2
1
2
1
1
1
0
1
2
1
2
1
2
1
1
0
1
1
1
0
1
1
2
1
1
1
1
0
1
0
0
2
2
2
0
1
2
2
1
1
1
0
1
1
0
0
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
0
2
2
0
1
1
2
0
2
1
1
1
2
2
0
2
2
1
1
1
2
1
2
1
2
2
1
2
0
1
2
2
2
1
1
1
1
1
1
2
0
1
1
1
2
1
2
1
0
1
1
1
1
1
2
1
1
2
1
1
1
0
0
2
1
1
1
2
1
2
1
1
1
2
0
1
1
2
1
1
1
2
1
2
1
1
0
1
1
1
1
3
1
1
1
1
2
1
0
2
1
1
0
1
2
1
1
1
1
1
1
1
1
1
1
0
1
1
1
0
0
2
1
1
1
1
1
1
2
1
2
1
0
1
2
1
1
0
1
1
1
1
2
1
1
0
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
0
1
1
1
0
3
1
1
1
1
0
1
1
1
1
1
1
0
1
1
1
1
1
1
2
1
1
2
1
1
1
1
2
2
1
1
0
1
1
2
1
2
1
2
2
2
1
2
1
0
0
1
2
0
0
1
1
1
1
2
1
1
1
1
0
1
0
1
1
2
0
2
2
1
3
2
2
0
2
1
1
1
2
1
1
2
1
3
2
1
1
0
1
0
1
0
1
1
0
2
1
2
2
1
0
1
2
0
1
1
1
2
2
1
1
1
2
1
1
1
1
1
1
2
1
0
1
1
1
0
2
1
2
1
2
1
2
2
2
1
1
0
1
2
1
1
2
2
1
0
1
1
2
1
1
1
1
0
1
0
1
2
1
2
1
2
1
2
1
2
1
2
2
1
1
1
1
0
2
0
1
1
1
1
2
0
1
1
0
1
2
1
2
2
2
1
2
1
1
0
1
0
1
2
1
1
1
1
1
1
1
2
1
0
0
1
1
2
1
0
1
1
0
3
2
0
1
1
1
1
1
1
2
2
2
2
0
0
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
0
1
1
1
2
2
2
2
1
2
2
1
1
2
1
1
1
1
2
2
1
1
1
1
1
2
2
0
2
1
0
2
0
1
1
2
1
1
0
1
0
2
1
1
1
2
1
1
2
0
1
0
1
0
2
1
1
2
1
2
2
1
2
1
2
1
1
2
1
1
2
1
2
1
0
2
0
1
1
2
1
1
1
2
2
1
0
1
1
2
2
2
2
2
0
0
1
2
1
1
1
1
0
1
1
1
2
1
2
0
1
1
1
1
1
2
0
1
2
2
1
2
1
1
1
1
1
1
0
1
2
2
0
1
0
3
2
1
1
2
2
0
2
1
1
1
1
0
0
1
2
1
1
1
1
1
2
1
2
1
1
1
1
0
3
2
1
1
1
0
1
2
1
1
1
1
1
2
1
0
1
1
1
1
2
1
1
1
1
2
0
1
1
1
1
1
1
1
0
1
1
1
1
1
2
1
2
1
2
2
1
1
1
1
2
2
1
2
1
2
1
1
2
1
1
1
1
1
2
0
0
3
1
2
1
1
1
0
1
1
0
3
2
1
2
1
2
0
3
1
2
1
1
1
1
1
1
2
0
2
1
2
1
1
2
2
1
1
1
2
0
1
1
1
2
1
2
2
1
1
1
2
1
2
1
1
1
1
1
0
2
1
1
0
1
0
2
0
1
1
1
1
1
0
1
1
2
2
1
0
1
1
1
2
0
2
1
1
1
1
0
1
1
0
1
1
2
1
2
2
1
3
2
2
1
2
1
1
1
1
2
0
1
2
2
0
0
1
1
2
1
0
1
1
1
2
1
0
1
1
1
1
1
1
1
0
2
3
2
1
1
0
1
1
1
1
1
2
2
1
1
1
2
1
1
1
1
1
1
1
1
0
0
0
1
2
2
0
1
0
2
1
2
1
2
1
1
1
1
2
2
1
1
0
2
1
1
1
1
1
0
1
1
1
0
2
1
1
2
1
1
2
1
1
1
1
0
2
1
1
1
2
0
1
1
0
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
0
0
1
1
1
0
0
1
0
2
0
1
1
2
1
1
0
1
1
2
1
0
1
1
0
2
1
1
3
1
1
1
0
2
1
1
1
2
2
0
1
1
2
1
1
0
1
2
0
1
1
0
0
2
1
0
2
1
2
1
1
2
1
2
1
2
1
1
0
1
1
1
2
0
1
1
2
2
1
7
2
1
1
2
1
1
2
1
1
1
0
1
1
0
0
2
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
0
1
1
1
1
2
1
2
2
1
0
1
2
1
1
2
0
2
1
2
0
2
1
2
1
1
2
1
2
2
1
0
1
2
1
1
1
2
2
0
2
0
2
0
1
0
1
1
1
0
1
1
0
1
0
1
2
1
2
1
1
0
0
2
1
1
1
2
1
1
2
1
1
1
0
2
3
1
1
2
1
0
1
0
1
1
1
1
2
1
1
1
1
1
1
2
2
2
1
2
2
0
2
2
1
1
1
2
1
1
1
0
3
1
1
1
2
0
1
1
1
0
0
2
1
1
1
1
1
1
1
2
1
2
2
2
1
1
2
2
1
1
1
1
1
1
1
1
0
1
2
2
1
1
1
1
1
1
2
2
1
0
0
2
0
1
1
2
1
2
0
1
3
1
1
0
1
2
1
2
1
2
0
1
1
0
0
1
1
2
1
0
2
2
0
1
0
1
1
1
2
2
0
1
0
1
2
1
0
1
1
1
2
0
1
1
1
1
2
1
1
1
0
1
1
1
2
2
1
0
0
0
1
2
1
1
0
0
1
0
1
1
2
1
2
1
1
1
1
1
1
1
2
2
1
2
0
1
2
1
1
0
1
1
1
2
1
0
2
2
2
1
1
1
1
2
1
2
0
0
1
0
1
1
2
2
1
1
2
1
1
0
3
1
1
1
0
2
1
2
1
1
1
1
1
1
2
1
0
1
1
1
1
1
1
2
1
2
1
0
1
2
1
1
1
1
1
1
1
1
0
1
0
3
1
1
1
2
1
1
2
0
2
2
1
1
2
1
1
1
1
1
2
1
1
1
1
1
0
1
1
1
1
0
1
0
1
1
1
2
1
1
1
2
1
0
1
1
2
2
1
1
2
2
0
2
1
1
1
1
1
2
1
1
1
2
0
2
1
1
2
2
1
2
1
2
0
0
0
1
1
0
1
0
2
0
1
1
1
1
1
0
1
2
1
1
1
1
1
1
0
1
2
1
2
1
0
0
2
2
1
0
1
2
1
1
1
0
1
1
0
1
0
1
2
1
2
2
1
0
1
2
1
0
1
1
1
2
2
2
1
1
1
1
1
1
1
0
2
1
0
2
1
2
2
1
1
1
0
2
1
0
1
0
1
2
1
1
2
1
2
1
2
1
2
1
1
1
2
1
1
1
1
2
0
1
1
1
0
1
1
1
1
1
1
1
0
1
2
1
1
1
1
1
0
1
2
1
0
1
2
1
2
0
2
2
2
1
0
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
2
1
1
2
1
1
0
1
0
1
2
2
0
1
1
1
1
1
1
1
1
1
1
0
1
1
1
2
2
0
2
1
0
2
1
1
1
2
1
2
1
1
2
0
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
2
1
2
1
1
2
1
2
0
1
1
0
1
1
0
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
0
1
1
2
1
1
2
1
2
1
0
0
1
1
1
1
1
1
1
1
2
1
2
2
1
0
2
2
1
1
2
1
0
1
1
2
1
1
1
1
2
2
2
1
2
1
2
1
1
2
1
1
1
1
1
2
1
1
1
1
2
0
1
1
1
0
2
1
1
1
1
1
1
1
2
1
1
2
1
1
3
1
2
0
1
2
2
1
1
1
1
1
1
1
1
2
1
0
1
2
1
1
0
1
1
1
1
2
1
0
1
1
1
1
1
1
1
0
1
2
1
2
2
0
1
2
1
1
1
1
1
1
1
2
1
1
2
0
2
2
0
2
2
0
1
2
1
1
0
1
0
1
1
1
1
1
1
3
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
2
1
1
2
2
2
1
1
1
1
1
0
0
1
2
1
0
1
2
2
2
2
1
1
2
2
2
1
2
1
1
1
1
1
2
0
2
1
1
1
0
2
1
1
1
1
0
2
2
1
1
2
2
2
1
1
0
2
1
2
2
2
2
1
1
1
1
2
2
1
2
1
1
2
2
2
1
0
1
1
1
2
1
1
3
1
1
1
3
2
1
1
1
1
1
1
2
0
1
2
1
2
2
1
1
0
1
3
1
0
1
1
1
1
2
0
2
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
0
1
1
1
1
1
1
1
1
2
1
1
1
2
1
0
0
1
1
1
1
1
0
1
2
0
1
1
1
2
1
1
1
2
1
2
2
2
2
0
2
0
0
1
1
1
1
1
1
1
1
0
1
1
1
0
1
2
2
1
1
1
1
1
2
2
1
0
1
1
2
1
2
1
1
1
1
1
1
1
1
1
0
2
1
1
1
1
1
2
0
0
1
0
1
1
1
1
1
1
2
2
1
2
0
2
1
1
1
1
2
1
1
1
1
1
1
1
0
2
1
0
2
0
1
1
1
1
1
1
1
1
2
1
0
1
1
2
3
2
3
0
1
0
2
1
2
1
1
1
1
0
1
1
1
1
1
2
1
1
2
2
1
1
1
1
2
1
1
0
2
1
2
2
1
1
1
1
2
1
2
2
2
0
2
1
1
1
2
0
2
2
1
2
2
1
1
0
2
2
0
1
1
2
1
0
2
1
1
1
0
1
1
2
2
1
2
1
1
3
1
1
0
0
1
0
1
0
1
1
1
2
1
1
1
1
1
2
1
1
0
0
2
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
2
1
1
1
1
0
1
2
1
0
1
1
2
2
1
1
0
1
1
1
2
2
2
1
1
2
1
1
1
1
1
0
2
1
1
1
2
2
1
2
0
1
1
1
2
1
1
1
2
0
1
1
1
1
1
1
1
1
2
1
3
2
1
1
1
2
2
1
2
1
2
1
0
2
1
1
1
1
1
1
1
1
2
0
1
0
1
0
0
0
2
1
2
0
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
0
1
2
1
1
0
0
1
1
1
2
1
0
1
1
1
1
0
1
3
0
1
1
1
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
0
0
0
1
2
1
2
2
1
2
2
2
1
1
1
0
1
1
2
2
2
1
0
1
2
0
1
1
1
0
1
1
1
2
0
1
1
2
0
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
0
1
1
2
2
1
1
1
1
1
0
1
1
1
2
1
1
1
0
1
1
2
0
1
1
1
1
1
1
2
1
1
2
0
2
1
1
2
0
1
2
0
1
1
1
2
1
2
1
0
2
2
1
1
2
1
1
1
1
0
2
0
0
1
1
0
1
0
2
1
0
1
2
2
1
1
1
2
0
1
1
3
1
2
1
1
1
0
0
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
0
1
1
1
0
1
1
1
0
1
0
1
1
2
2
1
1
2
2
2
1
1
1
0
1
1
2
0
1
1
1
2
2
1
2
1
0
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
0
1
1
1
2
1
1
0
1
2
1
1
1
1
1
1
1
2
1
1
2
2
1
1
2
1
2
0
2
1
1
1
0
1
2
1
1
2
2
1
1
1
1
1
2
1
2
1
1
2
2
1
1
2
1
1
1
2
1
3
1
1
2
1
1
1
2
2
1
0
1
1
1
0
1
1
1
0
1
1
2
1
0
1
2
1
0
1
2
2
1
2
1
1
1
2
2
2
1
0
0
1
2
2
1
2
2
1
2
2
1
2
0
2
1
2
1
1
2
1
0
1
1
2
1
1
2
1
1
2
1
1
1
1
2
2
1
0
0
2
2
2
1
1
1
2
1
1
2
1
1
1
2
2
1
2
1
2
2
2
2
0
1
1
1
3
1
1
1
0
1
1
1
1
1
1
1
1
1
1
2
1
0
1
1
2
2
1
0
1
1
2
1
1
2
1
1
1
2
1
0
1
2
2
0
2
1
0
1
1
2
2
1
2
1
2
1
0
0
1
1
1
1
2
2
1
1
2
1
1
1
0
2
1
1
2
2
1
2
1
0
0
1
4
1
1
2
1
1
1
2
1
0
0
1
1
1
1
0
0
2
1
1
1
2
2
1
2
0
1
0
1
1
1
1
2
0
2
0
2
2
2
1
0
2
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
3
0
2
1
1
2
1
1
1
1
1
0
0
2
2
0
1
0
1
2
1
0
1
2
0
1
0
1
2
0
1
2
1
1
0
1
1
2
1
1
1
1
1
2
2
1
0
0
1
1
1
2
2
1
1
2
1
1
1
1
0
1
1
1
1
1
2
1
1
0
2
2
1
1
2
2
1
0
1
1
2
2
1
1
2
1
1
2
1
2
1
1
2
1
2
1
2
1
2
1
1
1
0
2
1
1
0
2
1
1
2
2
1
2
0
2
1
1
1
1
1
2
1
1
1
1
1
2
2
0
0
1
3
1
1
1
1
1
1
2
0
1
1
1
1
2
1
0
2
2
1
0
1
1
1
1
2
1
1
1
0
2
2
4
1
1
1
1
1
0
1
0
0
1
0
1
1
2
1
0
1
1
1
1
0
0
1
0
1
1
1
2
0
1
1
1
2
2
0
1
2
2
1
1
2
2
4
0
1
1
1
2
2
1
1
1
0
1
0
1
1
2
1
2
1
1
1
1
0
1
1
1
1
1
1
1
1
1
0
1
2
0
0
1
1
1
1
1
2
2
1
2
1
1
1
1
2
0
0
1
0
1
2
1
1
1
1
2
1
1
1
0
2
1
1
1
0
1
2
2
1
1
1
1
1
2
1
1
1
0
2
1
1
2
1
1
2
1
2
1
1
0
2
0
1
1
1
1
1
1
1
2
2
2
2
1
1
1
0
2
2
1
1
1
1
2
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
2
0
1
0
2
1
0
0
2
2
1
1
0
0
1
1
1
2
1
1
2
1
1
1
0
1
1
1
1
1
1
1
0
1
1
1
0
2
0
1
3
1
0
1
1
1
2
0
1
2
1
1
2
2
1
0
2
0
2
1
1
2
2
1
0
1
2
1
1
1
1
1
1
2
1
0
0
1
1
1
2
1
2
0
2
1
2
1
1
2
1
2
2
2
1
1
1
2
1
1
1
1
2
1
1
0
1
2
1
0
1
1
0
0
2
1
1
1
2
0
2
1
1
2
1
1
1
2
1
1
2
1
1
2
1
1
0
1
0
2
0
2
1
1
1
1
1
2
1
1
1
0
0
1
1
2
2
1
1
2
1
1
2
1
2
2
2
0
0
1
1
1
2
1
1
0
1
1
2
1
1
2
1
1
1
0
0
1
1
1
1
0
0
2
1
2
2
1
0
1
2
2
2
2
1
1
1
1
2
1
1
1
1
1
1
2
1
0
2
1
0
0
1
1
2
1
1
1
2
1
1
2
2
1
0
1
1
1
1
1
1
1
0
2
1
0
3
1
2
0
1
0
1
0
2
1
0
2
1
2
1
3
0
2
1
1
1
1
1
1
2
1
1
2
2
1
1
1
1
1
2
0
2
0
1
1
2
0
0
2
2
1
1
0
1
2
1
1
1
2
2
1
1
1
1
1
1
2
1
2
1
1
1
1
2
1
2
2
2
2
1
2
1
0
1
2
1
1
1
0
0
0
1
1
2
2
1
0
2
2
1
2
0
2
3
1
1
1
1
1
1
0
1
1
1
1
1
2
0
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
4
2
1
1
1
2
2
1
2
1
2
2
0
1
1
1
1
0
0
1
1
1
1
2
1
1
2
1
1
0
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
2
1
0
2
2
2
1
1
1
1
0
1
1
2
1
2
1
1
2
0
1
2
1
2
1
1
1
1
2
1
1
1
1
1
2
1
1
2
2
1
1
1
1
2
0
1
1
1
2
2
1
0
0
0
0
1
0
1
1
1
1
1
1
1
1
1
2
1
0
2
0
1
2
2
2
0
1
1
1
2
1
2
2
1
1
2
1
1
1
1
1
2
2
2
1
1
1
2
2
1
1
1
1
2
1
2
3
1
0
0
0
2
2
2
1
1
0
0
1
1
0
1
1
1
1
2
2
1
1
1
2
2
1
1
1
1
0
1
1
2
1
1
0
1
0
1
1
2
1
2
1
1
1
1
1
1
2
2
1
2
2
1
1
1
2
1
2
2
2
1
1
2
1
0
1
1
0
2
1
1
1
2
0
0
0
0
2
1
2
1
1
2
1
2
1
1
2
0
2
3
1
0
2
1
1
1
1
1
2
1
0
1
1
1
1
1
1
1
2
2
2
1
1
2
0
2
1
3
2
0
1
1
1
2
1
1
1
0
2
1
1
0
2
1
1
2
2
1
1
1
1
1
1
1
1
1
2
1
1
0
0
0
2
0
1
2
1
1
1
1
0
1
0
1
2
1
0
2
1
1
1
2
0
2
2
1
2
1
1
1
1
2
0
2
0
1
1
1
1
1
1
1
2
1
1
1
0
1
1
1
1
0
2
2
1
0
1
1
2
1
1
1
1
0
1
2
1
2
0
0
1
0
1
2
0
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
3
2
2
1
1
1
1
0
0
2
2
0
2
1
0
1
2
0
2
1
1
1
1
2
2
2
2
0
2
2
1
1
1
2
2
2
1
1
2
1
2
0
0
1
1
0
1
1
2
2
2
1
2
1
1
1
1
1
2
1
2
2
1
1
2
0
1
1
0
2
1
1
1
2
1
1
1
1
0
1
1
1
1
1
0
1
1
2
0
1
1
2
1
1
1
1
1
1
0
1
2
1
1
2
2
1
0
2
1
0
1
2
2
2
1
0
2
2
1
2
0
1
1
1
0
1
2
2
1
2
0
2
1
0
1
1
0
1
2
1
2
1
1
2
2
1
1
1
2
2
1
2
2
1
1
1
0
2
2
1
0
1
2
1
0
3
1
1
1
2
1
2
2
2
1
1
0
1
2
2
2
1
1
2
0
0
0
2
1
1
3
1
1
1
0
1
0
1
2
1
2
2
2
1
0
1
2
1
1
1
1
1
1
1
0
2
1
0
0
0
1
1
0
0
1
2
1
1
2
1
2
1
1
2
1
2
1
2
0
2
2
0
1
1
0
0
1
1
0
2
1
1
2
1
1
2
1
1
2
1
0
0
0
1
1
0
0
2
2
1
2
1
2
2
1
1
1
1
2
2
1
1
2
1
0
1
1
1
1
1
1
1
2
0
0
1
1
1
0
0
1
1
1
1
1
1
2
1
2
0
1
2
2
0
0
2
0
2
1
1
1
2
3
0
1
1
1
2
1
0
1
2
1
1
0
1
1
2
2
1
1
2
1
1
2
1
2
1
1
1
1
1
2
0
1
1
1
1
1
1
1
1
1
1
0
2
1
1
2
1
1
1
1
2
2
2
1
0
1
1
2
1
1
1
1
0
1
2
2
1
1
0
1
0
2
0
1
1
2
1
0
1
2
1
1
2
2
0
2
2
1
1
1
2
2
1
1
2
0
1
2
1
1
1
1
1
2
2
0
0
1
0
2
0
1
1
1
1
0
2
1
0
2
1
2
1
2
2
2
2
2
0
1
1
0
2
2
1
2
1
2
1
0
1
0
1
0
1
1
1
1
1
0
1
1
2
1
0
0
1
2
1
1
1
1
2
1
0
2
0
1
1
1
1
2
1
1
0
1
1
1
2
2
1
1
1
2
1
1
1
1
1
1
0
1
1
2
2
2
2
0
1
1
2
1
1
1
1
0
1
0
3
1
0
2
1
1
2
2
1
3
1
1
1
0
2
1
1
2
2
2
2
2
0
0
1
2
2
1
1
0
1
1
2
2
2
1
2
1
1
1
1
2
1
0
1
1
1
1
1
1
0
1
0
1
1
1
0
1
1
1
0
1
0
2
1
0
0
1
1
3
1
1
1
1
1
1
1
2
2
0
0
0
2
2
4
0
2
1
1
0
1
1
1
1
1
2
1
1
1
1
1
0
2
2
2
1
1
1
2
1
1
1
1
1
2
2
1
0
1
1
1
1
1
0
1
1
1
1
2
1
2
1
0
2
2
1
1
2
2
2
1
2
0
1
2
2
2
1
1
0
1
2
0
1
1
1
1
0
1
2
0
0
2
2
2
1
2
1
2
1
1
1
1
0
2
1
1
2
1
1
1
0
1
2
2
0
2
1
2
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
2
0
1
2
1
2
2
1
1
1
1
1
1
2
1
2
2
1
2
0
1
1
1
1
1
1
2
2
2
0
2
1
1
2
1
1
2
1
0
2
2
1
0
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
0
1
2
1
0
2
1
1
1
1
0
2
3
1
1
1
1
1
2
2
1
1
1
1
0
1
1
1
1
0
1
1
1
1
0
1
1
1
1
1
1
1
2
2
2
2
1
1
1
0
0
0
0
0
2
2
2
1
2
1
1
0
1
2
1
0
1
3
1
2
1
2
1
1
0
1
1
2
1
1
1
1
2
2
1
1
1
0
1
0
1
0
1
1
1
1
1
1
2
2
3
1
1
2
2
2
2
1
1
2
0
2
1
1
0
1
1
1
1
0
1
3
1
1
1
2
2
1
1
1
4
1
0
0
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
0
1
1
3
0
1
2
1
1
1
1
0
1
1
2
0
1
0
1
2
1
2
1
1
1
1
1
1
1
1
0
1
1
1
1
0
1
1
1
1
1
2
1
0
1
2
2
2
0
2
1
0
1
1
6
1
1
1
2
1
1
1
1
0
1
1
1
0
2
2
2
1
1
2
1
1
1
1
1
0
1
0
1
2
1
2
1
2
2
0
2
1
2
2
2
2
1
1
1
1
1
2
1
1
0
1
1
1
1
2
1
1
1
1
1
1
1
1
1
0
1
2
1
1
1
2
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
0
1
0
1
1
2
0
1
1
0
2
1
1
1
2
1
1
2
1
1
1
1
1
1
3
1
0
1
2
1
2
0
2
0
1
1
1
1
1
0
2
2
1
0
1
2
1
1
1
1
2
1
1
2
1
1
0
1
1
1
1
2
1
1
0
2
1
0
1
1
2
2
2
2
2
2
0
2
2
1
0
1
1
1
1
1
1
2
1
1
1
0
2
1
1
1
2
1
1
1
1
1
2
2
1
1
1
1
0
2
2
2
1
1
1
2
1
1
2
2
1
1
1
1
0
2
2
1
2
2
1
2
2
1
1
0
1
1
1
1
2
1
0
1
1
1
0
1
2
2
1
1
1
1
1
0
2
1
1
2
2
1
0
1
1
3
1
1
1
1
1
1
1
1
1
0
1
1
1
0
1
1
1
2
2
2
1
2
1
1
1
0
1
1
2
1
2
1
1
1
1
0
1
1
0
2
2
1
2
2
1
2
1
1
0
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
0
2
1
1
0
1
1
1
1
0
0
1
1
2
0
1
1
0
1
1
1
1
1
0
1
2
1
0
2
2
1
1
1
0
1
2
1
1
0
1
1
2
1
1
1
1
1
1
2
1
0
2
1
1
2
0
1
2
1
2
1
2
2
1
0
2
1
1
2
1
1
1
1
1
2
0
1
0
2
0
2
2
1
0
1
2
1
2
2
1
2
0
1
0
1
1
1
1
1
1
1
3
1
1
2
1
1
1
1
1
2
1
1
0
1
2
1
0
2
1
2
1
0
0
2
1
1
0
1
1
1
1
0
1
1
1
2
1
0
1
1
2
0
2
1
2
1
2
1
1
1
1
0
1
1
1
1
0
2
1
1
1
2
1
1
1
1
1
2
0
1
1
0
1
0
1
1
1
0
1
1
1
1
1
0
1
0
2
2
2
1
2
1
1
2
1
2
1
1
2
1
1
2
2
0
1
2
2
4
0
1
1
2
2
1
2
1
1
1
1
1
2
1
0
1
1
1
0
1
0
0
1
2
1
1
1
1
2
2
1
0
1
0
1
0
1
1
1
0
1
2
2
2
2
0
2
1
0
1
0
2
1
2
1
2
1
2
1
0
1
2
1
1
1
0
1
1
2
1
1
2
2
0
1
1
2
1
1
3
0
1
0
2
1
1
1
1
0
2
1
1
0
1
1
1
1
1
0
1
2
1
2
1
0
2
1
1
1
2
1
1
2
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
0
2
1
2
1
1
1
2
1
1
0
1
2
0
1
2
1
1
1
1
2
2
1
0
1
1
1
1
1
0
1
1
1
1
1
1
1
1
2
2
0
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
1
1
1
1
1
0
0
1
1
1
0
0
1
1
2
2
1
1
1
1
0
0
2
1
0
1
1
2
2
1
2
1
2
1
1
2
1
2
0
1
1
1
1
1
1
2
1
2
1
1
0
2
1
0
1
1
1
0
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
0
1
1
2
2
2
2
1
1
2
1
1
1
1
0
1
1
0
1
1
1
1
3
0
1
2
2
2
2
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
1
2
1
1
2
1
1
1
0
2
3
1
2
0
2
1
2
1
1
1
0
1
2
2
1
1
0
1
0
1
0
1
1
2
2
1
1
0
1
1
1
1
1
1
1
1
2
1
2
1
0
2
1
2
1
1
1
1
2
0
2
2
0
0
2
1
1
0
1
1
1
1
0
1
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
2
2
1
1
1
0
2
2
1
1
1
1
1
0
1
1
1
1
1
1
1
1
2
1
1
1
0
1
0
2
1
1
0
1
2
1
1
1
1
1
2
1
1
2
1
2
1
2
2
1
1
1
2
1
2
1
1
1
1
2
2
1
2
1
1
0
2
1
1
1
1
1
0
0
1
0
0
2
2
2
2
1
1
1
1
2
0
1
1
2
0
1
2
1
1
1
1
1
2
2
1
1
1
2
1
1
1
1
1
2
0
1
1
1
1
1
0
2
2
0
0
1
2
0
1
1
0
0
1
1
0
1
2
1
1
1
2
2
1
2
1
2
1
1
0
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
0
1
1
1
1
1
1
1
2
1
2
0
1
1
0
0
1
2
0
1
2
1
2
2
2
0
1
2
2
1
1
2
1
1
1
1
2
1
1
1
1
1
0
2
2
1
1
0
1
1
0
0
1
1
1
0
0
1
1
1
1
1
2
1
1
1
1
1
2
1
0
2
1
1
1
1
1
1
1
1
1
0
1
2
0
2
1
1
1
1
2
1
1
1
0
1
1
2
1
2
1
2
2
4
0
0
0
0
1
1
2
2
0
2
1
2
2
1
1
1
2
1
1
2
1
2
1
1
2
0
1
2
1
1
1
1
1
1
2
1
1
2
1
1
0
0
1
1
1
0
1
1
2
1
2
1
2
1
2
1
1
1
2
1
1
0
1
1
0
0
1
1
2
1
1
1
1
1
1
0
1
1
1
1
2
2
0
1
2
1
1
2
1
0
2
1
1
0
1
0
1
2
0
1
1
2
2
1
1
2
0
0
1
1
0
1
0
2
2
1
1
1
2
1
0
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
0
0
1
1
2
1
0
0
0
2
2
2
1
2
1
1
2
1
2
1
2
1
1
1
1
1
1
0
1
1
2
1
1
1
2
1
1
2
1
2
1
1
1
1
3
1
1
2
1
1
1
1
1
1
1
1
0
1
1
0
1
2
0
1
1
1
1
1
2
1
1
0
2
2
2
2
1
1
2
1
1
1
0
0
1
1
2
2
0
1
2
2
2
1
2
1
1
1
1
1
1
3
1
1
0
1
1
1
1
1
1
0
1
1
2
1
1
1
1
1
0
1
2
2
1
1
2
0
1
1
1
1
2
1
0
1
1
2
0
1
0
2
2
2
1
1
1
1
2
1
1
1
3
0
1
1
1
0
1
1
0
1
1
1
1
0
1
1
2
1
2
0
1
2
1
1
1
1
1
2
1
1
1
1
1
1
3
0
1
1
1
1
1
1
2
2
2
1
1
1
0
2
1
2
0
1
1
1
2
2
1
1
1
2
1
0
1
1
1
2
2
2
1
0
1
1
2
1
0
1
1
1
1
2
1
1
1
1
0
1
1
1
1
1
2
1
0
1
2
0
0
1
2
1
1
0
2
1
1
2
2
1
2
1
1
1
2
1
1
0
1
2
1
1
1
1
1
0
1
1
2
2
2
1
1
3
3
2
1
1
2
0
2
1
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
1
1
0
0
0
1
2
1
0
1
2
1
0
1
1
1
0
1
1
1
0
2
1
2
2
1
1
2
2
1
2
1
1
1
1
1
2
1
0
1
0
2
1
1
1
1
1
0
1
1
1
1
1
1
1
0
1
1
1
1
1
1
2
0
1
1
1
1
0
0
1
1
1
0
2
2
2
0
2
2
1
1
3
1
0
0
2
1
1
0
2
2
0
1
1
1
2
1
0
1
1
2
1
1
1
2
2
1
1
2
1
0
1
1
1
2
1
0
1
2
0
2
0
1
1
2
1
1
1
1
1
1
1
0
0
1
1
2
1
1
2
1
0
1
2
2
1
2
2
2
0
0
1
1
1
1
1
2
1
1
0
2
2
1
1
1
2
2
1
1
1
2
1
2
2
2
1
1
0
2
1
2
1
1
1
0
2
1
2
1
1
2
1
1
0
1
1
2
0
2
1
2
1
1
1
0
1
1
1
1
1
1
2
0
2
0
0
1
1
1
0
1
2
1
0
2
1
0
2
3
1
1
2
0
1
2
1
1
1
0
1
1
2
1
1
0
2
1
1
1
1
2
1
1
1
0
1
2
1
0
1
1
2
0
1
1
1
1
1
0
1
1
1
1
1
1
1
1
2
1
1
1
1
0
2
1
0
1
1
0
2
0
2
2
1
2
0
2
1
1
1
1
1
2
1
1
2
1
1
2
2
2
0
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
0
2
1
2
0
1
1
2
1
1
2
1
1
1
1
1
1
1
2
1
1
2
0
1
1
2
1
1
0
1
2
1
1
1
1
2
2
1
2
1
1
1
0
2
1
2
1
2
1
2
1
2
1
1
1
1
1
2
1
1
0
1
2
2
2
1
1
2
2
1
2
1
1
1
1
2
1
0
1
1
2
2
1
1
1
2
2
1
1
1
0
2
1
1
2
2
1
0
0
1
1
2
2
2
2
1
1
1
0
1
1
1
1
1
1
2
0
1
1
1
1
1
1
0
1
0
1
1
1
2
2
1
1
2
1
1
2
0
1
1
1
2
1
0
0
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
2
0
2
2
1
1
0
1
2
0
1
3
1
1
1
1
2
1
2
1
2
1
2
1
0
2
2
1
1
1
0
2
1
1
2
2
2
0
1
1
1
2
2
0
1
2
1
0
2
1
1
1
1
0
1
1
1
0
1
1
1
0
0
1
3
1
1
1
1
1
2
1
1
1
0
0
1
2
2
2
1
1
1
1
1
1
2
2
1
1
2
1
2
1
1
1
0
1
1
1
2
1
1
0
2
2
1
2
0
1
1
2
1
1
1
1
1
2
1
1
1
2
0
2
1
1
1
0
1
1
2
1
2
0
1
1
1
1
1
2
1
1
1
2
0
1
1
1
1
1
0
2
1
1
0
2
2
2
1
2
1
1
1
2
0
1
1
2
1
1
0
1
1
0
1
1
1
2
1
1
1
2
1
1
2
1
1
0
0
2
0
1
1
0
1
1
2
1
2
0
2
2
1
3
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
1
1
2
1
2
2
1
1
2
1
0
0
0
3
2
0
0
1
1
1
2
0
1
1
2
1
1
2
1
2
1
2
1
0
1
1
2
0
0
1
2
2
1
0
1
1
2
1
1
2
1
1
0
1
2
2
0
1
1
1
2
1
1
2
2
1
1
1
0
2
1
0
1
1
0
1
0
1
1
1
1
2
1
1
1
2
1
1
2
0
1
1
2
0
0
1
2
1
2
2
1
1
1
1
1
1
1
1
2
1
0
0
1
1
1
1
0
1
1
1
0
1
1
1
0
1
1
1
1
1
1
1
1
2
2
2
1
1
0
2
2
2
1
2
2
1
0
1
0
2
0
1
1
1
1
1
2
2
1
1
1
1
2
0
0
2
1
2
1
2
1
0
2
2
1
1
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
0
1
2
0
1
1
0
2
0
1
1
1
0
1
1
2
1
2
2
1
1
1
2
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
0
1
2
1
2
0
1
1
1
1
1
2
1
1
1
1
1
2
2
2
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
2
1
0
1
1
1
3
2
1
1
0
0
1
1
0
1
1
1
1
2
1
2
1
1
2
1
1
1
0
1
1
1
2
1
2
1
1
1
2
0
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
2
1
1
1
0
2
1
1
1
2
2
2
1
1
1
1
1
1
1
1
1
0
1
1
2
2
1
1
1
1
1
1
1
1
1
1
0
0
2
2
1
2
2
1
2
1
1
1
2
0
1
1
1
1
2
0
1
1
2
1
1
0
2
1
2
1
1
1
1
1
2
1
0
2
0
1
2
0
0
2
2
1
2
1
1
1
2
1
1
1
1
1
2
1
1
2
2
1
1
0
2
2
0
2
1
1
2
1
1
1
1
1
0
1
1
2
1
0
1
2
1
2
2
2
0
1
1
1
0
2
1
0
3
1
1
2
1
1
1
1
2
1
1
0
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
1
1
0
1
0
0
2
1
1
2
4
2
1
1
0
0
2
2
0
2
1
1
1
0
1
1
0
0
1
1
1
0
1
2
1
0
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
2
1
1
1
1
1
2
2
0
1
0
1
2
2
1
2
1
1
1
1
1
1
2
2
1
1
1
2
0
1
1
0
1
0
2
1
1
1
1
2
2
1
2
1
1
1
1
1
2
1
2
0
1
2
0
1
2
1
1
2
1
0
1
1
1
1
1
2
0
1
2
0
1
1
1
1
1
1
1
1
2
1
1
1
1
2
2
1
1
2
1
1
2
2
1
2
1
1
2
2
1
1
1
1
1
0
1
1
0
1
0
1
0
0
1
1
1
1
1
1
0
2
1
1
1
1
1
2
2
1
1
1
0
1
1
1
1
1
2
0
1
4
1
2
0
2
1
2
1
0
2
1
1
1
1
0
1
2
0
0
1
0
1
2
1
2
2
1
1
2
1
0
0
1
0
1
1
1
1
1
1
1
2
0
0
2
0
1
1
0
1
1
0
1
1
1
0
2
0
1
2
1
2
1
1
1
1
2
0
2
2
1
1
1
0
2
1
0
1
0
1
1
1
1
1
1
1
1
0
1
1
2
1
1
1
1
0
1
1
2
0
0
2
1
0
1
1
0
1
1
1
2
1
2
1
2
1
1
3
1
1
1
0
2
1
1
0
1
0
2
2
1
2
1
2
2
1
1
1
1
2
0
1
1
2
1
2
1
1
1
1
1
1
1
1
1
0
1
1
2
1
1
0
1
1
1
1
1
1
1
1
1
2
1
1
0
2
1
1
1
2
1
0
1
1
1
1
1
1
1
1
1
1
1
0
2
1
1
0
2
0
1
1
1
1
0
2
1
2
3
2
1
1
0
2
1
2
1
1
1
2
0
1
1
2
1
1
1
1
2
1
1
2
1
2
2
2
0
0
1
1
1
2
1
1
1
2
1
0
1
1
1
2
1
2
1
2
1
1
1
1
2
1
1
1
2
2
1
2
1
0
1
2
1
1
2
1
3
1
1
1
1
0
2
2
1
1
1
1
2
1
1
1
1
0
1
2
1
1
1
0
1
1
0
0
0
0
1
1
3
1
1
1
1
1
2
1
1
2
1
1
1
2
2
2
0
1
1
1
2
1
1
1
2
2
2
1
2
1
0
1
1
2
1
2
1
1
1
1
1
1
1
0
2
1
1
0
1
2
2
2
1
1
1
0
1
2
1
2
1
0
2
1
2
1
1
2
2
1
1
1
1
1
1
0
1
1
0
1
2
1
2
1
2
2
1
1
2
2
1
0
2
0
2
1
1
2
2
1
0
2
1
1
1
1
1
1
1
0
1
1
1
1
2
0
1
1
1
1
1
0
1
0
2
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
2
0
1
1
1
1
1
1
1
1
1
2
2
0
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
0
1
1
1
0
1
2
2
1
0
1
1
1
1
1
1
2
2
1
1
0
1
1
1
2
1
0
0
0
2
2
1
1
1
1
1
1
0
2
0
0
1
1
0
1
1
0
2
1
1
1
2
2
1
1
1
0
1
2
2
1
1
1
1
1
1
2
1
1
0
1
1
0
1
1
1
1
1
1
0
2
1
1
1
0
1
2
1
1
1
2
1
0
1
1
1
1
1
1
1
1
1
1
2
1
0
1
2
1
1
1
1
2
1
1
1
1
1
0
1
2
1
1
2
1
2
1
2
0
2
1
0
2
0
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
0
1
1
1
2
1
1
1
0
0
3
0
0
2
1
1
2
0
2
2
0
1
1
2
0
2
2
2
0
2
1
1
1
2
1
0
1
1
2
1
2
2
2
1
0
2
1
2
2
1
1
1
2
1
2
0
1
2
1
1
2
0
1
2
1
1
0
1
2
1
1
2
1
1
1
0
0
1
1
1
1
2
1
2
2
2
1
1
2
1
1
1
1
1
2
1
1
1
2
0
1
0
0
1
2
0
0
0
0
1
1
0
1
2
1
1
1
1
2
1
0
0
1
1
2
2
0
1
1
1
1
1
1
2
1
2
2
1
2
1
1
2
2
1
0
2
1
1
0
2
1
2
1
2
0
1
1
1
2
1
1
2
2
0
0
1
1
1
1
1
2
0
1
1
0
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
2
0
2
1
1
2
1
1
2
1
1
1
1
1
0
2
0
1
1
1
2
2
1
2
0
2
2
0
1
1
2
1
1
1
1
1
1
1
1
1
2
1
2
0
2
1
0
2
1
1
1
1
2
2
1
0
2
1
1
1
2
1
2
2
1
1
2
1
1
1
1
1
1
1
2
1
1
1
0
1
1
0
2
2
1
0
2
2
1
0
1
1
1
2
0
1
1
1
0
0
1
1
1
2
1
1
2
1
0
2
1
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
0
1
1
1
1
1
1
1
1
0
2
0
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
0
1
1
1
2
2
1
0
1
1
5
1
2
0
1
1
2
1
1
0
1
2
1
1
2
1
2
2
1
2
0
2
1
1
2
1
1
1
0
1
1
0
1
1
2
1
1
1
1
1
2
1
0
1
1
2
1
1
2
1
2
1
0
1
1
1
0
0
1
2
2
1
1
1
2
1
2
1
1
2
1
2
1
1
2
1
1
1
2
1
0
1
1
1
1
1
1
2
1
1
1
1
0
1
0
1
1
2
2
1
1
1
1
0
2
1
1
2
1
1
1
1
1
2
1
1
1
2
1
2
1
2
1
1
0
0
1
2
1
2
1
1
1
1
1
1
0
2
1
0
2
1
2
1
1
2
1
1
2
2
1
1
1
1
2
2
0
2
1
1
1
1
1
1
1
1
0
2
1
1
1
1
2
2
2
0
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
2
2
1
1
1
1
1
2
1
0
1
2
3
2
2
0
1
1
1
1
1
0
2
1
0
2
1
2
0
2
1
2
1
1
1
1
1
1
0
1
1
1
0
1
1
1
1
2
1
0
1
0
0
2
1
1
3
2
1
0
0
1
1
1
1
0
1
1
1
0
1
1
0
1
0
2
1
2
1
1
0
1
2
1
2
1
1
2
1
1
0
0
1
1
0
2
1
1
0
1
0
1
2
1
1
0
1
0
1
2
0
1
1
1
1
2
2
1
1
0
2
1
2
1
1
1
1
1
1
0
1
0
0
1
1
2
3
1
1
1
1
1
2
1
1
1
1
2
1
2
1
2
1
2
1
2
1
1
1
0
2
2
1
1
0
0
1
1
2
1
1
2
0
1
0
1
0
2
1
1
1
1
1
1
0
1
0
1
1
1
2
1
1
1
1
1
1
0
1
1
2
2
1
1
1
1
2
1
1
1
0
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
0
2
2
1
1
1
1
0
1
1
1
2
2
0
1
1
0
2
0
1
2
1
2
1
1
1
1
1
0
0
2
1
2
0
1
2
1
2
0
2
0
1
1
1
1
2
2
1
1
1
1
0
1
0
0
0
2
1
2
1
2
0
1
1
2
2
0
2
1
1
1
1
1
0
1
1
2
2
0
1
1
1
1
1
1
2
1
2
1
1
2
1
2
1
0
1
1
1
2
1
1
2
1
1
1
2
1
1
0
1
1
0
0
1
2
0
1
2
2
1
2
1
2
1
1
0
2
1
1
1
1
2
0
2
1
1
2
1
2
2
2
1
1
1
2
2
1
1
1
1
2
1
2
0
1
2
2
2
2
1
1
1
1
1
1
1
2
1
1
0
1
2
2
1
1
1
1
1
2
2
1
1
1
1
0
1
2
1
2
1
2
1
2
1
0
2
1
1
1
1
0
1
2
2
0
1
2
1
1
1
2
1
1
1
2
1
1
0
1
1
1
1
2
1
0
1
2
0
1
1
1
1
1
1
1
1
0
1
0
1
2
0
1
1
1
0
2
1
1
2
1
1
0
1
1
1
1
0
2
1
1
2
1
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
2
2
1
2
1
1
1
1
1
2
1
0
1
1
2
1
1
1
2
1
2
1
2
1
0
1
0
1
1
1
2
1
1
1
1
2
1
1
3
1
1
1
2
2
1
0
2
2
1
1
0
1
1
2
1
1
1
1
0
1
0
1
0
1
2
2
1
1
2
1
1
1
2
2
1
0
1
1
2
2
1
0
2
1
2
0
2
1
2
1
0
1
1
1
2
1
2
1
2
1
0
0
0
1
1
2
2
1
2
2
1
2
1
1
1
1
2
2
1
1
2
2
0
1
0
1
1
2
1
1
2
0
2
2
1
0
2
1
1
1
0
0
1
0
0
1
1
2
2
1
2
1
1
0
1
0
1
0
2
1
2
0
0
2
1
2
1
0
2
1
0
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
0
0
0
1
2
2
1
0
1
2
1
1
0
0
2
0
2
2
1
1
1
0
0
1
1
1
1
1
2
1
2
1
0
1
1
0
1
0
2
2
0
1
1
1
1
1
1
1
1
2
0
2
2
1
0
1
1
1
1
1
1
1
1
0
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
0
2
1
1
2
1
2
2
2
1
2
0
1
1
1
1
0
2
2
0
2
2
1
1
1
1
1
1
2
2
0
1
1
1
0
2
2
1
1
0
1
1
1
0
0
1
1
1
1
2
1
1
2
1
1
2
2
2
2
2
0
1
2
0
2
1
1
1
1
2
2
1
1
1
0
1
2
1
2
2
1
1
2
0
1
2
1
1
2
1
2
2
2
1
2
2
2
0
1
1
2
1
1
1
1
1
1
1
1
0
2
1
1
1
1
1
2
1
0
1
1
0
0
0
2
1
1
1
1
1
1
0
1
1
1
1
1
2
0
1
1
1
1
0
2
1
0
2
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
0
1
1
2
0
1
2
2
1
0
1
2
0
1
2
1
1
2
1
1
2
2
1
2
1
1
1
1
0
2
1
1
1
1
1
1
2
1
1
1
1
0
1
2
1
0
1
1
0
0
2
1
1
1
0
1
2
1
1
1
1
2
0
1
1
1
1
2
1
1
1
2
0
2
1
1
2
0
2
1
1
1
1
1
2
2
1
1
2
1
1
1
1
1
2
1
2
1
1
1
2
0
0
1
0
1
1
1
1
2
2
1
2
1
1
1
2
1
2
1
2
1
1
1
0
0
2
0
1
1
1
1
1
2
2
2
1
1
1
2
1
2
2
2
1
1
0
2
1
0
0
1
1
2
1
3
1
2
0
1
0
1
1
2
1
1
1
2
1
1
2
1
2
0
2
1
1
1
1
1
1
1
1
1
2
2
1
1
2
2
1
1
1
1
2
1
1
2
2
1
0
1
0
1
1
2
0
2
1
1
1
1
1
2
1
2
2
1
0
1
1
1
1
0
1
1
1
1
0
1
1
1
0
2
1
1
1
0
2
2
2
2
1
0
1
1
1
2
1
0
1
0
1
0
1
2
1
0
1
1
1
0
2
0
0
2
1
1
1
0
1
1
1
1
2
1
1
2
0
1
1
1
1
2
2
1
1
1
2
1
1
2
1
2
1
1
1
1
1
2
2
1
1
2
0
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
0
1
1
2
1
1
0
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
2
1
1
2
1
0
1
1
1
2
0
1
2
1
1
1
1
1
2
2
0
0
1
0
1
1
0
2
0
1
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
0
0
1
1
1
1
1
1
1
2
1
1
2
0
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
0
1
0
1
1
2
2
0
1
1
2
0
0
0
0
1
1
2
1
1
2
1
1
1
1
1
1
2
2
1
2
1
1
1
2
2
1
1
1
1
1
2
1
1
1
2
1
2
2
2
2
1
0
1
1
1
2
0
0
1
2
0
0
1
2
2
1
2
1
0
1
1
1
2
2
1
1
2
0
1
1
1
1
2
2
2
2
2
1
1
0
1
1
2
1
1
1
2
1
1
0
1
1
1
2
1
1
2
2
0
0
1
1
2
1
1
2
1
1
0
1
1
1
1
1
1
1
2
1
1
2
1
1
1
2
2
0
1
0
1
2
1
1
1
1
1
0
1
1
1
0
2
1
2
1
1
2
3
2
1
1
1
1
1
1
0
2
2
0
1
1
1
0
2
1
1
1
0
0
0
1
0
2
1
0
0
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
0
1
1
1
1
1
1
2
0
1
1
1
1
2
1
2
1
1
1
1
1
2
2
1
2
1
2
2
1
1
1
1
1
1
1
0
1
0
1
1
1
1
0
1
1
2
1
2
1
1
1
2
1
0
2
0
1
2
2
0
2
3
2
1
1
1
1
1
1
2
1
1
1
1
2
2
1
1
1
1
1
1
0
1
1
1
1
1
2
1
1
1
2
1
0
1
2
2
0
1
2
1
1
2
1
1
1
1
2
1
0
0
1
1
0
1
0
1
1
0
0
2
1
1
2
0
0
2
1
1
2
2
1
1
1
0
1
1
1
0
1
1
1
1
1
1
0
1
1
1
1
1
2
1
1
0
1
1
1
1
0
1
1
1
1
2
0
2
1
1
1
1
0
0
1
2
1
0
3
1
1
2
1
1
0
2
0
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
2
1
0
0
1
0
0
2
1
1
1
2
2
5
1
1
1
1
1
1
1
1
2
1
0
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
0
0
2
2
1
1
1
1
2
1
2
1
1
1
0
2
2
1
0
1
1
2
1
2
1
2
1
0
0
1
2
1
1
2
1
0
0
2
1
1
1
1
1
3
1
0
2
1
2
1
0
1
2
0
0
2
1
1
1
0
1
2
1
2
2
1
1
3
1
2
1
0
1
1
2
1
1
2
1
1
0
1
1
0
1
1
2
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
0
1
1
1
5
1
1
1
1
1
1
2
2
1
1
1
0
1
1
0
2
1
1
2
1
0
1
1
1
2
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
0
2
1
2
1
1
1
1
1
2
2
1
1
1
1
1
2
1
2
1
1
1
1
1
0
1
1
1
1
2
1
1
2
2
2
1
0
0
1
0
0
1
1
1
1
2
1
0
2
0
2
2
1
2
1
2
1
2
0
1
1
1
1
2
1
1
1
1
1
1
1
0
1
2
2
1
1
2
2
1
0
1
1
1
2
1
1
2
2
1
0
1
0
1
1
2
1
1
2
1
2
2
2
1
2
1
2
1
1
1
2
0
1
2
2
2
2
1
2
0
1
1
1
1
1
1
2
1
1
1
2
0
2
2
1
1
2
1
1
0
1
1
2
1
3
1
2
1
2
1
1
1
1
1
1
1
1
1
1
2
1
0
1
1
0
1
2
0
1
1
2
1
1
1
1
1
1
2
1
1
1
0
0
2
1
1
1
1
0
1
1
2
1
0
1
1
0
2
1
2
1
0
1
1
1
0
1
2
1
1
1
1
2
1
1
3
1
0
1
1
1
1
2
1
1
1
1
1
1
0
1
1
1
0
1
1
1
2
0
0
2
2
1
0
0
1
1
1
2
2
0
0
1
1
1
1
2
1
2
0
1
2
0
2
1
2
2
1
1
1
0
1
1
2
2
0
1
0
1
1
1
1
0
2
1
1
0
1
1
1
1
1
0
1
2
2
2
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
2
1
1
1
2
2
0
3
1
0
1
1
1
1
1
1
2
1
1
1
2
2
2
2
1
1
2
1
1
1
1
2
1
2
1
1
0
1
1
0
2
1
0
1
2
2
1
3
1
1
1
1
1
1
1
1
1
1
1
0
1
2
0
2
1
1
1
2
1
1
2
2
1
1
1
1
2
1
1
1
1
1
2
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
0
1
2
1
1
2
2
1
1
1
1
2
1
2
1
0
1
0
2
0
1
1
1
1
0
2
2
1
1
2
2
1
2
2
0
1
0
2
1
2
1
1
0
1
1
1
1
1
3
1
1
1
1
1
0
1
0
0
0
1
1
2
1
1
2
2
2
1
2
0
1
2
2
0
1
2
1
1
1
1
1
2
1
1
2
1
1
1
1
2
2
2
2
1
1
1
2
2
0
2
1
2
0
2
1
1
2
1
1
1
1
0
1
1
1
1
0
1
1
1
1
1
1
1
1
0
2
1
0
2
1
2
2
1
1
1
2
2
2
1
1
3
1
1
1
1
1
1
1
0
1
1
1
2
1
1
0
1
1
0
2
1
2
1
1
1
0
1
0
2
1
1
0
1
1
0
1
1
1
1
1
2
1
1
0
1
0
1
1
0
1
2
1
2
2
1
0
1
1
1
2
1
1
2
3
2
1
2
1
2
1
2
2
1
2
2
1
3
1
1
2
1
2
1
1
1
1
1
0
1
1
2
1
1
0
1
2
1
1
1
0
1
1
2
2
1
1
1
1
2
1
2
2
1
1
1
2
2
1
2
2
1
2
1
0
1
1
2
0
1
0
2
2
2
1
1
1
2
1
1
1
2
1
1
1
0
1
1
0
2
1
2
1
1
2
1
1
2
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
0
2
2
0
1
1
2
1
2
2
1
1
1
2
1
1
1
1
1
1
1
0
0
2
2
0
1
0
1
0
1
2
1
1
2
1
2
1
2
1
1
1
2
1
2
1
1
2
1
1
1
0
2
2
1
1
1
1
1
1
1
1
2
1
2
1
2
1
1
0
1
1
1
0
0
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
2
2
1
0
2
1
1
1
0
2
3
1
1
1
1
2
0
1
2
2
1
1
2
2
1
0
1
2
1
1
2
2
2
1
1
0
1
1
1
4
2
0
2
1
2
1
1
1
1
1
1
1
1
2
2
2
1
2
0
1
0
0
1
1
2
1
1
2
2
1
0
1
2
1
0
1
1
0
1
0
1
1
2
2
1
1
1
1
2
0
1
1
1
2
2
2
1
2
1
0
1
1
1
2
2
1
1
1
0
1
1
2
2
1
1
1
1
1
1
1
2
0
2
0
1
1
0
2
2
1
1
1
1
2
1
1
0
2
2
0
2
2
1
2
2
2
0
1
1
2
0
1
2
4
1
1
2
0
1
1
0
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
0
1
1
1
2
2
1
1
1
2
1
1
0
1
1
1
1
1
2
1
1
1
1
1
0
1
1
1
2
1
2
1
1
1
1
1
0
1
1
1
1
2
2
3
1
1
1
0
1
1
0
1
1
1
0
2
0
1
1
2
1
0
1
1
2
2
2
0
1
1
2
0
1
1
0
1
1
1
1
2
1
1
0
1
2
2
1
1
1
1
2
1
1
1
2
0
1
2
1
1
2
1
1
1
1
0
2
4
0
2
1
2
0
1
1
0
1
1
1
0
0
0
2
1
2
1
1
1
0
2
1
0
2
1
3
1
1
1
1
1
1
0
1
1
0
0
1
1
1
0
1
0
1
1
1
1
0
0
1
2
1
1
2
1
1
1
2
1
2
1
2
1
1
1
1
1
1
2
1
1
2
1
1
1
0
1
1
1
1
1
1
1
1
2
1
1
1
2
0
1
1
1
1
1
2
2
1
2
0
1
2
2
1
2
1
2
1
0
2
1
2
2
1
1
2
1
1
1
2
1
5
0
2
1
1
1
1
1
1
2
2
1
1
1
2
0
2
1
0
2
2
0
2
1
1
1
2
2
2
0
1
2
1
1
1
0
1
1
1
1
2
1
0
1
1
1
0
1
2
0
1
1
2
4
2
1
1
1
1
1
0
1
1
1
2
1
1
1
1
1
2
1
0
1
2
1
1
1
1
2
2
2
1
1
2
1
3
2
1
0
1
0
1
2
2
1
2
1
1
2
1
2
1
2
1
1
1
1
1
2
1
1
1
0
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
1
0
0
1
1
1
1
1
1
1
1
0
0
0
1
0
1
1
0
1
1
1
1
2
1
2
1
1
1
0
1
0
0
1
1
0
2
1
1
0
2
1
1
0
1
1
2
2
0
1
2
1
1
0
1
1
1
2
1
1
1
1
1
1
0
1
1
2
1
1
2
1
1
1
2
2
1
0
3
2
1
1
1
2
1
0
1
1
2
2
2
2
2
1
1
1
1
1
1
1
2
2
1
0
0
0
2
0
1
2
1
2
1
1
0
2
2
2
1
1
1
2
1
1
2
1
2
0
1
0
1
1
2
2
1
1
1
1
1
1
1
0
1
1
1
1
0
1
2
2
1
0
1
2
2
1
2
1
2
0
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
2
0
0
2
1
1
0
1
1
1
2
2
2
2
1
1
1
1
2
1
0
0
0
1
1
2
2
1
1
1
1
1
1
0
3
2
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
0
0
1
2
1
2
1
1
1
2
2
1
1
1
1
1
0
1
1
1
1
1
2
1
0
1
1
1
1
1
1
2
0
1
1
0
1
1
0
1
1
1
1
2
1
1
1
1
1
2
1
0
1
1
1
1
2
1
2
1
1
0
1
2
0
1
1
1
1
0
1
0
1
0
1
1
2
1
1
0
1
1
1
2
1
1
1
2
1
1
2
1
2
1
2
2
1
1
2
1
2
1
1
1
1
2
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
2
2
2
1
2
1
2
1
1
2
1
2
1
2
1
1
1
0
1
1
0
1
1
1
1
1
2
1
1
1
2
1
1
1
0
0
1
1
2
0
1
1
2
1
2
2
1
1
2
1
1
2
1
2
2
0
2
2
2
1
2
2
0
1
1
2
2
0
1
1
1
1
2
1
1
2
1
0
0
1
1
1
0
0
2
2
1
2
2
1
1
0
1
1
2
2
2
1
1
1
1
1
1
2
1
0
2
2
2
1
1
1
1
1
2
1
1
0
2
2
1
0
1
2
2
1
0
2
1
1
2
2
2
2
1
1
0
1
1
1
1
1
1
1
2
2
1
1
1
0
1
1
0
1
2
1
2
2
0
1
1
0
1
0
2
0
2
1
0
1
1
1
1
1
1
0
1
1
1
0
0
2
1
1
1
1
2
1
1
1
2
1
1
1
1
1
2
0
0
1
1
1
1
2
3
1
1
1
1
2
1
2
1
2
2
1
2
1
1
1
0
2
1
1
0
0
2
1
1
1
1
1
1
1
2
1
2
1
2
1
1
1
0
1
1
1
1
1
2
2
0
1
2
1
0
0
1
1
1
1
2
1
0
1
0
1
1
1
1
2
1
0
0
1
2
0
3
2
2
2
2
0
0
2
1
1
2
0
1
1
2
1
1
1
0
0
1
2
2
1
2
1
2
2
2
1
1
1
2
1
1
1
1
1
2
0
2
1
1
1
1
2
1
0
2
1
1
2
1
1
1
2
2
1
1
1
1
1
1
1
1
1
0
1
1
1
0
2
2
1
1
2
1
1
1
1
0
1
0
0
2
2
3
1
1
1
2
1
2
2
1
0
2
2
1
2
1
1
1
1
0
1
2
0
1
1
2
1
2
0
0
1
2
0
1
1
1
0
2
2
1
2
1
1
1
1
2
0
2
0
1
2
0
2
0
1
1
2
2
2
1
1
1
0
1
0
1
2
1
0
1
1
1
0
1
1
2
1
2
0
0
1
2
1
0
1
3
1
1
1
1
1
1
1
2
2
1
1
1
1
2
2
1
1
1
1
1
1
1
1
2
1
2
1
1
0
1
1
1
1
1
1
3
1
1
1
3
1
1
1
1
0
2
1
2
1
1
3
1
1
2
2
1
1
2
2
1
1
2
1
1
1
1
2
3
2
2
1
2
1
0
1
1
1
1
1
1
1
2
0
3
1
2
2
0
1
1
2
1
1
1
0
2
1
2
0
1
1
1
0
1
1
1
1
2
1
1
1
1
1
0
3
1
1
1
1
1
2
1
1
2
1
2
0
1
1
1
1
2
2
1
1
2
1
1
1
2
1
1
0
1
1
2
1
1
1
2
1
2
2
1
0
1
1
2
2
1
1
1
1
2
2
2
1
2
1
0
1
1
1
1
2
2
1
1
1
1
0
1
1
2
1
1
2
1
2
1
1
0
1
1
1
1
1
0
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
2
2
1
2
1
1
1
1
1
2
1
2
0
0
1
2
2
5
2
1
1
2
1
1
0
0
2
1
2
1
0
1
2
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
0
1
1
0
2
1
2
1
1
0
0
0
2
0
1
1
1
1
0
1
0
1
1
1
1
2
1
1
1
2
1
2
1
1
2
1
1
2
1
2
1
2
1
1
2
1
2
1
2
1
2
2
1
1
1
1
2
1
2
1
2
1
2
1
2
2
1
2
1
1
1
0
1
1
0
2
1
1
1
2
1
2
1
1
2
1
0
2
1
1
1
1
1
1
0
1
1
1
1
2
1
1
2
0
1
0
1
1
1
0
0
0
2
1
1
1
2
1
1
0
2
1
1
0
1
1
1
2
1
1
1
1
1
0
1
1
1
0
1
1
1
2
0
1
1
1
2
3
2
1
2
1
2
2
1
1
1
0
2
1
1
1
1
3
2
1
2
1
1
2
0
1
1
1
1
1
2
1
0
2
1
1
1
1
2
2
1
1
1
1
1
1
1
1
3
2
1
2
1
0
2
1
1
2
1
1
0
1
1
1
2
2
1
1
1
1
2
0
2
1
1
0
1
0
2
1
1
1
2
1
0
1
1
1
2
1
2
1
2
2
2
1
2
2
1
1
2
1
1
1
1
1
1
1
1
2
2
0
1
1
1
1
1
2
2
0
1
1
2
1
1
1
1
1
2
1
1
1
1
1
0
0
1
1
1
1
0
1
1
2
1
1
1
1
1
0
1
0
1
1
2
2
2
1
1
0
1
0
1
1
1
0
1
2
1
1
1
2
1
1
1
2
0
0
2
2
1
1
1
2
1
2
2
0
2
0
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
2
1
2
1
1
1
2
2
1
1
1
1
2
1
2
1
2
3
1
0
0
2
2
2
2
1
2
2
1
2
1
1
2
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
5
1
1
2
1
0
2
1
1
1
1
2
1
1
2
1
1
2
1
2
0
1
1
2
1
2
1
0
1
1
1
3
1
1
1
1
2
1
1
0
1
1
0
1
1
0
0
1
1
2
2
2
1
2
1
2
1
1
1
1
1
1
2
1
0
6
0
3
0
1
2
0
1
1
1
1
1
2
1
2
2
1
2
1
1
0
2
0
2
0
1
1
1
1
2
2
1
1
2
1
2
1
1
1
1
0
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
2
2
1
2
1
2
0
2
0
1
1
1
2
1
1
1
1
2
1
2
2
1
0
0
2
1
1
1
1
1
1
2
2
2
2
2
2
1
1
1
1
2
0
1
1
1
2
2
1
1
1
0
1
1
1
1
1
0
0
2
1
2
1
1
1
1
0
0
1
2
0
2
1
1
1
1
1
1
1
1
0
2
1
1
1
0
1
2
1
1
2
1
1
2
1
2
2
2
1
2
1
1
1
2
1
2
2
2
2
1
1
2
2
2
0
1
0
2
1
2
1
1
2
2
2
1
1
1
2
1
1
1
1
0
1
1
1
2
1
2
1
1
1
2
2
2
1
1
2
1
1
1
1
1
2
1
0
1
1
0
1
2
1
2
1
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
0
1
2
2
1
1
1
1
1
2
1
2
1
2
2
1
2
0
0
1
1
1
2
2
1
1
1
2
1
2
0
1
1
2
2
1
1
0
1
1
1
1
2
1
1
0
2
2
2
1
2
1
1
1
1
2
1
3
1
1
1
1
2
2
1
0
1
1
0
1
1
1
1
2
0
1
2
1
1
1
1
1
1
2
1
1
1
2
1
0
2
1
2
1
2
1
1
2
1
3
0
2
2
1
2
2
2
1
1
1
0
0
1
2
2
1
1
2
0
1
2
1
0
1
1
1
1
2
1
1
0
1
1
1
2
1
1
1
2
2
1
0
0
1
1
0
1
2
2
2
1
0
0
1
1
2
0
1
1
1
1
2
2
1
2
1
1
0
3
1
1
1
1
1
2
1
2
1
1
1
1
2
1
2
1
1
1
0
2
1
1
1
1
0
1
1
2
1
2
2
0
1
2
2
1
1
1
1
3
1
2
2
0
1
1
1
1
1
1
1
1
1
2
1
1
0
2
2
1
1
2
0
1
2
1
2
1
1
2
1
2
1
0
1
3
1
0
1
1
1
1
1
1
2
0
1
1
1
1
1
2
1
1
2
2
1
1
1
0
2
1
1
1
0
1
2
4
2
2
1
2
2
0
0
0
2
1
1
1
1
0
1
2
1
1
0
1
1
1
0
1
1
1
0
1
1
0
1
1
1
1
2
1
1
1
1
0
1
2
2
0
1
1
1
1
2
1
2
2
1
1
2
1
0
1
1
1
1
1
1
1
1
1
4
1
1
2
2
2
1
2
0
1
1
1
1
1
1
0
1
1
1
0
1
2
0
1
2
1
2
2
1
2
1
1
1
1
1
1
0
1
0
1
1
2
1
2
0
1
0
0
1
2
1
2
0
0
1
0
1
1
1
2
1
0
2
2
1
1
1
0
0
2
2
2
1
1
0
1
2
2
1
2
1
1
0
1
1
1
2
1
2
2
1
2
0
1
1
2
1
1
1
1
1
2
1
2
2
0
2
2
2
1
1
2
1
0
1
1
0
2
1
1
1
1
1
1
2
2
1
1
1
2
1
1
2
2
1
1
2
1
1
2
1
2
2
0
1
2
2
2
2
2
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
0
1
2
1
1
2
2
1
1
1
1
2
0
1
2
1
1
1
1
1
1
1
2
1
2
2
2
1
1
2
2
0
1
1
1
0
1
1
1
1
2
2
1
0
0
3
1
0
1
1
1
1
0
1
2
2
0
1
2
2
2
1
1
2
2
1
1
1
2
2
1
1
2
1
1
1
2
1
2
2
1
2
2
1
0
1
2
2
1
1
2
1
2
2
1
1
1
1
0
1
0
0
1
1
1
1
1
2
1
1
1
1
2
2
1
1
2
1
2
1
0
1
1
1
1
1
0
1
2
0
1
2
1
0
1
0
1
2
1
0
1
0
2
2
1
1
0
1
1
2
1
2
1
1
2
1
2
1
2
1
0
1
1
2
1
1
2
1
1
1
1
1
0
1
2
2
1
1
1
1
1
1
0
1
1
0
0
1
1
1
0
1
2
1
1
0
2
1
2
2
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
2
0
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
0
1
1
0
0
1
1
2
5
2
1
1
0
0
1
1
1
1
1
1
1
1
1
1
2
3
1
1
0
1
1
2
0
1
2
1
1
1
0
1
2
1
2
0
1
1
2
1
1
1
2
1
1
2
1
2
1
1
1
3
2
1
1
1
1
2
2
2
2
1
2
1
1
1
1
3
1
1
1
2
1
1
2
1
2
1
0
2
2
2
2
2
1
1
1
1
1
1
2
2
2
1
3
1
0
0
0
1
1
2
1
1
1
1
2
1
1
1
1
1
0
0
2
1
1
1
2
1
1
1
1
2
0
0
1
2
1
2
1
1
2
2
2
2
1
2
1
1
2
1
1
1
1
2
0
1
2
1
1
2
2
2
1
2
1
2
2
1
1
1
1
1
2
2
1
1
0
2
1
2
1
0
0
1
1
1
1
1
2
1
2
0
2
1
1
2
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
2
0
1
2
2
1
2
2
1
1
2
2
0
1
1
1
1
1
2
3
0
1
1
2
2
2
1
2
1
0
1
1
1
1
1
1
1
2
0
2
1
1
2
1
1
2
1
0
2
1
1
2
1
1
2
2
1
2
1
1
1
1
0
2
2
0
1
1
2
1
2
0
2
1
1
1
2
2
1
0
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
0
2
2
2
1
1
1
2
2
0
1
1
1
2
0
1
1
1
1
0
0
1
1
0
2
2
0
1
2
0
0
1
1
1
2
1
1
1
1
2
1
2
2
1
0
2
1
1
2
1
2
1
1
1
2
2
1
0
1
1
0
1
1
0
1
1
1
1
1
1
2
1
2
1
1
1
2
1
2
1
0
2
2
1
1
1
2
1
0
1
1
1
3
1
1
1
2
2
1
1
1
1
1
2
1
1
2
2
2
2
2
1
1
2
1
1
1
2
3
1
2
2
1
2
1
2
1
2
1
2
1
1
1
2
2
2
1
1
2
0
1
1
1
0
2
2
1
1
2
1
2
0
1
1
0
1
2
1
1
2
1
1
1
1
0
1
2
1
1
2
1
1
0
30
0
1
2
2
0
1
1
2
2
2
0
0
1
1
1
2
1
1
2
1
1
0
1
0
1
1
1
0
1
1
1
2
1
0
1
1
2
1
1
0
1
1
1
2
1
1
2
1
0
1
2
1
1
1
1
2
1
2
1
1
2
1
1
1
1
1
0
1
1
2
2
2
0
2
1
1
1
1
2
2
1
1
1
1
1
1
1
1
0
1
2
1
1
1
0
1
1
1
1
1
1
1
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
2
2
1
1
2
1
0
0
1
1
2
1
0
1
0
1
0
1
1
1
1
1
2
1
1
1
1
0
2
1
1
2
0
2
2
1
2
1
1
1
1
2
1
1
1
0
1
1
1
1
0
1
1
1
2
2
1
1
1
1
1
1
0
0
4
1
1
2
1
1
2
1
1
2
2
1
1
1
0
2
1
1
1
0
1
1
1
1
1
1
1
1
1
2
0
1
1
2
0
1
2
1
1
1
2
2
1
1
0
1
1
0
1
1
1
2
1
1
1
1
1
1
2
1
2
1
2
1
1
2
1
0
1
1
2
1
2
2
1
1
2
0
1
2
1
2
2
1
2
1
1
1
1
1
2
2
2
1
2
2
1
1
0
2
1
2
1
1
1
1
1
1
1
1
0
2
2
0
1
0
2
1
2
2
1
0
0
1
1
1
1
1
1
0
1
1
1
1
2
1
2
1
1
1
1
2
2
0
1
0
1
1
2
2
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
2
0
2
0
1
2
0
2
1
2
1
2
1
2
1
1
1
0
2
2
0
0
1
0
1
1
2
2
2
0
1
1
0
1
2
2
2
1
1
2
1
1
1
1
1
0
2
0
2
1
2
1
1
2
0
1
0
1
0
1
1
2
0
0
1
2
1
2
2
1
2
1
1
1
1
1
1
1
2
1
1
2
1
2
2
1
1
1
1
2
2
1
0
2
0
1
2
0
1
2
1
1
1
1
1
0
1
0
1
1
2
1
0
1
1
0
1
0
2
1
1
2
1
1
1
2
2
1
2
2
2
1
1
1
1
1
2
2
1
1
1
2
1
2
2
1
1
2
1
0
2
2
1
1
1
2
0
1
1
1
2
2
1
1
1
1
0
1
2
2
1
2
2
1
1
2
2
0
1
1
1
1
2
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
0
1
1
0
1
1
2
1
1
2
1
1
0
1
1
1
0
2
1
1
1
1
2
2
1
2
1
1
1
0
1
2
1
2
1
1
1
1
2
2
1
3
2
0
0
1
2
1
1
1
0
2
1
1
1
0
0
1
1
2
1
2
1
0
1
2
2
2
1
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
0
2
2
1
1
1
1
1
0
2
1
2
1
1
2
2
1
1
1
1
1
2
3
2
0
2
1
2
1
0
2
1
1
1
1
2
2
1
1
2
2
1
1
2
1
1
1
2
0
1
2
1
1
1
2
1
1
1
0
1
2
1
0
1
1
1
1
0
1
1
2
1
1
1
1
0
1
2
2
2
0
1
1
1
1
1
1
2
1
1
1
2
1
2
2
1
1
2
1
1
2
0
1
1
2
1
0
1
2
1
1
1
1
1
1
1
0
1
3
1
1
0
0
1
1
1
2
0
1
2
2
2
0
2
1
0
1
1
1
1
1
1
2
1
0
1
1
1
1
1
1
1
2
1
0
0
2
1
0
2
2
1
1
2
1
2
1
1
2
2
1
1
0
2
0
2
1
2
2
1
1
1
0
2
1
1
0
1
4
1
1
2
1
2
1
1
1
1
2
1
1
2
2
2
0
1
1
0
2
1
1
0
2
1
2
2
0
0
1
1
1
1
0
1
2
1
1
0
1
2
1
1
1
0
1
0
1
0
1
2
2
1
1
0
1
1
1
1
2
1
0
0
2
1
0
1
2
0
2
1
2
1
1
1
2
0
2
1
1
2
2
1
1
1
1
0
1
1
2
1
1
2
1
1
1
2
1
1
1
3
1
2
1
1
1
0
1
1
1
2
1
1
0
1
1
2
1
1
0
1
1
1
2
1
1
0
1
1
2
1
1
0
2
1
0
2
1
1
1
1
1
1
2
2
1
1
2
1
1
1
1
1
0
2
1
1
0
1
0
1
1
2
1
1
1
2
0
2
0
1
1
1
1
0
1
0
2
1
2
1
2
1
1
0
1
1
0
0
0
1
2
2
1
2
1
1
1
1
1
1
1
0
1
0
1
1
1
1
1
0
2
1
2
1
0
2
1
0
1
1
2
2
2
0
2
2
2
1
1
0
1
1
2
1
2
1
1
1
2
1
1
1
1
2
0
1
1
1
1
1
0
2
2
1
1
2
1
1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
1
0
2
1
2
1
1
1
2
0
1
2
0
1
2
1
1
0
2
1
1
2
2
1
1
1
1
1
1
1
1
0
2
1
0
1
1
1
2
1
2
2
1
1
2
0
1
2
2
2
1
1
2
1
2
0
1
1
1
0
2
2
0
2
1
1
1
1
0
1
0
1
1
1
1
2
0
2
1
1
0
1
1
1
1
1
0
0
2
1
2
2
1
1
0
1
2
1
1
2
2
1
1
0
2
1
1
2
1
2
0
2
2
1
0
2
1
1
0
1
0
2
1
2
2
1
1
1
2
2
1
1
1
1
0
1
1
1
2
1
1
1
2
1
1
1
0
1
0
1
2
1
1
1
1
0
2
1
2
0
1
1
2
1
0
2
0
2
1
1
2
1
1
1
1
1
1
2
1
2
0
2
1
2
1
1
1
1
0
0
0
1
1
2
2
2
1
1
1
1
1
1
0
1
0
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
0
2
1
2
2
1
1
0
1
1
1
1
1
1
1
1
1
2
2
1
1
1
2
1
0
1
1
2
2
2
1
2
1
2
1
1
2
0
2
1
2
1
2
1
1
2
1
1
0
1
1
1
0
1
0
1
1
0
1
1
1
1
1
1
1
2
2
1
1
1
1
1
0
1
0
1
0
1
1
1
2
2
2
2
1
1
1
1
2
1
1
2
2
1
1
0
0
1
2
2
2
1
1
2
1
0
1
1
2
0
0
1
1
1
1
2
1
1
1
2
1
2
0
1
1
1
1
1
1
0
1
1
1
1
1
1
0
1
2
1
1
1
2
2
1
2
1
1
1
1
1
1
2
0
0
1
1
1
1
1
0
0
1
1
0
1
1
2
0
2
1
1
2
1
2
0
1
1
1
0
1
3
2
1
2
1
1
2
1
1
2
1
1
3
1
1
2
2
0
2
1
2
1
0
2
0
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
0
0
0
2
2
0
0
2
1
2
2
1
1
1
0
2
1
0
1
2
1
1
2
2
0
1
1
2
1
2
1
2
2
1
2
0
2
2
1
1
1
2
1
1
1
2
2
0
1
1
1
2
1
2
1
1
1
1
2
1
0
1
1
1
0
1
1
0
1
2
1
1
1
0
1
2
0
0
1
1
1
2
1
1
1
1
1
2
2
2
0
0
1
0
2
1
1
2
1
1
1
1
2
2
1
1
1
1
2
1
1
2
1
1
1
1
0
1
2
1
1
1
2
1
1
0
1
1
1
0
1
2
2
2
2
2
2
2
1
1
1
1
1
1
2
2
1
2
2
1
0
1
3
1
0
1
1
1
1
1
1
1
1
1
2
2
0
1
1
0
1
1
1
1
1
3
1
1
0
1
0
1
1
1
1
1
1
0
1
1
1
1
1
0
1
0
2
1
0
1
0
0
2
2
1
1
0
2
1
1
2
1
1
0
0
1
1
1
1
1
0
1
1
0
0
2
1
0
1
1
0
0
1
1
2
1
0
1
1
0
0
0
2
1
2
2
1
1
2
1
1
1
0
1
1
1
1
1
0
2
1
1
1
1
1
1
1
0
1
1
2
1
0
2
1
1
2
1
0
0
2
2
1
0
1
2
1
1
1
1
2
1
0
1
1
1
1
2
2
1
1
1
1
2
1
2
2
2
2
0
1
1
2
1
1
1
1
2
2
1
0
2
1
0
1
1
2
2
0
2
2
2
1
1
1
0
0
1
1
1
1
1
2
1
0
2
1
1
1
1
0
2
1
1
1
1
1
1
2
2
1
2
2
0
1
1
1
1
1
1
1
1
2
1
1
2
1
2
2
2
0
2
1
2
0
2
2
1
3
0
2
3
2
1
1
2
1
2
1
0
2
1
2
1
1
1
2
1
1
2
1
1
0
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
2
0
0
2
2
2
2
2
1
2
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
0
0
2
1
2
1
1
1
0
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
0
1
2
1
2
1
1
1
1
3
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
2
1
1
0
1
1
2
0
2
1
1
2
1
2
2
0
0
1
2
1
1
2
1
2
2
1
1
0
2
2
0
1
1
1
1
1
1
2
1
1
1
1
1
2
2
1
1
2
0
1
1
0
1
1
1
1
1
2
2
1
1
1
1
0
1
1
2
1
1
1
1
1
0
1
1
2
1
1
2
2
1
0
1
1
0
1
2
2
0
2
1
0
1
1
1
1
1
1
1
0
1
1
2
2
2
2
1
1
1
1
1
2
0
2
1
2
2
2
0
1
2
2
1
1
1
1
0
1
1
1
1
2
1
2
2
1
0
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
2
2
1
2
2
1
1
0
1
2
2
2
0
1
1
2
1
1
2
1
2
2
2
2
2
1
0
1
1
1
1
1
0
2
1
1
1
1
1
2
1
1
2
1
1
2
2
1
1
1
2
1
0
1
1
1
1
3
1
1
1
2
1
2
1
1
1
1
1
2
2
1
1
1
1
1
0
1
1
1
0
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
0
1
1
1
1
1
1
1
0
0
1
1
0
1
2
1
1
0
1
0
0
1
0
1
1
1
1
2
2
1
2
2
2
1
1
1
2
0
2
1
2
1
1
2
1
0
1
2
1
1
0
2
1
2
1
2
1
1
2
2
1
0
1
1
2
1
0
0
1
1
2
1
2
1
1
2
2
0
2
2
2
1
1
0
2
1
2
1
1
2
1
1
1
2
2
3
1
1
1
1
1
1
1
1
0
2
1
1
2
2
1
1
1
0
1
2
2
1
2
2
1
1
1
1
0
0
2
2
1
1
1
0
1
1
1
0
1
2
5
1
0
1
1
2
1
0
1
1
0
1
1
1
0
1
1
0
1
2
2
2
2
1
2
1
0
1
1
1
1
1
1
2
1
2
1
0
0
2
2
0
1
1
1
0
1
0
1
2
0
2
2
1
1
1
1
1
0
1
1
1
2
1
1
1
1
2
0
1
1
2
2
0
4
1
2
4
0
2
1
1
3
2
1
2
1
1
0
1
2
1
1
1
2
1
1
1
0
1
2
1
2
1
0
2
1
1
1
2
1
2
0
1
1
1
0
1
1
1
1
2
1
1
1
1
1
1
2
1
2
1
2
2
1
1
1
1
0
1
2
0
1
0
2
1
1
2
1
1
0
1
1
0
1
2
1
2
2
1
2
1
1
0
1
2
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
2
2
3
2
0
1
1
2
1
2
2
1
1
1
1
2
1
2
1
1
1
1
2
2
1
1
0
2
1
1
1
1
1
1
0
1
2
1
1
2
1
1
1
1
1
1
0
2
1
1
1
1
1
1
1
2
1
2
1
2
1
1
1
0
0
1
2
0
1
1
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
0
1
1
1
1
1
2
0
1
2
0
1
1
1
0
1
1
0
3
1
1
1
2
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
2
2
2
2
2
1
2
2
1
1
1
1
1
1
0
2
2
1
0
2
2
2
2
1
1
1
2
1
1
2
2
1
1
0
0
1
1
1
2
1
1
2
3
0
1
1
1
1
2
0
1
0
1
1
0
1
2
1
1
2
2
1
1
2
1
1
2
1
1
1
2
1
1
1
0
1
1
1
2
2
0
1
1
2
1
0
1
1
0
2
1
1
1
2
1
1
1
0
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
5
2
0
1
1
0
1
2
2
2
0
2
1
1
0
1
2
1
1
1
1
2
0
1
1
1
1
1
1
2
2
1
1
0
1
3
1
1
1
1
1
1
1
1
2
2
1
1
0
2
2
1
1
1
1
1
1
0
0
1
1
0
0
1
1
1
1
0
2
1
1
2
1
1
0
1
0
1
1
2
1
0
1
1
0
2
1
1
2
1
1
1
1
2
1
1
2
1
1
1
2
0
2
1
1
2
0
0
0
1
1
1
2
1
1
0
1
2
0
1
2
1
0
1
0
1
1
2
1
2
2
1
0
1
1
2
1
4
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
2
1
1
1
2
2
1
1
2
1
2
1
1
1
0
1
1
0
2
1
2
1
1
2
2
1
1
0
1
1
2
0
2
2
0
0
2
1
0
1
0
1
2
1
0
2
1
2
1
0
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
2
1
2
1
1
1
2
1
0
1
2
1
2
2
1
1
2
2
1
2
2
2
2
1
0
1
1
0
1
2
1
0
2
1
1
1
0
1
1
1
2
2
1
1
1
1
1
1
1
1
0
0
2
2
2
1
1
1
0
1
0
1
1
1
2
1
1
0
2
0
0
1
0
1
1
1
0
1
1
2
0
2
1
1
2
1
1
1
2
1
0
1
1
2
1
2
1
1
1
1
1
0
0
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
2
2
1
1
0
2
1
2
1
1
2
1
1
0
0
1
1
0
2
2
1
1
2
1
2
1
2
0
1
1
1
1
0
1
0
2
1
1
1
1
2
1
2
1
0
2
0
1
1
1
1
2
1
0
2
0
1
1
2
0
0
2
1
1
2
2
2
1
1
1
1
1
1
1
0
1
1
1
1
1
1
2
1
2
2
0
1
1
0
1
1
1
2
2
2
1
0
1
1
2
1
1
0
1
2
1
1
1
1
1
1
0
2
1
1
1
0
1
2
1
1
1
1
1
2
1
0
1
0
1
0
0
1
1
1
2
1
1
1
1
1
2
2
1
1
1
1
2
1
1
1
2
1
0
1
1
0
1
2
0
1
2
1
2
2
1
2
1
1
1
2
1
0
1
1
1
1
1
1
1
1
1
1
2
1
0
1
1
0
2
1
1
0
0
1
1
1
1
1
1
2
0
1
1
1
2
1
1
1
1
2
1
2
1
1
1
0
1
1
2
1
1
1
1
1
2
1
1
2
1
1
1
0
1
1
0
1
1
0
2
1
1
1
1
2
2
0
1
1
1
1
1
1
1
1
0
1
1
2
1
1
1
1
1
1
0
1
0
0
2
1
2
1
1
1
1
0
0
2
1
1
2
2
1
2
0
1
1
1
1
1
1
1
1
1
1
2
0
1
1
2
1
1
0
0
1
1
1
1
1
2
4
2
1
1
1
2
1
2
1
2
0
1
1
1
1
2
1
2
2
1
1
2
1
1
1
0
2
2
1
0
1
1
2
1
1
1
1
1
1
2
1
1
0
2
1
2
1
1
0
1
2
1
2
1
2
1
1
1
2
0
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
2
1
1
1
2
1
1
2
2
1
1
1
1
1
0
1
2
1
1
1
2
0
2
2
1
1
1
2
1
2
1
1
0
1
2
1
1
1
1
1
1
0
1
1
0
1
1
1
1
1
1
1
0
2
2
1
0
2
1
1
2
0
0
0
1
1
2
1
1
1
1
2
1
1
1
1
1
1
2
1
2
0
1
0
1
1
1
1
2
1
1
2
2
1
1
0
1
0
1
1
1
0
1
1
1
1
1
1
0
1
1
1
2
1
1
2
2
2
2
1
1
1
1
1
2
1
1
2
1
2
2
1
2
1
1
1
1
1
1
1
2
2
2
2
1
1
1
2
0
1
1
1
2
1
2
0
1
1
1
1
1
2
1
1
1
1
1
1
0
1
2
1
1
1
1
2
1
2
2
1
1
1
1
3
2
1
0
2
1
1
1
1
2
2
1
0
1
0
2
2
2
1
1
1
0
1
1
1
0
2
2
1
1
2
1
1
2
2
1
1
2
1
2
1
2
1
0
0
2
1
1
1
2
1
2
2
2
0
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
2
2
0
1
1
1
1
2
2
1
1
1
1
3
1
1
1
1
1
1
1
2
2
0
2
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
0
0
1
0
1
2
2
1
1
2
2
2
1
0
2
2
1
2
0
1
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
2
0
1
2
1
0
2
1
1
0
1
0
1
1
2
1
1
2
1
1
0
1
1
1
1
1
0
0
2
1
1
1
1
1
1
2
7
1
1
1
1
0
1
2
1
1
1
1
1
0
2
1
2
1
1
1
0
1
2
2
1
2
0
1
2
1
1
1
1
1
1
2
1
1
0
0
2
1
2
1
1
0
0
1
2
2
0
1
1
1
2
1
1
3
1
1
1
1
1
0
0
1
0
1
1
2
0
2
1
2
0
1
1
1
1
2
2
2
1
2
0
1
1
1
1
0
1
0
2
2
1
0
1
0
1
1
2
1
1
1
2
1
1
0
1
1
0
0
1
1
1
2
2
1
1
2
1
2
1
0
1
2
1
0
1
2
1
1
0
1
2
1
1
2
1
1
1
1
2
1
2
2
1
1
0
1
1
1
1
2
1
1
2
2
2
1
1
1
1
1
2
1
1
1
1
2
1
0
1
1
2
1
0
1
1
1
1
1
2
2
1
1
2
1
2
1
1
1
2
0
1
1
1
1
2
1
1
2
1
0
2
1
1
2
1
1
1
1
2
1
1
1
0
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
0
1
1
1
1
0
1
0
1
2
2
0
2
1
2
1
1
2
2
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
2
2
2
1
2
2
1
2
2
0
2
1
2
1
2
1
1
2
2
1
0
2
2
2
1
1
2
1
1
1
1
1
1
1
1
0
2
1
2
1
2
1
1
1
1
2
1
0
1
0
1
1
1
2
1
1
1
1
1
1
1
2
1
1
2
0
2
1
0
1
3
1
1
1
1
1
1
1
1
1
2
0
0
1
2
1
2
1
2
1
1
1
2
1
0
1
1
10
1
0
1
1
2
1
2
1
1
1
0
2
0
2
1
1
1
0
1
2
1
1
0
2
0
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
1
2
1
1
2
1
1
1
2
2
1
1
0
2
1
1
2
0
0
1
1
0
1
1
1
1
1
2
1
2
2
1
2
1
2
2
1
1
2
1
2
0
1
1
1
1
0
1
2
2
2
2
2
1
0
0
1
2
1
1
1
2
2
1
0
1
2
1
1
1
0
3
0
1
1
1
1
0
2
1
2
1
1
1
1
1
2
2
2
0
2
1
2
2
1
1
1
1
1
1
0
1
1
1
1
1
1
2
2
1
1
2
1
2
1
1
2
1
0
1
1
2
2
2
1
0
2
2
1
1
1
2
1
0
0
1
1
1
1
1
1
1
1
2
1
2
2
2
0
1
1
0
1
1
1
1
2
2
0
1
1
2
2
0
1
1
1
1
1
1
1
0
1
2
1
1
1
1
2
2
1
1
1
1
2
0
1
1
1
1
2
1
1
0
1
0
2
2
0
2
1
1
1
1
0
1
0
0
2
1
2
1
1
1
2
1
1
1
2
1
2
0
1
2
1
0
0
1
1
1
1
2
1
2
1
1
1
1
2
2
2
1
1
1
1
1
1
1
2
1
1
1
0
1
1
0
1
1
2
0
2
2
1
1
2
1
0
1
0
0
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
2
1
1
2
1
1
2
2
1
1
0
2
0
2
1
2
1
0
2
1
1
2
0
1
2
2
1
0
2
1
1
1
2
1
2
1
1
1
1
1
1
0
1
0
1
2
1
2
2
1
1
0
1
1
0
2
1
1
1
0
0
2
1
1
0
1
1
1
1
2
0
2
0
1
0
2
1
1
1
2
1
1
2
1
1
2
1
0
1
2
0
2
2
1
1
1
1
1
0
1
1
1
0
2
2
1
0
0
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
0
1
0
1
1
1
2
1
2
1
0
1
1
1
2
1
2
2
2
1
1
1
2
1
2
1
1
1
1
0
1
1
1
0
1
1
2
2
1
2
1
1
1
1
1
0
1
1
1
2
2
1
1
1
1
2
1
1
2
1
1
2
2
2
1
1
2
2
2
1
0
0
2
1
2
1
1
2
1
1
2
2
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
1
1
2
1
0
2
1
1
0
1
1
2
1
1
1
1
0
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
0
2
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
2
2
1
2
2
1
0
1
2
1
1
2
1
0
1
1
1
1
1
1
2
1
0
1
2
1
0
1
1
1
2
2
2
1
1
1
1
1
1
1
1
0
1
1
2
2
2
1
1
0
2
1
1
2
1
2
0
1
1
2
1
1
2
1
0
1
1
0
0
2
1
2
2
2
1
1
2
1
1
1
1
1
1
2
1
2
1
1
2
2
1
1
1
1
0
1
2
2
0
1
1
1
1
0
1
2
0
1
1
1
1
1
1
1
2
1
1
2
2
1
1
1
1
2
0
1
1
1
1
2
2
1
1
2
1
1
1
1
1
2
2
1
2
1
0
1
2
2
1
1
2
1
2
1
1
2
1
1
2
1
1
2
1
1
0
1
1
1
2
0
1
4
2
2
1
1
2
1
1
1
1
2
1
1
1
2
0
1
2
1
1
2
2
1
1
1
0
1
1
1
1
1
2
2
0
0
0
1
1
2
1
1
1
1
0
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
4
2
0
2
1
0
1
1
2
2
1
1
0
2
2
1
1
2
1
1
0
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
0
1
1
2
0
1
1
1
2
1
1
2
1
1
0
1
1
1
1
1
1
1
1
1
3
1
1
1
1
1
1
2
1
1
1
1
1
2
0
0
1
1
1
1
1
2
1
2
1
2
0
1
0
1
1
1
1
2
1
2
0
1
1
1
0
1
2
1
0
1
2
1
2
1
2
1
1
0
1
1
1
3
2
2
2
1
1
1
2
1
0
0
1
2
2
1
0
1
1
1
1
2
2
1
1
1
1
2
1
1
2
1
1
1
2
2
1
1
1
1
1
1
2
2
2
0
1
1
1
2
1
1
1
0
2
1
1
1
0
1
1
1
2
1
1
0
0
2
2
1
2
1
1
0
1
1
0
1
0
1
1
2
1
1
1
0
1
0
1
1
2
1
1
0
2
2
1
1
0
2
1
1
1
0
1
1
2
0
1
1
0
1
1
2
1
2
1
1
0
1
1
1
0
2
1
2
1
2
1
1
1
1
1
1
2
1
0
2
1
1
0
1
1
1
2
2
0
0
0
1
2
1
1
1
1
2
1
1
1
1
1
1
2
1
0
1
1
2
2
1
1
1
1
0
1
0
1
1
2
2
2
1
1
2
1
1
1
1
1
1
1
1
0
1
0
1
1
1
2
0
2
1
0
2
1
1
1
1
1
1
1
1
2
1
2
1
0
1
1
2
2
0
1
0
1
0
1
1
1
2
1
1
1
1
1
2
2
0
1
1
1
2
2
1
0
1
0
2
1
0
2
1
1
1
0
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
1
0
0
2
2
0
1
1
1
0
1
1
0
1
2
1
1
1
1
1
1
2
1
1
1
0
1
2
2
2
1
2
1
1
1
1
1
1
1
3
1
1
1
2
2
2
1
1
2
1
1
0
1
2
2
1
2
3
2
1
2
1
1
2
2
1
2
1
1
1
1
1
1
2
1
1
2
1
1
0
0
2
1
1
1
2
1
2
1
1
2
0
2
1
1
0
1
2
1
2
1
0
1
2
1
1
1
1
0
0
2
1
2
1
2
1
2
2
1
1
2
1
1
0
1
1
1
1
0
1
2
2
2
0
1
1
2
1
1
1
1
1
7
1
1
2
1
1
1
1
1
2
1
1
1
0
1
1
1
0
1
0
1
0
1
0
2
1
1
1
1
2
2
2
0
2
0
0
1
1
1
2
2
1
2
2
1
2
0
2
2
1
2
2
1
0
2
1
1
1
0
0
3
1
1
0
0
1
2
2
1
0
1
0
1
1
2
1
2
2
2
1
1
2
1
1
1
2
2
1
1
0
0
1
0
1
2
1
0
2
1
2
1
1
2
1
1
1
1
0
1
1
1
1
1
1
0
1
2
1
1
1
1
2
1
1
1
0
1
1
0
1
1
1
0
2
1
1
0
1
2
2
1
0
2
1
0
2
2
1
2
2
1
2
0
1
2
1
1
1
2
1
1
2
1
1
0
1
0
0
1
1
1
2
2
1
1
1
2
1
0
1
2
1
1
2
1
1
1
1
2
1
2
1
2
1
1
2
1
1
1
0
1
1
2
2
1
1
2
2
2
1
0
1
1
2
1
2
1
1
1
0
2
2
1
2
1
1
1
1
1
2
1
1
1
0
1
0
1
1
1
0
2
1
0
1
0
0
2
1
1
1
1
1
1
0
3
1
1
1
2
0
1
3
2
2
1
1
2
1
1
1
1
0
1
0
0
1
1
0
1
2
2
2
1
1
1
1
2
1
2
1
1
1
2
2
2
1
0
2
1
1
2
1
1
2
1
0
2
1
1
1
0
2
1
1
1
0
1
0
1
0
2
1
1
2
1
2
2
2
3
1
0
1
2
2
1
2
1
0
1
0
1
2
2
1
1
2
1
1
2
1
1
2
1
0
0
1
1
1
1
2
2
1
2
1
0
2
2
2
0
0
1
1
0
0
2
2
2
1
2
1
0
1
2
1
2
0
3
1
0
0
1
1
1
1
2
1
1
1
1
2
1
1
1
2
2
2
2
1
1
1
1
0
2
0
1
2
1
2
0
1
1
0
0
1
1
1
1
1
1
1
1
1
2
2
1
1
2
0
1
1
2
2
1
2
1
1
2
2
1
2
0
1
1
1
1
1
2
1
1
2
1
1
1
1
0
1
2
1
1
1
1
2
1
0
1
1
1
0
1
1
0
2
0
2
1
1
1
0
1
0
1
0
1
2
0
0
0
1
1
1
2
1
1
1
1
1
2
1
1
1
0
1
1
0
0
0
2
1
1
1
1
2
2
1
1
0
1
1
1
2
2
1
0
1
2
2
2
2
1
1
1
1
1
2
2
1
1
1
2
1
2
2
2
1
0
2
1
0
3
2
2
1
1
1
1
0
1
2
1
0
1
1
1
1
0
0
0
2
1
1
0
1
1
1
1
1
0
0
2
1
1
0
2
2
1
1
1
1
1
0
1
2
1
1
1
2
1
1
1
0
1
1
1
0
1
2
1
1
1
1
2
1
1
2
2
2
2
1
1
2
1
1
1
1
1
0
2
1
1
1
2
2
2
1
1
1
1
2
1
1
2
2
1
1
1
0
1
1
3
1
1
1
1
1
2
1
1
1
0
0
2
0
2
2
1
2
2
0
1
3
2
2
1
1
1
1
1
2
2
4
1
1
1
2
2
1
1
2
1
1
1
1
2
1
0
1
2
2
1
1
2
2
2
0
1
2
1
0
1
1
1
1
1
2
1
1
1
3
1
1
1
1
2
2
2
1
1
1
1
1
2
2
2
1
1
1
2
2
0
1
2
0
1
2
1
2
0
1
1
1
2
0
1
0
2
1
1
2
2
0
1
1
2
2
1
1
2
1
1
1
1
0
1
1
2
2
1
1
1
2
0
1
2
1
2
2
0
1
1
1
1
1
2
1
1
0
1
1
0
3
0
2
1
2
1
1
2
1
1
1
1
1
1
0
1
1
1
2
2
1
1
1
1
1
2
1
0
1
1
1
2
3
1
0
1
1
1
1
1
1
1
0
2
0
1
1
1
1
2
1
1
0
1
1
1
1
2
2
1
1
1
2
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
0
1
1
2
1
2
1
2
1
2
1
1
0
0
1
1
1
1
1
1
2
2
2
1
0
1
2
1
0
1
1
1
2
0
1
1
1
1
2
2
2
1
1
0
0
1
2
2
2
0
1
0
1
1
1
1
1
2
1
0
1
2
1
1
2
2
0
0
1
1
1
1
1
1
2
1
0
1
1
1
1
2
1
1
0
2
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
2
1
2
1
2
2
1
2
0
1
0
0
1
0
1
1
1
1
1
1
1
2
1
1
2
4
1
2
2
1
1
1
1
1
0
2
2
2
1
2
1
0
1
2
1
1
1
0
1
1
2
1
1
2
1
0
1
0
0
1
0
1
0
1
1
1
1
1
2
1
1
1
2
2
2
0
2
1
0
1
2
1
2
1
1
1
1
2
0
2
0
1
1
2
2
0
1
1
1
0
1
1
1
1
2
0
1
1
2
1
2
1
2
2
1
1
1
1
1
1
1
2
1
2
1
1
0
0
2
1
1
1
1
2
2
1
2
0
0
1
1
1
1
2
0
0
2
2
1
1
2
0
2
1
1
2
2
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
1
1
2
1
1
2
0
0
2
1
1
2
1
1
1
1
2
1
1
1
0
1
1
1
1
2
1
0
1
1
1
1
0
2
0
1
2
1
1
1
3
2
1
1
1
1
2
1
1
1
2
2
2
1
5
2
1
1
2
1
1
1
1
2
1
2
2
2
2
2
0
1
1
1
2
2
0
2
1
1
2
0
1
1
2
1
1
2
1
2
0
2
0
1
1
2
1
0
1
1
1
1
2
0
1
1
1
1
2
1
1
2
1
1
1
1
1
1
0
2
1
0
1
1
0
1
1
1
1
1
0
2
1
2
2
1
0
1
1
1
1
2
1
1
1
2
1
2
2
1
1
1
1
2
1
1
1
1
1
2
1
3
2
0
0
1
1
0
2
1
2
1
1
1
1
0
2
1
2
0
1
1
2
1
1
2
2
2
1
0
1
1
0
2
2
1
2
1
3
1
0
1
2
1
1
2
2
0
1
1
1
1
1
1
2
0
1
0
2
1
0
0
1
1
2
1
1
1
0
1
1
2
1
0
1
1
0
2
1
1
1
1
1
2
1
1
1
2
2
1
0
1
1
2
1
1
1
1
2
2
1
1
0
2
1
1
1
0
1
1
1
0
1
2
1
1
2
2
1
1
2
0
1
1
0
1
1
1
2
2
1
1
2
2
2
2
2
1
1
0
0
1
2
1
1
1
1
0
2
0
1
0
0
1
1
1
2
2
1
1
2
0
1
1
1
1
1
1
2
1
1
1
0
1
0
1
1
1
0
1
2
2
2
1
1
1
1
1
1
2
1
1
1
2
0
1
1
1
2
1
1
0
2
0
0
2
1
2
0
0
0
1
2
1
2
1
1
2
1
1
0
1
1
1
1
1
1
1
1
2
0
1
2
2
1
2
1
0
1
2
0
2
2
1
2
1
2
1
1
1
2
1
2
2
2
2
1
0
1
1
1
1
1
1
1
1
2
1
0
1
1
1
1
1
1
1
1
1
0
2
1
1
1
0
1
2
2
1
2
1
0
1
2
2
2
0
2
1
1
1
1
1
1
1
2
2
2
1
2
2
0
2
1
1
1
2
1
1
2
1
2
2
1
2
1
0
1
1
0
1
2
2
2
2
1
1
2
1
3
1
1
1
1
0
1
1
1
1
1
1
2
2
1
1
1
1
1
3
1
0
1
0
0
2
1
2
2
1
1
1
2
2
2
0
2
0
2
1
1
1
2
2
1
1
0
1
1
1
0
1
2
2
2
2
2
1
1
1
1
2
1
1
2
1
1
2
1
2
2
2
1
2
2
1
1
1
1
2
1
1
2
1
0
2
1
1
0
0
2
2
2
0
2
0
1
1
0
0
1
2
1
1
2
2
0
0
0
2
1
2
1
1
1
0
1
2
1
2
0
2
1
1
0
2
1
2
1
1
2
1
0
2
2
1
0
0
1
1
0
1
1
1
0
1
2
1
0
1
1
1
1
2
1
1
1
2
1
1
1
2
1
1
0
2
0
1
0
2
1
1
1
1
2
0
1
2
1
0
2
1
1
1
0
2
1
2
1
0
2
2
2
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
2
1
0
2
1
1
1
1
2
0
0
2
1
2
2
1
2
2
1
0
0
1
1
2
0
1
1
1
2
0
1
0
1
1
2
2
0
1
1
1
1
2
1
1
2
2
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
0
2
1
2
1
2
1
1
1
1
1
0
0
2
2
1
1
1
1
0
1
1
0
1
2
1
1
1
1
0
1
1
2
1
1
0
0
1
1
1
0
1
1
1
1
2
2
0
1
1
1
2
2
0
2
0
2
2
2
0
1
1
1
1
2
2
1
2
0
2
1
1
0
1
1
1
2
1
0
1
1
0
2
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
0
2
2
2
1
1
1
1
1
1
1
1
2
1
1
2
1
0
1
3
1
2
1
3
0
1
1
2
1
1
2
1
2
0
1
1
1
1
2
2
2
1
1
1
1
2
2
2
2
1
2
1
2
1
1
0
1
1
1
1
1
1
0
2
1
2
1
0
1
1
1
1
2
1
1
2
1
1
2
1
1
1
0
1
2
1
1
2
2
1
0
1
0
1
2
0
2
1
1
1
2
1
2
1
1
0
0
2
1
2
1
2
1
1
0
1
1
2
1
1
1
1
2
1
1
2
1
2
0
1
1
2
1
2
0
2
2
1
1
1
1
0
1
1
2
2
1
0
2
2
1
2
1
2
2
1
0
1
1
0
1
1
0
1
2
1
1
2
1
1
1
2
2
1
1
1
1
1
0
0
1
1
1
1
1
0
4
1
1
2
0
2
1
1
0
2
1
1
1
1
1
0
1
2
1
1
1
1
1
0
0
0
1
1
1
1
1
0
2
2
1
2
2
2
2
1
1
1
2
1
2
2
1
1
2
2
0
1
1
1
2
1
1
2
2
1
1
2
1
1
0
1
1
1
2
1
1
1
2
1
1
2
0
1
1
2
1
1
0
1
2
2
1
1
2
1
0
2
2
0
1
1
1
2
2
2
1
1
0
2
2
1
2
1
2
2
1
1
1
2
1
1
2
1
2
2
1
1
2
1
1
1
1
1
2
1
1
0
2
2
1
2
2
1
1
1
1
0
0
0
1
1
1
1
2
0
2
1
0
1
1
1
2
1
1
0
2
1
2
2
1
0
2
1
1
1
0
1
1
2
2
1
2
2
1
1
1
1
2
2
0
1
1
1
1
2
1
3
1
1
2
2
2
1
1
1
1
1
0
1
2
1
2
2
1
2
1
1
1
1
1
1
1
0
2
1
0
2
1
1
1
0
2
2
0
1
0
0
2
1
1
2
2
2
2
1
2
2
1
1
2
1
1
0
2
1
2
2
1
1
1
2
1
1
0
1
1
2
0
1
2
1
2
1
1
0
1
1
0
2
0
1
1
1
0
1
0
1
1
1
1
1
0
2
1
1
1
1
1
1
1
0
1
0
1
2
1
0
1
2
2
0
0
1
0
0
0
2
1
1
2
1
1
1
1
1
2
0
2
1
1
1
1
2
5
0
2
2
1
1
1
2
1
0
1
1
2
1
1
2
1
1
1
1
1
1
0
1
2
1
0
0
1
1
2
1
1
1
1
0
1
2
1
1
1
0
2
1
1
1
2
1
1
2
2
1
2
1
2
3
1
1
1
1
2
1
1
1
2
1
1
4
2
2
2
1
1
0
1
1
1
1
1
1
1
1
1
1
2
2
1
2
1
1
1
1
2
1
1
1
1
1
1
0
1
1
2
1
0
0
2
1
3
0
1
0
1
1
1
1
1
0
2
1
1
1
1
1
2
1
1
0
1
0
2
1
1
0
0
0
0
1
1
0
2
1
2
1
2
1
2
1
0
2
2
1
1
1
1
1
0
2
1
1
1
2
0
1
0
1
1
0
2
1
1
2
2
2
0
4
1
1
2
1
0
1
2
1
0
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
1
0
1
2
0
1
2
1
0
1
0
1
2
1
2
2
1
1
2
1
1
1
2
1
1
1
1
0
1
1
2
2
1
2
1
2
0
1
2
2
1
0
0
0
1
2
1
0
1
1
1
1
0
1
1
1
1
2
2
1
2
1
0
1
0
1
0
2
1
2
0
1
0
3
1
2
0
1
0
2
1
1
1
0
1
2
1
2
0
1
1
1
3
1
0
0
1
0
1
1
2
2
0
1
0
1
1
0
0
1
1
0
1
0
2
1
0
1
2
3
1
2
0
1
2
1
2
1
2
1
3
1
0
2
1
2
1
2
0
2
1
1
1
2
0
1
1
2
0
1
1
1
0
1
1
2
1
1
0
1
1
0
1
1
2
1
1
0
1
2
3
1
0
1
1
1
1
1
1
2
1
2
2
0
2
1
1
1
2
1
1
1
2
1
1
1
1
1
1
0
1
2
1
3
2
1
2
0
1
1
1
1
1
1
1
1
1
2
2
1
2
1
2
0
1
1
1
1
1
2
0
1
1
1
0
1
2
1
2
2
1
1
1
2
0
1
1
1
2
1
2
1
1
1
1
2
2
1
3
1
1
1
2
2
1
1
1
1
1
2
2
1
1
2
1
1
1
1
1
0
1
1
2
2
2
1
1
1
0
1
2
1
1
2
0
1
2
0
2
2
0
0
1
2
1
1
2
2
2
2
2
2
2
2
0
1
1
0
0
1
1
1
1
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
0
1
1
0
1
3
3
1
2
2
1
2
2
2
0
0
0
1
1
1
1
1
0
1
1
1
1
0
1
1
1
7
1
1
1
1
1
1
1
1
2
1
1
2
1
1
2
1
2
1
1
2
2
2
2
1
1
1
2
1
1
1
1
2
0
1
2
1
1
1
1
1
1
0
2
2
1
2
2
1
1
1
1
2
1
2
1
1
1
1
2
0
1
0
0
1
1
1
1
1
1
1
1
0
2
2
1
1
1
1
1
2
1
1
2
2
1
3
1
1
1
2
1
2
1
0
2
2
0
2
2
1
0
0
1
1
2
0
0
2
1
1
1
2
2
1
1
1
1
1
1
0
1
1
0
2
2
1
1
1
2
2
0
0
2
2
1
1
1
1
0
0
1
1
2
1
1
0
1
1
1
2
0
1
1
2
2
1
1
2
1
1
1
1
0
0
1
1
2
1
2
1
0
1
1
0
1
1
1
1
2
2
0
2
1
1
1
1
1
1
2
1
1
1
1
0
1
1
1
0
1
0
1
0
1
2
0
0
1
1
1
1
0
1
1
1
2
1
2
2
6
1
1
1
1
0
2
2
1
1
1
2
1
0
2
1
2
0
1
1
2
1
1
1
1
2
1
1
1
1
1
0
2
1
1
0
1
1
1
0
0
1
2
2
0
2
1
1
1
1
1
2
1
0
2
1
1
1
1
0
2
1
1
1
1
2
1
2
1
0
1
1
1
1
4
1
0
1
2
1
1
2
2
1
1
1
1
1
2
1
1
1
1
1
1
1
0
1
2
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
2
2
2
0
2
0
1
1
1
1
0
2
1
2
0
0
1
1
0
1
1
1
1
1
2
2
0
0
0
1
1
2
0
1
2
1
1
2
1
2
1
2
1
1
0
2
1
1
1
0
1
1
2
0
0
1
1
1
0
0
1
1
2
1
1
2
1
2
0
1
1
1
2
1
2
1
0
2
1
2
0
0
0
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
0
1
1
1
3
1
1
1
1
0
1
1
1
1
2
1
2
1
2
1
2
1
1
2
0
1
1
2
1
2
1
1
1
2
1
2
1
1
1
1
2
1
0
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
0
1
1
0
1
1
1
1
1
2
1
2
1
2
0
1
1
1
1
4
1
0
1
2
1
2
1
1
1
2
1
0
1
3
1
1
1
0
2
1
1
1
1
1
2
0
1
2
1
1
2
0
2
1
0
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
1
0
1
2
1
0
2
1
2
1
1
1
1
2
1
1
1
2
2
1
0
1
1
2
2
2
1
1
2
1
1
1
2
2
1
1
1
1
1
0
1
1
2
1
2
2
2
1
2
1
3
0
2
2
2
1
1
2
1
2
0
1
2
1
1
1
0
1
0
0
1
2
1
2
2
1
1
1
1
0
2
0
1
2
2
1
1
0
1
0
0
1
1
1
1
1
1
2
1
2
1
1
1
0
2
0
1
0
2
1
1
1
2
1
0
2
0
2
0
1
0
2
1
1
1
1
2
1
2
0
1
1
0
1
1
2
1
2
2
0
1
2
1
2
1
1
2
1
0
1
0
0
1
1
1
1
1
1
1
0
2
1
1
2
0
2
1
0
1
0
1
2
2
0
1
1
2
2
2
0
1
0
1
1
1
2
1
0
1
2
1
1
0
2
1
1
0
1
1
2
1
1
1
1
1
1
0
1
1
2
1
2
1
1
1
1
3
2
1
0
2
0
1
1
2
2
1
1
2
0
2
0
2
2
2
0
2
1
1
1
0
2
2
1
1
2
1
1
1
0
2
1
2
2
2
2
1
2
2
1
1
0
1
1
1
1
1
2
0
1
1
1
0
1
1
2
0
1
1
1
1
1
2
1
1
1
0
1
1
0
2
1
1
1
1
1
1
2
1
2
2
3
2
1
1
2
1
1
2
1
1
1
1
1
2
1
1
1
1
0
1
1
2
2
1
1
2
0
1
2
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
0
2
0
2
0
1
2
0
2
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
0
0
1
2
1
0
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
0
0
0
1
2
1
1
1
1
2
2
1
1
1
1
1
1
1
0
1
2
1
2
2
1
1
1
1
2
1
1
1
2
2
0
2
2
2
2
1
0
1
1
1
0
2
1
1
1
2
1
2
2
1
1
1
1
2
1
0
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
2
1
1
1
1
1
1
1
0
1
2
1
2
0
1
1
2
2
2
1
2
1
1
0
1
2
1
0
0
0
1
1
1
1
0
2
2
1
1
0
1
2
1
1
1
1
1
1
2
2
1
1
2
1
1
2
0
2
1
1
0
2
2
1
0
1
1
1
1
1
0
1
1
1
2
2
1
1
1
1
1
0
1
1
2
1
1
0
1
1
1
1
1
1
0
1
1
2
1
1
2
1
2
1
1
2
1
1
0
1
2
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
0
1
1
1
1
2
3
2
5
1
1
1
1
1
1
1
0
0
4
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
0
0
2
1
1
1
1
1
2
2
0
2
2
1
2
1
1
2
0
2
2
0
0
2
1
1
1
1
2
1
1
1
1
2
2
1
1
1
2
3
1
1
2
1
1
1
1
1
0
1
1
2
1
0
1
1
1
0
2
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
2
1
2
1
1
2
1
1
1
2
1
1
1
2
1
1
0
2
1
0
1
1
2
1
2
2
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
2
1
1
1
2
2
1
1
2
1
2
2
1
2
1
1
1
1
1
2
2
1
0
0
1
1
2
1
0
2
2
2
1
2
2
1
1
2
1
1
1
1
2
0
2
1
1
2
1
2
0
0
0
1
1
1
2
2
1
1
2
1
1
1
1
2
1
0
1
1
1
1
1
0
2
1
1
1
2
2
0
1
1
0
3
1
2
1
1
1
2
2
1
0
1
2
1
1
1
1
1
2
1
1
0
2
1
2
1
1
1
2
1
2
2
1
1
0
1
2
1
2
1
1
0
2
1
2
1
1
1
1
2
1
1
1
2
1
1
1
2
2
1
2
1
0
0
0
1
0
1
1
1
1
1
1
1
0
2
1
1
2
1
1
2
1
2
1
1
1
1
1
0
1
1
1
1
1
2
1
1
1
0
1
2
0
1
1
2
2
0
1
1
1
0
1
0
1
1
1
1
2
1
0
1
0
1
1
1
1
0
1
1
2
1
1
1
1
2
1
0
2
0
2
1
2
1
1
0
2
1
1
2
1
1
0
0
2
2
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
2
1
1
1
2
1
0
2
1
1
3
1
2
2
1
1
1
0
1
0
2
1
2
1
1
1
2
1
1
1
1
2
2
1
2
2
0
1
0
1
0
1
1
1
0
2
2
1
1
2
1
1
2
2
0
2
0
1
1
1
1
1
1
0
2
1
0
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
0
1
2
1
1
1
2
1
1
0
0
2
2
2
1
1
0
1
1
1
1
0
2
1
1
1
0
0
1
1
1
0
1
1
0
1
1
1
0
1
0
1
1
0
2
0
2
1
2
2
2
1
0
0
1
1
1
2
2
1
1
1
1
1
0
1
1
2
0
2
1
2
1
1
2
2
1
1
2
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
2
2
2
1
1
0
1
1
1
1
1
1
2
0
1
1
1
1
2
1
1
2
1
2
2
2
1
2
1
1
2
1
0
1
2
1
2
4
1
1
2
1
2
1
2
1
1
0
1
2
0
0
2
1
1
1
2
1
1
1
1
1
0
0
2
1
1
1
2
2
1
2
1
1
0
1
1
1
1
2
2
2
1
1
0
2
1
1
1
1
2
2
2
1
1
2
1
1
2
2
1
1
0
2
1
1
1
2
1
1
2
2
0
1
2
2
0
1
1
2
2
1
1
2
1
2
1
1
1
0
1
1
0
1
1
1
1
1
1
1
2
3
1
1
1
1
1
1
3
0
1
1
0
0
0
1
1
1
1
1
1
1
1
1
0
1
2
1
1
1
0
0
1
2
1
2
1
1
1
1
1
0
0
1
0
1
2
0
2
1
1
2
1
1
0
1
2
2
1
2
1
2
2
2
1
0
1
0
2
1
1
0
2
1
1
1
1
1
1
1
1
1
0
1
2
1
2
2
2
1
1
0
1
0
2
2
1
1
2
0
0
2
1
1
2
2
1
1
2
1
1
1
1
2
2
1
1
1
2
1
1
1
1
1
2
2
1
1
2
2
0
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
2
1
1
1
0
1
1
1
1
1
1
1
2
1
1
2
2
1
1
1
2
1
1
2
2
0
2
1
0
1
1
1
0
2
2
1
1
0
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
4
1
1
1
2
1
1
1
2
1
1
2
2
2
1
1
0
1
1
1
2
1
2
1
0
1
0
2
2
1
2
2
1
0
1
1
1
1
1
1
1
2
0
1
1
5
2
1
1
1
1
1
1
1
2
2
1
1
1
1
0
1
2
2
1
0
3
1
1
2
0
2
2
2
1
0
1
1
2
1
0
2
1
2
0
2
0
1
1
1
1
1
2
0
1
2
1
2
2
2
1
1
2
1
1
1
1
1
0
1
2
1
1
2
2
2
0
1
2
2
1
1
0
1
1
0
2
2
1
1
3
1
1
2
1
1
2
1
0
0
1
2
0
1
1
1
2
2
1
1
3
1
1
1
0
1
1
0
2
1
2
1
2
2
1
1
1
0
1
2
1
1
1
2
0
1
1
1
2
1
0
1
2
2
1
1
1
1
1
1
1
2
0
1
0
1
1
0
2
1
1
1
0
1
0
1
1
2
1
1
1
1
1
1
1
1
1
2
1
0
2
1
0
2
2
2
1
1
1
0
1
1
1
1
2
1
1
2
1
1
0
0
0
2
2
1
1
1
2
1
2
1
0
1
1
1
2
1
0
1
0
1
0
1
2
1
1
1
1
2
1
1
1
1
1
1
2
0
0
0
1
1
0
2
5
1
1
1
1
1
0
0
1
2
2
1
0
2
2
1
1
0
1
1
1
1
2
2
1
0
1
2
1
2
1
0
2
2
1
2
1
0
1
2
1
1
1
2
1
1
0
1
1
0
1
2
1
0
2
1
1
1
0
2
1
0
0
2
1
1
1
1
1
2
1
2
2
1
1
1
1
1
1
0
1
1
1
0
1
1
1
2
1
2
2
2
1
2
1
1
2
2
2
2
1
2
1
1
1
0
1
0
0
1
1
1
1
1
1
1
1
0
0
1
1
2
1
2
1
1
3
2
2
2
2
0
1
1
2
2
0
1
2
1
1
2
2
0
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
2
1
0
1
1
1
0
1
0
1
2
1
2
1
1
1
1
2
2
2
1
1
0
1
1
1
1
0
2
1
1
0
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
2
1
2
1
0
1
1
1
1
2
1
1
0
0
0
1
1
1
1
1
2
2
0
1
1
2
1
1
3
1
1
1
2
0
1
1
1
1
1
0
1
0
2
1
1
2
0
1
0
2
2
1
1
1
1
2
1
2
1
1
1
1
2
1
2
1
1
1
1
2
1
1
2
1
0
1
1
2
1
2
1
2
1
1
1
0
1
2
1
0
2
1
0
1
1
1
2
1
0
2
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
2
1
1
2
1
1
1
1
2
1
1
1
0
0
0
1
0
2
1
1
1
1
1
0
1
0
1
2
1
1
2
0
2
1
1
1
1
1
1
1
2
0
0
2
1
0
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
0
1
1
2
1
1
2
0
2
0
1
1
1
1
1
2
1
0
1
1
2
2
1
1
2
2
0
2
2
1
1
2
2
1
1
1
2
3
1
1
1
1
1
1
1
0
2
1
1
2
1
1
1
0
0
2
1
0
1
1
1
1
1
1
2
1
2
0
2
1
1
1
2
2
1
2
1
1
2
0
1
1
1
1
0
0
2
0
0
2
1
0
2
2
1
2
1
1
1
2
2
1
2
1
0
1
1
2
1
0
2
1
0
1
1
1
1
1
1
1
1
2
0
1
2
2
1
1
1
2
1
2
0
1
2
2
2
2
1
2
1
1
2
1
2
1
2
1
1
1
1
1
2
0
1
1
0
1
2
1
1
1
1
1
1
2
1
1
0
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
2
0
2
1
0
1
2
1
1
0
0
1
2
1
1
0
2
1
2
1
2
1
1
1
1
0
0
1
1
0
2
2
1
2
1
1
2
1
2
1
2
2
1
1
1
2
1
2
1
1
2
2
1
2
1
0
1
1
2
2
1
2
1
2
1
1
1
2
2
1
0
1
1
1
1
1
1
2
1
1
1
2
1
1
0
1
1
1
1
1
2
0
0
1
0
2
1
1
2
1
0
2
1
1
1
1
2
1
1
2
0
1
1
1
2
1
1
2
2
0
1
0
1
0
1
1
2
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
2
0
0
1
1
2
2
1
2
2
0
1
1
1
1
1
2
3
1
2
0
1
1
2
1
1
1
0
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
0
2
1
1
1
2
2
1
0
1
1
2
1
1
0
1
0
1
1
1
1
2
1
2
1
2
1
1
2
1
1
1
1
2
2
2
0
1
1
2
1
1
1
1
1
1
1
0
1
2
1
2
0
1
1
1
0
1
1
2
1
0
2
1
0
1
1
1
0
1
2
2
2
0
1
1
1
2
1
2
1
2
1
1
1
1
1
1
0
2
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
0
1
2
1
1
0
1
1
1
1
1
2
2
1
1
2
1
1
0
1
1
1
0
3
1
2
1
1
2
2
2
1
0
2
1
0
2
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
0
1
1
1
2
2
2
1
1
1
1
1
1
0
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
0
1
2
2
1
1
1
1
1
1
0
1
1
1
1
2
1
0
2
0
1
1
2
1
1
1
2
0
1
1
1
1
2
1
0
1
0
1
1
0
1
1
0
1
1
1
1
1
2
1
1
1
1
1
2
1
1
2
1
2
1
1
0
2
0
0
1
2
1
1
1
1
1
2
1
2
1
1
1
2
1
1
0
1
2
2
1
1
1
1
0
2
1
2
1
1
0
1
1
0
2
2
1
0
1
2
1
1
1
1
0
1
2
1
1
2
1
1
2
1
2
1
0
1
2
0
0
2
1
1
1
2
2
0
2
1
2
0
1
0
1
2
2
1
1
0
1
1
1
1
1
2
1
1
2
0
2
2
1
1
1
1
1
4
1
1
1
1
1
1
1
1
1
2
0
2
2
0
1
1
1
2
1
1
1
2
2
1
2
1
1
1
2
0
2
1
1
2
0
1
0
1
0
1
0
2
2
1
1
2
2
1
1
1
2
2
1
1
0
1
1
1
1
0
3
1
1
1
1
1
1
1
2
1
1
0
1
1
1
1
1
2
0
1
1
1
2
0
1
1
2
2
1
0
2
0
1
1
1
0
1
2
2
0
1
1
0
1
1
3
1
2
1
1
1
1
2
1
1
1
4
1
1
1
2
1
1
1
1
1
0
1
0
2
1
1
0
1
1
1
2
1
2
0
1
1
2
1
1
1
1
1
2
1
1
1
0
1
1
0
2
1
1
1
1
2
2
2
1
0
0
0
1
1
2
1
1
1
2
1
2
2
2
0
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
2
1
1
1
1
1
1
1
1
0
0
1
1
2
2
1
1
2
2
2
2
1
1
2
1
0
1
0
2
1
1
2
2
1
1
1
1
2
2
1
2
2
0
2
0
0
1
2
1
1
1
0
1
2
1
1
1
1
0
1
4
0
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
2
0
2
1
2
2
0
0
2
1
1
2
1
1
1
1
2
1
1
1
1
1
1
2
1
2
1
2
2
2
1
1
2
1
1
0
1
1
1
1
0
1
2
2
0
2
1
0
0
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
2
1
1
0
1
1
1
1
2
1
1
2
1
3
1
0
1
1
1
1
1
2
0
0
2
1
2
3
0
1
1
0
2
0
1
2
2
2
1
0
2
1
1
2
1
1
2
2
2
1
0
1
1
2
0
1
1
2
2
2
2
1
1
1
1
1
0
0
1
0
1
1
3
1
2
1
0
1
1
1
1
1
0
1
1
2
3
0
2
2
1
2
1
3
1
1
2
1
2
1
0
0
1
0
1
2
1
1
2
2
1
1
2
1
2
1
1
1
2
1
1
1
2
1
1
1
2
0
2
2
2
1
1
1
2
1
1
1
1
1
0
1
1
2
2
0
0
1
1
1
1
2
0
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
1
1
0
1
0
2
1
1
1
1
2
0
2
1
1
1
2
1
1
0
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
1
1
2
1
1
1
5
2
0
1
1
0
2
1
1
1
2
1
1
0
1
0
1
1
2
0
2
2
1
2
0
1
1
1
1
0
1
0
2
1
1
0
1
1
1
2
2
2
1
1
1
2
1
0
2
1
1
1
1
0
1
1
0
1
1
2
2
0
0
2
2
1
1
1
2
0
1
1
1
1
0
2
2
1
2
1
1
2
2
1
1
2
1
3
1
0
1
1
1
1
1
1
2
2
1
0
1
2
2
2
2
0
2
1
1
1
0
1
0
1
1
0
1
1
2
2
1
1
2
2
2
2
1
2
1
1
0
2
0
1
1
2
1
2
1
2
2
3
1
2
4
0
1
1
1
0
0
1
1
0
1
2
1
1
2
1
0
2
0
0
1
1
1
1
1
1
0
2
1
2
2
1
1
0
2
2
2
1
1
2
2
2
1
1
0
1
0
2
1
1
1
1
1
0
1
1
2
1
1
2
1
1
1
1
1
1
1
2
2
1
1
0
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
2
1
0
2
0
1
2
2
1
0
2
2
1
1
1
0
1
1
1
1
2
1
1
1
1
2
2
1
2
1
1
2
1
1
2
2
0
1
2
2
2
0
1
1
0
1
1
2
1
1
1
2
1
2
1
2
2
2
2
2
1
1
2
0
1
0
1
1
0
1
1
1
2
1
1
1
0
2
1
0
1
2
1
2
1
1
1
1
1
2
1
1
1
0
1
2
1
1
1
2
1
2
1
1
1
2
1
2
1
2
0
1
1
2
1
0
1
2
0
1
1
2
0
1
1
1
1
2
0
2
1
0
1
0
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
1
0
1
0
1
1
1
0
1
1
1
2
2
1
1
1
2
1
1
1
0
1
2
1
1
2
1
0
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
0
1
2
1
2
1
1
1
1
1
1
2
0
1
1
1
1
1
1
1
1
1
1
1
0
0
0
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
2
1
0
2
1
1
1
1
1
1
1
1
2
0
0
1
1
1
1
1
1
1
2
1
2
1
2
1
1
0
1
1
2
1
1
1
2
0
1
1
2
1
2
1
2
2
1
2
2
0
0
2
2
2
2
1
1
1
1
1
1
1
1
2
2
7
1
2
1
2
1
2
1
2
1
1
1
0
1
1
1
1
2
1
1
1
2
1
1
1
0
2
1
1
1
1
1
1
1
0
2
1
2
1
1
1
0
0
1
1
1
0
1
2
1
0
1
1
1
1
1
1
0
0
1
2
2
1
1
1
1
1
2
2
1
1
2
2
1
0
1
0
0
2
1
2
1
1
1
1
1
2
1
2
1
3
2
1
1
1
0
1
2
2
1
1
2
2
1
0
1
1
1
1
2
0
1
1
2
3
1
2
0
1
1
1
0
0
1
1
1
1
1
0
1
1
1
2
1
2
1
2
1
2
0
1
1
2
2
1
1
1
0
1
1
2
0
1
2
2
2
1
1
2
1
1
2
0
1
1
1
5
1
2
0
0
2
1
1
1
2
1
2
1
0
1
1
0
2
1
1
1
0
1
1
2
1
1
2
2
2
1
1
0
0
1
1
1
1
1
1
2
1
0
2
1
1
2
1
0
0
1
0
1
2
1
2
1
1
1
2
1
1
1
2
2
2
2
1
1
1
2
1
1
2
2
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
1
0
0
1
1
1
2
1
1
1
2
2
1
0
2
1
1
1
1
1
1
1
2
1
1
0
1
1
1
1
0
1
2
1
1
0
1
0
1
1
1
0
2
1
1
1
1
2
1
0
1
1
1
2
2
2
0
2
1
1
1
1
0
2
1
1
1
1
2
1
1
2
1
1
1
0
1
1
1
1
2
2
1
1
2
2
1
2
2
1
1
1
1
2
2
2
1
1
2
1
1
0
2
1
1
1
1
1
1
2
1
0
2
1
3
1
1
2
1
0
1
1
1
1
1
1
1
2
1
2
0
1
1
2
1
1
2
1
1
1
1
1
1
0
2
0
2
1
0
2
1
1
0
1
2
2
2
1
0
1
1
1
1
1
1
2
1
1
2
2
1
1
1
0
1
2
1
1
1
0
1
2
2
1
1
1
1
1
1
2
1
1
1
1
2
0
2
0
1
1
1
2
1
1
1
2
2
1
2
0
1
2
1
2
1
0
2
1
0
1
1
0
1
1
1
1
2
2
0
1
1
0
1
1
0
1
1
1
1
1
1
1
1
2
2
0
0
2
1
2
2
1
2
1
2
1
1
2
1
1
1
2
2
2
2
2
2
2
0
1
0
1
1
1
1
2
0
1
2
2
1
0
3
2
2
1
2
1
1
1
0
1
1
1
2
1
1
1
2
1
0
2
1
1
1
1
1
2
1
2
3
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
0
2
1
1
2
0
3
1
1
1
2
2
1
1
1
1
2
2
1
1
2
1
1
2
1
0
2
2
1
1
0
2
2
1
1
0
1
2
1
2
1
1
1
1
1
0
2
2
1
1
2
2
2
0
1
1
2
0
1
0
1
1
1
0
1
2
0
1
1
1
1
2
2
1
0
2
0
2
1
1
1
2
1
1
1
2
1
1
1
1
1
2
2
1
1
0
1
1
2
2
1
2
1
1
2
1
2
3
1
2
1
1
1
1
0
3
1
2
1
1
1
0
1
2
2
1
1
2
1
0
2
1
1
1
2
1
0
1
1
1
1
0
0
1
1
1
1
1
1
1
0
1
2
1
1
1
1
1
1
1
1
0
1
2
1
2
2
2
2
1
1
1
1
2
1
1
1
2
5
2
1
1
1
1
1
1
2
1
1
0
2
1
0
1
1
1
1
1
1
2
0
1
2
1
0
1
1
2
2
1
1
0
1
1
1
1
1
1
2
1
1
0
1
1
0
1
1
2
2
1
2
1
2
1
0
2
1
2
1
2
2
1
1
1
1
2
1
1
1
1
2
2
2
2
2
1
2
1
2
2
1
2
1
1
2
1
0
2
2
1
2
1
2
1
1
1
2
1
1
1
0
1
1
0
0
2
2
1
1
2
0
1
0
0
1
1
2
2
1
2
1
2
2
0
0
1
2
1
1
1
1
1
1
1
0
1
1
0
2
2
2
0
1
1
0
1
2
2
1
0
0
1
2
2
1
1
2
1
1
1
1
1
2
1
0
1
2
1
1
1
1
1
2
2
1
1
1
2
1
1
2
2
1
1
1
0
0
1
1
1
0
1
2
1
1
1
0
1
2
1
1
2
2
0
2
0
1
1
1
1
1
2
0
1
0
2
1
1
1
2
1
2
2
2
1
2
1
1
0
1
1
1
1
1
1
1
0
1
1
1
1
0
2
2
1
2
1
2
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
2
1
1
1
0
3
1
1
1
1
2
1
0
0
2
1
1
1
0
1
1
2
2
1
1
1
1
1
1
2
2
2
1
2
1
1
2
0
1
0
1
2
1
1
0
2
1
1
1
2
1
1
1
2
0
1
0
0
1
1
1
1
2
1
1
2
1
2
2
0
2
1
1
2
1
2
1
1
2
1
2
0
0
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
2
1
0
1
1
1
1
1
1
2
1
1
2
1
2
2
1
2
2
0
1
2
2
0
2
1
1
0
2
1
1
0
1
0
1
1
1
1
1
0
0
0
1
2
2
1
2
2
1
1
1
1
2
1
1
1
2
2
2
0
2
1
0
1
1
1
1
0
2
2
1
0
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
0
2
1
1
0
1
1
1
2
2
2
1
2
0
2
1
0
1
1
1
2
1
1
1
1
2
1
0
1
0
2
2
0
0
2
2
1
1
1
1
1
2
1
1
2
2
1
0
1
1
1
1
2
1
1
0
2
1
2
1
1
1
2
0
1
1
1
1
2
0
1
2
1
2
1
3
1
0
0
1
0
1
1
1
2
1
1
1
1
2
1
2
2
2
0
2
2
2
0
2
0
1
1
0
1
1
0
2
1
1
1
2
1
1
2
1
1
0
1
1
2
1
1
2
0
1
1
0
0
1
1
0
1
2
1
2
1
1
1
1
0
0
1
2
1
2
1
1
1
2
2
1
1
1
1
0
2
2
2
1
1
1
1
2
1
1
1
1
1
2
1
2
1
1
1
0
1
1
2
1
1
2
2
1
1
1
1
2
1
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
2
1
1
1
0
1
1
2
1
0
1
2
1
1
1
2
1
1
1
1
1
2
1
1
1
0
2
1
1
1
2
2
1
1
1
1
0
2
1
2
1
1
1
1
2
2
1
3
1
0
1
1
1
1
2
1
0
1
0
1
1
1
1
1
1
2
2
2
2
1
2
1
0
1
1
2
2
1
2
1
0
1
0
1
2
1
2
1
1
1
2
0
0
1
1
1
0
1
1
0
0
2
1
0
1
1
1
1
1
1
1
1
1
2
0
2
1
1
3
2
2
2
1
1
1
1
2
1
2
2
1
2
1
2
0
1
0
1
1
1
0
1
1
2
1
0
0
1
1
1
2
2
0
2
1
1
1
2
0
1
1
1
2
1
1
1
2
1
0
1
2
1
2
1
1
2
0
1
1
2
1
2
0
2
1
2
0
0
0
2
2
2
1
1
1
1
1
2
2
2
1
1
1
2
1
2
2
2
1
2
1
2
1
1
1
2
2
2
0
1
1
2
1
1
1
1
0
0
2
2
2
1
0
2
2
2
0
2
1
1
1
1
1
1
1
1
2
1
1
1
0
2
1
1
1
0
1
2
2
2
1
1
1
0
1
2
2
0
2
1
1
2
1
2
1
2
2
1
1
1
2
1
2
1
1
2
1
2
1
1
0
1
1
1
1
1
1
1
2
1
1
1
2
1
1
0
1
1
1
1
0
1
1
1
2
0
0
0
1
1
1
0
1
1
1
1
2
1
1
1
1
0
1
1
1
1
0
1
1
1
2
2
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
0
1
1
0
1
1
1
1
1
1
1
1
1
1
1
2
2
2
0
0
1
1
1
0
0
2
1
2
1
1
1
1
1
1
1
1
1
1
1
0
2
1
1
0
2
1
1
1
1
1
2
2
1
2
1
2
0
2
2
0
1
0
2
1
2
1
1
3
2
1
1
0
1
0
0
1
1
0
1
1
1
0
1
2
0
1
0
1
0
2
2
1
0
2
1
1
1
1
2
1
1
0
1
1
1
0
2
1
1
0
0
3
1
1
2
2
0
1
1
2
1
1
2
1
2
1
0
1
1
1
1
5
2
1
1
0
1
2
2
0
0
1
1
2
2
1
1
1
2
1
2
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
0
2
2
1
1
2
1
0
2
1
1
2
0
1
2
2
1
2
1
1
1
1
1
1
2
0
1
1
2
0
2
1
2
1
1
0
1
0
2
1
1
2
1
2
1
1
1
1
1
1
1
2
2
1
1
0
1
1
1
2
1
1
1
0
0
2
1
1
2
1
3
1
2
1
1
0
1
2
1
1
2
1
0
1
1
1
1
1
2
0
1
1
1
0
1
0
2
1
1
1
1
1
1
1
0
1
3
2
1
1
1
0
1
2
0
1
1
2
1
1
1
1
1
0
1
0
2
1
1
1
2
1
2
2
1
1
1
2
0
1
1
2
1
2
2
0
2
1
2
2
1
1
2
1
2
1
2
1
1
0
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
2
1
0
1
1
1
2
1
2
2
1
2
2
1
0
1
1
1
1
2
0
1
0
1
0
1
1
1
2
2
1
1
0
1
1
1
1
1
1
0
1
0
1
1
1
0
0
2
1
1
1
2
2
1
1
1
1
1
1
2
1
0
1
1
2
2
1
1
1
0
0
2
0
0
1
1
1
1
1
1
0
0
1
1
2
0
1
2
1
1
1
1
1
2
1
0
0
2
1
0
0
1
2
1
0
2
1
1
1
1
0
1
1
0
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
0
2
1
1
1
1
3
1
1
0
2
0
1
1
2
1
1
1
2
1
1
1
1
1
1
1
0
2
2
1
0
1
1
0
1
1
2
0
1
1
1
1
1
1
4
1
3
1
1
0
1
1
1
1
2
1
0
2
1
0
1
1
0
1
2
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
0
2
1
1
2
1
1
1
1
2
2
2
2
0
1
2
1
1
2
1
1
1
2
2
1
2
1
2
2
1
2
1
1
1
1
2
2
0
1
1
1
2
2
1
1
0
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
0
1
2
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
0
1
2
1
1
1
1
1
1
1
0
1
2
1
1
1
2
2
1
2
1
1
2
2
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
2
1
0
1
2
2
1
1
1
2
1
2
2
0
0
2
1
0
1
0
2
0
1
1
0
2
2
1
1
1
1
1
1
2
1
0
2
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
1
0
2
2
1
1
2
1
1
2
1
1
1
1
1
0
2
2
1
1
0
1
1
1
1
1
2
1
2
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
2
1
1
2
1
1
1
2
2
1
2
1
2
1
0
1
0
1
0
1
1
1
1
1
1
2
1
1
0
1
2
1
1
4
1
2
0
2
1
1
1
1
1
0
1
1
0
1
1
2
1
1
2
2
1
0
1
2
1
1
1
1
1
0
1
1
2
1
2
2
1
1
1
1
0
1
1
1
1
1
1
2
2
0
1
1
1
0
2
1
1
0
1
1
1
1
1
1
0
1
2
1
2
2
1
0
1
2
2
1
1
2
2
2
1
2
1
2
2
0
2
1
1
1
0
1
1
1
1
0
1
2
2
1
1
1
2
1
0
1
1
2
1
2
1
0
1
0
1
2
2
3
1
2
1
1
1
0
0
1
0
2
2
1
1
0
1
1
1
0
1
1
1
1
2
1
0
1
1
1
2
1
1
0
1
1
1
1
1
1
1
1
1
1
2
0
0
2
1
0
1
1
1
1
1
1
1
1
0
0
1
1
1
1
1
2
1
1
1
2
1
0
2
2
1
1
1
1
2
1
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
2
0
1
1
2
0
2
2
2
2
1
1
1
0
1
1
1
2
2
0
2
1
2
2
1
2
1
1
2
0
2
1
1
2
1
1
1
1
1
2
1
1
2
0
1
1
0
1
0
1
1
1
2
0
1
2
1
0
1
2
2
2
1
2
1
2
1
1
1
2
3
2
1
1
1
1
2
2
1
2
1
1
1
1
1
2
2
2
0
0
1
1
1
1
1
1
2
1
1
1
1
0
1
1
2
1
1
0
1
2
0
2
1
2
1
0
1
1
2
0
1
0
1
1
1
2
2
1
1
0
1
1
1
2
1
0
1
1
1
1
1
0
1
1
1
2
2
2
2
0
1
1
1
1
1
2
1
1
1
2
0
2
0
0
1
1
1
2
1
1
1
1
3
1
1
1
0
0
1
2
2
1
0
1
1
1
2
1
2
1
1
1
0
0
2
1
0
2
2
1
2
1
0
1
2
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
0
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
0
1
1
2
0
1
0
0
2
2
0
1
1
0
1
1
1
2
1
2
3
1
1
1
1
0
1
1
0
1
1
2
2
1
2
2
1
0
0
1
1
1
1
2
2
3
2
1
1
1
2
1
1
1
2
2
1
1
2
2
0
0
1
2
2
1
2
1
1
0
1
0
2
1
1
2
2
0
2
1
1
1
1
0
0
1
0
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
1
2
1
0
1
1
0
0
1
1
2
2
1
1
1
2
2
0
1
0
1
0
1
2
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
0
0
1
0
2
1
1
1
0
2
0
1
1
1
1
0
1
1
1
1
0
1
0
1
0
1
1
1
1
0
1
2
1
0
1
2
1
1
1
1
1
2
1
2
1
1
1
2
0
3
1
1
1
1
1
0
1
2
1
2
1
1
1
2
1
1
2
0
2
2
1
0
1
2
1
3
2
1
2
2
1
0
1
0
1
0
2
0
1
2
1
1
1
1
2
1
1
1
1
1
2
1
2
1
1
1
0
1
2
2
1
1
1
2
1
0
1
1
1
0
1
1
1
2
1
1
1
2
1
1
1
1
2
2
1
0
1
1
2
1
1
1
1
2
1
2
1
1
2
1
0
2
1
1
0
1
2
2
1
1
2
2
2
2
2
1
2
0
1
1
2
0
0
0
2
1
1
2
2
2
1
2
1
0
2
2
1
1
1
2
1
1
1
2
1
0
1
0
1
1
2
1
1
2
1
2
0
1
2
0
1
1
2
2
1
1
1
1
1
1
1
1
0
1
1
1
1
0
0
1
1
1
1
0
1
2
1
0
1
1
1
1
1
2
0
2
1
1
1
2
1
1
1
1
1
1
1
2
2
2
1
1
2
2
1
1
2
1
1
0
1
1
1
2
2
2
1
1
1
1
2
0
1
0
1
2
2
2
0
1
1
1
2
2
1
2
0
1
1
2
0
1
0
1
1
1
2
0
0
0
1
1
1
2
1
1
1
2
1
2
1
2
1
1
2
1
1
1
1
0
1
1
1
1
0
1
1
2
1
2
1
1
2
2
1
1
1
1
2
0
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
0
1
1
0
2
0
1
2
0
1
1
1
1
1
2
2
1
2
2
1
2
1
1
1
2
1
0
1
1
3
1
1
1
1
1
1
0
2
1
1
2
1
1
2
2
1
1
1
2
2
1
0
2
0
1
1
1
1
0
0
2
0
0
0
1
2
2
1
3
1
2
1
2
0
2
1
2
2
1
2
1
1
1
1
1
1
0
1
2
2
1
2
1
2
2
1
1
0
1
1
2
1
1
1
1
2
1
1
1
1
2
0
1
1
1
1
1
1
3
1
2
1
2
1
2
1
2
1
1
2
1
1
1
0
2
1
2
1
2
1
2
1
2
1
2
1
2
2
2
2
2
2
2
1
0
1
1
0
1
2
1
1
2
1
2
1
1
1
1
1
2
1
2
1
1
1
2
1
1
1
1
1
0
2
1
2
1
1
1
2
1
1
1
1
1
0
2
0
1
1
1
0
2
1
1
2
1
1
1
1
1
2
1
1
2
1
1
1
2
1
0
2
0
1
0
2
0
1
2
1
0
1
1
1
2
1
1
2
1
2
0
2
0
1
0
2
1
1
1
1
0
2
1
1
0
1
1
0
1
1
2
1
1
1
0
1
1
1
1
1
1
1
1
1
1
0
1
0
1
0
1
2
2
1
0
0
2
2
2
1
2
1
1
1
1
1
0
2
1
1
0
2
1
1
2
0
2
1
1
1
1
1
0
1
0
0
2
1
2
2
1
1
1
3
1
1
0
2
0
1
2
0
2
1
2
1
2
2
1
0
1
1
1
1
1
1
2
1
1
1
1
2
1
0
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
0
1
2
1
1
2
1
0
1
0
2
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
0
1
1
2
1
2
1
1
3
1
1
1
1
1
2
0
2
1
1
1
1
1
2
1
0
1
0
1
2
2
1
0
1
1
1
1
1
2
1
1
1
1
4
1
2
2
1
1
1
1
0
1
1
1
2
1
0
2
2
1
0
2
2
0
0
1
1
2
2
0
1
1
1
2
1
2
1
0
1
1
2
2
1
1
2
2
1
1
1
1
2
2
1
1
1
0
1
1
0
1
1
2
1
1
1
1
0
0
2
0
1
1
2
1
0
1
1
1
1
2
1
1
2
1
2
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
2
1
1
0
1
0
1
1
0
2
1
2
1
2
1
1
1
1
2
2
0
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
2
1
1
2
1
3
1
1
1
2
1
1
1
1
2
1
2
1
1
2
1
1
2
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
0
1
2
1
2
2
1
2
1
1
1
0
1
0
2
2
1
0
1
1
1
0
2
1
2
1
1
0
1
2
1
1
2
1
0
1
1
1
1
1
0
2
0
1
1
0
2
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
2
1
1
2
0
1
2
1
2
1
1
2
2
2
1
1
1
1
1
1
2
1
0
0
1
2
2
2
1
2
2
1
2
1
2
1
1
2
1
2
1
1
1
0
2
1
2
1
1
0
2
2
2
1
2
1
1
2
1
1
2
1
1
1
2
1
0
1
1
1
1
1
1
1
2
1
1
2
1
1
1
2
1
1
1
3
1
1
1
0
2
1
1
1
2
0
1
1
1
0
2
1
2
2
1
2
1
1
2
1
1
1
1
1
1
1
1
2
3
2
0
1
2
1
1
2
0
2
1
1
2
2
2
1
1
1
0
1
1
0
2
0
1
1
1
1
1
1
1
2
0
2
1
0
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
0
1
0
2
2
1
1
0
1
2
1
0
1
1
1
1
1
1
0
2
1
1
1
0
0
2
1
1
0
0
2
1
1
1
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
2
1
0
1
1
1
1
0
1
0
1
1
2
1
0
1
1
1
2
1
1
2
1
0
1
1
2
1
1
0
1
1
1
2
1
0
1
1
1
1
0
1
2
2
0
1
0
1
1
1
1
1
1
2
1
2
1
2
2
1
1
1
1
1
0
0
0
2
2
0
1
1
2
1
1
1
2
0
2
2
2
1
2
2
0
1
1
2
1
1
0
2
0
1
1
2
0
1
1
2
2
2
2
1
2
1
2
1
1
1
1
0
2
1
1
1
1
0
1
1
1
1
1
3
0
2
2
2
1
1
0
2
1
1
1
2
0
1
1
1
1
2
1
1
1
1
0
2
1
1
1
2
1
1
0
1
2
1
0
1
1
2
1
1
1
0
2
0
0
3
0
2
2
0
2
2
1
1
0
1
2
1
1
1
1
1
1
0
0
1
1
1
1
1
2
2
1
2
1
2
1
1
1
0
1
1
0
1
1
2
1
0
1
0
1
1
1
0
1
1
2
2
1
1
1
0
2
1
1
1
2
1
1
2
2
1
1
1
1
2
0
2
1
1
0
1
1
1
0
1
0
1
0
1
1
2
2
1
1
1
1
0
0
3
1
2
1
1
0
1
2
0
1
1
1
1
0
0
1
1
1
1
1
2
1
1
1
2
1
0
2
2
1
1
1
2
1
1
1
2
0
1
1
1
1
1
1
2
1
1
1
0
1
1
2
1
2
1
0
2
1
1
1
2
0
1
0
2
1
1
1
1
0
1
2
1
0
1
1
1
0
2
1
1
0
1
1
1
2
1
2
0
1
1
1
2
1
1
1
1
1
1
1
2
0
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
2
2
1
1
1
1
1
2
1
0
1
0
4
1
1
2
1
2
2
1
1
2
2
2
3
1
0
2
1
1
1
1
1
1
0
1
1
1
2
2
0
1
1
1
1
1
2
2
0
0
1
1
2
1
1
1
0
0
1
1
2
2
1
1
2
2
1
0
1
2
1
2
1
2
1
2
1
1
1
1
2
0
1
1
1
2
2
0
1
2
1
1
2
2
1
1
0
2
1
1
1
1
2
1
1
2
1
1
2
1
2
2
1
1
1
0
2
2
2
1
1
0
2
1
1
2
1
1
1
0
2
1
2
1
2
1
1
1
2
0
1
0
1
1
1
2
2
2
1
1
1
1
1
1
1
0
1
0
0
1
0
2
1
1
1
2
1
1
1
1
2
2
1
0
1
2
2
1
1
0
1
1
0
2
1
1
1
1
2
0
1
2
1
1
1
1
2
1
1
0
0
1
2
1
2
1
1
1
1
1
2
1
1
2
1
2
0
1
1
1
2
1
2
0
1
1
1
1
1
0
2
1
1
1
3
2
1
1
1
1
1
2
1
1
1
0
1
1
1
2
0
1
1
2
1
1
0
1
0
1
2
1
1
1
1
1
3
1
1
1
1
1
1
1
1
2
1
1
0
1
1
3
1
1
2
1
1
2
1
2
0
1
1
1
2
1
1
0
1
1
2
2
1
1
2
1
2
2
1
1
1
1
2
2
1
1
1
2
1
2
2
2
1
1
2
1
0
1
2
0
1
1
1
0
2
1
1
0
1
4
0
1
1
2
1
1
1
1
1
2
1
2
2
1
2
2
1
2
0
0
2
2
2
1
1
0
1
1
0
1
0
2
1
1
3
1
1
1
1
1
1
2
0
1
1
2
1
2
1
1
2
1
1
1
2
2
2
1
1
1
2
1
2
0
2
2
1
1
2
2
2
1
1
1
2
1
1
1
2
1
1
2
2
1
2
1
1
2
1
1
1
2
1
1
0
1
1
2
1
1
1
0
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
2
1
1
0
1
2
2
0
1
1
0
2
2
1
1
1
1
2
1
2
2
2
2
1
1
2
1
1
1
1
2
1
2
1
1
1
1
2
1
2
1
1
1
2
1
1
0
0
1
1
2
2
2
1
1
2
0
1
0
2
1
1
1
1
1
0
1
1
1
1
1
2
0
1
1
0
1
2
1
1
1
0
0
2
1
1
2
1
2
0
1
1
2
1
0
1
1
1
2
1
2
2
1
0
1
2
1
1
1
1
2
1
1
1
1
1
2
1
0
1
1
1
0
2
0
0
2
1
1
1
1
0
0
0
0
0
1
1
1
2
0
1
1
1
0
0
2
1
1
1
1
0
1
1
2
1
2
0
1
1
1
1
1
2
2
2
1
1
2
1
2
1
2
1
1
0
0
0
1
1
2
2
2
1
1
1
1
1
1
1
1
0
1
2
1
1
1
2
1
2
2
1
1
0
1
1
1
1
2
1
2
1
1
2
1
1
2
2
0
1
1
1
1
1
0
1
2
2
2
2
0
0
1
2
2
2
1
1
1
1
0
2
1
1
1
1
1
2
1
0
0
1
1
1
1
1
1
1
2
1
1
2
1
0
1
2
1
1
2
0
1
1
1
1
1
0
1
1
0
2
2
0
2
2
1
1
1
1
0
2
1
2
2
1
2
1
1
1
0
1
0
2
1
1
1
1
0
1
1
1
2
1
1
1
1
2
0
0
1
1
0
1
2
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
1
1
1
0
0
1
2
2
1
2
1
0
1
1
2
0
1
2
2
1
1
1
1
1
0
1
1
2
1
2
2
1
2
2
1
1
1
1
2
1
2
1
1
2
1
0
1
0
1
2
0
2
1
2
1
1
1
2
2
1
1
1
2
1
1
0
1
2
1
3
2
2
2
1
1
2
1
2
2
1
0
1
0
1
0
1
0
1
1
2
2
1
1
1
1
0
3
2
2
1
1
1
1
2
1
1
2
1
0
2
0
2
1
3
2
1
0
1
0
1
1
0
2
1
0
2
1
1
1
1
2
1
1
1
0
1
1
0
2
1
1
1
1
0
0
1
1
0
1
2
2
1
1
1
1
3
2
1
2
3
1
1
1
2
2
2
1
1
1
2
2
0
1
2
2
1
0
1
1
2
2
1
1
0
1
1
3
1
1
0
2
2
2
1
1
1
1
2
1
1
1
1
0
1
1
2
1
2
1
1
1
1
2
1
1
1
1
1
0
1
0
2
1
1
1
1
2
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
2
2
1
1
2
0
2
2
1
1
2
2
1
1
1
1
2
0
1
1
2
1
2
0
1
1
4
2
0
1
0
1
2
2
0
1
1
0
0
1
1
2
0
1
1
3
0
0
0
1
1
1
2
1
1
2
1
0
2
0
1
1
0
2
0
2
2
1
2
0
2
1
1
1
1
2
2
1
1
1
1
0
1
1
1
1
1
1
1
1
2
1
2
1
2
1
1
2
1
2
1
2
1
1
1
1
2
2
1
1
1
1
1
1
2
0
0
1
1
1
1
1
1
1
2
1
2
2
0
1
2
1
1
2
0
2
0
2
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
0
1
0
1
2
0
1
2
1
1
1
1
1
1
1
0
2
2
2
2
2
1
1
2
0
2
1
2
1
1
1
1
1
1
1
1
1
2
0
1
1
1
0
1
0
1
2
1
1
2
1
2
1
1
1
1
0
1
1
2
0
2
1
2
1
1
0
2
1
2
0
1
1
0
1
1
1
0
1
0
1
1
1
2
1
2
2
1
0
2
1
2
2
1
2
1
1
1
1
1
1
1
0
1
2
1
1
1
2
2
0
0
1
1
2
1
2
1
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
1
1
0
0
0
0
1
1
1
1
0
1
1
1
1
2
1
2
1
1
2
1
1
1
2
0
2
1
0
1
1
2
1
1
1
0
1
0
2
1
1
2
2
0
1
1
0
1
1
1
0
1
1
2
1
1
2
1
1
1
1
1
0
1
1
1
2
1
0
2
1
1
1
2
1
1
2
1
0
1
0
2
1
2
1
1
2
1
1
2
0
2
1
1
2
2
1
1
1
2
1
2
1
0
1
0
2
1
2
2
1
1
2
1
2
1
2
1
1
0
1
1
1
1
1
0
1
1
1
1
2
0
1
1
1
1
1
1
1
1
2
1
1
1
1
0
2
1
1
2
1
0
1
1
1
2
2
1
2
2
1
1
1
0
1
1
1
1
2
1
2
2
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
2
1
2
1
2
1
1
2
2
2
2
1
0
2
1
1
1
1
1
2
2
2
1
2
1
0
1
2
2
0
2
1
1
1
1
0
1
1
1
2
1
1
1
1
1
1
1
0
2
1
1
1
1
1
0
1
1
0
1
2
2
2
0
2
1
2
1
1
1
2
0
0
1
1
1
2
2
0
1
1
1
1
0
0
0
1
1
1
1
1
0
1
1
0
1
1
2
2
0
2
1
1
2
1
1
2
2
1
1
1
1
1
1
1
2
1
2
1
0
3
1
1
1
1
0
2
1
2
1
1
0
2
1
1
1
1
2
1
1
1
1
0
2
1
2
2
2
1
1
1
3
1
1
1
1
1
0
1
0
2
0
2
2
0
1
1
1
1
1
1
1
2
1
1
1
0
0
1
1
1
2
0
1
1
2
1
1
1
1
1
1
0
1
1
2
1
0
1
1
1
1
1
0
1
1
2
1
1
1
1
1
2
1
0
1
2
1
0
1
1
2
0
1
1
1
1
2
2
0
1
0
2
1
0
0
1
0
2
2
2
0
1
2
1
2
1
1
1
1
1
2
2
0
2
1
2
1
2
2
1
1
0
1
0
1
2
1
3
1
2
2
1
1
0
2
0
1
2
0
2
1
0
1
1
2
1
1
1
1
1
1
0
2
0
1
3
1
1
0
2
1
0
1
1
2
2
0
2
0
0
2
0
0
2
1
1
1
1
0
1
0
1
2
1
1
1
1
1
1
2
0
1
1
2
2
1
1
1
2
0
2
1
1
1
1
1
1
1
0
1
1
1
0
1
2
0
2
1
0
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
2
2
1
2
2
1
0
1
0
0
2
1
2
2
1
0
1
2
1
1
2
1
1
1
1
1
2
1
1
2
0
1
0
0
0
1
0
1
0
2
1
2
1
1
2
1
1
0
1
2
2
0
2
1
2
2
1
1
2
1
2
1
1
2
0
0
1
2
1
2
1
1
1
1
1
1
1
1
1
2
2
1
0
1
1
2
0
2
1
1
1
1
0
2
1
1
0
0
2
2
2
2
1
2
1
1
1
1
1
1
1
2
1
2
1
1
0
0
1
1
1
1
1
1
1
2
2
1
0
2
1
2
1
1
1
2
1
1
1
1
1
1
1
1
0
1
2
1
1
1
0
1
0
0
1
1
1
1
2
1
1
2
1
1
2
2
2
1
0
1
2
1
2
1
1
2
2
1
1
0
1
1
1
2
1
1
2
0
2
1
2
1
1
2
2
2
1
1
1
1
1
1
1
2
1
1
0
1
1
0
1
1
1
2
0
1
2
2
1
2
0
2
2
1
1
0
1
1
1
1
1
1
1
1
2
0
2
2
1
0
2
2
2
3
1
0
2
1
1
1
0
1
1
1
1
1
2
3
2
1
0
1
1
1
1
1
0
2
1
2
2
1
1
1
1
2
1
1
1
1
1
2
1
1
0
2
2
2
1
1
1
1
1
1
1
4
2
1
1
2
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
2
2
2
2
1
1
1
1
1
0
1
2
1
1
2
1
0
1
1
2
2
0
1
1
0
0
0
1
1
1
0
1
2
2
1
1
2
0
1
0
0
2
1
1
1
1
1
1
2
2
2
1
0
1
1
2
2
1
0
2
1
2
1
1
1
1
1
1
0
1
2
2
1
1
1
0
0
1
0
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
0
1
1
1
2
2
1
2
1
1
1
2
0
1
2
1
2
0
1
2
1
1
1
1
1
1
1
1
0
1
2
1
1
2
2
2
1
1
1
0
1
0
1
1
2
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
0
2
1
1
2
1
2
1
1
3
2
1
3
0
1
0
2
0
3
1
2
0
2
1
1
0
1
1
1
2
1
1
1
1
1
2
0
1
2
1
2
1
1
2
2
1
1
1
1
1
0
3
1
2
0
1
2
2
1
1
1
2
1
1
2
1
1
1
0
0
0
1
0
1
2
0
0
0
2
1
2
1
0
0
0
0
1
1
0
0
1
0
1
0
1
2
2
2
1
1
1
1
1
2
1
1
1
2
1
2
1
2
0
1
1
4
1
1
1
1
2
1
0
3
1
1
1
1
0
1
1
0
1
2
2
1
0
1
1
1
2
1
2
1
1
2
1
3
1
1
2
1
1
1
1
1
1
2
2
2
1
2
1
1
1
1
2
1
2
1
1
1
2
1
2
1
1
2
1
0
2
0
1
2
1
2
1
2
1
2
0
0
2
1
1
2
2
1
1
0
2
2
1
1
1
1
1
2
1
1
0
1
1
0
1
1
1
2
2
0
2
1
2
2
0
1
2
1
1
2
1
1
2
1
1
1
1
0
2
0
2
1
0
1
1
0
1
2
1
1
1
1
1
1
1
1
2
2
1
2
1
1
1
1
2
1
1
2
2
1
2
2
2
2
0
1
2
0
1
1
2
2
1
1
1
1
2
0
1
1
1
0
1
2
1
1
1
5
2
1
2
1
1
1
1
1
1
2
1
0
2
1
1
2
1
1
2
0
1
1
0
1
1
1
1
1
1
1
2
2
1
1
2
1
2
1
1
1
1
1
1
1
1
2
1
0
0
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
0
0
1
1
1
1
1
2
2
2
0
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
0
2
1
1
1
2
1
1
2
1
1
1
1
1
1
1
0
2
1
1
1
1
1
1
1
1
1
0
1
1
0
2
1
0
1
2
1
1
1
1
1
0
0
1
2
1
2
0
0
1
1
1
1
1
0
2
1
1
2
2
1
2
0
1
1
2
0
2
1
2
1
1
0
0
1
0
2
0
2
2
1
1
1
1
1
1
1
1
1
2
0
1
1
2
1
1
1
0
1
1
2
1
2
1
1
0
1
1
1
1
1
1
1
0
1
1
1
1
0
1
1
2
1
1
1
1
1
1
0
1
1
1
2
1
1
1
1
2
2
1
1
1
1
1
2
2
1
6
1
1
0
1
0
2
1
1
1
2
1
0
1
2
0
1
2
2
2
2
1
2
2
1
1
1
2
1
1
2
2
2
2
0
1
2
1
1
1
1
2
2
0
2
1
2
2
2
1
1
1
2
0
1
1
1
1
1
1
1
0
2
1
1
1
0
1
1
1
1
0
1
1
1
0
1
2
0
1
2
2
0
2
1
1
1
1
2
1
2
1
0
1
1
1
1
1
0
1
1
1
0
0
1
1
0
1
1
0
1
1
0
1
2
0
0
1
0
0
1
1
2
1
2
1
1
1
1
1
2
1
1
2
1
0
1
1
1
2
1
2
1
1
2
2
0
2
1
2
2
1
1
2
1
1
1
1
1
1
2
0
1
1
1
2
0
1
1
2
1
2
3
1
0
1
2
2
0
1
2
1
2
1
1
2
1
0
1
1
0
2
1
1
2
1
1
2
1
1
1
1
1
1
2
2
1
1
1
2
2
1
1
2
1
1
2
1
2
0
0
1
0
0
1
1
1
1
1
0
2
1
2
2
0
1
0
2
1
0
1
2
1
0
1
1
1
1
2
2
1
1
2
1
1
3
2
1
1
1
2
1
2
1
1
2
1
1
1
0
2
1
2
1
1
1
2
1
2
1
2
1
1
0
0
0
0
1
2
1
1
1
2
2
1
2
2
2
2
1
1
1
2
1
1
1
1
1
1
1
0
2
1
1
1
2
2
2
1
1
1
2
1
0
1
1
1
1
3
2
2
1
1
1
1
1
0
0
1
1
1
0
1
1
1
1
1
0
1
1
2
2
1
2
2
0
1
1
0
2
1
2
1
0
2
2
0
1
1
2
0
1
2
0
1
2
2
1
1
0
2
1
1
2
1
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
2
1
2
1
2
1
0
1
1
2
0
0
0
2
0
2
1
1
2
1
1
1
1
1
1
1
2
2
1
0
1
2
1
2
1
1
1
2
1
2
2
2
1
2
1
1
0
1
1
1
1
1
1
0
1
2
1
4
1
1
1
2
0
2
1
1
0
2
1
1
1
1
1
1
1
1
0
0
1
1
1
1
1
1
0
2
1
1
1
1
2
1
1
2
0
1
0
1
0
1
1
1
1
1
1
1
1
1
2
2
1
1
0
1
2
1
2
1
1
1
0
1
1
1
1
1
2
1
2
1
1
1
1
1
1
2
1
2
1
0
1
1
0
1
2
1
1
1
1
1
1
1
1
1
1
1
0
2
0
1
1
2
1
1
2
1
2
0
2
1
0
2
0
1
0
2
0
1
0
0
0
1
1
1
0
1
1
0
2
2
2
1
2
1
0
1
1
2
3
2
2
0
1
2
1
1
0
2
2
2
2
1
0
1
1
2
2
0
2
0
2
2
1
1
1
1
0
1
1
1
1
1
1
1
0
1
1
0
1
2
1
1
1
1
1
2
1
1
2
1
1
2
1
2
1
1
1
2
1
2
1
2
1
0
1
0
1
1
1
1
3
0
1
0
1
2
0
1
1
1
1
1
0
1
0
1
1
1
0
1
1
1
1
2
3
1
2
0
0
0
1
1
2
1
0
1
1
1
0
2
2
1
1
1
2
1
2
1
1
1
0
1
2
2
1
1
2
1
2
1
2
1
0
1
1
0
2
1
1
1
2
1
2
0
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
2
1
2
4
1
2
2
1
1
1
1
1
1
1
1
2
1
0
1
1
1
1
1
1
1
1
1
1
0
2
1
1
1
1
0
2
1
2
0
2
2
1
1
1
1
1
1
1
3
1
1
2
1
1
2
1
1
0
1
1
1
2
2
0
1
2
1
0
0
1
1
1
1
1
1
1
1
2
0
1
1
0
1
1
2
1
1
0
0
1
1
1
0
1
1
2
2
0
2
0
2
0
2
1
1
2
2
2
0
1
2
1
1
0
2
1
0
0
1
1
2
0
1
1
1
2
1
1
1
2
1
0
2
0
2
1
1
2
2
1
1
2
1
2
0
1
1
0
2
2
1
1
1
0
1
1
2
1
0
1
1
1
1
1
0
1
1
1
1
1
1
2
1
1
1
1
1
1
2
0
0
2
1
0
1
1
1
2
0
2
1
1
2
1
1
1
1
0
2
3
2
2
2
2
1
2
1
1
1
1
0
2
2
2
1
1
2
2
1
2
2
1
2
1
1
1
2
1
3
1
0
1
1
0
2
1
1
0
2
1
0
1
2
1
1
0
1
1
2
1
1
1
1
2
1
1
1
1
2
1
2
2
1
1
1
0
1
1
0
1
1
1
1
0
2
1
1
1
2
1
0
1
1
3
1
1
1
2
1
1
2
1
1
2
1
1
2
2
0
1
2
1
2
1
1
0
1
0
1
1
2
1
2
2
2
0
0
2
1
0
2
2
1
1
2
2
2
1
1
1
1
2
0
1
2
0
0
1
2
1
2
2
0
0
3
2
2
0
1
1
2
1
2
1
1
1
1
2
1
0
1
1
1
1
2
0
2
0
0
2
1
1
0
1
1
1
1
1
1
1
1
2
0
0
1
1
1
1
2
1
1
1
1
1
0
1
1
1
0
0
1
3
1
3
1
1
1
1
2
1
2
1
1
0
2
0
0
1
2
1
1
1
1
1
2
1
2
2
1
1
1
2
0
1
1
2
2
1
1
1
2
1
0
1
1
1
2
1
1
2
1
1
2
2
2
0
1
3
1
1
1
1
1
1
1
1
2
1
2
1
0
2
2
1
2
1
1
1
1
6
2
1
2
1
1
1
1
1
2
1
1
1
1
1
0
1
1
2
1
0
0
1
2
1
1
1
1
1
1
1
1
1
1
2
1
3
1
1
1
2
1
1
0
0
1
1
1
1
1
2
1
2
1
2
0
1
0
1
0
1
2
1
2
1
2
1
1
1
0
1
1
0
0
1
2
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
2
2
1
2
1
1
1
1
1
0
0
0
2
1
1
0
1
2
1
2
1
0
1
1
1
0
1
1
1
2
1
1
0
1
1
0
1
1
1
1
0
0
1
2
2
1
1
2
2
1
0
2
1
2
1
2
1
2
1
1
1
1
2
2
1
2
1
1
1
1
0
2
1
1
1
1
0
1
2
1
2
1
1
0
1
1
1
2
0
1
1
1
2
2
1
1
1
1
1
1
2
1
2
1
0
1
1
2
1
1
2
1
1
1
2
2
0
0
1
1
1
2
2
2
1
1
0
1
2
0
1
2
1
1
1
1
2
1
2
0
2
1
2
1
2
1
0
1
0
1
1
0
1
1
1
1
1
2
1
2
1
1
1
2
1
0
1
1
1
2
1
0
1
1
0
1
2
2
1
2
1
1
1
0
1
2
1
1
1
2
1
1
2
1
0
1
2
1
1
1
1
2
2
1
2
1
1
2
1
0
3
1
2
1
2
1
2
0
1
2
0
1
1
2
2
2
0
1
1
2
2
2
1
0
2
2
2
1
1
2
1
1
2
0
0
1
1
1
1
2
1
1
0
1
1
2
1
1
0
1
0
1
1
2
1
1
2
1
1
1
1
2
1
1
1
2
1
1
1
2
2
2
1
0
2
1
1
2
1
2
0
1
1
1
0
0
1
1
1
1
0
1
1
1
1
1
2
1
2
1
1
0
2
2
3
0
4
1
1
1
0
1
2
2
1
1
1
1
1
1
1
1
2
1
0
1
0
2
1
1
1
3
2
1
1
1
1
1
2
1
2
1
1
2
0
0
1
1
1
1
2
0
0
1
2
1
1
2
2
1
2
1
0
1
2
1
1
2
1
0
2
2
2
0
1
2
1
1
1
1
1
2
2
1
1
1
1
0
0
4
1
1
2
2
0
1
1
1
1
1
1
1
1
2
0
1
2
1
1
1
2
1
1
2
2
1
1
1
1
1
0
1
1
2
3
1
0
0
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
0
1
1
1
0
2
2
1
2
2
1
1
1
2
2
1
2
1
1
2
1
0
1
1
1
2
1
0
1
0
2
0
1
1
2
1
1
1
1
1
2
1
1
1
0
0
2
2
1
1
1
0
2
0
0
1
2
1
0
1
2
2
0
1
0
0
1
1
0
2
1
2
2
1
2
2
1
0
1
1
1
1
1
2
1
2
1
2
1
1
1
1
1
1
0
1
1
0
1
1
1
1
1
1
2
0
1
1
1
1
1
2
0
1
2
0
1
1
2
1
1
1
2
0
0
2
1
1
1
0
2
1
1
0
1
1
2
0
1
0
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
0
0
1
0
1
0
2
1
1
0
2
2
2
0
1
1
2
2
1
2
2
1
1
1
1
1
0
0
0
2
0
1
2
1
2
1
2
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
0
1
1
1
1
0
1
1
2
1
1
2
1
1
1
1
1
1
1
2
0
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
0
1
1
1
1
1
0
2
1
1
2
1
1
1
1
1
2
0
0
1
2
2
1
2
1
0
1
1
1
2
0
1
1
1
2
2
1
1
1
0
1
1
1
1
1
1
2
1
1
1
2
2
1
2
2
1
1
1
2
0
1
2
2
1
0
1
1
1
1
0
2
1
2
1
2
2
2
2
1
1
1
1
1
2
1
2
1
1
1
0
2
2
1
0
1
2
1
1
0
1
1
1
1
1
1
1
1
1
1
1
2
1
0
1
2
1
2
0
2
2
2
1
1
1
1
2
2
1
1
1
1
2
0
1
1
2
1
2
2
1
1
1
1
0
1
0
1
0
1
0
1
1
2
1
0
0
1
0
1
1
2
1
1
1
0
2
2
1
1
1
1
2
1
1
2
1
2
1
1
1
2
1
1
2
2
1
2
1
1
2
1
1
1
1
2
0
0
1
2
2
2
1
2
1
1
1
1
1
1
1
2
2
1
0
1
2
2
2
1
1
1
0
2
1
1
1
0
1
1
2
1
0
1
1
1
2
1
0
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
3
1
1
0
0
1
1
1
1
1
1
2
1
0
0
1
1
1
1
1
0
2
1
1
2
1
2
1
0
1
1
1
2
2
1
2
2
2
0
1
1
1
3
1
1
2
1
0
2
1
1
0
1
1
2
2
1
1
1
0
2
1
2
1
1
1
2
1
2
1
2
1
1
1
2
2
1
1
2
1
2
1
1
2
0
1
2
1
1
2
2
2
2
1
1
2
1
1
2
1
1
1
2
2
0
2
1
1
2
1
1
2
0
2
0
0
1
2
1
1
2
2
1
1
2
0
1
0
2
2
2
1
1
2
0
2
1
1
1
1
1
1
1
2
2
1
2
1
1
1
1
1
0
1
1
2
0
0
1
2
1
1
3
1
1
1
1
1
0
1
1
1
1
2
1
1
2
1
2
1
1
1
0
2
1
1
1
1
1
1
0
0
2
0
1
2
0
1
1
2
1
2
2
1
2
1
0
2
1
1
1
1
2
1
1
2
0
1
1
1
0
2
2
1
3
1
1
1
1
2
2
1
1
1
2
1
1
1
0
0
2
1
2
2
1
1
0
1
0
1
0
1
1
1
1
1
1
1
2
2
1
1
0
2
0
1
2
2
2
1
1
1
1
1
0
0
0
1
1
1
2
2
1
0
1
2
1
2
0
2
2
1
1
2
1
2
1
1
2
0
1
0
2
2
1
2
1
2
1
0
2
0
1
1
1
2
0
2
0
3
2
0
1
0
2
0
1
1
0
1
2
0
1
1
1
1
1
2
0
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
0
2
2
2
1
1
1
1
2
1
1
0
1
2
1
0
1
1
1
1
0
2
1
2
0
2
2
2
2
1
2
1
1
1
0
1
1
2
0
2
1
1
0
1
0
2
1
0
0
2
1
2
1
2
2
1
2
0
1
1
2
1
1
1
1
1
1
2
1
1
1
2
2
1
2
0
0
1
1
1
0
1
2
1
1
0
1
1
1
1
1
1
1
0
2
1
1
2
1
2
1
2
1
1
0
2
1
1
1
1
2
2
2
1
1
1
1
2
1
0
0
1
1
1
1
1
0
0
0
1
2
1
2
2
1
1
1
2
1
0
1
1
1
1
1
1
2
1
2
2
2
1
0
1
1
1
0
1
0
1
1
2
1
1
2
1
1
1
1
0
0
1
0
2
1
1
2
2
2
1
1
1
0
2
1
1
1
1
2
2
2
1
0
2
1
2
1
1
0
0
1
1
0
1
2
1
2
1
2
1
1
2
0
1
2
2
1
1
1
1
1
1
0
1
1
2
1
1
0
2
1
1
1
1
1
2
2
1
1
0
1
1
1
0
1
2
1
1
2
1
1
1
1
0
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
0
0
0
1
2
2
1
0
1
2
1
1
2
1
1
1
1
2
1
1
1
2
1
1
2
1
1
1
1
0
1
1
0
2
2
1
1
2
2
1
2
2
0
1
2
1
1
0
1
2
2
2
1
1
1
2
0
2
1
1
2
2
1
2
1
1
2
2
1
2
1
1
0
2
1
1
1
2
0
2
1
0
1
1
1
1
2
1
1
1
0
1
1
1
1
2
0
1
2
2
1
1
1
1
1
0
1
2
1
2
0
1
2
2
1
2
1
2
0
1
1
1
1
1
2
2
0
1
2
1
0
1
0
1
1
1
1
2
1
0
1
2
1
0
1
1
1
1
0
1
1
1
1
1
0
0
1
2
2
1
1
1
1
1
1
1
2
1
2
1
2
1
1
1
1
1
1
0
0
2
2
1
2
2
2
1
1
1
2
2
1
2
1
2
0
1
2
0
1
2
1
1
1
2
1
1
1
2
1
1
0
1
1
2
2
1
1
2
2
2
1
1
1
2
1
1
1
0
0
1
1
1
0
1
1
0
2
1
1
1
0
1
2
1
1
1
1
2
1
2
1
2
1
2
2
1
0
2
0
0
1
1
2
2
1
1
1
1
1
1
1
1
0
1
2
2
1
1
1
1
2
1
2
1
0
2
0
2
2
1
2
2
0
2
1
1
1
2
1
1
2
1
1
2
1
2
2
1
0
1
2
0
0
0
0
1
1
1
1
1
2
1
2
2
1
1
2
2
1
1
2
1
1
1
0
1
1
2
1
1
0
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
2
1
2
1
0
1
1
0
1
2
2
1
2
1
1
1
2
2
1
2
1
2
2
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
2
1
1
0
1
1
2
2
1
1
1
1
0
1
2
1
2
1
2
2
2
1
2
2
1
2
1
1
2
0
1
0
2
2
2
2
1
3
1
2
2
1
2
2
1
1
1
0
1
2
0
1
2
0
0
1
1
1
1
1
1
2
1
1
1
2
1
1
2
0
1
1
1
0
0
1
1
0
0
1
1
1
2
2
1
1
2
0
1
1
1
1
1
1
1
1
1
1
2
1
1
2
0
1
2
2
2
1
2
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
2
0
1
1
1
1
1
1
2
2
2
1
1
2
1
1
2
0
1
1
1
1
1
2
2
2
1
2
1
2
0
2
1
1
1
1
2
1
1
0
2
1
2
2
1
2
1
1
2
1
1
0
2
0
2
1
1
1
2
1
2
2
2
0
2
2
1
0
0
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
1
0
0
1
2
1
0
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
0
1
1
2
1
1
1
0
2
2
1
1
0
1
0
2
1
2
2
2
1
1
1
1
1
0
1
1
1
1
0
2
1
1
2
1
1
2
1
1
0
0
2
1
2
1
0
1
0
1
2
2
1
1
2
1
1
1
1
1
1
0
1
1
2
0
1
2
1
0
1
2
0
1
1
2
1
1
2
1
1
1
1
1
1
2
1
2
0
1
0
1
2
2
1
2
2
1
0
1
1
2
1
1
1
2
1
2
1
1
1
0
1
1
1
0
1
2
1
1
2
2
0
1
1
1
2
2
2
1
1
4
2
2
1
1
1
2
1
2
0
1
2
1
1
2
1
0
1
1
1
1
0
2
2
1
0
1
1
1
1
2
1
1
0
1
1
1
1
2
1
1
1
2
1
1
2
1
1
0
1
1
2
1
1
2
2
1
2
1
1
1
1
1
2
1
1
1
1
2
2
1
2
1
1
1
0
1
1
0
1
0
1
1
1
1
1
1
2
1
1
0
1
0
3
2
1
1
1
1
2
2
2
1
2
1
4
1
1
1
1
1
2
1
2
1
1
0
2
3
1
1
1
0
1
1
1
0
1
1
1
1
1
1
0
2
0
1
0
1
1
1
1
2
1
2
2
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
2
2
1
2
2
1
1
2
2
1
2
2
1
1
3
0
0
1
1
1
1
1
2
2
1
1
1
0
2
1
2
2
0
1
1
0
0
1
1
2
0
1
0
1
1
1
2
0
2
1
1
1
1
0
2
1
2
1
1
2
0
1
1
1
1
1
2
2
1
1
1
0
1
0
1
1
1
0
1
1
0
2
2
1
1
1
1
2
2
1
0
1
2
1
2
1
2
0
1
1
1
1
1
2
1
0
5
1
1
1
2
2
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
2
1
1
0
1
2
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
1
2
1
2
2
1
2
2
3
1
1
1
1
1
1
0
0
1
1
1
2
0
1
2
1
0
1
1
1
1
2
1
1
1
1
0
2
2
1
1
1
2
12
0
0
1
2
1
1
2
1
1
2
1
1
2
2
1
1
1
1
0
1
1
2
2
2
1
1
2
1
0
0
1
0
1
2
1
1
1
1
1
2
1
1
2
1
1
2
1
1
2
2
2
1
0
1
1
2
1
2
1
2
2
1
2
1
3
1
1
1
1
0
1
2
1
2
2
2
1
1
1
1
2
1
1
1
2
1
2
1
0
1
2
2
1
1
1
2
1
2
2
1
2
0
1
2
1
2
2
1
1
0
1
1
2
1
1
2
2
1
1
2
2
1
0
1
0
1
1
0
1
1
0
1
1
1
1
2
2
1
2
1
1
1
1
1
1
2
2
1
3
0
1
2
1
1
1
2
1
1
1
1
1
1
2
2
1
0
0
2
1
2
1
1
2
2
2
2
1
0
1
1
1
0
1
1
3
2
1
2
1
1
1
2
1
0
1
1
2
1
1
2
1
1
2
1
1
1
1
1
2
0
2
1
1
1
1
2
2
2
1
1
0
1
0
1
2
1
1
2
0
1
2
1
1
2
1
1
2
2
2
1
0
1
1
0
1
1
0
1
1
1
1
1
1
1
2
1
1
2
1
0
2
1
1
2
1
1
1
0
2
2
2
2
2
1
1
1
1
1
2
2
0
2
2
1
2
0
3
1
1
2
1
1
1
1
2
3
1
1
2
1
1
1
2
2
0
2
1
1
1
1
1
2
1
1
3
2
1
0
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
0
1
2
0
1
1
1
1
1
1
1
1
0
1
2
1
1
1
1
1
1
1
0
2
2
1
1
0
1
2
1
1
1
2
1
1
1
2
2
2
1
0
1
2
2
1
2
1
0
2
2
0
1
1
1
2
1
1
1
2
1
2
1
2
1
1
1
0
2
1
1
1
1
1
0
0
2
1
1
1
1
1
0
2
1
1
2
1
1
1
2
1
1
1
1
1
1
0
1
0
1
1
0
0
1
1
2
0
2
2
1
1
2
1
2
1
1
1
2
1
1
1
2
1
1
2
1
1
2
1
1
2
1
1
0
1
1
1
3
1
1
1
1
1
2
1
1
1
0
2
1
1
1
1
0
2
1
1
1
2
1
2
0
1
2
1
1
1
2
1
2
1
1
1
1
1
1
1
0
1
1
1
1
0
1
2
2
2
2
1
1
2
0
0
1
2
2
0
2
1
1
1
2
2
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
2
1
1
2
2
1
2
1
1
1
1
1
1
1
0
1
1
0
1
2
1
1
1
1
0
1
0
1
2
1
1
0
1
0
1
1
1
1
0
2
2
1
0
2
1
1
1
2
1
1
1
1
1
2
1
2
1
1
2
1
0
1
0
2
1
1
0
2
0
1
1
1
1
2
1
2
1
0
0
1
2
1
2
1
2
1
1
1
2
2
2
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
2
1
0
4
1
2
1
1
1
1
1
1
0
2
1
2
2
1
1
1
1
1
1
2
1
1
1
2
1
1
2
1
1
2
2
2
1
0
1
2
1
1
1
1
2
1
0
1
1
1
1
1
1
1
1
0
1
3
2
1
1
1
2
0
1
2
1
1
1
1
1
0
1
1
0
0
2
1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
1
2
2
1
1
2
2
1
1
2
0
1
1
1
1
1
2
1
1
1
1
0
0
1
1
2
1
1
1
1
2
5
1
1
1
1
1
2
1
1
1
2
2
2
2
1
1
1
2
1
1
0
1
1
2
0
1
2
1
1
1
1
2
0
1
1
1
2
2
1
0
1
1
2
1
2
1
1
2
0
1
1
1
0
1
1
1
1
2
1
1
2
0
1
2
1
2
0
1
1
2
1
2
1
2
2
1
2
1
1
1
2
1
1
1
1
2
0
1
0
0
1
0
1
2
1
1
1
1
2
1
1
2
2
0
1
2
1
2
1
0
2
1
1
2
1
1
2
2
1
2
2
2
1
0
2
0
1
1
2
1
1
1
0
2
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
0
1
1
2
1
1
1
2
2
2
1
0
1
1
1
1
1
1
1
1
2
1
2
0
1
1
1
0
1
0
1
1
2
1
1
1
1
2
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
0
2
0
1
1
2
1
0
1
2
1
1
0
2
1
2
0
2
1
1
1
2
1
1
1
2
1
2
2
2
2
1
2
1
2
1
1
1
2
1
1
1
2
2
2
2
1
2
2
0
0
1
0
2
1
1
1
1
1
0
0
2
1
1
2
1
0
2
1
1
1
1
1
1
1
1
2
2
1
1
0
1
1
1
1
1
1
1
0
2
3
1
1
2
1
2
0
0
1
1
1
2
1
1
2
1
1
1
1
0
0
1
2
2
1
1
1
0
1
1
1
1
1
2
1
1
1
2
1
2
1
1
2
0
1
0
1
1
2
1
0
2
2
0
1
1
2
1
2
2
0
1
2
2
1
2
2
1
2
1
2
2
1
2
1
1
1
3
0
1
1
1
1
1
2
1
2
0
1
1
1
0
1
2
3
2
2
0
1
1
1
2
1
1
1
1
2
1
0
2
1
1
0
1
2
1
1
1
1
1
0
1
2
1
1
0
2
1
1
0
2
0
2
1
1
2
1
2
1
2
1
2
2
2
1
1
1
1
1
1
3
1
1
2
2
1
0
0
0
1
1
1
1
1
1
1
0
1
1
1
2
1
2
1
2
1
1
1
2
2
2
1
1
1
1
1
1
1
2
2
1
1
1
1
2
1
1
1
2
1
2
0
2
0
2
1
3
1
1
1
1
1
2
1
1
1
2
2
1
1
1
2
2
1
0
2
1
0
0
1
0
1
1
0
1
2
1
2
1
0
1
0
2
0
2
1
1
1
1
1
1
2
1
1
1
0
2
0
1
0
1
1
1
1
1
2
0
1
1
1
1
1
1
1
2
1
2
1
1
1
1
2
0
1
1
2
1
1
1
2
2
1
1
1
1
1
1
2
1
2
1
0
1
1
1
0
1
1
1
2
1
2
1
1
1
2
1
2
1
0
1
1
1
1
1
0
1
1
1
1
0
1
1
0
1
1
0
0
1
1
0
2
1
1
1
0
1
1
2
1
1
1
1
0
1
0
1
2
1
2
1
2
0
1
1
0
1
2
0
1
0
2
2
2
0
0
1
1
1
1
2
1
4
1
0
1
1
2
1
1
1
0
1
1
2
1
1
1
1
2
1
1
1
1
2
2
1
0
2
1
2
1
1
1
2
1
1
0
2
2
1
1
2
2
2
1
2
1
1
2
1
0
2
2
1
1
0
1
1
2
1
0
2
1
1
2
2
1
1
2
1
2
1
2
2
2
0
1
2
1
0
2
1
2
2
1
1
1
0
2
0
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
2
1
1
1
2
2
1
1
2
1
1
2
1
1
1
2
1
1
2
1
1
1
1
2
1
1
0
1
2
2
1
1
1
1
0
2
1
1
0
1
0
0
1
1
2
1
0
0
2
0
1
2
1
0
2
1
2
1
1
1
1
1
2
1
3
1
2
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
2
1
0
2
1
1
2
1
0
1
1
1
1
1
1
1
1
0
2
0
1
1
0
1
1
2
2
2
1
1
2
1
1
1
3
1
1
0
2
1
1
1
2
0
2
1
2
2
1
1
2
1
1
0
1
0
1
1
1
1
2
2
1
1
0
1
1
2
1
2
1
1
2
1
2
2
1
2
0
0
2
1
0
1
2
1
1
2
1
2
1
1
2
1
3
1
1
2
1
2
1
0
0
1
2
1
1
1
2
1
2
1
1
1
0
0
0
1
1
0
1
1
2
1
1
0
1
0
1
2
1
1
0
2
0
1
0
2
0
1
2
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
2
2
1
1
2
1
1
0
1
1
2
1
2
1
1
3
2
1
2
2
1
1
2
1
1
1
1
2
0
2
1
2
1
1
1
3
1
0
2
1
3
1
0
1
1
1
1
1
2
2
2
1
1
1
1
0
1
0
1
1
1
2
1
3
2
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
2
0
2
1
1
1
1
2
2
1
2
1
1
0
0
1
1
1
0
1
2
1
1
2
1
2
1
1
1
2
2
1
2
0
1
1
2
2
0
1
2
1
0
0
1
1
2
1
2
1
1
1
1
1
0
1
1
3
2
1
1
2
1
1
1
0
2
2
1
2
1
2
2
1
2
1
1
1
1
0
1
1
2
0
1
2
0
1
2
1
1
2
2
2
2
1
1
1
2
1
0
1
0
0
2
1
1
2
1
1
1
1
2
1
2
0
0
1
2
0
1
0
1
2
2
0
0
2
1
1
2
1
2
1
2
1
0
2
1
1
1
0
1
1
0
1
0
1
1
1
1
0
1
1
1
1
2
0
0
0
0
2
1
1
1
1
1
1
2
1
2
1
2
1
1
1
1
1
1
1
0
0
2
1
2
2
2
2
2
0
1
1
1
0
1
2
1
1
2
1
1
0
2
1
0
2
0
1
1
1
3
1
1
2
1
0
0
1
1
1
1
2
1
1
2
2
0
1
2
2
0
2
1
2
0
2
1
1
2
1
2
2
2
1
1
1
1
1
1
1
1
2
1
1
1
1
0
1
0
2
1
1
1
1
1
1
1
1
1
2
2
1
2
2
1
2
1
1
1
1
1
1
0
1
1
2
1
0
1
1
2
1
0
1
1
1
1
1
0
1
1
0
1
2
1
1
2
1
1
1
1
1
2
1
1
1
1
0
2
2
1
0
0
1
1
1
0
1
0
1
1
1
2
1
1
0
1
1
1
2
2
1
1
1
1
1
1
1
1
2
1
2
1
1
2
2
1
2
1
1
1
1
1
1
0
1
2
1
1
1
2
0
1
0
2
0
0
0
1
2
1
1
0
0
2
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
0
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
0
2
1
1
1
2
1
1
1
1
1
1
1
2
1
2
2
2
1
0
2
2
0
0
1
2
1
1
1
1
0
1
1
1
2
0
1
1
2
1
1
2
0
2
1
2
1
2
0
1
0
2
1
2
2
2
2
0
1
3
2
0
2
2
1
1
1
1
2
1
1
1
1
1
1
1
1
2
0
1
1
1
1
0
0
0
0
2
1
1
2
2
1
1
0
1
3
1
1
1
0
1
1
1
0
1
1
1
1
2
1
1
1
0
1
1
2
1
2
1
2
1
2
1
1
2
2
1
1
1
1
0
1
1
1
2
2
1
1
0
1
1
2
1
0
1
1
2
0
0
1
0
2
1
1
1
1
0
1
2
1
1
0
1
1
0
1
1
1
1
2
3
2
2
1
1
1
0
1
1
2
0
1
2
0
1
1
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
2
0
0
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
2
0
2
2
0
1
1
2
1
1
0
1
1
1
2
1
1
2
1
1
1
1
0
1
1
1
0
0
1
1
3
1
1
2
0
2
0
2
2
2
1
1
2
0
1
1
1
2
1
1
1
2
1
2
0
2
3
1
1
1
1
1
2
2
1
1
1
1
1
2
3
1
1
1
2
1
1
1
1
0
1
1
2
1
1
2
1
1
0
1
0
0
1
2
2
2
0
1
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
0
1
1
2
3
1
0
2
1
1
1
0
0
0
1
0
1
2
1
1
1
3
1
0
0
0
2
0
1
1
1
1
2
0
0
2
1
2
2
1
1
1
1
1
1
2
1
1
1
0
2
1
1
2
0
1
1
2
1
1
2
1
1
2
0
2
1
3
2
0
2
1
1
1
0
0
1
1
1
1
0
1
0
1
2
2
1
2
2
1
1
1
1
1
2
2
2
1
2
1
1
1
0
1
1
2
1
1
1
1
2
0
2
2
1
0
2
1
2
0
1
2
2
0
2
1
2
1
1
1
1
1
2
1
1
2
1
1
0
1
1
0
2
2
2
0
0
2
2
0
2
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
1
2
1
1
0
1
1
1
0
0
1
1
1
1
1
0
1
1
1
1
1
2
2
1
2
2
2
0
0
0
1
2
2
1
0
2
2
2
1
1
2
1
2
2
1
1
2
1
1
1
2
1
1
1
1
1
2
1
1
1
0
0
2
4
1
1
2
2
1
1
2
1
1
0
1
1
0
1
1
0
1
2
1
0
3
1
2
1
1
2
2
1
0
0
0
0
1
2
1
0
2
2
2
0
1
1
1
1
2
1
0
0
3
1
1
1
1
2
0
2
1
1
1
1
2
1
1
2
1
1
1
2
1
1
0
1
0
1
1
1
4
1
1
0
2
1
0
1
1
1
0
1
1
2
1
1
0
1
1
1
1
1
1
1
1
2
1
0
0
1
1
1
0
0
2
0
1
2
1
0
1
1
2
2
1
1
1
1
2
1
1
1
2
2
1
1
1
2
0
2
2
0
2
1
2
2
2
1
1
0
0
2
2
1
2
2
1
2
1
0
3
2
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
0
1
0
1
1
2
1
1
1
2
1
0
1
1
1
2
2
1
0
1
1
1
1
1
1
1
1
1
0
2
1
1
1
1
1
0
1
0
1
2
2
0
2
2
1
1
1
1
1
1
0
0
2
2
1
2
1
2
1
2
1
1
2
1
1
1
1
2
0
0
1
1
1
1
1
1
2
2
1
1
0
2
2
1
1
2
2
1
2
1
2
1
2
1
1
0
1
1
1
1
2
1
1
1
1
0
1
2
2
1
1
0
1
1
2
1
2
1
1
1
2
1
1
1
2
1
2
2
1
0
0
2
0
1
0
1
1
1
1
2
1
1
2
1
2
1
1
0
0
1
1
1
1
1
1
1
1
1
0
1
1
2
1
1
1
1
1
1
0
1
1
1
1
1
2
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
0
1
0
1
0
1
2
1
2
1
1
0
1
1
2
1
1
1
2
1
0
1
1
1
1
1
1
1
0
0
1
4
1
1
1
0
1
1
1
1
2
2
2
1
1
1
1
1
2
2
1
1
2
2
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
2
1
0
1
2
1
1
1
1
1
1
0
1
0
1
1
0
3
1
1
2
1
1
2
2
1
1
1
0
1
2
1
2
1
1
2
0
1
1
1
1
1
2
2
2
1
0
1
1
1
1
1
1
1
0
2
1
1
1
1
1
1
1
2
1
1
1
2
2
2
2
2
2
2
1
1
0
2
2
2
2
1
1
2
2
2
1
1
1
1
1
2
2
1
1
2
2
1
2
1
0
0
1
0
2
1
1
1
1
1
1
1
2
1
1
1
1
0
1
1
2
2
1
2
1
2
1
0
2
2
1
0
2
0
1
1
1
2
1
1
1
2
1
2
1
2
1
1
1
2
1
2
1
1
1
1
3
1
2
2
1
0
2
1
2
2
1
1
1
2
0
1
1
0
1
1
0
1
2
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
0
2
1
2
2
1
0
1
0
1
0
1
1
1
1
1
1
2
1
0
2
1
1
2
1
1
1
2
2
2
0
1
1
2
2
1
1
2
1
0
1
1
2
1
1
0
1
1
1
0
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
2
0
1
0
1
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
2
1
1
1
0
2
0
0
1
1
1
1
1
1
0
1
1
1
0
2
1
1
1
1
1
1
1
1
2
1
0
1
1
0
1
1
2
0
0
1
1
2
1
0
1
2
2
2
2
2
1
1
0
1
1
2
1
1
1
2
2
1
2
1
1
1
2
2
1
1
0
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
0
1
1
2
1
2
0
1
0
1
1
1
0
0
0
2
2
2
2
1
1
1
0
1
2
1
1
1
1
1
1
0
1
0
1
1
2
0
1
0
1
1
1
1
1
0
1
2
2
1
1
1
1
0
2
0
1
2
1
2
1
1
1
0
2
2
0
2
1
0
1
0
1
1
2
2
1
1
1
1
0
1
1
1
2
1
1
1
1
1
1
0
1
0
0
2
0
1
1
1
0
1
0
1
2
0
1
1
1
1
1
1
1
1
1
2
2
1
1
2
2
2
1
0
1
1
2
2
0
1
1
1
2
1
0
1
2
0
2
2
2
1
1
1
1
0
1
1
1
1
2
1
2
2
2
2
1
0
2
2
1
0
1
1
0
0
1
0
1
1
2
1
1
2
1
2
1
1
0
0
1
2
2
1
0
2
1
1
1
1
2
0
1
2
2
1
1
0
2
1
0
1
1
2
2
1
0
1
2
0
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
2
1
0
0
2
1
1
2
2
1
2
2
1
2
0
1
0
2
1
1
1
3
0
2
1
1
0
2
2
2
1
1
1
1
1
2
0
1
1
2
2
1
1
0
1
1
2
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
2
2
1
1
1
1
1
2
1
1
2
1
1
2
1
1
2
1
1
1
1
1
1
2
0
1
2
1
1
1
2
1
1
2
1
1
1
1
1
1
1
0
1
2
2
1
1
2
1
1
1
1
2
1
1
1
0
1
1
2
1
2
1
2
1
0
2
0
1
1
0
2
1
0
1
1
1
2
1
2
1
1
1
1
1
1
2
2
1
1
1
0
1
2
1
1
1
3
1
2
2
1
1
2
1
2
0
0
1
1
1
0
1
1
1
1
2
2
1
2
1
1
1
1
2
1
1
1
0
1
0
1
1
1
1
2
2
1
1
1
2
1
0
2
2
2
2
1
2
1
0
2
2
1
2
2
2
1
1
1
1
0
1
1
0
1
1
1
1
1
2
1
2
2
1
1
1
2
1
0
1
2
1
1
2
1
0
1
1
2
1
1
1
2
1
2
1
1
0
1
0
1
1
2
1
1
0
1
2
0
1
2
2
2
1
1
1
2
0
1
2
1
1
2
1
2
1
1
0
0
1
1
1
1
2
2
1
1
1
1
0
1
1
1
0
1
1
2
2
1
1
0
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
2
2
2
2
1
1
1
1
2
0
1
1
2
1
1
0
1
1
2
2
1
0
2
2
1
2
2
2
1
0
1
2
0
0
1
2
2
6
1
1
1
1
2
1
1
1
1
0
0
1
1
2
1
0
1
1
4
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
0
2
1
0
1
0
1
1
2
2
1
1
1
2
2
1
1
1
1
1
1
1
1
1
0
1
0
3
1
1
1
0
2
2
1
3
1
1
0
1
1
1
1
2
3
2
1
2
1
0
2
1
1
0
1
1
1
1
2
1
0
1
2
0
2
1
1
1
1
0
4
1
1
1
2
0
1
2
1
1
1
1
3
1
1
0
1
1
2
0
2
1
1
1
2
1
1
1
0
1
2
1
2
1
0
1
1
0
1
2
2
1
2
1
1
2
1
2
2
2
2
1
1
0
1
1
1
0
2
1
1
1
1
2
2
0
1
1
0
1
1
1
1
1
0
1
1
1
2
1
2
1
2
2
1
2
2
1
0
2
1
1
1
1
1
1
1
1
1
1
2
2
1
1
0
0
1
1
1
1
1
1
1
2
1
1
0
1
2
3
1
1
2
1
2
1
0
2
2
2
1
1
1
1
2
1
1
2
2
1
2
1
0
1
2
1
1
1
1
1
1
0
2
1
2
1
2
1
1
1
2
1
0
0
1
2
2
0
2
1
1
1
0
2
2
1
1
2
1
1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
0
2
1
1
2
2
2
0
1
0
0
0
1
2
1
2
0
1
2
1
1
1
1
1
1
1
1
1
2
0
0
2
1
2
1
2
1
1
1
3
1
1
1
1
2
1
0
0
2
1
0
1
1
1
2
2
1
2
2
1
1
2
0
1
1
1
2
1
2
1
0
1
1
1
0
2
1
2
1
2
1
1
2
1
2
1
2
1
2
1
1
1
0
2
2
0
2
0
1
1
2
2
2
0
0
0
1
1
1
2
1
1
2
1
0
0
1
1
1
2
2
1
0
1
1
1
2
1
2
0
1
2
2
1
2
1
1
2
1
0
1
1
1
1
0
1
0
3
1
1
1
0
1
1
1
1
1
1
1
0
1
0
1
1
2
1
1
1
1
1
1
0
1
1
1
1
1
1
2
1
0
0
0
1
0
0
1
1
1
1
0
0
1
0
1
0
1
1
1
1
2
2
2
0
0
1
2
1
0
1
1
1
1
2
0
1
0
0
1
0
0
2
1
2
0
1
1
1
0
1
1
1
1
1
1
0
2
1
1
2
1
1
2
2
0
2
2
0
0
1
1
1
0
1
1
2
1
1
2
1
2
0
0
0
1
1
1
0
1
1
2
2
1
1
2
1
1
1
1
0
2
1
1
0
2
1
0
4
1
1
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
2
1
2
1
1
1
0
1
2
1
1
1
1
1
1
1
2
1
2
1
2
1
1
1
0
1
1
0
1
1
1
1
1
0
0
1
2
0
1
1
0
1
2
2
0
1
2
1
1
1
1
0
0
1
1
1
1
1
1
0
1
1
2
1
1
0
1
2
1
1
1
1
2
1
2
1
2
2
0
1
1
2
1
1
2
2
1
1
1
1
2
1
2
1
2
1
1
2
1
1
1
1
1
1
1
1
1
0
1
1
1
1
2
1
1
0
1
1
2
1
1
2
1
1
1
1
1
1
1
1
2
2
0
1
2
1
0
2
2
2
1
1
1
0
1
0
0
0
1
1
1
0
1
1
2
0
2
1
1
1
0
1
1
0
1
2
1
0
2
1
1
1
2
2
1
1
1
2
1
1
3
0
1
2
1
1
1
2
2
1
1
1
2
1
1
2
1
1
1
2
2
3
0
1
1
2
0
1
1
1
2
1
1
2
2
2
0
1
2
2
1
1
1
2
1
0
1
0
0
2
1
1
2
2
1
1
2
1
0
2
0
1
1
1
2
1
1
2
1
1
0
2
1
1
0
1
1
2
1
1
1
2
1
1
1
1
0
1
1
1
1
1
1
2
0
1
1
2
1
1
1
0
1
1
1
1
1
1
1
1
0
1
1
2
2
1
1
1
1
1
1
0
1
1
1
1
1
1
0
1
0
2
1
1
2
1
0
1
1
1
1
1
1
2
1
1
1
2
2
2
1
1
1
1
1
1
1
1
1
2
2
2
2
1
1
0
2
1
2
2
1
1
1
1
2
0
1
1
0
1
1
1
0
1
1
1
1
1
0
2
2
1
1
1
1
0
0
0
2
2
2
0
1
2
1
1
2
1
1
1
2
2
0
2
1
2
1
2
1
2
1
0
1
1
0
0
1
2
2
1
1
2
1
1
2
1
1
1
1
1
1
1
1
0
2
1
1
0
1
1
1
1
1
1
1
1
1
2
1
2
1
0
2
1
1
1
0
0
2
2
1
0
1
1
1
1
1
2
0
2
1
1
1
1
1
1
1
1
2
2
1
1
0
2
2
1
1
2
1
1
0
1
1
3
2
1
2
0
0
1
0
1
2
0
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
0
1
1
1
2
2
1
2
1
2
1
1
1
1
1
2
0
2
1
0
1
1
1
0
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
2
2
1
2
2
0
0
0
0
0
1
1
2
1
2
2
1
1
1
0
1
1
2
1
1
0
1
2
1
2
0
1
1
1
0
1
2
1
2
1
1
2
1
1
2
1
1
1
1
2
1
0
0
2
2
1
1
2
1
1
1
1
1
2
1
2
1
2
1
1
0
1
1
2
1
1
0
1
1
2
1
1
0
1
1
2
1
1
1
1
0
1
0
2
1
2
1
1
1
1
1
0
2
1
1
1
2
2
1
2
1
1
2
1
2
1
1
1
0
2
1
1
1
2
0
1
2
1
1
2
1
1
1
1
1
1
1
0
2
0
2
1
1
0
2
1
1
1
1
1
1
0
1
1
1
2
2
1
1
1
1
1
1
1
1
1
0
1
3
2
0
1
1
1
2
1
0
1
1
2
1
1
2
0
2
1
0
1
1
1
0
1
2
2
2
0
1
1
1
0
1
1
1
1
0
1
2
1
1
1
1
1
2
1
1
1
2
0
2
0
1
2
2
1
1
1
1
2
0
2
1
2
1
1
1
1
1
2
2
1
1
1
0
1
1
1
1
1
2
0
2
2
1
1
1
2
2
2
1
1
2
2
1
0
2
0
1
1
2
1
1
1
2
1
1
0
1
1
1
2
1
1
2
1
1
0
1
2
2
1
2
1
0
1
2
1
1
1
3
1
1
1
2
1
2
2
2
1
2
1
2
1
1
1
1
2
1
1
1
1
1
0
1
2
1
2
0
2
1
1
1
0
2
2
2
2
1
0
2
2
0
0
2
1
1
1
1
1
2
0
1
1
0
1
0
1
1
1
1
2
1
1
1
1
1
1
2
1
1
2
0
0
2
1
2
0
0
2
1
1
0
1
2
0
2
1
1
2
1
1
2
1
2
2
2
2
1
1
1
1
1
1
2
1
2
2
1
2
0
2
2
2
2
1
1
0
0
1
1
1
1
1
2
1
2
1
0
2
0
2
2
1
0
2
1
1
2
0
1
1
1
1
2
2
0
1
1
1
1
1
1
1
1
0
1
0
1
2
0
1
1
1
1
1
1
2
1
1
2
1
1
1
2
0
1
2
2
2
1
1
1
0
1
1
1
0
0
1
2
2
1
2
1
1
1
1
1
1
1
1
2
1
1
1
0
0
1
1
1
0
2
2
0
1
1
0
1
0
1
1
1
2
1
2
2
2
1
1
1
0
2
1
1
1
3
2
1
1
1
1
1
1
1
2
3
1
2
2
1
0
2
1
2
1
2
1
1
1
1
1
1
2
1
1
1
0
1
1
2
1
0
0
2
2
1
2
2
0
0
1
2
1
1
1
1
1
1
2
0
1
1
0
1
1
1
1
1
1
2
2
1
1
0
2
1
1
1
1
1
1
2
1
1
0
1
0
0
2
1
1
1
1
0
1
0
1
2
1
1
0
0
5
1
1
1
1
1
2
1
0
0
1
2
1
1
1
2
1
1
1
0
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
0
1
2
1
1
1
1
0
2
1
1
2
1
1
2
2
1
2
2
0
1
2
1
1
1
1
1
1
1
2
1
1
0
2
1
1
2
1
1
0
2
2
1
2
1
1
2
2
1
1
1
1
1
1
0
2
1
0
2
1
1
1
1
1
0
1
4
2
1
2
1
1
2
0
1
0
2
1
1
1
1
0
1
1
2
2
1
2
0
1
1
0
0
2
2
0
2
1
1
2
1
0
1
0
1
0
1
1
2
0
1
2
1
1
2
1
1
1
1
2
1
1
2
1
1
1
2
0
2
1
1
1
1
2
0
1
1
1
1
1
1
2
1
1
1
1
1
2
0
1
1
1
2
0
0
2
1
1
2
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
0
1
2
2
1
1
1
1
1
2
1
1
0
0
1
0
1
1
1
1
0
2
1
0
2
2
2
1
2
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
2
0
1
2
1
2
1
0
2
1
1
1
2
2
2
2
1
2
1
2
1
1
1
0
2
1
0
1
1
0
2
2
1
1
1
1
2
1
1
1
1
1
1
2
1
2
1
0
1
1
1
1
0
1
2
2
1
1
2
2
1
2
0
2
1
1
2
1
1
2
1
1
2
2
1
1
1
1
0
1
1
1
1
1
2
1
1
1
1
2
1
0
1
1
1
2
2
1
1
1
2
1
2
0
2
0
1
1
0
2
1
1
1
1
1
2
1
1
0
1
1
1
1
2
2
1
1
2
2
1
1
2
1
2
1
0
2
1
0
1
1
1
0
2
1
2
0
2
1
1
1
0
1
1
1
1
1
2
1
1
1
1
2
2
1
1
1
1
2
2
1
1
2
1
1
1
1
1
0
1
2
1
1
0
0
2
0
0
1
1
2
1
2
1
1
1
1
0
2
2
1
1
1
2
0
2
1
1
0
1
1
1
1
0
1
3
1
0
1
1
2
1
1
2
1
1
1
1
1
1
0
0
1
1
1
1
1
2
2
1
0
2
2
1
1
2
1
1
0
1
1
1
2
2
1
1
1
1
2
2
1
1
0
1
2
2
1
1
2
1
1
1
1
1
1
1
3
2
1
2
1
1
2
1
2
1
1
1
1
2
2
1
0
1
0
1
0
2
1
2
1
2
2
0
1
1
1
2
1
1
2
1
1
2
1
1
1
1
1
2
0
1
2
1
2
0
2
0
1
1
1
2
0
1
1
2
3
2
1
1
2
2
1
1
2
1
0
2
1
1
1
2
2
2
1
2
1
0
2
1
2
1
1
1
1
2
1
2
1
1
1
2
2
1
0
1
1
1
1
1
1
2
1
2
0
1
1
0
1
1
0
2
2
0
1
2
1
2
1
2
1
2
1
1
1
1
1
1
0
2
1
2
1
1
0
1
1
1
1
1
1
1
1
2
1
2
1
1
1
2
0
1
1
2
0
2
0
2
1
1
1
1
1
1
2
2
2
2
1
2
1
1
1
0
0
0
1
2
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
2
0
0
1
1
2
1
1
2
0
0
0
1
1
2
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
2
0
1
1
0
1
1
1
2
1
1
1
2
2
1
1
2
0
2
1
0
2
1
1
1
1
1
1
0
1
1
1
2
2
1
1
1
1
1
2
1
0
2
1
0
0
2
2
1
1
1
1
2
1
1
1
1
0
1
1
1
1
1
1
0
1
2
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
1
2
1
0
1
0
1
2
1
1
2
2
1
0
1
2
1
1
1
2
2
2
2
1
0
1
1
1
1
1
2
0
1
0
1
1
1
0
2
1
2
1
2
0
1
1
1
1
1
1
1
1
2
1
2
1
1
1
2
1
1
1
2
0
1
1
2
2
0
1
2
0
1
2
1
0
0
1
1
0
2
1
2
2
2
2
2
1
1
2
1
0
1
1
1
0
2
2
1
2
1
0
1
0
2
0
2
1
2
1
1
2
1
2
1
1
1
1
1
0
1
1
0
2
1
1
2
1
2
2
1
1
2
1
1
1
1
2
1
0
2
1
0
3
1
1
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
0
2
2
0
0
1
1
0
1
0
0
2
0
2
1
2
1
1
0
0
0
1
1
2
2
0
1
1
1
1
2
0
2
2
1
1
0
2
1
1
2
1
1
1
1
0
1
1
1
2
1
2
0
2
2
1
1
0
1
1
0
0
2
1
1
1
1
2
1
1
1
1
1
2
0
1
1
2
1
1
2
1
2
0
1
1
1
0
1
2
1
1
1
2
1
1
0
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
0
1
1
0
1
1
0
1
2
2
0
2
1
1
1
1
1
2
1
2
1
0
1
2
2
2
2
2
2
1
1
1
1
1
0
2
1
2
1
0
1
1
2
0
3
1
1
1
1
2
2
2
2
2
2
2
0
2
1
1
1
1
2
1
2
1
3
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
0
0
1
1
1
1
1
1
0
1
0
1
3
1
2
0
2
2
1
1
2
1
1
1
2
1
1
2
0
1
1
0
1
1
2
1
0
0
1
0
2
1
2
1
1
0
2
0
0
1
1
1
1
1
1
0
1
1
0
2
1
1
1
2
3
1
1
1
1
1
1
4
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
2
1
1
0
2
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
2
1
2
1
0
0
1
1
1
1
2
2
0
1
1
0
1
1
1
1
2
1
1
1
1
1
1
0
1
1
1
1
2
0
1
2
2
2
1
2
2
0
2
0
2
2
2
0
1
1
1
2
2
0
0
0
1
1
0
2
1
2
3
1
1
1
2
2
1
2
2
0
0
1
0
1
1
1
2
1
1
2
2
2
2
1
1
2
2
2
0
1
2
1
1
0
1
1
1
1
2
0
1
1
1
0
1
1
1
1
1
1
2
1
2
2
1
1
2
1
2
2
1
1
1
1
0
1
2
1
1
2
0
1
2
2
1
1
1
1
2
1
1
1
2
1
1
1
1
0
1
2
2
2
2
1
2
1
1
1
0
0
2
1
0
2
2
1
0
1
2
1
1
2
2
2
1
0
1
2
2
1
1
1
2
0
0
2
0
1
1
1
1
1
1
0
1
2
1
2
0
1
1
1
2
1
1
2
1
2
1
1
2
1
2
1
0
0
0
2
1
1
1
1
1
1
1
1
1
1
0
1
1
1
2
0
2
2
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
2
1
1
1
1
0
1
2
1
2
2
1
0
1
1
2
0
2
1
1
1
1
1
1
2
1
2
2
2
1
0
2
1
1
1
2
1
0
1
1
0
2
2
0
2
0
2
1
1
2
2
1
1
1
0
1
1
1
0
2
2
1
2
2
2
3
1
0
1
1
1
0
1
2
2
0
1
1
2
1
1
1
0
2
2
0
1
1
0
1
2
0
1
2
0
1
2
2
1
1
1
0
0
1
1
1
2
1
0
1
1
2
0
1
1
1
2
1
2
1
1
0
1
0
2
1
2
1
2
2
0
1
1
1
2
1
1
0
1
1
1
1
2
1
2
2
1
0
1
2
2
1
1
0
1
2
1
1
1
1
0
1
2
1
1
1
2
2
2
0
1
1
1
2
2
2
1
0
2
1
1
2
1
1
1
2
1
1
1
1
1
2
0
2
1
0
1
1
2
1
1
1
1
0
2
2
1
1
1
1
2
1
1
0
0
1
1
0
1
2
2
2
2
2
1
1
2
1
0
1
2
0
0
1
2
2
0
2
1
1
1
1
2
2
1
2
1
1
1
0
1
1
1
2
1
0
2
1
2
1
1
2
1
1
0
0
2
2
1
2
1
1
1
0
1
1
0
1
1
1
0
1
1
1
1
1
2
1
1
2
1
0
1
0
1
1
2
1
2
1
1
2
1
2
1
1
1
1
1
0
0
2
1
2
2
0
1
2
1
1
0
1
1
1
0
1
1
1
2
0
2
3
0
0
0
1
1
1
0
0
1
1
2
3
1
0
1
1
1
0
0
2
1
1
1
1
1
2
1
1
1
2
2
1
2
1
0
1
1
1
2
1
1
1
1
2
0
1
0
0
1
1
1
2
1
1
1
2
1
1
0
1
1
0
0
2
2
1
2
1
1
1
1
1
2
1
0
2
2
1
2
1
2
2
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
1
1
0
1
1
2
1
1
1
1
1
1
2
1
0
5
2
1
1
1
1
1
2
1
1
1
1
1
1
1
3
2
2
2
1
2
1
1
1
2
1
1
2
1
2
1
1
0
2
1
1
1
2
1
1
1
2
2
1
2
2
1
2
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
1
2
0
1
0
1
2
1
1
0
2
1
0
1
1
1
1
2
1
2
1
2
1
2
0
1
1
1
0
0
2
1
1
0
3
1
0
2
1
2
2
1
0
1
3
0
0
1
1
1
2
1
2
2
1
2
1
1
0
1
2
1
2
1
2
2
1
1
2
2
1
2
1
2
1
1
1
1
2
2
1
2
1
1
1
1
1
1
0
2
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
0
1
1
1
2
1
1
1
1
1
1
1
0
1
1
1
1
1
1
2
1
2
1
1
1
1
2
0
4
2
1
0
1
1
1
1
0
2
1
1
1
1
0
1
1
1
0
1
0
1
1
1
2
1
0
1
1
2
2
2
1
0
1
3
1
2
1
1
1
2
1
1
1
0
1
1
1
0
1
1
1
0
1
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
2
1
1
2
2
1
2
1
1
2
1
2
2
2
1
2
1
1
2
1
1
1
2
2
2
1
1
1
0
2
2
1
1
1
1
1
1
2
1
1
2
1
1
1
0
1
0
1
1
2
2
1
1
1
1
2
1
1
1
1
1
2
1
0
1
1
1
1
0
2
2
0
1
2
2
1
1
1
2
2
1
0
1
1
2
2
2
1
1
1
1
0
2
1
2
1
1
1
0
2
3
1
2
3
2
1
1
1
1
0
2
1
2
1
1
1
1
2
0
1
2
1
2
2
1
1
0
1
1
1
1
1
0
0
1
1
1
1
0
1
2
1
1
2
1
2
2
2
2
1
2
2
4
1
1
0
0
2
1
2
1
1
1
2
1
0
2
2
1
2
1
2
2
1
1
1
0
1
1
0
1
2
2
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
2
2
1
1
1
1
1
1
0
0
1
2
2
1
1
0
0
1
0
1
1
1
0
1
1
0
1
0
0
1
0
1
1
1
1
0
2
1
1
1
1
2
0
1
2
1
1
5
1
1
2
1
1
2
1
1
2
2
1
0
1
1
1
1
1
0
1
1
2
2
2
0
2
2
1
1
2
2
1
0
1
1
2
1
2
1
0
1
1
1
2
1
1
0
1
1
1
1
2
1
1
0
1
1
1
1
1
2
1
0
0
1
2
1
0
2
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
0
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
1
1
3
0
1
0
2
2
1
1
1
1
1
0
1
1
1
1
1
2
0
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
0
1
2
1
1
1
1
1
2
1
2
1
0
2
1
1
2
1
0
2
2
0
1
2
2
2
1
1
1
1
0
1
1
1
2
1
0
1
2
2
0
1
1
1
0
1
2
1
1
1
2
0
0
0
1
1
1
1
3
0
1
0
1
2
2
0
0
1
1
1
2
2
1
1
0
1
1
1
1
2
1
0
2
1
2
0
2
1
1
2
0
1
0
1
1
1
2
1
2
1
1
1
1
2
1
1
1
2
2
1
1
2
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
1
2
0
1
1
1
1
1
1
2
0
2
1
1
1
0
1
2
1
1
0
1
2
1
1
2
1
2
0
1
1
2
2
1
2
1
1
1
2
1
1
1
1
0
1
1
1
1
1
1
2
0
1
1
0
1
2
1
2
1
2
1
1
1
1
0
1
0
2
2
1
2
1
2
2
2
1
2
1
1
1
2
1
2
1
1
2
1
1
2
1
1
0
1
0
1
1
0
1
1
1
2
1
1
1
0
2
1
1
0
1
1
2
0
1
1
1
1
2
1
2
1
2
1
2
2
2
1
1
1
1
0
2
1
1
0
1
1
2
1
1
2
1
2
1
1
2
1
1
1
2
1
0
1
0
1
1
1
1
1
2
1
2
2
1
2
1
1
2
0
1
3
0
1
2
1
1
1
0
1
1
1
1
2
1
2
1
1
1
0
1
2
2
2
1
0
2
1
1
1
2
2
1
1
2
2
0
1
1
1
2
0
1
0
1
1
2
2
1
0
1
1
1
0
1
1
1
1
1
0
1
0
2
1
1
2
1
0
1
1
2
0
2
2
0
1
1
1
2
2
1
1
1
1
1
1
0
2
2
1
1
1
0
1
1
0
2
2
0
2
1
2
2
1
2
2
2
3
1
1
2
1
2
2
1
2
0
2
1
0
1
0
2
2
1
1
1
1
1
1
2
2
0
1
2
1
1
2
0
2
1
1
0
2
0
1
1
1
2
1
1
0
1
2
1
1
2
2
3
1
1
1
1
1
1
2
1
1
1
1
1
1
0
1
1
1
1
1
0
2
1
1
1
1
2
1
0
2
1
1
0
1
1
2
1
1
1
1
2
1
1
2
2
0
1
1
1
1
2
1
2
1
2
0
0
1
1
1
1
2
2
1
2
1
2
2
1
1
1
1
2
1
12
1
2
0
1
1
1
1
2
2
1
1
1
1
2
1
1
0
1
1
2
1
0
0
0
1
2
0
0
2
1
1
2
1
0
1
2
2
1
1
0
1
1
1
1
1
1
1
1
2
1
1
2
2
1
2
1
1
0
2
1
0
1
2
0
1
1
2
1
1
1
0
1
1
1
1
1
0
1
1
1
0
1
0
1
2
1
1
1
1
0
1
2
1
2
2
1
1
1
1
1
1
1
2
0
0
1
1
0
2
0
1
2
0
0
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
0
2
1
1
1
1
1
1
2
1
2
1
1
1
1
2
0
0
1
1
1
2
1
0
2
1
1
1
2
1
2
0
1
1
1
0
1
1
1
1
1
0
1
0
1
1
0
2
2
2
0
0
1
0
1
1
2
1
1
0
1
2
1
1
3
2
1
1
1
1
2
2
1
0
0
1
0
0
1
1
2
0
1
1
0
1
1
1
0
0
0
1
1
1
1
1
1
0
1
0
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
0
0
1
0
2
0
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
2
2
1
1
1
1
1
2
1
2
1
1
1
2
1
1
2
1
0
0
1
1
1
2
2
2
2
1
1
1
1
2
1
1
0
0
0
1
2
2
2
0
1
1
2
3
0
0
1
1
1
1
1
1
1
2
2
1
1
0
2
2
2
2
0
0
1
1
1
1
1
1
1
0
0
2
1
1
1
2
0
1
1
2
2
0
1
0
2
0
1
1
1
0
1
1
0
2
1
0
1
0
1
1
0
1
2
1
1
1
1
0
1
1
1
2
1
1
2
2
1
1
1
2
1
2
0
1
1
1
1
2
1
2
1
1
1
0
1
2
1
1
1
1
1
2
2
1
1
2
1
0
2
1
1
1
0
2
0
1
0
1
1
2
0
1
1
2
2
1
0
1
0
1
0
1
1
1
1
2
0
2
2
1
1
1
0
1
2
1
2
2
2
2
1
2
1
0
1
1
1
0
2
2
1
1
0
1
0
2
1
2
2
2
1
1
1
2
0
1
1
2
2
0
0
1
1
1
1
2
2
1
2
1
1
1
2
1
1
1
1
1
0
1
1
0
1
2
0
12
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
1
2
2
1
1
2
1
1
1
2
2
1
1
1
1
1
1
1
2
1
2
1
2
2
0
1
1
1
1
1
1
1
1
2
2
0
2
2
1
1
2
1
1
1
2
1
1
0
2
1
1
1
0
0
2
0
1
1
1
2
3
1
2
1
2
1
1
1
0
1
1
0
1
1
1
1
1
1
2
1
1
2
2
1
2
1
0
2
2
1
1
1
2
1
1
1
1
1
2
0
1
1
1
2
1
1
1
2
1
1
2
2
1
1
2
1
2
0
1
1
1
2
1
0
2
2
2
1
2
1
1
1
1
0
2
2
0
0
1
1
0
1
1
2
1
1
1
2
1
2
2
1
2
2
1
1
1
0
1
2
2
1
1
1
0
1
1
1
1
2
1
0
2
2
1
1
1
1
1
1
1
1
2
2
2
0
1
1
1
0
1
1
2
0
2
1
1
1
1
1
1
1
0
1
1
0
0
2
1
2
1
0
0
2
2
0
1
1
2
2
1
1
1
2
1
1
1
1
0
1
1
2
1
1
1
0
1
1
0
2
1
2
2
1
2
1
1
2
1
1
1
1
1
2
0
1
1
1
1
2
1
3
0
2
2
1
0
0
2
0
1
2
0
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
0
2
0
1
0
1
1
1
1
1
2
1
1
0
1
0
0
2
0
0
1
1
1
2
1
1
0
2
2
2
2
2
2
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
0
2
1
1
1
2
1
2
2
0
1
1
2
2
1
2
1
1
0
1
1
2
1
1
1
1
0
1
1
2
1
1
0
1
1
2
1
2
2
2
1
1
1
0
1
1
0
0
2
1
2
2
1
1
0
1
2
1
0
1
1
1
1
1
1
2
0
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
0
1
1
1
1
1
0
1
1
0
1
1
1
2
1
0
2
0
3
2
1
1
1
1
1
1
3
1
1
1
1
1
2
1
2
2
1
0
1
0
0
2
2
1
0
2
0
0
1
2
0
2
1
2
1
2
1
1
1
2
1
1
1
2
2
2
2
1
2
0
1
1
0
1
1
1
1
0
2
1
2
2
0
2
1
2
1
1
1
2
2
1
1
1
1
1
1
1
2
2
1
2
0
2
1
1
1
2
1
2
1
1
1
0
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
0
1
1
1
1
2
2
2
2
1
1
1
2
0
2
1
2
2
2
2
1
1
2
1
1
2
1
1
1
1
1
2
2
2
1
2
2
1
2
1
1
0
1
2
2
0
1
1
2
1
2
2
1
2
2
1
1
2
1
1
2
0
1
2
1
2
1
0
0
2
1
1
1
1
0
2
1
2
1
0
2
2
1
2
0
2
2
1
2
1
1
1
1
1
0
1
1
1
2
2
2
1
1
1
1
1
1
1
2
1
1
2
1
1
0
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
2
1
1
1
2
0
1
0
1
0
1
2
1
2
1
1
1
1
0
1
2
0
1
1
1
1
1
1
1
2
2
1
1
1
2
1
1
0
1
2
2
2
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
0
1
0
2
2
1
1
1
1
0
2
1
2
1
2
2
1
1
1
1
2
3
2
2
1
2
1
1
2
0
0
2
0
1
4
2
1
1
2
0
2
2
1
1
1
1
0
0
3
1
1
2
2
2
1
1
2
3
1
0
1
1
0
0
2
1
1
1
1
3
1
1
1
1
2
1
2
2
1
2
0
1
2
1
1
1
2
1
1
1
1
1
1
1
2
0
1
2
2
2
0
1
1
0
1
1
1
2
2
1
0
1
1
1
1
0
0
1
1
2
1
0
1
2
1
1
1
1
2
0
3
2
1
1
1
1
1
0
1
1
0
1
1
1
2
1
1
1
1
2
1
1
2
0
1
2
1
1
2
1
2
1
2
1
1
2
1
1
0
2
0
1
0
1
0
2
1
1
2
2
1
1
1
2
1
2
1
1
1
2
1
2
1
2
1
1
0
2
1
3
2
0
0
1
2
1
1
1
2
1
0
1
1
2
0
1
1
2
1
1
0
2
2
2
1
1
1
2
1
2
1
0
1
1
2
1
1
2
1
2
0
1
0
1
1
2
1
2
1
0
1
1
2
1
2
0
1
1
0
0
0
1
1
2
1
1
2
2
2
1
2
1
0
2
1
0
1
2
1
2
1
1
2
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
2
1
1
1
1
2
1
2
1
1
1
1
2
0
2
1
1
0
2
1
1
2
1
1
1
2
1
1
1
1
1
2
2
0
1
1
1
0
1
1
3
1
1
1
1
2
2
0
1
1
2
1
2
1
0
1
0
2
1
2
0
0
1
1
1
2
0
1
1
0
1
0
1
2
1
1
1
3
1
0
1
2
2
1
1
0
1
2
0
1
1
1
1
2
1
1
1
1
0
1
2
0
1
1
1
1
2
2
1
1
1
1
2
1
0
1
0
1
0
1
2
1
1
1
1
1
1
1
0
1
2
0
1
2
1
0
1
1
1
1
0
1
1
1
2
0
1
2
0
0
1
2
1
1
1
1
1
1
1
2
3
1
1
2
1
1
0
1
1
1
1
0
1
1
1
1
2
1
2
0
0
1
1
0
1
1
1
0
1
0
1
1
0
1
1
1
2
2
1
1
1
2
1
1
0
2
1
1
0
1
1
1
1
2
1
1
0
2
2
1
2
2
1
2
1
2
1
2
2
2
1
2
1
1
2
2
1
1
0
2
1
1
1
0
2
1
2
2
1
3
2
1
1
0
2
1
1
1
1
1
0
2
1
2
2
0
1
1
1
2
0
2
1
2
2
1
1
1
0
1
1
2
0
1
1
1
0
2
1
1
1
2
2
1
1
2
2
1
1
1
1
2
0
1
1
2
2
1
2
1
1
1
1
0
2
1
1
1
1
1
2
1
1
0
1
1
2
1
0
1
1
1
0
0
0
1
1
1
2
1
1
1
0
1
2
2
1
1
1
0
2
0
1
1
2
1
1
2
0
2
1
3
1
1
1
1
1
0
2
1
2
1
1
2
0
2
1
2
2
1
1
1
2
1
0
1
2
2
1
1
1
0
1
1
0
1
2
1
1
1
1
1
1
1
0
0
1
1
1
1
0
1
1
1
1
1
2
2
2
1
1
1
2
2
2
2
2
2
1
2
1
1
1
1
1
1
0
1
0
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
3
1
1
1
2
1
2
1
1
0
2
1
1
2
1
1
1
1
0
1
0
1
1
1
2
1
1
1
0
2
2
1
1
1
1
0
1
0
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
0
1
1
1
1
1
1
2
1
2
1
1
1
1
1
0
2
0
1
1
1
2
1
1
1
1
1
1
0
2
1
0
2
2
0
2
1
1
1
1
1
1
2
2
2
2
2
2
1
0
0
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
2
2
1
0
2
1
1
1
2
1
0
1
0
1
2
2
1
1
1
2
1
1
1
1
2
1
0
2
0
1
2
1
1
2
1
1
2
1
0
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
0
1
2
2
1
1
2
2
1
1
1
2
0
1
1
1
1
0
0
1
1
1
1
2
2
2
2
0
2
1
1
1
1
1
1
2
2
2
1
2
2
1
2
2
1
1
1
2
1
1
0
2
1
1
1
2
1
1
1
0
1
0
2
1
1
2
1
1
0
1
2
1
1
2
3
5
2
2
1
1
2
2
1
0
1
1
1
2
1
1
1
1
0
2
2
1
1
2
1
2
1
0
1
1
2
1
1
2
1
1
1
0
1
2
2
1
0
1
1
1
1
1
1
1
1
1
2
1
0
1
1
0
1
1
1
1
1
1
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
3
2
1
0
1
1
1
0
2
1
1
1
1
1
1
2
2
2
2
1
0
1
2
1
1
1
1
2
2
0
0
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
0
1
2
1
0
1
2
1
1
2
4
1
1
2
1
2
2
0
0
0
2
1
1
1
2
2
1
2
1
2
2
1
2
1
1
0
0
1
1
1
1
1
1
1
2
1
1
1
0
1
0
1
1
1
0
2
2
0
2
1
1
2
0
1
2
1
1
1
1
1
1
2
2
1
0
2
1
1
1
1
1
1
1
2
0
0
2
1
1
2
0
1
1
1
0
2
2
1
1
0
2
1
1
1
1
1
1
2
1
1
2
2
1
1
0
1
1
0
2
1
0
2
1
1
1
1
1
0
1
1
1
1
1
2
1
0
2
1
2
1
1
2
1
0
2
1
1
0
2
1
1
2
1
1
0
1
1
1
0
1
1
1
1
1
0
2
2
1
2
2
1
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
0
1
1
1
1
1
1
1
1
1
1
0
2
1
1
1
1
1
2
1
1
1
2
1
2
1
2
1
2
2
1
1
1
0
1
1
3
1
2
1
2
2
2
0
1
1
2
1
1
2
2
1
1
1
1
2
2
1
1
1
1
1
1
1
1
2
1
2
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
0
1
1
1
0
2
1
1
1
2
0
1
0
2
1
1
1
0
0
1
1
1
2
1
1
1
2
1
1
1
1
2
2
1
2
1
1
1
2
1
0
1
1
0
0
1
2
2
2
1
1
1
3
1
1
1
0
1
1
1
2
2
1
2
1
1
1
1
1
1
1
2
1
1
2
0
1
1
1
1
2
1
2
2
1
1
0
2
1
0
2
2
2
1
0
1
1
0
1
1
1
2
0
1
1
1
1
0
1
0
1
2
1
2
1
1
2
1
1
1
0
1
0
2
1
1
2
2
2
0
2
2
0
1
2
1
0
2
0
2
0
1
1
1
0
1
1
1
1
1
1
0
1
1
1
1
2
1
1
1
1
0
1
2
2
1
0
1
0
1
1
1
1
1
1
1
1
1
1
2
0
2
1
2
1
2
0
1
1
2
2
1
2
0
2
0
0
1
1
2
2
1
0
2
1
1
1
1
1
0
1
1
1
8
0
1
2
1
1
1
2
1
0
0
1
2
2
1
1
0
1
0
1
1
1
1
1
1
0
2
1
1
3
1
1
1
1
1
1
2
1
1
1
2
2
1
1
2
1
1
1
2
0
1
1
0
1
0
1
0
1
2
1
1
1
1
1
2
2
2
2
1
1
1
2
2
1
0
2
1
1
2
0
1
1
1
2
0
1
1
1
2
1
1
0
2
1
1
1
1
1
1
1
2
1
2
1
0
0
1
2
0
2
1
1
0
1
1
0
1
1
1
0
1
0
2
1
1
0
1
1
1
1
0
2
1
1
1
0
1
2
1
1
1
0
1
1
2
1
3
0
1
1
2
1
2
1
1
1
1
1
1
1
1
1
2
0
0
1
1
4
1
1
1
0
2
1
2
2
1
1
1
3
2
1
0
1
1
2
0
1
0
0
1
1
2
1
1
1
1
1
2
1
1
1
0
1
1
1
1
1
1
0
0
1
1
1
0
0
1
2
2
2
2
1
1
1
2
1
2
2
1
2
0
1
1
1
2
0
1
1
1
1
2
1
1
1
1
2
1
2
2
1
1
1
3
1
0
1
1
0
1
1
2
2
1
1
1
0
2
1
2
1
0
1
1
1
2
0
1
1
1
2
1
0
2
1
1
1
1
1
0
1
0
1
0
1
2
1
1
1
2
2
0
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
2
1
2
1
0
1
2
2
1
1
1
1
1
0
1
0
2
0
1
1
1
1
1
0
2
0
0
0
1
1
1
0
1
1
1
2
1
1
1
2
2
2
1
1
1
2
1
2
1
1
0
0
2
2
1
2
1
1
1
1
1
2
2
1
2
1
1
1
2
1
1
2
2
2
1
1
2
1
1
1
1
0
1
2
0
1
1
1
2
1
2
2
2
1
1
0
1
1
1
2
1
2
1
2
2
1
1
1
2
1
2
1
0
1
1
1
1
1
1
1
0
1
1
0
2
1
2
1
1
1
1
1
1
2
1
1
1
0
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
0
1
2
1
1
1
1
1
1
1
0
1
1
2
1
1
1
1
2
2
1
1
2
2
1
0
1
1
0
2
1
0
2
1
1
1
1
1
0
2
1
0
1
2
1
0
1
1
1
2
0
1
1
1
2
1
2
1
1
2
0
1
2
0
0
1
0
0
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
2
1
2
0
1
1
1
1
1
1
2
0
1
0
2
1
1
1
1
1
0
1
2
0
2
2
1
1
1
1
2
1
2
1
0
1
1
2
1
1
2
1
1
1
1
0
2
1
1
1
0
1
1
1
2
1
1
1
2
2
1
1
1
0
1
1
2
2
1
0
1
2
1
2
0
0
2
3
1
0
4
1
1
1
1
0
1
1
0
1
2
2
1
1
2
1
1
1
1
1
2
2
1
1
2
1
1
1
1
1
2
2
1
2
1
2
1
1
0
2
2
1
2
1
1
1
1
2
2
1
0
2
1
2
2
1
1
0
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
2
1
2
2
1
1
1
2
1
1
1
1
1
1
1
1
0
1
1
2
1
1
2
1
1
1
0
1
1
2
2
2
2
0
1
0
1
2
1
1
1
1
2
1
0
1
1
1
1
0
0
1
0
1
1
2
0
1
1
1
1
1
1
0
1
1
0
2
2
1
1
2
1
2
1
2
1
2
1
1
2
2
1
1
2
1
2
1
2
1
1
1
1
1
0
0
0
1
1
1
1
1
2
1
2
1
2
1
1
2
0
2
1
1
3
1
1
1
1
1
1
1
1
1
2
2
2
1
2
1
1
1
2
2
1
0
2
1
1
1
0
0
2
1
0
0
1
1
1
0
0
1
0
1
2
1
1
0
1
0
0
2
2
0
1
1
1
0
1
0
1
0
1
0
1
2
1
2
2
1
1
2
3
1
1
1
1
0
2
1
1
0
2
0
2
1
1
1
3
1
1
1
1
1
2
0
1
1
1
1
1
1
1
1
1
1
2
1
3
1
1
1
0
1
0
1
1
0
2
1
2
1
0
1
0
1
1
0
0
1
2
0
0
1
1
2
0
1
2
2
1
1
1
1
1
0
2
2
1
1
1
1
1
2
2
0
2
2
1
2
2
1
2
1
1
0
1
2
1
1
1
1
1
1
1
1
0
1
0
2
1
1
1
1
1
2
2
1
2
1
1
0
1
1
2
1
1
2
1
1
1
0
1
1
1
2
1
1
1
3
1
2
1
1
2
1
1
1
1
0
1
0
0
3
1
1
1
1
0
1
0
2
1
0
2
1
2
2
1
1
1
2
0
0
1
0
1
0
1
1
1
1
1
1
1
1
0
1
1
1
2
1
1
1
1
0
0
2
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
0
0
2
1
2
1
0
1
1
1
0
0
2
2
2
1
1
1
1
1
0
1
1
1
2
0
1
1
1
1
1
2
1
1
1
1
0
1
0
1
0
2
1
1
2
1
1
1
2
0
1
2
1
1
1
2
2
1
1
0
0
1
2
2
2
2
1
1
2
1
2
0
1
2
2
1
0
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
2
2
0
1
1
1
0
1
0
1
1
2
1
2
1
0
1
1
1
1
1
1
1
2
1
0
1
1
1
1
0
1
1
2
0
1
0
1
1
1
1
0
1
0
0
2
1
1
0
2
2
1
2
1
2
1
1
1
2
2
1
1
1
1
2
1
1
1
1
2
1
0
2
0
1
1
0
1
0
1
1
2
1
0
2
1
2
2
1
2
1
1
1
1
1
0
1
1
1
0
0
2
0
2
0
1
1
0
2
1
1
1
1
1
4
1
1
1
1
2
1
0
3
0
1
1
1
1
1
1
0
0
1
1
1
1
1
1
1
1
0
0
0
1
2
1
0
0
1
1
1
0
1
1
1
1
2
1
1
1
1
0
1
0
1
1
2
1
1
1
0
1
1
1
1
1
2
1
1
2
1
2
1
1
0
1
1
1
1
1
1
1
1
2
1
1
1
0
2
1
2
2
1
1
2
1
2
1
2
1
2
1
2
1
2
1
2
1
1
1
2
2
1
1
2
0
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
2
0
1
2
2
4
1
1
1
1
2
1
1
2
2
2
0
2
0
1
1
1
1
1
1
2
1
2
0
2
0
1
2
0
1
1
2
1
1
1
1
1
2
1
2
0
2
2
0
1
1
1
1
1
1
0
1
2
1
1
2
1
1
2
1
2
2
2
2
1
1
0
1
1
1
0
2
0
2
1
2
2
2
1
1
1
1
0
0
1
1
1
1
2
1
2
1
1
0
1
2
1
1
1
1
2
1
1
1
1
2
1
1
2
2
4
0
1
1
1
1
1
2
1
1
0
2
2
2
3
1
2
2
0
1
1
1
1
1
2
2
1
1
2
1
1
2
1
1
2
1
2
1
0
1
1
2
1
2
1
1
1
1
1
2
0
1
1
0
2
2
1
2
1
1
0
1
1
1
2
1
1
0
1
1
1
1
1
2
2
2
1
2
1
1
1
1
1
1
0
1
0
1
1
2
2
1
1
1
1
1
1
1
1
1
2
0
1
1
2
1
0
0
1
1
1
1
2
1
1
1
2
1
0
0
1
1
1
0
2
1
0
1
1
2
1
1
1
1
2
1
1
1
2
2
1
2
1
0
2
1
1
1
1
1
0
1
0
1
1
1
2
2
0
2
1
2
1
1
1
2
0
0
1
0
1
2
2
1
0
2
1
1
1
1
1
1
1
1
1
1
1
1
0
1
2
1
1
3
1
1
1
1
1
0
2
0
0
1
2
1
1
1
2
1
1
1
1
2
2
1
1
1
3
1
1
0
2
1
1
1
1
2
1
1
0
1
0
1
2
1
2
2
1
1
1
1
2
1
1
0
1
1
1
0
1
1
1
1
1
1
0
2
1
2
2
2
2
1
1
2
2
0
1
1
3
2
0
1
1
1
1
2
1
2
2
1
1
2
1
1
1
1
1
0
0
2
0
1
1
1
1
1
0
2
1
2
2
1
2
1
0
1
1
1
1
2
2
1
1
1
1
2
1
1
0
2
1
0
1
2
1
1
0
1
1
1
2
2
0
1
2
1
1
2
1
2
1
0
2
0
0
1
1
1
1
1
2
1
2
1
2
1
1
1
1
1
1
2
0
1
0
1
1
1
0
1
1
1
1
2
2
2
1
0
1
0
2
2
1
1
1
1
1
1
1
2
2
2
1
0
0
3
2
2
1
1
1
2
1
1
2
1
1
0
2
1
2
1
1
1
3
1
3
1
1
1
1
2
2
1
2
2
2
0
1
1
1
1
1
1
1
1
1
2
0
1
1
1
0
1
0
1
1
1
1
0
1
0
1
2
2
1
1
1
1
1
1
1
1
2
0
1
0
2
0
2
1
1
1
1
1
1
2
1
1
1
0
1
1
1
1
1
2
2
0
2
2
1
1
2
1
1
0
0
2
1
1
1
1
1
1
1
0
1
1
0
1
2
0
2
1
2
1
0
1
1
1
1
2
0
1
0
1
1
1
1
1
2
1
1
0
1
0
3
1
1
1
2
1
1
2
1
1
0
1
1
1
1
0
1
3
1
1
2
0
0
2
1
2
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
0
1
2
1
2
1
1
1
2
2
0
2
2
1
1
1
1
2
2
1
1
1
2
1
2
1
2
0
0
1
2
0
2
2
1
1
1
1
2
1
2
1
1
1
0
1
1
1
1
1
1
1
1
0
1
2
2
1
2
0
2
1
2
0
2
1
1
1
1
0
1
2
1
1
2
2
1
1
1
1
1
1
2
1
1
1
2
2
2
2
1
3
2
1
1
1
1
1
2
2
1
1
1
1
2
2
2
2
1
0
1
2
1
1
1
1
2
1
0
2
0
2
2
1
2
2
3
1
1
1
1
1
1
2
2
1
2
2
1
0
1
0
2
1
0
0
1
1
1
2
0
1
2
1
1
1
1
0
1
1
1
1
2
0
1
1
1
2
1
2
1
1
1
1
2
1
1
0
0
1
0
0
0
0
1
0
2
1
2
2
0
2
1
1
2
0
1
2
2
1
1
1
1
1
1
1
1
0
1
3
1
0
1
1
1
1
1
1
1
2
1
1
1
2
1
2
2
1
1
1
2
0
0
2
2
2
1
2
1
1
1
1
1
0
1
1
1
1
1
1
2
2
0
1
1
1
1
1
1
1
2
1
2
1
1
2
2
1
1
1
0
2
1
2
2
1
1
1
0
1
0
0
1
1
1
1
2
2
2
1
2
1
2
1
0
1
1
1
2
1
1
2
2
1
1
2
1
1
1
2
2
1
1
1
1
1
0
2
1
1
0
1
2
1
0
1
1
1
1
1
1
1
2
2
1
0
1
2
2
1
2
1
1
0
2
2
0
1
1
1
1
2
0
2
0
1
1
2
2
0
1
1
1
0
1
1
1
0
1
2
0
2
1
1
2
0
1
2
2
2
0
2
1
2
1
2
1
1
0
2
1
1
2
2
1
0
2
1
1
1
2
1
2
1
1
1
0
1
0
2
1
1
2
1
1
1
2
2
1
1
0
3
0
1
2
1
1
1
1
2
1
1
1
2
2
1
1
1
1
0
2
1
1
1
1
1
1
2
1
2
2
1
2
1
0
0
2
1
2
2
1
2
2
1
1
1
1
1
2
2
1
1
2
1
2
1
2
1
2
1
1
1
0
1
1
1
1
0
0
0
2
2
1
1
1
1
1
2
0
1
0
2
1
1
1
2
1
2
1
1
1
1
0
1
1
1
2
1
2
1
1
2
5
0
2
1
1
2
1
1
2
1
2
2
1
1
1
0
1
0
1
1
1
1
1
1
1
1
2
1
0
2
2
1
1
2
1
1
2
2
2
1
1
2
1
1
0
1
2
1
1
1
1
0
0
1
1
2
1
0
1
1
1
0
1
1
1
1
1
1
1
0
2
1
1
2
0
2
1
1
0
0
1
0
2
0
1
1
1
2
1
1
2
1
1
2
1
1
2
1
2
2
2
3
1
1
1
1
1
0
1
1
2
1
1
2
1
1
1
1
1
0
1
1
2
1
0
0
2
1
0
2
0
2
0
0
1
1
1
1
1
1
2
1
0
2
2
0
2
2
1
1
1
3
1
2
1
1
0
0
1
1
1
1
3
0
1
1
1
1
1
1
2
1
1
1
2
1
1
2
0
1
1
2
1
1
1
1
0
1
1
2
0
1
0
1
1
2
1
1
0
0
1
0
1
2
2
1
0
2
1
2
2
1
1
1
0
2
0
1
1
1
1
2
1
2
0
1
1
1
2
1
1
1
1
1
0
1
2
1
1
2
1
1
2
1
1
1
1
1
2
1
1
1
1
0
2
2
2
2
2
1
1
1
2
1
1
1
0
1
1
2
0
1
1
1
1
2
1
2
1
2
1
1
0
3
0
0
1
1
2
1
1
1
0
0
1
2
1
1
2
2
1
1
1
1
1
2
2
0
1
1
0
1
1
1
1
1
2
1
2
1
2
1
0
1
1
0
2
1
0
1
1
1
0
1
1
1
2
1
1
1
2
1
1
1
2
1
1
0
1
2
2
2
1
1
1
1
0
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
0
2
0
0
1
1
1
1
1
1
1
1
0
1
1
1
1
2
1
1
0
1
1
0
1
1
2
2
1
1
1
1
2
1
2
2
2
0
0
2
1
2
1
1
1
0
2
2
1
0
2
2
1
1
1
0
1
0
2
2
2
1
1
1
1
1
2
0
1
0
1
1
1
2
0
1
1
2
0
1
0
0
1
1
1
1
2
1
2
2
0
1
1
2
1
1
0
1
2
2
1
0
1
2
1
1
0
1
0
0
1
1
1
2
2
1
1
1
1
0
1
1
1
2
1
1
1
2
1
1
1
2
1
3
1
2
0
2
1
1
0
2
1
0
3
1
1
1
1
2
0
2
0
0
0
2
2
1
2
2
2
1
1
2
1
1
1
0
2
2
2
1
1
1
0
2
2
1
2
0
1
1
0
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
2
1
1
2
1
1
1
2
2
1
1
1
1
2
1
1
2
2
3
1
1
1
1
1
2
1
1
2
1
1
1
2
1
1
1
2
2
1
1
0
1
2
1
1
2
1
0
1
1
2
2
1
1
1
1
1
2
0
1
2
2
2
1
1
1
1
1
0
1
1
1
1
1
1
2
0
0
1
1
1
2
1
1
1
1
1
2
0
0
0
1
1
1
2
2
2
1
1
2
1
2
1
1
1
2
0
1
0
1
1
2
2
1
1
2
1
2
1
2
2
1
0
1
2
0
1
1
1
0
0
2
1
1
1
1
0
1
1
0
2
1
1
1
1
2
0
1
1
2
1
0
0
1
0
2
0
1
1
1
1
0
1
2
1
2
1
1
2
2
2
1
0
2
1
1
2
2
2
2
0
0
2
2
1
2
2
2
2
0
1
2
1
0
1
1
2
2
1
1
1
2
1
1
1
1
1
1
1
1
2
0
2
1
1
1
1
1
1
0
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
4
3
1
1
1
1
1
1
1
1
1
1
2
2
2
3
1
1
3
1
1
1
2
1
1
0
2
2
0
1
0
0
0
1
0
1
0
1
2
3
2
2
1
2
1
2
0
1
1
1
1
1
1
2
2
1
1
1
1
1
0
1
1
0
2
1
1
1
2
1
1
3
1
1
1
1
1
1
1
1
2
2
2
2
1
1
2
2
2
1
1
1
2
0
2
1
2
2
1
1
1
1
2
2
1
1
1
1
2
1
1
0
1
0
2
2
0
1
1
0
2
1
1
0
0
2
1
1
1
1
1
1
0
2
1
2
2
1
0
2
0
1
1
2
1
1
1
1
0
1
1
0
1
2
1
1
1
1
0
0
1
0
2
1
3
1
2
1
1
1
1
2
2
2
2
1
1
1
0
2
1
1
2
1
0
0
2
0
1
2
1
0
1
0
1
2
1
0
2
0
1
0
2
1
1
1
2
1
1
0
2
1
0
1
0
2
2
1
1
1
1
1
1
2
1
1
2
0
1
1
1
1
1
2
1
0
1
1
2
1
0
1
2
1
1
1
1
0
1
1
1
1
1
0
1
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
0
1
1
1
1
1
1
1
1
2
0
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
0
1
1
1
0
1
0
1
1
2
2
1
1
1
1
1
2
0
2
0
1
1
1
1
0
2
1
1
1
1
1
1
1
2
0
1
1
1
2
0
2
1
2
1
2
2
1
1
2
1
0
1
1
1
1
1
2
0
1
2
2
1
1
2
1
0
1
1
1
1
1
2
1
1
1
2
1
1
1
1
0
1
1
0
1
1
1
2
1
0
1
2
0
0
1
1
1
1
0
1
1
1
1
0
1
2
2
1
2
1
1
1
0
1
1
1
1
0
1
1
1
1
2
1
2
1
0
2
2
1
2
2
0
1
2
3
1
1
2
1
1
1
2
1
2
3
2
0
1
1
2
0
2
1
1
1
2
2
1
3
1
1
0
1
1
1
1
1
1
1
1
1
0
1
2
1
1
0
2
1
1
1
0
2
0
1
2
1
1
1
1
1
1
2
1
1
1
1
0
2
1
1
1
0
1
1
1
1
2
2
2
1
2
2
2
1
2
2
1
0
2
1
1
1
1
2
0
1
0
1
1
2
2
1
1
0
0
2
0
1
1
1
0
1
1
1
1
1
0
2
1
1
1
2
1
2
2
0
1
1
1
1
1
1
1
0
1
0
1
1
1
0
0
2
1
2
2
1
1
1
1
1
1
1
3
1
1
0
2
2
0
1
0
2
2
1
0
1
0
1
1
1
1
1
1
0
1
1
0
1
1
1
1
1
1
1
2
2
1
2
2
1
0
0
2
1
2
1
2
2
1
1
1
0
2
2
1
1
2
2
1
2
0
2
1
1
0
2
1
1
3
1
2
0
1
1
1
1
3
1
1
2
0
2
1
1
1
0
1
0
1
1
0
2
1
1
0
3
2
2
1
1
1
1
1
1
0
1
0
1
1
0
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
0
2
1
1
0
2
2
1
0
1
1
2
2
0
1
1
0
1
1
1
0
0
1
1
2
2
2
0
0
0
2
1
2
1
1
2
2
1
2
1
1
2
1
1
0
1
1
1
2
2
0
1
1
1
1
1
2
1
1
1
2
2
1
2
2
1
1
1
0
2
1
2
1
1
1
1
1
1
2
1
2
2
1
2
1
1
2
1
1
1
0
1
1
2
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
0
1
2
0
1
1
1
2
0
1
2
1
1
1
1
1
0
2
1
1
1
2
1
0
2
2
0
0
1
0
2
1
2
2
0
1
1
1
1
2
2
1
2
0
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
0
1
1
2
0
1
1
1
1
1
1
0
0
0
1
1
2
1
2
2
1
0
1
1
1
0
1
1
1
1
2
2
0
0
1
1
1
0
1
1
0
1
1
1
2
1
2
0
0
1
1
1
1
1
1
1
1
1
2
0
2
1
1
1
1
2
0
1
1
0
2
1
2
1
1
1
2
1
1
2
1
1
2
2
1
2
1
1
2
2
1
1
1
1
2
2
2
1
0
1
1
1
2
2
1
0
1
0
1
2
1
1
1
2
2
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
0
2
2
1
2
1
1
1
1
2
2
1
1
1
1
1
2
2
1
1
2
0
0
2
1
1
0
1
0
1
1
1
1
1
2
1
2
2
1
2
1
2
1
1
2
1
1
2
1
1
1
2
1
1
1
0
1
2
1
0
3
1
1
2
1
2
0
1
0
2
2
1
2
1
1
1
0
1
2
1
2
1
0
1
1
1
1
0
1
1
1
1
1
0
1
2
1
1
1
1
1
1
1
1
2
1
2
1
1
2
2
2
2
1
1
1
2
1
1
1
3
1
1
0
1
0
2
2
2
2
1
2
2
1
2
1
1
1
1
1
2
1
1
1
0
1
1
2
1
1
1
2
1
2
1
0
1
1
1
1
2
1
1
2
2
1
1
1
1
0
1
1
0
1
1
2
1
2
1
1
1
1
2
0
2
1
0
1
1
1
1
0
1
1
1
0
1
0
2
1
2
1
1
0
0
1
2
2
1
2
1
1
1
1
0
1
2
1
2
0
1
0
1
0
1
1
1
0
0
1
2
2
1
1
1
1
1
1
1
1
2
0
1
1
1
1
1
1
1
1
0
2
3
2
1
1
1
0
1
1
0
1
1
1
1
0
1
2
2
1
2
2
2
1
1
1
1
1
2
1
2
0
1
1
1
1
1
1
0
0
2
1
2
1
1
1
1
0
1
0
2
1
1
0
2
1
1
1
0
1
1
1
2
2
2
1
1
1
1
1
1
3
1
0
2
2
1
1
0
2
1
0
1
2
2
2
1
2
2
3
0
1
1
2
2
1
1
1
2
1
1
1
1
2
1
2
1
1
1
0
1
0
1
1
1
1
1
1
2
0
1
1
2
0
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
2
1
2
1
1
0
1
0
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
2
0
1
1
2
0
2
1
1
1
1
1
2
1
1
1
2
1
2
0
2
2
0
1
0
1
1
2
1
2
0
2
1
2
1
0
1
1
0
1
1
1
1
1
2
1
0
3
2
0
1
1
2
0
2
1
1
1
1
1
0
1
1
0
0
2
0
2
2
0
1
1
1
1
3
1
0
1
1
2
3
1
2
1
0
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
0
2
1
1
1
2
4
1
2
1
2
2
0
1
1
2
1
1
1
1
0
1
2
1
2
1
0
1
1
1
1
1
2
2
1
1
1
2
1
1
1
1
2
1
3
0
1
1
2
0
0
1
1
1
2
0
0
1
0
0
1
1
1
2
1
1
2
1
1
1
1
2
1
1
1
0
1
1
1
0
1
2
2
0
2
2
1
2
1
2
1
1
1
1
0
0
1
2
1
0
1
1
1
1
2
1
2
1
1
1
1
1
2
2
1
1
0
0
1
2
1
0
1
2
2
0
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
0
1
1
0
0
1
1
1
0
1
1
2
1
2
1
1
1
0
0
1
2
1
1
1
1
0
2
1
1
0
2
0
1
2
1
0
1
2
2
1
1
2
1
1
2
1
0
1
0
1
1
1
1
2
1
1
2
1
1
1
0
0
1
2
1
1
1
0
0
1
1
1
1
1
2
0
1
1
1
1
2
1
0
1
1
1
1
1
1
2
1
2
0
2
1
1
1
1
2
1
1
1
0
1
1
1
2
1
1
1
2
1
1
4
1
2
1
1
0
1
0
1
1
2
1
2
2
1
0
1
1
1
2
1
1
1
0
0
1
2
1
1
1
0
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
2
2
2
2
1
1
1
1
2
0
0
1
1
1
1
2
1
0
1
1
2
2
1
1
1
1
1
2
2
1
1
2
2
3
1
1
1
0
0
1
2
1
1
2
0
1
1
0
1
2
1
1
1
0
1
1
1
0
0
1
1
0
2
1
2
2
1
1
2
1
2
1
1
1
2
2
0
1
2
1
1
1
1
1
2
1
1
1
1
1
0
1
1
1
1
1
1
2
1
3
1
1
1
1
0
0
1
1
2
0
1
3
1
1
1
1
1
0
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
2
1
2
0
2
1
1
1
1
1
1
2
0
1
1
0
1
1
1
0
1
0
2
1
1
1
1
1
2
1
2
2
0
1
1
1
1
0
2
1
1
2
1
1
2
1
2
2
1
2
1
1
3
0
1
1
0
1
2
1
1
1
1
1
1
2
1
1
2
1
1
1
3
2
1
1
0
1
1
2
1
1
1
2
0
1
2
1
1
1
1
1
2
0
2
1
1
1
1
2
1
1
2
1
1
1
0
1
1
1
1
1
1
4
2
1
1
1
0
2
1
1
1
1
1
1
2
2
1
2
2
1
0
2
2
2
1
0
2
1
0
1
1
1
1
1
1
0
1
1
1
2
1
1
1
1
1
1
0
2
0
1
2
1
2
1
0
0
0
1
1
1
1
2
0
1
2
1
1
1
1
2
1
0
0
1
1
2
1
1
2
1
0
1
1
1
2
0
2
1
2
1
2
2
1
0
0
1
1
1
1
1
2
2
1
1
1
1
2
0
1
1
0
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
0
1
2
1
2
2
1
1
0
0
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
2
2
2
2
1
0
1
1
2
1
2
0
2
1
2
2
1
2
0
1
1
2
2
2
0
1
1
1
0
2
2
2
1
2
1
2
1
0
1
1
2
1
1
1
0
1
2
2
1
1
1
1
0
2
2
1
1
1
2
1
1
2
1
0
2
1
1
1
1
2
1
2
1
1
2
1
2
1
0
6
0
2
1
2
2
1
1
1
2
1
1
1
0
1
2
1
1
1
2
2
1
1
2
1
1
0
0
1
2
2
0
1
1
1
1
1
2
1
1
1
2
1
0
2
1
1
2
0
1
1
1
2
2
0
0
1
1
2
2
1
1
0
0
1
1
0
2
2
1
1
1
0
2
2
0
2
1
2
1
0
1
0
0
2
1
1
1
1
2
1
2
1
1
2
1
1
0
1
0
2
2
1
2
2
1
0
1
1
1
1
1
1
0
2
0
2
0
2
1
1
2
0
0
1
2
2
1
1
1
1
1
2
2
2
0
0
0
0
2
0
1
1
1
1
0
2
1
1
1
0
1
1
2
0
1
2
1
2
1
1
1
1
0
1
1
2
1
2
1
1
1
1
1
1
1
2
1
0
1
1
2
1
1
2
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
0
2
1
1
1
1
1
1
1
1
0
0
1
1
1
1
2
2
1
1
1
2
1
2
2
1
1
1
0
4
1
1
1
2
1
0
1
0
1
1
1
1
1
1
0
2
1
1
1
1
2
1
1
0
2
1
2
1
1
1
0
1
1
0
1
2
2
1
0
2
2
1
2
2
1
2
1
1
1
2
1
1
1
0
1
1
0
1
1
1
1
1
2
1
1
2
1
2
1
2
1
2
1
2
0
1
2
1
0
1
2
1
1
0
2
1
1
1
1
2
2
1
2
2
2
2
1
2
2
1
0
1
1
2
1
1
2
2
1
1
1
2
2
2
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
0
0
2
2
2
1
1
2
1
1
1
1
2
1
0
2
2
0
1
1
2
2
1
2
2
2
1
1
2
1
2
1
1
1
1
0
2
1
1
2
1
1
2
2
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
2
1
1
1
1
1
1
2
2
0
1
1
1
1
1
1
1
1
2
1
2
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
1
0
1
1
1
1
2
0
1
1
1
2
1
2
0
1
1
1
1
0
4
1
1
2
0
1
1
1
1
0
1
1
1
1
2
1
2
1
0
1
1
1
2
1
1
2
2
2
1
1
2
1
1
1
1
1
3
0
1
2
1
1
0
1
1
1
1
1
1
1
0
1
2
1
1
0
0
1
1
1
1
1
1
1
2
0
1
1
2
1
1
1
0
0
2
1
2
0
0
2
1
1
1
1
3
1
1
1
1
1
2
1
1
1
1
2
1
2
1
1
2
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
2
0
1
1
0
2
1
2
1
1
1
0
1
1
1
1
0
1
2
1
2
1
1
1
1
1
2
2
2
2
0
1
1
1
0
1
1
0
1
2
1
1
2
0
0
1
1
1
1
1
0
2
1
1
2
1
2
1
1
1
0
1
1
1
1
1
1
1
2
1
2
1
1
2
1
1
2
0
1
0
2
1
2
1
1
2
1
1
2
0
3
1
0
1
0
0
1
1
1
1
2
1
1
0
1
0
2
0
2
1
1
2
1
1
1
1
1
2
1
0
2
2
1
1
2
0
1
1
1
2
1
2
2
1
1
1
2
2
1
1
1
1
0
2
1
1
2
1
1
0
2
1
1
0
1
0
1
1
1
2
1
1
2
1
1
0
1
1
1
0
1
1
1
1
1
2
2
0
1
1
2
2
1
2
1
1
1
1
2
1
2
1
0
1
1
1
1
1
0
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
2
1
1
0
1
1
1
1
1
1
1
2
0
1
2
1
0
1
2
1
2
1
2
1
1
2
1
1
1
1
2
1
0
1
0
2
1
1
2
1
1
0
1
1
1
1
0
0
1
0
1
1
2
1
1
0
2
0
1
1
3
1
0
0
1
2
2
2
1
1
1
1
0
0
1
1
1
1
0
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
1
2
2
2
1
2
1
2
1
1
1
1
1
1
1
2
1
1
0
2
1
1
1
1
0
1
1
1
0
1
1
1
1
0
0
2
2
0
1
1
2
1
0
1
2
0
1
2
1
2
1
1
1
1
1
1
2
1
1
0
1
2
1
2
1
1
1
1
1
2
0
1
1
2
1
1
1
1
1
1
0
1
2
2
1
1
1
1
1
2
0
1
1
1
1
1
2
1
1
1
1
0
2
1
1
1
1
2
1
2
2
2
2
1
1
2
1
1
1
1
2
1
0
1
0
1
1
1
2
2
0
2
1
1
2
1
1
2
0
0
1
1
1
1
2
1
2
1
2
1
0
1
1
1
1
1
0
1
0
1
2
2
1
0
2
1
1
0
1
2
2
1
0
1
1
1
1
2
1
2
1
2
2
1
2
1
1
0
1
1
2
1
1
0
2
1
1
2
0
1
1
1
1
2
1
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
1
2
1
2
1
2
1
0
2
2
1
2
0
1
1
0
0
1
2
1
2
2
2
1
1
1
1
1
0
1
1
1
1
1
2
1
2
1
1
1
1
0
1
2
1
0
1
2
2
1
1
1
1
1
1
1
0
1
0
2
1
1
2
2
2
2
2
1
1
1
1
2
1
1
2
1
1
2
1
1
0
0
0
2
2
1
2
1
2
1
2
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
0
1
0
1
1
1
2
1
1
1
1
1
1
2
0
1
2
1
1
0
1
2
2
1
1
1
2
1
1
2
2
2
2
1
1
2
0
1
2
2
1
1
2
1
1
2
1
1
2
2
1
0
1
2
1
1
0
1
1
1
1
2
3
1
1
1
2
1
2
1
1
0
1
2
2
1
2
2
1
2
1
1
1
1
1
1
1
1
2
1
2
2
0
2
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
2
2
2
1
0
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
0
0
1
2
1
0
0
1
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
0
2
1
1
0
2
1
0
1
1
2
1
0
1
2
1
2
1
1
1
2
1
1
0
1
1
0
2
2
0
1
0
2
1
1
2
1
1
1
1
2
2
1
2
1
2
0
2
2
1
1
2
1
1
1
1
1
0
1
2
1
2
2
0
0
2
0
0
1
1
1
2
1
1
1
2
2
1
1
0
3
1
1
0
1
1
2
1
2
1
1
0
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
2
1
1
2
1
1
1
2
1
2
1
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
0
1
1
0
0
1
0
1
0
1
1
1
0
1
1
1
2
2
1
1
1
2
1
1
2
1
1
1
1
1
1
1
0
2
1
1
0
2
1
3
0
0
1
1
1
1
2
1
1
2
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
3
1
1
1
2
1
1
2
2
1
2
1
1
1
2
1
1
2
1
1
1
2
0
1
2
1
1
1
1
1
1
0
1
1
1
1
2
2
2
1
2
1
2
2
1
2
0
2
0
1
2
2
1
1
1
1
1
2
1
2
2
0
1
1
1
0
1
0
1
1
1
1
1
1
1
1
1
1
3
2
1
2
1
2
1
2
0
2
1
1
3
0
1
1
1
1
1
1
1
0
1
1
1
1
1
0
1
1
0
1
1
2
1
0
1
1
2
0
0
1
1
0
2
2
1
1
2
1
1
1
2
2
0
1
1
2
1
1
0
2
1
1
1
1
1
1
2
2
2
1
2
1
2
0
1
0
1
1
1
2
2
1
1
1
0
2
2
1
1
1
1
2
1
1
1
1
1
0
1
2
1
1
1
1
1
2
1
1
1
1
1
1
0
1
1
1
1
1
1
2
1
0
1
2
0
1
1
1
1
1
0
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
0
1
1
1
0
1
1
1
1
0
1
2
1
1
1
1
1
2
2
1
1
0
2
1
2
1
1
2
1
1
0
2
1
1
1
1
1
1
2
1
1
0
1
1
1
1
1
2
1
2
1
1
1
2
1
2
2
1
0
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
0
0
2
2
0
1
1
1
2
2
1
1
2
1
1
1
0
0
1
1
1
4
1
1
2
1
1
1
1
2
2
1
1
2
1
3
0
1
0
2
1
1
0
2
2
0
2
0
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
2
1
2
1
1
0
1
1
2
2
1
1
2
1
2
2
1
1
0
1
1
2
0
2
1
1
1
2
1
1
2
0
1
1
1
1
1
0
1
1
2
2
1
1
1
1
2
1
2
1
0
1
0
1
2
1
1
1
1
1
1
1
1
2
1
0
1
1
3
2
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
2
0
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
0
2
1
1
1
2
1
2
1
1
1
1
1
0
1
1
1
1
2
1
2
2
1
0
2
0
2
1
2
1
1
0
1
1
1
2
1
0
1
1
2
0
2
1
1
1
1
1
0
3
2
2
2
3
2
0
1
1
1
0
1
0
1
0
1
2
1
2
1
2
1
1
0
1
0
1
0
1
2
1
2
1
1
2
1
1
2
2
1
0
1
2
1
1
1
1
1
2
0
1
1
1
1
1
1
2
1
2
2
1
2
1
0
1
2
1
0
1
1
1
1
1
1
1
1
2
2
1
1
1
2
2
1
1
1
1
1
2
1
1
2
1
2
2
2
1
1
2
1
1
1
0
1
1
1
1
2
2
2
1
1
2
2
1
2
1
1
1
2
1
2
2
1
2
0
1
1
3
1
2
2
1
1
0
1
1
1
1
2
1
1
2
2
1
1
0
1
0
1
1
2
1
0
2
1
0
1
2
2
3
1
2
1
0
1
1
2
1
1
1
1
2
1
0
0
1
1
1
2
2
0
1
1
1
1
0
0
1
1
1
1
2
1
1
1
2
0
2
1
1
0
2
1
1
2
0
1
1
2
0
0
2
2
1
1
1
0
1
2
1
0
1
1
1
1
1
2
0
2
1
2
0
1
1
1
1
1
1
1
1
2
1
0
2
1
1
1
1
1
1
2
0
1
1
1
1
2
1
1
1
1
1
0
1
2
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
0
0
1
1
1
1
2
1
2
2
1
0
0
1
2
0
1
0
1
1
1
2
1
1
1
1
1
2
2
1
1
1
2
1
1
2
2
2
2
1
1
2
1
2
2
2
0
1
1
2
1
0
1
1
1
1
0
1
1
1
1
1
1
2
1
3
1
2
1
0
0
2
0
0
1
1
2
0
2
1
1
2
2
1
1
1
1
1
1
1
1
2
1
2
0
0
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
0
0
0
1
1
1
1
1
0
2
1
1
1
3
2
1
1
2
1
0
1
1
1
0
1
1
1
2
1
2
1
1
1
1
2
1
2
1
0
1
1
1
1
1
2
1
0
2
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
0
2
2
2
1
0
3
0
2
2
0
1
1
2
1
1
1
2
2
1
2
1
2
2
1
2
2
1
1
2
0
1
2
1
1
1
1
2
1
2
2
1
2
1
1
1
1
1
1
2
2
1
2
1
1
0
1
2
1
1
1
1
1
1
1
2
1
1
1
1
2
0
0
0
2
2
2
0
1
1
2
0
1
1
1
2
2
2
0
2
1
0
2
2
0
1
1
1
0
2
0
1
1
1
2
2
0
1
2
1
1
1
2
2
1
1
2
2
1
1
1
0
1
1
1
1
2
2
1
2
1
1
1
2
1
1
1
1
0
1
2
1
0
1
1
1
1
1
1
1
1
0
1
0
0
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
2
1
0
2
1
0
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
2
1
1
1
1
1
1
1
2
2
2
1
2
1
1
1
1
1
0
1
1
1
1
0
2
1
2
1
0
1
1
1
1
1
1
1
1
0
0
1
1
1
2
1
1
1
1
2
1
2
2
0
2
1
1
1
2
1
2
1
1
1
2
1
2
2
1
1
1
1
2
2
2
1
0
0
1
1
2
1
2
1
2
1
0
0
1
1
2
1
1
2
1
0
2
1
1
1
2
1
1
1
1
0
1
2
1
1
1
2
1
1
1
1
0
1
2
3
1
0
2
2
1
1
1
1
0
2
1
1
2
1
2
2
1
1
1
1
1
0
2
2
1
1
1
1
1
1
1
2
1
2
2
1
2
1
1
2
1
1
1
0
0
1
0
1
1
1
1
2
1
0
1
1
1
1
1
2
1
1
0
0
2
1
1
2
1
1
1
1
2
0
1
1
0
1
1
1
2
0
2
1
1
1
1
2
1
1
1
0
1
1
2
0
2
0
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
2
1
1
1
2
2
2
2
2
1
2
1
1
0
2
1
1
1
1
2
0
2
1
1
1
0
0
1
1
1
2
0
1
1
1
2
1
2
1
1
1
1
1
2
0
2
0
2
2
2
0
2
2
1
1
1
1
1
0
2
2
1
1
2
1
1
0
1
1
1
2
2
1
2
1
2
2
0
2
2
1
0
1
1
2
2
1
1
1
2
1
2
2
0
1
2
1
0
1
0
2
2
2
1
1
2
2
2
1
0
1
1
1
2
1
2
1
2
0
1
1
2
1
1
1
2
0
2
1
1
1
1
1
1
1
1
3
1
1
1
1
2
2
0
2
2
1
0
1
1
2
1
2
0
1
1
2
2
1
2
1
1
1
1
0
1
0
1
1
2
0
1
1
2
1
2
2
1
1
2
1
0
2
1
1
1
0
2
0
1
1
2
0
0
1
1
1
1
0
2
1
2
1
1
1
2
3
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
0
1
1
2
2
2
0
1
1
1
2
2
1
1
1
1
0
1
1
0
0
1
0
1
1
2
1
0
2
0
2
1
2
2
0
2
1
1
1
2
2
2
2
1
0
1
2
1
0
2
1
0
0
1
1
1
1
1
2
2
1
2
2
1
2
1
1
0
2
0
1
1
1
1
1
1
1
0
2
1
1
2
1
3
1
1
2
1
1
1
1
2
1
1
0
1
1
1
2
2
1
1
1
0
1
2
1
1
1
1
0
1
1
1
2
0
0
4
2
1
2
1
3
1
1
1
2
1
0
1
2
1
0
1
2
1
1
1
1
1
0
1
0
1
1
2
0
1
1
0
0
2
1
1
2
2
1
1
2
1
1
5
1
2
0
0
1
1
1
2
2
1
1
1
1
2
2
1
1
2
1
1
1
1
0
0
2
0
1
1
2
3
0
0
1
1
0
1
1
0
1
2
1
2
1
2
2
2
1
1
3
2
1
1
1
1
2
2
0
2
1
2
0
0
1
1
2
1
1
2
0
1
2
1
1
1
0
2
0
1
2
1
2
0
2
0
0
0
1
2
2
2
2
1
1
1
1
0
1
1
1
1
1
2
1
1
1
1
2
2
1
1
2
0
2
2
2
1
1
3
1
1
2
1
1
1
0
1
1
1
2
1
1
1
1
1
0
1
0
1
2
1
2
0
1
1
2
2
1
1
1
2
2
1
2
0
2
1
2
1
2
0
0
2
2
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
0
1
1
2
2
1
1
1
2
1
1
2
1
2
1
2
1
1
1
1
1
1
1
1
1
0
2
1
0
1
1
2
1
1
2
1
2
1
2
2
2
2
1
1
1
2
1
1
1
2
1
1
1
0
1
1
0
1
1
0
1
0
1
2
1
1
0
1
0
1
1
1
0
2
1
1
1
1
1
2
1
2
1
2
2
0
1
0
3
1
0
2
1
1
1
0
1
2
1
0
1
1
3
1
0
1
1
1
1
1
2
1
1
2
1
0
1
1
1
1
0
0
1
2
2
0
1
1
1
1
1
0
2
0
1
1
1
1
0
1
2
1
1
2
1
1
1
1
0
1
1
1
1
1
2
1
2
1
1
2
1
0
2
1
1
1
1
2
1
1
0
1
1
1
0
1
0
4
1
0
2
1
0
0
1
0
1
2
2
2
1
1
0
1
1
1
1
2
1
0
2
1
1
1
1
1
1
1
1
1
0
2
2
1
1
1
1
1
1
2
2
1
0
2
0
0
2
2
1
1
1
1
1
1
2
1
2
1
0
0
1
0
2
1
2
2
2
1
1
1
0
1
1
2
0
2
1
1
2
2
3
2
0
1
1
1
1
1
2
0
1
1
1
1
1
2
1
0
1
1
2
1
1
1
2
1
1
1
1
1
0
1
1
1
1
1
1
1
1
0
1
0
1
1
1
1
1
2
1
1
1
1
2
1
0
1
0
0
1
1
2
1
1
0
1
3
1
1
2
1
1
2
2
2
1
1
0
1
1
1
1
1
1
1
1
1
0
1
2
0
2
1
1
2
1
1
0
1
1
1
1
0
1
1
2
2
2
0
1
1
0
1
2
1
1
1
1
1
1
2
1
1
0
1
2
2
1
2
2
2
1
1
1
0
1
1
0
1
1
0
1
1
0
1
1
0
1
1
1
1
0
1
1
0
0
0
1
1
1
2
1
1
1
0
0
2
2
1
1
1
1
1
1
1
2
1
0
1
1
1
1
1
2
1
1
3
1
1
1
1
2
1
1
1
1
1
1
1
1
0
2
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
0
2
1
1
1
1
1
0
1
0
2
2
1
0
0
0
2
0
1
1
1
2
0
2
1
1
1
0
2
0
2
1
3
0
1
2
2
2
1
1
0
0
1
1
2
1
2
1
2
1
2
0
1
2
1
3
2
1
2
2
1
2
1
2
2
2
2
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
2
1
1
1
1
2
1
1
1
1
0
1
1
2
1
1
1
1
0
2
2
0
1
0
1
1
1
1
1
2
2
0
1
2
1
1
2
2
1
1
1
1
1
1
1
0
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
0
1
1
2
1
1
2
1
2
2
0
1
2
2
1
1
1
2
1
1
2
2
1
0
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
1
2
1
2
2
1
1
1
0
3
1
1
1
1
1
1
1
1
0
2
1
1
1
1
3
1
0
1
1
0
0
2
1
2
1
0
1
2
1
1
0
2
2
1
0
0
1
2
1
1
1
2
1
2
2
2
2
1
1
1
2
1
0
2
2
0
1
3
2
0
2
0
1
1
2
1
1
2
1
2
0
1
2
0
1
2
1
0
1
2
0
1
2
2
1
1
1
2
1
1
1
1
0
1
0
1
2
1
1
2
2
1
1
2
3
2
1
1
2
0
1
0
1
2
1
1
1
2
2
1
1
1
1
2
2
1
1
2
1
1
1
2
1
1
1
1
1
2
1
2
2
0
1
1
1
1
1
2
1
1
1
1
2
1
2
1
1
2
1
1
1
1
1
1
1
0
1
1
2
0
1
1
0
2
1
2
1
1
0
1
1
2
1
1
1
0
1
2
1
1
1
1
1
2
1
0
2
1
2
2
1
1
2
1
2
1
2
2
2
1
2
0
2
2
2
0
1
2
1
1
1
1
1
1
1
2
2
1
1
1
1
2
2
1
1
2
1
1
1
1
2
1
0
1
2
1
1
1
0
1
1
1
2
1
0
2
1
0
1
0
2
1
1
1
1
0
1
1
1
1
0
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
0
1
0
1
1
2
0
2
1
1
1
1
0
1
2
1
0
0
2
2
0
2
1
1
1
1
1
1
2
1
1
1
1
2
1
0
0
1
2
2
1
0
0
2
1
1
1
2
1
2
1
1
2
0
1
0
1
0
0
1
1
1
1
0
1
1
1
1
2
1
2
1
2
1
1
1
2
1
1
2
1
0
0
0
0
1
1
0
1
1
1
1
1
2
1
0
0
2
1
1
1
1
0
0
2
1
1
2
2
0
1
1
0
1
1
2
1
1
2
1
2
1
2
2
1
1
2
0
2
2
2
1
1
2
2
0
0
1
1
0
3
0
1
0
1
1
2
1
2
1
2
1
1
1
1
1
1
1
1
0
1
1
1
1
0
2
1
1
1
1
0
1
2
1
1
1
2
1
1
1
1
0
0
0
0
2
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
0
0
1
1
1
2
2
0
1
1
0
2
1
1
0
1
1
0
1
1
1
0
1
1
2
1
1
1
1
1
1
1
1
2
2
1
0
1
2
1
0
1
3
0
1
1
1
0
1
1
2
1
1
0
1
3
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
2
1
0
1
0
1
2
2
1
1
1
2
1
1
2
1
2
1
1
1
1
2
1
2
1
1
1
1
0
0
2
0
1
1
2
2
0
1
1
1
1
0
2
1
1
2
0
1
1
1
2
3
1
1
1
2
2
1
1
1
1
1
2
2
2
1
1
1
0
1
2
0
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
0
1
1
1
2
1
1
1
0
0
1
1
0
1
0
1
2
1
1
1
1
1
2
0
1
2
1
1
2
1
1
0
0
2
1
2
2
1
1
0
2
1
1
2
0
1
1
1
2
2
1
0
1
1
0
2
1
1
0
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
0
0
1
0
2
2
1
1
2
2
1
0
1
1
0
2
2
0
1
1
1
1
2
1
1
2
0
1
1
0
1
1
0
1
1
1
1
2
1
0
0
1
1
1
0
2
0
1
1
1
2
0
1
2
1
1
1
1
0
0
1
2
1
2
0
1
2
1
2
1
0
3
0
0
2
1
2
0
1
2
2
2
1
1
0
2
1
1
0
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
0
1
1
1
0
2
1
2
2
2
2
2
0
1
1
1
0
2
2
1
1
0
1
1
1
2
1
2
1
0
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
0
2
2
1
1
1
1
1
1
4
2
1
0
1
2
1
6
1
2
2
2
1
1
1
1
1
1
0
1
0
1
2
2
1
0
2
1
1
2
0
2
1
1
2
1
1
1
1
1
2
1
2
2
1
0
2
0
1
0
2
2
1
1
0
1
1
1
0
1
2
1
1
1
2
1
1
1
1
0
1
2
3
1
1
1
1
2
1
1
1
1
2
2
1
1
1
2
1
1
1
2
1
1
1
1
2
0
1
2
1
1
0
1
2
2
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
1
2
2
2
1
2
1
0
1
1
1
1
1
2
1
0
1
1
2
0
2
1
2
1
1
2
1
0
1
1
0
2
0
1
1
2
1
2
2
1
1
1
0
1
1
1
1
1
2
3
1
0
1
2
1
2
1
1
1
1
2
1
1
2
2
2
1
2
2
1
0
1
3
1
1
1
1
2
2
0
2
1
2
2
1
2
1
1
1
1
1
0
1
0
1
1
1
1
5
1
1
1
1
1
2
2
2
1
1
1
2
1
2
0
2
1
2
2
2
1
0
2
1
0
1
2
2
1
0
2
0
1
1
0
0
1
1
2
1
1
2
1
2
1
1
1
0
1
1
1
1
0
0
1
1
1
0
0
1
2
1
4
1
1
2
1
1
1
1
0
2
0
1
1
0
2
1
1
1
2
0
1
1
2
2
2
1
0
1
0
0
2
1
1
2
1
2
1
2
2
0
0
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
1
2
1
2
0
1
1
1
1
1
0
1
2
2
1
0
2
1
0
2
0
1
2
2
0
1
0
2
0
1
1
2
2
0
2
0
1
1
2
1
1
0
1
1
1
1
1
1
1
0
1
2
1
1
2
2
1
0
1
2
2
1
1
1
2
1
1
1
1
1
2
0
1
1
1
1
2
1
1
0
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
0
1
1
1
1
2
2
1
2
1
1
1
0
1
0
1
1
0
2
2
0
1
1
2
1
0
1
1
1
2
1
1
1
2
1
1
0
1
1
2
1
1
2
1
1
1
1
0
1
1
2
1
1
1
2
1
1
1
1
1
1
0
1
1
1
1
0
2
1
1
1
2
2
1
1
1
2
1
2
1
1
2
2
2
1
1
1
0
2
2
1
1
1
2
2
2
2
1
1
0
1
1
1
1
2
2
2
1
0
1
2
2
2
0
1
1
1
2
1
1
1
0
2
0
2
1
1
1
0
2
1
0
1
1
0
0
1
1
1
2
1
2
2
2
2
2
1
1
1
1
2
0
2
0
1
1
0
1
0
1
1
1
1
1
1
1
2
3
1
1
2
1
2
1
1
1
0
1
1
2
1
1
1
1
2
1
1
2
1
1
1
0
2
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
2
1
2
0
1
1
2
2
1
1
0
1
0
1
1
2
1
0
0
1
0
1
1
1
1
1
1
2
1
2
1
1
1
2
1
1
1
1
1
2
1
1
2
2
2
1
1
2
1
1
1
1
0
1
0
2
1
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
0
1
1
1
0
1
2
0
2
2
1
1
1
2
2
1
0
2
2
1
2
2
1
1
2
1
0
1
0
2
1
2
1
1
0
2
1
2
1
2
2
1
1
0
1
2
1
1
1
2
2
1
1
0
1
2
2
1
2
1
1
1
2
2
1
2
0
1
1
0
1
1
1
1
1
1
2
2
1
1
1
1
0
1
1
0
1
1
0
1
0
0
1
1
1
2
1
1
1
1
1
1
2
2
2
1
1
0
1
2
0
1
2
4
2
1
1
1
1
1
1
2
1
1
1
1
0
1
1
2
2
0
0
1
1
1
0
1
0
2
1
1
2
0
1
1
2
1
1
2
1
1
0
0
2
1
2
1
1
1
1
2
2
0
1
0
2
1
2
1
1
1
1
1
1
1
2
2
1
1
2
1
0
1
1
1
1
2
1
1
1
0
1
1
1
1
1
1
2
2
0
2
1
0
2
1
0
1
0
0
0
1
1
1
1
0
1
1
1
1
1
2
1
1
2
1
2
1
2
1
1
1
1
1
1
1
1
0
1
1
0
1
1
0
1
1
0
1
1
2
1
1
1
1
0
1
1
1
0
1
1
1
0
1
1
1
1
0
1
1
1
1
1
1
1
1
2
0
0
1
1
2
1
1
1
1
2
2
1
2
1
1
0
2
1
1
1
1
0
1
1
1
1
0
1
2
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
0
1
1
1
2
2
1
1
2
0
1
1
2
1
2
1
1
1
2
0
1
1
1
1
0
1
1
1
1
1
0
2
1
2
1
2
2
1
1
1
1
2
1
2
1
2
1
1
1
1
1
1
1
0
0
1
1
1
1
1
1
1
1
0
1
1
1
0
2
0
2
1
2
1
1
6
1
1
1
1
1
1
1
2
2
0
1
0
0
1
2
2
1
1
2
1
1
2
2
1
1
1
0
1
2
2
1
0
1
0
0
1
2
1
1
1
1
1
2
0
2
2
0
2
1
1
1
2
1
2
1
3
0
1
1
1
2
2
2
1
2
1
2
2
1
2
1
1
0
2
1
0
2
1
1
2
0
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
0
1
1
2
2
1
1
0
1
2
0
0
2
0
0
1
2
2
1
1
0
1
2
0
2
1
1
1
1
0
0
1
1
1
2
1
1
1
1
1
1
1
1
1
0
1
2
1
0
1
0
1
1
0
1
2
2
1
1
1
1
2
1
1
1
1
2
0
1
1
1
1
2
1
1
1
1
1
1
1
0
0
2
0
1
1
1
1
1
2
1
0
1
1
2
1
1
1
1
2
1
1
2
0
1
1
1
1
2
0
2
0
2
2
1
1
1
1
1
3
1
1
2
2
1
1
2
1
2
1
2
2
1
1
1
0
1
2
1
0
1
1
2
1
1
1
1
1
2
1
2
2
2
1
2
1
1
1
1
1
1
1
0
2
0
0
2
1
1
1
2
0
1
1
1
1
2
1
2
0
2
2
1
1
2
2
1
0
1
2
2
1
2
1
2
2
2
1
1
2
1
1
1
0
2
0
1
1
0
1
2
2
1
2
1
1
2
1
0
0
2
1
0
1
2
2
0
0
2
1
1
1
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
0
0
0
1
1
2
2
1
1
1
1
1
1
2
0
1
1
1
1
1
2
1
1
0
0
1
0
1
1
1
0
2
1
1
2
2
1
1
1
2
1
2
0
1
1
1
1
1
1
1
0
2
1
2
0
1
2
1
2
2
1
1
2
1
1
1
2
1
1
0
1
1
1
1
1
1
1
1
2
1
3
0
0
2
1
1
1
1
1
2
2
1
2
1
1
1
0
1
1
2
0
2
1
1
2
1
1
1
1
2
2
1
0
1
1
0
3
0
2
0
3
1
1
0
1
1
2
2
0
0
1
1
1
0
0
0
2
1
2
1
1
1
1
2
2
1
1
1
2
1
2
2
3
1
1
2
1
2
1
0
1
2
2
1
2
1
3
0
1
1
1
2
2
1
0
2
3
1
1
0
1
1
1
1
2
1
0
1
1
1
1
1
0
1
1
2
0
2
1
0
1
1
1
1
2
0
1
1
1
1
0
1
1
1
2
1
1
0
1
1
1
2
0
0
0
1
1
1
1
2
2
1
2
0
0
1
1
1
1
0
1
0
1
1
1
0
2
2
1
0
0
1
1
0
2
1
1
1
2
2
2
1
2
1
1
0
1
2
0
1
0
1
1
1
1
1
2
0
1
2
1
0
2
1
2
1
2
1
1
1
1
0
2
1
1
1
0
1
2
0
1
1
1
1
2
0
1
2
1
1
1
2
2
1
1
1
0
0
1
2
1
0
1
1
2
2
0
0
2
0
1
0
1
1
1
1
2
0
1
1
1
1
0
0
2
0
3
0
2
0
2
1
1
0
1
2
0
2
2
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
0
1
1
2
1
2
1
1
2
1
1
2
1
1
1
1
2
1
1
1
1
1
1
2
2
2
1
2
1
1
0
1
1
0
2
1
1
2
0
1
2
2
1
1
1
1
2
2
1
1
1
1
1
1
2
1
1
2
1
2
2
2
3
2
2
1
2
2
0
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
0
0
1
1
2
1
1
1
1
1
2
2
2
1
1
0
1
0
2
2
1
1
2
1
2
1
1
1
1
2
1
0
1
1
1
2
1
2
1
0
1
2
0
1
2
0
1
1
2
0
1
2
0
2
2
0
1
1
2
1
1
1
2
1
1
2
1
2
1
0
0
1
1
1
2
0
1
1
0
0
2
1
2
1
1
1
1
0
2
1
0
1
1
2
2
3
5
1
2
1
1
1
1
0
1
1
2
2
1
1
0
0
1
2
1
2
1
1
2
1
1
0
2
1
1
1
1
1
1
1
1
0
2
0
2
1
1
2
0
2
0
1
2
2
1
1
2
2
2
1
2
1
1
2
1
2
0
1
1
1
1
1
1
1
1
0
1
2
1
1
1
1
1
1
1
0
1
2
0
1
1
2
1
2
1
1
1
0
1
0
2
2
1
1
2
2
2
1
2
1
2
1
2
0
1
1
1
2
2
0
2
0
1
1
2
1
1
1
1
1
0
0
1
1
1
1
1
0
2
1
0
1
1
1
1
1
2
1
0
1
1
1
1
1
2
1
1
1
1
0
1
1
2
0
1
1
2
0
1
1
2
1
1
1
1
1
1
2
1
1
2
1
0
1
1
1
1
0
0
2
1
1
1
1
1
1
0
2
1
0
2
2
2
0
2
1
1
2
1
1
0
1
1
1
0
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
2
1
2
1
2
2
2
1
0
0
1
1
0
2
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
0
1
0
1
1
2
1
2
2
1
2
1
1
0
1
2
1
0
0
1
2
1
1
1
2
1
1
2
2
2
2
1
1
0
0
0
2
1
1
2
2
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
1
1
2
1
2
1
1
1
0
1
1
2
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
2
1
1
1
1
2
0
1
1
1
1
0
2
1
2
0
1
2
2
1
1
1
0
2
1
1
2
1
0
1
2
1
2
1
2
1
0
1
1
1
1
1
1
1
2
2
1
1
1
1
2
2
1
3
2
2
2
1
1
1
2
1
0
2
1
1
0
2
0
1
0
1
1
1
0
1
2
0
2
1
1
1
0
1
2
1
0
1
1
3
1
2
0
1
1
1
2
1
0
1
1
1
1
2
2
1
0
1
0
2
1
1
1
1
1
0
1
1
2
0
2
1
1
1
1
2
0
1
1
1
2
0
2
1
2
2
1
1
1
1
1
2
1
1
1
2
0
2
1
1
1
1
1
1
1
1
1
1
0
2
2
2
1
0
1
1
0
1
2
1
2
1
1
1
1
1
0
1
1
1
2
2
1
0
1
1
1
0
1
2
1
1
0
2
0
2
1
1
1
2
1
1
2
0
1
0
2
2
1
1
0
1
1
0
1
1
2
2
1
1
1
1
0
1
0
2
1
2
1
1
1
0
1
1
0
0
1
1
0
1
1
2
2
2
1
1
1
3
1
1
2
1
0
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
2
1
1
1
1
1
1
1
2
1
1
3
1
1
1
1
1
0
2
0
1
1
2
1
1
1
1
1
1
1
1
2
2
2
1
1
0
1
0
2
0
1
1
1
0
1
1
1
1
2
1
1
1
1
2
1
2
2
1
1
2
1
2
2
1
2
2
2
1
1
1
1
1
1
0
1
1
2
1
1
2
0
1
1
1
2
0
1
2
2
1
1
0
0
1
1
1
1
0
2
1
1
1
1
2
1
2
2
1
2
0
1
1
1
0
2
1
1
1
2
0
1
2
2
1
0
1
1
1
0
2
1
2
1
1
1
1
1
2
0
1
1
2
0
1
1
1
1
1
1
2
1
0
0
1
1
2
1
1
0
2
1
0
1
2
1
1
1
0
2
1
0
1
2
0
0
1
1
2
2
2
2
1
1
1
2
1
2
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
0
1
1
0
1
2
0
2
1
1
1
0
0
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
0
1
0
1
1
3
2
2
1
1
0
1
0
2
1
1
1
1
1
1
1
1
2
1
0
1
1
1
2
1
1
0
2
1
2
2
2
1
2
2
1
1
1
1
2
2
1
0
2
2
1
1
1
2
0
1
1
1
0
0
1
2
1
1
2
2
2
0
1
0
0
2
1
1
2
1
2
1
2
1
1
1
1
2
1
1
1
2
1
1
0
3
2
1
2
1
0
1
0
1
0
1
1
1
1
1
4
1
1
1
1
0
1
1
1
1
1
0
0
1
1
2
1
1
2
2
1
1
1
0
2
1
0
1
2
1
1
2
0
1
0
3
1
1
1
2
2
1
1
2
1
2
1
1
1
1
2
1
1
3
1
2
1
1
2
1
2
1
1
1
2
1
1
1
1
0
1
1
1
2
2
1
0
1
0
2
2
0
2
0
1
2
1
2
1
1
1
1
0
1
2
0
2
2
2
1
1
1
0
0
0
1
2
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
0
2
1
0
1
0
0
0
1
1
2
1
0
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
2
1
1
0
1
0
4
1
2
1
1
2
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
0
1
2
0
1
1
1
1
1
2
2
0
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
1
1
1
2
1
1
2
2
2
2
2
2
1
0
1
2
1
1
2
2
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
0
0
1
1
2
2
1
0
2
1
1
1
2
1
2
2
0
1
1
1
1
1
1
1
1
2
1
1
2
0
1
1
1
1
1
0
1
2
1
2
0
1
2
1
1
2
1
1
2
1
1
2
1
0
1
1
1
1
0
1
2
1
1
1
2
1
0
2
1
1
1
1
0
1
1
2
2
1
2
1
1
1
1
2
1
1
1
0
1
1
2
1
1
1
1
1
0
3
1
1
1
1
2
1
0
2
1
1
0
1
2
2
2
1
1
2
0
1
3
1
1
1
1
0
1
2
2
0
1
1
2
1
2
1
2
1
2
1
1
2
0
2
1
2
1
1
2
2
1
2
0
1
0
1
0
1
1
1
2
0
0
1
2
1
1
1
1
2
1
1
1
1
1
1
3
1
1
1
1
1
1
1
1
0
1
2
1
2
1
0
2
1
2
0
3
1
1
1
2
0
1
1
4
0
1
1
0
1
2
2
2
0
1
1
1
1
1
2
1
2
1
1
0
0
1
2
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
0
5
1
1
2
1
1
1
2
2
1
2
1
2
2
1
2
1
1
1
0
1
1
0
2
2
1
2
1
1
1
1
1
1
1
1
2
0
1
1
1
2
0
2
1
0
1
1
1
0
2
1
1
1
1
2
2
1
1
0
1
1
2
2
1
1
1
2
1
1
1
2
2
1
1
1
2
1
1
1
1
1
0
2
2
0
0
2
1
1
0
1
0
1
0
1
1
2
1
1
2
0
0
2
0
1
1
2
0
2
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
2
1
1
1
1
1
0
2
2
1
1
2
0
1
1
1
1
1
2
1
1
1
1
1
1
1
0
1
1
1
0
2
1
1
1
1
2
2
0
2
1
2
1
1
1
1
2
1
1
1
0
0
3
0
1
1
1
2
1
1
1
2
0
2
0
2
1
1
1
0
0
2
2
1
1
2
2
2
1
0
1
1
1
0
0
1
1
0
1
1
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
0
1
1
1
0
1
3
1
1
2
1
1
0
0
1
2
1
1
2
1
1
1
1
1
0
0
1
1
2
2
1
2
0
1
2
2
1
1
1
1
1
1
2
2
1
2
1
1
2
0
0
1
0
2
1
0
1
1
6
2
2
1
0
0
1
1
2
1
1
1
1
1
1
1
1
1
1
0
0
2
1
1
1
1
1
0
1
0
1
1
1
1
2
1
2
1
1
1
1
1
1
2
2
1
2
1
0
0
2
2
1
2
1
2
0
1
2
0
1
1
2
2
2
2
1
1
1
1
2
2
0
1
1
1
0
2
1
2
0
1
2
0
2
0
1
1
1
0
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
0
2
1
1
0
2
1
0
1
2
1
1
2
2
1
2
1
1
0
0
1
1
2
2
1
1
1
2
1
2
1
1
2
2
0
1
1
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
0
2
2
1
1
1
1
1
1
0
2
2
1
1
1
2
2
0
2
2
2
0
1
1
1
1
2
0
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
2
0
2
2
1
2
1
1
1
2
2
1
1
1
1
4
1
1
1
1
1
1
1
1
1
1
0
0
2
1
2
1
1
1
1
1
1
0
2
0
2
1
1
1
0
1
1
2
2
2
0
0
1
0
2
0
2
1
1
0
1
1
0
1
1
1
1
1
1
1
1
2
2
1
2
1
0
1
1
2
1
0
1
1
1
2
1
2
1
1
1
1
1
0
2
2
1
2
2
2
0
1
2
1
1
1
2
2
1
1
2
1
2
0
1
1
1
1
1
1
2
2
1
0
1
1
1
1
0
1
2
1
1
2
1
1
2
1
1
1
1
0
1
1
2
1
1
1
2
0
2
1
1
0
0
1
0
1
1
2
1
1
2
1
1
2
1
2
2
0
1
1
1
1
2
1
1
2
1
0
2
1
0
0
1
1
0
1
1
1
1
0
1
1
1
0
1
1
2
2
1
1
1
2
2
0
1
1
1
1
2
1
1
1
0
1
0
1
2
2
1
1
1
2
0
0
2
0
2
1
2
1
2
2
1
1
1
1
2
1
0
1
1
1
2
1
1
2
1
1
0
1
1
2
1
2
1
1
1
3
1
1
0
1
2
1
1
1
1
1
1
2
1
0
1
2
2
4
2
1
1
1
2
2
1
1
3
2
1
1
1
1
1
1
1
1
2
1
1
1
1
3
5
1
0
2
0
2
1
1
1
0
1
0
1
1
2
1
1
1
2
1
1
1
1
1
2
1
1
1
1
2
2
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
2
1
1
0
2
2
0
2
1
2
1
2
1
1
0
1
0
1
2
2
1
1
2
1
1
1
0
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
0
1
1
1
0
1
1
1
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
0
1
2
0
2
1
1
0
1
1
3
0
1
2
2
1
1
1
1
1
1
1
1
1
0
1
1
1
2
3
1
1
1
0
1
2
1
1
1
1
1
1
1
3
1
1
1
2
0
1
1
1
1
2
1
1
2
1
1
1
1
1
0
1
2
2
1
1
1
1
1
1
2
2
1
0
1
2
2
1
1
1
1
0
1
1
0
0
1
1
1
0
0
2
1
1
0
2
1
1
0
1
2
1
1
1
0
1
0
1
1
1
1
0
2
1
0
1
1
1
2
1
1
1
1
1
0
1
2
1
1
1
1
1
1
1
1
2
2
2
2
2
1
1
0
1
2
1
0
1
2
1
2
1
2
0
2
0
1
1
2
2
0
2
0
0
0
1
0
2
1
1
1
0
1
0
1
2
2
1
1
2
1
0
1
2
2
1
2
1
2
2
0
0
1
1
0
1
1
0
2
0
1
1
0
2
2
1
2
2
1
2
1
2
1
1
1
1
1
2
1
0
1
2
1
1
1
1
0
0
1
2
1
1
1
1
1
2
2
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
0
2
2
1
1
0
1
0
1
3
2
2
2
1
1
0
0
0
2
2
0
1
1
3
2
2
2
0
2
1
1
1
1
0
1
0
2
1
1
1
1
1
1
1
0
1
3
1
1
0
1
1
1
1
1
0
1
1
1
4
2
1
1
1
1
2
2
0
1
1
2
3
2
1
1
1
1
2
1
2
1
0
1
2
1
1
2
2
0
0
1
1
1
1
1
1
1
1
1
0
2
1
1
1
2
0
1
1
1
1
0
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
2
2
1
0
1
1
0
1
0
2
1
2
2
1
1
1
0
0
1
0
2
1
1
0
1
2
1
1
1
2
1
1
1
1
0
1
2
1
0
1
1
0
1
2
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
2
2
2
1
1
1
2
1
2
1
2
2
1
3
1
1
0
1
1
1
1
1
1
0
1
0
1
1
2
1
2
1
1
1
1
1
1
2
2
2
2
1
1
0
0
2
2
1
1
0
1
1
1
1
1
2
2
0
1
1
2
1
2
2
1
2
1
1
1
1
0
0
1
1
2
1
0
0
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
0
2
1
1
2
1
1
1
1
0
1
1
1
1
1
1
1
2
0
0
1
1
1
2
1
2
1
2
1
1
1
2
2
2
1
1
1
1
1
2
1
2
2
0
0
2
2
2
2
1
2
5
2
2
1
2
2
2
1
1
1
2
1
1
1
1
1
1
2
2
1
2
1
2
1
2
1
2
1
1
0
1
1
1
1
1
2
1
2
0
1
1
1
1
2
0
1
1
1
2
2
1
2
1
1
1
2
0
1
0
1
1
0
1
0
1
1
2
2
0
1
1
1
1
2
1
0
1
1
0
1
2
1
1
0
2
2
2
2
1
1
1
2
1
1
1
0
0
0
1
1
1
2
1
1
1
1
1
1
1
1
2
0
0
0
1
1
1
1
1
2
1
2
1
0
1
1
0
2
1
1
2
1
2
2
2
1
0
2
1
2
1
0
2
1
2
1
1
0
0
1
2
0
1
2
0
1
1
2
0
1
2
0
1
1
1
0
2
2
1
1
1
1
1
1
1
1
2
1
0
0
1
1
2
1
0
1
2
2
2
1
2
1
1
2
1
1
1
1
2
1
1
2
2
1
1
2
1
1
1
1
2
1
0
1
0
0
2
2
1
0
1
1
1
2
0
2
1
0
1
0
1
0
1
1
1
0
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
0
1
1
1
2
1
1
2
1
2
2
0
1
2
0
1
1
0
0
0
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
0
2
2
2
0
1
1
0
0
1
1
1
0
2
1
1
1
1
1
2
1
2
2
0
0
1
1
1
2
1
1
1
0
1
2
1
1
1
2
0
1
1
1
1
1
1
2
0
2
1
2
1
1
1
2
1
2
1
2
1
2
1
1
0
1
1
1
0
1
1
2
1
2
0
1
2
1
1
1
0
2
1
2
2
1
0
1
2
0
1
2
2
1
1
1
1
0
1
1
1
0
1
1
0
1
2
2
2
2
2
2
2
1
1
0
2
1
1
1
1
0
1
2
1
0
1
1
1
1
1
1
1
1
1
2
1
0
1
1
1
0
1
2
1
1
1
1
1
2
0
0
1
1
1
1
1
2
2
1
1
1
1
1
2
0
2
2
2
2
1
2
2
2
1
1
1
1
2
2
1
1
1
0
2
2
0
2
2
1
1
1
1
1
1
2
1
2
0
1
2
1
1
2
1
0
1
1
1
2
1
2
1
2
1
0
0
1
2
1
2
1
0
2
1
1
0
2
0
0
3
1
1
2
2
2
2
2
1
0
2
2
2
1
2
1
1
1
1
1
1
1
0
1
1
1
1
1
1
2
1
0
1
1
1
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
2
1
0
1
1
2
1
2
1
1
1
2
1
2
1
3
1
2
2
1
1
2
1
2
2
1
1
1
2
2
0
1
1
1
2
1
2
1
1
2
2
2
1
0
0
1
1
0
1
0
1
1
2
1
2
0
0
0
1
0
1
2
1
1
2
1
0
2
1
2
2
1
1
0
2
2
1
1
2
2
0
2
1
1
0
2
1
2
1
1
1
2
1
2
2
3
1
0
1
0
2
0
1
2
2
2
1
1
2
1
0
2
0
2
2
2
2
1
1
1
0
1
2
1
0
1
1
1
2
0
1
2
1
0
2
1
2
2
1
2
1
1
1
0
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
0
1
1
0
2
1
1
2
2
2
1
1
1
1
1
2
1
2
1
1
2
2
1
1
1
1
1
1
1
0
1
1
1
1
2
1
1
2
2
0
1
1
2
1
1
1
1
1
1
1
0
1
3
1
2
1
1
2
2
2
1
0
1
2
0
2
1
1
1
1
1
1
0
1
1
1
3
1
1
1
2
4
1
2
1
1
1
2
0
1
1
1
2
1
0
0
1
2
2
2
1
1
2
1
1
2
1
1
1
2
1
0
1
1
1
1
2
1
0
2
1
1
1
1
1
2
1
1
1
1
2
1
0
1
1
1
1
1
1
1
2
2
0
0
1
0
0
1
2
0
1
1
1
2
1
1
0
2
1
1
0
0
0
1
1
1
1
1
1
0
1
1
1
1
1
2
1
2
2
2
1
2
1
2
1
0
1
1
1
1
1
0
1
1
1
0
1
1
1
2
1
1
1
0
2
2
2
2
1
1
1
1
1
1
1
1
0
1
2
2
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
2
2
1
1
1
1
1
2
1
1
0
1
0
1
1
2
1
1
2
1
2
1
1
1
2
2
1
1
1
1
1
1
1
1
2
1
0
1
2
2
0
2
1
1
0
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
0
1
1
0
2
1
2
1
2
1
1
1
1
2
1
2
1
1
1
2
1
2
1
1
1
1
1
1
0
1
1
0
1
1
1
2
2
0
2
2
1
1
1
2
1
1
1
1
1
1
1
0
1
1
1
1
0
1
1
1
1
2
0
1
1
1
1
1
1
0
1
1
1
0
1
1
1
2
1
1
1
2
1
2
0
1
0
1
2
1
1
2
1
1
2
1
1
1
3
1
1
1
1
1
1
0
1
1
1
1
1
1
1
2
1
2
1
0
0
1
1
1
1
0
2
1
1
0
1
1
2
1
1
1
1
1
2
2
2
0
2
0
2
1
2
1
1
1
1
1
1
0
1
0
1
1
0
1
0
0
1
1
1
2
1
1
1
2
1
1
1
1
1
2
1
2
1
1
1
2
1
1
1
2
2
0
0
1
1
1
2
2
2
1
2
2
1
0
2
1
0
1
2
1
2
1
1
2
1
1
0
0
1
1
1
1
2
2
1
2
2
1
2
0
1
2
2
2
3
1
1
1
2
1
0
1
1
2
2
3
1
1
2
2
2
1
1
1
1
1
1
1
0
2
1
2
1
1
1
1
1
1
1
2
1
1
2
1
2
2
1
1
2
1
2
2
1
1
1
1
2
0
1
1
0
2
0
1
1
1
1
1
2
1
2
2
1
2
0
2
1
1
1
1
1
0
2
1
1
1
1
2
1
0
2
1
1
1
2
2
1
1
2
1
2
1
0
2
0
1
1
2
2
0
0
2
0
1
0
1
0
2
1
1
0
0
2
2
1
1
2
1
1
2
1
2
2
1
2
1
2
1
2
1
1
1
1
2
0
2
2
2
1
1
0
1
1
1
2
1
1
1
0
0
1
3
1
2
0
1
1
0
2
1
0
1
1
1
0
0
2
2
0
0
1
2
2
0
2
1
1
2
1
1
1
1
1
0
2
0
1
2
1
1
2
2
1
0
1
1
2
1
2
0
1
1
0
1
1
0
2
0
2
1
1
1
1
1
2
2
1
1
0
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
3
1
1
1
1
1
2
1
1
1
1
0
1
1
0
2
2
1
1
1
1
1
1
1
2
1
2
0
0
1
1
1
3
1
1
6
1
0
1
1
1
0
1
2
1
0
1
2
1
1
1
2
1
1
0
0
1
1
1
1
1
1
1
0
1
2
1
1
2
1
1
2
0
2
2
1
1
1
1
2
1
2
1
1
1
0
0
2
1
0
2
1
1
1
1
1
2
2
1
1
2
1
1
2
2
2
1
1
0
1
1
1
0
1
1
1
1
2
1
1
1
0
1
1
1
1
0
2
1
1
1
1
2
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
2
0
2
1
2
2
1
2
1
0
1
2
2
2
1
0
1
0
0
2
2
2
1
1
2
1
1
1
1
1
2
1
2
2
1
1
2
2
1
2
1
0
0
1
0
2
0
1
1
2
3
1
1
1
2
1
1
2
1
1
2
1
1
1
1
1
0
1
2
2
1
1
1
3
2
1
1
1
1
2
1
1
1
0
1
1
0
1
2
2
2
2
1
1
2
1
2
1
1
0
2
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
2
2
2
2
1
0
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
2
1
1
1
1
2
1
1
1
1
0
1
1
2
2
2
2
1
2
0
1
3
1
2
1
1
1
1
2
0
1
1
1
0
2
1
1
1
2
1
1
2
1
1
2
1
2
1
1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
2
2
1
1
1
1
2
1
1
1
0
0
2
0
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
2
1
2
2
2
2
1
0
1
1
1
1
1
1
1
0
1
1
2
2
1
1
1
1
2
2
1
1
1
1
0
2
1
1
1
1
1
2
1
1
1
0
0
0
1
1
1
1
1
2
2
1
1
1
0
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
0
1
1
1
1
0
0
1
2
1
1
1
1
2
1
1
1
1
1
0
1
1
1
1
2
1
1
2
1
1
1
1
2
2
1
1
1
2
2
1
2
1
0
1
1
1
2
1
1
2
0
0
1
0
1
1
0
1
1
1
1
2
2
0
1
1
2
1
1
1
2
1
1
1
2
1
1
0
0
1
0
1
1
1
1
1
1
2
1
1
1
1
1
0
1
1
1
2
0
1
2
1
1
1
0
0
1
0
1
2
1
1
1
2
1
1
2
1
1
1
1
2
1
1
1
1
0
1
1
2
1
1
0
11
0
2
0
2
2
1
0
1
0
2
1
1
0
1
1
0
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
1
2
1
1
1
1
1
2
1
2
0
0
1
1
2
2
1
1
2
1
1
1
2
0
1
2
2
1
2
0
1
1
3
2
0
2
1
2
1
1
1
1
2
2
0
1
1
0
2
0
0
1
0
1
1
1
1
1
2
1
2
1
1
2
1
1
0
0
2
1
1
1
1
2
0
0
0
1
0
0
1
1
2
0
1
2
2
1
1
1
1
1
0
0
1
1
1
1
2
1
1
1
1
1
0
1
0
1
1
2
1
0
1
0
1
1
1
1
1
2
2
1
0
1
1
1
2
2
2
1
1
1
1
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
2
0
1
0
2
1
1
1
2
1
1
1
2
1
1
2
0
0
1
1
1
1
1
1
2
1
2
0
2
1
1
1
1
1
2
1
1
1
0
1
1
1
0
1
1
2
2
1
1
1
0
1
0
0
0
2
1
1
0
1
1
0
1
1
2
2
1
2
2
0
1
2
1
2
0
2
1
1
1
1
1
2
2
1
1
2
0
1
1
2
1
1
0
1
0
1
2
1
1
1
1
1
1
1
0
1
1
2
1
1
3
2
1
2
1
4
1
1
2
1
1
1
1
1
0
1
1
1
1
1
1
0
2
1
1
2
1
1
2
2
2
2
1
1
1
2
1
1
0
1
1
1
2
1
1
1
2
1
1
2
2
2
2
2
2
1
1
1
1
0
2
2
0
1
1
0
2
1
1
2
1
2
1
1
1
2
0
1
1
1
1
1
2
1
2
1
1
0
0
1
2
1
0
1
1
0
0
1
0
1
1
1
2
1
1
2
1
0
0
1
2
2
1
1
1
0
1
1
1
1
2
2
2
1
1
1
1
2
1
2
2
1
1
1
1
1
2
1
0
1
2
0
1
1
1
2
1
1
2
1
2
1
0
1
2
1
1
2
0
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
1
2
1
1
1
1
0
0
1
2
1
2
1
1
1
2
1
1
2
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
2
2
1
2
1
2
1
1
1
1
1
1
2
1
0
1
1
0
1
1
1
1
1
1
0
3
1
1
2
1
2
1
1
2
1
1
1
2
1
3
1
1
1
1
1
1
0
3
1
2
1
1
0
1
1
1
2
1
1
1
2
0
0
1
1
0
1
1
1
2
1
1
1
1
1
0
0
4
1
2
1
2
2
1
2
2
2
2
1
1
2
1
2
3
0
1
1
1
1
1
1
1
1
1
0
1
1
0
1
2
2
1
0
2
2
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
0
2
2
1
1
1
1
1
1
1
1
2
2
1
1
0
1
0
1
1
1
1
0
0
1
0
1
1
1
1
1
1
0
1
0
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
2
2
1
1
1
2
2
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
3
1
2
1
1
1
0
1
1
2
1
1
2
0
1
2
1
1
1
1
2
2
1
1
1
0
1
2
1
0
2
2
0
2
1
1
0
1
0
1
1
1
2
2
0
2
1
2
0
1
1
1
0
2
0
1
2
2
1
1
0
1
2
0
1
1
1
1
0
1
1
1
1
1
2
1
1
1
1
1
0
2
1
1
1
1
1
1
2
2
1
2
0
1
2
1
1
0
1
1
1
2
1
0
2
0
1
1
1
1
1
1
1
2
1
2
1
1
3
1
2
1
1
1
0
2
1
1
0
2
2
1
0
2
2
1
0
1
1
3
1
1
1
1
1
2
0
1
1
0
2
1
1
1
2
1
1
4
1
0
1
2
1
1
2
1
1
0
1
0
1
1
2
1
1
0
1
2
2
1
1
1
1
1
1
1
1
1
3
1
1
1
0
1
1
1
2
1
2
2
1
2
1
1
1
0
1
2
2
2
1
1
2
1
1
1
2
1
1
1
1
1
1
0
0
1
1
0
2
2
1
1
1
0
0
2
2
1
2
1
1
1
1
2
0
0
1
1
1
1
1
0
2
0
1
1
0
0
1
2
1
1
0
1
2
2
1
1
2
2
2
1
1
1
1
1
2
2
1
0
1
1
0
0
1
1
1
1
1
1
1
0
2
1
0
2
2
2
1
1
2
2
2
0
1
2
2
1
1
1
2
1
2
1
1
1
1
2
2
1
1
2
1
1
0
1
2
1
1
1
1
1
1
2
1
0
1
2
0
2
1
1
0
1
0
1
1
1
2
2
1
1
1
2
1
1
2
1
1
1
1
1
1
1
0
0
2
1
1
1
1
1
2
1
1
1
0
1
2
0
1
1
2
2
2
1
2
1
1
0
1
1
2
1
2
1
1
1
1
2
1
2
1
1
2
1
1
1
1
0
1
1
1
0
1
2
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
0
1
1
1
1
0
0
1
1
1
2
1
1
1
1
1
2
2
1
1
2
2
2
1
2
1
1
1
2
2
2
2
1
1
2
1
1
2
1
1
1
0
2
1
2
2
1
1
1
2
0
1
1
1
1
1
1
1
1
1
2
1
3
2
2
2
2
1
0
2
1
1
2
1
1
0
2
2
1
1
1
2
2
1
1
2
1
1
1
2
2
1
1
1
1
2
0
2
1
2
1
1
1
1
0
1
1
2
1
1
1
1
2
2
2
1
3
2
1
1
0
1
1
1
2
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
0
1
2
2
1
1
1
2
0
1
2
1
1
1
1
1
0
1
0
0
2
1
1
1
2
2
1
2
1
1
1
0
0
0
1
0
1
1
2
1
2
1
0
1
2
1
1
0
2
1
1
2
2
1
1
2
1
1
1
1
1
1
2
1
1
2
0
1
1
2
1
1
1
1
1
0
2
1
1
1
2
1
1
2
1
1
2
1
1
1
1
1
1
1
0
1
1
2
2
1
2
1
2
1
0
1
2
1
1
1
1
0
1
2
1
2
1
1
1
1
0
1
2
1
1
3
0
1
2
1
1
1
0
1
2
2
1
1
1
2
0
1
2
6
1
1
1
0
1
2
1
1
1
1
1
1
1
0
1
1
2
1
0
2
1
1
2
2
1
2
1
0
1
0
1
2
1
1
1
1
2
0
1
1
1
0
1
1
1
2
1
0
1
2
0
1
1
1
1
1
2
1
1
0
0
1
1
1
1
1
1
2
0
1
2
1
1
1
2
1
0
2
1
1
1
1
1
2
2
1
1
2
1
1
1
1
0
1
1
0
1
1
0
1
1
1
0
1
1
1
2
2
1
1
2
2
1
1
1
2
2
2
2
1
1
1
1
1
2
2
1
1
0
2
1
1
1
0
2
1
2
1
1
1
1
2
1
2
0
1
1
1
2
1
2
2
1
3
2
0
2
1
2
0
1
1
0
1
2
1
2
2
1
2
1
1
1
0
1
1
2
1
2
1
0
1
1
1
0
1
1
2
1
2
2
0
1
1
1
0
1
1
2
1
1
1
1
1
2
1
1
1
0
1
2
2
2
2
1
1
1
1
2
1
1
1
2
1
1
1
1
0
1
1
1
2
1
1
1
2
2
1
2
0
1
2
2
2
1
2
0
2
1
2
1
2
1
1
2
1
2
1
1
1
2
2
1
0
2
1
1
3
1
1
0
1
1
1
1
0
1
1
1
1
0
2
3
1
1
0
2
2
2
0
1
1
2
1
1
1
1
1
2
1
1
1
1
2
2
2
2
1
1
1
1
1
2
2
1
1
2
2
1
1
2
1
1
1
1
1
1
0
1
1
1
2
2
1
0
1
1
2
1
1
1
0
1
2
1
1
1
1
1
2
1
0
2
1
1
0
0
1
0
1
2
1
1
1
1
1
0
1
2
2
1
2
2
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
0
0
1
1
1
2
1
2
2
1
1
2
2
2
1
1
2
1
0
2
1
2
1
2
1
1
1
1
1
1
0
1
2
1
1
2
1
1
2
2
1
1
1
1
1
1
2
2
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
0
1
0
2
1
1
2
1
1
2
1
0
1
1
0
1
2
1
2
1
1
2
1
2
1
2
3
1
2
0
1
1
0
1
1
1
1
1
1
0
1
0
1
1
1
2
1
2
1
2
1
1
1
1
0
4
1
0
0
1
1
2
1
1
1
1
0
1
1
2
1
1
1
0
1
1
2
2
2
0
1
1
1
2
2
1
0
1
2
2
1
1
1
2
1
1
1
1
1
1
1
1
1
0
1
1
0
0
1
2
1
1
1
1
2
1
2
2
1
0
1
2
1
1
1
1
1
2
2
1
1
1
1
0
0
2
0
1
2
0
3
1
1
1
0
1
1
1
1
1
1
2
1
1
1
2
1
1
1
0
1
1
2
1
0
1
1
1
1
2
1
2
2
2
1
1
1
1
2
0
1
1
1
1
0
1
1
1
2
0
1
2
0
2
1
1
2
2
1
1
1
0
2
1
1
2
1
2
1
1
1
1
1
1
0
1
1
1
1
2
0
1
1
2
0
1
2
0
2
1
1
1
2
1
1
2
1
2
1
1
1
1
1
2
1
1
1
0
2
1
2
1
0
1
1
1
1
1
1
2
0
2
1
0
2
1
1
0
0
1
1
1
2
1
1
1
1
2
2
2
1
0
2
1
0
2
1
2
1
2
2
2
2
1
1
2
1
1
1
2
0
2
0
1
2
2
1
2
1
1
1
0
1
2
1
0
1
2
1
1
1
2
1
1
1
0
1
3
1
1
2
1
1
2
2
1
2
1
2
2
1
2
1
1
1
1
2
1
0
1
2
1
2
1
1
2
1
1
1
1
1
1
0
1
0
1
2
2
0
3
1
1
1
2
1
1
1
2
1
3
1
1
1
0
1
1
1
0
1
2
0
0
1
1
1
1
1
1
2
1
0
1
2
2
3
2
1
0
1
0
2
1
1
1
2
1
1
2
1
1
2
2
2
1
1
1
1
2
1
2
1
2
1
1
0
1
1
1
2
1
0
1
1
1
1
2
0
1
1
1
1
0
1
2
2
2
1
2
1
1
1
0
0
1
2
1
1
1
0
2
1
0
0
1
1
2
1
0
1
1
1
2
1
2
1
1
1
1
1
2
2
1
1
2
1
2
1
3
1
2
1
1
1
0
2
2
2
1
0
1
1
1
1
2
0
1
1
2
1
1
2
1
1
1
1
1
1
1
1
0
1
0
2
1
2
1
0
1
2
1
1
1
2
1
0
0
0
1
1
2
1
1
2
1
1
2
2
2
1
1
1
0
0
2
2
2
2
1
2
0
0
1
1
0
1
1
1
1
1
1
2
1
1
1
2
1
1
1
0
1
1
2
0
1
0
2
1
0
1
1
0
2
1
0
1
1
1
2
2
1
1
2
0
0
1
1
1
1
2
1
2
1
1
2
1
2
0
1
2
2
1
1
1
0
0
1
2
2
1
0
2
1
2
0
1
1
1
0
1
2
1
3
0
0
1
1
2
2
1
1
1
0
2
1
1
1
1
1
1
0
0
1
1
1
1
1
1
1
0
2
1
1
0
1
2
1
1
1
1
1
1
2
2
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
0
1
1
0
1
1
1
1
1
1
2
1
2
1
1
0
1
0
0
0
1
1
2
0
1
1
0
2
2
1
2
1
1
2
2
1
2
2
1
2
2
2
1
1
1
2
2
1
2
2
1
1
0
0
1
2
1
1
1
0
1
2
1
1
2
2
2
1
2
0
1
2
1
0
2
1
1
0
1
1
1
1
2
1
1
1
1
1
1
2
2
1
2
2
1
2
2
1
1
0
2
1
1
1
1
1
0
1
2
1
1
1
2
2
1
1
0
2
1
2
1
0
2
1
0
1
2
1
1
2
1
1
1
1
1
2
4
1
1
2
1
1
2
2
1
1
2
2
1
2
0
2
2
1
1
2
1
1
1
1
1
1
2
2
1
0
1
2
1
1
1
1
1
2
1
1
2
2
0
0
1
1
1
2
2
1
1
1
1
1
1
1
0
1
2
1
1
1
1
1
2
1
1
1
1
1
1
0
1
2
2
1
1
2
1
1
1
1
1
2
1
2
2
0
1
2
1
2
1
1
1
2
1
2
2
1
1
1
2
2
1
2
1
2
1
1
1
1
2
2
1
1
1
1
1
1
0
1
1
2
2
1
1
2
1
1
1
2
2
1
2
0
0
1
2
1
1
2
0
2
2
2
2
1
0
2
1
1
2
2
1
1
1
3
1
0
2
2
2
0
1
1
1
2
1
1
2
1
1
1
1
2
1
1
0
1
2
0
1
1
2
2
1
2
2
1
1
0
1
1
2
1
2
0
1
2
1
2
1
2
0
1
1
0
2
1
1
1
3
1
0
2
2
1
0
2
1
1
2
1
1
2
1
1
1
0
1
1
2
0
1
2
0
0
1
1
1
1
1
1
1
2
0
1
2
1
2
1
0
3
1
1
2
0
1
2
1
1
1
1
1
1
0
0
2
1
1
1
1
2
1
0
2
1
2
1
1
1
2
2
1
1
0
1
1
1
1
1
1
1
2
1
2
1
1
0
1
2
1
1
1
1
0
2
1
1
0
2
1
1
1
1
2
1
1
1
1
1
0
2
2
0
1
1
0
1
1
2
2
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
0
1
0
2
1
2
1
2
0
1
1
2
1
1
1
1
1
2
1
1
0
1
1
1
0
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
2
2
1
2
1
1
2
1
1
1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
1
1
1
3
1
1
1
2
1
1
2
1
1
1
1
2
1
1
1
1
1
1
2
2
1
1
2
1
1
2
1
1
2
1
0
1
0
1
2
1
1
1
1
1
1
5
0
1
2
2
2
1
1
2
1
1
1
1
2
1
1
1
1
2
0
1
0
1
2
1
1
2
2
2
2
1
1
1
0
0
1
1
2
0
1
0
1
1
1
2
1
1
2
1
2
1
1
2
1
1
1
1
1
0
1
1
2
1
1
1
1
2
1
1
1
0
1
1
2
2
1
2
0
1
0
2
0
0
1
0
1
2
1
1
0
1
2
1
2
2
1
1
3
1
2
2
1
2
2
2
1
1
1
1
1
2
1
1
2
1
1
1
2
1
1
2
1
1
1
0
1
1
2
3
1
1
0
2
2
2
2
1
1
1
0
2
1
2
0
0
1
2
0
1
1
2
1
2
2
1
1
1
1
1
1
1
2
0
2
0
2
2
1
1
1
1
1
2
1
1
1
2
1
1
2
0
2
1
1
0
1
0
1
1
1
1
1
2
1
1
0
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
0
1
2
2
1
1
1
0
0
4
1
1
2
1
1
1
1
2
1
0
0
1
2
0
2
1
1
1
0
2
1
0
1
2
1
2
0
0
1
2
1
2
1
1
1
1
0
2
1
1
2
1
2
2
0
0
2
0
2
2
1
0
2
2
0
2
1
1
1
2
2
1
1
1
1
1
4
2
1
1
1
1
0
1
2
1
0
1
1
1
2
1
1
1
1
1
1
1
2
1
0
1
1
1
0
1
0
1
2
0
2
2
0
1
2
0
1
0
2
1
2
4
2
0
1
2
0
1
1
1
0
1
1
2
2
1
1
1
2
1
1
1
1
1
1
2
1
2
2
2
0
0
2
0
1
2
1
2
1
1
2
2
0
2
1
1
2
0
1
1
1
2
1
1
0
1
0
1
1
2
1
2
2
2
2
1
1
2
1
0
1
2
2
0
1
1
2
2
1
1
2
2
1
2
1
1
1
1
2
1
2
1
1
1
1
1
2
2
1
1
2
0
1
2
1
1
2
1
1
3
1
1
1
1
0
0
1
2
1
1
1
2
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
0
1
1
2
1
2
1
2
2
0
1
1
1
1
1
1
2
2
0
1
2
0
2
2
1
1
1
1
2
0
1
0
0
0
2
1
1
2
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
0
1
2
1
1
2
1
1
1
1
1
1
0
2
1
0
2
1
1
2
1
2
2
1
0
2
2
1
2
2
1
1
0
1
2
2
1
0
2
1
0
1
1
1
2
0
2
0
2
1
1
0
0
1
2
1
1
0
1
1
0
1
1
0
2
1
1
0
1
2
1
0
1
1
1
0
0
2
1
2
1
2
0
0
1
1
1
1
1
1
2
1
2
1
1
0
0
1
2
2
1
2
0
1
2
2
1
1
1
5
3
1
1
1
1
1
1
2
2
0
1
0
0
1
0
1
1
1
1
0
1
2
1
1
1
1
0
1
1
1
2
2
1
1
2
1
1
1
1
0
1
2
2
1
2
2
1
1
2
0
1
2
1
2
2
1
1
0
1
1
1
1
0
2
1
2
1
1
2
1
0
2
1
1
1
1
0
1
1
2
1
2
1
1
1
1
1
2
0
2
2
2
1
1
1
0
1
1
1
1
1
2
1
0
1
0
2
1
2
2
1
1
1
1
1
1
1
1
0
1
1
0
1
1
1
0
1
2
2
1
1
1
1
2
0
1
2
2
2
2
0
1
3
0
1
2
1
1
1
0
2
1
1
1
2
1
2
1
1
1
1
2
1
1
1
1
1
2
0
0
2
1
2
2
2
2
1
2
0
2
0
2
2
2
1
2
1
0
0
1
2
1
2
1
2
2
1
1
1
0
1
1
1
1
0
2
1
2
2
0
3
2
1
1
1
1
2
1
2
1
1
1
1
1
0
1
1
1
2
1
1
1
1
1
1
3
1
2
1
2
0
2
2
1
0
1
1
1
0
1
1
1
0
1
1
2
1
2
1
1
0
1
2
1
1
0
1
1
1
1
2
1
1
1
1
1
0
1
1
1
1
1
0
1
1
2
2
1
1
2
1
1
0
2
2
1
1
1
1
0
2
1
1
0
1
1
1
2
1
0
1
2
0
1
2
2
2
2
1
0
2
1
1
1
1
2
3
1
1
1
1
1
1
2
1
0
1
2
1
2
1
2
1
1
2
2
1
2
2
1
1
1
0
1
1
2
0
1
1
1
0
0
2
2
0
1
1
2
1
1
2
1
1
1
2
1
1
2
1
1
1
1
0
1
1
2
1
0
2
1
1
1
0
2
1
2
1
0
1
1
1
0
1
2
1
1
2
1
1
2
2
1
1
1
1
1
1
0
1
0
2
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
2
1
1
1
2
1
1
1
2
0
1
1
1
0
0
2
1
2
0
2
1
1
2
2
1
1
1
1
1
1
2
2
2
2
1
3
1
0
1
1
2
1
1
2
1
1
2
1
1
2
1
1
1
1
1
1
1
0
1
1
1
1
2
0
0
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
0
2
2
2
2
2
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
0
2
1
2
1
2
1
1
1
1
1
1
0
1
2
2
1
1
1
1
2
2
1
2
1
0
0
1
1
1
2
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
0
1
1
2
1
1
2
0
2
0
0
1
1
1
2
0
1
1
1
2
1
1
1
0
1
3
1
1
2
1
1
0
2
1
1
2
1
1
2
1
1
1
1
1
2
1
1
1
3
1
2
2
0
1
1
1
1
2
0
1
1
1
1
1
1
1
2
2
1
2
1
1
1
1
2
1
0
1
0
1
2
2
1
2
2
1
1
1
1
1
1
2
1
0
1
1
1
2
1
1
1
0
1
1
1
0
0
1
1
1
1
0
1
2
2
1
1
1
2
0
2
2
1
1
1
2
1
1
0
1
1
1
1
1
2
1
1
2
0
1
1
1
1
1
1
0
2
0
1
0
2
1
1
2
1
1
2
1
1
1
1
2
3
0
1
0
1
1
1
1
3
0
1
1
2
1
1
0
1
1
1
1
2
0
1
1
1
2
0
2
1
1
3
2
0
2
1
1
0
4
1
0
1
1
0
1
1
2
1
2
0
1
1
0
1
2
1
0
1
1
0
1
2
2
1
1
1
1
1
2
1
1
1
0
2
1
1
0
0
2
1
2
1
0
1
0
1
0
2
0
0
1
1
1
2
1
2
1
0
2
1
2
1
0
2
1
2
1
1
1
2
1
1
1
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
1
2
0
1
1
0
1
1
1
2
1
1
1
1
0
1
0
2
1
0
1
1
1
2
1
1
0
1
1
1
2
2
0
1
1
1
2
1
2
0
2
2
1
0
1
1
1
1
0
1
1
2
1
1
1
1
1
0
1
1
1
1
2
2
1
1
1
1
1
2
1
1
2
0
1
2
1
1
2
1
1
1
2
1
1
0
0
2
1
1
1
2
1
1
1
1
2
2
1
2
1
2
1
1
0
1
1
1
2
0
1
1
0
1
1
2
2
1
1
0
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
0
2
1
1
1
1
1
1
1
1
3
1
2
1
2
0
1
2
2
2
1
1
1
2
1
2
1
2
1
1
2
1
2
1
1
1
0
0
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
0
1
2
1
2
1
1
0
1
1
1
1
2
1
1
0
1
0
1
0
1
2
1
1
1
1
0
2
1
1
2
1
2
1
0
1
2
1
2
1
2
1
0
1
1
2
0
2
1
1
1
2
1
0
2
0
0
1
1
0
1
1
2
2
1
1
1
0
1
1
1
1
1
0
0
0
0
0
1
1
1
1
0
2
1
1
2
1
2
2
2
0
1
2
0
1
1
2
1
1
0
2
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
0
2
2
2
2
1
1
2
2
0
1
1
1
1
1
1
0
2
2
1
2
3
1
1
1
2
1
1
1
1
1
1
1
1
3
0
1
0
1
0
1
1
2
1
2
1
0
2
1
0
2
1
1
0
1
2
0
1
1
1
1
2
2
1
1
1
1
1
1
1
1
0
1
1
1
0
2
1
1
1
3
1
0
2
1
2
1
1
2
0
1
1
1
2
2
1
1
1
1
1
1
1
0
1
1
1
1
0
2
1
1
2
1
1
1
0
1
2
1
2
2
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
0
0
1
1
1
0
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
0
1
0
2
1
1
0
1
2
1
0
2
2
2
2
1
2
1
2
2
1
2
2
0
1
1
1
0
0
1
1
1
1
1
2
1
2
2
0
2
1
2
1
1
2
0
2
1
2
2
1
1
1
2
1
1
2
1
2
1
1
1
2
1
2
1
1
2
1
1
1
0
1
1
2
2
0
1
1
1
1
1
2
0
1
2
2
2
1
0
1
1
0
1
1
0
1
0
2
2
1
1
1
2
1
1
1
2
1
0
1
0
1
1
1
2
1
1
0
1
2
1
0
2
0
1
2
1
1
1
2
1
1
1
2
2
2
1
1
1
0
1
1
0
2
2
2
1
0
0
1
1
1
0
1
1
1
1
2
2
2
2
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
1
0
1
2
1
1
1
3
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
0
3
0
1
1
1
1
1
2
1
1
2
1
0
1
1
1
0
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
2
2
2
1
0
1
1
1
2
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
0
1
2
2
2
1
2
1
2
1
1
2
2
1
1
2
0
1
2
2
1
2
1
1
1
1
2
1
0
1
1
1
1
1
1
2
2
1
1
1
2
2
1
2
1
0
1
1
0
2
1
1
1
1
1
1
2
1
2
1
1
1
1
2
1
2
0
1
2
1
1
1
0
2
0
0
2
2
1
2
1
1
0
1
1
1
2
0
2
1
1
1
1
0
1
2
1
1
1
1
1
1
1
2
1
2
1
1
2
1
2
1
0
1
1
2
0
2
1
1
1
1
1
1
0
1
1
0
0
1
1
2
2
1
2
1
2
2
1
1
2
0
0
2
1
2
1
2
1
1
1
2
1
1
1
1
0
2
0
1
1
1
1
2
2
0
2
1
1
1
1
3
1
1
1
2
2
2
1
0
0
1
0
1
1
0
1
0
1
1
1
2
2
1
1
0
2
4
0
1
1
1
0
1
0
2
1
2
2
1
1
1
2
2
1
1
1
1
0
0
1
1
1
0
2
1
1
1
2
1
1
0
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
2
1
2
1
2
1
2
2
0
1
1
2
1
1
2
1
1
1
1
1
1
1
2
1
1
0
1
0
2
2
1
1
2
1
1
0
1
1
0
1
1
1
1
3
2
2
1
0
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
2
2
2
1
1
2
0
1
1
1
2
1
1
0
1
1
1
1
1
1
0
1
1
1
2
1
3
1
1
1
2
1
2
1
0
1
2
1
0
1
0
0
2
1
0
1
1
1
1
1
2
1
1
2
2
2
1
1
2
0
2
1
1
0
2
1
0
1
1
1
1
0
1
1
2
2
1
2
1
1
1
1
0
2
1
2
0
2
1
1
1
0
1
1
1
0
0
1
2
2
1
1
1
0
1
2
1
0
1
2
2
1
1
1
1
1
0
1
1
1
1
2
1
2
1
1
2
1
1
1
0
1
1
1
2
1
2
1
1
0
1
2
1
0
2
2
1
0
1
0
1
1
0
1
1
1
1
1
1
2
2
1
2
1
1
2
1
1
2
1
1
2
2
1
1
1
1
2
2
1
2
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
0
0
1
1
2
1
2
2
1
1
2
0
1
1
2
1
1
1
1
2
1
1
1
2
1
1
1
1
0
0
2
2
1
1
1
2
1
0
0
0
0
1
1
3
2
1
0
1
1
1
2
1
0
1
1
1
2
1
1
0
1
2
1
0
1
1
1
1
1
0
1
1
1
1
1
2
3
1
0
1
0
1
1
0
2
1
2
0
1
2
2
2
1
1
1
1
1
1
1
1
0
2
1
1
2
1
0
1
0
2
2
1
0
0
1
1
1
1
0
0
1
1
2
0
1
1
1
2
2
0
1
2
2
0
1
1
0
1
2
0
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
0
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
2
0
1
1
2
1
1
1
0
1
1
1
1
0
1
2
2
1
2
1
1
1
3
2
1
1
1
1
1
2
1
1
1
1
1
0
2
1
1
0
1
0
0
1
1
1
1
1
2
1
2
1
1
1
1
2
2
2
2
2
2
1
1
1
1
1
1
1
2
0
1
1
2
2
1
0
2
1
2
1
0
1
1
1
1
0
2
1
1
2
1
1
2
1
1
2
0
1
1
1
2
0
3
1
1
0
1
1
1
1
2
0
2
2
1
1
2
1
1
1
2
1
2
0
2
0
1
1
1
1
2
2
1
1
0
1
1
1
1
1
0
2
1
2
0
2
0
1
2
1
1
1
0
1
0
1
1
1
1
1
1
1
1
2
1
1
1
0
1
2
1
2
1
1
2
0
2
3
1
1
0
1
1
1
2
1
0
2
1
1
1
1
2
1
2
0
0
1
1
1
0
1
0
2
2
0
1
2
1
1
1
1
2
2
1
2
1
2
1
2
1
0
0
1
1
0
2
1
1
2
1
1
1
0
1
1
2
1
1
1
1
1
1
1
2
1
2
1
2
2
1
2
2
2
1
0
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
2
2
2
2
2
1
2
1
1
1
2
1
2
1
1
1
2
2
0
1
1
2
1
3
1
1
1
1
2
0
2
1
1
1
1
2
1
1
1
1
1
1
0
1
1
2
1
1
2
0
1
0
2
1
1
2
0
1
2
0
1
0
1
0
1
0
1
1
1
1
1
1
1
1
1
3
0
2
1
0
2
1
0
1
1
0
2
1
1
1
1
1
1
2
2
1
0
2
0
0
1
2
1
1
2
0
1
0
1
2
1
1
2
0
1
1
2
0
1
1
1
1
1
2
1
1
1
1
1
0
1
1
0
2
1
1
2
2
2
1
1
2
0
1
2
1
1
1
2
1
2
1
0
1
0
1
2
1
0
0
1
0
1
1
1
2
2
1
1
1
2
2
1
1
1
2
1
0
2
1
2
1
0
2
1
1
2
0
1
1
1
2
2
2
1
0
2
2
0
2
2
1
1
0
0
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
2
2
1
1
2
1
0
2
2
3
2
0
1
0
0
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
0
1
1
1
2
2
1
2
1
1
1
1
1
2
1
1
1
1
2
2
1
1
1
2
1
1
2
1
2
1
1
1
2
1
0
1
2
2
2
2
1
0
1
1
2
1
0
1
2
2
1
1
1
0
1
0
2
2
2
2
2
1
0
1
1
1
1
2
0
1
2
1
1
0
2
0
2
1
2
2
1
2
2
1
1
1
1
2
1
0
1
1
3
1
1
0
2
1
0
1
1
1
1
1
1
0
1
1
1
2
1
1
1
2
1
1
1
0
2
1
1
1
2
2
1
2
1
2
1
0
2
2
0
1
1
2
2
1
2
2
1
2
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
0
2
1
1
1
0
2
1
0
1
1
0
0
1
1
1
1
1
1
1
1
1
1
1
1
0
2
1
1
1
2
0
1
2
1
1
2
1
1
2
1
2
2
1
1
2
0
2
2
1
1
1
1
2
1
1
2
2
2
1
0
1
1
1
1
1
0
1
1
1
0
1
1
2
0
0
1
1
1
2
2
2
1
1
1
1
0
1
1
1
1
1
1
2
2
0
1
1
2
2
0
2
2
1
0
1
1
0
2
1
1
2
2
1
1
1
0
1
1
1
2
0
1
2
2
0
2
5
1
2
1
1
1
1
2
0
2
1
1
1
1
0
1
1
1
1
1
2
2
1
1
1
0
2
1
1
1
1
0
1
1
1
1
1
2
1
0
1
1
1
1
2
1
1
0
1
0
0
2
1
1
2
1
1
1
1
1
2
0
2
1
1
1
3
1
1
1
1
2
2
2
1
1
2
1
1
1
0
2
1
1
2
1
2
0
0
0
2
1
0
2
1
1
1
1
2
2
2
1
2
1
2
0
2
0
0
1
1
1
2
1
1
0
1
1
2
1
1
2
2
2
1
2
1
1
2
1
0
2
1
1
2
1
1
2
2
0
1
1
1
1
2
2
2
1
0
0
1
0
1
2
0
1
1
1
0
2
0
1
1
1
0
1
2
1
1
1
2
2
1
1
1
1
0
1
2
1
1
2
2
1
1
1
2
1
1
0
2
1
0
2
1
1
2
1
1
0
2
1
2
2
0
1
1
1
2
2
3
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
0
2
2
1
2
0
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
2
1
2
1
2
1
1
0
0
2
1
1
1
1
1
0
1
1
2
1
1
1
0
0
1
2
1
2
1
1
1
1
1
2
0
1
0
1
2
2
2
2
1
2
2
2
1
1
0
1
2
1
2
1
2
1
1
1
1
1
2
1
2
2
0
2
1
1
1
1
0
1
2
1
2
1
2
1
1
1
1
2
1
0
2
1
2
2
1
1
1
1
1
1
1
1
2
2
0
2
1
0
0
0
1
1
1
2
1
1
2
1
1
0
1
1
1
1
2
0
1
2
1
3
3
1
2
1
1
1
2
2
1
1
1
1
0
1
2
1
1
1
2
2
1
2
1
1
1
1
1
1
2
2
2
2
3
1
1
1
1
1
1
1
2
2
2
2
0
2
1
1
0
2
2
1
0
0
1
1
1
1
2
1
1
2
0
1
0
1
2
1
2
1
0
1
1
0
2
2
1
1
1
1
0
2
2
1
1
2
1
0
1
2
1
0
2
1
0
1
2
1
2
0
0
1
1
2
1
1
2
1
0
0
1
1
1
0
1
0
1
1
0
2
2
1
1
1
1
1
1
1
0
1
0
1
2
3
1
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
0
1
2
2
2
1
1
1
0
0
2
0
1
0
2
1
1
2
2
2
2
0
1
0
2
2
1
1
1
1
0
1
2
0
2
1
2
1
1
1
1
0
1
1
1
2
0
1
1
0
2
2
2
1
1
0
2
1
2
1
2
2
2
1
1
1
0
0
1
1
1
1
1
1
1
2
2
2
0
1
1
1
1
1
1
1
1
1
0
1
1
0
2
1
1
1
1
1
1
1
2
1
1
1
2
1
0
1
1
1
2
0
1
1
1
1
1
1
2
2
0
2
2
0
1
1
1
1
1
2
2
0
2
1
2
1
1
2
1
0
1
1
0
2
1
1
1
2
1
2
1
2
1
0
2
1
2
1
2
2
2
1
1
1
1
1
1
0
0
2
1
1
1
0
1
1
2
2
1
0
1
0
1
0
1
2
1
1
0
1
1
1
1
2
2
1
2
1
2
0
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
2
2
1
1
1
2
0
1
1
1
2
1
1
1
2
1
1
2
0
1
1
1
1
2
1
2
1
2
2
1
1
2
1
0
1
1
1
2
1
0
1
1
0
1
1
1
1
1
1
1
1
1
2
1
1
0
2
2
1
2
1
2
1
1
1
1
1
1
2
1
0
1
2
1
1
1
1
1
1
1
2
1
1
0
2
1
2
1
1
1
0
1
0
1
1
1
1
1
1
0
1
1
1
1
2
1
1
1
1
1
1
1
0
0
2
2
2
1
2
2
3
1
1
2
0
2
1
1
1
1
2
2
0
2
1
2
0
1
2
1
2
0
2
0
1
1
1
1
1
0
1
2
1
1
1
2
2
2
1
0
1
1
1
1
1
2
2
1
1
1
1
2
2
0
2
1
1
1
1
1
0
2
0
1
1
1
1
2
0
1
1
1
0
1
2
1
1
1
1
2
1
2
0
1
1
2
1
2
2
0
2
1
1
0
1
1
1
2
1
1
2
0
1
1
1
1
2
1
1
0
2
2
1
0
2
1
0
1
1
0
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
0
2
1
2
1
1
1
2
1
1
0
1
2
2
1
2
1
1
2
2
1
2
2
1
2
2
1
1
1
0
1
2
1
1
1
1
1
1
1
1
1
2
2
2
0
1
1
2
0
1
0
1
1
1
1
1
2
1
1
0
1
2
1
1
2
2
0
1
1
2
1
0
1
1
1
0
2
1
2
1
1
1
1
2
1
1
2
1
2
1
1
2
1
1
1
0
1
0
2
1
1
1
1
2
1
2
1
1
2
2
0
1
2
1
1
1
2
2
1
0
1
1
0
2
2
1
1
2
1
1
1
1
1
1
0
1
0
2
1
1
1
2
2
2
2
1
1
2
1
1
1
1
0
1
2
2
1
2
1
2
1
1
1
1
2
2
1
0
2
1
3
2
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
2
1
2
1
1
2
2
1
2
1
1
1
1
2
1
1
2
1
1
2
2
1
1
1
1
0
1
1
2
1
1
2
2
1
2
3
2
1
0
2
1
1
2
1
1
0
1
1
2
1
1
1
1
1
0
2
1
2
1
1
1
1
0
1
1
2
1
1
1
0
1
1
2
2
0
2
1
1
2
1
1
1
1
1
0
1
1
1
1
0
1
2
1
1
1
1
1
2
1
1
2
0
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
0
1
2
0
1
1
2
2
1
1
1
2
1
0
1
1
1
0
1
1
1
1
1
2
2
1
1
1
1
1
2
2
1
2
2
2
1
0
1
1
2
2
1
2
2
1
1
1
2
1
1
1
3
2
1
1
2
1
1
2
2
2
2
1
1
2
1
2
1
1
0
1
2
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
2
1
1
1
0
1
0
1
1
0
2
1
1
1
0
1
1
1
2
2
1
1
1
0
1
1
0
2
1
1
1
1
1
2
1
1
2
2
1
1
1
2
1
1
1
1
2
2
1
1
1
2
1
2
1
1
1
1
1
0
1
1
2
0
1
1
2
2
1
0
0
2
1
2
1
1
1
2
1
1
1
1
0
2
2
0
1
2
1
1
1
0
1
1
2
1
2
1
1
2
2
1
1
1
1
2
1
2
1
1
1
2
1
1
2
1
1
1
0
1
2
1
1
1
1
2
1
0
1
0
2
1
1
1
0
1
1
0
1
1
1
1
1
1
1
1
2
2
1
2
1
1
0
1
0
3
1
1
2
2
2
2
1
2
0
1
1
1
1
1
1
0
2
0
1
2
2
1
1
1
1
1
1
1
0
2
0
1
1
1
1
1
1
1
0
1
1
1
2
2
1
1
2
1
1
1
1
1
2
2
1
1
0
1
2
0
1
1
1
2
1
1
2
0
1
1
2
2
1
2
2
0
2
0
1
1
0
1
1
1
1
1
1
2
0
1
1
1
0
1
1
0
1
1
1
2
0
1
1
2
2
1
1
2
1
1
1
1
2
2
2
1
1
2
1
0
1
1
1
2
2
0
2
1
2
1
2
1
2
1
2
1
2
0
1
1
1
1
1
1
1
1
0
2
2
1
1
1
1
2
1
1
1
1
0
0
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
4
1
2
0
2
1
1
0
1
2
1
1
1
2
1
1
2
1
1
0
1
1
2
1
2
1
1
1
0
2
1
2
2
1
1
1
2
2
2
1
0
1
1
2
1
2
1
1
1
1
1
1
1
2
0
1
2
1
1
2
0
1
1
0
1
1
0
1
2
1
1
1
2
1
1
1
1
1
3
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
2
1
0
1
1
1
1
1
2
1
1
0
1
1
1
2
1
2
1
2
2
1
2
1
1
1
1
0
1
0
0
1
2
1
1
0
2
1
2
2
2
0
0
1
1
0
1
0
1
3
2
1
1
1
1
1
1
1
2
1
1
1
0
2
2
1
1
1
0
1
2
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
0
1
0
1
1
2
1
2
1
1
1
1
0
2
1
1
0
1
1
1
1
2
2
1
2
1
1
1
3
1
1
1
0
1
1
1
1
0
0
2
1
1
2
0
1
0
2
1
2
2
1
1
1
1
1
2
2
2
2
2
1
1
1
1
2
1
1
2
1
1
1
1
0
0
2
2
1
1
0
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
0
2
1
2
2
0
1
1
1
1
2
1
0
0
1
1
2
1
2
2
1
1
1
2
0
1
2
1
1
1
1
1
2
1
1
0
2
2
1
2
0
1
0
1
1
0
1
1
2
0
1
1
0
1
1
2
2
1
2
1
1
0
1
1
1
1
1
2
1
1
1
1
2
0
1
1
1
1
2
2
1
2
2
1
1
1
2
2
0
1
1
0
2
1
1
1
1
1
2
2
0
2
0
1
0
2
2
0
2
0
1
1
1
2
1
1
0
2
1
2
1
1
1
1
1
1
0
1
1
2
1
2
1
1
1
1
1
2
1
2
1
1
2
1
1
1
2
0
1
1
1
0
1
0
1
1
0
1
2
1
1
2
2
0
1
2
2
2
1
1
0
2
1
1
2
1
1
1
1
1
2
1
1
1
1
0
2
0
2
1
2
1
2
1
1
2
0
1
0
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
0
1
1
1
1
2
1
2
1
0
2
1
2
2
2
1
1
1
0
2
1
1
2
1
1
1
1
1
0
0
2
1
2
2
1
1
1
1
1
1
1
2
1
1
2
2
1
1
1
1
2
1
2
1
1
2
1
0
1
2
1
1
2
1
1
1
1
1
1
1
2
1
0
1
2
1
0
2
1
1
2
1
2
2
1
0
1
1
1
2
1
2
1
1
1
0
1
2
2
1
1
2
1
1
2
2
2
2
2
2
1
1
1
1
0
1
1
1
1
0
1
1
2
2
0
3
2
2
1
1
1
1
1
1
1
1
2
0
1
1
0
2
1
2
2
1
1
3
2
1
0
1
0
1
1
1
1
1
0
1
0
0
1
2
1
1
1
1
1
2
1
2
2
1
1
1
1
1
1
0
1
1
2
1
1
1
1
0
1
1
2
1
1
1
1
0
2
1
0
2
1
1
1
1
4
2
1
1
3
0
2
1
1
1
1
1
1
2
1
2
1
0
2
1
1
1
1
0
2
2
1
1
1
2
2
1
1
2
0
2
1
1
2
1
1
1
2
1
1
0
1
0
1
1
1
1
1
3
2
1
1
2
2
2
0
2
2
1
1
1
1
2
2
1
1
1
2
2
1
2
2
1
1
1
2
1
2
0
1
1
1
2
1
1
1
1
1
1
0
0
1
2
2
1
1
1
1
1
1
1
2
2
1
2
1
0
1
1
1
1
1
2
1
1
1
3
2
1
1
0
2
2
0
1
1
1
1
1
1
0
1
1
1
0
1
1
1
1
1
2
1
1
2
0
1
2
0
1
1
2
1
1
1
1
1
2
1
0
1
1
1
0
1
2
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
0
1
1
0
1
1
0
0
1
1
1
1
0
2
1
1
1
1
2
1
1
1
0
2
1
1
1
1
2
1
1
1
1
0
0
1
1
1
1
2
2
1
1
2
0
1
0
0
0
1
1
1
2
0
2
1
1
0
1
1
1
1
1
1
1
1
1
2
2
1
0
1
1
1
1
0
1
1
1
1
1
0
2
1
1
1
1
1
1
1
0
1
2
1
2
1
1
1
1
2
1
1
2
1
1
1
2
2
1
0
2
1
1
0
2
2
1
0
0
1
2
1
1
1
2
1
0
1
1
1
2
1
1
0
1
1
2
0
0
0
1
1
2
2
1
1
2
0
1
0
2
3
1
1
0
1
0
1
1
2
1
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
0
0
1
1
2
1
1
1
1
0
0
1
2
0
1
2
1
1
2
2
1
1
1
1
1
2
1
1
1
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
2
0
2
1
3
2
2
0
2
1
2
1
0
1
0
1
0
1
1
1
1
1
0
1
1
1
1
1
1
2
1
1
1
2
0
3
1
1
1
1
0
0
0
2
1
1
1
1
1
1
2
0
1
1
1
1
2
1
1
0
1
1
1
1
2
4
1
2
1
1
1
1
2
1
1
1
1
0
1
1
1
1
3
2
1
0
1
2
1
1
0
1
1
0
1
1
2
0
1
2
1
2
1
1
1
1
1
1
2
1
1
2
1
1
1
2
1
1
1
0
1
1
1
0
1
2
2
1
2
0
0
1
2
1
0
1
2
1
1
2
1
1
1
2
0
1
1
2
1
2
1
1
1
1
1
1
0
2
1
1
1
0
1
1
2
1
0
1
1
1
2
2
2
1
2
1
0
2
1
2
2
1
1
1
1
2
1
1
1
2
2
1
0
2
0
0
1
1
1
2
2
1
1
1
0
1
1
1
1
1
2
2
1
1
1
1
1
2
1
0
1
1
1
2
2
0
1
1
1
1
1
0
1
2
1
1
1
1
0
0
1
1
1
1
2
0
2
2
1
1
2
1
1
2
1
2
1
1
0
1
2
1
1
1
1
1
1
2
1
2
1
1
1
0
0
1
0
1
2
1
1
1
2
1
1
2
0
0
1
2
0
2
1
2
0
1
2
2
2
0
1
1
2
1
1
1
2
1
1
1
1
2
1
1
0
2
1
1
1
2
1
0
1
0
1
0
1
0
1
2
0
1
0
1
4
1
1
1
2
1
2
2
1
1
2
2
1
1
0
2
0
2
2
0
1
2
1
1
2
1
1
2
2
1
0
1
1
1
0
0
1
2
1
1
1
1
1
2
1
0
0
0
1
1
1
2
1
3
1
1
1
1
1
1
1
2
1
0
2
1
1
1
1
2
2
1
1
1
1
2
1
2
1
1
2
1
0
1
1
1
1
1
1
1
2
1
2
2
1
1
0
0
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
0
1
2
2
1
1
0
1
1
1
1
1
2
1
1
1
1
2
2
0
1
1
1
1
3
2
2
1
2
1
2
2
1
2
1
1
2
2
0
1
1
1
1
1
2
1
1
1
2
1
1
1
1
0
1
2
1
1
1
2
1
0
0
1
1
1
0
1
2
1
0
1
1
1
1
1
2
2
1
1
2
1
0
1
1
2
1
2
0
1
1
1
1
1
1
2
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
0
2
1
2
1
1
1
2
2
1
2
2
1
1
1
2
2
0
1
2
1
0
1
2
1
1
2
0
1
1
2
1
1
1
0
1
1
1
2
1
1
2
1
2
1
1
0
2
1
2
1
2
1
1
1
1
1
1
1
2
0
1
0
1
2
1
2
2
1
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
1
1
1
2
0
2
1
2
2
1
1
1
1
1
1
0
1
1
0
1
2
1
1
0
1
1
1
1
1
0
1
2
0
2
1
2
1
0
1
1
2
1
1
1
1
1
3
2
2
1
1
1
0
3
1
1
2
2
0
1
1
2
2
2
2
1
2
1
1
1
0
0
1
1
1
0
1
5
2
1
2
1
1
2
0
0
1
1
0
0
1
1
2
1
1
1
1
1
1
2
2
2
2
2
1
2
1
1
2
0
1
0
1
2
2
1
1
1
1
1
2
1
1
1
1
2
2
0
0
1
1
2
1
1
2
1
1
0
1
1
1
2
0
1
0
1
1
1
1
1
1
1
3
1
0
1
1
1
2
1
1
1
1
1
1
0
1
1
1
2
2
1
1
1
0
1
1
1
1
1
1
0
1
2
1
2
1
1
1
1
2
1
1
1
1
2
1
2
0
1
1
1
1
1
1
2
1
2
1
2
2
0
1
1
2
2
1
0
0
1
1
1
2
2
1
1
0
1
1
1
1
2
3
1
1
1
2
2
1
2
1
2
1
0
2
2
0
2
2
1
0
1
1
1
2
2
1
2
1
2
2
1
2
0
2
2
1
2
2
2
2
1
1
0
1
1
1
2
1
1
2
1
1
5
1
2
0
3
1
1
1
1
1
1
1
1
1
0
1
1
1
0
1
2
1
1
0
1
3
1
0
1
1
1
1
0
2
1
1
0
1
1
1
2
2
1
1
1
1
1
1
1
1
1
0
1
2
1
0
1
1
1
2
1
1
0
0
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
0
1
1
2
2
2
2
1
2
1
0
2
1
2
1
2
1
2
1
1
1
2
1
1
2
0
2
2
1
1
1
2
0
1
1
1
1
2
2
1
1
1
1
1
0
0
2
1
1
2
1
2
0
1
1
1
1
2
1
2
1
5
1
1
0
1
2
1
1
1
0
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
0
1
2
0
1
1
2
1
1
0
1
1
2
2
1
1
1
0
0
1
1
2
1
1
1
1
1
2
2
1
0
1
1
1
1
1
2
1
0
0
1
1
2
1
0
2
1
2
2
0
1
2
1
1
1
2
1
2
1
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
1
1
0
2
0
0
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
0
0
1
1
0
2
2
1
1
1
1
1
1
1
1
2
1
2
1
1
0
2
1
0
3
1
1
0
2
1
1
1
2
1
2
3
1
1
1
2
1
0
1
1
1
1
2
1
2
1
2
1
2
1
1
2
0
1
1
1
1
1
1
1
0
1
2
2
1
1
2
1
2
1
0
2
1
0
1
2
1
1
1
2
2
2
2
2
0
1
0
2
1
2
2
0
1
2
2
2
1
1
1
2
0
1
1
1
1
1
0
1
1
1
0
1
2
2
2
1
0
2
1
1
0
2
1
1
1
1
1
0
1
1
1
1
1
2
1
1
3
1
1
1
0
1
1
0
1
1
1
2
1
2
1
1
2
1
0
1
1
1
1
2
1
1
1
0
2
1
0
1
1
1
1
1
2
1
1
1
1
1
0
1
1
1
1
1
1
1
1
2
1
1
2
1
1
2
2
1
1
2
1
1
2
1
1
1
0
2
1
2
1
0
1
2
1
2
0
1
2
1
1
1
0
1
1
0
0
1
1
1
1
2
2
1
1
1
1
1
1
1
0
2
0
1
1
1
0
1
1
2
1
1
1
3
0
2
2
2
1
1
0
2
1
1
1
1
0
2
1
1
1
1
1
1
1
1
2
1
1
1
0
3
1
1
1
2
1
0
1
2
1
1
1
0
1
1
2
2
3
2
1
2
1
1
1
1
1
0
1
1
1
1
0
1
1
3
1
0
2
1
0
0
2
0
1
0
2
0
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
2
2
2
1
2
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
2
1
2
2
1
1
2
1
1
1
2
2
2
2
1
1
1
1
1
1
2
2
1
1
1
1
0
1
1
1
2
2
1
2
2
2
2
2
1
1
2
1
2
1
1
1
1
1
1
1
2
1
2
1
0
1
1
1
1
1
1
1
1
0
2
1
3
1
1
0
1
1
1
1
0
1
0
0
1
1
1
1
2
2
1
2
2
2
1
2
1
1
1
2
1
1
1
1
1
1
1
2
0
1
1
1
1
2
1
1
3
2
2
1
1
1
1
2
1
1
0
1
1
2
2
1
1
0
1
2
1
2
1
1
2
1
1
1
1
1
0
0
2
1
2
2
2
1
1
2
0
1
2
1
2
2
1
1
0
1
0
0
2
1
1
1
1
0
2
1
2
1
1
2
1
1
1
2
1
2
0
1
1
2
2
0
1
1
2
1
0
1
1
2
2
2
1
1
1
1
1
3
2
1
1
0
1
2
2
1
2
1
1
2
1
1
2
1
0
1
1
1
0
1
3
1
2
1
1
1
2
1
1
1
2
1
1
3
1
2
1
1
1
0
1
2
1
1
1
1
2
1
1
2
1
2
0
2
2
2
1
1
1
2
1
0
2
1
1
1
1
2
0
1
2
1
2
1
0
1
1
1
1
2
2
0
1
2
1
1
1
1
2
2
1
1
2
1
1
0
2
2
0
1
2
1
1
1
1
2
1
1
1
1
0
1
1
1
1
1
1
1
1
0
0
1
1
1
1
2
0
1
1
1
0
1
0
1
1
1
2
2
1
1
2
2
1
1
1
1
1
1
1
1
1
1
0
2
2
0
1
1
2
1
1
1
2
1
0
0
1
0
1
1
1
1
1
2
1
1
1
1
2
1
0
0
2
1
2
1
0
1
0
0
2
1
1
1
1
1
0
1
0
1
1
0
2
1
1
1
1
2
1
0
2
2
1
0
1
1
1
1
2
1
1
1
1
1
1
2
0
2
2
1
1
1
2
0
1
2
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
1
0
1
0
1
1
0
1
1
3
2
2
1
2
0
0
1
1
1
0
2
1
2
1
1
2
1
1
2
0
2
2
1
1
1
1
1
2
2
0
1
1
1
1
1
2
2
2
0
0
1
1
0
1
1
1
1
0
1
2
1
0
1
1
2
0
1
0
1
4
2
0
1
1
1
2
1
0
1
1
1
1
1
1
0
2
2
0
1
3
1
1
1
2
2
1
0
1
1
0
1
1
0
1
1
1
1
2
0
2
3
2
0
2
1
2
1
2
1
1
2
0
3
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
0
0
1
2
1
0
2
1
1
1
1
1
1
1
1
1
2
1
2
1
2
2
0
2
0
2
1
1
2
1
1
2
1
0
1
1
0
1
1
1
1
1
1
0
2
1
1
1
0
2
0
1
2
1
1
1
1
1
2
2
1
0
2
1
2
2
0
0
1
2
2
0
1
0
1
2
0
1
2
2
1
1
1
2
1
1
1
1
2
1
1
1
1
1
0
2
1
1
2
1
2
0
1
1
2
2
0
1
0
1
1
0
0
1
1
2
1
1
1
1
0
0
2
2
1
1
2
2
1
0
1
1
2
1
1
1
2
1
0
1
1
2
2
1
2
0
2
1
0
1
1
1
2
2
1
2
2
1
1
2
1
1
1
2
2
1
2
1
1
0
1
2
1
1
1
2
2
0
1
2
1
1
1
1
1
2
2
1
1
2
1
0
0
1
2
1
2
1
1
2
1
2
1
1
1
1
0
1
0
1
1
1
1
0
2
2
0
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
2
2
2
1
1
1
1
2
2
1
0
1
0
1
1
1
2
1
1
1
1
1
1
2
2
1
2
1
1
1
0
0
1
0
1
1
1
0
1
2
1
2
1
1
1
1
2
1
2
1
2
1
0
1
1
1
1
1
1
3
1
2
1
1
1
1
0
0
0
1
1
1
1
1
1
2
1
2
1
1
1
2
1
2
0
1
1
1
2
1
1
1
2
1
0
1
0
2
1
0
2
2
1
0
3
0
1
1
1
0
0
1
1
2
2
1
1
0
1
1
0
0
1
1
2
0
2
1
2
1
1
2
1
1
2
1
3
1
0
0
0
2
1
1
0
2
1
1
1
0
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
0
2
1
1
1
1
0
1
1
0
1
0
1
1
2
2
0
2
0
0
0
1
1
1
1
1
2
1
1
2
2
1
1
1
2
1
0
1
1
1
1
2
2
1
1
1
2
1
1
0
3
1
0
1
2
0
1
2
1
1
2
1
2
1
0
2
2
1
2
1
1
2
1
1
0
2
0
1
2
1
1
1
1
2
1
1
2
1
2
2
1
1
2
1
0
1
1
1
0
2
0
2
2
2
1
0
0
1
2
1
1
1
1
1
0
1
1
1
2
1
1
1
1
1
1
1
1
0
1
1
1
2
2
1
2
1
1
1
2
1
2
1
1
1
0
1
1
1
0
1
1
1
2
1
1
1
0
1
1
1
1
1
1
1
1
0
1
3
1
2
1
0
1
1
1
2
0
1
1
1
1
0
3
1
1
1
1
1
2
2
2
1
1
2
1
1
1
0
2
0
0
0
2
2
0
1
1
0
0
1
1
1
2
0
1
1
0
1
1
1
1
2
1
1
1
0
1
1
1
2
1
1
2
1
0
2
2
0
1
0
1
1
1
1
0
1
2
2
2
0
0
0
0
1
1
1
2
1
3
1
0
1
1
1
1
2
2
1
2
2
2
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
0
1
2
2
2
0
1
2
2
1
1
1
1
1
0
1
1
5
1
1
1
1
2
0
2
1
2
1
1
1
0
0
1
1
1
1
2
1
1
1
2
1
1
1
2
1
1
2
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
0
2
0
1
1
1
2
1
0
2
1
2
1
2
2
1
1
1
1
2
1
2
0
2
0
2
2
0
2
1
1
0
1
2
1
1
1
1
1
1
2
0
1
1
2
2
0
1
0
1
1
1
0
1
1
1
1
1
0
1
2
2
1
2
0
1
1
2
0
1
0
1
1
1
2
0
3
1
0
2
2
2
2
1
1
1
0
1
0
0
2
2
1
2
1
1
1
1
1
2
0
0
0
2
1
1
2
1
2
1
1
2
1
1
0
1
0
2
1
1
1
1
0
2
2
2
1
0
2
2
0
0
1
1
1
1
1
0
1
1
1
0
1
1
0
0
2
2
1
1
1
3
1
1
0
2
1
1
2
1
2
0
2
2
2
2
1
1
1
2
0
0
1
2
2
0
0
1
2
2
1
1
1
2
1
0
2
1
2
1
1
1
1
1
1
2
1
1
0
1
2
1
2
1
1
3
1
2
1
0
0
2
2
1
1
1
2
1
1
1
1
0
1
1
1
1
1
2
1
1
1
1
0
1
2
1
0
1
1
0
2
1
2
0
2
1
1
0
2
2
1
1
1
1
1
2
1
1
1
1
0
1
0
1
0
2
2
1
2
1
1
1
1
2
1
0
2
1
0
1
1
1
2
1
2
1
0
2
1
1
1
1
1
0
0
1
1
1
1
0
1
1
0
1
1
1
2
1
1
2
2
1
1
2
2
0
1
2
0
0
2
1
1
1
1
0
2
1
1
1
1
1
2
1
2
1
2
1
1
0
1
1
2
1
0
1
1
1
2
0
2
2
0
1
0
1
1
1
0
0
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
0
0
1
1
2
1
2
1
0
1
1
0
1
1
1
1
1
1
1
1
2
2
1
2
1
1
1
1
2
1
1
1
2
2
2
1
1
1
2
0
2
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
0
1
2
2
2
2
1
1
2
0
1
1
2
2
1
1
2
1
1
0
1
2
1
2
1
2
2
1
1
0
1
1
2
1
2
1
1
2
0
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
2
1
2
1
0
1
1
2
2
2
1
2
0
1
1
1
1
1
1
1
1
2
2
1
1
1
2
1
1
1
1
1
2
2
1
1
1
1
1
2
2
1
1
1
1
0
1
1
2
1
1
1
1
2
2
1
1
1
1
1
2
2
2
0
1
1
1
1
1
1
2
2
1
2
0
1
1
2
2
1
1
2
1
1
1
0
1
1
1
1
1
1
1
1
2
4
0
2
1
1
1
2
0
1
1
1
0
0
1
1
1
0
1
1
1
1
2
1
1
1
1
1
1
2
0
0
1
1
1
1
2
1
2
2
2
1
1
1
1
1
2
1
1
0
1
2
1
2
1
2
1
2
2
1
1
1
0
2
1
2
1
1
2
1
2
1
2
1
1
1
1
1
1
0
1
2
1
1
1
1
1
1
0
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
2
1
1
0
1
1
1
1
1
3
2
1
1
1
0
2
2
2
2
2
1
3
1
1
2
1
1
1
1
0
1
0
1
1
0
1
1
1
1
1
1
0
0
1
1
1
2
1
2
2
1
0
0
1
2
2
1
1
1
1
0
0
1
1
2
1
3
1
1
1
0
1
0
1
1
2
2
2
1
1
2
0
1
2
1
2
0
1
1
1
1
2
1
0
2
1
0
1
1
1
1
1
2
2
1
1
1
1
2
1
1
1
2
0
1
1
0
0
2
1
2
0
0
1
2
1
1
2
1
1
0
2
2
1
1
1
0
1
1
1
0
0
1
1
1
1
1
1
3
1
1
0
0
1
2
1
0
2
1
2
1
1
1
1
2
1
0
1
1
1
0
1
2
2
1
1
0
1
0
2
0
2
1
2
1
2
1
2
2
2
1
1
2
0
1
1
1
1
1
1
1
1
0
1
2
2
0
1
1
1
1
2
0
1
1
6
2
1
1
2
1
1
0
1
1
1
2
2
1
2
0
1
1
1
1
1
0
1
2
1
1
1
0
1
0
2
1
1
1
0
1
1
1
1
2
2
1
2
1
1
0
1
1
2
1
1
0
2
1
2
1
1
1
1
1
0
1
1
1
0
1
1
1
2
2
0
2
1
2
2
2
2
2
1
1
2
2
2
1
2
1
2
1
2
0
2
2
1
2
1
2
1
2
1
1
1
1
0
1
1
1
2
1
1
3
1
1
1
0
1
3
1
0
2
2
2
0
1
1
0
3
1
1
1
1
1
0
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
0
0
0
0
2
2
1
1
2
1
1
0
2
1
1
2
1
2
1
1
2
1
1
1
1
0
1
1
1
1
1
2
0
1
0
1
1
0
2
0
1
1
1
1
1
2
1
1
0
0
0
1
1
1
2
2
2
1
1
2
2
1
1
1
0
1
1
0
2
0
2
1
2
2
2
1
2
2
1
0
1
2
1
0
0
2
1
1
0
1
1
1
1
1
0
2
2
1
1
1
1
2
0
1
0
1
0
2
2
1
1
1
2
1
2
2
1
1
2
1
1
1
1
2
1
1
1
1
1
0
2
1
2
1
1
2
1
1
2
2
2
2
1
2
0
2
1
1
2
1
2
0
0
1
2
0
1
0
1
1
2
2
2
2
1
1
1
1
1
1
1
0
1
1
0
0
1
1
1
2
1
1
1
2
3
1
1
1
1
0
2
1
2
1
2
1
1
1
1
2
1
2
2
1
1
0
2
1
1
1
0
0
1
2
2
0
1
1
1
1
1
1
2
1
1
1
1
0
2
1
2
1
1
1
1
1
1
0
0
2
2
0
1
2
0
2
2
1
1
1
1
0
0
1
1
1
1
1
1
1
2
2
2
0
1
2
1
1
2
1
1
2
2
1
1
2
1
1
0
1
1
1
1
1
2
1
1
1
0
1
1
1
1
0
2
1
1
0
1
1
1
2
1
1
1
2
2
1
2
1
1
1
1
1
3
2
0
0
2
0
1
2
3
2
2
1
1
1
2
2
1
1
1
1
2
1
1
2
1
3
0
5
0
1
1
1
1
1
1
1
2
1
2
1
1
0
1
1
0
1
3
1
1
0
1
2
1
1
2
1
2
2
1
2
1
0
0
2
1
0
0
1
0
1
1
2
1
0
1
1
1
0
2
1
1
1
1
2
2
1
1
2
0
0
1
1
1
1
1
2
1
0
1
1
1
2
1
0
2
2
1
1
1
1
0
2
2
0
0
1
1
1
1
1
0
2
1
2
1
1
1
1
1
1
1
1
1
2
1
2
1
2
1
1
1
2
0
1
1
0
1
2
1
1
1
2
2
1
1
1
0
0
0
1
1
1
1
1
1
2
0
1
1
2
2
0
2
0
2
1
0
0
2
1
1
1
2
0
0
1
1
2
2
0
2
0
2
2
0
1
1
1
1
1
0
1
1
0
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
1
1
0
2
2
1
1
1
1
1
1
1
0
2
2
1
1
1
1
1
0
1
2
0
1
1
0
1
0
1
1
1
2
1
1
1
1
1
0
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
2
1
1
1
2
2
2
1
1
0
1
1
1
0
1
3
1
1
1
0
1
1
2
2
2
1
0
0
0
2
0
0
1
1
2
1
0
0
1
1
1
2
2
1
0
2
1
0
1
1
1
1
0
1
1
1
1
1
1
0
2
1
2
1
1
0
2
2
0
1
1
1
1
1
1
1
1
0
1
1
1
1
0
1
0
0
1
1
1
0
1
1
1
1
2
1
2
1
0
1
1
0
0
1
0
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
2
0
1
2
1
0
1
0
1
2
2
2
1
1
0
2
1
1
1
1
1
1
2
1
1
1
2
2
2
1
1
1
2
1
2
1
1
1
0
2
0
1
1
1
2
1
1
1
1
0
1
2
0
1
1
1
1
1
2
0
1
2
1
1
2
1
1
2
0
1
1
0
1
1
1
1
2
2
1
0
1
1
1
2
1
0
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
0
1
1
0
1
1
0
1
1
1
2
3
2
0
1
1
1
2
1
2
2
1
0
2
1
2
0
2
1
2
1
1
0
2
2
0
1
0
2
2
1
1
1
1
0
1
1
0
1
1
2
1
1
1
1
2
1
1
1
2
2
1
2
1
1
1
0
2
2
1
1
1
1
2
0
1
1
1
2
2
2
0
1
1
1
2
1
0
2
2
1
0
1
2
2
1
1
1
2
2
1
1
1
1
1
1
0
1
0
1
2
0
1
2
1
2
1
1
1
0
2
1
1
2
1
2
2
1
1
1
1
0
2
1
1
1
0
1
0
1
1
1
1
0
0
1
2
2
1
1
0
2
1
1
1
1
2
1
0
1
1
0
1
1
1
1
1
2
1
1
1
1
2
2
0
1
2
1
0
1
1
1
1
1
2
2
1
2
1
0
1
1
1
2
0
1
2
0
2
1
0
1
1
1
2
2
1
2
1
2
2
2
1
0
1
1
1
0
2
1
1
1
2
1
1
1
1
2
1
2
1
1
1
2
1
2
2
1
2
2
1
2
1
1
1
1
0
1
0
1
3
1
2
1
1
1
1
2
1
2
2
1
2
2
1
2
0
1
1
0
1
1
1
0
0
2
1
1
1
1
1
1
0
1
1
1
0
1
1
1
1
2
1
2
1
2
1
2
2
1
2
1
1
1
2
2
2
2
2
0
1
1
2
1
1
2
1
2
1
0
1
1
1
1
1
0
1
0
1
1
1
1
1
0
1
1
1
1
1
1
2
2
2
0
1
1
1
1
1
0
1
2
1
1
2
2
2
1
2
0
0
2
1
1
1
0
1
2
0
2
1
2
2
0
1
1
1
1
2
0
1
1
1
2
1
1
1
1
1
0
1
1
1
1
0
1
1
2
1
1
1
2
1
2
1
1
1
0
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
0
1
1
1
2
1
1
1
0
1
2
2
1
1
0
0
1
1
2
0
1
1
1
1
2
1
1
1
2
2
1
1
0
1
2
0
1
1
1
1
1
1
2
1
1
1
0
2
1
1
1
1
0
1
1
1
0
1
1
2
1
2
0
0
1
1
2
1
1
0
1
1
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
0
1
2
0
2
2
2
2
1
0
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
2
1
1
1
1
2
1
0
1
0
2
1
2
1
1
0
1
1
2
1
2
1
1
1
2
1
1
0
1
1
2
2
0
0
2
1
2
1
2
1
2
2
0
0
2
1
2
1
1
1
1
0
2
2
1
0
2
1
0
0
1
2
1
1
1
2
1
1
1
2
2
2
0
1
1
1
1
2
1
1
1
1
0
1
1
0
0
1
1
0
2
2
1
1
2
1
2
1
1
2
2
1
2
1
1
0
1
1
1
2
2
0
1
2
1
0
2
0
0
1
2
1
1
2
0
2
1
1
1
1
2
1
2
2
1
1
0
1
1
1
2
1
1
1
2
2
1
1
1
1
0
2
1
0
1
1
2
1
1
2
2
1
1
2
1
2
1
0
1
2
2
1
1
1
2
1
2
1
2
2
1
1
2
1
1
1
2
1
2
2
1
1
2
2
2
1
1
2
1
1
2
1
1
0
1
2
0
0
0
1
1
1
1
2
1
1
1
1
0
1
1
1
2
1
1
1
1
2
1
1
1
0
2
2
1
1
0
1
0
1
0
2
1
1
2
1
1
0
2
1
0
2
1
1
1
1
0
2
2
2
1
2
2
2
1
2
0
1
1
1
1
2
1
1
1
1
3
1
2
1
1
2
1
1
2
1
1
1
0
1
1
1
0
1
1
1
1
3
1
1
2
1
0
2
0
2
0
1
2
2
1
1
1
1
1
2
1
1
1
1
1
2
0
0
0
1
1
1
1
1
0
1
1
0
2
1
1
2
1
1
2
2
1
1
1
1
2
2
1
2
1
1
0
1
1
1
2
1
1
1
1
1
1
1
0
1
1
1
0
1
2
1
0
1
0
1
1
0
1
2
1
1
1
2
1
1
2
1
1
0
1
3
1
1
1
0
2
1
2
1
1
1
2
1
2
1
3
0
0
1
1
1
2
1
2
1
1
1
2
1
1
1
1
0
1
0
2
0
2
2
0
1
1
1
1
1
2
1
2
1
0
1
2
1
0
1
0
1
1
1
1
1
1
0
1
2
1
1
2
2
2
1
3
1
1
1
1
1
1
1
2
1
0
1
1
1
2
1
1
2
0
1
1
2
0
1
1
1
3
2
1
1
1
1
1
1
1
2
1
1
1
1
2
1
0
1
0
0
1
1
1
1
0
2
1
1
0
2
2
1
2
1
0
2
2
1
0
1
1
1
1
0
1
0
1
3
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
0
2
1
2
0
1
2
2
0
1
1
2
1
1
2
1
1
0
1
1
1
1
1
2
1
1
1
0
2
1
0
1
1
1
1
2
0
0
2
1
1
1
1
1
1
0
1
0
2
2
2
2
2
1
1
1
1
1
0
0
2
1
1
2
1
0
1
1
1
0
1
2
0
0
1
1
0
1
2
2
0
1
2
1
0
0
1
0
1
2
2
0
1
1
2
2
1
2
1
0
1
1
0
1
2
2
2
2
1
2
1
2
1
0
2
1
2
0
2
1
2
2
1
0
1
1
1
2
1
1
1
2
1
0
1
1
2
2
1
1
2
2
1
1
1
1
1
1
1
0
1
0
1
1
2
1
2
2
0
1
1
1
1
2
2
2
1
1
2
3
1
2
2
2
1
1
1
1
0
1
1
1
1
0
2
1
1
2
1
1
1
0
1
2
0
1
1
2
2
2
3
0
0
2
1
3
1
1
1
1
1
0
2
1
2
1
1
0
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
0
1
1
2
2
1
2
1
2
1
1
1
1
2
1
1
2
1
2
2
1
1
2
1
1
1
2
0
1
1
2
1
1
1
1
1
2
0
2
1
1
2
1
1
1
1
2
2
0
1
2
1
1
2
1
0
1
1
1
2
2
0
1
1
2
1
2
1
1
1
1
2
1
2
2
2
1
2
1
1
1
1
1
2
1
2
1
1
1
0
1
1
0
1
1
1
0
1
1
2
1
1
1
1
1
1
0
1
1
1
2
1
2
1
2
0
0
0
0
1
1
1
1
0
2
1
1
1
2
2
1
1
2
1
1
2
2
2
1
1
1
1
1
0
1
1
2
1
2
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
0
0
1
1
2
0
0
1
1
1
1
2
2
1
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
0
1
2
1
1
2
1
1
2
1
0
2
1
1
2
0
1
2
2
1
1
1
1
1
2
1
1
0
1
1
1
1
2
1
1
1
1
1
1
2
0
1
1
1
1
2
2
0
2
1
1
1
1
2
0
1
1
1
0
2
0
0
2
2
2
2
0
0
0
2
1
2
1
0
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
0
0
1
1
2
0
1
1
1
1
0
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
2
1
2
0
1
1
1
2
1
1
0
2
1
0
1
2
1
2
1
1
1
0
2
1
2
1
1
1
1
1
0
1
1
1
2
2
2
0
2
1
2
1
2
1
1
0
1
2
1
1
1
1
1
0
2
2
1
2
0
1
2
1
1
1
1
1
1
1
1
1
2
1
2
2
0
1
1
1
2
1
2
2
2
1
2
1
1
1
1
0
2
1
2
1
1
1
1
2
0
1
2
2
1
0
0
0
1
1
2
0
1
2
1
1
1
1
2
1
1
1
1
2
1
1
2
1
2
0
2
1
1
0
2
1
1
1
2
2
1
1
3
1
1
2
1
1
1
1
1
0
2
1
2
2
1
1
1
1
1
2
1
0
1
2
1
1
1
2
1
1
1
2
3
1
0
0
0
0
1
2
1
1
1
2
1
0
1
1
1
1
1
1
1
1
1
1
2
2
2
2
3
2
1
1
1
0
1
2
1
1
2
2
1
1
1
2
1
2
1
2
2
2
1
1
0
1
1
1
1
1
1
1
0
1
2
0
1
2
1
1
1
1
3
2
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
0
1
1
1
1
0
0
1
1
0
2
1
1
0
0
1
2
1
0
2
1
1
1
1
1
0
1
1
1
1
0
2
0
2
2
1
0
1
1
0
0
1
1
2
1
1
0
3
1
1
2
2
1
2
1
0
1
1
2
1
1
1
1
1
1
1
1
1
1
0
1
0
1
2
1
0
1
1
1
1
1
1
1
1
0
1
1
2
1
1
1
0
1
1
1
2
1
0
2
1
1
1
1
0
1
1
1
1
1
1
1
1
1
0
2
2
1
1
2
1
0
2
1
1
0
1
1
1
1
1
1
2
2
2
1
1
1
1
1
2
1
0
2
2
1
0
2
1
1
1
2
2
2
1
2
0
2
2
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
2
2
0
1
0
1
1
2
1
1
1
0
1
1
1
2
1
1
1
2
2
0
1
0
0
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
0
1
2
1
1
0
0
0
1
1
1
2
1
1
0
1
2
1
0
1
2
1
2
1
1
1
0
1
1
0
1
1
1
2
2
0
1
1
0
0
0
2
1
1
1
1
1
1
0
0
0
0
0
1
1
1
1
0
2
1
1
2
2
1
1
0
2
1
1
1
1
3
1
1
1
2
0
1
1
1
1
1
0
1
1
1
1
0
1
2
2
1
0
1
1
1
1
1
1
2
1
2
3
1
2
1
1
1
1
1
1
1
1
0
3
0
0
0
2
1
1
1
1
1
0
2
1
1
1
1
1
1
2
1
1
1
0
1
0
0
2
0
1
2
2
2
2
0
0
2
1
1
1
0
1
1
2
1
1
1
1
0
1
2
0
1
1
2
0
1
0
2
1
1
0
1
2
1
1
1
1
1
1
1
1
1
0
2
1
1
1
1
0
1
1
2
1
0
1
2
1
1
1
1
0
2
0
2
1
2
2
2
1
1
1
1
1
1
1
1
1
2
1
1
0
2
1
1
2
1
2
1
0
2
1
1
2
1
1
0
1
0
1
0
1
1
3
1
1
0
1
1
1
0
0
1
1
1
0
0
1
2
2
1
2
1
2
1
1
0
2
1
1
1
1
2
2
0
1
2
1
1
2
1
2
1
1
2
1
1
1
2
0
2
2
1
0
1
1
1
1
0
1
1
1
2
1
1
2
1
0
1
1
2
1
1
1
1
1
1
1
2
1
2
1
4
1
1
2
1
1
2
1
2
2
0
1
2
1
0
1
2
0
1
2
0
1
0
1
1
2
1
1
1
2
2
2
1
2
1
1
1
2
2
1
2
0
1
1
1
2
1
2
0
1
1
2
1
1
1
1
0
1
1
2
1
1
2
0
1
1
0
2
2
2
2
1
2
0
1
1
2
0
1
1
1
2
1
1
2
1
2
1
1
1
1
2
2
1
0
2
1
2
1
1
2
0
0
2
3
1
1
1
1
0
0
1
1
1
1
1
1
1
3
0
2
1
1
1
1
1
1
2
0
2
1
1
0
1
1
1
1
2
2
1
2
1
2
1
0
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
2
0
1
1
2
1
0
0
2
2
2
1
1
0
2
1
1
1
0
2
2
2
1
1
1
1
2
1
2
1
2
1
1
2
1
1
0
1
1
1
0
1
1
1
1
1
1
2
1
0
1
1
0
1
1
1
2
2
2
1
2
2
0
1
2
1
1
1
2
1
4
1
1
1
1
1
1
1
1
0
1
1
1
1
2
2
1
1
2
2
1
1
1
0
1
0
1
1
1
2
1
2
2
2
1
1
1
0
0
1
1
2
1
1
1
1
2
2
0
0
1
1
2
1
0
1
1
1
2
1
2
1
1
1
1
0
2
1
2
0
1
0
1
1
1
1
1
1
2
2
1
1
1
2
1
1
1
1
1
0
2
0
2
1
1
2
1
1
1
1
2
2
1
2
0
1
1
1
1
0
0
0
1
1
1
1
1
1
1
1
1
2
1
2
1
1
0
1
0
1
1
0
1
1
1
0
1
1
1
1
1
2
1
1
0
2
2
1
2
2
1
1
2
1
0
1
2
1
1
1
2
1
1
1
2
1
0
2
0
0
2
1
1
0
1
2
1
1
1
1
1
2
1
1
1
0
2
1
1
2
1
1
1
1
1
1
1
2
2
1
1
1
2
2
1
1
2
2
2
3
2
3
1
2
1
1
1
1
2
1
1
1
1
1
2
1
1
2
1
2
1
1
0
1
0
2
1
1
1
1
1
1
0
1
2
2
1
1
1
1
0
1
1
1
0
0
1
2
2
1
1
1
1
1
1
1
1
1
2
0
1
1
1
1
1
0
1
1
2
1
1
1
1
0
1
1
1
0
2
1
2
2
2
0
2
1
1
1
1
1
1
1
2
2
1
1
3
0
1
2
1
0
1
1
2
2
1
1
2
1
2
3
1
1
2
1
0
1
2
1
0
1
1
1
1
2
1
1
0
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
2
2
1
1
1
0
2
1
1
2
1
1
2
0
0
1
1
1
1
0
0
1
1
1
1
1
2
1
2
1
1
1
0
2
1
1
1
1
2
1
1
0
1
1
2
2
1
1
1
1
2
2
1
0
0
1
0
1
2
0
1
0
1
1
1
1
0
1
2
1
2
1
1
1
2
2
1
1
1
0
0
1
1
1
1
2
1
2
0
1
1
1
0
2
2
2
1
1
2
1
1
1
0
1
1
1
1
0
1
1
1
1
1
1
1
1
1
2
2
2
1
0
2
0
2
1
1
2
1
1
1
1
1
2
2
1
1
1
2
1
1
1
1
1
2
2
0
2
2
1
1
1
1
2
1
1
2
1
1
2
0
2
2
1
2
1
1
1
2
1
2
1
0
2
1
1
1
2
2
0
1
1
1
3
1
1
1
1
1
1
1
1
1
2
1
1
2
0
1
2
1
2
1
1
1
1
1
2
1
0
1
2
1
1
2
1
0
1
2
1
1
2
1
1
1
1
1
0
1
1
0
1
1
2
1
1
1
1
1
2
2
1
1
0
1
1
1
1
2
1
0
2
0
1
2
2
2
0
2
2
1
1
2
1
2
1
1
1
1
1
2
0
0
1
2
2
1
2
2
1
3
2
1
1
1
2
2
1
1
2
1
1
1
2
0
1
1
2
1
1
1
2
1
1
1
1
1
1
0
1
0
0
1
1
1
1
1
1
2
0
2
1
2
0
1
2
2
1
0
1
2
1
0
0
0
1
2
1
1
2
0
2
1
2
1
0
1
1
1
2
1
1
1
1
1
1
0
2
1
2
1
1
2
2
1
1
1
2
0
1
0
1
1
3
2
2
2
2
2
1
2
2
1
1
0
1
1
2
1
1
0
0
1
2
1
1
1
1
1
1
2
0
1
1
2
1
2
2
2
1
1
2
0
0
1
1
1
1
1
1
1
0
1
1
2
2
2
2
1
1
1
1
1
2
1
1
0
2
1
1
2
1
0
2
1
1
1
1
1
1
1
1
2
1
1
1
1
0
1
1
0
2
0
1
2
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
0
1
1
1
1
3
2
2
0
2
1
0
1
1
1
1
1
1
1
1
0
2
1
2
1
1
2
1
1
1
1
0
1
1
1
1
2
1
1
0
2
1
2
2
1
2
2
1
1
1
2
1
1
1
1
1
1
2
1
1
2
1
0
2
1
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
2
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
0
2
1
1
1
1
1
2
1
1
2
1
2
1
0
2
1
2
1
2
1
2
1
1
2
2
0
2
0
2
2
0
3
2
0
2
0
2
1
2
2
1
1
2
2
1
0
1
1
1
1
1
1
1
1
1
2
2
1
2
1
0
2
1
1
2
0
1
1
1
0
1
2
1
1
2
1
1
1
1
1
1
2
2
2
1
2
1
2
0
2
1
2
1
2
1
2
1
1
1
1
1
2
1
2
1
2
1
1
2
1
0
1
0
1
1
2
1
2
1
2
1
1
1
1
0
2
1
1
1
1
2
1
0
1
1
1
0
1
3
0
1
0
1
1
1
2
1
2
1
1
1
2
2
2
1
0
1
1
1
1
1
0
0
0
1
2
2
1
1
0
0
1
1
2
1
1
0
0
1
1
2
1
1
1
1
1
2
2
1
0
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
0
2
1
1
1
2
0
1
1
2
1
1
1
2
2
1
0
2
1
0
0
1
0
2
2
2
2
2
2
2
1
1
0
0
1
2
1
1
2
0
2
0
0
1
1
1
1
1
1
2
1
2
2
1
1
1
2
1
3
0
2
1
2
0
0
1
2
1
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
0
2
1
2
1
0
0
2
1
0
0
1
1
1
2
1
1
1
3
2
2
2
1
0
1
2
1
1
0
2
1
2
1
5
0
2
1
1
0
2
1
1
1
1
1
1
0
2
1
1
2
0
2
0
1
1
1
1
6
1
1
1
0
1
1
0
1
1
1
1
0
1
1
1
1
1
0
1
2
1
2
1
0
1
2
1
1
1
0
0
1
1
1
1
2
1
1
0
2
1
2
1
1
1
2
1
2
0
1
0
2
1
1
1
1
0
1
3
1
1
2
0
0
1
1
1
2
0
1
0
1
1
0
1
2
1
1
2
1
0
2
1
1
2
1
1
1
2
1
1
1
2
0
1
1
1
1
1
1
1
0
1
1
1
2
2
1
1
1
1
1
0
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
0
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
0
1
2
0
1
11
1
2
2
1
1
0
1
0
1
0
1
1
1
2
2
2
2
1
2
1
1
1
0
1
1
0
1
0
4
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
1
2
2
1
1
0
2
0
0
2
2
1
1
2
1
1
0
1
1
2
1
0
2
2
1
2
2
2
1
1
2
1
0
1
3
3
0
1
1
1
2
2
1
1
1
2
2
1
2
1
1
0
2
2
1
1
1
1
1
2
2
2
2
2
1
1
0
2
1
1
2
1
1
1
1
1
2
1
1
0
2
2
1
1
1
1
1
1
1
2
2
1
1
1
2
2
1
2
2
1
0
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
0
2
1
2
1
1
2
1
1
1
0
1
1
0
2
1
2
1
0
2
1
0
1
1
1
1
2
2
1
1
1
1
1
1
0
1
2
1
1
1
2
1
2
2
0
1
1
2
0
1
1
0
0
0
2
1
2
1
0
0
2
2
1
1
0
1
0
2
1
1
1
1
1
0
2
0
2
1
2
1
1
2
0
1
2
2
2
1
1
2
1
2
1
0
1
1
2
2
1
0
1
0
1
1
1
0
1
2
0
1
1
0
1
2
2
1
1
2
1
1
1
1
2
0
0
1
1
1
1
2
1
1
1
1
1
1
2
1
2
2
2
2
1
1
0
1
2
1
1
2
1
1
1
1
1
0
2
1
1
2
0
2
1
1
0
1
1
1
2
0
2
2
1
1
1
1
1
1
1
1
1
1
0
2
2
1
2
1
0
1
2
1
1
2
1
0
1
1
1
1
1
1
4
1
2
1
1
0
1
2
0
1
1
1
2
1
1
1
1
1
1
4
2
1
2
2
1
1
2
2
1
1
1
0
2
2
0
1
2
2
1
1
1
1
1
2
1
0
0
1
2
2
1
2
2
1
0
1
1
0
1
1
1
0
1
1
1
0
0
0
1
1
1
0
1
2
1
1
1
1
2
0
1
0
2
0
1
2
1
0
1
1
1
1
0
1
2
2
1
1
1
1
1
2
2
1
0
2
0
0
2
1
0
2
2
1
0
1
1
2
0
2
1
2
1
1
1
1
1
1
2
1
2
1
1
1
2
0
2
1
1
0
2
0
1
2
1
1
0
2
1
2
0
1
1
1
2
1
1
1
0
1
1
0
1
1
1
2
2
2
2
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
2
1
2
1
1
2
1
2
1
2
1
2
2
1
0
1
2
2
0
1
1
2
1
1
1
0
1
1
2
2
0
2
2
1
1
2
2
2
0
1
2
2
2
1
2
1
0
0
1
1
1
1
1
1
2
1
2
1
2
1
0
1
1
0
1
1
2
1
1
1
1
0
1
1
2
0
2
1
1
1
1
0
0
1
1
2
0
1
1
0
1
2
1
1
2
1
2
2
1
1
1
1
1
1
1
1
2
1
1
1
1
2
2
2
1
2
1
2
1
1
2
1
2
1
1
1
1
2
1
1
2
0
0
1
2
1
2
1
2
1
1
2
1
2
1
2
1
1
2
1
1
1
1
1
1
1
0
2
2
2
1
1
2
1
2
1
1
1
1
1
2
2
1
1
2
0
4
2
1
2
1
2
1
1
1
0
2
1
0
2
1
0
2
2
1
2
1
0
2
1
1
1
1
2
1
0
0
1
1
2
1
2
1
1
1
1
2
0
1
1
1
1
1
1
1
1
1
2
1
1
1
1
0
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
2
2
0
2
1
2
1
2
2
1
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
2
2
1
1
1
1
0
1
2
1
1
0
1
0
1
1
1
1
1
2
1
1
2
1
1
2
2
1
1
1
0
2
1
1
1
1
1
0
1
0
1
0
0
0
1
0
1
1
1
1
2
1
0
2
1
1
1
1
0
2
2
1
1
2
0
1
2
1
1
1
1
1
0
1
1
1
1
1
0
1
1
0
2
0
1
1
0
1
1
0
1
2
1
1
0
1
1
1
1
1
4
1
1
1
2
2
2
0
1
1
1
1
1
1
0
2
2
1
1
1
1
1
0
2
0
0
2
1
1
1
1
3
3
2
1
2
2
1
1
1
0
1
1
2
2
1
1
1
1
1
2
2
1
2
0
1
2
1
1
1
1
0
1
1
2
1
1
1
2
1
1
0
2
2
1
2
0
2
1
2
2
2
1
1
1
2
1
1
1
0
1
2
1
1
0
1
1
1
0
0
1
1
1
2
1
1
2
1
1
1
1
1
1
1
2
2
0
0
1
2
1
1
2
2
1
1
1
0
2
2
1
2
1
1
0
2
2
1
1
1
0
1
0
2
2
0
2
0
2
0
1
1
1
0
1
1
1
0
1
1
0
1
1
1
1
1
2
1
0
1
1
2
1
1
2
2
1
2
1
1
1
1
1
2
1
2
2
2
2
2
1
1
1
1
2
1
1
2
2
1
1
0
2
1
1
0
1
0
1
0
1
2
2
0
1
2
2
1
2
1
2
0
2
1
2
2
2
1
1
2
0
1
2
0
1
1
0
1
1
2
2
1
1
1
1
0
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
0
2
1
2
1
1
1
2
2
1
1
1
0
1
2
2
1
1
0
1
0
1
0
0
1
1
0
0
2
1
2
1
1
0
1
1
1
2
2
1
0
2
1
1
1
3
2
0
0
1
0
1
1
2
1
2
2
1
1
1
1
2
1
2
2
1
1
0
1
1
1
1
2
0
1
1
1
2
2
1
2
1
2
1
2
1
1
0
0
0
2
0
1
1
2
1
1
0
1
1
0
1
2
1
2
1
2
2
2
0
1
2
2
1
1
1
2
1
2
1
1
2
1
1
1
2
2
1
1
1
2
0
2
1
2
0
1
2
1
2
2
0
1
1
0
2
1
1
1
2
1
1
1
1
1
1
0
1
1
2
1
1
2
1
1
1
1
1
1
0
2
1
2
1
2
2
1
2
1
1
1
2
0
0
2
1
1
1
1
1
2
1
0
2
2
0
0
1
2
1
1
2
1
1
2
0
1
1
3
0
2
0
2
0
1
1
1
0
2
1
1
0
1
1
1
2
1
1
1
1
2
1
0
1
1
1
2
1
1
1
1
1
1
2
2
2
1
1
1
2
2
2
1
2
1
0
1
1
1
2
1
1
2
0
1
1
1
1
1
1
1
1
1
2
1
1
0
1
2
2
2
1
2
0
1
2
1
1
0
1
1
2
1
1
1
0
1
0
2
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
0
1
1
1
1
1
1
0
1
0
1
1
0
1
0
2
1
2
1
1
1
1
1
1
1
3
0
0
2
1
1
1
1
1
0
1
2
0
1
1
1
1
1
1
2
2
1
0
0
1
1
2
0
0
1
1
1
0
1
2
1
2
2
1
2
1
1
2
2
1
1
2
3
2
1
1
2
0
1
1
1
1
0
0
2
1
0
1
1
2
2
4
1
2
1
2
0
1
0
1
2
0
0
1
2
1
1
1
1
0
1
1
0
1
1
0
1
0
1
1
1
1
1
2
1
1
1
2
1
1
1
0
1
1
1
1
1
1
1
1
1
2
2
2
1
1
2
2
2
2
0
1
2
0
1
1
2
1
3
1
0
0
1
0
0
0
1
1
1
1
1
2
2
1
1
1
1
1
1
1
0
2
1
1
1
1
1
1
1
1
2
1
1
2
2
1
1
0
0
0
1
1
1
1
0
1
0
0
1
1
1
1
0
1
1
0
1
1
1
1
1
2
1
2
1
1
0
0
1
1
1
1
1
1
1
1
2
1
2
2
1
2
1
1
0
2
0
1
2
2
1
2
1
2
2
1
2
0
1
2
2
1
1
0
1
1
1
1
1
2
0
1
1
2
1
1
1
2
1
1
1
2
1
1
0
1
1
2
1
1
0
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
0
2
0
2
1
2
2
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
0
1
1
2
0
2
1
0
1
0
2
1
1
1
1
1
1
0
1
1
1
1
1
2
1
2
1
2
1
1
2
2
1
1
1
0
1
2
1
1
1
2
1
1
1
2
2
2
1
1
1
0
1
1
1
1
0
2
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
2
1
1
1
0
0
1
1
2
0
2
0
1
2
2
1
2
2
0
1
3
0
1
1
1
1
2
1
1
2
1
1
2
0
1
1
2
2
2
1
1
1
1
1
2
1
2
2
1
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
0
0
2
1
2
1
2
1
1
2
0
1
1
1
1
1
2
1
1
1
1
0
1
2
2
1
1
2
1
1
2
2
1
1
3
1
1
1
1
2
1
1
1
1
1
1
1
1
0
1
1
1
2
2
1
2
1
2
2
1
1
1
2
1
1
2
1
1
1
2
1
3
2
1
1
2
1
1
1
2
0
2
2
1
1
2
1
0
2
1
1
1
1
1
1
2
1
1
1
1
1
0
0
1
1
2
1
1
2
2
1
1
1
2
1
1
0
2
1
1
1
1
1
0
1
1
1
2
1
2
2
1
0
1
1
1
2
1
2
2
1
1
2
0
1
2
1
1
1
1
2
1
1
1
0
1
1
2
0
2
1
1
2
1
0
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
2
0
0
2
2
2
2
1
1
0
2
1
2
1
1
1
2
2
1
1
1
1
1
1
2
1
1
2
1
1
1
1
0
1
1
1
1
0
2
1
2
1
1
0
2
1
1
1
2
1
0
2
0
1
0
0
1
1
1
2
1
1
0
1
2
1
1
0
2
1
1
2
2
2
1
2
1
1
1
1
2
0
0
1
2
2
1
2
1
2
2
1
1
1
1
1
1
1
1
2
0
2
1
1
2
1
2
2
0
2
2
1
1
1
1
1
1
0
2
2
1
0
2
1
1
1
1
0
1
0
1
1
1
2
1
0
1
1
1
2
1
0
1
0
2
1
0
2
1
2
2
1
1
1
2
2
1
1
1
1
1
1
1
0
1
0
0
1
2
1
1
1
0
1
2
2
3
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
0
2
1
1
1
1
1
1
1
0
2
1
0
2
2
1
2
1
2
1
1
1
0
1
1
2
2
0
0
1
1
1
1
2
2
2
1
1
1
1
2
1
1
2
1
0
1
2
1
0
0
1
2
1
0
1
1
2
0
1
1
1
2
1
1
1
1
1
2
0
1
1
1
0
1
3
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
0
1
2
1
1
2
1
1
1
1
2
0
1
0
2
1
1
1
1
1
1
0
2
0
1
0
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
0
2
0
1
1
1
1
1
1
1
1
1
0
1
1
0
0
1
1
2
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
2
1
1
2
2
0
2
1
1
0
2
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
0
1
1
0
0
1
2
1
0
1
2
1
1
1
1
0
1
2
1
1
1
2
1
0
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
0
0
1
1
2
0
0
1
2
1
1
1
1
2
1
1
1
1
0
1
0
2
1
1
1
0
1
1
1
1
1
0
1
1
1
2
2
0
0
1
1
0
1
1
1
1
1
1
1
1
2
1
1
1
0
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
0
1
1
1
0
1
0
0
0
1
1
0
0
1
3
1
1
1
1
0
1
1
1
1
1
1
0
0
1
1
2
1
0
1
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
0
0
1
1
1
1
0
1
1
1
2
1
1
2
1
0
0
0
0
1
2
2
0
1
2
1
1
1
0
1
1
0
2
2
1
2
2
0
1
1
2
2
1
2
1
1
2
1
2
2
1
1
2
1
2
1
2
1
0
1
1
1
1
1
2
1
1
1
1
2
0
1
1
1
1
2
1
2
1
1
2
1
1
2
1
0
0
2
2
2
1
1
2
0
1
0
1
2
1
0
1
2
1
0
1
1
1
2
1
1
1
1
2
2
1
2
1
1
2
0
1
1
1
0
1
2
1
2
1
2
1
0
1
2
1
1
1
1
1
2
2
1
0
2
0
2
2
1
1
1
2
0
1
1
1
1
2
1
1
1
0
1
1
2
2
1
2
2
1
1
0
1
2
1
1
2
0
1
0
0
1
2
0
0
2
2
0
1
1
1
0
1
1
0
1
1
1
0
1
2
1
1
1
1
1
1
1
2
1
2
0
2
1
1
1
2
0
1
2
1
1
2
2
2
1
0
2
1
1
1
1
1
2
2
1
1
0
1
0
1
0
2
1
2
0
1
1
1
1
2
1
1
0
1
1
1
1
1
1
2
1
1
1
0
2
1
1
1
1
1
1
2
2
1
2
1
2
1
1
1
1
2
1
1
1
2
2
0
0
1
2
1
1
2
1
1
2
2
1
2
1
1
2
0
2
0
1
0
0
1
0
1
0
0
1
1
1
1
2
1
0
2
1
2
0
1
1
1
0
1
1
3
1
1
1
1
2
1
1
1
1
2
0
2
2
1
0
2
1
1
0
2
1
0
2
1
2
0
0
2
1
2
1
2
1
1
0
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
0
1
2
1
2
1
1
1
1
1
2
2
2
1
0
1
2
1
1
0
1
1
1
1
1
2
0
1
2
2
1
2
2
1
1
2
1
1
2
2
1
1
0
2
2
0
1
2
1
0
0
1
2
1
2
1
2
1
1
1
1
3
0
1
2
2
1
1
1
1
0
2
1
2
0
1
1
2
1
2
1
1
2
2
1
1
1
1
1
1
1
1
2
1
1
2
1
0
1
1
1
2
1
2
2
0
2
1
1
1
0
0
0
2
2
1
1
1
1
1
2
2
1
2
0
1
1
1
1
1
1
2
0
1
1
2
2
0
1
0
1
2
2
0
0
1
1
1
1
1
1
2
1
1
1
0
0
2
1
1
2
1
1
0
0
2
1
0
1
1
1
1
1
2
1
1
1
1
2
2
1
2
0
2
2
1
1
1
1
1
2
1
1
1
1
2
1
2
1
0
1
2
2
1
1
1
2
1
2
2
2
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
0
1
1
1
1
2
2
0
2
0
2
2
1
1
1
1
1
1
1
1
2
1
1
1
0
1
3
3
0
1
2
0
1
1
2
1
1
2
2
1
2
2
1
1
1
1
2
2
0
0
1
1
1
0
1
1
1
1
2
1
1
2
1
0
1
1
1
1
2
2
1
1
2
1
1
2
1
2
1
2
1
1
2
1
1
1
2
1
0
1
1
2
2
1
0
1
1
1
0
1
0
2
1
2
1
0
1
0
1
0
2
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
2
1
0
1
0
0
0
1
2
0
1
2
0
2
2
1
1
2
2
1
1
0
1
1
1
2
1
1
2
0
1
2
1
0
2
1
2
2
1
2
1
1
1
2
1
1
2
1
2
1
2
2
1
1
1
1
1
0
1
2
1
0
1
1
1
1
1
1
1
1
2
1
1
1
1
2
0
1
1
1
1
0
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
0
1
1
2
1
1
1
2
0
0
1
2
1
2
1
0
1
1
0
1
1
1
1
2
1
1
1
1
1
1
2
1
2
1
1
1
2
2
0
1
1
1
2
0
2
1
2
1
2
1
0
1
1
2
1
2
1
1
1
0
2
2
0
1
1
1
1
2
1
1
1
1
2
2
1
2
1
1
1
1
2
1
1
1
1
1
1
2
0
1
1
2
1
1
1
3
0
2
2
2
1
1
1
1
1
1
0
1
1
0
1
2
0
1
2
1
2
2
2
1
0
1
1
0
2
2
1
1
1
1
2
1
1
0
1
1
1
1
1
1
1
2
2
1
1
1
1
0
1
1
1
1
0
1
2
1
0
1
1
1
1
0
2
2
2
1
1
0
0
1
2
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
3
1
0
2
2
1
1
2
2
0
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
0
2
1
1
1
0
0
1
1
3
1
3
1
1
1
1
2
1
1
1
1
1
2
1
0
1
2
1
1
1
2
2
1
1
1
1
2
2
1
2
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
0
0
2
1
1
1
2
2
0
1
2
1
0
1
1
1
2
0
1
1
1
0
1
1
1
2
1
2
2
0
2
0
2
0
1
1
2
2
1
1
0
1
0
0
1
1
1
1
1
1
1
1
2
1
1
0
1
0
1
2
1
1
2
0
1
1
0
1
1
1
1
1
1
1
1
1
2
2
0
2
2
1
2
1
1
1
2
1
1
1
3
0
2
0
2
0
1
2
0
0
2
1
1
0
1
1
2
2
1
1
0
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
0
1
1
2
1
0
1
1
1
1
1
1
1
1
1
3
1
1
1
1
0
0
1
1
1
0
1
0
1
2
2
2
1
1
2
1
1
1
1
1
1
0
0
1
1
1
1
1
1
1
1
1
1
1
1
2
1
0
1
2
0
1
1
2
1
1
1
0
1
1
0
1
1
1
1
1
0
1
2
1
1
2
2
0
2
1
2
1
1
1
1
1
1
1
0
1
0
1
2
1
0
1
1
0
1
1
2
1
2
1
0
1
1
1
1
2
1
1
1
2
1
1
2
2
1
1
2
0
0
1
1
1
0
1
0
1
2
1
2
0
1
0
0
2
2
0
1
1
2
1
1
1
0
2
2
0
2
1
1
1
2
0
1
0
2
1
2
1
2
2
1
1
2
1
2
1
1
1
0
2
1
1
1
1
0
1
1
1
0
0
2
1
0
1
1
2
2
1
1
2
0
1
1
1
2
1
1
0
1
1
1
1
1
2
1
2
2
1
2
1
1
1
1
1
2
1
1
1
1
3
0
0
1
1
1
1
1
0
0
1
1
1
1
1
1
1
2
0
2
1
0
1
1
1
1
2
1
1
1
2
2
1
1
2
2
1
2
1
1
1
1
1
2
1
2
2
1
1
1
0
1
1
1
1
2
1
0
1
2
2
1
2
1
1
1
1
1
2
2
1
1
2
1
2
1
1
1
1
0
1
2
1
1
1
2
1
1
2
1
2
2
0
2
1
0
2
0
0
1
1
1
1
2
2
1
1
1
1
1
2
2
1
2
1
0
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
0
2
1
2
2
0
1
1
0
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
2
2
1
0
1
1
1
2
1
1
1
2
1
2
1
0
1
1
1
1
0
1
1
1
0
2
0
1
0
0
1
2
2
1
0
1
1
0
0
1
1
2
1
2
1
0
2
2
2
1
1
2
1
1
1
0
1
2
1
1
1
2
1
2
0
1
1
2
1
1
0
1
1
2
2
1
2
2
0
1
1
1
1
0
2
0
0
1
1
1
2
1
2
2
1
1
1
0
1
1
1
2
1
1
1
2
1
1
2
1
1
0
2
1
1
2
1
1
1
2
1
2
1
0
1
1
1
1
1
1
2
0
1
1
0
0
1
1
2
1
1
0
2
2
0
1
2
2
1
1
1
1
1
2
1
0
1
1
0
1
1
0
1
2
1
1
1
0
1
1
2
2
2
1
2
1
1
1
1
1
0
4
1
1
1
1
1
2
1
2
1
0
2
2
1
1
0
1
1
2
1
1
0
1
2
2
0
2
1
2
0
2
1
2
0
2
2
2
0
1
1
0
1
2
2
1
1
1
1
2
1
2
2
2
1
1
1
1
2
1
2
1
1
2
1
1
2
1
0
1
0
1
0
1
1
1
2
1
1
2
1
2
2
2
1
1
2
1
2
1
1
2
1
1
1
2
1
1
2
1
0
2
2
1
2
1
0
1
2
1
0
1
1
2
1
1
0
1
1
1
1
2
1
2
1
0
2
0
1
1
1
2
1
1
2
1
1
0
1
0
2
1
1
2
1
2
1
1
0
1
1
1
1
1
2
3
1
1
1
1
1
1
1
1
1
1
1
2
0
1
1
1
1
2
1
1
2
1
0
1
1
2
2
1
1
2
1
1
2
2
0
1
2
2
1
2
2
0
2
1
2
1
1
1
2
1
1
0
1
1
1
2
1
1
1
0
1
1
1
1
1
1
2
1
1
0
1
0
1
2
1
1
2
2
1
1
1
2
1
1
0
2
1
2
1
1
1
2
1
1
2
1
1
1
0
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
0
2
1
2
1
1
1
1
2
1
2
0
2
2
1
2
2
2
1
1
1
1
0
2
0
2
1
2
1
1
1
1
2
1
2
1
1
1
2
1
2
0
1
1
0
1
1
1
1
1
1
1
1
2
1
1
2
1
1
3
3
2
4
1
2
0
1
0
1
1
1
0
1
1
2
0
2
1
1
1
1
1
1
1
0
2
0
2
2
1
0
1
2
2
1
0
1
1
1
0
1
2
1
3
1
1
2
2
1
1
2
1
1
2
1
1
1
2
2
1
0
1
0
1
1
1
1
1
1
1
1
1
1
2
1
1
0
2
2
1
2
1
1
1
3
1
2
0
1
2
1
1
1
1
1
2
1
2
1
1
0
1
1
1
0
1
0
1
1
1
1
1
0
1
2
1
1
1
2
1
1
1
2
0
2
1
1
1
2
0
1
1
2
1
2
2
1
1
1
0
1
2
2
1
2
2
1
2
1
1
2
2
1
2
1
1
0
0
2
1
1
1
2
1
0
1
0
1
1
2
1
1
1
2
1
2
1
3
1
2
2
1
1
5
1
1
2
2
1
1
0
1
2
2
1
1
0
0
1
1
2
1
1
1
2
2
2
2
1
1
2
1
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
0
2
1
1
0
1
0
0
1
0
0
1
2
1
1
1
2
1
2
2
2
2
1
1
2
1
2
2
2
1
1
2
2
0
1
2
2
2
1
1
1
1
1
1
0
0
2
0
0
1
2
2
1
2
1
1
2
0
1
2
2
2
2
2
2
1
0
1
2
2
1
1
2
1
2
1
1
0
1
1
1
1
1
1
1
1
1
1
1
0
1
0
2
2
0
1
1
1
1
2
1
0
1
1
2
1
2
2
1
1
1
1
1
2
1
1
2
1
1
1
2
2
1
2
2
0
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
0
1
2
1
2
0
1
1
1
1
1
0
1
0
1
3
2
2
2
1
1
0
1
1
2
2
0
1
1
1
1
1
1
1
2
1
0
1
1
1
1
1
1
0
2
1
1
1
1
0
0
0
1
1
1
2
2
0
1
1
1
1
1
2
2
2
1
0
1
2
1
1
1
1
1
2
1
2
2
2
1
1
2
1
1
1
1
1
1
0
1
2
1
1
2
1
0
1
2
0
1
1
0
1
1
1
1
1
1
0
0
1
1
1
0
1
1
2
2
2
1
0
1
1
1
1
2
1
1
1
2
1
1
2
1
1
1
2
1
2
1
2
2
1
1
2
2
3
1
1
1
2
1
1
1
0
0
1
1
0
1
1
1
2
1
1
2
1
2
1
1
1
2
1
1
1
1
2
1
2
1
2
1
1
1
2
1
1
1
1
1
2
1
0
1
1
1
1
1
1
1
1
1
1
0
1
1
1
2
1
1
1
0
1
1
1
2
1
0
1
1
1
1
1
2
2
2
0
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
0
1
2
1
2
1
0
1
0
1
1
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
0
1
0
2
1
1
2
2
1
0
2
0
1
1
0
1
0
0
1
2
1
2
0
1
1
2
1
0
1
1
1
1
1
2
1
1
2
0
2
1
0
1
0
1
1
1
1
2
3
1
1
2
1
2
1
1
1
2
1
1
1
1
1
2
1
0
2
1
1
1
1
1
1
1
1
1
2
1
1
1
0
1
2
2
2
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
1
0
1
1
2
1
2
1
0
2
1
1
2
2
1
1
2
1
2
2
1
2
1
1
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
0
2
1
2
1
2
0
0
1
1
2
1
1
2
1
2
2
1
1
1
1
2
1
1
2
1
2
2
2
3
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
0
1
1
0
0
1
1
0
1
1
2
1
1
2
1
2
1
1
0
2
1
2
1
1
2
1
1
1
1
1
1
1
1
0
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
2
1
1
1
1
0
2
0
1
1
1
0
1
1
1
1
1
2
1
1
1
1
1
2
2
2
1
1
2
1
1
2
0
1
1
1
2
1
9
1
2
2
1
2
2
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
0
1
0
1
0
1
3
1
2
2
1
1
0
2
1
1
1
1
0
1
1
1
1
1
2
1
1
2
1
1
2
1
1
1
0
1
1
0
0
1
1
1
1
1
2
2
1
2
2
2
0
1
1
0
1
0
1
1
1
1
1
1
2
0
2
2
1
1
1
1
0
1
1
1
2
1
1
1
2
1
1
1
0
0
0
0
2
1
1
0
1
1
1
1
1
2
1
1
2
1
1
1
1
2
1
1
1
1
0
0
1
2
2
1
1
0
0
0
1
0
1
1
2
2
0
0
1
2
1
2
1
1
2
1
1
2
1
1
1
2
2
1
1
1
1
2
1
2
1
1
1
2
1
2
1
1
2
1
2
1
1
0
1
0
1
1
1
1
2
2
1
1
1
2
1
1
1
2
1
2
1
0
1
1
1
2
2
2
1
1
0
1
1
0
1
1
0
2
1
1
1
1
1
1
0
0
1
2
1
1
1
2
0
1
0
1
3
2
1
2
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
0
1
0
2
2
0
1
2
1
1
1
1
2
0
1
1
1
1
1
1
1
1
2
2
1
2
2
1
1
2
1
2
1
2
1
1
2
0
1
2
1
2
2
1
1
2
1
1
1
1
1
0
2
1
0
2
2
1
1
0
1
2
0
1
0
1
2
1
0
1
1
1
1
1
2
1
2
1
1
1
0
1
0
1
1
1
2
1
0
1
1
0
1
1
2
0
1
1
1
1
1
0
1
2
1
2
1
1
1
1
1
1
1
1
2
1
1
1
0
0
2
1
0
0
1
1
1
0
1
1
2
1
2
2
1
0
1
1
1
2
1
2
1
1
1
1
1
1
2
1
2
1
1
0
1
0
1
2
1
1
0
0
1
1
1
2
0
1
2
2
0
1
1
2
1
1
1
1
1
2
0
1
0
1
2
1
1
1
2
0
0
2
0
2
2
1
0
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
0
1
1
1
1
2
0
1
1
2
0
1
1
1
2
0
2
2
1
2
1
2
2
1
1
1
2
1
0
1
2
1
1
1
1
1
2
1
1
0
0
2
2
1
1
1
1
1
1
2
0
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
0
1
1
1
2
0
1
1
1
2
1
1
0
2
1
1
2
1
1
1
1
1
1
1
1
0
1
0
0
1
2
1
1
1
1
1
0
1
1
1
0
2
2
2
1
1
1
2
2
1
1
2
1
1
1
2
1
2
2
2
1
2
1
2
2
1
1
2
0
1
1
1
2
2
1
0
1
2
0
0
2
2
1
0
2
1
2
1
1
1
1
2
1
1
1
1
1
2
1
0
1
0
2
1
1
1
2
2
1
1
2
0
1
2
2
1
1
1
1
1
1
1
0
2
0
2
1
2
1
2
0
0
2
0
0
2
2
1
1
2
1
0
1
1
1
1
0
1
1
1
1
0
1
1
1
2
1
0
1
2
0
1
1
1
1
1
1
0
1
1
1
1
2
1
2
1
1
1
2
1
1
1
1
1
0
2
0
1
1
1
1
1
1
2
2
1
1
0
1
2
2
1
1
1
1
0
2
1
1
1
1
1
2
2
0
2
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
0
1
2
1
1
0
1
1
1
0
1
2
1
2
1
0
1
0
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
0
0
0
1
1
1
0
1
1
1
0
2
1
1
1
0
2
2
1
1
0
1
1
1
2
1
1
1
1
1
1
1
1
2
0
2
0
1
1
0
1
2
2
2
3
1
2
1
1
2
2
1
3
1
1
1
2
2
1
1
2
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
0
0
1
0
1
0
1
2
1
2
2
1
2
1
0
1
1
1
2
2
2
1
1
2
2
1
1
1
1
2
2
2
0
2
2
1
2
2
1
1
0
0
1
1
2
2
0
1
1
1
2
1
2
1
2
0
1
1
2
0
1
0
2
1
0
2
1
2
1
1
2
1
2
1
1
2
1
1
1
1
0
1
1
1
1
1
0
1
0
0
1
1
2
1
2
1
2
1
1
1
1
2
0
0
1
1
1
1
0
2
1
2
0
2
0
1
2
1
1
1
2
2
1
1
1
1
1
1
0
1
0
1
1
1
2
1
2
1
2
1
1
2
2
2
1
1
0
1
1
1
1
1
0
1
1
1
2
0
1
1
2
1
2
1
1
1
1
1
1
1
1
1
0
2
2
1
1
2
1
1
0
1
0
0
1
1
2
1
2
0
2
1
1
1
1
0
2
1
1
1
1
1
2
1
0
1
2
0
1
1
1
1
1
5
0
2
0
1
1
2
1
1
2
2
1
1
1
1
1
1
1
0
1
0
0
1
1
0
2
1
2
1
1
2
2
1
1
1
2
1
2
1
2
1
1
1
2
2
1
2
2
1
1
1
2
1
2
2
1
1
2
1
2
2
1
0
1
1
2
1
1
2
2
2
1
2
2
2
1
2
1
1
1
1
1
2
0
1
1
1
1
2
1
2
1
1
0
1
2
1
1
0
2
1
1
1
2
1
1
1
2
2
2
1
1
2
2
2
1
2
1
1
1
1
1
0
1
2
2
2
1
1
1
1
1
1
3
1
2
1
2
1
2
1
1
2
1
2
1
1
0
2
1
0
1
1
1
0
2
1
1
1
1
1
1
0
0
1
1
1
1
0
1
1
1
0
1
1
2
2
2
1
1
2
0
1
1
1
1
1
2
2
1
1
0
1
1
1
1
1
1
1
1
0
1
2
0
1
1
1
0
2
2
1
1
1
1
1
2
2
0
1
1
0
0
2
1
1
2
1
0
0
2
1
1
1
1
1
1
2
1
2
2
1
1
2
1
1
1
1
1
1
1
0
1
2
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
2
1
1
2
0
1
2
1
1
2
1
0
1
1
0
1
0
2
0
1
2
1
1
3
1
0
0
1
1
1
2
1
1
2
1
0
2
1
2
0
1
1
2
2
0
1
2
0
1
1
2
1
1
2
0
0
1
1
0
1
1
2
2
1
0
1
0
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
2
0
0
1
1
2
1
0
0
1
1
1
2
1
1
2
1
1
1
1
0
1
1
0
1
0
0
2
1
2
2
1
1
2
0
1
1
2
2
2
1
2
1
2
1
2
1
1
2
1
1
0
2
1
1
1
1
0
1
1
2
1
3
1
2
1
1
1
1
0
0
1
1
2
2
1
1
2
2
1
2
1
1
1
2
1
1
2
1
2
2
1
1
0
0
1
2
1
1
1
0
2
1
1
1
1
0
0
1
2
2
1
1
1
2
0
1
1
2
1
1
1
1
1
1
0
0
2
0
0
2
1
1
1
0
2
1
1
2
2
0
1
1
0
2
1
1
2
0
1
2
1
1
1
1
1
0
1
2
1
2
1
1
2
2
2
1
1
1
1
1
1
1
1
2
0
0
0
1
1
0
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
0
1
0
1
1
1
0
2
0
1
2
1
2
1
0
1
2
1
1
1
2
2
1
1
1
1
1
2
0
1
1
1
0
2
2
1
2
3
2
1
2
1
1
0
2
2
1
1
1
1
1
1
2
0
1
1
2
2
2
2
1
1
1
1
0
1
1
1
1
0
0
2
1
1
1
1
1
1
1
1
1
2
2
1
2
1
2
0
0
1
2
2
1
2
2
1
1
2
0
1
0
1
1
2
1
2
1
0
2
1
2
3
2
2
0
2
0
1
1
1
1
0
1
0
1
1
0
1
1
1
1
2
1
1
1
2
1
0
1
1
2
1
2
1
1
1
1
1
1
2
1
2
0
2
1
0
2
0
2
1
1
2
1
1
1
2
0
1
0
0
2
0
2
1
1
1
0
1
1
1
2
1
1
0
1
1
0
2
2
1
1
1
1
1
1
1
1
1
2
0
1
1
1
0
2
1
0
1
1
1
1
1
0
4
0
0
1
1
1
1
1
1
1
2
0
0
3
1
2
2
2
1
1
1
1
1
0
1
0
1
1
1
0
1
2
1
1
2
1
2
1
1
1
1
1
2
1
1
2
1
2
1
1
0
1
1
2
1
1
1
3
1
1
1
0
1
2
1
0
2
0
1
1
0
0
0
0
1
1
2
1
1
1
2
1
0
1
2
2
1
2
1
2
1
1
1
1
1
2
1
2
2
2
0
1
1
2
1
0
0
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
2
2
1
0
2
2
1
2
1
1
2
1
2
1
1
1
2
1
1
2
1
2
2
1
1
1
1
2
1
0
2
0
2
1
1
1
1
1
0
2
1
1
1
1
1
0
0
1
1
1
0
2
2
2
2
1
0
0
1
2
2
1
0
2
0
1
1
1
2
0
2
1
1
2
1
1
2
1
1
1
1
1
2
2
1
1
0
2
2
1
1
1
1
1
2
1
1
2
1
1
2
2
1
2
1
1
1
2
0
1
1
2
1
1
1
1
2
0
1
2
1
2
1
1
1
2
1
2
2
2
2
0
2
1
2
2
0
1
1
1
2
1
2
1
2
2
2
2
1
1
0
1
1
1
1
1
1
0
1
2
1
0
1
0
1
0
1
2
1
1
1
1
1
1
1
1
2
2
2
2
1
1
0
2
7
2
0
2
2
1
1
1
0
0
1
2
2
2
1
0
0
1
1
2
2
1
0
1
0
2
1
1
1
0
2
1
1
1
1
2
1
1
1
1
1
1
2
0
1
1
2
1
2
0
0
1
2
0
1
1
1
2
1
1
2
1
2
1
1
0
1
1
0
2
2
1
2
1
0
1
1
1
1
1
1
1
0
1
1
2
1
1
1
0
1
1
1
1
2
1
2
2
2
2
2
2
0
1
1
1
1
1
1
3
1
1
1
1
2
1
1
1
0
1
1
1
0
2
1
2
2
1
1
1
0
2
1
1
1
0
0
1
1
1
2
0
2
1
2
1
1
1
2
0
1
2
0
2
1
1
1
1
1
1
1
1
1
0
1
0
1
1
1
4
1
1
1
1
1
1
1
1
0
0
2
0
1
1
1
1
1
1
1
2
0
1
0
2
1
1
1
1
0
1
1
0
2
2
1
1
1
1
0
1
1
1
1
1
0
1
1
1
4
0
0
2
0
1
2
0
1
2
1
1
0
1
1
1
0
1
1
1
0
1
0
1
1
1
2
1
2
1
2
0
2
0
2
1
0
1
2
2
0
1
1
1
1
1
1
1
1
1
2
1
2
0
1
0
0
1
1
1
1
1
1
1
1
2
2
1
0
1
1
2
1
1
1
1
2
1
1
1
1
2
0
2
1
1
1
1
2
1
2
2
2
2
2
1
0
1
2
1
2
1
1
1
1
1
0
0
0
2
0
1
1
1
1
1
0
1
1
1
1
0
1
1
1
1
1
2
1
1
1
1
0
1
2
2
1
2
0
1
1
0
1
1
1
0
0
1
2
1
1
1
1
1
2
0
1
1
1
0
0
2
2
1
1
1
4
2
1
1
1
1
0
1
1
2
1
1
0
2
2
1
2
0
2
2
1
1
2
0
0
1
1
1
0
2
1
1
2
1
2
2
1
2
1
1
1
1
1
2
0
1
1
1
1
1
1
1
1
1
1
1
0
1
0
1
2
1
1
1
0
2
1
1
1
1
1
1
2
1
1
1
1
1
0
1
4
1
1
1
1
1
2
1
1
1
1
1
0
1
1
2
1
1
1
0
0
0
0
1
1
2
1
1
1
1
0
1
1
1
0
2
1
2
1
1
1
2
2
2
1
3
1
1
1
1
1
1
1
1
0
1
1
2
2
2
1
2
1
1
0
1
1
0
1
2
1
0
1
1
0
1
0
1
1
1
1
1
2
2
1
2
0
1
1
1
1
1
2
1
1
2
2
2
2
1
3
1
2
2
1
0
1
2
0
1
1
1
0
1
1
1
2
1
1
1
1
1
2
1
1
1
2
0
1
1
0
1
1
1
1
1
2
1
1
2
1
2
1
2
1
2
1
1
1
0
2
1
1
1
0
1
1
1
0
2
1
2
1
1
1
1
0
1
1
1
2
1
1
0
0
1
1
1
0
1
1
1
0
2
0
2
1
1
1
0
1
2
1
2
0
1
2
2
2
2
1
1
2
2
1
0
1
2
2
2
2
1
0
1
1
1
1
0
1
1
1
1
2
0
1
2
2
2
1
2
2
0
1
1
1
1
1
2
1
0
1
2
2
1
2
1
2
0
2
1
2
1
0
1
1
2
0
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
0
2
1
2
2
2
0
1
0
1
0
1
1
1
1
2
1
2
2
1
1
2
1
1
1
1
1
2
0
1
1
2
1
2
2
1
1
1
0
1
0
1
2
0
2
1
1
1
0
0
1
2
2
2
2
1
1
1
1
0
1
2
0
1
0
2
1
1
0
1
1
1
1
1
1
1
0
1
0
0
1
1
2
1
2
0
1
0
0
1
2
1
1
1
1
4
1
1
2
2
1
1
0
2
4
2
2
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
0
0
1
1
1
2
1
1
0
1
2
2
1
1
2
1
1
1
1
4
2
1
1
2
1
1
2
2
2
0
1
1
2
1
1
1
1
1
2
2
1
2
1
1
1
1
0
1
2
2
1
2
1
2
1
1
1
1
2
2
1
1
0
1
1
1
1
2
1
1
2
2
1
1
0
0
1
1
1
0
2
1
1
1
1
1
1
1
0
2
1
1
2
1
1
1
1
0
2
2
1
1
0
1
2
2
1
1
0
0
2
1
1
1
0
1
2
2
2
1
1
0
0
2
1
1
1
1
0
2
1
1
1
1
0
1
1
1
0
1
2
2
0
2
2
1
0
1
1
0
0
1
1
1
1
1
1
1
1
0
2
1
2
1
1
2
1
1
0
1
1
1
0
1
1
2
1
0
1
1
2
2
1
1
2
1
1
1
2
0
1
1
1
1
1
1
1
0
0
4
2
0
0
1
2
1
2
1
1
1
2
2
7
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
0
1
0
1
1
2
1
1
2
1
0
1
0
1
1
1
1
0
1
1
0
1
1
1
1
1
1
0
2
1
0
0
1
2
1
1
2
0
1
1
2
2
2
1
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
2
2
1
0
2
1
1
1
2
1
0
0
2
1
0
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
0
1
1
1
0
1
2
2
1
2
2
1
2
1
1
2
2
2
2
1
1
2
2
0
2
2
1
2
1
1
0
0
2
3
1
1
1
1
0
1
0
1
1
1
2
0
2
1
1
2
2
0
2
1
1
1
2
1
0
1
1
2
1
1
1
1
1
1
1
1
1
2
1
0
1
1
1
0
2
1
3
1
1
1
0
2
1
1
1
1
1
0
1
2
2
1
1
1
2
1
1
1
1
2
1
0
1
2
1
0
1
1
1
2
2
1
1
1
2
1
1
2
1
1
1
1
2
1
0
0
1
1
1
2
1
1
0
0
2
1
1
2
1
1
0
1
1
1
0
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
1
2
2
1
1
1
0
1
1
2
0
0
1
1
0
1
1
2
1
1
2
1
2
1
1
1
2
1
1
1
2
2
1
1
2
1
2
1
0
1
1
2
1
0
1
1
1
1
1
2
2
3
2
2
1
1
1
1
2
2
2
0
0
1
0
1
1
1
1
1
2
2
1
2
1
1
1
1
1
2
1
0
1
1
2
2
2
2
1
1
2
0
1
1
1
1
1
1
1
0
3
1
0
0
2
2
1
1
1
2
2
1
1
2
1
1
3
2
1
1
1
2
0
2
1
1
1
0
1
1
2
2
1
2
1
2
1
1
2
1
2
0
1
1
1
1
1
1
1
1
2
0
2
1
1
0
0
2
1
1
0
0
1
3
1
2
1
1
2
2
2
1
2
1
1
2
1
1
2
2
1
1
2
2
1
1
1
1
1
4
1
1
2
1
2
0
2
1
0
1
1
1
2
1
0
2
0
1
1
1
0
1
1
1
1
1
1
1
2
0
1
2
1
0
1
0
1
1
1
1
2
1
2
2
2
2
1
1
1
2
1
1
0
1
0
1
0
2
1
1
2
0
1
2
0
0
1
1
2
1
1
1
1
1
1
1
1
2
2
1
1
1
0
2
1
2
1
1
1
2
2
2
2
1
0
1
0
1
1
2
2
1
1
4
1
2
2
0
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
2
1
1
0
2
0
1
0
2
0
1
1
0
1
1
1
1
1
1
0
2
0
1
1
0
2
2
2
1
0
1
1
2
2
0
0
1
1
1
1
2
1
1
1
2
2
1
1
1
2
0
1
0
1
1
1
2
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
2
2
1
2
2
2
1
1
2
1
1
1
1
1
0
0
3
1
1
2
1
2
1
1
1
0
2
1
1
1
1
2
2
1
1
2
2
0
2
1
2
1
1
2
1
1
0
0
1
1
1
2
1
1
1
1
2
2
1
2
2
1
1
1
1
1
1
0
2
1
0
1
1
2
0
1
1
1
2
2
1
1
2
1
1
1
1
1
0
1
2
2
2
2
0
2
1
2
1
0
2
2
0
2
1
1
1
1
0
1
2
1
2
2
2
1
2
1
1
1
1
1
2
0
0
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
1
2
1
2
3
2
1
1
1
1
2
0
2
0
2
0
1
2
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
0
1
0
1
0
1
2
0
0
1
0
2
2
1
1
1
1
1
2
0
0
2
1
1
2
1
1
1
1
2
2
1
0
1
0
1
2
2
1
1
1
2
2
1
1
1
2
1
3
2
2
1
2
1
1
2
1
1
1
0
2
1
1
1
1
2
2
1
0
0
1
0
2
2
1
2
2
2
1
1
2
0
2
2
0
1
2
2
2
0
0
1
1
0
1
2
1
2
1
0
0
1
1
2
2
0
2
1
0
2
0
1
1
1
1
1
1
2
1
1
1
0
0
1
2
1
1
1
2
1
1
1
2
2
1
1
1
2
0
1
0
0
1
1
2
2
1
0
1
1
1
0
1
1
1
1
1
2
1
1
1
2
1
2
1
2
1
0
1
1
1
1
0
0
2
1
2
3
1
1
2
1
2
1
1
1
0
1
1
1
1
0
0
1
1
2
2
1
1
3
1
1
0
2
2
7
0
2
0
1
1
1
1
2
0
2
1
1
1
2
0
1
2
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
2
1
1
2
1
0
1
1
1
1
2
2
1
2
2
1
1
1
1
1
1
2
0
2
1
1
1
2
1
1
2
1
1
0
2
2
0
1
1
1
1
1
2
1
1
0
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
0
1
1
2
1
0
1
0
0
1
2
1
1
0
0
1
0
2
1
1
1
2
1
1
1
2
0
1
1
2
1
1
2
0
3
1
1
1
0
2
1
1
1
1
1
0
1
1
1
1
1
1
1
0
1
2
0
1
1
2
2
0
2
1
0
1
1
1
3
1
2
1
2
1
1
2
2
1
1
2
1
1
1
1
1
1
0
1
0
1
1
1
0
1
1
1
2
2
1
1
1
2
1
0
2
1
1
0
0
1
1
1
2
2
1
1
1
2
2
2
1
1
1
0
1
1
1
0
1
1
2
1
2
2
0
1
1
2
1
2
0
2
1
0
1
1
1
1
2
1
1
2
1
0
0
2
2
0
2
1
1
1
2
1
2
1
1
0
3
1
1
1
2
0
1
0
1
1
1
0
0
1
1
1
0
2
1
2
1
2
1
1
0
0
0
1
2
1
1
2
1
2
1
2
2
1
1
0
3
2
0
1
1
0
2
1
1
1
1
3
1
1
2
1
1
2
1
2
1
2
1
1
0
1
1
1
1
2
1
2
2
2
0
2
1
1
1
1
1
2
0
1
2
0
0
1
0
1
1
1
1
1
0
0
0
1
1
1
1
2
0
1
0
1
2
1
1
1
2
2
2
1
2
2
0
1
0
1
1
2
2
2
2
1
1
1
1
0
1
0
1
1
1
1
1
1
0
1
1
2
2
1
1
0
2
1
2
1
1
1
1
0
0
0
1
2
1
1
1
1
1
1
0
0
0
1
1
1
1
1
1
1
1
2
1
0
1
1
1
1
1
2
1
0
1
0
1
2
1
1
1
0
0
0
1
2
1
2
2
1
1
1
0
2
2
2
0
1
0
1
1
1
1
1
1
1
1
1
2
2
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
0
1
2
2
1
1
1
1
1
1
1
0
0
1
0
1
1
2
2
2
1
2
2
2
0
1
1
1
2
0
1
1
1
1
1
0
1
1
0
2
0
0
0
1
1
1
0
0
1
1
1
0
0
1
0
1
1
1
0
1
0
1
1
1
2
1
1
0
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
0
1
0
1
0
1
2
0
0
1
2
1
1
1
0
1
1
0
2
1
1
0
2
1
2
2
2
0
1
1
2
1
1
1
1
1
1
1
0
2
1
1
2
1
1
1
1
2
1
2
1
2
0
0
1
0
1
0
1
1
1
1
1
2
1
1
0
1
2
1
1
2
1
2
1
1
2
1
1
1
1
0
2
2
2
1
1
2
1
0
0
1
1
0
0
1
1
1
0
1
0
1
1
2
1
0
1
2
1
0
2
1
1
1
1
2
0
1
2
2
1
1
1
0
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
0
0
2
1
1
1
1
1
1
1
2
1
1
1
1
2
0
1
1
2
2
1
1
2
0
2
1
2
0
1
0
1
2
1
2
2
1
0
2
1
2
2
0
1
1
2
1
2
1
2
2
0
1
0
1
1
1
1
1
1
0
1
1
1
1
1
2
2
1
1
0
0
1
1
1
1
1
1
2
1
1
3
1
1
1
0
0
2
2
1
2
1
2
1
1
0
2
2
1
1
1
1
1
2
2
1
1
0
1
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
0
2
1
0
1
1
1
1
1
1
0
0
2
1
0
0
2
1
1
2
1
2
1
2
2
1
1
0
2
0
1
1
1
2
2
3
1
1
0
1
2
1
0
0
1
1
2
1
1
1
1
2
1
2
1
2
0
2
0
1
2
2
1
0
2
1
2
1
1
2
1
1
1
1
0
1
1
2
0
1
1
1
1
1
0
2
1
1
1
2
2
2
1
1
2
1
1
1
2
3
1
1
0
1
0
1
1
1
0
2
1
1
1
1
2
2
0
2
1
2
1
1
1
3
1
2
1
0
1
2
2
1
1
2
1
1
1
1
2
0
2
0
1
1
1
1
0
0
1
1
1
1
0
1
0
2
1
2
1
1
1
1
2
3
0
1
1
1
0
1
1
2
2
1
3
1
1
2
2
2
1
2
0
1
2
1
2
1
2
1
1
1
1
2
2
0
0
1
1
2
1
2
2
1
2
1
0
0
0
2
1
2
2
1
1
2
2
2
1
2
0
2
1
1
1
1
2
1
1
2
1
1
2
6
1
0
1
0
1
1
1
2
1
1
0
1
1
2
1
2
1
1
1
1
0
1
1
1
1
1
1
1
2
1
1
1
1
2
0
2
2
1
1
1
2
0
1
1
1
10
2
0
2
1
1
1
1
1
2
0
3
0
2
0
1
0
1
0
2
1
1
2
2
0
1
2
1
2
1
2
2
1
1
1
2
1
0
2
3
0
2
2
1
2
2
1
0
2
2
1
1
2
1
1
0
1
0
1
2
1
1
1
1
1
2
1
1
1
0
2
1
1
1
1
0
1
1
1
2
1
0
2
1
1
1
1
0
1
1
1
0
1
0
1
1
1
0
1
2
2
0
1
1
1
1
1
2
0
2
1
1
0
0
0
2
1
1
1
1
1
1
1
2
2
1
2
1
1
1
0
0
1
2
1
1
1
1
2
1
0
1
0
2
1
1
2
1
1
1
1
0
1
0
1
1
2
1
1
1
1
1
2
1
1
1
2
0
1
1
1
1
1
1
1
1
2
2
2
2
2
1
2
2
1
1
0
2
2
1
1
1
2
1
0
2
1
1
1
1
2
1
1
1
1
1
2
1
2
2
0
1
1
0
2
2
1
0
0
2
2
1
0
1
1
0
1
1
0
1
1
1
2
1
2
2
1
1
1
1
2
1
1
0
1
1
2
1
2
1
1
0
2
0
1
1
2
2
1
1
1
1
1
2
1
1
0
2
1
1
1
1
1
0
0
2
1
1
1
0
1
1
0
1
2
2
1
1
2
1
1
2
1
1
1
2
0
0
2
2
1
1
2
0
1
1
1
0
1
1
2
2
1
2
1
2
2
2
1
0
1
2
0
2
1
1
2
2
1
1
0
1
0
1
1
1
1
1
1
2
2
0
2
1
1
2
0
0
2
1
1
1
1
2
1
1
2
2
2
1
2
1
0
3
1
1
1
1
2
2
1
1
1
2
0
1
1
1
1
2
1
0
0
1
1
0
2
1
1
1
2
1
1
2
2
2
2
1
2
1
1
2
1
1
0
1
1
1
0
1
1
2
2
1
1
1
2
1
2
1
2
1
1
0
0
2
1
1
1
1
1
2
2
2
1
1
1
1
1
2
1
1
1
2
0
2
0
1
1
1
2
1
2
1
1
2
1
1
0
2
2
1
1
1
2
1
1
1
2
1
1
0
1
0
2
2
2
1
1
2
1
2
2
2
2
2
1
1
1
2
0
0
1
2
1
1
1
1
2
1
2
1
1
1
1
0
2
2
1
1
0
1
1
2
2
2
0
1
2
1
1
1
1
0
0
2
1
1
1
1
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
2
3
1
0
0
1
1
0
1
1
1
1
1
1
1
2
0
1
1
1
1
0
2
2
2
1
0
1
1
1
2
0
1
1
2
0
2
1
0
2
1
1
2
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
0
2
2
0
2
1
1
1
1
0
2
2
1
1
2
2
2
1
2
0
1
2
1
1
2
1
0
1
2
1
1
1
2
1
1
1
1
1
1
1
0
1
1
1
2
2
1
2
1
1
1
1
1
1
1
0
2
2
1
2
1
1
1
2
2
1
1
1
0
2
2
1
2
1
2
1
1
1
2
1
1
1
2
2
2
0
1
2
1
2
1
1
2
1
1
2
1
2
0
1
1
1
2
1
2
3
1
1
2
0
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
1
1
0
1
1
1
1
1
2
1
0
1
1
2
1
1
2
1
1
2
1
1
0
1
1
2
1
1
1
1
1
1
1
2
1
0
1
1
1
2
2
1
2
1
1
1
1
1
0
1
1
1
2
1
0
1
2
2
0
1
1
2
0
0
1
1
1
1
1
1
2
1
0
1
1
0
1
2
2
1
1
0
1
2
1
1
2
2
1
1
1
1
1
5
0
2
2
0
1
1
1
1
1
1
1
0
2
2
0
1
1
2
0
2
1
1
0
1
0
1
2
1
2
0
1
1
2
2
0
1
2
1
0
1
1
2
1
2
1
1
1
2
1
1
1
1
0
1
1
1
0
0
3
2
2
1
1
1
2
0
1
0
1
1
1
1
1
2
1
2
1
2
1
1
2
1
1
1
1
0
1
2
0
1
1
0
2
2
1
1
1
0
1
0
0
1
0
1
1
2
1
1
2
0
2
1
1
0
1
1
2
1
0
1
0
1
1
1
1
1
0
1
0
1
2
0
1
1
2
0
1
1
2
1
1
2
2
0
1
0
1
1
1
2
0
1
1
1
1
2
2
1
1
1
2
0
2
1
0
1
2
1
1
0
1
1
0
2
0
2
2
1
1
2
2
1
1
0
1
2
1
1
1
2
1
0
1
1
1
1
1
1
1
2
1
0
1
1
2
2
1
1
1
1
1
0
1
1
1
1
1
2
1
2
1
1
1
1
0
1
2
1
1
0
1
1
1
0
1
2
1
1
2
1
2
0
1
0
1
1
1
1
1
1
1
1
1
2
2
1
4
1
1
0
0
0
0
1
2
2
2
1
1
1
1
2
1
1
1
2
2
1
1
0
2
1
1
1
1
1
1
1
1
2
2
1
0
2
1
2
2
1
1
2
1
1
0
1
1
1
1
0
1
1
2
1
1
1
1
2
2
2
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
0
2
1
1
1
2
1
0
1
2
0
1
3
1
1
2
1
1
1
1
1
0
2
1
0
1
1
2
0
1
1
1
2
1
1
1
1
2
1
1
2
2
1
1
1
1
1
3
1
2
1
2
1
1
1
1
1
2
2
2
0
2
0
1
2
2
1
2
1
1
1
1
0
2
2
1
1
1
2
3
2
2
1
1
1
1
1
1
1
1
0
3
2
0
2
2
1
2
1
1
1
0
2
1
1
1
2
1
0
2
1
1
1
1
0
0
1
1
0
1
1
1
2
1
0
1
2
1
1
1
1
1
1
0
2
1
1
2
1
2
1
1
1
1
1
1
1
1
0
1
2
0
2
1
2
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
0
0
1
1
1
1
1
1
1
2
1
1
0
2
0
2
1
2
0
2
1
1
1
1
1
1
0
1
1
1
2
1
1
2
1
1
1
1
2
1
2
2
2
1
2
1
1
3
1
2
1
1
1
0
1
1
1
1
1
0
2
1
2
2
1
1
1
1
2
2
1
0
1
1
1
0
1
1
1
1
2
2
1
1
1
1
1
1
0
0
2
1
1
2
1
1
1
0
1
1
1
1
2
1
2
1
1
2
1
2
1
2
1
1
1
1
0
1
0
1
2
1
0
1
1
2
2
1
2
1
1
1
1
1
1
1
1
0
2
1
1
1
1
1
2
1
1
1
1
2
2
1
2
1
2
1
1
2
2
1
1
0
2
1
1
1
1
2
3
2
1
2
1
1
1
2
1
1
0
0
2
1
2
1
1
1
0
1
2
2
1
1
1
1
2
1
2
0
1
2
1
1
1
1
2
1
2
1
1
0
2
1
2
1
1
2
2
1
2
2
1
0
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
0
1
2
1
2
1
2
2
2
2
0
0
0
1
1
2
0
1
0
1
1
1
1
1
1
1
0
0
1
1
1
1
9
2
1
1
1
2
1
0
1
1
3
1
0
2
2
2
1
1
1
2
1
1
1
1
1
1
0
2
2
0
2
2
1
0
1
1
1
2
2
2
2
0
1
1
2
0
1
1
2
2
2
1
2
1
2
1
1
1
1
0
2
1
0
1
1
1
0
1
2
1
1
1
1
2
1
1
2
2
2
1
1
2
1
1
0
1
2
1
2
0
1
1
0
1
0
0
1
1
2
1
2
2
1
2
0
2
1
3
1
2
1
1
3
1
1
1
1
1
1
2
1
1
2
1
1
0
2
1
1
0
1
1
2
1
2
2
2
0
1
2
0
2
1
1
1
0
1
0
1
0
1
2
1
1
2
2
1
2
1
1
0
0
1
0
2
1
1
2
1
2
2
1
1
1
2
2
2
1
0
2
1
1
1
0
1
1
1
1
0
2
1
1
1
0
1
2
1
2
2
1
1
1
2
2
2
2
1
1
2
1
1
1
0
4
1
2
1
2
1
1
1
2
1
0
1
1
0
1
2
1
1
1
1
1
1
2
1
3
0
1
1
1
1
2
1
2
0
2
2
1
1
1
0
1
0
1
1
1
1
1
2
1
1
0
2
1
0
1
2
3
2
1
1
0
2
1
1
0
1
0
1
2
0
2
1
0
1
2
1
2
0
1
0
1
1
0
1
2
0
1
1
0
1
2
0
2
1
1
0
0
1
1
1
2
1
1
0
0
1
2
1
1
1
2
1
1
0
2
2
1
0
2
1
1
1
1
1
1
2
1
1
2
1
1
0
0
2
1
0
2
1
1
1
2
1
0
1
1
1
0
1
1
0
0
1
1
1
2
1
1
1
0
1
1
1
1
2
2
1
1
0
1
2
1
1
2
1
0
2
0
1
1
0
1
1
1
0
1
0
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
0
1
0
0
1
1
1
1
0
1
1
2
1
2
1
3
1
1
1
1
0
2
0
1
1
1
1
1
1
2
1
0
1
2
1
2
2
1
2
2
1
1
1
0
3
1
1
2
2
1
0
2
1
2
1
2
1
0
0
1
0
0
0
2
0
2
1
1
1
1
1
1
2
0
2
2
2
1
1
1
1
2
2
1
2
1
1
2
1
1
2
0
1
2
2
1
0
2
2
1
2
1
1
0
0
2
2
1
2
1
2
1
1
1
1
1
1
1
0
2
0
1
0
1
1
1
2
2
2
2
1
1
1
1
1
2
1
1
2
1
1
2
1
2
2
0
1
1
0
0
0
1
1
1
0
1
1
1
1
1
1
1
1
0
1
1
0
1
1
1
2
1
1
2
0
1
2
1
1
0
1
2
1
2
2
1
1
0
1
1
1
2
1
2
1
1
0
0
2
1
2
1
0
3
2
2
1
1
0
1
2
0
2
1
1
1
1
0
0
1
1
1
1
1
1
0
3
0
2
1
1
1
1
0
2
1
0
1
0
1
0
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
0
1
2
1
1
2
1
1
2
1
1
2
1
2
1
1
1
2
1
1
1
1
2
1
0
1
1
2
0
1
1
2
0
1
1
0
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
2
3
2
1
0
1
2
2
1
1
1
2
1
0
1
1
1
0
0
1
1
1
0
1
0
2
1
1
2
1
2
1
1
2
0
0
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
2
0
0
1
0
1
1
2
1
2
0
0
1
2
1
1
0
2
0
1
1
1
1
1
0
2
1
1
1
1
2
1
1
1
1
1
1
0
0
2
1
0
2
1
1
2
1
2
2
1
2
1
2
2
1
1
0
0
1
1
0
1
2
1
0
1
0
1
1
2
2
2
0
1
2
2
1
2
1
1
1
0
1
0
1
1
1
1
1
1
0
1
1
1
0
2
1
1
1
2
0
1
1
1
1
2
2
1
1
2
1
1
2
4
1
1
2
1
1
1
2
0
0
1
2
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
2
2
1
2
1
2
2
1
1
1
2
2
1
1
2
1
0
1
0
1
2
0
1
0
1
1
2
1
1
1
1
1
1
1
2
0
2
2
2
1
4
1
0
1
3
1
0
0
0
1
1
1
1
1
2
1
1
1
0
3
2
1
2
1
2
1
0
1
0
2
2
1
1
0
1
1
1
1
2
1
1
2
1
1
1
2
1
2
1
2
2
2
1
1
1
1
1
1
2
1
1
1
2
2
2
0
1
1
1
1
1
1
2
1
2
2
2
1
1
1
2
0
1
2
0
1
2
2
1
1
2
0
3
1
1
1
2
2
1
1
1
1
1
1
0
1
2
1
0
1
1
0
1
1
0
0
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
2
2
1
1
2
1
1
2
1
1
2
1
2
1
2
1
1
1
0
1
1
2
1
1
1
1
2
1
1
0
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
3
1
1
1
1
1
2
1
0
2
0
1
1
1
0
2
1
1
1
2
0
1
1
2
1
1
1
2
0
2
1
0
1
1
2
1
1
0
1
2
1
1
1
0
2
2
1
1
1
1
2
0
1
0
0
2
1
2
1
1
1
2
1
0
2
1
2
2
1
1
2
1
1
2
0
0
1
1
0
2
0
1
1
1
1
1
2
2
1
0
1
1
2
1
0
2
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
0
2
2
1
1
1
2
1
1
2
0
1
2
1
0
2
1
1
0
1
1
2
1
1
1
0
1
2
2
1
1
0
2
2
2
0
1
1
1
1
2
2
1
1
1
1
1
0
1
1
1
0
1
1
2
2
1
1
1
1
2
1
2
1
2
1
1
1
1
0
2
1
1
1
1
0
2
1
2
1
0
2
1
1
2
1
2
1
0
1
2
1
2
2
1
0
1
1
0
1
1
1
2
2
1
1
1
2
0
1
1
2
2
1
1
1
0
2
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
0
0
2
1
1
1
2
1
1
0
2
1
2
1
1
0
5
1
1
1
2
2
1
1
1
1
1
1
2
1
2
1
1
0
0
1
1
2
1
1
1
2
1
2
2
1
1
2
2
1
1
2
2
0
2
1
1
1
1
2
0
2
0
1
2
1
1
1
1
1
2
1
2
2
1
0
2
2
2
1
2
1
1
1
0
2
2
1
0
1
1
2
1
1
2
1
1
1
1
3
1
0
2
2
2
1
1
1
0
2
2
1
2
1
0
1
0
2
2
1
1
2
1
2
0
2
1
0
1
1
2
2
1
1
2
1
1
0
1
1
1
0
2
1
1
1
2
1
1
1
1
1
0
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
0
0
1
2
2
0
1
1
2
2
1
0
2
1
2
2
2
1
1
1
1
0
0
2
1
2
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
0
2
1
1
0
2
1
2
0
0
2
2
0
0
1
1
1
1
1
1
2
0
1
1
0
0
2
2
1
1
1
1
0
1
2
1
1
1
1
1
1
1
1
0
1
0
1
1
1
1
1
1
1
1
2
2
1
1
1
0
2
1
0
2
1
1
1
2
1
2
1
1
1
0
1
2
1
1
1
2
0
1
2
1
1
1
1
2
0
0
1
1
1
1
1
1
1
1
1
0
1
0
1
1
2
2
1
2
0
2
1
1
1
2
0
1
1
1
1
1
2
2
0
1
1
0
1
1
1
1
1
1
1
1
2
1
0
1
1
1
1
1
1
2
1
2
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
0
1
2
2
2
2
1
1
1
1
1
1
1
2
1
1
2
2
2
1
1
0
1
1
1
1
1
2
1
1
1
1
2
1
0
0
2
2
2
1
1
2
1
0
0
1
1
2
1
0
2
2
1
1
2
1
2
1
2
1
1
2
2
1
1
2
1
1
2
0
1
1
2
1
1
1
2
1
2
1
1
2
2
1
1
1
1
1
1
2
2
1
1
0
1
1
1
2
2
1
1
1
2
1
1
2
2
0
0
1
1
1
1
2
1
2
1
1
2
0
3
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
2
1
1
0
1
1
2
2
1
1
2
2
2
3
1
0
2
0
1
2
1
1
1
2
1
1
1
1
1
1
2
2
1
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
2
0
1
1
1
1
1
1
1
1
1
2
2
1
0
0
0
0
0
1
2
1
2
1
0
1
0
2
2
1
1
2
1
1
1
1
3
1
1
1
2
2
3
1
1
2
2
2
0
1
1
2
1
1
1
1
2
2
1
0
1
1
2
1
1
2
2
1
2
1
1
1
1
1
2
1
1
2
1
2
1
1
1
2
2
1
1
1
2
3
1
1
0
1
2
1
0
1
1
2
1
0
1
1
0
1
2
0
1
1
1
1
2
1
0
2
0
1
2
0
2
1
1
1
0
1
0
2
1
1
1
1
1
1
0
1
1
0
1
2
1
2
1
2
0
1
1
1
0
0
2
1
1
1
1
1
1
0
2
0
2
1
1
1
1
2
2
2
1
1
1
0
0
1
1
1
1
1
1
1
2
1
2
2
1
2
0
2
1
1
1
1
1
1
1
0
2
2
0
1
1
2
1
1
1
0
2
2
2
1
1
1
1
0
1
1
0
1
2
2
1
1
1
0
2
2
0
1
2
1
1
1
1
1
1
1
1
1
0
1
1
2
1
1
1
1
2
1
2
2
1
1
1
0
1
1
0
1
1
1
1
1
2
2
0
1
0
2
1
1
2
2
2
1
1
1
2
1
0
1
1
1
1
1
1
0
1
1
2
2
2
1
1
1
1
1
1
1
0
2
1
1
1
0
1
1
2
1
2
1
0
1
1
1
2
2
2
2
1
0
1
1
2
1
1
2
0
2
1
0
0
1
0
1
1
1
1
1
0
0
1
1
1
2
1
1
1
0
1
2
1
1
2
1
1
2
2
1
2
0
1
2
1
1
1
1
0
1
1
0
1
2
1
1
1
0
1
1
2
1
1
1
1
1
2
2
0
1
1
1
1
0
1
2
0
1
1
1
0
1
1
1
2
1
1
2
1
1
2
1
1
1
1
1
0
0
1
1
2
2
1
1
1
0
1
0
0
1
1
0
1
1
2
1
2
0
2
1
1
2
1
1
0
0
1
0
1
2
2
1
1
1
2
2
1
0
2
0
1
1
1
1
1
1
1
1
1
2
1
2
1
0
1
1
1
1
1
1
1
0
1
0
1
1
1
1
1
1
1
1
1
1
1
0
1
1
2
2
1
1
2
2
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
0
2
2
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
1
2
1
2
1
2
1
2
1
1
1
2
1
1
1
2
1
1
1
2
2
2
2
1
1
0
1
1
1
1
1
2
1
1
2
1
1
1
1
0
1
1
2
1
2
0
1
2
0
0
1
1
1
0
1
1
1
0
1
1
1
1
1
2
2
2
1
1
1
2
1
1
1
1
0
1
2
1
2
1
1
0
0
1
0
1
2
1
1
1
2
0
2
2
0
1
1
1
0
2
1
0
1
1
0
2
1
1
1
1
1
1
1
1
1
1
2
2
2
1
2
2
1
0
1
3
2
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
0
0
1
1
2
1
2
2
1
1
0
1
0
1
1
0
1
1
2
1
1
2
2
1
1
1
1
1
1
2
1
2
1
2
2
0
0
2
1
2
1
1
1
1
1
2
1
2
1
0
2
0
1
1
1
0
1
1
1
1
1
1
1
4
2
1
2
2
1
0
1
1
1
1
1
1
1
1
1
1
1
0
1
0
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
4
0
1
1
1
1
1
2
1
2
2
2
1
1
1
1
0
1
1
1
2
1
2
1
1
2
1
2
1
2
2
1
1
2
1
1
2
0
1
1
1
0
2
1
1
1
1
1
2
2
2
1
1
1
1
2
2
0
0
1
1
2
2
1
2
0
1
0
1
2
1
2
1
1
1
1
2
1
1
1
1
0
1
1
1
2
1
2
2
1
1
0
2
1
1
1
2
1
1
1
1
2
2
0
1
1
1
1
1
1
1
2
1
1
1
0
1
1
1
0
2
1
1
2
4
0
2
0
2
1
1
2
1
1
0
2
1
2
1
0
1
0
1
1
2
1
2
0
1
2
2
1
1
2
1
1
1
1
0
2
2
0
0
2
0
5
1
1
0
2
1
0
2
1
1
1
0
0
2
1
2
0
1
2
1
1
1
1
2
2
1
1
2
2
0
2
1
1
1
1
0
1
1
3
1
0
0
1
1
1
1
1
1
2
1
1
1
2
1
1
0
1
0
0
1
1
1
1
0
0
1
1
1
1
1
1
1
1
2
1
2
5
0
1
1
2
1
1
4
1
2
1
2
1
2
1
2
1
1
1
0
1
2
1
1
1
0
0
2
1
0
2
2
1
1
2
1
1
1
2
2
1
1
1
1
1
2
1
2
1
2
1
1
1
1
0
1
1
2
0
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
0
2
1
1
1
0
1
1
1
1
2
1
2
1
1
1
0
2
2
1
2
2
1
2
1
2
1
2
0
2
2
2
2
1
1
1
1
2
0
2
2
1
2
1
0
1
1
2
1
0
1
0
2
2
1
2
1
1
2
1
2
1
0
1
1
1
2
1
3
0
1
1
2
0
1
1
1
2
1
1
1
0
2
1
1
1
1
1
1
1
1
1
2
0
1
2
1
3
1
2
1
0
1
1
1
1
2
1
2
1
2
1
2
1
1
1
2
2
1
1
1
1
1
2
0
1
0
2
1
1
2
2
2
1
1
1
1
0
0
0
2
2
1
1
1
1
0
1
1
2
1
1
1
1
2
2
2
0
1
1
2
1
2
2
1
1
0
1
1
1
0
1
1
0
1
1
3
1
1
0
1
1
1
1
1
2
1
0
2
2
1
1
1
0
0
2
1
1
1
0
0
1
2
1
2
1
1
1
1
0
1
1
1
2
1
0
0
1
2
4
1
1
1
3
1
1
1
2
0
0
1
1
1
2
1
2
1
2
1
2
1
1
1
2
1
2
2
0
2
1
1
2
1
1
1
2
1
0
1
2
1
2
0
2
1
2
1
1
1
1
0
1
1
1
2
1
1
1
1
1
2
1
1
1
1
2
2
1
1
1
1
2
1
1
0
1
1
1
1
2
1
1
0
2
1
1
2
1
2
1
1
2
1
0
2
1
1
0
1
1
2
0
1
1
1
1
1
1
1
2
1
1
2
1
1
0
0
1
1
2
0
1
2
1
1
1
1
1
1
1
1
1
2
1
0
2
1
2
1
1
1
2
1
1
1
1
1
0
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
0
2
1
1
1
1
1
0
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
2
0
1
1
2
1
1
2
1
0
1
1
1
0
2
1
1
0
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
3
1
2
1
2
1
0
2
1
1
2
2
1
1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
2
0
2
1
1
1
2
2
2
1
2
1
2
1
0
1
1
1
2
1
0
2
1
1
2
2
1
1
2
1
2
1
2
0
2
0
1
1
0
1
1
1
1
1
0
1
2
1
1
1
2
0
2
1
1
1
1
1
1
1
1
1
1
1
0
1
1
2
2
0
2
2
1
1
1
0
0
1
0
2
1
0
1
0
2
1
0
1
2
1
1
1
1
0
1
1
1
0
1
1
0
1
1
1
1
3
2
2
1
0
1
1
1
2
0
1
1
1
1
1
1
1
1
1
0
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
0
0
2
2
0
1
2
2
1
1
1
1
1
2
0
0
1
2
2
1
0
1
2
2
2
1
1
3
1
1
1
1
1
0
1
2
2
1
1
2
1
2
1
1
1
1
0
2
0
1
2
2
1
0
5
0
1
0
1
1
2
1
2
0
1
0
0
1
2
2
0
4
1
1
2
1
1
2
1
2
2
1
0
2
1
1
1
0
0
1
2
1
1
1
2
1
0
1
1
2
0
1
1
1
1
1
2
1
1
2
1
2
1
2
1
2
1
1
0
1
2
1
1
1
2
2
0
1
2
1
1
1
1
1
4
2
0
1
0
1
2
0
0
1
1
0
2
0
1
2
2
1
1
2
2
0
2
0
1
1
1
2
1
1
1
0
1
2
2
1
2
1
1
2
1
1
1
1
2
1
0
1
1
1
1
1
2
1
3
1
2
0
2
2
0
2
2
1
0
2
2
1
0
2
1
1
2
1
0
0
0
0
1
1
2
1
1
1
2
2
1
1
1
0
0
0
1
1
1
0
0
1
1
0
1
1
1
1
1
2
2
2
1
0
2
1
2
1
1
0
2
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
1
2
0
1
1
0
1
1
1
1
1
1
0
1
2
2
2
2
1
1
2
1
1
1
1
2
1
3
2
1
0
2
1
2
2
0
2
1
1
1
1
1
2
1
1
0
1
1
1
1
1
0
1
1
1
0
1
0
2
1
1
2
2
1
1
1
2
2
0
2
1
0
2
1
1
1
1
1
2
1
2
2
0
1
1
1
1
1
2
1
0
1
0
2
1
1
0
1
1
1
1
1
1
0
1
0
0
1
2
1
1
1
2
0
1
2
1
1
1
2
1
1
1
1
0
1
2
1
0
1
1
2
2
2
1
3
1
1
1
2
2
2
2
0
2
2
2
1
1
2
0
2
2
2
3
1
1
2
1
2
1
1
2
0
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
2
0
2
2
1
1
1
1
1
0
2
2
1
2
1
0
1
1
1
2
1
1
1
2
2
0
1
1
1
1
1
1
1
2
2
1
2
2
1
1
2
1
2
0
1
2
1
1
2
1
2
1
1
0
1
0
1
0
1
0
2
2
0
1
1
1
1
1
2
2
1
1
2
1
0
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
0
1
1
1
2
1
1
0
1
1
1
2
1
1
1
1
1
0
1
1
2
0
1
1
2
0
1
2
2
2
2
1
2
2
1
1
2
1
1
2
0
1
1
1
1
0
1
1
1
2
2
1
2
2
1
1
0
1
1
1
1
2
2
2
2
2
1
0
1
0
2
0
1
1
2
1
1
1
1
2
1
1
1
2
2
1
1
1
0
1
1
1
0
0
1
0
1
1
1
1
1
2
2
2
1
1
1
0
1
1
2
0
0
2
2
1
1
1
0
0
0
1
0
2
1
1
0
2
2
2
0
1
1
1
2
1
2
1
1
2
1
1
1
1
1
0
2
0
0
1
2
2
1
0
1
1
2
1
2
1
1
1
2
1
1
1
2
1
0
1
1
1
1
1
1
1
0
2
1
1
1
1
2
0
2
0
0
2
2
1
1
1
2
2
1
1
1
2
1
2
0
1
0
1
2
0
2
1
2
1
1
2
1
1
1
0
1
0
1
0
2
2
1
1
0
0
1
1
2
1
1
1
1
1
0
1
1
2
1
1
1
2
1
2
2
1
1
1
1
1
0
1
2
1
1
1
1
2
1
1
1
1
1
2
2
0
1
2
1
1
1
1
2
0
1
1
1
1
2
2
2
2
2
1
1
1
1
1
0
1
2
1
2
1
1
0
0
1
2
1
1
2
1
0
0
0
1
1
1
1
2
1
2
0
1
1
3
0
2
0
1
1
1
1
1
2
1
1
1
2
2
0
1
1
1
1
1
1
1
2
1
1
1
1
1
0
1
0
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
2
1
1
1
2
1
0
1
2
1
1
1
2
1
0
2
1
1
1
1
0
1
2
1
1
1
0
1
0
1
0
2
1
1
0
1
1
0
1
1
1
1
2
1
1
2
2
1
1
2
1
1
1
1
1
2
0
1
0
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
0
1
1
2
0
0
0
1
2
1
1
0
1
1
0
1
1
1
2
2
1
1
1
2
2
0
2
1
1
1
2
1
1
1
1
0
1
1
1
2
2
8
2
0
1
1
1
1
2
1
1
1
1
2
2
2
2
1
1
1
2
1
2
1
2
1
2
1
2
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
2
2
2
2
1
1
1
1
1
1
0
2
1
2
1
2
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
0
1
1
0
1
2
1
1
1
2
2
1
2
2
2
0
1
1
1
1
2
2
1
1
2
2
2
1
2
1
1
2
1
2
2
1
1
0
1
2
1
1
1
1
0
1
2
1
1
1
1
1
1
1
2
2
0
1
2
1
1
1
2
1
1
1
1
1
1
1
2
2
1
2
1
1
1
1
0
1
1
1
2
0
2
0
1
1
2
1
1
3
1
1
1
1
1
2
1
1
2
2
1
0
0
2
1
0
1
2
1
1
0
1
1
2
0
2
2
2
2
1
2
1
2
0
0
1
1
1
1
1
1
1
2
1
1
1
2
2
1
2
1
1
2
1
1
1
1
2
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
0
1
2
1
1
0
1
2
2
2
1
2
1
1
1
0
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
0
0
0
1
1
0
1
2
1
2
1
1
1
2
1
2
1
1
0
1
2
2
2
2
1
2
1
1
1
0
1
0
1
1
0
1
1
1
1
1
0
1
2
1
1
2
0
1
1
2
1
1
0
2
1
1
2
1
0
1
2
1
1
1
1
1
1
0
1
0
1
2
1
1
1
2
1
1
1
0
2
1
2
2
1
0
1
2
1
1
0
2
1
1
1
1
2
2
1
2
1
1
1
1
1
1
1
0
0
0
0
2
2
1
1
2
1
2
1
1
1
2
2
2
1
1
1
0
0
1
1
1
1
1
1
1
0
2
2
1
2
1
1
2
0
1
2
1
1
2
2
1
1
2
0
2
2
2
2
1
2
2
1
2
1
0
0
2
1
1
2
1
1
1
2
1
1
2
0
2
0
1
1
1
0
1
1
1
1
2
1
1
1
1
1
2
1
2
0
1
1
1
1
1
0
1
2
2
1
2
1
1
1
1
1
1
1
0
1
2
1
1
1
1
0
1
1
1
1
1
0
1
1
2
2
1
0
2
2
1
1
1
1
1
2
0
0
0
1
1
2
1
1
1
1
2
2
1
1
0
0
1
2
1
0
0
1
1
2
1
1
2
2
1
1
2
0
1
0
1
2
1
1
2
1
0
1
1
2
2
2
1
1
1
2
1
1
1
1
1
1
2
0
1
0
2
2
2
0
1
1
1
2
1
1
1
2
3
1
1
1
0
0
2
1
2
2
1
1
0
1
1
1
2
1
1
1
2
2
1
0
1
0
1
1
1
1
0
1
1
1
1
2
1
1
1
1
1
1
1
2
0
1
1
1
0
2
2
1
1
1
1
2
0
1
1
1
0
2
2
0
0
2
0
2
1
0
1
1
1
2
2
1
1
1
2
1
0
1
1
1
1
1
1
0
1
1
2
1
1
2
0
1
1
0
1
1
1
1
2
1
2
1
1
2
1
3
0
2
3
1
1
1
2
2
0
1
0
0
1
2
1
2
1
2
0
2
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
2
2
0
1
1
1
1
2
2
1
1
1
1
1
2
1
1
1
1
1
0
1
1
1
1
2
2
1
2
0
1
0
1
1
1
1
1
0
1
1
1
2
0
1
2
1
1
1
0
1
1
1
1
2
1
1
0
1
2
2
0
1
0
2
1
1
2
1
0
1
1
2
1
2
1
2
1
0
2
1
1
2
1
0
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
1
1
2
2
1
0
2
2
1
1
2
1
1
1
2
1
2
0
0
1
1
1
2
1
1
2
1
1
1
1
0
1
1
2
0
1
2
1
0
1
1
2
1
1
1
1
1
1
1
1
1
0
1
1
2
1
1
1
2
2
1
2
1
1
1
1
1
1
2
1
1
1
0
1
1
1
0
0
2
2
1
1
1
0
1
2
1
2
2
1
1
1
0
2
2
1
1
1
0
0
1
1
1
1
1
1
1
2
0
2
1
2
1
1
2
2
0
1
2
0
2
2
1
0
2
0
1
2
2
2
0
3
1
1
0
1
1
1
1
1
2
1
1
0
1
1
2
1
1
1
1
1
1
0
1
0
1
1
0
2
1
1
0
1
0
2
1
2
2
2
1
1
2
1
2
2
1
1
2
2
1
1
0
1
0
0
1
1
1
1
1
1
0
2
1
1
1
1
1
1
1
1
1
1
1
1
0
0
2
1
1
2
1
1
1
0
1
1
1
1
2
2
0
1
1
2
1
1
2
2
1
1
1
2
2
1
1
0
0
2
2
1
1
1
1
1
1
0
1
1
1
1
1
1
2
3
1
2
1
1
3
1
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
2
1
0
1
1
1
1
0
1
1
1
2
2
2
2
1
1
1
0
1
1
1
1
1
1
1
1
0
1
2
1
0
1
0
2
1
1
1
1
1
1
1
2
1
1
0
2
2
1
2
1
0
1
1
1
2
1
1
0
1
0
2
1
2
3
2
1
1
1
1
1
0
0
1
1
1
1
2
1
1
1
2
1
2
0
2
1
1
2
0
2
1
1
1
2
2
2
2
2
2
1
2
1
1
1
1
1
1
1
1
1
1
1
0
2
0
1
1
2
1
0
1
2
2
1
1
2
1
1
1
1
2
0
0
1
1
1
1
2
1
2
1
1
1
0
1
1
0
1
2
1
0
1
1
1
1
2
1
2
1
1
2
1
1
2
2
1
0
1
1
5
2
1
1
2
1
2
1
1
1
0
0
1
0
1
1
2
1
1
1
2
1
0
0
2
1
1
2
1
2
1
1
1
1
1
1
2
1
1
2
1
1
2
0
2
0
1
1
2
2
1
2
1
1
0
1
1
2
1
1
1
1
1
2
0
1
1
0
1
0
2
2
1
2
1
1
1
1
2
1
1
0
1
1
1
1
1
0
1
1
1
2
0
1
2
0
0
1
0
2
1
1
1
2
2
0
0
2
2
0
1
2
2
1
1
0
1
2
2
0
0
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
0
1
1
1
0
1
1
1
1
1
0
1
2
0
1
2
1
0
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
0
0
2
1
1
1
1
1
1
1
0
2
1
1
0
1
1
2
1
1
0
1
0
1
2
2
0
1
2
3
1
1
1
1
1
1
0
1
1
0
1
1
2
1
4
2
1
1
1
1
2
1
0
1
1
1
0
1
2
0
1
1
0
2
1
0
1
1
0
2
0
0
1
0
1
1
1
1
1
2
0
0
0
0
2
0
2
0
1
1
1
2
1
0
1
1
1
1
1
1
1
1
1
0
2
2
2
2
1
0
0
1
2
2
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
2
0
0
1
1
1
2
2
1
0
1
1
2
2
1
1
1
1
1
2
1
1
1
2
0
1
2
1
1
3
1
1
0
1
2
1
1
0
0
1
1
1
1
0
1
1
2
1
0
1
0
1
1
2
2
1
1
2
2
1
1
2
1
0
1
1
1
1
1
1
2
1
0
2
2
1
1
1
1
2
2
0
0
1
1
0
3
1
1
1
0
1
1
2
1
1
0
1
0
2
1
2
1
1
0
1
1
1
2
1
2
0
1
1
2
0
2
1
1
1
1
1
0
1
2
1
2
1
1
1
0
0
2
1
0
1
1
0
1
1
1
1
0
0
1
2
1
2
2
1
3
1
1
1
1
0
1
1
1
0
2
1
2
2
2
1
1
1
1
1
0
2
0
2
0
0
2
1
1
1
1
2
2
1
2
1
1
1
1
1
1
1
2
1
1
1
0
1
1
1
1
0
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
0
1
0
0
0
2
1
1
1
1
1
1
1
2
1
1
1
1
0
1
1
2
1
1
1
0
2
2
1
1
2
2
2
0
0
2
1
1
1
2
2
1
1
1
0
1
1
0
2
2
2
1
1
0
2
2
1
2
0
3
0
2
2
2
1
0
0
1
1
1
1
1
0
0
1
1
1
1
2
1
1
2
1
0
1
1
1
1
2
1
1
1
2
2
1
2
1
0
1
1
1
2
1
2
0
1
2
1
2
1
2
1
1
2
0
1
1
1
1
2
1
1
2
1
1
1
2
1
2
2
1
1
2
1
1
0
1
1
1
1
1
0
2
2
1
2
0
0
1
1
1
0
1
0
2
1
0
2
1
1
1
2
2
1
0
2
1
1
1
0
2
1
1
1
0
0
2
0
1
2
2
1
1
1
1
2
1
1
0
2
1
1
2
0
0
2
1
1
2
1
2
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
1
1
2
1
3
0
1
0
2
2
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
2
1
1
2
2
1
1
1
0
1
1
1
1
1
2
2
1
1
0
1
2
1
1
1
0
0
0
1
1
2
0
0
3
1
1
2
1
2
2
1
1
2
0
1
1
0
1
0
1
5
1
0
1
1
1
1
1
1
1
1
1
2
0
1
1
1
1
1
1
0
1
1
0
0
1
2
2
1
2
1
1
1
1
4
1
1
1
1
2
1
1
1
1
1
0
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
0
3
1
1
1
0
1
2
2
1
1
2
2
1
1
1
1
2
0
1
2
1
3
2
1
1
1
1
1
1
1
1
1
2
2
2
2
2
1
1
1
0
0
2
0
1
0
1
2
1
1
1
0
1
2
1
0
1
1
0
1
2
1
1
1
2
0
1
2
1
1
1
1
1
1
1
1
2
1
2
1
1
2
1
2
1
1
1
1
3
1
1
2
8
1
2
1
2
1
1
1
2
2
1
2
1
2
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
0
2
2
2
1
2
2
1
2
2
1
1
1
2
1
2
2
1
1
2
3
1
2
1
2
1
0
2
2
2
0
0
0
1
1
1
1
0
1
1
1
2
1
1
2
2
2
0
1
2
2
1
2
1
2
2
1
1
1
1
1
0
0
1
1
1
2
1
1
2
1
1
1
0
1
1
1
1
1
1
2
2
2
1
2
1
0
1
1
2
1
1
2
2
1
1
2
1
2
1
2
0
1
1
1
0
2
1
1
0
1
2
1
2
1
1
2
2
1
0
2
1
1
2
1
0
2
1
0
1
2
2
2
1
1
1
1
0
1
1
1
1
0
2
1
1
1
1
2
2
1
1
1
1
0
1
2
2
2
1
2
2
1
1
1
1
1
1
0
2
1
0
0
0
1
1
1
2
1
1
2
1
2
1
1
1
1
1
2
2
1
2
0
2
1
1
1
2
0
1
1
0
0
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
2
1
1
1
1
1
1
1
0
0
1
1
1
2
0
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
2
4
1
1
1
1
2
1
1
0
1
1
1
1
1
1
2
2
1
1
2
0
1
2
1
1
1
1
0
2
1
1
2
2
1
2
1
1
1
2
2
1
1
1
1
2
1
1
0
1
1
1
1
1
2
0
2
2
0
1
2
1
1
1
1
1
2
1
1
1
2
1
1
2
0
1
1
0
1
1
1
1
2
1
1
1
0
1
2
1
0
1
1
1
1
1
1
1
0
0
1
1
1
1
1
2
1
1
1
2
1
2
1
1
0
1
1
1
2
1
1
1
2
2
1
1
2
2
4
0
1
1
1
1
2
1
1
1
1
1
2
2
1
2
1
2
1
2
1
1
1
1
1
0
1
1
2
1
1
2
1
1
1
1
1
2
0
1
1
1
0
2
2
1
1
1
2
2
1
1
2
1
1
2
1
1
2
1
1
2
1
1
2
1
2
1
1
2
1
1
1
3
1
1
2
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
5
1
1
1
1
1
1
1
1
1
1
1
1
0
1
0
2
1
1
1
1
1
0
1
2
1
1
1
1
2
1
1
0
0
1
3
1
1
2
1
2
1
1
1
1
2
2
1
2
0
1
2
1
1
3
1
2
1
1
1
1
0
1
1
2
2
0
0
1
0
1
1
1
2
2
2
1
2
3
1
1
2
1
0
1
1
0
1
1
1
2
1
0
2
1
1
2
1
2
1
1
1
0
2
2
1
1
1
1
1
1
1
2
1
1
1
0
2
1
0
1
2
1
2
0
2
1
2
1
1
2
1
1
1
2
1
4
2
1
0
1
2
1
2
2
2
2
1
1
1
1
1
1
1
2
1
2
1
0
1
1
1
1
1
2
2
1
1
2
1
0
0
1
2
1
1
1
2
2
2
2
1
1
1
2
2
1
2
0
0
1
0
1
2
1
1
0
2
1
0
1
1
1
0
2
2
1
1
2
1
1
1
1
2
1
3
1
1
2
1
1
2
1
1
1
1
2
1
1
1
1
0
1
0
1
0
1
2
2
2
1
1
2
2
1
1
1
1
1
0
2
1
1
2
1
2
1
1
1
1
1
0
1
2
2
1
1
1
1
1
1
0
2
2
1
1
1
2
1
1
2
1
1
1
0
1
1
1
2
1
1
1
1
3
2
2
0
1
2
2
2
0
2
2
2
2
1
1
1
2
1
1
1
1
1
1
0
2
1
1
1
1
1
0
0
0
2
1
1
1
2
0
1
1
1
1
0
1
0
1
2
1
1
1
0
2
2
1
0
2
1
2
1
2
1
1
1
0
1
1
2
0
1
1
1
1
1
1
1
1
1
1
2
1
2
2
2
1
0
1
0
1
1
2
0
1
2
2
2
1
1
1
0
1
1
0
1
1
1
1
2
1
1
2
1
2
1
1
1
0
1
1
0
1
1
2
2
1
0
1
2
2
1
1
1
2
2
1
1
2
0
1
2
1
1
0
1
1
1
1
2
1
1
1
1
2
0
1
1
1
1
2
1
1
1
2
1
1
1
0
1
0
2
1
1
1
1
1
1
1
2
1
1
2
1
1
2
1
1
2
2
1
1
0
1
0
1
1
2
2
1
0
2
1
2
1
1
1
1
0
1
1
1
1
1
2
0
1
1
0
1
0
2
2
2
1
0
1
1
1
0
2
0
2
0
1
1
1
1
1
1
1
1
1
2
0
0
0
1
0
2
1
0
1
2
1
2
2
1
2
2
2
1
1
1
1
2
1
1
1
2
2
1
1
0
1
2
1
1
2
0
2
1
2
2
0
2
1
1
1
1
2
0
2
3
1
1
1
0
2
2
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
2
1
0
0
2
2
1
1
1
2
2
1
1
0
2
1
1
1
0
2
1
1
2
2
2
2
2
0
2
1
2
1
2
2
1
1
2
1
1
1
1
2
1
2
1
1
0
0
1
1
1
2
1
2
1
3
2
2
2
2
2
1
2
1
2
1
1
1
2
1
2
0
0
1
0
1
0
1
1
2
1
1
1
1
2
1
2
2
2
0
1
1
0
0
1
1
2
1
1
1
1
1
1
1
2
2
1
0
2
1
1
1
1
2
2
1
1
1
1
1
1
1
1
3
1
0
2
2
0
1
1
1
1
2
1
1
1
1
1
0
1
1
1
1
2
1
2
1
2
1
2
0
1
1
1
1
2
4
1
0
1
1
1
2
1
1
1
0
1
1
1
2
2
1
0
1
1
2
1
2
1
1
0
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
0
1
2
1
2
0
2
0
1
2
2
2
2
1
1
1
1
1
1
1
0
0
2
2
2
1
1
1
2
1
2
1
1
2
0
1
0
2
2
1
1
1
1
0
0
1
1
1
1
2
1
1
2
0
2
1
1
1
2
1
1
2
0
1
1
1
1
1
1
1
2
1
0
1
0
1
1
1
2
2
2
2
1
1
0
0
1
1
1
1
1
0
0
0
0
1
2
1
2
1
2
1
0
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
0
1
1
1
1
1
1
1
1
2
0
1
0
0
1
2
1
1
1
1
2
2
2
1
1
1
2
1
2
2
1
1
1
1
0
1
2
2
1
1
1
2
1
1
1
0
1
2
1
1
0
2
2
1
1
0
1
1
1
1
1
2
1
1
2
1
1
1
2
0
0
2
2
1
1
1
1
1
1
2
1
2
1
1
0
0
2
2
3
2
1
1
2
1
1
2
0
2
1
1
1
1
1
2
1
2
0
1
1
2
1
0
1
2
1
1
1
0
1
0
2
1
1
0
2
2
1
1
1
2
1
2
1
2
1
1
2
0
1
0
2
1
0
2
2
1
2
1
1
1
1
1
2
2
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
1
2
2
1
1
3
1
0
1
2
2
1
0
1
2
2
1
2
1
0
2
0
1
2
1
0
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
0
1
2
1
2
0
1
1
2
1
2
1
1
2
0
2
1
0
0
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
0
1
1
1
2
1
1
1
2
1
1
1
2
1
2
2
2
1
0
2
1
1
1
2
0
2
0
1
2
4
0
3
1
1
1
1
0
2
1
1
2
2
0
2
1
2
2
2
2
2
1
0
1
0
2
0
1
2
1
1
1
2
1
1
2
0
1
1
3
2
1
1
0
1
2
1
1
1
2
1
1
1
2
1
0
1
1
2
1
1
2
2
2
2
1
0
1
1
1
1
2
1
3
3
1
2
1
0
0
0
1
1
1
1
1
2
0
1
1
1
1
2
1
1
2
0
0
3
1
1
1
1
1
0
2
2
2
2
1
1
1
2
1
2
2
1
2
1
2
1
2
1
2
0
2
0
1
2
1
1
1
1
1
2
1
1
1
1
1
2
2
1
0
1
1
1
1
1
0
1
2
2
2
1
2
1
2
1
1
1
1
0
1
1
1
2
1
2
2
1
0
1
1
0
0
1
1
1
1
2
1
2
2
1
1
1
1
2
1
2
1
0
1
1
2
1
1
1
2
1
1
2
2
2
2
1
1
2
0
1
0
1
1
1
2
1
1
2
1
2
2
2
1
1
0
2
0
1
0
1
2
1
2
0
1
2
1
1
1
2
1
2
1
1
2
2
1
1
1
2
2
1
2
1
1
0
2
1
1
2
1
2
2
2
1
1
1
0
1
2
2
1
2
2
1
1
1
1
0
1
2
1
2
0
2
1
1
1
1
2
2
2
1
1
2
1
0
2
1
1
1
1
1
1
1
0
2
2
1
1
2
1
1
2
1
2
1
1
1
0
0
1
2
1
1
1
1
0
1
3
2
2
1
2
1
2
1
2
1
1
2
1
0
0
0
2
0
1
1
1
2
2
1
2
1
2
0
2
1
0
1
1
2
1
0
1
0
1
2
2
1
0
1
1
2
1
0
0
1
0
2
1
2
0
1
1
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
2
0
1
2
1
1
1
1
1
0
0
2
1
2
1
2
1
1
1
1
1
2
1
1
1
1
0
1
2
1
0
1
0
0
1
0
1
4
1
1
1
1
1
0
2
1
2
1
0
1
0
2
1
1
2
1
1
0
1
1
1
1
2
1
2
1
1
1
1
2
1
2
1
2
2
1
1
1
1
2
1
1
0
1
0
0
2
2
2
2
1
1
1
2
0
2
1
2
1
1
1
2
1
1
1
2
0
2
1
2
0
0
0
2
1
1
1
1
2
2
1
1
2
1
1
1
1
1
1
0
2
1
1
2
1
2
2
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
0
1
1
1
1
2
2
1
1
1
2
0
2
1
1
1
1
1
1
0
1
2
2
0
0
1
1
1
1
1
1
0
2
1
1
1
1
0
1
2
2
1
1
1
1
1
1
1
0
1
1
2
1
1
1
3
2
1
1
0
1
1
1
1
1
1
2
2
1
1
2
1
2
1
1
1
1
1
1
0
1
0
0
1
1
1
1
1
2
1
1
1
2
1
0
2
2
0
2
1
1
2
1
2
0
0
1
1
2
1
1
1
1
1
1
1
2
2
2
1
2
2
2
2
1
1
1
1
2
0
2
0
2
2
0
1
1
1
2
1
0
1
1
1
1
1
2
1
1
1
1
0
1
2
0
1
1
2
1
2
0
1
1
1
1
1
1
2
1
0
1
2
0
0
1
1
1
1
1
0
2
1
2
2
1
1
1
1
2
1
2
0
1
2
1
1
2
0
2
1
1
2
1
1
0
2
1
1
1
1
1
0
1
1
1
0
1
2
1
2
1
2
1
0
1
2
2
1
1
2
1
1
1
2
1
2
1
1
1
1
2
2
1
1
1
1
1
1
1
1
2
1
1
0
3
1
0
1
1
0
1
1
2
1
1
1
1
1
2
2
1
1
2
2
0
1
0
1
2
1
0
0
1
1
2
1
0
2
2
1
2
1
0
1
2
0
2
1
1
1
1
1
1
1
1
2
1
0
1
1
2
0
1
2
1
2
2
2
1
2
1
1
1
2
1
1
1
1
1
1
2
1
0
2
2
2
0
2
1
2
2
0
2
2
1
2
1
0
1
1
1
1
1
0
1
0
1
2
1
0
0
0
1
2
1
0
2
1
2
2
2
1
2
2
2
1
1
1
1
0
2
1
1
2
1
1
1
1
1
2
1
2
2
1
1
1
1
2
0
0
1
1
1
1
2
2
1
1
1
1
2
1
1
2
1
2
2
1
2
1
1
2
1
1
1
1
1
2
0
1
2
1
0
1
1
1
1
0
2
1
1
2
1
1
1
1
2
1
1
1
1
1
1
2
0
1
1
1
1
1
1
1
2
0
1
0
1
1
0
2
2
2
1
2
1
1
2
1
2
1
2
0
0
2
2
1
1
1
1
2
1
2
1
2
2
1
2
1
1
1
1
1
1
1
1
1
1
1
0
1
1
2
1
1
2
0
2
2
1
1
1
1
1
1
1
1
1
1
1
1
0
2
0
1
1
1
0
2
2
0
1
1
1
2
1
1
1
1
1
2
1
1
2
1
1
2
2
1
0
1
1
1
2
1
1
1
0
1
1
1
1
1
1
1
1
1
1
2
2
0
1
1
1
1
1
1
1
0
2
2
2
1
1
1
1
1
1
2
0
1
2
2
1
1
1
1
1
2
0
1
2
1
1
2
1
0
2
1
1
1
0
1
1
1
1
1
1
0
0
2
1
1
1
1
1
1
0
1
1
1
2
2
1
0
2
2
1
1
2
0
0
2
0
1
1
0
1
1
1
1
1
1
3
2
1
2
2
1
1
1
0
1
2
2
1
0
3
1
2
1
0
0
1
2
0
0
2
2
1
1
1
2
1
1
2
0
2
2
0
1
1
1
0
1
2
1
1
2
2
2
0
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
0
1
1
1
2
2
2
1
1
1
1
1
3
1
1
1
2
2
1
1
2
1
1
1
0
1
1
1
2
2
1
1
2
0
1
1
1
1
1
1
1
2
1
0
1
1
0
1
2
2
1
0
2
1
1
1
2
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
2
1
1
2
2
0
1
1
1
1
0
0
1
0
1
4
1
1
1
1
1
1
1
1
1
2
1
1
2
2
1
2
1
1
0
2
0
2
2
0
2
1
1
1
1
1
1
2
1
0
1
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
2
0
2
1
1
2
0
1
0
0
2
1
1
1
1
1
0
2
0
2
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
0
1
2
2
1
1
1
1
2
1
2
2
1
1
2
1
1
0
1
1
2
1
1
1
2
1
0
1
1
1
1
1
2
2
1
1
0
2
1
1
1
0
1
2
1
1
2
2
2
2
2
2
1
1
2
1
0
2
1
1
1
0
1
1
1
2
1
1
2
2
1
0
1
2
1
1
2
1
1
1
1
1
0
0
1
1
1
1
0
1
1
1
1
1
2
1
1
1
1
2
1
2
0
1
1
1
0
2
1
0
0
1
2
2
2
1
1
1
2
2
1
1
1
1
1
1
2
0
1
1
1
1
1
1
0
1
1
1
2
1
2
1
2
2
1
0
2
1
1
2
1
0
1
1
1
1
2
1
0
1
2
1
1
0
2
1
1
2
1
1
1
1
1
2
2
0
2
2
1
1
1
0
4
2
1
1
1
2
1
2
1
2
0
2
0
1
1
1
1
1
1
3
2
0
1
1
1
2
2
0
2
1
0
0
1
1
2
2
2
2
1
2
1
0
2
1
2
1
2
1
1
1
1
1
2
1
2
1
2
0
1
1
1
1
1
1
2
1
1
1
1
1
1
0
0
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
2
0
1
1
1
1
1
0
1
1
1
2
1
1
2
1
0
2
1
1
1
1
1
0
0
1
0
2
0
2
1
1
1
1
1
0
2
1
0
0
1
1
2
1
1
1
1
3
3
2
1
1
1
1
2
1
2
2
2
2
2
1
2
1
1
1
1
2
1
2
0
0
1
1
1
1
0
1
2
1
2
1
1
1
1
2
1
0
0
1
1
1
2
1
1
1
1
1
1
2
2
1
1
2
1
1
2
2
1
1
1
1
1
0
1
1
0
1
2
1
1
1
1
1
1
1
0
1
1
1
1
0
1
1
1
1
1
2
2
0
0
1
1
2
1
0
1
2
1
1
2
1
2
1
0
1
1
1
1
1
1
1
0
2
1
1
0
1
1
1
1
1
1
1
2
0
1
1
2
1
0
1
1
2
2
1
2
2
1
0
1
1
2
2
1
1
1
1
1
1
0
1
0
2
1
0
2
2
1
1
1
1
2
2
2
2
0
1
2
1
1
1
1
1
1
1
2
1
1
1
0
1
2
2
1
2
1
2
1
2
1
1
0
1
1
1
1
2
1
1
2
2
1
2
1
1
0
1
2
0
1
1
1
1
1
1
1
1
1
1
1
1
0
2
2
2
1
2
1
1
2
1
1
1
1
0
2
1
2
1
1
1
1
2
1
0
1
1
1
0
2
1
1
2
1
1
1
0
1
1
1
1
1
1
0
1
1
2
0
1
1
2
2
1
1
1
1
1
1
1
0
0
1
2
1
1
2
1
1
2
1
1
1
1
0
1
1
1
1
1
1
2
2
2
1
2
1
1
1
1
1
2
1
2
2
1
1
2
2
1
2
1
1
2
1
1
1
1
2
1
0
1
1
0
1
2
0
0
1
1
1
1
0
1
1
2
1
1
1
0
1
1
1
0
1
1
1
1
1
1
1
1
1
2
1
1
0
1
2
1
1
1
1
0
1
2
1
1
1
0
1
1
1
2
1
1
2
1
2
1
1
0
1
1
1
1
1
1
1
2
2
1
2
1
1
0
0
2
2
0
1
1
1
1
2
2
0
1
1
0
2
1
1
3
2
1
2
1
1
1
1
0
1
2
2
0
1
1
1
0
2
1
0
1
1
2
1
1
1
1
1
0
1
2
1
1
1
2
1
1
1
0
1
1
2
1
1
1
1
2
2
3
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
0
2
1
1
1
2
1
1
1
1
1
2
1
1
1
1
2
2
1
1
1
0
2
1
1
0
0
2
1
2
1
1
1
2
1
2
1
1
0
2
1
0
1
1
0
1
2
1
0
2
1
1
1
2
1
1
1
2
1
0
2
1
1
1
1
1
2
2
1
1
1
0
0
1
1
1
1
2
1
0
1
0
1
1
2
1
1
2
1
0
2
2
2
1
1
1
1
1
0
1
1
1
0
2
1
1
1
1
1
1
1
1
0
1
2
0
1
1
1
0
1
2
1
1
1
1
1
1
1
1
0
1
2
1
1
1
1
1
2
1
0
1
1
1
2
2
1
1
1
1
2
2
1
2
1
1
1
1
0
2
1
2
1
1
1
2
1
0
0
1
1
1
2
1
1
0
2
1
0
1
1
0
1
0
2
2
2
0
1
1
0
0
1
1
0
1
2
1
0
3
1
1
0
2
0
1
1
1
2
2
2
1
2
1
0
2
1
2
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
0
1
1
1
2
0
1
1
0
1
1
2
1
1
2
1
1
1
1
0
1
1
2
1
0
1
1
2
1
1
1
1
1
0
1
1
1
1
1
2
1
1
1
0
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
2
1
0
1
1
0
0
2
1
1
1
1
2
1
1
1
1
1
1
0
1
1
0
1
1
1
1
1
2
1
1
1
1
2
1
1
0
2
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
2
0
1
2
2
2
1
1
1
0
1
2
1
0
2
1
1
0
1
1
1
1
1
1
2
1
2
2
1
2
1
2
1
0
1
1
1
2
2
1
1
1
2
1
2
1
0
1
2
2
2
1
2
1
1
1
2
2
1
1
0
1
1
1
1
1
0
1
1
2
1
0
1
0
1
1
1
1
1
1
1
1
1
0
1
0
0
1
2
0
1
1
1
1
1
1
2
2
0
1
1
1
2
3
2
1
1
1
1
0
0
2
1
1
0
2
1
2
1
0
1
1
0
1
1
1
0
1
2
1
2
1
2
1
1
1
1
2
2
2
0
1
1
1
2
0
2
2
1
0
1
0
2
2
1
2
2
1
2
1
1
2
2
1
2
1
2
1
0
1
1
1
2
1
1
2
2
1
2
1
1
1
1
2
1
1
1
1
3
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
2
2
1
1
0
1
2
0
6
0
1
1
2
1
0
2
0
1
2
2
2
1
1
1
0
1
2
2
2
1
1
1
2
1
2
1
0
0
0
0
1
1
1
2
2
1
0
2
1
1
2
1
2
2
1
1
1
2
1
1
0
1
1
1
1
1
2
1
1
1
0
0
0
1
0
2
2
1
0
0
1
1
3
0
1
1
1
2
0
2
1
1
0
1
1
1
1
0
1
0
2
0
2
0
1
1
2
1
1
2
0
1
1
2
2
1
1
1
1
2
1
1
1
2
1
2
0
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
2
2
2
1
2
2
2
1
1
2
1
2
1
0
0
0
1
0
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
2
1
1
1
1
1
2
1
1
0
1
1
1
0
1
1
1
1
1
2
1
1
1
1
0
1
1
1
1
1
1
2
1
1
1
2
1
2
1
0
2
1
2
2
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
0
2
1
2
2
1
1
1
2
0
1
2
1
1
2
1
1
1
2
2
1
1
0
0
1
0
2
2
0
1
1
1
1
0
1
0
0
2
2
1
0
1
2
2
0
0
1
1
1
1
2
1
1
1
0
1
1
0
1
1
1
3
1
1
1
1
1
1
2
1
1
1
3
2
1
1
1
1
1
1
0
2
0
0
2
2
1
2
0
1
1
1
1
2
0
1
1
1
1
2
1
1
2
1
1
2
1
2
1
2
0
1
1
1
1
0
1
1
0
2
1
1
2
2
1
1
2
1
1
1
1
2
0
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
2
0
0
1
1
1
1
1
2
1
2
1
1
1
2
0
1
1
0
3
1
1
1
2
2
1
1
1
1
1
2
1
1
2
2
1
2
0
1
1
2
0
1
1
1
0
2
1
1
0
1
1
1
1
1
1
1
2
1
1
0
2
1
2
2
2
1
2
1
2
1
1
1
1
0
1
1
1
1
0
1
1
1
1
0
1
1
1
1
1
0
1
1
1
2
2
1
2
1
2
1
0
1
1
1
1
1
0
1
1
2
2
1
1
1
2
2
1
1
1
1
1
10
1
0
2
1
0
1
1
2
1
2
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
2
1
1
2
1
2
2
1
1
0
0
2
1
1
1
1
2
1
1
1
1
0
1
1
1
1
2
1
1
2
1
1
1
2
1
1
1
2
1
2
1
2
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
2
2
0
1
0
1
1
1
2
1
1
1
0
1
2
2
1
1
2
2
1
2
1
0
1
2
1
0
0
1
1
0
0
1
1
1
2
1
2
2
1
2
3
2
1
1
1
0
2
2
1
1
2
2
1
1
0
1
1
2
2
0
0
1
1
0
0
1
1
3
1
2
2
2
1
1
1
1
1
1
2
0
2
2
1
1
2
2
1
1
2
1
1
0
1
1
2
1
1
0
1
1
2
2
0
1
1
1
1
1
1
2
1
1
2
1
2
1
2
2
0
2
1
1
1
0
1
1
1
1
2
2
2
1
1
1
1
2
1
0
1
1
0
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
2
0
2
2
1
1
1
1
0
0
2
1
0
1
2
1
2
1
1
1
2
1
1
1
2
1
1
1
1
1
2
2
1
1
2
1
1
2
1
0
2
1
1
1
1
2
2
1
1
2
0
1
1
0
2
0
1
1
0
1
2
1
0
0
2
2
2
2
0
0
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
0
1
1
2
0
0
1
1
1
2
0
1
0
1
2
2
1
0
2
1
1
1
1
0
1
1
1
2
1
1
1
1
2
1
1
2
0
2
1
1
1
1
1
1
2
2
1
2
2
2
2
1
0
1
1
1
2
1
1
2
1
2
2
1
1
1
1
1
1
2
2
2
1
2
0
1
1
1
1
1
1
0
2
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
2
1
1
1
1
2
0
1
2
1
1
1
0
2
1
1
1
1
1
1
1
1
1
1
0
2
1
4
2
0
1
1
1
1
1
1
0
1
1
0
1
1
1
1
1
1
1
0
0
0
2
1
2
1
2
1
0
1
1
1
1
1
1
1
2
2
2
0
1
1
1
2
1
1
2
2
3
2
1
0
1
2
2
1
1
1
0
0
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
2
0
1
1
2
1
2
1
1
1
1
1
0
1
2
1
2
1
1
1
1
2
1
2
0
1
0
1
2
2
0
0
0
2
1
0
0
1
1
2
1
1
2
1
1
0
1
1
2
1
0
1
1
1
0
1
1
2
1
2
1
1
1
1
1
1
2
2
2
2
1
1
1
2
1
1
1
1
1
1
1
1
1
2
0
2
1
2
1
1
1
0
1
1
1
1
1
2
2
1
1
2
1
1
1
2
0
1
1
4
1
0
1
1
1
0
1
2
1
0
1
1
1
0
1
1
1
1
0
2
1
1
1
2
1
1
2
2
1
1
0
1
1
1
1
1
1
1
1
1
1
1
2
0
1
1
0
1
2
1
1
0
2
1
1
1
1
2
0
1
1
2
1
1
1
1
0
3
1
1
0
1
2
2
0
0
1
0
1
1
0
2
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
3
2
1
0
1
3
2
1
1
1
1
2
2
1
1
2
1
2
2
1
2
1
1
1
2
1
2
1
1
1
1
2
2
1
1
2
0
2
2
1
1
1
1
1
1
2
0
2
1
1
1
0
0
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
1
1
2
0
1
1
2
0
1
0
2
1
1
1
2
1
1
2
2
1
1
1
2
1
0
1
1
1
2
1
1
2
1
1
1
1
0
1
2
1
0
0
1
0
2
1
2
1
2
1
1
2
1
1
0
2
0
1
2
1
1
1
2
1
1
2
1
2
1
1
1
1
2
2
1
0
0
1
1
1
0
1
1
2
1
1
2
2
1
1
2
1
1
1
1
1
2
1
0
1
1
1
1
2
1
1
1
2
0
1
1
1
0
1
1
1
0
1
0
0
2
1
1
1
1
1
2
0
1
2
2
1
0
1
2
1
1
1
1
2
1
2
2
1
1
1
2
2
1
1
1
1
0
1
1
1
1
1
0
1
2
1
2
1
1
1
1
1
3
2
1
1
1
2
1
1
1
2
0
1
0
1
2
2
1
1
2
1
1
1
1
1
2
2
2
1
1
1
0
1
1
2
0
1
1
2
2
1
1
1
1
2
1
1
0
1
1
1
1
0
1
0
1
1
1
1
1
2
1
1
1
1
1
1
2
1
2
2
2
1
1
1
1
0
2
2
1
2
1
0
2
1
2
0
1
1
1
0
1
0
1
1
2
1
1
0
1
1
2
1
0
1
1
2
1
1
2
1
0
1
1
2
1
1
1
1
1
2
1
2
1
2
1
1
1
1
1
1
2
1
2
2
1
2
0
1
0
1
1
1
1
2
1
2
2
2
1
1
2
1
2
1
2
1
1
1
1
1
1
2
2
2
1
0
2
1
1
1
2
0
2
1
3
2
0
1
1
2
2
1
0
0
2
1
1
0
2
0
2
1
1
0
1
1
1
2
1
1
0
1
1
1
1
2
2
1
2
1
1
1
1
2
0
2
1
1
2
1
2
1
2
2
0
1
0
1
2
1
2
1
1
1
2
1
3
1
1
1
1
1
0
1
2
2
1
1
2
1
1
0
1
1
1
1
1
1
0
1
0
1
1
1
0
2
1
2
1
1
1
1
1
1
0
1
1
1
1
2
1
1
1
1
2
2
1
1
1
2
1
1
2
1
1
1
1
0
2
1
1
1
0
4
2
1
1
2
1
2
1
2
2
2
1
1
1
1
2
1
2
2
0
1
1
1
2
2
0
1
0
2
2
1
1
1
2
0
2
1
1
2
1
1
1
1
1
0
1
1
2
2
1
1
1
1
2
1
0
1
1
1
1
1
2
1
2
2
1
0
2
1
1
1
1
1
1
1
0
1
1
2
1
1
1
1
2
0
1
1
2
1
1
1
1
2
1
1
1
2
1
2
2
2
1
1
2
1
2
2
1
0
1
0
0
1
0
1
1
0
2
1
2
0
0
1
0
1
1
2
2
1
0
1
1
1
2
1
1
1
1
1
0
2
2
1
0
2
1
1
1
0
1
0
1
2
0
1
2
1
2
2
1
2
1
1
2
2
1
2
0
1
1
2
1
1
1
2
2
0
1
1
1
2
2
2
2
1
1
2
1
1
1
0
1
2
2
1
0
1
2
1
1
2
1
1
2
1
1
0
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
2
0
1
1
1
1
1
2
0
0
1
0
2
1
1
1
1
1
0
1
2
1
1
1
1
1
1
1
1
2
2
1
1
1
1
2
1
1
1
2
2
0
1
2
1
1
0
2
2
1
1
1
2
2
1
1
1
3
1
2
1
0
1
2
1
0
1
0
0
1
1
1
2
2
2
0
1
1
2
2
2
2
1
1
1
1
1
1
2
2
0
1
1
2
1
2
1
1
2
1
0
1
1
1
1
1
1
2
1
2
0
2
1
1
1
1
1
1
0
3
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
2
2
1
1
0
1
0
2
1
1
1
1
1
0
2
2
1
1
0
1
1
1
1
2
2
0
1
2
2
0
1
1
2
2
1
2
0
1
2
0
1
2
1
2
1
2
1
1
2
1
0
1
1
2
2
2
1
1
1
0
0
1
2
0
1
1
1
4
2
2
1
0
1
0
2
1
1
1
0
1
1
1
2
0
2
2
1
2
1
2
1
1
3
1
1
1
1
1
0
2
1
0
0
2
2
2
1
2
2
2
1
1
2
2
2
1
0
1
1
2
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
0
1
0
1
2
2
2
1
1
1
2
1
1
1
1
2
1
1
2
2
2
1
1
1
1
1
1
0
1
1
2
1
1
0
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
0
1
2
1
1
1
1
2
1
1
0
0
2
1
1
1
1
1
1
1
1
2
1
2
2
1
0
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
2
2
1
1
1
1
2
3
1
1
1
1
1
0
1
2
2
1
2
2
0
1
2
2
1
0
1
1
1
1
0
2
2
1
1
0
1
2
2
0
1
1
2
1
1
0
1
0
2
0
1
0
1
1
1
0
0
1
0
0
1
1
1
1
0
1
0
2
2
1
2
1
2
1
1
1
1
1
1
0
1
1
2
1
1
1
2
1
1
2
1
1
0
0
0
0
1
2
1
2
1
1
1
0
2
1
1
1
1
2
1
1
1
1
1
1
1
1
2
0
0
2
2
2
0
1
2
2
1
1
1
1
1
0
1
1
1
1
1
1
2
1
1
2
2
1
2
1
1
1
1
1
0
2
1
2
0
1
2
1
2
0
1
1
1
1
0
0
0
2
2
2
1
0
0
1
1
2
1
0
0
0
0
2
2
1
1
1
2
1
2
1
2
2
0
1
0
0
2
1
1
1
1
1
2
0
1
2
1
2
2
1
1
1
1
2
1
1
1
1
1
2
2
1
1
0
1
1
2
1
1
1
1
1
0
1
2
1
1
1
2
1
2
1
1
2
1
1
2
1
1
1
2
1
0
1
1
0
1
1
2
1
1
1
2
1
2
1
2
2
2
1
1
1
2
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
2
2
1
2
2
1
0
1
1
1
1
1
0
1
1
0
1
1
1
2
1
0
2
1
2
2
1
2
2
1
1
2
0
1
1
1
2
1
1
0
1
1
1
2
1
2
1
1
0
1
1
0
2
2
0
1
2
1
0
2
2
2
2
1
1
1
2
1
1
2
2
1
1
2
1
2
1
1
1
2
1
2
1
2
2
2
1
2
0
1
1
2
1
2
1
1
0
2
1
1
2
1
1
1
1
1
1
1
2
1
2
1
2
2
1
1
1
0
0
0
1
1
1
1
1
1
1
2
1
2
1
1
1
2
0
1
2
0
1
1
1
2
1
0
1
2
1
1
2
0
1
1
0
1
0
2
2
1
1
1
2
1
1
1
1
1
1
0
1
0
1
1
2
1
1
0
1
0
2
1
1
1
1
0
4
1
0
1
1
2
1
1
1
1
1
2
1
2
0
2
1
1
1
1
1
1
1
1
1
1
2
1
0
1
2
1
2
1
1
2
0
2
2
1
0
2
1
1
2
2
0
1
2
2
1
1
1
1
1
1
1
2
2
2
3
0
1
1
1
2
1
2
0
1
0
0
0
0
2
2
2
2
1
1
1
2
0
1
1
1
0
1
1
1
1
1
2
1
2
1
1
1
1
2
1
2
0
2
2
1
1
1
1
1
1
2
2
1
1
2
0
1
1
2
1
2
1
1
2
1
0
1
1
1
3
2
2
2
1
1
0
2
2
1
1
1
2
1
1
1
0
1
1
1
1
1
0
1
0
1
2
1
1
1
1
0
1
1
2
2
1
2
1
2
1
1
1
3
1
1
1
1
1
1
0
2
2
1
1
1
0
1
1
1
1
0
1
1
1
2
1
1
2
1
2
0
0
1
1
1
1
0
2
1
1
0
1
2
2
1
1
1
2
2
1
2
2
1
1
2
2
1
1
1
0
2
2
2
1
0
2
0
1
0
2
1
1
0
1
1
2
1
1
1
2
2
0
1
2
1
1
1
1
1
2
2
1
2
1
0
2
1
1
1
1
2
0
1
2
1
2
2
1
1
1
2
1
1
0
0
1
0
0
1
1
1
1
1
1
1
0
1
1
2
2
0
1
1
1
1
1
1
0
1
1
2
1
1
2
2
1
1
0
1
2
1
0
0
1
2
1
2
1
2
1
1
1
1
1
1
1
1
1
2
0
0
2
0
1
1
1
0
1
2
1
1
1
0
0
1
1
0
2
0
0
1
2
2
0
2
1
2
0
1
1
1
1
2
1
1
0
1
2
2
1
1
1
1
1
1
0
1
2
0
1
1
2
1
0
2
1
1
2
2
0
2
1
0
1
1
1
0
1
1
1
1
1
2
0
2
1
1
1
1
1
1
1
2
1
1
2
1
0
1
1
2
2
1
2
0
1
1
1
2
0
1
1
1
0
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
0
1
0
1
0
1
2
0
1
1
1
0
1
2
1
1
2
1
2
0
1
2
0
2
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
2
1
1
1
1
1
2
2
1
1
2
1
1
0
1
2
3
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
0
1
2
1
1
1
1
2
2
1
1
2
1
0
2
1
1
1
1
1
2
2
1
1
1
0
1
2
3
1
0
0
2
2
1
1
0
1
2
2
1
2
1
2
1
1
1
1
0
2
2
0
0
1
1
1
1
1
1
0
2
1
2
1
0
2
1
0
0
0
1
1
1
0
2
1
1
0
1
1
0
1
1
2
2
1
2
2
1
2
2
2
2
1
2
1
2
1
1
0
1
0
1
0
1
1
0
1
1
1
1
0
1
1
1
1
2
1
0
1
1
1
2
2
0
1
1
0
2
1
1
2
2
2
1
2
1
1
1
12
2
1
1
2
1
1
2
2
2
1
1
0
1
1
2
1
2
1
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
2
2
0
1
1
1
2
1
1
1
2
1
1
2
1
2
2
1
1
1
1
2
1
0
0
2
1
1
1
2
1
1
0
1
1
2
1
1
1
1
2
0
1
1
1
2
1
1
1
1
2
1
1
2
1
0
1
1
0
2
0
1
0
2
1
2
2
1
1
1
2
1
1
0
1
2
1
1
2
2
1
1
0
1
2
1
2
1
1
0
2
1
1
1
1
1
0
1
1
1
0
2
1
1
1
2
1
1
1
1
1
1
1
1
0
0
1
2
1
0
0
0
0
0
2
1
0
1
1
1
2
1
1
2
1
1
1
2
1
2
1
2
1
1
1
2
1
2
0
1
2
1
2
1
1
1
2
0
1
2
1
0
2
2
1
0
1
1
2
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
0
0
2
1
0
1
1
1
1
1
0
2
1
1
1
1
1
1
1
0
1
1
1
1
1
2
1
0
1
1
1
1
0
2
1
1
1
1
2
0
0
2
2
2
1
0
1
1
1
1
0
2
1
1
1
1
1
1
1
0
0
1
2
1
2
2
2
3
0
2
2
1
1
1
2
1
2
0
1
0
1
1
1
2
2
1
1
2
1
1
1
1
1
0
2
2
1
1
2
1
1
2
0
1
2
2
1
1
0
1
1
1
1
1
1
1
1
1
2
3
1
2
1
1
2
2
1
2
2
1
1
1
1
1
1
1
2
2
1
0
2
1
1
2
1
1
1
0
1
1
1
1
2
2
2
2
1
2
2
1
1
1
2
2
1
2
1
1
1
1
1
0
1
1
2
1
0
2
1
1
2
2
1
1
1
1
2
1
0
1
0
0
1
2
1
1
1
1
2
1
2
2
1
2
2
0
1
2
1
1
0
2
1
1
1
0
1
1
1
2
1
1
1
1
1
0
2
2
2
1
1
1
0
0
1
2
1
1
0
2
1
1
2
0
1
1
2
1
1
2
1
0
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
2
1
1
1
2
0
0
1
0
2
1
1
1
1
1
1
0
0
2
1
1
1
2
1
2
1
1
1
2
1
2
0
2
1
1
0
0
0
2
2
0
1
1
1
1
2
2
1
1
0
1
0
1
1
1
0
2
2
1
0
2
1
1
1
1
1
0
2
1
1
1
1
1
1
2
1
1
3
2
1
1
1
1
2
2
2
2
0
2
1
0
0
2
3
0
1
1
1
1
1
1
1
1
1
1
2
1
1
0
1
1
1
1
1
1
2
1
2
1
0
1
1
0
2
1
0
1
2
1
1
1
1
1
0
1
1
1
1
1
2
3
1
1
1
2
2
1
1
1
0
1
1
1
2
2
2
1
2
1
1
1
1
0
1
0
2
1
1
1
1
1
2
2
1
2
1
1
1
2
1
2
1
1
1
1
2
2
1
1
1
0
1
1
2
0
1
1
1
0
1
2
1
0
1
2
1
1
1
1
1
2
2
1
0
1
0
0
1
1
2
1
0
1
2
1
1
1
1
1
1
0
1
2
1
1
2
0
1
0
2
2
1
0
1
1
1
2
2
2
1
1
1
0
1
1
1
1
1
1
1
2
1
0
1
0
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
0
1
1
1
1
0
2
1
2
1
1
1
1
1
1
1
2
1
1
1
0
1
2
2
2
0
0
1
1
1
2
0
1
1
1
2
1
1
1
1
1
1
2
0
1
1
0
1
1
2
2
1
1
2
2
2
1
0
1
1
0
1
1
1
1
2
2
1
1
2
1
1
2
2
1
1
0
1
0
2
2
1
2
1
1
1
1
1
1
2
0
1
0
0
2
1
1
0
0
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
0
0
2
1
1
1
1
1
1
0
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
0
1
2
0
1
2
0
2
0
1
1
1
1
1
2
1
1
1
1
1
2
1
1
2
0
1
2
1
1
2
1
1
1
1
1
1
2
2
1
2
1
2
1
2
0
1
1
0
0
1
0
0
1
2
1
1
1
2
1
1
0
0
1
1
1
2
1
1
1
2
1
1
1
0
1
0
1
1
2
2
2
1
1
1
2
1
1
0
1
1
1
1
0
2
1
2
2
1
1
1
1
2
0
2
1
1
1
0
1
1
1
1
1
1
2
0
1
1
0
1
1
1
1
0
1
1
2
1
1
1
1
1
0
2
0
1
1
1
2
1
1
1
0
2
2
1
2
1
2
0
1
0
2
0
2
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
2
0
1
1
2
1
1
1
1
2
1
1
1
2
2
1
1
2
1
2
1
1
1
1
1
2
2
1
2
1
0
2
2
0
1
2
1
1
2
1
1
2
1
2
2
1
2
2
1
1
0
2
1
2
2
0
1
1
1
1
1
1
2
1
1
1
2
1
1
1
2
1
0
1
2
1
1
2
1
1
1
1
0
1
1
2
1
1
1
2
2
1
1
1
0
1
1
0
0
2
2
1
1
1
1
1
1
1
2
1
0
2
1
1
1
0
1
2
1
0
1
2
1
2
2
1
2
1
1
2
1
2
1
1
2
1
1
1
0
1
1
0
2
1
2
1
2
1
2
2
1
1
1
2
0
1
1
2
2
3
1
1
1
2
1
1
2
1
1
2
0
2
2
2
1
1
0
1
0
1
1
1
1
2
2
1
2
1
2
1
2
0
2
1
1
2
1
2
0
0
2
1
2
1
2
0
1
2
1
1
1
1
1
2
1
0
2
0
1
2
1
2
0
1
0
1
1
1
1
0
2
2
2
1
1
1
1
1
0
1
1
2
1
1
1
0
1
1
1
0
1
1
2
1
1
1
2
1
1
2
1
1
1
2
2
1
1
1
1
1
1
2
2
1
2
0
0
2
1
1
0
1
1
1
2
1
1
2
1
1
2
1
1
2
1
1
1
1
0
2
1
1
1
1
2
2
1
0
1
2
2
2
2
0
2
0
1
2
2
1
1
2
1
1
1
1
2
2
2
0
1
2
1
1
1
1
1
0
2
1
1
1
1
1
2
1
1
1
0
1
1
2
2
1
2
1
1
1
1
2
1
1
1
1
0
1
2
1
0
1
0
1
1
2
2
4
2
1
1
1
1
1
1
0
1
0
2
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
1
1
1
1
0
2
1
1
1
2
2
1
1
1
2
0
1
0
2
1
1
1
1
1
2
1
2
1
2
2
1
2
2
1
0
1
1
1
1
1
2
1
2
2
2
1
2
1
1
1
1
1
1
1
1
1
0
0
1
1
2
2
0
1
2
2
1
2
2
1
0
1
1
1
1
1
2
1
2
1
1
1
1
1
1
5
1
0
1
0
1
1
1
2
1
1
2
2
1
2
1
0
0
1
2
1
2
2
2
2
1
1
1
1
2
1
1
1
1
1
0
1
1
1
1
1
1
2
1
0
1
1
2
1
2
1
2
1
1
1
2
1
2
1
0
2
1
2
1
2
0
1
1
1
0
1
1
1
0
1
1
1
1
1
1
0
1
1
0
0
1
1
2
2
1
1
2
0
1
1
1
1
1
1
2
1
1
1
1
0
2
0
1
1
1
1
1
2
1
1
0
1
1
1
1
1
1
0
2
1
2
2
2
0
0
1
1
1
0
1
2
1
2
1
1
1
2
1
1
2
1
1
0
1
1
1
2
1
0
1
0
0
2
1
0
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
2
1
3
0
2
2
1
2
1
2
1
2
0
1
1
1
1
1
1
1
1
0
1
2
1
1
1
1
1
1
1
2
1
1
1
0
1
2
1
1
1
1
1
1
2
1
3
2
1
1
1
1
1
2
1
1
1
2
1
0
2
1
1
2
2
1
2
1
2
1
0
1
1
2
2
1
0
1
2
1
1
1
0
1
1
0
1
2
1
2
2
1
1
1
1
1
1
1
2
2
2
1
2
1
1
1
1
1
1
2
2
1
2
1
1
1
1
1
0
1
1
1
0
1
1
2
1
1
1
1
1
1
0
1
1
2
1
1
1
1
1
1
2
1
2
1
2
2
0
1
1
2
1
2
2
0
2
0
2
1
1
1
1
0
2
0
0
1
1
0
2
1
2
2
1
1
1
1
2
1
2
2
1
0
1
1
1
2
0
1
1
1
1
1
2
1
1
3
1
1
2
2
0
0
1
2
1
1
1
1
2
1
1
1
1
0
2
1
1
1
1
1
1
2
2
0
1
1
2
2
0
2
1
1
1
1
2
1
1
2
1
1
1
1
1
0
1
1
1
2
1
1
4
0
1
1
1
2
1
0
2
1
1
2
1
2
1
0
1
2
0
1
1
2
1
2
1
1
2
1
2
1
2
2
1
0
2
1
1
1
1
1
1
1
1
1
1
2
1
0
1
1
1
2
1
1
0
2
0
1
2
2
1
1
1
1
0
1
0
2
1
0
1
0
1
1
1
1
0
1
2
1
1
2
0
1
0
0
1
2
2
0
1
1
1
1
2
1
2
1
1
0
2
2
0
0
2
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
2
2
1
2
2
1
1
2
1
2
1
2
1
1
1
2
0
1
0
2
1
0
1
2
1
2
1
2
2
2
1
0
2
1
1
1
2
1
1
1
2
1
2
0
1
1
1
1
2
0
2
2
1
1
2
2
0
1
1
1
1
1
0
2
1
1
0
2
1
2
1
0
0
1
1
1
2
1
1
2
1
1
1
1
1
0
1
1
2
1
0
2
2
1
0
1
2
2
0
2
0
0
0
1
2
1
1
1
2
0
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
0
0
1
1
1
2
1
0
1
1
1
1
2
4
1
1
1
1
1
2
1
1
1
1
0
2
1
0
2
2
2
1
2
2
0
1
0
1
1
1
1
1
0
2
0
1
1
0
1
2
1
1
1
2
1
1
2
0
2
1
2
2
1
1
2
2
1
2
2
1
1
2
1
1
2
2
1
1
2
1
0
1
1
1
2
1
1
1
2
1
2
1
1
0
1
1
2
1
4
2
1
2
1
2
1
1
2
2
0
0
1
1
1
1
1
1
1
2
0
2
1
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
1
2
2
1
1
1
2
1
1
0
1
0
1
2
1
2
2
1
1
1
1
1
2
1
1
2
1
0
1
0
1
0
2
0
1
2
1
1
1
1
2
1
1
1
2
0
1
1
1
1
1
2
0
3
2
1
1
2
1
2
2
1
1
2
2
0
1
1
1
0
1
1
1
1
1
1
1
1
1
1
2
1
2
1
2
2
1
2
0
2
1
1
2
0
1
1
0
1
0
2
1
1
1
2
2
1
1
1
1
1
0
1
0
1
1
1
1
1
0
1
1
1
2
1
1
1
1
2
1
1
1
2
1
0
1
1
1
0
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
2
1
2
2
0
1
1
1
1
0
1
1
1
2
2
1
1
2
1
1
1
1
1
1
0
1
1
0
1
1
1
1
1
1
0
2
1
0
1
1
1
1
1
2
1
1
1
2
2
2
1
2
2
0
1
1
2
2
0
0
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
2
2
0
1
1
2
2
1
2
1
1
1
2
1
1
1
0
1
2
1
2
1
2
1
0
0
2
2
1
0
1
0
1
1
1
1
1
2
1
1
1
1
0
1
2
0
1
1
1
1
1
1
1
1
0
1
0
1
2
2
2
1
2
1
1
1
0
1
1
0
1
1
1
2
1
1
2
1
2
0
2
3
1
1
1
1
2
1
1
1
0
2
1
1
1
1
1
1
0
2
1
1
1
1
2
2
2
1
1
1
2
1
1
0
1
2
1
1
0
2
1
1
2
1
1
1
1
1
1
1
1
0
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
0
1
2
1
0
1
2
1
2
2
1
1
2
0
1
2
2
1
2
1
1
2
1
1
1
2
1
1
1
0
1
1
1
1
1
2
1
0
1
1
1
1
2
2
2
1
2
2
2
0
1
2
1
1
2
1
0
1
1
0
1
2
2
3
1
1
1
1
1
0
1
1
1
1
1
1
1
2
1
1
1
2
1
2
2
2
2
1
1
0
1
0
1
1
1
0
2
1
2
1
1
1
1
2
1
2
1
1
0
2
2
2
1
1
1
1
1
2
2
2
2
0
1
2
1
2
1
1
2
1
2
2
2
1
1
2
2
2
0
2
1
1
1
2
1
2
1
1
2
1
0
1
2
1
1
1
0
2
1
1
1
1
0
2
2
1
1
1
1
1
0
0
0
2
2
1
1
2
1
1
2
2
1
1
1
1
1
1
1
0
0
2
1
1
3
1
1
1
0
0
2
1
1
2
1
1
1
2
1
1
1
2
2
0
1
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
0
2
0
1
2
1
1
1
0
2
1
2
1
0
1
2
1
1
1
2
0
1
1
1
1
1
2
0
2
1
0
2
0
1
1
2
2
1
0
0
1
1
1
0
2
1
2
1
1
1
1
2
2
0
0
1
2
1
1
0
1
1
1
2
1
0
1
1
2
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
2
2
1
1
0
2
2
1
1
1
1
0
1
2
2
1
0
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
0
2
1
1
1
2
1
1
1
1
1
1
1
2
2
2
2
1
2
2
2
1
1
2
0
1
1
0
2
2
2
3
2
0
1
2
1
1
1
2
2
1
2
0
1
1
2
1
1
1
1
1
0
1
1
2
0
1
2
1
0
1
1
1
3
1
1
1
1
1
1
1
1
1
0
2
2
2
0
1
1
0
0
0
1
1
1
1
0
1
1
2
1
0
1
1
1
1
1
2
0
1
2
1
1
2
2
2
1
0
1
1
1
1
2
1
1
1
2
1
1
2
1
1
2
1
2
1
1
2
2
2
2
1
2
1
1
0
1
2
1
1
1
1
1
1
0
1
1
2
2
0
2
1
1
1
1
0
1
1
1
1
2
2
1
0
2
2
1
1
2
1
1
2
1
1
1
1
1
1
0
2
1
0
2
1
0
1
2
2
0
1
1
1
2
2
1
2
0
1
2
2
2
1
2
2
1
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
3
1
2
1
1
1
0
1
2
2
1
1
0
1
2
2
2
1
0
1
1
1
0
1
1
1
1
1
2
1
2
2
1
2
0
1
1
2
1
1
1
1
0
1
1
3
1
0
1
0
1
0
1
1
1
1
2
2
1
1
1
2
1
0
1
2
2
1
2
2
1
1
1
2
2
1
1
1
1
1
2
2
1
2
2
2
2
1
0
1
1
2
1
2
1
1
1
4
1
1
1
0
1
1
1
2
1
1
1
0
1
0
1
1
1
2
1
1
1
2
1
0
2
2
0
1
1
1
1
1
1
1
1
1
2
1
1
1
0
1
2
2
1
2
2
1
1
2
1
0
1
1
2
1
1
1
1
1
1
0
0
1
1
1
1
1
2
1
0
1
1
2
0
1
0
1
2
0
1
1
1
2
1
1
1
1
1
1
1
0
1
1
2
1
0
2
2
1
1
1
1
2
2
1
1
2
1
1
1
1
1
0
1
1
3
0
2
1
1
1
1
2
1
1
2
1
1
3
1
0
1
2
1
1
1
1
1
1
1
0
2
0
1
1
1
0
2
1
0
1
1
0
0
2
2
1
2
1
0
1
2
1
1
1
2
1
0
2
2
1
1
1
1
2
2
1
1
1
2
0
1
1
1
1
1
1
1
1
1
1
1
1
2
1
0
0
1
2
2
2
1
2
2
1
0
1
1
2
2
4
0
1
1
1
1
2
1
1
1
0
1
3
1
1
2
2
1
2
1
0
1
1
0
1
2
2
1
2
1
1
2
1
0
1
1
2
1
1
1
1
1
1
1
0
2
1
1
1
1
3
2
1
1
2
0
1
0
1
1
1
1
1
1
0
1
1
1
1
1
2
1
1
1
1
1
0
1
0
1
0
2
1
1
1
1
1
1
0
1
1
1
1
0
2
2
0
1
1
1
2
2
1
1
1
0
1
1
2
1
2
2
1
1
1
1
1
2
2
1
1
1
1
0
1
1
1
1
2
2
1
1
1
1
1
0
1
0
0
1
0
1
2
1
1
0
1
2
2
2
1
1
1
1
1
1
2
1
1
1
2
0
1
2
1
1
1
1
1
1
1
0
0
4
2
2
1
2
2
1
1
1
1
2
1
2
1
0
1
1
1
2
1
1
1
1
2
1
2
1
2
1
2
1
2
2
1
2
1
2
1
1
2
1
2
2
0
1
1
1
1
2
1
1
2
1
2
3
2
1
1
0
1
0
1
1
1
2
2
1
2
1
1
0
2
1
1
0
2
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
0
1
1
1
1
1
1
1
1
2
1
1
0
0
0
1
2
2
1
2
1
2
2
0
1
2
1
2
1
1
2
1
1
1
0
1
1
1
1
2
1
1
1
0
1
2
2
2
1
1
1
1
1
1
1
4
1
1
2
1
0
1
2
1
2
0
1
1
0
2
1
1
0
1
2
1
0
1
1
1
1
1
1
1
2
1
2
1
1
2
3
1
1
2
1
3
1
2
1
1
1
2
1
2
1
1
1
1
2
1
2
2
1
1
1
1
2
1
2
1
1
1
1
2
1
1
2
1
2
4
2
1
1
1
1
1
2
1
2
1
1
1
2
1
1
0
1
1
1
1
1
0
1
1
3
1
1
1
1
1
1
1
1
2
2
1
2
1
0
2
1
1
1
3
1
2
1
2
1
2
1
2
2
2
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
2
2
2
2
1
2
1
2
1
1
1
4
2
0
3
1
1
2
1
1
1
1
2
2
2
1
1
0
1
1
1
0
1
1
2
2
1
2
1
1
2
2
2
1
1
0
0
1
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
2
1
2
1
2
1
0
2
2
1
2
2
1
2
0
1
1
1
1
1
1
2
1
1
2
1
2
1
1
1
2
1
2
0
0
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
0
1
1
1
2
0
1
1
2
2
1
2
1
1
1
0
1
1
2
0
1
1
2
2
1
0
0
1
1
1
1
2
2
2
2
3
1
0
1
2
1
2
2
1
2
2
1
0
1
0
0
1
2
1
1
0
1
1
2
2
2
0
1
0
0
2
1
1
0
1
2
0
2
0
0
2
1
1
1
1
0
1
1
1
1
1
2
1
1
1
1
1
2
2
1
1
2
0
1
0
0
1
1
0
1
1
3
1
2
0
2
0
2
0
1
1
2
1
1
1
2
2
1
0
1
1
1
2
1
1
1
1
1
1
2
1
1
0
2
1
1
1
1
1
2
2
1
2
1
0
2
1
1
1
0
0
1
1
2
1
1
1
1
2
0
2
2
1
2
1
1
1
2
1
1
2
1
1
2
1
1
1
0
1
1
1
1
1
2
1
0
2
2
1
1
1
2
1
2
1
0
1
1
2
1
1
2
1
1
2
1
1
0
0
1
1
2
1
1
1
2
1
2
1
2
1
1
2
2
1
2
2
1
0
1
2
0
1
1
1
1
1
2
1
1
0
1
1
1
1
1
2
0
1
0
2
1
1
1
1
1
2
1
0
1
1
1
1
0
2
2
1
1
1
2
1
2
1
2
2
1
0
0
0
1
1
1
0
1
1
2
1
2
2
1
1
1
1
0
1
1
1
2
1
2
2
2
1
1
2
2
1
1
1
1
0
2
2
2
2
2
1
1
2
2
0
3
1
2
1
1
2
0
1
2
1
2
0
2
0
1
1
1
1
1
1
1
1
1
0
1
2
1
2
1
2
0
1
1
1
2
1
1
1
1
0
1
1
1
1
2
1
1
1
1
1
1
1
1
0
1
1
1
2
1
1
1
1
2
1
1
2
1
2
1
1
2
1
2
2
0
1
1
1
1
1
2
2
1
1
1
1
2
1
1
1
2
1
0
2
2
1
1
1
1
1
0
1
1
0
1
1
1
0
1
2
1
0
1
0
1
1
2
2
2
1
1
1
1
1
0
0
2
2
2
1
1
1
1
2
2
2
0
2
0
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
0
2
2
1
1
2
2
2
1
2
0
1
1
0
1
1
2
1
2
2
2
1
0
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
0
1
1
1
0
1
2
2
2
1
1
2
2
2
1
1
1
1
1
2
0
1
1
1
1
2
2
1
1
1
1
2
1
2
1
1
1
1
1
1
1
0
1
1
1
1
1
0
1
2
2
1
1
1
1
1
3
2
2
1
2
1
2
2
1
0
2
1
2
1
1
2
1
1
1
1
1
2
1
1
0
3
1
1
2
2
1
1
1
1
1
2
2
1
1
0
0
0
1
0
0
1
1
2
1
1
1
1
2
1
1
1
1
0
2
1
1
0
0
2
2
0
1
1
1
2
1
1
0
1
1
2
1
2
1
1
1
1
1
1
1
1
0
0
2
2
2
1
1
1
1
2
0
1
0
1
0
0
1
2
0
2
2
1
1
2
2
0
0
1
2
1
1
1
1
0
0
1
1
1
2
1
0
0
1
1
1
1
2
1
1
1
2
1
2
1
2
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
0
2
1
1
1
0
1
2
2
1
4
1
2
1
1
1
2
1
1
0
1
1
1
0
2
1
0
2
1
2
0
2
1
1
1
1
2
1
2
1
2
1
1
1
1
0
2
0
0
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
2
1
0
1
1
0
1
1
1
1
2
1
2
1
1
1
1
1
1
2
1
2
1
1
2
2
1
2
1
1
1
1
1
2
1
1
1
1
0
1
1
1
1
1
1
1
1
1
2
2
3
2
1
0
2
1
2
1
1
1
0
1
2
2
1
1
1
2
1
1
1
2
1
0
1
0
0
1
0
0
1
2
1
1
1
0
0
2
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
2
0
1
2
2
2
1
1
2
2
0
0
2
2
2
2
1
1
0
1
1
1
1
2
1
1
1
0
1
0
1
0
1
0
1
0
1
1
1
1
1
2
1
1
2
2
1
1
1
2
2
1
2
1
1
0
1
2
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
0
1
1
0
1
1
1
1
0
1
1
1
1
2
2
1
2
0
2
1
1
2
1
2
1
1
2
1
0
1
1
1
0
1
1
1
0
1
2
1
1
1
1
1
2
0
1
2
2
0
2
2
0
1
0
1
0
2
0
1
2
1
2
1
1
2
1
2
1
2
0
1
0
1
1
1
1
1
1
2
1
1
2
1
3
1
2
0
2
1
1
1
1
2
0
1
2
1
1
1
0
1
2
1
1
1
2
1
1
1
2
0
1
1
2
2
1
0
1
1
2
1
1
1
1
1
2
1
1
1
1
1
0
0
1
2
1
1
0
1
1
2
1
0
1
2
1
2
2
1
1
1
2
1
1
2
1
1
1
0
1
1
2
1
2
1
0
1
2
2
1
0
1
2
1
2
1
4
3
0
1
1
1
1
1
1
1
2
2
1
0
1
2
1
1
0
1
1
1
2
0
0
1
1
1
1
1
2
1
1
2
1
2
2
1
1
1
0
2
1
2
1
0
0
1
1
2
1
0
1
2
1
1
1
2
1
1
1
0
1
2
1
2
1
1
2
2
1
0
1
1
2
1
0
1
0
1
1
1
1
2
1
0
2
3
0
1
0
1
1
1
0
1
1
1
2
2
1
1
2
1
2
2
1
1
1
1
2
0
2
1
2
1
0
1
1
1
1
0
1
0
1
2
0
2
1
2
1
2
2
2
1
1
2
1
1
1
0
2
2
1
1
0
0
1
1
1
1
1
1
1
1
0
2
0
1
1
1
3
1
1
1
1
1
1
1
2
2
2
2
0
0
1
0
2
1
1
1
2
1
2
1
0
1
1
1
1
2
0
1
1
1
0
1
1
1
1
2
1
2
1
1
2
1
1
1
1
2
2
1
2
1
1
1
1
2
1
1
1
1
1
2
1
1
0
2
1
1
2
1
1
2
1
1
0
2
2
1
1
2
0
2
2
2
0
2
0
1
0
2
0
0
1
1
1
1
1
0
1
1
1
1
1
2
1
0
1
1
1
0
1
2
1
1
1
1
1
1
1
1
1
1
0
1
0
2
2
2
1
1
1
1
2
1
1
1
1
1
2
2
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
0
1
1
2
2
2
0
1
0
1
1
1
1
1
2
1
0
1
2
1
2
1
2
1
2
1
1
1
2
1
1
1
1
0
0
1
1
1
1
1
1
1
1
2
2
1
2
1
0
1
1
1
2
1
1
1
0
0
1
1
1
1
2
1
1
1
1
1
1
1
1
2
0
1
2
1
0
1
1
1
0
2
2
2
0
1
1
2
2
1
1
1
1
1
1
2
1
1
1
2
1
2
1
0
1
1
2
0
0
2
1
2
1
1
2
1
1
2
1
1
1
1
1
1
2
1
1
0
2
1
1
1
1
2
1
0
2
1
2
1
2
1
2
1
0
1
1
1
1
1
1
0
1
1
1
1
1
2
3
1
0
1
2
1
2
2
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
2
1
0
1
2
2
1
3
1
2
1
2
0
1
2
1
1
0
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
1
2
0
2
1
2
1
1
1
1
1
1
1
0
2
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
2
2
1
1
0
1
1
1
1
1
1
0
2
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
2
1
1
2
1
2
1
2
0
2
1
1
1
2
1
1
1
1
1
0
1
2
2
1
2
1
0
2
0
2
1
2
0
2
1
1
1
0
2
1
0
1
1
1
2
0
2
1
0
2
2
3
1
1
1
1
1
1
1
2
1
2
1
2
1
1
1
1
1
2
1
1
0
2
2
2
2
2
2
1
1
1
1
1
1
2
1
2
2
1
1
2
1
2
2
1
1
2
1
1
1
1
1
2
1
0
2
0
0
1
2
2
1
0
1
1
1
2
0
1
2
1
0
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
0
1
2
2
1
2
1
1
2
1
1
2
0
1
0
1
1
1
2
2
1
1
1
2
2
2
1
2
1
1
1
1
1
1
1
0
2
1
1
1
1
1
2
2
1
1
1
1
1
2
1
2
0
1
3
1
1
1
1
1
0
2
0
2
0
0
1
1
2
1
1
1
1
2
1
2
2
2
1
2
1
1
2
1
1
1
2
0
1
1
1
0
1
1
1
2
1
1
1
0
1
1
1
2
2
0
1
1
0
1
0
0
3
1
0
1
1
1
1
1
2
0
1
1
1
1
1
1
1
1
1
1
2
1
0
1
1
2
1
1
1
1
1
1
2
0
2
2
1
1
2
0
1
1
1
1
1
1
1
1
0
2
1
2
1
2
1
1
0
1
1
2
1
1
1
0
2
1
2
1
1
1
2
2
0
0
1
1
1
2
1
2
2
2
1
1
1
1
2
1
1
2
1
1
1
1
2
1
1
1
1
0
0
1
0
1
2
1
0
1
1
0
2
1
1
1
2
0
1
1
0
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
2
1
2
1
2
2
1
2
1
2
1
1
1
1
2
1
1
1
2
1
1
2
1
1
1
2
1
0
1
2
0
2
1
1
1
1
0
2
1
1
1
2
0
1
1
1
2
1
2
0
1
2
0
1
2
2
1
2
2
0
0
0
1
2
1
1
1
2
1
0
1
0
1
2
2
1
2
1
1
0
1
1
2
2
2
1
1
1
1
2
2
1
1
1
2
2
0
2
1
1
2
1
1
2
2
1
1
2
2
2
1
1
2
1
1
1
0
2
1
1
1
0
1
2
1
2
1
1
1
2
1
1
2
0
1
1
2
1
0
0
1
0
1
2
1
1
0
1
2
0
3
2
1
1
1
2
2
1
2
1
1
2
0
1
2
1
2
0
2
2
2
1
0
0
1
1
1
0
1
1
1
2
1
1
2
1
2
3
1
2
1
1
1
1
1
1
2
0
0
0
1
1
0
0
1
2
2
2
1
1
1
0
1
1
0
2
1
1
2
0
1
1
1
1
1
1
1
1
2
1
0
1
1
1
1
2
0
1
2
1
1
2
2
1
2
2
1
2
1
1
1
1
2
1
1
1
0
1
1
2
2
1
1
2
1
0
1
1
0
2
1
1
2
1
1
2
1
2
1
1
0
1
2
0
2
1
1
1
1
1
1
1
0
2
1
3
1
2
0
1
1
2
1
0
1
1
1
1
0
0
1
2
1
1
2
2
1
1
1
1
1
1
1
1
2
1
1
1
2
1
0
1
1
0
1
0
1
1
0
2
0
1
2
0
1
2
1
1
1
0
2
1
1
1
2
1
3
0
0
1
0
1
1
1
2
1
1
2
1
0
1
1
1
1
2
1
2
2
1
1
1
1
2
0
1
2
0
2
2
2
1
2
1
2
0
1
1
1
0
2
1
2
0
2
1
1
0
0
1
1
0
0
2
1
1
2
2
1
0
2
1
1
2
1
1
2
1
0
2
1
1
2
1
1
2
1
1
1
0
1
2
2
1
1
0
1
1
1
1
2
2
2
1
1
3
0
2
0
1
0
2
1
1
1
2
1
1
2
1
1
1
1
1
0
2
2
1
2
2
1
2
2
2
1
1
1
1
0
1
1
1
0
1
3
0
1
1
1
1
2
1
1
0
0
1
2
0
1
1
1
2
1
1
2
2
2
1
1
2
0
0
1
1
1
2
1
1
2
2
1
0
2
1
0
1
1
0
1
0
1
1
2
1
0
2
1
2
1
2
1
2
0
1
1
1
1
1
2
0
1
2
0
1
1
1
1
2
1
1
1
1
1
1
1
2
0
2
1
1
1
1
2
0
0
0
1
1
1
2
1
1
1
0
1
1
2
1
1
0
1
1
1
1
1
2
1
0
1
2
0
2
1
1
1
0
0
1
1
1
1
1
2
1
1
1
2
0
1
0
0
1
0
1
2
1
2
1
1
1
2
1
2
2
1
0
2
2
1
1
2
1
1
2
1
1
1
1
1
1
1
1
2
2
1
1
1
0
1
1
1
1
1
1
1
1
1
2
1
1
1
4
0
1
1
1
1
2
1
1
1
0
2
2
0
1
0
0
1
1
1
1
1
1
1
2
1
1
2
3
0
2
1
2
1
0
1
0
0
2
1
1
1
1
2
1
1
1
1
1
2
1
1
2
1
2
1
2
1
1
1
1
2
1
1
2
1
2
0
1
1
1
1
2
2
1
1
0
1
1
4
1
1
0
1
1
2
1
1
2
0
0
1
2
0
1
2
2
1
1
1
1
0
1
2
1
1
1
1
0
1
1
0
1
1
1
1
1
2
2
1
1
0
1
0
2
1
1
1
1
0
2
2
0
1
1
1
0
0
1
2
0
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
0
3
1
2
0
1
1
2
1
2
0
2
3
2
0
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
2
1
1
1
0
1
2
0
1
1
1
1
1
2
1
1
1
2
1
2
0
1
1
0
0
1
1
1
1
1
2
1
2
2
1
1
1
1
1
1
1
2
2
0
1
1
1
0
1
1
1
1
1
2
2
1
2
1
0
1
0
1
1
1
0
1
1
1
2
2
2
1
2
1
1
1
3
1
1
2
1
1
1
0
1
0
1
1
0
2
0
2
1
1
1
1
1
1
1
3
2
1
1
0
1
1
1
2
0
1
0
0
0
2
1
2
1
1
0
1
2
1
1
2
1
1
1
0
2
1
0
1
2
1
1
1
1
1
1
1
0
1
1
1
1
0
1
1
2
1
2
1
1
2
1
1
1
2
0
1
2
1
2
1
0
1
0
2
0
2
1
2
0
1
1
1
1
1
2
1
2
1
2
2
1
1
2
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
0
0
0
1
0
1
1
1
1
1
1
0
2
1
1
0
0
1
1
1
2
1
1
1
2
1
1
1
1
0
2
2
2
1
1
2
2
1
2
1
1
2
1
2
2
1
0
1
1
1
1
3
1
2
0
2
1
1
1
1
1
2
1
1
0
0
1
0
2
1
2
2
1
1
2
1
1
1
2
2
1
2
1
1
1
0
2
1
1
1
1
0
1
1
2
1
2
2
1
1
1
1
1
2
1
0
2
1
2
1
0
1
1
1
1
0
0
1
1
2
1
1
1
1
1
0
2
1
1
1
0
1
1
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
2
1
3
1
2
1
1
2
1
2
1
1
1
1
2
1
1
2
1
1
2
0
1
1
1
1
1
1
2
1
2
1
1
2
1
2
1
1
0
2
0
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
2
1
1
1
1
1
2
1
1
2
1
1
1
2
1
0
1
2
0
1
2
1
1
1
1
2
1
1
2
1
2
0
1
1
1
1
1
2
1
2
1
1
2
0
1
1
0
1
1
1
2
1
0
0
0
1
1
2
2
1
2
0
1
0
1
2
2
0
1
4
1
2
2
1
0
2
1
2
2
0
1
1
0
1
0
1
1
0
1
1
0
1
1
1
2
2
2
2
1
0
2
1
1
1
0
1
0
1
0
1
2
1
1
1
1
1
2
1
2
1
0
2
1
2
1
1
1
2
1
2
1
1
1
1
0
1
0
0
0
1
1
1
0
1
2
1
1
1
1
0
1
2
1
1
1
2
1
1
1
1
1
3
0
1
2
2
1
0
1
1
1
2
0
2
1
1
1
2
1
1
0
2
2
0
1
2
1
1
1
1
1
1
1
2
1
1
0
1
1
1
1
1
1
0
0
2
2
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
2
1
0
2
1
1
1
2
0
2
1
2
1
2
2
1
1
2
1
1
1
1
1
2
1
1
0
1
1
0
1
1
1
1
1
2
1
2
1
1
2
3
1
1
2
2
1
1
1
0
1
2
1
2
1
0
1
0
2
3
1
1
1
2
1
2
0
1
2
2
1
2
2
1
1
1
1
1
1
1
0
1
1
2
1
0
2
1
1
1
1
2
1
1
1
1
2
1
1
2
2
0
1
1
1
1
0
1
1
1
1
1
1
0
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
0
2
1
1
1
1
0
1
1
1
2
1
2
1
1
0
1
0
2
2
1
0
2
1
1
1
0
1
0
1
2
0
0
1
1
1
2
0
2
1
0
1
1
0
2
2
2
1
0
1
2
1
4
2
0
0
1
1
1
2
1
2
0
2
1
2
1
1
1
0
0
0
1
1
0
1
2
2
2
0
1
1
2
2
1
1
1
2
2
0
1
1
2
1
1
1
1
0
1
1
1
1
1
1
1
2
2
1
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
0
1
2
1
0
1
2
2
3
1
1
2
2
2
1
1
1
1
0
1
2
1
1
1
1
1
1
1
0
2
2
1
1
1
1
1
1
2
2
1
1
1
1
0
1
0
1
2
1
1
1
1
0
0
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
2
2
1
1
2
2
1
2
0
0
1
2
1
2
1
2
1
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
1
0
1
0
2
1
1
1
0
1
1
1
1
1
2
1
2
1
0
1
0
0
2
1
1
2
0
1
1
1
2
1
1
1
1
1
1
0
1
1
1
0
1
0
0
1
1
1
1
1
2
0
1
2
1
2
0
1
1
0
2
0
1
1
1
1
0
0
1
1
1
1
1
1
1
1
1
1
0
1
2
1
1
0
2
1
1
1
1
2
1
1
1
0
0
2
1
2
1
0
1
0
1
1
0
1
1
0
1
1
2
1
2
1
2
1
1
2
1
0
2
1
1
1
2
0
1
1
2
1
1
0
2
1
1
0
1
0
1
0
0
1
2
1
1
1
2
1
1
2
1
1
1
2
1
2
1
1
1
1
0
1
1
1
1
2
0
0
1
1
1
1
0
1
1
1
2
0
0
1
1
1
2
0
2
1
1
1
2
1
1
2
1
1
2
2
1
0
1
1
1
0
2
1
2
2
1
0
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
1
2
1
1
3
1
1
0
1
0
0
2
1
2
1
1
1
2
2
2
1
1
1
2
1
0
1
1
1
1
1
1
1
1
1
1
1
0
1
1
2
1
1
1
2
0
2
1
1
1
2
1
1
2
0
2
1
2
2
2
2
1
0
1
2
1
2
1
1
0
1
1
2
2
1
1
1
1
1
1
2
1
2
1
1
1
0
1
0
2
1
0
1
1
2
2
2
1
0
2
1
0
1
1
1
1
1
1
2
0
1
1
1
1
1
2
2
1
1
2
1
1
2
1
2
1
0
1
1
2
1
1
1
2
2
1
1
1
2
2
1
2
0
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
0
2
1
1
2
1
1
0
1
0
0
2
0
2
1
1
0
0
2
1
1
2
1
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
0
1
1
2
1
1
1
2
1
1
1
2
2
2
0
1
2
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
3
1
1
0
1
1
2
1
1
1
2
1
1
0
1
0
1
1
1
1
2
2
1
0
0
0
1
1
1
1
1
1
2
0
1
1
0
1
2
2
2
1
1
1
1
0
1
1
1
1
1
1
2
1
1
1
1
2
0
2
2
1
1
1
2
0
2
2
1
0
1
1
1
1
1
0
1
1
1
1
0
2
2
0
0
1
1
1
1
2
1
1
1
2
2
0
2
0
0
0
1
2
2
0
0
1
2
1
1
1
2
2
2
1
1
1
0
1
1
0
1
1
1
1
2
1
1
1
1
1
1
1
1
2
0
2
0
1
2
1
2
1
2
1
1
0
1
2
1
1
2
1
1
0
1
0
1
1
2
0
1
1
0
1
1
0
1
0
2
1
0
1
0
0
2
1
2
1
1
1
1
1
1
0
2
1
2
1
1
2
1
0
1
1
0
2
1
1
1
1
2
1
1
0
2
2
0
1
0
0
1
1
0
1
2
2
2
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
0
1
1
2
1
1
1
1
1
1
1
1
0
1
1
0
3
2
2
1
1
1
2
1
1
2
1
1
2
1
2
0
2
1
2
1
1
1
2
1
2
2
1
1
2
1
1
0
2
1
2
1
1
1
1
2
1
0
1
2
0
1
1
1
1
1
1
2
0
1
1
0
0
1
1
0
2
1
1
1
0
2
2
1
2
1
1
1
1
1
1
2
1
0
1
1
1
1
1
1
2
1
2
0
2
1
1
1
1
2
1
1
2
1
1
1
0
1
2
0
0
2
0
2
1
1
1
1
1
1
1
1
0
1
2
0
2
2
1
0
1
2
1
1
1
0
1
1
1
1
1
1
0
2
2
1
2
1
1
2
1
2
2
1
2
1
1
1
2
2
1
1
1
1
1
2
0
1
2
1
2
1
2
1
1
1
1
1
1
1
2
1
0
1
0
0
1
1
1
2
0
2
1
2
2
1
0
1
1
1
1
1
2
1
2
1
1
1
1
1
0
2
0
2
1
1
1
0
2
1
1
1
1
1
2
1
1
1
2
2
0
1
1
1
0
1
2
2
1
1
1
0
1
1
0
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
2
1
2
1
0
0
1
1
2
1
2
1
1
1
2
1
2
0
0
1
1
2
1
1
1
1
1
0
2
1
1
1
1
0
0
1
2
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
0
1
1
1
1
2
2
0
1
0
1
0
2
2
2
1
2
1
1
2
1
1
0
2
2
0
1
1
2
2
0
5
1
1
1
1
1
2
1
1
2
1
2
2
1
2
1
1
0
1
2
1
1
1
1
0
1
1
2
2
1
2
0
1
2
1
1
1
1
0
1
1
1
1
1
1
2
1
0
1
2
2
2
1
2
1
1
1
1
1
0
1
1
1
1
2
1
2
1
1
0
2
0
1
1
2
1
2
1
2
1
1
0
1
1
1
1
1
1
1
1
2
2
1
2
1
0
1
1
0
1
1
1
1
2
2
0
1
1
1
1
1
0
1
0
0
2
2
1
2
1
1
1
1
0
1
1
2
1
1
1
2
1
1
1
2
0
1
2
1
2
1
1
1
0
1
2
2
1
1
1
1
2
0
1
1
1
1
2
1
1
1
1
1
2
2
0
2
2
0
1
1
1
1
1
1
1
1
1
0
1
1
0
0
1
1
0
2
1
1
0
2
1
1
1
1
1
2
1
1
1
1
2
1
1
2
2
1
1
1
1
0
1
2
2
2
1
2
1
1
1
1
1
1
1
2
0
1
0
2
1
1
2
0
2
1
1
1
1
0
2
1
0
1
1
1
2
1
0
1
1
1
1
1
1
1
1
1
0
1
2
2
1
0
2
0
1
1
1
1
2
1
1
2
1
0
1
2
2
1
4
2
1
1
1
2
0
1
1
1
1
2
2
0
1
2
2
0
1
2
1
2
0
2
0
1
1
2
1
1
1
2
0
2
1
1
1
0
1
1
2
2
0
2
2
0
1
1
1
2
2
2
1
1
1
2
1
1
1
0
2
1
2
1
0
1
1
1
2
1
0
1
0
1
1
1
0
1
1
1
2
1
2
1
1
2
1
0
1
1
3
1
0
2
2
1
1
1
1
1
1
1
1
2
0
1
1
1
1
1
1
2
1
1
2
1
0
1
1
1
2
1
2
2
1
1
1
3
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
0
2
0
1
2
1
2
1
0
2
0
0
1
1
2
2
2
1
1
1
2
2
1
1
2
1
1
1
1
2
1
2
1
1
2
2
2
1
2
2
1
1
1
2
1
2
1
1
1
1
2
1
2
1
1
1
0
1
2
1
1
0
1
1
0
0
2
1
1
1
1
0
1
2
1
1
2
1
0
1
2
2
2
1
2
2
1
1
2
2
0
2
0
1
1
1
0
0
2
2
1
0
1
1
2
1
1
1
2
1
1
1
1
2
2
1
1
2
1
2
2
1
1
0
1
1
0
1
2
1
1
0
1
2
2
1
1
1
2
1
1
1
2
1
1
0
1
1
1
1
1
1
2
0
2
2
2
1
1
0
0
0
1
0
1
1
1
2
2
1
0
0
0
1
1
0
2
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
0
1
1
1
1
1
1
2
1
1
1
1
1
1
0
1
2
1
1
1
1
2
0
1
2
1
9
2
2
1
2
2
0
1
2
1
4
0
2
0
2
1
2
1
2
2
1
0
1
1
0
1
2
1
1
2
0
1
2
1
2
2
2
0
0
1
3
1
1
1
1
1
1
1
2
1
4
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
0
1
1
2
1
1
2
0
2
1
1
1
2
2
1
1
2
1
2
1
0
2
2
1
0
2
1
0
2
0
1
2
1
1
1
1
0
1
1
1
1
0
1
0
1
2
2
1
2
1
1
1
3
2
1
1
2
2
2
1
2
2
1
2
1
1
2
1
1
1
1
1
1
1
2
1
2
0
1
2
0
1
1
2
0
0
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
2
2
2
1
2
1
2
1
0
2
0
1
0
1
1
1
1
0
1
1
1
1
1
1
2
1
0
2
1
1
1
1
1
2
0
1
1
1
0
1
2
1
2
1
2
1
1
1
2
1
1
1
1
1
2
1
1
0
1
1
2
1
1
2
1
2
2
0
2
0
0
0
1
1
1
0
2
2
2
0
1
1
1
1
2
0
2
1
2
2
0
1
2
2
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
0
1
1
0
1
1
2
2
1
1
1
1
1
0
1
1
1
2
1
1
1
0
1
2
0
1
1
1
2
0
1
0
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
0
1
0
1
0
1
1
1
1
1
1
1
2
1
1
2
1
1
0
1
2
2
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
0
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
1
1
0
1
1
1
2
0
1
2
2
1
0
1
2
0
1
2
1
1
2
1
1
1
1
1
2
1
1
1
1
0
2
1
2
2
1
1
1
0
0
0
0
2
0
1
1
2
2
1
1
1
1
1
1
1
2
1
0
4
1
7
1
1
0
0
1
1
2
1
0
1
1
2
1
1
2
1
1
1
1
1
1
0
2
2
2
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
2
1
2
0
1
1
1
1
1
1
1
0
1
2
1
2
1
0
1
1
1
1
0
1
2
0
0
1
1
0
2
0
2
0
2
0
1
1
1
1
3
0
0
0
2
1
0
1
2
1
1
1
1
2
1
1
1
1
1
2
1
1
2
2
2
3
1
2
2
1
1
1
1
1
1
1
2
2
3
1
1
2
1
0
2
1
1
1
1
2
0
1
0
1
1
1
1
2
2
1
1
1
2
1
2
1
0
1
1
1
1
0
3
0
0
1
2
1
2
2
2
1
1
1
1
1
1
1
2
1
1
1
0
0
1
2
1
2
1
0
2
1
1
1
1
1
0
1
2
0
1
1
0
1
1
0
1
1
1
1
1
1
1
0
0
2
2
1
1
2
1
1
1
1
1
1
1
1
2
1
2
1
1
1
2
1
3
1
2
0
2
0
1
0
1
1
1
1
1
1
1
0
1
1
1
1
1
1
0
2
1
1
1
0
0
0
2
1
1
1
1
2
0
1
1
0
0
2
1
1
1
0
2
2
1
2
2
0
1
1
1
1
1
1
1
1
1
1
1
0
2
0
1
2
2
1
1
0
0
0
0
1
1
1
1
0
1
2
1
0
1
1
2
2
1
1
2
2
0
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
2
2
1
2
0
1
0
1
1
2
2
1
2
1
1
2
1
1
2
1
0
2
1
1
0
2
1
0
1
2
0
1
0
1
1
1
1
1
1
1
2
1
1
0
1
2
0
1
0
2
2
1
2
2
1
1
1
1
1
2
2
2
1
1
1
1
1
2
1
0
2
1
2
1
0
2
1
1
2
1
1
1
2
1
2
1
1
2
1
1
2
3
1
2
1
0
1
2
0
1
1
1
2
1
1
2
2
2
1
1
1
2
2
1
1
0
1
1
1
1
2
1
1
2
2
0
2
2
2
1
0
1
2
2
1
2
2
1
2
1
1
1
1
1
1
1
1
0
1
1
1
2
1
1
0
1
1
1
2
0
1
1
1
1
1
1
1
1
1
1
0
2
0
1
1
1
1
0
1
2
4
1
2
1
1
0
1
1
0
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
0
2
1
2
1
2
2
2
2
0
1
1
4
1
1
1
2
2
1
1
2
1
0
1
1
1
2
1
0
5
1
0
2
2
1
1
1
1
1
0
1
1
2
1
1
1
2
1
2
2
1
2
0
1
1
1
2
1
1
2
1
1
2
0
1
2
1
2
1
2
2
2
1
1
1
2
0
1
2
1
1
0
1
1
1
1
2
1
2
0
1
1
2
1
2
1
2
2
1
1
1
1
1
1
1
1
1
0
0
1
0
2
1
0
1
1
1
2
1
1
1
0
1
1
0
0
2
1
1
1
2
2
1
1
2
1
1
2
1
1
1
1
2
1
2
0
1
2
1
2
1
1
5
0
1
1
2
1
1
2
1
1
1
1
1
1
0
1
2
1
2
1
1
2
2
1
1
2
2
0
0
1
1
2
2
1
1
2
1
2
1
2
1
1
2
2
1
2
1
2
1
0
1
2
2
1
1
2
1
1
0
2
1
1
2
2
0
1
1
1
1
1
2
1
2
2
1
2
2
1
1
0
1
1
2
1
0
1
1
0
1
1
1
2
1
1
2
0
2
0
1
2
1
1
1
0
2
1
1
0
0
1
0
1
2
1
2
1
5
2
0
2
0
0
1
2
1
1
1
1
1
1
1
0
1
0
1
0
1
1
1
0
2
1
0
1
1
1
2
2
1
2
1
0
1
1
1
1
1
0
1
0
1
0
1
2
1
2
1
1
1
2
1
1
1
1
0
1
2
1
2
1
1
0
2
1
0
0
0
1
0
1
0
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
2
1
1
1
2
1
2
1
1
2
1
1
1
2
1
1
1
1
1
1
2
1
2
1
2
1
1
1
1
0
2
2
2
2
1
1
0
1
2
2
1
2
2
2
2
1
2
2
1
1
1
1
0
1
2
3
0
0
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
0
1
1
0
2
1
2
1
1
1
1
2
1
1
2
1
1
1
2
1
2
1
1
1
2
1
1
1
2
0
1
1
1
1
1
1
1
1
0
1
0
1
2
1
2
2
1
2
0
0
1
0
1
0
1
1
0
1
1
1
1
1
2
2
0
1
1
2
2
2
1
1
1
1
1
0
1
1
0
1
1
1
1
0
0
1
1
1
0
1
1
1
1
2
0
1
1
0
2
0
0
1
1
2
1
1
1
1
2
2
0
1
0
2
2
1
2
2
1
1
1
1
1
2
1
2
1
2
1
0
1
1
0
0
0
0
2
2
0
1
3
2
0
1
2
1
1
1
1
1
1
0
2
1
1
1
1
2
2
1
0
1
1
0
1
0
0
1
0
1
1
1
1
1
1
3
1
1
1
0
0
0
1
1
1
2
1
0
1
2
0
2
1
0
1
1
2
1
1
1
0
1
0
1
1
2
2
0
1
0
1
1
1
1
0
1
1
1
0
2
1
1
2
1
1
1
1
2
1
1
1
2
0
1
2
1
1
2
1
1
0
1
2
2
1
1
2
2
1
2
2
3
1
0
2
1
1
1
1
1
1
2
1
0
2
1
1
0
2
2
0
1
1
1
1
1
1
1
1
2
1
1
2
1
0
2
0
1
1
2
1
1
0
2
1
2
0
1
0
0
2
1
1
1
1
1
1
1
1
0
1
1
1
2
1
1
2
1
1
2
2
1
2
0
1
1
1
2
1
2
1
1
1
2
1
1
2
14
1
2
0
1
1
1
1
0
1
1
2
1
2
1
1
2
1
0
2
0
1
2
1
2
1
1
1
2
0
1
1
1
1
3
2
1
2
1
2
1
0
1
1
1
1
1
2
1
1
1
1
1
1
1
2
2
0
1
2
1
2
0
1
2
2
0
2
1
1
2
0
1
2
1
1
1
1
1
2
1
1
1
2
1
2
1
2
2
4
2
1
2
1
0
1
1
1
1
1
2
1
1
2
2
0
1
1
1
2
1
2
1
1
1
0
1
1
1
1
1
1
1
1
2
2
2
2
0
1
1
1
2
0
1
0
1
1
2
1
2
1
1
1
1
1
2
0
2
2
1
1
0
2
1
2
1
2
0
2
1
2
2
2
1
1
1
1
1
1
3
1
1
1
1
0
2
2
2
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
2
1
1
1
2
2
2
2
2
1
2
0
2
1
1
2
1
0
1
2
1
2
1
2
1
1
1
1
2
1
1
1
1
2
2
1
2
1
2
2
0
2
3
1
2
1
0
1
0
1
0
2
1
1
1
1
1
2
2
1
2
2
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
0
1
2
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
2
1
2
1
2
1
1
0
2
1
2
1
2
1
1
1
1
1
1
1
1
0
1
1
1
1
2
1
1
1
1
1
0
2
1
1
1
2
1
2
1
1
1
2
2
2
1
1
1
1
2
1
1
1
1
0
0
1
1
1
1
1
1
1
1
0
1
1
1
2
1
1
1
0
2
1
0
1
2
1
1
1
2
1
2
1
1
1
1
0
1
2
1
2
1
1
1
1
1
0
1
0
1
1
1
1
1
2
1
1
1
2
2
1
2
2
1
1
1
1
1
2
2
1
2
2
1
1
0
1
2
1
2
1
1
1
2
1
1
1
1
1
0
1
1
1
2
0
1
0
1
1
2
1
1
1
1
1
2
2
2
1
2
2
2
2
2
1
1
1
2
1
1
0
1
1
0
1
2
1
1
1
2
1
1
1
1
2
0
2
2
1
2
2
1
2
2
2
0
2
1
1
1
2
2
2
2
1
1
2
1
0
1
1
1
1
1
1
0
1
1
2
2
0
2
2
1
1
1
1
1
0
1
1
1
1
2
2
1
1
1
1
2
1
1
0
2
2
2
2
1
2
1
1
0
1
1
1
1
1
0
0
1
1
1
1
1
2
1
1
1
2
2
1
2
1
2
0
1
2
2
1
1
1
1
1
1
0
1
2
1
0
1
1
2
1
1
1
1
1
1
2
1
1
0
1
0
1
0
2
1
2
1
1
1
1
3
1
0
2
1
2
2
1
0
1
1
0
1
1
1
2
1
0
1
1
1
1
2
1
2
2
2
2
2
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
2
2
2
1
1
1
2
1
1
1
1
1
0
1
2
1
1
2
1
1
1
2
1
1
1
1
0
0
2
2
1
1
2
1
1
2
1
1
0
2
1
1
4
2
2
1
1
1
0
1
2
0
1
2
2
1
2
1
1
1
2
1
0
1
1
2
1
0
1
1
1
0
1
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
2
1
0
1
1
1
1
1
1
2
2
1
1
1
1
1
1
0
2
1
1
2
0
2
2
1
2
2
0
1
1
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
0
2
1
0
1
2
2
2
1
2
1
2
0
0
1
0
1
1
1
2
1
0
2
1
1
1
1
1
0
0
1
1
0
1
1
1
2
1
0
0
1
1
1
1
0
1
2
1
1
2
2
1
1
2
2
1
1
0
1
1
1
2
1
1
1
1
1
0
1
2
1
1
1
1
1
1
1
1
2
1
1
1
3
1
0
1
0
1
1
1
1
1
1
1
2
2
1
2
1
1
0
2
2
1
0
0
0
1
1
1
1
1
1
2
1
1
1
1
0
1
1
1
1
0
2
1
1
0
1
1
1
1
1
2
1
1
1
1
0
1
2
2
1
3
1
0
2
1
1
1
1
1
2
2
1
1
1
1
0
1
1
2
1
1
1
0
1
0
1
0
2
1
1
0
1
2
0
1
1
2
1
1
2
1
2
1
1
1
2
1
1
1
1
2
2
2
1
1
1
2
0
2
1
2
2
2
1
1
1
1
1
0
1
1
2
2
0
1
1
0
1
1
2
1
1
1
2
1
2
1
1
1
1
0
1
0
0
1
1
0
1
1
1
1
0
1
1
1
0
2
0
0
2
1
1
1
1
0
2
1
1
1
1
1
2
2
1
1
1
2
1
1
0
1
1
0
1
2
1
1
1
1
1
1
2
2
1
1
1
2
1
1
2
2
2
1
1
1
2
2
1
1
1
2
1
2
1
2
1
0
1
1
1
1
1
0
1
2
2
2
1
2
1
3
1
1
1
0
1
2
1
1
2
2
1
1
2
1
1
1
1
0
1
1
1
1
1
2
1
1
2
1
1
1
2
1
3
1
2
2
1
1
1
2
2
2
0
2
0
1
2
0
2
2
1
1
1
1
1
0
2
1
1
1
1
1
1
1
0
2
2
2
1
0
1
2
0
1
1
1
1
1
1
1
0
0
1
1
0
1
0
0
1
2
1
1
1
1
1
1
0
1
2
1
1
1
1
1
2
1
2
0
0
1
0
2
0
1
1
1
1
2
1
2
1
1
2
1
2
1
1
2
2
1
1
1
0
1
1
1
1
1
2
1
4
1
1
1
1
1
1
1
1
2
0
1
1
1
1
1
0
1
1
1
0
2
2
2
1
1
1
0
1
0
1
1
2
1
1
1
0
2
1
1
0
1
1
1
1
1
1
1
0
2
0
2
1
1
2
0
1
0
1
1
0
1
1
2
2
2
1
1
1
1
2
1
1
1
2
2
2
1
1
1
0
1
2
2
1
1
1
2
1
0
2
1
1
1
0
1
2
2
2
1
1
2
2
1
1
1
0
1
2
1
1
0
2
2
1
1
2
1
0
1
1
1
1
2
2
1
2
1
2
1
2
1
1
1
2
1
1
0
1
1
1
1
0
1
1
2
1
2
1
1
0
1
0
0
1
1
1
2
1
2
1
2
2
2
1
1
1
1
1
1
1
0
1
1
1
2
1
0
0
1
2
1
1
2
2
1
1
2
2
1
1
0
1
1
1
1
1
1
1
2
0
2
1
1
1
0
1
0
2
2
1
1
1
1
1
2
2
1
1
2
2
0
2
1
2
2
0
2
2
0
2
2
2
1
1
1
1
2
1
1
1
0
1
2
0
1
1
2
1
2
1
1
1
2
2
2
1
1
2
1
1
1
2
0
2
2
0
1
1
1
2
0
1
2
1
0
1
1
1
1
1
1
1
2
2
1
2
2
2
1
1
1
1
1
1
1
1
1
2
2
1
1
1
2
1
0
0
1
1
1
1
1
1
1
1
1
2
1
0
1
0
1
1
1
2
2
1
1
2
2
1
0
2
1
1
1
2
1
1
1
1
0
1
0
2
2
0
1
6
2
1
1
1
1
0
1
1
1
1
0
2
1
2
1
1
1
1
2
0
1
2
1
1
2
0
2
1
0
2
1
1
1
2
1
1
1
1
1
2
2
2
1
1
0
0
1
0
1
1
1
1
1
1
0
1
1
2
1
2
0
0
1
1
1
2
1
2
2
1
0
0
1
0
1
2
1
0
1
1
2
2
1
0
0
2
1
0
2
2
1
1
0
1
1
0
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
0
1
0
2
1
1
2
2
1
1
1
2
1
1
0
2
1
2
1
1
0
2
1
1
2
1
1
0
0
1
0
0
2
1
2
1
1
1
1
1
2
2
1
1
2
1
2
1
1
0
1
2
1
1
0
0
1
1
1
1
2
2
0
1
1
1
1
1
2
1
0
1
2
2
1
0
1
2
1
2
0
1
2
2
1
0
1
1
1
1
0
1
1
1
2
2
1
2
1
1
2
2
1
0
1
1
2
1
1
2
1
0
1
1
1
2
1
1
3
2
1
1
1
2
4
1
2
1
1
1
0
1
2
2
1
1
2
1
1
1
1
1
2
2
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
2
2
1
2
1
2
1
1
1
0
1
1
2
1
1
0
1
1
1
1
2
0
1
0
1
1
0
2
2
1
0
2
2
1
1
2
1
1
1
1
2
1
2
1
1
1
2
0
2
2
1
1
1
1
2
1
1
1
1
1
0
1
1
1
1
1
0
0
2
1
2
1
1
1
1
1
0
1
1
1
0
1
1
2
1
1
0
1
1
0
0
1
0
1
1
1
2
0
1
1
2
1
1
1
2
2
1
0
1
1
0
2
0
1
1
2
1
1
1
2
2
1
2
1
1
1
0
2
1
1
1
1
1
2
1
1
1
1
2
0
2
1
1
1
1
2
0
2
1
1
1
1
2
1
2
1
2
2
1
1
1
0
1
1
0
2
1
1
1
1
1
2
1
0
1
1
1
1
0
1
1
1
1
1
1
1
1
2
1
0
2
1
2
0
2
1
1
1
1
2
2
2
1
1
1
1
0
1
1
0
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
3
0
5
1
2
1
2
1
2
1
0
1
1
0
1
0
1
2
1
1
1
0
1
0
2
2
2
1
1
2
1
2
2
1
2
2
1
2
1
2
1
1
0
2
2
1
1
2
1
1
0
2
1
1
1
1
0
0
1
2
2
2
1
1
0
2
1
1
1
2
1
1
1
0
2
1
1
2
1
1
0
1
1
1
2
1
0
1
1
2
0
1
0
0
1
1
1
1
1
1
2
2
2
1
2
2
1
1
1
1
1
2
1
1
2
1
0
1
1
1
2
0
2
1
1
0
1
1
1
2
1
1
1
1
1
1
2
0
1
1
0
2
0
1
1
2
1
1
1
2
1
1
1
2
2
1
1
1
1
1
2
2
1
2
0
1
1
1
1
1
1
0
1
0
1
1
1
1
1
2
1
1
2
1
2
1
1
2
2
0
1
2
2
1
1
2
1
0
1
2
1
1
1
0
0
1
1
1
1
1
1
0
1
1
1
2
2
2
2
2
2
2
2
1
1
1
2
1
0
1
0
0
2
2
1
1
0
1
1
0
1
1
2
2
2
1
0
1
1
1
1
1
1
1
2
1
0
0
1
1
1
1
1
1
1
1
2
1
1
0
0
1
1
1
1
2
2
1
1
1
0
1
0
2
1
0
2
2
1
2
1
1
1
2
1
1
1
1
1
1
2
0
2
0
0
1
1
2
1
2
2
2
2
1
2
0
0
0
1
1
0
2
1
1
2
1
1
1
1
0
1
1
2
0
0
1
0
0
0
0
1
1
2
1
1
2
1
1
0
1
2
1
1
1
1
2
1
1
1
2
2
2
1
1
2
1
0
1
1
1
2
0
1
1
2
1
1
1
1
2
1
0
1
0
0
1
1
1
0
2
1
0
1
1
1
1
2
1
1
0
2
1
1
2
2
2
2
1
1
1
1
1
2
1
1
2
2
0
1
1
0
1
1
2
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
0
0
1
1
3
1
1
1
1
1
2
1
2
2
1
1
1
1
1
1
2
2
1
1
1
1
2
2
2
1
1
1
1
1
2
1
2
2
1
2
2
1
1
2
1
0
1
1
1
1
0
2
2
1
1
2
1
1
0
2
1
1
1
1
1
1
1
0
1
2
1
1
0
0
1
1
2
1
1
1
0
1
0
2
2
1
0
2
1
1
0
1
2
1
0
2
1
2
1
0
1
0
0
1
1
1
1
3
2
0
2
2
2
0
2
2
1
1
1
1
1
2
1
2
1
0
1
0
1
0
0
1
1
1
1
1
1
2
1
0
2
2
1
1
1
1
2
1
2
0
2
0
1
1
1
2
1
2
1
1
1
2
1
2
1
1
0
1
1
2
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
2
0
1
1
2
1
1
1
1
2
1
1
1
1
2
2
2
1
1
2
0
1
1
0
1
1
2
1
2
1
0
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
0
1
1
1
2
1
2
1
0
1
0
1
1
1
1
1
1
1
2
2
1
2
2
1
2
1
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
2
1
1
2
1
2
1
2
1
2
1
2
1
2
2
1
1
0
2
2
1
1
2
1
2
1
1
2
0
1
1
0
2
0
1
1
2
1
1
2
2
2
1
1
1
1
0
1
1
0
1
1
1
1
2
1
1
0
1
2
1
0
1
1
1
1
2
1
0
1
1
1
1
1
2
2
2
1
0
1
2
2
0
1
2
1
2
1
0
2
2
1
2
1
2
1
2
1
2
1
1
2
1
1
1
1
1
2
0
1
1
1
1
1
0
1
2
1
1
0
1
1
1
1
1
2
2
2
2
1
1
1
1
2
1
2
2
2
1
2
1
1
0
1
2
0
1
2
1
1
2
0
2
1
2
1
5
2
2
1
0
0
0
0
2
1
1
0
2
1
0
1
2
1
2
2
2
1
2
1
1
2
2
1
1
1
1
1
1
2
2
1
3
1
0
1
0
2
0
1
1
0
1
0
1
1
1
0
0
1
1
2
2
1
1
1
1
0
2
2
1
1
1
1
1
1
1
0
2
1
1
0
3
2
2
1
1
1
1
1
1
2
1
1
1
2
0
2
1
1
1
1
1
1
1
1
2
1
2
2
2
2
1
1
0
1
2
2
1
1
1
1
1
1
2
1
2
0
1
1
2
1
1
2
0
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
0
1
1
1
1
2
1
1
2
1
0
1
1
0
2
0
1
1
1
1
2
1
1
1
1
1
1
2
1
1
0
1
2
1
1
0
2
1
1
1
1
2
2
1
2
1
1
1
2
2
1
2
1
1
2
1
3
2
1
1
1
2
2
1
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
0
0
1
1
1
1
1
1
1
1
0
1
1
2
2
1
0
0
2
2
2
1
1
1
1
2
1
1
1
2
1
1
1
2
1
0
1
1
1
1
1
2
2
1
1
9
1
1
0
1
2
1
1
0
2
2
1
1
1
1
2
3
2
2
2
0
1
1
1
1
1
0
2
2
0
1
1
1
2
1
1
1
2
2
1
1
2
1
1
0
1
0
2
2
1
1
0
1
1
1
1
2
1
1
2
1
1
1
1
1
2
2
2
1
1
1
1
1
1
2
1
0
0
1
1
2
0
0
1
0
1
1
2
2
1
2
2
1
0
1
1
2
1
1
2
1
1
0
1
0
1
2
1
1
1
1
1
2
0
1
1
1
0
0
1
1
1
1
1
1
2
1
1
1
1
1
0
1
1
1
1
0
2
1
1
1
1
2
2
1
1
1
1
2
1
2
1
1
1
1
2
1
1
1
0
2
1
1
1
1
1
1
3
1
1
1
1
1
1
0
1
1
1
2
1
1
2
2
2
2
0
1
2
1
2
2
0
2
1
2
1
1
1
1
2
1
1
1
2
2
0
2
1
0
1
0
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
0
2
2
1
1
1
1
1
2
0
2
2
1
1
1
2
1
1
1
1
2
1
1
2
1
2
1
4
2
1
1
1
1
1
2
1
3
1
0
1
1
1
1
1
1
1
1
0
2
1
1
1
2
2
1
1
0
1
1
1
1
1
1
1
1
1
0
2
1
1
1
1
1
2
1
1
1
1
1
2
1
2
0
2
2
1
2
2
0
1
1
1
1
1
1
2
1
2
2
0
2
1
1
1
1
1
1
1
1
0
1
2
2
1
0
1
0
0
2
1
1
1
0
1
0
1
1
2
2
1
1
1
1
1
1
2
1
0
0
2
0
2
1
1
2
1
1
1
2
1
1
0
0
1
1
2
1
2
2
1
1
1
1
0
1
2
2
2
0
1
1
1
2
1
1
1
2
0
2
0
0
1
1
1
0
1
0
1
2
1
1
0
2
2
1
1
2
2
1
0
1
2
1
1
1
1
0
0
2
1
1
1
1
1
1
1
2
1
1
2
2
1
1
1
1
2
2
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
2
2
1
0
0
2
1
0
0
2
2
3
1
0
1
1
2
2
2
1
2
1
1
1
1
1
0
1
1
1
2
1
1
2
1
2
1
2
1
1
1
1
1
1
1
0
1
1
1
2
1
1
1
1
2
2
1
0
1
1
2
1
1
2
1
1
0
0
3
1
1
1
2
1
2
0
2
2
1
1
1
1
1
2
0
1
2
2
1
1
0
2
1
2
0
1
1
1
0
1
1
2
2
1
2
1
2
1
1
1
0
2
1
2
1
1
0
2
2
2
1
1
1
0
2
1
2
0
0
0
1
1
2
1
2
1
1
1
1
1
1
0
1
0
1
2
1
1
2
1
1
0
1
1
1
2
1
1
1
1
1
1
1
1
1
2
0
1
1
1
0
2
1
1
2
1
1
1
1
2
2
2
1
2
1
0
2
2
2
1
2
1
1
2
1
2
0
1
2
1
0
2
1
1
1
1
2
1
1
1
2
1
0
1
1
1
2
1
0
1
1
1
1
2
2
2
2
1
1
1
2
1
1
2
2
1
1
2
1
1
2
1
1
1
2
2
2
1
1
0
0
1
1
1
1
1
0
2
1
1
1
1
1
1
2
1
1
1
1
0
1
1
1
1
1
1
1
2
1
3
2
2
0
1
1
1
1
1
2
0
1
2
1
1
2
1
2
0
1
1
2
1
0
1
2
1
1
2
1
1
1
1
1
2
2
1
1
1
1
2
1
2
1
2
2
2
1
0
1
1
2
1
1
0
2
0
1
1
0
1
1
2
1
0
2
1
2
2
1
1
1
0
1
1
1
0
0
1
1
1
2
2
1
1
1
1
1
2
1
2
1
1
1
1
2
1
2
2
1
2
1
1
3
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
0
1
1
1
0
1
1
2
1
1
2
2
1
1
0
1
2
2
2
2
1
3
0
2
1
1
1
2
1
1
1
1
3
2
2
1
0
0
2
1
0
0
1
2
0
1
1
1
2
1
1
2
1
1
1
1
1
1
1
0
1
1
2
1
1
1
2
1
0
1
1
2
1
0
1
2
1
0
2
1
2
2
1
1
1
1
2
2
1
2
1
1
0
2
1
2
0
2
1
0
1
0
1
2
1
2
3
1
1
1
1
2
1
2
2
1
1
1
1
2
0
1
0
2
1
2
1
1
1
0
0
1
0
2
1
1
1
2
1
1
1
2
0
1
1
2
1
1
1
0
1
1
1
0
1
2
1
1
1
1
2
3
0
2
2
2
0
1
1
0
1
1
1
1
1
1
0
2
2
1
1
1
1
2
1
1
1
2
1
0
2
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
2
0
1
2
1
1
1
0
1
2
1
1
2
2
1
1
0
1
0
2
1
1
0
0
1
2
2
2
1
1
0
1
1
0
2
2
1
1
2
1
2
2
0
1
0
1
2
1
2
2
1
1
1
2
1
1
2
0
1
1
1
0
1
2
1
1
0
1
2
0
1
2
1
2
0
2
0
1
1
1
1
1
3
1
2
1
1
1
2
1
1
2
1
0
0
1
1
0
1
1
1
1
0
1
1
1
1
0
1
1
1
1
1
0
0
0
3
2
2
1
1
1
0
2
2
1
1
1
2
1
0
0
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
0
2
2
3
2
1
1
1
2
1
1
0
1
1
1
0
0
1
1
0
1
1
1
2
2
1
1
1
2
0
1
1
2
0
1
1
1
0
0
2
3
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
0
0
1
2
0
1
2
1
1
1
2
2
1
1
1
1
0
1
1
1
0
2
1
1
0
1
1
2
2
2
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
2
0
0
2
1
0
1
0
1
0
2
1
0
0
1
2
2
0
2
2
2
0
0
1
1
2
1
2
2
1
1
1
1
1
1
1
0
0
1
1
2
1
1
2
1
2
0
2
1
1
0
1
1
1
1
1
2
1
1
0
2
1
0
2
1
1
1
0
1
1
1
0
1
1
1
1
2
0
1
1
1
2
1
1
1
1
1
2
4
1
2
1
1
0
1
1
1
1
2
1
2
1
1
1
1
1
1
1
2
1
2
2
1
1
0
1
1
1
2
1
1
1
2
1
1
2
2
1
1
2
2
1
1
1
1
1
1
2
0
1
2
2
1
2
2
2
0
0
2
0
1
2
2
2
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
2
1
0
2
1
2
1
1
0
1
1
2
0
2
1
2
2
1
2
0
1
2
2
1
1
0
1
1
1
1
1
0
1
0
2
1
1
1
1
1
1
0
0
1
1
1
2
1
2
2
1
2
1
1
1
2
0
1
2
1
2
1
1
1
2
1
1
0
2
2
1
1
1
2
1
2
1
2
2
1
0
1
0
2
1
0
2
0
1
1
1
1
1
1
1
0
2
2
1
1
2
2
1
2
2
1
1
2
1
0
1
1
1
2
0
2
1
1
2
1
2
2
1
0
0
2
2
0
1
0
2
0
1
0
1
1
1
2
1
1
2
1
0
2
0
1
0
1
1
1
0
2
1
1
0
2
1
1
0
0
0
0
2
1
0
1
2
0
2
1
1
2
1
1
2
2
1
1
1
1
1
0
1
1
2
1
2
1
2
1
1
1
2
0
1
0
1
2
1
1
2
2
1
1
1
1
1
2
1
0
1
0
2
2
1
2
0
1
2
1
1
1
2
2
2
1
1
1
1
1
2
1
1
0
2
1
2
1
0
0
0
1
0
1
1
1
2
1
1
2
1
0
2
2
1
1
1
2
0
2
0
0
2
2
1
1
1
1
1
1
1
1
2
0
2
0
1
1
1
2
2
0
1
1
1
0
1
1
1
1
1
1
0
1
0
1
1
2
1
1
2
2
1
1
1
0
1
1
1
0
1
1
2
1
1
1
1
0
1
2
1
0
1
2
2
1
0
1
1
1
1
1
2
1
1
2
2
1
1
0
2
1
2
2
1
2
0
2
0
2
1
1
1
2
1
1
1
1
2
1
1
1
1
0
2
1
1
2
1
1
2
1
1
1
1
1
1
1
1
0
1
1
0
1
0
1
1
1
1
0
1
2
2
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
2
1
2
1
1
1
0
2
0
1
1
1
1
1
2
1
2
1
2
2
1
2
2
2
0
1
2
1
0
2
1
0
1
1
1
2
1
1
1
1
2
1
1
2
2
1
2
1
2
1
1
1
2
2
1
2
2
1
1
1
2
1
2
1
2
1
1
2
2
1
1
1
1
1
0
1
1
1
2
2
1
1
1
2
2
2
2
1
0
0
1
1
1
2
1
1
2
1
2
2
1
1
1
1
1
2
1
0
0
1
0
1
0
1
2
1
1
1
1
0
1
1
2
1
1
2
2
2
1
1
1
0
1
2
1
2
1
0
1
1
0
1
3
1
1
1
2
0
1
2
1
0
2
2
0
1
2
2
1
2
1
1
1
0
1
4
1
1
1
1
1
2
2
1
2
1
1
0
1
2
1
1
1
0
1
1
2
2
1
2
1
2
2
1
1
0
1
0
2
1
1
5
1
0
1
2
1
2
2
1
1
2
1
1
2
1
1
0
1
0
2
1
0
1
1
1
1
2
1
2
1
1
1
1
2
0
2
1
0
2
2
3
2
1
1
1
2
1
2
1
1
2
1
1
0
1
2
2
1
2
2
0
2
0
1
1
1
1
1
1
1
1
1
1
1
0
0
1
2
1
2
2
1
1
2
2
1
1
1
2
1
1
1
2
1
1
1
1
1
2
2
1
0
1
2
1
2
1
1
1
1
2
1
0
1
1
0
0
1
1
1
1
0
0
1
1
2
1
1
2
0
1
2
1
2
1
2
1
1
1
1
1
2
2
1
2
1
0
1
1
1
0
1
0
3
0
1
1
1
1
1
0
1
0
2
1
1
2
1
0
1
2
0
1
0
1
1
1
2
1
0
2
1
2
2
1
1
2
1
1
1
1
1
2
1
1
1
1
0
1
0
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
0
1
1
0
0
0
0
1
1
2
2
1
1
2
0
1
0
1
2
1
1
1
0
2
1
0
1
1
2
1
1
2
0
2
1
1
1
1
0
1
0
2
1
1
1
1
1
2
1
1
0
1
1
1
2
1
1
1
1
1
1
2
0
2
2
1
1
1
0
1
2
1
1
2
0
0
2
2
1
2
1
1
2
1
1
1
0
1
1
1
2
1
2
1
2
1
1
1
1
2
1
1
0
2
1
2
0
1
2
2
1
1
1
0
1
2
0
1
0
2
0
1
1
2
1
1
0
0
2
1
1
2
2
1
0
1
1
1
1
1
1
0
3
1
0
2
1
1
2
0
2
1
2
0
1
1
1
1
1
2
1
0
2
1
1
1
1
1
1
1
1
1
1
1
2
0
2
2
0
1
1
1
1
1
1
2
1
1
1
1
2
2
1
1
1
1
2
0
1
1
0
1
1
2
1
2
1
0
0
1
1
2
1
2
1
2
1
1
1
1
2
2
0
1
1
1
2
1
1
1
1
2
1
1
2
2
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
2
1
1
2
1
1
2
2
1
1
0
1
1
1
1
1
1
1
2
1
1
2
0
2
1
1
1
1
0
1
2
0
1
2
0
1
0
1
0
2
2
2
1
1
1
2
0
2
1
0
0
1
1
0
1
0
3
1
1
1
0
0
2
1
2
2
1
2
1
2
2
0
1
1
1
3
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
0
1
1
2
1
0
1
1
1
2
2
1
1
0
0
1
1
1
0
2
0
1
2
2
1
1
1
1
3
0
2
1
1
1
1
1
1
1
2
1
0
0
2
2
1
1
1
1
1
1
1
0
2
2
2
2
2
2
1
1
2
1
1
1
0
0
0
1
1
1
1
0
2
1
1
1
1
2
1
1
1
1
2
1
2
2
0
2
1
1
1
2
1
1
2
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
1
0
2
1
2
1
1
1
1
1
1
2
1
1
1
0
2
0
2
1
2
1
2
1
1
1
0
2
1
0
1
1
0
2
1
1
1
0
1
2
2
1
2
2
2
2
1
1
1
1
1
1
2
2
2
1
1
1
0
1
1
0
1
1
0
1
1
1
1
1
1
2
1
1
1
1
1
1
0
1
1
0
1
2
2
2
0
2
1
2
1
0
2
2
2
1
0
0
1
2
1
1
1
2
1
3
0
1
1
2
2
1
2
1
1
1
1
1
2
2
0
1
0
1
0
1
1
1
2
1
1
1
2
2
1
0
0
2
0
1
2
1
2
1
0
0
1
1
1
1
2
1
1
1
0
1
1
1
0
0
1
2
0
1
2
2
2
1
2
2
1
1
1
0
2
1
1
2
1
2
1
1
2
1
1
1
2
0
2
1
2
2
1
2
1
0
1
2
1
0
1
1
1
0
1
1
1
1
0
1
1
1
1
0
0
1
1
1
2
2
1
0
1
0
1
1
3
1
0
2
1
0
0
2
1
1
2
1
1
2
1
2
1
2
1
1
2
1
1
1
1
0
1
2
0
1
2
1
1
1
2
1
1
2
1
0
1
2
1
1
2
1
1
2
2
0
1
1
1
1
0
2
1
2
0
1
1
0
2
0
2
1
1
2
1
2
2
1
2
1
1
1
0
1
1
1
1
1
2
2
1
1
1
2
1
1
2
1
2
1
1
2
3
1
2
1
1
2
1
2
2
0
1
1
1
1
1
2
1
0
1
1
0
2
1
1
1
1
1
1
2
1
1
2
0
1
2
2
2
1
1
1
1
2
2
1
1
2
1
1
1
2
0
2
1
2
2
1
1
1
1
0
1
0
1
0
1
1
2
1
1
2
1
2
0
1
1
0
2
0
1
2
1
0
1
1
1
1
0
1
1
1
2
2
2
1
2
2
2
1
1
1
3
0
1
2
2
1
2
1
1
1
2
0
1
1
2
2
0
1
1
1
0
1
2
2
1
1
3
1
2
2
2
1
2
1
1
1
2
0
2
1
2
0
0
1
1
0
0
0
2
1
2
1
0
2
1
2
1
0
2
0
1
1
1
2
1
1
0
1
0
0
0
1
0
1
1
1
1
2
2
1
1
1
1
1
1
1
1
0
1
1
0
1
1
2
1
1
2
1
1
1
1
1
1
2
2
2
0
1
2
1
0
2
2
1
2
0
1
1
1
1
1
0
1
1
1
1
1
0
1
2
2
1
0
1
2
2
1
1
0
2
1
0
1
1
1
1
1
1
0
2
1
1
1
2
0
1
1
0
2
2
1
2
1
1
1
2
1
1
1
1
0
1
2
2
1
2
1
1
2
1
1
0
1
2
1
1
0
1
1
1
1
1
1
1
1
1
2
2
2
1
0
2
1
1
1
1
1
1
2
1
2
1
1
2
2
1
1
0
2
3
2
1
1
2
2
1
2
2
1
1
1
1
1
1
2
1
2
2
2
0
1
1
2
1
1
2
1
2
1
1
1
2
1
2
0
1
1
1
1
1
1
1
2
0
0
0
2
1
1
2
1
1
2
1
1
2
2
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
0
1
1
2
1
2
2
1
1
1
0
1
1
1
1
2
1
2
2
0
2
0
1
0
1
2
1
1
1
1
1
1
1
1
2
1
0
1
2
0
1
1
2
1
1
0
2
1
1
1
2
1
0
1
2
1
0
0
1
2
1
2
1
1
1
1
1
2
1
1
1
1
1
1
0
1
1
1
2
2
1
1
2
0
2
0
1
1
0
1
1
1
1
2
2
2
1
0
1
1
1
1
2
1
2
2
0
0
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
0
1
2
1
0
1
2
1
1
1
2
1
1
2
2
1
1
1
0
1
1
2
1
1
0
2
2
2
0
2
1
2
2
1
1
1
2
1
0
2
2
1
1
1
0
1
2
0
1
2
1
2
1
2
1
2
1
1
1
2
1
1
2
1
1
1
1
2
1
1
0
2
1
1
1
1
1
2
1
2
2
0
2
1
0
0
1
2
1
1
1
2
1
0
2
1
2
1
1
1
2
1
2
1
2
1
0
1
1
1
0
1
1
1
1
1
1
1
2
1
2
1
1
1
0
2
1
2
0
1
1
2
1
1
1
2
1
1
1
1
1
1
0
1
1
2
1
2
0
2
1
1
0
1
1
2
2
1
1
1
1
1
1
1
2
2
2
1
2
2
2
2
1
1
1
1
1
0
0
2
1
1
1
0
1
1
2
1
1
0
1
1
1
1
0
2
1
1
0
1
1
1
1
1
1
0
0
1
1
2
2
0
2
1
1
1
2
0
1
1
1
1
2
1
1
1
2
0
2
1
1
2
0
1
0
1
0
1
1
1
1
0
1
1
1
1
1
1
2
2
1
2
2
1
0
1
0
2
1
1
2
1
1
2
1
2
1
1
1
1
1
1
0
1
1
1
1
1
0
1
2
2
0
0
1
2
0
2
2
2
2
2
1
2
2
1
0
2
1
2
1
1
2
2
2
1
0
1
1
1
1
1
2
1
1
1
2
0
1
1
1
1
1
2
1
1
1
0
2
1
1
1
2
1
2
2
1
2
2
2
1
2
2
1
1
0
0
1
0
1
1
2
1
0
2
2
2
1
1
0
1
1
2
1
0
3
1
1
2
0
0
1
1
2
0
1
2
1
1
1
2
2
1
1
1
1
1
0
3
1
1
1
1
1
1
0
0
1
1
1
1
1
1
1
0
1
1
2
1
1
2
1
1
1
2
1
1
2
1
1
2
1
0
0
2
2
2
1
1
1
2
1
2
2
1
2
2
1
1
1
2
1
2
1
1
1
1
0
1
1
1
1
2
2
1
1
1
1
2
0
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
2
0
3
0
0
2
2
1
1
2
0
2
2
0
0
2
1
1
1
1
1
1
2
1
1
0
1
0
1
2
2
2
1
1
1
1
1
1
2
1
2
1
1
2
2
1
1
0
1
2
2
2
2
1
1
2
0
0
1
1
1
1
0
1
1
1
2
1
0
2
2
2
1
0
1
1
1
1
1
1
1
0
2
0
2
1
1
1
1
1
1
1
0
2
2
2
1
0
2
1
1
1
1
2
2
1
1
1
1
2
1
1
1
2
0
1
0
2
1
1
2
1
2
1
1
1
0
1
1
1
1
1
1
0
2
1
2
1
1
2
1
0
1
1
1
1
2
0
0
1
0
2
1
1
1
1
1
0
2
1
0
2
1
1
0
1
3
1
1
2
1
1
1
1
2
1
2
1
1
2
1
1
1
1
0
1
2
1
1
2
1
1
2
0
1
0
0
2
2
0
0
1
2
1
0
1
1
1
1
1
1
2
1
2
1
1
2
2
1
1
1
1
1
2
1
1
1
1
1
1
3
1
1
1
1
1
1
1
2
0
1
2
1
1
2
1
1
2
1
1
1
0
0
1
1
1
1
1
1
1
0
2
1
1
1
1
1
1
0
0
1
2
1
1
0
2
1
1
2
1
1
1
2
2
1
1
1
1
1
0
1
1
0
0
0
1
1
2
2
0
1
0
1
1
1
0
1
2
2
1
1
1
0
1
2
1
1
1
2
1
1
1
0
2
1
0
2
1
1
2
0
2
0
1
1
1
1
2
1
1
1
0
1
1
1
1
1
2
2
1
1
1
1
3
1
1
1
2
0
1
1
1
1
1
0
0
1
1
0
2
1
0
2
1
1
0
1
2
1
2
3
2
1
2
1
0
0
2
2
2
1
1
2
1
0
1
0
1
1
1
1
1
1
1
1
1
1
2
1
0
1
1
1
1
1
1
0
2
1
2
1
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
2
2
1
1
0
1
1
1
2
2
0
1
1
1
1
2
2
1
0
2
2
2
2
1
1
1
2
0
1
2
1
1
0
1
1
1
1
1
2
1
1
0
0
0
1
1
2
1
1
1
0
0
1
1
1
2
1
1
2
1
3
1
2
0
1
1
1
1
1
0
1
0
2
2
1
1
2
2
1
1
1
1
1
2
1
2
0
1
2
1
1
1
1
2
1
2
1
1
1
1
0
0
1
2
1
1
1
1
1
2
0
2
0
2
1
2
1
0
0
2
1
2
0
1
1
1
1
1
0
1
2
1
2
1
2
2
2
1
2
1
1
0
1
1
2
2
1
1
2
0
1
1
1
0
0
1
1
1
1
1
0
1
2
1
0
1
1
2
1
1
1
0
2
1
1
1
1
1
0
1
1
1
1
2
0
1
1
2
1
2
1
2
2
1
2
0
1
1
1
0
1
2
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
0
2
1
1
0
1
0
0
1
0
0
2
1
0
1
1
1
1
0
2
2
2
2
2
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
2
1
1
1
1
2
0
2
1
1
1
1
1
1
1
1
1
1
2
2
2
2
2
1
1
1
0
4
1
1
1
1
1
2
0
1
1
2
1
2
1
1
4
0
2
2
1
2
1
1
1
2
0
1
2
1
0
2
1
1
1
1
1
0
2
1
0
0
1
1
1
2
2
1
1
1
1
1
1
2
1
0
1
1
1
1
0
2
1
1
1
1
1
0
0
1
1
2
1
1
2
1
1
1
1
2
0
0
1
1
1
1
2
1
2
2
2
0
0
1
2
2
1
1
2
0
1
1
0
2
1
1
1
3
1
1
0
1
1
2
1
0
2
1
1
1
1
1
2
0
2
1
2
1
1
2
2
1
0
0
1
1
0
1
1
1
1
1
1
1
0
2
1
2
1
1
1
1
2
1
1
2
1
0
1
1
2
2
1
1
1
2
1
1
2
0
1
1
1
1
1
2
2
1
1
2
1
1
2
2
0
1
1
2
1
2
1
0
1
1
1
0
2
1
1
1
1
1
0
2
2
1
0
2
1
1
3
1
1
2
0
0
1
1
2
1
1
1
2
0
1
1
1
1
1
2
1
2
1
0
1
3
1
2
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
2
2
2
1
0
1
0
1
1
1
2
2
1
0
1
2
1
1
1
1
1
1
1
1
0
1
1
2
1
2
1
1
1
2
1
2
1
1
1
1
1
1
2
1
2
1
1
1
2
1
1
2
1
1
1
1
2
1
1
1
1
2
2
1
0
0
2
0
1
2
2
1
1
1
1
1
1
1
2
1
1
1
2
1
0
0
2
1
1
2
2
2
1
1
1
0
2
1
1
1
1
1
1
0
1
2
2
0
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
2
1
2
1
2
1
1
2
1
1
1
0
2
1
0
2
1
1
1
2
1
1
1
1
2
1
1
1
1
0
0
2
1
2
1
1
1
0
2
2
1
2
1
1
2
1
1
1
1
2
1
0
1
0
1
1
0
1
1
1
2
1
1
1
1
0
0
1
0
1
1
1
0
2
0
1
1
1
1
1
2
2
1
2
1
2
0
1
1
0
2
0
1
2
1
1
1
1
2
1
0
1
0
1
0
1
1
1
1
2
2
1
1
1
0
1
2
1
0
1
1
1
1
1
2
2
1
2
2
1
2
1
2
3
1
2
2
2
1
2
1
1
2
1
0
1
2
2
1
1
0
2
1
1
0
1
1
4
2
1
2
0
0
1
2
1
1
0
1
1
1
1
2
2
1
2
0
1
1
1
1
2
1
1
1
2
1
1
2
2
1
2
2
1
2
0
1
0
2
0
0
2
1
1
1
1
2
2
1
1
1
1
1
1
0
2
1
1
0
2
1
2
1
1
1
1
1
2
1
1
0
1
2
1
2
2
1
2
2
1
1
2
0
2
1
0
1
1
1
0
2
1
2
1
1
1
1
1
2
0
1
0
0
1
1
2
2
0
1
0
1
0
2
1
1
2
0
1
2
0
1
1
0
1
0
1
0
1
1
1
2
1
1
0
0
2
1
2
2
0
1
0
1
1
0
1
2
1
1
2
1
1
1
2
1
1
1
2
1
1
2
2
1
0
0
1
2
1
0
0
2
0
1
1
0
2
1
1
1
2
1
2
1
1
2
0
1
2
1
1
1
1
0
1
2
0
1
2
2
1
2
1
1
2
2
1
1
1
1
0
2
1
1
1
2
1
2
1
1
1
1
1
1
1
1
2
0
1
1
0
1
1
2
1
1
2
0
1
2
0
0
1
2
2
1
1
2
1
1
2
1
0
1
1
1
0
2
1
2
1
1
1
2
1
1
1
2
3
1
2
0
1
1
2
2
1
1
1
1
2
1
1
1
0
0
1
0
2
1
2
1
1
0
0
2
2
1
1
2
1
2
0
1
2
0
1
1
1
2
1
1
1
2
0
1
1
2
1
1
1
1
0
2
1
2
1
1
1
2
2
1
1
1
0
0
1
0
1
2
2
1
2
1
2
1
1
2
1
1
1
2
2
2
1
1
2
1
2
0
2
1
0
0
1
1
2
2
1
1
2
1
2
1
1
0
1
1
1
1
2
2
1
0
0
1
1
1
1
1
0
1
2
1
2
1
1
1
1
1
1
0
2
2
1
2
1
1
0
2
1
1
1
1
1
2
0
1
1
0
1
1
1
2
2
1
2
0
1
1
1
1
1
0
1
1
2
2
2
1
2
1
1
1
1
1
1
1
0
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
0
0
0
1
2
1
1
1
2
1
1
1
2
1
2
0
0
1
1
1
0
1
1
1
1
2
1
2
0
1
1
1
0
2
1
1
1
0
1
0
1
0
1
2
2
1
1
1
1
1
2
2
1
1
2
1
0
1
1
0
1
1
2
1
2
0
1
1
1
1
1
0
2
1
1
1
1
0
1
0
2
2
1
2
1
2
0
1
1
1
1
2
0
1
1
1
1
1
2
2
1
1
1
2
2
1
1
1
1
1
1
1
2
0
1
1
0
1
1
1
1
0
1
2
4
2
0
0
1
1
2
1
2
2
1
1
1
1
1
1
1
0
0
2
1
0
0
2
1
1
1
0
1
1
2
1
2
1
1
1
1
2
1
1
1
1
0
1
1
1
2
0
0
2
1
1
1
1
1
1
2
1
2
1
2
1
1
0
1
2
4
1
1
1
2
2
1
1
1
2
1
2
2
1
1
1
2
1
0
1
0
1
1
1
0
2
2
0
1
1
1
1
1
1
0
1
1
2
2
0
1
0
1
2
1
2
1
0
2
2
1
1
2
1
1
1
2
1
0
2
1
2
2
2
1
1
0
1
0
1
2
1
1
2
1
1
2
1
0
1
1
1
2
2
1
1
1
1
2
2
1
2
1
1
0
0
1
2
1
1
1
0
2
2
0
2
2
0
1
1
1
1
1
1
0
7
1
0
1
1
1
1
1
1
1
1
1
2
1
1
0
2
2
1
1
1
1
2
1
1
1
2
0
1
1
1
1
1
1
1
2
1
1
1
1
2
2
1
3
1
1
1
1
1
1
0
2
0
1
1
2
1
1
1
0
1
1
1
1
1
1
1
1
2
3
1
1
2
1
2
2
1
1
0
1
1
2
2
1
0
1
0
1
2
1
1
1
1
2
2
2
0
0
2
1
1
2
0
1
1
0
1
1
1
4
2
1
2
1
1
2
0
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
2
2
2
0
0
2
0
2
1
0
1
1
0
1
1
2
1
2
0
0
0
1
1
1
0
1
0
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
0
2
1
1
0
1
0
1
1
2
0
1
1
1
1
2
1
1
2
1
1
2
2
1
2
2
0
1
2
1
1
1
2
1
2
0
1
2
2
1
1
1
1
2
2
1
0
1
1
2
1
1
1
0
2
1
1
1
1
2
1
1
1
2
1
1
1
0
1
0
1
1
2
1
0
1
2
1
1
0
0
2
1
2
7
0
2
1
0
1
2
1
0
2
1
1
1
1
1
1
1
2
2
0
0
1
2
1
1
0
1
0
1
1
1
1
2
1
1
2
1
2
1
2
2
1
2
1
1
2
2
1
0
1
2
1
1
1
2
1
2
2
1
1
1
2
1
1
1
2
1
1
0
1
1
2
1
0
0
0
1
1
0
1
1
0
1
1
0
2
1
0
1
1
2
1
0
0
1
2
0
0
1
0
1
2
1
1
1
0
1
1
2
0
2
2
0
1
0
1
0
1
2
1
1
1
1
1
2
1
1
1
2
2
2
1
2
2
1
2
2
1
1
2
0
0
1
0
2
2
1
2
2
0
1
0
1
0
1
2
2
1
2
1
1
2
1
1
0
2
1
1
0
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
0
2
1
2
2
1
1
2
0
1
2
1
2
1
1
2
1
1
1
2
1
2
1
1
1
1
0
1
2
1
0
0
1
1
1
2
1
1
1
1
2
2
1
1
2
1
1
1
2
1
0
1
3
1
1
1
1
1
0
2
1
1
1
1
0
2
1
1
2
1
1
2
0
1
0
0
2
1
0
1
2
1
2
5
2
2
1
1
2
1
2
1
1
2
2
0
3
1
1
2
1
0
0
1
1
0
1
0
0
0
0
2
1
1
1
2
2
1
1
1
2
1
1
1
1
1
1
1
0
0
1
1
2
2
0
2
1
2
1
1
2
0
1
2
2
0
1
0
1
1
1
1
1
0
2
1
1
1
1
2
1
0
0
2
2
1
1
2
0
1
1
1
1
1
1
1
2
1
2
1
1
1
2
1
0
0
1
2
1
1
2
1
1
0
1
1
1
1
2
1
2
2
1
2
1
0
2
1
0
1
1
1
0
1
2
1
1
1
1
1
1
1
0
1
1
1
0
1
1
1
0
1
1
2
1
2
1
1
2
1
1
0
1
1
1
2
0
2
1
1
0
0
2
2
1
2
1
1
1
1
1
0
1
1
0
1
1
2
1
1
1
1
1
1
1
0
1
1
1
1
0
1
2
2
1
2
1
2
0
1
1
0
1
2
1
0
0
1
0
1
1
1
0
1
1
0
2
1
2
1
2
2
2
1
0
1
1
1
1
1
0
2
0
0
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
0
1
2
1
1
0
2
3
1
1
1
2
1
2
0
1
1
1
2
1
1
1
2
2
1
2
1
1
1
2
1
0
2
1
2
1
1
2
1
1
2
0
0
0
0
1
1
1
2
2
1
2
1
2
2
2
2
1
0
1
1
1
1
1
1
2
2
0
1
1
2
2
1
0
2
1
1
1
2
1
0
0
2
1
1
1
0
1
2
0
1
1
1
1
1
2
1
0
1
0
2
2
1
2
1
1
1
2
0
1
1
1
2
1
1
2
1
2
0
2
1
2
0
1
0
1
1
1
1
1
2
0
1
1
1
2
0
1
2
1
2
2
0
2
3
1
2
2
1
1
1
1
2
0
1
2
2
2
1
1
1
1
1
1
0
2
1
1
1
1
1
2
1
1
0
2
1
1
2
2
1
1
2
1
0
1
1
0
0
1
2
1
1
0
2
1
2
1
1
1
1
1
2
0
2
0
1
1
2
2
0
2
1
1
2
1
2
1
0
1
0
2
1
1
1
2
1
1
1
0
0
2
2
1
1
1
2
1
1
1
1
1
0
1
1
2
0
1
0
1
1
0
1
2
1
1
2
2
2
1
2
2
0
1
0
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
0
1
2
1
1
1
2
1
1
1
2
1
2
1
0
0
1
0
1
0
2
1
1
0
1
1
1
1
2
1
1
1
1
1
2
0
0
1
1
1
1
0
0
1
0
2
1
2
1
2
2
2
1
2
1
1
1
2
2
1
1
2
2
1
0
2
1
1
2
2
1
1
0
2
1
1
1
2
1
1
1
0
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
2
1
1
0
2
1
2
1
1
2
1
0
2
2
2
1
4
2
0
1
1
1
1
0
2
2
1
1
0
2
0
2
2
2
0
1
1
0
2
1
2
1
2
0
1
1
0
1
1
0
1
1
1
1
0
2
1
1
2
1
1
0
2
2
2
1
1
1
3
1
2
1
1
1
1
1
0
1
0
1
1
1
1
1
2
1
2
0
1
1
1
2
1
2
1
2
1
0
1
1
1
1
2
2
1
1
0
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
0
1
1
1
1
1
2
0
1
0
2
0
1
1
2
2
1
1
1
1
1
0
1
1
2
1
1
1
1
2
1
0
2
1
2
1
1
1
2
1
1
1
1
2
2
1
1
1
1
1
2
0
1
1
0
1
1
1
1
2
1
1
0
1
2
1
1
0
1
1
1
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
0
1
2
1
2
1
1
2
2
1
1
1
1
1
1
1
1
2
1
2
1
2
1
0
0
1
1
0
2
0
0
1
1
1
1
1
2
1
1
0
3
0
2
2
1
2
2
1
1
0
1
1
1
0
1
1
1
1
1
2
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
2
1
0
2
0
1
0
1
2
2
1
1
0
1
1
1
2
1
1
1
1
2
0
1
0
1
1
1
1
0
3
1
0
1
1
1
1
1
1
1
1
0
1
1
0
1
1
1
1
2
0
1
3
2
1
1
1
1
0
1
2
1
2
2
1
2
0
2
1
2
0
1
2
2
2
2
2
1
0
2
1
1
2
2
1
1
1
0
1
0
1
1
1
1
2
1
1
1
1
1
2
0
2
1
2
2
2
2
2
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
2
1
1
1
1
1
0
1
1
1
2
1
1
0
1
2
1
1
0
1
1
1
1
1
1
1
1
2
2
1
1
1
2
1
1
3
2
1
2
1
0
1
4
2
1
1
2
1
1
1
1
2
1
1
2
1
1
1
2
2
1
2
1
1
2
1
2
0
1
0
2
2
1
1
2
1
2
0
2
1
0
0
1
0
1
1
2
1
2
2
2
1
1
1
1
1
2
0
1
1
1
0
1
2
1
1
1
0
1
1
2
1
2
1
0
1
1
1
0
1
3
1
1
1
2
1
0
1
1
2
1
1
2
1
1
1
1
0
1
1
1
0
1
2
1
2
1
1
2
1
1
2
0
1
1
0
2
1
1
1
1
1
1
2
1
1
1
1
1
1
0
2
1
2
2
1
2
2
2
1
1
2
2
2
1
1
2
1
2
1
1
1
1
1
1
1
1
0
1
1
1
0
1
1
1
0
0
1
0
2
2
2
2
1
1
1
1
1
2
1
1
0
2
2
1
1
2
2
2
1
1
1
1
0
0
1
1
1
0
1
2
1
1
1
1
2
1
2
1
2
0
0
0
2
0
1
1
1
2
2
0
0
0
1
1
1
1
1
1
2
0
1
1
2
1
2
0
1
2
1
1
1
1
1
1
2
1
1
0
2
1
1
2
2
1
0
1
1
1
1
2
1
2
1
1
2
1
0
1
0
0
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
0
1
1
3
1
2
2
2
1
0
1
2
0
2
1
0
1
1
2
2
1
2
2
1
1
2
2
1
2
0
2
1
2
1
1
0
1
2
1
1
2
2
2
2
2
0
1
1
2
1
1
2
0
1
1
1
1
1
1
2
1
1
1
0
1
1
1
0
2
2
1
1
2
1
2
2
1
0
1
0
1
1
2
0
0
1
2
1
2
1
2
1
1
2
2
1
1
1
0
1
1
1
1
1
1
2
2
2
1
1
1
1
0
1
0
1
2
1
2
2
1
0
0
0
1
1
2
1
2
1
2
1
0
1
1
2
2
1
1
1
2
1
2
1
0
1
2
2
2
3
2
1
0
2
1
1
1
1
1
2
1
1
2
2
1
2
0
1
1
1
1
1
0
1
1
1
1
1
1
0
2
2
1
2
2
2
1
1
2
2
1
1
1
2
2
1
0
1
1
1
2
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
2
0
2
1
0
0
1
1
1
2
1
1
1
2
0
1
1
1
1
0
1
1
2
1
0
2
1
1
1
1
1
1
0
2
1
2
1
1
1
0
2
2
1
2
1
1
1
1
0
1
2
1
1
2
1
1
1
1
1
1
1
1
0
1
1
2
2
1
0
1
2
1
1
1
2
2
0
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
0
2
1
1
1
2
0
2
1
1
1
1
1
0
1
2
1
0
1
1
1
2
2
1
2
1
2
2
1
2
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
0
2
1
1
2
0
1
2
1
1
1
1
2
0
1
0
1
1
0
2
0
2
1
1
2
1
2
2
1
0
0
2
1
2
2
1
1
0
1
1
1
2
2
1
0
0
1
1
1
0
0
2
1
2
1
1
0
1
1
1
1
0
1
1
1
2
2
1
1
1
0
1
2
1
1
1
1
1
1
1
2
1
1
0
1
0
1
2
2
2
2
1
1
1
1
2
0
0
2
1
1
2
0
1
2
1
1
2
0
0
1
1
1
1
2
1
2
2
1
0
1
0
1
1
1
1
1
2
1
1
1
1
1
1
0
1
2
1
2
1
2
2
1
1
1
1
1
2
2
1
2
0
1
2
2
1
1
1
2
1
1
2
1
2
1
1
2
1
1
1
1
3
1
1
1
1
2
1
7
1
1
2
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
2
2
1
1
1
2
1
2
2
2
3
2
1
1
0
1
1
1
1
2
2
2
2
1
1
1
1
1
1
1
4
1
1
1
2
2
2
0
1
2
1
1
1
0
1
1
1
1
1
1
0
1
1
0
1
1
0
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
2
2
1
2
1
0
2
1
1
1
0
1
1
2
1
1
1
1
2
1
0
3
1
0
2
1
1
2
1
1
1
1
1
1
0
1
2
1
1
1
1
1
0
0
3
1
2
1
1
0
2
1
1
2
2
1
1
2
1
1
2
1
2
3
1
1
0
1
2
1
1
2
2
1
3
1
0
1
1
2
1
1
2
2
2
1
1
1
2
1
1
1
1
2
3
0
0
1
2
2
1
2
1
1
1
2
1
2
0
1
1
1
2
1
1
2
2
1
2
1
0
0
1
1
2
1
1
3
0
0
2
1
2
1
1
2
1
1
1
1
1
2
2
2
0
1
1
1
1
1
1
0
1
1
1
1
2
1
0
0
2
1
1
1
1
1
0
1
0
1
2
0
1
1
1
1
3
1
1
0
2
1
2
1
1
1
2
2
3
1
1
2
1
1
1
1
2
1
1
1
1
1
0
1
1
1
2
1
1
2
0
2
2
0
1
0
2
1
0
1
2
0
2
1
2
0
1
1
1
1
1
2
2
2
1
1
1
1
1
2
1
0
1
1
2
1
2
1
2
1
2
1
1
2
1
0
1
1
1
0
1
1
1
2
1
2
1
1
1
1
1
1
1
2
1
2
2
1
2
0
1
1
0
0
2
2
1
1
1
2
1
1
2
0
1
2
1
2
2
1
1
1
1
1
1
1
2
1
1
2
1
2
2
1
1
2
2
1
2
2
1
1
2
1
1
1
1
0
1
2
2
1
1
1
1
1
1
1
1
1
1
3
1
1
1
2
2
1
1
1
2
2
2
1
1
5
2
1
0
1
0
1
1
2
2
1
2
1
2
2
1
1
1
2
2
2
1
1
1
1
1
1
2
1
2
1
2
0
1
1
2
2
1
2
2
2
2
1
0
1
1
2
2
1
2
2
2
1
0
0
1
2
1
1
1
1
1
1
2
1
1
2
2
0
1
2
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
0
1
1
1
1
1
0
1
1
2
1
2
1
1
1
1
1
2
2
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
2
2
2
0
1
1
1
2
1
1
1
2
1
0
1
0
1
1
1
0
2
1
1
1
1
1
0
0
1
1
1
1
2
1
0
2
2
1
1
2
1
1
0
1
1
1
1
3
2
1
0
2
1
1
1
1
2
0
2
1
1
0
1
1
1
1
1
0
1
1
2
2
1
1
1
1
2
0
1
2
1
1
2
0
1
1
0
1
1
1
2
0
1
1
1
1
1
2
2
1
1
0
2
2
2
2
1
1
0
1
1
1
1
2
2
2
0
1
2
1
1
1
0
2
0
1
2
1
1
1
2
2
2
1
1
0
1
2
1
1
0
1
1
1
1
0
0
1
0
1
1
1
2
0
1
0
0
2
2
0
2
1
1
1
2
2
2
1
1
2
2
1
1
1
0
1
0
1
0
1
0
1
1
1
2
1
1
1
1
1
1
2
1
2
0
2
0
1
0
1
1
1
1
0
2
2
1
1
1
1
0
1
2
1
0
1
1
1
1
1
2
1
1
1
0
1
1
1
1
1
1
1
1
2
1
1
1
1
2
2
2
1
0
1
1
1
1
1
1
2
0
1
1
1
1
2
1
2
1
0
2
1
1
2
2
1
1
1
1
1
0
0
0
1
1
0
0
0
1
1
2
2
1
1
2
2
1
1
1
2
1
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
0
1
3
0
2
1
2
1
1
1
1
1
1
1
0
1
1
1
2
1
0
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
0
0
2
1
1
1
2
1
1
1
2
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
3
1
1
2
1
1
0
1
1
1
1
0
1
1
2
1
1
2
1
2
1
1
1
1
1
0
1
1
1
1
0
0
2
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
1
0
0
1
1
2
1
1
0
2
1
1
2
1
1
2
1
1
1
1
2
2
1
2
1
0
2
1
2
1
1
2
1
0
1
1
2
1
2
2
1
1
1
0
1
0
1
1
1
1
1
1
0
1
2
1
1
1
1
1
1
1
1
2
1
1
0
1
1
1
2
1
1
1
1
0
1
1
1
1
2
1
2
0
0
1
0
1
1
1
0
1
1
1
1
1
1
1
2
1
1
1
0
1
2
1
1
1
0
2
2
1
2
0
2
1
1
2
1
2
1
2
0
1
1
2
1
1
1
1
2
1
1
1
1
1
2
1
1
0
1
2
1
0
2
0
1
0
1
1
0
1
2
1
1
1
1
0
2
1
0
2
1
1
1
1
1
1
2
2
1
2
0
2
3
1
0
1
1
0
0
2
0
1
1
1
1
1
2
2
0
1
2
2
1
0
1
1
2
1
2
2
1
0
1
0
2
2
2
1
1
2
1
1
3
1
1
1
1
1
1
1
1
1
1
1
2
1
1
0
1
1
1
2
1
0
1
1
1
2
2
1
2
1
0
1
1
1
2
1
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
2
0
1
0
1
0
1
1
2
2
1
1
1
1
3
1
1
0
1
1
0
2
1
1
1
1
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
2
0
1
1
1
2
2
1
1
0
2
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
2
1
0
2
2
2
1
1
0
0
1
1
1
1
1
1
1
2
0
1
1
0
2
1
2
1
1
0
2
1
2
1
2
1
1
0
0
1
1
2
1
1
1
2
1
1
2
2
1
1
1
1
2
1
2
2
1
1
2
0
1
1
1
0
1
1
1
1
1
0
1
2
1
1
0
0
2
1
1
1
2
1
0
2
2
1
0
0
1
1
0
2
2
1
1
2
2
1
2
1
2
0
0
1
1
2
1
1
1
1
2
1
1
1
1
0
1
1
1
0
1
2
1
1
1
0
1
0
1
2
0
0
2
1
1
1
1
2
1
2
1
1
0
1
2
1
0
2
1
1
1
1
1
1
2
2
1
1
1
1
1
2
2
0
0
1
1
1
1
2
1
1
1
2
1
0
1
1
1
0
1
1
1
2
1
1
1
0
1
1
1
1
1
2
0
1
2
1
1
1
0
1
2
1
3
2
2
1
2
2
1
2
0
2
1
0
1
2
1
1
1
2
1
1
0
0
2
2
0
2
1
1
2
1
0
2
1
1
1
1
1
1
1
1
2
1
2
0
1
0
1
1
1
1
1
1
1
1
1
0
1
1
0
2
1
2
1
1
1
1
1
1
1
0
1
2
1
0
0
1
1
1
2
1
1
2
2
1
1
2
1
1
2
2
2
0
2
1
1
1
1
1
0
1
1
1
0
2
1
2
0
1
1
1
1
1
1
1
1
0
1
1
1
1
1
2
2
2
2
1
1
2
0
2
1
2
0
1
2
1
0
1
1
1
1
2
1
0
1
2
0
1
1
1
0
2
2
1
2
1
1
1
0
2
1
1
0
1
2
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
2
0
1
1
1
1
1
1
0
1
0
2
1
1
1
2
1
2
0
1
2
1
1
2
1
1
1
1
1
1
1
2
1
1
0
1
1
1
1
1
1
1
1
1
2
1
1
2
2
1
2
1
1
1
2
1
2
1
2
1
1
1
1
2
1
0
1
2
1
1
2
2
1
1
2
1
1
1
1
2
1
1
1
1
1
1
2
1
2
1
0
1
2
1
1
1
1
1
2
1
1
0
1
0
2
1
2
2
2
1
1
1
1
1
0
1
0
2
1
2
1
1
1
1
0
2
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
2
1
1
1
2
0
2
2
2
1
0
1
1
2
2
1
1
2
1
0
1
0
2
1
1
0
1
2
1
0
2
1
2
1
1
2
2
1
1
1
2
2
1
1
1
1
0
1
1
1
1
1
1
2
1
1
0
0
1
1
1
1
1
1
1
1
2
1
2
1
1
2
2
1
2
0
2
1
1
1
1
2
1
1
0
2
1
1
0
1
2
2
1
2
1
2
1
1
2
2
0
1
1
2
1
1
1
2
2
1
1
0
1
1
0
1
1
2
2
2
1
1
1
0
2
2
0
2
2
1
1
2
1
1
1
1
2
2
1
1
1
1
1
0
1
1
0
1
1
0
1
2
0
1
0
2
1
1
1
2
0
1
2
0
1
1
1
1
1
1
0
2
0
1
1
0
1
2
1
1
1
1
1
2
2
0
0
1
2
0
2
1
2
0
1
1
1
0
0
1
2
1
2
1
1
0
1
1
1
1
1
2
1
0
1
2
0
1
1
1
1
1
1
2
1
0
1
1
1
2
1
1
1
1
1
1
0
1
1
1
1
1
0
2
1
2
1
1
1
2
2
1
1
1
2
2
0
1
1
2
1
2
1
1
1
1
1
1
1
0
1
2
1
1
2
0
0
1
1
2
3
0
1
0
1
1
1
1
2
1
0
1
1
1
1
2
1
2
2
2
2
1
1
1
0
1
1
2
1
1
1
1
1
0
2
1
1
1
1
2
0
0
1
1
1
2
1
2
2
2
1
1
1
1
1
1
0
2
0
1
0
1
2
0
3
1
1
1
1
1
1
1
2
1
2
0
1
2
1
1
1
2
2
1
2
0
2
1
2
1
1
1
2
1
1
2
1
0
1
1
1
1
0
1
5
1
0
2
1
2
1
1
2
1
2
1
1
0
1
2
2
1
2
1
1
1
1
1
0
1
1
1
1
2
2
1
1
1
2
0
0
1
2
1
1
1
1
2
1
2
1
1
0
1
0
1
1
3
0
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
0
1
1
1
0
1
1
1
0
3
1
2
2
0
1
1
0
1
2
2
1
1
1
1
2
1
2
1
0
2
0
2
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
3
2
1
1
1
1
0
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
0
1
2
1
1
0
0
1
1
1
0
1
2
1
2
1
1
2
0
1
1
1
1
1
1
2
3
2
1
1
0
1
2
2
1
1
2
1
1
1
0
0
2
1
1
1
0
2
1
1
0
2
1
1
1
2
1
1
1
1
1
2
1
0
0
0
0
1
1
2
2
2
1
1
1
1
1
1
1
1
2
1
3
1
1
1
2
2
1
0
1
0
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
5
0
1
1
2
1
1
2
1
1
0
2
1
0
0
2
1
2
1
2
0
1
1
1
2
1
1
1
2
2
0
1
0
2
1
1
2
1
2
1
2
0
0
1
2
2
1
1
1
2
1
1
2
1
1
1
2
1
1
2
1
1
1
1
1
2
0
1
2
1
1
1
2
1
1
1
2
1
1
2
2
2
2
1
0
1
1
1
2
2
1
1
1
1
2
2
1
1
1
1
2
1
1
2
1
0
1
1
1
1
1
1
1
1
0
1
0
1
1
1
1
1
1
0
2
1
1
1
1
1
1
1
1
1
2
2
0
1
1
1
0
1
2
2
1
2
1
1
2
1
1
0
2
1
2
1
1
1
1
1
1
1
2
2
2
2
1
1
1
1
1
2
1
1
0
0
2
0
1
1
2
2
2
2
2
1
2
2
1
0
1
1
1
2
2
1
2
0
1
1
1
1
1
2
0
2
2
1
2
2
0
0
2
0
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
0
1
1
2
2
2
1
1
2
2
2
0
1
2
1
1
0
0
2
1
2
1
1
1
0
1
1
2
2
2
0
1
2
2
1
1
0
1
2
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
2
2
2
1
1
0
1
1
2
2
0
1
1
2
1
0
1
1
0
0
0
1
1
0
1
2
1
1
1
2
2
1
0
1
1
1
1
1
2
1
1
1
2
0
0
1
1
1
0
1
2
1
1
2
2
2
2
1
1
1
0
2
2
1
0
1
1
1
1
1
1
1
0
1
1
2
1
1
1
1
1
1
1
2
0
1
1
1
1
0
1
1
1
1
2
1
0
1
1
1
0
0
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
0
0
1
2
1
1
2
0
1
1
1
1
2
3
2
1
0
1
1
2
0
0
2
1
2
2
1
2
2
1
1
0
1
2
1
1
1
1
1
1
4
2
1
2
2
1
1
2
1
2
0
1
1
1
1
1
2
1
0
0
2
2
1
2
0
2
1
1
1
0
2
0
2
2
1
1
2
2
1
1
1
2
1
2
1
1
1
0
1
1
0
1
0
1
1
1
1
1
0
1
2
2
1
2
2
0
2
2
2
1
0
1
1
2
1
1
1
2
1
2
1
0
2
2
1
2
1
1
2
2
0
1
1
0
1
1
0
3
1
2
2
1
1
2
1
0
1
1
2
1
1
1
1
1
2
1
1
0
1
1
2
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
0
2
2
1
2
0
2
2
2
1
1
0
1
1
1
1
1
1
2
2
2
0
1
2
1
0
1
1
1
0
1
0
2
2
2
0
1
0
2
0
1
1
1
1
1
2
0
1
2
1
1
2
1
1
1
1
2
1
1
1
1
0
1
1
1
2
1
5
1
1
1
2
1
0
1
2
2
1
0
1
1
1
1
1
2
0
2
1
1
2
0
2
1
1
2
1
1
2
1
2
2
1
0
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
0
1
1
1
0
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
2
1
0
2
1
2
1
2
1
1
2
2
1
1
3
1
1
1
2
1
2
3
2
2
0
1
0
1
0
1
1
1
1
2
2
1
2
1
0
0
2
0
1
1
1
1
1
1
2
0
2
1
1
2
1
1
1
2
2
2
2
2
1
1
1
1
2
2
0
2
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
0
1
0
2
1
1
1
1
2
2
2
0
0
1
1
0
0
0
1
1
0
1
1
1
1
1
2
0
1
2
2
1
1
1
1
1
1
3
2
1
1
1
1
2
2
2
2
1
0
2
1
1
1
2
2
2
1
0
1
2
1
2
2
2
0
2
1
0
2
1
2
2
1
2
1
2
1
2
1
1
1
1
1
1
0
1
2
1
2
2
2
0
1
2
0
0
2
1
1
2
1
1
2
1
1
1
1
1
1
0
0
0
1
1
1
2
1
0
1
1
1
1
1
0
1
1
1
1
0
2
1
1
2
1
1
0
1
1
2
1
1
2
0
1
2
2
1
0
1
2
1
1
1
2
2
2
1
1
2
1
1
2
2
2
1
1
2
1
0
1
1
1
1
1
0
1
2
1
2
2
1
1
2
2
1
1
1
1
1
2
2
2
1
1
1
1
1
1
0
1
0
2
1
1
1
0
2
1
1
1
1
1
1
3
1
1
1
2
1
2
0
0
1
1
1
0
1
1
1
1
2
2
1
0
2
1
1
0
1
2
1
1
1
1
1
2
1
1
1
1
1
1
2
2
1
2
1
1
1
2
1
1
1
2
1
2
0
1
1
1
1
1
2
1
1
1
1
2
1
0
2
2
2
2
2
1
1
1
1
2
2
1
1
1
2
1
2
1
0
1
1
1
1
0
2
1
1
2
0
2
1
1
2
1
0
2
1
1
1
2
2
1
1
0
1
2
1
1
1
2
1
1
0
1
2
1
1
1
2
1
1
1
1
2
2
1
1
1
0
0
1
1
2
1
1
1
1
2
1
1
1
3
1
2
1
2
2
1
1
1
1
2
1
0
1
1
0
1
1
0
2
1
1
1
1
1
2
1
1
1
1
2
1
2
2
2
1
1
1
2
1
1
0
1
2
1
1
0
0
1
0
1
2
1
1
1
1
1
1
0
2
2
1
2
2
1
0
1
1
1
1
1
2
0
1
1
1
1
2
2
1
2
1
1
2
2
0
1
1
1
2
1
1
0
1
1
1
1
1
1
2
1
2
1
2
2
1
1
1
1
0
1
2
1
1
1
1
2
1
1
1
0
1
1
1
1
1
2
1
1
1
1
2
1
1
0
1
1
1
1
1
1
2
0
1
2
1
1
1
0
1
0
1
2
1
1
1
0
2
1
2
0
2
1
1
2
0
1
1
1
1
1
1
2
1
1
1
1
2
0
2
1
1
1
2
1
1
0
1
0
3
1
2
0
1
1
2
1
1
1
2
1
1
0
1
1
1
0
1
1
2
0
2
2
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
0
1
2
2
1
1
2
1
2
1
2
1
2
0
2
2
1
2
1
1
1
1
1
1
2
1
0
1
1
2
1
2
2
2
2
1
1
1
1
2
2
1
2
1
1
1
1
1
2
1
1
1
1
2
1
1
0
0
2
1
1
2
1
1
2
0
1
2
1
2
1
2
1
2
2
2
1
2
1
2
1
1
2
1
0
1
1
1
1
1
0
1
0
1
2
1
1
0
2
2
4
2
0
1
2
2
2
1
2
1
2
1
1
1
1
2
0
1
0
1
1
0
2
1
2
2
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
0
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
0
2
1
1
1
1
1
1
2
2
1
1
1
2
1
1
1
1
1
1
1
1
1
0
0
1
2
2
1
0
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
0
1
1
1
2
1
2
1
1
1
1
2
1
1
0
1
1
1
1
0
1
1
1
2
2
1
2
1
2
0
1
1
1
2
2
0
1
3
1
2
1
2
1
0
1
1
1
1
2
1
2
2
2
0
1
1
2
1
0
1
2
0
1
1
1
1
2
1
2
2
1
1
1
2
1
1
0
1
0
2
3
1
1
2
2
1
2
2
1
2
0
1
1
0
0
1
1
1
0
1
1
1
1
1
1
2
1
1
1
1
1
0
0
0
1
0
1
2
0
1
1
1
1
1
1
2
1
1
1
1
2
2
1
1
1
0
1
1
1
0
1
1
1
2
1
0
1
1
0
1
3
0
1
0
1
2
1
0
1
2
2
2
1
2
1
0
1
0
2
2
2
0
1
1
1
1
1
1
0
1
2
1
1
2
1
2
2
0
3
1
1
2
1
1
1
1
1
2
0
1
1
1
1
2
1
1
1
1
2
1
2
0
1
2
2
2
2
2
0
1
2
0
1
1
2
1
1
1
1
2
2
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
0
1
2
2
1
1
0
2
2
1
0
1
1
1
1
1
1
2
2
0
1
2
1
1
1
1
2
1
1
1
0
1
0
2
2
2
1
1
2
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
2
1
2
1
2
1
1
1
2
1
1
0
1
1
1
1
1
1
1
1
1
1
2
0
1
1
0
2
3
1
1
1
2
0
2
2
1
2
1
0
1
1
2
2
0
0
1
1
1
2
1
2
2
0
2
1
2
1
2
1
0
1
2
1
2
2
1
1
1
0
0
1
0
1
1
2
2
2
1
1
0
1
1
1
2
0
2
1
1
2
1
2
1
2
0
1
1
1
1
1
1
0
1
1
1
1
0
1
2
1
1
1
1
1
1
1
2
1
1
1
1
0
2
0
1
2
2
2
1
2
2
1
2
2
1
1
2
1
1
2
2
2
1
1
1
1
3
2
1
0
0
1
1
1
1
2
0
1
1
1
0
1
0
2
1
1
2
0
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
0
1
1
1
2
1
0
1
2
1
2
0
1
0
2
1
1
0
1
1
1
2
2
0
1
1
1
1
0
2
2
1
1
1
1
1
1
1
0
1
1
1
1
2
2
1
0
2
0
2
2
1
2
0
1
0
1
2
2
2
2
2
1
1
2
2
0
0
0
1
2
0
2
2
1
2
1
1
2
1
1
2
1
1
2
1
1
2
2
2
1
2
2
2
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
2
2
2
1
1
1
2
2
1
1
2
1
2
3
1
1
0
1
1
1
1
1
1
1
1
1
1
2
2
2
1
0
1
1
1
1
1
1
2
0
1
1
1
1
0
2
1
0
1
1
1
1
2
0
2
1
1
1
1
0
1
1
1
1
2
1
1
1
1
1
1
1
2
1
0
1
1
0
0
2
2
0
2
1
1
1
1
1
1
1
2
1
0
0
0
2
1
1
1
1
1
1
0
2
2
1
0
1
2
1
1
1
1
1
1
1
2
0
1
1
1
1
2
1
1
2
2
1
2
0
1
1
0
0
1
2
0
2
1
1
2
1
2
2
1
2
1
1
1
2
1
1
2
2
1
1
1
1
0
1
1
1
2
2
1
1
1
1
1
1
1
0
1
2
1
0
1
1
2
2
0
1
1
2
0
2
1
1
2
1
1
2
1
1
1
1
1
1
1
0
1
1
1
0
1
1
1
1
1
2
2
2
0
1
0
1
1
2
1
2
1
1
1
2
1
2
1
1
2
1
2
2
2
2
2
0
1
0
2
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
2
1
1
1
1
0
2
1
2
1
1
1
1
1
2
0
1
2
1
1
2
1
0
1
2
2
2
1
1
2
1
2
2
1
1
1
1
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
0
0
1
1
1
1
2
1
0
1
1
1
1
1
2
2
1
1
2
2
1
1
2
1
2
1
1
1
2
1
2
2
1
1
0
1
1
2
1
0
1
1
1
1
2
1
1
1
1
1
2
1
1
2
2
1
1
1
1
0
2
1
2
1
1
2
0
2
1
1
1
1
1
1
0
2
2
1
1
2
2
1
1
1
2
1
0
2
2
1
1
2
0
2
1
2
1
1
2
2
2
1
1
1
0
0
1
1
2
1
1
2
1
1
1
1
0
1
1
1
2
1
2
1
1
2
1
2
1
1
1
1
1
1
1
2
2
1
0
1
1
1
2
1
1
2
1
1
0
1
1
1
1
1
1
0
0
0
1
1
1
1
1
1
2
1
1
1
2
1
0
1
2
2
1
2
2
0
2
1
1
1
1
1
0
0
2
2
1
0
1
1
1
1
1
2
1
1
1
1
1
2
1
2
1
0
1
1
2
1
1
2
0
1
1
2
1
1
1
1
2
2
2
2
0
0
1
2
1
1
1
1
1
2
1
1
1
1
2
1
1
1
0
2
1
2
1
2
1
2
2
4
0
1
2
0
2
1
1
1
2
2
1
1
0
1
1
0
2
0
1
1
2
2
0
0
1
1
1
1
1
1
2
1
1
0
1
1
2
1
2
2
1
0
1
2
2
1
1
0
0
1
1
2
2
1
1
1
1
1
1
1
2
0
2
1
1
1
2
1
2
2
0
2
1
1
0
0
1
1
1
0
1
1
2
1
0
2
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
3
0
1
1
2
1
2
1
2
2
0
1
1
1
2
2
1
0
0
1
1
1
1
2
1
2
1
1
0
1
2
1
1
0
1
2
1
2
1
1
1
2
1
1
0
0
1
2
0
2
2
1
2
2
1
1
2
1
2
2
1
1
1
2
1
1
1
1
3
1
1
0
1
1
1
1
1
2
2
1
1
1
1
2
2
0
2
2
2
1
2
1
1
1
1
1
1
2
2
1
2
1
1
0
1
0
1
1
1
1
2
2
1
2
1
0
1
1
1
1
2
0
0
2
1
1
0
0
1
2
0
1
0
1
0
1
1
1
1
0
2
1
2
1
2
1
2
2
1
2
1
1
2
1
0
2
2
0
1
1
1
2
2
1
1
1
1
1
1
1
1
2
1
1
2
0
2
2
2
2
1
1
1
1
1
1
0
2
1
1
1
1
1
0
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
2
0
0
2
0
0
2
2
0
1
1
2
2
1
0
2
1
0
1
2
2
2
1
1
1
1
1
2
1
2
0
1
2
1
0
0
1
1
1
1
1
1
1
2
2
2
1
1
1
2
1
0
0
2
1
1
2
1
1
1
1
2
1
2
1
1
2
2
2
1
0
2
1
1
1
1
1
0
1
1
1
1
1
1
0
1
1
2
2
0
1
1
1
1
2
1
0
1
2
1
2
2
2
2
2
1
0
1
1
2
1
1
1
1
1
2
2
2
2
2
2
2
2
1
1
1
1
1
1
1
2
2
1
2
2
0
1
1
1
1
1
2
1
2
1
0
2
1
2
2
1
1
1
1
1
1
0
1
2
1
0
2
1
1
0
1
0
2
0
2
2
1
1
2
2
1
1
1
0
1
0
1
1
1
1
1
1
3
1
0
1
2
2
1
2
1
0
2
2
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
2
1
2
1
1
1
2
1
1
1
1
0
1
1
1
1
1
0
2
1
2
2
2
1
0
2
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
0
1
2
1
1
2
0
1
1
1
1
0
0
1
1
0
1
2
1
1
2
1
1
2
1
1
1
1
1
1
2
2
1
2
2
1
1
1
2
2
0
1
1
1
1
1
1
1
1
0
1
2
1
1
1
1
0
2
2
1
1
1
1
2
0
2
2
1
1
1
2
1
1
0
2
0
1
1
1
1
2
0
1
1
1
2
1
1
1
1
1
0
2
2
1
2
1
1
1
1
0
1
2
1
1
1
1
1
1
2
1
1
0
2
1
1
1
1
1
2
1
2
2
1
2
1
2
1
1
2
1
1
0
0
1
1
1
2
0
1
2
1
2
2
2
1
2
1
1
1
1
0
1
0
1
1
0
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
2
0
2
1
2
1
1
2
2
1
1
1
0
1
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
2
2
1
2
1
2
1
2
1
1
0
0
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
0
0
1
2
2
1
2
0
2
1
1
1
1
2
1
2
2
1
0
2
1
1
1
2
1
1
1
1
1
2
2
1
2
4
1
1
1
1
1
2
1
2
1
1
2
2
2
1
1
0
1
1
2
1
1
2
1
2
2
2
2
2
1
2
1
2
1
1
7
0
1
0
1
2
1
0
2
2
2
2
1
1
2
1
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
2
1
1
1
2
1
1
1
1
1
2
1
1
0
0
1
1
0
1
2
1
0
1
0
1
1
1
2
1
1
1
1
1
2
1
1
2
0
0
1
0
0
1
2
1
1
1
0
1
0
2
2
1
2
2
0
2
2
1
1
1
1
1
2
1
2
1
0
0
1
1
2
1
1
0
1
2
2
1
1
1
1
2
1
1
1
2
2
2
2
1
1
1
1
1
1
1
1
2
2
1
1
1
1
0
1
1
1
2
2
1
1
1
1
1
1
0
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
0
1
0
3
0
0
1
0
1
5
2
1
1
1
2
1
1
1
1
1
1
1
0
1
1
1
1
1
2
0
2
0
1
0
1
0
2
1
1
1
1
1
2
1
0
1
2
2
2
1
1
1
2
1
2
0
0
2
1
1
2
2
0
2
1
0
2
1
0
1
1
1
1
1
1
2
3
2
1
1
1
0
1
1
0
0
0
1
1
1
1
1
0
1
2
1
1
1
2
0
1
1
1
0
0
2
1
1
2
2
2
2
0
1
1
1
0
2
1
2
1
2
2
1
1
1
2
1
2
0
2
2
2
2
2
2
2
0
1
2
1
1
1
1
1
1
1
1
1
0
1
0
1
2
1
0
1
1
1
0
1
0
2
1
1
0
2
0
2
0
2
1
1
1
0
0
1
0
0
0
2
2
1
1
1
2
0
1
0
2
1
1
0
2
2
1
0
1
1
1
1
2
1
1
2
1
1
0
1
2
2
2
0
1
0
2
2
2
1
1
2
2
1
2
1
1
1
1
1
0
1
1
1
2
1
2
1
2
2
1
0
1
3
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
2
2
0
1
1
1
1
1
0
0
1
1
0
1
1
2
1
1
1
2
1
1
2
2
1
0
1
1
0
1
2
3
2
1
1
2
2
0
1
1
1
2
2
2
2
1
2
1
1
1
2
2
2
1
1
2
1
1
1
0
2
2
2
0
1
1
2
1
1
1
1
1
1
2
2
1
1
0
1
1
2
1
2
1
2
1
1
1
5
1
1
1
1
1
1
2
1
1
1
2
0
1
0
1
1
1
2
1
2
2
1
2
2
1
2
2
0
0
1
1
1
1
2
2
1
1
1
1
1
0
2
2
1
1
1
1
1
0
2
1
1
1
1
0
1
1
1
1
1
1
2
1
1
1
1
0
0
1
1
1
1
1
1
1
1
1
2
2
2
0
1
2
2
1
1
2
0
1
2
1
1
1
1
0
1
1
2
1
1
1
0
1
2
1
1
1
2
2
1
0
2
2
2
2
1
1
1
0
2
1
1
2
1
3
2
0
1
1
1
1
1
1
2
1
1
1
1
1
1
2
0
2
2
1
1
2
1
1
1
2
1
1
0
1
1
1
2
1
3
1
2
2
0
0
2
1
2
1
1
2
0
1
2
2
1
1
0
0
1
2
1
0
1
1
1
1
1
0
1
1
1
1
0
2
1
1
1
2
1
2
2
1
2
1
0
1
1
1
1
1
1
1
1
1
1
2
0
1
2
1
1
1
1
2
0
2
2
1
0
2
2
1
1
2
2
1
2
1
2
2
1
1
2
2
1
2
1
1
1
1
1
1
0
2
1
3
1
1
2
2
2
2
1
1
0
1
1
0
1
1
1
1
1
1
1
1
2
2
2
1
1
2
1
1
1
0
1
2
1
1
2
2
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
2
2
1
0
2
1
2
0
1
2
2
1
1
2
2
1
0
1
1
1
1
0
1
1
2
2
2
1
1
1
2
1
2
1
0
2
2
0
1
0
2
1
1
1
2
2
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
2
0
1
1
2
1
1
1
2
1
1
1
1
1
2
2
4
0
1
1
1
1
0
0
1
1
1
0
1
2
2
1
2
1
1
0
2
2
1
1
2
1
1
0
1
1
2
2
1
1
2
2
1
1
1
0
2
0
1
0
0
1
2
1
1
1
1
1
2
1
0
2
1
1
2
1
1
2
0
2
0
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
2
2
1
1
1
2
2
1
1
1
1
0
1
2
1
2
2
0
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
0
1
2
1
0
1
2
1
0
1
2
1
1
1
2
1
0
1
1
2
1
1
1
0
2
0
2
1
1
1
1
2
2
0
0
1
1
0
1
1
0
1
1
2
1
3
0
0
1
1
1
2
1
1
1
1
1
2
1
1
3
1
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
0
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
0
1
1
1
1
1
1
2
1
1
2
1
1
1
1
0
0
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
0
1
1
1
1
2
2
1
1
1
2
1
1
2
2
2
1
2
1
0
1
1
2
1
1
1
1
0
1
1
1
1
2
1
2
1
1
1
1
1
2
2
2
1
1
1
2
1
1
2
1
1
2
2
1
2
2
1
0
1
1
2
1
2
1
1
1
0
1
2
1
1
0
1
1
1
1
1
1
1
2
1
2
1
1
1
2
1
2
2
1
1
1
1
1
1
1
0
1
1
2
2
2
1
1
2
1
2
0
1
1
2
1
1
2
1
0
1
2
0
0
2
1
1
1
1
1
2
1
1
0
0
1
0
4
2
1
1
0
1
1
1
1
1
1
2
2
1
2
2
1
1
2
1
2
1
2
2
2
2
1
1
1
1
1
1
1
1
2
2
1
1
1
1
2
2
0
1
1
1
0
1
1
1
1
0
2
1
1
0
1
2
1
1
1
2
0
0
1
3
1
1
1
1
1
0
0
1
1
2
2
1
1
2
1
1
1
1
2
0
2
0
1
1
2
1
2
2
1
1
1
2
1
2
1
0
2
1
2
1
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
2
2
0
1
1
0
1
1
2
1
0
0
1
1
1
1
1
0
1
1
2
1
2
2
1
2
1
1
1
1
2
2
1
1
2
1
2
1
1
1
2
0
1
1
1
1
2
1
2
1
0
0
2
0
1
1
2
1
0
1
1
2
1
1
1
1
0
1
0
1
2
2
2
1
1
1
1
1
0
1
2
0
1
1
2
1
2
1
1
2
1
1
1
1
1
2
2
3
1
1
1
1
1
1
1
1
0
1
2
1
1
1
2
0
2
0
2
0
0
2
1
2
3
2
2
1
2
2
1
2
1
2
1
1
2
1
1
1
1
1
1
1
2
1
3
1
1
1
0
1
2
1
2
2
1
1
1
0
1
2
1
1
2
1
2
0
1
1
1
1
1
1
1
1
1
1
1
0
0
2
0
2
1
1
2
1
1
1
2
0
1
0
2
1
1
1
1
2
2
0
1
1
1
1
2
5
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
2
2
2
1
1
1
1
1
2
1
2
0
1
1
1
1
1
1
1
1
1
0
2
2
1
0
1
1
2
1
2
1
1
1
2
1
1
1
1
2
1
2
1
1
0
1
1
1
1
2
2
1
3
0
0
1
1
0
1
2
1
1
2
3
1
0
1
1
2
1
1
1
0
1
1
1
1
1
1
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
2
1
2
2
1
2
0
2
1
2
2
1
0
1
1
2
1
1
1
2
1
0
2
1
1
0
1
1
2
1
0
2
0
1
2
2
1
2
2
1
1
1
1
0
1
0
1
2
0
1
1
1
1
2
2
1
0
1
1
1
1
1
1
1
1
1
2
1
0
1
1
2
1
1
2
1
2
2
2
2
1
1
1
2
1
1
1
1
0
0
1
1
0
1
1
1
1
2
2
1
1
1
1
0
0
1
2
1
1
1
1
1
1
1
2
2
0
1
1
1
1
1
1
0
2
1
2
2
2
2
2
0
2
1
2
2
1
1
1
1
0
0
1
1
1
1
1
1
1
1
0
1
1
1
0
1
2
2
2
1
1
0
1
2
1
1
0
1
2
2
1
1
1
1
0
1
1
0
0
1
1
1
1
1
0
2
1
0
1
1
1
0
1
2
1
2
2
1
2
1
1
1
2
1
1
1
2
1
1
2
1
1
1
1
0
1
1
1
1
0
1
2
1
2
2
1
0
2
2
1
1
1
1
2
1
1
2
1
2
1
1
1
0
2
2
3
1
1
2
1
1
1
2
2
1
0
1
0
1
1
2
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
0
0
1
1
2
1
1
0
1
2
1
0
0
1
1
0
2
1
1
1
0
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
2
0
1
0
1
2
1
1
1
1
0
2
1
1
2
1
1
1
1
1
1
2
1
1
0
1
1
0
2
2
1
1
1
1
1
1
1
1
2
1
2
2
2
2
0
2
1
1
2
1
1
1
1
1
0
1
1
1
0
2
1
0
1
1
1
1
2
0
2
1
1
2
1
1
0
1
2
1
1
1
1
2
1
1
2
1
1
1
2
1
1
2
1
2
2
5
1
1
1
0
1
1
1
1
1
0
1
1
1
2
0
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
0
2
1
1
1
1
1
0
1
2
1
2
1
1
1
0
1
2
1
1
1
1
1
1
1
1
0
1
2
1
0
1
1
1
1
1
0
1
1
1
1
1
1
1
1
0
2
1
1
1
1
1
1
1
1
2
2
3
1
2
2
1
1
1
2
2
0
2
2
1
2
2
1
1
1
2
2
0
1
1
1
1
2
2
1
2
1
0
1
1
0
2
1
2
1
1
1
1
1
2
1
1
1
2
0
1
0
0
2
1
2
5
2
1
0
0
1
1
1
2
1
1
1
1
2
1
1
0
1
1
1
2
1
1
2
0
2
1
1
1
0
1
2
0
1
2
1
1
1
2
1
2
1
1
1
0
2
0
0
1
2
2
0
2
2
1
1
0
2
2
0
1
1
1
2
1
0
2
0
1
1
0
1
1
1
1
2
1
0
1
2
2
2
2
2
1
1
1
2
1
1
1
3
1
0
1
2
1
1
0
1
1
0
1
2
2
1
1
1
0
0
2
0
1
0
1
1
0
2
1
2
1
1
1
1
1
1
1
1
2
0
0
1
0
2
2
0
1
1
1
1
1
1
2
1
1
2
2
1
0
2
0
1
1
2
1
2
1
1
2
0
3
2
2
1
1
0
1
2
1
1
2
2
2
1
2
1
1
0
1
0
1
2
1
2
1
2
1
1
1
1
1
1
1
1
1
2
1
2
5
1
2
1
2
1
1
1
1
0
1
2
1
2
0
1
2
3
1
2
1
1
1
0
2
1
2
1
1
1
1
2
2
1
1
2
1
1
2
1
1
2
0
2
1
1
1
2
1
1
0
0
1
2
1
1
2
1
1
1
1
1
1
1
2
1
2
2
2
1
1
1
1
0
1
1
1
0
1
1
1
2
1
1
1
2
1
1
0
2
1
1
3
1
1
1
1
1
2
0
1
2
1
2
0
1
2
2
1
2
1
1
2
1
1
1
1
0
1
1
1
2
2
2
1
2
1
1
1
2
1
1
1
1
1
0
1
1
0
2
0
0
2
2
2
1
1
1
0
1
0
2
1
2
1
1
1
0
1
1
1
0
1
1
1
2
1
0
1
2
1
2
1
2
1
0
1
1
1
3
2
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
2
2
0
2
1
2
1
0
1
1
1
1
1
2
1
1
1
1
2
1
2
0
2
1
1
0
0
1
1
2
1
1
1
1
1
1
0
2
0
2
0
0
2
1
1
1
1
1
0
1
1
2
2
1
2
1
1
1
1
2
2
1
1
0
1
1
1
2
2
1
1
0
1
1
1
1
2
1
1
0
2
0
1
1
0
0
1
1
1
2
1
1
1
2
1
1
1
1
1
0
2
2
1
1
1
1
2
0
1
1
1
1
1
1
1
0
1
2
1
1
2
2
0
1
1
1
1
2
2
1
1
1
1
1
1
0
1
1
0
1
1
1
1
1
1
2
1
1
1
1
1
0
1
2
2
1
1
0
1
2
2
1
1
1
0
1
0
0
1
1
0
1
1
1
1
1
0
1
1
2
1
1
1
1
1
1
2
1
2
0
1
2
2
1
2
1
0
0
1
2
0
2
1
0
1
1
1
1
1
1
2
1
1
1
1
0
1
1
2
1
2
1
1
0
1
1
2
1
1
2
1
2
1
0
1
1
1
2
1
1
2
1
1
1
2
1
0
1
1
1
1
1
0
0
2
1
1
0
0
0
1
1
1
1
1
0
1
0
1
2
0
1
1
1
0
2
1
0
2
1
1
1
2
1
1
1
0
1
0
2
1
1
2
1
1
2
1
0
1
1
1
1
1
0
1
0
2
1
2
2
2
1
2
1
1
1
1
1
1
1
1
1
2
2
1
2
1
1
0
1
1
2
2
6
2
1
1
2
1
2
1
1
1
2
1
2
0
1
1
1
1
0
1
1
1
1
1
2
1
2
1
0
1
1
2
2
1
1
0
1
1
0
1
1
1
1
1
2
1
1
1
1
1
3
1
1
1
1
1
1
1
2
0
2
0
1
1
2
1
2
2
1
1
1
1
2
0
2
0
1
2
1
2
1
2
1
2
0
0
1
2
0
1
2
1
1
0
2
1
0
1
1
0
2
2
1
1
0
0
1
1
2
1
0
2
1
2
1
1
1
1
2
2
2
0
1
0
2
1
1
1
1
1
1
0
2
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
0
2
2
0
2
1
2
2
2
1
1
0
1
1
1
2
2
2
0
2
1
0
0
2
1
0
1
2
2
1
1
0
0
2
1
1
2
2
1
2
1
1
1
2
1
1
2
1
0
0
2
1
2
1
1
0
1
1
2
2
1
2
0
1
2
1
1
1
1
1
0
0
0
0
1
1
2
0
1
1
1
0
1
0
2
1
2
1
1
1
1
2
1
1
2
1
2
1
2
1
1
2
1
1
1
2
1
1
2
2
2
2
1
1
2
0
1
2
1
1
2
1
1
2
1
2
1
3
2
2
0
1
1
1
1
1
2
0
1
1
2
2
1
1
1
1
1
1
1
0
2
1
3
0
0
1
1
2
1
1
2
1
1
2
0
1
1
2
2
2
1
1
2
0
2
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
0
0
2
1
1
1
2
2
1
0
1
2
1
1
1
1
1
1
1
2
2
0
1
1
2
1
1
0
1
1
1
1
0
1
2
0
0
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
2
1
1
1
2
1
1
1
1
2
1
0
2
1
2
1
1
2
1
2
1
1
1
0
2
1
1
1
1
1
0
1
1
0
1
1
2
0
1
1
2
1
2
1
2
2
1
1
1
1
2
0
2
2
2
1
2
2
1
1
2
2
1
1
1
1
2
2
2
2
1
2
2
2
1
0
1
1
0
1
1
1
3
1
1
1
1
2
1
0
1
0
1
2
2
1
1
1
2
2
0
2
2
2
0
0
1
1
1
1
1
1
2
1
2
1
1
1
1
0
1
0
1
2
1
2
1
0
1
2
2
1
1
1
1
1
1
0
3
1
1
1
1
2
1
1
1
2
1
1
1
1
1
2
1
2
1
3
1
1
1
1
1
1
0
2
1
0
2
2
1
2
1
1
0
1
1
3
1
2
1
1
1
1
0
1
1
1
2
2
1
1
0
1
2
1
1
0
1
1
1
1
2
1
1
2
1
1
1
2
1
0
0
1
2
2
0
1
1
2
1
2
2
2
1
0
0
1
1
2
0
0
2
1
1
1
1
1
0
0
1
1
1
1
1
2
1
1
2
2
0
1
2
1
1
1
1
2
2
2
1
1
1
2
1
1
2
1
1
0
2
1
1
2
3
1
1
3
2
2
0
1
1
1
1
2
1
2
1
2
1
1
1
2
1
0
0
1
1
1
1
1
1
0
1
1
2
0
1
0
1
1
1
2
2
2
1
1
2
2
2
1
1
2
2
0
0
0
2
0
0
1
1
2
2
1
1
1
1
1
0
2
1
1
1
2
1
1
1
0
1
1
2
1
1
2
1
1
1
1
1
1
1
2
1
0
1
1
0
1
1
2
1
0
1
1
1
1
2
0
1
1
1
0
1
1
2
2
2
1
0
2
0
1
1
1
1
2
1
1
2
1
1
0
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
0
1
2
1
1
1
1
1
1
2
0
2
1
1
1
1
0
1
0
1
1
1
0
1
1
1
1
1
1
2
1
2
2
0
1
1
1
1
1
1
1
1
1
1
0
1
0
0
1
1
1
0
1
1
1
1
1
0
1
0
1
2
1
2
1
2
1
1
0
1
0
1
2
2
1
1
1
1
2
1
0
1
2
1
2
1
0
1
1
2
1
1
1
0
1
1
1
2
2
1
1
2
1
2
1
1
1
2
2
2
1
0
1
1
2
1
1
1
1
2
0
1
1
2
0
1
2
1
0
1
1
0
1
1
0
0
1
1
1
2
2
2
1
1
1
2
1
0
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
2
1
0
1
1
1
1
1
1
1
1
1
1
1
1
2
0
1
1
1
2
1
1
1
2
1
1
1
2
2
1
0
1
1
1
2
1
3
1
0
0
0
1
1
1
1
0
2
1
1
2
1
1
1
1
0
1
1
1
1
1
1
1
1
1
3
2
1
2
1
1
1
2
1
1
2
1
1
1
2
2
1
1
0
2
1
1
1
0
0
1
1
1
0
1
2
2
1
1
1
2
1
1
1
1
2
1
1
2
2
1
1
1
2
1
1
1
1
0
2
2
1
0
2
2
1
1
1
1
2
2
0
1
1
2
0
0
2
0
1
1
0
2
1
1
0
1
0
1
1
0
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
2
1
2
1
2
3
1
2
1
1
1
2
1
2
1
1
0
1
1
1
1
1
2
2
2
2
1
1
1
2
3
1
1
1
1
2
0
1
0
1
3
0
1
1
1
0
1
1
1
1
2
1
1
0
2
1
2
2
1
1
2
2
2
2
1
1
2
1
2
0
1
1
1
2
1
2
1
1
1
2
1
1
1
1
2
2
1
1
1
2
0
1
1
0
1
1
1
2
1
0
2
1
1
2
1
1
1
1
1
0
1
1
1
1
1
1
1
0
1
1
2
1
1
1
1
1
2
1
2
0
0
1
1
1
1
1
1
0
1
2
2
1
0
1
1
1
1
2
1
1
2
1
1
1
0
1
0
1
1
1
0
0
5
0
2
2
1
1
2
1
1
1
1
2
2
2
2
2
2
0
2
2
1
1
2
1
1
2
0
1
1
2
2
1
1
1
1
2
1
1
1
2
1
2
1
1
1
0
1
1
1
1
1
2
2
1
1
1
1
2
1
1
2
0
1
1
0
1
1
0
2
1
1
1
0
2
0
1
1
2
2
1
1
0
1
1
1
1
1
0
1
1
1
1
2
1
2
1
1
1
0
1
1
1
1
2
1
1
1
1
1
0
2
2
0
1
1
1
1
2
1
0
2
1
1
1
2
0
1
1
1
1
0
2
2
1
1
2
2
1
1
1
1
1
1
1
1
1
0
1
1
2
1
1
0
2
0
2
1
2
1
0
2
1
0
1
1
0
1
2
1
1
2
2
1
1
2
1
0
1
2
0
2
2
1
2
0
1
2
1
2
1
0
1
1
1
1
1
2
2
0
1
1
1
1
1
3
1
2
0
1
1
0
1
1
1
1
1
2
1
1
1
1
0
1
2
1
1
1
1
1
1
1
2
1
2
2
2
3
0
2
0
2
2
1
2
1
1
2
1
1
1
1
2
1
0
2
1
0
2
2
1
1
0
1
1
1
2
1
1
1
1
0
1
1
1
1
1
2
2
1
1
1
1
1
0
1
1
2
0
1
1
1
1
1
0
1
1
1
2
1
0
1
1
1
0
2
0
1
1
1
0
1
0
2
2
1
1
2
1
3
1
1
1
1
2
1
1
1
1
0
0
0
0
2
1
2
2
1
2
2
1
1
2
0
1
1
2
1
0
1
2
1
1
0
2
1
0
2
1
1
2
1
2
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
0
0
1
1
1
1
0
2
1
1
1
1
1
1
1
0
1
1
0
0
1
1
1
1
1
1
0
1
2
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
0
0
1
0
2
1
0
1
1
2
1
0
1
1
2
1
0
1
1
1
0
1
2
1
1
1
1
1
2
1
1
2
0
1
1
1
0
1
2
1
1
1
1
1
1
1
1
0
2
1
0
1
1
1
1
1
1
1
2
1
2
1
2
1
1
1
1
2
1
0
0
1
1
2
2
0
0
1
2
1
1
1
0
1
2
1
2
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
0
0
1
1
1
2
0
0
1
2
0
1
0
0
1
1
1
1
1
2
1
0
1
1
2
2
1
2
2
0
1
1
1
0
1
1
1
0
0
1
1
1
1
0
2
2
0
1
1
2
1
0
2
2
2
1
0
0
1
1
1
1
2
2
2
2
1
1
2
2
2
0
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
0
1
2
1
0
0
2
2
2
1
1
1
1
2
2
2
0
2
2
1
2
1
0
2
1
1
1
1
0
1
1
1
1
1
1
2
1
2
1
1
3
1
1
2
1
1
0
0
0
1
2
1
2
1
0
1
1
0
0
1
1
1
1
3
1
0
2
1
1
2
1
1
1
2
1
1
0
1
1
2
1
1
1
0
1
1
2
1
1
1
2
1
1
2
2
1
1
2
1
1
0
2
1
0
1
1
1
1
1
2
1
2
1
0
0
0
1
1
0
2
1
2
0
2
2
0
1
1
1
1
1
2
0
0
1
1
1
1
1
0
0
1
1
1
1
1
1
1
0
1
1
2
2
0
1
1
1
1
2
2
2
1
1
1
2
1
1
1
1
1
2
2
2
1
1
1
2
1
2
1
1
1
2
1
0
0
2
2
2
1
1
1
0
2
2
2
1
2
2
1
1
1
1
1
1
1
0
2
2
2
1
1
1
1
2
1
1
1
1
2
1
1
2
1
2
1
1
0
2
1
0
0
2
1
2
2
2
1
1
1
1
1
1
1
2
1
2
1
2
1
1
2
2
1
1
1
1
1
1
0
1
2
1
1
1
1
0
1
1
1
1
1
0
2
1
1
1
1
1
1
2
0
2
1
0
1
2
1
1
1
2
1
2
2
2
1
1
2
1
1
1
2
0
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
0
1
0
1
1
1
1
1
1
1
2
2
1
0
1
1
1
1
2
0
2
2
0
0
1
2
0
2
1
2
2
2
0
1
1
1
2
2
1
1
1
2
0
0
2
2
3
1
1
3
1
1
1
2
1
1
1
1
1
0
2
1
1
2
0
1
0
1
2
2
2
1
2
1
1
2
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
3
2
1
2
1
0
0
1
1
0
0
2
1
1
1
0
2
1
2
0
2
0
2
1
2
1
1
1
0
2
2
1
1
1
0
1
1
1
1
2
1
1
1
1
1
1
0
0
1
1
1
1
0
1
2
1
1
1
0
0
1
2
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
0
2
2
1
0
1
1
0
0
2
0
1
1
2
1
1
2
1
1
0
2
1
1
2
4
1
2
1
1
1
1
1
1
1
2
2
2
1
1
2
1
1
1
2
1
2
1
1
1
1
1
2
1
1
2
1
1
1
0
1
1
1
1
1
0
1
1
1
2
1
2
1
2
1
0
1
1
0
1
1
1
2
1
2
1
0
1
1
2
2
2
1
1
2
1
2
1
2
2
0
2
3
2
1
1
1
1
1
1
1
0
2
1
2
1
1
3
1
1
2
1
2
1
1
1
1
1
1
1
1
2
0
0
2
1
1
1
2
2
2
2
1
1
1
1
1
2
0
1
1
0
1
1
1
1
1
1
1
1
1
2
1
0
0
1
1
1
2
1
1
1
1
1
1
0
1
1
1
1
1
1
0
0
1
2
1
2
1
1
1
1
0
2
3
1
2
1
1
1
2
2
2
1
1
2
2
1
2
1
2
2
2
1
1
1
0
1
1
2
1
2
2
1
2
1
1
0
1
2
0
1
1
1
1
2
2
2
2
1
3
1
2
0
2
0
1
1
1
1
0
2
2
2
2
1
2
1
0
2
2
2
1
1
2
2
1
1
2
1
1
0
1
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
0
1
2
1
1
2
0
1
2
2
0
1
1
1
1
1
1
1
1
2
1
1
1
0
0
1
2
1
0
2
1
1
1
2
1
1
1
2
0
2
1
2
1
1
0
2
1
2
2
0
2
1
1
1
0
1
1
2
1
1
1
1
1
1
0
0
2
1
1
2
0
1
1
1
2
0
1
2
1
1
1
2
1
1
2
1
1
1
1
2
1
1
1
1
1
1
0
0
1
1
1
1
1
2
0
1
2
1
1
2
1
1
1
0
1
1
2
1
2
2
1
1
1
0
1
1
0
2
2
1
1
1
0
1
0
2
1
2
1
1
1
1
1
2
0
1
1
1
1
1
1
0
1
1
2
0
2
2
1
0
0
2
1
1
1
1
1
1
1
1
1
0
0
2
0
1
1
2
1
0
1
0
0
1
2
1
1
1
1
1
0
1
0
1
1
0
1
1
0
2
2
1
1
1
1
2
2
1
1
1
2
1
1
0
2
1
2
1
2
2
1
0
1
1
2
2
1
1
2
1
1
0
0
2
2
1
0
1
2
2
1
2
1
1
1
1
1
0
1
2
1
1
1
1
1
1
1
0
1
1
0
0
1
1
1
1
1
1
1
0
2
1
1
1
1
2
2
1
2
0
0
1
1
0
2
0
1
2
1
1
1
1
1
1
0
2
2
1
0
2
1
0
0
1
1
0
1
1
2
1
1
0
1
1
1
0
1
1
2
1
1
1
0
1
0
1
1
2
1
0
0
1
1
1
1
1
1
1
1
0
2
1
2
1
1
2
2
0
0
1
1
0
2
1
1
2
1
1
1
1
1
1
1
1
2
0
1
1
1
2
1
1
1
1
2
1
1
0
1
1
1
3
1
2
0
1
2
1
1
2
0
1
1
1
1
2
1
1
2
1
0
2
1
2
0
2
2
1
3
1
2
1
1
2
1
0
1
1
1
2
1
1
1
1
0
0
2
1
2
1
0
0
1
1
1
2
1
1
2
1
2
2
2
2
2
1
2
2
1
1
1
2
1
1
1
2
1
2
2
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
0
1
1
1
2
1
0
2
2
0
1
2
1
2
2
1
2
1
1
2
1
2
1
0
0
1
1
0
1
1
1
2
1
1
2
0
1
2
2
2
2
0
1
1
2
2
1
1
1
2
1
1
1
1
2
1
1
1
2
1
1
2
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
2
1
0
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
1
1
1
2
1
1
2
1
0
1
1
1
1
2
1
2
1
2
1
1
2
2
1
2
1
2
1
0
1
1
0
0
1
1
1
1
1
1
2
2
1
1
0
1
1
2
2
0
2
0
1
1
0
1
1
1
1
1
2
1
1
1
2
2
2
1
1
1
0
0
1
1
1
1
1
1
2
1
1
1
1
1
2
1
2
2
2
1
0
2
1
1
1
1
1
1
0
1
2
1
1
1
0
1
1
1
1
3
1
1
1
2
1
1
1
0
2
1
2
0
1
2
1
1
2
2
0
2
1
1
0
2
1
3
1
1
0
2
0
2
1
1
2
1
0
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
2
1
1
1
2
1
1
0
1
1
2
2
1
1
1
1
1
2
2
0
1
0
1
1
0
1
1
1
0
1
1
1
1
2
2
2
2
1
1
1
1
1
2
2
1
1
1
1
2
1
1
1
2
1
1
1
1
0
0
1
2
1
2
1
1
1
1
1
2
2
2
2
0
2
0
0
2
0
2
1
1
1
1
2
1
1
1
1
1
1
1
0
1
1
1
2
1
2
1
1
1
2
1
0
2
1
1
1
1
0
1
1
1
1
1
1
1
2
1
0
1
1
0
1
2
1
0
1
1
1
2
2
1
1
1
2
1
2
1
1
1
2
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
2
1
0
1
2
0
2
1
0
1
1
2
2
1
1
1
1
1
1
1
0
1
1
1
2
2
1
1
1
2
2
1
1
1
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
2
2
2
1
1
1
1
2
2
1
1
1
2
2
2
2
1
1
1
1
0
1
1
2
1
1
1
1
1
1
1
1
0
1
2
1
1
0
1
1
1
0
0
1
0
2
0
1
1
0
0
2
1
1
1
2
0
2
1
2
0
2
0
1
2
1
1
2
1
1
1
1
0
1
1
1
1
2
2
0
0
0
2
2
1
1
2
1
1
2
1
1
2
1
1
1
1
2
1
2
1
2
0
2
1
2
1
1
0
1
0
1
0
0
0
1
1
2
1
2
1
1
0
1
1
2
2
2
0
2
1
1
1
1
2
2
1
0
1
2
1
1
1
1
1
0
1
1
1
2
1
1
0
2
1
0
1
0
0
1
2
1
2
1
2
1
2
1
1
2
1
2
2
2
0
0
1
1
1
1
2
1
1
1
2
1
1
2
1
0
2
1
1
1
1
1
2
1
1
3
2
1
1
1
2
2
1
1
2
1
1
1
1
0
1
1
2
1
1
1
1
2
1
1
1
1
0
1
1
1
1
2
1
2
1
2
1
1
2
1
2
1
2
1
0
1
1
1
1
1
1
1
1
2
2
1
1
3
1
1
0
1
1
1
1
0
1
0
1
0
1
1
0
2
1
1
2
2
1
1
1
2
0
0
0
7
1
1
1
2
1
0
1
1
1
1
2
0
2
2
1
0
1
2
1
0
1
2
1
0
1
1
0
1
1
1
2
2
2
1
1
2
1
1
1
1
2
2
0
1
1
0
1
1
1
1
1
1
1
1
1
1
1
0
1
0
2
2
2
1
1
1
2
1
1
0
1
1
2
2
2
2
2
0
1
1
1
0
2
1
1
1
2
1
0
1
1
1
2
1
1
0
1
0
2
2
1
1
1
0
1
1
3
1
1
0
1
1
2
1
2
1
1
0
1
2
1
2
1
2
0
0
1
2
1
2
1
1
2
1
2
0
2
1
1
2
1
2
1
1
2
2
1
1
1
1
2
1
1
0
2
0
0
1
1
2
2
1
5
0
2
1
1
1
0
1
2
1
1
2
0
1
2
1
2
1
1
1
1
0
1
1
1
2
1
0
1
0
0
1
0
2
1
3
1
1
1
1
2
0
0
1
2
2
1
1
1
1
1
0
0
1
1
0
1
1
1
1
0
0
1
1
1
1
1
2
1
1
2
1
1
0
1
1
1
1
0
1
1
1
2
0
1
1
1
1
0
0
1
1
1
2
1
2
2
2
0
1
2
1
1
0
1
0
1
1
1
0
1
1
0
1
1
1
0
0
2
2
2
1
0
2
0
1
1
0
1
0
4
2
2
1
1
0
1
0
1
1
1
1
1
0
1
1
1
1
1
2
1
2
1
0
1
1
1
1
2
2
0
0
0
2
1
1
1
1
0
0
1
2
1
0
1
0
1
1
1
1
2
2
1
2
1
1
1
0
1
1
2
1
1
2
1
1
2
2
2
2
2
0
0
1
1
1
1
0
2
0
0
0
0
1
0
2
2
1
0
1
2
1
1
1
2
1
1
1
1
2
1
1
1
2
1
1
2
2
1
2
1
1
1
1
1
0
1
2
1
2
1
1
1
1
1
2
0
2
1
1
0
1
1
2
2
1
0
1
2
1
1
2
1
1
0
2
1
1
1
1
1
1
1
1
0
1
1
1
2
1
2
1
2
0
0
0
1
1
1
1
0
1
1
0
1
0
2
1
1
2
2
2
1
1
0
1
1
1
2
1
1
1
2
1
0
1
2
1
1
1
2
2
1
2
2
2
2
1
1
0
0
1
1
0
2
1
2
0
1
1
1
1
1
1
1
1
1
1
2
2
4
1
0
1
1
1
2
0
1
0
5
2
2
2
1
1
2
1
1
1
1
1
2
1
1
1
0
0
1
1
0
1
0
2
2
1
1
2
1
2
1
2
1
1
0
1
2
2
1
2
0
1
1
1
2
0
2
1
1
1
1
1
2
1
1
2
1
1
1
2
2
1
2
1
2
0
1
1
0
1
1
1
0
1
1
0
1
1
1
0
1
1
0
1
1
0
1
2
2
1
1
0
1
1
1
1
2
2
1
1
2
1
2
2
2
1
1
2
2
2
1
0
0
2
3
2
1
1
1
2
1
1
2
0
1
2
1
1
1
1
1
2
1
1
1
1
1
1
0
0
1
1
1
1
0
2
1
1
0
1
1
1
1
1
1
2
0
0
1
1
2
1
1
2
1
0
1
1
1
1
2
1
1
1
2
1
2
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
2
2
0
1
0
1
1
2
1
1
1
0
2
0
1
1
0
1
1
1
1
1
1
1
2
2
1
2
2
2
1
1
2
1
0
0
0
0
2
2
2
1
2
1
1
2
2
0
1
2
2
2
1
1
1
0
1
1
2
2
1
1
2
1
1
2
1
1
0
1
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
1
1
2
1
0
1
1
1
2
0
0
1
1
1
1
1
1
1
2
0
1
1
1
1
3
2
1
1
3
1
1
1
1
1
1
1
0
2
0
2
1
1
1
2
1
0
0
1
1
1
1
1
1
1
2
0
2
1
2
1
1
1
0
2
1
1
1
2
1
1
1
1
2
1
0
1
1
2
0
2
2
1
2
1
1
1
2
0
0
0
1
2
1
4
1
1
2
0
2
1
1
2
1
1
2
2
1
1
2
1
0
1
2
1
1
1
0
2
1
1
1
0
2
0
1
1
1
1
2
0
1
1
1
1
1
2
2
1
1
1
2
1
1
1
1
1
1
1
2
1
2
2
1
1
1
2
1
1
1
2
0
1
1
1
2
1
1
0
1
2
0
1
1
2
1
1
1
2
2
1
1
1
1
2
2
2
1
1
2
1
0
2
2
1
1
1
0
2
1
1
1
1
2
1
1
2
1
1
2
2
1
1
1
1
0
1
1
2
2
0
1
0
1
1
0
1
1
1
0
1
0
1
1
0
1
1
1
2
0
1
1
1
0
2
0
1
1
1
2
0
1
2
1
1
0
1
1
1
2
1
0
1
2
1
1
0
0
0
1
1
2
1
0
2
1
1
1
0
0
0
1
1
0
1
1
1
2
1
1
1
1
1
2
0
1
1
0
0
1
2
1
1
1
2
1
0
1
1
1
1
0
0
0
1
1
1
1
1
0
2
1
1
2
0
1
1
2
1
1
2
1
1
1
1
2
1
1
1
2
1
1
2
1
1
1
2
2
1
1
2
1
2
1
1
1
2
2
0
1
1
2
2
1
1
0
1
0
0
3
2
2
1
1
1
0
2
1
2
0
1
1
1
1
0
0
1
2
1
0
1
1
1
0
1
2
1
2
2
2
1
2
1
1
1
1
1
1
1
1
0
1
1
0
1
1
1
1
1
1
2
0
1
2
0
1
2
1
2
0
1
1
1
1
1
2
1
1
1
0
1
2
2
1
1
1
1
1
1
2
2
1
2
0
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
0
0
2
1
0
1
2
1
1
0
0
0
1
1
1
2
2
2
2
1
2
1
1
1
1
2
0
1
0
0
1
0
1
0
1
1
1
1
1
1
1
0
0
1
2
2
1
0
1
0
1
1
2
2
2
1
0
0
1
1
0
0
1
0
2
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
2
1
1
1
2
1
2
1
2
1
1
2
1
1
2
1
2
1
2
0
1
2
1
0
2
1
1
1
1
1
1
1
2
1
1
1
2
1
1
2
1
1
1
1
1
2
0
2
1
1
1
1
2
1
3
2
1
2
1
0
2
1
1
0
2
1
2
1
1
2
1
1
2
2
1
1
1
1
2
1
1
1
2
1
2
2
1
1
1
1
1
0
1
1
1
1
1
2
1
2
0
1
1
1
1
2
1
1
1
1
0
1
2
1
1
2
1
1
2
0
2
2
2
1
0
2
2
2
1
1
1
1
2
0
0
2
1
2
2
2
2
1
1
0
1
2
0
1
0
1
2
2
1
1
1
0
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
2
1
0
0
0
0
1
2
1
0
0
2
2
1
0
1
3
2
1
2
1
2
1
2
1
1
0
0
1
1
2
1
2
0
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
2
0
0
1
1
1
1
1
0
1
1
1
1
2
0
1
1
0
1
2
1
0
0
2
1
1
1
1
2
1
2
2
2
1
1
2
1
1
0
1
1
1
1
1
2
2
1
0
1
1
1
2
0
0
2
2
1
1
1
1
1
1
1
1
2
1
2
0
2
1
1
1
2
1
1
1
2
1
1
1
1
0
1
1
1
2
1
0
1
1
1
2
2
1
1
1
1
2
0
2
1
1
1
1
1
1
1
1
0
0
2
1
1
1
1
1
1
1
1
1
1
0
0
1
2
1
2
1
2
2
2
0
2
1
1
2
0
1
0
0
1
1
1
1
2
1
0
1
1
1
1
1
2
1
2
2
1
1
0
1
2
1
1
1
2
1
0
1
1
2
1
1
1
2
1
1
2
2
1
1
1
2
1
1
0
1
0
1
1
1
2
1
1
1
0
1
1
3
1
0
1
2
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
2
0
2
1
2
1
2
2
1
2
1
1
1
0
2
1
1
0
0
1
0
0
2
2
1
3
2
1
1
1
1
1
2
1
1
1
1
1
0
1
1
1
1
1
2
0
2
2
1
0
1
1
1
1
1
1
2
0
1
1
0
0
1
1
1
0
1
1
1
0
0
1
0
2
2
2
0
2
1
3
1
1
1
3
2
1
1
1
1
2
1
2
2
1
1
1
1
1
0
1
0
1
1
1
2
0
1
0
2
1
0
2
0
1
0
1
1
1
1
1
1
1
0
2
0
0
1
0
2
1
2
1
1
2
1
1
0
1
2
2
1
1
1
2
2
1
0
1
2
1
1
2
0
2
1
0
1
1
2
0
1
1
0
1
1
1
2
1
1
1
2
1
1
2
1
1
0
1
2
1
1
2
1
1
0
2
1
2
1
2
1
1
2
1
1
2
3
2
2
1
1
1
1
1
1
1
1
2
1
1
1
1
0
3
0
1
0
1
1
0
1
1
0
1
1
0
1
1
1
2
2
1
0
1
2
1
2
2
0
1
1
1
1
1
0
1
2
2
1
1
1
2
1
1
1
1
1
1
2
2
2
2
2
1
2
2
1
1
0
1
1
1
2
1
1
1
1
1
1
0
2
1
2
2
1
2
1
1
2
1
2
0
1
1
0
0
1
2
2
1
0
1
1
2
2
1
1
2
1
0
2
1
1
1
0
2
1
1
1
1
1
1
1
1
1
1
1
2
0
2
2
0
2
1
0
1
1
1
1
1
2
1
2
1
1
1
1
0
1
2
0
2
1
1
2
1
1
1
1
1
0
1
2
2
1
1
1
1
2
1
0
1
1
1
1
1
2
1
1
0
0
0
1
1
1
0
2
1
2
1
0
1
0
1
1
3
2
1
1
1
2
0
0
2
2
1
2
1
0
1
2
2
2
0
2
1
1
0
2
1
1
0
2
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
2
0
1
1
1
2
1
2
1
1
1
1
1
1
0
1
2
1
1
1
0
2
1
1
1
1
1
1
0
1
1
1
1
1
1
0
1
1
1
1
1
0
1
2
2
2
1
1
1
1
1
1
1
1
1
1
3
1
2
1
1
0
1
1
1
1
1
2
1
0
1
2
1
1
1
1
1
2
4
1
1
1
1
1
0
1
1
1
1
2
1
1
0
2
2
2
1
1
2
1
1
1
1
1
2
1
1
0
0
1
1
2
1
1
1
1
1
3
1
1
1
1
1
1
1
2
2
1
1
1
0
2
0
2
1
1
1
0
1
2
1
1
1
0
2
1
1
0
2
0
1
2
2
1
0
1
1
3
1
2
1
1
1
1
1
2
1
1
1
1
2
1
1
2
2
1
2
2
1
1
0
1
2
1
2
1
1
1
2
0
1
2
1
0
2
1
1
1
1
1
5
2
2
1
2
2
2
1
1
1
4
1
2
1
2
1
1
2
1
1
1
0
1
1
2
0
2
2
1
2
2
1
2
1
2
2
2
0
1
0
1
1
1
1
1
1
1
1
2
1
2
2
2
3
2
1
1
1
1
2
0
1
0
1
1
2
1
2
0
0
1
0
2
1
1
3
2
0
1
1
1
0
1
1
1
2
1
1
2
1
0
2
1
1
1
0
2
1
1
1
2
2
1
1
1
2
1
1
1
2
1
0
1
1
1
1
1
2
1
1
0
1
2
1
0
2
1
1
2
2
2
1
1
2
1
1
0
0
2
1
2
2
1
1
2
1
1
1
1
1
0
2
4
1
1
2
1
1
2
1
1
2
1
2
1
1
1
1
2
1
0
0
1
1
1
2
1
3
1
1
1
1
1
1
1
2
1
1
2
0
2
1
1
1
1
1
1
0
1
1
1
1
1
0
1
1
2
0
1
2
0
1
2
2
1
2
1
1
2
0
1
1
1
2
1
1
2
2
0
1
1
0
2
1
0
0
1
1
1
2
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
0
1
1
1
0
2
1
1
1
2
2
1
0
1
1
1
1
1
1
0
1
1
0
1
0
2
2
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
4
1
1
0
1
1
2
2
1
2
1
2
1
1
1
1
1
0
2
1
1
0
0
1
1
1
2
1
1
1
2
1
1
1
1
1
0
1
1
2
3
1
0
1
2
1
1
0
2
1
2
2
2
1
1
0
1
1
2
1
2
1
0
1
1
1
1
2
2
2
1
2
1
0
2
1
1
1
2
2
1
1
1
1
1
2
1
0
1
1
2
1
1
1
1
0
1
0
0
1
1
1
2
2
2
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
2
2
1
1
2
2
1
0
1
1
1
1
1
3
1
1
1
1
1
1
0
1
1
1
1
1
1
3
1
1
2
2
0
1
0
1
1
0
1
2
1
1
2
2
1
2
2
2
1
1
1
1
0
2
1
0
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
0
0
1
1
2
2
1
1
1
1
1
1
1
1
2
1
0
1
2
1
1
0
2
1
2
2
1
1
1
2
2
1
0
0
1
0
1
2
2
2
1
1
1
0
1
1
2
2
1
0
2
1
1
1
1
1
1
2
1
1
2
0
1
1
0
2
0
0
1
1
1
0
1
1
1
2
1
1
1
1
1
1
1
2
2
1
3
1
2
2
1
1
1
1
0
1
0
1
1
1
1
2
1
2
1
2
1
1
2
1
1
0
1
1
2
1
1
1
2
1
1
2
2
2
1
2
2
2
1
1
1
1
0
1
1
1
1
1
1
1
1
0
1
1
1
1
2
1
1
1
0
1
1
0
0
1
1
1
2
1
1
1
0
1
0
2
2
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
2
1
2
2
1
2
2
0
0
1
1
0
1
1
2
3
1
0
1
2
1
1
0
1
2
2
2
1
1
2
1
1
2
1
1
2
2
1
1
2
1
1
0
0
1
1
1
1
1
1
2
0
0
2
2
0
1
1
2
1
0
2
1
1
1
1
1
1
1
1
0
2
0
1
1
1
2
2
1
1
2
1
1
2
2
1
2
1
2
1
1
2
1
1
0
1
1
1
2
1
1
1
2
1
3
2
1
0
2
0
0
0
0
1
1
2
2
1
1
0
1
2
1
2
2
2
0
1
1
1
2
1
1
1
1
0
0
1
2
1
2
1
2
1
1
1
2
0
1
1
1
0
1
0
2
2
1
1
2
1
1
1
1
1
1
2
1
0
1
1
1
1
2
1
1
1
2
2
1
1
0
0
2
1
0
1
1
1
1
1
1
0
1
2
1
1
1
1
1
1
1
2
0
0
2
0
1
1
2
2
2
0
1
2
1
1
1
1
1
1
1
1
0
0
2
2
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
0
1
1
0
1
1
0
1
1
2
1
2
1
1
0
1
1
0
0
1
2
2
2
2
2
0
1
1
2
1
0
1
2
0
0
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
3
1
1
1
0
1
3
0
1
2
1
1
2
1
1
1
0
0
1
1
1
0
1
1
1
4
1
1
1
1
1
1
1
1
1
0
1
0
1
0
2
1
1
1
0
2
1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
2
1
2
0
2
1
2
2
2
1
2
1
1
1
1
1
1
0
1
2
0
1
3
2
2
0
1
1
1
1
1
2
0
0
2
1
2
2
1
1
1
1
1
1
2
1
0
2
2
1
1
1
0
1
2
3
1
1
1
0
0
2
0
8
2
1
1
0
1
2
1
1
1
2
1
1
1
1
2
1
2
1
0
2
1
2
2
1
1
0
1
2
1
0
1
2
0
1
1
1
1
1
2
1
1
1
1
2
1
0
2
1
1
2
1
0
1
2
1
1
1
1
1
2
1
1
1
1
0
1
1
1
1
1
1
2
1
0
1
1
1
0
1
1
2
2
1
1
2
2
0
1
0
0
1
1
0
2
0
1
2
1
0
2
2
2
2
3
2
1
0
1
1
1
1
1
1
1
1
1
0
1
2
1
2
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
0
1
1
1
2
1
1
1
1
1
2
2
1
2
2
2
0
0
0
1
1
1
1
1
1
1
1
1
0
0
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
0
1
1
2
1
1
1
1
1
1
1
1
0
1
2
1
1
1
1
2
2
2
1
1
1
2
2
2
2
0
1
0
2
2
1
2
5
0
1
2
2
0
2
1
1
1
0
2
1
1
1
2
1
1
2
0
1
2
2
0
2
1
2
2
1
2
2
2
1
1
1
2
2
0
1
1
1
1
2
2
1
1
2
2
1
2
2
0
1
2
0
1
1
2
1
1
1
2
1
2
2
1
1
1
0
1
1
1
1
0
1
1
1
1
1
0
0
0
2
2
1
1
2
2
0
2
2
1
1
1
1
2
1
0
1
1
0
0
0
2
0
2
1
0
1
1
1
1
2
0
1
1
1
1
0
1
1
1
0
2
1
2
1
1
1
1
2
1
1
0
1
1
2
0
1
1
1
2
1
1
0
1
1
1
0
1
1
1
2
1
3
1
2
1
1
2
2
1
2
1
1
2
1
2
2
0
2
1
2
1
1
0
2
0
0
1
1
1
0
1
1
1
2
1
2
0
1
1
0
0
2
1
0
2
1
2
1
1
1
2
1
1
2
2
2
1
1
1
2
1
2
1
1
1
1
1
2
1
0
1
1
1
0
2
0
1
1
0
2
1
2
1
1
1
1
0
0
1
1
1
1
2
1
0
3
2
1
1
2
1
2
1
0
0
1
1
1
0
1
1
1
2
2
1
1
1
1
2
1
1
2
0
0
1
2
1
2
1
2
1
0
0
1
2
1
1
1
1
1
2
1
2
1
1
1
0
1
2
2
0
2
1
0
1
0
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
2
2
1
1
2
2
1
1
1
2
2
1
1
2
1
1
0
1
1
1
1
2
1
2
0
1
1
1
3
2
1
1
1
0
2
1
1
2
1
1
1
0
1
0
2
1
1
0
2
2
1
1
2
2
2
1
0
2
1
1
0
1
1
1
1
1
1
1
1
2
1
1
1
0
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
2
2
1
2
0
1
0
1
1
0
1
1
1
1
1
1
1
1
2
1
1
3
1
1
1
1
2
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
0
2
1
1
1
2
0
0
1
2
0
2
1
1
1
1
1
0
1
1
0
2
1
1
1
1
2
1
2
1
1
2
1
1
2
1
1
1
1
1
1
2
1
0
2
1
1
1
1
2
1
0
1
1
2
1
2
1
1
1
1
0
1
1
1
2
2
1
2
1
0
2
1
1
1
3
1
1
1
2
1
1
1
1
1
2
1
2
2
1
1
2
1
1
1
1
1
0
1
2
1
1
1
0
2
1
0
1
1
1
2
0
1
1
1
0
2
1
1
1
0
1
2
1
1
1
1
2
1
0
1
2
1
0
1
2
1
1
1
0
1
1
1
0
1
1
2
1
1
1
2
1
0
0
2
2
1
2
1
0
1
1
2
2
1
1
2
2
1
0
1
2
1
1
1
1
1
1
0
2
1
1
1
1
1
1
1
1
1
2
0
1
0
1
2
1
1
0
2
1
2
2
0
2
1
1
1
1
1
1
1
1
1
1
2
1
0
2
1
2
1
1
1
1
2
2
2
2
1
2
2
1
0
2
1
1
2
1
1
1
1
1
1
1
1
2
2
2
0
1
1
0
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
2
2
1
2
1
2
2
1
2
2
1
1
0
1
2
1
1
1
1
2
0
0
1
2
1
1
1
1
1
1
0
0
0
2
2
3
1
1
1
1
1
1
1
2
0
1
2
1
2
2
1
2
1
0
1
0
1
2
1
2
2
2
0
1
0
2
0
0
1
2
1
1
2
1
1
1
1
1
2
2
0
2
2
1
2
1
1
0
2
1
1
1
1
1
2
2
2
1
0
1
1
0
1
2
2
1
1
2
2
0
1
1
2
1
0
2
2
1
2
2
2
2
0
0
2
1
1
1
1
2
2
2
2
1
2
0
2
1
1
1
1
1
1
1
2
0
1
2
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
2
2
1
0
1
1
1
1
1
1
1
1
1
2
2
2
1
2
1
1
1
2
0
0
1
2
1
1
0
2
1
1
1
1
0
1
0
2
0
1
1
2
2
1
1
0
1
2
0
0
1
1
1
1
1
1
2
2
1
1
1
2
2
1
2
2
1
2
0
1
1
2
1
0
0
1
0
2
0
0
1
2
2
1
1
2
1
1
0
3
1
2
1
1
1
1
2
1
2
2
1
0
1
1
1
1
1
1
0
0
1
1
2
2
2
1
2
0
1
0
0
2
2
0
2
1
1
1
0
0
2
2
1
1
0
2
1
1
1
2
1
1
2
1
1
1
1
1
2
1
0
1
1
1
2
1
1
2
2
1
1
4
1
0
1
1
1
1
1
2
0
1
1
2
0
2
2
1
1
2
1
1
1
1
0
1
1
1
1
2
1
2
1
0
1
0
2
2
1
1
2
2
1
1
1
1
0
0
0
1
2
2
1
1
2
1
1
2
0
1
0
2
0
0
2
1
1
1
1
1
1
2
1
1
0
0
1
1
1
2
1
2
2
1
1
1
2
2
1
1
0
1
1
2
0
1
1
1
2
1
1
2
1
1
0
0
1
2
1
1
1
1
1
1
0
1
2
1
1
1
2
2
1
2
1
1
0
1
1
1
1
1
1
0
1
0
1
1
2
1
1
2
1
1
2
2
0
1
1
0
1
2
2
2
1
2
1
2
1
2
1
1
1
2
1
1
1
1
1
1
2
3
2
2
2
2
2
2
1
3
0
1
1
2
1
2
1
2
1
0
2
0
1
1
2
1
2
1
1
2
1
1
1
1
1
1
2
1
2
0
0
1
1
1
1
0
1
2
1
1
1
2
1
1
1
2
2
1
2
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
1
0
1
0
2
0
1
1
1
2
1
2
2
1
1
1
1
0
0
1
0
1
1
1
2
1
1
0
1
1
0
1
2
2
1
2
2
0
0
2
1
1
1
1
2
1
1
1
1
1
1
0
1
1
1
2
1
2
1
0
1
1
1
1
1
2
0
1
1
2
1
4
1
1
2
1
0
1
1
2
1
1
1
1
0
1
1
2
2
1
1
1
1
1
1
1
1
1
0
0
1
0
0
1
1
1
1
0
1
0
1
1
1
2
0
0
1
1
1
1
1
1
0
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
0
1
1
1
2
2
1
1
2
1
0
1
1
1
1
1
0
2
0
2
1
2
1
0
1
1
1
2
2
0
1
2
1
2
0
0
1
0
0
1
1
1
1
0
2
1
1
1
1
2
1
2
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
0
1
1
1
1
1
0
1
2
0
0
1
1
1
1
1
0
0
1
1
1
2
1
1
1
1
1
2
1
1
0
1
1
0
2
1
1
1
1
2
2
2
2
2
0
2
0
2
2
1
0
1
0
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
0
2
2
1
2
1
1
0
1
1
1
1
0
3
2
1
0
0
1
1
1
0
1
1
1
1
1
1
2
1
1
3
2
1
1
1
1
3
2
1
1
1
1
0
1
1
2
0
1
2
1
1
1
0
1
0
1
1
0
1
1
1
0
1
0
1
1
1
1
1
2
2
1
1
0
1
1
1
1
0
2
2
1
0
2
1
1
2
1
1
1
1
1
1
2
0
1
2
1
2
1
1
1
1
1
2
1
1
2
1
1
2
1
2
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
2
2
1
2
1
0
1
1
0
1
1
2
0
2
1
1
0
2
1
1
1
2
1
0
1
0
2
2
2
1
1
1
2
1
2
0
0
1
1
1
0
0
1
1
1
1
0
1
1
2
0
1
0
2
1
1
1
1
1
2
2
1
1
1
1
2
0
1
1
1
0
2
1
2
2
1
1
1
1
1
1
1
1
1
2
1
2
0
0
1
1
1
1
1
1
1
0
1
1
2
2
1
1
1
3
1
1
0
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
2
2
0
1
1
1
1
1
1
1
2
1
1
1
1
2
2
1
2
1
1
0
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
0
0
1
1
1
1
1
0
0
1
1
1
1
1
0
1
2
1
1
1
1
1
0
1
2
1
1
1
2
2
1
1
0
1
1
1
1
1
1
1
2
1
0
0
1
1
2
1
2
2
1
1
2
1
1
0
1
1
1
1
1
1
2
1
1
0
1
2
2
1
1
2
2
1
2
1
1
1
1
1
2
2
1
2
1
1
2
1
1
2
2
0
1
2
1
1
2
1
0
1
1
0
0
1
2
2
0
1
0
1
0
2
2
1
0
2
1
2
1
1
1
1
0
2
2
1
1
0
2
2
0
1
1
0
1
1
1
1
2
1
0
1
1
2
1
1
1
2
2
1
2
1
2
1
1
2
1
2
2
2
2
1
0
1
1
2
1
2
1
2
1
1
1
1
1
1
1
1
0
1
1
1
1
3
2
1
1
1
1
2
1
1
0
1
2
0
1
0
0
1
0
3
1
1
1
1
2
0
1
2
1
1
2
0
1
1
2
2
2
1
1
1
0
2
1
0
0
1
2
1
0
1
1
1
1
1
1
2
1
1
2
1
1
1
1
2
1
0
0
1
1
1
1
1
1
1
0
1
0
0
1
1
1
1
1
2
4
1
0
1
0
2
2
2
2
1
2
1
1
0
2
1
2
1
1
2
1
2
0
1
1
1
1
0
2
1
2
1
0
1
1
1
1
2
1
0
0
1
1
1
1
1
0
2
1
1
2
1
2
2
1
2
1
2
2
1
2
1
4
1
1
1
1
1
2
1
1
0
1
1
1
2
1
1
2
1
0
1
1
1
1
1
1
1
1
2
2
2
0
2
1
1
1
1
2
1
1
0
1
1
1
1
1
1
2
1
1
1
2
1
2
1
2
0
2
2
2
0
0
2
0
1
2
2
1
1
2
0
2
1
0
1
2
1
1
1
1
1
2
1
2
0
1
1
1
1
0
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
2
2
1
2
1
1
1
0
2
1
1
0
1
1
2
1
2
2
1
1
1
1
1
1
1
0
1
1
1
1
0
1
1
1
1
1
2
1
0
1
1
1
2
2
1
0
1
3
1
1
0
1
0
1
1
1
1
2
1
1
1
1
1
1
1
3
2
1
0
1
1
1
1
2
0
1
1
0
0
1
1
2
2
1
1
1
1
2
1
0
2
1
1
0
2
2
1
1
2
2
2
1
2
1
2
1
0
1
1
1
0
2
1
1
0
1
2
1
0
1
7
1
2
2
3
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
0
0
0
0
1
0
0
1
1
2
1
2
1
1
1
1
2
2
1
1
1
2
2
1
1
1
1
2
1
0
0
1
2
1
1
1
1
1
1
1
1
1
1
2
2
1
0
1
2
2
3
1
0
1
0
1
1
1
2
1
1
2
0
2
1
1
1
1
0
1
1
2
1
1
1
1
1
1
1
3
0
1
2
2
2
1
1
0
2
0
2
0
1
1
0
2
1
1
1
0
2
0
1
1
2
1
2
2
1
2
2
1
2
1
0
0
1
0
2
0
1
1
1
1
1
2
1
1
0
1
1
1
1
0
1
1
1
1
1
1
1
0
2
0
1
2
0
1
2
2
1
1
1
1
2
2
1
2
0
1
3
1
1
1
1
2
2
2
3
1
2
1
2
1
1
2
0
1
2
1
1
2
1
2
1
1
2
1
1
1
2
0
5
2
1
2
2
0
1
1
1
1
2
2
1
1
0
2
1
1
0
2
2
1
1
0
1
1
4
2
2
1
0
1
1
2
2
1
0
2
1
1
1
1
1
2
1
1
2
0
1
1
2
1
2
1
1
3
2
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
2
1
1
0
1
1
1
1
2
0
1
1
0
1
2
1
2
0
1
1
1
2
1
2
1
0
2
1
1
2
2
2
2
0
2
0
0
1
1
1
1
2
1
1
1
1
0
2
1
1
1
1
1
1
2
1
1
1
1
2
0
1
1
2
1
1
2
2
1
1
2
2
1
1
1
3
2
1
2
0
2
1
2
2
0
1
0
2
2
1
1
2
1
0
1
2
1
1
1
2
1
2
2
1
3
2
2
0
1
1
2
2
1
1
1
1
2
2
1
1
0
0
0
0
1
2
1
2
1
1
2
1
1
1
0
1
1
1
2
0
0
1
1
0
0
2
0
1
1
1
1
1
1
1
1
1
1
1
0
0
1
0
1
1
1
1
2
0
2
1
0
0
1
1
2
1
1
2
0
2
1
1
1
1
1
1
1
1
2
1
0
2
1
2
1
1
1
1
0
1
1
1
1
1
0
1
1
1
1
2
1
2
0
2
2
2
1
1
1
2
1
0
1
1
2
2
2
1
1
1
1
0
1
1
1
1
2
1
1
1
1
1
0
1
2
1
1
1
1
2
1
2
1
1
2
2
1
1
0
1
1
2
1
1
0
6
0
1
1
0
0
1
1
1
1
1
1
2
2
0
1
1
1
1
1
1
1
2
1
0
1
2
2
1
1
1
2
1
1
1
1
1
1
1
1
0
1
2
1
1
1
2
1
2
1
2
1
1
1
1
1
2
1
1
0
1
2
2
1
0
1
2
0
1
1
1
1
1
1
0
1
0
1
1
1
2
1
0
1
1
2
1
1
1
0
1
1
1
1
1
1
1
2
1
1
1
0
1
2
1
0
1
1
1
2
2
2
1
1
1
1
2
1
1
1
1
1
0
1
2
1
1
2
1
1
1
1
2
0
1
1
2
1
2
1
1
1
2
2
1
1
1
1
1
1
2
1
2
1
2
1
0
2
1
2
2
2
1
1
0
0
1
1
1
1
2
1
1
1
1
1
2
1
2
2
2
2
0
1
1
1
2
1
2
2
1
1
1
0
1
2
2
2
1
1
0
1
2
1
1
1
2
0
1
0
2
0
0
1
1
2
2
1
1
1
1
2
2
1
2
1
2
0
0
1
0
0
2
1
1
1
0
2
1
2
1
1
1
2
0
1
2
1
1
2
1
2
1
2
2
2
2
1
1
1
0
0
1
1
2
1
1
0
1
0
2
1
2
1
0
1
1
1
1
1
2
1
1
2
2
0
0
1
1
1
1
0
2
2
1
1
2
1
1
1
1
2
0
5
2
1
1
1
2
0
1
1
1
1
1
1
1
1
0
2
1
1
1
1
1
0
1
1
1
1
1
1
1
1
2
1
2
1
1
0
2
1
1
1
2
0
1
1
0
1
2
1
2
1
1
2
1
2
1
1
1
0
1
1
2
1
2
1
1
1
1
1
0
2
1
0
2
2
1
2
0
1
1
2
2
1
2
2
1
1
0
2
1
2
1
1
2
1
1
1
1
1
0
0
1
0
1
2
1
1
2
1
0
0
1
1
1
0
1
0
2
2
1
1
1
0
0
1
1
2
1
1
2
1
1
1
1
0
2
1
0
1
2
1
0
1
1
1
1
1
0
1
1
1
1
1
1
2
1
1
2
1
1
2
1
1
2
1
1
1
2
0
2
2
1
1
2
2
2
1
2
0
1
1
0
1
1
1
1
1
1
1
0
1
1
2
1
1
1
0
0
0
1
2
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
0
2
1
0
1
2
1
2
1
1
1
2
1
1
2
2
1
1
2
1
1
1
2
1
3
1
2
1
0
1
1
1
1
2
0
1
1
1
2
1
1
2
1
1
2
2
1
1
0
1
2
1
1
1
1
2
0
1
1
2
2
1
1
1
1
2
0
2
1
2
2
1
2
2
2
0
1
0
1
3
1
0
1
0
1
1
2
2
1
1
2
1
1
0
1
2
3
1
2
1
1
1
1
0
1
1
1
2
1
2
2
1
2
0
2
2
0
1
2
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
2
2
1
0
2
1
2
1
1
1
2
1
1
1
1
1
1
1
0
1
2
1
1
1
2
2
2
1
2
2
2
1
2
2
2
0
1
0
0
2
2
1
0
2
1
0
1
3
1
2
1
1
1
1
1
0
2
2
1
1
1
0
1
1
1
1
2
1
0
2
1
1
2
1
2
1
2
1
0
0
2
1
1
1
2
1
1
2
2
1
0
1
1
1
0
1
1
2
0
1
0
0
1
0
1
1
1
1
1
2
2
1
1
1
1
1
1
2
0
1
1
2
1
1
1
1
2
1
2
2
1
1
2
0
1
0
2
2
0
1
2
2
2
0
2
2
1
1
1
1
2
1
2
0
1
2
1
2
1
1
2
2
0
0
1
1
0
0
1
1
1
1
1
1
1
1
1
1
2
2
1
2
0
2
2
1
1
1
1
0
2
1
1
1
2
1
0
0
1
1
1
1
1
3
2
1
1
1
1
4
2
1
1
2
1
1
2
1
2
1
0
2
0
1
1
0
5
1
1
1
1
0
2
1
1
1
0
2
2
2
2
1
1
1
1
1
0
1
1
1
1
1
1
1
0
1
0
1
2
1
1
1
0
1
1
1
1
0
0
2
1
0
1
2
1
2
0
1
2
1
2
2
1
1
1
1
1
1
2
1
0
2
1
2
1
2
1
1
2
2
1
2
1
1
2
1
1
1
1
1
0
0
1
2
1
0
2
1
1
1
0
2
1
1
0
1
0
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
0
1
0
1
1
1
1
2
1
1
1
1
1
2
0
2
1
2
1
1
0
1
1
2
1
2
2
1
2
0
1
2
1
1
1
1
1
1
0
0
1
0
0
1
1
2
1
2
0
2
1
1
1
1
2
1
2
2
0
1
1
1
1
0
1
1
1
1
0
2
2
1
2
1
0
1
1
1
2
1
1
1
1
1
1
2
2
0
2
2
0
1
0
1
1
1
0
2
1
1
0
1
1
2
0
0
1
1
1
2
1
2
1
1
2
1
2
1
0
1
1
1
2
0
2
1
0
2
2
1
1
1
2
1
2
2
1
2
0
1
0
1
2
1
1
1
1
1
1
2
1
1
0
1
0
2
1
1
0
2
1
1
1
1
1
1
2
1
1
2
1
1
2
0
2
0
2
0
1
2
0
2
1
1
1
1
0
1
1
1
1
2
1
0
1
0
2
2
2
0
1
1
1
0
0
2
1
1
2
1
2
1
1
1
0
1
1
1
2
3
2
1
1
1
0
1
1
2
2
1
1
1
1
1
1
1
0
1
2
2
1
1
1
0
1
1
1
2
2
2
0
1
1
2
2
1
2
2
1
0
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
0
0
1
2
1
2
2
1
2
1
0
1
1
1
2
2
2
0
2
1
1
1
1
2
0
0
1
1
2
1
0
2
1
1
1
1
2
1
2
1
0
2
1
1
1
1
1
1
1
1
2
1
2
0
1
2
1
2
1
2
0
2
1
1
1
1
1
1
1
2
1
1
2
2
0
0
1
1
1
0
1
1
1
1
2
1
1
1
1
1
0
1
1
1
2
1
1
1
1
1
2
2
2
1
1
1
2
1
1
1
1
0
2
0
2
0
1
2
2
1
1
1
4
0
3
1
2
1
2
1
1
1
2
1
0
0
1
1
1
2
1
1
1
1
0
1
1
1
1
1
1
1
2
0
1
1
1
1
1
1
1
2
1
1
1
1
1
1
0
1
2
2
1
1
1
2
2
2
2
2
1
0
1
0
1
1
1
1
2
1
1
0
1
2
0
2
2
2
0
0
0
2
1
1
1
1
1
2
1
2
2
0
0
2
2
1
2
1
1
1
1
2
1
0
1
0
1
2
1
2
1
1
1
1
0
1
2
0
0
1
1
1
0
1
1
1
1
1
1
1
1
0
0
1
1
1
1
0
0
2
2
2
1
2
1
1
1
1
2
1
2
1
1
1
0
1
1
0
1
1
0
1
1
1
1
1
2
0
2
1
1
2
1
1
1
2
1
1
1
1
2
1
1
0
0
1
1
1
0
2
1
1
1
2
1
1
1
2
1
0
3
1
1
1
1
0
0
1
1
2
1
1
1
1
2
1
2
1
1
0
1
1
2
1
1
1
2
2
1
1
1
0
2
2
0
1
1
0
1
0
2
1
1
1
1
1
1
2
2
2
4
1
1
1
2
1
1
1
1
1
2
1
2
1
2
1
1
1
1
1
0
1
1
2
1
2
0
1
1
1
1
2
2
2
1
0
2
1
1
2
1
2
1
2
1
1
0
1
2
0
1
2
0
2
0
2
1
2
1
1
1
0
1
2
1
1
1
1
0
2
1
2
0
1
2
0
2
2
1
2
1
1
2
0
1
1
1
1
0
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
0
2
1
1
0
1
1
1
1
1
0
2
1
2
1
1
0
1
1
1
2
2
2
1
2
1
2
0
1
1
1
1
2
2
1
1
1
1
1
2
2
2
1
1
1
1
1
2
1
1
2
2
0
1
2
2
2
1
2
0
2
0
2
1
0
2
2
1
1
1
2
1
1
3
1
1
1
1
2
0
1
0
1
1
2
1
3
1
1
1
1
2
1
2
1
2
1
0
3
3
1
1
1
2
1
0
0
0
0
1
1
1
0
1
2
1
2
1
1
1
2
1
2
1
1
2
2
2
1
2
0
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
0
2
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
0
1
0
1
1
2
0
0
1
2
0
3
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
1
1
0
2
1
2
1
1
1
1
1
1
0
1
1
2
1
0
0
1
1
1
1
2
1
2
1
1
2
2
1
1
2
2
2
1
2
0
1
1
1
1
2
2
1
0
1
1
1
1
1
1
2
1
2
1
1
2
1
1
2
1
1
1
1
1
1
1
1
0
2
1
0
1
1
1
1
1
2
2
1
1
0
0
2
1
1
1
2
1
2
1
2
1
1
1
1
1
1
0
0
2
1
1
1
0
1
2
1
2
2
1
1
2
1
2
0
1
1
1
1
1
2
1
0
1
1
1
0
2
1
0
0
1
0
1
2
1
1
0
1
2
3
1
1
1
2
0
1
2
1
0
1
1
1
1
1
0
2
2
2
1
1
2
0
0
2
1
1
1
1
1
2
1
1
2
2
1
0
1
1
0
1
1
0
1
1
1
1
1
0
1
2
1
1
1
0
1
1
2
1
2
2
1
1
1
0
1
0
1
1
2
1
2
2
2
1
0
1
1
1
1
1
1
2
0
2
1
1
1
1
2
1
2
1
2
2
1
2
2
1
1
1
2
2
1
2
0
1
2
2
0
0
1
1
0
1
1
0
1
1
2
1
0
0
1
1
1
1
2
1
2
2
1
1
1
2
0
2
1
1
1
1
1
1
1
1
2
2
1
0
1
1
1
1
2
1
1
2
0
1
1
0
2
1
1
1
0
0
2
1
2
1
1
1
1
1
0
1
2
2
1
2
1
2
1
0
2
0
1
0
1
1
0
2
2
1
2
1
1
1
1
0
1
1
1
1
1
1
2
1
1
2
1
2
1
2
1
1
2
0
1
1
1
1
2
1
0
1
1
2
1
1
2
1
1
2
0
1
1
2
0
1
1
1
1
1
1
1
1
1
1
2
2
2
2
1
2
1
1
1
1
2
2
2
1
0
2
0
1
2
2
1
0
2
1
1
1
0
1
1
0
1
1
1
1
1
0
1
2
1
1
2
1
0
2
1
0
2
2
1
1
0
1
0
1
1
1
2
1
1
1
2
0
1
1
2
0
2
1
1
2
1
2
1
1
1
1
2
1
1
1
1
2
1
1
0
2
1
1
2
2
1
1
1
2
2
1
1
0
1
1
2
2
1
0
1
0
2
1
1
2
2
1
2
1
2
0
2
1
1
1
1
2
1
2
1
2
1
1
1
0
1
1
1
1
0
1
2
1
2
2
1
1
1
0
1
1
1
1
2
2
2
0
1
1
1
0
1
2
1
1
1
2
1
1
1
2
1
0
2
1
1
1
1
1
1
2
0
1
1
1
2
1
1
1
2
2
2
0
1
1
2
0
1
1
2
1
2
2
1
1
2
1
1
1
2
1
1
1
0
1
2
0
1
1
1
0
1
1
1
1
1
1
1
1
1
1
2
0
2
0
2
1
1
2
1
1
1
1
0
0
2
0
0
1
1
1
0
1
1
1
2
1
1
1
1
2
1
2
1
1
1
2
1
1
0
1
2
1
1
1
1
1
1
1
0
1
0
1
1
1
0
1
1
1
0
1
1
1
0
1
2
2
1
1
1
1
0
1
1
1
0
2
1
2
2
1
1
1
1
2
1
0
0
1
1
1
1
1
1
1
1
1
1
0
1
1
3
1
2
1
1
1
1
1
1
1
1
2
1
2
1
1
1
2
1
0
1
1
1
1
1
0
2
2
2
1
1
2
1
2
0
2
1
0
0
2
0
1
1
1
1
0
1
1
2
1
1
1
2
1
1
1
1
1
1
0
0
1
0
0
2
2
1
1
2
1
1
0
0
0
2
1
2
1
2
2
1
1
1
1
1
2
2
1
1
2
2
0
0
1
2
2
2
0
1
0
1
1
1
2
0
1
1
1
0
1
1
2
1
2
2
1
2
1
1
1
0
1
2
1
1
2
1
1
1
1
1
1
1
2
0
1
1
1
1
0
2
3
3
1
1
1
2
1
0
1
1
0
1
2
1
0
1
1
1
0
0
1
1
0
1
1
2
2
1
0
1
1
1
1
2
0
1
1
1
2
0
1
0
1
1
1
1
1
1
2
0
0
2
1
0
1
1
2
1
0
2
1
3
1
1
2
0
1
1
2
1
1
2
2
1
1
1
1
2
2
1
1
1
1
1
2
2
1
1
2
1
2
1
1
0
0
0
1
1
1
1
1
2
1
2
1
1
1
2
1
0
2
1
2
1
2
2
0
1
1
1
2
1
1
1
1
1
1
2
1
2
2
1
1
2
2
1
1
2
1
0
1
1
2
1
1
1
1
2
1
1
2
1
1
1
2
1
1
1
1
1
0
2
1
2
1
2
1
2
1
0
1
3
2
2
0
1
0
2
2
1
1
2
2
1
3
1
0
1
3
1
2
1
0
0
1
2
2
2
2
2
2
2
1
1
2
1
1
2
1
2
1
0
1
1
1
1
1
2
1
1
1
2
1
1
2
1
1
0
1
1
1
1
0
2
1
1
1
0
1
1
1
6
1
2
1
1
1
1
1
1
2
1
1
1
2
0
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
2
2
1
0
1
1
1
2
1
1
1
1
0
2
1
1
2
1
1
1
2
1
1
1
2
1
1
1
0
1
0
2
2
1
1
0
1
2
0
2
1
1
2
2
2
1
0
1
1
1
1
2
1
0
1
1
1
1
0
0
1
1
1
2
1
1
1
1
2
1
1
2
0
1
1
1
2
2
1
1
1
0
1
1
1
1
1
1
1
2
1
1
7
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
2
1
0
1
1
1
0
1
0
2
2
1
0
1
2
1
1
1
1
1
2
1
2
1
1
2
1
2
1
2
1
1
1
2
2
1
1
1
0
1
1
1
2
1
1
1
1
1
1
2
1
1
0
0
1
3
0
1
1
1
1
1
2
2
1
1
1
1
0
2
2
2
0
2
1
3
2
1
1
1
2
0
1
1
2
1
1
1
0
2
1
0
1
1
1
1
1
1
1
0
1
1
3
1
1
0
1
1
1
1
1
1
1
2
1
2
1
1
1
2
2
0
2
2
1
1
1
0
2
0
2
1
1
1
1
1
0
1
2
2
2
2
1
1
1
1
1
1
2
0
1
1
0
0
0
2
1
2
1
1
6
1
1
1
1
1
1
1
1
1
1
2
1
2
1
0
2
1
1
1
1
2
2
1
2
1
1
0
1
1
1
1
0
2
0
1
1
0
1
0
0
1
1
2
1
1
1
1
0
1
0
0
2
0
1
2
1
1
1
1
1
2
1
1
1
1
1
1
2
2
1
0
1
1
1
1
1
1
2
0
1
1
1
1
1
2
1
1
2
2
2
1
0
2
2
1
1
1
0
1
0
1
0
1
1
2
2
1
0
1
1
1
0
0
1
1
1
2
1
2
0
1
2
1
2
1
1
1
2
1
1
1
2
2
1
1
2
1
1
1
2
1
1
1
1
1
0
1
0
1
0
1
1
1
1
1
1
1
2
1
0
1
1
2
1
2
1
1
1
1
1
1
2
2
2
1
1
0
1
1
1
0
1
2
1
0
2
1
1
1
1
1
0
2
2
2
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
2
0
0
2
0
0
0
2
2
1
2
2
1
2
2
1
1
1
2
1
1
3
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
0
0
0
1
2
0
1
1
1
2
1
1
0
0
1
1
2
0
0
2
2
0
2
1
1
1
1
1
0
2
1
1
0
2
0
2
1
5
1
0
1
2
2
1
1
1
1
1
1
2
0
2
0
0
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
1
1
1
1
1
0
2
2
1
1
1
1
1
1
0
0
2
1
1
2
1
1
1
0
1
1
2
2
1
1
0
1
0
2
1
1
0
1
1
1
2
0
2
1
1
1
1
2
1
1
1
2
1
1
0
1
1
1
1
0
2
1
1
1
1
2
1
1
0
2
2
0
1
1
2
2
1
2
2
2
1
0
0
0
1
2
2
1
1
1
1
0
0
1
0
1
1
1
0
1
2
2
1
1
1
0
2
0
2
1
0
1
0
1
2
0
0
0
1
1
2
1
0
1
1
1
0
1
1
1
1
1
1
1
3
1
2
1
2
2
1
0
1
1
2
1
1
1
1
1
1
1
2
2
1
1
1
1
2
2
2
2
1
1
1
1
1
1
1
1
1
1
1
0
1
2
1
1
0
0
0
1
1
0
1
1
1
1
1
0
1
2
1
1
1
0
1
1
1
0
2
0
1
2
2
2
2
2
2
1
1
1
1
1
1
1
0
2
0
2
1
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
2
1
2
1
1
2
2
1
2
0
0
0
1
2
1
2
1
1
1
0
1
1
1
2
1
1
0
1
0
2
1
1
1
0
2
1
1
2
1
0
1
1
0
1
1
1
2
1
1
1
0
0
1
1
1
1
1
0
1
0
1
1
1
1
1
1
3
1
2
1
1
2
2
1
1
1
0
1
2
1
1
1
1
1
1
1
0
2
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
0
1
1
1
1
1
1
2
1
2
1
2
0
1
1
2
2
1
1
1
1
1
1
0
1
2
1
1
0
2
0
1
0
1
1
1
1
1
2
1
0
2
2
1
1
2
1
0
1
1
1
2
0
1
2
1
0
1
2
1
1
1
1
3
2
1
1
2
2
1
1
1
1
0
1
2
1
1
0
1
1
1
1
1
1
1
1
0
2
2
2
2
0
2
2
0
1
1
1
2
2
1
2
1
2
2
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
0
1
1
0
0
1
2
0
2
1
1
1
1
0
1
1
1
2
1
2
2
2
2
0
2
1
2
2
0
2
1
1
1
2
1
1
2
1
1
0
2
1
1
1
2
1
2
2
1
1
1
0
1
1
3
1
1
0
2
0
1
1
1
2
2
1
2
1
2
0
2
1
1
2
0
1
2
2
1
2
1
0
1
2
2
2
1
1
0
1
1
1
0
1
1
0
2
1
2
2
0
2
1
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
0
0
1
1
2
1
1
1
1
0
0
1
2
1
1
1
1
1
1
2
1
1
1
1
0
2
2
1
1
1
2
1
1
1
1
1
2
2
1
1
1
2
2
1
3
0
2
1
1
1
0
1
2
1
1
2
1
2
1
1
2
2
0
1
1
1
1
0
1
0
2
0
2
1
1
1
1
2
1
1
1
1
1
2
0
1
2
1
2
2
1
2
0
1
2
1
1
2
2
0
0
2
2
1
1
1
1
0
2
1
2
0
1
1
0
1
1
1
1
1
2
2
1
1
0
1
1
1
1
2
1
1
0
1
0
1
1
2
1
1
2
2
1
1
0
1
1
1
1
0
2
1
0
1
0
2
1
1
1
1
1
2
1
1
2
1
0
1
1
2
2
2
2
0
1
1
1
2
2
0
0
1
2
1
2
2
0
0
1
1
2
2
1
0
1
1
1
1
1
1
2
1
1
1
1
3
1
2
1
2
1
1
1
1
1
1
1
4
2
0
1
1
0
1
1
0
1
0
1
1
1
1
2
1
1
2
1
0
1
1
0
1
1
1
0
1
2
1
1
1
1
2
0
2
1
0
1
2
1
0
1
1
2
1
1
1
1
0
1
1
1
0
2
1
1
1
1
1
1
2
1
1
1
2
0
1
1
1
2
1
1
0
1
0
2
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
2
1
1
0
1
1
2
2
1
1
0
0
1
2
1
0
2
0
1
2
1
2
2
1
1
2
1
1
1
1
1
2
1
0
0
1
0
1
2
1
0
1
1
2
0
1
1
1
1
2
1
1
1
1
1
1
2
0
1
1
2
1
1
1
0
1
2
2
1
1
1
1
1
1
1
0
1
1
2
1
2
1
2
2
3
2
1
2
1
0
1
1
1
0
1
1
2
2
1
0
1
2
1
0
2
1
1
2
2
1
1
1
1
2
1
1
1
0
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
2
0
2
1
1
2
2
1
1
1
1
1
1
2
1
1
2
0
2
2
1
1
2
1
1
2
2
1
1
1
0
1
1
1
1
1
1
1
0
1
1
1
0
2
1
0
2
2
1
1
1
1
2
2
1
0
3
0
1
2
2
1
1
1
1
0
2
1
2
2
2
1
1
2
1
2
2
1
2
0
1
1
2
1
1
1
1
1
1
2
2
0
0
1
1
0
1
1
1
0
1
2
0
1
1
1
1
1
1
2
2
1
1
2
1
2
0
1
1
1
0
0
1
1
1
1
2
1
2
1
1
1
2
0
0
1
1
2
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
3
2
1
1
1
2
1
1
0
1
2
1
0
2
1
1
1
2
0
0
2
1
2
2
0
0
1
1
0
1
1
2
1
1
2
1
2
1
1
2
2
1
0
0
1
1
0
0
2
1
1
1
2
1
1
1
1
1
0
1
0
1
1
1
0
1
2
1
1
1
2
2
1
1
1
1
1
2
0
1
0
2
2
1
1
2
1
1
2
1
2
1
1
1
2
1
1
1
1
0
0
2
0
1
1
1
0
2
1
2
1
2
1
1
0
2
2
1
1
0
1
1
2
0
0
2
0
1
1
0
0
0
1
1
1
0
2
0
1
2
1
1
1
2
0
1
1
1
3
0
1
2
1
2
2
2
0
0
0
2
1
1
1
1
2
1
1
2
1
0
1
2
1
1
1
1
3
0
1
1
1
0
1
1
2
1
1
1
2
2
1
1
2
1
1
1
1
2
0
2
2
2
1
2
2
1
1
2
0
1
1
1
2
1
2
1
2
1
2
0
1
2
2
1
1
0
1
1
2
0
2
1
1
2
1
1
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
2
1
0
1
1
1
0
0
1
1
1
1
1
2
1
2
4
2
1
2
3
2
1
1
1
1
1
1
1
1
0
1
1
1
2
2
1
2
1
0
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
2
0
1
1
1
1
1
2
2
2
2
2
1
0
1
2
1
0
0
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
2
2
2
1
1
1
1
1
0
0
0
0
2
1
1
2
0
2
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
1
0
1
2
0
1
1
0
1
1
1
1
0
0
1
1
0
1
1
2
2
1
1
1
2
1
1
1
1
3
1
2
1
1
1
0
1
1
1
2
1
1
1
2
1
2
1
1
1
0
1
1
1
1
1
1
2
2
2
1
0
2
1
1
1
2
1
2
1
1
0
1
1
0
1
1
2
1
0
2
0
1
1
1
1
1
2
2
1
1
1
2
2
1
0
1
1
1
0
0
2
0
2
1
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
3
1
2
2
1
1
0
2
2
1
1
0
2
2
2
0
1
1
0
0
1
1
2
1
0
1
1
1
2
0
2
1
1
1
1
0
1
1
2
0
2
2
1
1
2
2
1
2
2
1
1
1
1
2
1
1
0
2
2
1
1
1
0
2
2
0
2
1
0
1
1
1
1
0
1
2
2
2
2
1
1
1
1
1
1
0
1
2
1
1
1
2
1
2
1
1
0
1
1
1
0
1
1
2
2
1
1
1
1
1
1
1
1
2
1
1
1
0
2
1
1
1
2
0
1
1
1
2
0
0
1
2
1
1
2
1
1
1
1
0
0
2
1
2
1
1
1
1
1
2
1
2
2
1
1
1
3
1
0
1
2
1
1
2
2
0
1
1
1
1
1
1
1
0
0
1
0
1
1
0
1
1
2
1
2
1
1
2
2
0
1
2
1
1
2
2
1
1
1
1
2
2
1
1
0
1
0
1
0
0
0
1
1
2
1
1
0
1
2
1
1
1
2
2
1
2
0
1
1
2
2
1
1
1
1
2
1
1
2
1
0
1
1
1
1
1
2
1
0
1
1
1
1
0
1
1
1
1
0
1
1
1
2
1
1
1
1
1
0
1
2
2
1
1
1
1
1
0
0
3
2
1
1
2
0
0
1
1
1
2
1
1
1
0
1
1
1
2
2
2
2
0
1
1
1
1
2
1
2
1
1
2
1
1
2
2
1
1
1
2
0
0
3
1
1
1
1
1
2
0
2
1
1
1
1
1
1
2
1
2
3
1
1
0
2
1
2
1
1
2
1
2
1
1
1
1
1
1
2
1
2
1
0
1
1
0
1
1
1
0
1
1
2
1
1
1
1
2
2
1
1
1
1
2
1
2
1
2
1
1
0
1
2
1
1
1
1
1
1
1
1
0
1
0
2
0
1
0
1
1
1
2
2
1
2
1
1
1
1
1
2
1
2
1
2
2
2
1
2
2
2
1
1
2
0
1
0
1
1
0
0
1
0
1
1
1
2
1
1
1
1
0
1
2
1
1
1
2
0
1
2
0
0
0
1
1
1
2
1
0
1
1
1
1
0
2
1
2
2
1
0
1
1
2
0
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
2
2
2
1
1
1
2
1
1
1
1
1
2
1
2
2
2
2
1
1
1
1
2
2
2
2
2
1
2
1
1
1
2
0
1
1
1
1
1
1
0
1
2
2
1
0
0
1
1
2
1
1
1
1
2
2
2
2
1
2
0
1
1
2
1
1
1
1
1
1
2
0
0
1
0
1
2
2
2
2
1
2
1
1
2
1
1
1
1
1
1
2
2
2
2
2
1
2
1
0
1
1
0
0
1
1
0
2
1
1
0
2
2
1
0
0
0
1
0
0
1
1
1
2
1
1
1
1
1
2
0
0
1
1
1
1
1
0
2
2
1
1
2
0
1
1
1
1
2
1
2
1
1
1
1
0
1
1
1
1
2
0
1
1
1
2
1
1
1
1
1
0
2
1
1
0
1
1
1
1
1
1
3
1
0
2
1
1
0
1
1
1
2
2
1
2
2
1
1
1
2
1
0
1
1
1
1
1
1
1
2
1
2
1
2
1
1
2
1
0
1
0
1
1
1
1
2
1
1
1
2
0
2
1
1
1
1
1
1
1
1
0
1
1
2
1
0
1
1
2
0
3
1
2
1
2
1
2
1
2
1
1
1
1
1
1
1
2
1
1
0
0
1
1
1
1
2
0
1
1
2
2
2
0
1
2
1
1
2
1
1
2
1
1
1
1
2
2
2
1
1
1
1
2
1
1
1
1
1
1
2
0
1
0
1
1
0
3
0
2
0
2
1
1
1
1
2
0
1
1
0
2
2
1
2
2
1
1
1
2
1
1
1
1
1
1
1
0
0
1
1
1
1
2
1
1
1
1
1
2
1
1
0
1
1
1
2
1
0
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
0
1
1
1
2
1
1
2
17
0
1
1
2
0
1
2
2
1
1
0
1
0
0
1
1
1
1
1
1
2
0
1
1
2
1
1
1
1
1
1
1
0
1
0
1
1
1
1
2
0
2
2
2
1
1
1
2
1
1
2
1
1
1
1
2
1
3
2
1
2
1
2
2
1
1
1
2
1
1
2
1
2
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
0
1
2
0
3
2
1
1
1
1
1
0
1
0
2
2
1
0
1
1
0
2
2
1
0
1
3
1
1
1
1
1
4
0
2
2
2
1
0
1
2
1
4
1
2
1
1
0
0
1
1
2
2
1
2
1
0
1
1
1
1
1
2
1
1
1
2
1
2
0
1
1
1
1
2
0
1
0
1
2
1
1
1
2
1
1
1
1
0
0
2
2
1
1
2
1
1
2
2
1
1
1
2
1
0
1
2
1
1
1
1
1
2
1
1
0
1
2
2
2
1
2
1
1
1
1
1
0
1
1
2
1
1
1
0
1
2
2
1
2
1
1
0
1
2
1
2
0
1
1
1
1
2
2
1
1
0
1
1
1
2
1
1
2
1
1
1
0
1
0
1
3
2
1
0
1
2
1
2
1
0
2
1
3
1
2
2
2
0
1
2
2
1
1
1
0
1
1
2
2
1
2
1
2
2
1
1
0
1
1
0
1
0
1
1
2
1
1
0
2
1
1
2
0
1
1
0
1
1
1
2
0
1
1
2
2
1
2
1
1
0
1
2
1
1
2
1
2
2
1
1
2
1
2
1
1
1
2
1
1
1
2
1
2
1
1
1
1
0
1
1
1
1
0
2
1
2
1
0
0
1
1
1
1
1
1
2
1
0
0
2
0
1
2
0
2
1
1
2
1
0
1
1
1
0
1
1
0
1
2
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
0
2
1
1
1
2
1
1
1
2
0
1
2
0
1
1
2
1
0
0
2
1
2
1
1
0
2
1
0
2
1
1
1
1
2
1
1
1
0
1
1
2
2
1
2
0
1
1
0
1
0
0
2
0
1
1
1
1
0
1
1
1
0
1
2
2
2
1
2
1
2
1
1
2
0
0
1
1
1
2
1
2
3
1
1
0
3
0
1
1
1
1
1
1
1
2
1
0
1
2
1
0
2
1
0
0
1
1
1
1
1
2
0
1
0
2
1
1
1
1
0
1
2
0
1
0
2
1
1
1
1
1
1
1
0
1
0
2
0
1
1
1
1
1
1
1
0
0
1
2
1
1
0
1
1
1
1
2
1
1
2
1
1
1
2
2
0
1
1
2
1
1
1
2
0
1
1
1
1
1
0
1
2
2
2
1
1
2
2
1
1
0
1
2
1
1
0
1
0
1
2
0
2
0
1
1
0
0
1
2
1
0
1
2
0
2
1
1
2
0
1
1
1
0
1
2
1
1
1
1
1
1
2
1
0
1
1
1
2
2
1
1
1
2
0
2
1
2
1
1
1
2
1
1
2
1
1
1
2
2
2
1
1
1
1
2
1
0
1
1
2
1
1
1
0
1
0
2
1
0
2
1
1
2
2
0
1
1
1
1
1
1
1
1
1
1
1
2
0
0
1
2
1
1
0
2
1
1
1
2
1
1
0
1
0
1
1
1
1
1
1
1
1
0
1
0
0
1
1
1
1
0
1
1
1
2
2
1
1
1
2
1
1
0
1
1
0
1
2
1
2
2
1
2
1
1
1
1
1
0
1
1
1
0
2
2
2
2
1
1
1
1
2
1
1
1
0
2
1
2
2
1
0
1
1
2
0
2
1
2
1
2
1
2
1
1
2
1
1
2
0
1
1
1
1
2
1
1
0
2
1
2
2
1
1
0
1
1
2
1
3
1
1
0
1
1
1
1
1
1
1
1
1
1
0
0
0
1
2
1
0
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
2
0
1
1
1
1
1
2
0
1
1
1
1
1
1
1
1
2
2
1
1
1
0
1
0
1
1
2
1
0
1
1
0
1
2
2
2
1
1
1
0
1
3
1
1
2
2
7
1
0
2
0
1
1
3
0
1
1
1
1
1
1
1
2
1
1
1
1
3
1
1
0
1
1
2
1
2
0
1
1
1
1
1
1
2
0
1
1
0
1
1
2
2
2
1
1
1
1
1
0
2
1
1
1
0
1
1
1
2
0
0
1
1
1
1
2
1
2
1
1
1
2
2
1
2
1
1
1
1
1
2
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
0
2
1
1
0
1
0
0
1
0
1
2
1
0
2
2
1
2
2
2
2
1
1
1
1
1
2
0
0
1
1
1
1
1
1
2
2
1
1
0
1
1
1
1
2
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
0
1
1
2
1
0
1
0
0
2
1
2
1
1
1
2
2
1
1
1
1
0
1
0
2
2
1
2
2
1
1
2
1
1
1
1
1
1
2
1
1
1
2
0
1
1
2
1
1
0
1
0
1
2
2
1
1
1
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
2
2
1
1
2
0
1
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
1
0
2
2
1
1
0
2
1
2
2
0
1
1
1
1
1
1
1
1
1
1
1
0
1
2
1
2
1
1
1
1
1
2
0
1
1
1
1
2
1
2
1
0
1
1
0
1
1
0
2
1
1
2
1
2
1
2
1
0
1
0
3
0
1
1
0
0
0
0
2
0
1
0
2
0
2
0
1
1
2
1
1
2
1
0
1
0
1
0
2
2
1
1
1
1
2
1
0
1
2
1
1
1
2
2
0
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
0
0
2
2
1
1
1
2
1
1
0
2
0
2
1
1
0
0
1
1
1
2
1
1
1
1
0
1
1
1
2
1
2
2
2
1
1
1
2
1
1
2
2
1
2
3
1
1
0
2
1
1
2
0
2
1
0
2
1
1
1
1
1
1
1
1
2
2
1
0
1
1
2
0
1
2
1
2
0
1
1
1
2
1
1
1
1
2
0
1
2
0
0
1
1
2
1
2
0
1
1
1
1
1
1
1
2
0
1
1
0
2
0
1
1
4
0
0
1
1
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
2
2
0
1
3
2
1
0
0
1
2
1
1
2
2
1
2
1
1
1
2
0
2
1
2
1
2
1
1
2
1
2
1
1
2
1
1
2
1
2
1
0
0
0
2
1
1
1
1
1
0
0
1
2
2
0
2
1
2
1
2
1
1
1
1
0
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
2
2
0
1
1
1
1
0
2
1
2
1
0
1
2
1
2
1
0
1
0
0
1
1
1
1
1
0
1
1
2
1
2
1
1
2
1
2
1
1
1
1
2
1
1
0
1
1
1
1
2
2
1
1
1
2
1
1
0
2
1
1
1
0
1
1
1
1
2
2
5
2
1
1
1
1
0
1
1
1
1
1
0
1
0
2
1
0
0
2
1
2
4
1
1
2
1
0
1
1
1
1
0
2
1
1
1
0
1
1
0
1
1
1
2
1
2
2
1
1
2
1
2
1
2
2
1
1
1
0
1
1
1
1
2
3
0
0
1
2
1
1
2
0
1
2
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
0
0
0
1
0
1
2
1
1
1
1
1
1
0
2
1
1
1
1
1
0
1
1
1
1
1
1
1
0
1
1
2
1
2
0
1
1
1
1
2
2
0
1
1
2
0
1
0
1
1
1
1
2
2
0
1
1
2
1
1
1
1
0
2
1
1
0
2
1
1
1
1
1
1
1
0
1
1
2
1
1
2
0
2
4
1
2
1
1
1
0
2
2
1
1
1
1
1
1
1
2
0
1
0
1
1
1
2
0
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
2
1
2
2
2
1
1
2
2
1
0
1
0
0
1
1
0
2
1
1
2
1
0
1
1
0
1
2
0
0
1
1
2
1
1
1
0
1
1
2
1
1
1
1
2
1
0
2
1
2
1
1
1
0
1
1
1
1
1
1
1
2
1
2
0
2
2
2
1
1
0
2
3
1
1
1
1
1
1
2
1
2
1
1
0
2
1
1
1
1
1
1
0
1
0
1
0
0
2
1
2
1
1
1
2
2
2
1
1
1
0
2
1
2
1
2
1
1
1
2
1
1
1
2
2
2
1
2
1
1
1
1
1
1
2
0
2
1
0
1
1
2
0
0
2
1
1
1
1
2
1
2
2
2
1
2
0
0
1
2
1
1
1
2
2
1
1
1
2
1
1
0
1
1
1
1
2
1
1
2
1
1
1
2
1
0
1
2
1
1
1
2
2
0
2
1
1
1
1
1
1
2
1
2
2
1
0
1
0
1
1
1
2
1
2
1
1
2
1
1
1
2
1
1
1
1
2
1
2
1
1
1
2
2
1
0
3
1
2
1
0
1
1
1
2
1
2
1
0
0
1
1
0
1
1
0
1
2
1
1
1
1
2
0
1
1
2
1
0
2
1
0
1
1
1
2
0
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
0
1
1
1
1
1
2
1
1
2
2
1
1
1
0
0
1
0
2
2
2
1
2
1
1
1
2
1
0
1
2
1
0
1
1
1
2
2
1
2
2
2
2
1
1
1
2
1
1
1
0
1
2
1
1
0
2
0
0
0
1
1
1
1
1
2
2
1
2
1
1
0
2
1
0
2
1
1
1
0
1
1
0
0
0
2
1
1
1
1
1
1
1
2
1
0
1
0
1
1
0
1
1
1
1
2
1
1
2
2
2
1
1
1
1
1
1
1
2
2
2
2
0
1
2
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
0
2
1
1
1
2
0
1
1
1
2
1
1
1
0
2
2
1
1
1
1
0
0
2
2
1
0
1
2
1
2
1
1
2
1
1
1
1
2
1
1
1
0
1
2
1
1
1
1
1
2
1
0
0
1
1
2
0
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
0
1
0
1
1
1
1
1
1
1
1
1
1
1
0
1
0
2
0
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
0
0
2
1
1
1
0
1
1
2
0
1
1
0
1
1
1
1
2
1
0
1
1
2
0
1
2
1
0
1
1
2
1
1
1
2
1
1
1
1
1
1
2
0
2
2
1
2
2
2
2
2
1
1
1
1
0
1
1
1
2
1
1
2
2
1
2
1
1
1
1
1
1
1
0
0
2
1
2
2
1
1
2
2
4
2
1
1
1
1
1
2
1
2
2
1
0
2
2
1
0
1
0
2
1
1
1
0
1
1
1
1
1
1
2
1
0
1
1
2
1
2
1
2
0
1
0
1
1
1
1
1
0
1
1
1
1
0
1
1
1
1
2
2
1
2
0
1
1
2
1
2
1
1
1
0
0
1
2
2
1
0
1
2
1
1
2
1
1
1
2
1
2
1
2
2
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
0
0
1
2
2
2
1
0
1
1
2
0
1
1
0
2
3
2
0
1
1
1
1
1
3
2
1
0
0
2
1
1
1
0
1
2
2
1
1
2
1
2
1
1
1
2
2
1
1
1
1
2
1
2
2
1
1
1
1
1
2
1
1
1
2
2
1
2
1
1
1
1
2
1
1
2
1
1
1
0
1
2
1
1
1
1
1
1
1
1
0
1
2
2
1
2
1
1
2
2
1
2
1
1
2
0
2
1
1
1
1
0
0
1
2
1
2
1
1
1
2
2
1
1
1
2
2
1
1
2
1
1
1
1
2
1
1
2
2
1
3
1
1
1
1
0
1
1
2
2
1
1
1
1
1
1
1
0
2
1
1
1
1
2
0
1
1
1
1
2
1
1
1
1
1
2
2
1
1
2
1
0
2
2
2
1
2
1
1
2
1
1
0
1
1
1
0
1
1
0
0
1
1
2
1
1
1
2
0
0
0
2
0
1
1
2
2
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
0
1
2
1
1
1
1
2
2
0
1
1
0
1
1
2
0
2
1
1
2
1
2
1
1
1
1
1
1
2
1
2
1
1
1
0
1
2
1
1
2
1
1
1
1
2
1
0
1
1
1
2
2
0
1
2
0
1
1
2
1
1
2
0
1
1
0
2
1
1
1
0
2
1
1
1
1
1
2
1
2
1
2
2
2
1
0
1
2
1
1
1
1
1
0
1
2
1
0
2
1
1
2
1
1
0
1
2
2
0
1
1
1
1
1
1
1
1
2
1
1
0
0
1
0
1
1
1
2
1
2
1
1
1
1
2
1
1
1
1
1
2
1
0
1
1
0
1
2
0
2
2
1
2
1
0
1
1
2
1
2
1
1
1
1
1
0
1
1
0
1
0
1
0
2
1
1
1
0
2
2
2
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
0
1
1
2
1
1
0
1
2
1
2
0
1
1
0
1
2
1
2
1
1
1
1
1
1
0
1
1
2
1
2
2
1
1
1
1
1
2
1
1
1
2
0
2
0
1
2
1
2
1
1
0
2
2
1
0
1
1
2
0
2
1
1
2
2
2
2
1
1
1
1
1
1
1
2
0
2
1
1
2
2
1
1
2
1
1
2
2
1
0
0
0
2
1
1
2
0
1
0
1
1
1
2
1
2
1
1
1
1
2
1
1
2
1
1
0
1
1
1
1
1
1
1
2
2
1
1
2
1
2
1
0
2
1
0
1
1
0
1
1
2
1
1
1
1
2
1
1
1
0
1
1
1
1
1
2
1
0
1
2
1
2
1
2
1
0
2
1
1
0
1
1
0
0
1
1
1
1
1
2
2
2
1
2
0
1
2
1
1
0
1
2
2
1
1
1
0
1
2
2
0
1
1
0
2
0
1
0
2
1
1
2
1
2
1
1
2
1
2
1
1
0
2
0
1
0
1
2
2
2
1
1
2
1
1
2
1
2
2
1
2
1
0
2
1
2
2
2
2
1
1
1
2
2
2
1
2
1
2
1
1
1
0
1
1
1
2
1
1
0
0
1
0
0
2
1
1
1
1
1
1
0
1
1
2
1
2
2
0
2
1
2
1
1
0
1
1
2
0
0
2
0
1
1
1
2
1
1
1
1
0
1
0
1
2
1
1
1
2
1
2
2
1
1
1
1
2
1
0
1
1
2
1
1
2
2
0
0
1
0
2
2
1
1
2
2
1
1
2
1
0
0
2
2
1
1
1
1
1
0
0
2
2
1
0
1
1
2
2
2
2
1
1
1
1
1
1
1
2
1
0
2
1
2
1
1
1
1
1
1
2
2
1
1
0
1
0
1
0
1
2
2
1
2
0
1
0
1
2
1
0
2
0
1
2
1
0
1
2
1
1
1
0
2
1
1
1
1
1
0
0
1
2
2
1
1
2
0
0
0
2
1
1
1
1
2
1
2
1
1
1
1
0
1
1
1
1
1
2
2
0
2
1
1
1
1
1
0
1
1
2
1
2
1
3
0
2
2
1
0
2
2
1
1
1
2
2
0
0
1
0
1
1
1
1
1
1
1
1
1
1
1
1
2
2
0
1
2
0
1
1
2
1
1
0
1
1
2
2
0
1
2
2
2
2
2
0
1
2
2
1
1
1
1
2
1
2
2
1
1
1
0
1
1
2
2
1
2
0
1
1
0
1
1
0
0
1
1
1
1
1
1
0
0
0
1
0
2
1
1
1
0
1
2
0
1
2
2
1
1
1
1
2
1
1
1
0
0
2
1
1
2
1
1
1
2
0
1
1
0
2
1
1
1
1
1
1
1
0
2
1
1
1
1
2
1
0
1
1
1
1
1
1
0
2
2
1
1
2
1
2
0
1
2
1
2
1
1
2
2
2
1
1
2
1
1
2
1
1
1
1
2
1
1
0
1
1
2
1
2
0
1
1
0
1
0
1
1
1
0
1
1
1
1
1
1
1
0
1
1
2
1
1
1
2
1
1
2
2
2
2
1
0
0
2
1
1
1
1
2
1
1
1
1
1
0
1
1
1
1
2
0
1
1
1
0
2
0
1
0
1
1
2
0
2
1
1
2
1
2
1
1
2
1
2
1
2
1
2
1
2
1
1
2
2
0
1
2
1
0
2
2
2
1
3
0
0
0
1
1
2
1
2
1
1
1
1
2
2
1
1
1
2
1
2
2
1
2
0
1
1
1
2
1
1
1
1
1
2
2
1
1
0
1
1
0
1
1
2
1
2
0
1
1
0
1
0
1
2
1
2
1
1
1
1
1
0
1
1
1
2
1
1
2
1
0
1
2
1
0
1
0
1
2
2
2
1
1
1
0
0
1
2
2
2
1
1
0
1
1
2
1
1
2
1
1
0
2
1
1
1
2
1
2
2
1
0
1
1
2
2
2
1
2
1
1
2
1
2
1
2
0
1
1
1
2
1
2
2
2
0
1
1
0
1
1
1
0
1
1
1
0
1
0
1
2
2
1
0
1
2
1
2
1
1
2
0
1
2
1
0
1
2
2
1
1
0
1
0
0
1
2
0
1
0
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
0
2
0
1
2
1
3
0
1
0
2
1
1
1
1
2
1
0
1
0
1
1
0
1
1
1
1
1
0
1
0
2
0
1
1
1
2
1
1
1
1
1
1
1
0
2
2
2
1
0
2
1
1
1
0
1
2
1
1
1
1
2
3
2
2
2
1
2
2
1
1
1
1
1
1
1
1
2
2
2
2
1
1
0
1
1
1
1
2
1
0
2
2
1
1
1
1
0
1
0
2
2
2
1
1
1
0
1
1
2
1
1
1
2
1
0
1
1
1
2
1
1
2
1
2
1
1
2
1
1
2
1
1
2
2
0
1
1
0
1
1
1
2
0
2
1
1
1
0
2
1
1
1
2
1
3
1
0
0
0
2
2
1
1
1
1
1
1
2
0
1
0
1
1
0
1
1
0
2
2
1
3
1
1
1
2
2
1
0
2
1
2
2
2
1
1
1
2
0
1
2
1
0
2
2
1
1
1
2
1
0
1
0
1
1
0
2
1
1
1
1
2
1
1
2
1
1
2
2
0
0
1
0
1
1
0
1
1
1
2
1
2
0
2
3
2
1
0
1
1
2
1
1
0
1
1
1
0
1
2
0
1
1
1
2
0
2
0
1
2
0
1
1
1
0
2
1
1
2
1
2
1
1
2
1
2
1
1
1
2
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
1
1
2
1
1
2
2
1
2
1
1
0
1
2
1
1
0
1
2
1
1
1
1
1
1
1
2
1
2
1
3
1
1
1
0
1
2
2
1
1
1
2
1
1
1
1
1
2
1
2
2
0
1
1
0
1
1
2
0
1
1
1
1
0
2
1
1
1
1
2
1
1
1
2
1
0
1
1
1
1
1
1
1
1
1
3
1
1
1
2
1
0
2
1
0
0
2
1
2
1
1
1
2
1
1
1
1
0
2
1
1
1
1
2
2
1
2
2
2
0
1
1
1
1
1
1
1
2
1
2
1
1
1
0
1
0
1
0
2
1
2
1
1
2
1
1
0
2
2
1
1
1
0
1
2
2
2
1
0
0
1
2
0
2
2
0
1
2
1
0
1
2
1
2
1
2
1
2
0
1
1
1
2
2
1
1
0
2
1
1
2
1
1
1
1
1
1
0
2
2
1
1
1
1
1
1
2
2
1
1
1
2
1
2
2
0
0
1
2
0
2
1
1
1
1
1
0
0
1
1
2
2
3
2
2
2
2
1
1
1
0
2
1
1
2
2
2
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
0
1
1
1
0
1
2
1
0
1
1
1
1
1
1
2
2
2
1
1
1
1
2
1
0
0
1
2
2
1
2
1
1
2
1
1
0
2
2
1
2
1
1
1
1
2
0
2
2
1
1
1
1
0
0
1
0
1
2
0
2
1
2
2
2
1
1
1
0
1
1
1
1
0
1
1
1
1
1
1
3
1
0
1
2
1
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
2
1
0
1
1
1
1
1
1
1
1
0
0
1
1
1
0
1
1
1
1
1
0
1
1
2
1
2
2
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
2
2
1
1
1
1
0
0
0
1
2
2
1
2
1
2
1
1
2
1
2
1
1
0
1
1
2
1
2
1
2
0
0
0
2
1
2
2
1
1
0
1
1
1
1
2
2
1
1
1
2
2
1
1
2
0
2
2
2
1
1
3
2
1
1
1
1
1
1
2
1
2
1
1
1
2
1
2
1
1
1
2
2
2
0
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
0
0
1
2
1
2
1
2
1
1
1
0
1
1
1
1
2
1
1
2
2
0
1
0
1
1
0
1
1
2
1
1
1
1
2
1
2
0
2
0
0
1
1
1
2
0
0
1
1
2
1
2
0
2
1
1
1
1
0
1
1
1
2
2
1
1
1
2
2
1
1
0
1
2
0
2
1
1
1
1
1
0
1
1
2
2
1
1
1
1
1
1
0
1
1
1
2
1
1
2
2
1
2
2
1
2
1
0
1
1
0
2
2
1
2
1
2
1
1
1
0
2
0
2
1
1
0
1
0
1
1
1
2
1
1
1
1
2
2
1
2
1
1
1
1
0
1
1
1
3
1
0
0
1
1
1
1
1
1
1
1
2
0
1
1
1
1
1
1
0
1
0
1
2
0
1
1
2
1
0
2
1
1
1
1
1
1
0
1
1
1
1
2
1
1
0
0
2
2
1
1
0
1
1
0
1
1
1
1
1
2
3
2
1
1
0
0
1
2
2
0
1
1
1
2
1
1
1
2
2
1
1
0
2
0
2
1
1
2
1
0
1
1
1
1
1
1
1
2
1
1
1
0
2
1
0
1
2
2
2
1
2
1
0
1
1
1
1
1
1
1
2
0
0
1
2
1
2
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
0
1
2
1
1
1
1
1
1
0
1
1
0
1
1
0
1
0
1
1
1
1
1
2
1
2
1
2
2
2
1
2
2
2
1
2
1
1
1
0
2
1
1
1
2
1
2
1
0
1
2
1
0
1
0
1
1
1
1
0
1
2
1
1
1
1
2
2
0
0
1
1
2
1
2
2
0
2
2
1
2
1
1
2
2
1
1
0
2
0
0
1
1
1
1
1
2
0
1
2
1
2
1
0
1
2
2
1
0
2
0
1
1
0
0
1
2
1
2
1
0
0
1
2
1
2
0
0
1
2
1
1
1
2
2
2
1
1
2
1
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
2
1
0
1
1
2
1
2
0
2
0
0
1
1
1
0
1
2
2
1
2
1
1
2
1
3
0
1
1
0
2
1
1
1
0
1
1
0
2
1
2
1
1
2
1
1
1
2
1
1
1
2
1
0
1
1
3
0
2
2
1
1
3
1
2
0
1
0
0
2
1
2
1
1
1
0
1
2
2
1
1
1
1
0
2
1
1
1
1
0
1
1
0
1
2
1
0
2
1
1
1
2
0
1
1
0
1
1
0
1
1
1
1
0
1
2
1
2
1
2
0
1
0
2
0
1
2
1
1
2
1
1
1
1
0
1
2
0
0
1
1
3
1
1
1
1
0
2
1
1
2
1
1
1
0
1
2
1
2
0
2
1
1
1
0
2
1
1
2
1
1
2
2
2
1
2
1
1
2
1
0
2
1
0
2
2
2
1
2
2
1
1
1
1
2
1
1
0
1
1
1
2
1
1
1
1
2
0
1
1
2
1
1
1
1
1
1
1
1
0
0
0
1
0
1
2
1
1
1
1
1
1
1
0
1
1
0
1
1
1
2
2
1
0
1
2
2
1
1
1
2
1
1
1
1
1
1
1
0
1
1
1
2
1
1
1
1
1
2
1
1
0
1
6
2
1
1
2
0
2
1
1
2
0
2
2
1
1
1
2
0
1
1
0
0
1
1
1
1
1
0
1
1
1
2
0
2
1
2
0
1
3
1
1
2
0
2
0
1
0
1
1
2
1
1
2
2
1
1
1
1
1
1
1
2
1
0
2
2
1
1
1
1
0
2
0
1
1
0
1
1
2
3
0
0
2
1
1
1
1
1
0
2
2
1
0
2
2
1
2
1
2
1
2
1
1
1
1
0
1
1
1
1
1
1
1
0
3
1
1
2
2
1
2
1
1
3
1
2
1
2
1
2
1
2
0
2
1
1
0
0
2
0
2
2
0
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
0
1
1
1
0
1
1
0
2
1
0
0
2
1
2
1
0
2
0
1
2
1
1
2
1
1
2
1
0
2
1
1
0
2
0
0
1
1
2
2
1
2
1
1
1
0
0
1
1
2
2
2
1
2
1
2
2
2
1
0
1
1
1
1
2
1
1
2
0
2
1
2
2
2
2
2
1
1
0
1
2
1
1
1
3
1
1
0
1
1
2
1
1
1
1
1
1
1
2
2
2
2
0
2
1
1
2
1
0
1
1
2
1
1
0
2
1
1
2
2
1
1
1
1
0
2
1
1
2
1
1
2
1
1
1
1
2
2
1
2
1
1
1
1
1
1
2
1
2
0
1
0
1
1
0
1
1
0
1
2
2
2
1
2
0
1
2
0
1
1
1
1
1
1
0
1
1
1
1
0
1
0
1
1
0
2
0
2
1
2
0
1
2
1
0
1
0
1
1
0
1
1
1
1
1
1
2
0
2
1
1
2
1
2
1
2
1
1
1
0
1
1
2
1
1
2
1
1
2
2
2
2
2
1
2
1
1
1
1
1
1
1
0
2
1
1
0
3
1
1
2
1
1
1
1
2
1
1
1
2
1
1
2
1
1
1
0
1
2
1
1
1
1
1
2
1
1
1
0
0
2
1
1
1
1
2
1
2
0
1
1
1
1
0
0
2
1
1
1
1
1
2
1
1
1
1
1
1
2
2
0
1
1
1
2
1
1
1
2
1
1
1
1
2
2
1
2
1
2
1
1
2
0
1
1
1
1
1
1
1
1
2
1
1
2
0
1
1
0
1
2
1
1
1
1
1
1
1
0
1
1
0
1
1
1
1
1
1
0
2
2
1
1
1
1
2
1
1
1
1
1
0
1
2
2
1
1
1
2
0
1
1
2
1
0
1
0
1
1
1
1
2
0
1
1
0
1
2
1
1
1
1
1
0
2
1
2
2
1
1
1
1
1
2
2
1
2
1
1
1
1
1
0
2
1
1
1
2
1
1
1
2
1
1
1
1
2
1
2
0
2
1
3
0
1
1
1
1
1
1
2
1
2
1
0
0
0
0
0
2
0
1
1
1
0
2
1
1
1
0
2
1
1
2
2
1
1
1
2
1
1
1
1
1
1
2
1
1
2
1
1
2
1
0
1
1
1
0
1
0
1
1
0
2
0
1
1
2
1
0
1
2
1
1
2
1
1
1
1
2
1
0
0
2
2
0
1
0
1
0
1
2
1
2
1
2
1
1
1
1
0
2
2
0
1
1
2
1
1
1
2
1
2
2
1
0
2
1
1
2
0
1
2
1
2
1
2
2
3
1
1
1
1
1
1
2
1
2
2
2
1
2
2
0
1
1
2
2
1
1
1
2
1
1
2
1
2
1
2
1
1
0
0
2
1
2
1
2
1
1
1
1
1
2
1
0
1
0
0
0
1
1
2
2
0
0
1
1
1
1
2
1
1
1
2
1
1
1
2
2
0
2
2
2
0
0
2
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
1
1
0
1
1
0
1
1
1
1
1
1
1
1
2
1
1
1
0
2
1
1
0
1
2
1
2
1
2
0
1
1
1
2
1
2
1
1
1
1
2
1
1
1
1
1
0
0
1
2
1
2
1
1
2
1
0
2
2
0
1
1
0
2
0
1
2
2
1
1
1
1
1
1
1
2
3
0
1
2
1
2
2
1
0
0
1
1
1
1
1
2
2
2
1
1
3
1
1
0
2
1
2
1
1
2
1
1
2
1
2
2
1
1
3
1
2
0
1
2
1
1
0
1
1
2
1
1
1
2
2
2
1
0
0
1
0
1
1
2
1
1
1
1
2
1
0
2
2
1
1
2
2
1
2
1
1
1
1
2
0
0
1
1
0
0
1
1
2
1
1
1
1
1
1
0
1
0
2
1
1
1
1
1
0
2
2
1
0
1
1
1
1
1
2
1
1
1
1
2
1
2
1
2
1
1
0
1
0
2
1
2
1
1
1
1
1
1
2
1
1
1
0
2
1
1
1
1
1
1
0
0
1
2
0
2
1
1
1
0
1
2
1
1
1
1
1
1
1
1
0
2
2
1
1
1
2
1
1
1
1
1
2
1
1
0
1
0
1
1
1
2
2
2
1
1
2
0
1
1
1
2
1
1
0
0
1
1
2
1
1
1
1
1
1
1
1
1
1
3
2
1
1
2
0
1
1
1
1
0
2
2
1
1
1
2
2
1
1
2
1
1
1
2
1
1
0
0
1
1
1
0
1
1
2
1
2
2
1
2
1
1
1
0
1
0
1
2
1
1
1
2
0
1
2
1
1
1
0
1
1
1
2
1
1
0
2
1
1
1
2
1
1
1
1
1
1
2
2
2
1
2
0
1
1
0
1
1
2
1
2
1
1
2
1
1
2
0
1
2
1
1
2
1
2
1
0
2
2
1
1
1
1
0
1
1
1
0
1
1
1
0
2
0
1
1
1
2
1
2
2
1
1
1
0
2
2
1
1
1
0
1
2
1
1
1
2
1
1
2
2
2
1
1
0
2
1
2
0
1
1
1
1
1
1
0
1
0
2
1
1
2
1
1
1
1
1
1
1
2
2
2
1
0
1
2
2
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
2
1
1
0
1
1
2
2
2
1
0
2
1
0
2
1
0
2
1
1
1
1
2
2
0
2
1
2
2
1
1
1
2
0
1
1
0
1
1
1
1
1
0
1
1
1
3
1
0
2
1
1
1
1
1
1
0
1
1
1
2
1
1
1
1
1
1
1
0
2
2
2
1
1
2
1
2
1
0
1
2
1
2
1
2
0
2
1
1
2
1
2
1
1
0
1
2
1
0
1
0
1
1
1
1
3
1
2
2
1
1
1
2
1
0
0
1
2
1
1
2
2
1
1
1
1
2
1
0
1
1
1
1
2
1
2
2
1
1
0
1
1
2
1
2
1
2
2
1
2
2
1
1
1
1
1
2
0
1
0
1
1
1
2
1
2
1
1
1
1
0
1
1
2
1
1
2
1
1
1
1
0
2
1
1
2
2
2
0
2
1
1
1
2
1
1
1
1
2
2
0
1
1
1
1
1
1
2
1
1
1
2
2
1
2
1
2
1
1
1
1
1
2
1
1
1
2
2
1
1
2
1
1
2
2
2
1
2
1
2
1
1
1
1
1
0
1
1
0
2
1
1
1
1
0
1
2
2
1
1
1
1
0
0
0
1
1
1
2
1
1
2
1
1
1
3
1
0
1
1
1
1
0
0
1
1
2
2
1
2
1
1
2
1
0
2
1
1
2
1
2
2
1
0
1
1
2
1
2
2
2
0
1
0
2
1
1
1
1
1
0
2
1
1
1
2
0
2
0
1
1
1
0
2
1
1
1
1
1
1
2
1
2
1
1
0
2
1
1
1
1
1
1
0
1
2
2
1
1
1
1
2
1
2
1
1
1
2
1
2
0
0
2
2
1
0
0
2
0
1
2
1
1
1
1
0
0
1
1
0
1
1
2
1
1
1
0
0
1
1
1
1
1
2
1
2
2
1
1
0
1
2
2
0
1
0
1
1
2
1
1
1
1
0
1
1
2
1
2
1
1
1
1
0
1
1
1
0
1
2
2
0
1
0
1
1
0
1
1
1
1
1
1
1
0
1
1
1
1
2
1
1
1
0
1
1
2
2
2
1
1
1
2
1
0
1
1
1
2
2
1
1
1
1
2
1
1
1
1
3
1
1
1
2
1
1
1
1
2
1
1
2
0
2
1
1
1
1
0
1
1
2
0
2
2
1
0
1
1
1
1
0
0
1
2
0
1
1
1
0
0
2
0
1
0
1
1
2
1
1
1
1
1
2
1
1
1
2
2
1
2
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
0
1
1
0
1
1
1
2
1
0
1
2
0
1
1
1
0
1
2
2
2
0
1
1
1
1
1
2
2
1
2
2
2
1
1
1
1
1
0
0
0
1
1
1
0
1
2
1
1
0
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
0
1
1
2
1
1
2
2
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
0
1
2
1
0
2
1
2
1
2
2
1
2
1
1
1
1
1
2
2
0
2
1
0
2
1
1
1
1
1
1
0
0
1
2
0
0
1
2
2
2
1
1
0
0
1
1
2
1
2
1
0
1
0
1
2
2
1
1
1
1
1
1
2
0
1
1
2
1
1
2
1
1
0
1
1
1
1
1
0
1
0
1
1
0
1
2
1
1
1
1
1
2
1
2
1
2
1
1
2
2
3
1
2
2
1
2
1
2
1
2
2
1
1
3
1
1
1
1
1
2
1
1
1
1
1
0
1
0
1
0
0
1
2
1
0
1
2
0
2
1
2
2
1
1
1
1
1
1
1
0
0
1
0
0
2
2
2
1
1
0
1
1
2
2
1
2
1
0
1
2
1
2
1
1
1
0
1
1
1
1
1
1
1
3
1
1
1
2
1
1
1
1
1
2
2
2
1
2
1
0
2
1
1
1
1
1
2
1
1
0
2
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
2
1
0
2
1
1
2
1
0
1
1
1
2
1
1
1
2
1
1
1
1
2
1
0
0
1
2
1
1
0
2
2
1
0
0
0
1
1
1
1
1
1
0
1
1
1
0
1
2
1
1
1
1
2
1
1
1
1
1
1
2
2
1
1
0
2
1
1
1
2
0
2
2
1
1
1
2
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
2
1
1
1
1
1
1
0
2
2
1
1
1
1
1
1
0
1
2
2
2
1
1
1
2
1
1
1
1
1
2
1
2
1
0
2
1
1
1
2
1
1
1
2
2
1
2
1
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
0
1
1
0
0
2
0
2
1
1
1
1
2
1
2
1
0
0
0
1
2
2
1
0
1
1
1
1
1
1
2
1
0
1
0
0
2
1
1
1
1
2
2
1
1
1
2
2
1
1
0
1
1
2
1
2
1
1
1
1
1
1
2
2
1
0
1
1
0
2
0
2
2
1
2
2
2
2
2
2
1
1
1
2
1
2
1
1
1
1
1
1
1
0
1
1
0
1
1
1
1
1
1
2
2
2
1
0
1
1
1
1
0
2
1
0
0
1
1
1
2
0
2
1
1
0
0
1
1
1
1
1
2
1
0
1
1
0
1
0
1
1
1
0
1
2
2
0
1
0
2
2
1
2
2
1
1
1
2
1
1
1
1
2
1
1
3
2
1
1
1
1
1
1
1
2
2
1
1
1
0
1
2
1
2
1
2
1
1
1
0
1
1
1
1
2
1
1
1
1
1
2
1
1
0
2
2
1
1
1
2
4
1
2
0
2
1
2
0
1
0
1
1
1
2
1
2
1
1
1
2
0
1
1
0
1
2
0
1
1
1
1
2
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
0
2
2
1
1
1
2
1
2
1
0
1
1
1
2
1
1
1
1
2
1
0
1
0
2
1
0
1
0
2
2
2
1
1
0
0
1
0
1
0
1
2
1
1
2
1
1
1
1
0
1
0
1
1
3
2
0
1
1
2
0
0
1
2
0
1
1
1
0
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
3
1
1
2
1
0
1
1
1
0
1
1
2
1
2
1
2
1
1
1
1
2
2
1
1
0
1
1
2
1
1
0
0
2
1
1
2
1
0
0
1
2
1
1
2
1
0
2
1
2
1
1
1
1
2
2
2
0
1
1
2
2
1
2
1
0
0
1
1
1
2
1
1
2
1
2
1
1
1
0
0
0
1
1
0
1
2
1
0
1
1
2
2
0
1
2
2
1
0
2
1
2
1
1
1
1
0
3
1
2
1
1
2
1
1
1
1
0
1
2
1
2
2
2
1
1
1
2
1
0
2
1
1
2
1
0
0
1
1
0
1
2
1
2
1
1
0
1
1
1
1
2
1
1
2
0
1
1
1
1
0
2
1
0
2
2
2
2
1
2
1
0
1
1
1
1
1
1
2
1
2
2
2
2
2
2
1
1
1
2
1
0
1
0
2
2
0
2
2
1
1
0
1
1
2
1
1
1
1
2
2
1
0
2
0
2
2
1
2
2
0
2
1
2
1
1
1
1
1
1
2
1
0
2
0
1
1
0
2
2
2
2
1
1
0
0
2
1
1
0
0
2
2
2
1
1
1
1
1
1
1
1
0
0
2
1
1
1
1
2
1
2
1
1
0
0
1
1
3
1
1
1
2
1
1
2
1
1
0
2
1
1
1
2
1
1
0
0
2
1
1
1
1
2
1
1
2
1
0
0
1
1
1
1
1
1
0
0
1
1
3
1
1
2
0
1
1
0
1
1
2
1
0
1
1
1
1
1
1
2
2
2
2
1
2
1
1
1
2
0
0
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
1
3
0
2
0
0
1
2
1
1
1
2
0
0
2
2
2
0
2
2
2
0
2
0
0
0
0
1
1
0
1
0
2
1
0
2
1
1
0
1
1
1
1
0
0
1
2
0
1
1
0
1
1
2
1
2
1
0
1
0
2
2
1
2
1
2
0
1
2
2
1
1
1
0
0
2
1
1
0
1
1
0
1
2
1
1
1
1
1
0
1
0
1
1
1
1
1
2
1
3
1
1
3
2
0
1
1
1
1
2
1
1
1
2
0
1
0
1
4
0
1
0
2
1
2
1
1
2
2
2
1
1
1
0
2
0
1
1
1
0
1
1
1
1
2
2
1
2
1
2
1
0
0
1
2
1
2
3
1
1
0
2
0
0
2
2
2
2
1
1
1
0
0
1
1
1
1
1
2
1
1
1
0
2
1
1
2
2
2
1
1
2
4
2
1
1
1
2
0
3
2
1
1
2
0
1
1
1
1
1
3
2
2
1
1
1
2
1
2
0
1
1
0
2
2
1
2
1
1
1
2
1
1
0
1
1
1
1
1
0
1
0
2
1
1
1
1
2
2
1
1
1
1
0
2
1
0
1
1
2
1
2
0
1
2
1
1
1
1
1
0
1
2
1
0
1
1
1
1
1
1
1
1
2
2
1
1
1
0
1
2
2
1
2
1
1
1
0
2
0
1
2
1
3
1
1
1
1
0
1
1
1
1
2
2
1
1
1
1
1
1
1
1
0
1
1
1
1
0
2
0
1
1
1
2
1
1
1
1
1
2
1
2
1
2
1
1
1
0
2
1
1
2
2
2
0
1
1
2
1
1
0
1
1
1
0
1
2
1
1
0
1
1
2
1
1
2
1
0
1
1
2
1
0
1
2
2
1
1
1
1
1
1
2
0
1
0
1
1
2
1
1
1
1
2
1
1
1
2
0
0
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
2
0
1
2
0
1
2
1
1
2
1
0
1
2
1
0
1
0
1
2
1
2
1
1
1
1
1
1
2
1
0
0
1
1
1
1
1
0
1
0
1
2
1
1
0
0
1
0
2
2
1
2
1
2
1
1
1
0
1
2
2
0
1
1
1
1
2
0
0
2
0
1
0
0
2
1
0
0
1
1
1
1
1
2
2
1
2
0
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
0
1
1
1
0
1
2
1
0
1
1
1
2
1
1
2
1
2
1
1
2
1
1
1
2
2
2
2
1
2
2
2
2
1
1
1
2
1
0
1
1
0
2
2
1
1
2
1
2
1
2
0
2
2
2
2
1
1
1
2
2
1
1
2
1
0
2
0
1
2
0
1
2
0
1
2
1
2
2
1
1
1
1
2
1
1
2
1
2
1
0
0
1
2
1
2
2
1
1
2
1
2
1
1
1
2
1
0
1
2
1
1
1
2
2
0
1
2
0
0
2
2
1
1
0
2
0
1
0
1
1
1
1
0
1
0
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
2
2
2
1
2
1
1
1
0
2
1
0
0
1
2
1
0
1
2
2
2
1
2
2
1
1
1
1
1
2
1
2
1
2
1
1
1
1
1
1
2
1
2
2
1
1
1
0
1
1
2
0
1
0
2
0
1
1
1
1
1
1
1
1
2
2
1
2
1
1
1
1
0
1
2
1
1
1
2
0
1
1
1
0
0
2
0
1
1
1
1
1
0
2
1
0
1
1
1
1
1
1
1
1
1
1
0
2
2
1
1
0
1
1
1
1
1
1
1
0
1
2
2
2
1
1
1
2
0
0
0
1
0
1
0
1
1
2
2
1
2
1
2
1
2
1
2
1
0
2
1
1
1
1
0
1
2
1
2
1
2
1
0
1
2
0
0
0
1
1
1
1
2
1
1
1
1
1
1
1
0
1
1
2
1
1
1
1
0
0
1
0
0
2
2
1
1
1
1
2
1
1
1
2
2
1
2
2
2
1
1
0
2
2
1
2
1
0
1
2
2
1
1
2
1
3
1
2
2
1
1
2
1
2
0
1
1
0
1
1
2
1
1
2
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
0
1
1
1
1
1
1
1
1
3
1
0
1
1
0
1
1
0
1
2
1
0
0
1
1
2
2
1
1
1
0
0
0
2
2
2
1
1
0
1
1
2
1
1
0
1
1
1
0
1
1
1
2
1
2
0
1
1
0
1
1
0
1
1
1
1
1
1
2
2
2
1
1
1
1
0
1
1
1
1
0
1
0
1
2
0
1
1
0
1
2
1
2
1
1
1
1
1
1
2
1
0
1
1
1
1
3
1
0
1
2
1
0
1
1
2
1
0
1
1
1
1
1
1
1
1
1
1
0
2
1
1
1
2
2
1
0
1
1
2
1
1
1
0
0
1
1
3
2
1
2
0
0
1
2
2
2
1
1
1
0
0
0
1
1
2
2
1
1
1
0
1
2
2
1
1
1
1
1
1
1
1
1
1
2
2
2
1
0
1
0
1
1
2
1
1
1
2
1
1
1
2
1
0
2
0
0
2
2
1
2
1
0
2
1
0
1
1
2
2
1
1
1
1
2
1
1
1
0
1
2
2
1
1
1
2
1
1
1
1
1
0
1
1
1
1
1
1
1
1
2
1
0
2
2
1
1
1
2
1
2
2
4
0
1
1
2
2
1
1
1
1
1
1
1
1
2
1
1
1
2
0
2
1
1
2
0
1
2
2
2
1
2
1
1
1
1
1
1
1
4
0
1
2
0
2
1
1
2
0
1
1
1
1
1
2
1
0
2
1
0
0
1
1
1
1
0
1
6
1
1
2
2
1
2
0
1
2
2
1
1
1
1
2
1
1
1
1
1
1
0
1
1
1
1
0
2
1
1
0
1
0
1
1
1
0
1
1
1
1
0
1
1
1
1
2
2
1
1
1
1
1
1
0
1
1
1
1
1
2
1
1
1
1
1
1
2
0
0
1
1
2
2
1
2
1
2
1
2
0
1
2
0
0
0
1
1
1
2
2
2
2
1
1
1
1
1
0
1
1
2
0
1
1
1
2
1
1
1
0
2
1
1
0
1
1
1
2
2
2
2
0
1
2
2
2
2
1
2
1
1
1
0
2
1
1
2
1
1
0
1
2
0
2
2
0
2
1
1
1
1
1
1
2
2
2
1
2
1
0
1
1
1
2
1
2
0
0
1
2
1
1
1
2
0
1
2
2
1
1
1
2
0
1
1
2
2
1
1
1
1
0
1
1
1
1
1
1
1
0
1
2
1
1
1
0
0
2
1
1
1
1
0
1
0
1
2
1
1
2
2
1
1
1
1
1
2
1
1
1
1
2
0
1
2
1
1
1
2
2
0
1
2
1
2
1
1
1
0
2
1
1
2
2
1
0
1
1
1
1
1
2
1
1
0
1
2
0
1
1
0
1
1
1
1
2
1
1
1
2
0
0
1
2
1
1
0
1
1
2
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
2
2
2
1
1
1
1
1
0
1
0
1
2
2
0
0
1
1
2
1
1
0
1
1
1
1
1
2
1
2
2
1
0
1
2
1
1
1
0
1
1
1
2
1
1
1
2
2
1
0
2
1
2
0
1
1
1
1
1
1
3
2
1
1
1
1
0
1
2
1
1
2
1
1
2
1
1
2
1
1
1
2
1
2
1
2
1
2
1
1
2
2
1
1
2
1
2
1
1
2
1
1
1
2
1
1
1
0
2
0
1
0
2
2
1
1
0
1
1
2
1
1
1
2
2
2
2
1
2
1
2
1
0
5
1
1
0
1
1
1
1
1
1
1
2
1
0
2
1
2
2
0
1
2
1
1
1
2
1
2
2
1
1
1
2
1
2
2
1
2
1
1
1
1
2
1
1
2
1
0
1
1
2
2
1
1
1
1
1
1
1
1
2
0
1
2
0
1
2
1
1
0
1
2
1
1
1
2
1
1
1
0
1
1
1
1
1
1
0
1
1
2
0
1
2
1
1
2
1
2
0
1
2
1
2
2
1
1
1
2
1
1
3
1
1
2
1
2
1
1
1
1
2
1
0
3
2
1
1
0
0
1
2
1
2
0
2
1
1
1
1
1
1
1
1
1
2
1
0
0
1
0
2
1
1
1
1
1
1
0
0
1
1
0
1
0
1
1
0
1
0
1
0
1
1
1
0
1
0
2
1
1
2
2
1
3
1
1
0
1
0
1
1
1
1
1
1
0
2
1
0
0
1
0
0
2
1
1
0
1
1
1
1
1
2
1
2
1
2
1
1
1
1
1
1
1
2
2
1
1
1
1
2
2
1
2
0
2
0
1
1
1
1
1
0
1
2
1
1
2
1
1
1
2
1
1
1
2
0
2
1
1
1
1
1
1
1
1
1
2
2
1
1
1
2
1
1
1
2
1
0
1
1
1
1
2
1
1
0
1
2
1
1
2
1
2
2
1
1
2
1
2
0
0
1
1
0
1
0
0
1
1
1
0
0
1
1
1
1
2
2
1
1
1
2
2
1
2
0
0
2
1
2
1
1
5
1
2
0
1
2
2
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
2
2
2
2
1
1
1
0
1
1
0
1
1
2
0
1
0
0
1
2
1
1
2
2
2
1
1
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
0
1
1
1
1
1
1
0
2
1
2
0
0
1
0
0
2
1
1
0
1
1
1
0
2
1
1
1
2
1
2
0
1
1
1
2
2
1
1
1
1
1
1
0
0
2
1
1
1
1
2
1
0
1
0
0
2
1
1
1
1
1
5
2
1
1
1
1
1
1
1
2
2
2
1
2
1
9
1
1
1
1
1
0
1
2
2
0
1
2
0
1
1
1
1
1
1
1
2
2
2
2
2
2
2
2
2
2
0
1
1
1
2
1
2
1
2
1
1
0
1
1
1
0
1
1
1
1
1
0
1
1
1
1
1
2
2
1
0
1
1
2
1
1
1
1
1
1
2
0
2
0
2
2
1
1
0
1
1
2
0
1
1
1
1
1
2
2
0
2
1
1
1
1
1
2
0
1
1
1
1
1
0
2
1
3
1
2
1
1
2
2
0
1
1
1
0
1
2
1
0
2
2
2
1
1
2
2
2
2
1
1
1
1
1
1
1
2
1
2
0
1
2
2
1
0
0
0
1
1
1
1
1
0
2
1
2
2
0
0
2
1
1
2
1
0
1
1
1
1
1
1
1
1
0
0
1
3
0
1
0
2
2
0
2
1
2
2
1
1
1
1
1
2
1
0
1
2
2
0
0
2
0
2
2
1
2
2
2
1
2
2
1
0
0
1
0
1
1
1
1
0
2
1
2
1
1
1
0
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
0
2
1
1
1
1
2
2
1
0
1
0
0
1
0
1
0
0
2
2
1
1
0
2
1
1
1
2
1
1
2
1
2
1
1
1
1
0
1
1
1
2
1
1
0
1
1
2
2
2
2
1
1
1
2
0
1
0
1
2
1
1
1
2
1
1
0
1
1
1
1
0
2
1
1
1
3
1
1
1
1
2
1
1
1
1
1
0
1
0
0
2
1
1
1
1
0
2
2
1
1
1
1
1
2
2
0
2
1
1
2
0
2
1
1
2
1
1
1
1
1
1
0
2
1
1
1
0
2
1
1
0
0
2
0
1
1
2
2
2
0
2
2
1
1
1
1
1
1
0
0
1
1
0
1
1
1
2
1
2
1
3
1
1
2
0
1
0
1
2
1
1
1
1
1
2
2
2
1
0
1
1
2
1
1
1
0
1
2
1
1
1
0
0
1
2
1
1
2
0
1
2
0
2
0
1
1
1
2
0
1
1
2
1
1
2
0
0
0
1
2
1
1
2
1
0
2
1
1
1
0
2
1
1
1
1
1
1
1
5
1
1
2
2
2
1
2
2
1
0
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
2
1
1
2
1
2
1
1
0
0
2
3
1
1
2
1
1
1
0
2
2
1
2
1
1
2
2
1
3
1
1
1
2
0
1
2
1
1
1
0
1
0
2
1
1
1
2
1
1
2
1
1
1
1
0
1
0
1
1
1
0
0
0
2
2
1
1
1
1
1
1
0
1
0
1
1
2
1
2
2
1
1
0
1
1
1
1
4
0
1
1
1
1
1
0
1
2
1
1
1
0
2
1
0
1
0
2
2
0
2
2
2
1
1
1
2
1
1
1
1
0
2
1
1
1
1
1
2
1
0
2
1
1
0
2
1
1
1
1
2
0
1
2
1
1
2
0
2
1
1
2
2
0
1
1
1
1
1
2
1
1
0
2
1
1
1
2
2
1
1
1
1
0
1
1
1
1
1
0
2
0
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
5
2
1
1
2
1
1
0
0
1
2
3
1
1
0
2
1
1
2
1
0
1
0
2
2
1
0
1
1
1
1
0
1
1
0
2
1
1
1
1
1
1
1
1
1
1
1
0
1
1
2
0
2
1
1
2
2
1
2
2
2
1
1
1
0
1
1
1
2
2
2
1
1
1
0
1
1
1
1
1
2
1
2
2
2
1
1
1
2
2
1
1
0
1
1
0
2
2
1
2
2
0
1
1
1
2
0
2
0
1
2
1
1
1
1
0
1
1
0
1
0
0
3
1
1
1
1
1
2
1
1
1
1
0
1
2
1
1
1
1
0
1
1
2
1
2
1
1
0
2
0
1
2
1
2
0
1
1
1
1
1
0
1
1
2
1
1
2
2
1
1
1
1
2
1
2
2
2
1
1
2
2
2
1
2
2
1
0
1
1
0
0
1
1
2
0
1
1
2
0
0
2
1
2
0
1
2
1
2
1
1
0
1
1
2
1
1
1
1
1
0
1
2
0
0
1
1
2
0
1
1
0
1
2
1
1
2
1
0
1
1
2
0
1
0
1
1
1
1
1
0
0
1
1
1
2
2
1
1
1
1
1
2
2
1
2
1
0
2
1
1
1
1
1
1
2
0
1
2
1
0
2
1
1
1
1
2
1
1
1
1
1
1
1
0
1
1
0
2
1
1
1
1
0
2
0
2
1
1
1
1
1
2
1
2
1
1
2
1
1
2
1
0
2
1
1
2
1
2
2
1
1
2
3
1
2
1
0
1
1
0
1
1
1
1
2
2
1
1
2
1
1
2
0
1
0
1
1
1
1
1
1
1
1
2
1
1
0
0
1
1
1
1
2
0
2
0
1
1
0
1
1
1
1
1
2
1
1
0
2
1
0
0
2
1
1
2
1
2
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
1
1
0
1
0
1
1
1
2
0
0
1
0
1
1
2
1
1
2
1
3
2
1
1
2
2
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
0
2
2
2
2
1
2
1
2
0
1
1
1
1
1
1
1
1
1
1
1
0
1
1
2
1
0
1
2
2
2
1
1
3
2
2
1
1
2
1
1
1
1
2
1
0
1
1
2
2
1
1
1
1
1
0
1
1
0
1
1
2
1
1
2
1
2
1
2
1
2
0
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
2
2
2
2
2
2
1
1
2
2
1
2
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
0
2
2
2
1
1
2
1
1
1
1
2
0
1
1
1
2
1
2
2
2
2
0
1
2
1
1
2
2
1
1
2
1
1
1
1
1
1
2
0
1
1
1
0
1
2
1
1
1
0
0
0
1
2
1
1
1
1
1
2
1
1
0
1
1
2
2
1
2
0
1
2
1
1
1
0
0
1
1
2
0
1
2
1
2
1
0
1
2
1
1
2
2
1
1
1
1
1
1
2
1
0
1
2
1
1
2
2
1
1
2
0
1
0
2
1
1
1
1
1
2
2
1
1
1
2
2
1
1
1
1
2
1
1
1
0
1
0
0
1
1
2
2
2
2
2
1
1
1
2
1
1
2
1
1
0
1
2
1
2
0
2
2
1
2
1
1
1
1
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
1
1
2
1
1
1
1
0
1
2
2
1
1
1
1
1
2
1
1
1
2
1
1
2
1
1
0
1
2
3
1
1
0
1
2
1
2
1
0
1
0
2
1
2
1
1
0
1
1
2
1
1
1
1
1
1
1
2
0
0
0
1
1
1
2
0
0
2
2
2
1
2
1
2
1
1
1
1
1
1
1
2
1
1
0
2
1
2
1
0
2
1
2
1
2
2
1
1
7
1
0
1
1
1
2
2
1
2
1
1
1
1
1
1
0
1
2
1
3
2
0
0
0
1
1
0
1
1
1
1
1
2
1
0
1
1
0
1
1
1
1
0
0
1
2
1
1
2
1
1
0
1
1
1
2
0
1
0
2
1
0
1
1
2
1
1
2
1
2
1
1
2
2
1
0
1
2
1
1
0
1
0
0
2
2
2
0
1
2
1
1
1
2
2
1
1
0
1
2
1
3
1
2
1
1
1
0
1
2
1
1
1
2
2
2
1
1
1
1
1
1
1
0
0
0
2
0
2
2
1
0
2
2
1
1
3
2
1
2
1
0
1
2
2
2
0
1
0
1
0
1
1
1
2
1
1
1
1
1
2
1
1
2
2
1
0
3
1
1
1
0
1
1
1
1
1
1
2
0
1
1
1
1
1
2
2
0
1
1
2
1
1
1
1
2
2
1
1
0
1
1
1
2
1
0
0
1
1
1
1
1
0
0
1
1
1
0
1
0
1
2
1
0
1
1
1
2
1
0
1
2
2
0
1
1
1
1
1
1
1
0
0
1
2
1
1
2
0
0
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
2
2
1
1
1
2
3
2
1
0
2
2
2
1
1
1
2
2
1
0
2
1
1
0
1
2
2
1
1
1
2
2
1
1
2
1
1
1
1
2
2
1
1
1
1
0
1
1
1
1
0
1
2
1
1
1
1
2
2
0
2
1
1
1
1
0
1
2
2
0
1
1
0
1
0
2
1
1
1
1
0
1
2
1
2
2
1
1
1
1
1
2
1
2
0
1
1
2
1
1
2
2
2
0
2
2
2
1
1
2
2
1
0
1
1
2
2
2
2
0
1
2
1
2
1
1
0
1
0
1
1
1
1
1
2
1
2
1
1
0
2
2
1
1
1
1
1
2
2
1
1
1
1
0
2
1
1
0
0
2
1
1
1
0
1
1
0
0
1
2
2
1
2
2
1
1
1
2
1
2
1
1
2
0
1
1
1
1
1
2
1
1
1
1
1
1
2
1
2
1
1
1
2
1
2
2
2
1
1
2
1
1
2
2
1
2
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
1
2
1
1
2
1
0
0
1
1
1
2
1
0
1
1
0
0
2
2
1
0
1
0
2
1
2
1
1
1
1
1
1
1
0
1
1
1
0
2
0
2
1
1
2
2
1
2
1
1
1
1
0
0
2
2
0
1
1
1
1
0
1
1
1
1
1
1
2
2
1
2
1
1
2
1
1
0
1
1
2
2
0
1
0
1
0
1
1
1
1
1
1
1
1
1
3
1
2
1
0
1
1
1
1
1
2
1
0
2
1
0
2
1
0
1
1
1
1
1
1
0
1
0
0
0
1
1
1
1
0
0
1
1
1
2
1
1
1
1
2
2
1
1
1
2
0
1
1
2
1
2
0
1
2
0
1
2
1
0
2
0
1
1
1
1
2
1
1
1
1
1
1
0
0
0
1
1
1
1
1
1
1
1
2
1
2
1
1
2
2
1
2
1
2
1
2
0
2
1
1
0
2
0
0
2
1
3
1
1
1
1
1
1
1
1
1
2
1
1
3
2
2
1
0
1
2
1
2
1
0
1
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
2
1
1
0
1
1
1
1
3
2
2
2
2
2
1
0
1
1
0
1
1
2
1
1
1
1
1
2
1
2
0
1
0
1
0
1
1
0
2
2
0
2
2
2
1
0
1
1
2
1
2
1
0
2
1
1
0
1
1
1
1
1
0
1
1
1
1
2
1
2
2
1
1
1
1
2
1
0
1
1
1
2
0
1
2
0
1
1
2
2
2
1
1
1
0
1
1
0
1
0
0
1
1
1
2
1
1
1
2
2
1
0
1
1
2
1
1
1
0
2
1
1
1
1
1
1
1
2
1
0
1
2
1
1
0
1
0
2
1
0
1
1
2
1
1
1
0
3
1
1
1
2
1
1
1
2
1
1
1
1
1
2
2
0
1
1
0
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
0
1
1
2
1
1
1
2
1
1
0
0
1
0
2
1
1
2
0
1
1
2
0
2
1
1
1
1
1
2
1
2
1
2
2
1
1
0
1
2
1
1
2
1
0
1
2
1
1
1
1
1
1
2
1
4
2
2
2
2
2
1
1
1
1
0
1
1
2
1
1
2
1
1
1
2
2
2
2
0
2
1
1
0
1
1
1
1
1
1
0
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
2
1
1
0
1
2
1
1
2
1
1
1
1
1
1
0
0
1
2
0
1
1
1
1
1
1
1
1
1
1
0
1
1
0
1
1
1
1
1
0
2
1
2
1
2
1
0
2
1
0
2
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
2
1
1
2
1
1
1
2
1
1
1
1
1
2
2
1
1
1
1
0
2
1
0
0
1
2
2
1
0
0
2
1
1
0
2
1
1
2
1
1
2
1
1
1
0
2
1
1
1
2
1
1
1
1
1
2
0
0
2
2
0
3
1
1
1
0
2
1
1
2
1
1
1
3
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
2
2
1
1
2
1
1
0
1
1
1
0
2
1
1
2
0
1
1
1
2
1
1
1
1
1
1
0
2
0
2
2
1
1
1
1
1
0
1
2
1
2
2
2
1
2
1
1
1
1
1
0
2
1
1
0
1
1
1
1
1
2
0
2
1
2
1
1
1
1
2
1
1
1
1
0
1
4
1
1
1
2
2
0
1
1
1
5
2
1
1
1
1
1
3
1
1
0
1
1
2
1
2
2
1
2
1
2
2
1
1
0
0
1
1
0
2
1
1
0
1
1
1
1
1
1
1
1
1
0
1
2
2
1
1
1
2
0
1
2
1
1
1
1
1
2
1
1
2
2
2
1
1
2
1
1
2
1
1
1
1
1
0
1
0
1
1
1
1
0
1
1
1
2
1
2
1
1
1
1
2
1
1
1
0
0
1
2
1
2
1
1
2
2
1
0
1
1
1
1
1
1
1
1
0
1
2
2
2
1
1
0
1
1
2
1
2
1
1
0
0
1
1
1
1
2
1
1
1
1
1
1
2
0
1
1
2
1
1
0
1
1
1
1
0
1
0
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
2
1
2
1
1
1
1
2
1
2
1
1
2
1
2
0
1
1
1
2
2
1
1
2
1
1
1
1
2
2
1
0
1
1
1
2
1
1
1
2
1
2
1
0
1
1
0
1
1
1
1
2
1
1
1
2
2
1
1
2
0
1
2
2
1
1
1
0
2
0
2
1
1
2
2
2
2
1
1
2
2
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
2
1
1
1
1
1
1
1
2
2
1
0
2
2
1
1
1
1
2
0
0
1
2
1
1
1
1
1
0
1
1
1
2
1
2
1
2
1
1
1
0
1
1
2
1
1
2
1
0
1
1
2
1
1
0
1
1
1
1
1
1
2
1
0
1
1
1
1
1
2
1
1
1
1
2
0
1
0
0
1
2
2
1
2
2
1
0
1
0
1
1
1
1
2
1
0
1
2
0
0
1
1
2
1
1
1
0
3
2
1
1
0
1
0
1
1
1
1
1
0
1
1
1
2
1
0
1
1
2
0
1
1
1
1
2
1
1
2
2
1
1
0
2
2
1
0
2
1
2
2
1
2
2
1
2
2
2
1
0
2
0
1
1
2
1
2
2
0
1
2
1
1
2
1
2
1
1
1
1
1
0
1
0
1
0
1
1
1
1
0
2
1
1
1
2
1
1
1
1
1
1
1
0
1
2
1
1
1
0
1
1
1
1
1
2
2
1
1
1
0
0
1
1
2
1
1
1
1
1
0
2
1
1
1
2
2
2
1
1
1
1
1
2
2
2
1
1
1
2
1
1
1
0
1
2
1
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
0
0
2
1
1
2
2
0
2
2
0
0
1
2
2
1
2
1
1
0
2
0
2
2
1
2
1
1
2
2
1
0
2
2
1
0
0
0
1
2
0
2
1
1
1
1
1
2
2
1
1
2
0
0
2
1
1
2
3
1
1
1
0
1
2
1
1
0
2
1
2
1
2
0
2
1
0
1
0
1
1
0
1
2
1
1
0
1
1
1
0
1
2
2
1
2
1
0
2
1
2
2
1
1
0
0
2
2
0
1
2
1
1
1
2
1
2
1
1
0
1
0
2
1
2
0
1
0
1
1
0
2
0
0
2
0
0
2
1
1
0
2
1
2
1
1
2
1
0
2
1
2
0
0
1
1
1
2
1
0
1
1
1
0
2
1
0
1
1
1
2
1
1
2
1
1
2
2
0
1
1
0
2
1
1
1
2
2
2
0
0
1
0
1
1
0
0
1
0
2
1
1
2
2
1
2
1
1
2
1
2
2
0
1
2
0
1
1
0
2
2
1
2
1
1
1
1
0
1
1
2
1
1
1
1
1
1
1
1
0
1
2
2
1
1
1
1
1
2
0
2
2
1
2
1
1
0
2
2
1
1
1
1
0
1
0
1
1
1
0
2
2
1
2
0
1
1
1
1
1
2
1
1
1
2
1
1
2
1
1
1
1
1
2
2
0
1
2
1
1
0
1
1
1
1
0
2
1
2
2
1
1
0
2
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
0
2
1
2
2
1
0
1
2
1
1
0
1
2
1
1
1
1
1
1
2
0
1
1
2
1
2
1
0
1
2
1
1
1
1
1
1
2
2
2
2
1
0
3
1
1
1
2
1
0
0
2
1
1
1
2
1
1
0
2
0
0
2
1
1
1
1
0
1
0
0
1
1
2
1
2
0
1
0
1
2
1
1
0
1
1
0
1
1
1
2
2
1
2
1
1
0
0
1
0
0
1
1
0
1
1
1
2
2
0
1
0
0
2
1
1
1
1
1
2
3
1
1
3
0
2
0
0
1
1
0
1
2
1
1
1
2
1
1
2
0
0
0
0
1
2
1
1
1
0
0
0
1
1
1
1
2
1
1
3
1
1
1
2
1
2
1
2
1
2
0
1
1
2
1
1
1
1
0
2
2
2
1
0
1
1
1
1
1
1
0
0
1
1
1
1
1
1
0
1
0
1
1
0
1
1
1
0
0
1
1
1
1
1
0
2
1
1
2
1
2
2
1
1
1
0
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
1
2
0
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
0
0
2
1
1
1
2
1
1
1
1
1
2
2
2
1
1
1
1
1
2
1
1
1
1
2
1
1
1
0
0
2
1
0
0
2
2
2
1
1
1
1
1
0
2
1
2
2
1
2
1
1
1
1
3
1
1
2
0
3
1
2
1
1
1
0
1
1
1
1
1
1
1
1
1
0
1
1
0
1
1
1
0
1
0
0
1
2
1
1
1
1
2
2
2
1
1
1
2
0
1
1
1
0
0
2
1
1
1
1
1
1
2
0
1
1
2
0
1
1
1
1
2
1
1
2
1
0
2
1
2
1
2
1
1
1
0
2
2
2
1
2
1
2
2
2
0
1
1
1
1
2
1
1
2
1
1
2
2
2
1
6
1
1
1
0
1
1
1
1
0
1
1
2
2
1
1
2
2
1
1
1
2
2
2
1
2
1
1
1
1
1
1
0
1
2
0
0
2
2
2
1
1
1
2
2
2
1
1
2
2
1
1
1
1
1
1
2
1
1
2
2
1
1
2
1
2
1
1
1
2
1
2
2
2
1
2
1
1
1
2
2
1
1
3
1
1
1
0
2
1
0
1
2
2
2
1
1
0
1
2
2
1
1
1
1
1
1
1
0
2
0
1
0
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
3
1
0
1
2
1
1
1
0
1
1
1
2
1
2
1
0
1
2
2
1
2
1
2
0
1
1
1
1
1
2
3
1
2
1
1
1
2
1
1
0
1
2
1
1
1
0
1
2
1
0
0
1
1
2
6
1
1
0
2
1
1
1
2
0
0
1
0
1
2
1
1
2
1
2
0
1
1
1
0
0
0
1
2
1
1
0
1
1
1
0
1
1
1
2
1
1
2
1
1
1
1
2
1
0
2
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
2
2
1
1
2
1
0
1
2
1
1
1
1
1
1
1
1
1
1
1
1
0
0
1
1
1
1
1
2
0
0
1
1
1
1
1
1
0
1
2
1
1
2
1
1
2
1
1
1
0
1
1
2
1
1
2
1
1
1
1
2
0
1
2
1
1
1
1
1
1
1
2
1
2
0
1
1
1
1
1
0
1
2
1
0
1
2
2
2
0
2
1
1
1
1
1
0
1
1
0
1
2
0
2
1
2
2
1
1
1
1
0
1
1
1
1
2
2
0
0
1
2
1
2
1
1
2
0
3
1
0
1
1
1
1
2
2
1
1
1
0
1
1
0
0
1
1
1
0
2
2
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
0
1
1
1
2
1
2
2
2
1
2
1
1
1
1
1
1
0
2
2
1
1
2
1
1
2
1
1
1
1
0
1
2
1
2
1
1
2
0
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
2
1
2
1
2
0
1
2
1
1
1
1
1
2
2
1
1
2
1
0
2
1
1
1
1
1
2
2
0
2
1
0
1
2
1
1
1
1
1
1
1
1
1
2
1
0
1
1
1
1
1
1
2
1
2
1
2
1
1
1
0
1
0
0
2
1
1
1
1
1
2
1
0
1
2
1
1
2
2
2
1
1
2
1
1
0
2
1
0
0
2
0
0
1
2
2
1
1
2
2
1
2
1
0
1
1
2
1
2
1
3
1
1
1
1
2
2
1
1
1
1
2
1
0
2
1
2
2
2
2
2
2
0
1
1
1
1
1
0
2
1
2
0
2
1
1
1
1
2
0
2
1
1
1
1
1
1
2
2
0
0
1
1
1
1
1
1
1
1
1
1
1
0
1
0
1
1
2
1
0
1
1
2
2
1
2
2
2
1
2
2
1
2
2
1
1
1
2
1
1
0
1
1
1
1
1
1
1
2
1
2
2
1
2
1
2
2
0
1
0
2
1
1
0
1
2
1
2
1
2
1
1
1
1
1
1
0
0
1
1
1
1
1
1
1
2
1
2
0
1
0
0
0
1
2
1
2
0
1
0
1
1
1
2
0
1
2
1
1
2
2
1
3
1
1
1
1
0
1
1
1
4
2
1
1
1
0
1
1
1
1
0
0
1
2
1
2
1
1
1
1
0
1
1
0
1
1
2
1
1
1
1
2
0
1
2
1
2
2
1
1
1
1
0
1
1
1
1
1
0
0
1
1
1
2
1
1
1
2
2
2
1
2
1
2
2
1
1
1
1
1
2
0
1
1
1
0
1
1
0
1
1
1
1
0
2
1
1
1
1
1
1
1
0
1
1
1
0
1
2
0
1
1
1
1
1
1
1
2
1
0
1
1
1
1
1
1
2
2
1
0
1
1
2
2
2
1
2
1
1
1
2
0
1
2
2
1
1
1
2
1
0
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
2
1
2
2
2
1
1
1
1
1
1
0
2
1
1
1
2
1
1
2
2
1
1
0
1
1
2
0
0
1
1
0
0
2
1
2
0
1
2
1
2
1
1
1
2
1
1
1
1
1
0
1
1
0
1
0
2
1
2
2
1
1
1
2
1
0
1
1
1
0
1
0
1
1
1
2
1
0
1
1
1
1
0
1
1
1
2
1
0
1
1
1
1
0
0
1
1
2
1
1
2
1
2
1
0
0
1
1
1
1
2
1
1
1
1
2
2
1
2
1
0
2
1
1
1
1
1
1
1
2
1
1
1
0
1
0
1
0
1
1
1
1
1
1
1
1
2
0
1
1
2
0
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
0
1
1
2
1
1
1
1
1
1
0
1
0
1
1
1
0
1
1
1
0
0
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
2
1
2
1
1
1
2
2
0
1
1
1
2
1
1
0
1
1
1
1
2
1
0
1
1
2
1
2
1
2
1
1
1
1
1
1
1
1
1
0
1
0
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
3
0
1
1
2
1
1
1
1
1
1
2
0
0
1
2
1
0
1
2
2
1
2
1
1
2
2
1
1
0
0
1
1
0
1
1
0
0
1
1
1
1
1
1
0
4
2
1
1
1
2
1
1
2
1
1
2
2
1
1
0
2
1
1
1
1
1
0
2
1
1
1
1
2
0
1
1
1
2
2
1
0
2
1
0
2
1
1
2
1
1
2
0
1
0
1
0
1
1
1
1
1
1
2
1
0
1
2
1
1
1
2
2
1
2
1
2
2
1
2
1
1
1
1
2
1
2
2
1
2
1
1
1
1
2
2
1
2
2
1
1
0
0
2
1
1
1
1
1
1
2
1
1
2
1
1
1
2
1
0
1
1
2
0
1
1
1
1
2
0
1
2
1
1
2
0
1
1
2
1
1
2
2
3
1
0
1
1
0
1
1
1
1
2
2
1
1
1
1
1
0
2
1
0
1
2
1
1
1
1
0
1
2
0
1
1
1
2
1
1
1
2
1
1
1
0
2
1
1
2
1
2
0
1
2
2
2
1
1
0
1
1
1
0
1
2
2
2
1
2
1
1
2
1
2
1
1
1
1
1
1
0
2
1
1
2
1
2
1
1
2
2
1
1
2
4
1
0
2
1
1
1
1
2
0
1
0
2
2
1
0
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
2
1
1
0
0
2
1
2
2
0
0
2
2
1
1
1
2
1
1
1
1
2
2
1
0
1
1
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
2
0
2
1
1
1
1
0
2
1
2
0
1
1
1
2
2
1
1
1
0
0
1
1
2
2
1
1
1
2
1
1
1
1
1
0
1
0
1
2
1
1
1
0
2
1
2
1
1
0
2
1
0
1
1
0
1
1
1
0
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
0
1
1
0
0
0
1
1
0
1
1
2
1
1
0
0
1
2
0
2
2
1
1
2
1
2
0
0
0
1
0
1
0
1
2
2
1
2
2
2
1
2
2
0
1
2
1
1
2
2
1
1
0
1
1
1
1
1
1
1
1
2
1
2
1
1
2
1
0
2
1
1
0
1
1
1
2
1
0
1
1
0
2
2
2
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
0
1
0
2
1
2
0
1
1
2
1
1
1
1
0
1
1
1
1
2
1
1
2
2
1
1
1
1
2
1
2
0
1
1
2
1
1
1
1
2
1
1
2
2
2
2
1
1
0
1
1
1
2
2
0
1
1
1
1
1
0
1
2
1
2
2
0
1
1
0
7
0
1
3
0
1
0
1
1
2
1
2
1
2
1
1
1
1
1
0
1
1
1
0
1
1
2
1
1
1
2
2
1
1
2
0
2
1
1
1
0
2
2
1
1
1
2
1
0
2
0
1
1
0
1
1
2
2
1
2
1
1
1
0
1
1
2
1
1
1
1
1
1
1
1
1
2
2
0
1
2
1
1
1
2
1
1
1
2
2
2
1
2
1
2
1
1
2
2
1
2
2
1
2
2
1
1
1
1
2
1
1
1
2
1
1
1
1
3
2
2
1
2
2
1
2
2
1
1
2
1
2
1
1
1
1
0
0
1
1
1
1
1
2
1
5
1
0
1
2
2
2
1
1
1
2
1
1
1
1
2
2
0
1
1
1
1
1
1
0
1
1
0
1
1
2
2
1
1
0
1
1
1
1
1
1
1
0
1
0
1
1
1
1
2
1
1
1
2
1
1
1
2
2
0
1
0
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
2
2
0
0
2
1
2
1
2
2
0
2
1
0
1
2
1
1
3
1
2
1
1
1
2
2
1
1
0
1
1
1
1
1
0
0
0
0
2
1
1
0
2
1
1
1
0
0
1
0
0
1
1
1
1
1
1
1
2
1
1
0
1
1
1
1
1
1
2
1
2
2
1
1
0
2
1
1
2
1
1
0
1
1
0
1
1
0
2
1
1
1
0
2
1
2
1
1
2
1
1
0
2
2
2
1
1
1
1
2
1
1
2
1
2
2
1
1
2
1
1
1
1
1
1
0
1
1
1
1
2
3
1
1
1
1
2
1
1
1
2
1
2
1
2
1
1
2
1
1
0
1
0
1
0
1
1
1
1
2
1
1
1
1
2
0
2
1
2
1
1
1
1
2
2
1
1
2
1
2
1
0
0
1
1
0
0
2
0
1
2
2
1
1
1
1
1
1
1
1
0
2
1
2
1
2
1
1
1
0
2
0
1
1
1
1
1
1
1
2
2
1
1
1
1
2
2
1
1
1
2
2
0
0
1
2
2
1
1
1
2
0
0
2
0
1
1
1
1
1
1
1
1
1
1
0
1
2
1
1
2
1
1
2
2
1
1
1
2
0
1
0
1
1
1
2
2
2
0
2
1
1
2
1
2
1
1
2
1
2
2
2
2
1
2
1
1
1
1
1
1
1
2
3
0
1
1
0
2
0
1
1
0
1
1
1
0
1
0
1
2
1
1
1
1
2
1
1
1
1
0
1
2
1
1
0
2
0
0
2
0
1
1
0
1
1
1
0
2
1
1
2
1
2
1
0
0
0
2
0
0
1
2
0
1
2
2
1
0
1
2
2
1
2
2
1
1
2
0
0
1
1
1
1
2
2
2
2
1
0
1
2
1
1
1
2
1
1
1
2
2
0
1
2
1
3
2
1
2
1
1
1
1
1
2
1
1
1
1
0
2
0
1
2
1
0
2
0
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
0
1
2
4
1
1
1
1
2
1
1
1
0
1
1
1
2
1
1
3
0
0
1
2
1
1
2
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
0
1
0
2
1
1
0
1
2
0
1
1
1
2
1
2
1
0
1
1
2
2
1
1
1
1
1
2
0
1
1
0
1
1
1
1
1
2
1
1
1
1
0
1
1
1
1
1
2
2
3
1
0
0
2
1
2
0
1
1
1
0
0
2
1
2
1
1
0
1
0
2
2
1
1
0
1
1
0
0
1
1
1
1
2
0
1
1
1
1
2
2
1
0
2
1
1
1
1
1
2
1
1
1
1
1
0
1
5
0
2
1
1
2
1
1
1
2
1
1
0
1
1
1
1
1
2
1
2
1
1
2
1
1
1
0
1
1
1
1
0
1
1
1
2
2
1
2
1
2
1
1
1
1
0
1
1
2
1
1
2
1
1
1
1
2
1
2
0
2
2
1
0
2
1
1
2
0
1
0
2
1
1
1
1
1
1
1
1
0
1
0
2
0
0
1
0
1
0
3
0
0
0
0
2
1
1
1
1
1
1
1
1
2
2
0
1
1
0
2
0
1
1
0
2
2
1
1
2
0
2
2
1
2
1
1
1
1
1
2
0
1
1
1
2
2
1
2
0
1
0
1
1
1
1
0
1
1
1
0
1
2
1
1
1
2
1
2
1
1
1
2
1
1
2
1
1
1
0
1
2
1
1
1
1
0
1
1
1
2
1
1
2
2
1
1
1
1
1
2
0
1
2
0
0
2
1
1
2
1
1
1
1
2
0
2
1
1
0
1
1
1
2
2
2
1
2
1
1
1
2
0
1
1
1
1
2
1
0
1
2
0
2
1
1
1
1
0
1
1
0
1
1
1
1
1
1
2
1
3
1
1
1
1
1
1
1
2
1
0
1
2
2
1
1
1
2
2
1
1
0
1
2
1
1
1
2
1
1
1
1
1
1
2
0
2
1
2
2
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
0
2
0
2
1
2
1
1
1
1
1
2
0
2
2
2
1
1
0
1
1
2
1
2
2
2
1
1
1
1
1
1
2
1
0
2
3
2
0
1
2
2
1
1
2
1
0
2
2
2
1
1
1
1
1
1
1
1
1
0
1
1
1
2
1
1
1
1
1
2
2
1
1
2
2
1
1
1
1
0
1
2
1
1
0
1
1
1
1
1
1
0
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
2
1
1
1
2
0
1
1
2
0
0
1
1
2
1
1
1
2
2
2
0
1
2
1
0
1
0
1
1
1
0
1
1
1
2
0
1
2
1
1
0
0
2
1
2
1
2
2
1
1
1
1
3
0
0
2
1
1
1
1
1
1
0
1
2
0
1
1
1
2
2
1
1
1
1
1
1
2
1
1
1
2
0
2
1
0
1
1
1
1
2
2
1
1
0
1
1
0
0
0
1
0
0
1
1
1
1
1
2
1
1
1
0
1
1
2
2
1
1
1
0
2
2
1
1
1
0
1
1
1
0
2
2
0
1
2
1
1
2
1
2
2
1
2
1
1
2
2
1
2
1
1
0
2
1
2
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
2
2
2
1
2
2
1
1
1
2
2
2
2
1
1
2
2
1
1
3
2
2
2
1
2
1
2
1
1
2
1
0
2
2
1
1
2
1
1
0
1
2
1
0
3
2
2
0
1
2
2
2
1
1
1
1
2
1
1
1
1
2
1
0
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
0
0
1
1
1
2
1
2
1
1
0
0
1
2
1
2
1
1
1
1
0
1
1
1
2
1
0
1
1
2
0
1
2
1
0
1
1
1
1
1
1
1
2
1
0
1
1
1
1
0
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
2
0
1
2
1
0
0
0
1
1
1
0
1
1
1
1
1
1
1
1
1
2
2
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
2
0
1
1
0
1
1
0
2
1
1
2
1
1
1
1
2
0
0
1
1
1
2
2
1
1
1
2
1
2
1
1
0
1
1
0
1
1
1
2
1
2
1
1
2
1
1
1
2
2
2
1
1
2
1
1
1
1
1
1
1
0
1
1
1
0
1
1
0
1
1
1
1
1
2
2
1
1
1
1
2
1
1
0
2
1
1
1
1
2
1
1
1
0
1
0
1
1
1
0
1
2
1
1
0
1
2
1
2
1
2
2
2
1
1
0
0
2
2
2
1
1
1
2
1
1
1
1
2
1
1
2
1
1
0
2
1
1
2
1
1
1
3
0
2
1
0
1
1
1
1
0
1
1
1
1
1
1
1
1
0
2
1
1
1
2
1
2
1
1
0
1
2
1
0
0
1
1
2
1
0
1
1
1
2
2
2
1
1
0
2
1
1
0
2
1
1
1
1
2
1
1
2
1
1
1
1
0
1
0
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
2
1
1
1
0
1
1
0
1
0
2
1
0
1
0
1
1
0
0
2
1
1
2
0
1
1
2
1
1
1
0
0
1
2
1
1
2
1
1
2
1
1
1
1
0
2
1
1
2
1
0
0
1
1
1
1
1
1
2
1
1
0
2
2
0
2
1
2
2
0
1
1
1
1
2
1
2
2
1
1
2
2
1
2
2
1
1
1
1
1
1
0
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
0
0
1
1
2
0
1
2
2
2
1
1
1
0
2
2
2
1
1
2
2
2
1
1
1
2
2
3
0
1
2
1
1
2
0
1
1
1
1
1
1
1
1
1
1
0
2
1
1
2
0
1
1
1
2
3
2
0
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
2
2
1
2
1
1
2
1
2
2
1
1
1
2
2
2
2
2
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
0
1
1
1
2
1
2
1
2
1
1
2
2
2
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
0
2
1
2
0
1
1
2
1
1
1
0
2
1
2
1
0
1
1
2
0
0
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
2
1
2
1
1
1
1
2
1
2
1
1
2
1
2
1
2
0
2
1
2
1
0
8
1
1
1
1
1
1
2
2
1
2
1
1
2
1
2
2
1
1
0
2
2
1
2
1
1
1
1
1
1
2
0
1
0
2
1
0
0
1
2
1
2
1
1
2
1
0
2
1
1
1
2
1
1
1
1
1
1
0
3
2
1
2
1
1
1
1
1
1
1
2
2
2
0
1
2
1
1
1
1
0
1
0
0
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
2
1
2
1
1
1
0
0
1
1
1
1
1
0
0
0
1
1
0
1
1
1
2
2
1
3
1
1
1
2
1
0
2
1
1
2
2
1
1
1
2
1
1
1
2
1
1
0
1
2
1
1
2
1
1
2
1
1
1
2
1
1
1
2
1
1
1
0
1
1
2
1
2
1
1
0
1
1
1
0
1
0
1
1
1
2
1
2
1
1
2
1
0
1
0
2
2
1
2
0
1
4
2
1
1
1
2
2
2
2
1
1
1
0
1
1
2
1
1
1
0
0
1
1
2
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
0
2
1
1
0
1
2
2
2
1
0
0
2
0
1
0
1
0
0
2
1
2
2
2
1
0
1
2
1
1
1
1
1
2
1
1
2
1
1
1
2
2
1
1
2
1
1
2
1
2
2
1
0
1
3
2
0
1
2
1
1
2
2
2
2
1
1
1
2
0
1
1
2
1
1
1
1
1
1
0
1
2
0
2
1
2
1
2
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
2
1
1
1
0
1
0
1
1
2
1
2
0
1
2
1
0
1
2
2
0
1
0
1
2
0
0
1
2
1
2
1
1
1
4
2
0
1
0
1
1
1
0
1
0
1
1
2
1
1
0
1
1
1
1
1
1
1
2
2
2
2
2
1
2
0
1
2
1
1
1
2
1
1
1
1
2
1
1
1
1
1
2
1
1
1
0
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
0
2
3
1
1
1
2
1
2
1
1
1
1
1
1
1
0
1
0
2
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
2
1
2
1
2
1
1
1
1
2
1
1
0
1
1
1
1
1
2
1
2
2
2
1
1
1
0
1
1
1
1
1
1
2
1
1
2
1
2
1
1
1
1
0
2
2
2
1
0
1
2
1
1
0
1
1
1
1
1
1
1
1
1
1
0
1
2
1
1
1
1
2
1
2
1
1
2
1
0
1
1
1
2
1
1
1
2
1
2
1
1
1
2
1
1
1
1
0
1
1
1
1
2
1
1
1
0
2
3
1
0
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
2
2
1
1
1
2
1
2
1
2
1
2
0
1
1
2
1
2
1
1
3
1
1
0
0
2
1
1
1
1
2
0
1
1
1
2
1
2
1
1
1
1
1
2
2
1
1
1
1
1
1
0
1
1
1
1
1
2
1
0
2
0
2
0
1
1
2
2
1
1
1
1
1
0
2
1
1
2
1
2
1
3
1
1
1
2
2
1
1
1
2
1
1
2
1
0
1
1
1
2
2
1
2
2
2
1
1
1
0
1
0
1
2
1
1
1
2
0
2
0
1
1
1
1
1
0
1
1
0
0
0
1
2
2
1
1
1
1
2
1
1
0
2
1
2
2
1
2
1
1
1
2
1
1
1
1
1
1
0
2
1
1
2
3
1
0
2
1
0
1
1
1
1
1
1
1
1
1
2
1
1
3
0
1
2
1
1
1
0
0
2
0
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
3
2
1
3
2
1
1
0
1
0
0
1
1
2
2
0
1
1
1
2
1
1
0
1
2
2
1
1
1
2
1
2
2
1
1
1
1
0
1
2
1
2
2
1
0
1
2
1
1
1
1
1
1
1
1
0
0
2
2
1
1
2
2
1
1
1
1
0
2
2
1
2
1
1
1
1
0
1
1
2
1
1
1
2
1
2
2
2
1
1
1
2
1
1
2
2
0
1
2
1
1
1
2
1
2
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
0
2
1
1
2
0
0
1
1
1
0
1
1
1
1
2
1
1
0
1
2
2
1
1
2
4
0
2
1
0
2
0
0
2
1
2
2
2
1
2
2
0
2
1
1
1
1
1
1
1
0
1
2
0
1
1
0
1
1
0
2
1
1
1
1
1
0
1
0
2
2
1
1
1
1
1
3
1
1
1
1
1
1
1
0
0
2
2
2
2
1
1
0
0
1
1
1
2
2
2
1
1
0
2
1
0
1
0
0
2
1
2
2
0
1
1
1
1
1
2
2
1
0
2
0
1
0
2
1
1
1
1
2
1
1
1
3
0
1
0
1
1
1
2
1
2
1
1
2
0
2
1
0
2
1
1
0
1
1
2
1
1
1
1
1
1
1
1
2
1
1
0
1
2
1
0
1
2
2
2
2
1
0
2
1
1
1
1
1
1
0
1
1
1
1
2
0
1
1
0
1
0
1
2
1
2
1
1
1
1
2
1
1
1
1
0
1
0
1
2
2
1
1
1
1
1
0
1
1
1
1
1
1
2
1
1
1
0
0
0
1
1
0
1
1
2
2
2
1
1
1
1
1
1
1
2
1
1
2
1
1
2
1
2
2
1
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
2
1
0
1
2
0
0
1
2
1
1
1
1
1
1
1
0
3
2
1
2
2
1
2
1
1
1
2
1
1
2
1
0
1
1
2
1
1
1
0
1
1
1
2
1
1
1
1
2
1
1
1
1
0
2
1
0
1
1
2
1
2
1
1
1
2
1
1
2
1
1
0
1
1
1
2
0
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
0
1
0
2
1
1
2
0
0
2
1
1
2
1
0
1
2
0
1
2
1
2
0
1
2
0
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
3
1
1
1
1
1
0
1
1
1
1
1
2
1
2
2
1
1
0
0
1
1
1
1
1
1
0
1
1
1
1
1
2
1
2
1
1
1
2
2
1
1
1
1
1
1
0
1
1
2
1
1
2
1
0
1
1
2
0
2
1
2
1
6
1
2
1
1
1
1
1
1
2
1
1
1
2
1
0
2
0
2
1
1
2
2
0
1
0
3
1
1
1
2
0
1
2
0
1
1
2
0
1
2
1
2
1
1
1
2
1
2
1
1
0
2
0
0
1
1
1
1
1
1
1
2
1
1
1
0
2
2
1
0
2
1
1
1
1
1
1
2
1
0
0
2
2
0
1
2
1
1
1
1
1
2
1
1
1
0
5
1
1
0
1
1
2
1
1
1
2
1
1
1
1
2
1
0
1
0
1
1
0
1
1
2
2
1
1
2
1
1
1
1
1
1
2
1
2
2
1
2
1
1
1
1
1
0
2
0
0
0
1
1
1
1
1
2
1
0
0
2
1
2
2
2
1
1
1
1
1
1
1
2
1
1
1
1
0
2
1
1
1
1
2
1
1
0
1
0
2
1
1
0
1
2
1
1
1
1
2
0
1
1
0
1
1
0
2
1
1
1
1
0
1
1
2
2
1
2
0
1
1
1
1
1
1
1
2
2
0
2
0
2
2
1
1
2
2
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
0
1
1
2
0
1
1
0
0
1
1
2
1
0
1
1
0
1
1
2
3
1
0
2
1
1
1
2
2
0
1
1
0
1
2
1
3
1
1
1
1
2
0
1
0
1
1
2
2
1
1
2
1
2
0
1
0
0
1
1
1
2
2
2
2
1
2
1
1
1
2
2
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
2
1
1
1
2
0
1
3
0
1
1
0
1
1
2
1
2
1
2
0
1
2
2
2
1
1
1
1
1
1
1
2
2
1
1
0
0
0
1
1
1
1
0
1
2
1
1
1
2
0
1
2
2
2
0
1
2
1
2
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
2
2
4
2
1
2
0
1
1
1
1
1
0
0
2
2
2
1
2
2
2
1
1
1
2
1
0
1
1
1
1
1
2
2
2
1
1
2
1
1
2
0
1
1
1
1
2
1
1
2
1
1
2
1
2
2
1
1
1
0
2
1
2
2
1
1
1
2
1
1
1
1
2
1
2
1
2
0
1
1
2
0
1
3
1
1
1
1
2
2
0
1
2
2
1
1
0
1
2
1
2
0
1
0
0
1
0
0
0
0
0
1
1
2
2
1
1
2
2
1
1
1
1
1
2
1
2
1
1
1
2
2
1
2
1
1
1
0
0
1
3
2
1
2
1
1
2
2
2
3
0
4
2
1
1
1
1
2
1
1
2
1
1
2
1
2
1
2
0
2
1
2
1
1
0
6
1
1
1
0
1
0
2
1
2
0
2
0
0
1
1
1
0
2
1
1
0
1
1
0
1
2
1
1
1
1
0
1
1
2
1
1
1
3
1
2
1
2
1
0
2
0
1
1
0
1
1
2
1
1
2
1
2
1
2
2
0
0
1
2
1
1
1
2
2
2
1
2
0
1
2
1
1
1
1
0
1
1
1
2
2
0
0
1
2
0
1
2
2
0
2
1
1
1
1
0
2
1
1
1
2
2
1
0
1
0
0
1
1
2
0
1
2
1
1
2
1
2
0
1
0
0
1
2
1
1
1
1
1
1
1
1
0
1
1
1
1
1
0
0
1
2
1
1
1
1
2
1
0
1
2
0
1
1
0
1
1
0
1
1
2
1
1
1
2
1
2
2
1
1
0
2
1
1
1
1
0
1
0
1
2
2
1
0
1
2
2
1
2
2
1
2
0
1
2
2
1
1
1
1
0
2
1
1
1
2
1
2
1
3
2
0
1
1
2
1
2
1
1
2
1
0
1
1
1
2
0
1
1
1
2
1
1
1
2
0
1
1
2
1
1
1
2
1
1
1
0
1
0
1
1
2
1
2
1
2
1
0
2
2
1
2
1
1
1
1
2
1
0
1
1
1
0
2
2
2
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
2
1
1
2
2
1
0
1
0
1
2
1
2
2
1
1
1
1
0
1
2
1
0
3
1
2
1
1
1
1
2
0
0
1
0
1
2
1
1
1
2
1
0
1
1
1
1
1
1
1
1
1
2
2
1
1
1
3
2
1
1
0
2
1
2
1
1
1
1
1
1
0
1
1
0
2
1
1
1
1
1
1
1
2
0
0
0
1
2
0
2
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
1
1
2
1
2
2
1
1
1
1
2
1
0
0
2
2
0
2
1
1
1
2
1
2
1
1
2
1
2
0
1
2
0
1
1
2
1
2
0
1
0
1
1
1
0
1
1
1
1
1
1
1
1
0
2
1
2
1
1
2
1
2
0
1
1
2
0
1
2
1
2
2
1
1
1
1
2
1
2
1
1
2
3
1
1
2
1
1
1
0
1
1
0
2
1
1
2
1
2
0
0
1
2
1
2
2
1
0
1
1
1
1
1
2
2
2
1
1
1
2
1
1
2
1
1
1
3
2
1
2
1
0
2
1
5
2
2
1
2
2
2
1
1
1
1
2
2
1
1
2
1
1
2
1
1
1
0
2
1
0
2
2
1
1
1
2
2
0
1
1
1
2
0
1
1
1
1
3
1
0
1
1
1
0
2
1
1
2
1
2
2
1
2
1
2
2
1
0
1
1
1
1
1
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
2
2
1
1
1
2
2
2
1
1
2
1
0
2
0
1
1
1
2
1
2
1
1
3
1
2
1
1
0
1
1
2
2
0
1
1
1
0
1
2
1
1
1
0
2
2
2
1
5
1
1
0
1
1
2
2
1
2
2
2
1
0
1
1
1
1
2
3
1
1
2
1
7
2
1
1
1
2
1
2
2
2
1
1
2
1
0
1
2
1
0
1
0
1
1
0
2
1
2
2
0
1
2
1
1
2
0
1
1
0
1
1
2
1
2
1
0
1
1
2
1
2
1
1
1
2
1
1
0
2
1
2
1
3
2
0
2
1
1
1
1
1
1
2
1
2
2
2
0
2
0
0
2
1
2
2
1
1
1
1
1
1
1
0
2
2
2
1
1
1
1
0
1
1
1
1
1
1
0
1
0
1
1
2
2
1
2
0
1
2
2
2
1
1
2
0
1
1
2
2
1
2
2
2
0
1
1
1
1
0
1
0
2
1
0
2
0
1
0
2
1
2
1
1
2
1
2
1
2
1
0
1
2
1
0
2
2
0
1
2
1
1
1
1
2
1
1
2
1
2
3
1
1
1
0
1
2
1
1
2
2
2
1
1
1
1
0
1
1
1
2
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
4
1
1
1
0
0
1
2
3
2
1
1
1
0
2
1
2
2
1
2
2
0
0
2
1
1
2
1
1
0
1
0
1
1
1
1
2
1
1
0
0
3
1
1
2
0
1
1
2
1
0
1
1
0
0
1
1
1
1
1
1
1
2
2
1
2
2
1
0
1
0
2
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
0
0
1
1
1
1
1
2
1
2
1
0
2
1
1
0
1
0
2
2
2
1
1
1
1
1
1
1
1
1
1
0
2
1
1
2
2
2
1
1
1
1
3
1
1
1
1
0
2
1
1
1
0
1
1
4
2
1
0
1
2
1
0
1
1
2
2
1
1
1
0
0
1
0
1
2
1
0
2
1
1
2
0
1
1
2
5
1
2
1
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
0
2
2
1
2
2
1
1
1
1
2
2
1
1
0
1
2
1
1
1
0
0
1
0
1
1
1
2
0
1
1
2
1
2
1
2
2
1
1
2
2
2
1
1
0
1
1
1
2
1
2
1
1
1
2
1
0
1
0
1
2
1
1
1
2
1
12
0
1
1
1
2
1
1
1
1
0
2
1
1
1
0
0
1
1
2
0
1
2
1
1
1
0
1
2
1
2
0
1
1
1
1
0
1
1
1
1
0
2
1
1
2
1
2
1
1
1
2
1
0
1
1
1
0
1
1
1
2
0
2
2
2
1
1
0
2
1
1
1
1
1
1
1
1
1
1
0
0
1
1
1
1
0
1
2
1
1
1
1
1
1
2
0
1
2
2
1
2
1
2
1
1
2
1
1
2
0
1
1
0
2
1
2
1
2
1
1
1
2
2
1
1
1
1
1
1
1
2
2
1
1
0
0
0
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
0
1
1
0
1
0
2
2
1
2
1
2
2
1
2
1
2
0
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
3
0
2
1
2
1
1
2
0
1
1
2
0
0
2
2
2
0
1
0
2
0
1
2
0
0
1
1
1
1
2
2
2
0
2
1
1
0
1
1
2
1
1
2
2
0
1
1
1
1
1
1
2
1
1
3
2
2
1
2
1
1
2
1
2
2
2
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
2
1
1
1
1
0
2
2
1
2
1
0
0
1
1
1
1
1
0
1
2
1
2
1
1
1
2
1
1
1
1
1
0
1
2
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
0
2
0
1
2
1
2
1
2
1
1
2
1
1
2
1
1
0
1
1
1
2
1
1
1
2
1
0
0
1
1
0
2
0
2
1
0
0
0
2
1
2
2
1
2
1
0
1
1
1
1
2
1
2
2
0
1
2
1
1
1
2
1
1
1
0
0
1
1
1
1
2
1
0
1
1
2
1
1
1
2
1
1
1
2
2
1
1
1
0
2
2
0
1
1
0
1
1
2
1
2
1
2
2
1
1
1
3
2
1
1
1
0
2
1
1
1
1
1
1
1
1
1
2
0
1
2
1
0
2
1
1
0
0
1
1
1
3
1
1
2
2
2
0
1
2
1
0
1
2
1
2
3
1
1
1
2
2
0
0
0
1
1
1
2
0
1
1
1
2
1
1
2
2
0
2
0
2
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
2
1
1
0
1
1
2
1
1
0
2
1
0
1
2
1
1
1
2
1
0
1
1
1
0
1
1
1
2
2
1
1
2
1
2
0
1
1
1
0
0
1
1
1
1
1
1
1
2
1
1
2
1
1
1
2
1
1
1
0
1
2
2
1
1
2
2
1
1
2
1
2
2
2
1
1
1
1
1
1
1
1
1
2
2
0
2
1
2
1
1
2
1
1
1
0
1
2
2
1
1
1
2
1
2
1
2
1
0
1
1
1
1
2
1
1
2
0
1
1
1
1
1
1
0
1
2
1
0
1
1
0
0
0
2
1
0
1
1
0
1
1
1
1
1
0
0
1
1
2
1
1
1
1
1
0
2
0
1
1
1
1
1
1
1
0
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
2
1
2
1
1
1
1
3
1
0
1
2
2
2
1
1
1
1
1
1
2
1
1
1
0
2
0
1
1
1
0
2
2
2
1
2
2
1
1
2
0
1
0
1
1
1
1
1
1
1
1
2
2
0
2
1
1
2
0
1
1
0
1
1
1
1
2
0
1
1
2
2
1
2
0
1
1
1
0
1
1
0
1
2
2
1
0
2
1
1
1
0
1
1
1
1
0
1
1
1
1
1
2
2
0
2
1
0
2
2
0
0
1
2
1
0
1
1
0
1
1
1
1
2
0
1
1
2
2
2
1
0
1
1
2
1
1
1
1
1
2
1
1
1
1
1
0
1
1
0
1
1
1
1
2
0
1
1
1
0
3
2
1
2
1
1
1
0
1
2
1
1
0
1
2
1
2
1
2
1
2
0
2
0
2
1
1
1
1
1
2
2
0
1
2
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
2
2
0
2
0
1
1
2
1
1
1
2
2
1
1
0
2
1
1
2
1
1
1
1
2
2
1
1
2
2
1
2
2
1
1
1
1
1
1
2
2
2
1
2
1
2
1
0
1
1
1
2
1
0
1
1
1
0
2
1
0
1
1
1
0
1
1
1
2
1
1
1
2
1
1
0
2
1
0
1
1
1
2
1
1
1
2
1
0
1
2
2
2
2
2
2
0
1
1
1
2
1
1
0
0
1
1
1
1
2
1
0
0
0
2
1
0
1
1
1
0
1
0
2
2
1
2
1
1
1
1
0
1
0
0
1
1
1
2
1
1
0
2
2
2
1
2
2
2
0
2
1
2
1
2
1
1
1
1
2
1
1
1
3
1
1
1
0
1
0
1
2
1
2
2
1
1
2
1
1
2
1
2
2
0
1
1
1
1
0
1
1
1
2
2
1
1
2
1
0
1
1
1
1
2
1
1
2
1
1
0
1
1
1
1
2
0
1
1
1
0
0
2
0
1
1
1
1
1
0
1
1
1
2
2
1
1
1
2
1
1
1
1
0
1
1
0
2
0
1
0
2
0
1
1
1
0
2
1
1
2
2
1
2
1
2
1
1
1
0
0
1
1
0
1
1
2
1
2
0
2
2
1
1
2
1
2
0
1
1
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
2
2
2
1
2
0
1
1
1
1
1
2
2
2
1
2
0
1
2
0
1
0
2
2
2
1
2
1
2
1
1
1
1
0
0
1
2
1
2
1
1
1
1
0
1
2
1
1
1
1
1
1
1
1
2
0
1
1
0
2
1
1
2
2
1
1
1
2
0
1
1
1
1
1
1
0
2
2
3
0
1
0
1
2
2
1
1
1
1
1
1
1
0
1
1
2
1
2
0
1
3
1
0
1
1
2
1
2
2
0
1
2
0
2
1
0
1
1
1
2
2
2
1
1
1
2
1
0
1
1
1
0
2
1
1
1
2
1
2
1
2
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
0
1
0
2
2
2
1
0
2
1
1
1
1
1
0
2
2
2
2
0
2
1
1
0
1
0
1
1
1
2
2
0
2
1
1
2
2
0
1
1
0
1
1
1
2
2
1
1
0
1
0
2
2
0
1
1
1
1
0
2
2
1
0
1
2
2
1
0
1
1
1
1
1
1
2
0
2
1
0
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
0
1
1
1
1
2
0
1
1
1
2
1
1
2
2
2
1
1
1
1
0
1
1
1
1
1
1
1
1
2
2
0
1
1
1
0
2
0
1
1
0
1
2
2
2
0
2
1
1
1
1
1
2
1
2
1
0
1
1
1
0
1
1
0
1
1
0
1
2
0
2
2
1
0
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
2
0
0
1
2
2
1
1
0
1
2
0
1
2
1
1
0
1
1
1
1
2
2
1
1
1
2
1
2
1
0
2
1
1
1
2
1
1
1
2
1
1
1
1
1
1
0
2
1
1
1
1
1
1
1
0
2
2
1
0
1
1
1
0
1
1
0
2
2
1
1
2
1
1
0
1
1
1
0
1
1
2
1
1
2
0
1
0
1
2
1
1
1
2
1
1
1
1
1
0
1
2
1
1
2
1
1
0
1
1
1
1
1
1
1
1
1
0
1
2
1
1
1
1
0
1
1
1
0
1
1
0
1
2
2
1
1
1
1
0
1
0
0
1
1
0
1
1
0
0
1
2
1
1
0
1
2
2
1
1
1
1
0
0
1
1
1
2
0
1
2
1
1
1
1
2
2
1
1
1
2
1
1
1
1
3
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
2
1
1
1
2
1
0
1
1
1
1
1
1
1
1
1
1
0
1
1
1
2
0
1
2
2
1
1
1
1
1
0
1
2
0
1
1
1
1
2
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
2
2
1
2
0
2
1
0
1
1
2
2
1
0
0
0
1
1
0
1
2
0
1
1
1
1
1
2
2
1
2
0
1
1
1
0
1
2
1
1
3
1
0
1
2
1
1
1
2
1
1
1
0
0
2
1
2
1
1
1
1
1
1
1
0
1
2
0
1
1
1
1
1
1
1
1
1
0
2
0
2
3
1
1
2
1
2
1
1
1
1
1
1
1
1
0
1
0
0
1
0
1
1
2
0
1
2
1
1
1
1
1
1
2
0
1
1
1
1
1
1
1
1
0
1
1
2
1
2
1
1
1
1
1
2
0
2
1
0
1
1
1
2
2
0
1
0
1
1
1
1
1
1
1
2
1
2
1
2
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
0
2
1
2
1
1
1
1
0
1
1
1
1
1
2
1
1
2
2
4
1
0
1
1
1
1
1
2
1
1
2
1
1
1
1
2
2
1
2
1
1
1
1
2
2
1
1
2
0
1
2
1
2
1
1
1
1
2
1
1
2
1
0
2
1
2
2
1
2
1
1
1
1
1
1
2
0
1
1
1
1
1
2
2
1
1
1
1
1
0
1
1
2
1
0
0
1
2
1
2
1
2
0
1
1
0
1
1
1
2
1
1
2
1
2
0
2
1
0
2
1
1
2
2
1
0
1
1
1
2
1
0
1
1
0
2
1
1
1
1
1
1
2
2
1
1
1
1
1
2
2
1
1
1
2
0
1
2
1
0
2
1
1
1
1
1
1
2
2
0
1
1
1
1
1
2
2
1
1
1
1
0
2
2
1
2
2
2
2
1
0
1
1
2
0
1
1
1
2
2
1
1
1
1
1
1
2
1
2
1
1
2
0
1
1
0
1
2
1
2
2
2
2
1
0
2
0
1
0
1
0
1
1
2
1
2
1
2
1
2
1
2
1
1
2
0
1
1
1
1
1
0
2
1
0
2
1
2
0
0
1
2
1
0
1
1
1
2
1
1
1
1
1
1
2
1
2
1
1
1
2
2
0
1
1
2
1
1
0
1
1
0
2
2
1
1
1
0
1
1
2
2
1
2
0
1
0
1
1
1
1
2
1
1
1
2
1
2
2
1
1
2
1
0
2
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
2
0
1
1
1
0
2
1
1
2
1
1
2
2
1
2
1
1
0
2
1
1
1
2
1
0
1
2
1
1
1
1
2
1
0
1
1
2
1
1
1
1
2
1
2
2
1
1
1
0
1
1
1
1
1
1
2
1
1
0
1
0
1
0
3
1
1
1
1
1
1
1
1
1
1
2
0
2
1
1
1
1
0
1
2
5
1
2
0
1
1
2
1
2
1
1
1
1
2
0
2
1
2
1
0
2
2
1
1
1
1
2
1
0
1
1
1
2
1
1
1
1
0
1
0
0
1
2
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
0
0
3
1
1
1
1
1
2
1
1
1
0
2
2
0
0
1
1
2
2
1
2
1
2
1
0
0
1
0
1
2
1
0
0
1
1
1
0
0
1
0
1
2
2
1
1
1
1
2
1
1
1
1
1
2
1
0
2
1
2
1
0
1
1
1
1
1
2
1
1
1
2
1
2
0
1
0
0
1
1
0
1
2
1
1
2
1
1
1
3
0
1
2
1
2
2
1
1
2
2
1
0
1
0
2
2
1
1
2
1
1
1
2
1
1
1
1
2
0
1
1
1
1
1
0
1
2
1
0
1
1
2
2
1
1
1
1
0
1
0
1
1
1
1
1
1
2
2
1
1
1
2
1
2
1
0
1
1
1
0
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
0
0
1
2
1
1
0
1
1
1
1
2
1
0
0
1
1
1
2
2
2
1
2
1
1
2
0
1
1
1
2
2
1
2
2
1
2
1
0
1
1
1
2
1
2
2
1
0
1
1
0
1
1
1
1
2
1
1
1
0
1
1
1
1
1
2
0
2
1
1
2
0
2
1
1
0
1
0
0
1
2
1
1
1
2
1
0
2
1
2
1
1
1
1
1
1
2
1
1
0
1
2
1
2
1
1
1
2
1
1
1
2
2
2
1
1
0
2
1
0
1
1
1
1
2
1
1
0
1
1
3
2
1
1
1
1
1
1
1
0
1
1
0
1
2
1
1
1
2
1
1
1
2
2
1
0
2
1
1
1
2
1
1
1
1
1
2
0
2
1
1
1
1
2
2
2
1
0
0
1
1
1
2
2
2
1
1
2
1
0
1
1
1
1
1
1
2
1
2
2
0
1
2
1
2
1
1
0
2
0
0
1
2
2
0
1
1
2
2
0
1
2
2
1
1
1
2
2
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
1
2
1
2
1
1
1
0
1
1
1
1
1
1
0
2
1
1
1
1
1
2
2
1
0
0
2
1
1
4
1
2
1
2
0
2
2
0
1
0
2
2
2
2
1
0
1
1
2
0
0
1
1
1
1
3
1
1
1
0
1
2
0
1
2
1
1
1
1
1
0
1
1
1
1
0
1
1
0
1
1
2
0
0
2
0
0
2
2
1
1
1
2
0
1
0
1
1
2
0
1
1
1
1
1
2
1
1
1
2
2
2
2
1
2
2
1
1
0
1
1
1
1
0
2
1
1
1
1
1
2
1
1
1
2
1
1
0
0
1
1
2
1
1
1
1
0
2
1
0
1
1
1
1
1
2
0
1
0
0
0
2
2
0
1
0
1
1
1
1
1
2
1
1
1
1
2
0
2
1
1
1
0
1
0
1
1
2
1
0
1
1
1
1
1
1
1
1
1
2
2
0
1
0
2
1
0
1
1
0
2
2
2
1
2
1
1
2
1
1
0
2
2
2
1
1
2
1
1
2
1
2
2
1
3
1
1
1
0
0
1
1
1
2
0
1
1
1
0
1
1
1
1
1
1
1
1
1
2
2
1
1
0
1
0
2
1
1
1
2
1
1
1
1
2
1
1
1
1
0
1
1
1
1
1
0
1
1
1
1
0
1
0
1
2
1
1
0
1
1
1
1
3
0
1
1
1
1
2
1
1
1
1
1
1
1
1
1
0
1
2
1
0
1
2
1
0
1
1
2
1
0
2
1
2
1
1
1
1
0
1
1
1
3
1
2
1
2
2
1
0
0
2
2
1
1
1
1
1
2
2
1
1
1
0
1
1
1
1
2
2
2
1
2
2
1
1
1
1
0
2
1
2
2
1
1
1
2
2
1
1
2
0
2
1
0
0
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
2
2
1
1
1
1
1
0
2
1
0
1
1
1
1
1
0
1
1
1
2
0
1
2
2
1
1
0
0
1
2
0
0
1
0
1
1
1
2
1
0
0
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
0
1
2
2
2
1
1
1
1
1
1
1
0
0
2
1
1
1
1
2
1
2
1
1
2
0
2
2
0
1
2
1
1
1
1
1
1
1
2
1
1
1
1
0
0
1
2
1
1
1
1
1
1
1
2
1
2
1
2
1
1
1
1
2
2
0
2
1
1
2
0
1
1
1
2
1
1
2
1
2
2
2
1
1
1
2
1
0
2
0
2
2
1
2
2
2
1
2
1
1
2
1
1
1
1
2
1
1
2
0
1
1
1
1
0
2
1
1
0
1
1
1
2
1
1
1
1
2
1
3
2
0
0
2
1
1
2
1
2
2
1
0
1
2
1
1
1
1
2
1
2
2
0
2
2
0
1
0
2
1
0
2
2
1
1
1
1
1
1
0
0
0
0
0
1
1
1
2
1
1
2
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
0
2
1
1
2
1
0
1
2
1
2
0
1
2
1
1
1
1
1
0
1
2
0
1
1
2
1
2
2
2
1
1
1
1
1
0
1
1
2
2
1
1
2
2
1
1
1
1
1
1
1
1
2
2
1
1
0
2
1
2
1
1
1
0
4
1
1
2
3
1
1
2
2
2
1
2
0
1
1
1
2
1
0
1
1
1
1
2
1
0
1
1
1
0
2
1
1
1
1
1
0
1
1
2
1
1
1
1
2
1
2
0
1
1
0
1
0
1
1
0
1
2
2
2
1
1
1
1
2
1
1
1
1
1
1
0
1
1
1
1
1
2
1
1
0
1
2
1
1
1
1
0
1
1
1
0
1
1
2
0
1
0
1
0
1
1
1
0
1
1
1
2
3
1
1
0
0
1
1
2
3
1
1
1
1
1
1
0
1
2
2
1
1
2
1
1
1
1
1
1
1
2
1
2
2
1
1
1
0
2
1
0
1
1
1
1
1
1
1
2
1
1
0
2
1
1
0
1
1
2
1
0
1
0
1
2
1
0
1
0
2
1
2
1
1
0
3
1
1
2
1
0
1
1
1
0
2
0
1
1
1
1
0
0
1
1
1
1
1
2
2
1
2
2
0
1
1
2
1
2
1
0
1
0
1
2
1
2
1
3
1
1
0
2
1
1
1
0
1
1
1
1
1
2
2
1
1
1
1
1
2
2
0
1
1
1
2
2
1
1
1
2
1
1
1
1
2
1
1
0
1
2
2
1
1
2
0
0
0
1
2
0
1
1
2
1
0
2
2
1
0
1
2
1
1
2
1
0
1
1
1
0
2
1
2
0
1
1
0
1
1
1
2
0
2
1
1
1
2
1
1
2
1
0
1
1
2
1
2
2
1
1
1
1
1
1
1
2
1
1
2
1
2
2
0
1
1
1
1
1
3
1
1
2
1
2
1
1
1
1
1
1
1
2
0
1
1
1
2
1
0
1
1
1
0
2
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
0
2
1
0
2
2
1
0
2
1
2
1
2
1
2
1
1
3
1
2
1
2
1
1
2
1
1
1
2
1
2
1
1
1
1
1
2
1
1
0
1
2
0
1
1
1
2
1
1
1
1
2
1
2
1
2
2
3
0
2
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
1
1
2
1
2
1
1
0
1
2
1
1
2
1
1
1
2
1
2
2
2
1
1
2
2
1
2
0
0
0
0
0
0
2
2
1
0
2
0
1
1
2
1
0
2
1
1
1
0
0
0
1
0
1
1
2
1
1
2
1
1
1
1
3
3
1
1
1
1
1
2
1
0
1
0
0
1
0
1
1
1
1
2
1
2
2
2
1
2
1
1
1
0
1
1
1
1
1
1
2
1
1
1
2
2
1
1
1
2
1
1
1
1
2
1
1
0
1
1
2
0
2
2
1
1
2
2
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
0
2
2
2
1
1
1
2
2
1
1
1
1
1
2
2
1
1
1
1
0
1
2
0
2
2
0
1
0
0
1
2
2
2
0
1
1
0
2
0
1
1
2
0
1
1
2
1
1
1
1
0
1
1
1
1
0
2
0
2
1
0
2
1
1
0
1
1
2
2
1
0
1
1
0
1
3
1
1
0
1
0
1
1
2
0
1
0
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
0
0
1
1
1
8
2
1
2
2
1
1
2
1
2
2
0
1
1
2
1
1
0
2
1
1
0
1
1
1
1
2
0
1
1
1
1
0
1
1
1
2
0
1
1
1
1
2
1
2
1
1
1
0
2
0
0
1
2
1
1
3
1
2
1
2
1
1
2
0
3
2
0
1
1
2
1
1
0
1
1
2
2
2
1
2
1
1
2
1
0
2
0
1
1
1
0
1
1
1
1
1
1
2
2
2
1
2
2
2
2
1
1
1
1
2
0
2
1
1
1
1
1
1
2
1
0
0
0
1
1
1
2
1
1
1
1
1
0
1
1
1
1
1
1
0
1
1
2
1
2
1
1
1
1
1
1
2
1
0
1
1
1
2
1
1
2
1
1
0
0
1
1
1
2
1
1
0
2
0
1
1
1
0
0
1
1
1
2
3
1
1
1
1
1
2
1
2
2
2
1
0
1
2
1
1
1
1
1
1
0
1
1
1
2
1
1
1
2
1
1
2
2
0
1
1
1
1
2
1
0
1
0
1
1
1
2
1
1
1
2
0
0
2
2
0
1
2
1
0
0
2
1
2
1
0
1
2
2
0
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
0
0
2
2
2
1
1
1
1
1
2
2
0
0
1
1
1
1
0
1
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
0
2
1
1
1
2
1
1
2
1
1
1
1
1
0
1
2
1
1
2
1
0
1
2
1
1
0
1
2
2
1
1
1
2
2
2
0
2
2
1
1
0
1
1
1
1
1
2
2
1
1
1
1
2
1
0
2
2
1
2
0
1
1
0
2
1
1
1
2
1
2
1
2
1
0
2
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
0
2
2
1
1
2
1
1
1
1
0
0
2
0
0
2
1
1
1
0
1
1
1
1
2
2
2
1
0
0
2
1
2
0
1
1
2
1
1
1
1
1
1
1
1
1
1
2
2
1
1
0
1
2
1
2
1
1
1
1
1
0
1
1
0
0
2
1
1
1
0
1
1
1
2
0
2
1
1
2
1
1
1
1
1
0
1
1
1
1
1
0
1
1
1
1
2
1
2
0
2
2
2
1
2
2
2
1
0
2
2
1
0
2
0
0
1
1
0
1
1
2
1
2
1
1
1
1
0
1
0
0
1
1
1
2
1
2
2
1
1
2
1
1
1
1
0
2
0
1
0
1
2
1
2
0
1
2
1
2
2
1
1
1
1
2
1
0
1
1
1
1
1
0
1
1
1
0
0
1
2
0
1
1
1
1
1
1
0
1
1
2
0
2
1
2
0
2
0
1
1
2
0
1
1
0
2
1
1
1
1
1
1
2
1
1
1
1
1
0
2
1
1
1
0
1
1
1
0
0
1
1
2
1
1
1
1
2
2
0
1
0
2
1
0
1
2
1
1
1
1
1
0
0
2
1
2
2
1
1
0
1
0
1
1
1
1
0
2
2
1
1
1
2
1
1
2
1
1
1
1
1
1
1
2
2
0
1
0
1
1
1
1
1
1
2
2
2
1
1
3
2
1
1
1
1
2
2
1
2
1
2
2
0
2
1
1
2
1
2
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
1
1
2
2
1
0
2
1
2
1
1
1
2
1
1
0
2
1
0
2
1
2
1
2
1
1
0
2
1
2
2
1
1
1
2
0
1
1
2
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
2
1
1
2
1
1
0
2
1
2
2
2
1
1
2
1
2
2
1
1
1
1
0
1
1
1
0
1
3
1
1
1
2
1
2
1
1
1
1
0
2
1
3
0
1
1
1
1
1
1
1
1
2
1
2
1
0
2
1
1
1
1
1
0
2
1
1
2
1
1
2
3
2
1
1
2
1
1
1
1
0
1
2
1
1
1
0
3
2
1
1
0
2
1
2
0
2
0
2
1
2
1
2
2
0
2
1
1
1
1
2
1
1
1
1
0
2
1
2
2
0
1
2
1
1
1
0
2
1
0
1
2
1
1
1
1
0
1
1
1
0
2
1
1
1
1
1
1
1
0
1
2
1
2
2
1
1
1
0
1
1
1
1
2
2
2
0
1
1
2
0
1
0
1
1
2
2
1
1
2
1
1
1
1
1
1
2
1
2
0
2
2
1
1
0
2
1
1
0
1
0
1
1
1
3
1
1
1
2
2
2
1
2
2
0
2
1
1
1
1
1
2
1
1
2
2
1
2
0
2
1
2
2
1
0
1
1
2
2
1
1
1
1
0
0
1
0
2
2
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
0
1
0
1
1
2
2
0
1
1
2
1
2
1
1
2
1
1
1
2
0
2
1
1
0
1
1
1
1
1
2
1
1
1
0
2
1
2
1
1
1
1
2
2
1
1
1
2
1
1
1
1
1
2
1
2
1
2
1
1
1
0
0
0
2
2
1
1
1
1
1
2
2
2
0
2
0
1
1
0
0
1
2
1
1
1
1
1
1
2
2
2
1
1
1
2
1
1
2
1
2
1
1
1
1
2
1
0
1
0
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
0
1
0
1
1
1
2
2
2
1
1
1
1
1
0
1
1
1
1
2
2
1
1
0
0
0
2
1
1
1
2
2
1
1
1
1
0
0
1
1
2
2
0
0
1
1
1
1
2
0
2
1
2
1
1
2
2
2
1
2
1
0
1
1
1
2
1
2
0
1
2
1
2
1
1
1
2
0
0
1
1
1
2
1
0
1
1
1
1
1
1
2
2
1
1
0
2
1
1
2
2
2
1
1
2
1
1
0
1
2
1
1
2
0
1
0
0
0
1
1
1
1
0
2
2
1
0
1
1
1
1
1
2
1
0
0
2
1
2
1
2
1
1
0
1
1
1
2
1
0
1
1
2
1
1
1
2
1
2
0
1
1
1
1
2
1
2
1
1
1
1
2
1
2
1
1
2
2
1
1
1
1
1
2
0
1
2
1
2
2
1
1
2
1
1
0
1
0
2
1
2
2
0
1
1
1
1
1
2
0
1
1
1
2
1
1
1
1
1
1
1
0
1
2
1
1
0
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
0
2
2
1
2
2
1
1
2
0
1
0
2
1
1
1
1
2
1
2
2
2
1
2
0
2
2
1
1
1
1
1
2
1
2
2
2
1
1
1
1
1
1
0
1
1
0
2
1
0
2
0
1
0
1
1
2
2
1
1
1
1
2
1
1
1
1
0
1
1
1
2
1
1
1
1
1
0
2
2
2
1
1
2
1
2
1
1
1
1
1
1
1
1
1
0
1
2
2
2
2
1
2
2
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
2
1
1
1
2
2
1
2
1
2
0
1
1
1
2
2
1
1
1
0
1
0
1
2
1
1
1
2
1
0
1
2
0
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
0
1
1
1
2
1
1
2
1
2
2
1
0
1
2
2
2
1
1
0
0
1
0
0
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
2
1
1
1
1
1
1
1
1
0
0
1
1
1
1
1
2
2
0
1
1
2
1
2
0
1
1
1
1
2
1
1
1
1
1
2
1
2
1
1
2
0
0
1
2
1
1
1
1
2
0
1
2
1
1
1
1
2
2
1
1
2
0
2
2
2
1
0
1
2
1
0
2
1
1
1
1
1
1
2
1
1
1
1
1
0
0
1
1
2
0
1
1
2
1
1
2
1
1
1
1
1
2
1
1
1
0
1
1
1
1
1
1
2
1
0
1
1
1
1
2
2
4
1
2
0
1
2
1
2
1
0
1
1
1
2
1
1
1
2
2
1
1
1
0
0
1
1
1
1
1
1
1
2
2
0
0
1
1
1
2
1
1
2
0
1
1
2
1
2
1
1
1
1
1
1
2
3
1
1
0
1
2
2
2
1
1
0
1
1
1
1
2
0
1
2
1
2
1
1
2
1
1
0
1
1
1
1
0
1
1
2
1
0
1
2
1
1
1
1
1
1
2
1
0
0
2
0
1
0
1
2
1
1
2
1
1
0
1
1
1
2
2
1
0
2
1
2
1
0
2
1
2
0
2
1
1
0
1
2
1
2
1
1
2
1
2
2
2
0
1
1
1
2
1
1
2
1
1
1
1
0
1
1
1
2
2
0
1
1
2
2
2
1
1
1
1
0
0
1
1
1
2
0
2
2
1
1
2
1
0
2
2
2
0
0
1
1
1
2
1
1
1
1
1
1
2
1
0
0
0
2
1
1
1
1
1
1
1
2
1
1
0
1
1
1
1
2
2
2
1
2
2
0
0
1
1
2
1
1
3
1
2
1
0
2
2
2
1
1
1
1
3
1
2
1
2
1
2
1
3
2
0
0
1
1
1
2
1
1
1
1
2
1
1
1
0
0
1
0
2
1
1
1
2
2
3
2
0
0
1
1
0
2
1
1
1
1
2
2
1
1
0
1
1
0
1
1
1
0
2
2
1
1
1
4
1
1
0
1
2
2
2
1
1
2
0
1
0
1
0
2
2
1
1
1
2
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
0
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
0
1
2
2
1
2
1
2
2
0
1
1
1
2
1
2
1
2
2
2
1
0
2
2
0
1
1
1
1
2
2
0
1
1
1
0
2
1
0
1
1
1
1
2
1
1
1
1
1
0
2
1
1
1
1
0
2
2
1
2
1
1
2
1
1
1
1
1
1
2
1
2
0
1
1
1
1
2
1
1
1
1
1
1
1
1
0
2
0
1
2
0
1
0
2
2
2
0
1
1
2
2
1
0
1
1
1
1
2
1
1
0
1
2
1
0
1
1
2
2
2
1
0
1
1
1
2
2
1
0
1
2
2
1
1
1
2
1
0
3
1
1
2
1
1
0
1
2
1
2
0
1
0
1
2
1
1
2
1
1
1
1
0
1
1
2
1
1
2
0
2
1
2
2
1
1
1
0
2
0
1
1
1
2
1
1
1
2
1
0
2
2
1
1
1
1
0
1
1
1
2
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
0
1
1
1
1
2
2
1
1
0
1
2
0
1
0
2
1
1
1
1
1
2
2
0
2
1
1
2
1
1
1
1
0
1
1
0
2
0
1
1
1
0
2
1
2
1
1
2
0
3
1
2
1
1
1
1
2
0
1
1
1
2
1
1
2
1
1
1
1
2
1
1
1
1
1
2
1
2
0
2
1
1
1
2
1
2
1
1
2
1
1
1
1
1
1
1
1
2
2
0
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
2
2
1
1
1
1
0
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
0
1
1
0
0
1
1
2
1
2
1
1
2
0
0
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
2
2
1
2
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
0
1
1
1
1
1
2
0
1
1
5
1
1
1
1
2
1
1
3
2
2
1
1
0
1
1
1
2
2
2
1
1
0
2
1
2
1
0
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
2
2
2
2
2
1
1
0
1
2
1
0
1
0
1
0
1
2
1
1
1
2
2
0
1
2
2
1
1
1
2
1
2
2
2
1
1
2
1
0
1
1
1
3
1
1
1
1
0
0
2
1
1
2
1
2
2
2
2
1
1
2
1
1
1
0
1
1
1
1
1
1
1
2
1
1
0
1
1
2
1
2
1
0
1
1
1
1
1
0
0
2
1
2
2
1
4
1
1
0
1
1
1
1
1
1
1
2
2
1
2
1
1
1
0
0
2
2
1
1
1
0
1
2
2
2
2
2
1
1
1
1
1
1
1
1
1
0
0
2
0
1
1
2
1
2
2
1
1
0
1
1
1
1
1
2
1
1
1
0
2
0
1
1
1
1
2
1
2
2
1
0
0
1
2
1
2
1
2
1
1
1
0
1
0
1
1
2
2
2
1
1
2
1
1
2
2
1
1
1
0
2
1
1
1
2
1
1
1
0
1
1
1
0
1
1
1
1
1
1
1
2
2
1
1
1
0
1
1
1
2
1
1
2
2
1
1
1
1
1
1
2
1
1
2
2
0
2
2
3
2
1
1
1
1
1
1
2
1
1
2
2
0
1
1
1
1
1
0
1
1
1
1
2
1
2
2
1
1
2
1
1
2
1
1
1
2
0
3
1
1
1
1
1
2
1
1
1
1
0
2
1
2
1
2
2
1
0
1
1
1
1
1
0
2
2
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
0
1
1
1
1
2
2
0
1
1
2
0
1
1
1
1
1
0
0
1
2
0
1
1
2
1
2
2
1
1
0
1
2
2
0
2
2
1
1
0
0
2
1
1
1
0
1
2
1
1
2
1
1
2
1
2
1
1
0
1
1
2
1
1
2
2
1
0
2
0
1
2
1
1
2
0
2
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
2
0
1
1
1
1
2
1
2
0
1
1
1
2
2
0
1
2
2
1
1
2
1
1
1
1
2
1
2
1
2
1
0
2
0
1
1
1
0
1
2
1
1
2
1
1
1
2
1
1
1
2
1
1
1
2
1
2
2
1
1
2
0
1
2
1
2
0
1
1
0
2
2
2
1
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
0
1
2
1
1
2
1
1
1
1
0
1
1
0
1
0
0
1
0
2
1
2
2
2
2
1
2
0
2
1
1
2
1
1
1
1
1
0
2
2
2
1
2
2
1
0
1
1
1
1
2
2
1
2
1
1
0
1
0
1
1
1
1
2
2
1
1
2
1
1
0
1
1
1
2
2
1
1
1
1
1
0
2
2
1
1
1
1
1
2
2
1
1
1
1
2
2
2
1
2
1
1
2
1
0
1
2
2
1
1
1
1
1
4
1
1
2
0
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
2
1
2
2
2
1
1
1
1
1
0
1
1
2
0
2
1
1
1
0
0
1
1
1
1
2
0
0
1
1
1
2
1
2
2
0
1
1
2
2
1
1
0
2
2
1
2
1
2
1
1
1
1
0
0
1
2
2
1
2
1
2
1
0
1
1
1
1
2
2
2
2
1
1
1
2
1
2
1
0
0
1
1
2
1
2
0
1
1
1
1
1
2
1
1
2
1
1
2
0
2
2
1
2
1
1
2
1
1
1
2
1
1
0
1
0
1
0
1
1
1
1
0
1
1
1
1
2
2
2
2
2
1
1
2
1
1
1
1
1
1
1
1
2
1
2
1
2
1
1
1
1
1
1
2
1
1
2
1
1
1
1
0
2
2
1
1
1
0
1
1
0
1
2
1
1
2
1
1
1
1
0
1
1
2
1
0
1
1
2
2
1
1
1
0
1
1
1
1
2
1
2
0
1
0
2
0
1
0
2
1
1
1
1
1
1
2
0
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
0
1
1
1
1
1
2
1
2
1
1
1
1
1
2
2
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
2
0
2
1
1
1
2
1
1
1
0
2
1
1
2
1
1
1
1
2
2
1
2
2
2
2
1
1
1
1
1
0
1
1
2
0
1
0
3
1
1
1
0
2
1
0
2
1
0
2
1
1
1
1
1
2
1
2
0
1
1
1
0
2
1
1
1
1
1
1
1
1
0
2
1
1
1
1
2
1
2
1
0
2
1
1
0
2
0
1
1
1
2
1
2
1
1
1
0
1
0
1
0
1
0
1
0
0
1
2
1
2
2
2
1
1
1
2
2
2
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
2
3
0
1
1
2
2
1
1
1
2
2
1
1
1
0
1
1
0
0
2
2
1
1
1
1
1
2
1
2
2
0
1
1
1
1
2
1
1
1
2
1
1
0
1
2
1
1
2
1
1
2
1
2
2
1
0
1
1
0
2
1
1
1
1
2
2
1
1
1
1
1
1
1
0
1
1
2
1
2
1
2
1
1
1
1
1
1
2
1
2
2
1
1
1
2
2
2
1
0
1
1
1
1
2
2
1
1
1
2
1
2
1
1
0
2
1
2
1
2
1
2
1
2
2
2
2
1
1
1
1
1
1
2
1
1
1
2
2
2
1
1
0
1
1
1
0
1
1
1
1
0
2
1
1
0
0
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
2
1
0
2
1
2
1
1
1
1
1
1
1
1
1
1
2
2
0
0
1
2
2
1
1
1
2
1
1
1
1
1
2
1
2
2
1
1
1
1
0
2
1
1
1
1
0
1
0
0
0
1
1
1
0
0
1
2
2
1
1
2
2
1
2
1
2
2
1
1
2
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
0
1
1
1
1
0
1
0
2
1
2
1
0
1
1
2
2
0
1
0
1
1
1
1
3
2
1
2
2
1
1
2
1
0
1
2
1
1
1
1
1
2
2
2
0
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
0
1
0
1
1
1
1
1
1
1
1
2
1
0
1
2
1
1
0
2
1
1
1
1
1
0
2
2
1
1
1
2
0
1
0
1
2
0
2
2
1
1
2
2
1
2
1
1
0
0
1
1
2
1
0
2
1
1
1
1
0
0
0
2
1
1
1
1
1
2
1
1
1
1
0
1
2
1
1
2
1
0
0
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
0
0
1
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
2
0
2
1
1
2
0
2
1
2
1
1
1
1
1
1
1
2
2
1
2
2
0
0
1
2
1
2
2
2
0
1
1
1
1
2
1
0
2
1
2
2
1
1
1
2
0
2
1
1
0
1
0
0
2
2
0
0
1
1
2
1
0
2
1
1
1
2
1
1
1
1
1
1
1
1
1
0
1
2
2
2
1
1
1
1
1
2
0
2
1
1
1
1
2
0
0
1
2
1
1
1
0
2
1
1
1
2
1
2
2
2
1
2
1
1
0
0
2
1
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
2
1
1
1
2
1
1
1
1
2
1
0
1
0
0
2
1
1
1
2
2
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
0
1
0
0
1
1
1
2
1
2
1
1
1
0
1
0
1
0
1
0
2
1
1
1
1
1
0
5
0
1
2
1
1
2
0
2
1
1
1
2
2
2
1
1
1
1
2
2
0
2
0
1
1
1
1
1
1
1
1
1
2
1
0
2
1
1
1
1
1
0
2
2
1
1
2
1
1
2
1
1
1
2
2
2
1
1
1
2
1
1
1
1
1
2
0
2
0
1
1
0
2
2
1
1
1
1
1
1
1
0
2
1
1
2
0
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
2
1
1
1
1
0
1
1
1
2
1
1
2
1
1
1
1
1
0
1
2
2
1
2
1
1
1
2
2
1
1
2
1
1
2
1
1
2
1
1
2
2
0
2
3
1
1
1
2
1
0
0
2
1
2
1
1
1
1
2
1
1
1
2
2
1
1
1
2
1
2
1
1
1
1
2
1
1
0
1
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
0
2
0
1
1
1
1
1
2
1
0
1
2
0
1
2
1
1
1
2
2
1
0
1
0
1
2
1
2
2
1
1
1
1
2
1
1
1
2
1
0
1
2
2
2
0
0
3
1
2
1
1
2
1
1
1
1
0
1
1
1
2
0
0
1
1
1
2
2
2
1
1
2
2
1
1
1
2
1
2
1
1
1
1
1
2
1
1
3
1
2
1
3
0
1
2
0
0
1
0
1
2
1
2
1
0
0
2
1
1
1
1
1
1
1
1
1
2
1
1
1
0
1
2
1
1
1
1
1
1
0
1
1
1
1
1
2
1
1
2
1
2
1
2
1
2
1
1
1
1
1
1
2
2
1
2
2
1
1
1
1
0
0
0
0
0
1
2
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
1
0
1
0
3
1
2
0
1
2
1
2
1
2
1
2
0
1
1
2
1
0
2
1
1
2
1
2
1
1
1
1
1
1
2
2
1
0
2
0
0
2
1
1
2
1
0
2
2
1
1
0
1
1
2
2
1
2
2
1
1
1
1
0
2
1
1
2
1
1
0
0
1
0
1
2
0
1
2
0
1
1
1
1
1
1
1
1
1
1
2
0
2
2
0
0
1
2
1
0
1
2
2
1
1
1
1
1
1
1
1
1
0
1
2
1
1
2
2
1
1
0
1
1
1
0
1
1
2
1
0
1
1
2
2
1
2
2
1
1
1
1
3
2
1
1
2
1
2
0
1
1
2
1
2
1
0
1
1
0
2
1
1
1
0
1
2
1
2
2
1
2
2
2
1
1
1
1
1
1
1
1
0
1
1
1
1
0
2
1
1
0
1
1
2
1
1
2
1
1
2
2
7
0
1
2
1
1
1
1
2
2
2
2
1
1
1
0
0
1
2
0
1
1
1
2
0
1
1
1
1
2
2
2
2
2
2
1
1
1
1
2
2
0
1
2
1
1
1
1
1
0
0
1
2
1
1
1
1
1
1
0
2
1
1
1
0
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
0
2
0
0
2
0
1
2
1
1
2
0
1
2
1
1
2
2
1
2
0
1
2
2
1
1
1
2
1
1
2
2
1
1
1
1
1
1
2
1
2
1
2
0
2
1
1
1
1
0
1
2
1
1
2
1
1
1
1
2
1
1
0
0
1
2
1
2
2
1
0
1
1
1
1
1
2
2
0
1
0
0
1
2
0
1
2
2
1
1
1
1
2
0
1
2
2
1
1
2
1
2
2
1
2
1
2
2
1
0
1
2
1
1
1
1
1
1
1
1
1
1
0
1
1
0
1
0
2
1
1
1
2
2
1
2
2
2
1
2
1
2
1
1
0
0
1
1
1
1
1
1
1
2
0
0
2
2
1
1
1
1
1
2
1
1
1
1
1
1
1
0
0
1
2
3
0
1
1
1
2
1
1
1
0
1
2
0
1
2
1
1
0
1
1
1
0
1
1
1
0
1
2
0
0
0
1
1
0
1
2
1
1
1
1
1
0
1
1
2
1
2
1
0
2
1
1
2
1
1
2
1
1
1
1
1
1
1
1
2
0
2
1
0
2
1
1
1
0
1
1
1
2
2
1
2
0
1
2
1
1
2
0
1
1
1
1
1
1
1
1
1
1
2
0
0
2
1
0
2
2
2
1
0
1
1
1
2
2
1
1
1
1
2
2
1
2
1
1
2
2
1
1
0
2
2
1
0
1
1
2
2
1
1
1
1
1
1
2
1
1
3
0
2
0
2
1
0
0
1
2
2
2
2
1
2
1
1
2
0
0
2
1
1
2
0
1
1
1
1
1
1
1
1
2
1
1
1
1
1
0
0
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
0
2
2
1
1
2
1
1
1
1
0
1
1
1
1
1
1
0
1
0
1
1
1
1
1
1
0
0
1
1
1
1
1
2
2
1
1
1
0
1
2
1
2
1
0
0
2
0
1
1
1
1
0
2
1
1
1
1
2
1
1
1
2
2
1
1
1
0
1
0
2
1
0
0
0
2
0
1
0
0
1
1
1
2
2
1
2
2
1
1
1
1
2
1
1
2
2
1
1
2
1
1
0
0
2
1
0
2
1
0
1
1
1
1
0
1
1
1
2
1
1
2
1
1
1
0
1
1
2
1
1
1
2
1
0
1
2
0
0
2
2
1
1
2
1
2
1
1
2
1
1
2
1
2
1
2
0
1
2
2
1
1
1
1
1
0
1
1
1
1
1
1
0
1
1
2
2
1
1
2
1
0
0
1
2
1
1
0
1
2
1
1
2
1
1
2
1
1
1
1
0
1
1
1
0
1
2
2
1
2
1
1
1
1
1
0
0
1
0
1
2
1
0
2
1
2
2
1
1
0
1
1
1
2
0
1
0
1
1
1
2
1
1
1
0
1
1
1
1
1
1
0
0
1
0
0
1
1
1
1
0
1
1
2
0
1
2
1
2
2
0
1
0
1
1
2
2
2
0
0
1
1
1
1
1
0
1
2
1
2
1
0
2
1
1
1
1
0
1
2
0
1
1
2
1
1
2
1
1
1
4
2
1
1
2
2
1
1
1
1
1
2
2
1
1
1
1
1
1
0
1
2
1
1
1
2
1
1
1
0
1
2
1
1
0
0
1
1
1
2
1
0
0
3
1
1
0
0
2
1
1
0
2
0
1
1
2
2
1
1
1
1
2
2
0
0
1
0
2
2
1
1
1
0
1
1
1
1
1
2
1
1
1
1
0
2
0
0
2
2
2
1
1
1
0
1
1
2
1
1
1
2
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
2
2
1
2
0
2
1
1
1
1
2
1
1
0
1
2
1
0
0
1
2
1
3
3
4
1
1
1
1
0
1
2
1
0
2
1
0
1
1
2
2
1
1
2
0
1
1
0
1
1
2
0
1
1
1
1
1
0
0
1
1
1
2
2
2
0
0
0
1
1
1
1
1
1
2
0
2
1
1
0
1
1
0
1
2
1
1
1
1
2
1
1
1
2
2
1
2
0
2
1
1
1
2
1
1
1
2
2
2
0
0
1
1
0
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
1
0
1
1
1
1
1
1
0
1
0
0
2
1
1
2
1
0
1
1
1
1
2
2
1
1
2
0
2
1
1
1
1
2
1
1
1
0
1
1
1
2
2
1
2
1
1
1
1
2
2
1
0
1
1
1
1
1
2
1
1
1
0
0
2
1
0
1
2
2
1
1
1
0
1
2
0
1
0
1
1
1
1
1
2
1
1
2
1
0
1
1
2
1
1
2
1
1
2
1
2
1
1
1
1
1
1
0
4
1
1
1
1
0
1
2
1
1
0
1
1
1
1
0
0
2
0
1
1
1
1
1
1
1
1
1
0
1
1
3
2
1
0
1
1
1
1
1
1
0
2
2
1
1
1
2
1
0
1
0
1
2
1
1
1
1
0
1
1
1
0
2
1
1
0
0
0
1
2
0
1
2
1
1
1
0
2
2
0
0
1
1
1
1
1
0
1
1
2
2
2
1
1
2
1
2
1
1
0
1
1
1
1
1
1
2
1
1
1
3
1
1
1
1
1
1
1
2
1
1
2
2
0
1
1
1
1
1
2
1
1
0
1
2
3
0
1
2
1
1
2
2
2
0
2
1
0
1
2
1
0
0
1
2
4
1
1
1
2
1
2
2
1
1
1
0
1
2
2
1
1
0
2
0
1
1
1
1
2
0
1
2
2
2
2
0
2
1
2
2
1
1
1
1
1
0
2
2
0
2
1
2
1
1
0
1
0
0
1
1
1
1
1
0
1
1
2
1
2
1
0
0
0
1
1
2
1
2
2
1
0
2
2
2
1
2
1
1
2
1
2
1
2
2
1
2
1
1
1
2
1
2
0
1
1
1
1
0
1
1
2
2
0
1
2
0
1
0
1
2
1
0
2
0
1
1
1
2
1
1
2
0
1
1
1
1
1
2
2
1
1
0
1
1
1
2
1
1
1
0
2
2
2
1
2
2
1
1
0
2
1
0
1
0
2
2
1
1
1
1
2
1
0
2
1
2
1
0
1
1
1
0
2
2
1
2
2
2
1
1
2
2
2
1
0
1
1
1
1
1
1
1
2
1
2
2
1
1
1
2
2
1
1
2
1
1
2
1
1
2
1
1
1
1
1
2
1
0
2
1
1
1
3
1
2
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
3
0
2
2
2
1
2
0
2
1
1
2
2
1
2
1
2
1
1
1
1
1
1
1
0
1
1
2
2
1
0
1
1
2
0
2
2
2
1
1
1
1
1
1
0
1
2
1
2
1
1
1
0
0
1
1
0
1
0
1
2
1
0
1
3
1
1
1
1
1
1
0
0
2
1
2
0
1
1
1
0
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
0
1
0
1
2
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
0
2
1
1
2
0
2
1
2
1
2
1
2
0
1
0
1
1
0
1
0
2
1
2
1
1
0
1
1
1
1
1
1
0
1
0
1
1
2
1
0
1
1
1
2
1
0
1
1
1
1
1
2
1
2
1
1
1
0
1
2
2
2
0
0
1
2
1
1
1
1
1
1
1
1
0
1
1
1
2
1
1
2
2
0
1
2
2
0
3
0
2
1
1
0
1
2
1
3
0
2
0
1
1
2
1
1
1
1
0
2
1
0
0
1
1
2
1
0
1
2
1
1
2
1
1
1
0
1
1
2
1
1
2
0
1
0
0
0
2
2
1
2
2
1
1
1
2
1
0
1
1
1
1
1
2
1
1
1
1
2
1
2
2
1
1
1
1
0
1
1
2
0
1
1
1
1
1
1
2
1
0
2
0
1
2
1
0
1
2
2
0
2
1
0
2
2
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
2
1
0
1
1
3
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
2
2
2
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
0
0
2
1
1
1
1
4
1
0
2
2
1
1
1
0
1
1
1
2
2
1
0
0
1
2
1
2
1
2
1
1
0
2
1
0
2
0
0
2
1
1
2
0
1
1
2
1
1
1
1
1
1
2
1
0
0
1
2
1
2
2
2
0
1
1
1
1
1
1
1
2
1
1
1
2
1
2
2
1
0
1
1
1
2
2
1
2
1
1
2
1
0
2
1
0
1
2
1
0
1
2
1
0
1
2
2
1
1
1
1
1
2
1
1
1
1
2
2
1
2
2
1
1
1
1
2
2
0
1
1
1
0
1
0
2
0
1
0
1
2
1
1
0
1
1
1
1
1
1
0
1
2
1
1
1
2
2
0
1
0
1
1
2
1
1
1
2
1
2
2
1
2
1
1
1
1
0
2
2
1
2
2
2
1
1
2
0
1
1
1
0
1
1
2
2
0
2
1
1
2
1
1
1
0
1
1
1
1
1
1
0
1
2
1
1
1
0
1
2
1
2
1
2
1
1
1
2
2
0
1
1
2
0
1
1
2
0
1
1
1
2
1
2
1
1
2
1
0
1
1
0
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
0
1
1
1
2
0
1
1
1
1
1
1
2
1
1
1
2
0
0
2
1
1
1
1
1
2
0
1
2
2
1
2
0
1
1
1
1
1
2
2
3
1
1
0
0
2
1
0
0
1
1
2
1
2
1
2
1
1
1
2
1
1
1
1
1
1
0
1
0
1
1
1
2
2
2
1
0
1
2
1
2
1
1
1
1
1
2
1
2
1
1
2
1
1
1
0
1
1
2
1
1
1
2
1
2
0
1
0
1
0
2
1
1
2
2
2
1
1
1
1
0
1
0
1
1
2
1
2
0
1
1
1
2
1
2
1
1
2
2
1
1
1
1
1
0
1
1
2
1
0
1
1
2
2
1
1
2
2
1
3
1
1
2
1
1
2
1
2
1
0
1
1
0
2
1
1
1
1
1
1
1
1
2
2
1
0
2
1
0
2
1
1
1
1
1
1
1
1
2
1
1
0
0
1
1
3
1
1
2
2
1
1
1
1
1
0
0
1
2
2
1
2
1
1
2
2
2
2
1
1
1
1
1
1
1
1
1
1
2
2
1
0
2
1
1
0
1
2
1
1
0
0
0
1
0
1
1
2
1
2
1
2
1
1
1
1
0
1
1
1
2
1
2
1
1
1
1
2
0
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
0
0
0
0
1
1
0
1
1
2
1
2
2
1
0
1
1
2
2
1
1
1
1
2
1
2
1
0
1
1
2
2
0
1
2
1
2
1
1
0
1
2
2
1
1
2
1
0
1
1
2
2
0
2
0
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
0
1
1
2
1
1
1
1
1
1
1
1
0
0
0
0
1
2
1
1
0
2
0
1
1
2
1
1
1
1
0
1
2
1
1
1
1
1
1
1
1
1
1
0
1
1
1
0
2
1
2
1
1
2
1
1
1
0
1
1
1
0
0
1
1
2
2
2
1
2
2
1
1
2
2
1
2
2
1
0
0
1
0
1
2
2
1
2
1
2
0
1
1
2
1
2
1
1
1
1
1
2
1
1
1
0
2
1
2
1
1
2
1
0
1
1
1
2
1
2
1
2
1
1
2
1
1
1
2
2
1
1
1
2
1
2
2
1
1
1
0
1
1
2
1
1
1
0
0
2
1
1
1
1
1
1
0
1
0
1
1
1
1
2
0
1
1
2
1
0
2
0
1
1
1
0
1
1
2
1
2
0
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
0
2
1
1
2
1
1
3
1
1
1
1
0
1
2
2
2
1
2
0
2
1
1
1
2
1
1
1
1
2
1
0
2
1
1
1
2
1
1
0
1
1
1
1
1
2
3
1
1
0
1
0
2
2
0
0
2
2
1
1
2
1
1
1
1
2
1
2
1
1
0
1
2
2
0
2
1
1
1
3
0
2
1
0
2
1
1
0
1
1
2
1
2
2
2
1
0
0
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
2
2
1
1
1
1
1
1
2
1
1
0
1
0
1
1
1
1
2
0
1
0
0
2
1
1
1
0
1
2
2
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
0
1
0
0
1
1
2
1
1
1
0
2
0
1
1
2
1
1
1
1
1
1
1
1
0
1
2
1
1
1
2
1
1
2
1
1
0
1
1
1
0
1
0
0
0
1
1
1
1
1
3
2
1
1
2
1
1
2
1
1
2
0
1
1
3
1
2
2
1
2
2
1
1
2
1
2
2
2
1
1
1
1
1
1
1
1
2
2
1
1
1
0
2
0
1
1
1
1
1
1
2
1
2
2
0
1
0
1
1
1
1
1
1
2
1
1
1
0
1
0
2
0
2
1
2
1
1
1
1
1
1
1
0
2
0
1
1
1
1
0
1
1
1
1
1
0
1
2
1
1
1
1
1
2
2
0
1
1
1
1
1
1
2
1
2
1
1
1
1
2
2
2
1
0
1
1
1
1
1
1
2
0
1
1
3
3
0
1
0
2
1
1
1
1
1
0
0
2
1
0
2
1
0
1
1
1
2
2
0
0
2
1
2
1
1
2
1
0
2
2
2
3
1
2
1
1
2
1
1
0
1
1
0
0
0
0
1
2
1
2
1
1
1
2
0
1
1
1
1
0
1
1
2
1
2
1
1
1
2
1
2
1
2
1
1
2
1
1
1
0
1
1
1
1
1
1
1
1
2
2
1
1
1
0
1
1
2
2
2
2
1
2
1
1
2
1
2
1
2
1
2
1
1
2
0
0
1
1
1
1
1
1
1
1
2
1
2
2
2
0
0
1
1
1
1
1
1
2
2
1
2
2
1
1
1
1
0
0
1
1
1
1
2
1
1
1
2
1
2
1
1
1
0
1
0
1
1
2
1
2
1
2
1
2
1
1
2
1
1
1
1
2
1
1
2
0
1
2
2
1
1
1
1
1
2
1
1
0
1
1
1
0
1
2
1
1
0
1
1
1
1
1
1
2
1
1
2
2
2
1
1
1
1
0
2
1
1
1
0
1
1
1
1
2
0
1
2
1
1
0
2
1
1
1
2
1
2
1
2
2
1
1
2
1
1
0
1
1
0
1
0
0
1
1
1
1
1
1
2
2
1
1
1
0
1
1
1
2
1
1
2
2
2
0
1
1
2
2
0
0
1
1
1
1
1
2
2
1
0
1
2
0
2
0
2
1
1
2
2
2
2
1
2
0
1
1
1
1
0
1
1
1
1
2
1
1
1
2
2
0
2
1
1
1
1
1
1
2
1
1
1
1
2
1
0
1
2
0
2
1
1
2
1
5
3
1
2
2
0
1
1
2
1
2
1
2
1
1
1
0
2
1
2
0
2
2
0
1
1
2
2
1
1
1
1
1
1
2
1
0
2
0
1
1
1
2
2
0
0
2
0
1
2
1
1
0
2
1
1
1
1
0
2
2
2
1
1
0
1
1
1
1
2
0
0
2
2
1
1
0
1
1
2
2
1
2
0
1
1
0
1
1
1
0
0
0
2
1
1
2
0
0
1
2
2
1
1
0
2
0
2
1
0
2
1
1
0
1
2
1
0
1
1
1
1
2
0
0
1
1
1
1
2
1
1
1
0
2
1
2
1
1
1
1
1
2
1
1
2
6
1
2
1
2
1
1
1
0
1
1
2
1
1
2
2
1
1
1
2
1
2
0
1
1
1
1
1
0
1
1
1
1
1
2
1
0
1
0
1
3
2
1
0
0
0
1
1
2
1
2
2
1
1
0
2
2
2
2
0
2
2
2
2
1
1
2
2
2
2
1
0
1
0
1
1
0
2
2
2
2
1
0
2
2
0
0
0
2
1
1
2
1
1
0
1
0
2
0
2
2
1
2
2
1
1
1
2
1
1
2
1
2
1
1
0
0
2
1
2
1
2
1
1
2
1
2
1
1
1
0
1
1
2
1
2
1
1
1
1
0
2
0
0
1
1
0
2
1
0
1
1
1
1
1
0
1
1
1
1
0
1
1
1
2
2
0
1
1
1
1
1
2
1
1
0
1
1
1
2
3
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
2
2
1
1
0
0
1
1
1
2
2
1
1
1
1
1
2
1
2
1
1
0
2
1
0
1
1
1
1
1
1
1
1
2
1
2
2
1
2
1
2
1
0
1
2
1
0
2
1
1
2
2
1
1
1
0
1
0
1
1
0
1
2
0
2
1
1
1
2
1
2
1
2
1
1
1
1
1
1
1
1
2
1
1
0
1
1
0
1
1
0
1
2
0
1
1
2
1
1
1
2
1
0
1
2
0
2
1
1
2
2
1
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
2
1
1
0
1
1
1
1
2
1
0
2
1
1
1
1
1
1
2
1
2
2
1
1
2
1
0
2
0
1
2
1
2
2
1
1
0
1
1
1
1
1
0
1
0
1
0
2
2
1
1
1
0
2
1
1
1
1
3
1
2
1
1
1
2
1
1
1
0
0
1
0
2
0
2
0
0
1
0
2
0
0
0
1
1
1
0
1
1
1
1
1
1
0
2
1
0
0
1
2
2
1
1
0
2
1
2
1
1
1
1
1
1
2
2
1
1
1
3
2
1
1
1
1
1
1
1
0
1
1
1
2
1
1
1
1
2
1
1
2
0
0
1
1
1
1
2
1
2
1
1
1
1
2
2
1
1
1
0
1
1
2
1
2
1
1
0
1
1
1
0
1
2
2
2
1
1
2
0
1
0
2
1
2
1
2
2
2
1
1
2
2
1
1
1
2
1
1
1
2
0
1
2
0
1
1
0
2
0
0
1
1
1
2
1
1
1
0
2
2
0
1
2
1
1
2
1
0
1
2
1
1
0
1
2
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
0
0
1
2
2
1
1
3
1
0
1
1
0
1
0
0
2
1
2
1
2
1
1
1
2
0
1
1
1
2
1
0
2
0
1
2
0
0
2
2
1
2
1
1
1
1
1
2
2
1
0
1
0
2
1
1
0
2
0
1
1
1
1
2
0
1
2
1
1
5
1
1
0
0
0
1
2
1
2
2
2
1
2
1
1
0
1
2
2
2
1
1
1
2
0
1
1
1
2
1
1
2
1
1
1
2
0
0
0
1
0
1
0
1
2
2
1
2
0
1
1
0
1
1
1
1
1
0
1
2
2
1
1
2
2
1
1
0
1
1
1
0
0
1
2
1
1
1
2
1
1
1
1
2
1
1
1
1
2
0
2
1
2
0
1
1
0
1
0
0
1
0
0
2
0
1
2
1
1
0
1
0
1
1
2
0
2
1
1
1
1
1
2
2
1
1
1
1
2
2
1
0
1
1
1
2
1
1
1
1
1
1
2
1
2
1
1
1
0
2
0
1
1
0
2
1
1
2
1
2
2
1
1
1
1
1
0
2
0
1
0
1
2
1
1
2
1
2
1
1
1
0
1
1
2
1
1
2
1
1
1
1
2
2
1
1
1
1
0
1
1
2
2
1
1
2
1
2
1
0
2
1
0
0
2
0
2
2
1
2
1
1
1
0
1
1
0
1
1
0
1
1
2
1
1
1
1
1
1
1
1
3
0
2
2
2
0
1
1
1
1
1
1
0
0
1
1
0
1
2
2
0
1
1
0
1
1
1
3
0
1
2
2
1
1
1
0
1
2
1
0
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
2
1
2
0
0
1
1
1
2
1
1
1
1
1
1
0
1
2
0
0
2
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
2
1
0
1
1
4
1
1
0
0
1
1
1
1
1
1
1
1
2
1
0
1
2
1
0
0
2
2
1
2
2
2
2
1
1
2
1
2
2
1
1
0
0
1
1
1
2
2
1
1
2
2
1
1
2
0
1
1
1
0
0
1
2
1
1
1
1
1
1
1
1
1
3
1
1
0
1
1
3
2
1
1
1
1
1
1
1
0
0
1
1
2
2
1
0
2
0
2
1
2
0
1
1
1
2
0
2
2
1
2
1
1
1
1
2
1
1
2
1
1
1
0
1
1
0
2
1
1
1
2
1
1
0
1
1
1
1
0
1
1
2
1
1
2
1
1
1
2
1
1
1
0
2
2
1
1
0
2
1
2
1
1
1
2
2
1
1
1
0
0
1
2
1
2
1
1
1
2
1
1
1
2
2
1
1
2
2
1
2
1
1
2
1
2
1
1
1
1
1
1
2
1
1
2
1
1
2
1
2
2
1
1
1
1
1
1
0
0
2
0
0
1
1
1
0
1
1
0
1
1
1
1
2
1
0
1
1
1
2
1
1
1
0
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
0
2
2
1
1
1
1
2
1
0
0
0
1
2
2
1
1
2
2
1
1
0
1
1
0
1
1
0
2
0
1
2
0
1
1
2
1
1
1
2
1
1
1
0
0
0
0
2
1
1
1
1
1
1
0
1
1
1
2
1
1
1
1
1
1
2
1
1
2
1
1
3
2
0
1
1
1
2
1
2
1
0
2
1
1
0
1
2
1
2
2
1
2
1
1
1
1
1
1
1
1
1
1
0
0
1
1
1
0
2
2
1
2
1
1
1
1
1
1
1
2
1
1
1
0
2
1
1
1
2
0
1
1
0
1
2
1
2
2
1
1
1
2
2
1
1
1
1
2
2
0
1
1
0
0
1
1
0
1
1
1
2
1
2
1
1
1
1
0
0
2
1
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
0
1
0
1
1
1
0
1
0
2
1
2
2
2
2
0
4
1
3
2
0
1
1
1
2
1
1
1
1
1
2
2
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
2
0
0
1
1
1
1
1
1
1
1
1
2
0
1
0
1
0
0
2
2
1
1
0
1
0
1
0
2
2
2
2
2
1
1
1
1
1
2
1
1
1
1
1
2
2
1
2
1
1
2
1
1
0
2
2
1
2
1
1
1
2
1
1
1
1
1
1
1
0
1
0
1
1
1
1
0
2
1
1
1
0
2
0
1
2
1
1
1
0
2
1
1
1
1
2
1
1
1
1
1
1
1
1
0
0
1
1
1
2
1
1
1
1
2
1
0
2
1
1
1
0
1
1
2
2
1
1
2
2
2
0
1
2
1
1
1
0
2
1
1
1
1
0
1
1
1
2
1
1
1
1
1
0
1
1
1
0
0
2
2
1
1
2
1
2
1
1
1
1
1
1
1
2
1
2
0
0
1
1
2
0
1
1
2
2
1
1
1
0
2
1
1
1
1
1
1
1
1
4
1
2
1
2
1
1
1
2
2
2
1
1
2
1
2
1
1
2
1
1
2
2
1
1
2
0
2
2
2
1
2
1
2
1
1
2
1
0
1
2
1
0
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
0
2
2
2
1
0
2
2
0
1
1
1
1
1
1
2
2
2
2
1
0
0
2
1
2
1
1
1
2
2
1
1
2
2
1
0
1
1
1
1
2
1
1
1
1
2
2
0
1
1
1
1
0
0
1
1
1
1
1
2
2
2
2
1
1
1
1
1
1
0
1
1
2
1
0
1
1
2
1
1
2
1
2
2
2
1
1
0
2
1
1
1
2
1
1
1
1
1
1
1
0
0
1
1
1
2
1
1
0
0
1
1
1
1
1
1
1
2
2
1
1
0
1
0
2
2
2
1
0
2
1
1
1
1
2
1
1
2
1
1
1
0
1
1
0
1
1
2
1
2
1
0
2
1
1
2
0
0
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
0
0
1
0
1
0
1
1
2
2
1
1
1
2
1
1
2
1
1
1
1
0
1
1
1
1
2
1
0
2
1
1
1
1
2
1
1
1
1
2
1
0
1
1
1
1
1
1
1
2
1
1
0
1
1
1
1
1
1
1
1
1
1
2
1
1
1
0
1
0
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
1
2
1
2
1
1
2
1
1
1
2
2
0
1
1
1
1
1
1
1
1
0
1
0
1
0
1
1
0
1
1
1
0
1
2
1
1
0
2
1
1
1
1
1
2
1
1
1
2
1
2
1
2
1
1
1
0
1
1
1
1
1
2
1
2
1
1
1
1
1
0
0
1
1
1
1
1
1
1
2
2
1
1
1
2
1
2
0
1
1
1
2
0
0
2
1
1
1
2
2
2
1
2
0
0
1
1
2
1
1
1
2
1
0
1
1
1
0
2
2
1
0
1
0
2
1
2
1
2
2
2
0
1
1
2
1
1
1
1
2
1
1
1
1
1
0
1
1
1
1
1
2
2
2
1
1
1
2
2
1
2
1
1
1
0
2
1
1
1
2
2
1
2
1
2
1
2
1
2
1
1
0
2
1
1
1
1
2
1
1
1
1
2
1
2
2
1
1
1
0
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
2
2
1
1
1
1
1
0
2
0
1
1
1
1
1
1
1
1
0
1
1
1
1
1
0
1
2
0
2
1
0
0
1
0
1
1
1
1
1
2
1
2
1
1
1
1
1
1
2
1
0
1
2
0
1
1
0
0
2
1
1
1
1
2
1
1
1
1
1
2
1
1
1
0
1
1
1
2
1
1
1
2
2
2
1
1
2
1
2
2
2
1
1
1
2
1
1
1
1
1
1
2
1
2
0
1
1
0
2
1
0
2
0
1
1
2
1
1
2
0
1
2
1
1
1
1
1
0
1
0
1
2
0
1
0
1
1
1
0
0
2
1
1
1
1
0
2
0
1
0
1
2
1
1
2
1
0
0
1
2
1
1
1
0
2
1
1
1
0
1
1
1
1
1
2
1
2
2
2
0
1
1
1
1
0
2
0
1
3
1
0
2
1
1
1
0
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
1
2
0
1
2
1
1
1
1
1
1
0
1
0
2
1
1
2
1
1
2
2
0
1
1
1
1
2
1
1
1
1
1
2
1
0
0
0
1
3
2
1
0
1
2
0
0
2
2
2
1
1
1
1
2
1
2
2
0
0
2
2
1
1
2
1
1
1
2
1
1
2
1
2
2
1
1
1
1
1
0
1
1
1
1
2
1
2
1
2
0
1
1
1
1
0
1
2
1
0
1
2
1
0
0
1
1
2
0
0
0
1
1
1
2
1
0
1
0
1
2
1
1
1
1
1
1
0
1
2
1
1
3
1
2
1
1
1
1
0
2
1
1
0
1
1
1
1
2
1
1
2
0
1
1
1
1
1
1
1
2
0
0
1
1
1
2
0
1
1
0
2
1
1
1
1
1
0
0
1
1
1
2
1
1
0
0
0
0
1
1
1
1
1
0
1
1
1
1
1
0
2
1
2
1
2
0
0
0
1
2
2
1
2
1
1
1
0
0
1
1
1
2
1
0
1
0
1
3
2
0
1
1
1
1
0
1
1
1
1
1
1
1
1
0
1
2
2
1
1
2
1
0
0
1
1
1
1
0
1
0
1
2
1
1
0
0
1
1
1
2
2
1
2
2
0
1
1
2
0
1
1
1
0
0
2
1
0
2
1
1
2
2
3
1
0
2
1
1
1
0
1
2
2
1
1
1
2
1
2
0
1
1
1
1
1
1
2
1
1
1
2
1
0
2
2
2
0
1
1
0
1
2
1
2
2
3
1
2
2
2
1
1
2
1
1
1
2
2
1
1
1
0
1
1
2
2
1
1
1
1
2
2
1
1
2
0
2
1
1
1
2
1
1
1
3
2
0
1
1
1
1
1
0
1
1
0
1
1
1
2
1
3
1
2
1
1
1
1
1
1
1
2
2
2
1
2
1
1
1
1
0
2
2
1
1
2
2
1
2
2
0
1
2
1
1
1
1
1
0
2
2
1
2
1
1
1
1
2
1
2
1
0
2
1
2
0
1
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
2
1
2
1
2
1
1
1
1
2
1
1
2
2
2
2
2
1
1
1
0
2
1
1
2
1
0
2
2
1
2
2
0
6
1
2
2
2
1
2
1
1
2
1
1
1
2
1
3
0
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
2
2
1
1
0
2
1
1
1
1
2
1
0
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
0
0
1
0
1
1
1
0
1
0
1
2
0
1
2
1
0
1
1
1
1
1
0
1
1
1
1
1
1
2
1
0
1
1
0
2
1
2
1
1
0
1
0
1
2
1
1
0
1
2
1
1
0
1
1
1
1
0
2
1
0
1
2
1
1
1
0
0
1
1
2
1
2
1
2
0
1
2
2
1
0
0
1
1
1
0
1
1
1
1
1
1
1
1
1
0
2
0
0
2
0
1
2
1
2
2
1
2
2
1
2
2
1
2
2
1
1
2
1
2
0
2
1
1
1
1
1
1
2
1
1
1
0
1
1
1
1
1
1
2
3
2
0
1
0
1
1
2
0
1
1
1
1
2
1
1
2
1
1
1
1
0
1
0
0
2
2
1
1
1
1
1
1
1
1
1
1
1
1
0
1
2
2
1
2
1
1
1
2
1
1
1
2
2
1
2
1
2
2
2
1
1
1
2
2
2
0
2
1
1
1
1
1
1
0
1
1
2
0
1
2
1
2
1
1
1
2
2
1
1
1
0
1
1
1
2
1
1
1
1
1
1
1
2
1
2
2
1
0
1
3
1
1
2
1
2
0
1
1
2
1
2
2
0
1
2
1
1
1
2
2
1
1
1
1
2
1
1
0
1
1
2
1
1
1
2
1
0
1
1
1
1
1
0
1
2
1
2
1
1
1
0
2
1
0
1
1
1
1
1
1
1
2
2
0
0
1
1
1
0
0
1
2
1
1
1
2
2
1
1
1
1
1
1
2
1
1
2
2
1
1
1
2
1
0
0
1
1
1
1
1
1
2
2
2
1
2
1
0
2
2
1
1
1
2
2
1
2
0
2
1
0
0
2
1
2
2
2
1
1
2
3
1
0
0
1
2
2
1
1
1
1
0
2
1
1
1
1
1
2
1
1
1
2
1
1
2
2
0
2
1
1
1
1
1
1
1
1
1
1
2
1
2
0
1
2
2
1
1
1
2
2
1
1
1
2
2
2
1
1
1
0
0
2
1
1
2
2
1
1
1
1
2
0
1
1
1
2
0
0
1
1
0
1
1
1
0
2
1
1
1
2
1
2
1
1
2
1
0
0
2
1
2
1
1
0
2
1
0
1
1
1
1
0
0
1
1
2
2
1
1
3
1
1
1
1
2
2
2
1
1
1
1
2
1
0
1
0
0
1
2
1
1
0
1
2
1
1
0
1
2
1
4
1
3
1
2
1
0
0
1
1
2
1
1
1
1
2
1
1
1
1
2
1
0
1
1
0
1
1
1
1
0
0
1
1
1
2
1
1
2
1
2
2
1
2
1
1
2
1
1
0
1
2
1
0
1
0
1
0
1
1
1
1
2
1
2
2
2
1
2
1
1
1
1
0
1
0
2
1
0
2
0
1
0
1
3
1
1
0
2
2
1
1
0
1
1
0
1
0
2
0
0
0
1
1
1
1
0
0
1
1
1
1
1
2
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
0
1
2
1
2
2
2
1
1
1
1
0
1
1
1
1
2
1
1
1
2
1
1
2
1
1
1
1
1
1
1
0
2
0
1
2
0
1
1
1
1
1
1
1
0
1
0
2
1
2
1
1
1
2
1
2
1
0
1
1
1
2
1
1
2
2
1
1
0
1
2
1
1
1
2
1
1
1
2
1
2
2
1
2
1
2
1
2
1
2
1
2
1
1
1
1
2
1
1
1
2
2
1
1
0
1
1
1
3
0
1
1
2
2
3
2
0
1
1
1
1
2
1
0
1
2
0
2
2
2
1
1
2
1
1
1
0
2
1
1
1
2
1
2
1
1
1
2
2
1
1
2
0
1
1
2
0
1
1
2
1
1
1
0
0
2
1
1
0
1
2
1
0
1
0
2
1
2
2
1
1
3
1
2
1
1
1
1
0
2
2
1
2
2
0
1
2
1
2
1
1
1
0
2
0
1
2
1
1
0
2
2
2
1
1
2
1
1
2
1
1
1
1
1
2
2
1
1
2
1
0
1
1
1
1
1
1
2
2
1
0
2
1
1
1
1
2
2
2
1
0
1
1
2
2
2
0
1
2
0
0
1
2
1
1
1
1
1
1
2
1
2
1
2
1
1
1
1
2
2
1
0
1
1
1
2
1
1
1
2
2
0
2
1
0
1
1
1
2
2
1
2
1
2
0
2
2
1
1
1
1
1
1
1
1
2
1
2
1
1
1
0
2
1
2
1
1
1
2
0
1
1
2
2
1
1
0
1
2
2
0
1
0
2
1
2
2
1
1
1
2
1
1
2
1
1
1
0
1
1
1
1
1
2
1
1
1
1
1
0
0
1
2
2
1
1
1
1
1
1
2
2
1
1
0
1
0
1
1
1
2
1
1
2
1
1
2
0
1
2
1
2
1
2
2
1
2
1
2
1
0
1
0
1
0
1
1
1
1
0
1
0
1
2
2
0
1
27
1
1
0
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
0
2
2
0
1
1
2
1
1
2
1
2
1
1
1
2
1
2
1
0
1
1
1
2
1
1
1
1
1
1
2
1
2
1
1
2
1
2
0
2
2
2
2
0
0
1
2
2
1
2
1
0
1
1
2
1
2
0
1
1
1
4
1
0
1
2
2
2
0
1
2
2
2
1
1
1
1
0
2
0
1
1
0
1
1
1
2
1
2
1
0
0
1
2
1
2
2
1
1
2
2
1
1
1
1
1
2
1
1
1
1
1
0
0
0
1
2
1
2
1
1
1
1
1
1
2
1
1
2
1
2
1
1
1
1
1
1
2
1
0
2
1
0
1
0
1
0
0
2
1
1
1
2
0
1
2
1
1
0
1
2
1
1
2
1
0
2
1
1
1
2
2
1
2
1
0
0
1
2
1
2
2
2
1
2
2
1
1
1
0
2
1
0
1
1
1
1
1
0
2
2
1
1
2
0
1
1
0
1
1
0
2
1
1
1
1
5
1
1
2
2
2
1
1
1
1
1
1
0
1
0
2
2
2
2
1
0
0
1
1
1
2
1
2
1
2
1
1
1
1
0
2
2
0
1
1
1
1
2
1
0
1
1
2
2
1
1
1
1
1
0
1
1
2
1
1
2
0
1
1
1
1
2
1
1
2
0
1
1
1
1
2
0
1
1
1
1
4
1
2
2
1
2
1
0
2
2
1
2
1
2
2
2
1
1
1
1
1
2
0
1
1
1
1
1
1
2
1
1
3
1
1
1
0
0
1
1
2
1
1
1
0
1
1
1
1
1
1
2
2
1
1
1
1
1
0
0
2
0
1
1
1
1
1
1
1
1
1
1
0
2
1
1
1
2
2
1
2
2
2
3
2
2
2
2
1
2
2
1
2
1
1
1
1
2
1
2
1
1
0
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
0
1
2
1
1
1
1
1
1
1
0
2
1
1
2
1
1
3
2
1
1
1
1
2
2
1
1
1
2
0
1
0
1
0
2
1
1
3
1
0
1
2
0
2
2
1
1
1
2
1
1
0
1
0
1
1
1
1
1
0
1
1
2
1
2
1
1
1
1
2
2
2
2
2
1
1
1
1
0
1
2
1
2
0
1
1
1
2
1
1
1
1
1
2
2
2
1
1
1
1
0
1
1
0
1
1
2
2
1
2
2
1
2
1
1
1
2
1
1
1
0
1
1
1
0
1
2
1
1
0
1
2
2
2
3
1
1
1
2
1
1
2
1
1
0
1
1
2
1
1
1
1
1
0
1
2
1
1
2
1
0
1
0
1
2
1
1
1
2
1
0
2
1
1
0
2
0
1
1
2
1
1
1
1
1
0
1
1
0
1
1
1
1
1
1
1
1
0
2
1
0
2
2
1
2
0
1
1
0
1
1
0
2
1
1
0
1
1
1
1
1
1
1
1
1
1
0
2
1
1
1
1
1
0
1
2
1
1
1
2
1
2
1
1
1
1
2
0
0
1
0
0
1
1
1
1
1
1
1
0
1
2
0
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
0
1
0
1
1
1
1
2
0
1
2
2
1
0
1
1
1
1
0
1
2
1
1
1
2
1
1
1
1
1
2
1
1
0
1
1
2
1
1
1
1
1
1
1
2
1
0
1
1
1
1
2
2
2
1
2
2
0
1
2
0
1
1
1
1
1
1
1
1
2
2
1
1
0
2
1
1
2
2
1
1
1
1
0
2
1
2
2
2
1
1
2
1
1
1
0
1
1
1
1
1
1
2
1
0
1
2
2
1
1
2
1
0
1
1
1
1
1
1
1
2
1
2
1
0
1
1
1
1
1
1
1
1
2
0
1
1
1
2
1
1
2
1
2
1
1
0
1
1
1
0
1
1
2
1
0
1
2
0
1
1
1
3
1
2
1
0
2
1
2
2
1
1
0
1
1
1
2
1
1
1
1
0
1
1
1
1
2
1
0
1
1
1
0
1
1
1
2
2
1
1
0
1
1
0
3
0
2
1
1
1
1
0
1
2
1
1
1
1
0
1
1
1
1
1
1
0
1
0
2
1
1
1
1
1
1
1
0
1
2
0
0
0
1
1
1
1
1
1
1
1
0
1
1
2
2
1
1
1
2
2
1
1
1
1
0
0
2
0
2
1
1
1
1
1
1
1
0
1
0
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
2
0
1
1
1
1
1
1
2
0
1
1
1
1
2
1
1
1
2
1
0
0
1
1
1
1
2
0
1
0
1
1
1
2
1
1
1
1
2
1
1
1
1
1
2
1
0
2
1
0
1
1
1
1
1
1
1
2
1
0
1
1
1
1
2
2
1
1
1
2
1
0
2
2
0
1
2
1
1
1
1
1
1
1
1
1
0
1
0
0
2
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
0
1
1
2
0
1
1
1
1
1
1
1
2
1
1
0
1
2
2
1
1
1
1
1
1
1
0
1
1
1
1
0
1
1
1
1
1
2
2
1
0
1
2
2
1
1
2
1
1
1
1
1
2
0
0
1
1
1
0
0
2
0
1
0
1
1
1
1
1
2
2
2
1
1
0
2
1
0
1
1
1
1
1
2
1
0
2
1
1
1
2
1
2
1
1
2
2
1
0
2
1
1
2
1
2
2
1
1
1
1
1
1
1
0
1
2
1
1
1
1
1
1
2
0
2
1
2
0
2
2
2
0
1
1
0
2
1
1
1
0
2
1
0
1
2
1
1
0
2
0
1
1
2
0
0
2
1
2
1
1
1
2
0
1
1
0
1
1
1
0
2
2
1
1
2
2
0
1
0
0
2
1
1
1
1
2
1
1
2
2
1
1
0
1
0
2
2
1
0
1
0
2
1
1
1
0
2
1
1
1
1
0
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
2
2
1
2
1
1
1
2
0
1
2
1
1
1
1
0
2
1
1
1
1
1
1
1
0
1
0
0
1
1
1
0
0
1
1
1
1
1
1
2
2
2
0
1
1
2
0
1
1
2
1
0
1
1
1
1
0
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
2
0
2
2
1
1
1
1
1
0
1
1
1
2
1
2
2
1
23
2
0
1
1
1
0
1
1
1
1
0
0
2
1
1
1
1
2
2
2
2
2
0
0
1
1
1
1
1
2
1
2
2
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
0
1
1
0
1
1
2
2
2
1
1
1
2
2
2
2
2
1
2
2
1
1
2
2
1
2
1
2
1
2
2
1
0
1
0
1
2
1
2
0
1
1
1
1
0
0
2
2
0
1
2
1
1
1
0
1
1
1
1
1
0
1
1
1
1
0
2
0
2
1
2
1
0
1
1
1
1
2
1
2
2
2
0
1
1
0
2
1
1
2
1
0
2
1
1
0
2
1
1
0
1
2
1
2
1
1
1
1
0
1
1
0
2
1
2
1
0
0
1
1
2
1
1
0
1
1
2
1
1
1
0
2
1
1
1
1
2
1
1
1
1
0
1
1
1
1
1
1
1
1
1
2
2
1
0
1
1
1
1
1
1
1
1
2
1
1
0
0
2
2
1
1
1
1
2
1
1
0
1
0
1
0
1
1
1
2
1
1
1
1
1
1
1
2
0
2
1
1
2
1
1
0
2
1
1
2
2
2
1
1
1
2
1
1
0
0
1
1
2
1
1
2
2
1
1
1
2
1
1
1
3
2
2
1
1
0
0
0
2
1
2
2
0
1
2
1
1
1
4
2
2
1
0
1
1
1
1
0
1
2
0
1
1
1
1
2
0
1
2
2
1
1
1
0
0
1
1
1
1
1
1
2
1
2
1
1
1
1
2
1
2
1
1
1
2
1
1
0
1
1
1
1
1
1
2
1
1
0
1
2
2
0
1
2
1
1
2
1
2
1
0
1
0
0
1
1
0
1
1
3
1
1
2
1
1
1
1
1
1
1
0
1
1
1
0
1
1
1
2
2
1
2
2
1
1
1
2
1
1
1
0
1
2
1
1
2
0
0
0
1
1
1
2
1
2
1
4
1
0
0
1
1
2
2
2
1
1
1
1
2
1
2
1
1
2
1
1
2
2
0
2
0
1
2
1
0
0
0
1
2
1
1
2
2
1
2
2
2
2
1
1
1
0
1
1
2
1
1
0
0
1
2
1
1
1
1
1
1
2
1
1
1
1
0
0
1
2
2
0
1
1
0
1
1
2
2
1
1
1
1
1
2
1
1
2
1
1
1
1
0
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
0
1
1
0
0
1
2
1
2
1
1
1
1
2
0
2
1
2
0
1
1
1
2
1
0
0
1
2
2
2
0
2
0
2
1
2
1
1
1
1
2
1
1
2
1
2
1
1
1
2
2
1
1
1
2
2
2
0
1
1
0
1
2
1
1
1
1
1
1
2
0
2
2
1
1
1
0
1
1
1
1
2
2
3
1
2
2
2
1
0
1
1
2
0
1
2
2
1
2
1
1
1
1
1
2
1
1
0
0
1
2
1
1
1
2
1
1
1
0
1
2
1
1
2
0
1
1
1
1
1
1
2
1
2
1
0
1
1
0
0
2
1
1
1
2
1
1
2
2
2
0
1
2
1
1
1
1
1
1
1
2
2
1
2
1
1
1
1
2
2
1
1
0
1
1
0
1
1
2
1
1
1
1
1
0
2
1
1
2
1
1
1
1
0
0
1
1
1
0
1
1
1
1
1
1
1
2
1
3
1
1
1
1
0
1
1
1
2
0
1
1
1
1
2
1
0
1
2
0
1
2
1
1
2
2
1
2
1
1
1
1
1
0
0
1
1
0
3
1
1
2
1
2
1
1
2
1
0
1
1
0
1
1
3
0
1
1
1
1
2
1
1
2
2
2
0
1
0
2
0
1
1
2
1
0
1
0
2
1
1
1
2
2
1
1
2
1
1
1
1
1
1
2
1
1
1
2
2
2
1
0
1
1
1
2
1
1
1
1
2
1
1
1
2
1
2
2
0
1
0
2
2
1
1
2
1
1
2
1
1
1
0
0
1
2
1
2
1
1
0
0
1
1
1
2
2
1
1
2
2
1
2
1
1
1
1
2
0
1
1
1
0
0
0
0
1
1
1
0
2
1
1
1
1
2
1
1
1
0
2
1
1
1
1
1
0
1
0
2
1
2
1
2
1
1
0
1
2
1
2
1
1
0
1
1
1
2
0
2
2
1
1
1
0
1
1
1
2
0
0
1
1
1
1
2
1
1
1
1
1
1
1
1
2
2
1
2
2
1
2
1
1
1
0
1
1
0
1
0
1
1
1
0
2
0
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
0
0
0
1
1
1
1
2
2
0
1
1
0
1
1
1
1
2
1
1
2
1
2
1
1
0
0
1
1
2
2
0
1
2
0
1
2
2
1
2
0
1
1
1
1
1
1
1
1
1
0
2
2
1
0
0
1
2
1
1
0
1
1
3
0
2
2
1
0
0
0
1
2
1
2
1
1
2
1
0
1
0
1
1
1
2
2
1
1
2
1
1
1
2
2
1
1
1
1
1
1
1
0
1
1
2
0
1
1
1
2
2
1
1
0
2
1
1
1
1
2
2
1
1
1
2
1
1
0
1
1
1
1
0
1
1
1
0
1
1
2
2
1
0
2
1
1
2
1
0
1
1
1
1
0
1
2
1
1
1
2
0
0
2
1
2
1
0
1
1
2
1
0
1
2
1
1
1
1
0
1
1
2
2
0
1
2
1
1
1
1
1
0
1
0
1
1
1
1
1
1
1
1
1
1
0
1
2
1
0
2
2
1
1
2
1
0
1
0
1
1
1
1
1
1
2
1
0
1
0
1
2
2
1
1
0
2
1
1
0
1
1
1
2
1
0
1
2
1
0
0
1
1
2
2
2
0
2
1
1
0
2
2
1
2
1
2
1
1
1
2
0
1
1
0
1
1
0
1
1
1
2
2
1
1
1
1
1
1
1
2
1
2
0
2
1
1
1
1
2
2
1
1
1
1
2
2
1
1
2
1
0
1
1
1
2
1
1
2
2
1
0
0
1
2
1
1
1
1
1
2
1
2
2
1
1
1
1
1
0
0
1
1
0
1
1
2
1
1
1
2
0
1
1
1
1
1
1
1
2
1
2
0
1
3
1
2
1
1
1
1
2
0
1
1
1
1
2
1
1
0
1
1
0
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
2
0
1
2
1
0
1
2
1
1
1
1
1
1
0
1
1
1
2
1
0
2
1
1
2
1
1
1
1
1
1
1
4
2
0
2
1
2
0
2
1
2
1
1
1
1
1
1
1
1
1
1
2
0
0
0
1
1
2
1
1
1
1
1
0
1
2
1
1
1
2
1
0
2
2
2
0
2
1
1
0
2
1
1
1
1
1
2
2
1
1
0
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
0
1
2
0
1
1
2
1
1
2
1
1
1
0
2
2
1
1
1
1
1
1
1
1
1
1
1
0
0
1
1
2
0
1
1
2
1
1
1
2
1
2
2
2
0
1
2
0
2
1
1
2
1
2
2
1
0
0
1
2
0
1
2
1
0
1
1
1
2
1
1
1
1
0
1
2
1
1
1
1
2
1
1
1
0
2
0
2
0
1
0
2
1
1
2
1
1
0
2
0
1
1
1
1
1
0
1
1
1
0
2
1
1
1
2
1
2
1
2
1
1
0
1
1
2
0
2
1
1
0
1
1
0
0
0
2
2
2
1
2
1
1
1
0
0
1
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
2
1
1
0
2
2
0
1
2
1
2
0
1
1
1
1
1
1
1
1
1
1
1
1
0
2
2
0
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
0
2
1
1
1
1
1
0
1
1
1
0
0
1
1
0
2
1
1
1
1
1
1
2
1
1
2
1
1
1
2
1
2
1
1
1
1
2
1
1
1
1
1
0
2
1
0
1
1
1
1
1
1
0
2
2
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
2
0
0
2
1
1
2
2
2
1
0
1
1
1
1
1
2
1
2
2
0
1
3
1
2
1
2
1
1
1
1
0
1
1
1
1
1
1
2
1
1
1
2
2
0
1
0
1
0
2
2
2
0
1
2
2
2
0
0
1
1
0
1
2
1
0
0
2
1
1
1
2
1
1
1
1
1
1
2
1
2
1
0
0
0
2
0
2
1
2
1
3
2
2
1
2
2
2
1
1
0
1
1
1
1
1
0
0
0
2
2
1
2
0
0
1
2
1
1
1
1
0
0
1
1
1
1
1
1
2
2
0
2
1
1
1
1
1
2
1
1
1
2
1
0
1
1
2
1
0
0
2
2
1
1
2
1
1
2
1
0
1
1
2
2
1
1
1
1
2
2
1
2
0
2
1
2
1
1
1
1
0
0
1
1
1
0
1
1
0
1
1
1
0
1
1
1
1
0
1
3
1
1
2
1
2
2
2
1
1
2
1
1
1
2
0
1
1
0
1
1
1
1
1
0
0
1
2
1
2
0
1
1
1
0
1
1
1
1
1
2
0
1
2
1
2
1
1
1
2
1
1
2
1
1
1
1
1
1
1
0
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
2
0
0
1
1
2
2
2
1
1
1
1
2
0
1
1
2
1
1
1
1
0
0
1
0
2
1
1
1
0
1
1
2
3
1
2
2
1
0
0
1
0
1
1
1
0
0
2
1
2
1
2
1
2
1
1
1
1
2
1
1
0
1
1
1
2
1
1
1
1
1
1
1
0
1
2
1
2
2
2
2
1
2
1
1
1
1
1
1
0
2
1
1
3
2
1
1
1
1
1
1
2
0
0
1
1
2
1
0
1
1
1
0
2
1
1
1
0
2
1
1
1
0
1
1
1
2
2
2
2
1
0
1
1
1
0
1
1
1
1
1
1
1
2
0
1
0
2
1
1
2
0
1
0
1
2
2
2
2
2
2
1
1
1
1
1
1
0
1
1
2
1
1
1
1
1
1
1
0
2
1
2
1
2
2
1
1
2
0
2
1
0
1
1
2
2
1
1
1
2
1
2
2
1
1
1
2
2
1
1
2
2
1
1
2
2
0
0
1
1
0
1
1
1
1
1
1
1
2
1
1
3
1
1
1
0
1
1
1
1
1
1
1
1
0
2
2
2
2
0
2
1
0
2
1
1
1
2
0
1
2
0
0
2
1
1
2
1
2
1
0
0
1
2
0
1
1
1
0
1
1
2
1
0
0
1
0
0
1
1
1
0
1
1
1
0
0
1
1
1
1
0
0
1
1
2
1
2
2
1
2
1
1
2
1
0
2
1
1
0
1
2
1
0
1
1
1
2
1
1
1
0
1
1
2
2
0
1
1
2
1
1
1
1
1
0
1
1
0
1
1
1
2
1
1
1
1
0
2
2
1
2
0
2
1
1
0
1
2
1
2
1
1
1
1
2
1
4
1
1
1
1
2
2
0
1
2
1
1
1
5
2
1
2
2
0
0
1
0
2
2
0
1
1
1
1
2
0
1
1
0
1
1
1
2
1
0
1
1
1
1
2
1
1
1
2
1
1
1
1
0
1
1
1
1
2
1
1
1
1
2
0
2
2
2
1
1
0
1
1
1
1
1
0
0
0
1
0
1
1
2
2
1
1
1
2
2
1
1
0
1
1
1
2
1
1
0
1
1
1
0
1
0
2
1
0
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
1
0
1
2
0
2
1
1
1
2
1
2
1
2
1
1
1
2
1
1
1
0
0
1
0
1
2
1
1
1
1
1
0
1
1
1
2
1
0
0
0
0
1
2
1
1
0
1
0
1
1
2
1
1
0
2
1
1
2
1
2
0
1
1
1
2
1
1
1
0
1
5
0
0
1
1
1
0
0
1
1
1
1
2
1
1
0
1
1
2
0
1
0
1
1
1
1
1
0
2
1
1
0
1
0
2
1
1
1
1
0
1
1
1
0
1
0
1
2
2
2
0
1
1
2
2
1
1
1
1
1
0
2
1
1
1
1
1
1
2
0
1
1
2
1
0
1
1
2
1
0
2
0
1
1
2
0
1
1
1
1
1
2
2
0
2
1
1
1
1
1
0
2
1
1
1
1
1
1
2
0
1
1
0
0
1
2
1
2
1
0
2
1
1
2
1
1
1
0
0
1
2
1
2
1
2
1
1
0
0
2
2
1
0
2
1
2
2
0
1
2
1
1
2
2
1
1
1
1
0
1
1
1
1
1
1
2
1
1
0
1
2
1
0
1
2
2
1
1
1
1
1
1
1
1
1
2
2
2
1
1
2
0
2
0
1
1
1
1
1
1
0
0
1
1
1
1
1
0
2
1
0
2
1
2
2
0
1
2
1
1
2
4
1
1
1
1
2
2
0
0
0
0
0
1
2
1
2
2
2
2
1
1
1
1
0
2
0
2
0
2
2
1
0
3
2
1
1
1
1
0
2
1
1
1
0
2
1
0
1
1
1
1
2
2
2
1
1
1
2
2
1
2
1
0
2
2
1
1
1
3
1
1
1
1
2
2
2
1
1
1
1
0
1
0
0
1
2
1
1
1
1
1
0
1
1
2
1
0
2
0
2
2
2
1
3
1
2
2
1
2
1
1
1
2
1
1
2
0
1
1
0
0
1
1
1
1
2
1
1
1
2
1
0
1
2
2
0
2
2
1
1
1
1
2
2
1
0
2
2
2
1
1
2
0
1
1
3
1
1
1
2
2
1
1
2
1
1
0
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
0
1
2
1
2
1
1
1
0
2
1
2
1
2
1
1
1
1
1
1
0
2
2
1
2
1
1
1
1
1
1
2
0
2
0
1
0
1
1
1
1
0
1
2
2
2
2
2
1
0
2
2
1
1
2
1
1
1
1
1
1
2
1
1
2
1
0
1
1
2
1
1
0
1
1
2
1
2
2
1
1
0
0
1
2
1
1
1
1
2
1
1
2
1
3
1
1
0
2
2
1
0
0
1
1
2
1
2
1
0
1
1
2
1
2
2
2
1
1
1
1
0
0
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
0
1
1
1
1
2
2
0
2
2
1
2
2
1
1
1
1
1
0
2
1
1
2
1
1
2
1
0
0
1
0
1
1
2
1
1
2
2
2
0
1
0
1
1
2
1
0
1
1
1
0
1
0
1
1
1
2
1
2
2
2
2
1
2
2
2
0
0
2
0
2
2
1
1
2
2
1
1
1
1
2
1
1
1
1
0
0
1
0
2
0
3
1
0
2
2
1
1
2
1
1
2
0
2
1
0
2
1
1
1
1
1
2
1
0
3
0
2
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
0
1
1
2
2
3
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
2
1
1
0
1
1
2
2
1
1
0
1
1
1
0
1
2
1
2
1
1
1
2
1
1
1
1
1
2
1
1
1
2
0
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
0
2
1
3
0
0
2
0
0
1
1
1
0
1
1
1
2
1
1
0
1
1
1
1
1
1
1
1
1
1
0
1
1
1
0
1
1
1
1
2
0
2
1
0
1
1
1
1
2
1
1
1
1
1
1
2
2
1
0
1
1
2
1
0
1
1
1
2
2
1
1
1
2
1
2
0
1
1
2
1
1
2
0
1
0
2
1
1
2
1
1
2
1
1
1
1
2
1
0
0
1
1
2
3
0
2
1
2
2
1
1
1
1
2
2
1
1
1
1
1
0
2
1
0
0
2
0
1
2
1
3
2
2
1
0
2
0
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
1
1
1
0
1
1
0
0
1
1
1
1
1
1
1
1
1
2
1
0
1
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
1
2
1
1
1
0
2
1
0
1
2
0
1
1
1
1
2
1
1
1
1
1
1
1
1
0
1
1
0
1
1
1
2
1
1
1
0
1
3
1
1
3
2
1
2
1
2
0
2
1
1
0
0
2
0
2
2
1
1
2
1
2
2
1
2
0
2
2
1
1
0
1
1
1
1
1
1
0
1
2
2
1
1
0
2
1
1
2
1
2
1
1
1
2
1
0
2
0
1
1
2
3
1
1
1
2
0
1
1
1
1
0
1
1
2
1
2
1
1
1
1
1
0
1
2
1
1
1
2
2
1
2
2
1
1
0
2
1
0
0
2
1
2
0
1
1
2
1
1
2
1
2
3
1
1
0
1
0
1
2
1
1
1
2
1
1
1
2
0
2
1
2
0
2
1
1
1
0
2
1
1
1
1
2
1
1
2
2
1
1
1
1
2
0
1
1
0
2
2
1
1
1
1
2
1
1
2
1
1
1
1
2
1
2
1
1
1
1
2
3
1
2
1
1
0
1
2
1
2
1
1
1
2
2
1
1
1
2
1
1
1
1
2
2
2
1
1
2
1
1
1
1
1
2
2
2
1
1
1
1
2
1
2
0
0
1
2
1
1
1
1
0
1
1
1
1
1
2
1
2
0
2
1
2
1
1
0
1
2
0
1
1
2
0
2
1
1
0
1
0
1
0
1
1
2
1
1
2
1
1
1
2
1
2
0
1
1
1
2
2
2
2
1
1
2
1
1
0
2
1
1
1
1
1
1
1
1
2
1
1
2
2
2
1
1
2
1
2
1
1
2
1
1
1
1
1
0
1
1
2
1
0
1
1
1
1
0
1
2
1
1
1
1
2
0
1
2
0
1
3
2
1
1
2
1
1
1
1
2
1
3
0
1
1
1
2
1
4
2
1
2
1
2
1
1
0
1
2
2
1
1
1
1
1
1
1
1
2
1
0
1
1
1
2
1
0
1
1
0
0
1
1
2
2
0
2
1
1
1
0
1
2
1
1
2
1
1
1
2
1
1
1
2
2
1
1
0
1
1
1
1
1
0
1
1
1
2
1
1
2
1
0
2
0
0
2
1
1
1
1
0
1
2
1
0
2
1
1
0
1
1
1
1
3
0
2
1
2
1
1
2
0
0
1
0
2
1
1
1
1
1
1
1
0
2
1
2
2
1
2
1
2
1
2
1
2
0
1
2
1
1
1
1
2
1
1
1
1
1
0
0
1
1
1
1
1
0
2
2
0
1
0
1
1
2
3
1
1
1
2
1
1
1
0
1
1
1
1
1
1
1
2
2
2
2
1
2
2
2
1
1
1
1
1
2
1
1
1
0
1
1
1
1
1
0
1
1
1
2
0
1
2
1
1
1
2
2
1
1
1
1
0
1
0
2
1
1
1
1
1
1
1
1
0
1
1
0
1
1
1
0
1
1
1
0
2
1
1
0
1
2
2
1
1
1
1
2
2
1
1
0
1
1
1
2
1
1
0
2
2
2
2
1
1
1
0
2
0
1
1
2
1
0
1
1
1
3
2
1
1
1
1
1
1
1
1
0
1
1
0
2
0
1
1
2
0
2
1
1
1
1
2
2
1
1
1
1
2
1
1
1
0
1
1
2
2
1
0
1
1
1
1
2
2
1
0
2
0
1
1
0
1
1
0
0
1
1
0
2
1
0
1
1
1
1
0
1
2
1
1
1
2
2
1
1
1
2
1
1
1
2
1
1
0
1
1
1
1
1
1
1
1
3
1
2
0
1
0
1
1
1
1
1
1
1
0
1
1
1
1
2
1
0
2
2
1
1
1
1
2
2
1
1
1
2
0
0
1
2
1
1
1
0
1
1
1
1
1
1
2
1
1
2
0
0
1
1
1
1
2
2
2
1
1
3
0
2
1
0
1
2
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
0
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
1
1
1
1
2
1
1
0
1
2
1
1
1
1
1
0
1
1
2
0
1
1
0
1
2
2
1
2
1
0
1
1
1
2
1
1
1
1
2
2
0
1
1
2
1
2
1
2
1
1
2
2
0
0
1
2
1
1
1
2
1
2
1
0
1
2
2
0
1
1
1
0
0
1
1
2
2
0
0
2
0
2
0
1
1
1
1
1
0
1
1
1
2
2
1
2
1
2
1
2
2
1
1
1
2
1
1
1
1
2
3
2
1
1
2
0
1
0
1
2
1
3
1
0
2
1
2
1
1
1
2
1
0
0
2
2
0
0
2
2
2
2
2
0
0
2
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
0
1
2
2
1
1
1
1
0
2
1
1
1
1
1
2
0
1
1
1
1
0
1
1
2
2
1
3
1
1
1
1
1
1
2
1
0
1
1
1
1
2
1
1
1
1
1
1
1
1
1
0
2
2
2
1
2
0
0
2
1
1
1
1
2
2
2
1
0
1
1
0
2
1
1
2
1
1
1
1
0
1
2
1
2
1
2
2
1
1
2
1
2
1
1
2
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
0
1
1
0
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
0
2
1
1
1
2
1
0
0
1
2
1
1
1
0
1
1
1
0
1
1
1
1
1
0
1
2
1
0
1
0
1
2
2
1
2
2
1
1
2
1
2
1
1
1
1
1
1
1
1
0
1
2
1
2
1
0
1
1
1
2
1
2
1
2
1
2
1
2
0
2
1
1
0
1
2
1
1
2
3
1
1
1
1
2
2
1
0
2
2
2
0
2
1
2
1
3
1
1
1
1
1
1
1
2
0
1
1
1
1
2
1
1
0
0
0
1
1
1
2
2
1
1
2
1
2
1
0
1
2
1
2
1
1
2
1
2
1
2
1
1
2
2
1
0
1
1
1
1
1
2
1
2
2
1
1
1
1
2
1
1
1
1
1
1
2
2
1
0
1
1
1
2
1
2
1
1
2
1
1
2
2
1
2
1
2
0
1
0
1
2
2
1
1
1
1
1
1
1
1
0
1
1
1
2
2
1
2
2
1
2
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
0
2
2
1
1
1
1
2
0
1
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
0
2
1
2
1
1
1
1
1
2
1
2
2
0
1
1
1
2
1
1
1
0
1
1
1
2
0
1
0
2
2
1
3
2
0
0
0
1
1
1
1
2
2
0
1
1
1
1
1
2
2
1
1
1
0
1
1
2
1
1
1
1
0
0
1
1
0
1
2
1
0
2
1
1
1
1
2
1
1
1
2
1
1
2
2
1
1
1
0
1
0
0
1
1
0
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
2
1
2
0
1
2
1
1
2
2
3
1
1
1
1
1
2
1
1
0
0
2
1
1
1
0
1
1
1
2
2
1
1
0
0
1
2
1
0
2
1
1
1
2
1
1
2
1
1
2
2
1
2
1
1
2
0
0
1
2
0
0
1
2
1
0
1
1
2
1
1
1
2
2
1
2
1
1
2
1
1
1
1
1
1
1
1
0
1
1
1
1
0
1
1
2
2
0
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
0
1
1
1
0
1
1
2
0
1
1
1
2
1
0
1
0
1
0
2
1
1
1
0
1
2
1
1
1
1
1
1
0
0
1
0
1
1
1
0
1
0
1
0
2
0
1
1
0
1
0
0
1
1
1
1
1
2
1
1
2
1
0
1
1
1
0
2
2
1
2
1
2
0
1
0
1
1
0
2
2
1
2
0
1
1
1
0
1
0
2
1
1
2
0
0
1
1
1
2
1
1
1
1
2
1
1
1
1
1
0
1
1
1
1
1
1
2
1
2
0
1
2
1
1
1
0
1
1
1
0
2
0
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
0
2
1
1
2
1
1
2
0
2
1
1
1
1
1
0
1
1
1
2
1
1
1
1
2
1
0
1
1
1
2
0
0
0
1
1
1
1
0
1
1
1
2
2
1
2
0
0
1
1
0
1
0
1
0
1
0
1
1
2
1
1
2
2
2
2
0
1
1
1
1
1
1
1
2
1
1
0
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
0
1
0
2
2
1
0
0
2
2
1
1
1
2
0
1
1
1
1
1
0
2
1
1
1
2
1
1
0
2
2
0
1
1
0
1
1
1
2
1
1
1
2
1
1
2
2
1
1
0
2
2
0
0
1
1
1
1
1
0
1
1
2
1
1
1
2
0
1
1
2
1
1
1
1
2
1
0
0
2
2
1
1
0
2
1
1
1
1
0
1
1
0
0
2
2
1
1
1
2
2
1
2
0
1
1
2
0
1
0
1
1
0
1
1
1
2
1
0
1
1
1
2
1
1
2
2
1
1
1
2
1
1
1
0
1
1
1
1
1
1
1
2
1
2
1
2
2
1
1
1
2
0
1
0
1
1
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
0
1
1
0
1
1
1
2
1
1
0
2
2
1
1
2
2
2
2
1
1
1
1
0
0
2
0
2
1
2
2
1
1
1
1
0
1
1
1
1
1
1
1
0
2
1
1
1
2
2
1
0
1
1
1
0
1
2
1
1
2
0
1
2
2
1
0
2
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
0
2
1
1
1
1
1
1
1
1
1
1
0
1
2
0
1
1
1
1
1
1
1
1
1
2
1
1
1
1
0
1
1
1
1
2
1
1
2
2
2
1
1
2
1
1
1
1
2
0
2
1
0
1
2
1
1
1
1
0
1
0
1
0
1
0
0
2
1
2
1
1
2
1
1
2
0
0
1
2
1
1
2
1
1
0
1
1
4
2
1
1
1
1
2
2
1
1
2
0
1
2
1
2
2
2
2
0
1
1
2
1
1
2
1
2
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
1
1
1
1
2
2
1
2
1
1
1
2
1
1
1
0
0
1
2
1
1
1
0
1
3
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
0
1
1
2
1
1
1
1
2
1
2
2
1
1
1
0
1
1
1
1
1
0
1
2
2
1
1
1
1
1
1
1
0
1
1
0
1
1
1
1
0
1
1
1
1
1
1
1
1
1
3
2
0
1
1
1
1
1
1
1
1
1
2
1
1
0
1
1
2
1
1
2
1
1
1
2
2
1
1
2
2
1
1
1
2
1
1
2
1
1
1
1
2
2
1
1
2
2
1
2
2
1
0
0
1
1
2
1
1
2
1
1
1
1
1
0
1
1
0
1
1
1
2
2
1
2
2
1
2
1
1
2
2
1
1
1
1
1
1
2
1
1
2
1
2
1
1
2
1
1
1
1
2
2
2
2
1
0
1
1
1
2
1
1
1
1
1
1
0
1
0
2
1
1
2
2
1
2
2
4
1
2
2
1
1
1
2
1
2
1
1
1
1
0
1
1
2
2
1
0
2
1
4
1
1
1
1
1
1
1
1
2
1
0
0
1
1
0
0
0
1
2
0
0
1
1
0
0
1
0
1
0
1
2
1
2
1
2
0
1
1
2
1
1
1
1
2
1
1
1
0
1
1
2
2
1
1
1
1
1
1
1
1
6
1
1
1
2
1
0
1
1
1
2
2
2
1
2
2
3
1
2
1
2
2
1
0
1
1
1
1
1
2
1
1
2
1
0
2
1
2
1
1
0
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
0
2
2
1
1
2
2
1
2
2
1
1
3
1
2
2
2
2
0
2
1
1
2
2
2
0
1
2
1
1
1
2
1
1
2
1
1
0
1
1
1
2
1
0
1
1
1
1
1
2
1
2
1
1
1
2
0
1
0
2
1
2
2
0
1
0
1
1
1
2
2
1
1
2
2
1
1
3
1
1
1
2
2
1
1
0
1
1
0
0
0
0
2
1
0
1
1
2
1
1
2
1
0
1
0
1
1
1
1
1
1
0
0
0
2
1
1
1
2
0
1
2
0
1
0
1
2
0
1
1
0
0
1
0
2
1
2
2
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
0
1
1
2
1
1
1
2
1
1
1
0
1
0
1
2
1
1
0
0
1
1
1
2
0
2
2
2
2
1
1
0
2
1
2
1
0
1
1
1
1
1
2
2
2
1
1
2
1
1
1
2
2
0
1
0
1
1
2
2
1
1
1
1
0
2
1
2
2
2
1
0
1
2
1
2
2
1
1
1
0
0
1
2
2
2
0
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
2
1
2
1
0
1
0
1
1
1
1
2
1
0
2
1
0
1
1
2
2
1
1
1
2
1
1
1
1
2
0
1
0
1
1
1
1
2
1
1
0
1
1
0
2
2
0
0
1
2
1
0
2
1
1
2
2
1
0
2
2
1
1
1
1
1
2
1
1
0
1
1
0
1
2
2
1
1
1
1
2
2
2
1
1
2
0
1
1
1
2
1
2
1
1
1
2
2
1
1
1
1
1
1
0
0
0
0
2
1
2
2
1
2
2
1
2
1
1
0
1
1
1
1
1
1
0
0
1
2
1
0
1
2
0
1
0
0
1
1
2
1
1
1
2
1
1
0
2
1
1
0
1
2
1
1
2
0
0
1
2
0
1
1
0
1
1
1
1
1
2
1
1
0
1
0
1
1
0
2
1
1
2
2
0
1
2
1
0
1
2
1
1
1
1
0
1
1
2
2
2
1
0
2
2
0
2
1
2
2
2
0
1
2
1
1
0
1
2
2
2
1
1
2
1
2
2
1
1
1
1
1
1
2
1
2
2
1
1
1
2
1
1
1
1
0
1
1
0
1
1
2
1
1
1
1
1
2
1
1
2
1
2
1
0
1
0
2
1
1
1
0
1
2
0
2
0
1
1
1
2
0
0
0
1
2
0
0
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
2
0
1
1
2
2
1
0
1
2
0
1
1
2
2
1
1
1
0
0
1
1
1
2
1
1
1
2
2
1
4
1
1
2
2
1
1
2
1
1
1
0
1
1
1
0
1
2
2
1
0
1
0
1
1
1
1
1
1
1
1
0
1
2
1
1
0
1
2
1
1
1
1
1
1
1
2
2
1
2
1
2
1
1
2
1
1
1
1
1
1
2
1
2
1
2
1
0
2
2
0
1
2
1
2
1
0
0
2
1
1
1
2
1
1
1
2
1
1
1
1
0
1
1
1
0
1
1
2
1
1
1
2
1
1
0
4
0
2
1
2
1
1
2
1
2
2
1
1
1
2
0
2
1
1
0
2
2
2
0
1
1
1
1
1
2
1
1
1
1
1
1
0
1
1
1
1
2
1
2
2
1
1
2
1
2
1
1
1
1
1
1
1
1
2
1
2
1
2
1
1
2
1
2
0
1
1
0
1
1
1
1
1
1
0
0
1
1
2
1
2
1
2
1
2
0
1
3
1
1
1
2
1
1
1
2
1
1
1
2
2
0
1
0
1
1
1
1
1
1
2
1
1
2
2
2
4
0
1
1
1
2
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
2
2
2
2
0
1
1
2
0
1
1
1
1
2
1
1
2
1
1
1
2
0
1
1
1
0
1
2
1
1
1
2
1
0
1
1
2
1
1
0
1
0
2
0
0
1
2
1
1
0
1
1
2
0
1
1
1
2
1
1
1
2
2
2
0
2
2
1
2
1
1
1
3
1
1
0
2
2
0
2
1
2
1
2
1
1
1
1
1
1
2
1
1
2
1
1
2
2
1
2
0
1
1
1
0
2
1
0
2
1
1
1
2
1
1
1
1
2
0
1
1
1
2
2
1
1
1
0
2
1
2
1
2
1
2
2
2
2
1
1
1
1
2
2
0
1
0
1
1
0
1
2
2
0
1
2
2
1
1
0
1
1
1
1
2
0
2
2
2
1
1
1
0
1
1
1
1
1
3
0
1
2
0
2
2
1
0
1
1
2
1
2
2
1
1
1
2
0
1
0
0
0
1
2
2
1
1
1
1
1
1
0
0
1
0
1
1
1
0
1
2
1
1
0
1
1
2
1
1
1
2
2
2
2
1
1
0
1
2
1
1
2
1
2
1
1
2
2
0
1
1
1
2
1
1
1
0
1
0
1
1
1
1
1
1
1
1
2
2
1
2
1
2
1
1
0
1
1
0
1
0
1
1
2
1
1
1
2
2
2
1
1
1
2
0
1
1
2
1
1
2
1
1
2
1
4
2
1
0
1
2
1
1
2
1
2
0
0
1
1
0
1
1
2
1
1
1
1
3
1
1
0
2
1
2
0
1
1
2
0
2
0
1
1
1
1
1
0
1
0
1
0
1
1
1
0
2
1
0
0
1
1
0
1
2
1
2
2
1
2
1
1
1
1
2
2
1
0
0
2
2
1
1
1
0
1
2
1
1
1
0
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
0
0
1
1
1
0
2
1
1
1
2
2
2
0
2
1
1
1
1
1
2
1
1
1
1
4
2
0
1
1
1
0
1
0
1
1
2
0
0
2
1
2
0
1
1
1
1
1
1
0
1
1
2
0
1
1
1
1
0
2
2
1
0
1
1
0
1
1
2
1
1
1
1
1
1
2
1
1
1
2
0
1
1
1
2
2
1
0
1
0
1
1
1
1
1
0
1
1
2
0
1
1
2
2
1
2
1
1
1
0
2
1
0
1
1
2
2
2
1
1
1
1
1
0
1
2
1
0
0
2
1
1
1
2
2
0
2
0
2
2
2
1
1
0
1
2
1
1
1
1
2
0
1
1
1
0
1
2
1
1
2
3
1
1
1
1
0
1
2
2
1
1
1
2
1
1
1
2
2
2
1
2
2
2
0
1
1
1
0
1
0
0
1
1
2
2
0
2
1
2
2
1
1
2
0
2
2
2
0
0
1
1
1
0
1
0
2
2
1
2
1
1
2
2
1
2
1
1
2
1
1
1
2
1
1
1
0
1
2
1
2
1
1
2
1
0
1
1
1
0
1
1
2
2
0
1
1
1
0
1
1
1
2
1
1
1
2
0
1
1
1
1
0
0
1
1
0
0
1
1
1
0
0
0
2
0
0
2
1
1
1
1
1
2
1
1
1
1
2
0
1
1
1
2
1
1
0
1
1
1
1
1
2
1
1
0
1
2
1
1
0
0
1
1
1
1
2
2
1
1
1
1
1
2
2
2
1
0
1
1
2
1
0
1
1
1
2
1
0
2
2
2
2
1
1
1
0
1
1
2
1
1
2
1
1
1
1
2
2
2
2
0
0
0
1
1
1
2
0
2
2
0
1
0
1
1
1
1
2
1
1
1
2
0
2
2
1
2
1
0
1
2
1
2
1
1
2
1
1
1
1
1
2
1
1
2
0
1
1
2
1
1
1
1
2
0
0
1
2
0
0
0
1
1
1
2
2
1
1
2
1
1
1
0
2
2
1
2
2
1
1
2
1
2
1
2
2
1
1
2
1
1
2
1
4
1
1
2
2
1
1
1
2
0
0
0
1
0
1
0
1
2
1
1
2
0
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
0
1
0
1
1
1
2
2
0
1
1
2
1
1
1
1
2
1
1
1
1
1
0
1
1
0
1
0
2
1
1
1
2
1
1
1
1
1
0
1
0
2
1
0
1
1
1
1
2
1
1
1
1
1
2
0
1
1
2
1
1
1
2
2
1
1
1
1
1
1
1
1
2
0
2
1
2
0
1
1
1
1
2
2
0
1
1
1
0
1
1
0
1
2
1
2
1
0
1
1
0
1
1
1
1
2
1
1
1
1
0
2
1
0
1
2
2
0
2
1
2
2
2
1
0
2
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
0
1
1
1
1
1
2
2
1
1
1
1
0
1
1
1
2
2
2
1
1
1
1
1
2
1
2
2
1
1
2
2
1
2
1
2
1
1
2
1
0
1
2
2
1
2
1
2
0
0
1
1
2
2
2
0
1
2
1
1
1
2
1
2
1
2
1
2
1
1
1
1
1
1
1
0
1
1
1
1
0
2
1
1
1
2
2
1
0
1
1
1
1
1
0
0
1
1
1
1
1
0
0
1
1
1
1
1
1
1
0
1
1
1
1
0
2
0
1
1
0
0
1
1
2
1
1
1
1
1
2
1
0
0
1
1
1
0
1
1
1
2
2
2
1
1
0
2
1
1
2
1
0
1
2
1
2
1
0
1
3
1
2
2
2
2
1
2
1
1
1
2
1
0
1
1
1
1
2
1
1
2
3
1
1
1
1
2
1
1
1
1
1
2
2
2
1
1
1
0
2
1
1
0
2
2
1
0
1
1
1
0
2
0
0
1
1
1
2
0
1
1
1
2
0
1
1
2
1
1
1
1
2
0
1
2
1
0
3
2
0
0
0
2
0
1
1
1
1
1
1
2
1
1
1
0
1
1
2
0
2
2
1
1
0
2
1
1
0
1
2
1
3
1
1
1
2
1
0
1
1
1
1
1
1
0
2
1
2
0
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
0
1
2
0
0
0
1
1
1
0
2
1
1
2
1
0
1
3
2
2
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
0
1
2
1
1
0
1
2
1
0
1
1
1
2
0
1
2
1
1
1
1
2
2
0
1
0
2
1
2
2
2
1
0
1
1
2
2
0
1
1
1
1
1
1
1
2
1
1
2
1
1
1
2
0
1
1
1
1
2
0
2
1
1
1
2
1
1
1
2
1
1
1
1
1
2
1
1
0
1
2
2
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
0
1
0
1
1
0
2
2
1
1
2
0
0
1
1
1
1
1
1
0
0
1
1
2
1
1
0
1
1
1
2
0
1
2
1
0
1
1
1
1
0
3
2
1
1
1
1
1
1
1
1
1
0
1
1
1
0
1
1
2
1
1
2
1
1
2
1
0
1
1
1
1
1
1
1
1
2
1
2
1
0
1
1
1
1
0
2
1
1
2
2
1
0
2
0
1
1
2
0
1
0
2
0
0
0
1
2
0
1
1
1
1
0
1
2
0
1
2
1
1
0
1
0
1
1
1
2
1
0
1
1
1
1
1
2
0
2
2
2
1
0
2
1
1
1
2
1
1
1
2
1
1
1
2
0
2
1
1
1
1
0
1
2
2
1
2
0
2
1
2
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
0
0
1
2
2
1
1
1
1
1
1
2
1
1
0
1
0
2
2
1
2
0
1
1
1
0
2
2
1
1
1
1
1
1
1
0
2
1
0
2
1
0
2
2
1
1
2
1
2
1
1
1
1
0
0
1
1
0
1
1
1
1
1
1
0
1
1
2
1
1
1
2
1
1
0
1
1
2
2
1
0
1
1
0
2
2
1
1
1
1
1
1
2
1
2
1
1
1
2
6
1
0
0
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
0
1
0
0
1
1
0
1
2
1
0
1
1
1
0
1
2
1
1
2
1
2
1
2
0
1
2
2
1
2
1
2
1
1
2
2
1
1
1
2
1
2
2
1
2
2
1
0
1
1
2
2
2
2
0
2
1
1
1
0
1
2
1
1
1
2
1
1
1
2
1
1
1
1
2
0
0
1
2
1
1
2
1
1
2
1
1
1
1
1
2
2
2
2
1
2
2
0
1
2
1
0
1
2
0
2
1
1
1
1
1
2
1
1
2
1
1
1
2
1
1
2
0
1
0
1
0
2
1
2
1
2
1
1
1
0
1
0
1
1
1
1
2
1
0
1
1
1
2
1
1
1
1
2
2
2
1
0
1
1
1
1
1
1
0
1
1
1
2
2
2
1
0
1
2
2
1
1
1
1
1
1
1
1
0
2
1
1
1
0
2
2
2
1
1
2
0
1
2
1
1
1
1
1
1
1
1
2
0
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
2
1
2
1
0
2
1
1
1
1
1
1
1
1
1
1
2
2
3
2
0
2
1
1
1
1
1
0
1
1
1
1
1
2
1
0
2
1
1
2
2
1
0
1
0
1
1
0
2
1
1
1
2
2
2
1
1
1
2
0
1
1
1
1
1
2
2
0
2
1
2
0
2
1
1
1
1
1
2
1
0
0
2
2
0
2
1
2
2
1
1
2
1
1
1
1
2
0
1
0
2
1
0
1
1
1
0
1
1
1
1
1
2
1
2
1
1
1
2
0
1
1
2
1
2
1
1
1
1
2
0
1
2
1
1
1
0
1
1
0
1
1
1
1
1
0
1
1
1
2
0
0
1
0
1
1
2
0
1
1
3
2
1
1
0
0
5
1
1
2
2
1
1
1
1
1
2
1
1
1
2
1
2
0
1
0
1
1
1
1
1
0
2
2
2
1
1
2
2
0
2
1
2
0
2
0
1
2
0
1
1
1
1
1
1
2
1
1
1
2
3
0
0
1
1
1
1
1
1
1
1
0
1
1
1
3
0
1
1
1
1
1
2
1
2
1
0
1
1
0
0
1
1
1
1
1
1
1
1
1
1
2
0
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
2
1
1
0
1
0
1
2
1
1
0
0
1
1
1
1
1
1
2
1
1
1
1
0
1
1
1
1
1
0
1
1
1
1
1
0
0
1
1
0
1
1
1
1
1
2
2
1
1
1
1
3
1
0
1
1
1
2
1
2
1
0
1
1
1
2
2
1
2
2
2
1
2
1
2
1
1
1
0
1
1
0
0
1
0
1
1
0
1
1
1
1
0
1
2
1
0
1
2
0
1
2
2
2
1
2
2
1
1
0
1
2
1
2
0
1
0
2
0
1
2
0
0
1
2
1
2
2
1
0
1
1
2
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
1
0
0
1
1
0
2
1
1
1
1
1
2
0
2
1
2
1
2
0
2
2
1
1
0
2
1
2
1
1
1
1
1
1
2
1
1
0
0
2
2
1
0
2
1
1
1
0
0
0
1
1
2
1
1
2
1
1
2
2
2
1
1
1
1
1
1
0
0
2
1
1
3
1
0
1
1
1
1
1
1
2
2
1
2
2
2
1
1
1
2
2
1
1
0
2
2
0
1
1
1
2
1
1
0
1
1
0
2
1
1
1
2
1
1
0
1
1
1
2
2
1
1
1
2
1
1
2
1
2
1
1
0
1
1
2
1
1
2
1
1
1
0
2
3
1
1
1
1
1
1
1
2
1
2
1
1
2
2
2
1
0
0
1
2
1
0
2
2
2
0
1
2
1
1
2
2
1
2
1
0
1
2
1
1
1
1
2
2
1
0
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
0
1
1
1
1
0
0
1
0
0
0
1
0
2
2
0
1
0
0
1
2
1
1
1
1
1
1
0
2
2
0
1
1
3
0
0
1
0
1
2
1
1
2
1
2
0
2
2
2
1
2
1
1
1
1
1
2
1
2
1
1
2
1
2
1
0
0
1
1
1
2
1
1
1
0
1
1
1
2
0
0
2
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
2
0
1
2
1
1
1
1
0
1
2
0
1
1
1
1
1
0
1
1
2
1
2
1
1
1
1
1
1
1
2
1
2
1
2
1
0
1
2
1
1
1
2
1
2
0
2
2
1
1
1
1
2
0
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
2
1
0
1
1
1
2
1
1
1
1
0
1
0
2
2
2
1
2
2
1
0
1
1
1
1
1
2
2
2
0
1
2
0
0
1
1
0
1
1
2
2
1
1
1
1
2
0
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
0
0
1
2
1
1
3
1
1
2
1
1
3
1
1
1
1
2
1
1
1
2
1
0
2
1
1
1
2
1
0
1
1
1
2
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
2
1
0
1
2
1
1
1
2
1
0
1
1
2
1
2
1
1
2
2
1
1
0
2
0
1
1
0
0
2
1
1
1
2
1
1
1
1
1
0
2
0
2
2
1
1
0
0
1
1
1
2
2
1
0
1
2
1
1
0
1
0
0
1
1
0
1
1
1
1
5
2
0
1
1
1
2
1
1
1
0
1
1
2
1
2
1
0
1
1
2
0
1
1
1
2
2
1
2
1
2
1
0
1
2
1
0
1
2
2
0
1
2
1
1
1
2
1
0
1
0
1
1
2
1
2
2
1
1
1
1
0
1
1
1
1
0
1
1
1
1
2
1
1
1
2
1
2
2
1
2
2
1
1
0
1
1
2
1
1
1
2
1
2
1
1
1
0
2
2
2
0
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
2
1
2
1
1
0
1
1
1
2
2
1
1
2
1
1
1
1
1
1
2
2
1
1
1
2
1
1
0
1
1
0
2
0
2
1
2
1
2
1
1
1
2
2
2
1
2
1
1
0
2
0
1
1
2
1
1
1
1
0
2
1
1
2
1
2
1
1
1
0
1
1
1
1
1
2
1
0
2
1
1
2
1
1
1
0
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
0
0
1
3
2
1
0
2
2
1
2
2
1
1
0
1
1
0
1
1
0
1
1
1
2
2
2
1
1
1
2
1
2
1
0
1
1
2
1
1
1
1
1
2
1
2
1
2
1
2
1
1
1
1
0
1
1
1
1
1
1
2
1
1
2
0
1
1
0
1
1
1
1
0
0
1
1
1
1
1
1
1
2
0
1
1
1
1
2
0
0
1
2
0
2
0
1
2
1
2
2
1
1
1
1
1
1
2
2
1
0
0
2
1
0
1
0
1
2
0
1
2
1
2
1
1
2
2
0
0
1
1
2
1
1
0
1
1
2
1
1
1
0
2
1
2
0
1
1
2
0
2
1
1
1
3
2
1
1
1
1
2
1
2
1
1
1
2
1
1
1
2
1
1
2
1
2
1
0
1
1
0
1
1
3
1
0
0
1
1
2
2
0
1
1
1
0
1
1
1
1
0
0
2
1
1
0
0
0
1
2
1
1
0
2
1
1
1
1
0
0
1
1
1
0
0
1
1
1
1
1
1
1
1
0
2
1
1
2
2
0
2
0
0
0
1
1
2
1
0
2
1
1
2
0
1
1
2
1
2
1
1
1
1
2
1
1
2
2
2
1
1
1
1
1
2
1
1
1
0
1
1
2
1
1
1
1
1
2
2
1
0
2
1
2
1
2
0
1
1
1
1
0
1
2
1
2
1
1
0
1
1
0
1
1
1
1
1
2
0
1
2
1
2
1
1
0
1
0
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
2
2
0
1
1
1
0
1
1
1
1
1
1
0
1
1
1
1
1
2
2
1
1
1
0
1
1
1
2
1
1
0
1
1
1
1
0
1
1
1
2
0
2
2
0
1
1
1
0
2
1
2
2
2
1
1
1
1
1
2
2
1
1
0
1
2
1
1
1
1
1
2
0
1
1
1
1
1
1
1
2
1
1
1
0
2
1
2
1
1
1
0
2
1
1
2
1
0
1
2
0
1
1
1
2
1
1
1
0
2
1
1
1
1
1
1
1
1
1
0
1
1
1
1
2
1
2
2
2
1
1
1
0
1
1
2
1
2
2
1
2
1
1
1
2
2
1
1
1
0
2
2
1
2
1
1
1
1
1
1
2
2
2
1
0
2
1
2
0
1
1
1
2
1
1
1
0
1
2
2
1
2
1
1
0
1
1
2
0
1
1
1
1
2
1
1
1
2
1
2
2
0
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
1
0
1
1
2
1
1
2
1
1
1
2
0
1
2
2
2
2
1
1
0
3
1
1
1
1
1
0
0
1
2
1
2
0
1
0
2
1
1
1
0
2
1
1
1
2
1
1
1
1
2
2
1
0
0
0
0
1
1
1
1
1
1
1
1
2
1
0
3
1
2
2
1
1
1
1
1
2
0
1
1
1
1
1
1
1
1
2
1
2
1
1
2
2
1
0
1
2
1
1
1
1
1
0
1
1
2
1
1
1
1
1
1
1
1
1
1
1
0
1
2
2
1
2
1
1
1
1
1
1
0
2
0
1
1
2
2
1
1
1
2
2
1
1
1
1
1
1
1
1
2
1
0
1
1
0
2
1
1
1
1
2
1
1
2
1
1
1
0
2
1
1
1
0
1
2
2
1
0
1
0
1
1
0
1
2
1
1
1
0
0
1
1
2
0
0
1
0
1
0
0
1
2
1
2
0
1
0
1
3
2
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
0
1
2
1
2
1
0
1
2
0
1
1
2
0
0
2
1
1
1
1
2
1
1
0
1
1
2
2
0
0
0
0
1
1
1
2
2
0
2
1
2
2
1
0
1
3
2
2
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
2
0
2
1
1
2
1
1
1
1
1
1
1
2
1
0
2
1
2
1
2
0
1
1
0
0
1
1
2
0
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
2
2
1
2
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
0
1
0
1
1
0
2
1
1
1
2
1
1
1
1
0
1
1
0
2
2
0
2
1
1
1
0
1
1
0
1
1
0
1
1
1
1
1
2
2
2
1
0
1
1
2
2
1
0
2
0
1
2
1
1
1
1
1
3
2
1
1
0
2
1
2
0
1
1
0
1
2
2
0
1
2
2
0
1
2
1
2
2
2
2
1
0
1
2
1
1
1
1
1
2
1
0
0
0
0
1
2
2
2
1
2
2
2
1
1
2
2
1
0
1
1
3
1
1
2
1
1
2
1
3
0
0
0
2
1
1
1
1
1
2
1
1
1
1
0
2
1
1
1
1
1
2
1
1
0
0
1
1
0
1
2
1
2
1
2
1
1
1
1
2
2
1
1
1
1
2
1
0
0
1
1
1
1
1
2
1
1
1
0
2
0
1
1
1
1
2
1
1
1
0
3
1
3
1
1
1
1
1
1
0
1
1
2
2
2
0
0
1
2
1
1
0
2
1
1
1
2
1
1
1
0
0
1
1
2
0
1
0
0
2
1
2
1
2
1
0
2
1
2
1
1
1
1
1
2
0
1
2
1
2
1
2
1
2
0
1
2
1
1
1
2
1
2
1
0
2
1
1
4
0
1
2
1
2
1
1
1
1
1
1
1
1
1
1
2
2
1
2
1
0
0
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
0
1
1
1
2
1
1
2
1
2
3
1
1
1
1
1
1
0
2
1
1
1
0
2
2
1
1
1
1
1
1
1
1
2
0
2
1
2
1
1
2
1
1
1
1
2
1
2
1
2
0
1
1
1
1
1
2
0
1
1
1
0
2
2
1
2
1
1
0
1
1
1
2
1
2
1
2
2
1
0
1
1
2
0
2
1
2
1
1
2
2
2
1
1
1
1
2
2
2
1
1
1
1
1
2
1
2
1
2
0
2
1
1
0
1
2
2
1
1
1
1
2
1
2
1
1
1
1
0
1
2
0
1
1
0
0
1
2
1
1
2
0
1
2
2
2
1
1
1
1
2
1
1
1
2
0
1
3
1
0
2
1
0
2
1
0
1
2
1
1
1
1
1
2
2
2
2
2
2
2
1
1
0
1
1
3
1
1
2
2
1
1
1
2
0
0
1
1
0
1
1
1
0
1
1
0
1
2
1
2
1
1
1
1
1
1
0
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
0
3
1
1
1
2
1
1
1
1
1
2
2
1
2
1
1
2
2
1
1
2
1
1
0
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
0
1
1
2
1
2
1
1
0
2
2
1
2
0
1
1
1
2
1
1
1
1
1
1
2
2
0
1
0
1
1
0
1
0
1
2
1
1
2
0
1
1
2
2
1
1
1
1
2
2
1
0
2
1
1
0
1
0
1
0
1
1
1
1
0
2
1
1
1
1
1
0
0
1
2
2
2
1
1
2
1
1
1
1
1
0
1
0
1
1
1
2
1
1
1
0
2
0
1
1
2
0
1
1
1
0
0
1
1
1
2
2
1
1
1
2
1
1
1
2
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
2
2
1
0
1
1
0
1
1
0
2
1
1
1
0
2
3
2
2
1
1
1
2
1
2
2
0
1
1
2
0
2
2
1
0
2
1
1
2
0
1
2
1
0
2
1
1
1
0
0
2
2
0
1
0
1
0
1
1
0
1
1
1
2
1
0
1
2
1
1
2
2
1
0
2
0
1
2
1
1
0
3
2
2
1
1
2
1
1
0
1
1
2
1
1
1
1
2
1
1
0
1
1
1
1
1
0
1
1
2
0
1
2
1
1
1
0
2
1
2
2
2
1
1
0
0
1
2
0
2
1
0
1
2
1
1
3
1
0
1
1
1
1
0
2
1
1
1
1
0
2
1
0
1
1
3
1
2
2
1
1
1
0
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
1
0
1
1
2
1
1
1
0
1
1
2
1
1
0
1
1
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
2
1
0
0
1
1
2
1
1
0
1
1
1
1
1
1
1
1
2
1
0
1
0
2
0
0
2
2
1
1
1
2
1
1
0
1
2
2
1
1
2
1
1
1
1
2
1
1
1
2
1
1
2
2
1
1
1
2
0
1
1
2
1
1
2
1
2
1
1
1
1
1
1
0
1
1
2
2
1
1
0
1
1
0
2
2
1
1
0
0
1
1
1
1
0
2
1
1
2
1
1
0
2
1
1
2
0
1
1
1
1
1
1
0
2
2
0
1
1
2
1
0
1
0
1
0
1
1
2
1
2
2
1
1
0
1
1
0
1
1
2
1
1
0
1
2
1
1
1
2
1
1
1
1
1
1
0
2
1
0
1
2
2
1
1
2
1
0
2
1
0
2
0
1
1
2
0
1
1
1
2
1
1
2
1
1
1
1
1
1
0
2
2
0
1
2
1
1
1
1
1
1
1
1
1
0
1
1
0
1
1
0
0
1
1
2
1
1
1
1
2
3
1
2
2
1
1
0
2
1
2
1
0
2
1
1
2
1
1
1
2
2
2
1
1
1
1
0
2
2
0
0
2
0
2
1
1
1
2
1
1
2
1
1
1
0
0
1
1
2
1
1
2
1
1
0
2
1
1
1
1
1
1
2
0
2
1
2
1
1
1
1
0
1
2
1
1
1
2
2
2
2
1
1
1
1
1
1
1
2
1
3
1
2
0
1
2
1
2
2
1
1
2
0
1
1
2
1
2
0
1
2
2
2
1
1
2
1
0
1
1
2
1
1
2
1
1
1
1
1
1
0
1
2
1
1
1
2
1
2
1
1
2
0
1
2
1
2
1
2
0
0
1
1
0
1
1
1
0
0
0
1
2
1
1
2
1
1
2
1
0
2
2
0
2
1
1
2
1
1
0
1
2
2
2
0
1
2
1
1
2
1
1
0
0
1
1
0
1
1
1
2
1
1
1
0
2
2
1
1
1
1
1
2
1
3
1
1
0
1
2
1
1
1
2
1
2
1
0
0
1
2
2
1
1
1
1
0
3
1
0
0
1
2
1
0
1
1
1
1
0
1
2
0
0
1
1
2
2
0
1
1
0
1
2
1
1
1
0
2
1
2
1
1
1
1
1
0
2
1
1
1
1
1
1
2
1
2
0
0
2
1
1
2
1
1
1
2
2
2
2
1
1
0
1
2
0
1
0
1
1
1
1
1
1
1
1
2
2
0
1
2
0
1
1
1
2
1
2
2
0
1
2
1
2
1
2
0
1
2
2
1
1
1
2
1
2
2
1
1
1
1
2
0
1
4
1
1
1
2
1
0
2
1
1
2
1
2
1
2
1
1
2
1
2
1
1
2
1
1
1
1
2
1
2
0
1
2
2
2
1
1
1
0
1
1
1
1
1
0
2
2
1
1
0
1
0
1
0
1
2
2
2
1
1
0
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
2
2
1
2
1
2
1
0
1
1
0
1
1
1
2
1
1
1
1
1
1
2
1
0
0
1
0
1
0
3
1
1
2
2
1
0
1
2
1
2
1
1
2
1
2
2
1
1
1
1
2
2
1
1
1
5
0
0
1
1
1
2
1
1
1
1
2
2
1
1
2
1
2
1
0
1
1
1
1
0
1
1
2
0
2
1
2
1
1
1
2
1
1
1
2
2
1
0
2
1
0
1
1
2
1
1
2
2
2
1
1
0
1
2
2
1
1
1
0
1
1
0
0
1
2
1
1
0
1
1
1
1
1
2
0
2
2
1
0
2
0
1
1
1
1
1
2
1
1
1
1
1
0
1
2
1
2
1
1
0
2
2
1
0
1
1
1
0
1
0
1
2
1
0
1
1
2
1
2
2
1
1
1
2
1
0
1
1
1
1
0
1
1
1
0
2
1
1
1
1
1
1
1
3
1
1
1
0
0
0
1
1
1
0
1
2
2
1
1
1
2
2
2
1
1
1
1
0
1
1
1
0
1
1
1
0
1
1
2
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
0
0
1
1
1
1
2
1
2
1
1
0
1
2
1
1
1
1
1
1
0
1
1
2
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
2
1
1
2
1
0
1
2
1
2
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
2
0
1
2
1
2
1
0
1
1
1
1
2
1
1
1
1
1
1
0
1
2
2
1
1
1
0
1
2
1
1
2
0
0
2
1
1
1
0
1
2
0
0
2
1
1
1
1
0
1
1
1
1
2
1
0
1
3
0
0
1
1
2
2
2
2
1
1
2
2
1
0
1
1
0
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
2
2
1
2
1
1
1
0
0
0
1
1
1
0
2
1
1
1
2
1
2
1
2
2
2
0
1
1
0
0
3
1
1
2
0
2
1
1
2
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
0
1
1
2
1
1
1
1
1
1
2
1
2
1
0
1
1
1
2
1
1
1
1
0
1
2
0
0
1
1
1
0
0
2
1
1
2
1
1
1
1
1
2
1
2
1
0
2
1
1
2
1
1
0
1
1
1
0
0
0
2
2
1
2
2
1
1
2
1
1
1
2
0
2
1
0
1
1
1
1
1
1
1
1
2
1
1
0
1
1
1
2
1
2
1
1
1
2
1
2
1
2
1
1
2
2
2
0
0
1
0
1
1
0
1
1
2
1
1
2
1
1
1
2
2
0
1
1
0
1
1
0
0
1
1
1
1
2
1
0
2
1
1
1
0
1
1
0
1
1
1
1
1
2
1
1
1
2
1
2
0
3
1
1
1
1
1
1
0
2
1
1
1
1
0
1
2
2
1
1
1
1
1
1
1
1
1
2
2
1
1
2
0
2
1
0
1
1
1
0
1
2
1
1
0
2
0
2
1
2
1
0
1
1
1
1
1
2
2
1
2
2
2
1
2
0
1
2
2
1
1
1
1
2
1
1
1
1
1
2
1
1
0
0
1
1
2
2
1
1
1
1
3
2
1
1
1
1
2
1
0
1
0
2
2
1
1
1
1
2
2
1
2
1
0
1
1
0
1
1
1
0
1
2
1
1
3
1
2
8
1
1
2
1
1
1
1
0
1
0
1
1
1
1
2
1
0
1
0
1
1
1
1
1
2
2
1
0
1
1
2
1
1
1
1
1
0
1
1
2
2
0
0
2
0
1
0
2
1
2
1
1
0
2
0
1
0
1
2
1
1
1
1
1
2
0
0
1
0
1
1
2
0
2
2
2
4
2
1
1
1
1
1
2
1
1
2
2
1
1
3
1
0
1
0
0
1
1
1
1
1
2
2
0
2
2
1
1
2
2
0
1
0
1
2
1
2
1
1
2
1
1
1
1
1
1
0
0
1
0
1
1
2
1
1
1
1
1
2
2
1
2
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
2
0
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
2
0
1
1
1
2
1
1
1
1
0
2
2
2
1
0
0
1
1
1
2
2
1
0
2
1
1
2
1
1
1
1
2
0
2
1
2
1
1
2
0
2
1
1
1
0
2
1
1
0
2
0
2
1
2
1
1
1
1
2
1
2
2
1
1
2
1
0
2
2
1
1
1
2
0
0
2
1
1
1
0
1
1
1
1
2
1
2
0
0
1
1
1
1
1
1
1
1
2
2
0
2
1
1
2
1
1
1
2
2
2
1
1
2
2
2
1
1
1
2
2
1
2
0
0
1
2
2
1
1
1
1
2
1
1
1
1
1
1
0
1
1
2
1
2
1
2
1
0
1
1
1
2
0
0
1
1
1
2
1
1
1
1
1
1
1
0
1
1
0
3
1
0
2
1
1
2
2
1
1
1
1
1
2
1
2
0
2
1
1
1
1
1
2
1
1
0
0
0
1
0
0
1
2
1
1
0
2
1
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
2
1
2
5
2
1
1
0
1
2
0
0
1
2
1
0
1
2
1
1
1
1
1
2
1
0
2
1
1
1
1
2
1
0
3
1
1
1
1
2
1
1
1
1
2
2
1
2
1
1
1
1
0
1
1
1
2
1
2
1
2
2
2
1
2
1
2
1
1
1
2
1
1
0
0
1
1
2
1
2
2
1
2
1
1
2
0
1
2
1
1
1
2
1
1
1
2
1
1
1
0
0
1
1
2
2
0
1
2
1
1
0
1
0
2
2
1
2
2
1
2
2
1
2
1
2
1
2
1
0
0
1
1
1
1
0
1
1
1
2
1
2
1
1
2
1
0
2
2
1
2
0
1
2
1
0
3
1
2
2
2
1
1
0
1
2
2
1
1
1
1
1
1
1
1
2
2
1
1
1
2
1
1
1
1
2
1
1
1
1
0
1
2
0
1
1
1
1
1
1
2
1
1
2
1
0
1
1
1
1
1
2
0
1
2
1
1
0
1
1
1
0
1
0
2
2
1
1
0
1
0
2
1
2
1
2
1
1
0
0
0
1
1
1
2
2
0
1
0
1
2
0
1
1
1
1
2
1
1
2
1
1
2
1
2
2
1
0
3
1
2
1
2
1
1
0
0
1
3
1
1
2
2
2
1
1
1
1
2
1
0
1
2
2
1
1
1
2
2
2
1
1
2
1
1
1
1
1
0
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
2
1
0
1
1
2
1
1
1
1
1
0
2
2
1
0
1
1
2
1
1
1
1
2
1
1
1
0
0
2
2
1
0
1
2
1
2
2
1
1
1
0
1
1
2
1
1
2
1
2
0
2
1
1
1
2
1
1
1
3
2
2
1
1
0
1
0
1
0
1
1
0
3
1
1
1
1
1
1
1
2
1
2
1
2
1
1
1
0
0
2
1
1
1
1
0
1
0
1
1
1
1
0
2
1
0
2
2
1
1
0
0
1
1
1
1
1
2
2
2
1
1
1
0
1
2
1
2
0
0
1
1
1
1
1
1
2
1
0
2
2
1
2
2
1
2
1
1
2
1
1
1
1
1
2
1
2
0
1
1
1
1
1
0
2
1
1
1
1
2
0
2
2
2
1
2
1
1
0
0
2
2
0
1
2
0
1
2
3
1
2
2
1
1
2
1
0
2
1
1
1
2
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
0
2
0
1
1
0
2
1
2
0
1
1
1
2
1
1
1
2
2
2
1
0
2
1
1
1
1
1
1
2
1
1
1
1
0
1
1
0
2
2
1
2
2
1
1
2
0
0
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
2
2
1
1
2
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
1
0
1
0
2
1
0
0
0
1
2
1
1
2
1
2
1
0
2
1
0
2
0
2
1
2
0
1
0
1
2
1
2
1
1
1
2
1
2
2
1
1
2
1
0
1
2
1
1
1
2
2
1
1
1
1
2
2
1
2
1
1
1
2
2
1
1
1
1
1
1
1
1
1
0
0
2
1
1
1
1
2
2
1
1
1
1
2
2
1
1
1
1
1
1
1
2
2
2
1
2
0
1
1
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
1
0
1
2
2
0
3
1
0
2
0
0
1
1
2
1
2
1
2
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
0
1
0
2
0
1
2
2
1
1
1
1
0
2
1
1
1
1
1
2
2
1
1
2
1
1
2
1
2
1
2
1
1
1
1
2
1
0
2
1
1
1
0
0
1
2
1
1
1
1
1
0
1
2
0
0
1
1
0
1
2
1
1
1
0
0
3
1
2
2
1
1
1
1
1
2
1
1
2
2
3
0
1
2
0
1
1
1
1
1
1
0
1
2
1
2
1
1
1
1
0
1
0
2
0
1
2
1
1
0
2
1
0
1
1
1
2
1
2
1
2
2
1
0
1
0
2
2
1
0
2
1
1
0
2
1
0
0
1
1
1
1
1
1
0
1
1
0
2
0
0
2
1
1
1
0
1
1
2
0
2
1
1
1
1
1
0
2
1
0
2
1
0
1
1
1
1
1
2
1
1
0
0
2
1
1
1
1
2
1
1
2
2
0
2
1
1
0
0
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
2
1
1
0
0
2
2
1
1
1
2
0
2
2
1
1
1
1
1
0
1
1
1
1
1
1
1
2
2
1
1
1
2
0
1
1
1
2
2
2
1
1
1
1
1
1
0
1
1
1
2
1
0
1
1
2
1
1
2
1
1
1
2
0
1
2
1
2
2
1
0
1
1
1
1
2
1
0
2
2
1
0
1
2
1
2
2
0
1
0
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
2
2
0
1
1
2
1
1
1
2
2
1
0
1
1
1
1
1
1
1
0
2
2
0
1
1
2
2
2
1
1
1
1
1
1
1
1
2
1
2
1
2
2
2
1
1
1
1
1
2
2
1
1
1
2
2
2
1
2
2
0
1
1
1
0
0
0
1
2
1
2
1
1
2
1
1
2
1
1
1
0
1
1
0
2
1
1
1
1
2
2
1
2
1
1
1
1
1
2
0
1
2
2
1
2
1
2
1
1
1
1
1
1
2
2
1
1
1
1
0
1
0
1
1
1
0
1
1
1
1
1
1
1
2
1
2
1
2
2
1
1
2
0
2
1
2
1
2
2
1
2
1
0
1
1
1
2
1
2
1
1
1
1
0
2
1
1
2
1
2
1
2
0
1
1
2
1
1
1
2
1
2
0
1
1
1
0
1
2
1
2
1
1
1
1
2
1
1
1
1
0
1
1
2
0
2
1
0
2
1
0
1
1
2
1
1
1
0
3
1
1
1
1
2
1
1
2
2
2
1
1
1
1
1
2
1
1
1
1
1
2
1
2
1
1
1
2
2
2
1
1
1
0
1
1
1
2
1
1
1
1
2
1
0
1
1
2
1
2
1
1
0
2
1
1
2
2
1
2
1
2
1
1
3
1
1
1
1
1
2
0
2
0
0
1
2
1
0
0
1
1
2
1
2
1
2
2
0
1
1
1
7
2
2
2
2
1
1
1
1
1
1
1
1
1
1
1
0
0
0
2
1
3
1
1
0
1
2
0
2
1
2
2
1
1
0
1
1
2
2
1
1
2
1
2
1
1
4
0
1
1
1
1
1
2
2
1
1
0
2
1
1
1
0
1
1
1
2
2
0
2
1
0
2
2
1
1
0
1
2
1
1
0
2
1
1
1
1
1
0
1
1
1
0
1
2
1
2
1
0
1
1
1
0
1
0
1
1
1
2
1
2
1
2
2
1
1
1
2
1
1
1
0
1
1
1
2
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
2
0
2
1
1
1
1
1
1
2
1
0
0
1
1
0
1
2
1
2
1
1
1
1
2
2
1
1
0
1
1
2
1
1
1
1
1
1
1
0
1
1
0
2
1
1
0
1
2
1
2
1
1
1
0
1
1
1
1
1
2
1
0
1
0
1
1
1
2
1
2
1
2
1
1
1
1
1
1
1
0
1
2
1
1
1
0
0
1
0
0
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
1
2
2
1
1
2
2
0
2
1
1
2
1
1
2
1
2
2
1
1
2
2
2
1
1
1
1
0
1
2
2
1
1
2
2
2
1
0
1
2
1
1
1
1
2
1
1
1
1
1
3
1
1
2
1
1
0
1
1
0
1
1
1
1
1
1
0
1
2
2
1
1
0
1
2
1
2
2
1
1
1
0
0
2
0
1
1
0
2
1
0
1
1
0
1
2
1
1
0
1
1
2
1
1
1
1
1
1
0
2
2
1
0
1
1
2
1
1
1
1
2
1
1
1
1
1
1
0
1
1
1
0
2
1
1
1
1
2
1
1
0
1
1
2
1
1
1
2
0
1
1
0
1
1
1
2
1
1
1
1
1
0
1
1
2
1
1
1
1
1
2
0
2
1
1
1
0
0
1
1
0
1
1
1
1
1
2
0
2
1
2
0
1
1
0
1
1
2
1
1
1
1
1
2
0
2
1
1
2
2
0
1
0
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
2
2
2
0
0
2
1
2
0
1
1
1
1
1
1
0
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
0
1
2
2
1
2
1
1
1
2
2
1
2
2
2
2
2
0
1
2
1
1
1
2
2
1
1
2
1
1
2
1
1
0
2
2
1
1
1
1
1
0
2
0
1
1
2
1
1
1
1
2
0
3
1
2
0
2
0
1
4
2
2
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
1
2
1
0
2
0
1
1
1
1
2
1
1
1
1
1
1
2
2
2
1
0
1
3
1
1
1
1
1
2
1
1
2
1
0
1
2
2
1
1
1
1
2
1
1
1
1
1
0
2
2
2
1
1
1
2
1
1
1
1
1
1
2
0
1
2
0
1
0
0
1
1
1
1
1
1
1
2
0
1
1
2
2
1
1
2
0
1
1
1
1
1
1
2
0
1
1
1
1
0
2
1
2
0
2
1
1
1
0
2
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
2
1
1
2
2
0
1
2
2
2
2
1
1
2
1
1
1
2
1
1
0
1
1
0
3
0
2
2
2
1
1
1
1
1
1
2
1
1
1
1
0
1
0
1
2
1
1
1
1
1
1
1
1
1
1
2
2
1
0
0
2
1
1
1
2
1
1
1
0
1
1
1
1
0
1
0
2
0
2
2
1
1
2
2
1
1
1
1
1
2
1
2
0
0
1
1
2
0
1
2
1
2
1
1
1
1
1
0
1
1
0
1
2
1
1
1
2
1
1
1
1
1
1
0
2
0
1
2
1
1
1
1
0
1
2
1
2
1
1
0
1
1
1
1
1
1
1
1
2
2
1
0
1
1
1
1
1
1
1
0
1
1
1
2
1
2
1
0
1
0
1
2
0
1
1
1
1
1
1
1
1
1
0
0
1
0
1
1
1
0
1
2
0
1
1
2
2
1
1
1
0
1
1
1
1
2
0
0
2
2
1
2
1
0
2
1
2
2
1
1
1
1
2
0
0
2
1
1
1
2
1
2
1
1
1
2
1
0
1
1
2
0
2
0
1
1
1
1
1
2
2
1
0
2
1
1
1
1
1
1
2
2
2
0
0
2
1
1
1
1
0
1
1
1
1
0
1
1
1
1
1
1
1
0
2
0
0
1
1
1
1
1
1
0
1
2
1
1
1
3
1
0
1
1
1
1
2
2
2
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
0
1
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
1
0
1
2
1
1
1
1
1
1
1
2
1
0
1
1
2
1
1
2
1
1
1
1
1
1
1
2
0
1
0
1
1
0
1
1
1
1
1
1
2
1
1
1
2
1
2
1
2
2
0
2
0
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
2
0
1
2
1
1
1
2
0
2
2
1
1
1
1
1
0
1
1
1
1
1
2
1
1
1
0
1
1
1
1
1
0
1
2
1
2
1
1
2
1
1
1
2
1
2
1
4
2
0
1
3
1
0
1
1
1
1
1
2
2
0
1
1
2
1
0
1
1
1
1
0
1
1
2
1
2
2
1
1
2
1
2
1
2
1
1
0
2
1
2
2
0
1
2
1
2
1
1
0
1
2
1
1
2
2
1
2
1
1
0
1
0
1
1
1
1
1
0
1
1
1
1
1
1
1
0
0
0
1
2
1
0
1
1
1
1
0
1
2
1
1
1
1
1
1
0
2
1
0
1
1
2
0
0
0
2
2
2
1
1
1
1
1
2
1
0
2
1
2
2
1
1
2
0
1
0
1
2
1
1
2
2
2
1
1
1
2
0
0
2
1
0
2
1
0
2
1
1
1
1
1
1
1
0
2
1
1
2
1
0
1
1
1
1
1
2
1
0
1
1
1
1
1
2
1
1
1
0
0
2
1
2
1
1
1
0
1
2
1
2
2
0
0
2
1
1
2
0
1
1
1
2
2
1
1
1
2
2
1
2
1
2
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
1
1
2
1
0
2
1
1
0
2
1
2
1
2
1
1
1
0
2
1
1
1
0
1
1
2
0
1
1
1
1
1
1
1
2
1
1
1
1
1
4
0
2
1
1
1
2
1
2
1
1
1
0
1
2
1
1
1
2
1
0
1
1
1
1
1
1
2
1
1
1
2
2
1
1
0
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
2
1
0
2
2
0
1
1
1
1
2
1
2
0
1
1
1
1
1
1
1
0
1
1
2
1
2
1
0
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
0
2
0
1
2
1
2
0
1
2
1
2
1
2
1
1
0
2
1
2
2
2
1
2
1
1
1
1
1
0
2
1
1
1
1
2
2
1
2
1
2
1
0
2
1
1
3
1
1
0
1
1
2
1
1
1
1
2
1
1
2
1
2
1
0
2
2
1
2
1
1
0
2
0
2
1
2
1
2
1
1
1
1
2
1
0
2
0
2
2
0
2
2
1
1
1
1
1
1
1
1
1
0
2
1
1
0
1
2
1
1
1
2
2
2
0
0
2
1
1
1
2
1
0
1
1
0
0
1
1
0
1
0
0
1
0
1
2
2
0
1
1
0
1
0
0
2
0
1
1
1
2
1
2
1
0
1
0
2
1
1
1
2
1
0
1
2
1
0
1
2
2
0
1
0
0
1
1
1
2
1
1
2
1
1
1
2
2
1
2
1
2
2
2
1
2
1
1
0
1
0
1
1
1
1
0
2
2
2
1
0
1
1
2
0
2
2
1
1
1
2
1
1
1
2
1
0
2
2
1
1
1
2
2
1
1
1
2
1
2
2
0
2
1
1
1
2
1
0
1
1
2
1
1
0
1
1
1
1
1
1
1
1
1
2
1
2
1
1
0
1
2
0
1
2
0
1
2
1
1
1
2
1
1
3
2
1
1
0
1
2
1
2
1
0
1
1
0
1
1
1
1
1
1
1
1
0
1
1
2
2
1
1
1
1
2
1
0
0
1
1
2
1
0
1
1
1
1
1
2
1
1
1
0
2
0
1
1
1
0
2
0
2
3
1
1
0
1
0
1
1
0
1
1
1
2
3
2
1
2
1
2
1
2
1
2
2
1
1
0
1
1
1
0
1
0
2
2
1
1
0
1
1
1
1
1
1
1
1
0
1
1
1
0
1
1
0
1
2
1
1
0
1
2
1
3
3
1
0
0
1
1
1
2
1
1
1
1
1
1
1
1
1
2
0
1
1
1
1
1
2
1
2
1
1
2
1
2
1
0
1
1
2
1
2
2
1
2
1
1
2
1
0
1
1
1
2
2
2
1
1
2
2
1
1
0
0
1
1
5
0
1
2
0
2
1
2
0
1
1
2
1
1
0
1
1
1
0
2
2
1
2
2
1
2
1
2
2
2
0
2
0
2
1
1
1
0
1
1
1
2
1
1
2
1
2
1
1
1
1
0
0
2
0
1
1
1
1
1
0
1
1
1
1
1
1
2
1
1
1
2
2
2
1
0
1
1
1
0
1
1
1
1
1
1
1
1
0
0
2
0
1
1
0
1
1
1
0
1
1
1
1
0
1
2
1
1
1
1
1
2
0
2
1
1
1
1
1
1
1
0
2
1
1
1
1
1
2
1
2
1
2
2
1
1
1
2
1
2
0
1
1
1
0
0
1
1
1
1
1
0
1
1
2
1
1
1
1
2
1
1
1
2
1
0
1
0
0
1
2
2
2
2
2
1
2
1
0
0
1
1
0
1
2
1
1
1
0
2
1
1
0
2
2
1
1
3
1
0
1
0
1
2
1
1
1
1
1
1
1
1
2
1
0
0
2
1
1
1
0
0
2
1
1
1
1
1
2
2
1
0
0
1
0
1
1
2
0
1
0
2
2
1
2
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
0
1
2
1
1
1
1
1
1
1
2
2
1
2
1
1
2
2
1
0
0
2
2
2
1
2
2
2
1
0
2
0
1
2
1
0
2
1
1
1
1
0
2
1
2
1
0
1
1
2
0
1
2
12
2
1
0
1
1
1
1
1
1
1
1
1
1
3
1
1
1
1
0
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
0
1
1
1
1
1
0
1
2
1
0
0
2
2
0
1
0
2
2
0
0
0
1
2
1
1
0
0
1
2
1
1
1
1
1
1
1
1
1
1
2
0
1
1
1
0
1
1
1
1
1
2
0
1
2
1
1
1
2
1
1
1
0
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
0
1
0
2
1
1
1
1
1
1
1
0
2
1
2
1
1
1
1
2
2
2
2
1
0
1
1
1
2
1
1
2
1
1
2
1
1
2
2
0
2
1
2
1
1
1
1
1
1
2
2
2
0
0
0
1
1
2
2
1
1
1
0
0
0
1
1
2
2
1
1
1
1
2
1
1
0
0
1
2
0
2
1
1
1
1
1
1
1
2
0
0
1
2
2
2
0
3
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
2
0
2
1
1
1
1
2
1
1
1
1
1
1
1
0
1
1
2
1
1
0
1
1
2
1
1
1
1
2
2
2
2
0
1
2
0
1
1
1
0
1
0
0
1
3
2
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
0
0
1
2
1
1
1
0
2
2
1
0
0
1
1
1
1
1
1
2
1
1
1
1
0
2
2
1
1
1
0
1
0
0
1
1
1
1
1
1
0
0
2
1
1
1
0
2
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
0
1
1
1
1
1
0
1
2
1
1
2
1
1
0
0
1
2
1
1
1
1
1
2
1
2
0
1
2
1
1
0
1
2
1
1
2
0
1
1
1
0
2
2
1
2
1
1
1
2
2
3
1
1
1
2
1
1
0
0
1
2
2
2
1
1
1
1
2
2
1
1
1
1
1
0
0
2
2
1
1
1
1
1
1
1
0
1
1
0
0
1
1
1
2
1
2
0
2
2
1
1
2
1
2
1
2
1
2
1
1
2
1
1
0
2
1
1
1
1
2
2
1
1
0
1
2
1
0
1
0
1
1
1
1
1
1
1
1
1
2
1
1
2
2
2
2
2
2
1
0
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
2
1
1
2
1
2
1
2
1
1
1
0
1
1
0
1
0
0
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
0
0
1
1
1
1
1
0
1
1
1
1
0
1
1
1
1
0
1
1
0
2
1
2
1
1
1
1
1
3
2
0
1
1
2
1
1
2
1
1
1
2
0
2
2
1
1
1
1
1
1
1
1
0
1
1
1
1
1
0
1
2
1
0
1
2
1
1
1
1
1
1
1
1
2
0
2
2
2
1
1
1
1
1
0
2
2
0
1
1
1
1
2
1
2
2
2
2
1
2
1
1
0
1
2
1
1
1
1
0
2
1
1
2
2
1
1
1
1
1
1
2
1
1
2
1
1
1
1
0
1
2
0
1
1
2
2
1
0
1
2
1
1
1
2
1
1
2
2
2
1
1
2
1
1
1
0
1
1
1
1
1
0
2
1
1
1
1
1
0
1
2
1
2
0
1
1
2
1
1
1
2
2
1
1
1
1
1
2
1
2
1
1
2
1
1
1
2
2
1
2
0
1
1
1
1
0
0
1
1
1
1
1
2
0
0
2
1
1
1
0
1
1
2
1
1
1
1
2
1
1
1
0
0
0
1
2
2
2
2
1
1
1
2
1
1
1
1
2
1
1
2
1
2
0
2
2
2
1
1
2
2
1
1
2
2
1
1
2
1
1
1
2
1
0
1
1
1
2
0
0
1
1
1
0
1
0
2
2
2
2
0
1
1
1
1
1
2
2
0
0
1
1
2
1
0
1
2
0
1
1
1
0
1
1
1
1
2
2
1
0
0
1
0
0
1
1
2
0
1
1
1
2
1
0
2
1
2
1
1
0
2
1
1
1
2
1
2
1
1
1
1
1
0
1
1
1
2
0
1
1
1
1
1
1
1
1
1
1
2
0
1
2
1
1
2
0
1
1
0
2
0
1
1
1
0
1
1
0
0
0
1
2
1
0
2
1
1
0
1
1
1
1
0
1
1
2
3
1
1
2
1
0
1
1
1
1
1
1
2
1
1
2
0
2
0
1
1
1
1
1
1
1
2
1
1
2
2
0
2
1
1
1
1
2
2
1
2
0
0
1
0
2
1
0
1
1
0
1
1
0
1
1
2
1
1
0
1
1
0
1
1
1
1
2
2
0
2
1
0
1
2
1
1
0
2
2
0
1
2
1
0
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
0
1
1
1
1
0
1
1
2
2
1
1
2
1
1
2
1
1
2
2
2
2
0
0
1
2
1
2
2
1
1
1
2
1
1
1
1
1
2
1
1
1
2
2
1
0
1
1
1
1
1
1
1
1
0
1
0
1
1
1
1
0
1
1
0
1
1
1
0
1
1
1
1
1
2
1
1
0
1
1
0
3
0
1
0
1
1
0
2
1
2
1
1
1
0
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
0
1
0
0
1
1
2
1
2
1
2
1
1
0
0
1
1
2
0
1
1
2
2
2
1
2
1
2
1
1
2
2
1
2
1
1
2
1
1
0
2
0
1
1
1
1
0
2
1
1
1
0
2
1
2
1
0
1
1
1
1
1
1
2
1
2
1
1
2
1
1
2
1
1
1
1
1
2
1
0
1
1
1
1
2
2
1
1
1
2
2
2
0
1
1
1
1
1
1
0
1
1
1
2
1
1
0
1
0
1
2
0
1
1
1
1
2
1
2
1
1
0
0
2
1
2
1
2
1
1
2
1
2
2
1
5
1
2
2
1
1
1
0
1
1
1
1
1
1
1
1
0
2
2
1
1
1
1
1
1
0
1
2
0
2
2
1
1
1
1
2
1
1
0
0
1
1
2
1
0
1
1
1
4
1
2
1
0
1
1
0
1
1
1
1
0
1
0
1
0
1
1
0
1
0
2
1
0
0
2
1
1
2
2
0
2
0
1
1
2
0
2
1
0
2
2
1
2
2
0
0
1
2
1
1
1
1
1
1
1
1
0
1
1
1
1
0
1
0
1
2
0
1
1
1
1
1
1
0
2
1
1
0
0
1
1
1
2
1
2
2
2
2
2
1
1
1
0
1
1
1
1
2
1
1
0
0
1
0
0
1
1
0
2
1
1
2
2
1
1
2
2
1
1
2
2
1
2
1
1
2
1
0
1
1
1
1
1
0
1
1
1
1
1
1
1
1
2
1
4
1
1
1
1
0
2
2
1
1
1
1
0
1
1
1
2
1
2
2
1
1
1
1
1
1
0
0
1
2
2
1
2
0
0
2
1
1
0
2
1
1
1
1
1
2
2
1
2
2
1
2
1
2
1
0
1
0
2
1
2
1
1
2
1
1
1
2
1
0
1
1
2
1
1
1
1
2
1
1
0
1
3
1
2
1
1
1
0
0
0
1
1
1
1
1
2
2
1
2
1
2
1
1
1
1
1
1
2
1
2
2
2
1
0
1
2
1
0
0
1
1
2
2
1
1
0
2
1
0
1
0
1
0
1
1
0
0
1
1
1
1
2
1
1
0
1
2
2
3
1
1
1
2
1
0
1
2
0
1
1
1
1
1
0
2
1
1
0
1
2
2
0
0
0
1
2
1
1
2
1
1
1
1
1
1
2
1
2
1
1
1
2
0
3
1
1
2
2
1
1
3
1
2
1
1
1
2
1
1
1
1
1
2
1
0
1
1
1
1
1
2
1
0
1
1
1
2
2
0
1
2
2
0
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
0
1
0
2
0
1
2
1
0
2
1
2
2
1
1
1
0
1
1
1
1
1
1
1
3
2
0
1
1
1
2
2
1
1
1
2
1
1
2
2
1
0
1
2
1
2
2
1
1
0
0
1
0
1
2
2
1
0
1
0
1
1
2
1
1
1
1
0
1
1
2
1
1
0
2
0
1
0
2
0
1
3
0
2
1
1
1
1
1
0
1
1
1
1
2
2
0
1
1
1
1
0
1
0
1
1
1
1
2
1
2
2
2
1
2
1
1
1
1
1
1
1
1
2
4
1
0
1
1
2
2
1
1
2
1
1
1
1
1
2
1
1
0
1
2
1
1
1
2
1
1
1
1
1
0
1
2
1
1
1
2
1
1
0
1
1
1
2
2
1
2
1
2
2
1
0
1
1
0
2
1
1
0
1
1
1
1
1
1
0
1
1
0
2
1
0
2
1
1
1
2
1
2
3
2
1
1
2
1
2
1
1
0
1
2
1
2
2
2
1
2
0
2
2
0
1
2
1
1
0
0
1
2
1
1
2
1
1
1
2
1
0
1
1
1
0
1
1
2
1
2
1
1
1
0
2
1
1
1
1
2
0
2
1
1
2
1
1
1
1
2
0
1
0
1
1
1
1
1
3
1
2
1
1
2
1
1
1
0
1
0
0
2
1
1
0
0
2
2
1
0
1
2
1
1
1
1
1
0
1
1
2
2
1
1
2
0
1
1
1
1
1
1
1
2
1
1
0
1
1
0
1
0
0
2
0
1
1
2
2
2
2
0
1
1
1
0
0
1
0
0
1
2
1
1
3
1
1
1
0
1
1
1
1
0
1
1
2
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
0
1
2
2
2
1
1
1
2
1
1
1
1
1
2
2
1
2
1
0
0
1
0
1
1
1
1
2
1
3
1
2
1
2
1
2
2
1
1
1
1
1
0
1
1
1
1
1
1
0
1
2
2
0
1
1
2
1
1
2
1
0
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
0
1
1
1
1
1
2
1
2
0
1
1
1
1
1
1
2
1
2
2
0
0
1
0
0
1
1
1
1
1
0
1
2
2
0
1
1
0
1
1
1
2
1
0
2
0
0
2
2
1
1
1
1
1
1
0
2
1
1
1
1
1
1
0
1
2
0
0
2
2
1
1
1
1
2
1
1
2
1
1
2
1
1
1
2
2
1
1
1
2
2
2
1
2
0
0
1
0
1
1
0
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
0
1
0
0
2
1
1
2
1
2
1
2
2
2
2
1
1
0
1
0
1
2
1
0
1
1
1
2
1
2
2
2
0
1
1
1
1
1
0
0
1
2
0
0
2
2
1
1
1
2
2
2
0
1
1
1
2
1
2
1
2
2
2
1
1
2
0
0
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
1
2
1
2
0
0
0
2
1
0
1
1
1
1
0
2
1
0
1
0
1
1
1
2
1
0
2
1
1
2
0
1
1
1
2
0
2
1
1
1
1
0
1
1
1
2
1
0
2
2
1
1
1
2
1
2
1
1
1
1
0
2
2
1
2
1
1
1
0
2
1
1
1
1
2
1
0
1
1
2
1
1
0
1
2
2
2
1
1
2
1
1
1
0
1
1
1
0
2
2
2
2
1
0
2
1
2
1
2
0
2
1
2
1
0
1
1
1
1
1
1
2
1
0
1
2
2
1
1
2
2
1
1
0
1
1
1
2
2
2
2
0
0
2
2
1
1
1
2
0
1
2
2
0
2
2
1
1
1
1
0
1
0
2
0
1
0
1
0
1
2
1
1
1
1
0
1
1
1
2
1
2
1
2
2
2
0
2
1
1
1
2
1
0
1
1
1
1
0
1
1
1
2
1
2
1
1
1
2
1
1
2
1
1
0
0
1
1
1
0
1
4
2
1
1
1
1
1
1
1
1
0
1
2
0
0
1
2
1
1
1
1
1
1
1
1
3
0
2
0
1
2
1
1
2
1
1
1
1
1
0
1
1
0
1
1
1
0
1
0
1
1
1
0
1
1
1
1
2
1
1
2
1
1
0
0
2
0
2
0
0
1
1
1
2
2
1
2
0
2
1
2
2
2
1
1
0
2
1
1
2
2
0
0
0
2
2
1
1
0
2
2
1
1
1
1
0
1
1
2
1
1
1
1
1
1
1
1
0
2
1
1
0
2
1
0
0
1
1
1
1
1
0
1
1
1
1
1
1
1
0
1
0
2
0
0
1
1
1
0
1
1
1
1
1
1
1
1
0
2
1
0
0
1
1
1
1
2
1
1
1
1
0
1
2
1
1
0
1
1
2
2
1
1
2
1
2
2
1
1
2
0
1
2
1
1
1
0
2
2
0
0
1
0
1
1
2
2
1
1
2
2
1
1
2
1
1
2
1
1
1
2
0
0
1
2
4
2
1
1
0
2
1
1
0
2
1
1
1
0
1
1
1
1
1
2
1
1
0
1
0
0
1
1
1
1
1
0
2
1
2
2
2
1
1
1
2
0
2
2
1
1
1
2
1
1
1
2
0
1
1
0
1
2
1
1
0
2
1
1
1
1
2
2
1
2
0
1
2
1
1
2
2
2
1
2
1
1
2
1
2
1
0
1
1
1
2
1
0
2
1
2
1
1
1
2
0
1
1
0
0
1
1
4
0
1
1
1
1
1
1
1
0
2
2
1
1
1
1
0
1
1
1
1
0
1
1
0
1
1
1
2
0
2
1
2
1
1
2
2
1
1
1
1
1
1
2
2
1
1
1
2
0
1
1
1
0
1
1
1
1
1
2
1
1
2
0
1
0
0
0
1
1
1
1
1
2
1
2
2
2
1
1
2
1
0
2
0
1
2
2
2
1
2
2
2
2
0
0
1
2
1
1
1
1
2
1
1
2
1
1
0
1
1
1
1
0
1
1
1
0
2
1
1
1
1
0
2
1
2
1
1
1
1
2
1
1
1
1
2
1
2
0
2
2
2
2
1
0
1
1
1
1
1
1
1
0
1
1
0
0
2
0
0
1
1
2
2
2
2
1
0
1
1
1
2
1
0
2
1
2
1
1
1
2
1
1
0
1
0
1
1
1
1
1
0
2
1
0
1
2
1
2
0
1
2
0
2
1
0
1
1
2
2
1
1
1
1
1
1
2
3
2
2
2
1
2
1
1
1
1
2
2
2
2
0
2
2
1
1
2
0
1
1
2
0
1
0
1
1
1
1
1
1
1
2
1
2
1
1
1
2
2
1
1
2
2
1
1
0
2
2
1
1
1
1
1
1
1
2
1
1
1
1
2
2
1
1
2
1
2
0
2
1
0
0
2
2
1
1
2
1
1
1
2
1
1
1
2
1
2
1
1
1
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
0
1
2
1
0
1
1
2
1
1
2
2
0
2
1
1
2
0
1
1
1
2
2
1
0
0
0
2
0
1
1
1
1
2
2
2
1
2
1
0
1
1
1
0
2
1
1
2
1
1
2
1
0
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
0
1
2
0
1
2
2
1
0
1
2
1
0
1
1
1
1
2
1
0
2
1
2
1
0
2
1
1
1
1
2
0
1
2
1
2
1
1
2
2
1
1
1
0
2
2
1
1
1
0
1
1
1
0
1
0
1
1
1
0
1
0
1
2
1
2
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
2
1
0
2
1
1
2
0
1
1
1
1
1
1
1
2
1
1
1
2
0
0
0
1
1
1
0
0
1
1
1
0
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
0
1
1
0
0
2
2
1
0
1
2
1
1
1
1
0
1
1
1
1
0
1
0
1
0
0
1
1
1
1
0
0
2
1
1
2
2
1
1
1
1
2
0
2
1
1
1
1
2
2
0
1
0
0
1
2
2
1
1
1
0
1
1
2
2
0
1
2
1
0
1
2
1
1
1
1
1
0
1
0
2
0
0
1
1
1
1
1
2
1
1
1
1
2
1
2
1
1
1
0
2
2
2
2
1
2
1
1
2
1
1
2
1
0
1
2
1
0
2
1
3
1
1
1
1
0
1
0
2
1
1
0
0
1
0
1
1
1
2
2
1
1
1
1
0
0
1
0
0
1
2
2
1
2
1
2
1
1
1
1
1
1
2
1
1
0
1
1
2
1
2
0
2
2
1
1
2
1
1
1
2
1
2
2
0
1
1
1
2
1
1
1
1
1
0
0
1
1
1
2
1
1
2
2
2
1
1
1
0
2
1
2
1
2
0
2
2
1
2
2
1
2
2
1
1
1
1
1
1
1
0
0
0
1
0
2
1
1
1
1
1
0
1
1
2
1
1
1
1
2
2
1
2
2
2
0
1
1
1
0
1
1
1
1
0
2
1
1
1
1
1
1
2
0
1
1
1
0
1
1
1
2
1
1
1
1
0
1
1
1
1
1
1
0
1
2
1
1
0
1
5
1
1
2
1
2
1
1
1
1
1
1
0
1
1
1
1
0
1
2
1
1
0
1
2
1
1
0
0
0
2
1
1
2
2
2
1
2
1
2
1
2
1
2
2
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
2
1
1
1
0
2
1
1
1
0
2
0
1
1
1
1
1
1
1
1
0
1
1
1
2
1
1
0
1
1
1
0
1
0
2
1
0
1
1
2
0
1
1
0
1
0
1
2
2
1
0
1
2
1
0
2
1
1
1
1
1
1
0
0
0
2
1
2
2
1
3
2
0
1
1
1
1
2
1
1
1
2
1
1
0
1
2
0
1
1
1
1
2
0
2
1
1
1
1
0
1
2
1
1
1
2
1
1
1
2
1
2
0
2
2
1
2
1
2
2
1
1
1
0
2
0
2
1
0
1
1
1
2
1
1
2
1
1
1
1
1
0
0
1
1
0
2
2
1
2
1
2
2
1
1
1
2
1
1
0
1
1
2
2
1
1
1
1
2
1
1
1
1
0
2
2
1
2
0
1
1
3
1
1
1
1
2
1
1
1
1
2
1
2
1
1
0
2
1
1
1
0
2
1
2
2
1
2
2
2
0
1
1
2
2
1
0
2
1
1
2
1
1
2
1
1
1
2
2
1
1
1
0
1
1
1
2
1
1
1
0
0
1
2
2
0
2
1
2
0
2
1
2
2
0
1
1
0
1
1
0
1
1
2
1
1
2
1
1
1
1
1
0
1
1
1
1
1
2
1
2
1
0
2
2
2
1
2
0
1
2
1
1
2
1
1
1
1
2
2
1
1
1
1
1
1
1
1
2
0
1
1
2
1
1
0
3
1
1
1
1
1
1
1
1
0
1
2
1
2
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
1
2
1
1
1
2
0
1
2
1
2
1
1
1
1
2
2
1
1
1
1
1
2
1
1
2
0
1
1
0
1
1
2
1
2
2
1
2
0
2
0
1
1
1
2
2
1
2
1
2
1
2
1
1
2
1
1
2
1
2
0
2
1
1
2
1
1
1
1
1
2
1
2
1
1
1
2
4
1
1
2
1
1
2
1
1
0
1
1
1
0
1
0
1
1
0
1
1
1
1
1
1
1
0
1
2
1
1
0
1
1
2
1
2
1
0
1
1
1
1
1
0
0
1
1
2
1
0
1
2
1
1
1
2
1
2
2
1
0
1
2
1
1
2
1
0
2
1
2
1
1
0
1
2
1
1
0
0
1
0
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
1
0
0
1
1
1
2
1
1
1
0
2
1
2
2
0
1
2
1
1
2
0
2
1
0
1
1
1
2
2
1
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
0
1
1
1
1
2
2
1
2
1
1
2
3
1
2
1
1
0
1
1
2
2
1
0
1
2
1
2
1
1
2
1
2
1
1
0
1
1
1
1
1
1
0
1
1
1
1
1
2
1
1
0
1
1
2
1
1
1
2
1
2
1
1
1
1
0
1
1
1
1
2
1
1
4
2
1
1
1
1
3
1
1
1
2
1
2
1
0
2
1
2
2
1
1
1
1
2
1
2
2
1
0
2
0
1
0
1
1
2
2
0
1
0
1
0
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
3
1
1
1
2
1
1
2
2
2
1
1
2
2
2
2
2
1
1
1
1
0
1
2
0
1
1
2
1
2
1
2
2
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
2
2
1
2
1
2
2
1
1
0
1
2
0
0
1
1
0
1
1
0
2
1
2
0
2
2
1
1
0
1
2
0
1
1
0
1
1
1
1
1
1
1
1
2
1
0
2
1
1
2
1
1
2
1
1
2
3
2
1
1
0
1
1
0
2
2
2
1
1
1
1
1
1
1
1
2
1
2
5
1
1
1
1
1
2
0
1
2
1
2
1
0
1
2
1
2
1
1
1
0
1
1
1
1
1
1
1
1
2
0
2
1
1
1
1
2
1
1
2
2
1
0
2
1
1
2
0
0
1
1
2
1
1
2
2
2
1
1
0
2
0
1
2
1
2
0
1
1
0
0
0
2
1
1
2
2
1
0
1
1
1
1
1
1
1
0
0
1
2
0
2
1
1
1
1
2
1
1
0
1
2
2
2
1
0
2
1
1
1
1
1
2
1
0
1
0
0
0
1
2
2
2
1
2
1
1
0
1
2
0
0
1
1
1
1
1
0
1
1
1
1
1
0
2
1
1
1
1
1
2
1
1
1
1
0
1
1
1
1
1
1
1
1
2
0
1
2
1
1
0
2
1
1
1
1
1
2
1
2
1
2
1
1
1
1
1
2
1
1
0
1
1
2
1
1
2
1
1
2
1
1
1
1
1
1
0
0
2
0
1
1
1
1
0
1
1
0
2
1
2
2
0
2
1
1
1
1
1
1
1
0
1
1
1
0
1
1
1
1
1
0
0
0
2
1
1
0
7
2
1
2
1
1
1
0
1
0
1
1
1
1
2
1
1
1
2
1
0
1
2
1
2
0
1
1
2
1
1
1
1
1
2
1
0
1
1
2
1
1
0
0
2
0
1
2
2
1
0
1
1
1
2
1
0
1
0
1
2
1
1
1
1
1
0
1
1
1
1
1
0
1
0
1
1
0
1
1
1
1
1
0
1
1
0
1
0
1
1
2
1
1
1
1
2
2
1
2
2
1
2
1
1
1
1
1
1
2
1
2
1
1
1
2
2
1
1
1
1
1
1
1
1
0
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
0
0
1
0
0
2
1
1
1
1
1
1
2
0
0
1
2
1
0
1
1
1
2
1
1
1
1
1
0
1
1
1
1
1
2
1
2
1
1
1
0
1
1
2
1
0
0
2
1
2
1
1
1
1
1
1
0
2
1
1
1
2
1
1
1
1
1
1
2
1
2
1
1
0
1
1
1
1
0
2
1
1
1
1
1
1
1
1
6
1
1
0
3
1
1
0
1
1
1
0
1
1
0
2
2
1
0
2
1
0
1
1
1
0
2
0
0
0
1
1
2
2
2
2
1
1
1
0
2
0
0
1
1
0
1
1
1
1
1
0
1
1
2
0
2
1
2
0
1
1
1
2
2
2
1
1
2
2
0
2
0
2
1
1
1
0
1
4
1
1
2
1
2
2
1
0
2
1
2
1
1
2
1
1
0
2
0
1
2
2
1
1
1
2
2
1
0
2
1
0
2
1
1
0
1
1
0
1
2
2
0
1
1
1
2
1
1
1
0
2
1
1
0
1
1
1
0
1
1
2
1
1
0
1
2
1
1
2
1
0
1
1
1
1
1
1
0
1
0
2
1
1
1
1
1
1
0
0
0
1
1
1
1
1
1
1
0
1
2
2
1
1
1
1
2
1
2
2
1
1
0
1
1
1
1
1
1
1
1
1
0
1
1
1
0
1
1
1
1
1
1
0
2
1
1
1
1
1
1
1
1
1
1
2
2
1
2
1
2
1
1
1
2
1
0
1
2
1
0
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
2
1
1
1
2
1
0
1
1
1
1
1
2
1
2
1
2
1
1
2
0
1
0
2
2
2
2
2
0
1
1
1
0
1
0
1
0
1
1
1
0
1
2
2
2
1
1
1
1
1
2
2
1
1
2
0
1
1
1
1
2
2
2
1
1
1
1
0
0
2
2
2
0
1
2
0
1
1
0
2
2
2
2
1
1
0
1
2
1
1
2
1
1
1
1
2
1
1
1
1
0
0
1
1
1
0
2
1
2
1
1
2
2
1
1
1
2
1
1
1
1
1
1
2
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
0
1
2
1
2
0
0
1
2
1
1
1
1
1
0
1
0
2
2
1
1
1
2
2
2
2
0
1
1
2
2
0
2
1
0
1
2
1
1
1
1
1
0
1
2
1
2
1
1
1
0
1
2
0
1
2
1
1
1
1
2
2
0
1
2
0
1
1
2
2
0
1
2
2
2
2
1
1
1
1
1
2
1
1
1
0
2
1
1
0
1
1
1
1
1
1
1
0
1
1
2
2
1
1
1
1
1
1
1
1
2
0
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
0
1
1
1
1
1
1
1
1
2
1
1
1
0
1
0
1
1
2
2
2
2
2
1
1
1
1
1
0
0
1
2
1
1
2
1
1
4
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
0
2
0
2
1
1
1
1
2
1
1
1
1
1
0
2
1
0
1
0
1
2
2
2
1
0
1
1
1
1
0
2
1
1
1
1
2
1
2
3
2
2
1
2
0
1
1
1
1
1
1
1
0
1
1
1
2
1
1
2
1
1
2
1
1
1
2
1
2
1
1
2
1
1
1
1
1
1
1
2
1
0
1
1
1
1
1
1
0
1
1
2
2
0
1
1
1
1
2
1
1
2
1
1
0
2
0
1
1
2
0
1
1
2
1
1
1
1
1
0
1
0
1
1
2
0
1
1
0
0
1
0
0
1
0
2
1
0
1
0
1
0
1
1
1
1
1
2
1
1
2
2
1
1
1
2
1
0
1
2
1
0
1
1
2
1
1
1
1
1
1
1
0
0
1
0
0
1
1
1
1
1
1
1
0
0
2
1
1
2
1
1
2
1
0
0
2
1
0
0
1
2
1
1
1
1
1
0
1
1
2
2
2
1
1
1
2
1
1
0
2
2
1
2
1
1
1
2
2
1
1
2
1
1
1
1
1
0
1
1
1
2
1
0
1
0
0
2
1
1
1
1
1
1
1
0
2
1
1
2
1
0
1
2
0
2
2
1
1
1
1
1
1
0
1
1
2
1
1
1
1
2
1
1
1
0
1
0
1
2
2
1
2
1
0
1
1
2
1
1
0
1
1
1
2
2
1
0
1
2
0
0
2
1
1
1
2
0
1
2
1
1
1
2
1
2
1
1
1
2
1
2
1
2
2
2
1
1
2
0
1
0
1
1
2
1
2
0
1
1
1
1
4
1
1
1
1
1
1
1
1
1
2
0
1
1
2
0
1
1
1
1
1
1
1
1
0
2
1
2
1
2
1
1
2
1
2
1
1
1
1
0
1
1
1
1
2
0
0
0
2
1
1
1
2
0
1
0
2
1
2
0
1
1
0
1
1
1
2
2
1
2
1
1
2
1
2
0
1
1
2
1
1
1
1
1
1
1
3
2
1
2
2
1
2
1
1
1
0
1
1
1
1
1
1
3
1
1
1
1
1
0
2
1
1
0
2
1
1
1
1
1
1
0
0
1
1
1
2
1
2
2
1
2
1
2
2
2
1
2
2
1
1
2
1
2
0
0
0
0
0
1
1
1
2
0
0
2
1
2
3
1
1
2
2
1
1
2
1
0
2
2
1
2
0
1
1
2
1
2
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
2
1
1
1
0
2
1
1
1
1
1
1
2
2
1
1
1
0
0
1
1
0
2
1
1
1
2
1
1
0
2
2
1
1
1
1
2
1
2
2
1
1
2
1
2
2
1
1
1
2
0
3
1
2
0
0
1
1
1
0
2
2
1
1
0
2
0
1
1
1
1
1
1
0
2
1
1
1
1
1
2
0
1
1
1
2
1
1
1
1
2
1
0
1
0
1
2
2
0
1
1
2
1
0
2
1
1
1
1
0
0
1
1
1
1
1
1
1
0
1
1
1
4
1
1
0
1
1
1
1
1
0
0
1
1
3
2
1
0
2
1
1
1
2
2
1
2
1
1
1
1
1
1
0
1
1
1
1
1
2
1
1
2
2
1
1
1
2
0
0
2
1
1
1
1
0
2
0
1
2
1
1
1
1
1
1
1
1
0
1
1
2
1
2
0
2
1
1
1
1
1
1
1
2
0
1
1
1
1
1
2
1
1
0
1
0
1
2
0
1
0
2
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
0
0
1
2
0
2
1
1
1
1
1
1
2
1
0
0
1
0
1
0
1
3
2
1
1
2
1
1
1
1
0
2
1
1
2
2
1
1
1
1
1
1
0
1
2
1
1
2
1
2
1
1
0
1
1
2
0
1
1
1
0
0
1
2
2
1
1
2
2
1
1
0
0
1
1
1
1
1
1
1
0
1
2
1
1
2
1
1
2
0
2
1
2
2
2
1
1
2
1
1
1
1
1
2
0
1
1
2
2
1
2
2
2
2
1
1
2
2
1
2
1
1
1
2
2
2
1
1
2
2
1
2
1
1
2
2
1
1
0
2
1
2
2
1
1
1
1
1
1
1
1
1
0
1
1
1
1
3
1
1
2
1
1
1
1
1
0
1
0
0
1
1
2
1
2
1
1
0
1
1
1
2
0
0
0
2
1
2
2
0
2
0
1
1
2
1
1
0
2
1
1
1
2
2
1
1
1
1
1
2
1
1
2
1
1
1
1
2
2
2
2
2
0
2
1
1
2
1
1
1
0
1
1
1
2
1
1
2
0
1
1
0
2
1
0
1
1
1
2
2
0
0
1
1
1
1
2
2
1
0
1
1
1
1
1
1
0
2
1
1
2
1
1
1
1
1
1
2
1
0
1
1
1
1
0
0
1
1
2
2
0
1
1
2
1
1
1
1
2
1
2
2
0
1
2
0
2
1
1
0
1
2
1
2
2
1
1
1
1
1
1
1
1
1
2
1
1
2
2
2
0
2
2
1
1
1
1
1
0
1
2
0
1
1
2
1
1
1
0
2
2
1
1
2
1
0
1
1
2
0
2
1
1
0
0
1
1
0
1
1
1
1
1
2
3
1
1
1
2
0
2
0
1
2
2
1
1
1
1
1
1
1
1
2
1
2
2
1
1
2
1
1
2
1
1
1
1
1
1
1
2
1
1
2
2
0
1
0
0
1
1
2
1
1
1
1
1
2
0
1
0
2
1
0
1
1
2
2
2
1
1
2
1
1
1
1
2
1
2
1
1
1
2
1
0
1
1
2
1
1
0
2
1
2
0
1
1
1
1
1
2
1
1
2
1
1
1
2
1
1
1
0
1
1
1
2
0
0
0
1
1
2
2
2
2
1
1
1
1
1
0
2
2
2
1
2
2
2
1
1
0
1
1
1
2
1
1
0
2
1
1
1
1
1
1
2
1
1
2
1
2
1
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
2
2
2
2
1
2
1
1
1
1
1
1
1
1
0
2
1
0
0
2
0
0
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
2
1
1
1
2
1
1
0
2
2
1
0
1
2
1
0
1
0
2
2
0
2
1
0
1
2
1
1
1
1
2
1
0
0
0
1
1
0
2
2
1
1
1
1
2
2
1
1
1
2
1
1
1
2
1
0
1
2
2
0
1
1
2
1
1
1
1
1
1
1
2
1
1
2
0
1
0
1
1
2
1
0
2
2
1
1
0
1
0
1
2
1
1
2
1
1
1
2
2
2
1
0
1
2
1
1
0
1
2
1
2
1
1
2
1
1
1
1
1
2
1
1
1
2
1
0
1
1
1
2
2
2
2
2
1
1
2
0
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
0
2
0
2
1
0
2
1
1
0
1
1
1
1
2
2
0
1
1
1
1
2
1
2
1
2
2
2
1
0
1
2
2
0
1
1
1
1
1
1
1
0
1
1
2
2
2
1
1
2
2
1
2
2
2
1
1
0
1
2
2
1
1
2
1
1
3
2
2
1
1
1
1
0
1
1
1
1
2
1
1
1
1
1
2
2
0
2
1
1
1
1
1
2
1
1
1
2
1
0
1
2
1
1
1
1
0
1
0
1
1
1
0
1
2
1
1
1
2
1
1
1
1
1
2
2
0
2
1
0
1
1
2
0
0
1
1
1
1
1
0
2
1
2
0
2
1
0
2
1
1
2
1
1
1
1
0
2
1
2
2
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
2
0
1
1
1
2
1
1
2
1
1
1
2
2
2
2
1
1
1
0
1
2
1
0
2
2
1
2
2
1
1
2
1
1
2
0
1
2
2
0
1
0
1
1
1
2
1
2
1
2
2
1
2
1
1
1
2
1
2
0
1
1
1
2
1
1
1
1
1
1
2
2
2
1
0
1
2
1
2
1
1
1
0
2
0
2
1
0
1
2
1
1
2
1
1
1
0
1
1
1
1
2
1
1
2
1
0
2
2
1
2
1
1
0
1
1
1
0
1
0
0
3
2
1
1
2
1
1
1
1
1
1
2
2
0
1
2
0
1
2
0
2
2
1
1
2
2
0
1
0
2
1
1
1
1
0
1
2
1
1
1
2
1
2
0
1
1
2
1
1
1
0
0
1
2
2
1
2
2
2
2
1
0
1
1
2
2
1
1
2
2
1
1
1
1
1
2
1
1
0
1
3
1
0
0
2
2
1
0
0
1
0
0
1
0
0
1
2
1
1
1
0
1
1
2
1
1
1
1
2
1
1
0
3
2
1
1
1
1
0
2
1
2
1
2
2
2
1
1
1
1
1
2
2
1
1
0
1
0
1
1
1
0
1
1
2
1
1
1
2
1
2
1
2
1
2
1
0
0
2
1
1
1
1
1
1
2
2
1
2
2
0
0
1
2
1
1
2
1
1
1
1
0
0
2
2
1
1
2
1
0
1
0
2
1
2
1
2
1
1
0
1
0
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
0
1
1
1
1
1
1
1
2
1
1
0
2
1
1
1
1
2
2
0
1
1
2
1
1
1
1
1
2
1
2
2
2
0
1
1
0
2
1
1
1
2
1
1
0
2
1
2
0
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
0
0
0
1
1
0
1
1
1
1
1
1
1
1
2
1
0
0
2
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
2
1
2
2
1
2
0
0
0
1
1
2
0
1
0
1
1
1
2
1
2
1
1
2
1
1
1
0
2
0
0
1
1
1
2
2
1
1
2
0
1
2
1
0
1
1
1
0
1
1
1
1
1
1
2
1
1
1
1
2
0
1
0
2
1
2
1
1
0
2
1
0
1
1
1
1
2
1
2
1
1
0
1
1
1
1
1
0
1
2
1
1
1
2
1
1
2
2
1
2
1
1
1
2
0
1
1
2
1
2
2
1
1
2
0
2
0
0
1
1
1
2
2
1
1
2
2
1
2
1
2
1
3
2
1
1
1
2
1
1
1
1
0
2
0
1
1
0
1
1
1
1
0
1
0
0
2
2
1
1
2
1
1
1
0
0
1
0
1
2
1
2
1
1
2
1
1
1
2
1
1
0
2
0
1
0
2
1
1
1
1
2
1
0
2
1
2
2
2
0
0
2
1
0
0
1
1
2
0
1
2
0
1
1
1
2
1
1
0
2
2
0
1
2
1
1
1
1
0
1
1
1
1
1
0
1
1
1
1
2
0
1
2
1
2
1
1
1
2
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
0
1
0
2
1
2
1
2
1
1
1
1
2
1
0
1
2
2
1
1
0
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
0
1
1
1
1
1
0
0
1
2
1
1
1
1
2
2
2
1
2
0
0
2
2
2
2
1
2
1
1
1
2
2
2
1
0
1
1
1
1
1
0
1
2
1
1
0
2
2
1
1
0
2
1
1
0
2
2
0
1
1
2
1
1
1
1
0
1
1
1
1
2
2
1
0
1
0
2
1
1
1
1
2
0
2
1
1
2
1
2
1
1
1
1
2
1
1
0
1
0
1
1
1
1
1
1
1
1
1
1
3
2
1
2
1
2
1
2
1
1
1
1
1
2
1
0
1
1
1
1
2
1
1
0
1
0
2
1
1
1
1
0
1
2
1
1
1
0
1
2
2
2
1
0
1
1
2
1
2
1
1
1
0
0
0
2
2
1
0
2
1
1
1
1
1
1
1
1
0
2
2
0
1
1
0
1
1
1
1
1
2
2
1
2
1
2
1
0
2
3
1
0
1
1
1
1
1
1
2
0
1
1
2
1
1
1
2
0
1
0
2
2
1
1
1
2
0
0
1
1
2
1
0
1
1
1
0
1
1
1
1
2
1
2
2
1
1
1
1
1
2
1
0
1
1
2
1
2
1
2
1
0
1
2
2
1
1
1
1
1
1
3
2
1
1
2
1
1
2
2
2
1
0
2
1
2
1
2
0
2
2
0
1
1
1
1
1
1
1
1
2
1
2
2
1
1
0
1
2
1
2
3
1
1
1
1
1
0
1
1
1
1
1
1
2
1
1
1
2
1
1
2
1
1
1
1
0
1
1
0
2
1
1
1
1
1
1
2
2
1
1
1
1
1
3
1
1
1
0
0
1
1
1
1
2
1
1
1
2
1
1
2
1
1
0
1
2
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
2
0
1
1
2
1
1
1
1
2
1
2
2
1
1
2
1
2
1
1
2
2
2
0
1
1
0
2
1
1
1
1
1
0
2
2
0
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
0
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
0
1
1
1
1
1
1
1
1
1
1
2
1
1
0
0
1
2
2
1
1
2
2
2
1
1
1
2
0
2
1
0
1
1
1
1
0
2
2
0
1
1
1
1
1
1
2
2
0
1
1
1
1
2
2
0
1
2
2
0
0
1
1
1
2
2
2
1
1
1
1
1
1
0
0
1
1
1
2
2
2
1
1
1
2
1
1
1
1
1
1
2
0
2
1
1
1
1
1
2
2
2
1
2
2
1
0
1
1
2
1
1
1
0
1
0
2
2
1
1
1
1
1
2
2
1
1
6
1
1
1
1
2
1
1
1
1
1
2
2
1
0
1
0
1
1
1
2
1
1
1
1
2
1
1
0
1
0
1
1
1
1
1
2
0
0
1
1
1
2
2
0
1
2
1
0
1
2
1
1
1
1
2
2
1
1
1
1
1
2
1
1
2
1
1
1
2
0
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
2
2
2
1
1
1
2
1
0
2
2
1
1
1
1
1
1
0
1
2
2
1
2
0
1
2
2
1
2
2
1
1
1
1
0
2
1
1
2
2
1
1
1
2
0
1
2
1
2
3
1
1
1
1
1
0
0
1
2
2
1
1
0
1
2
1
1
1
2
2
2
0
1
0
1
2
1
1
2
2
1
1
1
1
1
2
1
1
2
0
1
2
1
2
1
1
2
1
2
1
2
1
0
2
1
2
1
1
1
2
1
1
1
2
0
0
0
2
0
1
1
1
2
1
1
2
1
1
1
1
1
2
2
1
2
1
2
1
1
1
3
1
1
2
1
2
1
1
2
1
0
1
2
1
0
1
2
1
1
1
2
2
1
1
2
1
0
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
1
2
1
0
2
2
3
1
1
1
0
0
0
1
2
1
1
1
1
1
1
0
1
0
1
1
0
2
1
1
1
1
1
1
0
2
1
1
1
1
1
1
1
1
1
1
1
2
2
0
2
1
2
1
2
2
1
1
2
1
1
1
1
1
1
0
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
2
1
2
2
0
0
2
2
1
3
0
2
1
1
1
1
1
2
2
1
2
1
1
1
2
2
1
1
1
1
1
0
0
2
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
0
0
1
1
1
0
1
1
1
2
0
0
1
2
1
1
1
1
1
2
2
0
1
1
1
1
2
1
1
1
0
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
2
0
1
0
0
1
1
1
2
2
2
1
0
1
1
2
1
1
0
1
2
1
2
2
1
1
2
1
1
2
2
2
0
1
2
2
2
1
1
1
1
1
1
2
1
2
2
2
1
1
2
2
0
0
1
1
1
1
2
1
1
2
2
1
0
1
1
2
1
1
1
1
1
1
1
1
1
1
0
0
2
1
1
1
0
1
2
1
1
1
2
2
1
0
2
1
0
1
2
0
1
0
0
1
1
2
1
1
2
1
1
2
2
2
0
0
0
1
1
1
1
1
1
1
2
1
0
1
0
1
1
1
1
1
1
1
2
2
1
2
2
1
2
1
2
1
1
1
1
2
1
1
1
1
1
0
1
2
2
2
0
1
2
1
1
1
2
2
1
2
1
1
1
1
1
1
2
1
0
0
1
0
2
2
1
0
2
0
1
1
1
1
2
2
0
1
1
2
1
0
0
0
1
1
1
0
2
2
0
2
0
1
2
0
0
1
1
2
2
1
1
1
2
1
2
2
1
2
2
1
2
2
2
1
1
1
1
1
2
1
1
2
1
1
1
0
2
2
1
2
2
2
1
2
2
1
2
1
1
1
1
1
2
1
1
1
2
2
0
1
1
1
1
1
2
2
1
1
2
1
0
1
1
2
2
2
1
1
2
1
1
0
1
2
1
1
2
1
2
1
0
1
2
1
1
1
1
2
1
1
2
1
0
1
0
0
1
1
0
1
0
1
0
1
1
2
1
1
0
0
1
1
1
1
1
1
2
1
0
2
1
1
1
0
1
0
1
2
2
0
1
2
1
2
1
1
1
1
1
0
0
0
1
2
2
1
2
1
1
1
1
1
2
2
1
1
1
1
2
2
1
1
1
1
2
1
1
2
1
1
1
0
0
1
1
2
2
1
0
2
2
1
1
0
1
2
0
2
1
0
1
0
0
2
2
1
2
1
2
1
2
1
1
2
1
1
1
1
2
1
2
2
1
1
1
1
2
1
2
0
1
2
0
1
1
1
1
1
1
1
2
1
2
1
0
0
1
1
0
1
1
1
2
1
2
1
2
1
1
0
1
1
1
2
1
1
1
1
1
1
1
0
0
2
1
0
1
1
0
1
1
1
2
1
1
1
2
2
1
1
2
1
1
1
1
1
2
0
1
1
1
1
1
2
1
2
0
1
2
2
1
2
1
1
1
2
1
1
0
0
1
1
0
1
0
0
1
1
2
2
1
2
0
1
2
2
0
1
2
1
1
1
1
2
0
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
0
2
1
1
2
2
1
1
2
1
1
0
1
1
1
1
1
0
1
0
2
2
1
2
0
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
0
2
1
1
1
0
2
0
1
1
1
1
1
1
2
1
1
1
2
1
1
1
0
0
2
0
1
1
2
1
1
1
0
1
1
1
1
2
2
2
0
0
1
0
1
2
1
1
2
1
0
1
2
1
1
1
1
1
2
1
0
1
1
1
2
2
0
1
1
1
1
0
1
1
1
2
2
0
0
1
2
1
2
0
1
2
1
2
2
1
2
1
0
2
2
2
1
1
1
1
1
1
0
1
2
1
1
0
0
1
1
2
2
1
1
6
1
1
1
2
2
1
0
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
2
2
1
2
1
2
2
1
1
1
1
3
1
1
1
0
2
1
2
1
2
1
2
1
2
1
2
1
1
1
1
0
2
1
1
1
1
1
1
1
1
0
1
1
1
1
2
1
2
1
1
1
1
1
1
2
0
1
1
1
0
0
1
0
2
1
2
1
2
1
0
1
1
2
2
1
0
1
1
0
1
1
2
1
0
1
1
1
2
1
1
2
1
0
1
1
1
1
2
1
1
1
1
1
2
0
1
1
0
1
1
1
0
1
0
2
2
2
1
2
1
1
2
2
1
0
1
2
1
1
1
1
1
1
0
1
1
2
2
1
2
1
1
2
1
2
0
1
1
1
1
1
1
1
2
1
2
1
1
1
2
2
0
1
2
1
1
0
1
1
0
2
2
2
0
1
1
2
1
2
1
1
1
1
2
0
1
1
1
2
1
0
0
2
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
0
3
2
1
2
1
1
1
1
1
1
1
2
1
1
0
1
1
2
1
0
1
2
2
0
1
1
1
0
0
2
2
2
1
1
0
1
1
1
2
0
0
2
1
1
1
1
1
2
2
1
1
1
0
1
1
1
2
1
2
1
1
1
1
4
1
0
2
1
1
1
2
1
1
2
0
0
1
1
0
1
1
1
2
1
1
1
0
1
1
1
1
1
2
1
1
1
2
2
0
0
2
1
1
1
1
0
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
1
1
1
2
1
0
1
1
1
1
1
1
1
1
0
1
2
1
1
1
1
1
1
1
1
2
1
2
1
2
0
1
1
1
0
2
1
1
1
1
1
1
1
1
1
1
0
1
2
1
2
1
0
1
1
2
2
2
1
2
1
2
1
1
1
2
1
2
1
1
2
0
2
1
1
0
2
1
1
2
1
1
1
0
1
0
1
2
0
2
1
1
3
2
3
0
1
1
1
2
0
2
2
1
1
1
1
1
2
1
2
1
1
0
1
0
2
1
0
0
2
1
2
3
1
0
1
1
0
1
1
2
1
1
1
2
1
1
1
1
1
2
2
1
1
0
1
1
1
1
1
2
2
1
1
2
1
1
0
1
0
1
0
2
1
1
1
1
0
1
1
2
1
1
1
1
0
1
0
1
1
1
1
0
2
0
1
2
1
1
1
2
0
2
1
1
0
1
2
0
1
2
1
1
0
1
2
1
2
1
1
2
1
1
1
0
1
2
1
1
1
1
1
1
1
1
1
0
1
1
1
0
1
2
2
0
0
0
1
1
2
1
1
0
1
1
1
1
1
1
1
1
1
2
0
1
2
0
2
0
3
2
1
1
2
1
0
1
1
2
1
1
2
2
1
1
1
1
2
1
2
1
1
1
0
1
1
1
1
1
1
1
1
1
2
2
1
1
1
2
1
2
1
2
2
1
0
1
0
2
0
1
0
1
2
0
1
2
2
2
1
0
1
2
1
1
0
2
0
1
1
1
1
2
2
1
2
1
2
2
1
1
1
1
1
2
1
2
0
1
1
2
1
1
2
1
2
1
1
2
1
1
1
1
1
3
1
1
1
1
1
2
1
0
1
1
1
2
1
1
2
2
2
1
0
2
1
1
1
1
1
1
1
1
1
1
2
1
1
0
1
0
1
1
1
2
1
1
1
0
1
0
1
2
1
1
2
2
1
1
1
2
1
1
1
1
2
2
1
1
2
1
1
1
1
2
1
2
0
2
2
2
1
2
2
2
1
1
0
1
0
1
2
0
1
0
1
2
1
1
2
1
1
1
1
0
1
1
1
1
1
2
2
1
0
2
1
2
1
1
0
1
1
1
1
0
1
2
1
1
2
2
1
2
1
1
2
2
4
1
1
1
0
1
2
1
1
1
2
0
0
1
1
1
1
1
1
1
1
1
1
0
1
1
2
4
1
1
1
2
1
1
1
1
2
1
1
2
2
0
1
2
1
1
2
1
1
1
1
2
2
2
1
1
2
0
2
1
1
1
1
1
1
1
0
4
1
2
1
1
2
1
1
2
1
2
1
1
2
1
1
2
0
1
0
1
0
1
2
1
2
2
1
2
1
1
2
1
2
1
0
1
1
1
1
1
0
2
0
1
2
2
1
1
2
2
2
1
2
1
1
2
2
1
2
2
2
1
0
3
1
1
2
2
1
1
1
2
0
1
0
1
1
2
1
1
1
0
1
0
2
2
0
1
1
1
1
1
2
1
2
1
2
1
2
1
2
1
1
2
1
2
1
1
2
2
1
1
0
1
1
1
1
2
1
1
2
1
1
1
0
1
0
2
2
1
2
0
1
2
1
1
1
1
2
1
2
1
2
1
1
0
1
2
1
1
1
1
1
0
1
1
2
1
1
1
1
1
0
1
1
1
1
1
1
2
1
1
1
1
0
0
2
1
1
2
1
2
2
1
1
1
1
1
1
1
1
2
2
1
1
1
2
0
2
1
2
1
1
2
1
1
0
2
2
1
1
2
0
2
1
0
1
1
0
1
1
2
1
0
2
0
0
2
1
2
1
1
2
2
2
1
1
1
2
0
1
2
1
1
0
0
1
2
2
1
1
2
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
2
2
2
2
1
1
1
1
0
1
0
2
1
1
1
1
1
2
1
2
2
2
2
1
1
1
0
1
1
0
1
1
2
0
1
1
1
2
2
1
2
1
2
2
2
2
0
1
2
2
1
1
1
1
0
1
1
1
1
1
2
0
1
2
1
1
2
0
2
2
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
2
0
1
1
2
1
1
2
2
1
2
1
1
0
1
0
0
1
1
1
2
1
1
0
3
1
6
1
2
2
1
1
1
0
1
1
1
1
1
1
0
1
1
0
2
1
1
1
1
2
2
3
2
1
2
1
2
1
1
1
2
1
1
0
1
1
1
1
2
1
0
2
2
1
1
1
1
1
1
0
1
2
2
0
1
2
1
1
1
2
1
1
0
1
2
1
1
1
2
2
1
1
1
1
1
1
0
0
2
2
3
1
1
1
1
0
1
1
1
0
2
1
0
1
1
1
1
1
2
0
0
1
2
1
1
2
1
2
1
1
2
1
1
0
1
1
1
1
0
2
0
2
1
0
0
1
1
0
2
1
1
0
4
1
2
1
2
1
1
2
0
0
2
1
1
2
1
1
1
1
2
1
1
1
2
1
1
1
1
1
2
2
1
2
1
1
1
1
2
2
0
0
2
1
1
1
2
2
0
1
1
0
2
0
1
1
1
1
2
0
1
1
1
1
2
1
1
1
0
1
0
1
1
2
1
2
1
1
1
1
1
1
0
1
1
0
1
1
1
2
2
1
2
2
2
2
1
1
1
1
1
1
1
1
1
0
2
1
1
1
2
2
2
0
1
1
1
0
1
2
2
1
1
0
2
2
1
1
1
1
1
1
0
1
2
1
1
0
2
1
1
2
0
1
1
1
1
1
1
1
0
2
1
1
1
2
1
1
1
1
1
2
0
1
1
1
2
1
1
0
2
1
1
2
2
2
1
2
1
1
2
0
1
1
2
1
1
1
1
1
1
1
2
2
2
1
2
1
1
2
1
0
2
0
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
0
2
2
1
0
1
1
2
1
1
2
2
1
2
1
1
1
1
1
1
0
1
0
1
1
1
2
0
1
1
1
1
1
2
1
0
2
1
2
2
1
1
1
1
1
1
2
0
1
1
1
1
1
1
2
1
1
1
0
1
1
1
0
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
3
0
2
1
2
1
2
1
2
1
0
2
2
1
2
1
1
1
1
2
0
1
0
1
2
1
1
0
1
1
2
2
1
1
1
1
1
1
1
2
0
1
1
0
1
2
2
2
1
0
2
1
1
1
2
1
1
1
2
1
2
1
1
1
1
2
1
2
0
1
1
2
0
1
0
1
1
2
1
1
1
1
1
1
0
1
1
1
2
0
1
0
2
2
2
0
1
1
2
1
0
2
0
2
0
1
1
1
1
1
1
1
1
2
0
1
2
0
1
1
1
0
2
1
1
2
1
1
1
1
1
2
0
0
0
0
1
1
1
1
1
0
2
0
1
2
2
2
0
1
1
1
1
2
2
1
1
1
1
1
2
0
2
1
1
2
2
1
1
1
0
1
1
0
1
0
1
4
1
1
1
2
0
1
1
1
1
1
1
1
1
1
2
1
1
1
0
2
1
2
2
1
3
2
1
2
1
0
2
1
0
0
1
2
1
1
2
2
1
2
0
2
2
1
1
1
1
1
1
0
0
2
2
1
2
1
1
0
2
1
0
1
2
2
1
2
0
1
0
1
1
0
1
1
1
2
1
0
1
2
1
1
0
2
1
1
2
0
2
0
1
1
0
1
1
3
2
1
0
1
0
1
1
1
1
1
0
2
1
0
2
0
0
1
1
2
1
1
1
1
2
3
2
1
1
1
2
2
1
1
1
0
2
1
1
1
1
1
1
3
0
0
1
1
0
1
1
1
1
1
1
1
1
0
1
2
1
0
1
0
1
0
1
1
2
1
1
1
0
1
1
2
1
0
1
0
1
1
2
1
2
1
0
2
1
2
1
1
0
1
0
0
0
0
1
2
0
2
1
1
1
0
1
1
0
1
0
1
1
1
1
1
1
0
1
1
1
1
1
2
0
2
1
1
1
1
1
1
0
2
1
1
1
1
2
1
1
1
1
1
1
0
1
1
0
2
2
1
1
2
1
2
1
0
1
1
1
1
1
1
1
1
1
1
0
0
2
1
2
1
2
1
3
1
1
2
1
1
1
2
2
1
1
1
2
1
1
2
1
0
1
1
0
2
2
0
1
2
3
1
1
1
1
1
2
1
1
0
1
1
1
1
1
1
0
1
1
1
1
1
1
2
1
1
1
1
1
0
1
1
1
2
1
1
2
2
1
1
0
2
3
1
0
1
1
2
2
2
0
0
0
2
1
1
2
1
1
1
1
0
0
1
1
1
1
1
1
2
0
0
1
0
1
2
1
0
0
2
1
1
1
1
1
2
2
1
1
1
1
2
0
1
4
2
1
2
2
1
1
1
2
1
1
2
0
1
1
1
2
1
1
2
1
1
2
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
0
1
2
2
1
2
1
0
0
1
1
1
1
1
1
2
0
2
1
1
1
0
2
2
1
1
1
2
1
1
1
2
1
2
1
1
1
0
0
0
0
1
1
1
1
0
1
1
2
1
2
0
1
2
1
1
2
1
1
1
0
3
0
1
1
2
2
1
2
1
1
1
1
0
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
0
1
2
1
1
0
1
0
1
2
3
2
1
2
0
0
1
2
2
2
1
2
0
1
1
1
1
0
1
0
2
1
1
1
2
0
0
1
1
0
2
2
1
1
2
0
1
1
2
1
2
1
1
1
1
2
1
1
0
1
2
2
2
1
1
2
2
1
2
1
2
1
2
1
1
1
2
1
0
0
2
1
1
1
0
1
0
1
1
1
1
1
1
0
1
0
1
2
1
1
1
0
1
1
1
1
0
1
1
2
1
1
2
1
1
0
0
2
2
1
2
1
2
2
1
1
0
1
1
1
1
1
0
2
2
2
1
1
1
2
2
1
2
1
0
0
0
1
0
0
1
2
1
1
0
2
2
2
1
1
2
2
1
0
1
1
1
2
1
1
1
3
1
1
1
1
1
1
0
1
1
1
0
1
1
1
0
0
2
1
1
4
1
1
1
0
1
1
2
2
0
3
0
1
1
1
2
1
2
1
1
2
1
2
1
2
1
2
1
1
1
1
1
2
1
1
1
2
1
2
2
1
2
2
1
1
1
0
1
1
1
1
0
1
2
0
2
1
1
1
2
1
1
1
0
1
1
1
1
0
2
1
1
2
1
2
1
1
2
0
1
2
1
1
1
1
2
1
0
2
2
1
1
1
2
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
0
1
1
1
1
1
1
2
1
1
2
1
3
0
1
1
1
1
1
1
3
2
0
2
1
1
1
1
0
1
0
2
2
0
0
1
1
1
2
1
2
0
0
1
1
2
1
1
1
1
1
1
1
1
0
2
0
1
1
2
2
1
1
0
0
1
2
1
2
0
2
2
1
1
2
1
1
1
0
1
2
1
0
2
1
1
0
1
2
3
2
1
2
1
1
1
2
1
1
1
1
2
1
2
0
1
2
1
1
1
1
1
2
2
1
1
1
1
1
2
2
0
0
2
2
1
1
2
1
2
2
1
1
1
2
0
0
2
1
1
1
1
1
1
2
1
1
1
0
1
1
1
1
2
1
2
1
1
2
1
0
2
0
2
1
2
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
2
0
1
3
1
0
2
1
2
1
2
0
1
1
1
0
2
2
1
1
1
1
0
2
0
1
1
0
2
1
0
1
1
2
0
1
1
1
2
1
0
0
1
1
1
0
1
0
0
1
3
1
1
1
0
1
0
2
1
1
3
2
1
1
1
1
1
1
2
1
1
2
2
2
1
2
1
1
0
2
1
1
0
1
0
1
1
1
1
0
1
2
1
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
0
1
0
2
0
2
0
1
0
1
1
1
0
1
0
1
0
1
1
1
1
2
1
2
1
0
2
1
1
1
2
1
1
2
2
1
2
1
1
1
2
1
1
1
1
1
1
0
2
1
2
1
2
1
2
0
2
2
1
1
2
0
1
1
0
2
1
2
1
10
1
0
0
2
1
2
0
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
2
0
1
1
2
0
1
2
1
1
1
1
1
1
1
1
0
1
1
2
1
0
1
1
1
0
2
2
1
1
1
1
2
0
0
1
1
2
3
2
1
1
0
1
1
1
1
0
2
1
1
2
1
1
1
1
4
1
0
1
2
3
1
2
1
1
2
1
0
1
1
0
1
1
1
2
2
1
1
0
0
1
1
2
1
1
0
1
1
1
2
1
1
1
1
1
2
0
1
0
1
1
2
1
2
1
1
1
0
0
2
1
2
1
1
1
2
0
0
1
1
1
2
1
1
3
2
1
1
0
2
0
1
1
1
1
1
2
1
1
1
2
2
2
1
1
1
2
1
1
0
1
1
1
2
1
0
0
0
1
2
1
1
1
1
1
1
1
0
1
1
1
1
1
0
1
2
1
1
2
1
1
2
1
1
1
1
1
2
2
0
1
1
2
1
2
2
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
0
1
0
1
2
1
0
1
1
2
2
1
3
1
2
0
1
1
1
1
1
1
2
1
1
1
1
2
2
2
1
1
1
1
1
1
2
2
1
1
1
1
2
1
1
2
1
2
2
1
2
1
1
2
2
0
1
2
2
1
0
1
1
1
1
1
1
2
1
2
2
2
1
0
2
2
1
1
0
2
1
1
1
1
0
2
1
1
1
2
1
1
1
0
2
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
1
2
1
5
1
1
1
1
1
1
2
0
1
1
2
1
1
2
1
1
1
1
1
0
1
1
1
1
2
1
2
1
0
1
1
1
1
2
1
0
1
1
2
1
1
1
2
1
1
1
1
1
1
0
0
2
0
1
1
1
2
1
0
1
1
1
1
2
0
1
1
1
2
1
2
1
0
0
0
1
1
1
1
1
1
1
2
1
1
0
1
1
1
1
1
1
2
0
1
1
0
1
1
2
0
1
1
2
1
0
1
3
1
1
1
0
2
1
0
1
1
2
2
0
1
0
0
2
0
1
1
2
2
1
2
1
1
1
1
1
0
1
0
1
0
0
2
1
1
1
1
2
2
2
1
0
3
1
0
2
1
1
1
1
1
2
1
3
1
1
1
2
0
1
1
1
0
2
2
1
1
1
0
2
1
2
2
1
0
1
1
0
1
1
1
2
2
1
1
1
2
1
2
1
0
1
0
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
0
2
1
1
2
0
2
1
2
1
1
2
1
1
0
2
1
2
0
2
1
1
0
0
2
0
1
1
1
1
1
1
1
2
1
0
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
0
1
1
1
1
0
2
1
2
2
1
1
1
1
1
2
1
2
2
1
1
2
1
2
1
2
1
1
2
1
1
1
2
1
0
1
1
2
1
1
2
2
1
0
0
1
1
2
2
2
2
1
1
2
1
0
1
0
1
2
0
1
1
1
0
1
0
1
2
1
1
1
1
1
1
0
1
1
1
2
2
1
1
0
2
1
1
1
1
0
1
1
1
1
1
1
0
1
2
2
0
1
1
2
0
1
1
1
1
1
2
1
1
1
11
0
1
1
1
1
1
1
2
2
2
2
1
2
0
1
1
1
2
2
2
1
1
1
2
2
1
0
2
2
1
2
2
1
1
1
1
1
2
1
1
2
1
1
1
1
2
1
1
1
1
2
1
0
1
1
0
2
2
1
0
2
0
1
2
1
2
2
1
1
2
1
1
1
2
1
1
1
2
2
1
1
2
2
1
1
1
1
2
1
2
1
0
1
2
0
1
1
0
1
1
1
2
0
1
0
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
2
1
1
2
2
1
2
0
1
1
0
1
0
1
2
0
0
0
1
1
1
1
1
1
1
2
1
1
0
1
1
2
2
1
2
2
0
3
1
1
2
1
0
1
1
1
1
1
2
0
1
0
0
1
1
1
1
2
1
1
1
1
1
1
1
2
0
1
2
0
1
1
0
1
0
1
1
2
1
1
1
0
1
1
2
1
1
1
2
0
1
2
1
1
3
2
1
1
1
1
1
1
1
2
0
1
2
1
2
1
1
2
0
1
1
2
0
2
2
1
0
2
1
0
1
1
2
1
1
0
2
1
1
1
1
1
1
2
1
1
1
2
1
1
0
1
0
1
0
1
0
1
1
1
1
2
0
1
0
2
2
1
0
1
1
0
1
0
1
1
1
1
2
1
1
1
0
1
2
2
2
1
1
1
1
1
1
0
2
0
1
1
1
0
1
1
1
2
1
1
1
1
1
0
1
0
0
1
2
1
2
1
1
0
1
1
1
1
1
2
1
2
2
1
1
0
1
2
0
1
0
3
1
1
0
1
1
2
2
1
0
2
1
1
0
1
1
2
1
0
1
1
1
1
1
1
1
0
1
1
1
0
1
2
1
1
2
1
1
2
1
1
2
1
1
1
1
1
1
0
0
2
2
2
1
1
1
0
2
1
2
3
1
1
2
0
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
0
2
1
1
0
1
1
1
1
1
2
0
2
2
2
1
2
1
1
1
1
0
1
1
2
1
1
1
1
2
1
2
0
0
1
1
1
2
1
2
1
1
0
2
1
1
1
1
1
1
0
1
2
1
3
1
1
0
2
1
1
0
2
1
1
1
1
1
1
3
2
2
0
2
1
0
1
1
1
1
2
1
2
1
1
1
0
1
1
1
1
0
1
2
1
1
1
2
0
1
2
1
2
1
1
1
2
1
0
2
1
1
1
1
1
2
0
1
1
1
2
2
0
1
1
1
1
2
1
0
1
0
1
1
1
2
0
1
1
1
1
2
0
0
1
1
1
1
1
2
1
1
2
1
1
2
1
0
1
1
1
1
1
1
1
1
2
1
1
2
2
1
2
2
1
0
1
1
1
0
1
2
1
0
0
1
1
1
0
2
0
1
1
0
2
2
1
2
1
2
1
1
1
1
1
2
1
0
1
1
1
1
2
2
1
1
1
1
1
2
2
2
2
1
2
0
1
1
1
2
0
2
0
2
1
2
0
1
1
1
1
2
2
1
1
1
1
0
2
1
1
0
2
2
1
2
1
0
1
2
2
0
1
1
1
1
1
0
1
1
1
0
1
1
1
1
0
2
2
1
1
2
2
0
1
1
1
4
2
2
1
1
0
2
1
2
1
0
2
1
2
1
1
1
1
2
1
2
2
1
1
1
1
1
2
1
2
0
1
1
0
2
2
1
1
1
1
1
1
1
1
2
0
1
2
1
1
1
1
0
1
1
0
1
1
2
2
2
0
1
1
0
1
1
1
1
1
2
0
2
1
2
0
1
1
1
1
1
1
0
2
1
0
1
2
0
1
0
0
1
1
1
1
0
1
1
1
1
2
1
1
2
1
1
1
2
1
1
1
1
0
1
2
1
1
2
1
1
2
1
0
0
2
1
2
1
1
1
1
2
2
1
2
0
0
1
2
2
2
1
1
1
1
2
2
2
2
2
1
0
1
1
0
2
1
1
2
1
1
1
1
1
1
2
1
1
1
0
2
1
2
1
1
0
1
1
1
2
1
1
2
1
1
1
0
1
1
0
1
2
1
0
1
1
1
1
0
1
1
2
2
1
1
0
2
1
2
0
0
1
1
1
1
1
1
2
0
1
1
0
2
1
0
2
1
1
1
1
1
2
2
0
1
1
2
0
1
1
2
2
2
1
2
1
2
2
1
0
3
1
1
2
1
1
0
2
1
1
0
1
2
2
1
1
2
1
0
1
1
1
1
0
1
1
1
1
0
1
2
2
1
1
1
0
1
1
0
2
3
1
2
0
0
2
1
1
1
1
0
1
2
2
2
1
2
2
2
2
1
0
1
1
1
1
1
1
1
1
2
2
1
1
1
2
0
1
2
1
2
0
0
0
1
1
1
1
1
1
1
1
2
1
1
1
1
0
1
0
1
0
2
1
2
1
1
1
1
1
2
2
2
1
1
0
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
3
1
1
0
0
2
2
1
2
1
1
1
1
2
1
1
2
2
1
1
2
1
1
1
2
1
1
1
1
0
1
1
1
1
4
2
2
2
2
2
0
1
0
2
1
2
2
1
0
1
2
1
1
0
1
2
1
1
1
2
1
1
0
1
1
1
1
1
2
0
1
1
2
1
1
0
2
1
1
2
1
1
2
1
2
1
1
2
2
2
1
1
2
2
1
1
1
0
2
2
1
2
1
1
2
2
0
1
3
0
1
1
1
1
0
0
1
1
1
1
1
1
2
2
0
1
1
1
1
1
2
2
1
2
1
1
1
2
2
2
2
1
2
2
0
1
2
2
1
1
2
1
1
1
1
2
1
1
2
0
1
1
2
1
2
0
0
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
2
2
0
2
2
1
1
1
1
2
2
2
1
2
1
1
2
1
1
1
2
0
1
0
0
0
0
2
2
1
1
1
2
0
2
1
2
2
2
0
1
2
1
1
1
2
2
1
1
2
0
1
1
0
1
1
0
1
1
1
1
1
0
1
0
0
1
0
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
0
0
2
1
2
0
0
2
1
2
1
1
1
1
1
1
0
2
1
0
2
2
0
1
0
0
1
0
2
1
1
1
1
1
1
0
1
2
1
1
1
1
0
1
2
2
1
2
1
2
1
1
2
2
2
1
1
1
2
0
2
1
1
2
1
2
1
2
1
1
0
0
1
1
1
0
1
0
2
1
1
1
0
1
2
1
1
1
2
2
1
0
0
1
1
2
1
0
0
1
1
2
1
1
1
1
3
2
0
2
1
1
2
2
1
3
1
1
0
1
1
1
2
1
1
2
0
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
2
1
0
1
1
0
1
1
2
1
1
2
0
1
3
2
2
1
1
1
1
1
1
0
2
1
1
2
1
1
1
1
1
2
0
2
0
2
1
1
0
1
1
1
2
1
1
0
1
0
1
0
2
1
2
2
0
0
1
2
1
1
1
1
1
2
1
1
0
2
0
0
1
2
1
2
1
2
1
1
1
1
1
2
1
1
0
1
1
1
3
0
1
2
1
2
0
1
1
2
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
3
1
1
1
0
3
1
1
0
1
1
1
0
1
1
0
2
1
0
1
1
0
1
1
0
2
1
1
1
0
1
3
1
1
0
1
1
1
1
0
1
1
0
0
1
1
1
1
1
1
1
1
1
1
0
2
1
1
1
1
2
1
2
2
1
0
1
2
1
0
0
1
1
1
1
1
1
0
1
1
0
0
2
2
1
1
0
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
0
1
1
1
1
2
1
2
1
1
2
1
0
1
1
1
1
2
2
0
2
1
1
1
2
1
1
1
1
1
1
1
2
0
1
1
1
2
1
2
1
0
0
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
2
0
0
2
1
1
2
1
1
0
0
1
1
1
0
1
1
1
2
2
1
1
1
1
2
1
2
1
1
1
1
2
1
0
0
1
1
2
0
2
1
2
2
2
1
1
1
1
0
2
2
0
1
1
1
2
2
1
0
1
0
1
1
1
2
1
0
1
1
1
1
1
1
2
1
0
2
1
1
1
2
1
1
2
1
2
2
1
1
1
1
1
1
1
1
0
0
1
0
1
1
1
1
1
1
2
1
1
1
1
2
0
2
2
1
1
1
0
1
2
0
1
2
1
2
2
2
1
1
0
1
1
1
1
1
1
1
2
1
1
1
0
0
0
1
1
2
1
0
0
1
0
2
0
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
2
0
2
0
2
0
2
0
1
1
1
1
0
0
1
2
0
1
1
1
1
1
1
2
0
1
2
1
1
2
2
1
0
1
2
1
1
1
1
1
1
1
1
2
2
1
2
1
1
2
1
1
1
0
1
0
1
1
0
1
1
1
1
2
2
2
2
2
0
1
0
1
2
0
1
1
2
0
1
1
2
1
1
1
2
1
1
2
0
2
1
2
2
1
1
0
2
2
1
1
0
1
2
1
1
1
1
2
1
2
1
1
1
2
1
1
0
2
1
1
0
2
1
1
0
1
1
1
1
0
1
1
1
2
2
1
2
1
2
1
1
1
1
1
1
0
1
0
2
2
1
2
1
1
1
2
2
1
1
1
2
1
1
0
2
1
2
1
1
1
1
0
1
2
2
0
1
1
1
1
1
1
1
1
1
1
1
2
1
0
1
2
1
2
1
1
1
0
1
1
1
2
1
0
2
2
1
2
1
1
1
1
1
2
2
0
2
1
1
1
2
1
2
0
2
0
0
1
0
1
2
0
1
1
2
1
1
0
0
2
1
0
1
1
0
1
2
1
0
1
1
0
1
1
0
1
2
1
0
1
1
1
2
0
0
1
1
1
0
1
1
2
1
1
1
1
2
2
1
0
2
1
1
2
1
0
2
0
1
1
2
1
2
1
1
1
2
1
1
1
1
2
0
1
2
2
1
1
2
1
1
0
1
1
2
0
2
1
2
1
1
1
1
2
1
2
2
1
1
2
0
1
2
2
0
2
1
1
2
1
1
2
1
1
1
1
2
1
0
2
1
1
1
2
1
2
2
1
1
2
1
1
1
0
1
3
1
0
1
2
0
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
2
1
1
2
1
1
1
1
1
3
1
1
1
1
1
0
1
1
1
2
1
1
1
1
1
1
2
1
1
2
1
0
1
1
1
0
2
1
0
1
1
1
1
2
0
1
0
1
0
1
1
1
1
2
0
1
1
0
1
1
1
1
1
1
1
1
1
2
1
1
0
1
0
1
2
0
1
2
2
3
1
1
1
1
1
0
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
0
1
2
0
1
1
1
3
1
1
1
1
1
2
1
2
0
2
2
1
2
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
2
2
1
1
1
2
0
1
0
1
2
1
1
1
2
1
1
1
2
0
1
2
1
0
1
0
2
0
2
1
1
1
1
1
1
2
2
1
2
2
3
1
0
1
1
1
1
1
2
2
1
0
0
0
2
0
1
1
2
1
2
2
2
0
2
0
1
0
1
1
2
1
2
1
0
2
1
2
1
2
2
1
1
0
2
1
1
1
2
1
1
0
1
2
1
0
0
1
0
0
1
1
2
1
1
1
0
1
1
2
1
2
1
1
2
0
1
1
1
1
0
0
1
0
0
1
1
1
1
2
2
2
1
1
0
1
2
2
1
1
0
1
2
1
1
1
2
0
1
1
2
1
1
1
2
2
1
1
1
1
1
2
1
1
1
1
1
0
2
1
2
1
2
2
1
1
1
1
1
1
1
2
2
0
2
2
1
1
0
0
2
1
0
1
1
1
0
1
1
1
0
1
1
1
1
1
1
1
2
0
1
2
2
1
2
2
1
1
1
1
0
1
0
1
1
2
0
0
3
0
1
1
1
1
1
1
2
1
1
0
1
2
1
1
1
2
1
1
2
0
1
0
0
1
1
2
0
2
1
0
1
1
2
1
0
1
1
1
2
1
2
2
2
0
2
0
1
2
1
1
2
1
0
1
1
0
1
1
0
1
0
1
0
0
0
1
2
1
0
2
1
1
1
1
2
1
1
1
1
1
2
1
1
1
0
1
0
0
1
1
1
1
0
1
1
4
0
2
1
1
2
0
1
1
0
1
0
1
0
1
1
1
1
2
3
2
2
0
2
1
0
0
2
1
0
1
2
1
1
1
0
2
1
1
2
1
1
3
1
2
1
0
2
1
2
2
1
1
1
1
2
2
1
1
0
1
1
0
2
1
1
2
2
1
1
1
1
1
1
1
1
1
2
0
1
1
0
1
1
1
1
0
0
1
0
0
2
1
0
1
1
2
0
1
1
0
1
1
1
0
1
2
1
1
1
1
2
1
0
1
2
2
1
2
2
2
2
1
2
1
1
1
2
1
1
3
1
1
1
1
1
0
2
2
2
1
1
1
1
2
1
3
0
0
1
1
1
0
1
0
1
1
2
1
1
2
1
1
1
1
0
1
2
0
1
1
1
1
1
2
0
1
1
1
1
1
1
1
1
1
0
2
1
2
1
1
2
1
0
1
1
1
1
1
2
2
1
1
1
1
1
1
4
1
1
1
1
0
2
1
1
1
1
2
2
2
1
1
2
1
2
2
2
1
1
1
1
1
2
2
2
1
1
1
0
1
1
1
1
0
0
1
1
0
1
1
2
0
2
1
2
1
2
2
1
0
0
2
1
1
1
1
1
1
1
2
2
1
1
1
1
2
0
1
1
0
1
1
2
1
1
2
1
1
1
2
2
2
0
0
1
1
2
1
1
0
1
2
2
2
2
1
1
2
2
0
1
0
2
1
1
2
2
1
2
2
1
2
1
0
0
1
1
1
1
1
1
1
2
0
1
1
1
2
1
1
1
1
1
1
2
2
1
2
1
1
1
2
1
1
1
2
2
1
1
0
2
1
1
1
1
2
1
2
1
1
0
1
0
0
0
1
1
2
1
1
2
1
1
1
1
1
1
1
2
2
1
2
1
3
2
1
1
1
1
2
1
1
3
2
0
2
2
1
2
1
1
2
2
2
2
2
2
1
2
2
2
1
0
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
0
1
2
1
2
2
1
2
0
1
0
2
0
0
2
1
2
2
2
1
1
1
1
0
1
3
2
0
2
1
1
1
1
2
2
1
1
2
0
2
0
1
1
1
2
1
1
1
1
1
1
1
1
2
2
1
2
2
1
1
1
1
0
2
0
1
0
1
2
2
1
1
1
0
2
3
1
1
0
2
1
2
0
1
1
1
2
1
1
0
2
1
1
1
1
1
1
1
1
2
2
1
2
2
2
2
1
2
1
2
1
1
0
1
1
1
1
1
1
0
1
1
0
0
1
2
2
1
2
0
1
1
1
1
2
1
1
1
1
1
0
1
1
0
1
1
1
2
1
1
1
1
1
3
1
0
1
0
1
2
0
0
0
1
1
1
2
2
1
1
1
1
1
1
0
2
1
2
1
2
1
1
1
1
1
2
1
2
1
1
1
2
1
1
2
1
2
2
2
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
0
1
1
2
1
0
1
0
1
0
1
1
1
2
1
2
1
0
1
0
1
1
1
1
2
1
2
1
1
1
1
1
1
0
2
1
0
0
2
1
0
1
0
2
2
0
0
0
1
1
2
2
0
1
1
1
2
1
2
2
1
2
1
0
1
1
1
1
0
2
1
1
0
2
2
2
2
0
1
1
2
0
2
1
1
1
2
1
2
2
0
1
2
1
1
1
1
1
2
1
1
0
1
1
1
0
2
2
1
1
1
1
2
1
1
1
2
1
2
0
1
1
1
1
2
0
1
2
0
1
2
1
1
1
1
1
0
0
1
1
1
2
1
1
0
1
1
1
1
1
1
0
1
2
1
0
1
1
0
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
0
2
2
1
0
2
1
1
1
1
1
2
2
1
1
2
0
2
1
1
1
2
2
0
0
2
2
2
1
0
2
1
2
2
2
2
2
0
1
2
1
1
0
0
1
2
0
0
2
1
1
1
2
1
1
1
1
2
1
1
1
1
2
2
1
0
2
1
2
2
2
2
1
2
0
2
1
2
2
0
2
0
1
1
2
1
1
0
1
1
1
1
1
1
1
1
2
0
0
2
1
0
1
1
2
0
0
0
3
2
1
2
0
1
1
1
1
1
0
2
2
1
2
0
1
2
1
1
2
1
1
3
0
2
1
1
1
1
2
1
1
1
1
2
0
2
1
1
1
1
2
1
2
2
2
0
1
1
1
1
1
0
1
1
1
1
2
0
0
2
2
1
1
1
1
1
2
0
1
0
2
1
0
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
2
1
2
1
1
2
1
2
1
2
2
1
1
1
1
1
1
2
0
1
1
1
0
2
1
2
1
1
1
1
2
2
1
0
1
1
1
1
1
2
1
1
1
0
2
0
1
2
0
1
1
1
1
2
1
1
1
1
2
1
1
0
2
1
1
2
1
1
1
1
1
1
1
1
0
1
2
1
1
1
2
0
1
2
1
1
1
1
1
1
1
1
1
0
1
1
1
2
1
2
0
2
1
1
1
1
1
1
1
1
1
0
1
2
1
1
1
1
2
1
1
2
0
0
1
1
1
1
1
0
2
1
1
1
1
1
2
2
3
1
1
1
2
2
1
1
2
1
0
0
1
2
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
0
0
1
2
2
2
0
1
1
1
1
1
1
1
1
1
2
1
0
0
3
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
0
2
1
0
1
1
1
1
1
1
0
0
1
1
1
1
1
2
2
0
0
2
2
1
1
1
1
0
1
2
1
1
1
1
1
2
1
2
2
1
2
0
0
2
0
1
1
2
1
1
1
2
1
1
1
1
1
1
0
2
1
1
0
0
1
1
0
1
2
0
1
1
2
1
1
1
2
2
1
2
2
0
0
1
1
1
1
1
1
0
2
2
1
0
0
1
2
1
2
2
1
1
1
1
1
2
1
1
2
1
2
1
1
1
1
2
2
2
1
2
1
1
1
1
0
1
2
1
1
1
0
2
1
1
1
1
1
1
1
0
2
2
1
1
1
2
2
1
2
1
1
1
0
2
1
1
2
3
1
2
1
0
2
1
2
2
1
2
0
1
2
2
1
1
1
1
0
2
2
2
2
2
1
1
1
2
2
2
1
0
2
1
1
1
1
1
1
0
1
1
1
1
1
0
2
1
1
2
1
1
1
2
2
0
1
0
1
1
1
1
0
1
2
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
0
0
1
0
2
0
1
1
1
1
2
1
1
2
2
1
1
1
2
1
1
2
1
1
1
1
0
1
1
0
2
2
1
1
1
1
1
1
2
2
0
2
2
1
1
0
1
1
0
1
1
1
1
1
2
0
2
1
2
1
2
1
1
1
1
1
1
1
1
0
0
1
1
1
1
3
1
1
0
1
1
1
0
1
2
1
1
1
2
1
1
1
1
2
1
1
0
1
0
2
1
1
1
0
0
1
1
1
1
0
0
1
2
0
1
1
0
0
2
1
1
0
0
1
1
1
0
1
2
2
1
1
0
2
2
1
1
1
1
0
1
2
1
1
0
0
2
1
1
1
2
1
1
1
1
1
1
1
2
2
1
0
1
1
2
1
1
1
1
2
1
2
0
1
1
2
1
1
0
2
1
2
2
1
1
0
1
1
1
1
1
1
1
0
1
2
2
1
1
1
0
1
1
1
1
1
0
1
1
1
1
0
1
1
1
1
0
1
1
1
1
0
2
1
1
0
1
0
1
1
1
1
0
1
1
2
1
1
2
1
1
2
0
1
1
1
1
1
1
1
1
0
1
1
2
1
1
0
1
1
0
1
1
1
1
1
1
1
0
1
2
1
2
1
1
2
1
1
1
1
1
1
1
1
0
0
0
1
1
0
1
1
1
1
0
0
1
0
1
1
2
1
0
1
1
1
0
1
2
1
2
1
1
0
2
1
1
2
1
1
1
1
1
1
0
1
1
2
1
2
0
1
1
2
1
2
0
0
1
3
1
1
1
1
2
2
1
1
1
2
0
1
2
1
2
0
1
1
1
2
3
1
1
1
1
2
0
1
1
2
1
1
1
2
2
2
1
1
1
1
0
1
1
1
1
2
1
2
2
1
1
1
2
0
1
0
1
1
1
0
0
0
2
2
1
1
1
1
1
2
0
1
0
2
2
1
1
1
1
0
0
1
1
1
1
1
1
1
1
1
0
2
1
0
1
1
0
1
1
2
1
0
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
2
1
1
1
1
1
0
1
1
2
1
1
0
1
1
0
0
1
1
0
1
1
1
1
1
1
2
1
0
1
1
1
1
0
2
0
2
1
1
1
1
0
2
1
2
1
2
2
2
1
2
1
2
2
1
2
1
2
1
1
1
1
2
1
0
1
1
2
0
0
0
1
1
0
1
2
1
0
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
4
1
1
3
2
2
1
3
2
0
0
1
2
0
0
1
1
0
1
1
1
2
1
2
0
1
2
2
1
1
1
1
1
0
1
0
1
1
1
2
2
1
0
2
1
1
1
1
1
0
2
2
2
0
1
1
1
1
1
0
1
1
1
2
2
2
1
1
2
0
1
1
1
2
0
1
1
2
1
0
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
0
1
1
0
1
1
1
1
2
1
1
0
1
1
1
1
1
1
2
1
0
2
1
1
1
2
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
2
2
2
2
2
2
2
1
1
1
2
2
2
2
1
1
1
1
0
1
2
1
1
1
2
1
1
2
2
1
2
1
2
0
1
2
0
2
1
1
0
2
1
2
1
1
1
1
2
0
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
2
0
2
0
2
1
1
1
2
1
1
1
1
2
1
1
0
1
1
0
1
1
1
1
2
2
0
1
1
1
2
1
1
2
1
1
1
0
1
2
2
1
1
1
2
1
2
1
0
1
1
2
1
2
0
1
1
1
2
2
1
1
1
0
2
2
0
0
0
1
0
1
1
1
1
1
0
1
4
1
1
0
1
1
2
1
1
2
1
1
2
0
1
2
0
2
2
0
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
0
1
1
2
1
1
0
2
2
2
1
1
2
2
2
1
1
0
1
1
2
0
0
1
1
1
2
1
1
1
2
1
1
2
2
2
1
1
0
2
1
1
0
1
1
1
1
1
0
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
0
0
1
1
1
0
1
1
1
1
2
2
1
1
1
1
2
1
1
2
1
0
1
1
1
2
0
1
2
0
2
0
2
0
1
2
1
1
0
1
0
1
2
1
2
0
1
1
2
1
2
1
1
2
1
1
1
2
1
2
1
1
2
1
0
1
1
1
1
1
2
1
1
2
1
1
1
2
1
1
0
1
1
1
1
1
1
1
1
1
0
0
1
0
1
1
1
2
1
2
1
1
1
1
1
1
1
2
1
2
1
0
1
2
0
2
2
1
1
2
1
0
1
2
0
1
1
2
0
2
1
1
1
0
1
2
1
1
0
1
1
1
1
0
2
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
0
1
1
2
1
2
1
0
0
1
2
0
1
1
1
2
1
1
1
0
1
2
1
1
0
0
1
1
1
0
1
1
1
1
1
1
1
0
1
0
1
1
1
1
2
1
0
0
1
1
1
1
1
1
1
1
1
2
1
1
1
0
1
1
1
1
2
1
2
0
2
1
2
1
1
2
1
1
2
1
2
1
1
2
1
1
0
1
1
4
1
2
1
2
0
1
2
1
0
2
1
1
1
1
0
1
2
2
2
1
1
1
1
1
1
1
1
0
0
0
0
1
1
0
1
1
2
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
2
1
2
1
0
1
1
1
1
1
2
1
1
1
1
1
0
2
1
2
2
1
1
0
1
0
1
1
1
1
0
1
0
1
0
2
2
1
1
1
1
0
1
1
1
1
0
0
1
1
2
1
2
1
2
1
1
1
1
1
1
1
2
0
0
2
1
0
1
1
1
2
2
1
1
1
0
1
1
2
2
0
0
1
1
1
1
1
2
2
1
2
2
0
1
0
1
1
0
2
1
1
1
0
2
1
0
2
1
1
1
1
2
1
2
1
1
0
1
1
1
1
0
0
2
1
1
1
1
2
0
1
1
1
3
1
0
1
2
1
2
0
1
2
1
1
2
1
0
1
1
2
1
1
1
1
1
1
2
1
1
2
2
1
1
0
1
1
2
1
1
1
1
1
2
2
2
2
1
2
1
2
2
1
1
2
1
2
2
1
1
1
2
1
0
2
2
0
1
1
1
0
2
1
2
1
1
0
1
1
0
1
1
0
1
2
1
1
1
4
1
1
2
1
2
1
2
2
2
1
1
1
1
1
0
2
2
0
1
1
1
1
2
2
0
1
1
1
1
1
1
2
1
1
2
1
1
2
1
1
2
2
2
0
1
1
2
0
2
1
1
1
1
2
1
0
1
1
1
2
1
1
0
0
2
1
0
1
2
2
1
4
2
0
1
2
1
2
2
2
1
1
1
1
1
1
0
1
1
2
0
1
1
1
2
2
1
2
2
1
2
1
2
1
1
2
2
2
2
1
1
2
1
1
1
1
1
1
1
0
0
2
1
2
1
1
1
2
1
1
1
2
1
0
1
2
2
1
1
2
2
1
1
1
2
0
1
1
1
1
1
1
1
2
1
2
1
1
1
2
2
2
1
1
2
0
1
1
1
2
2
0
2
1
2
1
1
1
1
1
1
0
2
1
2
1
1
1
0
0
1
2
2
1
1
3
1
2
1
1
1
1
1
1
2
5
2
1
1
1
1
1
1
1
2
1
2
2
1
1
2
1
2
2
1
2
1
2
2
0
1
1
1
1
2
4
1
1
1
2
1
1
1
2
1
2
2
1
1
1
0
1
1
0
1
1
1
2
1
2
1
2
0
1
1
2
1
1
0
1
2
0
1
0
0
1
2
1
0
0
2
1
1
1
1
0
2
1
1
0
1
1
0
2
2
0
1
0
1
1
1
0
1
1
0
0
1
1
1
1
0
2
2
1
2
1
1
1
3
2
1
1
1
1
1
1
1
2
0
1
1
1
1
0
2
2
2
1
0
1
1
1
2
2
0
1
0
1
1
2
1
2
1
1
1
1
2
0
2
1
1
2
2
2
2
0
1
0
1
1
1
1
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
2
1
2
1
0
1
1
1
3
1
0
1
0
2
1
0
1
0
1
1
1
0
1
1
3
2
0
1
1
1
1
2
1
1
0
1
0
1
1
1
0
1
2
0
1
2
1
0
1
1
0
0
2
0
1
0
2
1
0
1
1
1
1
1
2
1
1
1
2
2
0
1
1
1
1
2
2
1
1
0
0
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
2
0
1
1
1
1
2
0
2
2
1
2
2
2
2
1
0
2
1
1
0
0
0
1
0
2
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
2
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
0
1
2
1
2
1
1
2
1
0
1
1
1
2
1
2
1
2
1
1
2
0
0
1
1
1
2
2
0
1
2
1
1
2
1
2
1
1
1
0
1
1
2
2
1
2
1
0
2
1
0
2
1
2
2
2
1
1
1
0
2
1
0
0
0
2
0
1
0
1
1
1
2
2
2
1
1
2
1
2
0
1
0
1
2
0
2
1
0
1
2
0
1
1
1
2
2
1
1
1
2
2
0
1
0
1
1
2
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
2
1
1
1
1
1
1
1
0
1
1
2
1
2
2
2
0
1
0
2
1
1
1
2
2
1
1
2
1
1
2
1
1
2
2
2
1
1
1
1
2
2
2
1
2
2
2
1
1
1
4
1
1
1
1
1
1
2
1
1
1
2
1
2
2
1
1
2
1
0
1
1
1
1
1
2
1
1
1
1
0
1
1
0
1
1
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
0
1
2
2
2
2
2
1
0
2
1
1
2
0
1
1
2
1
1
1
1
1
2
2
1
1
1
1
0
1
1
2
2
1
1
0
1
0
1
2
1
1
1
2
0
1
2
2
1
2
1
1
0
2
0
1
1
1
1
2
1
2
1
1
2
0
0
1
2
2
1
2
1
1
1
1
1
1
1
2
1
1
0
1
2
1
2
1
1
2
0
1
1
1
1
1
2
1
2
1
1
0
2
1
1
1
1
1
0
2
1
2
0
1
1
1
0
2
1
2
1
1
0
1
1
1
1
0
1
0
1
1
1
2
0
1
1
1
2
2
1
1
0
1
2
1
1
1
1
2
0
1
1
1
1
1
1
2
1
1
0
1
1
1
1
0
2
2
1
0
1
1
2
0
1
1
2
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
2
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
0
1
1
1
1
1
1
2
2
2
1
0
1
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
2
2
1
1
1
1
1
1
1
0
1
1
1
2
2
1
1
2
1
1
1
1
1
2
1
1
1
2
1
2
1
0
1
2
2
2
2
2
1
1
1
1
2
1
1
2
0
1
1
1
1
1
1
1
1
1
0
1
1
2
1
1
1
1
1
1
1
2
0
2
1
1
1
1
1
1
1
2
0
1
1
2
0
2
2
2
1
1
1
1
2
2
1
0
1
1
2
2
1
2
2
2
2
1
1
1
0
1
1
1
1
1
2
2
1
0
2
2
1
1
2
1
1
1
2
1
2
1
1
2
2
2
2
2
1
0
2
0
2
4
0
2
1
1
1
1
2
2
0
2
0
1
1
0
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
2
1
0
1
1
2
1
2
1
1
1
1
0
2
2
2
1
2
1
0
0
1
1
2
3
1
1
1
1
1
2
2
1
1
1
0
1
1
1
1
0
1
1
0
0
1
0
1
1
1
1
0
2
0
0
1
0
1
2
1
1
1
1
1
1
1
2
1
0
1
0
2
1
1
1
2
1
0
0
1
1
2
1
1
0
1
1
0
2
1
0
1
0
1
2
1
1
2
2
1
1
0
2
1
1
1
1
2
1
2
2
0
1
1
1
1
1
2
2
2
2
1
1
2
0
2
1
0
1
1
1
0
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
2
0
1
0
1
2
1
1
1
2
1
1
1
1
1
1
2
0
0
0
2
1
1
2
1
1
2
0
2
2
2
1
1
1
2
1
1
1
2
0
0
2
1
2
1
1
1
1
1
0
1
1
2
1
1
1
1
1
1
1
2
1
2
1
0
1
1
2
2
2
1
1
2
1
2
0
2
1
1
1
1
1
1
3
0
2
2
2
1
0
1
1
1
1
2
1
1
0
1
1
0
1
1
1
0
1
1
1
1
2
1
1
1
2
2
1
2
2
1
1
0
1
1
1
1
3
1
1
1
1
1
0
2
1
1
1
1
1
0
2
2
1
0
1
1
1
1
2
1
1
0
1
0
1
1
2
2
1
2
1
0
2
1
0
2
0
2
2
0
2
1
1
1
2
1
1
1
1
3
1
1
1
1
1
2
1
1
1
1
1
1
1
2
0
1
1
1
1
1
1
1
2
2
0
1
0
0
1
2
2
1
1
0
1
2
1
1
1
1
1
1
2
1
0
1
2
1
1
1
1
1
1
0
2
1
1
1
1
2
1
1
1
0
1
2
1
3
1
1
1
1
2
1
2
1
1
1
2
1
2
2
1
2
0
2
0
2
1
2
1
1
1
2
1
2
1
2
1
1
1
1
1
1
2
0
0
1
1
2
1
1
1
2
1
1
2
0
2
1
1
1
1
1
2
1
1
1
2
1
0
1
0
1
1
1
1
0
0
0
0
0
1
1
1
1
1
0
1
3
1
1
1
1
0
1
1
0
1
1
2
2
1
1
1
2
2
2
2
1
1
1
1
1
0
2
1
1
1
1
0
1
1
1
1
2
1
1
1
1
1
1
1
1
0
0
2
1
1
2
1
0
0
0
1
0
1
1
1
1
0
1
1
0
2
2
0
1
1
1
1
1
2
1
2
1
1
1
1
0
0
1
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
0
1
0
1
1
1
1
2
1
1
1
1
1
2
0
0
2
1
1
1
2
1
2
2
1
2
2
1
2
0
1
1
1
1
2
2
1
1
1
1
1
2
1
1
1
7
1
1
1
1
0
1
0
1
1
1
1
1
1
2
1
1
1
0
1
0
1
2
0
1
1
0
1
2
1
0
2
2
2
1
1
2
1
1
1
1
1
0
2
1
1
1
1
1
1
0
1
0
2
1
1
0
1
1
1
2
0
2
2
1
1
2
1
2
1
1
1
1
1
1
3
1
1
1
1
2
1
0
0
1
1
0
1
2
1
2
0
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
2
1
2
1
1
1
1
1
0
1
2
1
1
2
1
2
2
1
0
1
0
2
1
1
1
1
0
2
1
1
1
1
1
1
2
1
1
1
0
1
1
2
1
2
1
1
1
1
1
1
1
1
2
1
2
2
1
1
2
2
1
1
2
1
2
2
1
1
1
2
2
1
1
1
2
0
1
2
1
1
2
1
1
1
1
2
1
1
1
1
1
2
1
1
2
1
1
2
1
1
2
0
1
1
1
2
1
1
2
2
1
1
1
0
1
1
1
1
2
1
0
2
1
1
1
1
1
1
1
0
2
1
1
2
1
0
1
1
1
1
2
1
1
1
2
1
1
2
1
1
1
1
2
0
2
1
1
1
0
1
2
1
2
0
2
2
1
0
1
2
1
1
0
1
1
2
1
1
3
1
0
1
0
2
1
2
1
1
1
2
1
1
2
1
2
1
2
2
1
0
2
1
1
0
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
3
1
1
1
1
2
0
1
0
0
1
0
1
1
1
3
1
2
0
1
1
2
0
1
0
1
0
1
1
0
2
0
3
1
2
2
1
0
1
1
2
2
1
2
1
1
1
1
2
1
1
1
1
1
1
0
1
2
0
0
1
1
2
1
0
1
1
1
1
2
2
2
2
1
1
1
2
1
1
1
2
0
1
2
1
2
0
1
1
1
1
1
1
0
1
1
1
0
1
1
2
1
1
1
1
2
1
2
2
1
1
0
2
2
0
1
1
1
1
2
1
1
2
1
1
1
1
2
2
1
1
0
1
2
2
1
2
1
2
2
2
0
1
0
1
2
1
1
1
1
1
3
1
1
2
1
1
1
1
1
1
1
2
1
2
0
1
1
1
1
2
0
1
1
2
1
0
0
1
1
0
1
1
2
1
2
1
1
1
0
1
1
1
1
2
1
1
1
0
1
2
2
1
1
0
0
0
0
1
1
1
1
1
1
1
2
1
0
1
1
1
1
2
1
0
1
2
2
2
1
1
1
2
1
1
1
1
1
2
2
1
0
1
0
1
1
1
1
1
1
0
1
0
1
0
0
2
2
1
1
0
1
1
2
0
2
1
1
2
1
1
1
1
1
0
1
1
1
1
1
2
1
0
1
1
1
1
0
1
1
1
2
2
2
1
1
2
0
1
1
2
1
1
1
1
0
0
0
1
1
2
1
2
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
0
1
2
0
1
2
1
0
1
2
2
1
2
0
2
1
1
1
2
0
1
2
1
1
1
1
0
1
1
0
1
2
1
2
1
2
1
1
0
1
1
1
0
1
1
2
2
1
2
1
1
1
1
1
1
0
1
0
2
2
2
2
1
1
2
1
1
1
2
1
1
2
1
2
2
1
1
1
1
1
1
1
0
1
1
1
2
0
0
1
1
0
0
0
2
1
4
1
1
2
0
2
2
0
1
1
1
1
1
0
1
0
1
1
1
0
2
2
0
1
1
2
1
1
1
2
1
1
1
1
1
1
0
1
1
1
1
1
1
2
1
1
1
2
1
1
1
2
2
0
0
3
1
0
1
1
0
1
1
1
1
0
1
1
1
2
1
1
1
1
1
1
1
0
1
1
2
2
2
1
2
1
2
1
2
1
1
2
1
1
2
1
1
2
1
1
1
1
1
2
2
1
1
1
1
0
2
2
1
1
1
1
2
1
2
0
1
1
1
1
1
1
1
1
0
1
1
2
2
1
1
2
1
1
1
1
1
1
1
2
1
2
0
1
0
1
1
1
1
2
1
1
1
0
2
2
1
1
2
1
1
1
1
3
2
0
1
1
1
1
1
1
1
1
1
1
1
1
0
2
2
2
1
1
1
2
2
2
1
1
1
1
1
2
0
0
1
1
0
1
2
0
1
2
1
2
1
1
1
0
0
1
2
1
2
1
1
1
1
1
2
2
0
1
1
0
1
1
2
1
1
1
1
2
0
0
2
1
1
2
1
2
1
2
2
1
2
2
2
1
1
2
1
2
2
2
2
2
0
2
2
1
2
1
1
1
2
2
1
2
2
1
1
1
0
1
1
0
2
1
1
1
1
1
2
0
2
1
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
1
1
1
1
1
3
1
1
1
0
1
1
1
0
1
3
1
1
1
0
0
1
1
1
2
1
1
1
1
2
2
1
0
1
1
0
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
2
0
1
1
2
2
1
2
1
2
2
1
1
1
0
1
1
0
0
0
2
1
1
0
1
2
1
1
2
1
2
1
2
0
2
1
1
2
1
1
1
1
2
1
1
1
1
0
1
1
1
1
1
2
2
2
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
2
1
1
1
0
1
1
1
1
2
1
1
1
1
1
1
1
1
1
0
2
1
1
1
0
0
1
1
2
0
0
1
2
1
1
1
1
0
2
1
1
2
1
1
1
2
1
1
1
1
1
0
1
1
1
1
1
0
0
1
2
2
1
1
1
1
1
1
1
1
1
1
1
2
2
0
1
1
2
1
2
1
1
1
1
1
1
1
0
0
1
1
1
1
0
2
0
1
1
0
1
1
1
1
2
1
0
2
1
2
1
0
1
0
0
1
1
2
1
1
1
2
1
1
1
2
0
2
2
2
1
1
1
2
1
1
1
0
1
2
1
1
1
2
1
0
1
0
1
1
1
1
1
1
2
0
1
2
1
0
1
1
2
1
0
2
1
0
0
1
1
2
2
2
1
2
2
0
1
3
1
2
1
1
0
1
0
1
0
1
1
1
1
1
1
1
0
1
2
1
4
0
1
4
1
1
1
2
2
1
1
0
1
2
2
1
1
2
2
2
0
2
1
1
1
1
0
1
1
2
2
0
2
1
1
1
0
0
0
1
1
1
2
0
1
1
1
2
2
1
0
1
1
2
1
2
1
1
1
1
1
1
1
1
2
2
1
1
1
1
0
1
2
1
1
2
2
1
0
1
1
2
1
1
1
1
2
2
1
2
1
1
0
1
1
1
1
1
1
1
1
2
1
0
1
2
2
2
1
1
1
1
1
1
1
0
1
1
1
1
1
0
1
1
1
1
1
2
1
0
1
0
1
1
1
1
1
2
2
1
2
1
0
1
1
2
1
1
0
2
2
2
1
2
1
1
0
1
1
2
1
0
1
1
1
1
1
1
2
2
1
2
0
1
0
1
1
0
1
2
1
0
2
1
2
1
1
1
2
1
1
2
1
1
1
1
1
0
1
2
2
1
1
0
2
1
2
2
1
2
0
1
1
1
2
2
1
2
2
0
1
1
1
1
1
1
1
0
1
1
2
2
0
1
2
1
1
0
1
1
1
2
1
0
1
1
3
0
1
1
1
0
2
1
1
1
1
1
1
0
2
1
1
0
1
0
2
1
1
2
1
1
0
0
0
1
1
1
1
1
1
1
1
1
0
1
1
0
1
0
2
1
0
1
1
0
2
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
2
2
0
1
1
2
2
1
2
2
1
1
1
1
2
1
1
0
1
0
1
1
2
0
2
2
1
1
1
1
1
0
1
1
1
1
1
0
2
1
1
1
2
1
0
1
2
2
1
2
1
1
1
2
2
1
0
2
2
0
0
1
0
1
1
0
0
1
0
1
0
1
1
1
1
1
0
1
2
1
2
0
1
2
2
1
1
1
2
2
0
1
0
1
0
1
1
2
2
0
2
1
2
1
0
0
1
2
1
1
1
2
1
2
1
2
1
1
1
1
2
1
1
1
1
1
2
0
2
0
0
0
1
1
1
0
2
1
2
2
2
1
2
0
1
2
0
2
1
2
0
2
1
1
1
1
1
2
2
1
1
1
2
1
2
2
1
1
2
1
1
1
2
0
1
2
2
1
1
2
2
1
1
0
1
0
2
1
1
1
2
1
2
0
2
1
2
1
2
2
2
0
1
1
1
1
1
1
0
2
1
0
1
0
2
1
1
1
2
1
2
1
1
1
2
3
1
1
1
0
1
1
1
1
4
1
2
1
1
1
1
2
0
2
1
1
2
2
1
2
2
2
1
0
2
1
0
1
2
1
2
0
1
2
2
2
1
1
2
0
2
1
2
1
1
2
0
1
1
1
2
2
1
1
2
1
1
1
1
1
1
2
1
1
0
2
1
0
1
1
1
3
1
1
0
1
2
0
1
2
1
1
2
1
1
1
1
2
0
0
2
1
0
1
1
2
1
0
2
1
0
1
1
0
1
0
2
1
0
0
5
1
1
0
2
1
1
1
1
1
1
1
1
1
1
1
1
2
0
2
1
1
0
1
1
0
2
1
0
2
1
1
0
1
1
1
1
1
1
1
2
0
2
1
2
2
1
2
0
1
0
1
1
1
1
0
2
1
1
0
1
2
2
0
1
2
1
1
0
2
2
1
1
1
2
1
1
0
2
1
1
1
0
1
1
1
1
2
1
0
1
2
1
1
1
1
0
1
1
1
2
1
2
0
1
1
1
2
0
1
1
2
1
0
2
1
1
1
2
0
1
2
1
1
1
1
1
1
1
0
0
1
2
2
2
0
1
1
1
2
0
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
0
0
1
1
2
1
1
2
2
1
1
0
1
1
1
0
2
1
1
2
1
1
1
1
1
1
0
1
1
0
1
1
2
0
1
2
2
0
1
1
1
1
1
1
1
1
2
2
1
1
2
0
2
1
2
1
1
1
1
1
2
1
1
1
1
1
0
1
1
1
1
1
1
1
1
2
0
1
0
2
1
1
1
2
1
0
1
0
2
0
0
1
1
0
1
1
2
1
1
1
1
1
2
0
0
0
1
1
2
1
1
2
0
1
2
1
1
2
1
1
1
1
1
1
1
2
0
1
1
1
3
1
1
2
1
1
2
1
2
1
1
3
1
0
2
0
2
2
1
1
1
1
1
2
1
0
1
1
2
1
1
0
1
1
0
2
2
1
2
2
0
2
1
1
1
0
2
1
2
1
1
2
1
2
1
1
1
2
2
1
1
1
1
0
1
1
1
1
2
1
1
2
1
1
1
1
1
2
2
0
1
0
1
1
1
2
0
1
1
1
1
2
1
2
0
1
1
1
1
1
1
1
0
1
1
2
1
2
2
0
2
2
1
1
1
1
1
0
2
2
0
1
1
1
0
1
2
1
2
1
2
1
1
0
2
1
2
1
2
1
0
1
1
1
0
1
2
1
1
2
1
1
1
1
1
0
1
1
1
1
1
0
1
2
1
1
2
1
2
2
1
2
2
1
0
2
2
2
1
1
2
0
1
1
1
2
1
1
2
0
0
2
1
0
1
2
2
2
1
1
2
1
1
1
1
1
1
2
2
1
1
3
2
2
1
0
2
1
0
1
1
1
2
1
1
1
1
1
1
1
1
1
2
0
1
1
0
0
1
2
2
1
0
0
1
1
1
1
1
2
1
1
1
0
2
1
0
0
1
1
0
0
2
1
1
2
0
1
0
1
1
2
1
0
0
2
1
1
1
1
0
1
0
1
2
1
1
1
1
0
1
2
1
1
2
1
1
1
0
4
1
1
1
2
1
2
1
1
0
2
1
1
1
2
1
1
0
1
0
0
1
0
1
1
2
2
1
1
1
1
1
1
0
1
1
1
0
1
1
1
0
2
1
2
2
2
1
2
1
2
1
1
1
1
0
1
1
1
1
1
0
2
1
1
0
1
2
1
1
1
2
1
1
1
0
0
0
0
1
0
0
1
0
1
0
1
2
1
1
2
1
2
1
1
2
2
1
2
2
2
2
2
1
1
2
0
1
1
1
0
1
1
1
1
1
0
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
2
1
0
1
2
0
1
0
2
1
1
1
1
1
1
2
2
0
0
1
2
1
1
1
0
0
2
1
1
2
1
1
1
0
2
1
2
1
2
0
1
1
1
1
2
1
1
1
1
1
0
1
1
1
1
0
2
1
0
1
1
3
2
1
1
1
1
1
1
2
2
1
1
1
1
1
2
2
1
1
1
1
1
2
1
2
1
1
2
2
1
2
1
1
1
1
2
1
1
2
1
0
2
1
1
1
2
2
1
1
2
2
1
0
1
1
1
1
1
1
0
1
1
1
2
2
0
2
1
1
2
1
0
2
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
1
2
2
1
1
2
2
1
2
0
1
1
1
0
2
2
0
0
0
2
1
1
1
0
1
2
1
1
1
1
0
1
1
1
1
1
2
1
1
2
1
1
1
3
1
1
2
1
1
0
0
1
0
2
1
1
2
1
2
0
1
6
1
2
1
2
2
1
1
2
1
1
0
2
0
1
0
2
1
2
1
1
1
2
1
1
0
1
1
1
3
1
1
2
1
2
0
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
3
2
1
1
1
0
0
2
2
2
0
2
1
0
2
1
1
0
1
1
1
1
0
1
1
2
1
2
1
1
1
2
2
1
2
1
1
1
1
0
1
1
0
1
2
2
0
0
1
0
1
1
2
2
1
2
0
1
2
0
1
2
1
0
1
1
0
1
1
1
0
1
0
1
0
1
2
2
1
1
0
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
0
0
1
1
1
1
1
1
2
1
1
2
2
1
1
1
2
2
2
2
2
2
2
1
1
0
2
1
1
2
1
1
0
2
2
1
1
1
1
0
2
1
0
1
1
3
1
1
1
2
2
0
1
1
1
2
1
1
2
1
0
1
2
1
2
2
1
1
1
1
0
0
1
0
1
1
1
0
1
0
2
1
0
2
0
1
0
1
0
0
0
1
1
2
1
1
1
1
1
1
1
2
1
0
1
1
1
1
2
1
2
2
1
2
2
1
1
2
0
1
1
1
1
2
2
1
2
0
1
2
1
0
2
0
1
1
1
1
1
2
2
1
1
2
2
1
2
1
2
1
1
2
2
1
2
1
2
1
1
1
1
2
2
1
1
2
1
2
2
1
0
1
1
1
2
0
2
1
2
1
2
1
1
2
0
1
0
0
1
2
0
2
1
1
1
1
0
1
0
1
1
1
0
2
2
0
1
1
2
1
1
2
1
2
2
1
0
1
1
1
2
1
2
1
1
1
1
1
1
0
2
2
1
1
2
2
2
1
2
2
1
1
2
0
1
2
2
1
1
1
1
0
1
1
1
2
0
1
1
2
2
1
1
0
2
2
2
2
0
2
2
1
1
0
1
1
1
0
1
2
2
1
1
1
2
0
2
1
1
0
1
1
1
1
2
1
1
1
1
1
1
3
1
2
1
1
1
0
2
2
1
2
0
1
1
1
2
1
2
1
2
1
1
1
1
0
2
1
1
1
1
1
0
2
0
2
1
2
0
1
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
2
2
1
1
1
2
2
1
2
2
1
1
1
0
1
1
1
1
1
1
1
2
0
1
0
1
1
1
1
2
2
1
0
1
1
1
1
2
1
2
2
0
2
2
2
1
1
1
0
2
1
2
1
1
3
1
2
0
1
1
2
2
1
2
1
1
1
0
1
1
0
1
1
0
1
2
1
1
0
1
1
0
2
1
1
1
1
1
1
1
1
1
2
0
1
0
1
2
1
1
1
1
1
1
2
1
1
2
2
2
1
1
1
1
1
1
1
1
2
1
1
1
0
1
1
0
1
2
1
1
2
0
0
1
1
1
2
1
1
2
1
2
1
1
2
1
0
1
1
2
1
1
1
1
2
1
1
2
1
1
1
2
1
1
2
1
2
1
1
0
1
2
1
1
1
1
1
2
1
1
2
2
1
2
1
1
1
1
1
1
1
1
2
2
2
1
1
0
1
1
0
1
2
1
1
2
0
1
2
1
1
0
1
1
1
2
1
1
2
2
1
1
2
1
1
1
1
0
2
1
2
1
1
1
2
1
1
1
2
1
1
2
5
1
1
0
2
1
2
1
1
1
1
1
2
2
1
1
1
2
1
1
1
1
2
1
0
1
1
2
1
1
1
1
1
2
1
0
1
1
2
1
2
1
2
1
1
2
1
1
1
1
0
1
2
1
1
0
2
2
1
1
1
1
1
1
0
2
1
2
1
1
2
1
1
0
1
1
1
1
1
1
2
0
1
1
0
1
1
1
1
1
1
1
1
1
3
1
1
1
2
1
1
2
1
1
1
1
2
1
1
1
2
1
1
2
3
1
2
1
1
2
1
1
1
2
1
0
1
2
1
0
2
1
2
1
2
0
1
1
2
1
2
0
1
0
3
0
1
1
0
1
1
1
1
2
1
1
0
1
1
0
1
2
2
1
2
2
1
1
1
1
1
1
2
1
1
2
1
2
1
1
1
1
2
2
1
1
1
1
2
0
2
1
2
2
1
1
1
0
2
2
0
1
1
1
1
1
0
2
1
2
1
3
0
1
1
2
2
1
1
0
2
1
1
1
1
1
1
1
0
1
1
1
1
1
1
2
4
2
1
1
0
1
1
2
0
0
2
1
1
1
1
0
2
0
0
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
0
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
2
1
2
1
1
1
1
1
2
2
1
1
1
1
2
2
1
1
1
0
1
1
1
0
1
0
0
1
2
1
1
0
1
1
1
1
1
0
1
1
1
2
0
1
2
1
1
1
0
1
2
1
2
0
1
2
1
1
1
1
1
0
1
2
1
1
1
1
1
1
0
2
2
2
2
2
1
1
1
0
1
2
1
1
1
0
1
1
1
2
1
1
0
1
1
1
1
1
1
0
1
2
1
1
1
1
1
1
0
2
2
1
1
1
1
1
1
1
1
2
1
0
1
0
1
7
2
1
1
1
1
2
2
1
1
2
2
1
2
2
2
1
2
0
0
2
1
1
1
0
0
1
1
0
1
1
0
1
1
2
0
1
2
1
2
1
0
1
1
0
2
1
1
2
1
1
1
2
1
2
2
0
1
2
1
1
1
1
2
1
1
1
2
1
1
2
2
2
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
2
1
2
1
1
0
1
0
1
1
0
1
2
1
1
1
2
1
3
0
0
1
2
0
2
0
1
1
0
0
2
1
2
2
2
2
1
2
2
1
2
2
1
1
1
0
0
1
1
2
1
2
1
1
1
1
1
0
1
1
1
1
2
1
0
1
0
1
1
1
2
2
1
1
2
1
1
2
2
0
0
1
1
2
1
2
1
1
1
2
1
2
2
1
0
1
0
1
3
2
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
0
1
1
0
1
2
1
1
2
1
2
2
2
1
2
1
1
1
0
2
2
2
1
1
1
0
1
1
1
1
1
0
1
0
2
1
1
1
3
2
1
0
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
0
0
1
1
2
2
2
1
1
1
1
1
2
0
2
1
2
1
1
0
1
0
1
1
2
1
1
1
2
2
1
1
0
1
1
1
2
1
1
2
1
1
2
1
1
2
0
2
2
1
1
1
0
1
1
0
1
2
1
2
0
2
1
2
1
2
1
0
1
2
1
1
1
2
1
2
1
1
1
0
1
1
1
0
1
1
0
1
3
0
1
2
0
0
1
2
1
1
1
1
1
2
1
1
1
1
2
1
0
0
1
2
2
2
1
1
1
2
1
1
1
1
1
0
2
1
0
1
2
1
1
7
1
1
1
1
1
1
2
1
1
1
2
1
1
0
1
1
1
2
1
1
1
2
1
1
0
1
1
2
1
2
2
1
2
1
3
2
2
1
2
1
1
1
1
2
1
1
0
1
1
1
1
0
0
1
1
2
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
2
1
1
1
1
0
1
1
0
2
1
1
2
1
2
1
1
2
2
1
1
2
2
2
1
1
1
0
1
2
1
0
0
1
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
0
2
1
1
1
0
1
1
2
1
1
0
1
2
1
1
2
1
1
1
0
0
2
1
1
1
2
1
0
1
1
1
1
2
1
0
2
0
1
1
1
0
1
1
1
1
1
1
1
1
2
1
1
1
2
1
2
2
1
0
1
1
1
0
1
1
2
1
1
1
0
1
2
0
1
1
1
1
1
1
1
1
1
2
0
1
2
1
1
1
1
2
1
1
2
1
2
1
2
1
1
2
1
1
1
1
1
1
1
1
2
2
2
1
2
0
1
1
1
2
1
1
1
1
2
1
2
1
1
1
0
0
1
2
1
1
1
2
1
0
1
2
1
1
2
1
0
1
0
1
1
1
2
2
1
0
1
2
2
1
2
1
1
1
1
1
1
1
0
1
1
2
1
1
1
1
0
2
1
1
1
2
2
1
2
1
1
1
2
0
0
1
2
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
2
2
1
2
2
1
1
1
0
2
2
1
0
2
1
1
1
2
1
1
1
1
2
2
2
1
1
1
2
1
1
1
1
1
0
1
1
2
1
1
1
2
2
1
1
9
2
1
1
1
0
0
1
2
1
1
2
1
2
2
1
2
1
1
1
1
2
2
0
1
2
1
1
1
2
1
2
0
2
1
1
1
2
0
1
1
4
2
1
1
1
2
2
1
0
1
1
1
1
1
2
2
0
1
1
1
0
2
1
2
0
1
1
2
1
1
1
2
1
3
1
2
1
1
1
1
0
1
1
1
2
1
1
1
1
0
0
1
1
1
1
1
0
1
2
1
1
0
1
0
0
1
1
1
1
1
2
1
1
2
1
2
1
2
1
1
1
2
2
2
2
1
0
2
1
0
2
1
1
1
1
1
1
1
0
0
1
0
1
2
1
0
2
2
2
0
2
2
1
1
1
1
2
1
1
2
2
2
0
1
2
1
2
0
1
1
2
1
1
1
1
1
1
1
1
1
0
1
2
2
1
0
1
1
1
0
1
2
1
1
1
1
3
1
1
1
1
2
1
1
1
1
2
1
2
2
1
3
1
0
1
1
1
2
2
1
1
1
1
1
1
0
1
1
1
1
1
2
1
1
2
1
1
1
1
1
0
2
2
2
1
1
0
1
1
1
2
1
0
1
1
1
1
1
1
1
1
1
1
1
0
2
1
1
0
1
1
1
2
2
2
1
0
1
2
1
0
1
2
1
1
0
1
1
1
1
1
1
2
2
1
1
0
1
1
2
0
1
1
2
0
0
2
2
1
2
1
1
1
1
2
1
1
1
1
1
1
2
1
1
2
1
1
0
0
1
0
1
1
2
1
3
0
2
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
0
0
1
1
1
0
2
2
2
1
2
1
1
1
2
0
2
2
1
1
2
1
1
1
1
1
1
2
3
1
1
2
1
1
2
1
1
2
1
1
1
1
1
1
0
1
1
1
1
2
1
2
1
1
1
1
1
0
1
1
0
2
0
2
1
1
1
1
1
1
1
1
1
1
1
2
2
0
2
1
1
1
1
2
2
1
1
0
0
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
0
1
2
0
1
1
1
1
0
2
1
0
1
1
2
1
1
1
0
1
0
1
1
2
1
1
2
1
1
1
0
1
1
2
1
1
2
1
1
1
1
0
2
0
2
0
2
1
1
1
2
1
1
1
1
1
1
1
1
0
2
1
1
1
2
0
1
1
2
1
1
1
0
0
1
2
1
2
1
0
3
1
1
1
1
1
1
1
0
0
2
1
2
2
0
2
2
1
2
1
1
1
2
1
0
1
1
3
1
1
1
1
1
1
1
1
1
2
1
0
0
1
1
0
1
1
1
1
0
0
1
1
1
2
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
3
1
1
1
1
1
2
2
1
1
1
2
1
2
1
0
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
2
0
0
1
0
2
0
1
1
1
2
1
1
0
1
1
1
1
1
1
2
1
1
1
2
2
1
2
0
2
1
1
0
2
1
1
1
1
1
1
2
1
1
1
1
0
1
0
1
1
1
1
2
1
1
0
2
0
0
1
1
1
1
1
2
1
1
0
1
1
2
0
1
0
0
0
1
0
1
1
2
0
1
1
1
0
1
1
1
2
2
0
1
1
1
1
1
2
0
1
2
1
1
1
2
2
1
1
0
1
1
2
1
1
2
1
1
1
0
1
1
1
2
2
3
0
0
1
0
1
1
1
1
2
1
0
1
1
1
0
2
3
1
1
1
0
2
1
1
1
1
0
2
1
1
1
2
1
1
1
1
0
2
2
1
1
1
1
0
1
1
0
1
1
1
1
2
2
1
1
2
0
0
1
1
1
2
2
1
2
2
0
2
1
0
2
1
2
1
1
1
0
1
2
1
1
1
1
2
1
2
1
2
2
1
1
1
1
1
0
1
1
1
1
0
0
2
1
1
0
0
2
1
2
2
2
2
1
2
2
1
0
2
0
1
1
1
2
1
1
0
2
1
1
1
1
0
1
2
2
1
1
1
1
1
1
2
1
0
0
1
1
1
2
1
1
1
1
1
1
2
0
0
2
1
2
1
3
1
1
1
1
1
1
0
1
1
2
1
1
1
1
1
1
1
2
2
0
1
2
2
1
1
1
1
0
2
1
0
0
1
1
2
2
0
2
0
1
0
0
1
1
1
1
1
2
1
1
2
0
1
1
0
1
0
1
1
1
1
1
0
2
1
0
1
2
2
2
2
1
1
1
2
1
1
2
1
1
2
1
0
1
0
0
1
2
1
2
1
2
2
1
0
2
1
0
1
1
1
1
1
1
2
1
0
2
0
2
1
2
2
2
1
1
1
1
1
1
0
1
2
1
1
2
2
0
1
1
2
1
1
0
2
1
1
2
2
2
1
2
1
0
0
1
2
2
1
1
2
0
1
1
1
2
1
1
2
1
1
0
1
2
1
1
1
0
0
1
1
2
1
1
1
1
0
2
0
2
0
1
0
2
1
1
1
2
1
1
1
2
0
2
1
1
0
1
1
2
1
0
1
1
0
2
1
1
1
1
2
1
1
1
2
2
2
0
0
0
2
0
2
1
2
1
2
1
2
1
2
1
2
1
1
1
1
1
0
0
1
1
1
2
2
1
1
2
2
1
1
0
2
1
2
2
2
0
3
2
1
1
0
1
1
0
3
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
0
1
0
1
0
0
2
2
1
1
1
1
2
1
1
2
2
1
1
2
1
1
1
1
2
1
1
1
0
2
2
2
2
1
1
1
2
2
1
0
1
1
2
1
2
2
2
1
0
1
1
0
1
2
1
1
1
1
1
1
0
1
1
1
1
2
1
1
1
0
1
1
0
1
1
1
1
0
1
1
1
1
1
1
2
0
1
1
1
1
1
0
2
2
2
1
1
1
2
2
2
1
2
1
2
1
1
1
0
1
2
1
2
3
1
1
2
2
1
2
1
2
1
0
1
1
1
1
1
0
1
0
0
2
1
2
1
0
1
0
1
1
2
1
1
0
1
0
0
2
1
1
2
1
1
2
0
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
0
1
1
1
1
0
1
1
1
1
2
1
2
2
1
2
1
0
1
1
1
2
1
1
1
1
2
2
1
0
1
2
1
1
2
2
0
2
1
2
1
1
0
0
2
1
1
1
1
1
1
3
1
1
1
1
0
1
0
2
1
2
1
0
1
0
1
2
1
1
2
0
1
1
2
1
1
0
1
1
2
2
1
2
1
1
1
2
2
1
2
1
2
1
1
1
1
2
1
0
1
2
2
1
1
0
1
2
1
1
2
1
2
1
2
1
1
2
1
0
1
2
1
2
2
0
2
1
3
2
0
1
1
2
1
2
1
1
1
2
1
2
1
1
1
2
1
0
1
1
1
2
1
1
1
0
1
0
1
1
1
1
2
0
0
0
1
1
1
1
1
2
1
0
1
1
0
0
1
1
1
1
0
0
2
2
1
1
0
2
1
0
2
0
2
1
1
2
2
1
1
1
0
1
1
1
2
0
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
0
2
2
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
1
1
0
2
0
1
0
1
1
0
1
1
0
1
1
1
2
0
2
1
1
0
0
1
1
0
1
1
1
4
1
1
0
2
2
1
1
1
1
2
2
1
0
1
1
0
1
1
1
1
1
2
1
1
2
1
1
0
1
0
1
2
1
2
1
1
1
0
1
1
1
2
2
0
1
0
2
1
1
1
0
1
1
1
0
1
2
2
2
1
1
0
1
1
2
1
1
1
2
1
1
2
1
1
1
0
2
1
1
0
1
2
2
1
1
0
1
1
1
1
1
1
0
1
1
1
2
1
2
2
0
3
1
1
0
1
2
1
0
1
1
1
1
1
1
1
1
1
1
0
2
1
1
1
2
0
1
2
1
0
2
2
2
1
2
0
1
0
0
1
2
1
1
2
0
1
1
1
1
2
1
1
1
0
1
1
1
1
0
2
1
1
1
0
1
0
1
1
1
2
2
1
1
0
2
1
2
1
1
1
2
1
2
1
1
1
1
1
1
2
0
2
1
1
0
1
0
2
0
1
1
1
0
1
1
1
2
2
3
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
0
1
0
0
2
1
0
2
1
1
0
1
2
2
0
0
2
2
1
1
1
0
1
1
1
1
1
2
2
2
1
0
1
0
2
2
0
0
1
1
1
1
2
1
2
0
1
0
1
1
1
1
0
2
1
1
2
2
1
2
2
1
1
2
1
1
0
2
1
1
2
1
1
2
1
1
2
0
1
2
2
0
2
1
1
3
1
2
1
1
1
1
1
1
1
1
1
2
1
1
0
0
1
2
2
1
1
1
1
1
1
2
1
1
2
2
2
2
0
1
1
2
1
2
1
1
1
0
0
1
1
1
1
1
1
1
1
1
3
1
1
1
1
0
2
1
1
1
2
1
2
1
1
1
2
1
1
1
2
1
2
3
1
1
2
1
1
2
0
2
1
1
4
1
1
1
2
1
1
1
1
1
1
1
0
1
0
1
1
2
1
1
1
1
2
1
1
1
1
0
1
2
0
1
1
1
2
1
1
1
1
1
1
2
2
0
1
2
0
0
1
2
2
1
2
1
1
0
1
1
1
1
1
2
1
1
1
0
1
1
0
1
2
1
2
1
0
0
1
0
1
1
1
0
1
1
1
0
1
2
0
2
2
2
0
1
1
2
1
1
2
1
1
2
1
0
2
0
1
0
1
1
2
2
1
1
2
1
1
2
0
1
0
2
1
2
0
1
1
2
2
1
1
0
1
1
2
1
2
1
0
1
1
1
1
2
2
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
2
1
1
0
2
0
0
1
1
2
1
2
0
1
1
0
1
0
2
2
2
1
2
2
1
2
0
1
1
2
1
2
1
1
1
2
2
1
3
1
2
0
1
1
0
2
2
0
1
1
2
2
1
1
2
1
1
0
0
1
1
1
1
2
1
2
1
0
1
1
1
1
1
2
2
1
1
0
1
1
2
2
2
1
1
1
0
1
1
1
1
1
1
1
1
0
2
1
1
0
2
1
1
1
0
0
1
1
1
1
2
1
1
1
2
2
1
1
2
1
1
1
0
1
2
3
1
0
2
1
0
1
2
1
1
1
1
1
1
2
2
0
1
1
1
1
1
1
1
1
1
0
1
4
1
2
1
0
2
1
1
1
1
1
2
1
2
2
1
2
2
2
0
1
1
1
2
1
2
0
2
1
1
1
2
1
1
1
1
1
1
1
1
1
0
1
1
1
1
0
2
0
2
2
1
2
1
2
0
1
1
3
1
2
2
1
1
1
1
1
1
1
3
1
1
2
1
1
2
0
1
0
1
1
1
0
0
2
2
2
2
2
1
1
1
1
1
1
0
1
1
0
1
2
1
1
1
1
2
0
0
0
1
1
1
1
1
1
2
1
0
1
1
1
0
1
3
0
1
2
1
1
1
1
1
2
2
1
1
2
1
1
1
2
1
1
0
0
0
2
1
2
1
1
0
2
1
0
1
2
1
1
2
2
1
1
2
1
0
2
1
2
0
1
0
1
1
0
1
1
1
1
2
1
1
0
1
1
3
2
1
1
2
1
1
1
1
1
2
1
1
1
2
2
0
0
1
1
1
0
0
1
1
1
2
2
1
1
2
2
1
0
1
0
1
1
1
2
1
1
1
2
2
2
2
1
1
1
2
1
0
1
1
1
1
0
2
1
1
2
1
2
1
2
1
0
1
1
1
1
2
1
1
2
2
1
0
2
2
2
1
1
1
1
1
1
1
1
1
0
1
2
1
1
2
2
1
2
0
0
1
1
1
0
0
1
1
1
2
1
1
1
1
0
2
0
1
1
2
2
1
1
0
2
2
1
2
1
0
2
1
0
1
0
1
1
2
0
1
1
1
1
2
1
2
0
1
1
2
0
0
2
2
2
0
2
2
1
1
0
2
1
1
1
0
1
1
1
1
2
2
2
2
1
1
2
1
1
1
2
1
1
2
2
2
0
2
1
1
0
2
1
1
2
1
1
2
2
1
1
1
1
0
1
1
0
3
1
1
1
1
2
1
1
0
1
2
2
1
1
1
0
1
2
1
0
2
2
2
1
1
2
1
1
1
2
1
2
1
1
1
1
1
2
1
0
2
1
1
2
2
2
0
1
1
1
2
1
1
1
1
2
0
0
1
0
0
2
1
1
1
2
0
2
2
1
1
2
2
0
1
2
1
1
2
1
1
2
2
1
2
0
2
1
1
0
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
0
2
1
0
2
1
1
2
1
1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
1
1
2
2
1
1
1
2
1
1
2
0
2
0
0
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
0
1
2
0
1
1
1
2
2
2
1
1
1
2
1
1
2
1
1
2
1
1
1
3
2
1
2
1
1
1
1
1
1
0
2
1
0
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
0
1
1
0
1
1
0
1
0
0
0
0
2
1
1
2
1
0
0
2
2
1
1
0
1
2
1
2
2
2
1
2
1
2
2
2
1
0
1
1
1
1
0
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
2
2
1
1
1
1
2
1
1
2
2
2
1
2
1
0
1
1
1
1
1
1
1
1
1
2
0
1
1
1
1
1
1
1
1
1
1
2
1
0
1
2
1
2
0
1
1
1
2
2
1
0
2
2
1
1
1
0
1
2
1
1
1
1
0
2
2
1
2
2
0
2
1
1
1
1
2
0
2
2
1
1
1
2
1
2
1
1
0
1
1
2
2
2
1
0
2
1
1
1
1
0
2
1
1
2
1
0
1
1
1
1
2
1
2
1
1
1
1
0
2
2
1
2
1
0
0
0
1
0
1
1
2
2
1
1
1
2
1
2
1
1
1
1
2
1
2
2
1
2
1
1
1
2
1
1
1
1
2
2
0
1
2
0
1
1
1
0
0
0
2
0
0
1
2
1
2
2
2
1
2
1
1
1
2
1
2
1
1
2
0
1
1
1
1
1
1
2
2
2
2
1
1
1
2
1
0
1
0
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
2
2
1
1
1
0
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
0
1
1
1
0
1
2
2
2
1
1
1
1
2
1
1
1
1
1
1
0
1
1
2
2
1
1
3
1
1
2
2
0
1
2
1
11
1
1
2
0
0
1
2
1
1
1
0
1
1
2
2
0
0
0
1
0
1
2
1
1
1
1
1
2
0
1
0
0
0
1
1
1
0
0
0
3
1
4
2
2
2
1
1
2
1
2
2
1
1
0
2
1
1
0
1
1
1
1
1
1
2
1
2
0
2
1
1
2
2
0
2
1
1
2
1
1
2
1
1
1
2
1
1
2
1
1
0
1
2
0
1
1
1
1
1
1
1
1
1
1
2
3
2
2
1
1
2
2
1
2
2
0
2
2
2
2
0
1
1
0
1
0
1
1
1
2
0
2
1
2
1
1
0
1
2
2
1
2
1
0
1
0
2
1
1
1
1
0
1
1
1
2
1
0
1
2
1
1
0
1
2
4
1
1
1
1
1
0
1
2
1
1
1
1
1
1
0
1
1
1
2
1
1
1
1
1
1
1
1
1
0
1
1
0
1
2
4
1
0
1
1
1
1
0
0
0
1
1
2
0
1
1
2
2
2
2
1
1
1
1
1
3
1
1
1
1
1
1
1
1
1
1
2
1
2
1
2
0
0
1
0
2
2
1
2
1
1
2
1
1
0
1
1
2
2
2
1
2
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
0
2
1
2
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
2
2
2
1
1
1
1
0
1
1
0
1
0
0
1
1
1
2
1
1
1
2
0
1
1
0
2
3
1
1
1
1
2
1
2
1
1
1
1
2
2
1
1
2
2
2
1
1
1
1
1
1
1
1
1
0
1
2
2
1
2
0
1
1
1
1
1
1
0
1
0
1
1
2
1
1
1
0
1
1
0
1
1
0
0
2
2
1
2
1
0
1
2
1
1
1
1
1
2
1
1
2
2
1
1
1
1
2
1
2
1
2
1
1
2
0
1
1
0
0
1
2
1
1
2
1
2
2
2
1
0
2
1
1
0
1
1
2
2
2
1
1
2
0
0
1
1
2
1
0
0
1
2
1
1
0
0
1
1
2
1
2
1
1
2
1
0
1
1
1
3
1
2
0
1
1
1
1
2
0
1
1
1
2
2
1
0
2
1
0
0
1
1
0
1
1
1
1
0
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
0
0
1
1
0
2
2
1
1
1
2
2
2
1
1
2
0
1
1
1
2
1
1
1
1
0
1
2
2
2
1
1
1
0
1
1
0
1
1
2
2
2
1
1
1
2
1
1
0
1
1
1
2
0
1
1
1
1
0
2
1
1
2
2
2
1
1
1
1
1
1
2
1
1
2
0
1
1
0
1
2
2
2
1
2
1
1
0
2
1
1
1
2
1
0
2
0
1
2
1
1
0
2
0
0
0
2
1
0
1
1
2
1
2
2
0
2
1
1
2
2
1
1
1
0
1
1
1
1
0
1
1
1
0
0
1
0
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
2
2
1
2
1
1
0
2
2
1
1
1
1
3
3
2
1
2
1
1
1
1
1
0
1
1
0
2
1
2
1
2
1
0
2
0
1
1
1
1
1
2
1
1
1
2
2
2
1
1
1
1
2
1
2
1
1
1
2
1
1
1
2
1
1
1
2
0
1
2
1
1
1
1
1
1
1
0
1
0
2
1
0
0
1
1
0
0
1
0
1
1
1
1
1
1
0
1
2
1
2
0
1
1
2
1
1
2
1
1
1
1
1
2
0
1
1
2
2
1
1
2
1
1
1
1
1
1
0
2
1
1
1
1
2
1
1
0
0
1
0
1
1
2
1
0
1
2
1
1
2
1
1
1
2
2
1
0
1
1
0
2
2
1
1
0
1
1
1
0
2
0
0
1
2
2
2
1
0
1
1
1
2
1
1
1
1
1
0
1
1
2
1
2
2
2
0
1
2
1
1
2
2
0
1
1
1
1
1
1
2
1
1
3
2
0
1
1
1
1
0
1
1
1
2
1
1
1
1
1
1
1
0
1
1
0
1
0
1
2
2
2
0
1
2
1
0
2
1
0
2
1
1
2
1
1
0
1
1
1
1
1
1
2
2
1
1
2
1
1
1
1
1
1
2
0
2
3
1
1
2
0
1
1
0
1
1
1
1
1
2
1
2
0
0
0
2
1
1
1
1
2
2
2
2
1
2
1
2
0
1
1
1
0
2
0
0
1
1
1
1
2
0
0
1
0
1
1
2
1
1
2
1
1
1
1
1
2
2
0
1
1
2
1
0
1
0
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
3
1
0
0
1
1
1
1
1
1
1
1
1
1
1
1
2
0
1
1
2
1
1
1
1
2
1
0
1
1
2
2
1
1
1
1
1
1
2
0
1
1
1
2
1
1
2
1
1
1
1
1
0
1
1
0
2
1
1
1
2
1
1
1
1
0
1
1
2
1
1
1
2
1
1
1
0
1
2
0
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
0
0
1
1
2
1
1
1
1
1
0
1
2
1
1
0
1
1
1
2
2
1
0
2
1
1
2
0
2
1
1
1
2
1
1
2
1
2
1
0
1
2
1
0
1
2
1
2
2
2
2
1
0
1
1
1
1
3
1
1
1
2
1
1
1
1
2
1
2
1
1
0
1
2
2
1
2
1
1
1
1
2
2
2
1
0
1
1
2
1
2
1
1
0
2
1
0
1
1
2
1
1
0
0
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
2
1
0
0
1
1
1
1
1
2
1
0
1
1
0
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
0
1
0
2
2
2
1
0
2
0
1
1
1
2
0
1
2
1
1
1
1
1
1
1
0
0
1
1
0
1
1
0
1
2
1
2
2
0
1
1
1
1
0
1
1
0
2
1
2
1
1
0
1
2
2
1
2
2
1
1
0
0
0
1
1
0
1
1
2
1
1
1
1
2
1
1
1
0
2
1
2
2
0
2
1
1
2
1
1
0
1
2
1
1
1
1
1
1
1
1
0
1
1
0
1
0
2
0
1
1
1
2
1
1
1
1
1
0
2
1
1
1
1
0
1
1
2
1
2
0
1
1
2
2
1
1
0
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
0
2
2
2
1
2
1
1
1
1
1
2
2
1
1
2
1
2
1
1
1
1
1
1
1
1
1
2
2
0
1
1
1
1
1
2
0
1
2
2
2
2
1
1
1
1
1
2
1
1
1
0
1
1
1
0
2
1
1
2
1
2
1
1
1
1
1
2
1
1
2
0
2
1
1
1
1
1
1
1
1
0
2
5
1
1
1
0
1
1
1
1
0
2
2
2
1
3
1
2
0
4
2
1
1
0
0
1
1
1
0
2
1
1
2
2
0
1
1
1
1
1
2
1
1
1
0
0
1
1
2
1
1
1
1
0
2
2
1
2
2
0
1
1
0
2
2
2
1
2
0
0
1
3
1
2
1
1
1
0
0
1
1
1
0
1
2
1
1
2
1
2
2
1
0
1
0
1
1
2
1
2
1
2
1
1
1
1
2
0
1
1
2
2
1
1
1
2
1
1
2
0
1
1
1
1
1
2
2
1
2
1
1
1
1
1
2
0
2
1
1
1
1
1
1
1
1
1
1
1
0
0
1
1
1
2
1
2
1
0
1
1
1
1
0
0
1
0
0
2
1
1
0
0
1
1
1
1
1
0
2
1
1
2
1
2
0
1
1
1
2
1
0
1
1
2
0
1
2
0
2
1
1
2
1
2
1
1
1
0
1
1
1
1
1
1
1
1
2
2
2
2
1
0
2
2
1
1
0
1
1
1
1
2
2
1
1
1
2
0
3
1
0
2
2
2
2
1
1
2
1
1
1
1
1
1
1
0
1
1
2
2
1
1
2
1
0
2
1
0
2
1
0
2
1
1
1
2
1
2
1
2
2
1
1
1
1
2
1
1
1
2
1
2
1
1
1
0
1
1
1
1
0
0
1
1
1
0
1
1
2
1
1
1
2
2
1
0
1
1
2
1
1
1
1
0
1
0
2
1
1
1
2
1
1
2
0
1
1
1
1
1
1
1
1
0
1
1
1
1
2
1
1
2
1
1
1
0
1
2
1
0
0
1
1
1
1
2
1
1
2
0
0
1
0
1
2
2
1
2
2
2
1
0
1
2
1
1
1
0
1
1
2
0
1
1
0
0
1
1
3
1
0
2
1
1
1
2
1
1
1
1
1
2
1
1
1
2
2
1
2
0
2
2
1
1
1
1
2
1
1
2
0
1
1
2
1
2
1
1
1
1
1
1
1
0
2
1
2
1
1
1
0
0
2
2
2
1
1
1
1
0
2
2
1
1
1
1
1
1
1
1
0
1
1
1
1
1
0
1
1
1
1
2
0
2
0
1
2
0
1
1
1
1
1
1
0
0
1
1
1
1
1
1
1
2
0
0
2
2
1
2
1
1
1
0
1
1
1
2
1
1
0
1
1
1
1
1
1
1
1
2
2
1
0
1
1
2
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
0
0
1
1
1
2
2
1
0
1
1
1
2
2
1
0
2
1
3
1
1
2
0
2
1
0
2
0
2
2
2
0
2
1
0
1
1
1
1
2
1
0
1
0
0
1
0
2
1
0
0
0
2
1
1
2
1
0
0
1
2
1
2
1
1
2
2
1
1
2
0
2
0
1
0
1
1
1
1
2
1
1
1
1
1
2
1
1
0
1
1
0
1
1
1
0
1
1
1
2
1
2
1
0
2
1
2
1
2
0
1
1
2
1
1
2
1
1
0
1
1
0
0
2
1
1
0
1
2
2
1
1
2
2
1
0
1
0
0
0
1
1
0
1
1
1
1
2
1
1
0
1
2
1
1
1
1
2
0
2
1
1
2
1
1
1
1
1
1
2
1
1
2
1
1
2
2
2
1
3
2
1
1
1
1
1
2
1
0
1
1
2
1
1
0
1
1
1
0
1
2
0
0
0
2
2
0
1
1
2
1
1
2
1
1
0
1
1
2
1
2
0
1
2
2
0
1
0
1
1
1
1
1
1
1
1
1
1
0
0
0
1
2
2
1
2
2
1
1
2
1
1
1
1
0
1
1
1
0
2
0
1
1
2
1
0
1
1
1
2
1
1
1
2
0
1
1
0
1
1
1
1
1
2
1
0
1
2
1
2
1
1
1
1
2
2
1
1
2
1
1
1
1
1
1
2
1
1
0
2
2
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
2
0
2
0
1
1
1
0
1
1
2
1
1
1
3
0
1
1
1
2
1
2
1
2
1
0
1
2
1
1
2
1
1
2
1
1
0
1
1
0
1
0
1
2
2
1
1
2
1
0
1
0
0
1
2
1
1
2
1
0
1
2
1
0
1
0
1
0
1
1
1
0
1
1
0
1
1
1
0
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
3
0
1
0
1
0
2
1
1
1
0
1
2
0
2
1
1
1
0
0
1
1
2
0
0
1
1
0
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
2
2
1
4
1
2
2
2
0
1
1
1
2
1
0
1
1
1
1
2
1
1
1
1
1
0
1
1
1
0
1
2
1
2
1
2
1
1
1
1
2
1
1
2
1
0
1
2
2
2
2
2
2
1
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
2
0
1
1
2
2
2
2
2
1
0
1
2
2
2
2
1
2
1
1
0
0
0
0
2
0
1
0
0
1
1
2
1
1
1
0
0
0
1
1
2
1
1
1
2
1
2
2
1
2
1
1
1
1
1
1
1
2
1
0
2
1
1
2
1
2
2
1
1
1
1
2
0
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
0
2
0
1
2
0
1
1
2
1
1
0
2
2
1
1
1
1
1
1
1
0
1
4
1
1
1
1
1
1
2
2
2
1
1
2
1
0
1
2
1
1
2
1
1
1
2
1
2
1
0
2
1
1
1
0
1
1
1
1
1
2
1
0
2
1
1
1
1
2
1
2
1
3
1
1
1
1
2
1
2
1
2
1
1
0
1
2
2
1
2
2
1
1
0
1
1
1
0
1
2
1
0
2
1
2
1
1
1
2
3
1
1
2
1
1
1
1
1
0
2
1
0
2
2
2
1
1
2
1
2
1
1
1
1
2
2
1
1
1
2
0
2
1
2
1
1
0
0
1
1
2
1
1
1
2
1
2
0
1
1
1
1
2
0
2
1
1
1
1
1
1
1
1
2
2
0
1
1
2
1
1
1
1
1
2
1
0
1
1
0
1
1
0
1
1
1
1
1
2
1
1
1
2
1
0
1
1
1
1
0
2
2
1
1
2
1
2
2
1
1
1
2
1
1
1
0
1
1
2
1
2
1
1
1
2
1
0
1
2
2
1
2
1
1
1
1
1
2
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
3
1
1
2
1
1
0
1
2
0
1
2
0
1
4
2
1
1
1
1
2
1
1
1
2
2
1
2
2
1
2
1
2
1
1
1
1
1
1
1
0
0
1
0
1
1
4
0
2
1
2
2
2
1
1
2
1
1
1
1
2
1
0
2
2
1
0
3
0
0
2
0
1
1
1
0
1
0
1
2
0
1
1
0
2
0
0
2
1
2
1
0
1
1
1
1
2
1
1
0
2
2
1
1
2
0
0
2
0
1
0
1
1
1
1
2
1
1
1
0
2
0
1
1
1
1
1
1
1
0
0
1
1
2
1
1
2
1
1
0
2
2
1
1
2
1
0
2
1
2
3
1
0
1
1
2
1
1
1
0
0
2
1
1
1
1
1
1
1
0
1
1
1
0
1
1
1
1
2
1
0
1
1
2
1
0
1
1
2
2
0
1
1
0
1
0
2
0
2
0
2
1
2
0
1
1
1
2
0
1
1
2
2
2
1
1
2
2
1
1
2
1
0
1
2
1
1
1
2
1
1
0
1
2
1
2
1
1
2
1
1
0
2
1
1
1
2
0
2
1
1
1
1
1
1
1
1
2
2
1
2
1
2
2
1
1
1
0
1
2
1
1
2
1
1
2
1
2
1
1
0
0
1
1
1
2
1
1
1
2
1
1
2
1
2
0
1
1
2
1
2
1
1
1
1
0
1
2
0
2
2
1
0
1
0
0
1
0
1
1
1
2
1
1
1
1
0
1
2
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
0
0
1
1
1
1
2
1
1
2
1
1
1
0
1
2
1
1
1
1
0
1
1
1
1
1
2
1
1
0
2
2
2
1
1
1
1
1
1
1
1
0
1
2
1
0
1
1
1
1
0
2
2
1
1
2
1
1
1
1
2
2
2
1
1
1
0
1
1
1
1
2
1
1
1
1
2
0
1
2
1
1
1
0
2
1
2
1
1
1
1
1
1
0
0
1
3
1
0
1
1
1
2
1
1
1
2
1
0
2
1
1
1
1
2
2
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
0
1
0
1
1
1
2
1
1
1
1
1
0
1
1
1
2
2
1
0
2
0
1
2
0
1
1
2
1
0
1
0
1
0
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
2
0
0
0
1
1
1
2
1
0
1
1
0
2
2
1
1
1
1
2
0
1
2
1
1
0
2
1
0
1
2
1
1
1
2
2
1
1
2
2
1
2
1
1
1
1
1
1
2
1
1
1
2
0
2
2
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
2
1
0
1
1
1
1
1
2
1
2
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
1
0
0
1
1
1
2
1
2
1
0
2
0
1
2
1
1
1
1
1
0
1
0
1
0
0
0
1
1
1
2
2
1
2
1
1
2
0
0
1
0
1
0
1
2
1
0
0
1
2
1
1
2
1
1
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
2
1
0
1
2
1
1
1
1
1
0
1
1
0
1
1
1
2
2
1
1
0
1
1
1
2
1
1
1
0
1
1
2
2
1
1
1
1
2
1
2
1
1
2
1
1
2
0
1
2
1
2
1
1
2
1
0
2
2
1
1
1
2
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
1
1
1
1
2
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
1
1
2
2
1
2
1
1
3
2
1
2
0
1
1
1
2
1
1
0
1
1
1
1
1
0
1
0
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
2
2
1
1
1
1
0
1
4
1
1
1
1
1
1
1
2
1
0
1
2
1
1
1
1
2
1
1
2
0
2
1
1
1
0
1
1
1
1
2
1
1
2
1
0
1
2
0
0
1
1
1
2
1
2
1
1
2
0
2
2
1
1
1
1
0
0
1
1
2
1
2
0
1
2
1
4
1
1
1
1
1
1
1
1
2
2
0
1
1
1
1
2
1
2
0
1
1
1
2
2
2
1
0
2
1
1
1
1
1
1
0
2
1
2
1
1
1
1
1
0
0
1
1
1
1
1
2
0
1
0
1
2
1
1
1
1
2
1
1
2
1
1
1
2
2
2
1
1
1
1
2
1
2
2
1
1
1
1
2
1
1
2
0
2
2
1
1
1
1
1
1
1
1
0
1
0
1
3
1
1
2
2
1
2
1
1
2
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
0
1
1
0
1
2
1
2
1
1
1
1
0
2
1
1
1
2
1
1
1
1
0
2
1
2
0
1
2
1
2
1
1
2
1
1
1
1
2
1
2
2
1
2
2
1
1
1
1
1
1
1
1
2
1
1
1
1
2
2
2
1
1
2
1
1
1
1
2
1
1
1
1
0
1
2
1
1
1
1
1
0
1
0
1
2
1
1
1
1
2
1
0
2
2
2
2
1
0
1
1
0
1
2
1
1
1
2
1
0
0
1
1
1
1
1
2
1
1
2
1
0
2
2
1
1
2
1
1
1
1
1
0
1
1
2
1
2
0
3
1
1
1
1
1
0
1
1
1
2
2
1
2
2
1
0
0
2
2
1
1
2
1
1
1
0
0
1
2
0
0
1
1
1
1
2
2
1
1
1
2
2
1
0
0
1
3
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
2
1
1
1
2
1
2
1
2
0
1
1
0
1
2
1
1
0
1
1
1
1
1
2
1
1
0
1
1
2
3
2
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
2
1
1
1
2
1
1
1
1
1
3
2
1
1
1
0
0
1
0
2
1
1
1
2
2
0
1
1
0
1
1
0
1
1
2
1
2
2
1
2
1
2
1
1
1
1
1
1
2
1
1
2
1
1
1
0
2
2
2
2
1
2
1
1
1
1
1
1
1
0
1
0
1
1
1
2
1
0
1
1
2
2
1
1
2
0
1
0
1
0
0
1
1
1
1
2
0
1
2
1
1
1
1
1
0
1
0
1
1
1
2
0
2
1
1
1
2
2
2
2
2
0
0
1
1
2
1
1
1
0
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
0
1
2
2
0
0
1
1
2
0
1
1
1
0
1
1
1
1
1
1
0
1
1
1
0
1
1
1
1
1
1
0
1
2
1
1
1
1
1
2
1
1
2
1
2
1
1
1
1
0
1
1
1
1
1
2
1
1
0
1
1
2
1
1
1
1
0
2
1
2
1
1
0
2
2
0
1
2
0
0
1
0
1
2
0
2
1
1
1
1
1
2
1
1
1
0
1
1
2
1
1
1
1
0
1
1
2
2
2
2
1
4
0
1
2
1
0
1
1
1
1
1
2
1
1
0
2
1
0
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
0
1
0
1
1
1
2
1
2
1
1
3
1
1
1
1
0
1
0
1
1
1
2
1
1
0
1
1
1
1
1
2
2
2
0
0
1
0
2
1
1
2
1
1
1
0
1
1
1
1
1
1
1
1
2
1
1
1
1
2
2
2
0
1
1
1
1
1
1
2
1
2
2
1
0
1
0
1
1
1
1
2
2
2
1
1
0
1
1
0
1
2
1
2
1
3
2
2
0
1
1
1
2
1
1
1
1
0
0
1
0
2
1
1
2
2
0
2
1
2
2
1
0
1
2
1
0
1
2
2
1
1
2
1
1
1
0
0
1
1
1
1
0
0
1
0
1
2
1
2
1
2
1
1
2
1
1
2
0
1
1
1
3
1
1
2
1
0
1
1
2
0
0
1
2
1
2
1
1
1
0
1
1
1
1
1
1
1
1
2
1
2
0
0
1
1
2
2
1
0
2
2
2
2
1
1
1
0
2
1
0
1
0
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
2
1
0
2
1
4
2
1
1
2
2
1
0
1
1
2
2
1
1
0
1
2
1
1
1
1
2
1
2
2
1
1
1
0
1
1
1
1
1
1
1
1
0
1
0
1
2
1
2
0
1
2
2
1
1
0
2
1
0
1
0
0
0
1
1
1
0
1
2
1
0
1
1
2
0
1
2
1
1
1
1
2
1
1
1
2
1
1
1
2
2
2
1
1
1
1
0
0
1
1
1
1
2
1
1
1
1
3
1
2
1
1
2
2
1
1
0
1
1
1
1
2
1
1
0
1
1
1
1
0
0
1
1
1
1
1
1
2
1
1
2
0
1
2
1
1
1
2
1
2
1
1
1
0
2
1
2
1
2
1
0
2
2
1
1
2
0
1
2
1
1
2
1
1
1
0
0
2
0
1
2
1
1
1
2
2
2
1
3
1
0
1
1
1
1
0
1
0
1
1
1
0
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
0
0
2
1
1
1
2
0
2
0
1
2
1
2
1
1
2
1
0
1
1
2
2
1
1
1
1
2
0
2
1
0
1
1
1
0
1
0
1
2
2
0
1
0
1
1
2
1
1
1
1
0
1
2
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
1
2
1
2
1
2
0
1
1
1
1
2
1
1
1
1
1
2
2
2
0
0
2
1
1
2
0
1
2
1
1
1
2
1
0
1
1
2
1
0
0
0
1
2
0
1
0
1
1
1
1
2
1
1
2
1
1
1
1
1
2
2
1
1
1
2
2
0
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
2
1
1
2
6
2
1
0
2
2
1
2
1
1
1
1
1
1
1
1
1
2
2
1
1
1
0
1
1
1
1
1
2
1
1
1
1
1
1
0
0
0
2
1
3
2
1
1
1
1
1
3
1
1
1
1
1
2
1
1
1
1
0
1
1
2
1
2
2
1
2
1
0
1
1
1
1
1
2
2
2
1
1
1
2
0
1
2
1
1
2
1
1
2
1
1
1
1
0
1
1
1
1
2
2
0
2
0
2
2
1
1
1
1
1
1
1
1
1
2
2
2
2
1
0
1
0
1
2
2
1
2
1
1
1
1
2
1
1
1
0
1
2
1
1
1
2
2
2
2
2
1
1
1
1
1
2
1
1
1
1
1
2
1
2
1
2
1
2
0
1
0
1
0
2
2
1
1
1
2
0
1
1
1
0
2
1
1
1
1
1
2
2
2
2
2
1
1
1
1
2
1
1
0
0
1
1
2
1
1
1
2
1
3
1
1
0
0
1
2
2
4
2
1
2
1
1
1
1
1
2
1
1
1
1
2
2
2
3
2
2
2
0
2
2
1
1
1
1
2
2
2
1
1
0
1
1
2
2
1
1
1
1
2
1
1
1
1
0
2
1
2
2
0
2
1
1
0
1
1
2
1
0
1
0
1
1
2
2
2
0
2
2
1
2
1
1
2
1
2
1
1
1
1
1
2
1
0
1
1
2
1
1
0
1
1
1
1
1
1
0
1
2
1
2
0
0
1
1
1
1
0
1
1
1
0
1
1
1
1
1
1
1
2
1
1
1
1
1
0
1
1
1
1
0
1
1
1
2
0
0
1
0
2
0
1
1
2
0
2
1
1
2
1
1
2
1
0
1
1
1
2
2
1
0
1
1
0
2
2
1
2
1
1
2
1
1
1
1
0
1
0
2
0
0
1
0
1
0
1
0
2
1
1
2
0
1
2
1
0
1
1
1
1
1
1
1
1
2
2
2
2
0
1
2
1
2
2
1
1
1
1
1
1
1
1
0
1
1
2
0
1
1
1
2
1
0
1
1
1
2
1
2
0
0
1
1
2
1
2
2
1
2
1
0
0
1
2
1
1
1
1
2
2
1
1
1
3
2
0
1
1
1
1
2
2
2
1
1
1
1
1
1
2
2
1
1
2
2
0
1
0
1
1
2
1
1
0
0
0
1
1
2
1
1
1
1
2
2
1
2
0
1
1
0
1
1
2
1
1
1
1
1
1
1
0
1
0
2
2
1
2
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
2
1
2
2
2
1
1
1
1
2
1
1
2
2
1
1
0
1
1
2
1
0
1
1
2
1
1
1
1
0
1
1
1
1
1
1
1
0
1
1
1
1
1
2
0
0
2
1
0
2
1
2
2
1
1
1
1
0
0
2
3
2
1
1
2
1
1
2
1
0
1
2
1
0
2
2
1
1
1
1
1
1
1
0
1
1
2
1
1
1
1
1
2
1
2
1
2
2
1
2
1
1
1
2
2
0
2
0
0
1
2
2
1
2
1
2
1
2
1
1
1
1
1
1
1
1
2
1
2
1
2
1
1
2
1
1
0
1
1
1
0
2
1
1
0
1
1
2
0
1
2
1
1
0
1
1
2
1
2
1
1
2
0
1
1
1
1
2
1
0
1
1
1
1
7
1
2
1
1
0
2
1
1
1
2
2
1
0
2
2
0
1
1
2
2
2
1
2
1
1
2
1
2
1
1
1
1
4
2
1
1
2
1
1
0
1
1
1
1
1
1
2
2
0
0
2
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
1
0
2
2
1
1
1
1
1
1
2
0
0
1
2
2
1
1
1
2
1
2
0
0
1
1
2
1
2
0
1
1
0
2
2
2
1
1
2
2
2
1
1
1
1
2
3
0
3
1
0
2
0
2
1
1
0
0
1
1
0
1
1
1
1
1
1
1
2
0
0
1
2
1
1
0
1
1
1
1
3
2
2
2
2
1
0
1
1
3
2
2
2
2
1
1
1
2
2
1
1
2
2
2
1
0
2
1
1
1
1
1
1
1
1
0
1
0
2
1
0
1
1
1
1
1
0
1
2
0
1
2
0
1
2
0
0
1
2
1
1
1
1
1
1
2
1
1
2
1
1
1
2
1
2
1
1
0
1
1
1
0
1
1
1
0
1
1
1
1
1
2
1
1
1
1
1
2
0
1
0
1
1
0
2
0
1
2
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
0
1
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
2
1
2
1
1
0
0
2
2
2
0
2
1
0
0
1
1
1
2
1
1
1
1
1
2
2
1
1
1
0
1
2
1
0
2
1
1
1
0
2
0
2
2
3
1
0
1
1
0
1
1
2
0
1
1
1
1
0
0
1
1
1
2
1
1
2
2
2
2
0
1
1
1
1
1
1
1
0
1
1
2
1
1
2
2
1
1
2
2
1
1
2
2
1
0
1
1
1
1
1
1
0
0
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
2
0
2
0
0
0
2
1
0
2
0
1
2
1
1
0
0
0
2
1
1
1
2
2
1
1
1
1
1
0
2
2
1
1
2
1
1
1
1
2
2
2
1
1
1
2
1
1
0
2
0
2
2
1
2
1
1
1
1
2
0
1
2
1
1
0
0
1
1
2
0
1
1
1
2
1
0
1
2
0
1
1
1
1
2
1
3
1
2
2
1
1
1
1
1
0
1
0
2
1
0
1
0
1
1
1
2
1
2
2
0
1
0
1
1
1
2
1
1
2
1
1
1
1
1
0
0
2
2
2
2
1
1
1
1
1
1
0
1
2
1
0
1
1
1
1
2
1
2
1
1
1
2
1
1
2
0
1
1
0
1
1
1
1
2
1
1
1
1
1
2
2
1
1
2
2
2
1
2
1
2
2
1
1
0
2
1
1
1
1
1
0
1
1
1
1
1
1
0
3
1
2
2
1
1
2
1
2
0
0
0
2
1
1
1
1
1
1
0
0
1
2
1
0
0
1
1
1
0
2
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
2
1
1
0
0
2
0
1
0
1
1
3
1
1
1
0
1
0
1
1
2
0
2
1
2
2
2
1
0
1
1
1
2
1
1
1
1
1
1
2
0
2
1
1
1
1
0
2
1
1
1
1
1
1
0
1
0
1
2
1
1
1
0
2
1
0
1
1
1
0
0
1
1
1
2
1
2
2
1
2
1
0
2
1
1
1
1
1
2
1
1
0
2
1
2
1
2
2
1
1
1
1
0
1
1
1
1
1
2
1
1
0
2
0
1
1
1
0
1
1
1
2
1
1
0
2
0
1
1
1
1
0
2
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
2
1
1
0
1
1
3
1
2
1
1
1
1
0
1
2
1
1
1
1
0
1
1
2
2
0
2
1
1
0
1
1
1
0
0
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
2
0
1
2
1
1
2
1
1
1
2
0
0
2
1
0
2
1
1
1
1
2
2
0
1
1
1
0
1
2
1
0
1
1
1
1
1
1
2
1
1
2
2
1
1
1
1
2
1
1
1
2
1
1
1
0
1
1
2
1
1
1
1
1
1
1
1
1
0
2
2
1
1
1
1
2
1
1
2
1
1
0
0
2
1
2
2
1
0
2
2
0
1
1
1
2
1
2
0
2
2
0
1
1
1
2
1
1
0
1
1
1
2
2
1
1
2
0
1
1
2
1
1
0
1
0
1
1
2
1
1
2
1
2
2
0
2
1
1
1
1
1
0
1
2
1
2
2
0
2
0
1
2
1
2
2
1
1
2
1
0
1
0
1
0
2
2
1
2
1
1
2
1
2
1
2
1
1
1
2
0
1
0
1
0
1
1
1
1
1
0
1
2
0
2
1
2
2
2
1
2
0
2
1
2
2
1
1
0
1
1
0
0
1
1
1
1
0
2
1
0
0
2
1
1
1
1
1
1
1
1
1
2
2
2
1
1
0
1
1
1
1
1
1
0
0
1
2
0
2
2
1
1
0
1
0
1
1
1
1
1
2
0
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
1
0
2
1
1
2
0
1
1
1
1
1
1
2
1
1
2
1
1
2
1
0
0
2
1
1
1
1
1
1
0
1
2
2
1
1
1
1
4
2
1
1
2
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
0
0
1
1
1
1
2
0
0
1
2
0
0
1
1
1
1
2
0
2
1
1
2
1
0
1
1
0
1
1
1
0
0
2
1
1
2
1
2
3
1
1
2
2
1
2
1
1
2
1
1
1
2
1
1
1
1
1
2
0
1
2
1
1
2
1
1
0
2
2
1
1
1
0
2
2
0
1
2
0
1
2
2
1
0
1
1
1
2
2
0
1
0
1
1
0
0
0
0
0
2
1
0
1
1
1
1
2
2
1
1
0
0
1
0
1
0
2
1
1
1
2
2
2
1
1
0
0
2
1
1
1
1
1
1
1
0
1
1
3
1
1
2
1
0
0
1
2
1
1
1
1
2
1
1
1
1
1
2
2
2
1
1
2
1
1
1
1
2
1
2
0
1
0
0
1
0
1
2
1
1
1
0
1
1
2
0
0
1
2
1
0
2
1
2
1
0
1
1
0
1
2
1
0
1
1
2
1
1
2
1
1
1
2
1
1
1
1
1
2
0
1
1
0
1
2
1
1
0
0
0
0
2
1
1
1
2
1
0
1
1
1
1
2
1
1
2
2
2
2
1
0
1
2
2
1
2
2
1
1
2
1
2
2
0
1
2
1
2
2
2
1
2
0
1
2
0
1
1
1
1
3
1
0
1
2
2
0
1
1
2
1
0
1
0
1
1
1
1
1
0
1
1
0
1
1
2
1
1
1
1
1
1
2
1
1
2
1
1
2
1
2
2
2
1
1
1
1
1
1
2
2
1
2
1
1
0
1
1
2
2
1
1
1
0
1
1
1
2
0
1
2
0
1
1
1
2
2
0
1
2
1
1
0
1
1
1
2
5
1
2
2
1
0
0
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
0
2
1
2
2
1
0
1
2
1
1
1
1
1
2
2
1
0
1
1
1
0
2
1
1
1
2
2
1
2
0
1
1
1
1
1
1
1
1
2
2
1
1
2
1
2
1
1
0
2
2
1
2
1
1
1
1
0
1
2
2
1
1
0
1
1
1
2
1
1
0
1
2
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
0
1
1
0
1
1
1
2
2
1
1
1
1
0
1
2
1
1
0
0
1
1
1
1
1
1
1
1
0
1
1
2
2
1
1
2
2
2
0
1
1
1
1
1
1
2
1
1
2
1
2
2
0
1
2
1
1
1
1
1
1
0
1
1
2
1
2
2
1
2
2
1
2
1
1
2
2
1
0
1
1
2
1
1
1
1
1
0
0
2
2
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
1
1
1
2
2
1
0
1
2
1
1
1
0
2
0
0
1
1
2
1
1
1
1
3
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
2
2
1
2
2
1
2
1
2
1
0
1
1
1
0
1
1
0
2
0
1
1
1
0
1
1
1
1
2
1
1
1
0
2
1
0
1
1
0
2
1
2
1
1
1
1
2
2
0
1
1
1
0
1
1
2
2
1
2
1
1
2
1
1
2
1
1
1
1
1
0
2
1
1
1
1
1
0
1
1
1
2
1
2
1
2
2
1
1
2
2
1
1
1
1
1
2
2
1
1
1
0
1
1
2
1
2
2
0
1
2
1
2
2
0
1
1
0
1
2
2
0
2
2
1
1
1
1
1
0
1
1
1
1
1
2
0
2
0
1
1
2
1
1
1
2
1
2
1
2
0
1
1
1
1
0
1
2
1
1
1
2
1
2
0
1
2
0
1
0
0
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
2
0
0
1
2
1
1
0
1
1
1
2
1
1
1
1
2
1
1
2
1
2
1
2
2
1
2
1
3
1
0
1
1
2
1
1
1
0
0
1
1
1
1
0
1
0
2
2
1
1
1
0
2
2
2
2
2
1
2
2
1
1
0
1
0
1
1
1
1
1
0
1
1
2
1
1
1
0
1
1
1
2
1
1
1
1
2
2
2
1
1
2
0
0
1
0
1
1
1
1
2
2
1
2
1
1
2
1
1
2
1
1
0
0
1
0
4
1
2
1
1
1
1
2
0
1
1
2
2
1
2
1
2
1
2
1
1
0
1
1
1
1
1
1
1
1
0
2
0
1
1
0
0
1
1
2
2
1
1
1
2
1
2
1
2
1
1
1
0
1
1
2
1
1
2
1
1
0
1
0
2
2
0
1
0
0
1
0
2
2
2
1
0
1
1
1
0
2
0
1
3
1
1
1
1
0
0
0
1
1
1
1
1
1
1
1
2
1
0
1
1
0
1
3
0
1
1
1
1
1
1
2
1
2
1
2
1
1
2
1
1
1
1
2
1
1
1
1
0
0
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
2
2
1
1
1
2
1
1
0
2
0
1
1
1
2
1
1
2
1
1
2
1
2
1
1
2
1
1
1
2
0
1
1
2
1
1
2
1
1
2
1
2
2
1
1
2
2
1
1
0
2
0
0
1
2
2
1
2
1
1
2
1
0
1
0
1
1
0
3
1
1
1
2
0
1
1
1
2
1
0
1
2
0
1
2
1
0
2
0
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
2
0
1
1
1
2
2
0
1
1
1
2
0
0
2
2
1
1
1
2
1
0
1
2
1
1
1
1
2
2
1
1
0
1
2
1
11
1
1
1
0
1
1
2
0
0
1
2
2
1
1
2
1
1
1
2
1
2
1
1
2
1
2
1
1
2
1
2
0
1
1
2
1
1
2
2
1
1
1
2
1
1
0
0
1
0
2
1
0
2
1
0
1
1
1
2
1
1
2
2
0
1
2
2
1
1
1
1
1
1
1
1
0
1
1
2
0
2
1
2
1
2
0
0
0
1
2
1
2
1
1
1
1
1
2
1
1
1
1
1
0
5
1
1
2
0
1
1
1
1
1
1
1
1
2
2
1
1
0
0
2
0
0
1
0
1
1
1
1
1
2
0
0
1
2
1
0
1
2
1
1
1
0
1
1
2
1
1
1
2
2
1
1
1
0
1
1
0
1
2
1
2
1
2
1
1
1
1
2
1
0
0
1
1
1
1
1
1
0
1
1
2
0
2
0
2
1
0
2
1
1
0
2
1
0
1
1
1
1
1
2
2
1
2
1
1
0
1
1
0
0
1
2
1
1
1
1
1
1
0
1
1
0
1
1
1
0
1
1
1
1
1
0
2
2
1
2
2
1
0
0
2
1
1
0
1
1
1
2
1
1
2
1
2
2
2
2
1
2
1
2
1
2
0
2
1
1
1
0
1
1
1
1
1
1
0
0
2
0
2
2
1
2
1
2
1
0
0
1
1
1
1
2
1
1
2
1
1
1
1
1
0
1
0
1
2
1
1
1
2
1
0
1
1
2
1
0
2
1
1
1
1
1
1
2
2
0
1
2
1
1
2
2
1
1
0
2
1
1
0
1
2
1
1
1
1
2
1
2
1
1
1
0
1
1
0
1
1
1
1
1
1
1
0
0
1
1
1
1
1
1
1
1
0
1
2
2
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
2
1
1
0
1
1
1
2
2
1
1
1
1
0
1
1
1
1
2
1
1
1
2
1
2
1
1
0
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
2
2
2
0
1
1
0
1
0
2
1
2
3
1
1
1
1
2
2
2
1
0
1
1
1
1
2
1
2
2
1
1
1
1
1
2
1
1
0
2
2
2
0
2
1
1
1
1
2
1
1
1
2
1
1
1
0
2
0
1
1
1
1
1
2
2
2
1
1
1
1
1
0
0
0
0
1
1
1
1
1
0
1
1
1
2
2
1
2
1
1
1
1
1
2
1
0
1
1
1
0
1
1
0
1
2
1
0
2
2
1
1
0
2
0
2
1
1
1
0
1
1
0
1
1
0
1
0
1
1
2
2
0
1
1
1
1
1
1
1
0
2
2
0
1
1
1
1
1
1
2
2
0
1
1
2
1
0
1
1
1
1
1
1
1
2
1
2
1
0
1
1
1
1
2
0
1
1
1
1
1
1
0
1
1
0
1
1
1
1
1
2
2
1
2
1
1
2
1
1
2
0
1
1
1
0
1
0
1
1
1
2
1
1
1
1
0
1
1
1
0
3
1
1
1
2
0
2
2
1
2
1
0
1
1
2
1
1
1
1
0
2
1
1
1
1
1
1
2
2
2
0
1
1
1
1
1
1
2
1
1
2
1
1
0
1
1
1
1
1
1
0
1
1
1
1
0
1
2
1
1
2
1
1
1
1
2
1
2
1
1
1
0
1
2
1
1
1
1
1
1
1
1
2
1
1
0
2
1
1
1
2
1
1
1
1
1
2
1
1
0
0
2
1
1
2
2
1
1
2
1
1
1
1
0
1
1
0
1
1
1
0
2
2
1
2
1
2
2
2
1
2
1
2
2
1
1
1
0
1
2
0
1
0
0
0
1
2
1
1
0
1
2
1
0
1
1
1
2
1
1
2
1
1
0
1
1
1
1
2
1
2
0
0
2
1
1
1
1
1
1
2
2
2
1
2
2
1
2
1
1
0
1
1
1
2
2
1
0
1
2
1
1
1
1
0
1
2
0
1
0
0
2
1
2
1
1
1
2
1
0
1
1
1
0
2
1
1
1
2
2
1
1
1
0
0
2
0
2
1
1
1
1
1
1
2
1
1
1
1
0
1
1
1
1
2
1
2
1
1
1
2
1
1
1
0
0
1
1
1
2
1
0
0
1
1
0
2
1
1
1
0
2
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
2
2
7
1
2
1
2
0
0
1
2
1
1
1
0
1
1
2
1
1
1
1
1
1
1
0
1
2
0
1
0
1
1
1
2
1
2
2
1
1
0
0
1
1
2
1
1
1
1
0
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
0
2
2
1
1
1
1
1
1
2
1
0
0
1
1
0
1
2
1
2
0
2
2
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
1
1
2
0
0
1
1
3
1
1
1
1
2
1
0
1
2
0
1
1
1
0
2
1
1
1
1
1
1
2
1
0
2
0
1
1
2
1
2
1
1
1
0
0
1
1
2
1
2
2
2
1
1
1
2
1
1
0
1
3
1
2
0
2
1
0
0
1
1
2
1
1
1
2
1
1
1
0
2
1
1
3
2
0
1
2
1
0
1
0
1
1
0
2
1
1
2
0
0
1
2
1
2
1
1
2
1
1
0
1
2
1
0
1
1
2
1
1
0
0
0
1
1
0
0
1
2
2
2
1
0
2
1
0
2
0
1
1
1
1
2
2
1
1
1
1
1
2
1
1
0
1
0
1
2
2
2
0
0
2
0
1
1
0
0
1
0
0
1
1
1
1
1
1
0
1
1
1
0
2
0
1
0
2
1
1
1
2
1
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
0
2
1
2
1
1
1
0
1
0
2
1
1
1
1
1
2
1
0
2
1
1
1
1
2
1
1
1
1
2
1
1
1
1
0
1
1
2
1
1
1
1
1
1
2
0
1
1
1
1
0
1
0
0
2
1
1
1
1
0
0
0
1
2
2
1
1
1
2
0
1
1
1
1
1
1
1
0
2
2
1
1
1
0
1
1
0
2
1
2
1
2
1
2
1
1
0
1
1
0
1
2
2
1
1
1
1
1
1
1
1
2
1
1
1
1
0
0
1
1
1
1
1
1
1
1
1
1
0
1
2
2
2
1
1
1
0
1
1
2
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
2
2
1
0
1
1
2
1
1
2
2
1
1
0
2
0
1
2
2
2
0
1
1
1
0
1
2
0
0
1
1
1
1
1
2
2
2
0
1
2
1
2
1
1
0
1
2
1
2
1
2
0
1
1
1
0
1
1
1
2
1
0
2
0
1
0
1
1
2
1
2
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
2
1
1
0
1
1
1
1
2
1
1
1
2
1
1
0
1
1
2
1
1
2
1
1
2
1
1
1
2
0
1
1
3
0
2
2
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
1
0
0
1
1
1
0
1
1
0
2
0
1
1
1
1
0
1
1
1
2
1
1
0
1
2
2
2
1
1
2
2
0
1
1
1
0
1
0
0
2
0
1
1
2
2
1
2
1
0
1
1
1
1
1
2
1
1
1
1
1
1
0
1
1
1
2
0
1
2
1
2
1
0
1
0
0
1
1
2
2
2
1
1
1
1
1
1
0
0
1
0
2
1
1
1
1
1
0
0
1
2
1
0
1
1
0
0
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
0
1
1
1
2
1
0
1
1
1
1
1
1
1
1
1
1
1
2
1
1
0
2
1
1
1
0
1
0
0
1
1
1
2
1
2
0
1
1
0
0
1
1
1
0
0
2
1
1
1
0
1
1
1
1
2
2
2
1
1
1
1
2
1
0
2
1
1
0
1
2
1
1
1
1
2
1
2
2
1
2
2
1
1
2
1
2
1
1
0
2
1
0
1
0
2
0
1
0
1
2
1
1
2
2
1
1
0
1
0
2
1
1
1
1
1
2
1
2
1
2
1
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
0
0
1
1
0
1
1
1
1
1
1
1
1
1
1
1
2
1
0
1
0
1
1
2
1
2
1
1
1
0
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
0
1
1
0
2
1
1
1
0
1
1
1
1
1
1
1
0
0
1
0
1
1
2
1
0
0
1
1
1
1
0
0
1
4
1
0
2
0
1
1
1
2
0
2
1
0
1
0
0
2
0
2
1
2
1
1
1
1
1
1
2
0
1
2
2
1
2
2
0
1
2
1
0
1
1
1
1
1
0
1
1
1
1
2
0
1
1
1
1
0
1
1
1
1
2
2
0
1
2
1
1
1
1
1
1
2
1
0
1
0
1
1
1
1
1
0
1
1
1
1
0
1
1
1
0
2
1
1
1
3
0
1
0
1
1
1
2
0
1
2
1
1
1
0
1
2
1
0
2
0
2
1
2
2
1
1
1
1
2
2
1
0
0
1
2
2
1
2
2
1
1
1
2
1
2
2
2
1
2
1
0
1
2
1
2
2
0
1
1
3
2
1
2
0
1
1
1
1
1
1
1
1
1
2
1
1
0
1
1
1
1
2
2
1
2
1
2
2
1
0
1
1
2
1
1
1
1
1
2
1
1
2
1
1
2
2
1
1
2
2
2
2
1
3
2
1
1
1
2
1
1
0
1
1
0
1
1
1
1
1
1
0
1
2
1
2
2
0
1
1
0
2
2
1
2
2
1
1
0
1
2
1
1
2
1
2
1
2
1
0
1
1
1
1
1
1
1
1
1
0
1
1
2
1
1
1
2
1
2
1
0
1
2
1
1
0
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
2
1
1
2
1
1
2
1
0
0
1
1
1
0
2
1
1
2
1
0
1
0
2
2
1
1
0
1
2
1
1
1
0
1
1
0
1
1
1
0
1
2
2
1
1
2
1
1
1
1
2
1
2
1
2
1
1
0
1
1
2
0
1
2
1
2
1
1
0
0
1
2
0
1
2
1
2
0
2
2
0
0
1
1
1
1
1
1
1
2
0
1
1
2
1
2
2
1
2
1
2
2
2
0
2
1
2
1
1
0
2
1
1
1
2
1
2
1
1
1
0
1
1
2
1
1
1
2
1
0
1
1
0
1
0
0
1
0
1
1
2
1
0
0
1
1
1
1
0
2
2
1
1
1
2
2
1
1
1
2
1
2
1
1
2
1
2
2
1
1
1
0
0
1
1
2
1
1
0
2
1
1
0
0
1
2
1
1
1
2
0
0
2
1
0
1
2
2
0
1
1
1
1
1
2
1
2
0
1
1
1
1
2
0
2
1
1
0
1
0
1
1
1
0
1
2
1
2
0
1
1
1
2
2
2
1
1
0
0
1
0
1
2
2
1
0
1
1
1
0
1
1
0
1
0
2
2
1
1
1
1
1
1
0
2
0
2
1
2
1
1
1
2
1
1
2
2
0
2
2
1
2
1
1
0
1
1
1
1
1
1
2
1
2
1
1
1
1
1
2
2
0
1
1
1
0
1
1
1
2
1
2
2
0
1
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
2
2
1
2
0
1
1
2
2
0
2
2
1
1
1
1
0
1
1
1
2
2
1
2
2
0
0
2
0
1
0
1
0
0
2
1
1
0
0
0
0
0
2
1
2
2
2
1
0
1
1
1
1
1
1
1
1
1
2
1
2
0
1
2
1
1
2
2
1
0
1
0
1
0
1
1
1
2
1
2
1
3
2
2
1
1
1
1
1
1
1
1
2
1
1
1
0
1
1
0
0
1
1
1
0
2
2
1
2
1
2
1
2
2
2
2
1
2
2
2
0
1
1
1
2
0
2
1
1
1
1
1
1
1
1
1
2
1
2
0
1
2
2
1
2
1
2
2
2
1
1
3
1
1
2
2
1
1
1
1
1
1
2
2
1
2
1
1
0
2
2
3
1
1
2
1
1
2
1
1
1
1
1
2
1
1
1
2
2
2
1
2
2
1
1
1
1
1
0
2
0
2
2
2
0
1
1
2
1
0
2
1
1
2
1
0
2
1
0
1
2
0
1
1
2
1
2
2
2
1
1
2
1
1
1
0
0
1
1
1
2
1
1
1
1
0
0
1
1
0
2
1
1
2
2
1
2
0
0
1
2
1
1
1
0
1
1
1
2
2
1
2
0
2
1
1
1
2
1
1
2
2
2
1
1
2
1
2
1
1
1
0
1
1
1
1
2
1
2
2
2
2
1
0
0
0
1
1
2
2
2
1
0
2
1
1
1
1
1
2
1
1
2
0
1
1
1
1
1
1
2
1
1
2
1
1
0
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
0
2
1
0
1
2
2
2
1
1
1
1
1
0
2
1
1
1
1
1
1
1
1
2
2
1
1
0
1
2
1
2
2
1
1
1
1
0
1
1
1
1
0
1
1
1
2
1
1
2
2
1
0
1
1
0
1
1
2
1
0
2
1
2
0
0
1
0
1
2
0
1
1
2
0
1
1
2
2
1
2
1
0
1
1
1
1
1
0
2
1
0
1
1
1
2
0
0
2
1
2
1
1
1
1
1
1
2
1
1
2
1
1
1
2
1
1
2
1
1
1
2
2
0
1
2
1
1
1
0
1
0
1
2
1
1
1
1
1
1
1
1
2
1
1
0
1
0
1
0
2
1
2
1
1
1
2
1
1
2
1
1
2
1
2
1
1
0
2
1
1
2
0
2
0
1
1
1
2
1
2
2
1
0
1
1
2
1
1
1
1
2
1
1
2
1
2
0
1
1
1
1
2
2
1
1
0
1
2
1
1
2
1
2
1
2
1
1
1
1
1
1
1
1
0
2
1
0
1
1
2
2
2
1
1
1
1
2
2
1
2
2
1
2
0
1
1
1
1
1
2
1
1
1
2
2
1
1
2
1
2
1
2
0
2
1
2
0
2
1
1
1
1
1
2
1
2
2
2
1
2
1
1
1
2
1
1
2
0
1
1
1
1
0
2
1
1
1
0
1
1
0
1
1
1
1
2
0
3
1
1
1
1
1
1
2
1
2
1
2
2
1
2
2
1
1
0
1
0
1
1
1
1
1
1
1
1
1
1
2
2
2
0
1
1
1
1
0
1
1
2
1
2
1
1
1
1
1
0
2
1
0
0
0
1
2
1
1
1
0
1
1
1
2
1
1
0
1
2
2
2
1
2
1
1
2
2
1
1
1
2
1
1
1
0
1
1
1
1
1
2
1
1
1
1
1
1
2
1
0
1
1
1
0
2
2
1
0
1
2
2
2
1
1
0
1
1
1
1
2
1
1
2
2
1
1
1
1
0
1
1
1
1
0
1
1
0
1
0
0
1
0
1
2
1
1
1
0
0
0
2
2
2
2
1
2
1
0
1
2
1
1
2
1
0
2
1
1
2
1
2
1
2
0
1
2
2
2
2
0
1
0
0
1
1
1
1
0
2
3
1
1
1
1
1
0
1
1
2
2
1
0
2
1
1
1
2
1
2
1
0
1
1
0
1
0
1
1
2
2
1
2
1
1
2
2
1
1
1
1
1
1
2
1
2
2
1
2
2
1
1
2
0
1
2
1
1
1
2
1
1
2
1
1
1
1
1
2
1
1
0
1
1
1
1
0
1
2
2
1
2
1
1
1
1
2
0
1
1
0
1
1
0
3
1
0
2
2
0
2
2
1
1
2
1
0
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
2
1
2
2
1
1
1
1
0
2
2
2
0
1
1
0
0
1
0
1
2
1
0
1
0
1
2
1
1
1
1
1
1
1
1
0
1
1
1
1
0
1
1
1
1
1
1
0
0
1
2
1
1
0
2
1
1
0
0
1
1
1
1
1
1
1
1
1
0
2
1
2
1
2
1
2
1
1
1
0
1
1
1
1
1
1
2
1
2
1
1
2
1
2
1
2
1
0
1
2
1
1
1
1
1
1
0
1
1
2
2
2
1
2
1
1
2
1
1
1
2
1
2
1
2
1
1
0
0
2
0
2
1
2
2
0
1
1
1
2
1
1
0
1
0
1
1
0
0
1
0
1
2
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
2
2
1
1
1
0
2
0
1
0
3
2
2
1
0
2
1
0
2
1
0
1
1
1
2
1
2
1
2
1
1
1
0
2
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
1
1
2
2
1
1
0
1
1
1
1
0
1
1
2
1
1
1
1
0
0
1
1
1
0
1
1
3
1
1
1
1
1
1
1
2
1
1
0
0
1
2
1
0
2
1
0
1
1
1
2
2
1
1
1
1
1
1
1
2
0
2
1
1
1
1
2
1
2
1
1
2
1
1
1
1
1
2
2
1
1
1
0
2
2
2
1
2
2
0
0
1
1
2
2
2
1
1
1
0
1
0
1
1
0
0
1
1
1
1
1
2
1
2
2
1
1
1
1
0
2
1
0
1
2
1
1
1
0
1
1
1
0
1
1
2
1
1
1
2
1
0
2
1
1
1
1
2
2
1
2
1
2
2
1
2
1
2
2
3
2
1
2
1
0
0
1
1
1
0
0
1
2
2
0
0
2
1
1
1
2
1
1
1
1
1
0
0
1
2
2
1
2
1
1
1
2
1
1
1
2
2
1
2
1
2
1
1
1
2
2
2
1
1
0
2
0
2
1
1
1
0
1
1
0
1
0
0
1
2
2
1
1
1
1
2
1
1
1
2
1
2
2
1
2
1
1
1
1
2
0
1
1
2
2
2
1
1
1
0
1
1
2
2
2
1
1
2
0
1
1
1
1
2
1
1
3
1
1
1
1
0
2
1
3
2
2
1
0
2
1
2
1
0
1
1
1
1
2
1
2
2
2
1
1
0
2
1
0
1
1
1
1
1
1
1
2
0
1
1
2
1
1
1
2
1
2
1
1
1
1
1
2
1
2
2
1
0
1
0
4
2
0
1
2
1
2
2
0
1
1
1
3
1
0
2
1
1
2
1
1
2
1
1
0
2
1
1
1
1
1
1
0
1
2
1
1
2
2
0
1
1
1
0
1
2
1
2
0
1
2
2
1
2
0
1
1
1
2
1
2
1
1
1
2
2
1
1
1
2
1
1
2
1
1
2
1
1
2
1
1
1
2
1
1
1
1
1
0
1
1
1
1
0
1
2
1
2
2
2
2
1
2
2
1
0
1
1
1
2
1
1
1
1
0
1
1
0
2
1
1
1
2
1
2
0
2
1
1
1
1
2
2
1
2
2
1
2
1
1
2
1
1
1
1
1
2
2
1
0
1
1
1
1
0
0
0
1
1
1
1
0
2
1
1
2
1
1
2
1
2
0
1
1
0
0
1
1
1
2
1
1
1
1
1
1
0
2
1
1
1
2
1
1
1
1
1
2
1
1
2
1
1
1
0
1
2
2
1
1
0
2
1
2
1
0
2
0
1
2
1
2
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
0
1
2
1
1
2
1
1
2
1
1
1
1
0
1
2
2
2
2
2
2
1
1
2
2
2
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
0
2
2
1
1
0
2
2
2
1
2
0
1
1
0
0
1
2
1
2
1
1
1
1
2
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
3
1
1
1
1
0
1
2
1
1
2
2
1
2
1
1
1
2
0
1
0
0
1
1
1
1
0
2
2
2
2
2
1
2
1
1
2
1
1
1
2
2
2
2
1
1
1
1
0
1
1
1
2
1
2
2
1
1
1
1
2
2
1
2
2
2
1
1
1
2
1
1
0
2
2
1
2
1
2
1
1
1
2
2
1
1
2
1
2
2
1
1
1
2
0
1
2
2
1
0
1
2
1
1
1
1
1
1
2
1
1
2
1
0
2
2
1
1
1
1
1
1
0
2
1
0
2
1
1
1
2
1
1
1
0
1
0
1
1
1
0
1
1
1
2
2
1
2
1
1
1
1
1
1
2
1
0
1
2
0
1
0
1
1
2
1
2
0
2
1
2
0
1
1
1
1
2
1
0
1
2
2
1
1
2
1
0
1
1
0
2
1
1
1
1
2
1
1
1
0
0
1
1
2
1
2
1
1
2
2
0
1
0
2
2
1
1
1
1
1
1
1
1
1
1
1
0
1
2
1
2
0
2
1
1
2
1
1
2
0
1
1
2
1
0
2
1
2
1
0
2
0
0
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
2
2
2
1
0
1
1
2
2
1
4
0
1
1
1
1
1
1
1
1
2
0
3
1
2
2
1
2
1
1
0
2
1
1
0
1
2
1
1
1
2
0
2
2
0
2
1
1
1
1
2
2
0
1
2
2
1
0
1
1
1
2
1
1
2
2
1
2
1
1
1
0
1
2
2
1
1
1
2
0
1
1
1
1
1
1
0
1
1
1
1
2
1
1
1
1
1
1
2
0
1
1
2
2
2
1
1
0
2
1
2
1
2
1
1
1
1
1
1
2
1
1
0
1
2
1
2
2
1
1
0
2
1
1
1
5
1
1
1
0
2
2
2
1
1
2
1
1
1
1
1
1
1
1
2
0
2
1
0
2
1
1
0
1
2
2
2
1
2
2
1
0
1
0
1
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
1
2
0
2
2
2
1
1
1
1
0
0
1
1
1
1
1
2
1
2
1
1
1
3
1
1
2
1
0
1
1
1
0
1
1
0
3
1
3
2
1
2
2
0
2
1
2
1
2
2
1
1
2
0
1
2
1
2
2
1
1
1
0
0
1
2
2
1
1
1
2
1
0
2
1
2
2
1
2
2
1
1
1
2
2
0
2
2
1
1
2
0
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
0
1
1
1
1
1
2
1
2
2
2
0
1
1
2
2
1
1
2
1
1
1
1
0
1
1
1
0
1
0
2
2
2
2
1
2
1
2
2
1
1
1
1
1
0
0
1
2
2
2
2
1
1
2
1
1
2
1
1
1
1
1
2
1
1
2
1
1
0
1
1
1
1
1
2
1
2
2
1
2
1
1
1
1
1
2
2
2
1
2
2
0
1
0
1
1
2
1
2
1
1
1
2
2
0
1
1
1
0
1
2
2
2
1
1
0
2
1
1
2
2
2
2
1
1
2
0
0
1
1
1
0
1
1
1
1
1
0
1
1
1
2
1
1
1
1
2
2
0
0
1
1
1
1
1
1
2
1
1
1
1
1
1
1
0
2
2
2
1
1
1
2
1
2
1
1
1
2
1
1
0
1
1
0
1
1
1
2
1
0
1
1
2
0
2
2
2
1
2
1
1
1
2
1
1
2
1
0
1
2
2
1
1
0
3
2
1
0
2
2
1
1
1
1
1
1
1
1
0
1
0
1
2
1
1
1
1
2
1
0
1
1
2
1
0
1
2
1
1
2
1
1
1
1
1
0
1
0
0
2
0
1
1
1
1
0
2
1
0
1
2
1
2
1
2
0
1
1
1
2
2
1
0
1
1
1
0
2
1
1
2
2
1
1
1
1
0
0
1
1
1
2
1
1
1
2
1
1
1
1
0
2
1
1
0
2
1
2
2
1
1
1
1
2
1
0
1
2
2
1
1
2
0
2
2
1
1
2
0
0
1
1
2
1
1
1
2
0
1
1
0
1
0
1
1
0
1
1
1
2
2
1
2
1
0
1
2
2
0
1
1
2
0
0
2
2
1
2
1
1
2
1
0
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
0
2
2
1
0
1
2
2
2
2
2
1
1
1
1
1
1
2
1
2
1
2
1
1
2
1
0
2
2
1
3
0
1
1
1
2
1
0
0
0
1
1
1
1
2
0
2
1
1
2
1
2
3
1
1
1
2
1
2
1
1
0
1
2
1
1
0
2
1
1
1
2
1
1
1
2
0
1
2
0
2
1
1
1
1
1
1
2
0
1
0
1
1
2
2
1
1
1
2
0
2
2
2
1
1
2
1
1
1
2
2
1
2
2
1
1
2
2
0
1
1
0
0
0
2
1
1
0
1
1
0
1
1
0
1
1
2
1
2
0
1
2
2
1
2
2
2
1
1
2
2
1
0
1
2
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
2
0
0
1
0
2
2
1
1
1
1
1
1
1
0
1
2
2
1
0
1
0
1
0
1
0
1
1
1
0
1
1
2
2
0
1
2
0
2
2
2
1
0
1
1
1
1
0
0
1
1
1
2
0
0
1
1
0
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
0
2
1
0
1
1
1
2
2
1
2
2
1
1
2
0
0
1
2
1
1
1
1
1
1
1
1
1
3
1
1
2
0
2
2
2
1
2
1
1
2
1
1
0
1
2
1
1
1
1
2
1
2
2
2
2
2
0
1
2
1
1
2
1
1
1
2
0
1
1
0
1
1
2
1
1
2
1
2
2
0
1
1
1
1
0
2
1
1
1
0
1
1
1
1
2
1
1
1
0
2
1
1
2
2
2
2
1
1
1
2
1
1
0
0
1
0
2
2
0
0
2
1
1
1
1
2
2
0
2
1
1
1
0
0
1
1
1
1
1
2
2
1
2
1
1
1
2
1
2
0
0
1
2
1
1
0
2
1
2
2
1
0
2
2
1
0
1
2
1
1
1
2
1
1
2
2
1
1
1
0
1
1
0
2
2
2
1
2
2
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
2
1
1
0
0
1
0
0
1
1
1
1
1
1
1
1
0
1
2
2
1
1
1
1
1
1
1
0
2
1
1
1
2
2
0
1
1
1
1
2
1
0
1
1
1
1
2
2
1
1
1
1
2
1
1
0
1
1
1
1
1
1
0
1
2
1
1
1
1
1
1
1
1
2
1
1
0
1
1
2
1
0
1
1
1
1
1
1
2
1
0
2
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
2
1
1
1
1
1
1
1
0
1
0
1
1
0
2
1
1
2
1
0
1
1
2
1
0
1
0
1
1
2
2
1
0
0
1
2
2
1
0
1
1
2
2
1
1
0
1
1
1
2
0
1
1
1
1
1
1
0
2
2
2
1
2
2
1
2
1
0
0
0
1
1
0
2
1
1
1
1
1
1
2
3
1
1
1
1
2
2
0
2
1
2
0
2
0
0
2
1
2
2
1
1
2
1
1
2
1
1
2
1
1
0
2
1
1
1
1
0
0
2
1
0
1
2
1
1
1
1
2
2
1
1
2
1
1
2
1
1
2
0
0
1
1
1
2
1
1
1
0
1
1
1
1
0
3
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
1
2
1
0
0
0
0
1
1
2
1
0
1
1
1
2
2
0
1
1
1
1
1
2
1
0
1
1
1
1
1
1
0
2
2
2
2
2
1
2
0
0
0
1
1
1
2
1
0
1
0
1
2
0
2
0
1
1
1
1
1
0
0
1
0
2
1
1
2
1
1
1
2
0
1
1
2
2
1
1
2
0
8
1
1
1
2
1
2
0
0
1
1
1
1
1
0
1
2
2
1
1
2
2
2
0
2
2
2
2
1
0
0
1
1
2
1
1
2
0
2
2
1
0
2
1
1
1
1
2
1
0
2
1
1
1
2
2
1
2
1
1
1
2
0
1
2
1
0
1
1
1
0
1
1
0
1
2
1
1
1
1
1
1
1
2
2
2
1
1
0
2
2
0
1
1
2
2
0
2
1
1
0
1
1
0
1
2
2
2
2
1
2
1
2
1
2
1
0
2
1
0
1
1
1
0
2
2
2
1
1
1
1
0
0
1
2
2
1
2
1
0
2
0
0
1
1
1
1
0
2
2
1
2
1
1
0
0
1
1
1
1
1
0
1
1
1
2
2
0
2
1
2
1
1
2
1
1
1
1
1
5
1
1
1
1
0
2
1
1
1
1
1
2
2
0
1
1
0
0
2
1
1
2
2
0
1
0
1
0
2
1
1
2
1
1
0
0
2
0
2
1
2
0
1
1
1
0
1
1
0
1
0
1
0
1
1
1
2
2
1
0
0
1
2
1
1
2
1
0
0
1
2
1
0
0
2
2
1
2
1
2
1
0
1
1
1
1
1
1
1
0
0
1
1
2
0
0
2
0
0
0
2
1
1
0
0
2
2
1
1
1
1
0
2
1
1
2
0
1
1
1
1
1
1
2
2
1
2
1
0
1
1
0
1
2
2
0
1
0
1
2
1
0
1
1
1
1
1
2
0
1
1
1
1
1
1
0
2
1
1
1
1
2
2
1
2
1
2
1
2
2
1
1
1
1
1
1
2
1
2
1
2
1
1
2
2
2
1
1
1
0
1
1
0
2
1
0
1
0
1
0
1
2
1
1
0
1
2
2
1
1
1
1
1
1
2
2
1
0
0
2
0
1
1
1
1
1
1
2
1
2
1
2
1
1
2
1
0
1
1
1
0
1
0
1
1
0
1
1
3
0
1
0
1
0
1
1
1
2
2
1
1
3
0
0
1
1
2
0
2
1
1
1
0
1
0
1
1
1
1
2
2
1
2
1
2
1
1
1
2
1
0
2
1
1
2
1
2
0
1
1
2
1
2
0
0
1
1
1
0
1
1
2
1
1
1
2
1
1
2
1
1
4
0
1
2
1
1
2
0
1
1
2
1
2
1
1
1
2
2
2
2
2
1
1
2
1
1
1
0
0
2
1
1
2
0
2
1
1
2
1
1
1
1
1
1
1
1
0
1
1
2
1
1
1
1
0
1
4
1
1
1
1
2
2
2
1
2
2
5
1
0
1
1
1
1
2
1
0
0
1
1
2
1
1
2
1
1
0
0
0
1
1
0
0
2
1
2
1
1
1
1
2
1
1
1
0
1
1
1
0
2
2
1
2
2
1
1
2
0
2
1
0
2
1
2
1
1
1
1
2
1
2
0
1
2
1
1
0
1
1
1
0
2
2
1
1
2
1
2
1
1
2
2
1
3
2
1
2
2
1
2
0
1
1
1
2
1
1
1
1
1
2
2
1
2
2
1
1
1
1
1
1
1
2
1
3
0
2
1
2
0
1
1
1
1
2
0
1
1
1
2
1
1
1
0
1
0
1
0
1
1
2
2
1
1
1
1
1
1
2
1
2
2
1
1
1
2
0
2
1
0
1
0
2
2
1
1
2
1
1
1
2
0
1
2
1
1
1
1
1
1
1
1
2
1
3
2
1
0
1
1
2
0
1
0
2
1
3
1
2
2
2
1
0
1
2
1
2
1
1
1
2
0
1
2
1
2
1
1
1
1
1
1
1
1
1
0
1
1
2
2
1
1
1
2
0
0
0
2
0
0
0
1
1
1
1
6
1
2
1
1
1
1
1
0
2
1
1
2
0
2
1
1
2
1
1
1
1
0
2
1
1
1
1
2
1
2
1
2
2
2
2
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
2
1
1
2
1
2
2
1
1
1
1
1
1
0
2
0
3
1
1
0
0
1
1
2
1
2
1
2
1
1
0
2
1
1
2
0
1
0
1
1
1
0
1
1
1
1
1
0
1
1
2
2
2
2
1
2
1
1
1
2
1
0
1
0
1
2
1
1
1
1
1
1
1
1
1
2
2
1
2
1
1
2
1
1
2
2
1
1
1
2
1
1
0
1
0
2
1
1
2
2
0
0
1
1
0
1
1
1
1
1
2
1
2
1
1
1
0
1
1
2
1
1
1
0
1
1
1
1
1
1
0
0
0
1
2
0
1
1
2
3
2
1
0
1
2
2
1
1
1
1
0
1
2
1
1
1
1
1
2
0
2
1
2
2
2
1
1
2
2
0
2
2
1
1
2
1
0
1
1
1
2
1
0
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
1
0
1
1
1
2
2
0
2
1
1
1
1
2
1
2
1
2
2
1
1
1
0
2
1
1
0
1
1
0
1
1
1
2
2
0
0
2
1
2
2
1
1
1
1
0
2
0
2
2
1
1
1
2
2
1
1
0
2
0
1
1
2
0
1
1
1
1
1
1
2
0
2
1
1
1
1
1
2
1
1
1
2
1
2
2
1
5
1
1
1
1
2
1
2
1
3
1
1
1
2
1
2
0
1
2
1
1
2
0
1
2
1
2
0
1
1
1
2
1
1
1
1
1
0
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
0
2
1
2
1
1
2
2
1
1
1
1
1
0
2
2
1
2
1
1
0
1
1
0
0
0
1
0
2
2
2
1
2
1
1
2
1
1
2
1
3
1
0
1
1
2
1
2
1
2
1
1
1
1
1
1
0
2
1
1
1
1
0
1
1
2
2
1
2
0
0
2
1
1
1
1
1
1
1
1
0
1
0
1
0
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
0
1
1
1
1
1
2
0
0
2
2
1
1
1
0
1
2
1
2
1
1
1
1
1
2
1
1
3
1
1
1
1
1
0
1
2
1
1
2
2
1
1
0
0
2
1
2
1
1
2
0
1
2
1
1
1
0
0
1
3
1
1
2
1
1
0
2
1
1
2
1
1
1
0
0
1
1
1
2
2
1
1
1
1
1
0
2
1
2
1
1
2
1
2
1
1
2
1
1
2
0
0
2
1
1
2
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
0
1
1
2
1
1
1
1
2
1
1
1
1
2
1
0
1
1
2
1
1
1
1
1
1
0
1
2
0
1
1
1
1
1
1
1
1
2
1
0
1
2
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
2
0
1
1
0
1
1
1
1
1
2
1
0
1
1
1
2
1
2
1
1
1
2
2
0
2
1
2
1
1
1
1
1
0
1
1
1
1
1
1
1
2
1
1
1
1
0
0
2
1
3
1
1
0
1
2
1
2
1
1
1
1
1
1
2
2
1
2
1
2
0
1
1
1
2
1
1
2
2
1
1
1
1
1
2
2
2
2
1
2
2
1
1
2
0
1
1
1
2
2
1
0
1
1
0
1
2
1
4
1
1
1
1
2
0
1
2
1
1
1
1
2
2
1
1
1
1
1
2
0
2
1
1
1
1
2
0
1
1
1
1
2
2
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
2
1
2
1
0
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
2
0
1
1
1
1
1
1
1
1
1
1
2
1
0
1
1
2
1
2
0
2
1
1
0
3
0
1
2
1
1
2
1
0
1
2
1
1
1
1
2
1
1
1
1
1
0
2
1
1
1
0
1
2
1
1
2
0
1
1
1
1
1
1
1
2
2
0
2
0
1
1
2
1
2
1
1
1
0
1
1
1
0
0
1
1
2
2
2
2
1
1
1
2
2
1
1
1
2
1
1
1
1
2
2
1
2
1
2
1
1
1
2
2
1
1
1
1
1
2
1
2
1
1
1
2
2
1
1
1
2
1
1
2
1
2
1
1
2
0
0
1
1
1
1
1
2
1
1
1
2
2
1
1
2
1
2
1
1
1
1
1
1
0
1
2
0
1
1
0
0
1
0
0
1
0
2
0
1
1
3
1
1
1
2
1
1
2
2
2
1
2
1
2
1
1
2
1
1
0
2
1
0
1
2
1
1
2
1
1
2
1
0
1
2
1
1
1
1
1
2
1
0
1
0
2
1
3
2
1
1
1
2
1
0
1
0
0
1
1
1
1
1
0
2
1
1
2
1
1
0
1
1
1
1
1
2
1
1
3
1
1
2
1
1
1
2
1
1
0
0
1
2
2
2
1
1
2
1
0
1
1
1
2
2
0
1
1
1
1
1
2
1
2
1
2
1
1
2
2
1
1
1
1
1
0
1
1
0
1
1
2
2
0
1
1
1
0
2
1
0
1
2
1
0
1
2
1
1
1
2
2
1
1
2
1
1
0
1
0
2
1
1
1
1
1
2
1
1
1
1
0
2
1
1
1
2
1
0
1
1
0
1
1
1
1
2
1
0
2
1
2
0
0
1
0
0
1
2
0
2
1
4
2
1
1
2
1
0
0
1
0
1
1
1
1
3
2
1
0
2
1
2
1
0
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
1
1
0
2
2
10
1
2
1
2
1
2
1
1
1
2
1
2
1
2
0
2
1
1
1
2
1
1
2
2
2
0
1
1
2
1
0
1
1
2
0
1
1
1
0
1
0
2
1
1
2
0
0
1
1
1
2
0
1
1
1
1
1
1
1
2
2
2
1
1
1
0
1
1
0
1
1
2
1
0
2
1
2
0
1
2
2
1
2
1
1
1
2
0
2
0
1
2
1
0
1
1
1
1
1
0
1
1
1
1
2
2
0
1
2
1
2
2
1
0
0
2
0
1
1
1
1
2
2
0
1
0
1
2
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
2
1
2
0
1
1
1
1
1
1
1
1
0
2
0
1
0
0
1
1
1
1
1
2
0
1
2
1
1
2
1
1
1
0
1
1
1
1
1
2
1
1
2
1
2
1
2
2
1
1
0
1
1
1
1
1
2
1
1
0
1
1
2
1
1
0
2
1
1
1
1
1
0
1
1
2
2
1
1
0
1
1
1
2
1
1
1
1
1
1
2
2
2
1
2
2
1
1
1
1
1
1
2
2
1
1
2
1
1
2
1
2
1
1
0
1
1
1
1
2
1
1
1
1
0
1
1
1
1
1
1
0
1
2
2
2
0
1
1
2
1
1
2
1
1
2
1
1
1
0
1
2
1
2
2
2
1
0
2
2
1
1
0
2
1
2
1
1
2
2
1
1
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
0
1
1
1
1
2
1
1
2
1
1
1
1
2
1
1
1
2
1
1
2
2
2
1
1
0
2
0
1
1
2
1
1
0
0
0
1
0
1
1
1
1
2
0
1
0
2
1
1
2
1
1
1
1
1
2
2
1
1
2
2
1
0
1
2
1
1
1
1
1
1
2
2
0
1
1
2
3
2
2
1
1
1
1
1
1
2
1
1
1
0
3
0
1
1
2
1
1
2
1
1
1
1
2
1
2
1
2
1
2
1
2
2
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
0
0
2
2
1
2
1
2
2
2
0
0
2
2
2
2
1
1
2
2
1
1
1
1
0
0
2
1
1
1
1
1
1
1
2
0
1
0
2
2
1
1
1
0
1
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
2
1
1
0
1
2
1
0
1
0
2
0
1
2
0
0
1
2
1
1
1
1
0
1
1
1
1
1
2
0
2
1
1
2
0
1
1
1
1
1
1
1
1
2
1
2
1
0
1
1
1
1
1
1
2
1
2
1
0
2
1
1
1
1
0
2
0
0
1
1
1
1
1
1
1
1
0
1
0
1
0
1
1
1
0
1
1
1
1
1
1
0
1
1
0
1
1
1
1
1
1
1
1
1
2
1
0
1
0
0
2
1
1
2
2
0
1
2
2
0
2
2
1
1
1
1
0
1
1
1
1
1
1
0
1
0
1
2
1
2
0
2
0
1
2
1
1
1
1
0
1
2
1
0
2
1
1
1
0
1
1
1
1
1
2
0
1
2
2
1
1
1
1
1
2
2
1
2
1
0
2
1
1
2
1
1
1
1
0
1
1
2
0
1
1
2
2
2
1
1
0
1
1
1
0
1
0
1
2
0
1
1
1
2
1
1
2
1
2
2
1
2
2
2
1
1
0
1
2
1
0
2
2
1
1
1
1
0
1
1
2
2
0
1
1
1
1
1
2
1
2
2
1
1
1
1
2
1
1
2
2
2
1
1
1
0
1
1
2
0
2
1
1
2
1
2
1
1
0
2
2
0
1
1
2
2
1
2
0
1
1
1
1
1
2
3
1
1
1
1
2
1
2
2
1
1
1
0
1
1
2
1
1
1
2
1
0
0
1
1
2
1
1
2
2
1
2
2
2
2
2
1
1
1
1
0
1
1
0
0
0
1
2
1
2
2
1
1
2
1
1
2
1
0
2
1
1
1
1
1
0
2
1
1
1
0
1
2
1
2
1
0
0
1
1
2
1
2
1
1
1
2
1
1
1
2
2
1
0
1
1
1
1
0
0
0
1
1
0
1
2
2
2
1
1
0
1
1
1
1
1
2
0
0
1
0
1
2
1
0
0
1
2
2
3
0
2
1
1
2
1
2
1
1
2
1
1
1
2
1
1
1
1
1
1
0
1
1
0
2
1
1
0
1
0
1
0
1
1
1
1
1
2
1
2
2
2
2
1
0
1
2
1
2
1
1
2
2
1
1
1
1
2
1
1
2
2
1
1
1
5
0
1
0
1
1
1
1
2
1
2
1
2
1
1
2
2
2
2
1
2
2
0
1
2
1
1
1
1
1
2
1
1
1
0
1
0
2
1
1
1
1
1
1
0
1
1
1
1
1
1
1
0
1
0
0
1
1
2
2
1
2
1
0
1
1
0
3
1
1
2
1
2
1
2
1
0
1
1
0
1
2
1
2
1
1
2
1
2
0
1
1
2
1
1
2
0
1
1
1
2
2
1
2
2
2
2
1
1
2
1
1
1
1
1
1
2
1
1
2
2
0
1
1
1
1
1
1
1
2
0
1
1
2
1
1
2
1
1
1
1
1
1
1
1
0
2
2
0
1
1
2
1
1
1
1
1
2
1
1
1
1
1
0
1
1
1
1
0
1
2
0
1
1
1
0
1
1
1
1
2
1
0
0
1
0
2
2
2
2
1
2
1
1
1
2
2
1
1
2
0
1
1
0
1
2
2
2
1
2
2
1
1
2
1
0
1
2
1
1
1
0
1
0
0
2
1
0
1
1
0
0
1
0
1
1
1
2
0
1
1
1
1
1
1
2
2
1
2
0
1
1
2
2
1
1
0
1
1
1
1
1
2
1
1
2
1
0
1
1
1
2
1
2
2
1
1
2
2
1
2
2
1
2
2
1
2
1
1
1
1
1
2
2
0
1
0
2
1
1
2
2
1
2
1
1
1
2
1
0
1
0
0
0
2
1
2
1
0
2
2
1
2
1
2
1
2
1
1
1
1
1
1
1
0
1
1
2
1
1
1
1
1
1
2
1
0
3
2
1
1
1
2
0
1
2
2
0
1
1
1
0
1
2
1
0
1
1
2
0
1
1
3
1
0
1
1
1
0
1
1
2
1
2
0
2
0
1
1
0
1
1
1
2
1
1
1
2
1
1
0
0
0
1
2
3
2
0
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
0
1
1
2
1
1
1
2
2
1
2
1
2
3
0
0
0
1
1
1
1
2
1
2
1
1
1
1
1
2
1
0
1
2
1
1
1
1
1
2
1
1
2
1
0
1
1
1
1
2
1
2
1
2
2
0
2
0
1
1
0
0
1
1
1
0
1
1
1
0
1
1
1
0
1
1
1
1
1
1
2
0
2
1
1
0
1
1
1
2
2
2
0
1
2
1
0
1
2
1
1
1
1
0
0
2
0
2
1
1
2
1
1
1
2
1
0
1
1
1
1
1
0
1
2
1
2
0
0
1
1
2
1
0
1
2
0
1
1
0
1
2
1
1
2
2
2
1
2
1
1
1
1
2
2
1
1
1
0
1
1
1
2
2
1
1
2
0
1
1
1
0
0
1
1
2
2
1
2
1
2
1
1
1
1
1
0
2
2
1
1
1
0
1
1
1
0
1
1
0
1
1
2
2
1
2
1
1
1
2
1
1
1
2
2
1
1
2
2
1
2
1
2
1
1
1
0
1
1
1
1
1
1
0
0
0
1
1
1
4
1
0
2
1
1
0
1
1
1
1
1
1
1
1
1
1
1
2
0
2
1
0
1
1
2
1
1
1
2
1
1
1
0
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
0
2
1
1
1
2
1
1
1
1
1
1
1
1
0
1
1
0
1
0
2
1
1
1
1
0
1
0
1
1
0
2
1
1
1
1
1
2
1
0
1
2
2
0
0
1
1
0
1
2
1
1
1
2
1
2
2
0
1
0
0
1
1
1
0
1
0
1
1
1
1
1
1
1
0
0
2
1
2
1
1
1
1
1
0
2
0
2
0
2
1
0
1
1
2
1
1
0
0
1
1
1
1
1
1
1
1
1
1
1
0
2
1
2
2
0
1
1
1
0
1
1
1
2
1
1
1
0
1
1
1
1
0
1
1
1
0
1
1
1
1
0
2
1
0
1
2
1
1
1
1
1
1
1
1
1
2
2
0
1
1
2
2
1
1
2
1
1
1
2
1
2
1
1
1
1
1
0
0
2
1
1
1
1
0
1
2
2
2
1
1
1
0
0
2
1
1
0
2
2
2
2
2
2
2
2
1
1
1
1
1
1
0
1
0
1
1
1
1
1
0
1
1
1
1
1
2
1
1
2
1
2
0
2
1
1
0
1
1
0
1
2
2
1
1
1
1
2
2
1
1
1
1
2
1
2
1
0
1
2
0
1
2
1
1
2
1
2
1
1
1
2
2
1
2
2
0
1
0
1
1
1
0
0
2
1
2
1
1
2
1
1
0
0
1
2
1
1
2
2
1
1
1
1
0
2
1
2
0
1
1
1
0
0
1
1
1
3
2
1
1
0
2
0
2
0
1
2
2
2
1
1
1
1
1
1
1
1
2
2
1
1
1
0
1
1
3
1
1
1
1
3
0
1
2
2
1
0
2
1
2
1
0
2
2
2
1
1
1
0
1
0
2
1
1
1
1
1
1
0
1
2
1
1
2
1
1
2
1
1
2
1
1
2
1
1
1
2
2
2
2
1
0
1
1
1
1
1
2
2
1
2
1
1
1
0
1
2
1
1
1
1
1
1
2
0
2
0
1
0
2
1
1
0
1
1
1
1
2
0
1
1
1
2
1
2
1
2
1
1
2
0
1
1
1
1
0
1
0
1
1
0
2
2
0
1
1
1
1
1
1
0
1
0
0
2
0
2
1
2
1
1
2
1
1
0
2
0
1
0
2
1
2
1
2
1
0
1
1
1
1
2
2
2
1
1
1
2
1
1
2
1
2
2
1
1
2
2
1
2
1
1
1
1
1
2
1
1
1
0
1
0
3
0
2
1
1
1
0
1
2
1
1
1
1
2
1
1
1
1
2
2
1
0
1
0
1
1
1
1
1
0
2
2
2
1
2
1
1
0
2
1
1
2
2
0
1
0
1
1
1
0
1
1
1
2
0
1
1
0
0
1
3
2
2
2
1
1
1
0
2
2
1
2
1
2
1
1
0
1
2
2
2
2
1
2
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
2
2
1
0
1
1
0
2
1
1
1
1
1
1
1
1
1
2
1
1
1
0
1
1
2
0
3
0
0
1
0
1
1
1
0
0
1
1
1
1
1
1
0
0
1
0
1
2
2
1
1
1
1
2
1
0
2
1
1
2
0
0
1
1
0
1
2
0
1
1
1
1
1
0
2
1
2
2
1
1
2
1
1
1
1
1
1
1
2
2
1
2
0
2
1
1
1
1
1
0
1
1
0
1
2
1
2
1
1
1
1
1
1
1
1
1
1
2
0
1
0
1
0
0
1
0
1
1
1
0
2
2
1
0
2
0
1
1
2
0
0
1
1
1
2
2
2
1
1
2
1
2
2
1
1
0
1
1
1
2
1
1
1
1
2
2
1
1
1
1
1
1
2
1
0
1
2
2
2
1
1
2
1
1
1
2
2
0
1
2
1
1
3
2
1
2
1
1
2
1
0
1
1
1
1
1
1
2
1
1
1
1
0
0
1
2
1
1
1
2
2
2
1
1
1
0
2
0
2
2
1
1
1
2
1
1
1
1
2
1
3
1
2
2
2
1
1
2
0
2
1
1
0
1
1
0
2
2
1
1
1
2
1
1
1
1
1
0
2
1
1
0
1
1
2
2
1
1
0
1
1
2
1
1
1
2
2
0
0
4
1
1
1
0
0
1
0
1
0
1
0
2
2
1
2
1
1
1
1
1
0
1
1
0
1
1
1
0
1
2
1
1
2
2
2
1
1
1
1
0
1
1
1
2
1
0
1
1
1
1
1
0
1
1
1
1
1
1
1
0
0
1
2
1
1
1
1
1
1
1
1
1
1
1
2
2
0
1
1
2
1
2
1
1
0
1
1
1
2
1
1
1
1
1
1
2
1
2
1
2
2
1
1
0
0
1
0
1
1
1
1
2
2
0
2
1
2
0
1
1
2
2
1
0
1
2
2
1
2
1
1
2
0
1
1
0
1
1
2
1
1
0
2
2
1
1
1
2
2
1
0
0
0
2
1
1
1
1
1
1
1
0
1
1
2
1
1
1
2
2
0
2
1
0
1
1
2
0
2
1
1
1
2
1
0
1
1
1
2
2
2
2
1
1
1
1
1
1
2
2
2
0
1
1
1
1
1
1
2
1
0
1
1
1
1
2
2
0
1
2
2
1
0
1
1
0
1
1
3
1
1
1
1
1
0
1
2
1
1
2
1
0
1
0
2
2
0
0
3
1
1
2
0
0
1
0
2
1
1
1
1
1
2
1
1
1
1
0
1
0
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
2
1
1
2
2
2
1
2
1
1
2
2
0
1
1
1
1
1
1
0
2
2
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
0
1
2
2
2
0
1
1
2
1
1
2
1
1
1
1
0
1
1
2
1
0
0
1
0
0
0
2
1
1
2
1
1
1
2
1
2
2
1
2
1
1
1
1
0
1
1
0
2
1
2
0
1
2
1
2
2
2
2
1
1
1
1
1
1
0
2
1
2
1
0
1
2
1
1
1
1
1
1
2
2
1
2
2
0
1
0
1
1
2
1
2
2
0
0
1
2
1
1
2
1
2
2
2
2
2
2
1
2
2
1
1
1
1
0
1
0
1
1
1
1
1
0
2
1
1
0
0
2
1
1
0
1
1
1
1
1
1
1
1
2
1
1
1
2
0
1
2
1
2
1
2
1
2
0
1
2
1
1
1
1
1
1
1
1
1
2
1
2
0
1
2
0
1
2
0
2
1
1
1
1
0
1
1
1
0
2
1
1
1
2
1
1
0
1
2
1
1
1
0
1
0
1
1
1
1
2
1
2
0
2
0
1
2
1
1
1
1
2
1
1
2
2
1
0
1
1
1
1
0
1
1
2
1
1
1
1
1
1
1
1
4
2
2
2
1
1
2
2
0
2
1
1
1
1
2
2
2
1
1
1
1
1
2
1
1
2
2
0
1
1
0
2
2
1
2
1
1
1
2
1
2
2
0
0
1
1
1
2
2
3
1
1
1
2
0
2
0
2
0
2
0
2
1
0
1
1
0
2
1
1
2
1
0
0
0
0
0
0
1
1
1
0
1
1
2
1
2
2
1
0
1
2
2
2
1
1
1
1
1
2
1
0
1
2
2
1
1
1
1
0
1
1
2
2
2
1
1
1
1
1
2
2
1
0
1
1
1
1
1
2
1
0
1
0
2
1
2
1
1
2
1
1
1
1
1
0
2
2
2
1
1
0
1
1
1
1
1
1
2
0
2
3
1
2
3
1
1
1
1
2
1
1
0
1
2
1
2
1
2
1
1
2
0
1
1
1
1
2
1
2
1
1
1
1
2
1
1
1
2
1
1
0
1
1
2
0
2
1
0
1
1
0
1
1
1
1
1
0
1
1
1
1
2
0
2
1
1
2
1
1
1
0
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
0
1
0
1
1
1
0
2
2
2
0
1
2
1
1
1
0
0
2
0
1
0
1
1
2
1
0
2
1
1
1
2
1
2
1
0
1
2
2
1
0
1
0
2
2
1
2
0
1
1
2
1
1
1
1
2
0
1
1
0
1
1
1
1
1
2
1
1
2
1
3
0
1
1
1
1
1
2
1
1
1
0
1
1
1
2
1
1
1
1
2
0
2
2
1
0
2
2
0
1
1
0
1
0
2
1
1
1
1
2
1
1
1
2
1
0
2
0
3
1
1
1
0
1
2
1
0
0
2
1
1
1
2
2
1
1
1
1
2
1
1
1
1
0
2
1
1
1
1
2
2
2
1
2
1
1
1
1
0
1
1
1
0
1
2
2
1
1
1
1
1
1
0
1
0
1
1
1
1
1
1
1
0
1
1
1
1
0
1
1
2
0
2
0
1
1
0
1
1
2
1
1
1
2
1
0
1
0
0
1
0
2
2
2
1
1
0
2
1
1
1
0
1
2
1
1
1
0
1
1
1
2
2
2
2
1
1
1
2
2
2
2
0
0
1
2
1
0
0
1
1
0
1
2
1
1
0
0
1
2
1
1
1
2
2
2
1
1
1
1
1
1
2
2
1
1
2
1
2
1
1
1
0
1
0
2
2
1
1
2
2
1
1
0
1
1
1
1
1
0
1
1
2
2
2
1
1
1
2
1
2
1
0
0
1
1
2
1
2
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
2
1
0
1
1
1
0
1
0
1
1
2
0
1
1
1
1
1
1
1
2
1
1
1
0
1
1
0
0
2
1
2
0
1
2
2
1
1
2
2
1
1
1
1
2
2
1
2
2
1
1
1
1
1
2
1
2
2
2
1
2
2
1
1
1
1
1
1
2
1
1
0
1
2
1
2
2
1
0
0
1
1
1
2
1
1
0
1
1
1
1
1
1
0
2
1
1
1
2
1
0
1
2
2
2
2
2
1
1
1
1
1
1
3
2
1
2
0
1
0
2
2
1
2
1
1
0
1
1
1
1
1
1
1
2
1
1
1
1
1
0
1
1
1
0
1
1
1
1
2
0
1
1
1
1
2
1
2
1
2
1
2
1
1
0
1
2
1
0
1
2
3
1
1
1
1
1
2
1
2
1
1
1
1
2
2
1
1
0
2
1
1
2
1
3
1
1
1
1
1
2
2
1
3
1
1
1
1
0
1
1
2
2
1
2
1
1
1
1
1
3
0
2
1
1
1
0
1
2
2
1
1
1
2
2
1
1
2
1
1
0
2
1
1
1
0
1
1
1
2
1
1
1
1
1
1
1
1
3
1
2
0
1
1
2
2
1
0
1
0
1
1
0
2
2
2
0
1
1
0
1
1
2
1
2
1
0
1
1
2
1
1
2
0
0
1
1
1
0
0
1
1
1
1
2
1
2
1
0
2
1
2
1
2
0
1
1
1
2
1
0
1
1
1
2
1
1
1
2
1
2
2
1
2
1
1
1
1
1
1
0
2
1
0
1
1
2
0
0
1
1
1
1
2
1
0
1
1
0
1
2
2
1
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
0
2
1
0
0
2
1
1
1
1
2
1
1
0
1
1
1
0
0
1
0
1
2
1
1
1
0
2
1
1
0
1
0
2
1
2
1
1
1
1
1
1
1
2
1
2
2
1
0
2
0
1
0
1
2
1
2
0
2
2
1
2
1
2
1
2
0
0
1
1
1
1
0
1
1
1
0
0
1
1
0
2
1
2
0
4
2
0
1
1
2
2
3
1
2
2
1
0
1
0
1
1
1
1
1
1
1
0
1
1
1
0
1
0
2
2
1
0
1
1
1
1
2
1
1
2
1
0
1
1
2
2
1
0
2
1
1
1
2
2
1
1
1
1
1
1
0
1
2
1
1
2
1
1
1
1
1
1
0
1
1
0
1
2
1
1
0
1
1
2
1
1
2
1
1
1
1
2
1
0
2
0
1
1
0
0
1
2
2
1
1
1
2
2
0
2
4
2
1
1
1
1
2
1
0
1
2
2
1
0
1
1
2
0
1
1
1
1
1
0
0
2
1
0
2
1
1
1
0
0
0
2
2
2
0
2
2
1
2
1
0
2
0
1
1
1
1
0
2
1
2
1
1
1
2
2
1
2
2
0
1
2
1
2
1
0
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
0
1
1
0
1
1
0
1
2
1
2
0
0
2
2
1
1
1
1
0
1
2
0
1
1
2
0
2
1
1
0
1
1
2
2
0
1
2
2
2
0
2
2
1
2
1
2
1
1
1
5
1
0
1
2
1
2
2
2
1
1
1
2
1
1
1
1
0
1
2
2
1
1
0
0
1
0
0
0
1
2
1
2
0
1
2
1
1
2
1
1
2
1
1
1
1
0
1
1
2
0
1
1
0
0
1
3
0
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
0
2
0
0
1
1
2
1
2
0
1
1
1
0
1
1
0
1
0
0
2
1
0
1
2
0
2
1
3
1
1
1
1
0
1
0
0
1
1
1
1
0
3
1
1
2
1
0
1
1
1
1
0
0
0
1
0
1
1
0
2
1
1
1
0
1
1
2
1
1
0
1
2
0
1
1
1
1
1
1
1
1
2
2
2
2
1
1
2
2
1
1
0
0
1
1
2
0
1
0
1
2
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
2
1
1
1
1
1
1
1
0
2
1
1
2
1
1
1
1
1
1
2
2
2
2
3
2
0
1
1
1
1
0
2
2
1
1
0
2
1
0
1
1
2
2
1
2
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
2
1
1
1
0
2
1
1
2
0
1
2
1
1
0
1
2
2
1
2
0
1
0
1
2
2
2
1
1
1
1
1
1
0
1
1
1
0
2
1
0
1
2
2
1
1
0
2
1
1
2
1
2
1
2
1
2
1
0
2
1
1
2
2
0
1
2
1
2
0
1
2
0
1
1
1
2
1
1
0
1
1
1
1
2
1
0
1
1
1
1
1
2
2
0
1
1
2
2
1
2
1
0
1
1
1
1
0
0
1
2
2
0
0
2
1
0
2
0
1
1
1
1
1
1
1
1
2
2
1
2
1
1
1
1
1
0
2
2
2
1
0
0
1
1
2
1
2
1
1
2
1
0
1
2
0
1
0
0
0
1
1
1
1
1
2
1
0
1
1
2
1
3
1
2
2
1
2
0
1
1
1
1
2
1
0
1
2
1
2
2
1
1
2
1
1
1
2
1
0
2
1
1
2
1
1
0
1
1
1
1
2
1
0
1
1
1
2
0
2
1
1
2
2
1
2
1
2
1
1
0
1
1
1
1
0
1
0
1
2
1
0
1
2
1
1
1
2
1
1
2
2
1
2
1
1
1
1
2
1
1
0
1
2
1
2
1
1
1
4
0
2
1
1
1
2
1
1
1
2
2
2
0
2
1
1
1
1
1
1
2
1
0
2
1
1
1
2
1
0
2
1
1
2
1
1
2
1
0
1
2
0
1
2
2
1
1
1
2
1
0
2
2
1
2
1
1
1
0
1
2
0
2
1
1
1
1
1
0
1
1
0
1
1
2
0
0
1
0
1
1
0
1
3
0
1
2
2
1
0
1
1
1
1
0
2
1
1
0
0
1
1
1
1
2
0
2
2
1
1
0
2
2
2
1
2
1
1
1
1
1
1
1
1
0
2
1
1
2
1
2
1
0
1
2
1
0
1
0
1
0
1
1
0
0
1
3
1
2
1
1
1
1
1
1
1
1
0
1
2
0
1
2
1
2
2
1
1
1
2
0
0
1
1
1
1
1
1
1
1
1
1
1
0
0
1
2
1
0
1
2
1
3
1
2
1
1
1
2
2
2
2
2
1
0
1
1
1
2
0
0
1
0
2
1
2
1
1
2
2
0
1
1
1
1
1
1
1
1
0
2
1
1
1
0
1
1
1
0
1
1
1
1
0
1
0
1
2
0
2
1
1
2
1
2
1
2
1
0
1
2
1
0
1
0
1
2
1
2
0
1
1
1
2
1
1
0
2
1
0
2
1
1
2
0
2
1
1
3
1
1
1
1
2
1
2
0
1
1
1
2
1
1
1
1
2
1
2
0
1
1
1
0
1
1
2
1
1
2
1
1
1
0
2
1
1
2
1
0
1
1
2
1
0
0
1
1
1
1
1
0
1
1
2
0
2
2
2
0
1
0
2
2
1
0
1
0
0
0
1
1
3
2
2
1
0
1
1
1
1
1
0
1
1
0
0
1
2
1
0
1
1
1
2
1
1
2
2
1
2
2
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
2
1
2
2
1
0
1
1
1
1
1
2
2
0
1
2
1
1
0
1
0
1
0
1
2
1
0
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
2
1
1
1
2
2
1
2
1
1
1
1
2
2
1
1
0
1
0
1
1
2
1
2
2
1
1
0
1
1
2
1
1
0
2
2
1
1
1
0
2
1
1
1
1
1
1
2
0
2
1
0
1
1
4
1
1
2
1
1
1
2
0
0
1
0
1
2
1
2
1
1
2
1
1
2
1
1
0
1
1
1
1
2
2
0
2
2
1
1
1
1
1
2
2
2
2
2
3
2
2
0
2
2
0
1
2
1
2
2
1
1
1
1
1
0
1
1
0
2
2
1
1
1
1
1
0
0
1
2
1
0
0
1
1
1
1
0
1
1
1
0
2
1
1
1
0
1
2
2
1
0
2
1
1
1
1
1
1
1
1
1
2
0
1
1
1
1
1
2
1
1
2
0
1
2
2
0
0
1
1
2
0
1
1
1
2
0
1
1
0
2
1
0
1
1
1
2
1
1
0
2
2
1
1
0
2
2
0
1
1
1
1
1
1
2
1
2
2
1
1
0
1
1
1
1
1
1
0
1
2
1
2
1
1
0
0
2
2
1
1
0
0
1
2
2
0
1
2
0
1
1
0
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
0
2
1
2
2
2
1
1
2
1
1
1
1
2
1
1
1
1
1
2
1
0
2
1
1
1
2
1
2
1
2
1
1
1
1
1
1
2
1
1
2
0
2
1
1
1
1
0
1
1
1
1
0
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
0
1
1
1
1
2
1
1
1
0
0
2
1
2
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
1
1
1
2
1
1
2
1
1
1
1
2
1
1
1
2
2
1
0
1
1
2
1
1
1
1
2
2
1
1
0
1
1
2
1
2
1
2
0
1
1
1
1
1
1
0
1
1
0
1
1
1
2
1
1
0
2
1
1
1
0
2
1
0
2
1
2
1
1
1
1
1
2
1
1
0
1
2
1
1
1
0
2
1
2
0
1
1
1
2
2
2
2
1
1
0
1
1
1
1
2
1
0
1
1
2
1
2
3
1
1
2
2
2
2
0
1
1
1
1
1
1
1
2
1
1
1
1
1
1
0
2
1
1
2
0
2
2
1
1
1
1
1
1
1
1
1
2
1
1
2
2
1
2
1
1
1
1
1
0
1
2
1
1
1
2
2
1
1
2
1
1
1
2
1
0
1
1
2
0
2
0
2
0
1
0
1
1
2
2
2
1
1
2
2
1
2
1
2
1
0
1
1
0
3
1
0
1
2
2
2
1
1
2
0
0
2
2
1
1
1
1
1
1
1
0
2
1
2
1
2
2
1
0
2
1
2
1
2
1
1
2
1
0
1
0
2
0
0
2
1
2
1
1
2
1
1
1
2
1
1
1
1
1
1
0
1
1
2
0
2
1
1
0
1
2
1
2
2
1
0
1
1
1
1
2
1
2
0
1
1
1
0
2
1
1
1
2
0
2
2
0
1
1
1
1
2
0
0
2
1
1
0
1
0
1
0
2
1
1
1
1
0
0
2
1
0
1
1
1
1
2
1
0
2
2
1
1
1
1
1
3
2
1
2
2
0
1
0
1
1
1
1
1
1
2
1
1
1
1
0
1
1
1
2
1
2
1
2
1
0
1
1
1
1
1
1
1
1
1
2
1
2
0
2
1
2
1
0
1
2
2
1
1
2
2
1
1
2
1
1
0
1
1
0
0
1
1
2
1
1
1
1
1
0
1
1
1
1
0
0
1
1
1
1
1
1
1
1
1
1
0
1
1
2
1
1
1
1
1
1
1
1
0
0
1
1
1
0
1
1
1
2
2
1
2
2
1
1
0
0
1
0
1
0
2
0
1
1
0
1
1
1
2
2
1
1
2
1
2
2
2
2
0
2
1
1
2
2
0
1
2
1
1
2
1
1
2
1
1
0
1
1
0
1
2
0
0
1
2
1
2
1
0
1
0
0
0
1
1
3
1
1
2
1
1
1
1
1
1
2
1
1
2
2
2
0
1
3
0
0
1
2
1
2
1
0
0
2
0
2
0
1
1
2
2
1
1
0
2
2
2
1
1
0
0
1
0
1
0
0
2
1
2
1
2
1
1
1
1
2
1
1
2
0
1
1
2
1
2
2
1
0
1
1
1
1
1
1
1
1
2
1
1
1
1
2
0
1
0
1
2
2
3
1
2
1
1
2
1
1
1
2
1
1
2
2
1
1
1
1
1
1
0
1
2
2
1
1
1
1
1
1
2
1
3
2
2
1
2
1
1
1
0
1
1
1
1
2
1
2
2
2
1
1
2
1
1
2
2
1
0
2
1
2
1
2
2
2
2
1
1
2
1
1
0
1
2
1
0
1
2
0
1
3
0
2
1
0
0
1
0
1
1
2
1
1
1
1
0
0
0
2
1
1
0
1
1
1
1
2
1
1
0
0
0
1
2
2
1
1
6
1
1
1
1
1
1
2
1
3
2
1
2
1
1
2
0
1
1
1
1
1
3
1
0
1
2
2
2
1
1
1
1
1
1
1
0
2
0
0
1
2
1
1
1
1
1
0
1
0
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
2
2
2
1
2
0
1
1
0
2
2
1
1
1
1
1
1
0
1
1
0
2
1
2
1
0
1
1
3
1
1
1
2
1
2
0
2
2
1
2
2
2
1
1
2
1
2
1
1
2
2
2
2
2
1
1
1
1
1
1
0
2
1
2
2
1
2
2
1
2
2
2
2
1
0
1
1
1
1
2
1
1
0
2
1
1
2
2
1
1
1
2
1
1
1
1
2
0
1
1
1
1
1
1
1
1
0
1
2
1
0
1
1
2
0
2
1
2
2
0
2
1
1
1
2
1
1
1
2
1
0
0
1
0
2
1
1
1
0
0
0
1
0
1
0
2
1
0
1
0
1
2
0
1
0
2
0
0
0
1
2
1
1
0
1
2
1
2
1
1
1
0
1
0
1
2
2
1
0
2
2
1
1
1
1
2
1
1
1
2
0
0
1
2
1
0
1
1
0
1
0
1
0
1
1
1
1
2
1
1
2
2
0
2
1
1
1
1
1
1
1
0
0
1
1
2
1
1
1
1
1
2
0
1
0
2
2
0
1
3
1
2
0
1
1
2
2
1
2
1
1
2
1
1
0
1
2
1
1
1
2
1
1
1
0
0
1
2
1
1
0
0
0
1
3
0
2
1
1
1
1
1
0
1
1
1
1
0
0
1
1
1
2
1
1
0
0
0
1
0
1
1
2
2
2
2
2
2
1
1
2
2
2
1
1
0
0
1
1
2
1
0
1
2
1
1
1
1
1
1
1
0
2
1
1
0
1
2
0
1
2
0
0
2
1
1
1
0
1
2
2
2
2
1
1
1
1
1
1
2
1
1
1
2
1
0
2
0
1
0
1
1
1
1
2
2
1
3
1
1
1
1
1
1
2
2
1
0
0
1
1
1
1
2
0
1
2
2
2
1
2
1
1
1
2
0
1
0
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
0
1
1
2
1
2
1
2
1
1
2
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
2
0
1
1
1
0
2
1
1
1
1
2
0
0
2
2
1
0
1
1
2
1
1
0
0
1
1
1
1
2
0
1
2
2
1
1
1
1
0
1
2
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
2
1
0
0
0
1
1
2
1
1
2
1
2
2
2
1
1
1
2
2
0
2
1
1
2
1
1
1
1
2
1
1
1
1
1
2
0
0
1
1
1
2
1
2
1
1
1
1
1
0
1
2
1
1
1
1
1
0
1
1
1
2
2
2
0
0
1
2
1
0
1
2
1
0
1
2
1
2
1
1
2
2
1
1
1
1
1
2
1
0
1
1
1
2
1
0
2
2
1
1
1
2
1
1
1
1
1
2
1
1
0
1
1
0
2
2
2
1
1
1
1
0
1
1
1
1
2
1
0
0
1
2
1
1
0
1
2
1
0
2
1
2
2
1
1
0
1
1
1
0
1
1
1
2
1
1
2
1
0
2
1
2
0
0
2
0
1
0
2
1
0
2
0
2
1
2
2
0
2
1
1
1
0
1
0
3
2
1
1
0
1
1
2
0
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
2
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
2
3
2
1
1
0
1
0
1
1
1
2
2
1
0
1
2
2
0
1
1
0
1
2
1
2
1
1
2
2
0
0
1
0
2
2
1
1
0
1
0
1
1
1
1
1
2
1
1
0
1
1
2
0
2
2
1
1
2
1
1
1
0
2
1
2
1
1
2
0
1
2
2
1
2
0
1
1
2
1
1
0
1
0
2
2
2
0
2
3
2
1
1
1
2
1
1
1
2
1
1
0
0
2
1
1
1
0
2
1
1
2
1
1
2
2
1
0
1
1
2
1
1
1
2
1
1
2
1
0
1
1
2
1
1
2
1
2
2
2
1
1
1
1
0
1
2
1
1
0
0
1
2
0
1
1
2
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
0
0
2
1
1
1
1
1
1
1
1
1
1
0
1
1
2
1
2
1
0
1
1
1
1
2
1
1
1
2
1
1
2
1
1
1
0
2
0
0
1
1
2
0
1
2
2
1
1
1
2
2
1
1
1
1
1
2
1
1
1
2
1
1
1
2
1
0
0
0
1
1
0
1
2
2
1
2
1
1
1
1
2
2
1
1
2
2
0
1
2
1
2
2
2
0
1
1
1
1
1
0
1
1
1
2
1
2
1
1
2
1
0
1
1
0
0
1
1
0
1
1
2
1
0
1
2
1
1
1
2
1
1
1
2
1
1
1
0
1
2
1
2
1
0
1
1
0
1
2
1
1
1
2
1
2
0
1
0
0
1
2
1
1
1
1
1
0
1
0
1
0
1
1
2
2
0
1
2
2
0
0
1
1
2
1
0
1
1
2
1
1
2
1
1
1
1
2
0
1
2
0
2
2
1
0
1
1
1
0
1
2
1
2
0
0
2
2
1
2
1
1
2
1
0
2
1
1
1
0
1
1
0
0
0
1
1
1
0
1
1
1
0
0
2
1
0
1
0
1
2
1
1
2
1
1
1
1
2
1
1
2
1
2
1
1
1
0
1
0
0
1
1
1
0
1
1
1
2
0
1
1
2
1
2
2
1
2
2
2
1
1
1
2
1
1
1
1
1
1
1
0
1
2
0
2
1
1
1
2
2
2
1
1
1
2
1
2
2
2
2
0
1
1
2
1
1
1
1
1
1
1
2
1
0
1
2
2
0
2
1
2
2
1
2
1
2
1
2
1
1
2
0
0
1
2
1
1
2
0
1
1
1
1
1
1
2
1
1
1
1
2
0
1
2
2
1
1
1
2
1
0
1
2
1
1
1
0
2
2
0
2
2
1
1
1
1
0
1
1
2
1
1
1
0
1
3
0
0
0
1
0
1
2
1
1
1
2
0
0
2
1
1
0
1
1
1
2
2
1
3
1
2
1
0
1
1
2
2
1
1
0
1
0
2
2
1
2
2
1
0
1
1
3
1
1
1
2
1
1
1
1
2
1
2
2
1
2
2
2
1
2
1
1
1
1
0
1
1
1
1
1
1
1
0
1
2
2
0
0
1
1
1
2
1
0
0
1
1
1
1
2
1
0
2
2
1
2
1
2
1
2
1
0
0
0
2
1
2
1
1
0
1
0
1
2
1
2
1
1
2
0
2
0
1
1
1
0
0
1
2
1
0
1
2
1
0
1
1
0
1
2
2
1
2
1
1
2
0
2
1
1
0
2
1
1
0
2
2
1
1
1
1
2
1
1
1
1
1
1
1
1
0
0
1
1
1
1
2
1
2
1
2
2
1
0
0
1
2
1
1
2
2
1
1
2
2
1
1
3
2
1
1
1
3
2
1
1
2
0
2
1
2
1
1
2
0
1
0
2
1
1
1
1
0
1
1
0
0
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
0
2
0
1
1
1
1
1
1
2
0
1
1
0
1
1
1
2
1
1
2
2
2
2
1
0
1
2
0
1
1
1
2
1
0
1
1
1
1
0
1
1
1
1
2
1
1
1
0
1
2
1
1
1
1
1
0
1
0
0
1
1
1
0
0
1
0
1
0
1
1
1
1
2
1
1
0
1
1
2
2
1
0
2
0
1
1
1
1
1
0
1
1
0
0
1
1
1
1
0
2
1
2
1
2
1
0
1
1
1
1
1
1
1
2
1
0
0
1
1
2
1
1
1
1
0
1
1
2
1
1
2
1
0
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
0
1
0
1
2
1
1
2
1
1
1
1
1
1
2
1
1
2
2
3
1
1
0
0
1
2
1
1
1
2
1
1
1
1
1
1
1
1
0
1
1
1
2
2
1
1
1
2
1
1
1
2
1
2
1
1
2
2
2
1
1
1
2
0
0
2
2
2
1
2
2
1
2
1
1
1
1
1
0
1
1
1
1
2
1
2
2
1
1
2
1
1
0
1
1
2
0
0
0
1
1
1
1
1
1
1
2
1
1
2
1
2
1
0
1
0
0
1
2
2
2
2
1
2
0
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
2
0
0
1
1
1
1
1
2
1
1
1
1
1
2
0
1
2
1
0
2
2
0
0
0
0
1
1
1
1
0
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
0
2
0
1
2
1
2
1
0
1
1
0
1
1
2
0
2
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
0
1
1
1
0
0
1
1
2
0
1
1
2
1
1
1
2
0
2
1
2
1
1
1
1
1
2
1
1
0
2
1
1
1
1
3
1
1
0
3
1
2
1
1
2
1
0
2
1
1
0
1
1
1
2
2
1
1
0
0
2
1
0
2
1
1
1
1
1
2
1
1
0
1
1
2
2
1
1
1
2
0
1
1
1
1
1
1
1
0
0
1
1
1
1
1
2
1
1
1
1
0
2
1
1
2
1
1
1
0
1
1
2
2
1
0
0
2
1
0
1
0
2
0
1
2
1
2
2
2
2
1
1
1
2
2
1
1
1
2
1
1
1
2
2
1
1
2
0
2
0
2
0
2
1
2
1
1
1
1
2
1
2
1
1
1
1
0
0
1
1
0
2
1
1
0
2
1
2
0
2
0
0
0
1
0
1
1
0
0
2
1
2
2
1
1
2
1
1
1
1
1
0
2
1
1
2
0
1
1
2
0
2
1
1
2
1
1
1
2
1
0
1
1
1
1
2
2
1
2
1
1
1
3
1
1
2
1
1
2
2
1
1
1
1
2
1
1
1
1
1
2
2
1
1
1
1
1
0
2
1
1
2
1
2
0
1
1
1
2
2
0
2
1
1
1
2
2
1
4
2
2
1
2
1
0
1
2
2
0
0
2
0
2
1
1
2
0
1
0
1
1
1
1
2
1
1
1
0
1
1
0
1
2
1
2
0
0
2
1
1
1
2
1
2
2
1
2
2
1
2
1
1
2
1
1
1
2
2
1
1
2
1
3
1
1
2
2
2
1
1
8
2
2
1
1
0
1
1
2
2
1
0
2
2
1
1
2
2
1
1
2
1
0
1
1
1
0
1
1
1
1
1
1
2
1
1
2
1
1
2
1
2
1
1
2
2
1
1
1
2
1
1
1
1
1
0
1
1
2
1
1
2
1
1
1
2
0
1
1
0
1
2
0
1
2
1
1
1
1
1
1
2
0
1
1
2
1
1
1
1
2
1
1
1
2
2
1
1
2
1
1
2
2
1
1
1
1
1
2
1
1
1
0
1
2
1
1
1
0
2
1
2
2
1
1
2
1
2
2
0
1
0
0
1
1
1
1
2
1
1
1
1
0
1
2
2
1
1
1
1
3
1
1
1
1
1
3
1
1
0
2
1
2
2
1
0
1
1
1
1
1
1
2
1
1
0
1
1
1
0
1
0
1
2
1
1
1
1
0
1
1
0
1
1
2
2
1
2
1
2
1
1
1
1
1
2
1
2
0
1
3
1
1
1
2
1
1
1
1
2
2
1
2
1
1
1
1
1
1
2
1
1
3
1
1
1
1
1
2
2
2
2
1
1
1
0
1
1
1
1
2
1
1
1
1
0
1
2
1
0
1
1
1
1
0
1
2
2
1
1
1
1
1
1
2
1
0
2
1
1
1
2
0
0
1
0
0
0
1
1
2
0
2
0
0
1
2
1
1
2
0
0
0
1
1
2
1
2
1
2
2
2
1
2
1
1
0
1
3
1
1
2
1
1
2
0
1
1
1
1
2
0
2
2
0
2
2
0
2
2
0
1
1
1
2
1
1
2
2
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
0
0
1
0
0
1
0
0
1
1
0
2
1
1
1
0
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
0
1
2
3
1
2
1
1
1
1
1
1
0
1
1
0
1
0
0
1
1
1
0
2
2
1
2
1
1
1
1
1
2
2
1
2
0
0
1
1
0
1
1
1
3
0
1
0
1
1
2
2
1
1
1
1
1
2
2
2
2
0
1
1
1
1
1
1
0
0
1
1
0
2
0
1
2
1
0
2
2
1
2
1
1
1
1
1
0
2
1
1
2
2
1
2
2
1
1
1
1
1
1
1
1
1
1
2
0
0
0
2
1
1
2
2
1
1
1
0
1
1
1
2
1
1
3
1
2
1
2
0
1
1
1
1
1
1
2
2
1
2
1
1
1
1
2
0
1
2
1
1
2
1
0
1
2
0
1
1
1
1
1
1
1
0
3
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
1
0
0
1
1
1
2
1
1
2
1
1
1
1
2
1
1
2
0
0
1
1
1
2
1
1
1
1
0
0
2
2
1
1
1
1
2
2
1
0
1
1
1
1
1
2
2
1
1
1
1
1
2
2
2
0
2
1
0
1
1
1
1
1
0
1
0
2
2
1
1
1
1
2
1
1
2
1
1
1
1
1
3
0
1
1
2
0
2
1
2
1
0
2
1
0
2
0
1
2
2
2
1
2
0
2
1
1
1
1
1
2
1
1
1
0
1
1
2
1
2
0
1
1
2
0
2
0
2
1
1
0
1
1
0
1
0
0
2
1
1
2
1
1
1
0
1
1
2
1
0
1
1
1
1
1
2
1
2
1
2
1
1
1
1
2
0
1
2
2
3
2
2
1
0
1
2
2
1
1
1
0
2
1
2
2
1
1
1
1
1
2
1
2
1
2
1
1
1
0
1
1
1
2
2
1
0
2
3
1
1
1
2
1
1
1
1
1
2
1
2
2
1
1
2
1
0
0
1
1
4
0
0
1
1
1
0
1
1
2
2
2
1
2
1
2
1
1
2
1
2
2
0
1
1
1
1
1
0
1
1
1
1
1
2
2
1
1
1
1
0
1
1
2
1
1
1
1
2
1
1
0
0
1
2
1
2
1
1
0
1
1
2
1
2
1
2
1
0
1
1
1
3
1
1
0
0
1
1
1
0
1
1
0
2
1
1
1
2
1
1
2
1
1
1
2
0
1
2
2
0
1
2
2
2
1
0
1
1
2
0
2
1
1
1
1
1
1
2
1
0
0
2
1
2
2
1
0
1
0
0
1
1
2
2
1
1
0
0
0
1
1
1
1
0
1
1
1
0
2
1
2
1
2
2
2
1
0
2
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
2
2
2
1
1
1
1
1
2
0
2
1
1
2
1
0
1
2
2
1
1
2
1
1
1
2
2
1
1
1
1
2
1
1
2
1
0
1
0
1
2
1
1
1
1
1
1
0
0
1
0
0
0
1
2
0
1
0
1
0
1
1
1
1
1
1
2
1
0
2
0
0
2
1
1
2
0
2
2
2
2
0
0
2
1
0
0
2
1
1
1
1
1
1
1
0
1
2
0
2
2
2
1
1
2
1
2
2
1
2
1
2
2
1
1
1
1
1
2
2
2
1
0
1
2
1
2
2
2
2
1
0
1
2
1
0
0
2
1
1
0
1
1
1
2
0
1
1
1
2
1
0
0
1
2
2
0
1
0
1
0
1
0
2
1
1
1
2
1
1
2
0
2
1
1
1
2
0
1
2
2
1
1
1
2
1
1
0
2
1
1
1
1
0
1
2
2
2
1
1
1
1
1
1
1
0
1
2
2
0
1
4
2
2
1
0
2
1
1
0
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
2
1
2
1
2
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
2
0
0
0
2
1
0
1
1
0
2
2
0
2
1
1
1
1
2
2
1
2
1
1
2
0
1
0
2
0
0
2
1
1
1
1
1
1
2
2
1
1
1
1
0
1
1
1
1
2
2
1
2
1
2
0
2
1
1
1
2
1
1
2
1
1
0
2
1
2
2
0
2
1
2
0
2
1
1
1
1
1
1
1
2
1
2
1
1
1
2
1
1
1
1
2
1
1
0
1
1
1
2
1
1
1
0
1
1
1
1
1
0
1
1
2
1
1
1
1
2
1
2
1
1
1
2
1
1
2
2
2
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
0
2
0
0
1
0
0
0
1
1
1
1
5
2
1
1
1
1
1
2
1
2
2
1
1
1
1
1
1
0
1
1
1
1
1
2
1
1
2
2
1
2
3
1
1
0
1
1
1
1
1
1
1
1
1
1
0
1
1
1
2
1
1
2
1
1
1
1
0
2
1
1
1
1
1
1
0
1
1
1
2
1
1
0
1
2
2
1
1
2
1
1
1
1
1
1
2
1
0
1
0
2
1
1
1
1
1
0
1
1
1
2
1
1
2
1
1
1
1
0
1
1
1
1
2
1
1
2
1
1
2
1
0
1
0
1
0
1
1
1
2
1
2
1
2
2
1
1
2
2
0
1
0
1
0
1
1
0
1
2
1
0
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
0
2
2
1
1
1
0
1
1
1
0
2
1
1
1
1
1
1
1
2
1
1
1
0
1
1
1
1
1
1
1
1
0
1
1
2
2
1
1
1
1
2
1
0
1
1
1
1
1
1
1
2
0
2
1
1
1
1
1
2
1
0
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
0
1
2
0
1
1
1
0
1
2
1
2
2
3
2
0
1
1
1
1
1
1
1
1
2
1
2
1
2
1
2
1
1
2
1
2
1
1
0
2
2
1
0
1
1
2
1
1
0
1
2
2
2
2
1
0
1
0
1
1
0
0
2
1
2
2
2
1
1
1
1
2
0
1
2
1
1
1
1
0
0
1
1
1
0
1
1
2
1
1
2
1
1
1
1
1
1
1
1
0
2
2
1
2
1
0
2
1
1
1
2
1
0
1
0
2
1
1
1
1
1
1
0
2
2
1
1
1
1
1
1
2
1
0
0
0
1
2
0
1
1
1
1
2
1
2
0
2
1
1
1
1
0
0
1
1
2
1
1
1
1
1
2
2
1
2
2
1
1
1
1
2
1
4
1
1
0
1
1
1
1
1
0
0
1
0
0
1
1
0
1
1
1
2
0
1
1
1
1
1
1
1
1
1
1
0
2
0
2
1
1
0
1
1
1
1
2
1
1
1
1
1
0
1
1
2
2
2
1
1
1
2
2
1
0
1
1
1
0
1
2
1
1
3
0
1
1
1
1
1
1
1
0
0
1
1
1
1
1
2
1
2
1
2
1
1
0
1
1
0
1
2
1
1
1
1
2
2
1
1
1
1
1
0
1
1
2
1
2
1
1
0
1
1
2
1
1
1
2
1
1
1
2
2
1
2
2
1
0
2
2
1
1
1
1
0
2
0
2
2
1
2
1
0
1
1
1
0
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
4
2
1
1
1
0
2
1
0
2
1
1
1
1
1
1
1
2
1
2
2
0
1
1
1
1
0
2
1
1
1
1
2
1
1
0
1
1
1
1
1
2
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
2
1
2
1
0
1
2
1
0
0
1
1
1
1
0
1
1
1
1
2
1
1
2
0
1
1
1
1
2
2
1
0
2
2
1
1
2
2
1
1
1
1
1
2
1
1
1
2
0
2
2
0
2
0
1
0
2
1
1
1
1
1
1
1
0
0
1
2
0
0
1
0
1
0
1
1
1
2
1
1
0
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
0
2
0
1
2
0
2
1
1
1
1
2
1
2
0
1
1
2
1
0
1
1
2
2
1
1
1
1
1
1
1
2
0
0
2
1
1
2
2
0
1
1
1
0
1
1
2
2
1
0
1
1
0
0
1
1
2
1
1
0
1
1
1
0
2
2
1
1
2
1
1
0
1
0
1
1
1
1
1
0
1
1
1
2
2
1
1
1
0
1
1
1
1
1
1
0
1
1
2
1
0
1
1
1
2
1
1
0
1
2
2
1
1
0
1
2
0
1
2
1
1
2
1
1
1
0
2
2
1
1
1
1
2
2
1
1
2
1
2
0
2
2
1
0
1
1
0
1
1
1
1
1
1
1
1
0
2
1
0
1
1
0
2
2
1
0
1
1
1
0
2
1
2
1
1
1
1
0
1
1
1
1
1
0
0
0
1
1
0
1
1
1
2
1
1
2
1
1
0
1
1
1
1
0
1
1
0
2
1
0
1
2
0
2
1
1
2
1
1
1
0
1
1
1
1
2
1
1
1
1
1
1
1
1
0
1
1
2
1
1
1
2
1
0
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
2
0
2
2
2
1
1
1
1
1
1
0
1
1
1
2
1
0
2
1
1
1
1
1
1
0
1
1
2
1
1
1
1
1
1
0
1
1
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
0
1
1
0
1
1
1
0
1
1
1
1
1
1
2
0
2
2
1
1
1
2
2
1
0
2
1
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
1
0
1
1
0
1
2
2
2
2
0
1
1
1
1
0
1
1
2
0
2
1
2
1
2
1
1
2
1
1
0
1
0
1
1
1
1
1
1
1
0
1
2
2
1
2
2
4
0
0
0
1
1
1
1
1
1
1
1
1
2
2
1
2
0
0
1
1
1
1
0
0
1
1
1
1
2
2
1
1
1
1
1
1
1
0
0
1
1
2
1
1
1
2
0
0
1
1
1
2
0
2
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
2
2
1
2
1
1
1
1
0
1
0
2
0
3
1
0
1
2
1
1
1
1
2
0
1
0
1
1
2
1
1
1
1
2
0
1
1
0
1
1
1
1
2
0
2
1
1
1
1
1
1
1
0
2
2
0
1
2
1
1
1
2
2
1
1
2
0
1
0
1
0
1
1
1
2
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
0
1
2
1
0
1
1
1
1
0
1
1
2
1
1
1
0
0
1
0
1
1
1
1
0
1
1
1
1
1
3
1
1
1
0
1
1
1
1
1
1
3
1
2
1
1
2
1
2
1
0
1
1
1
1
1
0
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
1
0
1
2
2
1
2
2
1
1
0
1
1
1
1
0
1
1
1
1
1
1
0
1
1
0
0
1
1
1
2
0
0
1
1
0
2
2
1
1
2
0
1
1
1
2
1
2
1
1
1
1
0
1
2
1
0
1
1
2
1
2
1
2
1
1
1
2
1
1
1
1
0
2
1
0
1
1
1
2
2
1
1
1
1
2
1
1
2
2
1
1
1
2
1
1
0
1
2
2
2
1
0
1
0
2
1
1
1
2
0
2
0
1
2
1
1
0
1
0
2
1
0
1
1
1
1
2
1
1
1
1
1
1
0
1
1
2
1
1
1
2
1
1
2
1
1
3
1
1
2
1
1
2
1
1
1
0
1
1
1
2
1
1
1
1
1
1
1
0
1
1
1
1
0
1
0
1
1
0
1
1
0
1
3
1
1
1
1
2
1
1
1
1
1
1
2
0
2
2
1
1
1
1
1
2
0
1
1
1
2
1
0
1
1
2
1
1
1
1
1
1
1
2
1
1
2
1
0
1
0
1
1
1
2
1
1
0
1
1
0
1
2
1
2
2
1
1
2
2
0
1
2
1
2
0
1
1
1
1
1
2
1
1
0
2
2
3
2
1
0
0
1
2
1
1
0
1
2
2
2
0
0
1
1
2
1
1
1
0
0
0
1
1
1
1
1
0
0
0
1
2
2
2
1
1
1
1
0
0
1
2
0
1
1
1
0
1
1
2
1
1
0
1
2
1
5
2
0
1
1
2
2
2
2
1
2
2
2
2
1
1
2
1
1
1
1
0
1
0
0
2
2
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
3
2
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
0
1
2
0
1
1
2
1
1
0
2
1
1
0
1
0
1
1
2
0
1
1
1
1
0
0
1
1
1
1
1
1
2
1
1
2
1
0
1
1
2
3
1
1
1
0
1
1
0
1
1
1
0
2
2
2
1
2
0
2
1
1
2
1
1
1
1
2
1
1
1
0
0
2
2
2
1
1
1
1
1
1
1
1
1
2
1
1
1
0
2
1
2
1
1
1
2
2
2
1
1
2
1
1
1
0
1
2
1
1
1
1
1
1
1
2
0
2
0
1
1
0
2
2
1
1
1
1
1
2
1
0
0
2
1
1
0
0
1
1
2
1
1
2
1
1
2
1
1
1
1
1
1
1
1
0
1
0
1
2
1
1
0
1
1
1
1
1
1
1
1
2
2
1
1
1
2
1
1
1
1
1
2
2
1
1
2
2
1
2
1
0
1
1
1
2
1
1
2
1
1
2
1
1
1
0
1
0
1
1
2
2
0
0
0
1
0
2
1
1
1
1
1
1
2
1
1
1
2
2
1
1
0
2
1
0
0
2
1
2
2
2
1
1
0
0
0
1
1
0
1
2
1
1
0
2
1
1
1
2
0
0
2
2
1
1
1
2
1
0
2
2
1
0
1
1
1
2
0
1
2
2
0
2
0
2
2
0
1
1
2
1
1
4
1
0
0
2
1
2
1
0
2
2
1
2
1
1
2
1
0
2
0
1
1
1
1
2
1
1
1
0
2
2
2
1
2
2
1
1
0
1
1
1
1
1
1
1
1
2
1
0
1
1
1
1
0
1
2
2
1
1
2
1
1
1
0
1
1
1
1
1
2
0
0
1
2
1
1
1
0
1
0
1
0
2
0
0
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
0
1
0
1
2
1
1
2
1
1
1
2
1
0
1
1
1
2
1
1
1
1
2
1
1
1
1
1
2
2
1
2
1
2
1
0
1
1
4
1
1
0
1
1
0
0
1
1
1
1
1
1
2
1
1
0
0
1
0
0
2
1
1
1
1
1
1
1
2
0
1
1
1
1
1
1
1
2
1
0
2
2
2
1
1
2
2
1
1
0
1
1
1
1
0
2
1
1
2
1
1
1
0
1
1
1
2
1
1
1
1
1
1
1
2
1
0
1
1
1
1
2
1
1
1
0
1
2
1
0
0
1
1
1
1
1
1
2
2
1
1
1
2
1
3
2
1
2
0
1
1
0
1
1
2
1
1
2
1
0
1
1
2
0
1
2
2
1
1
0
1
0
1
1
1
1
1
1
2
2
0
1
1
1
1
1
0
1
2
1
2
1
0
1
1
1
1
1
2
1
1
1
0
0
0
2
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
0
1
1
1
1
2
1
1
1
1
1
2
1
1
0
0
1
1
0
2
1
1
1
0
2
2
1
1
0
1
2
1
2
1
2
2
0
1
1
0
1
1
1
0
1
2
1
1
1
2
2
1
2
2
0
0
2
1
1
1
1
1
0
1
1
1
1
1
2
1
2
0
2
1
1
0
1
1
2
1
1
0
1
2
2
2
2
1
1
0
2
1
1
0
0
2
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
1
2
1
2
2
1
2
0
1
1
1
1
1
0
2
1
3
0
1
1
1
1
0
1
1
0
1
1
1
2
2
1
1
2
2
1
0
0
1
1
0
1
1
0
1
0
1
1
1
2
1
1
2
2
0
1
0
2
1
1
1
1
1
1
1
1
2
0
2
1
1
1
0
2
1
0
1
0
1
1
1
1
1
1
0
0
2
1
2
2
1
0
2
1
1
1
1
1
2
0
1
2
1
2
2
2
2
1
1
0
1
0
0
1
1
1
1
1
2
2
1
2
0
1
2
0
3
1
1
2
1
1
2
1
1
2
1
1
1
2
2
1
1
1
2
0
1
1
1
1
1
2
2
2
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
2
0
1
1
2
1
1
1
1
2
0
1
2
0
1
1
1
2
2
1
2
0
1
2
1
1
2
0
2
1
0
2
1
0
0
2
0
2
1
2
2
0
0
1
2
2
1
1
1
0
1
1
1
1
1
0
2
1
1
2
2
0
1
1
1
2
1
1
2
0
1
2
1
1
1
1
0
1
0
2
1
1
1
1
1
1
2
2
1
1
1
1
1
0
1
1
1
0
2
1
1
1
1
1
1
1
1
0
0
1
1
1
3
2
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
2
1
2
0
1
1
1
1
1
1
1
1
1
1
1
1
1
2
0
2
2
0
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
2
1
2
2
1
1
1
2
2
2
1
1
1
1
1
0
2
1
1
2
2
1
1
1
0
1
1
1
1
1
1
0
0
0
1
2
2
1
0
1
0
1
1
1
1
1
1
2
1
1
1
1
2
2
1
1
1
1
1
1
0
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
0
0
2
1
1
1
3
1
1
4
1
1
2
1
1
1
2
1
3
1
1
1
0
1
2
1
1
1
1
0
1
1
0
1
1
1
1
0
2
0
1
2
1
1
2
1
1
1
2
2
2
1
1
0
2
2
1
0
1
1
1
1
2
0
1
0
1
1
1
1
1
1
1
1
2
2
0
1
1
1
0
1
1
1
1
2
2
2
1
1
0
1
1
1
1
1
2
0
1
0
1
2
2
1
2
2
1
0
2
1
0
2
2
0
1
1
1
0
1
1
1
0
1
1
0
3
1
1
0
0
1
2
0
1
0
2
2
2
0
1
0
2
2
2
0
1
0
1
1
1
2
2
1
2
2
0
0
2
2
1
1
2
1
3
1
2
2
1
0
0
1
1
0
1
1
1
1
1
0
2
1
1
1
2
1
0
2
2
1
1
1
1
2
1
1
2
1
1
2
1
2
0
2
1
0
1
2
1
2
2
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
0
1
1
1
2
1
0
2
0
1
1
1
1
1
0
2
1
1
1
2
0
0
1
1
1
1
1
1
1
0
1
1
1
2
2
1
1
1
0
2
1
1
1
1
1
0
0
0
2
2
2
1
0
1
1
1
0
1
1
1
1
2
2
2
2
1
2
1
1
1
2
1
1
1
1
1
1
2
4
1
1
0
1
1
2
1
2
1
1
2
2
2
2
1
1
1
0
1
1
1
2
1
0
1
2
1
1
2
2
2
2
2
2
1
1
0
1
0
1
2
2
1
1
2
2
1
3
1
1
1
1
2
0
1
1
1
2
1
1
2
1
0
1
1
2
1
1
1
1
1
1
1
0
1
1
1
1
1
2
1
1
2
1
0
1
0
1
1
1
1
1
1
0
1
2
1
1
1
1
2
1
0
2
1
0
2
2
1
1
2
2
1
1
0
2
2
1
2
1
2
2
1
1
2
0
1
2
1
1
1
2
1
0
1
1
1
1
0
3
1
2
1
1
2
2
0
2
1
1
1
1
2
1
1
1
0
2
1
1
2
1
1
1
1
2
2
1
1
2
2
1
1
1
1
1
1
0
0
1
0
2
2
0
0
0
1
1
2
1
1
1
1
1
2
1
2
2
0
2
1
1
1
1
0
1
1
2
1
0
2
1
1
1
0
1
1
2
2
2
2
0
1
0
1
1
1
1
1
1
1
1
0
1
1
1
1
2
0
0
1
1
0
1
0
1
2
2
2
1
1
1
1
0
1
1
0
1
1
1
1
2
2
1
1
1
1
1
2
1
1
0
1
2
2
1
2
1
1
1
1
0
1
1
1
1
2
1
2
1
1
2
2
2
1
2
2
2
2
2
1
1
1
1
0
0
1
1
2
0
2
1
1
1
1
1
1
2
2
1
1
1
2
0
1
4
1
1
1
2
2
1
1
1
2
0
1
2
1
0
2
1
2
1
1
0
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
0
1
0
1
2
1
2
0
1
2
0
1
0
2
2
2
3
1
2
1
1
1
1
1
1
1
2
2
1
1
2
1
1
2
2
0
1
1
0
0
1
2
1
1
1
1
1
1
1
2
2
2
1
1
1
2
1
2
1
1
1
1
1
1
1
0
0
0
1
0
2
1
1
0
1
1
0
0
2
1
2
1
2
1
0
1
2
1
0
2
1
1
2
1
1
0
1
0
1
2
2
2
1
2
2
1
1
1
1
1
1
0
1
1
1
1
1
0
1
1
0
1
2
1
1
0
1
1
0
0
3
1
1
2
1
2
1
1
2
1
1
1
1
0
1
1
1
1
2
2
0
2
2
2
2
2
1
1
0
1
1
1
0
1
1
1
0
2
1
1
2
2
2
1
2
1
1
1
2
1
2
1
2
1
1
2
1
1
1
1
0
1
2
1
1
1
1
1
2
2
1
1
1
0
2
1
1
1
2
1
1
1
0
1
1
2
1
0
1
1
1
1
2
1
1
2
0
1
0
1
1
1
1
1
2
1
1
1
2
1
2
1
0
2
1
2
1
0
1
2
2
2
1
2
1
2
1
0
1
1
1
2
3
2
1
1
1
0
1
2
1
1
1
3
2
1
2
1
1
1
2
1
1
1
3
1
1
2
1
1
1
2
0
1
2
2
1
1
0
1
1
2
1
2
1
1
1
1
1
1
1
1
1
0
2
1
1
1
2
2
2
2
1
2
1
0
0
1
1
0
1
0
0
2
2
1
1
1
1
2
1
2
1
2
1
1
1
1
1
0
1
1
0
1
1
1
2
1
1
0
1
1
0
2
3
1
1
2
1
1
2
1
2
2
2
0
2
2
1
1
1
1
2
1
1
2
1
2
1
0
0
0
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
0
2
1
2
0
1
2
1
1
1
2
1
1
2
2
2
1
1
1
2
2
2
0
1
1
1
2
0
1
2
1
1
2
1
1
1
1
1
1
2
1
2
0
1
1
0
1
1
1
1
1
2
1
0
1
1
1
1
1
2
1
1
2
1
0
1
1
1
1
1
1
1
1
0
0
1
2
1
0
1
1
0
2
1
0
2
1
1
2
1
2
1
1
1
1
0
3
2
1
0
2
0
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
0
1
1
2
1
1
1
1
1
1
1
0
0
1
4
1
2
1
1
1
1
1
1
2
1
0
1
1
1
1
1
1
2
2
1
1
2
2
0
1
1
1
1
2
1
0
1
1
1
1
1
2
1
2
2
1
2
2
1
1
1
1
1
1
0
2
0
2
1
1
1
2
2
2
1
2
1
1
0
1
1
1
0
1
0
1
2
1
2
1
1
1
1
2
0
1
1
1
2
2
1
1
2
2
1
1
1
0
2
1
2
2
1
1
2
0
1
1
1
0
2
2
2
1
0
2
1
2
1
0
2
1
1
1
1
1
1
0
1
1
1
1
1
0
1
2
0
1
1
1
1
1
1
1
1
2
1
1
1
0
1
2
1
0
2
0
1
1
0
2
0
0
2
1
1
2
1
0
1
1
0
1
2
1
2
1
1
2
2
1
0
1
1
2
2
3
1
1
2
1
1
1
1
0
1
0
1
1
0
1
2
2
0
0
0
1
1
1
0
1
1
1
2
1
1
0
1
1
0
1
1
1
1
0
1
2
1
2
1
1
0
1
1
1
1
1
2
1
0
1
1
1
1
1
1
2
1
2
2
0
1
2
1
0
0
1
2
1
1
1
2
2
1
0
1
1
1
0
2
0
2
1
1
1
0
2
1
2
0
1
1
1
1
1
0
1
1
2
0
2
2
2
2
1
2
1
1
1
1
2
2
1
1
1
2
2
1
0
1
3
0
1
0
1
1
2
1
2
1
2
1
0
1
0
1
1
1
1
3
1
1
2
1
2
1
1
1
0
0
1
2
1
1
1
2
1
0
1
3
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
1
0
0
1
2
0
0
1
3
1
1
2
2
0
1
1
4
1
1
1
2
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
0
1
1
1
0
1
2
1
1
1
1
1
1
1
1
1
0
1
2
1
2
1
1
1
0
1
1
1
1
1
1
2
0
1
1
1
2
1
1
1
0
1
1
0
1
1
2
1
1
0
1
1
2
2
2
2
2
0
0
1
1
1
2
2
2
2
0
1
1
1
2
1
1
1
1
1
0
0
0
0
1
1
2
1
1
1
1
1
1
2
1
2
1
2
2
1
1
1
2
1
0
1
0
1
1
0
1
1
1
1
1
1
1
2
2
1
1
0
0
1
1
1
2
1
1
2
1
2
0
1
0
0
2
1
0
1
1
2
2
2
1
0
1
1
1
1
1
3
0
1
1
1
1
2
1
1
1
1
2
1
0
0
1
1
1
2
1
1
2
0
0
1
1
1
1
2
1
2
1
2
2
2
0
0
2
1
1
1
1
1
1
1
2
2
1
1
1
3
1
1
1
1
2
0
2
1
1
1
2
1
2
1
1
1
1
1
2
2
2
1
1
1
0
1
1
1
1
0
1
1
2
2
1
2
1
0
1
1
2
2
1
1
2
1
1
0
1
1
1
1
1
1
0
1
1
0
1
1
0
1
1
1
2
1
1
1
1
2
1
1
1
1
2
0
2
2
0
0
2
1
0
1
2
0
1
2
1
1
2
1
0
0
0
1
1
1
1
0
0
1
0
2
1
1
1
2
1
1
1
1
2
1
1
0
0
1
1
2
1
2
1
1
2
0
1
1
2
1
1
2
0
1
1
2
1
1
1
1
1
1
2
2
2
2
1
2
1
0
1
1
1
1
1
2
1
1
2
1
2
1
1
1
0
1
1
0
1
2
1
1
0
1
1
0
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
0
2
1
1
1
1
1
2
1
1
1
1
2
2
1
1
2
2
1
1
2
1
1
0
1
1
1
1
2
2
1
2
1
2
2
2
1
1
1
0
1
1
0
2
2
2
1
2
5
2
2
2
1
1
1
1
1
1
1
2
1
2
1
0
2
1
1
1
1
1
0
2
2
1
2
0
1
0
1
2
0
2
2
2
1
1
0
1
2
1
2
0
0
2
1
1
2
0
1
0
1
1
2
0
1
1
2
1
1
1
0
0
2
1
1
1
2
1
0
1
2
1
1
1
1
2
1
1
1
2
2
0
1
1
1
1
1
1
0
1
1
1
1
1
0
2
0
1
1
1
0
1
1
0
1
0
1
1
0
2
2
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
0
1
1
1
2
1
2
1
1
1
1
1
1
1
2
1
2
2
1
1
0
0
2
2
0
0
1
2
1
2
2
2
1
1
1
2
1
1
1
0
1
2
1
2
2
1
1
2
2
2
1
1
1
2
2
2
0
2
2
2
1
2
2
1
1
1
0
1
0
2
2
1
1
1
1
1
2
2
1
2
1
2
1
1
1
0
1
1
1
2
1
0
1
1
1
1
1
2
1
2
2
1
2
2
0
1
2
1
1
0
2
2
1
1
0
2
1
1
1
1
2
1
2
1
2
1
1
2
1
1
1
2
1
1
1
0
1
2
1
2
1
0
1
1
2
1
0
1
1
1
0
1
1
1
1
1
0
1
2
0
1
0
0
1
1
2
0
1
1
1
0
1
0
2
2
1
1
1
1
2
2
2
1
1
1
2
1
0
2
2
1
1
0
2
1
1
0
2
2
1
1
1
2
2
2
1
0
1
1
1
2
2
0
1
1
1
1
2
1
1
0
0
1
1
2
0
0
1
1
1
2
0
2
1
0
1
2
1
1
2
1
2
2
0
2
1
1
2
1
1
1
2
2
1
1
1
1
1
1
1
0
1
2
1
1
2
1
0
2
2
2
1
1
2
2
1
2
2
1
1
1
2
2
1
2
2
1
2
1
2
1
1
2
1
2
1
1
0
2
0
1
1
2
1
1
1
1
2
1
1
0
1
0
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
0
1
1
1
1
0
1
0
2
1
1
0
1
2
4
0
0
1
1
1
1
0
2
1
2
0
2
2
1
2
0
0
1
1
1
2
2
1
0
1
2
1
1
1
0
2
1
0
1
1
1
1
4
2
1
0
1
2
1
1
2
1
2
0
1
1
1
2
1
1
2
1
2
1
2
0
1
1
1
1
1
2
2
2
1
1
1
1
2
1
1
2
1
0
1
2
0
1
1
1
1
0
1
1
1
1
0
1
0
2
1
2
1
2
0
1
1
1
2
2
2
0
1
0
1
1
1
1
1
1
0
1
2
1
1
2
2
1
1
2
0
1
1
2
1
1
1
1
1
0
1
1
0
3
1
1
1
1
1
1
0
1
1
1
0
2
0
1
1
1
2
1
1
1
0
1
1
2
1
2
1
1
1
0
0
1
1
1
1
1
1
1
2
1
1
0
1
2
1
1
2
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
3
1
1
1
1
1
1
1
0
2
2
1
2
1
2
2
1
0
2
1
2
1
1
1
0
0
1
3
1
1
1
1
1
2
2
1
1
0
0
1
1
1
1
1
2
1
1
1
3
1
1
2
2
1
1
1
0
0
5
1
1
3
1
1
1
1
1
1
2
1
0
1
2
1
1
2
1
0
1
1
1
1
1
1
2
2
1
2
1
2
2
2
2
1
1
1
2
1
2
2
2
1
2
0
1
1
1
1
2
0
0
1
1
1
1
1
1
1
5
2
1
2
2
1
1
1
1
1
1
2
0
0
2
0
1
1
1
1
2
1
1
1
2
1
0
1
0
1
2
1
1
0
0
2
1
1
1
1
1
1
1
1
1
1
1
1
0
0
0
2
0
1
0
1
0
1
1
0
1
1
0
1
1
2
2
2
1
1
1
2
1
1
1
1
1
2
2
2
1
1
2
0
1
1
1
2
0
1
2
1
1
1
1
1
2
1
1
2
1
1
3
2
1
1
2
1
0
4
1
2
0
0
1
0
0
0
1
1
1
1
1
0
1
1
2
1
2
2
1
0
1
1
2
1
2
1
1
2
2
2
0
1
2
2
2
1
4
1
1
0
1
1
1
2
1
1
3
2
1
2
1
0
1
1
1
1
2
0
2
0
2
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
0
1
0
1
1
0
0
0
1
2
1
1
1
1
1
1
0
1
0
1
5
1
1
0
1
0
1
2
2
1
1
1
1
1
2
1
0
1
1
1
2
1
1
0
2
1
1
1
1
2
1
0
2
2
1
2
2
1
1
0
2
2
1
2
2
0
1
2
1
1
1
1
1
1
1
0
1
1
0
2
2
1
2
1
1
1
0
3
1
1
1
1
1
2
1
1
2
1
1
1
2
2
1
2
1
1
1
1
1
0
1
1
0
2
1
3
2
1
2
1
1
1
1
2
2
0
1
1
1
1
1
1
2
2
0
2
1
1
0
2
2
1
1
2
1
1
2
0
2
0
2
1
2
1
1
2
1
1
2
2
1
0
2
0
0
2
2
2
1
1
1
1
1
1
1
2
0
0
1
2
2
1
0
1
0
1
1
2
2
2
1
2
2
2
0
1
1
1
1
1
2
2
1
2
1
1
1
1
1
2
0
1
2
1
0
0
1
1
0
1
1
1
0
2
1
0
1
1
1
1
1
1
1
2
2
1
1
1
1
2
1
1
2
1
1
1
0
1
1
2
1
1
1
1
1
0
1
1
1
1
0
1
1
1
1
1
1
1
2
2
2
2
1
1
2
2
1
1
2
2
1
0
1
0
2
1
1
1
2
2
1
2
1
1
2
1
2
1
1
2
0
2
2
2
1
1
1
2
1
2
2
1
1
2
2
0
1
2
3
2
2
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
2
0
0
1
1
1
1
2
2
1
2
1
2
1
0
0
2
2
1
0
1
2
1
1
1
1
1
1
1
0
1
2
1
2
1
1
2
1
1
1
1
1
1
2
1
2
2
2
1
1
1
1
0
0
1
2
2
1
2
0
0
1
1
2
2
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
0
1
1
1
1
1
1
0
1
2
2
0
1
2
1
1
2
0
2
1
0
0
1
2
1
0
1
2
2
2
1
1
1
3
1
1
1
2
0
1
1
1
1
2
1
1
1
1
0
1
1
2
1
2
2
1
0
2
2
1
1
1
0
2
1
1
2
2
2
2
0
2
1
1
0
1
1
1
1
1
1
1
1
1
2
2
2
1
2
1
2
0
0
1
1
2
1
2
1
2
0
2
1
2
2
2
2
2
2
2
1
1
2
2
0
1
0
2
0
0
1
0
0
1
1
1
1
2
0
1
1
0
1
0
1
0
2
1
1
1
2
1
0
1
1
1
1
1
0
1
2
1
1
2
2
1
1
1
2
1
1
1
0
1
2
2
1
1
1
1
2
1
1
1
2
2
1
0
1
2
1
1
1
1
1
1
1
2
1
1
1
0
1
2
2
0
0
1
1
0
1
1
1
2
1
0
0
1
2
2
1
1
1
2
1
0
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
2
1
2
2
0
1
1
1
1
1
2
2
1
2
0
1
1
1
2
1
1
0
1
0
0
1
1
1
1
1
1
1
0
2
2
0
1
1
2
1
3
2
1
1
1
2
1
2
1
0
1
1
0
2
2
2
2
2
1
1
1
2
0
2
2
2
1
1
1
0
0
1
0
2
0
1
1
1
0
2
1
1
1
1
2
1
0
2
1
2
1
0
1
0
1
2
2
1
2
1
2
2
1
1
1
1
2
1
1
1
1
1
1
2
2
0
1
1
0
1
2
1
1
1
2
0
0
1
2
1
1
2
0
1
1
1
1
1
2
1
3
1
1
2
2
2
1
1
1
1
2
1
1
1
1
0
1
1
1
1
1
1
1
0
0
2
2
2
0
2
1
0
0
1
1
1
1
0
1
1
1
0
2
1
0
1
1
1
1
1
0
1
3
0
2
2
1
1
1
1
1
1
1
2
1
1
2
1
0
2
3
1
0
1
1
1
1
1
1
0
1
1
1
1
1
2
1
0
1
2
2
1
1
2
1
2
1
1
1
2
1
1
1
1
1
2
2
1
1
1
1
1
1
0
1
2
1
1
1
1
1
1
1
1
1
2
0
2
1
1
2
1
1
0
1
1
2
1
2
1
2
0
2
1
2
1
1
1
1
2
0
1
1
2
2
1
2
1
1
1
1
1
1
0
2
1
0
1
0
0
1
1
0
1
2
2
1
0
1
1
0
1
1
2
1
1
1
1
2
1
1
1
1
0
1
1
0
1
0
1
0
1
1
1
1
2
1
0
1
1
1
1
1
2
2
1
2
2
1
0
0
2
1
2
1
1
1
1
2
2
1
1
2
0
1
1
1
2
1
0
2
1
1
0
1
0
0
1
2
1
1
1
2
1
1
1
0
1
2
2
0
2
1
1
1
2
2
1
1
1
1
1
1
1
0
0
2
1
0
1
1
0
1
1
1
2
1
1
1
2
1
1
1
2
0
1
2
2
2
1
2
1
1
1
2
1
1
1
1
1
0
1
2
1
1
2
1
1
1
1
0
1
0
1
0
1
2
1
1
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
1
1
2
2
1
1
2
1
0
2
1
1
1
2
1
2
1
2
0
1
2
1
1
0
1
1
1
1
2
2
2
1
1
1
1
1
1
2
1
1
1
1
1
0
1
2
1
2
0
1
1
1
1
0
1
0
2
1
1
0
1
0
1
1
0
1
0
0
2
1
2
1
1
1
1
2
2
1
1
2
2
1
1
1
1
1
1
0
0
0
1
1
1
0
0
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
2
0
2
1
1
2
1
2
1
1
2
2
1
2
1
2
1
1
1
1
2
0
1
1
2
0
1
1
1
0
2
0
1
2
2
1
2
2
0
1
1
1
1
1
1
2
1
2
2
1
2
1
1
1
1
1
2
2
1
1
1
1
1
0
1
1
1
1
1
1
1
2
0
2
2
2
1
1
1
0
0
2
0
2
1
1
1
1
1
1
2
1
0
1
2
2
1
0
1
2
1
2
1
1
1
1
1
0
0
1
0
2
0
0
2
1
2
1
1
0
1
0
0
1
1
2
1
1
1
1
1
0
2
2
0
2
0
1
0
0
1
1
1
2
1
0
1
1
1
1
2
2
1
2
1
0
1
2
1
1
0
0
1
1
1
0
2
2
0
2
1
1
1
2
1
1
1
1
0
1
0
2
1
1
1
2
1
1
2
1
2
1
0
1
1
1
0
1
1
1
1
1
0
1
1
1
1
2
1
2
1
1
1
1
2
1
1
1
2
1
1
1
1
2
2
1
2
2
0
1
1
1
1
0
1
1
1
1
1
2
1
1
2
1
1
2
2
1
3
1
1
1
1
1
1
2
1
1
1
1
0
1
1
1
2
1
1
1
2
1
1
1
0
1
0
1
2
1
2
0
1
1
1
1
1
2
1
1
1
1
1
1
0
1
1
2
2
2
0
0
1
0
1
0
1
0
1
1
1
1
1
0
1
1
2
1
2
1
2
1
1
1
2
1
1
2
1
1
2
1
2
2
2
0
2
1
2
1
2
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
0
1
0
2
1
2
1
1
1
2
2
0
1
2
1
1
2
1
2
1
1
2
1
1
2
2
1
1
0
0
1
0
1
1
0
2
1
1
1
1
2
1
2
1
1
1
1
1
1
2
2
1
0
1
3
2
1
1
0
0
1
1
1
0
2
2
0
1
1
1
1
1
1
1
1
0
2
2
1
3
1
0
1
2
0
1
1
1
2
0
2
0
1
2
1
2
2
1
0
1
0
1
1
1
1
2
2
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
0
2
2
1
1
2
1
0
0
0
1
1
2
1
2
1
1
1
0
0
1
1
1
3
2
1
1
0
1
1
2
1
1
1
1
1
1
2
1
1
0
1
1
2
0
2
1
1
1
2
0
1
1
0
0
1
0
1
0
2
1
1
1
2
1
0
2
1
1
0
1
2
0
0
1
0
1
1
0
1
1
1
2
1
1
0
1
1
1
2
2
0
2
1
2
1
2
0
2
2
1
2
1
0
1
2
1
1
2
1
1
2
1
0
2
1
0
1
0
1
2
1
1
2
1
1
2
1
0
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
1
2
1
1
1
2
1
1
0
1
0
2
2
1
0
1
1
1
2
1
1
0
1
1
1
1
1
1
1
1
1
2
2
2
1
1
2
1
1
1
1
1
2
2
1
2
2
1
1
0
1
2
0
2
1
2
1
0
1
2
1
1
1
1
1
1
1
1
0
1
2
1
1
1
1
2
1
1
1
2
1
1
1
2
1
2
1
1
1
2
2
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
2
2
0
1
1
1
2
1
0
1
1
0
1
3
1
0
2
2
2
1
1
2
1
1
1
1
2
1
2
1
0
1
1
0
1
1
1
2
0
2
1
2
1
0
1
1
2
1
1
2
1
1
1
1
1
2
1
1
1
3
0
1
1
2
1
1
1
1
1
1
0
1
2
2
0
1
0
2
1
2
1
1
2
0
1
0
1
1
2
0
1
1
0
1
1
0
1
1
2
1
1
1
2
0
1
2
1
1
2
0
2
1
0
2
1
0
0
2
1
1
1
1
1
0
2
1
1
2
1
2
2
1
1
2
2
0
3
1
1
1
1
1
0
1
0
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
0
1
2
2
1
1
1
1
2
1
1
2
2
2
1
2
1
2
1
1
1
0
2
2
1
0
1
1
2
1
1
1
2
0
2
2
1
2
0
2
1
0
1
1
1
2
2
1
1
1
2
2
1
1
1
2
3
1
1
1
1
1
2
1
1
0
1
1
1
1
1
0
1
1
1
1
0
1
1
2
1
1
2
2
1
2
0
1
0
0
2
1
1
1
1
2
1
1
1
2
2
1
1
0
1
2
1
1
1
1
0
1
1
1
1
1
0
1
2
1
2
1
1
0
1
1
1
1
1
1
1
1
1
1
2
1
0
1
1
1
2
1
1
2
2
1
1
1
0
1
1
1
1
1
1
1
1
2
2
1
1
1
1
0
1
1
1
2
1
1
0
1
2
1
2
2
0
1
1
0
1
1
1
1
1
0
1
0
1
2
1
2
1
1
0
2
1
1
1
1
0
1
0
2
2
1
2
1
1
1
2
0
0
1
1
0
1
1
1
1
1
1
2
1
0
1
1
1
1
2
2
1
1
0
1
1
2
0
1
1
0
1
2
1
2
1
2
1
1
1
0
0
2
2
2
1
0
2
1
1
2
1
1
2
1
2
1
1
2
1
1
1
0
1
1
1
1
1
2
2
2
2
1
2
2
2
1
2
2
2
1
1
1
2
1
1
0
1
1
0
0
1
0
1
1
2
1
1
1
0
1
1
1
0
1
1
1
1
1
2
1
1
2
1
1
1
2
1
2
0
1
0
1
0
1
1
1
2
0
1
0
2
2
2
1
1
2
1
2
0
2
1
1
1
1
1
1
1
1
2
0
1
2
1
0
1
1
0
1
0
1
1
1
1
1
1
2
1
0
0
1
1
1
1
2
1
2
1
2
1
2
1
2
2
0
1
2
2
2
0
2
1
2
0
0
1
1
1
2
0
1
1
0
1
2
2
0
2
2
2
1
2
1
1
1
2
2
1
1
0
1
1
1
1
1
1
1
1
0
0
0
0
0
1
0
1
0
1
1
1
1
2
2
2
1
1
1
2
0
1
1
0
1
1
2
0
1
0
2
1
1
1
1
1
2
0
2
0
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
0
1
1
1
1
1
2
2
0
2
0
1
1
1
2
1
1
1
0
2
1
1
2
0
1
0
2
1
0
1
2
1
1
1
2
1
1
2
1
0
1
1
0
1
1
0
1
1
1
1
0
1
1
1
1
2
1
2
1
1
1
2
2
1
1
1
2
0
0
1
1
3
1
0
2
0
2
2
1
1
1
2
2
0
1
2
1
1
1
2
2
2
2
1
1
1
2
1
1
1
1
0
1
1
1
1
0
1
0
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
2
1
1
2
1
1
2
1
1
2
0
0
0
1
1
1
1
0
1
1
1
0
1
1
1
2
1
1
2
2
0
1
0
1
1
1
1
1
2
2
1
1
1
1
1
1
2
2
2
1
1
1
2
0
1
1
1
0
1
1
1
1
1
1
1
0
1
1
2
1
1
2
1
1
2
1
2
0
1
0
2
0
2
1
0
0
1
0
2
0
1
1
1
1
1
1
1
0
2
1
2
1
2
1
1
2
1
1
1
0
2
2
1
1
2
2
2
0
3
1
2
1
1
0
1
2
1
0
2
0
1
1
2
2
0
1
1
1
2
0
2
2
0
2
2
0
1
0
1
1
1
2
1
1
2
0
1
1
1
1
1
1
1
0
1
0
1
0
1
2
1
2
1
2
1
1
1
0
1
1
0
0
2
1
2
1
1
1
1
1
2
0
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
2
2
1
0
1
1
1
2
1
2
1
1
1
0
1
1
1
0
1
0
1
1
1
2
1
1
1
0
0
1
1
1
1
1
0
0
1
0
2
1
0
1
2
0
1
0
1
0
1
1
1
0
1
2
0
2
1
1
1
2
1
2
1
2
2
1
1
1
1
1
1
1
2
1
1
1
2
1
0
1
2
1
2
0
0
1
1
0
2
1
1
2
0
1
2
1
0
2
1
1
1
1
0
1
2
1
1
2
1
1
1
1
0
1
1
1
1
2
0
0
1
2
1
1
2
1
3
0
1
0
0
1
1
1
2
1
2
1
1
1
0
1
2
1
1
1
0
1
1
1
0
1
2
0
1
2
2
1
2
2
1
1
1
1
0
2
2
1
2
1
0
1
0
2
1
2
2
1
1
2
1
0
2
0
1
1
1
0
1
2
1
2
1
1
2
2
0
1
1
1
1
0
2
1
2
2
2
1
0
1
1
1
1
1
2
1
1
0
1
1
1
1
2
0
2
1
2
1
2
1
1
1
2
1
1
2
1
1
2
1
2
1
0
1
1
2
1
1
0
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
0
1
1
2
2
1
0
0
1
1
0
1
1
1
1
0
1
0
2
1
2
1
1
0
2
2
1
0
1
1
1
1
1
1
1
1
1
0
0
1
0
1
1
1
1
1
1
1
1
2
1
1
1
1
0
2
1
2
1
1
2
1
2
1
2
1
2
1
1
1
1
1
1
2
1
1
2
1
2
2
2
1
0
1
1
1
1
2
1
1
1
1
1
1
3
2
1
2
1
0
2
2
2
2
2
2
1
0
0
2
0
2
0
2
0
2
1
1
1
1
0
0
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
0
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
2
1
0
1
0
1
1
1
1
1
1
1
0
0
1
2
1
1
1
1
2
2
1
1
1
1
2
2
1
1
0
1
1
1
1
1
1
1
1
1
0
1
2
1
2
1
1
1
2
1
1
2
2
2
1
1
1
0
1
1
2
2
1
1
1
0
0
1
1
2
2
2
1
1
2
2
0
2
1
1
1
1
1
2
1
1
1
1
2
1
2
1
1
2
1
2
1
2
2
2
0
1
1
1
1
1
0
1
2
1
2
1
1
2
1
1
1
2
1
1
1
0
1
1
1
1
2
1
1
2
0
2
1
1
1
1
0
1
0
1
0
1
1
1
2
1
2
0
2
0
1
2
1
2
1
2
0
1
2
2
0
0
2
1
3
2
2
0
2
1
1
2
1
2
1
1
2
2
3
1
2
2
1
1
2
1
2
1
1
1
2
1
0
0
1
0
2
1
2
1
0
1
3
1
2
2
1
1
1
1
1
1
2
1
0
1
1
1
2
1
1
1
2
0
0
2
2
2
1
2
2
1
0
1
1
1
2
1
2
2
0
1
1
1
1
1
1
1
1
2
1
2
2
0
2
1
1
0
1
0
1
1
1
1
1
2
1
1
2
2
0
1
1
0
1
2
1
1
1
2
1
1
2
1
2
1
1
1
2
0
1
1
2
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
2
0
0
1
1
1
1
1
1
2
2
1
2
1
1
2
1
2
2
0
1
2
1
1
2
1
1
1
2
1
2
4
1
2
1
1
0
1
1
2
1
1
1
2
0
1
0
1
1
1
1
2
2
1
1
1
2
1
1
0
1
2
2
1
1
1
0
2
1
2
2
0
1
1
1
2
2
2
1
1
2
1
2
2
0
1
1
0
2
0
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
0
0
1
2
1
1
1
1
1
1
0
1
1
1
1
2
0
1
0
1
1
1
1
0
0
0
1
2
1
0
1
2
1
1
1
1
1
0
1
2
2
1
2
1
1
1
2
1
1
2
1
0
2
1
1
1
1
2
0
2
2
1
2
1
2
1
2
2
1
0
1
0
0
1
1
1
2
1
0
2
1
1
0
1
1
1
1
2
1
0
1
1
2
1
1
0
1
1
1
2
1
1
1
1
1
1
2
0
2
1
0
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
0
0
1
1
1
2
2
2
1
0
1
0
1
0
1
1
2
1
1
1
2
1
2
1
2
2
2
1
1
2
1
1
1
1
1
1
2
1
1
1
0
1
0
2
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
2
2
1
2
1
1
0
1
2
0
2
2
1
1
0
1
1
2
1
0
1
1
0
1
1
1
1
2
2
1
0
0
1
1
1
2
1
0
1
1
0
1
1
2
1
1
2
1
1
1
2
3
1
0
1
2
1
0
1
1
1
0
1
1
1
1
2
0
0
1
1
0
0
1
0
0
1
1
0
1
0
2
1
1
2
0
1
1
1
1
1
1
1
1
1
1
1
1
1
0
2
1
1
1
1
2
1
2
1
1
1
2
0
1
2
1
1
1
2
0
1
1
2
0
1
2
2
1
1
2
2
1
1
0
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
0
1
1
0
0
1
1
1
2
2
1
0
2
1
1
2
2
1
1
2
0
1
1
1
2
1
2
1
1
2
1
0
0
1
2
2
2
1
1
2
1
1
1
0
1
1
1
0
1
0
2
2
2
0
0
1
2
1
1
1
1
2
1
2
1
2
1
2
0
2
1
2
0
1
1
0
1
1
2
1
1
0
0
1
2
2
4
1
1
1
3
2
0
2
2
1
1
2
1
2
0
2
1
2
2
2
1
0
1
0
2
1
2
1
1
1
1
3
1
1
1
0
0
2
2
1
1
2
1
1
2
1
2
0
0
2
1
2
1
2
1
1
1
1
2
2
2
2
1
2
2
2
2
1
1
1
0
2
1
1
1
1
1
2
0
1
1
2
1
1
1
1
1
1
2
2
1
0
1
1
1
1
1
2
2
1
1
2
1
0
2
2
1
1
1
1
1
1
0
2
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
2
2
2
1
1
1
1
1
1
0
1
1
0
1
2
1
2
1
0
0
2
1
1
0
1
1
1
1
2
3
2
1
0
1
1
2
2
1
1
0
0
1
1
1
1
1
1
1
0
1
1
1
1
1
0
1
1
2
1
1
1
2
1
1
1
2
1
0
0
1
2
0
1
0
1
1
1
1
0
1
2
2
2
1
0
0
1
1
1
1
2
2
2
1
1
2
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
2
1
1
0
1
1
1
1
2
1
2
0
1
1
2
1
2
1
0
1
2
1
0
1
1
1
1
1
2
1
1
1
0
0
1
1
1
2
2
2
1
1
0
1
1
1
1
1
1
0
1
2
2
0
1
2
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
0
2
1
1
2
2
1
1
1
1
2
1
1
1
2
0
0
0
1
1
1
1
2
1
0
1
1
1
1
1
1
2
2
2
1
1
1
1
1
2
1
1
0
1
0
0
2
1
2
1
2
1
2
1
1
2
2
1
1
1
1
1
2
2
1
1
2
1
1
0
1
1
0
2
1
1
1
1
1
0
2
1
1
2
1
1
0
2
1
1
1
1
1
1
0
2
1
1
2
1
2
1
1
1
2
0
0
2
1
2
0
1
1
1
0
1
0
1
2
2
2
1
0
0
2
2
1
2
1
1
1
2
2
1
1
1
2
1
2
1
1
1
2
1
3
1
1
0
1
2
1
1
2
1
2
0
1
1
2
0
1
0
0
1
0
2
2
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
0
1
2
1
1
1
1
4
1
1
0
0
1
1
1
2
2
1
1
1
1
0
2
1
1
2
1
1
2
1
1
1
2
2
1
1
2
2
1
0
1
0
1
3
0
1
1
2
0
1
1
1
1
1
1
1
1
0
1
1
1
0
1
1
1
2
1
1
1
1
1
2
1
2
1
0
1
1
1
1
1
2
1
2
1
1
1
1
0
1
1
2
2
1
1
2
1
1
1
2
0
2
1
1
1
2
2
2
1
0
2
1
0
2
1
2
1
1
2
1
1
1
1
1
1
2
1
1
2
0
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
2
2
2
1
2
2
1
1
1
1
1
1
0
2
1
1
2
1
1
1
1
1
0
1
1
2
2
2
1
1
1
1
1
0
2
2
2
1
1
1
1
2
0
1
2
2
1
1
2
2
1
2
2
1
2
1
1
2
1
1
1
1
1
1
2
0
0
0
1
1
1
0
1
1
1
1
1
1
1
1
2
2
1
1
0
1
1
1
2
1
2
1
1
1
0
1
1
1
0
2
1
1
1
1
1
2
1
2
2
1
2
1
2
1
2
0
1
1
1
2
0
1
1
2
0
1
1
2
1
1
1
2
0
1
1
1
1
0
1
1
2
1
2
1
1
1
3
0
0
2
2
0
1
1
2
2
1
1
2
2
1
1
1
0
1
1
0
1
1
0
1
2
1
1
1
1
0
2
0
0
1
2
1
2
1
2
1
1
0
1
2
1
1
1
2
1
1
1
0
1
0
2
0
1
1
2
2
2
1
1
0
1
1
1
1
1
1
0
2
2
2
2
1
0
1
0
1
1
1
1
1
1
2
1
2
2
1
1
2
1
1
0
1
1
1
0
2
1
2
1
1
1
1
1
1
1
2
1
2
2
0
1
1
1
1
1
1
1
1
1
0
1
0
1
0
1
1
2
2
2
2
2
1
1
2
0
1
1
1
2
1
2
1
1
1
1
2
2
1
1
1
0
1
0
1
1
2
1
2
2
0
0
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
2
2
1
0
1
2
0
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
0
1
1
2
2
1
1
1
0
0
1
0
1
1
1
1
1
1
1
1
1
0
1
0
1
0
1
1
1
1
2
1
0
2
1
2
0
1
1
1
2
2
0
1
1
2
1
0
2
1
1
0
1
2
1
1
1
0
1
1
1
1
2
0
1
1
1
0
1
1
1
2
0
1
1
0
1
2
1
2
2
1
0
0
0
1
1
2
1
1
0
0
1
0
1
1
0
1
0
1
1
1
0
3
1
0
1
1
1
1
1
0
1
0
1
1
0
0
1
1
1
1
2
0
1
1
0
1
1
1
1
1
1
3
2
1
2
1
1
1
1
2
2
0
1
2
0
2
0
2
1
2
1
0
0
2
1
1
1
1
2
0
0
0
1
1
2
1
0
1
1
2
1
0
2
1
2
1
0
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
3
1
2
1
1
1
1
1
1
2
1
0
1
1
1
0
2
1
0
1
1
1
1
1
0
1
0
1
1
1
1
1
1
2
0
1
2
2
2
1
1
1
2
1
2
1
1
1
0
1
0
1
2
1
2
1
1
1
1
1
1
2
2
1
2
2
2
1
2
2
2
0
1
1
1
1
0
2
1
0
1
0
1
1
0
1
1
1
1
2
2
1
1
1
2
1
1
0
1
2
0
1
1
1
1
2
1
1
2
0
2
2
2
1
2
1
2
1
1
1
0
1
2
1
2
1
1
1
1
1
2
1
0
1
1
0
1
1
2
1
1
1
1
1
1
1
1
2
2
2
1
1
0
1
2
1
1
1
1
1
0
2
1
1
2
1
2
1
1
1
1
0
0
2
1
1
2
1
1
1
1
1
1
0
2
1
1
1
1
1
1
1
1
0
2
1
2
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
2
0
1
1
1
1
0
1
1
1
0
2
2
1
1
1
1
1
0
1
1
1
1
2
1
2
2
1
2
1
1
1
2
1
2
0
2
2
1
2
1
1
0
2
1
0
2
1
1
1
1
1
0
1
0
1
2
1
1
1
1
2
1
1
1
0
2
0
1
1
1
1
1
1
0
1
0
0
1
1
0
1
0
1
1
1
0
1
1
1
1
2
1
1
2
1
0
0
1
1
1
2
1
1
2
0
1
1
2
2
2
1
2
0
2
1
1
2
1
1
1
1
2
0
2
1
1
2
1
1
1
0
1
1
0
1
1
2
2
1
1
1
2
1
0
1
2
1
1
0
1
2
2
2
1
2
0
1
1
2
0
1
1
1
1
0
1
2
2
1
2
2
1
1
1
1
1
1
0
1
1
2
1
2
0
0
2
1
2
2
1
1
0
3
0
2
1
1
1
0
0
1
2
1
1
1
0
1
1
2
2
1
1
2
0
1
2
2
1
1
2
1
2
2
0
2
1
1
1
2
1
2
0
2
1
1
1
1
1
2
2
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
0
2
0
2
1
2
2
1
1
1
0
1
0
1
0
2
2
1
1
2
0
1
1
1
1
2
2
1
0
1
2
2
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
2
2
2
1
0
2
1
1
0
2
1
2
1
0
0
1
2
2
1
0
1
2
1
2
1
1
0
2
1
1
1
1
1
1
2
1
1
1
0
2
2
1
1
0
3
1
0
1
1
1
1
1
1
1
1
2
2
0
2
1
1
2
0
1
3
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
2
0
2
2
1
2
1
2
1
2
1
2
1
1
1
1
1
1
2
1
0
1
2
0
0
1
0
1
1
1
2
1
2
2
1
2
0
1
1
1
1
1
1
0
1
1
1
2
1
0
1
1
0
1
0
1
1
2
1
2
1
2
1
1
1
0
2
0
1
1
2
1
1
1
2
1
1
1
0
2
2
1
2
0
1
1
0
2
2
0
1
1
1
1
1
2
2
0
1
1
1
0
2
2
1
1
1
0
1
2
1
1
1
2
2
1
2
0
1
2
1
0
3
0
1
1
2
1
1
2
2
1
0
2
1
0
1
1
1
0
1
1
1
2
1
2
1
2
2
1
1
0
1
1
2
2
2
1
2
1
1
2
1
1
2
1
2
2
1
2
1
0
0
0
1
1
1
1
1
1
1
1
1
0
2
0
0
1
0
1
1
0
1
1
0
2
0
0
1
1
1
1
1
2
2
1
5
1
2
1
1
1
1
2
2
0
1
1
1
1
1
1
2
1
0
0
1
1
1
2
1
0
1
0
1
2
1
1
1
2
1
1
2
0
2
2
1
1
1
2
1
1
1
2
2
1
2
2
1
1
1
1
1
1
1
0
1
2
3
2
2
1
1
1
2
1
1
1
1
1
0
0
1
1
1
1
0
1
0
1
1
0
0
1
2
1
0
1
2
1
1
2
1
0
1
0
1
1
0
1
1
3
0
2
6
2
2
1
1
2
1
3
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
0
2
0
1
2
1
2
1
1
2
0
1
1
1
1
1
1
2
1
0
1
1
2
1
1
2
1
2
1
1
1
0
1
2
1
2
1
1
0
1
0
2
0
1
2
1
1
2
2
1
1
2
0
2
1
0
2
2
2
1
1
1
1
1
1
2
1
1
1
2
2
1
2
1
1
2
1
1
1
1
0
0
1
1
1
2
2
2
1
2
1
1
2
2
1
1
1
0
1
1
1
2
0
0
1
1
1
1
1
1
1
1
2
2
1
0
1
1
0
2
1
2
2
1
1
1
0
1
1
1
0
1
0
1
2
2
1
1
1
1
1
1
1
1
2
1
1
0
2
1
1
1
1
1
2
0
1
2
1
2
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
1
2
0
0
1
1
1
2
1
0
1
1
1
1
2
1
1
1
2
1
2
1
1
1
2
2
1
1
1
2
2
0
2
1
1
1
1
1
1
1
0
1
0
0
2
0
2
1
1
1
0
1
0
2
2
0
1
1
1
0
1
1
1
1
1
1
0
1
1
1
0
1
1
0
1
1
2
1
1
2
0
1
2
1
1
1
1
2
1
1
1
1
0
2
0
1
2
1
1
1
1
0
1
1
0
1
1
1
1
1
1
0
2
0
2
1
2
2
1
2
1
1
2
1
1
1
1
1
0
2
3
1
1
0
0
2
1
2
1
1
2
1
2
1
1
1
2
0
1
1
2
1
0
1
1
1
1
1
0
0
2
1
1
1
1
1
1
1
2
2
1
1
1
1
2
0
0
2
0
1
1
1
2
2
1
1
1
1
2
1
2
2
1
1
2
2
2
2
0
1
0
2
2
1
1
1
1
2
0
1
1
1
1
2
3
1
0
2
1
1
1
2
1
1
2
2
2
1
0
1
2
1
2
2
1
2
1
1
0
2
1
1
1
1
1
1
0
0
1
1
0
2
1
1
1
1
2
1
2
0
0
1
2
1
1
2
1
0
1
2
1
1
2
1
1
1
2
0
1
1
2
0
0
0
1
2
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
2
1
1
1
0
1
2
1
1
1
1
1
2
2
2
1
2
1
2
2
1
1
1
1
1
0
2
1
1
1
2
1
2
2
1
1
1
1
1
0
2
1
1
2
1
1
2
1
1
1
1
1
1
1
2
2
0
1
1
0
1
1
1
1
1
1
2
1
1
0
1
1
2
1
1
1
1
1
2
1
0
1
1
0
2
1
1
1
2
2
1
1
1
1
3
0
1
1
2
2
1
1
1
1
1
0
1
1
2
2
2
1
2
0
1
2
2
1
1
1
1
1
2
2
1
1
1
1
1
0
1
2
5
1
1
1
1
1
1
2
2
3
1
1
1
0
1
2
1
1
1
2
1
1
1
1
2
2
2
1
1
2
2
0
0
3
2
1
1
1
1
2
2
1
0
1
2
1
1
0
2
1
1
1
1
1
0
2
1
1
1
0
1
1
1
2
3
0
2
1
1
1
2
1
1
2
1
2
0
2
1
0
2
1
1
1
1
2
2
0
1
1
2
2
2
1
2
1
1
0
1
1
1
2
1
2
0
1
1
1
1
2
1
2
1
0
1
1
2
2
1
3
2
1
2
0
1
1
0
2
2
1
0
3
2
1
1
2
1
1
0
2
2
1
1
0
0
2
1
1
1
0
2
0
0
1
1
1
1
2
1
0
2
1
1
2
1
1
2
1
1
1
1
2
1
1
1
1
1
1
0
0
2
2
1
0
1
1
2
1
0
1
1
2
1
2
1
1
2
1
2
1
0
0
1
1
1
1
1
1
1
1
2
0
1
2
3
0
1
0
1
2
2
1
1
2
1
0
1
1
1
2
1
1
0
1
0
0
1
1
1
1
1
0
1
0
1
1
1
1
2
1
1
1
1
0
0
1
0
1
1
1
0
1
2
1
2
1
1
1
1
1
1
1
1
1
2
0
1
1
1
1
2
0
2
1
1
3
1
1
0
1
0
0
0
1
2
1
2
1
2
1
2
1
1
2
0
1
1
1
1
1
2
1
2
0
3
1
2
1
1
2
2
2
2
0
1
1
1
1
2
2
1
0
1
0
1
0
2
1
1
1
0
0
2
1
0
0
1
1
1
0
0
1
1
2
1
1
1
1
1
2
1
1
1
2
1
2
1
1
0
2
2
1
1
1
2
0
2
1
1
1
1
1
2
1
1
0
1
0
1
0
3
1
1
1
0
2
1
2
2
1
1
1
1
1
0
0
2
1
1
1
1
1
1
2
2
0
2
1
1
0
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
2
1
1
1
1
1
1
1
0
2
1
1
1
2
3
1
1
1
1
1
2
1
0
1
0
0
2
1
0
1
1
0
2
1
1
0
1
1
2
1
1
1
1
1
1
1
1
1
2
1
2
6
1
1
1
1
1
2
1
1
2
1
0
1
1
1
2
1
0
1
1
2
1
2
0
1
3
1
1
0
2
2
1
1
2
1
1
1
1
0
0
1
0
2
1
1
2
1
1
1
2
0
1
1
1
1
1
2
2
1
1
2
1
1
1
1
2
1
0
1
1
2
2
1
1
1
1
2
1
0
2
0
1
1
1
0
1
1
1
2
1
2
1
1
0
1
0
0
0
1
1
1
0
1
2
1
1
2
2
0
0
1
2
0
1
1
0
0
3
1
2
1
1
1
2
1
2
1
2
1
1
1
2
1
1
2
0
1
1
1
2
2
1
0
0
2
1
1
0
1
0
0
0
1
0
1
2
0
0
1
1
2
3
1
0
1
1
1
2
1
1
1
1
0
1
1
1
1
0
1
1
1
1
3
1
1
2
2
0
1
2
2
1
1
2
0
1
0
1
1
0
1
1
1
1
1
1
1
1
1
1
1
2
1
1
3
1
1
1
1
1
1
0
2
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
2
1
1
0
1
1
1
2
1
1
1
2
0
1
2
2
1
1
2
0
0
0
2
2
2
1
2
0
2
2
1
3
1
0
1
1
2
1
1
2
1
2
1
1
1
1
0
0
0
1
2
2
1
1
2
2
1
2
1
2
0
1
2
2
1
1
1
2
1
1
1
1
2
1
1
1
1
1
2
1
0
1
2
1
1
1
0
2
0
0
0
1
0
1
1
0
2
1
1
1
1
1
0
1
2
1
1
1
1
0
1
1
2
1
1
1
2
0
0
1
1
2
0
1
1
1
1
0
2
2
2
1
1
1
1
2
1
2
1
2
0
2
1
1
1
1
0
0
0
1
1
1
1
1
1
1
1
1
2
1
0
1
1
1
0
1
1
2
2
1
0
1
1
1
2
1
2
0
2
1
2
0
0
0
0
1
1
0
1
2
2
2
1
1
0
1
1
0
2
2
1
1
0
0
2
1
1
1
1
1
1
2
1
0
1
1
0
0
1
0
1
2
1
1
0
1
1
1
1
2
2
1
2
1
0
1
2
1
3
1
1
1
1
1
0
1
2
1
1
1
1
0
0
1
1
1
2
2
1
1
1
2
2
1
2
2
1
1
1
0
2
1
1
2
0
1
0
2
1
1
0
1
1
1
1
1
1
2
0
2
1
2
1
1
1
1
1
0
1
1
1
2
0
1
1
2
1
1
1
2
1
1
0
1
2
0
1
1
1
0
2
1
1
1
1
2
2
0
0
1
2
2
1
0
2
2
1
2
0
1
0
1
2
0
0
0
1
2
2
2
2
1
1
2
1
1
1
1
2
2
1
1
1
2
1
0
1
1
1
1
2
2
1
1
3
2
1
1
2
0
2
2
0
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
2
0
1
2
1
1
2
0
0
1
1
0
2
0
0
1
0
2
1
2
2
1
1
0
1
2
0
0
0
0
0
1
2
1
1
1
2
1
1
3
1
1
1
1
1
1
0
1
2
1
2
0
1
1
1
1
1
0
1
1
1
0
1
2
2
1
0
1
1
1
1
1
0
1
3
1
1
2
1
2
1
0
1
1
0
1
1
2
1
2
2
2
0
1
1
1
1
2
1
2
0
1
1
1
2
1
1
2
0
1
1
2
2
1
1
0
1
1
1
2
1
2
1
1
0
2
1
1
1
2
2
1
0
0
0
0
1
1
1
2
1
2
1
2
1
1
1
1
0
1
1
1
1
1
2
1
1
1
1
0
0
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
0
2
2
1
0
1
1
1
1
0
1
1
1
3
0
1
1
1
1
2
2
1
1
1
0
1
2
1
1
1
4
1
1
1
2
1
1
1
1
2
2
1
2
2
1
1
2
2
1
1
1
1
1
2
0
1
0
2
1
1
2
2
1
1
2
2
2
1
2
1
2
1
2
1
1
1
1
2
1
3
1
1
2
0
2
0
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
1
2
1
1
1
1
2
1
2
0
1
1
1
2
1
1
1
1
1
1
1
1
2
2
1
2
2
2
1
2
2
2
2
1
1
1
2
1
1
0
1
1
1
0
1
0
3
1
2
1
2
1
2
1
1
2
2
1
1
1
1
2
1
0
1
2
1
2
1
2
1
2
2
1
1
0
1
1
1
1
1
0
0
1
2
1
1
1
0
1
0
2
2
1
1
2
1
2
2
2
1
1
1
1
1
0
2
1
0
1
1
2
1
1
2
0
2
2
1
1
1
1
1
2
0
2
1
1
1
0
1
1
1
1
0
1
1
1
2
1
1
0
2
2
0
1
1
2
2
0
1
2
1
0
0
1
1
1
1
1
1
1
2
1
1
1
0
2
1
1
1
0
0
1
1
2
2
2
1
1
2
1
2
2
1
0
0
1
0
1
0
2
2
1
2
1
1
1
1
0
1
2
1
0
2
2
1
0
1
2
2
1
1
1
1
1
1
1
1
0
1
1
1
0
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
0
0
2
1
1
1
1
1
0
2
3
1
1
2
1
1
1
1
2
2
0
2
2
2
0
1
1
1
1
1
2
0
1
1
1
1
1
1
1
0
2
1
2
2
2
1
2
1
1
2
2
2
1
1
1
1
1
2
2
1
1
2
1
1
1
1
1
1
2
1
0
1
0
2
1
1
1
2
1
1
1
2
1
0
1
0
1
1
1
2
1
2
2
0
1
0
2
0
1
0
2
1
1
2
1
1
1
2
1
1
1
1
1
1
2
1
1
0
1
1
1
1
1
1
1
0
2
1
1
1
1
1
1
1
1
2
1
0
1
1
1
1
1
1
1
1
2
0
1
2
1
1
1
0
0
2
2
1
1
2
0
0
2
2
0
0
1
1
2
1
1
2
1
1
1
1
1
2
2
1
1
0
1
2
1
2
1
2
0
0
1
2
1
0
1
2
1
1
1
1
2
1
1
1
2
1
2
1
2
1
2
0
1
1
0
1
2
1
0
1
1
2
1
1
0
2
2
1
1
1
1
0
1
1
2
0
1
0
1
1
1
2
1
0
1
1
1
0
0
2
1
1
0
4
1
0
0
2
2
1
1
0
2
2
1
1
1
1
1
1
1
1
1
1
2
2
0
2
1
1
2
2
1
1
1
1
1
1
2
2
1
1
2
1
1
0
2
1
1
2
1
1
2
1
0
2
2
1
1
0
2
1
0
2
0
1
1
1
2
1
1
1
1
2
1
1
1
1
1
2
1
2
0
1
1
1
1
1
1
0
1
2
2
1
2
1
1
1
0
1
1
1
0
1
2
2
1
1
1
2
1
0
1
1
0
1
1
2
1
1
2
2
1
1
1
2
1
1
1
0
0
1
1
1
1
1
1
2
0
1
2
2
3
1
1
0
1
1
2
0
1
0
2
2
0
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
1
1
0
0
1
1
1
1
1
1
0
0
1
1
1
2
2
0
1
1
1
1
1
1
1
1
1
2
2
1
1
0
0
1
0
1
0
1
1
1
1
2
2
1
1
1
1
1
1
2
1
1
2
1
0
1
1
1
0
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
0
1
2
1
1
0
1
1
1
1
2
1
1
1
1
1
3
1
0
1
2
0
2
1
1
2
1
1
1
2
2
1
2
2
1
2
2
0
2
1
1
2
0
2
1
0
2
2
1
1
2
0
0
1
1
0
2
0
0
2
2
1
2
0
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
1
0
1
2
0
1
0
0
1
1
0
1
1
1
1
0
0
2
1
0
2
1
1
0
1
2
1
2
0
1
3
0
2
0
2
2
1
1
1
0
1
1
1
2
2
2
1
2
1
2
2
1
1
2
2
1
1
1
1
0
2
2
2
2
1
1
1
0
1
2
1
0
0
1
2
0
1
2
0
1
1
1
2
1
1
1
1
2
1
1
0
1
1
2
1
2
1
1
2
2
1
2
2
2
0
1
0
1
1
0
1
1
2
1
0
1
2
1
1
1
1
2
1
1
0
1
1
1
1
2
2
1
1
2
1
1
1
2
1
1
2
1
1
1
1
2
0
1
1
2
2
1
1
1
1
0
1
1
2
2
1
0
2
0
2
1
1
1
2
1
1
2
1
1
1
1
1
1
2
2
1
0
1
1
1
1
1
1
1
1
1
1
0
0
1
1
1
0
0
1
1
0
1
1
2
2
1
1
1
2
1
2
2
1
2
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
2
0
1
1
2
1
1
0
1
1
1
2
1
2
2
2
2
2
1
2
1
1
1
0
2
1
1
0
1
1
0
1
1
1
0
1
1
2
1
1
0
1
2
2
1
0
1
2
1
1
1
1
2
1
1
1
1
0
2
2
1
1
0
1
1
0
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
0
1
1
0
0
1
1
1
1
1
2
1
1
1
1
2
1
2
1
1
0
2
1
2
0
1
2
1
2
2
2
2
1
2
1
1
0
1
2
1
1
1
0
2
1
2
1
1
1
1
0
1
1
1
1
2
1
0
1
1
1
2
1
1
1
2
1
2
1
1
2
1
1
1
3
2
1
2
1
1
1
2
1
1
1
1
1
0
2
1
3
1
1
2
2
2
1
1
1
2
0
1
2
1
1
1
1
1
1
1
2
2
1
1
0
1
1
2
2
2
1
1
0
1
1
2
0
1
1
1
1
0
1
4
1
1
0
4
0
1
1
1
1
1
1
2
1
1
0
0
1
0
2
1
1
1
1
1
1
1
0
2
1
1
1
1
0
1
1
1
1
1
2
2
0
2
1
2
0
1
2
2
0
1
2
2
1
1
1
0
1
1
2
1
0
2
1
1
4
0
1
1
2
1
1
1
1
2
2
0
1
0
2
0
0
2
1
1
2
1
2
1
1
1
1
1
1
1
0
1
2
0
1
1
1
0
0
1
0
0
2
1
0
0
1
1
1
1
2
2
1
0
1
0
0
1
1
1
1
1
1
1
0
1
2
1
1
1
1
2
1
2
1
1
1
1
0
1
0
2
1
1
2
1
1
2
1
2
1
1
2
0
1
1
1
2
0
0
1
0
1
0
1
1
1
0
1
1
1
1
2
2
1
1
1
0
0
2
0
1
1
2
2
2
1
0
1
0
0
1
2
0
1
0
2
0
1
2
1
1
1
1
1
2
2
2
2
1
2
2
1
1
1
1
1
1
1
0
0
0
0
1
0
2
1
0
1
0
2
1
1
2
1
2
1
1
1
0
1
1
1
2
1
1
1
1
1
2
2
1
2
1
0
1
1
1
1
1
1
1
0
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
0
2
1
1
1
0
0
2
1
1
1
1
2
1
1
2
1
1
1
2
1
1
1
1
0
2
1
1
1
1
2
1
2
2
2
1
1
1
1
1
0
1
1
1
1
2
1
2
1
0
1
1
2
1
1
0
0
1
0
0
2
0
1
1
1
2
1
1
2
2
2
0
1
2
2
1
1
0
2
2
1
1
1
1
0
1
2
0
1
2
1
1
2
1
2
1
2
0
0
2
0
1
1
1
1
1
1
2
2
2
0
1
1
1
2
1
1
0
2
1
2
1
0
2
1
1
2
1
1
0
1
2
1
1
2
2
0
1
1
2
1
1
1
0
1
1
2
1
1
2
1
2
2
0
1
1
1
2
0
1
2
1
2
1
2
1
0
0
2
1
1
1
1
2
1
2
1
1
1
0
1
1
1
1
1
0
4
2
1
2
0
1
0
0
1
2
2
2
2
1
1
2
2
1
1
1
1
1
1
2
2
1
1
1
1
0
1
1
3
0
1
2
2
2
1
1
1
1
2
1
1
1
1
1
0
0
1
2
0
0
1
2
2
1
1
1
0
1
1
1
1
1
1
1
1
2
1
2
0
1
1
2
2
1
1
1
1
2
1
1
1
2
0
1
1
1
1
1
2
0
2
0
2
1
1
2
1
1
1
1
1
1
1
1
2
2
0
1
1
1
1
0
0
1
1
1
2
1
1
0
1
1
1
1
0
1
0
2
1
0
1
1
0
2
1
1
1
1
1
0
0
1
1
2
1
1
1
2
1
0
1
1
1
1
2
1
2
0
2
1
1
0
1
1
1
1
1
1
2
1
1
1
1
0
2
1
1
1
1
1
1
1
1
1
1
1
0
1
1
2
2
1
1
1
1
1
0
1
2
1
1
1
2
1
1
3
2
1
1
2
1
0
1
1
1
1
2
1
1
1
0
1
1
2
1
1
1
0
1
1
1
2
1
2
1
0
1
0
1
2
1
1
1
1
1
3
2
1
1
2
2
0
2
2
2
0
0
1
1
1
1
2
1
1
1
0
1
1
1
1
1
2
0
1
1
1
2
0
0
1
1
0
2
1
2
2
2
0
1
1
1
1
2
1
1
0
1
1
1
1
1
1
1
1
2
1
1
0
2
1
1
1
1
1
1
1
1
1
1
1
1
0
1
2
1
1
0
1
0
1
1
1
0
1
1
1
1
2
0
0
0
0
1
2
0
1
1
1
1
2
1
1
1
0
0
1
1
1
1
2
1
1
2
1
2
2
2
1
1
1
1
2
2
1
1
1
1
2
1
1
2
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
0
2
1
1
2
0
1
2
1
1
1
1
1
0
1
2
1
1
2
1
0
2
2
0
1
1
1
0
1
1
2
1
2
1
1
1
2
1
1
1
1
1
2
2
2
1
2
1
1
1
1
2
2
0
2
0
1
2
0
1
1
1
2
2
1
1
1
1
1
0
2
2
1
2
1
1
1
1
2
1
1
2
1
2
2
2
1
1
1
1
1
0
1
2
0
2
1
1
1
2
1
1
1
0
2
2
1
1
0
1
1
2
1
1
1
0
1
0
1
1
1
1
1
1
1
1
0
2
0
2
0
2
0
1
1
0
2
1
0
1
1
2
0
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
0
1
1
1
1
1
2
2
1
1
1
1
1
2
0
0
2
1
0
1
2
1
1
2
1
5
2
2
1
1
3
1
0
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
0
2
2
2
1
1
2
2
0
1
1
2
2
2
2
0
1
1
2
1
1
0
1
0
1
1
0
1
2
1
2
2
2
2
1
1
1
2
1
1
2
0
1
1
0
1
0
2
2
1
1
1
1
0
1
2
1
1
2
1
2
2
2
2
1
1
1
0
1
1
1
0
2
1
1
1
1
0
1
1
1
1
0
1
1
1
0
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
2
0
1
2
2
2
2
2
1
2
1
2
1
2
0
1
2
1
1
1
1
2
1
1
2
2
0
1
1
2
1
0
1
1
1
2
1
1
1
1
1
1
2
1
1
1
0
1
1
1
2
3
1
1
2
2
1
1
2
2
1
1
1
1
2
1
1
1
1
0
1
2
2
1
1
1
2
1
2
1
2
0
0
1
0
1
2
1
1
0
0
2
2
1
1
0
1
1
1
2
1
1
1
1
1
1
1
2
2
2
1
1
1
2
0
1
2
1
2
2
1
2
1
1
1
1
2
0
1
1
1
1
2
2
2
1
1
1
0
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
2
0
1
2
2
2
2
0
1
2
0
1
0
1
2
0
2
2
2
2
1
2
1
0
2
1
0
2
1
1
2
1
2
1
0
1
2
2
2
1
1
0
0
1
1
1
2
1
1
1
2
1
2
2
0
2
0
1
1
1
1
1
2
1
2
0
1
1
1
1
2
1
2
1
1
1
0
0
0
0
1
1
1
1
2
1
2
1
0
1
1
2
1
1
2
1
2
0
1
1
2
1
2
2
1
0
1
1
1
2
0
1
1
1
0
0
1
1
1
2
2
1
1
1
1
0
2
2
1
1
1
1
1
1
1
1
0
2
1
1
1
1
1
1
2
1
1
0
1
1
1
0
1
1
1
1
1
2
1
0
1
1
1
1
1
1
2
2
2
1
2
2
0
1
1
2
0
1
4
1
3
0
1
1
0
1
1
2
1
2
0
2
0
0
1
2
1
1
1
2
1
1
1
1
2
1
2
2
2
2
2
2
1
0
0
1
1
1
1
1
1
1
2
1
1
0
1
2
1
1
2
1
1
1
2
2
1
2
2
1
2
1
2
1
1
1
1
1
2
1
0
2
1
1
0
1
2
1
2
1
1
2
0
0
1
1
0
1
1
1
1
0
1
0
1
0
1
0
0
2
2
1
2
1
1
2
1
2
1
1
1
1
0
1
1
0
2
2
1
1
2
1
1
1
3
2
1
1
2
1
0
1
1
1
1
1
1
1
1
1
1
2
2
0
2
1
1
1
1
1
2
1
0
0
2
1
2
1
1
1
1
1
2
1
0
0
1
0
1
1
1
1
1
2
0
1
1
1
1
1
0
2
0
0
1
1
1
2
1
0
1
2
1
1
2
1
1
2
2
1
2
1
1
1
1
2
0
1
0
1
1
2
0
1
1
2
1
0
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
0
1
1
0
2
1
1
1
2
2
1
2
1
1
1
1
1
0
1
0
1
1
1
1
1
2
1
0
1
1
2
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
2
0
1
1
1
1
1
2
1
2
0
1
1
1
1
2
2
1
1
1
1
2
2
1
0
1
1
1
1
1
2
1
2
1
1
1
1
0
2
1
0
2
1
1
1
0
2
1
1
2
2
2
0
1
1
1
2
2
1
1
0
1
0
1
1
0
2
1
1
1
2
1
1
2
2
1
1
1
2
1
1
1
2
1
0
0
1
1
0
1
1
1
1
2
1
1
1
1
1
1
1
2
2
0
1
0
0
2
0
2
1
1
1
0
1
1
1
1
0
0
1
1
2
0
0
2
1
1
1
1
0
1
1
1
2
1
2
1
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
2
2
2
1
2
1
2
1
1
1
1
2
2
1
0
0
1
0
1
1
1
2
0
1
1
1
2
2
1
0
1
1
2
1
1
1
0
1
1
1
1
1
1
1
2
0
2
1
1
1
0
0
1
1
1
1
0
2
2
1
2
1
1
1
2
1
1
1
1
0
1
1
1
1
1
1
1
2
2
1
2
1
1
1
1
2
1
2
1
1
2
1
2
2
1
1
0
1
1
1
1
1
0
2
1
2
2
1
2
1
1
1
1
1
2
1
2
1
1
1
1
2
2
1
1
2
2
0
0
1
2
2
2
2
1
1
1
2
1
0
0
2
1
1
1
2
1
1
2
1
0
1
1
1
2
2
2
2
2
1
2
1
1
1
2
0
0
1
1
2
2
1
1
1
0
2
1
1
1
1
1
1
1
1
1
1
0
1
0
2
0
2
1
1
2
1
2
0
0
2
2
0
0
0
0
1
0
1
1
1
1
1
2
1
0
2
1
1
1
1
1
0
1
1
1
0
0
1
1
1
2
2
2
2
1
0
1
2
1
4
2
2
1
1
2
2
0
1
1
0
1
1
1
2
1
1
1
2
1
2
1
2
1
2
1
2
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
2
0
1
0
2
1
1
0
1
1
1
1
2
0
0
1
0
1
0
1
1
0
1
1
1
2
2
1
0
0
1
0
0
1
0
1
1
2
1
1
1
1
0
1
1
0
2
1
1
1
2
2
2
1
1
2
1
2
1
1
4
0
2
1
2
0
1
0
1
1
1
3
1
2
1
2
2
1
0
1
1
1
0
1
0
0
1
2
2
1
2
1
1
0
0
1
1
1
2
1
1
1
1
1
1
0
2
0
1
1
1
1
2
0
1
2
1
1
0
2
1
1
0
1
1
1
0
2
1
0
2
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
2
1
2
1
0
2
1
0
1
1
1
0
1
0
2
0
2
2
1
0
0
2
0
2
1
1
1
1
1
1
2
1
1
1
1
0
1
2
2
0
1
1
0
0
1
0
2
0
1
1
0
1
2
1
0
2
1
0
1
1
1
1
1
1
0
2
2
0
2
1
1
1
1
1
1
1
1
1
1
0
0
2
1
0
2
1
1
1
1
2
0
2
1
1
2
1
0
1
1
0
2
1
1
0
2
1
1
1
1
1
0
1
1
1
1
0
2
1
1
0
2
1
2
1
1
2
1
0
1
1
1
2
0
2
1
0
1
1
1
2
2
1
1
0
1
2
1
1
2
2
1
1
2
1
2
1
1
1
1
1
1
2
1
1
2
2
0
1
0
2
1
0
1
1
2
1
1
1
0
2
2
1
1
1
1
1
1
0
1
1
1
1
0
1
1
2
2
1
1
1
1
1
0
1
0
2
1
0
2
1
1
1
1
2
2
1
0
1
1
2
1
1
1
0
0
1
2
2
2
2
2
0
1
1
0
2
1
1
1
1
1
0
1
1
1
1
0
1
1
2
2
0
1
2
1
1
1
1
1
1
2
2
2
1
2
2
1
0
2
0
0
2
1
2
1
1
1
0
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
0
2
1
0
1
1
2
1
0
2
0
2
1
0
2
1
2
1
1
1
2
1
0
1
1
0
1
1
0
1
1
1
2
1
1
0
2
1
2
1
2
1
1
1
1
0
1
1
1
1
1
2
1
2
1
2
1
1
2
2
3
1
1
2
1
2
1
1
1
1
1
0
1
1
0
0
2
1
1
1
1
1
0
1
0
1
1
1
1
0
1
1
1
1
2
2
0
1
1
2
2
2
2
2
1
1
1
2
2
2
1
1
1
1
2
0
1
2
1
1
1
1
1
2
1
2
0
1
1
1
1
1
1
1
2
0
0
1
1
1
1
0
1
1
0
2
1
1
2
1
2
2
1
0
1
2
1
1
1
0
0
1
1
1
0
1
1
1
2
1
1
2
1
0
2
2
2
1
1
1
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
0
1
1
1
0
1
1
2
1
2
0
1
1
0
0
1
1
1
1
0
0
1
2
1
1
1
0
2
1
2
2
1
1
1
1
2
1
1
2
1
1
1
1
2
1
2
1
0
1
1
1
2
2
2
3
2
2
0
2
1
0
1
1
1
1
1
2
0
1
0
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
2
2
1
2
1
2
2
2
1
2
1
0
1
0
1
1
0
0
1
1
1
1
2
0
1
1
1
2
0
1
0
1
1
0
1
1
1
1
1
2
2
0
1
2
1
1
1
1
0
1
1
1
1
1
1
0
1
1
1
1
0
2
1
2
1
1
0
2
2
1
1
0
1
0
1
2
1
2
1
2
1
1
1
1
1
1
1
2
0
2
3
0
1
1
2
0
2
2
1
0
1
2
1
1
1
2
1
2
1
2
1
0
1
1
2
1
2
0
1
0
1
1
1
0
0
0
1
0
2
1
1
1
1
2
1
1
1
2
1
1
2
1
1
2
0
1
1
2
1
2
1
1
1
1
1
0
1
1
2
1
1
1
1
1
0
2
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
1
1
2
2
1
0
1
2
2
2
1
1
2
1
1
1
1
1
0
2
1
0
2
2
2
1
1
0
1
1
1
1
2
2
2
1
1
1
2
1
2
1
1
1
1
1
1
2
1
2
1
1
1
2
0
0
1
2
1
1
1
1
0
2
1
1
2
1
2
0
1
2
1
2
2
1
2
1
1
2
2
1
2
2
1
1
1
2
1
1
2
1
2
2
1
1
1
1
1
0
1
1
2
2
1
1
1
1
0
1
1
1
0
2
1
0
1
2
1
1
1
2
2
2
2
2
1
0
3
1
2
2
1
2
1
1
1
2
1
0
1
2
2
2
1
1
0
0
1
1
1
1
2
1
0
1
1
1
2
2
1
0
2
1
2
1
1
2
1
2
1
1
1
1
1
2
1
2
1
0
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
0
2
0
1
1
2
2
1
2
1
0
1
1
1
1
1
1
1
0
2
1
2
1
1
1
1
1
1
1
1
0
1
1
1
2
0
0
1
1
1
2
1
0
1
1
0
1
2
0
2
2
1
2
2
1
1
1
1
1
0
2
1
1
1
2
2
2
2
0
2
2
1
0
1
1
1
2
1
1
1
1
2
1
1
2
1
1
2
0
2
0
1
1
2
0
1
1
1
2
2
1
1
2
0
1
1
1
1
1
0
1
1
1
2
1
1
1
1
1
2
1
1
2
1
1
1
1
1
2
0
1
2
1
1
2
1
1
0
2
2
1
1
1
2
1
2
2
1
1
1
1
2
1
1
0
1
0
0
1
2
1
0
0
1
1
0
1
0
1
1
1
1
2
1
1
1
2
0
1
1
1
2
1
2
2
2
2
1
1
1
2
1
1
1
1
0
1
1
1
2
1
1
1
0
1
1
1
0
2
1
1
1
2
1
1
2
1
2
1
0
1
1
1
1
2
2
0
1
1
1
1
1
2
1
1
1
1
4
1
1
2
1
1
1
1
0
1
1
1
0
1
2
1
1
1
2
2
1
2
1
2
2
1
2
0
0
3
0
2
1
5
1
2
1
1
1
0
1
1
1
0
1
1
1
2
1
1
1
1
1
1
1
1
0
1
0
1
2
1
1
0
1
1
1
2
1
2
1
1
2
2
0
1
0
0
1
1
2
1
1
1
1
0
1
1
1
1
1
1
1
1
1
2
1
0
1
1
1
1
2
2
1
1
2
0
1
0
1
2
0
0
0
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
0
2
1
1
2
0
2
1
1
0
2
2
1
0
2
2
1
1
1
1
1
2
2
1
1
1
1
2
2
1
1
2
3
1
0
1
2
1
1
1
2
1
0
2
2
2
1
1
1
2
1
1
1
2
0
1
1
1
1
3
1
1
1
1
1
1
1
1
1
1
1
2
1
3
0
1
1
2
2
1
1
1
1
1
2
1
0
2
1
2
1
1
1
1
1
2
3
1
0
1
2
1
2
1
1
2
1
1
1
2
1
2
2
1
0
2
1
1
2
1
1
1
1
1
0
1
1
2
1
0
1
1
1
1
1
1
1
1
1
1
2
1
1
0
1
1
0
2
1
2
0
1
1
1
2
0
1
1
2
1
1
1
2
1
1
2
0
1
0
1
1
1
1
2
1
1
1
0
1
1
1
2
2
2
0
1
1
1
1
1
0
1
0
1
1
1
0
1
2
0
2
0
1
1
2
0
1
1
2
2
1
2
1
1
1
1
1
1
2
0
2
2
1
2
2
2
1
2
2
1
1
1
1
1
2
2
1
1
0
1
1
2
1
1
0
1
0
1
2
0
1
1
1
1
1
1
0
0
1
1
0
1
2
1
2
1
1
1
0
1
1
1
1
1
2
2
1
1
1
2
1
1
2
2
0
2
1
1
2
1
2
2
2
0
1
1
2
1
0
0
2
2
1
0
0
0
1
2
1
1
0
0
2
1
2
1
0
2
1
1
1
2
2
2
1
2
1
1
3
1
2
0
1
2
2
1
1
1
1
1
1
0
1
2
2
1
1
1
2
5
1
1
2
1
2
2
0
1
1
2
1
1
1
1
3
1
2
1
0
2
2
0
1
2
1
2
1
1
1
1
2
1
1
2
2
1
0
0
1
1
2
0
1
2
1
2
1
2
1
1
1
1
1
1
1
1
0
1
1
0
1
0
2
1
0
1
1
1
2
0
1
1
1
2
2
1
1
1
1
1
1
2
2
1
2
2
1
0
2
2
1
2
1
2
1
1
1
2
2
1
2
1
0
0
1
0
2
1
2
1
1
1
2
0
2
1
1
1
1
1
0
1
2
1
1
1
1
0
0
1
2
2
0
0
1
2
1
1
2
2
0
0
1
1
0
2
1
1
0
0
1
1
1
2
1
1
1
2
0
0
2
1
1
0
1
1
1
0
1
1
2
1
1
1
0
1
2
1
1
2
2
2
0
1
1
0
1
2
2
0
1
2
1
0
1
2
1
1
1
1
1
1
2
1
1
0
1
2
2
1
0
2
1
1
1
1
0
1
0
1
1
0
1
1
2
1
1
0
1
1
1
0
1
0
2
1
1
1
1
2
1
0
1
1
1
2
1
0
2
2
1
1
2
1
1
3
2
2
1
1
1
1
1
1
1
0
4
1
1
2
2
2
1
1
0
0
1
2
1
2
0
2
2
0
2
1
3
1
1
2
2
2
0
1
2
2
2
1
1
1
1
2
0
0
0
0
1
1
1
1
1
0
2
0
1
1
1
1
1
2
1
1
1
0
2
2
0
1
2
0
1
2
1
1
1
1
0
1
2
0
1
1
0
1
2
2
1
1
1
1
4
2
2
2
1
1
1
1
1
2
0
1
2
1
1
2
1
1
1
2
2
1
1
1
1
2
1
2
0
1
1
2
1
1
1
0
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
2
1
3
2
0
2
0
2
0
1
1
2
2
1
1
1
1
1
2
1
1
2
1
2
0
1
1
1
1
1
2
1
1
2
1
1
2
1
2
0
2
1
1
2
0
1
2
1
1
0
1
1
1
1
1
1
1
2
1
2
0
1
1
1
0
1
0
1
2
0
1
0
2
1
0
2
2
1
1
1
1
1
1
0
1
1
0
2
1
1
1
1
1
1
0
2
1
1
1
1
2
1
1
2
1
0
1
1
1
1
2
1
0
1
2
2
2
1
1
1
1
1
0
2
1
2
2
1
1
1
1
2
1
2
1
1
2
1
1
2
1
1
0
2
1
1
1
1
0
1
2
1
1
1
2
2
0
1
1
1
2
1
1
2
1
1
2
2
0
1
1
2
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
0
2
1
1
1
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
0
2
1
1
2
1
1
1
2
1
1
1
0
2
0
0
1
1
0
0
1
1
1
1
1
0
1
1
1
2
1
2
2
0
1
0
1
1
2
1
1
2
1
2
1
1
0
1
1
1
1
2
1
1
1
1
0
2
2
1
2
1
1
1
0
1
1
1
2
1
0
2
1
1
1
0
1
2
0
1
1
1
1
2
1
2
2
1
0
1
1
2
2
1
1
1
1
0
2
1
1
1
1
1
1
1
1
1
0
2
2
1
1
1
2
0
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
0
1
1
0
1
1
1
0
0
1
0
1
1
2
2
1
2
1
1
1
2
0
1
2
1
1
1
2
1
1
1
2
1
2
1
1
0
2
1
2
2
1
1
1
1
1
1
1
1
2
2
0
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
0
0
2
1
1
1
2
1
2
1
0
1
0
0
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
3
0
1
2
1
0
1
2
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
2
1
1
2
0
1
0
1
1
0
1
0
2
0
2
2
2
1
1
2
1
0
1
0
1
0
2
1
2
1
1
2
1
1
0
2
0
1
2
1
1
0
2
1
2
1
1
2
2
1
2
2
2
1
1
2
1
1
2
2
2
2
1
1
2
1
1
1
1
1
1
0
2
1
1
2
1
2
1
1
0
1
2
1
0
2
1
1
1
1
1
2
2
1
0
2
2
1
3
1
1
1
1
1
0
2
1
2
1
2
1
1
1
1
1
1
0
1
1
1
1
1
0
1
1
1
1
1
2
2
1
1
0
1
1
1
1
0
1
2
2
0
1
0
0
1
2
0
1
1
1
1
1
1
1
1
1
2
2
1
1
1
0
0
1
0
1
2
1
2
2
1
0
1
1
1
1
1
1
0
2
2
0
1
1
1
1
2
1
2
2
1
0
0
1
0
1
1
1
1
1
0
2
2
1
1
1
1
1
0
2
2
1
1
2
1
1
1
1
1
0
0
2
2
1
3
1
0
1
1
2
1
1
1
1
1
2
0
0
2
1
0
2
1
1
0
2
0
1
1
2
2
1
2
1
1
1
2
1
1
1
0
2
1
1
0
2
2
2
2
1
2
0
2
1
1
1
1
1
2
0
2
0
1
1
1
0
1
2
1
1
0
1
1
1
1
2
1
2
0
2
5
1
1
1
1
1
2
1
1
2
1
1
1
0
1
1
1
2
1
0
1
1
0
1
1
0
0
2
1
1
1
1
1
0
2
1
0
1
0
1
1
1
1
1
1
1
2
1
1
0
0
0
1
1
1
1
1
1
0
2
1
1
1
2
1
1
2
1
0
1
2
1
1
1
2
1
1
0
1
2
1
1
2
1
0
2
0
1
1
2
0
2
1
2
1
1
2
0
1
2
1
1
1
1
2
0
0
2
1
1
0
2
1
0
0
1
1
0
1
1
1
1
0
2
0
1
1
1
2
2
2
1
2
1
1
2
1
2
1
1
1
1
1
1
1
0
1
1
2
1
2
0
1
1
1
2
1
2
1
2
5
1
2
0
1
1
2
1
1
1
0
0
0
1
1
0
0
2
1
0
1
1
2
1
1
1
1
1
1
1
0
1
2
1
0
1
2
1
2
1
2
1
1
1
1
0
1
1
0
1
1
1
1
1
1
2
0
2
1
0
2
1
1
2
1
1
1
0
1
1
2
1
2
2
2
1
0
2
0
1
1
2
1
2
0
3
1
2
1
0
1
0
1
0
1
1
1
1
1
0
1
1
1
0
1
1
2
2
1
0
1
2
1
1
1
2
2
0
1
2
1
1
1
1
0
2
0
2
2
0
2
2
2
1
1
1
0
2
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
0
1
0
1
2
1
1
1
2
2
1
2
1
2
1
1
1
1
0
1
2
1
1
1
1
1
2
0
2
1
1
2
2
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
0
1
1
2
1
1
0
2
0
1
1
0
1
1
1
2
2
0
2
1
1
2
0
1
2
1
1
2
1
1
2
1
1
2
1
1
0
1
1
1
2
1
2
1
1
1
1
0
0
1
2
2
1
1
2
1
2
1
2
1
0
1
1
1
1
2
1
1
0
1
1
1
1
2
0
1
2
1
1
1
2
1
1
0
2
1
1
0
1
1
1
4
2
1
0
1
1
0
0
0
0
2
1
1
1
2
0
1
1
0
0
1
1
1
1
1
2
1
1
1
1
0
1
1
1
1
0
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
1
2
0
2
1
2
2
1
1
1
1
1
1
1
1
2
1
1
2
0
1
1
2
0
1
2
1
1
1
1
2
2
0
1
1
2
1
1
2
1
2
1
1
2
0
1
2
2
1
0
1
1
1
0
1
1
1
1
1
2
1
2
0
0
1
3
2
0
1
1
1
1
2
2
1
2
1
2
0
1
1
1
1
0
2
1
2
1
2
1
2
1
2
2
1
1
0
1
1
1
1
0
1
1
0
2
1
1
0
1
1
1
1
1
1
0
1
1
2
0
1
2
1
1
1
1
1
1
1
0
1
2
0
0
2
1
1
0
0
3
1
1
1
1
2
1
1
1
1
2
1
1
2
1
2
1
1
1
1
2
2
1
1
2
1
1
0
1
1
1
2
1
0
1
1
1
1
1
1
1
1
1
1
2
1
2
0
1
2
1
0
0
1
1
1
1
1
2
1
2
1
1
2
0
0
2
2
3
1
0
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
0
1
2
1
1
0
1
0
1
1
2
1
1
2
1
2
1
0
1
2
1
1
1
1
1
1
1
1
0
2
0
1
1
1
0
2
2
2
1
0
1
1
2
1
2
1
1
2
1
1
1
1
0
2
1
1
1
1
1
2
1
1
1
2
2
2
2
1
5
1
1
2
2
2
1
1
2
1
1
2
1
1
0
1
1
2
1
0
1
1
0
2
1
1
1
2
1
0
0
2
2
1
1
2
2
1
1
1
1
0
2
1
0
2
2
1
1
1
2
1
1
1
0
1
2
2
2
1
1
1
1
1
2
1
1
1
1
0
0
1
1
2
1
1
1
1
1
1
1
1
0
2
1
1
2
2
2
1
1
2
1
2
1
1
2
1
1
2
1
1
1
0
2
1
1
1
1
2
2
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
2
1
2
2
0
1
1
1
1
2
1
1
2
2
2
1
1
1
1
1
2
1
1
0
1
2
1
1
1
2
2
1
1
1
1
1
1
2
2
1
1
1
0
1
1
1
1
1
1
1
2
2
1
1
2
1
0
1
2
0
1
1
0
1
2
2
1
2
1
2
1
2
2
1
1
2
0
1
1
2
1
1
2
0
2
2
1
1
1
2
0
1
2
1
1
1
2
0
2
2
1
2
1
1
1
1
2
2
1
1
1
2
1
1
2
2
2
0
0
2
2
1
1
1
0
1
1
1
1
0
1
2
1
1
0
1
1
1
1
1
1
1
2
1
0
1
0
1
2
2
0
1
1
2
2
0
1
1
0
1
1
1
2
0
1
0
2
1
1
1
2
2
2
3
1
1
1
1
1
0
1
2
1
2
0
0
1
1
1
0
1
1
0
2
1
1
1
1
1
1
1
1
1
1
1
2
0
1
1
1
2
1
2
1
1
1
2
2
2
1
1
1
2
1
1
0
0
1
1
0
2
1
1
2
1
1
2
2
2
1
0
1
1
1
2
1
1
2
0
1
2
2
1
1
0
1
2
1
1
2
2
1
0
1
0
0
1
0
1
1
1
2
1
0
1
0
2
0
1
1
1
1
2
0
1
2
2
2
1
1
2
1
1
1
1
1
2
1
0
1
1
2
2
1
2
1
0
1
1
2
1
1
2
1
1
0
1
0
1
1
1
2
1
1
1
1
1
2
1
0
2
1
1
1
2
1
2
1
1
1
2
1
0
2
1
1
2
1
1
0
1
1
1
1
0
2
1
1
1
1
1
1
2
1
0
0
2
0
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
3
1
1
1
1
2
2
1
0
0
1
2
2
2
0
0
1
2
1
1
1
2
2
1
2
1
1
2
1
2
1
2
2
2
1
0
0
1
2
1
1
1
2
1
0
1
2
1
2
1
2
1
2
1
2
1
1
0
0
1
0
1
0
1
1
1
0
0
1
1
1
1
2
1
1
1
2
0
1
1
2
1
1
1
1
1
0
1
1
1
1
1
1
1
2
1
0
1
1
1
0
1
1
0
0
0
2
1
1
0
1
2
0
1
2
1
0
1
2
1
1
0
2
0
0
0
0
1
1
3
1
1
2
1
2
1
1
0
0
1
1
1
1
2
1
1
1
0
1
2
1
1
2
1
1
1
2
1
1
0
0
2
1
0
1
1
2
2
2
2
1
1
1
1
2
1
1
1
1
0
0
2
2
0
1
0
1
1
1
2
1
0
0
2
1
0
1
1
2
1
0
2
1
1
1
2
2
1
0
1
2
1
1
2
1
1
1
1
1
1
1
0
2
1
2
1
1
0
1
1
1
1
0
2
1
1
0
1
1
0
1
1
0
0
0
1
0
0
1
1
1
0
2
1
1
1
1
1
2
0
2
1
1
1
0
1
1
1
1
2
1
0
1
0
1
2
1
1
2
1
1
0
2
1
0
1
1
1
2
2
1
0
1
1
2
1
0
1
1
2
1
1
4
1
2
1
0
0
2
0
1
1
1
1
1
0
1
1
1
2
1
1
0
2
2
2
1
1
1
0
0
1
1
2
1
1
2
1
0
1
2
2
1
1
1
0
1
1
1
2
1
1
1
1
1
1
1
0
1
2
2
0
1
1
2
2
2
1
2
1
2
2
2
1
2
1
1
1
2
2
1
1
1
1
1
1
1
1
0
1
0
2
1
2
1
1
0
1
1
2
1
1
1
1
2
1
1
1
1
0
1
1
1
1
1
1
2
2
1
1
0
1
0
0
2
1
1
1
1
1
2
0
1
0
1
2
0
2
0
2
0
0
2
2
2
2
1
1
1
1
1
1
2
1
1
2
2
1
2
1
1
2
1
2
1
1
1
1
2
1
1
2
1
2
1
1
2
2
1
0
1
1
2
2
2
0
1
2
1
1
1
1
1
1
1
0
1
1
1
2
1
2
1
2
2
1
1
1
1
1
1
1
1
1
0
1
1
1
1
2
0
2
1
2
2
1
0
2
0
1
1
1
1
0
0
2
2
1
2
2
1
1
1
1
1
0
1
2
0
0
1
1
1
2
1
1
2
1
1
2
2
0
2
2
2
1
1
0
0
1
1
1
1
1
1
1
1
1
1
2
1
0
1
0
1
1
0
1
2
0
1
1
1
2
2
0
1
1
1
1
2
2
1
2
1
1
1
1
2
2
1
1
0
4
2
1
1
2
2
1
1
2
1
2
2
2
1
2
1
1
1
1
2
3
0
0
0
0
1
2
1
0
2
2
1
2
1
2
1
0
1
2
1
1
0
2
1
1
0
3
1
1
1
2
2
4
1
2
1
1
1
2
0
1
2
0
1
1
1
1
1
1
1
0
2
0
1
0
2
1
2
1
3
1
1
1
0
2
0
1
1
2
0
1
1
1
1
1
2
0
1
1
2
1
1
1
1
1
1
1
0
1
0
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
3
2
1
2
1
1
2
1
2
2
1
2
1
1
1
1
1
1
1
0
2
1
0
1
2
1
1
2
1
1
2
1
2
1
1
1
1
3
1
2
2
1
1
2
2
1
1
1
1
1
1
2
0
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
2
2
1
1
0
2
0
1
1
2
1
2
2
1
0
2
1
0
0
1
1
2
1
1
1
1
1
1
1
1
1
2
1
2
0
1
1
0
1
0
1
0
1
1
1
1
1
3
2
1
1
1
2
1
2
2
1
1
1
1
1
0
1
2
1
2
2
1
1
1
2
1
1
2
0
2
1
1
1
1
0
2
1
2
1
2
1
2
1
1
1
1
1
1
0
2
1
1
2
1
2
0
2
2
1
1
1
1
2
1
1
1
1
1
1
0
1
1
2
1
1
1
0
1
2
1
2
1
1
1
1
1
1
2
2
1
1
1
2
1
2
2
1
1
0
2
2
1
2
1
1
3
0
1
1
1
2
1
1
1
0
1
1
1
1
2
1
1
1
2
1
0
0
1
0
0
1
1
2
2
1
1
2
1
1
1
2
1
1
0
1
1
1
1
1
1
1
2
0
1
1
1
1
1
0
1
1
1
1
0
2
1
1
2
2
0
2
2
0
0
1
1
2
3
1
0
1
1
1
2
1
1
1
1
1
0
1
0
0
1
1
2
1
1
2
1
1
1
2
1
1
0
1
1
1
1
1
4
1
2
2
1
2
0
0
1
1
1
0
1
0
1
2
1
0
2
1
1
1
2
1
1
2
1
1
0
2
1
1
1
1
2
1
2
0
1
1
2
0
1
1
1
2
1
1
1
1
1
1
0
1
2
0
1
1
1
1
2
2
1
1
1
1
1
1
1
0
1
0
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
2
2
1
2
1
0
2
1
1
2
1
0
1
2
1
1
1
1
2
2
1
2
1
0
1
1
0
2
1
1
1
1
1
1
0
1
1
2
0
2
2
2
2
0
2
2
2
3
0
3
2
2
1
2
2
0
1
1
2
1
1
1
1
2
0
2
1
1
0
1
2
0
1
0
1
1
1
2
0
1
0
1
1
1
0
1
2
1
1
1
1
1
1
1
2
4
0
1
1
1
3
2
1
0
1
1
1
1
1
1
0
1
1
1
1
2
1
1
2
2
0
1
1
1
1
0
1
0
1
3
1
1
0
1
1
0
1
0
1
2
2
2
1
1
0
1
1
1
1
0
1
0
2
0
1
2
2
0
3
1
1
0
1
1
1
1
2
1
2
1
1
1
1
1
1
2
2
2
1
1
1
1
2
1
2
2
2
2
1
0
2
4
2
1
2
4
1
1
1
2
1
1
1
1
2
1
2
2
1
1
0
2
0
1
1
1
2
2
1
2
1
1
1
1
1
0
1
2
1
2
1
0
0
2
1
2
2
1
2
2
1
1
0
1
1
1
0
1
1
1
1
1
1
1
1
1
1
0
2
2
0
1
0
1
1
0
1
1
2
1
1
1
0
0
2
1
2
1
1
1
1
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
0
0
1
1
0
1
1
1
1
1
1
1
1
1
0
0
1
1
1
2
1
1
1
0
2
1
0
0
1
1
2
1
1
2
1
1
2
2
1
2
2
1
0
2
1
1
1
1
0
1
1
2
1
2
2
0
1
1
1
1
2
1
1
1
0
1
1
2
2
1
1
1
1
2
2
1
1
1
2
2
1
1
1
1
2
1
2
1
1
2
1
1
0
0
1
1
1
1
1
1
1
1
1
2
2
1
2
2
2
2
1
1
2
1
2
1
0
1
0
1
2
1
2
1
1
2
0
1
1
1
1
0
1
0
1
1
0
1
1
2
0
2
1
1
0
1
1
1
1
2
2
2
1
1
1
0
1
1
0
1
1
1
2
1
2
1
1
2
1
1
2
2
2
0
1
1
1
0
0
2
2
1
1
1
1
2
0
2
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
2
2
1
0
2
1
1
1
2
1
1
1
1
0
1
1
1
0
2
1
1
1
2
0
2
1
1
1
1
1
1
1
2
2
2
1
1
1
1
2
1
2
1
1
1
1
2
2
2
1
1
1
2
0
2
0
2
1
1
2
1
1
2
2
1
1
2
2
1
2
0
1
1
2
2
2
0
1
1
0
1
1
1
0
2
2
2
1
0
1
1
1
2
1
2
2
2
1
1
1
1
1
1
1
1
0
0
1
1
1
0
3
2
1
2
2
1
0
1
1
1
2
2
1
0
1
1
0
1
1
2
0
1
1
1
1
1
2
0
1
1
2
2
1
1
1
1
1
1
1
1
1
2
1
2
1
1
0
2
1
1
2
1
1
1
0
2
2
2
1
2
2
1
0
1
0
2
1
1
1
1
2
1
1
1
1
2
2
0
1
1
2
1
1
1
1
1
1
1
1
0
2
2
0
1
1
1
1
1
0
2
1
2
1
2
1
2
1
1
2
1
1
2
1
1
2
1
1
2
2
1
1
2
1
0
2
1
2
1
2
1
0
1
2
2
0
1
1
1
1
3
2
1
1
2
0
1
1
1
1
0
2
1
1
1
1
1
1
2
1
1
2
1
0
1
1
2
3
1
0
1
1
1
1
1
2
2
1
1
1
1
2
2
1
2
1
2
1
2
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
0
0
0
1
1
1
1
2
1
2
0
1
1
1
2
0
1
1
0
1
0
2
2
1
1
1
0
1
1
2
1
1
2
1
1
2
2
2
0
0
0
1
2
3
1
1
2
1
0
0
1
2
1
2
1
1
1
1
1
2
1
1
0
1
0
0
2
1
1
2
1
1
1
1
1
1
0
1
0
1
0
1
1
1
1
2
2
1
2
2
2
1
1
1
1
0
1
1
0
0
1
0
2
0
1
2
2
1
1
1
2
1
1
2
1
1
1
1
1
2
2
1
1
0
0
1
0
1
2
1
0
1
0
1
1
2
1
0
0
1
1
1
1
1
1
1
1
0
0
2
0
1
1
1
1
0
1
1
2
1
2
1
1
1
2
2
1
1
2
1
1
1
0
1
1
1
1
1
0
1
1
2
2
2
1
1
2
1
1
2
1
0
1
0
1
2
0
1
1
2
2
1
1
1
2
2
1
2
2
1
1
1
1
2
1
2
1
1
1
2
1
1
1
2
1
1
1
0
1
1
2
0
1
1
1
1
2
0
1
1
2
1
1
0
1
0
1
2
2
1
1
0
0
1
1
2
1
1
2
1
1
2
1
1
1
1
2
0
1
2
1
1
1
0
1
1
0
3
1
1
2
1
0
1
0
1
1
1
1
2
1
1
2
1
2
1
1
1
1
1
2
0
1
1
2
1
1
1
1
1
2
1
1
2
0
1
1
2
1
1
2
2
0
1
1
1
0
0
2
1
1
1
2
1
0
1
1
1
1
1
0
1
2
1
1
2
0
0
1
1
1
1
1
1
0
0
1
1
1
1
1
2
1
1
1
1
1
1
1
1
0
1
1
1
1
1
0
1
1
1
0
1
1
1
2
1
1
1
2
0
1
0
2
0
1
1
1
0
0
1
2
1
2
1
0
3
1
2
1
1
1
1
1
1
2
0
2
1
1
1
1
2
1
0
2
1
0
1
1
2
1
0
1
2
1
2
1
1
1
1
1
1
1
0
2
2
1
2
1
2
1
0
1
0
1
1
1
1
2
1
1
1
0
1
1
1
2
1
0
1
2
1
1
2
2
1
1
1
1
1
4
1
1
1
2
2
1
1
1
1
1
1
1
0
2
3
1
0
0
2
1
1
2
0
1
2
1
1
1
1
1
1
1
0
1
1
1
2
1
1
0
1
1
2
1
1
1
2
1
2
2
1
0
1
1
1
2
1
3
2
2
1
1
1
1
1
0
1
1
1
1
2
1
0
1
1
2
1
3
1
1
2
0
0
0
1
1
0
2
1
1
1
2
1
2
1
2
2
0
2
1
1
1
1
1
1
1
2
1
1
1
1
0
1
1
1
0
2
0
1
1
1
1
1
1
1
2
1
2
0
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
0
1
1
2
1
0
1
1
1
2
2
0
2
1
1
1
1
2
1
0
0
1
1
1
2
1
1
2
1
2
1
0
2
2
1
2
2
1
2
1
1
1
1
2
1
1
1
1
1
1
0
1
2
1
1
1
1
1
3
1
1
2
1
1
0
0
2
1
1
2
1
2
1
1
1
3
2
1
1
2
2
1
1
1
1
2
1
2
2
2
0
1
1
2
1
0
0
1
1
0
1
2
1
1
1
1
2
0
2
2
1
1
1
1
2
2
0
1
1
2
2
1
1
1
1
2
2
1
1
1
1
2
2
1
2
2
1
1
2
2
0
2
1
0
2
1
1
1
2
1
2
1
1
1
1
1
0
1
1
2
0
1
1
1
2
1
1
2
1
0
0
0
1
2
1
1
1
1
1
2
1
1
0
0
2
1
1
1
1
1
1
2
1
1
0
1
2
1
1
1
1
1
2
1
1
1
1
1
0
2
1
2
0
1
0
2
2
0
3
1
2
1
1
1
2
2
0
0
2
2
0
1
1
2
2
1
2
1
2
1
2
0
1
0
2
1
2
0
1
1
1
1
0
1
1
1
2
1
1
1
1
0
0
1
1
1
0
1
1
0
1
0
1
1
1
1
2
1
0
1
1
1
1
1
2
0
1
1
1
1
1
1
1
1
0
1
0
1
1
1
2
1
1
0
0
1
1
1
0
2
1
1
1
2
0
1
1
1
0
2
0
0
1
1
1
1
0
3
2
2
1
2
1
1
1
2
0
1
1
2
1
2
1
2
1
1
1
3
1
0
1
0
1
1
0
2
1
1
2
1
1
1
1
1
1
1
2
1
2
2
2
2
1
2
1
2
3
1
1
1
2
1
0
1
2
0
1
2
1
0
1
0
1
0
1
2
1
1
2
1
2
1
1
2
1
1
0
1
2
1
1
1
2
2
1
1
1
1
1
2
0
1
1
2
2
0
1
1
1
0
2
1
1
1
1
2
1
1
1
1
1
2
1
1
0
1
2
0
0
0
1
1
1
0
3
0
2
0
2
1
1
1
1
1
0
2
0
0
1
1
1
0
1
2
1
1
1
0
1
1
2
0
1
2
1
1
1
2
0
2
1
1
1
0
0
2
1
2
1
0
1
3
1
1
0
1
1
2
1
2
2
1
1
1
1
2
2
1
0
1
1
1
1
1
2
1
1
2
1
1
1
1
2
1
2
0
1
1
2
0
2
1
2
2
1
1
1
2
1
1
1
0
3
1
2
1
1
1
2
1
0
1
1
1
0
0
1
0
0
1
0
0
1
2
1
0
1
0
0
1
2
1
0
1
0
1
0
2
1
2
0
1
1
2
1
1
2
1
1
2
1
1
2
1
2
2
2
1
1
2
2
1
2
1
2
1
1
2
1
1
1
1
1
1
0
1
2
0
1
0
1
1
2
1
0
2
1
1
2
1
1
1
1
2
1
1
1
1
1
2
1
2
1
0
1
1
2
1
2
2
1
1
1
1
1
1
1
2
0
1
1
1
0
1
1
1
1
2
1
2
1
0
0
2
1
1
1
2
0
3
1
2
2
1
2
1
1
0
0
1
1
0
1
1
1
1
1
2
1
2
0
2
2
2
1
1
1
3
0
1
2
1
1
2
0
1
0
1
2
1
1
1
1
2
1
1
1
1
3
1
2
2
1
2
0
1
1
1
0
0
2
2
1
3
0
1
0
1
1
1
2
0
1
2
1
1
2
1
1
1
1
1
1
1
1
0
1
1
2
1
0
0
0
1
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
2
1
2
0
0
0
1
2
1
1
1
1
1
0
0
1
1
1
1
2
1
2
1
1
1
1
2
1
1
1
1
2
2
1
1
2
1
1
1
1
1
0
1
1
2
1
1
1
1
1
0
2
1
2
2
0
1
1
1
0
1
1
2
2
2
2
2
2
0
1
1
3
1
1
1
1
1
2
2
1
1
2
1
0
0
2
0
1
1
1
1
2
0
1
1
2
2
1
0
1
0
2
2
0
0
1
1
1
1
1
0
2
2
2
1
1
2
2
0
1
1
2
1
1
2
2
0
0
0
1
2
1
1
1
1
2
2
2
1
2
1
2
2
1
1
1
1
0
1
1
3
1
2
0
0
2
2
0
1
1
0
1
2
1
1
1
2
1
4
1
2
2
1
1
1
2
0
1
1
1
2
2
0
2
1
1
0
1
2
1
1
2
0
1
1
1
2
1
1
1
1
0
2
1
2
1
1
2
2
1
1
3
2
2
1
1
1
2
1
1
1
2
1
2
2
2
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
0
1
2
1
1
1
2
1
1
1
2
0
0
1
1
0
1
1
2
1
1
1
1
0
1
1
1
2
1
2
1
1
1
1
1
1
1
0
1
1
1
2
1
0
0
1
2
1
2
2
0
2
1
0
1
1
2
1
2
1
0
1
1
1
1
1
0
1
1
1
1
1
1
2
2
0
1
1
1
0
2
1
2
2
1
2
0
1
1
2
1
1
2
2
2
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
0
2
1
0
2
1
1
1
2
0
1
2
2
1
1
0
1
1
1
1
1
2
1
0
2
1
2
1
1
1
0
1
2
1
2
1
1
1
0
1
1
2
1
1
2
0
1
0
1
1
2
1
0
1
1
1
1
0
0
2
1
2
2
0
2
2
1
1
1
2
2
1
1
0
1
1
1
2
0
1
1
1
1
0
1
1
1
1
1
1
0
2
2
1
1
2
1
1
1
1
2
0
0
1
1
1
2
2
0
1
1
1
1
1
0
2
2
1
1
2
0
1
1
2
1
1
1
2
4
1
1
1
1
1
2
1
1
2
1
0
1
1
1
2
1
2
1
1
1
1
2
1
0
2
1
1
2
2
1
2
1
1
2
1
1
2
1
1
1
2
1
2
2
1
1
2
0
2
1
1
2
1
2
2
0
1
2
1
1
1
1
2
2
1
0
1
2
0
0
2
0
2
1
1
1
0
1
1
1
2
1
0
1
1
0
1
1
1
2
2
1
2
1
1
2
0
2
1
1
2
2
2
1
1
3
1
2
0
1
1
1
1
2
1
0
2
1
1
0
1
1
1
2
1
1
0
2
1
1
2
1
1
0
1
1
1
2
1
1
2
1
1
2
0
2
1
2
0
1
1
2
1
1
2
1
1
1
0
1
1
3
2
1
1
1
1
1
1
0
2
1
0
0
1
1
1
2
0
2
1
2
1
1
1
0
1
1
1
1
2
2
1
1
1
0
0
1
1
1
2
0
1
1
1
2
2
1
1
2
1
1
1
2
0
0
2
1
1
1
2
0
1
1
2
1
0
2
1
3
1
2
1
0
0
1
3
2
2
1
2
1
1
1
2
2
2
0
2
2
1
1
1
2
1
0
1
2
1
1
1
1
2
3
1
2
0
1
0
1
1
1
2
1
1
0
3
1
1
2
2
2
2
1
1
1
2
1
1
0
1
1
0
1
1
1
1
2
1
1
1
0
0
2
0
1
0
1
1
1
1
2
1
1
1
1
0
2
1
1
2
1
1
0
1
1
2
0
2
1
1
2
1
1
1
1
1
0
0
1
1
1
1
1
1
0
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
0
1
0
1
1
0
1
1
2
2
1
0
1
1
0
1
1
2
0
1
1
0
2
1
1
1
0
1
1
1
0
2
1
2
0
1
1
2
0
1
0
2
2
1
0
2
2
1
1
1
0
1
2
1
2
1
1
0
1
2
1
0
2
2
0
2
1
1
1
0
0
0
1
1
1
1
1
1
0
4
1
1
1
1
1
0
1
2
1
1
1
0
2
1
1
1
1
2
1
1
1
1
1
1
0
2
1
2
1
1
1
1
1
2
2
1
1
0
0
1
1
1
2
2
2
0
3
1
1
2
1
0
0
1
1
1
2
1
0
2
1
1
2
2
1
1
1
1
2
2
1
1
0
1
0
2
1
1
1
1
1
1
0
1
1
2
1
0
1
2
1
1
2
1
2
1
2
0
2
1
1
1
1
1
0
2
1
1
1
2
2
1
1
2
1
1
1
1
0
2
1
1
1
1
2
1
2
2
2
1
1
1
1
1
1
1
0
0
1
1
1
1
1
1
2
2
2
2
1
1
2
1
2
1
1
1
1
1
1
1
1
0
2
1
1
1
1
2
1
1
0
2
1
2
0
1
1
2
1
2
1
3
1
1
1
1
0
1
1
1
1
0
2
1
1
0
1
1
1
1
0
1
1
1
2
1
1
1
1
1
2
0
0
1
1
0
1
1
1
1
1
1
2
1
1
2
1
0
1
2
2
1
1
2
1
0
1
0
1
1
2
1
2
1
0
1
1
0
1
1
1
2
1
0
1
1
1
2
1
1
1
0
1
3
2
1
1
2
2
1
1
2
2
0
1
1
1
2
1
1
2
1
1
2
2
1
1
1
2
1
1
1
2
0
1
1
1
0
1
1
2
2
2
2
1
1
2
1
2
1
2
0
0
2
1
1
1
1
1
1
1
2
2
0
1
1
1
0
2
1
1
1
0
1
0
1
2
1
1
1
1
1
1
2
2
1
2
1
1
3
1
0
1
1
2
2
1
1
0
0
2
1
1
1
2
0
0
1
2
1
2
2
1
1
2
1
1
2
2
1
2
1
1
1
1
1
1
0
1
1
1
0
2
1
1
1
1
0
1
2
1
2
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
0
1
1
2
1
0
2
0
2
2
2
1
1
2
1
1
1
1
1
1
1
0
1
1
1
2
2
2
2
1
1
1
0
1
2
2
1
1
2
1
2
1
1
0
2
1
2
2
1
1
1
2
2
2
1
0
1
1
1
0
1
1
1
0
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
0
2
1
2
2
2
1
1
2
1
1
2
1
2
1
1
1
0
1
1
0
0
1
1
2
2
1
2
1
1
1
2
0
0
1
1
0
1
2
1
1
0
2
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
0
1
2
0
0
0
1
1
1
2
1
2
1
1
1
2
2
1
2
1
3
1
0
1
1
1
0
1
1
0
1
1
0
1
1
1
2
1
0
1
1
1
0
1
0
1
2
1
1
1
1
0
1
2
1
0
1
1
1
0
0
2
0
2
1
1
1
0
1
0
0
1
1
1
1
1
1
1
1
0
1
1
1
1
2
0
1
1
1
1
2
1
1
2
1
0
2
2
1
1
1
1
1
1
0
0
1
1
1
1
1
1
1
1
1
2
1
2
0
0
1
1
1
1
1
1
0
1
0
1
0
1
1
2
0
0
1
1
1
1
1
0
2
2
1
1
2
1
2
2
1
1
2
2
1
1
2
3
1
0
1
1
1
1
2
0
1
1
1
1
0
0
1
0
1
0
2
2
3
1
1
1
1
2
1
1
0
2
1
2
1
1
1
2
1
1
2
1
0
1
2
2
1
2
1
1
1
2
0
2
1
1
1
2
1
1
2
0
2
2
1
1
1
1
2
0
1
1
1
2
0
0
2
2
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
0
0
1
2
0
2
1
0
1
1
1
1
2
4
2
2
1
2
1
2
2
1
2
1
1
0
1
2
0
2
1
2
0
1
0
1
2
2
1
1
0
1
1
1
2
1
1
0
2
0
1
0
0
2
1
1
1
2
0
0
0
0
1
0
2
2
0
1
1
2
0
1
2
0
2
1
1
1
2
2
0
1
2
0
1
3
1
1
0
2
1
1
1
1
2
2
1
2
0
1
1
3
1
2
0
1
0
1
1
1
2
1
1
1
1
1
1
2
0
0
2
1
1
1
2
1
2
1
1
1
0
0
1
1
1
2
1
1
2
0
0
2
1
1
1
1
2
1
1
1
2
1
0
2
0
0
1
2
2
1
0
2
0
1
1
2
1
1
2
1
2
1
1
1
1
0
2
1
2
2
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
1
1
0
1
1
0
1
2
2
1
0
1
0
1
1
2
1
0
1
1
1
1
2
3
1
1
1
2
2
2
1
1
1
2
1
1
1
1
1
1
1
3
2
0
2
1
1
2
1
2
1
1
1
1
1
0
1
0
3
1
2
2
1
1
1
0
1
1
1
2
2
1
0
1
1
0
2
1
1
2
1
1
1
1
2
0
1
0
1
2
1
2
1
1
2
1
2
2
1
1
1
2
0
1
1
1
1
2
1
2
1
2
2
1
1
2
2
1
1
2
1
1
1
1
3
2
1
1
1
2
2
1
2
1
1
1
0
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
0
1
1
1
0
1
1
1
0
1
1
2
1
1
1
1
1
1
1
0
0
1
1
2
2
1
1
1
1
2
1
1
1
0
0
0
0
1
1
1
1
1
1
1
1
2
1
2
1
1
4
0
1
1
1
1
2
2
0
1
1
1
1
1
1
1
2
0
1
1
1
1
1
1
2
0
0
1
1
2
1
1
1
1
1
1
1
0
1
1
2
1
1
1
1
0
2
2
2
1
2
1
0
2
1
2
0
0
1
1
1
1
1
2
1
1
0
1
0
1
2
1
0
2
1
1
1
1
1
1
1
2
1
1
2
0
1
1
1
2
1
1
1
2
1
1
1
2
1
1
2
2
0
0
2
2
2
2
0
1
2
2
1
2
1
1
1
1
1
2
1
1
0
2
1
1
1
2
2
2
1
0
2
2
2
2
1
2
1
2
0
1
1
2
1
1
1
1
1
2
2
0
1
1
1
1
2
0
1
0
2
0
0
2
1
1
0
2
1
2
0
1
1
1
1
1
1
1
0
0
2
1
5
1
1
1
1
1
2
1
1
2
1
3
1
1
1
0
2
0
2
2
2
1
2
1
0
1
1
1
2
1
1
2
1
2
2
2
2
1
1
3
0
1
1
2
1
0
1
1
1
0
1
1
1
0
1
2
0
2
1
1
2
1
0
1
1
2
1
1
0
1
1
2
1
1
2
2
1
1
1
1
2
0
0
2
2
1
1
0
1
1
1
1
1
0
1
2
1
0
1
1
1
0
1
2
1
1
2
1
2
1
2
1
2
1
1
1
1
1
1
0
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
0
1
2
2
1
2
1
1
1
3
1
2
2
1
0
1
2
0
1
0
1
1
2
2
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
0
1
2
0
2
1
1
1
0
0
1
1
1
2
1
2
1
1
1
1
1
1
1
0
1
1
1
1
0
2
1
2
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
0
2
2
1
2
1
2
2
0
2
0
2
2
0
1
2
1
1
1
2
0
1
1
0
2
3
2
2
1
1
1
1
1
1
1
1
0
1
1
1
2
1
2
1
1
1
0
2
0
2
1
3
1
1
2
1
1
0
1
1
1
1
1
1
1
1
2
1
1
1
1
1
0
1
0
2
1
2
0
1
1
0
0
1
2
1
0
1
1
2
2
2
1
2
1
1
1
2
1
1
1
2
1
1
1
0
1
1
0
1
1
1
2
0
0
1
1
2
1
2
2
1
1
1
1
1
1
0
1
2
1
2
1
1
1
1
2
1
0
2
1
1
1
0
1
1
1
1
1
1
1
3
2
0
0
1
2
0
2
1
2
1
1
0
0
1
1
2
1
0
0
2
1
2
0
2
1
2
0
1
1
2
1
1
1
1
0
1
1
1
0
1
1
1
1
1
0
1
1
1
1
0
1
2
2
1
1
2
1
1
2
1
0
0
1
1
1
0
1
2
1
0
0
0
1
1
0
2
1
1
1
2
1
1
1
0
2
1
1
1
2
2
1
2
1
3
1
2
1
1
1
1
1
1
1
1
1
0
2
1
1
1
2
1
1
2
1
1
2
1
1
3
2
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
2
1
2
1
0
1
1
1
2
1
2
1
1
1
2
2
1
2
1
0
1
2
1
0
1
1
1
1
1
1
2
2
1
1
0
2
2
1
1
1
1
1
1
1
1
0
1
2
1
1
1
1
1
2
0
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
1
0
2
0
2
1
1
1
1
2
0
0
2
2
1
2
2
0
1
2
1
1
0
1
1
2
0
0
1
1
0
1
2
1
0
1
1
1
1
1
1
1
2
1
1
0
1
1
1
1
1
1
2
2
1
1
1
2
1
2
1
1
1
1
1
1
2
2
1
1
0
1
1
0
2
2
2
1
1
0
2
0
0
1
1
2
2
1
1
1
2
0
1
0
2
0
1
1
2
2
1
1
0
2
2
2
1
1
1
2
1
0
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
2
1
1
1
1
2
1
1
1
2
1
1
0
1
1
1
2
1
1
1
1
1
0
1
1
1
1
1
1
0
1
1
0
0
2
1
1
2
2
2
1
1
1
2
2
1
1
1
1
1
3
1
1
0
1
1
1
2
1
1
1
1
0
2
0
2
0
2
2
1
1
2
1
1
0
2
1
1
2
1
0
1
0
2
1
1
0
2
1
1
1
1
2
1
0
1
2
1
1
1
1
0
1
1
1
1
1
2
1
1
1
1
0
3
1
1
1
1
1
1
0
2
1
1
1
2
1
1
1
2
1
1
2
0
2
1
1
1
1
1
1
2
1
1
0
1
1
1
1
1
2
1
2
2
1
2
2
1
1
1
0
2
1
1
1
2
2
1
1
1
1
2
1
2
1
2
1
2
1
1
1
1
2
1
1
1
1
0
1
1
0
2
2
1
1
1
2
1
0
1
1
1
2
1
3
2
2
2
1
1
1
2
1
1
1
1
0
1
1
3
1
2
1
2
2
2
1
0
2
1
1
0
2
1
2
1
1
1
2
2
1
1
2
1
1
0
0
2
2
1
1
1
2
0
1
2
1
1
0
1
2
2
2
1
1
1
1
2
2
0
0
0
1
2
0
2
1
0
1
1
1
2
2
1
1
1
1
2
2
1
0
2
0
1
1
1
1
1
1
1
1
1
2
1
0
2
1
2
1
2
2
0
2
1
1
1
1
2
2
2
1
1
1
1
1
2
1
2
1
2
1
0
2
1
1
1
1
2
1
1
1
1
1
0
1
1
1
1
1
2
0
2
1
3
1
1
1
1
4
2
1
1
1
1
2
1
1
1
1
2
1
2
1
1
1
1
2
0
1
2
1
1
1
1
0
1
1
2
1
1
1
1
0
2
0
1
1
2
2
1
1
2
1
1
2
0
2
1
1
2
2
1
0
1
1
0
2
1
2
0
1
1
1
0
2
1
1
2
2
1
1
1
0
1
0
1
1
1
2
1
0
1
2
1
1
1
2
1
1
0
1
1
2
1
2
0
1
1
2
2
1
2
1
1
1
1
3
1
1
1
0
1
2
0
2
2
0
1
2
0
1
1
1
1
1
2
0
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
2
2
1
2
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
0
1
2
2
0
1
1
2
1
1
1
1
0
1
0
0
1
1
1
2
1
0
0
1
1
0
2
1
0
1
1
1
2
1
0
1
2
1
0
3
1
1
1
0
1
1
2
0
1
2
1
1
1
1
1
2
1
2
0
0
1
1
1
2
1
1
1
1
2
2
1
2
2
1
1
1
0
1
0
1
1
2
1
1
1
1
1
2
1
1
3
1
1
1
1
1
1
0
1
2
1
1
1
1
2
1
1
1
1
2
1
4
1
1
1
2
0
1
2
2
1
2
1
2
0
2
3
2
1
2
2
1
1
1
0
1
1
1
1
1
0
1
0
1
1
1
1
0
1
2
1
1
1
0
1
1
2
1
1
0
1
2
2
1
2
1
1
2
1
2
0
0
1
1
1
1
2
1
0
1
1
1
1
1
1
0
1
2
2
0
2
1
1
1
0
1
2
1
2
0
1
1
2
1
0
2
1
1
0
0
2
0
1
2
1
0
0
2
1
0
2
2
2
1
0
2
2
3
2
1
2
1
0
1
1
1
2
1
2
2
1
2
1
1
0
2
1
1
0
1
1
3
2
1
1
3
1
2
2
1
2
1
1
1
1
1
1
2
0
1
1
2
0
0
1
2
2
1
2
0
0
2
1
1
1
1
1
1
0
1
2
2
1
1
1
1
1
2
1
0
1
0
1
1
2
0
1
0
1
1
1
1
1
1
2
2
1
0
2
1
1
0
0
1
0
1
1
1
2
1
2
1
2
2
0
1
0
1
1
1
1
1
1
2
0
2
2
1
0
1
0
1
1
2
1
0
1
0
1
2
1
1
1
2
1
1
1
2
1
2
2
1
2
2
1
1
1
2
1
1
2
2
0
1
1
2
1
2
2
1
2
2
1
2
2
1
1
2
1
1
1
4
1
2
0
1
1
1
1
1
1
0
1
1
1
2
1
0
1
1
1
2
1
1
1
2
1
1
2
1
1
0
1
0
1
1
2
2
1
1
2
2
1
2
0
2
1
0
1
1
2
1
1
1
1
1
1
0
1
1
1
2
2
2
1
1
1
1
1
1
0
1
1
1
2
1
1
2
1
0
0
1
1
1
1
1
1
1
0
0
2
1
1
1
1
2
2
1
1
1
1
1
1
1
1
2
2
2
1
1
0
2
1
1
1
1
2
1
1
2
0
0
1
2
0
1
1
1
2
0
1
1
1
2
1
1
2
0
1
2
2
1
2
1
2
0
2
1
1
1
0
1
2
1
1
1
2
2
1
1
0
2
1
2
2
1
2
1
1
1
0
1
1
1
2
2
1
0
1
1
2
2
2
1
1
2
2
2
1
1
2
1
0
2
1
2
1
2
1
2
2
1
2
1
2
1
1
0
1
1
2
1
1
1
2
1
1
1
0
2
1
0
1
2
2
2
1
0
1
1
1
1
0
1
0
0
1
1
2
0
2
2
1
1
1
2
0
2
2
1
1
1
0
1
0
1
1
2
1
1
2
1
1
1
1
1
1
0
1
1
1
1
1
0
1
1
1
1
1
1
0
1
1
1
0
1
0
1
2
1
1
2
1
1
1
0
1
0
2
1
2
1
1
1
0
0
1
1
0
1
0
0
1
1
1
2
1
1
1
2
1
1
2
0
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
1
1
2
2
1
1
2
1
0
0
2
0
1
1
1
2
0
1
1
1
1
1
2
1
1
0
2
1
2
2
0
0
1
1
1
2
1
1
1
0
2
1
2
2
1
1
1
2
1
0
1
1
1
1
2
1
1
2
0
1
1
2
1
2
2
1
1
2
3
0
1
1
1
1
1
1
0
1
1
1
1
0
1
2
2
1
1
1
1
2
2
1
1
1
2
1
1
1
1
0
1
0
2
1
1
1
1
1
2
1
1
2
2
2
1
2
0
2
1
1
0
2
0
2
2
2
2
0
0
1
2
2
1
1
1
1
1
1
0
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
2
0
1
1
1
1
0
2
2
1
1
2
1
1
1
1
1
1
0
1
1
0
2
1
1
2
0
1
2
1
0
1
1
1
1
0
2
2
1
1
0
1
1
1
2
0
1
2
2
1
0
1
1
2
1
1
1
2
2
2
1
0
1
1
0
1
0
1
1
2
2
1
2
1
5
2
2
2
1
2
1
2
1
1
1
1
1
1
1
0
1
0
1
1
1
1
2
0
1
1
1
0
1
2
2
1
2
0
1
2
0
1
2
2
1
2
1
0
1
0
2
2
2
2
1
1
1
1
1
1
1
1
2
0
1
2
1
1
1
1
1
0
0
1
0
1
1
1
1
1
1
1
1
1
1
0
1
2
1
1
1
1
1
0
2
1
0
1
1
0
2
0
1
0
1
1
2
2
1
1
1
1
1
1
2
1
2
2
2
2
1
1
1
1
0
1
2
2
2
1
0
1
1
2
1
2
2
2
2
1
1
1
1
1
0
2
1
2
2
1
2
0
1
1
1
2
0
1
2
1
1
1
2
0
2
1
2
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
2
1
1
1
1
1
2
4
1
1
1
1
0
1
2
1
0
2
1
1
1
1
1
2
1
1
1
2
2
1
1
1
2
1
2
3
1
2
1
2
0
1
1
1
1
1
1
1
2
1
2
1
1
1
0
2
1
1
1
2
1
1
2
1
1
0
2
1
1
0
1
1
1
1
1
1
0
1
2
1
1
1
1
2
1
2
1
1
1
0
1
1
1
2
1
1
1
1
1
1
2
1
1
1
0
1
1
1
1
1
1
1
0
1
1
1
1
1
2
1
1
0
1
1
1
0
1
1
2
1
2
1
1
1
1
0
1
1
1
0
1
1
0
1
1
1
2
2
1
1
0
0
0
1
2
2
1
1
1
1
1
0
1
1
1
1
1
1
1
1
0
1
1
2
1
1
2
1
1
1
1
1
1
0
1
2
1
0
0
1
2
1
1
0
1
1
1
1
1
1
0
1
2
1
1
1
2
2
1
1
1
0
2
1
1
0
0
1
1
1
1
1
1
1
1
3
2
1
1
1
1
1
1
0
1
2
1
2
2
1
2
1
2
2
0
2
1
1
6
2
2
2
1
2
1
1
1
0
1
1
2
2
2
1
1
1
2
1
1
1
1
2
2
2
1
1
1
1
1
2
1
1
1
1
1
0
0
1
0
2
1
0
0
2
0
0
0
1
2
1
2
0
1
2
2
1
2
1
2
1
2
2
1
2
1
1
2
1
1
0
2
1
0
2
1
1
1
1
2
1
1
0
2
1
1
2
0
1
1
1
2
2
1
1
1
2
1
2
3
2
1
1
1
1
0
0
1
0
1
0
1
2
1
1
1
0
0
1
1
2
0
1
1
2
0
2
1
0
0
0
0
1
1
1
0
1
2
0
1
1
1
1
1
2
1
1
2
1
1
1
1
1
0
0
1
0
1
0
1
2
1
1
1
1
0
1
0
2
2
2
1
1
0
3
0
1
2
1
1
1
1
2
1
0
2
2
2
1
1
1
1
1
1
2
2
1
2
2
1
1
0
1
0
1
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
2
1
2
1
1
1
2
1
2
1
1
1
1
0
1
2
0
1
1
1
2
1
1
2
1
1
2
1
0
2
0
1
1
1
1
1
2
1
2
2
1
2
1
1
1
0
1
1
1
1
1
1
1
2
1
1
0
2
2
1
0
2
1
1
2
1
2
1
1
1
1
0
2
2
2
1
1
0
0
2
1
2
2
1
1
0
1
2
0
1
1
2
1
0
0
0
2
0
1
1
1
1
2
1
1
2
2
1
0
1
1
1
1
0
2
1
1
2
1
2
1
1
0
1
1
1
1
4
1
2
1
1
1
2
0
1
1
2
0
1
1
1
1
1
1
1
2
1
1
1
2
2
2
1
0
1
1
1
1
0
1
0
0
0
1
2
1
1
1
2
1
2
1
1
2
1
1
2
2
1
2
0
1
2
2
1
1
1
2
0
1
1
2
1
2
1
2
1
1
0
2
1
1
0
1
1
1
1
2
0
1
2
1
2
1
2
1
0
1
2
1
1
1
1
2
0
0
2
2
2
1
0
1
2
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
1
1
2
0
2
1
2
1
2
0
2
2
1
1
1
1
1
1
1
2
1
0
1
1
0
1
0
1
2
1
1
0
1
1
2
2
0
0
1
1
1
1
2
1
1
0
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
2
1
1
1
2
0
2
1
1
1
2
1
2
1
1
0
1
0
2
1
1
1
0
1
1
1
2
2
2
2
0
0
1
1
2
1
2
1
2
1
1
1
0
1
2
0
2
2
2
1
2
1
1
1
2
2
0
1
0
1
2
0
1
1
1
1
1
1
1
1
0
0
1
1
1
1
2
1
0
1
1
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
0
1
1
1
1
1
2
2
1
2
1
1
1
2
1
2
2
0
1
1
2
1
2
1
0
2
2
1
0
1
1
1
1
1
0
2
2
2
2
1
2
1
2
1
1
1
1
2
0
1
1
1
1
0
1
1
1
0
1
1
2
1
2
1
1
1
2
1
2
1
1
1
0
2
0
1
1
0
0
1
1
0
1
2
2
1
1
1
1
2
0
1
1
0
1
0
1
1
2
1
2
1
1
2
2
1
0
1
2
1
1
1
1
1
2
1
2
1
1
1
0
1
1
0
0
2
2
1
1
1
2
1
1
1
2
1
0
1
1
1
1
1
1
2
0
0
3
1
1
2
0
2
1
1
1
0
2
1
1
1
1
1
1
2
1
1
2
2
0
1
2
1
2
1
1
1
0
1
1
1
1
1
1
0
2
0
2
2
2
1
2
1
1
2
1
1
0
0
1
1
2
1
2
1
1
2
1
0
2
0
1
0
1
1
1
0
2
1
2
2
0
1
1
0
1
2
2
1
2
1
2
1
1
1
2
1
1
2
1
1
1
1
1
1
1
2
1
1
2
1
0
1
2
2
1
2
1
1
2
0
1
2
2
1
1
0
1
2
1
1
2
1
0
1
1
1
1
1
0
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
0
1
2
1
1
2
0
0
1
1
0
1
1
0
1
1
1
1
1
1
1
2
1
0
1
2
2
1
2
1
1
1
1
1
1
0
1
1
2
2
1
2
1
2
1
2
1
2
2
1
2
1
1
2
0
1
1
1
2
1
1
1
1
1
1
0
1
2
2
0
2
1
1
1
2
1
1
1
1
1
1
1
1
1
2
0
1
1
0
1
1
1
1
0
1
2
1
0
1
0
1
1
1
1
1
1
2
1
0
1
1
2
2
0
0
1
2
1
2
1
1
2
1
1
2
1
1
0
1
1
2
2
2
2
1
1
1
0
2
0
1
1
1
2
1
2
2
0
2
1
1
1
1
2
1
1
1
1
1
0
0
2
2
1
2
1
1
1
1
2
2
2
1
2
1
1
1
2
1
1
1
2
0
0
0
2
1
1
1
1
1
1
1
1
2
2
1
0
1
1
2
2
2
1
1
2
1
2
2
2
2
1
2
1
1
1
2
1
2
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
0
2
2
2
1
1
1
3
0
1
1
1
1
0
2
1
2
2
1
1
1
1
0
0
1
0
1
0
1
0
1
1
1
1
1
1
1
1
1
2
0
0
1
1
0
2
1
1
0
1
1
1
1
2
1
2
1
1
1
1
2
1
2
1
0
1
1
1
1
1
1
1
0
1
1
1
0
1
2
1
1
2
1
1
0
3
2
2
2
0
1
2
1
1
1
1
1
2
2
2
1
1
1
2
1
3
1
2
1
1
1
2
1
1
1
0
0
2
0
0
1
2
1
1
1
2
2
1
2
1
1
0
0
0
1
1
0
0
1
1
2
1
2
2
2
2
2
2
1
1
2
1
0
1
2
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
2
0
1
2
0
2
1
1
1
1
1
1
1
2
1
0
1
1
2
1
0
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
2
1
1
1
2
1
1
0
2
1
2
2
0
0
0
1
1
1
1
1
1
0
2
2
1
1
0
2
1
1
1
1
1
1
1
1
1
0
1
1
1
1
0
1
0
1
1
1
0
1
1
0
1
1
1
2
0
1
0
2
2
2
1
2
1
1
1
1
2
2
1
2
2
1
2
1
1
2
0
1
1
2
2
1
1
1
1
1
0
1
1
0
1
1
1
2
2
0
1
1
1
0
2
1
1
1
1
0
1
1
1
2
0
1
1
2
2
1
2
0
1
1
2
1
1
2
2
1
1
2
1
1
2
1
0
1
1
1
1
1
2
2
1
1
1
2
1
1
1
1
1
1
2
1
2
1
0
2
0
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
0
0
1
1
1
1
1
2
2
2
2
1
1
1
0
1
0
1
1
1
1
1
1
1
1
1
2
2
0
2
1
2
1
1
0
1
1
1
1
1
1
2
1
2
2
1
2
1
2
2
0
1
1
1
1
1
1
1
1
0
1
2
1
1
2
2
1
2
1
2
1
1
2
2
1
1
1
1
1
1
2
0
2
1
1
1
1
0
0
1
1
1
1
0
1
1
0
2
1
2
1
1
1
2
2
2
1
1
0
0
0
2
0
1
1
0
2
1
1
1
2
1
1
0
1
1
0
1
1
2
2
2
1
1
0
1
1
0
0
0
0
1
2
2
1
1
2
1
0
1
1
2
0
1
4
2
0
1
2
2
2
2
0
0
2
1
2
2
2
1
2
0
2
2
1
0
0
2
0
2
1
1
1
1
2
2
1
1
2
2
2
1
1
1
1
1
1
2
2
2
1
2
1
1
0
0
1
2
2
0
1
0
2
1
1
1
1
2
1
1
1
1
1
1
1
0
1
1
1
2
0
0
1
2
0
2
1
1
2
2
1
2
1
2
0
2
1
1
0
1
1
1
1
0
0
1
2
2
1
2
1
2
1
0
1
2
2
1
1
2
2
1
2
1
1
1
1
1
1
0
2
1
1
2
0
1
2
1
1
1
2
1
1
2
1
1
1
1
2
2
0
1
1
1
0
2
0
1
1
1
2
1
2
2
1
3
2
0
1
1
1
1
1
0
0
2
0
1
1
1
2
1
1
0
1
2
1
0
1
2
1
1
1
0
1
1
1
1
1
1
1
1
0
2
1
2
1
1
1
0
1
2
1
1
1
2
1
1
0
0
2
0
2
1
1
1
1
1
0
1
1
1
1
0
1
1
2
2
1
2
1
1
1
0
1
1
1
1
2
1
1
1
2
1
2
2
1
2
2
0
1
1
2
2
1
1
1
0
2
0
2
1
1
2
1
2
1
1
2
1
1
1
2
1
1
1
1
1
1
2
2
1
1
2
2
1
2
2
1
2
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
2
1
1
1
2
1
1
2
1
0
1
1
1
1
0
0
2
0
1
1
3
1
1
2
1
2
1
0
1
1
2
1
0
1
2
1
2
2
1
2
1
2
1
0
1
1
1
2
1
1
1
2
0
2
1
2
2
2
1
0
0
1
0
1
1
1
2
1
1
1
2
1
1
2
1
0
1
1
2
0
1
2
1
1
1
2
1
2
2
1
0
1
0
1
1
2
1
1
1
1
0
1
1
1
1
0
1
1
2
1
0
1
1
1
2
1
1
1
1
1
2
0
1
1
1
0
2
1
2
0
2
2
2
2
2
2
3
1
1
1
2
2
1
2
1
1
1
1
2
2
1
1
2
1
1
1
1
2
2
2
1
1
1
1
1
1
2
2
2
1
0
0
1
1
1
1
1
2
1
1
1
0
2
1
1
1
1
4
0
2
1
0
0
0
1
1
1
0
1
1
2
1
2
1
2
1
1
1
2
2
1
1
1
1
1
1
1
2
1
0
0
1
1
1
1
2
1
2
2
1
0
2
0
1
1
1
1
1
1
2
1
2
1
2
1
2
1
1
0
1
1
1
1
1
0
1
1
1
0
1
1
2
0
1
2
1
0
1
1
2
2
1
1
1
1
2
3
1
0
2
1
1
1
1
1
1
1
0
1
1
1
1
1
1
0
2
1
0
0
0
1
2
2
1
2
1
2
1
1
1
2
1
1
1
0
2
1
0
1
1
1
1
1
1
0
2
0
2
0
1
1
1
1
1
2
1
1
1
1
1
1
0
0
2
1
1
1
0
2
2
2
0
1
1
2
1
1
1
1
1
1
2
0
1
2
1
2
2
0
1
2
2
2
0
1
1
1
1
1
1
1
0
1
1
0
1
1
1
1
0
1
0
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
2
1
1
1
1
1
1
1
1
1
2
1
2
1
2
0
1
2
1
1
2
0
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
2
3
1
0
1
1
1
1
2
1
1
2
1
1
1
1
2
1
0
1
1
1
1
1
2
1
1
1
1
2
1
0
2
1
1
2
1
2
1
1
0
1
1
1
1
1
1
1
1
1
1
1
3
1
1
1
1
1
1
1
2
1
0
2
1
1
2
1
1
0
1
1
1
2
1
1
1
0
1
0
1
1
2
1
1
1
1
2
1
1
2
0
1
1
1
1
1
1
0
1
1
2
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
0
0
2
1
1
2
1
1
2
1
1
1
1
0
1
0
1
0
0
1
1
1
1
1
1
1
1
0
1
1
1
1
1
2
1
1
1
1
2
2
0
1
1
1
2
1
1
2
2
0
0
1
2
2
1
1
1
0
0
2
1
2
1
1
1
1
1
2
2
1
1
0
1
1
0
1
0
2
2
0
1
1
1
1
1
0
2
1
1
2
2
1
2
1
1
1
2
0
1
2
2
1
1
1
1
1
2
0
0
1
1
1
1
1
1
1
1
1
0
1
1
1
0
1
0
1
1
1
1
1
0
1
1
2
0
1
1
1
0
1
1
2
1
2
2
1
2
1
1
3
1
1
1
1
1
2
2
1
0
1
1
1
1
1
2
7
1
1
2
1
1
0
1
0
1
1
2
3
2
1
2
1
0
0
1
0
1
1
0
2
1
0
2
2
1
2
1
2
1
0
0
0
1
2
2
1
1
1
2
1
0
2
1
1
1
2
1
1
1
1
2
1
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
2
1
2
1
1
1
1
1
0
1
0
0
1
1
1
0
1
2
1
2
1
1
1
0
0
0
1
2
2
1
0
1
1
2
0
1
2
1
1
1
2
2
0
1
1
2
1
1
1
0
1
1
3
1
1
1
1
1
1
2
1
1
1
0
1
0
1
1
1
1
1
0
0
1
1
2
1
1
2
2
0
1
1
2
1
1
2
1
0
1
1
1
2
2
1
0
2
1
2
1
1
1
0
0
1
3
2
1
2
2
1
3
2
1
1
2
1
2
1
2
1
1
2
1
2
2
1
2
2
1
1
1
1
2
1
2
0
1
2
2
0
0
1
3
1
2
1
2
1
1
1
2
2
1
1
1
1
1
1
1
0
1
1
2
0
2
1
1
1
2
1
1
2
1
2
2
1
1
1
2
0
1
1
2
1
2
1
1
2
1
0
1
1
2
0
0
1
1
1
0
2
0
1
1
2
1
1
0
0
1
1
1
0
1
1
1
2
2
1
2
1
1
1
2
0
1
1
2
1
2
2
2
3
1
1
1
1
1
2
1
1
1
1
1
1
0
0
1
1
2
1
1
1
1
1
2
1
2
1
2
1
1
1
0
1
1
1
1
2
2
1
1
0
1
1
1
1
1
1
1
1
1
1
0
1
0
0
1
1
1
2
0
1
1
1
0
1
2
1
2
2
0
1
2
1
0
1
1
1
1
1
1
1
1
1
1
0
2
2
1
2
1
2
0
1
1
1
1
0
1
1
1
1
2
0
1
1
1
2
1
1
0
2
1
0
1
2
1
1
1
1
1
1
2
1
1
1
0
2
1
2
0
2
2
1
3
1
1
1
1
1
1
0
1
1
2
1
2
1
0
0
1
0
1
2
1
1
0
1
1
1
0
1
1
0
1
0
2
1
1
2
1
1
1
1
2
1
1
0
1
1
1
1
1
1
1
1
1
4
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
0
1
0
0
1
3
2
1
2
1
0
1
1
1
1
1
2
2
1
1
1
2
1
1
1
5
2
1
2
1
1
1
2
1
1
2
2
0
0
2
2
1
2
1
1
0
1
2
0
1
1
0
2
1
1
1
2
0
0
1
1
1
1
2
1
1
1
1
1
0
2
1
0
2
1
1
2
0
1
1
1
1
1
1
0
1
2
1
0
1
2
1
1
1
1
1
1
0
1
0
1
1
2
1
1
1
2
1
2
0
1
1
0
2
0
0
1
2
1
1
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
2
0
1
1
1
1
1
1
1
1
2
1
1
2
0
2
1
1
2
1
0
0
1
1
1
1
2
1
1
1
1
1
1
0
1
2
1
1
1
1
1
2
1
1
0
1
0
1
1
1
1
1
0
1
1
1
1
2
1
0
1
1
1
2
2
1
1
1
0
1
1
1
2
1
3
2
1
1
1
0
2
1
1
1
2
1
0
1
2
1
2
2
0
1
2
1
1
2
2
0
2
0
1
0
1
1
1
1
1
1
1
2
1
0
1
3
1
1
2
1
0
0
1
1
1
1
2
0
2
1
2
1
1
1
2
2
1
1
1
1
1
1
1
1
2
0
2
1
1
0
2
2
0
1
1
1
1
1
0
1
2
0
0
1
0
1
1
1
2
2
1
1
1
1
1
2
1
0
1
1
1
1
1
2
2
1
1
1
1
1
0
1
1
1
1
1
1
1
2
1
2
1
2
1
0
1
0
1
2
1
2
1
1
2
2
1
2
1
0
0
1
1
1
2
1
1
1
2
1
1
0
3
1
1
1
1
1
0
2
1
2
1
2
1
2
1
1
1
1
1
1
2
0
0
1
1
1
2
1
2
1
1
0
2
0
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
0
2
1
1
1
1
1
1
2
1
2
1
1
0
1
0
1
1
1
1
0
2
1
1
1
1
1
1
0
2
0
1
1
1
2
1
0
1
2
2
1
1
1
2
1
0
1
1
1
1
0
2
1
0
2
0
1
1
1
0
1
1
1
1
1
1
1
1
0
1
0
2
1
2
1
1
1
1
0
1
2
1
3
0
0
2
1
1
2
0
1
1
1
1
1
0
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
2
1
2
0
1
0
2
1
1
1
1
2
1
0
1
1
1
1
0
1
0
1
1
1
2
2
1
2
1
2
0
1
1
1
2
0
1
2
0
1
0
1
0
1
3
0
1
2
1
2
2
1
1
2
1
1
2
1
2
1
2
2
1
1
0
1
2
0
1
1
1
2
1
1
2
2
2
1
1
1
1
1
1
2
1
1
1
0
1
1
1
2
2
1
1
1
1
1
1
1
0
1
1
1
0
1
2
1
2
1
1
2
1
0
2
1
2
1
0
2
1
2
1
1
2
1
1
2
1
1
1
3
1
1
1
2
3
0
1
2
1
0
1
1
2
2
2
0
1
1
1
2
0
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
0
1
2
1
1
0
2
1
2
1
2
2
1
0
1
1
2
1
0
1
1
1
1
1
1
0
1
0
2
2
1
2
2
2
0
1
2
1
0
2
2
1
1
2
1
1
0
0
1
0
2
1
1
1
1
1
1
1
1
1
2
2
1
1
1
0
2
1
2
1
2
1
0
0
1
1
0
1
2
1
1
1
1
1
2
0
0
1
0
1
2
1
2
1
1
2
1
1
1
1
1
2
1
2
1
2
1
1
1
0
0
2
0
2
1
0
0
1
1
1
0
1
1
2
1
1
1
1
0
1
2
1
1
1
2
1
1
0
2
1
1
1
1
1
0
1
1
1
1
1
2
1
1
2
1
1
2
1
1
0
1
1
2
2
1
1
0
1
2
1
2
2
1
1
2
0
2
1
1
0
1
1
0
2
0
1
1
1
2
0
2
1
1
2
2
2
0
1
1
2
1
1
1
1
1
1
1
2
2
2
2
0
1
2
1
0
1
0
1
1
1
0
1
0
2
1
3
2
1
2
1
1
1
1
1
1
1
2
2
1
1
2
1
0
3
0
2
0
1
1
1
0
0
0
2
0
0
2
1
0
2
2
0
1
1
1
2
1
1
2
1
1
1
0
1
1
0
0
1
0
1
2
2
0
1
0
2
1
1
1
1
1
2
1
1
0
1
1
1
1
1
1
2
2
1
2
0
2
0
2
2
0
1
1
2
1
1
1
1
0
1
1
1
1
0
1
1
1
2
1
1
1
1
0
1
0
1
1
1
1
1
0
1
2
1
1
1
2
1
0
2
0
1
1
2
2
2
2
1
1
0
1
1
2
1
2
1
2
1
1
2
2
1
0
2
1
1
0
1
1
2
1
1
1
0
1
2
2
1
0
2
1
1
2
1
1
2
2
0
0
1
1
1
1
1
1
1
2
1
1
1
2
1
1
0
0
1
0
1
1
1
1
1
1
3
1
2
1
1
1
0
0
0
2
1
0
0
2
2
0
1
1
1
1
1
2
0
1
0
1
1
2
1
1
2
1
1
0
1
1
1
1
1
1
2
2
2
0
1
0
1
1
1
1
1
1
1
2
2
1
0
1
1
1
1
1
1
2
1
1
1
2
2
1
1
2
0
1
1
1
2
2
2
1
2
0
1
1
1
1
1
1
0
1
1
1
0
2
2
2
0
1
1
0
1
1
1
1
1
0
2
1
2
0
0
1
1
1
2
1
1
2
2
1
1
2
1
1
0
1
2
0
0
2
1
1
1
1
0
1
1
1
1
1
1
1
2
1
2
1
0
1
2
2
1
2
1
2
2
3
1
2
1
2
1
0
1
1
0
2
2
1
2
2
2
1
0
1
1
0
1
1
2
1
2
1
1
1
1
0
1
0
1
2
1
1
1
1
2
0
1
2
1
1
2
0
1
0
1
1
0
1
1
1
0
2
0
1
2
2
1
1
2
1
0
2
2
0
1
1
1
0
1
1
0
2
2
1
1
2
1
1
0
1
1
1
0
1
1
1
0
2
0
1
1
1
0
2
1
0
1
2
2
2
1
1
2
1
1
0
1
1
2
1
1
1
0
2
0
1
0
1
1
1
2
2
1
1
1
0
1
1
0
1
1
1
1
0
1
0
2
2
1
1
2
0
1
1
1
0
1
2
1
1
2
1
1
0
0
1
1
2
1
1
1
1
1
1
1
1
0
1
1
1
1
2
1
1
1
2
1
2
1
1
1
2
1
1
1
0
1
1
0
0
1
1
2
1
1
1
1
1
3
2
1
4
1
1
1
0
0
1
2
1
1
0
0
0
1
2
1
1
2
0
0
1
1
0
1
2
1
0
1
2
2
1
1
0
1
1
1
1
1
1
2
2
2
2
1
1
1
1
1
1
1
0
1
1
1
0
1
2
0
3
1
1
1
2
1
0
0
1
1
1
1
2
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
0
1
1
1
3
2
2
1
0
1
1
1
1
1
2
1
2
1
1
2
1
2
1
1
1
0
1
0
1
2
1
2
1
1
1
2
2
2
1
1
1
0
1
1
1
2
0
0
1
1
1
1
2
1
2
0
1
2
1
1
1
1
1
0
2
1
1
2
1
0
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
0
2
1
1
1
3
1
1
2
1
2
2
1
1
1
1
1
1
1
1
2
0
1
1
1
0
2
1
0
1
1
1
1
2
1
1
1
1
1
1
2
1
2
1
1
1
0
1
0
1
0
0
1
1
1
1
2
0
0
1
1
2
2
1
2
2
1
1
1
1
0
1
1
0
1
2
1
0
2
1
1
0
1
1
2
3
0
2
1
0
1
1
1
1
1
2
0
2
1
2
2
0
2
2
1
0
2
1
1
1
2
0
0
1
0
1
1
0
0
1
2
0
2
1
2
2
0
2
1
2
1
1
1
1
2
2
1
1
1
1
1
0
1
1
1
1
0
1
1
1
1
2
1
2
0
1
1
2
2
2
1
1
0
0
2
1
1
1
2
0
0
2
1
0
1
2
2
1
1
2
1
1
2
0
0
1
1
1
1
1
1
1
2
0
0
1
3
1
2
1
1
1
1
0
2
0
1
1
1
2
0
0
2
1
1
1
3
0
2
1
1
1
1
1
1
0
0
1
1
2
1
2
1
2
1
1
2
1
1
0
1
1
1
2
0
2
1
1
2
0
1
1
2
2
1
0
1
0
2
1
1
2
1
2
1
2
1
0
2
1
1
1
1
1
1
1
1
2
1
1
1
0
1
1
1
1
1
2
0
0
1
2
2
0
1
1
0
1
1
1
2
1
1
1
1
2
2
2
1
2
1
2
1
2
2
2
1
1
1
2
2
0
1
1
1
2
1
1
1
1
1
2
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
2
0
1
1
2
1
1
2
1
2
0
1
1
1
1
2
2
1
1
1
1
1
1
0
1
1
2
2
2
0
2
2
1
2
2
1
1
1
1
1
1
2
1
2
2
0
1
3
1
1
2
1
0
1
0
2
1
1
2
0
1
2
0
1
1
1
1
1
1
1
1
1
2
1
1
0
2
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
0
2
1
0
0
1
0
1
1
1
1
0
2
2
2
2
1
1
1
1
1
2
2
0
1
1
2
2
1
2
0
1
2
1
0
1
1
1
2
1
1
0
1
1
1
0
2
2
1
1
1
0
2
1
2
3
1
2
2
0
2
1
1
0
0
0
1
1
2
1
0
0
2
2
1
2
2
0
1
0
1
1
0
1
1
1
1
1
1
1
2
0
2
2
2
2
2
2
1
1
2
1
1
1
1
1
0
2
1
2
1
2
0
2
1
2
0
2
2
1
1
1
2
0
1
2
2
1
2
1
1
1
1
1
1
1
1
2
2
1
1
1
1
2
0
2
1
1
2
1
1
1
2
0
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
0
2
1
2
1
2
1
0
1
1
0
1
2
1
2
1
1
1
1
2
0
1
1
1
1
1
1
1
1
0
1
1
1
1
1
2
1
2
1
2
1
1
2
1
2
2
2
0
2
2
0
2
1
0
1
1
1
0
2
1
1
1
0
0
2
1
2
0
0
0
1
1
1
1
1
1
1
1
1
1
0
1
1
1
0
1
2
1
2
1
1
2
0
1
1
2
2
0
1
1
2
1
1
1
1
1
1
2
1
1
1
2
0
2
1
1
1
1
1
2
1
1
0
1
0
1
1
1
2
1
1
1
2
0
1
1
1
1
1
0
1
0
1
1
2
0
1
2
2
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
1
2
2
1
2
2
1
1
1
1
2
1
1
1
2
1
0
1
2
2
2
1
1
1
1
1
1
1
1
1
0
1
2
2
1
2
1
0
1
1
1
2
1
1
1
2
2
1
1
1
2
1
1
1
1
1
1
2
2
0
0
1
0
1
1
1
2
1
1
1
1
0
1
1
1
1
2
0
2
0
1
1
2
1
2
1
1
2
3
2
1
1
1
0
1
1
2
1
2
1
1
0
0
1
1
1
1
2
1
0
1
2
1
0
1
1
1
1
2
1
1
0
1
1
1
1
1
2
1
2
1
0
2
2
1
1
1
1
2
1
1
1
1
1
1
2
1
2
0
0
1
2
1
2
1
1
1
2
1
1
0
2
1
1
2
1
0
1
2
1
1
1
1
0
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
2
1
2
1
2
1
0
1
1
1
0
2
2
0
1
1
2
2
1
1
1
1
0
2
2
1
2
0
1
1
2
1
1
1
2
0
1
1
1
1
0
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
1
1
2
1
1
1
1
2
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
2
1
0
0
1
1
1
1
1
1
1
1
1
1
2
0
2
0
2
2
1
1
1
2
2
1
0
1
1
1
2
1
1
1
1
1
1
2
3
1
2
1
1
0
1
1
1
0
1
1
2
1
2
2
1
1
1
1
1
2
1
0
1
0
0
2
1
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
2
1
1
1
1
2
1
2
2
1
1
1
2
3
1
2
2
2
1
1
2
1
1
1
1
1
2
0
0
0
1
1
1
2
1
1
2
0
0
1
1
2
1
1
2
1
1
0
1
2
1
1
1
1
1
2
1
0
0
0
2
0
1
0
1
1
1
3
1
1
1
1
1
1
1
0
1
2
1
2
2
1
1
2
2
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
1
2
0
0
1
2
1
2
2
0
1
1
0
1
0
1
1
1
1
2
1
0
0
0
1
2
1
1
1
1
2
1
3
1
3
1
1
1
1
0
0
2
1
2
2
1
1
1
1
1
0
1
1
1
2
0
2
1
2
1
1
0
1
2
1
1
3
2
0
1
1
1
2
1
1
1
1
1
1
2
1
1
1
0
2
1
1
1
0
1
1
2
1
2
2
0
1
1
2
1
1
1
1
0
1
2
1
2
0
2
1
1
0
0
2
1
1
1
1
1
1
1
2
4
2
1
2
1
1
2
0
1
1
1
1
1
1
1
1
1
1
1
0
1
1
0
0
1
1
1
1
2
0
2
0
2
0
1
2
1
2
1
1
1
2
0
2
1
2
2
1
1
2
2
2
1
2
1
1
2
2
0
1
1
2
2
3
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
2
1
1
4
1
1
2
1
1
0
1
1
2
1
1
0
2
1
1
2
1
0
2
1
0
1
1
1
2
1
1
1
0
1
2
1
2
1
2
2
1
2
1
1
0
1
1
1
2
2
1
1
1
2
0
2
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
0
0
2
1
1
1
1
0
2
2
0
1
1
2
1
1
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
0
2
1
1
2
0
1
1
2
2
1
1
1
2
1
2
1
2
1
1
1
1
2
1
1
1
1
2
2
1
1
1
1
2
2
1
1
0
2
1
1
2
1
1
3
2
0
0
3
1
1
1
2
2
1
2
5
0
2
1
0
1
0
1
2
2
1
1
1
1
2
0
0
2
2
2
2
1
0
2
1
1
1
1
2
1
1
2
1
2
3
1
1
0
1
0
1
2
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
0
2
2
1
2
1
1
1
1
2
2
2
0
1
1
1
1
1
1
0
1
1
1
1
1
1
2
1
1
1
1
0
1
2
2
2
1
1
1
1
1
2
0
2
0
1
1
1
2
1
2
1
1
2
1
1
0
1
0
2
1
2
2
2
1
1
1
1
2
1
2
1
1
0
2
0
1
2
2
2
2
2
1
2
1
1
0
1
0
1
2
1
0
1
0
1
1
1
2
1
0
2
1
1
1
1
0
1
2
1
2
1
1
1
0
1
1
1
0
0
1
1
1
0
2
2
1
0
1
2
0
1
1
2
1
1
1
1
1
2
2
0
1
1
2
0
1
1
2
1
2
1
1
0
1
0
2
2
2
1
2
2
1
1
2
2
1
1
0
1
1
1
1
1
1
0
0
1
1
1
1
2
1
1
1
1
1
2
1
1
1
0
1
1
1
1
1
2
0
1
1
1
1
1
1
1
2
1
2
1
1
2
1
1
0
1
1
0
1
1
1
1
1
1
2
1
0
0
1
0
0
1
1
0
2
0
1
2
1
1
2
0
1
0
2
0
1
2
1
2
1
0
1
1
1
1
1
0
0
0
1
1
1
2
1
2
2
2
2
2
1
1
0
1
2
0
2
1
2
2
2
2
1
2
1
1
2
1
0
0
2
1
1
0
1
0
1
2
1
2
2
1
1
1
1
2
2
1
1
1
2
1
1
2
1
1
1
0
2
2
1
2
1
1
1
1
2
2
1
3
2
1
1
0
1
1
1
1
1
0
1
2
1
0
0
2
0
2
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
0
1
4
1
1
2
2
1
2
1
1
1
2
0
2
0
2
1
1
1
2
1
1
1
1
2
0
0
1
1
1
1
0
1
1
2
1
2
1
0
1
1
0
1
1
1
1
0
1
2
1
1
0
1
2
2
1
2
2
0
1
0
1
0
2
2
2
0
1
1
2
1
2
1
1
1
1
1
1
1
0
2
2
1
2
1
1
1
1
1
1
2
1
1
1
1
2
2
0
2
1
0
1
1
2
2
1
2
1
0
1
1
0
2
1
1
1
1
2
1
1
2
1
1
1
2
2
1
2
2
1
0
0
1
1
2
1
1
1
1
2
1
2
1
1
2
1
1
0
2
1
0
1
2
0
0
1
2
2
1
1
0
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
2
1
1
3
4
1
2
1
1
0
1
1
1
0
2
2
2
1
1
2
1
1
1
1
0
2
2
1
0
2
1
2
2
1
2
2
1
1
1
1
1
2
1
1
1
1
1
1
0
1
1
0
0
1
1
2
0
1
1
1
1
1
1
0
1
0
0
1
1
1
0
1
1
1
3
1
1
1
1
2
1
0
1
1
2
2
2
1
0
1
1
1
2
2
2
1
1
1
1
0
1
1
2
1
0
2
2
1
1
1
2
1
1
2
1
0
4
2
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
0
2
0
1
1
1
1
2
1
2
0
2
1
1
1
1
2
1
1
2
0
1
2
1
1
0
1
0
1
1
0
1
0
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
0
2
1
1
1
1
1
1
1
1
0
0
1
1
1
1
0
0
0
1
1
0
1
1
1
1
1
2
1
1
1
1
2
2
1
1
3
1
1
1
0
1
1
2
1
1
2
1
2
1
0
1
2
2
2
2
1
1
1
1
1
2
0
1
2
2
1
2
1
1
1
1
1
1
2
1
1
1
2
1
2
2
2
2
1
0
2
1
2
2
1
2
1
1
2
2
1
0
1
0
1
1
2
1
2
0
0
0
1
0
1
2
0
1
1
1
1
1
1
1
0
1
1
0
2
2
1
1
2
2
0
2
0
0
2
1
1
1
1
2
1
2
2
1
1
1
1
2
1
0
1
1
2
1
0
1
1
1
2
2
1
1
1
1
2
1
0
0
0
0
2
1
2
0
1
1
1
1
2
0
1
2
2
1
1
1
1
1
1
2
0
0
0
2
1
1
1
1
1
0
1
1
2
0
1
1
2
1
0
1
2
1
1
0
0
1
1
2
1
1
2
1
0
1
1
1
0
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
2
1
2
1
0
0
2
1
2
1
0
1
2
0
0
2
2
1
1
2
1
2
2
2
1
2
2
2
1
1
1
0
1
1
1
1
0
1
0
1
1
1
1
1
2
2
1
2
0
2
1
1
0
0
1
2
1
1
1
1
1
1
0
1
1
1
0
1
0
1
0
1
1
1
1
2
2
1
0
2
1
0
2
2
1
2
2
2
1
1
1
1
1
0
1
1
2
1
1
1
0
3
0
1
1
2
1
1
2
2
2
1
0
0
2
0
2
1
1
0
1
2
1
1
2
0
1
1
1
0
1
2
2
0
2
2
1
4
0
2
1
0
1
2
2
2
1
2
1
1
1
2
2
1
1
1
2
2
2
1
2
2
1
1
2
1
2
1
1
2
2
1
1
0
0
1
1
1
2
1
1
0
1
2
4
2
1
0
1
1
1
0
0
1
2
1
0
2
1
2
0
0
0
1
1
2
2
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
2
1
0
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
0
1
1
0
0
1
2
2
1
2
1
0
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
0
1
2
1
1
1
2
1
1
2
2
1
1
0
2
1
1
1
2
1
1
0
1
1
1
1
2
1
2
1
2
1
1
2
2
0
1
1
2
1
0
2
1
1
2
1
1
2
2
1
1
2
1
1
1
0
2
1
1
2
2
2
1
1
2
1
2
0
2
1
0
1
1
1
0
2
2
1
1
1
0
2
1
2
1
0
1
1
2
1
1
2
1
0
2
1
2
0
1
0
2
1
0
1
1
1
1
1
2
1
1
0
2
2
1
1
1
1
2
1
2
1
1
1
2
1
1
2
1
1
1
0
2
2
1
1
1
1
1
1
1
0
1
2
1
2
1
1
1
1
1
0
1
0
1
2
1
1
2
1
1
1
1
1
0
0
1
1
2
2
2
1
1
1
2
1
1
2
1
1
2
2
1
1
1
0
1
2
2
0
1
2
2
1
1
1
2
1
1
1
2
1
1
2
2
1
2
2
0
1
2
2
0
1
2
0
2
2
1
2
1
1
1
1
0
0
1
2
2
1
1
1
1
2
0
1
2
0
1
2
2
1
1
0
2
1
1
3
1
1
2
1
2
1
1
2
1
2
0
2
1
0
1
2
1
2
2
1
2
1
0
2
0
2
0
1
1
1
1
1
2
1
2
1
2
0
0
0
1
1
2
2
1
2
1
0
1
2
2
2
1
1
1
2
0
1
1
0
1
0
1
1
2
0
2
1
2
2
1
2
0
1
2
1
0
0
1
1
1
1
1
2
2
1
0
2
1
2
1
0
1
1
1
1
2
2
1
1
0
2
2
1
0
1
1
2
1
2
0
2
1
2
1
0
0
2
2
2
1
1
1
1
1
0
1
2
1
1
1
2
1
2
1
1
2
0
1
1
1
2
1
2
1
1
2
1
1
1
0
0
1
1
0
2
1
1
1
0
1
1
0
1
1
1
0
1
1
2
2
1
1
1
0
2
1
1
2
0
1
2
1
2
2
0
1
2
1
1
1
1
2
1
2
1
2
1
0
1
2
1
1
1
2
2
1
1
1
1
2
1
2
1
1
1
2
1
1
2
2
1
1
1
1
3
2
1
2
0
2
1
2
2
1
1
1
1
1
1
1
2
1
1
2
1
0
1
2
2
2
2
1
1
2
2
2
1
0
1
2
1
1
0
1
0
2
0
0
1
1
1
1
1
2
1
1
0
1
0
1
0
2
0
2
2
2
1
1
1
2
1
0
2
1
0
1
1
1
1
1
0
0
1
1
2
1
1
2
2
1
0
1
1
2
2
1
0
1
2
1
1
0
0
1
2
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
2
1
1
0
1
2
0
2
2
1
1
1
1
1
1
1
1
1
0
2
0
1
1
1
2
1
0
0
2
0
0
2
1
1
1
0
2
2
2
2
0
1
1
1
1
1
2
1
1
1
1
0
1
1
1
1
2
1
0
1
1
1
2
2
1
2
1
1
2
1
2
1
2
1
0
3
1
1
1
2
1
1
0
1
2
1
2
1
0
2
0
1
2
1
1
1
1
2
1
1
0
1
1
0
2
2
1
1
1
1
0
1
2
0
1
1
1
1
1
1
1
1
2
1
0
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
0
1
2
0
2
1
1
0
1
1
0
0
1
1
0
1
1
2
1
1
2
1
0
1
1
1
1
1
1
1
2
1
3
2
1
1
1
2
1
0
0
2
1
1
2
2
1
1
2
1
1
1
2
1
1
1
1
0
0
1
2
1
0
2
0
1
1
1
1
1
1
0
1
3
1
1
2
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
0
1
0
1
1
2
1
1
2
1
0
2
1
1
1
1
1
2
1
1
1
1
0
1
2
1
1
1
1
2
2
1
2
1
0
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
2
1
2
0
1
2
0
1
0
1
1
2
2
1
2
0
2
1
1
1
1
1
1
1
0
1
2
1
1
1
1
2
1
2
0
2
1
1
1
0
2
1
1
2
1
1
1
2
1
1
1
1
2
0
1
2
1
1
2
0
2
2
1
1
1
2
1
1
1
1
1
2
1
0
1
1
2
2
1
1
1
2
1
1
2
1
2
0
0
1
0
1
2
2
1
1
0
0
1
1
2
2
0
2
1
0
2
1
1
0
2
0
1
1
2
1
1
1
2
1
1
2
2
0
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
2
2
0
2
2
1
2
2
0
1
2
1
1
1
1
2
1
2
1
1
1
2
2
1
1
2
1
2
9
2
1
0
1
2
1
1
1
1
1
1
1
0
1
0
0
2
0
1
1
1
1
1
2
0
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
2
1
1
1
2
1
1
1
1
1
0
1
2
1
1
2
1
0
2
1
2
0
1
1
0
1
1
1
1
1
1
1
1
3
2
2
1
1
1
1
1
1
1
1
1
2
2
1
1
2
0
1
1
1
1
1
1
2
1
1
1
0
1
2
1
1
0
1
0
0
2
1
1
2
1
1
1
1
2
1
1
1
2
2
1
2
1
2
2
1
1
0
1
0
2
2
0
1
1
0
1
2
1
1
2
1
1
1
1
2
1
1
1
1
1
1
2
1
1
0
1
2
2
1
2
0
1
2
1
0
2
1
0
2
1
2
0
2
0
1
1
1
2
1
1
1
1
2
0
0
1
1
1
1
1
1
1
1
0
1
0
2
1
1
2
1
2
2
1
1
1
1
1
2
2
1
1
1
2
1
2
0
1
1
1
1
2
1
1
1
1
2
1
1
2
0
1
3
2
0
1
2
1
0
1
1
0
1
0
1
2
1
1
0
1
2
1
1
1
1
1
0
1
2
2
2
1
1
2
1
1
1
1
2
1
1
1
1
1
0
2
0
1
1
1
2
1
1
1
1
0
1
1
1
1
2
1
2
0
1
2
2
1
1
1
1
1
2
1
0
1
1
1
1
1
2
2
1
1
1
2
1
1
1
1
2
1
2
1
2
2
2
1
1
1
1
1
1
0
1
1
1
2
1
2
1
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
0
2
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
0
2
2
0
0
1
2
2
0
1
2
1
1
1
1
1
2
0
2
2
1
2
1
1
0
0
2
1
1
0
2
1
1
0
1
2
0
1
1
1
0
1
2
2
2
1
2
1
2
1
1
2
2
0
1
1
0
1
1
2
1
1
1
1
1
1
1
2
2
2
1
3
2
1
1
1
1
1
2
0
1
2
1
1
1
1
1
1
1
2
0
2
2
1
2
1
1
0
1
1
2
1
1
1
1
0
1
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
0
1
1
0
1
1
1
1
2
0
1
2
1
2
1
2
1
1
1
1
2
1
0
2
2
1
1
1
1
1
1
2
1
1
1
2
1
1
2
1
1
0
1
1
1
1
1
0
1
2
1
1
1
1
1
0
0
1
1
2
1
1
0
0
1
1
2
1
1
2
2
1
1
1
2
0
1
2
0
2
2
1
2
0
1
1
0
1
0
2
2
1
1
1
1
1
1
1
2
1
2
1
2
0
1
1
1
1
1
1
2
1
2
1
1
1
2
1
1
2
0
1
2
2
1
0
0
2
2
1
1
1
1
1
1
1
0
1
2
1
1
2
2
1
1
0
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
0
2
1
2
1
0
2
1
1
1
2
2
1
1
1
1
1
1
0
1
1
2
1
2
2
2
2
1
1
0
0
1
0
1
0
1
1
2
1
1
1
2
2
2
1
1
0
2
2
2
1
1
1
1
2
1
2
2
1
2
1
1
2
1
0
1
0
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
0
1
1
2
2
1
1
1
1
1
1
1
1
1
2
1
0
2
0
0
0
0
1
1
1
2
1
6
1
3
2
2
2
1
1
1
1
1
2
1
0
1
0
0
0
0
1
0
2
2
0
1
1
2
1
2
2
0
2
0
1
1
1
1
2
2
1
2
0
2
1
2
1
2
1
1
1
0
0
1
2
0
1
2
1
1
1
1
0
1
2
1
1
1
2
2
0
1
1
2
1
0
1
2
2
1
2
2
1
2
1
1
1
1
0
2
1
1
2
2
1
0
1
2
1
2
1
0
1
0
1
1
1
1
1
0
1
0
1
1
1
0
1
1
1
0
2
1
2
1
1
1
1
1
1
2
2
0
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
0
1
1
1
1
2
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
0
2
2
2
2
2
2
0
2
2
1
2
1
2
2
0
2
1
2
1
0
1
1
3
1
1
1
1
0
1
1
1
1
1
1
1
1
1
0
1
1
2
1
2
0
2
1
2
1
1
1
1
0
2
1
1
1
1
3
1
1
0
2
1
1
2
1
1
0
0
1
1
1
0
2
1
0
2
1
1
0
1
1
1
1
0
1
1
1
0
1
1
0
0
0
1
0
1
1
1
1
2
2
1
1
1
1
1
1
0
1
1
2
1
0
1
1
2
2
1
1
1
0
0
2
1
2
2
2
1
1
2
0
1
2
1
1
1
1
0
1
1
1
1
0
1
1
0
2
1
1
1
1
1
1
2
2
1
1
1
1
1
1
0
1
2
1
2
1
1
1
1
1
1
2
2
1
0
1
2
0
1
2
2
2
1
2
0
1
1
1
1
1
1
1
1
1
0
2
0
1
2
1
2
1
1
2
1
0
2
2
1
2
2
1
1
2
2
1
2
1
0
1
0
1
1
1
1
2
1
0
2
0
1
1
2
1
2
2
2
2
1
1
1
1
1
1
1
2
2
0
2
1
1
0
0
2
0
2
1
1
1
2
0
0
2
2
1
2
0
1
2
0
1
1
1
0
1
2
0
1
2
1
1
4
1
2
1
1
2
1
2
2
1
2
1
1
2
1
0
1
1
1
1
2
1
1
2
1
2
1
1
1
1
0
2
1
1
0
1
1
0
1
1
1
1
1
1
1
2
1
1
1
0
1
1
1
1
1
1
1
1
0
1
0
1
1
2
1
2
1
1
2
0
1
2
1
1
1
1
0
0
1
2
1
1
1
1
2
0
1
1
0
1
1
0
1
1
1
1
1
2
0
1
1
0
1
2
2
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
3
1
1
2
0
0
1
1
2
1
1
1
1
1
0
2
1
1
2
2
1
1
2
1
1
1
0
0
1
2
2
1
1
1
1
2
1
1
1
1
1
0
0
1
0
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
0
1
0
1
1
1
0
1
2
1
0
1
0
0
1
1
1
1
2
1
1
1
0
1
1
1
0
1
1
2
1
1
2
0
2
1
1
0
2
1
1
1
1
1
1
2
1
3
1
1
1
2
2
1
0
1
1
1
1
1
1
2
1
1
1
1
0
1
0
1
1
1
2
2
1
1
0
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
0
1
2
1
0
2
2
0
1
2
2
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
0
2
1
1
0
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
2
1
2
2
1
2
2
2
2
1
0
2
1
1
1
2
1
1
1
0
1
1
1
1
1
1
1
3
1
1
1
1
1
1
1
2
1
0
1
2
0
1
2
1
1
1
1
1
2
0
1
1
2
0
1
1
1
0
1
1
1
2
1
0
1
1
1
2
1
0
1
2
1
1
2
1
1
2
2
1
1
1
1
1
1
1
0
1
1
0
1
0
1
1
2
0
0
1
2
2
2
3
1
1
0
1
1
2
1
1
1
1
2
2
0
1
0
1
1
1
1
0
1
1
1
2
1
1
1
0
2
2
2
0
2
1
1
1
1
2
2
1
1
2
1
2
2
1
2
2
1
1
1
1
1
1
2
0
0
2
1
0
1
1
2
1
0
1
1
3
1
1
1
2
1
1
1
1
1
2
2
1
1
0
1
1
1
0
2
1
1
1
2
2
1
1
2
1
0
2
2
1
0
1
0
2
1
1
1
0
0
1
1
0
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
0
1
3
1
1
1
1
1
1
1
1
1
0
1
1
1
1
2
2
1
0
1
2
1
2
1
1
1
1
2
1
1
0
1
1
1
1
2
1
2
1
1
0
1
2
1
1
0
1
1
1
0
1
1
2
2
1
1
2
0
1
2
2
2
0
2
2
0
2
2
2
1
1
1
1
1
0
1
0
1
1
2
1
1
2
1
2
2
1
1
3
1
0
1
0
0
2
1
1
2
1
1
1
1
1
1
0
1
1
1
1
1
1
2
1
2
0
1
0
2
1
1
1
1
2
1
0
0
1
1
1
2
1
1
1
0
2
2
1
2
1
2
2
2
1
1
2
2
1
1
0
1
1
1
2
1
1
1
2
1
1
0
2
1
0
1
0
2
2
0
1
0
1
2
2
2
0
1
1
2
1
1
1
1
0
1
1
1
1
0
1
2
1
2
1
1
1
2
1
1
1
0
2
1
1
1
1
1
2
1
1
2
1
1
1
2
0
1
1
1
1
1
1
0
1
1
0
1
1
1
1
2
2
1
1
1
1
0
1
1
1
1
2
1
2
0
1
1
1
1
1
2
2
2
1
1
1
2
2
2
0
2
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
0
1
1
0
1
1
1
2
1
1
1
2
2
1
2
0
1
1
1
1
2
2
1
1
2
0
0
1
1
1
1
1
0
2
2
1
1
2
1
1
1
2
1
1
1
1
1
3
1
2
1
2
0
1
0
1
1
1
4
1
1
1
1
0
0
1
2
0
2
1
1
1
0
1
2
2
1
2
0
2
2
1
2
2
2
0
1
2
2
2
1
1
0
0
1
1
1
1
1
1
1
2
1
1
0
0
1
0
1
1
1
1
2
1
1
2
1
1
0
1
1
2
0
1
1
1
1
1
1
1
1
1
1
1
1
2
1
0
1
0
2
2
1
1
1
1
2
0
1
1
0
1
1
1
0
2
1
2
0
1
1
0
0
2
2
2
1
2
1
2
1
2
2
0
1
1
1
1
1
1
2
0
2
1
1
1
1
2
1
0
1
2
0
2
2
1
1
2
1
0
0
1
1
0
1
1
2
2
2
1
0
1
1
2
2
1
1
0
1
3
2
2
2
2
0
1
2
1
1
1
2
1
1
0
0
1
1
0
2
1
0
1
2
1
2
2
2
1
1
1
1
1
1
2
2
1
2
0
2
1
1
1
1
2
2
1
1
1
1
1
2
1
1
2
1
1
1
0
1
1
2
1
1
0
2
0
1
0
1
1
1
0
2
2
2
0
1
2
0
0
1
2
1
1
0
1
1
1
2
0
2
1
1
1
2
2
1
1
1
0
1
2
2
1
2
1
1
0
0
1
1
2
1
1
1
2
2
1
2
1
0
2
1
1
1
1
1
1
1
1
1
1
1
2
1
0
1
1
1
1
1
2
1
1
0
2
2
2
1
1
1
1
2
1
2
1
1
1
0
1
0
1
1
1
2
1
1
1
1
1
0
1
2
1
1
0
1
2
2
1
1
2
2
1
1
2
2
1
0
1
2
0
1
1
2
1
1
2
2
2
1
1
1
0
2
2
1
0
2
1
1
1
1
1
1
2
2
2
1
1
1
1
2
0
1
1
0
1
1
1
1
1
1
2
1
2
1
1
1
2
1
0
1
2
2
1
2
1
1
1
1
0
1
0
1
1
1
1
1
1
2
1
1
1
0
2
2
1
2
1
2
2
0
1
2
2
1
1
2
1
1
1
1
1
1
1
1
2
2
1
1
1
2
1
0
1
0
0
1
1
1
1
1
1
0
2
2
2
1
0
1
1
2
1
2
2
1
1
1
2
1
0
0
1
1
0
0
1
3
1
1
2
0
1
1
1
1
2
1
1
0
1
1
1
2
1
2
1
2
2
1
1
0
1
2
0
0
1
2
1
1
1
1
0
1
1
2
2
1
0
1
1
2
1
1
0
0
1
1
1
1
1
1
1
1
2
0
1
1
0
1
1
2
1
1
1
0
1
2
1
1
1
1
2
2
1
2
1
2
1
2
2
1
0
0
2
1
1
1
1
1
1
1
2
1
2
2
0
1
2
1
2
1
1
1
1
2
1
1
1
0
1
1
1
2
2
1
2
1
2
2
1
2
1
1
1
1
2
1
2
0
1
2
1
0
1
1
2
2
1
3
0
1
2
0
1
0
1
1
1
1
2
1
2
1
0
1
1
0
1
1
0
1
1
1
1
1
1
1
0
1
1
1
2
2
2
2
1
1
2
2
2
1
1
0
1
0
0
1
1
1
0
1
1
2
1
0
1
1
1
0
2
1
1
2
1
0
1
0
2
2
1
1
2
2
2
2
1
0
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
0
1
1
0
1
2
1
1
2
1
1
1
2
2
2
2
0
1
1
0
0
2
1
2
0
0
0
1
0
2
1
1
2
1
1
1
1
1
0
1
0
2
1
0
1
2
0
2
1
1
1
1
1
0
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
2
1
1
2
1
1
1
0
0
1
2
1
1
1
2
1
2
1
1
1
1
1
1
2
0
1
1
1
1
2
2
0
1
0
1
0
1
2
2
1
2
1
2
0
1
1
1
1
1
1
2
0
1
1
1
1
1
2
1
1
0
1
0
1
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
0
1
1
1
2
1
1
1
2
1
1
1
1
2
0
2
1
1
1
1
0
2
2
1
1
2
4
1
1
0
1
1
1
2
1
1
1
0
1
1
1
1
1
2
1
2
2
1
1
0
0
2
1
1
1
1
1
1
1
1
1
0
0
2
1
2
1
1
0
1
0
1
0
1
1
1
1
0
1
2
1
1
1
1
1
0
2
1
1
1
0
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
0
1
1
1
1
0
1
0
1
0
0
0
0
1
2
2
1
1
0
1
2
1
1
1
1
0
0
1
1
1
1
1
2
1
1
2
0
1
1
2
0
1
2
1
1
1
1
2
1
1
2
1
2
1
0
1
2
2
1
1
1
1
0
1
2
1
1
0
1
2
0
2
2
1
1
1
2
1
0
1
1
1
2
1
0
0
1
1
1
2
0
2
1
1
2
1
5
1
1
3
1
1
0
2
1
1
1
1
1
2
2
0
1
1
2
1
2
2
1
1
1
1
1
1
2
0
0
0
1
2
1
1
1
2
2
1
1
2
1
1
1
1
2
1
1
1
0
1
0
1
1
1
1
2
1
1
1
0
1
2
0
2
1
2
1
1
2
2
2
1
2
1
0
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
2
1
1
2
1
0
1
2
1
2
2
2
2
1
1
1
1
0
1
1
1
2
1
2
1
1
1
1
1
0
1
0
1
0
0
1
1
1
1
2
2
1
1
1
2
2
1
0
1
1
1
1
1
2
1
1
1
1
1
2
2
1
1
1
1
1
0
1
2
2
2
2
1
0
1
2
1
1
1
0
1
2
1
1
1
2
0
1
2
1
1
1
1
1
2
0
1
1
2
0
0
1
1
1
2
1
1
0
1
1
0
1
1
1
1
1
2
1
0
2
0
1
1
2
1
1
2
1
1
1
1
2
0
0
2
1
0
2
1
1
1
0
1
1
1
0
2
0
1
1
1
1
2
2
1
2
0
1
2
1
1
2
1
2
0
1
2
0
1
1
1
2
1
1
1
2
1
2
2
1
1
0
2
2
1
1
1
1
0
2
2
1
0
3
0
1
1
0
1
1
1
0
2
1
1
1
1
2
0
1
2
2
1
2
2
1
3
1
0
1
1
1
1
1
1
2
0
1
2
2
1
1
1
1
0
2
1
1
1
1
1
0
1
0
1
1
1
1
1
1
1
1
2
2
0
0
1
0
0
1
1
1
2
2
2
1
2
2
1
2
2
1
1
1
2
1
2
2
1
2
1
2
2
1
1
1
1
0
2
1
1
0
0
1
0
0
1
2
1
2
2
2
2
1
2
1
1
1
1
1
1
1
2
1
1
1
0
1
1
1
1
1
0
1
2
1
2
1
2
2
1
2
1
1
0
1
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
2
2
2
0
1
2
1
1
1
1
1
0
2
0
1
1
2
1
1
2
0
1
1
1
2
0
2
1
1
0
2
1
2
1
2
2
2
1
2
2
1
1
1
0
0
1
2
2
1
2
2
1
2
1
1
0
0
1
2
0
1
1
1
2
1
1
1
1
0
1
0
2
1
0
1
1
0
1
1
1
1
2
1
1
1
0
1
2
1
2
1
0
1
1
1
1
0
1
1
1
1
0
2
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
0
1
0
0
1
2
1
1
3
1
1
0
2
0
2
0
2
1
1
1
1
2
1
0
1
0
0
2
1
1
1
1
2
1
0
1
0
0
0
1
1
1
2
0
2
1
1
1
1
0
0
1
1
1
2
0
1
2
1
1
1
0
2
0
0
1
1
2
1
1
2
1
1
1
1
2
2
1
0
1
0
0
2
0
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
0
1
2
1
0
1
2
1
1
1
1
1
1
1
1
0
1
2
0
1
1
1
2
1
1
1
0
1
1
1
1
0
1
2
0
2
1
1
1
2
1
1
1
1
1
2
2
1
1
1
2
1
1
0
0
1
1
1
0
1
0
1
1
1
1
0
1
1
1
1
1
1
1
2
1
0
0
1
1
1
2
2
2
0
2
0
1
1
1
2
1
1
1
2
0
1
1
1
1
1
1
0
1
1
2
1
2
1
0
2
1
1
1
1
1
1
2
3
1
2
2
1
2
1
1
1
1
1
1
2
1
1
0
1
1
2
1
2
0
2
0
1
1
1
1
2
2
0
1
1
1
1
3
2
1
1
1
1
2
1
1
2
2
2
2
1
1
3
1
2
2
1
1
1
2
1
1
0
1
2
0
2
2
2
1
1
0
2
1
1
1
1
1
2
2
1
2
1
0
1
1
1
1
1
1
1
2
1
1
1
1
0
1
1
1
1
1
1
2
0
2
1
1
0
2
1
2
2
1
1
1
2
1
1
0
1
1
1
2
1
0
2
1
2
0
3
1
1
0
1
2
1
1
1
1
1
1
2
2
0
2
2
2
1
1
1
0
1
1
2
0
1
1
0
2
1
1
1
1
3
1
1
2
2
0
1
2
1
1
2
1
1
1
1
2
2
2
1
2
1
1
1
0
2
1
0
2
1
0
2
2
2
1
1
0
2
2
2
2
2
1
1
1
2
1
1
1
2
1
2
2
1
4
1
1
1
0
1
1
2
1
1
1
1
0
1
1
2
1
1
2
1
1
0
1
1
2
2
2
1
1
1
1
1
0
1
1
2
1
1
1
0
0
2
1
1
2
0
1
0
0
1
2
1
1
2
1
1
1
1
1
1
1
1
0
2
1
0
2
2
1
1
2
1
1
0
1
0
2
1
2
2
1
1
2
1
2
1
0
0
1
1
2
0
2
0
0
2
1
1
3
1
0
1
1
2
1
2
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
1
2
1
2
2
1
0
2
2
1
1
1
1
0
2
1
2
2
1
1
2
1
1
1
1
1
1
1
1
2
1
0
1
2
2
1
1
1
1
1
1
0
1
1
0
1
2
2
1
1
1
1
1
1
1
1
1
2
2
2
1
0
1
2
0
1
0
0
1
1
1
1
0
1
2
0
2
2
2
1
1
2
2
2
1
0
2
1
0
1
1
1
1
0
2
1
1
1
2
2
0
1
2
1
2
1
1
1
1
1
1
0
0
0
1
2
1
1
1
1
1
2
0
1
1
2
0
1
0
2
2
0
1
1
1
4
2
2
1
1
1
1
1
1
1
1
2
0
1
0
1
1
1
2
2
2
0
1
1
1
1
1
1
2
2
1
1
0
1
1
1
1
1
1
1
1
0
1
1
1
1
3
1
1
1
1
1
0
1
0
0
1
2
1
2
1
0
1
3
1
1
1
0
1
1
0
2
1
2
1
2
1
2
0
1
1
2
1
1
1
1
1
1
1
2
1
0
1
2
0
1
1
1
1
0
1
1
0
1
2
1
1
2
1
1
1
2
1
1
1
2
1
1
1
2
1
2
1
2
0
1
0
0
2
0
1
1
2
2
1
1
1
1
0
2
1
0
2
1
0
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
2
1
2
0
1
2
2
1
1
1
2
1
0
0
1
1
1
1
1
1
1
1
0
1
1
1
0
2
1
0
1
1
0
2
1
1
1
2
1
2
2
0
1
2
1
2
1
0
2
1
1
1
2
1
1
2
2
1
1
1
1
2
0
0
1
1
2
2
1
1
1
1
1
1
1
2
0
1
1
1
1
0
2
1
2
2
2
1
1
1
2
1
1
1
2
0
1
1
1
0
3
2
0
1
1
1
1
2
1
1
2
1
2
1
1
1
1
0
1
1
1
2
1
1
1
0
1
2
1
1
1
1
1
1
0
0
1
2
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
2
1
1
1
1
2
1
1
2
0
0
2
1
1
1
1
2
1
1
1
2
1
1
0
1
1
1
2
2
1
1
1
0
1
1
1
1
1
2
2
0
0
1
1
2
1
1
1
2
1
1
1
2
2
1
1
1
0
1
1
2
1
1
1
1
2
0
0
1
1
2
2
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
3
1
2
1
0
2
0
0
2
0
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
0
2
0
2
1
1
0
0
1
1
1
2
0
0
0
1
2
2
1
1
2
1
0
1
1
2
0
1
1
2
1
1
0
2
1
0
1
2
1
1
2
1
2
2
2
1
0
2
2
0
1
1
1
1
1
2
0
1
1
2
1
0
0
1
1
1
1
0
2
1
2
3
0
1
1
1
0
0
2
1
1
2
1
1
2
2
1
2
2
1
1
1
1
1
0
2
0
2
0
1
2
1
0
1
1
1
0
1
2
1
2
2
1
1
1
1
2
1
1
1
1
1
1
2
1
1
2
1
1
2
1
2
1
1
1
1
1
2
0
2
2
1
1
0
1
1
1
2
1
0
1
0
2
2
1
1
1
1
2
1
1
1
0
2
1
1
1
1
1
1
1
1
1
2
1
1
0
1
1
1
0
1
1
2
1
1
1
1
1
2
1
0
1
1
2
1
0
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
2
0
1
1
1
0
0
1
0
1
1
0
1
2
2
0
1
1
1
1
1
1
1
2
1
2
1
1
0
0
2
1
1
1
2
0
0
1
2
1
1
0
2
2
0
1
1
0
0
1
1
1
1
1
1
2
1
2
2
1
2
1
1
1
1
1
1
2
2
2
1
2
0
1
2
2
1
0
1
1
0
1
2
2
0
1
0
2
1
0
0
1
1
1
0
2
1
2
2
0
1
1
1
0
1
1
1
0
1
2
1
2
1
1
0
2
1
3
2
0
1
2
1
1
1
0
0
1
1
1
1
1
1
1
1
1
2
3
1
1
0
3
0
1
2
0
1
0
1
1
1
1
1
1
0
1
1
0
0
2
1
1
1
1
2
1
1
1
2
1
2
2
1
2
1
2
1
2
2
1
0
1
1
1
1
2
1
1
1
2
0
1
1
1
1
1
2
1
1
2
3
1
1
1
1
2
1
1
1
1
1
2
1
2
1
2
1
2
0
0
1
1
1
1
2
2
1
1
2
1
1
1
1
1
1
2
2
1
1
1
2
1
1
1
0
1
2
2
2
1
1
1
1
2
2
0
1
1
2
0
2
1
2
1
1
2
2
0
1
0
2
1
1
0
1
1
1
1
1
0
1
2
1
1
1
1
2
1
1
1
2
1
0
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
0
1
2
1
2
1
2
1
1
1
0
1
2
2
0
1
1
1
2
2
2
2
3
0
1
3
1
1
0
1
1
1
1
1
0
1
2
1
2
0
1
2
2
2
2
1
2
1
1
1
1
1
1
0
2
2
1
1
1
1
2
1
0
1
1
0
2
1
1
1
1
1
2
1
1
0
1
1
1
1
1
1
1
1
2
1
1
0
0
1
1
1
1
0
1
1
1
1
1
1
1
1
2
2
1
2
1
1
1
2
1
2
1
1
1
2
2
1
2
1
0
1
1
1
1
0
1
2
1
1
1
1
1
2
2
1
2
2
2
0
1
1
1
1
1
0
0
2
1
0
1
2
2
2
1
0
1
2
1
1
2
1
0
1
1
1
1
1
1
1
1
1
1
1
2
1
2
0
2
1
1
2
1
1
2
0
1
1
1
1
0
1
1
2
1
1
0
1
2
1
1
1
2
1
1
2
1
1
0
1
1
1
1
0
0
0
1
2
2
2
2
1
1
0
1
2
0
2
2
1
1
2
1
1
1
1
2
1
0
2
1
1
2
1
2
1
0
1
1
1
2
0
1
2
1
2
0
2
2
1
2
1
2
2
1
2
0
0
1
1
1
1
1
1
1
2
1
1
2
0
1
0
1
1
1
2
0
1
1
2
1
1
0
0
0
1
2
1
1
0
1
1
1
1
0
0
2
1
1
1
0
1
1
1
2
1
0
1
1
1
2
1
1
1
1
0
1
0
0
2
2
0
1
1
1
2
1
1
1
2
0
1
2
1
1
1
1
1
0
2
0
2
1
2
1
1
1
2
1
0
2
0
1
1
1
2
1
1
1
0
3
0
1
2
2
2
1
1
1
1
2
1
1
1
3
0
1
1
3
1
1
1
1
1
0
1
1
2
1
1
1
2
1
1
2
1
1
1
0
1
0
1
0
2
2
0
0
0
1
2
1
1
1
0
0
1
2
1
2
1
2
1
1
1
1
1
1
0
1
2
2
1
1
1
1
1
0
0
1
1
1
1
2
1
2
2
0
1
1
1
1
1
0
1
1
0
0
1
1
2
2
2
1
2
0
1
1
1
1
1
3
1
1
2
2
1
2
2
2
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
2
2
1
0
1
1
1
0
0
1
1
1
1
1
2
1
1
1
1
1
0
1
2
2
1
0
1
0
1
0
2
1
1
1
1
1
1
1
1
0
2
2
2
1
2
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
0
0
1
1
1
2
0
1
1
2
1
1
1
1
2
2
2
1
2
0
1
1
0
1
1
1
2
2
1
1
0
1
2
1
1
2
1
1
2
1
1
1
2
2
1
1
1
1
0
1
0
2
2
2
1
2
2
1
2
1
1
1
1
0
0
0
1
1
0
0
2
0
1
1
0
1
0
1
1
1
2
2
0
1
2
0
1
2
2
2
2
0
1
1
1
0
1
1
1
1
0
1
1
1
2
1
1
2
2
1
1
1
0
1
1
1
1
1
1
2
2
0
1
1
2
1
1
2
0
1
0
1
1
1
1
2
2
1
1
1
1
1
0
0
0
2
1
1
1
1
2
1
2
1
2
2
0
1
1
1
0
1
1
1
1
1
2
0
1
0
1
1
0
1
1
1
1
2
1
1
0
2
2
1
1
1
1
2
1
0
1
0
1
1
1
1
0
1
2
0
1
2
2
1
1
1
1
1
1
2
2
1
1
1
2
1
1
1
1
1
1
1
0
0
1
1
2
1
1
1
1
0
1
1
0
1
1
1
1
2
1
1
1
1
1
0
1
1
1
0
2
2
1
1
1
1
1
0
1
2
1
0
2
1
1
1
1
1
1
2
1
2
1
1
2
1
1
2
1
1
0
1
1
2
1
1
1
1
1
1
0
2
2
0
1
2
1
1
1
1
1
0
1
1
1
0
1
2
1
1
1
2
1
1
2
1
1
2
2
0
1
1
0
3
2
1
2
1
1
2
2
2
2
2
1
1
1
2
2
2
0
1
1
2
2
2
1
1
2
1
1
1
1
0
0
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
2
1
1
1
0
1
1
1
1
0
1
2
1
0
2
1
1
1
1
0
1
1
1
1
2
0
1
1
2
1
1
1
1
1
0
0
0
1
1
2
1
1
2
1
1
1
1
1
2
1
1
0
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
2
1
0
4
1
1
2
0
1
1
1
1
2
1
2
1
2
1
1
2
0
1
1
1
0
1
2
2
2
0
0
1
1
1
1
1
3
1
1
0
2
0
1
2
1
2
1
1
1
1
1
1
2
1
0
1
1
1
1
1
1
0
0
1
1
1
2
0
1
1
2
2
2
1
1
2
1
1
2
0
1
2
2
1
1
1
0
1
1
1
1
2
1
2
1
1
2
2
1
2
2
2
1
1
1
1
1
2
1
1
1
1
2
2
1
1
2
0
1
0
1
1
1
1
1
0
1
1
2
1
1
1
1
1
0
1
1
1
0
2
2
1
1
1
0
1
1
1
0
2
1
0
2
2
1
1
1
1
1
1
1
0
1
1
1
1
1
2
2
1
1
2
2
0
0
1
1
1
1
1
1
1
1
2
1
1
1
2
3
1
1
1
1
1
1
1
1
2
1
0
0
1
1
1
1
1
1
1
1
1
3
0
1
2
2
1
2
2
1
2
0
1
2
0
0
1
1
1
2
1
0
2
0
2
1
1
1
1
1
1
1
2
1
1
0
1
2
2
1
2
1
2
2
1
1
1
2
1
1
0
0
2
1
1
1
2
0
1
0
1
2
1
2
1
1
1
2
1
2
1
0
2
0
1
1
1
1
1
1
2
0
1
1
2
1
1
2
1
2
1
1
1
1
0
1
1
1
1
2
1
1
0
0
2
1
2
2
2
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
0
1
2
0
0
1
1
1
1
2
1
2
1
1
0
2
1
1
1
1
0
1
2
1
1
2
1
1
0
1
1
1
1
1
2
1
1
1
2
2
1
1
0
1
1
1
1
1
1
1
2
3
1
1
1
1
1
2
0
2
0
1
1
2
2
2
2
0
0
1
1
1
1
1
0
1
2
1
1
1
1
1
1
1
2
1
2
1
2
2
2
1
2
1
1
0
1
0
1
1
2
2
1
0
1
1
2
1
1
0
0
0
1
1
1
2
1
2
0
1
1
2
1
1
1
1
1
1
2
1
2
1
1
1
2
2
1
1
0
2
1
1
1
1
0
1
1
1
1
2
2
0
1
2
1
1
1
1
0
2
1
1
0
1
2
1
2
1
1
1
2
1
1
1
1
1
0
0
2
0
0
2
2
0
1
1
2
1
1
1
1
2
0
1
2
1
2
1
1
1
1
1
0
2
2
2
1
2
1
2
1
1
2
2
1
2
1
2
0
0
2
1
1
2
1
1
2
1
2
1
1
1
0
1
2
1
2
1
1
1
1
1
1
2
1
2
1
2
1
0
1
0
1
1
1
1
1
1
1
1
1
1
3
0
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
0
1
1
0
1
1
0
1
2
1
2
2
0
2
1
1
1
1
0
1
1
2
2
2
1
1
1
2
2
1
1
1
2
1
1
2
4
2
2
0
1
1
2
2
1
1
2
1
1
2
2
1
2
1
3
0
1
1
1
2
2
2
2
2
1
1
2
1
2
1
2
1
0
2
2
0
0
1
0
2
1
1
1
1
1
2
0
1
1
0
2
1
1
1
1
2
0
1
0
0
2
1
1
0
1
1
2
2
1
2
1
0
1
0
1
1
1
4
1
1
1
2
1
1
0
2
1
1
1
0
1
1
0
2
1
1
1
1
0
0
1
1
1
2
2
1
1
2
1
2
0
0
1
1
0
1
1
0
2
0
1
1
1
1
1
1
1
0
1
1
0
2
0
1
1
0
1
0
1
1
1
0
1
2
0
1
1
2
1
1
2
1
1
0
1
2
0
1
1
1
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
2
2
1
0
1
2
1
0
1
2
1
1
0
1
1
3
1
0
1
0
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
0
1
1
1
2
1
2
2
1
2
2
1
1
1
1
1
1
1
1
2
1
1
2
0
1
1
1
1
1
2
1
2
2
1
2
2
1
2
0
1
1
0
1
1
2
1
1
1
1
1
0
2
2
0
1
1
1
2
1
2
1
1
1
1
1
2
1
1
0
1
0
1
2
2
1
2
1
1
1
1
2
1
2
2
2
2
1
1
1
1
1
0
1
1
2
1
1
2
0
2
2
1
1
2
1
2
0
2
2
1
1
2
1
2
1
1
2
1
1
2
1
1
1
1
0
2
1
1
2
1
1
1
3
0
1
1
1
2
1
1
1
1
1
1
1
1
0
2
2
1
1
2
0
2
1
0
1
1
1
0
1
1
1
0
1
1
2
3
1
1
2
1
1
2
1
2
2
1
1
2
1
1
0
0
0
2
1
2
2
1
0
1
1
0
1
2
1
1
2
1
1
1
1
1
1
1
1
0
1
2
2
0
1
1
1
2
1
1
1
1
0
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
2
1
1
1
2
1
1
1
1
1
2
2
1
2
2
1
2
1
1
2
0
1
1
1
0
1
1
1
2
1
1
2
2
1
1
1
1
1
1
2
1
1
1
0
1
2
0
1
1
1
2
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
0
1
1
0
0
0
0
1
1
1
1
1
1
2
1
0
1
2
2
1
0
0
0
1
0
0
1
1
1
1
1
3
1
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
0
2
2
1
2
1
2
1
1
1
2
1
1
2
1
1
0
1
1
1
2
1
1
2
2
1
0
1
1
1
1
1
2
1
2
1
3
2
0
1
2
2
2
1
0
1
1
0
0
0
1
1
1
1
2
1
0
0
1
1
1
0
1
1
0
1
1
0
2
1
2
1
0
1
2
0
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
0
1
1
2
1
1
0
1
1
2
1
0
1
1
1
2
1
1
2
1
1
1
0
1
1
1
1
1
1
1
2
1
1
2
1
1
2
2
2
1
1
1
1
1
2
1
1
0
1
3
2
1
0
1
1
1
2
2
1
2
2
2
2
2
2
1
2
1
1
2
0
1
1
1
1
1
1
1
6
1
2
1
1
1
1
2
1
1
1
1
0
2
1
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
2
0
1
0
1
2
0
0
1
2
1
1
2
1
1
2
1
2
1
0
1
2
0
1
1
1
1
1
1
1
1
1
1
0
1
2
2
1
2
1
0
1
0
1
1
1
1
1
0
1
1
2
2
1
1
1
1
2
1
1
1
1
0
1
0
0
1
2
2
0
2
1
0
2
2
1
0
2
1
1
1
1
1
1
5
0
1
1
1
0
0
1
2
1
1
1
2
2
2
1
2
2
2
2
0
1
2
1
1
2
2
1
2
1
1
1
1
0
2
0
1
1
1
2
1
2
1
0
1
1
1
1
1
2
1
1
2
1
1
1
0
2
2
2
0
2
2
2
1
1
1
2
2
1
2
2
1
1
1
2
1
1
1
1
2
0
1
2
2
0
0
1
2
1
1
1
1
1
2
1
1
0
1
1
1
2
0
1
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
0
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
0
1
2
1
2
1
2
1
2
1
0
0
1
1
1
1
2
1
1
1
0
1
1
1
2
1
1
1
1
1
2
2
1
1
2
0
1
2
1
1
1
1
1
1
1
0
2
1
1
1
2
1
2
1
0
1
1
0
1
1
0
1
1
1
1
1
1
1
1
1
1
1
2
1
0
1
2
1
1
1
1
2
1
1
1
0
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
0
1
2
2
1
1
1
1
1
2
0
1
2
1
1
1
2
2
1
1
1
1
0
1
1
1
1
2
1
1
1
1
1
1
1
0
1
2
2
1
1
2
2
0
1
1
1
0
1
1
0
2
1
1
1
0
0
1
0
2
2
2
2
2
0
1
1
1
1
1
2
2
2
2
0
1
1
2
3
0
2
0
0
0
0
0
1
2
1
2
1
0
2
1
2
1
2
1
1
1
1
1
1
1
1
2
2
0
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
2
1
0
1
0
1
2
2
2
0
2
1
1
2
0
1
1
1
2
2
1
1
1
1
1
2
1
1
0
1
0
2
1
1
2
1
2
1
1
1
0
1
2
0
2
1
2
1
1
1
2
1
0
2
0
1
2
2
1
1
1
1
1
1
4
2
1
1
1
1
2
1
1
2
1
0
1
1
7
1
2
2
2
1
0
1
1
1
2
0
1
1
2
1
1
1
2
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
3
1
1
0
0
2
1
0
1
0
1
1
0
2
2
1
0
1
1
1
2
1
1
1
1
2
0
1
1
1
1
2
1
0
1
0
0
2
1
1
1
1
3
2
1
1
2
1
2
1
1
2
1
2
2
1
1
1
1
1
0
2
1
1
2
1
1
2
2
1
1
2
1
2
0
1
0
2
1
2
2
1
1
1
2
1
0
1
1
0
1
1
1
2
1
2
2
2
1
2
3
3
0
1
2
1
1
1
2
1
1
2
2
1
1
1
1
1
2
1
1
2
2
1
1
2
0
1
1
1
1
1
0
0
1
0
1
1
1
1
1
1
1
2
1
1
0
2
1
1
1
2
1
1
1
2
1
1
1
1
1
0
1
0
0
2
1
1
0
1
1
2
1
1
2
0
1
1
1
0
2
1
0
1
1
1
1
1
3
1
1
1
1
0
0
3
2
2
1
1
1
1
0
1
2
0
1
0
1
0
1
2
2
2
1
2
0
2
2
1
1
1
2
0
0
1
1
2
1
1
0
1
1
1
1
1
2
1
0
2
1
0
1
1
1
1
1
0
0
1
1
2
1
1
2
1
0
0
1
1
1
1
1
0
1
1
0
1
1
1
0
1
1
2
1
1
2
1
1
1
1
1
1
1
2
2
0
1
2
1
0
1
1
2
2
1
1
0
1
1
1
1
2
1
1
0
1
2
1
2
1
1
2
2
2
1
1
2
1
1
1
2
1
0
0
3
2
1
2
2
1
2
0
1
1
1
2
1
1
0
1
1
1
1
0
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
3
2
0
1
1
1
0
2
1
1
2
1
1
0
1
1
2
0
1
0
1
0
1
1
0
1
1
2
2
2
1
1
1
0
0
2
2
1
1
1
1
1
2
1
1
1
2
0
1
1
0
1
1
1
1
1
0
1
1
1
1
1
1
0
0
1
1
1
0
1
1
1
0
1
2
1
1
0
1
1
1
1
2
1
0
2
1
1
1
2
2
1
0
1
2
0
1
1
1
2
1
1
0
2
1
1
0
2
1
3
1
2
1
1
0
1
1
2
2
2
1
0
1
1
2
1
1
0
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
2
0
1
1
1
2
2
1
2
2
1
1
0
1
1
1
2
0
1
1
2
2
2
1
2
2
1
1
1
2
1
1
2
2
0
2
1
1
2
1
1
1
1
1
0
2
1
1
1
0
1
1
2
2
2
1
2
2
1
1
1
1
1
0
0
0
1
0
2
2
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
2
1
1
2
0
1
1
2
0
1
2
1
2
2
1
1
0
1
1
1
0
1
1
1
1
1
2
2
1
0
2
1
0
2
1
3
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
2
1
1
0
1
2
1
0
1
1
2
2
1
1
3
2
2
2
1
1
1
1
1
1
2
0
0
1
1
4
1
0
2
2
1
2
2
2
1
0
1
1
1
1
1
1
1
1
1
0
2
0
2
1
1
1
2
1
2
1
1
1
2
0
0
1
2
1
2
2
2
2
1
1
1
2
2
1
1
1
2
1
1
1
2
1
0
0
1
2
2
1
2
1
2
2
1
1
1
2
2
0
1
1
1
2
1
2
1
1
1
1
0
0
1
1
1
0
1
1
1
1
1
1
1
0
2
0
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
0
1
0
1
2
1
1
3
2
0
1
0
2
2
1
2
1
2
1
0
0
2
0
1
1
2
2
1
1
1
2
1
1
1
1
2
2
2
1
1
2
1
1
0
1
1
0
1
0
1
0
1
0
1
1
2
1
0
2
2
3
1
1
1
0
2
1
1
2
1
0
2
2
1
1
1
0
1
0
1
1
1
1
1
1
0
2
1
1
2
1
0
1
1
1
1
0
1
2
0
1
0
1
1
1
2
3
1
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
2
1
1
1
1
1
2
1
1
1
0
2
1
2
1
2
1
2
2
1
1
0
2
2
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
2
2
1
0
2
1
2
1
1
1
1
1
2
2
1
2
1
1
0
2
1
2
1
1
1
0
3
1
0
0
1
2
1
1
1
2
2
1
0
0
1
1
1
1
0
1
1
1
2
1
1
1
1
1
1
1
2
1
1
3
1
2
1
0
0
0
1
0
1
1
1
1
0
0
1
0
1
1
1
2
2
1
1
1
0
1
2
1
2
0
0
0
2
2
2
1
0
1
1
0
1
0
1
2
1
2
2
0
0
2
2
0
1
2
0
1
1
1
1
0
1
0
1
2
2
1
0
0
0
1
0
1
2
0
1
0
2
1
1
1
1
2
1
2
1
2
1
2
1
1
1
1
1
1
1
1
2
1
0
2
1
0
2
2
1
1
2
2
1
1
2
1
1
2
2
1
1
0
2
0
2
2
1
1
2
2
1
2
1
1
1
1
0
2
0
2
0
1
2
2
2
1
2
1
0
1
1
1
1
1
2
1
1
2
0
1
1
1
1
0
1
1
2
1
1
0
1
2
2
1
1
1
1
1
2
1
0
1
1
1
0
2
1
1
1
1
1
1
1
0
1
0
1
2
1
4
1
2
2
2
1
1
1
1
1
1
1
2
2
2
2
0
1
1
1
1
2
2
1
1
0
1
1
2
0
2
1
1
1
2
1
1
1
1
2
1
1
2
1
1
2
1
1
2
2
1
2
1
1
0
2
1
0
1
1
1
0
2
1
2
1
0
1
1
1
1
1
1
1
2
1
2
2
2
2
1
0
1
1
2
1
1
1
1
1
1
2
1
1
2
1
1
2
2
0
2
1
0
1
1
1
1
1
1
2
1
1
2
2
2
2
2
1
1
1
0
2
2
0
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
0
2
2
0
1
0
1
2
1
0
0
0
1
2
1
1
1
1
2
1
1
0
1
1
1
2
1
2
0
2
1
1
2
2
1
1
0
2
1
2
1
1
2
2
0
1
2
0
1
1
0
1
0
1
1
0
1
1
0
1
2
1
0
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
0
1
0
2
2
1
1
1
1
1
1
1
0
2
0
1
1
1
2
1
2
1
0
2
1
1
3
1
2
1
0
1
0
1
2
0
0
1
0
1
1
1
0
2
0
1
2
1
1
0
2
0
1
0
2
1
1
1
1
2
1
1
1
2
1
1
0
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
0
1
1
0
1
0
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
0
1
1
2
1
1
0
2
0
2
1
1
0
1
1
0
1
2
1
1
0
0
0
0
1
1
2
1
0
0
0
2
1
2
1
1
1
2
2
2
0
1
2
2
1
0
1
2
0
1
2
1
0
1
1
0
0
1
1
1
2
2
1
0
1
1
1
2
1
2
1
1
1
1
1
0
1
1
1
1
1
2
0
0
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
0
2
1
1
1
1
1
1
1
1
1
0
1
1
1
0
2
1
0
2
1
0
1
2
1
2
1
1
1
1
2
1
2
1
0
1
1
2
1
1
1
1
1
2
1
2
2
2
0
1
2
2
1
2
2
1
1
1
0
1
1
2
2
2
1
1
2
1
1
1
2
1
2
1
2
1
3
0
1
2
1
1
0
2
0
1
1
2
1
1
1
2
2
0
2
1
2
1
0
2
1
1
1
1
1
1
0
1
2
2
1
1
0
1
0
2
1
2
2
0
1
1
1
2
1
0
2
0
2
1
1
1
1
1
2
1
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
0
2
0
1
1
2
1
2
1
2
1
1
1
1
1
1
1
0
2
0
0
1
1
2
1
0
0
1
1
2
1
0
1
2
1
1
1
3
0
1
1
1
1
1
2
1
1
2
2
1
0
0
1
1
1
2
2
1
0
1
1
1
2
1
1
1
1
0
1
1
1
1
1
1
2
1
2
1
2
1
2
2
1
0
2
1
2
1
2
1
1
2
1
0
0
2
0
1
1
0
0
1
2
2
1
1
1
1
2
0
1
2
2
2
2
1
0
1
2
2
1
1
1
2
1
3
2
1
1
1
1
1
1
1
1
2
1
0
1
1
0
1
1
2
1
1
1
1
1
0
1
0
1
1
1
0
1
0
1
1
1
1
1
2
0
0
0
1
0
1
1
1
1
2
0
1
1
2
0
1
1
0
2
1
1
1
1
1
2
1
1
2
2
2
1
2
1
0
2
1
2
1
2
1
1
1
2
1
1
1
1
1
2
1
0
1
1
1
2
0
1
1
2
1
1
2
1
0
1
1
1
1
2
1
0
1
1
2
1
0
1
2
0
0
1
1
2
0
1
1
1
0
2
0
2
2
1
1
1
1
0
1
1
1
2
0
1
1
0
1
4
1
1
2
0
1
1
1
2
1
0
2
2
1
1
1
2
1
0
1
1
0
1
2
0
2
1
1
1
1
1
1
1
1
1
2
1
2
4
0
1
1
0
0
1
2
1
2
1
2
1
1
1
0
1
1
1
1
1
0
1
1
2
1
0
1
1
1
1
1
1
1
1
2
0
0
1
1
2
1
2
2
1
1
0
1
1
0
2
0
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
0
2
2
1
1
1
2
1
1
1
0
0
1
1
2
0
1
1
0
0
2
1
1
1
1
0
2
1
2
0
2
1
1
1
2
2
2
2
1
1
1
2
1
2
1
2
1
1
0
1
0
1
1
2
1
1
1
1
1
2
1
1
1
1
2
2
2
1
0
1
2
1
1
1
1
2
2
0
2
2
2
1
1
2
1
1
2
1
1
0
2
1
0
1
1
1
1
2
0
2
0
1
1
2
0
1
1
1
2
2
2
1
2
2
1
1
2
1
1
2
1
2
0
0
1
1
1
3
0
1
1
1
0
0
1
1
0
1
1
1
2
1
1
2
1
1
1
1
1
1
1
2
3
2
1
2
1
1
1
1
1
1
2
0
1
2
2
2
1
1
1
0
2
1
1
1
2
2
1
2
2
0
0
1
2
0
2
1
2
0
1
1
2
1
1
1
0
2
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
1
2
1
1
2
0
0
1
1
0
0
1
2
2
0
2
1
2
1
1
2
1
2
2
0
0
1
0
1
1
1
1
0
1
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
3
1
1
1
1
0
1
2
1
0
1
0
1
2
1
1
1
0
2
1
1
2
1
0
2
2
2
1
0
1
0
1
1
1
1
0
1
2
1
0
1
0
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
0
2
1
0
0
2
1
0
1
1
0
1
1
2
0
2
1
1
2
1
1
1
3
1
1
1
1
0
2
1
1
1
2
1
1
0
1
2
1
1
1
1
1
0
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
2
2
1
1
1
1
0
2
2
2
2
1
1
0
1
2
1
0
1
1
1
1
1
0
1
1
2
1
1
1
1
1
1
1
0
1
1
1
1
0
3
1
1
1
1
0
0
1
1
1
1
0
1
1
1
1
1
2
0
1
1
1
2
1
0
2
1
1
0
0
1
1
1
2
2
0
1
1
0
1
2
2
0
1
1
1
0
1
1
1
1
1
2
0
2
0
0
1
1
1
1
1
2
1
2
0
1
0
1
1
1
2
1
1
1
1
1
2
1
1
1
2
0
1
0
1
0
2
2
1
2
1
2
2
2
1
1
1
1
1
1
1
0
2
1
1
2
2
1
2
1
1
1
1
0
0
2
2
1
3
2
1
1
1
0
0
2
1
2
2
1
0
1
1
1
1
1
2
0
1
2
0
1
2
1
1
1
1
2
1
0
0
1
1
1
1
1
1
1
1
1
1
0
1
1
2
2
1
1
2
1
0
1
0
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
2
3
0
2
1
0
1
1
1
1
1
2
2
1
1
1
2
1
2
1
2
1
0
1
0
1
1
1
2
1
0
1
2
2
1
1
0
1
0
1
2
1
2
0
1
2
1
1
0
1
1
1
1
0
2
0
1
2
1
0
1
2
0
0
1
1
1
2
2
1
1
1
1
2
0
1
1
1
1
2
1
2
1
1
1
2
1
2
2
2
2
2
1
2
2
1
1
1
1
2
2
0
1
1
1
1
1
2
0
0
1
1
2
1
2
1
1
1
0
1
2
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
2
1
2
2
1
1
1
1
2
2
1
1
1
1
0
1
1
0
1
1
1
1
1
2
2
1
2
1
1
1
1
0
1
1
0
1
1
1
1
1
1
0
1
1
2
2
2
0
3
1
2
0
1
1
0
1
2
0
2
1
0
1
1
2
1
1
1
1
1
2
2
0
1
1
1
0
1
1
1
2
0
1
1
0
1
1
2
1
2
1
0
1
2
1
1
2
1
1
2
0
2
1
1
0
1
1
1
2
2
2
1
1
0
1
0
1
1
0
1
1
1
1
3
2
0
1
2
0
1
1
2
0
1
2
2
0
1
1
1
1
1
2
0
0
1
2
1
1
0
1
1
0
1
1
0
2
1
2
0
2
1
2
0
1
2
1
2
1
2
1
2
1
2
0
1
1
1
3
2
2
2
1
1
2
1
2
1
1
2
1
1
1
1
2
0
2
1
2
2
1
2
1
1
1
1
0
0
2
1
1
2
2
1
2
0
1
1
2
2
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
2
1
0
1
1
1
2
2
2
1
0
1
1
1
1
1
1
2
1
1
0
1
1
0
1
0
1
1
0
2
0
0
1
1
1
1
0
1
2
1
1
1
1
1
1
1
2
1
1
1
1
0
1
0
1
2
2
1
2
2
1
0
1
1
2
1
1
0
1
1
0
2
1
1
3
1
1
1
2
1
1
2
1
2
1
1
1
2
2
2
1
2
2
1
1
1
1
1
1
1
1
2
1
2
1
1
1
0
0
1
1
1
0
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
2
1
3
1
3
1
0
0
1
0
1
2
1
1
1
2
1
1
1
1
1
3
1
0
1
1
1
1
2
1
1
1
2
1
1
1
0
0
2
1
1
1
1
1
2
1
1
2
1
1
0
0
2
1
1
2
1
1
1
2
1
2
1
1
0
2
2
2
1
2
2
1
2
1
2
2
1
0
1
2
1
1
0
2
1
1
2
1
1
2
1
0
0
2
2
1
1
1
1
0
1
2
0
2
1
1
0
2
1
1
1
1
2
1
1
1
1
0
2
1
1
1
1
2
2
1
0
1
1
1
0
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
2
1
2
1
0
1
1
1
0
0
1
2
1
1
0
1
1
2
0
0
1
2
0
0
1
1
1
0
0
2
2
1
0
1
1
1
1
1
2
2
1
2
0
1
2
1
1
2
1
1
2
2
1
1
1
1
2
1
2
1
1
2
1
0
1
1
1
2
1
1
1
1
1
0
1
2
1
1
1
2
2
2
1
1
1
1
2
2
1
2
0
1
3
1
2
1
0
1
2
1
1
1
0
1
1
2
1
1
1
1
2
1
1
2
2
1
1
0
2
2
2
0
2
1
1
1
1
1
2
1
2
2
1
1
1
1
3
1
2
2
1
1
2
2
1
1
1
0
2
2
1
1
1
0
2
1
1
2
1
1
0
2
0
1
0
1
2
2
1
1
1
1
1
2
2
1
1
2
1
1
1
0
0
1
1
2
1
1
1
1
1
2
0
1
1
1
1
0
0
0
1
1
1
1
1
1
1
0
1
1
1
2
2
1
2
0
0
1
1
1
1
2
2
1
1
0
1
1
1
2
1
0
2
1
1
1
1
4
2
1
1
0
0
2
0
1
0
1
1
1
0
1
1
1
1
1
0
1
2
1
1
2
1
1
0
1
1
1
1
0
1
1
0
1
0
2
1
1
1
2
2
1
1
0
1
1
1
2
1
1
1
1
1
2
1
1
2
0
1
0
2
1
2
2
1
1
1
2
1
1
1
2
1
0
1
2
0
1
1
1
2
1
1
1
2
1
2
1
2
1
1
1
1
0
1
1
2
2
2
1
1
0
1
1
2
1
1
1
1
1
0
1
1
0
1
1
2
0
1
0
2
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
0
2
2
2
1
0
1
2
1
2
0
1
1
2
2
1
2
2
1
1
1
0
1
2
0
2
1
1
1
1
2
1
1
1
2
1
1
0
0
1
2
1
1
1
1
1
0
1
1
0
2
0
1
1
1
0
1
1
1
1
1
2
2
2
2
1
1
1
1
1
2
1
0
1
1
1
1
1
2
2
1
1
1
2
1
2
1
1
1
1
1
2
1
0
1
2
1
1
2
0
1
2
2
1
2
2
1
2
1
1
1
2
1
2
1
1
1
1
0
1
2
0
0
0
2
2
0
2
2
2
2
1
1
2
1
1
1
1
1
2
1
0
1
1
2
2
0
1
2
1
1
1
1
1
0
2
2
1
1
1
0
1
1
1
0
1
1
2
1
0
1
1
1
1
2
0
0
2
2
1
1
1
2
0
0
0
2
1
2
0
2
1
1
1
2
1
0
2
0
1
0
1
1
0
2
1
1
1
0
1
0
0
1
1
0
0
1
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
2
1
1
1
0
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
2
1
0
1
2
0
0
1
1
0
2
1
2
2
0
2
1
1
1
1
1
1
1
1
2
1
1
3
1
2
2
2
2
0
3
1
1
0
1
1
1
1
1
2
1
0
2
0
2
1
2
2
1
1
1
1
1
2
1
2
1
0
2
2
1
0
1
2
1
1
1
1
2
1
1
1
0
2
1
1
0
1
1
1
1
1
2
0
1
1
1
1
1
1
0
1
1
1
0
2
2
1
1
1
1
1
1
1
2
1
1
2
0
2
1
2
1
2
1
2
1
1
2
1
2
1
1
2
0
2
1
1
2
1
1
1
0
1
1
0
0
1
1
0
1
2
1
1
2
2
2
1
1
1
0
1
2
0
1
1
2
1
0
1
1
1
1
1
0
1
1
1
1
1
1
2
1
1
2
1
0
1
1
2
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
2
1
2
1
1
1
2
1
1
0
1
2
1
1
1
1
1
1
1
2
2
1
1
2
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
2
2
1
1
0
1
1
2
1
0
1
1
1
1
0
1
0
1
1
1
2
1
2
2
1
0
0
1
1
2
0
1
1
1
1
2
1
1
1
1
1
2
2
2
1
1
2
2
1
1
0
0
1
0
2
0
2
1
0
2
1
1
1
0
1
0
2
1
2
1
1
1
1
1
1
1
1
1
1
2
0
1
1
1
2
2
1
0
2
1
0
1
2
0
1
1
2
2
1
1
1
1
1
0
0
1
1
1
1
2
1
1
2
2
2
1
2
2
1
1
2
1
2
1
1
1
4
1
1
1
2
3
1
1
1
1
1
2
1
1
0
1
1
0
1
2
2
0
0
2
1
1
1
1
1
2
2
1
2
1
0
1
2
1
0
2
1
1
2
2
1
2
2
0
2
1
2
0
0
1
0
0
2
1
2
1
1
1
2
2
1
1
1
3
2
0
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
0
2
1
1
2
0
1
1
1
1
2
1
2
0
0
1
1
2
1
0
0
1
0
2
2
1
1
1
2
1
2
0
1
1
1
2
2
2
0
1
1
1
2
1
2
2
1
0
2
2
2
0
1
0
1
1
1
0
0
1
2
1
1
0
1
1
1
1
1
1
1
1
0
1
2
1
1
0
2
1
2
2
2
1
1
1
0
2
1
1
1
1
2
1
1
1
1
1
1
2
1
2
1
1
1
0
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
2
1
3
0
2
0
1
1
0
2
1
2
1
0
1
0
2
1
2
1
1
2
1
2
1
1
1
1
1
2
2
1
2
2
1
1
1
1
1
1
1
0
0
0
2
1
1
1
2
2
0
1
2
2
1
0
1
1
0
2
1
2
1
1
1
0
2
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
0
1
2
4
1
0
1
2
1
1
2
1
1
1
0
1
1
2
2
2
1
2
2
1
2
1
2
2
2
1
2
2
1
1
0
1
2
0
1
1
2
2
1
2
1
1
2
1
1
1
1
1
1
2
1
0
1
2
1
1
1
2
2
1
1
2
0
1
0
0
1
0
1
1
1
1
0
1
2
0
1
1
1
2
2
1
1
0
2
1
2
0
1
1
0
0
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
0
2
2
1
1
1
1
1
2
2
1
2
1
1
0
0
2
2
2
0
1
2
2
2
1
0
1
1
1
2
1
1
2
0
2
2
1
2
0
0
2
2
1
1
1
2
1
1
1
1
2
1
0
1
1
0
2
1
2
2
1
1
1
1
1
1
2
0
1
2
0
2
1
1
0
2
1
1
1
1
1
0
1
1
2
2
0
2
1
1
1
1
2
1
1
1
1
0
0
0
2
2
2
1
1
1
2
2
1
1
1
2
0
2
0
1
2
0
0
2
1
2
2
1
2
1
1
2
1
0
1
1
2
2
1
2
2
1
2
6
1
1
1
1
0
1
1
1
2
1
2
1
1
2
1
1
1
0
2
0
1
1
2
0
2
2
0
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
2
0
1
1
1
1
1
1
1
1
1
1
2
2
1
3
1
0
2
0
1
0
1
1
1
1
1
1
1
1
0
2
1
2
2
1
2
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
2
2
3
0
1
1
1
1
2
1
2
1
1
1
1
2
1
1
1
2
2
1
2
1
2
1
1
1
1
1
1
1
1
2
0
1
1
2
1
2
1
2
3
1
1
1
1
2
2
2
0
3
1
1
1
1
1
2
0
3
0
1
1
0
2
1
1
2
1
1
0
1
0
1
1
1
1
1
1
0
1
2
1
0
0
0
0
1
0
1
1
1
1
2
1
1
2
0
1
1
0
1
1
1
1
1
1
1
1
0
2
1
2
0
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
0
1
1
1
1
2
2
2
1
2
1
0
1
2
2
1
0
1
1
1
2
1
1
1
1
0
2
2
1
1
1
2
2
2
1
2
0
1
0
1
4
1
1
0
2
1
0
0
1
2
0
2
1
2
1
1
1
0
2
1
1
1
0
1
3
0
1
1
0
1
2
2
1
1
1
1
2
0
3
2
1
1
1
1
1
1
1
1
2
2
1
1
1
0
1
1
1
1
1
2
1
1
0
1
1
2
1
1
2
2
0
1
1
1
1
1
0
1
1
0
0
1
1
1
2
1
1
0
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
2
1
1
0
1
1
1
1
0
0
2
3
1
1
1
1
1
0
2
2
1
1
1
1
1
2
2
2
2
1
1
1
1
1
0
1
1
2
2
1
1
1
2
2
1
1
1
0
1
2
1
1
1
1
2
0
1
1
1
1
1
1
0
1
1
1
2
1
1
2
2
2
1
2
1
0
1
1
1
1
1
1
0
1
1
0
2
1
1
0
2
2
0
2
1
0
2
0
2
2
1
1
1
0
1
0
2
1
1
0
1
1
1
1
1
2
1
0
0
1
1
1
0
2
1
1
0
2
1
1
2
2
1
1
1
0
2
2
1
0
2
1
1
1
1
1
0
1
0
0
0
1
1
1
2
1
1
0
2
2
0
1
3
1
1
2
2
1
1
0
1
1
1
1
1
1
1
1
2
1
1
3
1
2
1
1
1
1
1
2
2
2
1
1
0
1
0
2
1
2
2
5
1
2
1
1
2
1
1
1
1
2
1
2
0
1
1
1
1
1
2
1
0
1
2
1
0
1
1
1
2
1
1
3
0
2
1
1
1
2
2
2
1
1
1
2
1
1
1
2
0
1
1
0
1
2
0
2
1
1
2
0
1
1
1
2
1
1
1
2
2
2
1
1
0
1
0
1
2
1
2
1
1
1
1
1
1
0
1
1
0
2
0
1
1
1
2
1
1
1
1
2
1
0
0
1
1
1
1
1
1
2
1
1
1
1
1
1
0
1
1
1
1
0
1
2
0
2
2
1
1
1
1
1
1
1
1
2
0
1
1
2
1
2
2
1
0
2
1
1
0
1
2
1
1
0
1
1
1
2
2
0
2
2
1
1
1
1
2
1
1
2
1
1
2
2
1
1
1
2
1
1
0
2
1
0
1
1
2
1
0
1
2
1
0
1
2
1
1
2
1
1
0
1
1
0
1
1
1
1
2
1
1
2
1
1
1
0
1
1
1
2
1
1
1
1
1
0
1
1
1
0
1
1
2
1
1
2
1
2
1
1
1
1
2
1
0
2
2
2
1
1
1
1
1
1
2
1
1
1
0
0
1
1
0
2
0
1
2
2
1
1
1
2
1
2
1
0
2
1
2
1
0
0
2
2
1
1
1
0
0
1
1
1
1
0
1
2
1
0
0
1
1
2
1
1
1
1
1
0
0
0
1
1
0
1
0
1
2
1
2
1
1
0
2
2
1
1
1
2
2
1
1
1
1
0
2
1
1
1
2
2
1
1
1
2
1
1
1
1
7
1
2
1
2
1
1
2
1
1
1
2
1
1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
2
1
0
1
2
1
0
2
1
1
0
1
1
2
0
2
1
1
1
1
0
1
1
0
1
2
1
1
1
1
0
1
2
1
2
1
1
2
0
1
2
1
0
2
0
1
1
1
2
2
1
1
0
2
1
1
2
0
1
0
1
1
1
1
1
1
1
2
1
1
1
2
1
1
2
1
2
1
1
1
2
1
0
0
1
1
2
1
1
1
1
2
1
1
1
2
1
2
0
1
2
1
0
0
1
1
2
2
1
1
1
2
2
1
1
1
1
2
1
0
2
1
2
1
1
1
2
1
1
1
1
1
0
1
1
0
1
1
1
1
0
2
1
1
1
1
2
1
1
1
1
2
1
2
1
2
1
1
1
0
1
1
1
2
1
1
2
1
2
1
0
1
0
1
1
1
0
1
1
1
2
2
1
1
1
2
1
0
1
0
1
2
1
1
1
1
2
2
2
1
1
2
1
0
1
1
2
0
1
0
1
1
2
2
2
1
0
2
1
2
2
1
2
0
1
0
0
2
1
1
1
1
1
2
2
1
0
1
0
1
1
1
1
1
1
2
1
1
0
1
1
1
1
2
1
1
1
1
0
1
1
2
1
2
1
2
2
2
1
1
1
1
1
2
1
1
1
2
2
0
0
1
1
1
1
1
1
2
1
1
2
1
2
1
1
1
1
1
1
2
2
1
1
2
1
1
1
1
1
1
0
2
1
1
1
1
1
2
0
1
1
1
0
1
1
1
2
1
0
2
1
1
2
1
0
1
1
2
1
1
2
2
2
1
0
2
1
0
1
2
1
1
2
0
0
1
2
1
2
1
1
2
1
0
2
0
2
1
2
0
1
1
2
1
1
0
1
0
1
1
1
2
2
1
0
1
2
0
1
0
1
1
1
1
1
2
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
2
2
0
1
0
2
2
1
0
1
2
1
1
1
1
2
2
0
1
0
2
2
1
1
1
1
2
1
2
2
1
1
1
1
1
1
0
1
1
1
2
1
1
1
1
1
1
0
2
1
1
2
1
1
2
1
1
1
2
2
1
1
0
1
0
1
2
1
1
0
1
1
1
1
1
1
2
1
0
2
1
2
1
1
1
1
1
1
1
1
1
0
0
1
0
0
1
2
1
1
2
0
2
1
2
1
0
1
1
1
1
2
1
0
1
1
0
2
0
1
2
1
0
1
2
0
1
0
1
1
1
1
1
1
0
1
1
0
2
0
1
1
0
1
1
0
1
1
0
2
1
1
1
1
1
2
0
0
2
2
0
1
2
2
1
1
1
2
2
2
2
1
1
0
2
1
1
1
1
1
1
2
1
1
1
2
1
1
2
2
1
1
1
1
1
1
0
1
2
2
0
0
0
6
1
2
1
0
1
0
1
2
3
1
1
2
1
1
1
1
0
0
2
1
2
0
1
1
1
2
1
0
2
2
1
1
1
1
1
1
2
2
1
1
1
2
1
1
1
1
1
0
1
1
1
1
1
0
1
0
1
1
1
1
1
1
1
1
2
2
1
1
1
0
1
2
1
0
1
2
2
2
0
1
2
1
1
1
1
2
0
1
2
0
2
1
1
1
1
1
2
1
1
2
0
0
2
2
1
1
0
1
2
0
1
1
0
1
1
1
1
1
2
2
0
1
0
1
1
2
0
1
0
2
1
1
1
1
1
1
1
1
1
2
1
2
1
1
0
1
1
0
2
1
1
1
1
2
1
0
1
2
2
1
1
1
1
1
1
2
0
2
2
2
1
1
1
2
0
0
1
0
2
1
1
1
1
0
1
1
1
1
1
1
0
1
1
1
2
1
1
2
1
2
0
2
1
1
0
1
1
1
1
1
1
1
1
2
1
1
1
1
0
1
0
1
1
1
1
1
1
2
1
1
1
2
0
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
0
1
1
0
2
1
0
1
1
1
1
2
2
0
1
2
1
1
1
1
1
2
0
1
1
1
1
0
1
1
1
1
2
0
2
1
0
1
2
1
2
1
2
1
0
1
1
1
1
1
0
1
2
2
1
1
1
2
2
1
1
1
4
2
1
1
2
1
0
1
0
1
1
1
2
2
2
1
1
1
1
0
1
0
1
2
1
1
1
1
1
1
2
0
1
1
0
1
1
1
1
1
1
1
0
2
1
2
2
1
2
1
1
2
1
1
2
1
1
1
1
2
1
1
2
1
1
1
0
2
2
1
1
1
1
1
0
1
0
1
1
1
1
0
4
2
3
0
1
0
2
1
2
0
2
2
1
1
0
1
2
1
0
1
1
1
1
0
1
2
1
2
2
1
1
1
1
1
1
1
2
1
2
0
1
1
0
2
1
1
0
1
1
1
2
1
0
1
1
1
3
2
2
2
2
2
0
1
1
1
1
1
1
1
1
1
2
1
1
0
1
1
1
1
1
2
1
1
1
0
2
1
1
1
1
2
1
1
1
0
0
2
2
1
2
2
0
1
1
2
1
1
0
0
0
1
1
1
2
2
1
1
2
0
0
1
2
1
1
1
0
1
1
1
2
1
2
2
1
2
1
2
0
1
2
1
0
1
0
2
2
1
1
1
2
0
1
2
1
2
2
2
1
1
1
1
1
2
0
1
1
1
1
1
1
1
2
2
1
1
2
1
2
1
1
1
1
2
1
2
0
2
1
0
2
1
1
1
0
2
1
1
2
2
0
1
0
1
0
3
1
2
2
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
0
0
1
0
2
1
2
1
2
1
1
1
2
1
0
0
1
1
0
1
1
0
1
2
0
1
0
1
2
1
2
1
1
1
1
2
1
1
1
0
1
1
1
2
1
1
1
1
0
2
1
2
0
0
1
1
1
2
1
1
1
1
1
2
2
2
0
1
0
1
1
1
2
2
2
2
0
1
0
0
0
2
1
1
1
1
2
2
1
1
1
1
1
2
3
1
1
2
1
1
1
1
1
1
1
0
1
1
1
1
0
1
1
1
2
0
1
1
0
2
1
2
1
2
2
0
1
1
0
1
0
2
1
1
0
2
2
0
1
1
1
1
1
1
1
2
1
1
1
1
2
1
0
1
0
2
0
1
2
1
1
2
0
1
1
1
1
2
1
1
0
1
1
0
1
1
2
1
2
1
2
1
1
2
1
1
1
0
0
0
2
1
1
1
2
2
1
1
2
1
1
1
1
0
2
2
1
0
1
2
3
1
1
1
1
1
1
1
2
0
1
2
2
2
1
1
1
2
1
1
1
2
1
1
0
0
2
1
2
1
1
1
3
0
1
2
1
1
1
1
1
1
2
2
1
1
1
1
2
1
2
1
1
1
2
1
0
1
1
1
0
2
1
2
2
1
1
0
0
1
2
2
0
0
1
1
0
0
0
1
2
1
1
2
1
1
0
1
1
1
1
0
1
1
1
1
1
1
1
0
1
1
1
1
1
2
1
1
1
2
1
1
2
1
1
1
1
2
2
2
1
2
1
2
3
1
0
0
1
2
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
2
1
1
2
1
1
1
2
0
1
0
1
1
2
2
1
2
1
2
1
0
1
0
1
2
2
2
1
1
1
0
0
1
1
0
1
2
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
2
1
0
1
1
1
2
0
1
1
2
2
1
0
1
1
1
1
2
3
1
2
1
2
2
1
1
2
2
2
0
1
2
1
1
0
1
1
1
1
1
2
2
0
1
2
2
0
1
2
2
1
0
1
1
1
1
1
1
1
1
1
1
2
1
1
0
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
0
1
1
1
0
0
1
1
1
1
2
1
0
2
1
2
0
0
1
2
2
2
0
1
1
2
1
1
2
2
0
2
2
1
2
3
2
2
2
1
1
2
2
0
2
1
1
0
1
2
1
2
0
2
1
0
1
1
0
2
1
2
1
1
1
0
1
1
1
0
2
2
1
2
1
0
1
1
1
1
1
2
1
1
1
0
1
2
2
1
2
1
0
1
1
0
1
1
2
0
0
2
1
1
1
1
1
1
0
1
2
2
1
2
2
1
0
2
2
1
2
1
1
1
1
2
1
1
1
2
3
2
2
2
0
1
2
1
2
1
1
1
0
1
2
2
1
1
2
0
1
1
2
1
1
1
1
2
1
1
1
1
2
1
2
1
1
2
1
0
1
1
2
1
1
1
2
0
1
0
2
2
2
2
1
2
0
2
1
1
1
2
1
0
2
1
1
0
1
2
1
1
1
2
1
1
2
1
2
2
5
1
1
2
2
1
2
1
1
1
0
1
1
2
2
1
1
1
2
2
2
0
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
0
1
1
1
1
1
0
2
1
1
0
1
3
1
1
1
1
1
2
1
2
1
0
2
1
1
1
1
1
2
0
2
1
2
1
1
2
2
1
2
1
1
1
2
0
1
2
1
2
1
1
1
1
0
2
0
1
1
1
1
1
0
1
1
2
0
1
1
1
2
1
2
1
1
1
0
0
0
1
2
1
1
1
1
1
1
1
2
1
2
1
2
1
1
1
2
2
1
1
0
1
2
1
2
1
1
2
0
1
2
1
1
1
0
2
2
1
1
0
0
1
1
1
1
0
2
1
1
2
2
2
1
1
1
1
0
2
1
1
1
1
1
3
0
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
0
1
1
1
0
1
0
1
2
2
1
3
2
2
1
1
1
2
1
2
2
1
2
1
2
2
2
2
1
1
2
1
1
1
0
2
2
0
1
1
2
1
0
2
1
1
1
0
1
2
1
3
2
1
1
1
1
1
2
1
1
0
1
1
1
1
1
1
1
0
1
1
2
1
1
1
2
0
2
0
2
1
1
2
1
1
1
1
1
1
2
0
1
2
0
0
2
1
1
1
1
0
1
1
0
1
2
2
2
1
1
0
1
1
2
1
1
1
1
1
0
2
2
1
1
1
2
0
0
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
1
2
0
1
2
1
2
1
1
1
0
1
1
1
1
1
1
1
1
1
2
2
1
1
1
2
1
1
1
2
0
2
2
1
1
1
1
2
1
0
1
1
1
2
1
0
1
2
1
0
2
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
2
1
2
1
1
1
1
1
2
1
2
2
0
1
1
1
0
1
1
1
1
1
1
1
1
0
1
1
0
1
0
1
1
0
1
0
0
2
1
2
2
1
2
1
1
1
0
1
1
1
0
0
1
1
2
2
1
2
1
1
1
0
1
2
2
2
2
0
1
1
2
1
1
2
1
1
1
1
2
0
1
1
2
1
1
0
1
1
1
0
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
0
1
1
0
1
1
2
0
2
1
2
1
0
1
1
2
2
1
2
1
1
1
0
1
1
2
0
1
1
0
1
1
1
1
0
1
1
1
2
2
1
2
2
1
0
0
1
2
1
1
1
0
1
1
2
1
1
3
2
2
2
1
2
1
2
1
1
2
0
1
0
0
2
1
1
2
0
1
2
2
1
0
2
1
1
2
0
1
1
1
2
2
2
2
1
1
1
0
1
1
0
1
2
1
2
0
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
0
2
2
1
1
2
1
1
1
1
2
1
1
2
2
1
1
0
0
1
1
1
0
1
1
1
1
1
0
2
1
1
2
1
1
1
0
1
1
1
0
1
2
1
1
0
0
1
0
1
1
1
0
1
1
1
0
2
2
1
1
2
0
1
1
1
0
1
0
1
1
1
0
1
2
0
1
0
2
2
1
1
1
0
1
1
2
0
1
1
1
1
0
1
1
1
1
1
1
1
1
1
2
1
1
0
1
1
1
1
0
2
1
2
1
1
3
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
3
2
2
0
1
1
1
1
1
1
0
1
2
0
1
1
2
1
1
1
0
1
2
2
1
2
2
1
1
2
1
1
0
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
2
2
2
1
2
2
0
1
1
1
1
1
1
0
1
2
2
0
1
0
2
0
1
2
2
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
0
0
2
1
2
3
1
1
1
1
1
0
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
0
1
1
1
1
1
0
0
1
0
1
1
1
1
1
1
1
1
2
1
1
1
2
2
2
2
2
1
1
2
2
1
1
2
1
0
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
0
2
1
1
1
1
1
1
1
1
1
1
1
0
1
2
0
1
2
1
1
2
1
1
1
2
2
2
1
0
2
1
1
2
1
1
1
2
2
1
1
1
1
2
1
1
1
0
1
1
1
0
2
0
1
0
1
1
0
1
1
2
1
2
1
1
1
1
1
0
4
1
1
0
2
1
1
1
1
2
1
2
2
1
0
1
1
1
1
1
0
1
1
1
1
0
1
2
2
1
1
1
1
2
0
1
1
2
0
1
2
2
2
1
3
2
2
1
2
1
0
1
2
1
1
1
1
1
1
2
1
1
1
0
1
1
0
1
2
1
2
1
0
2
1
0
1
2
1
1
2
1
1
1
1
2
1
1
1
1
1
2
2
0
0
0
1
1
2
1
1
1
1
1
1
0
1
0
1
1
1
2
1
0
1
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
0
1
1
3
0
1
1
2
1
2
2
1
0
2
2
1
2
1
1
1
0
2
2
1
1
1
2
0
1
1
1
1
1
2
0
2
2
2
1
0
1
0
2
2
1
2
2
1
1
0
0
1
1
1
1
1
2
0
1
1
1
2
1
2
2
2
1
0
1
1
1
1
1
0
2
2
1
1
0
0
0
1
2
2
1
0
1
2
0
1
1
0
1
1
0
1
1
1
1
1
2
1
1
2
2
1
1
2
1
1
0
2
1
2
1
1
2
0
2
1
1
2
1
0
0
2
0
2
1
1
2
1
2
2
1
1
2
1
2
1
1
1
1
1
1
2
1
2
1
1
0
1
1
0
1
2
1
1
2
1
2
2
1
1
1
2
1
1
1
2
1
1
0
1
0
2
1
1
1
2
1
0
0
0
0
1
2
1
1
1
1
1
1
2
2
1
2
1
1
1
2
2
1
2
1
1
1
1
1
1
0
1
1
1
1
1
1
2
0
2
2
1
0
2
2
1
2
2
1
2
1
0
1
0
1
1
2
1
1
1
1
1
1
1
1
2
2
1
2
1
2
1
1
1
2
1
1
2
1
0
1
0
1
1
2
1
0
1
1
1
1
2
2
1
0
1
1
1
1
1
2
1
1
0
1
2
1
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
0
1
1
1
1
1
0
0
1
1
0
2
2
0
1
2
0
1
2
0
1
2
0
1
1
1
1
2
1
1
1
1
1
1
2
0
1
1
2
1
1
1
1
1
2
1
1
1
2
0
0
0
2
1
1
0
2
1
1
2
2
1
1
1
2
1
0
0
1
2
1
2
0
1
0
1
1
2
2
1
1
0
1
1
1
1
0
2
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
2
2
1
0
1
1
0
1
1
2
1
2
1
2
0
2
2
1
0
1
0
1
1
1
1
1
2
2
1
1
0
1
1
2
1
2
1
1
2
1
1
1
2
1
1
2
1
1
1
1
1
2
2
1
0
1
0
2
1
2
1
1
2
2
2
1
0
1
2
0
1
1
1
2
2
0
1
1
2
1
2
2
1
3
2
1
1
2
0
0
1
2
1
2
2
2
2
1
1
1
1
1
2
1
1
1
1
1
1
0
0
1
2
2
1
1
2
1
2
2
1
1
1
0
1
1
0
0
2
2
2
1
0
1
1
1
1
2
0
1
1
2
1
2
1
1
1
0
0
0
1
1
2
1
1
1
2
0
2
0
1
2
2
1
1
1
0
1
1
1
1
1
1
0
1
3
1
1
2
2
0
1
1
0
1
0
1
2
0
0
1
2
1
1
1
1
1
2
2
1
1
1
1
1
0
2
2
1
2
2
1
1
1
0
1
1
0
1
2
2
1
2
1
1
2
1
2
2
0
1
1
0
1
1
2
0
2
1
1
1
0
1
2
2
1
1
1
0
1
1
2
1
2
1
1
2
1
3
0
0
1
0
1
0
1
1
2
2
1
2
1
1
1
1
2
2
1
1
0
0
0
1
1
0
0
0
0
1
1
2
2
2
1
2
2
1
1
0
0
0
2
1
2
1
1
2
1
1
1
2
2
0
1
2
1
1
0
0
2
2
2
1
1
2
1
2
1
0
1
2
1
4
0
2
1
2
1
1
1
0
2
2
1
1
1
1
1
1
1
2
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
2
1
1
1
2
1
1
1
1
1
2
0
3
0
1
1
2
1
1
2
1
1
0
2
1
2
1
2
0
1
1
1
1
0
1
1
1
1
1
1
1
3
2
0
0
2
2
1
1
1
1
2
0
1
0
2
2
1
2
2
1
1
0
1
1
1
1
1
1
2
1
1
3
1
1
1
2
1
1
1
2
2
1
2
1
1
0
2
1
1
3
1
2
1
1
2
1
2
0
2
2
2
1
1
2
2
2
2
1
1
2
0
1
1
2
1
1
0
1
1
0
1
1
1
1
4
2
1
1
1
1
2
0
1
1
1
2
1
1
2
1
1
2
1
2
0
1
1
0
1
2
1
1
2
1
1
2
1
1
1
2
1
1
1
0
1
0
1
2
1
2
1
1
1
1
1
1
1
2
0
1
2
1
1
0
1
1
1
1
0
1
1
1
2
2
1
1
2
1
0
1
1
2
1
1
2
1
0
1
0
0
2
2
1
1
1
0
1
1
1
1
1
0
1
1
1
2
1
1
1
1
2
2
1
1
1
2
1
0
1
1
1
1
1
2
0
1
1
0
1
2
1
2
1
1
2
0
1
1
0
2
1
1
1
1
0
2
1
1
1
1
2
1
2
1
0
1
2
1
2
0
1
1
0
1
0
1
1
2
1
1
2
1
1
1
0
1
2
1
4
0
1
2
3
1
1
1
1
1
1
1
2
0
1
1
1
2
0
1
1
1
0
1
1
1
1
1
1
0
0
1
1
1
2
1
1
1
2
2
0
2
0
2
1
1
1
1
1
0
0
2
2
2
2
0
1
0
1
1
1
2
1
2
0
1
1
1
2
1
1
2
0
2
0
0
1
1
1
0
2
1
0
0
1
1
1
1
0
1
1
0
0
0
0
2
1
1
2
2
1
1
1
2
3
1
1
2
1
2
2
2
2
1
2
2
2
2
0
1
1
2
2
1
0
2
2
2
1
0
1
1
2
1
0
1
1
1
1
1
2
1
2
2
1
2
0
2
0
1
2
1
1
2
2
0
1
1
1
1
2
1
2
0
1
1
2
1
2
1
1
1
1
6
2
2
2
0
1
1
2
2
3
1
1
1
1
1
2
2
1
1
1
2
1
1
2
1
2
2
0
2
2
1
1
2
1
1
1
1
1
1
1
0
1
2
1
1
1
2
1
0
1
1
2
1
1
1
1
1
2
1
3
0
0
1
1
1
1
2
1
1
1
1
1
1
1
2
1
0
1
0
1
2
0
1
0
1
0
1
1
2
2
2
1
0
2
2
1
0
2
1
1
1
0
2
3
1
1
1
1
0
2
1
1
1
0
0
1
0
0
0
1
2
2
1
1
1
2
1
1
1
2
1
1
2
1
1
1
0
1
2
1
1
1
1
2
2
2
2
2
0
7
1
1
1
1
2
0
1
1
1
0
1
0
1
1
0
3
1
2
0
1
0
1
1
1
0
2
2
0
2
1
0
1
0
1
0
0
1
1
2
2
2
1
1
1
1
0
1
0
0
1
1
2
1
0
1
0
0
2
1
1
2
1
0
1
1
1
1
1
0
1
1
2
2
0
0
2
1
1
1
1
1
1
2
1
1
1
1
1
0
1
1
1
1
2
2
0
1
2
1
2
0
1
2
0
1
1
2
0
0
2
1
1
1
0
0
0
1
1
1
2
0
2
2
1
1
2
1
0
2
2
1
1
1
2
1
0
1
1
2
0
0
1
1
2
1
1
1
2
2
2
1
2
1
1
1
2
2
2
1
1
1
1
1
1
0
1
1
2
1
4
1
1
1
1
2
2
1
0
1
0
1
1
2
2
0
1
1
1
1
1
2
1
2
1
1
1
1
2
2
1
2
0
1
1
1
1
1
1
1
0
0
1
1
0
1
2
0
1
1
1
3
1
0
1
1
1
1
0
2
2
2
2
2
1
1
0
2
1
1
0
1
2
1
2
1
0
1
0
1
2
1
2
0
0
0
2
1
1
1
2
2
0
1
2
2
0
1
2
1
1
1
2
1
2
1
2
2
1
1
1
1
2
1
2
1
1
0
1
1
2
1
1
2
1
2
1
2
1
1
1
1
1
1
1
1
0
0
0
1
2
1
1
1
1
2
1
0
2
1
0
1
1
2
2
2
1
0
1
2
0
2
1
1
1
1
1
1
1
1
2
2
1
1
0
0
1
2
2
0
1
1
1
1
1
2
1
1
2
1
0
0
1
2
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
2
1
1
0
0
0
0
0
0
2
1
2
2
2
1
0
0
1
2
1
0
2
2
0
1
1
2
1
1
1
1
0
2
1
1
0
1
1
1
2
0
2
1
1
1
1
2
0
2
1
1
1
1
1
0
1
1
0
2
0
2
0
1
1
2
2
1
1
1
1
2
2
1
0
1
1
1
1
1
1
1
1
2
2
1
1
1
2
1
1
0
1
0
0
1
0
0
1
1
1
2
1
1
2
1
0
2
1
1
2
2
2
1
1
1
1
1
1
1
2
2
2
2
2
1
1
1
0
1
1
1
1
0
1
1
1
3
1
1
2
0
0
1
0
1
1
0
2
2
2
1
0
1
2
0
2
0
2
2
2
2
1
1
1
1
0
1
1
2
1
2
1
2
1
1
2
2
1
0
0
1
3
1
1
1
0
2
2
1
1
2
1
1
2
0
1
1
1
1
2
2
1
2
2
4
2
1
1
1
1
0
0
1
2
2
3
1
1
1
1
0
1
1
1
1
2
1
1
1
2
1
2
1
1
1
2
1
1
0
1
1
0
0
1
1
0
1
1
2
1
1
2
2
1
2
1
1
1
0
2
1
0
1
1
0
1
1
2
1
1
0
2
1
0
1
2
0
1
1
1
1
2
1
1
0
1
1
0
1
0
1
1
2
1
2
1
1
1
0
1
1
2
2
1
0
1
1
1
0
2
1
1
0
0
2
2
1
1
1
1
1
0
1
2
1
1
0
1
1
1
1
0
2
1
1
1
1
1
1
2
2
0
1
1
1
1
2
1
0
2
1
1
0
2
1
1
2
0
1
1
1
1
0
1
1
2
0
0
1
2
0
0
1
1
1
1
1
2
2
1
1
1
2
1
1
1
0
0
2
2
1
1
1
1
0
0
2
2
2
1
2
3
2
2
0
0
1
2
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
2
1
0
0
1
1
2
1
2
1
1
2
2
0
1
0
2
2
1
1
1
1
1
1
1
1
2
0
1
2
2
0
1
1
2
1
0
0
1
2
1
1
1
1
1
1
2
2
2
0
1
1
1
2
2
1
1
0
1
1
2
1
1
1
1
4
1
2
0
0
2
2
0
1
1
0
2
0
2
0
2
2
0
1
2
2
0
0
1
1
1
1
1
2
2
2
1
0
1
1
1
1
1
1
1
1
2
0
1
2
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
0
1
1
2
1
1
1
1
1
1
1
1
1
1
3
1
2
1
0
2
1
2
1
2
2
1
0
1
1
1
1
2
1
1
0
1
1
3
1
0
2
1
1
0
1
1
1
1
0
0
2
1
1
1
1
2
1
1
1
1
1
1
2
1
1
2
0
0
2
1
0
1
0
1
2
1
0
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
1
1
1
2
1
0
2
2
1
1
1
1
1
1
1
1
1
1
1
0
1
1
2
1
1
2
1
2
1
1
2
0
1
1
1
1
1
1
0
2
1
1
2
2
2
1
1
1
1
1
1
0
0
1
0
2
2
1
1
1
1
1
1
4
1
2
2
1
2
0
2
2
0
1
1
1
1
2
1
0
0
0
0
1
2
1
1
1
1
0
0
1
1
2
0
1
2
1
2
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
0
2
1
1
1
2
1
2
0
0
1
1
1
1
2
1
1
2
1
1
0
1
2
1
1
1
1
1
0
1
0
1
0
1
0
1
1
1
1
2
0
1
0
1
1
0
1
2
1
1
1
0
0
2
1
3
2
2
1
1
1
2
1
1
1
1
1
0
2
0
1
1
2
2
1
2
1
1
1
2
1
2
0
2
1
2
2
1
2
1
1
2
2
1
2
1
0
1
1
1
1
1
1
1
3
1
1
1
1
2
2
1
1
1
1
2
1
1
1
0
0
2
1
1
1
1
2
2
0
1
1
0
1
1
1
2
2
1
2
0
1
2
2
1
1
1
2
1
4
1
0
1
2
0
1
2
1
1
1
1
1
2
1
8
2
1
1
1
1
1
2
0
0
1
1
1
2
0
1
2
1
1
2
1
2
1
1
2
2
1
0
1
1
1
1
2
1
3
1
1
0
0
0
1
1
2
1
2
0
2
1
1
1
1
0
1
1
1
1
1
1
0
1
1
1
1
1
2
2
2
1
0
2
1
1
2
1
1
1
0
1
1
1
1
1
0
2
0
1
1
1
1
1
1
1
1
1
1
1
2
2
0
1
2
1
2
1
2
1
1
1
2
2
1
0
1
1
1
2
0
2
1
1
1
1
1
1
1
1
0
1
0
1
1
2
2
1
2
2
1
1
0
2
2
1
1
2
2
1
1
2
1
2
2
1
2
1
1
2
1
2
1
1
2
0
1
2
1
2
1
1
2
0
2
0
1
1
1
2
1
1
1
1
1
1
0
1
1
0
2
1
1
2
2
1
1
2
1
1
1
1
1
1
0
2
2
2
1
1
1
1
1
1
0
1
0
1
1
1
5
1
1
1
2
2
2
0
1
1
1
1
1
1
1
1
2
1
1
1
1
1
0
1
1
1
2
2
0
2
1
0
2
1
1
1
1
1
5
1
1
1
1
1
1
1
1
0
1
2
1
1
1
1
2
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
0
0
2
0
2
1
0
1
0
1
0
2
1
1
0
2
2
3
0
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
0
2
1
2
2
2
2
3
1
2
1
1
1
1
2
1
0
2
1
2
1
1
1
1
1
0
0
1
1
1
2
0
1
1
1
1
0
1
2
2
1
1
1
1
1
1
1
0
2
1
3
2
1
1
2
2
0
1
2
1
2
1
2
1
1
1
1
1
1
2
1
1
0
1
2
1
1
1
3
2
0
2
2
2
1
0
1
2
0
1
1
1
2
2
1
1
1
0
0
1
1
2
1
2
1
1
1
0
1
1
1
1
1
1
1
2
1
1
1
0
2
1
1
2
2
1
0
0
1
2
1
1
1
1
1
2
2
2
2
1
2
3
0
1
1
1
1
1
1
2
1
1
0
1
1
2
1
2
1
1
2
1
1
0
1
2
1
0
1
1
0
1
1
1
2
2
1
0
0
0
1
2
1
1
2
0
1
0
1
1
2
1
0
1
1
1
0
1
0
1
1
0
1
1
1
1
2
1
1
1
2
1
2
1
1
0
1
1
1
1
2
2
1
1
1
1
2
2
1
2
2
1
1
1
2
2
1
1
1
1
1
0
2
2
1
1
2
1
1
1
1
2
1
1
2
1
1
0
1
1
0
1
1
1
1
0
2
2
1
1
1
1
1
0
1
1
1
2
1
1
1
1
0
1
1
4
1
1
3
1
1
1
2
1
2
0
0
1
1
2
1
1
1
2
1
1
0
2
1
1
2
2
0
1
1
2
0
0
1
1
1
1
0
1
0
1
1
1
1
2
1
1
1
1
1
2
0
2
1
1
2
2
1
2
1
1
0
1
1
1
2
2
2
0
2
1
0
1
1
1
1
1
2
1
0
1
1
1
1
2
1
0
2
2
1
1
1
0
1
0
2
1
2
1
3
2
2
2
0
2
1
2
2
1
2
1
2
1
2
1
2
1
1
1
1
1
3
2
1
2
1
1
1
1
2
1
1
1
1
1
1
2
2
1
2
1
2
0
1
2
2
1
2
1
1
2
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
2
2
2
2
1
1
1
1
2
0
1
2
1
1
1
1
2
1
1
1
0
1
1
1
1
1
1
2
1
1
1
2
1
1
1
2
1
1
2
0
0
2
1
1
1
1
1
2
1
2
1
2
1
1
0
0
0
2
1
1
1
1
2
0
1
0
1
1
1
0
0
1
1
2
2
0
1
2
1
0
1
1
1
1
2
1
2
0
2
1
1
1
1
0
1
1
1
2
2
1
1
1
1
3
1
1
2
2
1
2
1
0
1
1
2
2
1
1
1
1
2
1
1
1
2
1
1
1
2
2
1
1
1
2
2
0
1
2
2
1
0
1
1
1
1
1
1
1
0
1
1
2
2
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
2
2
2
0
1
1
2
2
2
1
2
1
1
0
2
1
1
1
1
1
1
1
2
1
2
0
1
0
2
2
1
1
2
1
1
0
1
2
0
1
1
2
1
1
1
1
0
1
0
1
2
1
2
1
2
1
2
1
2
0
1
2
1
1
2
1
1
1
1
1
1
2
1
1
0
2
1
1
1
1
1
0
2
1
1
1
1
1
1
1
2
0
2
0
1
2
1
1
2
1
0
1
0
0
2
0
1
1
1
0
0
2
2
2
2
0
1
2
1
1
1
1
0
0
2
1
1
1
1
0
1
1
2
2
1
1
2
1
1
2
1
2
2
1
3
2
1
2
1
1
1
2
2
1
2
1
1
2
1
2
0
1
0
1
1
0
1
1
1
1
0
1
2
2
1
1
0
1
1
2
1
1
1
1
1
0
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
1
1
0
0
0
0
2
2
1
2
1
2
1
1
1
1
1
2
2
1
2
2
1
1
1
1
2
1
1
0
1
0
0
2
1
1
1
1
1
2
1
1
2
0
1
1
1
0
1
1
3
2
1
1
2
0
1
1
0
1
2
0
1
1
1
2
1
2
1
1
0
1
1
1
1
2
2
1
1
1
1
1
1
1
1
2
2
1
0
1
1
2
1
1
2
2
1
3
1
0
1
1
1
1
1
2
1
1
0
2
1
1
1
1
1
1
1
0
0
1
1
1
0
1
1
2
0
1
1
0
2
2
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
2
1
1
0
1
1
1
2
0
2
1
0
0
1
1
1
0
2
2
1
1
1
1
1
1
1
0
1
1
1
0
1
1
1
1
1
1
1
1
2
1
1
2
2
1
1
2
0
1
3
2
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
1
2
2
1
2
1
2
1
1
2
0
0
1
0
0
1
0
0
2
2
1
2
2
1
2
2
0
1
1
1
1
2
2
1
2
1
1
0
1
1
2
1
1
2
2
1
1
1
1
0
1
0
1
1
2
1
1
0
1
1
1
0
2
2
1
1
1
1
1
1
1
0
1
0
2
0
2
1
1
1
2
1
1
0
0
2
0
1
2
1
1
0
1
1
0
1
2
1
1
0
1
2
1
0
1
1
1
1
1
1
2
0
1
0
1
1
1
1
0
0
2
1
1
0
1
1
1
1
2
0
0
1
1
1
1
1
1
0
1
1
1
2
0
1
1
1
1
1
1
3
1
1
1
2
1
1
2
0
2
2
1
1
1
1
2
2
0
1
1
1
1
1
1
2
2
2
1
2
1
0
0
2
1
0
1
2
2
1
0
1
1
1
0
1
2
0
2
1
1
0
2
1
1
1
0
1
1
1
1
1
2
1
1
1
1
1
1
1
1
0
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
2
1
1
0
1
0
1
2
0
2
1
2
2
2
0
0
0
0
1
1
0
2
1
1
0
1
1
2
0
2
1
1
1
0
1
1
1
1
1
0
1
0
1
1
1
1
1
1
1
1
2
2
1
1
1
0
2
0
1
1
2
2
2
1
2
0
1
1
1
0
0
2
1
1
1
2
1
0
0
0
1
1
2
0
0
1
1
2
1
0
1
0
1
1
1
1
1
1
0
0
1
2
1
0
1
1
1
0
0
1
1
1
1
1
2
1
1
2
1
1
1
2
1
1
1
2
0
1
1
1
2
2
1
2
1
0
1
1
1
1
1
1
2
1
1
1
0
1
2
2
1
1
1
2
1
0
1
1
1
2
1
1
2
1
1
1
2
1
1
2
1
0
2
1
1
1
1
2
0
1
2
0
2
1
0
1
1
1
1
1
2
1
1
1
2
1
1
2
2
1
2
2
1
2
1
1
0
1
2
0
1
1
1
1
1
1
1
0
1
2
1
1
2
2
1
1
1
1
1
1
2
0
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
2
2
2
1
1
0
1
0
0
1
2
1
2
2
2
0
1
1
2
1
1
0
1
1
1
1
1
2
0
1
1
1
2
3
1
1
1
0
1
2
2
1
1
2
2
1
1
2
1
0
0
1
1
1
1
0
2
1
2
0
0
1
1
1
1
1
2
1
1
2
1
1
0
1
1
1
1
1
1
1
1
1
0
1
1
0
1
1
1
2
1
1
1
1
1
2
0
1
1
1
1
2
2
0
1
1
1
2
2
2
1
2
1
1
1
1
1
1
1
1
1
2
2
1
0
1
1
1
2
0
1
1
2
2
2
1
1
2
2
0
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
0
2
1
2
1
2
1
1
2
1
1
1
2
1
1
0
1
1
1
1
1
0
2
1
2
1
1
1
1
1
1
1
2
2
0
2
1
1
1
1
1
1
2
1
0
2
0
1
0
1
1
1
1
1
1
1
1
1
2
2
1
1
1
2
1
1
2
0
2
1
1
1
1
2
2
0
1
1
0
2
2
2
0
2
1
0
0
1
1
1
1
0
1
0
0
1
2
1
1
1
2
1
2
1
3
0
1
0
1
1
1
1
1
1
1
1
1
1
1
1
3
1
1
2
1
1
1
1
1
2
2
1
2
1
1
1
0
1
1
1
1
1
1
1
0
1
1
1
2
1
2
1
1
2
1
1
0
1
1
1
1
1
1
2
1
1
1
1
0
1
1
0
0
1
2
1
1
1
2
1
2
2
1
2
1
2
1
2
1
1
1
1
0
2
1
2
1
0
2
1
2
2
1
2
1
2
1
2
2
1
2
1
1
1
2
1
1
1
1
1
1
1
0
2
1
1
1
1
1
1
2
2
1
2
2
1
1
1
2
1
1
1
1
1
0
2
0
0
1
0
1
1
0
1
2
1
1
1
1
1
2
0
1
0
1
2
1
1
1
1
2
1
0
1
1
0
1
2
0
2
1
1
2
2
2
1
2
1
2
0
1
1
0
1
1
1
2
1
1
2
2
2
1
1
1
2
0
2
1
0
2
0
1
1
0
2
1
2
0
1
1
1
0
1
1
0
1
1
1
0
1
1
1
1
2
0
1
2
1
2
2
1
0
2
1
3
1
1
0
1
1
2
1
1
2
1
0
2
2
1
0
2
1
1
1
1
2
1
0
1
1
1
1
0
1
1
1
1
1
0
2
1
0
1
2
1
1
1
1
2
1
2
1
0
2
2
1
1
0
0
2
1
1
1
1
2
1
2
2
2
1
2
1
0
2
1
1
2
2
0
2
2
2
1
1
1
1
1
1
1
0
0
2
2
1
1
1
2
2
1
0
1
2
1
1
1
1
0
0
1
2
2
1
4
0
2
1
1
2
2
1
0
0
0
0
0
2
1
2
1
0
0
2
2
2
1
1
1
1
1
0
2
1
2
0
0
1
1
1
1
1
0
1
2
1
1
2
1
1
0
1
1
2
2
2
0
1
2
1
0
0
1
1
1
0
2
2
1
1
1
1
2
1
1
1
1
1
5
1
1
1
0
1
0
1
1
1
1
1
1
1
1
2
2
2
1
2
2
1
1
1
1
1
1
0
1
1
1
1
1
2
1
1
1
1
1
0
1
0
1
1
1
2
1
2
2
1
2
1
1
1
1
2
1
1
1
2
1
2
1
2
1
0
1
1
2
2
2
0
1
2
1
1
2
0
1
1
1
0
1
0
1
1
1
5
1
0
1
1
0
2
2
2
0
1
0
1
2
2
2
2
2
2
1
1
1
2
1
1
1
1
2
2
0
1
1
2
1
0
1
1
2
1
0
1
1
1
2
1
1
1
1
0
2
1
1
1
1
0
1
1
1
2
1
0
2
0
1
2
2
1
1
0
2
1
1
0
2
1
1
2
0
0
2
1
1
2
0
1
1
0
0
1
1
1
2
0
1
0
1
1
1
2
0
1
1
1
0
1
2
1
1
1
1
2
1
0
1
2
2
1
2
0
2
2
0
2
0
2
2
2
1
1
1
2
1
1
1
0
0
1
2
0
1
2
1
1
1
1
2
1
1
2
1
2
1
0
1
1
1
0
2
1
1
2
0
1
1
2
1
1
1
2
1
1
2
1
1
1
1
0
1
0
2
1
1
1
1
1
1
1
1
0
1
0
2
1
1
2
1
0
1
0
1
1
2
2
1
1
1
2
2
1
1
2
2
1
1
2
2
1
2
1
0
1
1
2
1
0
1
1
1
1
1
2
1
1
1
1
2
2
1
1
2
1
0
1
2
1
1
1
2
1
2
2
2
2
2
1
2
2
1
1
1
1
1
1
2
2
1
1
2
1
2
2
1
1
2
1
2
1
1
1
1
1
0
1
1
1
0
1
2
1
1
2
1
1
2
1
2
1
1
1
2
2
2
1
1
1
2
1
1
1
2
1
2
1
2
1
2
0
0
1
1
1
0
2
1
2
2
2
1
2
0
1
1
2
1
1
0
1
2
2
2
0
1
1
1
1
1
2
1
1
1
1
1
1
2
1
0
2
1
2
1
2
1
1
1
1
2
1
3
1
1
2
1
0
2
1
0
0
1
1
1
2
0
1
1
1
1
1
1
1
3
0
0
0
1
1
2
1
1
1
2
2
2
2
0
1
1
1
0
2
1
0
2
1
2
1
1
1
1
2
1
1
1
2
1
1
1
2
2
2
2
1
2
1
1
1
0
1
1
0
1
1
1
2
2
1
1
1
1
1
1
1
1
0
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
1
0
2
0
1
1
2
1
1
1
1
1
1
1
1
1
1
2
0
0
0
1
1
2
1
2
1
1
2
1
1
0
1
1
1
1
0
1
1
1
1
1
1
1
2
2
1
0
1
1
2
1
1
1
0
1
1
1
1
1
1
1
1
2
2
0
2
1
1
1
1
0
1
0
1
2
1
2
1
2
1
1
1
2
2
2
1
1
1
1
1
1
1
0
0
0
1
1
1
2
2
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
2
3
1
1
1
1
1
2
2
1
1
2
2
2
1
2
1
1
0
1
1
1
2
0
1
1
1
1
2
1
2
2
0
0
1
0
1
1
2
1
1
1
1
0
1
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
2
1
1
1
1
0
1
1
1
2
1
1
2
1
1
1
1
1
0
1
1
1
2
1
1
1
1
0
1
2
1
0
1
1
1
1
1
3
2
0
0
1
1
1
1
2
1
0
2
1
2
1
1
2
1
1
1
0
1
2
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
2
2
2
1
1
0
1
2
1
0
2
2
1
1
0
1
1
1
1
2
1
2
2
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
2
1
0
1
1
1
1
1
1
0
0
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
0
1
1
2
3
2
2
1
2
2
1
1
2
1
1
1
2
1
3
2
1
1
1
1
0
2
1
1
1
1
2
2
1
1
0
2
1
2
1
1
2
2
2
1
1
1
0
2
2
1
2
1
1
1
1
2
1
1
2
2
1
2
1
1
1
4
0
0
1
1
2
1
1
1
1
2
2
2
1
1
1
1
2
2
0
1
1
1
1
1
1
1
1
1
0
0
1
2
1
0
1
0
1
0
1
0
1
0
2
1
1
2
2
0
1
1
2
1
1
3
1
2
1
1
2
2
1
1
2
1
2
1
2
1
1
1
0
0
2
1
1
1
1
1
1
0
2
1
1
1
0
2
1
0
1
1
1
0
0
1
2
1
1
0
1
1
2
2
1
1
1
2
1
2
0
2
1
2
1
0
2
1
1
0
2
1
1
0
1
1
1
1
2
1
0
1
1
2
2
1
2
1
2
2
1
1
1
1
1
2
1
1
1
1
1
0
1
1
1
2
1
1
1
0
1
0
2
2
1
1
1
0
1
1
1
1
0
1
1
1
0
0
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
0
2
0
1
1
2
2
1
2
1
1
1
1
1
2
1
1
2
2
1
2
1
1
1
1
1
1
0
1
1
2
1
1
2
1
1
1
1
1
2
1
2
1
1
2
2
2
0
1
2
2
1
1
1
0
1
1
1
1
1
1
1
0
2
1
1
1
1
1
1
1
2
1
2
1
0
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
2
1
2
1
1
2
1
2
0
1
0
0
2
1
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
5
1
1
1
1
2
2
2
2
1
1
1
2
2
1
1
1
2
0
1
1
2
2
1
1
1
1
1
1
2
1
1
2
1
1
1
0
1
2
2
0
1
1
2
1
1
1
1
1
0
2
2
1
1
1
1
2
1
1
1
0
2
1
1
2
1
1
0
1
1
2
2
1
2
0
1
1
1
1
0
0
1
1
2
2
0
1
0
0
4
1
1
1
1
1
1
2
1
1
1
2
1
1
1
2
1
2
1
1
2
1
1
1
1
1
1
0
2
1
2
2
1
1
1
2
0
1
1
1
0
1
2
0
1
2
1
1
1
1
2
2
2
2
1
2
1
0
2
1
2
0
1
2
1
1
1
1
2
1
2
2
1
2
1
1
2
1
1
1
0
1
1
1
1
2
2
0
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
2
1
0
1
1
2
2
1
1
1
3
1
2
1
2
1
2
1
2
1
1
2
1
0
2
1
1
3
1
1
1
0
0
2
1
1
1
2
2
2
1
0
2
1
0
1
1
1
1
1
1
2
2
0
1
1
1
0
1
1
0
0
0
0
0
1
1
0
1
2
2
0
0
1
2
1
1
1
0
2
2
1
1
1
2
2
1
2
1
2
1
1
2
1
1
1
1
0
1
2
0
1
1
1
1
1
1
1
0
1
1
1
1
1
2
2
2
1
1
0
2
2
1
2
1
2
0
1
1
1
1
1
2
1
1
1
1
2
0
1
1
1
2
0
1
1
1
1
0
1
1
1
2
1
1
2
1
1
2
1
1
1
1
1
3
1
1
1
1
1
1
2
1
1
1
2
1
2
1
0
2
1
1
1
1
1
2
2
0
2
0
1
1
1
2
2
1
2
0
1
2
2
1
1
1
1
1
2
2
2
1
0
0
2
1
0
1
0
1
1
2
1
2
1
1
1
3
1
1
1
2
2
1
1
2
1
1
1
1
1
1
0
1
1
2
1
1
1
1
1
1
1
1
1
1
0
1
1
1
0
2
1
0
1
1
1
1
1
1
2
0
0
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
2
1
2
1
1
1
0
1
1
2
1
1
1
2
1
1
1
0
2
2
1
1
1
1
1
1
2
1
2
1
2
1
1
1
1
1
1
0
1
1
1
1
2
2
2
2
1
2
2
1
1
1
1
1
1
1
1
1
2
1
1
1
0
1
1
1
1
0
1
2
1
2
1
1
2
1
2
1
0
2
0
1
1
2
1
1
1
0
1
1
1
1
0
1
1
1
0
1
1
2
1
2
1
1
1
1
1
2
1
1
0
1
2
0
1
1
0
2
0
1
1
2
2
2
0
0
1
0
1
1
1
1
0
0
1
2
0
0
0
1
1
1
2
1
0
1
1
1
0
0
1
0
2
1
0
1
1
0
2
1
1
1
1
1
2
1
0
1
0
1
2
1
1
1
1
2
1
1
2
0
2
2
2
1
1
1
2
1
1
1
1
1
1
0
3
0
1
1
1
0
1
2
1
0
1
0
1
1
1
2
1
2
1
0
1
0
0
1
1
1
1
1
1
0
1
1
2
1
2
1
2
1
1
1
2
2
2
1
1
0
1
1
2
1
2
2
1
1
0
1
1
1
1
1
2
1
3
1
0
0
1
1
1
1
1
1
2
2
2
1
1
2
1
0
1
1
1
1
2
0
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
0
1
1
1
0
1
2
1
1
2
2
1
2
1
2
1
2
1
0
2
2
2
1
1
1
1
1
0
1
1
1
1
1
0
2
0
1
1
1
1
1
0
1
3
1
0
0
1
1
0
1
2
0
2
1
0
0
2
0
2
2
2
2
1
1
2
1
0
1
1
3
1
1
0
1
1
0
0
1
0
1
1
1
1
0
1
1
0
0
1
0
1
1
1
1
1
1
1
2
0
1
1
1
1
0
0
1
0
2
0
1
1
0
1
0
2
2
2
2
1
1
1
1
1
1
2
1
1
1
1
0
1
1
0
1
2
2
0
1
1
2
1
2
1
1
2
1
1
0
2
1
2
3
1
2
0
1
1
1
1
2
2
1
1
1
2
2
1
2
1
0
2
2
2
0
1
1
2
1
1
0
2
1
2
2
2
1
2
0
0
1
1
1
1
1
1
1
1
2
1
2
3
1
0
1
1
2
1
1
0
2
3
1
0
1
1
1
1
2
1
1
1
1
0
1
1
1
3
1
1
1
1
2
1
0
1
1
2
1
2
1
2
1
1
1
1
2
2
1
1
1
0
1
2
2
1
2
2
1
2
1
0
1
1
1
1
1
2
1
1
2
1
0
2
1
1
1
1
1
1
0
2
1
0
2
1
2
1
4
2
1
1
1
0
1
2
2
2
2
1
1
1
1
0
2
0
1
1
2
1
1
1
2
2
1
2
1
2
1
1
1
1
1
0
1
1
1
2
1
1
2
1
1
1
1
0
2
2
2
2
0
2
1
2
1
2
1
2
2
1
1
2
0
1
1
1
1
1
1
1
0
1
2
3
1
1
1
2
2
1
1
2
1
2
1
0
1
1
0
1
1
0
0
1
2
1
1
2
1
1
2
1
2
2
2
2
1
1
2
1
1
1
2
1
1
1
1
0
2
0
2
1
2
2
1
2
2
1
1
2
2
1
0
1
0
2
2
1
1
1
1
1
1
1
1
0
0
1
1
2
1
1
0
1
2
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
0
1
1
1
2
2
1
1
1
1
1
1
2
1
1
1
2
2
1
1
2
1
1
2
1
0
1
1
2
2
1
1
1
1
1
2
1
2
1
1
1
2
1
2
1
0
1
1
1
2
1
1
2
1
2
1
2
1
1
1
1
1
1
1
0
2
2
1
1
0
0
1
1
1
1
0
0
0
1
2
2
0
2
1
1
2
2
1
1
1
1
1
2
0
0
2
1
2
1
1
1
1
2
1
1
0
0
1
1
1
1
1
0
2
1
1
1
0
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
0
1
1
0
1
2
2
1
1
1
0
1
2
1
1
1
2
2
1
0
1
2
1
0
2
1
1
1
1
0
1
2
1
0
1
1
1
0
0
1
0
1
1
1
1
0
2
1
2
1
2
0
1
1
1
1
2
0
0
0
1
1
2
1
0
2
1
1
0
1
1
1
2
1
1
1
1
1
0
1
1
1
1
1
2
2
1
1
2
1
1
1
2
1
2
1
1
2
1
1
1
1
2
1
1
1
1
0
1
1
1
1
1
2
2
1
1
1
2
2
2
1
2
1
0
2
2
0
1
2
1
1
1
2
2
2
2
2
0
1
2
1
1
1
0
1
1
0
2
1
0
1
2
1
2
2
2
1
2
2
1
2
2
2
1
1
1
1
1
1
0
1
1
1
1
1
0
0
1
1
1
1
1
2
1
1
1
1
0
0
1
1
0
1
1
1
2
1
1
1
0
1
1
2
0
1
1
1
0
1
0
1
1
2
2
1
1
1
0
1
2
2
0
1
1
2
1
1
1
1
1
1
2
1
0
1
2
1
0
1
1
1
1
1
1
1
1
2
1
0
0
2
2
1
2
1
1
1
1
1
2
1
1
1
2
1
1
2
1
0
2
1
1
1
1
0
2
0
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
2
2
1
1
2
1
1
1
0
1
2
1
2
1
1
2
1
2
0
1
1
1
1
1
1
1
1
1
0
2
1
2
1
1
1
2
2
1
1
1
2
0
2
0
2
1
1
0
1
0
1
0
1
1
0
1
0
1
1
1
1
1
2
1
1
1
1
0
0
2
1
2
1
1
0
1
1
1
0
1
2
1
0
1
2
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
0
1
1
1
1
2
1
2
2
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
2
1
0
1
0
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
0
1
1
1
0
1
1
1
1
2
1
1
1
1
1
0
0
1
1
1
0
1
2
2
1
1
2
4
1
1
2
2
1
0
1
2
2
0
1
2
1
1
1
1
1
0
0
1
1
0
2
0
2
2
1
2
1
1
1
1
1
0
2
2
1
1
1
3
2
1
2
1
2
1
1
2
2
1
2
1
1
1
1
1
0
0
1
2
1
0
0
1
1
0
1
2
1
2
1
1
2
0
1
2
1
1
1
0
1
1
1
2
1
1
1
1
1
2
1
2
2
0
1
0
1
1
2
1
1
2
3
0
1
0
2
1
1
1
2
1
1
1
1
1
1
1
1
1
0
1
1
1
2
0
1
1
2
1
0
4
0
1
0
0
1
0
1
1
0
0
1
1
1
2
0
1
1
1
1
2
1
1
1
0
0
1
2
0
1
1
1
1
1
1
2
1
2
1
0
1
2
0
1
1
0
1
1
1
0
1
0
1
1
0
1
2
1
1
1
1
2
0
0
1
1
0
0
1
2
1
1
1
1
1
0
1
1
0
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
0
3
2
1
2
1
0
1
1
1
1
2
1
1
1
0
1
0
2
2
2
1
1
1
1
1
1
1
0
2
0
1
1
1
1
2
1
1
1
1
1
2
2
1
1
1
2
1
1
2
1
2
1
1
0
0
1
2
2
1
1
0
0
1
2
1
1
1
1
1
0
1
1
1
2
1
1
1
1
1
1
0
1
1
1
1
0
1
1
1
0
1
1
1
2
1
1
1
0
1
1
1
1
0
2
1
2
1
1
1
2
0
2
2
1
2
1
3
1
0
2
1
1
1
1
1
1
1
1
2
1
0
2
1
1
2
1
2
1
1
1
1
1
2
1
2
2
1
2
1
1
1
2
2
0
2
2
1
2
0
1
1
2
1
1
1
0
2
1
1
1
1
2
1
2
1
1
1
1
1
1
0
1
1
1
1
0
1
0
1
2
0
2
1
1
1
0
1
1
2
0
2
1
1
2
2
1
0
1
2
1
1
0
2
2
1
1
1
2
1
2
0
1
1
1
2
1
2
1
1
1
1
1
0
2
0
1
1
1
1
2
0
1
1
1
1
1
1
1
1
2
0
1
0
0
1
0
1
1
1
2
0
0
1
1
0
1
1
1
1
1
1
1
1
0
0
1
1
1
1
2
1
2
0
1
1
1
3
1
1
2
2
1
1
1
1
1
0
1
1
1
0
0
1
1
2
2
2
1
1
2
1
1
1
2
2
2
1
1
1
1
0
2
1
1
1
1
1
1
3
1
2
0
1
1
2
1
1
1
2
2
1
1
1
1
1
2
2
1
0
1
2
1
0
1
1
1
1
1
2
0
1
0
1
1
1
1
1
1
0
1
1
1
1
0
0
2
2
1
1
1
1
1
2
1
1
3
2
0
2
1
1
1
0
2
1
2
1
1
2
1
1
1
0
1
1
0
1
1
2
1
1
1
0
0
1
2
1
1
2
0
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
0
1
1
2
1
0
2
2
2
2
1
1
0
1
1
1
1
0
1
1
0
1
1
2
1
1
1
2
2
0
1
1
0
1
1
0
0
1
0
2
1
2
1
1
1
1
1
2
2
1
2
1
0
2
1
1
0
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
1
2
1
1
1
1
1
0
1
1
0
1
2
1
0
1
2
1
1
1
2
2
1
1
1
1
1
1
1
2
0
2
0
2
1
2
2
2
1
1
1
1
1
2
1
0
1
1
0
2
2
2
1
2
1
2
1
1
2
1
1
1
2
1
1
1
2
1
1
2
2
1
1
1
1
2
1
1
3
2
1
1
1
1
2
1
2
1
1
1
1
1
2
1
2
1
2
1
1
1
1
1
1
1
0
2
1
0
2
2
1
2
2
1
1
1
1
0
1
1
0
2
1
1
1
0
2
1
1
1
1
1
0
2
1
0
1
1
2
1
1
2
1
2
2
1
1
2
0
1
0
1
1
1
1
1
1
1
1
0
0
1
1
0
1
0
2
1
0
1
1
1
0
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
0
1
1
1
1
2
2
0
1
1
0
2
1
0
1
0
1
1
1
1
1
0
1
1
0
2
2
1
1
1
1
2
1
1
1
0
2
1
0
2
2
1
1
1
0
1
2
1
2
0
1
2
2
1
0
2
2
2
0
2
0
1
1
1
4
1
1
1
1
0
5
1
0
2
1
2
1
1
1
1
1
0
1
1
2
0
1
1
1
1
2
1
0
2
2
1
0
1
2
1
1
1
1
1
1
1
0
0
1
1
1
1
2
2
2
1
2
1
1
2
1
2
1
2
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
0
1
1
0
1
1
2
1
0
2
2
2
1
2
1
1
1
1
1
1
0
2
1
2
1
1
0
2
0
2
1
2
1
1
1
1
2
0
1
1
1
2
0
1
1
1
2
1
1
1
0
2
2
1
1
2
1
1
1
1
1
0
2
1
1
2
0
2
1
2
4
2
1
1
0
0
1
1
1
1
1
1
1
1
1
2
1
0
2
1
3
2
2
1
0
1
1
0
2
2
1
2
1
2
1
1
1
0
1
2
1
1
1
1
0
1
1
1
2
1
1
1
1
0
0
0
2
1
2
2
1
2
1
0
1
1
0
2
1
0
0
1
0
1
1
1
1
2
2
1
0
0
0
2
1
2
1
2
1
1
0
1
0
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
0
0
2
1
2
1
2
1
1
1
1
0
1
2
1
2
0
1
1
1
1
1
1
1
0
1
2
2
0
1
1
0
2
2
1
1
1
0
1
2
1
2
2
1
1
1
0
1
1
0
0
1
1
1
1
2
1
1
0
1
2
0
1
0
2
1
1
1
4
1
2
0
2
1
1
1
1
2
1
0
0
2
1
0
2
1
2
1
1
1
2
1
2
2
1
1
1
1
2
4
1
1
2
1
2
1
0
1
1
0
1
0
2
2
1
1
0
2
1
2
0
2
1
1
1
1
1
1
1
1
2
2
1
1
2
1
2
1
1
2
1
1
0
1
2
1
1
1
2
2
0
1
1
1
1
1
1
0
1
0
0
1
2
1
1
0
1
2
1
1
1
2
1
2
1
2
1
0
2
1
1
1
1
2
2
0
1
1
1
0
2
1
0
1
1
1
1
1
1
1
2
0
1
1
1
1
1
0
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
0
2
1
1
1
2
1
1
0
0
2
1
1
1
2
0
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
0
1
2
0
1
1
1
0
1
0
1
2
1
1
0
1
2
1
1
1
0
2
1
1
1
1
1
1
3
1
1
1
1
1
1
1
1
1
1
1
1
2
1
0
1
1
0
2
2
1
1
2
1
2
1
1
2
1
1
2
0
1
1
1
1
1
1
2
1
1
1
1
1
0
0
2
2
1
1
1
1
1
2
1
2
2
1
1
1
1
2
1
0
2
1
0
0
1
2
0
1
0
1
1
1
1
2
2
1
2
1
1
1
0
1
1
1
2
0
1
1
1
1
1
1
2
0
0
1
2
1
1
1
1
2
1
2
2
1
1
2
0
1
1
2
2
1
1
1
1
1
1
1
1
0
1
1
1
2
0
0
1
1
2
1
1
1
2
1
2
1
0
1
2
1
2
1
2
1
2
0
2
1
1
1
1
1
1
2
1
2
2
1
1
1
2
0
0
2
1
0
1
1
0
2
2
0
1
2
2
1
1
1
2
1
1
1
1
1
0
2
1
1
1
2
1
2
1
1
2
1
0
1
1
1
1
1
0
2
1
0
1
1
2
1
1
2
1
1
2
2
1
1
2
1
2
1
3
1
2
1
0
1
1
1
2
1
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
0
1
1
0
1
1
1
1
0
1
1
1
2
1
0
0
1
1
2
1
1
1
1
1
1
2
2
2
1
2
2
0
1
1
2
1
2
1
1
2
2
1
0
1
2
1
1
2
2
1
1
1
1
6
0
2
2
2
0
1
1
2
2
0
1
1
1
2
1
2
4
1
1
1
1
2
1
1
1
1
1
1
1
4
1
1
0
1
1
0
1
2
2
2
2
1
0
1
2
1
2
1
1
1
0
1
1
1
0
0
1
1
1
0
2
2
1
2
1
2
1
2
0
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
0
2
0
1
2
2
2
1
1
2
1
1
1
2
1
1
1
1
1
2
2
1
0
1
1
2
0
1
1
1
2
1
1
2
1
1
2
1
2
0
2
1
2
1
1
1
1
1
0
1
1
1
2
1
1
2
2
2
1
1
1
1
1
1
1
0
1
1
1
1
1
2
1
2
1
2
0
1
1
2
1
1
1
1
1
1
1
0
2
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
0
2
0
2
0
2
1
2
0
1
2
2
1
1
0
1
1
1
2
2
1
2
1
1
1
2
1
1
1
1
1
1
1
1
0
1
1
2
1
1
0
1
1
1
1
2
2
1
2
2
1
1
0
1
1
1
1
2
2
1
2
1
2
0
1
1
1
1
2
1
1
1
2
0
1
1
1
1
1
1
1
1
1
1
0
1
1
2
0
1
1
1
1
0
1
2
1
0
1
2
1
1
1
1
0
0
1
2
2
1
2
1
1
2
1
1
2
1
0
2
1
1
2
1
2
1
0
1
2
1
1
1
0
1
1
1
1
1
0
1
1
1
0
1
1
1
1
1
1
1
0
1
2
0
0
2
2
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
2
1
1
1
1
1
2
2
1
1
1
2
1
2
2
1
0
2
2
1
1
0
1
0
1
1
2
2
1
1
1
1
1
1
1
1
2
2
1
1
1
1
0
0
1
0
1
1
1
2
2
1
2
2
1
0
1
1
0
1
2
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
2
1
1
1
2
1
1
0
2
1
2
1
1
1
1
0
1
2
1
2
1
1
0
1
1
1
1
0
1
1
3
2
2
1
0
1
1
0
1
0
0
0
2
0
1
0
2
1
2
1
1
2
1
1
1
1
1
0
0
1
0
1
0
1
1
1
0
2
0
1
1
1
2
2
2
2
1
1
0
1
1
1
1
1
1
1
1
1
2
0
1
1
2
1
0
1
2
1
0
0
1
0
0
0
2
1
1
2
1
2
1
2
0
0
1
1
0
1
1
1
0
2
2
2
1
1
2
1
1
2
1
1
1
1
2
1
0
1
1
2
0
0
0
2
1
1
2
2
1
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
2
0
2
1
2
1
0
1
2
1
2
2
0
2
1
1
1
1
0
1
1
2
1
1
1
1
0
1
1
1
1
2
1
2
2
2
1
1
2
0
1
1
1
1
1
1
1
1
0
1
2
0
0
0
1
0
1
1
2
1
1
1
1
1
0
1
1
1
1
1
1
2
1
1
1
1
0
2
1
1
1
2
0
1
1
0
1
1
2
1
1
2
1
2
1
1
0
1
1
1
1
2
2
0
1
1
1
2
1
1
1
0
1
2
1
1
2
1
2
1
1
1
2
1
1
1
1
1
0
1
1
0
2
1
1
0
1
1
1
1
1
2
1
0
2
2
1
1
2
1
1
1
1
0
2
1
1
1
0
1
1
1
1
1
1
0
1
0
0
0
1
1
1
2
1
2
1
1
1
2
1
1
2
1
1
2
0
3
3
1
3
1
1
2
1
0
2
2
1
0
2
1
1
1
1
1
1
0
1
2
2
1
0
2
2
1
1
1
1
0
1
1
1
0
2
1
0
1
1
1
1
1
1
2
2
1
2
1
0
1
2
2
2
2
1
2
1
1
1
0
1
2
1
1
1
2
2
1
1
2
0
0
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
2
0
1
0
0
1
1
1
1
0
3
2
0
1
1
2
1
1
0
2
1
1
1
2
0
1
2
2
1
1
2
0
0
1
1
2
1
1
2
1
1
1
0
0
2
1
1
0
2
2
0
2
1
1
1
1
2
0
2
1
2
1
0
1
1
1
1
1
0
1
1
1
1
2
1
1
1
1
1
2
0
1
1
2
2
0
1
2
2
1
1
1
1
2
1
1
1
0
1
1
1
1
0
0
1
1
1
1
1
1
1
0
1
2
2
1
1
2
1
2
1
1
1
2
1
2
1
1
2
2
1
1
1
1
1
1
0
1
1
1
0
1
1
2
1
1
1
2
1
1
1
1
1
1
0
0
0
1
1
1
1
1
0
0
1
1
1
2
2
2
0
2
0
0
2
0
1
1
2
1
2
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
0
1
1
1
2
2
1
1
1
1
1
1
2
3
2
1
1
0
0
1
2
0
0
0
2
1
2
0
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
0
1
2
1
2
2
2
1
2
1
1
2
2
2
0
1
1
1
1
2
2
2
2
2
2
1
1
1
1
1
1
2
2
1
2
1
1
1
1
2
1
0
0
0
2
1
0
1
2
1
1
1
1
2
1
1
0
2
2
1
1
2
1
1
0
2
1
1
1
1
0
1
2
0
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
2
2
2
0
1
2
0
0
0
1
1
1
1
1
2
1
0
1
1
0
2
2
0
1
1
1
1
2
1
1
1
1
2
0
1
0
1
0
1
1
2
1
1
2
1
1
0
1
1
1
1
1
2
1
1
1
2
1
2
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
0
0
1
1
2
2
1
0
1
1
1
1
1
1
2
1
2
1
2
1
1
2
2
1
2
1
1
1
1
1
1
2
3
1
1
1
2
1
1
1
1
1
2
1
1
0
2
1
1
1
1
1
1
0
1
1
1
2
0
0
1
1
1
1
2
2
1
1
2
1
1
1
1
2
1
1
1
1
2
2
2
1
1
1
1
2
0
0
2
1
2
2
1
1
1
1
1
0
2
1
1
0
1
2
0
0
1
1
0
2
1
2
2
1
0
1
1
2
2
1
0
2
2
1
1
0
2
1
1
1
1
2
1
2
1
1
1
1
0
1
1
1
2
1
1
1
1
2
1
2
1
1
1
1
2
0
1
2
1
1
1
1
2
1
2
1
1
2
1
1
1
1
1
1
0
1
1
1
1
2
2
1
1
1
2
1
0
2
1
1
1
2
2
1
1
1
1
1
0
2
1
1
1
1
1
2
2
1
1
2
1
1
2
1
1
2
0
1
1
2
1
1
2
1
0
2
2
2
1
1
1
2
1
1
0
1
2
0
1
3
1
2
1
1
1
0
0
1
1
1
1
1
2
0
1
0
1
1
0
2
1
0
2
1
1
0
0
2
2
0
1
1
1
1
1
1
1
0
1
2
1
1
1
1
1
2
1
1
1
0
1
1
1
1
2
2
1
1
1
1
2
0
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
2
1
1
2
1
1
0
1
0
1
2
2
0
1
2
1
1
1
2
1
2
1
1
2
1
1
1
1
0
0
1
0
2
1
1
2
1
1
1
1
1
0
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
0
2
1
1
1
2
1
1
1
2
1
1
1
0
2
0
2
1
1
1
2
1
2
0
0
1
2
1
2
1
1
1
1
2
1
2
1
1
0
1
2
1
1
1
1
1
0
0
0
2
0
1
1
1
1
1
0
2
1
1
1
1
0
0
1
0
2
1
1
1
1
0
1
0
1
1
0
1
1
1
2
0
1
1
1
1
2
1
2
1
1
1
1
1
0
1
1
1
1
1
1
1
1
0
1
1
1
0
2
1
1
1
2
0
1
1
1
2
1
2
2
2
0
2
1
2
2
1
1
0
1
0
0
0
1
1
0
2
2
0
1
1
1
1
1
1
1
1
1
0
1
1
1
2
1
1
0
2
0
1
2
1
2
2
1
2
1
1
0
1
0
2
2
1
1
1
1
1
2
1
1
1
0
1
1
2
2
0
1
1
2
0
1
2
2
1
1
2
2
0
2
1
1
1
1
1
1
0
2
1
1
2
0
0
0
1
1
2
1
1
1
1
1
1
1
0
1
1
1
0
1
1
1
1
2
1
2
0
0
2
2
1
1
2
0
2
2
2
1
2
0
1
2
1
0
2
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
3
0
1
1
1
0
0
1
0
1
1
1
1
1
2
1
2
2
1
0
1
1
1
2
0
1
0
2
2
1
1
1
1
1
2
1
1
1
0
0
1
1
1
1
1
1
1
1
1
1
0
0
2
1
1
1
1
1
0
1
1
1
1
2
1
2
2
1
2
1
0
2
1
2
1
1
2
1
1
1
1
2
1
1
1
1
2
1
0
2
2
1
1
2
2
2
2
1
0
1
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
2
1
2
1
1
2
1
1
2
2
3
1
1
0
1
2
1
1
2
1
1
2
1
1
1
1
2
1
1
0
2
1
1
1
2
1
2
2
1
1
2
1
1
0
1
1
1
2
1
0
2
1
1
1
0
0
1
3
0
1
1
1
1
0
1
1
1
0
1
2
1
2
0
2
0
2
1
1
2
1
1
1
1
1
1
1
1
0
0
2
1
2
1
1
1
1
1
1
2
1
3
2
0
2
1
1
2
1
0
1
2
1
2
2
0
1
0
1
1
1
2
1
0
1
0
2
1
1
1
1
2
1
2
1
1
2
1
2
2
2
2
2
1
2
1
1
1
1
0
2
1
1
1
1
2
1
2
2
2
1
1
1
1
0
1
1
1
2
1
2
0
0
0
1
1
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
0
1
2
1
2
1
1
1
2
1
1
1
1
1
1
0
1
2
2
2
1
2
1
3
2
0
1
2
1
1
1
2
1
2
1
0
0
1
1
3
1
1
1
1
1
1
1
1
1
1
2
2
0
2
1
1
1
0
1
2
0
1
1
1
1
1
1
1
1
1
2
0
3
2
1
1
2
1
2
1
1
2
0
1
0
0
1
2
1
5
2
1
0
1
2
0
0
1
1
1
1
1
2
2
1
0
3
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
1
0
2
1
1
1
2
0
2
1
1
1
1
1
1
1
1
0
2
2
2
1
1
2
2
1
0
1
1
1
0
0
2
0
1
1
0
1
1
2
2
1
1
1
2
1
2
1
2
1
2
1
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
0
0
0
1
1
2
1
1
1
2
1
1
1
2
1
1
2
2
1
0
1
2
1
1
1
1
1
2
0
1
2
1
1
1
1
1
1
2
1
1
1
1
0
2
1
1
1
2
1
1
2
1
1
1
0
1
1
2
1
2
2
1
2
1
1
1
0
0
1
2
1
1
0
2
1
1
2
2
1
2
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
0
1
1
0
0
2
2
0
1
0
1
2
0
0
1
0
2
1
1
1
1
2
1
1
1
1
1
2
1
2
1
0
2
0
1
2
1
1
2
0
1
2
1
2
1
1
1
2
1
1
1
1
1
2
1
2
1
0
1
2
1
1
1
0
0
1
0
1
1
1
1
2
0
1
1
1
1
2
1
2
2
1
2
1
1
1
2
2
0
2
2
1
2
1
2
1
1
1
1
1
1
0
0
1
1
1
1
1
1
0
0
2
1
1
1
1
1
1
2
0
1
1
1
1
1
1
1
2
1
1
1
1
0
1
2
1
1
2
1
1
1
2
1
1
0
2
0
1
1
2
1
2
4
1
2
0
1
0
2
2
2
0
0
1
3
2
1
0
2
1
1
1
2
1
1
1
1
1
1
3
1
1
1
1
0
1
2
1
1
1
2
1
1
2
1
2
1
2
1
1
2
1
2
1
2
1
1
1
1
1
1
1
3
1
1
0
1
3
2
0
2
1
1
2
1
0
1
0
1
0
1
2
1
1
1
1
2
1
1
2
2
1
0
2
1
1
1
1
0
0
1
2
1
1
0
1
0
1
2
2
0
1
2
2
1
1
1
1
0
0
1
1
1
1
2
1
1
0
0
1
1
1
0
1
1
1
0
2
1
2
1
1
1
1
1
2
2
0
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
2
2
0
1
1
0
1
0
1
2
2
1
1
0
2
1
2
0
1
1
0
1
1
1
0
1
0
0
2
0
1
2
1
1
1
0
1
1
1
1
1
0
1
1
2
1
1
1
1
1
0
0
1
2
1
1
0
1
1
2
1
1
1
2
2
1
1
1
1
1
1
2
2
1
1
2
0
0
1
1
1
0
1
2
1
0
2
1
1
1
1
1
2
2
1
2
1
1
1
1
1
0
2
1
2
2
1
1
0
0
1
1
2
1
1
1
1
1
1
2
2
0
1
2
2
1
1
1
1
1
1
1
1
1
0
1
1
0
0
1
1
1
2
1
0
0
2
1
1
1
0
1
1
0
1
1
1
1
0
1
2
1
1
2
1
2
2
1
1
2
1
2
1
1
1
0
0
2
0
2
1
1
2
0
2
1
1
1
1
2
1
1
2
0
1
1
2
1
1
2
2
0
1
0
2
1
0
2
1
2
0
1
1
2
1
1
1
2
1
2
2
2
0
1
1
1
0
1
1
1
1
0
1
2
0
3
0
2
1
1
1
1
1
2
0
0
2
0
2
1
2
1
2
1
2
2
1
2
0
1
2
1
2
1
2
1
1
1
1
1
1
1
1
2
2
1
0
2
0
0
1
1
2
1
1
2
2
1
0
2
1
0
2
2
1
1
1
1
1
1
1
2
0
1
2
1
1
1
2
1
0
2
2
0
1
1
1
1
1
1
1
1
1
1
1
0
1
0
1
2
1
1
1
1
0
2
2
1
2
1
1
1
1
1
1
1
1
2
1
2
0
1
1
1
0
1
1
1
1
1
2
2
0
2
2
1
1
1
1
2
2
1
1
1
1
1
2
0
2
1
0
1
0
1
1
1
1
0
1
1
1
2
0
1
2
1
1
0
1
1
2
1
0
1
2
1
2
1
1
1
2
1
2
1
1
0
1
1
1
1
1
1
1
0
1
1
1
1
1
0
1
1
2
1
0
0
1
1
1
1
1
1
0
1
2
1
1
1
1
1
1
1
1
2
0
1
2
1
2
1
2
1
1
2
1
2
1
2
2
2
0
1
1
0
1
2
1
2
1
0
2
0
2
1
0
2
1
1
2
1
1
0
1
1
1
0
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
1
1
2
2
0
0
1
2
0
1
2
0
2
1
2
0
2
1
1
1
1
1
2
1
2
2
1
1
1
1
1
2
1
2
2
2
1
1
1
1
1
1
1
0
1
2
1
1
2
1
0
2
1
2
1
1
1
2
1
1
1
2
1
2
1
2
1
1
2
1
2
1
2
0
1
2
2
1
1
1
1
1
1
1
0
1
1
2
1
0
0
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
2
1
2
1
1
2
1
1
2
2
1
1
1
1
1
1
1
1
2
2
0
2
2
1
1
1
1
1
1
1
0
1
2
1
1
1
1
2
1
1
1
0
2
2
2
2
1
2
2
2
2
1
0
1
1
1
1
1
1
0
1
1
1
2
2
0
2
1
1
1
1
1
2
2
1
1
2
2
1
1
1
1
0
2
0
1
1
1
2
0
1
1
0
1
2
1
2
0
1
3
1
1
1
2
1
0
2
1
1
1
1
2
2
1
1
2
1
1
1
0
2
2
0
1
1
1
1
0
1
1
2
2
1
0
0
1
0
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
0
1
1
1
1
2
2
1
2
0
0
2
2
1
0
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
0
0
1
2
1
1
1
0
1
2
0
1
1
1
2
1
2
1
1
0
0
1
2
1
0
1
1
1
0
1
0
2
1
1
0
1
0
1
1
1
1
2
2
1
1
1
1
1
1
2
0
1
1
2
2
1
2
1
2
1
2
2
1
1
1
0
2
2
2
1
1
0
1
1
1
0
1
0
1
1
1
0
0
0
1
0
1
2
1
1
2
1
0
1
1
1
1
1
1
1
1
2
1
1
0
1
2
1
0
0
2
1
1
0
1
0
0
3
1
1
1
1
1
2
2
1
0
2
2
2
0
1
1
1
1
0
1
2
0
1
0
1
1
2
2
1
2
1
1
1
0
1
0
1
1
0
1
1
2
0
1
2
0
2
1
2
2
1
1
2
1
1
1
1
1
1
0
1
0
0
3
1
1
1
0
1
1
0
1
2
1
2
2
2
1
1
2
1
1
3
2
1
2
1
1
1
2
1
0
1
1
1
1
0
1
0
1
2
2
2
1
1
3
1
1
1
1
1
1
1
1
1
1
1
0
2
1
1
0
1
1
0
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
0
2
1
1
1
1
1
1
1
1
0
0
1
0
2
0
2
1
2
1
2
2
1
1
0
1
2
2
1
2
1
1
0
2
1
1
1
1
0
1
1
2
1
2
2
2
1
1
2
2
0
1
1
0
2
1
0
0
1
2
1
2
1
0
1
1
2
0
1
1
2
1
1
1
2
1
1
0
1
0
1
1
1
1
1
1
2
1
1
2
2
2
2
2
1
2
2
1
1
1
1
2
1
1
0
2
1
2
2
0
1
1
1
0
0
1
1
1
2
1
0
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
2
0
1
0
2
2
1
0
1
1
2
2
1
0
1
0
1
2
1
2
1
1
1
1
2
1
4
1
0
1
3
0
1
1
1
0
0
2
1
1
1
2
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
0
2
2
2
1
2
1
1
1
1
1
1
1
1
2
1
0
1
1
2
2
2
1
1
0
1
2
0
1
2
2
0
1
2
1
1
1
2
1
2
1
2
1
2
1
1
2
1
1
2
0
2
1
2
2
1
2
1
0
2
1
0
1
2
1
1
2
1
1
0
1
2
1
1
1
2
1
1
1
1
0
1
1
1
1
1
0
1
1
1
2
2
1
1
1
0
1
1
2
1
0
1
1
3
2
2
1
1
1
1
0
1
1
2
0
1
1
1
0
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
0
1
0
0
1
1
1
2
1
1
0
1
1
1
1
2
0
2
1
2
1
1
0
2
1
1
2
2
1
1
0
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
0
0
1
2
0
0
2
0
2
1
2
2
0
1
1
1
1
1
1
1
2
0
1
2
1
2
2
2
1
2
1
1
0
1
2
1
1
0
1
0
1
1
2
1
1
1
2
1
1
2
0
2
1
1
0
1
1
2
2
1
1
1
2
2
1
1
0
2
1
2
1
0
1
0
1
1
1
2
1
1
1
1
0
0
1
1
1
0
1
1
1
0
1
2
0
1
0
1
1
1
1
1
2
3
2
2
2
0
1
2
1
2
2
1
1
0
1
2
2
1
1
1
0
1
1
2
1
0
1
1
0
2
0
1
2
2
0
0
0
2
1
2
1
1
2
1
0
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
3
1
1
1
1
0
0
0
1
1
1
1
1
0
1
2
0
1
1
3
1
2
0
1
1
1
0
1
1
2
2
1
0
0
1
1
1
1
1
2
1
1
0
2
0
1
1
1
1
1
1
2
2
1
1
1
1
1
1
2
0
2
1
1
1
1
3
1
2
1
1
2
1
1
1
0
1
2
0
1
2
1
2
1
0
0
1
2
1
1
2
1
1
1
0
1
2
0
1
1
1
1
1
0
1
2
1
2
1
1
1
1
1
2
0
1
0
1
0
1
2
1
1
2
0
1
0
1
0
1
1
2
1
2
2
1
1
1
1
1
3
2
1
1
1
1
1
1
2
1
1
2
1
1
0
0
1
2
1
3
2
1
1
1
1
0
0
1
0
0
1
1
2
0
1
2
2
0
1
1
1
2
1
0
1
1
2
2
2
2
1
2
2
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
2
1
3
1
0
2
1
1
2
2
1
1
2
2
2
2
2
0
2
2
2
0
1
2
0
1
2
2
1
2
1
2
1
1
1
2
1
1
0
0
2
0
1
1
1
2
1
2
0
1
2
1
2
1
2
1
1
2
1
1
0
1
1
2
2
2
1
1
1
2
0
0
0
1
1
2
1
1
2
2
2
1
2
1
1
1
2
1
1
1
2
2
0
1
1
1
1
1
1
2
1
0
2
0
0
1
0
1
1
2
2
1
1
1
2
0
1
2
1
0
2
1
1
1
2
2
1
1
1
1
0
1
1
1
2
1
0
1
2
2
2
2
1
2
1
1
1
1
1
1
1
1
1
0
1
0
1
2
1
2
0
2
2
1
2
1
2
1
1
1
1
0
1
0
2
1
0
0
1
1
0
2
1
0
1
1
0
1
2
1
2
0
0
1
1
1
1
1
1
2
2
2
2
1
1
1
1
1
0
1
1
1
2
1
2
1
1
1
2
1
0
2
1
1
2
1
1
1
2
1
1
1
1
2
0
1
1
1
2
0
0
1
1
1
1
2
1
1
2
2
0
1
1
0
1
1
1
1
0
0
2
2
1
1
1
2
1
0
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
0
2
1
0
2
1
1
1
2
1
2
1
1
1
1
0
1
2
0
1
0
1
1
2
1
1
3
1
1
2
1
2
1
1
1
1
1
2
1
0
1
2
1
1
1
1
0
2
1
1
0
1
1
1
2
1
1
1
2
1
1
1
2
1
0
1
2
1
1
0
1
2
1
0
1
1
1
1
3
0
1
1
2
1
1
2
1
0
1
1
1
1
2
2
0
1
1
2
1
1
2
2
0
1
1
1
0
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
0
1
1
1
1
1
1
1
1
1
2
2
2
1
1
2
0
1
0
1
1
2
2
1
2
1
1
0
1
0
2
1
1
2
1
1
1
0
0
1
2
2
1
1
0
1
2
2
2
1
1
1
2
2
1
1
2
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
2
2
1
1
1
1
2
1
2
2
2
2
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
2
1
2
0
1
2
1
1
2
1
1
0
2
1
1
2
1
1
2
1
1
0
1
1
0
0
1
2
1
2
1
2
1
0
1
2
1
2
1
1
1
1
1
1
0
0
1
1
1
2
1
0
2
1
1
1
1
0
0
1
1
2
2
1
2
1
2
0
0
1
1
0
2
1
1
0
1
1
0
1
1
1
2
1
1
1
3
1
1
1
1
1
2
0
0
1
1
1
2
2
1
1
2
1
1
1
1
0
1
1
2
1
1
0
0
2
1
1
1
1
1
1
1
1
1
2
1
1
2
2
1
0
2
2
0
2
2
1
1
0
1
0
1
0
1
0
1
1
2
1
0
1
1
1
0
1
1
1
1
1
1
1
1
1
2
1
1
1
0
1
0
1
0
0
1
0
0
0
2
1
1
1
0
0
1
1
2
1
1
1
1
2
1
2
0
1
1
1
1
0
2
1
2
2
2
1
2
1
1
1
1
2
2
2
1
2
2
0
1
2
1
0
0
1
1
2
1
1
1
3
1
2
1
1
1
1
0
1
1
1
1
2
1
1
2
1
0
1
1
1
0
1
1
2
1
2
1
1
1
0
0
1
2
1
1
1
3
0
1
0
2
1
1
1
0
1
2
0
2
2
0
1
1
2
0
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
2
1
2
1
1
1
2
2
1
1
2
2
2
1
1
1
0
1
1
1
2
1
1
1
2
1
2
1
0
1
1
1
1
0
2
2
1
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
2
1
2
2
1
1
0
1
0
2
2
1
2
1
1
1
2
1
1
2
1
1
1
2
1
1
1
2
0
0
1
2
1
1
2
1
1
1
2
1
1
0
2
1
1
0
2
1
1
0
0
1
1
1
1
1
0
0
1
2
2
0
2
1
1
1
0
1
0
1
2
1
1
2
1
1
2
1
2
2
1
2
2
0
2
1
0
1
2
1
1
1
1
1
1
1
1
1
0
1
1
1
1
2
1
1
1
2
1
1
2
0
0
1
0
1
1
2
1
1
1
2
1
1
1
1
2
0
2
1
1
1
2
1
1
0
2
1
1
1
2
3
2
1
1
1
1
1
1
1
1
1
0
1
1
1
1
2
1
2
1
0
1
0
1
1
1
2
1
1
2
2
1
2
1
2
1
1
2
2
1
1
2
2
2
1
2
1
1
1
1
2
0
1
1
2
2
2
1
2
2
1
1
1
1
1
2
1
0
1
0
0
1
2
1
1
2
1
2
0
0
1
1
1
2
3
1
1
1
2
2
1
1
1
0
2
1
1
1
1
1
1
0
1
0
1
1
1
1
1
2
1
0
1
1
1
1
1
1
1
1
0
1
2
0
0
1
1
1
1
2
1
0
1
1
1
1
1
2
1
1
0
1
1
1
0
1
1
1
2
0
2
0
0
1
1
0
1
1
1
1
1
1
1
2
0
1
1
0
2
0
1
1
0
1
1
2
0
1
1
2
1
1
1
0
1
1
1
1
0
0
1
2
1
1
0
1
1
1
0
1
1
1
1
1
1
1
2
1
1
2
1
2
1
0
0
1
2
1
2
1
0
1
1
1
0
1
2
0
1
2
2
2
1
1
1
1
1
1
2
1
0
1
1
0
0
1
0
2
1
0
1
0
2
1
1
2
2
2
0
1
1
1
0
1
1
2
1
1
1
0
0
1
1
2
1
1
1
2
1
2
2
1
2
2
1
2
1
2
1
2
2
1
2
1
1
1
0
2
2
2
1
1
1
1
1
2
1
0
1
2
1
1
1
1
1
2
2
1
1
1
1
1
0
2
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
0
1
0
1
1
1
1
2
0
1
0
2
1
1
2
0
1
2
1
0
1
1
1
0
0
1
1
2
1
1
1
1
1
1
0
1
1
1
1
1
1
1
2
1
2
0
1
1
3
1
1
1
1
1
2
1
2
2
1
0
1
0
1
1
1
1
1
1
1
1
2
0
1
2
1
0
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
0
1
1
1
1
0
1
2
2
2
2
0
2
2
1
0
2
1
2
0
0
1
1
2
1
1
1
1
1
2
2
1
2
1
1
1
1
0
1
3
1
1
2
1
1
1
1
1
0
1
2
0
2
2
1
1
1
1
1
2
1
1
0
1
1
1
1
2
2
1
1
1
0
0
1
0
1
1
1
1
2
1
1
1
2
2
2
2
0
1
1
1
1
1
1
1
1
0
2
1
1
1
1
1
1
1
1
1
2
1
2
0
1
2
1
1
0
2
1
0
1
2
2
0
1
2
1
1
2
0
1
2
1
0
1
1
1
0
1
1
1
0
2
1
1
0
0
1
1
0
2
0
1
2
1
1
0
2
1
1
2
1
0
2
0
1
2
1
2
1
2
2
1
0
1
1
0
1
1
0
1
1
1
1
2
1
0
2
1
1
1
0
1
2
1
1
0
1
1
1
1
1
1
0
1
1
1
1
1
1
2
1
1
1
0
1
2
1
1
0
0
0
1
1
1
1
1
1
0
1
2
1
2
2
1
1
1
1
1
1
1
2
2
0
1
1
2
0
1
1
1
1
2
1
1
1
0
2
1
1
1
2
1
1
1
3
2
1
0
2
1
2
1
1
1
1
1
1
2
2
1
2
1
1
1
1
0
1
1
1
1
1
1
1
1
1
2
1
3
2
1
2
1
0
1
1
1
1
0
1
1
2
0
1
1
1
1
1
1
0
1
1
2
1
0
2
1
1
0
0
1
1
1
2
2
1
1
2
2
1
1
0
1
1
1
1
1
1
1
1
1
0
2
1
2
2
0
1
1
1
1
0
1
0
0
1
2
1
1
1
1
1
1
2
1
1
1
0
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
0
1
2
1
1
1
1
2
2
2
1
2
1
1
1
0
0
0
1
1
1
2
1
2
2
2
2
2
0
1
2
0
1
2
1
1
1
1
0
1
2
0
0
1
2
0
1
0
2
2
2
1
1
0
1
1
2
1
1
1
1
2
1
2
1
2
2
1
1
1
1
2
1
0
1
0
2
1
1
1
0
0
1
0
1
2
1
1
1
1
1
2
0
1
2
1
2
1
1
0
1
2
1
1
1
2
1
2
1
1
1
1
1
1
1
2
0
1
1
2
1
1
0
1
0
2
2
2
1
0
1
0
0
0
1
1
1
1
1
2
2
1
0
1
2
0
1
1
1
1
1
2
1
1
2
1
0
2
1
2
1
1
1
1
2
1
2
1
2
2
0
2
0
1
1
0
1
1
2
1
0
1
2
2
1
1
1
2
2
0
1
1
1
0
0
0
1
1
2
1
2
0
2
2
0
2
1
1
0
1
0
2
1
1
2
1
2
1
1
0
1
2
1
0
1
2
1
1
2
1
1
1
0
2
1
1
1
1
1
1
1
1
1
0
0
1
1
1
1
0
1
1
1
1
0
2
1
0
0
1
1
2
1
1
1
1
1
1
1
0
1
0
1
1
2
2
1
2
2
1
1
1
1
1
2
0
1
1
1
2
1
0
2
1
2
1
1
1
2
2
1
1
0
0
0
1
2
2
1
2
1
2
1
1
1
2
1
0
1
2
2
1
1
1
2
1
2
1
1
0
1
2
1
0
0
0
1
2
2
1
1
0
1
1
1
0
1
2
1
0
2
1
2
0
1
1
1
1
1
1
0
1
1
1
1
2
1
2
0
2
1
1
2
1
2
1
1
1
2
0
2
2
1
1
2
2
2
2
2
1
1
2
1
1
1
0
2
2
2
1
0
1
1
1
1
1
1
2
2
1
2
1
1
2
1
2
2
1
1
2
2
1
0
1
1
1
0
1
0
1
1
1
1
2
1
0
1
1
2
2
0
1
2
1
1
2
4
2
2
0
1
1
0
1
1
1
1
2
1
1
0
1
0
1
0
1
1
1
2
1
0
1
1
1
2
2
1
0
2
1
0
2
0
2
0
1
1
1
0
2
2
1
0
1
2
1
1
0
0
2
0
1
0
2
2
1
0
1
1
1
1
0
1
1
1
2
1
2
1
1
1
1
1
0
0
1
1
1
1
1
1
1
0
1
1
1
0
2
1
2
1
2
1
1
1
1
0
0
1
1
1
0
3
1
2
1
1
2
1
1
1
0
1
2
2
0
1
2
1
1
1
2
1
2
2
1
1
2
1
0
2
1
1
0
1
2
1
2
1
2
2
1
0
1
1
2
0
2
1
1
1
1
1
2
1
0
1
1
2
1
1
1
0
1
1
0
2
1
0
0
1
2
1
1
2
1
1
2
0
2
1
1
2
1
1
1
1
2
1
1
0
1
1
1
2
2
2
1
1
2
0
1
1
3
1
2
1
1
2
1
0
1
2
4
0
2
2
1
1
1
2
1
0
1
1
0
0
1
1
2
2
2
0
1
0
2
1
2
2
1
1
2
2
1
2
1
1
1
2
0
1
1
0
1
1
1
2
2
2
1
1
1
1
1
1
1
0
0
1
1
1
1
1
1
0
2
1
0
1
1
2
1
1
1
1
2
2
1
2
1
1
0
1
1
1
2
2
2
0
1
1
0
0
2
2
1
1
2
2
2
1
2
1
2
1
1
1
1
0
1
2
2
1
1
1
1
1
1
0
2
1
2
1
1
2
2
2
2
1
3
2
1
1
1
1
1
1
2
1
1
0
2
0
2
2
0
2
0
2
1
1
0
1
0
1
0
1
2
1
1
1
1
0
1
2
0
1
2
1
1
2
0
1
0
1
1
2
1
2
1
0
1
1
2
2
1
1
1
1
0
1
1
1
1
2
1
2
2
1
2
1
1
0
1
2
2
1
1
1
2
1
1
1
1
1
1
1
0
1
0
2
0
0
1
1
1
0
1
1
1
1
1
2
1
0
2
0
0
2
1
1
1
2
0
1
1
0
1
1
1
2
2
1
1
1
1
1
1
1
1
2
2
1
2
2
1
1
0
1
1
0
1
2
1
1
2
1
1
0
1
2
1
1
1
1
1
2
1
2
0
1
1
0
1
0
2
1
1
0
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
2
2
1
1
1
1
0
1
1
2
0
1
2
1
2
0
2
1
2
1
0
1
1
0
0
2
1
2
2
1
0
1
2
1
1
1
0
2
1
1
1
1
1
0
1
2
0
1
2
0
1
1
2
1
2
2
2
1
3
1
2
0
2
2
2
1
1
1
1
1
1
1
1
1
2
1
2
2
1
1
2
1
2
0
1
1
2
1
1
2
1
2
1
1
0
1
1
1
1
2
1
2
0
1
1
2
0
1
0
1
0
0
0
1
2
1
2
0
0
1
0
1
1
1
1
2
2
1
1
1
2
1
0
1
1
0
0
2
0
1
1
2
1
2
1
1
2
1
2
2
2
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
0
1
2
0
1
1
0
1
0
1
1
0
1
1
1
1
1
1
1
1
0
2
1
2
1
2
1
1
1
2
2
1
2
0
0
1
0
0
1
0
1
0
0
0
1
2
1
1
1
2
1
2
0
0
2
1
2
1
1
1
0
2
1
1
2
1
1
0
1
1
1
0
1
0
1
1
2
1
2
1
0
2
1
2
0
1
1
1
1
1
2
2
2
1
1
1
1
2
1
1
2
2
2
1
1
1
0
1
1
0
1
2
1
3
1
1
1
0
1
1
1
1
1
1
1
1
1
2
0
1
1
1
2
0
1
1
1
1
1
1
0
1
1
2
1
1
1
1
1
2
1
0
1
1
1
1
1
0
1
1
0
2
1
1
2
2
1
1
0
1
1
1
0
1
1
1
0
1
1
1
2
0
0
1
1
1
0
1
1
2
2
0
1
1
2
1
1
1
1
1
1
2
0
2
2
1
2
1
1
2
1
2
2
1
2
1
0
1
1
1
1
0
2
1
2
1
0
2
2
2
1
2
1
1
1
1
1
1
1
1
0
1
0
1
3
0
1
1
1
0
1
2
0
1
1
1
1
1
1
1
1
0
1
1
0
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
0
1
0
1
1
1
1
2
0
2
1
2
1
1
1
1
1
2
1
1
1
2
0
1
1
1
2
1
0
1
1
2
1
2
0
0
2
1
1
0
2
1
0
1
1
1
0
0
1
1
0
2
2
0
2
1
2
1
1
1
2
1
1
1
0
1
2
0
1
1
2
2
1
1
1
2
1
1
2
0
0
1
1
1
0
1
0
2
2
2
1
1
1
1
0
1
5
0
1
0
1
0
2
1
1
1
2
1
2
1
1
2
2
1
2
2
2
1
0
2
2
2
2
0
2
1
2
1
1
2
1
0
2
2
1
0
2
1
2
1
1
1
2
1
1
1
0
1
2
0
1
1
1
2
0
0
1
0
2
1
1
1
1
1
1
1
0
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
1
1
2
1
1
1
1
0
1
2
1
1
2
1
2
0
1
1
2
1
1
1
1
2
1
0
1
1
1
0
1
2
1
1
1
1
1
1
1
2
2
1
1
1
1
2
2
5
1
2
2
1
1
0
1
1
0
2
0
1
1
1
0
0
1
1
2
1
1
0
1
1
2
2
1
1
1
1
0
0
1
1
1
1
1
2
1
2
2
1
2
1
0
2
1
0
1
1
1
1
1
1
2
2
1
0
2
2
1
1
1
2
1
2
1
2
1
1
2
1
1
0
0
0
1
2
1
1
1
1
1
1
1
2
1
0
1
2
2
2
0
0
1
1
1
1
2
1
1
1
2
1
0
1
1
0
1
1
1
0
2
2
2
1
1
2
1
1
1
1
2
1
0
1
0
1
0
2
2
2
0
0
2
1
1
1
1
1
2
1
0
0
1
2
1
1
1
1
1
2
2
2
1
2
0
2
1
1
1
0
2
1
0
1
1
1
3
1
0
1
0
0
1
1
1
1
1
2
1
1
1
3
0
2
2
2
2
2
2
1
1
2
1
1
1
0
1
1
1
1
2
2
1
0
3
1
0
0
1
2
1
2
2
1
1
1
0
2
1
0
2
1
1
0
2
1
1
1
0
1
0
2
1
1
1
1
1
2
1
1
1
2
0
1
0
1
1
1
2
1
0
0
1
1
1
1
1
0
1
1
1
2
1
1
2
1
2
1
0
1
1
1
0
2
1
1
2
1
1
1
1
1
2
2
2
2
0
1
2
1
1
2
2
1
1
1
1
1
1
2
0
2
1
2
1
1
1
0
1
0
1
1
2
1
1
1
2
1
1
1
1
2
0
1
2
0
1
0
0
1
1
1
1
1
0
1
1
1
2
1
5
0
1
1
2
1
2
1
1
1
2
2
0
2
1
1
0
2
0
1
1
0
0
1
2
1
1
0
1
3
1
1
2
1
1
2
2
2
2
0
1
1
1
2
1
2
1
1
1
0
0
1
1
1
0
0
0
0
1
1
1
1
0
1
2
1
2
0
2
1
2
1
3
0
1
1
1
1
1
1
1
1
1
2
1
1
0
1
1
2
1
0
1
1
1
1
2
1
1
1
1
0
2
1
1
1
2
0
1
1
1
1
2
1
1
1
1
1
2
1
2
1
0
2
0
1
1
1
1
1
1
1
1
1
1
0
2
1
1
0
1
1
2
1
0
1
1
1
1
2
1
1
2
1
0
0
2
2
1
2
1
1
2
2
1
0
2
2
1
1
1
2
1
2
1
2
1
2
1
1
2
2
2
1
1
2
2
1
1
1
1
2
1
0
1
0
0
1
2
1
1
3
2
0
1
1
0
2
0
1
1
1
1
1
1
0
1
1
1
2
1
2
1
1
1
1
1
1
0
1
1
1
1
1
0
1
2
0
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
0
2
0
1
1
1
1
1
0
2
1
2
1
1
1
1
2
2
0
1
0
1
2
1
1
1
1
1
1
1
1
1
2
1
3
1
2
1
1
2
2
3
1
2
2
2
0
2
0
1
1
1
1
1
2
1
1
1
2
1
0
0
2
1
1
1
2
1
0
1
1
1
1
0
0
1
2
1
0
1
1
1
1
0
0
1
1
0
2
2
1
1
1
0
2
1
0
1
1
2
2
1
0
1
0
2
0
0
0
1
1
1
1
3
2
2
2
1
2
1
1
0
2
1
0
1
1
1
1
2
1
1
0
1
2
1
1
2
1
2
1
1
1
1
2
2
1
1
1
2
2
1
1
1
2
1
0
1
1
1
1
2
2
2
2
0
0
1
2
1
2
1
2
1
2
2
2
1
1
1
1
1
1
1
2
2
3
1
1
2
2
1
2
2
1
1
1
0
2
1
1
2
1
1
1
1
1
1
3
1
0
3
3
1
2
2
0
1
2
1
1
0
1
1
0
0
1
1
1
1
1
0
1
4
2
0
1
1
0
2
1
2
0
0
1
1
1
1
1
1
1
1
1
0
1
1
1
2
2
2
1
2
1
0
1
1
1
0
1
0
1
1
2
1
2
1
1
1
1
1
1
1
1
1
0
1
0
2
2
1
1
1
1
1
0
1
1
0
1
2
1
0
2
0
1
1
2
0
1
1
2
1
2
1
1
2
0
1
2
2
1
2
1
1
1
1
1
1
1
1
2
1
1
0
0
2
2
2
0
2
0
1
1
1
1
0
0
1
2
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
1
0
2
2
2
1
1
1
0
2
2
1
2
1
0
1
1
1
1
0
1
1
1
2
2
1
3
1
1
2
2
1
1
2
1
1
0
2
1
1
2
1
1
1
0
0
0
1
2
1
1
2
1
1
1
2
1
1
1
1
1
1
2
2
1
2
2
3
1
2
1
1
1
1
1
1
1
1
1
1
0
1
1
0
2
1
2
2
1
1
2
2
0
1
1
1
1
1
1
2
2
1
1
2
1
1
1
1
1
0
1
0
0
1
1
2
1
2
2
1
2
2
1
1
1
2
2
1
2
1
2
1
2
1
0
2
0
1
1
1
1
0
1
0
0
2
1
1
1
1
0
1
0
1
0
0
1
1
2
1
2
2
2
1
1
2
2
0
1
2
0
1
1
2
1
0
1
2
1
1
2
1
1
1
0
3
0
1
2
0
1
1
1
1
2
1
0
1
2
1
1
1
2
1
1
1
2
1
1
2
0
1
0
1
1
1
2
1
1
1
0
0
1
0
2
0
2
2
2
0
1
1
2
1
1
1
2
1
2
1
1
0
1
1
0
2
1
1
1
1
2
1
1
1
0
2
1
2
2
1
1
1
1
1
0
3
1
1
1
1
1
0
1
1
2
1
1
1
1
1
2
1
0
1
1
3
0
0
1
1
1
2
1
0
2
2
1
1
2
2
1
1
2
1
1
0
1
1
1
1
1
1
1
1
2
1
1
1
0
1
1
1
1
1
0
0
1
2
2
1
0
1
1
1
2
1
2
1
1
1
1
2
1
1
1
2
1
1
1
1
2
2
0
1
1
1
1
1
2
1
2
2
1
0
1
1
2
1
1
0
0
0
1
1
0
1
1
0
2
1
1
2
2
2
1
1
1
1
1
2
1
1
0
1
1
2
1
1
2
0
0
0
1
0
0
1
2
1
1
2
1
2
1
0
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
2
2
2
1
0
1
2
1
2
1
1
1
1
0
0
0
1
2
1
1
1
1
2
0
2
1
1
1
1
0
1
1
2
1
0
2
1
2
0
0
4
1
1
2
1
2
1
1
2
2
1
1
1
1
1
1
2
2
1
1
1
1
1
2
2
1
0
1
2
1
2
2
1
2
0
1
1
1
1
0
2
1
0
1
1
1
0
1
1
1
1
0
1
2
1
1
1
2
1
2
0
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
2
1
0
1
1
1
2
1
0
2
1
1
1
0
1
2
1
1
1
2
0
1
1
0
2
1
1
1
1
1
2
0
1
1
0
0
1
0
2
2
1
1
2
1
2
1
1
2
1
1
1
0
1
1
1
1
1
2
1
0
1
2
1
1
1
2
1
1
0
2
1
2
1
1
1
2
2
0
1
1
1
1
2
0
1
1
2
1
1
1
0
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
2
0
0
2
1
2
1
1
1
2
1
1
1
1
1
2
1
0
1
2
2
0
1
1
2
1
1
2
2
2
1
1
1
0
1
1
2
1
0
1
0
1
1
2
1
1
0
1
1
0
1
1
1
1
2
2
1
2
1
2
1
1
1
1
1
0
1
1
0
0
1
1
1
2
1
1
0
1
2
1
2
3
1
1
1
1
1
1
2
2
1
1
2
1
0
0
1
0
0
2
0
2
1
2
0
1
2
1
2
0
1
1
0
2
2
1
1
1
1
0
1
1
2
1
1
1
0
1
1
1
2
0
0
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
2
1
2
1
2
0
1
1
0
1
2
1
1
0
0
1
1
2
1
1
1
2
2
1
0
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
2
2
1
1
0
3
1
1
2
0
2
1
0
2
1
2
1
1
1
1
1
0
0
0
1
0
1
2
1
2
1
2
1
1
1
2
1
0
0
0
2
1
2
2
0
1
1
1
1
1
1
2
1
1
2
1
2
1
1
1
0
1
1
1
1
1
2
2
0
1
1
1
1
1
1
0
1
1
2
1
1
2
1
2
0
1
1
1
1
1
2
1
2
1
1
0
1
0
0
1
1
1
1
1
1
2
1
0
1
1
1
1
0
1
1
1
2
1
1
2
1
2
2
0
1
2
1
0
1
1
1
1
2
2
2
1
2
1
1
0
1
2
1
1
0
0
2
0
1
1
0
3
2
0
1
1
1
1
2
0
2
1
1
1
1
0
0
1
2
1
0
0
1
2
1
1
1
1
1
0
1
2
1
2
1
1
1
1
1
1
0
1
1
1
1
1
2
1
0
1
1
1
0
1
1
1
1
0
1
0
1
0
1
1
1
2
1
2
2
1
1
3
1
1
2
1
1
1
0
1
1
1
1
1
1
1
1
0
1
1
2
2
1
1
1
1
1
1
1
2
2
1
2
0
2
1
1
2
1
1
1
0
2
1
2
0
1
3
0
1
0
1
1
2
2
1
1
1
0
1
1
1
0
1
1
2
0
0
2
2
1
3
2
0
0
0
2
2
1
0
2
1
1
0
1
1
1
1
1
1
2
3
1
0
0
1
1
0
2
1
1
2
1
2
0
0
1
1
1
1
1
1
1
1
2
1
2
2
2
2
1
2
1
1
2
0
1
2
1
2
1
2
0
1
0
2
1
1
1
0
2
0
0
0
2
1
2
1
1
2
1
1
1
1
0
1
1
1
0
1
1
0
2
1
1
1
1
0
2
1
1
1
2
1
2
1
2
0
1
0
2
3
0
1
0
1
0
1
2
0
1
0
1
2
1
0
1
1
0
2
0
1
0
2
2
1
1
1
1
1
2
1
1
1
1
2
2
1
1
1
1
0
1
1
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
0
1
1
2
1
0
1
1
1
2
1
1
1
2
2
1
0
1
0
1
0
1
2
1
1
2
1
1
1
1
1
0
2
1
1
0
0
1
0
1
1
0
0
2
0
1
1
0
2
1
1
0
1
1
1
2
1
1
1
1
1
2
1
2
0
1
1
1
1
0
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
3
2
1
1
1
1
1
2
1
2
2
1
2
1
0
1
1
1
0
1
1
1
0
1
1
1
2
1
2
1
0
2
1
1
1
2
1
1
1
1
0
1
2
0
0
2
1
1
1
1
2
1
1
1
0
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
0
1
1
2
1
2
1
1
0
1
1
0
1
1
1
1
1
2
1
1
2
1
0
2
1
1
0
1
1
2
1
2
1
2
1
2
1
1
0
2
1
1
3
1
2
1
2
1
1
2
2
1
1
3
1
0
1
1
2
2
0
1
1
0
1
1
2
2
1
1
1
0
1
2
2
1
1
1
1
1
1
1
0
2
2
1
1
1
1
1
2
1
2
0
1
1
1
1
2
2
1
1
0
2
1
1
2
1
0
0
1
3
2
2
1
0
2
0
1
1
1
1
1
1
2
1
1
2
1
1
1
1
0
0
2
1
1
1
1
1
2
2
1
1
0
1
1
1
1
2
2
1
1
1
2
1
2
1
2
1
1
1
1
0
0
0
1
1
1
1
1
2
2
1
1
1
1
0
1
1
2
1
1
2
1
0
1
1
1
1
1
1
1
1
0
1
1
1
2
2
1
1
1
0
0
2
1
1
1
2
0
0
1
1
2
1
1
1
1
1
0
1
2
0
1
1
0
1
0
1
2
1
1
0
0
1
1
1
0
0
1
0
1
0
2
1
1
1
2
2
0
3
1
2
2
2
2
2
1
1
1
1
1
1
1
1
1
1
2
2
1
1
4
1
1
2
2
1
0
0
2
1
1
2
1
1
1
1
1
1
1
0
1
2
1
2
1
1
1
1
0
2
1
2
1
2
1
0
1
0
1
1
1
1
1
1
2
2
1
0
1
2
1
1
1
1
1
1
0
1
0
1
1
0
1
1
1
0
1
1
2
1
1
2
2
2
1
1
2
1
1
1
0
0
2
1
1
0
1
2
0
1
1
1
1
1
2
2
1
1
1
2
2
1
2
1
2
1
1
2
1
0
1
2
2
1
2
1
2
2
1
1
2
1
2
0
2
1
1
2
0
1
1
1
2
1
2
1
1
1
1
1
2
0
2
1
1
0
2
2
1
1
1
1
1
1
2
0
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
2
2
1
1
2
2
0
1
2
1
2
2
2
2
1
1
1
2
2
1
1
1
0
0
2
0
1
2
1
0
2
0
1
1
1
2
1
1
1
0
1
1
2
1
1
1
1
1
1
2
2
1
1
2
2
1
0
1
1
1
1
2
1
2
1
1
2
1
1
1
1
0
2
1
1
0
1
1
2
0
1
1
1
1
0
2
1
2
1
1
0
1
2
1
1
1
2
2
1
4
1
1
2
0
1
1
2
1
1
2
1
1
0
1
2
1
1
0
1
0
2
1
1
1
2
2
0
2
2
1
1
1
2
1
2
1
0
2
2
2
1
2
0
2
2
1
0
2
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
0
1
1
1
2
1
1
1
1
1
1
1
1
0
1
1
0
1
1
0
1
0
1
0
1
2
0
2
1
1
1
2
1
1
2
1
1
2
1
1
1
0
1
2
1
1
1
1
1
2
0
2
1
1
1
2
1
1
0
1
1
0
1
1
0
1
1
1
1
0
1
1
2
1
1
1
1
1
1
1
0
0
1
2
1
0
1
1
0
2
2
2
2
1
1
0
2
2
1
2
1
1
1
1
0
2
1
0
1
1
1
1
1
1
1
1
2
1
3
1
1
2
1
1
1
1
0
1
1
1
2
0
1
2
1
2
2
1
0
1
1
1
1
1
2
1
1
1
1
2
1
0
1
1
0
0
2
1
0
0
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
0
1
1
1
2
1
1
1
0
1
1
1
1
0
1
1
1
1
1
1
2
1
2
1
0
1
2
1
1
1
0
1
2
0
2
1
1
0
1
1
0
1
2
0
1
1
0
1
1
1
1
1
1
1
1
0
2
1
1
1
0
1
1
2
2
1
2
1
1
1
1
0
1
2
1
1
2
2
1
1
2
1
1
1
1
2
1
1
0
2
1
1
2
0
0
1
2
2
1
1
1
2
1
1
1
3
1
1
1
1
1
1
2
2
1
2
0
2
1
1
2
1
2
2
2
1
2
1
1
1
2
1
1
1
0
0
1
2
1
1
1
2
2
1
1
0
1
1
1
1
1
1
1
2
1
2
1
2
1
2
1
1
1
1
2
2
2
3
1
2
2
1
1
1
1
1
2
1
2
0
1
1
1
1
1
1
2
1
2
1
2
0
1
1
1
1
1
1
0
2
1
1
1
1
1
2
1
1
2
1
0
1
1
0
1
0
1
1
1
0
1
0
1
1
1
2
1
0
1
2
1
1
1
1
1
2
0
1
1
0
0
0
1
1
1
1
1
2
2
0
2
2
1
1
1
2
2
1
1
0
1
1
2
1
2
1
1
1
1
2
1
1
1
0
1
1
1
1
1
2
1
1
0
0
1
0
1
1
2
0
1
1
1
1
2
1
0
0
1
2
2
2
1
1
1
0
1
2
1
0
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
0
2
1
1
1
1
1
0
1
1
1
1
1
1
2
1
1
2
2
1
2
1
1
2
2
0
0
1
0
1
1
1
1
1
1
0
2
1
1
2
1
1
1
0
0
1
2
0
0
2
2
0
1
1
1
1
1
0
1
1
1
1
1
0
1
3
1
1
2
1
1
2
1
1
1
1
2
1
0
1
1
2
1
1
0
0
2
1
1
1
2
2
1
0
2
2
2
0
2
1
1
1
1
1
1
1
2
1
0
1
1
0
1
1
1
1
1
2
2
0
2
2
2
1
2
2
1
0
0
1
1
1
1
1
1
2
2
2
0
2
0
1
2
1
1
1
2
0
2
1
0
1
1
2
1
1
2
1
1
1
1
2
1
1
0
1
1
1
0
2
1
0
2
2
2
0
1
1
0
1
0
0
0
1
1
1
1
1
0
1
1
1
0
1
1
1
1
2
1
2
1
1
0
1
3
1
1
0
1
1
1
2
1
1
1
1
0
1
1
2
2
2
1
2
1
1
2
2
1
1
0
1
2
1
1
2
2
1
1
1
1
2
1
2
0
1
0
0
2
1
1
1
1
1
1
2
1
1
1
2
2
2
0
1
2
1
1
0
1
1
0
1
2
0
1
1
1
1
0
2
0
2
1
2
1
2
2
1
2
2
1
1
0
1
1
2
0
1
2
0
0
2
1
1
0
1
1
1
1
2
0
1
1
1
1
0
0
0
2
1
1
1
0
1
2
1
0
1
2
2
2
1
1
2
0
1
2
2
1
1
1
0
1
2
1
1
1
1
1
1
1
2
1
1
1
1
2
1
2
1
1
0
1
1
0
1
1
1
1
2
0
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
0
1
1
0
0
1
1
1
0
1
1
1
2
2
1
1
1
1
1
1
1
1
2
1
0
1
0
1
1
1
1
1
2
1
2
1
2
2
1
0
1
2
1
1
1
2
0
1
1
2
2
1
0
2
0
1
1
2
1
2
1
1
1
1
1
1
0
1
2
1
1
1
1
1
2
1
1
2
1
1
2
1
2
1
2
2
0
1
1
2
0
0
1
2
0
0
2
3
1
2
0
1
2
1
1
1
2
1
0
1
0
2
1
1
1
1
2
0
0
2
2
2
2
0
1
1
1
1
1
0
1
1
2
2
2
1
1
1
1
1
1
1
1
1
1
1
2
2
2
2
1
1
1
0
0
2
2
0
2
1
1
1
1
1
2
1
2
1
4
2
0
1
1
2
2
2
1
1
0
2
1
1
0
1
1
2
0
2
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
2
1
2
1
2
2
0
1
1
0
1
1
2
0
2
2
1
0
0
2
1
1
1
2
0
2
1
1
0
2
1
0
2
1
1
3
2
1
1
1
0
0
2
2
1
1
2
1
2
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
0
1
0
1
1
1
1
2
1
2
1
1
1
2
2
1
1
1
3
1
1
2
1
1
0
1
1
1
1
1
1
1
1
1
2
2
1
0
2
1
2
1
1
2
0
2
2
1
1
1
1
1
2
1
2
1
2
2
2
0
2
1
1
1
0
2
0
1
0
0
0
2
0
1
1
0
1
0
2
1
1
2
0
2
0
2
1
0
1
0
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
0
2
1
1
1
1
1
0
1
1
1
2
2
2
2
1
2
1
1
1
2
2
1
1
2
1
1
2
3
1
0
1
2
1
1
1
1
1
0
1
1
2
1
2
1
0
2
2
1
1
1
1
2
0
2
0
2
0
0
1
2
0
1
1
1
2
1
1
2
1
2
0
2
2
0
1
1
1
1
1
1
1
1
0
1
1
1
0
1
2
2
1
0
1
1
1
2
1
1
0
1
1
1
1
0
0
1
1
1
1
1
1
2
1
0
0
0
1
1
1
1
1
1
2
2
0
1
2
1
1
1
2
0
1
1
2
2
1
1
0
1
1
0
1
0
0
1
2
2
1
2
1
1
1
1
1
1
2
2
1
1
1
2
1
1
1
1
0
1
1
2
2
0
1
2
1
1
2
1
4
2
1
1
0
1
1
2
1
2
0
1
0
2
1
2
0
0
1
2
1
1
1
0
1
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
2
1
0
1
1
1
2
1
1
1
1
2
1
2
1
0
1
2
1
1
1
1
2
2
1
2
1
1
2
2
1
2
1
1
0
2
1
1
1
1
1
0
1
2
1
1
1
1
0
1
1
0
1
0
1
0
1
2
2
2
0
1
1
2
1
1
1
2
2
1
1
1
1
1
2
3
1
2
2
1
2
1
1
1
1
0
1
2
2
1
1
0
1
0
0
1
1
2
1
1
1
1
1
2
1
1
2
1
1
1
1
2
1
1
1
1
1
2
2
2
1
1
2
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
0
1
2
1
1
0
2
1
2
1
2
1
1
1
1
2
1
2
0
0
1
0
2
1
2
1
2
2
1
2
2
1
0
2
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
0
2
2
0
0
2
1
3
1
2
1
1
2
2
0
1
1
2
2
1
1
2
2
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
0
1
1
2
0
1
0
1
1
1
0
0
0
1
1
1
1
1
1
1
2
1
1
2
1
1
0
0
1
1
1
1
0
1
1
0
1
1
1
1
2
0
0
1
1
1
1
1
1
2
2
0
0
1
1
0
0
1
2
1
2
1
1
2
2
2
1
1
0
0
2
1
2
2
0
1
2
1
2
0
2
0
2
2
1
1
1
1
2
1
1
1
0
2
0
0
1
2
1
1
1
1
0
1
2
1
1
2
1
0
1
2
1
2
2
1
1
1
1
2
1
1
1
1
0
1
1
2
0
2
1
2
1
0
1
0
1
1
3
0
1
1
2
1
1
1
1
1
2
2
2
2
1
0
2
0
1
1
1
1
0
2
1
0
0
1
2
1
1
1
0
0
1
1
1
2
1
2
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
0
2
1
1
1
1
2
2
1
1
1
1
1
1
1
2
2
1
1
1
2
2
1
0
1
1
1
2
1
1
1
0
1
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
3
1
1
2
1
0
1
1
0
1
1
2
2
2
1
1
0
0
1
2
0
2
1
2
2
1
1
1
1
1
2
0
0
1
1
1
0
1
0
1
2
1
1
3
2
1
1
1
2
1
1
2
2
1
2
2
2
1
1
1
0
2
1
0
1
2
1
1
0
2
2
0
2
1
2
1
1
1
1
1
2
0
2
0
1
1
1
0
2
2
2
0
0
1
0
0
1
2
1
1
1
0
1
2
1
1
1
0
1
1
0
1
2
1
1
2
1
2
0
1
2
1
2
3
1
0
1
2
1
1
2
1
2
2
2
1
0
1
0
0
1
0
2
0
2
1
1
1
1
2
2
1
1
0
1
1
2
2
1
2
2
2
2
0
1
0
1
1
1
0
1
1
2
1
0
1
0
2
1
1
1
2
1
1
1
1
1
2
1
2
2
1
1
2
2
1
0
1
0
2
1
1
1
1
1
1
1
1
1
0
2
2
2
1
0
0
1
1
1
1
2
0
1
2
2
2
0
1
1
1
0
1
2
2
2
1
1
2
1
1
2
1
1
0
2
2
2
1
0
1
1
1
1
1
0
1
1
0
1
0
1
1
1
1
1
1
1
1
1
1
0
1
1
2
1
1
2
0
1
2
1
1
2
1
1
2
0
1
1
2
0
1
1
1
2
1
1
1
0
1
0
2
1
2
1
1
1
2
1
2
1
1
1
0
1
1
2
1
1
1
1
1
1
2
1
0
1
0
1
2
1
2
2
1
2
2
1
0
1
1
2
1
1
1
1
1
1
2
2
0
1
1
1
0
0
2
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
2
1
0
1
1
1
2
0
1
2
2
2
1
1
1
2
1
1
2
1
2
1
1
1
1
0
1
2
1
2
1
1
1
1
1
1
1
1
1
2
2
1
2
1
1
2
1
1
1
0
2
1
1
1
1
1
1
1
0
2
0
1
1
1
0
1
2
1
1
1
0
1
2
1
1
1
1
1
0
1
0
1
2
1
1
1
1
2
0
0
2
2
2
2
1
3
1
1
1
0
1
1
0
2
1
1
1
1
1
1
1
2
1
1
2
1
1
0
1
1
1
2
0
1
0
1
0
0
2
1
1
2
1
1
2
1
1
1
1
0
0
0
2
1
1
1
1
2
1
0
1
2
1
2
1
1
1
2
2
2
1
1
0
2
1
1
1
0
1
1
2
1
1
2
1
2
1
2
1
1
2
1
1
1
1
2
2
2
1
2
1
1
2
1
1
2
2
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
0
1
0
1
0
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
2
1
2
1
1
2
1
1
2
2
0
1
1
1
0
1
2
1
1
0
1
1
1
1
1
1
1
2
0
1
1
0
1
1
1
2
2
2
1
1
2
2
0
0
0
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
3
1
2
1
0
2
1
0
0
1
2
1
0
2
1
2
0
2
1
1
1
1
2
3
1
2
1
2
1
2
1
1
2
2
0
0
0
0
1
0
0
0
1
1
1
1
0
1
2
1
1
1
2
1
1
0
1
1
2
1
1
1
1
0
1
2
1
1
2
1
1
1
2
1
2
2
1
2
1
0
2
1
1
0
1
1
2
1
1
0
1
1
1
1
0
1
1
1
0
2
1
1
0
1
0
1
1
1
0
0
0
1
1
1
1
1
0
1
1
1
1
2
1
0
2
1
0
0
0
1
1
0
2
0
1
2
1
2
1
2
1
1
1
1
1
1
0
1
1
2
1
1
1
1
1
2
1
2
0
1
1
1
0
0
2
1
2
1
1
2
1
1
1
1
0
1
1
1
2
2
1
2
1
2
1
1
0
1
1
1
1
2
1
1
0
1
1
2
1
0
1
2
0
0
1
1
1
1
1
1
1
1
0
2
1
2
0
0
1
1
0
2
1
2
1
2
1
1
0
2
1
1
1
2
1
2
2
2
2
1
1
1
1
1
1
1
1
1
1
2
2
1
2
0
1
1
1
1
1
1
1
1
1
1
3
2
2
1
1
0
1
1
3
0
2
1
1
2
1
1
2
2
2
1
0
2
1
1
1
1
1
1
1
0
1
0
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
0
1
2
2
0
1
1
2
0
1
2
1
0
1
1
2
1
2
2
0
1
1
1
1
2
2
2
2
2
1
2
1
2
0
1
0
1
1
1
1
1
1
1
2
1
2
1
1
0
1
0
2
2
2
0
1
1
0
2
1
0
2
1
1
0
2
1
0
1
1
1
1
1
1
2
1
1
1
1
1
1
0
1
2
2
1
0
1
1
0
0
0
1
1
2
1
0
2
1
1
2
2
2
0
1
2
1
0
0
1
1
1
0
2
0
1
1
0
1
1
2
1
1
1
1
1
1
2
1
2
1
2
1
2
1
1
1
1
1
2
2
2
1
2
1
1
2
2
0
2
1
1
0
1
0
1
0
0
3
0
1
1
2
0
3
1
0
2
1
2
1
1
1
1
2
2
1
0
2
2
0
1
1
1
1
0
2
1
1
2
1
0
2
2
1
2
1
0
1
2
1
1
2
1
1
1
1
1
2
1
2
1
2
2
2
1
1
0
1
1
1
1
2
1
2
0
1
2
1
0
2
1
0
2
1
0
1
1
1
1
2
1
2
2
1
1
1
1
2
0
2
1
1
2
2
2
1
1
1
2
0
1
1
0
1
1
1
1
2
2
1
1
1
1
2
3
1
1
2
1
0
1
2
1
1
2
1
1
1
1
0
1
1
2
1
2
1
1
1
1
2
0
1
1
0
1
1
1
1
1
1
1
1
1
0
1
0
1
1
1
1
2
0
1
1
0
1
2
2
1
0
0
0
2
2
2
1
2
2
1
1
0
1
3
0
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
0
2
2
1
1
1
1
2
1
1
1
0
1
1
0
1
1
1
1
0
2
1
1
1
0
1
0
1
0
2
1
0
0
1
0
1
1
1
1
2
0
0
1
1
0
0
1
1
2
2
0
2
1
2
3
2
1
1
1
1
1
1
1
1
2
0
1
1
2
2
1
2
1
2
1
2
1
1
2
1
1
1
1
1
1
1
2
2
1
3
1
1
1
1
0
1
1
1
0
1
2
2
1
1
0
2
1
1
1
0
1
1
0
2
1
0
1
1
2
0
0
0
0
0
2
1
1
1
2
2
2
1
2
1
2
1
1
1
1
1
0
1
2
1
2
2
0
1
1
0
1
1
1
2
1
0
1
2
1
1
0
2
2
1
1
2
1
0
0
0
1
2
1
1
1
1
2
1
1
1
2
1
2
1
1
2
1
1
1
1
1
2
1
1
1
2
0
3
2
1
2
1
1
2
0
1
0
1
2
2
2
2
2
1
1
1
0
1
1
1
1
1
2
2
0
1
1
1
1
1
1
1
1
2
2
2
1
1
1
0
1
2
1
2
2
2
2
1
1
0
1
1
1
1
0
0
2
1
1
1
2
1
1
2
1
2
0
1
2
1
1
2
1
0
1
1
2
2
2
0
1
0
1
1
1
2
1
1
0
1
2
2
0
1
1
1
1
1
2
2
1
0
1
2
2
1
1
1
2
0
0
1
2
2
1
1
1
2
1
2
1
1
2
1
1
1
2
0
1
1
0
1
1
1
1
0
0
1
1
1
2
0
2
1
1
1
1
1
1
0
1
1
1
3
3
0
1
1
1
1
2
1
2
1
0
1
2
1
2
2
0
1
0
2
0
1
1
1
1
1
0
1
1
1
2
2
1
1
1
1
0
1
1
1
0
0
0
0
0
2
2
2
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
1
2
1
2
1
1
2
1
1
1
2
2
0
1
1
1
1
0
1
1
2
2
0
1
2
1
1
0
0
1
2
1
1
1
0
2
2
0
1
0
1
0
0
0
1
1
1
2
0
1
2
1
1
2
2
1
1
1
0
2
1
1
0
2
1
2
1
0
2
1
1
1
1
1
1
1
1
1
2
1
1
1
3
2
1
2
1
1
1
1
0
1
1
1
1
3
1
1
1
0
0
1
1
0
1
1
0
2
2
0
1
1
0
1
1
1
1
1
1
2
1
2
0
1
1
0
2
1
1
2
0
1
1
0
1
2
1
1
1
1
1
2
2
1
1
2
1
1
1
0
2
2
2
1
1
2
1
1
1
2
1
2
1
1
0
2
1
1
1
2
1
1
2
1
0
1
0
1
1
2
3
1
1
0
1
0
0
0
2
1
2
1
1
2
1
0
1
1
2
0
5
1
1
0
0
1
0
1
1
1
3
1
2
1
1
1
1
1
1
1
2
1
1
2
0
2
1
1
1
0
0
1
1
0
1
1
0
1
1
1
2
1
0
1
1
1
1
2
1
1
1
2
1
2
1
1
0
1
1
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
2
2
2
0
0
1
2
1
1
1
2
2
2
1
2
1
2
1
2
1
2
2
1
1
1
2
1
0
1
1
1
1
1
1
1
1
0
1
1
1
0
1
2
1
1
1
1
1
1
1
2
2
2
1
2
1
0
1
1
1
0
0
1
1
2
1
2
2
1
1
0
1
0
1
2
1
0
2
2
2
2
1
1
2
2
0
1
2
2
1
2
0
1
1
1
1
0
2
1
1
1
1
2
1
2
1
1
0
1
1
2
2
1
1
1
2
1
1
1
1
1
1
0
1
1
0
1
1
0
1
1
1
1
1
2
2
1
1
1
1
1
2
1
0
0
2
2
1
1
2
0
1
2
1
1
1
1
2
1
1
2
1
1
1
2
0
1
0
0
0
1
1
1
1
1
0
1
1
1
0
1
1
1
1
1
1
0
1
1
1
2
2
1
2
1
1
1
2
1
1
1
1
1
1
1
1
0
1
1
1
1
1
2
1
2
2
1
1
3
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
0
1
1
0
1
2
1
1
2
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
0
2
1
1
1
0
2
1
1
1
2
1
2
2
0
2
1
2
1
1
1
0
1
1
1
1
0
2
2
2
2
1
1
1
2
0
1
1
2
1
2
1
1
1
2
2
1
1
0
1
1
1
2
1
1
2
0
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
0
2
1
1
1
1
0
1
1
1
1
2
1
2
0
1
1
1
2
1
1
2
2
1
1
1
0
1
1
1
0
1
2
2
3
1
1
1
1
1
1
1
1
1
3
2
1
1
2
1
2
2
1
2
0
2
2
1
1
0
1
1
1
1
1
1
1
1
1
0
2
1
1
1
1
1
2
1
1
1
2
0
0
1
2
1
1
1
0
2
0
1
1
1
0
2
1
1
2
1
0
1
1
1
1
1
2
1
2
1
1
1
0
1
1
1
2
2
1
1
1
1
1
1
2
2
1
2
1
2
0
1
0
1
2
1
0
2
1
2
2
1
2
1
1
1
2
1
1
2
0
0
1
2
1
2
0
2
1
1
1
2
1
1
0
0
1
1
1
1
1
2
2
1
1
1
1
2
2
1
1
1
1
1
2
0
1
0
1
1
1
1
1
2
1
1
1
2
1
1
0
1
1
1
1
1
2
2
1
1
1
2
1
2
1
2
0
1
2
1
1
1
1
1
1
2
2
1
2
2
1
1
2
1
1
0
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
0
0
1
1
0
1
1
0
0
1
1
1
2
1
1
2
0
1
1
1
2
1
1
2
1
1
1
1
1
1
2
2
2
2
1
0
1
1
1
2
2
1
2
1
1
1
2
0
1
1
0
0
1
1
0
1
1
1
1
2
3
1
2
0
0
0
1
2
0
1
1
2
1
1
1
1
1
1
1
1
1
2
2
0
1
1
1
1
1
2
1
2
1
0
1
1
2
1
1
2
1
2
1
0
1
0
1
1
1
0
1
1
1
0
1
1
1
1
0
2
2
1
0
1
1
1
2
0
2
2
0
0
2
2
2
0
2
1
2
2
2
2
1
1
1
1
1
1
0
2
1
2
1
0
2
1
2
2
4
0
1
1
1
2
1
2
0
0
1
1
1
1
2
0
2
2
1
1
2
1
2
2
1
1
1
1
0
2
1
2
0
1
1
0
2
0
2
1
0
0
2
1
1
2
1
2
1
2
2
1
1
0
1
2
0
1
1
0
2
1
1
1
1
1
1
0
1
0
1
1
1
1
1
1
1
2
1
1
1
1
1
0
1
1
1
1
2
2
0
0
0
2
1
1
0
1
1
1
2
1
1
1
1
1
1
1
1
0
1
1
0
1
1
1
2
0
2
1
1
1
1
1
0
1
1
1
2
1
0
1
2
2
0
2
1
1
1
2
1
1
0
0
1
1
1
1
2
1
1
0
2
1
1
1
1
2
2
1
2
0
0
2
1
1
1
0
2
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
0
2
1
2
1
0
0
2
2
1
1
1
1
1
1
2
1
1
2
1
1
0
1
2
1
2
1
2
1
1
1
1
1
2
1
2
1
1
1
1
0
0
1
1
0
1
1
0
0
2
1
1
2
1
1
2
1
1
1
1
1
2
2
2
2
1
1
0
0
2
2
1
1
1
2
1
1
2
1
1
2
1
0
1
1
1
1
2
2
1
1
1
1
0
2
2
2
1
1
1
1
1
2
1
1
1
0
1
1
2
2
1
1
0
2
0
1
0
0
1
1
1
0
1
0
1
1
0
1
2
1
1
1
1
1
1
1
1
0
1
2
1
1
2
0
1
1
1
1
1
0
2
1
1
2
0
1
1
1
1
2
1
1
1
1
1
2
0
0
0
1
2
1
1
1
1
0
1
1
1
1
1
2
1
1
0
2
2
1
0
1
1
1
1
2
0
2
1
1
1
2
2
1
0
1
2
2
1
1
1
0
1
1
2
2
2
1
2
1
2
0
1
1
1
1
1
0
2
1
1
0
1
2
0
1
2
1
0
1
1
1
1
1
1
0
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
0
0
2
1
1
1
2
2
1
1
0
0
1
1
2
0
0
2
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
3
1
1
0
0
2
1
1
1
2
1
1
2
1
1
1
1
4
1
2
0
2
1
2
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
0
1
1
1
1
2
0
1
2
0
2
1
2
0
0
1
1
1
1
1
1
2
2
2
1
1
1
1
1
2
1
1
1
0
0
1
2
1
2
1
1
2
2
2
2
2
2
2
0
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
0
2
2
2
1
1
1
2
1
0
2
1
1
2
2
2
1
0
2
2
1
0
1
2
0
1
1
2
1
1
1
1
1
0
1
1
1
1
1
0
2
1
1
0
1
0
2
1
1
3
1
1
2
1
2
1
1
2
0
1
1
1
0
1
1
1
0
2
1
1
1
1
1
0
1
0
1
1
1
2
2
1
1
1
1
1
2
1
0
1
1
0
2
2
1
1
1
1
2
1
0
2
1
2
0
0
2
1
1
0
1
1
1
2
1
2
1
1
1
0
1
1
1
2
1
1
2
0
2
1
1
0
2
1
1
1
3
1
2
1
1
2
1
2
1
2
1
0
1
1
2
2
1
2
0
1
1
0
1
0
1
1
0
2
2
1
1
1
1
1
1
1
0
1
2
1
1
2
0
1
1
1
1
2
1
1
1
1
1
2
1
1
1
0
1
1
1
2
0
2
2
1
1
1
1
1
3
1
0
1
1
2
1
2
1
1
2
2
1
1
1
1
1
0
1
1
1
2
1
0
1
2
1
1
1
1
1
0
1
2
1
0
2
1
0
1
2
1
1
1
2
1
1
1
1
1
1
2
1
0
0
1
2
1
2
1
2
1
1
1
1
2
1
1
2
1
1
2
1
1
0
2
1
1
1
1
1
0
1
1
1
0
0
2
1
1
1
2
2
1
1
1
2
0
1
2
2
1
0
2
1
0
1
1
0
1
1
1
0
1
2
1
0
1
1
1
1
2
0
2
1
1
0
1
1
0
1
2
0
2
1
1
0
2
0
2
2
1
1
0
0
2
1
1
1
1
1
1
2
1
1
2
1
1
1
2
1
1
1
1
0
1
1
1
1
1
0
1
1
1
2
1
1
2
2
1
1
1
0
1
1
2
1
0
1
2
2
2
1
2
1
2
2
2
2
0
1
2
1
1
2
1
0
1
2
1
1
1
1
1
2
1
2
2
2
2
0
2
1
2
1
1
1
2
1
1
2
0
1
0
3
1
1
0
1
2
1
0
2
0
0
1
0
2
2
1
1
2
1
1
1
1
1
0
1
2
1
1
1
1
1
1
2
1
0
1
1
2
2
1
2
1
2
0
1
2
1
1
1
1
1
1
1
1
0
0
1
1
0
2
1
2
1
1
1
1
1
1
2
0
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
2
2
0
1
1
2
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
2
0
2
2
2
1
1
2
1
1
1
2
0
2
2
1
0
0
1
1
1
2
1
1
1
1
1
0
2
1
2
1
1
1
1
1
1
3
1
1
2
2
1
2
0
0
2
2
1
1
1
0
1
1
2
0
1
0
1
1
1
1
0
1
2
2
2
2
1
0
1
2
0
2
2
1
1
2
3
0
1
2
1
1
1
0
1
2
1
2
1
1
1
2
0
0
2
2
2
1
1
1
2
0
1
1
1
1
1
1
0
1
1
1
1
2
2
0
1
1
0
1
2
0
2
2
3
1
1
1
1
2
3
2
0
1
0
2
1
2
2
1
2
1
2
1
1
1
1
1
2
0
1
1
2
1
1
1
2
2
2
0
1
1
1
0
1
1
1
2
0
0
0
1
0
1
1
1
1
1
1
1
2
1
1
2
2
1
1
1
2
1
0
1
2
0
2
2
1
1
2
0
1
1
2
0
1
2
1
1
0
1
0
1
1
1
1
0
1
1
1
1
0
1
2
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
1
2
1
2
1
1
0
1
2
1
0
1
1
1
1
2
2
0
1
0
0
1
1
2
2
1
1
1
0
1
0
2
1
1
2
2
1
2
1
2
2
2
1
1
2
0
1
1
0
2
1
2
1
1
1
1
1
2
2
1
1
1
2
2
2
0
1
0
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
1
0
2
1
2
0
2
1
1
2
0
1
0
1
0
1
1
1
1
1
1
1
1
2
1
2
1
2
1
0
2
2
1
2
0
2
1
1
1
1
1
1
1
2
2
1
2
1
2
1
1
0
1
1
1
1
1
2
1
0
2
1
1
1
2
1
1
1
1
2
1
0
2
2
0
0
0
2
1
1
1
0
2
1
2
0
1
0
0
1
2
1
2
1
1
1
1
1
1
1
2
0
2
1
2
1
1
2
1
0
1
2
0
1
0
1
2
0
0
2
1
1
1
2
1
2
0
0
1
1
1
2
1
0
0
1
0
1
1
1
2
1
1
0
0
2
1
2
1
0
1
1
1
1
1
1
2
1
0
1
3
1
2
1
1
1
1
2
1
1
1
1
2
1
1
0
0
1
1
2
2
2
1
2
2
2
1
2
1
0
1
1
0
0
2
1
1
1
1
1
1
1
2
1
2
1
2
0
1
2
1
1
1
1
2
1
1
0
2
1
1
1
1
2
1
1
2
1
1
1
0
5
0
0
1
2
0
1
0
1
1
2
1
0
2
2
1
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
0
0
1
1
0
1
2
1
0
2
1
2
0
2
2
1
2
1
0
2
1
2
1
1
1
2
1
1
1
0
4
2
2
1
0
0
1
1
1
2
2
0
0
2
1
0
2
1
2
1
1
0
2
1
1
1
1
1
0
1
1
1
2
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
2
3
1
1
3
1
2
1
2
1
1
0
1
1
1
2
1
1
0
0
2
1
1
1
1
1
2
1
0
1
2
2
2
3
0
1
2
2
1
2
2
1
2
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
0
2
1
1
1
1
2
1
0
2
1
2
2
1
2
1
2
0
1
1
1
1
2
1
1
2
1
1
2
0
1
2
1
2
0
1
1
1
1
2
1
2
0
1
1
1
1
2
1
1
2
1
1
1
1
1
0
1
0
2
0
2
1
1
1
1
1
2
1
2
1
0
2
0
2
0
1
2
2
2
0
1
1
1
2
2
1
1
1
1
1
1
1
2
2
1
1
1
0
0
1
0
1
1
2
2
0
2
0
2
1
0
1
0
0
1
1
1
1
1
2
2
0
1
1
2
1
1
2
1
1
1
0
1
2
0
1
1
0
2
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
2
0
1
1
1
0
2
2
1
1
2
0
1
2
1
1
1
2
0
2
1
2
1
1
1
0
1
1
2
1
1
2
1
1
1
0
0
0
1
1
1
2
0
2
1
4
1
1
1
0
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
2
1
1
0
1
2
2
1
1
2
1
0
1
1
2
1
0
2
1
0
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
0
1
0
1
2
2
1
1
2
2
1
1
1
0
1
1
2
1
1
0
1
1
2
1
1
1
2
0
1
2
1
1
1
0
1
0
1
1
1
0
2
1
1
1
1
1
1
1
2
2
2
2
2
1
1
2
2
1
1
1
1
2
2
1
2
1
1
2
1
1
1
0
1
1
2
1
2
1
0
1
1
1
0
0
1
2
1
0
2
1
1
1
1
2
2
2
1
0
0
1
1
1
2
1
1
1
1
2
1
0
2
1
1
1
2
0
1
0
1
1
1
1
1
0
1
0
1
1
1
1
2
1
2
2
2
1
2
2
1
1
0
2
2
1
1
1
1
0
1
1
0
0
1
2
1
2
3
1
0
0
1
1
2
0
2
0
1
1
1
2
2
1
2
0
2
1
1
1
1
1
1
2
2
1
2
1
2
1
1
1
1
1
1
1
1
2
0
0
2
1
2
2
2
2
1
2
2
0
2
1
1
1
1
1
1
1
1
2
2
1
2
1
0
1
2
1
1
0
2
1
1
2
2
1
1
1
2
2
2
1
0
1
0
1
1
1
1
1
1
0
1
1
1
2
1
2
2
1
1
0
1
1
2
1
1
1
3
1
0
1
0
3
1
1
1
0
1
2
1
0
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
0
1
1
2
1
1
1
1
2
1
2
1
1
2
2
1
2
2
0
2
2
1
2
2
1
1
0
1
1
1
0
1
1
1
1
1
1
1
0
2
2
1
1
1
0
1
1
1
2
2
2
1
1
1
2
2
1
1
1
1
0
1
1
2
2
1
1
1
1
2
1
0
1
1
0
2
1
2
1
0
2
1
0
1
1
2
1
2
1
1
2
1
1
0
1
1
0
2
1
2
2
0
1
2
1
2
1
1
2
1
1
0
1
2
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
2
2
1
0
2
2
1
1
1
1
0
2
2
1
1
1
1
1
1
1
1
1
1
1
1
2
0
1
0
1
1
1
0
2
1
1
2
1
1
1
1
2
2
1
1
1
3
0
1
0
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
0
1
1
2
2
1
0
2
2
2
1
1
0
1
2
2
2
0
2
1
2
2
1
1
1
1
2
0
1
2
0
1
1
1
1
2
0
1
0
0
2
1
1
0
2
1
2
1
0
1
1
1
1
1
1
1
1
1
1
2
0
2
1
2
1
1
1
2
1
2
1
1
1
1
1
0
2
2
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
0
1
3
1
1
1
1
0
2
1
1
1
2
2
1
1
0
1
1
3
0
1
1
1
1
1
1
1
2
2
1
1
1
2
1
1
1
1
2
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
5
4
1
0
1
1
1
2
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
0
2
0
1
1
1
1
0
1
1
1
1
2
1
1
2
1
0
0
0
2
1
1
1
1
1
1
0
1
2
1
0
1
1
1
0
1
1
1
1
0
1
1
1
1
2
1
1
0
1
1
1
2
1
2
2
2
2
2
1
1
1
0
2
0
1
0
1
2
1
1
1
0
2
2
2
1
2
2
2
1
2
1
0
0
1
2
1
2
2
1
1
1
1
0
1
1
2
1
1
1
2
0
1
2
1
1
0
0
1
1
1
1
1
0
2
1
0
1
2
1
1
0
2
1
1
0
0
1
1
1
3
1
1
1
1
0
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
2
1
2
1
1
1
2
2
1
2
1
1
1
2
2
1
2
1
2
1
1
1
0
1
1
1
1
1
1
1
1
2
0
1
1
2
0
2
1
1
1
2
1
0
1
0
1
1
2
1
0
1
2
1
2
0
1
2
2
2
2
2
0
1
0
1
1
2
1
3
2
0
1
1
1
2
2
0
1
1
0
1
1
2
1
1
1
0
2
2
1
1
1
2
3
2
0
0
2
1
1
1
2
1
1
1
1
0
0
1
2
0
0
2
1
2
0
1
1
2
2
1
2
1
1
2
1
1
1
2
0
1
1
1
1
2
2
0
1
1
2
2
1
1
2
1
1
1
1
0
1
2
0
2
0
1
2
1
1
1
1
1
1
1
1
0
1
1
1
0
1
1
1
1
1
0
1
2
1
1
1
1
1
1
1
2
2
1
2
2
1
1
1
2
1
1
1
1
2
2
1
1
1
0
1
2
2
2
1
2
2
1
1
1
2
1
1
0
1
1
1
1
2
1
2
2
1
1
1
2
0
2
1
1
2
2
1
0
1
1
2
1
1
0
2
1
1
1
0
1
2
1
1
1
2
2
1
1
1
1
0
0
2
1
0
2
1
2
2
1
0
1
2
1
0
1
1
1
1
2
1
1
1
0
0
2
1
1
1
1
0
0
1
2
1
2
2
1
1
0
2
0
1
2
1
1
1
1
1
0
1
1
2
1
0
1
1
2
1
1
0
2
2
2
1
1
1
1
1
2
1
0
1
1
1
2
0
1
0
0
2
0
0
2
1
0
1
1
1
0
2
1
1
1
2
1
2
0
2
0
1
1
0
1
2
1
0
8
1
0
2
1
1
1
1
2
1
1
1
2
1
5
0
1
1
1
1
1
1
1
2
2
1
0
0
2
2
1
1
2
1
1
2
1
1
0
2
2
2
1
2
0
1
0
1
1
1
2
1
1
1
1
0
2
1
2
1
1
1
1
1
2
1
1
1
2
1
2
0
0
1
1
1
2
1
2
2
1
1
1
0
1
2
1
1
1
1
1
1
1
1
0
1
1
0
1
1
0
1
2
1
1
2
1
1
1
1
0
0
1
0
1
2
1
1
1
1
0
0
2
1
0
1
1
0
1
0
1
1
1
1
2
1
1
1
1
0
1
2
1
2
2
1
1
0
0
1
1
0
1
0
1
1
0
1
1
1
1
2
2
2
0
1
0
1
1
1
1
1
2
1
1
0
2
2
1
0
1
2
0
1
1
1
0
1
1
2
0
2
1
1
1
1
2
2
1
2
2
0
2
2
1
1
0
1
3
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
2
0
0
1
2
2
2
0
2
2
2
2
2
1
1
1
0
2
1
2
1
1
1
1
2
1
2
1
1
1
1
1
0
1
2
0
2
1
2
1
1
2
0
0
1
1
2
9
1
2
1
0
1
1
1
1
1
1
2
1
0
0
1
0
1
1
1
2
0
2
1
1
1
1
0
2
2
1
1
1
0
2
1
1
1
1
2
2
1
2
0
2
1
1
1
2
1
0
1
1
1
1
1
2
1
1
1
1
0
1
2
0
1
1
0
0
2
0
2
1
1
2
0
1
0
2
2
0
1
1
2
0
2
1
1
1
2
1
2
2
1
1
2
1
3
2
2
1
2
2
1
1
0
2
0
2
1
1
1
1
2
2
1
0
0
1
1
2
0
0
1
1
1
1
0
0
1
1
0
1
1
1
1
0
0
0
0
0
1
1
1
0
1
1
1
1
1
1
1
0
2
2
0
2
0
1
1
2
1
1
1
1
0
1
2
2
0
1
1
1
2
1
2
1
1
1
0
1
2
1
1
1
2
1
1
2
1
2
1
1
1
2
2
1
1
1
0
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
0
1
1
1
2
1
0
2
1
0
1
1
1
2
0
1
2
1
1
1
1
1
1
1
0
1
0
2
0
2
2
1
1
2
1
1
1
1
1
1
0
1
2
2
2
1
0
1
1
2
0
2
1
2
0
1
2
1
1
1
1
2
1
2
0
1
0
0
1
1
2
1
0
2
1
1
0
2
0
1
1
2
0
1
1
2
1
0
2
1
1
0
2
1
1
2
1
0
1
1
2
2
1
1
1
1
1
1
0
0
2
0
3
1
1
1
2
0
1
1
2
1
1
1
1
3
2
0
0
2
2
2
1
1
1
1
1
0
0
1
2
1
2
2
1
2
2
2
2
0
1
1
1
1
1
1
1
1
1
1
1
2
1
1
0
0
0
1
1
2
1
1
0
1
1
1
1
0
1
1
1
1
2
1
1
1
1
1
1
0
1
1
1
2
2
2
2
1
1
1
0
1
1
0
1
1
0
1
1
1
2
1
0
0
2
1
1
2
2
0
1
1
2
1
0
2
1
2
2
1
2
1
1
0
1
0
1
1
1
1
0
2
2
2
2
2
1
2
2
2
1
1
2
0
1
0
1
2
2
1
1
1
1
2
1
0
1
1
0
1
1
1
1
2
1
1
0
2
2
1
1
1
0
2
1
2
2
2
2
1
3
2
1
1
1
1
2
1
1
1
0
1
1
1
2
0
1
1
1
0
1
1
1
0
2
2
1
1
2
2
1
1
2
1
1
2
0
0
2
2
1
0
1
1
2
2
0
1
2
1
2
1
1
1
1
1
2
1
2
2
0
1
1
0
1
1
1
1
1
0
0
1
2
0
1
0
2
1
1
1
1
1
1
2
2
0
2
1
1
0
1
2
2
1
1
1
1
1
1
1
2
1
2
1
1
1
0
2
1
0
1
0
2
2
1
2
1
2
1
0
2
1
1
1
1
1
1
0
2
1
2
2
1
2
1
1
1
1
1
2
0
1
1
4
2
2
0
1
1
2
1
2
1
2
1
1
2
1
0
1
1
1
2
2
2
1
2
2
2
1
1
1
1
1
1
1
2
2
1
0
2
2
1
2
2
1
2
1
1
2
1
2
3
1
0
1
2
1
1
1
0
1
1
2
1
0
1
1
0
2
0
1
0
1
1
1
1
0
1
1
2
2
1
2
1
1
0
1
0
1
0
1
2
2
1
1
2
1
0
1
2
1
2
1
1
2
1
1
2
0
0
2
2
2
2
1
2
0
0
0
2
2
2
2
1
1
0
1
1
0
2
0
2
1
2
0
1
2
2
1
1
1
1
1
1
1
2
1
0
1
1
2
0
1
2
1
1
1
2
1
0
1
1
1
2
1
2
1
1
1
2
2
1
0
1
1
1
2
1
1
1
1
2
2
1
0
2
4
1
0
1
1
1
1
2
2
2
2
1
0
1
2
2
2
0
0
2
2
2
0
1
1
1
1
2
1
1
0
0
1
4
1
1
0
1
1
1
2
1
1
1
1
1
0
1
2
1
1
2
1
0
0
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
0
0
3
0
2
0
0
1
1
0
0
1
1
1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
2
0
1
1
1
2
2
2
1
2
1
1
1
1
0
2
1
1
1
1
1
2
1
0
1
2
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
0
2
1
1
1
1
2
0
1
1
2
1
2
2
0
2
1
1
1
2
2
0
1
1
0
2
2
1
0
0
1
1
1
0
2
1
1
0
1
1
0
2
2
0
1
1
1
2
2
2
1
2
2
1
1
1
1
0
1
1
1
1
0
1
1
1
2
2
1
1
2
0
1
0
1
0
1
2
2
1
1
1
1
0
1
2
1
1
2
0
1
0
1
1
1
1
2
2
0
2
1
1
1
1
2
0
1
0
1
1
1
0
0
2
2
2
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
0
1
1
1
1
1
1
1
0
2
0
1
2
0
1
1
1
1
1
1
3
1
0
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
2
2
1
1
1
1
2
1
1
0
1
1
1
1
1
1
1
1
1
2
0
1
1
0
1
2
2
1
1
1
1
2
2
0
1
2
1
2
1
0
1
2
2
1
1
2
2
1
1
1
1
1
2
0
2
1
1
1
2
0
1
0
1
1
1
1
0
1
0
1
1
0
1
1
1
1
1
2
0
1
1
1
2
0
1
1
1
1
2
2
1
1
1
0
1
1
1
1
1
2
0
0
2
1
2
1
1
2
1
1
2
1
1
1
2
1
2
1
1
0
2
1
2
1
1
0
1
1
1
1
1
2
0
1
1
1
1
1
1
2
0
2
1
0
2
1
1
0
0
2
2
1
1
1
1
0
1
0
2
1
1
1
1
1
2
2
0
2
2
1
0
0
1
1
1
1
0
1
1
1
1
1
2
1
2
2
1
1
0
1
2
3
2
2
2
1
1
0
1
1
2
1
1
2
1
1
2
2
1
1
1
1
1
2
1
2
0
2
1
0
2
0
2
1
2
1
0
1
1
1
1
1
1
0
1
1
1
1
1
2
1
1
0
1
0
2
1
1
2
2
1
1
0
2
1
1
1
1
0
1
1
2
1
2
2
2
1
1
1
1
2
1
1
1
2
0
2
2
1
2
1
1
2
2
0
0
2
1
1
1
2
0
2
2
1
2
1
1
1
1
2
2
2
1
1
1
2
1
1
1
1
0
2
1
1
2
0
1
1
1
1
0
1
1
2
1
1
2
1
2
0
1
1
1
2
1
0
0
1
1
1
3
2
1
1
1
1
0
0
2
1
1
1
2
0
1
2
2
1
2
1
0
2
1
2
1
1
2
1
1
1
1
1
2
1
0
1
1
2
1
2
1
2
0
1
1
1
2
1
2
1
2
1
0
1
2
0
2
2
1
2
1
1
2
1
0
1
2
1
1
1
2
1
1
1
1
1
0
1
1
1
1
6
2
0
1
1
1
1
2
2
1
1
1
1
1
1
1
0
2
1
2
0
0
1
1
0
0
0
1
0
2
2
2
1
2
0
1
1
1
1
2
1
1
1
1
1
2
2
1
2
1
2
2
1
1
1
1
2
2
0
2
2
1
1
2
1
1
1
1
0
1
1
1
0
2
2
1
1
0
1
1
1
2
1
1
2
0
1
2
1
1
1
1
1
2
1
1
1
1
1
2
2
1
1
1
2
1
1
1
1
2
2
1
1
1
1
0
2
1
2
1
0
0
1
0
1
2
1
0
0
1
2
1
1
3
2
3
1
1
1
1
1
0
0
1
1
1
1
2
1
1
1
1
1
3
1
2
2
1
0
1
0
1
1
0
1
1
2
2
1
2
3
1
1
1
2
1
2
2
1
1
1
1
2
1
2
0
2
1
1
2
1
0
2
1
1
1
1
2
1
1
2
2
1
1
1
1
1
2
2
1
2
1
0
0
1
0
1
1
1
0
2
1
1
1
2
1
1
1
1
1
1
0
1
1
0
0
0
1
3
1
0
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
0
1
0
1
1
1
1
1
2
1
0
1
0
1
1
2
1
2
0
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
0
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
2
0
2
1
1
2
1
0
1
1
0
0
0
1
2
0
1
1
1
1
1
1
0
1
1
1
2
2
1
1
2
1
1
1
0
1
2
2
2
2
1
1
1
1
1
2
1
3
1
0
1
1
1
2
0
1
2
1
1
0
1
1
1
2
1
0
1
1
2
1
1
0
0
1
0
1
0
0
1
1
0
1
0
1
2
0
1
1
0
1
1
2
0
1
0
0
1
1
1
0
2
1
2
0
2
2
2
1
2
1
1
1
1
1
1
1
1
3
1
1
2
2
1
1
1
1
1
0
0
2
0
2
1
0
0
1
1
1
0
0
1
1
1
1
1
1
2
0
2
1
1
1
2
4
1
2
1
1
1
2
1
1
2
1
1
1
0
1
0
0
2
1
2
0
1
1
0
1
1
1
1
1
0
1
1
1
1
2
1
1
1
0
1
0
2
2
1
1
0
1
1
2
1
1
1
0
0
1
2
1
1
0
1
1
1
1
1
0
2
2
0
1
2
1
2
1
1
0
1
1
1
1
1
1
0
1
0
2
2
1
2
2
2
2
1
0
2
1
0
0
1
0
1
3
2
2
1
2
1
2
1
0
2
2
3
1
2
1
1
2
1
1
1
0
1
0
1
1
1
1
2
1
0
1
2
1
2
1
1
1
0
1
1
1
1
1
0
1
0
2
1
1
1
1
1
1
1
1
2
2
1
1
1
2
1
1
1
1
2
2
2
1
0
0
1
0
0
2
2
0
1
2
1
1
2
1
2
0
2
1
1
0
0
1
2
0
1
1
1
1
1
0
1
1
2
2
1
1
1
1
2
0
0
1
2
1
1
2
0
1
0
0
1
1
1
1
0
1
1
1
1
2
1
2
1
0
2
2
1
2
1
0
2
2
2
0
2
2
0
0
1
0
1
2
0
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
0
2
1
1
1
1
2
0
2
1
1
0
2
1
0
1
1
1
2
2
1
2
1
1
1
2
0
2
2
1
2
1
1
1
2
0
1
1
1
1
1
1
1
1
1
2
2
1
1
2
0
1
0
1
1
1
0
1
1
1
1
1
2
1
2
1
1
0
1
1
1
1
2
0
2
1
1
2
2
1
1
1
1
1
1
1
2
1
2
0
1
2
2
2
1
1
1
1
1
3
2
0
0
1
0
1
1
2
1
1
1
1
0
2
0
2
2
1
1
1
2
1
2
1
0
1
1
1
1
1
1
1
1
0
0
1
1
1
1
1
1
2
0
0
1
1
2
1
2
1
0
1
0
0
1
1
1
1
2
1
1
2
1
2
1
2
1
1
2
1
1
1
0
1
1
1
1
1
2
1
1
1
1
2
1
0
1
0
1
0
1
1
2
1
1
1
2
2
2
0
1
2
0
1
0
1
1
0
1
1
2
1
0
1
1
1
0
1
1
1
0
1
1
1
0
1
0
1
1
1
2
1
1
1
1
1
1
1
1
1
1
0
2
1
2
2
2
2
2
1
0
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
0
0
2
2
2
1
1
1
1
2
2
1
1
1
1
1
2
2
1
1
2
1
2
2
1
1
1
0
1
1
1
1
2
2
1
1
1
2
1
2
1
1
0
1
1
2
0
2
1
1
1
1
1
1
2
1
1
1
1
1
2
2
0
0
1
0
1
0
1
0
2
1
1
2
1
1
1
2
1
1
1
1
0
2
2
1
2
0
1
2
1
1
1
1
1
0
2
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
2
2
1
2
1
2
2
1
2
0
2
0
1
1
2
1
0
2
1
2
2
1
1
2
2
1
1
1
1
0
1
1
1
0
1
2
1
1
1
1
1
2
1
1
2
1
1
1
1
0
1
1
0
1
2
1
1
1
1
0
1
2
2
2
1
1
1
1
0
0
1
1
4
1
1
1
0
2
1
1
1
1
0
1
2
2
1
2
2
1
2
2
1
1
1
0
1
2
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
0
1
1
1
2
1
1
1
1
1
2
2
2
1
0
1
1
0
0
2
2
1
2
1
1
1
2
2
1
2
1
1
1
1
2
0
1
2
2
1
2
1
1
1
2
2
0
1
1
1
1
1
1
2
1
1
2
1
1
1
1
2
2
2
3
1
0
2
2
2
1
2
1
2
1
0
1
2
1
1
1
1
2
1
2
3
2
1
1
2
1
1
1
1
1
2
1
1
2
1
1
2
0
1
2
2
1
1
1
2
1
1
1
1
1
2
2
2
1
2
2
2
1
1
1
0
2
1
2
1
1
2
1
1
1
2
0
2
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
2
2
1
1
1
1
1
2
0
0
2
1
1
0
1
0
1
1
1
1
1
2
1
0
2
1
0
0
1
1
2
1
1
1
2
0
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
2
1
1
0
0
1
2
1
2
0
0
1
2
1
1
1
1
2
1
2
0
1
1
1
1
1
1
1
1
1
0
2
1
1
0
1
1
0
2
2
1
1
1
1
1
0
0
1
1
2
2
1
1
0
1
2
1
1
1
1
2
2
1
3
1
0
1
1
1
1
1
1
2
1
1
1
3
1
1
2
2
1
1
0
1
0
2
1
1
0
0
1
2
2
1
0
1
0
0
1
1
4
1
1
2
2
0
2
0
1
0
1
0
2
1
2
1
1
2
1
1
0
3
1
1
2
0
1
1
2
2
0
0
1
2
1
2
2
1
2
1
1
1
2
2
1
1
1
2
1
1
1
1
1
1
0
1
2
2
0
0
2
0
1
1
1
1
2
1
1
1
2
0
0
1
1
1
0
1
2
1
0
1
1
0
1
1
1
0
1
2
2
2
1
1
1
2
1
0
2
1
2
1
1
1
1
2
1
1
1
1
1
1
2
2
1
1
3
2
0
1
2
1
1
1
2
1
0
2
1
1
1
1
1
1
2
1
1
1
2
2
2
1
1
1
2
1
0
1
1
0
1
0
1
0
2
1
1
2
1
1
1
0
2
1
1
2
1
2
1
1
1
2
1
1
0
2
2
2
1
2
1
1
1
0
1
2
1
1
1
2
2
1
2
1
1
2
0
1
1
1
1
0
1
1
1
2
1
0
1
1
1
1
1
2
1
1
1
1
1
1
2
0
1
1
2
0
0
1
1
1
2
0
1
2
2
1
0
1
1
1
1
1
0
0
1
1
0
0
1
0
2
1
1
1
1
1
1
1
1
0
2
1
2
2
1
1
2
1
1
1
2
0
2
2
0
0
2
2
1
0
1
1
2
1
0
0
1
1
2
2
1
2
1
1
1
1
1
1
0
1
1
1
1
0
1
2
2
2
2
1
1
1
1
2
0
1
2
1
1
1
1
1
1
1
2
2
1
2
2
0
2
1
2
1
1
1
0
1
1
1
1
1
2
2
2
2
0
1
2
2
1
2
2
1
1
0
1
2
2
0
2
1
1
2
2
1
2
1
1
2
2
0
0
3
1
2
1
1
1
1
1
1
1
1
1
2
1
2
2
2
1
1
0
0
1
1
1
0
1
1
0
1
1
1
0
2
1
1
1
1
1
2
1
1
2
2
1
1
2
0
1
1
2
2
2
1
1
2
2
0
1
1
1
1
1
1
1
1
1
0
2
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
2
2
1
1
0
2
1
2
1
1
1
1
2
1
2
2
1
2
1
1
1
1
1
2
2
1
0
1
1
1
1
0
1
2
2
1
1
1
1
1
1
2
1
1
1
0
1
0
1
2
2
0
0
0
1
2
1
1
2
1
1
2
1
1
1
1
1
0
2
1
2
1
1
1
2
1
0
1
1
2
0
0
1
2
1
2
1
1
2
1
2
0
0
2
1
1
2
1
1
1
2
1
1
2
3
1
0
1
1
2
1
1
1
2
1
2
0
0
1
1
1
2
0
2
1
0
1
1
1
1
1
1
2
2
1
1
2
1
2
1
1
2
0
0
1
2
1
1
0
1
1
1
1
2
1
2
1
1
2
1
1
1
1
0
0
2
1
2
0
0
1
1
2
1
2
1
1
1
1
2
1
1
2
1
0
1
1
2
2
2
2
0
1
1
0
2
0
1
2
1
1
1
2
3
0
1
1
2
1
1
1
2
1
1
2
2
1
1
2
2
2
1
1
1
0
1
1
0
2
0
0
2
0
1
2
1
1
1
1
0
2
2
2
0
1
1
1
1
1
3
2
1
2
2
1
2
1
1
2
1
1
2
0
1
0
0
1
1
2
1
3
2
0
1
1
1
1
1
0
1
1
2
1
0
1
1
2
1
2
1
1
1
1
1
1
1
1
0
1
2
2
1
1
0
1
1
1
2
0
2
0
1
2
1
0
1
1
0
0
1
1
1
2
1
1
2
1
2
2
1
2
1
0
1
2
2
1
2
2
1
1
1
1
1
0
2
2
1
1
1
1
1
1
1
2
2
1
1
0
0
2
0
2
2
1
1
2
1
1
1
2
1
0
1
1
1
0
1
1
0
2
1
1
2
2
1
2
2
1
1
1
2
1
1
0
1
1
0
1
2
1
1
1
2
1
0
1
1
1
2
2
1
1
1
1
1
1
2
2
1
2
2
2
2
0
0
2
1
1
1
2
2
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
2
2
2
1
0
1
1
2
1
1
1
1
1
1
1
1
2
0
1
1
0
1
0
2
1
2
1
1
0
0
0
1
1
3
1
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
2
2
0
1
2
1
1
1
2
1
1
0
1
1
1
2
1
1
1
1
1
1
1
2
0
0
0
2
1
2
1
1
1
0
0
1
0
2
1
1
1
1
0
2
1
1
1
2
1
2
1
0
1
1
1
1
2
1
1
1
1
1
1
2
2
1
1
2
1
2
1
1
0
2
2
0
0
1
0
1
1
1
1
1
1
1
1
2
2
1
1
0
1
1
1
2
2
1
1
1
1
2
1
1
0
1
1
1
2
0
1
1
2
2
0
1
1
1
1
9
1
1
1
2
0
2
2
1
1
1
1
1
1
2
1
0
0
1
1
1
2
1
1
1
1
2
1
2
2
1
1
1
1
1
0
2
1
1
2
1
1
1
1
2
0
2
1
1
1
2
1
1
1
0
1
0
1
0
1
1
2
1
1
1
2
1
1
1
2
0
1
1
2
1
1
2
1
1
1
0
1
1
1
2
1
1
0
1
1
2
2
1
0
1
1
1
3
1
1
1
1
2
1
0
1
2
1
1
2
1
2
2
1
2
2
2
2
2
1
1
1
2
2
1
1
2
1
2
2
2
1
1
1
2
1
0
2
0
1
1
1
1
1
2
0
0
1
0
1
2
1
1
1
1
2
2
1
1
1
0
2
1
2
1
1
2
1
3
1
2
1
2
1
0
0
1
2
1
2
1
2
1
0
1
0
0
1
2
1
2
2
1
1
1
2
2
1
1
0
2
1
1
2
0
0
1
1
0
2
1
0
1
1
0
0
1
2
0
1
0
1
0
2
2
1
1
1
1
0
0
1
1
1
1
0
1
1
2
1
2
2
1
0
1
2
0
2
0
3
2
1
1
1
1
1
1
2
1
2
2
1
1
0
1
1
1
1
1
1
2
1
1
1
2
0
1
2
2
2
1
1
1
0
1
1
1
1
2
1
2
1
2
1
1
1
1
2
2
1
1
1
2
1
2
2
2
1
1
1
0
1
0
2
1
2
2
0
2
1
0
0
2
1
1
1
1
1
1
2
1
1
1
1
1
0
1
1
2
1
0
1
2
2
1
1
4
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
2
1
1
1
1
2
1
2
1
1
2
2
1
1
1
1
1
0
1
0
0
1
2
2
1
1
1
0
0
1
2
1
1
0
0
1
1
2
1
2
1
1
1
1
2
3
1
0
1
1
2
1
1
2
0
0
2
2
1
2
1
0
1
0
1
1
2
1
2
1
1
2
1
0
1
1
1
0
1
2
2
2
1
2
1
1
1
0
2
2
0
0
1
1
2
2
1
1
2
1
2
1
1
2
2
0
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
1
0
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
0
2
2
1
0
1
1
2
2
1
1
0
1
1
0
1
2
0
1
1
1
1
1
1
1
2
2
1
2
1
1
1
3
2
1
2
2
1
2
1
2
1
1
1
2
1
2
1
1
1
1
1
0
1
1
1
1
1
2
1
3
1
1
2
1
2
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
2
2
0
1
1
1
2
1
1
0
1
0
2
1
0
2
1
1
1
0
1
2
1
1
2
1
1
1
2
1
1
1
1
1
2
2
2
1
1
0
1
1
3
1
2
0
2
1
1
1
2
1
1
1
1
0
1
2
2
4
1
1
1
0
1
1
1
1
1
0
1
1
2
1
0
1
1
1
1
0
0
2
1
2
1
2
1
1
1
1
0
2
0
1
1
1
1
1
1
1
2
2
3
2
1
2
1
0
1
0
1
1
1
2
2
2
1
1
2
1
1
1
1
1
1
1
0
0
2
1
2
1
1
2
1
1
0
1
1
1
1
2
1
1
0
1
2
1
2
1
1
1
1
0
2
1
2
1
1
2
1
1
1
2
2
2
1
0
1
1
0
1
0
1
2
1
1
1
1
1
1
2
1
1
1
0
1
1
1
1
2
1
2
1
1
0
1
1
1
1
0
0
2
1
1
1
2
0
2
1
2
2
1
1
1
1
1
2
1
1
2
0
1
1
2
2
1
1
1
0
1
0
1
2
2
1
1
2
1
1
0
2
2
1
2
2
0
1
2
1
0
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
2
0
2
0
1
0
2
1
1
0
2
1
1
0
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
0
1
1
2
2
1
0
3
1
1
1
0
1
2
1
1
2
0
1
1
2
2
1
1
2
3
0
0
1
1
2
1
0
1
0
1
2
2
1
1
2
2
1
1
1
0
1
1
1
2
1
1
1
1
0
1
2
2
0
1
1
2
0
1
1
1
0
1
1
1
1
1
0
2
1
1
2
2
1
2
2
1
1
1
2
0
1
1
1
1
2
1
1
1
1
1
1
0
1
2
1
2
1
2
1
1
1
1
1
0
1
1
2
1
3
2
0
1
1
0
0
1
1
1
2
2
2
1
1
2
2
0
1
1
3
1
1
1
1
0
0
1
1
1
1
2
0
1
0
1
0
1
1
1
2
2
0
1
0
1
2
0
1
2
2
0
1
1
1
1
2
2
1
1
0
2
1
1
2
2
0
1
1
2
2
0
1
1
1
1
2
1
1
1
1
1
1
2
2
2
1
2
1
1
2
1
1
1
1
1
1
1
2
0
2
2
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
0
0
1
1
1
0
1
0
0
1
1
1
1
0
2
1
1
1
1
2
0
4
1
1
3
1
1
1
1
2
0
1
0
0
1
1
2
1
2
2
1
1
0
1
1
1
2
1
2
1
2
0
2
1
1
1
1
1
1
1
1
1
1
1
1
1
0
2
1
1
2
2
1
0
1
0
1
1
1
0
1
0
1
2
2
0
1
1
2
0
0
1
0
0
1
2
0
1
0
1
1
1
2
0
1
1
0
1
1
2
1
1
1
2
2
2
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
0
2
1
2
2
0
1
1
0
1
2
1
1
0
1
0
1
0
1
1
2
0
2
1
0
1
1
1
0
1
1
1
2
2
2
0
2
1
0
2
1
1
2
0
1
1
0
2
0
1
1
1
2
2
1
2
2
0
2
1
1
0
1
1
2
2
0
1
2
2
1
0
3
1
1
0
0
2
0
0
1
1
0
0
1
2
2
2
2
1
1
2
2
1
1
2
1
3
2
0
1
1
1
1
2
2
1
1
1
2
1
1
2
2
1
1
1
1
0
1
1
1
2
1
1
1
2
1
1
1
0
1
0
2
0
1
1
0
1
1
0
2
1
2
1
2
1
1
2
2
1
1
0
2
1
1
0
1
1
1
1
1
0
1
0
0
1
2
1
1
1
0
1
1
1
2
1
1
0
1
1
1
1
1
0
2
1
0
1
2
0
0
0
1
1
1
0
1
1
1
1
2
1
2
2
0
2
1
0
2
1
1
1
1
1
3
1
1
1
2
1
1
1
1
2
0
2
1
1
1
1
1
0
1
1
1
1
0
1
1
1
1
2
1
0
2
2
0
1
1
1
0
0
1
2
1
2
1
1
2
2
0
2
2
1
0
1
1
0
1
3
2
1
2
1
1
1
1
1
1
1
1
1
2
1
2
2
1
2
1
2
1
2
0
2
1
1
0
1
1
0
2
2
1
1
2
1
1
0
1
3
2
1
1
1
0
1
1
1
1
0
1
1
1
1
0
1
0
0
1
2
1
2
1
1
1
1
1
0
1
1
1
1
2
0
2
1
1
1
1
1
1
1
1
2
0
0
1
2
1
0
1
0
1
1
1
1
1
2
2
1
0
2
1
1
0
1
1
1
2
1
1
2
1
1
1
1
1
2
1
1
0
2
0
1
1
1
1
1
1
1
1
2
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
2
1
1
0
1
0
2
1
1
1
1
1
1
1
0
1
1
1
0
0
2
2
1
1
0
2
2
2
1
1
1
1
1
1
0
1
0
1
1
1
1
1
1
0
1
1
1
2
1
1
0
1
0
2
0
1
1
2
1
1
0
1
1
2
0
2
1
2
1
0
1
1
1
1
2
1
1
1
1
1
0
1
1
2
1
1
1
0
1
1
1
1
1
2
0
1
1
1
2
1
1
1
2
0
2
1
1
1
1
1
2
1
1
1
0
1
2
1
0
1
1
1
2
1
1
1
1
0
1
1
1
1
0
1
0
4
1
1
1
0
1
2
0
1
2
0
2
1
1
1
1
1
1
1
2
2
1
0
1
1
1
1
1
2
2
1
1
1
0
1
1
1
1
1
1
1
6
1
1
1
1
0
0
1
2
2
1
2
1
1
1
1
1
2
2
0
1
2
2
1
1
2
1
1
0
1
1
1
2
2
2
1
2
2
1
1
1
2
1
1
0
2
2
1
1
2
1
2
1
1
0
1
0
1
1
1
1
2
1
2
1
1
1
1
0
1
1
0
2
1
1
2
1
1
2
0
1
1
2
2
2
1
2
1
1
2
2
1
0
2
1
2
1
0
0
1
1
1
1
1
1
0
1
0
1
2
1
1
1
2
2
1
2
1
1
1
2
1
0
2
0
2
1
2
1
1
1
1
2
1
1
1
2
1
0
1
1
1
2
2
1
2
0
0
2
2
1
0
2
2
1
2
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
0
2
0
0
0
1
1
2
1
1
1
1
1
1
2
2
2
1
1
1
1
2
1
1
1
1
0
1
2
1
2
0
1
1
1
1
2
1
1
1
1
2
1
1
2
1
2
2
1
1
2
1
1
1
1
0
2
2
2
1
0
1
2
1
2
2
0
1
2
1
2
2
2
1
2
1
0
1
1
1
1
1
1
1
2
2
2
2
1
1
1
0
2
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
2
0
1
1
3
1
1
1
2
1
1
1
1
1
1
1
1
2
0
2
2
2
1
0
1
1
1
1
0
1
2
2
1
2
2
1
1
2
1
0
2
1
1
1
1
1
1
1
0
1
2
1
0
1
0
2
1
1
1
1
1
0
1
0
1
2
2
1
2
1
1
2
2
1
1
1
2
1
1
1
1
0
0
1
1
0
2
2
0
1
2
2
2
0
1
1
1
0
1
2
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
0
1
0
1
2
1
1
2
1
1
0
1
1
1
0
1
0
0
2
1
1
1
1
1
2
1
2
1
2
1
1
1
1
1
1
1
1
1
2
2
1
1
2
2
1
0
0
1
1
2
0
2
1
2
2
1
0
2
2
0
0
1
2
2
2
1
2
2
2
0
1
1
1
1
1
2
2
0
0
0
1
1
1
2
1
1
0
1
2
1
1
2
2
1
1
1
1
2
1
2
1
1
2
2
3
1
0
0
1
1
2
0
2
1
2
1
2
1
2
1
2
0
1
1
1
2
2
1
0
1
1
1
1
1
1
1
0
1
0
1
2
1
1
2
1
1
0
2
1
0
2
1
0
1
1
1
1
1
2
1
1
1
0
2
1
0
1
1
1
1
2
1
1
1
0
1
1
1
0
2
0
2
1
2
1
0
1
0
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
0
1
1
2
1
1
2
1
2
1
1
2
1
2
2
1
1
1
2
1
1
1
0
1
1
1
1
1
1
1
2
2
0
1
2
2
1
1
1
2
2
1
3
1
1
1
2
1
1
0
0
2
1
2
1
1
1
1
2
1
0
2
1
1
1
2
1
1
2
1
2
2
2
2
1
1
2
2
2
1
1
1
0
1
1
2
2
2
1
1
2
0
2
1
1
0
1
1
1
1
2
1
1
0
0
2
0
2
1
1
1
1
2
2
1
2
1
1
1
0
1
1
1
0
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
3
1
2
0
1
0
1
1
1
2
2
1
2
1
2
1
0
0
1
1
0
1
1
1
1
1
1
1
1
1
2
1
0
1
2
2
0
1
1
1
1
1
1
1
1
1
2
1
2
1
0
1
2
2
1
1
1
1
1
1
2
2
0
1
1
1
2
1
1
1
1
2
1
1
2
1
1
4
1
0
0
1
1
2
2
2
0
3
2
2
1
1
2
1
1
1
1
2
2
2
0
1
2
2
1
1
1
1
2
1
1
1
0
1
0
1
1
1
1
1
1
2
1
1
2
0
1
1
1
2
2
1
1
1
1
1
1
2
2
1
4
1
1
2
1
2
0
2
1
0
1
1
3
1
1
1
1
1
1
1
1
1
1
2
1
2
0
1
1
1
2
2
1
2
2
2
0
1
1
0
2
2
1
2
2
0
1
3
2
0
1
1
1
0
2
2
1
1
1
2
1
2
1
0
2
2
1
1
2
2
1
1
1
4
2
0
1
1
0
1
2
0
2
1
0
2
0
2
1
2
1
1
2
0
0
1
1
1
1
1
0
1
1
1
1
0
1
1
1
1
1
1
1
2
0
1
0
1
2
1
1
0
1
2
1
1
2
1
1
2
2
1
0
2
1
1
1
0
1
1
0
2
2
1
1
1
1
1
2
1
1
0
1
0
2
1
2
1
0
1
2
1
1
1
3
2
1
1
2
1
2
1
1
0
1
2
1
2
1
1
2
1
2
0
1
2
1
1
0
1
1
1
2
2
1
2
2
1
1
0
2
1
2
2
2
2
0
2
1
1
2
1
1
1
1
0
2
2
1
2
1
1
2
2
0
1
1
0
1
1
1
2
2
1
1
1
1
1
1
1
1
1
2
1
0
1
1
0
0
1
0
0
1
2
0
0
1
2
2
2
1
2
1
1
1
0
2
1
0
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
0
1
0
1
1
1
2
1
1
0
1
1
1
0
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
0
1
1
1
1
0
1
0
2
1
0
2
2
3
2
1
0
1
2
2
1
2
1
1
1
2
1
2
2
1
2
2
2
2
1
1
2
1
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
0
1
1
2
1
2
1
1
1
1
1
3
1
2
0
0
1
1
0
1
0
2
0
0
0
1
0
1
2
0
0
1
1
1
2
1
1
1
1
1
2
0
1
2
1
1
1
2
1
1
1
0
1
1
0
2
1
0
1
1
2
2
1
2
1
1
2
1
0
1
2
1
1
1
1
1
1
1
2
2
0
2
2
2
1
1
0
1
2
1
0
1
0
1
0
2
2
0
1
1
1
2
1
2
1
1
0
1
1
0
1
0
1
0
1
2
1
1
1
1
1
0
2
2
2
1
1
1
0
1
1
1
1
1
2
0
2
2
1
2
2
1
1
1
2
1
2
1
1
1
2
1
1
2
1
2
1
1
0
1
1
2
1
1
1
1
2
2
2
1
0
1
1
1
2
1
1
1
1
1
2
1
1
0
0
1
2
1
1
1
1
2
0
1
1
1
1
0
0
1
0
1
0
1
2
1
1
0
0
0
1
2
1
1
1
3
1
2
2
1
2
1
1
1
1
2
1
1
1
1
1
1
2
1
0
2
2
1
1
1
1
1
2
1
0
1
1
2
1
0
1
3
1
1
1
1
2
2
0
1
1
1
1
2
1
1
1
0
1
1
2
1
1
1
1
1
1
2
2
1
2
2
2
1
1
2
1
0
2
1
0
2
1
0
1
2
1
1
1
0
1
1
1
1
0
1
0
1
1
1
1
0
1
2
1
1
1
1
2
1
0
1
1
0
1
1
2
1
0
1
1
1
1
1
1
1
1
1
1
2
2
1
2
1
1
2
1
2
1
2
1
0
2
1
1
1
1
2
1
1
1
2
2
2
2
1
1
1
1
3
1
1
1
1
0
2
1
3
2
0
1
1
0
2
0
1
0
1
2
1
1
0
1
2
1
1
1
1
1
1
1
1
1
2
1
0
1
1
2
1
1
2
2
1
2
2
1
1
1
0
1
1
1
0
1
2
2
0
1
1
1
1
1
2
1
2
2
1
1
1
2
2
1
1
1
1
2
1
1
1
2
2
0
2
2
2
1
1
1
1
0
0
1
2
2
1
2
2
1
1
1
1
1
1
0
2
1
1
1
1
1
1
1
2
2
0
1
2
2
0
1
1
1
0
1
2
2
1
1
2
2
1
1
2
1
0
1
1
1
1
2
0
2
1
2
1
1
0
1
1
1
1
0
2
2
1
1
1
2
1
1
2
1
1
1
0
1
1
0
1
2
1
2
2
2
1
0
1
1
1
1
2
1
0
0
0
2
1
2
1
1
1
2
1
1
0
1
1
1
2
1
1
1
0
1
2
1
1
0
2
2
1
1
1
1
2
0
2
1
2
1
1
0
0
1
1
2
1
1
1
2
2
1
1
2
2
1
1
2
1
1
0
2
2
2
0
2
1
2
2
1
1
1
0
1
1
1
0
2
1
1
1
0
2
0
1
1
2
1
1
1
2
1
2
2
2
2
2
1
1
2
1
1
0
1
1
0
2
1
1
1
0
1
2
1
3
1
1
1
1
1
1
1
1
1
0
1
2
1
1
1
2
2
1
1
1
2
1
2
1
1
3
1
1
1
1
2
1
1
1
1
1
0
1
1
2
1
1
1
2
2
0
1
1
1
0
0
2
1
0
0
1
1
2
1
1
1
1
3
1
1
1
1
2
1
1
1
1
1
2
0
2
2
1
2
2
4
1
0
1
1
2
1
1
1
1
1
1
0
2
1
1
1
1
1
0
1
1
2
1
2
2
1
1
1
1
0
1
1
0
1
0
1
1
0
1
1
1
0
2
1
1
1
2
0
0
1
0
1
0
1
0
2
1
1
2
1
0
2
0
1
2
1
0
0
1
0
1
1
0
1
0
2
0
2
1
0
1
1
1
1
0
1
1
2
1
2
1
1
1
0
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
2
0
2
1
1
0
2
1
1
1
1
2
1
1
1
1
2
4
1
2
0
1
2
1
0
1
1
1
1
1
1
0
2
2
2
2
1
1
0
1
1
0
2
2
1
2
2
2
1
1
2
1
0
1
2
1
1
1
1
2
1
1
1
1
1
2
0
1
1
2
1
2
3
0
1
2
2
0
1
2
1
1
2
1
1
1
2
1
1
2
0
1
1
1
1
1
1
2
1
2
1
1
1
0
3
1
1
2
2
1
0
0
1
0
1
1
1
1
1
2
2
1
1
1
1
2
2
1
2
1
1
1
1
2
2
2
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
0
1
0
1
1
2
1
0
1
1
2
1
0
1
2
0
1
2
0
2
2
1
1
1
1
1
1
1
2
0
1
1
1
1
2
1
1
1
1
1
1
2
0
2
1
0
1
0
1
1
1
1
1
0
1
2
2
1
1
1
0
0
1
1
2
1
2
1
0
1
2
0
1
0
1
1
2
0
1
2
1
1
0
2
1
1
1
1
2
1
1
1
0
1
1
0
0
1
0
1
1
2
2
0
1
1
1
1
1
2
1
1
2
1
0
1
1
1
1
1
1
0
1
1
1
0
1
2
2
1
1
1
0
2
1
1
1
2
1
1
2
1
2
0
1
2
2
1
1
1
1
0
2
1
1
1
1
1
2
1
1
1
1
2
1
2
2
0
0
2
1
1
1
0
1
1
2
1
0
2
1
1
2
2
2
1
0
0
2
2
2
2
2
0
1
1
2
1
1
2
1
1
2
1
2
2
1
2
1
1
1
2
2
2
2
1
2
1
1
1
2
1
1
0
1
1
2
2
2
1
1
2
1
3
0
1
1
1
1
2
0
0
1
1
1
1
1
0
1
1
1
1
0
2
1
0
1
1
2
1
1
2
1
0
2
1
2
1
1
1
1
1
2
2
1
1
1
2
1
2
0
1
1
1
1
2
1
1
2
1
2
1
0
1
2
1
1
0
2
2
2
2
2
1
2
2
1
1
2
1
1
1
0
1
1
3
1
1
1
1
2
1
0
1
0
2
1
1
1
0
1
2
1
1
1
1
1
1
1
1
2
1
1
1
0
3
1
1
1
1
1
2
1
2
2
0
1
2
1
1
0
0
1
0
2
1
1
2
1
0
1
0
1
1
1
1
2
0
1
1
1
1
1
1
0
1
1
2
1
0
0
1
2
1
2
2
2
1
0
2
1
2
1
1
1
1
1
1
0
2
2
1
1
1
2
2
0
2
2
1
1
1
2
1
0
1
0
2
1
1
2
1
0
1
1
1
1
2
2
1
1
0
1
1
1
0
1
0
0
1
2
1
0
0
1
1
1
1
1
2
1
1
2
1
1
1
1
2
0
1
1
1
1
1
1
0
2
0
2
1
2
2
2
0
1
1
1
2
1
2
1
1
1
2
1
1
0
2
1
2
1
1
0
1
0
1
1
2
2
1
1
2
2
1
1
2
1
2
1
0
1
1
1
1
2
0
2
1
0
0
1
1
1
1
1
1
2
1
0
0
1
2
1
1
0
0
1
0
2
2
1
1
1
0
1
2
1
1
1
2
1
1
1
0
1
1
2
4
1
2
1
1
2
1
1
1
1
1
1
0
1
0
1
2
2
0
1
2
1
1
1
1
1
2
1
0
0
2
1
1
0
0
1
1
1
2
0
1
4
2
2
1
2
2
1
1
1
1
1
1
2
1
2
1
1
0
2
1
1
1
1
1
2
1
1
0
1
1
2
1
1
0
1
1
0
1
0
2
1
2
1
0
2
2
1
1
1
0
1
1
2
2
0
1
1
1
1
2
2
2
2
1
2
1
1
2
1
2
1
0
1
1
0
2
1
2
1
2
1
0
1
1
1
1
1
1
0
0
0
1
1
1
1
0
1
0
1
2
1
2
1
0
1
0
1
0
1
0
0
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
2
0
1
2
1
1
1
1
2
2
1
1
1
1
1
1
1
0
2
2
2
1
2
2
1
2
1
2
2
1
0
1
1
0
2
2
0
2
1
1
2
1
2
0
2
1
1
0
2
1
1
1
0
0
1
1
2
2
1
0
1
2
1
2
0
2
1
1
2
1
1
1
0
2
0
2
0
1
0
2
1
1
2
0
2
1
1
1
1
1
1
2
1
1
2
1
1
0
2
2
1
2
1
1
1
2
1
1
4
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
1
2
1
3
1
1
1
2
1
2
1
1
1
1
2
0
1
0
0
0
1
0
0
1
2
1
1
1
1
2
2
1
2
1
1
2
2
1
1
0
1
1
1
1
1
1
2
1
1
1
1
1
2
2
1
1
1
1
2
1
1
1
2
2
7
1
1
1
1
1
1
2
1
2
1
2
1
2
1
1
0
1
1
2
1
2
1
2
2
2
2
1
2
2
0
1
1
2
1
1
2
2
1
2
1
1
1
2
2
1
2
1
1
1
1
2
2
1
2
1
1
2
2
1
2
1
1
2
1
2
1
0
2
1
1
2
1
2
1
2
1
1
1
1
2
1
1
0
0
2
1
0
2
0
0
1
1
1
2
1
1
1
1
0
2
2
1
1
1
1
1
1
0
2
0
2
1
1
1
1
1
0
0
0
1
1
1
1
2
2
1
1
1
2
1
1
1
2
2
1
0
1
1
1
2
0
1
2
2
2
1
1
0
2
1
2
0
0
0
0
1
1
1
2
2
2
1
1
1
1
2
1
1
1
1
0
2
0
2
1
2
1
0
0
0
2
1
0
2
2
1
0
1
0
1
0
1
1
1
1
0
2
0
2
0
0
1
1
0
1
1
0
1
1
1
2
2
1
1
0
2
1
1
1
1
2
1
1
1
0
1
1
0
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
0
2
0
1
2
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
2
1
0
2
1
1
1
2
1
1
1
1
0
0
2
1
1
0
2
1
1
1
1
0
1
2
1
1
2
0
0
2
1
1
2
1
0
2
0
2
1
1
1
1
1
1
1
1
1
2
1
2
1
2
0
2
0
2
0
2
2
1
2
2
0
2
1
1
1
1
1
1
0
0
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
0
0
1
1
1
2
1
2
1
0
0
1
1
1
1
2
2
2
2
0
0
1
1
1
0
1
1
1
1
1
1
2
0
1
2
1
1
1
1
2
1
0
0
1
1
1
1
1
1
2
1
1
2
1
1
0
2
1
1
2
1
1
0
1
1
2
1
1
1
1
1
1
1
0
1
2
2
1
2
2
1
2
2
2
2
0
1
2
1
1
2
0
2
1
2
1
1
1
2
1
0
2
1
1
1
0
1
1
0
2
1
2
1
1
1
1
1
1
1
1
1
0
1
1
1
1
0
2
1
1
2
0
1
1
1
2
2
2
1
1
1
2
1
1
1
2
1
2
1
1
2
0
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
2
1
2
0
1
2
1
2
2
1
1
1
0
2
3
2
1
1
1
1
2
1
2
0
2
1
2
0
0
2
2
1
1
2
2
1
2
1
1
1
2
1
1
1
0
1
1
2
1
0
0
1
0
2
2
2
1
1
1
1
2
1
0
1
2
2
1
0
1
1
1
2
2
1
1
1
2
1
0
1
0
0
1
1
1
2
2
0
0
1
1
1
0
2
1
1
1
0
1
1
2
0
2
0
2
0
1
2
1
1
1
0
1
1
2
1
1
1
2
1
2
1
2
0
1
2
1
0
1
1
1
1
0
1
2
1
2
2
2
1
2
1
0
2
2
0
2
1
1
0
0
1
2
2
1
1
2
2
2
1
1
2
2
1
2
2
1
1
0
0
1
2
1
0
1
0
0
1
0
2
2
2
0
1
1
1
1
2
1
1
0
1
0
0
1
0
1
1
1
1
2
2
1
1
1
2
2
1
1
1
0
1
2
2
0
0
1
0
1
1
1
2
1
1
1
2
0
0
2
1
2
0
1
0
1
2
1
1
1
1
1
1
1
1
0
1
1
2
1
1
1
1
0
1
1
1
1
1
1
1
1
1
2
2
1
2
0
2
1
0
2
1
1
2
1
1
1
1
2
1
1
2
1
1
1
0
2
0
1
0
1
1
1
2
1
1
1
1
1
1
2
2
2
0
1
1
0
2
1
1
2
0
2
1
1
2
1
1
0
1
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
3
1
3
0
2
1
1
0
1
1
1
2
1
1
1
0
1
2
1
2
0
0
1
1
0
0
2
1
0
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
2
1
1
0
1
1
0
1
0
1
1
1
1
1
2
1
1
1
0
1
2
1
1
1
1
0
1
1
0
2
1
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
2
2
0
0
1
1
1
0
2
2
2
2
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
0
0
1
2
2
2
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
0
1
1
0
1
1
2
2
1
1
0
0
0
1
1
1
1
2
1
2
2
1
2
2
2
2
1
0
1
2
1
2
0
1
1
1
2
0
2
0
2
1
1
2
1
1
1
0
1
0
1
0
1
1
1
1
1
1
1
1
1
1
1
1
0
1
2
1
1
1
0
1
1
1
1
1
2
1
1
1
2
0
2
0
1
1
1
1
1
1
0
1
2
1
1
1
2
1
1
1
1
1
2
1
1
2
1
3
0
1
1
1
1
0
2
2
1
2
1
0
1
1
1
2
1
1
2
1
2
2
1
0
1
0
0
2
0
1
2
1
1
2
2
1
0
2
1
0
1
1
2
1
2
1
1
1
2
2
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
1
1
0
2
0
0
0
1
1
1
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
3
2
2
2
2
0
2
2
1
2
1
2
1
2
1
1
1
2
1
0
2
1
1
1
1
0
0
1
1
1
1
1
1
2
1
2
0
1
1
1
2
2
1
2
1
1
1
1
2
2
0
1
2
2
1
1
2
2
2
1
1
1
2
1
0
1
1
3
1
0
2
0
0
1
2
5
2
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
0
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
2
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
0
2
2
1
0
1
1
1
2
1
2
1
0
1
2
0
1
2
1
2
1
1
2
1
1
1
1
2
2
1
1
1
2
1
0
1
1
2
0
2
1
1
0
1
2
2
1
1
1
1
1
1
2
3
1
2
0
1
2
2
1
1
0
1
1
1
3
0
1
2
0
1
1
2
2
0
1
2
1
1
1
1
1
2
0
1
0
0
1
1
1
1
2
1
1
1
1
1
1
2
2
0
2
1
1
1
1
1
1
1
1
1
1
1
1
0
1
2
1
2
1
0
2
2
1
1
2
1
2
1
1
0
2
1
3
1
1
0
2
2
0
1
0
1
1
1
0
1
2
1
1
1
1
1
1
1
2
1
2
2
0
1
1
0
1
1
1
0
2
2
2
2
1
1
1
1
0
2
1
1
1
0
1
1
1
2
2
0
0
1
1
1
1
1
2
1
1
1
1
0
1
0
0
0
1
1
1
5
1
3
1
1
1
1
2
2
1
1
2
2
2
1
1
2
1
0
1
0
1
1
1
2
1
1
2
1
1
1
1
2
2
1
1
0
1
0
2
1
1
1
1
1
1
1
1
1
1
0
0
1
0
0
2
0
1
1
1
2
1
2
2
1
1
2
1
2
1
1
1
1
2
1
0
1
0
1
2
2
0
1
1
1
2
1
2
1
0
2
1
1
1
1
1
1
0
1
0
1
2
1
2
1
2
2
2
0
0
2
1
2
0
1
1
0
2
1
0
1
1
2
2
1
1
2
1
2
1
1
1
1
0
0
1
2
1
1
1
1
1
0
1
1
1
2
2
1
1
1
1
1
2
2
1
1
2
2
2
1
1
1
2
2
1
1
2
1
2
0
1
1
1
1
1
0
0
1
0
1
1
0
1
2
2
1
1
1
2
1
1
1
0
1
1
3
2
2
1
2
1
2
1
1
0
2
2
1
1
2
1
2
1
1
1
2
2
1
0
1
1
1
1
2
2
1
2
1
1
0
1
0
1
2
2
1
2
1
1
1
2
1
1
1
2
0
0
1
1
2
1
2
1
1
2
1
2
1
1
1
2
1
1
1
1
2
1
2
2
1
0
1
1
1
1
0
2
1
0
1
2
1
1
1
1
1
1
0
1
1
1
1
2
1
0
1
2
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
1
0
2
1
1
1
0
1
1
1
1
2
1
2
2
1
1
1
1
1
1
0
1
1
0
2
1
0
0
2
0
1
2
0
1
1
2
2
3
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
2
2
2
2
1
1
1
0
1
1
1
0
2
2
1
1
1
2
0
0
1
1
1
1
1
1
1
1
1
1
0
1
1
2
1
0
1
1
1
1
3
1
1
2
1
0
1
1
1
1
2
0
1
2
1
2
1
1
2
1
2
2
1
1
0
3
0
1
1
1
1
0
1
1
2
1
1
0
2
1
1
1
1
1
2
1
0
0
1
1
1
1
2
1
2
0
1
1
1
1
1
1
0
1
2
1
1
1
2
0
1
0
1
1
1
1
1
2
0
1
0
1
0
1
2
1
1
1
1
2
1
1
0
1
1
2
1
1
0
1
2
0
1
0
2
1
0
0
1
2
1
1
3
1
1
0
1
1
2
1
2
1
1
2
0
2
1
1
1
1
1
1
1
1
1
0
2
1
1
1
1
0
1
2
2
0
0
1
2
1
4
1
1
2
1
1
2
2
0
0
2
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
0
1
1
2
2
1
0
1
2
1
1
1
2
0
2
0
0
0
1
0
2
2
2
1
2
1
1
0
1
1
0
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
0
1
1
1
1
2
0
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
2
1
1
0
1
2
2
2
2
1
1
2
1
1
1
2
2
1
2
0
1
0
2
0
1
1
0
1
2
1
2
0
1
1
1
1
1
1
1
2
1
1
1
2
2
1
2
1
2
1
1
1
1
0
1
0
0
0
0
3
2
0
1
0
1
1
2
0
1
1
1
1
1
2
1
2
1
2
2
1
2
1
1
1
0
1
1
1
1
1
1
2
2
2
1
2
2
1
2
2
1
0
2
1
1
1
0
3
1
1
1
2
1
2
1
2
0
1
1
2
2
1
1
0
1
2
1
2
1
1
1
1
1
1
1
2
1
0
0
0
1
2
1
1
2
1
1
0
1
1
1
2
1
1
0
1
1
1
0
1
2
1
2
1
2
2
2
2
1
1
1
2
0
4
0
1
1
0
2
0
2
2
2
2
2
2
0
1
1
0
2
1
1
2
0
2
0
2
2
2
1
2
1
0
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
0
1
2
1
2
2
1
1
1
2
1
0
2
1
2
1
2
1
0
2
1
1
2
1
1
1
1
1
1
1
1
3
1
2
2
1
1
0
2
1
1
2
1
1
1
0
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
2
1
1
0
1
0
2
1
1
1
1
1
1
2
0
1
2
1
1
1
2
1
2
1
0
1
0
1
2
1
1
0
1
0
2
1
0
1
1
1
2
1
1
1
1
0
1
1
1
1
0
1
2
1
1
1
0
1
0
1
1
1
1
1
0
1
2
0
0
2
1
0
1
1
1
0
1
2
0
1
1
1
0
1
1
1
1
2
1
1
1
1
1
2
1
1
2
1
1
0
2
1
2
1
2
2
2
1
1
2
1
2
1
1
0
1
1
1
0
2
1
1
1
1
1
1
2
2
1
1
1
1
0
0
1
1
2
1
1
0
2
1
1
2
0
2
1
0
1
0
1
1
1
2
1
1
2
1
1
0
1
1
2
1
1
0
1
2
1
0
2
1
0
1
1
2
2
1
1
2
1
2
2
2
1
1
0
1
1
1
1
2
1
1
2
2
0
0
1
1
1
1
2
1
2
1
2
1
1
1
1
1
1
2
2
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
0
1
1
0
2
2
0
1
3
1
1
1
1
2
1
1
1
0
1
1
1
1
1
0
0
2
1
2
2
2
2
1
1
1
1
2
2
2
2
3
1
1
1
2
1
2
1
1
1
0
2
2
1
2
1
1
1
1
2
1
1
1
1
0
1
2
1
0
2
1
2
1
0
1
2
1
0
0
1
1
1
1
2
1
2
1
1
0
0
0
1
1
1
1
0
1
1
2
1
1
2
1
2
1
0
0
1
1
1
1
2
0
1
1
1
1
1
0
1
1
1
1
1
2
2
1
1
1
0
1
1
2
1
1
1
1
0
1
1
1
2
0
1
2
0
2
1
1
1
2
1
1
2
0
0
2
1
2
1
2
1
1
1
1
1
0
1
1
2
1
1
1
1
1
2
0
0
1
1
1
1
1
2
1
1
1
1
1
2
1
0
1
1
1
1
0
1
2
2
1
0
0
1
1
1
2
1
0
1
1
2
1
1
2
1
1
2
1
1
2
1
2
1
2
2
1
2
0
1
1
1
2
1
2
1
0
1
1
1
1
1
2
1
2
2
1
1
1
2
1
1
1
2
1
1
1
1
0
1
1
0
1
1
2
1
1
2
2
1
1
1
2
2
1
0
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
0
1
2
2
1
1
2
1
2
1
1
1
0
2
1
0
1
2
1
1
1
0
0
2
0
1
0
1
1
1
2
1
1
2
2
0
0
2
2
2
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
4
1
1
1
2
2
1
1
1
2
1
1
2
2
0
0
2
1
1
1
1
0
2
1
1
1
1
2
0
1
0
1
1
2
0
1
1
2
1
1
1
1
1
1
1
1
2
2
0
0
2
1
1
0
2
1
2
1
1
1
2
1
1
1
1
2
1
1
2
2
1
1
1
1
0
2
1
2
1
0
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
0
1
1
3
2
1
1
1
2
1
2
2
1
1
1
2
1
1
2
1
1
0
1
1
1
2
0
1
1
1
1
2
1
0
1
0
0
1
2
1
0
1
0
2
1
1
2
1
2
0
1
0
1
2
2
1
0
2
1
2
1
1
1
0
0
2
1
1
2
1
0
1
0
0
1
2
1
2
2
1
1
2
1
1
1
2
1
2
1
2
3
2
1
0
1
2
1
2
2
1
0
1
0
1
2
2
1
1
0
0
1
1
0
1
2
1
1
0
1
1
2
0
2
2
0
1
2
2
1
2
0
0
1
3
1
2
2
1
2
1
2
1
2
2
1
2
1
1
1
1
1
1
1
2
2
1
1
2
1
1
2
2
2
1
1
2
0
1
1
0
2
1
1
1
1
1
1
1
1
0
2
2
1
1
1
1
1
0
1
1
2
1
1
3
3
1
1
1
2
2
1
1
2
1
1
2
0
1
1
2
1
1
0
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
0
1
1
1
0
1
1
1
1
2
1
1
2
1
1
1
2
0
1
1
0
2
1
2
1
1
2
2
2
1
1
1
1
1
0
1
1
1
1
1
1
2
1
1
1
0
1
2
1
1
1
1
2
2
2
1
1
0
0
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
0
2
1
2
1
1
1
2
1
2
2
1
1
2
1
1
2
2
1
1
1
1
1
0
0
1
1
1
1
1
1
1
1
0
2
0
1
2
1
1
1
2
0
1
1
0
2
1
1
1
1
1
2
1
1
0
2
1
1
1
2
3
2
1
0
1
0
1
1
1
0
2
2
1
1
1
1
0
0
1
2
1
1
2
0
0
2
1
1
2
1
1
1
0
2
2
1
1
1
1
1
2
0
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
2
0
1
1
0
1
1
1
2
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
2
1
2
1
1
2
1
1
0
1
1
0
1
2
0
1
1
1
0
0
1
1
2
1
0
1
2
1
0
1
1
2
2
0
2
1
2
1
0
1
2
0
2
2
2
2
1
1
2
0
1
2
1
1
1
1
1
0
1
1
1
2
0
0
0
1
1
2
1
1
1
1
1
0
1
1
1
1
1
1
1
1
0
1
1
1
1
0
1
1
2
0
1
0
2
1
2
1
2
2
1
1
1
1
0
2
1
1
2
1
1
1
1
2
2
1
0
0
2
2
2
2
1
1
2
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
2
2
2
1
1
0
1
2
2
1
1
1
1
1
2
2
1
2
0
1
1
1
1
2
1
1
1
1
0
1
1
1
0
2
2
1
2
1
0
1
1
1
0
1
1
1
1
0
1
2
0
2
1
1
0
0
1
0
2
1
1
2
2
2
0
2
2
1
1
1
1
2
1
0
0
1
2
1
1
2
1
1
1
1
1
2
2
3
1
1
0
0
1
2
2
2
1
1
0
1
1
0
2
1
0
1
0
1
2
2
1
0
1
0
2
1
0
2
1
1
0
1
1
2
1
4
2
1
1
1
2
2
2
2
1
2
1
1
2
1
1
2
2
2
1
1
1
2
2
1
0
2
1
1
0
0
1
1
1
1
1
1
0
1
1
1
1
1
1
2
1
1
1
1
1
0
1
1
1
1
1
0
1
1
0
2
1
1
1
1
1
2
2
1
1
1
2
2
1
1
2
1
1
1
2
1
1
1
2
0
0
2
0
0
1
1
0
2
1
1
1
0
0
2
0
2
1
2
1
1
2
1
0
1
1
2
2
1
1
1
1
2
1
1
2
2
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
2
2
0
1
1
0
1
1
1
1
1
2
1
1
0
2
0
1
0
2
1
2
1
1
2
1
1
1
2
1
1
1
0
0
1
1
1
2
1
2
2
1
0
1
1
0
2
1
1
1
1
1
2
1
2
0
1
2
1
1
1
1
0
0
1
0
2
1
2
0
1
1
2
2
1
1
2
2
1
1
1
0
2
1
2
1
2
0
1
2
1
2
2
2
1
1
1
1
1
2
1
1
1
2
1
1
2
0
2
1
2
0
1
1
1
1
0
0
1
2
1
1
2
1
0
0
1
1
2
1
1
1
0
3
2
1
2
1
0
1
0
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
2
1
2
1
2
1
1
0
2
1
2
1
1
1
1
1
2
0
2
1
1
1
1
1
0
1
1
0
1
1
2
1
2
2
1
2
1
1
2
1
1
1
0
1
2
1
1
1
0
1
1
1
0
1
1
1
1
2
1
1
2
2
1
2
2
1
1
2
2
2
1
1
1
0
1
2
2
1
2
1
1
1
1
1
2
0
1
2
1
1
0
1
1
1
2
1
1
1
2
1
1
2
1
2
1
0
1
1
2
2
1
1
1
1
2
0
1
1
2
1
2
2
0
1
1
1
1
2
0
1
2
0
0
2
0
0
2
2
2
1
1
1
1
1
2
1
1
1
0
1
0
2
1
2
1
0
0
1
1
2
1
2
1
1
1
2
1
1
1
0
0
1
0
2
1
0
1
1
2
1
1
1
1
2
1
1
1
1
2
2
1
2
2
1
1
1
1
0
0
1
0
1
1
2
1
2
2
2
1
1
1
1
1
1
1
3
1
0
2
1
1
0
2
1
1
1
2
1
2
1
1
2
1
0
1
1
0
1
0
1
1
1
2
1
2
2
1
2
1
1
2
1
0
1
0
2
1
1
2
1
1
0
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
0
2
1
1
1
1
2
1
2
2
2
0
1
1
1
2
1
1
2
2
1
1
1
0
1
1
0
1
1
1
1
1
1
2
1
1
1
1
1
2
1
2
1
2
1
0
1
1
1
2
1
1
1
1
1
1
1
2
1
1
0
1
1
1
1
2
1
2
2
2
2
2
1
1
2
1
1
1
2
1
1
1
1
2
1
2
1
1
0
2
0
0
1
1
2
2
1
1
2
1
2
1
1
1
0
0
0
0
1
2
1
1
2
1
1
1
0
2
1
1
2
1
0
1
2
2
1
2
1
1
1
2
1
1
1
1
1
0
0
0
1
1
0
0
1
1
2
1
1
1
1
1
1
0
2
2
1
1
0
1
1
1
2
1
1
1
2
1
1
1
1
1
2
2
1
1
2
0
2
0
2
0
1
2
1
2
1
1
0
0
1
0
1
1
1
2
1
2
0
1
2
1
1
1
0
1
0
1
2
1
1
2
1
1
1
2
0
1
1
1
0
0
2
1
1
0
0
1
1
2
1
0
2
0
2
1
1
2
1
1
2
1
2
2
1
1
0
1
1
2
1
1
0
1
1
0
0
0
1
1
2
1
2
0
1
1
1
0
0
2
0
1
2
1
2
1
1
2
1
1
1
1
1
3
0
1
2
1
1
1
1
0
1
0
1
2
1
1
2
1
1
1
1
1
1
2
1
1
0
1
1
1
2
1
2
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
0
0
1
1
1
0
2
0
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
2
0
1
0
2
2
1
0
0
1
1
1
1
1
1
1
1
1
2
1
3
1
1
1
1
2
1
2
1
1
2
1
2
1
0
2
1
0
1
1
1
1
2
1
2
1
2
0
2
2
2
1
1
1
0
2
1
2
2
1
1
1
1
1
0
3
1
1
1
1
1
2
1
1
1
2
1
1
1
1
0
1
1
2
1
2
2
2
1
2
1
1
1
1
1
1
1
3
2
2
1
2
1
1
2
1
1
1
1
2
2
0
1
1
0
1
1
0
1
0
1
0
1
0
1
1
2
0
1
1
1
1
1
1
1
2
2
0
0
1
1
1
0
0
1
0
2
0
1
1
2
0
0
1
2
2
2
1
1
2
1
1
1
1
1
1
1
2
0
0
0
1
0
1
2
1
1
1
0
2
1
1
1
2
1
2
0
1
1
2
1
1
0
1
2
1
1
1
2
2
1
2
1
2
1
1
1
1
0
1
0
1
2
0
2
2
2
2
1
2
2
1
1
1
1
0
1
1
2
0
2
1
2
1
1
2
1
1
1
1
2
1
3
1
1
1
1
2
2
2
1
1
1
1
1
1
2
1
1
1
1
0
0
1
2
1
2
1
1
1
1
0
1
1
1
1
2
0
2
2
1
1
2
2
2
1
2
1
1
0
2
1
2
1
1
1
1
1
1
1
0
0
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
2
1
0
1
2
1
1
1
1
2
2
1
2
0
2
1
1
2
1
0
1
2
1
1
1
1
1
1
1
0
2
1
1
2
1
1
1
1
2
1
1
2
1
2
1
1
1
0
0
1
1
1
0
2
2
1
1
1
0
1
2
1
1
1
1
2
1
1
1
1
1
1
1
0
2
1
2
2
1
1
2
1
1
1
1
1
2
1
1
1
1
2
2
2
2
1
2
1
2
1
1
1
1
1
0
1
1
1
2
2
1
2
2
1
1
1
1
0
1
1
1
1
2
1
2
0
1
1
1
1
1
1
1
0
2
1
1
1
1
1
0
2
1
2
1
1
1
2
1
2
0
1
1
0
0
1
1
0
2
1
1
1
0
1
0
2
2
1
1
1
0
1
1
1
2
2
0
1
1
1
1
2
1
1
1
0
1
1
1
1
2
1
1
2
1
1
1
1
2
1
1
0
0
0
0
1
0
1
2
1
1
1
2
1
1
1
1
1
1
1
0
0
1
1
2
1
1
1
1
1
1
0
1
2
1
2
0
1
2
1
2
1
1
1
1
1
1
1
1
1
1
2
0
0
1
1
2
1
2
1
2
1
1
1
2
1
1
1
1
2
1
1
2
2
2
2
0
1
1
1
1
1
0
0
1
1
1
2
2
0
0
1
1
1
0
1
0
2
1
0
1
2
1
1
1
0
1
1
2
1
1
1
2
1
0
1
0
0
1
1
1
1
1
1
2
1
1
1
2
2
1
2
2
2
1
1
1
1
1
2
1
2
2
2
1
1
1
0
2
0
1
2
0
1
1
1
2
1
2
0
2
1
1
1
1
2
1
2
0
2
2
2
1
2
2
1
1
1
1
1
1
0
0
2
2
1
0
2
1
2
4
2
2
1
1
1
2
1
0
1
2
1
2
1
0
1
1
1
1
1
1
1
0
1
1
2
1
1
1
1
2
1
1
1
1
0
1
1
1
0
2
2
1
1
1
1
2
2
0
1
1
2
1
1
1
0
1
1
2
1
1
1
0
1
0
2
1
2
1
1
1
1
0
1
1
1
1
1
1
3
1
1
2
1
1
1
1
1
2
1
0
1
0
1
1
2
2
1
2
1
1
2
1
0
2
2
1
1
2
1
1
0
1
1
1
1
1
1
0
0
1
1
0
1
2
2
2
2
2
1
2
0
0
1
2
1
0
2
1
2
1
0
3
1
1
2
0
0
0
1
1
2
1
1
1
2
1
2
1
1
2
2
1
1
2
1
1
1
2
1
1
1
0
2
1
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
2
0
2
0
1
1
2
1
1
1
0
1
1
2
1
1
0
1
2
1
2
1
2
2
2
1
1
1
1
0
1
1
1
1
1
1
0
2
1
0
2
1
0
2
2
2
1
0
1
2
1
1
1
1
1
2
1
1
2
2
2
2
1
0
0
1
2
2
1
2
1
2
1
1
2
1
2
1
1
1
1
1
1
1
0
1
2
1
1
1
2
0
1
2
1
2
0
1
1
1
1
1
1
1
2
1
1
1
1
1
1
0
1
1
1
1
1
2
1
1
1
1
2
1
1
1
0
2
2
1
1
1
1
1
1
0
1
6
1
1
1
2
2
2
0
1
1
0
2
2
0
1
1
1
1
1
2
2
0
2
1
1
1
1
1
1
1
1
2
0
2
2
1
0
2
1
0
1
1
2
1
1
1
1
2
1
1
2
2
1
2
1
2
1
1
2
2
1
2
1
1
2
1
1
2
2
1
1
2
1
1
0
1
1
2
0
1
1
0
1
1
1
2
2
2
1
1
1
2
1
1
2
1
1
1
1
1
1
2
0
2
1
1
2
0
0
1
1
1
1
1
0
1
2
2
2
2
1
2
1
1
0
2
1
1
2
1
1
1
1
2
1
0
1
1
0
1
1
1
0
2
1
2
2
1
1
0
1
1
1
2
1
1
1
0
1
1
1
1
2
2
1
1
2
0
1
1
2
2
2
2
1
2
1
1
2
1
3
1
1
1
0
1
1
1
2
1
2
1
1
1
1
2
2
2
2
0
0
0
1
1
1
1
1
0
2
1
1
2
1
2
1
2
0
2
2
1
1
1
1
1
3
1
1
2
0
2
1
1
0
1
1
1
1
2
1
1
2
1
1
1
1
2
1
2
2
0
0
2
2
0
0
1
0
1
1
3
2
1
1
2
2
1
0
2
2
2
1
1
1
1
2
1
1
1
1
1
1
2
2
0
1
0
1
1
1
2
0
1
1
2
1
1
2
2
1
2
1
1
1
2
2
0
1
2
1
1
1
1
1
1
2
1
1
0
1
0
2
0
0
2
1
1
2
1
1
1
0
2
1
1
0
1
1
2
1
1
1
2
0
0
1
1
1
2
2
2
1
1
1
1
2
1
1
1
1
2
2
1
0
1
2
0
1
0
2
1
1
1
1
1
2
2
1
1
1
0
1
1
2
0
1
1
0
1
1
0
1
1
1
1
1
1
2
1
2
1
1
2
0
2
2
1
1
2
1
1
3
2
1
2
1
1
1
1
2
0
2
1
1
2
0
1
2
2
1
1
1
0
1
1
1
1
2
1
1
2
3
1
1
1
1
2
1
1
1
2
2
1
1
1
2
1
2
0
1
2
1
2
0
1
2
2
1
1
1
2
0
1
1
1
0
1
1
1
1
1
2
1
0
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
2
2
1
2
2
2
0
1
1
2
1
2
0
1
2
0
0
1
2
1
1
1
2
1
0
0
1
2
1
1
1
1
1
1
0
1
1
1
1
0
0
1
0
1
1
1
2
2
1
2
1
0
2
1
1
1
1
0
0
2
1
1
1
1
2
1
1
1
2
1
1
1
2
0
1
1
1
1
0
1
0
0
2
2
2
1
1
0
1
1
1
1
1
0
0
1
2
2
1
1
1
1
0
1
1
3
1
2
1
2
1
1
1
1
1
1
0
0
1
1
1
1
1
1
1
1
0
1
0
1
1
1
1
1
1
2
1
0
0
1
1
0
1
2
1
2
2
1
1
1
1
1
1
1
0
0
0
1
1
1
1
2
1
0
1
1
2
0
1
1
2
1
2
2
2
2
0
1
1
1
1
1
2
1
0
2
1
1
1
1
2
1
0
1
1
1
0
2
2
2
1
1
2
1
1
0
1
1
0
1
1
1
1
1
2
1
0
1
1
1
1
0
1
0
1
0
1
1
2
1
2
1
1
1
1
3
0
1
1
1
1
1
2
1
2
1
2
1
1
2
0
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
1
1
2
0
0
1
2
1
0
1
1
2
0
2
1
1
1
1
1
2
1
1
1
1
1
1
0
1
1
1
1
1
2
1
2
1
0
2
2
2
2
0
0
1
2
1
0
1
1
1
1
1
1
1
1
2
0
0
1
1
2
1
3
2
2
1
1
1
2
1
2
2
0
1
1
1
0
1
1
1
1
1
1
1
2
1
1
1
2
1
2
2
1
1
1
1
1
1
2
2
2
1
1
1
2
1
2
2
1
2
0
2
1
1
2
1
1
0
1
1
0
1
2
0
0
2
1
2
2
1
1
0
1
2
0
1
1
1
2
1
1
1
1
0
1
1
2
0
1
1
1
1
1
0
1
1
1
0
2
1
0
1
1
1
1
2
1
1
2
3
1
1
1
1
0
2
1
2
2
0
2
1
1
1
1
1
1
1
0
1
0
1
1
1
1
1
2
1
0
1
2
1
2
1
1
1
2
2
2
1
1
1
2
1
1
1
1
1
2
1
2
1
0
1
1
2
1
1
1
0
1
1
2
1
1
2
1
1
1
1
1
1
1
2
1
3
3
1
1
0
2
1
1
1
2
1
1
2
1
3
2
0
1
1
1
2
1
0
1
1
0
1
0
2
0
1
1
2
1
0
0
2
1
1
1
1
0
1
0
0
1
0
1
0
0
1
0
0
1
1
1
2
1
1
0
1
1
1
0
0
1
1
1
1
1
1
2
2
1
1
0
1
2
1
0
1
0
2
2
1
1
1
1
1
1
1
0
1
2
1
1
1
2
1
2
1
1
1
1
2
1
2
1
2
1
0
1
1
0
1
2
2
1
1
2
1
0
1
1
2
1
2
2
1
1
1
1
0
1
0
1
1
1
1
0
0
1
1
1
1
2
0
2
1
1
1
1
0
2
2
2
1
1
1
2
1
2
2
1
0
1
1
2
2
1
1
1
1
1
2
1
1
2
1
1
1
2
1
2
0
1
1
2
0
1
1
1
2
1
1
1
2
2
1
0
1
1
1
1
1
1
0
1
2
1
1
1
1
2
2
1
1
0
1
1
1
2
1
2
2
2
1
1
2
2
2
2
1
2
2
2
2
0
0
1
1
1
1
2
1
1
1
1
1
2
1
2
1
1
2
0
3
1
1
1
1
1
1
1
2
2
2
1
1
2
1
1
2
1
0
1
1
1
1
0
1
1
1
2
0
1
1
1
1
1
0
1
1
1
1
1
1
2
2
1
1
2
0
1
2
1
1
1
1
1
0
2
2
1
1
1
0
2
1
1
0
1
1
1
1
1
1
2
1
1
1
2
1
1
1
0
1
3
2
1
2
1
0
1
1
1
0
1
1
0
1
0
0
1
1
0
1
2
2
2
1
2
1
1
0
0
1
2
1
2
2
1
0
1
1
0
1
1
2
1
1
1
0
2
1
0
0
2
1
0
1
2
1
1
1
1
2
1
1
2
2
0
1
1
1
2
1
1
1
1
2
1
2
1
1
0
1
1
1
1
1
2
2
1
5
2
1
0
2
2
2
0
0
1
1
2
1
1
1
2
1
2
2
2
2
1
0
1
1
1
1
1
1
1
1
0
2
1
1
2
2
1
2
1
1
1
2
1
0
2
1
2
2
1
1
1
2
2
0
1
1
2
1
1
1
1
2
2
1
2
2
1
1
3
1
1
1
2
1
2
1
1
0
1
1
0
1
1
1
2
2
0
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
0
1
1
3
1
2
1
2
2
2
2
2
0
2
2
1
1
2
1
1
2
2
1
2
1
1
1
1
1
1
2
0
2
2
1
1
1
1
1
0
0
1
1
2
1
2
2
1
1
0
2
2
1
0
1
1
1
1
2
1
1
1
0
2
1
2
1
2
1
1
2
1
0
1
1
2
0
1
1
2
0
2
1
2
1
0
1
0
1
1
2
1
0
1
1
1
0
1
2
2
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
0
1
1
3
1
1
1
1
1
1
1
1
2
1
0
2
1
2
0
1
0
1
1
0
1
3
1
1
1
0
1
1
1
0
2
0
1
2
0
1
0
2
1
1
1
0
2
1
1
0
2
1
1
1
1
1
1
1
2
0
1
0
0
1
1
2
1
1
1
0
1
1
1
2
1
0
1
1
1
1
1
2
2
0
1
1
0
2
0
2
2
1
0
1
2
1
2
1
0
1
1
2
1
1
1
0
2
0
3
2
2
1
0
2
1
1
2
1
1
2
1
0
2
2
1
1
1
1
1
1
1
1
1
1
2
0
1
1
1
1
1
0
1
1
1
2
1
1
1
0
1
1
1
1
1
0
2
2
0
2
1
1
3
1
1
2
1
1
2
1
1
1
2
1
1
1
0
1
1
1
1
1
2
2
2
1
1
1
2
1
1
0
0
1
1
0
2
1
2
1
1
2
1
2
1
2
1
1
1
1
2
1
0
1
1
1
2
1
2
1
1
1
1
2
1
1
2
1
1
2
1
0
1
2
1
1
0
2
1
1
2
1
0
0
2
1
1
2
1
2
1
1
2
1
2
2
1
0
2
1
2
0
1
0
2
1
1
1
1
0
1
1
0
1
2
0
1
1
0
1
2
1
1
0
1
1
1
1
1
2
0
1
1
2
1
0
1
0
1
1
2
1
2
1
2
1
1
0
1
1
2
1
0
2
1
0
1
1
0
2
1
2
1
1
2
1
0
1
0
2
0
2
2
0
0
2
1
1
1
2
1
1
0
2
2
1
2
2
1
3
1
1
0
1
0
1
1
1
2
1
1
0
1
0
0
1
2
2
1
1
2
1
1
0
1
1
1
2
0
1
1
1
1
1
0
1
1
1
1
1
1
1
2
2
1
1
2
1
1
0
2
0
1
2
1
2
2
1
0
0
2
0
1
1
2
2
1
2
1
1
2
2
2
2
2
0
1
1
2
1
1
1
2
2
1
1
0
1
0
0
2
0
2
1
0
1
0
0
2
2
1
2
1
0
0
1
1
1
1
1
2
1
1
2
1
2
0
1
1
1
1
0
1
1
1
0
1
1
2
1
1
1
2
1
2
1
1
2
2
2
2
1
1
0
1
1
2
1
1
1
1
1
2
1
2
1
1
0
1
2
2
1
1
1
1
1
0
0
0
1
2
1
0
0
1
2
1
1
1
1
1
1
1
1
2
1
2
2
1
1
2
1
2
2
1
1
1
1
1
1
1
1
1
2
1
0
1
1
0
2
0
2
1
1
2
2
0
0
2
1
2
1
1
1
2
2
2
2
1
1
1
0
2
0
2
2
1
1
1
1
1
1
2
1
0
1
1
1
1
2
1
0
0
1
2
1
1
1
1
1
1
1
0
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
0
1
2
2
1
1
1
0
1
1
1
1
1
1
1
2
2
1
1
1
0
1
1
1
2
1
1
0
1
1
1
1
0
1
2
2
2
1
1
0
4
1
2
1
1
1
1
1
1
1
0
3
1
1
1
0
1
1
0
1
1
1
1
1
2
1
1
1
1
1
2
1
2
1
2
1
2
2
2
1
1
2
1
1
2
1
1
1
2
1
2
0
1
1
2
0
2
1
1
1
2
1
1
1
1
1
2
1
2
1
1
2
1
2
2
1
3
1
1
2
1
2
1
1
1
1
0
2
2
2
2
0
0
2
1
2
1
1
1
1
1
1
1
1
1
1
2
2
1
0
2
2
2
1
1
1
1
1
1
2
2
0
2
1
2
2
1
3
0
1
1
0
1
1
1
1
1
1
2
2
2
1
0
1
1
1
1
0
1
1
0
1
1
1
1
1
2
1
1
1
1
1
0
1
1
2
1
1
1
1
2
1
1
1
1
1
1
0
0
1
1
1
0
1
1
1
2
1
0
1
1
2
1
0
1
0
1
2
2
2
1
2
1
1
2
2
2
1
1
1
1
1
1
0
2
2
0
1
1
1
1
0
0
0
2
1
1
2
1
0
1
2
1
1
1
2
1
1
1
1
2
1
1
1
2
1
1
2
1
0
1
2
2
2
1
1
0
1
1
2
3
0
2
1
1
2
0
1
0
1
1
1
1
1
1
1
1
2
2
1
1
0
1
1
1
1
1
0
0
1
1
2
1
0
1
2
1
2
1
1
0
1
1
1
1
1
1
1
1
1
2
0
2
2
0
2
1
1
1
1
1
1
0
1
1
2
1
1
0
1
2
1
1
1
1
2
1
2
1
1
1
1
2
0
1
1
0
1
0
2
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
2
1
2
0
1
2
1
1
1
0
1
0
0
2
1
0
2
2
0
0
1
1
1
1
1
1
0
2
1
1
1
1
1
2
1
2
1
2
1
0
1
0
2
1
0
2
1
1
2
1
1
1
1
0
1
1
2
0
1
1
2
1
0
1
2
1
1
0
1
1
0
0
2
1
2
1
1
2
1
2
0
1
1
1
1
2
1
1
1
1
2
2
1
1
2
2
2
1
1
1
1
2
2
1
2
1
1
1
0
1
2
1
1
2
1
0
0
1
1
2
2
1
2
0
1
1
1
1
1
1
1
0
1
1
1
0
2
1
1
1
1
1
1
2
1
2
1
2
1
1
2
2
2
2
1
1
1
0
1
1
1
1
1
1
1
1
1
0
0
2
1
1
0
1
1
1
1
1
1
3
2
1
0
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
2
0
1
1
1
0
0
1
1
1
1
2
1
2
0
1
1
1
1
0
1
1
0
1
2
2
1
1
0
1
1
0
2
2
1
1
2
1
0
1
0
2
1
1
2
0
2
1
1
2
1
1
1
2
1
2
2
1
1
2
1
1
1
1
1
1
2
0
1
1
2
2
2
0
1
1
1
0
0
2
1
1
1
2
1
0
0
1
0
0
1
2
1
1
1
2
0
0
1
1
2
1
1
1
1
0
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
1
2
2
1
2
0
0
0
1
1
1
1
1
2
0
1
1
1
1
1
1
2
1
2
1
1
2
0
1
1
2
1
2
1
1
1
0
1
1
2
1
1
2
2
1
1
1
2
2
1
1
1
0
1
1
0
1
1
1
2
2
1
1
1
1
0
2
2
1
1
1
2
1
1
0
2
1
1
2
1
1
1
1
0
2
2
1
1
0
1
1
1
1
1
0
1
1
1
1
2
2
1
2
2
2
0
2
1
1
2
1
0
0
1
1
2
1
2
0
1
0
2
3
1
1
1
1
2
1
2
2
1
2
1
1
1
2
2
1
1
2
1
0
1
1
1
2
1
0
2
1
1
1
1
1
1
2
1
1
0
1
1
1
1
0
1
2
1
1
2
1
1
1
2
1
0
1
2
1
1
2
1
2
0
2
2
2
2
1
0
0
0
1
1
1
6
1
1
1
1
2
2
2
1
1
2
1
1
1
2
2
3
1
1
1
0
2
1
1
1
1
2
2
1
1
1
0
1
2
1
1
0
1
2
1
1
2
2
1
2
1
0
2
1
1
1
0
1
0
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
0
1
1
1
2
2
2
2
1
1
2
1
1
1
1
1
1
1
2
1
2
0
1
1
0
1
1
1
2
1
2
3
0
1
1
1
1
1
1
0
2
1
2
2
1
1
2
1
1
1
1
2
0
1
2
1
2
3
1
2
0
1
2
1
2
1
2
1
1
0
1
2
0
1
1
0
2
1
2
1
2
1
1
1
1
1
1
2
0
2
1
0
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
2
1
0
2
1
0
1
1
2
1
0
0
1
1
1
1
1
1
1
0
1
1
1
0
1
2
1
1
1
1
2
0
1
2
1
1
1
2
0
1
0
1
2
1
0
2
1
0
1
1
0
0
1
2
1
1
1
1
1
0
1
2
1
2
1
2
1
1
2
1
1
1
0
2
2
1
1
1
1
2
1
2
1
1
1
2
1
1
2
2
1
1
1
1
1
1
1
0
1
2
1
2
2
1
1
0
1
1
2
2
2
0
1
1
1
1
1
2
1
0
1
0
1
0
0
1
2
2
0
0
2
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
2
0
0
2
1
2
0
2
1
1
2
0
1
1
1
2
1
0
1
1
2
1
2
2
2
1
2
0
2
2
1
0
1
1
1
1
4
1
2
1
1
2
2
1
1
1
1
0
1
1
1
1
2
2
1
1
1
1
1
0
2
0
1
1
2
1
1
2
1
1
1
1
0
2
2
2
1
2
1
1
2
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
2
1
1
1
1
2
2
1
1
1
2
1
1
0
1
1
1
2
2
1
1
2
3
1
2
2
1
1
2
1
1
0
1
1
1
2
0
2
1
0
1
0
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
2
2
0
1
1
2
1
1
1
1
2
2
2
0
1
2
2
2
1
2
1
0
1
0
2
1
1
1
1
1
1
1
2
0
0
1
1
1
0
1
1
1
1
1
1
0
1
2
1
1
2
0
1
1
1
1
2
1
1
1
0
1
1
1
1
0
1
1
1
1
2
0
2
1
2
2
1
1
0
2
1
0
1
0
2
1
1
3
0
1
2
1
2
1
1
1
1
1
1
2
1
2
1
2
0
0
2
1
1
2
2
1
0
2
1
1
1
1
1
2
2
1
2
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
0
1
0
2
0
2
0
1
2
2
1
1
0
1
2
1
1
0
1
1
0
2
2
2
0
0
1
1
1
0
1
1
1
2
2
1
1
2
2
2
1
2
1
1
2
1
0
2
1
1
1
2
0
1
1
1
1
0
0
2
2
1
1
2
2
1
0
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
2
2
2
1
2
1
0
1
0
1
1
1
1
1
1
1
1
2
2
1
0
2
2
0
1
2
1
2
1
2
2
1
1
1
2
0
1
1
2
0
2
1
1
1
2
1
1
1
2
2
1
2
0
2
1
1
1
1
1
0
1
0
1
0
1
2
0
1
0
2
2
5
1
0
1
1
2
2
1
1
1
1
1
1
0
0
2
0
0
2
2
2
0
2
1
2
2
3
0
0
2
2
0
1
1
0
0
2
2
0
1
1
1
1
1
1
2
0
1
2
2
1
2
1
1
1
0
1
1
1
1
1
1
1
2
2
1
1
0
1
1
2
1
2
1
2
2
2
0
2
2
0
2
2
1
1
2
1
1
1
2
2
1
1
1
1
2
2
1
1
0
1
2
1
2
0
0
2
1
0
1
1
1
1
2
1
2
1
1
1
0
1
1
1
1
1
2
0
2
1
1
1
0
1
1
1
2
2
1
1
1
2
1
1
0
0
1
1
1
2
0
2
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
0
1
1
0
1
1
1
1
1
1
0
1
1
1
2
1
2
0
1
2
1
2
1
1
1
2
1
2
1
2
2
1
1
1
0
0
2
1
0
1
0
1
1
2
1
1
2
1
1
1
0
1
2
1
1
1
1
0
2
2
1
1
1
2
1
1
1
0
1
2
0
1
1
1
2
2
2
2
2
2
1
1
2
1
0
0
1
1
1
1
0
1
1
2
0
0
0
1
1
1
1
1
0
1
1
1
2
2
1
1
1
1
1
0
1
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
1
1
0
1
2
1
1
2
0
1
2
1
0
1
3
1
2
1
2
1
1
1
1
2
1
2
2
1
2
1
0
1
1
2
1
1
1
0
1
2
1
2
1
0
1
1
1
1
1
1
1
0
1
0
1
2
1
1
2
0
0
1
2
1
2
1
2
0
3
1
0
2
1
2
1
1
1
1
1
1
0
0
0
1
1
0
0
1
1
1
1
2
2
1
1
1
2
2
1
1
0
1
0
1
0
1
2
1
0
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
0
0
1
1
0
1
1
2
1
1
1
1
1
2
2
1
1
1
1
1
0
1
1
1
1
1
0
1
1
1
1
2
1
1
1
1
1
1
0
2
1
0
1
1
2
1
1
2
0
2
1
0
2
1
2
2
2
1
1
1
2
1
0
0
0
2
0
1
0
2
0
2
1
1
1
1
1
1
1
2
1
2
1
1
1
2
1
2
2
0
1
1
0
1
1
2
2
2
1
1
2
1
0
2
1
1
2
2
0
2
2
1
1
1
1
1
1
1
0
2
2
0
2
1
0
1
0
1
1
0
1
1
2
0
0
2
2
2
1
0
1
1
1
1
1
1
1
1
0
1
1
0
1
1
1
2
0
1
1
1
1
1
1
1
0
1
1
2
1
1
1
0
2
1
1
0
1
1
1
2
1
0
2
1
1
1
1
2
1
0
1
1
2
1
2
1
1
2
0
0
1
1
1
2
1
1
1
1
2
0
2
1
1
1
0
2
1
2
1
1
1
1
1
1
0
0
0
0
1
2
2
2
1
1
1
1
1
2
1
2
2
2
1
2
1
2
1
1
2
1
1
1
2
1
2
1
1
3
1
2
1
1
1
2
0
1
1
1
1
1
1
1
1
0
1
1
1
2
2
1
1
0
1
2
1
1
2
2
1
2
1
2
1
0
1
1
1
1
1
2
2
0
1
2
1
0
1
1
1
0
1
2
1
1
2
2
1
2
1
1
1
1
0
1
1
2
1
2
0
1
1
1
1
0
2
1
0
1
1
2
1
2
1
1
1
0
1
1
1
2
1
1
1
2
1
1
2
2
1
1
1
1
0
1
1
2
2
1
1
0
0
1
1
0
0
0
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
0
1
1
1
0
1
2
2
2
1
1
0
0
1
1
1
1
2
1
2
1
2
1
0
0
1
3
1
1
1
1
1
2
2
2
2
1
1
1
1
1
0
0
1
1
0
1
1
1
2
1
1
0
1
1
1
2
2
1
0
1
1
2
2
1
2
1
1
1
1
0
1
1
2
1
1
1
2
0
1
1
1
1
2
1
1
1
1
1
1
1
0
1
1
1
2
2
0
2
1
1
1
1
1
1
1
1
2
0
1
1
0
1
1
1
1
2
1
1
1
1
1
1
1
1
1
0
1
1
2
1
1
2
1
1
1
1
1
0
1
1
2
1
0
1
2
0
1
1
2
1
2
1
0
2
2
0
1
1
1
2
0
1
1
1
1
2
2
1
0
3
0
1
1
2
0
1
2
1
1
1
1
2
1
1
0
2
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
0
1
1
2
1
2
1
1
1
1
1
1
2
1
2
2
1
2
1
1
2
2
1
1
1
0
1
1
0
1
2
1
2
1
1
2
1
1
2
1
3
1
2
1
0
1
1
2
1
1
1
1
1
1
1
1
2
0
2
1
2
1
1
1
1
2
1
1
1
2
1
2
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
0
2
2
0
1
2
0
0
1
0
1
0
2
0
1
1
1
1
1
1
1
0
2
1
1
1
2
2
2
2
1
2
0
2
2
2
1
2
1
1
2
1
1
1
1
1
1
0
0
0
1
1
0
1
1
2
2
1
2
1
2
1
1
1
1
2
2
1
0
0
1
1
2
1
1
1
2
1
0
1
2
1
1
0
1
0
2
0
3
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
0
1
0
1
2
1
1
1
0
0
1
1
1
1
1
1
1
1
1
0
2
1
1
2
1
1
2
1
1
1
1
1
1
1
2
2
0
1
2
1
1
1
0
1
0
1
1
1
1
2
1
2
2
2
0
0
0
1
1
1
1
2
1
2
1
0
1
1
1
2
1
1
1
1
0
1
1
2
0
2
0
2
1
1
2
2
0
1
0
1
0
1
1
1
2
1
2
1
1
1
0
2
2
0
1
0
1
1
1
1
2
1
1
1
1
1
0
2
1
1
0
2
1
0
1
1
1
1
2
1
1
1
0
0
1
1
1
1
1
1
1
1
0
0
1
0
1
1
0
1
1
1
0
2
0
1
1
1
1
2
1
1
1
1
1
0
1
0
1
2
0
1
1
2
2
1
2
1
2
1
2
1
1
1
0
1
0
2
2
1
1
1
0
1
1
1
1
1
2
0
1
1
1
1
0
1
2
1
2
2
2
1
0
1
2
1
2
1
2
0
1
2
0
0
1
1
1
0
3
1
1
2
2
2
1
1
1
2
1
2
1
1
1
1
0
3
1
3
1
2
2
2
1
2
1
2
1
0
2
0
1
2
1
1
0
2
1
2
1
1
2
1
1
1
1
1
1
1
0
1
1
1
0
1
2
2
1
1
1
1
1
0
2
2
1
1
2
1
2
2
2
0
0
1
2
1
2
2
2
1
0
1
0
0
2
1
1
2
1
1
2
1
1
1
1
1
1
2
1
1
2
2
0
1
2
1
2
0
1
1
1
0
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
0
2
1
1
2
1
2
1
2
1
1
0
2
1
2
2
2
1
1
1
1
2
2
1
1
1
1
1
1
1
0
2
1
1
2
4
1
1
0
0
0
2
1
0
1
1
1
1
2
1
1
2
2
1
1
1
2
0
2
2
2
1
0
1
1
0
1
1
1
1
2
0
1
0
1
1
1
0
1
0
1
1
1
2
1
0
1
1
1
1
0
0
1
0
2
1
1
1
0
2
1
1
2
0
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
0
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
0
2
1
1
2
0
1
1
1
1
1
0
0
2
2
2
0
2
2
1
0
1
1
1
1
2
2
1
1
0
1
1
2
1
0
1
2
1
1
1
1
1
1
1
0
1
1
2
1
2
2
2
1
2
1
2
1
1
1
1
0
1
2
1
1
0
2
1
0
1
1
1
1
1
1
1
2
2
1
1
0
1
1
0
1
1
1
1
1
1
1
1
1
2
0
0
1
0
0
1
2
2
2
1
2
2
1
1
2
1
1
1
1
1
1
2
2
2
1
1
0
1
1
1
2
2
1
0
2
1
2
2
2
0
0
1
1
1
1
1
1
1
1
1
2
1
1
1
2
0
1
1
1
1
1
1
1
0
1
2
1
1
2
1
0
1
1
2
1
1
1
1
1
1
1
1
1
1
0
2
1
1
2
1
1
1
2
0
1
2
1
1
1
2
0
1
1
1
1
1
1
2
1
2
2
2
2
1
1
1
2
1
1
1
2
1
1
2
1
1
2
1
1
1
2
1
1
3
2
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
0
1
1
1
1
1
1
1
0
1
1
1
1
2
2
1
0
0
2
0
1
1
1
1
1
0
1
1
3
0
2
1
3
1
1
1
1
0
1
1
1
1
2
2
1
0
1
2
1
1
2
2
1
1
1
1
2
0
1
1
0
2
1
0
0
1
2
1
2
1
2
2
1
1
1
2
2
2
1
1
1
1
1
1
1
2
0
2
1
1
1
1
1
0
1
1
2
2
1
2
2
2
1
1
2
1
0
1
2
0
1
0
1
2
1
1
2
2
2
1
1
0
1
0
1
0
2
0
1
2
2
1
0
2
1
2
2
1
2
2
1
1
1
1
0
1
2
1
1
0
1
1
1
0
1
1
1
0
1
2
1
2
1
0
1
1
0
1
0
2
1
1
1
0
1
2
2
1
1
1
1
1
1
2
0
0
2
1
0
2
1
0
0
1
1
0
1
1
2
1
1
2
1
1
2
1
1
0
2
1
2
0
0
1
1
1
0
1
1
1
2
0
1
0
1
1
0
2
2
1
1
2
0
1
1
1
2
1
1
2
1
1
1
2
1
1
2
1
1
1
0
1
1
1
1
1
1
0
1
0
2
1
1
1
2
2
1
2
1
1
1
1
1
1
1
2
2
0
0
2
1
2
0
0
0
1
2
1
1
1
1
1
2
1
2
0
1
2
2
1
1
1
1
1
1
1
1
1
2
0
1
2
0
2
2
2
1
1
1
1
2
1
1
0
2
0
0
2
1
1
2
1
2
2
1
2
1
2
1
1
0
1
0
1
1
3
1
2
0
1
1
2
1
0
1
0
1
2
1
1
2
0
3
1
0
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
0
2
1
1
0
2
1
0
0
1
1
1
0
1
0
2
1
1
2
1
2
1
1
2
1
1
2
1
2
1
2
2
0
0
1
2
0
2
2
1
2
1
0
1
1
1
1
1
1
1
1
1
0
1
1
1
1
2
0
2
1
1
2
1
1
0
1
0
1
0
2
1
0
1
2
1
0
0
2
1
2
1
0
2
1
1
0
1
2
1
1
0
0
2
1
2
1
2
2
0
1
2
1
0
2
1
2
1
2
2
3
2
0
2
2
1
1
1
1
1
1
1
3
1
1
1
1
0
1
0
1
1
0
1
1
2
2
0
2
2
1
1
2
1
1
1
1
1
2
1
1
1
1
0
1
1
2
1
2
2
1
2
1
0
2
1
2
0
1
2
1
1
1
1
2
0
2
2
1
1
1
0
2
1
1
2
1
1
2
1
1
0
1
1
2
1
1
1
2
5
2
0
1
2
1
1
2
1
2
0
1
2
1
1
2
1
2
1
1
2
1
1
1
0
1
2
1
2
1
1
0
1
1
0
1
1
1
1
2
1
1
1
2
1
0
1
2
2
0
0
1
1
2
1
1
0
2
1
2
0
1
2
1
1
2
2
0
0
1
1
1
1
0
1
1
1
1
1
1
1
1
2
2
2
1
1
1
2
2
1
1
1
1
2
1
1
0
0
0
2
1
1
1
1
2
1
1
0
0
1
0
2
0
0
0
1
0
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
4
2
2
1
0
2
0
1
1
1
1
1
2
2
0
1
1
1
2
1
1
0
1
2
1
3
1
1
1
1
2
1
1
1
0
1
1
0
1
2
2
1
2
1
1
1
1
1
1
1
0
1
1
3
2
1
1
0
1
2
1
0
2
0
1
1
2
1
2
1
1
2
1
1
1
1
1
0
1
0
1
0
2
1
1
1
2
2
1
1
2
2
1
1
1
2
2
2
1
1
1
1
1
1
1
0
0
7
1
1
0
1
1
2
2
1
1
1
1
0
2
1
1
2
1
0
1
1
0
2
1
1
1
1
1
1
2
2
1
2
0
0
0
1
1
1
1
1
1
1
2
1
0
1
1
2
1
1
1
1
2
2
0
1
2
1
1
1
3
1
1
1
0
1
1
1
2
1
1
0
1
1
2
1
1
1
2
0
1
1
1
1
1
1
2
3
2
2
3
2
1
1
1
2
1
1
1
1
1
2
1
3
1
2
1
1
1
1
0
2
2
1
0
1
1
2
2
1
1
1
1
1
1
2
2
1
2
1
1
1
0
1
2
1
1
1
0
1
1
1
1
1
1
2
1
2
1
0
2
2
0
1
1
1
2
1
1
1
2
2
1
0
2
2
0
1
1
1
1
1
1
2
1
2
1
2
1
0
2
2
1
1
1
1
1
1
1
1
1
2
0
1
2
1
1
2
2
0
2
1
1
0
0
2
1
1
1
1
2
2
0
1
1
2
1
1
2
2
1
1
1
1
1
1
1
0
0
1
2
1
1
1
1
0
1
1
0
1
1
1
2
1
2
1
2
0
2
3
1
2
1
1
1
1
1
1
2
0
1
2
2
0
2
1
1
1
3
1
1
0
1
1
1
1
0
2
2
0
0
2
1
2
1
2
1
1
1
1
1
0
1
1
1
1
1
2
1
1
1
0
1
2
1
1
1
1
2
0
1
0
1
2
1
1
1
1
1
1
2
0
0
1
1
1
0
2
0
2
1
0
1
2
1
1
1
1
1
0
0
1
1
1
1
0
2
1
1
1
0
1
1
2
0
2
2
1
1
1
2
2
1
1
2
1
0
1
2
0
1
2
1
1
1
1
1
2
1
2
2
0
1
1
1
1
1
1
1
1
1
0
1
1
1
2
2
1
2
1
1
1
1
2
2
1
1
2
0
1
1
0
1
0
0
1
1
1
1
1
2
1
1
2
1
1
0
0
2
1
1
2
2
1
1
1
1
1
1
1
1
1
2
1
0
1
1
1
1
1
1
1
2
2
1
1
1
1
2
2
2
0
1
0
0
0
1
2
2
0
1
0
0
1
1
1
0
2
0
2
2
0
1
1
2
1
1
2
1
2
0
1
3
1
1
2
1
1
1
1
0
1
2
1
2
0
0
1
2
1
2
1
2
1
0
1
1
2
1
0
0
1
1
2
1
1
0
2
0
1
2
1
1
1
2
1
2
2
0
1
1
0
1
1
1
0
1
1
1
1
2
1
1
0
1
1
1
0
2
1
2
1
0
0
0
0
1
2
1
1
0
1
1
1
1
2
1
1
1
1
0
1
1
1
2
1
1
1
1
1
2
1
1
0
0
1
1
1
1
0
2
1
2
0
1
1
0
0
2
1
1
1
0
1
1
1
1
1
2
1
2
2
1
1
1
2
1
0
2
2
1
1
1
1
1
1
1
1
1
2
0
2
1
1
1
2
0
1
1
1
2
2
1
0
1
2
1
1
2
1
1
2
1
1
1
1
2
1
0
1
1
1
0
1
2
2
1
1
1
1
1
1
2
1
1
0
0
1
0
1
1
1
2
1
2
1
0
1
1
0
1
1
2
2
3
2
1
2
1
2
0
2
0
1
1
1
1
2
0
2
0
1
1
1
2
0
2
1
2
2
3
2
0
1
2
1
0
2
3
2
1
0
1
1
1
2
1
1
2
1
1
1
1
1
1
0
1
1
2
1
1
2
1
2
1
1
0
0
0
1
1
1
0
1
1
1
1
1
1
2
2
1
1
1
1
2
1
0
1
2
2
1
2
1
2
0
1
2
1
1
1
1
2
1
1
1
2
2
0
1
3
2
1
1
1
1
1
1
1
1
0
1
2
0
0
1
0
0
2
1
1
1
0
1
2
1
1
2
2
1
1
1
0
0
0
1
1
0
1
2
2
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
2
2
2
1
0
2
1
0
1
1
1
1
2
1
1
1
1
1
0
1
1
2
2
2
1
1
2
1
1
1
2
2
1
0
1
1
2
2
0
2
1
2
1
0
2
2
1
2
2
1
0
1
2
1
1
1
1
1
2
2
2
2
1
0
2
2
2
1
1
1
1
0
2
2
2
1
1
1
0
1
2
1
2
1
2
1
1
0
1
1
1
1
2
2
2
7
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
0
0
1
1
1
2
1
1
1
1
1
2
0
2
1
1
1
2
1
2
1
1
2
1
1
1
2
1
1
1
1
1
0
1
2
1
1
0
2
1
1
1
2
1
2
1
0
2
1
1
2
1
1
0
1
1
1
1
2
2
2
1
0
2
1
1
2
1
2
0
1
1
1
2
1
0
1
1
1
2
1
1
0
1
1
1
1
1
1
1
0
0
1
1
1
0
1
1
1
1
1
0
1
1
1
1
2
2
2
1
2
1
0
2
1
1
2
0
1
1
1
1
1
1
2
2
2
0
1
2
2
0
1
0
2
0
0
1
2
1
1
1
2
1
1
0
1
0
2
2
1
1
1
1
2
0
1
1
0
2
2
1
0
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
0
1
1
1
0
2
1
2
1
1
1
1
1
1
2
1
2
2
1
2
2
1
1
1
2
1
1
1
1
0
0
1
1
1
0
2
0
1
0
1
2
0
1
1
0
3
1
1
1
1
2
1
1
1
1
0
2
1
2
1
1
1
1
0
1
1
0
0
1
1
2
2
1
1
2
2
1
1
1
2
1
1
1
1
1
2
1
1
1
1
2
0
1
1
1
1
1
1
1
1
2
2
2
1
0
2
1
0
1
1
1
1
1
2
1
2
0
1
0
1
1
1
1
0
2
1
0
1
0
1
1
2
1
2
1
2
1
2
1
1
1
1
1
1
1
1
0
1
0
1
1
1
0
2
0
1
0
2
2
2
1
0
1
1
1
0
1
0
1
0
2
2
1
2
1
1
1
1
2
2
1
1
1
0
0
0
1
1
0
2
0
2
2
2
1
2
2
1
2
1
1
0
1
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
2
1
1
1
1
0
1
1
1
1
1
1
2
1
2
1
1
1
1
1
2
2
1
1
3
1
2
1
1
2
1
1
2
0
1
1
0
2
2
0
2
1
2
1
1
1
1
1
1
1
1
1
1
0
1
1
1
0
1
1
1
1
0
1
0
1
1
2
1
1
1
1
1
1
1
1
0
2
1
1
2
2
1
1
1
2
1
2
1
2
1
1
0
0
2
1
2
1
1
1
0
2
2
1
1
2
1
2
2
1
0
1
1
0
1
1
0
1
1
1
0
0
1
2
1
1
1
1
1
2
1
2
1
2
1
0
1
2
1
1
2
1
1
1
1
1
0
1
1
1
1
1
2
2
1
2
1
1
0
1
1
1
1
1
1
1
0
1
2
1
1
1
0
1
1
2
1
0
1
1
1
2
1
1
3
0
2
1
1
1
1
1
1
1
2
1
0
1
2
1
1
1
2
1
1
1
1
1
0
2
1
0
1
0
0
1
1
2
2
1
1
0
0
2
1
0
1
0
1
1
1
0
1
2
1
1
0
0
2
1
0
1
0
1
1
1
2
2
0
1
3
1
0
1
1
1
1
1
1
1
1
3
1
0
1
1
1
1
1
1
1
1
0
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
0
1
2
1
0
2
2
1
1
0
1
1
1
0
1
0
1
1
4
2
1
1
2
1
1
1
0
1
0
1
0
1
1
1
1
0
1
2
1
2
1
0
1
2
1
2
1
2
1
1
3
1
2
1
0
1
1
1
1
1
1
0
1
1
1
2
1
1
1
2
1
2
2
0
0
0
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
2
1
2
1
2
1
1
2
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
0
1
1
0
1
1
2
1
1
1
1
1
1
6
0
0
2
0
1
2
2
0
2
2
2
0
1
1
1
0
2
2
1
1
0
2
1
1
1
2
0
1
2
1
1
2
2
1
1
2
1
2
1
1
1
2
1
1
2
1
1
2
1
1
1
1
1
2
1
1
0
0
2
2
1
2
1
1
1
2
1
0
1
1
0
1
1
2
0
1
1
0
1
1
1
1
1
2
0
1
2
1
1
1
1
1
2
1
2
1
2
1
1
0
1
0
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
0
1
1
1
2
2
2
2
1
0
1
0
2
1
1
1
0
1
1
1
2
1
0
1
2
1
2
1
1
0
1
0
0
0
2
1
1
1
1
1
2
1
1
2
0
1
1
2
0
0
2
1
1
2
2
2
2
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
0
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
2
1
2
1
2
1
0
1
1
0
1
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
0
2
2
1
1
1
1
1
1
1
1
0
1
1
1
2
1
2
2
2
1
1
2
1
1
1
0
1
2
1
1
3
1
0
1
1
0
1
0
1
1
2
2
2
1
0
1
1
1
1
2
0
1
1
0
1
1
2
1
1
1
4
2
1
2
1
1
1
1
0
0
0
1
1
1
0
1
1
1
2
2
1
2
1
1
2
2
1
2
3
0
2
0
1
1
1
0
2
0
1
1
0
1
2
2
1
0
2
1
0
1
2
1
2
1
1
2
1
1
1
1
1
1
1
2
1
0
1
1
1
1
2
0
1
1
1
0
2
1
1
1
1
2
2
1
1
1
2
1
1
2
1
1
1
0
0
1
0
1
1
2
1
1
2
1
0
2
1
1
1
1
1
1
1
1
0
2
1
2
1
2
2
1
2
1
1
1
1
1
2
2
2
1
2
1
1
1
2
1
0
0
1
0
1
2
1
1
2
1
1
1
2
0
1
2
1
2
2
2
2
1
1
1
1
1
1
0
1
1
1
2
1
2
1
0
1
1
1
0
2
1
1
2
1
2
1
1
1
1
1
1
1
0
1
1
2
0
1
2
2
1
1
1
1
1
1
2
1
2
0
1
2
1
1
2
1
1
1
1
1
2
2
2
0
2
1
0
1
2
1
2
1
0
1
1
1
1
1
0
1
1
2
1
1
1
0
1
0
1
1
1
1
2
1
1
0
1
0
1
1
1
1
2
2
1
1
2
2
0
1
1
1
1
2
2
1
1
1
1
0
1
1
2
1
0
1
0
1
1
1
1
1
2
2
0
1
0
1
0
1
1
1
1
1
1
0
1
1
1
1
1
2
2
1
0
1
1
2
2
1
1
0
1
1
2
2
1
1
1
1
2
1
2
1
1
1
1
1
0
2
1
1
2
1
1
1
2
1
1
1
1
1
0
0
2
1
2
1
2
1
0
1
1
3
2
1
2
0
0
0
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
2
1
2
2
2
1
1
0
1
2
1
1
1
1
0
1
0
1
1
1
1
1
1
1
2
1
1
0
1
1
1
2
0
1
2
1
2
1
1
1
1
1
0
0
1
1
1
1
1
2
1
1
2
2
1
1
1
1
1
2
1
1
1
0
0
1
1
1
1
2
1
1
2
2
1
1
1
2
1
0
2
1
0
2
2
1
1
2
1
0
1
0
1
2
1
1
1
2
0
1
1
1
0
1
1
0
1
2
1
1
0
2
1
2
2
2
1
2
1
0
1
1
1
2
0
1
1
1
0
1
0
0
1
1
1
1
0
1
0
1
1
1
1
0
1
1
1
1
1
1
2
2
1
1
1
2
2
2
1
0
1
0
1
2
1
2
2
2
1
0
1
2
0
1
2
1
0
1
1
1
0
1
2
1
0
3
1
1
2
1
1
1
0
0
1
2
1
0
1
1
1
1
2
1
2
1
2
1
1
1
2
0
2
2
2
2
1
1
2
1
1
1
1
1
2
0
1
2
2
1
1
0
1
2
2
1
1
2
1
1
1
1
1
1
1
2
2
0
1
0
2
1
1
1
1
1
1
1
2
1
1
1
0
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
2
0
1
1
1
2
1
2
0
1
1
1
1
1
1
2
2
2
1
1
0
1
0
1
2
1
1
1
1
1
1
0
1
1
2
1
2
1
1
1
1
1
1
0
2
1
1
1
0
1
1
1
1
1
1
1
1
1
2
2
2
1
0
2
2
1
1
1
2
1
2
2
1
2
1
2
1
2
1
1
1
0
1
1
2
1
2
1
1
0
2
1
2
1
1
1
2
0
2
0
1
1
1
1
1
2
1
0
1
1
0
1
1
1
1
0
2
1
1
1
1
1
1
2
2
1
0
2
1
1
1
1
0
1
2
2
2
2
2
0
1
1
2
0
0
2
2
0
2
2
2
1
1
1
1
1
1
3
2
2
1
1
1
1
2
1
0
1
1
2
1
0
1
2
0
1
2
1
1
1
1
2
0
1
1
1
0
1
1
2
1
1
1
2
1
0
1
1
1
1
1
2
1
1
2
2
1
0
0
1
1
2
1
1
1
2
2
1
2
1
1
0
1
1
0
1
2
2
1
0
0
1
1
1
0
2
1
1
1
1
1
1
1
1
1
0
1
2
2
2
1
1
1
1
2
2
2
1
0
1
0
2
1
1
1
0
10
1
1
0
0
1
1
1
0
1
1
1
1
2
1
2
2
2
0
1
1
1
2
1
1
1
1
1
1
1
1
2
0
2
1
1
1
1
1
1
1
1
2
1
0
1
1
1
2
2
2
1
1
2
2
1
1
1
2
1
1
2
1
1
1
1
2
1
1
2
0
1
1
2
0
0
2
2
2
1
0
2
0
0
1
1
1
1
0
1
0
1
1
0
0
1
2
1
1
1
1
1
0
0
1
1
2
1
2
1
2
0
1
0
1
1
1
1
2
2
1
1
1
0
0
1
0
1
1
1
1
0
2
2
1
1
1
0
2
1
0
0
1
1
1
1
1
1
1
1
1
1
2
1
0
0
1
2
1
1
1
1
1
1
1
2
1
0
1
2
4
2
1
2
1
1
1
2
0
1
2
2
2
1
1
1
2
1
1
2
2
2
2
0
1
1
2
1
1
0
2
1
1
1
0
2
0
1
1
1
0
0
1
0
0
1
1
2
1
2
1
1
1
2
1
1
0
2
1
1
2
1
1
0
1
2
2
0
1
0
1
2
1
2
1
1
1
1
0
1
2
1
1
1
1
1
1
2
1
5
1
2
1
2
1
1
1
0
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
1
1
2
1
1
0
1
1
1
2
2
1
0
1
1
2
1
1
1
1
4
1
1
0
0
2
0
1
1
1
2
2
1
1
0
1
1
1
1
0
1
2
2
1
0
1
1
1
1
1
2
2
2
1
2
1
1
1
2
1
2
1
1
1
1
1
0
2
2
1
1
1
2
1
1
1
1
1
2
0
1
2
1
2
1
2
1
2
1
1
1
1
0
1
1
2
2
1
1
2
1
2
1
1
1
2
2
2
1
0
1
2
1
1
1
1
1
1
1
0
1
0
1
1
1
0
0
2
1
1
1
1
0
1
1
1
1
2
1
1
0
0
1
0
0
2
1
1
2
2
1
2
2
1
1
1
2
0
2
1
1
0
2
1
2
1
1
1
2
1
1
0
1
0
1
2
0
1
1
1
0
1
1
1
0
0
0
1
0
1
1
1
1
2
1
0
1
0
1
1
1
1
1
1
1
1
1
2
2
2
2
0
1
1
1
0
1
0
2
0
2
1
1
2
0
2
1
2
2
1
1
1
2
1
0
1
1
2
2
1
2
0
1
0
0
1
0
0
1
0
1
1
0
1
1
1
2
1
1
1
0
1
1
1
1
1
1
1
1
2
1
2
0
1
1
2
1
2
2
1
1
1
1
1
0
1
0
2
2
1
1
1
1
2
1
0
1
2
1
2
1
2
2
1
1
1
2
1
1
1
2
1
0
1
1
1
2
1
1
1
1
0
1
2
2
1
1
1
1
1
0
2
2
1
1
1
1
1
0
2
2
0
0
0
1
2
1
0
2
1
1
1
1
1
2
0
0
1
0
1
1
1
1
2
1
1
1
1
2
0
2
1
0
1
1
1
2
0
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
3
2
0
2
1
2
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
0
2
1
1
1
1
2
1
1
1
2
1
2
2
1
3
1
1
1
1
1
1
0
2
0
1
1
1
1
1
1
1
1
1
0
1
1
1
0
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
2
1
1
2
1
1
1
2
2
2
1
2
2
1
1
1
1
1
1
1
1
1
0
1
1
1
0
1
1
1
1
2
1
1
1
2
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
0
2
1
2
2
1
0
0
1
2
1
0
0
2
0
0
1
0
1
1
1
0
2
2
0
1
1
1
1
1
1
0
1
0
1
0
1
1
1
4
1
0
5
1
1
2
1
2
1
1
1
1
0
1
1
3
2
1
2
0
1
1
2
1
2
1
1
0
1
1
2
0
1
1
1
2
0
0
1
0
2
1
0
0
1
2
0
0
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
2
1
1
2
1
2
1
1
3
2
1
1
1
1
1
0
1
2
1
1
1
1
0
0
2
1
2
1
1
1
1
1
1
0
1
1
1
1
1
1
0
1
1
1
1
1
2
0
1
2
1
2
2
0
1
1
1
1
1
2
1
2
1
1
1
0
0
1
1
3
1
1
0
1
2
0
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
0
2
1
1
2
1
1
0
1
2
2
1
1
0
1
1
1
0
1
2
1
1
1
2
1
2
1
1
1
0
1
0
1
0
0
1
1
0
1
1
0
1
0
1
1
2
1
0
1
1
1
1
0
1
1
1
1
2
1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
0
1
2
2
1
2
1
1
2
2
1
1
1
3
2
0
1
0
1
2
1
1
1
1
0
1
0
1
1
2
0
2
2
1
2
1
1
1
0
1
2
0
1
1
1
0
0
1
0
2
2
1
1
1
1
1
2
1
1
0
1
2
1
1
1
0
1
1
1
1
0
2
1
1
0
0
1
1
1
2
0
1
1
1
2
1
1
1
1
1
1
1
0
1
1
1
1
2
0
1
1
2
1
2
1
2
0
1
0
1
0
1
1
1
2
1
2
1
0
1
0
2
1
0
1
1
2
1
1
2
2
1
2
0
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
2
1
2
2
1
0
1
1
1
1
1
1
1
1
1
1
0
2
1
1
1
0
2
2
0
1
2
1
2
1
2
1
0
1
1
1
0
1
1
1
0
1
0
2
1
1
1
2
0
2
2
1
4
1
1
2
0
2
1
1
1
1
1
0
1
1
0
2
2
1
1
1
1
0
1
1
2
1
0
1
2
1
0
1
0
1
1
1
1
1
2
1
1
2
1
1
0
0
2
1
1
2
1
1
1
2
1
1
1
0
1
0
1
2
1
1
2
1
2
1
1
2
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
2
0
1
1
1
1
1
2
1
1
1
0
2
1
2
1
2
0
1
1
1
2
2
2
1
1
1
1
0
1
1
2
2
2
2
1
1
1
2
1
2
1
1
0
0
0
1
1
2
0
2
1
2
1
0
1
0
0
1
2
1
1
1
0
2
1
0
1
1
1
1
2
0
1
2
1
1
1
1
1
2
1
1
0
2
1
2
1
1
1
0
2
0
1
1
1
1
1
1
1
2
1
0
1
1
2
1
1
2
1
2
2
0
2
1
1
1
1
1
1
1
1
1
2
0
1
1
1
2
1
1
1
7
2
1
1
1
2
1
1
1
1
2
1
2
1
1
0
0
1
1
1
1
1
2
1
1
0
1
1
1
1
0
0
1
2
0
1
2
2
0
2
1
0
1
2
1
2
0
2
1
1
0
1
1
1
1
0
0
2
1
1
1
0
1
1
1
1
1
1
0
2
1
2
1
1
0
0
2
2
1
2
1
1
1
2
0
2
1
2
1
1
2
1
1
1
1
1
0
1
0
2
1
1
1
1
2
1
2
0
2
0
0
1
1
2
1
1
1
1
1
1
0
1
1
1
2
1
1
2
1
1
0
1
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
2
1
2
1
0
1
1
0
0
2
1
2
1
1
1
1
0
1
1
1
1
1
1
2
2
2
0
1
1
1
1
1
1
1
1
0
1
2
0
1
1
1
1
1
0
2
1
1
1
1
2
1
2
1
2
2
0
2
1
2
1
2
1
1
0
2
2
1
1
1
0
1
2
1
1
1
1
1
0
1
1
1
1
1
1
1
2
1
2
1
0
1
1
1
1
2
1
1
1
3
2
1
1
1
1
1
0
2
2
2
0
1
1
1
1
1
1
1
2
1
2
0
2
2
1
0
1
1
1
2
0
2
2
1
2
1
2
1
0
2
1
0
1
1
1
1
1
2
1
2
1
2
1
1
2
1
0
2
1
1
1
0
1
2
1
0
0
2
1
2
1
1
1
0
2
2
1
2
1
1
2
1
1
2
1
1
1
2
1
1
2
1
1
1
1
1
2
1
1
2
3
1
1
1
1
2
1
1
1
1
0
1
1
1
2
1
1
1
1
1
0
1
2
1
1
1
1
0
1
2
1
0
0
1
1
2
1
1
1
0
1
1
1
2
1
2
2
2
1
2
2
2
1
1
2
1
0
2
1
2
2
1
0
1
2
2
2
1
1
2
1
0
0
1
1
2
0
1
1
1
1
1
2
2
2
1
1
1
1
1
2
2
0
1
1
2
0
0
1
0
1
1
1
0
2
1
1
2
1
2
1
1
1
2
1
0
1
2
1
0
0
0
2
1
1
1
0
0
2
1
1
1
2
0
2
0
2
0
2
2
1
1
1
1
1
1
2
1
0
1
0
0
1
0
1
1
0
1
1
1
2
1
0
1
1
1
2
0
1
2
1
1
1
1
1
0
2
0
2
1
1
1
0
1
1
2
2
2
1
0
2
1
2
0
1
2
1
1
1
2
1
0
1
1
1
0
2
1
1
1
2
1
1
1
1
2
1
0
2
1
2
2
1
1
1
1
1
1
1
0
1
1
1
1
2
1
1
1
2
1
1
0
2
1
2
0
1
1
1
1
0
2
0
1
1
2
1
0
2
1
1
2
1
1
0
1
1
1
2
2
1
1
1
1
1
2
2
1
1
2
2
2
1
2
1
1
2
2
2
1
1
2
1
2
1
1
2
0
1
1
0
0
2
1
1
1
1
1
2
2
1
1
2
1
1
1
1
1
2
0
1
0
1
0
1
2
2
1
1
1
0
1
2
1
1
2
1
0
2
1
0
2
1
1
0
2
2
2
2
0
2
0
0
1
0
1
1
1
0
1
2
0
1
1
1
0
2
2
0
1
0
2
0
2
2
1
1
1
5
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
2
1
2
2
0
2
1
2
1
1
1
2
1
1
1
1
1
0
1
1
2
1
0
1
0
1
1
0
1
1
1
0
1
2
1
1
1
1
0
1
2
1
1
2
1
1
2
1
1
2
1
1
1
2
2
2
1
1
0
2
2
2
1
1
1
1
2
1
2
2
1
0
2
1
1
0
1
1
0
1
0
2
1
1
1
2
1
0
2
1
1
1
1
2
2
1
0
2
1
1
1
2
1
2
1
1
1
0
1
1
1
2
1
2
1
1
2
1
2
2
1
1
1
0
1
2
2
1
2
2
0
2
1
1
1
1
2
1
1
1
0
2
1
1
1
1
0
2
2
1
1
2
0
1
0
1
1
1
1
0
1
2
1
2
0
1
1
1
1
2
1
2
1
2
1
0
2
0
1
2
1
1
1
0
0
1
0
1
1
1
1
1
1
1
1
2
2
1
1
1
2
1
1
3
1
1
1
0
1
3
1
1
1
1
1
1
0
1
1
2
0
1
1
1
0
4
1
2
2
1
2
1
0
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
0
0
1
0
1
2
1
1
0
2
2
0
1
2
0
1
1
2
2
1
1
1
1
2
2
0
1
1
0
1
1
1
2
1
1
0
0
1
2
1
2
2
1
1
1
0
2
1
1
1
1
1
1
1
1
2
2
1
3
1
2
1
0
1
2
2
2
2
1
1
3
1
1
0
2
1
0
1
1
0
2
1
1
1
0
1
1
1
2
1
2
1
2
1
2
0
0
1
1
1
1
0
1
1
1
1
2
2
1
1
1
1
0
1
0
1
2
1
1
1
1
0
2
2
1
1
0
1
1
2
1
2
2
1
1
1
1
1
1
1
1
0
1
1
0
0
1
1
1
1
2
1
0
2
0
1
1
0
1
1
1
2
1
1
1
1
1
1
2
1
0
1
1
1
1
2
1
1
2
1
1
1
0
0
1
1
2
2
2
1
1
1
1
2
0
2
0
2
1
1
1
2
1
2
1
0
1
0
1
1
1
1
0
1
1
0
2
1
1
0
1
1
1
0
1
0
1
1
1
1
1
1
1
1
0
1
2
2
1
1
0
0
1
1
2
0
1
1
2
1
1
1
2
1
2
1
2
0
1
2
1
1
2
1
2
1
2
2
2
1
1
3
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
2
1
0
1
2
0
2
2
1
1
1
0
1
2
3
0
1
1
0
1
2
1
2
1
1
1
1
1
0
0
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
0
1
1
1
1
2
1
1
1
2
1
0
1
2
2
1
2
2
1
2
2
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
1
0
1
2
1
1
2
1
1
0
1
2
1
0
2
1
1
1
2
1
1
0
1
0
1
1
1
0
0
1
1
1
2
1
2
2
2
1
1
1
1
2
1
1
2
2
0
2
1
1
1
1
2
1
1
1
2
0
1
1
1
1
1
1
1
1
1
1
0
0
1
1
1
3
2
2
1
0
1
2
1
2
1
0
1
2
1
0
2
1
2
1
1
1
1
1
1
0
2
1
0
1
1
1
1
0
1
1
0
2
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
0
1
1
3
1
1
2
0
1
2
2
2
2
2
1
1
2
1
1
0
2
1
1
1
2
1
2
2
1
1
1
1
2
2
1
1
2
1
2
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
3
1
1
1
1
1
1
1
2
2
0
1
2
1
1
0
0
1
0
0
2
6
0
2
1
1
2
1
0
1
1
2
0
1
0
2
0
1
1
2
1
1
0
2
2
2
1
1
0
1
0
1
2
1
2
1
1
3
1
1
2
1
2
2
1
2
1
1
1
0
1
1
0
1
1
1
1
2
1
1
2
1
1
1
1
2
0
2
0
2
1
2
1
1
0
1
1
0
2
2
1
2
1
2
1
2
2
2
1
2
1
0
1
2
2
1
1
1
2
1
2
0
0
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
0
1
2
1
1
1
0
0
2
1
2
0
0
1
0
1
1
1
1
0
1
2
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
2
2
1
2
1
1
3
1
0
1
2
2
1
2
2
2
1
1
1
2
1
2
0
1
1
2
1
2
1
1
1
2
1
1
2
1
0
0
0
0
1
1
0
1
1
1
1
1
1
2
1
1
1
1
2
0
1
2
1
0
1
2
2
2
1
2
0
1
1
0
1
1
1
0
2
1
2
1
1
2
2
1
1
1
2
1
0
1
2
1
1
1
0
2
1
0
2
1
0
2
1
1
2
1
2
1
2
1
1
1
1
2
0
1
1
1
1
1
1
1
0
1
1
0
1
1
0
1
0
1
0
2
1
1
1
2
2
1
1
1
1
1
2
1
0
2
1
2
1
2
1
0
0
1
1
1
1
1
2
1
1
1
0
1
2
1
2
1
2
1
2
2
2
0
1
1
1
2
1
0
0
1
1
0
1
1
0
2
0
2
2
0
2
1
1
1
1
1
2
4
2
0
1
2
0
1
1
1
1
1
2
0
2
0
1
3
1
1
0
2
1
1
1
1
0
1
2
1
1
2
2
1
2
2
1
0
2
1
1
2
1
2
0
1
2
0
1
2
0
0
2
1
2
1
1
1
1
0
0
1
2
1
1
1
1
0
2
1
1
1
3
1
1
1
1
0
0
1
2
1
2
1
0
0
1
2
2
1
1
2
0
1
2
1
1
2
0
2
1
0
2
1
1
2
1
1
1
2
1
2
1
1
1
2
0
1
2
1
1
1
1
1
1
2
0
2
0
1
1
1
1
1
2
1
0
0
1
1
1
0
1
2
1
1
2
2
0
1
1
2
2
0
1
1
2
1
0
2
2
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
2
2
2
2
2
2
2
1
0
0
0
2
1
1
1
2
1
1
2
2
0
1
1
1
1
1
1
0
1
1
2
1
1
1
1
1
1
0
2
1
2
1
1
1
1
0
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
0
3
1
2
2
0
0
1
1
0
2
0
0
1
1
1
1
1
0
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
0
1
2
1
1
2
2
1
1
1
2
1
1
0
1
1
1
1
2
2
1
1
1
1
0
0
1
1
0
1
2
1
1
1
1
1
1
1
1
2
2
1
1
1
2
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
0
2
2
1
0
1
1
1
1
2
1
1
1
0
2
1
1
1
1
2
1
1
1
1
1
2
1
0
1
0
1
1
0
2
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
2
0
0
1
1
2
2
2
2
1
0
0
2
1
1
2
1
1
1
1
1
1
0
1
1
2
1
2
0
1
2
1
0
1
1
2
2
1
2
1
1
0
0
1
2
1
2
1
1
1
1
0
1
1
1
1
1
2
2
1
2
1
1
2
0
1
0
1
2
1
1
1
1
1
0
2
1
1
1
2
1
2
2
2
0
2
2
1
0
1
2
0
1
2
1
1
1
1
1
1
2
1
2
1
2
1
0
0
1
2
1
0
2
2
1
1
1
0
0
0
1
1
1
1
1
1
1
1
0
2
2
0
2
1
2
2
2
0
2
1
1
2
1
1
1
1
1
0
2
0
2
1
1
1
1
1
1
1
0
1
1
2
1
1
1
1
1
1
1
1
2
1
0
1
2
2
1
1
1
2
2
1
2
4
1
1
1
0
0
1
1
1
1
2
1
2
0
2
0
0
0
1
1
2
2
1
0
1
1
1
1
1
1
1
1
0
2
1
1
2
1
1
1
1
1
0
2
2
1
1
1
2
1
2
2
2
1
2
1
2
2
1
2
2
0
2
2
2
2
1
2
2
1
2
0
2
1
2
2
1
1
1
1
0
1
2
4
2
1
1
0
1
1
1
1
1
0
2
1
2
1
2
1
1
2
2
0
2
1
1
1
1
0
1
1
1
1
2
1
2
0
2
1
1
1
1
2
0
0
2
0
2
1
1
1
2
1
1
1
1
1
0
1
1
1
2
1
2
1
1
1
2
1
2
1
2
1
2
2
1
1
2
2
1
1
1
1
2
1
2
1
1
1
2
0
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
0
1
0
2
2
1
2
1
1
2
1
1
1
0
2
1
1
1
2
2
1
1
1
2
1
1
2
0
2
1
1
1
1
1
1
1
1
1
0
1
0
1
1
0
0
1
2
1
1
2
1
2
0
2
1
1
1
1
1
0
1
2
1
2
0
2
2
2
1
2
1
0
0
1
1
1
1
1
1
0
1
2
0
1
1
1
1
2
2
1
1
1
2
1
2
2
1
1
1
0
0
1
1
2
0
2
2
1
1
1
1
1
0
1
1
1
2
2
0
1
1
1
1
0
1
1
1
0
2
1
0
1
1
1
2
2
0
1
1
1
1
2
1
2
1
1
0
1
1
1
1
1
1
1
0
1
1
1
2
1
2
1
1
1
1
2
1
1
1
0
1
2
2
2
1
2
3
0
1
2
2
1
2
1
1
1
1
1
1
0
1
2
2
1
1
0
2
1
2
1
1
2
2
2
1
1
1
1
0
1
1
1
1
0
2
0
2
0
2
1
1
2
0
2
1
2
1
0
1
1
2
0
2
1
2
1
2
0
1
1
1
1
1
1
1
1
1
0
1
2
1
1
3
2
1
1
0
1
1
2
1
0
1
0
1
1
3
0
1
1
1
1
1
2
2
2
1
2
2
1
2
2
1
1
0
1
1
1
1
2
2
1
1
1
1
2
2
1
1
2
1
2
0
0
1
1
1
0
1
0
1
2
2
1
2
1
1
1
2
1
2
0
1
1
1
1
1
0
1
0
0
1
2
1
2
1
2
1
1
1
1
2
1
2
1
2
2
1
1
0
0
0
1
1
0
1
1
1
0
0
1
1
1
2
0
0
1
1
1
2
0
1
0
2
2
1
1
1
1
1
2
1
2
2
1
2
1
0
1
2
1
1
0
1
0
0
1
2
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
2
0
1
1
1
1
2
2
1
1
2
2
3
1
2
1
1
1
1
1
1
0
1
0
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
2
1
2
2
1
1
2
0
1
2
1
1
1
1
1
1
2
1
0
1
0
0
1
1
1
1
1
1
1
1
1
0
2
1
1
2
1
1
1
1
0
1
1
2
1
0
1
1
1
1
2
2
1
1
1
0
1
1
1
0
0
2
1
1
2
1
0
0
1
2
1
0
1
0
0
2
2
2
1
2
1
1
0
2
2
0
2
0
1
2
1
2
1
1
1
2
1
1
0
1
1
1
1
1
0
1
2
0
1
0
2
1
1
1
1
2
2
1
2
1
1
1
2
2
1
1
1
1
1
2
1
2
2
0
1
1
1
1
1
0
1
1
1
1
1
1
1
1
2
0
0
1
1
1
1
2
2
0
2
2
0
1
2
1
2
1
1
1
1
2
2
1
1
1
1
1
2
1
2
0
0
1
0
1
1
1
1
1
1
1
1
1
1
2
2
0
0
2
1
1
1
1
1
1
1
1
2
1
0
1
2
1
0
1
1
1
0
2
1
2
0
1
2
1
1
1
0
1
1
1
1
1
0
1
1
1
1
0
1
1
1
1
1
1
1
2
0
2
2
1
2
0
1
1
1
0
1
1
1
1
1
1
2
2
1
0
1
2
1
1
1
1
1
1
1
2
2
1
2
1
2
1
2
0
1
2
2
0
0
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
0
0
1
2
1
2
2
1
1
2
1
1
1
0
0
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
0
0
0
1
1
2
1
1
1
1
1
1
2
2
1
2
1
0
1
0
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
0
1
1
0
2
2
1
1
0
1
1
2
1
1
1
1
2
1
2
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
0
1
2
2
1
1
0
1
1
1
2
2
1
0
1
1
2
2
2
1
2
1
1
1
1
2
2
1
1
1
1
0
1
2
1
1
1
2
1
1
2
2
1
1
1
2
1
0
1
1
1
1
1
1
1
2
1
2
2
1
2
2
1
0
1
2
1
2
0
1
1
2
1
1
2
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
0
2
1
1
2
2
1
1
1
1
0
1
2
1
1
1
0
1
1
1
1
1
1
0
2
1
1
1
1
1
1
2
1
2
1
2
1
0
1
1
2
0
1
3
1
2
1
2
1
2
1
1
2
1
1
0
0
2
1
1
1
2
1
1
1
0
1
0
2
1
0
1
2
2
0
1
2
1
1
2
1
1
1
0
1
0
0
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
0
0
1
1
0
2
1
1
1
1
1
1
2
1
0
1
1
1
1
1
4
1
1
1
1
2
0
1
1
0
2
1
1
2
0
1
1
1
2
2
1
1
0
1
1
2
1
1
1
1
2
2
3
1
1
1
2
0
1
1
1
1
1
1
1
2
0
2
1
1
1
1
2
1
1
1
2
1
2
1
1
0
1
0
1
1
2
1
1
2
2
1
0
1
1
0
1
1
1
1
0
1
1
2
2
1
2
2
1
1
1
2
1
1
2
1
1
1
0
2
1
2
2
1
2
1
2
1
2
1
1
0
2
3
2
2
1
1
1
1
0
2
1
1
1
1
2
0
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
2
1
2
0
0
2
1
0
1
1
1
1
1
1
2
1
1
1
0
0
1
1
2
2
1
0
0
1
2
1
1
1
1
0
0
1
2
1
1
1
1
2
2
1
1
2
2
0
1
1
0
1
1
2
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
0
0
2
0
2
1
1
2
0
2
2
0
1
1
2
1
2
1
1
1
1
0
2
1
1
2
0
2
0
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
2
2
0
1
2
1
1
1
2
0
1
1
0
1
1
0
1
1
1
1
1
1
1
0
1
0
1
1
2
1
1
1
0
1
1
1
0
0
2
0
1
2
0
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
2
2
2
0
1
1
0
1
1
1
1
2
1
1
2
2
1
1
0
2
1
1
1
1
1
1
1
2
1
1
1
1
0
1
1
1
2
1
1
2
1
1
0
1
0
1
0
1
1
1
1
2
0
1
1
0
1
1
1
1
2
2
1
1
1
2
1
1
0
1
1
1
0
0
1
0
1
2
2
1
0
2
2
1
1
1
2
1
1
1
0
1
2
2
1
3
0
2
1
1
1
1
2
0
2
1
2
1
1
1
2
1
1
1
1
1
2
1
2
1
1
2
2
1
1
1
1
0
1
0
1
0
1
1
2
2
2
0
1
1
2
0
2
2
1
2
1
1
2
2
1
1
1
0
0
1
2
1
1
1
1
0
0
1
1
1
1
1
1
3
1
2
1
1
2
0
1
1
2
1
2
1
0
2
2
0
0
2
1
1
1
0
2
1
2
1
1
1
0
1
1
1
1
1
2
2
1
1
1
0
1
1
1
2
2
2
0
1
1
1
1
2
2
2
1
1
0
3
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
2
2
1
0
1
1
1
1
2
1
1
1
1
0
2
1
2
1
1
1
1
2
1
1
1
0
1
2
2
2
2
1
2
1
1
0
1
2
0
1
0
2
1
1
1
2
1
1
1
1
1
2
1
0
1
1
2
1
1
0
0
2
1
1
1
2
1
2
2
1
0
1
1
0
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
2
2
1
1
1
2
1
0
1
1
3
1
1
2
1
2
1
1
1
1
2
1
1
1
0
1
0
2
2
0
2
0
2
0
2
2
2
0
1
1
2
0
1
0
2
0
1
1
1
2
2
1
2
1
2
1
1
1
0
1
1
1
2
1
3
1
1
1
1
0
1
2
1
0
2
2
2
0
2
2
1
2
1
0
1
2
1
3
1
2
2
1
0
2
2
1
2
1
0
1
2
2
1
1
1
1
1
2
1
1
0
1
1
0
2
2
2
2
2
0
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
0
1
1
0
2
1
1
1
1
1
0
1
1
1
1
1
1
1
1
0
1
1
2
1
1
1
2
1
1
1
0
2
1
0
1
1
1
1
0
1
1
1
2
1
1
1
1
0
2
2
0
2
1
1
1
1
0
1
1
2
2
1
1
2
1
1
3
2
1
1
1
1
1
0
1
1
1
2
0
1
1
1
0
2
1
2
2
2
1
2
1
0
1
1
1
1
2
1
1
1
1
2
0
1
1
2
2
1
1
1
1
1
1
1
1
2
0
1
1
1
1
2
2
1
1
2
2
1
2
1
2
1
1
1
2
1
1
1
2
0
1
1
1
1
1
2
1
1
0
1
1
0
0
0
1
1
1
2
1
1
3
1
1
1
2
1
2
2
2
1
1
1
2
1
1
2
1
1
2
1
1
1
2
1
1
2
1
1
1
2
1
1
0
2
1
1
1
1
1
0
1
2
1
1
1
2
1
1
2
0
1
1
1
2
1
1
1
0
2
1
2
0
0
1
2
0
0
1
2
0
1
2
1
2
2
1
1
1
1
1
3
0
1
2
1
2
1
2
1
1
1
0
1
1
2
1
1
1
1
2
2
1
1
1
0
1
1
1
1
0
1
1
1
3
1
1
1
0
0
0
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
0
1
1
2
0
0
1
1
2
2
1
1
1
1
1
1
0
1
2
1
0
1
0
2
1
1
0
1
2
1
1
2
1
1
1
1
2
2
1
2
1
1
1
1
1
0
1
1
0
1
1
1
2
0
2
1
1
1
1
0
1
2
2
1
1
1
1
1
1
1
2
1
0
2
1
3
2
1
2
1
1
1
0
1
1
1
1
1
1
2
2
0
2
2
2
0
1
1
1
1
1
1
1
1
2
1
2
2
1
1
0
1
2
1
0
0
2
1
1
2
1
1
2
0
1
1
2
1
1
1
4
1
1
1
2
1
1
0
2
1
1
0
1
2
2
2
2
1
1
0
0
1
0
0
0
1
1
1
1
2
1
2
2
2
1
1
1
2
1
0
2
1
2
1
2
2
1
1
1
2
1
1
2
1
1
0
1
1
1
1
0
2
1
1
1
0
1
2
2
0
2
1
2
1
0
2
1
1
0
2
1
1
2
2
2
0
1
1
1
0
1
1
3
1
0
1
1
1
1
0
1
1
1
1
1
1
0
1
1
1
1
1
1
1
2
1
1
0
1
2
1
0
0
2
2
1
1
1
2
2
0
2
1
1
1
0
1
2
1
0
2
0
0
2
0
1
1
2
2
3
0
1
1
2
0
2
1
1
0
2
1
2
2
2
1
1
1
1
1
2
2
1
1
1
1
1
2
0
1
1
2
2
0
1
1
2
2
1
1
1
1
1
0
1
0
1
1
2
2
2
1
2
1
1
7
1
2
2
1
2
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
0
0
1
1
1
1
1
2
0
2
1
1
1
2
0
2
1
1
0
1
2
1
0
1
2
0
1
2
2
1
0
1
0
1
1
1
1
1
1
3
0
0
1
2
0
1
1
2
0
1
1
1
1
0
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
0
2
0
1
2
2
1
0
1
1
1
0
1
1
1
1
0
1
2
1
2
2
1
0
2
1
0
0
1
1
1
2
0
1
1
0
1
1
2
1
0
1
0
2
2
1
1
2
2
2
1
1
2
0
2
2
0
1
1
0
1
0
1
1
1
1
1
1
1
1
1
1
2
0
2
1
1
0
1
1
2
2
2
1
1
1
1
1
0
3
2
1
1
1
1
2
2
2
1
0
0
1
1
1
1
1
2
2
2
1
1
0
0
0
1
0
1
1
1
0
1
2
0
0
1
1
0
1
2
2
0
1
1
1
1
1
2
1
2
2
1
1
2
0
2
1
1
1
2
1
1
3
1
1
1
1
0
1
1
0
2
1
1
1
0
1
1
2
2
1
1
2
0
1
1
1
0
1
1
2
1
1
1
1
1
1
1
1
0
0
1
1
2
2
1
1
1
2
3
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
0
1
1
2
0
1
0
1
1
2
1
0
1
2
1
2
2
1
0
1
1
2
1
2
0
1
1
2
1
1
2
0
2
0
1
2
2
1
1
1
1
2
1
1
2
0
1
1
1
2
0
2
1
2
1
1
1
2
2
0
1
1
2
0
1
2
1
1
1
1
1
1
1
0
1
2
1
1
1
1
1
1
0
1
1
1
1
1
2
1
2
0
1
1
2
2
1
1
2
0
0
1
0
1
1
1
1
0
0
2
1
0
1
1
1
1
1
1
1
1
1
2
2
1
2
2
1
0
2
1
0
2
3
1
1
2
1
1
0
2
2
2
1
2
2
2
1
1
1
0
2
1
1
1
0
1
1
0
1
1
1
0
1
0
1
2
1
1
1
1
1
2
2
1
1
0
2
2
1
0
2
2
1
0
1
1
1
0
0
1
1
2
0
0
1
1
1
0
2
3
1
1
0
1
1
1
1
1
2
1
2
1
1
1
1
0
2
1
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
2
2
1
1
3
2
1
2
1
1
1
1
1
1
0
2
1
2
2
2
2
0
2
1
1
1
1
2
2
1
2
1
1
2
1
2
0
1
1
1
2
1
1
2
2
0
1
2
1
1
2
1
2
0
1
2
1
1
2
2
2
1
2
0
1
1
1
2
1
2
1
0
2
1
1
0
0
1
1
1
1
2
1
2
2
2
2
2
1
0
0
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
1
0
2
1
1
1
0
1
0
1
2
1
2
1
1
1
0
1
1
1
1
1
1
2
1
1
2
1
2
1
1
2
2
1
1
1
1
1
0
2
2
2
2
1
1
1
0
1
0
1
0
2
0
1
1
1
2
1
0
1
2
1
1
1
2
1
1
2
1
0
1
1
1
1
0
1
1
1
2
1
1
2
1
2
1
2
1
2
2
0
0
2
1
1
1
2
1
2
2
1
1
2
1
1
1
2
1
0
1
1
1
2
2
0
1
0
1
2
1
1
2
1
1
1
2
2
1
1
1
2
2
1
1
1
1
2
1
0
1
1
1
0
1
2
0
2
1
2
1
1
0
1
1
1
1
1
2
1
1
1
1
2
0
1
0
1
1
1
1
1
1
2
1
0
2
1
1
1
0
1
1
1
2
2
2
1
1
2
2
0
2
0
1
1
0
1
1
1
0
2
1
1
2
1
1
0
0
1
2
0
1
1
1
1
1
2
1
1
1
1
1
2
1
0
1
2
1
1
2
1
1
2
2
0
1
2
1
1
1
2
1
1
1
2
2
0
0
2
2
1
2
1
1
1
1
1
2
1
1
0
1
2
2
1
0
1
2
1
1
1
1
1
1
1
1
1
0
1
1
1
2
1
1
1
1
1
0
1
1
1
0
2
2
2
1
1
2
0
0
0
2
2
1
2
1
0
1
2
1
0
1
0
1
1
0
1
2
0
1
2
1
1
1
0
1
0
2
1
1
1
2
1
1
0
1
1
1
1
2
1
2
1
1
2
0
1
1
2
1
0
1
0
0
2
2
2
2
1
1
0
1
0
0
1
2
1
1
1
1
1
1
2
1
0
1
1
1
0
0
1
1
1
0
2
2
1
1
1
0
0
2
1
1
1
0
1
1
2
2
1
2
0
2
1
1
2
1
1
1
1
0
1
0
2
1
0
1
0
0
1
1
0
1
1
2
0
2
2
0
0
1
1
1
0
1
1
1
1
1
0
1
1
1
2
1
1
0
2
1
1
2
1
0
0
1
1
2
1
1
0
1
0
1
1
2
1
2
2
2
1
1
1
1
0
2
2
0
1
1
1
0
1
1
1
1
2
2
1
1
1
2
0
1
1
2
1
1
1
1
1
1
1
1
1
1
2
2
0
2
2
2
0
2
2
1
0
0
1
2
0
1
2
1
0
0
1
2
0
1
1
2
1
3
1
1
2
1
1
0
0
1
1
1
2
1
1
0
1
1
0
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
1
0
1
1
1
1
1
1
2
1
1
1
0
2
1
1
0
1
1
1
2
1
1
1
0
0
0
1
0
1
2
1
1
1
1
1
1
1
1
0
0
1
2
1
2
1
1
2
0
0
1
1
1
1
1
1
1
1
1
0
0
0
0
1
1
2
1
1
1
1
1
0
1
2
1
0
1
1
2
0
2
1
2
2
1
2
0
1
1
2
1
1
2
2
2
1
1
2
2
2
2
0
1
1
1
2
1
1
1
1
1
2
1
2
1
1
1
0
1
2
0
1
1
2
1
2
2
2
1
1
2
1
1
1
2
0
1
0
1
1
2
1
0
1
1
1
1
1
1
2
1
1
0
2
0
1
1
2
1
0
2
1
2
1
2
2
2
1
1
1
2
0
1
2
1
1
2
0
2
2
0
1
1
2
2
1
1
1
1
1
1
2
1
2
2
0
1
2
1
1
2
1
2
1
1
2
1
1
0
0
1
1
1
1
0
1
1
2
1
1
1
1
0
1
2
1
1
1
1
2
2
2
1
2
1
2
0
1
1
0
1
2
1
2
1
0
1
2
0
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
1
1
1
2
0
1
1
0
1
0
2
2
1
1
1
1
1
2
1
1
1
2
1
1
0
1
1
1
2
1
2
2
1
1
1
0
1
0
1
2
2
1
1
1
2
2
2
1
1
1
2
1
2
1
0
0
1
0
1
2
2
0
2
1
1
3
1
1
1
1
1
1
1
1
2
2
2
2
1
1
0
0
1
0
1
1
0
1
1
1
1
1
1
2
1
1
1
0
0
1
0
1
0
1
2
1
2
1
2
2
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
2
2
2
0
1
2
2
1
2
2
2
2
0
1
1
2
1
1
1
1
0
1
1
0
1
1
1
1
1
0
2
1
1
1
2
2
1
1
2
3
2
1
1
1
1
1
2
1
2
1
2
1
2
0
2
1
1
1
1
1
2
0
1
1
1
1
2
1
1
1
2
1
1
2
2
1
2
0
1
1
1
1
1
1
1
1
1
2
1
1
0
1
2
1
2
1
1
0
0
1
1
2
1
2
2
1
1
1
1
1
1
0
1
1
2
0
0
2
2
0
2
1
2
1
1
1
1
1
2
0
1
1
1
2
2
1
2
1
1
1
3
1
2
1
2
2
1
1
1
1
1
2
1
0
2
1
1
1
1
1
1
1
1
1
0
1
1
0
1
1
1
1
0
1
1
0
1
1
1
1
1
1
3
2
1
1
1
2
0
2
2
1
2
2
0
0
1
1
1
0
0
1
1
0
1
1
0
2
1
1
1
1
1
1
2
0
1
1
1
2
0
1
1
1
1
1
0
0
1
0
1
1
2
1
1
0
2
2
1
1
1
1
1
1
2
1
1
1
1
1
2
2
1
0
1
2
1
1
2
2
1
1
1
1
1
1
0
0
0
2
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
2
1
1
1
1
1
1
2
2
1
1
1
2
1
0
2
1
1
0
1
1
1
2
1
1
2
1
0
1
0
2
0
1
1
1
1
1
1
2
1
0
1
1
1
2
1
0
1
1
2
1
1
1
1
2
1
0
0
1
1
1
1
1
2
1
1
0
1
0
1
0
1
1
2
1
2
1
0
2
1
1
1
1
1
1
1
1
0
2
2
2
0
0
1
2
1
1
1
0
0
1
1
2
0
1
1
1
1
1
0
1
1
1
1
1
2
2
1
1
1
2
1
1
1
1
3
1
2
0
1
1
0
1
1
0
2
1
1
1
1
1
2
1
0
1
1
1
2
1
2
1
1
2
2
2
1
1
0
1
1
4
2
1
1
0
2
2
0
1
2
1
1
1
1
1
2
0
1
1
1
1
2
1
1
1
1
0
2
1
0
1
2
1
2
0
1
1
1
1
1
1
1
1
1
0
2
1
1
1
0
1
1
1
2
1
1
1
2
2
1
2
1
0
1
2
2
0
1
1
1
2
1
2
1
1
1
1
0
2
1
0
1
2
0
1
1
1
0
2
1
1
1
1
1
1
1
0
1
1
1
1
0
1
0
1
0
2
0
1
1
1
2
1
0
2
2
3
1
1
1
1
1
1
1
2
1
2
2
1
2
2
2
1
2
1
1
1
1
1
0
3
2
0
1
1
1
1
0
1
2
0
1
2
0
0
1
1
1
2
1
2
0
1
2
1
1
2
2
0
0
1
0
1
1
1
1
1
1
2
2
1
2
0
1
2
1
1
0
2
2
1
1
0
1
1
1
1
1
1
0
2
1
1
1
1
2
1
1
1
0
1
1
1
2
1
1
1
1
2
0
2
1
1
2
2
2
2
1
2
1
1
1
1
1
1
1
1
0
1
1
1
3
1
1
1
1
1
1
1
1
0
1
2
0
1
2
1
1
2
0
1
1
1
1
1
2
0
0
2
1
0
1
1
1
2
2
1
1
1
1
1
1
0
1
1
1
1
1
2
1
1
1
1
2
2
1
2
2
2
1
3
0
0
1
1
1
1
1
1
1
0
1
0
1
1
1
0
2
2
2
2
0
2
1
2
1
1
0
1
2
2
2
1
0
2
0
1
2
1
1
0
2
2
1
1
1
1
2
0
1
1
1
2
1
1
1
2
2
1
1
0
1
2
1
1
2
1
1
1
1
2
0
2
1
2
0
0
1
1
1
2
1
1
1
1
0
1
2
1
2
1
2
1
1
2
1
0
2
1
2
1
1
1
0
2
1
1
0
2
1
1
2
2
2
1
2
1
1
1
1
1
2
1
1
1
1
1
0
0
1
1
0
1
1
1
2
2
0
0
2
1
0
0
0
1
1
0
2
2
2
1
0
1
1
1
1
1
0
1
1
1
2
1
1
2
0
1
2
1
3
0
1
1
1
0
1
0
1
1
0
1
1
2
1
2
1
1
2
1
1
1
1
4
1
1
2
1
1
1
0
0
1
1
1
2
3
1
2
1
1
1
1
1
2
1
2
2
2
1
2
1
0
1
0
1
2
1
0
0
2
1
2
3
1
3
1
1
1
1
2
1
1
1
1
1
0
1
2
1
1
0
2
1
1
2
1
1
0
1
0
2
0
1
1
0
2
2
1
1
1
0
2
1
2
2
1
0
1
1
0
0
1
1
2
2
1
2
1
0
2
1
1
1
1
2
0
2
1
0
1
1
1
0
1
1
3
2
0
1
1
2
1
1
1
1
2
0
2
2
2
1
1
0
1
2
2
0
1
1
1
1
2
1
1
1
0
1
0
2
1
2
0
1
1
1
2
1
1
1
1
1
1
0
1
2
1
1
1
2
1
1
1
1
0
1
2
1
1
2
1
1
2
1
1
1
1
2
0
2
1
2
1
0
1
0
2
1
0
1
2
4
1
0
0
1
1
2
1
2
2
1
1
1
1
1
2
1
1
1
0
0
1
1
1
2
1
2
2
1
0
2
0
2
1
1
1
0
1
0
2
0
1
0
1
2
2
1
1
2
1
1
1
2
1
1
2
1
0
2
0
1
2
1
2
1
1
1
1
0
1
1
1
0
0
1
1
2
1
0
1
1
0
1
1
1
2
0
2
1
0
1
2
1
0
1
1
1
1
1
2
2
1
2
1
0
1
0
1
2
1
1
1
1
2
2
2
2
1
1
0
0
1
0
1
1
2
0
1
1
1
2
1
2
0
1
2
1
0
1
1
2
1
0
1
1
1
1
0
1
2
1
0
1
1
1
1
0
2
1
0
2
1
2
2
1
1
1
0
1
1
1
1
0
1
1
0
1
1
1
1
2
1
1
1
0
0
1
2
2
1
2
2
1
2
1
1
1
0
0
1
2
1
1
1
1
1
1
2
0
0
1
2
0
1
1
0
1
0
2
3
0
2
1
1
0
0
1
0
2
2
1
1
1
0
1
1
2
2
0
1
2
1
0
2
1
1
1
2
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
0
2
1
0
1
1
2
0
0
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
0
1
2
2
1
0
1
1
1
1
0
1
2
1
1
1
1
2
1
2
1
1
1
2
1
1
2
1
1
2
1
1
2
2
2
1
1
0
1
1
1
1
2
2
1
1
1
0
0
1
1
0
2
1
1
1
1
2
0
0
1
2
0
1
1
0
1
0
2
1
2
1
1
2
1
1
2
0
2
1
1
2
2
1
1
0
1
1
1
1
1
1
1
1
1
2
3
1
1
1
1
2
2
2
1
1
1
1
0
0
1
1
2
1
1
1
2
1
0
1
1
1
1
2
1
1
1
1
1
0
3
1
1
1
2
0
2
1
1
1
1
1
0
1
2
2
0
1
1
0
1
1
1
1
4
2
1
1
1
2
2
1
1
1
2
1
2
1
1
1
0
1
1
1
0
1
1
1
0
2
1
1
0
1
1
1
1
1
2
1
1
0
2
2
1
2
0
2
1
3
0
0
2
2
1
0
1
2
1
1
0
1
1
1
1
1
1
3
2
2
1
1
2
2
1
2
2
2
2
1
1
1
1
1
1
0
1
1
0
2
1
1
1
2
2
1
1
1
1
1
1
2
1
2
1
2
1
0
1
1
1
2
1
1
0
2
1
1
1
1
2
1
1
1
2
2
1
2
1
1
0
0
1
1
1
1
1
1
1
1
2
1
1
1
1
1
0
2
2
2
1
2
1
2
1
1
1
0
2
1
2
1
1
0
2
0
2
2
2
0
0
1
1
1
2
1
2
1
2
1
2
1
1
1
1
1
1
0
1
1
1
2
1
1
1
1
1
0
1
0
2
2
1
1
1
0
1
1
1
1
0
1
1
0
1
0
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
0
0
0
1
1
1
2
0
1
1
1
1
1
1
1
1
0
2
1
0
1
1
1
2
1
0
2
1
1
3
1
1
0
1
0
1
1
2
1
0
1
1
1
1
2
1
2
1
1
0
2
2
0
2
1
0
1
1
1
1
2
0
1
1
1
1
1
2
0
2
1
1
2
2
1
2
1
1
1
2
0
2
2
1
2
0
1
1
1
2
1
1
1
1
1
1
0
0
0
1
1
1
2
1
2
2
1
1
1
2
1
1
1
1
0
1
1
1
1
1
1
1
1
2
2
1
2
0
2
2
1
1
2
1
2
1
1
3
1
1
1
1
1
0
2
1
0
1
2
1
2
2
1
2
1
1
1
2
1
1
1
2
2
1
1
1
0
2
1
1
2
1
1
1
1
0
1
1
2
1
1
1
0
1
2
1
1
1
2
0
2
2
0
1
2
1
2
1
0
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
0
1
1
1
2
1
1
1
0
1
1
1
1
0
1
1
0
1
1
0
1
2
1
1
1
1
1
1
1
1
1
1
0
1
1
1
0
1
1
2
2
1
1
2
1
0
1
0
0
2
0
1
3
2
0
0
1
0
2
1
1
2
1
1
0
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
1
0
1
1
0
0
2
1
1
2
1
2
0
1
1
1
1
1
2
2
2
1
2
2
1
1
2
1
1
0
1
1
1
2
0
2
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
0
1
1
2
1
2
1
1
1
1
1
1
1
0
2
1
1
1
1
1
1
2
1
1
2
2
2
0
1
1
1
1
1
0
1
1
1
0
1
1
0
1
0
1
0
1
2
2
3
2
1
1
1
1
1
1
1
0
2
1
2
1
1
0
0
1
1
1
0
1
1
1
1
2
2
1
2
1
1
0
1
1
1
1
1
1
2
1
1
2
1
1
2
1
1
2
1
1
1
1
1
1
2
2
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
0
1
0
0
2
2
2
1
1
2
2
1
0
2
1
0
1
1
2
1
1
1
1
1
0
1
1
0
2
1
2
0
2
2
2
1
0
1
0
0
1
2
1
2
1
1
1
0
2
0
1
2
1
1
1
1
2
1
2
0
0
1
1
0
2
1
1
1
1
2
0
2
2
1
1
1
1
1
1
1
1
0
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
0
0
1
2
1
1
1
1
2
1
1
1
2
1
2
1
1
2
2
1
2
1
2
1
2
1
1
2
2
1
1
0
2
1
1
1
0
2
2
1
0
0
0
0
0
0
2
1
1
1
1
1
2
1
1
1
1
1
1
0
1
1
2
2
1
2
1
1
1
2
1
1
2
2
1
1
1
1
1
0
1
1
1
1
1
1
1
1
2
1
1
1
0
2
1
1
1
1
1
1
2
2
1
0
1
0
0
2
2
0
1
1
2
2
2
1
0
1
1
2
1
1
0
1
1
1
0
1
0
1
1
2
1
1
1
1
1
0
1
0
1
1
1
1
0
1
2
1
2
0
2
2
2
1
1
2
1
0
1
1
1
1
1
1
2
1
1
3
2
1
1
2
1
1
2
1
1
1
0
2
1
0
0
1
1
1
1
1
2
1
1
1
1
1
4
1
2
2
1
1
1
1
2
1
1
0
1
1
1
1
0
1
1
2
1
1
1
2
2
1
1
2
2
1
1
2
1
1
2
0
1
2
1
1
1
2
1
1
1
1
1
1
1
0
2
2
1
0
0
1
1
0
1
0
2
1
1
1
1
1
1
1
0
1
2
1
1
1
0
0
1
1
1
0
0
1
3
0
2
2
1
0
2
2
1
1
1
4
2
1
1
1
1
1
2
1
3
1
1
1
1
1
1
2
1
1
1
0
1
1
2
1
0
1
1
2
0
1
1
2
1
1
2
2
2
1
1
2
1
2
1
1
0
1
1
2
1
1
1
1
0
0
2
1
1
2
0
1
1
1
1
1
1
0
1
1
1
2
1
1
1
1
1
0
0
1
1
1
1
1
1
1
2
2
1
1
2
0
1
1
1
1
1
2
0
1
1
0
1
1
2
1
1
3
1
2
0
2
0
2
2
0
1
1
1
1
1
1
2
1
1
0
1
1
2
1
1
0
1
0
0
2
1
1
1
1
2
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
0
1
1
1
2
1
2
1
0
2
2
0
1
2
1
1
1
2
2
2
1
1
2
0
1
1
1
1
1
1
1
1
0
1
1
2
1
1
0
1
2
1
1
1
1
1
1
0
1
1
2
1
1
1
1
1
1
1
2
0
0
1
0
1
1
0
0
1
1
1
1
1
1
0
1
1
1
1
1
2
1
1
1
1
2
1
1
2
2
1
0
2
0
1
1
1
1
1
2
1
2
1
1
0
1
2
1
1
2
1
1
1
2
0
1
1
1
2
2
1
1
1
1
4
1
1
1
1
0
1
1
2
2
2
2
1
2
2
1
1
1
2
1
1
1
1
2
1
1
1
2
1
2
1
1
1
2
0
1
1
1
1
1
1
1
2
1
0
2
1
1
2
2
1
2
1
0
1
0
2
1
1
1
1
1
0
1
1
2
2
2
0
1
0
1
0
2
1
1
2
2
2
1
1
0
2
1
1
2
3
2
1
1
1
1
0
1
1
0
1
1
0
1
2
1
0
1
2
1
0
1
2
2
1
1
2
1
0
1
1
1
0
2
1
2
0
1
1
1
2
1
1
2
1
2
1
0
0
1
1
2
0
0
0
1
0
0
0
1
1
1
2
2
1
0
0
1
1
1
1
1
2
1
0
1
1
3
1
2
1
1
2
0
1
1
1
1
1
1
2
0
1
1
1
1
0
1
1
1
1
2
1
2
0
2
1
0
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
0
2
1
0
2
0
1
2
1
1
1
1
2
2
0
1
1
2
1
2
2
0
1
1
1
1
2
2
1
2
2
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
0
1
2
2
1
1
1
1
1
0
1
1
1
1
1
1
2
2
1
2
1
1
1
1
1
2
1
2
1
1
0
1
1
1
1
1
1
1
2
0
1
1
1
3
1
1
1
2
1
1
1
1
1
0
2
2
2
1
1
3
0
2
0
1
0
0
2
1
2
0
1
1
1
2
2
0
0
1
1
2
2
1
2
1
1
2
2
2
1
2
1
1
1
1
0
1
2
1
1
1
2
1
1
1
2
2
2
1
1
1
1
1
2
2
1
1
0
2
1
1
2
1
2
2
2
1
0
2
2
1
1
1
2
1
1
0
1
0
1
1
2
0
0
0
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
0
1
1
0
1
1
0
1
1
1
1
1
2
1
1
2
2
2
1
0
1
0
1
1
2
1
1
0
2
2
1
1
1
1
1
1
1
1
1
1
2
2
0
1
1
0
1
1
1
2
1
0
1
1
1
1
3
1
1
2
2
2
1
1
0
0
1
1
0
2
1
1
2
1
0
0
2
1
1
0
1
1
1
1
1
1
2
1
1
2
0
1
1
1
2
2
1
2
1
0
1
1
2
1
1
2
1
1
1
1
1
0
1
1
2
1
1
1
2
1
1
1
1
1
1
1
0
1
0
2
1
0
2
1
1
1
1
1
1
0
2
1
0
1
2
0
1
0
1
1
0
2
0
1
1
1
0
1
2
0
2
1
2
2
1
0
1
2
1
2
1
0
0
1
0
1
2
2
1
1
1
1
1
1
4
0
0
1
1
2
1
1
1
0
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
0
1
2
2
1
2
0
1
1
0
1
0
1
1
1
2
1
1
1
1
2
2
1
2
1
2
0
2
2
1
0
1
2
0
1
0
1
0
0
2
2
1
1
0
2
1
2
1
0
0
1
2
1
2
1
1
2
2
0
1
1
1
1
1
1
1
0
2
1
1
1
2
1
1
1
3
1
2
1
1
1
0
1
2
1
1
0
2
0
1
1
1
2
0
1
1
1
1
1
0
1
2
1
1
1
1
0
1
1
1
2
2
1
1
1
2
1
1
1
0
1
1
3
1
0
2
1
2
2
2
1
0
2
1
1
0
1
1
1
2
1
1
2
2
1
2
2
1
2
1
1
1
1
1
1
0
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
2
0
2
2
1
0
1
1
2
2
0
1
1
1
0
1
1
2
2
2
2
1
1
1
1
2
1
0
1
1
1
1
1
2
0
1
2
1
3
1
2
0
2
1
0
1
2
2
2
1
1
0
1
2
0
1
1
1
0
0
2
1
1
1
0
2
1
0
3
0
1
1
1
1
1
1
1
1
1
1
1
1
0
2
1
2
0
1
2
1
1
1
1
0
1
1
1
1
0
1
1
0
1
2
1
1
2
2
2
0
4
2
1
2
1
2
0
1
1
1
0
1
2
1
1
0
1
2
1
2
1
0
1
2
2
1
2
1
1
1
1
2
2
1
1
1
1
1
1
1
2
0
1
1
0
1
1
2
0
2
1
1
2
1
1
1
1
2
1
1
0
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
0
1
1
2
1
0
1
2
1
1
1
0
1
1
1
1
2
2
2
1
1
2
1
1
1
1
1
0
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
0
1
1
1
1
0
1
2
2
1
0
1
0
1
0
1
1
1
1
1
1
0
1
1
1
0
1
1
2
1
1
1
1
1
2
1
2
1
2
0
1
0
1
1
1
0
1
0
0
1
1
0
1
0
1
1
1
1
1
1
1
2
1
0
1
1
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
0
2
2
1
1
1
2
0
2
2
1
2
1
0
1
0
1
2
1
2
1
1
0
1
0
1
1
1
2
1
0
1
1
1
1
1
0
1
2
1
2
2
1
1
2
1
2
1
2
1
1
2
1
1
1
1
1
1
2
2
2
1
1
1
1
2
1
1
1
0
1
1
0
2
2
2
2
1
3
0
1
1
1
1
1
1
0
1
1
2
2
1
1
1
0
1
2
0
3
1
1
1
1
1
0
2
2
1
0
2
2
1
1
2
2
0
1
2
1
2
2
1
1
2
1
1
1
1
1
2
1
2
1
0
1
1
1
1
1
1
1
1
1
1
1
2
1
0
1
1
1
3
1
1
2
1
2
2
1
1
2
1
1
2
1
1
2
0
1
1
1
1
1
0
1
1
0
2
1
1
2
0
2
2
2
2
2
1
1
2
1
0
2
2
1
1
1
2
0
1
0
1
1
0
2
1
1
0
2
1
2
1
1
1
1
1
1
1
1
2
2
1
0
2
1
1
1
1
0
1
1
2
1
2
1
1
1
1
2
2
1
1
0
1
2
1
2
0
1
1
1
1
1
1
0
2
2
2
1
1
1
3
1
1
2
2
1
2
2
1
1
2
1
2
1
1
1
2
1
3
1
1
1
1
1
1
1
1
1
1
2
3
1
1
2
1
1
2
2
0
1
1
2
1
1
1
1
2
1
1
1
1
0
2
1
1
2
2
1
1
1
2
0
2
0
0
0
0
1
1
1
1
2
1
1
1
2
2
1
1
1
2
1
1
1
2
2
1
2
0
2
1
0
1
2
1
2
1
1
1
2
1
1
2
0
0
1
0
1
1
0
1
1
2
2
1
2
0
1
0
1
1
1
3
1
0
1
1
1
1
2
1
1
1
1
0
1
1
1
0
1
1
1
2
2
1
1
1
1
0
1
0
1
1
1
2
2
0
0
2
1
0
2
0
2
1
2
1
1
1
2
1
1
1
1
1
0
2
1
1
1
0
1
1
1
1
1
1
1
1
2
2
1
2
0
1
1
1
0
0
1
1
1
1
0
1
1
1
0
0
1
2
1
1
1
1
1
1
2
1
2
1
0
0
2
2
1
1
2
0
1
1
2
1
2
1
2
1
2
1
1
2
1
1
0
0
2
1
1
1
1
1
1
1
0
1
0
1
1
0
1
1
0
1
0
1
1
2
1
1
1
1
2
0
2
2
1
0
1
2
2
0
1
1
1
1
2
1
2
1
1
0
1
1
1
0
1
1
2
1
1
1
1
2
0
0
1
1
2
1
2
1
1
0
1
2
2
2
1
1
1
1
1
1
1
1
1
0
4
1
1
1
1
1
2
1
1
1
1
2
1
2
2
1
2
2
1
0
2
1
2
1
1
1
0
2
1
1
1
1
1
1
1
1
2
2
0
0
2
1
2
2
0
1
1
0
2
1
1
2
1
2
0
1
1
1
1
2
1
1
1
1
1
1
1
2
2
2
0
1
1
0
2
1
0
0
1
1
1
2
1
1
0
0
1
2
1
1
2
0
1
1
0
1
2
2
0
1
2
0
1
1
0
1
1
1
1
3
2
1
1
2
0
1
1
0
1
2
1
1
2
1
1
2
1
1
2
2
2
1
1
2
1
1
2
2
1
1
1
1
1
0
1
1
2
1
1
1
1
0
1
1
1
1
1
2
1
1
0
1
1
1
2
1
2
1
1
1
2
1
0
1
0
2
2
1
1
1
1
1
1
2
2
1
0
1
2
1
1
0
1
2
1
1
0
2
1
2
2
2
2
1
2
1
2
1
0
2
1
1
2
1
1
0
0
0
1
0
0
1
1
0
0
1
1
1
2
2
1
1
2
2
1
1
1
2
1
1
1
2
1
2
2
0
1
1
2
1
1
2
1
1
2
0
1
1
2
1
1
1
1
2
2
1
1
1
1
1
1
1
1
2
1
3
1
1
1
1
2
2
1
1
2
1
1
2
1
2
1
0
1
1
1
1
1
1
1
1
1
1
2
0
2
1
1
1
2
2
1
2
2
2
1
1
1
2
1
1
1
2
1
1
1
1
1
1
0
2
1
2
0
2
1
1
1
1
1
2
0
2
0
2
1
0
1
0
1
2
1
0
1
1
1
2
1
1
2
1
1
1
1
1
2
1
2
1
1
2
1
1
1
2
2
2
1
1
1
2
2
1
1
1
0
1
0
1
2
1
0
1
1
1
2
1
1
0
1
1
1
1
1
1
2
2
1
1
1
2
1
1
1
2
0
1
1
1
1
1
1
0
1
2
1
1
1
2
2
0
0
2
1
1
1
2
0
1
0
2
2
0
1
0
1
1
2
1
1
0
0
2
1
1
1
1
1
1
0
1
2
1
0
1
1
1
1
1
2
0
2
2
1
1
2
1
2
1
2
1
1
1
1
1
1
1
1
2
0
2
1
1
2
1
0
2
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
2
2
2
1
1
1
1
1
2
1
1
2
1
1
1
0
2
1
1
2
2
1
1
1
2
1
1
0
1
1
1
1
2
0
1
1
2
1
0
1
1
1
1
2
2
1
2
2
0
1
1
1
1
2
1
0
2
2
2
1
2
1
1
1
1
0
0
1
2
1
1
1
2
0
1
1
2
1
1
1
2
1
1
1
1
1
5
1
0
1
2
0
1
1
0
2
2
1
1
1
1
0
1
2
2
1
2
0
0
1
1
1
1
1
2
0
1
2
1
1
3
2
0
1
1
0
2
1
2
1
1
0
2
1
1
1
0
0
1
1
1
0
0
1
1
2
1
1
0
0
1
1
0
2
1
2
2
2
1
1
1
1
1
1
1
1
1
2
2
0
2
3
2
1
0
2
1
1
1
2
2
0
1
2
1
2
2
1
2
1
2
2
0
1
1
1
0
2
1
2
1
0
2
1
2
1
0
1
2
1
2
1
0
0
1
1
2
0
1
1
0
2
0
1
2
1
1
1
0
2
1
1
2
1
1
0
2
1
1
0
2
2
1
1
3
2
1
1
1
1
1
1
1
1
2
0
2
2
2
1
1
1
1
0
2
2
0
0
2
2
2
2
0
2
0
1
0
1
1
1
1
1
2
0
2
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
0
0
1
1
1
0
2
0
1
0
2
1
1
2
1
1
2
2
2
1
2
1
1
1
2
1
0
1
1
1
1
1
2
0
0
2
0
1
1
2
1
1
1
1
1
1
0
0
2
2
2
0
2
1
3
1
1
1
0
1
1
1
2
2
2
1
0
2
1
0
1
1
1
0
1
2
1
0
1
1
0
1
1
1
1
1
2
0
1
0
1
1
0
1
1
1
2
0
1
2
1
2
1
1
0
0
1
1
1
1
1
2
2
2
0
2
1
1
1
1
1
0
1
1
1
2
1
0
0
1
1
0
1
1
2
1
0
1
0
1
1
0
2
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
2
1
0
1
0
2
1
0
1
1
2
0
1
1
2
1
1
0
2
1
2
1
0
1
1
1
2
0
2
2
1
1
2
1
1
0
2
2
0
1
1
0
2
1
2
2
1
2
1
1
0
1
0
1
1
0
1
2
1
1
0
2
1
1
1
0
0
1
2
2
0
1
1
2
1
2
1
1
1
1
2
0
0
0
1
0
1
1
2
2
1
1
1
1
1
2
1
2
1
1
1
2
2
1
2
0
0
0
1
2
1
2
1
2
1
1
1
2
2
1
2
0
1
1
2
1
2
1
1
2
0
1
1
0
2
2
1
1
2
1
1
0
0
1
2
2
1
1
0
1
0
2
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
0
1
2
1
1
2
0
1
1
3
1
1
1
1
1
0
1
2
1
1
2
1
1
1
2
1
2
2
1
0
2
1
1
1
1
1
0
1
2
0
2
1
2
1
0
1
2
2
0
0
1
0
0
1
3
1
1
1
1
1
2
1
1
0
2
2
1
1
1
2
1
1
2
1
1
1
0
2
1
1
0
1
0
1
0
1
2
1
1
0
2
0
1
1
1
1
2
1
1
1
1
1
1
2
1
1
2
1
0
2
2
2
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
0
1
2
1
1
1
2
1
2
1
1
1
1
1
2
1
0
1
2
1
2
1
1
2
1
1
1
2
1
0
1
1
1
2
1
0
1
2
0
2
0
1
1
1
1
1
1
1
1
1
1
0
1
1
2
1
1
2
0
1
1
2
0
1
2
2
1
1
2
2
2
1
1
1
1
0
1
2
0
1
2
0
2
1
1
2
0
1
2
1
1
1
0
0
1
1
1
1
1
0
1
1
2
1
1
0
0
2
0
1
1
1
1
2
2
1
1
1
1
0
1
1
0
2
0
1
1
2
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
0
2
0
0
0
1
0
1
2
1
1
1
1
1
1
0
1
0
0
1
2
0
1
3
2
1
2
1
1
1
1
1
2
1
1
1
2
4
1
1
1
1
1
2
0
1
1
1
1
2
1
1
1
1
1
0
1
0
0
3
1
2
0
2
1
2
1
1
1
1
1
1
2
2
1
1
2
0
1
1
2
2
1
1
1
1
1
1
2
2
1
1
2
2
2
1
1
2
1
3
2
1
1
1
1
1
1
2
2
1
1
1
2
2
1
2
0
2
0
2
2
2
0
1
1
1
1
2
1
1
1
0
0
2
1
1
1
2
0
1
1
0
1
0
1
1
2
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
0
1
1
1
2
1
2
2
2
1
1
2
2
1
0
2
0
1
1
1
1
1
1
1
2
1
1
1
1
2
2
1
1
1
2
1
1
1
1
0
1
2
1
2
1
1
2
2
1
2
1
1
1
1
1
2
2
1
1
1
1
2
0
1
2
1
1
1
0
1
0
0
2
1
1
2
1
1
1
1
1
0
2
1
1
2
2
3
1
1
1
2
2
0
1
1
1
1
2
2
1
1
2
2
0
1
1
1
1
1
2
2
1
2
1
2
1
1
1
2
1
2
1
1
1
1
2
2
1
1
0
2
2
1
2
2
0
2
1
2
0
1
1
1
1
0
1
2
1
1
1
2
1
1
2
1
1
1
2
2
1
1
1
2
1
2
1
2
1
0
1
0
1
2
1
2
1
1
2
0
0
1
1
1
3
1
2
2
1
0
2
1
1
2
1
2
1
1
1
1
1
2
2
1
1
2
0
1
0
0
1
1
1
1
1
0
1
1
2
1
1
0
1
3
1
2
1
1
1
2
1
1
2
2
1
2
2
1
1
0
1
1
0
1
0
1
1
1
1
1
0
2
2
1
1
2
2
0
2
2
1
2
1
0
1
1
2
1
1
2
2
1
1
1
1
1
1
1
2
0
1
1
1
1
1
1
1
1
1
1
1
2
0
1
1
2
0
1
2
0
2
1
2
1
1
0
3
1
1
1
1
1
2
2
1
1
3
2
0
1
0
1
1
0
1
1
2
0
1
1
0
1
0
1
1
0
1
0
1
1
1
1
1
2
1
1
1
2
1
1
2
1
0
1
0
1
2
2
1
1
0
2
2
0
1
1
1
1
1
1
0
2
2
1
1
1
2
1
1
1
1
2
1
1
2
1
2
1
1
2
1
2
1
2
1
2
1
1
2
0
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
2
1
0
2
1
1
2
1
1
0
1
1
1
1
1
2
1
0
1
0
1
1
1
1
3
1
1
1
0
1
0
1
0
1
0
1
1
0
1
2
1
2
1
3
1
2
2
1
0
2
2
1
1
1
1
2
1
1
2
2
1
1
1
1
1
2
1
1
2
1
2
0
1
1
1
0
1
1
1
1
2
1
1
1
0
0
1
1
2
2
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
0
0
1
2
1
1
1
1
1
2
1
1
0
1
2
2
2
1
1
1
1
2
2
1
2
2
1
1
1
0
0
2
1
0
2
1
2
1
2
1
2
2
2
1
1
1
1
2
1
2
1
2
2
1
1
1
2
2
2
2
1
1
2
1
1
1
2
1
1
1
2
1
0
0
1
0
1
2
1
1
2
1
1
1
1
1
1
0
2
1
1
2
0
2
1
2
2
1
2
2
0
2
1
0
2
2
1
0
1
1
1
1
1
0
1
0
1
1
1
1
1
1
0
1
1
0
1
1
1
0
2
1
2
2
2
2
2
2
2
1
1
3
1
1
1
1
1
1
2
1
2
2
2
1
1
1
0
1
1
2
1
1
2
2
2
1
0
2
1
2
1
0
1
2
1
0
0
0
2
0
1
1
2
2
1
1
2
2
2
1
1
2
1
1
1
2
0
2
1
2
1
1
1
2
1
0
0
1
1
1
1
2
1
2
1
0
2
1
1
0
1
1
0
2
2
0
0
1
2
2
1
2
2
3
1
2
1
1
1
0
0
1
1
0
1
2
1
1
1
1
1
1
1
2
2
0
2
2
1
1
1
2
1
2
1
1
1
1
2
1
1
1
1
0
1
2
1
1
1
0
2
1
1
2
1
0
2
1
1
2
1
1
1
0
2
2
1
2
2
1
1
1
1
1
2
1
1
1
2
1
1
1
0
1
1
0
2
0
2
2
1
2
1
1
1
1
0
0
1
1
0
1
2
1
1
1
2
2
1
1
1
1
0
3
0
1
2
0
4
1
1
0
1
2
2
1
1
1
1
1
1
2
1
1
1
1
0
0
2
1
0
1
1
1
1
1
1
1
1
1
1
1
0
0
1
1
0
2
1
1
1
1
1
2
1
1
1
0
1
1
1
1
1
2
1
1
2
1
1
1
0
1
0
2
1
0
1
1
2
2
1
1
1
2
1
2
1
1
1
1
2
1
2
1
2
1
1
1
0
1
1
1
0
2
1
2
1
2
0
1
1
2
1
1
1
1
1
2
0
1
2
1
2
1
0
0
1
1
1
2
0
1
1
1
1
0
1
1
0
0
1
1
0
0
1
2
2
1
1
2
2
1
2
2
0
1
2
1
1
2
2
1
0
1
1
1
1
0
1
1
1
2
2
1
1
2
1
2
2
0
1
2
2
2
1
1
1
2
0
2
1
1
1
2
1
1
1
1
1
0
1
1
1
2
1
0
1
1
1
3
1
1
1
0
2
1
1
1
0
2
0
1
1
1
2
2
0
1
2
2
1
1
2
1
2
2
1
1
2
2
1
2
1
2
1
2
2
2
1
1
2
1
1
1
1
2
2
2
1
0
1
2
1
0
0
1
1
1
3
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
2
1
2
2
1
1
1
0
2
0
1
1
1
1
1
1
2
2
0
1
2
1
1
1
1
1
0
1
1
1
0
2
1
0
0
1
2
2
1
0
1
1
2
0
1
1
2
1
1
1
1
0
2
1
2
2
1
1
2
2
2
1
1
1
1
1
0
0
1
0
2
1
1
1
1
0
1
1
1
1
3
1
0
2
0
0
1
0
0
1
1
1
1
2
0
1
1
2
1
0
1
2
2
1
1
2
2
2
2
0
3
2
2
1
0
2
1
1
1
1
3
1
1
1
2
1
1
1
3
1
2
1
2
1
2
1
0
1
0
0
0
2
2
2
1
1
2
0
1
1
1
0
1
1
2
1
1
1
1
1
2
1
1
1
1
2
0
0
1
1
1
2
1
1
1
1
2
1
1
3
1
2
0
1
1
0
0
2
2
2
0
1
2
1
0
2
2
2
0
1
1
1
1
2
0
0
0
0
0
1
0
2
1
1
1
2
1
2
1
1
1
2
0
1
1
2
2
1
1
1
1
1
1
1
1
1
2
1
0
2
1
0
2
1
2
2
1
0
2
2
1
1
0
1
1
1
2
0
1
1
1
1
1
2
0
0
1
1
2
1
1
1
1
2
2
1
1
1
2
0
2
1
0
1
1
1
0
2
1
0
1
1
2
1
1
0
0
2
1
1
1
0
1
1
1
2
2
1
0
1
0
1
2
1
1
0
1
1
0
0
2
1
0
2
1
1
1
1
2
0
1
1
1
0
1
1
1
1
1
0
0
1
2
0
1
2
1
1
1
1
1
1
0
2
1
2
0
1
0
1
2
1
1
2
1
1
1
1
1
1
2
1
1
2
1
1
1
2
1
2
1
1
0
0
2
0
1
2
1
1
1
2
1
1
2
0
1
1
0
2
0
0
0
1
2
1
1
1
1
0
0
0
5
0
2
1
2
1
1
1
1
1
2
0
1
1
1
1
1
1
2
1
1
2
1
1
0
2
1
0
2
1
1
1
1
2
1
1
0
2
1
0
0
0
1
2
1
1
0
1
1
1
1
1
1
2
2
1
1
0
1
1
1
0
1
2
2
1
0
1
0
0
1
0
1
1
1
0
0
1
1
0
1
1
0
1
1
1
2
4
1
1
1
1
0
2
1
1
1
1
1
1
1
1
1
0
1
1
2
0
0
1
0
2
1
2
2
0
2
1
0
0
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
0
0
1
0
2
1
1
0
1
1
1
1
2
0
1
2
1
2
2
1
1
2
1
1
1
1
0
1
1
1
2
2
0
1
2
2
0
2
1
2
1
2
1
1
2
2
1
1
1
1
0
2
1
1
0
0
0
1
1
0
1
1
1
1
1
2
1
1
1
1
1
2
2
1
1
1
1
2
1
2
2
1
1
1
1
1
1
2
1
2
2
1
0
0
2
1
2
2
1
1
1
2
1
1
1
0
0
1
0
1
2
1
1
0
1
2
1
2
1
2
2
2
2
3
1
1
2
1
2
1
1
1
2
0
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
0
1
0
1
0
2
2
0
1
0
0
1
1
1
0
1
1
2
1
0
1
0
1
2
2
0
1
2
1
2
1
1
1
1
0
3
0
2
2
1
2
1
2
1
0
1
1
1
1
0
1
1
1
2
2
1
1
2
2
0
1
2
1
0
0
1
1
1
1
0
1
2
1
1
1
1
1
0
1
2
1
2
1
1
2
1
1
1
1
0
1
2
2
0
2
0
3
0
1
1
0
1
1
1
1
1
2
1
0
1
1
2
1
0
1
1
2
1
2
2
1
1
1
1
1
1
1
0
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
0
2
1
1
1
2
0
1
1
2
1
1
0
1
1
1
2
1
0
0
1
0
1
1
1
1
1
1
1
1
1
0
1
1
0
1
1
1
2
2
2
1
2
2
1
0
1
1
2
1
2
1
0
0
0
1
1
1
1
1
2
0
1
1
2
0
2
1
0
2
2
2
0
1
1
1
0
1
2
1
0
1
1
1
0
2
1
0
2
1
1
1
2
1
1
1
1
2
1
2
2
2
0
2
1
2
1
1
2
1
2
1
1
1
3
1
1
0
0
1
1
0
0
1
1
1
0
1
1
1
1
1
1
1
1
2
0
0
0
2
0
1
1
0
1
2
1
1
2
0
1
2
0
2
2
1
1
1
0
2
1
0
1
1
1
0
0
1
1
1
1
0
1
0
1
1
1
0
1
2
1
1
1
1
2
1
1
1
1
1
2
2
1
1
1
2
2
1
1
1
0
1
2
1
1
1
1
1
1
2
1
1
2
0
0
0
1
1
2
0
2
2
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
0
2
0
1
1
2
1
1
1
0
1
1
1
0
2
2
1
0
2
1
1
2
1
2
0
1
1
1
2
2
0
1
2
2
1
2
1
1
2
0
1
2
1
1
2
1
1
0
1
1
1
0
2
1
1
1
2
2
1
1
1
1
1
0
0
0
1
0
1
1
0
2
2
1
2
2
2
2
1
1
2
1
2
1
2
0
1
1
0
2
1
1
1
2
2
2
1
2
0
2
1
0
1
2
0
1
2
1
1
1
1
1
1
1
2
0
1
1
1
2
1
1
1
1
0
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
0
1
1
2
1
1
1
3
2
1
1
2
1
1
1
1
1
3
1
2
0
1
1
1
1
2
1
0
1
1
1
2
1
0
1
1
1
1
2
2
1
0
2
1
2
1
1
0
0
1
0
1
0
2
0
2
0
1
1
1
2
0
1
1
2
2
0
1
2
0
1
1
1
1
1
1
1
1
2
1
2
1
1
0
0
1
0
1
1
1
1
2
1
1
0
1
1
1
0
0
0
1
1
1
2
1
1
1
2
0
1
2
1
1
2
1
2
1
0
1
2
1
0
1
1
1
2
2
1
0
1
1
1
1
1
1
2
1
0
1
1
1
2
2
2
1
1
0
1
1
0
2
2
1
0
1
2
0
1
2
2
1
0
1
2
1
2
2
1
2
1
2
1
1
2
1
1
1
1
1
2
2
2
0
1
1
2
1
1
1
1
0
1
1
0
1
0
1
0
2
1
2
2
2
1
2
1
0
0
2
1
1
3
0
0
2
2
1
2
2
2
1
2
2
1
0
1
1
1
0
0
2
2
1
0
0
1
2
1
1
1
1
1
1
1
2
1
2
2
1
1
2
0
1
1
1
2
2
1
1
1
1
1
1
0
1
0
1
2
1
1
1
1
0
1
1
1
0
1
2
1
1
2
2
0
1
1
1
2
1
1
1
2
1
2
2
0
2
1
2
0
2
2
1
1
1
1
2
1
2
2
2
2
2
2
1
0
2
2
3
1
1
2
3
1
1
0
1
1
1
1
1
1
1
1
0
2
0
1
1
0
1
1
1
1
1
1
1
2
1
1
2
1
1
2
2
1
1
2
1
1
1
2
1
0
0
1
1
1
1
1
1
1
1
1
2
1
2
1
2
1
0
2
1
1
2
0
1
1
1
1
1
1
0
1
1
1
2
0
6
1
0
2
1
1
1
1
1
0
1
2
2
1
1
2
1
2
1
2
1
1
1
1
1
2
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
0
4
1
2
1
2
1
1
1
1
0
1
1
2
1
1
0
2
0
2
1
1
1
2
0
1
2
1
0
2
3
2
2
1
1
1
2
1
2
0
0
1
3
1
0
1
1
2
2
0
2
2
2
2
1
0
0
1
2
2
1
0
1
1
0
1
1
1
2
1
1
1
1
1
2
2
1
1
1
0
1
2
1
0
1
1
1
2
0
1
2
1
1
1
2
2
1
2
1
1
1
2
1
2
1
1
1
1
0
1
0
1
1
1
0
1
1
1
0
0
1
1
1
1
1
1
0
1
1
0
2
1
1
1
1
1
1
0
1
1
2
1
1
1
1
1
1
4
1
0
2
0
2
1
1
1
1
2
2
1
1
1
1
1
2
1
4
1
1
1
2
1
1
2
1
2
1
0
1
1
0
1
1
1
2
1
0
2
1
0
1
1
0
2
1
1
0
2
0
1
0
1
1
2
2
2
1
2
1
1
2
0
0
1
0
2
1
2
1
2
1
2
1
2
1
0
2
1
1
0
0
1
1
2
1
1
0
0
2
2
0
0
1
0
1
1
0
0
1
1
1
0
2
2
1
1
1
1
1
1
2
1
1
1
1
2
2
0
2
1
2
1
1
0
2
1
1
1
1
1
1
1
0
2
1
2
1
2
1
1
0
1
2
2
1
0
1
0
2
1
1
0
1
0
0
1
1
1
2
1
0
2
0
1
2
1
2
1
1
1
1
0
1
1
0
1
1
1
0
2
2
0
2
2
1
0
1
0
1
2
2
1
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
1
4
2
2
2
2
0
1
1
1
1
0
0
0
2
1
1
2
1
1
1
0
1
1
0
2
1
2
2
0
0
1
0
2
1
0
1
1
1
0
1
1
2
1
2
1
0
1
2
0
1
1
0
1
1
2
1
1
2
1
1
1
0
0
1
1
0
0
0
1
1
1
1
1
1
1
2
1
1
2
1
0
1
1
1
1
1
0
1
1
1
2
2
1
2
1
2
1
0
1
1
0
1
1
1
2
1
1
2
1
2
1
1
0
1
1
1
1
2
2
0
1
0
1
1
0
1
0
1
1
0
1
0
2
1
0
0
2
1
1
1
1
2
1
1
1
1
1
1
1
0
0
2
1
1
1
0
0
1
1
1
1
1
0
1
1
1
2
2
1
1
2
2
2
1
2
1
0
1
2
1
0
1
1
1
1
1
1
1
1
2
0
1
2
0
0
1
2
1
0
1
1
2
1
0
2
2
0
0
1
1
2
1
0
1
1
1
2
1
1
1
1
1
1
0
1
1
1
1
0
1
0
1
1
2
1
0
1
1
1
2
2
1
1
0
1
2
1
1
1
1
1
1
1
1
0
2
1
1
2
1
1
2
1
1
2
2
1
1
2
1
1
2
0
1
1
1
0
1
0
1
1
1
1
0
1
1
1
2
1
1
1
1
0
0
0
2
1
1
2
1
1
1
0
0
2
1
2
1
1
1
1
1
1
0
1
0
1
1
1
0
2
1
1
2
0
0
2
1
1
1
1
1
2
1
1
1
2
1
1
2
1
2
1
1
0
1
1
1
1
2
2
1
1
1
1
1
0
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
0
1
2
1
0
2
0
1
1
2
1
2
1
1
2
1
2
1
2
1
1
1
1
1
0
2
1
1
1
1
1
1
1
1
0
1
1
0
1
2
1
1
1
2
1
2
1
1
4
0
0
1
1
1
1
1
1
0
2
1
2
2
1
1
1
0
2
1
0
1
1
1
1
1
1
1
2
2
0
1
1
2
0
0
1
1
0
0
1
1
1
3
1
2
1
0
2
1
0
1
1
1
2
1
2
2
0
1
1
2
1
1
2
2
2
1
1
1
2
1
0
1
1
2
2
1
0
0
1
2
1
1
1
2
1
2
1
2
0
2
1
2
2
1
2
1
0
2
1
0
2
2
1
1
0
2
1
2
1
2
1
1
1
1
1
1
1
1
0
2
0
1
2
2
1
0
1
2
1
1
0
1
2
1
2
1
1
2
1
0
1
1
1
1
1
1
1
2
2
2
2
0
1
1
1
1
1
1
3
1
1
1
0
2
0
2
1
1
1
2
1
0
2
1
1
1
0
2
1
0
1
1
0
1
0
1
2
1
1
1
0
1
1
1
1
2
1
1
3
1
0
0
2
1
1
1
1
0
1
2
1
1
1
2
1
1
2
1
2
1
2
1
1
1
2
1
1
1
0
0
1
1
2
1
1
1
2
0
1
2
1
1
1
1
1
2
0
2
2
1
2
0
1
1
1
1
1
1
0
2
2
1
1
2
2
1
2
1
2
1
1
1
1
1
2
2
1
1
1
1
1
0
1
1
1
0
2
0
2
0
1
2
1
1
1
1
1
1
0
0
1
1
1
1
1
1
1
1
2
2
1
2
2
1
2
1
1
1
0
1
1
1
1
2
2
1
1
1
1
1
0
1
1
0
1
1
1
1
2
1
1
0
0
1
2
1
2
0
2
1
1
2
1
2
1
1
1
1
0
1
2
1
2
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
2
1
1
1
2
1
2
0
2
2
2
1
0
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
0
1
1
0
1
1
2
0
1
1
1
1
1
2
1
2
1
2
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
2
1
1
2
1
1
1
0
1
1
1
2
0
1
0
2
1
1
1
2
1
1
1
2
2
1
2
1
1
1
1
1
0
1
0
1
1
1
2
1
2
0
1
0
1
1
1
1
1
1
2
0
1
1
1
1
0
1
1
1
2
2
2
0
1
1
1
0
1
2
1
1
1
0
1
2
1
1
1
1
1
1
1
2
1
0
2
1
1
0
1
1
1
1
1
1
1
0
1
2
1
1
0
2
1
2
2
1
1
1
0
0
2
1
1
1
1
1
1
2
1
0
2
1
1
2
1
0
1
1
1
0
1
1
0
1
2
2
1
1
1
0
1
2
2
1
1
0
1
1
0
2
0
1
1
1
1
1
1
2
3
1
1
2
1
1
1
1
1
1
1
2
0
2
1
1
2
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
2
1
1
1
1
2
2
1
2
0
1
1
1
2
1
0
0
1
0
2
1
1
0
1
1
1
1
1
2
1
1
1
1
1
1
0
2
1
1
0
1
1
1
1
2
0
2
1
2
0
1
1
1
1
2
2
1
1
2
1
1
2
2
1
2
2
1
1
2
2
0
0
2
1
1
1
2
2
2
2
1
1
1
2
1
1
0
1
1
0
2
1
5
2
1
1
1
1
1
1
2
2
0
0
1
1
1
3
1
1
2
1
1
1
1
1
1
2
1
2
1
0
1
2
0
1
0
1
0
1
1
2
1
1
1
1
1
1
0
1
1
1
2
1
0
2
0
2
1
0
1
2
2
1
2
2
2
2
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
0
1
0
1
0
1
1
0
1
0
1
1
1
2
1
3
1
1
1
1
2
2
1
0
1
1
1
2
1
0
1
1
1
1
1
1
1
2
1
0
1
0
0
0
1
0
1
1
0
0
2
0
0
1
2
1
1
0
2
1
0
1
1
2
1
1
1
1
1
2
1
2
2
1
1
1
1
1
1
1
0
1
1
2
1
1
2
3
2
0
1
2
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
0
1
1
1
1
0
2
0
1
0
2
0
2
1
1
2
2
2
2
1
2
0
1
2
2
1
1
1
1
2
1
1
1
2
1
1
0
1
1
1
1
2
0
2
1
2
0
1
1
1
3
1
1
2
2
1
1
1
1
1
0
1
1
1
2
0
1
1
1
1
1
1
1
1
1
2
2
2
2
1
0
1
2
0
1
1
0
2
1
1
0
2
1
1
2
2
1
1
0
1
1
1
2
1
1
1
1
2
0
2
1
1
2
2
1
1
1
1
1
1
0
1
1
1
2
2
1
0
1
1
1
2
2
0
1
1
1
1
1
0
1
0
1
1
1
1
3
2
1
0
1
1
1
1
1
1
1
1
0
1
2
1
0
2
1
1
0
0
1
0
2
1
2
0
2
2
0
1
2
0
1
2
0
2
1
0
0
1
0
1
1
1
0
2
1
2
1
2
0
2
0
2
1
1
1
1
1
0
2
1
2
2
1
1
1
1
1
2
1
1
1
2
1
1
0
1
2
1
1
2
1
1
1
0
1
0
1
2
0
2
0
1
2
1
1
1
1
1
1
0
1
1
1
0
1
0
1
1
1
1
1
1
1
1
1
2
0
2
0
1
1
1
0
1
1
1
1
1
1
0
2
1
1
1
2
1
1
2
2
1
1
1
1
0
1
2
2
1
1
1
1
1
1
2
2
1
2
1
1
1
1
2
2
0
0
0
1
2
1
1
2
1
2
0
0
1
1
1
0
0
1
1
1
2
2
1
1
1
1
2
3
1
1
1
2
1
1
1
1
2
1
2
1
2
1
2
1
2
0
1
1
1
1
1
1
1
1
0
0
1
1
1
1
2
0
2
0
1
1
2
1
1
2
1
1
1
0
1
2
1
1
1
1
1
6
1
0
1
0
1
2
2
1
1
1
1
1
1
1
1
1
1
1
2
2
2
2
2
2
1
1
1
1
1
1
2
1
2
1
1
1
1
2
1
2
1
1
1
1
0
1
1
3
1
1
2
1
2
0
2
1
1
2
2
2
1
2
2
0
0
0
1
1
1
1
2
2
2
1
2
2
3
1
0
1
1
0
1
1
2
1
2
1
0
2
2
2
2
1
2
1
0
1
1
1
2
1
2
1
1
2
2
2
0
1
1
2
1
2
0
1
1
1
1
0
2
1
2
1
0
2
1
2
1
2
1
1
1
1
1
0
1
1
2
0
1
2
1
1
1
1
1
2
0
0
0
1
1
0
1
1
2
1
2
1
0
0
2
0
2
1
0
1
1
2
1
1
1
0
1
1
0
1
1
2
2
1
1
1
2
1
1
2
2
1
2
1
2
0
1
1
1
2
1
2
2
2
1
1
1
2
1
1
1
1
2
1
0
1
1
1
1
0
1
1
1
1
1
2
1
0
2
1
0
2
2
1
1
1
1
1
3
1
1
1
2
1
2
1
1
0
1
2
2
1
1
0
2
1
2
0
1
1
2
1
2
1
2
1
0
2
1
1
1
1
2
0
1
1
1
0
1
0
1
1
0
0
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
0
1
1
2
0
1
1
1
1
0
0
1
1
2
1
1
0
1
1
2
1
1
2
1
1
1
1
1
1
1
1
0
0
2
1
1
1
1
1
0
1
2
2
1
1
1
1
1
1
1
0
1
0
2
1
1
1
1
2
1
1
2
1
1
2
1
2
1
1
1
1
1
2
2
1
1
1
2
2
1
2
0
1
1
1
1
1
1
2
1
1
0
1
1
0
0
1
1
1
1
1
2
1
1
0
2
0
1
0
2
1
2
1
2
2
1
2
1
2
1
1
2
1
1
1
2
0
2
1
1
2
1
1
1
2
1
2
2
1
1
2
0
2
0
1
1
1
1
2
1
1
2
1
1
2
1
2
1
1
0
1
2
1
1
1
1
0
1
0
1
1
1
1
1
1
2
0
1
1
2
2
2
2
0
2
2
2
2
1
1
1
1
1
2
0
2
1
2
1
0
1
1
1
2
1
2
2
0
1
1
1
1
1
0
1
2
1
1
1
1
2
1
2
2
2
2
2
1
2
1
2
1
1
2
1
1
1
1
1
2
2
0
1
2
1
1
1
1
1
1
2
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
0
1
1
0
1
1
1
2
2
1
2
1
1
2
1
1
1
2
2
1
1
1
0
2
1
0
0
1
2
2
1
0
1
2
1
1
1
1
2
1
2
2
1
1
2
1
1
3
1
2
1
0
2
1
1
1
1
1
2
1
1
2
0
1
1
2
1
1
0
2
2
1
2
1
2
0
1
1
0
1
1
1
1
1
1
0
1
1
1
1
1
0
2
1
1
1
2
2
1
1
0
0
1
2
1
1
2
1
1
1
2
2
1
1
0
2
1
0
1
1
0
1
1
0
1
1
2
1
1
0
1
0
1
2
1
1
1
1
2
1
2
0
2
2
1
1
1
0
1
0
2
0
1
2
1
1
1
0
2
1
2
1
2
1
1
1
2
2
1
1
1
2
1
1
1
0
1
1
1
1
1
1
2
2
1
2
0
1
1
1
1
1
1
1
1
2
1
0
2
2
1
0
2
1
1
1
1
1
1
2
2
1
2
1
1
2
1
1
0
0
1
2
1
1
2
0
2
2
1
2
1
1
1
0
3
1
2
2
1
0
0
1
1
1
1
2
1
1
1
1
2
1
0
2
1
1
1
1
1
1
1
1
1
2
0
1
2
1
2
1
2
1
1
2
0
3
2
0
1
2
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
2
1
2
1
1
1
0
1
0
0
1
1
1
1
1
0
1
2
1
1
0
1
1
1
1
2
1
1
2
2
1
1
2
1
1
2
1
1
0
1
0
2
1
2
1
2
1
2
1
1
1
2
1
1
2
1
2
1
1
1
0
2
1
1
1
1
0
2
2
1
1
0
1
1
1
2
1
1
1
0
1
2
2
1
1
1
2
1
1
1
0
2
1
1
1
3
1
1
1
0
1
2
1
1
2
1
0
1
1
1
1
1
0
0
0
2
1
0
1
2
1
2
1
1
2
2
3
3
2
2
1
0
1
0
1
2
1
2
0
1
2
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
2
2
0
1
0
1
2
1
2
1
1
1
2
1
1
1
1
1
2
1
0
3
0
1
0
1
1
1
0
2
1
1
1
1
2
1
1
2
1
1
1
2
1
1
2
1
1
1
0
1
1
0
1
2
2
2
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
0
1
2
0
1
1
1
1
1
2
1
1
2
1
1
2
1
2
1
2
1
2
1
1
2
1
1
2
1
1
1
1
1
2
1
0
1
1
1
0
1
1
1
2
1
1
1
1
0
1
2
2
1
0
1
1
4
0
2
1
1
1
1
1
0
0
1
1
1
0
1
1
1
3
1
1
1
2
2
2
1
1
3
0
2
2
2
1
2
2
1
1
1
1
1
1
1
2
0
1
1
2
0
1
1
1
1
2
2
0
2
2
2
1
2
1
0
1
1
1
3
1
2
1
0
2
0
0
0
1
1
2
1
2
1
1
1
2
1
1
1
1
0
1
2
0
1
4
2
2
2
1
1
1
1
1
1
2
2
1
1
1
2
2
4
2
2
1
2
1
0
1
0
1
1
1
0
2
1
1
0
2
0
0
2
1
1
1
1
0
2
2
1
1
1
2
1
0
0
2
2
1
1
1
1
1
1
2
2
2
1
1
2
1
1
1
0
1
0
1
1
0
1
1
1
0
0
1
1
1
1
1
1
1
1
1
1
1
0
1
2
1
1
2
1
0
2
1
1
2
1
1
1
1
1
1
2
1
2
1
2
1
1
2
2
0
1
2
1
2
0
2
0
2
1
0
1
2
2
1
1
1
2
1
1
2
1
1
2
1
1
0
1
1
1
1
0
2
2
2
2
2
2
1
2
0
2
1
1
1
0
1
1
1
1
1
1
1
1
1
0
0
1
0
2
2
1
1
2
1
2
1
1
1
1
1
1
1
0
1
0
2
0
2
1
0
1
2
1
1
0
1
0
0
1
2
1
1
1
1
1
1
1
2
1
1
0
1
1
1
1
1
1
1
1
1
1
2
1
1
0
0
0
1
1
0
2
1
0
1
0
1
1
2
1
2
1
2
2
1
1
1
1
1
2
0
1
2
2
2
0
1
1
1
1
2
1
1
2
2
0
1
1
1
2
2
1
1
1
1
2
0
2
2
0
2
1
0
2
1
1
1
1
0
1
1
1
0
1
2
1
1
1
1
1
1
2
1
1
1
5
2
1
1
1
0
1
1
1
0
2
0
1
1
1
1
1
1
1
1
2
1
2
0
2
1
0
1
0
1
1
2
1
1
2
1
1
2
1
1
2
1
1
1
1
1
2
0
2
1
1
1
2
2
1
2
1
0
1
1
2
1
1
1
1
2
1
1
1
2
2
1
1
0
1
1
2
0
1
2
1
1
1
2
0
0
1
1
1
0
1
1
1
1
1
2
1
2
1
3
1
1
1
1
1
0
2
3
1
1
2
2
1
1
1
0
0
1
2
1
2
1
2
1
1
1
0
2
0
1
1
2
1
2
1
1
0
2
1
1
1
1
0
2
1
2
1
1
1
1
2
0
1
1
2
1
1
0
0
1
1
1
1
1
1
2
0
2
2
1
2
2
1
0
1
1
1
1
1
1
0
0
1
0
0
1
2
2
1
1
1
2
1
1
1
2
2
1
0
1
1
2
2
3
1
1
1
1
1
0
1
1
1
0
1
1
2
1
0
1
2
1
0
2
1
0
1
0
0
1
1
1
2
2
1
1
1
0
1
2
1
1
2
1
2
1
1
1
1
1
0
2
1
2
2
1
0
0
1
0
1
2
0
1
1
1
2
1
1
1
1
2
1
2
0
1
1
1
1
0
2
2
1
1
1
1
1
1
1
1
2
2
2
1
0
0
2
1
2
1
1
2
1
1
1
1
0
1
1
1
2
0
2
1
1
1
1
2
1
1
1
2
1
1
1
2
1
2
1
1
1
2
2
2
0
1
1
0
0
1
2
1
1
2
1
1
1
0
1
1
1
0
0
1
1
1
2
2
0
1
1
2
1
1
1
1
1
2
1
2
1
1
1
0
2
1
1
0
0
1
0
0
0
2
2
0
2
2
1
1
2
1
2
2
1
0
1
1
0
1
1
1
2
1
1
1
0
1
2
1
1
1
1
1
1
1
2
1
1
1
1
0
2
2
2
2
1
0
2
2
2
1
1
1
2
1
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
2
0
2
1
1
2
2
2
1
0
1
0
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
2
2
1
1
1
1
0
0
1
1
1
1
1
2
3
1
2
1
1
1
2
1
0
0
1
1
1
1
0
2
2
1
2
1
0
2
2
1
1
0
1
2
2
2
2
1
1
1
1
2
0
1
0
1
1
1
1
1
1
1
2
1
2
1
2
1
1
1
1
1
1
0
0
1
1
1
1
2
1
1
1
1
1
1
1
0
0
1
1
0
1
1
1
0
1
1
1
1
1
1
0
1
1
0
1
1
2
1
2
2
0
0
2
1
1
1
1
1
2
1
1
1
1
0
1
1
2
1
0
0
1
2
1
2
1
1
1
1
2
2
2
1
1
1
1
2
1
0
3
1
0
1
1
1
1
1
1
1
1
2
0
2
2
0
0
2
1
1
1
1
1
1
1
1
2
1
1
1
1
2
2
0
1
0
0
1
0
2
1
2
1
0
1
1
0
0
1
1
1
2
1
1
2
1
1
1
2
1
1
2
0
1
1
2
2
2
1
1
1
0
2
1
1
1
2
0
1
1
1
1
1
1
1
0
2
0
2
2
1
1
1
0
1
1
2
1
1
1
2
1
1
1
1
2
2
1
2
1
1
1
2
0
1
1
0
0
0
2
1
4
0
1
2
0
1
1
0
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
1
2
1
0
0
2
0
2
1
2
1
1
2
2
2
1
2
0
1
2
0
2
2
2
1
2
1
2
0
1
1
0
1
1
1
2
1
1
1
1
1
0
1
2
1
3
2
2
1
1
1
2
1
2
1
1
2
1
1
0
2
1
1
1
2
0
1
1
0
1
2
1
1
1
1
1
0
1
1
0
1
0
2
1
2
1
1
2
1
0
1
1
1
1
1
1
1
1
1
2
1
1
1
0
2
2
0
1
1
1
1
1
2
2
1
1
2
1
1
1
2
1
2
1
1
0
1
0
1
0
1
2
2
0
1
0
0
1
2
1
5
0
2
2
1
0
0
1
0
3
1
1
1
0
1
1
0
1
1
2
2
1
1
1
1
0
1
1
0
2
1
2
1
1
1
0
2
2
2
1
1
1
1
0
0
0
1
1
1
1
1
1
1
1
2
1
1
0
2
1
1
1
1
1
2
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
0
1
1
2
1
0
1
0
1
2
1
0
1
0
2
0
2
2
0
1
1
1
0
1
0
1
1
0
1
1
0
1
1
1
1
1
1
2
1
1
2
0
1
1
1
1
1
2
1
1
2
1
0
2
0
1
1
1
1
1
1
0
1
2
2
2
1
2
1
1
2
0
1
1
1
0
0
1
1
1
1
1
1
2
0
0
1
1
0
1
1
1
0
1
1
0
1
1
2
1
1
0
1
1
0
2
1
1
1
2
1
2
1
1
0
2
2
1
2
2
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
2
1
0
2
1
1
1
1
0
1
1
2
2
1
2
0
1
0
1
2
2
1
1
1
1
2
1
2
1
1
2
1
1
1
1
1
2
2
1
1
1
0
1
0
1
2
2
1
2
0
1
1
1
3
2
1
2
1
2
1
1
2
1
1
1
2
2
1
1
0
1
1
1
1
1
0
3
1
1
2
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
3
1
1
2
1
1
1
0
1
0
2
1
1
2
1
1
1
2
0
1
1
0
1
1
1
2
2
2
1
1
1
1
1
0
2
1
1
2
1
1
1
1
1
2
1
1
0
1
2
0
2
1
1
2
1
1
1
2
1
0
1
1
0
2
1
1
0
0
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
2
2
1
1
2
2
1
1
1
0
2
0
1
0
1
0
2
0
1
1
0
1
2
2
1
2
2
1
0
0
2
2
2
3
1
1
2
2
2
1
2
1
1
1
2
0
1
2
0
2
1
1
2
1
1
1
5
2
1
1
1
1
1
1
1
1
2
2
2
1
1
1
2
1
2
1
2
1
1
1
0
2
1
2
1
1
0
1
1
1
0
2
1
2
1
1
1
0
1
1
2
1
1
1
0
0
1
2
1
2
3
1
2
0
1
0
2
0
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
0
2
0
0
0
1
1
2
1
0
1
1
1
1
2
1
1
2
1
2
1
1
2
1
1
1
1
1
1
0
2
0
0
1
1
2
1
2
0
1
1
1
1
1
1
1
0
1
1
0
0
1
1
0
0
1
1
1
2
1
2
2
2
1
1
0
1
0
2
1
1
2
1
2
1
2
1
1
2
0
0
1
1
1
2
2
1
1
1
0
2
1
1
1
1
2
0
1
1
1
2
0
0
2
1
2
1
1
0
2
1
1
2
0
1
3
0
1
2
0
1
2
0
2
1
1
2
1
2
1
2
1
1
2
1
2
1
1
1
2
1
1
2
1
1
2
1
2
1
1
2
2
1
1
1
1
0
2
1
1
1
1
0
0
0
0
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
2
1
1
2
1
1
1
2
1
1
1
1
1
0
1
1
1
2
1
1
1
1
1
1
2
1
1
1
0
0
2
2
1
2
1
2
2
1
0
0
1
1
1
1
0
1
1
1
1
1
1
2
2
1
1
2
2
1
1
1
2
0
0
0
1
1
1
2
1
1
1
1
2
0
1
0
1
2
1
2
1
1
1
1
1
0
0
1
2
1
1
0
2
1
0
1
1
0
2
1
2
0
0
1
1
2
1
1
1
0
1
1
2
0
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
0
1
2
1
1
1
1
1
1
1
1
1
1
2
0
1
1
1
0
2
1
0
1
2
2
1
2
0
0
2
2
1
2
2
1
1
1
0
1
2
2
2
1
1
2
1
1
1
1
2
2
1
0
1
1
1
2
2
1
1
1
1
1
2
4
3
0
1
0
1
0
1
0
1
1
2
1
1
1
2
2
1
1
0
1
1
1
1
1
1
1
2
1
1
0
1
2
1
2
1
1
1
1
0
1
1
1
1
1
1
0
2
1
1
1
2
2
2
1
1
0
2
1
1
1
0
1
1
0
1
0
2
1
1
1
1
1
0
1
1
1
2
1
2
1
2
2
2
0
2
2
0
2
0
0
0
1
2
2
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
0
1
2
1
1
1
1
1
0
0
1
1
0
2
2
1
0
1
1
2
1
1
1
2
1
1
1
1
2
1
0
1
1
0
2
2
1
1
1
1
0
1
0
1
1
3
1
2
1
1
2
2
1
2
2
1
2
1
1
2
1
1
1
1
1
1
2
1
1
0
1
0
1
1
1
1
1
1
0
1
0
2
2
1
2
2
2
0
1
1
1
1
1
2
2
1
1
1
2
1
0
1
1
1
1
1
0
2
1
1
1
1
1
1
2
0
1
1
1
1
1
1
1
2
1
1
1
2
1
1
0
2
1
1
1
1
1
1
1
1
2
1
2
2
1
1
1
2
2
2
1
1
1
2
1
2
2
1
1
1
0
1
1
1
0
2
1
0
1
1
1
1
1
1
1
1
0
0
2
2
1
1
1
1
0
0
2
1
1
1
1
1
0
1
1
2
1
1
2
0
1
1
1
0
1
1
2
1
2
1
1
1
1
1
1
0
1
1
1
2
1
0
1
1
1
1
1
2
2
1
1
1
2
1
1
1
2
1
1
0
2
1
2
1
1
0
1
0
1
1
1
1
2
2
0
0
0
0
2
1
2
2
1
2
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
0
1
1
1
1
0
2
1
0
2
2
0
1
2
1
1
0
0
1
2
0
1
1
0
1
2
1
2
2
1
1
1
1
1
2
1
2
1
1
1
2
1
1
1
0
1
1
1
1
0
2
1
2
1
1
2
1
1
1
1
1
1
3
1
1
1
1
1
0
2
2
2
2
2
2
2
1
1
1
1
1
2
1
0
1
1
1
1
1
0
1
1
1
1
0
1
2
1
1
0
1
1
0
2
2
1
1
1
1
1
1
2
1
0
1
2
1
2
1
1
2
2
1
1
1
2
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
2
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
0
2
0
1
1
2
0
1
1
2
1
1
0
1
2
1
2
2
2
1
1
2
1
0
2
1
1
1
2
2
2
1
0
0
0
1
1
1
1
1
1
0
0
1
1
0
1
1
1
1
1
2
2
2
1
1
0
0
1
2
1
1
1
1
1
1
0
1
1
2
2
1
1
2
1
1
1
0
1
1
1
4
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
0
1
2
0
2
1
0
1
1
2
2
1
2
2
1
1
1
1
2
1
1
1
1
1
1
0
1
2
1
2
1
1
1
0
2
2
1
2
1
1
0
1
0
0
2
2
1
1
1
2
1
1
1
1
0
2
2
1
1
1
1
1
2
1
0
2
1
1
2
1
1
2
0
1
1
2
1
1
2
1
1
1
1
2
1
1
2
2
1
1
1
1
2
2
1
1
1
1
2
0
2
0
1
1
1
2
1
2
1
2
1
1
1
1
2
1
2
1
2
1
1
1
1
2
1
1
1
1
0
2
1
1
1
1
0
1
2
0
1
1
1
2
1
0
1
1
2
1
0
1
1
1
0
0
0
0
2
1
2
0
0
0
2
1
1
0
1
1
3
0
1
1
2
1
1
1
1
1
0
1
1
1
1
1
1
1
1
2
1
1
1
2
3
1
2
1
2
1
2
1
1
1
2
1
1
0
1
1
1
2
2
0
2
1
1
1
0
0
1
1
1
1
2
2
1
2
1
1
1
1
2
1
2
1
1
1
2
1
3
1
1
0
1
1
2
1
2
2
2
1
0
1
1
1
2
1
1
1
0
2
2
0
1
1
1
1
0
2
2
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
0
1
2
1
2
2
1
1
1
1
1
1
2
1
1
1
2
1
1
0
1
1
1
1
2
2
1
1
1
1
1
0
0
2
1
0
0
2
0
1
2
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
0
0
0
2
1
1
1
1
0
0
1
1
0
1
2
1
2
0
2
1
1
2
1
1
0
1
1
0
1
1
1
2
2
1
1
2
2
1
1
2
1
2
1
1
2
0
0
1
2
1
0
2
2
2
1
1
1
0
1
0
1
0
1
1
0
1
1
1
2
1
1
0
1
2
1
0
1
1
1
1
1
1
2
1
0
1
1
1
2
1
1
0
2
2
0
2
1
1
1
0
1
1
0
1
0
1
1
1
1
0
1
1
1
2
2
1
1
1
1
1
1
1
1
0
1
1
0
1
1
1
1
1
1
1
1
2
1
0
2
1
1
1
1
1
2
1
2
1
0
2
1
2
0
1
1
1
1
1
2
2
0
2
2
1
2
1
2
0
1
1
1
1
1
2
1
3
0
2
0
2
0
1
1
1
2
0
2
1
1
0
2
2
1
1
1
1
1
1
2
1
2
0
1
2
2
1
2
1
2
2
1
0
3
2
1
0
1
2
0
1
0
1
0
1
1
1
1
1
1
1
1
0
1
0
1
2
1
1
1
2
2
1
1
1
1
1
0
0
1
1
1
0
0
1
2
1
0
0
2
2
0
1
2
1
1
1
1
1
2
1
1
1
2
2
0
2
1
1
1
0
2
1
1
0
0
1
1
2
1
1
1
1
2
1
1
1
0
2
1
0
1
1
1
2
1
2
0
2
2
2
1
1
1
1
0
2
2
1
2
1
2
0
1
1
1
1
1
1
1
2
2
1
1
2
1
0
2
1
2
0
1
1
1
2
0
1
2
2
1
1
1
2
1
1
0
2
1
1
0
1
1
1
2
2
1
1
2
1
1
1
0
1
2
1
1
1
1
1
1
1
1
1
0
2
1
1
1
0
0
2
1
2
0
0
0
1
1
1
1
0
0
1
1
2
2
0
1
0
1
1
0
1
1
2
1
0
0
1
1
1
1
2
0
2
1
1
1
1
1
2
1
1
0
1
2
0
1
1
2
2
1
1
1
1
1
1
2
2
1
1
2
1
2
1
1
2
0
1
1
1
1
0
1
1
1
2
1
1
1
2
2
1
2
1
1
1
1
0
4
2
1
1
1
1
1
1
1
1
0
1
1
1
1
2
1
0
2
1
2
2
0
1
1
1
1
0
1
2
1
1
2
0
2
1
1
1
0
1
1
1
2
1
1
1
1
0
2
1
0
2
0
1
2
1
1
1
3
0
2
1
1
0
0
1
1
2
1
1
1
1
0
2
0
1
1
1
1
1
1
0
2
2
1
1
0
1
1
1
1
1
0
1
2
1
1
2
1
2
0
1
1
1
1
1
0
1
2
2
1
1
1
2
1
1
1
1
4
0
1
0
0
1
1
2
0
2
2
1
1
1
1
0
1
2
2
1
2
1
0
1
1
0
2
1
0
0
1
1
1
1
0
1
1
2
1
1
1
1
2
1
1
1
0
1
2
1
0
1
1
1
0
2
2
1
1
1
2
1
1
1
1
2
1
1
2
1
0
2
1
2
1
1
1
1
0
2
1
1
0
2
0
1
0
1
2
1
1
1
1
1
1
1
1
1
1
1
2
0
1
1
5
1
1
1
1
1
1
1
0
2
2
0
1
1
0
1
1
0
2
0
2
2
1
0
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
0
1
2
1
2
1
2
1
1
1
1
0
1
0
0
1
1
2
0
1
2
0
1
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
2
2
2
2
2
1
1
1
1
1
1
1
2
2
2
1
2
1
1
0
1
1
1
0
2
2
1
1
1
2
1
2
2
2
2
1
1
0
0
1
1
1
2
1
1
0
2
1
0
1
1
1
2
1
1
2
3
0
1
1
0
1
2
2
2
1
0
1
0
2
1
1
1
1
0
1
1
1
1
1
2
1
1
2
1
2
1
2
2
1
1
1
2
0
1
0
2
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
0
1
2
1
1
1
2
1
3
1
1
2
1
0
1
1
0
2
2
1
1
2
1
1
1
1
1
2
2
2
2
2
0
1
1
1
1
1
1
2
0
0
1
1
1
1
1
1
1
1
2
0
1
1
1
1
1
0
1
1
1
1
1
1
1
2
0
2
1
1
2
2
1
0
0
1
1
1
1
1
2
4
0
0
1
1
1
1
1
3
1
1
1
1
0
0
1
2
2
1
1
1
1
1
0
1
1
1
0
1
1
2
1
1
1
1
0
1
0
1
1
1
1
1
2
3
2
1
1
1
1
1
0
2
1
1
2
0
1
2
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
2
3
1
2
1
1
1
1
0
2
1
0
1
1
2
2
1
2
1
1
2
1
1
1
2
2
0
1
2
1
2
2
1
1
1
1
2
1
1
1
0
1
1
0
0
0
1
1
2
1
2
2
2
1
2
1
1
1
0
1
2
1
1
1
1
2
2
2
0
1
0
1
1
0
1
2
1
1
1
2
1
2
0
1
1
1
1
1
2
1
0
0
2
1
2
0
2
1
2
2
2
1
1
1
1
0
2
1
0
1
2
1
1
0
1
1
1
2
0
1
1
2
2
0
2
1
1
2
1
2
1
1
1
1
1
2
2
1
1
1
1
2
2
0
1
0
1
1
1
1
0
1
1
1
1
0
0
2
1
1
0
2
2
2
0
1
2
0
1
1
1
0
0
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
2
1
1
0
1
2
1
1
1
0
1
0
2
1
1
1
0
2
1
2
1
2
1
1
0
1
2
2
1
1
1
1
1
1
1
1
0
0
1
1
1
2
1
1
2
1
1
0
0
2
1
2
1
1
1
0
1
1
1
1
0
1
1
1
2
1
1
1
1
1
1
2
0
2
1
1
1
1
2
1
2
0
1
1
2
2
1
0
1
1
2
1
1
2
1
2
2
2
2
1
1
2
1
0
2
1
2
0
1
2
1
2
2
0
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
0
2
1
1
1
0
0
1
1
1
1
1
2
2
1
1
2
1
1
1
1
2
1
0
1
1
1
1
1
1
2
2
1
2
1
1
2
2
1
3
0
1
1
2
1
1
2
1
2
1
1
2
1
1
1
2
1
1
1
0
2
1
1
1
1
0
1
1
2
1
0
2
1
2
2
1
1
0
1
0
1
1
1
0
1
2
1
2
1
0
1
1
2
1
1
1
1
1
1
1
1
2
2
1
1
0
2
1
1
6
2
0
1
1
1
2
1
1
3
0
1
2
1
0
0
1
2
1
1
0
1
2
1
3
0
1
0
1
2
1
1
1
0
1
1
1
1
1
2
1
1
1
1
2
1
1
1
0
1
1
1
1
2
1
1
1
0
1
1
2
1
1
1
1
1
1
1
0
0
1
1
2
1
1
1
1
1
0
1
1
1
2
1
0
1
0
0
2
1
1
1
1
1
1
1
0
1
1
1
1
2
1
1
0
1
1
2
2
1
1
2
2
2
1
1
2
1
1
2
1
2
1
1
0
1
1
1
2
1
1
1
1
2
2
1
1
1
0
1
1
0
0
1
1
1
2
2
0
2
1
1
0
1
1
1
2
1
1
2
1
2
0
1
1
4
2
2
1
1
1
1
1
1
2
1
1
2
1
1
1
3
1
2
1
1
1
1
1
1
0
1
2
0
0
2
2
1
1
1
1
1
0
1
1
0
0
0
1
0
2
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
2
1
2
0
1
1
0
1
1
0
0
1
1
0
1
0
1
2
2
1
1
0
0
1
1
1
2
1
1
0
1
1
1
0
0
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
0
1
1
0
0
0
2
0
1
2
0
2
0
1
1
1
1
1
2
1
0
1
1
0
1
1
1
2
2
2
1
1
1
1
2
1
1
2
1
2
1
2
1
1
1
1
1
1
1
1
0
1
1
2
2
0
2
1
1
0
1
1
1
2
1
2
1
1
1
1
0
1
1
0
0
1
1
1
1
2
2
0
1
1
0
0
2
1
1
1
1
1
1
2
1
4
1
2
1
2
2
2
2
0
1
1
1
1
2
1
0
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
0
2
1
1
2
2
1
1
2
0
1
2
2
1
1
1
2
1
0
1
1
1
2
1
1
1
1
0
1
1
1
0
1
1
1
0
2
1
1
1
1
1
1
0
1
1
1
1
2
1
2
0
2
0
0
0
1
0
1
2
1
2
2
1
1
1
2
1
1
2
2
1
1
1
2
1
1
2
1
1
2
1
2
1
0
2
1
1
1
1
1
1
1
0
1
2
1
1
2
1
0
1
1
1
1
1
0
1
1
1
1
1
1
0
2
1
2
1
1
1
0
1
2
1
1
2
1
1
1
1
2
1
2
2
1
1
1
2
1
1
0
1
0
0
0
1
2
1
2
1
0
1
0
2
1
1
1
1
2
2
1
1
2
1
1
1
2
1
1
2
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
0
0
2
1
1
2
1
2
2
1
2
1
1
1
0
0
1
2
2
1
1
1
1
0
1
1
1
2
1
1
2
1
2
4
5
1
1
1
1
1
0
1
1
1
1
1
1
2
1
1
2
0
1
1
1
2
2
1
2
1
1
2
1
1
1
1
1
1
1
1
2
0
2
1
1
2
1
1
1
1
1
2
2
1
4
0
1
1
0
2
1
1
1
2
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
0
1
1
2
1
1
1
2
0
1
1
1
0
1
1
1
1
0
1
1
2
2
1
2
1
0
2
1
2
2
2
1
2
1
3
2
1
1
1
0
1
1
1
1
1
1
2
1
1
1
1
0
1
1
0
2
1
1
1
0
1
2
1
1
2
1
1
1
1
1
1
2
1
1
0
1
1
1
1
1
0
1
1
2
1
1
0
2
0
1
0
1
1
1
1
2
1
1
1
1
1
0
1
0
2
1
1
1
1
2
1
2
1
1
1
1
2
1
1
2
1
1
0
1
1
2
1
1
0
1
2
0
1
1
0
2
1
2
1
2
0
1
1
1
1
0
2
1
1
2
0
2
0
1
1
1
1
1
1
2
3
2
1
1
1
1
1
2
1
1
1
1
2
2
2
1
2
1
0
1
1
1
2
1
1
0
1
2
1
1
1
1
1
2
1
1
2
2
1
1
1
0
0
1
1
1
2
1
1
0
1
1
1
1
1
1
1
1
0
1
1
2
1
1
2
2
1
1
2
1
2
2
1
1
1
2
1
2
2
1
1
1
2
1
2
1
2
1
2
0
1
0
0
0
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
5
0
1
0
1
1
2
2
1
1
0
1
2
2
1
1
1
1
1
1
0
1
0
1
1
1
1
1
1
2
1
1
1
1
2
1
2
2
0
0
1
0
0
1
2
2
1
2
1
1
1
1
2
2
1
1
1
1
2
1
1
1
0
1
1
1
0
0
1
0
1
1
1
1
1
1
2
1
2
1
0
1
3
1
1
1
0
1
0
0
1
1
2
1
1
1
0
1
1
2
1
1
1
2
1
1
2
1
1
1
1
1
1
0
1
3
1
1
2
2
1
2
1
1
2
2
1
1
0
2
1
1
1
0
1
0
1
0
0
1
1
1
2
0
2
0
1
1
0
1
0
0
1
1
1
1
0
2
1
1
1
2
2
1
1
1
2
1
1
0
1
1
1
1
1
1
2
2
1
1
2
1
1
2
1
1
1
0
1
1
1
1
0
1
2
2
1
1
1
0
0
1
1
2
1
2
1
1
2
0
1
2
1
1
2
1
1
0
1
0
1
1
2
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
0
1
1
1
1
0
1
2
1
1
0
0
1
2
1
1
1
2
2
1
0
0
1
2
1
2
1
2
1
0
1
1
1
2
1
1
2
2
0
2
1
1
1
0
1
1
1
1
0
1
1
1
1
2
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
2
2
2
1
2
2
1
1
1
2
1
1
1
1
1
2
2
2
1
2
1
1
1
1
2
2
2
1
2
1
2
0
1
1
2
2
1
1
0
1
2
0
1
2
2
0
1
2
0
1
2
1
2
1
0
0
0
0
2
0
2
1
1
1
0
1
2
2
2
1
2
2
1
1
2
0
1
2
1
2
1
1
2
1
1
2
1
0
1
3
1
0
0
1
0
3
1
0
1
1
0
1
2
0
2
1
1
1
1
1
1
1
1
1
0
0
2
2
1
2
1
1
1
1
1
2
1
2
2
1
1
1
2
1
0
2
2
2
2
1
0
1
2
2
1
1
1
1
2
1
2
2
2
2
1
1
1
1
1
1
1
0
1
2
1
1
1
1
1
1
0
0
0
2
2
2
0
1
0
1
0
2
1
0
0
1
1
0
0
1
1
1
2
0
1
0
2
0
1
1
2
0
0
2
1
1
2
1
1
1
1
1
1
1
2
0
0
1
1
1
1
1
2
1
1
1
1
1
1
0
0
1
1
1
2
0
1
3
2
1
1
0
1
2
0
1
0
1
1
1
0
1
1
0
0
1
1
0
1
1
1
0
1
1
0
2
0
1
1
1
0
2
2
1
1
1
1
2
1
1
2
1
1
1
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
0
1
2
1
1
1
0
1
0
0
1
2
1
2
1
1
1
1
1
2
2
1
1
0
2
1
1
1
2
2
2
1
1
1
0
1
1
1
1
0
1
1
2
2
2
2
1
1
2
1
1
1
2
2
2
2
1
1
1
1
2
0
2
1
1
2
1
2
1
2
2
1
1
2
1
2
1
1
2
1
1
2
0
2
1
1
2
1
1
1
0
1
1
1
1
1
2
1
1
0
1
1
1
2
1
1
2
1
2
0
2
2
2
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
2
1
2
2
1
0
1
1
1
0
1
0
0
2
1
0
2
1
0
2
1
1
1
0
3
0
2
1
0
1
1
2
0
1
1
0
1
2
1
2
1
0
4
1
2
1
1
2
2
1
1
2
1
1
1
2
1
1
2
2
0
1
0
1
0
1
1
4
0
1
1
0
0
2
1
0
1
1
1
2
2
2
1
0
1
1
1
1
1
2
2
1
0
1
0
1
0
1
1
2
1
1
2
2
2
1
1
1
2
2
1
1
1
1
2
0
1
2
1
2
1
2
1
2
1
2
2
0
1
2
1
2
0
1
1
0
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
0
1
1
1
2
2
1
1
1
1
1
0
2
2
2
1
1
1
1
1
2
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
2
1
1
1
0
1
1
1
2
1
0
2
1
1
1
2
1
1
2
1
0
1
0
1
2
1
2
0
1
1
1
1
1
2
1
1
0
2
2
1
1
2
1
0
0
1
1
2
2
1
1
1
0
2
1
1
1
1
1
1
1
1
1
1
2
0
1
2
1
1
0
1
1
2
2
1
2
1
1
1
0
0
1
2
1
1
0
2
7
0
1
2
1
1
1
2
1
1
1
2
1
1
2
1
1
2
1
0
0
1
1
1
2
1
1
1
1
1
2
2
1
2
1
2
1
1
0
2
2
1
1
2
2
1
1
2
2
1
2
1
2
0
1
0
2
1
1
1
1
1
1
2
1
1
1
0
0
1
0
2
2
1
1
2
2
1
2
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
0
0
0
2
2
1
1
2
1
2
1
0
1
2
2
1
1
0
1
0
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
0
1
1
0
1
1
1
2
2
1
2
1
0
0
0
2
1
0
1
1
0
1
0
0
1
2
1
0
1
2
1
2
0
1
1
1
0
2
0
0
1
1
0
0
1
1
2
1
1
1
0
2
2
2
2
1
1
1
1
1
0
1
1
2
1
1
1
1
0
1
1
1
1
1
2
2
1
1
1
1
2
1
1
2
1
1
1
2
1
1
0
2
2
3
0
1
2
1
1
2
1
2
2
1
1
2
0
1
2
1
2
0
1
1
0
1
2
0
1
1
0
2
0
2
1
2
0
1
1
1
1
1
2
0
2
0
0
1
2
1
0
0
0
1
1
1
0
2
2
1
0
2
2
1
1
2
2
1
1
3
1
1
1
1
1
2
2
1
1
0
2
2
1
1
0
1
1
1
1
1
1
2
2
0
1
0
2
1
2
1
1
0
2
1
2
1
1
2
2
1
1
1
2
1
2
2
1
1
1
1
1
1
1
0
1
0
1
1
0
1
2
1
2
1
1
1
0
1
1
1
1
1
0
2
2
2
1
2
1
1
1
0
1
1
1
1
0
2
1
1
1
1
2
0
2
1
1
1
2
1
1
1
1
1
2
2
2
1
1
0
0
1
2
1
3
1
0
1
1
2
1
1
2
1
1
0
0
1
1
1
1
1
2
1
1
1
3
1
1
2
2
1
0
1
1
1
1
1
1
1
2
1
0
2
1
2
1
1
1
1
1
1
0
1
1
2
1
0
1
2
1
1
1
1
2
1
1
2
1
1
2
1
1
2
1
1
1
1
0
1
1
2
1
1
1
1
1
2
1
1
2
1
1
0
0
2
1
1
0
2
1
0
1
1
1
1
1
0
2
1
1
1
2
1
1
1
1
3
2
1
1
2
2
2
1
1
0
1
1
2
1
1
1
0
2
1
1
1
2
1
2
2
1
1
1
2
2
1
2
1
1
1
1
1
2
2
2
0
1
2
2
1
1
0
2
0
3
1
1
1
2
1
1
2
2
1
2
1
1
2
0
1
1
1
1
1
2
0
1
1
1
1
1
1
2
0
0
2
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
2
1
1
1
1
1
1
0
1
0
1
2
1
1
1
1
2
1
0
2
1
1
1
1
1
1
1
1
2
2
2
1
1
2
1
1
1
2
2
1
1
0
0
1
1
1
1
1
0
1
1
1
1
1
2
1
1
1
1
1
2
0
1
1
1
1
1
1
0
1
1
2
0
1
1
1
2
1
2
1
1
2
1
1
1
1
1
2
0
1
1
1
2
1
1
1
1
2
2
2
1
0
1
1
1
1
1
2
1
1
0
0
1
0
1
2
2
2
2
1
0
2
1
1
1
0
1
1
1
1
1
2
1
1
1
1
1
0
1
1
2
2
0
1
1
2
1
2
1
2
1
2
1
1
2
1
1
1
1
2
2
2
2
1
1
1
0
1
1
1
1
1
0
1
0
2
0
1
1
1
1
0
1
1
2
1
0
1
1
1
0
1
1
1
1
1
2
1
3
1
1
0
1
1
1
0
0
2
1
2
1
1
1
1
1
1
2
1
2
2
1
2
2
1
1
2
2
2
1
1
2
1
2
1
1
1
1
0
1
1
2
0
1
1
1
2
0
0
2
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
0
0
1
1
0
1
1
1
1
2
2
1
2
3
0
1
0
1
1
1
1
1
2
2
1
1
2
2
0
1
1
0
1
1
1
1
1
2
2
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
0
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
0
1
1
2
2
1
0
1
0
1
1
1
1
1
1
1
0
2
2
1
1
2
1
2
1
2
2
1
1
1
0
2
1
1
2
1
1
1
1
1
0
2
0
1
1
0
2
2
1
1
1
0
2
0
1
1
1
2
2
1
1
1
1
2
1
2
0
1
1
1
1
1
1
2
1
1
1
1
1
2
1
0
0
2
1
1
2
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
2
0
2
1
1
2
1
2
2
1
1
1
1
1
1
0
1
1
2
0
1
1
1
1
1
1
1
1
0
1
1
0
1
1
1
1
2
1
2
1
2
1
2
1
1
1
1
1
2
2
2
1
3
0
2
1
2
1
1
1
0
1
1
2
1
1
1
2
1
1
1
2
1
1
2
1
0
2
0
1
1
1
0
2
1
1
1
1
0
1
1
1
2
1
1
1
2
2
1
0
1
2
2
1
0
1
2
2
2
1
2
1
1
1
1
1
2
2
1
0
2
2
1
1
1
1
1
2
1
1
1
0
2
1
0
1
1
2
2
1
1
2
1
1
2
1
1
0
2
0
0
2
1
1
1
1
2
2
1
0
1
1
0
2
1
1
1
1
1
1
1
0
0
2
1
1
1
2
1
2
1
2
1
2
0
1
2
1
1
3
1
1
1
1
1
1
1
1
1
0
1
1
1
2
1
1
1
1
2
1
0
1
1
1
2
2
2
1
0
2
1
1
1
2
1
0
1
1
0
2
1
2
2
1
1
2
1
1
1
1
1
2
1
1
1
1
2
2
0
2
1
1
0
1
1
1
0
2
1
1
1
1
0
1
1
1
1
2
1
1
2
2
1
0
0
1
0
1
2
2
1
0
1
1
1
2
1
1
2
1
0
2
2
2
0
1
1
1
1
2
2
1
1
1
1
0
1
1
1
1
0
2
1
2
2
2
0
1
1
1
6
0
0
0
2
0
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
2
2
1
0
0
1
1
2
1
0
2
1
1
2
0
0
1
1
1
2
2
0
2
0
1
1
2
2
1
1
1
1
1
1
1
2
1
0
2
2
0
1
0
0
1
1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
1
2
0
0
1
1
2
1
0
1
0
2
2
2
1
1
1
1
2
0
2
1
2
2
2
1
1
1
2
1
1
1
2
1
0
1
2
1
1
1
1
2
2
1
0
1
1
1
2
1
1
2
0
1
1
2
1
0
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
0
0
1
2
1
1
1
1
1
0
1
1
1
1
1
0
1
2
0
1
1
1
2
1
0
0
1
1
1
0
0
2
2
0
1
1
2
1
1
0
0
2
2
1
1
2
3
1
0
1
2
1
1
2
1
0
1
1
1
1
1
1
0
1
1
1
1
1
2
0
1
0
2
2
1
1
1
1
2
1
1
1
1
1
2
2
2
1
0
2
1
1
1
0
2
1
1
1
0
1
1
2
1
0
1
0
2
2
1
2
2
2
2
1
1
2
1
0
1
0
1
1
1
1
1
1
1
1
0
1
2
2
1
1
1
1
2
1
1
2
1
1
1
1
2
1
1
1
0
1
1
1
0
1
2
2
1
0
1
2
1
0
1
1
1
1
1
1
1
2
0
1
0
1
1
0
0
1
1
0
0
0
0
1
1
1
2
2
1
1
1
2
2
0
1
1
1
1
1
1
0
2
1
1
1
1
2
1
1
3
1
1
1
1
1
1
2
0
1
1
1
2
1
2
2
0
0
2
1
0
1
1
2
2
0
1
0
1
1
0
1
2
1
1
2
1
1
1
1
1
0
1
1
2
1
1
1
1
1
1
0
1
2
1
2
1
2
4
1
1
3
1
1
1
1
0
2
1
1
0
1
1
1
1
1
1
1
1
1
1
0
2
2
2
1
1
2
1
1
1
1
1
2
1
1
1
0
1
0
1
1
1
2
2
1
1
1
1
2
2
1
2
2
1
0
0
1
1
2
2
1
1
1
1
0
1
1
1
1
1
2
1
2
2
2
2
1
1
1
1
0
1
1
2
2
1
2
1
1
1
2
2
2
1
2
1
1
0
2
2
1
1
2
1
1
1
0
2
0
1
2
1
1
1
1
1
2
0
0
2
0
1
1
1
1
0
1
1
1
3
1
0
1
1
1
1
1
1
1
0
1
1
1
1
2
2
0
0
0
2
1
1
0
2
1
1
1
1
1
1
1
2
1
1
2
1
0
1
1
1
1
1
1
1
1
1
0
1
1
1
3
1
2
2
2
1
1
1
2
1
2
0
1
0
1
1
2
1
1
1
1
1
0
1
2
1
0
2
2
1
1
1
1
0
1
1
1
1
1
2
1
1
1
1
0
2
2
1
1
0
1
1
1
1
0
1
2
1
1
1
1
1
1
1
2
1
1
1
2
1
0
2
2
0
2
1
1
2
2
1
1
2
1
1
1
1
1
0
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
0
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
0
1
1
0
1
1
2
2
1
1
1
2
0
1
2
1
0
2
1
1
2
0
2
2
1
1
0
0
2
2
0
1
0
2
1
1
1
1
1
1
1
2
1
2
0
1
2
0
2
1
0
2
1
2
1
0
0
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
0
2
2
0
1
1
2
1
0
1
0
1
0
0
1
2
4
1
1
1
1
1
2
1
1
2
1
2
1
2
1
0
2
1
0
1
2
1
2
1
1
1
1
1
1
1
2
1
1
0
1
1
1
2
1
1
2
1
1
2
1
1
0
1
2
1
1
1
1
1
2
0
2
0
0
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
0
0
1
1
1
1
2
1
0
1
2
0
1
2
1
1
0
1
1
1
2
0
1
1
1
2
2
2
1
1
0
2
1
2
1
2
2
1
1
0
1
0
2
1
2
2
2
1
1
1
0
1
1
1
2
1
1
1
2
1
2
1
0
1
2
1
3
1
1
1
1
1
1
1
1
1
1
1
2
2
2
2
0
1
1
2
2
0
0
0
1
1
0
2
1
1
2
1
1
1
1
1
1
4
0
2
1
1
1
2
1
1
2
2
0
2
1
1
1
2
1
1
1
1
0
1
1
1
1
2
1
2
1
1
2
0
2
0
2
1
1
0
1
1
2
1
1
2
1
1
0
0
2
1
1
1
0
2
1
1
1
1
1
0
2
1
2
0
1
1
1
0
1
1
1
2
1
1
2
1
0
1
1
0
2
2
1
2
1
1
1
0
1
2
1
1
1
2
1
0
1
1
1
0
1
1
1
1
2
1
1
1
2
2
2
2
1
4
1
0
1
1
1
1
2
0
1
1
6
1
1
1
1
0
0
1
1
1
2
1
2
1
1
2
1
1
0
1
1
1
1
1
0
1
2
2
2
0
1
1
1
1
1
0
1
0
1
1
1
1
1
1
0
1
1
0
1
1
0
0
1
1
1
2
2
1
1
2
1
1
0
1
2
0
1
1
1
1
1
1
1
1
2
2
1
1
1
1
0
1
1
1
2
0
1
1
1
1
1
1
1
1
0
0
0
2
1
1
1
1
1
2
2
2
0
1
1
1
1
1
2
1
2
0
0
1
1
2
0
2
0
2
2
2
1
2
1
2
1
2
1
1
1
0
0
1
1
1
1
2
2
1
0
1
0
1
1
1
0
0
1
2
1
1
1
1
2
1
2
1
1
2
1
1
1
3
1
2
0
1
1
2
1
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
5
1
1
1
1
1
1
1
0
1
2
2
2
1
1
1
1
1
1
2
1
1
1
1
0
1
1
0
1
2
1
0
1
2
1
3
2
1
1
0
1
0
1
1
1
1
1
2
2
2
1
0
1
2
1
2
1
1
2
0
1
2
0
0
1
1
1
1
2
1
1
1
0
1
2
0
1
0
1
2
1
1
1
0
2
2
1
0
2
1
0
2
3
1
1
0
1
1
0
1
1
1
1
2
1
0
2
0
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
2
0
1
0
1
0
1
0
1
0
1
1
1
1
2
1
2
2
1
1
1
1
1
1
2
1
1
1
0
0
1
1
0
2
2
1
1
2
2
1
0
1
1
1
1
1
1
2
1
0
0
1
1
1
0
1
0
3
2
1
1
1
1
1
1
1
0
1
1
1
2
1
0
3
1
1
1
1
2
1
1
0
2
0
1
1
0
1
1
1
2
0
1
2
1
1
1
1
1
1
1
2
1
2
1
0
0
1
2
1
1
1
1
1
1
1
1
2
1
2
1
1
0
1
1
2
2
1
1
1
1
1
2
1
1
1
2
0
2
1
2
1
2
2
1
1
1
0
1
2
0
1
0
1
0
2
1
1
1
1
1
1
0
1
1
1
0
1
1
1
1
0
1
2
2
1
1
1
1
1
1
1
2
2
1
2
1
1
1
1
2
1
2
2
1
1
0
1
0
2
2
2
0
1
2
1
1
1
1
1
1
1
1
2
0
0
1
1
1
0
2
1
1
0
2
3
1
2
2
1
1
1
2
1
0
2
1
1
0
2
2
0
1
1
2
1
1
1
2
2
2
0
1
2
2
1
2
1
1
0
1
1
1
1
1
1
2
0
1
1
1
1
1
1
2
2
1
2
1
0
1
1
1
3
1
0
2
1
1
1
1
0
1
0
1
1
1
2
0
1
0
2
2
1
1
0
1
0
1
2
1
1
1
1
1
2
1
1
3
1
2
0
1
0
0
0
1
1
1
0
0
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
0
1
1
0
1
1
1
1
1
1
1
1
1
2
0
1
2
1
2
2
2
0
2
0
1
0
0
0
1
1
2
1
2
1
1
2
1
1
0
1
2
0
0
0
1
2
1
1
2
0
1
1
1
1
0
0
0
1
1
2
2
1
1
1
1
1
1
0
0
1
2
2
2
1
1
2
1
0
2
1
0
2
2
0
0
1
2
0
1
0
1
1
2
1
2
2
1
0
2
1
1
1
2
1
1
2
0
1
1
1
1
2
0
2
1
1
1
2
2
1
1
2
1
2
1
1
2
1
1
1
1
0
1
1
0
1
1
1
1
3
0
1
2
1
1
1
1
1
1
1
1
2
0
1
1
1
1
1
0
0
0
2
1
0
1
1
1
1
1
1
0
2
2
1
0
1
1
2
2
1
1
1
0
0
1
1
1
1
3
2
1
1
1
2
1
1
0
0
1
1
1
2
1
1
1
2
0
2
2
1
1
1
2
2
1
1
0
1
1
2
0
1
1
1
1
2
0
2
1
0
1
2
1
1
1
1
1
1
2
2
2
1
1
2
0
2
1
1
0
1
1
1
2
2
1
3
0
1
2
2
1
1
1
2
1
2
0
0
1
1
1
1
1
1
1
2
1
1
0
1
2
1
1
1
2
2
2
1
0
2
1
2
1
2
0
0
1
2
3
1
1
0
1
1
1
2
1
1
2
1
0
1
0
1
0
1
1
1
1
1
2
1
1
1
2
2
2
1
1
1
1
1
1
1
0
1
2
1
1
2
1
1
2
2
1
1
2
1
1
2
1
1
1
1
2
2
1
2
1
1
1
1
0
1
1
2
1
2
1
2
1
2
1
1
0
1
2
1
2
1
1
1
2
1
2
0
1
1
1
2
0
2
1
1
0
1
2
1
1
1
1
1
2
1
0
1
2
1
1
1
1
1
1
2
1
2
2
2
1
2
2
1
2
1
2
1
0
1
1
2
1
2
2
1
0
2
1
2
1
0
1
2
1
2
1
2
2
0
2
1
1
1
2
1
1
3
1
1
1
2
2
1
1
0
1
1
1
2
2
1
1
1
0
1
1
1
1
2
0
1
0
1
2
0
2
2
1
1
1
0
0
1
1
1
2
1
2
1
0
2
1
2
1
1
1
1
1
2
0
1
1
1
1
1
1
0
1
1
1
0
1
0
1
1
1
1
2
2
1
1
1
2
1
1
1
1
2
2
1
0
1
1
1
2
1
1
0
1
0
2
0
1
1
1
1
1
0
0
2
1
2
1
0
1
2
2
1
2
2
1
2
2
0
1
2
1
0
2
1
1
1
1
1
0
2
1
0
1
2
0
1
0
1
0
1
1
1
0
1
2
1
1
1
2
1
2
0
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
0
0
0
2
2
1
3
1
0
2
1
1
1
1
2
2
1
1
1
0
1
2
1
2
1
0
1
1
1
2
1
1
1
2
2
1
2
0
0
2
2
0
0
1
1
1
2
2
1
1
2
1
0
2
2
0
1
1
1
1
1
1
0
0
2
2
1
1
0
1
2
1
1
1
1
1
1
1
1
0
0
0
3
2
1
2
0
1
2
1
1
1
0
0
0
2
0
1
1
2
1
1
1
2
1
1
2
2
1
2
1
2
2
1
1
0
1
1
2
1
0
1
2
1
2
1
1
1
2
2
1
1
1
1
1
0
1
1
0
0
1
2
1
1
1
1
1
1
1
0
1
1
2
0
1
1
1
1
2
2
1
1
0
1
2
0
1
0
1
1
1
1
1
2
0
2
0
1
2
0
1
1
2
2
0
2
1
1
2
2
1
2
1
2
0
2
0
2
1
0
1
1
2
2
1
2
1
1
0
1
1
1
1
2
0
2
1
1
2
1
2
1
1
2
1
2
0
1
1
2
1
1
1
1
0
0
2
2
1
2
1
1
2
1
2
1
2
1
1
2
0
0
1
0
2
1
2
1
1
1
0
1
1
0
1
0
0
0
2
1
1
1
2
2
0
2
1
2
1
1
1
0
2
1
0
1
1
0
1
1
1
2
1
1
1
0
1
2
2
2
2
1
2
0
1
0
0
1
2
1
1
2
1
1
1
1
1
1
1
0
1
0
1
1
1
1
2
1
1
1
1
1
2
2
1
1
0
2
2
1
1
2
2
1
2
1
1
1
2
1
2
2
1
1
1
2
1
1
1
2
0
1
0
1
1
0
1
0
0
1
0
2
1
1
0
0
0
1
1
0
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
0
2
1
1
0
1
1
1
2
1
1
2
0
1
1
2
3
1
1
1
2
1
1
2
2
1
1
1
1
2
1
1
1
1
1
2
0
2
1
2
1
1
2
2
0
0
1
1
1
1
0
1
1
2
1
1
1
1
1
2
1
2
2
2
1
1
0
0
1
1
1
1
0
0
2
2
1
1
1
1
1
0
2
1
1
1
1
2
1
1
2
1
1
1
0
1
2
1
1
1
1
1
1
1
2
2
1
1
0
1
1
1
1
1
1
1
2
0
2
1
1
1
1
2
1
1
1
0
0
2
1
1
2
1
0
1
1
1
1
1
1
1
1
2
1
1
1
1
2
0
1
1
1
1
1
2
1
1
1
2
1
2
1
2
1
0
1
1
2
1
1
2
1
2
1
1
1
1
0
1
1
1
1
1
0
0
1
1
1
2
0
0
0
1
1
1
2
1
1
1
1
1
1
0
2
2
1
1
1
2
1
0
1
0
1
1
1
1
1
2
2
2
1
1
1
1
0
1
2
2
2
1
1
2
2
1
2
1
2
1
1
2
1
1
2
2
2
1
2
1
1
0
0
1
1
1
1
1
1
2
2
1
0
0
1
2
1
1
2
1
1
2
2
2
2
0
1
1
2
1
1
1
1
1
1
0
1
2
1
0
1
1
1
1
0
1
0
2
2
2
1
1
2
0
2
1
2
1
1
1
1
1
1
0
0
1
0
1
2
1
1
2
2
1
1
2
2
2
0
1
0
1
1
2
1
1
0
1
0
2
2
1
0
1
0
2
1
2
0
1
0
1
2
1
1
1
0
2
1
1
1
2
2
1
1
1
1
1
0
1
1
1
1
1
1
1
2
2
2
2
1
1
1
1
0
1
2
1
2
0
2
1
2
1
2
1
2
1
1
2
1
2
1
1
1
1
2
2
1
1
2
1
1
1
1
2
1
0
2
1
1
2
1
1
2
1
1
1
1
1
1
0
1
2
1
1
2
2
2
1
1
1
0
1
1
1
1
1
1
1
2
2
1
1
0
1
2
1
1
1
0
1
0
1
1
2
1
1
2
1
1
1
1
0
2
1
0
1
1
1
1
1
1
1
1
1
1
1
2
2
1
0
1
1
2
1
1
0
1
1
0
1
1
1
1
1
2
1
1
2
2
1
2
1
1
1
2
1
1
0
1
1
2
1
1
1
2
0
1
1
1
1
1
2
0
1
1
1
1
0
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
0
1
2
2
2
1
1
1
1
2
1
2
2
1
1
1
1
1
1
2
1
0
2
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
2
0
2
2
2
2
1
3
1
1
2
1
2
1
0
2
1
1
2
1
2
1
1
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
1
1
1
2
0
2
1
0
2
1
1
2
1
1
1
0
2
2
0
2
0
1
1
2
2
1
2
1
2
1
2
1
2
2
1
1
1
3
2
1
1
1
0
0
2
0
2
0
1
1
0
1
1
1
2
1
2
2
2
1
0
2
2
1
1
2
1
2
1
0
2
0
1
1
1
1
1
2
1
2
1
2
1
1
1
0
1
1
2
1
0
2
1
1
1
2
2
1
1
1
1
1
0
1
1
1
1
1
1
2
0
1
2
1
2
1
1
1
1
1
2
1
2
2
1
1
1
3
1
1
1
1
0
0
2
1
0
1
1
2
2
3
2
1
1
1
1
2
0
1
0
0
1
2
0
1
1
1
1
1
1
2
1
1
0
1
1
1
0
2
0
1
0
1
1
2
2
1
1
1
2
2
1
0
2
1
1
1
1
1
2
1
1
1
2
1
1
1
0
0
1
1
0
2
1
1
1
1
1
1
1
2
1
2
2
2
2
1
2
1
0
0
2
2
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
3
2
1
0
1
1
2
2
1
7
1
2
0
2
1
1
1
1
0
1
1
1
1
2
2
0
1
1
2
1
1
2
2
1
3
2
1
0
1
1
0
1
0
2
1
1
1
2
1
1
0
1
1
0
1
2
1
1
0
1
2
0
1
2
1
1
1
2
1
1
1
1
1
2
1
1
1
1
0
2
2
1
0
1
1
0
1
2
0
1
1
1
1
1
0
0
1
2
0
2
1
0
1
0
1
2
1
2
1
1
0
1
0
1
2
0
1
1
1
1
1
0
1
1
1
2
1
0
2
6
2
1
0
0
1
1
1
1
1
0
1
1
1
2
1
1
1
1
1
0
1
1
1
2
2
1
2
1
2
0
2
1
2
0
1
0
0
2
0
1
2
1
1
0
1
2
2
0
2
0
1
1
0
1
1
2
2
2
0
1
1
2
1
1
1
2
1
2
1
2
0
2
1
1
1
1
1
1
1
0
1
2
1
0
1
1
0
3
1
1
1
1
1
1
1
1
1
1
1
1
0
2
1
1
0
1
1
0
1
1
2
1
1
2
2
1
1
1
1
1
2
0
1
1
1
1
0
2
0
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
0
1
1
2
1
1
1
1
2
1
2
1
2
1
1
2
0
1
0
2
1
1
1
1
2
2
1
2
1
1
0
0
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
2
2
0
0
1
0
1
0
1
2
2
0
1
1
1
0
2
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
2
1
0
1
2
1
2
1
2
1
0
2
1
1
0
2
2
2
1
0
1
1
0
1
1
1
1
0
1
1
1
1
0
0
0
1
1
0
0
3
1
1
0
1
1
1
0
2
2
1
1
1
2
1
1
1
1
1
1
2
1
2
1
2
1
0
1
1
1
1
1
1
1
1
0
0
1
2
2
1
1
1
1
0
1
2
1
2
1
0
3
1
1
2
1
2
1
1
2
1
0
1
1
1
1
1
0
1
1
1
1
1
1
3
2
2
1
2
1
1
2
2
2
0
1
2
2
0
1
1
0
1
1
0
2
1
2
1
1
1
1
0
3
2
0
1
1
0
1
1
2
1
1
2
1
2
2
1
0
1
1
1
1
2
1
0
1
0
2
2
0
1
0
2
2
2
1
2
1
1
0
0
1
2
2
0
1
0
1
1
2
1
2
1
1
1
2
1
1
1
1
1
0
1
1
1
1
2
0
2
1
1
2
1
1
0
1
1
1
1
1
0
1
1
1
1
1
1
2
1
1
0
1
5
0
1
1
1
1
1
1
1
1
0
1
2
2
1
1
2
1
2
2
1
1
1
1
1
2
1
1
1
1
1
1
0
2
1
1
0
0
1
1
1
1
1
1
0
1
1
1
1
2
1
0
1
1
0
2
0
1
1
1
1
0
1
1
2
1
2
1
1
0
1
0
2
0
1
1
2
2
0
1
1
1
1
2
1
2
1
3
2
1
0
1
2
2
2
1
1
0
1
1
1
2
1
2
2
1
1
1
1
1
0
0
1
2
0
1
3
2
0
1
2
2
0
3
1
1
0
1
2
2
1
1
2
1
1
2
1
2
1
1
1
1
2
1
2
2
1
1
2
2
1
1
0
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
2
0
2
0
1
1
1
1
1
1
2
1
1
0
1
1
1
1
1
1
1
1
0
2
1
2
1
1
2
0
0
1
1
1
1
1
0
0
1
1
2
1
1
0
2
2
1
1
1
2
1
1
1
1
1
0
1
2
0
0
2
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
0
1
1
0
2
1
0
1
1
1
1
1
1
1
0
1
3
1
1
1
1
1
1
1
1
2
0
1
1
1
1
1
2
1
1
1
1
1
1
1
3
1
0
1
1
1
1
1
0
1
1
1
1
0
1
1
2
1
1
1
1
0
0
2
1
2
1
1
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
2
1
1
1
0
2
1
1
1
2
1
2
1
0
1
2
1
0
1
0
2
1
0
1
0
1
2
1
1
1
2
1
0
0
2
1
1
2
0
1
2
1
0
1
2
1
1
2
1
3
1
1
1
2
0
0
1
1
0
1
1
1
1
1
1
1
1
1
1
1
2
2
2
2
0
1
0
2
2
2
1
0
2
2
1
1
1
0
1
1
1
1
0
0
1
2
1
1
1
1
2
1
2
1
1
1
2
1
2
1
1
2
1
1
1
0
1
2
1
0
1
0
2
1
2
1
0
2
1
1
1
0
1
1
0
1
0
0
1
2
1
1
2
1
1
1
1
1
1
2
1
2
1
0
1
1
2
1
1
1
2
1
2
1
2
0
2
2
2
1
1
2
0
1
1
1
1
0
1
1
1
1
2
1
1
1
0
1
2
1
2
2
0
1
0
1
0
0
0
2
1
1
2
1
1
2
2
1
2
1
1
1
2
0
1
1
1
0
1
0
1
1
0
1
2
1
1
1
2
0
2
1
1
1
1
2
1
1
1
1
0
1
1
1
1
2
1
0
1
1
0
1
1
1
1
1
2
1
1
2
1
1
2
2
2
1
1
1
1
3
1
1
2
1
1
1
0
2
2
2
1
1
2
2
1
1
1
1
0
1
2
3
0
1
1
2
1
1
0
2
1
2
1
0
1
1
2
2
0
2
1
1
1
2
1
2
2
2
1
2
2
1
1
1
1
0
1
1
1
0
1
1
1
2
2
1
1
1
0
1
2
4
1
2
2
1
1
1
0
1
1
1
1
0
1
2
1
1
1
2
1
1
2
1
2
1
1
0
1
0
1
1
1
1
1
1
3
2
1
2
2
2
2
1
2
1
1
1
1
0
2
1
1
1
1
0
1
2
1
0
1
1
1
1
2
0
1
1
1
1
2
1
2
1
2
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
0
2
1
2
2
2
1
1
0
0
1
1
1
1
1
1
1
1
0
0
1
1
2
1
2
2
2
2
1
2
3
2
1
1
5
1
1
1
1
1
1
1
2
1
1
2
1
2
2
1
1
1
1
0
1
0
1
1
2
1
2
1
0
2
1
1
1
1
2
1
2
1
2
0
0
1
1
1
1
0
0
1
1
1
1
0
0
1
1
2
1
0
0
2
0
1
1
1
1
1
0
1
0
0
1
1
2
0
1
1
1
1
1
1
2
2
2
2
1
0
2
2
1
2
1
1
1
1
2
2
1
0
2
1
1
1
1
0
2
0
0
0
1
0
0
1
1
2
1
1
1
2
0
1
1
1
2
0
1
2
1
1
1
2
1
1
0
0
0
1
1
1
1
2
1
1
1
1
1
0
0
1
1
1
1
1
2
0
2
1
0
2
1
1
1
2
0
0
2
2
0
2
1
1
0
0
1
1
1
0
1
1
0
2
2
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
1
2
2
2
0
2
1
1
2
1
2
1
1
0
0
1
1
0
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
0
1
2
2
1
1
1
1
1
2
1
1
1
1
1
1
1
0
2
0
1
1
2
0
1
1
0
1
1
2
2
0
1
1
1
1
3
2
1
0
1
1
1
0
1
1
1
1
1
0
0
1
1
2
1
0
1
1
2
2
0
1
1
0
4
1
2
1
1
1
1
2
1
1
0
0
1
1
2
1
1
1
1
0
3
1
1
2
2
0
1
0
0
1
1
2
1
3
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
0
1
1
1
1
1
1
1
1
2
2
0
2
2
1
1
1
1
1
3
1
0
2
1
2
0
0
2
1
1
2
1
1
2
1
1
2
1
0
1
1
2
0
2
1
1
1
2
2
0
2
0
0
1
2
1
1
0
0
2
1
1
1
1
2
2
0
1
1
1
1
1
1
2
0
1
1
1
1
2
1
1
2
1
1
1
0
1
2
2
1
1
2
1
1
1
0
0
1
1
1
2
1
1
2
1
1
0
1
2
1
2
0
0
2
1
1
2
1
1
2
1
1
0
1
0
1
1
1
1
2
1
1
1
1
1
1
0
0
0
1
1
2
0
1
0
0
1
1
1
1
1
1
1
0
0
1
1
1
0
2
1
2
0
0
0
0
1
0
2
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
0
1
1
1
0
2
1
1
1
1
0
1
1
1
1
2
2
1
2
2
1
0
1
0
1
1
1
1
2
0
2
1
1
1
1
0
1
1
1
1
2
0
2
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
0
2
0
1
1
2
1
0
2
2
0
0
1
0
1
1
1
1
1
2
1
1
1
1
0
3
1
2
0
0
1
1
1
1
2
0
1
0
2
2
1
1
1
2
2
1
2
0
1
0
1
2
0
1
1
0
1
1
1
1
1
0
1
2
1
1
1
2
1
1
1
0
0
1
2
1
2
2
1
1
1
1
2
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
1
2
1
1
1
2
1
2
2
1
1
2
1
2
1
1
1
1
1
1
0
1
0
1
1
1
1
2
1
1
1
1
3
1
2
2
1
0
1
0
1
1
1
1
2
1
1
2
2
2
1
0
1
1
1
1
2
1
1
1
1
1
1
1
0
1
2
0
2
2
1
2
0
1
2
1
1
1
0
0
1
2
1
1
2
2
2
2
0
1
0
2
2
0
2
1
3
1
1
1
1
1
1
1
1
1
1
2
1
1
1
0
1
2
1
1
0
0
0
1
0
2
2
1
0
0
0
2
2
2
0
1
1
1
2
1
2
1
1
2
1
0
1
0
1
1
1
1
1
1
0
1
1
2
1
1
1
2
0
1
0
2
0
3
1
2
2
1
1
2
1
1
1
1
1
1
2
0
0
0
1
0
0
2
2
2
2
1
0
1
1
1
1
1
2
2
1
1
2
1
1
1
1
2
2
2
2
0
0
0
1
0
2
1
2
1
1
1
1
1
1
2
1
1
2
1
1
1
0
1
1
3
1
2
1
1
1
0
2
1
1
1
0
0
1
0
1
0
1
0
3
0
1
1
1
1
1
2
2
0
0
1
0
2
2
2
2
2
1
0
1
1
1
2
2
2
0
1
1
2
0
2
1
1
1
1
1
1
1
3
2
2
0
2
2
1
1
2
2
1
1
1
1
1
0
2
1
2
2
2
2
2
1
0
0
2
1
1
0
1
1
2
1
1
1
2
1
1
2
2
1
0
2
1
1
1
1
1
1
1
1
1
0
1
1
1
1
0
1
2
1
0
0
1
0
1
0
1
1
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
0
1
0
0
1
1
0
2
1
2
2
1
1
1
1
2
1
1
2
1
2
2
1
1
1
0
1
1
1
0
1
1
1
1
1
2
1
1
1
1
1
0
0
1
1
2
0
1
1
1
1
2
1
2
1
2
1
2
0
1
2
2
0
2
2
1
1
1
1
1
2
1
0
0
1
1
1
1
2
1
0
1
1
1
2
0
1
1
1
1
1
2
2
0
2
1
1
0
1
1
0
2
1
2
1
0
1
1
0
1
2
1
1
1
1
4
1
1
1
0
1
1
1
2
1
2
2
1
1
2
0
2
1
1
1
1
2
2
1
2
0
0
2
3
0
1
2
1
0
1
2
2
1
1
0
0
1
1
1
1
2
1
1
1
1
0
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
0
1
1
2
1
0
1
1
1
0
0
1
1
2
1
2
2
0
2
0
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
1
0
2
2
1
2
0
1
2
1
1
0
2
1
2
1
1
1
1
1
1
2
1
0
1
1
1
1
1
1
1
0
0
2
1
1
1
0
1
0
1
0
1
2
0
1
2
2
1
0
1
1
2
1
0
1
1
1
1
0
2
1
1
2
0
1
1
1
0
2
1
2
2
2
1
1
1
1
0
1
1
1
2
2
1
2
2
0
1
1
0
2
1
2
0
1
1
1
0
1
2
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
0
1
2
1
1
1
0
1
1
0
2
1
1
0
0
1
2
2
1
1
5
2
1
1
4
0
1
1
1
1
1
2
2
1
1
1
1
2
1
1
0
1
1
1
1
2
1
1
1
2
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
0
8
0
1
1
1
1
2
1
2
1
1
0
1
1
1
1
1
1
1
1
0
1
1
1
2
1
2
1
1
1
1
1
1
1
1
2
2
1
0
1
2
0
0
1
1
1
1
2
1
2
1
2
1
1
1
1
1
0
1
1
2
2
1
2
2
2
1
1
1
2
2
0
1
1
2
2
1
1
2
2
1
1
2
1
1
0
2
2
1
1
1
0
1
1
1
1
2
1
0
1
1
1
2
1
0
2
0
2
1
0
1
1
1
2
0
2
4
0
0
2
0
2
0
1
1
1
2
1
1
1
1
2
1
2
1
1
2
0
0
0
2
1
1
1
1
0
1
1
1
0
1
1
1
1
2
1
1
1
1
1
0
2
1
1
1
1
0
1
1
1
1
1
1
1
1
1
0
0
2
2
0
1
1
1
1
2
0
1
1
0
1
1
2
2
1
1
0
1
2
2
1
0
0
2
0
2
0
1
1
1
1
1
1
1
1
0
0
1
2
1
0
1
2
1
1
1
2
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
0
1
1
1
1
1
2
2
1
1
2
2
1
0
1
1
2
1
2
2
1
1
1
1
1
0
0
1
0
1
2
2
2
1
1
2
1
1
1
1
1
1
2
2
1
1
0
1
2
2
1
1
2
1
1
1
2
2
1
1
1
1
0
1
1
2
1
1
2
1
1
1
1
2
1
2
2
1
1
1
2
0
1
0
2
1
1
1
1
2
2
0
1
2
0
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
0
1
1
0
1
1
1
0
1
1
1
0
1
2
1
0
1
0
1
0
1
1
1
2
0
1
1
1
1
1
2
1
0
1
1
2
1
1
1
1
1
2
1
0
2
1
0
1
1
0
1
0
1
2
1
1
1
1
0
0
2
1
1
0
0
2
1
1
1
2
2
2
2
2
1
1
1
1
1
0
2
1
1
1
0
1
2
2
2
1
3
1
1
1
0
0
1
1
1
1
2
0
2
1
1
0
1
1
1
1
0
1
0
2
2
1
1
1
1
1
1
0
1
1
1
2
0
1
1
1
0
1
1
0
0
1
1
0
1
0
1
1
1
1
1
2
1
0
2
1
1
1
2
2
1
0
2
1
0
1
1
1
2
1
2
1
0
1
0
1
1
1
2
0
1
2
2
0
1
2
2
1
1
0
1
0
1
1
2
1
1
3
2
1
1
1
1
1
1
1
1
1
0
1
1
2
1
0
1
2
2
1
0
0
1
2
1
1
1
0
2
1
1
1
1
1
1
2
2
2
2
2
1
1
1
2
1
1
0
1
1
1
2
2
1
1
2
1
1
2
1
2
0
0
1
1
0
1
1
0
1
1
1
0
2
1
0
2
0
1
1
1
0
0
1
1
1
1
0
0
0
0
1
1
1
2
1
0
1
2
1
2
1
2
1
1
2
0
2
0
1
1
1
0
1
2
2
1
1
0
2
1
1
2
1
0
0
1
1
1
0
1
1
0
1
2
0
1
1
0
1
1
2
0
2
1
1
1
1
1
2
2
1
2
1
1
1
1
0
1
2
1
2
1
1
1
0
1
1
1
0
1
1
0
1
1
1
1
2
0
2
1
1
0
1
1
2
2
1
0
1
2
0
1
1
1
1
0
0
2
1
1
1
1
2
1
2
1
1
1
1
1
2
0
1
2
1
1
0
1
2
3
1
1
1
1
2
1
1
1
2
0
1
1
2
1
1
1
1
0
1
1
1
2
1
2
0
1
1
1
2
1
1
2
1
1
1
1
1
2
1
1
2
1
1
0
0
1
1
0
1
1
1
1
1
0
0
1
2
1
1
1
1
1
1
1
2
1
1
1
2
1
0
0
1
1
2
1
2
2
0
1
1
1
1
1
1
2
1
1
0
1
1
2
0
1
2
1
2
2
2
1
0
1
1
2
2
1
2
1
2
0
0
2
0
2
0
0
1
0
0
2
1
1
0
1
1
0
1
0
0
1
1
1
1
1
2
1
1
1
2
2
2
1
1
1
1
0
2
2
1
2
2
1
1
1
1
1
0
2
2
0
1
1
1
2
1
2
1
1
2
0
1
0
1
1
1
1
0
1
1
0
2
1
1
1
1
1
1
0
1
1
1
1
2
2
1
2
1
1
2
1
2
0
1
3
1
1
1
7
1
2
1
1
0
1
0
2
1
2
0
1
1
0
0
1
1
1
2
1
0
1
2
1
2
1
1
2
1
2
1
2
2
1
2
2
1
1
1
1
1
0
2
1
0
1
1
0
2
1
1
2
2
1
2
2
1
0
1
1
0
2
1
1
1
0
1
2
1
1
0
1
2
1
1
2
2
2
1
1
1
2
0
1
1
2
2
2
1
1
1
0
1
2
1
1
0
1
0
2
0
1
2
1
1
1
2
2
0
2
1
1
0
0
1
1
2
1
1
2
0
0
1
1
0
2
1
2
2
1
1
1
1
1
1
1
0
1
0
1
2
1
1
1
0
1
1
0
1
1
1
1
2
1
1
2
2
1
1
1
0
0
1
2
1
1
1
3
1
0
1
1
1
0
1
1
2
1
1
2
0
2
1
1
1
1
1
1
2
2
1
2
2
0
2
1
0
0
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
2
1
0
2
1
2
1
1
1
1
1
2
1
0
2
1
1
2
1
1
1
2
1
1
0
1
1
1
1
1
1
2
1
1
0
1
1
1
2
2
1
1
2
1
1
2
1
1
1
0
1
0
2
2
1
1
1
0
1
1
1
1
2
2
0
1
1
1
1
3
1
1
1
1
1
1
1
1
0
2
1
1
1
1
2
2
1
1
1
1
2
2
1
0
1
1
2
0
2
1
1
1
2
2
1
1
1
2
1
1
1
1
0
1
1
1
1
1
1
0
1
2
1
2
1
2
0
1
2
2
1
1
1
0
0
1
1
1
1
1
1
2
1
0
2
5
1
1
0
0
1
1
0
1
2
0
1
1
1
1
1
1
1
1
1
1
1
1
0
1
0
1
2
1
0
1
1
1
2
1
1
1
2
1
1
1
1
2
2
1
2
2
2
2
1
0
1
1
1
1
0
1
2
1
6
2
2
0
0
0
1
1
0
1
2
1
1
1
1
0
1
1
0
1
1
1
1
2
1
1
2
1
1
0
1
1
1
1
2
0
0
1
1
1
1
1
2
2
1
1
1
0
0
1
1
1
0
2
1
1
0
1
2
1
1
4
0
2
2
1
1
1
1
2
0
1
1
2
1
1
1
1
1
1
2
1
0
1
1
1
2
1
2
1
0
0
1
1
2
0
1
1
2
2
1
1
1
0
1
1
1
1
1
2
1
1
2
1
1
1
2
1
1
0
2
0
1
2
1
1
0
1
1
1
1
1
1
1
2
1
0
0
0
0
1
2
1
1
2
2
2
1
1
2
2
1
0
1
1
1
1
2
1
2
1
1
2
2
2
1
0
1
2
2
1
1
2
0
2
0
0
2
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
2
0
2
1
1
0
1
2
1
2
1
1
1
2
1
1
2
1
2
1
1
1
2
2
1
2
1
0
2
1
1
0
1
2
2
1
2
1
2
1
0
1
1
2
1
1
1
1
1
2
1
1
1
0
2
1
1
0
1
1
1
1
1
2
1
2
2
2
1
2
1
1
1
1
2
1
1
1
2
1
2
1
1
0
1
1
1
1
1
1
1
2
1
1
1
1
2
2
2
1
2
1
1
2
1
1
1
1
1
1
2
0
2
1
0
0
1
0
0
1
2
1
1
1
1
1
1
1
1
2
0
0
2
2
2
1
2
2
1
1
1
0
2
1
1
0
2
1
0
1
1
1
0
1
1
1
1
0
1
1
2
1
2
1
2
0
0
1
0
1
1
0
1
1
2
2
1
1
1
1
1
2
2
2
2
1
1
2
2
1
2
1
1
2
1
0
2
2
1
2
2
2
1
1
1
1
0
2
2
2
2
1
1
0
1
1
2
2
2
1
1
2
1
1
1
1
1
1
1
1
1
0
0
1
0
1
0
1
1
2
1
1
1
1
2
1
2
0
0
1
1
1
1
0
1
2
1
1
2
1
1
1
2
0
1
1
1
1
2
1
1
1
2
2
1
1
0
2
1
2
2
0
1
1
2
2
1
2
1
1
1
2
2
1
1
2
1
2
0
0
2
2
1
2
1
1
1
1
1
1
2
1
2
2
2
0
2
1
1
1
0
2
0
1
1
0
1
1
1
1
2
2
2
1
1
1
1
1
0
2
1
1
1
1
1
2
1
1
2
2
1
1
1
2
1
2
1
1
1
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
0
2
1
2
0
2
2
1
2
1
1
1
1
1
1
1
1
0
0
1
0
1
2
0
2
1
1
1
0
1
0
1
1
2
1
2
2
1
1
1
1
0
0
1
2
0
1
2
1
1
1
1
1
2
1
1
0
1
1
1
1
0
2
2
1
2
0
1
2
1
2
1
1
1
2
1
2
1
0
0
1
1
1
1
0
2
1
1
1
1
1
2
0
1
1
1
2
1
1
2
1
0
0
1
0
0
1
2
0
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
0
2
2
0
1
2
1
1
1
1
2
1
2
1
0
2
2
1
1
1
1
1
1
1
1
2
1
1
2
2
1
0
1
2
1
1
2
2
0
1
1
1
1
0
1
1
1
2
1
1
1
1
1
1
1
1
0
2
0
1
1
1
1
2
1
2
1
1
1
1
1
1
2
1
0
2
1
2
1
1
1
1
2
1
1
1
0
1
2
1
0
0
1
1
1
1
1
2
0
1
1
1
1
1
1
1
1
2
2
1
2
1
1
0
0
1
1
1
2
1
1
1
0
0
1
1
1
2
2
1
1
1
1
1
1
1
0
2
2
1
2
1
1
1
1
1
1
1
2
1
1
2
2
1
0
3
1
0
1
1
1
1
2
1
1
1
0
0
0
1
1
2
1
1
1
1
1
1
2
0
2
1
1
1
1
1
1
1
0
2
1
0
0
1
3
1
0
0
2
1
2
0
1
1
2
2
0
1
2
1
0
2
0
2
1
1
1
1
2
2
1
1
2
1
1
1
1
1
1
2
0
2
1
2
1
1
0
2
1
1
2
2
2
1
2
1
1
1
0
1
1
2
1
1
2
1
0
1
1
1
1
1
1
2
2
0
1
1
1
1
2
1
2
2
2
0
1
1
0
2
1
0
1
1
2
0
1
1
1
3
1
1
1
1
1
2
1
2
1
1
2
2
0
2
1
2
2
1
2
0
1
1
1
1
1
1
2
1
0
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
0
2
1
1
0
1
9
1
2
0
1
1
1
1
1
1
2
1
1
1
1
0
1
1
1
2
1
2
1
1
1
1
0
0
2
1
1
1
1
1
1
2
2
2
0
1
1
1
0
1
2
2
1
1
1
1
1
1
2
1
0
2
1
2
1
0
1
0
1
2
1
1
0
1
1
1
1
2
1
2
1
2
2
1
1
0
0
0
1
1
1
1
1
2
1
1
2
1
2
0
0
1
2
1
2
1
0
1
1
0
0
1
0
1
1
2
2
1
1
2
1
1
1
1
1
2
2
1
2
1
2
1
0
2
0
1
2
1
0
1
1
1
1
2
1
1
2
0
1
2
1
1
0
2
2
1
1
1
1
2
1
0
0
1
2
2
1
2
1
1
1
1
1
1
2
0
1
1
1
2
1
1
2
1
2
0
2
1
1
1
1
2
1
1
1
1
2
1
2
1
2
1
2
1
2
2
1
1
2
1
1
0
1
1
0
1
1
0
1
1
2
2
0
1
1
1
1
1
1
1
1
0
1
1
1
0
1
1
0
1
1
1
1
1
0
0
0
2
1
1
1
1
1
1
1
2
2
1
1
0
1
1
1
1
0
0
1
1
2
1
1
1
2
1
1
1
1
0
1
1
1
1
1
1
1
1
2
1
1
1
2
0
2
0
0
1
1
0
1
2
1
2
1
0
0
0
1
1
2
1
0
1
1
0
2
1
1
2
2
1
1
0
1
1
1
1
2
0
0
1
2
1
3
1
1
1
2
2
2
1
2
1
2
2
1
1
1
1
1
2
1
1
1
1
1
1
1
3
1
0
2
1
1
0
1
1
1
2
1
1
2
1
1
2
1
2
2
1
0
0
0
1
1
1
2
2
1
0
1
2
1
0
2
1
2
1
0
1
1
0
1
1
1
0
1
1
2
1
1
2
1
1
1
1
1
0
2
1
1
1
1
1
2
2
0
1
1
1
0
0
2
1
1
1
1
1
1
2
1
0
1
1
2
1
1
0
1
1
1
1
2
0
2
1
1
1
2
0
0
2
0
2
0
1
2
1
1
0
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
2
2
1
1
2
2
1
1
1
2
2
2
0
1
0
2
1
1
1
1
1
2
1
0
1
1
1
1
1
2
2
0
1
0
1
3
1
1
1
1
2
1
1
1
1
1
0
0
2
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
0
1
1
3
1
2
0
2
2
1
0
1
1
0
1
2
2
1
1
1
2
2
1
1
1
1
0
1
1
2
1
1
2
2
1
1
2
1
0
1
1
2
1
1
1
1
2
1
1
2
2
1
2
1
2
1
2
1
1
1
1
1
2
1
0
1
2
1
1
1
2
2
1
1
1
2
2
1
2
2
1
0
2
1
6
0
1
2
0
2
1
1
0
1
1
1
2
1
1
1
1
0
1
1
2
2
1
0
0
1
2
1
1
1
2
1
1
1
1
1
1
2
2
2
2
1
1
2
1
1
1
2
1
2
1
2
3
2
1
0
0
0
1
1
1
1
2
1
0
2
2
1
1
1
2
1
1
1
0
1
2
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
2
1
2
1
1
0
1
0
0
1
1
0
1
1
0
1
0
1
1
1
1
0
1
2
1
0
1
2
1
1
0
1
1
1
2
1
1
1
2
1
0
1
0
0
1
1
1
1
0
1
1
0
1
0
1
1
2
1
1
1
1
2
1
2
0
1
1
1
2
0
1
0
1
1
1
1
2
0
1
1
1
1
1
3
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
2
2
1
1
1
1
2
1
2
0
2
1
1
1
1
0
2
1
1
2
2
1
0
0
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
0
1
1
1
1
0
1
0
2
2
1
1
2
1
1
2
1
1
1
0
1
0
0
0
1
1
1
1
1
1
1
2
1
0
1
2
1
2
1
1
2
1
2
2
1
2
2
3
1
1
1
1
1
1
1
1
1
1
2
2
0
1
1
1
1
1
1
1
0
2
1
2
2
1
0
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
0
1
1
1
1
1
1
1
1
1
1
1
2
1
2
0
5
1
0
1
1
0
0
1
1
1
1
0
1
2
3
1
1
1
1
1
1
1
1
1
0
1
2
1
0
0
1
1
1
1
1
2
1
1
2
2
0
2
0
2
0
2
1
3
1
1
0
1
2
2
1
1
1
1
1
2
2
0
0
1
0
2
1
1
1
2
1
1
1
1
1
1
0
1
1
1
1
1
1
1
2
1
1
2
1
1
1
3
1
1
1
1
0
2
1
1
0
1
1
1
2
1
2
2
2
1
2
1
1
1
2
0
1
0
0
1
2
1
1
1
1
1
1
2
1
1
0
2
0
1
2
1
1
1
2
1
2
1
2
0
1
2
1
2
1
1
1
1
1
2
1
0
2
1
0
1
1
1
2
2
1
1
0
2
1
1
1
1
2
1
1
0
1
1
1
2
1
0
1
2
1
1
1
1
1
2
1
2
2
1
2
2
1
2
1
2
0
1
1
2
2
0
1
1
2
2
2
1
1
1
0
1
1
0
1
0
2
1
1
1
0
1
1
1
1
2
1
2
0
1
1
6
1
1
1
2
2
1
1
1
2
2
1
2
1
1
1
2
0
0
0
2
0
1
0
2
1
1
2
1
1
0
0
0
2
1
1
1
2
1
2
1
1
2
2
1
2
1
1
2
1
2
2
1
2
2
2
0
1
1
2
1
2
1
0
1
1
2
2
1
1
1
1
2
1
1
2
1
2
1
2
1
1
1
1
1
2
1
2
1
1
2
2
1
2
1
1
2
1
1
2
1
1
2
2
1
0
1
1
1
1
0
3
0
2
0
2
1
2
1
0
1
1
2
2
1
2
0
0
1
1
1
1
0
1
1
1
1
2
0
1
1
1
0
2
2
1
1
0
1
0
2
1
1
1
0
1
2
1
0
2
1
1
1
1
1
1
1
1
2
0
1
1
2
2
1
3
1
2
2
1
0
0
1
0
2
1
0
1
2
2
0
1
2
1
1
0
0
2
1
1
2
1
1
1
1
1
1
0
2
0
1
1
2
1
0
1
1
1
1
2
1
1
1
2
1
1
1
1
1
2
1
1
1
0
1
0
1
1
2
1
2
1
1
2
2
0
1
2
1
0
2
1
1
0
2
1
1
0
1
1
1
2
1
0
3
2
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
0
1
0
1
1
0
1
1
0
1
2
2
1
1
1
1
1
1
2
1
1
1
0
1
1
1
2
0
1
1
0
2
1
1
2
0
1
0
0
1
1
1
1
1
0
1
1
1
0
1
1
1
1
1
2
1
3
0
1
0
0
0
0
1
0
1
1
1
2
1
2
1
1
1
1
1
1
1
0
1
1
2
0
2
1
0
1
2
2
1
1
1
1
2
1
2
1
0
1
1
1
1
0
1
1
2
1
1
0
1
1
0
1
2
1
2
1
1
1
1
0
0
2
1
1
1
1
1
2
2
1
3
0
2
0
0
1
1
0
2
2
1
1
1
2
1
10
1
2
2
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
0
0
2
1
1
1
2
1
0
1
1
1
1
1
1
1
0
1
2
1
1
1
1
1
1
1
1
1
2
1
2
1
1
0
1
2
0
1
1
2
1
1
1
1
1
1
1
0
1
0
1
2
1
1
1
0
1
1
0
1
0
1
2
1
1
1
0
1
1
1
1
1
1
1
0
1
2
1
1
1
1
1
1
1
1
1
0
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
0
1
0
1
1
0
1
1
2
2
1
1
1
1
1
1
1
0
1
1
2
2
1
1
1
0
1
0
2
2
2
1
0
1
1
0
1
1
1
0
2
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
0
2
1
1
1
2
2
1
1
1
0
0
0
2
1
2
1
2
2
1
1
1
1
0
1
1
1
1
2
1
1
1
0
1
1
0
2
2
2
1
1
1
2
1
1
1
2
1
2
1
1
2
1
1
1
1
1
2
2
2
1
1
1
1
1
2
0
2
1
1
0
2
2
0
1
3
1
0
1
1
2
2
0
0
2
0
1
2
0
1
1
2
1
1
1
1
1
1
1
2
2
1
2
1
1
2
1
1
0
1
1
1
2
1
1
1
1
2
1
1
1
1
1
0
1
1
1
1
1
0
1
1
2
1
2
1
1
2
1
1
1
1
2
1
1
0
1
1
0
1
1
1
1
1
1
2
1
2
1
0
1
1
1
2
0
1
1
1
1
1
1
1
2
0
1
1
1
1
1
0
1
0
1
1
2
0
1
2
2
0
1
1
1
2
1
0
2
2
2
2
1
1
1
1
2
1
1
2
1
1
1
2
2
1
1
3
1
1
0
1
1
2
2
1
0
2
1
1
1
0
1
0
1
1
1
1
2
2
0
2
2
3
0
0
1
1
0
1
1
1
1
0
0
2
1
1
1
0
1
2
2
1
1
2
1
2
1
1
1
2
1
2
1
1
1
2
1
0
1
1
0
2
1
2
0
1
0
0
1
1
0
2
1
0
1
1
1
2
1
0
2
1
2
1
1
1
2
2
1
1
2
1
1
2
1
1
1
1
1
1
1
1
0
1
0
1
1
2
1
1
1
2
2
1
2
1
2
1
0
2
1
1
2
1
2
1
2
1
2
1
1
2
1
0
0
2
1
1
1
2
1
0
1
2
2
2
1
1
1
0
1
1
1
3
2
1
2
1
1
1
1
1
2
2
1
1
0
0
1
0
0
2
1
1
2
1
1
2
2
2
1
0
1
3
1
1
1
0
2
1
2
3
1
1
1
2
1
2
2
0
0
1
0
1
0
2
1
0
0
2
2
2
1
1
1
1
1
2
1
0
1
2
1
1
0
1
1
1
1
1
1
1
1
0
2
1
1
3
1
2
1
1
1
1
1
2
2
0
2
0
2
1
1
0
1
2
0
1
1
0
1
1
0
0
2
2
1
1
1
1
0
2
0
1
1
1
2
2
1
0
1
0
1
1
1
0
1
1
2
2
1
2
0
1
1
2
2
1
1
0
1
1
1
1
1
1
0
1
1
2
2
1
1
1
1
2
1
2
1
1
1
2
0
1
2
1
1
0
1
1
2
1
1
1
0
2
2
1
1
1
1
2
1
1
1
1
2
0
2
2
2
1
0
1
1
1
1
2
1
2
2
2
3
1
1
2
0
1
1
1
0
2
0
1
1
2
1
1
2
0
1
2
1
1
1
1
0
1
2
2
2
1
2
2
2
2
1
2
0
2
0
2
2
0
1
1
1
1
1
0
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
0
1
0
1
2
1
1
1
1
1
1
1
1
2
1
2
1
1
0
1
1
1
0
0
1
1
1
1
1
1
0
1
2
1
1
1
2
0
0
1
1
2
0
1
0
1
1
1
1
2
2
2
1
2
0
1
1
1
1
1
1
1
1
1
1
1
2
0
0
1
2
0
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
0
1
2
1
2
2
1
0
1
1
2
2
1
1
2
1
1
1
0
2
1
2
2
1
1
1
1
0
2
1
2
1
1
1
1
1
1
1
0
3
1
1
1
0
2
2
1
0
2
1
2
1
2
1
2
1
0
1
1
2
1
1
2
2
2
2
1
1
1
0
1
0
1
1
1
1
2
2
1
1
2
1
1
0
0
1
1
2
2
0
0
2
1
1
1
1
1
1
0
3
1
2
1
0
4
1
2
1
1
1
1
0
1
2
1
1
1
0
1
0
1
1
2
1
1
2
1
1
1
1
2
2
1
1
2
1
0
1
1
1
1
2
1
1
2
0
1
1
1
1
0
2
1
1
1
1
1
3
1
2
1
1
2
1
1
1
1
0
2
1
2
1
2
0
1
1
1
1
0
2
1
0
1
1
1
0
2
2
1
2
1
1
1
0
2
2
0
0
1
2
2
1
2
2
2
2
2
1
1
1
0
1
0
2
1
0
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
2
1
1
1
2
1
2
3
1
0
1
2
1
0
1
0
1
1
2
1
1
1
1
1
0
1
2
1
2
1
1
1
1
1
0
1
1
0
1
2
3
0
1
0
1
1
1
4
2
1
0
1
1
2
0
1
1
1
1
2
2
1
1
1
1
1
1
2
1
2
1
0
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
1
2
2
1
2
2
1
1
1
1
0
2
1
0
1
3
1
1
2
1
1
2
1
1
1
1
0
1
1
0
1
2
0
2
1
1
1
2
1
1
1
1
1
1
2
0
1
2
0
1
0
1
1
0
0
1
2
1
1
1
1
1
1
1
2
1
3
1
0
1
1
2
1
1
1
2
2
1
1
2
1
1
1
2
0
1
1
1
1
0
2
1
1
1
2
1
1
1
1
2
2
1
1
0
1
1
1
2
1
1
2
1
1
1
2
0
2
0
1
1
2
1
1
1
0
1
2
1
2
1
1
2
1
1
1
1
1
2
1
1
1
2
1
2
2
1
1
1
1
0
1
1
1
1
2
1
2
0
1
2
1
2
1
2
1
0
2
1
1
1
0
1
0
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
0
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
0
1
0
0
1
1
1
2
2
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
2
0
1
2
1
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
1
1
2
1
2
1
1
0
1
1
1
1
1
2
2
1
1
1
1
2
1
2
2
0
0
1
1
1
1
1
1
2
1
1
2
2
0
2
0
2
1
1
0
1
1
1
1
1
1
0
2
2
0
1
1
1
2
1
1
2
1
3
2
1
1
0
1
2
2
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
2
0
1
1
2
2
1
1
1
2
2
1
1
2
0
2
2
1
2
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
2
2
2
1
1
2
2
1
1
2
2
1
1
2
0
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
3
0
1
0
1
1
1
1
1
1
1
2
2
2
3
1
1
1
1
2
0
1
1
2
1
1
2
1
1
0
1
1
2
2
1
2
2
1
0
1
1
2
2
0
2
1
2
0
1
2
1
2
1
2
1
2
2
2
2
1
2
1
1
1
1
2
1
1
1
2
1
3
0
1
1
1
2
1
1
1
1
1
1
1
1
1
1
0
1
2
1
1
2
1
1
1
0
1
2
1
0
1
2
1
2
1
1
2
2
1
1
2
2
2
1
1
1
1
0
2
0
2
1
1
1
1
1
1
1
1
1
0
0
1
2
1
1
1
1
1
1
2
1
1
3
1
2
1
0
2
2
1
1
2
2
2
1
1
2
1
1
2
2
1
1
1
1
1
1
2
1
0
1
2
0
2
1
1
2
1
0
2
1
1
2
2
0
1
1
0
0
2
2
1
1
1
1
1
1
2
2
1
1
1
1
0
1
1
1
1
1
0
2
2
1
1
2
0
1
1
1
2
1
1
2
1
1
2
1
1
1
2
1
1
1
1
1
2
1
0
2
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
2
1
0
0
0
1
0
2
1
1
1
2
1
1
1
1
1
1
1
1
0
1
1
0
0
2
1
2
1
2
1
1
1
1
1
1
0
2
1
2
1
1
0
1
1
0
1
2
1
1
0
1
1
1
1
1
1
2
1
0
1
1
1
1
1
1
1
1
1
1
0
0
1
1
1
1
0
2
2
1
1
2
0
0
1
2
1
1
1
2
1
1
1
0
1
2
1
2
1
2
2
2
2
2
1
1
2
1
1
1
2
1
1
0
1
1
2
0
3
2
1
0
2
1
2
0
1
1
1
1
3
1
1
1
2
0
1
1
1
1
1
1
1
1
2
1
0
1
0
1
1
2
0
2
1
2
0
0
0
1
1
2
0
1
1
1
2
1
0
0
1
1
2
0
1
2
1
0
1
0
2
2
2
1
1
1
1
0
1
1
2
1
1
1
3
1
1
1
0
1
1
1
0
1
2
1
1
1
1
2
1
2
1
2
1
2
1
2
1
2
2
0
0
1
0
2
0
1
1
1
1
3
1
1
1
1
0
1
1
2
2
1
0
1
0
1
1
1
1
2
0
1
1
2
1
1
1
2
1
1
0
1
1
1
2
1
1
2
2
1
1
1
0
1
1
1
1
1
1
1
1
1
0
1
2
1
1
1
2
1
1
1
1
1
2
0
2
2
0
1
1
2
1
1
2
1
0
0
2
2
1
1
1
2
0
1
1
1
1
2
0
1
2
2
0
1
1
1
1
1
1
1
1
0
1
1
2
1
0
3
1
0
2
1
0
1
1
2
2
0
2
1
2
1
1
2
0
1
2
2
2
1
1
1
0
2
1
1
1
2
1
2
1
2
1
1
1
1
0
1
0
0
0
1
1
2
2
0
2
0
2
1
2
1
1
2
1
2
2
1
0
1
1
2
1
1
1
1
1
1
2
0
0
1
2
1
1
1
1
0
1
0
1
2
1
0
1
1
1
2
1
1
2
1
2
2
1
1
2
1
0
1
0
1
1
1
2
0
1
2
1
1
1
0
2
1
2
1
1
1
1
1
1
2
0
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
0
2
1
1
1
1
1
1
1
2
2
1
1
1
2
2
2
1
0
1
1
1
0
1
1
1
1
1
1
1
2
1
1
1
2
0
1
1
1
0
1
1
1
1
2
1
2
0
2
1
1
1
3
1
2
1
1
1
1
1
1
0
3
3
1
1
1
1
2
0
2
1
1
0
2
2
1
1
0
0
1
1
1
1
2
1
2
1
1
1
2
1
1
0
0
2
2
1
2
2
0
1
1
1
1
1
2
1
1
1
0
2
1
1
1
1
2
1
1
2
0
1
2
2
1
1
2
1
1
0
0
1
1
1
1
1
1
1
0
0
1
1
2
1
1
2
1
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
2
1
2
2
3
1
1
2
1
2
1
1
1
0
2
1
2
2
2
1
1
1
2
1
2
1
3
1
1
1
1
2
1
1
1
2
1
1
0
1
2
0
2
1
1
1
0
1
1
1
1
2
1
1
1
2
1
1
0
2
1
1
1
1
0
2
1
2
0
2
0
1
1
1
2
2
2
1
1
1
2
2
1
1
1
2
1
1
1
2
0
1
1
0
1
1
0
1
0
2
1
2
1
1
1
2
1
2
0
2
0
2
1
1
1
1
2
0
1
2
1
2
1
0
0
1
2
1
1
0
2
1
2
2
1
2
2
2
1
2
1
2
1
2
0
0
2
1
1
1
1
1
1
2
1
1
1
0
2
0
1
2
2
1
1
2
1
1
2
2
1
2
2
1
2
0
1
1
2
0
1
1
1
1
1
1
0
1
2
1
2
1
1
5
0
1
0
1
2
1
0
1
1
1
1
2
1
1
1
2
1
2
0
1
1
1
0
1
1
0
1
2
1
0
2
1
1
1
1
1
1
1
0
2
1
1
1
0
0
0
1
1
2
0
1
1
1
1
0
1
1
1
1
1
2
1
1
1
1
1
0
0
0
1
1
0
1
2
1
2
1
1
1
0
0
1
1
2
1
1
1
2
0
2
0
2
0
2
2
1
1
1
2
2
2
1
1
1
2
1
1
1
0
1
1
1
1
2
2
1
0
1
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
0
1
2
1
1
2
2
1
1
1
1
2
0
2
1
1
2
0
0
1
1
1
1
0
1
0
0
1
1
1
1
2
1
1
2
1
1
1
1
1
2
0
1
0
1
0
2
2
1
2
2
1
2
3
1
2
0
0
1
0
1
1
2
2
1
2
0
1
2
1
1
2
1
1
0
0
1
1
1
0
1
2
1
2
0
1
2
1
1
1
1
1
1
0
1
1
1
2
2
1
1
1
1
1
1
1
2
2
1
1
2
1
0
1
1
1
1
1
1
1
1
2
2
1
2
1
1
1
2
1
1
1
1
1
2
2
1
0
2
2
2
2
0
2
1
1
1
2
1
1
0
1
1
2
0
0
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
2
1
2
1
1
1
2
1
1
2
1
1
2
2
1
2
1
0
0
1
2
2
1
2
2
1
1
1
1
1
2
1
1
0
2
2
1
2
2
4
1
1
1
2
2
2
1
1
0
2
2
1
0
1
0
2
2
1
1
0
0
2
1
1
1
1
1
2
1
1
2
1
2
2
0
1
2
0
2
2
1
2
2
2
1
1
2
1
2
3
1
1
0
1
1
1
1
1
1
0
2
1
0
1
1
1
2
2
2
1
1
2
1
1
2
1
1
1
1
2
1
2
1
0
2
0
2
1
1
1
0
2
1
1
1
2
1
2
2
2
2
1
1
0
0
1
1
0
1
0
2
1
1
1
0
1
1
2
1
1
2
0
0
1
4
1
1
1
1
0
1
1
0
0
1
1
1
1
1
1
2
2
0
2
1
2
2
0
1
2
1
2
0
1
1
1
1
1
0
1
0
0
0
1
2
1
1
1
1
0
2
1
1
1
2
0
1
2
1
2
1
2
1
1
1
1
1
0
1
1
2
1
1
1
2
0
2
2
0
2
0
1
1
1
1
2
2
1
1
2
0
0
1
1
1
2
1
1
1
0
0
2
2
2
1
1
1
1
1
2
2
1
0
2
1
1
1
2
0
1
1
1
1
2
2
2
1
1
2
1
1
1
1
0
1
2
1
0
1
2
1
1
0
1
1
1
1
2
1
2
0
1
2
1
0
1
1
0
1
2
1
1
0
1
1
2
0
1
1
2
1
0
2
2
2
1
1
2
1
1
1
1
1
2
1
1
1
1
1
0
6
1
2
0
1
1
1
2
2
1
1
1
1
2
2
1
1
1
1
1
0
1
2
2
2
1
0
1
1
1
1
2
0
1
1
1
3
1
1
1
2
1
2
2
0
1
1
1
1
2
1
0
2
1
1
3
0
0
1
1
2
2
1
2
1
1
2
1
1
1
2
2
0
1
1
3
0
2
0
2
2
2
1
1
1
1
1
1
1
1
2
0
1
0
1
1
1
0
1
1
1
0
1
1
1
0
1
1
1
0
1
1
0
1
2
1
1
1
2
1
2
0
1
0
1
1
1
1
1
1
0
2
1
1
1
2
1
1
2
1
0
1
1
1
6
1
2
0
0
2
1
0
3
2
1
1
2
1
2
0
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
0
1
0
2
0
1
1
1
2
2
1
1
1
0
0
1
1
1
1
1
2
2
1
2
1
2
1
1
0
2
2
1
1
1
1
1
2
2
1
1
0
1
0
1
2
2
2
0
2
1
2
2
2
1
2
0
1
1
1
1
2
1
1
1
0
1
2
1
1
1
1
1
1
1
1
1
1
2
2
1
2
1
0
1
1
3
1
1
1
2
1
1
1
2
1
1
1
1
1
0
2
1
1
1
1
1
2
2
1
2
1
0
2
1
2
1
2
1
0
0
1
1
1
0
2
1
1
1
2
2
1
2
1
1
0
0
1
1
1
1
2
1
1
1
1
1
1
2
1
0
2
1
0
0
2
1
1
0
0
1
1
1
1
1
1
1
0
0
2
2
1
1
2
1
1
1
1
1
2
2
2
1
1
2
2
2
2
0
2
1
2
1
4
1
1
2
1
1
1
2
0
1
2
1
1
0
1
1
1
1
1
1
1
1
2
0
1
2
1
2
1
1
1
1
2
1
2
0
1
2
1
2
1
1
2
2
1
2
1
2
1
1
2
1
0
1
2
2
1
1
1
1
2
3
1
0
1
1
1
1
2
2
1
2
2
1
1
1
1
2
0
1
2
1
1
1
2
2
1
2
0
1
1
1
1
0
2
2
1
0
0
1
0
2
0
2
1
1
0
2
1
1
0
1
1
1
1
2
0
1
1
2
2
1
1
0
2
0
0
0
2
1
1
2
2
1
1
1
2
1
2
1
0
0
2
1
3
1
1
1
0
1
0
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
0
1
1
2
1
1
1
1
1
1
2
1
2
1
1
2
2
1
1
0
1
0
1
1
0
2
1
2
1
2
1
1
0
1
1
1
1
1
0
1
1
2
1
1
0
0
2
1
2
2
1
1
1
0
0
2
2
2
1
1
1
2
2
0
2
2
2
0
2
1
1
2
0
0
1
1
1
1
1
2
1
2
1
2
0
1
2
1
1
1
1
0
0
1
1
1
1
0
1
1
1
2
1
0
2
1
1
1
2
1
1
1
1
0
1
2
1
1
1
2
0
1
0
1
2
2
2
2
1
3
1
1
0
1
1
2
1
1
1
2
1
1
1
1
1
1
2
2
1
0
2
2
1
1
1
1
1
0
1
3
0
2
0
1
1
1
1
0
2
1
1
2
1
2
1
1
2
1
1
1
1
0
1
1
1
3
0
2
2
2
0
1
2
1
0
1
1
1
0
1
1
1
1
1
1
2
1
2
2
1
2
0
1
1
1
1
0
1
1
2
2
1
1
1
2
1
0
1
2
1
1
0
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
0
1
2
1
1
2
1
1
1
2
2
0
2
1
1
3
1
0
1
2
1
2
2
1
1
0
1
1
1
1
2
1
2
2
1
1
1
1
2
1
2
1
2
1
1
4
2
1
0
2
0
0
0
1
1
1
1
3
1
1
1
1
0
1
0
0
2
2
2
1
1
1
1
1
1
0
2
1
0
1
2
2
1
2
1
1
1
1
1
0
1
0
1
1
1
0
2
2
0
0
1
1
2
1
1
0
2
2
2
0
2
2
1
1
2
0
2
1
0
3
0
1
0
2
1
2
2
1
1
1
1
1
1
1
0
1
2
2
1
1
2
1
1
1
1
1
2
0
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
0
1
0
1
1
1
0
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
2
2
1
1
2
0
2
1
1
0
1
2
1
1
1
2
1
1
0
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
0
1
2
2
1
2
0
0
1
1
2
1
1
1
2
1
1
2
0
1
0
1
1
1
0
1
2
3
2
1
1
0
2
1
0
1
1
1
1
1
1
2
2
1
2
0
2
1
1
1
1
1
1
0
1
0
1
1
1
1
1
2
1
1
1
1
0
1
2
1
1
1
2
1
2
1
1
1
2
2
0
2
2
1
1
1
2
1
0
1
1
1
1
0
2
1
2
1
3
2
1
1
0
1
1
1
1
1
1
1
2
1
1
2
1
1
2
1
1
2
1
0
1
0
0
1
1
2
1
1
1
1
0
0
2
1
2
0
0
2
2
1
2
0
1
1
1
0
2
0
1
1
1
1
1
2
1
2
1
1
0
1
1
2
2
1
2
1
1
1
0
1
2
0
1
1
0
1
1
0
1
2
1
2
1
2
7
1
1
1
2
1
1
0
1
1
2
1
1
1
2
1
0
1
1
1
0
1
0
1
2
0
1
1
1
1
1
1
1
1
2
2
1
2
1
0
1
2
1
1
1
1
2
2
2
1
1
2
2
0
0
1
2
0
1
2
1
2
0
1
1
0
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
0
1
2
2
1
2
0
2
2
2
1
1
1
1
1
2
1
1
2
2
1
1
0
1
1
1
1
2
2
1
2
2
1
1
0
1
1
1
1
2
2
1
1
2
1
1
2
1
2
1
2
1
2
1
0
2
2
2
1
1
1
2
2
1
1
1
1
2
3
1
2
1
1
1
2
1
1
0
2
1
1
0
2
1
1
2
1
1
1
2
2
0
1
0
1
0
2
1
1
1
2
0
0
2
2
2
1
1
0
1
1
1
1
1
0
1
1
1
1
1
1
0
1
1
0
1
1
1
1
1
2
0
1
0
1
2
2
2
2
1
1
1
1
1
0
2
2
1
0
1
1
1
1
1
1
1
1
2
1
2
1
1
0
1
1
1
2
1
1
1
1
1
1
1
2
2
1
2
2
0
1
0
2
1
1
1
1
2
1
1
1
1
0
1
2
1
2
1
1
0
1
1
1
1
1
1
1
1
0
0
1
1
1
2
1
1
1
1
1
1
1
1
1
1
0
2
1
1
1
1
2
0
0
1
1
2
0
2
1
1
2
1
1
0
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
0
1
1
2
0
2
2
1
0
1
1
2
1
1
2
1
1
1
1
1
1
1
2
0
2
1
1
1
0
1
2
1
1
2
0
2
1
2
0
1
2
2
1
1
0
1
0
1
1
0
1
1
1
2
1
0
1
1
1
2
1
0
1
1
1
1
1
1
0
1
0
2
1
2
1
0
1
1
1
1
1
1
1
1
1
1
0
1
2
2
1
1
1
1
2
1
1
2
2
0
2
1
2
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
1
0
1
1
1
1
1
1
2
1
0
2
1
2
2
1
1
1
1
1
1
0
1
1
1
1
1
2
1
2
1
2
2
1
2
1
1
2
2
1
1
1
1
2
0
1
1
1
0
0
2
1
1
0
1
1
1
2
1
1
1
1
1
1
1
1
1
0
1
2
2
1
2
0
1
2
1
1
1
2
1
1
2
0
1
1
1
2
0
1
2
1
1
1
1
1
2
1
1
1
2
2
1
1
1
2
2
2
1
1
0
1
2
1
1
2
2
1
0
2
1
1
0
1
1
1
1
2
2
1
1
2
1
2
1
1
2
0
1
1
1
0
1
1
1
1
2
1
2
2
2
1
0
2
0
1
1
1
2
1
0
1
1
1
1
2
1
1
0
2
2
1
0
1
0
1
1
0
2
1
2
1
2
1
1
1
1
1
1
1
1
2
0
1
1
1
1
1
0
1
1
2
0
1
1
1
1
0
0
2
1
2
1
1
0
2
1
2
1
1
1
1
2
1
1
1
1
0
0
2
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
2
1
0
1
1
2
1
1
2
2
0
1
0
1
1
1
1
0
1
1
0
1
1
1
1
1
2
0
1
0
1
1
1
1
1
0
2
1
1
1
2
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
0
1
1
2
1
1
1
1
2
1
0
2
2
1
2
2
2
0
1
1
1
1
1
0
1
2
1
2
0
0
2
0
2
1
2
1
1
1
2
1
1
2
1
1
1
0
1
1
1
2
2
1
1
0
2
1
1
1
0
1
2
1
2
1
0
2
1
3
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
0
1
1
1
1
0
3
1
1
2
1
0
1
0
0
2
1
1
1
3
2
2
0
1
1
2
1
0
1
1
1
2
1
1
2
0
0
1
2
1
2
0
2
1
1
2
1
1
0
1
1
1
2
1
1
1
1
1
0
2
2
1
1
1
0
2
1
1
1
1
1
1
0
1
1
2
1
1
0
2
1
0
0
2
1
1
1
1
1
1
1
1
0
1
2
1
2
0
1
2
1
1
2
2
1
1
1
4
1
2
1
1
1
1
1
1
1
0
2
1
2
2
0
1
2
1
1
1
1
1
1
0
2
1
2
1
2
2
0
2
1
0
2
2
2
1
1
2
0
1
2
0
1
2
1
1
1
1
1
1
1
0
1
1
1
1
2
1
1
0
1
1
2
1
1
1
2
2
1
1
1
2
1
0
1
1
1
2
1
0
0
1
2
1
1
0
1
1
1
0
0
1
2
2
1
2
2
1
0
1
2
2
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
2
1
0
1
2
1
1
2
1
0
1
1
1
1
2
1
0
2
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
0
1
1
1
1
3
2
1
2
1
2
0
1
1
1
1
2
1
2
0
2
2
1
1
1
2
1
1
2
1
2
1
0
2
1
2
2
2
1
1
2
2
1
0
3
1
1
2
1
1
1
1
1
1
0
1
1
1
0
1
2
1
1
1
2
0
1
0
2
1
0
0
1
2
1
1
1
0
2
2
1
1
1
1
2
0
1
2
2
1
0
2
2
1
2
1
2
0
1
1
1
1
1
1
1
1
1
2
0
1
1
1
1
3
1
1
1
0
1
1
0
1
1
2
2
1
2
2
1
2
1
0
1
2
0
1
1
1
1
1
2
1
1
2
1
1
0
2
1
1
1
2
0
1
2
2
1
2
2
2
1
1
1
1
2
1
2
1
1
1
2
1
2
1
0
1
1
1
1
1
1
1
1
1
0
1
1
0
1
1
1
1
1
0
1
2
2
2
1
2
1
2
1
1
1
1
1
2
1
0
2
1
0
1
1
0
1
1
1
1
2
0
0
1
1
1
2
1
0
0
2
2
1
1
1
1
0
0
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
2
1
1
1
0
2
1
1
1
1
2
1
1
1
1
0
2
1
1
0
2
1
1
1
1
2
1
1
0
0
1
1
1
1
2
2
1
2
0
1
1
1
1
1
0
1
2
1
1
1
2
2
0
2
1
1
1
2
2
1
1
2
0
0
2
0
1
1
3
0
1
1
0
2
1
1
2
2
0
1
0
0
1
1
1
1
1
2
2
1
1
1
1
0
2
0
0
1
2
1
1
1
1
2
0
1
1
1
1
1
1
3
2
0
0
0
0
0
2
1
1
1
0
1
1
1
1
1
1
1
1
0
1
1
0
0
2
1
1
1
2
1
3
2
1
2
1
2
2
0
1
1
1
1
0
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
0
1
1
1
1
1
0
0
1
1
1
2
2
2
0
13
1
2
1
1
2
1
1
2
0
1
1
2
1
1
1
2
2
2
2
1
0
2
2
1
2
1
0
1
1
2
1
0
2
2
1
1
1
1
1
2
1
0
1
1
1
0
1
1
1
2
0
2
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
2
0
1
0
1
1
1
1
2
2
1
2
2
2
1
1
1
1
0
0
1
0
1
1
1
1
2
2
2
2
1
2
0
0
0
0
0
1
1
1
1
2
0
1
1
2
0
0
2
1
0
1
1
0
2
1
1
2
1
1
0
1
0
2
0
1
1
1
1
2
1
2
1
0
2
1
0
3
1
0
1
1
2
2
2
2
1
2
1
0
2
2
1
2
2
1
1
0
1
2
0
1
1
1
2
1
0
1
1
2
2
0
1
1
1
1
1
1
0
1
1
1
1
1
0
2
1
2
0
1
1
1
2
1
2
1
1
0
2
4
0
1
2
0
1
1
1
1
1
1
1
2
1
1
3
1
1
1
2
1
0
0
2
0
2
1
1
1
1
2
1
1
2
1
0
1
2
1
0
2
1
1
1
1
1
1
2
1
1
2
1
1
1
0
1
1
2
1
0
1
1
2
1
1
1
1
1
1
0
1
1
1
1
0
2
1
1
1
0
1
2
2
1
0
0
1
2
1
1
1
0
2
1
0
1
0
0
2
1
0
1
1
1
1
1
1
1
1
1
2
1
1
0
1
1
1
1
1
2
1
1
1
1
0
2
1
2
1
1
1
2
1
0
1
1
2
1
1
0
0
1
1
2
1
1
0
0
2
1
2
1
1
2
1
0
1
0
2
1
1
1
0
2
1
2
2
2
1
1
1
1
1
2
1
1
2
1
0
1
2
2
1
0
1
1
2
1
2
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
0
1
0
2
1
1
2
2
2
2
1
1
1
1
1
1
1
1
2
1
2
2
0
1
2
3
0
1
1
1
1
2
0
1
1
1
1
1
1
0
1
0
1
2
1
2
1
0
1
1
0
1
1
1
1
2
1
2
0
1
1
1
2
1
1
1
1
1
1
1
1
4
1
3
1
0
0
2
1
2
1
1
1
2
1
1
0
0
0
1
1
1
1
1
1
1
1
1
1
2
0
1
1
1
2
1
1
1
1
2
2
2
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
2
1
1
2
2
0
1
1
0
1
2
1
1
1
1
1
1
1
0
1
1
1
0
1
2
1
2
1
1
1
1
2
1
2
2
2
2
1
1
2
1
1
0
1
2
1
1
2
1
2
1
1
1
2
3
1
1
1
1
1
2
1
2
0
1
1
1
1
0
2
0
0
1
1
1
1
0
1
1
1
0
1
2
1
2
2
1
1
1
0
1
1
0
2
1
1
2
1
0
2
1
1
0
1
1
1
1
2
1
2
1
2
1
0
0
1
2
2
2
2
1
2
1
2
1
2
1
0
1
1
1
1
2
1
1
1
0
1
1
2
1
1
1
1
1
1
2
0
2
1
0
1
2
2
1
1
1
1
3
1
1
2
1
1
0
1
2
1
0
1
1
1
1
2
2
1
1
1
1
2
2
1
2
0
1
1
2
1
0
0
1
1
1
0
1
2
2
2
1
2
1
1
2
1
1
1
1
2
1
1
1
1
0
2
0
1
1
1
0
1
1
1
2
1
1
1
1
1
1
2
2
2
0
1
2
1
1
1
0
2
2
0
1
1
1
1
1
2
2
1
1
0
1
1
1
1
1
1
1
0
1
2
1
1
1
1
2
1
1
1
0
1
1
1
1
2
2
1
1
1
2
2
2
2
0
2
2
2
1
1
2
2
2
0
1
1
1
2
2
1
1
2
2
0
0
1
1
2
2
1
1
2
1
2
1
0
2
0
1
2
2
2
2
1
1
2
1
1
0
1
0
1
1
1
1
1
1
2
1
2
1
1
1
1
0
2
1
0
1
1
2
1
2
0
1
1
1
0
2
1
0
1
1
1
1
2
0
1
0
1
1
1
2
1
1
1
1
1
2
1
1
0
1
1
1
1
0
1
1
3
1
0
1
1
0
0
1
2
1
1
1
2
1
1
1
1
1
2
1
1
0
1
1
2
1
1
1
1
3
1
1
2
1
1
1
0
2
0
2
1
1
1
1
0
0
2
1
1
1
2
1
1
1
1
2
1
2
1
0
1
1
3
1
2
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
3
2
0
1
1
1
1
0
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
0
1
1
1
0
1
1
0
1
1
1
1
1
0
1
1
1
3
1
1
1
1
1
0
1
1
2
1
1
1
2
1
2
1
1
1
0
0
2
1
1
1
1
0
2
1
2
0
1
1
1
1
2
0
2
1
0
1
2
1
1
2
2
1
0
2
2
0
1
1
1
1
1
1
0
1
1
1
2
0
0
1
2
1
0
1
1
1
1
1
1
1
1
1
1
1
2
1
2
0
2
1
2
1
1
1
1
1
1
1
1
2
0
1
2
1
1
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
0
1
2
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
0
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
0
1
1
1
2
1
2
1
0
2
2
2
2
2
1
1
0
1
2
2
1
1
0
0
1
1
1
0
1
2
1
0
1
1
1
0
1
1
1
2
0
1
1
0
1
1
1
1
2
1
1
1
1
1
1
1
2
3
1
2
0
1
2
2
1
1
0
1
1
2
1
1
2
0
1
2
1
1
2
1
2
1
2
1
2
1
1
1
2
2
1
1
1
1
0
1
1
1
2
0
1
2
1
1
1
2
1
0
1
0
0
1
2
2
1
1
1
2
0
1
1
2
1
1
2
1
1
2
2
1
0
0
1
1
2
1
1
1
1
1
1
1
1
1
1
1
0
2
1
3
1
2
1
0
1
1
1
0
2
1
1
1
0
0
2
0
1
1
0
1
1
1
2
1
1
2
1
1
1
2
2
1
1
1
1
2
2
1
2
1
2
1
1
1
1
1
2
1
0
2
1
1
1
2
0
2
1
2
1
1
1
0
1
1
2
1
0
1
1
1
2
2
1
2
1
2
2
2
1
2
1
1
2
1
2
0
0
1
1
2
0
1
1
1
2
2
0
1
1
1
1
2
1
1
1
1
0
0
0
1
1
2
0
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
0
2
1
1
1
1
1
0
1
2
1
0
2
2
0
2
1
1
1
1
1
2
1
1
2
1
1
2
1
1
1
2
2
1
2
1
1
0
0
1
1
1
1
1
2
0
2
0
1
2
1
2
0
1
1
1
1
2
1
0
1
0
1
1
2
1
3
1
1
0
2
1
0
2
3
1
1
1
1
1
2
1
1
2
0
1
2
1
1
1
1
2
1
2
0
1
1
1
1
1
1
1
1
1
1
2
0
1
2
1
2
1
4
1
2
2
1
2
1
1
1
1
2
1
1
1
2
1
1
1
0
1
1
1
2
1
1
1
0
1
2
0
1
1
1
1
2
1
1
2
0
1
0
1
1
2
1
1
1
1
2
2
1
1
1
1
1
0
1
1
0
1
1
1
0
1
1
1
2
1
1
0
2
1
2
1
1
0
1
1
1
1
1
2
0
1
0
2
1
1
0
1
1
0
1
2
1
2
1
2
2
2
2
1
1
0
0
1
0
1
2
1
1
1
3
0
1
1
2
3
2
2
1
2
1
1
1
1
1
1
1
1
0
2
0
1
2
0
1
1
2
2
1
2
0
1
1
2
1
1
1
0
1
1
1
0
0
1
1
1
1
1
1
0
0
1
0
1
1
2
1
1
0
2
2
1
1
1
1
1
1
1
0
1
0
1
1
0
1
2
1
0
3
2
1
1
3
1
0
1
1
2
1
2
1
1
1
1
0
2
1
1
2
2
1
2
0
1
1
0
0
1
1
1
2
1
1
1
1
0
2
1
2
1
1
1
1
1
1
2
3
2
1
1
1
2
1
2
1
1
2
2
0
1
1
2
2
1
0
1
0
1
0
2
1
1
1
2
0
1
1
1
2
1
1
0
2
1
1
2
1
2
0
1
1
2
1
1
0
1
1
0
1
1
2
0
1
1
1
1
2
1
1
1
2
2
1
0
2
1
1
1
1
1
2
2
1
1
1
2
2
1
1
1
1
0
2
1
1
0
1
2
1
1
2
1
1
1
0
1
1
0
1
1
1
1
0
1
0
1
1
1
2
2
1
2
2
1
0
1
2
2
1
1
2
2
1
0
1
1
0
1
1
1
1
2
2
2
0
0
2
2
0
2
0
2
1
0
2
2
0
1
1
1
2
0
1
1
2
2
2
1
2
1
1
1
0
2
1
0
2
0
1
0
1
1
1
2
1
1
1
0
1
2
2
2
1
1
1
1
2
1
0
0
2
1
1
1
1
1
0
2
1
1
1
2
1
2
2
1
0
2
1
1
1
2
1
1
2
1
1
0
2
1
2
1
2
1
1
1
1
1
1
1
2
0
2
1
1
1
2
2
0
1
1
1
2
1
2
2
0
2
1
2
2
1
1
2
2
1
0
1
1
1
1
2
1
1
1
1
1
1
1
0
1
2
0
1
1
1
1
2
1
2
2
1
1
2
2
2
1
2
1
1
1
0
0
3
1
1
2
2
1
1
1
2
1
1
1
2
1
0
1
0
1
1
1
0
1
1
0
1
2
1
1
2
1
1
2
1
2
2
1
0
2
1
1
1
1
2
1
0
1
0
0
1
1
3
2
1
1
2
1
1
0
0
2
0
1
1
2
1
1
1
1
1
1
2
2
0
2
2
1
0
1
1
1
2
1
1
2
3
2
1
1
1
1
1
1
1
1
1
1
1
3
2
1
1
1
1
2
2
1
0
1
1
1
0
2
1
1
2
2
2
2
2
1
0
2
2
1
1
1
1
1
0
1
1
2
1
2
1
2
1
2
1
2
0
1
0
2
1
1
1
1
1
0
1
0
1
0
1
0
0
1
1
2
0
1
1
1
1
2
1
1
0
2
1
2
2
1
1
1
0
1
1
1
2
1
0
1
1
1
1
1
2
2
1
2
1
1
1
2
1
1
1
0
1
2
0
0
2
1
2
0
1
1
1
1
1
0
0
0
1
2
0
1
1
1
2
1
2
1
1
2
0
1
1
0
1
1
1
2
1
0
1
1
2
0
2
1
0
1
1
2
0
1
1
1
1
1
1
2
3
1
1
0
1
2
2
2
2
1
1
0
2
1
0
2
2
1
1
1
2
1
1
1
0
1
1
1
1
1
1
1
2
2
2
1
1
2
2
1
1
1
1
0
1
1
1
2
1
1
0
0
1
1
1
2
1
2
0
1
2
1
2
1
1
1
1
1
2
1
0
2
1
1
1
2
0
0
1
1
1
1
1
1
1
2
1
2
1
2
0
2
1
3
1
1
0
1
1
1
1
2
0
1
2
2
0
2
2
1
2
1
3
1
1
1
1
1
1
0
0
2
0
2
2
0
1
2
2
2
0
1
1
2
1
1
0
1
1
1
1
1
1
1
2
1
2
1
2
2
2
1
1
1
2
1
1
1
1
1
0
2
1
1
2
1
1
2
2
2
1
1
2
1
1
1
1
1
1
1
1
2
1
2
2
0
0
1
1
1
0
1
1
2
1
2
0
1
1
1
2
0
1
1
1
2
0
2
0
1
1
1
2
1
2
1
2
2
1
0
0
1
1
1
1
1
0
0
2
1
0
1
1
1
0
1
1
1
0
2
2
2
1
1
0
1
1
1
1
1
2
2
1
1
1
1
1
0
2
1
1
1
2
1
0
1
0
1
1
1
2
1
1
2
1
1
1
0
1
1
1
1
1
1
2
1
2
2
0
2
1
0
0
1
0
1
1
0
2
2
1
1
1
0
2
2
1
0
2
1
1
2
2
1
1
2
2
1
2
1
2
1
1
1
1
1
0
1
1
2
1
2
1
1
2
1
1
1
0
1
1
1
1
2
0
1
1
1
1
2
0
2
0
2
1
1
0
1
1
2
1
1
1
1
1
1
0
1
1
2
1
1
1
0
1
1
1
2
1
2
1
1
1
2
2
2
0
0
1
0
0
1
1
2
1
1
1
1
1
1
0
0
0
2
1
1
1
2
0
1
2
2
1
1
0
2
1
0
1
0
1
1
1
1
1
0
2
2
2
1
2
0
2
1
1
2
1
1
2
2
1
1
2
2
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
0
0
1
1
1
1
1
1
1
1
0
1
2
1
2
2
0
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
2
1
1
1
2
1
2
1
0
1
1
0
0
2
1
1
2
1
0
1
1
1
1
0
1
1
2
1
1
1
1
1
1
2
2
1
2
1
1
0
1
0
1
1
2
1
2
2
2
2
2
1
1
0
2
2
1
1
2
1
2
1
1
1
1
1
1
2
1
2
1
1
1
2
2
2
1
2
1
1
1
1
1
1
1
2
1
1
1
0
1
2
1
0
1
1
1
2
1
1
2
1
0
1
1
0
1
0
1
1
2
1
0
1
2
2
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
0
2
1
1
2
1
2
0
0
1
1
0
1
1
1
1
1
2
2
1
2
2
2
0
1
0
2
1
0
1
1
1
1
2
1
0
0
2
1
0
6
1
2
1
1
2
2
1
0
1
0
1
1
1
0
2
1
1
0
1
2
0
1
0
1
1
2
1
1
1
2
1
1
2
2
1
1
1
2
1
0
2
1
0
2
2
1
1
0
1
1
1
1
1
2
0
1
1
2
2
2
1
1
2
1
2
1
1
1
1
2
0
1
1
1
2
0
1
1
2
1
0
1
1
1
2
0
1
1
1
1
2
1
0
1
2
0
1
2
1
1
2
2
1
0
1
1
2
2
1
1
1
1
1
1
0
2
2
1
1
1
2
0
1
1
1
0
2
2
1
1
0
1
1
1
1
0
2
1
1
1
0
1
1
1
1
2
2
0
2
1
2
1
0
1
1
1
1
1
0
1
2
1
2
0
1
1
1
0
1
2
1
1
0
0
2
1
1
1
1
1
2
2
0
0
2
1
2
1
1
1
0
1
2
2
1
1
2
1
1
1
1
1
1
0
1
2
1
1
1
1
0
1
3
2
1
1
2
1
1
2
2
0
2
1
1
1
2
0
1
1
1
1
0
1
1
1
1
0
2
1
2
0
1
1
1
2
2
1
1
1
1
2
1
0
2
1
1
2
2
1
1
1
0
2
1
1
0
0
2
3
1
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
2
1
2
0
1
1
1
1
1
2
2
1
0
0
2
1
2
1
1
0
2
1
1
1
0
1
1
1
1
1
1
2
1
1
0
1
1
0
1
2
2
2
1
0
1
3
1
1
1
1
1
2
0
1
1
1
1
1
2
0
2
1
2
1
2
0
2
1
1
0
1
1
0
1
1
1
0
1
0
0
2
1
2
1
1
1
1
2
2
2
1
1
1
1
2
1
0
1
0
1
1
1
2
1
1
1
1
1
1
1
2
1
1
0
1
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
0
1
2
0
2
1
1
1
2
1
1
0
1
1
0
1
2
1
1
1
1
1
1
1
0
2
2
1
0
1
2
1
1
2
1
1
1
1
1
0
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
0
2
2
1
1
1
1
0
1
1
1
2
0
0
1
0
1
0
1
3
2
1
1
1
1
1
1
0
1
1
1
1
1
1
1
2
1
1
2
1
1
0
0
0
0
2
2
1
2
1
2
1
1
1
1
3
1
1
1
1
1
1
1
2
1
2
1
1
1
0
1
1
1
0
2
1
2
1
0
0
0
2
1
2
1
1
0
1
1
2
1
1
1
2
2
1
2
1
2
1
0
1
0
1
1
0
0
1
1
1
3
1
1
1
0
2
0
3
0
0
2
1
1
1
1
2
0
1
2
2
1
0
1
1
0
0
2
1
1
1
0
1
0
2
1
1
2
1
0
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
1
1
2
1
1
1
1
2
1
1
0
2
1
1
1
1
2
1
1
2
0
1
2
1
2
2
2
1
0
1
1
2
1
1
1
1
1
2
2
2
2
2
0
1
1
2
0
1
0
2
2
2
1
1
1
2
2
2
2
0
1
2
1
2
1
2
2
1
2
1
1
0
1
1
1
1
2
0
2
2
0
1
1
1
1
1
1
2
2
0
0
1
1
0
0
2
1
1
0
1
2
0
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
1
1
0
1
0
2
1
1
0
1
2
1
1
2
1
2
1
0
2
0
0
1
1
2
1
1
1
2
1
2
1
1
2
1
1
2
1
1
1
2
1
1
0
2
1
1
1
2
1
1
1
2
2
1
1
1
2
1
2
1
1
2
1
1
1
1
1
0
1
2
1
0
1
1
1
2
2
2
1
1
1
1
1
0
1
0
2
1
1
1
0
1
0
2
1
1
1
1
0
0
2
2
2
1
2
0
0
1
1
2
0
1
2
2
2
0
0
1
1
0
2
1
2
1
2
1
2
1
1
0
2
2
1
1
2
1
1
1
2
1
1
1
1
2
1
1
0
2
1
2
0
0
0
0
1
1
1
1
2
1
1
1
2
1
0
0
1
2
1
1
2
2
1
2
2
0
2
1
0
2
2
2
1
1
1
1
0
1
1
1
1
1
0
2
1
1
1
2
6
1
1
1
1
1
2
1
1
1
0
1
1
1
2
1
1
2
1
1
1
1
1
0
1
2
2
1
2
3
2
1
1
2
1
1
1
2
0
1
2
1
1
1
0
2
2
1
1
1
1
1
1
1
1
2
2
0
2
1
0
0
0
1
0
0
1
1
2
1
2
2
1
0
1
1
1
1
1
2
0
2
1
1
0
2
1
0
0
1
1
1
1
1
1
1
2
0
1
0
1
0
1
1
2
1
2
1
1
2
1
2
0
1
2
1
2
2
1
2
1
1
0
2
2
2
1
0
1
0
0
0
1
1
2
1
1
1
1
1
1
1
1
1
1
0
1
2
0
2
1
1
1
1
1
2
1
2
2
1
1
2
0
0
1
0
2
2
2
1
1
2
1
1
0
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
0
2
1
1
2
2
0
1
1
1
1
0
1
1
2
2
1
1
0
1
2
1
1
1
1
1
0
1
1
2
1
1
0
1
1
0
1
1
1
0
1
1
1
2
1
1
1
2
1
1
1
2
1
1
2
1
1
2
1
0
2
2
1
1
1
1
2
0
1
1
0
1
0
2
0
0
1
1
2
1
2
1
1
0
1
2
1
1
1
1
0
2
1
1
1
2
2
1
1
1
1
1
5
1
2
1
0
0
1
0
1
0
2
1
2
1
1
1
1
0
2
0
2
1
1
2
2
1
2
2
1
1
1
1
2
1
0
1
0
4
0
1
1
1
1
0
1
0
2
2
2
1
1
0
1
1
2
2
1
1
1
1
1
1
1
3
1
2
2
1
0
2
2
1
2
1
1
1
0
3
1
2
1
1
1
0
0
0
1
1
1
0
0
1
2
1
1
2
2
2
1
0
2
2
2
2
1
1
2
1
1
1
1
1
0
1
1
1
1
2
2
1
2
0
1
2
2
1
1
1
1
1
1
2
1
1
2
1
2
2
1
1
1
0
0
1
1
1
1
1
1
2
2
1
0
1
1
0
1
1
1
0
0
1
1
1
1
1
1
1
1
1
2
0
1
1
1
2
2
1
1
1
2
2
2
2
1
1
0
1
1
1
0
1
2
0
0
2
1
1
1
1
1
1
1
2
1
1
1
1
0
1
0
0
2
2
1
2
1
1
1
1
1
0
1
2
1
1
2
2
1
1
1
1
0
1
0
2
1
1
2
2
1
1
1
2
1
2
0
1
0
1
1
2
1
2
1
2
2
1
2
0
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
2
1
0
2
1
1
1
1
2
1
2
1
1
0
1
0
2
1
2
1
1
1
1
0
2
1
1
0
2
1
0
2
1
2
1
0
1
0
1
1
1
0
1
0
2
1
2
1
1
0
1
1
0
1
0
1
1
1
0
1
2
1
0
0
1
1
1
2
0
1
1
2
1
1
2
1
1
1
0
1
1
1
2
1
2
2
1
1
2
1
1
1
3
1
1
1
2
1
1
3
2
2
1
1
0
0
1
1
1
1
2
1
0
2
1
1
1
2
0
2
1
1
1
1
1
1
1
1
1
2
1
2
1
1
0
1
1
2
1
1
1
1
1
2
2
1
2
2
1
1
1
1
1
2
2
0
1
1
1
1
0
1
1
1
0
2
2
1
0
1
1
0
1
0
2
1
1
0
0
0
1
1
1
1
1
0
1
1
2
1
1
1
1
2
4
0
0
2
1
0
2
0
0
2
1
1
1
1
2
2
1
1
1
0
1
1
2
0
1
1
1
1
2
0
1
2
1
0
2
0
0
1
1
2
1
2
1
2
2
0
0
0
1
0
2
2
1
1
1
1
1
0
1
1
2
2
1
1
1
1
1
1
1
1
2
1
1
0
1
1
1
2
0
2
1
1
1
1
1
2
2
2
2
1
1
1
1
2
2
2
1
0
1
1
1
1
1
1
1
1
1
1
0
1
1
1
2
2
1
1
1
1
0
2
1
1
0
1
1
1
1
1
2
2
1
1
2
0
2
2
1
1
1
2
1
1
1
0
1
1
2
1
0
1
2
0
1
1
3
0
1
1
1
1
1
3
1
1
1
2
1
1
2
2
2
1
2
1
1
1
0
1
1
2
1
1
1
2
1
1
1
4
1
1
1
1
1
1
1
1
1
1
0
2
1
1
1
0
1
1
1
1
2
1
1
1
1
1
1
1
0
2
1
1
1
0
1
0
1
1
2
0
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
0
1
1
2
1
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
3
1
1
2
1
2
1
1
1
1
2
1
1
0
1
1
0
2
2
1
2
1
1
2
0
0
1
3
1
2
1
2
2
1
1
0
2
2
2
2
2
1
2
2
0
0
1
1
1
1
1
1
2
1
2
1
1
1
2
1
0
1
1
1
1
2
1
0
1
1
1
2
1
1
0
1
1
0
0
2
1
1
1
2
2
2
1
1
0
1
1
0
2
1
1
0
2
2
0
2
0
1
2
1
2
1
1
1
0
1
1
2
1
1
1
1
1
2
2
1
1
0
1
1
2
1
2
1
2
1
0
1
1
0
1
2
1
1
1
3
0
1
2
2
1
2
3
1
1
2
0
0
1
2
1
1
2
1
2
4
1
1
0
2
1
2
0
1
1
3
2
0
1
1
0
1
2
1
1
2
0
1
0
0
1
5
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
0
1
1
1
1
2
1
1
0
0
1
1
1
1
0
1
1
1
1
1
1
2
2
1
1
0
1
0
1
1
1
2
2
1
2
2
1
1
2
2
2
1
2
0
1
1
1
1
1
1
2
2
0
1
1
2
1
1
1
1
1
0
1
1
0
1
0
2
0
2
1
2
0
1
0
1
2
2
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
0
1
1
1
1
2
1
1
1
2
0
1
1
2
1
2
2
1
1
2
2
0
1
1
2
0
1
1
1
1
1
1
1
0
1
1
2
1
1
2
1
2
1
1
2
1
1
1
1
1
2
1
1
1
1
0
2
0
0
1
0
1
1
2
1
2
3
1
1
0
1
1
2
2
1
0
2
1
2
1
1
1
1
2
0
1
2
0
2
1
0
2
1
1
1
2
1
2
1
1
1
1
2
2
2
1
0
1
0
1
2
0
1
1
2
1
2
1
1
1
0
0
2
1
1
2
0
0
1
1
0
1
0
2
1
1
1
1
2
1
0
2
1
1
2
2
0
2
1
1
1
2
0
0
1
2
2
1
1
1
2
1
2
1
1
1
1
2
0
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
2
1
1
0
2
0
1
1
0
1
1
1
1
0
1
1
0
2
1
1
1
1
1
2
2
1
0
1
0
1
0
2
1
0
1
1
2
2
0
1
1
1
1
0
0
1
1
0
1
1
1
1
2
2
1
1
1
1
0
2
1
1
1
2
1
2
2
2
0
1
0
1
1
1
2
1
2
0
1
1
1
2
1
2
1
2
1
1
2
1
1
1
2
0
0
1
1
2
1
0
0
1
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
0
1
1
1
1
2
2
0
2
1
0
1
1
1
1
0
0
2
0
0
1
2
1
0
1
1
1
1
1
1
1
0
4
1
1
2
0
1
2
3
1
2
1
2
1
1
2
0
2
1
2
1
1
0
1
2
2
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
0
1
1
1
1
2
1
3
1
2
1
1
1
2
1
0
2
0
2
2
2
2
0
2
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
1
0
1
1
1
2
1
1
1
2
1
1
1
1
0
1
1
1
1
0
1
0
1
1
1
1
1
1
1
1
2
1
1
1
1
2
0
1
0
2
1
0
0
1
2
0
0
2
1
1
0
1
2
1
0
1
1
1
1
1
1
1
1
1
2
1
1
1
0
1
0
1
1
1
1
0
0
0
1
2
0
2
1
1
1
1
1
1
1
0
1
1
2
1
2
1
1
1
2
1
1
0
0
0
1
1
1
1
2
1
1
1
1
0
1
0
1
1
1
1
2
0
1
1
3
2
1
1
0
2
1
2
1
1
2
2
1
2
1
2
2
1
2
1
0
1
0
1
0
1
1
2
1
2
1
2
1
1
1
1
2
1
1
1
1
1
2
1
1
1
2
0
0
1
1
1
1
0
1
1
1
2
0
2
1
2
1
2
2
1
1
1
0
1
0
2
2
1
1
1
1
1
1
0
2
0
1
1
3
1
0
4
0
2
0
2
1
2
1
0
1
2
2
1
2
2
0
2
6
1
0
1
2
1
1
0
1
0
1
0
1
1
1
1
1
0
1
1
1
2
1
3
1
2
0
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
0
0
0
1
2
1
0
1
2
1
2
1
1
1
1
1
1
1
2
2
2
2
2
1
1
1
1
0
1
1
1
0
1
2
1
2
1
1
1
2
2
0
0
2
1
0
2
1
2
0
2
2
1
1
2
2
0
2
2
1
1
1
1
0
0
0
1
0
1
0
1
1
1
2
1
1
2
2
1
2
2
2
1
1
1
1
1
1
1
1
0
0
1
1
2
2
1
1
2
1
0
2
2
1
0
2
1
1
2
2
1
1
1
2
1
1
2
2
1
1
1
0
1
1
0
1
2
1
0
1
0
1
0
1
1
1
2
1
1
3
1
1
0
0
1
2
2
1
2
1
2
2
1
1
0
1
2
1
2
1
1
1
1
1
2
1
1
0
1
0
2
1
1
0
1
1
1
1
2
1
1
1
1
1
1
2
1
2
1
1
2
1
1
2
1
0
0
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
0
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
0
1
2
0
1
1
2
2
0
1
2
1
1
3
1
1
2
0
1
0
2
2
1
1
0
1
8
2
1
1
2
0
1
1
0
0
1
1
1
1
2
0
1
0
1
1
1
1
0
1
1
0
1
1
1
1
0
1
1
1
2
1
2
0
0
2
2
1
2
2
1
2
2
0
2
1
2
1
0
1
1
1
2
1
0
1
2
1
1
2
1
1
1
3
2
2
0
2
2
2
1
1
0
2
1
0
1
1
1
2
1
0
1
1
1
1
4
1
1
1
1
2
2
1
1
1
2
0
1
0
1
2
1
2
2
1
1
2
1
2
1
0
0
1
1
1
2
1
1
0
1
2
1
1
1
1
2
1
1
0
1
0
1
0
1
0
2
2
1
1
1
0
2
2
1
0
2
1
2
2
1
1
2
0
1
1
2
1
0
1
1
1
1
0
2
1
1
1
2
2
1
1
2
1
1
1
2
2
2
1
1
1
2
1
2
1
1
1
1
2
0
0
0
1
1
1
1
1
2
1
1
1
2
1
1
1
2
2
1
0
2
1
0
4
2
1
1
1
1
1
2
0
0
2
1
1
2
1
2
0
2
1
1
1
1
1
0
1
2
0
1
1
1
2
1
1
0
1
0
1
1
1
0
2
1
0
2
1
1
1
2
1
1
1
2
1
1
1
1
1
2
2
1
1
1
0
1
1
2
1
1
3
0
2
0
0
1
1
4
1
1
0
1
2
2
1
0
1
1
1
2
1
0
1
1
2
0
1
2
1
1
1
1
0
1
1
1
2
2
1
1
2
1
1
1
2
1
2
1
2
1
1
1
2
0
1
1
0
2
1
0
0
1
1
1
2
1
1
1
1
1
1
1
1
1
0
2
1
1
1
0
0
2
1
1
1
1
2
1
1
0
1
2
0
0
2
0
2
1
1
0
1
3
2
2
0
1
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
2
1
2
2
0
2
1
1
1
0
1
0
1
1
0
0
1
0
1
1
1
1
2
1
1
0
1
1
2
0
1
0
1
1
1
1
1
0
1
1
1
1
1
1
0
1
1
2
1
1
1
2
1
0
2
1
1
1
1
2
1
1
2
1
1
2
0
0
1
1
1
2
0
1
1
2
2
2
2
1
1
1
1
0
1
2
1
0
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
0
1
0
1
0
1
2
0
2
1
0
1
1
2
2
2
0
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
2
1
2
1
1
0
1
0
1
1
0
1
1
1
2
4
1
2
2
1
2
0
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
2
1
1
0
1
1
1
1
0
1
1
1
1
1
1
1
0
2
1
1
2
1
1
1
1
1
2
1
1
0
1
2
0
0
0
0
1
1
0
1
2
1
2
1
1
1
2
2
1
1
2
0
1
0
1
1
2
2
1
1
0
1
0
1
2
1
1
1
0
2
1
2
3
1
2
2
2
1
0
1
2
1
1
1
2
3
1
1
1
2
1
2
1
1
1
2
0
1
1
3
1
1
1
0
1
2
1
2
1
1
1
2
4
1
1
1
0
1
1
0
1
1
2
1
1
1
2
1
1
1
1
0
1
1
2
1
1
2
0
1
1
2
0
1
1
1
1
1
0
2
1
0
1
2
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
2
2
2
2
2
1
2
0
2
1
1
2
2
0
1
2
2
1
1
1
0
1
1
1
1
0
1
1
1
1
2
3
2
1
0
1
1
1
0
2
1
0
1
0
1
1
1
2
1
0
1
1
1
1
1
1
2
1
1
0
1
2
1
1
0
0
2
1
1
1
1
1
2
1
0
2
1
1
0
0
1
2
1
0
2
1
1
1
1
1
1
2
0
0
0
1
1
0
3
2
1
0
1
1
1
2
1
1
0
1
1
1
0
1
7
2
1
1
1
2
1
0
1
1
2
0
2
0
0
1
1
2
2
1
2
1
1
0
1
1
2
1
2
2
1
2
0
1
1
1
1
0
1
1
1
1
0
1
2
2
1
1
0
2
0
2
1
1
1
2
1
1
1
0
1
1
1
2
1
1
1
1
2
2
1
1
1
1
1
2
1
1
2
1
1
1
1
0
1
1
2
1
0
1
1
0
1
1
1
4
2
1
0
1
1
1
1
1
2
1
0
1
0
1
2
1
1
2
0
1
1
2
1
1
2
2
1
2
1
2
0
2
1
1
1
1
1
0
1
1
2
2
1
0
2
2
0
0
2
2
1
1
0
1
1
1
2
1
1
0
1
2
0
1
2
0
1
2
1
2
2
0
2
1
2
2
1
0
2
0
2
2
1
1
1
0
1
1
1
1
1
1
1
0
0
1
1
2
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
0
2
0
7
1
0
1
1
2
1
0
1
2
1
1
2
1
1
1
2
1
1
1
2
0
1
1
0
1
2
2
1
1
1
1
1
0
1
0
1
1
1
1
1
1
2
1
2
1
2
1
2
1
0
0
2
2
0
1
1
1
1
0
1
0
1
1
0
1
1
2
3
1
1
2
1
1
2
2
1
1
2
0
2
1
1
1
1
1
1
1
1
1
1
1
0
0
1
1
1
1
0
1
2
0
1
2
1
0
1
1
1
1
2
1
1
1
1
1
1
1
2
1
0
1
1
2
1
2
1
0
2
1
1
1
1
0
1
2
2
1
1
1
1
1
0
1
1
1
2
1
1
0
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
0
1
1
1
0
2
1
1
1
1
2
0
1
1
1
1
2
2
2
1
1
2
1
0
1
2
1
4
2
1
1
1
1
1
2
0
1
1
1
2
1
0
2
1
1
1
2
1
1
1
0
1
1
1
1
1
1
2
1
1
2
2
0
1
1
0
1
1
1
2
2
0
1
1
1
2
2
0
0
1
2
0
1
2
2
2
1
1
2
1
1
2
2
2
1
2
1
2
1
0
1
1
2
1
1
1
2
1
0
1
1
2
1
1
1
2
1
1
1
2
2
1
2
1
2
1
1
1
0
1
1
1
1
1
2
1
1
2
1
1
0
2
2
0
1
0
2
0
0
1
2
1
2
0
0
1
2
1
1
1
2
1
2
2
0
1
2
0
1
1
2
2
1
0
1
1
1
1
2
2
4
1
0
1
0
0
1
1
0
2
0
2
2
1
1
1
1
2
1
1
1
2
1
1
0
1
2
1
1
0
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
2
1
0
2
1
1
1
1
1
2
0
0
1
1
1
0
1
1
1
1
1
2
1
1
1
1
1
0
0
2
1
1
0
0
2
2
1
1
1
1
2
1
1
0
1
1
1
1
1
0
1
0
1
1
1
1
2
1
2
2
1
2
2
1
1
1
0
1
0
2
1
0
1
2
1
2
0
1
0
2
1
1
1
2
1
2
0
1
1
2
1
0
1
0
1
1
0
2
1
2
2
0
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
2
2
1
1
2
2
1
2
1
2
1
1
1
1
0
2
1
0
0
1
1
1
2
1
1
1
1
1
2
1
0
1
1
2
0
1
2
2
0
0
1
0
0
1
1
1
1
1
0
1
1
2
1
1
0
1
0
2
1
0
1
2
1
2
1
1
1
0
1
2
0
0
0
0
1
1
1
2
0
1
1
1
0
1
0
0
3
1
0
1
1
1
1
1
1
1
0
1
1
0
0
1
1
1
1
1
1
1
1
2
1
1
1
1
0
1
0
0
1
1
2
0
0
1
1
1
1
1
2
2
0
1
2
2
2
1
1
2
1
1
2
1
0
1
0
2
1
0
1
1
1
1
2
2
1
2
2
1
1
1
1
1
1
1
1
0
1
3
1
2
2
1
0
1
1
2
0
1
1
2
0
1
0
1
1
1
1
1
1
0
2
1
0
1
1
1
1
2
1
0
2
1
1
1
1
1
1
2
0
2
2
1
1
1
1
0
1
1
1
0
2
1
2
3
0
0
1
2
1
1
1
0
1
1
2
1
1
1
1
2
1
2
1
2
2
1
1
1
0
1
0
2
2
1
2
1
1
1
1
1
2
1
2
0
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
0
2
0
2
1
1
1
1
1
2
2
2
1
2
1
1
1
2
1
1
2
1
1
2
1
0
1
1
1
1
1
0
0
2
1
1
1
1
2
2
1
2
0
0
0
1
0
1
1
2
2
1
0
1
1
1
1
1
1
1
1
0
0
2
1
1
1
1
1
1
1
1
1
2
2
0
1
2
2
1
2
1
1
1
1
0
1
1
0
1
1
1
2
1
1
1
2
1
1
0
1
1
1
1
1
2
1
2
1
1
0
1
1
1
1
1
1
1
2
0
1
1
2
1
1
0
1
1
1
2
1
1
1
1
1
2
1
0
0
1
1
1
2
0
1
1
1
1
2
2
1
1
1
2
0
1
1
1
2
1
1
2
1
1
0
2
1
1
2
1
1
0
1
1
1
1
1
3
1
1
1
1
1
0
2
1
1
1
1
1
1
2
1
2
1
0
1
2
2
1
0
1
1
0
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
0
1
1
0
2
1
0
1
0
2
0
1
1
1
2
2
0
1
1
2
2
1
1
1
1
1
1
2
2
1
2
1
2
1
1
1
1
2
1
2
1
0
0
1
1
2
1
1
1
1
2
2
0
0
2
1
0
1
1
1
2
1
0
1
2
1
2
1
2
1
1
1
2
1
1
1
1
2
0
1
1
1
1
2
1
0
2
2
2
1
1
1
1
1
2
0
2
0
1
1
1
1
2
1
1
2
1
1
1
1
0
1
1
1
2
2
1
1
2
2
2
0
1
0
1
1
1
1
1
1
1
2
1
2
2
1
0
2
1
2
1
1
1
1
2
1
1
0
1
1
2
1
1
0
2
1
2
1
1
1
1
2
0
1
1
2
1
0
2
1
2
1
1
1
1
1
1
2
0
2
1
1
1
2
2
1
1
2
1
1
1
1
1
0
1
1
1
2
1
0
2
1
1
0
2
1
2
1
1
1
2
0
1
1
2
1
1
1
0
0
1
1
1
2
2
1
1
1
1
1
1
1
2
2
1
1
2
1
2
1
1
1
1
1
1
1
1
1
0
2
2
1
1
2
0
0
1
1
2
1
1
1
2
2
1
1
2
2
1
1
2
1
1
2
1
0
1
0
1
2
2
1
1
2
0
1
1
1
0
2
2
0
1
2
1
1
2
1
2
1
0
1
0
1
0
2
2
1
1
1
0
0
2
2
1
0
1
0
1
1
2
1
0
2
2
1
0
2
1
1
0
0
1
1
1
1
1
1
1
0
1
1
3
1
2
1
1
0
1
2
2
1
1
0
2
1
0
0
2
1
2
1
1
2
2
1
2
2
2
1
2
2
1
2
1
1
0
1
1
2
1
1
1
0
2
2
2
1
2
1
1
0
1
1
1
0
0
1
2
1
1
1
1
1
1
1
1
0
2
1
1
3
1
2
1
2
1
1
1
0
1
0
1
1
2
1
2
1
1
1
2
1
1
0
2
2
2
1
1
1
1
2
0
2
1
1
2
0
1
0
2
1
0
1
0
0
1
2
1
1
0
0
0
1
1
1
1
2
1
1
1
1
0
1
1
2
1
2
2
1
1
1
1
0
1
0
1
1
0
1
2
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
0
2
1
1
0
1
1
1
2
2
1
1
2
2
1
1
1
2
1
0
1
0
1
2
1
0
1
1
1
0
1
2
1
1
0
2
1
2
1
1
1
0
1
3
1
0
2
1
2
1
2
1
0
1
1
1
0
0
1
0
1
1
2
1
1
1
1
2
1
2
1
1
0
2
0
1
2
0
1
0
1
1
1
1
2
2
1
1
1
0
0
0
1
0
1
0
0
1
2
0
0
1
0
2
1
1
0
1
1
0
0
2
1
2
1
1
0
1
1
2
1
1
1
1
0
1
1
2
1
1
0
1
1
1
0
2
1
1
1
2
2
1
0
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
2
0
1
0
1
1
2
1
1
1
1
1
1
2
2
2
0
2
1
2
0
2
1
1
1
1
1
1
1
2
1
0
1
2
1
1
0
1
1
1
2
2
2
1
1
2
1
0
1
1
1
1
1
1
1
1
0
2
1
1
1
1
1
0
1
0
1
1
1
1
2
1
1
1
1
1
0
2
1
1
1
1
1
2
1
2
0
1
1
0
2
1
2
1
2
1
0
1
2
0
2
2
2
1
1
1
2
0
2
0
0
1
0
1
1
2
1
2
1
0
1
0
3
2
1
1
1
1
2
2
1
1
1
1
1
1
0
0
1
1
0
0
1
1
0
0
0
1
0
1
2
1
2
1
2
1
2
0
0
1
2
2
0
1
1
1
2
2
0
1
0
1
0
1
1
1
1
1
0
0
0
2
0
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
0
0
2
1
1
1
2
1
1
1
0
1
1
1
2
1
1
1
2
2
2
1
2
2
1
1
1
2
1
1
1
1
0
1
1
2
1
1
1
0
1
1
2
1
2
1
1
1
0
0
1
1
1
2
2
1
0
1
2
1
0
1
1
1
1
1
1
1
0
1
1
1
1
1
1
3
1
1
0
1
1
1
0
3
1
2
1
1
1
0
1
1
2
1
1
2
0
1
1
3
1
1
1
1
0
1
2
1
1
1
2
1
0
1
3
2
0
1
1
2
1
1
1
1
0
2
1
2
1
2
1
2
1
2
0
1
1
0
0
2
2
0
2
1
2
1
1
2
1
1
0
1
2
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
2
0
0
0
0
2
2
1
3
1
1
2
2
1
0
2
1
2
1
1
2
1
1
0
2
1
1
0
2
1
0
1
3
1
0
1
1
1
0
2
1
1
2
1
1
0
1
2
1
1
1
1
1
0
1
1
0
1
1
1
1
1
1
2
1
1
1
1
1
2
1
0
1
2
1
0
1
0
2
0
2
1
1
1
0
2
1
1
2
1
2
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
3
1
1
2
0
1
1
1
2
0
0
2
0
0
0
1
2
2
2
0
1
0
0
0
1
2
2
1
2
1
2
1
1
1
0
1
0
2
1
1
1
2
2
2
1
2
0
3
1
2
1
2
2
1
1
2
2
1
2
0
1
1
1
1
1
1
1
1
1
0
1
2
1
0
2
1
1
1
2
0
1
2
2
0
1
1
1
2
0
1
2
1
1
0
1
0
2
1
1
1
1
2
1
2
2
1
1
2
0
1
1
1
1
1
1
1
1
0
0
1
2
2
2
2
1
1
2
0
2
1
1
2
0
2
1
1
1
1
1
2
1
1
1
0
1
1
2
1
0
1
2
1
2
1
1
1
2
1
1
1
1
1
1
2
0
2
1
1
1
1
2
1
1
1
2
1
1
2
2
2
0
1
1
1
2
0
0
1
2
1
2
1
1
1
1
1
0
0
1
2
1
2
2
0
1
2
2
0
1
1
0
2
1
0
1
2
1
2
1
1
2
1
2
1
0
2
0
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
2
1
5
1
1
0
1
1
1
2
2
2
1
1
2
1
1
2
1
1
0
0
0
2
1
1
0
1
1
2
1
1
0
1
1
2
0
2
1
2
1
1
0
2
1
1
2
1
2
2
1
1
1
1
1
1
1
1
0
1
1
1
0
1
1
1
1
2
1
1
2
1
1
2
2
1
1
0
1
1
1
2
1
2
1
1
2
2
0
1
1
1
1
2
0
1
2
0
0
0
2
1
1
0
1
1
1
1
2
1
0
0
1
1
2
1
2
1
1
1
0
2
1
2
1
1
1
1
1
1
0
1
1
0
1
1
1
2
2
0
1
1
2
0
1
1
1
2
2
1
0
0
0
1
1
1
1
1
1
1
1
1
0
1
2
2
0
1
2
1
1
1
1
1
1
2
1
1
1
1
0
0
1
2
1
1
0
1
1
1
2
2
1
1
1
1
2
1
2
1
1
0
1
1
2
1
1
1
1
1
1
2
0
2
1
2
1
1
0
1
1
0
2
1
1
1
2
0
0
0
1
1
1
2
1
1
2
2
1
1
1
2
2
1
1
1
0
0
2
1
2
1
1
1
0
0
2
2
2
1
1
1
1
1
0
1
2
1
2
2
1
2
1
0
1
1
1
1
1
1
1
0
1
1
1
1
2
0
1
1
2
1
0
1
1
1
3
2
1
1
1
1
1
1
2
1
1
1
1
1
1
0
2
0
1
0
1
2
2
2
3
1
1
1
2
2
1
1
2
1
1
0
1
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
2
1
1
2
2
1
1
0
1
1
0
1
2
1
1
0
2
2
1
1
2
1
0
1
0
1
1
0
1
1
2
2
1
1
1
0
1
2
1
1
1
1
2
1
1
1
1
1
2
1
2
1
2
2
1
2
2
2
1
0
2
3
1
2
1
2
1
1
1
2
1
1
2
1
1
0
0
1
1
1
1
1
0
1
1
1
1
1
1
2
1
0
1
1
1
1
2
1
1
2
1
2
1
2
1
2
1
1
1
0
1
1
1
1
1
2
1
0
1
1
1
1
1
1
2
2
2
0
1
1
1
0
0
0
1
1
1
2
2
1
0
1
1
2
2
2
2
1
1
1
0
0
1
1
1
1
2
2
1
0
2
1
2
1
2
0
2
0
1
1
1
1
2
1
0
2
2
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
2
1
2
0
2
2
1
1
1
1
0
2
0
1
1
0
0
1
1
0
0
2
2
0
1
1
1
1
1
1
2
2
1
1
1
1
0
1
0
2
0
2
0
1
1
0
2
1
1
2
1
2
1
1
0
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
2
1
0
1
1
2
0
0
2
0
2
0
1
2
2
2
1
1
1
1
2
1
1
1
1
2
0
0
0
1
1
0
2
1
1
1
3
2
1
1
1
1
1
1
1
3
1
0
2
2
1
0
1
0
2
2
0
2
1
2
2
1
2
1
2
1
2
1
1
0
0
1
1
1
1
1
0
0
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
0
2
1
2
1
0
1
1
1
2
1
1
1
1
1
1
1
0
2
1
1
1
2
2
1
1
1
1
1
1
1
2
0
1
2
2
0
1
0
2
1
1
1
1
1
1
0
1
1
1
2
0
2
1
0
0
1
2
1
1
2
1
1
1
2
1
1
3
1
2
1
1
2
1
1
1
2
1
1
1
2
0
1
1
1
2
0
0
1
0
1
1
1
2
1
0
1
1
1
0
2
1
1
1
3
1
1
1
1
1
2
1
1
0
1
1
1
2
0
2
2
1
2
1
0
1
1
1
0
2
0
0
2
2
1
1
1
1
1
1
0
2
2
2
1
0
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
0
1
1
1
1
1
0
1
1
2
1
1
2
0
0
1
1
1
1
1
1
2
1
1
1
0
1
1
1
1
1
2
1
1
1
1
1
0
3
1
2
2
0
1
1
1
1
0
2
1
0
1
1
0
1
1
1
1
1
1
1
2
2
1
1
0
1
0
1
1
1
2
0
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
0
2
1
1
0
0
1
1
0
1
2
2
1
1
1
1
1
1
2
2
1
1
1
2
1
1
2
2
1
1
2
1
2
1
1
2
2
2
1
1
1
1
1
1
1
0
1
7
1
1
1
2
2
0
2
1
1
1
1
0
2
2
1
1
1
2
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
1
2
1
0
1
0
0
1
1
1
1
1
0
1
2
1
2
0
1
2
0
3
1
2
1
1
1
1
2
2
1
1
0
1
1
0
1
1
2
2
0
1
0
0
1
1
2
2
2
1
1
1
1
1
0
2
1
1
1
1
1
2
1
1
2
1
1
1
2
0
1
1
2
1
2
2
1
1
2
1
2
1
1
1
2
1
1
1
1
0
1
2
0
2
1
2
0
1
2
1
2
2
0
2
2
1
0
1
1
1
1
2
2
2
1
1
2
2
1
0
1
1
1
1
1
2
1
1
0
1
1
2
1
2
0
1
1
1
2
2
2
1
2
1
2
0
3
2
0
1
2
1
2
1
1
1
2
1
1
2
1
0
1
0
1
2
1
1
1
1
1
2
1
1
2
0
2
1
0
2
0
0
1
1
1
1
1
2
1
0
1
1
2
2
1
1
1
0
1
1
1
1
2
2
1
2
2
1
0
0
1
1
1
1
2
0
1
1
1
1
0
2
1
1
1
1
2
1
1
2
1
1
0
0
1
2
2
0
1
2
2
0
0
1
2
2
1
1
2
0
0
0
0
2
0
1
2
1
0
2
1
0
1
0
1
2
2
2
2
1
1
2
1
2
1
1
1
0
1
2
0
2
1
2
2
2
1
1
1
2
1
1
0
0
1
1
2
0
1
4
2
1
2
1
2
1
0
1
1
1
0
0
2
1
1
2
2
1
2
1
2
1
0
1
1
1
1
2
1
2
1
1
1
1
2
0
1
1
1
1
1
2
1
1
2
1
1
0
1
1
0
2
1
1
1
0
2
2
1
0
1
1
1
1
1
1
1
1
0
0
1
1
1
2
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
1
2
2
1
1
1
1
2
2
0
1
1
1
1
1
1
2
1
1
2
1
1
1
0
1
1
1
0
2
1
0
1
1
1
2
1
0
0
2
0
1
0
1
1
1
1
2
0
2
1
1
1
1
1
1
2
1
0
0
1
1
1
0
1
0
1
2
0
1
1
2
1
0
1
0
2
1
0
2
1
2
1
1
1
3
0
0
1
1
1
1
0
0
1
1
1
1
2
1
1
2
2
1
1
1
1
2
1
1
1
1
1
0
1
1
1
1
0
0
1
1
2
1
1
1
1
1
0
2
1
1
1
1
1
0
0
2
1
1
1
1
0
3
1
1
1
1
0
1
2
2
0
1
2
2
1
2
2
1
2
1
1
0
1
1
1
0
0
2
0
0
2
1
7
2
1
0
0
1
1
1
1
1
2
0
1
2
1
1
1
1
1
1
1
1
2
1
1
1
0
2
1
3
1
1
1
0
1
1
1
0
1
0
1
1
2
1
2
1
1
1
0
0
2
1
0
0
2
0
2
1
2
1
1
2
1
1
2
0
2
1
1
1
1
2
2
1
1
2
1
1
1
2
2
1
1
1
1
1
1
1
2
1
2
2
2
1
1
1
1
0
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
0
2
0
2
1
1
0
2
2
1
0
0
1
2
0
1
1
0
2
1
1
2
2
1
1
0
2
2
1
0
1
1
1
1
2
1
1
0
0
1
1
0
1
2
1
0
1
1
1
2
2
3
1
2
1
0
3
1
2
0
1
1
1
0
1
2
2
1
1
1
2
1
0
2
0
1
2
2
1
2
1
1
1
2
1
3
1
1
1
0
1
1
1
1
0
1
0
0
2
1
1
2
1
0
1
1
1
0
0
2
1
1
1
1
1
1
1
2
1
2
2
2
1
2
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
1
1
1
1
1
0
1
1
1
2
0
2
1
1
1
2
0
1
2
1
1
1
0
0
2
2
1
1
2
1
0
1
1
3
1
1
1
1
0
2
2
1
1
1
2
1
1
0
1
1
1
2
1
1
0
2
2
1
2
1
1
1
0
1
1
2
2
2
1
2
1
1
1
0
2
0
2
1
1
1
2
2
1
1
2
1
1
1
1
1
0
0
0
1
1
0
1
1
1
2
1
1
1
1
1
1
2
2
0
1
1
2
1
2
1
2
1
1
1
2
2
0
0
2
2
1
1
2
1
1
0
1
1
0
1
1
1
2
1
2
2
1
1
1
1
1
1
2
0
1
2
2
0
2
1
0
1
1
1
1
1
1
2
1
1
1
2
0
1
1
0
1
1
2
1
1
1
1
1
2
1
1
1
1
2
2
1
1
1
2
1
2
2
1
0
2
1
1
0
2
2
0
0
2
1
1
1
1
2
1
0
1
2
1
1
2
1
1
2
1
1
1
1
1
2
1
1
1
1
2
0
1
1
2
1
1
1
0
1
2
1
1
1
1
2
0
0
2
3
2
1
2
2
1
2
2
2
1
1
2
1
1
1
1
1
1
2
1
1
1
0
1
2
0
0
0
0
2
4
1
1
1
1
0
1
1
1
0
3
2
1
2
1
1
1
0
1
1
1
1
1
1
2
1
1
2
0
2
2
1
0
1
2
1
1
2
1
2
1
2
1
1
0
1
1
1
1
2
1
0
2
1
0
1
2
1
1
1
1
1
1
0
1
1
1
1
1
2
1
1
1
1
2
2
0
1
1
1
1
1
1
1
1
0
1
1
2
1
2
1
0
2
1
1
1
1
2
1
1
1
0
2
1
1
2
1
1
1
1
0
2
0
1
2
0
1
1
0
3
0
1
0
1
2
2
1
0
1
1
1
2
1
0
0
2
1
1
2
2
1
1
2
1
1
1
1
0
1
1
1
2
1
1
1
0
2
1
0
1
1
1
1
2
2
0
2
0
1
1
0
0
2
1
0
1
1
2
1
1
2
0
1
0
1
1
1
2
0
2
1
2
1
2
0
1
1
1
1
1
1
1
1
1
2
1
0
2
1
1
1
0
2
1
1
2
0
1
1
0
0
1
1
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
0
1
2
2
1
1
0
2
1
1
1
2
1
0
1
1
1
2
1
1
1
2
1
0
2
1
0
0
1
2
1
1
1
2
0
1
2
1
1
2
1
1
0
0
1
2
1
1
0
2
1
2
0
1
2
2
0
3
2
1
1
1
1
2
0
1
1
2
2
0
2
1
1
2
0
0
2
1
1
1
0
2
1
1
1
1
0
7
1
1
1
1
0
1
2
0
2
1
1
2
1
1
2
1
1
1
1
1
2
1
2
0
2
0
2
2
2
1
1
2
1
2
3
1
1
0
1
1
1
1
1
2
2
2
1
1
2
1
1
0
0
1
1
1
1
1
1
1
0
2
1
0
1
0
2
1
1
1
2
1
1
2
1
2
1
1
1
0
1
2
1
0
2
1
1
1
1
1
0
0
1
1
0
1
1
1
2
1
1
2
1
1
1
2
0
1
2
2
0
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
0
0
0
2
1
1
1
1
1
0
0
1
1
1
2
1
2
1
1
1
2
2
1
2
1
0
0
1
1
2
2
1
0
2
1
1
1
1
3
0
1
2
0
1
1
1
1
1
1
0
1
0
1
1
2
1
1
1
1
1
1
1
1
0
1
0
1
1
1
1
1
2
2
1
2
0
0
0
1
1
2
1
1
1
2
2
1
1
2
1
1
1
1
2
0
0
1
1
1
0
0
1
0
2
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
0
1
0
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
2
3
1
1
1
1
2
1
2
1
1
0
0
1
1
1
1
2
2
1
1
2
2
1
1
1
1
2
1
1
2
1
1
1
0
0
1
1
1
2
2
0
0
1
1
1
2
2
1
1
1
2
2
2
1
1
2
0
1
0
1
1
1
1
0
1
1
1
0
1
1
1
0
1
4
1
1
1
1
2
1
1
1
0
0
1
1
0
0
1
0
1
2
1
3
2
1
1
1
2
1
2
1
2
1
1
1
1
0
1
1
1
0
0
1
1
0
1
1
1
1
1
2
2
0
2
1
2
2
1
0
1
1
0
2
1
1
1
1
1
2
2
1
0
1
1
2
1
1
2
2
1
1
0
2
2
1
1
1
2
1
1
2
1
1
1
1
2
1
1
0
1
1
1
1
2
2
1
0
2
2
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
2
0
0
1
2
1
1
1
1
0
1
2
1
1
0
2
1
1
2
2
1
1
1
1
1
1
2
1
1
0
1
1
2
1
1
1
1
1
1
0
0
1
0
2
1
0
2
1
2
1
1
1
1
1
1
1
1
1
1
1
0
1
1
2
1
1
0
1
2
1
1
1
2
1
1
1
1
1
2
0
0
2
2
0
2
1
1
0
1
0
1
1
1
2
1
2
2
1
2
1
0
0
2
1
1
2
1
1
1
2
0
1
0
1
1
2
1
1
0
1
0
0
1
2
2
1
2
1
2
1
1
1
2
2
1
1
1
0
0
1
1
1
1
2
1
1
1
2
1
0
2
1
1
1
1
1
1
1
1
0
1
1
1
0
1
1
1
1
1
1
2
0
1
1
0
2
1
2
1
2
2
1
1
1
1
2
1
0
1
0
1
2
2
2
1
1
1
0
1
1
1
0
1
2
3
1
1
2
1
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
1
2
0
2
1
1
2
1
0
1
0
1
2
0
1
1
1
0
1
0
0
2
3
1
0
2
2
1
1
0
1
1
0
0
2
1
2
2
1
0
2
1
2
2
0
1
0
1
1
1
0
1
1
1
2
1
2
1
1
1
1
2
2
2
0
2
1
2
1
1
2
1
1
0
1
2
0
1
0
2
1
2
1
1
1
2
1
1
1
2
1
1
2
1
2
0
1
1
1
1
1
1
1
1
1
2
1
2
1
2
1
2
1
1
0
1
0
2
1
1
1
1
1
1
1
2
0
1
2
0
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
0
0
1
1
1
1
1
1
0
1
2
0
2
2
1
1
0
0
1
1
1
2
1
1
1
1
1
1
2
1
1
0
1
0
1
0
1
0
1
1
1
1
0
1
2
1
1
2
1
0
2
0
1
1
0
1
2
1
3
1
0
2
1
1
2
0
2
1
1
1
2
0
0
1
1
1
1
2
1
1
1
1
1
1
1
0
1
1
0
1
1
2
1
1
0
1
1
1
0
1
1
1
1
1
1
2
1
1
1
1
1
2
2
1
0
2
1
1
1
2
2
1
1
1
1
1
2
1
1
1
0
2
2
0
1
1
1
1
1
2
1
0
1
1
1
1
1
2
1
1
1
0
1
2
1
1
2
1
2
2
1
1
1
1
0
1
0
2
1
2
1
1
2
2
1
1
2
1
1
0
1
1
1
1
1
1
1
1
1
1
1
0
1
2
2
2
1
1
1
2
1
2
1
2
2
1
2
1
1
2
2
0
1
0
1
2
1
2
2
1
1
0
1
0
0
1
1
2
2
1
0
2
1
1
0
2
0
1
1
1
1
2
2
2
2
2
1
1
1
0
1
0
1
0
1
0
2
1
1
1
0
1
1
2
1
2
1
1
1
1
3
2
2
1
2
2
1
1
1
2
2
1
1
1
2
2
1
1
2
1
1
1
2
1
1
2
0
2
2
1
1
1
0
0
1
1
2
1
1
0
1
1
4
1
1
1
0
1
1
1
0
1
1
1
2
1
2
1
2
2
2
1
1
1
1
0
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
2
1
2
1
2
1
1
2
1
1
2
2
2
1
1
1
1
1
2
1
0
2
0
1
3
2
1
1
0
1
0
1
2
2
1
1
1
2
1
2
1
0
2
1
1
1
1
2
2
1
1
2
1
1
2
1
2
2
1
0
2
1
0
1
1
1
1
1
1
1
2
0
1
1
1
1
1
2
1
1
0
2
2
0
1
1
1
1
1
1
0
1
0
1
1
0
1
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
2
1
1
0
1
1
1
1
1
0
0
1
2
1
0
2
0
1
1
1
1
0
1
2
2
3
2
1
1
2
2
0
1
2
1
1
1
2
2
1
1
2
1
0
1
1
2
1
1
2
1
2
1
2
0
1
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
2
0
1
1
1
0
1
1
1
1
1
1
2
2
2
1
0
1
0
2
1
1
1
1
1
1
1
2
1
1
1
2
0
1
2
0
1
1
1
2
1
2
1
2
0
1
2
3
1
2
1
2
1
1
0
1
0
1
1
0
1
0
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
2
1
0
0
1
1
2
1
1
0
1
2
1
0
2
2
1
0
1
1
1
2
1
1
1
1
1
1
0
0
2
1
2
2
0
1
1
0
0
1
2
2
0
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
2
0
1
1
0
1
1
1
1
0
0
0
1
1
1
1
1
1
0
2
1
1
1
1
1
1
1
0
1
1
1
1
2
1
1
0
2
2
0
1
0
1
1
1
1
2
0
0
0
1
1
1
1
0
1
1
1
1
1
2
1
1
1
1
1
0
1
0
1
2
0
1
0
1
1
1
2
1
1
1
2
2
2
1
1
1
2
2
2
1
0
2
0
1
2
1
1
1
2
2
1
1
1
1
0
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
2
1
1
0
1
1
0
1
1
1
1
1
1
1
1
0
0
1
1
2
2
1
1
0
1
1
1
1
1
1
1
2
1
1
2
2
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
0
2
1
1
1
1
0
1
1
1
1
2
0
0
1
1
1
2
1
1
1
0
2
1
1
1
1
1
0
1
2
1
0
0
2
1
1
1
2
2
2
1
2
2
1
0
0
1
2
1
1
0
1
0
1
1
0
1
0
1
2
0
1
1
0
2
0
1
1
2
0
1
1
1
2
0
1
1
1
0
1
0
1
1
1
1
2
1
0
1
1
2
2
1
0
2
0
1
2
2
1
1
1
1
0
0
1
1
1
1
2
1
1
1
1
1
0
1
1
2
1
2
2
0
2
1
1
1
1
2
2
1
1
1
3
1
0
1
1
0
1
2
2
0
2
0
1
1
1
1
2
2
1
1
0
2
1
1
1
1
2
1
2
2
2
2
2
2
0
2
1
1
0
1
0
1
2
1
1
1
1
0
1
2
1
1
0
2
0
2
2
1
0
1
1
1
1
1
1
1
2
0
0
1
1
1
1
1
1
2
0
1
2
1
1
0
1
1
2
0
1
2
1
0
1
1
0
1
1
0
1
1
2
1
1
1
1
0
2
1
1
2
1
0
0
1
1
1
1
1
0
1
1
1
1
1
0
1
1
0
2
3
0
1
1
1
2
1
1
1
1
1
1
1
0
1
1
0
1
1
2
1
1
1
1
2
0
1
2
1
1
0
1
0
2
1
3
1
1
0
1
1
2
1
1
1
0
1
2
2
2
1
1
0
2
0
1
1
1
1
0
0
0
2
1
2
1
1
1
1
1
2
2
1
1
1
1
2
1
1
1
0
1
1
1
0
1
1
1
2
2
1
2
1
0
0
2
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
0
1
1
2
2
1
2
1
1
1
1
0
1
1
1
1
1
2
1
0
0
1
2
2
1
1
1
2
1
2
1
1
1
1
1
0
1
1
1
1
0
1
2
1
2
1
2
1
0
1
0
1
2
1
2
0
2
1
0
2
1
0
1
1
1
1
2
1
1
2
0
2
2
2
1
1
2
1
1
2
2
1
1
0
2
2
0
1
2
1
2
2
0
2
2
1
0
1
1
1
0
0
0
1
1
1
2
1
2
2
0
1
1
1
1
1
1
1
1
2
2
1
1
1
2
2
1
2
1
1
0
1
0
1
2
0
0
1
1
1
0
0
1
1
1
1
1
1
0
2
1
1
1
0
2
1
1
1
1
1
1
1
1
2
1
2
1
1
1
2
1
2
1
0
1
2
1
1
1
1
1
1
2
1
1
2
1
1
1
0
1
1
1
1
1
0
1
1
0
0
1
1
1
1
1
1
1
1
0
1
1
1
2
2
1
1
2
2
1
2
1
1
2
0
2
1
1
0
1
1
1
1
1
1
1
0
1
2
1
2
0
1
1
1
2
1
1
1
1
1
2
1
1
2
1
0
2
1
1
1
0
1
1
0
1
1
2
1
0
0
2
1
1
1
1
0
0
1
1
1
2
2
1
1
1
0
0
2
1
1
1
1
1
2
1
1
2
1
2
0
1
0
3
1
2
2
2
1
0
1
1
1
2
2
2
1
0
1
1
2
2
2
1
1
0
1
2
1
0
1
1
2
0
0
1
1
2
1
1
1
2
1
1
1
0
1
0
1
1
1
1
1
2
1
2
1
1
2
1
1
1
0
1
1
1
2
1
1
1
2
1
1
1
1
2
1
0
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
0
2
2
1
1
1
3
1
1
1
0
1
1
1
1
1
1
1
2
1
0
2
1
1
1
2
1
1
1
1
1
2
1
1
1
2
0
0
1
2
1
1
1
1
1
1
1
3
1
2
1
2
1
2
1
1
1
2
2
1
2
2
0
1
2
1
1
3
1
0
1
0
1
1
2
2
1
1
1
2
1
0
2
1
1
1
1
1
1
0
1
1
1
1
2
0
2
1
2
0
1
1
1
2
1
1
2
2
1
1
2
2
2
1
1
1
1
2
2
1
1
2
1
0
2
1
1
1
1
1
0
1
2
0
2
2
1
1
2
1
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
1
0
0
0
1
1
2
1
2
1
2
1
1
1
1
1
2
2
1
1
1
1
0
1
1
2
0
1
0
1
1
1
1
0
1
0
1
1
1
1
1
2
2
1
0
2
1
1
1
1
1
2
1
2
1
1
0
1
2
1
1
0
1
1
2
0
1
1
0
1
1
0
1
0
0
2
1
2
1
1
1
1
1
2
1
1
1
1
1
2
2
1
0
1
2
2
1
0
1
1
1
0
1
2
1
2
1
0
1
1
1
1
2
2
1
2
1
1
1
1
1
1
2
2
1
1
0
1
2
0
1
1
2
1
1
0
1
0
3
1
1
1
1
1
2
0
1
1
0
1
1
1
1
2
1
1
1
1
2
1
1
0
0
1
1
2
1
1
2
1
1
1
0
1
2
1
2
1
2
1
1
2
1
1
1
1
1
2
1
2
0
0
2
1
0
0
1
1
1
1
1
1
0
2
1
1
0
0
1
1
1
2
2
0
1
1
1
0
2
1
0
0
1
2
2
2
1
1
1
2
1
1
2
1
1
1
2
1
1
1
3
1
1
1
2
0
2
2
1
1
0
1
1
0
1
1
0
1
2
1
1
1
2
1
1
2
2
0
1
1
0
0
1
1
2
2
2
2
2
1
1
1
1
1
0
1
2
1
1
1
2
2
1
3
2
2
2
1
2
2
2
1
1
1
2
1
1
1
2
2
1
1
1
1
0
1
1
1
1
2
0
1
1
2
1
1
1
1
1
0
1
1
1
1
1
1
0
1
2
2
1
1
1
0
1
1
0
1
0
1
0
2
0
1
1
1
2
1
1
2
0
1
1
1
1
1
2
1
1
1
0
1
1
2
0
2
2
2
0
2
0
2
1
0
0
1
1
1
2
0
1
1
1
1
1
0
2
1
0
1
1
1
2
2
2
1
2
1
0
1
0
2
0
2
2
1
1
2
1
1
1
1
1
0
1
2
2
2
1
2
0
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
0
3
2
1
1
1
1
0
1
4
1
0
2
2
1
1
1
1
1
2
1
1
1
2
1
0
1
2
1
1
1
2
1
1
1
0
0
0
1
1
0
1
2
1
2
2
2
1
1
1
1
1
1
1
0
0
2
1
1
1
2
1
1
1
2
2
1
1
1
2
1
1
0
1
2
1
1
0
2
0
1
2
1
1
0
1
1
1
1
1
2
2
0
1
1
2
2
1
1
2
2
1
2
2
2
0
1
2
0
2
1
1
1
1
2
1
1
1
1
1
1
2
0
0
1
1
0
1
2
1
1
0
2
0
1
1
1
2
1
2
1
1
1
0
2
1
1
0
0
1
1
2
1
1
3
1
1
1
1
2
1
0
1
1
2
0
2
1
2
1
1
1
1
1
0
2
0
1
1
2
1
1
1
1
1
2
3
0
0
1
1
1
1
1
1
1
1
1
1
2
1
0
2
1
1
1
1
1
1
1
1
1
0
1
1
2
1
2
1
1
0
1
1
1
1
2
1
2
1
1
2
1
0
2
1
1
1
2
0
1
2
2
1
2
1
1
2
1
2
2
1
0
0
1
2
1
1
1
0
1
0
1
1
2
1
0
1
1
2
2
2
0
1
1
1
2
1
1
1
2
2
1
2
0
1
1
1
2
2
1
1
1
1
1
1
2
1
2
2
0
1
2
1
1
1
1
0
1
0
1
1
0
1
0
1
1
2
1
0
1
1
1
1
0
1
2
1
0
1
1
1
0
2
2
1
2
1
1
1
1
1
1
1
0
0
2
1
0
1
0
1
0
1
2
1
0
2
1
1
0
1
0
0
1
2
1
1
2
1
2
2
0
1
1
2
1
0
1
0
0
1
1
0
2
0
1
1
1
1
1
1
2
1
1
2
1
2
2
2
0
1
0
1
2
1
1
1
0
1
1
2
0
1
0
2
1
1
2
1
2
2
1
1
1
1
2
1
2
2
2
0
1
1
1
1
2
2
2
2
1
1
1
1
1
0
2
2
0
1
2
0
0
1
1
0
1
2
1
2
1
1
2
1
1
1
1
1
1
1
2
1
0
0
1
0
0
2
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
0
1
1
1
0
1
0
1
3
1
0
1
1
2
1
1
1
1
1
0
2
0
1
1
0
2
2
1
1
1
1
1
1
2
1
2
1
3
1
0
3
1
0
1
1
1
1
1
2
1
0
1
0
1
0
1
1
2
1
1
1
2
1
2
1
1
0
1
0
0
2
1
0
1
1
1
1
1
1
0
2
2
0
2
0
1
1
1
2
1
2
1
1
1
1
2
1
1
0
0
1
0
2
1
1
1
2
1
1
0
1
1
1
1
0
1
0
0
1
1
2
0
1
1
1
0
1
2
1
2
1
1
2
1
0
1
1
1
1
1
1
2
0
1
1
2
2
1
2
0
2
1
1
1
1
1
2
1
0
2
2
1
0
2
2
1
1
1
1
1
1
1
1
1
2
1
1
1
0
2
1
0
1
1
2
2
2
1
1
1
1
2
1
1
2
2
1
1
3
2
1
0
1
1
1
1
1
1
2
2
2
0
2
0
1
1
2
0
1
1
2
1
0
1
1
2
1
1
2
1
2
1
1
1
1
1
3
1
1
0
1
1
1
2
0
0
2
0
1
0
1
1
1
2
2
0
1
0
0
1
0
2
1
2
0
1
1
1
1
1
2
0
1
2
1
0
1
1
1
2
1
1
1
2
1
2
0
2
1
2
1
1
0
1
3
1
2
1
0
0
1
1
2
2
2
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
2
2
1
0
1
1
1
1
1
2
1
0
0
0
1
0
1
1
0
2
0
1
1
2
1
1
1
2
2
2
2
1
1
1
2
1
1
1
1
1
1
2
0
1
0
2
1
1
1
2
1
1
2
0
0
2
1
0
1
1
1
1
2
1
0
1
1
1
2
1
1
0
0
1
2
2
1
1
0
0
2
1
2
2
2
2
1
1
1
1
1
0
1
1
1
1
2
0
2
0
2
1
1
2
1
1
1
1
0
1
1
1
1
1
1
2
1
1
1
1
2
1
0
1
1
1
1
1
0
1
0
1
1
0
2
1
1
2
1
0
0
1
1
1
1
1
1
1
1
0
1
2
1
0
2
1
1
1
1
0
1
2
1
3
1
1
2
1
1
1
2
1
1
1
0
1
1
1
1
1
2
1
1
2
1
2
0
1
0
1
1
2
1
1
1
1
2
1
1
2
0
1
1
2
1
1
0
1
2
1
2
0
1
1
0
1
1
1
2
2
1
0
0
0
1
1
0
2
2
1
1
1
1
2
1
1
1
2
2
2
1
0
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
0
0
1
1
0
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
0
2
1
1
0
0
1
1
0
1
1
0
0
1
0
2
2
0
1
1
1
1
0
1
0
0
0
1
1
0
1
1
2
1
1
1
1
1
2
1
1
2
1
2
1
1
1
1
1
2
1
1
1
1
0
1
1
1
2
2
1
1
1
1
1
0
0
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
2
1
1
0
2
1
2
2
2
2
1
2
1
1
1
1
1
1
1
2
1
0
1
2
4
1
0
1
1
0
2
2
1
1
1
1
1
2
0
1
2
1
2
1
0
1
1
1
0
1
2
2
2
1
1
0
1
1
1
1
1
0
1
1
1
1
0
1
1
0
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
2
2
2
1
1
0
1
0
1
0
1
1
1
1
0
0
1
1
3
1
2
1
1
1
1
1
1
0
2
2
0
1
0
1
2
0
2
0
3
1
1
2
1
0
1
1
2
2
1
2
1
1
2
1
2
2
1
1
0
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
0
0
1
1
0
0
1
1
2
1
0
2
1
0
1
1
1
1
1
1
0
1
1
1
2
1
2
1
1
1
2
1
1
1
1
0
1
1
1
2
1
0
1
2
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
2
0
1
1
1
1
3
1
1
2
1
1
1
1
2
2
2
1
1
2
1
2
1
1
2
4
1
1
2
0
0
1
1
0
0
2
1
2
1
0
1
2
2
1
1
3
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
2
2
2
2
2
2
1
1
1
2
2
1
1
1
1
1
1
1
2
0
0
2
1
1
2
1
1
0
0
0
1
1
1
0
1
1
0
1
1
2
2
2
1
1
1
1
1
0
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
0
1
1
0
0
2
1
2
1
1
2
1
2
2
1
0
1
0
2
1
1
1
2
1
1
4
1
1
1
2
1
1
0
1
1
1
1
0
3
2
2
0
0
0
0
0
1
1
1
0
1
1
2
1
1
0
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
0
1
1
2
1
1
1
0
1
0
1
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
2
0
2
1
1
2
2
1
2
2
1
1
1
2
1
2
1
2
1
1
1
0
1
1
1
2
2
2
1
1
0
1
2
2
1
0
1
0
1
0
0
1
1
1
2
1
1
0
1
1
2
1
1
1
1
1
0
1
1
1
1
2
2
1
1
2
2
1
2
1
1
0
1
2
1
1
2
2
1
1
1
1
1
1
1
1
1
0
0
1
1
2
1
2
1
1
1
1
1
0
0
1
1
1
0
1
2
2
2
1
1
1
1
1
1
1
1
1
1
2
2
1
2
1
2
1
1
2
1
1
1
0
1
1
1
1
1
2
2
1
1
2
0
1
1
1
2
1
2
2
0
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
0
0
1
1
1
2
1
2
2
1
1
1
1
1
1
0
0
2
1
2
1
1
1
2
1
1
1
1
2
2
1
2
1
1
1
0
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
3
2
2
0
1
1
2
0
1
1
1
0
2
0
1
2
1
2
1
1
1
1
2
1
3
2
0
1
1
0
2
1
1
0
1
1
1
1
1
2
2
2
0
1
2
1
2
1
1
1
0
1
1
2
1
2
0
2
2
1
0
1
1
1
1
1
1
0
2
0
1
2
2
1
2
2
1
1
1
0
1
0
2
2
1
2
1
1
1
1
1
2
1
2
1
1
0
1
1
2
1
1
1
1
1
1
2
1
1
0
2
1
1
1
1
1
0
1
1
1
2
0
1
1
1
0
1
1
1
0
1
0
2
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
2
1
2
2
1
2
1
0
1
1
1
1
1
1
1
2
1
2
1
2
2
1
2
1
2
1
1
0
1
0
1
0
2
1
1
1
2
0
1
2
0
1
1
1
2
1
1
1
1
2
1
1
2
1
2
2
1
1
1
0
0
1
1
1
1
1
1
1
2
0
1
0
1
0
1
1
0
2
2
1
1
2
1
0
1
1
2
1
0
1
1
2
2
2
1
1
0
1
1
1
1
1
1
1
2
2
2
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
0
1
1
2
1
1
0
0
1
0
2
1
2
1
1
0
1
1
2
1
2
1
1
1
1
2
1
1
2
1
1
0
1
1
1
2
1
1
1
2
0
1
1
0
1
2
2
1
1
2
1
2
2
1
1
1
2
0
1
1
2
2
1
2
0
2
1
2
1
0
1
1
0
2
1
1
1
2
0
1
0
2
1
2
0
1
1
2
0
2
2
0
2
0
2
2
1
1
1
0
0
0
1
1
2
2
1
0
0
0
2
1
2
1
0
1
2
1
2
2
0
1
1
1
0
1
1
1
0
2
1
2
0
1
1
1
0
1
1
0
0
1
1
1
0
1
1
2
2
0
1
1
1
0
1
2
1
1
1
0
1
2
1
2
0
1
1
1
2
1
2
1
1
0
1
0
1
0
1
1
1
1
2
1
1
0
1
1
1
1
1
1
0
2
0
1
2
1
1
2
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
0
1
1
1
1
1
1
1
1
1
0
2
5
1
0
1
1
2
1
2
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
2
1
1
0
1
2
1
2
1
0
1
0
2
0
2
1
2
2
0
0
2
0
1
1
1
2
1
1
1
2
1
2
1
0
1
1
1
1
0
2
1
1
1
2
2
1
0
1
2
2
1
1
2
1
1
0
1
1
1
1
1
1
2
1
1
1
0
1
0
1
1
1
2
1
2
0
2
1
2
1
2
1
1
1
1
1
2
1
2
1
1
0
1
1
2
1
2
2
2
0
1
1
2
1
1
0
1
1
1
2
1
1
1
1
2
1
1
2
0
1
2
1
0
0
0
1
0
2
1
0
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
2
2
1
2
0
2
1
1
1
1
1
2
1
1
1
1
1
2
2
1
2
1
0
2
2
2
1
2
1
1
1
1
1
1
0
0
1
2
0
2
1
0
1
2
2
1
2
1
2
0
1
1
1
1
2
1
0
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
1
4
0
2
0
1
1
2
3
2
2
1
1
2
0
1
1
0
2
1
1
2
1
1
2
2
1
1
1
0
1
1
2
1
0
1
2
1
1
1
0
0
2
2
1
1
1
1
0
1
2
1
1
1
0
0
1
1
0
1
1
0
2
2
1
2
1
1
1
0
1
0
1
0
2
0
2
0
2
1
2
2
1
0
1
1
2
2
1
1
1
2
1
1
1
1
1
1
2
1
0
1
1
1
1
1
1
1
1
1
0
1
2
1
1
0
0
1
1
1
1
0
2
2
1
1
1
0
1
2
1
1
1
1
1
1
0
1
1
1
2
2
0
0
2
0
1
1
1
2
0
1
2
2
1
1
1
1
1
2
2
1
0
0
0
3
1
1
1
2
2
2
1
2
1
1
1
1
1
2
1
2
0
1
1
1
1
1
1
1
1
1
1
0
1
2
1
0
2
3
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
0
1
0
1
2
1
2
1
1
1
1
1
1
2
1
2
1
1
1
2
1
2
1
1
1
1
1
1
1
1
0
1
1
1
1
0
1
2
1
2
0
0
1
0
2
1
2
1
2
1
2
1
0
2
1
1
1
2
1
1
0
2
0
2
2
1
1
0
1
1
1
0
1
1
1
1
1
1
1
2
0
2
0
2
1
1
1
1
1
2
2
1
0
1
1
0
1
1
2
1
1
2
1
1
2
0
2
1
2
0
2
1
0
2
1
1
1
2
2
0
1
1
1
1
1
0
1
0
1
2
2
0
2
2
1
1
1
2
1
1
1
1
2
0
2
1
2
0
1
1
1
1
1
0
1
1
1
2
0
1
1
1
1
2
1
3
0
1
1
0
1
1
1
1
2
1
0
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
0
2
0
2
2
1
1
1
1
2
1
3
0
0
1
0
1
1
2
1
2
2
2
1
1
2
2
1
0
0
2
2
1
2
1
2
1
1
1
1
2
1
1
2
1
2
2
0
0
2
0
1
1
1
2
2
1
0
1
1
2
0
1
1
2
0
1
0
0
0
1
1
1
1
0
1
0
0
1
1
0
1
1
2
1
1
0
1
1
2
0
1
0
1
1
1
2
1
2
2
2
2
1
1
2
2
1
1
1
1
2
2
2
1
1
1
2
1
1
1
2
2
2
1
0
2
1
1
1
1
0
1
1
1
2
2
0
0
1
1
1
0
1
0
1
1
0
2
1
1
1
1
0
2
1
1
1
2
1
1
1
0
0
1
1
1
1
1
1
1
1
2
2
0
2
1
1
2
0
1
0
2
1
1
1
1
1
0
1
0
1
0
1
1
2
2
2
1
0
2
2
1
2
1
1
2
0
2
2
2
2
1
0
1
1
1
1
1
1
1
2
2
0
1
2
2
1
2
0
1
0
1
2
0
0
1
1
0
1
2
2
1
1
1
1
0
0
1
0
1
2
1
2
2
1
1
1
2
0
1
1
1
1
1
1
2
1
1
2
2
2
1
1
2
1
1
2
1
1
2
1
2
1
1
2
1
2
1
1
2
0
2
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
0
2
1
1
1
1
0
1
1
0
0
1
1
1
1
1
1
1
0
2
1
2
1
2
1
1
1
1
2
0
2
1
1
1
1
1
0
0
1
0
1
2
1
2
0
1
1
1
2
1
1
1
1
1
0
1
1
1
0
2
1
1
1
2
2
2
1
1
0
2
2
1
1
0
2
1
1
0
0
0
1
1
1
1
1
1
1
1
1
0
1
1
0
1
1
1
2
1
0
1
2
1
1
1
1
2
1
1
2
0
0
2
1
1
1
2
1
1
1
0
1
2
1
2
1
2
2
1
1
2
1
1
2
2
1
2
1
1
0
1
1
3
0
2
1
0
1
1
2
1
1
1
0
1
1
2
2
1
1
0
1
1
2
2
2
1
2
1
1
1
0
1
1
2
1
1
2
2
1
1
2
2
1
1
2
1
2
2
1
2
0
1
2
2
1
1
1
1
0
1
1
2
1
1
1
2
1
1
1
2
0
2
1
2
1
1
1
1
1
1
1
0
0
1
2
1
2
2
0
1
1
1
0
2
1
0
1
1
1
1
1
0
2
0
1
1
1
1
1
2
2
2
2
2
1
1
0
0
1
0
1
1
1
0
0
2
1
1
1
1
1
2
1
2
2
1
2
1
2
1
1
1
0
1
1
1
1
2
1
1
1
1
0
1
1
1
1
1
1
0
2
1
2
1
1
2
1
1
0
1
1
2
2
2
1
2
1
1
2
2
0
1
0
1
1
2
2
1
1
1
1
1
0
0
1
0
2
1
0
0
1
1
1
1
1
2
1
1
0
1
1
1
2
0
2
2
1
1
1
1
0
0
0
2
1
0
1
0
1
1
1
2
1
2
1
1
1
1
0
1
2
2
2
1
0
1
1
1
1
1
1
1
1
1
2
1
0
1
1
1
1
2
1
2
1
0
1
1
1
2
0
1
0
2
1
2
1
0
2
1
0
1
1
1
2
2
0
1
1
1
0
2
0
1
1
0
1
1
1
1
1
1
2
1
1
0
1
1
2
2
1
1
2
1
2
1
1
1
1
0
2
2
1
0
2
1
0
1
2
1
1
1
0
1
0
1
0
1
1
1
2
1
2
1
1
1
1
2
2
1
0
0
2
2
1
2
1
1
0
2
0
1
1
2
1
2
1
1
1
1
0
1
1
1
0
1
1
1
3
0
1
1
1
1
2
2
2
1
0
1
2
2
1
2
1
1
1
0
2
1
1
1
1
2
1
1
0
0
1
1
1
1
1
1
2
1
1
1
0
1
1
1
2
1
0
1
1
1
0
1
1
1
1
2
0
1
1
2
1
1
0
2
1
1
0
2
1
1
2
1
0
1
1
1
2
2
2
1
2
1
2
1
1
2
1
1
1
1
0
1
2
1
2
1
1
1
1
1
1
0
1
2
1
2
1
2
2
1
1
4
2
0
1
1
2
0
1
2
2
1
1
1
1
0
1
2
0
2
2
2
1
2
1
2
1
1
1
2
2
2
1
1
1
1
1
1
1
0
1
2
1
3
1
0
1
2
1
1
1
2
1
2
2
1
1
1
0
1
2
0
1
1
0
0
1
5
1
2
1
1
0
1
0
1
1
2
1
1
0
2
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
2
1
1
0
1
3
1
1
1
1
1
2
0
3
1
1
2
0
1
2
1
1
1
0
1
1
1
0
1
1
1
2
2
0
1
1
1
2
2
0
2
1
1
1
0
1
2
1
2
2
2
1
1
1
2
2
0
1
1
1
1
1
1
1
0
1
2
1
2
1
0
1
1
1
0
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
0
1
1
2
1
3
2
0
1
1
2
1
1
0
1
1
0
2
1
2
0
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
0
1
0
2
1
2
1
0
2
1
1
1
2
1
1
1
1
1
1
2
2
0
1
1
1
1
0
2
0
2
1
1
1
1
1
2
0
1
1
1
1
1
1
2
2
1
2
1
2
1
1
1
1
1
2
2
0
0
0
1
1
1
1
0
2
1
2
1
2
0
1
0
1
1
1
2
1
1
1
1
2
1
2
2
1
1
0
1
1
1
1
1
1
1
0
1
1
1
1
2
2
1
1
2
2
2
2
2
1
2
1
1
1
1
2
2
1
2
1
2
2
0
2
2
2
1
0
0
1
1
1
1
1
0
2
2
1
1
1
1
1
1
0
1
2
1
1
1
0
0
0
1
1
1
2
0
1
1
0
1
1
2
1
1
1
2
2
1
1
0
2
1
1
1
2
0
0
2
0
1
0
2
1
1
2
0
1
1
1
3
2
2
1
1
1
1
1
1
1
1
0
1
1
1
0
1
2
1
2
3
2
1
2
2
1
1
1
2
0
1
1
2
1
1
2
0
2
1
1
1
2
1
1
1
2
2
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
1
1
2
2
1
0
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
0
1
0
2
1
1
0
1
1
2
2
0
1
0
0
2
1
1
1
1
1
2
1
1
1
2
1
0
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
2
1
1
1
1
2
2
1
0
1
0
0
2
2
1
1
1
1
1
1
0
1
0
1
2
1
1
3
1
2
1
1
1
1
0
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
5
2
1
1
1
1
1
1
0
1
1
1
1
1
1
1
0
2
1
1
2
0
1
1
1
1
2
2
1
2
2
1
1
2
2
1
1
2
0
0
1
1
0
0
1
1
2
0
1
1
1
0
0
0
6
0
1
1
1
2
1
1
1
1
2
1
1
2
1
1
2
2
1
1
1
2
2
1
0
2
1
1
2
2
1
0
0
2
2
1
0
1
2
1
1
0
1
1
1
1
2
1
1
1
0
0
0
1
1
2
1
2
1
1
1
1
2
2
1
2
3
1
1
1
1
2
1
1
0
1
0
0
1
0
1
1
1
2
2
1
0
0
1
0
1
1
1
2
1
1
1
0
1
2
0
1
1
1
1
2
2
0
0
1
1
2
0
1
2
2
2
1
1
1
1
1
1
1
1
1
2
2
2
1
2
0
1
1
1
1
1
0
2
0
0
2
2
1
1
2
1
0
0
0
0
1
1
2
1
1
0
1
1
1
1
2
1
1
1
2
0
1
2
1
1
1
1
0
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
0
2
1
1
2
1
2
1
0
1
1
2
2
1
0
1
1
2
2
0
0
2
2
0
1
1
1
2
1
2
1
1
2
1
1
0
1
0
0
2
0
1
1
1
1
1
1
1
1
2
2
1
1
2
2
1
2
2
1
1
1
0
1
1
1
1
1
1
0
1
1
1
1
1
0
1
2
0
0
2
1
0
1
1
1
1
2
1
0
1
0
1
0
1
1
2
1
1
0
0
2
1
2
1
2
1
1
1
1
1
2
1
1
2
1
1
0
2
1
0
1
0
1
2
1
0
0
0
0
1
1
1
1
1
1
1
0
2
2
1
1
1
1
2
2
2
1
2
0
3
1
2
1
1
1
1
1
1
2
0
0
1
2
1
2
1
1
1
1
1
2
1
1
2
1
0
1
1
1
1
0
1
2
2
2
0
1
1
1
2
1
1
1
1
1
1
0
1
1
1
1
1
2
1
2
2
2
2
1
1
2
1
1
1
1
1
0
1
2
2
2
1
1
2
1
2
0
1
1
1
2
1
2
1
3
1
1
1
1
1
1
0
2
1
4
2
1
1
0
1
1
0
1
1
2
1
1
1
1
1
1
1
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
0
1
2
0
1
2
2
0
2
4
1
0
2
2
1
1
2
1
1
1
1
0
0
1
1
2
2
1
0
1
1
1
2
1
1
1
1
1
1
0
1
0
1
1
1
2
2
2
0
1
1
1
0
0
0
1
1
0
0
1
1
0
1
0
1
1
1
0
1
2
2
1
1
1
1
0
1
1
1
1
1
1
2
1
1
1
1
1
2
0
1
2
1
0
1
2
1
2
2
2
1
1
0
2
1
1
2
2
0
2
1
1
1
0
1
1
1
1
1
0
0
1
1
1
1
1
1
0
1
0
2
1
0
2
2
2
1
1
1
1
2
1
1
1
1
1
2
1
0
1
1
0
0
1
2
0
1
1
1
0
0
1
2
2
2
1
0
0
1
2
1
1
0
1
2
1
1
1
0
1
2
1
1
2
1
1
1
0
1
1
1
1
1
1
0
1
1
1
1
4
2
1
1
2
1
2
1
1
1
0
2
2
1
1
2
1
1
1
1
1
0
1
1
1
1
1
1
2
0
1
2
1
1
2
1
1
1
1
0
1
1
1
2
1
2
1
1
1
1
2
0
3
1
1
1
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
2
0
1
2
1
2
0
1
2
0
1
1
1
1
1
1
2
1
1
1
1
2
1
2
2
1
1
1
2
1
1
1
1
1
0
1
1
1
1
0
2
1
0
1
1
2
1
2
1
1
2
0
2
1
3
1
1
2
1
1
2
2
1
1
1
2
1
1
1
1
3
1
0
2
1
2
1
1
2
1
1
2
1
1
1
2
2
2
1
1
1
1
1
2
1
1
1
1
1
1
0
1
1
2
2
1
1
1
1
2
0
2
1
1
1
1
1
0
2
1
1
0
1
1
1
2
1
1
1
1
2
1
2
1
1
2
1
2
1
1
1
1
1
1
2
2
1
1
0
0
2
1
2
2
1
1
1
1
0
0
1
0
2
0
1
1
1
1
1
1
1
1
0
2
1
1
0
1
0
1
1
1
1
1
0
0
1
2
1
1
1
1
0
1
2
1
0
1
2
1
2
1
1
2
0
1
3
0
1
1
1
2
2
1
1
1
1
2
1
1
1
1
0
1
1
1
1
1
0
1
1
0
1
2
1
1
1
1
1
1
0
0
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
0
2
1
0
2
1
2
0
0
0
0
1
1
2
0
0
1
0
0
2
2
1
1
2
1
0
1
1
2
2
1
0
1
1
2
0
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
3
1
1
1
1
1
1
2
0
1
1
1
0
2
1
2
2
1
1
1
1
2
2
1
2
2
1
2
1
1
2
0
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
0
1
2
1
1
2
0
1
2
1
2
1
1
0
1
1
0
1
1
1
1
1
1
1
2
2
2
0
1
1
2
1
0
0
1
1
1
1
1
0
0
0
2
1
1
0
2
1
1
1
1
1
1
1
1
1
0
2
1
2
0
2
1
1
2
1
1
2
3
1
1
0
2
0
1
2
1
2
2
1
1
1
1
1
1
1
0
0
0
1
0
1
0
1
0
1
2
2
0
2
1
1
1
2
0
2
1
2
2
1
1
2
1
1
2
1
2
2
0
1
2
1
2
1
0
2
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
0
1
2
2
1
2
2
1
2
1
1
1
1
1
1
1
0
2
1
1
0
0
1
1
1
1
1
1
2
0
0
1
1
0
0
1
1
1
1
2
1
1
1
1
1
2
2
1
1
0
1
1
0
2
2
2
0
0
2
2
2
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
0
2
1
1
2
1
1
2
2
1
1
1
0
1
2
1
1
2
0
0
1
1
1
2
2
1
1
1
2
1
2
1
1
1
0
2
0
1
2
2
1
1
2
1
1
0
1
1
1
1
1
2
2
2
2
1
1
2
2
1
1
1
2
1
1
1
1
2
1
1
1
1
2
2
1
0
1
1
1
1
1
2
1
2
1
0
1
1
1
2
1
0
1
1
1
3
2
1
1
2
1
0
1
1
1
1
1
1
0
1
1
1
1
1
2
0
1
1
0
2
1
1
1
1
1
1
2
1
2
1
1
0
1
2
1
0
3
1
2
1
1
2
0
1
1
2
0
2
2
1
1
1
0
2
1
2
1
2
1
1
1
1
1
1
0
2
2
1
0
1
2
1
1
1
1
1
1
1
1
1
2
0
1
1
0
2
1
0
1
2
1
1
1
0
0
2
1
1
0
0
1
2
0
1
2
1
0
1
1
2
1
0
0
1
2
2
2
1
1
1
1
2
0
2
1
2
2
1
1
1
0
1
1
1
1
2
2
1
1
2
2
0
1
2
1
1
1
1
2
1
2
1
1
2
0
1
1
2
1
1
1
2
2
1
1
1
1
0
1
1
1
0
1
1
1
2
1
2
1
1
2
1
2
1
2
1
1
2
1
2
0
1
2
2
2
1
0
1
1
1
2
1
2
1
1
0
1
2
2
2
1
1
1
1
1
1
1
1
1
1
0
1
1
1
0
1
2
0
2
2
1
2
1
1
1
1
1
1
1
2
2
1
1
1
2
1
2
1
1
0
2
0
2
1
1
1
2
1
1
2
1
1
1
1
0
1
1
2
1
0
1
0
1
1
2
1
0
1
4
2
1
2
0
2
1
1
1
1
1
1
2
1
1
1
0
1
1
1
1
1
1
1
1
4
1
0
2
3
1
1
0
1
0
0
1
1
1
1
1
1
2
1
1
1
1
0
1
2
1
1
2
1
1
1
2
1
1
0
1
2
1
1
0
1
3
1
1
0
1
1
1
0
0
1
2
1
1
0
2
1
2
2
0
1
0
1
1
1
2
1
2
2
1
1
1
0
1
0
1
3
0
1
2
1
1
0
0
1
1
2
2
1
2
2
1
2
2
1
1
0
1
1
2
1
1
0
1
1
1
2
2
2
1
1
1
1
2
1
0
1
0
1
1
1
1
1
1
0
0
2
1
1
1
1
1
1
0
3
1
2
1
0
0
1
1
2
1
2
1
1
2
1
0
3
1
2
1
1
1
1
0
0
0
0
1
1
1
0
2
1
1
0
0
0
2
0
1
2
1
0
1
2
1
1
1
1
1
1
2
2
1
0
1
1
1
2
1
2
1
0
1
1
2
2
2
0
1
2
1
0
1
1
1
2
1
2
1
0
1
2
2
2
1
2
1
2
1
0
1
1
1
1
0
1
1
1
1
0
2
1
0
1
1
1
1
2
2
0
1
1
1
1
1
2
1
2
2
1
1
1
2
1
2
2
1
1
1
2
0
1
0
1
1
1
2
1
2
1
1
1
1
1
2
1
1
0
1
1
1
1
1
1
0
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
1
1
1
2
1
0
1
2
1
2
1
1
2
1
2
1
2
1
1
1
1
1
2
0
1
2
1
1
0
1
1
1
1
1
3
2
0
2
0
1
1
2
1
2
1
1
1
2
2
2
2
2
1
1
1
1
1
1
2
1
1
1
0
1
1
2
1
2
1
1
1
2
0
1
1
1
1
1
2
0
0
2
1
1
1
1
2
1
1
2
1
2
1
2
1
1
2
1
2
0
1
0
1
2
1
2
1
1
1
3
1
1
1
2
2
0
1
1
1
1
0
0
1
0
1
1
1
1
2
0
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
0
1
1
1
1
0
1
2
2
1
2
1
1
1
1
2
1
1
0
2
1
1
2
2
1
1
0
2
0
2
1
1
0
1
0
2
2
1
1
2
1
1
1
0
0
1
2
1
0
1
1
2
0
1
1
2
1
1
1
2
1
0
1
1
1
2
2
1
1
1
1
2
1
0
2
1
1
1
1
0
1
0
2
2
2
1
1
1
1
1
2
1
1
1
1
0
1
2
1
1
1
2
0
2
1
2
1
1
1
1
1
1
1
1
1
1
0
1
0
0
2
2
1
1
1
0
0
1
1
1
1
1
0
0
1
2
3
2
0
1
0
1
2
1
1
1
2
2
2
1
2
2
1
2
1
1
2
1
2
2
2
2
2
2
1
1
2
1
2
1
2
1
1
1
2
2
1
1
2
2
2
2
2
1
1
1
2
0
2
0
0
1
0
1
1
1
1
2
1
2
2
2
1
1
1
2
1
0
0
0
0
2
1
1
1
2
2
1
1
0
1
1
0
2
2
1
0
2
1
1
1
2
1
1
1
2
1
1
0
0
1
1
1
0
1
1
2
1
1
1
1
2
1
1
1
2
2
1
0
1
0
2
0
1
1
1
1
1
3
2
0
2
1
0
1
2
1
2
1
1
1
1
1
1
0
1
1
1
1
1
2
1
2
1
0
2
0
1
3
1
1
1
2
1
1
1
2
0
1
1
1
1
2
1
2
1
2
2
3
2
1
2
1
1
1
1
2
1
1
3
2
1
1
2
2
1
0
1
1
1
2
2
1
0
1
1
1
2
1
1
2
1
1
1
1
1
1
2
0
0
1
2
2
1
1
1
1
0
2
1
1
0
2
1
2
1
1
2
1
2
2
1
0
1
2
1
2
1
2
1
2
0
1
1
0
1
1
2
2
0
0
1
0
2
2
2
1
0
2
2
1
1
1
1
1
1
1
0
2
1
2
1
1
1
1
0
1
2
2
1
1
2
0
1
0
2
0
1
0
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
0
1
2
1
2
1
0
1
1
1
2
1
0
0
0
1
2
2
2
1
1
1
1
0
1
0
1
2
2
2
1
1
2
1
1
1
2
1
1
1
1
1
0
2
1
0
0
1
2
2
0
1
1
1
1
0
1
1
2
1
1
2
1
1
2
1
0
2
0
1
2
2
1
2
1
1
1
2
2
1
1
0
1
2
2
4
0
1
2
2
1
1
2
1
2
0
1
1
2
2
0
2
1
1
2
1
1
3
1
1
2
1
1
1
1
1
1
2
1
1
0
1
1
0
1
2
2
1
1
1
0
1
1
2
2
1
1
1
1
2
1
1
1
2
1
1
1
1
0
1
1
2
2
1
2
1
2
2
1
1
1
1
1
2
1
2
1
2
0
0
1
0
1
1
2
0
1
1
4
1
1
1
1
2
1
1
1
1
1
1
3
0
1
1
2
2
1
1
1
2
1
0
1
0
0
1
1
2
1
1
1
2
1
1
1
1
2
1
1
0
1
2
2
1
0
1
1
1
1
2
1
2
1
1
2
1
2
1
2
1
2
0
0
0
2
1
1
1
1
1
0
1
1
2
2
2
1
2
0
1
1
0
1
1
1
1
1
2
1
1
2
1
1
1
1
2
1
2
2
2
2
1
1
2
1
1
1
1
1
1
1
2
1
2
0
1
2
0
1
1
0
0
1
1
1
1
0
1
1
1
1
2
1
2
1
2
2
1
1
1
1
1
1
1
1
2
1
1
0
1
2
1
2
1
1
2
2
2
1
2
1
1
1
2
1
2
2
2
2
1
1
2
1
1
1
1
1
1
0
1
1
2
2
1
2
1
0
1
1
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
3
0
1
1
1
2
1
0
1
2
1
1
0
2
1
1
2
2
0
1
1
0
1
1
0
1
1
1
1
0
1
1
1
1
2
2
0
1
2
1
1
2
2
2
0
2
1
1
2
2
1
1
1
1
2
1
0
1
1
1
1
0
1
2
2
0
1
0
2
2
2
0
2
1
0
2
0
2
1
2
1
2
1
1
1
1
1
1
0
1
1
1
1
1
0
1
2
1
2
1
0
1
1
1
0
2
2
2
2
1
2
1
0
1
0
1
1
0
0
2
2
1
1
1
0
1
2
1
0
1
1
1
0
2
1
1
1
1
1
1
1
0
1
2
0
1
0
1
2
2
1
1
1
0
0
1
1
2
2
1
2
0
1
2
1
0
2
0
1
1
0
1
1
1
1
2
0
1
1
1
1
2
0
1
1
0
1
1
1
1
1
2
1
1
1
0
1
0
1
1
1
1
1
0
1
0
1
2
1
2
1
2
2
1
2
2
1
0
1
1
0
1
0
1
1
1
2
0
0
2
1
2
1
2
1
1
1
1
1
1
1
2
2
1
1
1
1
0
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
0
2
1
1
1
0
2
1
2
2
2
1
1
2
0
1
2
1
0
0
1
2
2
0
1
0
1
1
2
2
1
2
2
2
1
1
0
0
1
2
0
0
2
0
1
1
2
1
1
1
1
1
1
2
1
1
0
1
1
1
1
1
2
2
1
2
2
2
2
2
2
2
2
0
1
1
1
0
2
1
2
1
2
0
1
1
1
2
1
1
2
1
0
1
0
1
1
1
0
2
1
1
0
0
1
1
2
1
1
0
2
2
1
0
1
1
1
1
1
1
1
1
2
1
1
2
0
1
1
0
1
1
1
2
1
1
0
1
1
1
0
2
1
2
1
2
1
1
2
1
1
0
1
0
1
1
1
0
1
0
1
2
1
1
1
2
1
2
1
1
0
2
2
1
0
2
2
1
1
1
1
2
1
1
0
1
1
1
0
2
1
2
2
0
1
1
2
0
1
1
1
1
0
0
0
0
1
1
1
0
1
1
0
1
3
2
1
1
1
0
0
2
0
0
1
1
1
1
1
1
0
1
0
2
1
2
2
1
2
1
0
2
1
1
1
2
1
2
2
2
1
0
1
1
2
1
0
2
1
1
1
2
0
1
0
1
1
1
2
0
3
1
0
1
2
1
1
0
1
1
1
1
2
0
1
0
1
1
1
2
1
0
2
2
1
0
2
1
0
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
0
0
1
2
2
2
2
1
0
2
0
1
2
2
2
2
1
1
1
1
2
0
2
1
1
2
2
2
0
1
1
2
1
2
1
1
0
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
1
2
1
1
1
0
1
1
1
1
1
1
1
2
0
2
1
1
1
1
1
0
2
2
1
1
1
2
1
3
1
1
1
4
1
2
2
1
1
2
0
1
1
1
1
1
2
0
1
1
1
0
0
1
1
1
1
1
2
2
1
0
1
1
1
1
0
2
1
1
1
1
0
1
1
1
1
1
1
0
1
0
1
1
2
2
1
1
1
2
2
1
1
1
2
0
2
1
0
0
0
1
0
2
1
0
1
1
1
2
1
2
2
1
1
2
2
1
1
1
1
1
1
1
2
1
1
2
2
1
2
1
1
1
1
1
1
1
1
0
0
2
1
1
2
1
1
0
1
2
1
2
0
0
0
2
2
1
0
0
1
1
1
2
1
0
1
0
0
1
1
1
1
1
2
2
2
0
1
1
1
0
1
1
0
2
0
2
2
0
2
1
0
1
0
1
1
1
1
2
2
0
1
2
1
1
1
1
1
1
1
0
0
1
2
1
1
2
2
0
2
2
0
2
0
2
1
1
1
0
0
1
3
2
1
1
2
2
1
0
2
1
2
0
1
1
0
1
1
2
1
0
1
1
1
1
1
1
1
2
1
2
1
2
1
2
1
2
2
2
1
1
2
1
2
2
1
1
1
0
0
2
1
2
1
2
1
1
1
1
2
2
2
0
1
1
2
2
1
1
1
1
1
1
1
0
1
1
2
1
1
1
2
1
1
1
2
2
1
1
1
1
1
2
2
0
2
0
0
1
1
1
2
1
2
2
1
0
1
1
0
2
1
1
1
0
1
1
3
0
2
1
0
1
2
0
1
1
2
0
1
1
2
1
0
0
1
1
1
1
1
2
1
0
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
0
0
1
2
2
1
1
0
1
0
2
2
1
0
1
1
0
1
2
1
2
2
0
2
1
1
1
0
2
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
0
1
2
2
1
1
1
1
0
2
0
1
1
0
1
0
1
1
1
2
1
1
2
1
1
1
2
1
1
1
2
0
1
0
1
0
1
0
2
1
2
2
1
1
1
1
1
2
1
1
2
1
2
1
1
1
0
2
0
1
2
1
1
0
0
1
0
2
1
0
1
0
1
1
1
0
1
1
1
1
1
1
1
2
1
3
1
1
2
2
2
0
1
0
1
1
0
1
1
1
2
1
1
2
1
2
1
2
2
1
1
1
1
2
1
1
1
2
0
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
0
1
2
1
2
1
2
1
1
1
2
2
0
1
2
1
2
2
1
0
1
0
2
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
2
0
1
1
1
1
2
1
1
2
1
2
0
2
1
1
2
2
0
1
1
2
2
0
1
1
2
2
1
1
1
1
0
0
2
1
0
1
1
2
2
1
1
1
1
1
1
1
2
1
2
1
2
1
2
0
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
0
2
0
2
1
1
1
1
1
0
1
0
0
1
2
0
1
1
0
1
0
4
1
1
1
0
1
0
1
1
0
0
1
2
1
1
1
1
1
2
0
0
1
1
2
2
1
1
1
0
1
1
1
1
0
1
2
1
1
1
0
1
0
0
1
1
1
1
2
1
1
1
0
1
2
1
1
2
1
2
1
1
1
1
1
1
0
1
2
2
1
1
2
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
2
1
1
1
2
1
1
2
2
0
1
1
0
2
1
3
1
2
0
1
2
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
2
1
1
1
1
2
0
1
2
1
1
1
0
1
1
1
1
1
2
1
0
0
0
1
1
2
1
1
0
2
1
0
3
1
1
2
1
2
1
1
0
0
0
1
1
0
3
2
1
2
1
2
0
1
1
1
0
1
2
2
0
2
1
2
1
1
1
1
1
1
2
2
1
2
2
1
1
1
1
0
0
1
2
1
1
2
1
1
1
0
2
1
1
1
1
1
2
1
0
1
1
1
1
0
2
1
0
1
1
0
1
1
1
0
1
1
3
2
0
2
1
1
2
1
1
1
1
2
1
0
1
2
1
0
1
1
0
0
1
2
1
2
2
2
1
0
0
1
1
1
1
1
2
1
1
1
1
0
0
1
1
1
1
1
1
1
1
2
1
1
1
0
0
0
1
2
1
2
1
0
1
2
1
2
1
1
0
1
2
2
1
2
2
0
1
1
1
0
0
1
1
1
2
1
2
2
2
2
2
1
1
2
2
2
1
0
1
0
1
1
2
1
1
1
2
0
1
1
0
2
1
1
2
2
1
0
2
1
1
0
0
1
1
1
0
2
1
0
2
2
0
1
2
1
1
1
1
1
1
1
2
1
0
1
1
1
1
2
2
1
1
1
2
1
2
2
1
1
1
0
1
2
1
1
0
1
0
1
2
1
1
1
1
0
0
1
1
0
2
0
1
1
1
1
1
1
1
2
2
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
2
1
2
0
2
1
2
1
2
1
2
0
2
1
1
1
1
0
2
1
1
0
1
0
1
0
1
1
0
1
1
1
1
1
1
0
1
1
0
1
1
1
2
1
1
1
1
1
1
0
1
1
1
1
1
1
1
2
2
2
1
0
2
1
1
0
1
1
1
1
0
0
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
0
1
1
0
2
1
2
2
1
2
0
1
1
2
1
2
2
2
1
1
1
2
1
0
0
0
1
1
1
1
2
1
1
1
0
1
1
2
0
1
1
1
1
1
1
1
1
2
1
0
1
1
1
2
2
2
1
1
3
0
1
1
0
2
2
1
1
1
2
1
1
1
1
1
0
1
2
2
2
2
2
1
2
2
2
2
0
2
1
2
2
0
1
2
0
0
1
2
1
0
1
1
1
1
0
1
0
0
1
1
1
0
1
2
1
0
1
2
1
1
1
1
1
1
2
1
1
1
0
1
1
1
1
1
1
2
0
1
1
1
1
2
0
1
1
1
1
0
1
2
1
1
1
1
2
1
0
1
1
0
1
1
1
1
2
1
2
1
1
1
3
1
1
1
2
1
1
2
0
1
1
0
0
1
2
1
0
1
2
1
0
2
1
2
1
1
0
2
2
2
2
0
1
0
0
1
2
1
1
1
1
0
0
2
2
2
1
1
1
1
2
1
2
0
1
2
1
1
1
1
1
1
0
1
2
1
2
0
2
1
2
1
2
1
1
0
1
1
1
1
1
1
1
1
1
1
1
2
0
1
0
1
0
2
1
1
0
1
2
1
2
1
1
1
1
2
0
0
1
2
0
1
1
1
1
1
1
1
2
1
1
2
0
1
0
1
0
1
1
2
2
0
1
1
1
1
2
1
2
1
1
1
2
1
1
1
1
2
2
2
2
1
2
0
1
2
1
0
1
1
2
1
1
0
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
2
0
1
1
0
0
1
1
1
1
1
4
2
0
2
2
2
0
1
2
1
2
1
1
1
3
1
1
1
0
1
2
1
2
2
1
2
1
1
1
1
2
0
2
0
1
1
2
2
2
2
2
1
1
1
2
2
1
1
1
2
2
0
2
1
1
0
1
1
1
2
1
1
1
2
1
1
0
2
1
1
1
1
1
1
1
2
0
1
1
1
1
0
1
2
1
1
1
1
2
0
0
2
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
0
0
0
0
0
1
1
1
0
1
1
1
0
1
1
1
1
1
0
1
2
1
2
1
1
1
1
1
1
1
1
1
1
2
1
0
0
0
1
2
2
2
0
2
1
1
1
1
2
0
1
2
1
1
2
2
2
1
1
3
1
2
1
2
1
1
1
1
2
2
1
0
2
2
1
2
2
2
1
2
1
2
1
1
1
1
1
2
1
2
1
1
1
0
1
1
1
1
2
2
1
1
0
2
1
1
1
0
2
1
1
1
0
1
0
1
0
1
0
1
2
1
1
0
2
0
2
2
0
0
1
2
2
0
1
1
1
2
1
1
2
2
2
1
1
1
1
0
1
1
1
2
1
1
1
1
2
0
1
2
1
1
2
1
1
1
1
1
0
2
2
2
1
1
0
1
3
2
1
1
1
1
1
0
1
1
2
1
2
1
1
0
1
0
2
0
1
0
1
0
1
1
1
1
0
2
1
2
2
1
0
2
1
0
0
0
1
0
1
1
2
1
1
2
1
1
2
1
1
1
2
2
1
1
1
0
1
1
1
1
0
2
1
0
1
2
1
0
1
1
1
1
1
1
1
0
0
2
0
2
1
0
1
0
1
1
0
1
2
2
0
1
1
1
0
2
1
2
1
1
0
1
2
0
0
2
1
1
1
2
1
0
2
0
2
1
2
1
0
1
1
1
1
4
0
1
1
1
1
1
2
0
1
0
1
1
2
0
1
1
2
1
1
1
1
1
1
0
1
2
1
1
1
1
0
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
0
1
2
1
2
1
1
1
2
1
1
1
1
2
2
1
1
1
1
2
2
1
1
1
1
0
2
2
0
2
0
1
1
1
1
0
0
1
1
1
1
0
1
1
0
1
0
1
1
1
1
2
0
1
1
1
1
2
0
0
0
1
1
1
0
0
1
2
0
2
1
1
0
1
1
0
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
1
0
0
1
3
1
0
0
1
0
1
1
1
1
1
2
2
1
0
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
2
1
2
1
1
2
2
2
1
1
2
0
1
0
1
0
2
1
1
2
0
1
1
1
2
1
2
0
2
2
0
0
2
2
0
1
1
1
1
0
0
0
2
1
1
1
1
1
0
0
1
3
2
1
1
0
2
0
1
1
1
2
2
1
0
1
1
1
1
1
1
2
1
2
2
2
1
1
2
0
2
2
1
1
2
2
1
1
1
1
0
1
1
1
1
1
1
1
0
1
1
2
2
2
1
1
2
0
1
1
1
1
1
3
2
2
1
1
1
2
1
1
3
1
1
1
1
1
1
1
0
0
1
0
0
1
1
1
2
2
1
1
2
1
2
1
1
0
1
2
1
0
2
1
1
2
2
2
2
1
1
1
0
1
0
1
2
1
0
1
2
0
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
4
1
0
2
1
1
2
1
1
1
1
1
1
1
1
0
2
0
0
2
1
1
0
2
1
1
2
0
1
0
1
1
0
2
1
2
1
1
1
1
1
1
1
2
2
1
1
0
1
1
0
2
2
1
2
0
1
2
0
1
1
1
2
1
2
1
1
1
2
2
1
2
0
1
1
2
2
1
1
1
0
1
1
1
1
2
1
1
1
1
1
2
2
2
2
1
1
2
1
1
1
1
2
2
2
1
1
1
2
1
1
2
1
1
1
0
1
1
2
2
0
1
2
1
1
1
1
0
1
2
1
1
0
2
1
0
1
2
1
1
1
2
2
1
0
1
1
2
1
1
1
2
2
2
1
1
0
1
1
2
2
2
1
2
0
0
1
1
0
2
2
0
1
2
1
1
1
1
0
0
1
1
1
1
2
1
1
0
0
2
0
0
2
0
1
1
1
0
3
0
2
1
1
1
2
2
1
0
2
2
1
1
1
2
1
2
1
1
0
1
2
1
2
1
0
1
1
1
0
2
1
0
2
1
1
2
0
1
0
1
1
2
2
1
2
1
1
2
1
1
1
2
1
1
1
1
2
1
0
2
1
4
1
1
0
1
1
1
2
0
1
1
2
1
1
1
0
1
1
0
0
0
2
2
0
2
1
2
1
1
2
1
2
1
1
1
2
1
2
1
1
1
1
0
2
1
1
1
2
2
1
1
1
1
1
1
2
2
1
1
1
1
1
0
0
1
1
0
1
1
1
2
1
0
0
0
1
1
0
0
1
1
1
1
2
1
1
1
2
2
2
2
1
1
0
1
1
2
1
2
0
1
1
0
1
1
2
1
0
1
1
1
1
2
1
1
1
1
0
0
2
1
1
1
2
1
1
2
1
1
2
1
2
1
1
0
1
2
2
1
2
1
2
0
1
1
1
2
0
2
1
2
1
2
1
1
0
1
1
1
2
1
1
1
1
2
1
0
1
1
2
1
2
2
1
0
1
1
2
1
1
1
2
1
2
1
0
1
1
1
1
1
1
1
1
2
1
1
2
2
2
1
2
0
1
0
1
1
1
0
2
1
2
1
2
1
0
2
1
1
1
1
0
1
1
2
1
0
1
2
2
0
0
1
0
2
1
0
1
2
1
1
2
1
0
2
0
1
1
1
1
1
0
1
0
1
1
0
1
1
1
1
1
1
0
1
0
2
0
2
2
1
0
1
1
1
0
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
4
1
1
0
1
1
1
1
1
2
1
2
2
2
0
1
1
0
1
1
1
1
1
1
1
1
1
1
2
2
0
1
1
2
0
1
2
1
2
1
1
1
1
1
1
1
1
1
1
0
2
2
1
1
1
2
1
1
2
0
0
2
1
2
1
0
3
0
1
1
1
0
2
1
1
1
2
1
1
2
2
1
0
1
1
2
2
2
2
2
2
1
0
1
1
2
2
1
1
2
1
2
1
1
2
1
1
1
1
2
1
1
1
0
1
1
0
1
0
1
1
0
0
1
1
2
1
1
2
2
1
1
2
1
1
1
0
1
0
1
2
1
1
2
1
1
1
1
1
0
1
1
1
1
1
1
1
1
0
0
0
0
1
1
1
2
1
1
0
1
1
1
0
0
2
1
2
0
0
1
1
1
1
1
2
1
2
1
1
1
1
2
1
2
0
1
2
2
1
2
1
1
1
1
1
2
1
0
2
1
1
0
1
0
2
1
1
0
1
1
1
1
0
2
3
1
1
2
0
1
2
2
2
2
1
1
0
1
1
1
0
1
1
1
1
0
1
2
1
1
2
0
1
0
0
2
1
0
1
2
1
1
2
0
1
1
1
0
2
1
1
1
2
1
2
2
0
1
0
2
0
1
2
1
1
1
1
1
1
2
2
0
1
1
2
0
1
1
0
1
1
1
1
2
1
1
1
1
1
1
2
1
1
2
0
1
0
2
1
0
2
0
1
4
1
1
1
2
2
2
1
2
0
1
1
2
1
3
1
1
0
2
2
0
0
2
1
2
1
0
1
1
1
1
1
1
1
1
1
1
1
2
2
0
0
1
0
1
1
2
1
2
0
1
1
1
1
0
0
2
2
1
2
1
2
0
1
1
1
1
1
2
1
1
2
1
1
1
2
1
2
1
1
1
1
1
0
0
0
0
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
1
0
1
1
2
1
1
1
1
1
1
1
0
1
1
1
1
1
0
1
1
1
2
0
0
1
0
2
1
2
1
1
1
1
1
1
2
2
1
1
0
1
2
1
1
2
2
1
1
2
0
1
1
1
2
0
2
1
0
1
2
1
1
0
1
0
1
1
1
1
2
2
0
2
1
2
1
2
1
1
0
1
1
0
2
1
1
1
1
1
1
1
2
1
1
0
1
1
2
1
0
0
0
1
0
0
0
2
2
0
1
1
2
1
2
1
0
1
1
0
2
0
2
0
1
2
1
2
2
1
1
1
0
1
1
0
1
0
1
0
2
1
1
1
1
2
1
0
0
0
0
2
1
1
2
1
1
2
0
1
1
2
1
2
0
1
1
2
1
2
1
2
1
1
1
2
0
1
1
1
2
1
1
0
1
1
1
1
1
1
2
1
1
1
1
1
1
0
1
1
0
1
1
1
2
0
0
1
0
1
1
1
1
1
0
1
1
0
2
2
1
0
1
2
1
0
1
1
1
1
1
2
2
2
1
0
1
1
0
1
2
2
1
0
2
1
1
0
2
0
3
2
1
1
2
1
1
2
1
2
0
1
0
0
1
1
2
1
1
1
1
1
1
1
1
2
3
1
1
2
0
1
1
1
1
0
1
1
1
1
1
2
1
2
1
1
1
1
1
0
0
1
1
3
1
1
1
1
1
1
1
1
1
1
0
2
1
1
1
1
1
0
1
1
1
0
2
1
0
1
0
1
1
0
1
1
1
1
0
1
1
3
1
1
2
1
2
0
2
1
1
2
1
1
0
1
1
2
2
1
0
2
1
1
2
1
1
1
2
0
1
2
0
1
0
0
1
2
1
1
1
1
1
1
2
0
1
1
1
1
1
1
1
1
0
1
0
1
1
1
2
1
1
1
1
1
1
1
1
2
2
2
1
2
1
1
0
1
2
1
2
2
1
1
1
2
0
0
1
1
1
1
2
1
0
1
1
2
2
1
2
1
0
2
2
1
1
1
6
1
1
1
1
0
0
2
1
1
1
1
1
1
1
1
1
2
1
2
1
2
0
2
2
1
1
1
1
2
2
1
1
1
1
0
1
1
2
2
1
1
2
0
1
2
0
2
1
1
1
1
0
1
1
2
1
1
0
2
1
1
1
1
1
1
1
2
1
0
2
2
2
0
0
1
2
1
2
0
1
2
2
0
0
1
1
1
1
2
1
2
2
1
2
1
1
1
2
0
2
1
1
1
1
1
1
1
1
0
1
1
2
1
0
1
1
1
1
2
2
0
1
2
1
2
1
2
2
1
1
0
2
0
1
2
1
2
2
1
1
2
1
2
1
4
1
1
1
1
1
0
2
1
1
1
1
1
2
0
1
3
1
1
1
0
0
1
2
1
0
1
1
0
1
1
0
2
2
2
1
0
1
2
1
1
0
1
1
1
1
1
1
2
2
0
0
1
0
1
2
0
2
1
0
1
0
1
1
1
1
1
3
2
1
2
1
1
1
0
2
2
1
1
1
1
2
2
2
2
1
1
2
2
1
1
2
1
2
1
1
0
1
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
0
1
1
2
1
2
0
1
1
1
2
2
1
0
2
2
2
1
2
0
1
1
0
1
1
2
1
1
0
2
2
1
1
2
0
1
1
1
0
1
1
1
0
1
2
1
2
0
1
1
2
0
1
1
2
1
1
1
1
1
2
1
0
0
1
1
1
1
0
2
1
1
0
2
1
1
1
1
1
0
1
1
3
2
0
0
1
2
1
0
1
1
2
1
1
1
1
1
2
1
1
2
2
0
1
1
0
1
1
2
1
1
1
1
1
1
1
1
1
2
0
0
1
2
0
1
1
2
0
2
1
2
1
1
0
1
1
1
1
0
2
0
1
1
0
1
1
1
0
0
1
1
2
0
1
1
1
1
1
1
2
0
1
2
0
1
2
1
1
1
0
2
0
1
1
2
1
1
2
1
1
2
1
0
0
0
3
1
1
1
1
1
2
2
1
1
1
2
2
1
1
2
2
2
2
1
0
1
1
2
2
1
0
1
2
1
1
1
1
1
1
0
1
1
1
2
1
1
1
1
1
1
2
1
2
0
0
1
1
1
1
0
1
1
1
1
1
1
2
0
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
2
0
0
1
1
2
2
1
2
2
2
1
1
2
1
0
1
1
1
2
1
2
0
0
1
1
1
1
2
1
1
1
1
1
1
0
2
2
1
0
1
2
0
2
2
2
1
1
1
2
1
1
1
1
1
2
1
2
1
2
4
1
2
0
1
1
2
2
2
1
1
0
1
0
0
1
2
2
1
1
0
2
1
1
1
1
0
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
2
0
1
2
2
1
1
0
2
1
1
2
1
1
1
1
1
2
2
1
1
2
2
1
1
1
1
1
1
1
2
1
1
0
1
1
0
1
1
1
1
2
1
1
1
1
1
2
1
1
1
0
1
1
1
1
1
2
2
1
1
2
1
0
2
0
1
1
0
1
2
1
0
1
1
2
1
1
2
1
2
2
0
0
0
1
2
2
0
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
0
1
1
1
1
1
2
1
0
3
1
1
2
2
2
1
1
2
2
1
0
1
1
1
2
2
1
1
0
1
1
0
0
1
1
1
1
1
1
1
2
0
2
1
1
1
1
1
1
1
0
2
1
1
1
1
2
1
2
1
1
1
0
1
2
2
2
1
1
2
1
1
2
1
1
1
2
1
1
2
2
0
2
2
1
1
1
0
1
1
1
1
1
0
1
1
1
2
1
0
2
1
2
2
1
0
1
2
0
1
1
1
0
1
0
1
1
1
1
1
1
1
1
0
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
0
2
2
1
1
1
1
1
1
2
0
0
1
1
1
1
1
1
1
2
1
1
0
1
0
1
0
1
2
1
2
1
2
0
1
1
1
2
2
1
1
1
2
2
1
1
0
0
1
2
1
1
0
1
1
1
2
1
1
1
1
1
0
2
2
1
2
1
2
1
1
1
1
1
1
1
0
0
0
1
2
1
1
1
1
1
1
1
0
1
2
2
2
1
1
1
1
2
1
1
1
0
1
1
1
1
2
1
1
1
1
2
0
0
0
1
1
1
0
1
2
1
2
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
0
2
2
0
1
0
2
2
1
0
2
1
2
1
0
1
2
2
2
0
1
1
2
1
0
1
2
1
2
1
1
1
1
1
2
1
0
1
2
0
1
1
0
1
1
0
1
1
2
0
2
0
1
1
0
1
1
2
1
1
0
2
1
2
0
2
2
2
1
1
0
3
1
0
1
1
1
1
2
1
1
0
1
1
2
1
2
0
0
1
1
1
2
2
3
1
1
1
0
1
2
1
1
1
1
2
1
1
2
2
0
0
1
1
0
1
1
1
1
2
1
1
1
2
1
2
2
0
1
2
1
1
0
2
2
1
2
1
1
0
1
1
1
1
1
1
0
1
1
2
0
0
1
1
1
1
1
1
0
1
1
2
2
0
2
1
1
0
1
1
0
1
0
0
2
1
1
2
1
1
2
1
2
1
1
1
0
1
1
1
1
0
1
1
1
1
1
1
0
1
1
2
1
1
1
1
1
1
1
2
0
2
1
1
1
1
1
2
2
2
2
0
1
2
1
1
1
1
2
1
1
0
1
1
1
1
2
1
1
2
2
0
2
3
2
1
1
0
1
1
1
2
1
1
1
1
2
0
1
1
1
1
2
0
1
1
2
1
1
2
1
2
1
1
2
1
1
2
1
1
1
1
1
1
1
2
1
0
1
2
2
2
1
1
2
1
0
1
1
1
1
1
1
1
1
2
1
0
1
0
1
2
1
1
1
3
2
1
0
2
1
1
2
0
1
2
1
2
0
1
2
0
1
1
0
1
1
1
1
3
2
2
2
1
1
2
2
1
2
1
1
1
2
1
1
1
0
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
0
0
2
0
2
1
2
0
1
1
2
1
1
0
0
1
1
1
1
0
2
2
2
1
3
1
2
0
2
1
1
1
1
1
2
1
0
2
2
1
2
1
1
2
1
1
1
1
1
2
0
1
2
0
2
2
2
1
0
2
2
1
1
2
0
2
2
1
1
1
2
2
0
2
1
1
2
1
2
1
1
1
2
1
1
2
1
2
1
2
1
1
1
2
1
1
2
1
1
1
0
1
1
1
1
1
1
1
2
1
1
0
1
1
1
1
2
1
1
0
1
2
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
3
2
2
1
1
0
0
2
1
3
1
1
2
2
1
2
1
0
2
2
1
1
1
1
1
1
2
2
1
1
1
5
1
2
1
1
1
1
1
2
2
2
2
2
5
1
1
0
1
2
3
1
1
1
1
2
1
1
2
1
1
2
2
1
0
1
2
1
1
1
1
2
1
0
1
1
1
1
0
2
2
2
1
1
1
1
1
1
0
0
1
1
1
2
1
1
2
0
1
1
0
1
1
2
2
1
1
1
0
1
1
2
0
1
2
1
1
1
2
1
2
1
1
2
1
2
2
1
1
1
2
1
1
1
1
2
2
0
1
1
1
1
0
2
2
1
0
2
2
1
1
2
1
2
1
2
2
1
1
2
1
1
1
1
1
1
2
1
2
0
0
1
2
1
0
1
1
2
1
1
1
1
1
2
2
1
0
1
1
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
2
1
0
0
1
0
0
1
2
1
0
2
1
2
2
2
1
1
1
2
1
1
1
3
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
0
0
5
2
2
1
0
0
1
2
1
0
2
2
1
1
2
1
1
1
2
1
2
1
2
2
1
1
1
1
0
0
1
0
0
0
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
0
1
1
1
2
1
2
1
4
1
3
1
2
1
1
1
0
1
0
0
1
2
2
2
2
3
1
2
2
1
0
2
1
2
1
1
1
0
0
1
1
1
2
1
1
0
0
1
2
2
2
1
2
1
3
0
0
2
2
1
2
1
2
0
2
2
1
1
2
1
1
2
1
1
0
2
0
2
1
1
1
1
1
1
0
2
1
1
1
1
2
1
1
1
1
2
1
0
0
0
1
1
1
1
1
1
2
1
1
1
1
1
2
2
1
1
1
1
1
0
1
1
1
1
1
1
1
2
0
1
1
0
1
2
2
2
1
1
1
1
1
1
1
1
0
2
2
1
2
1
1
1
0
1
1
1
1
1
0
0
1
1
2
1
1
2
1
2
1
1
2
0
1
2
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
2
2
0
2
1
1
1
1
2
1
2
1
1
1
1
2
1
0
1
2
0
1
1
0
1
1
1
2
0
0
0
1
1
1
2
2
2
1
2
1
1
1
2
1
1
1
0
1
2
2
0
2
1
1
1
2
1
1
1
1
1
1
2
1
0
1
0
2
2
2
1
2
0
0
1
2
1
1
0
0
0
1
1
1
1
1
2
1
0
2
1
1
0
1
1
1
2
1
1
0
2
2
1
0
0
0
1
0
1
0
0
0
2
0
1
2
1
2
1
1
1
1
2
1
0
1
1
2
3
1
1
0
2
2
1
1
1
1
2
1
2
1
1
1
1
0
0
0
1
0
1
2
1
0
1
0
1
1
0
1
1
1
2
2
1
1
1
1
1
2
1
0
0
1
1
0
1
1
2
1
1
0
1
0
2
1
2
2
1
1
0
1
1
1
1
1
1
1
1
1
1
0
1
1
1
2
1
1
1
0
1
1
1
1
2
2
2
1
1
0
1
1
1
0
1
1
1
0
0
1
1
1
2
1
0
1
2
1
2
1
2
1
1
1
2
1
1
0
2
0
2
1
2
0
1
1
1
2
1
1
1
1
1
1
1
0
1
1
1
0
2
1
0
1
1
1
1
0
1
1
2
0
2
1
1
1
1
2
1
1
1
0
1
1
2
1
1
1
1
1
1
1
1
1
1
2
2
1
0
1
1
1
0
2
2
1
1
1
2
2
1
1
0
2
1
1
0
1
1
1
2
2
1
0
1
1
0
1
1
2
1
1
1
1
1
1
1
0
1
1
1
2
0
1
1
1
2
1
1
1
1
1
1
2
0
0
1
1
2
1
0
0
1
1
1
2
2
1
1
1
0
1
2
1
1
2
1
1
1
1
2
0
1
1
1
1
0
2
1
2
1
1
2
2
0
0
1
0
1
2
1
0
1
2
1
1
2
1
2
1
2
1
1
2
1
1
1
1
1
2
2
1
2
2
1
1
2
2
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
0
2
1
1
0
1
1
0
2
2
1
1
1
1
1
1
0
2
0
1
1
1
2
1
0
1
1
1
1
1
0
1
1
2
1
1
1
1
1
1
2
1
1
2
1
1
2
0
1
1
1
1
0
2
1
1
1
0
1
1
1
1
1
1
1
1
0
0
2
1
1
1
1
1
1
2
1
2
4
2
1
2
0
1
1
1
2
1
2
1
1
1
0
1
2
1
1
1
1
2
1
1
1
2
1
2
1
1
1
2
0
0
0
1
1
1
1
2
1
1
1
2
0
2
0
0
0
0
1
1
0
0
2
2
2
1
0
1
3
1
1
1
1
0
1
1
1
1
1
1
2
1
1
2
1
1
0
2
1
1
2
1
0
0
1
1
1
1
0
0
0
1
1
1
1
2
0
2
1
0
2
2
1
2
2
1
1
1
1
2
1
1
2
1
1
1
2
1
1
1
1
0
1
1
0
1
0
0
2
1
1
1
0
0
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
0
2
1
1
2
2
1
1
1
2
1
0
1
1
0
1
2
1
2
2
1
1
1
1
2
1
2
1
1
2
1
1
2
1
1
1
1
1
2
1
1
2
1
2
1
2
2
1
0
1
0
2
1
1
1
2
1
1
2
0
1
1
0
1
0
1
1
1
0
1
1
2
1
1
0
0
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
2
2
1
1
1
1
2
3
1
1
1
1
2
1
1
1
1
2
2
1
2
3
0
1
1
1
1
1
1
0
1
2
0
1
1
0
1
0
1
1
2
0
1
0
1
2
0
1
0
1
2
1
2
1
1
2
1
2
1
0
1
0
1
1
2
1
1
1
2
1
1
1
0
0
1
1
1
1
1
2
0
1
1
1
0
2
1
2
2
2
0
1
1
0
2
2
0
2
1
2
1
2
2
1
1
0
0
1
2
0
2
1
1
1
1
2
1
1
2
2
1
2
2
2
1
1
2
2
0
1
2
1
1
1
0
1
0
1
1
2
2
2
1
0
1
1
1
1
1
1
0
1
1
1
2
1
2
2
0
1
1
0
1
1
0
1
0
1
1
1
0
1
1
1
3
1
0
1
1
0
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
2
1
1
1
0
2
2
1
1
0
1
1
1
3
1
1
1
0
0
1
4
0
1
1
1
1
2
1
0
1
2
0
1
1
0
1
0
0
0
1
2
1
1
1
3
2
2
1
2
1
1
1
1
1
1
1
1
1
0
2
1
1
1
2
0
1
2
1
2
1
1
1
1
2
1
0
1
1
0
0
1
1
1
1
0
3
1
2
1
2
1
1
1
2
0
2
1
2
1
1
2
1
1
0
1
1
1
1
1
2
1
2
2
1
1
2
1
1
1
2
1
1
1
1
1
2
1
2
0
2
1
1
1
1
1
0
1
1
1
1
3
3
2
2
1
0
1
1
3
2
1
0
1
2
1
2
2
1
1
1
1
1
2
1
1
1
2
1
1
2
1
1
0
0
0
1
2
1
0
1
2
2
2
1
1
2
0
1
1
1
1
1
1
0
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
2
0
2
1
1
1
2
1
3
1
1
2
2
1
1
1
1
2
2
0
0
1
1
1
1
2
0
1
0
1
1
1
4
2
1
0
2
1
1
2
1
1
0
1
1
1
1
1
1
1
1
0
0
0
2
1
2
1
1
1
1
1
1
2
1
1
1
0
1
1
2
1
1
1
1
0
0
0
1
1
0
1
1
1
1
2
1
0
2
0
1
0
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
2
1
1
1
0
2
1
1
1
1
1
1
3
1
1
0
2
1
1
1
0
1
0
1
0
1
0
0
2
1
2
1
0
0
1
2
1
1
0
1
2
1
1
1
1
1
0
0
0
2
2
2
1
1
1
2
1
1
1
1
0
1
1
1
0
0
0
0
1
1
2
1
1
1
1
0
2
2
2
1
0
1
0
2
0
1
2
1
1
2
2
1
1
1
0
0
1
0
0
2
1
1
0
0
1
1
2
2
2
2
1
1
0
1
2
1
1
1
0
1
1
2
0
1
1
0
1
0
1
2
1
1
1
1
1
1
2
2
1
0
2
3
1
2
1
2
2
0
1
2
1
0
1
1
2
1
2
1
2
1
1
0
2
1
1
1
1
1
1
2
0
2
2
1
1
1
1
2
1
1
1
2
2
1
2
0
1
1
1
1
0
1
2
2
0
1
2
1
1
1
3
1
2
1
2
2
0
2
1
1
1
1
1
1
1
1
2
1
1
2
0
1
0
1
2
1
0
2
2
1
2
1
1
1
1
2
2
1
1
1
2
1
1
0
1
1
2
1
0
1
1
1
1
1
1
2
1
0
0
1
2
1
1
0
0
1
0
2
2
2
1
0
0
1
2
2
1
2
1
2
0
1
2
1
0
0
1
1
1
0
0
1
1
2
1
1
0
2
1
1
0
1
1
1
1
2
1
1
0
1
2
1
1
1
1
1
4
1
1
1
0
1
1
0
1
2
0
1
1
1
0
1
1
1
1
1
0
1
1
1
1
4
1
2
1
1
2
1
1
2
1
1
1
2
2
2
0
0
0
0
2
1
1
1
1
1
1
0
1
1
2
2
2
3
1
1
1
0
1
1
0
2
1
0
1
1
1
1
1
0
1
1
1
2
0
1
2
1
1
2
2
1
1
1
2
0
2
1
0
1
1
2
0
0
2
1
2
2
1
2
1
2
2
2
1
1
1
1
1
1
1
1
1
1
2
2
0
1
1
1
2
0
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
0
2
1
1
1
1
1
0
2
1
2
1
1
1
1
2
2
2
1
1
1
1
1
2
2
0
1
1
1
1
1
1
2
2
1
1
1
2
1
2
1
1
0
1
1
1
0
1
1
2
2
1
0
1
2
2
2
1
2
2
1
1
1
1
0
1
1
0
2
2
1
0
1
2
1
2
0
1
0
1
0
0
1
2
1
1
0
1
2
2
1
2
1
1
2
2
2
1
1
1
2
1
1
2
2
1
2
1
1
1
1
1
1
0
2
1
0
2
1
2
1
1
1
0
1
0
1
1
1
1
1
2
1
2
1
1
1
1
0
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
2
2
1
1
1
2
1
0
2
1
1
1
2
0
1
1
1
1
2
0
0
1
2
0
2
1
1
1
1
1
1
1
1
0
1
2
1
1
2
0
1
2
1
2
2
1
2
1
2
1
0
1
0
2
1
1
0
2
1
1
2
1
2
1
2
1
1
2
2
1
1
0
1
1
1
1
1
1
1
0
0
1
1
1
2
1
1
1
1
1
1
2
1
0
1
0
1
1
1
1
1
2
1
1
0
2
0
1
1
1
1
0
2
2
1
1
1
2
1
2
1
1
0
1
2
3
2
2
2
1
1
1
1
2
2
0
1
1
1
1
0
1
1
1
1
2
1
1
1
0
1
2
1
1
1
1
1
2
1
2
2
1
1
2
1
0
1
0
1
2
1
1
2
1
1
1
0
0
1
1
0
2
1
1
1
2
2
0
1
2
0
1
1
1
1
1
1
1
1
1
2
2
1
0
1
1
1
1
1
1
2
1
1
0
2
0
1
1
1
1
1
2
1
0
1
1
1
1
1
1
1
2
1
1
0
1
1
1
1
1
1
1
2
1
1
1
0
1
0
1
1
2
1
1
1
1
2
2
1
1
2
1
2
2
0
1
1
0
1
1
1
1
1
2
2
1
1
1
2
2
1
2
1
1
1
0
0
1
0
1
0
0
2
1
1
2
1
1
2
2
0
1
1
1
1
1
0
2
0
2
0
0
1
1
2
1
0
1
1
2
1
0
0
1
1
1
1
1
0
1
2
0
1
0
1
1
1
2
2
1
0
2
1
1
1
1
1
0
1
1
2
1
1
2
1
0
1
1
1
1
1
2
2
2
1
1
1
1
1
1
2
1
2
1
1
1
1
0
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
0
0
2
1
2
2
0
2
1
1
1
1
1
1
1
2
0
1
1
0
1
0
1
1
2
1
1
1
1
1
1
1
1
1
1
0
0
2
2
1
1
0
1
1
1
1
1
1
0
1
1
2
1
0
1
1
2
1
2
1
1
1
2
1
1
1
0
1
1
1
0
2
0
1
2
1
1
1
1
2
2
0
1
1
0
2
3
1
1
2
1
0
1
1
0
0
1
0
1
1
2
2
2
1
0
1
1
1
2
1
2
1
1
1
2
0
0
2
1
1
0
1
0
1
1
1
2
1
2
2
1
1
1
2
1
2
1
1
1
2
1
1
2
1
1
1
1
0
1
2
1
2
1
1
1
0
2
2
1
2
2
1
0
1
1
1
0
0
1
0
2
0
1
1
1
0
1
2
2
1
2
0
1
1
1
1
0
1
2
0
1
2
1
1
2
2
1
1
0
1
2
2
0
1
2
1
0
1
1
2
0
1
1
1
2
1
2
1
1
1
0
0
2
1
1
1
1
1
2
1
1
2
1
1
1
1
1
0
1
1
0
2
1
1
0
1
1
1
1
2
2
1
2
1
1
1
2
0
1
1
0
1
1
0
1
1
0
1
0
2
1
1
1
1
1
2
1
1
1
2
2
2
2
0
1
1
1
1
2
0
2
1
1
1
1
1
1
2
1
1
1
1
1
2
0
1
1
1
2
1
1
2
1
2
1
1
1
0
0
2
1
1
1
1
2
2
1
0
1
1
2
1
1
2
1
1
1
1
1
1
0
1
1
2
1
2
1
1
1
1
1
1
2
2
1
1
1
2
2
1
1
1
1
2
2
2
0
1
0
1
2
1
0
1
2
0
0
1
1
0
2
2
1
1
0
1
1
2
0
1
1
1
1
1
1
1
1
0
2
2
2
0
1
2
0
2
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
1
0
1
2
1
1
2
1
0
2
1
1
2
2
1
1
0
1
1
1
0
1
2
1
1
2
1
0
2
2
1
0
0
1
1
0
1
1
1
2
1
1
2
1
1
1
0
0
1
0
1
1
2
2
1
1
1
1
0
0
2
1
1
1
2
1
0
1
0
2
1
1
1
2
0
1
2
1
1
0
2
1
0
1
1
1
0
1
0
1
1
2
1
2
0
1
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
2
0
1
1
1
1
1
1
1
1
2
0
1
1
2
1
1
1
1
0
0
2
1
2
1
0
2
2
2
1
1
1
1
0
2
0
1
1
1
1
1
1
1
0
1
2
2
1
1
2
1
1
1
1
1
1
0
1
2
1
0
0
1
1
1
1
1
1
1
1
0
1
2
2
0
1
1
1
1
1
1
0
1
1
0
1
2
1
1
1
1
1
1
0
1
2
2
1
2
1
1
1
1
2
2
3
1
1
0
1
2
1
0
2
1
0
2
1
1
1
1
1
1
2
0
1
2
1
2
1
1
2
2
0
1
1
0
1
0
1
2
1
0
2
1
1
1
2
1
0
0
1
2
2
2
1
1
0
1
2
1
1
1
2
2
0
1
2
1
1
1
1
1
0
1
0
1
0
0
1
1
0
1
2
0
2
2
1
1
2
2
1
2
1
1
1
2
1
1
1
3
2
1
1
1
0
1
0
0
3
1
1
1
1
1
0
2
1
1
2
1
1
2
2
0
2
1
1
1
1
0
0
1
0
1
1
1
0
1
1
0
2
2
1
1
2
0
1
1
1
1
1
2
1
1
0
0
1
0
1
1
1
0
2
2
1
2
1
0
1
1
1
1
1
2
2
2
1
1
0
1
1
1
1
0
0
1
1
0
1
1
0
2
1
1
2
2
1
1
2
1
1
1
0
1
1
1
2
1
1
1
1
1
1
1
2
1
0
2
2
1
2
1
4
0
1
1
0
1
0
1
1
1
1
1
2
1
1
2
1
0
1
0
1
1
2
2
1
2
2
1
1
1
1
0
1
1
0
1
1
1
0
2
1
1
2
0
2
1
1
0
2
2
1
1
1
2
6
1
1
2
0
1
1
2
1
1
2
2
0
2
1
1
1
0
1
1
2
1
2
1
0
0
2
1
1
1
1
1
1
1
0
1
1
0
2
1
2
1
1
1
0
1
2
1
2
0
1
2
1
2
1
1
0
1
2
1
1
1
0
3
0
2
1
1
1
1
1
2
0
0
1
1
1
1
1
1
0
2
1
1
2
1
1
2
2
1
2
1
2
1
1
1
1
1
1
0
1
1
2
1
1
1
1
1
1
1
2
0
1
1
2
2
1
1
1
1
1
2
0
2
1
2
0
0
0
2
1
0
2
1
1
2
1
1
2
2
1
1
1
0
1
1
2
1
1
0
1
2
2
2
0
1
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
2
1
2
1
2
1
0
1
1
1
1
1
1
0
1
1
1
1
1
2
2
1
2
1
1
0
0
2
1
0
1
1
1
1
1
1
1
2
1
2
1
0
1
2
1
1
1
1
1
2
0
1
1
0
1
2
2
2
0
1
0
1
0
1
1
1
2
2
1
1
0
0
1
1
1
1
1
2
2
1
1
2
1
2
1
2
0
1
0
1
1
0
1
1
1
1
2
0
2
1
1
2
2
1
1
1
1
1
2
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
2
2
1
0
1
1
1
2
2
1
1
2
1
0
2
0
1
2
1
2
1
2
2
2
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
0
2
0
1
2
2
1
1
0
1
1
2
2
1
0
1
1
2
2
1
1
2
2
2
1
2
0
1
1
2
2
1
2
2
1
0
1
1
1
0
1
1
0
2
1
2
1
1
1
2
2
1
1
1
1
1
1
1
1
1
0
1
1
1
2
1
0
1
1
2
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
0
1
1
1
1
1
1
1
0
1
1
1
1
1
1
2
1
1
2
2
2
0
1
1
0
0
1
2
1
1
1
2
1
1
1
1
0
1
0
1
0
2
2
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
0
0
1
0
0
1
2
1
1
1
1
1
2
1
1
1
0
0
1
1
2
1
1
1
2
1
1
2
1
1
1
2
1
1
0
1
1
2
1
1
1
1
1
0
2
1
1
1
1
0
1
1
1
1
1
1
2
0
1
2
0
2
1
0
1
2
1
2
1
1
1
2
1
2
0
2
1
1
1
1
0
1
0
0
1
1
1
2
1
2
0
1
1
2
2
2
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
2
0
0
1
0
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
2
0
1
1
3
1
1
1
1
1
1
1
2
0
1
0
1
1
2
2
1
2
2
1
1
1
1
1
1
1
1
2
1
2
1
1
1
2
1
0
2
1
0
2
1
2
2
1
1
2
3
0
1
1
2
1
2
2
1
2
2
1
2
1
1
1
1
2
1
1
1
1
2
2
2
1
1
0
1
1
1
1
0
1
2
2
1
2
1
1
1
0
1
1
1
2
1
2
1
1
1
2
0
1
1
1
1
1
1
2
1
1
1
1
1
2
1
0
1
1
1
1
1
1
0
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
2
2
1
1
1
1
1
1
1
0
2
2
0
2
1
0
1
1
1
1
0
1
3
1
1
2
1
0
0
2
1
0
1
1
1
1
1
2
1
1
2
0
2
1
2
0
1
1
1
1
2
2
1
1
0
2
0
1
1
0
0
2
1
2
2
2
1
1
1
3
1
1
0
0
1
0
0
1
1
0
2
2
1
1
0
1
2
2
2
0
0
2
1
0
0
1
1
1
0
0
1
1
2
0
1
1
1
1
1
1
1
1
0
0
1
0
1
1
1
1
1
1
1
1
2
2
1
1
0
2
2
1
1
1
1
1
1
1
1
1
1
0
2
1
2
0
2
3
1
1
2
2
1
1
1
1
1
0
1
1
1
0
1
1
1
2
1
0
2
1
1
1
2
1
2
2
1
2
1
2
1
1
1
0
1
1
1
2
0
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
2
1
2
1
1
1
1
0
1
0
2
2
1
1
1
0
1
1
1
1
1
1
1
2
2
1
3
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
2
0
2
1
2
1
1
2
0
1
0
1
1
1
1
0
1
1
2
1
2
1
1
0
1
2
1
1
1
1
1
0
2
2
1
1
2
2
1
1
1
1
1
1
1
0
1
1
1
0
0
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
0
1
1
0
1
2
1
1
1
1
1
1
0
1
2
2
1
1
1
1
2
2
1
0
0
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
2
0
0
2
2
2
1
1
2
1
0
1
2
1
1
2
2
1
1
1
2
1
0
1
1
1
2
0
1
2
1
2
2
1
1
2
1
2
1
1
0
1
1
1
1
2
1
1
2
1
1
2
0
2
1
1
2
1
2
7
2
0
1
1
1
1
1
1
1
2
1
1
2
2
1
2
0
1
1
1
0
0
2
2
0
2
1
1
1
1
2
1
0
1
0
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
0
1
2
1
1
2
1
1
1
0
2
0
0
1
1
0
1
1
1
1
2
2
1
2
1
0
1
2
2
1
2
1
1
2
1
2
1
1
0
1
2
1
2
1
1
1
2
1
1
1
2
2
0
0
1
0
2
2
1
2
1
2
1
1
0
1
2
1
1
2
1
1
2
2
2
1
2
2
2
1
2
1
0
1
1
5
1
1
2
1
0
0
1
1
1
0
2
1
1
2
2
2
1
1
0
1
1
0
2
2
2
1
1
0
0
2
0
2
1
1
1
1
1
1
2
0
2
1
2
2
1
2
1
1
1
1
0
1
1
1
1
1
1
0
1
1
1
0
1
0
1
2
1
1
2
1
1
0
1
2
2
1
3
1
1
1
1
1
1
1
1
1
1
0
1
0
1
0
0
1
1
2
0
0
1
2
3
2
2
1
5
1
2
1
1
1
2
1
1
2
0
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
3
2
1
1
1
1
1
1
0
0
1
1
1
2
2
1
1
1
1
1
2
1
1
1
1
2
1
1
2
0
1
0
2
0
2
0
1
1
2
2
0
1
0
1
1
2
2
1
1
1
1
1
0
1
1
1
1
1
1
1
1
0
2
1
2
0
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
0
1
2
1
1
1
1
2
1
0
2
1
0
1
1
1
1
1
1
2
2
1
2
1
1
2
1
2
0
1
1
1
1
0
1
0
1
1
2
1
0
1
1
1
1
2
1
2
1
1
1
1
1
0
1
2
1
1
1
1
1
1
1
2
1
1
2
2
2
2
1
1
1
2
1
0
1
2
2
1
0
2
2
1
0
1
1
0
1
1
1
1
1
2
1
1
2
0
1
1
0
1
0
1
0
1
1
1
1
2
1
1
1
1
1
1
0
2
2
1
1
2
2
1
1
1
2
0
2
1
1
2
0
1
1
0
1
0
1
1
1
0
2
1
1
2
1
0
1
1
2
0
2
1
0
1
5
2
2
1
1
1
1
1
1
2
2
1
1
1
0
1
1
1
1
1
1
2
1
0
1
1
1
1
1
1
0
1
2
0
1
1
1
1
1
2
1
0
1
1
2
1
1
2
1
1
1
0
2
1
2
0
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
0
1
1
0
1
0
0
2
1
1
1
2
0
2
2
0
2
1
2
2
1
1
1
1
2
1
1
2
1
1
2
2
1
0
1
1
1
1
2
2
1
1
1
0
2
1
1
2
1
2
1
2
2
1
1
2
1
0
2
1
3
1
1
2
0
0
0
1
1
2
0
1
2
1
1
1
1
1
0
1
1
2
2
1
2
1
1
1
2
1
2
1
1
1
1
1
2
1
2
2
1
1
1
2
0
0
1
1
1
2
1
1
1
2
1
0
0
0
1
0
1
1
1
2
0
2
0
0
1
0
2
1
0
0
2
1
2
0
1
1
1
0
0
1
0
1
1
2
1
0
2
1
0
1
0
1
1
1
1
2
0
0
1
5
1
2
0
3
2
1
2
1
2
1
1
2
1
2
1
0
1
0
1
1
1
2
1
2
2
1
1
1
1
0
1
0
1
1
0
0
1
1
1
1
1
0
1
2
0
1
0
2
1
1
1
1
1
2
2
1
2
1
1
2
1
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
0
0
0
2
1
1
1
1
0
1
1
2
2
1
1
1
1
1
1
1
1
1
1
2
0
0
1
1
4
1
1
2
1
2
2
1
0
2
2
1
1
2
0
1
2
1
1
1
1
0
1
1
2
1
1
1
1
4
2
1
1
0
1
1
0
2
2
1
0
1
1
1
1
1
1
1
0
0
0
1
2
2
1
2
1
1
0
1
2
2
1
1
2
2
1
2
1
1
2
1
2
0
1
1
2
2
1
1
1
1
0
1
1
2
1
1
2
1
1
1
0
1
2
1
0
1
1
1
1
2
1
1
1
2
0
1
2
0
2
2
2
1
1
1
1
1
1
1
1
1
0
0
1
2
0
2
0
2
2
2
1
1
1
2
1
2
1
1
1
2
1
1
1
2
1
1
1
2
0
1
1
2
1
1
1
1
1
1
2
1
0
1
0
1
0
1
1
1
1
0
0
1
2
1
2
1
1
1
1
1
1
2
2
2
1
2
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
2
1
1
2
1
1
1
1
0
1
1
0
2
0
1
1
1
1
1
1
1
1
2
1
1
2
0
2
1
1
2
1
1
1
1
0
2
1
1
2
2
1
1
1
0
2
0
1
1
1
1
1
2
0
1
1
1
1
1
2
2
2
1
1
0
0
1
1
2
1
1
1
1
0
0
1
2
1
1
0
1
1
1
2
2
1
2
1
1
1
1
2
0
1
1
1
1
0
1
1
1
2
2
1
0
1
0
2
0
1
1
2
2
0
1
1
2
1
2
1
2
2
1
1
1
1
0
1
1
1
0
1
1
1
1
1
0
1
2
1
1
1
0
0
1
1
1
1
1
1
0
1
1
0
1
1
2
2
1
2
2
0
0
1
1
2
1
2
2
0
1
1
2
1
1
1
1
1
0
1
1
2
1
2
1
0
1
1
1
1
1
1
2
2
2
1
1
0
1
1
2
2
1
1
0
0
1
2
1
1
1
1
1
1
1
2
2
2
0
1
1
1
1
1
1
0
2
1
1
1
2
0
2
2
1
2
1
1
1
1
2
1
1
1
1
2
1
0
1
1
0
0
2
1
0
2
1
1
1
1
1
1
2
1
1
1
2
1
0
1
1
1
2
1
0
2
1
0
1
1
2
1
2
1
1
1
0
1
1
1
2
1
1
1
1
1
1
2
1
0
1
1
1
2
1
0
1
1
0
2
1
1
1
0
1
1
1
1
1
1
2
2
1
1
2
1
1
1
2
1
1
2
1
1
2
1
1
1
0
1
1
1
0
1
1
0
1
1
0
1
2
2
2
2
1
2
1
1
2
1
2
1
1
1
2
0
0
1
1
1
1
1
2
1
0
1
0
1
2
0
2
2
0
2
2
0
1
0
2
2
1
1
0
2
1
1
1
0
0
1
1
1
1
2
2
1
2
1
1
1
1
0
1
1
1
3
1
1
1
1
0
1
2
1
1
1
1
1
2
1
2
2
2
1
1
0
1
1
1
0
1
1
1
1
1
2
2
1
1
0
1
1
1
1
1
1
1
1
1
1
2
1
1
0
1
2
1
0
0
1
0
2
0
0
1
1
2
1
0
1
1
1
0
2
1
2
1
2
1
1
0
1
0
0
2
1
1
1
1
1
2
0
2
0
1
1
1
0
0
0
1
0
1
1
2
1
1
1
0
0
1
0
2
0
2
2
1
1
1
1
2
1
2
1
0
1
1
0
1
1
1
1
0
2
1
1
1
1
2
1
1
2
1
0
1
1
2
1
1
1
1
1
0
1
0
1
0
1
2
1
1
1
1
1
2
1
2
0
2
1
1
1
1
1
1
1
2
0
1
1
1
1
2
1
1
1
1
2
1
1
2
1
2
1
2
1
1
0
1
3
2
1
1
1
0
0
0
0
1
2
2
0
2
2
1
1
1
2
2
2
2
1
2
2
2
1
1
2
0
1
1
1
0
1
1
1
2
2
2
1
0
2
2
1
1
1
0
1
2
1
0
0
0
1
1
1
1
2
1
2
0
1
1
1
2
1
1
0
2
2
1
0
2
2
2
1
1
1
1
0
1
1
1
1
0
1
1
0
2
0
1
1
1
1
1
1
0
0
0
0
0
2
1
0
1
2
0
1
1
1
0
1
1
0
1
2
1
2
0
0
1
1
1
1
2
1
2
0
1
1
1
1
2
1
1
0
1
1
2
1
2
0
2
1
0
2
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
2
0
2
0
2
1
1
1
0
2
1
1
0
0
1
0
1
1
2
2
2
1
0
0
1
0
2
0
2
0
2
2
2
0
0
1
1
1
1
1
1
1
2
1
2
1
1
0
1
1
2
0
1
1
1
1
0
1
0
0
1
2
1
0
1
1
1
1
2
1
1
1
1
1
2
0
1
1
0
1
0
2
1
1
1
1
1
2
2
0
2
2
1
0
1
2
1
1
1
0
1
2
0
2
2
2
2
1
2
4
1
1
2
1
1
1
1
2
1
1
1
2
1
1
2
1
1
2
1
1
0
1
1
1
0
0
2
1
1
2
0
0
1
2
1
1
0
1
2
1
1
3
2
1
1
1
0
0
0
1
1
1
1
1
0
1
1
1
2
1
1
0
1
0
2
1
1
0
2
1
2
1
1
0
1
0
1
2
2
1
1
1
0
0
1
1
1
1
1
0
2
2
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
2
1
1
1
1
1
1
1
2
2
2
2
0
1
0
1
1
0
2
1
1
1
0
1
0
0
1
1
1
2
1
2
2
1
1
1
2
0
2
2
1
2
1
1
1
1
2
1
2
1
1
2
2
1
1
1
1
1
1
2
0
1
1
0
1
1
1
0
1
1
1
1
2
0
2
1
1
0
1
2
1
2
1
2
2
0
0
1
0
1
1
1
2
1
1
1
1
1
0
1
1
1
2
1
1
2
1
3
1
1
1
1
1
1
0
2
1
1
1
1
1
1
0
0
2
2
1
1
2
1
1
1
2
1
1
1
1
1
2
0
0
1
1
2
0
2
0
1
2
1
1
1
0
1
2
2
1
1
1
1
1
1
2
2
1
1
2
2
2
1
0
1
1
1
1
2
1
1
1
2
1
2
2
2
2
0
2
1
1
1
1
2
0
1
0
1
1
0
0
1
2
1
1
2
1
1
0
1
2
1
1
0
0
1
1
1
1
1
2
0
2
2
2
0
1
2
0
1
1
0
1
1
1
1
1
1
0
0
0
1
1
1
1
2
2
1
2
1
2
1
1
1
1
0
0
1
1
1
1
3
1
1
2
1
1
1
1
1
2
2
2
2
2
1
1
2
1
1
1
0
2
1
2
0
2
2
1
1
0
0
1
0
1
1
0
0
1
1
2
1
2
0
1
1
1
1
1
2
2
2
2
1
2
2
1
2
0
0
1
1
2
1
1
1
1
1
1
1
1
1
0
1
1
1
1
2
2
2
0
0
0
0
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
0
1
1
2
2
0
1
1
0
1
1
1
1
1
1
1
2
1
1
2
2
2
0
0
4
2
0
1
1
0
1
1
1
1
0
1
1
1
1
1
2
1
1
1
1
1
0
1
1
0
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
0
1
2
1
1
1
1
1
1
1
1
2
2
1
0
0
1
1
2
2
2
1
2
1
0
2
1
2
2
1
2
1
1
1
2
0
2
0
1
2
1
1
1
2
1
1
2
2
1
3
1
0
1
1
1
1
1
2
2
2
1
1
1
2
2
1
0
1
1
1
1
2
2
0
2
1
1
0
1
1
1
1
0
2
1
2
0
1
1
1
1
1
1
1
1
0
1
1
2
0
2
1
1
1
1
1
1
0
1
1
0
2
1
2
1
1
0
1
1
1
2
2
2
2
1
2
1
1
2
0
1
1
2
1
2
1
2
2
0
1
3
0
1
1
1
2
1
1
2
1
2
1
2
1
1
1
1
1
2
2
1
2
1
1
1
0
2
0
2
2
1
2
1
2
2
0
1
1
1
1
1
1
1
2
1
1
1
1
0
1
1
2
1
2
1
1
2
1
2
1
1
1
0
0
1
1
1
1
2
1
1
2
1
1
1
1
1
2
2
1
1
2
1
0
1
2
1
1
0
1
1
1
1
1
0
0
2
0
1
0
2
2
1
2
1
1
2
1
1
1
1
1
1
0
1
1
0
0
0
2
1
1
0
2
0
1
2
1
0
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
1
2
1
1
1
2
0
0
2
1
2
1
2
1
2
1
0
1
1
1
1
1
0
0
1
1
1
2
0
1
1
1
0
0
1
2
2
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
3
1
2
1
1
1
1
1
1
2
4
1
1
1
2
0
2
2
2
2
1
0
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
0
1
2
0
1
1
1
1
1
2
2
2
1
2
1
1
2
1
2
1
1
1
1
0
2
1
0
1
2
2
1
1
2
1
0
1
1
1
0
1
1
1
2
1
2
0
1
2
0
1
0
1
1
2
1
1
1
2
2
1
2
2
1
4
2
0
2
1
1
2
1
1
0
1
0
1
1
1
1
1
1
0
0
1
1
1
1
1
0
1
0
1
1
1
1
1
1
1
1
2
2
1
1
2
1
2
2
0
1
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
2
1
2
1
2
2
1
1
1
0
0
1
1
2
1
1
2
1
2
1
1
1
1
2
2
1
1
2
0
1
1
1
1
2
0
1
0
0
1
0
1
1
1
1
2
0
0
2
0
0
2
1
1
1
2
2
2
1
2
1
1
1
2
1
2
1
2
2
2
0
1
2
1
0
1
1
4
1
2
2
1
1
2
1
1
0
1
1
2
3
1
0
0
2
3
2
2
1
0
1
1
0
1
1
0
1
0
2
0
0
0
1
1
2
0
1
2
1
1
1
0
2
1
0
1
1
1
1
1
2
1
3
1
1
0
1
1
0
1
1
1
2
1
0
2
1
1
2
0
1
1
2
2
1
1
1
1
0
1
1
1
1
1
1
1
1
1
2
1
1
1
0
1
1
2
2
1
1
1
2
0
2
1
2
1
1
2
1
1
2
1
1
1
0
1
2
1
1
1
2
0
1
1
0
1
1
1
0
1
0
1
2
1
1
1
1
2
0
1
1
1
1
1
1
1
2
1
1
2
0
2
1
1
1
2
1
0
1
2
1
1
2
2
1
0
1
2
2
2
2
2
0
2
0
2
0
1
2
2
1
0
2
1
2
1
1
0
1
1
1
1
1
2
0
2
0
2
1
1
1
1
1
0
2
1
1
1
2
1
1
2
2
1
1
1
0
1
2
1
1
1
0
2
1
2
0
1
1
1
0
2
1
1
1
1
1
1
2
1
2
1
2
2
0
2
1
2
1
0
0
2
1
1
1
1
2
2
1
1
2
1
0
1
1
2
1
1
1
1
1
1
1
2
0
1
2
1
2
1
1
1
1
2
1
2
2
2
2
0
2
1
0
0
1
1
1
1
1
0
1
0
2
1
1
1
1
1
1
0
1
0
2
1
2
2
2
0
2
1
1
1
1
0
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
1
0
2
1
0
1
2
2
1
1
0
2
2
2
1
1
1
1
2
1
1
0
2
1
1
1
1
1
2
1
2
0
1
1
0
1
0
2
2
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
0
2
0
1
1
2
1
1
0
0
1
1
2
1
1
0
1
1
1
1
2
1
2
0
2
1
1
1
1
1
0
1
1
1
1
1
1
1
0
0
1
1
1
1
2
1
1
2
2
1
0
1
0
1
0
1
1
1
1
0
1
1
1
1
2
1
2
1
0
2
0
1
1
0
1
1
0
1
0
1
1
1
1
1
1
1
1
1
3
0
1
0
0
1
1
2
0
0
0
1
1
2
1
2
1
1
1
1
1
2
1
1
1
1
0
1
1
1
1
2
1
0
2
1
2
1
1
1
1
1
1
1
2
1
0
1
0
1
1
2
0
1
0
1
2
1
1
0
1
0
1
1
1
1
1
0
2
1
0
1
1
3
1
2
1
1
1
1
0
1
1
2
2
0
1
2
1
0
1
0
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
1
2
1
1
1
1
1
0
1
0
1
1
1
1
2
1
1
1
1
2
2
0
1
1
0
0
1
1
1
2
1
2
2
1
2
1
1
2
2
1
2
2
2
1
2
1
1
2
1
2
1
2
1
2
1
1
0
1
2
1
0
1
1
2
2
5
1
2
2
0
1
1
2
2
1
1
1
2
0
0
2
2
2
1
1
2
1
3
2
2
1
1
2
1
2
1
3
1
2
2
0
0
2
1
1
1
1
2
1
1
1
1
3
0
0
0
1
2
0
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
0
2
0
1
2
1
3
1
0
1
2
2
0
2
0
1
1
2
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
0
0
2
1
1
1
2
0
1
0
2
0
0
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
0
1
1
0
1
1
2
1
0
1
1
2
2
0
1
1
2
1
1
1
1
1
2
2
2
0
1
1
2
1
1
2
1
1
1
1
1
0
1
0
1
1
0
2
1
1
0
1
0
1
2
1
1
0
0
1
2
2
1
1
1
1
1
1
2
0
1
1
1
1
1
0
2
2
1
1
1
1
1
2
0
1
1
0
0
1
1
2
2
2
1
1
1
2
1
2
2
0
2
2
0
1
1
0
1
2
2
0
1
2
1
0
1
2
0
1
1
1
1
0
0
1
2
0
2
1
1
0
1
2
2
2
1
1
1
1
1
0
2
2
1
2
0
0
1
2
2
1
1
0
1
1
2
1
0
0
2
0
0
1
1
0
2
1
1
1
2
1
1
2
0
1
1
1
2
0
1
1
1
1
1
2
1
1
2
0
1
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
2
2
1
1
1
2
1
1
1
1
1
0
0
1
1
1
1
1
2
1
1
0
1
1
1
2
1
1
2
0
0
1
1
1
1
2
1
0
2
2
2
1
0
1
2
1
2
0
1
0
1
0
2
2
0
1
1
1
1
1
0
0
1
3
1
1
3
2
0
0
0
1
2
1
1
1
4
2
1
0
1
1
0
1
1
0
0
2
1
1
1
0
1
1
1
1
2
1
0
0
1
1
1
0
0
1
1
1
2
2
1
1
1
1
1
1
1
0
0
2
2
2
1
0
1
1
0
1
0
2
2
1
2
2
1
0
2
1
2
1
1
0
0
1
1
0
2
1
1
1
1
2
1
2
1
2
1
0
1
7
1
1
1
1
2
1
2
1
2
0
1
1
1
1
0
1
1
2
1
1
1
1
1
1
4
1
0
1
1
1
1
2
0
2
0
1
2
2
0
1
1
1
2
1
0
1
1
1
1
1
2
2
0
0
1
1
0
1
1
1
1
2
1
1
1
2
2
2
1
1
1
1
1
1
1
2
1
1
0
0
1
0
1
2
1
1
1
1
1
1
1
1
1
2
1
0
1
1
1
1
1
1
1
1
1
0
0
1
2
1
2
1
1
1
2
1
1
0
1
1
1
1
2
0
1
1
1
1
1
1
1
2
1
2
1
1
1
2
1
1
2
1
1
0
1
1
1
1
2
1
1
0
1
2
2
1
1
1
2
2
1
1
1
2
1
1
1
0
0
2
1
2
1
1
1
1
1
0
2
1
2
1
1
0
2
0
2
1
2
1
1
1
1
2
1
1
1
1
2
0
1
1
2
1
1
1
1
2
0
1
1
1
1
2
0
1
1
1
2
1
2
1
2
2
4
1
1
1
1
0
1
1
1
1
1
3
1
1
1
2
1
0
0
0
2
1
1
1
1
2
2
1
1
2
1
1
0
0
1
0
1
1
1
2
2
2
2
1
1
1
1
1
1
2
2
1
1
1
1
2
2
1
2
1
2
1
0
1
1
1
1
0
1
1
0
1
2
1
2
1
2
0
2
2
2
1
1
1
1
1
2
2
1
1
4
1
1
1
2
0
1
0
0
0
1
1
1
1
1
1
1
1
2
0
0
1
2
1
1
2
1
1
1
0
1
1
1
2
2
1
2
2
1
2
1
1
1
1
0
1
2
1
1
2
1
0
2
0
1
1
2
0
2
1
1
1
1
1
2
1
1
2
2
2
2
1
1
1
2
1
1
2
1
1
1
1
1
0
1
1
0
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
0
0
1
2
0
1
0
2
1
1
0
1
3
1
1
0
0
1
1
1
0
1
0
0
1
0
1
1
1
1
0
1
1
2
1
1
0
1
1
1
0
0
1
0
1
2
0
0
1
1
0
1
1
1
0
1
1
1
1
1
0
2
1
1
1
1
1
2
1
1
1
2
1
1
1
3
2
0
1
0
1
1
2
1
0
0
1
2
1
1
1
0
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
2
0
1
1
1
1
1
1
2
0
2
1
1
2
1
1
2
1
2
1
2
1
1
1
3
1
1
1
1
1
1
1
2
1
1
2
1
1
2
1
2
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
0
2
0
1
0
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
2
1
1
0
1
0
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
1
1
1
0
1
1
1
1
1
1
0
0
1
0
0
1
1
1
2
2
1
2
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
0
1
1
1
1
1
0
0
2
1
1
2
2
1
1
1
0
0
2
1
1
1
1
1
0
1
0
0
1
1
1
1
1
1
2
2
0
2
2
2
1
0
2
1
0
2
1
1
2
1
1
1
1
0
1
1
0
1
2
1
1
0
1
1
1
0
2
2
2
1
0
1
2
1
1
1
1
1
2
2
1
1
2
1
1
1
1
3
2
1
1
1
2
1
1
1
2
1
2
2
2
2
1
1
0
2
2
1
1
1
1
1
2
1
2
1
1
2
1
1
0
2
1
0
1
1
2
1
1
1
1
2
2
1
1
1
0
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
0
1
2
1
0
0
1
2
1
1
1
1
1
2
2
0
1
1
1
0
1
1
1
1
1
1
2
2
1
1
1
1
2
0
1
1
1
2
1
1
3
2
2
1
2
1
1
1
2
1
1
2
1
1
1
1
2
2
1
1
0
1
2
0
2
1
2
1
0
1
2
1
1
1
1
1
1
2
1
2
1
2
2
0
0
1
2
1
1
1
0
0
2
2
0
0
2
0
0
1
1
1
2
2
1
2
0
0
1
0
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
3
1
1
1
2
1
2
1
2
1
1
1
1
0
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
0
1
0
1
0
1
1
1
1
1
1
1
1
2
1
2
0
1
1
2
1
1
1
6
1
1
1
0
1
0
1
0
2
0
0
0
1
1
1
0
0
1
2
1
1
0
2
0
1
1
1
1
0
1
1
0
2
1
1
2
1
2
0
2
2
2
1
1
2
1
0
1
1
0
1
1
0
1
1
0
2
2
0
1
1
1
1
1
1
1
2
0
1
2
2
1
1
1
1
1
0
1
0
1
1
1
1
1
1
1
1
1
0
2
0
0
1
2
3
1
1
1
1
1
0
2
1
0
1
1
2
1
0
1
1
2
1
1
1
1
2
1
0
0
1
1
1
0
2
1
1
1
1
1
1
1
2
2
1
0
1
0
0
1
1
0
0
0
1
1
2
2
1
0
1
1
1
2
1
2
1
0
2
0
1
1
1
2
1
2
1
1
2
0
0
1
2
1
1
2
0
1
2
1
2
2
1
1
1
0
1
1
2
1
2
0
2
2
2
1
2
0
1
1
1
2
1
1
1
2
1
1
1
2
1
0
0
1
1
2
1
1
1
1
2
2
1
1
1
0
1
1
1
0
1
1
1
1
1
2
2
1
1
2
2
0
2
1
0
1
4
1
1
0
1
1
1
1
1
1
1
1
1
1
1
0
1
1
0
1
0
1
0
1
1
2
0
1
1
2
1
1
1
0
1
1
1
0
1
1
1
1
1
1
0
1
2
1
2
1
1
0
2
2
2
2
2
2
2
1
1
2
1
1
1
0
1
1
0
1
2
1
1
0
1
1
0
1
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
1
2
1
1
2
1
1
1
1
2
0
1
2
0
2
0
1
1
0
1
2
0
0
2
1
1
1
1
1
2
0
1
2
1
1
1
2
1
0
1
1
1
2
1
1
1
1
1
2
0
1
0
1
1
1
1
2
2
2
1
1
1
2
1
1
1
1
2
1
0
1
2
2
1
2
0
1
1
1
1
1
1
1
2
1
2
1
1
1
1
0
1
1
1
2
1
0
2
1
2
2
2
1
0
0
1
2
1
1
2
0
2
2
0
2
2
1
2
1
1
0
1
1
2
1
0
1
1
1
2
1
0
2
2
0
1
2
2
1
2
0
0
1
1
1
1
2
1
1
1
1
1
1
2
0
2
0
2
1
1
0
1
0
1
1
1
1
1
1
2
2
1
1
1
1
2
1
1
2
0
2
0
2
1
1
0
0
1
1
1
2
1
0
0
2
1
1
1
0
2
1
1
1
0
2
1
2
1
2
2
1
1
1
1
1
0
1
0
2
1
1
1
1
1
1
1
1
1
2
1
1
2
0
1
2
2
1
1
2
0
2
1
2
1
1
1
1
2
2
1
1
0
1
2
1
1
1
2
1
1
1
1
1
1
1
1
0
1
1
2
2
2
2
2
1
2
2
2
1
1
1
1
1
1
1
1
2
1
1
1
1
2
2
2
0
1
2
1
2
2
1
1
1
2
1
1
1
0
0
0
2
2
1
0
2
1
3
2
0
2
1
2
3
1
0
1
1
1
2
1
1
2
2
2
1
2
1
1
0
1
1
2
1
1
0
2
1
1
1
0
2
1
1
1
1
2
1
2
1
1
0
1
1
1
1
2
1
1
1
1
1
1
1
1
1
3
1
2
2
1
2
1
0
1
1
2
2
1
1
0
0
0
2
2
1
1
2
1
2
1
1
1
1
1
2
1
0
2
0
1
1
1
1
1
0
2
2
1
1
2
1
1
1
1
1
1
1
2
1
0
1
2
0
1
2
1
1
1
0
2
1
1
2
1
2
1
2
1
1
1
2
2
1
2
2
1
1
2
2
1
1
2
1
1
1
1
0
1
1
1
1
1
1
1
1
1
2
1
1
2
2
1
1
1
1
2
1
1
2
1
0
1
1
1
1
1
2
1
1
2
0
1
1
2
1
0
1
1
1
1
1
0
1
0
1
1
2
2
1
1
1
1
2
0
1
1
1
1
1
0
1
0
1
1
2
2
2
1
1
1
1
2
1
2
2
1
1
1
0
1
1
2
1
0
2
1
0
0
2
2
2
2
1
0
0
1
2
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
2
2
0
1
2
1
1
2
0
0
2
0
1
2
1
2
1
2
1
2
1
0
1
0
0
1
0
1
1
1
1
1
0
2
1
1
1
1
1
1
2
2
1
1
2
1
1
1
1
2
1
1
1
0
2
1
0
0
1
2
0
1
1
1
1
2
2
1
1
1
2
2
0
1
1
1
0
2
2
1
2
2
0
1
0
2
1
2
1
1
1
2
1
1
3
2
1
1
1
1
0
1
1
1
2
1
0
1
1
1
1
1
1
1
1
2
2
1
0
1
1
1
1
2
1
2
1
2
1
1
1
1
1
2
1
1
1
1
1
0
2
1
0
1
1
1
2
1
1
2
2
2
0
0
0
2
1
1
1
1
2
2
2
2
1
1
0
1
1
1
2
1
1
0
1
1
1
1
1
0
0
0
1
1
1
2
1
1
1
0
2
1
2
1
1
2
1
2
1
2
1
2
3
1
1
0
1
1
1
0
1
1
0
1
2
1
2
0
2
2
1
2
2
1
1
1
2
0
2
0
2
2
1
0
1
0
1
1
2
2
1
1
1
1
1
1
1
2
2
2
3
1
1
1
2
0
2
1
1
2
1
1
1
1
0
1
1
2
1
2
2
1
0
1
1
0
1
1
0
1
1
1
2
1
2
1
1
1
1
0
0
1
0
2
2
0
1
0
1
1
2
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
0
1
2
0
1
1
1
1
1
2
0
2
1
2
2
1
1
2
2
0
1
2
1
1
2
2
2
0
1
1
1
1
1
1
1
1
1
1
1
0
1
1
2
1
1
1
2
1
0
1
1
1
1
1
1
1
0
0
2
1
1
1
1
2
2
1
1
2
1
2
1
1
1
1
2
1
0
1
1
1
0
3
2
1
2
1
0
1
0
1
1
2
1
1
1
1
1
2
2
1
1
3
0
0
1
1
0
2
0
1
1
2
2
2
1
2
1
0
1
1
1
0
2
2
0
0
1
0
1
0
2
1
2
2
1
1
2
2
1
1
1
1
2
1
1
1
0
1
1
1
2
1
1
1
2
2
1
1
2
2
1
1
0
1
1
1
1
0
1
1
0
0
1
2
0
2
1
2
1
1
1
2
1
2
1
1
2
1
2
0
1
1
1
1
2
1
1
2
0
1
1
1
1
1
2
1
2
1
1
1
1
2
1
0
1
1
1
0
1
0
1
1
1
1
2
1
1
2
2
1
1
1
2
2
1
1
1
1
2
2
1
1
0
0
1
1
2
1
0
2
0
0
1
0
1
0
1
0
0
1
2
1
1
0
1
1
1
0
0
1
2
1
1
0
2
1
1
1
1
2
0
1
2
1
2
1
1
1
1
0
2
1
1
0
2
1
1
2
1
1
1
0
1
1
1
0
2
1
1
1
2
0
1
0
1
1
2
3
1
1
2
1
0
1
0
1
1
1
1
1
0
2
1
1
1
1
1
1
0
2
0
0
0
1
1
0
1
2
2
1
1
1
1
0
1
2
1
2
1
1
1
0
0
1
2
2
1
0
1
1
2
0
1
2
1
2
1
1
0
0
2
1
1
2
1
2
0
2
1
1
1
1
0
2
2
1
1
2
1
0
1
4
1
1
1
1
1
1
1
1
2
0
2
1
1
1
2
1
1
0
1
1
2
0
1
2
1
1
0
1
1
2
1
0
1
0
1
0
1
1
1
1
1
2
2
1
1
0
1
0
2
1
0
2
2
0
2
0
2
2
1
1
1
1
1
1
2
1
1
2
1
0
0
2
0
0
2
2
1
0
2
0
0
1
2
0
2
1
1
2
1
2
1
2
1
2
1
1
1
0
0
0
2
1
0
1
2
1
0
0
2
1
2
1
1
1
2
2
0
1
1
2
1
1
2
1
2
1
1
1
0
1
2
1
1
1
1
2
1
1
1
1
2
1
0
1
2
2
1
2
1
2
1
1
1
1
2
1
1
0
0
2
0
0
1
1
0
2
1
2
2
1
0
2
1
0
0
0
1
1
1
0
1
2
1
0
1
1
1
1
1
1
0
0
2
2
1
0
2
1
2
2
3
0
1
1
1
1
1
0
2
1
2
1
1
2
1
2
1
2
1
1
2
2
2
2
1
2
0
1
2
1
1
0
1
1
0
0
1
1
2
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
1
2
1
0
1
0
1
1
0
2
0
1
1
1
1
1
1
1
2
2
1
2
1
2
0
1
1
1
1
0
0
2
1
2
1
1
1
1
1
2
0
1
0
0
1
2
1
2
1
1
2
0
0
0
1
1
2
2
1
1
0
1
2
0
1
1
0
1
1
1
1
1
1
2
2
1
0
0
2
0
1
2
2
1
1
0
1
1
2
1
1
1
1
1
2
2
0
1
1
2
1
1
1
1
1
0
1
1
1
1
0
1
2
1
1
1
0
1
1
0
1
0
1
1
1
2
2
1
1
1
1
2
1
1
2
1
0
2
1
1
3
1
1
1
1
1
1
2
1
1
1
0
1
0
1
1
1
2
1
1
1
1
0
0
1
2
1
2
1
0
3
1
1
2
1
0
1
2
1
1
1
0
1
2
0
1
1
2
1
0
1
1
0
2
2
1
2
2
1
1
1
0
2
1
0
1
1
1
2
2
0
0
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
0
1
2
1
2
1
1
3
1
2
1
1
2
1
1
2
1
0
1
1
2
0
1
1
1
1
2
1
1
1
1
1
1
1
0
2
2
2
1
1
2
4
2
2
1
1
1
1
1
1
1
0
1
1
2
0
7
0
0
2
1
1
1
0
0
2
1
2
1
1
2
2
2
2
2
2
2
2
1
1
1
1
1
1
1
2
1
1
0
1
1
1
2
0
0
1
1
0
1
2
2
1
0
1
1
1
1
1
2
2
1
0
2
0
1
1
0
1
1
1
1
1
2
2
0
1
2
1
2
1
1
1
2
1
1
2
2
2
1
1
1
1
1
2
2
1
1
0
0
1
1
3
0
1
0
1
1
1
2
1
3
0
1
2
2
2
1
2
2
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
0
0
0
1
1
2
1
1
2
2
2
2
1
1
1
1
0
1
1
2
2
1
2
1
1
2
1
1
1
1
1
2
1
1
1
2
2
1
2
2
1
1
1
1
0
1
1
2
1
1
1
1
0
1
1
1
1
1
1
0
1
0
1
1
1
2
1
1
1
2
1
0
1
1
1
1
1
0
0
2
1
1
1
0
1
1
0
2
0
1
2
1
0
0
1
1
0
2
0
1
1
1
0
1
1
2
1
2
0
1
1
1
1
1
1
1
1
0
1
1
1
2
1
2
2
1
1
2
1
2
1
1
0
2
1
1
2
1
2
1
2
2
0
0
1
0
1
2
1
1
2
1
0
0
0
0
0
1
1
1
0
1
1
1
1
1
2
1
0
1
1
2
1
1
2
1
1
2
2
1
1
0
2
2
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
0
2
1
1
1
0
0
0
1
1
0
2
1
0
0
2
1
2
0
2
1
1
0
0
1
0
2
1
2
2
2
2
1
1
1
1
1
1
1
0
0
0
1
1
1
2
0
1
1
1
1
2
1
2
2
1
1
1
1
1
2
1
2
1
1
2
1
2
2
0
1
1
1
2
1
1
2
1
2
0
2
0
1
2
1
1
2
1
1
1
1
0
0
1
1
0
1
0
1
2
0
0
1
0
0
0
0
1
2
1
2
1
0
1
1
1
1
1
0
1
1
1
1
2
1
1
2
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
2
3
1
2
1
0
0
1
1
2
1
1
1
2
1
2
1
2
1
1
0
1
1
1
0
1
1
0
2
1
1
1
0
0
2
1
1
2
1
2
1
2
1
1
1
1
1
1
1
1
2
2
1
1
2
2
1
2
0
1
1
1
2
0
2
2
1
2
1
1
2
1
1
1
0
0
2
0
1
1
2
1
1
2
1
2
1
1
2
0
1
1
2
1
2
1
1
2
1
2
1
0
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
0
2
1
1
1
0
1
2
0
2
1
1
0
1
1
2
1
1
1
2
0
1
1
1
1
0
2
1
1
0
1
1
0
2
2
1
1
1
2
1
0
1
1
1
0
1
2
1
1
1
1
1
1
0
1
1
1
1
2
1
1
1
1
1
0
0
1
1
0
1
1
1
2
0
1
1
1
1
2
1
2
2
1
0
0
2
2
1
1
0
2
1
1
2
1
2
1
1
0
2
1
1
1
1
1
1
2
1
1
3
1
2
1
1
1
0
1
0
1
1
2
1
1
2
2
0
2
0
1
0
1
2
1
3
1
1
1
1
0
2
2
1
1
1
1
0
1
2
1
1
1
0
0
1
0
1
2
1
0
2
2
1
2
1
0
2
2
2
1
1
2
1
1
1
2
2
1
2
1
1
2
1
2
2
0
2
1
0
1
2
2
0
0
1
1
1
1
1
1
2
1
1
1
1
2
0
1
1
1
1
0
1
1
2
0
1
1
0
1
1
1
0
1
2
2
1
0
1
2
1
1
2
2
2
1
1
1
1
1
0
1
1
2
1
1
1
1
3
1
1
1
1
1
1
2
1
1
2
1
1
1
1
0
1
0
1
1
1
2
1
2
2
2
1
1
2
1
1
1
2
0
1
1
1
1
1
1
2
2
1
0
2
3
1
2
1
1
1
0
0
1
1
1
1
2
1
1
1
1
2
1
2
2
1
2
0
1
1
2
1
0
0
1
1
0
1
1
2
3
1
1
1
0
1
2
2
2
1
1
0
1
0
2
1
2
2
2
1
1
1
1
2
2
1
1
2
1
1
0
0
1
1
1
1
0
1
0
2
1
0
2
0
1
2
2
2
1
1
1
1
2
1
0
2
0
2
1
1
2
1
1
1
2
1
2
1
2
2
1
1
1
0
2
1
1
2
3
1
1
1
0
1
2
0
1
2
2
1
1
1
2
2
0
0
1
1
1
1
2
0
1
1
2
2
1
2
2
0
0
1
1
1
2
1
1
2
1
1
1
2
1
1
1
0
2
1
1
2
1
2
1
2
1
2
1
0
1
1
1
1
2
1
1
2
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
2
2
0
1
1
2
2
1
1
1
1
0
1
2
1
0
1
2
1
1
3
1
1
2
1
1
2
2
2
1
1
0
1
0
1
0
1
1
1
1
1
1
0
1
1
0
2
2
1
1
1
1
0
2
2
1
0
2
1
1
1
2
1
2
1
1
1
2
1
1
2
0
2
2
2
1
2
2
1
1
1
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
0
2
1
2
2
1
1
1
1
1
1
3
0
7
1
0
1
3
1
1
1
1
1
1
2
1
1
2
0
2
1
2
1
2
2
2
2
1
1
1
1
1
0
2
1
2
1
0
1
1
2
1
0
1
1
1
0
1
1
1
1
1
1
1
1
2
1
1
1
0
2
2
2
1
1
0
2
2
1
1
1
1
1
2
1
0
1
1
1
2
1
1
2
0
0
2
1
2
1
1
0
2
2
0
2
1
1
1
2
0
1
1
2
1
2
1
1
1
1
1
0
0
1
1
1
1
1
1
2
2
0
1
1
2
0
1
0
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
2
1
2
2
1
1
1
0
1
1
0
0
1
1
1
1
2
1
0
2
0
0
1
2
1
1
1
1
2
0
2
2
1
1
1
1
1
1
2
2
2
2
1
2
1
2
2
1
2
0
1
0
1
1
1
2
2
1
1
2
0
1
1
0
1
0
1
1
2
1
3
2
0
0
1
1
1
1
1
2
1
1
1
0
2
0
1
1
2
1
0
0
1
1
2
1
1
1
1
0
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
2
1
2
1
1
1
1
0
2
1
2
1
2
2
1
1
1
1
1
1
1
1
0
2
2
1
1
0
1
0
2
1
0
1
1
1
0
2
1
2
2
2
1
1
2
1
2
2
1
1
1
1
1
1
1
0
1
0
0
1
2
1
2
0
2
2
2
0
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
0
1
1
2
0
2
1
1
1
1
1
1
2
1
2
2
2
1
1
1
1
1
0
1
0
1
1
1
1
2
2
2
1
0
1
1
1
2
2
1
2
1
2
1
1
1
2
0
1
2
1
1
1
1
0
2
0
0
0
1
2
1
0
2
2
2
2
1
1
2
0
1
2
1
0
1
1
1
1
1
1
1
2
1
1
1
2
0
1
1
2
2
2
1
1
2
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
0
2
1
1
1
2
0
2
2
1
2
1
1
1
1
1
0
0
1
1
1
1
1
2
2
1
1
1
1
1
1
0
2
2
2
1
1
1
2
0
1
1
1
1
1
1
1
0
1
1
2
2
1
1
2
1
1
1
1
2
0
2
0
1
2
1
1
1
2
2
1
1
1
2
0
2
1
2
0
1
0
2
2
1
1
2
1
1
1
0
1
1
1
1
0
1
0
0
0
2
2
0
1
2
1
1
1
1
1
1
2
2
2
2
1
0
0
2
2
0
0
1
1
1
2
1
0
1
0
1
1
2
1
2
1
2
1
0
2
2
1
1
2
1
1
2
1
2
2
1
2
2
1
2
1
1
1
1
0
1
2
2
1
1
1
2
2
1
2
2
0
1
0
1
1
1
1
0
1
1
1
0
1
0
1
1
1
0
1
1
1
1
1
1
1
0
1
1
2
2
2
0
0
2
1
1
1
1
0
1
1
1
1
1
2
2
1
1
2
2
1
1
2
2
1
2
1
1
2
1
1
2
0
1
1
0
1
1
1
2
1
0
1
1
0
0
1
1
1
0
1
1
1
1
1
1
1
0
1
2
1
1
1
1
2
0
1
1
1
2
1
2
1
1
0
1
1
2
1
1
1
1
2
2
0
2
1
1
2
1
1
2
0
1
2
2
1
0
1
1
0
0
1
1
1
1
1
2
2
1
1
1
0
1
1
0
1
1
1
2
1
1
1
0
1
1
1
2
1
1
0
1
2
1
1
1
2
1
1
2
1
1
1
1
1
2
2
1
2
2
1
1
2
1
2
1
1
1
1
1
0
1
1
1
1
1
1
1
1
2
1
1
1
1
0
1
1
1
1
1
0
1
0
2
0
1
2
1
1
0
2
1
1
1
0
1
2
1
1
2
1
1
3
1
1
1
2
1
0
1
1
1
2
0
0
1
1
1
2
0
1
1
1
2
1
1
1
1
0
1
1
1
1
1
0
0
0
2
2
2
1
1
0
0
0
1
2
1
0
0
0
2
1
1
1
1
1
1
1
1
0
1
1
1
2
1
1
1
1
3
0
2
1
1
1
1
1
1
1
1
2
1
1
1
1
0
1
2
2
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
2
1
0
2
1
1
1
0
1
1
1
0
2
1
1
1
1
1
1
0
1
0
2
1
1
1
2
2
2
1
1
1
1
2
0
1
1
2
2
1
2
1
1
0
1
1
1
1
0
1
2
1
1
1
1
1
1
1
1
1
1
1
0
2
2
1
1
1
2
2
1
1
1
1
2
2
2
0
0
1
1
1
1
3
1
1
2
1
2
1
1
2
1
1
1
3
0
0
0
1
2
1
0
2
0
1
1
2
1
2
1
1
1
1
1
1
1
0
1
1
1
2
1
1
1
2
1
1
2
1
3
1
1
2
1
1
1
1
1
2
1
2
1
1
0
1
2
2
0
2
1
1
0
0
1
1
0
0
0
0
2
1
2
2
1
1
1
1
2
1
1
0
2
1
1
1
1
1
1
2
1
2
1
2
2
1
2
1
1
1
1
1
2
1
1
2
1
1
1
1
2
0
0
1
0
1
2
1
1
1
1
2
1
1
1
1
1
0
2
1
2
1
0
2
1
0
2
0
1
1
1
1
1
1
1
1
2
0
1
2
1
1
1
1
0
1
1
2
1
1
1
2
2
0
1
0
1
1
1
0
0
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
0
1
1
1
2
1
1
1
1
1
1
1
3
2
1
1
2
1
2
1
1
0
1
1
1
0
2
1
1
2
1
2
1
1
2
1
1
1
1
1
1
2
1
1
2
0
2
2
1
1
2
1
1
1
1
1
0
1
1
1
1
1
1
2
2
1
0
0
2
1
2
2
1
1
2
1
1
1
1
1
1
2
0
2
2
0
0
1
1
2
0
1
2
1
1
1
1
2
1
2
1
0
2
1
1
2
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
1
0
2
1
1
1
0
1
1
1
2
1
1
2
2
1
1
1
2
1
1
1
2
1
0
1
0
1
2
2
1
1
1
2
0
1
2
2
1
1
1
0
2
0
2
1
2
0
1
0
1
1
1
2
2
1
1
1
1
1
0
1
1
0
1
1
1
1
1
1
0
1
1
1
1
2
1
2
0
1
0
1
2
1
2
1
1
2
1
0
0
1
1
1
1
1
1
1
0
1
0
1
1
1
0
1
2
0
1
1
1
2
0
1
1
0
1
1
1
0
1
1
1
2
1
4
1
2
1
1
2
1
2
1
1
1
0
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
2
2
1
2
2
1
1
2
1
2
2
1
2
1
2
0
1
1
0
1
1
1
1
3
2
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
0
1
1
0
1
1
1
2
2
2
0
2
1
1
1
0
1
1
2
1
1
1
1
1
1
0
0
2
1
1
1
1
1
1
0
1
0
2
2
1
1
1
0
1
1
1
1
1
1
1
1
1
1
0
0
2
2
0
1
2
0
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
2
2
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
0
1
1
1
1
3
0
1
1
1
1
2
1
1
2
1
1
2
1
1
2
1
2
1
2
1
1
1
0
1
1
1
1
1
1
0
1
0
1
1
1
0
1
2
1
1
2
2
1
2
0
1
0
0
1
1
2
1
1
2
1
1
1
2
0
0
0
1
1
0
2
0
1
1
0
1
0
1
0
1
1
1
2
1
1
0
0
1
2
1
1
1
1
1
2
1
1
2
2
1
1
0
2
2
1
1
1
0
1
1
1
2
1
1
2
1
2
1
1
1
1
2
2
1
0
1
2
2
1
2
2
2
2
2
2
1
1
2
2
1
1
1
2
0
1
0
1
1
1
1
2
0
1
0
1
1
2
2
1
2
1
0
1
1
1
1
1
2
1
0
1
1
0
1
1
1
1
0
2
0
1
1
1
1
1
1
2
0
1
1
1
1
1
0
1
1
1
0
1
0
1
1
1
2
0
2
2
1
1
1
1
2
1
2
1
1
1
0
1
0
1
1
1
1
2
2
1
1
2
1
2
2
0
1
1
4
1
1
1
1
0
1
1
2
0
1
1
1
2
1
0
0
1
1
1
2
1
2
2
1
1
1
2
1
1
1
0
2
1
1
2
1
0
1
2
2
1
1
1
1
2
1
0
2
0
1
2
1
2
1
2
2
0
0
2
1
1
1
1
0
1
1
1
1
1
1
1
0
0
2
0
1
1
2
1
1
1
0
1
2
1
0
1
1
2
0
1
1
2
1
2
0
1
1
1
2
2
2
1
1
1
1
2
1
1
0
2
2
1
1
0
1
2
1
1
0
1
1
1
1
0
1
1
2
0
2
1
1
0
1
1
2
1
1
1
2
1
1
0
2
0
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
3
1
1
2
1
1
0
1
2
1
1
0
1
2
1
2
0
0
1
1
1
1
1
0
1
2
1
1
1
2
2
1
1
1
1
2
0
1
2
2
1
1
0
2
2
1
0
2
2
2
1
1
1
0
0
1
1
2
1
1
1
1
2
1
1
1
2
2
2
1
1
1
0
1
1
1
2
2
1
1
1
0
0
1
0
0
1
1
1
1
1
2
1
2
1
1
2
1
1
0
1
1
1
1
1
1
2
2
1
1
1
1
1
1
0
1
0
1
1
1
1
1
1
1
1
2
1
0
1
0
0
1
0
1
1
1
1
0
1
0
1
1
1
1
2
1
0
0
1
1
1
1
2
1
1
0
1
1
1
2
2
2
1
1
1
1
0
0
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
0
2
1
1
1
2
1
1
2
1
1
1
2
1
0
2
1
1
2
0
2
0
3
2
1
0
1
2
0
1
1
2
0
0
1
2
1
1
0
0
1
1
1
0
1
2
1
1
1
1
2
1
1
2
2
1
2
1
2
2
0
1
1
1
0
1
1
2
1
1
2
1
1
1
1
2
1
1
1
1
1
0
1
0
0
2
0
2
0
1
0
0
1
0
1
0
1
1
0
1
1
1
1
1
1
1
1
2
2
1
2
1
1
2
1
1
3
1
2
2
2
1
1
0
1
1
1
2
1
1
2
1
0
2
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
0
2
2
1
2
1
1
1
0
1
1
1
1
2
2
2
2
1
1
1
1
1
2
0
1
1
1
0
1
2
2
2
2
1
0
2
2
1
1
1
2
1
1
1
1
1
0
1
2
4
1
1
1
1
2
1
2
2
1
1
0
1
2
1
1
1
0
1
0
2
2
1
0
1
0
1
2
0
2
2
1
1
2
1
1
2
1
1
0
1
1
2
0
1
1
1
1
1
1
1
2
2
2
0
1
2
2
2
1
1
0
1
2
2
1
2
1
1
2
0
0
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
0
1
1
1
0
1
1
0
2
0
1
0
2
2
2
1
1
2
2
1
2
2
1
1
1
1
1
2
1
1
0
1
0
1
2
3
2
0
1
1
1
1
1
1
1
1
1
2
1
1
2
2
1
1
0
1
1
1
0
1
0
2
2
1
0
1
1
0
1
1
1
1
1
1
2
1
0
2
1
2
1
1
1
1
1
1
1
1
2
1
1
2
0
1
1
0
1
1
2
1
1
1
2
2
1
1
1
1
1
1
0
1
1
1
0
0
1
1
1
1
1
2
1
1
2
1
1
2
0
2
0
1
1
1
1
2
1
1
1
1
1
1
1
1
1
0
2
1
1
1
1
0
1
1
1
1
1
2
0
2
1
1
0
1
1
1
1
1
1
1
2
1
2
1
1
2
1
2
1
2
1
0
1
1
1
2
1
1
1
2
1
1
1
0
1
1
1
1
1
1
0
2
2
1
2
1
2
0
1
0
1
0
0
0
1
1
1
1
1
2
1
1
0
1
2
0
1
1
1
2
1
1
2
0
1
1
0
1
1
1
0
2
2
2
6
1
1
2
0
1
0
1
1
2
2
1
2
2
1
2
2
1
2
1
2
1
1
2
0
1
1
2
1
0
1
1
1
2
1
1
1
1
1
1
0
2
1
1
2
1
0
1
1
0
1
0
1
1
1
2
2
1
1
0
1
2
2
1
0
1
1
1
2
1
2
2
1
2
1
1
0
3
2
2
1
1
0
0
2
1
1
1
0
1
0
2
1
2
1
1
2
2
2
0
2
2
0
2
1
1
1
2
1
1
0
0
1
1
1
2
0
1
1
1
2
2
0
1
0
1
1
2
1
1
1
2
2
1
0
1
1
1
1
0
1
2
1
1
0
1
0
1
0
2
1
1
1
1
1
1
1
1
1
1
2
2
1
1
0
2
1
0
2
1
1
1
1
2
1
1
0
1
1
1
1
1
1
1
2
1
2
1
1
1
0
2
1
2
1
2
1
1
1
1
1
0
1
1
1
2
1
2
0
1
1
0
1
1
1
1
0
1
0
1
1
1
0
1
1
1
1
1
1
0
2
1
1
1
2
1
0
2
2
1
0
1
1
1
1
1
1
1
1
1
1
0
2
0
2
0
2
1
1
0
0
2
1
1
1
1
0
2
2
3
1
1
1
2
2
2
1
2
1
0
1
2
1
0
2
2
1
1
1
0
1
2
1
1
2
1
1
0
1
1
1
2
1
2
2
0
1
1
2
2
1
1
0
0
1
1
2
1
0
1
2
0
2
1
1
2
2
2
1
1
1
2
2
1
1
0
1
1
2
1
1
2
1
0
1
1
1
2
1
1
1
1
1
1
0
2
1
1
1
2
2
2
1
1
1
0
1
1
1
1
1
1
0
2
1
0
0
1
1
2
0
1
1
1
1
1
2
2
0
1
2
2
1
2
2
2
1
1
2
1
0
1
0
1
0
1
1
2
1
1
1
1
1
1
2
0
1
2
1
2
1
1
2
1
0
1
2
1
1
2
1
0
1
0
2
1
1
1
1
1
1
0
2
0
2
1
2
1
2
0
2
0
0
2
0
1
1
2
0
1
2
2
1
1
1
1
1
2
2
1
1
1
1
0
1
2
0
1
2
1
1
1
1
1
0
1
2
1
3
2
1
1
2
2
2
1
2
1
1
2
2
0
2
1
1
2
2
0
2
1
1
2
1
2
2
1
0
1
1
3
1
2
1
2
1
1
1
1
1
0
1
1
0
1
0
2
1
1
1
1
1
1
1
1
1
0
2
1
1
1
2
0
2
1
1
2
1
1
1
2
1
1
1
0
1
1
1
2
1
2
1
2
0
1
1
2
1
2
2
1
1
1
2
2
2
1
2
2
1
1
1
0
1
0
1
1
2
1
2
1
1
1
0
1
2
1
0
0
1
1
1
1
1
1
1
2
1
1
1
1
1
0
0
2
1
1
2
0
1
2
0
0
1
0
1
0
1
1
0
2
1
1
2
1
0
1
0
1
2
1
2
1
1
1
2
1
0
1
2
0
1
1
1
1
0
1
1
0
1
2
0
0
1
1
1
1
1
1
1
1
1
0
1
1
0
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
0
1
2
1
1
1
2
0
1
1
0
2
2
2
0
2
2
2
1
2
2
0
1
2
1
1
1
1
1
1
1
0
1
1
1
1
0
0
1
2
1
1
2
1
1
1
1
1
1
1
0
2
1
1
1
2
1
1
1
2
0
1
2
1
2
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
0
1
1
1
1
2
2
0
0
2
1
1
2
1
1
1
0
2
2
0
0
1
2
2
1
1
0
1
1
1
0
0
1
1
1
1
0
1
1
1
0
1
1
1
2
1
1
2
2
14
1
1
0
1
0
2
1
2
1
1
0
2
1
2
1
1
0
1
0
0
1
0
1
1
1
2
1
2
2
0
0
2
1
1
1
0
1
1
2
2
1
1
1
1
1
1
1
1
0
1
2
1
0
2
2
2
2
1
2
1
1
1
0
1
2
1
1
0
1
1
1
3
1
1
1
1
1
2
2
1
1
1
1
2
1
0
1
1
2
1
1
1
2
1
1
1
2
1
1
1
2
1
2
2
1
1
1
0
1
1
1
1
0
1
1
1
1
0
2
1
2
1
1
1
0
1
2
1
0
1
1
2
1
1
1
2
2
1
2
1
1
2
3
1
2
2
1
2
0
1
1
2
1
1
0
1
1
1
1
1
1
1
3
1
2
1
1
0
1
1
2
2
1
1
0
1
2
2
1
1
1
2
1
2
2
1
0
1
1
1
1
2
1
1
2
2
1
1
1
2
1
1
0
1
0
2
1
1
0
1
2
1
1
1
1
2
1
1
0
1
1
1
0
1
1
1
1
2
0
1
1
0
2
2
1
2
1
1
1
1
1
2
1
0
1
1
0
1
0
1
1
1
0
1
2
2
1
1
1
0
1
0
1
1
1
1
1
0
0
0
1
2
2
1
2
2
1
1
0
0
1
1
0
1
1
1
2
1
0
1
1
1
1
1
0
2
1
2
1
1
1
1
1
1
1
1
0
2
1
0
1
1
0
2
2
1
1
1
2
1
2
1
1
2
1
1
1
1
1
1
4
2
1
0
1
1
1
1
1
1
1
1
2
0
1
2
2
1
2
0
1
2
1
1
1
1
2
2
1
3
1
2
1
2
1
0
2
1
1
1
2
1
1
0
1
2
1
2
1
0
0
1
1
0
1
1
2
2
1
2
1
3
1
1
2
1
1
1
1
1
1
0
2
2
1
2
1
2
2
1
0
2
2
1
2
1
1
0
2
1
1
1
2
1
1
1
0
1
1
1
1
2
2
2
1
1
0
0
2
1
1
1
1
2
1
1
1
1
1
1
0
2
2
1
1
1
2
1
2
2
1
1
2
1
1
1
2
1
0
1
1
2
1
2
2
1
1
1
1
0
2
1
1
0
1
2
2
1
0
1
0
3
1
0
1
1
2
1
1
2
1
1
1
1
1
2
0
0
1
1
1
1
0
2
1
1
0
2
1
0
1
1
0
1
1
2
1
2
1
2
2
1
1
2
1
0
2
1
0
1
2
2
0
0
0
1
1
2
2
1
2
1
2
1
2
1
2
1
0
1
1
1
2
2
2
0
1
2
1
2
1
1
2
1
0
1
1
1
1
2
2
1
3
1
2
1
1
2
1
1
1
1
1
2
5
2
2
0
2
1
2
2
1
1
0
1
1
1
1
1
1
2
1
0
2
1
0
2
1
1
1
2
0
1
0
2
1
1
1
1
1
1
1
2
2
1
1
0
1
2
1
1
1
2
1
1
1
0
1
0
2
0
1
1
1
1
1
1
1
1
2
2
1
1
1
2
2
0
1
1
1
2
2
1
1
0
2
2
2
2
1
1
1
1
0
1
2
1
0
1
0
2
1
1
1
1
1
0
1
0
1
2
0
1
2
1
1
2
1
1
1
1
2
2
1
1
0
0
2
1
1
1
1
0
1
1
1
1
2
1
1
0
2
1
1
2
1
1
1
0
2
2
1
1
1
0
1
1
1
2
1
2
2
1
2
0
1
2
1
1
1
1
2
1
1
1
2
1
0
0
1
0
1
1
1
0
1
1
1
1
2
1
1
2
1
2
2
1
1
1
0
1
0
1
2
1
1
0
1
0
1
0
1
1
1
1
1
1
2
2
0
1
2
1
1
1
1
1
1
1
0
2
1
3
1
1
2
1
0
1
1
2
2
1
1
1
0
2
1
2
2
1
0
1
1
1
1
2
1
2
1
1
1
1
1
2
1
0
0
2
1
1
2
1
1
1
1
1
1
2
2
1
1
0
1
1
1
0
2
1
1
1
1
1
1
1
0
2
1
2
1
2
1
2
1
1
1
1
1
1
2
0
1
1
2
2
1
2
1
1
1
1
0
2
3
1
1
1
2
1
1
2
1
0
2
1
2
1
0
1
2
1
1
2
0
1
1
1
1
0
2
2
0
2
1
1
0
1
2
1
2
2
0
1
0
2
1
1
1
1
1
1
1
1
2
0
1
1
1
1
1
1
1
2
2
1
0
2
0
2
3
2
1
0
1
1
1
1
1
1
1
2
1
0
2
2
2
0
1
1
1
1
2
2
2
1
1
2
1
1
1
1
2
1
0
1
2
2
1
2
2
2
2
1
1
1
1
2
1
1
1
1
1
1
2
1
0
1
1
2
1
1
1
1
2
1
2
1
0
2
2
1
1
2
1
1
1
1
2
0
1
2
1
1
2
2
1
1
2
0
2
1
1
0
1
1
2
1
1
0
1
2
0
1
1
4
2
0
1
1
1
0
1
1
2
1
1
1
1
1
1
1
2
2
1
2
2
0
1
1
1
1
2
1
1
2
2
1
0
1
1
1
1
2
1
2
1
1
1
2
2
2
0
3
2
1
2
1
1
1
0
1
1
1
1
1
1
1
1
1
2
1
0
1
1
3
1
1
1
1
0
2
1
1
1
2
1
1
0
1
0
0
0
1
1
2
1
1
1
1
1
2
1
1
1
1
2
2
1
1
1
0
1
0
1
1
1
2
2
2
1
1
1
1
2
0
1
1
1
1
1
2
1
1
4
1
2
2
1
1
2
1
1
0
1
1
1
2
1
1
1
1
1
1
2
1
1
2
0
0
2
2
2
0
1
0
0
1
1
1
2
1
1
1
2
1
0
1
1
2
1
0
1
2
2
1
2
2
1
2
1
1
1
0
2
0
2
1
2
2
2
4
1
1
1
1
2
0
2
1
2
0
1
2
1
1
1
2
2
3
1
2
2
1
0
2
1
1
1
2
2
1
1
1
0
1
2
1
1
0
1
2
1
1
1
1
1
1
0
2
2
1
1
1
2
0
1
1
2
1
0
1
1
1
1
0
1
1
2
1
2
0
1
1
1
2
2
1
1
1
1
2
1
0
1
1
1
1
0
1
1
2
0
1
1
1
1
0
2
1
1
2
1
1
1
1
1
1
2
1
2
1
0
0
2
1
2
2
2
2
0
2
2
0
2
1
1
0
1
2
1
0
1
2
0
1
1
1
2
1
1
0
2
1
1
2
1
1
0
1
2
1
1
2
1
2
1
2
1
1
2
1
1
3
1
5
1
1
1
1
1
1
1
1
1
2
0
1
2
1
2
1
1
1
0
1
1
2
1
1
3
1
1
1
1
2
0
1
0
1
1
0
0
1
1
1
1
1
1
2
0
1
1
1
0
2
0
1
1
1
1
1
1
1
1
0
1
1
1
1
1
2
1
1
1
2
1
1
0
1
0
0
1
1
0
1
1
2
1
1
1
2
1
2
1
1
1
2
2
1
2
0
1
1
0
0
1
0
2
1
1
1
0
2
2
1
2
0
1
1
2
2
1
1
1
1
1
2
0
1
1
1
2
1
1
1
1
0
2
2
1
2
0
1
2
1
1
2
0
2
1
2
1
0
0
1
1
1
1
1
1
1
1
1
2
0
1
0
2
2
1
1
0
1
1
2
1
0
0
1
0
2
1
0
1
1
1
1
2
2
0
1
1
2
1
1
1
1
3
1
1
1
1
1
2
1
1
1
2
1
1
1
2
1
1
1
0
1
0
0
1
2
0
1
1
0
1
1
0
1
1
0
2
1
1
1
1
1
1
1
2
2
1
1
0
1
1
3
1
1
1
1
1
2
1
1
1
2
1
2
1
0
1
1
0
1
2
1
1
1
1
2
1
1
2
1
1
0
1
1
2
1
0
0
2
2
2
0
1
1
1
1
1
2
0
1
2
0
1
1
2
1
1
1
1
2
1
2
1
1
0
1
2
1
1
0
1
1
1
0
0
1
1
2
2
1
1
0
0
2
0
1
1
1
1
1
2
2
2
2
1
1
0
0
1
1
2
1
1
1
1
0
1
0
0
1
2
2
1
0
1
1
1
1
0
1
1
1
0
1
1
1
2
2
1
2
2
2
1
1
1
1
1
1
0
1
1
1
1
0
0
1
1
2
1
1
2
1
1
0
0
2
1
1
2
1
1
1
0
1
1
2
1
0
2
0
1
0
0
1
0
1
1
1
2
1
2
1
1
1
1
0
0
2
0
1
0
1
2
1
1
1
0
2
0
0
1
2
1
2
2
1
2
1
2
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
2
1
0
1
2
2
2
2
1
0
0
1
1
1
1
1
1
1
1
3
0
2
1
1
1
1
1
2
1
1
1
1
0
1
2
1
1
2
1
1
1
1
2
1
2
1
1
0
2
0
1
1
2
2
2
2
1
3
1
1
1
1
1
2
2
2
2
2
1
1
1
1
1
2
2
1
1
1
2
0
1
1
2
1
1
1
0
2
1
1
2
2
0
2
2
1
0
2
1
1
1
1
1
1
0
1
2
1
1
2
1
0
2
2
2
1
1
1
0
1
1
0
1
2
1
0
2
2
1
1
1
1
1
1
2
1
2
2
1
1
2
2
1
0
2
1
0
1
1
1
1
1
1
1
1
1
1
0
1
1
0
2
1
2
2
2
2
2
1
2
0
0
1
1
2
1
0
1
0
2
2
0
1
0
0
1
1
2
2
0
1
1
1
1
1
1
0
0
2
2
1
1
1
2
1
1
0
1
1
1
1
2
2
2
0
1
1
1
1
0
1
1
1
1
2
1
0
2
1
2
0
0
2
1
1
2
2
1
1
1
1
1
1
0
1
1
1
1
0
1
1
1
1
0
1
1
0
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
2
0
1
1
1
0
0
1
1
1
0
2
1
1
3
1
1
2
2
1
1
1
1
1
1
0
1
1
2
2
2
2
2
2
1
0
0
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
0
1
1
1
1
1
1
1
0
1
1
1
1
1
1
2
1
1
1
1
2
1
1
0
1
1
1
1
2
1
2
0
0
2
1
0
1
1
2
0
1
1
1
1
1
1
3
1
1
0
1
0
2
2
1
1
1
1
1
2
2
2
1
1
2
1
0
1
1
2
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
0
1
0
1
1
2
2
1
1
1
1
1
2
1
1
0
1
1
1
2
1
1
1
2
2
1
2
1
0
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
0
2
1
2
2
1
1
0
0
2
1
1
1
1
0
2
1
1
1
2
1
1
1
1
0
2
2
1
2
1
1
2
1
1
2
1
0
2
1
1
1
0
1
1
1
1
0
2
2
1
1
1
0
1
1
1
2
1
1
1
1
2
1
1
1
2
1
0
0
1
1
2
1
1
0
2
1
1
2
0
0
2
1
1
2
1
1
1
2
1
1
0
0
0
2
1
2
2
1
1
1
1
1
0
2
1
1
1
2
0
1
1
1
1
1
0
0
0
1
1
2
1
1
1
1
2
1
1
2
2
0
1
1
1
2
1
1
1
1
0
1
1
0
1
1
2
1
1
2
1
2
1
1
0
2
0
0
1
1
1
0
2
1
1
1
2
0
1
0
1
1
1
1
1
2
1
1
0
3
1
1
2
4
1
1
2
0
1
1
0
1
1
1
2
2
1
1
2
1
2
1
0
0
1
1
1
1
0
0
1
2
1
1
2
1
1
2
2
2
1
1
0
1
0
0
2
2
1
1
1
1
2
2
0
0
2
1
0
3
2
2
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
0
1
0
1
1
2
1
2
2
2
2
1
0
0
1
1
0
2
2
1
6
2
1
1
2
2
1
1
1
2
1
1
2
2
1
2
0
2
0
1
1
2
1
1
1
2
1
1
0
2
2
2
2
2
0
2
1
2
0
1
0
1
1
0
2
1
1
0
2
1
1
1
2
2
1
1
2
1
0
1
1
1
2
2
2
1
0
2
1
2
1
1
0
2
1
2
1
1
2
0
1
1
2
0
1
1
1
1
1
0
0
1
1
2
0
1
0
5
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
1
1
0
0
1
1
1
2
1
1
2
1
0
0
0
1
2
0
0
1
2
1
0
2
1
1
0
2
1
1
1
2
1
1
2
1
1
2
0
1
1
1
2
1
1
1
2
1
1
0
2
0
2
2
1
2
2
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
0
0
0
0
1
1
0
1
1
1
2
1
1
1
1
1
0
2
1
1
1
0
1
1
0
2
2
1
2
0
1
2
1
1
2
1
1
2
1
1
2
2
0
1
1
2
1
1
2
2
1
1
1
1
1
1
1
1
1
0
2
1
1
1
1
0
1
1
2
1
0
1
1
1
1
1
1
0
0
1
2
1
0
1
2
1
0
1
1
0
2
2
1
1
0
0
2
2
1
2
0
0
1
1
0
2
0
1
1
1
1
1
1
0
1
1
2
0
0
1
0
1
0
2
1
2
0
2
2
0
2
0
1
1
1
2
0
1
0
2
2
1
1
2
1
1
0
0
1
1
1
1
0
1
1
1
0
0
2
2
1
1
1
1
1
0
1
1
0
1
3
0
0
2
1
1
0
1
1
1
1
1
2
1
1
1
1
1
2
2
1
1
2
2
1
1
2
2
1
1
1
1
2
1
1
1
1
1
2
1
0
1
0
1
0
2
2
2
0
1
1
1
1
1
1
2
2
0
1
1
1
2
1
0
1
1
2
1
2
1
2
1
2
1
2
1
1
2
0
1
1
1
0
0
1
1
1
2
1
0
1
1
0
1
1
2
0
1
1
2
2
0
1
1
0
1
1
1
0
0
2
2
1
1
1
1
2
2
1
1
2
1
2
1
1
1
2
1
1
2
1
2
1
1
1
2
2
1
1
0
1
2
2
1
2
1
0
1
1
3
1
1
0
0
2
1
2
1
1
2
1
0
2
0
1
1
0
1
1
2
1
1
1
0
1
1
0
2
2
1
2
1
1
1
1
1
1
1
1
2
0
1
1
0
1
0
1
1
2
2
1
0
2
1
1
1
1
2
1
1
2
2
2
1
1
1
1
1
1
2
0
2
1
1
2
1
1
0
1
1
1
1
1
0
0
1
0
1
1
1
2
1
2
2
1
2
1
1
2
0
1
1
1
0
0
1
1
2
0
1
1
1
1
1
2
1
1
1
1
2
1
2
1
1
1
2
1
2
2
2
0
0
1
1
1
1
1
1
2
1
1
2
1
1
1
0
0
1
1
1
2
1
1
2
1
0
3
0
1
1
1
1
1
1
0
1
0
1
0
1
2
2
2
2
1
1
2
2
1
0
2
1
1
2
0
2
1
1
2
0
1
1
0
1
1
2
0
1
1
1
1
1
1
1
2
1
1
0
1
1
1
1
1
1
3
1
1
1
1
2
0
1
1
1
1
1
1
1
1
2
2
1
0
1
1
0
1
1
1
2
1
1
0
0
1
1
2
1
2
2
1
1
1
1
1
0
1
1
1
0
2
0
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
2
1
1
0
1
2
2
1
1
2
0
0
1
2
1
2
1
0
0
1
1
1
1
1
1
0
2
1
1
0
1
1
2
2
1
2
1
2
1
1
2
2
1
2
1
0
0
2
1
1
0
1
1
0
1
0
1
1
0
1
2
2
2
1
0
1
1
1
0
1
1
1
1
1
2
1
1
1
0
2
1
0
1
0
1
1
1
1
0
0
1
1
1
1
0
1
2
1
1
1
1
0
0
1
1
2
1
2
2
1
2
2
0
1
1
4
2
0
1
1
0
1
0
2
2
1
2
1
1
1
1
2
2
1
1
2
0
1
2
1
1
1
2
1
1
2
1
1
1
2
2
1
1
1
2
1
1
0
0
1
0
2
1
1
1
1
1
0
1
1
1
0
1
1
1
2
1
1
1
0
0
1
2
1
0
2
1
2
2
2
2
1
1
0
1
1
1
2
1
0
1
2
0
1
1
0
1
1
1
1
2
1
1
1
1
2
0
1
2
1
1
0
1
1
1
0
1
2
2
2
1
1
0
1
1
1
1
2
2
1
1
3
1
2
1
1
1
0
1
1
1
1
2
1
1
1
2
2
1
1
2
0
0
1
0
1
1
1
1
2
0
2
1
1
2
2
2
1
1
0
1
1
1
1
1
1
0
2
1
2
1
0
2
0
1
1
1
1
1
1
1
1
0
1
2
2
1
1
0
1
1
2
2
1
0
2
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
0
1
0
2
2
0
1
1
1
1
2
1
0
2
2
2
2
2
1
2
2
1
1
0
1
1
0
2
2
2
1
1
1
2
1
1
2
2
1
1
1
1
1
0
1
2
1
0
1
1
2
2
0
1
1
1
2
2
2
1
1
1
1
2
2
2
2
1
1
2
1
2
2
2
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
0
1
2
0
1
1
1
2
0
1
1
2
1
2
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
0
1
1
0
1
2
1
0
0
1
1
1
0
0
1
1
1
1
0
0
2
1
0
1
1
1
0
1
2
2
1
1
2
1
1
1
0
2
2
1
2
1
1
2
1
1
0
2
1
1
0
0
1
1
2
1
1
2
1
1
0
1
1
0
0
2
1
1
1
2
1
2
1
1
1
0
2
1
1
2
1
0
1
1
1
2
0
1
2
1
0
1
1
1
0
2
1
1
2
1
0
2
2
0
2
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
1
1
2
2
1
2
1
3
0
1
1
1
2
2
2
1
1
1
0
1
0
2
0
2
2
0
1
1
1
1
1
1
1
1
2
1
1
0
2
1
2
2
1
1
1
1
1
1
1
0
1
0
2
1
1
0
2
2
2
1
1
2
2
1
2
1
1
2
1
2
1
1
0
2
1
2
1
2
1
1
1
2
2
1
0
1
2
2
1
1
2
2
1
1
2
1
1
2
2
0
1
2
1
0
1
0
1
1
1
1
0
1
1
0
2
1
1
1
2
2
0
1
0
1
1
1
1
1
2
1
1
2
2
1
0
1
2
0
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
0
2
1
0
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
0
1
1
1
2
0
2
1
1
1
0
1
2
1
1
1
1
1
1
1
1
2
2
1
2
1
1
0
1
1
0
0
0
2
1
1
1
0
1
1
0
1
2
1
0
2
1
1
1
1
0
2
1
0
1
1
0
1
1
0
1
0
0
2
2
1
2
0
1
2
2
2
0
2
1
1
0
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
0
1
1
1
1
1
1
2
2
1
1
0
1
1
2
1
1
1
1
2
0
1
1
3
1
1
0
1
2
1
1
1
2
1
0
2
2
1
2
1
1
1
1
1
1
0
1
1
1
1
1
1
1
0
1
2
1
1
1
1
1
2
1
1
2
1
2
1
0
1
2
1
1
2
0
1
1
1
2
1
1
1
1
1
2
1
1
0
1
2
1
0
1
0
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
0
1
1
1
1
0
2
1
2
1
1
0
1
0
1
1
2
2
2
1
2
1
2
1
1
1
1
0
1
1
1
1
0
2
1
2
2
1
1
0
1
1
0
1
1
1
2
0
2
1
1
1
2
1
1
1
1
0
1
2
1
1
1
2
2
0
1
1
2
0
1
1
1
1
2
1
1
2
1
0
2
1
2
2
1
0
1
2
0
1
1
0
1
2
1
2
2
1
1
2
1
1
1
1
1
2
1
2
1
2
1
2
2
2
1
1
1
1
0
1
1
1
1
0
2
1
1
0
2
0
2
1
1
1
1
0
1
1
0
1
1
1
0
1
1
1
0
0
0
1
2
0
1
1
1
1
2
0
1
0
1
1
1
1
1
1
1
2
1
2
2
1
1
2
0
0
2
1
1
2
2
1
1
0
1
1
2
2
1
1
1
1
1
1
2
2
0
1
1
1
1
1
1
1
2
1
1
1
1
1
2
0
2
2
1
1
2
0
2
2
0
0
1
1
1
1
1
1
1
1
2
0
1
1
1
2
1
1
2
0
1
1
1
1
1
2
1
2
1
1
1
1
1
1
0
1
1
1
0
1
1
1
1
0
0
1
1
2
0
0
1
1
0
1
2
2
1
0
1
1
1
1
2
0
0
1
1
1
2
1
1
2
1
1
1
1
0
2
2
1
1
1
1
1
1
1
1
2
0
1
1
1
1
1
1
1
1
2
2
1
0
0
1
0
1
1
1
1
3
1
1
1
1
1
1
2
1
2
1
2
0
1
1
1
0
1
1
1
0
2
2
1
2
1
1
3
1
2
1
2
0
1
1
2
2
0
2
2
1
1
1
1
1
1
1
1
1
1
1
1
3
0
1
2
2
0
2
1
1
1
2
0
0
1
1
1
0
1
2
2
1
1
1
1
1
1
1
2
1
2
1
1
0
1
1
1
1
1
1
1
2
2
1
2
1
2
2
1
0
1
1
2
2
2
1
0
1
1
1
1
2
2
1
1
1
1
1
1
1
0
1
0
2
1
1
1
1
1
2
2
2
1
0
1
1
1
1
1
1
2
1
1
2
0
0
1
1
5
1
1
1
2
1
2
2
1
0
1
1
1
1
0
2
2
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
2
2
2
2
1
1
1
1
1
1
2
2
1
0
1
2
2
1
2
2
2
1
2
1
1
1
1
2
0
1
2
1
1
1
1
1
1
1
1
1
0
1
2
0
1
2
1
1
2
1
1
1
2
1
1
0
1
1
2
1
1
1
1
1
2
1
1
2
2
1
1
1
1
0
2
0
1
2
0
1
1
1
1
1
1
1
1
1
0
1
2
1
1
1
1
1
0
1
1
1
1
0
1
2
1
1
1
0
1
1
1
2
0
1
2
1
1
2
2
1
1
1
1
1
2
1
1
1
2
1
1
1
0
1
1
1
1
2
0
1
1
2
0
1
2
1
1
1
1
0
2
2
1
0
1
1
1
0
1
4
2
1
1
2
1
2
1
1
1
1
2
2
2
1
2
1
1
2
3
2
0
1
1
1
1
1
1
1
2
2
1
2
1
2
1
2
1
2
2
1
1
1
1
1
2
1
1
2
1
0
1
1
0
1
1
1
1
1
0
1
0
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
2
1
0
1
1
1
0
1
0
1
1
0
2
0
0
1
1
1
2
1
1
1
1
0
1
1
0
2
0
1
1
1
2
0
0
0
0
1
0
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
0
2
1
1
2
1
0
2
2
2
1
1
1
1
2
2
1
2
1
1
0
1
1
1
1
0
1
2
1
1
2
2
2
1
2
1
1
0
1
1
2
1
0
1
0
1
0
1
2
1
1
1
1
1
1
0
1
0
2
1
0
1
0
1
1
1
1
2
1
0
1
3
2
0
1
2
1
2
1
1
0
1
1
1
0
0
1
1
1
2
0
2
2
2
2
1
1
0
1
0
1
1
1
0
1
1
0
1
1
1
1
2
1
1
1
1
2
1
1
4
0
1
1
1
2
1
0
0
2
0
1
3
1
0
1
1
2
0
2
1
1
1
2
1
2
2
2
1
0
1
2
2
1
1
0
1
1
1
2
1
1
1
0
1
2
2
2
1
1
1
1
2
1
0
1
1
2
2
1
1
2
2
0
2
0
1
2
2
1
0
0
1
1
0
2
2
1
1
1
1
1
1
2
1
1
1
1
1
0
1
0
1
1
2
0
2
1
2
1
0
2
2
0
0
1
1
1
2
2
1
0
3
0
1
1
1
2
1
1
1
1
1
1
1
1
1
1
0
1
1
2
1
0
1
0
0
1
0
2
1
2
0
1
2
1
1
2
1
2
1
1
1
0
1
0
2
1
1
1
1
1
1
0
2
2
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
0
1
1
2
2
1
1
1
2
1
0
1
2
0
1
1
1
1
3
1
1
1
1
2
0
3
1
2
1
1
1
1
1
1
1
1
2
1
2
1
2
1
0
0
0
1
1
1
1
2
2
0
2
1
1
0
1
1
1
0
1
2
1
2
0
0
1
1
1
0
1
1
0
1
1
2
1
2
1
2
2
2
1
1
2
1
1
1
1
1
1
1
0
0
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
2
0
2
1
2
1
1
0
1
1
1
1
0
2
1
1
2
1
2
2
2
1
0
1
1
1
2
2
1
1
1
1
1
1
1
2
2
1
1
2
1
0
1
0
1
0
1
1
1
1
1
1
1
0
2
1
1
1
1
1
1
1
0
2
0
1
1
2
2
1
2
2
1
2
2
1
2
0
1
1
1
1
1
0
0
1
2
1
1
2
1
1
1
2
2
2
2
2
0
1
1
1
2
2
1
2
1
0
2
1
1
1
1
0
1
1
1
2
1
1
1
1
1
1
1
1
0
2
1
1
1
0
1
1
1
0
2
2
1
2
1
2
1
1
2
1
2
1
1
2
1
2
1
1
1
1
1
2
0
1
1
1
1
0
1
0
1
2
0
1
1
1
1
0
1
1
2
2
1
2
1
2
2
2
1
2
2
1
1
1
1
2
1
1
0
2
1
1
0
1
1
2
1
0
2
1
6
1
0
2
1
1
2
2
1
0
1
1
1
2
0
0
1
1
1
0
0
2
1
1
1
1
1
1
2
2
0
1
1
2
1
2
1
1
1
1
2
0
2
2
1
2
1
1
1
2
1
2
1
1
1
1
2
0
1
2
1
0
2
1
0
1
1
2
0
1
2
2
2
1
2
1
2
1
1
1
2
1
1
0
1
2
2
2
0
0
1
0
0
1
1
1
2
0
1
1
1
2
2
2
2
0
1
1
1
2
1
0
0
1
1
2
1
1
2
2
1
0
1
1
1
1
2
0
1
1
0
1
1
2
1
1
1
1
1
0
2
1
1
0
1
0
1
1
1
1
1
1
1
0
1
1
0
1
2
0
2
1
2
1
2
2
1
1
0
1
0
1
1
2
1
1
1
2
1
2
1
1
1
0
1
0
2
1
1
1
0
1
1
1
1
2
1
0
0
1
1
1
2
2
2
2
2
1
1
0
1
2
1
1
1
1
0
1
1
2
1
1
2
1
1
1
2
2
2
1
2
1
2
1
2
1
1
1
1
2
2
2
1
1
1
1
0
1
1
1
2
1
1
2
1
1
1
1
2
1
2
1
2
1
0
2
1
1
1
2
2
2
2
1
2
1
1
0
2
1
0
1
1
1
2
1
1
1
1
2
1
2
1
1
1
1
0
0
1
1
2
2
1
1
1
2
2
2
2
1
1
1
3
1
2
2
2
1
0
1
1
1
1
1
1
1
0
2
1
0
0
2
1
2
2
0
1
2
1
1
1
1
2
1
2
1
1
2
1
1
1
1
1
1
1
2
0
1
1
0
0
0
2
1
0
0
1
2
1
2
0
1
2
1
2
1
1
0
1
0
1
1
1
1
1
0
1
2
1
2
0
1
2
1
2
1
1
2
1
1
2
1
1
1
1
2
1
2
1
0
1
1
2
2
1
1
0
2
0
2
2
2
0
0
1
1
1
0
1
1
1
2
1
1
1
0
1
1
0
1
0
1
2
1
1
1
0
2
0
2
0
2
0
1
1
1
1
2
2
1
1
1
1
1
1
1
2
2
2
1
1
0
2
2
1
2
2
0
1
1
2
1
1
3
1
2
1
2
0
0
1
1
1
1
1
0
2
1
1
1
1
0
0
2
2
1
1
2
0
2
1
1
0
1
0
1
1
2
1
1
0
1
1
2
1
1
0
2
1
2
1
0
1
1
1
2
2
2
0
1
1
1
1
1
0
3
2
1
1
2
2
1
2
2
2
2
1
1
1
1
2
2
2
1
1
1
0
1
0
1
1
0
2
1
1
0
0
1
2
1
1
1
2
0
1
0
1
1
1
1
3
1
1
1
1
1
1
2
1
1
1
1
2
0
2
2
1
1
1
2
1
1
1
1
0
2
2
0
2
2
1
1
0
2
2
2
0
2
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
0
2
0
1
1
2
1
1
2
1
1
2
0
1
1
2
0
0
1
1
1
2
2
1
1
2
1
5
2
1
0
2
1
2
2
2
1
1
2
1
1
1
3
1
1
1
1
1
1
2
0
1
2
1
2
1
1
1
1
1
0
1
1
1
2
1
1
0
2
4
1
2
1
1
2
2
1
1
1
0
1
1
1
2
1
2
2
2
1
2
0
1
1
0
1
1
1
1
1
2
2
0
1
1
0
1
2
1
1
1
0
2
1
1
1
0
0
1
0
0
1
2
1
0
1
1
9
1
0
1
1
1
1
1
1
1
1
1
2
1
0
1
0
1
1
1
0
1
2
1
1
2
1
1
2
1
1
2
0
1
1
1
1
1
0
0
1
0
1
2
2
1
1
1
1
1
1
1
1
1
0
0
2
2
2
0
1
1
2
1
1
2
1
1
2
1
1
2
2
1
1
1
2
2
1
1
2
1
1
1
1
1
1
0
1
1
1
1
2
1
1
1
0
1
1
0
1
1
1
1
1
1
1
0
2
1
2
1
2
1
2
2
1
2
2
2
0
1
0
1
1
1
1
1
1
1
2
1
2
1
1
0
1
1
1
0
1
1
3
1
1
1
1
1
2
1
0
0
1
1
1
2
1
1
2
1
2
2
1
1
0
1
1
1
0
2
1
1
2
1
0
0
2
1
1
1
1
1
0
0
1
2
1
2
1
0
1
1
1
2
0
1
0
2
1
1
1
2
1
1
2
2
0
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
2
0
1
1
0
0
2
1
1
2
2
2
1
1
2
1
2
0
2
1
1
1
2
2
2
1
2
1
1
2
2
2
1
1
0
2
2
2
0
2
1
1
2
1
1
1
1
1
1
0
2
2
2
1
1
1
1
2
1
1
1
1
2
0
1
1
1
1
1
0
1
1
1
1
3
2
1
1
1
1
1
2
2
1
1
2
2
1
2
1
1
1
2
1
1
2
1
1
1
0
0
1
0
1
1
1
1
0
1
2
1
1
2
1
2
2
1
1
2
0
1
0
1
1
2
1
1
1
1
2
1
1
0
2
1
2
1
1
2
1
1
0
0
1
3
1
0
1
1
0
1
1
2
0
2
1
0
1
1
1
0
2
1
3
1
1
1
1
0
1
0
2
1
1
2
2
0
1
2
2
1
3
2
1
1
1
2
2
1
0
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
0
1
0
2
0
2
1
1
1
0
1
1
1
1
2
2
1
2
0
1
2
1
1
1
2
0
1
1
1
2
1
0
1
0
1
1
1
2
0
2
2
1
1
1
2
2
1
1
2
1
1
2
0
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
0
1
1
1
1
1
1
2
2
0
1
0
1
1
1
1
2
1
1
1
2
1
1
1
1
1
0
0
1
1
1
2
1
1
2
1
0
0
1
1
2
1
1
2
0
1
1
1
1
1
0
1
1
0
1
1
2
1
1
2
1
2
1
1
1
2
1
1
1
2
1
1
1
2
1
2
1
1
1
2
1
2
1
2
1
3
0
1
0
1
1
1
1
1
1
1
1
0
2
1
0
1
1
1
1
2
1
2
1
2
2
1
1
1
1
1
1
0
2
2
2
1
1
1
2
1
2
2
1
0
1
2
0
4
1
1
1
2
0
0
1
1
1
2
0
0
2
1
1
1
0
2
0
1
1
1
1
1
1
2
1
1
0
1
1
0
1
1
0
0
1
1
0
1
1
1
1
1
1
2
1
0
1
1
1
2
1
0
0
1
1
2
0
1
1
1
0
0
0
1
2
1
0
0
2
1
2
1
1
1
2
1
0
1
1
1
1
1
2
0
1
1
2
1
1
3
1
0
1
1
1
2
1
1
2
1
1
2
1
1
2
0
1
2
1
2
2
1
2
2
2
0
0
0
0
1
2
3
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
0
1
0
1
1
1
1
2
2
1
0
1
6
1
1
1
3
1
1
0
1
0
1
1
1
1
1
1
1
1
2
0
0
0
1
2
0
2
1
1
1
1
1
1
2
1
2
1
0
1
1
1
2
0
1
0
2
1
1
1
1
1
1
1
0
1
1
0
0
1
1
1
1
1
3
1
2
2
1
2
1
1
1
1
2
0
1
1
1
2
1
0
1
2
1
2
1
2
1
1
1
0
1
1
1
1
1
2
1
1
1
0
1
1
2
1
1
1
1
1
2
1
1
1
0
0
1
2
2
1
1
1
1
1
2
1
1
2
1
1
2
2
0
2
1
1
2
1
1
2
3
0
1
1
2
1
0
0
1
2
1
1
2
0
1
0
2
2
2
1
1
0
0
1
2
1
3
1
2
1
2
1
1
2
2
1
0
1
1
0
1
2
1
1
1
2
3
1
1
0
2
2
0
1
1
1
1
1
1
2
2
0
1
1
1
1
2
2
0
1
1
1
1
1
0
1
0
1
2
2
1
1
1
2
1
1
0
1
1
1
2
1
1
2
1
2
0
1
1
1
1
2
1
1
2
1
2
1
0
1
1
1
1
2
1
1
2
0
1
1
2
1
2
0
2
2
2
1
2
1
1
1
1
2
2
2
1
1
0
2
1
1
1
0
0
0
0
2
1
0
1
1
1
1
1
1
1
0
0
1
1
1
1
1
1
1
1
1
2
2
1
1
2
2
1
1
1
1
2
1
1
0
0
2
1
1
1
3
1
2
2
0
2
1
2
0
1
1
0
1
0
0
1
0
1
2
1
1
2
1
0
0
1
1
1
0
0
0
1
1
1
2
1
1
2
0
1
1
1
1
1
1
2
1
1
2
1
1
1
1
0
1
1
1
1
1
0
1
0
0
2
1
1
1
1
1
1
1
2
1
0
1
1
1
0
1
1
1
1
1
1
2
1
1
1
1
2
1
2
1
1
2
2
1
1
2
1
1
2
2
5
0
1
0
1
2
2
2
0
1
2
0
2
1
1
0
2
0
1
2
1
1
1
1
1
2
1
1
1
1
1
0
1
1
1
1
2
1
1
0
2
2
1
0
0
2
1
0
0
2
1
1
1
1
2
1
1
0
1
1
1
1
1
1
2
1
1
1
0
0
2
1
1
1
1
2
2
2
1
1
0
1
1
2
1
2
1
1
1
1
1
1
1
0
2
0
0
1
2
2
1
1
1
1
1
0
2
1
1
0
1
0
1
2
0
2
1
1
1
2
1
1
1
1
1
1
1
1
0
2
1
1
1
0
2
2
1
1
2
1
1
1
2
1
0
1
1
2
1
1
2
1
1
1
1
2
2
2
2
2
2
1
1
2
0
1
1
1
1
1
1
1
1
1
1
2
1
1
0
1
1
2
0
1
1
1
1
1
1
1
2
1
1
1
2
1
1
2
2
0
2
1
2
0
1
2
1
1
1
1
2
1
0
1
1
1
1
1
1
2
1
2
1
1
1
1
1
0
2
1
1
1
2
2
2
1
0
1
1
1
1
1
2
2
1
2
2
1
1
0
0
1
2
1
1
1
0
1
1
1
2
1
1
0
1
2
1
1
1
1
2
0
1
1
1
2
0
2
0
1
2
1
0
1
0
1
2
2
0
1
0
1
1
1
1
1
1
1
1
1
1
0
1
1
1
2
1
2
1
1
1
1
0
1
0
2
2
1
1
1
2
1
1
3
1
1
1
1
2
2
1
1
1
1
0
2
2
2
0
0
2
2
1
2
1
1
2
1
1
1
1
2
1
2
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
0
1
1
1
1
0
1
1
2
1
1
2
1
1
2
1
1
0
2
1
1
1
2
2
1
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
1
2
1
1
1
0
1
1
1
1
1
1
3
2
1
0
1
2
1
1
1
1
1
1
2
1
3
0
1
1
2
2
0
1
0
1
1
2
1
1
1
1
2
1
2
0
2
2
1
1
1
1
1
1
1
0
1
1
1
0
2
1
1
0
1
1
1
1
2
1
1
1
0
2
1
1
1
1
2
0
0
1
1
1
2
1
1
2
2
1
0
1
0
2
4
0
1
1
2
1
1
1
1
0
2
2
2
1
1
1
1
2
1
1
1
1
2
2
1
1
1
1
1
2
1
1
1
0
2
0
1
1
1
1
1
2
1
0
2
1
2
2
1
0
1
0
0
0
2
1
2
2
1
1
1
1
0
1
1
0
1
1
1
1
1
1
1
2
1
1
1
1
2
2
1
1
2
0
1
0
2
1
2
2
2
1
1
1
2
1
1
1
1
0
1
0
1
0
1
1
2
1
1
1
0
1
1
0
0
1
2
2
1
2
1
1
1
0
0
1
2
1
1
1
2
1
1
1
2
0
2
1
1
1
1
2
1
1
0
1
2
1
2
1
1
1
1
1
2
2
1
1
1
2
1
1
0
1
1
1
1
0
1
2
1
2
1
1
1
0
0
2
2
1
1
0
1
1
2
2
2
1
2
2
1
1
1
2
0
0
1
2
1
1
0
1
1
2
1
2
1
2
1
2
1
1
1
2
2
0
1
0
1
1
1
0
1
1
1
1
0
1
1
0
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
0
1
1
2
1
2
1
1
1
1
3
1
1
2
1
1
2
1
1
2
0
0
0
1
1
0
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
0
2
1
0
2
1
1
0
0
2
0
1
1
1
1
1
1
0
1
1
1
2
1
1
2
0
1
1
1
2
0
1
1
1
1
1
0
1
1
1
2
0
1
2
1
1
1
1
2
2
0
2
1
1
1
1
1
2
1
0
1
2
1
2
1
2
1
2
1
1
1
2
1
2
1
0
1
0
1
2
2
1
1
0
2
1
0
1
1
1
2
1
1
0
1
2
1
2
1
1
2
2
0
1
1
2
2
1
2
1
1
2
1
2
0
0
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
2
0
1
0
1
0
1
1
1
0
1
2
1
1
1
0
2
1
1
2
2
2
1
2
1
1
1
1
0
1
1
0
2
1
1
1
2
1
2
0
1
0
1
1
2
1
1
0
0
2
1
1
1
0
0
1
2
1
3
0
0
2
1
1
1
2
1
0
2
1
0
2
1
2
2
1
1
3
2
1
0
1
0
2
1
2
1
1
1
1
1
1
2
2
1
0
2
1
1
1
0
1
2
0
2
1
1
1
2
1
2
1
1
1
1
1
2
2
1
2
0
1
1
1
2
1
0
2
1
1
1
1
3
0
1
1
0
1
2
1
2
1
1
1
0
1
0
1
2
2
1
1
1
1
1
1
1
1
2
2
1
1
0
1
0
0
1
1
1
1
0
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
0
1
1
1
3
2
1
1
2
0
1
1
1
2
1
2
1
1
2
0
1
0
1
0
1
1
1
1
2
2
0
1
2
1
2
1
1
1
1
1
0
1
2
2
2
1
1
1
1
0
0
5
2
0
1
0
1
2
1
0
1
1
1
0
0
1
2
0
1
0
1
1
0
1
1
1
1
0
1
0
1
1
1
1
1
1
1
1
2
1
2
2
1
1
0
1
2
1
1
0
2
1
1
1
1
1
1
1
2
1
2
0
1
2
1
0
0
2
1
1
0
1
1
0
1
3
2
1
1
1
1
1
1
1
1
1
2
1
2
0
1
2
2
2
2
2
1
2
1
0
0
0
0
2
0
1
1
3
1
0
0
0
0
1
0
2
2
1
2
1
1
2
1
2
1
1
1
2
1
2
1
1
3
1
1
1
2
1
1
2
1
1
0
1
1
1
0
1
1
1
2
1
2
0
2
1
0
1
1
0
1
2
1
0
2
1
1
2
2
1
0
0
2
2
0
0
2
0
1
2
1
0
2
1
0
0
0
1
1
2
1
0
0
1
0
1
2
1
3
1
1
1
2
1
1
1
2
2
2
2
2
0
1
1
0
1
1
0
1
1
1
2
2
2
1
0
1
1
0
2
1
2
1
1
1
1
1
1
1
2
2
2
1
1
1
1
0
1
2
1
1
2
1
1
1
1
2
1
1
1
1
1
0
1
1
1
1
1
1
0
1
1
1
1
1
1
1
2
2
0
2
1
1
0
1
2
0
1
1
1
1
1
0
1
1
2
1
1
0
1
1
1
2
0
1
2
1
2
0
0
2
1
1
1
1
1
1
2
2
2
0
2
1
0
2
2
1
2
2
1
1
1
1
2
1
3
0
1
1
1
0
1
2
1
1
0
0
2
1
0
2
2
1
1
1
1
1
0
1
0
0
2
2
2
2
1
1
2
0
0
1
2
1
1
2
1
2
2
1
1
1
1
1
2
2
0
1
1
1
1
0
1
1
2
1
1
2
0
2
1
1
1
1
1
1
1
2
0
2
0
2
0
1
1
1
0
2
1
1
0
0
0
1
1
2
1
1
2
1
1
2
1
1
1
1
1
1
2
1
1
0
1
2
0
2
2
1
1
0
1
1
1
0
1
2
2
1
1
1
0
0
1
1
1
0
3
0
1
0
1
1
0
1
2
1
1
2
1
1
1
2
2
0
1
0
2
1
1
1
2
1
1
1
1
0
2
0
1
1
2
1
2
1
0
1
1
2
1
1
0
0
2
1
0
1
1
1
1
1
1
2
1
1
1
1
0
2
0
1
1
2
1
1
2
2
1
1
1
2
0
2
0
0
1
0
1
1
2
2
2
1
1
1
1
1
2
1
1
1
2
1
2
1
1
0
2
1
1
1
1
2
1
1
1
2
2
1
1
2
1
1
0
1
1
0
1
0
1
2
2
1
1
1
2
1
2
1
0
2
3
2
2
2
1
1
1
2
0
1
0
2
1
1
1
1
2
1
2
0
1
2
1
1
0
1
1
2
2
1
1
2
1
1
0
2
1
1
1
1
0
1
1
1
0
2
0
2
1
1
2
1
2
1
0
1
1
1
1
1
1
1
0
1
1
1
2
2
2
1
1
2
1
1
1
1
1
2
2
0
0
2
2
2
1
0
0
0
1
1
1
1
1
0
1
1
0
2
1
2
1
1
1
2
2
2
1
2
0
1
2
1
2
1
1
1
1
1
1
1
3
1
0
1
0
1
1
1
1
1
1
1
1
0
2
1
1
1
1
1
0
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
0
3
1
1
1
1
2
1
1
2
2
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
0
1
1
1
1
2
1
2
1
1
2
2
1
1
3
2
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
2
1
2
1
2
1
0
2
0
2
1
1
1
2
2
1
1
1
0
1
2
1
2
1
1
1
1
1
0
1
1
1
2
1
0
0
2
1
0
1
1
1
1
1
1
1
2
2
0
2
0
0
2
1
0
2
2
1
1
0
1
1
1
0
1
0
0
1
1
1
1
1
1
2
1
0
1
2
1
0
0
1
2
2
1
1
0
1
1
0
2
1
1
1
1
0
1
2
3
1
2
2
1
1
1
1
1
2
0
1
1
1
2
1
1
1
1
1
1
1
2
0
1
0
1
1
1
2
1
1
1
3
1
2
2
2
2
1
2
2
2
1
2
0
0
1
0
1
2
0
1
1
1
2
0
0
1
2
1
0
1
1
0
0
1
0
1
1
1
1
2
1
2
1
2
1
1
1
1
1
0
1
1
1
1
0
1
1
1
2
0
2
2
1
1
2
0
1
1
1
2
2
2
1
2
0
1
1
1
1
2
1
2
0
2
1
1
1
2
2
1
1
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
1
2
2
2
1
1
1
2
2
1
1
2
2
2
1
1
0
2
1
1
1
1
1
1
0
1
2
1
1
1
1
0
1
2
2
2
1
0
2
1
2
0
2
1
1
2
1
1
1
1
1
1
2
0
2
2
1
1
1
1
0
2
1
2
0
1
1
1
0
1
1
1
2
1
2
2
1
2
1
2
1
1
1
1
1
0
2
1
1
2
1
1
2
2
1
1
0
1
2
1
1
2
2
1
1
2
1
1
1
1
1
2
0
2
2
1
0
1
1
1
2
1
1
1
1
1
1
2
1
2
1
0
1
1
0
2
1
2
1
0
2
2
2
1
1
3
2
1
1
1
0
1
1
0
1
1
1
1
1
1
2
1
1
1
3
3
0
1
0
1
0
0
0
2
1
1
1
1
1
2
1
2
0
0
2
1
1
2
1
1
2
2
1
2
2
2
1
2
2
1
2
2
2
0
2
2
1
1
1
2
1
1
1
1
0
2
1
1
1
2
2
2
1
1
2
2
0
1
2
2
1
1
2
0
2
0
1
1
1
1
1
1
1
1
0
1
1
1
0
0
1
1
2
2
1
2
1
2
1
1
2
0
1
1
0
2
1
0
2
3
1
1
2
2
2
1
0
1
1
2
1
1
1
1
1
0
1
0
2
0
0
1
1
1
0
1
1
2
2
1
1
0
1
0
1
1
1
2
2
2
1
2
0
0
0
0
1
1
0
1
0
0
2
1
1
0
0
1
0
2
2
1
2
0
1
1
1
2
1
1
1
1
1
1
2
2
1
1
0
1
2
1
0
0
1
1
0
1
0
0
1
0
2
2
1
1
2
1
1
2
1
1
1
0
1
1
1
3
1
2
1
1
1
1
1
1
2
1
0
0
2
1
2
2
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
2
2
1
1
2
0
0
1
1
2
1
1
1
0
1
1
0
1
1
2
1
1
1
1
2
0
0
1
2
1
3
2
1
1
1
1
1
1
3
2
2
0
1
1
1
1
1
1
1
2
0
1
2
1
1
1
1
1
1
1
1
0
1
1
1
1
2
1
1
2
1
5
2
1
1
1
0
1
0
1
1
1
2
2
0
0
0
2
2
1
2
1
1
1
1
0
2
0
2
1
1
2
1
2
1
1
0
1
1
1
1
1
2
2
1
1
2
2
1
1
2
1
2
1
1
1
1
2
1
0
0
1
1
0
0
1
1
1
0
1
1
1
2
1
1
1
1
0
2
1
2
2
1
1
2
1
1
1
1
0
0
2
2
1
3
1
1
2
1
2
1
1
1
1
1
1
1
1
1
2
2
0
0
1
1
1
1
1
1
0
2
0
1
1
1
1
2
1
1
1
1
0
2
2
1
0
3
2
2
1
2
1
0
1
1
0
1
1
1
0
1
1
1
1
1
0
1
0
1
2
1
1
2
1
1
1
1
0
1
1
1
1
2
1
2
0
2
0
0
2
2
1
2
1
1
2
1
1
2
0
1
2
1
2
1
1
1
0
0
1
1
1
1
1
1
1
1
1
2
1
1
0
1
1
1
1
2
1
1
2
1
1
1
1
2
0
1
1
1
2
1
1
1
1
1
2
2
2
1
1
2
1
1
1
2
0
1
0
2
2
1
2
2
1
2
0
2
1
0
1
1
1
1
1
1
2
1
2
1
0
0
1
1
2
2
2
2
1
1
2
1
1
0
0
1
1
0
1
1
1
1
1
1
1
1
1
2
0
2
0
13
1
0
1
1
1
1
2
2
1
1
1
2
1
0
3
2
2
0
1
1
1
1
2
1
2
1
1
1
1
1
2
2
1
1
2
0
1
1
1
1
2
2
1
1
2
2
2
1
0
1
1
1
1
1
0
1
1
1
1
0
2
1
2
0
2
1
1
1
1
0
1
2
0
1
4
1
2
1
0
1
1
1
2
2
1
2
1
0
1
0
1
0
1
2
2
1
1
1
1
2
1
1
2
2
2
2
0
1
1
1
1
1
0
2
2
1
1
2
2
0
1
1
1
2
1
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
0
0
0
2
1
1
2
0
1
0
2
1
1
1
0
0
1
2
0
1
2
2
2
0
1
1
1
1
2
2
0
1
1
2
1
0
1
1
2
1
1
2
1
0
0
2
1
1
1
2
1
1
0
1
2
2
1
2
1
2
0
1
1
1
2
1
1
0
1
0
1
1
0
1
1
1
1
0
1
1
1
1
1
0
0
1
1
1
1
2
1
2
1
1
2
1
1
1
1
2
0
2
1
0
2
2
2
1
2
2
2
2
1
1
1
1
1
1
1
1
0
2
1
1
1
1
0
1
1
1
1
1
1
1
1
1
0
1
1
1
1
2
1
0
1
0
1
1
1
1
1
0
0
2
1
1
2
1
1
1
0
2
2
0
1
1
1
1
1
1
1
2
1
1
1
1
2
0
0
1
1
1
1
0
2
1
1
1
1
2
2
0
2
2
1
0
1
1
1
3
2
1
0
1
1
0
1
1
1
2
1
1
1
3
1
1
1
0
1
1
1
2
0
1
1
3
1
1
1
1
2
1
1
2
1
2
1
1
1
1
2
1
1
2
1
0
1
1
0
1
1
2
0
1
1
2
1
0
1
1
2
1
1
1
1
1
1
1
1
1
1
2
0
1
1
2
0
0
2
1
1
2
1
0
2
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
2
2
1
1
0
1
2
0
1
1
1
1
2
1
1
1
1
2
1
1
2
2
2
1
2
0
1
1
1
0
0
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
0
2
2
2
2
1
3
2
1
1
0
1
1
1
1
1
1
1
0
2
1
2
1
2
1
0
2
1
2
2
3
1
1
1
1
1
1
1
0
1
1
1
1
0
1
1
1
2
0
2
1
0
2
1
2
0
1
1
2
1
1
1
1
0
1
0
0
0
1
2
1
1
0
1
2
1
1
1
2
0
1
2
1
2
2
1
1
2
1
1
1
1
1
1
1
2
1
1
2
2
1
1
1
1
0
1
2
1
2
2
1
1
1
1
1
0
1
1
0
0
1
2
1
1
1
1
0
1
1
1
0
1
1
2
2
0
1
1
2
2
1
2
0
1
1
2
1
1
3
0
2
1
1
1
1
0
2
2
2
0
2
1
2
1
1
1
1
2
1
1
1
1
0
1
2
1
1
2
2
1
1
1
2
2
1
1
2
1
1
1
1
0
1
1
1
2
1
1
1
1
2
0
0
1
0
0
1
2
1
2
1
1
0
1
1
1
1
2
1
1
2
0
1
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
2
0
0
0
1
1
1
2
1
1
1
2
2
1
1
0
1
1
2
1
1
2
1
1
2
1
1
0
1
2
2
1
0
1
1
1
1
1
1
1
1
0
1
1
1
2
1
1
1
1
2
1
1
2
1
2
1
1
2
0
2
2
1
0
2
1
2
1
1
1
0
0
0
1
2
1
1
0
1
1
2
0
2
1
0
1
1
1
1
1
2
0
1
1
1
1
1
2
1
1
2
1
1
1
2
1
2
1
1
2
2
2
1
2
1
3
1
1
0
1
1
1
0
2
1
1
1
2
1
1
1
1
1
1
1
1
1
0
2
1
2
1
2
0
2
1
2
1
1
1
1
1
2
1
1
1
2
1
0
1
0
1
2
1
1
0
2
1
1
1
1
0
0
1
1
1
0
1
0
1
2
1
2
1
1
1
1
1
1
1
2
1
1
0
1
0
1
0
2
2
1
1
1
3
2
1
1
1
1
2
1
1
1
2
2
0
2
1
0
1
2
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
1
0
0
1
0
1
1
1
1
0
2
1
1
1
1
1
1
1
1
1
0
1
2
1
2
1
1
2
2
1
2
1
1
1
1
1
0
1
1
1
1
1
0
1
1
1
1
1
2
1
0
2
2
1
0
1
1
2
1
0
0
1
1
1
1
1
1
1
1
1
1
0
2
1
1
0
1
1
0
2
1
2
1
1
0
0
0
1
1
2
2
1
1
0
1
1
2
1
1
0
1
2
1
1
0
1
2
2
1
1
0
1
2
1
1
1
1
0
0
1
1
1
1
1
1
0
1
1
2
0
1
1
2
1
0
1
1
2
2
2
0
1
1
1
1
2
0
1
1
2
3
2
0
1
0
2
1
2
1
2
2
1
2
0
2
1
2
0
1
1
1
2
2
1
1
0
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
2
0
1
1
1
1
2
1
2
2
1
1
2
1
1
1
1
0
2
2
2
2
0
1
0
2
1
2
2
1
1
1
1
0
0
1
1
0
1
0
1
0
1
0
2
1
1
1
1
1
1
2
0
0
1
2
1
1
0
2
1
1
1
2
0
1
1
1
1
1
1
2
1
1
1
1
2
0
1
0
0
1
1
2
0
1
1
1
2
1
2
2
1
1
0
0
1
1
2
0
1
1
2
1
2
1
2
1
1
2
0
1
1
2
2
1
1
1
2
2
0
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
0
2
1
1
0
2
1
1
2
1
1
1
1
2
1
1
1
0
1
1
1
1
2
2
1
0
3
0
2
0
1
0
2
2
2
1
2
1
1
0
1
1
1
1
1
2
1
1
1
2
1
0
1
3
1
1
0
1
1
2
1
2
1
1
2
1
0
1
1
2
1
0
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
0
2
0
1
2
2
1
0
3
1
2
1
2
1
2
1
0
0
2
1
1
1
0
1
0
1
2
1
3
1
1
1
1
1
1
1
1
1
2
0
0
0
1
1
1
1
1
1
2
1
1
1
1
2
1
2
1
1
2
1
1
1
2
0
2
0
0
0
0
1
1
2
2
1
1
2
1
1
1
1
1
2
2
1
0
1
1
0
1
1
2
3
2
1
0
1
1
1
2
2
2
2
2
2
2
0
2
2
2
0
1
0
2
1
1
2
1
1
1
0
2
1
1
1
0
1
0
0
2
1
6
1
1
1
0
1
1
2
1
2
1
1
2
1
1
1
1
1
1
1
0
1
1
1
2
1
1
2
2
1
1
2
2
1
0
2
1
1
0
1
0
2
1
2
0
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
3
1
0
1
2
1
1
0
1
0
1
3
3
1
1
1
2
1
1
2
2
1
1
1
1
1
2
1
1
2
1
1
2
1
0
2
1
1
2
1
1
1
2
0
1
1
0
1
1
1
2
1
1
2
1
2
0
1
1
1
1
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
0
1
1
1
2
2
2
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
0
1
0
1
1
2
1
1
2
1
2
1
2
1
1
1
2
1
1
2
0
1
1
2
1
1
2
1
1
1
0
1
1
1
1
0
1
2
0
1
2
1
1
2
2
1
2
1
0
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
2
1
1
1
0
1
1
1
0
1
1
0
1
2
0
1
1
1
2
2
2
0
1
1
2
1
2
1
0
2
1
1
2
1
2
0
0
1
0
0
1
1
1
1
1
0
0
1
1
1
0
1
2
2
1
1
0
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
2
0
1
1
2
1
2
1
1
1
1
1
1
1
2
0
2
1
1
1
1
1
2
1
2
2
1
1
1
1
0
1
2
0
0
1
1
2
1
1
2
2
1
2
2
0
1
1
1
2
1
7
1
2
1
1
1
1
1
3
1
1
1
2
0
1
1
1
1
0
1
1
1
1
1
1
1
1
2
2
0
2
0
1
0
1
2
1
0
1
1
2
1
2
1
0
1
1
1
1
1
1
1
2
2
2
0
0
2
1
1
1
1
1
1
0
1
0
1
0
2
1
2
2
1
1
2
1
1
1
1
1
2
2
2
1
1
2
1
2
1
3
0
0
1
2
1
2
1
2
1
0
1
2
1
2
1
1
1
0
0
0
1
0
1
2
1
1
1
0
2
2
1
2
0
1
0
1
2
1
1
1
2
2
1
1
1
2
1
1
1
1
2
0
1
1
2
2
1
2
2
2
0
1
0
1
1
2
1
2
1
1
1
0
2
0
2
1
0
2
2
1
0
2
1
1
1
1
1
2
2
1
0
1
2
0
1
1
1
1
2
1
1
1
1
1
0
2
0
0
1
2
0
1
1
1
2
1
1
0
1
2
2
1
1
0
1
2
1
1
2
1
1
1
1
1
1
1
0
2
0
1
0
1
2
1
1
1
2
2
2
2
1
1
1
2
1
1
1
2
1
1
1
0
1
1
1
0
2
1
1
0
1
1
1
2
0
1
1
2
1
1
1
1
1
1
0
1
0
1
1
2
1
0
2
1
1
1
1
2
1
1
1
1
2
1
1
0
1
2
1
0
1
1
0
1
1
1
2
1
1
1
2
0
1
2
1
0
1
1
1
1
1
1
0
1
1
1
1
1
2
0
1
1
1
0
1
1
1
1
1
0
1
1
1
2
0
1
2
1
1
1
1
0
2
1
1
1
1
2
1
2
1
1
1
2
2
2
1
1
1
1
4
1
2
1
1
1
1
1
2
2
1
2
0
1
1
1
1
2
2
0
1
1
0
1
1
0
2
1
0
1
1
1
1
1
0
1
1
1
1
2
2
1
1
2
2
2
1
1
0
2
1
1
1
1
1
1
1
1
0
0
1
0
1
0
1
0
2
2
2
1
1
1
2
1
1
2
1
1
0
1
1
1
2
2
1
1
1
1
1
0
1
1
1
1
0
2
1
1
0
1
2
0
1
2
2
1
1
1
2
0
1
2
2
2
2
1
1
0
2
1
0
1
1
1
1
2
2
1
0
1
0
0
0
1
1
2
1
2
1
0
1
1
2
3
1
1
0
1
1
1
1
1
2
0
1
2
1
1
0
0
1
2
1
1
1
1
1
2
0
1
2
0
1
1
1
1
1
2
2
2
1
1
2
1
0
1
2
0
2
2
3
1
1
2
1
2
1
1
1
3
1
1
1
1
2
1
1
2
1
1
1
1
2
1
2
1
0
2
0
2
1
1
1
1
1
1
1
2
2
1
1
1
2
0
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
0
2
2
2
1
0
2
2
0
1
1
1
1
1
2
1
1
1
0
1
2
2
0
2
0
2
1
2
1
1
1
1
2
1
1
2
1
2
1
1
1
1
0
2
1
1
1
1
1
0
2
1
1
2
1
1
1
2
2
1
0
2
2
2
0
2
1
2
2
0
1
0
2
1
1
0
1
1
1
1
1
1
1
2
1
1
1
1
0
0
1
1
1
2
1
2
1
1
0
2
1
2
2
2
0
2
0
2
1
1
1
2
2
2
1
1
1
0
1
1
0
1
2
0
0
1
1
2
1
1
1
1
2
1
1
1
2
1
1
0
1
1
1
2
2
1
1
1
1
2
2
1
1
2
2
2
1
1
2
1
1
2
1
1
1
1
2
0
1
1
1
1
1
1
1
1
1
1
2
1
1
1
0
1
1
1
0
1
1
1
1
1
0
1
0
0
2
0
2
1
2
2
0
1
2
2
1
0
1
1
2
2
1
0
2
1
1
1
2
1
3
1
0
2
2
1
0
0
1
1
1
2
1
1
0
0
0
1
1
0
2
2
1
1
1
2
1
1
1
1
2
2
1
2
1
2
2
1
1
0
1
1
1
1
1
0
0
1
1
0
2
1
2
1
1
1
2
2
1
1
0
2
1
1
2
1
2
1
1
1
0
1
1
1
1
2
1
1
1
1
1
1
1
1
0
2
1
0
1
1
2
0
2
1
2
1
1
1
1
1
1
0
1
1
1
2
1
1
1
0
1
1
2
1
1
0
1
1
1
0
1
1
1
2
1
1
2
2
1
1
2
2
3
0
0
1
1
1
2
0
1
2
1
0
1
2
1
2
2
1
1
0
1
2
1
1
1
1
2
0
1
1
1
0
1
1
1
2
1
1
1
1
1
1
2
1
1
0
1
1
1
1
1
1
1
2
1
0
1
2
2
1
2
1
1
2
2
1
1
2
0
1
1
1
2
2
0
1
1
1
1
2
1
1
1
1
1
1
0
2
1
1
0
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
0
1
1
1
1
2
1
1
0
2
2
0
2
2
1
1
0
1
1
0
1
1
2
1
0
1
0
2
1
1
1
1
1
1
1
2
0
1
0
0
1
1
1
1
0
1
1
1
2
2
1
0
1
1
1
1
1
1
0
2
1
1
2
1
1
2
1
1
2
2
1
1
2
2
1
2
1
1
1
2
2
0
2
1
1
0
1
1
2
1
1
0
2
1
1
1
2
0
1
1
1
0
0
0
0
1
1
0
0
2
0
0
1
2
2
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
1
0
2
2
1
1
0
1
0
2
1
2
1
1
1
2
2
1
1
1
1
1
1
0
1
2
1
0
0
2
2
0
1
1
2
0
2
1
1
1
2
1
0
0
3
1
1
2
2
1
1
1
1
3
1
1
0
0
1
1
1
1
2
1
2
2
1
1
1
1
0
0
3
1
1
1
2
2
1
0
1
2
1
0
1
1
2
2
0
3
2
1
1
2
2
2
1
2
1
2
1
2
0
1
1
1
1
2
1
1
0
0
1
2
1
1
1
1
1
1
1
0
1
1
0
1
1
1
2
1
1
0
1
2
0
0
0
1
0
2
1
1
0
1
2
1
1
1
1
1
1
2
0
0
1
1
1
1
2
1
1
1
1
0
2
1
2
1
2
0
0
1
2
1
1
0
1
1
1
1
1
1
3
1
2
1
1
1
0
1
1
2
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
0
1
0
1
2
1
1
1
0
2
1
1
1
1
0
1
2
1
2
1
1
1
0
1
1
2
2
2
2
2
1
1
0
1
2
1
2
1
0
2
1
1
1
2
1
2
1
2
3
1
1
2
1
1
1
2
1
1
1
2
1
1
1
2
1
2
1
1
1
1
2
1
1
1
2
1
2
1
1
2
0
1
1
0
2
0
1
1
1
1
1
2
2
2
2
1
1
1
2
1
0
1
1
1
3
0
1
0
0
1
1
1
0
1
1
2
2
0
1
1
1
1
2
1
0
1
2
0
0
0
2
1
2
1
1
0
2
1
1
2
1
1
2
1
1
0
1
0
1
1
1
1
2
1
1
1
2
1
0
0
1
0
1
1
0
2
0
1
1
0
2
1
1
0
1
1
1
1
2
2
1
1
0
1
1
1
1
1
0
1
0
0
1
1
2
2
2
1
0
1
0
1
2
2
1
0
2
1
0
2
0
1
2
0
1
0
1
1
1
2
1
1
1
2
1
2
0
1
0
2
1
2
1
2
1
1
1
0
1
2
0
1
1
1
1
1
1
1
1
1
2
2
2
0
1
0
0
1
1
1
1
1
1
1
1
1
1
0
1
1
0
4
1
0
1
2
1
1
2
1
1
2
1
2
1
1
0
2
1
2
1
0
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
0
1
1
1
0
1
0
2
2
0
2
1
1
1
1
2
1
1
2
1
1
1
1
1
0
1
2
1
0
1
1
2
2
1
1
1
0
2
1
2
1
1
2
1
1
1
1
1
1
0
1
2
1
1
2
1
0
1
1
0
0
0
3
2
1
2
1
1
0
0
1
1
1
2
1
1
2
1
1
1
1
0
1
0
0
2
2
2
0
0
1
2
2
1
1
1
1
2
1
1
1
1
1
1
2
0
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
2
1
1
1
1
2
1
1
2
2
1
1
2
2
2
1
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
0
1
0
1
1
1
1
1
2
1
2
2
0
0
1
0
1
1
1
0
1
0
1
1
1
0
1
1
2
0
0
2
1
1
1
1
2
1
1
0
1
2
1
2
1
2
1
1
2
2
1
1
1
1
1
0
1
2
0
1
1
0
0
1
1
1
1
1
1
1
3
1
2
1
2
1
2
1
1
1
1
2
2
0
2
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
0
2
1
0
1
1
1
1
0
1
1
0
0
2
1
2
0
2
0
2
1
2
2
1
2
0
0
1
1
0
0
2
2
2
1
1
0
1
1
0
2
1
2
1
0
1
1
0
1
2
2
0
2
1
1
1
1
1
1
1
2
2
1
2
2
1
2
1
2
1
1
1
0
0
1
2
1
1
1
1
2
1
2
1
1
1
3
1
1
2
1
1
2
0
1
2
2
1
2
2
2
0
1
2
1
2
1
1
1
0
1
2
1
1
1
2
0
1
1
1
1
1
1
2
2
2
0
1
1
1
1
0
1
0
1
0
1
1
1
2
2
1
1
1
2
1
0
1
1
0
2
1
1
1
1
1
1
0
2
1
2
3
1
1
2
1
1
1
0
1
1
1
1
2
0
1
2
1
2
1
1
0
1
2
2
1
1
2
1
0
0
1
1
0
0
2
1
1
0
1
1
1
1
2
2
1
1
2
1
1
1
0
1
1
1
1
1
0
1
0
0
1
1
1
0
2
1
1
1
2
1
2
1
2
1
1
0
1
1
2
0
1
2
1
1
0
1
0
1
2
1
0
1
1
1
1
1
2
1
1
2
0
1
0
1
1
0
1
2
1
2
2
1
1
1
1
1
1
1
1
2
2
1
0
3
2
1
1
2
1
2
1
1
1
2
1
2
1
1
3
1
1
1
2
2
1
2
2
0
0
1
1
1
0
2
1
2
2
1
0
2
1
1
1
2
1
0
2
1
1
1
2
2
0
2
1
1
1
1
0
1
0
2
1
1
0
1
1
0
0
2
0
1
1
1
1
1
2
1
1
0
0
1
1
1
2
0
1
1
2
1
2
1
2
2
2
1
1
1
2
2
2
1
0
1
1
1
1
0
2
2
1
0
1
2
1
2
2
1
2
1
2
0
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
2
2
2
1
0
1
1
0
1
1
1
0
2
0
1
1
1
1
2
0
1
2
1
2
1
1
0
1
1
1
1
2
0
1
1
1
2
2
0
2
2
0
1
1
2
1
1
2
1
1
0
2
1
1
1
2
1
1
1
1
0
1
1
1
1
2
1
1
2
0
1
2
1
1
1
1
2
1
1
1
1
2
1
1
0
1
1
1
1
2
0
2
0
1
0
2
0
0
1
1
2
2
1
1
2
1
1
2
0
1
1
1
2
0
2
1
1
1
1
1
1
0
2
1
1
1
1
0
1
1
1
0
1
0
2
1
1
1
2
1
0
1
1
0
2
1
1
1
3
0
1
1
1
2
1
0
0
2
1
2
0
1
2
0
0
1
1
1
1
2
0
1
1
0
1
1
1
1
1
1
1
0
1
0
1
2
1
0
0
1
1
2
1
1
0
1
1
1
1
1
0
2
2
3
1
1
2
0
1
1
2
1
0
2
2
2
1
1
1
0
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
0
1
2
0
2
1
2
1
1
1
0
0
2
1
1
0
1
1
1
1
1
1
2
1
1
0
1
1
1
1
1
1
1
2
1
1
2
2
1
2
2
1
1
2
1
1
2
0
2
1
2
1
1
2
0
1
2
1
1
1
1
2
2
0
1
1
2
1
0
1
2
0
1
1
1
2
1
1
2
1
1
0
1
1
2
1
1
2
1
1
1
2
1
2
0
1
1
1
1
2
1
1
2
1
2
0
1
0
1
1
1
0
1
0
2
2
2
1
1
0
2
1
1
1
0
0
3
1
1
1
0
0
1
2
2
0
1
1
1
1
1
0
1
1
1
0
0
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
2
0
1
1
0
1
2
2
1
0
0
2
1
1
1
2
1
1
1
1
1
2
0
2
1
2
1
1
1
2
2
1
1
2
1
1
1
2
1
2
1
1
1
2
0
2
2
0
1
1
1
1
3
2
1
1
0
1
1
2
1
1
3
2
1
2
1
1
1
0
2
1
1
1
1
2
1
1
2
1
1
1
1
2
1
1
0
2
1
1
1
0
1
1
0
2
1
1
1
0
0
1
1
0
2
1
1
1
1
2
1
1
2
2
1
2
1
0
1
0
2
1
1
2
2
1
1
1
2
0
0
0
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
2
1
2
2
1
2
2
1
1
2
0
1
1
1
1
1
2
0
1
0
1
1
1
1
1
2
0
0
1
1
2
1
2
1
0
2
1
1
1
1
0
0
0
0
1
1
1
2
1
1
1
0
1
1
1
1
0
1
1
1
2
1
1
2
1
1
1
1
2
0
1
2
1
1
2
1
1
1
1
0
1
1
1
1
1
2
2
1
2
0
1
1
1
1
1
2
2
1
1
2
2
2
1
0
2
3
1
0
2
2
1
1
0
1
1
0
2
1
1
1
1
2
1
1
0
0
1
1
2
2
0
1
0
1
0
1
0
1
2
2
1
1
2
2
2
1
1
1
1
2
1
2
0
0
1
2
1
1
1
0
1
1
2
2
1
1
2
2
0
2
2
1
2
1
2
1
1
1
2
1
2
2
1
0
0
1
1
1
0
1
2
2
2
2
1
0
3
0
0
1
1
2
1
1
1
1
1
0
2
1
1
1
1
2
1
2
0
1
1
1
1
1
2
1
1
2
0
1
1
2
1
1
1
0
2
1
0
1
1
2
2
1
2
1
1
0
1
2
1
1
2
1
1
0
1
0
1
2
1
1
1
1
1
1
1
2
1
2
2
0
1
1
1
2
1
1
2
0
0
1
2
2
2
1
1
0
1
1
0
0
2
1
0
1
1
1
2
1
1
1
1
1
2
1
1
2
1
1
2
1
1
2
1
1
3
1
0
0
0
1
1
1
1
1
1
0
2
0
1
1
1
2
0
1
1
1
2
1
0
1
2
1
1
0
2
1
0
0
1
1
1
1
2
2
1
2
0
0
1
0
1
2
0
2
1
2
1
1
2
1
2
2
1
2
0
1
1
1
1
1
0
1
1
1
1
1
1
1
0
0
0
2
1
2
1
1
2
1
1
0
1
2
2
1
0
1
1
1
1
1
2
1
1
3
1
1
1
0
1
1
1
2
1
1
2
2
1
1
1
1
0
2
1
1
2
1
0
1
2
1
1
1
1
2
1
1
0
1
0
1
1
2
2
0
0
1
2
1
2
2
2
0
0
1
1
3
1
1
2
1
1
1
0
1
2
1
1
1
1
1
1
1
1
1
3
1
1
2
0
1
2
1
1
1
2
0
1
1
0
1
1
2
1
1
1
0
1
1
2
0
1
2
1
0
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
0
1
1
0
1
1
1
2
2
0
1
2
2
1
1
1
1
1
1
1
1
0
1
1
1
0
1
2
1
2
1
2
2
2
1
0
1
0
2
1
1
1
1
1
1
1
2
1
2
1
1
0
2
2
1
1
1
1
2
0
1
1
0
1
2
1
0
1
1
2
1
2
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
0
1
1
1
1
0
0
1
1
1
2
2
1
1
0
1
1
1
2
1
1
3
1
2
1
1
2
1
1
1
2
0
0
1
2
1
0
1
0
1
1
1
1
1
0
1
2
1
1
1
1
2
2
1
1
1
0
2
2
1
1
1
1
1
2
2
2
2
1
1
0
1
2
2
2
1
2
1
1
0
0
0
2
1
1
1
1
1
2
2
1
1
1
2
2
1
0
1
1
1
0
1
2
1
0
1
2
1
1
2
2
1
1
4
2
1
1
0
1
1
2
1
1
1
1
2
2
2
2
0
1
1
0
0
1
2
1
2
2
1
1
0
1
2
1
1
1
1
1
1
2
1
1
2
1
0
2
1
2
1
2
4
2
1
2
1
2
2
2
1
1
1
0
1
2
1
0
1
2
1
0
1
1
1
1
1
2
2
2
1
1
0
1
1
2
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
2
2
1
1
2
1
2
1
2
1
2
2
1
1
1
1
1
2
1
0
0
1
0
1
0
1
1
2
1
2
1
1
1
1
1
1
1
1
0
1
1
1
1
1
0
2
2
1
1
1
1
1
1
2
1
2
1
0
1
1
2
1
1
1
1
1
1
1
1
0
1
1
1
0
1
1
1
1
1
2
1
0
1
2
1
1
1
1
0
1
1
2
2
1
1
1
1
1
1
0
1
1
1
2
1
1
2
1
1
1
1
0
1
2
1
2
1
2
2
1
1
0
1
2
1
1
1
1
2
1
1
1
2
2
2
1
1
1
1
1
1
2
2
1
1
0
1
2
2
1
3
1
2
2
1
2
1
1
1
1
1
1
2
1
0
1
2
2
1
2
1
1
1
2
3
1
1
1
1
1
2
1
1
2
1
2
0
0
1
1
2
1
0
1
2
2
1
1
1
1
1
0
1
0
1
2
0
1
1
1
1
2
1
1
0
1
1
1
2
1
1
1
2
2
1
1
0
2
0
1
1
1
1
1
1
1
1
2
0
1
0
1
0
0
1
1
1
1
1
1
1
1
1
2
2
1
0
3
1
0
1
0
0
2
1
1
2
1
1
2
1
1
1
2
1
2
1
2
1
1
2
1
1
1
1
1
2
1
1
1
0
1
1
1
2
1
1
1
2
1
1
2
1
0
1
1
0
0
2
2
1
0
1
0
2
1
1
1
1
1
0
0
2
1
1
1
1
0
1
1
1
1
1
0
0
1
1
0
1
0
1
0
1
1
2
1
2
2
2
1
2
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
1
0
1
1
0
1
1
2
1
0
0
1
1
0
1
1
2
1
1
2
1
0
1
1
1
1
0
1
1
1
1
1
1
1
2
1
1
1
1
1
2
0
0
2
1
1
0
0
2
1
1
1
1
0
1
1
0
1
1
1
0
1
1
0
0
1
1
1
1
1
2
1
0
1
2
1
1
1
1
1
2
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
2
0
1
1
0
2
0
1
1
2
2
1
2
0
1
2
1
1
1
1
1
0
1
1
0
2
0
1
1
2
1
0
1
0
2
2
2
1
1
1
1
0
0
0
1
1
1
3
1
1
0
0
2
0
2
1
2
2
1
1
1
2
1
1
1
0
1
1
1
0
2
1
2
1
1
2
2
2
1
0
0
1
1
2
1
1
0
0
2
1
1
1
1
1
1
2
1
1
2
1
1
2
1
2
1
2
1
0
0
1
1
1
1
2
2
2
2
1
1
1
1
2
2
1
1
1
2
1
1
1
1
0
1
2
1
1
1
1
0
1
2
2
0
1
1
1
1
1
2
1
0
2
1
2
1
1
1
2
1
1
2
1
2
1
1
2
2
2
1
0
0
2
2
0
2
2
1
1
1
1
1
3
1
1
2
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
2
1
1
1
0
1
1
1
2
2
1
1
2
1
2
1
1
1
1
2
1
1
1
2
0
2
2
1
1
0
1
1
1
1
2
2
1
2
0
1
0
1
1
1
0
0
1
1
1
1
1
1
0
1
1
1
1
3
2
1
1
1
2
1
0
0
1
0
0
1
1
1
0
0
1
2
1
1
1
1
1
1
0
1
1
2
1
1
2
1
2
1
1
2
1
1
1
2
1
2
1
1
0
2
1
2
2
2
1
1
2
0
1
0
1
2
0
2
1
2
1
1
1
1
1
0
1
1
2
0
1
1
2
3
2
2
0
1
0
2
2
0
0
1
0
1
1
2
1
0
0
0
0
0
1
2
0
1
1
1
1
1
1
1
2
1
1
3
1
0
1
2
1
1
0
1
2
1
1
1
2
0
1
2
2
0
2
1
1
1
1
1
1
2
0
1
0
1
1
2
1
1
1
2
1
1
1
2
0
2
1
2
2
2
1
1
1
1
1
1
1
2
0
1
1
2
1
1
1
1
1
1
3
2
1
0
2
2
0
2
2
2
0
0
1
2
1
1
1
1
1
0
0
2
0
1
1
1
0
1
1
0
2
2
0
1
1
2
1
1
1
1
1
2
1
0
2
1
1
1
0
1
1
1
1
1
1
1
0
2
2
1
1
2
1
0
1
2
2
2
1
1
1
2
2
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
0
2
0
1
1
1
2
1
1
2
2
1
0
2
1
0
1
0
1
1
2
1
0
2
0
2
2
1
1
1
1
0
0
2
1
1
0
2
1
1
1
1
1
1
2
1
2
1
1
1
1
2
0
1
1
0
1
1
1
2
2
1
1
2
1
1
1
1
2
2
1
2
1
2
2
1
0
1
1
1
2
1
1
1
1
1
1
0
2
0
0
0
1
0
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
2
0
2
2
1
2
1
1
2
1
1
1
0
0
2
0
1
2
1
1
0
1
1
2
1
0
1
2
2
1
1
1
1
1
1
1
2
2
1
1
2
1
2
0
0
2
1
1
1
0
1
1
1
1
2
1
0
0
2
1
1
1
1
1
0
2
1
2
1
2
2
2
2
1
1
1
1
1
2
2
1
1
1
0
2
2
0
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
0
1
2
0
1
0
1
1
1
2
2
1
1
1
2
1
0
0
1
1
1
1
2
1
2
1
0
1
2
1
1
1
1
2
1
1
2
0
1
0
2
2
2
1
1
1
1
1
0
2
1
2
1
1
1
0
2
1
2
1
0
1
2
1
0
1
1
1
2
2
0
1
1
1
2
2
1
1
2
1
1
0
2
1
2
2
1
1
2
0
2
1
1
1
0
0
0
2
1
1
0
1
1
1
2
0
1
2
1
2
0
0
2
2
1
1
1
2
0
1
0
2
1
0
2
1
1
2
1
2
1
1
0
1
2
2
1
2
1
1
1
1
1
2
1
2
1
2
1
1
2
1
1
1
1
1
1
1
1
1
0
0
2
1
1
2
1
1
1
1
1
2
2
1
2
1
2
1
2
1
1
2
1
1
2
1
2
0
1
2
1
0
2
1
2
2
1
1
1
1
0
2
1
2
2
1
0
1
0
2
0
1
1
1
2
1
1
2
1
2
1
1
2
0
1
1
0
2
1
0
2
0
1
3
0
0
1
1
1
1
1
1
1
1
1
1
0
1
0
1
1
2
0
2
2
2
2
1
1
0
1
1
2
1
2
1
1
1
1
1
1
0
1
1
2
2
2
0
1
1
1
3
2
1
2
0
2
1
1
0
1
2
2
1
1
1
1
1
2
0
1
1
1
1
1
2
0
2
1
1
1
1
1
2
1
1
1
0
1
2
2
1
1
1
1
1
0
1
2
1
1
2
1
1
1
2
1
0
1
1
1
2
1
1
1
2
0
1
1
1
0
2
1
2
1
1
1
1
1
1
1
2
1
0
1
1
1
1
0
1
2
1
0
0
1
1
0
1
1
2
1
2
1
1
1
2
1
1
1
2
1
1
1
4
1
2
0
0
2
2
0
1
2
0
2
2
2
1
1
2
1
2
1
1
1
1
1
1
1
2
0
1
2
0
1
0
2
0
2
2
2
1
0
1
2
1
2
2
2
2
1
1
1
0
0
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
2
1
1
1
1
1
2
0
0
1
1
2
1
2
1
1
1
2
1
1
0
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
0
2
2
1
1
0
1
2
1
1
1
1
1
1
1
2
1
0
1
0
2
2
1
2
1
2
1
2
3
1
1
1
1
1
1
1
1
1
2
2
1
2
1
2
1
1
2
1
0
1
1
0
0
1
2
2
2
2
0
1
1
2
2
2
1
2
0
1
1
1
1
2
1
1
0
2
1
1
2
2
1
1
1
2
0
2
0
1
2
0
1
1
1
2
1
0
2
2
1
1
1
0
1
1
0
1
2
1
1
1
1
1
2
2
1
2
1
1
1
1
0
1
1
1
1
1
0
1
2
2
2
1
1
2
1
1
1
1
2
1
1
1
1
0
0
2
1
0
2
0
0
0
1
1
2
2
2
1
1
1
1
2
2
1
1
1
1
1
1
0
2
1
1
1
1
2
2
1
1
2
1
2
1
1
0
1
2
1
1
1
2
1
1
0
1
1
1
0
1
1
1
1
1
2
1
1
2
0
0
0
1
1
2
2
1
1
1
1
1
1
1
2
1
1
0
1
1
1
2
1
1
2
1
1
1
0
1
2
2
1
1
1
1
1
1
1
0
0
1
1
0
1
0
1
0
2
0
2
1
0
1
1
0
1
1
1
0
1
0
2
1
1
1
1
1
0
1
2
1
2
1
0
0
1
1
0
2
1
1
1
0
1
1
1
0
1
1
1
2
1
1
2
1
2
1
0
1
3
2
2
1
0
1
2
1
1
1
1
1
0
1
1
1
1
0
2
1
0
2
1
1
2
1
2
2
1
2
1
0
1
1
2
1
1
2
1
0
0
0
1
1
1
1
1
2
1
1
1
0
2
1
2
1
1
0
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
1
1
0
1
2
1
1
1
2
2
1
0
1
2
1
1
1
1
2
0
0
1
2
2
1
1
2
1
2
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
0
2
0
1
0
2
2
2
2
1
2
0
2
1
0
0
0
1
0
1
2
1
0
1
0
0
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
2
2
0
1
0
1
2
0
1
1
1
1
1
1
1
1
2
1
2
1
1
0
2
1
2
1
2
1
0
1
1
1
0
1
2
1
1
1
1
0
0
0
2
1
2
1
1
0
1
2
2
0
1
1
1
2
1
1
1
2
2
2
1
1
0
2
2
2
0
1
1
1
1
0
1
1
1
1
1
2
1
1
3
1
2
1
1
1
1
2
1
1
0
1
2
0
2
1
0
1
2
2
1
1
1
1
1
1
2
1
1
2
1
0
1
2
1
2
2
2
1
1
1
2
1
1
0
1
0
1
2
0
1
0
1
2
1
1
4
2
2
1
1
1
1
2
2
0
2
1
1
1
1
0
0
1
0
1
1
1
1
1
1
2
0
2
1
1
1
2
1
1
1
1
2
0
2
1
0
1
1
2
1
0
1
2
0
0
2
2
2
1
1
3
0
1
1
1
1
1
1
1
0
2
1
1
2
1
2
1
1
1
1
1
1
1
2
1
0
1
1
0
1
2
1
1
1
1
2
1
1
2
0
0
1
1
1
2
1
2
2
1
1
1
1
1
2
1
0
1
2
1
1
1
0
0
1
2
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
2
0
1
1
1
2
1
2
1
1
2
1
2
1
2
1
1
0
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
2
1
1
1
1
1
0
1
1
1
0
1
1
0
1
1
2
2
1
2
1
1
1
1
1
1
1
1
0
0
1
0
2
0
1
1
1
1
1
1
2
2
1
2
0
1
1
0
0
1
1
1
1
2
1
1
1
1
2
1
0
1
1
1
1
2
2
1
1
1
1
0
0
1
1
1
0
0
1
0
2
0
1
1
2
1
2
1
0
2
2
2
1
1
2
1
1
1
1
2
2
1
2
1
2
1
1
2
1
1
2
1
2
0
1
2
1
1
1
1
1
2
1
0
1
1
2
1
2
1
2
1
1
1
1
1
1
1
1
0
1
1
2
2
0
2
2
2
1
1
2
1
1
1
2
1
1
0
1
1
2
2
0
2
1
1
0
2
1
1
1
1
1
1
0
1
1
1
1
1
1
0
2
0
2
1
0
1
1
1
1
0
1
1
0
1
1
1
2
0
1
1
1
2
1
0
1
0
0
1
1
1
1
1
1
0
1
2
1
0
1
1
3
2
1
2
4
1
1
1
1
1
1
1
1
1
0
1
1
0
1
2
1
2
1
1
2
1
0
2
1
1
2
1
1
1
2
1
1
1
3
2
0
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
2
2
1
2
1
1
1
1
2
2
1
2
2
2
1
3
0
2
1
1
0
2
1
1
1
1
1
2
2
2
1
1
2
1
2
2
1
2
0
1
2
1
1
1
1
1
1
1
1
1
1
1
2
0
1
2
0
2
1
1
1
1
1
1
0
2
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
0
1
2
2
2
1
1
1
1
2
0
1
1
1
1
1
1
2
0
0
2
1
0
1
1
0
0
1
1
1
2
1
1
1
2
2
1
1
1
1
1
2
2
1
1
1
2
1
1
0
1
2
2
1
1
1
1
1
0
1
1
2
2
2
0
1
1
0
1
1
2
1
1
2
2
1
0
2
1
1
1
1
1
1
1
2
1
1
2
1
0
2
1
1
0
1
1
2
1
1
1
0
2
0
3
2
1
1
2
1
1
1
2
0
1
1
2
2
1
0
2
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
2
1
1
1
1
2
1
1
0
1
0
1
0
1
2
1
1
1
1
1
1
1
0
1
1
2
1
0
0
1
1
1
2
1
2
2
1
1
0
0
1
4
0
2
2
1
1
1
1
2
1
1
1
2
1
0
2
1
0
0
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
0
2
1
0
1
1
1
2
4
1
1
1
1
0
0
1
1
0
1
2
1
1
2
1
1
0
1
2
1
2
0
1
1
2
1
1
1
1
2
2
1
1
1
1
1
2
1
1
1
1
1
1
2
2
1
0
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
2
1
0
1
1
2
2
0
1
1
0
1
1
0
1
1
1
1
1
2
0
2
2
1
0
1
0
0
1
1
2
1
1
1
2
1
0
2
0
0
1
1
2
1
1
1
1
1
0
0
0
1
0
1
1
1
1
1
2
2
1
1
1
2
0
0
1
2
1
1
0
1
1
1
0
1
0
0
1
1
2
1
1
0
1
1
1
1
2
2
1
1
1
1
1
1
0
2
0
1
1
2
1
1
2
1
2
1
2
2
2
1
2
2
1
2
2
1
1
0
2
2
1
0
2
1
1
1
2
1
2
1
0
1
1
1
1
1
1
2
2
0
1
0
1
1
1
0
2
2
0
1
2
1
3
2
0
1
1
2
1
1
1
1
2
2
0
1
2
1
1
0
1
1
1
1
1
1
1
0
2
2
2
1
1
1
2
0
1
2
2
0
2
1
1
1
1
1
1
1
0
2
1
1
0
1
1
0
1
1
0
0
2
1
2
1
1
1
0
1
1
2
1
1
2
0
1
1
0
1
0
1
1
1
1
0
0
2
1
2
0
0
2
1
1
1
1
1
2
0
1
1
0
2
0
1
2
2
1
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
0
1
0
2
0
1
2
1
0
1
1
0
1
1
2
2
1
1
0
1
1
1
1
2
2
2
2
2
1
1
1
1
1
2
1
1
2
1
1
2
0
1
1
1
2
1
1
2
1
1
2
1
1
1
1
1
0
1
1
2
0
0
1
2
1
1
2
2
1
2
1
1
1
1
1
0
1
1
1
1
1
1
0
0
1
1
1
1
2
1
1
2
1
2
1
1
2
2
1
1
1
0
1
1
1
1
1
2
0
1
1
2
1
0
0
2
1
1
2
1
1
1
2
2
1
2
1
2
1
1
1
1
2
1
1
0
1
1
2
1
1
1
1
2
1
1
1
1
1
1
0
1
1
1
1
1
1
2
2
1
1
2
1
2
1
1
1
2
1
4
1
1
1
2
2
2
1
1
1
1
2
1
1
1
1
1
1
0
1
2
2
0
1
3
1
3
1
1
1
1
1
0
0
0
0
1
1
1
1
1
1
1
0
1
1
1
2
2
1
1
1
1
1
2
1
0
1
1
1
2
0
1
1
2
1
1
0
1
1
1
1
1
1
1
1
0
2
2
1
1
2
2
2
2
1
1
1
1
1
1
1
1
1
1
2
2
0
0
2
1
0
0
1
0
1
0
2
1
1
1
1
1
2
1
2
2
2
1
2
0
2
1
1
1
1
2
0
2
1
1
0
0
0
1
2
1
2
2
0
0
1
2
1
1
2
1
1
1
0
1
2
1
1
0
1
1
1
1
0
1
1
1
0
1
1
2
0
1
1
2
2
1
2
2
0
1
1
1
2
1
1
0
1
1
1
2
2
1
1
1
1
1
1
0
2
1
1
1
2
2
0
1
1
2
1
1
0
1
0
1
1
1
2
2
1
2
2
1
1
2
2
1
1
0
1
2
0
0
0
1
2
1
0
0
1
1
1
2
1
2
1
1
1
1
2
1
2
2
0
1
1
2
1
2
1
1
2
2
1
1
1
0
1
1
0
1
1
0
0
2
1
1
0
2
1
1
1
1
0
2
1
0
2
1
1
2
1
1
1
1
0
1
1
1
1
0
1
2
1
0
1
1
3
1
1
1
1
1
1
1
1
0
0
1
1
3
1
1
1
1
1
2
0
1
1
1
2
1
1
1
1
1
1
2
1
2
2
0
1
2
1
1
0
1
1
2
0
3
1
1
2
1
2
1
0
0
0
1
1
1
1
1
0
2
1
0
1
1
1
1
1
2
1
1
0
1
1
0
3
2
0
1
1
1
0
1
2
1
0
1
2
1
0
1
1
2
1
0
1
2
1
1
1
2
2
1
1
1
0
1
1
2
1
1
2
2
1
0
0
0
1
0
1
1
1
1
1
1
0
1
2
1
1
2
0
2
2
2
0
1
1
1
1
0
1
2
2
1
1
0
1
2
1
1
2
1
0
1
1
1
1
0
2
0
2
2
1
1
0
1
1
1
2
0
1
1
2
1
2
1
1
1
2
1
1
1
2
1
1
1
1
2
1
2
1
1
3
2
1
1
1
2
1
0
1
1
0
1
2
0
1
1
2
0
1
1
2
1
1
1
0
1
1
1
1
2
1
0
1
2
1
2
2
1
1
1
1
1
1
1
2
1
2
1
3
1
1
1
1
2
0
0
1
1
1
0
2
1
1
1
1
0
1
1
1
2
1
1
0
2
1
0
1
2
1
1
1
1
2
0
1
1
2
2
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
0
1
1
1
0
1
1
1
1
0
1
1
1
1
0
2
2
1
0
1
1
1
1
2
2
2
1
1
2
2
2
1
1
1
1
1
2
1
1
1
2
1
2
1
2
2
1
2
2
1
1
1
2
2
1
1
1
2
1
2
2
1
1
1
1
0
2
0
1
2
1
2
1
1
1
0
2
1
0
1
1
0
1
1
0
2
1
2
1
1
1
1
1
2
1
1
1
0
1
1
0
1
2
1
2
2
0
2
2
2
0
2
1
0
1
1
1
0
1
1
1
1
1
1
2
1
2
1
1
1
1
1
0
1
1
2
1
2
1
2
1
1
2
1
1
0
1
1
1
1
0
2
1
1
1
1
2
1
1
0
2
2
1
1
1
1
2
0
1
1
1
0
2
1
0
1
2
1
2
1
2
1
1
0
1
2
2
1
1
1
1
2
0
1
1
1
0
1
2
1
2
0
1
1
2
1
2
1
0
1
0
1
2
1
0
0
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
2
1
2
1
1
2
0
0
1
0
1
1
0
1
0
1
1
1
0
2
1
1
1
2
1
1
1
2
2
1
1
1
1
1
2
1
2
1
0
2
1
1
1
2
1
0
1
1
1
1
0
1
1
1
2
1
2
1
0
2
1
1
1
2
1
2
2
2
1
1
1
2
0
1
1
2
1
1
1
1
1
1
1
1
1
1
0
2
1
0
1
1
1
2
1
1
1
1
1
1
2
0
1
1
1
1
1
2
1
2
1
0
2
2
0
1
0
2
4
2
2
0
2
1
2
1
1
0
1
2
2
1
1
1
1
1
1
1
0
1
1
1
1
1
2
1
1
0
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
2
1
1
1
1
1
1
0
1
2
1
1
2
1
0
0
1
1
2
2
2
1
0
1
1
1
2
2
2
1
2
1
2
0
2
1
2
1
2
1
0
1
1
1
1
2
2
1
2
1
1
1
2
1
2
2
1
1
1
0
2
2
0
0
1
0
1
2
2
2
1
2
2
1
1
1
0
1
2
1
1
1
1
0
0
1
1
1
0
2
1
1
1
0
0
1
1
1
1
2
2
0
1
0
0
1
1
1
2
1
1
2
1
1
1
0
2
0
0
0
2
2
2
0
1
0
2
1
1
2
1
2
0
2
0
1
1
1
1
1
1
0
1
1
1
1
1
1
1
0
2
1
3
1
1
1
1
1
1
2
2
1
0
2
2
1
0
2
2
1
1
2
0
1
2
1
2
1
1
1
2
1
1
0
1
1
1
1
1
1
2
1
1
1
1
1
0
1
2
1
1
1
2
2
1
2
1
1
1
0
2
1
1
1
1
2
2
1
1
1
2
1
0
1
1
2
2
0
1
2
1
1
2
1
1
1
1
2
2
1
2
0
0
1
1
1
0
1
1
2
1
1
1
1
1
1
1
1
0
1
2
1
2
1
1
1
1
1
1
2
1
1
0
2
2
2
1
1
3
0
2
0
2
2
2
1
1
1
0
1
1
1
2
1
1
1
1
1
0
1
1
0
2
1
1
2
2
1
1
1
1
1
2
2
0
1
1
1
1
2
2
2
1
1
1
1
1
2
2
1
0
2
1
0
0
1
1
2
1
1
2
2
2
2
1
2
1
1
1
3
1
1
1
2
0
1
2
1
2
1
2
1
1
3
1
2
1
1
1
2
1
2
2
2
1
1
1
0
1
2
1
0
1
2
1
1
2
1
2
1
2
1
1
3
1
1
2
1
2
1
2
1
1
0
1
1
1
0
2
1
0
1
1
1
2
0
1
1
1
2
1
1
1
0
1
2
1
1
2
1
1
1
0
0
1
1
0
1
1
1
2
1
2
1
1
1
0
1
1
1
1
2
1
2
1
1
1
1
1
2
2
0
0
2
1
0
2
2
1
8
2
1
0
1
1
1
2
2
2
2
2
1
1
2
1
1
1
2
0
1
2
1
1
2
1
0
1
2
0
1
2
2
1
1
2
2
1
1
1
2
1
2
1
1
1
1
2
1
1
2
1
2
2
2
1
0
2
1
1
2
1
1
1
1
2
1
1
1
1
2
2
2
1
1
2
1
2
2
1
1
1
2
0
1
1
2
1
1
1
1
1
2
2
1
1
1
2
2
1
0
1
2
2
1
1
0
1
1
2
2
2
2
1
0
1
1
2
1
1
1
0
1
1
0
1
2
0
1
2
1
2
1
2
1
1
0
1
1
0
1
2
1
0
1
0
1
2
2
1
1
1
1
2
2
2
1
2
0
1
0
2
2
2
1
0
1
1
1
1
3
2
1
2
1
1
0
2
2
1
1
1
1
1
1
1
2
2
2
1
1
2
0
1
1
0
1
0
0
2
1
2
1
2
1
2
1
1
1
1
1
0
2
1
0
1
1
1
0
1
1
1
2
1
1
1
2
2
1
1
1
1
2
2
2
1
2
1
0
1
1
1
1
0
1
1
1
1
1
1
2
1
1
2
1
1
1
2
2
1
0
2
1
0
1
1
2
1
2
1
1
1
2
1
1
1
1
0
0
0
1
0
1
2
1
1
2
1
1
0
1
2
1
2
1
2
0
1
1
1
2
1
1
2
2
0
1
1
0
1
1
1
1
1
2
0
1
1
1
1
1
1
1
2
1
0
1
1
1
1
1
1
1
1
2
2
0
0
2
1
2
1
1
0
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
0
1
2
0
2
1
2
0
1
1
0
1
1
2
2
1
1
1
1
1
1
1
1
2
1
0
1
1
1
1
1
1
0
2
0
2
1
1
1
0
1
1
2
1
1
1
1
1
1
1
1
2
1
1
0
1
1
0
1
1
1
1
0
1
2
2
1
1
1
1
1
0
2
1
1
2
2
1
1
0
1
2
1
2
1
2
1
1
2
1
1
1
1
1
1
1
0
2
1
1
1
2
1
1
0
2
0
2
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
0
2
1
1
1
2
0
1
1
1
0
1
0
1
1
1
0
1
1
1
2
1
0
2
1
0
1
0
2
2
1
1
1
1
1
1
1
1
2
1
2
0
2
1
1
1
1
2
1
1
2
2
1
1
2
1
1
1
1
2
1
1
0
1
0
1
1
2
1
1
2
1
2
1
1
1
1
1
1
0
2
1
2
1
1
2
1
1
1
0
1
2
1
1
1
2
2
1
1
2
2
1
2
1
2
1
1
0
0
1
2
1
1
1
1
1
2
2
1
1
2
1
2
1
1
0
2
0
1
2
1
1
1
1
1
0
2
0
1
0
1
2
0
2
1
0
1
3
1
1
1
1
2
1
1
1
1
2
1
1
0
1
2
1
2
1
2
2
0
0
1
2
1
1
0
1
1
1
0
0
2
1
2
1
1
1
0
2
1
1
1
1
1
1
1
1
1
2
1
1
0
1
0
1
1
1
2
1
1
0
1
1
1
0
2
1
0
1
0
1
1
1
2
1
1
1
1
2
0
0
1
1
0
2
2
0
2
2
1
0
2
1
2
1
2
1
2
1
1
1
2
2
1
1
1
1
1
2
2
1
1
1
1
1
0
2
0
2
1
1
1
1
2
1
1
1
0
2
0
1
2
1
2
2
1
1
1
2
1
1
1
1
1
2
2
1
1
1
2
2
2
2
1
1
1
1
2
1
1
2
1
0
1
1
2
2
1
1
2
1
0
2
0
2
1
0
1
1
1
1
1
1
2
1
0
2
2
1
1
1
1
2
2
1
0
0
0
2
1
1
5
0
1
1
3
2
2
2
1
2
1
2
1
2
1
1
0
2
1
1
1
1
1
1
0
1
2
2
2
2
1
1
1
1
2
2
1
1
1
1
1
1
1
2
0
1
1
0
1
2
1
0
2
1
1
1
1
2
2
0
2
0
1
1
2
2
1
2
1
2
1
1
1
1
0
0
0
1
0
0
1
1
0
2
1
1
1
3
2
1
1
1
0
2
1
0
1
1
1
2
2
1
0
2
1
0
1
1
2
1
0
1
1
2
1
0
1
2
1
2
1
1
1
1
1
2
1
1
1
2
1
1
2
1
2
0
1
1
3
1
1
1
1
1
0
0
1
1
2
1
3
1
1
2
1
1
1
1
1
1
0
2
1
1
1
1
0
2
2
1
1
2
1
1
2
2
0
1
2
1
1
0
2
0
2
2
0
2
0
2
1
1
1
2
2
1
1
1
1
2
1
1
2
1
1
2
1
2
1
1
1
0
2
0
1
2
1
1
1
1
0
2
2
2
2
1
1
1
2
3
1
1
1
1
1
1
1
1
1
1
2
1
1
1
0
1
1
1
1
1
1
1
1
1
0
2
0
1
1
2
1
2
2
1
2
2
1
1
2
2
1
1
1
1
1
0
1
2
1
1
0
1
2
1
2
1
3
2
2
0
2
1
1
1
2
1
0
1
2
1
1
7
2
0
0
1
1
1
1
1
1
2
0
1
1
2
0
1
2
2
1
0
2
1
2
1
2
2
1
0
1
2
1
1
0
0
1
2
1
1
0
1
1
2
1
1
2
1
4
4
4
1
1
1
1
0
0
1
1
1
1
1
1
2
1
1
2
1
2
1
1
1
1
1
0
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
0
1
1
0
1
0
2
2
2
0
1
1
1
1
1
2
1
1
2
0
1
1
0
1
1
1
2
2
1
1
1
2
1
1
1
1
1
1
1
0
2
0
1
1
1
2
2
2
2
2
0
1
3
1
1
1
2
0
0
1
1
0
1
0
1
3
1
1
2
1
0
0
0
0
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
2
0
2
1
1
1
2
1
0
1
1
2
1
2
2
1
1
1
1
1
1
0
2
1
0
0
0
2
1
1
1
1
1
2
1
2
1
2
1
2
1
1
2
0
1
1
1
2
1
1
1
2
2
0
0
2
1
0
1
0
1
2
1
1
2
1
2
1
1
1
2
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
0
0
1
1
0
1
1
1
0
1
1
1
2
1
2
2
1
1
2
1
2
1
2
1
1
1
2
1
2
2
1
2
0
1
2
1
2
1
1
0
3
2
1
2
0
2
1
1
1
1
1
0
1
0
1
1
1
0
1
0
1
0
2
1
2
1
1
0
0
1
0
2
0
1
2
0
1
1
1
1
2
1
2
1
1
1
1
2
1
0
1
2
1
2
2
1
0
2
1
1
0
1
0
0
0
0
1
1
0
0
1
1
2
1
2
1
0
2
2
1
1
1
1
2
2
1
1
1
1
2
0
1
1
0
2
2
0
0
1
0
0
1
1
1
1
1
0
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
0
1
1
1
1
2
1
0
1
1
2
1
1
1
1
1
1
1
1
2
2
1
0
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
2
2
2
1
2
1
1
1
0
1
1
1
1
1
1
2
2
1
0
1
0
1
1
1
1
1
0
1
1
1
0
1
0
1
2
1
1
1
0
2
1
0
2
0
0
1
0
2
1
2
1
2
0
0
1
1
2
1
1
1
3
2
2
2
1
1
1
0
1
1
2
1
1
1
2
2
1
0
1
1
0
1
0
1
0
1
2
2
2
0
1
0
1
1
1
1
0
1
2
1
2
1
0
1
1
0
2
0
1
1
1
1
0
0
1
2
1
1
0
1
1
1
1
0
1
2
1
0
0
2
1
1
1
1
0
2
2
1
1
2
3
0
1
1
1
0
1
1
1
1
1
1
1
1
0
1
1
2
2
1
2
1
1
1
1
0
2
1
1
2
1
2
1
1
1
1
2
1
2
1
1
2
0
1
1
2
2
1
1
1
1
0
1
2
2
1
0
1
1
2
1
1
1
1
0
1
1
1
1
2
1
2
1
2
1
0
0
2
0
1
1
1
1
2
0
2
1
0
0
1
0
2
1
1
1
1
2
1
1
1
2
1
2
1
1
0
1
1
1
1
1
1
1
3
1
2
1
1
2
1
1
0
1
1
1
1
2
2
2
1
0
2
1
1
0
1
1
1
1
1
0
1
1
1
2
1
2
1
1
1
1
2
2
0
1
2
1
1
1
1
1
1
2
1
1
2
1
1
2
2
1
1
1
2
0
1
1
1
3
1
1
2
0
1
1
1
2
2
2
1
1
1
1
1
0
2
0
2
1
1
0
0
1
1
2
1
2
2
1
1
2
1
1
1
1
1
1
2
1
1
0
1
1
1
1
1
1
1
0
1
1
1
1
2
2
2
1
1
1
1
1
1
0
1
1
1
2
0
0
0
0
1
1
1
1
1
1
2
1
1
1
3
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
1
0
1
0
2
2
2
1
0
1
1
1
1
1
2
2
1
1
1
1
1
1
1
0
1
1
1
1
1
2
2
2
2
2
1
1
1
0
1
1
1
1
1
1
1
2
2
2
2
1
1
1
1
1
1
1
1
0
1
2
1
2
1
2
1
0
1
1
1
1
1
1
0
3
1
0
0
2
2
2
1
1
2
0
2
2
2
1
1
1
1
1
1
1
1
0
1
1
1
1
0
1
1
0
1
3
1
2
2
1
1
1
2
1
2
2
1
0
1
2
1
1
2
1
1
1
1
0
0
0
2
1
1
1
1
1
1
1
2
2
2
1
1
2
0
1
0
1
1
1
2
0
1
1
2
2
1
0
1
1
0
0
1
1
2
1
1
1
2
2
1
1
1
2
1
1
2
2
1
1
1
1
0
1
2
2
2
1
0
1
2
1
1
1
0
1
0
1
1
1
1
1
1
2
0
1
2
1
1
1
1
1
1
2
1
1
1
1
2
2
1
2
2
0
1
0
0
2
0
2
1
0
1
1
1
1
1
0
2
1
1
1
2
1
0
1
0
0
2
2
2
2
1
2
2
1
2
2
2
2
1
1
1
1
1
1
0
2
1
0
1
2
0
0
0
1
1
2
1
1
1
1
1
2
1
2
1
3
1
1
2
1
0
1
1
1
1
0
0
2
2
1
1
0
1
1
1
1
2
0
1
0
1
2
1
0
1
1
1
1
1
1
0
1
1
1
2
0
0
0
1
2
1
2
1
1
2
0
1
1
1
1
1
1
1
1
2
3
0
1
0
2
1
0
1
1
1
2
0
2
1
1
2
2
1
2
1
1
3
1
0
2
2
2
1
0
2
0
2
0
2
1
0
1
1
1
1
1
1
1
1
0
2
1
0
1
1
1
1
1
1
1
1
1
1
2
0
1
2
2
1
0
1
1
1
1
0
1
1
1
2
0
2
2
2
1
1
1
1
0
1
1
1
1
2
1
1
2
3
1
1
1
1
2
1
1
0
2
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
2
1
2
1
1
0
1
2
1
1
1
0
1
1
1
1
2
1
2
2
0
1
2
1
1
1
1
1
1
2
1
1
2
1
1
0
0
1
1
1
0
1
1
1
1
0
0
1
1
1
1
1
1
1
2
1
2
0
1
1
0
0
1
1
1
2
2
2
2
1
1
1
2
2
1
1
2
1
1
0
1
0
1
1
0
0
1
1
0
1
1
1
1
2
2
1
2
1
1
1
2
1
2
1
2
0
0
1
1
1
2
1
1
1
2
2
1
0
0
1
2
0
2
1
1
2
0
0
1
1
0
1
1
0
2
0
0
1
0
0
1
1
1
1
1
2
2
2
0
1
1
2
2
1
1
1
1
1
2
1
0
1
2
1
2
2
1
3
1
2
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
2
1
1
1
0
1
2
0
1
1
2
2
0
1
1
2
1
1
2
2
1
1
2
1
1
1
0
1
1
1
2
1
2
1
1
1
1
0
1
2
1
1
1
1
1
1
1
0
2
0
0
2
1
1
1
1
1
2
2
1
0
1
1
0
2
1
1
1
1
4
1
1
1
1
1
0
1
1
1
2
0
1
1
0
2
2
1
1
1
1
1
1
1
1
2
1
2
1
1
2
1
0
1
1
5
1
2
1
1
1
2
1
1
1
1
2
1
2
1
1
2
1
3
0
2
1
0
1
2
2
1
1
2
1
0
1
0
1
1
2
1
1
1
1
1
3
2
1
1
1
1
1
1
1
1
2
1
0
1
1
1
1
1
0
0
0
2
1
2
1
1
1
1
2
1
2
1
2
2
2
1
2
2
1
1
0
1
0
2
1
2
2
1
1
0
1
1
1
1
1
0
1
1
1
2
1
0
1
1
2
1
1
0
1
1
0
2
1
0
2
1
0
2
1
1
2
2
2
0
0
2
1
1
1
1
2
1
2
2
0
1
2
1
1
1
0
1
0
1
1
0
0
1
1
1
0
1
1
1
0
1
1
1
1
1
1
0
2
2
1
1
2
1
1
0
0
1
1
1
1
1
1
2
1
2
1
1
1
0
1
1
1
1
1
1
2
1
2
1
1
1
2
2
1
1
2
1
1
1
2
1
2
2
1
1
2
0
1
2
1
1
1
2
1
2
1
1
1
1
5
1
1
0
2
1
1
2
2
1
1
1
1
2
2
1
2
1
1
2
2
1
1
1
0
1
1
0
2
1
1
2
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
0
1
1
1
2
1
1
2
2
0
0
1
1
1
1
1
0
2
2
1
1
2
2
1
1
1
1
1
0
2
1
2
1
1
1
2
1
1
2
1
2
0
1
1
3
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
2
1
1
3
1
2
1
1
1
2
0
2
1
1
1
1
1
1
1
2
0
1
2
0
2
1
1
0
2
0
2
2
0
0
1
1
1
1
1
2
0
1
1
1
1
2
1
2
2
1
1
1
1
2
1
1
1
0
2
1
1
0
3
2
1
1
2
1
1
1
1
1
0
1
2
1
3
1
2
1
1
0
1
1
1
1
2
0
2
0
1
1
1
2
1
1
2
1
0
2
1
1
1
0
1
1
2
0
1
1
1
1
2
2
2
1
1
1
1
2
1
1
1
0
2
1
1
1
2
1
1
1
2
0
1
0
2
0
2
1
1
2
2
2
0
2
2
1
2
1
0
1
1
1
0
1
1
1
1
2
1
1
0
2
0
1
2
0
0
1
0
0
1
0
1
1
1
2
2
1
1
1
0
1
1
1
2
1
2
1
1
2
2
1
1
0
1
2
0
0
1
1
2
1
1
1
1
2
0
1
1
1
2
1
0
2
1
1
1
1
2
1
1
2
2
0
1
1
2
0
1
1
0
1
1
2
1
1
1
0
2
1
2
0
1
1
0
3
0
1
1
2
0
1
2
1
0
1
1
1
0
1
0
0
1
2
1
2
1
1
2
2
1
1
1
1
0
0
2
1
0
1
1
0
1
1
1
1
2
1
1
0
2
1
2
1
2
1
0
1
1
1
0
1
1
1
1
1
0
1
2
1
1
1
2
1
1
1
1
1
0
5
1
1
0
2
2
2
1
1
2
2
1
2
0
2
1
1
2
0
1
1
1
1
1
1
2
2
1
1
1
2
2
1
2
1
0
1
1
2
2
1
0
1
1
0
2
2
1
1
2
2
2
2
1
1
1
1
1
0
0
1
1
2
1
1
1
1
1
1
1
1
1
0
2
1
2
1
1
1
1
2
0
1
2
2
1
2
1
1
1
1
2
1
0
1
0
1
1
2
1
2
1
1
1
1
1
1
2
1
0
1
2
1
1
0
1
1
1
0
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
0
1
1
0
0
2
1
1
1
2
0
1
1
1
0
1
1
0
1
0
1
1
1
1
0
1
1
2
1
1
1
1
1
1
2
1
2
2
2
1
0
1
1
2
1
1
0
2
2
1
2
1
0
1
0
1
1
1
1
1
1
2
1
1
1
2
1
1
1
0
2
0
1
1
1
1
1
1
0
1
1
0
2
1
1
1
2
1
2
1
1
1
0
1
2
1
1
1
1
0
1
2
1
1
1
1
1
1
1
1
1
1
0
2
0
2
1
2
2
0
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
0
1
1
2
1
1
1
2
0
0
1
1
3
1
1
3
1
2
1
1
2
1
1
2
0
1
1
1
1
0
1
1
2
1
1
1
1
2
2
2
0
1
1
1
1
1
1
2
2
2
1
1
1
2
0
2
2
2
2
2
2
0
2
1
2
1
1
1
1
0
2
2
1
1
1
1
1
1
1
2
1
1
2
2
2
1
2
1
0
1
1
1
1
1
2
0
1
1
3
2
1
1
0
1
2
1
1
0
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
0
0
1
2
1
1
1
1
2
1
0
1
0
1
1
2
2
1
1
1
0
2
1
2
1
1
1
2
1
1
1
1
1
1
3
0
2
1
2
2
0
1
1
1
1
1
1
0
1
1
1
2
1
1
2
1
1
1
1
1
2
2
1
1
0
1
1
1
2
1
2
2
1
2
1
2
2
1
1
1
1
1
2
0
1
1
1
3
1
0
0
1
1
0
1
1
1
2
1
1
2
1
1
1
1
2
2
1
1
2
2
0
1
1
1
1
1
2
2
1
1
0
2
1
1
2
1
1
1
1
1
1
1
2
2
0
1
1
0
1
1
1
1
0
1
1
1
1
1
1
1
1
1
0
1
2
1
1
0
0
1
1
1
1
0
1
1
2
2
0
0
1
1
2
0
1
1
2
1
1
1
1
2
1
0
1
2
0
1
0
0
2
1
2
2
1
1
1
1
1
0
1
0
1
1
1
2
1
2
1
2
2
2
1
1
1
1
0
3
1
1
2
1
2
0
2
2
0
1
0
1
1
2
1
2
3
1
1
0
0
2
1
0
1
2
2
2
1
1
1
1
2
1
1
1
2
1
0
1
1
1
1
1
1
1
1
2
1
0
2
2
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
3
1
0
1
1
0
1
1
1
1
1
2
2
1
1
1
1
2
2
2
0
1
0
2
1
1
1
2
2
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
0
2
0
1
1
1
2
1
1
1
1
1
0
2
1
1
1
1
1
1
2
1
1
2
0
1
1
0
2
1
1
1
2
1
2
3
1
0
1
1
1
1
2
0
2
3
0
2
2
0
1
1
2
1
0
2
1
0
1
1
0
0
1
1
1
0
1
0
1
2
2
1
2
0
2
2
1
2
1
1
0
1
2
1
1
0
1
0
1
1
1
0
0
1
1
1
1
1
2
2
1
1
1
1
2
0
1
1
1
2
2
2
1
2
0
2
1
2
1
1
1
0
1
1
1
2
1
0
1
1
1
1
2
1
2
1
1
2
1
1
1
2
1
1
2
0
1
1
1
1
1
1
0
1
2
1
2
1
0
1
2
1
0
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
2
1
0
1
1
2
0
2
0
2
1
2
2
2
1
1
0
1
1
2
0
1
0
1
2
1
1
1
2
1
2
2
2
1
0
1
1
1
1
2
0
0
2
1
1
2
0
1
1
1
1
1
1
2
1
1
1
1
1
2
2
0
2
1
1
1
1
1
1
2
0
2
1
0
2
2
1
2
2
1
1
1
2
1
4
0
1
1
2
2
2
1
1
2
0
1
2
2
1
1
1
1
1
1
2
1
0
1
1
1
0
1
1
1
1
2
0
1
1
1
1
2
1
2
1
1
1
2
2
1
1
0
0
1
1
2
2
1
1
1
1
2
2
1
2
1
1
2
1
1
2
1
0
1
1
1
1
1
2
1
1
0
1
0
1
0
1
0
2
1
1
1
2
1
0
0
2
1
1
1
2
1
1
1
1
1
1
1
1
1
0
1
1
2
1
0
0
2
1
2
1
1
0
2
1
1
2
1
1
2
2
1
1
1
1
1
1
2
2
2
1
2
1
1
1
0
1
0
0
1
0
1
1
1
0
1
1
1
1
2
1
1
2
2
1
0
1
1
1
2
2
1
2
2
2
1
1
0
2
1
1
5
1
2
1
1
2
1
1
2
1
2
1
1
2
1
1
1
2
1
0
2
1
1
0
0
1
1
1
1
1
1
0
1
1
1
0
2
1
2
1
1
0
1
2
1
1
1
1
1
1
1
1
1
3
2
1
1
1
0
0
2
1
1
1
1
2
2
1
0
1
1
0
0
2
1
0
1
0
1
0
2
1
1
1
2
1
0
2
1
2
1
1
2
1
1
1
0
2
1
1
1
1
1
1
0
1
1
0
1
1
1
1
2
1
1
1
2
1
2
0
1
1
1
1
1
2
1
1
2
1
2
1
2
1
1
0
1
1
0
1
1
0
1
0
1
0
0
1
1
2
1
1
1
1
1
1
2
2
1
1
2
0
1
1
1
2
1
1
2
1
1
1
1
2
1
1
1
1
1
2
1
1
0
1
0
2
1
1
1
2
2
1
2
1
2
1
0
1
0
0
1
2
1
1
1
0
1
1
1
0
1
1
1
1
0
1
1
0
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
0
2
1
1
2
2
1
2
1
1
1
0
1
1
0
1
1
1
1
2
0
1
2
0
1
2
2
1
1
1
0
0
2
1
2
1
1
1
2
1
2
0
1
2
1
1
1
2
1
1
0
1
2
2
2
1
1
0
1
0
1
0
2
1
2
0
1
1
2
0
2
1
1
1
0
1
1
2
1
1
1
1
1
2
1
0
1
1
1
1
0
0
1
1
1
1
1
1
1
1
0
2
1
1
1
1
0
2
1
1
2
1
1
1
0
1
2
1
1
0
0
1
2
1
0
2
0
1
1
2
1
1
0
2
1
1
1
1
1
1
1
1
1
1
0
1
1
0
1
0
1
1
2
0
1
2
1
1
0
1
1
1
1
1
0
0
1
0
2
2
1
0
1
1
2
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
0
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
3
2
1
1
2
2
2
3
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
1
1
4
1
1
1
2
0
1
1
1
1
0
2
1
0
0
1
1
1
0
1
1
1
1
1
0
2
2
1
1
2
2
1
1
2
0
1
1
1
1
1
1
2
1
2
2
1
1
1
0
1
1
1
2
1
1
1
2
1
0
0
0
1
1
2
1
0
0
0
1
2
1
1
0
0
1
1
1
2
0
2
2
2
2
0
1
1
1
1
2
0
2
1
2
1
1
1
1
1
1
1
1
1
0
1
2
2
0
1
1
1
1
2
2
2
1
2
1
2
1
2
0
1
0
1
1
0
1
1
1
1
1
0
0
1
2
1
1
1
1
0
1
2
1
1
1
1
0
1
1
1
1
2
0
2
1
1
1
1
1
0
1
1
1
1
0
1
1
2
2
1
0
2
1
0
1
1
0
0
1
0
1
1
1
1
2
2
2
0
1
2
1
0
1
1
1
1
1
2
1
1
0
1
0
1
2
2
1
2
1
2
1
1
1
1
0
2
1
1
2
2
0
2
1
1
1
1
1
2
1
1
1
1
0
1
1
1
1
1
1
0
1
1
1
0
1
5
1
1
0
1
2
1
2
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
0
1
1
1
1
1
1
2
0
1
1
1
1
1
1
0
2
1
1
0
2
1
2
2
1
1
0
2
1
2
1
2
1
1
2
2
1
0
1
2
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
0
1
1
2
1
1
2
1
1
0
1
1
2
1
2
1
1
0
0
1
1
1
1
1
1
0
2
1
0
1
1
1
3
0
1
1
1
1
2
0
0
1
1
1
1
1
2
0
2
1
1
2
1
1
1
3
0
0
2
2
1
1
2
1
1
1
1
2
1
2
1
2
1
2
2
2
1
1
1
1
0
1
0
1
1
2
1
1
1
1
2
1
0
1
1
2
1
2
2
1
1
2
1
1
2
1
2
1
1
1
1
0
1
0
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
1
2
2
1
1
1
0
0
1
1
0
2
1
0
1
1
2
1
1
0
1
0
1
1
1
1
0
1
1
1
2
2
1
1
1
2
2
1
1
1
0
2
2
0
1
1
1
0
2
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
0
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
2
0
1
1
1
2
2
1
2
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
0
1
1
1
1
0
1
1
2
1
1
2
1
1
2
2
0
2
0
0
1
1
2
1
1
2
1
1
1
2
0
1
2
1
1
0
2
1
1
2
0
1
1
1
1
1
0
1
1
1
0
1
1
2
1
1
1
2
1
1
0
1
1
1
1
1
1
0
1
1
2
1
1
1
1
1
0
1
2
2
1
1
1
1
1
0
0
1
0
1
1
1
1
0
0
1
1
1
1
1
0
0
1
0
2
0
1
1
1
1
1
2
0
1
0
1
2
1
2
2
1
1
2
0
1
0
1
1
1
2
3
1
0
1
0
1
2
1
0
0
0
1
1
1
0
1
1
0
2
2
2
1
1
0
1
1
1
1
2
1
1
4
1
1
1
1
0
2
1
1
2
0
2
1
1
1
1
0
0
0
2
1
1
1
1
1
2
1
0
1
1
3
1
1
1
1
1
0
0
0
1
2
2
0
1
0
1
2
2
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
2
0
1
1
1
1
1
2
2
1
2
1
1
2
1
1
2
1
2
1
1
2
2
0
2
2
1
0
1
2
0
1
1
1
1
2
2
1
1
2
1
1
2
2
1
2
2
1
1
0
1
0
1
0
0
3
1
1
1
1
1
2
1
0
2
0
1
2
2
1
0
1
2
1
0
2
2
1
2
1
0
1
2
1
2
1
0
1
1
0
1
1
0
0
1
1
1
1
2
1
2
1
0
2
1
2
1
0
2
1
2
1
1
1
1
2
1
1
1
1
1
2
1
1
0
1
1
1
1
0
2
1
1
2
2
1
1
1
0
1
1
1
2
2
2
1
0
2
2
1
1
1
0
1
1
1
1
2
1
1
1
1
1
0
1
1
1
1
1
0
2
2
1
1
1
1
2
1
0
2
1
1
1
1
1
1
2
1
1
2
1
1
1
1
2
1
2
1
1
1
2
0
2
1
1
0
1
2
2
0
2
1
1
1
1
1
1
1
1
1
1
1
0
2
1
1
1
1
0
2
2
0
1
1
1
2
2
1
1
0
0
2
1
1
0
1
1
1
1
1
0
1
1
1
1
1
1
0
1
0
1
1
1
0
2
1
1
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
1
0
2
2
1
2
1
2
2
1
1
2
1
2
0
1
2
2
2
1
4
2
2
1
2
1
1
1
1
0
1
2
2
2
1
2
2
1
1
2
1
1
1
1
1
0
1
1
2
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
2
1
1
0
0
1
0
1
1
2
0
1
1
1
0
1
2
1
2
1
2
2
1
1
1
1
1
2
0
1
1
1
1
2
1
1
1
0
1
0
1
1
2
1
1
1
1
2
2
1
1
1
1
1
2
2
0
1
1
0
0
2
1
1
1
1
2
2
1
1
1
1
1
1
1
0
1
0
1
1
1
1
1
2
1
1
1
2
0
2
1
3
1
1
2
2
0
0
2
0
1
2
1
1
0
2
1
0
1
0
1
2
2
1
1
1
2
0
1
1
0
2
1
1
1
2
0
1
1
1
1
1
1
2
1
2
2
1
2
2
1
0
1
1
1
1
1
1
1
1
1
2
0
1
1
1
1
2
1
0
2
2
2
1
0
0
1
0
1
2
1
1
2
1
2
1
1
0
0
1
1
1
1
1
2
1
1
2
1
1
0
2
0
2
0
2
1
1
2
2
2
1
0
0
1
1
2
0
1
1
1
1
1
1
1
1
1
0
2
1
2
2
2
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
0
1
1
0
2
1
1
1
1
0
1
2
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
2
1
0
1
1
1
1
1
1
1
1
1
2
1
1
1
0
1
0
1
1
1
1
2
2
1
2
1
1
1
1
2
2
1
1
0
1
1
1
2
2
1
1
2
0
1
1
1
1
1
1
1
1
1
2
2
2
1
1
2
1
1
1
0
1
1
1
2
0
1
1
1
1
1
2
2
1
1
1
2
1
1
1
0
1
2
2
1
2
2
0
1
0
1
2
1
2
1
1
1
1
1
1
1
1
2
1
0
1
2
1
0
1
1
2
1
1
1
0
1
0
1
2
1
0
2
1
0
2
2
2
1
1
0
2
0
1
1
2
2
1
1
2
1
1
0
2
1
1
1
1
1
1
0
0
1
2
1
1
0
2
1
0
2
1
1
1
1
0
1
1
1
0
1
0
2
1
0
1
1
2
1
2
1
2
2
1
2
1
0
2
1
1
1
1
1
0
0
2
4
1
1
1
2
1
0
1
2
0
0
0
1
1
1
1
1
1
1
1
2
2
2
0
1
1
1
1
1
0
0
2
4
1
1
3
4
1
2
0
1
1
0
1
1
1
0
0
0
1
1
1
1
0
1
0
0
2
1
1
1
2
1
2
0
0
2
1
1
1
1
1
2
0
0
1
1
1
0
1
0
1
2
1
0
0
2
1
2
0
1
2
1
1
2
1
1
2
1
0
0
1
2
1
0
1
1
1
0
1
1
0
1
2
0
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
0
2
1
1
2
2
1
1
1
1
1
2
0
1
1
0
2
1
1
1
2
0
0
2
1
1
1
2
0
1
1
1
1
2
1
1
1
1
1
0
2
2
1
2
1
1
1
1
1
2
1
1
1
1
3
1
1
1
0
1
1
0
2
1
1
2
0
2
1
2
1
1
1
1
2
0
2
0
1
1
2
2
1
2
2
2
1
1
1
2
0
1
1
0
2
0
1
1
2
1
3
2
2
0
2
2
3
0
1
1
1
1
2
1
1
1
1
1
1
1
0
1
1
2
1
1
1
2
1
1
1
2
1
1
0
1
0
1
2
1
0
1
1
1
1
1
1
1
1
1
2
2
1
0
1
1
2
1
1
1
1
1
2
0
1
1
1
0
1
1
1
1
1
0
2
1
0
0
1
2
1
0
1
1
1
1
1
0
1
1
1
0
1
1
1
1
2
1
2
2
0
1
1
1
1
0
2
1
2
1
0
0
1
2
1
1
2
1
2
2
1
2
1
1
1
1
1
1
1
1
3
1
2
2
1
2
1
2
2
2
0
1
1
0
1
2
2
1
1
2
1
1
1
2
0
0
2
1
1
1
1
2
0
1
1
2
1
1
2
2
1
1
1
0
1
1
1
1
1
1
0
2
2
2
0
1
1
2
1
1
1
3
1
1
2
2
2
1
0
1
1
1
0
2
1
1
1
2
1
0
2
1
2
1
0
2
1
0
2
1
2
1
1
3
1
1
1
0
1
1
1
0
1
1
1
1
2
1
1
1
2
1
0
2
1
1
2
0
1
3
1
1
1
0
1
1
1
1
1
1
2
1
1
1
3
0
1
1
1
1
1
1
2
1
1
1
2
2
1
2
1
1
0
1
2
1
1
1
1
1
0
0
2
0
1
2
0
1
2
1
2
1
0
1
1
2
0
1
1
1
1
1
1
1
2
0
2
1
1
0
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
0
1
3
2
2
1
1
0
1
1
0
1
1
1
1
0
1
1
4
1
1
1
2
0
1
1
1
1
1
2
1
1
2
1
0
1
0
1
1
1
2
0
1
2
1
2
0
1
0
0
1
2
2
1
1
1
0
0
1
1
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
2
1
1
1
1
1
1
1
2
0
1
1
1
1
0
2
1
1
0
0
1
1
2
1
1
1
1
2
2
1
1
1
1
0
1
0
2
0
0
1
1
2
1
0
0
2
1
0
2
1
1
1
1
2
1
1
1
1
2
2
1
1
1
2
0
2
1
1
1
1
1
2
1
1
2
1
2
1
1
1
0
1
1
2
1
2
1
1
2
1
2
3
1
1
1
1
1
1
2
0
1
1
1
2
1
2
0
0
2
0
2
1
1
2
1
0
1
2
1
1
2
0
0
2
2
2
1
1
1
1
2
0
1
0
5
1
0
0
1
1
0
0
1
1
1
1
2
0
1
0
0
1
1
1
1
1
0
0
0
0
2
1
1
0
1
0
1
2
2
1
2
1
0
1
1
2
1
1
1
0
0
1
0
1
1
1
0
1
0
0
1
0
1
1
1
1
2
2
1
2
2
2
1
1
1
1
1
1
2
1
2
1
1
1
1
0
1
1
1
2
1
2
2
1
1
2
1
0
0
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
2
1
1
1
1
1
2
0
2
1
1
2
1
1
2
1
1
1
1
2
1
2
2
1
2
1
2
1
2
1
1
1
1
1
1
1
2
2
2
1
1
1
1
0
1
1
1
1
1
2
1
1
1
1
1
2
2
2
0
2
0
1
1
1
0
1
1
1
2
1
1
1
2
1
2
2
0
1
0
1
0
2
2
2
0
1
2
2
1
1
0
1
1
1
2
0
1
2
2
2
2
1
1
2
1
0
2
1
1
1
1
1
1
1
1
2
1
0
1
1
1
2
1
1
1
1
0
2
1
1
1
2
1
2
1
1
1
1
0
1
1
1
1
1
1
0
1
1
0
2
1
1
1
2
1
1
1
0
1
1
1
2
3
1
1
2
1
2
1
1
2
1
1
2
1
2
1
2
2
0
2
0
1
1
1
0
0
1
0
2
1
1
1
1
1
1
8
1
2
1
0
1
1
1
1
1
1
1
0
2
1
1
0
2
1
1
2
2
1
1
2
0
1
1
2
1
1
1
1
1
0
2
1
2
1
0
0
2
0
1
1
1
2
2
0
1
1
1
2
2
1
0
0
1
2
1
1
1
0
1
2
2
1
1
0
1
1
0
1
2
0
1
0
1
0
0
1
1
2
0
1
1
1
1
1
0
1
1
1
2
1
2
2
1
1
1
3
1
1
1
2
2
1
1
1
2
1
2
1
1
0
2
1
2
1
1
1
1
2
1
1
0
1
2
2
1
1
1
1
2
1
0
1
1
1
1
0
1
1
1
1
1
1
1
1
1
2
0
2
1
1
2
1
2
1
1
0
2
1
1
0
1
1
2
1
2
2
1
1
1
2
1
2
0
2
1
2
0
2
1
0
2
1
1
1
2
1
1
1
1
1
2
0
1
1
0
0
1
0
1
0
1
1
0
2
1
1
1
1
2
1
1
0
0
0
1
2
2
2
1
1
1
1
1
1
1
1
0
1
1
1
1
2
0
1
1
2
2
2
1
2
1
1
2
1
3
1
2
2
2
1
1
1
1
1
1
2
2
1
0
1
2
1
1
2
2
2
2
2
2
1
2
1
2
1
1
0
1
1
1
1
3
1
1
1
0
1
1
1
1
0
1
2
1
1
2
1
2
2
1
1
1
2
1
0
0
1
1
1
2
1
2
0
2
2
2
2
2
1
1
0
1
0
1
1
1
1
2
1
1
1
2
0
2
1
1
1
1
1
1
1
0
1
0
1
0
1
1
2
1
1
0
2
1
1
1
2
2
1
1
2
1
2
1
1
0
1
1
1
1
2
2
1
2
2
1
2
1
1
1
1
1
1
1
0
1
1
0
0
1
1
0
2
1
1
1
1
1
0
2
0
2
2
1
0
1
1
2
1
1
1
2
1
1
1
0
1
1
0
1
2
1
1
2
1
1
1
1
1
2
1
1
1
1
0
2
1
3
2
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
1
1
2
2
1
1
0
1
1
0
2
2
0
2
1
1
0
1
2
2
1
1
1
1
1
1
1
1
0
2
1
1
0
2
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
1
1
3
1
1
2
2
0
1
1
1
1
1
1
1
1
1
1
0
1
2
1
1
1
1
1
1
2
1
1
1
2
2
0
1
0
2
2
1
1
2
1
0
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
3
1
1
1
1
1
1
2
2
1
1
1
1
2
1
1
1
0
1
2
0
1
2
2
1
1
3
1
1
1
1
2
1
1
1
1
1
2
1
1
0
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
0
0
1
0
1
2
0
1
0
1
1
1
1
0
2
0
2
1
1
2
1
2
1
1
0
0
1
1
2
1
1
1
2
2
1
0
2
0
2
0
1
2
2
2
1
2
1
1
1
1
1
1
2
0
1
1
2
1
1
1
1
1
1
2
1
1
2
1
2
1
1
2
1
0
2
1
1
2
1
1
1
2
1
3
2
2
1
1
1
1
2
2
1
1
1
0
1
1
2
2
1
1
1
0
1
0
1
0
1
1
0
2
1
1
2
2
2
2
0
1
1
1
1
2
1
0
1
1
1
1
2
1
0
1
0
1
1
2
2
1
0
2
1
2
1
2
1
1
1
1
1
2
1
1
1
0
1
1
1
2
0
1
1
1
1
1
2
1
0
1
2
1
1
0
1
1
2
1
2
1
2
1
2
1
1
1
2
1
1
1
1
2
1
2
1
1
0
0
0
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
0
0
0
1
0
1
0
1
1
1
1
5
2
1
1
1
0
1
2
1
2
1
0
1
2
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
0
0
1
0
1
2
2
1
1
2
2
1
0
1
2
1
0
0
1
2
0
1
1
1
2
2
1
1
1
1
2
1
1
1
2
0
1
2
1
2
0
0
0
2
0
1
1
1
1
1
1
1
2
1
1
0
1
1
1
0
1
1
1
1
1
1
1
1
2
1
0
2
1
2
1
1
1
2
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
0
1
1
1
1
2
1
0
0
2
2
1
1
0
2
1
1
2
0
1
1
1
0
3
1
2
1
1
0
2
2
1
1
2
1
1
2
0
1
1
0
2
1
2
1
1
1
1
1
1
1
1
1
0
1
1
1
2
2
1
1
1
2
1
1
0
2
1
1
2
1
1
1
1
2
1
2
2
2
1
2
1
1
1
2
2
2
1
1
2
2
1
2
1
2
1
1
1
1
1
1
1
1
2
1
0
2
1
1
1
0
1
1
1
2
1
0
1
0
1
1
1
1
2
1
0
1
1
2
2
2
1
1
1
1
1
1
1
1
0
1
1
2
1
1
1
1
1
1
1
1
1
1
1
0
1
1
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
0
2
2
1
2
1
1
1
1
1
2
1
1
0
1
1
2
1
1
1
2
0
1
0
2
1
1
1
2
1
1
1
1
1
0
2
0
1
1
1
1
1
2
2
1
1
1
0
0
2
2
0
0
1
2
1
1
1
1
1
0
2
1
2
1
0
1
1
1
2
1
2
0
1
1
2
1
2
1
2
1
1
1
2
1
1
1
1
2
1
2
1
2
1
1
2
0
1
2
2
2
0
2
2
2
1
1
1
2
1
1
1
1
1
0
1
0
1
0
2
1
2
2
0
0
0
1
1
1
1
0
2
1
1
3
2
4
0
2
1
1
1
1
2
2
0
1
2
1
1
2
2
1
1
0
1
0
2
1
1
0
1
0
1
2
1
2
2
2
2
1
2
2
0
1
1
2
1
2
1
1
2
1
1
1
1
0
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
0
0
1
2
1
2
2
1
1
1
1
1
2
1
2
2
2
2
2
2
1
1
1
1
1
1
2
2
0
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
2
1
1
1
1
1
2
1
1
1
1
0
2
2
1
0
0
1
0
1
1
1
0
2
0
1
1
1
2
2
2
1
0
0
0
0
1
1
1
1
0
0
2
1
0
1
2
1
2
0
1
2
1
2
2
1
0
1
1
1
1
2
2
1
1
2
1
0
1
0
1
1
2
1
1
1
1
1
1
1
2
1
1
0
4
2
0
1
1
1
1
1
2
1
1
2
1
2
1
1
0
0
1
1
1
1
1
1
1
1
1
1
1
0
0
0
1
2
1
1
0
1
1
1
0
1
1
1
1
0
1
0
2
1
1
3
1
1
1
0
1
1
2
1
1
1
2
2
0
2
2
0
2
2
0
2
1
1
1
1
1
1
1
1
1
1
1
2
2
0
2
1
1
1
1
2
2
0
2
2
2
0
2
1
0
1
1
1
1
1
1
2
2
0
1
1
2
0
1
1
0
1
1
1
2
0
1
2
2
1
2
1
1
1
2
1
2
2
1
2
1
2
2
1
2
1
1
2
2
0
2
1
1
2
2
2
1
1
1
1
1
1
2
1
1
1
0
1
2
1
2
1
2
0
1
1
1
1
2
2
1
2
1
1
1
1
1
0
1
1
1
1
0
2
1
1
1
1
2
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
4
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
2
1
1
2
1
0
0
2
1
0
1
2
1
2
2
2
0
0
1
1
2
1
2
2
1
1
0
1
1
2
0
1
1
1
1
2
1
1
2
0
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
0
0
1
1
0
1
1
1
2
1
1
1
1
1
1
0
1
1
2
2
0
0
2
2
1
1
1
0
0
1
4
1
2
2
0
1
1
2
1
1
0
2
0
1
1
1
1
1
1
1
1
1
2
1
1
1
0
8
2
1
1
2
2
2
2
2
2
0
1
0
1
2
0
2
1
2
2
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
2
0
0
1
2
1
1
2
1
0
1
2
2
1
1
1
2
1
2
1
1
1
1
1
0
2
1
0
2
1
2
2
0
1
1
1
1
2
3
1
1
2
1
1
1
2
2
1
1
0
2
1
2
1
1
1
1
2
0
1
2
1
1
1
2
1
2
1
1
0
1
1
1
1
0
0
1
1
1
2
1
1
1
2
1
1
2
1
1
1
1
1
0
1
2
1
2
2
0
1
2
3
0
2
0
0
1
2
2
1
1
1
0
1
1
1
1
1
0
1
2
1
1
1
0
1
0
2
1
1
2
1
0
1
1
0
1
0
1
1
2
1
1
2
1
2
2
1
0
1
2
1
1
1
1
0
1
1
0
1
1
2
1
2
1
2
1
1
1
1
1
2
1
1
2
1
2
2
0
1
1
5
0
1
0
1
0
1
1
1
1
1
0
1
0
2
1
0
2
1
1
1
0
1
1
1
1
2
0
1
0
1
1
1
1
1
0
0
1
2
1
0
1
1
1
2
2
1
2
1
1
1
0
1
4
1
2
1
0
1
0
0
1
1
2
1
1
1
1
1
1
2
1
1
0
2
2
1
1
2
2
0
1
0
2
1
0
1
1
1
1
1
1
1
1
2
2
1
2
1
1
1
0
1
2
1
2
2
2
1
1
1
1
1
1
1
2
0
2
1
1
1
2
0
1
1
2
1
1
0
1
0
0
0
1
3
1
1
1
2
0
1
1
0
1
1
1
2
1
1
0
0
1
1
2
2
1
1
1
1
1
1
1
0
1
1
1
2
1
1
0
0
2
1
1
1
0
1
1
2
2
1
2
0
2
1
0
1
0
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
0
1
1
2
1
1
2
2
1
2
1
1
2
2
3
0
0
1
1
1
1
1
2
1
2
1
2
2
1
0
2
0
2
0
2
1
2
2
2
2
1
1
2
2
0
2
1
1
1
1
2
2
2
1
1
1
2
2
2
1
1
1
1
2
1
1
1
1
2
1
1
1
2
0
1
1
1
1
1
1
2
1
2
1
0
1
1
1
2
1
1
2
2
1
1
1
1
1
1
2
2
1
1
2
2
2
1
2
2
0
1
1
1
1
1
1
2
2
2
1
0
1
1
1
1
1
1
1
1
2
2
2
2
1
2
1
1
1
1
0
3
2
1
0
1
2
0
1
1
1
2
1
2
1
2
1
2
1
1
1
1
1
0
2
1
0
1
1
1
1
1
0
1
1
4
2
1
2
2
2
2
2
2
1
1
2
1
1
2
1
2
3
1
1
2
1
1
1
3
2
0
1
2
1
0
2
1
1
1
1
1
2
1
0
2
0
0
1
2
2
1
1
1
1
4
0
2
1
0
0
1
1
2
1
1
1
1
1
1
2
1
2
1
1
2
0
1
2
1
1
1
2
1
1
1
2
1
1
0
1
1
2
1
1
1
1
1
0
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
4
2
2
1
1
1
2
1
1
1
1
1
0
1
0
1
1
1
1
0
1
2
1
1
0
1
1
1
1
2
1
1
1
0
1
1
2
1
1
0
0
1
1
1
0
1
1
2
2
0
1
1
1
1
2
1
1
1
1
1
1
2
2
1
1
2
1
1
2
0
1
1
1
1
1
1
0
1
0
2
2
1
1
2
1
2
0
1
2
2
1
2
1
1
1
1
2
1
1
1
1
1
0
2
1
0
1
1
0
1
2
0
0
1
1
1
1
1
2
2
2
0
1
1
0
1
1
1
1
1
1
1
0
1
1
1
1
1
1
0
1
1
1
2
2
0
2
1
2
1
1
0
1
0
1
1
1
2
1
1
2
1
1
1
1
2
1
1
0
0
1
1
0
1
2
1
0
1
1
1
0
1
1
2
1
1
2
2
0
1
1
2
1
1
1
1
1
2
1
1
1
1
1
0
2
4
0
2
1
1
0
1
1
2
2
0
1
1
1
0
1
1
9
1
0
1
2
3
1
0
1
1
0
0
1
1
1
1
2
1
1
2
1
1
1
2
1
1
1
1
0
2
2
1
2
1
2
1
1
0
0
0
0
1
0
1
1
1
1
1
2
0
0
2
3
2
2
2
2
1
1
2
0
2
2
0
1
2
0
1
2
2
1
1
2
0
1
2
2
1
1
2
1
0
1
0
1
1
1
1
3
0
1
2
1
1
0
5
1
0
1
1
0
1
1
2
1
0
2
1
1
1
1
1
1
2
1
1
1
2
2
0
0
1
0
1
0
2
1
1
0
1
1
1
1
1
0
1
0
1
1
1
1
1
2
0
1
1
1
2
2
1
1
1
1
1
2
0
3
1
1
1
1
0
1
1
2
1
2
0
0
1
0
2
0
1
1
1
1
2
1
1
0
2
1
1
1
1
1
1
1
1
1
2
1
1
2
2
2
2
2
2
1
1
1
2
1
1
2
1
1
2
1
1
2
2
2
2
1
2
1
2
2
0
2
1
1
2
2
2
2
1
1
2
1
2
0
1
0
2
1
1
1
1
2
1
1
0
1
1
1
1
0
1
1
2
1
1
2
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
2
0
2
1
1
1
1
1
2
0
0
0
1
1
0
1
1
1
1
2
2
1
1
1
1
2
2
1
2
1
1
2
1
1
2
1
1
1
1
0
1
0
1
0
1
1
1
1
1
1
2
2
0
1
2
1
0
1
0
1
1
1
1
1
1
1
1
2
1
2
0
0
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
2
1
0
0
1
2
1
1
1
1
1
1
1
1
1
2
2
1
1
0
2
1
1
0
1
2
0
1
1
2
1
0
1
1
2
1
1
1
1
0
1
1
2
1
0
1
1
1
1
1
2
2
2
2
1
0
1
2
1
1
0
1
1
1
1
4
1
2
1
2
1
2
1
1
2
3
2
0
1
1
1
0
1
1
1
1
1
2
1
1
1
1
0
0
2
2
0
2
1
1
1
1
1
2
1
1
2
2
1
1
0
1
1
1
1
2
1
1
2
1
0
0
2
1
2
2
1
2
1
0
0
0
1
1
2
1
1
1
2
1
1
2
1
2
0
2
1
1
1
1
2
1
1
0
0
2
1
1
1
1
0
2
2
0
0
1
0
1
1
1
1
2
1
2
1
1
1
2
0
1
0
1
2
1
1
1
2
0
0
1
2
1
1
2
0
1
2
2
1
1
0
1
1
0
1
1
0
1
0
1
2
1
1
1
0
2
0
1
2
2
1
1
0
2
1
1
1
2
1
0
1
2
1
2
1
0
1
1
1
1
1
1
2
0
1
2
1
1
1
1
0
2
2
2
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
0
1
3
2
1
1
2
2
1
2
2
0
2
1
2
1
1
1
1
2
0
1
1
1
2
1
1
0
1
1
1
0
1
1
1
2
0
1
1
1
0
1
1
1
2
1
2
2
2
2
2
1
2
0
1
2
1
1
1
1
0
1
0
1
2
0
2
0
2
1
2
2
0
2
1
1
2
2
0
1
2
2
1
1
1
1
1
2
2
1
1
1
1
2
1
1
0
1
1
1
1
1
0
1
1
1
0
0
2
1
1
0
1
1
1
0
1
2
1
1
0
1
2
1
1
1
0
1
1
0
1
1
2
1
0
0
1
1
0
3
1
1
1
0
1
2
1
0
0
1
1
2
0
2
0
0
1
1
0
1
1
1
0
1
1
1
1
1
2
2
1
0
1
1
1
1
2
1
0
0
0
0
1
1
0
0
2
2
2
1
1
1
1
1
1
1
1
1
0
0
1
1
1
1
1
1
1
1
0
1
2
1
1
0
0
0
2
2
1
2
0
1
1
1
1
1
2
0
2
0
0
2
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
0
2
1
0
1
1
1
0
1
1
0
0
1
2
1
1
1
2
1
2
2
1
1
1
2
1
2
2
1
1
1
1
2
1
1
1
1
1
1
2
2
1
2
2
1
1
2
2
2
2
1
1
0
2
1
0
2
2
1
1
1
0
1
1
1
2
0
1
2
1
1
0
2
1
2
1
1
1
1
1
0
1
2
1
1
2
2
1
1
2
1
1
1
0
1
1
1
1
1
1
1
1
2
1
1
1
2
0
1
2
1
0
0
1
1
1
1
1
1
1
0
2
0
1
1
2
1
2
1
1
0
1
1
1
1
1
1
1
1
0
0
0
1
0
2
1
2
0
2
0
1
1
1
0
0
1
0
2
1
1
0
1
1
2
1
1
0
1
0
2
0
1
0
1
1
1
2
0
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
2
1
2
1
1
1
2
2
0
2
1
0
1
1
1
2
0
2
2
1
0
1
2
1
1
1
1
1
2
2
0
1
0
1
1
1
1
1
2
2
1
2
2
1
1
1
1
1
1
1
1
0
0
2
2
1
2
1
1
2
1
2
2
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
0
2
2
2
0
0
1
3
2
2
1
2
0
1
1
0
1
1
0
2
1
1
0
1
2
2
1
2
1
1
1
2
1
2
2
0
1
1
1
1
1
2
0
1
1
1
1
1
1
1
1
1
2
1
0
2
0
1
1
0
1
0
2
0
1
0
0
3
1
1
1
1
1
2
0
1
2
2
2
2
1
1
1
0
1
2
1
0
2
1
0
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
2
1
0
2
0
2
0
2
2
2
0
1
1
2
2
1
1
1
1
2
2
1
1
2
0
0
1
0
1
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
0
1
1
1
1
1
0
1
1
1
0
2
2
0
1
2
1
1
0
1
2
1
2
1
1
1
1
1
2
0
1
0
1
1
1
1
0
0
1
2
2
1
1
1
1
1
1
1
1
1
1
2
0
2
1
1
1
2
0
3
0
1
2
2
1
0
1
2
1
1
2
2
0
0
2
1
2
1
1
2
2
1
1
1
1
1
2
1
1
2
1
2
2
1
2
1
1
1
1
1
1
1
1
0
2
2
0
1
1
1
0
1
1
2
1
1
2
0
1
2
1
1
2
1
1
2
0
1
0
2
1
1
1
1
1
1
1
1
1
2
2
0
1
1
1
2
1
1
1
2
2
0
2
2
0
1
2
0
1
1
1
1
1
1
1
1
1
2
1
1
1
0
1
1
0
0
1
1
1
1
1
2
2
0
2
2
2
1
0
1
1
1
1
1
0
2
1
0
1
1
1
2
2
1
1
1
1
0
1
0
1
1
0
0
1
1
1
2
0
0
2
0
1
2
2
2
1
1
2
1
1
1
0
0
2
2
0
1
1
1
1
2
1
1
0
1
1
2
3
0
1
2
1
0
3
1
1
1
0
1
1
2
1
1
0
0
2
2
2
1
1
1
2
1
0
1
3
1
1
1
0
0
2
1
1
1
1
2
2
1
1
2
0
2
1
2
1
1
2
1
1
1
2
2
0
1
2
0
0
3
1
0
1
1
1
1
1
0
1
0
2
1
3
2
2
1
0
1
1
2
1
0
1
2
1
1
2
1
0
2
0
1
1
1
1
2
1
1
2
1
2
1
1
2
1
1
1
2
1
1
1
0
1
1
2
0
2
0
1
1
1
1
2
1
1
1
4
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
2
0
0
2
1
1
1
1
1
0
1
1
1
1
1
1
2
1
0
1
1
2
1
1
1
2
2
0
2
1
1
2
1
1
1
0
1
1
2
1
1
2
1
2
1
1
0
1
0
1
0
2
0
1
1
1
2
1
1
2
1
0
0
0
2
0
0
2
1
1
1
0
1
1
2
2
2
1
0
2
1
2
0
1
1
2
1
1
2
2
1
0
1
1
1
1
1
1
0
1
1
1
2
2
0
2
1
2
1
1
1
1
1
1
1
1
2
2
2
1
1
0
1
2
1
1
0
2
1
0
1
2
1
1
1
1
1
2
1
2
1
1
2
1
0
1
0
0
3
1
2
2
0
1
1
1
2
2
2
1
1
2
2
1
1
2
0
2
0
1
1
1
1
1
0
1
2
2
1
3
2
1
2
2
1
2
0
2
1
2
2
2
1
2
1
2
1
1
2
2
0
2
1
1
2
3
0
0
2
1
1
1
0
1
1
1
1
1
1
1
1
1
2
1
1
0
0
1
1
1
1
0
2
1
1
1
1
1
1
1
1
1
1
4
1
1
1
2
2
3
1
2
1
2
2
1
1
2
1
1
1
1
2
0
1
0
1
1
1
2
1
1
0
1
2
1
1
1
2
1
1
1
1
2
1
1
1
0
1
1
0
1
1
1
1
1
2
2
0
0
1
1
3
2
1
1
1
1
0
2
1
1
1
1
2
1
1
1
1
0
0
1
4
0
2
0
2
0
1
1
1
2
1
2
2
1
1
1
2
1
0
2
1
1
1
1
1
3
2
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
0
0
1
1
1
2
2
0
1
1
1
1
2
1
2
1
2
1
1
2
1
1
1
3
1
2
0
1
1
1
1
2
2
2
1
1
1
2
0
1
0
1
1
0
1
0
1
1
1
1
1
1
1
1
2
0
1
2
1
0
2
2
0
1
1
1
1
1
1
2
1
2
1
1
1
1
1
2
2
1
2
2
0
0
1
0
1
1
2
2
1
1
1
2
0
2
2
2
1
2
1
0
2
1
2
1
1
1
2
1
1
1
1
2
2
1
1
0
0
2
1
1
1
1
2
2
1
1
1
1
1
1
1
2
2
1
0
1
2
1
1
2
1
1
2
1
0
2
1
1
2
1
2
2
1
2
1
2
0
1
1
0
0
0
1
0
1
1
1
1
2
1
1
0
2
2
0
2
0
3
1
1
1
1
1
2
1
0
1
1
0
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
2
2
1
1
1
2
1
1
2
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
7
0
0
1
1
0
1
2
1
1
1
1
1
2
2
0
1
1
2
1
2
2
1
1
2
1
2
1
2
2
2
1
0
1
0
1
1
1
1
1
1
0
1
1
0
1
1
0
0
1
1
1
1
1
2
2
1
1
1
2
1
2
1
2
2
1
2
2
2
1
1
1
1
1
2
2
1
0
1
2
1
0
2
2
2
1
2
1
1
0
2
1
1
1
0
1
1
1
2
2
1
1
0
0
1
1
1
1
1
2
1
0
1
2
1
2
1
1
1
1
1
0
1
0
2
1
2
3
1
0
1
0
1
0
1
1
2
2
0
2
2
1
1
1
2
1
1
2
1
0
1
1
1
1
2
1
1
0
2
1
2
2
2
1
1
1
1
2
0
1
0
1
0
2
1
1
1
1
2
1
1
2
1
1
1
2
2
1
1
1
1
1
2
1
2
1
2
1
2
1
1
2
1
2
1
1
2
2
1
1
0
1
2
1
1
1
1
1
1
1
1
1
1
1
0
1
2
1
1
0
0
1
1
1
1
1
1
1
1
1
1
1
0
1
1
0
1
0
2
2
2
2
1
1
0
1
1
1
2
1
2
1
1
2
2
1
1
2
1
0
0
0
1
1
2
1
1
1
1
1
1
0
0
1
2
2
1
2
3
1
3
1
1
2
1
1
3
1
1
1
1
1
0
1
2
2
1
0
0
1
2
2
0
1
1
1
1
1
1
0
2
2
0
0
0
1
1
2
2
1
1
1
1
1
0
2
1
1
2
1
1
1
2
2
0
1
1
2
1
1
0
0
1
1
0
1
0
0
1
1
1
1
1
1
2
1
5
2
1
1
1
2
1
1
2
1
0
1
1
1
1
1
1
2
1
1
1
1
0
1
1
1
1
1
0
1
1
1
1
2
1
1
1
1
2
1
1
1
1
0
1
1
3
1
0
3
1
1
1
3
0
1
2
0
1
1
1
1
1
1
1
2
1
1
1
1
2
1
0
1
1
1
1
2
1
1
1
1
0
1
1
0
1
1
1
2
1
0
2
1
0
1
0
1
2
1
0
1
2
2
2
1
1
1
1
0
2
1
1
0
1
0
1
0
2
0
1
1
1
2
1
1
1
0
1
1
0
1
2
1
1
2
1
2
1
1
1
2
1
1
0
1
1
1
1
1
1
1
1
1
0
1
1
1
2
0
1
1
2
1
1
0
1
1
1
2
2
2
1
1
1
2
2
2
1
2
1
1
1
1
1
2
1
2
2
1
1
1
1
2
1
1
1
0
2
1
0
1
2
2
1
1
2
1
2
1
1
1
1
1
1
2
0
0
0
1
1
0
1
2
1
0
2
1
1
1
2
1
2
1
2
1
1
1
0
1
1
2
3
0
3
1
1
1
1
1
1
1
0
2
0
1
1
1
1
1
1
1
1
2
1
1
1
1
1
0
1
1
1
1
1
2
0
1
0
1
2
0
1
0
1
2
0
2
1
1
1
0
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
0
1
2
2
2
1
2
2
1
1
0
1
1
2
1
2
1
1
1
2
1
1
1
1
0
0
1
1
1
2
0
1
1
2
1
1
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
2
2
0
1
0
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
0
1
1
1
1
0
2
1
1
1
0
2
1
1
1
1
2
1
1
1
1
1
0
2
1
1
1
1
1
2
1
0
4
1
0
1
1
1
1
1
0
2
1
1
2
1
1
2
1
1
2
1
1
1
1
2
1
2
1
2
1
1
1
1
2
2
1
1
1
1
1
1
2
1
1
2
1
0
1
1
1
0
1
2
2
2
1
1
2
2
1
2
1
0
1
2
1
2
2
0
1
0
1
1
1
1
0
1
0
0
1
2
1
1
1
1
1
0
1
1
1
1
2
1
0
1
1
2
1
2
1
2
2
1
1
2
1
2
0
0
1
0
2
1
1
1
0
1
2
0
0
1
2
1
1
1
1
1
2
0
1
1
2
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
2
1
2
1
0
0
1
1
1
1
2
1
1
1
0
0
0
2
1
1
2
1
2
1
0
1
0
2
2
2
2
2
1
0
1
2
2
1
1
1
1
2
1
1
2
1
1
1
1
2
1
1
2
1
2
1
1
1
2
1
2
2
2
2
1
1
0
2
0
1
1
1
1
1
1
0
1
2
2
1
1
1
1
0
2
1
2
1
0
1
2
1
2
1
2
2
0
2
2
2
1
2
1
1
1
1
1
1
0
0
2
2
0
1
0
1
1
1
2
0
0
1
1
2
1
1
1
1
2
1
2
0
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
0
1
1
2
2
1
1
1
1
0
1
1
1
1
2
1
2
1
2
0
2
1
1
1
2
2
1
2
0
1
1
0
0
1
1
0
1
1
1
1
2
2
1
2
1
1
1
2
1
1
1
2
1
3
1
2
1
1
2
1
0
2
1
1
0
0
1
1
2
2
1
1
1
1
1
3
1
1
2
1
0
1
1
1
0
1
1
0
1
1
1
1
0
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
0
2
1
0
1
1
1
0
1
0
1
3
1
1
1
1
2
2
1
1
0
2
2
1
1
1
2
2
2
2
0
1
1
1
2
2
0
1
1
1
1
2
2
1
1
1
2
1
2
0
3
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
0
2
2
1
1
1
2
1
1
1
1
1
0
1
0
1
0
2
1
1
1
1
1
0
3
2
1
0
1
0
1
1
0
0
0
2
1
1
2
1
1
1
2
1
1
1
3
0
2
1
1
2
1
1
1
1
0
1
1
1
2
1
2
1
0
0
0
1
2
1
2
2
1
0
0
1
1
0
1
1
1
2
0
2
1
1
1
2
1
2
1
1
0
1
1
1
1
0
1
1
1
1
0
2
1
1
1
1
1
1
1
1
0
2
1
1
2
1
0
1
1
2
0
1
1
0
1
1
1
0
2
1
1
0
1
0
1
1
1
1
1
1
2
0
2
1
2
0
1
1
1
0
1
2
1
1
1
1
2
1
1
2
1
1
0
1
1
0
1
1
1
1
2
1
1
0
1
2
1
2
1
2
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
2
1
1
1
1
1
2
1
1
2
1
1
0
1
1
1
0
1
1
0
2
2
0
0
1
2
1
1
1
1
2
1
1
1
0
0
2
1
0
0
1
1
1
1
1
2
1
1
1
1
1
0
1
1
2
1
1
2
1
0
1
1
1
2
1
2
1
1
1
3
1
1
1
1
1
0
1
1
1
2
1
1
0
1
1
0
1
1
1
1
2
2
0
1
1
1
0
0
1
0
1
2
1
1
2
2
1
1
1
1
1
2
2
1
0
0
0
1
1
1
2
1
1
1
0
1
0
1
1
2
0
2
1
0
2
1
1
1
1
0
1
0
1
1
1
1
1
1
1
1
2
1
0
0
0
1
0
0
2
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
2
2
2
1
1
0
1
2
1
2
1
2
2
3
0
4
1
1
1
1
1
2
0
0
2
0
2
1
2
1
2
1
2
0
0
1
1
2
1
1
2
1
1
1
1
2
2
1
1
2
1
1
0
1
0
1
1
2
0
1
2
1
2
2
3
0
1
1
1
1
2
1
1
2
2
1
1
1
1
1
2
1
1
3
1
2
2
1
1
1
1
0
1
0
2
1
1
1
0
1
1
1
1
1
1
1
2
1
1
1
0
1
1
1
1
0
1
0
0
2
0
2
2
1
1
1
2
1
1
1
0
1
1
0
1
1
1
0
2
1
2
0
1
2
1
2
1
1
2
2
1
1
1
2
1
1
2
1
1
0
2
1
1
1
0
1
0
1
2
0
0
1
1
1
1
2
0
1
1
1
0
1
1
1
1
1
1
1
0
1
2
1
1
1
1
2
2
0
2
1
3
1
1
1
1
1
1
0
1
3
0
2
1
2
2
0
1
0
1
1
1
2
2
1
1
1
1
1
1
0
1
0
2
1
1
1
1
2
1
1
2
1
1
2
2
1
2
1
1
1
2
2
1
2
0
1
1
2
0
2
1
2
1
1
1
1
1
1
1
2
1
2
1
0
2
1
2
0
1
1
1
1
1
1
1
2
1
2
0
1
1
1
1
1
1
2
2
1
0
1
1
1
1
0
1
1
1
0
1
1
2
1
1
0
1
1
1
1
2
1
1
1
1
0
1
1
1
1
0
1
0
0
0
1
2
1
1
1
2
1
1
1
1
1
1
1
1
0
1
2
1
1
1
0
1
1
2
2
1
1
1
0
2
2
1
2
1
1
0
0
1
2
0
2
1
2
2
1
1
2
0
2
1
0
2
0
0
2
1
3
1
0
1
1
1
2
2
1
1
1
2
1
1
2
0
1
2
2
2
0
1
0
1
1
1
1
2
1
1
1
1
2
0
1
1
1
1
1
1
0
1
1
1
2
1
1
1
2
1
2
1
0
1
1
1
1
1
1
1
0
1
1
2
2
1
1
1
2
2
1
1
1
1
1
1
2
1
0
0
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
0
1
1
0
0
1
2
2
1
2
2
2
1
2
1
2
1
1
1
1
1
2
1
3
2
1
1
1
1
1
1
0
0
1
2
1
1
2
1
0
1
1
2
1
1
1
1
0
1
0
1
1
0
2
0
2
0
1
0
2
2
0
1
1
1
2
2
1
1
0
1
3
0
1
2
1
0
0
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
0
0
0
2
0
1
2
0
1
1
1
1
1
1
0
2
2
1
2
1
1
0
0
2
1
1
1
2
1
2
1
0
0
1
2
1
2
1
2
2
1
1
1
1
2
1
1
0
3
2
0
2
2
2
2
1
1
1
1
2
0
1
0
0
2
1
1
1
1
0
2
2
1
1
1
1
1
1
1
2
1
1
0
1
2
1
2
1
2
2
1
1
2
0
1
1
1
2
1
2
1
1
2
1
2
1
2
1
1
0
1
1
1
1
1
1
2
1
2
0
2
1
1
1
1
1
1
0
1
1
1
1
1
0
1
1
1
1
1
2
1
1
2
1
0
1
0
0
1
1
1
1
1
1
2
1
1
1
0
0
2
1
2
1
2
1
1
0
1
1
1
1
1
1
1
1
2
0
0
0
0
0
2
1
1
1
1
1
2
2
2
1
0
1
0
1
1
1
2
3
1
1
2
1
2
0
2
1
2
1
2
2
1
2
0
0
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
0
1
2
1
0
0
2
2
1
1
1
0
2
1
2
1
1
2
1
2
1
1
1
2
2
0
0
1
5
1
0
2
1
2
1
2
1
1
0
2
2
2
2
1
1
2
2
2
2
1
0
2
0
0
0
1
1
2
1
1
1
1
2
2
1
3
2
1
1
1
1
1
1
2
2
0
1
1
1
1
0
0
0
1
1
2
1
2
1
1
0
0
1
1
1
0
1
2
0
1
1
1
1
1
1
1
1
2
0
1
1
0
0
1
1
1
2
2
1
1
1
0
1
0
1
2
1
2
0
1
2
0
1
0
1
2
1
2
1
0
1
0
1
0
1
1
0
1
2
1
1
1
2
0
1
1
1
1
1
1
0
2
0
2
1
1
1
2
1
2
0
2
1
1
2
1
1
1
1
2
1
0
1
1
1
1
1
1
2
0
2
1
1
1
2
0
0
1
2
1
1
1
0
1
1
1
2
1
1
1
1
2
1
0
1
2
2
0
1
1
1
2
1
2
1
1
1
2
1
1
0
1
1
2
1
0
1
2
1
1
1
2
0
2
1
1
1
1
1
0
2
1
1
1
2
1
1
2
1
1
6
0
0
1
0
1
2
1
1
1
1
1
2
2
1
1
1
1
3
0
0
2
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
2
3
1
0
2
0
2
1
1
0
1
3
0
1
1
1
2
1
1
1
0
1
1
1
1
1
2
0
2
0
1
0
1
0
1
1
1
0
2
0
1
0
1
0
1
2
1
1
2
1
0
1
1
1
1
2
0
1
4
2
2
2
0
0
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
0
1
2
1
1
1
1
1
1
0
1
1
1
1
1
0
0
2
1
1
1
1
1
0
1
1
1
2
2
1
1
1
0
1
0
1
1
1
1
1
0
1
2
1
1
1
0
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
2
1
1
1
1
0
0
2
1
0
0
1
1
2
1
2
1
1
2
1
2
1
1
0
2
1
2
1
1
1
1
1
1
0
1
1
1
2
2
2
1
2
1
2
0
1
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
3
2
1
2
1
1
1
2
1
2
1
0
2
1
1
1
1
1
2
0
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
0
1
0
1
2
1
1
1
0
1
1
1
1
1
1
2
0
2
2
2
1
0
1
0
2
1
1
1
2
2
1
2
0
1
0
1
1
0
1
1
2
1
2
2
2
1
2
1
2
0
1
1
1
1
2
1
1
0
0
1
2
1
0
1
0
1
0
1
1
0
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
2
0
2
0
1
1
2
2
2
1
1
0
1
1
1
1
1
1
1
1
0
1
2
1
0
1
2
2
2
0
0
1
1
1
1
1
1
1
2
1
1
1
1
0
1
2
0
1
3
1
1
1
1
2
1
2
0
1
1
1
2
1
0
3
1
2
2
1
2
1
2
2
1
1
2
2
1
2
1
1
1
1
1
1
1
1
2
0
1
1
2
0
0
1
1
2
1
0
1
2
1
1
0
1
1
2
2
1
1
1
1
0
1
0
3
0
0
1
1
0
1
1
0
2
1
1
0
0
0
0
1
1
2
0
0
1
1
1
1
1
2
2
2
1
1
0
1
1
1
0
1
2
1
1
1
1
1
0
1
1
1
1
0
2
1
1
2
1
1
0
2
0
1
1
1
1
2
1
1
0
0
0
1
1
2
1
1
0
1
2
1
1
2
1
0
1
1
1
2
1
2
2
0
1
0
1
1
2
1
1
1
1
1
1
1
0
1
1
1
1
0
1
0
1
1
0
1
1
1
1
1
1
2
1
2
1
1
1
0
0
2
1
0
2
1
1
1
1
2
0
1
0
1
1
1
1
1
2
1
1
1
2
1
1
0
1
1
2
1
0
2
2
1
0
1
1
1
2
0
0
1
2
1
1
1
2
2
1
1
2
0
0
0
1
1
2
1
1
1
1
2
1
1
1
0
0
1
0
1
0
1
1
2
0
2
1
1
1
0
0
1
1
1
1
1
2
2
1
1
1
2
1
1
1
1
1
2
2
1
0
2
1
1
1
1
1
1
1
0
2
2
1
1
1
0
1
1
1
1
1
1
1
1
2
1
0
1
0
1
1
0
1
2
1
1
0
1
1
1
1
1
1
1
0
2
0
2
2
2
2
2
1
1
0
0
2
2
2
1
1
1
1
2
1
2
1
1
1
2
1
1
2
1
2
1
1
4
1
2
2
1
1
0
1
2
2
1
1
1
1
1
1
0
2
1
2
1
1
1
1
2
1
1
0
0
0
1
1
1
1
1
0
1
1
0
2
1
2
1
1
2
0
0
0
2
2
1
1
0
0
1
0
1
1
0
1
1
1
1
1
1
1
1
2
1
1
0
2
1
1
1
2
1
1
1
1
2
2
2
1
0
1
1
1
0
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
2
0
2
2
1
1
0
2
0
1
1
1
2
0
2
1
1
2
2
2
2
1
1
2
2
1
1
1
1
1
0
2
1
3
1
2
1
1
1
1
1
1
1
0
1
1
0
1
2
1
2
1
2
2
1
1
1
2
1
1
1
1
2
1
1
2
1
1
2
2
2
2
2
1
0
1
1
1
0
2
1
2
1
1
2
2
2
2
1
2
3
1
1
2
2
1
0
1
2
1
1
1
1
2
1
1
0
1
1
1
2
1
2
0
0
0
2
1
2
1
1
1
2
2
1
0
2
2
2
0
1
1
1
2
1
0
1
0
1
0
1
0
0
1
1
0
1
1
1
1
1
0
2
1
1
0
0
1
1
1
1
1
2
1
0
0
2
0
0
1
1
2
1
1
1
2
1
1
1
2
2
2
0
1
1
1
1
2
0
1
0
1
1
1
2
1
2
1
1
1
1
1
1
0
1
1
2
0
1
2
1
1
1
1
1
1
1
0
1
2
1
1
1
1
2
1
0
1
2
1
0
2
2
1
2
1
1
2
2
0
2
1
0
1
2
2
1
1
1
1
1
2
1
1
1
2
4
1
2
1
2
1
2
1
0
1
2
2
1
1
0
1
0
1
1
1
1
1
1
2
2
1
2
0
1
1
0
0
1
1
1
1
1
2
1
0
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
2
2
1
1
1
0
1
1
2
1
1
1
0
1
1
1
2
3
2
1
0
0
1
1
1
1
1
1
0
1
0
2
2
1
1
1
0
0
1
2
0
1
0
1
1
2
0
1
0
2
1
0
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
0
0
1
1
0
1
1
1
1
0
2
1
1
2
1
1
0
2
2
0
1
2
1
2
1
1
1
1
1
0
1
2
0
2
0
0
2
1
2
1
1
2
1
0
2
1
1
1
2
1
0
0
1
0
1
1
2
1
1
1
1
1
1
1
1
0
1
1
1
1
1
0
2
1
0
1
1
0
1
0
2
2
2
1
1
1
3
1
1
2
2
1
1
0
1
1
1
1
1
0
2
1
1
1
1
0
2
2
1
1
1
0
2
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
0
1
2
2
4
1
1
0
1
1
3
1
2
1
2
1
2
0
2
1
1
1
1
1
1
1
1
2
1
0
0
1
1
1
1
1
1
0
1
2
1
1
1
0
2
1
1
1
0
1
1
1
2
1
1
0
2
1
2
2
1
1
1
0
1
0
2
1
1
1
0
1
1
1
1
2
2
1
1
1
1
0
1
1
2
2
2
1
3
2
2
0
1
1
1
2
2
1
1
1
1
2
1
1
1
0
2
1
1
1
2
0
1
1
1
1
1
0
1
0
1
2
0
1
0
1
0
1
2
2
0
1
0
1
1
1
1
1
1
1
1
2
1
0
1
1
1
0
2
1
0
0
1
1
1
1
1
1
2
1
1
2
2
1
0
2
0
1
1
2
1
1
2
1
1
3
0
1
1
1
0
2
2
0
0
0
2
2
2
2
0
1
1
1
1
1
1
0
1
1
2
2
1
1
1
2
1
1
1
1
1
1
0
1
2
1
2
1
2
1
1
0
1
1
1
1
1
2
1
1
1
2
3
2
1
1
0
1
0
1
1
1
1
1
1
1
1
1
2
0
1
1
1
0
2
1
1
1
2
1
1
1
2
1
2
1
1
1
2
1
1
2
2
1
0
1
2
2
0
0
1
1
2
2
1
0
2
1
2
2
2
0
1
1
2
2
2
1
2
2
2
1
1
2
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
0
0
2
1
2
1
0
1
1
1
2
1
2
2
2
1
2
1
0
2
1
2
2
1
0
1
0
1
1
1
1
1
0
1
1
2
1
0
1
1
1
1
1
0
0
2
1
1
1
1
1
0
1
1
0
1
1
2
1
2
2
1
1
0
1
0
0
1
1
1
2
1
1
1
1
2
1
0
1
1
1
0
0
1
2
2
2
1
1
1
1
1
1
1
1
2
0
1
1
1
1
1
0
0
2
0
1
1
1
2
1
0
1
1
1
2
1
1
1
2
1
1
3
2
1
1
2
1
1
1
1
0
1
2
1
0
1
2
1
2
1
1
1
0
2
1
1
2
1
1
1
1
0
1
1
1
1
2
2
0
1
1
1
1
2
1
1
0
2
1
1
1
1
2
2
2
1
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
0
1
0
1
1
1
2
1
2
1
2
1
1
0
1
1
1
1
2
0
2
2
2
1
2
1
1
1
1
1
2
1
1
2
0
1
2
1
1
1
1
2
1
1
1
1
2
0
1
2
0
1
1
0
0
0
1
1
0
2
2
2
1
1
1
1
1
0
1
0
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
0
2
1
1
0
1
1
1
1
2
1
2
0
1
2
0
1
1
2
1
2
2
1
2
1
0
1
1
1
1
1
0
1
0
2
1
1
1
1
1
1
2
1
0
0
1
0
2
2
2
1
2
1
2
1
0
0
1
1
1
1
1
1
1
0
1
1
1
2
0
1
2
2
1
1
1
1
1
1
1
1
1
2
1
1
1
0
1
0
0
1
1
1
1
1
0
0
1
1
2
2
1
1
1
0
0
2
2
1
0
2
1
1
2
1
0
0
1
1
1
0
2
3
1
2
2
1
0
2
2
1
1
1
1
0
1
0
0
2
1
2
1
1
3
0
0
1
1
1
1
2
0
1
0
0
1
2
1
1
1
1
2
0
1
1
2
1
1
1
1
1
1
2
1
0
1
1
1
1
1
1
1
2
1
2
1
1
1
2
1
2
1
1
1
0
1
1
1
0
2
1
2
0
2
0
1
1
1
2
2
2
2
1
2
1
2
0
0
2
1
1
1
1
2
1
1
2
2
2
2
1
1
1
2
2
1
2
1
2
1
1
0
1
1
1
1
2
2
2
2
1
1
2
1
1
1
0
4
2
2
2
1
2
0
2
2
0
1
1
0
1
2
2
1
2
1
1
0
1
2
0
1
1
1
1
1
3
0
2
2
2
1
2
1
1
0
1
1
1
1
1
1
1
1
1
2
1
1
2
2
1
1
0
0
1
2
0
1
3
1
2
1
1
2
1
1
1
1
2
1
2
0
0
1
1
2
2
4
0
2
0
2
1
2
1
1
1
1
2
0
0
1
1
0
1
1
2
1
0
1
1
0
1
0
1
2
1
2
2
2
1
1
0
1
2
1
1
1
1
0
0
0
1
1
2
0
1
1
2
2
1
1
1
0
1
2
1
1
2
0
2
1
1
0
1
1
2
2
3
1
1
0
2
2
0
1
1
1
1
0
1
1
1
2
2
1
1
1
2
1
1
2
1
2
1
0
1
2
0
1
1
1
1
0
1
1
1
1
1
1
0
1
2
1
1
1
1
0
1
0
1
1
2
1
0
1
1
0
2
1
2
0
1
1
1
1
0
0
1
1
1
1
1
3
2
1
1
2
2
1
2
1
0
1
0
1
1
1
1
1
0
1
0
1
1
1
1
1
2
0
1
1
1
1
0
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
0
1
1
2
2
2
1
1
1
1
1
2
1
1
1
1
0
1
1
1
1
0
1
1
2
1
0
1
0
2
2
1
1
1
0
0
2
1
2
1
0
1
0
1
1
2
1
1
1
1
1
2
1
0
0
1
1
2
1
1
2
1
1
2
1
1
1
1
1
1
3
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
2
0
1
2
1
1
1
2
0
1
2
1
1
1
1
1
0
1
2
1
1
0
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
0
1
1
2
1
0
1
1
0
1
0
1
2
0
1
1
2
0
1
1
1
1
1
1
1
0
0
1
2
1
1
1
1
1
0
1
1
0
2
1
0
1
0
2
2
1
0
0
1
1
1
1
2
0
1
1
1
1
1
0
1
1
1
2
2
2
1
1
1
1
2
2
1
2
1
1
1
1
0
1
1
0
1
2
2
1
2
1
1
1
2
2
1
0
1
1
2
1
1
1
0
2
1
0
1
1
1
0
1
1
1
1
0
1
2
1
1
0
1
1
1
2
0
1
2
1
2
0
2
1
1
2
1
1
1
1
2
1
1
2
0
0
1
1
1
1
2
0
2
1
1
1
1
1
1
0
1
1
0
1
1
0
1
1
1
2
1
1
2
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
2
1
1
1
0
1
0
1
1
1
1
1
2
1
0
1
1
2
2
1
1
2
1
0
1
2
0
1
1
1
2
1
2
1
1
1
2
1
2
2
1
1
1
1
2
1
1
2
2
4
0
2
1
1
1
0
2
1
1
1
1
0
1
2
2
1
1
2
0
1
1
2
2
1
1
0
1
0
0
1
2
1
2
2
1
1
1
1
2
1
1
2
2
0
2
1
1
2
2
1
0
1
2
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
0
2
1
1
1
0
1
1
2
0
1
2
2
2
1
1
1
2
1
2
0
1
1
0
1
1
2
0
1
1
2
0
1
1
1
0
2
1
1
0
1
2
1
0
1
1
1
2
2
2
2
1
0
1
2
0
1
2
2
2
1
1
1
2
0
1
1
0
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
0
1
0
1
2
0
1
1
2
2
1
1
1
2
0
1
2
1
0
0
2
1
0
1
1
3
1
1
1
2
1
0
2
1
2
1
0
2
1
1
1
1
0
1
1
0
2
0
1
0
0
1
1
0
1
1
1
1
1
1
2
2
1
1
1
2
1
2
0
2
1
1
1
1
1
2
1
1
1
2
1
2
1
2
1
2
1
1
1
2
1
0
1
1
1
1
0
1
1
0
1
1
2
1
2
2
4
1
1
1
2
1
1
0
1
0
1
1
1
1
2
2
1
0
1
1
1
1
0
1
2
1
1
1
2
0
1
0
1
0
1
0
1
1
1
2
0
1
1
1
1
2
2
2
1
1
0
1
0
0
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
0
1
1
1
1
1
0
1
1
1
1
1
0
2
1
1
1
1
1
1
2
1
0
2
2
1
2
1
1
3
1
2
1
2
1
1
0
1
1
0
0
2
2
2
1
1
1
0
1
1
1
2
1
0
1
1
2
1
2
1
1
1
1
1
0
1
2
2
1
3
0
0
2
1
1
1
2
1
1
1
0
2
0
1
1
1
2
1
1
2
1
1
1
1
0
1
1
1
1
1
1
1
0
1
1
2
2
1
1
1
1
1
1
1
1
2
2
1
1
0
1
2
1
1
0
1
0
1
1
1
2
0
0
1
0
2
1
2
1
1
0
0
0
1
1
2
1
1
1
1
1
1
0
1
1
1
1
1
2
1
2
1
2
2
0
1
1
2
0
2
1
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
1
0
1
1
0
1
2
1
2
1
2
1
1
1
0
2
1
1
1
0
0
1
1
1
1
1
1
1
0
0
1
0
1
1
0
1
1
1
2
2
2
1
1
2
1
1
2
1
1
1
2
2
1
0
0
2
2
1
1
0
2
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
0
2
0
1
0
2
1
1
1
0
1
1
1
2
1
2
1
1
1
0
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
0
1
2
0
2
1
0
2
2
0
1
0
2
1
1
1
1
1
1
1
2
0
2
2
0
2
2
1
0
1
1
2
2
2
0
1
0
2
2
1
1
1
1
1
1
1
0
1
0
1
1
1
1
1
1
1
1
1
1
0
1
2
0
1
2
1
0
2
1
2
2
1
1
2
2
1
1
1
0
1
1
1
2
2
0
1
1
2
1
1
2
1
1
1
2
1
1
2
1
1
2
1
0
1
2
1
1
1
1
0
1
1
2
0
1
1
1
1
2
1
2
1
0
2
1
1
1
0
1
2
0
2
1
0
1
0
1
0
1
1
2
0
1
0
2
2
1
1
1
1
1
1
2
1
1
1
0
4
0
1
1
0
1
1
2
1
1
1
1
1
1
0
2
1
1
1
1
1
1
1
2
1
0
1
1
0
0
2
1
0
1
1
1
0
2
2
1
0
1
0
1
1
0
2
1
0
1
1
1
2
1
1
1
1
1
1
1
1
2
2
1
0
1
1
0
2
1
2
1
2
2
0
0
2
1
1
1
2
1
0
0
1
1
1
1
1
1
1
1
2
1
0
1
1
2
1
1
1
1
1
1
0
2
0
2
1
1
1
1
2
0
1
1
1
1
0
1
1
1
2
2
2
1
2
1
1
1
1
1
2
1
2
2
0
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
0
1
1
1
3
1
1
1
2
2
1
1
0
1
1
1
1
2
1
2
0
1
1
1
2
1
1
2
1
0
1
1
1
3
1
1
1
1
1
2
0
1
1
1
1
1
2
2
0
2
1
1
1
2
1
0
1
2
0
1
0
1
1
1
1
1
1
2
0
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
1
1
1
0
1
1
1
1
1
0
2
0
1
1
1
0
2
1
3
1
2
0
0
0
1
1
0
2
2
1
0
2
2
0
1
1
1
0
1
1
2
1
1
1
0
1
1
1
1
1
1
1
2
1
1
1
0
1
1
1
1
2
1
1
1
1
2
1
1
0
1
1
1
0
2
1
1
1
1
0
2
1
1
0
2
2
2
1
2
2
1
2
1
2
0
1
1
2
0
2
1
1
0
1
1
1
2
2
1
1
1
1
2
2
1
1
1
2
1
1
0
1
1
2
1
1
0
1
2
1
2
1
1
1
1
1
2
0
2
1
1
1
2
1
1
2
1
1
2
1
0
0
1
1
1
3
1
1
1
1
1
1
0
2
2
1
0
1
1
2
1
2
2
1
0
1
0
1
3
1
1
1
2
1
1
2
1
1
2
1
1
1
0
1
0
1
2
1
2
1
1
2
1
2
2
2
1
1
1
1
1
0
2
1
1
1
2
0
1
1
1
1
2
1
1
1
1
2
1
2
0
1
1
1
2
1
1
2
1
1
1
0
2
0
0
2
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
2
1
2
1
2
1
0
1
0
0
2
1
2
1
2
1
1
1
1
1
2
1
0
2
0
1
1
1
2
2
1
2
1
1
1
1
2
0
1
1
2
2
1
0
2
0
1
2
1
0
1
2
2
1
1
2
0
2
2
1
2
2
2
2
1
1
1
2
2
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
0
1
1
1
2
1
1
1
2
0
2
1
1
0
1
1
2
0
1
1
1
2
1
1
2
1
1
2
1
1
1
1
1
1
1
0
2
1
1
0
2
1
1
1
1
1
1
1
1
2
2
2
1
2
1
1
1
2
1
1
1
1
2
1
1
1
0
2
2
1
0
1
1
2
1
1
0
2
1
1
2
1
1
1
1
1
1
1
1
1
1
0
1
0
1
1
2
2
1
2
0
1
2
0
2
1
1
1
2
2
1
1
1
1
1
2
1
5
1
1
2
0
2
2
0
1
1
1
1
1
1
2
2
0
0
2
2
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
0
1
2
1
1
1
1
1
1
1
1
1
1
0
1
1
2
1
1
1
0
2
1
1
2
0
1
1
1
1
1
0
1
1
2
1
1
0
0
0
1
1
0
1
0
3
1
1
1
0
1
1
2
2
1
1
1
1
1
0
2
0
1
0
1
1
1
2
1
1
1
1
1
0
2
0
2
2
2
1
0
1
1
0
1
1
1
1
1
2
1
3
0
0
1
1
2
1
1
2
1
2
1
0
2
1
0
1
2
1
1
2
1
1
0
1
2
1
1
1
1
1
1
1
1
1
2
1
1
2
0
0
0
1
2
0
1
1
1
2
1
1
1
1
2
1
1
1
1
1
2
1
2
1
2
1
1
1
1
1
1
1
0
0
1
2
1
1
1
1
1
2
1
1
2
1
1
2
2
0
1
0
0
1
2
1
2
1
1
2
2
0
1
2
1
0
1
2
1
2
2
1
2
2
1
2
0
0
0
1
1
1
0
0
2
1
1
1
1
1
0
1
2
1
1
2
1
2
2
1
0
2
1
1
1
2
1
1
1
2
3
3
2
1
2
1
2
1
1
1
0
1
1
2
1
1
1
2
1
0
2
1
1
2
1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
2
1
2
1
1
2
1
1
1
1
2
2
2
2
0
2
2
1
1
0
1
0
1
1
1
2
0
2
1
0
2
1
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
2
1
1
3
2
0
1
1
1
1
1
1
2
1
2
2
1
2
2
1
1
1
1
0
1
0
1
1
1
1
2
1
1
2
0
1
2
2
1
0
3
1
1
0
1
1
1
1
1
1
1
1
2
0
1
1
1
2
0
2
1
2
2
1
2
0
2
2
2
1
1
2
2
0
1
2
2
0
1
0
2
2
1
2
2
1
1
2
1
2
1
0
2
1
2
1
0
1
2
0
2
2
1
0
1
0
0
1
1
1
1
2
1
0
2
1
1
2
1
1
0
0
0
1
1
1
1
1
1
1
0
2
2
1
2
2
0
2
1
1
1
1
1
1
1
2
1
1
1
0
1
1
1
1
2
1
2
1
2
0
2
1
2
1
1
1
2
0
2
0
1
2
1
0
1
0
1
2
1
1
1
1
2
1
2
1
2
2
1
0
2
2
0
1
1
2
2
0
1
1
1
2
1
1
1
2
2
1
0
1
1
0
1
1
2
2
1
2
1
2
2
2
1
2
1
2
2
1
0
1
2
1
1
2
2
1
1
1
0
1
2
1
1
0
0
2
1
0
1
0
1
1
0
0
2
1
2
1
2
2
1
1
1
2
1
1
1
2
2
2
2
0
2
2
1
1
2
1
1
1
2
1
1
1
1
0
1
2
2
2
1
1
1
2
1
0
2
1
2
1
0
1
2
1
1
2
1
1
2
1
2
1
2
2
1
2
0
2
1
1
0
1
1
0
2
1
2
1
1
1
1
1
1
1
0
1
1
1
0
1
1
1
0
1
1
1
2
0
1
1
1
1
1
1
1
3
1
0
1
1
1
2
1
1
1
1
1
1
1
2
2
1
0
2
0
0
1
1
1
2
1
0
1
1
1
1
0
1
2
2
1
1
2
1
1
1
0
0
2
1
1
2
1
2
1
2
2
0
1
1
0
1
1
1
2
1
0
1
1
1
1
1
1
1
0
4
0
2
1
1
2
0
1
2
1
1
2
1
0
1
2
1
2
2
1
0
2
2
2
0
1
1
1
2
1
0
1
2
2
2
1
2
0
1
1
2
1
1
3
1
1
1
1
1
0
0
1
1
0
1
1
1
2
0
0
2
1
2
0
2
1
2
0
2
1
1
0
1
1
1
0
1
2
1
2
2
0
2
2
1
2
1
2
2
0
2
1
2
1
1
1
1
1
1
0
1
1
2
1
0
3
1
1
1
2
1
1
1
2
1
1
1
1
1
2
0
1
0
1
1
0
0
1
1
2
2
0
1
1
1
1
1
2
1
1
0
1
2
2
1
3
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
0
0
1
3
1
1
0
1
1
0
1
2
1
2
2
1
1
1
2
1
2
2
0
1
1
0
0
1
1
2
0
2
1
2
1
0
2
0
0
1
1
1
0
1
1
1
1
2
1
2
1
1
2
1
1
1
1
2
1
1
2
0
2
1
0
0
2
2
2
1
0
1
1
1
2
1
1
1
2
2
2
2
0
2
1
2
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
0
1
2
2
1
1
0
0
0
1
1
1
1
1
1
0
2
1
2
1
2
0
1
2
0
1
2
1
2
2
0
2
1
1
0
1
2
1
2
2
1
0
1
1
1
0
1
1
1
1
1
1
1
0
1
1
1
0
2
1
0
1
1
1
0
1
1
1
1
2
1
1
1
1
1
2
1
1
2
1
1
2
2
0
1
1
1
3
0
1
2
2
0
2
0
2
1
2
1
2
2
1
1
0
2
1
1
1
1
1
3
1
1
0
1
2
0
1
1
2
2
1
0
0
1
2
1
2
2
0
1
1
1
1
2
2
1
1
1
1
0
2
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
0
2
0
0
3
2
1
1
2
2
2
0
1
1
1
1
2
0
1
1
2
1
2
2
0
1
1
1
2
0
1
0
2
1
1
1
1
1
2
1
0
1
1
2
1
2
2
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
0
2
1
1
2
2
1
1
0
1
2
0
1
1
1
1
0
1
0
1
3
1
0
1
1
2
2
1
2
0
1
1
0
1
1
1
0
1
0
1
0
1
0
0
1
1
0
2
2
1
2
0
1
1
1
1
2
2
0
1
1
2
2
1
1
1
1
2
2
0
2
1
1
0
1
1
1
1
1
2
1
0
1
1
2
1
1
1
1
0
2
0
2
1
2
1
1
1
1
1
0
1
2
2
1
1
2
1
2
1
0
1
2
1
1
2
1
2
1
0
1
1
1
0
0
2
1
1
2
1
2
1
2
1
1
1
1
2
1
2
0
1
1
2
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
0
1
1
0
0
4
1
2
1
1
2
1
0
0
2
1
0
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
0
2
1
2
1
0
1
2
1
1
1
1
1
2
0
1
1
1
2
1
2
1
2
1
1
1
2
1
1
1
1
1
2
1
2
1
0
1
2
2
1
0
2
2
1
2
1
1
1
2
1
2
1
1
1
1
0
1
0
1
1
1
2
1
0
1
0
1
1
1
1
1
1
2
2
0
1
1
2
1
1
1
1
1
1
2
0
1
1
1
0
2
0
1
1
0
2
1
2
2
1
1
1
1
1
0
1
2
1
1
1
1
2
1
1
1
0
1
2
1
0
1
0
1
1
0
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
0
1
0
0
2
0
1
2
0
0
1
1
1
1
1
1
0
2
1
0
2
1
1
1
1
2
2
1
1
2
0
1
1
1
0
1
1
1
1
2
1
0
2
0
1
1
1
1
1
1
1
1
1
0
2
1
1
1
0
0
3
0
1
1
2
2
1
2
2
2
2
0
2
1
2
1
1
0
2
1
1
2
2
0
0
2
0
2
0
1
1
1
2
2
1
2
1
2
2
1
1
1
1
1
1
2
1
0
0
1
1
2
0
1
2
0
1
1
0
1
2
0
1
1
1
2
1
1
1
1
2
2
1
1
2
1
2
1
1
0
1
2
1
1
0
1
1
1
0
2
1
1
1
1
1
1
0
2
1
1
2
2
1
0
1
1
1
2
2
0
2
1
1
2
1
1
0
1
1
2
2
1
2
1
1
2
1
1
1
1
1
1
1
0
2
1
0
2
1
1
0
1
2
1
2
1
1
1
1
1
1
1
1
1
2
0
0
1
1
1
1
1
2
2
2
1
1
1
2
1
2
1
0
1
2
2
0
1
1
1
1
1
1
2
1
2
1
1
1
0
1
1
1
0
2
0
1
1
0
1
1
0
1
1
1
1
1
1
1
1
0
1
1
1
0
1
1
1
2
2
1
2
2
1
1
2
1
2
0
1
1
2
1
1
1
0
1
2
1
2
0
3
1
1
1
0
1
0
2
2
1
2
1
1
0
1
0
1
2
1
0
0
2
1
1
1
1
1
1
1
1
0
2
1
0
2
1
1
2
1
0
1
1
1
1
0
0
1
1
0
0
2
2
0
1
2
1
1
0
0
1
1
1
2
0
2
2
2
1
2
1
1
2
1
2
2
1
1
1
1
1
1
0
1
1
1
1
1
1
0
1
1
1
0
1
2
1
2
2
0
1
1
0
1
2
1
1
1
0
1
0
0
1
1
1
2
2
1
0
1
0
1
1
1
2
2
2
1
1
1
1
1
2
1
1
0
1
1
1
1
0
2
1
1
2
2
1
1
1
1
1
1
1
0
1
1
1
0
0
2
0
1
0
2
1
1
2
2
1
2
1
1
0
2
1
1
1
0
1
1
2
0
0
2
1
1
1
1
0
0
1
1
1
1
1
2
1
2
2
2
0
2
1
1
1
1
0
1
1
1
1
1
0
1
1
1
1
2
2
3
1
0
0
1
1
1
1
3
1
2
2
1
1
1
1
0
1
1
1
2
1
2
1
1
1
1
0
1
0
1
2
0
1
1
1
2
1
0
1
1
1
1
1
0
1
2
1
1
1
1
2
0
1
2
1
1
1
0
2
1
1
0
1
1
0
0
1
1
1
1
1
2
1
2
1
1
0
1
2
1
1
0
1
1
3
1
1
1
1
0
1
1
1
1
1
1
1
1
2
1
0
1
2
2
1
0
0
1
0
2
1
1
1
1
1
1
2
1
2
2
1
1
1
1
0
1
2
1
0
1
1
2
1
2
1
1
1
2
2
0
1
2
1
1
1
2
0
1
1
1
1
0
1
1
2
1
2
1
1
1
1
0
0
1
2
1
1
1
0
1
2
1
2
1
0
1
1
0
2
0
2
2
2
0
1
2
1
2
0
2
1
0
1
1
1
1
0
1
1
2
2
1
0
2
2
0
1
2
1
1
1
1
2
2
1
1
0
2
0
0
1
1
1
1
1
1
1
1
1
1
1
0
2
2
0
1
1
0
1
2
1
1
0
2
1
0
1
1
2
1
0
1
2
2
1
1
1
1
2
0
0
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
2
2
1
1
1
0
2
2
1
2
1
1
1
1
2
1
1
1
0
2
1
1
1
1
0
0
1
1
1
2
1
1
1
1
1
1
1
0
2
1
0
0
1
1
1
1
1
2
0
1
0
2
1
0
1
2
1
1
2
1
2
2
1
1
1
2
1
1
0
0
0
1
1
0
1
1
1
0
1
1
2
1
1
2
1
2
2
1
2
1
1
1
1
1
1
0
0
1
2
2
1
1
1
2
1
1
1
1
1
1
2
2
0
1
1
2
1
1
1
2
1
2
0
1
1
1
0
0
1
0
1
2
0
1
1
1
2
1
2
1
1
1
2
1
1
0
1
1
0
2
2
1
1
0
0
2
2
2
2
1
1
0
1
2
0
2
1
1
0
1
1
1
0
0
1
2
0
1
0
1
1
2
1
1
0
1
1
1
1
1
2
2
1
2
2
1
1
2
1
1
1
2
1
1
1
1
1
2
2
0
0
1
2
1
1
1
1
2
1
1
0
2
1
2
1
2
2
1
1
1
2
1
1
1
1
1
2
2
1
1
2
0
1
1
1
1
1
2
1
1
1
1
1
1
1
2
0
0
1
2
1
1
0
2
2
1
1
0
2
2
1
1
1
1
0
1
1
1
1
2
1
0
1
1
1
1
2
1
1
1
2
1
0
2
1
1
0
1
1
1
1
1
1
0
1
1
0
1
1
0
1
2
0
2
0
1
0
1
2
1
2
1
1
1
1
2
2
0
1
1
1
1
1
2
1
1
2
2
1
1
1
1
0
1
1
2
1
1
1
2
2
1
2
0
1
2
1
2
2
1
0
1
1
2
1
1
1
1
1
3
1
2
1
0
1
1
1
1
3
1
1
2
1
1
1
1
1
1
2
0
1
1
1
1
0
0
1
1
2
2
2
0
1
0
2
0
1
1
2
1
2
1
2
1
1
1
1
1
1
1
1
1
0
2
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
2
2
1
0
1
1
1
0
1
0
0
1
1
1
0
1
2
1
1
0
1
2
2
1
1
2
1
0
0
2
0
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
0
2
0
1
1
1
1
1
1
1
2
1
0
1
1
1
1
1
1
1
1
1
0
1
1
1
1
2
1
2
1
2
1
1
1
3
1
0
1
2
1
1
2
1
0
2
1
1
0
2
0
1
1
1
1
2
1
0
0
1
1
0
0
1
2
1
0
1
0
0
1
2
0
1
1
1
1
3
1
1
1
1
1
1
2
1
1
2
1
0
1
2
3
1
1
0
1
1
0
1
1
1
0
2
1
1
1
1
2
1
1
1
2
3
1
1
2
2
0
2
1
2
1
0
1
1
1
0
1
2
1
0
3
1
1
2
1
1
1
1
1
0
2
1
2
1
1
1
2
0
1
2
1
1
1
1
1
1
2
1
1
2
1
1
1
2
1
3
1
2
2
0
1
1
1
2
1
1
0
2
1
1
1
1
1
1
1
0
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
0
2
1
0
0
2
1
0
1
1
0
1
2
0
2
1
1
0
1
2
2
2
1
4
1
1
1
0
0
1
0
2
2
2
0
1
0
1
1
1
1
1
2
1
0
2
1
0
1
2
1
1
0
2
1
1
2
1
1
0
1
1
1
2
1
1
2
2
1
2
1
0
1
0
1
0
2
1
0
1
1
2
2
2
1
1
0
0
1
1
1
1
1
1
0
1
1
2
1
0
1
0
0
2
1
1
0
2
1
1
0
1
1
1
1
2
2
1
1
2
1
1
2
1
1
0
2
1
1
0
1
1
2
1
2
1
0
1
2
1
2
1
1
1
0
1
1
1
2
1
2
1
1
0
1
1
1
1
1
1
1
1
2
0
1
1
1
2
1
2
1
0
2
1
1
1
1
0
1
1
2
1
2
2
1
1
0
1
2
1
2
1
1
0
2
1
1
1
1
2
0
2
2
2
0
2
1
1
0
1
1
1
1
1
1
1
0
1
1
1
2
0
1
0
1
2
2
1
2
2
1
0
1
1
0
0
1
1
1
1
1
2
0
1
1
1
1
1
0
1
2
0
2
1
2
1
1
2
2
2
1
1
1
1
1
1
1
1
1
0
2
0
0
1
2
1
0
0
0
2
1
2
0
0
1
1
1
1
2
1
1
2
0
0
1
1
2
1
1
1
0
1
1
2
0
0
1
1
2
2
2
1
4
2
1
0
0
1
0
1
0
2
0
2
2
1
3
1
2
2
1
2
1
1
1
2
1
2
1
2
1
1
1
1
1
1
1
0
2
1
1
1
1
2
1
1
0
1
0
1
1
2
1
2
1
1
1
0
2
3
1
2
1
2
1
1
2
0
1
1
2
1
2
1
1
1
1
1
1
1
0
1
2
2
1
0
1
2
0
3
1
2
1
1
1
0
1
1
1
0
1
1
2
1
2
1
2
1
2
1
1
0
0
0
1
0
1
1
1
2
1
2
2
0
1
1
1
1
1
2
2
1
2
1
1
0
2
0
2
1
1
1
1
1
1
2
0
1
0
1
1
2
0
1
1
0
1
1
2
2
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
0
2
1
2
2
0
2
0
1
1
1
2
0
1
1
2
2
1
1
2
2
3
0
0
2
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
0
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
0
2
1
1
1
2
0
1
1
1
1
2
2
2
2
1
2
1
2
1
1
1
1
2
1
0
1
2
1
1
0
1
2
1
1
1
2
1
2
1
0
1
0
0
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
0
0
0
0
1
2
1
1
2
1
1
2
1
1
2
1
1
0
0
1
1
2
1
1
0
2
1
0
1
0
1
1
1
2
1
1
2
0
2
0
0
0
1
0
1
2
1
1
2
0
1
1
1
2
1
1
1
1
0
2
0
1
1
0
0
2
1
2
1
1
1
2
1
2
0
0
1
1
2
0
2
1
1
2
1
1
0
1
2
2
0
1
0
1
1
0
1
1
1
1
0
1
0
2
2
1
2
1
0
2
0
2
2
1
1
1
1
1
0
1
5
0
2
1
1
2
1
1
1
2
2
1
1
1
0
2
2
1
1
0
2
1
1
1
1
0
0
1
0
0
2
1
1
2
1
1
0
1
1
1
2
1
1
0
0
0
1
0
1
1
2
2
1
1
1
1
1
1
1
1
2
3
1
1
1
1
2
1
0
2
0
1
2
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
2
1
0
1
1
2
2
1
2
0
1
1
2
1
2
0
1
1
1
1
2
1
1
1
2
1
2
0
2
1
1
1
1
1
1
0
2
0
2
1
1
2
2
1
1
1
1
1
0
1
2
1
2
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
0
1
1
0
0
0
1
0
1
1
2
2
2
1
1
1
1
1
1
1
1
2
1
2
0
1
2
1
0
2
1
1
1
2
1
0
0
1
0
2
2
1
0
1
1
1
1
1
2
1
1
2
1
2
1
2
1
2
1
2
1
1
1
1
2
0
1
1
0
1
0
2
1
2
2
0
1
2
0
2
0
0
0
0
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
0
1
2
1
2
0
2
1
1
1
1
1
0
0
1
1
1
2
0
1
1
1
1
1
1
1
2
1
1
0
2
1
1
1
0
1
1
1
1
2
1
0
1
1
2
2
1
1
2
1
0
1
1
1
1
1
1
2
2
1
1
1
1
1
2
1
0
0
2
1
1
2
1
1
0
1
2
1
1
1
1
1
2
2
2
1
2
1
1
1
1
1
2
1
1
1
2
1
1
2
1
1
0
0
1
0
1
1
0
2
1
1
2
2
1
2
1
0
2
1
1
1
2
1
0
1
1
1
2
1
1
1
2
0
1
1
1
0
2
0
2
2
0
1
1
1
1
1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
1
1
0
1
0
1
1
2
2
1
0
1
2
1
2
1
0
2
2
1
1
1
0
1
1
0
1
1
1
1
2
2
1
0
1
1
1
2
2
2
1
1
1
1
1
1
1
1
1
2
1
2
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
2
1
1
1
0
1
1
1
0
2
1
1
1
0
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
0
1
2
1
1
1
1
0
1
1
2
1
1
1
1
1
2
0
1
3
1
1
0
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
2
1
0
1
2
1
0
2
1
2
2
1
1
10
2
1
1
0
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
2
1
2
2
1
2
1
2
1
1
0
1
2
0
1
1
1
1
1
1
1
0
1
1
0
1
1
0
0
2
0
0
2
0
1
2
2
1
0
1
2
1
2
1
1
1
0
0
2
1
1
0
2
2
1
0
0
1
1
0
1
1
1
1
0
0
0
2
1
1
0
1
1
4
0
1
1
2
2
1
2
1
1
2
1
1
1
2
2
2
1
1
0
1
1
1
0
2
1
2
1
1
1
1
1
1
2
1
1
1
0
1
2
1
1
0
1
1
1
1
1
1
1
1
1
2
1
1
0
2
1
1
2
2
1
1
2
1
2
0
1
2
1
1
2
2
1
1
1
1
1
2
0
2
1
2
4
1
1
1
2
1
2
1
1
1
2
2
0
2
1
0
1
1
2
2
1
1
1
1
1
1
1
1
0
0
1
0
1
2
1
1
1
0
1
1
2
1
1
1
1
1
1
1
1
2
2
1
1
1
1
0
2
1
1
1
7
2
1
0
0
0
1
3
0
1
1
0
1
1
1
1
0
2
0
2
1
1
1
1
1
2
1
1
2
0
1
0
1
1
1
0
1
1
1
1
0
1
1
2
2
1
2
1
0
1
2
2
2
0
0
2
1
1
1
2
1
2
2
1
2
0
0
1
1
1
1
2
0
2
1
2
1
1
2
0
1
1
1
1
1
1
2
0
2
1
1
1
2
1
1
2
1
1
1
2
2
3
0
1
1
1
2
2
1
2
0
2
1
0
2
0
2
1
1
1
1
1
1
2
1
1
0
2
2
1
1
1
2
0
0
1
1
1
2
2
1
1
1
2
1
1
1
2
1
1
2
1
1
2
1
1
2
2
2
1
2
1
1
0
1
2
2
1
2
1
1
2
2
1
2
2
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
0
1
2
2
2
1
2
2
1
1
1
1
2
0
2
1
1
2
0
2
1
1
2
1
2
1
1
1
1
1
3
0
2
1
1
1
1
1
0
0
1
1
1
2
1
1
2
1
1
1
1
1
1
1
0
1
1
2
1
1
1
0
0
1
0
1
1
1
2
1
1
0
0
1
2
1
1
1
1
1
1
1
1
0
2
0
3
0
1
0
0
0
0
1
1
1
2
1
1
1
1
1
0
2
1
2
1
2
1
2
1
2
2
2
1
1
1
2
2
1
1
1
2
1
1
2
1
0
1
1
2
1
0
1
1
1
2
1
0
1
1
3
1
0
0
2
2
2
2
1
1
1
2
1
1
1
2
1
3
2
1
1
2
1
3
1
0
2
2
1
0
1
1
1
2
1
1
2
1
1
1
1
2
2
0
2
1
2
1
1
1
1
1
0
1
2
1
0
2
0
0
2
1
1
0
0
1
2
1
2
1
2
0
1
1
2
1
2
1
2
2
2
2
0
1
0
1
1
2
1
1
1
2
1
1
0
2
1
1
1
1
1
2
1
1
1
1
1
0
1
1
1
1
0
1
2
0
1
2
0
1
2
1
0
2
2
0
1
0
1
0
1
1
2
1
1
2
1
1
2
1
2
1
1
2
1
2
1
2
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
2
1
1
1
0
1
1
2
1
0
0
1
1
1
1
2
1
2
2
1
1
2
1
1
2
1
1
2
1
2
1
2
2
1
1
0
1
0
1
1
1
1
1
1
2
2
1
1
1
0
1
1
2
1
0
2
1
2
0
2
1
1
0
1
1
1
1
1
1
0
0
1
1
2
1
1
1
1
1
0
1
1
1
1
0
2
1
1
1
1
1
0
1
1
1
1
0
0
2
0
2
1
1
0
0
0
1
0
1
0
0
1
2
1
0
1
1
1
1
0
1
0
2
0
1
1
1
1
1
1
1
2
0
2
2
0
1
2
1
2
2
0
1
1
1
1
2
1
1
1
1
1
1
1
0
0
0
1
1
1
2
1
1
1
1
2
1
2
2
2
1
1
2
1
1
1
1
1
1
0
2
2
3
1
2
0
1
0
1
0
1
1
1
1
1
2
1
1
1
2
1
2
1
1
2
1
1
1
0
1
1
1
1
2
2
1
1
1
1
1
1
0
1
2
1
1
2
0
2
0
1
1
1
2
2
1
1
2
1
2
2
1
1
0
0
1
2
1
1
1
1
2
1
4
1
0
0
1
1
2
0
1
2
2
1
0
1
1
1
2
1
2
1
1
1
2
1
2
1
2
1
1
0
2
1
1
2
1
1
0
1
0
1
0
2
1
1
1
1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
1
2
1
0
0
1
1
0
1
1
2
1
2
2
1
1
1
1
0
0
1
1
1
2
1
2
2
1
0
1
0
1
1
2
2
0
1
1
1
1
0
0
2
1
1
0
2
0
1
1
1
2
0
1
2
1
0
1
1
2
1
0
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
2
2
1
1
1
2
1
1
1
0
1
2
1
1
1
2
0
2
1
1
1
1
1
2
1
1
1
0
2
1
1
1
0
1
1
2
0
1
1
2
1
1
2
2
2
2
2
2
2
0
1
2
1
2
0
0
1
1
2
2
2
2
1
1
2
1
2
2
2
2
1
1
1
1
2
1
0
0
1
2
0
1
0
0
0
1
1
1
1
0
1
1
1
0
1
1
0
1
1
1
1
0
0
2
0
1
2
1
1
2
2
1
0
1
1
2
0
1
0
1
1
1
2
1
1
1
0
1
1
2
1
1
1
2
0
0
0
1
1
1
1
2
1
2
1
0
0
1
1
1
2
1
1
1
2
1
0
2
2
2
1
1
1
2
2
1
2
0
1
1
2
2
1
1
0
1
2
0
1
0
1
1
2
3
1
2
1
1
0
1
1
1
1
2
0
1
1
1
0
2
1
1
0
1
2
1
1
0
1
1
1
1
1
2
0
1
0
1
2
2
2
1
2
0
1
2
0
2
1
1
1
1
1
2
2
0
1
2
0
2
2
2
0
0
2
1
1
1
1
1
1
0
2
1
0
1
1
1
2
0
2
1
1
0
1
0
0
2
1
0
2
2
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
0
2
0
1
1
1
2
1
1
1
0
1
1
3
2
0
0
2
1
0
1
2
1
1
1
1
2
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
2
1
1
1
1
2
1
2
2
1
0
1
1
2
0
1
0
1
1
1
2
1
1
1
1
0
1
0
2
2
2
1
1
1
1
2
1
1
2
1
1
2
1
0
1
0
2
2
1
2
1
2
2
1
1
1
0
2
2
2
2
2
1
0
1
1
1
2
0
1
1
1
1
1
1
1
1
2
1
2
0
0
1
1
1
1
1
3
1
1
0
1
2
0
1
1
2
1
1
1
1
1
2
1
2
1
1
1
2
1
1
2
0
1
2
1
1
2
1
1
1
0
1
0
1
2
2
1
1
1
1
1
1
1
1
1
1
2
2
1
2
2
0
0
0
1
1
2
1
1
0
2
1
1
1
1
1
2
2
1
0
0
2
1
3
1
0
2
3
1
2
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
2
1
1
3
1
2
1
2
1
1
1
2
2
0
1
0
1
0
1
0
1
2
1
0
1
1
0
1
1
0
0
1
2
2
0
1
1
0
2
0
1
1
2
0
1
1
0
0
1
1
1
2
1
2
2
0
1
1
2
1
2
2
1
0
1
1
1
1
1
0
1
1
1
2
1
1
2
2
1
1
0
1
0
1
1
0
1
1
1
1
2
2
2
1
0
1
1
2
1
0
2
0
1
0
1
1
1
0
2
1
0
1
0
2
1
2
1
1
0
1
2
0
1
1
2
2
1
3
2
2
1
2
1
1
2
1
2
2
1
2
1
0
0
1
1
1
1
0
2
2
1
0
2
0
1
2
1
1
1
1
2
1
1
2
2
2
1
1
1
2
0
0
1
1
1
1
1
1
2
0
1
0
1
1
2
1
1
0
0
1
2
2
1
1
0
0
1
1
1
4
1
1
1
2
1
2
2
0
2
2
1
1
0
1
1
1
2
0
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
2
0
1
2
2
1
2
1
1
1
1
1
1
2
1
0
1
0
1
1
1
1
0
2
1
1
0
1
1
1
0
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
0
0
1
0
1
0
1
2
2
2
1
1
0
1
0
0
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
0
0
2
1
1
1
0
0
2
1
0
1
0
1
1
2
1
1
0
2
2
1
0
1
1
1
1
0
2
1
1
2
2
2
1
1
1
2
2
0
1
1
0
1
1
1
2
1
0
2
1
1
1
0
0
1
2
1
0
2
1
1
1
1
1
1
1
2
1
1
2
1
1
2
1
0
1
2
1
1
1
1
1
1
1
1
1
0
1
1
0
2
2
1
1
1
2
2
2
1
2
0
1
2
0
1
2
0
1
1
1
0
2
1
1
1
1
1
1
0
2
2
1
0
2
2
2
1
1
2
0
1
2
1
0
1
1
1
0
1
0
0
2
1
1
1
0
2
2
1
1
1
1
2
2
0
2
1
2
1
1
1
1
2
1
1
2
1
2
2
0
2
1
0
1
1
1
1
1
1
0
2
1
0
1
2
1
0
0
1
1
1
2
1
0
1
0
0
1
0
1
1
1
0
0
1
1
0
0
1
2
2
2
1
1
1
1
0
0
2
1
1
2
1
1
1
1
1
2
0
1
1
1
1
2
2
2
2
1
1
2
1
2
2
1
1
1
2
2
1
2
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
2
0
1
1
1
0
2
1
0
0
1
1
1
1
1
1
1
1
1
0
2
1
2
2
2
1
2
1
2
2
1
2
1
3
1
2
1
2
0
1
1
2
2
3
0
1
0
1
0
2
1
2
1
1
1
1
0
1
1
1
1
0
1
1
1
1
1
2
0
0
1
0
1
1
1
0
2
1
1
2
1
1
1
1
1
0
1
2
2
0
0
1
1
1
1
1
2
0
0
0
1
1
3
2
2
1
1
1
1
1
1
0
0
2
1
1
1
1
1
1
1
1
1
1
1
2
0
0
0
1
2
2
1
1
2
1
1
2
1
1
1
2
1
2
1
0
1
1
2
1
1
2
1
2
2
1
1
2
1
2
1
0
2
2
0
0
2
0
0
1
1
1
1
1
1
2
0
1
1
2
1
1
2
1
0
1
0
1
1
1
1
2
0
1
0
1
2
2
1
0
1
1
2
1
0
1
2
2
1
1
2
1
1
1
2
1
2
2
1
1
2
1
1
2
1
0
1
1
1
1
1
1
0
1
1
1
1
2
0
2
2
2
1
1
2
1
2
2
2
1
1
1
0
1
0
2
1
2
1
2
0
1
1
0
1
1
1
1
2
1
1
2
1
2
2
0
0
1
2
2
1
1
0
1
1
0
0
1
1
2
1
1
1
1
1
2
1
1
2
2
2
1
2
1
1
1
1
1
1
1
1
2
1
1
0
1
0
1
1
1
1
0
2
1
1
2
1
1
1
0
1
1
0
2
0
1
2
1
2
1
1
1
1
2
2
2
1
1
1
2
1
0
1
1
1
1
2
1
1
1
0
0
0
2
2
2
1
1
1
0
1
2
1
0
1
1
1
1
1
0
1
1
0
2
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
0
1
1
1
1
1
2
0
1
2
1
1
2
1
0
1
1
1
2
1
1
1
1
1
0
1
0
0
0
1
2
1
0
1
1
1
2
1
1
2
2
2
2
2
1
1
0
1
0
1
1
1
1
2
1
0
3
1
1
0
0
0
1
1
0
2
1
1
1
2
2
1
1
1
2
0
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
3
1
1
1
0
2
2
1
1
1
1
0
2
2
1
2
1
1
0
1
2
0
0
1
1
0
1
1
2
2
1
0
1
2
1
1
2
1
1
1
1
0
1
1
1
1
1
1
1
2
0
1
2
0
1
2
1
2
1
1
1
2
0
2
2
2
1
0
0
2
1
2
2
1
1
2
1
1
1
0
0
1
1
1
1
1
1
0
1
1
1
1
2
2
0
0
2
1
0
1
1
2
1
1
2
1
1
2
2
3
1
1
1
1
1
3
1
2
3
2
1
1
1
1
1
1
1
1
1
0
2
1
1
1
1
1
1
1
1
1
0
1
1
1
0
0
2
2
0
1
2
2
2
2
1
1
2
2
2
1
2
1
1
1
2
1
1
2
0
1
2
2
0
2
1
2
1
2
1
1
2
1
1
1
1
1
0
2
1
1
2
1
0
1
1
2
0
1
2
2
0
0
0
1
1
2
2
1
2
0
1
1
1
1
2
0
2
1
1
1
2
1
2
2
0
0
0
1
1
1
0
1
0
1
1
1
1
2
2
2
1
1
0
2
2
1
2
1
2
2
1
1
2
1
1
1
1
1
1
1
1
2
1
2
1
2
2
2
1
1
1
1
1
1
2
0
1
2
1
1
1
2
0
1
2
0
1
2
2
1
1
1
1
0
1
1
2
8
1
1
1
1
0
1
2
1
1
2
2
1
1
1
1
2
1
1
1
1
2
1
2
2
0
0
2
2
1
2
1
1
0
1
1
1
1
1
1
2
1
1
1
2
2
1
1
1
0
1
1
0
1
0
2
1
1
2
1
1
1
1
2
1
1
1
0
2
1
2
1
0
1
2
1
2
1
0
1
0
1
2
2
1
0
1
1
2
1
1
1
1
0
2
1
1
1
0
1
1
1
0
1
2
1
1
2
1
1
2
1
0
1
2
1
1
1
2
2
1
0
1
2
1
1
1
2
1
1
1
2
0
0
1
2
1
1
1
1
2
2
1
0
2
0
1
1
1
2
0
1
1
1
0
1
1
2
0
2
1
1
2
0
0
1
1
1
1
1
1
1
1
0
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
0
0
1
0
1
2
1
1
1
1
1
1
2
2
1
1
2
1
1
2
0
1
1
1
0
1
1
1
2
2
0
1
1
2
2
1
2
2
1
0
1
1
0
1
1
1
2
1
1
2
1
1
1
1
1
2
2
0
2
2
2
1
0
2
1
1
1
1
2
1
1
1
1
2
2
0
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
2
0
2
2
1
1
1
1
1
1
1
2
1
1
0
1
2
1
1
2
1
0
2
1
1
3
1
1
1
1
2
1
2
0
1
1
1
0
2
1
1
2
2
1
1
1
1
2
2
2
1
1
1
1
1
1
2
1
2
0
1
1
3
1
1
1
1
0
1
2
2
1
2
1
0
2
1
1
1
2
0
2
1
2
2
0
1
1
2
1
2
1
1
1
0
1
2
1
0
2
2
1
1
1
2
1
1
2
1
0
1
0
1
0
1
1
0
1
2
1
1
0
2
1
2
1
1
1
1
0
1
1
1
1
1
1
1
2
1
1
2
1
0
2
1
1
0
1
1
0
0
1
1
1
2
0
1
1
0
1
2
4
1
2
1
1
1
1
2
1
1
1
1
0
2
1
1
1
2
1
2
1
1
1
1
2
1
1
0
2
1
1
0
1
1
1
0
2
1
1
1
1
1
0
1
1
1
1
1
2
1
1
0
0
1
0
1
2
1
2
2
1
1
1
1
1
1
2
1
1
0
1
0
0
2
1
2
1
2
1
1
0
1
0
1
2
2
1
1
2
1
1
1
1
1
1
1
2
0
1
2
1
1
1
0
1
1
2
0
1
1
2
1
1
1
1
2
0
1
1
1
0
1
1
1
1
1
2
0
1
1
1
1
0
2
1
1
1
1
0
1
1
1
1
2
0
1
1
1
0
1
2
1
1
2
1
1
1
1
1
1
1
1
0
1
0
2
2
2
1
0
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
0
1
2
1
1
2
1
2
2
1
1
2
2
2
1
2
0
1
1
2
2
1
1
2
1
1
2
1
1
0
0
2
1
1
0
1
1
1
1
2
1
1
1
1
1
1
1
1
1
0
1
1
1
5
0
1
1
1
1
0
2
1
1
1
1
1
1
1
1
1
0
1
0
1
2
2
1
1
1
2
2
0
1
1
1
1
1
2
2
1
0
1
1
0
1
0
1
0
2
1
2
1
1
1
1
2
2
1
1
1
2
2
1
1
1
1
2
1
1
2
1
2
1
2
0
1
1
1
1
1
1
2
1
0
1
1
0
2
1
2
1
1
0
1
1
0
1
1
1
1
0
1
1
1
1
1
2
1
1
2
0
1
1
0
1
2
1
1
1
1
1
0
1
2
0
1
0
1
1
1
1
1
1
1
1
1
1
1
0
1
1
2
1
3
1
1
1
0
0
0
1
1
1
1
1
2
2
1
1
1
2
1
2
1
0
1
1
2
1
2
1
1
1
2
1
2
2
1
2
1
1
2
1
1
1
2
1
1
2
1
2
2
0
2
2
2
2
2
2
1
1
1
1
0
1
0
1
0
2
1
0
2
2
0
1
1
1
1
1
1
0
0
4
1
1
1
1
3
1
1
1
2
2
1
1
3
1
0
1
2
1
1
0
0
0
2
2
1
2
2
1
0
1
2
1
1
2
1
1
2
1
2
0
1
1
0
1
2
2
1
2
1
2
0
2
2
1
2
2
0
1
0
1
1
0
1
2
1
2
0
2
0
0
1
1
1
0
2
1
1
2
1
4
1
0
0
2
1
2
2
2
2
1
1
2
2
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
2
1
1
0
2
1
1
1
1
1
2
2
1
1
3
1
1
2
2
1
1
0
2
0
1
1
1
1
1
1
1
1
0
1
1
1
1
2
1
1
1
1
1
1
1
0
0
2
0
1
0
2
1
1
1
2
1
1
2
1
0
1
2
0
2
1
1
0
1
0
1
1
1
1
1
2
0
1
0
1
0
1
0
2
0
0
1
1
1
1
0
2
1
1
1
0
1
2
1
1
1
2
1
1
2
2
1
0
1
1
2
1
0
0
2
1
0
2
1
1
1
0
0
2
1
0
1
1
1
1
1
1
1
0
1
1
1
1
1
0
2
1
1
2
1
1
2
2
1
1
1
1
2
0
1
2
1
1
1
1
2
1
1
2
2
2
1
1
1
2
1
1
1
2
2
1
1
1
0
1
1
1
2
1
0
1
2
0
2
1
1
0
1
2
1
1
1
1
2
1
1
2
2
0
1
1
0
1
2
1
1
1
1
2
1
2
0
2
2
1
1
1
0
1
1
1
0
1
1
1
1
1
1
1
2
1
1
2
1
1
0
1
1
2
2
1
2
1
1
1
1
0
1
2
1
2
1
1
0
2
1
2
1
1
0
2
2
2
2
2
1
0
1
2
1
1
1
1
0
2
2
1
0
2
2
1
2
1
0
2
1
1
1
2
1
1
1
1
0
1
1
1
1
0
2
2
2
1
2
1
1
0
1
0
1
1
1
0
0
1
2
1
2
0
0
1
2
1
2
0
1
1
1
1
0
0
1
1
2
2
1
2
1
1
0
1
1
2
1
0
1
2
2
1
1
0
0
2
0
0
2
1
1
1
1
2
1
1
0
1
1
2
2
2
1
1
0
1
1
1
1
1
1
2
1
1
1
1
1
2
1
2
1
2
1
1
2
2
1
0
1
0
0
1
1
1
1
1
0
0
1
1
0
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
0
1
0
2
0
1
1
2
1
1
2
0
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
0
2
0
2
1
2
1
2
1
2
1
2
2
1
0
2
1
2
0
2
1
1
2
1
1
2
2
1
1
1
1
1
2
1
1
0
1
2
0
2
2
1
2
2
0
1
2
2
1
1
0
1
0
1
0
1
1
1
0
1
1
2
1
1
1
1
3
1
2
2
2
1
1
1
2
1
1
1
1
2
1
1
1
2
1
1
1
0
1
1
1
0
1
1
1
2
1
0
1
1
0
1
1
1
2
1
1
2
1
1
0
1
1
0
1
0
1
1
2
1
1
0
2
2
2
1
1
1
0
2
2
1
0
2
1
2
1
1
1
1
1
2
1
3
0
1
1
2
1
1
1
1
2
0
1
1
1
0
1
1
1
0
1
2
2
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
0
0
2
1
2
1
1
2
1
1
1
0
0
1
0
1
1
1
1
1
1
1
0
2
0
1
1
1
1
1
1
1
0
1
0
0
0
1
1
1
2
0
1
1
1
2
0
2
1
1
1
1
2
2
2
1
2
1
2
0
0
0
1
2
1
0
2
1
1
1
0
2
1
2
3
1
1
2
1
1
1
1
0
2
1
1
0
2
1
1
1
1
1
1
1
1
0
1
1
2
1
1
1
1
2
1
1
1
1
1
2
1
2
2
1
1
1
2
0
1
2
0
0
1
0
1
2
0
1
0
2
1
0
1
1
1
1
2
2
1
2
1
0
1
2
2
2
1
0
1
1
1
0
2
1
0
1
0
1
1
1
1
2
2
2
1
1
2
1
1
1
0
1
1
0
2
1
1
1
1
1
1
0
1
0
2
1
0
1
1
0
1
0
1
0
2
1
0
1
1
1
2
1
1
1
1
3
1
1
1
2
1
1
1
2
1
2
2
2
1
1
1
2
2
1
2
1
2
2
1
2
1
1
2
1
2
0
1
2
1
1
1
2
0
1
1
1
1
1
0
0
2
1
1
1
1
2
1
1
2
1
1
1
1
0
1
1
0
1
0
1
2
2
2
1
1
0
2
1
1
1
0
2
1
0
0
1
1
1
2
3
1
1
2
0
1
1
2
1
1
3
2
0
2
1
1
1
1
2
1
0
0
1
1
1
1
1
1
0
1
2
1
2
0
1
2
2
3
0
1
1
1
1
0
1
1
1
0
2
1
1
1
0
1
1
1
2
1
2
2
1
1
0
1
1
0
1
1
1
2
1
1
1
2
0
1
2
3
1
2
2
1
1
1
1
2
1
1
0
1
1
1
2
1
2
0
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
0
1
1
1
1
1
2
1
2
0
1
2
1
1
1
2
0
2
1
2
0
1
2
0
0
2
1
1
0
1
2
0
1
1
0
1
2
2
1
1
1
1
2
1
0
1
1
1
1
2
1
1
1
1
1
0
2
0
1
1
1
1
0
1
1
0
1
1
1
2
1
1
1
1
1
1
1
3
1
1
1
1
1
1
1
1
1
1
2
1
0
1
1
1
1
2
2
2
1
1
3
1
1
0
1
2
1
1
2
1
1
1
1
1
2
1
1
2
2
1
2
2
1
1
1
2
1
0
1
0
1
2
1
1
0
1
1
1
0
2
1
3
1
1
1
1
1
1
2
1
2
0
1
2
2
2
0
2
1
2
1
1
2
1
2
2
1
1
1
1
2
2
1
1
2
2
2
1
1
1
2
1
2
1
1
1
1
1
1
0
1
0
1
1
1
1
2
1
1
1
0
0
1
1
1
1
1
1
1
1
1
2
1
1
1
0
1
1
2
1
0
1
2
1
0
2
1
0
1
2
1
2
1
1
2
1
2
2
4
1
0
1
0
2
1
2
1
0
1
1
2
2
0
1
1
0
1
2
0
1
1
0
1
2
1
1
1
0
1
0
1
2
1
1
1
1
1
1
2
1
2
1
2
1
2
2
1
0
0
2
2
1
1
1
1
1
2
1
1
1
0
1
2
1
1
1
1
1
0
1
1
1
1
1
1
1
0
1
0
1
1
1
1
1
1
0
2
1
1
0
1
2
1
0
0
1
1
1
2
1
0
2
1
0
1
1
2
1
0
0
1
2
1
0
1
2
0
1
1
1
1
0
1
0
1
2
1
1
0
1
1
1
2
1
1
3
2
2
1
2
2
0
2
2
1
1
1
2
1
2
1
1
1
0
1
1
1
0
1
2
1
1
2
1
1
1
2
1
2
1
2
0
1
0
1
1
1
0
1
1
0
1
0
2
2
1
1
2
1
1
1
1
2
1
2
1
2
1
2
1
2
2
1
0
1
1
0
1
1
2
0
1
2
1
1
2
0
2
2
2
2
1
2
1
1
1
2
1
1
1
0
1
1
0
2
1
1
1
2
2
1
1
0
2
0
2
1
1
2
3
2
2
2
1
2
2
1
1
0
0
2
2
1
2
0
1
0
1
2
1
1
2
1
1
1
1
2
1
1
0
0
1
1
1
1
2
1
1
1
1
1
2
1
0
1
1
1
1
2
1
1
1
0
1
0
0
1
0
2
1
2
1
2
2
1
0
0
2
1
1
1
1
0
2
1
2
2
2
2
0
1
1
1
1
0
1
1
1
2
1
1
2
2
1
1
1
1
1
1
2
1
0
1
2
1
1
2
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
1
2
0
1
1
1
0
1
1
2
1
1
2
1
2
2
1
2
1
0
2
0
1
2
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
2
1
2
0
1
2
1
0
0
2
1
2
1
1
1
1
0
1
0
0
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
0
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
0
1
2
1
0
1
1
1
1
2
1
1
0
2
1
1
3
1
1
1
1
2
2
1
1
0
2
0
1
1
1
0
2
1
1
1
1
1
1
1
2
2
0
3
2
1
1
1
1
1
1
2
1
1
2
1
1
1
1
2
1
2
0
1
1
1
1
2
0
1
1
1
1
1
1
0
1
0
1
0
2
2
0
0
0
1
0
1
1
0
0
1
2
0
2
1
3
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
0
2
2
1
1
1
2
0
1
1
2
2
2
1
0
1
1
1
1
1
2
1
0
0
2
1
2
1
2
1
1
2
2
1
2
1
0
1
1
0
1
1
0
2
1
1
2
1
0
1
1
0
1
2
2
2
1
0
1
1
1
1
1
1
2
2
2
1
1
2
2
1
1
1
2
1
1
1
2
1
1
1
2
1
0
2
0
2
1
1
1
1
0
1
1
1
1
1
0
0
1
1
0
3
1
1
1
1
1
2
1
1
0
1
2
1
1
1
2
1
2
1
2
0
2
1
1
0
1
2
1
1
1
1
1
1
1
1
1
1
2
1
0
1
0
1
0
2
1
1
1
1
0
1
1
2
2
2
1
1
2
0
1
2
1
2
0
1
1
1
0
0
0
1
2
0
1
2
1
2
0
2
2
1
1
1
1
1
2
1
1
2
1
1
0
0
1
1
2
2
0
1
0
1
1
1
1
1
0
1
0
1
1
1
1
0
2
2
1
2
1
1
1
2
2
2
1
1
1
1
2
1
1
1
1
1
1
1
0
1
0
1
1
1
1
1
2
1
2
2
1
2
1
1
2
1
1
3
2
1
0
0
2
1
0
1
2
2
1
1
2
1
1
0
1
2
1
1
1
0
2
1
1
2
1
1
2
1
1
0
1
1
1
1
1
1
2
0
2
1
1
1
1
2
1
1
1
1
0
2
1
2
2
2
1
2
1
1
0
0
1
2
2
0
1
2
1
1
1
1
2
2
1
1
0
1
1
1
1
1
2
2
1
0
1
0
1
2
1
0
0
1
2
0
1
1
1
1
1
2
1
2
1
1
0
0
2
0
0
1
1
1
2
0
1
2
1
2
2
2
1
1
2
2
1
2
0
2
1
1
1
1
0
1
0
2
1
2
2
2
2
4
0
1
2
2
0
2
1
1
1
1
1
1
0
1
1
0
2
2
1
1
1
1
1
1
2
1
2
1
2
2
1
2
1
1
1
0
1
1
2
2
0
2
1
1
1
0
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
0
1
1
2
2
1
2
1
2
1
1
2
1
1
2
0
0
0
2
0
2
0
2
2
2
1
1
1
2
1
1
0
1
1
1
1
2
1
1
2
1
0
1
1
0
1
1
0
2
2
1
1
2
1
2
1
1
0
1
2
1
1
2
1
2
0
1
1
1
1
1
1
1
1
2
1
2
1
2
1
2
1
2
0
0
0
1
2
1
1
1
1
2
1
2
1
1
1
1
2
0
0
1
1
1
3
2
1
2
1
2
2
1
0
1
2
0
2
1
1
1
1
2
2
1
2
1
1
0
2
0
1
0
1
2
1
0
2
2
2
2
2
1
1
1
2
1
0
1
0
0
0
1
1
1
1
2
2
3
1
1
1
1
1
1
1
1
3
1
0
1
2
2
1
1
2
1
1
4
1
1
2
2
2
2
1
0
1
1
2
2
3
3
0
0
2
1
2
1
0
1
0
2
0
0
0
1
2
1
2
1
2
2
2
0
2
0
0
1
2
1
2
0
1
2
1
1
1
2
1
2
0
1
1
1
1
1
2
2
2
1
0
1
2
1
1
2
1
2
1
1
1
1
1
0
1
1
1
1
2
1
1
1
0
1
0
0
2
0
0
1
1
1
1
1
2
1
2
0
1
1
0
1
1
1
2
0
1
1
2
0
1
1
1
1
1
1
1
1
2
0
1
0
2
0
1
2
2
1
0
1
1
1
2
1
1
0
0
1
1
1
1
0
1
1
2
2
1
1
1
2
1
1
0
1
1
1
0
2
2
0
0
0
1
1
2
2
1
2
0
1
1
1
1
1
2
1
2
1
0
1
0
1
1
1
1
0
1
2
2
1
1
0
1
1
0
2
0
2
1
1
1
1
1
1
2
1
1
2
1
3
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
1
1
0
2
2
1
2
2
1
1
2
1
2
1
1
2
1
1
1
1
1
2
1
1
1
1
1
0
2
0
1
2
0
1
0
1
1
2
1
1
2
1
1
2
0
1
1
0
1
2
1
2
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
2
1
2
1
1
1
1
1
2
0
0
2
0
2
1
1
1
1
1
1
1
1
2
1
1
0
1
2
1
1
0
1
2
3
1
1
1
0
1
1
1
1
1
1
2
1
1
0
1
1
2
0
0
0
1
1
2
2
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
0
0
0
1
1
0
2
2
0
1
1
1
1
0
1
2
2
1
1
2
1
2
1
1
1
0
2
1
2
1
1
0
1
1
0
1
2
0
2
1
2
2
1
2
0
1
1
1
1
0
2
0
2
0
1
0
2
2
1
0
1
1
1
1
2
1
1
2
1
1
1
1
2
1
2
1
3
1
1
1
0
2
2
1
1
2
0
1
1
0
1
1
1
0
1
2
2
1
1
1
1
2
1
1
1
1
1
1
0
1
1
2
1
0
1
2
2
1
1
2
2
1
1
1
0
2
0
2
3
1
1
0
1
1
1
1
1
1
1
1
2
1
1
1
1
1
0
1
2
2
2
2
1
1
1
1
1
0
0
0
0
1
0
1
1
2
2
0
1
2
2
1
1
0
1
1
1
1
1
2
1
2
2
2
1
1
0
2
1
1
1
1
1
2
0
1
2
1
2
1
1
0
2
1
1
1
1
2
1
2
1
1
0
2
1
1
1
0
1
1
2
2
1
1
1
2
1
2
2
1
1
0
1
1
1
2
1
1
2
1
0
0
1
1
1
1
2
2
1
2
0
2
0
0
1
0
1
2
2
1
1
1
1
0
1
1
1
2
0
1
1
0
1
0
0
1
1
1
0
2
1
2
2
0
1
1
1
1
2
1
0
1
2
1
1
0
1
1
1
1
1
0
1
1
1
0
1
1
3
2
2
1
1
1
0
1
1
2
0
2
1
2
1
0
1
0
1
1
2
1
0
1
1
1
2
1
0
1
2
0
1
1
0
1
2
2
2
1
1
2
2
1
1
2
1
2
1
0
1
0
2
2
2
1
1
2
1
0
1
2
2
2
2
2
1
1
2
2
1
2
0
1
1
1
0
1
1
1
2
1
1
2
0
1
2
1
1
1
1
2
2
1
0
1
1
1
1
2
1
2
1
2
1
0
1
1
2
1
1
0
1
1
1
2
2
1
1
0
1
2
1
2
1
2
0
2
1
2
1
1
2
2
1
0
2
0
1
2
1
2
1
2
2
1
0
0
1
2
2
1
1
1
2
2
1
1
2
1
2
1
1
1
1
1
0
1
2
1
2
1
1
2
1
2
1
1
1
1
2
1
1
1
1
1
2
1
1
2
1
0
2
1
0
2
1
2
1
1
1
1
1
1
1
2
2
1
1
1
2
1
1
0
2
1
1
1
0
1
2
0
1
2
1
1
2
2
2
1
0
1
1
2
2
1
1
2
0
1
1
1
2
0
1
0
2
1
1
1
1
0
2
0
1
2
1
2
1
2
1
1
1
3
2
1
1
1
0
2
1
2
1
1
1
1
2
1
1
1
1
1
0
1
0
1
0
1
0
1
0
1
1
2
2
0
1
0
1
1
1
1
1
1
1
1
2
2
0
1
0
2
1
0
1
1
1
1
2
0
2
1
0
1
1
1
0
2
1
1
0
2
1
0
1
1
2
1
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
0
1
1
2
1
0
1
1
1
1
2
1
1
1
0
1
1
2
2
0
0
1
1
2
1
1
1
0
1
1
1
0
2
1
1
1
1
2
1
0
2
2
1
2
1
2
0
2
1
0
1
1
2
2
1
2
1
1
2
0
1
2
2
1
1
1
1
1
2
1
1
1
2
1
2
2
1
0
0
1
1
2
1
1
2
1
1
2
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
0
2
1
0
2
1
1
2
1
1
1
0
1
2
1
1
0
2
0
1
1
0
0
2
1
1
1
2
1
1
1
1
1
2
2
2
1
2
0
2
2
1
1
2
0
1
2
1
1
2
0
1
1
1
2
2
0
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
2
1
1
1
0
0
0
1
1
1
1
1
1
2
1
2
1
1
1
2
1
1
1
1
1
2
0
2
1
1
1
0
1
9
1
2
1
1
2
1
1
1
1
1
1
1
0
1
1
0
0
0
2
0
1
1
2
1
1
1
1
0
2
1
2
1
2
1
1
0
2
1
1
1
1
1
2
1
1
3
1
1
1
1
0
1
1
1
2
1
1
2
1
1
2
2
2
0
1
0
2
1
1
1
2
1
1
1
0
1
2
2
2
1
1
1
2
1
2
1
2
1
2
0
1
1
1
0
2
1
1
2
1
1
1
1
1
2
1
2
1
1
0
1
2
1
1
1
2
1
1
2
0
0
1
2
0
0
1
0
0
1
1
2
2
1
1
1
0
2
0
0
1
1
1
0
2
1
2
0
1
0
0
1
1
2
1
1
2
1
0
1
0
4
2
1
2
0
2
0
2
1
1
0
2
0
1
1
1
0
2
1
2
0
2
1
1
1
2
0
1
0
1
0
1
1
2
3
1
1
1
2
1
1
0
0
1
2
1
1
0
2
1
1
1
1
0
1
1
1
1
1
0
2
0
0
0
1
1
1
0
1
1
2
2
0
1
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
0
2
2
1
1
2
1
2
2
1
1
2
2
0
1
2
1
1
1
1
1
0
1
2
1
1
0
2
1
1
0
1
1
0
0
1
2
1
1
2
1
1
1
2
0
0
1
1
2
2
1
0
1
1
1
1
1
1
1
1
1
2
2
1
1
1
2
1
1
1
1
1
1
1
1
2
0
0
1
2
0
1
1
1
1
1
3
1
1
1
1
2
0
1
1
1
0
1
2
2
2
1
1
1
0
1
0
0
1
2
2
0
2
0
2
1
1
0
6
2
1
0
0
1
2
1
1
1
0
1
2
0
2
0
1
1
0
1
1
1
1
1
1
0
1
1
1
1
1
0
0
2
1
1
1
0
1
1
2
2
1
1
1
0
2
0
1
1
1
2
1
1
2
1
1
1
1
0
2
1
1
2
2
1
2
0
3
1
1
1
1
2
0
1
2
1
1
0
1
1
1
1
1
1
1
1
1
0
2
2
1
2
2
1
1
2
1
1
1
0
0
1
1
1
1
2
1
0
1
2
2
2
1
1
1
2
1
2
1
0
1
2
1
0
0
0
1
1
1
0
0
2
1
0
1
0
1
1
1
1
1
0
1
2
1
1
0
1
1
1
1
1
1
0
2
0
2
1
2
1
2
1
1
1
0
1
2
1
1
1
0
1
1
1
1
1
2
1
1
3
2
1
1
2
1
2
1
0
0
1
1
0
1
1
1
0
1
2
0
1
0
2
1
1
1
2
1
1
1
1
0
2
1
1
2
1
1
1
1
1
1
0
1
2
1
1
1
2
0
2
2
2
2
1
1
1
0
0
1
1
2
1
1
1
2
1
0
0
1
2
1
1
2
2
0
0
1
0
0
1
1
1
2
1
1
2
1
1
0
1
0
1
2
1
0
1
2
0
1
2
2
0
1
2
1
1
1
2
2
1
0
2
1
2
2
0
1
0
2
1
2
1
0
1
1
2
1
3
1
2
1
1
1
1
1
2
2
1
1
1
2
1
2
1
2
1
1
0
2
1
1
1
1
1
1
2
2
0
1
2
1
1
1
2
0
1
2
0
1
1
1
0
0
1
1
1
1
1
0
1
2
2
1
1
2
0
1
0
0
2
1
1
1
1
1
2
1
1
1
1
1
0
1
1
2
2
2
1
0
1
0
2
2
1
0
1
1
1
0
1
3
1
2
2
1
1
1
0
1
2
1
1
0
1
2
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
2
2
1
1
0
2
1
0
1
1
1
1
2
2
1
1
1
1
1
2
2
2
1
1
1
0
0
1
1
1
0
2
1
1
0
0
1
1
0
1
2
2
2
0
2
1
0
2
1
1
2
1
2
1
1
0
0
1
2
1
1
2
2
2
1
1
1
1
2
2
0
0
1
0
2
1
0
1
1
1
0
0
1
1
1
0
1
1
1
1
1
2
0
2
1
1
1
1
2
1
1
2
1
2
1
2
0
1
1
0
0
1
1
0
1
1
1
0
0
0
1
0
2
1
2
1
1
1
0
1
0
2
2
2
1
1
1
1
2
1
2
2
2
2
1
1
0
1
1
1
1
1
0
2
1
1
1
0
0
2
1
2
1
2
2
1
1
1
1
1
1
1
1
2
1
3
2
1
1
0
1
1
0
2
1
1
0
1
1
1
0
2
2
1
1
1
2
1
0
2
2
1
1
1
1
0
1
2
1
1
1
1
1
1
2
0
0
1
2
1
2
1
1
2
2
1
3
1
2
0
1
1
0
1
1
1
1
1
0
1
1
2
2
1
1
1
1
0
1
0
0
1
2
1
1
1
0
2
1
0
1
1
1
1
1
1
0
2
1
2
1
1
2
0
1
0
1
1
1
2
1
1
1
1
2
1
1
1
0
0
2
1
2
1
1
0
1
1
2
1
1
1
0
1
2
2
2
1
1
1
2
2
1
0
2
1
0
1
1
1
2
2
1
1
1
2
1
1
1
1
1
2
1
1
2
0
4
1
1
1
1
1
0
1
0
1
1
1
1
1
0
1
1
1
2
0
1
1
2
1
1
1
2
1
4
1
2
1
0
1
1
1
0
1
1
2
1
1
1
1
1
0
3
2
1
1
1
0
1
1
1
2
1
0
3
1
1
1
0
1
1
3
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
0
0
2
2
1
2
1
2
1
3
2
1
2
1
2
0
1
1
1
0
1
1
1
1
3
1
2
2
1
1
1
1
2
1
1
2
0
2
2
0
1
0
0
1
1
0
1
2
0
2
2
1
2
1
1
1
0
1
2
1
2
0
0
2
2
1
1
1
0
1
1
2
2
2
2
1
1
1
1
1
1
0
2
1
2
1
1
0
2
1
1
1
0
2
1
1
1
0
1
2
1
2
1
1
2
2
1
1
1
0
2
1
2
2
2
2
1
0
1
1
1
1
1
1
1
2
0
1
0
0
1
2
0
1
2
1
2
1
0
1
1
1
1
1
2
1
2
1
1
1
2
2
1
1
1
2
0
0
1
0
0
2
1
2
0
1
0
1
1
1
1
0
1
1
3
2
1
1
1
1
1
0
0
2
2
1
1
0
2
1
1
2
1
2
1
2
0
1
0
0
1
1
1
1
0
1
1
2
1
2
2
2
2
1
1
1
1
1
1
0
1
1
0
0
1
2
1
1
2
1
1
2
1
1
2
1
1
1
2
1
1
1
0
1
0
1
2
1
1
1
2
2
2
0
0
1
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
2
1
1
2
1
1
2
2
1
2
2
2
0
2
2
0
1
1
1
1
0
2
1
1
1
0
1
0
1
1
1
1
0
2
2
1
1
1
2
0
1
1
1
1
1
2
0
1
1
1
1
1
1
2
1
1
0
1
0
1
2
0
1
1
2
1
1
1
1
1
2
2
0
1
1
1
0
1
1
2
2
2
1
1
1
1
2
2
0
2
2
0
1
0
1
2
2
2
1
1
0
0
1
0
2
1
1
1
1
1
1
2
2
2
2
2
1
0
2
2
0
2
2
2
1
1
1
2
1
1
1
1
2
2
0
1
1
1
1
0
2
0
1
2
1
1
3
1
0
2
1
0
1
1
1
0
1
1
1
0
1
1
2
0
1
2
0
1
1
2
1
2
1
0
1
2
0
0
1
1
1
1
1
0
1
1
1
1
2
1
1
2
0
1
1
1
0
1
1
1
0
2
2
2
1
1
1
1
1
1
1
0
0
2
2
1
1
1
2
0
1
2
1
2
1
2
1
1
2
1
1
2
2
1
1
1
1
1
1
2
0
1
1
2
1
1
2
0
1
1
0
0
2
2
1
1
1
1
1
1
2
1
2
0
1
2
1
1
1
1
1
1
2
3
2
1
1
1
0
2
1
1
1
0
1
2
0
0
1
1
1
1
0
1
1
1
1
0
2
2
1
2
1
1
1
0
1
1
1
0
1
1
1
1
0
1
1
1
0
0
1
1
2
0
1
0
1
1
1
2
1
1
1
1
1
1
1
0
2
2
0
1
0
1
2
2
1
1
1
1
1
1
2
1
1
1
1
2
0
1
1
1
1
1
1
1
1
1
1
0
2
0
1
2
1
1
1
1
2
0
0
1
2
1
1
2
1
1
0
1
1
1
1
2
1
2
0
0
1
2
1
1
2
0
0
2
1
1
1
2
1
2
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
2
1
0
1
0
2
1
1
0
0
2
2
1
1
1
2
2
2
1
1
1
1
0
2
3
1
1
1
2
1
2
1
2
2
1
1
2
1
1
0
1
0
3
0
1
2
1
1
1
0
0
1
1
0
2
1
0
1
1
1
1
1
2
1
2
2
1
1
2
1
2
1
2
1
0
1
1
1
1
1
1
2
1
2
0
2
2
2
1
1
1
2
2
0
2
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
0
2
1
1
1
0
2
1
1
1
0
1
0
2
2
2
2
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
2
0
3
1
1
2
2
2
1
0
1
1
0
0
1
2
1
1
2
1
1
2
1
2
1
1
1
0
1
2
1
1
2
1
0
1
1
2
1
2
0
0
1
1
2
1
1
0
1
1
1
1
2
2
2
1
1
1
1
2
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
0
0
1
1
2
1
1
2
2
0
1
0
1
1
2
1
0
1
2
1
3
2
1
1
1
1
1
1
2
2
1
1
2
1
0
0
1
0
1
0
1
1
1
2
1
2
0
1
1
1
1
1
1
2
1
2
1
1
2
2
1
1
0
1
1
1
2
2
0
0
2
2
0
1
1
1
1
1
1
1
0
1
1
2
1
1
2
1
1
2
1
1
1
3
1
2
2
1
1
1
1
1
2
1
1
0
1
1
1
1
0
1
0
0
1
2
0
0
1
1
1
2
1
1
0
1
1
1
1
2
1
1
2
1
1
0
1
1
3
0
1
1
2
1
1
1
1
1
2
1
1
2
2
1
0
1
0
0
1
1
1
1
1
1
1
0
1
0
1
2
2
2
1
1
1
1
1
0
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
0
2
1
0
1
1
1
2
2
2
1
2
2
1
0
2
1
0
1
0
1
0
1
0
1
2
1
1
0
1
1
2
2
0
1
1
1
1
1
1
1
2
0
1
2
2
1
1
2
1
2
1
1
1
0
1
1
2
1
1
1
1
1
2
0
2
2
1
2
1
1
2
2
1
2
1
0
1
2
1
2
2
1
1
2
1
2
2
1
1
1
1
2
2
1
1
1
1
0
0
1
0
2
0
2
1
0
1
0
1
1
1
1
1
1
2
1
1
0
0
0
2
1
2
2
2
2
2
2
0
1
1
1
1
1
0
2
1
1
0
2
2
1
1
2
1
2
1
1
1
1
1
3
2
1
2
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
2
1
2
1
2
1
1
0
0
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
0
1
2
1
2
1
1
1
1
2
1
1
2
0
1
1
1
1
2
2
1
2
1
1
0
1
0
0
1
1
2
1
0
0
1
1
1
2
0
1
2
1
2
1
1
2
2
1
1
1
2
1
1
2
1
1
1
2
2
0
1
2
2
0
2
2
0
1
0
1
0
1
2
1
1
1
1
0
1
1
1
1
1
1
0
2
1
2
1
1
1
2
2
1
2
1
1
2
3
1
1
1
1
1
1
2
1
2
0
2
0
1
1
1
0
1
1
2
0
0
1
1
0
1
0
2
1
1
0
0
0
1
2
1
1
0
2
1
2
2
2
2
2
1
2
2
1
1
1
1
1
1
0
0
2
1
1
0
1
1
1
1
1
0
1
1
0
3
1
2
2
1
2
1
2
2
2
0
1
2
1
0
1
2
1
3
1
1
1
1
1
2
2
1
2
2
2
0
1
1
1
1
0
1
1
2
1
2
0
0
1
2
1
0
1
1
1
2
1
1
2
1
0
1
1
1
1
1
1
1
2
1
2
0
1
2
2
2
1
0
0
1
0
1
1
2
1
1
2
1
2
1
1
1
2
2
1
2
2
2
0
2
1
1
1
1
1
0
1
1
1
2
1
1
0
2
0
1
2
2
2
2
2
1
1
1
1
1
1
1
2
1
2
0
2
1
2
0
1
1
1
1
2
1
2
0
2
1
2
1
2
1
0
0
1
2
0
1
1
2
1
0
1
1
1
1
2
1
1
2
0
2
1
1
1
2
2
1
1
1
2
0
0
1
0
2
2
0
1
1
2
1
1
2
2
2
1
2
0
1
1
0
1
0
2
1
2
2
1
0
0
1
1
1
1
1
1
2
2
2
2
1
2
1
0
2
0
3
1
2
2
2
1
1
2
1
2
2
1
1
0
2
2
2
2
1
2
2
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
2
2
2
1
1
1
2
1
1
1
1
2
2
1
2
1
0
1
1
2
1
2
0
1
1
1
1
1
0
1
0
2
1
2
2
1
1
1
1
1
2
1
2
1
0
2
1
1
1
1
1
1
0
1
0
0
1
1
0
1
1
1
0
1
0
1
0
2
1
1
2
2
1
1
1
1
1
0
0
2
1
1
0
1
1
0
1
2
2
1
0
2
0
1
0
2
1
1
1
1
1
1
1
1
2
1
0
2
0
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
0
1
1
2
0
1
1
2
1
0
1
1
1
1
1
1
1
2
1
1
1
2
1
0
1
1
1
1
1
1
1
1
0
1
1
1
1
0
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
0
1
1
1
1
0
2
1
1
3
2
1
1
1
1
1
6
1
1
0
1
1
0
1
0
1
3
2
1
2
2
0
1
1
0
2
0
1
1
0
0
0
1
3
1
2
2
1
1
1
2
1
2
2
2
1
1
1
1
1
1
1
2
1
1
1
0
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
1
2
1
0
1
2
1
0
1
1
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
2
2
0
1
2
1
1
2
1
1
2
1
1
1
0
2
1
1
1
1
1
2
1
1
0
2
1
1
2
0
2
1
2
2
2
1
1
0
1
1
4
2
1
1
1
1
1
2
0
1
1
1
2
1
1
1
0
1
1
2
1
1
1
1
0
1
2
1
2
2
2
1
1
2
0
0
1
2
2
2
1
1
2
2
1
1
2
1
0
1
2
1
1
1
1
2
1
1
0
1
1
0
2
1
1
2
2
2
1
2
1
1
2
1
1
2
1
0
2
0
2
1
1
1
1
2
1
0
1
0
1
2
1
1
1
1
2
2
2
3
1
1
2
2
1
1
1
1
1
1
1
0
1
1
1
1
2
2
1
0
2
1
1
1
1
1
2
1
1
0
2
1
1
1
1
2
1
1
1
1
0
0
2
1
1
2
2
0
1
1
1
2
1
1
1
2
2
1
2
1
2
2
4
0
1
1
1
2
1
1
2
0
1
1
1
2
1
1
0
0
0
1
0
1
0
1
1
1
1
2
1
2
1
1
1
1
1
1
1
2
1
2
1
0
0
1
1
1
1
2
1
1
3
1
0
1
1
1
1
2
1
3
2
1
1
1
2
1
1
1
1
1
1
1
0
2
2
2
1
0
2
2
2
1
1
2
2
2
0
1
2
0
1
1
1
1
1
1
1
1
1
2
1
1
0
1
2
2
1
0
1
0
1
1
2
1
2
0
1
2
1
1
2
0
2
1
1
1
1
1
0
2
1
0
1
1
0
1
1
2
1
0
2
1
2
1
1
2
1
0
0
1
0
2
1
1
1
0
1
4
1
1
1
1
0
0
2
0
1
2
1
1
1
1
0
0
2
1
3
2
1
0
1
0
2
0
1
1
1
2
0
1
0
1
0
2
1
2
1
1
2
1
1
1
0
0
1
1
3
1
1
1
2
0
1
1
0
1
1
1
2
1
1
1
2
2
1
2
1
1
1
1
0
1
0
2
0
0
1
1
1
2
3
1
1
1
1
1
2
1
1
0
1
1
1
1
0
1
2
1
2
1
1
1
1
1
1
1
2
1
2
0
2
1
1
2
1
1
1
2
1
2
2
1
2
1
1
1
1
1
1
1
1
0
1
1
0
1
1
1
2
1
1
1
1
0
2
1
0
2
1
1
0
2
1
1
1
1
1
1
0
1
1
3
2
1
2
2
2
1
1
2
1
1
1
0
2
0
2
2
2
2
1
1
1
1
1
0
1
1
0
1
1
2
0
0
1
1
1
0
2
1
1
1
2
1
2
2
1
2
4
0
1
1
1
0
2
1
1
2
1
1
2
2
0
0
1
1
1
1
2
0
1
1
1
1
1
1
2
2
1
2
1
1
1
2
2
2
1
1
1
1
2
2
1
1
1
1
0
0
2
1
1
1
1
2
2
2
1
1
1
0
1
1
1
1
1
1
1
0
2
1
1
1
1
0
1
0
2
2
1
1
1
1
0
1
1
1
1
1
0
1
1
2
1
0
0
0
2
1
0
0
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
0
2
1
1
1
1
1
1
1
1
2
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
1
1
2
1
1
2
1
2
1
0
1
1
0
2
1
1
1
0
1
1
2
1
2
1
0
0
1
1
2
0
2
1
1
1
2
1
2
1
2
1
1
2
1
2
1
1
0
2
0
0
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
0
2
1
2
1
1
0
1
1
0
1
0
1
1
1
2
1
1
0
0
0
1
0
1
2
0
2
0
2
2
2
1
1
3
2
0
2
1
1
0
0
2
1
2
2
1
1
2
0
2
0
1
0
2
1
1
2
0
0
2
1
1
1
1
2
0
1
3
1
0
2
2
0
1
2
1
2
0
0
2
1
1
1
0
1
1
1
1
1
1
1
1
1
1
0
2
1
2
2
1
2
1
1
1
1
2
0
1
1
0
1
1
1
2
1
1
1
1
1
0
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
0
1
1
1
0
1
1
0
1
2
1
3
1
1
1
1
2
0
1
1
0
1
2
1
0
2
2
1
2
1
1
1
1
0
1
2
1
1
1
1
2
1
2
1
0
1
1
1
2
1
1
1
1
1
0
1
1
1
2
1
1
1
1
1
0
0
1
1
2
1
2
0
1
0
2
1
2
2
2
0
0
1
1
2
0
2
0
1
1
1
1
1
1
1
0
2
1
1
1
1
0
1
3
2
1
0
2
1
1
2
0
2
1
0
2
1
1
2
1
2
1
1
2
1
1
2
0
1
1
1
2
1
1
1
1
0
1
1
1
1
1
0
1
1
1
2
1
1
1
1
1
0
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
0
1
2
1
1
1
2
0
1
1
1
0
1
1
1
0
1
1
2
0
1
2
1
1
1
1
0
2
1
1
2
1
2
2
2
2
2
1
1
1
2
2
1
1
1
0
1
1
0
2
2
1
1
1
1
1
1
1
1
1
2
2
1
1
1
0
1
3
2
1
1
0
1
1
1
1
1
1
2
0
1
1
2
1
1
1
0
2
1
1
1
1
1
2
1
0
1
0
0
2
0
2
1
1
1
1
0
2
1
2
2
1
1
2
1
1
1
1
0
1
0
1
1
3
2
1
1
2
0
1
1
1
1
1
1
1
0
2
1
1
2
1
1
0
1
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
2
2
1
1
2
0
1
1
0
1
0
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
2
1
0
2
0
1
1
1
1
1
2
2
0
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
2
1
0
0
1
1
1
2
0
1
1
0
2
1
1
1
1
1
1
2
1
1
1
2
2
4
1
2
1
0
0
2
1
2
1
2
1
1
1
1
1
1
1
0
1
2
1
0
0
2
0
1
2
2
1
0
2
2
1
1
1
2
1
2
2
2
1
1
1
1
0
1
2
1
1
2
2
2
0
1
2
0
1
2
0
0
1
1
2
1
1
2
1
2
0
1
2
1
1
1
1
1
1
1
1
1
1
0
1
1
2
0
1
1
2
0
2
1
1
2
0
0
2
2
1
0
2
1
2
1
2
1
0
1
1
1
1
1
0
2
1
1
0
1
1
1
2
1
1
1
0
0
0
0
2
1
2
0
1
0
1
2
1
0
1
0
1
0
1
1
0
2
1
2
1
1
1
1
1
2
1
0
1
1
1
1
0
1
2
1
1
0
1
1
2
0
1
1
2
2
2
0
1
1
2
0
1
1
0
0
1
1
2
1
0
1
1
1
1
1
1
0
1
1
1
1
0
1
1
2
1
1
3
1
1
2
1
2
1
1
0
0
1
1
0
1
1
2
0
0
2
2
1
2
1
1
1
2
1
2
1
2
2
1
2
2
1
1
2
1
0
0
1
1
1
2
1
0
3
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
1
2
1
2
2
2
2
1
3
0
2
1
0
1
1
0
1
1
1
2
1
1
1
1
0
1
2
1
0
1
1
1
2
2
1
2
2
1
0
1
1
2
1
2
1
0
2
1
0
1
0
1
2
2
0
1
2
1
2
2
0
0
2
0
1
1
2
3
0
1
1
1
1
0
1
1
1
2
2
0
0
2
2
1
1
2
1
2
2
0
1
1
0
2
1
2
1
3
1
0
2
0
2
2
1
0
1
1
1
0
1
1
1
1
1
2
2
1
1
1
1
1
1
1
0
0
1
0
0
0
1
1
1
1
1
1
1
2
2
1
1
1
1
2
1
0
1
1
1
1
1
1
1
1
0
1
1
0
1
2
1
1
1
1
2
1
2
0
1
4
1
1
0
2
0
0
2
1
1
2
1
1
1
1
1
2
1
2
1
1
0
2
1
2
1
1
1
1
1
1
1
2
1
0
1
1
8
1
2
1
1
2
3
1
2
1
1
1
1
2
2
2
1
1
1
1
0
1
2
2
1
0
2
1
1
0
1
1
1
2
2
2
2
2
2
1
1
1
1
0
1
1
1
1
4
2
1
1
1
1
0
1
2
1
0
1
1
1
0
1
1
1
2
1
1
1
1
1
1
1
2
1
0
2
0
1
0
0
2
2
1
0
2
0
1
0
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
2
1
0
2
1
1
5
1
1
2
1
2
0
2
1
1
1
1
1
1
2
2
0
1
1
2
1
2
1
1
1
1
1
0
1
0
1
1
2
0
1
2
1
1
1
1
1
1
0
1
1
2
2
0
2
1
1
1
1
2
0
2
1
1
2
1
2
0
0
1
1
1
1
1
1
1
1
0
0
1
2
2
1
1
3
2
1
2
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
0
1
1
0
1
1
1
1
2
2
2
1
1
2
1
0
1
0
1
1
1
1
1
2
1
1
1
1
2
1
0
1
1
1
1
2
1
0
2
1
0
1
1
0
1
1
0
0
1
1
0
0
1
1
2
1
1
1
1
0
1
1
1
1
0
1
0
1
1
1
1
1
2
1
1
1
2
0
2
1
1
2
0
0
2
0
0
1
2
1
1
2
1
0
1
1
2
1
2
1
1
1
2
0
0
2
0
1
0
2
1
2
1
1
2
1
2
2
2
1
1
2
0
2
2
1
2
4
0
2
1
0
1
2
1
1
1
2
1
1
1
0
1
0
1
1
1
1
1
0
1
1
1
2
1
0
2
2
2
2
1
2
1
1
2
0
1
3
1
2
2
1
2
0
1
2
1
2
2
1
1
1
1
1
1
1
2
2
1
1
1
2
1
1
2
2
1
1
1
1
2
2
1
1
0
1
2
1
1
0
0
2
2
1
2
1
1
2
0
2
1
1
2
1
2
1
0
1
1
1
0
1
2
1
2
1
2
1
0
1
1
1
1
2
2
1
0
1
2
1
2
2
2
2
1
0
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
0
2
1
1
1
1
2
2
1
1
0
1
1
0
2
1
2
2
1
1
1
2
1
1
1
1
1
1
1
1
1
0
2
1
1
0
1
0
1
2
0
1
1
0
0
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
2
1
1
0
1
1
1
1
1
2
0
1
1
2
1
1
2
2
1
1
1
1
1
1
1
0
1
1
2
1
1
1
1
0
1
2
1
1
1
1
2
1
1
1
2
1
1
1
1
1
2
1
1
0
1
2
2
1
2
1
1
1
1
2
1
0
1
1
1
0
1
0
1
1
0
1
2
1
1
1
1
0
1
1
1
1
1
1
2
2
2
2
0
1
1
1
1
1
0
2
0
1
1
3
1
1
1
0
0
1
0
1
0
1
2
2
2
1
1
1
1
1
2
1
2
0
1
1
1
1
1
1
1
2
1
1
2
2
2
1
3
1
0
2
1
1
2
2
1
0
1
1
3
1
1
2
2
1
1
0
2
1
1
2
0
1
2
1
2
2
0
1
2
1
1
4
0
1
1
1
0
2
2
0
1
1
1
1
2
1
2
2
1
1
1
1
2
1
0
2
2
1
1
2
2
0
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
0
1
1
1
2
1
2
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
0
1
1
2
2
1
0
1
1
1
1
1
0
2
0
2
2
1
0
1
2
2
1
1
0
1
1
1
1
2
1
2
1
4
1
1
0
0
1
1
1
2
1
0
1
1
1
1
1
0
2
2
0
1
2
2
1
1
1
1
0
0
1
1
2
1
1
2
2
1
1
0
2
1
1
2
1
2
2
1
1
1
2
2
2
1
1
1
2
0
1
1
1
1
1
1
1
2
0
2
1
0
1
2
0
1
0
2
1
0
0
2
2
1
0
1
1
1
1
1
1
1
2
1
2
1
1
0
2
0
1
0
1
1
1
1
1
2
1
1
0
2
0
0
1
1
1
2
2
0
0
0
2
1
2
1
1
1
1
1
0
2
1
1
0
2
2
1
1
0
2
1
1
1
1
1
1
2
1
0
1
2
1
1
2
2
3
1
1
1
1
1
1
1
1
0
1
2
1
0
0
1
1
1
0
1
2
1
1
0
2
2
1
1
1
0
1
1
1
0
1
1
2
1
1
2
2
1
0
1
1
1
1
1
1
1
3
1
1
1
1
1
2
0
0
1
1
1
1
1
1
1
2
0
1
0
1
2
1
2
0
1
1
1
1
1
0
1
2
1
1
1
1
0
1
1
2
1
0
2
1
1
1
2
0
1
1
0
1
1
1
1
1
0
0
1
1
1
1
0
2
1
1
1
0
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
1
1
0
1
1
1
0
1
1
1
2
2
1
2
1
1
1
1
2
1
1
1
2
0
1
2
2
1
1
1
1
1
1
0
1
1
1
2
1
2
1
2
1
2
1
1
1
1
3
1
2
1
2
1
0
2
1
3
2
0
1
1
0
0
2
1
1
0
2
0
1
2
1
1
1
1
1
1
1
1
2
2
1
1
0
1
1
2
2
1
1
1
1
1
2
1
1
1
1
2
2
1
1
1
2
1
1
1
1
2
1
1
2
0
2
1
0
2
2
2
1
1
2
2
1
1
2
1
2
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
0
2
1
2
1
1
1
1
2
1
2
1
0
1
2
2
1
2
1
1
1
0
1
1
1
1
1
1
2
1
2
1
2
1
0
1
0
2
2
2
1
2
1
2
0
1
0
2
2
2
1
0
2
2
0
2
0
1
1
1
2
2
1
1
2
1
2
2
1
1
1
1
2
2
2
1
1
1
1
2
1
2
1
1
1
2
1
1
0
1
2
1
1
1
2
1
0
2
1
1
2
2
1
1
1
2
0
2
2
0
2
1
1
0
2
2
1
0
1
1
1
2
1
1
1
0
2
0
1
2
2
2
1
1
0
1
1
2
2
2
1
1
3
1
1
1
1
0
1
1
1
1
2
1
1
1
1
1
0
2
1
1
1
1
2
0
1
2
0
1
1
2
1
2
2
2
1
1
0
2
1
1
0
1
2
2
1
2
1
1
1
0
1
0
0
1
1
1
1
1
1
1
1
2
1
2
1
0
2
1
2
1
0
2
1
1
1
0
1
2
0
1
1
1
0
1
2
2
2
1
1
1
1
1
0
1
1
0
2
1
1
0
0
1
0
1
0
0
2
0
1
0
0
1
1
1
1
1
2
1
1
2
1
1
1
1
2
0
0
1
1
1
1
2
0
1
0
1
3
0
2
0
1
1
2
1
2
1
1
1
1
2
1
1
0
1
2
1
1
1
0
1
1
1
2
1
1
1
1
1
1
1
1
0
1
0
2
0
0
2
1
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
0
1
0
2
1
1
1
1
1
1
1
0
1
1
1
1
2
2
1
1
2
0
2
2
1
2
2
1
0
1
2
2
1
0
2
2
1
2
4
1
2
2
1
0
2
1
2
1
1
2
2
1
1
1
0
0
3
1
1
1
1
1
1
1
1
0
0
1
1
2
2
0
0
1
2
1
1
0
1
1
1
1
0
1
0
1
1
2
0
2
1
1
2
1
2
2
1
0
0
1
2
1
1
1
1
2
0
1
1
1
2
1
1
1
2
2
2
0
0
1
2
1
1
0
1
0
1
0
0
0
0
1
1
1
1
0
0
0
1
1
1
2
1
1
1
1
1
1
1
2
2
1
0
1
0
2
1
0
1
2
1
2
2
1
2
2
1
2
1
1
1
1
1
2
1
2
0
1
1
1
2
1
2
2
2
1
2
1
1
0
1
1
2
1
1
2
1
1
0
2
1
2
2
2
1
1
0
1
0
2
2
1
0
1
0
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
0
0
1
1
1
1
2
0
1
1
1
1
1
1
1
1
0
1
0
1
0
1
1
0
1
1
1
1
0
2
0
1
1
1
2
2
0
1
0
1
1
0
0
1
1
1
1
0
1
1
0
2
0
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
0
1
1
0
1
1
1
0
2
2
0
1
0
1
1
1
0
1
1
2
0
1
1
1
1
0
3
2
2
1
1
1
1
0
1
1
2
2
1
1
1
1
0
2
2
2
2
1
1
1
0
1
1
1
2
0
1
1
2
1
1
1
1
1
2
1
2
0
2
1
2
1
1
1
2
1
2
1
2
1
1
1
0
1
1
1
2
1
1
0
0
1
0
1
0
0
1
1
1
2
1
0
1
1
2
0
1
2
1
1
2
1
1
0
1
1
1
2
1
2
2
1
2
1
2
1
2
2
0
1
1
2
1
1
1
1
1
1
1
2
1
1
3
1
1
1
2
1
1
1
2
0
2
1
0
1
2
1
0
1
0
1
1
1
2
2
1
1
0
1
2
0
2
2
2
1
1
2
2
1
1
1
1
1
1
0
0
1
0
2
1
1
1
0
1
1
1
2
0
0
1
1
0
1
1
1
1
2
0
1
1
2
1
1
0
1
2
1
0
1
1
2
2
2
1
0
1
1
0
1
1
1
1
1
1
1
0
0
0
2
1
1
2
1
0
1
2
1
1
0
2
1
2
1
0
1
1
1
2
2
1
0
2
1
1
1
0
1
2
0
1
1
1
0
1
1
1
1
2
2
2
2
1
1
2
1
1
1
0
2
0
1
1
1
2
1
1
0
0
2
1
1
1
2
1
1
2
1
1
2
2
1
2
2
1
0
2
1
2
1
1
1
0
1
2
2
2
1
1
0
1
1
1
1
0
0
2
1
1
2
1
1
0
2
1
1
1
0
0
0
1
1
0
2
0
2
1
1
2
1
2
0
0
2
0
1
1
1
1
1
2
5
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
0
0
2
1
2
1
1
2
1
1
1
2
0
2
1
2
2
2
2
1
1
1
1
2
1
0
2
0
1
1
1
1
0
1
1
1
1
1
0
2
0
1
0
2
2
0
1
0
2
1
2
0
2
1
2
1
1
1
1
1
1
1
2
0
2
1
2
1
1
1
1
1
1
0
2
0
1
0
2
1
1
1
1
1
2
1
2
0
1
1
1
1
1
1
0
1
2
0
1
1
1
2
2
1
2
1
2
1
2
1
1
0
1
1
0
1
2
1
0
1
1
2
1
1
4
1
2
1
1
1
2
1
1
1
1
1
0
2
2
1
2
2
1
1
1
1
1
1
1
1
2
2
2
1
1
0
1
1
1
1
0
2
1
2
1
0
2
1
2
1
2
1
1
2
2
2
3
0
0
1
2
0
1
1
2
0
1
0
1
1
0
0
1
2
2
1
1
1
1
1
2
1
0
1
2
2
2
1
2
1
1
2
0
1
2
0
1
1
1
1
1
2
1
1
2
1
1
2
1
2
2
1
2
1
2
1
0
1
1
1
2
0
0
1
1
0
0
0
2
1
1
1
1
1
0
1
1
2
2
0
2
2
1
1
1
0
2
2
1
1
1
1
2
0
2
1
2
1
2
0
1
1
1
2
0
1
0
1
1
1
1
1
2
1
1
1
1
1
2
1
2
0
1
1
2
2
1
0
1
1
1
0
1
1
2
1
2
2
1
2
1
2
2
2
1
0
2
1
1
2
2
1
2
1
1
1
2
0
1
1
1
2
1
1
0
2
0
1
1
0
0
1
2
1
0
1
1
1
2
3
1
1
0
2
1
1
1
1
1
1
1
1
1
1
1
0
1
2
1
2
0
2
1
1
3
2
1
1
1
1
0
2
1
2
0
1
1
1
1
2
1
2
1
1
1
1
2
1
1
1
1
1
2
2
1
0
1
1
1
1
1
1
1
1
1
0
1
5
1
1
2
1
1
0
1
1
6
2
2
1
1
1
1
1
1
0
0
2
1
2
1
1
0
1
2
0
1
2
2
1
1
1
1
2
1
0
1
2
1
0
0
0
2
1
1
1
1
2
2
1
2
0
1
2
2
1
1
0
1
1
1
2
2
1
1
2
0
2
1
1
0
1
1
1
2
1
2
1
1
0
1
0
2
2
1
0
1
0
2
1
0
2
2
2
1
1
1
0
2
1
1
0
1
2
2
1
1
1
1
1
1
1
1
1
1
2
0
1
1
1
1
1
0
1
2
2
1
1
1
1
0
1
1
2
1
1
1
1
0
2
1
1
1
1
1
2
0
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
0
2
2
1
2
1
1
1
2
1
1
0
1
1
1
0
2
2
1
1
2
1
1
2
1
1
0
1
1
1
2
1
1
1
1
0
1
2
1
0
1
1
0
2
2
2
1
2
1
0
1
0
1
1
1
2
1
0
1
1
0
1
1
1
2
1
1
1
1
1
1
3
1
1
2
1
1
2
0
2
1
1
0
1
1
2
1
2
1
2
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
2
1
2
1
1
1
1
0
3
1
1
0
2
2
2
1
0
2
1
1
2
1
1
2
2
2
1
1
2
0
1
1
1
1
1
0
1
1
0
1
2
1
1
1
2
2
1
3
0
1
1
0
1
0
1
2
2
2
1
1
1
1
1
1
1
1
2
1
1
0
1
0
1
1
1
0
1
2
1
2
1
1
1
1
1
1
4
1
0
1
2
0
1
2
2
1
1
1
1
1
1
2
1
1
0
1
2
1
2
1
1
1
1
0
1
1
2
0
1
2
0
1
1
1
1
1
1
1
0
1
1
0
0
1
1
1
1
1
0
1
2
1
1
1
0
1
2
1
1
1
1
1
1
1
1
0
0
2
1
1
0
1
1
2
0
1
2
2
2
1
3
2
2
0
0
2
1
1
1
1
1
1
1
1
1
2
2
0
1
1
1
1
0
0
1
2
2
2
2
1
1
1
2
1
1
1
1
4
2
1
0
0
2
1
1
2
1
1
2
1
1
0
2
1
1
0
1
1
1
2
1
1
1
0
2
1
1
1
1
0
1
1
1
2
1
0
1
1
1
1
1
2
0
0
0
1
0
2
2
2
1
0
1
2
2
1
2
1
2
1
1
1
1
1
2
1
1
1
1
1
0
1
0
2
0
0
0
1
1
0
1
1
1
1
1
1
1
1
0
2
1
1
2
1
2
0
1
2
1
1
2
1
1
0
2
1
2
2
1
1
1
1
1
1
1
1
1
3
1
1
0
1
2
1
1
2
0
1
2
1
1
0
1
1
1
2
2
1
0
2
2
0
0
1
1
3
1
1
0
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
1
0
1
1
1
1
1
0
1
1
1
0
1
1
2
0
1
4
1
1
1
1
2
1
1
1
0
1
2
1
1
0
1
0
1
1
2
1
1
2
1
0
1
1
0
1
0
2
1
1
1
2
1
1
1
2
1
1
1
1
2
0
0
0
1
2
1
1
1
1
2
2
1
1
1
0
1
1
1
0
1
0
1
1
1
1
1
2
1
1
0
1
1
2
1
2
1
1
1
1
1
1
2
1
2
1
2
1
2
1
1
1
1
1
2
2
1
1
1
1
0
1
1
2
0
1
3
0
1
0
1
1
1
1
2
1
1
1
1
2
2
1
0
1
0
1
1
2
0
1
2
2
2
2
1
1
2
0
1
2
1
0
2
1
0
1
0
1
1
2
1
1
0
0
0
2
2
1
2
1
1
0
1
1
2
0
1
0
0
1
2
1
1
2
1
1
0
1
2
1
1
0
0
2
1
0
2
1
2
2
2
2
1
2
1
1
1
1
0
2
1
1
2
1
2
1
2
1
1
1
0
0
2
0
1
0
1
1
1
1
2
1
1
1
2
1
1
1
1
2
0
1
0
2
2
0
1
0
2
1
2
0
0
2
0
1
2
2
1
0
2
1
1
1
1
1
1
2
0
2
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
0
1
1
1
0
0
1
1
1
2
1
0
1
1
1
1
1
2
2
1
2
0
1
1
1
1
1
1
1
1
1
1
1
0
1
1
2
1
2
1
1
2
2
0
1
1
0
1
1
1
1
1
1
2
1
1
0
1
2
1
0
1
1
1
1
2
1
1
1
0
5
0
2
1
2
1
0
0
1
0
1
1
2
1
1
1
1
1
2
1
2
1
1
1
2
2
1
3
1
1
2
0
1
1
2
1
1
2
1
1
1
1
0
0
1
1
2
1
2
0
2
1
1
1
1
2
2
0
1
1
1
1
0
1
2
1
0
1
1
1
2
1
2
1
1
2
1
2
1
1
2
2
2
1
1
1
2
0
1
1
2
1
2
1
1
1
1
2
1
1
0
1
1
1
2
1
1
1
1
2
1
1
1
0
1
2
2
0
1
1
1
1
2
1
1
0
2
1
2
1
1
0
0
2
1
1
1
2
1
1
1
1
2
1
2
1
0
0
1
2
2
2
1
1
1
2
2
1
1
1
1
2
1
1
2
1
1
1
2
1
1
1
1
1
0
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
0
1
1
1
2
2
1
1
0
1
0
0
2
1
1
1
1
2
2
2
1
1
2
1
1
1
2
2
1
0
2
1
2
1
0
1
1
0
1
1
1
0
1
0
1
1
1
2
1
1
2
2
1
2
2
2
1
1
1
0
2
2
1
1
2
2
0
1
2
2
2
1
1
1
1
0
2
0
1
1
1
1
2
0
2
2
1
1
2
1
0
2
1
1
1
1
1
2
1
1
0
1
1
1
1
0
1
1
1
1
0
1
1
1
0
1
1
1
2
0
2
2
1
2
0
2
1
1
1
0
2
1
1
2
2
3
2
1
1
2
1
1
2
1
1
1
2
1
1
1
2
0
1
1
1
1
1
1
1
4
1
1
2
2
1
2
0
1
1
0
1
1
1
1
2
1
2
1
1
1
0
1
0
1
2
0
1
2
2
1
0
1
1
0
1
1
2
1
1
0
2
1
0
1
2
1
1
0
2
1
1
1
1
1
1
0
1
1
1
1
1
1
2
1
0
2
2
1
2
0
0
1
1
2
1
1
2
1
1
1
1
1
2
0
1
2
0
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
2
2
1
1
1
0
2
1
2
1
1
1
1
1
0
1
0
1
1
1
0
1
1
1
2
1
2
0
1
2
1
1
1
1
1
1
1
1
2
1
2
1
1
1
0
0
0
1
1
1
1
1
2
1
2
0
1
2
1
1
2
1
1
1
0
1
1
2
1
1
2
0
1
0
1
1
1
1
1
1
1
2
1
2
2
2
1
2
1
1
1
1
1
1
1
0
1
0
1
2
2
2
1
1
1
0
2
1
1
1
1
0
0
2
0
0
2
1
1
2
2
1
1
1
1
2
2
1
0
0
2
0
1
2
1
2
1
2
2
1
1
0
2
1
1
2
1
1
1
1
1
1
2
1
1
2
1
2
0
2
0
1
0
0
1
1
0
1
1
2
1
1
1
1
1
0
1
1
1
2
0
1
1
1
1
0
1
1
1
0
0
0
0
1
1
2
1
1
1
1
1
1
2
1
1
0
2
2
1
0
2
1
1
1
2
2
1
1
1
3
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
2
2
1
1
0
0
1
0
2
0
1
4
0
1
0
1
1
1
1
1
2
0
0
1
1
1
2
1
4
1
1
1
1
1
1
2
2
0
0
2
1
1
1
1
2
1
1
2
1
2
1
2
1
0
1
2
2
1
1
1
0
1
1
2
1
1
2
0
2
1
1
2
2
1
1
1
0
0
1
1
1
0
1
1
1
0
1
3
0
2
0
1
2
1
1
1
1
0
1
1
1
2
1
1
1
1
1
1
1
1
2
1
2
2
2
1
1
1
0
1
2
2
1
1
1
2
2
1
0
1
1
1
1
0
2
2
1
1
1
1
1
1
0
2
1
1
1
1
1
1
2
2
1
1
1
1
1
1
0
1
1
0
1
1
0
0
1
1
1
2
2
1
2
0
0
1
0
1
2
0
2
1
1
1
2
1
2
1
2
1
1
1
1
2
0
1
1
1
1
1
1
2
2
1
1
2
2
1
0
2
1
1
1
0
0
2
0
1
1
1
0
1
1
1
2
2
1
1
1
2
0
2
0
1
1
1
0
1
1
1
1
1
1
1
2
2
1
1
1
2
0
2
1
1
0
1
2
2
2
1
1
1
1
1
0
1
1
1
2
1
1
0
1
1
2
1
0
2
1
0
1
2
1
1
1
1
1
1
1
1
2
2
1
0
1
1
1
2
2
0
1
2
1
1
1
1
0
2
3
1
1
2
2
1
0
0
2
0
1
1
0
1
1
1
1
2
1
1
1
1
0
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
0
1
1
1
0
3
0
1
1
1
1
1
1
1
1
0
3
1
1
1
0
2
1
0
2
1
2
1
1
1
2
1
0
0
1
1
1
2
2
1
2
0
0
0
1
1
1
1
2
1
1
1
0
2
1
1
1
1
0
0
0
1
1
0
1
1
2
1
1
1
2
2
0
1
0
0
1
1
0
2
0
1
0
2
1
1
0
1
2
2
1
1
1
2
1
1
2
2
0
1
1
2
1
2
1
2
1
1
2
1
1
1
2
0
1
1
1
1
0
1
1
2
1
1
1
1
1
1
2
1
2
2
2
2
1
1
2
1
1
0
1
2
1
2
1
1
2
2
0
1
0
1
1
2
2
0
2
2
0
1
1
0
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
2
1
0
1
0
1
0
1
1
0
1
1
2
1
1
1
0
0
1
1
0
1
0
2
1
2
0
1
2
2
1
0
1
1
1
1
1
1
1
1
1
1
2
2
3
1
1
0
0
2
2
1
1
1
1
1
0
1
2
1
2
1
1
2
2
0
1
1
1
2
1
0
1
2
0
1
3
1
1
1
1
1
1
0
3
0
1
0
0
2
1
1
1
2
1
1
1
1
1
2
1
1
0
1
1
1
0
1
2
1
1
1
2
1
1
1
2
2
1
2
2
1
0
1
1
1
1
1
0
1
1
0
2
2
1
1
2
1
2
2
1
1
2
1
1
2
0
2
1
1
1
1
1
0
2
1
3
1
1
1
1
1
1
0
1
1
2
0
0
2
2
1
0
0
1
2
0
2
1
1
2
1
0
1
0
0
0
2
1
0
0
1
1
1
2
1
1
2
0
0
1
1
1
0
2
1
1
1
1
1
1
1
1
1
1
1
1
0
1
2
0
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
2
1
1
1
1
1
1
3
1
2
0
1
0
1
0
1
0
0
0
1
1
1
2
2
2
0
0
1
1
1
0
1
1
2
1
0
1
0
2
1
1
1
1
2
1
2
2
2
2
1
2
0
2
2
1
1
1
2
2
2
1
1
1
1
1
1
1
1
3
1
0
1
1
1
1
1
1
2
1
1
1
2
1
2
1
2
1
1
2
0
1
0
2
0
1
1
1
0
1
0
1
1
2
1
1
2
1
1
0
2
1
1
1
2
2
1
2
2
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
2
2
1
3
1
1
1
2
0
2
1
1
1
1
2
2
1
1
2
2
1
1
2
1
1
1
1
1
1
2
1
1
0
1
2
1
2
1
1
2
2
1
1
1
2
1
2
0
1
2
1
1
2
2
1
2
1
1
2
1
1
1
1
2
1
1
1
1
1
1
2
1
0
1
1
1
2
0
0
1
0
2
0
1
2
0
1
1
1
1
0
1
1
2
2
1
1
1
1
1
1
4
1
0
2
1
1
1
1
1
0
1
1
1
0
1
1
1
0
0
1
1
1
1
2
0
1
0
2
2
1
1
1
2
1
2
0
1
2
1
2
1
1
1
1
2
1
2
0
1
1
1
0
1
1
1
1
1
1
2
2
0
2
2
1
0
1
2
1
1
2
1
1
0
2
1
1
1
1
1
0
1
1
0
2
2
2
1
1
2
1
0
1
1
0
1
1
0
1
2
1
0
1
1
2
1
2
1
2
1
2
2
2
1
1
0
1
0
2
2
1
0
1
1
1
1
1
1
2
0
1
1
0
0
2
2
1
1
1
1
1
1
1
1
1
0
1
2
1
0
1
1
0
1
1
1
1
2
1
1
3
1
1
1
1
2
1
1
0
1
2
2
1
1
1
1
2
1
2
1
2
2
2
1
2
1
1
1
1
2
1
1
1
1
1
0
0
0
1
0
1
1
1
1
2
1
1
1
1
2
0
0
1
1
1
2
0
1
3
1
1
1
1
1
0
1
1
2
1
0
1
0
2
0
2
1
1
2
1
1
2
1
1
1
1
1
0
2
0
2
2
1
2
1
1
1
0
1
1
1
1
0
2
1
1
1
2
0
1
0
2
2
2
0
1
2
1
1
1
1
1
1
0
2
1
3
1
1
1
1
1
2
1
1
1
1
1
1
3
0
2
1
0
1
2
1
1
0
1
0
0
0
1
0
0
2
0
1
1
1
2
2
1
1
1
2
1
2
1
2
0
1
2
1
1
1
1
1
1
1
1
0
1
2
0
1
1
1
2
2
0
1
1
1
1
1
2
1
0
1
2
2
2
1
1
1
1
1
2
0
1
1
0
0
1
1
1
1
0
1
1
1
2
2
2
1
0
2
0
2
1
2
1
0
0
2
1
1
1
1
0
1
2
1
0
2
1
2
1
1
1
2
1
1
0
0
2
2
0
2
2
1
2
1
1
1
2
1
1
1
0
1
2
1
1
1
2
2
1
0
2
1
1
0
0
0
1
1
2
1
0
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
2
0
1
1
1
2
1
1
1
0
2
0
1
3
2
1
0
1
2
2
1
0
1
0
1
1
1
1
1
2
2
1
0
1
1
1
1
1
1
1
0
2
2
1
1
1
1
2
1
2
0
1
1
1
1
1
1
2
2
1
1
1
2
0
1
1
0
1
2
1
0
1
0
1
1
2
1
2
1
2
1
2
1
1
0
1
1
1
0
2
0
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
0
1
1
0
1
1
1
1
1
1
1
1
2
2
1
2
1
0
1
1
1
1
1
0
1
1
0
2
1
1
1
1
0
2
1
1
2
1
1
1
1
2
2
0
2
1
1
2
1
1
1
1
2
1
0
2
1
2
1
1
1
2
2
1
2
2
2
0
0
1
1
2
0
2
1
0
1
0
1
1
1
0
1
1
2
1
0
1
2
1
3
1
2
1
1
1
1
2
2
1
2
2
0
1
2
1
1
1
1
1
1
0
2
1
1
1
1
2
1
1
1
1
1
1
1
1
2
0
1
1
2
0
2
2
1
1
2
0
0
2
1
0
1
0
0
0
1
1
0
1
1
1
1
1
1
1
0
1
0
2
0
1
1
1
2
1
3
1
2
1
1
0
0
1
1
2
2
1
1
1
2
1
1
0
0
2
1
1
1
1
1
1
1
1
2
1
0
1
1
1
2
2
1
1
1
2
2
2
1
1
1
1
1
2
2
1
1
0
1
1
1
2
2
1
1
1
1
1
2
1
1
2
1
2
1
1
1
1
0
1
1
2
2
1
2
0
0
0
1
0
2
0
2
0
1
0
1
1
1
0
1
0
1
1
3
2
0
1
0
1
1
2
1
0
0
1
1
1
1
1
2
1
2
0
2
1
4
0
0
1
0
1
0
1
0
0
1
1
1
2
1
1
1
1
1
2
0
0
0
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
4
1
1
1
1
2
1
1
1
1
0
0
1
2
1
2
0
1
1
1
2
1
0
2
1
2
2
1
2
1
2
2
1
2
2
1
2
1
2
1
1
0
1
1
2
1
1
1
1
1
2
1
1
1
2
2
0
2
1
1
0
1
1
1
2
2
3
2
1
1
1
1
2
1
1
0
1
0
1
2
1
1
0
1
1
1
3
1
0
1
1
1
1
1
1
2
1
2
1
2
2
1
1
0
1
1
2
2
2
1
1
0
2
1
1
0
1
1
2
1
0
1
1
0
2
1
1
1
3
1
1
1
2
2
1
2
2
2
2
1
2
1
1
1
1
0
2
2
3
1
0
2
1
0
1
1
1
1
0
1
1
0
1
2
2
2
0
0
0
2
0
0
0
2
1
0
0
0
1
0
2
2
2
1
1
1
1
1
1
2
2
1
2
1
1
1
1
1
0
2
1
1
1
1
0
2
1
2
0
0
1
1
1
0
2
1
2
0
3
1
2
0
1
1
0
1
1
1
0
1
2
2
1
2
1
2
1
2
0
1
0
2
1
1
1
1
0
2
1
2
1
1
1
0
1
1
1
1
2
1
1
2
2
2
1
0
1
1
2
1
1
2
2
0
1
2
1
2
2
1
1
1
1
0
1
2
1
1
1
0
0
2
1
1
2
1
1
1
2
1
1
2
2
1
0
1
0
1
1
1
1
2
2
1
1
1
0
2
2
2
1
1
0
1
1
1
1
0
0
1
2
2
1
1
0
1
1
2
2
1
1
1
0
0
1
1
1
1
0
1
1
1
0
2
1
1
1
1
1
0
1
1
1
0
1
1
1
1
1
1
1
1
2
2
1
0
1
1
1
0
1
2
1
0
1
2
1
1
1
1
1
0
1
2
1
1
1
0
1
1
0
1
1
0
0
1
0
1
2
1
2
1
2
1
0
1
1
1
2
1
2
1
1
2
1
1
1
2
0
1
0
1
1
0
0
2
1
1
1
0
1
1
1
1
1
2
1
2
1
1
1
1
1
2
0
2
2
3
1
1
2
0
1
1
1
1
2
1
1
1
1
1
1
1
0
1
2
1
0
1
1
1
1
1
1
1
2
1
2
1
0
1
0
1
1
2
1
0
2
1
1
1
1
2
1
2
0
1
2
1
2
1
2
2
1
2
1
2
1
2
1
1
0
1
1
1
0
1
1
1
1
1
1
2
2
1
1
1
1
2
1
0
2
1
1
1
1
1
1
1
1
1
1
2
1
0
0
1
1
1
1
2
2
1
0
1
1
1
1
1
0
1
1
2
1
1
1
2
2
1
1
1
2
1
1
1
2
1
2
1
1
2
1
1
2
0
2
1
1
1
2
0
1
0
2
0
1
0
1
1
1
0
1
2
1
1
2
1
2
1
0
1
0
0
1
2
1
1
1
1
1
0
1
1
2
1
0
0
1
2
1
0
1
1
2
1
1
2
2
1
1
1
0
0
0
1
1
0
1
1
1
1
2
1
2
2
1
1
1
1
1
1
2
1
1
1
2
1
2
1
2
1
1
2
2
2
2
2
2
1
1
2
2
2
0
1
2
1
2
1
1
0
2
1
1
0
0
2
1
0
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
2
2
1
1
1
1
1
0
1
1
0
0
1
1
2
1
1
1
1
1
3
2
3
1
1
1
0
1
1
1
1
2
1
2
1
0
1
1
1
2
2
1
1
2
0
2
2
1
1
2
0
0
2
0
2
1
1
1
1
2
1
1
1
1
0
1
1
2
1
1
1
1
1
0
2
1
0
1
0
1
1
2
1
1
1
0
0
1
1
2
1
1
1
2
1
1
0
1
2
1
1
1
1
2
2
1
0
1
1
2
1
0
0
0
2
0
1
1
1
2
2
1
1
1
1
1
1
0
0
2
0
1
1
1
0
1
1
2
0
1
2
0
1
0
2
1
2
3
0
1
1
1
1
2
1
1
2
1
1
1
1
1
0
2
1
1
2
2
1
1
1
1
1
1
1
1
1
1
0
1
1
2
1
0
1
1
2
0
1
2
2
1
1
1
1
0
1
1
1
1
0
1
2
2
0
1
2
1
1
1
1
2
1
2
1
1
0
1
1
1
1
1
2
1
1
1
0
2
1
0
0
2
2
0
0
1
2
1
1
0
1
2
2
1
1
2
0
2
2
1
1
1
1
2
1
1
1
1
1
2
0
2
1
0
1
1
1
2
2
2
0
2
2
1
1
1
1
1
1
0
1
1
1
2
0
1
2
0
0
0
1
1
0
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
2
1
0
1
2
1
1
1
1
2
2
1
1
2
1
0
2
2
1
1
1
1
0
0
0
1
1
1
1
2
1
2
2
1
1
0
1
1
0
1
2
1
2
0
2
2
0
1
1
2
1
1
1
1
1
1
1
2
2
2
2
3
2
1
0
2
1
1
0
1
1
1
0
1
2
1
1
0
1
2
0
2
1
2
2
1
1
1
1
1
1
2
2
1
1
2
0
1
2
1
1
1
2
1
1
0
1
1
0
1
1
1
1
1
1
1
1
1
1
2
1
2
1
2
1
2
1
1
0
1
1
1
1
1
0
1
1
0
1
0
1
0
1
1
0
0
1
1
2
0
1
1
2
2
0
1
2
1
1
1
2
1
0
2
1
1
1
2
1
2
1
0
1
2
0
2
0
1
2
2
1
1
0
2
1
1
1
0
2
2
0
1
1
2
0
1
0
1
0
2
2
2
0
1
2
2
1
1
2
1
1
1
2
0
1
1
1
1
1
1
2
1
2
2
1
2
1
0
2
0
1
1
1
1
1
1
1
1
1
1
2
0
2
1
1
1
1
1
1
1
1
2
1
1
1
0
2
1
1
1
2
1
1
1
2
2
1
3
0
1
2
2
1
1
0
0
2
1
1
2
0
0
2
1
0
2
0
1
1
2
1
1
2
0
1
1
1
1
1
2
1
1
2
1
3
2
1
1
1
1
2
1
2
1
1
2
1
1
0
0
2
2
1
1
1
1
2
1
1
2
1
1
2
1
2
2
1
1
1
1
1
1
1
1
2
0
0
2
1
0
1
2
2
0
1
0
2
0
2
1
1
0
2
1
1
1
1
1
2
1
2
1
0
0
1
1
1
0
2
2
1
1
0
2
2
1
1
0
1
1
2
2
2
1
1
1
2
1
2
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
2
2
2
0
1
1
1
1
1
1
1
1
1
1
0
1
2
1
1
0
0
2
1
1
2
1
1
1
1
2
2
1
1
1
1
2
1
1
2
2
1
2
1
2
1
2
0
0
2
2
1
1
0
1
1
1
1
1
1
2
2
2
2
1
1
1
2
1
1
0
1
2
1
1
1
1
0
1
0
1
0
2
1
2
2
1
0
1
2
1
1
1
1
1
1
0
1
4
1
1
1
0
1
1
2
2
1
1
1
1
0
0
2
1
1
1
1
1
1
2
1
2
1
2
1
2
0
1
2
1
2
1
1
2
2
0
0
1
1
2
2
2
0
1
1
2
1
2
1
2
2
1
1
3
0
1
1
1
0
1
2
1
2
1
2
0
1
1
1
1
1
1
2
2
1
1
2
0
2
2
1
1
1
1
1
2
2
1
1
1
0
3
1
1
1
2
1
1
1
2
1
1
1
1
4
0
1
2
0
1
2
2
1
1
1
1
1
1
1
1
1
0
0
2
1
2
1
1
1
1
1
1
1
2
1
1
2
1
0
1
1
1
1
1
1
0
1
1
1
0
2
1
0
0
2
1
1
1
2
1
0
0
2
1
2
1
1
0
1
2
1
1
1
2
0
2
1
1
2
1
1
1
1
3
1
1
1
1
1
2
0
0
1
2
1
2
1
2
2
2
1
1
1
1
2
1
2
2
2
1
1
1
1
1
2
1
1
2
2
1
4
1
1
1
2
1
0
2
1
1
1
0
2
1
1
0
1
1
1
2
1
0
1
1
1
1
1
0
1
1
0
1
0
1
2
1
1
1
2
2
0
2
1
1
1
1
1
2
1
1
1
0
0
1
2
1
1
1
0
2
1
1
1
1
1
1
2
1
1
1
0
2
0
1
1
1
0
2
0
1
1
1
1
2
2
1
2
0
2
2
1
0
3
2
2
2
1
1
2
0
0
0
1
1
1
1
1
2
1
0
1
0
0
1
1
0
1
0
2
1
1
1
2
1
0
1
2
1
0
1
1
2
0
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
0
1
0
1
1
1
1
0
0
0
0
2
1
2
2
1
1
1
1
1
1
1
2
1
2
1
0
1
1
0
1
1
1
1
0
2
2
2
1
1
0
0
1
1
2
2
1
1
1
1
1
1
2
2
1
1
1
2
1
0
2
0
1
1
0
1
1
0
1
2
1
2
1
1
0
1
1
1
2
1
1
1
2
1
1
1
1
0
1
1
2
1
1
1
1
1
1
1
1
3
2
1
1
0
1
2
0
1
0
1
0
1
1
1
1
1
2
0
4
0
0
2
2
1
0
1
2
1
1
2
2
0
1
1
0
2
0
2
1
1
1
0
2
2
1
0
1
2
1
1
2
2
1
1
2
2
0
2
1
0
2
1
1
1
1
2
1
1
0
1
2
2
1
2
0
1
0
1
0
2
1
2
2
0
1
1
2
1
1
1
0
1
1
2
1
2
2
1
0
1
1
0
1
0
1
1
1
2
1
0
1
1
1
1
1
1
1
2
0
1
1
0
0
2
1
2
2
2
2
1
2
2
1
2
0
2
1
1
1
1
1
1
1
0
1
2
1
0
1
1
1
1
1
2
0
1
1
0
1
2
1
0
2
1
1
0
1
1
2
1
0
2
1
1
1
2
1
2
1
1
0
1
1
2
1
1
1
1
1
1
1
1
1
0
1
1
0
2
1
1
1
1
2
1
0
1
1
1
1
1
1
2
2
1
2
2
1
1
1
0
1
0
2
1
1
1
2
0
0
1
3
1
2
1
0
0
1
1
1
1
1
1
1
1
0
1
1
1
0
1
1
2
1
1
2
1
1
0
2
1
2
1
2
1
1
1
1
1
1
2
1
1
0
1
0
2
1
0
0
1
0
0
1
2
1
2
0
2
2
2
1
1
1
0
0
2
1
1
1
1
1
1
2
2
1
0
1
2
1
1
1
1
2
2
1
0
1
1
0
0
1
2
1
1
1
2
1
0
1
1
2
1
0
1
1
0
1
2
1
1
1
2
1
1
0
0
2
2
1
2
1
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
1
1
0
1
1
0
1
1
1
1
1
1
1
0
1
1
2
1
0
1
1
1
2
1
2
1
1
1
1
3
1
1
2
1
2
0
2
1
1
2
1
1
1
1
1
1
2
0
1
1
1
1
1
2
1
2
1
2
1
1
1
1
0
2
2
0
2
0
2
2
1
1
0
2
2
1
1
1
1
1
2
0
1
2
0
1
3
2
0
1
1
0
1
1
1
1
0
0
0
1
1
1
1
2
1
1
1
1
1
1
2
1
0
1
2
0
2
1
0
1
1
0
0
2
1
1
2
2
0
1
2
1
1
1
2
1
1
1
1
1
0
1
1
1
1
1
1
2
1
1
1
1
1
0
2
2
1
0
1
0
2
1
1
2
1
1
1
2
0
1
2
1
2
2
0
2
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
0
1
1
1
4
2
1
2
0
1
1
2
1
1
0
2
1
0
0
1
1
0
2
2
2
2
1
1
0
1
2
5
1
1
2
1
2
1
0
2
1
1
1
0
1
1
2
1
0
0
0
1
2
1
1
1
1
0
1
1
1
1
1
1
2
1
2
1
1
1
1
0
2
1
0
2
1
1
1
1
2
2
1
1
2
1
1
1
2
1
0
1
0
1
0
1
2
1
1
1
0
2
2
1
1
2
0
2
2
1
4
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
1
2
0
2
1
2
2
2
1
1
0
2
1
1
1
2
1
0
1
0
1
1
2
2
0
2
1
1
2
1
2
1
0
1
2
1
1
2
1
1
1
1
0
1
0
0
1
1
2
1
1
1
1
2
2
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
2
1
1
2
1
0
0
2
1
1
1
1
1
1
0
1
2
1
1
1
1
1
2
1
1
1
0
1
1
1
1
1
1
1
2
1
0
2
1
1
1
1
0
1
1
2
1
2
1
2
1
1
1
0
1
1
2
1
1
3
0
2
1
2
1
1
1
1
1
0
0
1
0
1
0
2
1
2
1
1
2
1
1
1
1
2
2
0
1
1
2
2
1
1
1
1
1
1
1
1
0
2
1
1
0
1
2
1
1
1
2
1
1
1
1
0
2
0
1
0
2
1
1
1
1
1
2
2
1
1
0
2
1
0
2
1
1
1
1
2
1
2
1
0
2
1
1
2
1
1
2
2
1
1
1
2
1
1
1
1
1
2
2
2
1
2
1
2
1
2
1
1
4
0
0
1
2
2
1
2
1
0
1
2
1
1
1
0
1
2
1
1
1
0
1
2
1
2
0
1
4
0
1
1
1
2
1
1
2
1
1
2
3
1
0
0
2
0
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
0
1
2
1
0
1
2
1
1
1
1
1
0
0
1
2
1
1
1
1
1
1
1
1
1
1
0
0
0
2
1
1
1
0
2
1
1
2
0
1
1
1
2
2
1
1
1
1
2
2
1
2
1
1
1
1
1
2
1
0
2
1
1
1
1
1
1
1
3
1
1
2
1
2
2
0
1
2
1
1
1
1
2
2
1
2
1
1
1
2
1
2
1
2
1
1
1
1
1
2
1
1
2
1
1
1
2
2
1
1
1
0
1
1
1
1
1
1
0
2
1
2
2
2
0
1
0
1
0
1
1
1
0
0
2
1
1
2
2
1
1
2
2
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
2
1
1
0
1
2
2
3
1
2
2
1
1
1
2
1
1
1
0
1
2
1
1
1
1
1
1
0
2
1
2
6
2
1
1
0
1
0
1
2
1
0
1
0
1
1
1
0
1
1
2
1
1
1
1
1
0
3
1
1
0
2
1
1
0
1
1
1
2
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
0
0
1
5
1
1
1
2
2
1
2
1
1
2
1
1
1
2
0
1
2
1
0
1
0
1
0
2
1
2
1
2
0
1
0
1
1
1
0
0
1
1
0
1
0
1
1
1
1
1
1
2
0
1
1
1
0
2
1
1
2
1
1
0
1
1
1
1
1
1
2
1
2
0
1
0
1
1
1
1
1
1
1
1
0
1
1
1
0
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
2
1
1
2
0
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
1
0
1
1
2
1
2
0
1
1
2
2
2
0
2
1
1
0
0
1
1
1
0
1
1
1
2
1
1
1
2
0
1
1
1
0
0
1
1
0
1
2
1
1
1
1
1
2
0
1
0
1
2
1
1
1
1
2
1
1
2
1
2
1
2
0
1
1
1
1
2
2
1
1
0
1
1
2
2
1
1
1
1
1
1
2
0
1
1
0
1
1
2
0
1
1
2
1
0
2
2
0
3
1
1
1
1
1
1
2
1
2
0
2
2
2
1
1
2
2
1
2
1
2
1
1
2
1
1
0
1
1
1
1
1
1
2
1
0
1
0
2
0
1
2
2
1
0
1
0
2
1
0
2
1
1
1
2
0
0
1
2
0
0
0
2
1
1
1
1
0
1
1
1
1
0
1
0
1
1
2
1
1
2
1
1
0
2
1
1
2
1
1
2
1
1
1
1
1
1
0
1
2
1
0
1
1
1
0
1
0
1
1
2
1
1
1
2
2
2
1
3
1
2
1
1
1
1
0
1
0
0
1
0
2
1
1
2
1
0
1
1
2
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
2
0
1
1
1
1
1
1
1
1
2
1
1
2
1
0
0
0
1
0
1
1
1
1
1
0
0
2
0
0
2
1
1
1
1
1
1
1
2
1
1
1
0
1
1
0
1
1
1
2
1
2
1
1
2
2
1
2
1
1
2
1
2
1
1
0
1
2
2
2
1
0
1
2
2
1
1
2
1
1
2
1
0
1
1
1
1
1
2
2
1
1
0
2
1
2
1
1
0
2
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
0
2
2
1
1
1
1
1
2
1
1
1
0
0
2
2
1
0
2
2
2
1
2
0
1
1
0
0
1
0
1
3
2
1
1
1
1
1
0
1
1
3
2
1
1
1
2
1
1
2
2
2
0
2
1
1
1
1
1
2
1
0
1
0
1
2
2
0
1
1
2
1
2
0
1
2
0
1
0
1
1
1
1
0
2
0
1
0
2
1
2
0
0
2
2
2
1
1
1
2
1
1
1
1
1
0
1
1
1
1
2
1
1
1
0
1
1
1
2
2
1
1
2
1
2
1
1
2
1
2
2
1
1
1
1
2
0
1
1
0
1
1
1
1
1
2
1
1
3
1
1
2
2
0
1
1
1
1
1
1
1
1
1
2
1
1
0
0
0
1
0
1
2
1
2
1
1
1
1
1
1
2
2
1
2
1
0
0
0
2
1
2
1
1
1
1
2
1
1
1
0
2
1
1
2
1
3
2
2
2
2
1
2
2
1
1
1
1
1
1
1
1
1
2
1
1
0
0
2
0
1
1
1
2
1
1
1
2
1
1
1
1
2
2
2
1
1
0
0
1
2
1
2
1
1
0
1
0
1
1
1
3
1
1
1
1
1
2
1
2
0
2
1
1
1
1
1
0
1
2
1
1
1
1
2
0
0
1
1
0
1
1
1
1
0
1
1
2
1
1
2
2
1
0
2
1
1
1
2
1
1
0
1
0
1
1
1
1
1
2
1
1
0
1
2
2
1
1
3
3
2
1
1
2
1
1
0
0
1
1
1
2
0
2
1
0
1
1
1
2
0
1
1
0
1
2
1
1
2
2
0
1
0
0
1
1
1
1
1
2
2
1
1
2
0
2
1
2
0
0
1
1
2
0
1
1
1
1
2
2
1
3
1
1
0
2
2
2
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
2
1
2
2
0
2
2
2
1
1
1
1
1
0
2
1
1
1
1
2
0
0
1
1
1
1
1
1
1
2
1
0
1
2
0
1
2
1
1
0
1
0
1
0
2
1
1
1
1
1
1
0
1
2
2
1
1
0
0
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
2
0
1
2
1
1
1
1
1
1
1
1
2
2
2
1
2
1
1
1
1
2
2
1
2
1
1
1
1
1
2
2
2
0
2
2
1
2
0
2
1
0
1
2
1
0
1
1
1
1
1
1
1
1
0
2
1
1
2
1
1
1
0
2
1
1
1
0
1
1
1
2
1
1
1
1
1
1
2
1
0
1
1
1
1
1
0
1
1
1
1
1
2
1
1
1
0
0
1
1
1
1
1
1
1
0
1
1
1
1
2
1
1
1
0
1
1
1
1
1
1
1
1
0
1
2
0
1
1
1
2
1
1
1
1
0
1
2
0
2
2
1
1
2
1
0
1
1
1
1
0
0
2
2
1
1
0
0
0
1
2
1
1
1
2
1
0
0
2
2
2
2
2
2
1
1
0
2
2
2
1
1
0
1
1
1
0
1
1
1
2
1
0
1
2
1
1
2
1
2
0
1
1
2
2
0
0
0
0
1
1
2
1
1
2
2
1
2
2
1
1
0
2
1
0
2
1
1
0
1
1
1
1
1
1
0
1
1
1
1
1
2
1
1
1
0
0
2
0
0
1
0
2
1
1
0
1
1
2
1
1
1
1
1
2
2
1
1
1
2
1
0
2
0
2
1
1
2
0
1
1
2
1
2
1
1
0
1
1
1
1
1
1
2
1
1
1
2
1
0
0
2
1
2
0
0
1
2
0
2
3
1
1
2
2
1
1
1
1
1
1
2
0
1
1
1
1
1
2
1
1
2
1
2
1
1
1
1
2
1
2
1
0
0
1
2
2
1
2
2
1
2
1
1
1
2
1
2
1
0
0
1
1
1
0
1
1
1
1
2
2
2
1
1
1
2
1
1
1
1
1
0
2
1
1
0
0
2
2
1
2
2
1
0
1
1
2
1
1
1
2
1
1
2
1
1
1
1
1
1
1
0
1
0
1
1
0
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
2
0
0
1
1
2
1
1
2
1
1
1
2
1
1
1
1
2
2
1
2
2
0
1
1
0
1
0
1
1
2
2
1
0
1
1
1
1
2
0
1
1
1
1
0
2
1
3
1
2
2
1
1
2
1
1
1
2
1
3
1
2
2
0
0
1
1
1
1
1
2
0
2
2
2
1
2
1
0
1
1
1
2
1
1
2
1
1
1
0
1
1
2
0
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
0
2
1
2
1
1
2
1
1
1
0
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
0
0
1
1
1
1
2
2
0
2
0
1
2
0
1
2
2
2
0
2
2
2
1
0
1
1
1
3
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
2
2
1
2
1
1
2
1
2
1
1
2
1
2
2
2
2
2
2
1
1
1
1
1
2
0
2
1
1
1
1
1
1
1
1
0
1
0
2
2
1
1
2
1
1
0
1
0
1
3
1
2
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
2
0
1
1
1
2
1
2
1
1
1
1
1
0
2
1
1
1
0
1
0
0
0
2
1
2
2
4
1
1
1
0
1
1
1
1
2
2
1
2
0
1
1
2
2
1
1
1
1
1
0
0
1
1
2
1
2
1
1
1
1
0
2
2
2
0
1
1
1
0
1
1
1
2
0
2
0
2
1
1
1
2
0
1
1
0
2
1
1
1
0
1
1
1
2
1
0
1
1
1
0
1
2
2
2
1
1
2
2
2
0
0
10
0
2
1
2
2
1
2
1
2
0
0
2
2
1
1
1
1
1
1
1
1
1
2
2
0
1
0
2
1
0
1
1
2
1
2
2
1
1
1
1
2
2
0
2
1
1
1
1
2
1
1
1
2
1
2
1
0
1
1
1
2
1
1
1
2
1
2
1
2
1
3
2
0
1
1
0
1
2
1
1
1
1
0
2
2
2
0
1
2
1
0
1
2
0
0
1
1
1
0
1
1
1
2
1
1
1
0
1
1
1
1
1
2
1
0
1
1
2
1
2
2
1
0
1
1
1
1
1
1
0
1
1
1
1
1
1
2
2
0
1
1
1
0
1
2
0
2
0
1
1
1
1
2
0
1
2
1
2
2
1
1
2
1
1
1
1
0
1
2
0
1
1
1
2
2
1
2
2
2
1
1
0
1
2
1
1
0
2
2
1
1
2
1
1
1
1
1
2
1
1
1
1
0
2
2
2
2
1
2
1
1
1
1
0
2
1
2
1
2
2
2
2
1
1
1
1
2
2
2
1
0
0
1
0
1
1
2
1
1
0
2
2
1
2
2
1
1
2
2
1
1
1
0
1
2
0
0
2
2
1
0
1
1
1
1
0
2
1
2
1
2
1
1
0
0
1
1
2
1
1
1
2
2
2
2
1
0
2
2
2
0
2
1
2
2
1
1
1
1
1
0
2
3
1
2
0
1
1
1
2
1
2
2
1
2
0
0
1
1
1
2
2
2
1
1
1
0
0
1
1
1
1
1
1
1
1
0
2
2
1
1
1
1
2
1
0
0
1
0
0
1
2
1
0
1
2
2
1
1
2
1
1
0
2
1
2
1
1
2
1
0
1
0
0
1
1
2
1
2
0
0
1
2
0
2
1
2
2
1
2
0
1
1
2
1
1
1
0
1
1
1
1
1
0
1
1
0
0
0
0
0
0
1
1
1
1
0
0
2
0
1
1
1
1
1
1
0
1
1
1
1
0
2
2
2
1
1
1
1
1
1
1
1
2
1
1
0
2
1
0
1
1
2
1
2
1
1
1
1
2
1
1
2
0
0
1
1
2
1
1
2
1
1
2
1
1
2
1
2
1
2
1
1
2
2
1
1
1
1
1
0
1
1
1
1
0
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
0
2
1
0
2
2
2
1
2
1
1
1
1
1
1
1
0
0
0
1
0
1
0
1
1
1
1
1
2
1
0
1
1
1
1
1
2
2
2
1
1
0
1
1
1
1
1
1
0
1
2
1
1
1
1
0
2
1
2
1
1
1
0
1
2
2
1
2
2
1
1
1
1
1
2
1
1
2
2
1
1
1
1
1
0
2
1
1
0
2
0
2
1
2
1
2
1
1
2
1
1
1
1
0
2
1
2
1
1
0
2
2
1
2
2
1
1
1
2
2
3
2
1
1
2
2
2
0
1
0
2
2
1
2
1
2
0
1
1
1
2
1
1
2
1
1
0
0
1
0
1
2
1
1
0
1
1
1
0
1
2
2
0
1
1
1
2
1
0
0
1
2
2
2
1
2
1
3
1
0
0
2
3
2
2
2
2
0
4
2
1
1
1
0
1
1
0
1
1
1
1
1
2
1
1
1
1
2
1
0
1
1
1
2
2
1
1
1
0
1
0
1
1
1
1
2
2
1
1
1
3
1
1
2
1
1
1
1
0
2
1
0
1
1
1
1
2
1
0
1
1
1
0
1
0
1
1
1
1
1
1
1
0
1
1
2
1
1
1
0
2
1
2
0
1
0
1
2
0
1
1
2
0
2
1
1
0
1
2
2
1
2
2
1
2
1
2
2
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
2
0
2
0
1
1
0
2
1
2
1
1
1
1
2
1
1
2
4
1
1
2
1
1
1
1
0
1
2
1
0
1
0
1
1
1
1
1
2
2
2
2
2
1
1
2
1
2
1
1
2
2
2
1
1
2
1
1
1
0
0
2
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
2
0
2
1
1
1
1
1
2
2
0
0
0
1
1
1
1
1
0
2
1
1
1
2
2
1
2
0
2
1
1
1
1
1
1
2
2
0
1
2
1
1
0
1
1
1
1
1
1
1
1
2
0
1
2
2
1
2
2
1
1
0
1
1
1
1
1
0
0
2
1
1
2
1
1
1
2
0
1
1
1
2
1
1
0
0
2
1
1
1
0
1
1
1
0
1
2
0
2
2
2
1
1
1
0
0
1
1
0
1
1
2
0
0
1
2
1
0
1
1
1
2
2
1
0
1
1
1
2
1
0
0
1
0
1
1
2
2
1
0
1
1
2
1
1
0
2
1
1
1
1
1
1
0
1
1
1
0
1
1
1
0
1
2
0
3
1
0
1
1
1
1
1
1
0
1
1
1
1
1
1
2
1
1
1
1
1
0
2
0
1
0
1
2
1
1
1
1
1
0
1
2
1
2
1
1
1
1
0
2
1
1
2
1
1
0
1
0
1
1
1
2
1
1
1
2
2
1
2
1
2
1
0
1
1
1
2
0
1
1
2
1
1
1
1
1
1
1
1
2
2
1
1
1
1
2
1
2
2
1
1
2
1
1
1
0
1
1
1
1
0
2
0
2
1
2
2
0
2
0
1
2
1
1
1
0
1
1
1
0
1
1
2
2
1
1
1
1
2
1
1
0
1
1
2
0
1
1
1
2
1
1
2
0
1
1
1
1
1
1
0
2
1
2
1
1
1
0
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
0
2
2
1
1
2
0
0
1
1
1
1
0
0
1
1
1
1
0
0
2
2
0
1
0
1
1
1
2
2
0
0
1
1
1
1
1
1
1
1
1
1
2
0
2
1
1
1
1
1
1
0
2
1
1
1
1
2
1
1
0
1
1
2
2
1
1
1
2
1
2
2
2
1
2
2
0
1
2
1
1
2
1
2
1
1
1
1
2
1
2
2
1
1
1
1
2
1
2
1
1
0
1
0
3
1
2
1
0
2
2
1
1
1
2
2
0
1
0
2
1
0
1
1
1
1
1
1
3
1
1
1
2
1
3
1
2
1
0
1
2
1
0
0
1
1
2
1
2
1
1
1
1
1
0
1
1
1
2
1
4
2
1
1
1
1
1
2
0
0
2
1
1
0
2
1
1
1
1
1
0
2
1
0
1
1
0
2
2
1
0
0
1
2
2
1
0
2
1
0
1
1
1
1
1
0
0
1
1
2
2
1
1
1
1
1
2
0
2
1
0
1
2
1
2
1
1
2
1
1
1
1
2
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
0
1
1
1
4
1
1
1
1
1
2
1
2
1
0
2
0
1
1
1
1
2
1
2
1
2
0
1
1
0
1
1
2
1
0
1
1
2
0
1
1
1
2
2
1
2
2
2
1
2
1
1
1
2
1
1
2
0
2
1
1
1
1
1
1
2
1
1
1
1
0
0
1
2
0
1
1
1
1
1
1
1
2
2
2
1
1
2
1
2
1
0
1
0
1
1
1
1
1
2
1
1
1
2
1
1
3
1
1
0
1
1
1
1
1
1
1
1
2
1
0
1
1
1
1
0
2
1
2
2
1
2
1
2
1
0
0
1
1
0
2
0
1
0
1
1
2
1
1
1
1
1
1
1
2
0
2
0
2
1
1
1
2
1
0
1
3
1
2
0
2
1
1
1
1
1
2
1
2
2
1
1
1
1
2
1
0
2
2
0
1
1
2
1
1
2
1
1
0
1
1
1
1
1
1
2
2
1
1
2
1
1
2
1
1
0
0
1
1
1
1
2
1
0
1
1
1
1
0
0
1
2
2
0
2
1
2
1
2
1
1
0
1
1
1
0
0
2
2
0
1
1
0
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
2
1
0
1
1
1
1
1
1
2
1
0
1
1
1
1
1
0
1
2
1
1
1
0
1
1
1
0
1
1
1
1
2
1
1
1
1
1
1
1
1
2
0
1
1
1
1
2
1
2
0
1
1
1
0
1
2
1
1
1
1
2
1
1
3
2
2
3
1
2
1
1
1
2
1
1
1
2
1
1
2
0
2
1
2
1
2
1
0
2
2
2
1
1
1
1
1
1
1
2
1
0
0
0
3
1
0
1
1
2
1
2
1
1
1
1
1
1
2
2
1
2
0
2
1
1
1
2
1
1
0
1
1
1
2
1
2
1
1
1
1
2
1
1
2
2
2
1
1
1
0
4
2
1
1
2
1
1
2
1
0
1
1
1
1
1
1
2
2
0
2
1
1
2
0
1
1
1
0
2
1
1
1
0
1
0
1
0
1
2
1
1
2
0
0
2
1
2
1
1
2
0
2
1
1
1
1
1
0
1
2
1
0
1
1
0
1
0
1
1
1
2
1
1
2
0
1
1
1
1
1
1
1
1
1
2
1
1
1
1
0
2
2
1
2
1
1
2
2
1
1
2
1
0
1
0
0
1
0
0
1
0
2
0
2
2
1
1
1
2
2
1
1
1
2
0
1
1
1
2
2
1
0
0
2
1
1
1
1
1
1
1
1
1
1
1
0
0
2
1
2
1
1
2
1
1
1
0
1
1
2
1
0
1
1
1
0
1
3
0
1
1
0
1
1
0
1
2
1
2
1
2
1
1
1
1
1
2
0
0
2
1
2
1
2
1
1
1
0
1
0
2
1
1
1
2
2
0
1
1
4
0
1
2
1
2
2
1
1
1
1
2
0
1
1
0
2
1
1
2
2
2
1
2
1
1
2
1
0
1
4
1
2
1
1
2
1
1
2
1
1
1
1
0
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
2
2
0
1
1
1
1
2
1
2
1
2
1
1
0
1
1
1
2
2
1
0
1
1
1
1
2
1
2
1
2
1
1
1
1
1
2
1
2
1
2
1
1
1
1
2
1
0
1
1
1
1
2
1
1
1
1
2
1
0
1
0
1
1
2
0
1
1
1
2
0
2
0
1
1
1
2
1
1
2
1
1
1
1
0
1
1
2
1
2
0
1
0
3
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
2
1
0
0
1
1
2
1
2
1
1
0
1
0
1
2
1
1
1
1
1
1
2
1
1
1
2
0
1
1
0
0
1
0
1
0
0
1
0
2
1
2
1
1
2
1
0
1
2
1
2
1
1
1
0
2
2
2
1
1
0
0
1
1
1
1
1
1
2
2
1
1
1
1
2
1
0
1
0
1
1
2
2
1
1
2
1
1
2
1
2
1
1
0
1
2
2
1
0
0
0
1
1
1
1
1
1
1
0
1
1
0
0
1
1
1
0
1
2
2
2
1
2
0
1
0
1
1
1
1
2
0
1
0
2
1
2
2
1
1
1
1
2
1
1
1
1
1
2
2
2
2
1
2
2
1
0
0
0
1
1
2
2
1
0
1
2
2
2
1
0
2
1
1
1
2
0
0
1
1
2
0
1
1
1
1
1
1
1
1
1
1
0
2
1
0
2
1
0
1
2
1
1
2
2
1
1
1
1
1
0
0
1
0
2
0
1
2
1
1
1
0
1
1
2
0
1
1
2
2
0
1
0
1
0
1
1
1
2
3
1
1
1
2
1
2
1
1
1
1
1
1
0
2
2
1
1
1
2
1
1
2
1
1
1
1
1
1
1
0
0
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
0
1
0
2
1
1
1
2
1
1
1
0
1
1
1
1
1
1
1
1
0
0
1
0
1
0
1
0
1
1
2
0
2
1
1
1
1
2
1
0
1
1
0
0
0
1
1
1
1
1
2
1
0
1
1
0
0
2
2
1
1
1
0
2
1
2
1
2
1
1
2
1
0
1
1
0
1
1
1
1
2
1
1
2
0
1
2
1
2
1
6
1
1
1
0
1
1
1
1
1
1
1
1
1
0
0
1
1
0
1
1
0
1
1
2
0
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
1
1
0
1
0
1
1
1
1
1
1
2
1
0
1
2
1
2
1
0
0
1
1
0
1
2
1
1
0
2
2
1
0
1
1
0
0
1
1
0
2
0
1
1
1
1
1
2
2
1
1
1
1
1
2
1
2
2
1
0
1
1
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
2
1
2
2
1
1
2
2
0
2
0
1
0
0
0
1
1
1
1
0
1
2
1
1
0
2
1
1
1
1
1
1
2
2
2
0
0
1
0
2
1
2
1
1
1
2
1
2
1
1
1
1
1
1
1
2
1
0
2
2
2
1
2
1
1
2
2
1
2
1
2
1
2
0
1
1
1
0
1
1
2
1
2
1
1
2
2
1
1
1
2
0
1
1
1
1
1
2
1
1
1
0
1
1
1
1
1
0
1
1
1
1
1
1
1
1
3
1
1
2
0
2
1
1
1
1
3
2
1
1
1
1
2
0
1
2
1
0
2
1
1
0
2
2
1
0
1
1
2
1
0
0
2
1
0
1
2
1
1
2
1
1
2
2
1
1
0
1
1
0
1
0
2
2
4
1
1
2
1
0
0
0
1
1
1
1
1
1
1
2
2
2
1
1
0
1
2
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
0
1
2
2
1
1
1
2
1
1
1
1
2
2
1
1
0
2
0
1
1
1
0
1
0
2
2
1
1
1
1
0
1
0
1
0
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
2
0
2
0
3
1
2
1
2
1
1
1
1
1
1
1
2
1
1
0
1
2
0
1
2
2
2
1
1
1
2
0
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
2
1
1
2
1
0
1
1
1
1
1
1
1
1
2
0
1
0
1
1
2
2
1
1
1
1
1
1
0
2
1
2
2
2
1
1
1
1
1
1
2
1
1
2
1
1
1
2
2
1
2
2
1
2
1
2
1
1
1
1
0
2
0
1
2
1
1
1
1
2
1
2
2
1
1
1
1
2
1
1
2
2
1
2
1
2
2
1
0
1
0
1
1
1
0
0
2
2
1
1
1
2
1
1
1
1
1
1
2
2
2
1
1
2
1
1
1
1
1
1
1
1
2
2
1
2
0
2
1
1
1
1
1
1
2
1
1
0
1
2
1
2
1
1
1
1
2
0
0
2
2
2
1
2
1
1
1
2
1
2
1
1
1
1
1
2
1
1
2
2
1
1
2
0
1
1
1
2
1
1
2
1
1
0
3
2
1
1
1
1
1
1
2
0
0
1
2
1
2
1
1
2
2
2
1
3
1
0
1
1
0
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
0
1
1
1
0
1
0
0
0
2
1
1
0
0
2
1
0
1
1
1
2
1
0
1
1
2
1
1
1
1
2
1
2
1
1
2
1
1
0
1
1
1
1
1
2
2
1
2
1
2
2
3
1
0
2
2
1
1
1
1
1
1
2
2
1
2
1
1
1
1
0
0
0
1
2
2
2
0
1
2
2
0
1
1
1
1
1
1
1
0
1
2
1
1
1
1
1
1
2
0
1
0
1
1
1
2
1
1
0
2
1
1
2
0
1
1
1
1
2
1
0
2
2
2
0
1
1
2
1
1
3
0
2
1
1
1
0
1
0
2
2
2
2
1
1
1
1
1
1
2
1
0
1
1
1
2
1
0
0
1
2
1
1
2
2
0
2
1
1
1
1
0
1
3
1
2
1
1
1
1
1
4
1
1
1
1
1
1
0
2
2
1
1
1
2
1
2
0
1
2
1
1
1
2
2
2
1
1
1
1
1
0
1
1
2
1
1
2
2
2
0
2
1
1
0
1
2
2
1
1
1
1
1
1
0
1
1
2
2
1
1
1
1
2
1
0
1
0
1
2
0
1
1
2
1
1
0
1
2
2
1
1
2
1
1
0
1
1
1
1
2
0
1
2
1
1
2
1
1
1
1
1
0
1
0
2
2
1
2
1
1
0
1
1
1
2
2
2
1
0
0
1
1
2
1
1
1
1
0
1
1
2
1
1
1
1
2
1
1
1
1
1
1
2
2
1
0
1
1
2
2
1
1
1
0
1
0
1
1
2
2
1
2
2
1
1
2
1
0
0
1
2
1
1
2
1
1
1
0
0
0
1
3
1
1
1
0
1
2
0
0
0
1
1
1
1
0
1
1
2
1
1
1
1
2
2
1
1
1
2
2
0
1
1
1
0
1
1
1
1
0
2
1
2
1
2
1
1
1
0
1
0
1
2
1
1
0
0
2
2
1
1
1
0
1
2
1
1
0
2
2
1
1
2
0
0
1
3
1
1
2
2
1
0
1
1
1
1
1
1
2
0
2
1
2
1
1
2
1
1
1
0
0
1
2
2
2
2
1
1
1
2
1
2
1
1
1
1
2
0
1
1
2
2
2
2
1
1
0
2
2
2
1
1
2
1
2
0
2
1
1
0
1
4
1
2
1
2
1
1
0
1
1
2
1
0
2
0
2
2
2
2
0
1
1
2
1
2
1
0
0
1
1
2
1
1
1
1
1
0
0
3
0
2
1
0
1
2
1
2
1
1
1
0
1
0
1
1
2
1
1
0
1
2
1
1
2
1
0
2
1
1
2
1
2
1
2
0
1
2
1
1
1
0
2
1
1
1
1
2
1
0
1
0
1
1
1
1
0
2
2
1
1
1
2
2
2
1
1
1
2
1
0
1
2
1
1
1
1
2
1
2
0
2
2
2
0
2
1
1
1
0
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
4
1
1
0
1
1
1
1
1
2
2
1
1
1
2
1
1
1
0
1
0
1
1
1
1
1
2
1
1
2
1
0
0
1
0
2
1
1
0
2
2
1
2
1
0
2
1
1
1
0
2
1
1
2
2
1
2
1
1
1
1
2
0
0
2
1
2
1
1
1
1
1
2
1
0
3
2
1
1
2
2
1
1
3
1
2
1
4
3
1
2
1
1
1
2
1
1
0
1
0
1
1
0
2
2
0
1
1
1
1
2
2
2
0
0
0
2
1
1
2
1
1
1
0
1
1
1
0
1
0
2
0
1
1
1
1
2
2
0
0
2
1
1
2
1
1
2
1
1
1
2
1
1
1
4
0
2
2
2
1
1
1
2
1
0
1
1
0
0
1
3
1
0
2
1
1
1
1
0
2
1
1
1
1
1
2
1
1
0
1
0
1
1
1
1
1
1
1
0
2
1
2
1
2
1
1
2
2
2
2
1
2
1
3
1
0
1
0
3
2
1
2
1
1
1
1
2
0
1
1
0
0
1
2
0
2
0
1
0
2
0
1
1
2
1
2
2
1
2
1
1
1
1
1
0
0
1
0
1
1
0
0
1
2
2
2
1
1
0
1
1
1
1
1
4
2
2
0
1
1
1
1
2
1
1
0
1
0
2
2
1
0
1
1
1
2
0
1
1
0
1
1
1
1
1
1
1
1
2
1
1
0
1
1
1
1
0
0
1
1
1
0
1
1
2
2
2
2
2
1
2
0
1
1
2
1
2
1
1
2
2
1
1
0
1
0
1
1
1
2
2
2
1
0
1
2
2
2
1
2
1
2
1
1
1
2
0
2
2
1
1
2
1
2
1
2
1
0
1
0
0
1
1
1
2
0
2
1
1
1
1
1
2
1
1
1
0
1
2
2
0
1
1
2
2
2
2
0
2
1
1
0
2
2
0
1
2
1
2
1
2
1
1
1
1
1
0
2
0
1
1
1
1
2
1
1
1
1
2
1
1
2
2
1
0
1
0
2
1
2
2
2
1
2
1
1
1
1
1
2
2
1
1
0
0
1
2
0
1
1
1
1
1
0
1
1
2
2
0
1
2
2
2
2
1
1
1
1
1
2
1
1
1
0
1
1
1
2
2
1
1
1
1
1
1
2
3
1
0
0
2
1
1
1
2
1
1
1
0
0
1
1
1
1
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
1
0
2
1
1
1
0
1
1
1
2
1
1
4
2
1
1
2
2
2
1
1
1
1
2
1
0
1
2
1
1
1
1
2
1
2
0
0
1
0
1
1
1
1
0
2
1
2
1
1
2
1
2
1
1
2
1
2
0
1
1
1
0
1
1
2
1
1
2
1
1
2
1
0
0
1
1
2
1
1
3
2
2
2
1
0
1
2
1
1
1
1
2
2
1
2
2
1
1
1
1
0
0
1
0
2
1
1
1
1
1
1
0
3
0
1
1
0
2
1
1
2
0
1
1
0
1
1
1
1
1
1
2
1
2
1
2
1
1
1
1
0
2
2
2
2
1
1
1
1
0
0
0
1
2
1
1
0
1
0
2
1
2
2
1
1
1
2
1
1
0
0
1
1
2
1
2
2
1
1
2
1
0
1
1
2
2
2
1
1
0
2
1
1
1
1
1
1
0
1
0
2
2
2
1
1
0
1
1
1
1
1
1
1
2
1
1
2
2
1
1
1
1
0
0
1
1
1
1
1
1
2
2
2
1
1
1
2
1
1
0
1
0
1
2
1
1
1
0
1
0
1
1
1
1
2
2
1
1
2
1
0
0
2
1
1
1
2
1
1
1
2
2
2
2
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
0
2
1
0
1
1
0
2
0
1
0
2
2
0
1
1
1
0
0
1
1
2
2
1
1
1
0
1
1
1
1
2
2
1
1
2
1
2
1
2
1
1
0
0
1
2
0
1
1
1
1
1
1
0
1
1
2
1
1
1
1
1
1
0
2
0
1
1
0
1
1
1
1
1
0
1
0
0
1
1
1
1
2
2
1
1
2
1
1
1
2
1
1
2
2
1
1
2
1
1
1
2
2
2
0
2
1
1
1
1
2
1
1
0
2
1
1
1
1
1
0
0
2
1
2
2
2
2
1
1
0
1
1
1
1
0
2
0
2
0
1
1
2
2
2
1
1
0
2
0
2
0
0
1
0
1
1
1
0
1
2
2
1
1
1
1
2
0
2
2
2
1
2
1
1
0
1
0
2
1
2
2
0
1
2
1
2
1
1
1
1
0
1
2
1
0
0
1
1
1
1
3
1
1
2
3
1
1
1
2
0
1
0
0
2
2
2
0
1
2
2
1
0
2
1
1
1
1
1
1
1
2
2
2
0
1
1
1
1
1
2
2
2
1
2
2
1
0
1
1
1
2
0
0
2
1
1
1
1
0
1
1
1
0
2
1
0
1
2
1
0
0
2
2
0
1
1
2
1
2
1
1
0
2
1
0
2
0
1
0
1
2
2
1
1
1
2
0
1
1
1
2
1
1
1
2
2
0
2
1
1
1
1
0
2
2
1
1
1
1
1
1
2
1
0
1
1
1
2
1
2
1
1
1
1
2
2
1
1
1
1
1
1
0
0
1
1
1
1
1
0
1
1
0
1
0
1
2
0
2
2
1
1
1
1
1
2
1
2
0
1
1
1
2
1
0
1
1
2
1
1
2
1
2
1
1
2
0
2
3
2
2
0
1
2
1
1
2
1
0
1
0
2
0
1
1
1
0
1
0
1
1
0
1
2
1
2
1
1
1
2
2
0
1
5
2
2
1
2
3
1
0
3
1
1
1
0
0
2
1
1
1
1
1
1
1
0
2
2
1
2
0
1
1
1
1
1
1
1
2
2
2
1
1
1
0
2
2
0
2
0
1
1
2
0
1
1
1
1
1
0
1
1
1
1
1
1
1
1
2
0
1
2
1
1
1
1
2
2
1
1
1
1
2
2
2
1
0
2
0
1
1
1
2
2
2
1
1
1
2
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
2
1
2
1
1
2
1
1
2
2
1
0
1
1
1
0
2
2
1
2
1
0
1
0
0
1
1
1
1
1
1
1
1
3
2
1
0
0
1
1
0
1
1
2
2
0
1
2
1
1
1
1
1
2
1
0
1
1
0
1
1
1
1
1
1
0
1
1
1
2
0
1
1
1
1
1
1
2
1
2
1
1
2
2
2
1
1
0
2
2
0
2
2
1
1
1
2
1
0
0
2
1
2
1
1
1
1
2
0
1
0
1
0
0
2
1
2
2
2
0
1
2
1
0
1
0
2
4
1
0
1
1
1
0
2
1
0
1
0
0
2
2
0
1
1
1
1
1
1
0
1
0
1
1
2
2
1
1
2
1
0
1
1
0
0
0
0
0
2
1
0
1
1
1
2
1
3
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
0
1
1
1
1
2
1
2
0
1
1
0
1
1
2
1
1
2
1
0
1
1
2
0
2
1
2
1
1
1
1
1
2
1
1
2
1
2
1
1
2
0
1
1
2
1
2
2
1
1
1
1
1
1
1
1
1
2
1
0
2
1
1
1
2
1
1
1
2
2
2
1
1
2
1
1
1
1
2
1
0
1
2
1
1
1
1
1
1
0
1
2
2
1
0
1
1
1
1
1
1
1
0
2
0
0
1
2
1
2
1
1
1
1
1
0
1
1
1
1
5
1
2
1
1
1
1
1
1
1
2
1
1
2
0
1
0
1
1
2
1
1
2
1
1
1
2
1
0
1
0
1
0
2
2
1
1
1
0
0
1
1
0
2
1
2
1
1
1
1
1
0
2
2
2
1
1
2
0
2
1
1
2
2
1
2
1
1
1
2
1
1
2
1
1
1
1
2
2
1
1
1
2
1
1
1
2
0
2
2
1
1
0
1
0
1
1
1
1
1
1
2
1
1
1
2
2
1
0
2
1
1
1
2
1
0
1
2
1
1
1
2
1
1
0
2
0
2
1
2
0
1
1
2
1
0
2
1
2
1
1
1
2
2
1
1
0
0
1
0
1
2
2
2
2
1
1
1
1
1
1
1
1
1
1
1
0
2
1
1
1
1
0
1
1
1
0
1
1
0
1
2
1
1
1
1
1
1
0
1
1
2
1
0
1
0
2
1
2
0
2
1
1
0
2
2
1
1
1
1
2
0
1
0
1
1
2
2
1
1
0
1
2
1
2
1
2
0
1
1
2
2
1
1
1
1
1
1
0
1
2
1
1
1
1
0
1
0
1
2
0
1
2
0
1
2
1
1
0
2
0
1
1
1
1
1
0
2
0
2
0
0
2
0
1
1
2
2
2
1
2
1
1
1
1
1
1
3
1
1
1
1
1
1
1
1
1
1
1
1
2
1
0
2
1
2
2
1
1
1
1
1
2
1
2
2
2
0
2
1
1
1
2
1
2
1
0
1
1
2
2
2
2
1
1
2
1
0
1
0
2
2
1
2
1
1
1
0
2
2
3
1
0
1
1
1
1
0
1
1
1
1
1
1
0
1
1
1
1
2
1
1
2
0
0
1
1
1
1
0
2
1
1
1
2
0
1
0
2
0
1
1
1
1
1
0
1
2
2
1
1
0
2
1
1
1
2
1
1
1
1
1
1
2
1
0
1
2
1
2
1
0
1
2
2
2
1
1
0
0
1
1
1
1
0
1
1
1
1
2
2
1
2
1
1
2
2
2
1
1
1
1
1
2
1
1
2
1
1
0
2
1
1
1
0
0
1
1
1
1
1
0
1
0
2
1
1
1
0
2
0
2
2
1
1
1
2
2
2
2
2
1
0
1
1
1
2
1
1
0
2
2
1
1
0
0
1
1
1
1
1
2
1
2
1
1
1
0
1
0
1
1
1
3
1
1
1
0
2
1
1
2
0
1
2
2
1
0
0
2
1
2
1
2
1
1
2
1
2
2
2
2
1
3
2
1
1
2
1
1
1
0
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
0
0
2
1
1
0
2
0
1
1
6
2
2
1
0
1
1
1
2
0
2
1
0
1
2
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
2
0
1
0
2
2
0
2
0
1
1
0
1
0
1
2
1
1
1
1
1
2
1
0
0
1
2
1
1
2
1
2
0
1
1
1
2
0
0
1
1
0
1
1
1
1
1
1
1
1
1
2
1
2
0
1
1
1
2
1
0
0
0
1
1
1
1
1
1
1
2
0
1
0
2
2
2
2
2
1
1
1
1
2
5
1
1
2
2
2
1
0
0
1
0
2
1
0
0
1
0
1
1
0
0
4
1
0
0
1
1
0
0
1
1
1
1
0
1
1
3
2
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
2
2
2
1
2
1
2
1
1
2
0
1
0
2
1
2
1
2
1
1
2
1
1
1
1
1
1
1
1
0
0
2
2
1
0
1
2
1
2
1
1
2
2
1
2
0
2
2
0
2
1
0
1
1
0
0
2
2
0
1
2
1
1
1
2
1
0
1
1
1
1
1
2
0
1
0
1
2
2
1
1
1
2
2
0
1
0
2
1
1
0
1
1
2
1
0
2
1
1
2
1
1
2
0
2
1
1
2
1
0
2
0
2
1
2
1
0
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
0
1
2
0
0
2
0
1
2
1
1
1
1
1
1
1
1
2
1
2
1
0
1
2
1
0
1
0
2
0
1
0
1
1
1
1
0
1
0
0
1
0
1
1
0
1
1
1
1
1
1
2
2
1
1
1
0
1
0
1
1
0
1
0
2
2
1
1
1
1
1
1
0
0
0
1
2
2
1
1
1
1
1
1
1
1
2
1
1
1
2
2
0
1
1
1
2
1
1
2
1
1
1
1
1
0
1
1
1
0
1
1
1
1
1
3
2
1
1
1
1
2
1
0
1
1
1
2
1
2
0
1
1
1
1
1
2
1
1
1
2
1
1
1
1
2
1
0
1
1
2
0
2
2
1
2
2
1
1
2
1
0
1
1
2
2
1
2
0
0
1
1
1
1
0
1
2
1
0
1
1
0
0
0
1
2
1
1
1
2
1
1
2
1
1
0
1
2
2
1
1
1
1
0
1
2
0
2
2
2
1
1
0
1
2
1
0
2
1
1
1
1
1
1
1
0
0
2
0
2
2
2
2
1
0
1
1
1
1
1
2
2
1
0
0
1
2
1
2
1
1
1
1
1
0
1
2
1
1
2
2
1
1
1
1
2
1
1
1
1
2
1
2
0
0
1
1
2
0
0
1
1
2
2
1
0
1
2
1
1
2
1
2
2
2
2
0
1
1
0
2
1
1
2
1
0
1
1
1
1
0
0
1
2
2
1
1
1
1
1
0
1
1
2
1
1
1
0
1
0
3
0
1
1
1
0
2
0
2
1
1
2
2
1
1
0
1
1
1
0
1
0
0
0
1
1
1
2
2
1
0
1
1
1
1
1
0
1
0
2
1
2
2
1
1
0
1
1
1
2
1
2
2
2
1
1
1
1
1
1
1
1
2
0
1
1
1
1
0
1
2
2
1
1
1
1
0
1
2
1
3
2
1
2
1
2
2
1
1
1
2
2
0
2
1
1
2
1
1
0
2
1
1
0
1
1
0
1
1
0
0
1
0
1
0
0
2
3
1
0
2
1
0
1
0
1
1
2
2
1
1
1
1
1
0
1
1
0
1
1
0
0
2
1
1
1
1
1
1
1
2
1
1
1
2
1
1
2
1
2
1
0
1
2
1
1
1
1
0
1
0
0
1
1
1
1
2
1
1
2
2
0
1
1
1
0
0
1
2
2
1
1
1
0
0
1
0
1
4
0
1
0
2
1
1
1
0
0
2
0
1
2
1
1
1
0
1
2
1
1
2
1
1
2
1
0
1
1
2
1
2
1
1
1
2
1
1
1
2
1
1
1
1
0
0
1
0
1
0
0
1
0
2
2
1
1
2
0
0
1
1
1
1
2
0
2
1
1
1
2
1
2
1
1
1
1
1
1
1
0
1
2
1
1
1
1
1
0
1
1
1
2
0
2
1
1
1
0
1
2
1
1
1
0
0
0
2
1
1
1
1
2
1
1
1
1
0
1
1
2
2
2
0
1
1
1
1
1
2
1
0
2
2
2
2
0
0
1
1
0
1
3
0
0
1
0
0
2
2
1
1
3
2
2
1
1
2
1
1
2
0
1
2
1
1
1
1
0
1
0
4
2
2
1
2
1
1
1
1
1
2
1
1
2
2
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
0
1
1
0
2
1
1
2
1
2
1
2
1
2
1
1
2
1
2
1
1
1
1
2
2
1
0
1
2
0
1
2
1
2
1
1
1
2
0
1
2
1
1
1
1
1
1
1
1
1
0
1
0
1
2
2
1
2
2
1
0
1
1
1
3
2
1
1
1
1
1
0
0
1
2
1
0
1
1
1
2
1
1
1
1
1
1
1
1
2
2
1
1
0
0
1
1
2
1
2
1
2
2
2
2
1
1
1
0
1
1
1
1
1
1
1
1
2
0
1
0
0
1
2
0
2
0
1
1
1
0
1
1
1
1
2
1
2
2
1
1
1
2
1
0
2
1
1
0
1
2
0
1
1
1
1
1
1
1
1
2
1
1
1
0
1
1
2
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
2
1
1
2
0
1
2
2
1
1
1
1
2
0
1
1
2
0
1
1
2
1
1
0
0
2
1
2
0
2
0
1
1
2
1
1
2
2
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
0
1
2
1
1
0
0
0
0
0
1
1
2
2
0
0
2
0
1
1
1
1
1
1
1
0
2
1
1
1
2
2
2
1
0
1
1
1
1
2
1
1
1
2
2
1
1
1
2
0
1
0
1
1
2
1
1
1
2
1
1
1
1
2
2
2
1
1
0
1
2
1
1
0
1
1
1
1
1
2
1
1
1
1
0
2
1
2
1
1
1
1
1
1
1
1
1
1
2
2
2
1
0
1
1
1
2
1
1
2
1
1
1
2
1
1
1
1
2
1
0
1
1
1
1
0
1
0
1
1
1
1
1
1
1
2
1
0
1
2
1
1
2
1
1
0
2
1
2
1
1
1
2
1
2
2
0
0
1
2
2
2
2
1
2
0
0
1
0
1
2
1
1
0
1
0
1
1
1
1
1
0
1
0
1
0
3
1
1
2
1
0
3
1
4
1
1
0
2
1
1
1
1
1
1
2
1
1
1
2
1
1
0
1
1
1
1
1
2
1
0
1
1
2
1
4
1
2
1
1
2
0
2
1
1
2
0
1
1
0
1
0
1
1
1
1
1
1
0
1
1
1
1
1
1
2
2
1
1
2
1
1
0
1
0
1
1
1
1
1
0
1
1
1
1
1
1
0
1
2
2
1
1
1
0
1
1
0
1
0
1
2
1
2
1
1
1
0
1
0
1
2
1
1
1
1
1
1
1
2
1
2
4
1
1
2
1
1
1
2
1
0
1
1
3
2
1
1
1
1
1
1
0
1
0
2
2
1
1
2
1
1
1
1
1
1
2
1
1
0
0
1
1
1
1
2
2
2
1
1
2
1
2
2
1
0
1
1
2
1
0
2
1
2
1
2
1
1
1
1
2
2
2
1
1
1
1
1
1
1
2
0
1
2
1
0
0
2
1
2
2
4
1
2
1
1
1
0
1
1
1
1
2
2
2
1
1
1
2
1
1
0
1
1
2
1
1
2
1
1
1
2
1
1
1
0
1
1
0
1
1
1
1
1
1
2
0
1
1
1
4
1
2
1
1
1
1
2
1
1
0
1
2
2
0
2
1
1
1
1
0
2
1
2
1
1
1
1
1
1
2
2
2
1
1
2
1
0
1
2
0
2
1
1
1
2
2
2
2
1
1
0
2
1
0
0
2
0
1
1
0
1
1
0
0
1
2
0
2
2
1
2
2
2
1
2
1
1
1
2
1
2
1
3
2
1
1
3
1
0
1
1
2
1
0
1
1
2
1
1
1
2
1
1
1
1
0
1
1
1
0
2
2
2
2
1
2
1
2
0
1
1
1
1
0
2
2
1
1
1
2
1
1
0
1
1
2
0
0
2
0
1
0
2
0
1
1
2
1
1
1
2
2
1
1
2
1
2
0
1
1
2
3
1
1
1
2
2
1
1
2
2
3
2
1
1
1
0
1
1
2
2
2
1
0
1
1
0
2
1
1
1
2
0
1
2
1
1
1
3
0
1
2
2
2
2
2
1
2
1
0
1
1
1
2
1
1
1
2
1
1
1
0
2
1
1
0
2
2
1
0
2
1
1
1
1
1
1
0
1
1
1
1
1
1
1
0
3
1
0
1
1
0
2
0
1
2
0
2
2
0
1
2
2
0
2
1
0
1
1
2
1
0
0
0
1
1
2
1
0
1
1
1
1
2
1
1
1
1
1
0
2
2
2
1
1
1
1
0
1
2
0
1
1
2
1
1
1
2
1
2
1
2
1
1
2
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
0
1
1
1
2
1
1
0
1
1
0
1
1
2
0
1
2
1
1
0
1
1
0
2
1
2
1
1
1
1
0
1
1
2
2
2
0
2
1
1
1
2
0
1
1
2
2
2
1
2
2
1
2
1
1
1
2
1
2
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
2
2
0
1
2
2
2
1
1
1
0
1
2
1
2
1
2
2
1
1
1
1
1
1
1
1
2
2
2
1
1
2
2
0
1
0
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
0
2
1
1
2
1
2
0
1
1
2
0
1
0
0
1
1
1
2
1
1
2
0
0
1
3
0
2
1
1
2
2
0
1
1
1
1
1
1
0
1
1
2
1
1
1
0
1
2
1
2
1
1
1
2
2
1
2
1
0
0
1
2
1
2
2
3
1
2
1
1
1
1
1
0
2
1
1
1
1
2
1
1
1
1
1
2
3
1
1
0
1
1
0
1
2
1
1
2
1
0
1
2
1
1
1
2
0
1
1
0
1
1
1
1
1
1
2
1
1
1
0
1
2
1
1
2
1
0
2
1
0
0
1
1
3
1
1
1
1
1
1
2
0
1
1
2
1
1
2
1
1
1
2
1
1
1
1
1
0
1
1
1
0
2
2
1
1
0
1
1
1
2
0
1
2
0
2
1
2
2
1
1
0
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
0
2
1
2
1
1
1
1
1
1
1
0
1
1
1
1
2
0
1
0
1
2
1
1
0
1
2
1
1
1
0
2
1
1
1
2
1
1
1
1
2
1
1
0
1
0
2
1
1
2
1
2
1
1
1
1
1
0
1
1
0
1
1
2
1
1
1
1
1
2
0
1
1
0
2
2
2
2
2
1
2
1
1
0
1
0
2
1
1
1
1
1
0
1
0
1
1
2
1
2
1
1
1
1
1
1
0
1
0
2
1
2
1
2
2
0
1
1
1
1
1
2
1
1
0
1
1
2
2
1
1
1
1
1
0
1
1
1
2
2
1
0
2
0
0
1
1
1
1
1
1
1
2
2
2
2
1
1
0
2
1
1
1
1
0
1
1
2
2
2
2
1
2
1
2
2
1
1
2
0
1
1
0
2
1
1
1
1
1
1
3
0
1
1
1
1
1
1
1
0
1
1
2
1
1
2
1
0
1
1
1
1
0
1
0
2
1
2
1
1
1
1
1
2
1
1
1
0
1
2
2
1
1
1
0
1
0
1
1
1
0
1
1
1
1
1
2
1
1
0
1
2
1
2
1
1
1
1
2
0
1
2
2
1
1
1
2
2
2
0
0
0
1
2
1
1
1
1
2
2
1
1
2
2
2
1
2
1
1
1
1
1
1
2
1
0
0
2
2
1
1
2
1
0
2
1
1
0
1
1
2
2
2
1
1
3
1
1
1
1
0
1
0
1
1
1
1
0
1
1
1
1
1
0
2
2
2
1
2
2
1
1
1
2
2
1
1
1
2
1
0
2
1
1
1
1
0
1
0
0
1
1
2
0
1
2
1
1
2
2
2
4
1
1
1
1
0
2
1
1
2
2
1
2
1
1
0
1
1
2
1
0
1
1
1
1
1
1
0
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
2
2
1
1
1
1
2
1
1
2
1
1
1
0
1
0
1
2
0
2
1
0
1
1
1
2
1
1
1
1
1
0
1
1
1
1
1
2
0
1
1
1
2
0
1
1
1
0
1
1
1
1
1
1
1
2
1
1
2
1
1
2
1
1
1
0
1
1
2
1
0
0
1
1
1
1
0
2
2
1
2
3
2
2
1
1
1
1
1
1
1
3
1
1
2
1
2
1
1
1
1
0
2
1
1
1
1
0
2
2
1
1
0
0
1
1
2
0
2
0
0
1
1
1
1
1
0
1
2
1
1
1
1
2
1
1
1
2
2
0
0
1
2
2
1
2
1
1
1
2
1
1
1
1
1
2
1
1
0
1
0
2
0
1
0
1
1
2
2
1
1
1
1
1
0
1
2
0
1
1
2
3
2
0
0
2
1
1
1
2
0
1
1
1
0
1
1
2
5
0
2
1
1
2
2
1
1
1
1
1
1
1
0
2
0
0
2
1
1
0
1
1
1
0
1
1
1
0
0
1
1
1
2
0
1
1
1
1
2
1
1
1
1
1
1
2
3
1
2
1
2
1
0
1
1
1
1
0
1
1
0
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
0
1
0
2
1
2
1
1
1
1
2
1
2
1
1
1
2
1
0
0
2
2
1
1
1
0
1
1
1
1
1
2
1
2
0
1
1
2
1
0
1
0
1
1
1
1
2
0
2
1
1
2
0
2
1
1
2
2
1
1
1
1
2
1
0
2
1
1
2
1
1
0
1
1
0
1
1
1
1
1
3
1
1
1
2
2
1
1
0
1
0
1
0
0
1
0
1
2
1
1
0
2
1
1
1
2
0
1
1
2
1
2
0
2
1
2
1
1
1
1
1
2
1
1
1
0
1
1
2
1
1
1
2
2
1
1
0
1
0
1
1
1
1
0
1
2
1
1
2
1
1
0
2
1
1
1
1
1
0
0
2
2
1
1
2
0
2
0
2
1
1
1
1
1
1
1
2
2
1
1
1
1
0
2
1
1
1
1
3
1
3
1
2
1
1
1
1
2
1
1
1
1
2
0
1
2
1
0
1
1
1
1
1
2
1
0
0
1
1
2
1
1
1
1
1
2
2
1
0
1
1
2
0
1
2
1
1
2
0
1
1
1
1
2
1
1
2
1
2
1
0
2
0
1
1
1
2
1
1
1
1
2
0
1
0
1
1
1
1
2
1
1
2
0
1
1
1
1
1
0
2
2
1
0
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
0
0
0
1
1
1
1
2
1
0
1
2
1
1
1
1
2
2
1
1
1
0
1
0
2
0
2
2
1
2
1
1
1
2
1
1
0
1
0
2
2
1
1
0
1
1
0
1
1
1
0
1
2
1
1
0
1
1
0
2
2
0
2
2
1
0
2
1
1
2
1
2
1
1
1
1
0
1
2
1
1
2
0
2
0
1
2
1
1
1
2
3
1
2
1
1
2
2
1
1
0
2
1
1
1
0
1
1
0
1
0
2
0
1
1
1
2
1
1
1
0
2
1
1
2
1
1
2
0
2
1
1
2
1
2
1
2
1
1
1
0
2
1
0
1
1
2
1
0
0
1
1
1
1
2
1
0
2
2
2
1
0
1
1
1
1
0
1
1
1
1
1
0
1
1
1
0
1
2
1
1
1
2
0
1
1
1
1
2
0
1
1
1
1
3
2
2
1
2
0
1
1
2
1
1
2
1
1
0
2
0
1
1
2
1
1
1
2
1
1
0
2
2
1
0
2
1
1
2
1
1
1
1
0
0
2
2
0
1
1
1
1
2
1
1
1
2
1
1
0
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
0
1
1
1
1
2
1
1
1
2
2
0
1
2
2
1
1
2
1
2
0
1
1
2
1
0
1
1
1
2
0
2
1
1
2
1
0
0
1
1
1
0
1
2
1
1
1
0
2
3
1
0
0
1
1
1
2
0
1
1
1
2
2
2
2
0
0
1
0
0
0
1
1
1
0
1
1
1
1
1
1
0
1
1
0
1
2
1
1
0
1
1
0
1
1
1
1
1
1
2
1
1
0
2
1
1
1
0
1
1
3
1
1
1
2
0
1
0
1
0
1
1
2
1
1
0
0
2
2
0
1
2
0
0
1
2
1
1
1
1
1
1
2
2
2
2
1
0
2
0
2
1
2
0
2
0
2
1
1
1
0
1
1
0
1
1
1
2
1
1
1
1
1
1
0
2
3
1
1
1
2
0
1
0
1
1
1
1
0
2
1
1
1
1
1
1
0
1
2
1
1
2
0
1
1
1
0
3
3
3
2
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
2
1
0
0
0
1
1
1
1
1
1
1
0
1
2
0
1
0
1
2
1
1
2
1
1
1
1
1
1
1
1
1
0
1
2
1
2
1
1
0
1
0
1
1
2
1
1
0
1
0
1
1
1
1
1
0
1
1
1
2
1
2
0
1
1
2
2
2
1
0
1
0
1
2
1
2
1
0
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
0
0
0
1
2
1
2
2
1
1
2
1
1
2
1
0
1
1
2
2
1
2
1
1
1
0
1
1
2
1
1
0
1
2
2
10
1
0
1
1
1
0
1
1
2
0
2
1
1
0
1
3
1
1
1
2
0
2
1
0
1
2
0
1
2
0
0
2
1
0
1
1
0
1
2
2
2
2
2
0
1
2
1
2
1
1
0
2
1
1
1
1
1
1
1
1
1
1
2
0
1
1
0
1
1
1
1
1
1
1
1
1
1
1
0
2
2
1
0
1
1
0
1
1
2
1
1
2
1
1
0
2
5
0
1
1
1
1
1
0
1
0
2
1
0
1
1
0
1
2
1
2
0
2
0
1
0
2
1
0
1
1
1
0
2
1
0
2
1
1
1
1
1
0
1
2
2
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
0
1
1
0
1
0
0
1
1
1
1
1
0
1
0
1
0
1
0
1
0
1
2
1
0
0
1
3
1
0
1
2
1
0
1
1
1
2
0
3
0
1
1
0
1
0
1
1
0
1
2
0
0
1
1
2
1
2
1
1
1
0
1
0
1
1
1
3
1
1
1
2
1
2
2
2
1
1
2
1
1
2
1
2
1
1
0
0
0
2
1
1
1
0
1
0
1
1
1
1
3
0
0
1
1
1
1
1
0
0
1
0
2
2
2
1
2
0
0
1
1
2
1
0
1
1
2
0
0
1
2
2
1
1
2
2
0
1
2
0
1
2
1
1
1
1
1
1
0
1
1
1
1
1
1
0
1
1
3
0
2
2
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
0
1
2
0
2
0
1
1
1
1
1
1
1
1
0
0
1
0
1
0
1
0
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
0
0
0
1
0
1
1
1
1
0
2
1
1
1
1
2
1
1
0
1
1
1
1
1
0
2
1
1
1
1
1
1
1
2
1
1
2
0
2
0
1
0
2
0
1
1
1
2
2
1
0
1
1
1
1
0
1
1
2
1
1
1
0
2
1
1
1
0
1
1
0
1
1
1
0
0
1
1
2
2
1
1
1
1
0
2
1
2
2
0
0
0
2
1
1
1
1
1
2
1
0
1
2
1
1
2
0
1
1
1
2
1
1
1
1
2
1
0
1
2
2
2
2
1
1
0
3
1
1
1
1
1
2
1
1
0
1
1
2
1
0
2
1
1
1
1
1
1
0
0
1
1
0
1
1
2
1
1
1
0
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
0
0
1
1
1
0
1
2
1
2
1
2
2
2
1
1
1
2
1
2
1
0
0
0
2
1
1
2
1
0
0
1
2
1
1
1
2
1
1
1
1
1
3
0
1
1
1
1
1
1
2
1
2
1
2
2
0
1
1
1
1
2
0
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
0
1
0
1
0
2
1
1
1
1
1
0
1
1
1
0
2
2
1
1
1
1
1
2
0
1
1
1
2
1
1
1
0
1
0
1
2
1
2
2
0
0
1
0
0
2
1
1
1
1
1
1
1
0
1
1
1
1
1
1
0
1
1
1
2
1
2
1
2
1
0
0
1
2
1
2
0
1
0
0
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
1
0
2
2
1
1
1
2
1
0
1
1
0
1
1
0
0
2
1
0
2
1
2
2
1
1
1
2
2
0
0
1
1
1
0
0
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
0
0
1
1
2
0
1
0
1
1
2
0
1
2
2
2
2
1
0
0
1
0
1
2
1
1
2
1
1
1
2
1
2
1
2
2
1
1
1
1
2
0
1
0
0
1
1
0
0
0
1
2
2
1
2
1
1
3
1
1
2
1
0
1
1
0
1
0
1
1
2
0
2
3
1
1
2
1
2
2
2
1
1
2
1
2
0
1
1
1
1
0
1
2
1
1
2
1
1
2
1
0
1
3
1
1
1
1
1
1
0
0
1
0
1
1
1
2
0
1
1
1
1
0
2
2
2
1
1
1
1
1
1
2
1
0
2
1
2
1
1
1
0
1
1
1
1
1
2
1
1
1
0
1
1
1
1
1
1
2
1
1
0
1
0
2
2
1
1
1
2
1
2
0
2
1
1
1
1
2
1
1
1
1
2
2
1
0
2
0
0
1
2
4
1
1
1
0
1
2
2
1
0
1
2
0
0
0
1
0
2
1
1
1
1
1
1
1
2
2
1
0
2
1
1
1
1
1
1
2
1
0
0
1
0
0
1
2
1
1
1
1
2
1
1
1
1
1
2
1
2
1
1
2
2
2
2
1
1
1
1
2
1
0
1
1
1
2
0
0
2
1
1
1
1
2
2
0
2
1
2
1
1
1
2
0
2
1
1
0
1
0
0
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
2
1
1
0
0
1
1
1
1
0
1
0
0
0
1
1
2
1
1
2
1
1
2
2
0
2
2
0
1
0
1
0
1
2
1
1
1
1
1
0
0
1
1
1
1
1
1
2
1
1
1
1
2
1
2
0
2
1
1
0
2
0
2
2
1
1
0
1
0
1
1
1
0
1
1
1
2
2
0
1
1
1
0
1
1
2
1
1
0
0
1
1
1
2
1
1
1
1
1
1
1
2
0
1
0
1
1
0
0
1
1
0
0
1
0
1
1
1
1
1
0
1
1
0
2
1
1
1
1
1
2
0
1
1
2
1
2
1
1
1
1
0
1
1
1
1
3
1
2
2
1
1
1
1
1
1
1
1
1
1
0
1
1
1
0
1
1
1
2
1
1
2
2
2
1
1
2
1
1
2
0
2
1
1
1
1
2
0
2
1
1
2
1
1
2
1
2
2
0
1
1
2
0
2
1
1
1
1
2
1
1
1
0
1
0
2
1
2
1
0
1
2
2
2
2
2
1
1
0
1
2
1
1
2
1
1
1
1
1
0
1
1
1
1
2
2
2
1
1
0
1
2
1
1
2
1
0
1
1
1
1
1
1
0
1
1
2
1
1
1
1
2
1
0
1
1
1
1
0
2
1
1
1
1
2
1
1
0
0
2
1
1
0
0
0
1
1
0
1
1
1
2
1
1
2
1
2
1
1
1
1
1
2
1
1
2
2
1
1
1
1
1
2
0
2
2
1
1
2
1
2
1
1
1
2
0
2
1
0
1
1
0
2
1
1
2
1
2
1
0
0
1
1
0
0
1
2
1
1
1
1
1
1
0
0
1
1
1
2
1
0
1
1
1
1
2
1
1
1
1
1
1
1
2
0
0
1
1
1
1
1
0
1
1
1
2
1
1
1
1
0
0
1
1
0
1
1
0
1
2
0
0
2
3
0
2
1
1
1
1
1
1
1
1
1
0
2
1
1
0
1
0
1
2
2
1
1
1
0
1
1
1
1
2
0
1
1
1
0
2
1
1
0
2
1
2
0
2
1
1
3
1
0
2
2
0
3
1
1
1
0
1
2
0
1
1
1
1
2
0
1
0
1
1
2
1
1
1
1
1
1
1
1
0
1
0
2
1
1
1
2
1
0
1
0
1
2
1
2
1
1
2
1
1
1
1
1
0
1
1
0
0
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
2
1
1
1
1
1
0
1
0
2
1
1
2
2
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
1
2
2
2
2
0
0
2
1
1
1
1
1
1
1
1
1
1
1
0
1
2
2
1
1
0
2
0
1
1
1
1
1
1
0
2
2
1
1
1
0
1
2
2
1
1
2
0
2
0
0
1
2
2
1
0
2
1
2
1
2
0
1
1
1
2
1
2
3
1
1
2
1
1
1
1
1
1
1
0
2
2
2
1
1
1
2
1
1
2
1
1
1
1
2
1
2
1
1
1
1
2
2
1
0
2
0
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
0
1
1
4
0
1
0
1
1
1
0
1
1
1
1
0
1
0
0
1
2
2
2
1
1
1
1
0
0
1
1
1
2
2
1
1
0
1
2
1
1
1
1
1
1
2
2
1
1
1
2
1
1
0
1
1
2
1
1
1
1
2
0
0
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
0
1
2
1
1
2
1
1
0
2
1
1
2
1
0
2
1
1
1
1
0
1
2
1
1
1
2
0
1
2
0
0
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
1
1
2
1
1
2
2
1
2
2
0
0
2
1
1
1
1
1
1
0
0
2
1
1
0
0
1
2
2
1
1
2
1
0
1
1
2
0
1
1
1
2
1
1
2
1
2
2
2
1
1
1
1
1
0
1
1
1
2
1
1
1
0
1
2
1
1
1
0
2
1
1
0
2
2
1
1
1
1
2
1
2
2
2
1
1
0
1
2
2
0
2
1
1
2
0
0
2
1
1
2
1
0
1
2
1
1
1
1
1
1
1
1
1
2
2
1
2
1
1
2
1
1
1
1
1
1
1
0
1
1
2
1
0
1
1
2
2
1
0
2
1
0
1
1
1
1
2
2
1
0
1
1
0
0
0
1
2
1
1
1
1
1
2
1
1
2
1
1
1
2
3
2
2
1
2
2
1
1
1
0
1
1
1
3
3
1
0
2
2
1
2
1
1
1
2
0
1
1
1
1
2
0
1
1
1
1
1
1
2
2
2
1
1
0
1
1
1
1
2
0
2
1
1
1
1
1
1
1
2
2
1
1
2
1
2
2
1
0
1
2
1
2
1
2
2
1
1
0
2
0
1
1
1
1
1
2
1
0
2
2
2
0
2
1
0
1
1
2
1
1
1
1
0
2
1
1
0
1
1
1
1
1
0
0
1
1
1
1
1
0
1
2
2
1
0
2
1
1
1
0
2
0
1
1
1
1
1
1
2
1
2
1
1
1
0
2
1
0
1
1
2
1
2
2
1
0
1
2
2
2
0
1
1
2
0
1
2
0
2
1
1
1
1
0
1
1
2
0
1
0
1
2
0
1
0
1
1
1
1
2
2
1
0
1
1
1
1
1
1
0
0
2
0
1
1
1
1
1
1
1
0
1
0
1
1
1
2
2
0
2
0
1
1
2
2
1
0
0
2
1
1
1
1
1
1
3
2
2
2
0
0
0
1
1
2
1
1
1
2
1
0
0
1
1
2
0
1
1
2
1
1
0
2
1
1
1
2
1
1
1
2
0
1
1
1
1
1
1
2
1
2
2
2
0
1
1
2
1
1
1
1
1
1
2
1
1
1
1
0
1
0
2
1
2
1
1
0
1
1
0
1
1
1
0
0
1
1
1
2
1
2
1
0
0
2
2
0
1
1
1
1
0
1
1
1
1
2
2
2
1
1
0
0
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
0
1
0
1
1
2
1
1
1
1
1
1
0
1
1
1
1
1
1
1
2
1
1
0
1
1
0
1
1
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
2
1
0
0
1
1
0
2
2
1
0
1
1
1
2
0
1
3
1
1
1
1
0
1
2
1
1
1
1
0
1
1
1
2
0
1
1
2
2
1
0
1
1
1
2
1
2
2
1
2
1
0
1
1
1
1
2
1
0
3
2
0
1
1
2
1
1
0
0
2
0
1
1
2
0
1
2
1
1
0
1
1
1
0
1
0
1
1
2
0
1
1
1
2
1
1
2
1
1
1
1
0
2
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
0
1
1
1
1
1
1
2
2
0
1
1
1
1
1
1
1
2
1
1
2
0
1
2
0
0
1
0
1
1
1
1
2
1
1
1
0
1
1
1
2
1
1
1
1
0
0
0
1
2
1
1
1
1
1
2
1
2
1
1
2
0
2
1
1
2
2
2
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
2
2
1
1
1
2
1
1
1
1
0
1
1
0
0
1
0
2
1
1
1
1
1
1
1
1
2
0
2
0
0
2
1
2
0
1
0
1
2
1
1
2
1
1
2
1
0
1
2
1
1
1
1
1
0
2
1
1
2
1
0
1
2
2
1
1
0
1
1
1
1
1
0
2
2
1
2
0
2
1
1
2
1
2
1
1
1
1
2
2
1
1
1
2
2
0
0
2
0
1
1
1
1
1
2
1
1
1
0
1
2
2
2
2
1
2
1
2
0
1
1
2
1
1
1
2
1
2
1
1
0
2
1
1
2
3
2
2
1
2
2
1
0
0
1
1
1
4
0
0
1
2
1
1
0
0
2
3
0
2
1
1
2
1
1
0
0
2
2
2
2
2
2
0
1
1
2
0
0
1
1
1
1
0
0
2
1
2
2
1
2
1
2
2
2
1
1
0
0
2
2
1
0
1
2
1
1
2
1
0
1
1
1
1
2
3
1
1
1
0
1
2
1
2
1
1
1
0
1
1
2
0
1
1
2
1
2
1
2
1
0
2
1
1
2
2
1
1
1
1
1
2
1
2
1
0
4
1
1
2
0
1
2
1
1
1
1
1
3
1
2
1
1
0
0
2
2
0
1
0
1
2
1
1
2
2
2
0
1
1
2
1
1
1
1
0
1
2
1
2
1
1
0
1
1
2
1
1
1
0
1
1
1
0
1
1
1
2
1
1
1
0
0
2
2
4
1
1
1
1
1
2
1
2
8
1
2
0
1
2
0
1
2
1
1
2
2
1
2
0
0
1
1
1
1
1
2
1
0
1
1
1
1
1
1
1
2
1
1
0
1
0
1
1
1
1
1
1
0
2
1
1
2
2
0
1
1
1
1
2
1
1
2
2
1
1
1
0
2
1
1
2
2
1
2
2
2
1
2
2
0
2
2
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
2
1
0
1
1
1
1
1
1
2
1
2
0
1
1
1
1
2
1
0
2
1
2
0
2
0
1
1
1
1
1
1
1
2
1
0
2
1
1
1
2
1
2
1
1
1
1
1
2
2
0
1
1
1
1
2
2
0
1
1
1
1
2
2
0
1
2
2
0
2
1
0
0
1
0
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
0
2
1
1
0
2
1
2
2
1
2
2
1
2
1
1
1
0
1
2
2
0
1
1
1
1
2
1
1
1
0
1
1
1
1
2
1
1
2
1
2
1
2
1
1
1
2
1
1
1
1
2
3
1
1
1
1
2
1
2
2
0
1
1
1
0
0
1
1
0
1
0
0
0
1
1
1
1
1
1
0
1
0
1
1
1
2
1
3
1
0
0
1
1
1
1
0
1
0
1
0
1
2
0
1
1
2
1
2
1
1
1
2
1
1
1
0
0
1
1
2
2
2
0
2
1
2
1
1
0
0
2
1
1
2
1
2
1
0
1
1
1
1
0
2
1
0
1
1
0
1
2
1
2
2
1
1
1
0
1
2
1
2
1
0
1
1
2
0
0
1
2
2
1
1
1
1
2
0
2
1
2
0
1
2
1
1
0
2
1
2
1
2
1
1
1
1
2
1
2
1
1
1
0
1
1
1
1
2
0
1
1
0
1
1
1
1
2
2
1
2
0
0
1
0
1
1
2
2
1
2
1
2
2
1
0
2
1
1
1
2
1
1
1
0
1
1
0
1
1
0
2
3
1
1
1
2
2
1
1
0
1
1
2
1
1
1
2
2
1
1
1
2
1
0
1
1
1
2
1
1
0
1
1
1
1
1
1
1
1
2
0
2
1
1
1
1
1
1
1
1
0
1
0
1
1
0
1
1
1
1
0
1
1
1
1
1
2
1
1
2
1
0
1
1
0
2
1
1
1
1
0
2
1
0
1
1
0
1
2
1
0
2
2
1
2
1
1
0
1
1
1
1
2
1
1
0
1
1
2
2
0
2
1
1
1
2
0
1
1
1
1
1
1
0
2
1
1
1
0
1
1
1
1
1
0
1
1
1
0
0
1
1
1
2
1
2
1
2
1
1
2
1
1
2
1
1
1
1
2
2
1
1
2
1
0
1
0
1
2
1
0
1
1
1
2
1
0
1
1
1
0
1
1
1
0
0
0
1
2
1
0
1
1
1
1
1
1
0
1
2
1
2
2
1
0
1
1
2
0
1
1
1
1
0
1
0
0
2
1
0
2
1
0
2
0
1
0
1
1
1
1
0
2
1
2
2
1
2
0
1
1
1
1
1
1
1
0
0
1
2
1
1
0
1
1
2
1
1
2
2
2
1
1
0
1
1
2
1
1
1
2
1
1
1
0
1
1
1
0
2
1
1
1
1
0
1
1
1
0
1
1
1
0
1
0
1
1
1
2
2
1
1
2
1
2
1
1
0
1
1
0
1
1
1
1
1
1
2
1
0
1
0
2
0
1
1
1
1
2
0
1
1
0
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
0
1
3
0
0
1
1
1
1
0
1
1
2
0
1
1
2
1
1
2
2
1
1
1
0
2
1
2
1
1
0
1
1
2
0
1
1
0
1
1
2
1
2
1
1
1
2
1
1
1
2
1
1
3
2
1
1
0
1
1
1
0
1
1
1
1
1
1
1
1
2
1
2
2
2
0
1
0
1
1
2
0
2
1
3
1
2
0
2
1
2
0
1
1
1
1
1
1
1
1
1
1
0
0
0
1
1
1
1
2
2
2
1
2
1
0
1
1
1
1
1
1
1
0
2
1
1
0
1
3
1
1
1
1
1
1
0
1
0
4
1
1
2
0
1
1
2
1
1
2
0
1
0
0
2
1
1
1
1
2
1
1
0
1
2
2
0
2
2
0
1
1
1
1
0
2
2
1
1
2
1
1
1
2
1
0
1
0
2
1
1
2
1
1
1
0
1
2
0
1
1
0
0
2
1
0
1
1
1
1
1
2
0
0
1
1
2
2
2
1
1
1
1
1
1
1
1
2
0
2
0
1
1
1
2
1
1
0
1
1
2
1
2
0
1
0
2
2
2
0
0
1
0
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
2
0
0
1
1
0
1
2
1
1
1
1
2
0
1
1
1
1
0
0
1
1
2
1
1
1
1
1
2
0
1
2
1
1
2
0
1
1
1
1
2
0
1
1
0
1
0
3
1
1
2
1
1
1
1
0
1
3
1
1
0
1
1
0
1
2
1
1
0
1
1
2
2
1
0
2
1
1
1
1
1
1
1
1
1
1
1
1
0
0
2
1
1
1
1
1
1
1
1
2
1
2
0
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
0
2
1
0
1
1
1
1
1
2
1
0
2
1
1
1
2
2
3
2
1
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
1
0
1
1
0
0
1
1
1
1
2
1
1
2
0
1
1
1
1
2
0
2
1
2
1
2
1
1
1
2
1
2
1
0
2
0
0
2
2
1
1
2
2
2
0
0
0
1
1
2
1
2
0
1
1
1
1
1
2
1
2
1
0
0
1
2
0
1
1
2
0
1
2
1
2
1
0
1
1
1
2
1
1
1
0
0
1
1
2
1
1
1
1
1
1
0
2
1
0
0
1
1
1
1
0
0
1
0
1
1
1
2
1
1
1
2
1
1
1
0
1
2
1
1
2
1
2
1
1
3
1
1
0
0
1
2
1
0
1
0
0
2
1
0
1
1
1
1
0
0
1
1
1
2
1
2
2
2
2
1
1
2
0
1
0
1
1
0
1
1
1
1
1
0
1
1
2
1
0
1
0
2
2
1
1
1
1
1
1
1
0
1
1
1
1
1
1
0
2
2
1
1
1
0
1
1
1
1
2
0
1
1
2
1
1
1
1
1
0
2
1
1
1
2
1
1
1
0
2
1
0
0
2
1
1
1
1
2
1
2
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
0
2
1
3
2
1
0
1
1
2
0
0
1
1
2
0
1
2
1
2
0
1
1
2
1
1
0
1
0
1
2
0
2
1
2
1
1
1
2
1
2
1
1
1
1
1
0
1
1
1
1
1
1
2
1
0
0
1
1
0
1
2
0
2
1
2
1
1
1
1
1
1
3
1
1
1
2
1
1
1
1
1
1
1
1
0
2
1
1
2
1
1
1
1
2
1
0
0
1
2
1
2
2
1
1
1
3
2
1
1
2
1
1
1
1
1
1
1
1
1
0
0
1
1
1
1
1
2
1
2
1
1
1
1
0
1
1
1
0
1
0
1
0
2
1
1
0
1
0
0
1
1
0
2
1
0
1
2
3
1
1
1
1
1
2
1
1
1
1
1
2
1
2
1
2
1
1
1
1
1
0
2
1
1
2
0
1
0
2
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
2
2
1
1
1
1
1
2
1
1
0
1
0
0
1
0
2
1
1
2
1
1
1
2
0
1
2
0
0
1
1
1
1
1
2
0
2
0
1
1
0
1
2
1
0
1
1
0
1
1
1
1
1
1
2
1
1
1
1
2
1
1
0
0
1
0
2
2
1
1
1
2
1
1
1
1
2
2
1
2
1
1
2
1
1
1
0
0
1
1
1
1
1
1
1
0
1
2
2
1
1
1
1
1
1
1
0
2
1
1
1
2
2
1
1
2
0
0
1
0
1
1
2
1
2
2
2
0
2
1
2
1
1
1
1
1
1
0
1
1
1
1
1
0
2
2
1
1
2
4
1
2
1
1
1
1
1
2
2
2
1
1
2
1
0
1
0
1
1
1
0
2
1
2
2
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
4
1
1
1
1
1
1
0
1
2
1
1
1
1
1
2
1
1
2
1
1
1
0
1
1
1
1
2
1
2
1
2
0
1
1
2
2
2
1
3
0
1
1
1
1
2
1
1
2
1
2
1
2
2
1
2
2
0
2
1
1
1
1
1
2
0
1
1
1
1
0
1
2
1
1
1
2
0
2
1
0
2
1
1
2
0
1
1
2
2
1
1
1
2
2
2
1
1
0
2
2
2
2
2
2
1
1
2
0
2
1
1
1
1
2
2
1
1
2
0
3
1
1
0
0
1
2
1
1
1
2
0
1
1
2
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
0
2
1
1
1
2
1
1
2
0
1
0
2
1
0
1
1
1
2
1
0
1
1
1
2
1
2
0
1
0
1
1
0
1
0
2
1
1
1
0
1
1
2
2
0
1
1
1
0
2
1
1
1
0
2
2
3
0
1
1
1
0
0
2
2
2
2
1
2
2
1
1
2
1
0
1
1
1
1
1
2
0
2
0
1
0
2
1
1
0
1
1
1
1
1
2
1
1
0
1
2
1
1
1
1
1
2
1
1
1
1
2
1
2
1
1
2
0
0
1
1
2
1
0
2
0
1
0
2
1
0
1
0
1
2
2
1
1
1
1
1
1
0
1
1
2
1
0
2
0
1
1
0
0
1
1
1
1
0
0
1
1
1
1
1
1
1
2
2
1
2
2
0
1
1
1
1
1
1
1
0
1
0
1
2
3
1
1
2
1
1
1
3
1
1
1
0
2
1
2
2
1
0
1
2
1
1
1
0
2
1
1
0
1
2
1
1
1
1
1
1
2
1
1
3
2
1
1
0
0
2
1
1
0
4
0
1
1
1
2
1
1
1
1
1
0
2
0
0
0
2
1
0
1
2
2
1
2
1
1
2
2
1
1
2
1
1
1
1
1
1
2
1
2
1
2
0
1
1
1
1
1
1
1
2
0
1
0
3
0
1
0
2
0
1
1
1
1
1
1
0
2
0
1
1
1
1
0
1
0
1
1
1
1
1
1
0
2
0
2
1
1
2
2
1
1
2
1
2
2
2
1
2
1
1
1
1
1
1
1
1
1
1
0
1
2
1
1
1
0
2
2
2
0
2
1
0
1
2
1
1
0
1
1
0
0
2
1
1
2
2
0
0
1
1
0
1
2
1
2
1
1
2
1
1
0
1
1
0
1
1
1
1
0
2
1
1
1
1
0
0
1
1
1
1
1
2
1
2
2
2
1
0
1
1
1
1
1
2
1
1
2
2
2
1
1
2
1
1
1
0
1
1
0
1
1
1
1
1
1
2
1
1
1
2
2
1
2
1
0
1
1
1
0
2
1
1
2
1
1
1
1
1
1
0
0
1
1
1
2
1
1
1
1
0
0
1
1
1
1
0
1
1
1
1
2
1
2
1
1
1
0
2
1
1
0
1
1
2
1
0
1
2
0
1
1
1
2
2
2
1
1
0
1
2
1
1
2
1
0
2
1
1
1
1
0
1
1
1
2
1
1
1
1
1
1
1
0
1
1
1
1
0
0
1
1
1
2
0
1
2
1
0
0
1
2
1
0
0
1
1
1
1
1
2
1
2
1
0
1
2
1
1
1
1
0
0
1
2
2
2
1
1
2
1
1
1
1
2
1
2
1
1
1
2
1
1
2
1
1
1
1
1
1
0
0
1
1
0
1
1
1
2
2
1
0
1
1
1
1
0
1
0
2
1
1
1
2
2
1
1
1
0
2
1
1
1
1
1
2
1
1
2
1
2
1
1
0
0
1
1
2
1
0
2
1
2
1
0
2
2
0
0
1
2
2
0
1
0
1
1
0
1
2
1
1
1
1
1
0
0
0
1
1
2
1
1
1
1
0
1
2
1
2
0
0
2
2
1
2
3
0
1
1
1
1
1
1
2
1
0
0
1
1
1
2
1
2
1
2
2
1
2
2
1
1
2
2
1
1
1
1
0
2
0
1
2
1
1
1
1
1
1
1
1
2
1
0
1
1
1
1
2
1
1
1
2
0
1
2
1
1
1
1
1
1
1
1
1
1
1
3
2
1
1
1
1
1
1
1
1
0
1
2
1
1
1
1
2
1
1
1
2
1
1
1
0
1
1
2
1
1
1
1
2
1
2
0
1
0
2
1
2
2
1
2
0
2
0
1
1
1
1
1
2
2
1
1
2
1
1
0
1
1
0
1
1
2
1
2
1
2
1
0
0
1
1
0
1
2
1
1
0
1
1
1
1
1
0
2
1
1
0
0
1
1
4
1
0
0
1
2
1
2
1
1
1
2
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
0
0
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
2
0
1
1
1
2
2
1
1
1
1
1
2
1
1
0
1
2
3
1
0
0
1
1
1
0
1
1
2
1
0
1
1
1
0
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
0
1
3
1
0
1
0
1
1
1
1
1
0
1
1
1
2
1
0
2
1
1
1
1
1
2
1
1
1
2
0
1
1
3
1
2
2
1
2
0
2
1
0
1
1
2
0
1
2
1
1
1
1
1
1
1
2
1
0
1
2
0
0
1
2
1
1
2
2
1
1
1
0
1
2
1
1
0
1
2
1
1
1
1
1
2
1
1
2
0
1
0
1
2
1
2
1
1
2
2
1
1
1
2
1
1
1
0
2
1
0
0
1
1
0
0
1
0
1
1
0
2
2
1
0
2
1
1
1
1
1
1
1
1
2
0
0
2
1
2
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
2
2
2
1
0
0
0
0
2
1
1
1
0
2
2
0
1
2
2
2
1
2
1
1
1
1
0
2
1
2
1
1
1
1
2
1
1
1
1
1
1
0
1
1
1
2
1
1
2
0
1
2
1
1
1
2
1
1
0
1
3
2
1
1
1
0
2
1
0
1
2
0
1
0
1
0
0
1
1
0
0
1
2
0
1
1
1
0
2
0
1
1
1
1
1
1
0
0
2
1
2
1
1
1
0
1
0
2
1
1
2
1
1
0
2
2
2
1
0
0
1
1
1
1
1
2
1
2
1
1
1
2
1
1
1
2
2
1
1
1
2
1
1
1
0
1
1
1
2
1
0
1
1
1
1
1
1
1
1
2
1
2
3
1
2
0
1
1
0
2
2
1
1
2
2
1
0
2
1
2
2
1
0
2
1
1
1
0
1
1
2
0
1
1
1
0
1
1
2
2
1
1
0
1
1
0
1
0
1
1
2
1
1
1
2
2
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
5
2
1
0
2
1
2
1
1
2
2
0
1
0
1
1
1
2
2
2
1
1
1
1
1
2
0
1
1
1
1
1
1
0
1
1
0
1
1
1
1
1
1
1
1
1
0
1
1
1
2
1
0
1
2
1
1
1
2
1
1
1
2
1
0
2
1
1
1
1
1
0
1
1
2
0
1
1
2
1
1
2
0
1
1
1
2
1
0
1
1
1
1
1
1
0
1
1
2
1
1
2
1
1
1
1
1
2
2
1
2
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
0
2
1
2
1
2
1
1
0
1
1
0
1
1
2
3
1
1
1
2
2
0
0
2
1
1
2
1
2
2
1
1
1
1
1
1
2
1
0
1
1
1
3
2
2
1
1
3
0
1
2
0
0
1
0
1
1
1
1
1
2
1
2
0
1
0
1
0
0
2
2
1
3
1
1
1
1
1
2
1
0
2
1
0
1
1
1
1
0
0
0
1
1
1
2
2
1
1
0
1
2
0
1
0
2
1
1
1
0
2
1
1
1
1
0
0
2
1
1
1
1
1
1
1
0
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
0
1
1
1
1
0
0
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
2
2
1
1
1
1
1
1
2
2
1
1
2
2
1
2
1
1
1
0
1
1
2
1
1
2
1
0
2
1
2
1
1
1
1
2
0
2
1
0
0
2
1
2
1
1
2
1
1
1
2
2
2
1
1
2
1
0
1
1
1
0
1
1
2
1
1
1
2
1
2
1
1
1
2
0
1
2
2
1
0
2
0
1
1
1
1
1
2
2
2
2
1
1
1
1
1
2
0
1
1
0
1
2
2
1
1
2
1
1
1
1
2
0
2
1
0
2
1
0
1
1
1
0
1
1
2
0
1
1
1
1
1
2
2
1
1
1
2
1
2
2
2
0
1
1
1
0
1
1
0
1
2
0
1
2
2
1
0
1
2
1
2
2
0
1
0
1
2
1
1
2
0
1
1
2
1
1
1
0
1
1
1
1
1
1
2
2
1
1
1
0
1
0
1
2
1
1
2
0
1
2
2
1
0
1
0
0
2
3
1
2
1
0
0
2
1
1
0
1
1
1
2
1
1
1
1
2
0
1
1
1
1
1
2
1
0
1
0
1
2
1
1
0
1
2
0
2
2
1
0
1
2
0
1
2
1
2
1
1
0
1
2
1
2
1
2
1
1
0
0
1
2
1
2
1
0
0
2
1
1
0
0
1
1
1
1
1
0
1
2
1
0
2
1
2
1
1
1
2
0
2
2
2
0
0
1
1
1
1
2
1
1
1
1
0
2
2
3
1
0
2
2
2
1
1
1
2
0
0
2
2
1
2
1
2
0
2
1
1
2
1
1
1
1
1
2
2
2
1
1
1
1
1
2
2
1
2
2
1
0
1
1
0
1
1
2
1
0
1
1
1
1
1
1
1
0
2
2
1
0
1
2
2
2
1
1
0
1
2
1
1
2
3
2
2
1
0
0
2
2
1
1
1
1
1
1
1
1
0
0
1
1
2
2
1
1
2
2
0
2
2
2
2
1
1
1
0
0
1
1
0
1
1
1
1
2
1
2
1
1
1
1
2
0
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
2
1
1
1
0
1
2
0
1
6
1
0
1
1
2
1
0
1
1
1
1
0
0
2
1
1
1
0
1
1
2
1
0
2
1
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
0
1
2
1
1
0
1
1
2
1
1
2
0
1
1
1
2
1
1
0
1
0
2
2
1
0
1
1
0
0
1
1
2
0
1
1
1
0
1
1
2
2
1
2
1
1
1
1
1
2
0
1
1
2
1
1
2
1
1
0
1
1
2
1
1
1
1
1
2
2
1
1
2
1
2
1
0
1
2
1
1
1
2
0
1
1
1
2
1
2
1
0
0
1
2
2
2
1
2
1
1
1
1
1
1
2
0
2
1
1
1
1
1
1
0
1
1
1
1
1
1
2
2
1
1
1
1
2
1
0
0
1
1
0
0
1
2
1
1
1
1
2
2
1
1
1
2
0
2
1
2
1
0
1
0
0
1
1
1
1
1
0
2
1
0
2
1
1
1
1
1
2
1
2
2
0
2
1
2
0
2
1
2
1
0
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
0
1
1
2
1
1
1
1
1
1
1
1
2
1
2
1
1
1
2
1
1
1
1
0
0
1
2
2
1
0
1
1
1
1
1
1
2
0
1
1
0
1
2
1
1
1
1
1
1
0
1
1
1
1
2
0
1
0
1
1
1
1
0
1
0
1
1
1
1
1
1
1
0
2
2
2
2
1
1
1
1
1
0
0
1
1
2
1
1
2
1
0
1
0
2
2
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
0
2
1
0
1
0
1
0
1
1
1
1
1
1
2
0
1
1
1
0
1
2
1
1
0
2
2
1
1
2
1
1
1
2
1
1
1
0
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
0
1
0
1
0
1
0
1
1
1
2
2
2
0
1
1
0
1
1
1
1
1
0
1
1
2
1
2
1
2
0
1
0
0
1
1
2
2
1
2
1
1
1
1
2
0
1
0
0
1
1
0
0
1
1
1
2
1
0
1
1
2
2
1
1
1
2
1
1
1
0
1
2
3
1
1
1
2
1
1
0
0
2
1
2
1
1
1
1
1
1
1
1
0
1
1
2
1
1
1
2
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
0
2
0
2
1
2
0
1
1
1
0
0
2
1
2
1
1
1
1
1
1
2
1
0
1
1
2
1
1
1
1
0
1
1
1
2
1
2
0
1
1
0
1
2
0
2
1
1
1
1
1
1
1
1
4
1
0
0
1
2
1
0
1
1
1
1
1
1
1
1
3
1
1
2
1
1
1
0
2
0
0
1
2
2
1
1
1
2
1
2
1
0
0
0
0
1
2
0
1
1
1
1
1
1
1
0
1
1
1
1
2
3
1
1
0
1
1
2
1
1
2
2
1
2
1
1
0
3
1
1
1
1
1
1
1
0
2
0
1
0
1
1
1
1
1
0
1
1
1
1
1
1
0
1
1
0
0
1
2
1
1
1
2
2
1
1
1
3
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
0
0
2
2
1
2
0
1
2
2
1
1
1
2
1
1
1
1
0
0
0
0
1
1
1
1
0
1
2
2
0
0
0
1
1
1
1
1
2
1
0
2
0
1
1
1
2
1
1
0
1
0
0
1
2
2
1
1
2
1
1
0
1
1
1
2
0
1
0
1
1
0
1
1
1
2
1
1
1
1
1
0
1
1
2
1
1
1
1
1
2
1
1
2
1
1
0
1
1
1
1
1
1
3
1
1
0
2
1
1
2
1
1
1
0
2
0
1
1
1
1
2
2
0
1
2
3
1
1
1
2
0
2
1
2
1
2
1
0
1
2
2
2
2
0
1
1
1
1
1
1
1
2
1
1
1
0
1
1
0
1
1
2
1
1
2
2
2
0
1
1
0
1
1
2
1
1
2
2
1
1
1
1
1
0
2
0
2
1
1
2
1
0
1
1
1
2
1
0
1
1
1
1
1
1
1
1
2
1
2
1
2
0
1
1
1
1
1
2
1
2
1
2
2
2
1
0
1
2
1
1
0
1
2
1
2
0
0
1
2
1
0
2
1
1
0
1
2
0
2
0
0
1
1
2
3
1
1
1
0
0
1
3
1
1
3
2
1
1
2
0
3
0
0
1
0
2
1
0
1
1
1
1
1
0
1
2
1
1
1
1
1
1
1
1
1
2
1
0
1
1
1
1
1
1
2
2
1
2
2
1
1
1
1
1
1
1
1
1
2
1
1
0
1
1
2
0
1
1
1
1
1
0
0
1
2
2
2
1
1
1
0
1
2
0
0
1
2
1
2
1
1
1
2
1
0
0
2
2
0
1
1
1
1
1
1
1
2
1
2
1
1
2
2
1
1
1
1
3
1
2
1
0
1
1
1
1
2
1
2
1
1
2
1
1
1
0
1
1
1
2
2
1
1
0
1
1
2
1
1
1
0
1
0
2
2
0
1
1
1
2
1
0
2
1
2
1
1
1
1
2
1
1
1
0
2
1
2
2
1
1
1
0
2
0
1
1
1
1
1
1
1
2
2
2
2
1
1
1
1
1
2
1
1
0
1
1
1
1
1
1
0
2
1
2
1
2
1
1
2
1
1
0
1
0
2
2
1
1
1
1
0
2
2
1
1
1
1
1
1
0
1
1
2
1
0
1
1
1
2
1
2
2
1
0
1
1
1
1
1
1
1
0
0
1
2
2
1
1
2
0
1
1
1
1
1
2
1
2
1
1
1
1
1
2
1
0
2
2
1
0
1
2
1
1
1
2
1
1
1
2
0
2
1
2
1
1
1
1
2
1
1
1
2
2
0
1
1
0
2
2
2
2
1
2
2
2
1
5
1
1
0
2
0
1
1
1
1
1
2
2
0
1
1
0
2
2
1
2
1
0
2
0
1
2
1
2
2
0
1
1
1
2
1
1
0
0
1
2
1
0
1
1
2
2
2
1
2
1
0
0
1
1
1
1
2
1
1
2
1
1
0
2
1
0
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
6
2
1
1
0
1
2
0
1
1
0
1
3
1
0
2
1
1
1
0
2
2
2
1
1
2
0
0
0
0
2
1
1
1
0
1
0
1
2
1
2
0
2
1
0
1
1
1
2
1
2
1
1
1
1
0
1
1
1
1
1
1
1
0
1
0
1
2
2
2
2
1
2
1
1
2
2
1
1
1
2
1
0
1
1
2
1
0
1
0
2
1
1
0
2
1
1
1
1
2
1
0
0
0
1
1
1
2
1
1
1
2
2
1
1
2
0
1
1
1
0
2
1
1
1
1
1
1
1
1
2
0
0
1
1
2
0
1
1
1
2
1
2
1
1
0
1
0
2
1
0
0
2
1
0
1
1
1
2
1
0
1
1
2
1
0
1
2
1
1
1
0
1
1
1
1
1
1
2
2
1
2
2
1
1
1
0
1
0
0
1
1
1
1
1
2
2
0
2
1
0
3
1
1
1
1
1
1
0
1
1
1
2
2
2
0
2
1
2
2
1
2
1
0
1
1
1
2
2
1
1
2
1
1
2
1
1
1
1
1
1
0
1
1
1
1
0
1
1
0
2
1
1
1
2
0
1
1
2
1
1
0
1
1
0
0
1
1
1
1
1
0
2
2
1
1
0
1
1
2
1
1
1
0
2
1
2
2
1
1
2
2
1
2
0
1
1
1
2
1
2
1
1
0
0
1
1
2
1
1
1
1
2
0
1
0
1
1
1
0
1
1
1
1
1
1
1
0
1
1
1
1
1
1
2
0
0
2
1
0
1
1
1
1
2
2
0
1
2
0
1
1
1
1
1
0
3
1
1
1
2
1
0
1
1
2
0
0
1
1
0
1
2
1
2
2
1
1
1
1
2
1
1
2
1
0
1
2
1
1
1
1
1
2
1
1
0
1
0
2
0
1
1
1
1
1
2
1
0
2
1
2
0
1
2
1
1
2
1
1
1
0
2
0
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
2
1
0
2
0
1
1
1
0
0
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
0
1
1
0
2
1
1
2
2
1
1
1
1
1
2
1
1
1
2
1
1
1
2
2
1
0
0
0
1
1
2
0
1
1
0
0
1
1
2
1
1
2
1
1
1
1
2
1
1
1
2
1
1
0
1
1
1
1
1
0
1
1
1
1
0
1
2
2
0
1
0
1
1
1
2
1
1
2
0
1
1
1
1
1
1
1
2
1
1
0
0
2
1
1
1
2
2
1
0
0
1
1
0
1
1
2
2
1
1
2
2
1
1
1
0
1
1
1
1
2
1
1
2
2
1
0
0
1
1
1
1
1
2
2
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
2
1
1
1
0
2
2
1
1
1
1
1
2
0
1
1
2
0
0
1
2
1
1
1
1
2
1
2
1
1
1
2
1
1
2
2
1
2
2
2
2
2
2
1
2
1
1
1
1
2
1
2
1
0
1
0
1
2
1
1
0
1
1
0
1
1
2
1
1
1
1
1
2
2
2
1
0
1
0
0
1
1
1
0
2
1
2
2
1
1
1
1
0
1
1
1
1
1
1
1
2
2
1
1
1
0
1
1
1
1
2
2
2
2
1
1
1
1
1
0
2
2
1
1
1
1
2
2
2
0
1
1
1
1
1
0
1
2
1
2
0
1
1
1
1
0
1
1
2
0
0
1
2
0
2
0
1
2
0
2
0
2
1
0
1
1
1
1
1
1
0
2
1
1
1
1
1
0
1
1
2
1
0
2
0
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
0
2
0
1
2
0
0
0
2
1
1
0
2
1
2
2
0
1
2
1
1
1
0
1
1
0
2
1
1
1
0
2
1
1
1
1
1
2
1
2
1
1
1
1
1
2
0
0
1
1
1
1
1
2
1
2
1
1
1
0
1
1
1
2
1
1
0
0
2
1
2
1
1
2
2
2
1
0
2
2
0
0
1
2
1
2
1
1
1
1
1
1
1
0
0
2
2
1
0
1
1
2
1
0
1
0
0
1
1
1
1
0
1
0
1
2
1
1
2
1
1
1
1
1
2
0
1
1
1
1
1
0
1
1
1
1
0
1
1
1
2
1
1
1
0
1
0
1
2
1
0
1
0
1
0
1
1
1
1
0
1
1
1
1
2
1
0
1
1
1
0
1
1
1
1
1
2
1
2
1
2
0
1
1
1
1
0
1
1
2
1
0
0
2
1
0
2
0
1
1
1
1
2
1
2
1
1
1
0
1
1
2
1
1
1
1
0
1
2
2
1
1
1
1
1
1
1
1
1
2
0
0
1
1
2
0
1
2
1
1
1
1
2
0
1
0
1
0
0
1
1
1
1
1
0
1
1
1
1
1
0
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
0
1
2
0
1
2
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
2
0
1
0
1
1
2
1
1
1
2
0
1
0
0
1
0
2
2
2
1
1
1
1
1
0
2
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
2
1
1
1
0
1
2
1
0
2
1
2
1
1
1
1
1
3
2
1
1
2
1
1
2
1
1
1
2
1
2
0
0
0
2
0
1
1
3
1
2
1
2
1
1
2
1
2
1
0
1
1
0
0
1
1
2
1
2
1
2
1
2
0
1
2
1
1
2
1
1
1
1
1
0
2
2
1
1
0
1
0
1
0
2
2
1
2
1
2
2
1
1
0
1
1
1
2
1
1
1
1
1
0
1
1
0
1
1
2
1
1
0
1
1
1
1
1
2
1
2
2
3
1
1
2
1
0
2
1
2
1
1
1
1
0
0
1
1
2
0
1
0
2
1
0
1
1
1
1
1
0
0
1
1
1
2
1
1
1
0
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
1
2
0
2
1
0
1
1
1
2
1
1
2
2
1
2
2
0
1
2
1
1
1
1
0
1
0
0
1
2
1
1
1
1
1
1
1
1
1
1
1
1
0
1
2
2
3
1
0
1
0
2
1
1
1
1
0
2
0
1
1
2
1
0
2
0
0
0
1
1
1
0
1
1
1
0
1
2
1
1
2
1
1
2
1
1
0
1
0
2
1
2
1
2
1
1
2
1
0
1
2
2
0
0
4
2
2
0
1
1
1
2
1
2
2
0
0
1
1
1
1
1
1
1
0
1
1
1
2
1
1
1
1
0
2
0
2
1
1
2
0
1
2
2
1
1
1
1
1
1
1
0
1
2
2
1
1
1
1
2
1
1
1
2
1
2
1
1
0
2
2
1
1
0
2
1
1
1
1
2
1
1
2
0
1
1
1
1
1
1
1
1
1
8
1
2
0
1
1
1
1
1
1
1
1
2
1
0
1
2
1
2
1
1
1
2
1
1
2
1
1
2
2
1
1
0
0
1
2
2
1
1
1
2
2
1
1
1
0
1
1
0
1
1
1
1
0
2
0
1
1
1
1
0
1
1
1
1
1
1
1
2
1
0
1
1
0
2
0
0
0
1
2
2
2
1
2
2
0
1
1
1
2
1
1
0
1
1
1
1
2
1
1
1
0
1
0
1
1
2
1
1
1
1
2
1
1
1
1
0
1
2
1
1
1
1
1
1
1
1
2
0
1
2
1
2
2
1
2
1
1
1
2
2
1
1
0
2
1
0
0
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
0
1
2
1
2
2
0
1
2
1
1
0
1
0
0
1
1
2
2
1
1
0
1
2
1
0
1
1
1
1
2
1
2
1
2
1
2
1
0
2
0
0
1
0
1
1
1
1
1
2
1
2
0
2
1
2
1
2
1
1
1
2
1
1
2
0
2
1
1
2
1
1
1
2
2
1
2
0
1
1
2
1
1
1
1
0
1
0
1
1
1
1
0
0
0
1
1
1
0
1
1
1
1
0
1
1
1
1
2
1
1
1
0
1
1
2
1
1
2
1
1
0
1
1
1
1
1
1
4
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
0
2
1
2
1
1
2
1
2
2
1
1
2
0
0
1
1
1
1
0
2
1
1
1
0
2
1
1
1
0
1
1
1
0
1
2
0
0
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
0
1
0
2
0
1
1
0
1
1
1
2
1
1
2
1
1
0
1
1
1
1
0
2
1
0
1
2
1
0
0
1
1
0
2
0
1
1
1
1
1
1
1
2
1
2
1
1
1
0
2
1
1
1
1
1
1
1
2
2
0
1
1
1
1
0
1
1
1
1
2
1
1
2
1
2
2
1
2
1
1
1
1
2
0
0
2
1
1
2
1
1
2
2
0
1
1
2
1
1
1
2
1
1
2
1
0
1
2
2
1
1
2
2
1
2
2
1
0
1
1
0
2
1
1
1
1
1
1
2
0
1
1
0
1
2
0
1
1
0
2
2
0
1
2
2
0
1
1
2
1
0
0
1
1
1
1
1
0
1
2
1
1
2
1
1
2
1
2
1
0
1
2
2
0
1
1
0
3
2
2
1
1
1
2
1
1
1
3
2
1
1
1
1
1
1
0
1
2
1
1
1
1
0
2
1
0
1
1
0
2
1
1
1
1
2
2
2
1
2
2
1
1
1
2
1
0
1
1
1
1
2
0
0
2
0
2
1
1
2
1
1
1
0
1
1
2
1
1
1
0
0
0
1
1
1
1
1
0
1
1
1
2
0
1
2
0
1
1
1
2
1
1
1
2
1
1
1
0
1
2
1
1
2
1
2
1
1
0
2
1
1
2
0
1
1
0
1
2
0
1
1
0
1
1
1
1
1
0
1
1
2
1
1
0
0
1
1
1
1
1
2
1
1
2
1
2
1
1
2
1
1
1
3
3
2
1
1
2
1
1
0
3
0
1
1
1
1
1
1
2
1
0
3
2
2
2
2
0
1
0
0
0
0
0
1
2
1
1
2
0
1
2
1
1
2
1
2
1
2
2
1
2
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
0
1
1
1
1
2
1
0
1
1
1
1
2
1
1
2
2
2
1
1
0
2
1
2
2
1
1
1
1
2
1
1
2
1
2
1
1
1
1
2
1
1
0
0
1
0
0
1
0
0
0
1
1
2
1
0
1
1
3
1
2
2
1
2
0
2
1
1
1
1
1
1
1
0
0
1
2
1
0
1
2
0
0
1
1
2
2
0
2
0
0
2
0
1
1
1
1
0
0
2
1
2
2
1
1
1
1
0
1
0
1
1
1
1
1
0
0
1
0
1
0
1
2
2
1
2
1
1
2
3
1
2
2
1
0
1
2
0
1
1
1
1
2
1
2
1
1
0
1
2
1
1
1
1
1
1
0
3
1
2
0
0
2
2
1
1
1
2
1
0
1
1
2
1
1
2
2
2
1
2
1
0
1
1
0
0
2
1
1
0
2
2
2
2
1
1
1
1
1
0
1
1
1
1
1
2
3
2
1
1
1
1
1
2
1
1
0
1
0
0
2
2
1
1
1
1
1
1
1
1
0
2
2
0
0
1
1
0
0
2
2
0
2
1
1
0
1
0
2
1
1
2
1
0
0
0
0
1
2
2
1
1
1
1
1
2
1
1
2
1
2
3
0
2
1
1
2
1
1
2
0
0
0
0
1
1
1
0
2
1
2
1
2
2
1
1
1
2
1
2
0
1
0
0
1
0
0
1
2
1
1
2
2
1
1
1
1
1
1
0
1
1
1
1
1
0
0
1
1
1
0
1
2
1
1
1
1
2
1
1
2
1
1
1
1
2
1
2
1
2
0
1
2
1
0
1
1
1
2
1
2
0
1
1
2
2
2
1
2
2
1
1
2
1
1
1
2
1
1
2
1
1
2
1
1
0
0
2
1
0
2
0
1
2
1
2
1
1
1
1
1
0
2
1
0
1
1
0
1
1
1
2
1
1
3
1
0
1
1
1
1
1
0
1
1
0
1
1
2
2
1
2
0
0
2
1
1
0
0
1
1
2
1
1
1
1
1
1
2
1
1
2
1
1
1
2
2
0
1
1
2
1
1
0
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
0
0
1
2
1
2
2
1
2
1
1
2
1
2
0
1
1
1
1
2
1
0
1
0
1
1
1
0
0
1
0
2
2
1
1
1
1
1
2
2
1
2
1
1
0
1
2
2
2
0
1
1
1
2
2
1
1
1
1
1
1
2
1
2
1
1
1
0
1
1
3
1
1
2
0
1
1
0
1
1
1
1
1
3
0
1
1
1
2
1
2
1
2
2
0
2
1
2
1
2
2
0
1
1
1
2
1
1
2
1
1
1
1
0
1
1
1
1
1
1
0
0
0
2
0
1
1
2
1
1
1
1
1
1
1
0
0
2
1
1
1
2
2
2
1
2
2
2
2
1
1
2
2
1
0
1
1
1
0
0
0
3
2
0
2
1
1
1
1
1
0
1
1
2
2
2
0
0
0
0
1
2
1
1
1
2
1
1
1
1
1
0
1
1
1
1
1
1
1
1
2
1
2
1
1
2
2
0
0
1
1
1
1
1
1
1
1
1
1
2
1
0
1
1
1
2
1
2
1
2
1
1
2
1
1
1
2
1
0
2
2
1
1
1
1
2
3
1
1
1
1
0
1
0
1
1
1
1
2
1
1
2
2
0
0
1
0
1
0
1
2
2
1
0
1
2
1
0
2
1
1
2
2
4
0
1
1
1
0
1
1
0
2
1
0
0
1
1
1
1
1
1
0
1
0
2
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
0
1
2
1
2
0
1
1
1
2
2
1
1
1
0
0
2
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
0
1
1
1
2
1
1
0
1
2
1
1
1
2
2
1
1
0
1
1
0
1
1
1
1
2
2
2
1
2
1
2
1
1
1
1
1
2
1
1
1
0
1
2
0
2
2
1
1
2
1
1
1
1
1
2
1
3
1
2
1
2
2
1
1
1
1
1
1
1
1
2
1
1
2
0
0
2
1
1
1
1
2
1
1
1
0
1
0
2
2
1
1
1
1
1
2
1
1
0
2
0
1
0
1
1
1
1
1
0
2
2
1
0
1
1
1
1
2
1
1
1
1
1
1
1
2
2
2
1
1
1
1
2
1
0
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
2
1
0
2
2
2
1
1
1
0
1
1
2
1
2
1
1
0
1
1
1
0
2
1
1
1
1
2
2
1
1
0
1
1
1
2
2
1
2
0
1
2
1
1
1
0
2
1
1
1
1
1
1
1
1
2
0
1
1
3
1
2
0
1
1
0
0
1
0
2
0
2
1
2
1
1
0
1
1
1
2
2
1
1
1
1
1
3
2
1
0
1
1
1
0
1
1
2
1
0
1
1
1
0
2
1
1
2
2
1
1
2
1
1
2
1
1
1
1
2
1
1
0
1
0
2
0
0
2
1
1
1
1
0
2
1
1
1
1
1
1
1
1
1
1
0
1
2
2
1
0
2
2
2
1
0
0
1
1
1
0
2
0
1
2
1
1
1
1
2
2
2
1
1
1
1
0
1
2
2
2
2
1
1
2
1
1
0
2
1
2
1
1
1
0
1
2
1
1
1
2
1
1
2
1
1
1
2
0
1
2
1
1
2
1
0
1
0
2
1
1
1
1
1
2
1
1
1
0
1
0
1
1
1
1
1
1
0
0
2
1
2
0
1
1
2
1
1
0
0
2
1
1
0
1
1
1
1
1
1
0
1
1
1
1
1
1
1
2
1
1
8
1
1
1
1
0
0
2
1
1
1
2
1
1
1
2
1
2
1
1
2
1
2
0
2
1
1
1
1
0
0
1
1
1
1
1
1
0
1
0
2
1
2
1
2
0
1
1
3
1
1
1
1
1
2
1
1
2
1
1
1
2
1
1
1
0
0
2
1
1
1
1
1
1
2
2
0
1
1
1
0
0
1
2
1
1
0
1
1
2
2
1
1
1
1
0
2
2
0
2
2
1
1
2
1
1
2
2
1
1
1
2
1
2
1
1
1
1
1
1
0
1
0
1
1
0
1
1
1
2
1
1
0
1
2
2
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
2
1
2
0
0
0
1
2
5
1
0
1
0
1
0
1
2
1
1
1
0
2
2
1
1
2
1
1
1
2
1
1
2
0
2
1
0
1
1
1
1
0
1
0
1
1
1
0
0
2
1
1
2
1
2
1
1
0
1
2
0
1
0
2
2
1
1
2
1
1
1
1
0
0
0
1
1
0
1
2
1
0
1
1
0
2
2
2
1
2
1
2
0
1
1
1
1
0
0
2
1
2
1
0
0
1
2
2
0
1
0
2
2
1
2
1
1
1
1
2
2
0
1
1
2
1
0
1
1
1
2
1
0
1
3
1
0
1
1
2
2
1
1
1
1
1
2
1
0
1
1
1
2
2
0
1
2
2
1
0
2
1
1
1
1
1
0
1
1
1
1
2
1
1
0
2
1
1
2
2
1
2
2
1
2
1
1
1
1
1
1
1
0
0
2
1
0
2
1
2
1
1
1
2
1
1
0
1
0
1
1
1
1
1
0
1
1
1
0
1
0
2
2
2
1
1
1
0
1
0
2
1
1
1
0
1
1
1
2
1
1
2
2
2
0
1
1
1
0
1
2
1
0
1
1
2
1
1
2
2
1
1
1
1
2
2
1
0
2
1
1
1
1
1
2
2
1
1
3
0
1
1
1
1
1
1
0
1
1
2
1
1
1
1
1
1
2
1
2
0
1
2
1
1
0
1
2
1
2
0
1
0
1
1
1
1
0
1
2
1
1
1
0
2
1
1
1
1
2
1
0
0
1
1
1
2
1
1
2
2
1
1
1
2
0
2
1
1
2
2
1
2
1
0
2
1
1
1
1
1
1
1
0
0
1
0
1
2
0
1
2
0
2
1
0
1
1
1
1
2
3
0
1
0
0
1
2
2
7
0
1
1
2
1
0
0
2
1
2
0
2
2
1
1
0
1
1
2
1
0
2
2
2
1
1
1
1
1
1
0
1
2
1
2
1
2
1
1
2
1
1
1
0
2
1
1
1
0
0
1
2
1
0
1
3
2
1
1
0
1
1
1
1
1
2
1
1
2
0
2
2
2
2
1
1
1
1
2
0
2
0
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
1
0
0
0
1
1
1
1
0
0
0
1
2
1
2
1
2
1
1
2
1
2
0
1
1
1
1
0
2
2
2
1
1
2
1
2
0
0
1
2
2
1
0
2
0
0
0
1
2
1
1
1
0
0
1
1
1
2
1
1
2
1
0
1
0
1
0
2
1
1
1
1
0
1
2
1
1
1
1
1
1
2
0
1
1
0
1
1
1
0
0
2
2
1
1
1
0
0
1
1
0
1
2
1
1
1
1
1
2
1
2
1
1
2
1
1
0
2
1
1
1
2
2
1
1
2
2
2
1
1
2
1
2
0
1
1
2
1
1
1
2
1
1
0
0
1
2
1
1
0
1
1
0
1
1
1
1
0
2
2
1
1
1
1
1
1
2
1
2
0
1
2
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
0
2
1
0
1
1
1
3
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
0
1
0
1
2
1
1
1
1
2
1
1
1
1
0
0
0
1
1
1
1
2
1
1
2
0
2
0
1
1
1
1
1
1
2
2
1
1
1
1
0
1
0
2
1
2
1
1
0
1
0
1
1
1
2
1
2
2
1
1
0
1
1
1
1
0
2
1
2
1
0
1
1
2
1
1
1
2
1
1
2
1
1
1
1
0
1
2
1
1
1
0
2
1
1
1
2
1
1
2
1
0
1
0
2
1
2
2
1
1
2
1
0
2
1
1
0
1
1
2
2
1
1
1
2
2
1
1
0
1
1
2
2
2
0
2
0
1
1
0
2
1
1
0
1
1
1
0
1
1
1
1
2
0
2
1
1
2
0
1
1
1
1
1
2
1
1
1
2
2
0
1
0
1
0
1
1
1
1
1
1
1
1
0
1
0
2
1
1
1
2
2
1
1
3
0
2
2
0
0
1
2
0
2
1
2
1
1
0
2
1
2
0
1
0
2
2
0
0
2
2
1
0
0
0
1
2
1
0
1
0
2
0
2
2
2
1
1
0
1
2
1
1
2
1
1
1
2
1
2
4
0
2
1
2
1
1
1
1
1
2
1
1
0
1
1
1
1
0
0
1
0
2
2
1
1
0
1
1
1
1
2
2
1
1
0
1
1
1
0
1
1
0
2
1
1
0
1
0
1
2
1
2
0
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
2
0
1
1
2
1
1
1
1
1
1
1
0
2
2
2
0
1
1
0
2
2
2
2
2
1
1
2
0
1
1
2
1
1
1
1
1
0
1
2
2
0
2
1
1
0
0
2
1
0
1
0
1
1
1
1
1
1
1
2
1
1
0
1
1
1
2
2
1
1
1
0
2
2
0
2
1
1
2
1
0
1
0
1
1
2
2
1
1
1
0
1
0
1
0
1
0
2
1
2
1
1
2
0
1
1
1
1
0
1
0
0
2
1
2
2
1
1
1
1
0
1
0
1
1
2
1
2
2
2
1
0
0
1
1
0
1
0
1
3
1
0
1
1
2
1
2
2
1
2
2
1
1
0
0
1
2
2
1
1
1
2
1
1
1
0
1
1
1
1
1
0
2
1
1
1
1
1
0
1
1
2
1
1
1
2
2
1
1
2
1
1
1
2
1
1
1
0
1
1
2
2
1
0
1
1
0
1
1
2
2
1
1
1
2
0
0
1
1
2
2
1
0
1
1
1
1
1
2
1
0
1
1
1
2
1
1
0
2
1
1
1
1
1
1
0
2
2
2
1
1
1
2
1
1
1
1
1
2
0
1
1
1
1
2
1
1
2
1
1
2
2
0
2
0
2
0
2
0
1
2
1
1
1
2
2
1
1
1
1
1
1
1
1
1
2
0
3
1
1
1
1
1
2
1
2
1
1
1
2
0
2
0
1
2
2
1
1
1
1
1
2
3
1
0
0
1
2
1
2
1
1
1
2
0
2
1
1
1
0
1
1
1
0
0
1
0
1
0
0
1
1
2
0
0
1
1
0
1
2
1
2
1
1
1
1
2
2
1
2
1
1
2
1
1
1
1
0
4
1
2
2
1
1
1
2
2
1
2
2
2
2
1
1
1
1
1
1
0
2
2
0
1
1
2
1
1
1
0
2
1
1
1
1
1
2
1
1
1
2
0
1
1
1
1
1
1
1
0
2
1
0
1
1
1
2
1
0
1
2
2
2
1
2
1
0
2
1
1
1
2
2
9
1
2
1
1
1
2
2
1
1
1
1
1
1
0
1
1
0
0
2
1
1
0
2
1
1
1
1
0
2
2
1
1
2
1
1
1
0
0
1
1
1
2
1
0
2
1
1
1
1
1
2
2
1
1
1
0
1
1
0
1
1
1
1
2
0
2
0
1
1
2
1
1
2
1
2
0
1
1
1
1
1
1
1
1
1
1
1
1
0
1
0
2
1
1
1
2
2
2
1
2
1
1
1
1
1
1
1
0
2
1
1
2
2
1
1
1
1
2
0
2
2
1
1
2
2
1
1
1
2
1
1
1
1
0
2
1
1
1
0
1
1
2
1
2
2
1
2
1
1
1
1
0
2
1
1
0
1
2
1
1
0
2
1
0
2
2
2
2
1
1
1
1
2
1
1
2
2
0
2
1
2
2
1
2
1
1
0
1
1
1
1
1
1
1
0
3
2
2
0
1
0
1
2
1
1
1
2
0
1
2
1
1
1
0
2
1
1
1
0
2
1
2
1
2
2
1
3
1
1
0
1
1
1
1
2
1
1
1
1
1
1
1
0
1
1
1
1
1
1
2
0
0
1
1
1
0
1
1
1
1
0
0
2
1
1
1
1
1
1
1
1
1
2
1
2
1
0
0
1
1
1
2
0
1
1
1
2
1
2
2
0
1
1
1
1
1
0
1
0
1
1
1
1
2
0
1
1
1
1
1
2
2
0
1
2
2
0
1
1
1
1
1
2
1
2
2
0
2
2
2
1
1
2
1
2
1
2
1
1
1
1
0
2
0
1
2
2
0
1
2
1
0
1
1
1
1
2
1
1
1
0
2
1
2
3
1
0
1
1
1
1
1
0
2
0
2
1
0
1
1
2
1
0
1
1
1
2
1
0
2
1
1
1
0
1
1
1
2
0
0
1
0
0
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
0
2
2
1
1
1
1
1
2
1
1
1
2
2
1
1
2
1
1
1
2
2
1
1
1
0
1
2
2
2
1
1
0
1
1
2
2
1
2
2
1
1
2
2
1
0
1
1
1
0
2
1
0
1
1
1
1
2
1
2
1
2
1
1
2
1
0
1
0
2
1
2
2
2
1
1
1
1
1
0
1
0
1
1
1
2
0
1
1
1
1
1
1
1
1
2
1
1
2
1
2
2
1
0
1
1
1
1
1
0
2
0
1
2
1
2
0
0
0
1
1
1
1
3
2
4
2
2
1
1
1
1
0
2
1
1
1
1
0
2
0
1
1
1
1
1
2
1
2
0
1
1
1
1
1
0
1
1
1
1
2
1
1
1
1
1
2
2
2
2
1
0
2
1
2
1
3
1
1
1
2
1
1
0
2
1
1
1
2
0
0
1
2
2
1
1
2
2
2
0
1
1
2
1
1
1
1
0
2
3
2
1
2
2
0
0
1
1
0
1
1
1
1
1
0
1
1
0
2
2
1
1
1
1
2
1
0
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
0
1
2
2
1
0
2
0
1
2
1
2
2
0
1
2
0
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
2
1
2
1
0
1
1
0
2
1
2
2
1
1
1
1
0
0
1
1
1
1
2
2
2
1
0
1
1
2
1
1
0
0
1
1
2
1
1
1
1
1
0
0
1
2
3
2
1
1
1
1
1
1
1
2
0
1
2
1
1
2
1
3
2
1
2
0
1
1
1
1
2
1
1
0
1
1
2
0
0
1
1
1
1
1
1
0
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
0
1
1
2
2
1
1
1
2
0
1
1
1
2
2
1
1
1
1
1
2
1
1
0
1
1
2
1
1
0
1
0
1
1
1
2
2
1
2
1
1
0
1
2
1
1
2
0
1
0
0
2
0
0
1
1
1
3
2
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
0
1
0
1
1
2
2
1
1
2
1
2
1
1
1
1
1
0
1
2
1
1
1
1
0
1
0
1
1
0
2
2
2
1
2
2
0
0
1
0
2
1
2
2
1
2
1
2
2
1
1
1
1
1
1
1
0
1
1
2
2
2
0
1
0
2
2
2
1
1
2
1
1
1
0
2
1
1
0
0
1
2
1
1
2
1
0
0
1
3
0
1
1
0
1
1
1
1
2
2
1
1
1
1
0
1
1
1
1
0
1
1
2
2
2
1
2
1
2
1
2
0
1
2
1
1
1
2
1
1
0
0
1
1
1
2
1
0
1
0
1
1
2
2
1
0
1
0
2
2
0
0
1
1
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
2
0
2
0
1
1
1
0
1
1
1
2
0
1
2
1
1
0
1
2
0
0
1
2
2
2
1
1
1
1
1
1
0
1
1
1
2
1
2
0
4
1
1
2
2
1
1
1
0
1
1
1
0
2
1
1
1
1
0
1
2
1
1
1
1
0
1
1
2
1
0
1
0
1
0
1
1
1
2
1
1
0
1
1
1
1
1
1
2
0
0
2
1
1
0
1
1
0
1
1
1
2
1
1
1
1
2
1
1
1
2
0
0
1
1
1
1
0
1
2
0
2
0
1
1
0
2
1
0
1
1
1
1
2
1
2
1
1
0
1
2
1
2
2
1
1
1
1
1
2
0
2
3
2
1
1
2
2
1
1
2
1
1
1
0
1
1
0
1
1
1
0
1
0
1
1
2
1
1
2
0
1
0
1
1
0
2
1
2
1
1
2
1
1
1
1
1
2
1
1
2
0
1
1
1
0
2
1
1
1
1
1
0
1
1
1
1
0
1
1
1
1
2
1
0
1
2
0
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
1
2
1
2
1
2
2
1
2
3
1
2
1
0
1
0
2
1
0
1
2
1
1
1
1
1
0
1
2
0
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
0
1
1
0
1
1
1
2
1
1
2
0
0
1
0
2
1
2
2
2
1
1
1
2
0
0
1
1
1
2
2
1
1
1
2
0
1
0
1
1
0
0
1
2
1
1
1
2
1
0
2
1
0
1
2
1
0
1
1
2
1
1
2
1
1
2
1
1
2
1
1
1
0
1
0
1
0
1
2
2
1
1
2
0
1
1
1
0
0
0
1
1
1
1
1
1
1
1
2
1
1
1
0
1
0
1
2
0
0
1
1
1
0
1
2
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
2
0
0
0
1
2
0
1
2
2
1
0
1
1
0
1
0
1
2
2
1
2
0
1
0
1
1
1
2
2
1
1
0
0
1
2
1
1
1
2
2
1
0
1
2
0
1
1
2
1
1
0
2
1
1
1
2
1
1
2
0
2
2
0
0
0
2
0
1
3
2
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
1
0
1
2
1
2
0
1
2
1
1
0
1
1
1
2
1
1
0
0
1
0
0
1
0
2
1
1
2
1
1
2
0
0
1
1
0
0
1
1
1
1
2
2
2
2
1
1
1
1
2
1
1
0
1
2
2
1
1
1
1
1
2
1
2
1
1
1
1
0
0
1
1
1
1
1
1
2
1
0
1
1
0
1
0
2
0
2
1
0
1
1
2
1
2
3
1
1
1
2
0
1
1
1
1
1
0
1
2
1
0
2
1
0
2
1
1
1
1
1
0
2
2
1
1
2
1
2
0
1
3
1
1
1
0
2
1
0
1
1
0
2
1
1
2
1
2
1
1
2
1
0
1
1
1
1
1
1
1
2
2
2
2
1
1
0
1
1
1
2
2
0
2
1
1
1
1
1
2
1
1
1
1
0
1
1
2
1
1
1
1
2
0
0
2
1
2
1
3
1
1
2
1
1
0
2
1
2
2
0
2
0
1
2
2
1
2
2
1
2
2
1
1
0
1
1
1
1
1
1
1
1
0
2
1
1
1
1
1
0
2
1
1
0
1
1
1
1
1
0
2
0
1
1
1
1
1
2
1
2
2
2
0
1
1
1
1
3
1
1
1
1
0
1
1
2
0
0
0
1
1
1
1
1
1
0
2
1
0
1
1
1
1
2
1
0
1
1
1
0
2
2
1
2
1
0
0
1
1
1
2
2
2
0
1
1
1
1
1
2
2
1
2
1
1
0
3
1
2
0
2
1
0
2
2
1
2
1
1
0
1
1
1
1
1
2
0
0
2
0
1
1
1
1
1
1
1
2
1
0
2
1
2
0
1
0
1
0
1
1
1
0
2
2
2
1
2
2
1
1
1
1
0
1
1
0
1
1
0
1
1
1
1
1
1
0
0
1
1
2
1
2
1
1
2
1
1
2
1
1
1
1
1
1
1
2
2
1
2
1
2
0
2
1
1
0
1
1
0
2
1
1
1
1
0
1
1
1
2
1
1
1
1
1
1
1
1
2
1
0
1
1
1
2
2
1
1
1
2
0
1
1
2
2
2
1
1
2
1
2
2
1
1
1
2
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
2
1
2
1
2
0
1
1
2
1
1
1
0
1
1
0
2
1
2
1
2
1
1
2
1
2
1
1
1
0
2
1
2
1
1
1
3
1
1
1
2
1
1
1
1
1
2
1
1
0
1
1
1
1
0
0
1
0
0
1
1
1
1
2
4
1
2
2
1
1
2
1
0
1
1
1
1
1
1
1
1
2
1
0
0
1
1
2
1
1
0
1
1
3
2
1
1
1
2
1
1
1
1
1
0
1
1
1
1
2
1
1
1
1
1
2
1
2
2
1
2
2
0
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
0
1
2
2
2
1
1
1
1
1
2
1
1
1
2
1
2
2
1
2
2
1
1
1
1
1
2
1
2
0
1
1
2
1
1
1
2
1
2
0
1
1
1
0
2
2
1
2
1
1
1
1
1
0
1
0
2
2
2
0
2
1
2
1
1
1
1
1
1
1
2
2
1
1
0
1
1
2
1
1
1
1
1
2
1
0
1
1
2
2
1
2
1
1
0
1
1
1
1
1
2
1
1
1
2
0
1
2
1
0
2
1
2
1
1
1
1
1
1
0
1
2
0
1
0
1
2
2
1
1
1
1
2
1
2
1
1
0
0
1
1
1
1
1
1
2
0
2
1
2
2
1
1
2
2
2
2
1
1
1
2
1
1
1
1
2
2
1
1
0
1
0
0
1
2
2
1
2
1
0
2
1
3
1
1
0
1
2
1
1
2
1
1
1
2
1
1
2
1
1
1
2
1
2
2
1
1
1
1
1
1
0
1
1
2
0
2
2
1
2
2
2
1
1
1
1
1
1
0
1
2
0
0
2
1
1
1
0
1
1
1
3
0
1
2
1
1
2
1
1
1
2
0
1
1
1
1
2
1
1
2
1
1
0
2
1
2
1
2
1
1
0
2
1
1
2
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
0
1
1
2
1
1
1
2
0
2
1
1
1
1
1
0
1
1
1
0
1
2
2
1
0
2
2
1
1
2
0
1
1
0
1
2
0
2
0
1
2
1
2
1
1
0
2
2
1
2
2
0
0
1
1
1
1
0
2
1
3
0
2
1
1
1
2
1
0
1
2
1
0
1
0
1
0
1
1
1
1
2
1
0
1
0
1
2
2
2
0
1
1
1
2
1
1
2
0
1
1
0
1
0
2
0
1
1
1
1
1
1
0
1
0
0
2
1
2
1
1
2
2
2
1
1
1
1
0
1
1
0
0
2
1
1
1
0
1
2
2
1
1
2
0
0
2
1
1
1
1
1
1
0
1
1
2
0
0
1
0
2
1
0
1
1
1
1
1
1
0
1
1
1
0
0
1
2
1
1
0
0
1
1
2
1
1
0
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
0
0
1
0
1
1
2
1
2
0
0
1
1
1
1
1
1
1
0
0
1
1
2
1
2
1
3
2
2
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
0
2
1
1
2
1
2
2
2
2
0
1
1
1
0
0
1
1
2
0
1
1
0
1
2
1
1
0
1
1
1
0
2
2
1
1
1
0
1
1
2
3
2
1
1
1
1
1
1
0
2
2
0
1
2
2
1
0
1
1
0
2
1
1
1
1
4
1
1
0
2
1
2
1
2
1
2
1
1
2
1
1
2
1
1
2
2
0
2
1
0
1
1
1
0
0
0
1
1
1
1
3
1
2
1
2
1
1
1
0
0
1
0
1
0
1
2
1
1
1
1
1
1
1
0
1
0
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
0
2
0
1
0
2
2
1
2
2
2
2
1
1
1
1
2
1
1
1
1
0
1
1
1
0
1
1
1
1
0
1
2
0
0
1
2
2
2
2
2
0
1
1
1
1
1
1
1
2
1
2
1
2
1
1
1
1
2
1
1
0
2
1
2
1
1
2
1
1
2
1
2
1
1
1
0
2
1
2
1
1
1
1
1
1
1
0
1
2
1
1
2
2
1
2
1
0
2
0
0
0
1
1
1
0
1
1
0
1
1
1
2
2
1
1
0
2
3
2
1
2
1
1
1
2
1
1
1
1
0
1
1
1
0
2
2
1
1
2
1
2
0
1
1
2
1
0
0
1
2
0
1
1
1
0
1
1
0
1
0
1
0
1
1
1
2
1
2
1
1
1
1
2
1
1
1
0
1
0
2
1
0
2
2
0
2
1
2
2
1
1
1
1
1
1
1
1
0
0
1
0
2
0
1
2
1
1
2
1
2
1
2
1
0
2
1
2
1
1
1
0
2
2
1
0
2
1
2
1
1
0
1
0
1
1
2
0
1
1
0
1
1
2
2
1
0
1
2
1
2
2
1
2
1
1
1
1
1
0
1
1
1
2
1
2
1
1
0
1
1
0
2
1
1
2
0
0
1
0
1
1
1
1
1
1
1
1
1
2
1
1
1
0
1
0
1
1
2
0
2
1
2
0
2
1
1
1
1
1
2
1
2
2
1
1
0
1
1
1
1
0
1
1
2
2
1
0
0
2
2
1
2
2
1
2
2
0
1
2
2
1
2
2
2
2
1
1
1
0
1
1
1
1
1
2
1
2
1
0
1
2
1
2
2
1
1
0
0
2
1
1
1
1
1
1
2
0
1
1
1
1
1
2
2
1
1
1
1
1
1
1
0
1
1
0
1
1
1
1
2
1
0
1
1
1
1
0
2
2
1
2
1
1
0
1
0
1
2
2
1
1
2
1
1
2
1
0
1
0
0
0
1
1
0
1
2
2
1
2
1
2
1
1
1
1
2
2
1
1
2
2
1
2
2
1
0
1
2
2
1
1
1
1
0
1
2
1
1
2
1
1
1
2
0
1
1
0
1
1
1
1
1
1
1
1
0
2
2
1
1
2
1
2
0
2
1
1
1
1
1
1
1
0
0
2
1
2
1
1
1
1
1
0
1
1
1
1
1
0
1
2
1
2
1
1
0
1
1
0
1
2
0
3
1
2
1
0
1
0
1
2
1
0
2
2
1
1
1
0
1
1
1
1
2
1
1
1
2
2
2
2
1
1
1
1
1
2
1
0
0
1
0
1
2
1
1
0
2
2
1
1
1
2
1
2
1
1
1
0
2
2
1
1
1
0
1
3
1
1
2
0
2
1
1
0
0
1
1
2
2
1
2
1
1
1
1
1
2
1
2
1
1
1
1
0
1
1
0
0
1
1
0
1
0
2
1
2
0
2
0
0
1
2
1
0
1
1
2
1
1
1
1
1
1
1
1
0
1
2
1
1
1
2
1
1
1
1
1
1
1
0
1
2
1
2
0
1
1
1
2
2
2
1
1
2
0
1
2
1
1
1
1
2
0
0
1
1
2
1
1
1
1
0
1
2
1
1
2
1
2
1
1
1
1
0
2
1
0
1
0
1
2
0
2
1
3
1
1
1
1
1
1
2
1
1
2
1
0
1
1
1
0
2
1
1
1
1
1
1
1
1
0
0
1
1
0
2
2
2
2
1
1
0
2
2
1
1
1
2
1
1
1
2
1
1
1
2
1
2
1
1
0
0
2
1
1
1
1
1
1
1
2
0
2
2
2
0
1
0
1
1
1
1
2
1
1
1
0
2
1
3
2
1
1
1
2
1
0
1
1
2
1
1
0
1
2
2
1
1
2
1
0
0
1
1
2
2
2
1
1
1
1
0
1
2
1
2
2
1
1
1
1
1
2
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
0
2
1
2
0
1
2
2
0
1
2
1
2
0
2
1
2
1
0
1
1
1
1
1
1
1
0
1
2
1
1
1
1
1
1
1
1
2
2
2
1
2
2
0
1
2
2
2
1
2
0
1
1
1
1
1
1
2
0
1
1
1
2
1
1
1
1
0
1
1
2
1
1
1
1
2
2
1
0
2
1
2
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
0
1
2
1
1
2
2
2
1
1
0
1
0
1
2
2
1
1
0
1
1
1
0
1
1
1
1
1
1
1
2
2
1
2
1
0
2
1
1
1
2
1
1
1
1
1
1
0
2
1
2
1
0
1
1
1
1
1
1
1
2
0
0
1
1
1
1
1
1
1
1
1
1
1
2
0
1
2
1
2
1
0
2
1
0
1
1
2
1
2
1
1
1
1
0
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
2
2
1
2
1
2
0
2
2
0
1
1
2
1
3
1
1
1
2
2
2
1
1
1
1
2
1
2
1
1
0
1
1
1
0
1
1
2
1
0
1
2
0
0
1
1
2
2
1
1
1
1
2
0
1
0
0
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
0
1
1
1
1
2
2
1
1
1
2
2
2
1
1
1
0
1
1
1
1
1
0
1
0
1
1
1
1
1
0
0
1
2
1
1
2
1
0
1
1
2
1
1
2
1
1
1
1
0
2
2
2
1
1
1
1
2
0
1
2
1
1
1
1
2
1
1
1
1
1
2
0
2
1
1
1
0
0
0
0
1
3
1
0
1
1
0
0
2
1
2
1
1
1
1
1
1
1
1
1
1
1
0
0
1
1
2
3
2
2
1
2
1
2
1
0
0
2
1
2
2
0
1
0
1
2
2
2
1
1
2
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
0
2
1
2
1
1
1
1
2
2
1
1
1
2
1
0
0
2
1
2
1
1
1
0
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
0
1
1
2
1
1
1
0
0
1
1
1
0
1
1
1
0
1
1
2
1
1
1
1
1
0
2
1
2
1
1
1
0
2
2
1
1
1
1
1
1
2
1
0
2
1
0
1
1
1
1
1
1
1
1
2
0
1
1
2
1
1
0
1
1
1
1
1
1
2
2
2
0
4
1
0
2
2
1
1
1
1
2
0
1
1
0
2
2
1
1
1
1
1
1
0
1
1
0
1
1
1
3
2
1
1
2
1
0
1
1
1
1
0
0
1
1
0
0
1
2
0
1
1
1
1
1
0
1
0
1
1
1
1
2
0
2
1
0
2
2
2
0
2
0
0
1
1
1
0
1
1
1
1
1
0
1
2
1
2
2
2
1
1
2
1
2
2
2
0
1
2
0
1
1
1
1
1
1
2
0
2
1
1
1
2
2
1
2
1
2
2
2
1
2
1
1
1
0
2
1
1
1
1
1
1
1
1
2
1
0
2
1
1
0
1
2
1
1
0
1
1
2
2
1
1
1
0
1
2
1
1
1
1
1
1
1
0
2
1
1
1
1
0
1
1
2
1
1
1
0
0
0
1
1
2
1
1
1
1
1
0
1
1
1
0
2
1
1
1
2
0
1
1
1
1
2
0
1
2
1
1
1
1
2
1
0
1
2
1
1
2
1
1
1
1
2
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
2
1
0
2
1
0
1
2
0
1
2
1
1
0
1
1
1
1
2
1
1
2
1
1
0
1
1
0
1
0
2
1
2
1
1
1
1
1
1
1
0
1
1
1
2
2
2
1
1
1
1
2
2
1
1
0
2
0
1
0
2
0
1
1
1
1
1
1
1
0
1
1
1
0
1
0
2
1
1
0
2
1
1
1
1
1
2
0
2
1
1
1
0
0
1
1
1
2
1
1
2
2
1
1
1
1
0
1
0
2
1
1
2
1
1
3
1
1
1
1
1
0
1
1
1
1
1
2
2
1
0
1
1
0
2
2
2
2
2
1
2
1
1
1
1
1
0
3
2
2
2
1
1
1
1
1
1
1
2
0
1
2
1
2
0
0
1
1
1
1
1
1
1
2
2
1
2
1
2
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
0
0
2
2
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
2
1
1
1
1
0
1
1
0
1
2
1
1
2
1
0
1
1
0
0
1
2
1
2
4
0
1
1
1
1
1
2
1
1
1
1
2
1
0
1
2
0
0
1
2
0
1
1
0
1
1
1
1
2
1
1
0
1
1
1
0
1
1
1
1
1
1
1
1
2
2
0
2
1
0
1
1
1
1
1
0
1
1
1
0
2
1
3
0
2
3
0
1
1
2
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
2
1
1
1
1
3
2
1
1
1
2
0
1
2
0
1
1
2
1
1
1
1
1
0
1
1
2
0
2
1
1
0
0
2
1
0
0
1
1
2
1
2
3
2
1
1
1
1
2
1
1
2
1
1
2
2
3
0
1
1
1
2
1
2
1
0
1
0
2
2
2
1
2
1
0
1
0
1
2
1
0
1
1
1
2
1
0
0
1
1
1
1
2
1
1
1
0
1
1
1
0
1
1
2
0
2
2
1
1
1
0
1
1
1
0
1
1
1
2
2
0
1
1
2
2
1
1
1
1
1
1
2
2
1
1
1
1
1
0
2
0
2
1
0
1
1
1
1
1
0
0
1
1
1
1
1
1
1
1
2
2
1
0
1
2
1
0
0
0
1
2
1
0
1
2
2
1
2
1
2
0
1
1
1
1
0
1
0
2
1
3
0
1
2
1
0
1
1
2
2
0
1
1
1
1
0
1
1
2
0
1
1
2
2
2
1
1
0
2
0
1
1
2
2
0
1
1
1
2
1
1
1
1
0
0
0
1
2
1
1
1
2
1
1
1
2
0
2
1
2
2
1
1
1
1
1
1
1
1
0
2
0
2
1
2
0
1
1
1
1
1
1
2
1
1
2
2
2
2
2
0
1
2
1
1
0
0
1
1
1
2
2
0
1
2
0
0
1
0
1
1
1
1
1
1
0
1
2
1
0
2
1
0
1
1
1
1
1
2
1
0
1
1
1
1
2
0
1
1
2
1
1
2
1
1
1
1
0
0
1
1
1
1
2
1
1
1
1
2
1
0
1
2
0
2
2
1
1
0
1
1
1
2
1
2
2
1
1
1
0
2
1
1
1
1
2
0
2
1
1
0
1
2
1
0
0
1
2
2
2
1
1
1
0
1
2
2
1
2
0
1
2
2
2
1
1
2
1
0
2
1
2
1
1
1
1
1
2
1
0
1
0
1
0
2
2
1
1
1
1
1
2
1
2
1
2
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
0
2
1
1
1
1
2
1
1
1
1
0
1
2
2
4
1
0
1
0
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
0
2
1
2
1
0
1
1
2
0
1
1
0
1
1
1
0
2
2
1
1
1
1
1
0
2
1
2
0
1
1
1
1
1
2
2
1
1
1
1
2
0
2
1
2
1
1
0
1
1
1
0
1
1
0
1
1
1
2
2
2
1
1
1
1
0
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
0
1
2
2
1
1
1
1
2
1
1
1
1
1
0
1
2
1
1
1
2
1
1
0
1
1
1
1
1
1
1
0
1
0
1
0
2
2
0
1
1
2
2
1
0
0
1
1
1
1
1
1
1
2
2
0
1
1
1
0
1
4
1
1
1
1
1
0
2
1
1
0
0
1
0
1
1
2
2
2
1
1
1
2
1
1
2
2
0
1
1
0
2
1
1
1
1
2
2
3
1
1
1
2
0
1
0
2
1
0
0
2
1
1
2
1
1
1
0
1
1
1
1
2
1
1
1
1
1
0
1
1
1
2
1
2
1
1
1
2
0
1
2
0
2
0
1
1
2
2
0
1
0
1
2
1
1
1
1
0
0
0
1
2
0
1
1
1
1
1
2
1
1
1
1
1
1
1
1
0
1
2
2
1
1
2
2
2
0
1
2
1
0
1
1
2
2
3
3
1
2
1
1
1
2
2
1
1
2
1
2
2
0
2
1
2
2
1
1
1
1
2
0
0
2
1
1
0
2
0
1
0
1
1
1
2
2
1
2
1
1
1
1
1
2
0
1
2
1
1
0
0
2
1
1
2
2
1
1
1
1
1
1
1
2
2
1
1
2
1
1
2
1
1
0
1
0
2
1
1
1
1
1
0
1
1
0
1
1
0
0
2
1
1
2
0
0
0
1
2
1
1
0
1
1
2
1
1
0
2
0
2
2
2
1
0
2
2
0
1
0
0
1
1
2
1
1
1
1
0
0
1
2
1
1
1
1
1
1
1
1
0
1
0
1
1
1
1
2
1
2
1
1
1
1
2
1
2
1
1
2
0
1
1
0
1
2
1
3
1
2
1
0
3
0
0
0
0
1
1
0
1
1
1
0
2
1
2
2
2
1
0
1
2
0
1
1
1
1
1
0
0
1
2
2
2
1
0
1
0
1
0
2
1
1
1
1
1
0
1
1
2
0
0
2
1
1
2
1
2
2
1
1
1
1
6
1
1
1
1
1
1
0
1
1
1
1
0
1
1
1
1
1
1
1
1
1
2
2
1
1
1
2
1
1
1
1
2
2
1
2
1
2
2
1
3
0
2
1
1
1
1
2
1
0
2
0
1
0
1
0
1
1
1
0
1
0
1
1
2
1
0
2
2
1
1
1
1
1
2
1
1
1
1
0
1
1
2
1
1
1
1
1
1
0
1
1
1
1
2
0
1
1
3
2
2
1
2
2
1
1
3
1
2
1
0
0
1
0
1
1
0
1
1
1
1
2
1
1
1
1
1
2
2
2
2
2
1
1
0
2
1
0
1
2
2
1
1
2
2
1
2
1
1
1
1
1
1
1
1
2
0
1
0
1
1
1
1
1
1
1
2
0
1
0
1
0
1
0
1
1
1
2
1
2
1
1
1
1
1
0
1
0
1
2
2
1
1
2
1
2
1
2
1
1
1
0
2
1
0
2
1
0
1
1
2
1
1
1
0
1
1
2
1
2
1
0
2
1
1
1
2
0
1
2
1
1
0
1
2
1
1
1
2
1
1
0
1
1
1
1
1
2
1
1
1
1
1
0
1
1
1
1
0
1
2
0
1
1
0
0
2
1
2
0
1
1
1
1
1
1
1
2
1
1
1
0
2
0
1
1
1
0
1
1
0
0
1
1
0
0
0
0
1
2
1
1
0
2
0
1
2
0
1
2
1
1
2
0
0
0
2
2
1
1
1
2
1
1
1
1
1
1
1
3
1
1
0
1
0
2
2
1
2
1
0
2
1
1
2
0
2
0
2
1
1
2
1
0
1
2
1
1
0
2
2
1
1
0
1
1
1
1
0
1
1
1
0
0
1
2
0
2
1
0
1
2
2
1
1
1
1
1
1
0
0
2
1
2
1
0
2
1
1
1
1
1
2
1
1
1
0
1
1
1
1
1
0
1
0
2
0
0
1
1
1
1
1
0
1
1
1
1
1
1
1
1
2
0
1
1
2
2
2
0
1
1
1
3
1
1
1
1
1
1
1
1
1
0
2
0
0
2
2
1
1
2
2
1
1
1
1
2
1
2
0
0
2
1
1
2
2
0
1
1
2
2
2
0
1
0
1
1
1
2
0
2
1
2
1
1
0
2
0
2
1
1
0
2
2
1
1
2
1
2
2
2
1
0
0
0
2
2
0
1
3
1
1
2
1
1
2
2
1
2
1
1
1
1
0
0
0
1
0
2
1
2
1
2
1
1
1
1
1
0
3
1
1
2
1
0
2
2
2
1
2
1
0
2
1
2
1
0
1
1
0
1
1
2
2
1
1
1
1
1
2
2
0
2
1
0
0
1
1
1
1
2
2
2
2
1
1
0
0
2
1
1
2
2
1
2
1
1
0
1
1
1
2
2
1
0
1
2
0
1
1
1
1
1
2
2
2
2
1
0
1
2
2
2
0
2
1
1
1
2
1
2
1
2
2
1
1
2
2
1
1
1
2
1
2
0
1
1
1
1
0
1
1
2
1
2
1
1
1
1
1
1
2
1
2
0
1
2
2
1
1
2
1
2
2
1
4
2
1
0
1
2
0
1
1
2
1
1
1
1
0
2
0
0
2
0
2
2
0
2
0
1
0
2
1
1
2
1
1
2
2
1
1
2
0
2
1
1
2
1
1
2
1
1
0
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
0
1
2
1
1
1
3
1
0
2
1
0
2
0
1
1
1
1
2
1
2
0
0
1
1
1
1
2
1
1
1
0
0
1
1
2
1
1
1
1
1
1
1
0
1
3
2
1
1
0
1
1
1
2
0
1
1
1
1
2
0
1
2
1
1
1
1
2
2
2
0
2
2
1
1
1
1
2
2
1
0
2
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
0
1
1
1
1
1
2
1
1
2
1
2
2
1
1
1
1
1
2
1
2
1
0
2
1
2
2
1
0
1
1
1
2
2
1
1
0
1
0
1
1
1
2
1
2
1
1
0
1
1
1
1
1
1
0
2
0
2
1
1
0
1
1
0
1
1
2
1
1
2
1
1
1
1
1
2
2
1
2
1
1
1
1
2
2
2
1
2
1
2
2
0
0
2
1
2
1
1
2
0
2
0
2
1
1
2
2
0
1
2
1
1
2
1
2
1
0
2
1
0
1
1
1
1
1
1
1
0
1
0
1
1
1
2
1
2
2
1
1
1
1
1
1
2
2
0
2
2
2
1
1
2
1
1
0
0
0
2
1
0
1
0
1
1
1
2
0
1
1
1
2
1
1
2
0
2
2
2
1
2
2
1
0
1
0
1
2
2
2
0
0
1
2
2
1
2
2
0
2
0
2
1
2
0
2
0
1
1
1
2
2
2
2
2
2
1
1
1
1
1
1
2
2
2
0
1
1
1
2
1
1
0
0
0
1
2
0
0
2
1
1
2
1
1
2
2
2
2
2
1
1
1
0
1
1
2
1
2
2
1
1
0
0
1
1
1
0
1
1
2
2
1
1
1
2
1
2
2
1
1
1
1
1
0
2
2
1
0
1
2
0
2
0
1
1
1
1
0
1
0
1
1
0
1
1
0
1
1
1
0
1
2
1
0
0
0
0
0
2
2
0
1
0
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
2
1
1
1
2
1
1
1
1
1
1
2
1
1
0
1
1
2
1
2
1
1
1
1
0
1
1
1
1
1
1
1
2
2
1
1
1
0
1
2
1
1
1
1
1
1
1
1
2
0
1
0
1
1
2
2
1
1
1
2
1
1
1
2
1
1
0
2
1
1
0
1
1
2
1
1
1
1
1
1
2
1
2
1
1
0
1
2
1
0
2
1
1
1
2
0
1
1
0
1
1
0
1
1
0
6
2
2
1
1
2
1
2
1
2
0
1
2
1
2
1
2
1
1
2
1
1
0
2
1
1
2
2
2
2
1
1
1
1
0
1
1
1
1
2
1
1
2
1
1
1
3
1
1
2
2
2
2
1
1
2
1
1
1
0
1
2
1
2
0
1
2
1
0
2
1
1
0
0
2
1
1
1
0
0
1
1
2
2
0
2
2
1
1
1
2
2
2
2
0
0
1
1
1
1
0
1
1
3
1
1
2
1
1
1
1
2
2
2
2
1
2
1
1
2
1
2
2
1
1
1
1
1
2
0
2
1
1
0
1
2
0
1
1
1
1
1
1
1
0
2
2
1
0
1
1
0
1
0
1
1
0
1
1
1
2
1
1
1
2
2
0
1
1
1
2
1
1
1
1
2
0
1
2
1
1
1
1
0
1
1
1
1
1
1
2
1
2
1
1
2
2
1
2
1
2
1
1
1
1
1
1
1
1
1
2
1
2
1
1
0
1
1
2
1
2
2
2
2
1
1
1
2
0
0
1
1
1
1
1
2
1
2
1
2
1
1
0
2
1
1
1
1
2
2
1
2
1
1
2
0
1
1
1
1
2
1
1
1
1
1
0
1
1
2
1
2
0
1
1
1
1
2
1
1
1
1
2
0
1
1
1
1
2
1
1
2
1
1
1
3
2
1
0
2
2
2
2
2
1
1
0
1
0
2
2
2
1
0
2
0
1
0
2
1
1
2
2
1
1
1
2
1
1
2
1
1
1
2
0
0
1
1
0
2
2
1
1
1
0
0
1
1
0
2
1
1
1
0
1
2
1
2
1
1
0
1
1
2
2
0
0
1
1
2
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
2
0
1
1
1
0
1
1
2
1
1
2
2
2
1
2
1
2
1
0
2
1
1
1
2
1
1
1
0
0
1
1
0
1
1
1
1
1
2
1
2
1
1
1
1
1
2
1
0
1
2
1
0
1
0
1
2
0
1
1
1
2
1
0
1
1
1
1
1
2
1
1
2
1
1
0
1
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
1
2
1
1
1
1
2
1
1
0
1
1
1
0
2
2
2
1
1
1
1
1
0
1
1
0
1
1
2
1
0
1
0
2
1
0
1
2
1
0
1
2
2
2
1
1
2
1
1
1
1
0
1
1
1
0
1
2
1
3
1
0
1
1
1
2
1
2
1
2
1
0
2
2
1
1
3
0
2
0
1
2
1
1
0
2
1
2
3
0
1
1
1
0
2
2
0
1
1
1
2
1
1
1
1
1
0
1
1
2
2
1
1
1
1
1
1
1
0
2
2
0
0
1
2
1
2
1
0
0
1
1
1
2
3
1
1
0
3
1
1
2
1
0
1
0
2
1
0
1
1
2
1
2
2
1
1
1
0
2
1
2
0
0
2
2
2
2
1
1
1
1
2
3
0
1
2
1
1
1
2
0
1
2
1
1
1
2
0
1
1
2
1
0
0
2
2
1
2
2
2
2
2
1
2
0
0
1
1
0
1
0
2
2
1
1
1
1
0
0
1
2
1
2
1
1
1
2
1
1
1
2
1
1
1
1
1
0
1
1
2
0
2
0
1
2
2
2
1
1
0
1
1
1
2
1
1
2
1
2
1
1
0
2
2
0
2
0
1
1
2
0
1
1
1
1
1
2
1
1
0
1
1
1
1
0
1
1
1
1
1
2
1
0
2
1
0
0
0
1
2
1
2
1
0
2
1
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
0
1
2
2
2
1
2
0
0
1
0
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
0
3
1
1
2
0
1
2
1
1
2
1
1
2
1
1
1
2
0
1
1
1
0
1
0
1
1
1
2
1
0
0
2
2
1
1
1
1
1
2
2
2
1
1
0
2
1
1
1
1
1
1
2
1
1
0
1
1
2
2
2
1
1
1
1
1
2
2
1
1
1
1
1
2
2
1
1
1
1
2
1
1
0
1
1
1
0
3
1
1
1
1
1
0
2
1
0
2
1
2
1
0
2
1
1
1
0
1
0
0
4
0
1
1
0
1
2
1
0
1
1
2
2
1
1
1
2
1
0
1
2
1
1
1
1
2
1
2
1
0
1
1
1
1
2
2
1
1
2
1
2
1
0
2
1
1
1
2
1
2
1
1
0
1
1
1
0
1
2
1
1
1
1
1
2
0
1
1
1
0
0
1
1
1
1
1
0
1
0
1
1
2
1
0
1
0
2
1
2
1
1
2
2
0
1
0
0
1
1
1
2
1
1
2
1
0
0
0
2
1
0
1
1
0
2
1
2
1
0
1
1
3
1
0
0
2
1
1
1
2
1
1
1
1
2
2
1
2
0
1
1
2
2
2
0
1
0
0
2
2
0
1
1
1
1
0
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
0
2
1
1
1
1
2
0
2
1
1
1
0
0
2
0
2
1
2
0
1
1
1
1
1
0
1
1
1
0
1
0
2
2
1
1
1
3
1
0
2
0
2
0
1
1
0
1
1
2
2
1
1
0
1
1
1
1
2
1
1
1
1
1
2
0
2
2
2
1
1
1
0
0
2
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
2
1
1
2
2
0
1
1
2
1
1
1
0
2
0
1
1
1
1
1
0
1
1
1
0
1
1
0
0
1
2
2
1
0
1
1
0
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
0
2
1
1
2
1
2
3
2
1
1
2
1
1
1
1
1
1
0
1
1
1
2
1
1
1
1
1
1
1
0
0
2
2
1
1
2
1
1
1
2
1
0
2
0
1
2
1
1
1
1
2
1
1
2
1
1
0
0
1
0
2
1
1
1
1
1
2
1
1
1
2
2
0
1
2
1
1
1
2
1
1
2
1
1
1
2
1
1
1
1
0
1
1
0
1
0
1
0
2
1
1
1
0
2
1
0
2
2
2
1
1
0
1
0
0
2
1
1
0
2
1
1
1
0
1
1
2
1
1
1
1
1
1
1
2
0
2
1
2
1
1
1
2
1
1
0
1
2
1
1
1
1
1
2
1
1
2
1
1
2
2
2
1
1
1
1
1
1
0
1
1
1
2
1
1
0
1
1
2
1
1
1
1
1
0
2
1
2
2
1
1
0
1
1
0
1
1
1
0
1
1
1
2
1
1
1
1
2
1
1
1
2
1
1
1
1
0
0
0
1
1
4
1
1
1
1
2
1
1
1
0
1
1
1
1
1
0
1
0
2
0
1
1
2
2
1
1
2
2
1
1
1
1
1
0
1
2
2
0
1
2
2
0
0
1
1
2
2
1
1
0
0
2
1
2
1
1
0
1
0
1
1
2
1
2
1
0
1
1
0
1
1
2
3
1
1
0
1
1
1
1
0
1
1
1
2
0
1
1
1
0
2
1
1
1
2
1
2
1
1
1
1
0
1
0
1
1
1
0
0
1
0
2
2
1
1
1
2
1
1
1
1
1
2
1
2
2
2
0
2
1
1
1
1
1
1
1
1
1
0
1
1
1
2
0
1
2
1
2
0
0
0
1
2
2
2
1
0
2
2
1
1
1
2
2
2
0
1
1
0
0
1
1
0
1
2
0
1
2
1
1
0
2
2
0
1
1
0
2
2
1
0
1
0
1
0
2
2
2
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
0
1
1
1
2
2
2
0
1
0
2
2
1
1
1
1
2
1
2
0
1
2
0
1
1
1
0
1
1
2
2
1
1
1
1
1
1
1
0
1
2
1
2
1
1
1
1
1
2
1
1
0
1
2
2
2
1
2
0
1
1
1
1
1
1
2
1
2
0
0
1
1
2
1
2
0
0
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
0
1
1
1
0
2
2
0
2
2
2
1
0
1
1
2
2
1
1
1
2
1
1
0
2
1
1
0
1
1
2
2
1
1
1
1
1
1
1
2
2
1
1
2
1
1
2
1
0
1
2
0
2
0
1
1
1
1
2
0
1
0
2
0
1
1
0
0
1
1
1
1
2
1
1
2
1
0
1
1
1
1
1
2
1
0
1
1
1
1
2
2
2
1
2
0
2
1
1
1
0
1
1
2
1
1
0
1
1
1
1
2
2
2
1
1
1
1
1
1
2
1
1
2
0
1
2
0
2
1
1
1
1
1
1
0
2
1
1
1
0
0
1
2
0
0
1
1
1
1
2
1
0
1
1
1
2
1
2
1
1
0
1
2
1
2
2
1
0
2
1
1
2
1
0
1
2
1
1
1
1
0
1
1
2
1
1
2
2
2
1
0
1
1
1
0
1
1
1
3
1
1
1
1
2
1
1
1
1
1
2
1
2
0
1
2
1
1
1
2
0
1
1
1
2
0
1
2
2
1
2
2
2
1
1
1
1
1
1
1
2
0
2
1
1
1
1
2
1
1
0
1
2
1
1
1
1
1
0
1
2
2
1
2
1
1
2
1
1
2
2
1
1
2
1
1
2
1
1
2
0
1
1
2
1
1
1
1
2
2
3
1
1
1
1
0
2
1
1
2
0
1
1
2
1
1
0
1
1
1
1
1
2
2
2
0
1
1
0
1
2
2
1
1
0
1
1
0
1
1
2
1
1
2
0
1
1
1
0
1
1
2
1
1
1
1
1
1
0
0
2
2
0
2
1
1
1
2
1
2
2
0
1
1
0
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
0
2
1
2
1
2
2
1
1
1
1
2
1
1
0
1
1
0
3
2
1
1
1
1
1
2
1
1
0
1
0
1
1
0
1
4
2
1
2
1
1
0
1
0
2
2
1
1
2
1
1
2
2
1
1
1
1
1
1
1
3
0
2
1
1
1
0
1
2
2
1
2
2
0
0
1
1
1
1
2
0
2
1
2
0
2
1
1
1
0
1
2
1
1
2
1
0
1
1
1
1
0
1
2
1
1
2
1
0
2
1
0
1
1
2
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
0
0
2
2
1
1
0
1
1
0
1
2
1
2
2
1
0
2
1
0
1
1
1
1
1
1
0
1
1
2
0
1
1
0
2
1
1
1
1
2
1
1
0
2
2
1
2
2
0
1
2
0
1
2
2
1
2
1
2
2
1
1
1
2
0
2
2
1
1
2
2
1
1
2
0
0
1
1
1
3
1
1
1
2
2
0
1
1
1
0
0
1
1
1
0
1
1
2
1
1
2
0
1
1
2
0
1
1
0
1
0
1
0
1
1
1
1
2
1
1
1
1
1
0
1
2
0
1
0
2
2
0
1
0
1
1
1
1
1
0
2
1
3
1
2
1
2
2
1
1
1
2
0
1
1
1
1
2
1
1
2
2
1
2
2
1
1
1
2
1
2
2
1
1
1
2
2
1
2
2
1
1
2
1
1
1
1
2
0
1
2
2
1
1
2
2
1
0
3
1
1
1
2
0
1
1
1
2
1
2
2
1
0
2
1
1
0
1
1
1
2
0
2
1
2
2
2
1
2
1
1
1
1
1
2
1
2
3
2
1
0
2
1
1
1
0
1
1
1
1
0
0
2
0
1
1
2
1
1
2
1
1
2
1
1
0
0
1
1
1
1
1
1
1
2
0
0
1
1
2
1
1
1
1
2
1
1
1
1
1
2
2
1
0
2
2
1
1
1
1
1
1
1
0
1
1
1
1
2
2
1
2
1
2
0
1
2
0
1
2
1
0
1
2
0
2
1
1
2
1
1
1
1
1
0
0
2
2
2
1
1
0
0
1
1
1
1
2
0
1
1
2
0
0
1
2
1
1
1
1
1
2
0
0
1
2
1
1
1
1
2
0
2
1
1
1
1
1
0
2
2
1
1
2
1
1
1
0
1
1
0
1
1
2
1
1
1
1
2
2
0
0
1
1
1
2
2
2
2
1
2
1
1
1
2
1
0
1
1
0
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
0
0
2
1
2
1
1
1
0
2
1
1
1
1
1
1
1
2
1
2
0
0
1
1
1
2
1
1
1
1
0
1
2
2
1
0
1
1
0
2
0
1
1
1
0
1
1
1
0
1
2
1
2
1
1
1
2
1
2
1
1
1
1
1
1
1
1
0
1
1
1
1
2
1
2
1
1
1
1
1
1
1
2
2
1
2
2
2
1
2
0
1
0
1
1
1
2
0
1
7
2
2
1
0
1
1
1
1
1
0
1
1
1
2
0
1
2
2
1
2
1
1
0
1
1
1
0
0
1
0
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
2
0
1
1
1
0
1
2
2
1
1
1
1
1
1
1
0
2
1
0
0
2
1
2
1
1
1
1
1
1
1
2
0
1
1
1
1
1
0
1
0
1
1
2
1
1
1
0
1
5
2
1
1
1
2
1
1
0
2
1
0
0
1
1
2
2
3
1
0
2
0
1
1
1
1
0
2
1
1
2
0
0
2
0
1
0
1
1
0
1
1
1
1
2
0
1
1
1
3
1
1
2
1
2
2
1
0
1
2
1
0
2
2
0
2
2
1
1
0
2
2
2
1
1
1
1
2
1
2
1
1
1
1
1
0
1
1
2
1
0
1
1
1
1
1
2
1
1
2
1
1
2
1
2
1
0
1
2
0
1
1
2
0
0
1
1
1
1
1
1
1
1
1
2
1
0
0
2
0
1
1
2
0
1
1
1
4
1
1
1
1
0
2
1
1
0
2
2
2
0
1
2
1
1
0
1
1
1
2
2
1
1
1
1
0
1
1
2
1
1
1
0
2
1
2
1
2
3
0
1
1
2
0
2
3
1
1
1
1
1
1
1
0
2
1
1
1
1
2
0
2
1
1
0
1
1
1
2
2
0
0
1
1
0
1
0
1
1
1
1
2
1
1
0
2
1
1
1
2
1
1
1
0
1
0
0
1
1
0
1
2
1
0
1
1
1
1
1
1
2
1
0
1
1
2
1
0
3
2
1
1
2
2
1
2
0
2
1
1
1
1
1
1
1
0
2
2
1
2
1
0
2
2
1
2
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
2
1
1
0
1
2
1
0
0
1
0
1
1
1
1
1
0
1
2
1
0
1
2
2
1
1
1
1
1
1
0
1
0
1
1
1
2
2
1
2
1
0
2
1
0
0
1
2
1
1
1
2
1
1
2
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
0
0
0
2
1
1
1
1
2
2
1
2
2
1
1
1
1
1
1
0
1
1
1
0
1
1
0
0
1
0
0
1
1
2
0
2
1
2
0
2
1
2
2
1
1
2
0
2
2
1
1
0
2
1
1
2
2
1
1
2
1
1
2
2
1
0
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
2
1
2
2
2
0
1
1
2
1
1
0
2
1
1
1
1
1
1
2
1
1
0
1
2
1
0
1
1
1
2
2
1
2
0
1
2
1
1
1
1
1
2
1
1
2
1
1
0
1
1
2
0
1
1
1
1
2
1
1
1
1
1
1
1
1
2
0
1
1
0
2
1
2
2
0
1
2
1
1
2
1
1
2
1
2
1
1
0
1
1
1
0
2
1
1
1
1
1
1
1
1
0
2
1
1
1
2
2
1
2
2
1
2
1
1
1
2
2
1
2
1
1
1
2
1
0
1
1
2
1
1
0
1
2
0
1
1
2
1
1
2
0
1
1
2
1
0
2
2
1
2
1
2
2
1
1
2
1
2
2
2
0
1
0
1
2
2
1
2
2
1
1
2
1
1
1
2
2
1
2
1
2
0
1
1
0
1
1
1
2
1
0
2
1
1
2
2
1
2
1
2
2
1
1
1
1
0
0
1
1
1
0
1
1
0
2
1
0
2
1
1
1
2
1
1
1
1
2
2
1
1
1
1
1
1
1
0
1
0
2
1
2
1
1
2
0
1
1
0
2
1
0
1
1
2
0
1
2
1
1
0
1
1
1
2
0
1
0
1
1
2
3
1
0
2
1
0
1
1
0
1
1
2
1
0
2
1
1
1
2
1
1
1
1
0
0
0
1
1
1
1
1
1
2
1
1
2
1
0
1
1
1
1
1
2
1
1
1
1
1
2
1
2
2
1
1
1
1
2
2
2
1
1
3
1
0
1
1
0
2
1
1
0
1
1
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
2
0
2
1
1
2
0
1
2
1
0
1
1
0
1
0
1
2
2
1
0
2
1
1
1
1
2
1
1
2
0
1
1
2
1
1
1
1
0
1
1
2
1
1
0
2
0
1
1
1
2
2
2
1
2
0
2
2
1
1
2
1
1
2
1
1
1
1
1
1
0
1
0
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
0
2
1
1
2
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
2
0
1
1
1
1
2
2
1
0
1
1
1
0
1
1
2
1
0
1
1
0
2
1
2
0
1
1
1
1
1
1
1
1
2
0
2
0
1
1
2
0
1
1
1
1
0
1
2
2
1
1
1
1
1
2
0
1
1
2
2
1
0
2
3
2
1
1
2
1
1
1
1
1
1
2
2
2
1
1
0
1
0
1
2
1
1
1
2
0
1
2
1
1
1
2
1
1
1
0
1
1
1
1
0
2
1
2
1
2
1
1
2
1
0
1
2
1
2
2
1
2
0
1
1
0
1
2
2
1
2
1
1
1
0
1
1
1
1
0
1
1
0
1
2
1
0
1
2
1
1
0
2
1
2
1
1
1
0
0
1
2
0
2
2
0
1
1
0
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
2
2
1
2
1
1
2
1
1
1
0
2
1
2
1
1
1
1
0
1
0
0
2
0
0
1
1
1
3
2
1
1
1
1
1
0
1
1
1
1
1
0
0
1
1
2
0
2
0
1
1
1
0
4
1
0
1
1
2
1
1
1
2
1
1
0
1
1
0
1
1
1
1
0
1
2
1
1
0
1
2
0
2
1
1
1
0
2
1
2
0
2
2
3
1
2
2
0
2
2
2
2
1
1
1
0
2
2
2
1
2
2
0
1
1
1
1
0
0
0
1
1
1
2
1
1
1
1
1
2
3
1
1
0
2
2
2
1
1
1
1
2
1
2
1
1
1
1
2
0
1
1
1
2
3
2
1
1
1
1
1
1
1
1
1
1
1
2
0
1
1
2
2
2
1
0
1
1
1
2
1
1
1
1
1
1
1
2
2
0
1
1
1
1
1
2
0
1
1
1
2
1
1
1
1
0
1
2
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
2
1
2
1
2
1
1
2
3
1
2
1
2
2
2
2
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
0
1
1
0
1
2
2
2
2
1
1
2
2
1
1
0
1
1
2
0
1
1
1
0
1
1
1
2
1
2
1
1
2
1
1
0
1
1
1
1
1
2
2
1
1
1
0
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
2
1
1
1
2
1
1
1
1
1
2
1
2
2
0
2
1
1
0
2
1
2
1
1
0
3
1
1
1
1
1
0
1
1
2
2
2
2
2
1
1
2
1
1
2
1
2
0
0
1
1
1
1
1
0
1
1
2
1
1
1
2
1
1
1
0
2
1
1
1
2
2
2
1
1
2
1
1
1
2
1
1
1
1
1
0
1
1
1
1
1
1
1
2
0
2
2
2
2
1
1
0
1
0
2
1
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
0
3
1
1
2
1
1
1
1
1
1
1
1
0
1
1
1
0
2
1
2
2
1
1
1
2
1
1
1
1
0
1
2
1
2
1
0
1
1
0
1
1
2
2
0
1
0
1
1
1
0
0
0
1
2
1
1
1
1
0
1
0
1
1
1
1
1
1
1
1
0
1
1
0
1
1
1
1
1
0
1
1
1
2
1
2
1
1
0
1
2
1
2
2
1
1
0
2
2
2
1
1
1
0
1
1
1
1
1
1
1
1
1
1
0
2
1
1
1
1
2
2
2
1
1
2
1
1
1
1
2
1
1
2
2
0
1
0
1
1
1
2
1
2
0
2
1
1
1
2
1
1
1
1
1
0
1
2
1
1
0
1
1
2
0
1
1
2
2
1
2
0
0
1
1
1
1
1
1
1
0
3
1
0
1
0
1
2
1
2
1
1
1
2
1
1
1
1
1
2
2
2
2
2
1
2
1
1
0
2
1
2
0
1
1
2
2
1
1
1
2
1
2
1
1
2
1
2
0
2
1
1
1
1
2
1
1
1
2
1
1
0
2
1
2
1
1
1
1
1
1
1
1
2
2
2
1
2
0
2
1
2
2
2
2
1
1
1
1
0
1
1
1
1
2
0
1
1
3
0
2
1
2
1
1
2
2
1
1
1
2
0
1
1
0
1
1
2
1
0
1
1
2
1
2
2
0
2
1
2
1
1
2
2
1
0
2
1
1
0
2
1
1
1
2
1
1
0
1
1
1
1
1
2
0
1
0
1
1
1
2
1
1
0
1
1
2
0
1
1
2
1
2
2
2
1
1
2
1
0
1
1
2
2
1
2
2
2
1
2
0
1
2
1
1
1
1
1
2
1
1
0
1
2
1
1
1
3
1
1
1
1
2
2
2
1
2
2
0
1
3
0
1
0
1
2
1
2
1
0
2
2
2
2
0
1
2
1
1
1
1
1
2
0
0
0
2
0
1
1
1
1
1
0
1
0
1
1
1
1
1
2
2
1
0
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
2
2
1
1
0
1
1
0
0
0
2
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
3
2
2
1
1
1
1
1
1
1
2
1
2
1
0
2
2
1
1
1
0
1
2
2
0
1
1
2
2
0
1
2
1
1
1
1
1
2
1
1
1
1
1
0
1
1
1
1
1
2
2
1
2
2
1
1
1
1
2
1
0
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
2
1
2
1
1
0
2
2
1
1
1
1
1
0
1
1
1
1
1
1
2
2
1
2
1
2
0
1
4
1
2
1
1
1
1
1
1
0
1
0
1
0
1
2
1
2
1
1
1
1
2
1
1
1
2
2
2
1
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
0
0
1
2
0
1
1
0
1
2
2
2
1
2
1
1
1
1
1
0
2
1
2
1
0
1
0
1
1
0
1
1
1
1
1
1
1
0
1
1
0
0
2
1
2
1
2
2
2
1
1
0
1
0
1
1
2
0
1
1
2
2
0
1
0
0
0
1
1
1
1
0
2
1
2
1
0
0
1
1
1
1
1
1
1
1
2
1
2
2
1
2
1
2
1
1
2
1
1
1
1
2
1
1
2
1
1
2
0
2
1
2
1
1
2
1
3
0
0
1
1
1
0
0
1
2
1
1
1
1
1
2
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
2
2
1
1
2
2
1
1
0
1
2
1
1
0
1
1
1
0
1
1
1
2
1
1
1
1
1
1
1
1
0
0
0
1
1
2
1
3
1
1
0
1
2
2
1
2
0
1
0
2
1
0
1
1
1
1
1
1
1
0
0
1
1
2
2
1
1
2
0
1
1
1
1
1
2
0
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
2
1
2
1
2
1
1
2
1
1
0
1
1
0
1
2
1
1
2
1
1
0
0
2
1
2
1
2
0
2
2
1
1
0
2
0
2
1
2
1
2
2
1
1
1
1
2
3
1
0
1
1
1
1
0
1
1
1
1
1
1
1
2
1
2
1
0
1
1
2
1
2
2
1
1
1
1
1
1
2
1
2
2
1
2
0
1
1
1
1
1
1
1
1
2
1
1
1
2
0
1
1
0
1
1
1
1
0
1
1
2
1
2
3
1
1
2
1
1
1
1
2
1
2
2
1
2
1
1
0
1
1
0
1
0
1
1
1
1
1
1
2
1
1
0
1
2
1
1
2
1
1
2
1
1
1
2
1
0
2
1
2
1
1
1
1
0
2
1
1
1
1
1
0
1
2
2
1
2
1
1
0
2
0
1
2
2
1
2
1
0
1
1
1
0
1
1
0
2
0
2
1
2
1
1
1
2
1
1
2
1
2
0
0
0
0
1
2
1
1
1
2
0
1
0
1
2
0
1
2
2
2
1
1
1
2
1
1
0
1
1
0
2
1
1
0
1
2
2
1
1
0
2
1
1
2
1
1
2
1
1
2
1
0
1
1
2
2
1
0
1
1
1
1
1
1
2
2
0
0
1
2
1
1
2
0
0
1
1
1
1
0
2
2
0
1
1
0
0
2
1
2
1
1
2
2
1
2
2
1
1
1
2
1
2
0
1
1
1
1
1
1
1
0
1
1
1
1
1
1
2
2
0
2
1
1
1
1
0
2
1
1
1
1
4
0
1
1
1
1
2
2
1
1
1
1
2
2
1
1
1
0
1
1
1
0
1
2
1
1
1
1
2
1
2
2
2
0
0
2
0
1
2
0
2
1
2
1
1
1
2
1
0
0
0
1
1
1
2
1
2
0
1
1
1
2
1
0
2
1
1
1
0
2
1
1
0
1
1
1
1
1
2
1
1
1
1
2
1
2
2
3
1
0
1
1
1
2
0
2
0
1
1
1
1
1
0
2
0
1
2
1
1
1
0
2
1
2
2
2
1
2
1
1
1
1
2
1
1
1
1
2
0
2
2
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
0
1
2
1
1
1
0
2
2
1
1
1
1
1
1
2
0
1
1
2
2
3
2
1
1
1
2
1
1
1
1
0
0
1
1
1
1
1
2
1
1
0
2
2
1
0
2
1
2
1
1
2
1
1
1
1
1
2
1
1
1
0
1
2
2
2
0
0
4
2
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
0
2
0
0
1
1
1
2
1
0
1
2
2
1
2
1
2
1
1
1
2
2
2
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
0
2
1
1
1
1
2
1
1
2
2
1
1
0
0
1
0
1
1
1
1
1
1
0
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
0
2
1
0
2
1
1
1
1
0
0
1
1
1
2
1
2
0
1
1
2
0
2
1
1
0
2
1
1
0
2
1
1
2
0
2
1
1
2
1
1
1
0
1
1
0
1
2
2
1
2
1
1
1
0
0
1
0
1
1
2
1
1
1
1
1
0
2
1
1
2
0
2
1
2
1
1
1
1
2
1
1
1
0
0
1
2
2
2
0
2
1
1
1
1
1
4
2
1
1
1
1
2
1
2
1
1
2
1
1
1
1
1
0
1
1
1
0
1
1
0
1
1
1
2
2
1
1
1
0
1
2
1
1
0
1
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
1
2
1
2
1
0
1
1
2
1
1
1
1
1
0
0
1
1
3
0
2
1
1
1
1
1
1
2
1
1
0
1
1
0
1
1
2
1
1
2
1
1
1
2
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
0
1
1
1
1
1
2
1
1
1
1
1
1
1
0
2
1
1
2
0
2
0
1
1
1
1
2
2
1
2
1
0
1
1
0
1
1
1
1
1
1
1
1
1
0
2
1
1
2
1
0
1
0
2
0
2
2
2
1
1
2
2
0
3
1
1
1
0
0
1
1
1
1
1
2
0
1
1
1
0
1
2
1
1
3
2
0
1
0
1
1
0
1
2
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
2
1
2
2
2
2
1
0
1
1
0
1
1
1
0
1
1
1
0
1
1
1
1
1
1
1
2
1
0
1
1
1
1
1
0
0
1
1
1
1
2
1
1
0
2
1
1
1
1
2
1
2
2
2
1
1
1
2
1
1
1
1
2
1
2
1
1
1
0
1
1
1
0
1
1
1
0
1
2
0
0
2
1
1
2
1
2
0
0
0
1
1
2
0
1
0
1
1
1
1
1
0
1
2
0
2
0
2
1
1
1
1
0
1
2
0
1
0
2
1
1
2
2
1
1
1
1
2
1
0
0
1
1
1
1
2
1
1
1
1
3
1
1
1
1
1
1
2
1
1
2
1
0
0
1
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
0
0
1
1
1
2
2
1
0
1
2
2
2
1
2
0
1
1
1
1
1
0
1
0
1
1
1
0
1
1
1
2
2
0
1
1
2
2
1
1
1
0
1
1
2
1
1
1
2
1
1
1
1
1
1
0
0
1
1
1
1
3
1
1
2
0
0
1
1
0
0
1
1
2
2
2
2
2
1
1
0
1
1
1
1
2
0
1
1
1
1
1
1
1
1
0
1
1
2
0
1
0
0
0
1
2
1
1
2
1
2
1
2
2
1
1
2
0
0
0
2
0
1
1
1
1
1
0
0
2
2
0
2
2
1
1
1
2
1
2
1
2
1
2
2
0
2
1
2
2
2
1
1
1
1
2
0
1
1
1
0
1
2
2
1
5
0
1
1
2
0
1
1
0
2
1
1
1
1
0
2
1
1
1
1
1
1
1
1
1
1
1
2
0
1
1
1
1
1
0
1
0
1
0
0
1
0
1
1
2
1
1
1
1
3
0
1
1
1
0
2
2
1
1
1
1
1
1
1
2
0
0
1
2
2
1
2
0
1
1
0
1
1
1
2
2
1
1
1
2
1
1
0
1
0
1
1
0
1
2
1
2
1
1
2
1
1
1
1
0
1
1
1
0
2
1
2
1
0
2
0
1
1
2
0
0
1
1
0
0
1
2
2
2
2
1
1
1
2
1
1
1
0
1
0
1
1
0
1
1
2
1
1
1
1
1
1
0
2
2
1
2
2
1
2
1
2
1
1
0
2
2
1
2
1
1
1
1
2
2
1
0
2
1
0
2
1
0
1
2
0
2
1
1
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
2
0
1
1
2
1
0
1
1
1
1
1
2
1
1
1
1
1
2
2
4
2
1
2
0
1
2
1
1
1
0
1
1
0
2
1
1
2
1
1
2
1
1
1
0
2
0
1
2
1
0
0
1
1
2
0
2
1
1
0
2
2
1
1
1
1
0
1
2
2
1
1
2
2
1
1
0
1
1
1
2
1
0
1
2
2
1
1
1
1
1
0
1
1
1
1
1
2
1
2
2
0
1
1
1
1
1
1
1
1
0
1
1
1
2
2
2
2
1
1
2
1
1
0
2
0
1
1
1
2
0
1
1
2
1
0
1
1
1
2
1
1
1
2
2
1
2
2
1
0
0
1
1
1
0
1
1
1
1
1
1
1
1
0
1
2
2
0
1
1
1
1
2
3
0
1
1
0
1
0
1
1
2
1
2
1
0
1
1
1
1
1
1
1
2
0
1
0
1
0
1
2
1
1
1
1
1
1
2
1
1
0
2
1
1
0
1
1
1
1
1
0
1
1
0
2
2
1
1
2
2
0
1
1
3
2
1
1
1
2
1
1
1
1
2
1
1
2
0
1
1
1
1
0
1
0
0
2
1
1
1
1
2
1
1
1
1
1
2
1
1
2
2
1
1
2
2
2
2
0
2
2
0
1
2
2
1
1
1
1
2
1
1
0
2
0
2
1
1
1
2
1
1
2
1
0
1
1
1
1
2
1
2
1
1
1
1
0
1
1
0
1
1
2
0
1
1
1
2
2
1
2
1
0
1
1
2
0
2
0
0
2
1
2
1
1
2
3
1
1
0
1
1
2
1
2
1
1
1
1
1
2
1
2
2
2
2
2
1
1
2
1
2
2
1
1
2
2
1
1
2
1
2
1
1
1
1
2
1
0
1
0
2
2
1
1
0
1
0
1
1
1
1
1
2
1
2
1
0
1
2
1
2
1
1
1
0
1
2
1
2
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
0
1
1
1
0
1
1
2
1
1
1
2
2
1
1
1
1
1
1
2
1
0
2
0
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
0
0
1
1
0
2
1
2
1
2
0
1
1
1
0
2
1
1
1
1
1
2
1
1
1
2
1
2
0
1
1
1
2
1
1
1
2
1
0
1
0
1
1
2
0
1
1
0
0
1
0
0
1
2
2
2
0
0
0
1
0
1
1
1
1
1
1
1
1
1
1
1
2
0
1
1
0
2
0
0
1
0
1
0
1
0
2
2
0
1
2
0
1
1
1
2
1
1
1
1
1
0
0
1
0
1
1
1
2
1
1
1
1
1
1
1
0
1
1
1
1
1
0
2
1
1
1
2
1
1
1
1
0
1
1
0
1
2
2
1
1
1
2
1
1
1
2
1
0
1
2
1
0
1
2
2
2
1
2
2
0
1
1
1
0
2
1
1
0
1
1
1
1
2
1
2
2
2
1
2
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
1
1
2
1
2
2
1
1
1
1
2
1
1
2
1
1
2
0
0
1
0
1
1
0
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
1
1
1
0
0
1
1
0
1
1
1
0
1
2
2
2
1
1
1
1
2
1
1
2
1
0
2
1
2
1
0
0
0
2
2
2
0
1
1
2
1
2
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
2
1
1
2
0
2
1
1
1
2
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
0
1
1
1
0
0
1
1
1
1
1
2
1
0
1
0
2
0
1
0
1
0
1
0
1
1
1
1
1
2
1
2
1
2
1
1
1
1
0
1
1
2
1
2
1
2
1
1
2
1
1
0
1
1
1
2
2
1
0
1
1
1
1
1
1
1
2
2
1
1
2
2
1
1
1
2
2
2
2
2
2
0
2
0
0
2
1
1
1
1
1
2
1
1
0
1
2
1
0
1
1
2
2
1
1
1
2
1
2
1
1
1
1
0
2
1
0
1
1
1
1
2
1
2
0
1
2
0
1
0
1
1
2
0
1
2
2
0
1
2
2
0
0
0
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
2
2
2
1
1
2
2
2
0
2
1
1
2
0
1
1
1
2
1
1
0
1
1
1
1
1
2
1
1
2
1
0
1
0
2
1
2
2
1
3
1
1
1
1
2
0
1
1
2
1
1
1
1
1
1
2
1
2
1
1
1
2
1
1
2
0
0
2
0
1
1
1
0
1
1
2
1
2
1
1
1
1
2
0
1
1
1
2
2
1
2
2
1
2
1
1
2
0
2
2
0
1
2
1
1
1
2
1
1
1
0
1
1
2
0
1
1
1
1
2
1
1
0
1
1
1
2
1
2
1
2
0
1
1
2
1
2
2
0
0
1
1
1
1
0
2
0
2
1
1
2
1
1
1
1
1
1
2
0
0
4
1
0
1
2
1
2
1
1
1
1
2
2
0
1
1
0
1
1
2
1
2
1
1
2
1
1
2
1
1
1
1
0
1
1
2
0
1
1
1
1
1
1
1
0
1
1
1
0
1
1
2
1
1
1
2
1
0
0
2
0
1
1
0
1
1
1
0
2
1
0
3
2
1
1
2
2
1
1
1
0
1
2
1
2
2
1
1
1
1
1
2
1
1
0
2
1
0
2
2
0
0
1
1
0
1
0
1
1
1
0
2
1
1
1
0
0
1
1
2
1
1
0
0
1
0
1
1
0
1
1
2
1
1
0
2
1
1
0
1
1
1
1
2
1
0
1
0
1
2
1
2
0
0
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
2
0
1
0
0
1
1
2
0
1
2
1
2
1
1
1
1
0
1
4
0
1
1
1
1
1
1
1
1
1
1
2
0
0
1
1
1
0
1
1
1
1
2
2
2
0
1
1
2
1
1
1
1
0
2
1
1
1
1
2
1
1
2
2
1
2
1
1
1
2
2
1
2
1
1
0
2
1
1
1
2
1
0
2
1
1
2
1
2
1
0
2
1
1
1
2
1
1
1
1
2
1
2
1
1
1
2
2
1
1
2
1
0
1
2
1
1
1
2
1
1
2
1
1
1
1
0
0
2
1
1
2
2
2
2
1
1
0
1
1
0
1
1
1
1
1
1
1
0
1
1
1
1
4
1
1
1
1
2
1
1
0
1
0
1
2
1
1
2
1
0
2
2
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
0
1
2
0
1
1
5
2
1
2
1
1
1
1
1
1
2
1
2
1
2
2
1
2
2
1
1
2
2
1
1
1
1
1
1
1
2
0
0
1
1
2
1
1
1
3
1
1
1
1
1
1
1
0
1
2
1
1
1
1
1
1
2
1
1
1
0
0
2
1
1
1
0
1
1
1
2
2
1
1
2
1
2
2
1
1
1
2
0
1
1
2
1
1
1
2
1
2
2
1
1
1
0
1
1
1
1
1
0
1
1
1
0
1
0
1
0
0
0
0
1
1
1
1
1
1
2
2
1
0
1
0
1
1
1
0
1
1
0
1
1
2
1
1
1
1
1
1
1
2
2
0
0
1
2
2
2
1
1
1
1
1
1
1
1
2
2
2
1
1
2
0
1
1
2
2
2
0
2
1
1
1
2
1
1
0
2
2
1
0
1
2
2
1
1
2
1
1
2
1
0
0
1
1
1
1
0
2
1
1
2
1
1
1
1
1
1
3
2
1
2
1
1
1
3
1
1
1
1
1
1
0
1
2
1
1
1
1
1
1
1
2
1
0
1
1
1
3
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
0
0
2
2
1
2
1
0
1
2
1
1
2
2
1
2
1
1
2
1
2
0
1
1
2
2
0
0
1
1
1
1
3
0
1
1
1
2
1
1
1
2
1
1
1
0
1
1
0
1
1
2
1
0
1
2
1
2
2
1
1
1
2
2
2
0
1
2
0
1
3
1
1
1
2
1
1
0
2
1
2
1
2
2
1
1
0
1
2
1
1
1
2
1
2
2
1
1
2
1
2
2
0
1
0
0
1
1
2
1
1
2
2
1
1
2
1
1
1
2
0
1
1
1
1
1
1
1
1
1
2
1
2
1
1
0
1
1
0
2
2
1
1
1
1
1
1
2
2
2
2
2
1
0
1
0
2
1
2
1
1
1
1
1
1
0
2
1
1
2
1
2
0
1
1
1
0
1
1
0
1
1
1
1
2
1
1
2
2
1
1
1
2
1
2
0
2
1
1
2
1
1
0
2
1
2
1
1
1
1
0
1
1
0
1
0
1
0
1
1
0
1
1
2
1
1
1
1
1
1
2
2
1
1
2
2
1
2
0
0
0
1
2
2
0
1
1
1
1
1
2
0
1
0
2
0
1
1
1
1
2
1
2
2
2
1
0
2
1
1
1
1
1
1
1
0
1
0
1
2
1
2
0
1
1
1
1
1
1
1
1
2
0
1
2
2
1
0
2
1
1
1
1
1
2
2
1
2
1
0
1
2
0
1
1
1
1
1
2
0
2
1
1
2
1
1
1
2
1
1
2
1
1
1
2
1
1
0
1
2
1
1
0
1
1
2
0
1
2
1
1
2
0
2
0
1
1
2
2
0
2
1
1
1
1
1
1
1
0
2
2
0
1
1
1
1
0
1
2
1
1
1
0
1
1
2
0
1
1
1
1
2
1
2
1
1
0
2
2
2
1
1
1
0
1
0
1
1
1
2
1
1
0
1
2
0
1
1
1
2
2
1
2
1
0
2
0
2
1
2
1
0
1
1
1
2
1
1
0
1
1
1
1
1
1
2
1
1
1
0
1
0
1
1
2
2
1
0
1
1
1
0
1
2
1
1
1
1
1
1
1
2
1
0
1
1
1
1
1
2
0
0
1
1
1
1
1
1
1
2
1
2
1
1
1
2
1
1
2
1
1
2
1
1
0
1
0
1
2
0
1
1
1
1
1
1
1
1
0
1
1
1
1
2
1
0
0
1
2
1
2
2
1
2
1
1
2
1
0
1
1
1
0
2
0
1
2
2
1
2
1
1
2
1
1
1
1
2
1
1
2
2
2
1
1
1
1
0
2
0
1
1
2
1
1
1
1
1
0
0
1
1
1
2
0
2
1
1
1
2
1
1
1
3
1
1
1
1
1
1
2
2
1
0
1
1
1
1
1
2
1
2
1
1
1
2
1
2
2
1
1
1
1
1
0
2
0
2
1
0
1
0
2
0
1
0
0
1
0
1
2
1
0
2
2
1
1
1
1
1
1
0
2
1
2
1
1
1
1
1
0
2
2
2
1
1
2
1
1
1
1
3
1
1
1
2
2
1
1
0
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
0
1
1
1
1
2
3
1
1
1
1
0
1
1
2
1
1
1
1
1
2
1
0
1
0
1
1
0
2
1
2
0
3
2
1
1
2
1
2
1
1
1
0
1
3
2
1
1
2
2
1
1
1
1
1
2
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
0
3
2
1
1
1
1
2
2
0
0
1
2
0
1
1
0
1
1
1
1
0
1
1
0
1
0
1
1
1
1
1
2
1
1
1
1
0
1
0
0
1
1
1
2
2
1
0
1
1
1
0
1
2
1
4
1
4
1
0
1
2
1
1
1
1
0
1
1
1
1
1
0
0
2
5
1
1
1
2
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
0
1
2
1
2
2
2
1
1
1
0
1
1
0
0
1
1
1
1
4
2
1
0
0
1
2
1
1
2
1
1
2
2
1
1
1
1
0
1
1
1
1
1
1
1
1
3
1
1
2
2
1
1
1
0
0
1
1
1
1
2
1
1
1
2
1
2
1
3
1
1
2
1
2
1
1
2
1
1
1
1
2
0
1
1
0
2
1
1
1
2
1
2
0
2
1
1
2
2
1
2
1
2
2
2
0
1
0
1
1
1
1
1
2
2
2
2
1
2
0
0
2
0
1
2
1
3
1
2
0
1
1
2
0
2
1
1
2
0
2
1
2
1
0
2
1
1
2
0
1
1
2
0
0
1
2
1
1
1
1
1
1
0
1
2
1
0
1
0
0
1
1
0
1
2
1
0
0
2
1
2
1
1
2
2
1
1
1
2
1
1
0
1
1
1
2
0
1
1
1
1
2
1
1
1
2
1
2
1
1
1
2
0
0
1
1
2
2
1
0
1
2
1
2
1
2
1
0
1
1
1
0
1
1
1
2
0
1
2
1
2
2
0
2
1
2
1
2
1
1
1
1
3
1
1
1
2
1
2
1
2
2
2
1
2
2
1
0
2
0
1
2
1
1
0
1
1
0
2
1
2
1
1
1
1
0
1
1
2
1
2
1
0
0
1
1
2
1
1
1
1
0
2
2
1
2
2
1
2
1
2
0
0
0
1
1
2
1
2
2
1
1
0
1
1
1
0
1
1
0
1
2
1
2
2
1
1
0
0
1
2
0
0
1
1
1
1
0
1
2
1
2
1
1
0
0
1
0
1
1
1
2
1
1
1
0
0
0
0
0
1
2
2
1
0
1
1
0
2
1
1
1
1
2
1
0
1
2
1
2
1
0
2
1
0
1
0
1
1
0
2
1
1
3
0
1
2
0
1
1
2
0
2
1
0
1
1
0
1
0
2
2
2
2
1
1
1
2
1
1
1
1
1
1
0
2
1
2
1
1
1
1
1
1
2
1
0
1
1
1
1
1
0
0
1
1
2
1
1
2
1
1
1
1
0
1
0
0
1
2
2
1
2
1
2
0
1
0
0
2
1
1
0
1
1
1
2
1
2
1
2
1
0
1
2
1
1
1
1
1
0
1
0
0
2
1
2
1
1
1
1
2
1
1
1
1
1
1
0
2
1
1
1
1
2
0
1
2
1
1
0
1
2
0
2
0
1
1
1
1
1
1
1
1
1
1
2
2
1
2
1
0
2
1
1
2
1
2
1
1
2
1
1
2
1
1
1
2
0
0
2
1
1
2
0
1
1
1
1
2
1
2
0
1
1
2
2
1
1
1
1
0
1
1
2
1
0
1
1
0
0
1
0
1
0
1
1
0
1
1
0
2
1
2
1
1
0
1
2
1
2
1
2
0
2
2
1
1
1
2
2
0
2
1
2
1
2
1
1
2
1
2
1
1
2
2
0
1
2
2
1
1
1
2
0
1
1
1
1
0
1
0
1
1
1
1
1
1
1
2
1
2
0
1
0
2
2
0
2
1
1
1
1
2
1
1
1
2
1
2
0
1
1
1
0
1
1
1
0
2
2
1
1
1
1
1
1
1
1
0
1
1
1
0
1
1
1
2
1
2
1
1
1
0
1
3
1
0
1
2
1
1
0
0
1
1
1
0
1
1
1
2
1
2
0
1
0
2
1
1
2
1
1
2
1
2
1
1
2
1
1
1
2
1
1
2
0
1
1
2
1
1
2
0
2
1
1
1
1
1
1
1
2
1
2
1
1
2
0
1
1
1
1
1
0
1
0
1
2
1
1
1
1
1
1
1
1
2
0
2
1
1
1
2
1
0
1
1
2
1
1
2
2
1
1
1
1
3
1
2
0
0
1
1
1
0
1
1
1
1
2
2
1
0
2
2
0
0
2
2
1
2
1
1
0
4
1
1
2
1
1
0
3
2
0
0
1
1
1
2
2
1
2
2
1
1
1
0
1
2
1
2
1
2
0
0
2
0
1
1
1
1
2
2
1
0
1
1
1
1
1
1
1
1
1
2
0
1
1
2
1
1
1
0
1
2
2
2
0
2
0
2
1
1
1
2
1
2
2
1
2
1
1
2
4
1
0
2
1
1
1
1
2
1
2
2
1
1
1
6
1
2
0
1
1
1
2
1
1
1
1
1
2
1
1
2
1
1
1
2
1
2
2
1
1
2
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
0
2
1
1
1
1
1
1
1
2
1
1
1
1
1
0
2
2
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
2
1
1
2
1
1
1
2
1
1
0
1
0
1
1
0
1
0
1
2
0
1
1
1
2
0
2
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
2
2
1
1
0
1
2
2
1
1
0
2
1
0
2
1
2
2
1
1
2
1
1
1
1
1
0
1
2
2
1
0
1
1
1
1
0
1
1
3
1
0
0
2
0
1
1
1
2
2
1
0
2
0
2
1
1
1
1
0
1
0
1
2
1
1
1
1
1
2
1
1
1
2
2
1
2
1
2
1
1
0
1
0
1
2
1
6
2
1
1
1
1
0
2
2
1
1
0
0
2
1
1
3
0
2
1
2
2
2
1
1
2
1
0
1
2
1
1
0
1
1
0
1
1
2
0
0
2
1
1
0
1
0
1
1
1
1
2
2
1
2
1
1
1
1
0
1
1
1
1
2
2
0
1
1
1
1
1
0
1
1
1
2
1
2
2
2
0
1
1
2
2
1
2
1
1
2
1
2
0
0
1
1
1
0
1
2
1
1
1
1
1
1
0
1
1
1
1
1
2
0
2
2
2
2
0
0
1
1
0
1
1
1
1
1
2
1
0
0
0
2
0
2
0
1
1
1
1
1
1
1
0
0
0
1
0
1
1
0
2
2
2
0
2
0
2
1
2
1
1
1
1
2
1
0
2
1
1
0
2
0
1
1
1
1
1
2
1
2
0
1
1
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
0
0
1
1
1
3
1
1
1
2
2
2
1
1
0
1
1
0
1
0
2
2
1
1
2
2
1
1
0
1
0
0
1
1
2
1
0
1
0
0
1
1
1
0
1
1
1
1
1
1
0
1
2
1
2
1
1
1
1
0
1
0
1
2
1
1
1
1
0
1
1
1
2
0
2
2
1
1
1
2
1
2
2
0
2
1
1
1
1
2
2
1
2
1
1
1
0
1
1
0
2
1
0
1
0
2
1
2
1
1
2
2
2
1
2
1
0
1
0
2
1
1
1
2
1
0
0
1
0
1
2
1
1
1
0
2
0
1
3
0
2
2
1
1
1
2
1
1
0
1
1
2
0
1
1
1
0
1
1
0
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
0
0
2
2
1
1
1
1
1
3
1
1
1
1
1
1
1
2
2
2
1
1
1
1
0
1
1
1
2
1
2
2
3
0
2
1
0
1
0
2
1
1
1
3
1
2
2
0
1
2
2
1
0
1
1
2
1
1
2
0
1
1
1
1
0
1
1
1
1
1
2
1
1
1
0
0
0
1
1
1
1
2
2
2
2
2
2
1
1
1
2
1
1
1
0
1
1
1
1
1
1
0
2
2
1
1
2
1
0
1
2
2
0
1
1
1
0
1
1
1
0
1
1
2
1
1
1
2
1
2
1
2
1
2
1
2
1
0
1
1
0
2
1
0
0
1
1
1
2
1
1
1
1
1
1
2
2
0
2
1
1
2
1
1
2
0
0
0
1
1
1
1
1
2
2
2
0
1
1
2
1
1
1
0
1
1
2
1
0
2
1
2
0
2
1
1
1
2
1
1
1
2
1
2
1
0
1
2
1
1
1
1
2
2
1
1
0
2
0
2
0
1
1
1
1
0
1
1
0
1
2
1
1
1
1
1
1
1
2
2
1
2
1
1
2
1
1
2
1
1
1
1
1
1
1
1
0
1
0
2
1
1
1
1
1
1
1
1
2
0
1
1
1
2
1
2
2
1
1
1
1
1
5
2
1
2
2
1
2
2
1
1
1
0
1
1
2
1
1
1
1
2
1
1
1
1
1
0
2
1
1
2
1
2
2
2
1
1
1
2
1
0
1
1
1
1
1
2
1
1
0
1
1
1
1
1
2
0
1
2
2
1
1
0
1
1
1
2
1
3
1
1
2
0
1
1
1
0
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
2
2
2
1
2
1
2
1
1
1
1
0
1
2
1
2
0
1
0
2
0
0
1
0
0
1
0
1
1
1
0
1
2
1
1
2
2
2
1
1
1
1
1
1
1
1
0
1
0
1
1
1
1
2
1
1
2
0
1
1
1
1
2
1
1
0
0
1
1
1
0
1
1
1
0
2
1
1
0
0
1
1
2
1
1
1
1
1
0
1
2
1
2
2
1
2
1
1
0
2
1
1
1
1
0
1
1
1
1
0
2
2
1
1
1
1
2
0
0
1
2
1
1
1
1
1
1
1
1
2
2
2
0
1
1
2
1
2
0
1
2
2
2
2
1
2
0
2
2
1
1
1
1
1
1
1
3
1
1
1
2
2
1
0
1
0
1
2
2
1
1
0
0
0
2
1
1
2
1
1
0
2
1
1
0
0
1
1
2
0
1
1
2
0
1
1
1
2
1
1
1
2
2
0
0
1
1
1
1
1
1
2
0
1
1
2
1
1
1
2
1
1
2
2
1
2
0
0
0
1
2
1
2
1
1
0
0
1
1
1
0
1
1
2
2
1
0
1
1
2
2
1
1
1
1
1
1
1
2
2
2
1
2
0
1
1
1
1
1
0
1
1
1
2
1
2
1
2
0
0
2
2
1
0
1
0
0
1
3
1
1
0
1
1
2
1
1
2
1
1
3
1
2
0
1
1
1
2
1
1
1
1
2
0
1
1
1
2
2
1
1
1
1
2
1
0
1
1
0
1
0
1
1
1
1
1
1
2
0
1
1
1
0
1
2
0
1
1
1
2
1
1
2
1
1
0
2
1
1
1
1
1
2
2
1
1
1
0
0
1
2
1
1
1
2
0
1
1
1
1
1
1
2
1
2
1
1
2
2
1
1
0
0
2
1
1
1
2
2
1
2
1
1
1
2
2
2
1
1
2
0
2
1
1
1
0
1
1
0
1
2
1
1
0
2
1
2
1
1
1
2
2
1
0
1
1
1
1
1
1
2
1
1
2
1
1
2
2
1
0
1
2
2
1
1
1
1
2
1
2
2
1
1
2
1
1
1
1
0
0
1
0
1
2
1
1
1
4
0
0
0
0
2
1
2
1
1
1
0
2
2
1
0
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
0
0
1
0
1
1
2
0
1
2
2
2
1
2
2
1
0
1
1
0
2
0
2
0
0
1
1
1
1
1
2
1
2
1
1
2
2
1
1
2
1
1
2
2
2
1
1
2
1
1
1
2
1
0
1
4
1
1
2
0
2
1
1
1
1
2
1
2
2
2
2
1
1
1
2
2
1
1
2
1
1
1
1
1
2
1
4
1
1
2
1
1
2
1
2
2
2
1
1
1
1
2
3
0
1
2
2
1
2
1
1
2
2
1
0
2
1
2
1
1
1
1
2
2
1
1
1
1
0
1
1
0
2
1
1
1
1
2
2
2
0
1
2
1
1
1
1
2
2
2
2
1
1
2
1
2
0
2
2
1
0
1
2
1
1
2
1
2
2
1
0
1
0
2
0
2
2
1
1
1
1
1
2
1
0
1
1
2
1
1
1
2
1
2
1
2
1
1
2
1
1
1
2
1
0
2
1
2
1
2
0
1
1
1
0
1
1
1
1
2
1
1
1
2
1
1
2
0
1
1
1
1
1
0
2
0
1
0
1
0
2
1
2
0
1
1
0
0
1
2
0
1
0
2
1
1
1
1
1
0
1
2
2
1
2
1
1
0
1
1
0
1
1
1
1
1
0
2
0
2
2
1
1
1
1
1
2
0
0
0
1
2
1
2
2
1
2
0
0
0
0
2
1
2
2
1
1
1
0
1
1
2
1
1
1
2
2
1
2
0
1
0
1
1
1
2
1
1
1
1
1
2
1
2
1
1
2
2
2
1
1
0
3
1
0
2
2
1
1
0
1
2
0
0
2
1
1
2
2
1
1
1
0
1
0
1
1
1
1
1
1
1
1
1
1
1
0
1
1
0
2
0
1
1
1
1
1
1
0
1
1
1
1
2
2
0
0
1
1
2
0
0
2
2
2
1
1
2
1
1
0
1
0
2
1
1
1
0
1
0
1
1
2
1
1
1
1
1
2
1
2
2
1
1
1
0
1
1
2
1
1
1
0
1
0
1
1
2
1
2
2
1
1
1
1
2
3
2
1
0
0
1
1
1
1
1
1
2
2
2
1
1
0
0
0
2
3
1
1
0
0
2
1
0
2
1
1
1
1
1
1
1
1
1
0
2
1
0
1
1
2
2
2
1
1
0
0
2
2
0
1
1
1
1
1
1
1
1
1
1
1
2
2
1
0
0
0
1
2
1
2
0
2
0
0
1
1
1
1
2
1
0
1
2
2
1
1
1
0
1
1
2
1
1
2
1
0
1
2
1
1
1
1
1
0
1
1
1
0
1
1
0
1
0
1
2
1
2
2
1
1
2
0
2
1
1
1
2
1
1
0
1
1
1
1
1
1
2
1
1
1
2
1
0
2
1
1
1
2
0
1
2
1
1
1
1
2
1
1
1
3
1
2
1
1
2
2
1
2
1
1
1
1
0
1
1
1
1
1
0
1
1
3
2
1
2
1
1
0
2
3
1
0
1
1
2
1
1
2
2
2
1
1
1
1
1
1
1
1
1
1
1
2
0
1
1
0
0
0
1
1
1
2
2
1
1
2
1
2
1
1
1
0
1
1
1
2
3
1
1
0
2
1
1
0
1
1
1
2
2
0
1
0
1
1
2
1
0
1
0
1
1
1
2
2
1
2
2
1
2
1
0
0
0
1
1
1
1
1
1
1
2
2
1
1
0
0
1
0
1
1
1
1
1
1
1
0
2
1
1
1
1
1
2
1
0
2
1
2
1
0
0
1
1
2
0
1
2
0
2
1
0
1
1
2
1
1
1
1
1
0
1
2
1
1
3
1
0
1
1
1
1
0
2
1
1
2
1
0
2
0
2
1
1
2
1
2
1
1
1
1
2
0
1
1
2
2
1
2
0
1
0
1
1
2
1
0
0
1
0
2
1
2
0
1
2
1
2
0
1
1
2
1
2
0
2
1
3
0
0
1
0
1
1
1
1
1
1
0
0
1
1
0
2
1
0
1
1
1
2
1
2
1
1
2
1
1
1
0
0
2
1
0
2
1
0
2
2
1
0
1
1
2
1
2
1
1
1
1
1
2
1
1
2
1
0
1
1
0
2
1
1
1
0
1
2
0
2
2
1
1
2
2
1
1
1
0
1
1
1
2
0
1
1
1
1
1
0
1
1
3
1
1
0
2
1
1
2
0
2
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
1
2
1
1
0
1
1
1
1
2
1
1
2
0
1
1
1
1
0
1
2
1
1
0
1
0
2
1
1
1
1
1
2
1
2
0
1
1
1
1
1
1
1
1
1
2
1
0
1
1
1
1
1
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
2
0
2
1
1
1
1
1
1
1
0
2
1
1
1
1
1
1
1
1
2
2
2
1
2
2
1
1
1
3
0
0
1
1
1
1
2
0
0
1
2
2
1
1
2
1
1
2
1
2
0
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
0
2
1
2
1
2
1
0
2
1
2
2
4
2
0
7
0
2
3
2
1
0
1
1
0
1
1
1
1
2
1
1
1
1
2
0
1
0
0
0
0
0
1
0
2
1
1
1
1
2
1
1
0
1
1
1
2
1
1
1
0
1
1
1
0
0
1
2
1
1
1
0
1
2
0
2
2
1
1
2
0
1
1
0
1
1
2
0
1
1
1
1
1
1
2
0
1
1
2
0
1
0
1
2
2
1
3
0
1
0
1
0
1
1
1
2
1
1
0
1
1
1
0
1
0
1
2
0
1
1
1
1
2
1
0
1
2
1
1
1
1
2
1
2
1
1
0
1
2
2
2
2
1
1
1
1
1
2
1
1
1
1
1
0
0
1
1
1
1
2
1
0
2
1
2
2
1
1
2
1
0
1
1
2
1
1
2
2
1
0
0
1
3
1
1
1
2
0
1
1
2
1
0
1
1
1
2
2
2
1
0
0
2
1
1
1
2
0
1
1
2
1
1
2
2
2
1
1
1
1
1
0
2
0
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
0
1
0
2
0
2
2
0
1
1
1
1
2
1
0
1
2
2
0
2
1
1
0
0
2
2
1
1
2
2
1
1
2
1
1
1
1
0
1
1
1
1
0
2
1
0
1
1
1
2
1
1
1
1
1
2
1
1
1
2
0
1
2
1
1
1
1
3
1
1
1
1
1
2
2
1
1
1
1
1
1
0
1
1
1
2
0
2
1
1
0
1
1
1
2
0
1
2
0
0
2
2
2
1
0
1
2
2
1
1
1
1
1
1
1
1
1
1
2
2
2
2
2
1
2
1
1
1
1
2
2
1
0
1
2
2
0
1
1
2
0
1
1
1
1
1
1
1
1
2
0
2
2
0
1
0
1
0
2
1
2
1
1
0
1
1
2
1
2
1
0
1
1
0
1
1
0
1
1
0
2
1
1
1
1
0
1
0
1
1
2
1
0
0
2
1
1
0
1
1
1
0
1
2
1
1
2
0
1
1
1
1
1
1
2
1
1
2
1
1
2
1
0
2
2
2
0
1
1
1
2
1
1
1
2
1
0
1
1
1
1
0
2
1
2
1
1
0
1
0
1
2
2
0
1
1
1
1
2
0
2
0
1
1
2
1
1
1
2
2
1
1
0
2
2
2
1
2
1
2
1
1
3
0
1
1
0
1
2
0
0
1
1
1
1
2
1
0
1
1
1
1
2
1
1
1
1
2
2
2
1
3
1
2
2
1
1
0
1
0
1
1
1
1
2
1
0
1
1
1
2
1
1
2
1
1
1
1
2
1
1
1
2
1
0
0
1
4
1
1
0
1
2
1
1
1
2
1
1
1
2
2
1
2
0
1
0
0
1
1
1
1
1
1
1
1
1
2
0
0
1
1
1
0
1
1
2
1
1
1
1
2
1
1
1
2
1
1
2
2
1
1
1
1
1
2
1
1
2
1
2
1
1
1
0
0
1
2
2
1
2
0
1
1
1
1
0
2
2
1
1
1
3
0
2
1
1
2
1
2
2
0
1
0
1
1
1
2
2
1
1
2
0
1
1
1
1
1
1
1
1
0
1
0
1
2
1
1
3
1
1
0
2
1
2
0
1
1
1
1
1
1
1
1
1
0
1
2
1
2
2
1
0
1
2
1
1
1
2
1
1
1
1
2
1
1
1
0
1
0
2
1
2
1
2
0
0
1
1
0
1
1
1
1
1
0
1
1
1
1
1
1
0
2
2
1
1
1
1
1
1
0
0
1
2
1
2
1
1
1
1
2
1
1
1
1
0
1
1
1
2
2
1
2
1
1
2
1
1
2
0
1
1
0
1
2
2
1
0
1
1
1
1
1
2
1
2
2
2
1
0
2
1
1
1
1
2
2
2
1
2
1
1
2
1
2
2
2
1
0
6
1
0
1
2
1
1
1
2
0
2
2
2
0
0
2
0
0
2
1
1
1
1
0
1
1
2
1
1
0
1
1
2
1
1
1
1
1
2
1
1
0
1
3
2
1
2
2
2
0
1
1
2
2
2
1
0
1
1
1
0
2
1
1
1
2
1
1
2
1
2
0
2
1
2
1
1
1
2
0
1
2
1
0
2
1
0
1
2
1
2
1
1
1
1
1
1
1
0
1
1
1
1
1
0
3
1
1
2
0
1
1
1
1
1
1
2
1
2
2
1
2
1
1
0
2
2
0
1
0
1
0
1
2
1
1
2
1
2
1
1
1
1
1
2
0
2
0
2
1
2
1
1
1
2
1
1
1
2
2
1
2
1
0
2
1
1
2
1
0
0
1
1
1
0
1
1
2
1
2
0
2
1
1
2
1
1
2
0
1
1
2
1
0
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
0
2
1
1
0
1
1
1
0
1
0
0
1
0
1
1
2
1
1
0
1
2
1
1
2
1
2
1
1
1
2
0
1
2
2
2
2
1
1
1
1
2
1
2
2
2
2
1
1
0
1
1
1
1
2
2
1
2
0
2
1
1
1
1
1
0
1
0
1
0
1
2
1
1
2
0
2
1
2
2
1
1
2
1
0
1
1
2
0
0
1
1
0
2
1
1
1
1
2
0
1
1
1
1
1
0
1
2
1
1
0
1
1
1
1
1
1
2
1
1
0
2
2
0
4
1
3
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
0
0
1
1
1
1
2
0
1
1
1
1
0
2
2
1
1
2
2
0
1
1
1
0
1
1
1
1
1
0
1
1
1
2
1
0
2
1
1
1
0
2
2
0
1
1
1
1
0
2
1
1
0
1
1
0
1
1
1
0
1
2
1
0
1
1
2
1
1
1
1
0
1
1
1
1
1
1
2
2
1
1
0
1
1
2
1
1
1
2
1
0
1
0
2
1
2
2
1
1
1
1
1
2
2
2
0
2
0
2
1
2
1
1
1
2
2
1
1
2
1
0
2
2
0
1
2
1
1
2
1
0
1
2
1
1
1
1
2
1
1
2
0
1
1
1
1
1
1
1
0
1
1
1
1
1
0
1
0
1
1
2
1
1
0
2
1
1
1
2
2
0
1
2
1
1
2
1
2
1
1
0
2
2
1
0
1
0
1
1
1
2
1
1
2
1
1
1
1
1
0
1
1
2
2
0
1
1
1
0
2
1
1
1
1
1
2
2
1
0
1
1
2
1
1
0
2
0
1
2
0
2
1
1
1
3
1
0
1
1
1
1
1
1
2
0
1
0
2
1
1
2
2
1
1
1
0
0
1
1
1
0
2
1
1
1
1
1
2
1
0
2
1
1
1
1
1
2
1
1
1
1
1
1
2
2
1
2
1
1
0
1
1
1
2
1
1
2
1
1
1
1
1
1
0
2
1
1
1
1
1
0
0
1
1
1
2
2
0
1
1
1
1
1
2
1
2
2
1
1
1
1
1
1
1
2
1
0
1
1
1
1
1
2
1
1
2
2
1
1
2
1
2
0
1
0
0
1
1
1
2
0
0
1
2
1
1
1
1
1
2
0
1
1
0
2
1
1
1
1
2
1
0
1
1
1
0
1
1
0
1
1
0
2
1
0
4
1
2
1
1
1
1
2
0
1
2
1
1
1
2
1
2
2
0
1
0
0
1
0
1
1
1
1
2
1
1
1
0
2
5
2
0
1
1
2
1
1
2
0
1
1
1
1
2
1
2
1
1
1
2
0
2
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
0
1
1
2
1
1
2
0
1
1
1
1
1
1
1
1
0
1
1
1
1
2
1
2
3
1
0
0
2
2
1
1
1
1
1
2
1
1
1
1
2
1
2
1
1
0
0
1
1
1
1
2
1
1
1
1
2
2
2
0
1
1
2
1
1
2
1
1
2
0
1
0
2
0
1
2
1
2
1
2
1
1
2
1
1
2
1
0
1
2
1
2
1
1
1
2
3
1
2
1
2
1
1
1
1
1
2
1
1
1
1
1
0
1
1
1
0
1
0
1
0
1
1
2
1
1
2
1
1
0
0
1
1
1
2
1
2
2
1
2
1
2
1
1
2
1
1
0
1
0
1
1
1
1
2
2
1
2
1
1
1
1
0
1
1
1
0
0
1
2
1
0
0
1
2
1
2
1
1
1
0
2
0
2
1
2
1
1
1
1
1
1
2
1
1
1
2
0
1
1
1
2
1
1
1
1
1
1
2
0
0
1
2
0
1
1
1
1
1
2
1
2
1
1
1
2
1
2
3
1
1
1
1
2
1
2
1
2
2
1
2
1
1
2
2
1
0
1
1
1
1
1
2
2
0
1
1
1
1
2
1
1
1
2
1
1
2
1
0
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
2
4
2
1
1
2
1
2
2
2
1
1
2
1
2
1
0
1
2
1
1
2
0
2
1
1
1
2
1
1
1
0
2
1
1
2
2
2
2
1
1
0
2
1
1
2
1
2
0
1
0
1
1
1
1
1
1
1
1
1
5
1
0
1
2
1
1
1
0
2
1
1
1
1
0
1
1
2
1
2
0
1
0
1
0
1
0
1
2
0
1
0
2
1
1
2
1
1
2
1
1
1
1
1
2
0
2
1
2
1
2
1
1
1
2
2
2
1
2
1
0
2
1
1
1
0
1
1
1
2
0
1
2
2
1
1
1
1
0
0
2
1
0
1
2
2
1
1
0
0
1
2
1
2
2
1
2
1
1
1
2
0
2
2
0
1
2
1
2
2
0
0
2
1
2
0
1
1
1
2
1
2
2
2
1
1
0
1
1
1
0
1
1
1
0
2
1
1
1
2
1
1
1
0
2
1
2
1
1
1
1
1
0
1
1
0
1
1
2
1
1
2
1
0
1
1
1
2
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
0
2
2
0
1
1
1
1
1
0
0
1
1
1
1
1
1
0
2
2
0
0
1
2
1
1
1
2
2
0
1
1
1
1
1
0
1
1
2
1
1
1
2
1
1
1
1
1
1
1
0
1
1
1
2
1
1
2
2
2
2
1
1
1
1
1
1
1
1
1
1
0
0
1
0
2
1
0
2
1
1
2
1
1
2
1
1
1
2
1
0
0
2
2
2
1
2
1
0
1
1
1
2
1
1
1
1
1
1
0
1
1
0
2
1
2
1
1
2
1
1
1
1
5
1
1
1
1
2
2
0
2
1
1
1
1
1
2
1
2
1
2
0
1
1
1
1
1
1
2
1
1
1
1
0
0
1
1
2
2
1
1
0
2
2
2
1
2
0
1
2
1
1
1
0
1
2
0
1
1
1
1
1
1
2
3
0
1
0
2
2
0
1
1
1
1
2
1
0
1
1
2
1
0
0
0
2
1
0
1
0
1
1
1
2
0
3
1
2
1
1
2
2
1
2
1
2
1
1
1
1
1
1
1
0
0
1
1
1
1
1
1
1
1
1
1
1
0
2
1
2
1
0
2
1
0
1
2
0
2
1
0
1
1
1
0
2
1
1
1
2
1
0
2
0
1
0
1
0
1
0
2
2
2
1
1
1
1
1
2
1
1
0
2
2
1
0
1
1
2
1
1
1
1
1
2
1
1
1
2
0
0
2
1
1
0
1
1
1
2
0
0
1
1
1
1
1
1
1
1
2
1
1
1
0
1
1
1
1
1
1
1
0
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
2
1
1
0
1
1
1
2
2
0
2
1
1
1
0
1
2
1
1
2
1
1
1
0
0
2
0
2
0
1
1
0
1
0
2
1
0
1
1
1
1
1
0
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
0
1
1
2
1
1
2
1
1
1
2
0
1
1
2
2
1
1
0
1
1
2
1
1
1
0
1
1
1
2
0
1
1
2
1
2
0
1
1
1
1
2
1
2
1
1
2
1
0
0
1
1
1
2
1
1
3
1
3
1
1
2
2
0
0
2
1
2
0
1
0
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
0
2
1
0
2
1
1
2
3
0
1
0
1
0
0
2
1
0
1
1
1
1
1
2
1
0
1
2
1
2
1
0
1
1
0
1
1
2
1
1
1
1
1
0
1
1
0
1
1
1
2
2
1
1
2
1
1
2
1
4
1
1
1
1
1
2
1
0
1
1
1
2
2
1
0
0
2
2
1
2
1
1
2
2
2
2
1
1
1
1
1
2
1
1
0
0
1
1
2
1
1
1
2
0
3
1
2
1
1
1
1
0
2
1
1
1
0
1
1
1
2
2
1
1
3
1
1
1
1
1
1
2
1
0
1
0
1
1
0
1
1
1
1
1
1
1
1
2
1
1
1
1
1
0
1
2
0
2
1
1
0
2
3
1
1
1
1
1
2
1
1
1
1
2
1
1
0
1
0
1
2
1
1
1
0
1
2
1
0
1
2
2
2
1
2
1
1
1
3
1
1
1
0
0
1
1
1
1
2
2
0
1
1
1
1
2
1
2
1
2
0
1
1
2
1
1
1
1
1
1
1
1
1
1
0
1
1
2
0
1
0
2
1
1
1
2
1
1
0
2
1
1
1
2
1
1
0
1
1
0
1
1
1
0
1
1
1
1
1
2
1
0
1
2
1
1
0
1
1
1
0
1
0
1
1
1
0
1
1
2
0
0
1
1
1
0
1
1
1
1
1
1
1
1
2
2
1
0
0
1
2
2
1
2
2
1
1
1
1
1
2
1
1
0
0
1
2
1
1
2
1
2
1
1
0
2
1
0
2
3
0
1
1
1
0
2
1
2
0
2
1
1
2
2
0
1
1
1
0
1
1
0
1
2
1
1
1
1
1
1
1
0
0
1
1
1
0
2
1
1
1
2
3
2
0
2
1
2
1
0
1
1
2
1
1
1
3
2
1
2
2
1
1
2
0
1
1
0
1
1
2
1
1
1
2
1
1
1
0
0
1
1
1
1
2
2
2
1
1
0
0
1
1
1
1
0
1
1
2
1
1
0
1
1
1
1
1
1
1
1
1
0
1
1
2
1
1
1
2
1
2
2
1
1
0
1
2
1
1
0
1
1
2
1
1
1
0
1
0
1
2
0
1
0
0
1
1
1
1
1
0
2
0
0
1
1
1
2
0
0
1
1
0
2
2
0
2
0
1
1
1
2
0
1
1
1
1
1
0
2
1
1
1
0
1
0
1
1
2
2
0
1
2
0
2
1
1
1
2
1
2
2
1
1
2
2
0
2
1
1
1
1
2
2
1
2
1
1
1
1
2
1
2
1
1
2
1
1
0
2
2
1
1
1
0
1
1
1
1
1
1
2
1
1
1
1
0
1
1
1
2
2
1
2
1
1
1
1
0
0
1
2
1
1
1
0
2
1
2
1
1
0
2
2
2
1
0
1
1
1
1
2
1
2
0
1
1
1
1
1
1
2
1
1
1
1
1
1
1
0
1
2
2
1
1
1
1
2
2
0
1
1
1
2
2
1
3
1
1
0
1
0
1
1
1
1
1
2
1
1
1
2
1
1
1
2
0
1
1
1
2
1
2
1
1
1
1
2
1
1
1
2
2
1
1
2
2
1
1
1
1
0
1
0
1
2
1
1
2
2
1
2
2
0
1
1
1
0
0
1
1
1
1
1
2
1
2
0
1
1
2
1
1
2
1
1
1
1
2
1
1
0
0
1
0
0
1
1
1
1
1
0
1
2
2
2
0
2
2
0
1
1
1
1
2
1
0
1
4
1
1
1
1
1
2
1
0
1
0
2
1
1
2
1
1
0
2
1
0
1
2
1
0
1
0
1
2
1
1
1
1
2
1
1
2
0
1
2
1
2
1
2
0
1
2
3
1
0
2
1
1
2
2
2
2
1
1
0
0
0
1
1
1
0
1
1
1
1
1
2
1
1
2
1
2
2
2
2
1
2
1
1
1
1
0
1
1
1
1
1
1
1
0
0
1
2
0
1
1
0
1
2
1
1
1
3
1
1
1
1
2
2
2
1
2
2
0
2
1
2
0
2
2
1
1
1
1
1
1
2
1
1
1
0
2
0
2
1
1
2
0
2
2
1
2
2
0
0
1
2
1
0
2
0
1
2
2
1
2
1
1
1
1
1
2
1
0
0
1
1
1
1
0
1
0
2
1
1
2
2
1
1
2
1
1
1
0
0
1
0
2
1
1
1
1
2
1
0
2
1
2
1
1
2
0
1
2
2
2
1
1
1
2
2
0
2
1
1
1
1
1
1
1
0
1
1
2
2
1
2
2
1
1
1
1
2
3
0
1
1
2
1
2
0
2
1
2
1
1
1
0
1
0
1
1
0
1
1
1
2
1
2
2
1
2
1
1
1
2
2
3
2
0
1
1
0
2
2
1
1
0
1
2
2
1
0
1
1
2
0
1
1
1
1
1
1
1
1
1
0
2
2
2
1
1
2
1
2
1
1
1
2
1
2
2
0
2
2
2
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
2
0
0
1
2
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
0
0
1
2
0
1
1
0
0
3
1
2
1
0
1
1
1
1
1
2
1
2
1
0
1
1
1
1
0
0
1
1
1
2
1
0
1
1
1
0
1
0
0
0
0
0
1
1
1
2
2
0
1
2
1
0
1
2
1
0
2
2
2
1
1
1
2
1
1
2
1
2
1
1
2
1
1
2
1
2
1
2
1
0
1
1
0
2
0
2
1
1
1
0
1
1
2
1
0
1
2
1
1
0
0
1
1
1
0
1
1
1
2
1
0
1
1
1
1
1
0
1
2
1
2
0
1
1
2
1
1
1
0
1
1
1
0
2
0
1
2
2
1
1
1
1
2
2
1
2
1
1
1
2
1
0
2
0
0
1
1
1
1
0
0
1
0
0
1
1
2
0
1
1
1
1
1
0
1
1
1
2
0
1
1
1
1
2
1
2
1
1
2
1
1
1
1
0
2
1
1
1
1
0
1
1
2
1
0
0
1
1
1
0
0
1
1
1
0
1
0
1
0
0
1
1
2
0
1
2
1
0
1
1
2
1
2
1
0
2
1
1
0
1
0
1
2
1
1
1
2
2
2
2
1
1
1
1
1
1
2
2
0
2
1
0
0
2
1
1
0
1
0
1
1
0
1
1
1
1
2
1
0
0
1
1
0
2
1
1
1
2
2
0
2
1
2
2
2
1
0
1
2
0
1
1
1
1
1
1
1
1
1
0
1
2
4
1
1
1
2
1
1
1
1
0
0
2
0
1
1
2
1
0
1
2
1
2
2
1
1
1
1
1
1
1
2
1
1
0
2
1
2
2
0
2
2
1
0
1
1
2
0
0
1
1
1
0
2
1
1
2
1
0
1
1
2
2
1
1
1
2
1
0
1
1
1
1
1
1
0
2
1
2
1
2
1
2
1
1
1
1
2
0
1
1
1
1
1
1
1
2
1
2
2
0
1
1
2
1
2
1
2
1
2
1
2
1
1
0
0
1
1
1
0
1
2
1
0
0
1
1
0
1
1
1
1
1
1
0
0
0
1
1
1
1
1
1
0
1
1
1
2
2
2
2
1
1
1
1
1
2
2
1
2
2
0
1
1
0
2
1
2
2
1
0
1
1
1
1
2
2
3
1
0
1
1
0
1
2
1
1
1
1
2
2
1
1
1
0
2
2
1
2
1
0
0
1
1
1
1
2
1
1
0
0
1
1
2
1
2
1
2
2
1
0
1
1
0
1
0
0
1
1
0
1
1
2
0
2
1
1
2
1
1
0
2
1
1
1
2
1
1
3
2
1
1
1
2
1
2
0
1
1
0
2
0
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
2
2
1
2
1
1
1
2
1
1
1
1
0
1
2
1
0
2
1
1
2
1
1
0
2
2
1
0
1
2
0
2
1
1
1
0
1
1
1
1
2
1
1
1
2
1
2
1
2
0
1
1
2
2
2
1
1
2
1
0
1
0
0
2
1
1
2
1
1
1
1
1
1
2
1
1
1
0
0
1
2
1
0
1
1
0
2
1
1
1
1
2
1
2
1
1
2
1
2
1
1
2
0
1
1
1
1
2
1
0
1
1
1
2
1
2
2
1
1
1
0
1
1
1
1
1
2
2
1
1
0
0
1
2
1
1
0
1
0
1
0
1
2
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
0
1
1
1
2
1
2
1
1
1
1
1
1
2
1
0
0
2
1
0
1
0
1
2
1
2
2
1
0
1
0
0
1
1
1
2
1
2
1
1
1
0
1
1
2
1
1
0
0
1
1
1
2
2
1
1
1
1
0
1
1
1
2
2
2
1
1
2
1
1
0
1
2
2
1
1
1
1
2
1
1
1
1
0
1
0
0
1
2
2
2
2
2
1
2
1
2
0
1
1
2
1
1
2
1
1
2
2
2
1
0
1
1
1
1
2
2
2
1
1
2
2
1
1
1
1
1
1
1
1
2
1
0
1
1
2
1
1
2
2
0
1
2
0
2
2
1
1
1
1
1
1
0
2
1
1
1
1
2
1
1
1
1
2
2
1
1
0
0
1
1
1
2
1
2
0
2
2
1
1
1
2
2
1
1
1
1
2
1
1
2
1
1
1
1
0
1
0
2
0
1
1
1
2
1
1
1
1
1
2
2
1
1
1
0
2
2
1
1
1
2
1
2
1
1
0
1
1
1
1
2
0
0
2
0
2
1
2
1
1
2
0
1
1
1
1
1
1
2
1
1
1
1
1
1
0
1
1
2
1
0
2
1
1
1
1
2
0
2
2
2
2
1
2
2
0
1
1
1
0
1
2
1
1
1
1
1
0
1
2
0
2
1
1
2
1
2
0
0
1
1
0
2
2
1
1
1
1
2
0
1
1
1
1
2
2
0
1
2
0
2
1
2
1
0
1
1
1
1
1
2
1
2
1
1
1
1
2
1
2
1
1
1
2
1
1
1
2
2
1
2
1
1
0
1
2
0
0
3
0
1
1
2
1
2
1
1
1
1
2
1
1
1
1
0
0
2
1
1
0
1
1
1
1
1
1
1
0
1
1
2
1
2
2
1
2
1
1
0
2
2
1
2
1
1
1
2
4
2
1
1
2
0
1
2
1
1
1
2
2
1
2
1
1
1
1
2
5
2
1
1
1
0
1
1
2
0
1
1
1
1
1
0
0
1
1
1
1
1
1
1
0
1
1
2
1
2
1
2
1
2
0
0
1
2
1
2
2
1
1
1
2
1
1
1
2
1
1
0
1
1
1
1
1
1
0
2
2
2
2
1
1
2
1
0
1
1
1
1
1
1
0
0
1
1
1
2
0
2
2
1
1
0
1
0
1
2
2
0
2
1
0
1
1
1
1
1
0
1
2
1
1
1
2
1
1
1
2
1
0
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
0
1
2
1
1
1
1
1
1
2
1
1
2
2
0
0
0
0
0
1
1
1
1
1
2
2
1
2
2
1
1
1
1
1
1
1
1
2
1
1
1
2
0
2
1
2
1
1
1
1
1
0
1
1
2
1
1
2
2
2
2
1
2
1
2
2
2
2
1
1
1
0
0
0
1
0
1
1
1
1
1
1
1
1
2
0
0
0
2
1
1
0
0
1
0
1
1
2
2
1
1
2
1
1
1
1
1
1
2
1
2
1
2
1
2
2
2
1
1
1
0
1
1
2
2
2
1
1
2
1
1
2
1
0
1
0
2
0
0
1
1
2
1
0
1
3
1
1
1
2
0
2
2
0
0
1
1
2
1
1
1
3
1
2
1
1
1
1
0
0
2
2
1
1
2
1
1
1
1
2
1
1
1
1
0
2
1
2
1
2
1
0
0
1
1
1
1
1
1
1
1
0
1
1
1
2
1
1
1
2
1
2
1
2
1
1
2
1
2
1
2
2
0
1
1
0
1
1
1
1
1
0
2
1
2
1
0
1
1
1
1
2
2
1
1
1
0
1
0
1
1
1
1
2
2
1
0
2
2
1
0
0
2
1
1
1
0
1
2
1
3
1
1
0
1
0
1
1
1
2
1
2
1
0
1
2
2
3
0
2
1
2
0
2
0
1
1
1
1
1
1
0
1
1
1
1
1
2
1
1
1
0
2
0
1
1
1
1
1
1
2
0
0
1
1
1
1
0
1
1
1
0
1
0
0
2
1
2
1
0
2
1
0
1
1
1
1
2
0
1
1
2
1
1
1
2
1
1
2
2
1
3
0
2
1
2
1
1
2
1
2
1
2
2
1
2
2
1
1
2
2
1
1
1
1
1
1
1
0
2
2
0
1
0
1
0
0
1
1
1
1
1
0
1
1
2
1
2
2
1
1
1
1
0
1
1
2
0
3
1
1
1
1
1
0
1
1
0
1
1
2
1
0
1
1
0
1
1
2
1
1
1
0
1
2
3
0
1
1
0
2
2
2
2
1
1
0
1
0
1
1
0
2
2
1
1
1
2
1
1
1
2
1
2
1
0
3
0
2
1
1
1
1
1
1
0
1
1
2
1
1
1
1
1
1
0
0
2
1
0
1
2
1
1
2
0
0
1
2
1
1
1
0
0
1
0
1
2
1
1
2
0
1
1
1
1
1
2
1
2
1
2
1
0
1
1
1
2
2
1
0
3
2
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
1
1
2
0
1
1
1
1
2
1
0
2
1
0
2
1
0
1
1
1
0
1
1
1
1
0
0
0
2
1
1
1
1
1
1
1
1
2
0
0
1
1
1
2
1
0
1
2
2
0
1
1
0
1
1
1
1
1
1
0
0
2
1
2
2
2
1
1
2
0
0
0
1
1
1
2
2
1
1
2
2
1
2
1
0
1
2
1
1
1
1
1
1
2
1
3
1
1
1
1
0
2
1
2
1
1
2
1
1
1
1
1
1
1
1
0
1
2
2
0
1
1
1
2
2
1
2
2
1
2
2
1
1
0
1
2
1
2
1
1
1
1
2
0
1
1
1
2
2
1
0
1
1
1
3
0
1
1
1
0
1
2
0
2
1
1
1
2
2
1
1
1
2
1
1
1
1
1
1
2
2
3
2
1
1
1
1
1
1
1
2
2
1
2
1
1
1
1
0
1
2
0
0
1
1
1
1
1
2
1
2
2
1
2
1
1
1
0
2
1
0
0
1
1
0
1
1
2
1
1
2
1
1
2
0
1
1
0
1
2
1
0
1
1
1
0
1
1
0
0
1
1
1
3
1
2
0
1
1
2
1
2
0
0
1
1
1
1
1
0
2
0
1
1
1
1
1
0
1
2
0
1
0
0
1
1
1
2
1
1
1
2
1
0
1
2
1
1
0
1
1
1
1
1
0
1
2
1
1
2
1
1
3
1
1
1
1
1
0
1
0
1
1
1
1
1
0
0
1
1
0
1
1
0
2
2
0
1
1
1
2
1
1
1
1
2
0
1
0
1
0
1
1
0
0
1
2
1
1
1
1
1
0
1
2
2
1
1
1
1
1
2
0
1
1
1
1
0
1
1
1
1
2
1
2
2
1
1
1
2
1
1
1
1
1
1
3
2
0
2
1
1
1
1
1
2
2
1
1
1
1
0
2
2
0
2
1
0
1
1
1
0
0
0
1
0
1
1
1
2
1
2
1
2
0
1
1
1
1
1
1
1
1
1
1
1
0
1
0
1
2
1
1
1
1
1
1
2
2
0
1
1
1
1
1
1
2
1
1
0
2
2
1
1
1
1
1
0
1
2
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
0
1
3
2
1
1
1
0
2
1
0
1
1
2
2
1
1
1
0
2
0
2
1
1
1
0
1
1
1
2
0
1
0
2
2
2
1
0
1
0
1
2
2
1
2
2
2
2
1
1
0
0
2
2
0
1
1
2
1
5
2
1
1
2
2
1
1
2
2
2
1
1
1
1
1
2
1
0
0
0
2
0
1
0
0
0
1
1
2
1
2
1
1
0
0
2
1
2
2
1
2
1
1
1
1
1
2
1
1
1
1
0
0
1
2
1
1
1
0
0
1
1
1
2
1
2
1
1
1
2
2
1
1
1
0
1
1
1
1
1
2
1
2
1
2
0
2
1
1
2
2
0
0
1
1
1
1
1
1
1
1
2
2
1
0
1
2
1
1
1
3
0
2
2
1
2
1
2
0
1
2
1
0
1
2
1
1
1
1
1
0
1
1
2
2
1
1
1
1
1
1
2
2
1
0
2
2
1
1
1
2
1
1
2
2
1
2
1
1
2
2
1
1
1
1
1
3
2
1
2
1
1
1
2
1
0
1
1
1
0
2
1
1
3
1
1
1
0
1
1
1
0
1
0
1
0
2
2
1
0
0
0
1
2
1
1
0
1
0
1
1
2
2
0
1
1
1
1
2
0
0
1
1
1
1
0
1
1
1
2
0
1
1
1
0
1
0
1
0
2
1
1
0
1
2
1
1
1
2
1
1
2
1
0
2
1
1
1
1
1
1
1
1
0
1
2
1
2
1
1
1
1
1
1
1
1
1
0
1
0
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
2
1
0
1
1
0
2
2
1
2
2
0
2
2
1
0
1
1
0
0
2
1
1
0
0
1
1
2
1
0
1
2
2
1
2
1
1
1
2
0
1
1
1
1
1
1
1
2
1
1
2
2
1
2
2
2
1
1
1
0
1
1
1
1
1
2
2
2
2
1
1
0
0
2
1
1
1
1
2
2
1
1
1
0
1
1
1
1
1
1
1
2
2
2
0
2
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
0
1
2
0
0
2
1
2
2
2
1
2
1
2
2
1
1
0
1
1
1
0
2
1
1
2
2
2
1
0
2
2
1
2
1
1
1
2
1
1
2
2
1
1
1
0
1
1
2
1
0
1
5
1
1
1
1
0
2
0
1
1
1
1
2
1
2
1
3
1
0
1
1
1
0
1
1
1
1
0
1
2
1
1
0
0
0
1
1
1
1
2
0
2
2
3
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
0
1
1
1
2
3
1
0
2
1
1
1
1
1
1
2
1
0
1
2
1
2
2
2
1
1
1
1
1
1
1
1
1
1
1
0
2
0
0
0
1
1
0
1
1
1
2
2
2
1
1
2
2
0
1
2
1
1
0
1
1
1
0
2
2
0
1
1
1
1
0
2
2
1
0
0
1
1
2
2
0
2
0
2
1
2
1
2
1
1
2
2
1
1
1
1
1
1
2
0
2
1
1
1
0
1
2
1
1
0
1
2
1
1
1
1
2
0
1
0
1
1
0
1
1
1
2
1
1
1
2
1
1
2
2
2
2
1
0
1
1
1
0
1
2
2
1
1
1
1
1
2
1
1
2
1
0
0
1
1
2
0
1
1
2
2
1
1
1
1
1
2
1
1
2
2
0
1
1
1
2
1
1
1
1
0
1
2
0
1
2
1
1
2
0
1
1
2
1
1
1
2
0
1
0
1
1
2
2
1
1
1
1
2
1
0
1
2
1
2
2
0
1
1
1
1
1
1
1
2
1
2
2
2
1
2
1
1
1
1
1
1
1
1
0
1
1
2
2
0
2
2
0
1
1
0
2
1
1
1
0
1
2
1
1
1
0
2
1
1
1
0
1
0
0
1
0
4
1
1
1
0
1
0
2
1
0
2
1
0
1
4
2
2
1
1
1
2
2
1
1
1
0
1
1
1
2
2
2
1
1
1
1
0
1
1
2
2
1
2
0
1
0
1
1
1
1
1
1
2
2
1
2
1
0
0
1
0
0
1
1
2
1
1
1
0
1
1
1
1
1
1
1
1
1
1
0
1
2
1
0
1
3
1
1
1
0
1
0
1
0
2
2
0
1
1
1
1
1
2
1
1
0
0
1
0
1
1
2
2
1
1
1
2
1
2
1
2
1
2
1
0
1
1
0
1
1
2
1
2
1
1
2
0
2
2
1
1
1
1
1
2
2
0
1
0
2
2
1
2
2
1
2
1
1
0
0
1
1
1
1
2
1
2
1
2
1
0
1
2
2
1
2
1
1
0
0
0
1
1
1
1
1
1
2
1
1
1
1
0
1
1
1
2
0
1
1
1
1
1
2
1
1
1
1
0
1
0
2
2
1
0
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
0
1
0
1
2
1
1
0
4
1
1
1
1
1
0
2
0
0
1
1
1
1
1
1
1
2
0
1
1
2
2
2
1
0
2
1
0
2
1
0
0
1
2
1
0
1
1
4
1
1
2
1
2
1
1
2
1
1
0
1
2
1
1
1
1
1
1
0
2
1
1
2
1
1
1
1
1
2
1
2
0
2
2
1
1
0
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
0
1
1
2
1
0
0
2
1
1
1
1
1
1
1
1
2
1
2
0
1
0
2
1
0
1
1
1
1
1
2
1
1
0
2
0
1
2
1
1
1
1
1
2
2
1
2
1
1
2
0
1
1
2
2
1
0
1
1
1
1
2
1
1
1
2
2
1
1
2
1
1
1
2
2
1
1
0
1
3
1
1
2
6
1
1
1
2
1
0
1
1
1
2
1
0
1
0
1
2
3
2
0
1
2
0
1
1
1
1
2
2
0
1
0
1
1
1
1
0
1
2
3
1
1
1
1
1
1
1
2
2
2
2
0
1
1
2
2
2
1
0
0
2
2
1
2
1
2
1
2
0
1
1
1
2
2
1
1
1
1
1
0
2
2
1
2
2
1
2
0
1
1
2
2
1
0
0
0
0
1
1
1
1
1
1
3
1
1
1
0
2
1
2
1
0
1
1
1
0
1
0
1
1
1
1
1
1
1
1
1
1
2
1
1
1
0
1
1
2
2
1
1
1
0
1
1
1
1
1
0
1
1
1
2
1
1
1
1
2
0
0
0
1
1
0
1
0
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
1
1
2
1
1
0
1
2
1
1
1
0
0
1
2
0
0
2
2
2
1
1
2
1
2
1
0
2
1
1
1
2
1
2
1
2
2
1
0
1
1
1
1
2
1
1
2
0
1
1
2
1
1
1
1
1
0
2
1
2
0
2
1
1
0
1
0
1
1
1
1
0
1
1
1
1
0
1
0
1
2
0
1
2
0
1
1
1
2
1
2
2
2
1
1
0
1
1
1
2
1
1
1
1
2
1
1
1
1
1
0
1
1
1
1
0
1
1
1
1
1
1
2
0
2
2
3
2
2
0
1
2
2
1
2
1
2
1
0
2
1
1
1
2
1
2
2
1
1
1
1
0
1
1
1
1
1
1
1
1
1
2
1
0
2
0
1
2
1
1
2
1
2
3
0
0
0
1
2
0
0
0
1
0
2
0
2
0
1
1
1
1
1
1
1
2
1
1
0
1
1
1
2
0
0
1
1
1
2
1
1
1
2
2
2
1
1
0
0
1
1
6
0
1
1
2
1
1
1
1
1
1
1
2
1
0
2
1
2
1
1
2
1
1
0
1
4
1
0
1
1
1
2
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
1
1
0
1
1
1
1
2
1
1
0
1
1
0
2
1
1
0
1
0
0
1
0
1
1
1
1
0
1
1
1
1
1
0
2
1
0
0
1
2
2
1
1
1
1
2
0
1
1
1
1
0
1
1
2
1
1
0
1
2
1
1
1
1
1
0
0
1
1
1
1
2
1
2
0
2
1
2
1
1
0
1
1
2
2
0
1
0
2
0
1
1
1
1
1
1
1
1
0
1
1
1
0
2
1
1
1
1
1
1
0
1
1
1
1
0
1
1
1
1
1
1
1
0
1
1
2
1
1
1
2
1
1
1
1
2
1
2
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
0
0
2
1
1
1
1
2
1
4
2
0
2
1
1
1
2
1
1
0
1
1
1
0
0
2
1
1
1
0
2
2
2
1
2
2
1
1
0
1
1
1
1
2
2
1
0
0
0
2
1
1
1
0
1
1
1
2
1
0
1
1
2
0
1
1
2
1
0
1
1
0
1
1
0
1
1
1
1
2
1
2
1
1
2
0
1
1
0
2
1
1
1
1
0
1
0
1
1
0
0
2
0
1
1
2
1
1
1
1
0
0
0
2
2
1
0
1
2
0
2
2
1
1
1
1
1
1
1
1
3
1
0
2
1
1
2
2
1
1
1
1
1
1
1
1
0
1
3
1
1
2
2
1
2
1
2
1
2
1
1
0
1
1
1
1
1
2
1
1
2
0
1
0
2
1
1
0
1
1
1
2
1
1
1
0
1
1
1
1
1
1
1
1
2
1
0
1
1
2
1
2
2
1
1
1
2
1
1
0
2
2
1
2
0
1
1
1
0
1
1
1
1
1
1
2
1
1
1
1
2
1
2
2
2
0
1
1
1
0
2
2
1
2
2
1
1
1
0
1
1
0
3
1
1
1
0
1
1
2
2
1
1
1
1
1
1
3
0
2
1
1
1
1
1
1
2
1
1
1
1
2
2
1
2
1
1
1
2
1
1
1
0
2
1
2
1
1
1
1
2
2
1
1
1
2
2
1
2
1
0
2
1
1
1
1
0
2
1
1
1
1
2
0
2
3
1
1
2
0
1
2
2
1
1
0
2
2
1
1
0
0
1
1
1
1
1
1
1
1
1
2
1
1
1
2
0
3
1
1
0
2
2
1
1
1
0
1
2
1
1
1
2
1
2
1
0
2
2
0
2
1
1
0
2
1
2
1
1
1
0
0
1
1
1
2
0
1
1
1
1
1
1
1
2
1
2
2
2
2
2
1
2
2
0
1
1
1
2
1
2
1
1
1
1
1
2
1
1
0
2
1
1
0
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
2
1
1
0
2
1
1
0
1
2
1
1
2
2
0
1
1
1
0
2
0
1
1
2
1
1
2
1
1
1
2
1
1
1
2
1
2
1
1
1
2
1
2
0
2
1
1
0
0
1
0
1
2
1
0
1
1
1
2
1
1
1
1
1
2
0
0
2
0
1
1
1
2
1
2
1
2
1
0
1
1
0
1
2
1
0
1
1
2
1
0
1
1
2
1
1
1
1
1
1
2
2
2
1
1
1
2
1
2
1
1
0
2
2
0
1
2
1
2
1
2
1
2
0
1
1
1
2
0
1
2
1
2
1
1
2
1
1
1
2
1
2
2
0
1
1
2
2
1
3
2
1
2
2
1
0
1
1
1
2
1
2
1
1
1
0
1
2
1
0
0
1
2
0
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
2
1
1
1
2
2
2
2
0
1
0
0
1
1
1
1
1
1
0
1
2
2
1
1
1
1
1
1
2
1
2
2
2
1
0
2
2
1
2
1
0
1
1
1
0
1
1
1
0
1
1
2
2
1
1
1
1
2
1
1
1
2
2
1
0
0
2
1
0
0
2
2
1
1
1
1
2
1
0
1
2
2
2
0
2
1
1
2
1
1
0
1
1
1
1
1
1
1
0
1
1
2
1
2
1
1
1
1
0
1
2
1
1
2
1
1
2
0
2
1
1
0
1
1
1
0
2
2
0
0
1
2
1
0
1
1
0
2
2
2
1
1
1
2
1
1
1
1
1
0
0
1
2
1
0
1
1
1
2
2
1
1
0
1
1
1
0
1
1
2
2
1
1
1
1
1
0
2
2
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
0
1
1
2
0
1
0
1
1
1
1
2
0
1
2
1
1
1
1
0
2
1
2
2
0
0
1
1
1
1
2
0
1
1
1
0
2
1
1
1
2
1
0
1
0
0
1
2
1
2
2
1
2
1
1
0
2
0
0
2
1
1
2
1
0
1
1
2
1
1
2
0
1
1
1
1
2
1
2
1
1
1
2
1
1
1
0
1
1
2
1
1
0
1
1
2
1
1
2
2
0
0
1
0
1
1
2
2
2
2
2
1
1
1
0
2
1
2
0
0
0
1
2
0
1
1
2
2
2
1
0
2
2
1
1
1
1
1
0
1
0
1
1
1
0
2
2
2
2
2
1
0
1
0
1
1
2
2
2
2
1
1
0
1
2
1
1
1
2
2
2
1
1
0
2
2
3
1
1
1
0
2
1
1
0
2
1
1
0
1
1
1
1
1
2
1
0
1
1
1
1
2
2
1
2
1
1
0
2
1
0
1
1
1
1
1
2
1
2
1
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
2
1
1
0
1
2
1
1
3
1
1
2
1
1
1
1
2
1
0
0
2
1
0
1
1
2
0
1
1
1
2
1
1
0
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
2
1
1
2
2
0
1
1
2
1
2
1
2
2
1
1
1
1
1
2
1
0
1
0
2
1
0
1
2
2
0
1
1
0
1
2
2
1
1
1
1
1
1
1
1
0
1
2
0
1
1
1
0
2
0
1
0
1
1
1
1
0
2
1
1
1
1
1
1
1
0
1
1
2
1
0
1
0
1
2
1
1
2
2
0
1
1
1
0
1
1
1
2
2
2
1
1
2
2
2
2
2
1
1
1
2
0
1
2
1
1
1
1
2
0
1
1
2
0
1
1
2
1
1
0
1
0
1
1
1
1
2
1
0
1
1
0
0
4
1
1
1
0
0
1
1
2
1
1
2
0
1
1
1
1
1
1
1
2
1
1
2
2
2
1
1
0
2
1
1
2
1
1
1
2
0
1
4
1
1
1
2
2
1
2
1
2
2
1
1
1
2
0
0
1
1
1
2
1
0
2
1
2
1
1
0
2
1
2
1
1
1
2
1
0
3
1
1
2
2
1
1
1
1
2
1
1
1
2
1
0
1
0
0
1
1
2
1
1
1
3
0
1
1
2
1
2
1
1
1
1
2
1
1
2
0
1
2
2
1
1
0
1
2
0
0
0
1
2
1
1
0
0
0
1
1
1
2
0
2
1
0
1
1
1
1
1
1
1
1
2
2
1
0
1
1
2
2
1
2
0
1
1
1
1
1
2
0
2
1
2
1
1
1
1
1
2
1
1
2
1
1
2
1
0
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
1
2
1
2
1
1
1
2
5
1
1
2
1
0
1
1
1
1
1
2
2
3
1
1
1
4
0
1
1
1
1
1
2
1
1
1
1
0
0
0
1
1
1
1
1
1
1
1
1
2
0
1
1
2
1
1
1
2
1
1
1
0
1
0
1
2
2
1
1
2
0
1
1
1
1
1
2
1
0
1
1
1
0
1
1
1
2
0
1
1
1
1
2
1
2
1
1
2
1
1
1
1
2
2
1
0
2
2
1
2
1
1
1
1
1
1
0
1
1
1
0
1
0
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
0
1
0
1
1
2
1
1
1
1
2
1
1
0
1
1
1
1
1
1
1
1
1
1
1
2
1
2
3
0
0
1
1
1
2
1
1
0
1
2
2
1
1
1
1
1
2
1
0
0
1
1
1
2
2
1
1
2
1
2
1
2
1
2
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
0
1
3
2
1
0
1
1
2
1
2
2
0
1
2
2
2
0
1
0
1
1
0
1
1
1
1
2
1
0
2
1
2
0
2
1
1
1
0
1
1
1
1
2
1
1
1
2
0
0
1
0
1
1
1
1
1
1
1
1
1
1
2
1
2
0
1
1
1
1
0
0
1
2
2
1
1
1
2
1
1
2
0
2
0
0
1
0
0
1
1
2
1
0
1
1
2
1
2
1
1
1
1
2
1
0
1
1
1
1
2
1
1
1
1
0
2
1
1
1
2
2
0
1
1
1
1
0
1
0
2
1
2
1
0
1
1
2
0
1
1
1
2
1
0
0
0
1
1
0
1
1
2
1
1
1
1
1
1
1
1
0
1
2
1
1
1
1
0
1
1
0
0
0
2
2
0
1
1
1
2
1
1
0
1
2
1
1
1
1
1
1
1
2
1
1
2
0
2
1
1
1
1
1
2
1
1
2
1
1
0
1
1
2
1
2
0
1
1
2
2
0
1
2
1
2
1
2
1
1
1
1
1
2
1
0
0
1
1
1
2
0
0
1
1
1
1
2
0
1
1
0
2
1
1
0
1
1
1
3
1
1
0
1
1
1
1
1
1
2
1
1
1
2
1
2
2
1
1
0
1
1
2
1
1
2
1
1
2
1
1
2
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
2
1
1
1
1
2
3
1
1
1
1
1
1
2
2
1
1
0
1
0
1
0
0
1
2
1
1
1
1
0
1
0
1
1
2
0
0
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
2
2
2
1
1
1
1
1
1
3
1
1
2
1
1
0
1
0
1
2
1
2
1
1
1
2
1
1
2
0
0
2
2
2
1
1
1
2
2
1
1
2
1
1
1
1
1
1
2
1
0
2
0
2
1
1
2
1
1
1
1
1
0
0
1
1
1
0
1
1
0
1
1
1
1
1
0
2
1
0
2
2
1
1
1
1
1
0
1
1
2
1
2
0
2
1
2
1
2
0
1
1
2
1
1
1
1
1
1
1
1
0
1
2
1
0
1
1
0
0
1
0
0
2
1
2
1
1
1
2
2
0
0
2
1
1
0
0
0
2
0
0
2
1
1
1
1
1
2
2
2
2
0
2
1
1
2
1
2
1
1
2
1
1
1
1
0
0
2
1
2
1
1
2
0
0
0
1
1
1
1
1
2
2
1
2
2
2
1
1
1
1
1
1
2
1
1
2
2
2
1
0
1
1
1
1
9
1
1
1
1
1
1
0
0
1
1
0
1
1
1
3
2
1
1
1
1
0
1
2
1
1
1
2
0
1
1
1
1
1
2
0
1
1
1
1
1
1
1
0
1
2
1
1
1
1
1
1
0
1
1
1
2
0
1
1
1
0
2
2
1
2
2
1
1
2
0
1
1
1
2
3
1
1
1
1
1
1
1
1
1
1
2
1
1
2
2
2
2
4
1
2
2
1
1
1
1
1
1
0
1
1
1
1
0
2
0
2
1
2
2
1
0
0
2
0
1
1
2
2
1
0
1
1
0
1
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
0
1
2
1
1
1
1
1
0
0
1
1
1
1
0
1
2
1
1
2
2
1
1
1
0
2
0
0
1
1
1
2
1
2
1
0
2
0
2
2
1
2
0
2
0
1
0
1
1
1
2
1
1
1
2
0
1
1
1
0
2
1
2
1
1
1
2
2
1
1
1
1
0
1
1
2
1
1
1
1
0
1
1
1
0
1
0
1
2
1
1
1
0
1
1
2
1
0
0
3
1
0
1
1
1
1
1
0
1
1
2
1
0
1
1
2
3
1
1
1
1
2
1
0
1
1
1
0
1
1
1
1
1
1
1
1
1
2
1
1
3
2
2
1
1
1
1
0
1
0
1
3
1
1
1
1
1
0
0
3
1
0
1
1
2
1
1
2
0
1
1
1
1
1
2
0
2
2
1
1
1
2
2
1
1
1
1
1
2
1
2
1
2
1
1
0
1
1
2
1
2
2
1
0
1
0
1
0
1
1
2
2
2
1
1
1
2
2
1
2
1
0
2
1
2
1
2
2
1
2
0
0
2
2
1
1
0
2
1
2
2
1
1
2
1
2
3
0
2
1
2
2
1
1
1
2
1
2
1
0
1
1
2
2
1
2
1
1
1
2
0
1
1
0
1
2
2
1
0
1
1
1
2
1
1
1
1
2
0
1
0
2
2
0
2
1
1
2
1
3
1
1
2
2
1
1
0
0
1
2
0
1
4
1
1
2
2
2
1
3
0
1
1
0
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
1
0
0
1
1
2
1
1
1
2
0
0
1
2
1
1
0
1
0
0
1
0
1
2
0
1
1
1
2
0
0
1
1
0
0
6
2
2
1
1
0
2
1
1
1
1
1
0
1
2
1
0
1
1
2
1
1
1
0
1
1
2
2
1
1
0
2
1
0
0
1
1
2
2
1
1
1
1
2
1
2
1
0
1
0
2
1
1
2
1
1
1
1
2
1
0
1
1
0
1
0
2
0
2
2
1
1
1
1
2
1
1
2
1
1
2
2
0
1
2
1
2
1
1
2
2
2
1
1
2
2
1
1
1
1
2
1
0
1
2
2
1
0
1
1
1
2
0
0
0
2
1
1
1
3
2
1
1
1
2
2
2
1
1
2
2
0
0
1
1
2
1
1
1
0
1
1
0
0
1
1
2
1
1
1
1
1
0
0
0
2
0
2
1
0
1
0
1
1
1
1
2
0
0
1
0
1
2
1
1
1
1
2
1
1
1
1
1
1
2
2
0
1
0
1
1
1
2
1
1
1
1
0
1
1
1
2
1
1
1
1
1
2
1
0
1
2
1
2
0
2
2
0
2
2
1
1
2
1
0
1
0
1
1
2
1
1
0
1
1
2
2
1
1
1
2
1
0
0
0
2
1
1
1
2
2
1
1
1
1
2
0
1
1
1
1
1
1
1
1
1
1
0
1
1
2
1
1
1
2
0
1
1
0
2
1
1
1
2
2
1
1
1
0
1
1
0
1
1
1
1
1
1
2
1
1
0
1
2
1
0
1
1
1
1
2
1
1
0
0
1
1
2
1
1
2
2
2
1
1
1
1
1
0
1
2
1
0
2
1
0
0
2
2
0
1
0
0
2
2
1
1
0
2
1
0
1
1
0
1
1
1
1
2
2
1
1
1
1
0
2
0
0
0
2
1
1
1
1
1
2
1
1
1
0
1
0
0
1
1
0
1
2
1
0
1
0
1
1
1
1
1
0
1
1
1
1
1
2
1
1
0
1
0
1
2
1
1
1
2
1
1
2
1
1
1
1
1
1
2
0
1
0
1
2
0
1
1
0
4
1
1
1
0
1
1
2
1
1
1
2
1
0
2
1
1
1
1
0
1
1
1
1
2
2
2
0
2
1
1
1
2
0
2
2
1
1
2
2
2
1
1
1
2
2
1
1
0
1
1
1
2
0
2
0
1
1
1
2
1
1
1
1
0
2
1
1
2
1
0
2
2
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
0
1
1
1
2
1
1
3
1
2
1
1
1
1
1
1
0
1
1
0
0
0
1
2
1
1
2
1
1
1
0
1
0
1
1
1
1
1
1
2
1
2
2
1
1
1
2
1
1
1
1
1
2
0
0
2
1
2
0
2
1
1
1
0
1
1
1
0
1
2
1
1
0
2
1
1
2
2
1
1
3
1
0
0
2
1
1
1
1
1
1
1
0
0
1
1
2
0
1
1
0
2
0
1
1
1
1
1
2
1
2
1
1
2
2
2
1
0
1
1
1
1
1
2
0
1
1
2
1
2
1
1
1
1
0
1
3
2
0
1
0
1
1
1
1
2
1
1
1
3
2
1
0
1
1
0
1
0
1
1
0
1
1
1
2
1
1
0
2
1
1
0
0
1
1
2
0
2
1
2
1
1
2
0
1
1
1
2
1
1
1
1
2
1
1
3
1
2
2
2
1
1
1
2
1
0
2
0
1
0
0
2
0
0
2
1
1
2
1
1
0
1
1
1
1
1
0
2
0
2
2
0
0
0
1
1
0
2
1
1
1
0
0
2
1
2
0
1
2
1
1
3
0
1
2
2
1
0
1
1
1
1
1
1
2
0
1
0
2
1
2
0
2
0
1
2
2
1
1
1
2
2
1
1
1
1
0
0
2
3
1
1
1
1
1
0
0
1
1
1
0
1
1
1
2
1
2
0
1
2
2
1
1
1
1
1
1
0
1
1
1
1
2
2
2
0
1
1
2
1
2
0
1
1
1
1
1
1
1
0
2
1
2
1
1
1
1
1
1
1
0
1
2
2
2
1
1
2
1
3
0
1
1
2
1
1
1
1
1
2
1
1
2
2
0
0
2
1
1
2
1
1
1
2
1
1
1
1
1
0
1
2
0
1
2
1
1
0
2
1
1
1
1
2
0
0
0
2
1
1
1
1
1
2
1
1
1
3
0
1
2
2
1
1
2
1
1
1
2
1
1
1
1
1
1
2
1
1
2
2
0
1
1
1
0
1
1
1
1
0
1
1
2
1
1
1
1
1
2
1
1
2
1
1
2
0
1
2
2
1
1
1
1
1
1
1
1
1
0
2
2
1
1
1
2
0
1
0
1
2
2
0
1
2
1
2
2
2
1
1
0
2
2
1
1
2
1
1
0
0
1
2
1
1
2
1
2
2
1
0
1
1
1
1
1
2
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
2
1
0
1
0
1
2
1
0
3
1
1
1
2
0
1
1
0
2
1
1
1
2
2
1
2
1
1
1
1
2
2
1
1
0
1
2
2
1
1
0
1
2
1
2
1
1
1
1
1
1
1
0
1
1
1
1
2
0
1
2
2
0
1
2
1
1
0
1
2
1
0
2
2
2
2
0
2
1
0
1
1
0
1
1
1
1
2
2
1
1
1
0
2
2
1
1
2
2
1
1
0
2
1
1
0
1
1
2
1
1
0
2
1
1
2
1
1
1
1
0
2
1
2
2
1
2
1
1
1
1
0
1
1
1
0
1
2
1
1
2
1
0
1
2
1
1
0
2
2
1
0
0
1
1
0
0
1
0
1
4
2
1
1
0
0
2
1
1
1
1
1
2
1
1
0
1
1
1
1
1
0
1
1
2
0
0
1
2
1
1
1
1
1
0
0
2
1
0
1
2
1
1
2
1
2
1
1
1
2
2
1
1
1
2
1
0
1
1
2
1
1
1
2
2
1
1
1
1
1
0
1
0
1
1
1
1
0
2
1
1
1
1
2
1
2
2
1
1
2
1
2
2
1
1
2
1
1
1
1
1
1
0
2
1
1
2
1
1
2
1
2
1
0
2
1
2
1
1
0
1
1
0
1
1
0
0
0
1
1
1
2
2
0
0
0
1
1
0
1
1
1
1
0
2
1
1
1
1
1
1
1
1
0
2
1
1
1
2
1
1
2
0
2
1
1
1
0
1
1
1
1
1
0
1
1
1
1
1
2
2
2
1
2
0
2
1
1
1
1
1
0
1
1
0
0
0
1
1
1
1
1
2
0
0
2
1
1
0
1
1
1
2
0
2
2
1
2
1
1
2
0
1
2
1
1
1
1
1
2
2
1
1
1
0
2
2
2
1
1
1
1
1
2
1
0
1
0
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
2
1
2
1
1
1
1
2
1
2
2
1
0
1
0
1
2
1
2
2
0
0
0
1
0
1
1
1
1
0
2
2
1
1
2
1
1
2
1
0
1
2
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
2
2
3
0
1
1
0
1
0
2
0
0
2
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
0
1
0
1
1
1
2
1
2
1
1
1
0
2
1
1
0
1
1
2
1
1
1
2
0
1
1
1
2
1
2
2
0
1
1
1
1
2
2
2
1
1
1
1
2
2
1
1
1
2
1
1
0
1
1
2
1
0
1
0
0
2
0
1
1
1
2
1
1
2
2
1
1
1
0
1
0
1
1
0
1
1
0
1
1
2
2
1
1
2
1
1
1
2
0
0
2
1
2
1
0
1
1
1
0
1
1
1
1
1
1
0
1
1
2
1
1
2
0
1
2
1
2
3
1
0
1
0
2
1
2
0
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
0
1
1
2
1
1
1
2
2
2
1
1
1
1
2
1
2
1
1
1
0
1
1
2
2
0
1
1
0
1
1
1
1
1
2
2
0
0
1
1
2
2
0
1
1
1
1
0
3
1
1
2
1
2
1
1
0
2
2
1
1
1
1
1
0
1
1
1
0
1
1
1
1
2
1
1
1
2
1
1
1
0
2
1
0
1
2
1
1
1
2
1
2
1
0
1
0
1
1
1
0
2
0
0
1
1
1
0
1
0
1
1
1
1
1
1
2
0
0
1
2
0
2
1
1
2
0
2
0
1
1
1
1
2
2
1
2
1
0
0
1
1
1
1
5
2
1
1
0
1
2
1
1
1
2
0
1
1
1
2
1
1
1
1
0
1
1
1
1
2
1
2
2
1
0
2
2
2
0
1
1
1
1
1
1
0
0
1
2
1
1
0
1
1
2
2
1
2
2
2
1
0
1
1
1
1
2
0
1
1
0
1
1
1
1
1
1
1
0
2
0
2
2
1
2
1
0
2
1
0
0
2
2
2
1
1
1
1
1
0
1
1
0
1
1
2
1
1
1
1
1
1
1
1
1
0
2
1
1
1
0
1
2
1
0
1
1
0
2
0
2
2
0
2
1
2
2
2
0
1
0
2
0
1
1
1
2
2
2
0
3
1
1
1
2
1
0
1
1
1
0
2
2
1
0
2
1
1
1
1
1
1
1
1
1
1
0
2
1
1
1
0
1
2
1
1
1
2
0
1
1
1
0
1
1
1
0
2
2
0
1
1
1
1
1
1
1
1
1
2
2
2
2
1
2
1
2
1
0
1
1
1
2
1
2
1
1
2
1
0
1
1
2
1
1
1
1
2
2
1
1
1
0
1
2
2
1
2
2
2
1
2
1
1
2
2
2
2
1
2
1
2
1
0
1
1
1
2
1
0
1
1
1
1
1
0
2
1
0
1
1
1
1
1
1
1
1
1
0
1
1
3
2
2
1
1
0
2
1
1
1
1
1
2
1
2
1
2
1
1
0
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
0
1
1
1
1
2
1
0
2
1
3
1
0
2
1
1
1
2
2
1
1
1
2
0
2
1
2
1
1
1
1
2
2
1
0
1
1
2
0
2
1
0
0
1
1
2
2
1
1
1
0
2
1
1
0
1
1
1
2
1
1
1
1
0
2
1
1
1
1
1
2
0
1
2
2
0
1
1
1
2
2
1
1
3
1
1
0
1
1
0
1
2
1
1
1
0
2
1
0
1
1
2
0
1
1
2
1
1
1
0
1
2
1
1
2
0
1
0
1
1
1
1
1
1
1
2
0
2
1
2
1
2
0
2
0
1
2
1
2
1
2
1
1
1
0
1
1
1
1
2
1
2
1
1
0
0
1
1
0
2
1
0
1
1
0
2
0
1
1
2
1
1
1
0
1
1
1
2
1
2
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
0
1
1
0
2
2
3
0
1
0
1
1
0
1
0
0
1
1
1
2
2
2
1
1
1
2
0
1
2
2
1
0
0
1
2
1
1
2
1
0
1
1
0
0
2
1
2
1
5
1
1
1
1
2
0
0
0
1
1
2
0
0
1
2
2
0
1
1
2
1
1
0
2
1
2
1
1
0
1
2
0
1
2
2
2
1
1
1
1
1
0
1
1
0
0
0
1
1
2
2
1
1
0
1
2
1
1
2
0
0
1
0
1
1
1
1
1
1
1
0
2
1
1
1
2
1
1
2
0
2
1
2
1
1
1
1
1
1
2
2
1
1
0
0
0
1
1
1
1
1
0
1
0
0
1
2
2
1
2
0
1
1
2
3
2
0
1
2
0
1
1
1
2
1
1
1
1
2
0
2
0
1
1
1
1
2
0
1
1
1
1
1
2
2
1
1
1
0
3
1
1
0
1
1
2
1
2
0
0
1
2
0
0
1
0
1
2
0
0
0
1
1
2
2
1
2
1
0
1
2
2
1
0
1
1
1
1
1
1
0
1
1
2
1
2
1
1
1
2
1
1
1
1
0
1
1
1
1
1
0
2
1
1
2
0
1
1
2
2
1
0
0
0
1
1
2
0
1
2
1
1
1
0
1
2
1
1
2
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
3
1
1
1
0
1
1
0
2
0
0
2
1
2
1
2
1
2
1
2
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
0
1
1
1
1
1
2
1
0
0
2
2
0
2
2
2
1
1
1
0
2
0
2
2
2
1
2
1
1
1
1
1
2
3
1
0
2
2
0
1
1
1
1
1
1
2
0
1
2
2
1
1
1
1
2
1
0
1
0
2
2
1
1
1
1
0
1
0
1
0
1
1
2
1
1
0
1
1
1
1
1
0
1
1
2
2
2
2
0
1
1
2
0
0
1
1
2
1
1
1
1
1
1
0
1
2
1
1
0
2
0
2
2
1
1
0
1
1
2
0
1
1
1
1
1
2
1
1
1
1
2
0
1
1
1
0
1
2
1
2
1
1
2
0
1
1
1
1
2
0
1
2
2
2
2
1
1
0
1
1
0
2
1
1
1
1
1
0
1
1
1
0
1
2
1
2
1
0
1
1
0
2
1
0
1
1
1
0
1
1
1
1
0
1
1
2
1
2
1
1
1
0
1
2
2
1
1
1
2
0
1
1
1
1
1
1
1
1
0
1
2
1
0
2
1
1
1
0
1
0
1
1
1
1
1
1
1
0
1
2
1
1
2
0
0
1
0
1
0
1
1
1
2
1
0
1
1
1
1
2
0
1
2
1
1
0
1
1
0
0
2
1
1
1
1
0
1
2
1
2
1
0
1
1
2
2
1
0
2
1
1
1
1
0
1
1
2
0
1
2
1
1
1
1
1
0
1
1
0
0
1
2
1
1
1
1
0
2
2
0
2
1
1
1
0
1
1
1
1
1
1
1
1
2
1
0
1
1
1
0
1
1
0
1
2
1
1
2
0
2
0
1
1
2
1
1
2
1
1
0
2
2
1
1
1
1
1
2
2
1
0
1
2
0
0
2
1
0
2
0
1
1
1
2
1
2
0
2
1
1
1
2
2
1
1
1
1
2
2
1
2
1
1
1
1
1
2
0
1
2
0
0
0
1
2
2
1
0
2
1
1
2
1
0
1
1
1
3
1
1
1
1
2
1
1
1
0
1
1
0
0
1
1
1
2
1
2
1
1
0
1
1
0
0
2
1
0
1
0
1
1
2
2
2
1
1
1
1
1
2
1
1
0
2
1
1
1
1
0
2
1
1
1
1
0
1
2
1
2
1
2
0
1
1
1
1
2
0
2
1
1
1
1
1
1
1
1
2
1
2
1
3
2
1
1
0
2
1
2
2
0
1
0
1
1
2
0
1
1
2
2
0
2
2
1
2
2
1
0
1
1
1
1
2
1
1
2
1
0
1
1
2
1
1
1
2
0
0
1
1
1
1
1
1
0
2
1
2
2
0
0
1
1
2
1
1
0
0
2
1
0
1
1
1
1
1
0
1
0
0
0
1
2
1
2
1
1
0
2
1
2
1
0
0
2
2
1
1
1
2
2
1
5
0
2
0
1
1
1
2
1
1
1
0
0
1
1
2
1
2
1
1
0
2
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
2
1
1
0
1
1
0
1
0
1
0
0
1
0
1
1
3
2
1
0
2
1
1
2
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
1
2
1
0
1
1
2
1
1
2
1
0
1
2
2
0
0
0
1
1
1
1
2
1
0
2
1
2
1
1
0
0
1
1
1
2
2
2
1
1
1
0
1
1
2
1
1
2
1
2
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
0
1
1
1
1
1
0
1
2
0
1
2
1
1
1
1
0
1
0
0
1
2
2
2
1
1
2
2
1
2
2
0
1
1
1
1
2
0
1
1
1
2
0
2
1
1
0
1
1
1
1
1
0
1
1
1
1
1
2
1
2
1
1
2
1
1
2
0
1
1
1
0
1
1
0
1
1
1
1
1
2
1
0
0
1
1
0
2
1
0
2
1
1
2
2
1
2
1
2
2
1
1
1
1
1
1
1
1
2
0
1
0
1
1
1
1
0
1
2
1
1
0
1
2
2
1
1
1
1
1
1
1
1
2
2
2
1
2
1
1
1
0
1
1
2
1
1
0
1
1
1
1
1
1
1
1
1
1
3
1
2
1
1
1
0
0
1
0
1
1
1
1
0
1
1
1
1
0
1
0
0
2
2
1
2
1
1
2
0
0
2
1
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
0
1
1
2
1
1
1
2
1
0
2
2
2
0
1
1
0
2
1
1
0
0
1
2
1
1
1
0
1
1
1
0
1
1
2
2
2
1
1
1
1
1
1
0
2
1
0
2
0
1
1
1
0
2
2
0
0
2
1
2
2
1
0
2
1
0
1
0
1
1
1
3
1
1
2
1
2
1
0
0
1
1
2
0
1
2
0
2
1
1
1
1
0
0
1
1
1
0
0
1
0
0
1
2
3
1
1
1
1
1
1
1
1
1
1
0
2
2
1
0
1
1
1
2
1
1
1
0
0
1
1
0
0
1
1
2
1
2
1
2
1
0
1
1
0
2
1
0
1
1
1
0
1
0
2
1
1
1
1
1
2
1
1
2
0
2
0
2
1
1
0
0
0
2
3
1
2
1
0
1
2
1
1
0
2
0
1
2
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
0
1
0
1
1
0
1
1
1
0
0
1
1
2
2
2
1
1
1
1
0
2
1
2
2
1
1
1
1
2
4
0
2
2
0
1
1
1
1
1
1
0
1
1
1
1
2
1
2
0
1
2
0
1
0
2
1
0
1
1
1
0
2
1
1
1
1
0
1
1
1
1
1
0
1
1
0
1
0
1
1
1
1
2
0
1
1
2
1
1
1
1
0
2
2
1
1
2
2
2
1
1
2
0
1
2
2
1
2
1
2
2
0
0
2
1
1
0
1
2
1
0
1
1
0
2
2
0
1
2
1
2
2
1
1
1
0
1
1
1
1
1
1
1
1
1
1
0
2
1
2
1
0
1
1
1
1
1
0
1
1
1
2
1
1
1
2
1
1
0
2
1
1
1
5
3
1
2
1
0
0
1
1
0
1
1
0
1
1
2
1
1
0
0
0
1
1
1
2
1
1
1
1
1
1
0
1
1
2
1
0
1
1
0
2
0
1
1
1
1
1
1
1
1
2
1
1
1
2
1
0
2
2
1
0
1
1
1
2
1
1
0
1
1
1
0
1
1
1
1
1
1
1
2
1
1
2
0
1
2
0
1
0
1
2
1
2
0
2
1
2
0
0
2
2
0
1
1
0
1
1
1
1
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
0
1
0
1
1
1
1
1
1
0
0
1
1
1
0
1
1
2
0
1
2
1
2
1
1
1
2
2
1
0
2
0
0
1
2
1
2
0
3
0
1
1
2
2
0
1
2
2
1
1
1
1
2
0
2
1
1
1
1
2
1
2
1
1
2
2
2
2
1
0
1
1
1
1
1
0
2
1
1
0
2
1
1
2
1
1
1
2
1
2
1
1
2
5
1
2
2
0
1
1
1
1
1
0
2
1
2
1
1
2
0
2
1
1
2
1
2
2
1
1
2
1
1
1
1
0
1
1
1
0
0
0
1
1
1
1
1
1
1
1
0
2
1
1
1
0
0
1
0
3
2
0
1
1
0
1
1
2
7
1
2
1
1
1
0
1
1
1
1
1
1
0
1
0
1
1
2
1
1
1
0
1
2
2
1
1
1
2
1
1
2
1
1
1
2
1
0
2
0
1
2
2
1
1
0
2
2
1
0
1
1
1
1
1
1
2
1
1
0
1
1
0
1
2
0
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
0
1
2
1
1
1
1
1
1
1
1
2
1
2
1
2
1
1
2
1
0
1
1
2
1
1
2
1
2
0
1
1
1
2
1
1
1
0
0
1
0
1
1
1
2
1
1
1
1
1
0
1
0
1
0
1
2
1
1
0
1
2
1
2
2
0
1
1
1
1
1
0
0
1
2
0
0
1
2
0
1
1
0
1
0
0
1
1
1
2
2
1
1
1
1
2
2
0
1
1
1
1
2
0
0
1
1
0
1
0
1
1
1
1
1
0
1
1
1
2
1
1
2
2
1
1
1
1
1
1
0
1
2
0
2
2
0
0
0
1
0
1
2
1
2
7
1
0
1
1
1
1
0
1
2
3
1
1
1
2
1
1
1
2
2
2
2
1
1
2
1
2
1
2
2
1
1
1
0
0
1
1
0
1
1
0
0
2
1
2
0
1
1
0
2
2
0
1
2
1
1
2
2
4
1
2
2
1
1
1
1
1
1
2
1
2
2
0
1
1
1
2
1
1
0
1
1
0
1
1
2
2
2
1
0
1
2
1
1
1
1
2
1
0
0
1
1
0
1
0
1
0
1
3
2
1
1
1
1
1
2
1
2
0
1
0
0
2
2
1
2
1
0
1
1
0
0
1
1
1
1
1
1
2
2
1
0
2
1
1
1
2
2
2
1
2
0
1
2
2
2
0
1
0
2
1
0
1
2
2
1
1
1
2
1
1
2
1
1
1
1
2
2
1
1
0
1
1
2
1
2
1
1
1
0
1
1
0
1
1
1
2
2
0
2
0
2
0
2
2
2
0
2
1
1
1
1
1
2
2
1
0
2
2
1
3
2
1
2
2
1
2
1
1
2
0
1
1
2
1
1
2
1
1
1
1
0
2
2
2
1
0
1
0
1
1
1
1
1
2
0
1
1
2
0
0
2
1
1
2
1
0
0
1
0
1
0
0
2
2
2
1
0
1
2
1
1
0
0
0
1
0
0
0
1
2
1
0
1
1
1
1
1
1
1
1
2
1
1
1
1
2
2
1
2
0
1
1
2
1
2
2
0
1
1
1
1
1
1
1
1
1
0
1
2
2
1
0
1
0
1
2
1
2
0
2
1
1
1
1
0
1
2
1
1
1
1
0
3
0
2
1
1
0
1
2
0
0
1
1
1
1
1
1
1
1
0
1
1
2
1
2
0
2
1
1
1
0
0
1
1
0
1
1
0
2
1
1
2
1
0
1
1
1
2
2
0
1
1
1
1
1
0
2
2
1
1
2
0
1
0
1
1
1
1
0
1
0
2
1
1
1
1
0
1
1
2
1
2
1
1
2
1
1
2
2
1
1
1
2
1
1
1
1
1
0
2
2
0
2
0
1
2
1
1
1
2
2
0
1
2
2
0
2
1
1
2
1
1
1
1
2
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
2
1
2
1
2
2
1
1
1
2
1
0
1
1
0
1
2
1
1
1
2
2
2
1
3
1
1
0
1
0
1
2
1
0
1
1
1
0
0
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
0
2
0
2
1
1
1
0
2
2
1
2
1
1
1
1
2
2
1
5
1
0
1
1
1
1
1
1
1
0
1
0
1
1
1
1
0
1
1
2
0
1
2
1
2
1
1
1
1
1
1
1
1
2
1
2
1
1
0
0
1
2
2
2
2
0
1
0
2
1
1
2
1
0
1
1
2
1
2
1
1
2
1
2
2
1
3
1
2
1
1
2
1
1
0
1
0
1
1
1
1
1
2
3
1
0
2
1
1
1
1
1
1
0
1
1
2
2
0
0
1
0
0
0
1
2
2
2
1
1
1
2
1
0
0
2
1
2
1
1
2
1
1
1
2
1
1
0
0
1
0
0
1
0
1
2
1
3
1
0
1
0
1
1
1
2
1
1
2
0
1
0
2
1
1
1
2
1
1
0
0
2
2
1
0
1
2
1
1
1
2
1
3
0
1
1
1
2
1
2
1
1
1
1
0
0
2
2
1
2
0
2
2
2
2
1
3
1
1
1
2
1
2
1
1
2
1
1
0
0
1
0
1
2
0
1
1
2
1
1
2
1
1
1
1
1
2
0
2
2
2
1
1
1
1
1
1
1
0
1
1
1
0
1
2
2
2
1
0
2
0
1
1
0
1
1
0
1
1
2
2
1
1
1
2
1
0
3
1
1
0
0
1
1
1
1
1
1
1
0
0
1
1
2
2
2
1
1
2
1
1
1
1
1
2
1
0
1
1
0
2
2
1
2
0
1
2
1
2
0
1
2
1
2
0
1
6
2
1
0
1
2
2
1
1
1
1
1
2
2
1
1
2
1
2
2
1
1
1
1
0
2
2
2
0
1
0
1
2
1
0
0
1
2
0
1
1
1
2
0
1
1
1
2
1
1
1
2
2
4
1
0
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
0
2
1
1
1
1
1
1
1
1
1
2
2
1
0
1
0
1
2
1
2
1
1
1
1
2
1
2
2
1
1
1
1
0
1
2
1
1
1
2
1
1
1
2
2
0
1
1
1
2
2
1
0
1
0
1
0
0
1
2
1
1
1
1
0
2
1
2
1
1
1
1
0
1
1
1
1
0
1
1
1
1
1
1
1
0
1
1
2
2
0
1
1
2
1
0
2
2
0
2
1
0
1
0
0
0
1
0
0
0
2
2
0
2
1
0
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
0
1
0
1
2
1
1
2
1
2
2
1
1
1
1
1
1
2
0
1
1
1
0
1
1
1
1
1
1
1
2
0
1
1
0
1
0
2
1
1
1
0
1
1
1
1
1
4
2
1
1
1
1
1
1
1
1
1
0
1
1
1
2
1
1
0
2
0
1
0
1
0
1
1
1
2
1
2
2
1
1
1
0
2
1
0
1
2
1
0
2
1
1
0
1
1
2
1
0
1
1
1
0
1
1
2
1
1
1
1
1
1
1
1
1
2
0
2
1
2
1
1
1
2
2
0
1
2
1
1
1
1
2
1
2
2
1
2
1
5
2
2
0
2
2
0
2
0
0
1
0
0
1
1
1
1
1
0
1
2
1
1
0
1
1
1
0
1
0
0
1
2
2
2
1
2
1
1
1
1
2
1
1
1
1
0
1
1
0
2
2
2
2
1
1
2
0
1
1
1
1
1
1
1
1
2
0
0
1
0
1
1
1
0
1
2
2
1
0
1
0
0
0
2
0
1
0
2
2
1
1
1
1
1
1
1
1
1
0
2
1
2
1
1
1
2
0
1
1
2
2
1
2
1
1
0
2
0
1
1
0
1
2
0
2
1
1
0
2
0
2
2
0
2
1
2
2
1
1
1
0
1
2
1
1
2
2
1
2
1
1
1
1
1
0
1
2
1
1
1
1
0
2
1
0
0
1
1
1
1
2
0
0
1
2
2
1
1
1
0
0
1
1
1
2
1
0
1
1
1
1
0
2
1
1
1
1
1
0
1
1
1
1
2
1
2
1
1
2
2
0
1
1
0
0
2
2
1
1
2
2
2
2
2
1
2
1
2
2
1
1
1
1
2
0
1
1
0
2
1
0
2
1
2
1
2
1
1
1
1
1
1
1
1
0
0
1
0
2
2
1
0
2
1
1
1
3
2
1
1
1
2
1
2
2
2
1
1
1
2
2
0
1
1
1
2
2
2
1
1
1
2
1
0
1
2
2
1
1
2
1
2
0
0
2
0
2
1
1
0
2
0
2
0
0
1
0
2
2
0
1
0
1
1
1
1
1
0
3
2
2
1
1
1
0
1
1
2
1
1
2
2
1
1
1
1
1
2
1
0
0
1
2
1
1
1
1
1
0
1
1
0
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
2
0
1
1
1
1
1
2
1
1
1
0
0
1
2
1
0
2
1
2
1
1
0
1
2
1
1
1
1
1
1
1
1
1
1
2
0
2
2
0
0
2
1
1
1
0
1
1
1
1
0
1
1
1
1
1
1
1
2
0
1
2
1
1
1
1
1
1
1
0
0
2
2
0
1
2
0
2
1
0
1
1
2
0
0
0
0
1
0
1
1
1
1
1
1
1
0
1
2
0
1
1
1
1
0
1
0
1
0
0
2
1
1
1
0
0
1
2
1
1
0
1
1
2
2
0
1
1
1
2
1
1
1
2
1
1
0
1
1
1
2
0
1
1
2
1
1
1
2
0
2
1
1
0
1
1
1
1
1
1
1
2
1
1
2
2
2
1
2
2
1
2
1
1
0
1
2
1
2
1
0
1
1
1
1
1
1
1
1
1
2
0
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
1
0
0
1
1
2
1
1
1
0
1
1
1
1
2
0
1
1
2
1
2
1
1
1
1
2
1
0
2
1
2
1
1
1
0
2
2
0
0
1
2
1
2
0
2
1
2
1
1
2
1
0
1
1
2
2
0
1
0
1
1
1
1
1
1
1
1
1
2
1
0
1
0
0
1
1
1
1
1
1
1
1
0
2
1
0
1
1
1
1
2
1
1
1
2
2
1
2
2
1
0
2
0
1
0
1
1
1
1
0
2
2
1
1
1
2
1
0
2
2
1
1
1
1
0
2
0
2
1
0
1
1
1
0
0
1
2
1
1
0
2
1
2
1
1
1
1
2
1
2
1
1
0
1
1
0
2
1
2
1
2
2
2
0
1
2
1
2
1
1
0
1
1
1
1
1
0
2
1
1
1
1
0
1
1
2
1
2
1
1
1
2
2
1
1
1
1
0
1
2
1
1
1
2
1
1
1
1
1
2
1
2
1
1
1
0
1
1
1
0
1
1
1
2
1
1
1
2
1
0
2
1
0
1
1
2
1
2
0
0
1
1
1
2
1
1
1
0
2
2
1
1
1
1
2
1
1
1
3
0
1
2
1
2
1
1
1
1
1
1
1
1
2
1
2
0
1
1
1
0
1
1
0
1
1
1
2
1
1
0
1
1
1
1
1
2
2
1
0
2
1
1
0
1
1
1
1
1
1
10
1
1
2
1
1
1
3
1
0
1
2
1
1
1
2
2
2
1
1
2
1
1
1
1
2
1
0
1
0
1
2
1
2
1
1
2
1
1
1
2
1
1
0
1
1
2
1
1
1
0
1
1
2
1
2
2
2
2
1
1
1
1
1
1
1
1
1
1
1
0
0
2
2
1
2
1
2
1
1
2
1
1
1
0
2
1
2
2
2
1
1
0
1
1
1
0
1
4
1
2
1
1
1
2
1
1
0
2
1
2
1
1
1
2
1
1
2
0
1
0
1
1
0
2
1
2
2
1
1
1
1
1
1
1
0
1
0
1
1
0
1
1
0
0
1
0
1
1
1
1
2
2
0
1
2
0
2
1
1
1
1
1
2
2
0
1
1
0
2
1
1
1
1
1
1
2
2
1
2
2
0
0
1
1
1
2
0
1
1
0
1
1
1
0
1
2
1
1
1
0
1
0
1
2
2
2
2
2
1
1
2
1
2
1
2
0
2
1
1
1
0
2
1
1
1
1
1
1
1
2
1
0
2
2
1
3
0
2
1
1
0
1
1
1
2
1
1
1
0
2
2
2
2
0
1
0
1
1
0
1
1
1
0
0
2
1
0
1
1
1
1
1
2
0
2
0
1
1
2
1
0
1
0
1
0
1
1
0
1
1
2
2
1
1
1
1
2
0
0
1
2
1
2
0
2
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
0
1
1
1
2
0
1
1
1
2
0
1
1
0
1
2
1
1
1
0
0
1
1
1
2
1
1
1
1
1
2
0
1
1
1
2
1
2
1
1
1
1
1
2
1
1
2
1
2
1
2
1
2
0
2
1
1
0
2
1
0
1
1
2
2
2
1
1
0
0
1
1
1
1
0
1
1
3
1
0
1
5
1
1
1
0
0
2
1
1
0
1
0
1
2
1
1
1
0
1
1
1
1
2
2
1
1
1
2
0
1
1
2
1
1
2
2
1
0
1
1
1
0
2
1
2
1
1
2
1
1
2
1
0
1
0
1
1
1
1
1
1
1
1
1
1
2
1
1
0
1
1
1
1
0
1
0
2
1
0
1
2
1
1
1
2
1
1
1
1
2
1
2
3
0
0
2
0
2
1
2
3
0
2
1
1
2
2
0
1
1
0
2
1
1
2
1
0
1
3
2
1
2
1
1
1
1
0
0
1
1
1
2
1
0
1
1
0
1
2
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
0
1
1
1
1
0
2
1
2
1
1
0
2
1
1
0
1
1
1
1
4
0
2
1
2
0
0
0
1
1
1
2
1
1
1
1
2
1
2
1
1
1
2
2
2
1
1
2
1
2
2
3
1
0
0
2
1
1
1
1
2
2
1
2
1
2
2
1
1
1
0
0
0
2
1
5
0
1
1
1
0
1
2
0
0
1
1
2
0
1
1
1
0
1
1
0
1
1
1
2
2
1
2
0
1
2
0
1
0
3
1
2
1
1
1
0
1
2
1
1
1
2
1
1
1
0
0
2
1
0
1
2
1
2
1
1
2
1
1
1
1
2
1
1
1
0
1
3
2
1
1
2
1
1
1
1
1
1
1
1
1
1
0
1
1
1
0
2
2
2
2
3
0
2
1
0
1
1
1
1
1
1
2
1
1
1
1
2
2
1
2
1
1
1
1
1
1
1
2
1
2
1
2
1
1
1
1
1
1
1
2
2
2
1
1
0
1
0
2
2
1
0
1
1
1
1
2
1
0
2
1
0
1
2
1
2
1
1
1
2
2
0
1
0
0
1
1
1
1
2
1
1
2
0
1
1
1
0
1
1
1
0
0
2
1
1
0
1
2
1
2
1
2
1
0
0
1
2
1
1
0
2
1
2
2
1
1
2
1
1
1
1
0
2
1
1
0
0
1
3
1
1
1
0
0
1
2
1
1
0
0
1
1
1
1
1
2
1
1
2
0
1
2
1
1
2
2
1
0
2
2
1
1
2
1
1
1
2
2
1
2
0
1
2
1
1
1
1
1
1
1
0
2
1
2
2
2
1
1
0
1
0
1
1
2
0
1
2
2
1
1
2
1
2
2
2
1
0
1
0
1
2
1
1
2
1
3
1
1
1
2
1
1
2
1
0
2
2
2
1
1
1
1
0
0
2
1
1
0
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
0
1
1
1
2
1
2
1
2
1
1
1
0
1
1
1
2
1
2
1
2
2
1
1
1
0
1
1
1
1
1
1
2
2
1
2
2
2
1
1
1
2
2
1
0
1
2
1
1
2
1
1
1
0
1
1
2
1
2
2
1
1
2
0
0
1
2
1
0
1
2
2
1
0
1
2
1
0
2
1
2
2
1
1
1
0
0
2
0
1
2
1
1
1
1
0
2
1
0
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
0
1
0
0
1
1
1
2
1
2
2
1
1
1
2
1
1
2
2
1
1
0
1
1
1
1
1
2
2
1
1
2
1
2
2
0
1
1
0
1
1
2
2
1
1
1
0
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
2
1
2
2
1
1
1
0
1
3
1
0
1
2
1
1
1
2
1
2
1
1
1
1
1
1
0
2
0
1
1
0
0
2
2
0
1
1
1
1
1
1
2
2
1
1
1
1
2
1
1
0
1
1
1
2
1
1
1
2
2
1
1
1
1
2
1
0
1
2
1
2
1
2
1
1
1
3
1
1
0
1
1
1
0
2
0
0
1
2
1
1
0
1
0
1
1
0
1
0
0
2
1
0
1
1
1
1
1
0
0
1
1
2
2
1
2
2
2
2
1
2
1
2
1
1
1
1
1
0
1
1
0
1
0
1
1
1
0
0
1
2
1
1
0
1
1
1
1
1
2
1
2
2
2
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
0
2
1
1
1
2
0
1
2
1
1
1
0
2
2
1
1
0
0
1
2
1
2
1
2
2
0
1
0
1
1
1
2
1
0
1
1
0
2
1
0
1
1
1
1
0
0
1
1
1
0
0
1
1
2
0
2
1
2
1
1
1
0
1
1
2
0
0
1
2
2
1
1
2
1
1
2
2
1
0
1
1
1
1
1
1
1
1
2
1
2
2
2
1
1
0
1
0
1
1
1
1
2
1
0
1
0
1
0
2
1
1
1
1
2
1
1
0
1
2
1
1
1
2
1
1
2
0
1
1
2
0
2
1
1
2
1
1
1
0
1
2
1
0
2
1
1
0
1
1
2
2
1
1
1
1
1
1
1
2
0
0
1
1
2
1
2
1
3
2
1
0
1
1
1
2
1
1
1
0
0
1
2
0
1
2
2
2
0
1
1
1
0
1
1
0
2
1
1
1
2
1
0
1
1
2
1
1
0
2
2
2
1
2
1
1
2
1
0
1
1
2
1
1
1
2
1
3
1
1
0
2
2
0
1
2
1
1
1
1
0
2
2
2
1
1
0
1
2
1
1
1
2
2
1
1
0
1
2
1
1
2
1
1
1
1
1
0
2
1
0
1
1
2
1
2
2
1
1
1
2
1
1
2
0
1
2
1
1
1
1
2
1
1
1
1
1
1
2
1
2
1
1
1
0
2
1
1
2
1
1
1
1
2
1
1
0
1
1
1
2
1
1
1
1
2
1
2
2
0
0
1
1
1
2
1
2
1
0
2
1
0
1
1
1
2
1
2
1
1
1
2
4
1
0
2
1
1
1
1
2
1
1
1
1
0
2
2
2
1
2
1
1
1
1
1
0
3
1
1
1
2
2
2
1
1
0
2
1
1
0
1
1
1
0
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
2
1
2
2
1
1
0
1
2
1
1
2
1
1
1
1
1
1
2
4
0
0
0
1
1
1
2
2
1
2
0
1
1
2
1
2
0
0
1
1
0
0
0
1
0
2
2
2
2
2
1
1
1
2
0
2
1
1
2
1
1
2
1
1
1
2
1
6
1
1
1
1
0
2
2
2
0
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
1
0
1
1
1
2
1
2
0
2
1
2
1
2
1
1
0
2
1
1
1
1
1
1
1
1
1
1
1
0
1
0
1
2
0
1
1
3
1
1
1
1
2
1
1
2
1
0
1
1
2
2
1
1
1
2
2
1
1
1
1
1
2
2
1
2
1
0
0
1
1
0
1
2
1
1
1
1
1
1
1
1
0
1
2
1
0
0
1
0
1
1
1
0
1
0
1
0
1
1
0
2
0
0
2
1
1
2
1
1
1
1
1
1
0
1
1
1
1
1
2
1
1
0
1
3
1
1
2
1
2
1
1
1
1
1
1
1
2
0
2
2
0
1
1
1
2
1
1
1
0
1
2
1
1
1
1
0
1
1
1
2
1
1
1
2
1
2
1
1
2
1
0
1
1
1
1
2
2
1
1
0
1
2
1
1
2
1
1
0
2
1
2
1
1
1
1
1
0
0
2
1
0
2
1
2
1
0
2
2
0
1
1
2
1
0
1
2
1
1
1
1
1
2
2
2
2
1
1
2
1
0
0
1
2
1
1
1
2
0
2
1
2
1
2
1
0
1
1
1
3
2
2
1
1
0
0
2
1
1
1
2
1
0
0
1
2
2
1
2
2
1
0
0
1
1
2
2
0
1
2
0
1
1
2
0
1
1
1
2
1
1
1
1
1
1
2
0
1
1
1
1
1
2
0
0
2
1
0
2
1
2
0
2
2
1
1
1
0
1
1
2
1
1
0
1
1
2
1
1
1
1
1
1
1
1
1
2
1
0
2
2
1
1
1
2
0
0
1
1
1
1
1
2
2
1
1
1
1
1
0
2
1
2
1
2
1
2
1
1
1
2
1
1
1
0
0
5
2
1
1
2
1
1
1
2
1
2
2
1
3
2
0
2
1
1
1
1
1
1
0
0
1
2
1
0
0
1
1
0
0
1
1
1
1
1
0
1
1
2
1
1
1
0
1
1
1
1
2
1
2
1
2
1
1
0
0
1
1
1
2
1
0
1
1
1
1
1
1
1
1
0
2
2
1
2
2
0
1
1
2
1
2
1
1
2
2
1
0
1
0
2
1
1
1
1
0
2
3
0
1
1
2
2
2
1
1
2
2
0
2
1
2
2
0
0
1
3
1
1
1
1
1
1
1
0
0
2
1
2
0
1
0
0
1
1
1
1
2
1
1
0
1
0
2
1
1
1
2
1
0
2
0
0
0
2
1
0
1
1
1
0
1
1
0
1
1
1
1
1
2
1
0
0
1
1
1
1
1
1
1
1
0
1
1
2
2
1
1
1
1
1
2
0
1
1
1
1
1
1
1
0
1
2
2
2
1
0
2
2
1
1
2
1
1
1
1
1
0
1
2
1
1
1
1
2
1
0
1
2
2
1
1
0
1
1
1
2
1
1
1
2
2
1
1
1
0
1
1
1
1
0
1
2
1
1
2
1
1
1
1
0
1
2
1
1
1
1
1
0
2
1
1
1
1
0
0
1
0
0
2
1
1
2
0
1
1
2
1
2
1
1
1
1
0
0
1
1
1
1
0
1
1
2
1
1
2
1
0
0
2
1
1
1
1
2
0
0
0
1
0
2
2
0
1
2
0
1
0
0
1
1
0
1
1
1
1
1
1
1
1
0
1
1
2
1
1
1
2
1
1
1
1
2
2
1
2
2
1
1
2
1
1
1
1
0
1
1
1
1
2
2
2
1
2
2
1
2
2
2
0
0
1
0
2
0
0
1
0
1
1
1
1
2
0
1
1
0
2
2
1
0
2
1
1
1
0
1
1
1
1
1
1
1
0
3
1
1
0
1
2
2
2
1
1
2
2
1
1
1
1
1
1
1
3
1
1
0
0
1
2
2
1
1
1
1
2
0
1
1
1
0
1
2
1
1
2
1
2
1
1
2
1
1
1
1
0
1
1
1
2
1
2
1
1
1
2
0
1
1
2
1
1
1
1
1
1
1
0
2
1
1
1
1
0
1
1
1
1
2
2
2
1
2
1
0
2
0
1
1
2
0
1
1
1
1
1
0
1
0
2
1
1
1
1
2
0
1
1
2
0
1
0
0
0
0
1
0
2
1
1
0
2
0
1
1
1
1
2
1
1
1
1
1
1
0
1
2
1
1
3
1
2
1
0
0
1
1
2
1
1
2
0
0
2
1
0
0
1
1
1
0
1
1
2
1
1
1
2
0
0
1
2
1
2
1
0
0
1
1
2
1
1
0
1
1
2
1
1
1
2
0
1
1
1
0
1
0
2
1
1
2
1
1
1
2
1
1
2
2
1
1
1
1
0
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
0
2
2
0
1
1
1
0
1
1
1
2
2
2
1
1
1
0
2
1
1
1
1
2
1
2
1
2
2
2
1
0
2
0
0
0
0
1
2
0
2
2
1
1
2
2
1
1
2
1
1
1
1
1
2
1
1
0
2
2
2
1
2
0
1
1
1
0
1
0
1
2
1
1
1
2
1
1
1
0
1
0
2
0
2
1
3
1
0
0
2
2
1
0
2
1
1
2
1
1
1
1
2
1
1
1
1
0
1
1
1
0
0
0
1
1
4
1
1
1
2
2
1
0
1
1
1
0
0
1
2
1
0
1
1
0
1
1
1
1
1
0
0
2
1
1
2
1
1
1
1
0
2
1
1
1
2
1
1
0
1
2
1
0
1
2
2
0
1
1
1
1
0
2
2
1
1
0
1
1
0
2
1
2
1
2
1
0
1
0
0
2
1
1
1
0
0
1
1
2
0
1
1
2
1
1
1
0
0
1
2
1
1
1
1
2
1
1
1
1
2
2
1
1
1
1
1
1
0
1
2
1
2
2
0
1
1
2
1
1
1
2
1
2
1
1
1
1
2
2
2
1
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
0
1
0
4
1
1
1
1
1
2
2
1
1
0
0
2
1
1
1
1
2
1
1
2
1
0
1
1
1
2
1
1
0
0
1
1
1
1
0
2
0
1
1
2
1
2
1
1
2
0
1
0
1
0
2
2
2
2
1
0
1
1
2
1
2
0
0
1
4
1
2
2
2
2
8
2
1
2
1
1
1
1
1
2
1
1
1
1
1
0
2
1
1
1
1
2
3
1
1
2
2
0
1
1
2
1
1
0
1
0
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
2
1
0
1
1
0
2
1
0
1
1
2
1
0
1
2
1
1
1
1
1
0
0
1
1
2
1
1
1
1
2
1
1
1
2
0
2
2
1
1
2
1
1
1
2
0
0
1
1
2
2
0
0
0
1
1
1
0
1
2
1
1
1
0
2
1
0
0
2
1
4
1
1
1
1
2
1
2
1
2
1
0
1
0
2
1
3
1
1
1
0
1
1
1
2
2
1
1
1
2
1
2
2
1
2
0
2
1
1
1
1
1
0
2
1
1
1
1
1
2
2
0
1
1
1
2
1
1
0
2
1
2
1
2
1
1
2
2
1
1
0
2
0
1
1
1
1
1
1
1
2
0
1
0
1
1
1
2
2
0
0
2
0
2
1
2
1
1
1
2
1
2
1
1
2
2
1
1
0
0
2
0
1
1
0
1
1
2
1
1
2
1
1
1
1
1
1
1
0
1
1
0
0
0
1
1
1
1
1
0
2
1
1
1
1
2
1
0
3
1
1
1
1
0
0
0
2
1
1
2
2
1
1
1
0
1
2
1
1
1
1
1
1
2
1
3
2
1
1
1
1
1
1
1
1
1
2
2
2
1
1
0
2
3
1
1
1
1
0
0
0
0
1
1
1
2
1
1
2
2
1
1
2
2
0
2
1
2
2
1
1
1
2
2
1
1
2
0
2
0
1
1
1
1
1
1
1
0
1
1
1
1
0
1
1
0
1
2
1
1
1
1
2
1
1
1
1
1
2
0
1
0
1
2
0
1
1
2
1
2
1
1
0
1
1
1
1
1
0
1
1
1
0
0
2
0
1
1
1
1
1
1
1
1
1
1
1
0
1
0
0
2
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
0
2
1
1
0
1
1
1
1
1
0
1
1
1
0
2
2
1
0
1
1
1
1
1
1
1
1
1
1
1
0
2
1
2
0
1
1
1
0
1
0
2
0
0
2
2
1
1
1
2
1
0
1
1
1
1
2
2
1
1
1
2
1
1
1
1
1
1
1
1
2
4
2
1
1
1
1
2
1
1
1
1
1
1
0
2
1
0
1
2
2
1
1
1
2
2
1
0
1
1
1
0
1
2
1
0
1
1
2
1
1
2
0
1
1
0
1
2
2
0
1
1
1
1
1
1
1
0
1
1
1
2
1
1
2
1
1
1
0
1
1
1
2
1
1
1
0
1
1
2
1
0
1
1
1
1
1
0
1
1
2
0
2
1
1
1
0
1
2
1
1
3
1
1
1
1
1
1
2
1
0
1
2
2
1
1
1
1
0
1
2
1
1
1
0
0
1
0
0
1
1
2
1
0
1
1
0
2
1
0
1
0
1
1
2
1
1
1
1
1
2
1
1
1
0
0
2
1
2
2
1
2
2
0
1
1
1
1
1
0
2
1
0
1
1
1
1
2
2
1
1
2
2
1
1
1
1
1
2
1
2
2
1
2
0
0
1
2
1
0
1
0
1
1
1
2
1
2
0
1
2
3
1
0
2
1
1
1
1
1
1
1
2
1
1
1
1
0
1
2
1
1
1
1
1
0
0
1
2
2
2
1
1
0
1
1
1
2
1
1
2
2
2
1
1
1
1
1
2
2
0
1
0
1
1
1
1
3
2
1
2
2
1
1
2
1
1
2
2
2
1
1
1
1
2
1
1
2
1
0
2
1
1
2
1
0
2
1
1
2
1
2
1
2
1
1
1
1
2
2
1
0
2
1
0
0
2
0
1
0
1
1
1
1
0
1
0
2
1
0
1
1
1
1
1
1
1
1
1
1
2
2
0
2
1
0
2
2
1
1
1
1
1
2
1
0
1
1
1
1
0
1
1
2
1
1
1
1
1
1
1
1
0
1
0
1
1
1
1
0
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
0
0
0
1
1
2
1
1
1
0
1
0
1
1
1
1
0
1
0
1
2
1
1
1
1
1
1
0
1
1
0
0
1
1
1
1
2
1
0
1
2
2
1
0
0
2
1
2
0
2
1
2
1
0
2
2
2
2
1
0
0
2
2
1
0
2
1
1
1
1
2
1
1
1
2
1
4
2
1
1
0
0
1
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
2
2
2
2
1
1
1
2
2
1
2
0
2
2
1
1
1
2
1
1
1
2
0
2
1
0
1
1
1
0
1
0
1
1
2
0
1
0
1
1
0
0
1
1
2
1
2
1
2
1
1
1
1
1
1
0
1
0
1
1
1
0
1
1
1
1
0
2
1
3
0
1
1
2
1
1
1
1
1
1
1
1
3
2
1
1
1
0
1
0
1
0
1
1
1
1
0
1
2
1
1
2
0
1
1
2
1
1
1
1
1
1
1
0
0
1
1
1
1
1
2
1
0
1
0
1
1
1
1
2
2
1
2
2
1
1
1
0
1
1
1
1
1
2
2
1
1
1
1
0
1
1
1
1
0
1
1
1
1
1
1
2
1
2
0
1
2
1
1
2
0
1
2
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
2
2
1
1
1
1
1
2
1
2
1
1
2
0
2
1
1
1
1
1
1
0
2
0
1
0
1
1
2
0
1
1
2
1
1
2
1
1
1
2
1
1
1
1
1
0
2
1
1
1
1
1
1
1
2
1
0
2
2
0
1
2
0
2
2
1
2
0
1
1
2
1
0
2
1
1
0
1
1
1
2
1
1
2
1
0
1
1
1
1
1
0
1
1
1
1
1
1
1
2
1
2
0
1
1
1
1
1
1
1
1
0
0
2
0
2
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
2
1
1
2
1
0
1
1
2
1
2
1
1
2
0
0
0
1
1
1
0
0
0
1
2
1
1
1
1
1
2
1
0
1
1
2
1
1
1
1
2
1
1
1
1
2
1
2
1
1
2
1
1
2
1
0
2
1
1
1
1
1
1
0
2
1
1
2
1
0
1
1
0
1
1
1
2
1
1
0
2
1
1
2
1
1
0
1
1
1
1
2
1
3
1
0
2
1
1
2
0
1
1
0
2
1
1
2
1
0
1
1
2
1
1
2
1
1
1
0
1
1
1
1
2
0
0
1
1
1
1
1
2
1
2
2
1
1
2
1
2
2
2
1
1
1
2
1
1
1
1
1
1
0
2
0
1
2
1
1
1
1
1
0
2
1
0
1
1
0
1
1
1
1
1
1
2
1
1
1
2
1
2
2
0
2
0
1
1
1
2
0
1
0
1
1
1
2
2
1
1
2
1
3
2
1
1
1
2
0
1
2
1
1
0
0
1
1
2
1
1
1
2
1
0
0
1
1
1
1
0
2
1
2
2
1
2
1
1
1
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
1
0
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
0
2
1
2
1
0
1
1
1
1
2
1
0
0
1
1
1
1
1
2
1
2
1
1
2
1
0
2
1
2
1
0
1
1
1
1
1
1
0
2
0
1
2
0
2
0
1
2
1
1
1
1
1
1
1
2
2
1
1
2
1
0
0
1
1
0
1
0
1
1
2
0
1
1
1
2
1
1
1
2
0
1
2
1
1
1
1
1
3
1
1
1
0
0
1
0
2
1
2
1
0
1
2
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
0
1
2
1
1
1
1
2
1
1
1
0
1
1
1
1
0
1
0
1
1
1
3
2
1
1
1
1
1
2
1
2
2
1
0
1
1
2
1
1
2
1
1
0
1
1
1
1
2
1
1
1
0
1
1
2
1
2
1
2
1
1
0
1
1
1
2
0
1
0
2
1
1
0
1
1
1
2
1
0
2
2
2
1
1
1
2
1
1
2
2
1
0
1
1
2
2
0
1
1
2
4
1
1
1
2
2
1
2
0
1
1
1
2
1
1
1
1
0
2
1
0
2
1
1
0
1
2
0
0
1
1
1
0
0
3
1
1
1
1
0
1
1
2
0
2
1
1
1
2
2
1
1
1
2
2
1
1
2
1
1
1
1
1
0
1
0
1
2
0
1
1
0
1
2
1
1
1
2
1
0
1
1
1
2
1
1
0
1
2
1
2
1
0
1
1
2
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
2
2
0
1
2
1
1
0
1
1
1
1
1
1
1
2
2
1
2
1
2
1
1
0
0
1
1
1
2
1
2
0
1
1
2
0
1
1
1
1
1
1
1
0
1
0
2
1
1
1
2
1
1
1
2
1
1
2
0
1
1
2
1
1
1
0
1
1
0
1
1
0
0
2
1
0
1
2
2
1
1
2
1
1
0
1
1
2
1
1
0
2
0
1
1
1
1
2
1
2
1
2
0
2
1
1
1
1
0
1
1
1
3
1
1
1
1
0
1
1
1
1
1
2
2
0
1
2
1
1
1
1
1
2
1
0
2
2
0
0
1
1
0
1
1
2
1
1
2
1
2
1
1
2
2
2
2
1
1
1
1
1
1
1
1
1
1
2
1
0
1
1
1
2
1
1
2
1
1
0
1
2
1
2
1
1
1
3
1
1
1
2
1
2
2
1
2
1
2
1
1
1
2
1
1
0
2
2
1
1
1
1
0
1
1
1
1
1
0
2
2
1
1
0
1
0
2
0
1
1
1
2
0
2
0
2
1
1
0
2
1
2
1
2
0
2
1
2
1
1
1
1
1
1
0
1
2
0
1
1
1
3
1
1
1
1
2
2
2
1
2
2
1
0
2
1
0
0
1
0
1
1
1
1
1
0
1
1
2
2
1
1
2
1
1
0
2
0
1
1
1
0
1
1
1
1
2
0
1
1
2
1
1
1
1
0
0
1
1
1
1
2
0
2
1
1
0
1
2
0
2
2
2
0
2
0
1
2
1
1
2
2
1
2
1
1
2
1
2
0
2
0
1
1
1
1
1
0
1
0
2
1
1
1
2
0
0
1
1
1
0
0
1
1
0
1
2
1
1
1
1
1
0
1
0
0
1
1
2
1
1
0
0
1
1
1
2
2
2
0
1
0
1
1
1
1
2
2
1
1
2
0
2
0
1
1
1
2
1
1
1
1
0
1
1
2
1
2
1
1
1
0
0
1
2
1
2
3
1
1
1
0
1
1
1
2
2
0
2
1
1
1
1
1
1
2
1
1
1
0
0
1
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
0
2
2
1
0
1
1
2
0
2
2
0
2
1
0
1
2
1
2
0
2
0
1
2
2
2
1
0
1
0
2
1
2
1
3
1
1
1
1
1
1
1
1
1
1
1
1
0
1
0
1
1
1
0
2
2
1
0
1
0
1
1
1
1
1
1
1
2
0
1
1
1
0
1
2
1
1
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
3
1
1
1
1
2
3
2
1
1
1
1
2
1
2
1
1
2
1
1
1
1
1
1
2
2
1
2
1
2
1
2
1
0
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
0
1
1
1
3
1
1
1
1
0
2
0
1
2
1
1
1
1
1
0
0
2
1
1
1
1
1
1
1
2
2
2
0
1
1
1
1
1
1
0
2
2
1
1
1
1
0
0
2
1
2
1
2
0
0
0
0
0
1
2
1
1
2
1
1
2
2
2
1
1
1
1
3
1
2
2
0
1
1
1
2
2
1
2
1
2
2
2
2
0
2
2
2
1
0
1
2
1
2
2
1
2
1
1
1
1
1
1
1
1
1
1
1
0
1
3
2
1
2
3
1
1
1
3
3
1
2
1
2
2
1
1
1
2
1
2
2
1
1
0
1
2
2
1
1
0
1
0
1
1
1
2
2
1
1
0
1
2
1
1
1
1
2
1
2
0
2
1
1
1
1
2
1
1
1
2
0
2
0
1
2
1
0
1
2
2
1
1
1
1
1
1
1
0
0
2
1
1
1
0
1
1
1
1
2
1
1
1
2
1
0
1
1
1
1
1
0
2
0
2
1
2
1
1
0
1
2
0
0
1
2
1
1
1
2
1
0
1
0
2
1
2
2
0
0
0
0
1
0
1
2
2
2
1
1
2
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
1
0
2
1
1
1
1
1
1
1
1
1
2
2
2
1
1
0
1
0
1
1
2
1
1
2
1
1
0
1
1
1
1
1
1
1
2
0
0
1
1
2
2
3
0
1
1
1
0
0
2
0
2
1
1
1
1
2
2
1
1
2
1
0
0
1
1
1
1
1
2
1
2
2
1
2
0
1
2
0
1
1
2
2
1
2
1
1
1
1
1
2
0
0
0
1
2
1
0
1
1
0
1
0
0
1
1
1
2
2
0
1
1
1
1
2
0
1
1
0
1
0
2
1
3
1
1
1
1
1
1
1
1
1
2
1
1
0
1
1
1
1
1
1
1
0
1
1
1
2
2
1
2
1
1
0
0
1
1
1
1
1
1
3
1
2
1
2
2
1
2
2
2
0
0
1
1
1
1
1
1
2
2
0
2
2
1
1
0
0
2
1
1
3
2
1
1
1
2
2
1
1
1
0
2
2
2
1
1
1
1
1
2
1
1
2
1
0
2
1
1
1
1
2
1
2
1
1
1
2
1
1
1
1
1
2
2
0
0
2
1
0
1
2
1
1
1
2
2
1
1
1
1
0
3
0
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
3
0
1
2
1
1
2
1
1
0
1
1
1
1
2
1
1
1
2
0
1
1
1
0
1
1
2
1
2
2
0
0
1
1
1
1
1
2
2
0
1
2
0
1
1
0
2
1
1
1
0
2
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
0
1
1
1
1
2
1
1
2
0
1
1
1
0
2
1
1
1
2
2
1
2
1
1
1
0
1
1
1
2
2
1
0
0
1
1
1
1
0
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
2
1
1
1
0
0
2
1
1
1
1
1
1
3
1
2
1
1
1
0
0
1
1
1
0
1
0
2
1
2
2
2
1
2
1
1
2
1
1
1
1
1
1
0
1
1
1
1
2
1
0
1
0
0
2
0
2
1
1
1
1
1
2
1
1
2
1
1
3
0
0
1
1
1
1
2
1
1
1
1
1
0
1
1
1
1
2
2
1
1
1
2
1
2
2
1
0
0
1
2
1
0
1
1
1
2
1
2
1
0
1
0
1
1
1
1
1
2
0
1
2
0
1
0
0
1
0
0
1
1
2
1
1
1
1
3
1
1
1
1
1
1
2
1
1
1
1
1
2
2
2
1
1
1
3
2
1
2
0
2
2
1
1
1
0
1
1
1
1
0
1
1
2
1
0
1
2
1
0
1
2
1
0
1
1
0
1
2
1
2
2
1
1
1
1
2
1
0
2
1
2
1
2
2
2
2
1
1
1
2
2
0
2
0
0
1
1
2
1
1
0
1
1
1
1
0
0
2
1
1
1
0
2
2
1
1
2
2
1
1
2
1
2
1
1
2
1
0
0
1
1
1
2
1
0
1
1
2
1
2
2
1
1
2
1
1
1
0
0
2
0
0
1
0
0
1
1
1
1
0
1
3
0
1
0
0
1
2
2
1
1
1
2
0
1
0
1
3
2
0
1
2
1
1
1
2
1
0
0
1
0
0
1
1
1
2
1
2
1
1
0
2
1
1
1
1
2
0
0
1
1
2
2
1
0
1
2
0
2
1
1
1
1
1
1
2
1
2
2
2
2
1
2
1
1
1
1
1
1
2
2
0
1
1
2
0
1
3
1
1
1
1
1
1
2
1
1
2
2
1
1
0
0
1
0
1
1
1
0
0
1
1
0
1
0
2
2
1
1
0
0
2
2
1
1
1
2
2
1
0
1
2
1
1
1
2
2
1
1
1
0
0
1
1
1
0
1
1
2
2
1
1
1
1
2
2
1
1
1
0
2
1
2
1
0
1
1
2
1
1
1
1
1
0
0
1
0
0
1
1
1
1
1
2
0
1
1
1
1
0
2
1
2
1
1
0
1
1
1
1
2
1
1
1
2
1
0
1
1
1
1
1
1
1
1
1
12
1
1
2
1
1
1
1
1
0
2
1
1
0
1
1
2
1
2
1
1
1
0
1
1
2
1
1
0
1
2
2
2
1
2
1
1
1
0
1
2
1
1
0
1
0
2
1
1
0
2
2
1
0
1
1
0
1
1
2
2
0
1
1
1
1
2
1
1
1
1
2
1
1
2
1
0
2
2
1
1
1
0
1
1
1
1
2
1
1
1
1
0
0
1
2
1
1
1
1
2
2
1
1
0
1
1
2
1
2
0
1
2
1
1
2
1
1
2
1
1
0
0
2
1
2
1
1
2
1
2
1
2
1
2
0
1
1
2
1
1
1
1
2
1
1
0
2
1
0
2
1
2
1
0
1
1
1
1
2
0
2
0
0
1
1
0
1
2
0
2
0
1
1
1
0
1
2
2
1
2
2
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
0
0
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
2
1
1
1
1
0
1
0
1
1
2
2
1
1
0
1
2
0
1
1
0
0
1
2
2
1
1
1
2
1
1
2
1
1
1
1
0
1
1
2
2
1
1
1
0
1
0
1
1
0
1
1
1
2
0
1
1
1
1
1
1
2
1
2
1
1
1
2
2
2
2
1
0
1
1
1
2
1
1
1
0
2
1
0
2
0
2
1
1
2
1
2
1
2
2
2
1
2
1
1
1
1
2
1
0
0
1
1
0
2
1
1
1
2
1
0
1
1
0
0
0
1
2
2
1
2
1
1
1
0
2
2
1
1
1
0
2
1
1
1
1
1
1
1
1
0
1
0
1
1
0
1
1
1
1
1
1
1
0
1
1
2
0
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
2
0
1
1
2
2
2
2
0
0
1
2
2
2
1
2
1
1
1
2
1
2
0
2
1
1
2
2
0
0
1
2
1
1
1
0
1
1
2
1
1
2
1
1
0
1
1
0
2
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
2
1
2
1
0
2
2
2
1
1
1
1
1
1
1
3
2
1
1
1
2
1
0
2
2
2
1
2
2
2
1
1
1
1
0
1
2
1
3
1
2
2
1
1
1
1
1
2
2
1
1
0
1
1
1
2
1
1
0
1
1
1
2
0
2
1
1
1
1
2
1
2
0
1
0
2
1
0
1
1
1
1
1
1
0
1
1
1
2
1
0
1
1
2
1
0
1
1
1
2
1
1
1
1
0
1
1
1
1
2
2
1
2
2
1
0
1
1
0
2
1
1
1
1
1
1
0
1
2
0
1
0
0
1
1
1
1
1
1
1
2
1
2
0
1
2
1
1
2
0
0
1
1
1
0
1
1
2
1
1
0
0
2
1
1
2
0
1
0
1
0
1
2
2
1
1
2
1
1
1
0
0
1
2
2
1
1
2
1
0
1
1
1
1
0
1
1
1
1
0
1
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
0
1
2
1
0
2
1
1
1
1
0
2
2
2
2
0
0
1
2
1
1
1
1
1
2
2
2
2
1
1
1
2
2
0
1
1
2
2
2
1
1
1
1
1
1
1
1
2
2
1
1
1
1
0
1
0
2
2
1
2
2
2
1
2
1
1
2
2
6
2
1
1
2
1
1
1
1
1
0
0
1
2
2
1
2
2
0
2
1
1
1
1
2
1
1
0
0
0
2
1
2
2
1
0
1
1
2
1
1
1
0
1
1
1
2
1
1
1
1
1
0
2
1
3
1
2
1
2
1
1
1
1
0
1
1
3
2
0
1
1
0
0
1
2
1
1
2
0
2
0
1
1
1
0
1
1
0
2
2
1
2
1
1
0
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
0
0
2
0
1
2
1
1
0
1
1
1
0
1
1
1
0
1
1
1
1
0
2
2
0
1
1
1
1
2
2
1
1
2
1
1
2
0
0
1
1
2
0
0
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
0
1
2
0
2
1
2
1
2
2
2
1
1
1
0
1
0
1
1
1
1
1
1
0
2
1
1
1
2
1
0
1
2
1
1
1
1
1
1
1
1
1
0
1
2
2
1
1
2
0
1
2
1
2
2
2
1
0
1
0
0
1
1
1
1
0
1
1
1
1
0
2
0
1
0
1
0
1
1
1
1
1
0
1
0
0
1
1
1
2
1
1
2
1
1
0
1
1
1
0
1
1
3
1
0
2
1
0
0
1
1
0
1
1
1
1
1
1
1
2
1
0
1
2
1
1
1
1
1
2
0
1
1
1
2
0
2
2
2
0
0
0
0
0
1
1
2
1
1
1
0
0
2
2
1
0
1
1
0
1
1
1
1
1
1
0
2
1
1
0
2
1
1
2
1
0
2
1
1
2
1
2
0
1
1
1
1
2
2
7
1
1
2
1
0
1
1
2
1
1
1
0
2
1
1
1
1
1
1
1
1
1
2
0
0
2
1
1
0
1
1
1
0
1
1
1
1
1
1
2
1
0
0
1
1
0
1
2
1
0
0
1
0
1
0
0
1
2
1
1
1
1
3
2
2
2
0
0
2
2
0
1
0
0
1
2
1
2
1
1
1
0
1
1
1
0
2
1
0
1
1
0
0
2
3
1
2
1
1
1
1
0
1
1
1
0
2
2
1
0
2
0
1
2
2
1
1
1
2
1
0
1
1
2
1
2
1
1
0
1
0
2
1
1
1
1
1
0
1
1
2
0
0
0
1
0
1
1
2
2
1
0
1
1
1
1
1
2
2
2
2
1
1
0
2
1
1
1
0
0
2
1
1
1
0
1
1
2
2
1
2
1
2
1
1
1
1
1
1
2
1
1
0
1
1
2
2
1
1
1
0
2
1
1
2
2
2
2
0
2
1
1
1
0
0
1
1
1
0
1
2
1
1
1
1
0
2
2
0
0
2
2
1
1
2
1
1
1
1
2
1
1
2
2
1
0
1
1
1
2
1
1
2
1
1
2
1
1
2
0
1
1
2
0
0
1
1
1
1
0
1
2
1
0
1
1
0
0
2
1
1
1
0
1
2
1
0
0
1
1
1
1
4
0
0
2
1
2
1
2
1
0
2
1
2
1
1
0
0
0
1
0
1
1
1
1
1
1
2
2
2
2
2
4
1
1
0
1
0
2
0
0
2
1
0
0
1
1
0
2
0
2
2
2
1
1
2
1
1
1
0
1
0
2
0
1
1
2
1
0
1
2
0
1
2
1
2
2
0
2
2
2
2
1
0
2
1
1
2
1
1
0
2
1
0
1
1
1
1
2
1
1
1
0
1
2
2
1
1
1
1
1
1
1
2
2
1
1
1
1
2
0
2
0
1
2
1
1
0
2
2
2
1
1
2
1
1
1
1
1
2
1
1
1
2
1
0
0
1
2
1
1
1
2
1
0
1
1
1
1
0
1
0
1
1
1
1
2
1
0
1
1
3
2
1
1
2
2
0
1
0
1
1
1
3
1
1
1
2
1
2
0
2
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
1
1
2
1
2
0
1
1
2
1
1
1
2
2
1
1
2
2
1
0
1
1
1
2
1
0
1
0
1
1
1
1
1
1
0
0
2
1
2
1
1
1
0
1
1
1
2
0
1
1
1
1
1
1
1
0
1
1
2
0
0
2
1
1
0
1
1
1
0
1
2
1
1
2
1
2
1
1
1
1
2
2
0
1
1
2
0
1
1
1
1
2
1
2
1
1
0
1
0
1
2
2
1
2
1
2
1
1
1
1
1
2
1
0
1
1
2
1
2
1
0
1
1
1
2
0
2
1
1
1
1
1
2
1
0
1
1
2
1
1
0
1
2
2
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
2
0
2
2
1
1
2
1
1
2
1
2
1
2
1
1
1
1
0
1
1
0
1
1
2
1
2
1
0
1
1
1
2
1
1
0
1
1
1
1
1
1
1
1
1
2
2
1
0
1
1
0
0
1
1
0
2
2
1
1
0
1
0
1
2
1
1
1
0
2
1
1
1
1
1
2
2
1
2
0
1
1
0
1
2
1
2
1
1
1
0
1
1
1
1
1
0
1
1
2
1
1
0
0
1
2
1
1
1
0
1
1
2
2
2
2
2
1
1
1
1
1
1
2
1
1
2
1
2
2
2
1
1
0
2
2
2
2
1
2
1
0
6
0
2
2
1
2
1
2
1
0
2
1
1
1
1
1
1
1
1
2
2
1
1
0
0
1
1
2
1
1
1
1
0
2
0
1
1
2
1
2
1
1
2
2
2
1
1
1
1
2
2
1
3
1
1
1
2
1
0
1
2
1
1
0
2
1
1
1
1
2
1
0
2
2
2
2
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
0
1
1
0
2
0
2
1
1
1
1
0
1
1
1
0
1
1
0
1
0
1
1
0
1
1
1
2
1
2
2
1
1
2
0
0
1
1
1
1
2
2
2
0
1
1
1
1
0
1
2
2
1
1
2
0
2
1
2
1
1
1
2
0
1
1
2
0
0
1
1
3
1
2
1
0
2
1
2
1
1
1
1
1
0
1
1
1
1
1
2
2
1
2
0
1
1
1
2
2
1
2
1
2
5
0
1
1
1
1
2
0
2
1
0
0
1
1
1
1
2
2
1
0
1
0
1
0
2
0
2
1
1
2
1
1
1
1
1
1
1
1
1
1
0
2
1
1
2
2
1
0
0
1
1
0
0
1
0
1
1
2
2
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
0
1
1
2
0
0
1
0
1
1
1
1
1
1
1
1
1
1
1
1
0
2
0
2
1
0
2
1
1
1
0
1
2
1
2
2
0
2
1
1
2
1
1
1
1
1
1
1
1
1
1
0
1
1
1
2
1
1
1
1
0
1
0
1
0
1
2
0
2
2
2
1
2
2
1
1
2
1
1
0
2
2
2
0
2
1
2
1
2
1
1
1
1
1
1
1
2
0
1
1
2
1
2
2
0
2
1
1
2
1
2
1
3
1
3
2
2
1
0
2
0
1
0
1
2
2
4
1
2
1
1
1
1
1
1
1
1
0
2
1
1
2
0
1
1
1
1
0
1
0
2
1
1
1
1
1
1
2
2
1
1
0
1
0
2
2
1
1
2
1
2
1
2
0
0
1
1
0
1
0
1
1
0
1
1
1
1
0
2
2
2
1
1
2
1
1
1
1
2
2
1
1
1
1
1
1
1
1
2
1
2
1
2
1
1
1
0
2
1
3
1
1
0
1
1
1
1
0
0
1
2
2
1
1
0
0
2
1
1
0
1
1
1
0
2
2
0
1
1
2
0
1
1
0
2
2
2
0
1
1
2
2
2
2
1
1
2
0
1
1
1
0
0
1
1
1
1
1
2
0
0
1
0
1
2
2
2
1
1
1
1
1
1
0
1
2
2
1
2
1
1
1
1
1
2
1
2
1
1
1
2
2
1
1
1
0
0
1
1
1
0
2
1
1
2
1
1
2
2
1
1
1
1
1
0
1
1
1
2
1
1
2
1
2
1
1
2
1
1
1
2
1
2
2
1
1
2
1
1
0
2
0
1
2
3
2
1
3
1
1
1
0
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
0
1
1
2
0
1
2
1
1
2
1
1
1
1
2
0
2
1
1
1
0
1
1
1
2
1
2
1
0
2
1
1
1
0
1
2
1
2
2
1
0
2
1
1
0
1
3
1
1
0
1
1
1
1
2
3
1
1
2
2
1
1
1
2
2
1
1
2
1
0
0
1
1
2
1
1
2
1
0
0
0
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
2
2
1
1
1
1
0
0
1
2
2
1
1
1
1
1
1
0
1
1
1
1
0
1
1
0
1
0
0
0
2
1
1
2
0
1
1
2
1
1
2
2
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
3
1
1
0
0
2
0
1
1
1
1
1
1
1
1
2
2
1
3
0
2
1
1
1
1
1
1
1
2
1
1
5
2
0
1
2
1
1
0
2
0
1
0
1
2
2
1
1
0
2
2
0
0
1
3
1
1
1
2
1
2
1
0
1
1
0
1
1
2
1
0
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
2
0
0
0
2
1
1
1
0
1
1
1
1
1
1
1
1
1
1
2
1
1
0
1
1
2
2
1
1
0
1
1
2
1
2
2
1
1
1
1
1
2
0
1
1
1
2
1
0
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
0
0
2
0
1
1
2
0
1
1
1
1
2
1
2
1
2
2
2
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
2
1
1
1
1
0
1
2
0
1
2
1
1
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
2
2
1
1
0
1
1
1
1
1
2
2
1
1
2
1
1
2
1
1
2
1
2
1
1
1
1
2
0
1
1
0
2
1
1
1
2
0
2
1
1
1
2
0
1
1
2
2
1
2
2
2
1
1
0
0
1
1
1
2
1
1
1
0
2
0
1
1
1
1
2
1
1
0
1
1
1
1
0
2
1
2
1
1
1
2
1
1
0
1
2
2
2
1
1
0
1
2
1
2
1
1
1
0
2
0
0
1
0
2
0
0
2
1
1
1
1
2
1
1
1
1
1
0
3
1
1
1
1
1
1
1
1
1
2
1
1
2
2
1
1
2
2
2
1
2
1
1
0
1
1
1
2
1
1
1
2
1
0
2
0
1
1
2
0
2
1
1
2
1
1
2
1
2
2
1
0
1
1
1
1
1
0
1
1
1
2
1
1
1
1
1
3
2
2
1
0
1
2
1
1
1
2
1
1
0
1
0
0
1
1
1
1
0
0
1
1
1
0
0
1
1
0
0
1
0
1
2
0
2
2
1
1
1
0
1
1
1
1
1
1
1
0
0
2
1
2
1
0
1
0
0
1
1
1
2
1
1
1
2
0
0
1
1
1
1
2
1
1
0
1
1
1
1
1
2
2
1
1
2
1
1
2
1
1
2
1
1
0
1
1
1
2
1
1
1
2
2
2
1
1
0
1
1
1
2
2
1
0
1
1
1
0
1
0
1
1
1
1
2
2
2
1
2
2
0
0
2
2
1
2
1
1
1
1
2
0
1
1
1
1
2
1
2
0
1
1
1
1
1
1
1
1
1
1
0
0
1
0
0
1
2
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
0
1
0
1
1
2
0
1
1
0
0
2
2
1
1
1
1
1
2
1
1
2
0
1
1
2
0
1
1
1
1
1
0
1
1
1
0
1
1
1
1
0
1
1
1
1
0
1
2
2
1
2
1
2
1
1
0
1
1
2
1
2
1
1
1
1
2
1
1
1
1
0
1
2
1
2
2
2
1
1
2
1
0
1
1
0
1
1
2
1
1
0
1
1
1
0
0
12
1
1
1
0
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
0
1
2
2
1
2
1
1
1
1
2
1
0
1
1
2
0
2
0
1
1
2
1
2
1
2
2
1
1
1
0
2
2
1
0
1
0
1
0
1
1
1
1
1
0
1
2
1
1
1
0
1
1
1
1
1
1
2
1
3
2
1
0
1
1
1
1
2
1
1
0
1
1
2
1
1
2
1
1
2
2
0
1
0
1
0
1
0
4
1
2
1
2
1
2
2
2
2
1
0
1
1
1
1
1
1
2
2
0
0
1
1
3
0
1
0
1
1
2
1
1
1
1
0
0
1
1
1
1
1
2
0
2
1
2
0
2
0
1
0
1
2
2
2
1
1
1
2
1
1
1
1
2
1
2
1
1
2
1
2
2
1
2
1
0
1
2
2
1
1
0
1
1
2
1
1
1
2
2
2
1
1
1
0
1
2
0
1
1
0
0
2
2
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
0
1
1
0
1
1
2
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
0
0
0
2
2
1
1
1
0
1
1
1
2
1
1
2
2
0
1
2
1
2
1
1
1
1
0
2
1
0
2
1
1
1
1
2
2
1
1
1
1
1
2
0
2
1
1
1
1
1
2
1
1
0
1
1
1
2
1
2
1
2
0
4
1
0
0
2
2
0
1
1
2
1
1
1
1
1
1
1
1
0
2
2
1
2
1
2
2
0
1
0
1
1
1
1
0
2
1
2
2
1
3
1
1
1
3
3
1
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
1
2
1
1
2
0
2
1
1
2
1
0
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
0
1
0
2
1
0
2
1
2
1
2
1
1
1
2
1
2
1
1
2
1
2
1
2
1
2
1
1
1
0
2
0
2
1
1
1
1
1
2
0
2
1
1
1
2
1
1
0
1
0
2
1
1
1
1
2
1
1
2
1
0
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
0
2
2
1
0
1
1
1
1
2
2
1
2
1
1
0
0
1
2
2
1
0
1
1
1
0
0
2
1
0
2
1
0
2
1
2
2
1
1
1
1
2
1
1
1
1
2
1
1
1
0
2
1
0
1
1
0
1
0
1
1
1
1
1
1
1
0
2
2
0
2
1
2
2
2
2
1
1
2
1
0
1
0
1
1
6
0
1
1
2
1
2
1
1
1
1
2
1
0
0
1
1
2
1
0
0
1
0
1
1
1
2
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
0
1
1
0
2
2
0
2
1
1
2
1
2
2
1
2
1
2
0
1
2
1
1
1
1
0
1
1
0
1
2
1
1
0
0
1
1
1
1
0
1
1
2
2
2
2
0
2
2
0
1
0
1
1
1
1
1
2
1
2
2
2
1
2
1
1
2
1
1
1
0
5
1
2
1
1
1
1
1
2
0
2
1
2
2
2
2
1
2
2
1
1
2
2
1
1
2
1
1
1
1
1
1
0
1
2
1
1
0
1
1
1
1
2
0
2
1
1
1
1
1
1
1
2
1
1
0
1
1
2
2
1
2
2
2
0
0
1
0
1
1
1
1
1
0
1
2
1
1
1
1
1
1
1
1
1
1
0
0
2
0
1
1
1
0
1
1
1
2
1
0
0
1
0
1
1
1
2
1
1
1
2
0
1
2
2
1
0
2
1
1
1
1
1
0
1
1
2
1
0
1
2
1
0
1
1
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
1
0
0
1
1
1
2
1
1
2
2
0
2
1
1
1
2
1
1
0
2
2
0
1
1
2
2
1
2
2
2
1
1
2
0
2
0
1
2
2
2
1
1
1
1
1
0
2
1
1
2
1
1
1
1
0
1
1
1
0
2
1
2
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
0
2
1
2
1
1
1
1
0
2
1
1
2
1
2
2
1
1
2
2
1
1
2
1
1
0
2
1
0
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
2
1
2
1
1
0
2
0
6
1
1
1
1
2
0
1
1
1
1
1
1
1
1
2
0
0
1
2
2
1
2
1
2
0
2
0
1
2
1
2
1
0
1
1
0
1
0
2
1
1
0
2
1
2
0
0
1
1
2
1
2
0
0
1
1
2
1
3
0
1
1
2
0
2
2
1
1
1
0
1
1
1
2
1
0
1
1
1
1
1
1
1
1
0
1
1
1
1
1
0
1
1
1
1
2
1
2
1
0
1
0
1
2
3
1
0
1
2
1
2
1
1
1
2
2
1
1
1
0
1
1
0
2
0
2
0
2
1
1
0
2
2
1
1
1
1
1
1
1
2
0
2
1
1
1
2
1
1
1
1
2
1
1
2
1
2
2
2
2
2
1
2
2
2
2
0
1
1
0
2
1
2
0
2
2
1
1
1
1
1
2
2
1
2
1
2
1
2
1
1
1
0
1
2
0
1
0
2
1
2
1
1
1
1
1
0
1
1
1
1
2
1
3
1
0
0
2
1
2
2
2
1
1
2
0
1
0
1
1
0
2
1
0
1
1
1
1
2
1
1
1
2
1
1
2
1
2
1
1
1
1
1
0
1
2
1
2
1
1
2
1
2
1
1
1
0
1
1
1
2
1
1
1
1
2
1
1
1
0
1
1
1
1
1
1
0
1
0
1
0
0
2
0
1
1
2
1
2
1
2
1
0
1
1
1
2
1
1
1
2
1
1
1
0
1
0
2
2
2
2
2
2
1
0
1
1
2
1
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
0
1
2
1
2
2
1
1
1
0
2
1
1
0
2
2
0
1
1
2
1
1
1
1
1
2
1
1
2
0
1
0
1
1
1
1
2
1
1
2
1
2
1
1
0
1
2
1
2
1
1
1
1
1
1
2
1
1
1
2
2
1
1
2
1
1
1
0
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
3
1
2
1
1
1
0
1
2
1
1
1
0
2
2
2
1
1
1
2
1
2
1
2
2
0
2
0
2
2
1
1
2
1
1
1
0
0
1
1
1
1
1
2
1
2
1
1
2
2
2
0
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
0
2
1
2
1
2
1
0
2
2
1
1
1
1
2
0
1
0
0
0
1
1
1
1
2
1
1
1
1
2
1
1
1
2
2
1
2
1
1
2
1
1
1
0
1
1
1
0
1
2
1
0
1
1
2
2
1
0
1
2
1
1
1
0
0
3
0
1
2
1
1
1
0
1
1
2
1
1
2
1
1
1
2
2
1
2
2
2
2
2
2
2
1
1
0
1
2
2
1
1
1
1
1
2
0
1
1
1
1
1
1
1
2
1
3
2
1
0
1
1
1
1
1
2
1
2
0
1
1
1
2
2
1
2
2
1
2
1
1
1
1
1
1
1
1
1
1
0
1
1
2
1
2
2
1
2
0
2
2
0
1
1
1
1
1
1
2
1
0
1
1
1
2
0
0
1
0
1
1
2
2
1
1
1
1
1
0
2
2
1
1
0
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
0
1
1
1
2
1
1
0
1
2
1
0
2
1
1
2
1
1
1
2
2
3
0
0
2
2
1
1
2
1
1
1
2
1
1
1
1
1
1
2
1
0
1
1
2
0
2
1
1
1
1
1
0
0
1
1
1
1
2
1
0
2
1
1
1
2
1
2
1
1
2
1
1
2
0
0
2
1
1
2
1
1
1
0
1
2
1
1
1
1
0
0
1
2
1
2
2
1
1
2
2
1
2
0
2
1
2
2
1
2
1
1
3
2
2
1
0
1
1
2
3
1
2
0
2
1
0
1
2
1
1
0
1
1
1
1
1
1
1
1
1
2
2
1
1
2
2
2
1
2
0
1
2
0
1
2
1
1
1
1
1
1
0
0
1
1
1
1
2
1
1
1
1
1
1
2
1
1
0
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
2
1
1
1
2
0
0
1
1
1
0
1
1
1
0
0
1
2
2
1
0
1
1
2
0
1
0
1
1
0
1
1
0
1
1
1
0
0
1
1
1
1
1
2
1
1
1
2
1
1
0
2
2
1
0
1
1
1
1
0
1
0
1
2
1
1
1
1
1
2
2
2
1
1
1
1
0
1
0
1
1
1
2
1
1
1
1
2
2
1
0
2
2
2
2
1
1
2
0
0
1
2
1
1
2
1
1
1
1
2
1
1
1
1
3
1
0
1
1
1
1
0
2
4
1
0
1
1
1
1
1
2
1
1
1
1
0
1
0
0
1
2
2
1
0
1
1
1
0
0
2
2
2
1
1
1
1
1
1
1
2
1
2
0
2
2
2
1
1
1
2
2
1
2
1
1
2
1
1
0
2
2
1
1
2
1
2
1
1
1
3
3
2
1
1
1
2
2
0
0
1
1
1
1
1
1
2
1
1
2
1
1
2
1
0
0
1
1
1
1
0
1
0
2
1
1
1
0
1
1
1
2
2
0
0
1
2
1
0
2
1
3
1
2
1
1
2
0
1
0
0
0
2
1
1
1
1
1
1
2
1
2
2
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
2
1
1
2
2
1
2
1
1
2
1
1
2
1
1
2
1
2
1
4
2
1
1
1
1
0
1
1
2
1
1
2
1
1
0
2
2
0
2
0
2
2
0
0
1
1
2
1
0
1
1
1
0
1
1
1
1
2
1
1
1
0
2
1
1
1
1
1
2
1
0
2
1
0
1
1
1
0
0
2
1
1
0
0
0
1
0
1
1
1
1
1
1
1
2
1
2
1
0
1
3
1
1
1
1
1
2
1
1
1
1
2
2
2
2
2
1
2
1
1
1
1
1
2
1
1
0
1
0
0
0
2
1
1
1
1
1
1
0
1
1
1
2
0
0
1
2
1
2
2
0
2
1
1
1
0
1
1
2
1
1
1
1
1
1
1
2
1
2
1
2
0
1
2
1
2
1
1
1
1
0
1
1
1
2
1
2
1
0
2
1
2
1
1
0
1
2
2
1
1
0
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
1
1
2
2
2
2
1
0
2
1
0
2
0
1
2
1
2
1
1
1
2
0
0
1
2
1
2
2
3
1
2
2
1
1
1
0
1
0
1
2
2
1
1
2
2
1
1
2
2
0
2
0
1
0
1
1
1
1
1
1
1
1
2
1
1
1
1
0
2
1
1
2
2
2
1
1
0
0
0
2
1
2
1
1
0
1
1
0
1
1
2
1
2
1
2
1
0
0
1
0
1
2
1
1
1
0
0
2
1
2
0
0
1
1
1
1
1
0
1
0
1
2
1
1
0
1
1
0
2
0
0
1
0
2
2
1
2
1
1
0
0
1
2
2
1
2
2
1
1
0
0
0
1
1
0
2
2
1
1
1
1
0
1
1
1
1
1
1
2
1
1
1
2
1
1
1
2
2
1
2
2
1
1
1
1
1
1
2
1
1
2
0
1
1
1
1
1
1
0
1
1
2
1
1
1
2
1
1
2
1
1
1
1
1
0
1
1
3
2
1
1
1
1
0
0
1
1
1
1
2
1
1
1
1
1
0
1
0
1
1
0
2
0
1
1
0
1
0
3
2
1
2
1
2
1
1
1
0
2
1
1
1
1
1
1
2
0
1
1
2
1
2
1
0
1
1
2
1
1
1
1
2
1
0
2
0
1
2
1
0
1
0
1
1
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
0
1
1
1
1
2
0
2
1
1
2
1
1
0
1
0
1
1
2
1
1
1
2
0
2
1
1
2
0
1
1
1
0
1
0
1
2
1
2
1
0
1
0
2
1
1
2
2
1
0
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
2
1
0
0
1
1
0
1
2
2
2
2
1
1
1
1
1
0
2
2
1
1
1
1
0
1
1
1
2
1
0
1
4
0
1
3
1
2
1
2
2
2
1
1
1
0
1
2
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
1
2
1
2
1
1
1
2
1
2
2
1
1
1
1
1
1
0
1
1
1
2
1
1
1
2
1
1
1
1
1
2
1
2
0
1
1
1
2
1
1
2
2
0
2
0
2
1
1
2
2
2
2
2
0
1
1
2
1
1
1
2
1
1
2
1
1
1
0
2
1
1
1
2
1
2
1
2
1
2
0
1
1
1
1
1
0
1
2
1
1
2
2
2
0
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
3
1
1
1
1
2
2
2
1
0
0
2
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
0
2
0
1
2
1
1
1
1
1
2
0
1
1
0
2
2
0
0
2
0
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
0
1
5
1
2
2
0
1
1
2
1
2
1
1
0
0
1
1
2
1
1
0
1
2
2
1
1
1
1
1
0
1
1
1
2
1
1
0
2
4
1
1
0
3
1
1
1
1
1
0
1
1
1
1
5
2
2
1
1
2
1
1
2
1
1
2
2
2
0
1
1
2
1
2
0
0
1
1
2
0
1
2
0
3
1
1
1
1
2
1
1
1
1
1
1
0
0
1
1
2
0
1
0
0
1
2
2
1
1
2
1
1
2
2
1
2
2
1
3
1
0
1
0
1
1
1
2
2
1
1
2
0
2
1
0
1
2
2
0
2
1
0
0
3
2
2
2
2
1
1
1
0
1
2
0
0
1
0
1
2
1
2
2
1
2
1
1
1
2
0
1
1
1
1
1
1
1
1
1
2
1
0
1
1
1
1
1
2
2
2
2
1
1
1
1
2
2
1
0
1
0
1
1
1
1
1
1
2
2
2
1
0
1
1
1
1
1
1
2
0
2
1
1
2
0
1
2
1
1
1
1
0
2
1
1
1
1
2
1
2
0
1
2
2
2
2
0
2
2
1
0
2
1
1
1
1
2
1
1
1
1
2
2
2
1
0
0
1
2
1
0
1
1
1
1
1
1
0
1
1
1
0
0
1
1
1
2
1
1
1
1
0
1
1
2
0
2
3
1
1
1
1
1
1
1
2
0
1
1
2
2
1
1
0
2
2
0
2
2
0
1
2
1
2
1
1
2
0
1
2
2
1
1
2
1
2
1
1
1
1
1
0
1
2
0
1
1
1
2
0
1
1
1
1
2
0
1
1
0
2
2
1
0
2
2
2
1
1
0
1
1
2
1
0
2
0
1
1
0
0
1
1
1
2
1
2
1
1
1
2
1
0
1
2
1
1
2
2
0
1
1
1
1
1
1
1
1
1
2
1
0
1
0
1
1
2
1
2
1
2
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
0
1
2
2
1
1
1
1
2
3
1
2
1
0
2
2
1
1
1
2
2
0
2
1
2
1
2
1
0
0
1
0
2
3
1
1
1
0
2
2
1
1
1
1
2
1
1
0
2
2
1
1
1
1
0
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
0
1
1
1
1
1
0
1
1
1
1
1
2
1
1
0
0
1
2
1
2
1
1
1
2
1
1
1
1
1
1
0
2
2
1
0
1
1
1
1
2
2
1
1
1
1
0
2
2
1
1
1
1
0
0
1
1
2
1
1
0
1
1
1
2
1
2
1
0
0
0
1
2
1
1
0
1
2
1
1
2
2
0
1
2
1
2
1
1
1
2
0
0
2
0
2
1
1
2
1
0
1
1
1
1
2
1
1
1
1
0
2
2
1
2
1
1
2
1
2
2
2
1
2
2
1
1
2
1
1
0
2
0
1
2
1
2
1
2
1
1
0
1
1
1
2
1
2
1
1
1
2
1
1
1
2
2
2
0
1
2
1
1
1
1
1
1
1
1
1
2
1
2
0
1
0
1
1
1
4
1
1
1
1
0
2
1
1
2
1
1
2
2
1
2
1
1
0
1
0
2
1
1
1
1
1
0
2
1
1
0
1
1
2
1
1
1
1
1
1
1
0
2
2
1
1
1
3
2
1
1
2
1
1
1
1
1
0
0
2
1
1
1
1
1
2
0
1
0
1
1
2
0
1
2
2
1
1
1
1
2
0
1
1
0
1
1
0
1
1
1
1
2
0
1
1
1
1
1
1
2
0
1
1
2
1
0
1
1
2
1
1
2
3
1
2
1
1
3
1
0
2
3
1
1
2
2
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
0
2
1
0
1
2
1
0
1
1
2
2
0
1
1
2
1
1
2
2
1
2
1
1
1
0
2
1
0
1
2
1
1
1
0
1
2
2
1
1
2
3
0
0
0
1
0
1
1
2
0
2
1
1
2
1
1
2
1
2
2
1
1
1
1
2
1
1
2
1
1
1
1
0
2
1
0
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
0
1
0
1
1
1
2
1
1
2
1
1
1
0
1
1
2
0
1
1
2
1
2
0
1
1
1
1
2
1
1
2
1
1
1
0
2
1
2
1
0
2
1
1
1
0
1
1
2
1
1
0
1
3
2
1
1
1
1
1
2
0
1
1
1
2
1
1
2
1
1
1
0
1
1
1
2
2
1
2
1
1
1
0
1
2
1
1
0
0
2
2
1
1
1
0
1
2
1
1
1
2
1
1
0
2
1
1
0
1
2
2
0
1
0
0
1
0
1
1
2
2
2
1
1
1
0
1
1
0
2
0
1
1
2
1
1
2
1
1
1
2
1
1
1
2
0
2
1
1
1
1
2
2
2
1
2
1
0
0
1
1
0
2
1
1
2
1
0
1
0
0
1
1
1
1
1
0
1
1
1
2
0
0
1
1
2
1
1
1
1
2
1
0
1
2
2
2
0
0
0
1
2
1
2
2
1
1
1
1
2
1
0
2
1
2
1
0
1
1
1
1
1
1
2
1
0
1
0
2
0
1
2
1
2
1
1
1
1
2
1
1
1
2
1
0
2
0
1
0
1
1
2
2
1
1
1
1
2
1
2
0
2
1
1
0
2
0
1
1
1
1
0
0
1
2
1
1
0
2
1
0
2
1
1
1
0
1
1
1
1
1
1
0
1
0
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
0
1
0
2
0
2
1
1
0
2
1
4
0
0
1
1
1
1
1
1
1
0
1
0
1
0
0
1
1
1
1
0
0
1
1
0
1
1
2
1
1
1
2
2
0
0
1
1
0
1
2
1
1
2
2
2
1
2
2
2
2
1
1
1
2
1
0
1
2
1
1
1
1
0
2
1
1
2
2
1
0
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
0
0
1
0
2
2
1
1
1
1
2
0
1
2
1
0
0
1
1
1
1
1
1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
0
1
2
2
0
1
1
1
1
0
0
2
1
2
1
0
1
2
1
2
2
1
1
1
1
1
1
2
3
2
1
1
1
1
1
1
1
2
1
1
1
1
2
1
0
1
1
2
0
2
2
2
2
1
1
1
1
2
1
2
0
1
1
1
1
1
0
1
0
1
2
1
0
2
1
1
2
0
1
1
1
0
1
2
2
0
1
2
2
1
0
1
1
0
1
1
1
2
0
0
1
1
1
2
1
2
2
1
1
1
1
0
0
1
2
2
2
1
1
2
2
1
1
1
1
1
0
1
1
1
0
1
1
1
0
2
2
1
2
2
1
1
1
1
1
2
2
0
1
1
0
1
1
0
1
1
2
0
1
0
2
1
1
1
1
0
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
2
1
1
2
2
1
1
1
1
0
1
1
0
1
1
0
0
0
0
1
1
1
0
2
2
0
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
0
1
1
0
1
1
2
1
1
0
1
1
1
0
0
0
1
1
0
1
1
0
1
1
1
1
1
1
2
1
0
1
1
1
1
1
1
1
0
1
1
0
1
2
0
1
1
0
1
1
1
2
1
2
1
1
0
1
1
1
0
1
1
0
0
2
1
1
2
1
1
1
0
1
2
1
2
1
2
2
1
2
1
2
1
2
1
2
0
1
2
1
2
0
1
0
1
0
0
2
2
1
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
2
1
2
1
2
0
2
2
1
1
1
0
0
0
1
2
2
2
1
2
0
0
1
1
0
2
1
1
1
2
0
0
1
0
1
2
1
1
2
2
0
1
2
1
1
1
1
1
0
1
2
2
0
1
1
1
1
1
2
1
1
0
1
0
1
0
2
1
1
0
1
1
1
2
0
0
1
1
1
1
1
2
0
1
1
1
1
1
1
2
0
2
0
1
1
1
1
1
1
2
0
2
2
2
1
1
1
1
1
1
1
1
1
1
2
1
0
2
1
2
1
1
1
0
2
0
1
0
2
2
0
1
2
2
1
1
2
1
0
1
1
1
2
2
1
1
0
1
1
1
0
1
0
2
0
0
1
1
2
0
1
0
1
0
1
0
1
1
1
0
2
2
1
1
2
1
2
0
0
1
1
0
1
1
0
1
1
1
1
1
1
2
1
1
0
0
2
1
1
1
0
1
1
0
0
1
2
1
1
1
2
2
1
1
1
1
0
1
1
1
2
2
2
1
1
2
1
0
1
1
1
1
1
0
1
2
1
2
1
1
0
1
0
1
0
3
1
1
2
1
1
1
1
1
2
2
1
2
1
1
1
1
2
1
0
2
2
1
1
1
0
0
1
0
1
2
2
0
1
1
2
1
1
2
1
2
1
0
1
1
1
2
1
1
1
1
1
1
0
1
1
1
1
0
1
1
1
1
2
1
1
1
1
1
0
2
0
1
1
2
1
3
1
0
1
1
1
2
1
1
1
1
0
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
2
1
2
1
1
1
0
2
1
1
1
1
1
1
0
2
2
2
2
1
1
1
2
2
2
1
2
1
1
2
1
2
0
0
1
1
0
1
1
1
0
1
2
1
1
1
0
1
1
1
0
1
2
0
1
2
0
1
1
0
1
1
1
1
1
1
1
1
2
1
2
2
1
3
1
0
2
0
1
2
2
1
2
2
3
1
1
2
0
1
1
2
2
0
2
0
1
1
1
1
0
1
1
2
1
1
1
1
2
1
1
1
1
0
0
0
1
2
2
1
0
1
1
1
1
1
1
2
2
1
1
1
3
1
2
1
1
1
1
1
1
1
1
1
1
2
1
0
1
1
0
0
1
1
0
0
0
0
2
1
0
1
1
1
0
1
3
1
0
2
2
1
1
0
1
0
1
1
0
2
1
2
1
1
1
1
0
2
2
0
1
1
1
2
1
2
1
0
2
2
1
0
1
1
1
4
1
1
1
0
1
0
1
1
1
1
1
1
1
1
1
2
1
2
1
1
0
1
2
1
2
1
1
2
0
1
1
2
2
1
2
2
1
2
1
1
1
1
1
0
1
1
2
1
1
1
0
1
2
1
1
2
2
1
2
1
0
2
1
1
1
1
1
0
2
2
1
1
2
1
1
1
0
1
1
0
0
2
1
2
0
1
1
1
1
1
2
1
1
2
1
1
2
1
1
2
1
1
0
1
1
1
2
1
2
2
1
1
0
1
0
1
1
0
0
1
2
1
2
1
1
1
1
1
1
2
2
1
0
1
1
0
1
1
1
0
1
0
2
1
1
2
0
1
2
2
1
1
0
0
0
1
0
1
1
1
0
2
1
1
2
1
2
0
0
2
2
1
0
1
1
1
0
2
1
1
1
0
1
2
1
1
2
1
1
1
1
2
1
0
1
1
1
1
1
2
1
2
1
2
1
2
1
0
1
0
2
2
1
1
1
1
0
2
2
1
3
0
1
2
1
0
1
2
1
1
1
1
0
1
1
2
1
3
1
1
2
2
1
0
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
2
1
1
1
0
1
1
1
1
1
0
1
1
1
2
2
1
1
1
0
1
1
2
2
1
0
1
2
2
1
1
2
0
1
4
0
0
1
1
0
1
1
1
2
1
1
1
2
1
1
0
1
2
2
2
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
0
2
2
2
1
1
2
1
0
1
2
1
1
1
1
1
2
1
1
1
0
1
1
1
1
1
0
2
1
0
0
1
1
1
1
2
1
1
1
1
2
2
1
1
1
1
1
2
1
1
0
2
0
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
0
0
1
0
1
1
1
1
0
1
2
1
1
2
1
1
1
1
1
1
2
1
2
1
2
1
0
1
1
2
2
2
1
2
0
1
0
2
2
1
1
2
1
2
1
1
2
1
1
2
1
1
1
1
1
2
1
1
1
2
1
2
2
2
0
1
1
1
2
1
0
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
0
1
1
1
1
0
1
1
2
0
1
0
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
4
2
1
2
2
1
1
1
2
2
1
1
1
2
1
1
2
0
2
1
0
0
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
2
3
1
1
1
1
1
1
2
1
0
2
1
1
2
1
2
0
1
1
1
1
2
1
2
0
2
1
2
1
1
0
1
0
1
2
1
2
2
1
2
1
1
1
1
1
1
1
1
1
0
1
1
1
0
1
1
1
1
1
1
1
1
1
0
0
1
0
1
1
1
1
2
1
0
2
2
2
2
1
0
2
0
2
1
0
3
0
1
2
1
1
1
1
0
1
2
1
3
3
2
1
1
0
1
0
2
1
1
1
1
2
1
1
1
1
1
2
0
0
1
0
1
1
1
0
0
1
0
1
2
2
1
1
2
1
1
2
1
1
1
1
1
1
1
2
2
1
1
1
2
2
1
1
1
0
2
2
1
2
2
1
2
2
0
0
1
1
1
1
2
1
1
1
0
1
1
1
0
1
2
1
1
1
0
2
1
1
0
1
1
1
2
2
1
1
1
1
0
1
2
2
0
0
2
1
1
1
0
1
0
1
2
2
1
2
4
1
0
1
1
1
1
1
1
1
1
1
2
0
1
1
1
1
1
2
2
1
1
1
1
1
1
1
0
1
2
1
1
1
2
1
1
1
1
1
1
1
2
0
1
0
2
0
1
0
1
2
0
1
2
12
2
2
2
1
1
1
2
2
0
2
2
1
1
0
1
1
3
1
1
2
1
1
0
1
1
2
1
1
1
2
1
0
1
2
1
0
0
1
0
1
1
2
0
1
1
1
1
1
1
2
0
1
2
1
3
1
1
2
1
1
1
1
0
1
0
1
0
1
1
0
1
1
2
2
0
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
4
4
2
1
0
1
1
0
2
1
1
2
1
1
1
2
1
2
0
1
1
1
1
1
2
1
1
2
1
2
1
1
1
2
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
1
0
1
0
1
1
1
1
1
2
0
2
2
1
1
1
0
1
0
1
1
1
0
0
0
1
1
0
1
0
1
1
2
1
1
1
1
1
2
1
0
1
1
2
1
0
1
1
2
1
0
1
1
1
1
1
1
1
1
2
0
1
2
1
1
1
2
0
3
1
0
1
1
1
1
2
2
0
2
1
1
2
2
1
1
2
1
1
0
2
2
2
1
2
1
1
2
1
2
0
2
0
2
1
1
1
0
0
0
1
1
1
1
0
1
1
0
0
1
0
0
0
0
1
1
1
1
1
1
1
2
1
0
1
1
1
1
2
3
1
0
2
1
1
1
2
1
1
2
2
2
2
1
2
1
1
1
1
1
1
1
1
2
2
1
2
1
1
1
2
2
2
1
1
0
1
2
2
2
1
0
0
2
1
0
1
0
2
2
1
1
0
1
2
2
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
0
0
1
2
1
1
2
1
1
1
1
1
0
1
1
0
2
2
1
0
1
1
0
1
1
1
2
1
2
1
1
2
1
1
2
1
1
0
1
1
2
1
1
1
1
1
2
2
1
1
0
0
2
1
1
1
2
2
2
1
1
2
1
1
1
2
1
1
1
1
1
0
2
1
2
0
1
1
2
1
1
1
2
2
2
1
1
1
1
1
2
2
0
2
0
1
1
1
2
0
2
2
1
1
1
2
1
0
1
1
1
2
0
1
1
1
0
0
2
2
1
1
3
1
0
2
2
1
1
1
1
1
0
0
1
1
1
0
1
2
0
1
1
1
0
1
1
2
1
0
1
2
2
2
1
1
1
2
1
2
2
1
2
1
4
1
1
2
0
1
2
2
0
1
1
1
0
2
0
1
0
1
2
2
2
1
1
1
1
1
1
1
1
1
2
1
1
0
1
1
1
2
1
0
0
1
1
1
2
2
1
1
1
2
1
1
1
1
2
1
1
2
2
1
2
2
1
3
1
2
0
1
1
2
0
1
0
2
0
2
2
2
1
1
1
1
1
2
2
2
1
1
1
2
1
2
2
2
2
2
1
1
1
1
1
2
1
1
1
2
0
1
1
1
0
2
1
1
1
2
0
2
1
0
1
2
1
1
2
2
0
0
1
1
1
1
2
0
1
0
2
1
1
1
0
2
2
1
1
0
1
2
2
1
1
1
2
1
0
1
1
1
1
1
0
1
1
2
1
1
0
1
1
2
2
1
1
2
1
1
2
1
1
1
1
2
0
1
1
1
0
1
1
1
1
1
0
1
1
2
1
1
0
1
2
1
1
1
1
2
2
1
1
1
2
1
2
8
2
1
1
1
1
1
2
2
0
1
0
1
1
1
1
1
2
1
2
0
1
0
0
1
1
2
2
0
1
0
1
1
1
2
1
2
1
1
0
1
1
1
1
1
1
1
1
0
2
1
2
1
1
2
1
1
1
2
1
1
0
0
1
2
0
2
1
0
1
1
1
1
1
1
2
1
0
2
1
1
0
1
1
0
1
2
1
1
1
1
2
1
2
0
0
1
1
1
1
1
1
1
1
1
2
0
1
0
0
2
0
1
1
0
1
1
1
1
2
2
1
0
1
0
1
2
2
1
1
2
0
1
2
2
0
0
2
1
1
1
1
1
1
0
2
1
1
2
2
1
2
1
1
1
1
2
1
0
1
0
1
1
1
1
1
0
1
1
1
1
0
2
1
0
1
1
2
0
1
1
1
0
1
1
2
1
1
0
1
1
1
0
1
2
1
2
2
1
1
1
2
0
0
1
1
1
1
1
1
2
1
0
1
1
0
1
1
1
1
1
1
0
2
0
1
1
0
1
1
1
1
0
2
1
1
2
2
1
2
1
1
1
0
1
2
1
1
1
2
1
1
1
2
1
0
0
1
0
1
1
1
1
1
2
1
0
0
1
1
1
2
1
1
1
1
1
2
0
1
1
1
1
2
0
2
2
0
0
1
2
1
1
1
1
2
1
2
2
1
1
2
1
1
1
2
1
2
0
2
2
0
1
1
1
1
1
1
2
1
1
0
1
1
2
0
1
1
1
2
2
1
1
1
0
2
0
0
2
0
2
1
1
0
1
2
1
2
1
1
0
1
1
1
2
1
1
0
1
1
0
2
1
1
1
0
1
1
0
0
2
2
2
1
2
0
1
1
1
2
2
2
1
1
1
0
2
1
1
1
1
1
1
2
0
0
1
1
2
0
1
1
2
1
2
1
1
0
2
2
1
1
1
2
1
1
2
0
1
1
2
0
0
1
1
1
1
1
1
1
1
2
1
1
2
2
2
0
0
0
1
2
1
1
0
1
2
1
2
1
0
1
1
1
0
1
1
2
1
2
1
1
0
1
1
1
1
1
1
2
1
1
1
1
0
1
2
1
0
1
1
2
1
1
2
1
1
0
1
0
1
1
0
1
1
2
1
1
1
1
1
1
1
1
0
2
1
1
1
1
2
1
1
1
0
1
1
0
2
0
0
1
1
1
1
1
1
0
0
1
1
2
1
2
1
0
0
1
0
1
0
1
1
1
1
0
2
2
2
1
1
1
1
0
1
2
1
0
1
1
1
1
0
2
1
1
1
1
1
1
1
2
1
1
2
2
0
0
1
1
1
1
1
2
1
2
1
0
2
1
2
1
1
1
1
1
1
0
1
2
0
2
2
2
1
13
0
1
2
2
1
1
2
1
1
1
1
2
1
2
0
1
1
2
0
2
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
2
1
1
2
1
1
2
1
3
1
1
2
1
1
1
1
2
1
2
1
1
1
1
2
1
2
0
2
1
1
1
1
1
0
2
1
1
1
1
1
1
1
1
0
2
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
2
0
1
1
0
1
0
2
1
2
2
1
0
1
2
2
0
2
0
0
1
1
0
2
1
2
2
0
1
0
1
1
1
0
2
1
2
2
2
0
1
1
1
1
0
1
1
1
0
1
2
1
2
0
1
1
1
0
0
1
2
2
0
2
2
1
1
1
0
0
0
0
2
2
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
0
1
1
0
1
1
1
1
2
0
1
1
1
0
0
0
1
1
1
1
3
1
1
1
2
1
1
1
1
2
1
1
2
2
1
1
1
2
1
3
1
0
2
1
1
2
1
1
0
1
1
1
2
2
1
0
0
1
1
1
0
0
1
1
2
1
1
0
2
1
1
2
1
2
1
1
0
1
1
1
0
1
3
2
1
2
0
2
0
2
1
1
0
2
1
1
2
1
2
1
1
1
1
0
1
0
2
0
1
2
0
1
1
2
0
1
1
2
2
1
0
0
0
1
1
1
1
1
0
2
2
1
1
0
2
1
0
1
1
1
1
1
1
1
1
2
1
0
2
2
1
1
1
0
1
1
1
1
1
2
0
1
1
0
0
1
3
2
1
0
0
1
2
1
2
1
1
1
2
1
2
1
1
1
1
0
2
1
1
1
0
1
2
1
1
1
0
1
2
1
1
1
2
1
2
2
0
1
2
0
2
1
2
2
2
1
1
1
2
1
0
1
1
1
2
0
1
1
2
1
0
0
1
1
0
1
2
1
2
2
2
1
1
2
2
0
1
2
2
1
2
0
0
0
1
1
0
1
1
0
2
1
1
1
1
2
0
1
1
1
1
1
0
1
2
2
1
1
0
2
1
0
2
1
1
2
1
1
3
1
0
1
2
1
2
1
0
2
2
1
1
1
0
1
2
1
2
1
1
1
1
1
2
1
2
0
1
1
2
2
1
0
1
0
0
0
0
1
1
1
1
1
1
1
0
1
1
1
1
1
2
1
2
1
2
0
0
1
2
0
1
1
1
1
0
1
1
1
1
1
0
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
0
2
1
1
2
1
1
1
1
2
2
5
0
2
1
1
2
1
0
0
2
1
0
0
1
1
2
1
2
1
1
1
1
1
1
2
0
1
1
1
1
0
1
1
1
0
1
1
1
0
2
0
1
1
1
1
1
1
2
1
1
0
6
1
2
1
1
2
3
2
1
1
1
1
1
1
4
1
1
0
1
1
2
1
1
1
1
1
1
1
0
1
2
1
0
1
0
2
1
1
1
1
1
1
1
2
2
1
1
1
1
0
2
0
2
1
1
0
0
1
1
1
1
1
2
1
1
2
2
1
0
1
2
2
2
1
1
0
0
2
2
0
1
0
0
2
2
1
0
2
1
2
2
1
1
1
2
1
1
0
1
1
1
2
1
2
2
1
2
1
2
2
1
1
1
0
1
1
1
2
0
2
2
1
0
1
2
2
2
0
1
1
1
0
1
1
0
1
2
1
1
1
0
1
2
2
0
1
2
2
1
2
0
0
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
0
2
0
0
2
2
2
2
1
2
1
2
1
0
2
1
1
1
1
0
1
1
0
1
2
1
1
0
2
1
1
0
2
0
1
1
1
2
1
1
1
2
2
1
1
0
0
1
0
1
0
1
1
0
0
1
1
2
0
1
1
1
1
1
1
1
2
1
1
2
1
1
1
2
1
1
1
1
2
1
2
1
2
1
1
2
1
1
1
1
0
1
1
1
1
1
1
1
2
1
1
1
0
1
1
1
2
3
1
0
1
1
2
1
1
1
1
1
0
1
1
0
1
0
1
1
3
1
2
1
1
2
2
2
1
0
1
1
1
1
1
1
0
1
0
2
0
3
1
1
0
0
3
1
1
1
1
0
2
1
1
0
1
1
1
1
1
1
1
1
1
1
0
1
2
1
1
1
2
2
1
1
2
0
1
0
1
2
1
2
1
1
0
1
3
1
1
1
0
1
1
0
2
1
0
0
1
1
1
2
0
1
2
2
1
1
1
1
1
2
1
1
0
1
1
2
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
0
1
2
1
1
2
1
0
2
1
1
1
1
1
1
1
1
1
0
0
1
1
1
0
0
1
2
1
2
1
1
2
1
2
2
2
2
2
1
0
0
1
1
1
1
2
2
1
1
1
1
2
0
2
0
1
2
1
0
0
1
1
1
1
2
1
1
1
0
2
1
0
1
2
1
2
1
0
2
2
2
1
1
1
0
2
1
2
1
2
3
1
0
1
1
0
1
1
1
0
0
1
1
1
1
2
1
2
1
1
0
2
2
1
1
1
1
2
1
1
1
1
2
2
1
1
1
0
1
1
0
1
0
1
1
1
1
1
1
1
1
1
0
1
0
1
1
1
2
1
1
2
1
1
0
1
1
2
1
1
0
1
0
2
2
1
0
0
1
1
1
0
1
0
1
0
2
1
1
0
1
1
0
0
1
1
1
0
0
1
2
1
1
1
1
1
0
1
1
3
1
0
1
1
1
0
0
0
1
1
2
0
1
1
1
0
0
0
1
0
1
1
2
1
1
2
1
3
1
1
1
1
2
2
1
2
1
0
1
2
0
1
2
0
0
1
0
0
1
2
1
1
0
1
1
2
1
1
1
0
2
0
2
1
1
2
0
0
1
1
1
1
2
2
1
1
2
1
0
1
1
2
1
1
2
1
1
2
1
1
1
2
1
2
2
1
0
1
1
1
1
1
1
1
2
1
2
1
1
0
1
1
1
1
0
1
1
2
2
1
1
1
2
1
2
1
1
1
1
0
2
1
1
1
1
1
2
1
0
2
1
2
1
1
0
1
2
2
1
1
0
1
1
1
2
2
1
1
1
1
1
1
2
1
0
1
2
1
1
0
2
1
1
0
2
2
2
1
1
2
1
2
1
1
2
1
2
0
1
1
1
1
1
0
0
2
1
1
2
1
1
1
1
1
0
1
0
1
2
1
2
0
1
1
1
2
2
1
1
2
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
0
1
0
1
2
1
2
1
1
1
1
2
2
2
2
2
1
1
1
2
2
1
1
1
1
0
1
1
2
2
1
1
1
1
1
1
1
2
1
0
1
1
2
1
1
2
1
1
1
1
1
2
1
0
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
0
0
2
1
1
1
1
1
0
2
1
0
1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
1
1
1
1
0
1
1
0
0
1
0
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
0
0
1
2
1
2
2
0
1
1
2
1
1
1
2
1
1
1
0
1
1
0
1
1
1
1
0
1
0
1
1
2
1
1
1
1
1
1
1
0
1
1
0
2
1
1
1
0
1
1
1
0
1
0
1
1
1
1
2
0
1
1
2
0
1
1
1
1
1
1
1
2
1
2
1
1
1
0
3
0
0
2
8
0
2
0
2
1
1
1
1
1
1
1
1
2
0
2
2
0
2
1
1
0
0
1
1
1
2
0
1
0
1
1
1
1
0
1
1
1
1
2
1
1
1
1
0
2
1
1
1
1
1
1
2
0
0
0
1
0
2
1
1
2
1
1
0
1
1
2
1
1
1
2
1
1
1
1
2
1
1
2
1
2
1
1
1
2
2
1
1
0
1
2
1
1
0
2
1
2
1
1
1
1
0
2
2
2
1
1
2
1
1
1
1
3
2
0
1
0
1
1
1
1
0
1
1
1
2
1
1
2
1
0
1
2
2
1
1
0
1
1
1
1
1
1
1
2
2
1
1
1
0
1
1
1
1
2
1
1
1
1
0
1
1
1
2
1
2
1
1
1
1
2
2
0
1
1
2
1
0
2
1
2
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
2
0
2
1
1
1
1
1
1
1
2
1
1
2
1
1
2
1
0
1
1
1
0
1
1
1
0
2
1
1
0
1
1
0
0
1
1
1
1
2
0
1
2
1
0
1
0
1
1
1
1
1
1
1
0
0
1
0
2
1
1
1
2
2
2
2
0
1
1
2
2
2
1
1
1
1
1
1
1
2
1
2
1
0
1
2
1
2
1
1
1
1
1
1
2
2
1
1
2
2
1
1
1
1
2
1
0
1
1
2
1
1
2
0
1
1
1
1
2
0
1
1
2
1
2
1
1
2
2
1
2
1
0
0
1
1
1
2
1
1
1
0
0
1
1
1
1
1
0
1
1
1
2
1
1
2
2
2
1
1
1
0
2
1
2
0
2
2
1
1
1
2
1
1
1
1
0
1
2
2
1
1
1
2
1
1
2
2
1
1
1
1
1
2
2
0
1
1
2
1
1
0
1
1
1
2
2
2
1
1
1
1
1
1
1
2
0
2
2
1
2
1
1
1
0
1
1
2
1
2
1
2
2
1
0
1
1
1
1
1
1
1
1
2
0
1
0
0
2
2
1
1
1
2
1
2
1
2
1
2
1
0
0
2
2
0
1
1
2
1
1
2
1
0
1
1
2
1
2
1
1
1
2
2
1
1
1
1
1
2
2
1
1
1
1
2
2
2
1
2
1
1
2
1
1
1
0
2
2
1
1
2
1
0
1
1
1
1
1
1
2
0
2
0
0
1
2
1
1
1
1
2
1
1
1
0
1
1
1
1
1
2
3
1
1
2
1
1
1
0
1
0
1
1
0
1
2
1
2
1
2
1
0
2
1
1
2
1
3
0
1
1
2
1
2
1
1
1
0
2
2
2
1
2
2
0
2
2
1
1
0
1
1
2
0
1
0
1
1
2
1
0
2
1
0
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
3
1
1
2
2
1
1
0
1
2
1
1
1
1
3
2
2
1
0
0
1
1
2
0
1
1
1
2
1
0
0
1
2
2
1
0
1
1
0
1
1
2
1
1
1
1
0
1
0
2
0
2
2
0
1
1
0
1
3
2
1
2
1
1
2
1
1
0
2
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
1
2
2
2
1
1
2
1
0
1
1
2
1
2
2
2
1
0
1
2
1
2
1
2
1
1
1
1
1
0
1
1
1
2
2
1
1
0
2
2
1
0
0
2
1
1
1
1
1
1
0
1
2
1
2
1
2
1
1
1
2
1
1
1
1
1
1
1
0
0
0
1
1
2
1
2
2
1
1
1
1
1
1
1
1
2
1
2
1
0
2
1
2
2
2
1
2
1
0
2
0
2
0
1
1
1
1
1
0
4
1
1
1
0
1
1
1
0
1
2
0
0
0
3
0
2
2
1
1
1
1
2
1
0
2
0
1
2
1
1
2
2
2
1
1
1
1
2
1
1
2
2
1
1
1
2
0
1
1
1
2
1
0
1
1
1
2
1
1
2
1
1
1
2
1
1
1
0
1
1
1
2
2
2
1
1
1
1
1
1
2
1
2
2
0
1
0
0
2
1
1
0
1
1
2
1
2
1
1
0
1
2
2
1
1
1
1
1
1
0
1
1
2
2
1
2
2
3
1
2
1
1
1
1
2
0
1
1
0
1
1
1
2
1
1
2
1
2
2
0
2
1
2
1
2
2
1
1
0
1
1
1
1
1
1
2
1
1
0
2
0
1
2
1
1
2
1
1
1
1
1
2
1
2
0
2
1
1
1
0
1
1
2
0
2
1
2
2
1
1
3
1
1
2
2
1
2
0
0
1
1
1
2
2
1
1
0
1
0
0
1
2
1
1
1
2
1
1
1
1
2
2
1
1
2
2
1
1
0
1
0
1
1
1
0
1
1
0
2
1
1
1
0
0
1
2
2
1
0
0
1
1
1
2
1
0
2
2
1
2
1
1
1
2
0
2
0
1
1
1
1
0
2
1
0
2
1
1
1
1
1
0
1
1
1
2
2
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
0
1
1
1
1
0
1
1
1
1
1
0
2
1
2
1
1
1
2
1
2
1
2
1
1
1
1
2
2
1
1
1
1
0
1
1
2
0
1
1
1
0
1
1
1
1
1
2
2
1
0
1
1
0
0
2
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
0
1
2
1
1
1
2
1
1
1
1
1
2
2
3
0
1
1
1
1
1
1
1
1
1
1
0
1
1
2
1
1
1
1
1
1
1
2
1
1
0
1
1
2
1
1
2
2
1
2
2
0
1
1
1
1
1
1
2
0
1
1
1
0
0
1
3
2
1
1
1
1
1
1
2
2
1
1
2
1
2
1
0
1
1
1
2
2
1
2
1
1
2
2
1
1
2
2
1
5
1
1
0
1
1
1
0
1
1
1
2
2
0
1
1
1
2
1
1
0
1
1
1
1
2
2
2
2
1
1
1
2
1
1
0
1
2
2
0
2
0
1
0
1
2
1
1
1
1
2
1
1
1
1
2
0
1
2
2
1
1
1
0
0
2
1
1
2
1
1
2
1
0
1
1
1
1
1
1
1
2
1
1
0
1
1
1
1
1
1
1
1
0
0
1
2
1
1
1
2
1
0
0
1
1
1
1
1
2
2
1
1
0
1
1
1
1
0
2
0
2
1
1
1
1
2
0
1
0
0
2
1
2
2
1
2
2
2
2
1
1
1
2
1
2
0
0
1
0
0
0
1
2
2
2
1
2
1
1
1
1
1
0
1
0
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
2
2
2
1
0
1
2
2
1
1
1
0
1
0
1
1
0
1
2
1
1
1
1
2
0
0
1
1
2
0
1
0
2
0
2
1
1
0
1
0
2
1
1
1
1
1
1
0
0
2
2
3
0
1
1
1
1
1
1
2
1
2
2
2
1
2
0
1
0
1
1
0
1
2
1
1
1
1
0
1
2
1
1
1
1
0
1
1
1
1
1
2
1
1
1
0
1
0
1
1
2
1
1
1
1
2
1
1
2
2
1
2
3
1
3
2
1
0
1
1
2
1
2
0
2
1
1
2
3
2
1
0
0
1
1
0
1
2
1
1
2
1
0
0
0
2
1
1
2
1
1
1
1
1
1
2
1
1
1
0
1
1
1
1
1
1
2
1
1
1
0
1
1
1
1
1
0
1
2
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
0
2
1
0
1
2
1
1
1
0
2
2
1
1
2
1
2
0
1
3
2
2
1
1
2
1
1
1
1
0
1
1
1
2
2
2
1
0
1
1
1
1
0
2
1
1
1
1
1
2
1
1
2
0
1
0
0
1
1
1
1
2
0
1
0
2
1
1
2
2
1
1
3
2
3
1
1
3
0
2
1
1
1
1
1
1
1
1
1
0
1
0
0
0
1
1
0
1
0
2
1
1
2
2
1
1
2
1
0
2
1
2
0
0
1
0
1
0
2
1
2
1
1
1
2
1
2
1
1
1
3
1
1
2
1
2
2
1
1
0
1
2
0
1
2
1
0
2
0
0
1
1
1
0
0
1
2
2
1
1
2
1
1
1
0
1
1
2
1
2
1
1
2
2
0
1
2
1
2
2
1
2
1
1
0
2
1
0
2
1
0
1
1
0
2
1
1
1
1
1
1
2
2
2
1
2
2
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
2
2
1
1
1
1
0
1
2
2
1
1
3
0
1
0
1
1
2
2
1
1
2
1
1
1
0
2
2
4
1
1
1
1
2
2
1
1
2
1
1
1
1
1
1
2
1
0
1
2
0
2
1
1
0
2
0
1
1
1
2
0
1
1
1
0
2
2
1
0
1
1
1
2
1
2
1
1
1
1
0
0
1
0
1
2
1
0
0
1
1
1
2
1
2
1
2
1
1
1
1
1
0
1
1
1
1
1
2
1
1
1
0
2
1
1
1
1
1
2
1
1
0
1
2
1
1
1
0
2
1
2
2
1
2
1
0
2
1
2
1
2
1
2
1
1
1
2
1
1
2
1
1
3
0
1
1
1
2
1
2
2
1
1
1
1
0
1
2
1
0
1
2
1
1
1
0
1
1
2
1
1
0
0
1
2
0
1
0
0
1
1
1
1
1
1
2
2
1
2
1
1
1
0
2
1
0
1
1
1
0
1
1
1
1
1
0
1
0
1
1
1
1
1
1
2
1
1
2
2
1
1
1
1
1
0
2
2
1
2
1
2
2
0
0
1
1
2
2
2
1
1
2
1
0
1
2
1
1
2
0
0
0
1
1
2
2
0
1
0
2
1
1
1
1
1
0
0
1
2
1
1
1
0
2
0
1
0
1
1
2
0
1
1
2
1
1
2
1
1
1
1
1
1
0
1
0
1
1
1
0
0
2
1
2
0
1
1
2
1
2
1
1
0
1
1
0
1
1
2
2
1
1
0
1
1
1
1
1
1
0
1
2
1
1
0
2
1
0
1
0
1
1
2
1
1
1
1
1
0
2
2
1
1
2
1
1
1
1
3
1
0
1
1
1
1
0
0
1
1
2
2
1
1
0
0
2
1
1
0
2
1
2
1
1
1
1
1
1
0
0
6
1
1
1
1
1
1
1
2
2
1
0
1
1
2
2
0
1
2
1
1
1
0
2
1
2
1
1
2
1
3
2
2
1
1
1
1
1
2
2
2
1
1
1
2
2
0
1
1
0
1
2
1
2
2
0
1
2
1
2
1
1
1
1
0
1
1
0
1
1
1
2
2
1
1
2
2
1
1
1
1
1
1
2
2
1
1
2
0
2
2
2
0
1
2
1
1
1
1
1
1
1
1
2
1
2
2
1
2
1
1
1
1
0
1
0
2
2
1
1
0
0
1
1
1
1
1
2
1
0
1
1
1
4
1
1
1
1
1
1
1
2
1
1
2
0
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
0
1
2
1
1
0
1
3
0
1
2
1
1
1
1
1
2
1
1
1
1
0
0
1
1
2
2
1
1
1
1
1
0
0
2
1
1
0
2
1
2
1
2
0
1
0
2
1
0
2
2
1
1
1
2
1
1
2
2
1
1
1
2
2
1
2
1
1
1
1
0
2
2
1
1
1
1
2
0
2
1
2
1
1
1
2
1
0
2
1
1
0
1
1
2
1
1
1
1
0
0
1
1
1
0
1
2
2
2
1
1
0
1
1
1
1
1
1
1
1
1
1
1
0
2
0
1
2
1
2
1
2
0
1
2
1
2
1
1
1
0
1
0
2
1
1
1
1
1
1
1
0
1
2
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
1
0
1
2
1
0
2
1
1
1
2
1
2
1
1
2
1
1
2
2
1
0
1
1
0
1
2
0
1
2
0
1
2
1
1
1
0
1
1
0
1
1
1
2
1
2
0
1
1
1
1
2
1
1
1
2
2
0
1
0
0
1
1
1
0
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
0
2
1
2
2
0
1
1
1
2
1
0
1
0
0
1
1
1
2
0
2
1
1
1
0
2
1
1
0
0
1
2
0
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
0
1
1
1
1
1
1
0
1
2
2
2
1
1
1
1
2
0
1
1
1
1
2
1
2
1
1
1
2
1
1
0
1
1
1
2
1
1
2
2
0
0
0
1
1
0
1
1
0
0
1
1
0
1
2
1
1
0
2
0
2
1
1
1
0
1
1
1
1
2
1
1
1
1
1
1
1
1
1
0
1
5
1
0
2
2
0
1
1
1
1
1
1
1
1
0
1
1
1
1
2
1
0
2
1
1
2
1
1
1
1
1
1
2
1
2
2
0
1
1
1
1
0
2
1
1
2
1
1
1
2
2
2
2
1
1
1
1
1
2
0
1
1
1
0
2
0
2
1
1
2
1
1
1
1
1
1
2
1
2
0
1
0
0
2
1
0
1
2
1
1
1
2
1
1
1
1
1
1
0
2
1
1
1
1
1
1
2
2
1
1
0
0
0
1
1
1
1
1
2
2
1
0
1
1
1
2
1
0
1
1
0
2
1
2
2
1
0
0
1
1
1
1
1
2
1
2
0
1
1
1
1
1
1
2
1
2
3
1
1
1
0
1
1
1
1
1
1
1
0
0
0
2
2
1
2
2
2
2
2
1
1
1
1
2
1
1
1
1
2
2
1
2
0
1
1
2
1
2
0
1
2
1
2
1
2
0
1
0
0
1
1
1
1
1
1
1
1
1
2
1
1
0
2
1
1
1
1
1
1
1
2
2
0
1
1
2
1
1
0
1
1
2
4
2
1
1
0
2
2
1
2
1
2
2
0
1
1
2
0
1
1
1
2
1
2
1
1
0
2
1
0
2
1
2
1
2
2
1
2
0
2
0
2
1
2
2
1
1
2
2
1
1
2
1
1
1
1
0
0
0
1
1
2
1
1
1
0
1
1
0
2
1
2
2
0
1
1
1
0
2
2
1
1
2
0
1
2
1
2
1
0
2
0
2
2
1
1
2
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
0
0
2
1
1
1
0
0
0
1
0
2
3
2
0
1
0
1
1
1
0
0
2
1
1
2
2
1
0
0
1
1
2
1
2
1
2
2
1
2
1
2
2
1
0
1
2
1
2
1
1
2
0
1
1
0
1
1
1
0
1
0
0
1
2
1
0
0
1
2
1
1
1
0
1
0
1
1
1
1
1
1
1
0
1
1
2
1
2
1
0
2
1
1
0
1
2
1
1
1
1
1
1
1
1
1
1
1
0
2
2
2
1
1
1
3
1
0
2
1
1
2
1
1
0
1
1
2
1
1
1
1
1
1
0
1
2
1
1
1
2
1
0
3
1
0
1
2
2
1
1
2
0
0
1
1
1
1
1
1
1
1
2
1
2
1
0
1
2
1
0
2
1
2
2
1
1
1
2
2
1
1
0
1
1
1
1
2
1
2
2
1
1
2
1
1
1
2
1
2
0
1
1
2
1
1
1
2
1
1
2
1
1
2
3
1
1
2
1
0
2
2
0
0
0
2
2
0
1
1
1
0
1
1
2
1
0
0
2
0
2
1
0
2
2
1
1
0
0
1
1
1
1
2
2
0
1
1
0
0
0
1
1
1
0
1
1
1
1
0
1
1
1
2
1
2
1
2
1
1
2
1
1
1
0
2
2
1
1
1
1
2
1
1
1
1
3
1
1
2
1
1
1
0
0
0
1
1
0
0
2
1
0
2
2
1
1
1
0
1
1
2
0
1
2
1
3
0
0
1
1
1
0
1
1
1
1
1
1
1
2
1
2
1
1
1
2
1
1
0
0
0
0
2
1
1
0
1
1
0
1
2
1
1
1
1
1
1
1
1
2
1
0
2
1
0
0
2
1
1
1
1
1
1
1
1
1
2
1
2
1
1
0
1
1
2
1
2
1
1
1
1
1
0
1
2
1
1
3
1
1
2
1
1
1
3
1
0
1
1
1
2
0
0
2
0
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
2
1
2
1
1
2
1
1
2
1
2
0
2
1
2
1
5
1
0
1
0
1
1
0
1
1
0
1
2
0
1
3
0
2
1
1
2
2
1
1
0
1
2
1
1
1
1
1
2
2
1
1
1
1
1
3
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
0
1
1
0
2
1
2
1
0
0
1
1
1
1
1
1
0
1
0
1
2
0
2
0
1
1
1
2
1
1
1
2
2
1
1
1
2
2
1
1
1
2
0
2
1
2
1
0
1
1
1
2
1
1
0
1
1
1
1
1
1
1
2
1
1
1
0
2
1
1
2
1
0
2
1
1
2
2
2
1
1
1
1
1
2
1
0
2
1
0
1
0
1
0
1
2
2
1
1
0
1
1
2
1
1
1
1
1
2
2
1
0
1
1
2
2
1
0
2
0
2
0
1
1
1
2
0
2
2
1
0
1
1
0
1
1
0
1
1
1
0
2
1
1
1
2
1
1
2
2
1
1
1
0
0
1
0
0
1
2
1
0
1
1
2
1
1
0
0
2
1
2
2
2
1
0
1
1
2
1
2
1
1
1
0
0
2
1
1
2
2
1
2
2
1
1
1
1
1
1
1
2
2
1
1
0
1
1
0
2
1
1
0
1
2
1
1
1
0
2
0
0
2
1
1
2
2
0
1
1
2
0
1
1
1
1
2
1
0
1
1
1
1
0
1
2
3
1
1
1
0
0
1
2
0
1
1
1
0
1
1
2
2
0
1
2
1
1
1
2
2
1
1
0
0
1
1
1
0
0
0
1
1
1
0
1
2
1
1
1
1
1
1
1
1
1
1
1
2
0
1
1
1
2
1
1
0
0
1
1
2
1
1
1
2
2
2
1
1
1
1
2
1
1
1
1
2
1
3
1
1
1
1
2
2
1
1
2
2
1
1
1
1
1
1
2
1
0
1
0
2
2
0
1
1
2
1
2
2
1
0
1
2
1
1
0
3
1
1
0
1
1
0
1
1
2
1
3
2
1
4
1
2
0
1
1
1
2
2
1
0
1
1
1
2
1
0
1
1
1
1
1
1
3
1
1
1
2
1
1
2
2
4
1
1
1
1
2
4
0
1
1
0
2
0
1
1
1
2
1
1
1
2
1
1
1
1
1
0
0
1
1
1
1
2
1
1
1
1
2
1
1
0
1
1
1
1
0
1
1
1
0
1
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
0
1
2
1
1
1
2
1
2
0
1
1
2
0
2
0
1
1
1
1
1
0
2
1
2
1
1
1
2
1
2
1
2
2
1
2
1
1
2
1
2
1
2
0
0
2
1
1
1
1
2
2
0
1
0
1
1
2
1
2
0
1
2
1
1
2
3
2
0
1
1
1
1
1
0
1
0
1
0
2
2
1
2
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
0
0
1
2
1
1
2
1
1
1
0
1
1
2
0
0
0
1
1
1
2
1
1
2
1
2
2
1
1
1
0
1
2
2
1
1
2
1
1
1
0
1
0
1
0
2
2
1
2
1
1
1
1
0
1
0
1
2
2
2
1
2
0
1
1
0
1
1
0
1
1
1
1
2
1
1
1
0
1
2
1
1
2
1
1
0
1
2
0
1
2
2
0
0
0
0
3
1
1
1
1
1
1
2
1
1
0
1
1
0
1
1
1
2
1
2
1
2
2
1
1
1
1
0
1
1
0
1
0
2
1
1
2
1
0
2
2
2
1
1
1
0
2
0
1
1
1
1
1
1
0
1
2
1
1
2
0
1
1
1
2
0
0
2
1
1
1
1
1
2
2
0
2
0
2
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
1
0
1
1
1
2
0
1
1
1
2
1
2
0
2
1
1
1
1
1
1
2
1
1
0
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
0
1
2
0
0
1
1
1
1
1
1
2
1
2
2
0
2
1
0
1
0
1
1
0
0
1
0
1
0
1
1
1
1
1
1
0
2
2
1
1
1
2
1
1
1
2
2
1
1
0
1
1
1
0
1
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
1
0
0
1
1
1
1
1
1
1
1
1
2
0
1
0
1
1
0
2
2
1
1
1
2
3
0
1
1
2
1
1
1
2
0
1
1
1
1
1
1
1
1
2
1
1
2
1
3
1
1
1
1
1
1
1
1
2
1
1
1
2
1
2
2
1
2
1
1
0
1
0
2
1
1
2
1
2
1
0
0
1
1
1
2
1
0
1
1
1
1
1
1
1
1
1
2
1
0
1
2
1
1
2
1
2
1
1
0
1
1
2
1
0
0
1
5
1
2
1
2
1
1
1
0
2
2
0
2
2
1
1
1
0
1
2
2
1
2
2
0
0
2
1
0
2
0
1
0
1
1
2
1
1
2
2
1
0
1
2
2
1
2
1
1
1
1
2
2
1
1
1
1
2
2
0
2
0
1
0
1
1
2
2
1
1
2
0
1
2
1
1
1
1
2
1
2
0
2
0
1
1
1
1
2
1
1
1
2
2
3
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
0
1
1
1
2
0
1
2
2
2
2
1
1
2
1
1
1
2
0
1
0
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
0
1
1
1
0
1
1
1
2
0
1
2
1
2
0
2
2
0
1
1
0
2
1
1
1
1
1
1
0
1
2
1
1
1
1
1
0
1
1
2
2
1
0
1
0
0
2
1
2
2
0
0
1
1
2
1
1
2
2
1
2
1
1
1
0
2
1
2
1
0
1
2
0
1
1
1
1
2
1
1
2
2
2
2
0
1
1
0
1
1
1
1
0
1
0
1
1
1
1
1
0
2
2
0
1
1
0
1
1
1
0
2
2
1
1
0
1
2
1
1
1
1
1
1
1
0
1
1
1
1
1
2
1
1
1
2
0
1
1
1
1
1
1
0
2
5
1
2
1
0
1
0
1
1
1
2
1
1
0
2
0
1
1
1
1
1
1
1
1
1
0
1
0
2
2
1
2
1
1
0
1
1
1
1
1
1
1
1
2
1
1
2
1
0
1
2
2
2
2
1
2
2
0
2
1
2
2
1
2
0
1
1
1
1
1
1
0
2
2
1
0
1
0
1
0
1
0
2
1
1
1
2
2
2
2
1
1
1
2
2
2
2
2
0
1
0
0
1
1
1
0
1
1
1
1
2
1
0
0
1
2
1
0
1
1
1
1
0
1
1
0
1
1
1
2
1
0
1
1
1
1
2
2
3
1
2
1
0
2
0
1
2
2
0
1
1
2
1
2
2
1
1
1
2
2
0
2
1
0
1
2
1
1
1
1
0
2
1
1
1
1
0
1
1
0
2
0
1
1
2
0
1
1
2
1
1
1
1
2
2
1
2
1
2
2
1
2
2
1
1
0
1
0
1
1
1
1
1
1
2
1
1
0
0
1
2
2
0
1
1
1
1
0
1
2
1
0
1
1
2
1
2
1
1
1
0
1
2
1
1
2
2
0
0
1
1
0
1
1
0
1
1
1
2
1
1
1
1
1
2
1
2
1
1
0
2
1
2
1
2
1
1
1
2
1
1
0
2
2
2
0
1
1
1
1
1
2
2
2
1
0
0
0
0
1
1
0
1
0
2
1
1
1
2
0
1
1
1
2
1
2
0
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
2
1
2
2
1
1
2
2
0
0
0
2
0
1
1
1
2
1
1
1
2
1
0
1
1
1
2
0
1
1
0
1
1
2
1
1
0
0
2
2
1
1
1
1
1
0
1
1
1
1
0
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
2
0
0
0
2
1
1
0
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
0
1
1
1
1
0
1
1
2
2
1
2
1
1
2
1
1
1
0
3
1
1
2
1
0
1
1
1
0
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
0
0
0
0
2
0
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
0
0
0
2
2
1
1
1
2
1
2
1
1
2
1
1
2
1
0
0
2
1
1
1
1
0
2
1
1
2
1
1
2
0
3
1
1
1
1
1
1
1
1
1
0
1
0
1
1
1
0
0
1
2
1
2
1
1
1
2
2
1
1
2
1
2
0
0
0
1
1
2
1
0
0
1
1
0
1
2
0
1
2
0
1
1
1
0
2
2
1
1
2
1
1
0
2
1
2
1
1
1
0
2
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
2
2
1
1
2
2
1
1
1
0
0
0
2
1
2
2
1
0
1
1
1
1
1
2
1
1
0
1
0
1
2
2
1
2
1
1
1
1
1
2
2
2
1
1
2
2
0
0
2
1
1
1
0
1
1
1
1
2
2
2
2
2
1
2
1
1
2
1
1
1
1
1
2
2
1
1
0
1
0
0
1
2
1
2
0
2
1
0
2
1
0
1
1
1
1
1
1
1
0
2
0
1
1
1
2
1
2
1
2
1
1
1
1
0
1
1
2
1
0
1
2
2
1
1
1
1
0
1
1
0
2
0
1
1
0
1
2
2
1
1
2
0
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
0
1
1
0
1
0
1
1
0
1
1
0
1
1
1
0
1
1
2
1
0
0
2
1
1
0
1
1
2
1
1
1
1
2
1
1
0
2
1
1
2
0
1
2
0
2
0
2
1
1
0
1
2
1
2
1
1
1
0
2
2
1
2
2
1
1
2
1
1
0
0
1
1
0
1
0
1
2
1
2
1
2
0
1
1
1
1
2
1
0
1
1
1
2
1
1
0
2
2
1
1
1
2
1
0
1
0
1
1
2
2
1
1
1
1
0
1
1
0
1
2
1
2
1
1
1
0
2
0
1
2
0
2
1
2
1
1
2
1
0
1
1
1
1
0
0
2
1
1
0
0
0
1
2
2
1
2
1
0
0
2
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
0
0
2
2
2
1
1
1
2
2
1
1
1
2
1
0
1
0
1
1
1
2
2
1
1
1
1
1
1
1
2
0
1
2
1
0
1
0
1
1
1
1
2
2
0
2
1
1
1
2
1
0
0
1
1
1
2
2
1
2
1
1
1
0
1
2
0
1
1
1
2
1
1
1
1
0
2
1
2
1
2
0
1
1
1
1
1
2
1
1
1
2
0
1
2
1
1
1
0
1
1
1
2
1
0
1
2
1
1
1
2
1
1
2
2
1
0
2
1
1
1
1
1
1
1
0
0
1
2
2
0
2
0
2
2
1
1
1
1
1
1
0
1
1
2
1
1
0
1
2
2
1
1
1
1
0
2
2
2
0
1
1
1
1
3
1
1
1
1
1
1
1
1
2
1
0
2
2
1
2
1
1
2
1
2
0
1
1
1
2
1
1
1
2
1
1
1
2
1
1
0
1
2
1
1
1
1
1
1
1
2
1
2
1
0
0
1
1
1
2
1
1
2
1
1
2
1
1
1
1
2
1
2
1
1
0
2
0
1
0
1
1
2
1
1
1
1
1
0
2
1
1
1
1
1
2
1
0
1
2
2
2
1
1
1
0
2
1
2
0
1
0
1
2
1
1
2
2
1
2
1
1
1
0
0
2
0
1
1
1
1
0
1
0
1
1
1
1
1
0
1
2
1
2
1
0
2
1
2
1
2
1
1
1
1
1
2
1
2
2
1
1
1
1
0
1
0
0
2
1
1
1
1
1
1
1
1
2
1
1
2
2
1
2
1
2
1
0
1
2
2
1
1
1
2
1
1
2
0
1
1
0
1
1
2
1
1
1
1
1
1
1
0
1
1
2
1
1
2
1
1
1
2
3
1
1
1
1
1
2
1
1
0
1
1
2
1
0
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
0
1
2
1
2
1
1
0
1
1
1
2
1
1
0
2
2
1
2
2
2
1
0
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
1
1
0
1
2
0
1
0
2
1
1
1
1
1
1
1
1
2
1
1
2
1
2
2
1
2
1
1
1
1
0
1
2
1
1
1
0
2
2
1
2
1
1
0
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
2
1
1
1
0
0
1
2
1
1
1
2
0
1
1
1
1
1
2
1
0
1
1
2
1
1
2
1
1
2
1
1
1
1
1
1
2
2
2
1
1
1
2
0
0
2
0
1
0
1
0
1
1
1
1
1
1
2
0
0
1
2
0
1
1
2
1
1
1
1
1
1
1
0
1
1
1
2
3
0
1
1
0
1
1
2
2
1
0
1
1
0
1
1
1
1
1
1
1
2
0
2
2
1
2
1
3
0
1
2
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
0
1
1
2
1
1
1
1
1
1
3
1
2
1
2
1
2
1
1
0
1
1
2
1
1
2
0
2
2
0
2
1
1
1
2
1
2
1
1
1
2
1
1
1
2
1
1
1
1
0
1
1
1
1
0
1
0
0
2
0
1
1
2
1
1
1
1
1
1
2
1
0
2
1
1
2
2
1
1
0
1
1
0
2
1
1
1
1
2
1
1
3
1
1
1
1
2
2
1
1
0
2
1
2
1
1
1
1
1
0
0
2
2
1
2
1
0
1
0
1
1
2
2
1
2
1
1
1
1
1
2
2
1
2
0
1
1
0
0
0
2
2
1
1
1
0
1
1
1
1
2
2
2
1
1
1
1
2
1
1
2
1
1
1
2
1
0
1
0
1
1
1
0
2
2
1
2
1
0
0
1
1
1
1
2
1
1
1
0
1
1
0
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
0
0
1
1
1
2
1
1
1
2
2
2
0
2
1
1
0
2
1
2
2
1
0
2
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
1
0
1
1
0
0
2
3
1
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
0
1
1
0
1
1
1
2
1
1
2
0
1
1
0
1
1
1
1
1
1
1
1
0
1
1
2
1
1
1
1
0
0
2
1
1
0
1
1
2
2
2
1
2
2
1
1
1
2
1
1
2
1
1
2
2
1
1
1
1
1
1
2
0
0
2
1
2
1
1
1
2
1
0
2
2
1
1
1
1
1
1
1
0
1
1
1
1
0
1
1
1
2
0
1
1
1
1
1
2
2
0
1
2
1
1
2
1
2
1
1
1
0
2
2
2
1
1
1
1
1
2
2
1
1
2
1
2
1
2
1
2
0
0
1
2
1
2
1
1
1
1
1
1
2
0
2
0
1
2
2
1
2
1
1
1
0
0
1
1
0
2
1
1
2
2
3
1
1
1
1
1
1
2
1
1
1
1
1
2
2
2
1
1
1
2
0
1
1
2
1
1
2
1
0
1
2
1
0
0
1
1
0
2
1
2
1
1
1
1
2
3
0
0
1
0
1
1
2
1
1
1
0
0
1
1
0
1
1
1
2
1
1
1
2
2
1
1
1
1
1
0
2
1
2
1
1
1
0
0
1
2
0
1
0
2
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
0
1
1
1
1
1
1
2
0
0
1
1
2
1
0
1
1
2
1
1
2
2
1
2
2
1
1
1
2
1
2
2
1
2
2
2
1
2
0
1
1
2
0
1
0
1
2
0
0
1
1
2
1
1
1
0
1
1
2
1
1
1
1
2
2
1
1
1
1
1
1
2
1
1
2
1
1
1
2
2
2
1
2
1
1
0
2
1
0
1
0
1
1
0
2
0
1
2
0
0
1
1
2
2
0
1
2
2
0
2
1
1
8
1
0
2
1
1
0
0
1
1
1
1
0
0
2
1
2
1
1
2
1
1
1
1
0
1
1
2
1
1
1
0
2
1
0
1
1
1
0
0
1
0
1
1
2
2
2
1
2
2
2
3
0
2
1
2
2
1
2
0
2
1
2
0
2
1
1
2
1
0
1
0
2
0
0
1
0
1
0
1
2
0
2
2
2
0
0
1
0
1
1
1
2
1
0
0
0
1
2
1
1
1
0
1
1
1
1
0
1
1
1
1
2
1
1
1
0
1
0
1
1
1
1
2
0
1
1
1
1
1
1
1
2
1
2
1
0
2
2
1
1
1
2
1
0
1
1
2
1
2
1
1
2
1
1
1
2
1
1
1
1
1
1
0
0
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
0
2
1
1
1
3
2
1
0
1
1
0
2
1
1
1
2
1
1
2
1
3
1
1
1
1
1
1
2
1
0
1
2
2
1
1
1
1
2
2
1
1
1
1
0
0
1
2
1
2
0
1
1
2
2
1
0
2
0
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
0
0
1
1
1
0
2
1
1
1
1
2
1
1
2
1
2
1
1
1
1
1
2
1
2
0
2
0
1
1
0
0
2
2
1
1
1
1
1
1
1
1
2
0
0
1
2
0
1
0
1
0
1
1
2
1
0
0
0
1
1
2
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
2
0
0
2
0
2
1
1
1
1
2
1
1
2
1
1
1
2
1
1
1
1
0
1
0
1
0
2
0
1
1
0
1
2
0
1
2
1
2
0
1
1
1
2
0
1
1
1
1
1
1
1
0
1
1
1
2
1
1
2
2
1
1
1
1
1
0
1
1
0
2
1
2
1
2
1
2
1
1
1
4
1
2
2
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
1
1
1
2
1
2
1
1
1
1
2
1
1
1
1
1
0
2
1
1
1
1
1
0
1
0
0
1
1
0
1
1
0
0
2
1
1
2
2
2
1
2
0
1
0
1
2
1
1
1
1
0
1
1
1
1
0
1
1
1
1
1
1
0
1
2
1
1
1
1
1
2
1
0
2
2
1
0
1
1
1
0
2
0
1
1
2
1
1
1
1
0
1
1
0
2
0
1
1
2
2
2
0
1
2
0
1
2
1
2
1
1
2
1
0
0
1
1
1
0
1
1
0
1
1
2
1
1
1
1
1
2
1
1
1
1
1
0
1
2
1
0
1
0
2
0
1
1
0
1
1
2
0
1
2
1
0
1
1
2
1
0
1
0
0
0
1
1
0
2
1
2
2
0
1
0
1
2
1
0
1
1
3
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
0
2
1
1
1
3
1
0
1
0
1
1
1
1
1
1
1
0
1
1
1
1
2
2
1
2
1
1
0
1
1
1
2
2
2
2
1
0
1
1
2
1
1
1
1
1
2
1
1
1
1
2
2
1
1
1
1
2
1
2
2
1
2
2
1
0
1
1
1
1
2
0
1
1
0
0
1
1
1
0
1
1
1
1
1
0
2
2
2
1
1
1
1
1
2
1
2
1
2
2
0
2
2
1
1
2
2
2
1
2
1
4
1
1
0
1
1
0
2
1
1
2
1
3
1
1
1
0
1
2
2
2
1
1
1
2
1
2
0
1
2
1
2
1
1
1
1
0
1
1
2
1
2
1
2
1
3
2
1
2
1
1
1
2
5
1
1
2
1
1
1
2
0
1
1
0
1
2
0
0
0
1
2
1
1
2
1
2
1
1
1
1
1
1
1
2
0
1
2
1
1
0
1
1
2
1
1
1
2
1
1
1
0
1
0
1
2
1
2
2
1
2
1
1
2
1
0
1
0
1
1
1
2
0
1
1
3
1
2
2
1
1
0
1
1
1
1
1
2
1
0
0
1
2
1
2
1
1
1
0
1
0
1
1
0
2
1
2
1
1
2
2
2
1
1
1
1
1
1
2
0
1
0
1
1
2
1
1
2
1
1
0
1
0
1
0
1
1
2
0
1
1
2
2
1
2
1
1
1
0
0
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
1
0
0
0
2
1
1
1
1
1
1
0
1
1
2
1
1
2
1
1
1
1
2
1
1
0
2
1
1
0
1
1
1
1
1
1
1
1
1
2
1
0
1
1
0
1
1
1
1
0
1
0
0
1
1
0
1
2
1
0
0
0
1
2
1
1
2
1
1
0
1
1
2
2
1
1
1
1
0
1
2
0
2
1
2
1
2
1
1
1
1
2
1
1
2
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
0
0
1
1
1
0
1
2
1
1
0
1
0
1
2
1
1
0
0
0
1
1
2
1
1
1
1
1
1
1
1
2
2
0
1
2
0
2
0
1
1
0
1
1
1
2
1
1
2
0
2
1
1
1
1
2
2
1
2
1
2
2
1
1
0
1
1
2
0
1
1
1
2
1
1
1
2
2
1
2
1
2
2
1
1
2
1
2
2
2
1
2
1
1
1
0
2
1
2
1
2
2
1
1
1
1
1
2
0
1
1
1
0
1
1
2
1
1
0
1
0
1
0
2
1
0
2
1
2
1
0
1
0
1
2
1
0
1
1
1
0
1
1
0
1
1
0
0
0
1
1
2
1
1
0
0
2
2
1
0
1
0
1
1
1
2
1
1
1
1
1
2
1
1
0
1
1
1
1
1
0
1
1
1
1
0
1
0
1
1
2
1
2
0
1
2
2
1
2
1
1
1
1
2
1
0
1
1
2
2
0
2
1
0
1
2
2
1
1
1
2
2
0
1
1
0
1
2
1
2
1
2
2
0
1
0
1
1
1
1
2
1
0
1
1
0
1
1
2
2
2
1
2
2
1
1
2
1
0
1
2
1
0
0
1
0
1
0
2
1
2
3
1
1
1
1
1
1
0
1
0
1
2
2
1
1
1
2
0
2
0
0
2
2
2
2
2
1
0
0
1
1
2
2
1
1
1
1
1
1
1
1
1
3
1
2
1
1
0
1
1
1
1
2
1
2
1
2
2
0
1
1
0
1
2
1
2
2
1
1
1
0
0
1
2
1
1
1
1
2
1
1
2
1
1
2
1
2
0
2
0
1
1
1
1
1
1
1
1
2
3
2
0
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
2
2
2
0
1
1
1
2
0
2
1
1
1
1
1
1
1
2
1
1
1
2
0
1
1
1
1
1
1
1
2
1
0
1
1
1
0
2
1
2
1
1
0
1
1
1
1
1
1
1
0
1
2
1
1
1
1
1
0
1
1
1
2
1
1
1
1
2
0
2
1
2
1
1
1
1
2
1
1
0
2
2
0
0
1
0
1
2
1
1
0
1
2
1
1
1
1
1
1
2
2
2
0
0
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
0
0
1
1
1
1
1
1
2
1
1
2
1
3
1
1
2
1
1
2
2
2
1
1
1
2
1
1
1
1
1
1
1
0
1
1
1
0
2
1
1
1
1
2
2
1
1
2
0
1
1
2
0
2
1
1
1
0
2
1
1
1
1
2
1
1
1
0
1
1
1
1
1
1
2
1
1
1
1
1
0
1
1
2
1
1
0
1
1
2
1
2
1
1
1
0
1
0
1
2
1
1
2
1
1
2
1
0
1
2
2
0
0
2
1
1
0
1
2
1
1
2
0
2
1
1
1
2
1
1
1
1
1
1
2
1
2
1
1
1
0
2
2
1
1
2
2
1
1
1
1
1
0
1
1
2
0
0
2
0
0
1
1
1
1
2
1
2
2
1
2
2
1
1
1
1
0
2
0
1
1
0
1
2
1
2
1
2
1
1
2
2
1
2
2
2
2
1
2
2
1
1
1
1
1
1
1
1
0
1
1
1
1
1
2
2
2
1
2
1
0
1
2
1
1
1
2
1
1
1
2
1
1
1
0
2
1
1
1
2
2
1
1
1
2
0
1
2
1
0
1
0
1
1
2
1
1
2
2
2
1
2
2
1
2
0
1
1
1
1
1
0
2
1
1
1
1
2
1
0
1
1
1
2
2
2
2
1
2
1
1
1
2
1
1
2
1
1
1
2
1
1
1
0
2
1
1
2
1
1
1
2
0
1
1
0
1
2
1
1
2
1
2
1
2
0
2
1
1
1
1
1
0
1
2
2
0
2
2
1
0
1
2
1
1
1
0
1
1
2
1
2
1
2
2
1
2
1
0
2
1
0
0
1
1
1
2
1
0
1
0
2
1
1
1
1
1
1
1
2
1
2
1
1
1
0
2
0
1
1
1
1
1
0
2
1
2
0
1
1
1
1
1
2
1
1
1
1
1
2
1
2
1
2
1
1
2
1
2
1
1
2
1
0
1
1
0
0
2
1
2
1
1
1
1
2
0
1
1
2
1
1
1
1
1
1
2
1
1
2
1
0
1
2
1
1
1
2
1
7
1
1
1
1
1
1
1
1
1
1
0
2
0
1
1
1
2
4
1
1
1
2
0
1
1
1
1
0
1
3
1
0
1
1
2
1
0
0
1
0
0
0
2
2
1
2
2
1
1
2
0
1
1
1
2
1
2
1
1
2
1
1
1
1
1
1
2
0
1
2
1
1
1
2
2
1
2
0
1
1
1
2
1
1
0
1
2
1
2
0
2
1
1
1
2
0
1
1
2
1
1
1
0
2
1
2
1
1
1
1
1
1
0
1
0
0
1
1
1
1
1
1
0
2
1
1
1
2
2
1
1
1
2
1
2
1
2
1
1
1
1
2
2
1
2
2
1
1
1
1
1
1
2
2
1
2
2
1
1
1
1
1
1
0
1
1
1
1
2
0
1
2
1
2
0
1
2
1
2
1
1
0
1
2
0
2
2
0
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
2
2
1
2
0
2
1
2
1
1
1
1
1
0
0
1
2
1
2
1
2
1
1
1
2
2
1
2
1
0
2
1
2
1
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
2
1
2
2
2
2
1
0
1
4
1
0
0
1
1
1
0
1
2
2
2
1
1
2
2
2
1
0
1
2
1
1
0
1
1
2
1
1
2
1
1
1
1
1
2
1
2
1
1
1
0
2
1
1
2
1
1
1
1
1
1
2
1
0
1
2
1
1
0
2
1
0
2
3
1
2
1
1
1
1
2
0
2
1
1
0
0
1
1
1
1
2
1
0
1
1
1
2
1
1
1
1
1
2
1
1
1
1
0
1
1
1
1
1
0
1
1
0
1
1
1
0
1
1
1
1
1
1
2
0
0
4
1
2
1
1
2
1
2
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
0
2
1
0
2
1
2
1
1
1
1
2
2
2
1
0
0
0
1
0
1
1
2
0
1
1
0
0
2
2
2
1
1
1
2
0
0
2
2
2
1
0
1
1
0
1
1
1
2
1
1
0
1
0
0
1
0
1
2
1
1
1
0
1
1
1
0
2
1
1
0
2
2
1
0
2
1
1
2
0
1
1
1
2
0
1
1
1
1
1
1
1
0
1
1
0
1
0
1
2
1
2
2
1
1
0
1
1
1
1
1
1
1
2
2
1
2
1
1
2
2
1
1
1
1
1
1
1
2
0
2
1
1
1
1
1
0
3
1
0
1
1
1
1
1
2
1
2
1
2
0
1
2
1
2
1
1
1
2
0
1
1
0
1
1
2
2
1
0
0
0
1
0
1
2
1
1
0
1
1
2
1
2
2
1
2
1
1
1
1
0
0
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
2
1
1
6
1
0
1
1
2
2
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
0
1
0
1
1
2
2
2
1
2
1
1
1
1
0
0
0
2
2
0
1
1
0
2
1
1
2
1
2
2
1
1
1
0
0
1
2
2
1
2
1
1
2
1
2
1
1
1
2
1
2
2
1
1
0
1
2
0
1
1
2
2
2
2
1
2
0
1
1
1
0
1
0
1
0
1
1
2
1
0
1
2
1
0
2
1
2
1
0
1
2
1
1
1
0
1
1
1
1
2
2
2
1
1
1
2
1
1
1
1
1
0
1
1
1
1
1
1
1
2
2
1
1
2
1
2
1
1
1
1
2
0
0
2
2
2
2
3
0
1
2
2
1
2
1
0
1
1
1
2
2
2
1
2
0
0
0
1
0
1
1
1
0
2
2
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
2
1
0
1
1
1
1
2
1
1
2
1
0
0
1
1
2
2
2
1
0
1
0
0
1
1
1
1
1
2
1
1
1
0
1
1
1
1
1
0
1
1
1
1
2
1
1
2
1
0
1
2
2
1
2
1
1
1
0
1
1
2
1
1
1
1
0
2
1
2
1
1
0
1
1
1
1
0
1
1
1
2
1
1
1
1
0
1
1
1
0
1
1
2
1
2
0
2
0
2
1
1
1
0
0
2
1
2
0
1
2
2
0
1
2
1
2
2
1
1
0
1
1
2
2
2
1
1
5
0
1
2
1
1
1
1
2
0
1
0
1
1
0
1
1
1
1
2
1
1
2
3
0
2
1
1
1
1
1
1
0
1
2
2
1
2
1
1
1
0
1
0
1
2
2
1
1
1
2
1
1
1
1
0
1
1
1
1
1
0
2
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
0
1
1
1
2
1
1
1
1
1
1
2
1
0
2
2
2
0
1
2
1
2
1
1
0
1
2
1
2
1
1
1
1
2
2
1
1
0
2
1
1
2
0
2
1
2
2
1
0
1
2
1
1
2
0
0
1
1
2
1
1
0
0
1
0
0
1
1
1
1
2
1
1
0
2
0
1
2
1
2
0
1
1
1
1
2
1
1
2
2
1
1
1
0
1
2
1
2
1
1
0
2
2
1
1
0
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
0
0
1
1
1
2
2
1
2
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
2
2
1
0
1
0
1
1
2
2
1
1
1
0
1
1
1
0
0
1
1
1
0
1
2
1
1
0
1
1
1
1
3
2
1
2
1
1
1
1
1
1
1
1
1
0
1
1
0
1
0
1
1
2
1
1
1
0
3
1
3
1
1
0
1
1
2
1
1
1
2
1
1
2
0
1
0
1
1
2
2
1
1
1
2
0
2
1
1
0
2
0
2
1
1
1
0
1
1
0
2
1
1
1
1
0
1
0
1
1
2
2
1
2
0
1
1
2
1
1
2
0
1
1
0
0
2
0
1
1
0
1
1
1
1
1
1
0
1
1
1
0
1
1
1
2
1
2
2
2
1
1
1
1
1
0
2
1
2
2
1
1
1
1
0
1
3
1
1
2
0
2
1
2
2
1
2
2
2
1
2
1
1
1
1
2
1
2
1
1
0
1
0
2
2
1
1
1
1
0
1
0
1
1
1
1
0
0
2
0
1
1
0
1
2
1
1
1
1
1
1
1
1
1
2
0
1
2
1
2
1
1
1
1
1
1
1
1
0
0
2
2
0
1
1
1
0
1
0
1
2
1
1
1
2
1
1
2
2
1
2
4
2
1
1
1
2
1
2
1
2
1
1
1
1
2
1
1
2
2
1
1
0
1
0
1
1
6
1
1
1
1
2
1
1
1
0
1
1
2
0
2
1
1
1
1
1
1
1
1
1
1
2
2
1
2
0
0
0
0
2
2
1
2
3
1
1
2
2
0
1
1
1
0
1
1
2
2
2
1
2
1
1
1
0
0
2
0
1
2
0
2
1
1
2
1
1
2
1
2
1
0
2
2
1
0
1
2
1
2
1
2
1
0
1
1
1
1
2
0
1
2
2
1
0
2
0
1
2
1
1
1
1
2
1
1
1
1
1
0
3
2
2
1
1
1
2
0
1
0
0
1
1
0
0
1
1
0
1
5
1
1
0
2
1
1
2
0
2
2
1
1
2
2
0
0
0
1
0
1
2
1
2
1
1
1
1
2
1
1
1
1
0
1
1
1
2
2
1
1
1
1
1
1
2
2
1
1
1
0
2
1
2
2
1
1
1
2
1
2
0
2
1
1
2
1
1
2
1
1
1
2
1
2
0
0
1
0
2
1
1
1
1
1
2
1
0
0
2
1
0
1
1
2
1
1
1
1
0
1
1
1
1
1
1
0
1
2
1
0
1
2
1
1
2
1
1
1
1
0
1
2
0
1
1
1
0
1
1
1
1
1
1
0
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
0
2
1
1
1
1
2
0
2
2
1
1
1
1
2
1
1
2
1
1
1
2
1
0
1
1
1
1
2
2
2
1
0
0
2
1
0
0
1
1
1
1
1
1
1
1
0
2
1
1
1
0
2
0
1
1
1
0
1
1
1
1
2
0
1
1
1
1
1
1
1
2
0
2
0
1
2
1
2
0
2
1
1
0
0
2
0
2
1
1
1
1
2
1
1
1
1
1
0
2
1
2
1
2
0
1
1
2
2
1
1
0
0
0
2
1
1
0
2
1
0
1
2
2
1
2
1
1
1
1
1
2
2
2
1
1
0
2
2
1
0
1
1
0
1
1
1
2
1
1
1
1
1
1
2
1
0
1
1
1
1
1
1
1
2
1
1
2
2
0
1
0
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
3
1
1
0
2
2
1
1
2
2
2
1
1
0
1
1
0
1
0
2
0
1
0
1
2
1
2
1
1
1
2
0
1
2
1
1
2
1
1
0
1
0
1
1
1
1
0
2
2
1
0
1
0
0
0
0
0
2
1
2
1
2
2
0
0
0
0
1
1
2
1
1
2
1
0
0
1
0
1
2
0
1
1
1
1
1
0
1
0
1
1
0
1
1
1
0
2
1
1
1
2
1
1
1
1
2
1
1
1
0
2
2
1
2
1
1
2
0
1
2
2
1
1
0
2
1
2
0
2
2
1
1
0
1
2
1
2
1
1
2
1
1
1
1
1
2
2
1
0
2
2
1
2
1
2
1
0
1
0
3
1
1
2
0
2
1
3
1
1
0
1
1
1
2
1
1
0
1
2
0
1
1
2
1
0
1
1
1
0
1
2
0
1
1
0
1
2
1
2
2
1
2
0
1
2
2
0
1
1
1
2
1
1
1
2
0
1
2
0
1
2
1
2
1
1
1
2
2
2
2
2
0
1
1
2
1
1
1
2
1
1
1
3
1
1
1
1
1
1
1
1
1
2
2
1
0
1
2
1
2
1
1
2
0
1
1
1
1
2
1
2
1
0
1
1
1
1
1
2
1
2
1
1
1
2
1
1
1
1
0
1
1
1
1
1
1
1
1
1
2
1
2
2
2
1
1
1
2
3
1
0
1
1
1
2
0
0
0
3
1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
1
0
0
1
1
2
1
0
1
2
1
2
1
0
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
0
0
2
2
1
1
1
1
1
0
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
0
1
2
2
2
2
2
1
0
1
2
2
1
1
1
1
1
0
2
2
1
1
1
1
0
1
1
1
2
1
1
1
2
2
1
1
0
0
1
1
1
1
2
2
1
1
1
1
0
0
0
2
1
1
2
1
0
2
1
0
1
2
1
1
1
0
2
2
1
1
1
0
2
1
2
2
1
1
1
1
1
1
1
2
2
0
1
2
1
1
0
1
2
1
1
2
1
1
1
1
3
1
2
1
1
2
2
1
0
1
0
0
1
2
2
1
1
2
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
0
0
1
2
0
2
2
1
0
1
1
1
2
0
1
1
1
1
2
2
2
2
1
0
0
1
1
1
1
2
1
2
2
1
2
0
1
3
1
0
2
2
2
0
0
1
2
1
0
2
1
1
1
0
1
1
1
0
1
0
1
2
1
1
2
2
1
0
0
1
1
1
2
1
1
1
1
2
1
1
1
1
1
0
1
0
0
1
0
0
0
1
2
1
2
2
1
1
1
1
2
0
1
0
2
1
0
1
0
4
1
1
0
0
2
1
0
0
0
0
1
2
1
0
0
1
1
1
1
1
1
2
1
1
0
0
1
0
0
0
2
2
0
2
0
1
2
1
1
2
1
1
1
2
1
0
1
2
1
1
1
1
2
1
1
1
2
1
0
1
1
2
5
1
2
2
2
2
1
2
1
1
0
1
1
1
1
1
0
1
2
1
1
2
1
2
0
1
1
2
1
1
1
1
0
1
1
1
0
1
0
1
0
1
2
0
1
1
1
1
0
2
1
1
1
0
1
1
1
1
1
0
1
1
0
1
0
1
1
1
1
2
1
2
1
1
0
0
1
1
1
1
2
2
2
1
0
1
1
0
1
1
1
1
1
1
1
0
1
1
1
1
1
0
1
1
0
0
1
0
2
1
0
1
0
1
1
1
2
1
1
2
1
1
2
0
2
1
2
1
1
1
1
1
0
2
2
0
2
0
1
1
0
2
2
1
1
0
1
1
2
1
1
1
2
1
0
1
1
1
2
1
1
0
1
0
2
1
2
1
1
2
1
0
3
1
0
1
1
1
2
1
1
1
1
1
1
3
1
1
2
2
1
1
1
0
3
1
1
0
0
1
1
0
1
2
1
1
0
1
2
1
0
0
1
1
1
2
2
1
0
1
2
0
1
2
1
2
0
0
2
1
0
1
0
3
2
2
1
0
2
0
0
1
1
1
0
1
1
0
1
1
2
2
1
1
1
0
0
1
1
0
1
1
1
1
1
1
0
2
1
1
1
1
1
1
2
1
1
0
1
2
2
2
2
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
0
0
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
2
1
1
0
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
2
1
2
1
1
1
1
1
0
2
1
1
1
0
1
1
1
2
0
0
1
2
1
2
1
1
2
1
1
1
1
1
1
0
1
1
2
0
0
2
1
1
0
0
1
2
1
2
1
1
1
1
1
1
1
1
0
1
1
2
1
0
2
1
2
1
1
2
2
0
1
1
1
0
1
1
1
1
0
1
1
1
1
2
1
1
1
1
1
2
2
2
0
2
2
0
1
1
1
1
2
1
2
1
1
1
1
2
0
1
1
1
2
1
1
0
1
1
2
1
2
0
2
0
0
1
1
1
1
1
1
1
1
1
1
1
0
1
2
1
2
2
0
2
2
2
0
2
1
0
0
1
1
1
1
2
1
0
2
2
2
1
2
0
2
1
0
1
0
2
1
0
1
0
2
1
2
3
1
2
1
0
1
2
0
1
0
2
0
2
1
4
1
1
1
1
1
0
1
0
1
2
0
2
3
1
1
0
1
2
1
1
0
1
1
1
1
0
1
2
0
1
1
1
1
0
2
1
0
1
0
1
1
1
1
1
1
1
1
3
1
1
2
1
1
0
2
0
1
1
1
0
0
1
1
1
1
1
2
1
1
1
1
2
1
1
2
0
2
1
1
1
1
2
1
1
0
1
0
1
2
3
2
1
0
2
2
1
1
1
1
2
1
2
0
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
0
0
0
1
1
2
2
1
1
2
2
1
1
0
1
0
2
2
1
1
2
1
1
2
0
1
1
1
1
1
1
1
1
2
1
1
2
2
1
2
1
5
0
1
1
2
1
1
1
0
0
2
1
0
2
2
1
2
0
2
0
2
1
1
2
0
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
0
2
1
1
1
1
1
0
2
0
1
2
1
0
2
0
1
0
1
1
1
0
1
1
1
2
1
1
1
1
0
0
2
2
1
0
1
1
1
2
1
0
1
1
1
1
1
1
1
1
1
1
2
0
2
1
1
1
1
1
1
1
2
2
0
1
1
1
1
1
1
1
2
1
1
1
0
0
1
2
1
0
1
0
1
2
1
1
0
1
2
1
1
0
1
0
2
0
2
0
0
1
2
0
2
1
0
0
0
2
1
0
1
1
0
1
2
1
1
1
1
1
1
1
1
0
0
2
1
0
1
2
1
1
1
1
1
1
1
1
2
2
1
0
1
1
1
1
2
2
2
0
0
0
0
1
0
1
1
1
1
2
0
0
1
2
1
1
0
1
1
0
1
1
1
2
1
1
1
0
1
1
2
1
2
0
2
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
0
2
1
1
1
2
0
2
1
1
2
1
2
1
1
1
0
1
1
1
0
1
1
1
1
2
1
0
2
1
2
1
2
0
2
1
10
1
3
1
1
1
2
1
2
0
2
0
1
1
0
1
1
2
1
1
1
2
1
2
1
0
1
1
1
1
1
2
1
1
1
1
1
1
1
0
1
0
1
1
2
1
0
1
2
1
1
2
1
1
1
1
1
1
1
1
1
0
2
0
2
0
1
1
1
1
1
2
1
1
1
1
1
2
2
0
1
2
0
1
2
1
1
1
0
1
1
2
1
1
2
0
2
1
2
2
1
1
2
2
1
2
1
1
1
1
2
1
2
1
2
1
1
1
2
2
2
1
1
2
1
1
1
0
0
1
1
1
1
1
1
1
1
0
0
1
0
1
2
2
1
1
2
2
1
2
1
1
2
1
1
1
1
0
1
1
0
0
1
2
1
0
0
2
2
1
2
1
1
1
1
0
1
1
2
1
1
1
0
2
1
0
2
1
2
2
2
1
0
2
1
2
1
1
1
1
1
1
0
1
2
2
2
1
2
1
1
1
2
1
2
2
1
2
3
2
1
1
1
1
1
0
2
1
0
0
2
1
1
1
2
1
1
0
0
1
1
1
1
1
1
1
0
1
1
2
0
1
1
0
0
1
1
1
1
1
2
0
2
1
1
1
1
1
0
4
1
0
1
2
1
1
2
2
1
1
0
1
2
2
1
1
2
1
1
1
0
0
1
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
0
1
1
0
1
1
1
2
1
1
2
1
1
0
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
2
3
1
1
1
1
1
1
1
1
1
1
2
1
1
0
2
1
1
1
1
2
0
2
1
2
1
0
1
1
1
1
1
2
1
1
2
2
0
2
1
1
1
1
1
0
2
0
0
1
2
1
1
1
1
1
0
2
1
0
1
1
1
1
2
2
1
0
2
1
1
2
1
1
1
1
1
1
2
1
1
0
2
1
1
1
1
1
0
2
1
0
0
2
1
1
0
1
1
1
1
0
1
0
0
1
1
0
1
1
2
1
1
1
1
1
1
0
1
0
1
2
0
1
1
2
1
2
1
1
1
1
1
2
1
2
1
2
1
1
1
1
0
1
0
1
0
1
1
2
0
1
1
1
1
2
1
2
0
1
1
1
1
2
1
1
1
1
1
1
1
0
0
2
1
1
2
1
1
2
2
2
1
1
1
0
0
1
1
0
1
2
1
1
1
0
0
2
1
0
1
2
2
0
1
1
0
1
1
1
1
1
1
0
1
1
1
2
1
1
1
2
2
0
1
1
1
1
1
2
1
1
2
1
0
1
0
1
1
1
1
1
2
2
1
2
2
2
2
1
1
1
1
2
0
3
0
1
1
1
1
2
2
3
1
2
1
2
1
1
2
1
1
1
2
2
1
0
1
1
1
1
0
0
1
0
1
0
2
2
0
0
1
1
1
1
1
1
1
1
0
2
1
1
1
1
0
1
1
2
1
2
0
1
2
1
2
0
1
1
1
2
1
0
1
0
1
1
2
0
1
1
1
1
0
1
1
1
0
2
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
0
0
1
1
1
1
1
1
2
0
2
1
1
1
1
1
2
1
0
1
1
0
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
2
1
1
1
0
0
1
1
1
1
2
1
1
0
2
2
1
2
1
1
1
1
2
1
2
2
1
0
1
1
1
2
1
0
1
0
1
1
2
1
0
0
1
0
1
1
1
1
1
1
1
1
2
2
1
1
1
2
0
1
2
0
0
2
1
1
1
2
2
2
2
1
1
0
1
1
1
0
0
1
1
2
0
1
1
1
2
0
1
1
2
2
1
2
1
1
1
2
1
1
1
0
1
1
2
1
1
1
1
1
1
1
2
1
1
0
1
1
2
1
2
2
1
2
2
1
2
1
1
2
1
0
2
1
1
1
2
1
2
0
0
2
2
1
1
2
1
1
1
0
1
0
1
2
0
1
0
1
1
1
0
1
2
1
0
1
0
1
2
1
1
1
1
1
1
0
3
2
0
1
0
2
1
1
5
0
2
2
1
1
2
1
1
1
1
0
1
2
1
1
1
0
1
2
1
1
2
0
2
2
1
1
2
2
2
1
1
0
1
2
1
2
1
1
0
2
2
0
2
0
0
2
1
1
2
1
1
1
2
1
1
1
1
0
1
1
1
1
0
0
1
0
0
2
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
0
1
2
2
0
2
2
1
2
1
2
2
3
1
2
1
1
1
2
1
2
2
2
1
1
0
1
1
1
1
1
1
1
1
1
2
2
2
1
2
1
1
1
1
2
2
1
1
1
2
1
1
1
1
1
1
2
1
2
1
1
1
2
1
1
1
2
0
1
0
2
2
1
2
1
1
1
1
1
3
1
1
0
1
2
0
0
0
2
1
1
0
1
0
1
1
0
1
2
1
1
1
2
2
2
1
0
1
0
1
1
1
1
1
1
1
2
1
1
0
1
1
1
1
2
1
1
1
2
0
1
1
2
1
0
1
2
1
1
1
1
1
1
1
1
0
0
0
1
2
1
1
2
1
2
2
2
2
1
1
1
1
0
0
0
1
1
1
0
1
1
2
1
1
2
1
1
1
1
1
2
1
1
1
1
0
3
2
2
0
1
0
1
1
2
1
0
2
1
1
1
1
1
2
2
0
1
2
1
1
2
0
2
1
2
1
1
1
0
1
1
0
1
1
1
2
1
2
2
1
1
1
0
2
1
1
1
1
1
1
2
2
1
1
1
0
1
2
1
1
1
0
0
0
2
1
1
1
0
1
1
1
2
1
1
1
1
1
2
2
2
1
1
0
1
0
0
1
1
2
2
2
2
1
1
2
1
1
0
2
1
1
0
2
2
0
1
1
2
1
1
1
2
0
1
0
1
0
1
1
2
2
1
2
2
1
2
2
1
2
1
0
0
1
2
0
2
1
1
1
1
2
0
1
1
0
1
2
1
0
1
2
1
0
1
0
2
1
2
0
1
1
2
0
1
1
2
1
1
1
1
0
1
1
2
1
1
0
1
1
0
1
1
1
1
0
1
2
0
2
1
2
1
1
1
1
2
0
1
0
1
1
1
1
2
0
2
1
2
1
1
1
2
1
0
1
0
1
1
1
1
0
0
1
1
1
1
0
1
2
1
1
1
1
1
1
1
2
1
0
1
2
2
0
1
2
1
1
1
2
2
2
2
2
0
0
0
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
0
1
0
1
1
0
0
0
1
0
1
0
1
1
1
3
1
1
0
1
1
0
1
1
1
1
1
2
1
2
1
2
1
1
1
0
0
0
2
1
0
1
1
1
1
0
1
2
1
1
1
1
0
3
2
1
2
1
1
2
0
1
2
1
1
1
1
1
1
1
2
2
1
1
0
1
2
1
0
1
1
1
2
1
2
1
1
1
0
0
2
1
1
2
2
1
1
1
1
2
2
0
2
2
1
1
2
1
1
2
2
0
1
2
1
1
1
2
1
1
4
2
2
2
1
1
0
1
1
0
1
2
1
1
2
1
1
1
1
0
1
0
1
1
2
1
1
2
1
1
0
1
2
1
2
0
1
2
1
1
1
1
1
2
1
1
1
2
2
0
1
2
1
1
0
0
2
1
1
1
2
1
1
1
1
1
1
1
1
0
1
0
2
0
0
2
0
1
2
0
2
2
1
1
1
2
1
0
2
1
1
1
1
1
1
1
2
1
0
1
1
2
0
0
0
2
1
0
1
0
0
2
1
1
2
2
0
1
0
2
1
2
2
3
1
2
1
1
1
0
1
0
2
0
0
2
1
2
2
1
1
1
1
1
1
0
0
1
1
1
0
1
1
1
2
1
1
2
1
0
2
1
1
1
0
2
1
1
1
0
0
2
0
1
2
1
1
2
2
1
0
1
1
1
1
2
1
1
2
1
1
0
0
3
2
2
1
0
1
1
1
2
2
1
1
1
1
1
1
2
0
1
0
1
1
2
1
1
1
0
0
1
1
1
1
1
2
2
1
2
0
1
1
1
0
0
2
1
1
1
1
1
2
2
1
1
2
1
1
1
2
0
3
1
2
1
1
1
1
2
0
2
1
0
1
1
1
0
2
1
1
2
0
2
1
1
1
2
2
0
1
1
2
1
2
1
1
1
0
1
1
2
2
1
1
1
1
2
1
2
1
2
1
1
1
1
0
1
2
1
1
3
2
1
1
1
2
2
0
1
1
0
1
1
0
0
0
0
2
1
1
1
1
1
1
1
1
1
2
2
1
1
1
2
1
1
1
0
1
1
1
1
2
2
1
1
2
1
1
0
1
0
1
1
1
1
0
1
3
0
2
1
0
1
2
1
1
1
1
1
1
1
1
2
0
1
1
1
1
1
2
2
1
0
1
1
1
1
1
1
1
2
0
1
0
0
1
1
2
0
1
2
0
1
1
1
1
1
0
2
1
1
1
2
0
0
0
1
1
1
2
1
1
1
2
1
1
2
1
0
1
2
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
2
2
1
1
1
0
1
1
1
1
1
0
2
1
2
1
0
1
0
1
1
1
2
1
1
1
2
0
1
0
1
1
2
1
2
2
1
2
0
1
1
1
0
2
0
1
2
1
0
2
2
0
0
1
1
1
1
2
1
2
2
2
1
1
1
2
2
0
1
2
1
2
2
0
1
2
0
0
1
1
1
2
1
1
1
1
1
1
0
0
2
1
0
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
0
1
1
0
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
2
1
2
1
1
2
2
1
2
0
1
2
2
1
0
1
0
1
1
1
1
1
1
2
1
1
2
1
4
0
2
1
1
0
1
2
1
1
1
1
0
0
2
1
1
1
2
1
1
1
0
1
2
2
1
1
1
1
0
1
2
1
1
1
2
2
1
2
0
0
0
2
1
2
2
0
0
0
0
2
2
1
1
2
0
0
2
1
2
1
1
2
1
2
1
1
2
1
1
2
1
1
2
0
1
2
1
2
1
1
1
2
0
1
1
0
1
0
0
0
1
1
2
1
1
1
1
1
3
2
1
1
1
0
2
1
1
1
0
2
0
1
1
2
1
1
1
2
1
1
0
2
1
0
2
1
2
1
0
1
1
1
0
1
1
2
1
1
1
1
1
0
1
0
1
0
1
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
2
0
2
1
1
2
2
1
0
2
2
0
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
0
1
1
1
2
0
0
1
1
1
1
1
1
2
1
1
1
2
2
1
2
1
2
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
2
0
1
1
1
1
0
1
2
1
0
1
0
2
1
1
1
1
2
3
1
1
1
1
0
1
0
1
2
1
2
1
0
1
2
1
2
1
2
1
1
1
2
1
1
1
0
1
1
1
1
1
4
1
1
1
2
2
1
2
1
1
2
2
1
1
2
0
1
1
1
1
2
2
2
1
1
1
1
2
0
2
1
1
1
1
1
1
1
1
2
1
2
2
1
1
1
0
0
1
2
1
1
1
1
2
2
2
1
1
1
1
2
1
1
2
2
2
1
1
1
2
1
0
1
2
2
0
0
2
1
1
1
0
1
1
1
1
2
0
2
1
0
2
1
0
1
2
1
1
1
1
1
2
1
0
1
1
2
2
1
1
0
2
2
2
1
1
2
2
2
0
1
2
1
0
1
1
0
1
1
1
1
1
0
2
0
1
0
1
1
0
1
1
1
2
2
1
1
2
2
1
1
1
2
1
1
0
0
1
0
1
2
2
1
1
1
1
1
0
2
1
1
2
1
1
1
1
1
1
2
1
1
0
1
1
2
1
1
0
1
1
1
1
1
1
1
1
0
1
1
1
1
0
1
1
1
1
0
1
0
1
0
1
2
1
1
0
1
1
1
1
1
2
1
1
1
1
1
1
0
2
1
1
0
1
2
1
2
2
0
1
1
1
1
2
1
2
1
1
1
1
2
1
1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
0
1
1
2
3
1
2
1
1
0
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
2
1
1
0
1
1
1
2
2
2
0
1
1
1
1
1
1
1
1
0
1
0
1
1
1
1
0
1
1
2
1
1
1
1
1
2
1
1
2
1
1
1
0
1
1
0
0
1
2
1
2
0
0
1
1
1
1
2
0
1
1
0
0
1
1
1
1
1
0
2
2
1
2
2
0
2
1
0
2
2
1
1
0
1
1
1
1
2
0
1
1
2
1
1
2
0
1
0
0
2
1
0
1
1
1
2
0
1
2
2
0
1
2
1
2
2
1
1
1
1
0
1
0
1
1
2
1
1
1
1
1
1
1
1
1
2
0
1
0
2
1
1
0
0
2
1
2
2
1
1
3
0
0
1
0
1
0
2
1
1
1
1
0
1
1
2
1
1
0
1
2
1
0
0
1
2
1
0
1
2
1
0
1
2
1
2
0
0
1
2
1
2
1
1
2
1
1
2
1
2
1
1
0
1
0
2
1
1
2
2
0
0
1
1
2
1
1
1
1
1
1
2
1
2
1
0
1
1
1
1
1
1
2
2
2
1
1
1
2
2
1
1
1
1
1
1
1
0
1
1
1
1
1
0
2
1
1
1
1
1
0
1
1
2
2
1
2
1
3
1
1
1
2
2
1
1
0
1
2
1
1
1
0
2
1
1
1
1
1
2
1
2
0
2
1
0
1
2
2
1
0
1
2
2
2
1
2
2
2
1
1
1
1
1
0
1
2
1
1
0
1
2
2
1
1
0
2
1
1
0
1
2
0
1
1
1
2
0
1
1
1
1
1
1
1
1
1
2
0
1
2
2
1
2
0
1
1
1
2
2
1
2
2
2
1
1
2
1
2
0
1
0
1
2
1
1
1
0
1
1
0
1
1
2
2
1
1
2
1
1
1
1
2
0
1
2
2
1
1
1
2
1
2
0
1
1
1
2
0
0
1
2
1
1
0
1
1
2
0
1
1
1
1
1
1
1
2
2
1
1
0
1
1
0
1
1
1
1
2
2
2
2
0
2
2
2
0
1
2
1
0
1
1
2
1
1
1
1
1
0
1
1
0
0
1
7
2
2
0
1
1
0
0
1
1
1
1
1
1
1
1
2
0
1
1
1
0
0
2
1
2
1
1
0
2
1
1
1
0
1
1
1
1
1
1
1
0
1
1
1
2
1
1
1
1
1
2
1
1
1
0
1
1
0
1
1
0
1
1
2
2
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
2
1
0
1
1
1
2
1
1
1
2
1
0
1
2
2
0
2
0
1
1
0
2
1
1
1
2
1
2
1
2
2
0
0
0
0
1
1
0
1
1
1
1
0
1
2
1
2
2
1
1
1
1
1
0
1
2
2
1
1
1
0
1
1
2
0
1
1
1
1
2
0
1
1
0
2
1
1
2
1
2
2
1
0
1
1
0
1
1
2
1
1
2
2
2
2
1
1
1
1
0
1
0
1
1
1
1
2
1
0
2
1
2
1
1
1
2
1
1
1
2
2
1
0
1
1
2
0
2
1
1
1
1
1
1
2
2
1
1
2
2
1
0
2
1
2
1
2
1
1
1
1
2
1
1
1
2
0
1
0
1
2
1
1
1
1
1
1
2
1
1
0
1
0
1
0
0
1
1
2
1
1
1
0
1
1
1
1
1
2
1
1
1
1
1
1
0
2
2
0
1
2
1
0
1
1
0
2
1
1
1
2
1
2
1
1
0
1
1
1
1
1
1
1
2
1
0
1
1
1
1
0
0
1
0
0
2
1
0
1
1
1
1
1
1
0
1
1
1
2
1
1
1
0
0
1
0
0
1
1
0
2
2
2
2
2
2
1
1
1
1
1
2
1
1
1
1
1
0
1
1
1
1
1
1
0
1
0
1
1
1
1
0
1
1
2
0
1
2
1
1
1
1
1
0
1
2
1
1
3
1
2
1
2
1
1
1
1
2
2
0
2
0
1
1
1
1
0
2
1
1
2
1
1
0
0
0
2
2
2
0
2
0
1
0
1
1
2
1
0
2
2
2
1
1
1
1
0
1
0
2
1
1
0
1
2
1
2
2
2
2
2
1
2
0
2
0
2
1
1
1
1
1
1
2
1
1
1
1
1
2
2
2
1
1
1
1
1
1
3
0
0
2
1
1
2
1
1
1
1
1
0
0
3
1
1
1
1
1
2
2
2
2
2
1
1
1
1
1
1
1
0
1
1
2
2
2
1
1
1
1
1
1
1
0
1
1
0
1
2
0
2
1
1
1
1
2
2
0
2
1
1
0
2
0
1
1
0
0
1
1
1
2
1
2
1
0
0
1
1
2
1
1
0
0
1
0
2
1
1
2
2
1
2
0
1
1
2
2
1
1
1
2
1
1
0
1
1
2
1
1
0
1
0
1
1
2
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
0
1
1
0
1
1
1
2
1
1
2
2
2
2
1
1
0
1
1
2
1
1
1
1
2
1
1
1
1
1
0
1
1
1
1
1
1
0
2
1
1
2
1
0
0
1
0
2
1
1
1
2
3
2
1
1
1
1
2
1
1
2
0
1
2
1
0
0
1
0
1
1
1
1
2
0
2
1
1
1
2
1
0
1
1
0
2
1
0
1
1
3
1
1
1
1
1
0
1
2
2
2
1
0
1
1
2
1
1
2
1
1
2
0
1
1
1
1
0
1
1
0
2
1
2
1
2
0
1
1
0
1
1
0
2
2
1
1
1
1
1
1
1
1
1
2
1
1
0
0
2
1
1
1
1
2
2
1
2
0
1
2
0
2
2
0
1
1
2
1
0
2
1
1
2
1
2
1
1
2
2
1
0
1
2
1
1
0
0
2
1
1
1
1
2
0
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
2
0
2
2
1
1
2
1
0
0
1
2
1
1
1
2
0
1
2
0
1
1
2
1
1
2
2
1
1
1
1
1
2
1
1
1
2
1
2
2
1
2
1
2
2
1
0
0
2
1
1
1
1
1
1
1
1
1
0
1
1
1
1
2
0
0
1
1
2
1
2
1
0
2
1
1
1
2
2
2
0
0
2
1
0
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
0
1
2
1
0
1
1
1
1
2
1
2
1
1
1
1
2
2
1
1
1
1
0
1
1
1
0
1
0
1
2
0
1
1
1
1
0
1
1
2
1
1
0
2
1
1
1
1
1
1
0
2
1
1
1
1
1
1
1
1
1
0
2
1
1
1
1
1
2
2
2
0
1
1
1
2
1
1
0
1
1
1
1
1
0
1
1
2
1
1
1
1
1
1
0
2
1
0
1
1
1
1
2
1
0
1
1
1
3
0
1
2
1
1
1
1
1
1
2
1
1
0
1
2
1
2
2
2
0
2
1
1
1
0
1
1
2
1
1
2
1
2
1
1
0
1
0
1
1
0
1
0
0
0
0
1
0
0
0
1
1
1
1
0
2
1
1
1
1
2
0
2
1
2
0
1
1
0
1
1
1
1
1
1
1
0
1
2
1
1
1
1
1
1
1
0
1
1
1
2
0
0
1
2
0
1
2
1
1
1
1
1
0
0
1
1
1
1
1
1
1
0
2
2
1
1
1
1
2
1
1
0
1
2
2
1
1
1
2
1
2
2
0
2
1
2
2
1
1
3
0
1
2
2
1
1
1
1
1
1
1
1
1
2
1
2
1
2
1
1
2
1
2
0
1
1
2
0
1
0
1
0
1
1
0
2
1
0
1
1
2
1
1
0
2
1
0
1
1
1
1
0
1
0
0
2
2
1
1
1
1
2
1
1
0
2
1
0
1
1
1
2
1
2
2
0
2
2
1
1
1
0
1
1
1
1
1
1
1
1
0
1
1
1
1
1
2
1
0
0
1
0
1
1
1
1
3
3
0
1
1
1
1
2
0
2
1
1
0
1
1
1
0
1
1
2
1
1
1
1
1
0
0
0
1
2
1
0
2
1
1
2
2
1
0
2
1
0
1
1
0
1
1
2
1
2
1
2
2
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
2
1
0
2
2
1
1
1
1
1
2
1
1
1
1
0
1
1
1
2
1
1
0
1
1
5
1
1
0
2
1
1
1
1
1
0
1
1
0
1
0
1
1
1
2
1
2
2
2
1
1
1
0
0
1
1
2
1
1
1
3
1
1
1
0
0
1
1
2
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
0
2
1
1
1
1
2
1
1
1
1
2
1
2
1
1
0
2
1
1
0
2
1
2
2
1
2
1
0
2
2
1
2
2
1
2
2
1
1
1
1
2
0
1
1
0
2
1
0
2
1
1
0
2
0
2
2
0
1
1
1
1
0
2
1
2
1
1
2
2
3
1
2
1
1
1
1
2
1
0
1
1
1
2
2
1
0
1
2
1
2
0
2
2
2
0
1
1
1
1
1
2
1
2
2
1
2
1
1
1
2
1
1
1
1
0
1
2
1
1
1
1
0
2
2
1
0
1
2
0
2
0
1
2
1
1
2
1
2
1
1
1
1
1
0
1
2
2
1
0
1
1
2
1
1
0
2
1
2
2
0
1
2
1
1
1
2
1
1
2
2
2
1
2
1
1
1
2
1
1
0
1
1
2
0
1
0
2
2
1
1
1
1
1
1
1
1
1
1
0
1
1
0
1
1
2
1
1
1
0
0
2
2
0
1
0
0
1
1
1
1
2
1
1
1
1
1
2
1
1
3
0
2
0
1
1
0
1
0
2
2
1
1
1
1
2
1
0
2
0
2
1
0
1
1
1
1
1
1
2
0
3
1
2
2
2
2
1
0
1
1
1
0
2
1
1
1
0
2
2
0
2
1
2
2
1
2
1
1
1
1
1
1
0
1
1
2
1
0
1
2
1
1
0
1
1
1
0
1
1
0
1
0
1
2
1
2
1
1
1
1
1
2
2
1
1
0
0
0
0
1
1
2
3
0
2
2
2
1
2
2
0
1
2
1
1
1
1
0
0
1
0
1
1
1
0
1
1
1
2
0
2
0
1
1
0
0
1
1
0
1
1
2
1
1
1
2
0
1
1
1
1
2
2
1
2
2
0
1
1
2
1
2
1
0
2
1
1
1
1
1
1
2
1
1
0
1
0
1
0
2
1
1
1
1
1
0
1
1
1
1
2
2
2
1
1
2
2
1
1
2
2
1
0
2
2
1
1
1
2
2
1
1
1
2
1
2
1
1
1
0
1
1
1
1
0
2
1
1
1
0
2
1
0
1
0
1
1
1
1
2
2
2
1
2
2
1
0
1
1
1
1
0
1
1
2
2
1
1
1
1
0
2
2
1
0
1
1
1
1
1
1
1
0
1
0
1
2
2
1
1
2
0
1
0
1
1
1
2
0
1
2
1
1
1
1
2
3
1
1
2
1
2
1
1
2
2
2
2
1
1
1
2
1
2
1
1
2
1
0
2
2
2
1
2
2
0
0
0
1
1
0
1
2
1
2
2
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
0
1
1
1
1
2
2
2
1
1
1
4
1
1
2
1
1
1
0
0
1
1
1
2
1
1
1
2
0
1
1
2
1
2
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
0
1
1
2
1
1
1
1
1
0
0
1
1
2
1
1
1
0
2
4
1
1
1
1
1
2
1
1
1
2
2
1
1
0
1
2
1
2
1
1
1
0
1
2
2
2
2
1
2
2
1
1
1
1
2
1
1
1
2
3
1
2
1
0
2
2
0
1
2
1
0
1
1
1
0
0
2
2
2
2
2
1
1
0
2
1
1
2
1
1
1
1
0
1
1
1
2
1
1
1
2
2
2
1
1
2
1
1
1
2
1
3
1
1
0
1
2
2
1
1
1
1
1
1
0
0
1
2
1
2
1
1
2
1
1
2
1
1
0
1
0
1
1
1
2
1
1
1
1
1
1
1
0
1
2
1
0
2
1
1
1
1
1
1
1
1
0
1
1
2
1
1
1
1
2
1
1
3
0
1
1
1
2
2
2
2
1
2
2
2
0
1
1
0
2
2
2
1
1
0
2
1
1
2
2
0
1
0
1
0
1
1
1
1
1
1
0
2
1
0
2
1
1
3
1
1
1
1
1
2
1
0
1
1
1
1
1
2
0
1
1
2
2
0
1
0
1
1
0
1
1
1
2
0
0
1
1
1
1
1
0
0
1
2
1
1
2
1
1
1
1
2
0
1
2
1
1
2
0
1
1
2
2
1
1
0
2
1
1
2
1
2
2
1
1
1
0
3
1
2
2
2
2
1
2
0
1
1
1
1
1
1
1
2
2
2
1
1
2
1
1
1
2
1
3
1
0
1
0
0
2
0
2
1
1
2
1
2
1
1
2
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
0
0
1
2
2
1
1
3
2
0
0
1
1
1
2
1
1
1
1
1
0
1
1
0
1
2
1
2
1
0
1
1
1
1
1
2
1
0
1
0
1
1
1
1
2
2
2
1
2
1
0
1
2
2
1
2
1
1
1
1
1
1
1
1
1
0
1
2
1
1
2
1
1
2
1
1
1
2
1
1
0
1
1
0
2
1
0
1
1
1
0
2
1
2
1
2
1
1
1
1
1
0
1
1
0
0
1
1
2
2
1
1
1
1
1
2
0
0
1
1
3
1
1
1
1
1
0
2
0
1
0
1
1
1
0
2
1
1
0
1
2
1
1
2
2
1
2
1
0
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
2
1
1
1
2
1
2
1
1
2
2
1
1
1
0
0
1
1
1
0
1
0
1
0
1
1
1
1
1
0
1
0
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
0
0
1
1
1
1
2
1
1
0
1
1
1
1
2
2
2
1
1
1
2
1
2
2
1
1
1
1
2
0
1
0
2
1
1
1
1
2
2
1
2
2
0
1
1
1
1
1
0
0
1
0
2
2
1
1
1
1
1
1
1
2
2
2
0
2
1
1
0
1
1
0
1
2
1
1
2
0
0
1
2
2
1
1
1
2
1
1
0
1
1
1
1
1
1
1
0
1
1
1
1
1
2
2
2
1
1
1
2
1
1
1
1
1
1
0
1
1
0
1
0
0
1
1
2
1
2
1
1
2
1
1
1
1
1
2
0
2
1
0
1
1
2
2
0
1
2
4
1
1
1
0
1
2
1
1
0
1
1
2
1
1
1
0
1
1
2
1
2
2
2
0
2
2
1
1
0
2
2
1
2
1
1
1
2
1
1
1
1
1
2
2
0
1
2
2
2
3
1
1
2
2
1
1
1
0
1
1
0
2
1
1
0
1
1
2
0
2
2
2
2
0
4
1
1
0
1
1
0
2
2
0
1
3
1
0
0
1
1
1
0
1
1
1
1
1
0
1
0
1
1
1
2
1
1
2
1
2
2
0
0
0
1
1
1
1
1
0
2
2
1
2
2
2
1
2
1
1
1
2
1
2
1
2
1
0
1
1
1
1
1
1
0
1
2
2
1
1
2
1
1
1
1
1
1
1
1
0
1
1
1
1
1
0
1
1
1
1
1
1
2
2
1
1
1
2
1
1
1
1
0
1
2
0
1
1
1
1
1
1
2
1
1
1
1
1
1
0
1
1
2
1
2
1
1
1
0
2
1
1
1
0
1
0
1
1
1
1
2
1
1
1
2
1
1
2
2
1
1
0
1
1
1
1
2
1
3
1
0
1
1
1
1
0
0
2
1
1
2
2
2
0
0
2
2
1
0
0
2
1
1
1
1
2
1
2
1
1
1
0
1
0
1
1
1
1
2
1
1
1
1
1
2
1
0
1
2
2
0
2
2
1
1
0
1
1
2
2
2
2
2
1
1
1
2
2
1
2
0
1
0
1
2
1
1
1
2
1
1
1
0
2
0
1
1
1
2
2
2
1
1
1
1
1
0
0
1
1
2
2
1
1
1
0
1
1
1
1
1
0
1
0
2
1
0
1
1
1
1
1
0
1
1
2
1
1
1
1
1
1
1
1
1
1
0
2
0
2
1
0
2
1
0
1
2
1
1
0
2
0
1
1
0
1
1
0
2
1
1
0
1
2
1
1
1
1
2
2
2
1
2
0
2
1
1
1
1
0
0
1
1
4
2
2
2
2
1
2
1
0
0
1
1
1
2
1
1
1
1
2
1
1
2
0
1
1
2
2
1
2
1
1
1
1
1
1
1
2
0
1
1
0
0
1
0
2
1
1
1
2
2
1
1
1
1
1
1
0
1
0
1
0
2
1
1
1
1
1
2
1
1
1
1
2
1
1
3
1
1
2
2
1
1
1
0
0
1
0
0
2
1
1
0
1
1
1
1
0
1
2
1
1
1
1
1
1
2
1
2
2
0
2
2
2
2
3
0
0
0
1
1
0
1
1
0
0
0
1
1
1
2
0
0
2
1
1
1
1
1
1
1
0
1
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
2
1
1
2
1
1
2
0
1
2
1
0
2
0
1
0
1
2
0
1
1
0
1
1
0
1
1
1
1
1
0
1
2
2
1
1
1
0
0
2
2
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
0
2
1
1
1
1
1
0
2
1
1
1
1
1
0
1
1
1
0
2
1
2
2
0
2
0
0
2
1
1
2
1
0
2
1
1
1
0
2
1
1
1
2
0
1
2
1
1
2
1
1
1
1
1
0
1
1
2
1
1
0
1
2
2
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
0
0
2
1
0
1
1
2
1
1
1
1
1
2
0
1
2
2
1
1
3
1
0
2
0
0
2
1
1
0
2
2
1
1
1
2
1
0
0
1
0
2
2
1
0
0
1
1
1
0
1
0
1
1
1
2
0
1
1
1
1
1
0
1
2
1
0
0
1
1
1
2
0
1
1
2
2
1
1
2
2
2
1
1
1
0
1
0
1
0
1
2
2
1
2
1
1
1
1
2
1
0
1
1
1
1
0
1
1
1
2
0
2
2
1
1
1
1
1
1
1
2
1
1
3
1
0
0
2
1
1
1
0
0
1
2
1
1
2
1
1
1
0
0
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
0
0
2
1
1
1
1
1
2
2
1
1
1
1
3
2
1
1
1
0
1
2
0
1
1
1
2
0
1
0
0
0
1
2
0
2
0
1
1
0
1
1
0
1
1
1
1
0
2
1
1
1
0
1
0
0
0
1
1
2
1
0
2
0
2
1
1
1
1
2
2
1
1
2
1
1
1
2
1
1
2
1
1
1
1
1
2
2
0
1
1
1
2
1
1
1
1
1
0
1
2
2
2
1
0
1
1
1
2
3
0
1
1
1
1
2
2
2
2
1
1
1
1
1
0
1
1
2
1
1
0
1
2
2
2
1
2
1
0
0
1
1
1
1
1
1
1
1
2
0
1
1
2
1
1
1
1
0
1
1
1
1
1
1
0
0
1
2
2
1
1
0
1
1
1
1
2
1
0
1
1
2
1
1
1
1
0
1
1
1
2
2
1
0
1
1
1
1
1
2
1
2
1
1
2
0
0
0
0
3
0
1
0
2
1
2
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
0
1
0
1
1
0
0
1
2
1
1
1
1
1
0
2
1
2
1
1
0
1
2
0
0
1
1
1
2
2
1
0
0
1
2
2
1
2
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
2
2
1
1
3
1
1
1
0
1
2
1
0
1
1
2
1
0
0
1
1
0
2
1
1
1
1
2
0
0
2
1
0
1
1
2
1
1
2
1
1
1
1
2
1
1
2
0
1
2
1
1
2
2
0
2
1
1
0
0
0
2
2
2
2
2
1
2
1
1
1
1
1
2
1
2
0
1
1
1
1
1
1
1
1
2
2
1
2
1
1
0
1
1
1
0
1
1
1
1
1
0
1
2
1
2
1
1
2
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
2
3
1
1
0
1
2
1
2
2
1
1
0
1
1
1
1
2
2
0
1
2
2
1
2
1
0
2
3
1
1
1
1
0
2
1
1
0
1
1
1
0
0
1
0
2
1
2
1
1
1
1
1
1
0
0
1
2
0
1
1
2
0
1
1
2
1
1
1
1
2
0
1
0
1
1
0
0
2
1
2
1
0
0
1
2
0
1
1
1
1
2
0
1
1
0
1
0
0
2
0
0
1
1
1
1
2
1
1
1
1
1
2
1
1
0
1
1
2
2
1
1
1
0
0
1
2
1
2
2
1
1
1
1
2
0
2
1
1
2
1
1
1
0
1
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
0
1
2
0
1
1
2
1
2
1
1
2
1
1
2
2
1
1
2
0
0
2
2
2
1
2
1
1
1
2
1
0
1
2
1
0
1
2
1
0
1
2
0
2
0
1
1
1
1
1
1
2
1
2
1
1
9
2
2
0
1
1
1
0
2
1
1
1
2
2
0
1
1
0
0
1
2
2
2
2
1
1
1
1
1
1
3
1
1
2
1
1
2
2
1
2
1
1
2
1
1
2
1
1
1
1
2
0
0
1
1
1
2
0
1
0
1
1
1
0
2
0
1
2
1
2
1
2
2
1
1
1
0
3
1
1
0
1
1
2
1
1
1
0
1
1
1
2
0
1
2
0
1
2
1
1
0
1
2
1
1
2
1
1
1
1
2
1
2
2
1
2
1
1
1
1
1
0
1
1
0
1
1
0
2
1
2
1
0
1
1
1
0
2
2
1
2
1
1
1
1
0
1
1
1
1
1
2
1
2
2
1
2
1
1
2
1
1
0
1
2
1
1
1
1
0
1
1
2
1
1
1
2
2
2
0
2
1
2
2
1
1
1
1
0
0
2
2
1
2
0
0
1
1
1
2
1
1
1
1
0
1
1
1
1
1
1
2
1
2
1
2
1
3
0
1
2
2
1
2
2
1
3
1
1
1
1
2
1
2
1
1
2
1
2
1
1
1
0
1
0
1
0
1
2
0
0
1
2
2
2
0
0
2
0
1
1
1
1
2
2
2
1
1
1
1
1
1
0
1
0
1
1
3
2
1
1
1
3
2
1
0
1
1
0
2
0
2
1
1
0
0
2
1
0
1
1
1
1
0
0
2
2
1
1
1
1
1
1
1
1
1
1
2
1
2
0
2
0
1
2
2
2
1
0
1
1
2
1
2
1
1
1
2
1
1
1
0
1
1
1
2
1
2
1
2
2
1
1
2
1
1
1
2
2
1
1
0
1
2
1
0
1
2
1
2
1
1
1
1
0
1
0
1
2
1
1
0
1
1
1
2
0
1
2
1
2
2
0
1
2
0
1
1
1
1
1
1
1
2
1
2
0
1
1
1
1
1
1
1
2
1
0
1
1
2
1
3
1
0
1
2
1
1
1
1
2
0
2
1
3
1
0
1
3
1
2
1
2
0
2
2
1
0
2
1
2
2
2
2
0
1
1
1
1
1
0
2
2
2
2
0
0
2
2
2
2
1
1
1
2
2
0
3
2
1
1
1
0
1
1
2
1
1
0
0
3
1
3
2
1
2
1
1
1
1
1
2
0
2
1
1
0
0
2
1
2
1
1
1
1
1
1
1
2
1
1
2
2
1
1
2
1
1
2
2
2
1
1
0
2
1
1
1
2
1
1
2
2
1
1
0
2
2
2
0
0
2
1
2
0
1
1
1
1
2
1
1
2
1
1
2
1
1
2
1
0
1
1
1
0
2
0
2
1
1
2
1
1
1
1
1
1
0
1
1
2
1
2
2
1
1
1
2
1
2
1
1
1
1
2
2
0
1
1
1
2
2
2
1
1
1
1
1
1
1
1
0
1
1
1
1
1
0
2
1
1
1
1
1
2
0
1
0
1
1
2
1
1
2
1
2
0
1
0
1
1
1
2
0
1
0
0
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
0
1
1
0
1
2
1
1
1
1
1
2
2
1
0
0
1
0
2
1
0
1
2
0
1
0
1
1
2
0
0
0
2
1
2
0
2
0
1
1
1
0
1
1
1
2
1
1
1
1
1
1
2
0
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
0
1
1
2
2
1
0
1
1
2
1
1
2
2
1
1
1
2
0
2
1
1
1
1
1
1
1
1
0
1
1
2
1
1
2
1
1
1
2
0
1
1
1
2
1
1
1
1
2
2
0
1
2
1
2
1
1
1
1
1
1
2
1
0
1
1
1
0
1
1
2
1
1
0
2
1
2
2
1
2
1
1
2
1
2
1
7
2
2
0
1
3
2
1
0
1
1
1
2
0
1
2
2
2
0
1
1
1
2
2
1
1
2
2
1
0
2
2
1
1
1
1
1
2
0
1
2
1
1
1
1
1
1
2
2
0
0
1
0
0
1
1
0
2
1
1
2
2
2
0
2
1
1
1
1
1
1
1
1
2
1
1
0
0
1
1
2
1
1
2
1
2
2
1
1
1
2
1
1
1
2
2
2
0
1
1
1
2
2
1
1
0
0
1
1
1
3
1
2
1
0
3
0
2
0
1
1
1
1
0
2
1
1
0
1
1
1
0
1
1
2
2
1
2
1
2
1
1
1
0
0
0
2
1
2
1
0
1
1
1
1
1
1
1
1
1
1
1
0
2
3
2
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
1
0
0
1
0
2
1
0
1
0
2
1
1
1
1
1
1
0
0
1
2
2
1
1
1
1
1
1
2
1
0
1
2
1
1
0
1
1
1
1
1
1
2
1
1
1
1
1
2
2
2
1
2
1
1
1
1
2
2
2
0
2
1
1
2
0
1
1
0
1
2
1
2
1
0
2
1
0
1
1
1
1
1
0
1
1
1
1
1
1
0
1
1
1
1
2
2
2
1
0
1
1
0
1
1
1
1
0
2
1
1
1
2
1
2
1
0
1
1
2
1
1
1
0
1
1
0
2
1
1
1
1
1
1
1
1
0
0
1
0
1
1
1
1
1
1
2
1
1
0
2
2
1
1
0
2
1
1
1
1
1
2
1
2
1
2
1
0
2
2
2
1
1
1
1
1
2
0
1
2
1
1
1
1
0
1
1
1
2
0
1
1
0
1
1
1
1
0
1
0
1
1
1
5
1
1
1
1
1
2
1
1
2
0
1
1
1
1
1
0
1
0
2
1
2
1
1
1
1
0
1
1
1
2
1
0
1
1
1
1
1
1
1
1
1
2
0
1
1
1
1
0
1
2
0
2
0
1
2
2
2
1
1
3
0
1
1
2
2
1
1
1
1
1
2
0
2
0
1
1
1
0
2
2
1
1
2
1
2
0
1
0
2
0
2
0
2
1
1
0
1
0
1
1
1
1
0
0
1
1
1
1
2
2
1
1
1
1
2
1
0
1
2
1
2
1
1
1
1
2
0
0
0
2
2
1
1
1
0
1
2
1
1
1
1
0
0
3
1
1
1
1
1
2
0
1
1
0
2
2
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
0
0
0
1
0
1
1
1
1
1
1
1
1
2
0
1
1
2
1
0
0
1
1
1
0
2
1
1
4
1
1
2
0
1
1
0
2
1
1
1
2
2
1
1
1
1
2
1
1
2
1
0
2
1
2
2
2
2
0
1
1
1
2
1
1
1
1
1
2
1
2
1
1
0
2
1
0
0
0
1
1
2
0
1
1
1
1
1
1
2
0
0
1
1
1
1
1
0
1
1
1
1
1
2
1
1
0
1
0
1
1
0
1
2
1
2
1
2
1
1
0
1
1
0
1
1
1
1
2
0
1
1
0
2
1
1
1
1
1
1
1
1
1
1
0
2
2
1
1
1
1
2
1
1
0
1
1
1
1
1
2
1
0
2
1
1
2
1
0
1
2
0
2
1
0
2
1
1
1
1
1
2
1
2
1
0
0
1
1
1
2
2
0
1
2
2
0
2
1
1
1
1
0
1
0
1
1
0
1
2
1
1
1
2
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
0
1
2
1
1
1
0
1
1
1
1
1
1
1
0
1
2
1
1
0
0
2
1
1
1
0
0
1
2
0
1
0
1
2
1
0
1
1
1
1
0
1
1
1
1
1
2
1
0
1
1
0
0
1
2
0
2
1
2
1
1
1
1
1
1
1
1
2
1
0
1
1
2
3
0
2
1
0
1
0
0
2
1
2
1
1
3
0
0
1
1
0
1
1
2
1
1
1
2
2
1
1
1
1
0
1
2
1
1
1
2
2
2
1
2
2
1
2
0
0
1
1
0
0
1
1
1
2
0
1
1
1
1
1
1
1
2
1
2
1
1
1
0
0
2
1
1
1
1
1
1
1
1
0
1
1
1
2
1
0
1
1
2
2
2
1
0
0
1
2
1
2
1
1
2
1
2
1
2
0
1
1
2
0
1
1
2
1
1
0
2
0
1
1
1
2
1
0
1
1
1
0
1
1
1
0
2
1
2
0
1
0
1
2
1
1
1
0
2
2
0
2
3
2
2
0
1
2
1
2
0
1
2
0
1
0
0
1
1
0
1
0
1
2
2
2
2
1
1
2
1
0
2
1
2
1
1
1
1
1
2
0
1
2
1
0
1
1
2
1
2
2
1
1
2
1
1
0
2
2
0
2
2
2
1
1
1
2
2
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
2
0
1
1
1
1
1
1
1
1
1
2
1
0
1
1
0
1
1
1
0
1
1
2
2
1
1
1
1
1
0
1
2
1
1
1
2
2
0
0
1
0
0
0
2
2
2
2
1
1
2
0
1
1
1
1
2
2
1
2
1
2
1
1
1
1
2
1
1
0
1
0
2
1
3
1
0
1
1
1
1
2
1
2
0
2
2
0
1
1
1
0
1
1
2
2
1
2
1
1
1
1
2
1
1
1
1
0
2
1
2
1
1
1
1
1
1
2
2
1
0
1
0
0
1
2
1
1
1
3
1
1
1
1
2
1
1
2
1
0
2
2
0
1
0
1
1
1
0
1
2
1
0
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
0
2
1
2
1
1
1
1
1
1
1
1
1
2
1
0
0
1
1
1
1
2
2
0
1
0
0
1
0
1
1
2
2
0
2
2
1
0
1
1
1
1
0
1
1
0
1
2
2
1
1
1
1
1
1
1
0
1
1
0
2
0
1
0
2
3
1
1
2
1
1
2
1
1
1
1
1
0
1
2
1
0
1
0
2
0
1
2
2
0
1
1
1
1
1
1
1
2
0
1
1
2
1
1
1
1
1
1
2
2
1
2
1
1
1
2
1
1
2
1
1
1
2
2
1
1
2
1
2
1
1
2
1
1
2
0
2
2
2
1
0
0
1
1
0
2
1
2
1
1
1
0
1
1
0
1
2
1
1
0
2
1
1
2
1
1
2
1
1
2
1
1
2
2
1
1
1
1
1
1
1
1
1
2
2
0
1
0
1
1
2
4
2
1
0
2
0
1
1
1
2
0
0
1
2
0
1
1
1
2
1
0
1
1
2
1
1
1
2
2
0
1
1
1
1
1
1
1
1
2
1
0
3
3
1
1
0
1
0
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
0
1
1
1
1
1
1
0
1
2
1
2
2
1
0
1
1
1
2
1
1
1
2
1
0
1
1
2
2
1
1
1
2
2
2
1
1
1
0
1
2
0
2
1
0
2
1
1
1
2
1
2
1
2
1
1
1
1
2
2
2
0
1
1
1
1
2
1
1
2
2
0
2
1
1
1
2
1
1
0
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
2
1
0
2
1
0
0
0
1
2
1
1
1
0
2
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
2
2
1
1
1
1
1
1
1
3
2
1
2
1
1
1
0
1
1
2
1
0
0
1
1
1
1
2
1
0
1
1
1
1
1
2
2
1
0
1
2
1
2
0
1
1
1
1
1
2
1
2
0
0
1
2
1
1
1
2
1
1
1
1
0
1
2
1
1
2
1
1
1
1
0
1
1
0
0
2
0
2
1
2
2
2
1
1
2
1
2
1
1
0
0
1
0
1
2
1
2
1
1
1
2
0
1
1
1
0
0
0
1
1
1
1
1
1
1
1
1
1
2
0
2
1
2
2
1
1
1
0
1
0
1
0
0
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
2
2
2
1
1
1
2
1
1
1
1
0
2
1
1
1
1
1
1
0
1
0
1
2
1
1
1
1
1
2
1
1
1
0
1
2
1
2
1
2
2
0
1
1
0
1
0
1
1
2
2
1
2
1
0
1
1
2
1
0
0
1
2
1
2
1
0
0
1
1
0
0
1
1
2
1
2
1
1
0
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
0
1
1
1
2
2
1
1
2
1
1
0
1
1
0
1
1
1
0
1
1
1
1
0
1
1
1
1
1
2
3
1
1
0
2
2
3
1
1
2
1
2
2
1
1
1
2
0
1
2
1
2
1
1
0
1
1
1
1
1
1
0
0
3
1
1
1
1
1
1
1
1
0
1
2
1
1
2
1
1
0
1
1
2
1
0
1
1
1
0
1
1
1
1
0
1
1
2
2
2
2
1
1
1
1
2
2
1
0
1
0
2
1
2
2
2
1
1
1
1
1
0
1
1
0
1
1
1
0
1
0
1
1
2
2
1
1
0
1
1
1
2
1
2
1
1
1
1
1
1
1
1
2
2
1
1
2
2
1
0
2
1
1
0
1
2
1
2
2
2
0
1
1
1
1
1
1
1
2
1
1
1
2
0
2
1
1
1
1
2
1
2
2
1
1
2
0
0
0
2
2
0
1
1
1
1
0
1
1
0
1
1
1
2
1
2
1
0
1
1
1
2
1
0
1
3
0
2
1
1
0
1
2
2
1
2
0
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
1
1
0
1
0
1
0
1
1
1
1
0
1
2
2
0
2
1
1
1
2
1
0
1
0
2
1
1
1
1
2
0
2
0
1
0
1
1
1
2
1
2
0
0
1
2
1
1
1
1
1
0
0
2
0
0
0
1
1
1
1
2
1
1
1
1
0
2
0
1
1
0
2
1
1
1
1
2
1
2
1
1
0
1
1
1
1
1
2
1
2
1
1
2
1
1
1
0
1
1
0
1
1
2
2
0
1
0
0
1
2
1
1
1
1
1
0
1
0
1
0
0
1
3
1
2
1
1
1
1
2
1
2
2
0
3
1
1
0
1
1
2
1
1
1
1
1
1
1
1
2
1
0
1
1
2
2
2
1
2
1
0
1
2
1
1
1
1
1
1
1
1
2
1
2
1
2
2
1
1
1
1
2
2
1
1
1
1
1
2
1
0
2
2
0
2
1
2
1
1
0
0
1
2
1
1
1
1
1
1
1
1
1
1
2
2
2
2
1
1
1
1
2
1
2
0
1
1
2
1
1
1
1
2
1
1
1
2
1
0
1
1
1
1
1
0
1
1
3
1
2
1
1
1
1
2
1
1
1
1
1
1
0
0
1
0
0
1
1
0
2
1
1
1
1
1
2
1
0
2
2
1
1
0
1
1
1
0
1
1
1
2
1
1
0
2
2
1
2
0
2
2
1
1
1
1
1
0
1
1
1
1
2
2
0
2
1
1
1
2
1
1
2
2
2
0
1
1
0
0
0
1
1
1
2
1
1
2
2
1
0
1
0
2
0
2
0
2
1
2
0
1
1
2
0
2
1
1
1
1
1
1
0
1
1
1
1
1
2
2
1
0
1
2
1
2
0
2
2
2
1
1
1
0
0
1
1
1
0
1
1
2
2
1
1
1
2
1
0
1
2
1
1
1
1
1
1
1
1
1
2
1
2
2
2
1
1
1
1
2
1
1
0
1
2
1
1
1
2
1
1
0
0
1
1
1
0
0
1
2
2
0
1
2
0
2
0
1
0
1
1
2
1
2
1
1
0
0
1
1
1
0
1
0
1
1
1
1
2
1
0
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
0
2
1
1
2
1
2
1
1
1
2
2
2
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
1
1
0
2
1
1
2
0
1
2
1
1
1
0
2
2
1
0
2
2
0
1
1
2
2
1
2
1
2
1
1
2
0
0
0
1
0
0
1
1
3
2
1
1
2
2
1
1
1
1
2
1
1
1
2
1
1
1
1
1
0
2
2
2
1
1
1
3
1
1
1
1
1
1
1
2
1
1
1
2
1
0
0
1
2
1
1
1
2
1
1
1
2
1
1
2
1
1
2
1
2
2
2
2
0
0
2
2
1
0
1
1
0
0
1
1
1
1
0
1
1
1
1
2
0
1
1
1
0
1
1
0
1
1
1
2
1
1
1
2
1
2
0
1
1
1
2
0
1
1
0
1
1
1
1
1
1
0
1
1
2
2
1
1
1
1
1
1
1
0
1
2
1
1
1
3
1
2
1
1
1
1
1
1
0
2
1
2
1
0
0
2
1
1
2
1
2
1
1
1
2
2
1
1
1
0
1
1
1
1
1
1
0
2
2
2
2
1
0
1
1
1
1
1
1
1
0
0
1
2
1
1
1
2
2
0
0
1
2
1
1
1
1
2
1
1
1
1
1
1
0
1
1
0
2
1
1
2
1
1
2
1
1
1
2
0
1
1
2
1
2
1
1
2
1
1
1
1
0
0
1
3
2
1
1
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
3
1
1
0
1
1
1
1
2
0
1
2
1
1
2
0
1
1
1
1
1
0
0
1
2
0
1
1
0
1
1
2
2
2
1
1
1
2
2
1
2
1
2
0
2
1
2
0
2
1
1
1
1
2
1
2
1
1
1
1
1
2
0
1
1
1
0
1
1
0
1
2
0
2
1
1
1
1
1
1
2
1
1
2
0
0
1
1
1
1
1
2
2
1
1
1
2
1
1
1
1
1
1
0
0
1
0
1
2
1
1
1
1
1
1
1
1
0
1
1
1
2
0
1
2
1
1
0
0
0
0
1
1
0
2
1
1
1
1
2
0
0
1
1
0
2
0
2
2
1
2
0
1
1
1
1
1
2
1
1
1
1
1
1
0
1
0
1
2
1
0
1
1
1
1
0
1
1
1
1
2
1
1
0
1
1
1
1
1
2
2
0
1
1
1
0
1
1
2
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
2
1
1
2
1
2
1
1
2
1
1
1
1
1
0
0
1
1
1
0
1
1
1
2
0
2
1
2
0
1
1
0
2
1
2
1
2
1
2
2
1
0
2
1
2
1
1
2
1
1
1
1
0
1
1
2
1
2
2
0
1
0
1
1
0
1
3
1
1
2
1
1
2
1
1
1
1
1
1
1
2
2
0
2
1
1
1
1
1
2
0
0
1
2
2
2
1
2
2
1
1
1
2
0
0
1
1
1
0
5
1
1
0
1
1
1
1
1
0
1
1
1
3
2
1
1
1
1
1
0
1
0
2
2
1
2
1
0
1
2
2
1
0
1
1
2
0
0
0
1
1
1
1
0
1
1
1
2
1
2
0
1
1
1
1
1
2
1
1
0
0
1
1
1
2
1
1
0
1
1
2
0
1
2
1
1
1
0
1
2
2
1
1
1
2
0
1
1
2
2
2
2
1
1
4
1
0
0
1
1
1
2
1
0
1
1
0
0
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
0
1
1
3
1
0
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
0
0
1
2
0
2
2
1
1
0
2
1
1
1
2
1
0
2
0
0
2
1
1
2
2
1
1
2
1
1
2
0
1
1
0
0
1
1
1
1
1
1
1
1
2
1
0
1
2
0
1
2
1
1
1
1
1
0
2
1
1
2
0
2
2
0
2
1
2
1
2
1
1
0
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
0
1
1
2
1
0
0
0
1
1
0
1
2
1
1
2
1
1
1
2
1
2
1
1
0
4
2
0
2
1
1
1
0
1
1
2
1
1
0
1
2
1
0
1
1
0
1
2
1
1
2
1
1
1
2
1
2
2
2
3
1
2
2
1
1
1
1
0
0
2
1
2
1
2
2
1
1
2
3
0
1
0
1
1
2
1
2
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
2
2
2
2
1
1
1
0
1
0
1
2
0
1
1
2
2
1
1
1
1
1
1
0
2
1
0
1
1
1
1
1
1
0
1
0
2
1
1
2
2
0
1
1
1
0
1
2
2
1
2
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
0
2
1
1
1
2
2
1
2
2
1
2
1
1
1
1
1
0
2
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
0
1
1
0
1
1
1
0
0
1
1
1
2
2
1
1
2
1
1
1
2
1
1
1
2
1
2
1
1
0
2
2
1
1
1
2
1
1
2
0
1
0
1
1
2
1
1
2
0
0
1
1
2
1
1
1
1
2
1
1
1
1
2
1
2
0
1
1
1
1
0
1
2
1
2
1
0
1
1
1
2
2
1
2
1
1
1
1
1
1
1
2
2
1
1
1
2
1
1
2
1
1
1
1
0
2
1
1
0
1
4
1
1
0
1
2
2
0
1
1
2
1
0
1
2
1
1
1
2
2
0
2
1
2
1
2
2
1
1
1
2
0
1
1
1
1
1
0
1
1
1
2
1
1
2
1
2
2
1
1
0
2
1
0
1
0
2
0
1
2
0
1
2
1
2
0
1
1
1
2
1
1
2
0
1
2
1
1
2
2
1
2
2
2
0
1
0
2
1
1
2
0
2
0
2
1
0
2
1
1
2
1
2
1
0
2
1
1
1
1
0
1
1
1
2
1
2
0
1
2
1
1
1
1
0
0
2
1
2
2
0
0
1
1
2
1
1
0
1
1
3
1
1
1
2
1
1
2
1
0
1
0
2
0
0
1
1
0
3
2
1
1
1
1
1
0
1
2
0
1
1
2
1
2
1
0
1
1
1
1
1
0
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
0
1
1
1
0
1
1
0
0
1
1
0
1
1
1
1
1
2
0
0
1
0
2
1
1
1
1
0
0
1
1
0
2
0
0
1
1
1
1
1
1
1
0
1
0
2
1
2
1
1
0
2
0
1
0
1
2
1
1
0
1
0
2
1
1
1
1
1
1
1
1
1
1
0
0
1
2
1
2
1
1
1
1
1
0
1
0
0
1
0
2
1
0
2
1
1
2
2
0
1
1
2
2
0
2
1
0
1
2
1
0
1
2
2
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
2
1
2
0
1
0
1
0
2
1
1
1
2
2
2
1
0
2
1
1
2
2
1
1
1
1
1
1
1
1
1
0
2
1
1
0
1
1
1
1
1
1
1
1
2
2
0
1
1
2
1
1
0
2
1
2
1
1
1
1
0
1
1
1
1
2
1
1
1
2
2
1
1
1
2
2
0
1
2
1
0
1
1
1
1
1
1
0
2
2
1
1
1
1
2
2
1
1
1
2
1
1
2
1
1
0
2
2
1
1
1
1
1
1
1
1
2
1
0
1
2
0
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
2
2
1
1
1
1
0
2
0
1
1
1
0
1
0
1
1
0
1
1
1
1
1
1
2
1
1
1
1
0
0
2
2
1
2
1
0
1
1
1
1
1
1
2
1
2
1
2
0
1
0
0
1
1
1
1
2
0
1
0
1
2
1
1
0
2
0
0
1
1
0
2
1
2
0
0
1
1
1
1
2
0
1
2
2
1
1
1
0
1
1
0
1
1
1
2
1
5
1
0
1
1
1
1
2
1
1
1
0
1
1
2
2
0
2
2
1
2
1
2
1
1
0
0
2
1
1
1
0
1
2
2
0
1
1
1
1
0
1
2
1
2
1
1
1
2
1
1
2
2
1
2
1
0
1
1
1
2
1
2
1
2
0
1
1
1
0
3
2
1
1
1
2
1
1
1
1
0
2
2
1
1
2
1
0
1
1
1
0
1
1
2
1
0
2
1
2
0
2
1
0
0
1
2
0
1
2
2
2
1
1
0
0
1
1
1
2
1
2
1
1
1
1
1
1
1
1
0
1
1
2
1
0
1
1
1
0
1
2
0
0
2
1
1
2
0
0
2
2
2
2
2
2
2
1
2
2
1
1
1
1
1
1
1
2
1
1
1
0
3
2
1
1
2
1
1
1
1
2
2
2
2
1
1
2
0
0
1
1
2
1
1
1
1
2
2
1
2
2
0
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
2
2
1
1
1
0
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
0
1
2
2
2
2
2
1
0
1
1
0
1
1
2
0
0
1
1
0
0
1
0
2
1
0
1
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
1
0
2
1
1
0
1
1
1
1
1
2
2
2
1
2
1
1
0
2
0
1
1
1
1
0
2
2
1
1
2
1
2
1
2
0
1
1
1
2
4
2
1
1
2
1
0
0
0
2
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
3
2
0
2
0
2
1
1
2
0
1
2
2
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
1
0
1
2
1
2
0
1
1
1
1
1
1
0
1
1
1
2
2
0
1
1
2
1
2
0
2
1
1
1
1
1
2
1
0
0
1
1
1
2
1
1
2
2
1
2
1
0
1
1
2
1
1
1
2
1
1
1
0
1
1
1
1
0
1
0
1
1
1
1
0
2
2
1
2
1
1
0
1
1
2
4
2
2
0
1
1
1
1
1
0
1
1
1
2
0
1
2
2
2
2
1
1
1
2
2
1
1
0
1
0
1
1
2
2
1
2
1
1
0
1
1
1
1
1
0
0
2
1
1
1
2
2
0
1
1
1
0
1
1
1
1
1
1
1
1
1
1
2
1
1
0
1
1
2
2
1
1
0
1
2
1
0
1
0
1
0
1
2
1
2
0
2
0
1
0
1
1
2
2
1
1
2
1
0
1
2
2
0
1
0
0
1
0
0
0
1
0
1
1
1
1
0
2
1
1
2
1
2
2
0
1
2
0
1
2
1
1
1
0
1
1
1
0
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
2
1
1
1
1
0
1
2
1
1
2
1
0
1
0
1
1
2
0
1
1
0
0
2
2
0
0
0
1
1
1
1
2
2
2
2
1
0
2
0
0
1
2
0
0
0
0
1
3
1
2
1
1
2
1
2
2
2
1
1
1
2
1
2
2
0
1
2
1
1
0
1
0
2
1
1
0
1
1
1
1
0
1
2
2
2
1
1
2
1
0
2
1
2
1
1
1
0
1
2
2
1
1
1
1
1
2
2
1
1
1
1
2
0
0
1
1
1
0
1
2
3
1
1
0
0
1
1
1
2
2
2
1
1
1
1
1
1
2
1
1
0
0
1
0
0
0
1
0
0
0
1
1
3
1
1
1
1
1
1
2
2
2
1
2
1
1
1
1
1
1
1
2
1
1
2
0
1
1
0
1
1
1
2
1
1
1
1
1
2
1
2
1
2
0
1
2
2
1
1
1
2
1
1
1
1
1
2
1
1
2
1
2
1
0
1
1
0
2
2
1
1
1
1
2
1
1
1
2
1
2
1
1
1
2
1
1
2
1
1
2
1
2
1
0
0
1
1
1
2
1
2
1
2
1
1
2
2
1
1
1
1
1
2
1
1
1
1
0
2
1
2
1
1
0
1
1
1
0
1
1
1
0
0
2
1
2
2
0
1
0
2
1
2
1
0
2
1
3
2
2
0
2
1
1
1
1
1
1
1
0
2
2
1
1
1
1
0
1
1
1
1
1
1
2
2
1
2
2
1
0
0
0
3
0
0
2
2
1
1
2
0
1
2
1
1
1
1
1
1
1
1
1
0
1
1
0
1
0
1
1
2
1
1
1
0
2
0
1
2
1
0
0
1
2
4
0
1
0
1
1
2
0
1
1
1
1
0
1
1
0
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
1
2
1
2
0
0
1
2
2
1
2
1
1
1
1
1
2
1
1
1
0
0
1
1
1
1
2
1
1
2
0
1
1
1
2
1
1
2
0
1
2
2
1
1
2
0
0
0
2
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
2
1
2
1
1
0
1
0
1
2
2
0
2
0
0
1
1
8
1
1
1
1
1
1
1
1
2
1
0
1
1
0
2
2
1
2
1
1
1
1
2
1
1
2
1
1
1
0
1
1
1
1
1
1
1
2
0
2
1
1
2
2
2
1
2
1
1
2
0
1
1
2
1
1
1
1
0
1
0
1
2
1
1
0
1
1
1
1
1
1
1
2
1
1
1
1
1
2
2
0
2
2
1
0
1
2
2
1
1
2
0
0
0
1
1
1
1
2
2
0
2
1
1
2
0
1
1
1
2
1
1
2
1
3
3
0
2
1
2
1
1
2
1
2
1
0
1
1
2
0
2
1
1
1
0
1
1
1
2
1
0
1
2
0
1
1
1
1
2
0
2
2
1
1
2
1
1
1
2
1
1
1
1
1
0
2
2
2
1
1
1
0
1
1
1
1
1
2
1
1
2
1
1
0
0
1
1
1
0
2
1
0
1
1
1
1
1
0
1
1
0
2
0
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
1
0
2
1
1
1
2
1
0
2
1
0
1
1
2
2
1
0
1
1
1
1
1
2
0
1
2
2
1
2
1
0
2
1
1
0
2
1
1
1
2
1
1
2
2
1
1
0
1
1
1
1
1
1
1
0
1
2
0
0
0
1
1
2
1
1
1
1
0
1
1
2
2
1
1
1
0
1
0
2
0
0
1
1
1
1
2
1
2
1
2
1
1
1
1
1
0
1
1
1
2
1
1
1
1
1
0
1
2
2
0
2
1
1
0
1
1
0
1
0
0
2
1
1
1
1
1
1
0
2
1
1
0
2
2
1
2
2
0
2
0
1
2
2
2
2
0
1
0
1
1
2
0
1
1
2
1
1
1
0
2
1
1
0
1
2
1
0
0
0
1
0
1
1
2
1
0
1
2
1
0
1
1
2
1
1
1
2
2
1
0
1
1
1
1
1
2
2
2
0
1
1
0
3
1
2
1
0
1
1
1
1
2
1
0
1
2
2
1
2
0
1
0
1
1
1
1
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
2
1
0
2
2
2
2
2
2
0
2
1
1
1
1
1
1
0
1
1
2
0
1
2
1
1
1
1
2
6
2
2
1
2
0
1
2
1
1
1
1
0
0
1
0
2
0
2
1
1
2
0
1
1
1
2
3
2
1
0
1
1
1
2
0
2
1
2
2
1
1
2
1
1
1
2
1
2
0
2
1
2
1
0
1
2
0
1
2
2
1
0
2
1
0
1
1
1
2
1
2
2
0
1
3
1
2
2
1
1
0
0
2
1
1
1
1
1
1
1
0
2
2
1
1
1
1
1
1
1
1
1
1
2
0
1
2
0
2
1
0
1
1
2
1
1
1
2
1
2
0
1
2
0
1
0
0
1
1
2
1
2
0
2
0
0
0
2
1
1
2
2
1
2
1
1
1
1
1
2
2
1
0
1
2
1
2
1
1
2
1
0
1
1
0
0
1
0
1
1
2
1
2
1
1
1
0
1
1
2
2
1
1
1
2
1
2
0
0
2
0
1
1
1
1
1
0
2
2
0
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
0
1
1
1
2
1
1
2
1
1
0
2
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
2
2
1
1
2
1
4
1
1
1
1
2
1
0
1
1
1
1
1
0
1
1
1
2
1
1
0
1
1
1
1
1
2
1
1
2
2
0
2
1
0
4
1
1
1
1
1
0
1
1
1
1
1
1
2
2
1
1
1
2
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
3
1
0
1
1
1
1
1
1
2
0
0
1
1
2
1
1
1
1
1
0
2
1
2
0
0
0
2
1
1
1
0
1
2
1
2
1
1
0
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
3
2
1
1
1
1
1
1
2
2
1
2
0
1
1
3
1
2
1
1
1
2
0
1
1
2
1
1
0
1
2
2
1
0
1
1
1
1
2
1
2
2
1
1
1
1
0
1
2
1
1
2
0
1
2
1
0
1
2
1
1
0
1
1
1
1
1
1
2
1
1
1
1
1
1
0
1
2
2
1
2
0
1
1
0
1
1
1
1
2
1
1
1
1
2
1
1
1
0
1
1
1
1
1
2
1
1
1
1
2
0
1
1
2
1
3
2
2
1
1
0
1
2
1
2
1
1
2
0
2
1
1
1
1
1
2
1
2
1
1
1
0
2
1
2
1
1
2
0
3
0
1
1
1
0
0
1
1
1
1
1
0
1
0
2
2
2
1
0
1
1
1
1
1
1
1
2
2
1
2
0
2
0
1
2
1
1
1
1
0
2
1
2
1
1
1
1
0
1
1
1
1
2
1
2
1
1
1
1
1
1
0
2
1
2
0
2
0
0
1
1
1
1
1
0
0
1
1
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
0
2
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
2
1
1
1
0
1
2
2
0
0
2
1
0
1
0
1
0
1
2
1
1
1
0
0
2
0
2
1
0
1
1
1
1
1
0
1
1
1
2
2
2
0
2
3
1
2
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
3
1
1
1
2
1
2
1
1
1
1
1
1
2
2
1
0
1
1
0
0
2
1
1
1
0
1
0
1
2
1
1
1
1
1
1
0
2
1
0
1
0
1
1
1
0
1
2
1
1
0
2
1
1
1
2
1
2
0
1
0
1
2
1
1
1
1
1
1
2
0
0
2
1
0
1
1
1
0
0
1
2
1
1
2
1
2
0
2
3
1
1
1
1
1
1
0
2
1
1
1
0
1
1
1
1
1
1
2
0
1
1
2
1
2
0
1
0
1
1
0
1
1
0
0
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
3
1
1
1
2
1
1
2
2
1
1
2
1
1
0
2
1
0
0
1
2
1
1
1
1
2
1
1
1
1
1
2
1
1
2
1
1
1
3
1
0
1
1
1
1
1
1
1
1
2
0
2
2
1
1
1
2
0
0
1
2
1
1
1
1
0
2
1
2
2
1
1
1
2
1
3
2
1
1
1
2
1
2
1
2
2
1
2
2
0
1
1
1
1
0
1
1
1
2
2
0
0
2
1
1
1
0
1
1
1
2
1
0
0
0
1
1
1
1
1
1
1
1
1
1
2
1
1
2
2
1
1
1
1
0
2
0
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
1
0
1
1
1
0
2
1
0
1
1
0
0
2
2
0
1
1
1
0
1
2
1
1
0
0
0
1
1
1
1
2
0
0
1
1
1
1
1
2
1
2
1
1
3
1
1
1
1
2
2
2
1
2
1
0
0
1
2
1
2
1
1
2
2
1
1
1
2
1
1
1
2
1
2
1
0
0
1
1
1
2
1
1
0
2
0
2
1
1
0
1
0
1
0
1
0
1
2
1
1
0
0
0
2
2
1
1
2
1
3
1
1
2
1
1
0
1
0
2
1
2
2
1
2
1
1
1
1
2
0
0
1
1
2
2
3
1
1
1
1
1
1
1
1
1
1
1
1
1
2
0
2
2
1
1
2
0
2
1
2
2
2
1
2
1
1
1
1
2
2
1
2
0
0
2
1
1
2
1
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
0
1
1
1
1
1
1
1
1
1
2
0
1
1
1
2
2
1
0
1
2
2
1
1
1
1
2
1
1
1
0
0
1
2
1
1
1
0
1
1
1
2
1
1
0
1
1
0
1
1
2
1
1
1
0
1
1
0
1
1
1
1
2
2
0
1
2
1
0
2
2
2
1
1
1
0
1
2
1
1
1
0
2
2
1
0
1
1
1
1
1
2
1
0
1
2
0
1
1
2
1
2
0
1
1
0
0
1
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
0
2
1
1
1
0
1
2
1
1
1
1
2
1
1
2
2
1
1
1
1
2
0
1
2
2
1
1
1
1
1
2
1
1
1
1
0
0
1
1
1
2
0
1
2
1
1
1
1
0
1
1
0
1
1
1
1
1
0
0
0
0
2
2
0
1
2
1
2
1
2
0
0
1
2
2
1
1
2
1
0
1
6
1
1
1
1
2
1
1
1
1
1
1
1
0
2
2
1
0
2
1
1
2
1
1
1
1
1
2
1
1
1
0
1
1
1
1
1
1
1
2
0
1
3
1
1
1
2
0
2
1
1
1
0
0
2
1
1
2
1
0
0
1
1
0
1
1
1
1
0
2
2
0
1
0
1
1
1
1
1
2
2
1
2
2
1
1
0
1
0
1
1
2
2
1
0
1
1
1
1
1
1
1
0
2
1
1
1
2
1
1
1
1
1
0
1
0
1
1
1
2
1
0
1
1
1
0
1
2
1
1
1
1
0
1
0
1
1
2
1
0
1
0
2
2
0
1
2
2
0
1
2
2
1
2
1
1
0
2
1
1
2
1
2
2
2
2
1
0
2
2
1
0
0
1
0
1
1
1
1
0
1
1
2
0
0
1
1
3
1
1
1
1
1
2
1
0
1
1
1
2
1
2
1
1
2
0
0
1
2
4
0
1
1
1
2
1
1
2
2
0
2
1
1
1
1
1
2
2
1
1
1
1
1
0
3
2
0
1
1
1
1
1
1
1
2
1
0
1
1
1
2
0
2
2
1
0
2
1
1
1
1
1
2
0
2
0
1
2
2
1
1
1
1
1
2
0
2
1
1
0
1
1
2
0
2
2
1
1
1
1
1
1
1
1
1
2
0
2
1
1
1
1
1
1
1
1
2
1
2
1
1
1
0
2
0
2
1
1
1
1
2
1
0
1
2
2
2
1
0
1
1
0
2
2
2
1
1
1
1
1
1
2
2
2
2
1
1
1
2
0
2
1
0
2
1
1
1
2
0
2
1
1
1
1
0
2
2
2
2
1
1
0
0
1
1
0
1
1
1
2
1
2
1
2
2
0
2
1
0
1
0
0
1
1
1
1
1
2
0
1
1
1
1
2
0
1
2
2
1
2
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
2
1
1
2
1
1
2
2
1
1
0
2
1
1
0
1
1
2
1
0
1
1
1
1
1
2
1
0
1
1
0
2
1
1
0
1
1
2
2
1
0
0
1
2
1
2
1
0
1
1
2
1
1
1
2
1
0
0
1
1
2
2
1
1
2
1
0
1
1
2
2
1
2
1
2
0
1
2
1
1
0
0
2
1
1
1
2
1
2
2
1
0
1
1
1
0
1
1
1
2
0
1
1
1
2
2
1
1
3
1
1
1
1
3
1
0
1
2
1
1
1
1
0
1
0
0
0
1
1
1
1
1
1
0
1
0
1
1
1
2
0
2
1
2
2
0
1
2
2
1
2
1
1
1
2
0
2
0
1
1
1
1
1
0
1
1
1
1
0
0
0
0
1
2
2
2
1
1
1
2
1
1
0
2
0
2
1
0
0
1
2
2
1
2
2
1
0
2
1
2
1
2
2
0
1
1
2
2
2
0
1
1
1
2
8
1
1
1
2
1
1
0
1
0
1
2
1
1
1
2
1
0
2
2
1
1
1
0
3
1
0
2
1
0
0
2
1
1
2
1
1
2
1
1
1
1
0
2
1
2
1
1
1
1
2
1
2
1
1
2
1
0
1
2
2
1
1
1
0
0
2
1
1
1
1
1
1
1
1
0
2
2
1
1
1
0
2
2
1
1
1
1
1
1
0
2
1
1
0
1
0
1
1
2
1
2
1
1
0
1
2
0
2
1
2
0
1
1
1
1
1
2
1
1
1
0
1
1
1
1
1
1
0
2
1
2
2
0
0
2
1
1
1
2
2
1
1
1
2
1
0
0
0
2
1
1
1
1
1
0
2
2
2
1
2
0
2
0
1
1
1
1
1
1
2
2
1
1
0
1
2
0
1
1
1
1
1
1
2
1
2
1
1
0
2
1
0
1
1
1
1
1
1
2
2
0
2
2
1
0
1
1
2
2
1
0
2
1
1
2
0
2
3
1
2
1
2
1
2
2
1
1
2
2
3
1
1
0
1
1
1
2
1
2
1
2
1
2
1
1
1
1
1
2
1
1
1
0
0
1
1
2
0
1
1
1
0
1
2
0
1
1
1
1
0
1
1
0
1
0
1
1
1
2
2
2
1
1
1
0
1
1
1
0
1
1
1
0
0
4
0
0
1
2
0
1
2
1
2
1
1
1
2
1
1
1
0
0
1
1
2
1
1
1
1
1
0
1
1
2
1
1
0
1
0
1
1
1
2
2
1
1
2
0
0
0
1
1
1
1
2
1
0
1
1
1
1
2
1
0
0
2
1
1
1
1
0
1
2
2
1
1
1
0
2
1
2
1
1
1
0
2
1
0
1
2
2
2
1
1
1
1
1
0
1
1
1
0
1
0
1
2
1
2
1
1
1
0
1
1
2
0
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
2
2
0
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
2
1
2
1
2
3
1
0
1
0
2
1
1
0
1
2
1
1
1
0
1
1
1
0
0
1
1
1
2
2
2
1
2
0
1
0
0
2
0
0
1
1
1
2
2
1
1
1
1
1
0
2
1
2
1
1
1
1
0
0
1
1
1
2
1
0
3
1
2
1
0
1
2
0
2
1
1
1
0
2
1
1
1
1
2
2
0
1
2
1
1
2
1
1
1
1
1
1
0
1
1
1
2
0
2
1
0
1
2
2
2
2
1
1
1
0
1
1
1
1
1
2
1
2
1
1
0
1
1
2
0
1
1
1
0
0
1
1
0
2
2
1
1
1
2
1
1
0
1
2
1
1
1
1
0
1
1
1
1
2
1
1
0
1
2
1
1
1
1
2
1
1
1
1
1
2
2
1
0
1
1
1
1
1
1
1
1
0
1
0
2
1
1
1
1
0
1
1
1
1
2
1
0
1
1
2
1
1
1
1
0
1
1
1
1
2
1
1
2
2
1
1
1
1
2
2
2
2
1
2
1
2
1
1
1
1
0
0
2
1
0
2
2
2
1
1
1
1
1
2
0
1
1
0
1
1
1
0
1
0
1
3
1
2
1
2
2
2
0
0
2
1
1
1
1
1
1
1
1
2
1
2
1
1
1
2
1
2
1
0
2
1
1
1
1
1
1
2
2
1
0
1
1
0
1
1
1
0
1
1
0
1
0
2
1
2
1
2
1
2
1
1
2
1
0
1
1
1
1
1
2
2
0
1
1
1
2
0
0
2
1
1
2
0
1
1
1
1
1
1
1
1
0
2
1
1
0
1
1
1
1
1
2
1
1
2
1
2
2
2
0
1
1
1
1
1
1
2
7
2
1
1
1
1
1
1
1
1
2
0
2
2
1
1
2
1
1
1
1
1
1
3
1
1
1
2
0
1
2
1
0
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
0
2
2
1
1
1
2
1
1
2
1
1
2
0
1
1
1
2
1
0
1
0
2
1
1
0
0
2
1
1
1
1
1
2
2
1
1
1
2
1
0
1
1
1
1
1
1
1
3
1
1
2
0
1
2
0
1
1
1
1
1
2
1
2
1
1
2
1
2
1
1
1
2
2
2
1
0
2
1
0
2
1
1
2
2
2
1
1
1
2
2
1
1
2
1
1
2
1
2
1
1
1
1
0
1
1
1
1
2
2
1
0
1
1
1
1
2
2
0
1
1
1
1
1
1
1
1
3
1
0
1
2
0
4
0
1
1
1
1
1
1
1
0
1
1
1
1
1
1
2
2
1
0
1
2
1
1
1
2
1
3
2
1
2
1
2
1
2
1
0
0
1
1
2
1
1
1
2
1
1
1
1
1
0
2
1
1
2
1
1
1
1
1
0
1
1
0
2
1
0
0
0
2
1
1
1
0
0
1
0
2
1
1
1
2
2
2
0
1
1
2
0
1
0
2
2
0
1
0
2
1
2
1
2
2
1
1
1
1
1
0
1
2
1
1
1
2
1
1
0
1
1
2
1
0
1
1
2
0
0
0
2
1
1
1
1
1
2
1
1
0
2
0
1
1
1
2
2
1
2
2
2
1
0
0
1
1
1
1
1
0
2
2
2
0
0
2
1
1
1
0
2
0
1
0
1
0
1
2
0
0
1
1
0
0
2
1
2
0
2
1
2
1
0
1
2
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
0
0
1
1
1
1
1
2
1
2
1
0
1
1
0
1
1
1
0
2
2
1
1
3
1
2
1
1
1
2
1
0
2
1
1
0
2
1
0
1
1
1
2
2
1
1
1
0
1
1
1
2
1
1
1
1
0
1
1
2
1
2
2
1
1
1
0
2
0
1
2
2
2
0
1
0
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
2
1
0
1
2
2
2
1
2
1
1
1
1
2
1
1
1
0
2
1
1
0
1
2
2
1
2
1
2
1
1
2
2
1
1
1
0
1
1
2
1
1
1
1
2
1
1
2
0
0
1
0
2
1
9
0
0
1
1
1
2
2
1
1
1
2
0
1
2
2
2
1
1
2
1
1
1
2
1
2
0
1
1
2
2
2
2
1
0
0
1
1
0
2
1
1
0
1
1
2
2
2
1
1
0
1
1
1
1
0
2
0
1
1
1
1
1
1
0
1
1
0
0
1
1
1
1
2
1
1
0
0
0
2
1
1
2
2
2
0
0
1
1
1
2
1
0
2
1
1
1
0
1
1
1
1
1
2
1
2
1
1
1
1
1
2
1
2
2
1
1
2
1
1
3
1
1
1
1
2
1
2
1
1
1
2
1
1
1
1
1
0
1
2
1
1
2
2
1
1
1
0
2
1
1
1
0
1
1
1
2
1
2
1
1
1
2
2
2
1
1
2
2
1
1
0
1
1
1
1
1
0
2
1
0
1
0
1
2
2
1
1
0
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
0
2
2
2
2
1
1
0
1
2
1
1
1
0
1
0
0
1
1
1
2
1
1
1
1
1
0
0
1
2
1
0
2
0
1
0
2
0
2
2
1
1
2
1
0
1
1
1
2
1
0
2
1
0
1
1
1
1
1
1
0
1
2
1
1
0
2
1
1
2
1
0
1
1
1
1
2
1
0
1
1
2
2
1
1
1
2
1
2
1
1
2
0
0
2
2
0
1
0
1
2
0
0
2
1
0
1
0
2
1
2
1
0
2
1
1
1
0
2
1
2
2
1
2
1
0
2
1
1
1
1
1
1
1
2
2
1
1
2
2
1
1
2
1
1
1
2
2
0
3
2
2
2
0
0
1
2
1
1
1
1
1
1
2
1
1
1
2
1
2
2
1
2
1
1
0
2
1
1
1
2
0
1
1
1
2
0
0
2
2
2
1
2
1
1
2
0
1
2
2
1
1
1
2
2
2
1
1
1
1
1
2
0
2
1
0
1
2
0
1
2
1
1
2
1
1
0
1
2
0
2
2
1
0
1
1
2
2
2
1
1
2
1
1
2
0
0
2
2
2
2
1
2
1
1
1
1
1
2
1
0
1
2
1
1
1
0
2
1
1
2
1
0
2
2
1
1
1
0
1
1
0
1
1
1
1
1
2
1
1
1
2
1
1
2
0
0
1
0
1
1
1
1
2
2
2
2
2
1
0
2
0
0
2
0
1
0
0
1
1
2
1
0
0
1
0
2
0
1
0
1
1
0
2
1
1
1
0
1
1
1
2
2
1
1
1
1
1
0
1
0
2
1
0
0
1
2
1
2
2
1
2
1
2
1
1
1
1
2
1
1
1
2
2
2
1
1
2
2
1
1
2
2
0
0
1
2
2
1
1
1
1
1
1
1
1
3
1
1
2
1
1
1
1
1
0
0
1
1
2
1
2
1
2
2
2
0
1
1
1
1
0
1
1
0
0
1
2
1
1
2
0
2
0
2
1
1
1
1
1
1
3
2
1
2
0
2
1
1
2
0
1
0
0
2
2
0
2
2
1
0
1
1
1
1
1
3
1
2
1
1
2
1
1
2
0
2
1
1
2
0
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
2
1
1
1
1
1
1
0
1
2
1
1
1
1
1
2
0
2
1
1
0
1
1
1
1
1
1
1
1
1
1
2
0
1
1
1
2
2
1
2
0
1
2
2
1
1
0
1
0
2
2
1
0
1
1
0
1
2
0
1
2
2
1
0
1
1
1
2
1
1
1
2
1
1
2
0
1
1
1
0
1
0
2
2
1
1
1
1
1
1
1
1
0
0
1
1
1
0
1
1
0
1
4
0
1
1
0
1
2
1
1
2
1
2
2
1
1
2
2
2
1
2
1
1
1
1
2
1
1
2
0
1
1
1
0
2
0
1
1
1
1
1
0
0
1
0
1
1
2
1
1
1
3
0
1
1
1
0
2
0
1
1
0
1
0
1
3
1
4
2
1
1
2
3
1
1
1
1
2
0
1
1
2
1
1
1
2
0
1
1
1
0
1
1
1
1
0
2
1
1
1
2
1
2
1
2
0
1
0
2
1
2
0
1
0
2
1
1
1
2
0
2
1
0
0
1
2
2
1
2
1
2
0
0
1
1
2
1
2
1
2
1
2
2
1
1
1
1
0
1
1
1
0
1
0
1
1
1
1
1
1
2
0
2
1
2
1
1
1
1
1
1
2
2
1
1
1
2
0
2
0
1
4
1
1
1
1
0
1
1
1
1
1
2
1
2
1
1
1
2
2
1
1
1
2
0
2
0
1
1
0
2
2
0
0
1
0
2
1
0
2
0
1
1
1
1
1
1
1
1
3
0
1
1
2
1
0
0
1
1
2
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
2
1
0
0
1
1
2
1
1
1
1
1
1
1
1
0
1
0
1
1
2
2
1
1
3
0
1
2
2
1
2
1
2
0
1
2
2
2
1
1
1
1
0
1
2
1
1
2
1
2
1
1
0
2
1
0
1
2
1
2
0
1
0
2
1
1
1
0
0
0
0
1
1
1
1
1
1
1
1
2
2
2
0
1
1
1
2
1
2
1
2
1
1
1
1
1
0
1
2
1
2
1
0
1
2
1
0
1
2
2
1
2
1
2
1
1
1
1
1
2
0
5
2
2
0
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
3
0
2
1
2
1
0
1
2
1
1
0
1
1
1
1
1
1
1
0
0
2
2
1
0
1
1
1
1
2
1
0
0
1
1
1
0
1
1
1
1
1
2
0
1
2
0
0
1
1
2
0
1
3
1
2
1
1
0
1
1
1
2
1
0
1
1
1
2
0
2
1
1
1
1
1
1
2
1
0
1
0
1
1
2
2
1
2
1
1
1
1
2
1
1
2
1
1
0
0
1
1
1
1
1
1
0
1
1
1
0
0
1
2
1
2
1
1
1
2
0
1
2
1
2
2
1
1
0
1
2
1
1
1
2
1
2
1
1
1
1
1
2
0
2
0
0
4
2
1
0
1
1
1
1
2
1
0
1
0
1
1
0
1
1
2
3
1
2
1
2
1
0
2
1
1
1
1
1
2
1
0
2
2
1
1
1
1
2
1
1
1
1
1
1
2
1
1
2
0
2
1
1
0
0
1
1
1
2
1
2
0
1
1
0
1
2
2
2
1
2
0
0
0
1
1
1
0
1
0
1
2
1
2
0
1
0
1
1
3
2
2
1
1
0
0
0
0
1
1
0
2
2
1
0
1
3
1
1
2
2
0
1
2
2
2
2
1
0
1
1
0
0
1
1
1
1
1
0
1
1
1
1
0
1
2
1
1
1
1
1
2
1
1
0
2
1
1
1
2
1
2
1
2
1
0
0
1
1
1
1
2
1
1
1
2
0
4
1
1
1
1
1
0
0
1
1
2
2
2
1
0
1
1
0
2
1
1
1
1
1
1
0
1
1
1
3
2
1
2
1
0
1
1
0
1
0
1
1
1
0
1
1
1
1
1
0
1
1
1
1
1
2
3
0
0
1
1
1
1
2
0
0
1
1
1
1
0
2
1
2
1
1
1
1
1
1
1
2
1
0
1
0
1
1
2
1
2
1
0
1
1
1
2
1
2
1
1
1
0
1
1
0
0
1
2
0
1
1
1
2
0
1
1
1
1
1
1
1
1
1
2
1
1
0
1
2
2
1
0
0
2
2
1
2
2
1
1
0
1
2
1
1
0
1
1
1
1
1
2
0
1
1
1
0
2
1
1
2
1
1
1
1
3
2
1
1
2
1
1
1
0
2
1
1
1
1
2
0
1
1
1
0
1
1
2
1
2
1
0
2
0
1
2
2
1
1
2
2
2
1
1
1
1
1
1
1
2
1
1
1
1
2
1
0
1
0
1
1
1
1
1
1
2
1
2
1
1
2
1
0
0
1
1
1
1
1
2
1
1
2
2
2
1
1
0
1
1
1
1
2
1
1
1
2
0
2
1
1
1
1
1
1
1
1
1
3
1
1
1
1
1
1
2
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
1
1
2
1
1
2
0
1
1
1
1
1
2
1
1
1
1
1
0
1
1
2
1
2
1
1
0
0
0
1
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
5
1
0
1
0
1
1
2
1
0
1
1
1
0
1
1
1
0
0
2
1
1
1
1
2
2
1
1
1
0
1
1
1
1
1
1
2
1
1
1
1
2
1
0
1
1
1
1
1
1
0
2
2
0
1
1
0
1
2
1
2
0
2
2
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
0
0
0
0
1
0
1
1
2
1
1
0
1
1
1
2
1
1
1
1
2
2
2
1
0
2
2
0
0
1
2
0
3
1
1
2
0
2
1
1
0
1
0
0
1
1
2
0
1
1
1
0
1
1
1
1
0
1
2
1
1
0
1
1
0
0
2
2
0
0
1
1
1
1
2
2
1
2
1
2
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
1
0
1
1
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
2
1
1
0
2
0
1
0
1
1
1
1
1
2
2
1
1
0
0
4
0
0
1
1
1
3
2
1
1
1
1
2
2
1
1
1
0
1
1
2
1
0
1
0
0
0
1
0
1
2
1
1
1
2
1
0
0
0
2
0
1
2
2
1
1
1
1
1
2
1
0
1
0
2
1
2
1
1
2
1
2
1
0
1
0
0
1
0
0
1
2
1
2
2
2
1
1
1
2
2
1
2
2
1
1
2
1
1
1
1
0
0
2
1
1
0
1
0
0
1
0
2
0
1
2
1
1
0
2
1
1
1
2
1
0
1
1
1
2
0
2
2
1
1
2
1
1
1
0
1
1
1
2
1
0
2
1
0
1
1
1
1
1
0
1
1
1
0
1
1
2
1
2
1
2
1
1
2
0
2
2
2
1
1
1
11
1
0
1
1
0
1
0
1
1
2
0
1
1
2
1
1
2
1
1
1
1
1
1
0
1
1
0
1
2
2
1
1
1
1
1
1
0
1
1
1
1
0
1
0
1
1
1
2
0
1
1
0
1
2
1
1
2
2
1
0
1
2
0
1
0
2
2
1
5
2
1
1
1
0
1
2
2
1
0
1
1
1
2
0
0
0
2
0
0
1
0
0
1
1
1
1
1
2
0
1
0
1
1
0
2
0
0
2
1
0
2
2
1
0
0
1
2
1
2
2
2
0
1
1
2
1
0
0
0
0
2
0
2
1
1
0
1
1
0
2
2
1
2
1
0
1
1
2
2
2
2
1
1
1
1
1
0
1
1
0
1
1
1
2
1
0
1
1
1
1
1
1
0
1
1
2
0
1
1
2
1
1
2
1
1
1
0
2
1
1
0
1
2
1
0
1
1
2
1
1
1
1
1
2
0
2
1
0
1
1
1
1
1
0
1
1
1
0
1
1
2
0
1
2
1
0
1
1
1
2
1
2
1
1
2
2
1
1
1
0
2
2
2
1
1
1
1
2
1
1
1
1
0
2
2
0
1
1
3
1
0
2
2
0
1
2
1
1
1
2
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
2
0
1
1
2
2
0
1
1
1
1
1
1
1
2
1
1
1
0
1
1
1
0
2
2
1
2
2
1
0
1
1
1
2
0
3
0
0
0
1
1
1
0
0
1
1
1
2
2
2
1
2
1
1
1
1
1
2
1
2
1
1
0
1
1
1
2
0
1
2
1
1
2
1
2
1
1
2
1
2
0
2
1
1
2
2
2
2
1
0
0
1
1
0
1
3
0
1
1
1
1
1
1
0
1
2
2
2
2
0
1
1
1
1
0
1
1
1
1
2
1
2
1
1
0
1
1
1
1
1
0
1
0
1
1
3
1
1
1
1
1
2
1
0
1
1
0
1
1
2
1
1
1
0
1
1
1
2
2
2
1
0
0
2
1
2
1
1
2
1
1
2
1
1
0
0
1
0
1
1
0
1
0
1
2
3
1
0
0
1
1
2
1
1
1
0
1
1
1
1
2
1
1
2
0
1
2
0
2
1
1
0
1
1
1
0
2
1
2
1
1
1
1
1
2
0
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
6
1
2
1
0
1
2
1
2
3
1
1
1
2
2
2
0
1
1
2
2
1
1
1
1
1
1
1
0
1
2
2
2
1
1
1
1
1
0
1
0
2
0
0
0
1
1
0
1
1
1
1
1
2
2
2
1
1
1
1
0
1
1
1
1
1
0
0
2
3
1
1
1
0
1
1
1
1
0
2
1
1
1
3
1
2
1
2
1
1
0
2
1
1
1
1
1
1
1
1
1
2
1
1
1
0
1
1
0
1
1
0
2
2
1
1
1
1
2
0
1
2
0
1
0
1
2
1
2
1
1
1
0
1
0
0
1
1
1
2
1
1
1
1
1
1
1
1
2
2
2
1
2
1
0
2
1
0
1
1
1
1
1
1
1
1
2
0
1
2
0
0
0
1
1
0
1
2
1
2
1
1
1
1
1
1
2
0
2
1
1
2
1
1
1
1
2
1
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
2
1
2
2
0
2
1
2
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
0
2
1
1
2
1
1
1
0
1
2
0
1
1
1
2
1
0
1
1
1
1
1
1
1
1
1
1
0
0
1
2
2
0
1
1
1
0
0
1
2
1
1
0
1
1
2
0
2
0
1
1
2
1
1
2
1
1
1
0
0
3
2
0
1
2
2
1
1
2
1
2
1
1
0
2
1
1
1
1
0
1
1
1
1
0
1
2
1
2
1
0
1
1
1
1
1
1
1
2
2
1
1
1
1
0
0
0
1
2
2
1
1
2
1
1
1
1
0
1
2
2
1
2
1
1
1
1
1
1
2
2
1
2
0
1
2
1
0
1
1
1
2
0
0
1
1
1
0
1
1
1
0
1
2
1
1
1
1
2
0
2
1
2
1
1
2
1
2
2
1
0
1
1
2
1
2
1
1
1
2
2
0
1
0
1
1
1
2
0
2
1
1
2
1
0
2
1
1
2
2
2
0
0
1
2
1
2
1
1
1
0
1
0
2
1
2
1
2
1
0
1
0
1
2
1
1
0
1
1
1
1
3
1
0
1
0
1
1
1
3
1
1
1
1
1
1
2
1
2
1
2
1
2
1
0
1
1
1
1
2
1
1
0
1
1
2
1
1
1
1
2
1
1
1
1
0
1
0
1
0
0
1
2
1
0
2
1
1
0
1
2
1
1
1
1
1
1
0
1
0
2
2
0
1
0
3
1
1
1
2
1
0
1
2
1
2
0
2
1
1
1
0
1
2
1
2
1
1
2
1
2
1
2
1
1
2
0
1
1
0
0
1
1
1
0
2
1
1
2
1
0
1
0
1
1
0
1
1
1
1
0
1
1
0
2
2
2
0
1
1
2
1
1
1
1
0
1
2
1
1
1
2
1
1
2
1
0
1
0
1
1
1
0
1
0
0
1
2
1
1
1
1
0
0
2
1
1
2
0
2
2
1
0
0
1
0
1
1
0
1
2
2
1
1
1
1
2
1
1
2
0
0
0
1
0
1
1
2
1
0
1
0
0
1
1
1
1
0
2
1
0
1
1
2
2
1
1
1
1
1
0
0
1
2
1
1
1
2
1
1
0
1
1
1
1
1
1
1
0
1
2
1
1
2
2
1
2
1
0
1
2
1
2
1
1
2
2
1
1
1
1
1
0
0
1
1
1
1
2
1
1
0
1
1
1
2
0
2
1
1
1
1
0
1
2
1
2
1
1
2
2
1
1
1
1
1
1
1
0
1
1
0
2
3
0
0
1
2
1
1
2
1
1
1
1
1
1
1
0
2
1
1
1
1
1
2
1
0
1
1
1
0
1
0
1
2
0
1
0
2
2
1
1
1
0
1
1
0
1
1
1
2
2
0
1
2
1
1
0
1
1
2
1
1
2
1
1
2
1
1
0
1
1
2
1
1
2
1
1
1
1
2
1
1
1
2
1
0
1
1
1
1
1
1
1
2
2
1
1
1
2
1
1
2
1
1
2
0
2
1
1
1
2
1
0
1
1
2
0
2
1
2
1
0
0
2
1
2
2
2
0
1
1
1
0
1
1
0
1
1
2
1
3
0
1
1
0
2
2
2
1
0
2
1
1
0
1
1
1
0
3
0
2
1
2
1
1
1
0
2
2
1
1
2
0
2
2
3
0
2
1
1
2
1
1
0
1
1
1
0
1
2
1
1
1
2
2
1
1
0
0
1
1
2
2
0
2
1
0
1
1
1
1
1
2
0
1
2
1
2
1
2
1
1
0
2
0
2
1
0
2
0
1
2
1
2
1
1
1
1
1
1
1
0
1
2
0
2
1
1
1
0
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
2
1
1
1
1
1
0
2
1
0
0
1
2
0
1
1
2
1
1
2
1
0
1
1
3
1
1
1
1
2
1
2
2
1
2
1
1
1
1
1
1
1
0
0
1
1
0
0
1
1
2
1
2
1
0
1
2
1
1
2
1
1
0
1
1
1
1
1
1
1
1
0
1
2
2
1
1
2
2
0
1
1
1
1
0
1
2
2
1
1
0
0
1
0
2
1
2
0
1
1
2
2
0
1
2
2
3
1
1
2
2
1
0
1
1
2
2
1
1
1
2
1
2
2
1
0
1
1
2
0
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
0
0
1
1
1
1
2
1
2
1
0
1
1
1
1
0
3
0
1
2
1
0
0
1
1
1
0
2
1
1
1
1
1
1
1
1
1
0
2
1
1
1
1
1
2
2
0
1
0
1
0
0
1
2
1
2
1
0
1
1
1
1
2
0
1
1
1
1
0
1
1
1
1
0
2
2
0
1
1
0
0
2
0
1
1
1
1
0
1
1
2
1
1
2
1
1
1
1
2
2
0
1
2
1
1
1
1
1
1
1
2
1
2
2
1
2
1
2
2
2
1
1
1
2
2
1
1
0
1
1
1
2
1
1
1
1
2
1
1
0
1
1
0
2
1
1
1
1
2
1
2
1
1
1
0
0
2
1
1
1
0
2
1
1
1
2
0
2
1
1
1
1
0
2
1
0
1
2
1
0
1
2
2
2
2
1
1
1
0
1
1
1
0
2
2
2
1
1
1
0
2
1
1
1
0
0
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
2
1
2
0
2
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
1
2
1
2
2
1
1
1
2
1
1
1
2
1
1
1
0
1
1
2
1
1
1
1
1
1
2
2
2
1
2
1
2
1
1
0
1
1
1
1
1
2
1
3
2
1
1
1
1
2
3
1
1
1
1
0
1
0
1
1
2
1
2
1
1
1
2
0
2
2
1
1
3
0
1
3
1
2
2
1
2
1
1
1
0
2
1
1
1
2
1
2
1
2
1
1
1
2
2
1
1
2
1
1
1
0
1
1
1
1
0
1
1
1
2
2
1
1
0
2
1
1
1
0
1
0
0
0
1
2
0
1
1
1
1
1
1
0
1
2
1
1
1
1
2
1
1
2
1
1
1
0
1
1
2
2
1
1
1
1
2
1
1
2
0
1
1
1
2
1
1
0
1
2
0
1
1
0
2
1
1
1
1
0
1
1
1
2
1
1
2
1
2
2
2
2
1
1
1
1
2
1
1
1
1
2
1
2
1
1
0
1
1
0
1
2
1
1
1
1
0
2
2
1
1
1
1
1
1
0
1
1
1
1
2
1
1
1
2
0
1
2
2
2
1
2
1
1
1
1
1
1
1
1
0
2
1
0
2
1
1
2
0
1
1
1
1
1
1
2
1
2
3
2
0
1
1
2
1
2
1
1
2
0
2
1
1
2
1
2
2
1
1
2
1
1
2
1
1
1
1
2
1
1
2
2
2
1
1
1
1
1
1
1
2
1
2
2
2
2
2
2
1
1
2
0
0
1
1
1
1
0
0
1
2
0
5
1
2
2
1
1
2
1
1
0
1
1
0
1
1
1
2
1
1
1
0
2
0
0
0
1
1
1
2
1
1
2
2
2
2
1
1
1
0
0
1
1
0
1
2
3
1
2
2
1
0
1
1
1
0
1
1
0
1
1
0
2
0
1
1
0
1
2
1
1
2
1
1
1
1
0
0
1
1
0
1
3
1
1
2
1
1
1
0
2
1
1
0
1
2
1
1
1
1
1
1
2
1
1
1
3
1
1
1
1
1
1
1
2
3
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
2
1
1
2
1
1
2
3
0
2
1
1
2
2
2
1
1
2
1
1
1
1
2
1
1
1
1
1
3
1
1
1
1
1
0
1
1
0
0
1
0
0
2
1
1
1
2
1
2
2
1
2
2
1
1
1
1
2
0
2
1
1
0
0
1
1
0
1
1
2
2
0
1
1
0
1
2
0
1
1
1
1
1
0
1
2
1
1
2
1
0
1
1
1
2
0
1
1
2
2
1
1
0
0
0
1
1
1
1
0
2
1
1
1
1
1
2
0
2
1
1
2
1
1
1
2
1
2
1
2
2
2
0
2
2
0
2
1
1
2
2
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
0
1
1
1
1
1
1
2
1
0
1
2
1
1
2
0
1
1
1
0
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
0
1
1
2
2
1
2
1
1
1
2
1
1
1
1
1
1
0
2
1
1
1
1
0
0
1
1
0
1
2
0
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
0
1
1
0
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
2
1
2
1
1
1
2
1
1
2
0
2
1
0
2
1
1
1
0
0
1
1
2
1
1
1
0
1
1
1
2
1
2
1
2
1
1
0
2
2
1
0
3
2
2
2
2
1
1
1
1
1
1
0
1
0
1
1
0
1
1
1
0
2
2
1
1
1
1
1
1
0
5
1
0
1
2
1
0
1
1
1
2
1
2
1
2
1
0
1
1
1
1
2
2
1
0
1
1
2
1
2
1
1
1
1
1
1
1
1
1
0
1
1
2
1
2
0
2
1
1
1
1
0
2
1
0
2
2
2
1
0
1
1
1
1
1
1
0
2
0
1
1
1
2
0
2
0
1
0
1
1
1
2
0
2
2
1
1
0
1
0
1
1
1
2
2
1
2
0
1
0
0
1
1
1
0
1
1
1
0
1
1
1
1
1
2
1
1
1
2
2
2
1
1
1
1
1
0
1
2
1
1
1
1
1
1
2
1
1
1
1
0
1
2
2
2
0
2
0
2
0
1
1
0
1
1
2
1
0
2
0
1
0
1
2
1
1
0
1
1
1
1
0
1
1
1
1
1
2
0
0
0
1
1
2
0
1
1
1
2
1
2
2
2
1
2
1
1
1
1
1
0
1
0
1
1
1
2
1
1
1
2
1
1
1
0
2
2
0
2
1
1
1
1
2
1
1
1
0
1
1
0
2
1
1
1
1
3
2
1
1
1
1
1
1
2
1
1
2
1
1
2
0
1
1
2
1
1
0
2
1
1
0
2
1
0
1
2
2
1
0
0
1
2
1
1
2
1
2
1
2
1
1
1
3
1
1
2
2
2
2
1
2
2
1
1
0
1
1
1
1
2
1
0
1
2
0
2
1
0
1
1
2
1
1
2
1
1
1
2
1
2
1
1
1
1
0
1
0
1
2
1
1
2
2
0
0
1
2
2
1
1
2
2
2
1
2
1
0
2
2
1
1
2
2
2
1
2
1
2
0
1
0
2
2
1
1
1
1
2
1
0
1
2
1
1
1
2
1
1
1
1
1
1
1
0
1
1
2
1
2
1
2
1
2
1
0
1
2
0
1
0
1
2
1
1
2
0
2
2
0
2
1
1
1
2
0
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
0
0
1
2
1
0
1
0
2
1
2
2
2
1
2
1
1
0
2
1
0
1
1
2
0
1
2
1
2
1
1
0
1
0
2
5
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
0
2
2
1
1
0
1
1
1
1
0
2
1
1
0
2
2
2
2
2
1
1
1
1
1
1
1
2
1
1
1
1
2
2
1
1
1
2
1
2
1
1
0
1
1
2
1
1
1
2
1
1
1
1
2
1
2
2
2
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
0
1
1
2
1
0
1
1
1
2
1
2
1
2
0
1
1
1
1
2
1
1
1
2
1
1
2
1
2
2
1
0
1
2
1
0
0
2
1
1
1
1
1
1
1
2
2
1
0
1
1
2
1
0
2
1
1
1
0
2
1
2
0
0
1
1
1
2
1
1
1
1
2
1
0
1
1
1
0
1
1
1
1
1
1
0
1
0
1
1
0
1
0
1
2
1
2
1
1
1
1
2
1
2
1
1
1
1
1
0
1
1
1
1
0
1
0
1
2
1
2
2
1
0
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
0
1
1
2
1
0
1
2
1
0
2
0
0
1
2
1
1
1
1
2
2
1
1
0
1
1
2
1
2
2
2
1
1
1
1
1
1
1
0
1
1
0
1
2
1
1
1
1
1
0
1
1
2
2
1
1
3
1
2
0
1
1
1
1
1
0
2
1
2
1
1
0
1
2
2
0
1
2
1
1
1
1
1
1
1
1
1
1
0
1
0
2
0
1
2
1
2
1
1
0
2
2
1
1
1
2
1
1
0
1
1
0
1
1
1
2
1
0
1
0
2
2
1
1
0
1
1
0
1
2
1
2
1
0
1
1
1
1
1
2
1
1
1
2
1
2
1
1
0
2
1
2
1
0
2
2
1
0
2
1
1
1
1
0
1
0
1
1
1
0
1
1
2
2
1
1
2
1
1
2
1
0
1
1
0
0
1
0
2
1
2
1
1
2
2
1
2
0
1
1
2
2
1
0
1
2
1
1
1
0
2
2
1
0
1
2
2
2
2
2
2
1
0
1
2
2
1
1
1
1
1
2
1
1
1
1
1
1
1
0
1
1
1
1
2
1
1
1
1
2
1
0
0
1
0
1
1
1
2
1
1
1
1
1
1
2
1
0
1
2
0
0
2
2
0
0
1
2
1
1
1
1
1
1
0
1
1
2
0
2
2
2
1
0
1
1
0
1
2
2
1
1
0
2
1
2
0
0
1
1
2
1
2
2
1
2
2
1
2
0
1
2
1
2
2
1
1
0
0
1
0
1
2
0
1
1
1
1
1
2
2
1
2
2
2
2
0
0
1
1
1
1
1
1
1
0
1
2
1
1
1
1
0
1
0
0
1
1
2
1
1
2
1
2
1
1
1
1
2
1
0
1
1
1
2
1
1
2
1
2
1
2
1
0
1
1
1
1
0
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
2
1
1
0
2
1
2
2
1
2
1
1
1
1
1
0
1
0
2
2
1
0
1
2
1
1
1
1
1
1
0
0
1
2
1
2
0
1
4
1
1
1
1
1
0
1
1
2
0
2
2
0
1
1
1
0
2
1
1
2
1
1
0
1
2
3
1
2
0
1
1
0
1
2
1
0
0
2
0
2
1
1
1
2
0
1
2
1
0
1
1
1
1
1
0
1
1
2
2
3
1
0
1
2
1
2
2
1
1
2
1
2
1
1
1
2
1
0
1
1
1
2
0
1
3
2
1
1
2
1
1
1
2
1
0
1
1
1
1
1
0
0
0
0
2
1
0
2
1
2
0
2
0
1
1
1
1
1
2
1
1
3
2
1
0
2
2
1
1
2
2
1
0
1
1
1
1
2
1
1
2
2
1
3
1
0
1
0
3
0
1
2
2
1
0
2
1
1
1
1
1
0
1
0
1
2
1
1
0
1
2
0
1
1
1
1
2
0
1
1
1
1
2
1
2
1
1
1
1
1
1
1
0
0
0
2
0
1
1
2
1
2
2
2
2
1
1
1
0
0
1
2
2
1
1
2
1
2
0
1
0
2
2
1
1
1
1
1
1
0
1
1
2
2
1
2
1
1
1
1
0
1
1
1
1
3
0
2
0
2
2
1
1
2
2
1
0
0
1
0
2
1
1
0
1
2
2
1
1
1
1
2
1
1
1
1
2
1
1
2
3
2
1
1
2
1
1
1
0
1
1
2
1
2
1
1
1
1
2
1
2
1
0
2
1
1
1
1
2
2
0
0
2
1
1
2
0
1
2
1
1
1
1
0
0
1
1
2
0
0
1
1
0
1
2
2
1
1
2
1
2
1
0
0
1
1
1
2
0
0
1
2
2
1
0
2
0
1
1
1
2
2
2
1
1
1
0
1
2
1
2
0
1
1
0
2
2
1
1
1
1
0
1
1
1
1
2
1
0
2
1
2
0
1
0
1
1
2
2
1
0
1
0
1
0
1
3
2
1
1
1
1
1
0
1
1
1
2
2
1
2
1
1
1
1
1
2
2
1
0
1
1
1
2
1
1
1
0
1
1
2
1
1
1
2
1
1
1
2
1
1
1
0
1
2
0
1
1
1
1
2
2
0
0
2
1
2
1
2
0
1
1
1
2
1
1
1
1
0
0
0
2
2
0
2
2
1
1
2
1
1
1
0
1
1
0
0
1
1
1
1
1
1
0
1
0
2
1
0
2
0
2
1
1
1
2
1
1
0
1
1
2
0
0
2
1
1
2
0
0
1
1
1
1
2
2
1
1
2
1
2
2
2
1
2
1
2
1
2
1
1
1
0
2
2
0
1
2
0
1
1
1
2
2
0
1
1
1
2
1
2
1
2
0
2
0
1
1
2
1
1
1
2
2
2
2
1
0
2
1
0
1
1
1
1
1
2
2
0
2
1
0
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
2
0
1
1
2
0
0
1
1
1
2
1
2
2
1
1
0
2
1
0
1
2
0
1
1
1
1
1
2
1
1
3
2
1
1
0
1
1
1
0
1
0
1
1
1
1
1
2
1
2
1
0
0
2
1
2
1
0
0
0
1
1
1
2
2
2
0
2
2
1
1
0
2
1
2
1
1
1
1
0
1
1
1
1
2
1
1
1
2
1
1
1
2
2
0
1
1
0
1
1
1
0
1
1
1
0
1
2
1
1
1
1
1
2
1
2
2
1
1
2
1
1
2
1
1
0
1
2
1
2
1
1
1
0
2
1
0
2
1
1
1
1
2
1
1
2
1
1
0
1
1
1
1
1
1
1
0
0
1
1
1
1
1
2
0
2
1
1
1
1
0
2
2
1
0
0
0
2
1
2
0
1
1
0
1
2
1
1
0
1
1
1
2
2
1
1
2
0
2
2
1
0
1
1
1
1
2
1
1
0
1
0
1
1
1
1
1
1
0
2
1
0
1
1
0
2
1
1
2
1
1
2
1
2
0
1
0
1
2
0
1
2
1
0
1
1
1
1
1
1
3
1
1
2
0
1
1
1
2
1
1
2
0
2
1
0
0
2
1
1
1
2
1
0
0
0
1
1
1
1
0
2
2
0
1
1
1
1
1
1
2
0
1
1
1
2
2
1
0
2
1
0
0
0
0
0
0
1
2
1
1
2
1
1
1
0
1
0
2
2
1
1
1
1
0
1
1
1
1
2
1
1
2
3
3
2
0
1
2
1
0
1
1
2
2
2
1
0
0
2
2
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
0
2
1
2
1
1
1
1
2
2
2
1
1
1
2
1
2
1
1
1
1
1
0
1
2
2
1
0
1
1
1
2
0
1
1
1
2
0
0
2
2
0
1
0
0
1
1
1
1
1
1
2
2
1
0
1
1
0
2
2
1
1
1
2
2
1
1
2
2
2
1
1
1
0
1
1
1
0
1
0
1
1
1
0
1
1
1
1
2
2
2
2
0
1
1
2
2
0
1
0
2
1
2
0
1
0
1
2
1
1
2
1
0
2
1
1
1
1
1
1
1
0
0
2
2
1
2
1
2
1
2
1
1
0
1
1
0
1
1
1
2
1
1
1
1
0
2
0
1
1
1
0
2
0
2
1
1
0
1
1
2
1
1
0
1
1
1
1
2
0
0
1
2
1
1
1
0
1
1
1
1
1
0
1
1
1
1
1
2
1
1
1
1
2
2
1
1
1
1
1
1
0
1
1
0
1
2
2
1
1
2
1
0
1
1
1
1
1
1
2
0
1
1
0
0
1
2
1
1
2
0
1
0
2
1
1
1
2
0
1
1
1
0
1
1
2
0
2
0
1
2
1
1
2
1
1
1
2
1
1
0
1
1
0
1
1
2
1
1
0
1
1
1
1
1
1
2
2
1
2
1
1
1
1
1
0
1
0
2
1
1
2
1
1
2
1
1
1
1
1
1
1
0
2
2
2
2
1
0
2
2
2
1
1
2
0
2
0
1
5
1
0
2
0
1
1
1
2
1
1
0
1
1
2
2
1
1
1
2
1
2
2
0
1
1
2
1
1
0
2
0
2
1
1
1
1
1
1
0
1
1
1
2
1
2
0
0
1
0
2
0
2
1
0
0
2
1
1
2
0
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
0
1
1
2
0
1
1
2
1
2
2
1
1
1
0
1
1
2
0
1
2
1
1
2
2
1
0
2
2
1
1
0
1
0
2
1
1
0
1
2
1
1
1
0
1
0
1
1
1
0
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
0
0
0
1
1
2
0
2
1
1
2
1
1
2
2
0
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
0
1
0
1
1
2
1
1
1
3
2
2
0
1
0
2
1
0
2
2
1
1
1
0
1
0
1
1
1
0
1
1
1
1
1
2
1
2
1
1
1
2
1
1
1
2
1
0
1
2
2
1
1
1
1
2
1
2
1
1
1
0
1
1
2
1
1
2
1
1
2
1
1
2
2
1
2
1
0
1
1
2
2
1
2
1
1
0
1
1
2
1
0
2
2
2
2
1
1
0
2
2
1
2
1
2
1
0
1
2
2
0
1
1
0
1
2
1
1
2
1
1
1
1
1
1
2
0
1
0
0
1
2
1
2
0
2
1
1
1
1
1
2
0
1
1
1
2
1
1
1
2
0
1
0
1
1
2
1
1
1
1
1
1
2
0
6
1
2
0
1
1
1
2
1
1
1
1
1
0
1
0
1
1
1
1
1
3
0
1
0
1
1
1
1
1
1
2
1
1
2
1
2
1
1
1
2
0
2
1
2
2
0
2
1
3
2
2
1
2
1
0
1
1
1
1
1
1
1
2
2
1
2
2
2
1
2
1
2
2
2
1
1
0
1
2
1
1
0
1
2
0
2
1
0
1
2
1
1
1
1
1
2
1
1
2
0
1
1
1
3
2
2
2
0
2
1
2
2
1
1
2
0
0
2
1
1
1
0
0
1
1
0
1
2
1
1
1
1
1
2
1
3
0
2
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
2
0
1
1
1
2
2
0
0
1
2
2
1
1
0
1
1
1
1
1
1
2
0
1
1
1
2
2
0
1
1
1
2
1
1
1
1
1
1
0
1
0
1
1
1
2
0
1
0
2
1
1
1
2
0
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
0
2
0
1
1
1
1
1
1
1
1
1
0
0
1
2
1
0
1
1
1
1
0
1
1
1
1
1
1
2
1
2
1
1
1
2
0
1
1
1
0
1
0
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
0
2
0
1
1
1
2
1
1
1
2
2
1
0
1
1
2
0
1
1
1
2
0
1
1
1
1
1
1
0
3
1
1
0
0
1
2
1
2
1
1
1
0
2
1
1
2
0
2
1
0
1
0
1
2
2
0
0
2
2
1
1
1
1
1
1
0
1
1
1
0
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
0
3
1
1
1
1
1
1
1
1
1
2
2
1
0
1
1
2
1
1
2
2
1
0
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
0
1
2
1
2
0
2
1
1
1
1
0
1
2
2
1
0
2
1
1
1
1
1
1
1
1
1
0
1
1
2
1
2
1
1
2
1
1
1
2
0
2
1
2
1
1
1
2
0
2
1
1
1
1
1
2
0
2
1
1
0
1
1
2
2
2
1
1
2
2
1
1
0
2
0
1
1
0
1
1
1
1
2
3
2
1
1
1
0
0
2
0
1
1
2
1
0
1
1
1
2
1
1
0
1
1
0
1
1
1
0
0
1
2
1
0
1
1
1
1
1
1
1
0
1
1
0
1
2
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
0
0
1
2
1
1
0
1
1
5
1
1
2
1
1
1
0
1
1
2
1
0
1
1
1
2
0
2
1
0
2
1
1
1
1
2
1
1
0
1
1
1
0
2
1
1
1
0
0
2
1
1
2
1
1
1
1
1
2
1
2
0
1
1
1
1
1
2
2
1
1
1
1
2
2
2
0
1
2
0
1
2
2
1
1
1
1
1
1
2
0
1
1
1
0
1
2
1
1
1
1
1
0
1
1
0
1
1
2
1
1
1
2
1
2
1
1
1
1
0
1
2
2
1
2
2
2
0
1
0
1
1
1
1
1
2
2
2
1
2
1
1
1
1
2
1
1
1
1
1
2
0
1
1
1
2
1
1
1
0
1
0
0
2
2
1
1
1
0
1
0
1
1
1
2
1
1
2
0
1
1
2
1
0
1
1
1
1
1
1
1
1
1
1
0
1
1
1
0
1
2
1
2
2
2
1
1
1
1
1
2
1
0
0
1
0
1
2
2
1
1
1
0
1
0
1
1
2
0
1
1
1
1
1
2
0
1
1
2
1
3
0
0
1
1
1
1
1
1
1
2
1
0
1
0
1
1
2
1
1
1
1
1
1
1
2
2
1
2
1
1
2
2
1
2
1
1
2
1
2
1
0
1
1
0
1
1
1
1
2
1
2
1
0
1
2
1
1
1
1
2
0
1
2
1
0
0
2
0
1
1
1
1
1
1
1
0
1
1
1
1
0
0
2
1
1
2
1
1
2
1
1
1
2
1
1
1
2
1
2
2
2
0
2
1
0
1
2
0
0
1
2
1
2
0
1
2
0
0
1
1
0
1
1
1
2
1
0
3
1
0
1
1
1
1
0
2
1
2
2
1
1
1
1
1
1
2
1
1
1
1
2
2
1
1
1
1
1
2
1
1
0
0
1
1
1
0
1
1
1
3
1
1
2
1
2
1
0
1
0
1
1
0
1
1
1
1
1
1
1
1
0
3
1
1
1
2
0
1
0
1
0
1
0
0
0
1
2
1
1
1
1
2
1
2
2
1
0
1
0
1
1
2
1
2
0
1
1
2
0
1
1
1
1
2
2
1
1
1
1
1
1
1
1
0
0
2
2
1
0
2
1
1
0
0
1
2
1
1
1
1
1
1
1
0
1
1
1
2
0
1
2
1
2
1
1
4
1
2
1
1
0
1
1
2
1
1
3
0
2
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
1
0
1
1
0
1
0
1
1
0
2
1
1
1
0
1
1
1
1
1
1
0
1
1
1
2
1
1
0
2
2
1
1
0
1
0
1
1
1
2
1
1
0
1
1
1
0
0
1
2
2
0
2
1
1
1
1
0
1
1
1
2
0
2
1
1
1
1
1
2
2
1
0
1
1
2
1
0
2
1
0
1
2
2
2
1
2
1
1
1
0
3
1
1
1
1
1
2
1
0
1
1
1
1
2
1
1
1
1
1
2
2
1
1
0
2
1
1
2
1
1
1
0
2
2
1
1
1
0
1
0
1
0
1
1
0
2
1
1
1
2
2
0
1
2
1
2
1
2
2
1
2
0
1
1
1
3
1
1
1
1
1
1
1
2
2
2
1
1
0
2
2
2
1
1
2
1
0
1
2
1
2
0
1
2
1
1
0
1
1
1
1
2
0
1
1
1
0
1
1
2
2
1
0
2
2
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
2
1
0
1
0
1
1
1
1
1
2
5
1
2
1
1
0
1
1
1
1
1
1
1
1
1
0
2
1
1
0
1
3
2
2
1
1
2
2
0
2
0
0
1
2
1
1
0
0
1
1
1
1
0
3
2
1
0
1
1
1
1
1
1
1
1
2
1
1
2
1
0
2
0
1
1
0
1
2
1
2
1
0
2
1
1
1
1
2
1
2
2
0
2
2
2
1
1
1
2
1
2
1
0
2
0
1
1
2
2
0
1
1
1
1
0
0
1
1
1
1
1
1
1
1
1
0
1
0
2
1
1
1
1
1
1
1
1
1
1
0
1
1
2
2
1
1
1
2
1
0
0
1
2
2
0
0
1
0
1
1
2
1
1
2
1
0
1
1
1
1
1
1
1
2
1
1
0
0
1
2
1
1
1
1
2
0
1
1
1
0
0
1
2
2
0
6
1
1
2
1
1
1
1
0
1
0
1
1
1
1
1
1
0
1
1
1
1
0
1
0
1
2
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
1
1
1
2
1
1
1
0
1
0
1
1
1
0
1
2
1
1
1
1
1
1
1
1
2
2
2
1
1
0
1
1
2
1
1
0
2
2
1
2
2
2
2
1
0
1
1
1
0
2
1
1
1
1
1
0
1
1
1
1
0
1
1
1
1
1
1
0
1
1
1
0
0
1
2
1
1
1
0
1
2
1
0
2
1
1
0
2
1
1
1
1
1
1
1
1
0
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
0
2
1
1
1
2
1
2
1
2
1
1
1
1
1
1
2
2
1
2
1
0
1
1
2
1
0
0
1
0
0
1
1
1
1
2
2
1
1
0
1
2
1
2
2
0
0
2
2
1
1
1
0
1
1
1
5
1
2
1
0
1
2
2
1
0
1
0
2
1
1
0
0
1
1
1
1
1
1
1
0
1
1
1
2
0
1
0
1
1
2
1
1
1
1
0
1
1
1
1
2
2
1
1
2
1
1
1
1
1
2
2
1
0
1
2
2
0
0
1
1
0
2
2
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
5
1
2
2
1
2
2
1
2
1
1
1
2
2
1
1
0
2
1
1
2
1
1
2
1
1
1
2
1
1
0
0
1
0
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
0
0
2
1
2
1
1
0
0
0
0
2
1
1
0
1
1
1
1
1
1
2
1
2
0
2
1
1
1
0
2
0
1
0
1
2
1
1
1
1
2
1
1
1
1
1
1
0
2
1
1
1
0
1
1
1
1
2
1
1
1
1
1
1
2
1
1
0
1
2
1
2
1
1
1
0
2
0
2
1
2
1
0
2
1
1
1
1
0
1
1
1
0
1
2
1
1
1
1
1
1
2
1
1
1
0
1
2
1
2
1
0
1
1
1
2
1
2
1
1
1
0
0
1
1
1
0
1
1
1
2
1
1
1
0
1
2
2
1
1
1
0
1
1
1
2
2
1
0
2
0
2
1
0
1
2
1
1
2
1
1
1
1
2
1
1
0
2
1
1
1
1
1
1
0
0
2
2
1
1
2
1
1
1
0
1
1
1
1
2
2
1
1
1
2
1
1
2
1
1
1
2
0
1
1
1
1
0
1
2
1
1
1
1
1
2
0
1
1
2
1
1
2
1
2
1
1
0
1
2
2
1
0
1
1
1
1
0
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
0
1
2
0
0
1
1
1
2
1
1
2
0
2
0
1
1
1
1
1
0
1
1
2
1
1
0
2
1
1
0
2
1
1
1
1
1
2
1
1
1
2
0
1
1
1
0
1
2
2
1
2
0
2
1
1
1
1
1
0
2
1
1
1
1
1
2
0
1
2
1
2
1
2
1
1
1
2
1
0
0
0
1
2
1
1
1
2
0
1
1
1
1
2
0
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
0
1
1
0
1
2
2
2
1
1
1
1
2
2
2
1
0
2
1
2
1
2
2
0
1
1
1
1
1
0
2
1
1
1
0
2
1
1
1
1
3
1
1
1
1
0
1
1
3
1
1
1
2
1
2
1
1
2
1
1
3
0
1
1
1
0
1
0
1
1
0
2
1
2
2
1
1
1
1
0
0
2
1
1
1
3
1
0
2
2
3
2
1
1
2
1
2
1
0
0
2
2
1
1
2
0
1
1
1
1
2
1
0
1
1
0
0
0
1
1
1
2
1
1
2
0
1
1
1
1
3
1
2
2
1
1
1
2
1
1
1
2
1
0
0
0
2
2
2
0
0
1
1
1
0
2
1
2
1
2
1
1
2
1
2
1
1
1
1
1
1
2
1
0
1
2
1
0
3
0
2
2
0
1
2
1
2
1
1
1
1
1
2
1
1
0
1
0
2
1
2
2
1
1
0
1
1
2
1
1
2
0
2
1
1
2
1
1
1
0
0
1
2
2
2
1
1
1
2
1
0
2
0
1
0
2
0
2
1
2
2
0
2
1
1
1
2
1
1
2
0
1
0
1
1
1
2
0
2
1
2
1
2
2
1
0
0
1
0
2
1
1
1
1
2
2
1
1
1
1
0
1
1
1
1
1
2
1
2
1
1
1
2
0
2
1
1
1
2
2
1
1
1
2
1
1
1
2
2
0
1
0
1
2
1
0
1
0
2
1
2
1
0
2
1
1
1
1
2
1
1
0
1
1
1
1
1
2
0
1
1
1
1
0
0
1
1
2
2
1
0
1
1
1
1
1
1
1
2
2
1
1
1
2
1
1
1
1
1
1
0
1
1
2
1
1
2
2
1
0
0
2
2
1
1
1
0
2
0
1
1
1
2
1
1
1
0
2
2
0
1
1
1
1
1
2
1
1
2
2
1
1
1
0
1
0
1
0
1
1
1
2
1
2
0
1
1
0
2
1
1
1
1
1
1
1
0
2
1
2
1
1
2
2
1
1
1
1
2
0
1
1
1
1
1
1
1
1
2
2
1
2
1
0
1
2
2
1
2
0
1
0
0
1
1
0
1
2
0
2
2
1
1
0
1
0
0
1
3
2
0
1
1
2
0
0
1
0
1
2
2
1
1
0
1
1
1
1
1
1
2
1
1
1
1
1
0
1
2
1
2
0
0
3
1
1
1
1
2
2
1
1
0
1
0
1
1
2
1
2
1
3
1
1
1
1
2
0
2
1
1
1
1
1
1
1
1
1
1
0
2
1
2
1
2
0
1
1
1
2
1
1
2
2
1
0
2
1
1
2
1
1
2
1
1
1
1
2
1
1
2
1
1
1
2
2
2
1
1
2
1
0
1
1
2
1
0
1
1
1
1
1
1
1
2
2
2
1
2
2
1
1
0
2
0
1
2
1
1
2
1
1
1
1
1
1
1
1
1
0
1
0
1
1
1
1
1
1
0
1
1
1
1
1
2
0
1
2
1
1
1
1
0
2
1
1
1
2
1
1
1
0
1
1
1
2
2
2
2
2
1
2
1
2
0
0
1
1
1
1
0
1
0
0
1
1
1
1
1
1
1
1
1
2
1
1
0
1
0
1
0
2
1
1
2
2
1
1
1
1
1
0
1
1
1
2
2
2
1
2
1
2
1
1
1
1
1
1
1
0
0
1
1
1
1
1
1
1
0
1
1
1
0
1
1
2
1
0
1
2
1
2
1
3
1
0
0
2
1
1
1
1
2
1
1
2
1
1
1
2
0
1
2
2
1
1
1
1
2
2
1
1
2
1
1
2
2
1
1
1
2
1
1
2
1
1
1
1
1
1
0
2
1
0
1
1
1
0
2
2
0
1
1
1
2
1
1
1
2
1
1
0
1
0
0
1
1
1
1
1
1
1
1
2
0
2
1
1
0
2
1
1
0
1
2
0
1
2
1
1
1
3
1
0
2
2
0
1
4
0
1
0
2
0
1
2
0
1
1
2
1
2
2
2
2
0
1
0
1
2
1
1
1
1
2
1
1
2
1
1
2
2
2
2
1
2
1
1
0
0
0
2
0
0
2
1
1
0
1
1
0
1
1
1
2
0
1
1
0
1
1
2
1
0
2
3
1
1
1
1
1
2
1
2
0
1
1
2
1
1
0
2
0
2
1
0
1
1
1
1
1
0
2
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
3
0
0
1
2
1
1
0
1
1
1
1
1
1
1
0
1
0
1
1
0
1
1
1
1
1
2
1
1
1
0
1
2
1
1
0
2
0
2
2
1
2
1
2
1
1
2
1
1
2
2
1
1
1
1
1
1
0
0
1
2
0
2
1
1
0
2
1
2
1
0
2
0
1
1
1
1
1
0
1
1
0
1
1
2
0
0
2
1
1
1
2
1
1
4
0
2
1
2
1
0
2
1
1
1
2
2
3
1
2
1
0
1
0
0
3
2
0
2
3
2
1
2
0
1
1
1
0
2
1
2
2
0
0
0
2
1
1
2
1
2
1
2
1
1
0
2
2
1
0
1
1
1
1
1
1
2
1
0
1
1
1
0
0
1
1
1
1
1
2
0
1
1
2
1
0
2
1
0
0
1
1
2
1
2
1
1
2
2
1
1
1
2
1
1
1
2
1
0
1
0
1
2
0
0
1
1
2
1
1
0
1
1
1
1
2
2
1
0
1
1
1
2
1
1
2
1
1
1
1
0
1
1
1
2
1
1
1
1
1
2
2
1
0
1
1
2
0
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
1
2
0
2
1
1
2
1
1
2
1
1
1
2
0
2
0
1
1
1
1
1
2
1
1
1
0
2
1
2
0
1
0
1
0
1
1
0
1
0
1
1
0
1
1
1
1
1
2
1
0
2
1
0
0
0
0
2
1
2
1
1
2
2
1
2
2
1
1
2
1
1
1
2
1
1
2
1
1
1
0
1
0
2
0
1
1
0
1
2
1
0
1
1
1
1
1
1
2
2
1
0
1
0
1
1
1
1
2
1
2
1
1
1
1
0
1
0
1
1
0
1
2
1
2
1
2
0
1
0
0
2
1
0
1
2
1
1
1
1
1
1
2
1
1
0
1
1
2
1
1
1
1
1
0
1
1
1
0
1
0
2
1
2
1
2
1
1
1
1
1
3
1
1
1
1
1
1
2
0
1
1
0
2
0
1
1
1
1
0
1
0
0
1
0
0
0
0
0
0
2
0
1
1
2
2
1
1
1
1
0
3
2
2
1
1
2
2
2
1
1
1
1
2
2
0
2
1
1
1
1
0
2
1
2
2
1
1
1
1
2
1
1
1
1
0
1
1
1
2
0
1
2
1
2
0
2
2
2
1
0
2
2
1
2
1
2
0
1
0
1
1
2
1
1
1
2
1
1
0
1
1
1
2
1
1
1
1
1
1
2
1
0
1
3
0
1
0
2
1
1
2
2
1
1
2
2
1
0
1
1
1
1
1
1
1
1
1
1
1
0
0
0
2
0
0
2
1
1
1
1
1
0
1
1
1
1
2
2
0
2
5
1
0
2
2
1
3
1
1
2
1
0
1
0
1
1
1
1
1
1
1
0
1
0
2
0
2
1
0
1
1
0
1
2
0
2
1
1
2
2
2
1
2
1
1
2
1
1
0
2
0
1
1
1
2
1
1
1
1
2
0
0
2
1
1
1
2
1
2
2
3
1
1
1
1
0
1
1
0
1
1
1
1
2
1
0
2
0
1
1
1
1
1
1
0
1
1
1
1
2
1
1
1
1
1
2
1
1
1
0
2
1
2
1
1
2
1
1
1
1
1
1
0
0
0
1
2
0
1
0
1
0
1
0
1
1
1
1
0
2
0
1
0
1
1
1
1
2
2
1
2
0
1
1
2
1
2
2
1
2
1
0
4
2
1
2
1
1
2
2
1
1
1
1
1
0
1
1
0
1
1
2
1
1
5
0
1
1
1
1
2
1
1
1
0
1
1
1
0
2
1
1
1
1
1
1
2
1
0
1
1
2
0
2
1
1
2
1
1
1
1
1
1
0
2
2
2
1
0
1
1
1
1
1
1
0
1
1
2
1
1
2
2
0
1
1
1
1
1
2
2
2
0
1
2
1
1
2
2
1
1
2
1
0
2
2
0
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
0
0
1
1
2
1
1
1
0
1
1
2
2
1
1
1
2
1
0
1
2
1
1
1
1
1
1
1
1
1
0
0
1
0
1
0
2
2
0
2
2
1
2
1
2
0
1
1
1
1
0
0
1
0
2
1
2
0
1
1
1
1
0
1
2
0
1
2
1
1
1
1
2
0
2
1
1
1
1
0
1
0
1
1
2
1
2
2
1
1
1
2
2
3
0
1
1
0
0
2
1
1
1
1
1
4
0
0
1
1
1
0
1
1
2
1
1
1
0
1
1
1
1
1
1
1
0
1
1
2
0
2
0
1
1
1
1
2
2
2
2
3
2
1
1
1
1
1
0
1
1
2
1
2
1
0
2
2
2
1
1
0
1
2
1
2
1
1
1
1
2
1
1
2
0
1
2
2
1
0
0
1
0
1
0
0
1
1
1
1
2
2
1
0
0
2
1
1
2
1
2
1
2
1
1
1
1
1
1
1
1
2
2
1
1
2
1
2
1
1
1
1
1
2
1
1
1
1
1
0
2
1
1
0
2
2
1
2
0
1
1
0
0
1
1
1
2
1
2
1
2
1
1
2
1
2
1
1
3
1
1
1
1
2
1
1
1
1
2
1
2
1
2
2
2
1
2
0
1
0
2
1
1
1
0
0
0
0
1
0
1
1
1
1
1
1
1
1
1
1
2
1
1
3
0
0
1
2
1
2
1
1
1
1
2
1
1
2
1
0
1
1
1
2
1
1
1
1
1
1
2
2
1
1
2
0
2
2
2
1
1
2
0
1
1
1
1
2
2
2
0
2
1
1
1
1
1
1
1
1
2
2
0
1
2
1
1
1
1
0
1
0
0
2
1
0
1
0
1
2
1
1
1
1
1
1
2
2
0
1
2
2
1
1
1
1
1
1
0
1
0
1
1
1
0
1
2
1
1
1
1
1
1
1
1
0
2
1
1
2
2
1
1
1
2
0
1
1
2
1
1
2
1
0
1
0
0
1
2
2
1
2
1
2
1
1
2
0
2
0
1
2
2
2
1
2
2
1
1
1
1
2
1
1
0
2
1
1
1
1
1
0
3
1
1
1
2
1
2
0
2
1
1
1
1
1
1
1
2
1
2
0
2
2
2
0
2
2
2
2
1
2
1
2
2
2
2
2
1
1
1
1
2
0
1
2
1
2
0
2
1
2
1
1
1
2
1
2
1
1
1
1
1
2
2
1
1
2
2
0
1
2
1
1
2
2
1
1
0
0
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
7
1
1
1
1
1
2
0
2
2
1
1
2
0
0
1
2
1
1
1
2
2
0
2
2
1
2
1
1
1
1
1
1
2
0
1
2
2
0
2
1
1
2
1
1
1
0
1
1
1
1
1
1
0
1
1
1
1
1
1
2
2
0
1
1
2
0
4
1
2
1
1
0
1
2
1
1
1
1
1
1
1
2
1
0
1
1
3
1
0
2
1
1
2
0
1
1
0
1
1
1
1
2
1
2
0
2
1
1
0
1
1
0
2
1
2
2
0
2
1
1
3
1
0
1
1
1
1
0
2
1
2
1
2
1
2
1
1
1
0
1
0
1
1
1
1
1
1
1
0
1
2
2
2
1
2
1
1
2
1
1
2
2
1
1
1
0
1
3
0
1
2
1
1
0
0
1
2
1
1
1
1
1
2
2
1
1
1
1
1
1
0
1
1
1
0
2
1
2
1
1
1
2
1
2
2
1
1
1
1
0
0
0
1
1
1
0
2
1
1
2
1
0
1
2
1
0
1
1
1
1
1
0
2
1
1
1
2
1
1
2
2
2
2
2
1
0
1
0
1
0
2
1
1
1
1
0
2
1
0
2
1
1
1
0
2
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
2
0
1
1
0
1
1
1
2
0
2
1
1
1
1
1
0
2
1
1
1
1
0
0
1
1
2
0
1
1
0
1
1
2
1
0
1
1
1
2
1
0
0
1
1
0
1
2
1
1
1
1
1
1
1
2
2
2
1
1
1
1
2
2
1
1
0
1
1
1
2
0
3
1
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
2
1
2
2
2
2
1
1
1
1
0
0
2
0
0
1
1
1
1
1
1
0
1
1
1
0
2
1
1
1
1
0
3
0
1
2
1
0
1
0
1
1
1
1
0
1
1
2
1
1
0
1
2
1
1
1
0
1
1
1
2
1
1
2
0
1
2
2
1
1
0
1
2
0
1
1
1
1
1
1
1
1
1
1
0
0
2
1
1
2
1
2
0
2
0
1
1
1
1
1
1
2
1
1
1
2
1
0
2
1
1
0
1
1
2
2
0
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
0
1
0
1
2
0
0
1
1
1
1
1
1
1
1
1
1
1
1
3
0
1
2
1
2
0
1
2
1
1
1
1
1
2
2
1
1
1
2
2
1
0
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
0
0
2
1
1
2
1
1
0
1
1
1
0
1
1
2
1
1
2
0
2
1
1
1
3
1
1
2
0
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
0
2
1
2
1
1
1
2
1
1
2
1
2
1
0
2
2
1
1
0
1
2
1
0
1
1
1
1
0
1
1
1
0
2
0
0
1
2
0
2
1
0
2
2
0
0
0
1
0
2
1
1
1
1
2
1
2
0
2
2
2
0
2
0
1
1
1
1
1
0
1
1
1
0
0
0
1
1
1
1
2
2
1
1
1
1
2
2
1
1
0
2
1
0
1
2
0
1
0
0
2
1
0
1
1
1
1
0
1
2
0
1
0
0
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
2
0
2
1
1
1
0
0
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
1
2
0
1
1
2
2
2
2
1
0
2
1
2
1
2
2
0
1
0
2
2
1
1
2
1
1
2
1
1
1
1
2
2
2
1
1
1
2
2
1
2
0
0
1
2
1
1
1
1
2
1
0
0
1
1
1
1
1
2
1
2
1
1
1
1
1
0
0
1
1
2
1
2
2
2
0
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
0
2
1
1
1
1
1
1
2
1
1
2
1
0
1
1
0
1
1
1
1
0
0
1
1
1
1
1
1
2
1
1
1
1
1
0
1
1
1
2
1
1
1
1
2
2
1
1
1
2
0
1
1
2
0
2
1
0
0
2
2
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
2
2
1
3
0
1
2
1
1
1
2
2
1
1
1
2
1
1
2
1
1
1
1
2
1
1
1
2
1
1
2
0
2
0
0
0
2
1
2
1
1
2
1
0
1
1
1
1
1
1
1
0
1
2
1
1
1
1
2
1
1
1
2
1
0
2
2
1
1
1
2
0
0
0
1
1
0
1
1
2
1
1
1
1
2
1
1
2
2
2
1
1
2
1
2
2
1
0
1
0
0
0
0
1
2
2
1
1
1
0
0
1
0
2
0
1
1
1
1
2
1
1
1
1
1
2
2
1
2
2
1
2
1
1
3
1
0
2
1
1
2
0
0
0
2
1
2
1
2
1
1
2
1
1
0
1
1
2
1
1
1
2
1
2
1
2
0
1
0
0
1
1
1
1
0
2
1
2
0
2
2
1
1
0
1
0
1
1
0
0
0
0
1
3
2
2
1
1
1
1
1
1
1
1
0
1
1
0
1
1
0
1
0
1
0
1
1
2
2
1
0
1
3
2
1
1
0
1
1
1
1
1
1
0
2
1
1
0
1
1
1
1
3
2
0
1
1
1
1
2
1
1
1
1
1
2
1
0
2
2
2
1
1
2
1
1
0
1
0
1
1
2
2
1
1
2
1
1
2
1
1
2
0
1
2
0
1
2
1
1
0
1
1
1
0
1
1
2
1
0
1
1
2
0
1
0
2
2
1
1
1
0
0
0
2
1
1
0
1
1
1
2
2
0
2
1
2
1
0
1
1
1
1
1
1
0
2
1
1
1
0
0
0
2
1
0
1
1
1
1
1
1
1
2
0
1
1
0
1
2
1
2
1
0
0
1
0
1
1
1
0
1
1
0
1
1
0
2
0
1
3
0
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
0
2
1
1
2
1
1
1
1
1
1
0
1
2
0
2
1
1
1
1
1
2
1
1
2
1
1
2
1
1
2
0
0
1
2
1
2
1
1
1
1
1
2
2
1
2
0
0
1
2
1
1
1
0
1
1
1
1
1
0
2
0
1
0
1
1
1
2
1
2
3
2
2
2
2
1
1
0
1
1
1
0
2
2
2
2
2
2
1
1
1
1
2
2
1
2
2
1
2
1
2
1
0
0
2
1
0
1
1
1
1
1
0
1
0
1
1
1
1
0
1
1
1
1
1
1
1
1
1
0
1
1
1
1
0
1
1
2
1
0
2
0
2
0
1
1
1
2
0
2
1
2
1
0
1
1
0
1
2
1
2
2
1
2
1
1
1
0
2
2
1
1
3
1
2
1
2
2
1
1
0
2
2
1
1
1
2
1
0
2
1
2
1
1
2
1
3
1
1
1
1
0
0
2
2
1
1
1
2
2
2
0
0
2
1
1
0
1
1
1
0
1
1
1
0
1
1
0
2
1
1
0
1
1
2
0
1
1
0
2
1
1
1
0
2
1
1
1
1
2
0
1
1
3
0
1
1
2
2
2
1
1
2
2
1
2
1
0
1
3
1
2
2
1
1
0
2
1
0
1
1
1
1
0
1
2
1
0
0
2
0
0
2
0
1
1
1
1
2
1
1
2
0
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
1
0
2
0
1
1
1
2
1
2
0
1
1
0
2
1
0
1
2
2
1
2
1
2
1
1
2
0
1
0
1
1
1
2
1
1
1
1
0
1
1
0
1
1
1
1
1
1
2
1
1
1
1
2
1
0
2
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
0
2
1
0
1
1
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
3
1
1
1
1
2
5
1
1
0
1
0
1
1
0
1
1
2
1
2
1
2
2
1
1
0
1
1
2
2
1
1
2
1
2
2
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
0
1
1
1
1
2
0
0
1
1
1
2
1
2
1
1
1
2
1
1
0
1
2
1
2
2
1
2
1
1
1
1
1
1
1
1
0
1
1
2
1
2
2
1
1
1
1
2
1
1
2
0
1
1
2
2
1
1
0
2
2
0
1
1
0
1
1
1
0
1
1
1
1
1
1
1
2
1
0
2
1
2
1
2
1
2
1
0
1
1
1
1
0
1
1
0
1
1
1
1
2
1
1
2
2
2
2
1
0
2
1
0
0
1
2
1
2
2
1
0
1
1
1
1
0
2
2
0
2
2
2
0
1
1
1
2
0
0
1
0
0
2
1
0
1
2
1
1
2
2
2
1
1
2
2
1
0
1
2
1
2
1
1
1
1
1
2
1
1
1
0
1
2
0
1
1
1
1
1
0
1
2
1
1
1
0
1
1
2
1
2
1
1
1
2
0
2
2
1
1
1
1
0
2
0
1
1
0
0
1
1
1
1
1
1
0
1
0
1
1
1
2
1
3
2
1
0
1
1
1
1
1
1
1
1
2
1
1
1
0
2
1
2
1
1
2
1
0
2
1
2
1
0
1
1
1
2
1
1
2
1
2
1
1
2
2
1
1
3
0
1
1
1
1
1
1
1
1
2
1
1
2
0
2
0
0
1
2
1
2
1
1
1
1
0
0
1
1
1
0
1
1
1
1
1
0
2
2
1
3
0
1
2
1
1
1
0
1
0
1
1
2
1
0
0
1
1
1
0
1
0
1
0
0
1
2
0
1
2
1
2
1
3
1
0
1
2
2
1
2
1
2
0
2
2
0
1
1
0
2
1
1
1
0
0
0
2
1
2
1
1
0
1
2
0
1
1
1
1
2
1
1
1
0
2
1
1
0
1
2
2
1
1
2
1
1
2
0
1
1
1
2
1
0
1
1
2
2
1
1
1
2
1
1
1
1
1
2
2
1
2
1
3
1
1
2
1
2
1
1
1
1
0
0
2
1
2
1
0
1
2
1
1
1
1
1
1
1
1
1
1
0
1
1
1
2
2
2
1
2
1
2
0
1
1
1
1
1
1
2
1
2
1
2
1
0
1
2
2
1
0
2
2
2
1
1
2
1
2
1
0
2
1
1
1
1
1
1
2
1
0
1
1
1
1
1
1
0
0
2
1
1
0
2
1
1
2
1
1
0
2
2
1
1
1
3
2
1
0
0
2
1
1
2
1
1
2
2
1
1
1
1
0
0
1
1
1
2
1
1
2
2
0
2
1
1
2
1
2
1
1
1
1
1
0
0
1
2
1
2
2
2
0
1
2
1
1
2
1
0
1
2
1
1
2
1
1
2
1
1
1
1
1
1
0
1
0
2
2
1
2
1
1
1
1
0
0
0
1
1
1
1
1
2
2
1
2
2
0
1
2
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
0
1
2
1
2
1
0
1
2
1
1
0
0
1
1
1
1
1
0
0
1
0
0
1
2
1
2
2
2
2
2
1
0
0
1
0
2
1
1
2
1
0
1
1
1
1
1
1
1
1
2
2
2
0
1
1
0
1
1
1
2
0
0
1
2
0
1
0
1
1
2
2
1
0
0
1
1
1
1
0
0
1
1
1
1
1
2
1
0
0
2
1
1
2
1
1
1
1
1
1
1
1
0
2
1
0
1
1
1
2
1
0
0
0
2
1
2
1
0
1
1
2
2
1
1
1
1
1
2
1
1
1
1
2
0
1
2
1
2
1
1
1
1
2
1
0
1
1
1
1
1
3
1
1
2
0
1
1
1
1
0
0
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
1
0
1
0
1
2
2
2
2
2
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
0
1
1
1
2
0
1
1
1
1
2
1
1
0
2
1
0
1
1
1
1
2
1
1
2
1
2
1
0
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
2
1
0
0
1
0
2
2
0
0
1
0
1
2
2
1
1
2
1
2
1
1
1
0
1
0
1
2
1
1
2
1
1
1
2
0
1
1
1
1
2
1
1
2
1
1
1
0
0
1
1
2
1
1
1
0
1
1
2
1
2
1
1
1
2
0
1
1
1
1
0
2
0
1
1
1
2
0
2
1
2
2
2
1
1
2
1
0
1
2
1
0
1
2
2
2
1
1
1
2
1
2
1
1
2
1
1
1
2
0
2
1
2
2
1
1
1
1
1
1
1
1
0
2
0
1
1
1
1
1
1
0
2
2
0
0
1
2
1
2
1
1
0
2
1
2
1
1
1
1
1
1
1
1
2
1
0
2
0
1
1
2
1
1
1
2
1
2
2
0
1
1
1
1
1
1
1
0
0
1
1
2
1
2
2
0
1
1
1
2
2
2
1
2
1
1
1
1
0
1
1
1
1
1
1
1
1
2
0
1
1
1
1
1
2
1
1
1
1
0
1
2
0
1
2
2
1
0
0
0
1
1
1
1
2
1
2
1
1
2
1
1
1
1
1
2
1
0
1
1
2
2
0
1
2
2
2
1
3
1
0
2
2
1
0
1
1
2
0
1
4
1
1
2
0
2
2
5
2
1
0
2
1
0
0
1
2
2
2
2
0
2
1
1
0
1
1
2
1
0
2
2
1
1
1
1
1
1
1
2
1
1
2
0
1
2
2
0
1
1
0
1
2
1
1
0
1
1
1
2
1
1
1
1
2
1
0
1
1
1
1
0
0
1
1
2
1
1
1
2
1
1
1
0
1
1
0
2
0
2
2
1
1
1
0
2
1
0
1
1
2
1
2
1
0
1
1
0
0
2
2
1
1
2
1
1
1
2
2
1
1
1
3
2
2
2
1
1
1
1
1
0
0
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
0
2
1
1
0
0
1
1
1
1
1
1
1
2
1
1
0
1
1
2
1
2
2
1
2
1
1
1
1
1
1
1
1
1
0
0
2
1
0
1
1
1
1
2
2
1
1
1
1
0
1
2
1
1
1
2
2
1
1
1
1
0
1
1
2
1
2
1
1
2
0
1
0
1
1
1
1
2
1
1
2
1
0
1
0
1
1
1
1
2
2
1
2
1
0
1
1
1
2
2
1
0
1
0
1
1
0
1
1
0
1
2
1
1
1
1
1
1
1
0
2
2
0
1
2
1
1
1
1
2
1
1
2
1
1
2
2
0
1
2
1
1
1
0
1
1
4
2
1
3
1
2
1
1
2
2
1
0
1
1
1
0
2
1
1
1
1
1
1
1
0
2
1
0
1
0
1
1
0
2
2
2
1
0
1
1
1
2
2
1
0
1
1
1
1
2
1
1
1
1
1
1
1
2
1
0
0
1
1
0
1
1
1
1
1
0
1
1
2
1
2
0
1
1
1
1
1
2
1
2
1
1
2
1
1
1
0
1
1
0
2
2
2
1
2
1
1
1
1
2
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
2
1
1
1
0
2
1
1
2
2
1
2
1
1
0
2
2
1
0
0
1
1
1
2
2
1
2
2
0
1
2
2
1
0
2
2
1
1
2
0
1
1
1
1
1
2
0
2
2
2
1
0
1
1
1
1
0
1
1
0
1
1
1
1
1
1
2
2
2
2
2
1
0
1
2
1
1
0
1
1
1
2
2
1
1
1
1
1
2
1
1
2
0
1
2
1
1
1
0
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
2
0
1
0
2
2
1
2
2
2
1
2
1
1
2
1
0
1
1
1
1
0
0
1
1
1
1
2
1
1
1
2
1
1
1
1
2
2
1
1
1
1
2
1
0
1
1
2
2
2
0
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
2
2
1
0
1
1
2
0
0
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
2
1
1
2
2
1
1
2
1
2
2
1
1
1
0
1
2
2
3
2
1
1
1
0
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
2
1
2
1
1
1
1
1
2
1
1
0
1
0
1
1
0
1
0
2
2
1
2
1
2
2
1
2
1
2
1
1
1
1
1
2
2
1
1
0
1
1
2
1
0
0
2
1
1
0
1
2
1
1
1
1
2
1
1
1
1
2
0
2
1
1
1
0
2
0
0
2
1
2
1
0
1
2
1
1
0
1
1
1
1
2
1
2
2
1
1
0
2
1
1
1
1
1
1
0
1
1
1
0
0
2
1
1
2
0
1
1
2
0
1
1
2
0
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
0
2
2
1
2
2
1
2
0
2
0
2
1
2
2
1
1
1
1
2
2
0
1
1
2
1
1
2
1
1
0
2
1
0
1
1
1
2
3
2
2
1
0
1
1
1
1
1
0
1
1
2
1
1
1
0
1
1
2
1
1
1
1
2
1
1
1
1
0
1
1
1
1
0
1
2
1
1
1
2
1
1
1
3
1
0
0
0
1
2
2
1
1
2
1
0
2
1
1
1
1
2
1
1
1
1
2
1
2
2
2
1
2
2
2
1
1
1
2
2
0
1
0
1
1
2
0
0
1
0
1
1
0
1
1
1
1
1
0
1
2
0
1
1
1
1
2
2
1
1
1
1
1
1
1
2
0
1
1
1
0
1
1
2
1
1
1
0
1
1
2
1
1
0
1
1
1
2
1
1
0
0
1
1
0
3
1
1
2
1
1
0
1
2
2
1
1
2
1
1
1
0
0
1
0
1
1
1
2
1
0
1
2
1
1
1
0
1
1
2
1
1
1
1
1
2
2
1
1
2
1
1
1
0
1
1
2
0
1
0
2
1
1
0
1
1
1
1
1
1
0
2
1
1
1
0
2
2
1
1
1
1
1
1
1
0
2
1
2
1
1
0
1
2
1
1
2
1
2
1
1
1
1
0
0
1
2
0
0
2
2
0
1
1
2
1
1
1
1
1
1
1
1
2
2
2
1
1
0
1
1
1
1
1
1
2
1
0
2
2
0
0
1
1
1
1
1
1
2
2
0
1
1
1
1
2
2
2
2
0
1
1
1
0
1
0
1
1
1
0
1
1
2
1
2
0
2
1
1
1
2
0
1
1
1
1
1
1
1
2
1
1
2
1
1
2
2
3
0
0
1
0
0
1
2
1
1
0
0
1
2
1
1
2
2
0
0
2
1
1
1
2
1
2
1
1
1
1
1
1
2
1
2
1
0
1
0
2
2
0
1
1
1
1
2
1
1
2
1
2
1
1
0
1
1
2
2
1
2
0
1
1
1
1
1
1
1
1
1
2
0
1
0
1
1
1
1
1
1
1
2
1
2
0
2
1
1
0
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
0
2
0
2
2
1
2
1
0
1
2
0
1
1
2
1
1
2
1
1
0
1
1
1
0
1
1
1
0
1
1
1
1
1
2
2
1
0
0
2
2
2
0
0
0
1
1
2
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
1
2
2
2
1
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
2
1
2
1
1
0
2
1
1
2
1
1
1
2
1
1
1
2
1
1
2
1
1
0
1
1
1
0
2
0
2
1
0
1
2
1
0
1
1
2
2
0
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
0
1
1
1
2
2
1
1
1
1
1
1
4
2
1
1
0
1
2
1
1
1
1
1
1
1
2
1
0
2
1
1
1
0
1
2
1
2
0
2
2
1
3
0
2
1
1
2
1
2
2
2
1
1
1
1
1
1
1
2
1
1
1
0
1
2
1
1
1
0
2
1
0
0
1
1
1
2
2
1
1
1
0
1
1
1
2
1
1
1
2
2
1
1
1
2
1
1
1
0
1
2
2
1
0
1
0
2
2
1
1
1
1
1
2
1
1
1
1
0
1
1
1
1
1
1
1
0
0
1
0
1
1
1
2
1
1
1
1
1
1
1
0
0
1
2
1
1
2
2
1
2
2
1
1
1
1
0
2
2
1
1
1
1
2
1
1
1
1
0
1
1
1
1
0
2
1
1
1
1
2
1
1
2
2
1
1
1
1
2
0
1
1
2
1
1
2
2
1
1
2
0
1
1
1
1
2
1
1
1
2
0
1
1
1
2
1
0
2
1
1
1
1
1
1
1
0
2
1
2
0
1
0
2
1
1
0
1
2
0
1
1
0
4
1
1
2
2
2
0
2
2
2
1
2
1
2
1
1
2
2
2
2
1
1
1
2
1
2
1
0
0
1
2
2
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
0
2
1
0
2
1
1
1
0
1
0
1
1
1
1
2
2
1
1
1
2
1
1
1
1
1
1
2
1
2
2
1
1
2
2
2
3
1
1
2
1
2
2
1
2
1
0
2
1
1
1
1
1
1
2
1
1
0
1
0
1
0
1
0
2
1
2
0
1
1
1
1
1
1
2
1
1
1
1
1
0
1
2
1
1
1
0
1
2
0
0
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
2
0
2
0
1
0
4
2
0
2
0
2
0
1
0
1
1
1
1
1
2
2
1
0
1
1
0
0
2
1
1
2
2
1
1
1
1
1
1
1
2
1
1
2
1
1
2
0
2
1
1
1
1
1
1
2
1
1
1
0
0
2
1
0
2
1
2
1
2
1
2
2
2
1
1
2
1
1
0
2
0
1
2
0
1
1
1
1
1
2
2
2
0
1
1
1
1
2
1
2
2
0
2
1
1
1
1
1
0
2
1
1
1
1
2
3
1
1
1
0
1
2
1
2
1
2
2
1
2
0
1
1
2
1
5
1
1
2
1
1
1
1
1
1
2
1
2
1
1
0
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
2
2
1
1
1
1
0
0
1
2
2
1
2
1
2
2
1
0
1
1
2
1
0
1
1
0
0
2
2
2
1
1
1
1
2
1
2
1
0
1
0
0
1
1
1
1
2
1
1
1
1
1
2
1
1
2
1
1
1
1
2
1
0
2
1
2
0
1
0
1
1
0
1
0
1
2
1
1
1
1
2
2
1
1
2
1
1
1
2
2
2
0
0
0
1
1
1
1
2
1
1
1
3
1
1
0
1
1
1
1
2
1
1
2
1
1
2
0
2
1
2
1
1
2
2
1
1
2
1
1
1
2
2
2
1
2
0
0
1
1
2
1
1
1
1
1
1
0
0
1
1
2
0
1
2
1
1
2
1
1
1
1
1
2
1
1
2
2
1
1
1
1
0
1
0
0
1
2
2
1
2
1
2
0
0
1
2
2
1
1
1
1
2
2
2
0
1
2
1
2
1
0
1
1
0
1
1
0
0
2
1
1
1
0
1
2
1
1
2
1
1
1
1
1
1
0
1
0
1
2
1
2
1
2
2
1
0
0
2
1
1
1
1
1
1
2
1
2
2
1
2
1
1
1
2
2
2
1
1
0
1
1
1
1
1
1
1
1
1
1
2
2
1
2
0
1
0
1
2
1
1
0
0
1
1
0
1
1
1
2
2
2
1
1
2
1
0
1
2
1
2
2
1
1
1
1
1
1
2
1
1
1
0
1
1
1
0
0
1
1
2
1
0
0
1
1
1
0
1
1
0
1
1
0
1
1
1
1
0
2
2
2
1
2
1
1
1
1
1
0
2
0
2
1
1
1
1
1
1
0
1
0
1
1
2
2
1
0
1
0
2
1
0
0
0
4
1
1
1
2
1
2
1
1
2
1
1
1
0
2
1
2
1
2
1
1
1
2
2
1
0
1
1
1
1
1
0
1
2
1
1
1
0
0
0
2
1
1
1
1
1
1
0
1
1
1
1
1
1
1
2
2
2
0
1
0
1
1
1
0
1
0
2
2
2
1
1
1
1
1
1
2
1
1
1
0
1
1
1
1
0
1
1
1
0
1
1
1
1
1
1
1
0
1
1
1
2
2
2
0
0
1
1
2
1
1
1
1
2
1
3
0
1
1
1
0
1
2
2
1
0
1
2
1
1
2
2
1
2
0
1
0
1
1
1
1
1
1
0
1
1
0
1
0
1
0
1
2
2
2
1
2
0
0
0
1
2
0
2
1
1
1
1
1
1
1
1
1
2
0
1
1
1
1
2
1
1
1
1
2
1
1
0
1
2
1
1
1
0
1
2
2
1
1
1
1
2
1
2
1
2
1
1
0
0
2
1
0
1
1
0
1
1
0
2
1
1
2
1
1
1
1
1
2
1
2
1
2
1
1
1
1
2
2
1
1
2
1
2
1
2
2
0
2
2
1
1
2
0
1
0
1
1
1
2
1
2
0
1
1
2
2
1
0
1
2
2
1
1
2
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
1
2
1
1
2
0
2
4
1
1
2
2
1
1
1
1
1
1
1
2
2
1
1
1
1
2
0
1
2
0
1
1
0
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
0
1
1
1
1
2
1
1
1
1
1
1
1
0
1
0
2
1
2
1
1
1
1
1
1
1
0
0
1
1
0
1
1
1
0
2
1
2
1
1
1
1
2
1
2
2
1
0
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
0
1
1
3
1
1
1
2
1
2
1
1
2
1
1
1
0
0
1
1
2
1
1
1
1
1
2
0
2
1
1
1
1
1
0
1
1
0
2
2
2
1
0
1
2
3
1
0
1
2
1
1
1
1
2
2
2
1
1
1
1
1
0
1
1
2
1
2
2
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
2
2
1
1
1
0
1
2
1
1
1
1
1
1
1
1
1
0
1
1
0
1
1
1
1
0
1
1
1
2
2
1
0
1
1
2
2
1
0
1
2
0
1
0
1
2
2
2
1
1
1
1
1
0
2
1
1
2
0
1
0
1
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
0
1
2
1
1
0
1
1
1
1
1
2
2
1
2
1
1
1
1
0
2
0
1
2
1
1
2
2
1
1
1
2
1
2
1
1
2
1
1
1
0
1
2
1
2
0
2
0
1
2
1
2
0
1
1
2
1
1
1
2
1
1
2
1
2
0
0
1
1
1
1
2
0
2
1
2
1
2
1
1
0
0
3
1
2
1
2
1
0
0
1
1
2
1
1
1
2
1
1
1
2
2
1
1
1
1
0
1
0
1
2
2
1
1
2
0
0
1
1
1
2
3
1
1
0
1
2
1
1
2
1
1
1
0
2
2
1
1
1
1
1
2
2
3
1
2
1
2
1
3
2
0
2
1
1
1
0
0
1
1
1
1
2
0
1
1
2
0
2
1
0
1
1
0
1
1
1
0
1
1
2
0
1
0
0
1
0
2
0
0
1
0
0
1
1
1
0
0
1
1
1
0
1
1
1
1
1
1
1
2
3
1
2
1
2
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
8
1
2
0
1
0
1
1
1
1
2
1
1
1
1
1
1
3
1
2
1
1
1
1
2
1
0
0
1
2
1
1
1
1
2
0
2
1
1
1
0
2
1
0
0
0
0
1
2
1
1
1
0
2
2
1
1
2
1
1
1
1
1
1
2
0
1
1
1
1
1
0
0
1
2
1
1
1
1
0
1
2
1
2
2
1
1
1
2
1
1
1
2
1
1
2
1
1
1
2
2
1
1
1
1
1
1
2
1
0
1
1
1
0
1
0
0
2
0
2
1
0
1
0
2
1
1
1
2
0
1
0
1
1
2
1
1
1
0
1
1
1
0
2
1
2
1
2
1
5
1
0
1
1
0
1
1
0
2
1
0
1
2
1
1
2
1
1
2
2
1
0
2
1
1
1
2
1
1
1
1
1
0
0
1
1
1
2
2
1
1
0
0
1
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
1
1
1
3
0
1
1
0
2
2
2
2
1
1
0
1
2
1
2
2
1
1
1
1
1
1
0
1
1
1
2
2
1
1
0
1
1
1
1
2
2
1
1
1
1
0
1
0
1
2
1
1
4
0
1
1
2
1
1
1
1
1
1
2
1
2
1
2
1
1
0
1
1
1
1
0
1
2
1
1
0
2
1
1
2
1
2
1
1
2
1
2
1
1
1
2
1
0
1
1
1
1
1
0
1
1
1
1
1
2
1
3
1
1
0
1
2
1
2
1
1
1
2
0
1
1
1
1
1
2
1
1
1
2
1
1
1
0
0
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
2
2
2
1
0
2
1
1
2
0
1
2
1
2
2
1
1
1
1
0
1
2
0
2
1
2
2
1
1
2
1
1
1
0
2
2
0
0
0
0
1
2
2
1
2
1
1
0
2
1
1
1
2
1
1
1
1
1
2
2
2
1
1
1
1
2
2
1
1
1
1
2
1
1
0
1
1
2
1
1
1
1
2
1
1
1
0
0
2
1
0
1
0
1
1
2
0
2
2
1
2
1
2
1
1
1
0
1
1
1
1
2
2
1
1
0
0
2
1
1
1
1
1
1
3
0
1
0
1
1
1
1
1
1
2
1
2
0
1
1
1
0
1
2
0
1
1
1
1
2
2
1
1
2
2
1
0
1
0
3
1
0
1
1
1
1
0
1
1
1
1
1
2
1
1
1
0
1
1
0
1
2
1
1
1
1
1
1
1
2
1
1
0
2
1
1
2
2
1
1
0
2
2
2
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
0
0
2
1
1
0
2
7
1
3
1
1
2
1
1
2
1
1
0
1
0
0
0
1
1
1
2
1
1
0
1
0
2
1
4
2
1
2
2
1
1
2
1
1
0
1
1
1
2
1
1
1
1
0
1
0
1
1
1
2
1
1
1
1
1
1
1
1
1
2
0
0
1
1
0
1
2
0
1
2
1
0
1
1
1
2
2
1
2
2
0
1
0
1
1
1
0
1
1
2
2
1
1
1
1
1
0
1
1
0
1
1
1
1
2
0
2
1
0
1
1
1
1
2
0
1
1
1
1
0
0
1
1
1
1
1
2
1
1
1
1
2
2
2
1
2
2
2
0
1
1
1
0
1
1
1
1
1
2
1
1
1
2
1
2
3
2
1
1
1
2
0
1
1
1
2
1
1
1
1
1
1
2
1
0
1
1
1
0
1
1
1
1
2
1
2
2
1
2
1
2
2
1
1
1
0
1
1
0
1
3
1
0
1
2
1
1
2
2
3
1
1
0
2
2
1
0
1
1
1
1
2
0
1
1
1
1
1
1
1
1
1
0
2
2
2
1
2
1
2
2
1
1
1
1
2
1
1
1
2
0
2
0
1
2
1
2
1
0
0
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
0
1
1
2
2
2
1
2
1
0
1
1
2
1
2
1
1
1
0
1
2
1
1
2
1
2
2
0
2
1
2
1
1
1
1
1
1
2
4
1
1
1
1
2
0
1
2
2
1
1
1
1
2
1
2
1
1
1
0
1
1
1
2
1
1
0
2
1
2
2
0
1
1
2
1
1
1
0
1
1
1
2
0
1
1
0
1
1
0
1
2
1
2
2
2
2
2
0
1
2
1
2
1
1
1
2
1
1
1
1
1
1
0
1
0
2
1
1
2
2
2
1
1
0
1
0
2
2
0
1
1
1
1
1
0
0
2
1
1
1
1
1
0
2
0
1
1
2
1
1
2
1
2
0
2
1
1
1
0
2
2
0
2
0
2
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
2
1
2
2
2
1
1
1
1
1
2
2
1
1
0
0
1
1
0
1
1
0
1
0
1
2
1
0
1
2
2
1
2
2
1
1
1
1
2
0
1
2
0
1
1
0
1
2
1
2
1
3
0
1
2
2
2
1
1
0
2
1
2
1
1
1
2
1
1
0
1
0
1
2
0
1
1
2
2
1
1
0
0
1
0
1
1
2
1
2
1
1
2
2
1
2
0
2
0
2
0
2
1
1
1
2
1
0
0
1
2
1
1
1
0
1
0
1
1
1
1
1
2
1
0
1
2
0
1
0
1
0
2
1
1
0
1
1
1
1
1
1
2
0
1
0
2
1
1
1
2
1
1
0
1
1
2
2
1
1
1
2
1
1
1
2
1
1
1
1
2
2
1
2
1
0
1
0
1
1
1
0
1
1
1
0
1
1
1
0
2
3
1
0
1
0
2
1
1
1
1
0
2
1
1
2
1
1
0
1
2
6
1
0
1
5
1
2
0
1
1
2
1
1
0
1
1
1
1
1
2
1
1
2
2
1
1
1
0
1
0
1
4
2
0
2
1
1
2
1
2
1
1
1
1
1
2
0
0
1
1
1
1
2
0
1
0
1
1
2
2
0
1
2
1
0
1
2
1
2
1
1
0
1
0
1
0
1
1
1
1
2
1
1
1
2
2
1
1
2
3
0
0
1
2
1
2
1
1
2
0
2
1
1
0
1
2
1
1
1
1
0
0
1
2
1
0
0
2
1
1
1
1
1
1
1
2
2
2
1
1
2
0
1
2
3
2
1
0
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
0
2
1
1
1
2
2
0
2
0
2
1
0
0
1
1
1
1
1
0
0
1
1
0
1
1
1
1
2
1
1
1
1
0
1
1
2
1
1
1
1
2
1
1
1
2
0
1
2
1
1
2
1
1
1
1
1
2
2
1
1
2
1
1
1
2
1
1
1
2
0
1
2
2
1
1
1
1
0
0
2
1
1
1
1
1
0
2
0
1
2
1
1
2
2
0
0
1
1
0
1
0
1
1
1
1
0
2
1
1
1
1
1
0
1
1
1
1
2
0
1
1
1
0
1
2
1
1
1
0
1
1
0
2
1
2
2
1
2
0
0
2
2
2
2
0
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
2
1
1
1
1
2
2
0
2
2
1
1
1
2
1
1
1
0
2
1
1
0
2
2
1
1
1
1
1
1
1
2
1
2
0
0
2
1
0
2
2
1
0
1
0
1
2
0
1
1
1
0
1
2
1
0
1
1
2
1
2
1
2
1
0
1
2
0
0
1
0
1
1
1
1
1
1
2
1
2
1
2
2
2
1
0
1
1
1
1
0
1
1
1
1
2
1
1
0
2
1
1
1
2
1
2
3
2
2
0
1
0
2
1
1
1
0
1
1
0
2
1
1
1
1
0
1
1
0
2
2
1
1
1
1
1
0
2
2
0
0
1
2
0
1
1
0
2
1
1
1
2
1
0
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
0
1
2
1
2
1
1
1
1
1
1
1
1
1
1
2
0
0
2
0
1
1
1
1
1
1
1
2
0
2
1
1
1
2
1
0
0
2
2
0
1
1
1
2
1
0
0
0
1
0
1
1
1
0
1
1
0
1
2
1
0
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
0
1
1
1
3
2
1
2
2
1
1
1
1
1
1
1
1
1
1
0
2
0
2
2
1
1
0
1
0
1
2
2
1
0
1
1
2
1
2
1
1
1
1
1
2
1
0
0
1
1
0
1
1
1
2
1
1
2
1
1
1
1
1
1
1
2
0
1
1
1
1
1
2
1
1
0
1
1
2
2
1
0
1
2
2
1
1
1
0
0
1
1
0
1
1
1
0
2
2
1
1
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
2
0
1
2
2
1
1
2
1
1
0
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
3
1
1
1
1
2
1
1
1
1
1
2
3
1
1
1
2
1
1
1
0
1
1
2
1
2
2
2
1
1
2
1
1
1
2
0
1
0
1
0
1
1
2
1
1
2
0
1
1
1
1
1
1
1
2
1
1
0
1
1
1
1
0
1
1
1
1
1
2
1
0
2
1
1
1
2
0
2
1
0
1
1
2
2
0
1
1
2
2
1
0
2
1
1
2
2
1
2
1
0
1
0
2
1
1
1
0
2
2
2
1
2
1
0
1
1
0
2
1
1
2
2
2
1
1
1
0
1
1
2
0
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
2
1
2
0
1
2
1
1
2
2
2
2
2
1
2
1
1
0
0
1
1
2
1
2
2
1
0
2
1
2
1
1
0
0
1
2
1
1
1
1
1
1
1
1
0
1
1
1
1
1
2
2
1
1
1
0
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
2
1
2
1
2
1
2
1
0
1
2
1
0
2
2
1
1
1
1
2
2
0
2
0
1
1
1
1
0
1
1
0
2
1
2
1
1
1
1
0
1
1
2
1
1
1
2
1
1
1
1
2
1
1
0
1
1
1
0
2
1
1
5
2
1
1
1
1
0
2
1
1
0
2
2
0
1
1
1
2
2
2
1
0
1
1
2
1
2
1
0
1
1
2
2
2
1
1
1
1
1
1
1
2
0
1
1
1
1
1
1
1
1
1
2
0
0
0
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
0
0
0
5
2
2
1
1
1
1
1
0
1
1
1
0
1
2
0
0
1
1
1
1
0
1
2
1
1
1
2
1
1
1
2
1
0
1
1
2
0
1
1
1
1
1
1
0
0
1
2
1
1
0
2
1
1
2
1
2
1
1
0
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
0
0
1
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
0
1
1
2
1
1
2
1
1
1
1
1
1
1
2
2
2
1
1
1
1
2
4
1
0
1
1
1
2
2
1
1
2
0
2
2
1
1
2
1
1
2
1
0
2
1
2
1
2
1
2
0
2
1
1
1
1
1
1
0
1
1
1
1
2
1
1
1
1
1
2
1
0
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
0
1
1
2
0
2
1
2
1
2
2
2
2
2
1
1
1
2
2
1
1
1
2
1
2
1
1
1
1
1
2
0
1
1
2
1
2
2
1
2
0
2
1
1
1
2
1
2
1
2
0
2
2
1
1
1
2
0
0
0
1
1
2
0
1
0
2
0
1
2
1
0
1
1
2
2
1
1
1
2
2
0
2
1
1
0
1
2
0
1
1
0
2
1
1
1
1
2
2
0
2
2
3
1
1
1
1
1
1
1
1
0
2
1
0
2
1
0
2
1
1
1
1
1
2
1
0
1
2
1
2
0
1
0
2
0
1
2
1
2
1
1
0
1
1
1
0
1
0
2
0
1
1
1
2
2
0
0
1
1
1
1
1
1
1
2
0
2
1
2
1
2
1
1
2
0
2
1
1
2
0
1
1
1
2
0
1
2
0
2
1
1
0
2
1
1
2
1
1
1
1
1
0
1
0
1
1
0
0
1
1
1
1
1
2
2
0
1
1
0
1
0
0
2
0
1
1
1
2
1
1
1
1
1
1
1
1
2
1
0
1
1
1
1
1
1
1
1
0
2
1
1
1
1
2
1
2
1
1
1
2
1
1
2
2
1
1
2
2
0
1
1
2
1
2
0
2
1
1
1
1
0
1
0
1
2
0
1
1
2
1
0
1
0
2
0
1
1
2
1
2
0
1
1
1
2
1
1
1
0
0
2
2
1
1
1
1
0
2
0
0
2
0
1
1
1
8
1
2
1
2
2
2
1
2
1
0
1
1
2
1
1
1
1
1
1
1
1
0
0
2
1
1
1
2
2
1
1
4
2
1
2
1
0
1
1
0
1
1
1
1
2
2
2
2
2
1
1
1
1
1
1
2
1
2
1
2
1
1
1
2
0
1
1
1
0
1
2
1
1
1
2
1
1
2
1
1
1
0
1
1
1
1
1
2
0
2
1
2
1
1
1
1
1
1
1
2
1
2
1
1
0
1
1
1
0
2
1
2
2
0
2
0
1
1
2
1
1
1
1
1
1
2
1
1
2
2
0
1
0
2
1
2
1
1
2
2
2
1
1
1
1
1
1
2
1
1
1
2
2
2
1
1
1
1
1
3
0
1
1
1
1
2
1
1
1
1
1
0
1
2
0
1
1
5
1
1
1
1
1
0
1
1
1
0
2
1
1
1
1
1
1
0
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
0
1
1
0
0
1
1
2
1
1
2
1
0
2
1
1
1
1
1
1
1
0
1
2
1
2
1
1
2
2
1
1
1
0
0
1
1
1
2
1
1
1
2
1
1
1
1
0
0
2
1
1
1
2
1
1
1
2
2
1
1
1
0
3
1
1
1
1
2
2
1
1
0
1
1
1
1
0
2
0
1
1
2
0
1
2
1
2
1
1
3
1
0
1
1
2
2
2
1
2
0
2
1
2
1
1
0
1
1
1
0
1
1
1
1
1
1
0
2
1
0
2
2
0
1
1
1
1
3
2
1
1
0
0
2
0
2
1
1
2
1
2
1
1
1
0
1
1
1
1
1
2
2
2
1
2
1
2
2
0
0
0
1
1
2
1
1
2
1
2
1
1
1
0
0
1
0
1
1
1
0
1
2
2
1
0
2
0
2
1
1
2
0
1
1
2
2
1
1
1
0
1
1
1
1
0
1
1
1
2
2
1
2
0
1
1
1
2
0
2
1
0
2
2
2
1
1
1
1
2
1
1
1
1
1
0
1
2
1
2
1
1
1
1
1
1
2
0
0
2
1
1
0
2
1
1
1
0
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
2
2
1
2
0
2
2
1
1
2
3
0
1
1
0
0
2
2
1
0
1
0
2
2
2
2
1
0
2
2
1
2
1
1
1
0
1
0
1
1
0
2
1
1
1
1
2
1
1
0
1
2
1
2
1
0
0
0
2
1
1
1
2
1
1
2
2
1
1
1
1
1
1
0
1
1
1
1
1
1
1
2
1
1
2
0
2
1
2
2
1
1
0
1
0
0
1
1
1
1
1
1
1
1
1
2
1
0
1
1
1
1
1
1
1
2
1
0
1
0
1
1
1
1
0
1
1
0
2
1
2
2
1
1
1
1
2
1
1
1
0
0
1
1
0
0
1
1
2
1
0
1
1
1
2
1
0
0
2
1
1
1
2
1
1
3
2
1
0
1
0
0
1
1
2
1
2
1
2
1
1
2
2
0
2
1
0
2
0
1
1
1
1
1
1
1
1
1
1
3
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
0
2
1
2
2
1
1
1
2
1
1
2
2
1
1
1
1
1
2
0
2
2
1
2
1
0
2
1
0
2
0
1
1
2
1
1
1
0
0
1
1
0
0
1
1
1
2
1
1
1
2
0
1
0
0
2
1
2
2
0
1
2
3
0
1
1
2
1
2
2
1
1
1
1
1
2
2
1
0
2
0
0
1
2
1
2
2
2
1
1
2
0
2
2
2
0
1
1
0
1
1
2
1
1
2
2
1
1
1
1
0
2
0
2
2
1
1
1
1
1
0
0
1
1
1
1
2
1
1
0
1
0
2
1
1
1
1
0
1
0
0
2
0
1
1
2
1
2
0
2
2
2
1
0
2
2
1
2
0
1
0
2
1
2
2
1
1
1
2
1
2
0
0
0
2
2
1
2
3
0
2
0
1
1
2
1
2
2
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
2
0
1
1
1
1
2
1
1
1
0
0
2
1
1
1
1
1
1
1
2
2
1
1
1
1
0
2
1
1
1
1
1
0
2
0
2
2
0
1
1
0
1
1
0
1
0
2
1
0
1
1
2
0
2
0
1
1
0
1
2
2
1
1
2
1
1
1
1
1
2
2
2
1
1
1
0
2
2
1
0
1
1
1
1
1
0
1
2
2
2
1
1
1
0
0
2
1
1
1
0
3
2
2
2
1
1
2
1
1
1
0
1
1
1
1
2
2
1
0
1
1
1
1
1
0
1
1
1
0
0
1
1
1
1
2
1
0
1
1
0
1
1
2
2
0
1
2
1
1
2
2
1
1
2
2
3
1
1
0
1
1
1
0
3
1
1
1
2
1
0
1
0
2
1
1
2
1
1
1
1
1
0
2
2
1
2
1
1
1
1
0
1
1
2
1
2
1
3
1
1
2
1
1
1
2
1
1
1
0
1
1
1
2
2
1
1
0
2
2
1
1
1
2
1
1
1
2
1
2
3
1
1
2
0
1
1
1
1
0
1
1
1
0
0
1
2
2
0
1
1
0
2
0
2
1
1
1
1
1
1
0
2
1
1
1
1
1
1
2
0
0
1
2
1
1
1
1
0
0
2
2
2
1
0
1
2
1
1
1
1
0
1
2
1
1
0
1
2
2
1
1
1
1
2
0
0
2
2
1
1
1
1
1
2
1
1
0
1
1
2
1
0
0
1
1
1
1
2
1
2
1
0
1
0
1
1
1
0
1
2
1
0
1
1
2
2
1
1
2
2
1
2
1
1
2
0
1
1
2
2
0
1
1
1
1
2
1
1
1
1
1
1
1
0
2
1
1
1
1
2
1
2
0
0
1
1
0
2
1
1
0
2
0
1
0
1
0
2
2
2
2
0
1
1
0
2
2
1
1
0
1
1
1
1
1
2
1
0
0
1
1
1
1
1
1
1
0
1
0
1
1
0
1
0
1
1
2
1
1
1
2
2
2
2
1
2
0
1
1
1
1
0
1
1
1
0
2
0
0
1
0
2
1
1
0
0
1
2
1
0
1
1
1
0
1
1
1
2
1
1
1
1
1
1
2
1
1
2
1
1
2
1
2
0
4
0
0
1
1
1
2
1
1
1
1
1
1
0
2
1
2
1
2
1
1
2
0
0
2
1
0
1
1
1
1
1
1
0
1
1
1
0
1
1
0
1
2
0
1
1
1
1
0
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
0
1
1
1
0
1
1
2
2
0
1
1
1
1
1
0
1
1
1
1
0
0
2
2
2
1
0
1
1
2
0
1
1
1
0
2
1
1
0
1
2
1
2
1
1
1
1
3
1
2
1
0
1
3
2
1
1
1
1
0
1
2
1
0
1
2
2
1
1
1
1
1
2
2
2
1
2
1
1
0
1
1
1
0
2
1
2
1
1
1
2
1
1
1
1
1
0
1
2
2
1
0
1
2
1
1
1
1
0
2
0
1
0
1
1
2
0
1
0
0
0
2
1
2
1
1
1
2
0
2
1
2
1
1
1
1
0
1
1
0
1
1
2
1
2
1
1
2
1
0
2
0
0
1
1
2
1
1
1
2
2
1
1
2
2
1
1
2
1
1
1
2
0
1
2
2
1
1
2
1
0
1
1
0
1
1
0
0
1
2
1
2
1
1
0
1
2
1
1
3
3
4
1
1
1
1
2
2
1
1
2
0
0
1
2
0
1
2
1
2
1
2
0
1
1
1
1
3
2
2
1
2
1
0
1
1
2
2
1
3
1
2
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
0
2
2
2
1
1
2
1
2
1
1
2
1
1
1
2
1
2
1
1
1
2
0
1
1
1
1
2
1
1
1
1
0
1
1
1
1
2
1
1
1
2
1
1
1
1
1
2
2
0
1
1
1
1
1
0
0
2
1
2
0
1
1
2
1
2
1
1
1
0
0
1
1
1
2
0
1
1
1
0
1
1
1
1
1
1
1
0
1
1
1
1
4
2
1
1
1
1
1
1
1
1
2
0
1
0
1
2
3
1
1
1
1
1
0
0
1
2
1
1
1
1
1
1
1
2
2
1
1
1
2
1
1
1
1
1
2
1
1
0
2
1
2
1
1
1
2
2
2
1
1
1
1
1
2
1
0
1
1
1
1
1
2
1
0
2
1
1
1
1
1
0
0
1
2
1
1
2
1
1
1
1
1
2
2
1
1
1
0
0
1
2
3
1
1
1
1
2
1
2
0
2
2
1
1
2
1
1
2
0
1
2
2
1
1
0
2
2
2
1
1
0
1
1
3
1
1
1
2
0
0
1
2
1
0
1
1
0
0
0
1
1
1
2
2
1
2
0
2
1
1
1
1
1
1
2
0
1
0
2
1
2
0
2
1
2
2
1
0
0
1
1
1
0
1
1
1
1
1
2
0
1
1
1
2
1
0
2
1
1
1
2
2
1
0
1
1
1
2
1
1
1
0
0
2
1
0
1
1
0
1
1
0
2
2
1
1
0
1
1
1
2
1
1
0
1
1
0
2
1
1
2
0
2
0
0
2
1
2
1
0
2
1
1
1
1
2
2
2
1
2
2
2
1
1
2
0
1
1
2
0
2
1
1
1
1
1
1
1
2
2
1
3
2
1
1
1
1
2
1
1
1
1
2
1
2
0
1
0
1
2
1
0
1
1
1
1
2
0
1
1
1
0
1
1
0
1
2
2
1
0
2
1
2
0
2
1
1
1
1
1
1
1
2
1
0
0
1
1
1
0
1
1
3
1
1
2
1
1
1
2
1
0
2
1
1
1
2
1
1
1
0
0
1
2
1
1
1
1
1
0
1
0
0
1
1
1
2
0
3
1
1
1
2
1
1
1
2
1
1
2
1
0
1
3
1
1
0
1
1
2
1
1
0
1
2
0
2
2
1
1
0
0
1
0
0
1
2
1
2
4
2
2
0
1
1
1
2
1
1
2
1
1
0
2
1
0
0
2
1
1
1
0
2
2
2
1
1
1
0
2
1
0
1
1
1
1
1
1
1
2
0
1
2
1
1
2
0
1
1
4
1
1
2
1
0
2
1
1
1
1
1
0
0
1
1
1
2
1
1
1
0
0
1
1
1
1
2
0
2
1
1
1
2
0
1
0
1
0
1
0
2
2
1
2
1
0
2
0
1
1
2
0
2
1
2
0
0
1
2
1
1
1
1
2
1
1
1
1
0
0
1
0
1
1
1
1
2
1
1
2
1
1
1
1
2
0
1
2
0
1
2
1
1
2
2
1
2
1
0
1
1
1
2
1
1
1
1
2
0
1
1
0
1
1
2
0
1
1
1
1
2
2
1
1
1
2
2
0
2
1
1
1
1
2
2
0
1
1
2
1
1
1
1
2
1
2
1
2
1
1
1
1
0
2
0
2
1
0
1
2
0
1
1
1
1
2
1
1
2
1
2
1
1
2
2
2
2
1
0
2
1
1
2
1
1
1
1
1
0
1
1
0
1
1
1
1
1
1
2
2
1
1
1
0
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
2
2
1
2
1
1
0
2
1
2
0
1
2
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
0
1
2
0
2
0
1
2
1
0
0
1
1
1
1
1
1
1
1
1
1
0
2
1
0
2
1
1
1
1
1
1
1
0
1
2
1
1
0
1
1
2
1
1
1
1
1
0
2
1
2
2
1
1
1
1
1
2
3
0
2
0
1
1
1
2
1
1
2
0
0
1
1
2
2
0
1
1
1
1
1
1
2
1
0
1
1
1
1
1
1
2
1
1
0
1
1
1
1
3
1
3
1
1
2
1
1
2
2
1
1
2
2
2
2
2
1
0
1
1
1
1
1
1
2
1
1
1
1
1
2
1
0
1
1
2
1
1
1
0
1
2
2
1
2
1
1
2
1
0
1
0
1
1
1
2
1
1
0
0
1
1
1
2
1
0
0
2
1
1
1
1
1
1
1
0
1
2
1
0
3
1
2
1
0
0
1
2
2
1
1
1
1
1
0
1
0
2
1
2
1
1
2
1
1
1
1
2
2
1
2
1
1
0
1
1
2
0
1
0
0
1
1
1
1
1
1
1
1
1
1
1
2
1
1
0
1
2
0
1
2
2
1
1
1
2
2
1
1
1
4
1
0
0
0
1
2
1
1
2
1
0
1
1
2
2
1
0
2
1
1
1
1
1
1
2
1
1
1
1
2
1
2
0
1
2
1
1
2
0
0
2
1
1
2
1
1
1
0
1
1
1
1
0
1
1
1
1
1
0
0
0
0
0
2
1
1
1
1
1
3
1
1
2
1
2
1
1
2
1
1
1
2
2
1
1
1
1
1
3
1
2
0
1
1
0
1
1
1
1
1
2
2
1
0
1
1
1
1
0
1
1
1
1
2
0
0
1
2
1
1
1
1
2
2
2
1
0
1
0
2
1
2
2
1
1
1
2
1
0
1
1
1
0
0
1
1
2
1
2
1
0
1
1
1
0
1
2
1
1
1
0
2
1
1
2
1
0
0
2
2
1
0
0
1
1
0
2
1
1
1
1
0
0
1
2
2
1
2
2
1
1
1
2
0
1
1
0
1
1
2
2
2
2
1
2
1
1
1
1
1
0
1
2
1
0
2
1
1
1
1
1
1
2
0
2
0
2
1
2
1
1
3
1
1
1
0
1
2
1
0
1
1
0
1
1
1
2
1
1
1
1
0
1
0
1
0
2
0
1
2
1
2
1
2
1
1
1
0
1
2
2
1
1
1
1
1
1
1
1
0
1
2
1
1
2
2
1
0
2
0
2
0
1
1
0
1
1
1
1
2
1
1
0
2
1
1
2
1
3
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
1
1
2
0
2
1
2
1
1
0
1
1
2
1
2
1
1
1
2
1
1
2
1
0
1
1
1
2
0
0
1
2
1
0
1
1
0
1
1
2
1
1
1
2
1
4
1
2
1
1
2
1
1
1
0
1
1
1
2
1
1
1
2
1
2
1
1
0
2
1
1
1
1
0
2
2
1
0
0
1
1
1
0
1
2
1
2
2
1
1
1
1
2
2
0
2
1
1
2
1
1
1
2
1
1
2
2
2
1
0
1
1
1
1
0
2
1
0
2
1
1
0
1
0
1
2
0
1
1
1
2
1
0
2
0
3
1
1
0
1
2
1
1
1
1
1
1
1
1
1
0
2
2
1
0
0
2
2
2
2
2
1
0
2
1
1
1
1
0
1
1
1
1
2
0
2
0
2
1
2
0
1
1
1
1
2
0
0
1
2
1
1
2
2
2
1
1
1
2
2
1
0
1
1
1
1
3
0
1
2
1
1
1
1
1
1
0
0
1
0
1
2
1
1
0
1
2
0
1
2
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
0
1
1
1
1
2
1
2
1
2
2
2
1
1
0
2
2
1
1
0
2
1
1
1
2
0
2
0
1
1
1
1
1
1
1
0
1
1
2
1
0
0
0
1
0
1
1
2
1
2
2
1
0
1
1
1
0
1
1
2
2
0
1
0
2
1
2
2
1
2
1
1
1
1
0
2
1
2
0
2
1
1
2
1
0
0
1
1
1
1
1
1
2
0
1
1
0
1
1
1
1
2
1
0
1
1
1
2
2
2
2
1
0
2
1
2
2
0
2
1
2
1
1
2
2
2
0
1
0
2
2
2
1
3
1
1
1
1
1
1
1
1
1
1
1
1
2
0
0
1
1
0
3
2
1
1
1
1
1
0
2
2
1
1
1
1
0
1
1
2
1
2
0
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
1
1
0
0
1
2
2
2
1
1
1
1
1
3
0
1
2
2
1
2
1
1
0
2
2
1
1
1
0
0
0
2
1
1
1
2
1
1
2
2
1
0
2
0
2
0
1
1
1
3
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
1
0
1
1
1
1
1
2
1
0
1
1
2
1
0
1
0
0
0
1
0
1
2
1
1
0
0
1
1
1
2
1
1
1
1
1
1
1
1
0
1
2
0
0
1
1
0
0
1
1
1
2
1
0
1
1
0
2
0
1
1
1
2
0
0
1
2
1
1
1
1
0
1
1
2
1
1
1
1
1
1
2
1
2
1
2
1
1
1
1
2
1
2
2
2
2
0
2
1
1
1
1
1
2
0
1
1
0
2
1
0
1
1
1
2
1
2
1
1
1
2
2
1
1
0
1
1
1
0
0
1
1
1
2
1
1
0
2
1
1
1
2
2
0
1
2
1
1
1
2
1
1
1
2
2
0
1
1
0
1
1
2
1
2
2
1
0
1
1
1
1
1
1
1
1
2
1
0
2
2
0
1
1
1
2
0
1
1
1
0
1
1
1
1
1
1
2
1
1
0
1
0
2
2
1
2
2
1
2
1
1
1
1
1
2
1
2
1
1
1
1
2
1
0
1
0
1
1
1
1
1
1
1
1
0
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
0
1
0
2
2
1
0
2
1
1
2
1
2
1
1
0
1
1
1
1
2
0
1
2
1
1
1
1
1
1
1
1
0
2
1
1
1
2
1
1
2
1
1
1
1
2
1
1
1
1
0
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
0
2
1
1
2
1
1
2
1
2
1
0
1
2
2
2
0
1
1
0
2
1
2
1
1
0
1
2
2
1
0
0
2
0
2
2
2
0
2
1
1
0
1
2
1
2
1
0
1
0
0
0
1
2
1
1
1
1
1
2
1
0
1
2
1
0
1
0
1
2
2
0
0
2
1
0
1
1
1
1
1
1
1
0
1
2
2
1
0
0
1
1
1
1
2
1
2
1
2
1
1
0
0
2
2
1
2
1
0
1
1
0
2
2
1
1
0
0
2
1
2
1
1
0
1
1
1
2
1
2
1
1
1
1
1
1
0
1
1
1
2
1
1
2
0
1
1
1
2
2
2
0
1
2
1
1
2
1
1
1
1
1
1
1
2
1
2
1
2
1
1
1
1
1
2
1
1
1
1
1
1
0
2
2
0
2
2
0
1
0
1
2
2
1
2
1
1
1
1
1
2
1
1
1
2
1
2
1
1
2
1
1
1
0
2
1
1
1
1
0
1
1
1
1
1
2
1
1
2
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
2
1
2
1
1
2
2
2
1
1
1
1
1
2
1
1
2
2
1
1
1
1
1
2
1
1
1
2
1
1
0
2
1
1
1
0
1
1
1
0
2
0
1
2
2
2
1
2
0
1
2
0
0
1
0
1
1
1
2
1
2
1
2
1
2
2
1
2
1
1
1
0
1
0
1
1
2
2
0
2
1
1
1
1
1
0
0
1
2
2
2
2
1
1
1
1
1
2
1
2
1
1
0
1
1
1
2
2
1
1
1
0
1
1
1
1
1
1
1
2
1
1
1
1
2
1
2
1
1
1
0
0
2
2
0
1
0
0
0
1
0
0
2
1
1
0
1
1
4
1
0
2
2
1
1
1
1
0
0
2
1
1
0
3
1
2
1
1
0
1
1
1
2
2
1
2
1
0
2
2
1
2
1
1
2
1
1
2
1
1
2
1
1
1
2
1
1
2
1
1
1
0
2
1
0
1
1
1
1
1
2
1
2
1
1
0
1
2
1
1
1
1
0
1
1
1
1
1
2
1
0
2
1
1
0
2
1
1
2
1
2
2
0
1
1
1
2
0
2
2
2
1
2
0
1
1
0
1
0
1
2
2
1
2
0
1
0
1
1
1
1
1
1
2
1
1
1
2
2
0
1
2
1
1
1
1
2
1
1
1
1
0
2
2
1
1
1
1
2
2
1
1
2
0
1
1
1
0
1
1
1
0
1
1
0
2
2
2
1
2
1
1
1
1
1
0
1
1
1
1
1
2
1
1
1
1
1
2
1
2
0
0
1
1
1
1
2
1
2
1
0
1
1
1
0
0
1
1
1
1
1
2
0
1
1
2
0
1
1
1
0
1
1
0
2
1
1
0
0
1
2
1
1
1
1
1
1
1
0
1
1
0
2
1
1
2
0
1
1
0
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
2
1
2
1
0
1
1
1
1
2
1
1
1
0
0
1
1
1
1
1
0
1
1
0
1
1
3
2
1
1
0
1
0
2
2
1
2
2
1
1
1
1
1
0
0
1
2
0
1
1
0
1
2
1
1
2
1
2
1
1
1
2
1
1
2
1
1
0
0
1
2
2
0
1
1
1
2
1
2
1
1
2
3
1
1
1
1
0
1
2
1
2
0
1
1
1
0
0
2
2
1
1
1
1
1
1
1
0
1
2
1
1
1
2
1
1
1
1
2
2
1
2
1
2
0
0
1
2
0
1
1
1
1
1
0
1
1
1
1
1
0
1
1
1
0
1
1
2
2
2
1
1
0
1
1
1
1
1
1
1
1
1
0
2
2
1
2
0
1
0
2
2
2
0
1
1
1
2
1
2
1
0
2
1
1
1
1
0
1
2
2
0
1
1
1
1
1
1
2
1
1
0
1
3
1
1
1
1
1
1
1
0
1
1
2
1
2
1
1
1
0
1
2
1
2
2
2
0
1
0
2
1
1
1
0
1
2
0
2
1
1
0
1
2
2
1
1
1
1
1
1
1
0
1
2
1
0
1
1
1
2
1
2
2
2
1
1
1
2
2
0
1
1
2
1
1
1
0
1
0
1
0
0
2
0
0
0
2
1
2
1
1
2
1
1
0
1
1
2
1
1
0
1
1
1
1
1
0
1
1
2
0
1
1
2
1
2
1
1
1
1
2
1
1
0
1
0
1
1
2
1
1
2
1
1
0
1
1
1
0
1
1
1
1
1
2
1
2
1
1
0
0
1
1
1
2
1
2
1
1
1
0
1
2
2
1
1
0
2
1
2
2
1
2
2
1
1
0
0
0
0
1
1
2
1
1
1
1
2
0
1
1
1
2
1
2
0
0
0
1
1
0
1
1
0
1
1
1
1
1
1
0
2
1
1
0
2
1
1
1
2
1
2
0
1
1
2
2
3
1
1
2
1
1
1
1
0
1
1
1
2
0
0
0
0
1
0
1
1
0
1
2
1
2
1
1
0
1
1
2
0
1
1
1
0
1
1
2
3
1
0
0
0
0
2
2
2
0
1
1
1
1
2
2
1
0
1
1
1
0
1
0
1
0
1
0
1
2
1
2
2
1
0
1
0
1
1
3
1
1
1
1
2
1
1
0
2
1
1
1
1
1
1
0
1
1
1
0
2
1
1
2
1
1
2
1
1
2
1
0
2
1
2
1
2
1
2
1
2
2
0
1
2
0
1
1
3
1
2
2
0
1
2
1
2
1
0
1
1
2
1
1
0
2
3
1
2
1
2
1
1
2
1
0
2
0
2
2
2
1
1
0
1
1
1
0
2
1
0
2
1
1
1
2
1
1
1
1
2
1
0
1
1
1
2
1
0
1
1
0
2
1
1
1
1
0
2
1
2
0
1
1
2
1
3
1
1
1
1
2
1
1
2
1
1
1
2
1
1
0
0
1
1
1
1
1
2
1
1
1
1
0
1
1
1
1
2
2
0
2
1
1
1
0
1
1
1
1
1
1
1
1
0
0
2
1
2
1
1
1
1
1
2
1
2
1
2
0
1
1
1
0
1
0
1
2
1
1
1
1
0
1
1
0
2
1
1
3
1
1
1
0
1
1
1
1
1
0
1
1
2
2
1
2
1
2
0
1
1
1
1
2
1
1
1
1
1
2
2
2
2
1
0
1
2
1
1
1
1
0
1
2
1
1
1
1
1
0
2
0
1
0
1
1
1
2
0
1
0
1
1
1
1
1
1
2
0
1
2
1
1
2
1
1
1
1
1
2
1
1
2
0
1
1
2
1
1
1
1
1
1
1
0
0
1
1
1
2
2
2
2
1
1
0
1
1
2
0
0
2
1
1
1
0
0
2
1
1
1
1
1
0
0
0
1
1
1
1
1
0
1
0
1
1
2
1
2
1
1
1
2
1
1
1
0
2
1
1
1
1
1
1
0
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
0
1
1
2
1
0
0
0
2
2
0
2
0
1
1
2
1
1
1
1
1
1
2
2
2
1
2
2
1
2
2
0
0
0
1
2
2
2
1
1
1
1
2
2
2
1
1
1
3
2
1
0
0
1
1
1
1
1
2
1
2
1
0
0
1
1
1
2
1
1
1
1
2
2
1
1
2
2
0
1
1
1
0
1
2
1
0
1
0
1
0
1
1
1
1
1
1
1
1
1
2
2
1
0
1
1
2
1
0
1
2
1
0
1
1
1
1
2
2
1
2
1
1
1
2
2
1
1
0
1
2
1
1
0
1
1
1
0
1
0
1
2
1
1
0
1
1
1
1
2
0
1
1
1
1
2
1
1
2
1
1
1
1
2
0
1
1
2
1
1
1
0
1
1
2
1
2
2
0
1
2
1
2
1
1
1
1
1
1
2
2
2
2
2
1
0
2
0
2
0
1
1
0
1
1
2
0
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
2
1
1
2
1
1
0
1
2
0
1
1
1
1
2
2
1
1
1
0
2
2
1
2
2
2
1
1
0
1
1
2
0
1
0
1
1
2
1
2
1
1
1
1
2
1
1
0
1
0
1
2
1
1
1
0
1
1
2
1
2
0
2
1
1
0
0
2
2
1
2
2
1
1
1
1
0
2
1
1
2
1
1
1
0
0
1
1
0
1
1
1
1
2
1
1
0
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
2
0
2
1
2
2
0
2
1
2
1
1
1
2
1
1
1
1
1
2
2
1
0
0
1
2
0
1
0
1
1
1
2
1
1
1
1
1
1
3
2
1
1
2
1
1
0
1
3
2
0
0
1
1
0
1
1
2
1
1
1
1
1
1
2
1
2
1
0
2
2
1
1
0
0
1
2
1
1
1
1
2
0
1
0
2
0
1
1
0
2
1
1
0
2
2
2
1
2
1
1
1
1
1
0
1
0
1
0
2
2
1
0
1
1
1
1
1
1
1
0
2
1
0
1
2
2
1
2
1
0
0
2
1
9
2
1
1
2
1
1
2
0
1
1
1
2
1
1
1
0
0
1
1
0
1
2
1
2
1
2
1
1
2
0
1
1
1
1
1
1
1
1
1
1
0
0
2
1
0
1
2
1
1
1
2
1
1
1
1
1
1
1
2
2
0
2
1
0
0
0
2
2
1
1
0
2
1
0
2
2
1
1
0
2
1
2
1
1
0
1
1
1
0
2
0
1
2
2
1
1
1
1
1
1
1
2
1
1
1
2
1
1
2
1
2
1
1
1
1
2
1
1
2
0
1
2
1
1
2
2
1
2
1
1
1
1
1
1
2
1
0
2
1
1
1
1
0
1
2
1
1
1
3
1
1
1
2
1
1
1
0
2
1
1
1
1
0
1
1
2
0
0
0
2
1
1
0
1
1
1
1
1
1
1
1
0
1
1
1
0
1
1
1
0
1
2
2
1
1
1
1
1
1
2
1
2
1
1
1
2
4
1
1
1
0
1
2
1
2
1
2
2
1
1
2
2
0
1
2
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
0
2
1
1
1
2
1
1
0
2
1
1
1
2
1
2
0
1
2
1
1
1
1
1
2
2
1
0
1
1
0
1
1
0
1
1
3
2
1
2
2
1
1
1
1
0
2
1
1
1
0
1
2
1
2
1
1
1
2
1
1
1
0
2
2
1
2
1
2
2
1
2
0
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
2
1
0
0
1
1
0
0
1
2
0
0
1
0
1
1
1
2
0
1
1
0
1
1
2
0
1
0
1
2
1
1
1
1
2
0
1
1
2
2
0
2
2
0
6
2
2
1
1
1
1
2
0
2
0
2
1
1
1
1
1
1
1
2
2
1
1
0
1
2
0
2
2
1
2
0
1
2
2
0
1
1
0
1
0
2
4
1
1
1
2
2
2
2
1
1
2
0
1
1
0
1
0
0
1
1
1
1
0
1
2
0
1
0
2
1
2
2
2
2
0
1
1
1
1
1
1
2
0
2
6
1
1
2
1
0
1
0
0
1
1
0
2
2
1
1
0
1
1
1
1
1
2
1
0
0
0
1
1
2
0
1
0
2
1
1
0
2
1
0
1
1
1
1
1
1
1
1
0
1
2
1
2
2
1
2
0
1
1
2
1
2
2
1
2
1
1
1
1
2
1
1
0
1
1
1
1
0
1
1
1
1
0
1
2
1
1
1
1
2
1
1
1
1
2
1
0
1
1
1
2
1
1
1
0
0
0
0
1
1
0
0
1
1
1
1
1
1
2
1
1
0
2
1
2
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
2
0
0
2
1
3
1
1
1
1
2
1
1
2
1
2
1
1
1
2
1
1
1
2
1
2
1
1
2
2
1
1
2
1
1
1
1
1
1
1
0
0
0
2
1
1
2
2
1
0
2
1
1
1
1
1
1
2
1
1
1
1
1
1
0
1
1
0
1
1
1
1
0
1
2
0
2
2
1
1
0
1
1
1
1
2
2
1
0
1
2
1
1
1
2
2
1
1
2
2
1
1
2
2
1
1
1
0
1
1
0
2
1
0
1
1
0
1
0
1
0
1
1
2
1
1
0
0
1
1
0
2
2
1
1
0
1
1
1
1
1
1
0
1
1
1
1
2
2
2
0
2
2
0
1
1
0
1
0
0
1
2
1
0
1
0
0
1
2
1
1
2
1
2
2
2
1
2
0
0
2
1
2
1
2
1
0
3
1
1
2
0
1
2
2
1
2
2
0
1
1
3
1
0
1
2
1
0
1
2
1
0
2
1
1
1
1
2
1
2
2
1
2
1
1
1
2
2
1
1
1
1
1
1
1
0
1
2
1
1
0
0
1
1
1
1
2
1
1
0
3
1
1
2
0
1
1
2
1
1
2
1
2
1
1
1
1
2
1
0
1
2
1
1
2
1
0
1
1
1
1
1
1
1
2
1
1
1
1
1
1
0
1
1
1
1
2
1
1
2
1
2
1
1
2
1
1
0
1
1
1
1
1
0
0
1
1
1
1
0
2
2
1
1
2
1
1
2
1
0
1
0
1
1
1
0
1
1
1
1
1
0
1
1
1
1
2
0
1
1
1
0
1
0
2
1
1
2
1
0
1
1
1
1
2
1
1
1
2
1
1
2
1
2
1
0
1
1
0
2
1
1
1
0
2
1
2
1
2
1
1
0
2
1
1
2
2
2
1
0
1
1
1
1
1
0
2
1
2
0
2
1
1
2
2
1
2
2
0
1
1
1
1
1
1
2
1
1
0
1
1
1
0
0
1
2
1
1
1
1
2
2
1
0
1
2
1
1
1
1
2
2
0
1
1
1
0
1
0
1
1
1
1
2
0
1
1
1
2
1
1
1
1
1
0
1
1
1
0
1
1
0
1
2
1
1
1
1
1
1
2
1
0
0
1
1
1
2
1
1
1
1
2
1
1
1
2
0
0
1
1
2
3
0
1
0
1
1
1
0
1
0
1
2
0
1
0
2
1
1
2
0
1
1
5
1
1
2
1
2
2
0
1
2
2
0
1
1
2
1
2
2
0
1
1
1
2
1
1
0
1
0
1
0
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
2
2
1
0
0
1
1
1
1
1
2
2
2
1
1
2
0
1
2
2
1
1
0
3
1
1
2
1
2
1
4
0
2
0
2
1
1
1
1
2
1
1
1
1
2
1
0
0
1
1
2
2
1
0
1
3
0
2
1
2
1
0
0
1
1
1
2
1
1
1
1
3
1
1
1
0
1
1
1
2
1
1
1
1
1
1
1
0
1
5
1
1
1
1
2
2
2
1
1
0
1
1
1
2
1
1
0
0
1
0
0
1
2
2
0
1
1
2
1
2
1
1
1
1
1
2
2
1
2
1
2
1
2
1
1
1
1
0
1
1
1
1
1
2
1
1
1
2
1
1
1
1
2
0
0
1
1
0
1
2
1
0
1
2
1
1
1
0
2
2
1
1
1
0
1
1
2
1
2
0
0
0
1
4
2
0
2
2
1
1
1
1
2
1
1
1
1
1
0
2
0
1
1
1
0
2
1
1
2
1
0
2
2
1
1
2
2
0
1
1
2
1
0
1
1
1
2
0
1
2
1
1
1
1
2
1
1
1
1
2
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
0
2
2
1
2
1
2
1
1
1
1
2
0
0
1
0
1
1
2
0
1
1
0
2
1
2
0
2
1
0
1
1
0
2
2
1
2
2
1
1
0
2
2
0
1
1
0
0
1
1
1
1
1
1
1
1
2
1
2
1
1
2
2
1
0
2
0
0
2
1
1
1
2
1
0
1
1
1
2
1
1
0
1
2
0
2
1
1
2
2
1
1
1
1
1
2
1
0
1
0
1
1
1
0
2
2
1
1
1
2
1
2
2
2
1
1
1
0
2
1
0
1
2
1
1
2
1
1
2
2
1
1
1
1
1
1
1
1
0
2
1
1
0
2
1
1
1
0
1
2
1
3
1
2
1
1
1
1
2
1
1
1
1
1
1
0
1
1
0
0
1
2
3
2
1
1
1
1
1
2
1
1
2
1
0
1
0
1
2
1
1
0
2
1
2
2
1
2
1
0
0
2
1
2
2
1
1
2
1
0
1
1
2
0
2
1
0
0
1
1
1
1
2
2
1
1
1
2
1
1
2
1
1
0
0
5
2
2
2
1
0
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
1
1
2
0
1
1
1
1
0
2
2
3
1
1
0
1
1
1
2
1
1
2
1
1
1
1
0
1
1
1
1
1
1
0
1
1
0
1
1
1
1
0
2
1
2
1
2
0
2
1
1
1
1
1
1
1
1
1
2
2
2
2
2
1
1
1
2
1
1
1
2
2
2
1
1
2
1
0
2
2
1
1
0
1
1
1
2
1
1
3
0
0
1
1
2
0
1
2
1
0
2
1
2
2
0
1
1
2
1
1
1
1
2
1
2
1
2
1
1
1
1
1
1
1
2
2
0
1
2
2
1
2
1
0
1
1
2
0
1
1
1
1
1
1
1
0
0
1
0
0
2
1
2
1
0
2
2
2
2
0
0
1
1
1
1
0
2
1
0
1
1
1
2
2
2
1
1
2
1
1
0
1
0
1
1
2
2
1
1
1
2
1
2
1
0
1
6
1
1
0
1
2
1
2
2
2
1
2
1
1
1
2
1
2
1
2
2
1
2
1
0
2
2
1
1
1
1
1
0
1
2
2
1
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
0
1
2
2
2
1
1
1
2
1
2
0
1
1
0
1
2
0
0
1
2
1
2
1
2
2
2
1
1
2
1
1
1
1
2
1
1
1
0
2
1
1
0
2
2
1
2
1
0
1
1
1
1
1
1
1
0
1
1
0
2
2
2
1
1
2
2
1
1
1
2
0
2
1
1
2
4
2
2
1
1
2
1
1
2
1
1
1
1
1
1
2
2
1
0
0
1
0
2
2
1
1
2
1
1
1
1
1
2
1
0
1
0
2
1
1
1
2
2
1
1
1
1
2
1
3
2
2
1
2
4
2
1
1
1
0
1
1
2
1
0
2
1
1
1
1
0
1
1
2
1
1
1
2
1
2
1
1
0
1
1
2
1
1
2
1
1
1
2
1
0
1
1
0
1
0
1
1
4
2
2
1
0
1
0
1
2
1
2
1
1
2
1
1
1
1
1
0
2
2
0
0
2
1
0
0
0
1
1
1
1
1
0
2
1
2
1
1
0
1
1
2
1
1
1
0
1
2
1
1
1
0
0
2
1
1
1
0
1
2
1
2
2
1
2
1
2
1
1
1
1
1
2
1
0
1
3
2
1
1
1
1
1
1
1
1
2
1
1
2
0
1
0
1
2
0
1
1
2
1
0
1
1
2
1
1
0
2
1
0
2
1
2
0
1
3
0
1
2
2
1
3
1
1
1
1
1
1
2
0
1
1
2
0
0
1
1
2
2
1
1
1
2
1
1
1
1
1
2
2
2
2
1
1
2
2
1
2
1
1
1
1
1
2
1
2
0
0
2
1
1
2
1
1
1
2
2
1
1
0
1
0
2
1
2
0
1
1
2
1
1
2
1
1
0
1
1
0
1
1
1
1
1
1
1
1
2
1
1
1
1
0
1
1
1
1
2
1
2
1
1
1
1
2
2
1
1
1
1
1
1
2
2
1
1
1
2
0
2
0
1
1
0
1
1
0
1
1
1
1
2
2
1
1
2
2
1
1
1
1
2
1
2
2
2
0
3
1
2
2
1
1
1
2
2
0
1
0
2
2
1
2
1
1
1
2
1
3
1
1
1
2
1
0
1
1
0
0
0
2
1
1
1
1
2
0
2
1
1
1
1
2
1
2
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
0
1
1
1
1
2
1
2
1
2
1
1
1
2
1
2
0
0
2
0
1
2
1
2
1
0
1
2
1
1
2
1
0
1
1
1
1
1
1
1
1
2
1
2
1
1
1
0
1
1
2
1
1
0
1
1
1
1
2
1
1
2
2
1
2
0
1
1
1
0
1
1
2
2
2
1
1
1
2
2
1
2
1
1
1
1
0
1
2
1
2
2
2
1
1
0
0
1
0
2
1
0
0
1
0
1
0
1
2
1
0
1
0
1
1
1
1
2
1
0
2
1
2
0
2
0
1
1
1
1
1
2
1
1
0
1
1
1
1
0
1
1
0
2
0
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
2
1
2
0
0
2
0
1
1
2
0
1
1
1
1
0
0
2
1
1
2
0
1
1
1
1
2
1
0
1
2
2
1
2
1
1
1
2
0
1
1
1
1
0
0
1
2
2
0
2
1
1
1
1
0
0
1
1
3
2
2
1
2
0
0
1
1
2
0
2
1
2
0
1
0
0
1
2
2
1
1
2
2
0
0
1
1
0
1
2
2
1
1
0
1
1
1
2
1
1
2
0
1
1
1
1
0
1
0
2
2
1
0
1
1
1
1
1
2
1
1
1
2
2
1
1
2
2
1
0
1
2
1
1
1
1
2
1
0
1
0
2
1
0
2
2
1
2
1
1
0
1
1
1
2
2
1
2
2
1
1
1
2
1
1
2
2
1
1
1
2
1
1
1
0
0
1
1
1
1
1
1
1
1
2
0
2
1
0
0
2
1
1
1
1
1
1
0
1
1
2
1
1
1
1
1
2
1
1
1
1
1
0
1
1
2
2
1
1
3
1
1
1
1
2
0
1
1
1
1
2
2
2
1
1
0
2
2
1
1
2
1
1
1
0
1
2
1
1
1
1
1
0
0
1
2
1
1
0
1
1
1
1
1
1
2
0
1
2
2
2
2
1
1
1
0
2
2
1
1
1
0
1
0
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
1
1
1
1
0
1
0
2
2
1
2
1
1
1
0
1
1
2
2
1
1
1
2
1
2
1
1
1
1
2
1
0
1
0
1
1
0
1
2
2
1
1
1
1
1
1
4
2
0
1
1
1
0
2
1
0
0
0
2
1
1
2
1
1
1
2
1
2
0
0
1
0
1
1
1
1
2
1
1
1
2
0
1
0
1
1
2
1
1
1
1
2
2
0
2
2
1
0
2
0
1
2
2
2
2
2
0
2
2
1
0
1
1
1
2
1
2
0
0
1
1
2
1
1
1
1
2
1
0
1
1
2
2
2
1
2
1
1
0
1
1
1
2
0
1
1
1
1
1
0
1
0
2
2
1
0
1
2
2
1
1
1
0
2
0
1
0
0
1
1
1
1
1
1
2
1
1
0
0
1
1
1
1
1
0
2
1
2
2
1
1
1
2
1
1
1
1
1
1
0
2
1
2
1
1
1
0
1
2
2
1
1
1
1
2
1
2
1
2
1
1
1
0
2
0
2
2
1
1
0
0
2
1
2
1
1
2
1
1
2
1
1
2
2
2
2
0
2
2
2
1
1
1
0
1
2
2
2
1
1
1
0
2
0
1
1
0
0
1
2
1
1
0
1
1
1
1
1
2
1
2
0
0
1
1
1
0
2
1
1
0
1
2
1
1
0
1
1
2
1
1
0
0
1
1
1
0
1
0
0
0
2
2
4
1
1
1
2
2
1
1
2
2
2
1
0
1
0
1
1
0
2
0
0
2
2
0
2
0
2
2
1
1
0
2
3
1
1
2
1
1
1
0
0
1
2
2
2
1
1
1
2
2
2
0
1
0
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
0
1
2
1
1
0
2
1
1
1
1
1
1
0
0
1
1
0
2
1
1
1
2
0
1
1
1
1
1
0
1
1
2
2
1
2
0
1
2
2
2
2
1
1
0
1
1
1
0
1
2
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
0
1
1
1
2
1
1
2
2
1
1
1
1
1
2
1
1
2
2
2
1
1
1
1
1
1
0
1
0
1
1
1
1
2
1
1
1
1
2
1
1
1
0
1
1
1
1
0
1
1
0
1
1
1
1
1
1
2
2
1
0
1
1
1
2
1
1
1
1
1
2
1
1
2
1
0
1
0
1
1
2
1
1
1
2
3
0
1
2
1
1
2
2
1
1
1
1
1
2
2
1
1
1
0
1
1
1
1
1
0
0
2
1
1
1
1
1
2
1
2
1
1
0
2
0
1
0
1
1
1
0
0
0
2
2
1
1
0
2
2
1
0
1
1
1
2
0
1
1
1
1
1
1
0
0
2
2
1
2
1
2
1
2
1
2
0
2
1
2
0
2
2
1
2
1
2
1
2
1
1
1
1
2
1
1
0
2
2
1
1
2
0
0
2
1
1
1
1
1
1
1
0
0
1
0
1
1
0
1
1
1
1
1
1
1
1
1
2
1
1
2
2
1
0
1
1
0
2
1
2
1
2
2
1
1
2
2
1
0
2
1
1
2
0
2
1
1
1
2
2
2
1
2
1
0
1
1
2
1
1
0
0
2
0
1
1
1
1
2
1
2
1
2
0
1
1
1
0
6
1
1
2
0
1
2
1
1
1
1
1
1
1
1
1
2
1
1
2
1
0
1
1
1
1
1
0
0
1
0
1
1
1
2
2
1
1
1
0
1
1
0
0
1
1
2
2
1
1
1
1
1
1
1
0
0
2
2
1
2
1
0
1
1
0
1
2
1
1
1
1
0
1
1
2
1
1
1
0
1
2
0
1
2
1
2
2
2
2
1
1
1
1
2
1
2
1
1
2
1
1
1
1
2
0
1
1
1
0
1
1
2
1
2
1
1
2
2
1
1
0
1
1
0
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
3
1
1
1
1
2
1
1
1
2
2
1
1
1
1
2
1
1
2
1
1
0
1
1
1
4
2
1
1
1
1
1
2
0
1
0
1
0
1
1
2
0
1
1
2
2
1
1
2
2
1
1
1
1
1
1
0
1
2
2
1
2
0
2
1
0
1
1
1
1
2
1
0
1
1
0
2
1
1
1
1
1
1
2
1
2
2
2
2
2
1
0
1
1
1
1
0
1
1
2
2
1
0
1
0
2
0
2
2
2
1
1
2
1
2
1
2
2
1
2
1
0
1
0
1
1
0
1
1
1
1
1
1
2
0
1
1
1
1
0
1
0
2
1
1
1
0
0
1
1
1
2
1
1
1
1
2
1
1
2
1
0
1
1
0
1
1
2
1
1
1
2
1
1
1
0
0
1
0
1
2
3
1
1
2
1
2
1
1
1
2
2
0
1
2
2
3
2
0
0
1
1
2
2
1
2
0
0
1
1
1
0
1
1
1
1
2
2
1
2
2
0
1
1
2
1
2
0
1
1
1
2
1
1
1
1
1
2
2
1
0
2
1
2
1
2
2
2
3
1
1
1
2
1
1
0
2
1
1
1
1
1
1
0
1
0
1
2
1
1
1
1
2
1
1
0
1
2
1
2
1
1
1
0
1
3
0
1
2
1
2
0
0
1
1
3
1
0
2
1
2
1
2
1
1
1
0
0
2
0
1
1
0
1
1
0
2
1
0
1
2
1
0
0
1
1
2
1
1
1
2
1
2
1
2
2
1
1
1
1
1
0
1
1
1
2
1
1
1
2
1
1
0
1
0
1
1
1
2
1
0
1
0
1
1
1
2
2
1
2
2
0
1
1
1
0
0
1
1
1
1
1
2
1
2
1
1
2
2
1
1
0
1
1
2
1
1
2
2
2
0
1
0
1
1
1
1
0
1
1
2
2
2
2
2
1
1
1
2
0
0
1
2
1
2
1
1
0
2
1
1
1
1
1
1
1
1
1
1
1
2
1
0
1
1
0
1
3
1
2
2
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
0
1
0
2
1
2
2
2
1
2
2
2
1
1
1
0
1
1
1
2
0
1
1
2
1
1
2
0
0
1
2
1
2
1
1
1
1
1
1
1
1
0
1
1
1
0
2
2
1
1
2
2
1
2
2
2
1
1
1
1
1
1
2
1
1
1
0
1
1
1
1
0
1
0
1
1
2
1
1
1
2
1
0
1
1
0
2
0
1
1
1
1
0
1
2
0
0
0
1
2
0
1
1
0
1
1
1
1
2
0
1
1
0
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
0
1
1
1
1
1
1
1
0
1
1
2
1
1
1
2
2
0
2
1
1
1
2
0
1
0
1
1
0
0
1
2
0
1
0
0
1
1
1
2
2
1
1
0
2
0
1
1
0
1
1
1
2
1
1
1
1
1
1
0
2
1
2
1
2
1
1
1
1
0
2
1
1
0
1
0
0
0
1
2
1
2
1
1
2
1
2
2
1
1
2
1
2
1
1
2
2
1
1
3
0
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
0
1
1
1
0
2
1
1
1
1
2
0
0
1
1
0
1
1
1
2
8
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
0
1
2
2
1
2
0
1
0
2
1
2
1
2
2
1
1
2
1
1
0
1
2
1
0
0
2
2
1
0
0
1
2
1
3
2
1
2
0
1
1
1
2
1
1
0
1
1
0
0
1
2
2
1
1
2
2
2
1
2
1
0
2
1
1
1
3
1
2
1
1
2
1
1
1
1
2
1
0
1
2
1
2
1
0
1
1
2
0
1
1
1
1
1
1
1
2
1
0
1
1
2
1
1
0
1
1
1
1
1
1
0
2
1
1
2
1
1
1
2
2
1
1
2
2
2
2
1
1
1
2
1
1
2
1
2
1
1
2
1
1
0
1
0
0
0
1
2
2
1
2
2
1
0
2
1
1
1
1
0
2
1
1
2
2
2
2
0
0
0
1
1
1
1
2
1
0
2
0
1
1
1
0
1
2
2
2
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
0
2
0
2
1
1
2
0
0
1
0
2
1
1
1
1
1
0
3
0
2
1
1
1
1
1
1
1
1
0
1
0
2
2
1
1
0
3
2
2
1
1
0
1
2
0
1
0
2
1
1
1
1
1
0
1
0
1
0
1
1
1
1
0
2
1
2
1
1
1
2
1
1
1
2
1
1
2
2
1
2
1
1
2
2
0
1
0
3
1
1
2
1
1
0
1
1
1
2
2
1
1
1
2
1
0
1
0
1
2
1
1
0
2
1
1
2
1
2
0
1
2
1
1
1
1
1
2
2
1
0
1
0
2
2
2
2
2
1
2
1
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
3
1
0
2
1
2
2
1
1
0
3
1
2
1
1
1
1
2
0
1
1
1
1
2
2
1
2
1
1
0
1
1
1
1
1
1
2
1
1
1
2
0
1
1
1
2
0
1
2
1
1
0
2
1
1
1
1
1
1
2
0
0
1
1
2
2
1
0
1
1
2
2
0
1
1
0
1
1
0
1
1
0
2
2
1
2
1
1
1
2
2
1
0
2
1
2
1
1
1
2
1
0
1
0
1
2
2
1
2
0
2
1
0
1
1
1
2
1
0
1
1
0
2
1
1
1
1
0
1
1
2
2
0
2
1
2
1
0
3
2
0
1
1
1
2
2
1
1
0
1
1
1
1
1
1
0
0
1
1
2
2
0
2
1
1
2
2
2
0
1
2
1
1
0
1
2
1
1
3
2
1
1
2
1
1
1
1
0
2
2
2
1
2
2
1
1
0
2
1
2
1
2
0
1
1
2
1
2
1
1
1
2
1
1
2
2
2
1
2
1
2
1
0
1
1
1
1
4
0
1
1
1
2
1
1
0
1
1
0
2
1
2
1
1
1
1
2
1
0
1
1
0
1
1
1
1
1
0
1
1
2
1
2
1
1
2
1
1
2
2
1
1
2
1
1
1
1
1
1
2
1
0
1
1
1
1
1
1
1
1
0
1
0
1
1
1
2
1
1
0
1
1
1
1
0
1
1
1
1
2
0
1
0
1
2
1
1
0
1
1
2
0
2
1
2
0
1
2
1
1
1
3
1
0
2
1
2
1
1
0
1
2
2
2
2
2
1
2
0
1
2
1
2
1
1
1
2
1
1
2
1
2
1
2
1
1
1
1
0
1
2
1
1
1
2
2
1
1
2
1
2
0
1
1
1
2
1
2
1
2
1
0
1
1
1
1
1
1
2
1
2
0
1
1
0
0
1
0
0
2
1
1
0
1
1
2
1
1
1
1
0
0
1
3
2
2
1
0
2
0
0
0
0
2
1
1
2
1
1
1
1
1
0
1
1
1
2
1
0
0
2
1
1
1
1
1
1
2
1
0
2
1
1
0
0
2
1
1
1
2
1
1
0
1
1
1
0
1
1
1
0
3
0
2
2
1
2
2
1
2
2
1
0
1
1
2
0
1
2
2
0
2
2
2
1
1
0
1
1
2
1
1
1
1
2
0
3
1
1
1
2
1
0
1
1
2
1
1
1
1
1
1
1
2
1
0
2
1
2
1
1
0
2
0
1
1
0
1
1
1
1
1
2
1
1
1
2
1
1
0
2
1
2
0
0
0
1
0
1
2
1
1
2
0
0
1
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
0
1
1
1
1
2
3
1
1
1
2
2
0
1
1
1
0
0
2
1
1
0
1
0
1
1
1
0
1
1
1
1
0
1
1
1
0
1
2
1
1
1
2
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
3
2
0
1
1
2
1
2
1
1
0
2
0
0
2
0
2
2
2
2
1
2
0
1
2
2
1
2
1
1
0
0
1
1
1
2
2
1
2
2
1
1
1
1
0
1
1
2
1
0
1
1
1
1
1
1
1
1
1
2
2
2
1
1
2
2
1
0
2
1
0
2
2
0
0
1
1
2
1
1
2
1
0
2
1
1
2
1
1
2
2
1
0
2
2
0
1
1
0
2
2
1
1
0
2
1
1
1
1
0
0
1
0
1
1
1
0
1
1
1
2
1
3
1
1
1
1
1
0
1
1
2
2
2
2
0
1
1
1
2
1
2
1
0
2
1
0
3
0
1
1
2
1
1
1
1
2
1
2
2
0
1
0
0
1
1
1
1
1
2
2
1
2
2
1
2
1
1
1
1
1
0
1
1
0
0
1
1
1
2
2
1
0
1
0
1
1
1
1
2
1
2
0
1
1
1
2
3
2
0
0
2
1
1
0
1
1
1
1
1
1
2
1
0
2
0
0
2
2
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
0
1
1
2
1
1
2
0
2
1
1
1
2
0
1
0
0
1
2
1
2
0
1
1
1
2
1
0
1
1
3
1
1
2
0
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
2
0
2
0
1
1
1
0
2
2
0
1
1
1
2
1
2
1
1
2
0
1
2
0
1
1
1
1
1
2
1
1
2
2
1
1
1
1
2
0
1
1
1
1
1
0
2
0
1
1
1
2
1
1
1
0
0
2
2
1
1
1
1
0
2
1
2
1
2
2
1
0
2
1
1
2
1
2
1
0
1
1
1
3
1
1
1
1
0
1
2
2
1
1
1
1
1
0
1
1
1
1
3
2
1
1
2
1
0
1
1
1
1
1
2
2
2
1
1
0
2
1
1
3
2
0
2
1
0
2
1
0
0
1
1
1
1
2
1
1
0
1
2
1
2
1
1
1
0
0
2
1
2
1
2
1
0
0
1
2
1
1
2
1
1
1
1
1
0
1
2
2
1
1
1
1
1
1
2
0
1
2
1
1
2
1
1
1
1
0
1
0
1
1
1
1
1
1
1
1
0
1
1
2
0
1
2
1
1
2
1
2
1
1
0
2
1
1
1
0
1
1
0
1
1
1
1
1
1
1
2
0
1
1
0
1
1
2
1
1
1
1
2
0
1
2
2
1
1
2
2
1
2
1
2
1
2
1
2
1
1
1
0
1
0
2
2
1
1
1
1
2
0
1
0
1
0
0
2
1
1
1
1
1
1
2
1
0
2
2
1
1
2
1
1
1
1
1
1
2
0
1
2
0
1
1
1
2
1
1
1
0
1
2
1
1
1
2
2
0
1
0
1
0
0
1
1
0
0
0
1
0
1
1
1
1
2
2
1
1
0
1
1
2
0
2
0
1
1
1
0
1
1
1
1
1
2
1
1
2
1
2
2
1
2
1
2
1
0
4
2
1
2
1
1
1
1
2
2
2
1
1
1
2
1
2
2
1
1
1
0
1
1
1
2
1
1
1
1
1
2
1
1
2
2
0
1
2
1
1
1
1
0
1
0
1
0
0
2
2
2
2
1
1
1
1
2
1
1
2
1
1
0
0
2
1
2
1
0
0
1
1
1
2
1
1
1
1
1
0
2
2
2
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
2
1
1
1
2
1
1
1
0
1
1
0
1
1
2
1
0
1
0
2
1
2
1
2
1
0
0
1
1
2
1
1
2
2
1
2
0
1
1
2
0
1
1
1
2
1
1
2
2
1
0
1
2
1
2
1
3
1
1
0
2
2
3
2
0
0
1
1
1
0
0
1
1
1
1
2
2
1
1
0
1
1
1
1
1
1
1
0
0
0
2
1
1
1
0
1
1
2
1
2
1
1
1
0
0
1
1
2
2
1
1
1
2
0
1
1
0
0
0
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
2
1
0
1
0
1
1
2
1
3
2
1
1
2
2
2
2
1
0
0
1
1
1
1
1
1
2
0
0
0
0
0
1
0
2
2
2
1
1
1
0
1
1
1
1
1
2
2
2
4
2
1
2
2
1
1
1
0
1
1
2
1
1
2
2
1
1
2
1
2
2
1
1
1
1
0
2
7
2
1
0
2
1
0
2
1
1
1
2
1
2
1
1
1
1
0
1
2
2
2
1
1
1
2
0
1
1
2
1
0
0
1
2
1
2
1
1
1
1
1
0
1
1
2
0
0
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
0
1
1
1
1
1
1
2
1
2
2
2
1
1
2
0
0
1
2
2
0
2
1
1
2
0
1
1
2
1
1
1
1
1
1
1
1
1
1
0
0
1
1
1
0
0
1
0
1
1
1
1
1
1
1
1
0
1
0
1
2
1
1
1
0
1
1
2
2
1
1
1
0
0
2
1
2
1
2
1
1
1
1
2
0
2
1
2
1
1
2
1
0
1
1
1
0
1
1
0
1
2
2
2
2
1
2
2
1
2
1
0
1
1
1
2
1
1
0
0
2
1
0
2
1
1
1
0
1
2
1
2
1
1
2
0
1
0
2
1
1
1
1
1
1
1
1
2
2
1
1
1
1
0
0
2
1
0
1
3
1
1
0
2
1
1
2
2
2
1
1
2
0
1
1
0
1
1
1
1
2
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
2
2
2
2
0
2
1
1
2
1
1
0
2
1
1
2
1
2
1
2
0
0
0
2
1
1
1
6
1
0
2
2
1
1
2
1
1
1
2
1
2
1
0
2
1
2
0
1
2
1
1
2
2
1
2
1
1
0
1
1
0
1
1
1
1
0
2
1
1
1
1
2
1
1
1
1
1
1
2
1
1
2
1
0
0
1
1
0
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
0
1
1
1
1
2
2
1
1
1
2
0
0
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
0
1
1
1
1
2
1
3
1
1
2
1
0
2
0
1
1
1
2
2
1
1
0
2
1
1
2
2
1
0
1
2
1
1
0
2
2
1
1
1
2
1
1
1
1
2
2
1
1
1
2
1
2
1
0
1
1
1
1
2
1
1
1
2
0
2
1
1
1
1
1
1
1
1
1
1
0
1
2
2
1
2
1
1
0
1
1
0
0
1
1
1
2
1
1
1
1
0
0
1
2
0
2
0
1
1
1
0
0
1
1
1
0
2
0
0
1
1
1
1
2
1
1
1
1
1
2
1
1
2
2
1
0
1
0
2
2
1
0
1
0
2
1
2
1
2
2
1
1
1
2
1
2
2
2
0
1
1
2
1
1
0
1
1
1
1
1
1
2
1
0
2
1
0
2
1
2
1
0
0
2
1
1
1
1
0
2
0
2
1
2
1
0
1
0
1
1
2
2
2
1
1
1
0
2
1
1
0
0
1
2
0
1
1
1
2
2
2
2
1
1
1
2
1
1
2
1
1
0
1
2
1
1
1
2
2
1
2
1
1
2
2
2
0
1
1
1
1
1
2
1
0
1
0
2
1
0
1
2
2
1
2
1
1
1
2
1
2
1
1
1
1
0
1
1
1
2
0
1
2
2
1
0
2
1
1
0
1
1
3
1
1
1
1
2
0
1
0
2
1
1
1
2
2
0
1
1
1
1
2
2
0
0
2
1
2
1
1
1
2
0
1
1
1
1
1
1
1
0
1
2
1
0
1
2
2
1
2
1
1
1
1
0
0
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
0
2
1
1
0
0
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
1
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
0
1
1
1
1
2
0
1
1
2
1
1
1
1
0
1
1
1
1
0
2
0
1
2
1
1
0
1
1
1
2
2
1
1
1
1
2
2
1
0
1
1
1
0
1
2
1
1
1
0
0
1
1
1
1
1
2
2
0
1
1
2
0
2
0
1
1
0
0
1
2
1
1
1
1
1
1
1
1
0
1
1
1
1
0
0
0
2
1
2
1
2
1
1
1
2
1
1
1
2
1
2
1
0
1
2
1
1
1
1
2
0
1
0
2
2
1
1
1
1
2
2
1
2
0
1
1
2
1
1
1
2
1
1
1
1
1
2
1
1
1
0
1
1
2
1
2
1
1
0
1
1
1
2
1
0
1
1
0
0
2
1
0
1
1
1
1
1
2
1
1
2
1
0
2
1
1
1
2
0
1
1
2
1
1
2
0
2
1
2
1
2
2
2
1
1
1
0
1
1
1
1
1
2
3
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
0
0
0
1
2
2
2
1
1
2
0
2
1
1
2
2
2
2
1
2
1
2
1
2
1
1
2
1
1
1
1
1
1
2
0
1
1
1
1
2
1
2
1
1
1
2
1
2
1
2
1
1
2
1
1
0
2
1
1
1
1
2
2
0
1
1
1
0
2
1
1
1
0
0
1
1
0
4
0
2
0
1
2
2
1
2
2
1
1
1
2
1
1
1
0
1
0
1
1
1
1
1
1
0
1
1
1
1
2
2
2
2
1
0
1
1
1
2
0
2
2
1
0
2
5
1
1
2
1
2
1
1
1
2
1
0
1
0
1
1
0
1
0
1
2
2
1
1
0
1
0
0
0
1
1
1
1
2
1
0
0
1
2
1
2
0
0
0
1
0
2
1
1
1
2
1
2
0
0
0
1
1
0
2
1
1
1
2
1
0
2
1
2
2
2
1
1
0
0
1
0
2
1
2
1
2
1
2
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
0
1
2
2
1
0
1
1
1
1
1
2
0
0
1
2
2
2
1
1
1
0
1
1
0
0
1
2
0
2
1
2
1
1
2
1
1
1
2
0
1
2
2
1
1
1
3
1
1
1
0
1
1
2
0
1
2
1
1
1
2
2
1
1
1
2
2
2
1
2
1
1
1
2
4
0
1
2
2
0
2
0
1
1
1
2
1
0
0
2
1
0
0
1
1
1
1
1
0
1
1
2
1
3
1
1
1
2
1
1
2
1
2
1
1
1
1
1
0
2
1
1
1
2
0
1
0
2
0
2
1
2
2
1
1
1
1
1
1
1
0
2
1
1
2
0
1
0
0
2
2
0
2
2
1
1
1
1
2
1
1
1
0
1
1
1
1
1
2
2
0
1
0
1
1
0
1
1
1
0
1
0
0
1
0
1
2
1
1
1
1
2
2
1
1
2
1
1
1
2
0
0
1
1
1
1
1
1
1
2
1
1
1
1
2
0
1
0
1
2
1
1
1
1
1
1
2
2
2
2
0
1
1
1
0
2
1
1
1
2
1
1
1
1
2
3
2
2
1
1
2
2
1
2
1
1
1
1
1
1
2
1
2
1
1
0
0
1
0
0
2
0
1
0
2
0
1
2
1
1
2
0
1
1
2
1
2
1
1
0
0
1
1
1
1
2
1
1
1
1
1
1
1
1
1
0
1
2
1
2
1
1
1
0
1
1
0
4
1
1
1
1
1
1
1
1
1
2
1
1
0
1
2
1
2
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
0
1
1
1
0
1
1
2
0
1
1
1
1
1
1
1
1
1
0
1
2
1
1
1
2
0
0
1
2
0
1
2
2
1
1
1
1
1
1
1
0
1
2
1
2
2
2
0
1
2
6
1
2
1
2
1
0
1
1
1
1
1
1
0
1
0
0
1
1
1
1
1
1
2
2
2
1
2
1
2
1
2
2
1
2
2
1
1
1
1
1
2
1
1
2
1
2
1
2
1
2
2
2
1
1
1
1
0
1
1
0
0
1
0
0
1
2
1
1
1
3
2
2
1
0
1
1
1
2
1
1
1
1
2
1
1
1
2
0
1
1
2
1
1
1
1
1
0
2
1
1
1
1
2
1
0
1
0
1
1
2
1
2
1
1
2
1
1
1
2
0
1
1
1
2
1
1
0
1
1
1
1
2
2
2
1
1
1
1
2
1
1
2
2
2
1
0
1
1
1
2
2
1
1
0
1
1
1
1
1
1
0
1
1
2
3
1
2
1
1
1
0
1
1
1
1
1
2
1
1
1
2
1
1
1
1
2
2
2
1
2
0
1
1
2
2
1
0
0
2
1
0
0
1
1
1
1
1
1
0
0
1
0
2
2
2
1
1
2
2
1
0
1
0
1
1
1
1
2
0
1
2
2
1
1
1
2
2
1
0
2
1
2
1
0
2
1
0
1
1
1
1
1
0
1
1
2
1
1
1
1
1
2
1
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
0
2
2
0
1
1
1
1
1
2
1
2
1
1
2
2
1
2
2
1
1
1
1
1
1
2
1
2
0
1
1
1
1
1
2
1
2
1
1
1
0
1
1
1
1
2
0
2
2
0
2
1
0
1
1
2
0
1
0
1
0
1
1
2
4
1
1
0
0
2
1
1
1
2
0
2
1
1
1
2
2
1
1
0
2
1
1
1
0
1
2
1
3
3
2
1
1
2
0
1
1
1
1
0
2
1
2
1
1
2
1
2
1
1
1
1
2
1
1
1
1
2
1
1
0
1
1
1
1
2
0
2
1
1
1
2
1
1
0
1
1
2
3
1
2
0
1
1
1
1
1
1
0
1
2
1
1
1
2
1
1
2
1
2
2
1
1
1
2
1
1
2
1
0
1
2
1
1
2
1
1
0
1
1
1
1
1
1
1
2
1
1
2
0
1
2
1
2
2
1
1
2
1
1
1
1
2
0
2
1
1
1
1
2
1
1
0
1
1
2
1
2
1
1
1
2
1
1
1
1
2
1
1
1
2
1
2
1
1
2
1
0
1
2
1
2
2
1
1
1
1
2
1
2
2
2
2
0
1
2
2
1
1
2
1
2
1
1
1
1
1
1
2
1
2
1
0
3
2
1
0
1
1
1
1
1
1
2
2
2
2
2
2
1
1
1
1
1
1
1
0
2
2
1
1
1
1
1
1
0
1
0
0
2
2
0
1
1
1
1
2
2
0
0
0
2
2
0
0
1
2
1
0
1
1
0
0
1
1
1
0
1
1
1
0
1
1
1
1
1
1
0
2
1
2
2
0
1
1
1
1
1
2
2
1
2
1
1
1
1
1
0
1
1
2
1
0
2
1
2
1
0
1
0
1
1
1
1
1
1
1
1
2
1
2
2
2
1
2
1
1
2
1
0
4
2
1
0
1
0
1
1
1
0
1
1
1
0
1
0
0
1
1
0
2
2
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
1
2
1
3
1
1
0
1
1
1
0
1
1
1
1
1
2
2
1
1
3
0
0
2
1
1
1
1
2
0
1
1
1
1
1
1
1
1
2
1
1
2
1
1
2
1
1
2
1
1
1
1
2
2
0
2
2
1
1
1
2
1
2
1
1
1
2
0
2
1
0
1
2
1
2
1
1
1
0
0
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
2
1
2
1
1
1
1
1
1
1
1
1
0
2
2
1
2
1
2
1
1
0
0
2
1
1
0
1
1
1
1
2
2
1
1
4
0
1
1
0
1
0
1
1
1
1
1
2
1
0
1
1
0
1
0
2
1
1
1
1
1
1
1
0
2
1
1
1
1
1
2
1
0
0
1
2
2
1
0
2
1
1
0
1
1
0
1
0
1
2
0
0
2
0
0
2
2
1
3
1
1
1
1
1
1
0
1
2
1
1
1
2
1
1
1
1
2
8
1
1
1
1
2
2
1
2
1
1
0
1
2
1
2
1
0
0
1
1
1
1
1
2
2
1
2
2
1
1
1
1
1
1
1
0
1
2
1
1
1
1
2
1
2
1
0
1
0
2
1
1
1
1
1
1
1
1
1
1
0
2
1
2
1
2
1
1
1
1
1
2
2
1
2
2
1
1
1
1
1
1
0
1
1
1
1
1
1
0
1
1
1
1
0
2
1
1
1
1
1
1
1
1
0
1
1
1
2
1
2
1
2
2
1
2
2
1
1
1
1
1
2
0
0
1
2
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
0
1
0
0
1
2
0
1
2
2
1
1
0
1
1
1
1
1
1
1
2
2
1
0
2
1
1
2
1
1
0
1
1
1
1
0
1
0
1
1
1
2
2
1
0
1
1
1
1
1
1
1
1
1
1
2
2
0
2
2
1
2
1
2
1
0
1
1
1
0
1
0
0
0
2
0
2
2
1
1
1
1
1
1
1
1
2
2
1
0
0
1
2
1
1
2
1
0
0
0
4
1
1
2
1
1
1
1
1
2
0
1
1
0
0
2
1
1
1
1
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
3
0
1
1
1
1
1
1
1
0
0
0
1
0
1
1
2
2
2
2
2
1
1
0
1
1
1
2
2
1
1
1
1
2
2
1
0
0
1
1
0
1
1
0
0
1
1
2
2
0
2
0
1
1
1
0
2
1
2
2
1
1
1
1
2
1
2
2
1
1
1
1
1
2
1
2
2
1
1
0
0
1
1
2
2
2
2
1
1
1
2
1
1
1
1
0
1
1
2
1
1
1
1
1
1
1
0
0
1
0
1
1
1
1
2
1
2
1
0
1
1
1
2
1
1
0
1
1
0
1
2
1
1
1
1
1
1
2
0
2
1
0
1
0
1
2
2
2
2
2
1
2
1
1
0
2
1
1
1
2
1
1
1
2
0
1
2
1
1
0
1
1
0
1
0
1
1
1
1
2
1
0
1
2
2
1
0
0
2
1
0
2
1
1
2
3
1
2
1
2
2
2
1
1
1
1
0
1
0
2
1
1
1
1
0
2
1
1
0
1
0
1
1
1
1
1
1
2
0
2
1
1
1
2
1
1
2
1
0
2
0
1
1
2
1
1
1
1
2
0
0
2
1
0
2
0
2
1
0
1
1
0
2
2
2
1
2
2
1
1
2
2
1
1
2
0
1
1
2
1
1
1
1
1
3
1
1
0
1
1
1
1
2
1
2
1
1
1
0
0
2
1
1
2
1
1
0
1
1
2
1
1
1
1
1
2
1
2
0
0
1
1
1
0
0
1
2
1
1
2
1
1
1
1
1
0
2
1
0
2
1
0
1
0
0
1
1
1
1
0
1
1
0
0
1
1
1
0
2
0
1
1
1
1
1
1
2
2
2
0
1
1
1
1
2
1
1
1
1
1
1
2
1
1
0
1
0
2
0
1
2
0
2
2
2
1
1
2
2
1
1
1
0
2
1
2
1
1
1
1
2
1
1
1
1
0
1
2
0
0
1
1
2
1
1
1
1
2
1
0
2
2
1
1
2
1
0
2
2
1
2
0
1
1
1
2
0
1
0
1
2
2
0
1
0
1
1
1
0
1
0
0
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
1
1
1
0
1
0
1
1
1
1
2
1
1
1
1
1
1
1
1
1
0
0
2
1
1
0
1
1
2
2
1
2
0
2
2
0
1
1
1
2
1
2
0
0
2
1
1
1
2
1
1
2
2
2
2
2
1
1
1
0
1
2
1
2
1
1
1
2
0
1
1
1
1
2
1
0
1
1
2
1
1
2
2
1
1
1
1
2
1
2
1
1
2
1
1
1
2
0
0
1
1
1
1
1
2
2
1
1
2
1
3
0
1
0
1
1
1
1
1
1
1
1
1
3
1
1
1
1
2
1
2
2
1
1
2
2
0
1
1
2
1
1
2
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
0
0
1
2
0
2
1
1
1
1
1
1
2
1
2
0
2
1
2
1
2
1
1
0
2
1
2
0
1
0
0
2
0
2
1
2
1
1
1
1
1
0
1
2
2
1
0
1
1
1
2
1
1
0
1
0
0
1
1
1
1
2
2
1
1
1
2
2
1
0
2
1
2
0
1
0
2
1
2
0
0
2
1
2
0
1
1
2
2
0
2
1
1
2
1
2
0
0
1
1
1
0
2
1
1
1
1
1
2
2
1
1
0
0
1
1
1
1
1
1
2
0
2
1
1
2
1
1
1
1
1
2
1
1
1
1
2
0
1
2
1
1
1
0
1
1
1
2
2
1
2
1
1
2
1
1
1
2
1
1
1
1
2
2
2
2
1
1
1
1
1
2
2
0
2
1
1
0
2
1
0
2
1
0
1
1
2
1
0
1
1
1
0
2
1
1
1
1
1
1
1
0
1
0
0
1
1
1
1
1
1
1
1
0
2
1
1
2
1
1
1
1
1
1
2
1
1
2
1
0
1
1
2
1
1
2
0
1
1
1
1
1
1
1
1
2
1
1
1
0
1
1
1
1
1
1
2
1
0
2
1
1
1
1
2
0
1
2
1
1
1
1
2
0
1
1
0
1
2
1
0
1
1
0
2
0
1
1
1
2
1
2
2
1
1
1
1
2
1
1
1
2
2
1
1
1
2
1
1
1
1
1
1
2
1
2
1
0
1
1
1
2
1
0
1
1
1
2
1
1
1
2
0
1
2
2
2
2
1
1
0
1
2
3
1
1
1
1
1
1
1
1
2
2
1
1
1
2
1
2
1
1
2
2
0
1
1
0
1
1
0
1
1
1
2
1
1
1
0
1
1
0
1
1
1
2
1
1
1
2
1
1
2
2
1
2
1
0
1
1
1
0
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
2
0
0
0
1
0
2
1
1
0
1
2
2
5
1
0
2
1
2
1
1
0
1
0
1
1
1
2
1
2
2
2
2
1
0
1
2
1
0
1
1
2
1
0
2
1
3
1
0
2
0
1
1
1
1
0
1
1
2
1
1
1
3
1
1
1
1
2
0
2
1
2
1
1
1
1
1
2
1
1
2
0
0
2
3
1
1
2
0
1
0
1
2
2
0
1
1
0
1
1
0
2
1
1
0
0
2
1
2
2
2
2
1
1
1
1
1
2
1
2
1
1
1
1
2
2
1
2
1
0
1
1
4
1
2
2
1
2
2
1
1
1
1
1
2
2
1
2
2
1
1
1
2
1
4
2
2
0
1
0
1
1
2
0
1
1
0
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
0
2
2
1
1
1
1
1
2
1
0
2
1
1
1
2
1
0
2
1
1
1
1
1
1
2
0
0
1
1
2
1
2
1
0
1
1
1
2
0
2
2
1
1
1
0
1
2
1
1
1
0
1
2
2
0
1
0
0
0
1
0
1
1
2
2
2
2
1
2
1
0
2
0
1
0
1
1
0
1
2
2
2
2
2
1
1
1
1
1
2
1
1
1
2
2
0
1
1
1
0
1
0
0
2
3
0
1
0
1
1
1
2
2
1
1
1
2
1
0
0
1
2
1
1
0
1
1
2
1
1
0
1
1
1
1
1
1
1
1
2
4
1
1
2
1
2
1
1
1
1
1
1
2
2
0
1
1
0
1
2
1
2
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
2
0
1
1
0
1
2
2
1
1
2
1
3
1
1
0
2
2
2
0
1
1
0
0
1
1
1
1
0
2
1
2
0
1
2
0
2
1
1
1
1
1
2
1
2
1
1
1
1
1
4
1
0
2
0
2
1
2
2
0
2
1
1
2
1
0
2
1
1
0
0
2
1
1
2
0
1
1
1
2
0
2
1
1
1
1
2
1
1
0
1
0
1
1
0
2
1
2
2
1
2
1
2
1
0
1
1
1
1
1
1
1
0
1
1
0
1
2
1
1
2
1
0
1
1
2
2
1
2
1
2
1
1
0
1
0
1
2
1
1
1
2
1
1
2
1
2
2
0
0
1
1
0
1
1
1
1
2
1
2
1
2
1
1
0
0
1
1
1
1
0
1
0
2
0
1
1
1
1
1
0
1
2
1
1
1
1
1
1
0
1
0
1
0
0
2
2
1
1
0
1
1
1
1
1
1
1
2
1
0
2
1
2
1
1
1
1
1
1
1
0
2
0
2
2
1
1
0
0
1
1
1
1
1
1
1
1
1
2
1
1
0
1
0
1
0
1
2
0
2
0
2
0
2
2
1
1
2
2
0
1
1
0
1
0
1
2
2
0
1
0
3
1
2
2
1
1
2
1
1
1
2
1
1
0
2
2
1
1
1
2
1
2
1
0
1
2
1
2
2
2
1
0
1
1
1
2
0
1
1
1
1
0
0
1
0
1
2
2
1
1
2
1
1
0
2
2
1
0
1
2
1
2
1
2
1
1
4
1
1
1
1
1
2
1
1
1
1
3
1
1
2
0
0
1
1
1
0
1
2
2
1
1
1
4
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
1
1
0
1
0
2
1
1
2
1
1
1
1
1
2
1
1
1
1
1
0
1
1
2
1
2
2
2
1
1
1
1
2
3
1
2
2
0
1
1
1
2
0
2
2
1
0
1
2
2
1
1
2
1
1
0
1
0
2
1
1
2
2
2
2
1
1
1
1
2
1
1
1
1
0
1
2
2
1
1
1
1
0
0
0
0
1
1
2
0
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
1
0
1
0
1
0
1
1
1
2
2
1
1
1
1
1
1
1
1
1
2
2
0
1
2
2
1
1
1
1
1
2
1
1
1
1
0
0
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
2
0
1
1
1
1
1
2
0
1
1
1
0
1
2
0
1
1
2
0
2
1
0
1
2
1
2
1
1
2
1
0
0
1
1
2
1
1
0
0
1
2
1
1
2
1
1
2
0
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
11
0
1
1
2
3
1
1
1
1
1
2
1
1
1
2
1
1
1
2
1
2
1
1
1
2
0
1
0
2
1
1
1
1
1
1
2
1
2
0
1
1
0
0
1
1
2
1
1
1
1
2
0
1
2
1
1
0
0
0
1
1
2
1
1
1
2
1
0
0
2
2
2
0
2
1
1
2
1
1
1
1
2
0
1
0
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
2
2
1
1
1
1
1
1
1
1
2
2
1
1
1
1
2
0
2
1
1
1
0
1
1
1
2
1
1
1
1
1
1
2
1
1
2
1
1
1
1
0
0
0
2
0
1
0
1
1
0
1
0
0
0
1
2
1
2
1
2
1
0
1
1
2
2
0
2
1
1
1
1
1
1
1
1
1
1
1
1
0
0
2
1
1
1
1
1
2
1
1
2
1
1
1
1
0
0
0
1
1
1
0
2
1
2
1
1
1
1
2
1
2
2
1
2
1
0
2
1
1
1
0
0
0
0
1
2
0
0
1
1
2
1
1
0
0
1
1
1
1
2
1
0
1
2
1
2
2
1
1
2
0
1
2
1
1
1
1
2
2
0
1
1
2
2
1
0
2
1
2
2
1
2
2
2
1
0
2
1
0
0
2
1
2
1
0
1
0
1
1
1
2
2
2
1
1
2
1
2
0
1
1
1
0
1
1
1
1
2
2
1
1
2
2
1
1
1
1
2
0
1
0
1
1
0
2
1
0
1
1
1
2
1
1
0
2
1
1
1
1
1
2
2
1
2
1
1
1
1
2
0
2
1
1
2
0
2
1
2
0
2
1
2
1
1
2
1
0
1
2
0
0
1
1
1
1
1
2
1
1
1
2
2
1
2
2
2
1
1
0
2
1
1
2
2
2
1
1
1
0
1
1
1
0
1
1
0
1
1
2
1
0
2
2
1
2
2
1
2
1
2
1
1
1
0
1
2
0
0
1
1
1
1
0
0
2
1
2
1
1
0
2
1
1
1
1
1
1
1
2
1
1
2
0
1
1
1
0
1
0
1
1
1
2
2
1
1
1
0
1
2
1
2
0
1
1
1
1
2
2
1
1
2
1
1
1
1
0
2
1
1
0
2
2
1
0
0
2
1
1
1
1
1
2
1
1
1
2
2
1
1
1
2
0
1
2
0
1
2
2
2
1
0
1
2
1
1
2
1
1
2
2
1
2
1
1
1
1
2
0
1
1
0
1
1
2
1
0
1
1
1
1
1
1
2
2
2
0
1
1
1
2
1
1
1
1
1
1
1
1
0
1
1
2
1
1
1
1
2
2
1
2
0
1
1
1
1
2
1
1
1
0
2
1
1
1
1
2
1
0
1
1
1
1
0
2
1
1
1
0
0
1
2
1
0
1
0
1
1
1
1
1
0
2
0
1
1
2
1
1
0
1
1
2
1
1
1
1
0
1
0
1
4
1
1
2
2
1
2
2
2
1
0
1
2
0
2
1
2
1
1
1
1
1
2
1
1
0
2
1
2
1
2
1
1
1
1
2
0
2
1
0
1
2
2
1
1
2
1
0
2
1
1
1
2
2
0
1
2
0
2
1
2
1
1
1
1
0
1
1
0
1
1
1
1
0
1
1
0
1
1
1
1
1
1
1
0
1
1
2
0
2
2
0
1
1
1
2
2
1
1
0
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
0
1
1
1
1
1
1
0
1
1
1
2
1
1
1
1
2
2
2
1
1
1
1
2
0
0
1
1
2
2
0
0
1
1
2
1
1
1
2
0
1
2
1
0
0
1
1
1
2
1
1
0
1
0
0
0
0
0
2
2
0
0
1
0
1
2
1
0
1
1
1
0
0
0
1
0
1
0
1
1
1
1
1
1
1
2
1
0
1
1
2
2
1
1
0
1
1
1
0
2
2
0
1
2
1
0
1
0
2
3
1
0
2
1
2
1
1
1
2
1
2
0
1
2
1
1
1
0
1
1
1
1
2
1
2
2
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
0
0
1
1
1
1
2
1
1
1
1
2
2
0
2
1
2
2
2
1
1
2
1
0
1
2
1
2
1
0
1
1
1
1
1
1
1
1
1
0
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
0
1
1
2
2
0
2
1
2
1
2
1
1
1
1
2
1
1
1
0
1
1
0
2
1
0
1
1
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
0
1
1
2
1
2
0
1
1
2
1
1
1
1
1
1
0
0
2
1
2
1
2
1
1
1
0
2
1
2
1
2
2
2
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
2
0
1
1
1
1
0
1
2
2
2
0
2
1
0
0
1
1
1
4
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
2
1
2
0
0
0
1
1
1
1
1
1
2
1
2
1
1
1
2
0
1
0
0
1
0
0
1
4
1
1
2
2
1
1
0
2
1
2
2
1
1
2
2
2
1
1
0
2
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
0
1
2
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
0
2
1
1
2
1
1
1
0
1
1
1
2
1
1
2
2
1
1
1
2
2
1
1
2
1
1
1
1
1
2
2
2
1
1
2
1
1
1
1
1
1
0
0
1
0
2
1
1
1
1
2
1
1
1
2
1
2
1
1
0
1
1
2
0
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
2
0
1
2
0
1
0
0
1
2
1
2
0
1
1
0
1
1
1
2
1
1
1
2
1
0
1
0
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
0
1
0
1
0
1
2
1
0
1
1
2
2
3
1
1
1
0
0
0
1
1
1
2
0
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
2
0
1
1
0
1
1
1
1
1
2
1
1
1
1
1
1
0
2
1
1
1
2
1
1
1
1
2
2
2
0
0
1
1
2
1
2
0
1
1
1
1
2
1
0
1
1
1
1
1
1
0
1
1
2
1
1
0
2
0
0
1
1
1
1
1
2
2
0
2
1
1
1
1
1
2
2
1
1
1
1
1
0
1
1
2
1
1
0
0
0
0
1
2
2
1
0
2
1
1
1
2
0
1
1
2
1
2
0
1
1
1
0
1
1
2
2
1
0
1
1
2
1
1
2
3
0
0
1
1
1
1
1
1
2
0
2
0
0
1
2
1
1
1
0
2
2
1
1
2
1
0
1
1
1
1
1
1
1
2
1
2
0
1
1
0
2
0
2
0
1
2
1
1
1
0
1
1
2
1
2
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
0
0
2
1
1
1
1
1
1
0
1
0
2
2
1
1
3
0
2
0
1
0
2
1
1
1
1
2
1
1
1
2
2
1
1
1
1
2
0
1
2
1
1
2
0
2
2
0
0
0
1
2
1
1
1
1
0
1
1
1
2
1
1
2
1
0
1
0
1
2
1
1
1
0
1
1
1
2
1
1
2
2
1
1
1
0
2
1
1
1
1
1
1
1
0
1
1
0
2
0
0
2
0
2
0
2
0
1
1
0
1
1
0
3
2
1
1
2
1
1
1
2
1
1
1
0
1
1
1
1
1
1
1
1
1
2
0
1
2
1
1
2
1
1
1
1
1
0
0
1
1
0
2
1
1
1
0
0
1
0
1
1
1
0
2
1
0
0
2
0
2
1
1
1
0
1
0
1
2
1
1
1
0
1
2
1
1
1
1
2
1
1
1
1
0
1
1
1
1
1
2
1
2
1
1
2
0
2
0
1
1
1
1
1
2
1
0
2
1
0
1
2
0
1
1
2
1
2
1
1
2
2
1
2
1
2
2
1
1
0
1
1
1
1
1
1
0
1
1
2
1
2
2
1
2
1
2
2
0
1
1
1
2
0
1
1
0
1
1
1
1
0
1
2
1
1
2
2
1
1
0
1
2
2
1
1
1
1
2
2
1
1
1
1
2
2
2
0
2
1
1
1
0
2
0
0
1
1
1
1
2
1
0
1
1
1
1
1
2
2
1
0
0
2
0
2
1
1
1
1
2
0
1
1
1
0
1
1
2
1
1
1
2
2
3
1
3
0
1
1
1
1
2
2
1
0
2
1
2
2
0
2
1
1
1
1
1
0
0
1
2
2
1
0
2
2
1
0
1
2
0
2
1
1
1
1
1
1
0
2
1
0
1
1
1
0
1
1
2
2
1
2
1
1
2
1
1
0
0
1
2
0
2
1
1
1
1
1
0
1
2
1
1
1
0
1
2
1
0
1
1
2
1
1
2
2
1
1
2
1
2
1
1
1
1
1
0
2
1
1
2
0
1
1
1
0
0
2
1
8
2
1
1
1
1
0
1
1
2
1
1
2
1
0
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
0
1
2
1
1
1
3
0
0
1
2
1
0
2
2
1
1
1
1
2
2
1
1
2
1
1
1
0
1
2
1
2
2
0
2
1
1
1
2
1
2
1
1
1
0
2
0
1
2
0
1
1
1
1
1
2
0
2
0
1
2
2
1
2
1
2
0
0
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
2
0
1
1
1
1
0
1
2
2
0
2
0
1
2
2
0
2
2
1
2
1
2
1
0
0
0
1
0
1
1
1
0
1
1
1
1
2
1
2
2
1
1
1
1
2
0
0
1
1
1
0
1
1
1
1
0
0
2
1
1
1
1
2
2
1
1
1
1
1
2
1
2
1
2
1
1
1
1
1
2
1
3
0
1
1
1
1
1
0
1
1
2
2
3
1
1
2
1
0
1
1
2
1
1
1
2
2
2
0
1
1
1
1
1
1
2
1
0
1
1
2
1
1
1
1
1
1
1
1
1
1
1
0
1
1
2
1
1
1
2
2
1
1
1
1
1
0
0
1
1
1
1
1
1
0
1
1
0
1
0
1
1
2
2
2
1
1
1
1
2
0
0
3
2
1
2
0
2
2
1
1
0
2
0
1
2
1
1
1
0
1
0
1
0
1
0
1
0
1
0
1
2
2
1
1
1
2
2
1
1
0
1
1
2
0
1
1
1
1
0
1
2
1
1
1
1
1
1
2
1
1
2
2
1
1
1
2
1
1
1
1
0
2
2
1
1
1
1
2
1
1
0
1
1
1
1
2
1
1
1
1
1
1
2
1
1
2
1
2
2
2
1
2
1
1
2
0
1
1
1
1
1
2
1
1
2
0
2
1
0
2
2
1
0
1
1
2
1
2
1
0
1
1
2
1
1
1
1
1
0
1
1
1
2
2
0
2
0
0
1
1
2
0
0
0
1
2
2
2
0
2
1
2
1
1
1
2
1
0
0
2
1
1
1
0
2
1
2
2
1
1
1
1
1
1
0
2
1
1
1
1
1
2
0
0
1
1
1
1
1
1
1
1
0
1
1
2
2
2
1
2
1
2
1
1
0
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
0
1
1
2
1
1
1
1
1
2
2
2
1
1
1
1
1
2
1
1
1
2
1
1
1
0
2
0
1
1
1
1
2
0
2
1
2
1
1
1
1
1
1
1
1
2
1
0
1
2
1
1
1
2
1
1
2
1
1
1
0
1
1
3
1
1
1
0
0
1
1
0
1
0
1
0
2
1
1
2
2
1
1
2
1
1
1
2
2
2
2
0
0
0
1
2
0
0
1
1
2
0
2
2
1
1
1
1
1
1
2
1
0
2
1
1
2
2
2
0
1
0
1
0
2
1
0
1
1
1
1
1
1
1
1
2
1
0
1
0
2
1
0
2
0
1
0
0
0
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
2
1
1
0
2
0
1
1
1
2
0
1
1
1
1
1
2
2
1
2
2
1
1
1
1
0
1
1
2
1
2
1
1
2
1
1
1
2
2
1
0
1
1
0
0
2
2
0
1
2
2
2
0
1
2
1
1
0
1
1
1
1
2
3
1
1
1
2
2
0
1
1
1
2
2
0
1
1
0
1
2
0
0
0
2
1
1
1
2
1
1
1
0
2
1
1
2
1
2
1
0
0
2
1
2
0
1
0
1
1
1
1
2
2
1
1
0
2
2
1
2
1
1
1
1
2
2
1
1
0
1
2
1
0
1
1
2
1
1
2
2
1
2
2
1
1
1
1
2
0
0
2
1
1
1
1
1
1
1
1
2
2
0
0
1
2
0
1
0
2
2
1
1
2
0
0
1
1
2
1
2
1
2
1
3
2
1
0
2
1
1
1
0
2
1
1
3
0
1
3
1
0
1
2
1
1
0
1
1
1
1
1
1
0
1
1
2
0
1
1
1
1
0
2
0
1
1
0
0
2
1
1
1
2
1
3
1
1
1
0
0
2
0
1
2
0
2
1
0
1
1
1
1
0
0
2
2
1
1
1
1
1
1
1
1
1
0
0
3
1
1
2
1
1
1
0
2
0
1
1
1
0
1
2
2
1
1
1
1
1
2
1
1
1
1
2
2
1
1
1
0
1
1
1
1
1
0
1
1
2
0
1
2
1
1
0
2
0
1
1
1
1
1
2
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
0
1
2
1
1
2
3
0
1
1
0
1
1
1
2
1
2
0
0
1
2
1
0
2
2
1
1
1
1
1
0
1
2
1
2
1
1
1
2
2
1
2
2
1
1
2
1
1
0
1
1
0
1
1
1
2
0
1
1
1
0
1
2
0
0
0
1
1
2
1
1
0
1
1
1
1
1
0
1
1
0
2
1
1
0
0
0
1
1
1
2
1
0
1
0
1
2
2
2
1
2
1
0
2
1
2
0
2
0
1
2
1
0
1
1
1
1
1
1
1
2
1
2
1
1
1
0
2
0
1
2
1
0
1
2
2
1
1
2
2
1
2
1
1
2
1
0
1
1
1
0
1
2
2
0
0
1
1
1
1
0
0
1
0
1
1
1
2
1
1
1
2
0
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
0
1
1
1
1
0
0
2
1
1
0
1
1
1
1
2
0
1
2
1
1
1
1
2
2
1
1
1
1
1
1
0
1
1
1
1
1
1
3
1
2
1
1
1
0
0
1
1
2
1
1
1
1
2
2
1
1
1
1
2
1
1
0
1
1
1
2
1
1
1
1
2
0
2
1
1
0
1
0
1
1
1
1
1
1
1
2
1
2
1
0
0
1
0
1
1
1
0
2
1
1
1
2
1
1
1
0
2
1
2
2
1
0
1
2
1
2
1
2
0
1
2
0
1
1
2
0
1
2
1
1
1
1
1
2
2
1
1
2
1
1
1
1
1
1
2
1
0
1
0
1
1
1
2
0
1
1
2
2
3
1
1
1
0
1
1
1
1
1
0
1
0
2
1
1
1
1
1
1
1
0
2
1
1
1
0
1
1
0
1
0
0
1
1
0
1
1
2
1
3
1
1
1
2
2
0
0
1
1
2
1
2
1
0
1
2
0
1
1
0
2
1
1
0
1
1
2
0
1
0
1
1
2
2
1
2
1
1
1
1
2
1
1
1
1
1
2
1
1
1
0
2
1
1
2
1
0
1
1
1
1
1
1
1
1
0
1
1
1
0
0
2
2
0
1
2
1
2
1
1
0
1
0
2
1
2
1
2
1
1
1
1
1
1
1
0
1
2
1
1
0
1
1
1
1
1
1
1
1
2
2
2
2
1
1
1
0
1
1
1
1
2
2
1
2
1
1
1
1
0
1
0
1
2
2
1
2
3
0
2
0
1
3
0
1
1
1
1
4
1
1
1
0
1
1
2
2
1
0
2
1
0
1
1
0
1
1
2
1
1
1
2
1
1
0
2
1
2
0
2
0
2
0
2
2
0
0
1
0
1
1
1
1
1
2
1
1
1
2
1
1
0
0
1
2
2
0
1
1
2
1
2
1
1
1
1
1
1
1
2
1
0
2
0
1
2
1
2
1
1
1
2
0
1
1
1
1
1
1
1
1
1
1
1
1
2
0
0
2
1
1
1
2
1
2
2
1
0
1
0
1
2
2
1
1
2
2
1
1
0
0
1
1
0
0
2
1
1
1
1
1
1
2
1
1
2
2
2
1
0
2
0
1
2
1
3
2
2
1
1
1
2
2
2
0
1
1
0
2
0
1
1
1
1
1
0
1
1
0
2
1
2
0
1
1
1
2
1
1
2
0
0
1
1
0
1
2
0
2
2
1
2
1
2
1
1
1
2
2
1
2
1
2
1
2
0
1
1
1
0
2
0
1
1
1
2
1
1
1
1
0
0
1
1
1
1
1
1
1
2
1
0
0
0
2
1
0
1
1
1
1
1
1
2
1
2
2
1
0
2
2
1
1
1
2
2
1
2
0
1
2
0
1
1
0
1
1
1
1
1
1
2
2
1
1
1
1
1
0
1
1
1
1
0
1
2
2
2
2
1
1
1
0
0
1
2
1
0
0
0
2
1
1
1
1
2
2
2
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
2
2
2
1
1
1
1
2
2
2
0
1
1
1
2
1
1
1
2
1
2
0
1
2
2
0
1
1
0
1
2
2
0
1
1
2
2
2
1
1
2
0
1
0
1
1
1
1
1
1
1
2
1
1
1
2
0
1
1
2
0
0
1
1
0
1
1
1
1
1
0
1
1
1
2
2
1
1
1
0
2
0
1
1
1
2
1
0
1
2
2
1
1
1
1
0
1
1
1
0
1
2
2
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
0
0
2
1
1
1
1
1
1
2
0
1
1
1
1
1
1
1
0
2
1
1
1
1
0
1
0
1
1
1
2
0
0
2
1
1
1
2
1
1
1
0
2
1
0
0
3
2
2
1
0
1
1
1
2
2
0
1
2
0
0
2
2
0
0
2
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
0
1
1
1
2
1
1
2
1
0
2
1
0
2
2
1
2
1
2
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
2
1
1
1
2
1
2
0
1
2
1
1
2
1
0
0
0
0
0
2
1
1
1
1
1
2
0
2
0
0
1
1
1
2
0
2
1
0
1
1
1
2
1
0
1
0
1
1
1
2
2
2
2
2
1
1
1
2
1
0
2
1
1
0
1
1
1
1
2
0
1
0
1
0
1
1
1
1
2
1
1
2
2
2
1
2
0
1
1
1
1
0
0
0
0
1
1
1
1
1
1
2
1
1
1
2
1
1
0
0
2
1
1
1
2
1
1
2
1
1
1
1
2
2
1
1
2
0
1
2
1
1
1
1
1
0
1
1
1
2
1
1
1
2
1
1
1
0
1
1
1
1
1
0
1
1
1
1
1
0
1
1
0
0
0
1
1
1
2
1
2
2
1
1
2
1
2
2
2
0
2
0
0
1
2
0
2
2
0
2
1
2
1
1
0
2
0
1
1
1
0
1
0
1
0
1
2
1
1
1
2
1
1
1
2
0
2
1
2
2
2
0
2
0
1
1
1
1
1
2
1
0
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
2
1
0
1
1
2
1
1
1
0
1
1
0
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
0
2
0
1
2
1
0
1
1
1
2
1
3
1
2
1
1
2
1
1
1
2
0
1
1
0
2
2
1
1
1
1
1
2
1
2
0
0
1
0
1
1
1
1
1
2
1
1
1
1
1
1
0
1
2
1
2
1
1
1
2
0
1
0
1
0
1
0
1
1
2
2
2
1
1
1
0
1
0
2
2
1
0
1
1
2
1
2
1
1
2
1
0
1
1
2
1
0
0
1
0
2
0
1
1
1
1
2
1
1
1
1
2
2
1
1
1
1
2
1
1
1
0
1
1
1
2
2
2
1
1
1
1
0
2
0
2
2
0
2
1
1
2
0
0
1
0
1
1
1
1
1
1
2
2
1
1
1
1
0
0
0
2
1
1
1
0
1
0
1
2
1
2
2
1
1
1
1
1
1
1
1
0
1
2
1
0
1
1
1
2
1
2
1
2
1
1
2
1
2
1
1
1
1
2
1
0
2
0
1
0
1
2
1
2
2
2
1
1
1
0
2
0
1
1
1
1
1
2
1
0
0
1
1
2
2
2
2
1
1
2
0
1
1
1
1
0
2
1
1
0
1
1
1
1
2
1
2
1
1
1
0
1
1
1
2
1
1
1
2
1
1
1
1
1
2
2
1
2
1
1
1
1
1
0
2
2
2
0
1
1
1
1
1
1
1
1
1
1
0
1
2
1
0
2
0
1
1
2
3
0
2
1
1
0
0
1
1
1
1
2
0
0
0
3
0
3
0
1
1
1
1
0
1
2
2
1
1
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
0
1
2
0
1
2
1
1
1
1
1
2
2
0
1
1
1
1
1
1
1
1
1
0
1
1
4
1
2
2
1
1
2
0
1
2
2
1
0
2
1
1
1
1
1
1
1
1
1
2
0
0
1
1
2
1
0
1
0
1
1
1
1
2
0
1
1
1
1
1
1
1
0
1
1
1
1
1
0
1
1
1
1
1
2
2
1
0
1
1
1
2
1
2
0
0
1
0
1
1
1
2
2
0
1
0
2
1
2
1
2
0
1
1
1
1
0
1
1
1
2
1
2
1
1
3
1
1
1
1
2
1
1
1
1
1
1
2
2
1
0
1
1
1
2
1
1
0
1
1
1
1
0
0
0
1
0
1
1
1
2
1
2
1
1
1
2
1
1
1
1
2
0
1
2
2
1
5
2
2
1
2
1
1
0
1
1
1
1
0
1
1
1
0
1
2
1
2
1
2
2
1
2
2
1
2
1
2
2
3
1
1
1
1
1
1
1
1
1
2
3
1
1
0
1
1
2
2
1
1
1
1
2
1
1
1
1
2
2
1
1
2
2
1
1
1
1
1
0
0
1
1
2
1
1
1
2
2
1
1
1
1
0
1
0
1
1
0
2
1
1
1
0
0
0
1
2
0
1
0
1
1
1
1
1
2
1
1
0
1
1
2
2
0
1
1
1
0
2
1
1
0
0
2
1
2
1
1
1
1
1
0
1
1
2
2
1
1
2
1
1
1
2
2
1
2
1
2
1
0
0
1
1
1
2
0
1
2
2
0
2
1
1
1
0
1
1
1
1
1
2
1
1
1
2
0
2
1
1
2
2
1
1
1
1
0
2
1
2
1
1
2
2
1
1
1
1
2
0
1
1
1
1
1
1
1
1
1
1
1
0
1
1
2
2
2
2
3
2
1
0
1
1
0
0
2
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
0
2
2
1
1
0
2
0
1
1
0
2
1
1
1
1
1
1
1
1
1
2
1
1
0
1
0
0
1
1
1
1
1
0
0
2
2
1
1
1
1
1
1
1
1
2
1
2
1
1
1
0
1
1
1
2
1
0
1
1
8
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
1
2
0
0
2
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
0
1
1
1
0
2
2
1
1
0
1
1
1
1
1
0
2
0
1
1
1
1
2
2
1
0
2
2
0
0
1
0
1
1
2
1
2
1
1
1
1
1
2
1
1
1
1
0
1
2
1
0
0
1
1
0
2
1
0
1
1
2
0
1
1
0
1
1
1
0
1
0
0
0
0
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
3
0
0
1
1
2
2
1
1
0
1
0
1
1
1
0
1
1
2
2
2
1
1
0
1
0
0
2
2
2
0
0
2
1
0
0
1
2
1
2
1
2
1
0
1
1
1
1
0
2
1
1
1
2
1
1
1
1
1
1
0
2
1
1
2
1
1
1
1
2
1
1
2
0
1
1
2
2
1
1
1
0
2
1
1
1
2
0
1
2
2
1
1
1
0
1
2
0
0
1
1
0
1
2
1
1
0
1
1
0
1
2
2
1
0
0
2
1
2
1
2
1
0
1
1
0
2
2
2
0
1
0
1
0
1
1
1
1
1
0
2
1
1
3
1
2
1
1
1
1
1
1
0
2
1
1
1
1
1
2
1
2
2
1
1
0
2
1
0
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
2
0
1
2
0
1
2
2
0
1
1
1
1
0
2
1
1
0
1
2
1
2
0
1
3
1
1
0
0
1
2
2
1
1
1
1
2
2
1
1
1
1
1
2
2
1
0
1
1
1
1
2
1
1
0
3
1
1
1
1
2
1
1
1
2
2
0
1
2
1
1
2
1
2
1
3
1
2
1
0
1
2
1
1
1
1
1
1
1
4
0
0
1
1
1
1
2
1
1
0
0
2
1
1
0
1
2
1
1
1
1
0
1
1
1
1
1
0
1
1
0
1
2
0
1
0
1
1
2
1
1
1
2
1
1
1
0
0
1
2
0
1
1
0
2
1
0
1
2
1
1
1
1
1
2
1
0
1
1
1
0
1
1
0
2
1
0
1
1
1
1
1
2
0
0
0
1
1
1
2
0
1
2
2
2
1
2
1
0
1
2
1
2
2
0
2
1
1
2
1
1
0
2
1
1
2
1
1
1
2
0
1
0
1
2
2
0
0
2
1
1
2
1
1
1
1
1
0
1
1
1
1
2
1
1
2
1
1
0
2
1
1
1
1
1
2
2
1
2
1
1
1
0
1
1
2
2
2
1
2
2
1
2
2
1
0
0
1
0
1
1
1
1
1
0
1
1
2
1
2
0
0
0
2
1
2
1
0
2
0
2
1
1
2
1
1
0
2
1
1
2
1
1
0
2
1
0
1
1
1
1
4
1
1
2
1
2
1
1
1
1
0
1
0
2
1
1
1
1
2
1
2
2
1
2
1
1
1
1
1
1
1
1
0
2
1
1
1
1
1
2
2
1
1
1
1
1
1
2
2
1
1
1
1
0
1
1
0
2
1
0
1
1
1
2
1
0
1
1
1
2
1
1
1
1
2
0
2
0
1
0
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
0
1
1
2
1
2
1
1
1
1
0
1
0
0
1
2
1
1
1
1
0
1
1
2
0
0
1
2
1
1
1
1
1
0
3
1
0
1
1
1
1
1
0
1
1
1
1
1
0
2
0
1
2
2
1
1
1
1
2
1
1
2
1
2
1
1
1
2
1
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
2
1
2
0
1
1
1
1
2
1
2
1
1
1
2
1
0
0
2
1
1
1
2
0
1
1
1
0
2
1
1
1
1
0
2
2
1
2
1
1
1
2
1
1
3
1
0
1
0
1
1
1
2
0
1
0
1
0
2
1
1
1
2
0
1
1
1
1
1
0
0
2
0
1
2
1
1
1
1
0
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
2
2
1
0
2
0
1
1
1
1
2
1
1
2
1
1
1
2
2
1
1
2
1
1
1
0
2
1
2
1
0
1
0
1
0
1
1
1
1
1
1
1
2
0
1
1
2
1
2
2
1
0
1
0
1
2
1
2
2
0
2
1
0
1
3
1
1
1
1
2
1
1
0
1
0
1
1
2
0
1
2
1
1
1
0
1
1
1
2
3
2
1
1
1
1
0
1
2
2
0
0
2
1
2
2
0
1
0
2
0
1
1
1
1
2
1
1
0
1
2
1
2
1
2
0
1
1
1
1
0
1
2
2
1
0
1
1
2
2
1
1
2
1
0
1
1
1
2
0
0
2
1
0
1
2
1
1
1
1
2
2
1
2
1
1
2
1
2
0
2
0
1
2
2
4
1
1
1
2
2
1
0
1
1
1
0
1
1
2
1
1
2
1
1
1
1
1
2
1
1
0
1
1
1
1
1
0
1
1
0
0
1
1
0
0
2
0
1
2
2
0
0
0
1
1
1
0
1
1
1
1
2
0
1
1
1
2
1
2
1
2
2
1
1
1
1
1
1
0
2
1
0
1
1
1
1
1
0
1
2
2
1
0
1
2
0
1
0
1
1
2
1
0
1
0
2
0
1
1
1
2
1
1
1
1
1
2
1
0
1
1
0
2
1
1
2
1
1
1
1
1
2
1
0
1
2
1
2
1
1
1
1
0
0
2
2
1
2
2
1
1
1
0
1
1
0
2
0
0
1
1
2
2
0
1
0
1
2
1
1
1
0
1
1
1
2
1
1
1
2
1
1
2
1
0
2
2
2
0
2
2
1
1
1
1
2
0
1
1
1
2
0
1
1
0
1
1
2
2
2
1
2
1
1
1
1
1
1
1
1
1
0
1
1
2
1
1
1
1
2
2
2
1
1
0
1
1
2
1
1
2
1
1
1
0
0
1
1
1
2
1
0
0
0
0
1
2
1
1
1
0
0
1
2
1
0
1
1
0
2
0
1
2
2
2
2
1
1
0
2
1
1
2
1
1
1
2
1
2
2
2
1
1
1
2
2
2
2
2
2
1
0
1
0
2
1
1
1
2
1
2
0
2
0
1
1
2
1
1
0
1
1
2
2
1
1
1
1
6
2
3
2
2
1
2
2
2
1
1
2
1
1
2
1
1
1
1
0
2
1
2
2
1
0
2
1
0
1
1
1
1
1
1
0
2
2
1
1
1
1
0
1
2
0
1
2
0
1
0
2
1
1
1
2
1
1
0
0
1
1
2
3
1
0
1
2
1
1
0
1
0
2
1
2
1
1
0
1
2
2
1
2
2
1
2
2
2
0
0
0
1
2
1
0
1
1
1
1
2
0
1
1
1
1
1
0
1
1
1
1
2
0
1
0
2
1
2
1
1
0
1
0
2
1
1
1
1
1
2
1
2
2
2
1
2
1
1
2
1
1
1
1
1
1
2
1
0
1
1
2
0
1
1
0
1
1
2
1
1
2
0
1
1
1
1
1
1
1
1
1
2
1
1
0
1
2
0
2
1
1
1
0
1
1
1
1
2
0
2
1
2
0
2
1
1
1
2
2
1
0
2
1
1
1
0
1
0
1
0
1
1
1
2
1
2
1
2
1
2
3
1
0
2
2
1
1
2
1
1
1
1
2
2
1
1
0
2
0
1
1
1
1
1
1
1
2
2
2
2
1
2
1
1
2
2
1
1
1
1
1
1
1
1
3
2
1
1
1
1
1
1
1
0
0
1
0
2
0
1
1
1
0
1
2
2
2
1
1
1
2
1
2
0
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
2
1
1
1
1
0
0
1
0
2
1
1
1
1
1
1
2
1
0
1
1
1
1
2
1
1
2
2
2
1
1
2
1
1
1
0
1
1
2
1
2
1
2
1
1
1
2
2
1
2
2
1
1
0
1
1
1
2
1
1
1
1
2
1
1
1
1
0
1
1
1
1
1
2
1
2
1
0
0
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
2
1
1
2
0
1
2
1
2
2
0
2
1
1
1
1
0
1
2
1
2
1
1
0
1
2
0
1
1
1
2
1
2
1
2
1
2
3
1
1
1
1
0
0
2
1
2
2
0
0
1
0
1
1
1
1
1
1
1
1
0
1
1
1
0
1
0
4
1
1
1
1
2
1
1
1
1
0
2
1
1
1
1
1
2
1
0
0
1
1
1
1
1
0
1
0
2
1
1
1
1
0
1
2
0
1
1
1
0
1
0
2
1
2
2
1
1
1
0
1
1
1
1
1
0
1
1
1
1
2
0
1
2
1
0
1
1
1
1
0
2
1
1
1
2
1
1
0
1
1
1
1
1
1
2
1
0
2
1
1
1
1
1
1
0
0
0
1
1
1
2
1
1
0
1
1
0
2
2
1
1
2
1
1
0
2
1
1
1
1
1
2
1
2
1
0
1
0
1
1
1
1
2
1
2
1
1
2
1
1
0
1
1
1
1
2
1
1
1
2
2
1
2
1
2
2
1
0
1
1
1
1
2
1
2
1
1
2
1
2
2
1
2
1
1
1
1
1
2
2
1
0
2
1
1
2
1
1
1
0
5
1
2
1
1
2
1
1
2
0
1
1
0
1
1
1
1
1
1
1
0
1
1
0
0
2
1
1
1
2
1
1
1
2
2
1
1
1
2
1
1
1
1
0
1
1
0
1
1
0
2
1
1
1
1
0
1
1
1
2
2
2
1
1
2
1
1
2
0
1
2
2
0
1
3
1
1
2
0
0
1
2
1
2
2
1
1
2
1
0
2
1
1
2
1
0
1
1
2
1
1
1
2
1
1
1
2
1
2
2
0
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
2
1
2
2
1
0
1
2
0
1
1
1
1
0
2
1
2
2
0
1
1
1
1
1
0
2
0
1
2
1
1
1
1
0
0
1
1
1
2
1
1
2
1
1
0
1
1
1
1
1
1
1
2
0
1
1
1
1
1
1
0
2
1
1
2
2
1
1
0
1
1
1
0
2
0
1
1
1
1
2
1
0
1
2
1
3
1
1
1
1
0
1
2
1
1
2
0
2
1
2
1
0
2
1
0
2
1
0
0
1
1
1
2
2
0
1
1
1
2
1
1
2
2
2
1
1
1
2
1
1
0
1
2
1
1
1
1
1
3
1
2
0
0
1
1
0
1
2
2
1
1
1
1
2
1
2
1
1
1
1
2
2
1
1
1
1
1
1
1
1
0
2
2
1
0
2
1
2
1
1
2
2
1
1
1
0
0
1
0
2
1
2
2
1
1
0
1
1
0
1
0
1
1
2
2
1
1
2
1
2
1
2
1
2
1
2
0
1
1
1
1
2
1
1
1
2
1
1
2
0
1
0
2
1
1
2
1
1
1
1
2
0
0
1
1
1
1
2
1
1
0
1
2
2
1
1
1
1
1
1
0
1
1
1
1
2
0
2
2
1
1
0
1
1
1
1
2
1
1
0
1
2
0
0
2
1
2
2
1
2
0
2
1
2
2
1
1
2
2
2
0
1
1
1
2
0
2
1
1
0
0
2
2
1
2
1
1
1
0
1
0
2
1
1
2
0
0
1
1
1
1
2
1
0
0
1
2
0
0
3
1
1
1
1
1
0
2
1
1
1
1
2
0
2
1
1
1
2
1
1
1
1
0
2
2
1
1
1
2
2
1
2
3
1
2
1
1
1
0
1
1
1
0
0
1
1
1
1
2
2
2
1
1
1
2
2
0
1
0
2
1
2
2
1
2
1
2
2
1
2
1
1
1
1
2
1
1
0
0
1
1
2
2
2
1
1
1
1
0
0
1
1
1
1
2
1
1
0
1
1
0
1
1
0
1
2
0
1
1
0
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
0
1
1
2
0
0
2
1
0
1
0
2
1
0
1
1
0
2
1
2
2
2
1
1
1
1
1
0
1
1
2
0
1
2
1
2
1
1
1
1
1
1
2
0
2
1
2
1
1
1
1
1
1
2
2
0
1
1
2
1
2
1
1
2
2
2
2
1
0
2
4
1
1
1
2
2
2
1
1
1
0
1
1
1
1
1
1
2
2
1
1
0
2
1
2
2
2
1
1
1
0
1
1
2
1
1
0
1
1
2
1
1
1
1
0
2
1
0
1
1
1
2
1
1
0
1
2
1
0
1
2
1
1
2
1
0
1
1
2
2
2
2
2
2
1
1
0
1
2
1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
1
1
1
2
1
1
3
0
1
1
2
2
1
2
2
1
0
0
1
1
1
1
1
1
2
1
1
1
1
2
2
0
1
2
1
1
2
1
2
1
1
1
2
1
2
1
1
2
1
2
1
1
2
1
0
0
1
1
0
2
1
1
1
1
1
0
2
1
1
0
2
1
2
0
1
1
2
2
1
1
1
0
1
1
1
1
2
1
1
2
1
1
1
2
2
2
1
0
2
1
1
1
0
1
1
1
0
1
0
0
2
1
2
1
1
3
2
0
1
1
2
2
1
1
2
0
2
2
2
0
3
1
1
0
1
1
1
2
1
0
1
1
1
2
0
1
0
0
1
2
1
2
3
1
2
1
1
1
0
1
1
1
0
0
1
1
1
1
1
1
0
2
1
2
3
2
1
2
0
1
1
0
1
1
1
2
2
1
1
2
0
0
0
1
0
0
1
1
1
0
1
0
1
2
2
1
2
1
0
1
1
1
2
0
1
2
2
2
1
1
1
1
1
1
2
2
1
1
2
1
1
1
2
0
0
1
0
1
1
1
1
1
2
1
2
1
0
1
1
1
0
2
0
2
1
1
1
2
1
0
0
1
2
1
1
1
1
1
1
1
1
2
0
1
2
1
0
1
1
1
2
1
2
1
1
1
1
0
2
1
1
1
2
2
2
1
1
1
1
1
1
1
0
2
0
0
1
1
1
1
1
1
0
2
1
2
1
2
0
2
0
2
0
0
1
1
1
1
2
0
1
1
1
0
2
0
1
2
1
2
2
0
1
1
1
1
2
1
1
1
1
1
2
1
1
2
1
1
1
3
1
1
1
1
2
2
1
0
1
1
2
2
1
0
2
0
1
2
1
0
1
1
1
1
1
1
1
2
2
2
2
1
0
1
2
2
1
1
0
1
1
1
1
1
2
2
2
2
1
1
2
0
1
2
2
2
2
1
0
1
1
2
2
2
1
2
1
1
0
1
1
1
1
0
2
0
2
0
1
1
2
2
2
1
1
2
0
1
1
2
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
2
0
1
1
0
2
1
1
1
1
1
1
2
1
0
1
1
1
2
2
1
2
0
1
0
0
2
2
2
0
1
2
2
1
1
1
0
1
2
2
2
1
0
1
2
0
2
2
1
1
2
2
1
1
2
2
0
2
2
1
1
1
1
0
0
1
1
1
1
1
1
0
2
1
1
0
1
2
2
2
0
1
1
0
1
2
1
1
2
1
1
1
0
2
0
1
1
1
0
1
1
0
0
1
1
2
1
0
1
1
2
1
0
1
2
1
2
1
1
1
1
1
1
1
2
0
2
2
1
1
1
1
1
1
2
1
1
0
0
1
1
1
1
2
1
0
1
1
1
1
0
1
2
2
0
1
1
0
1
1
1
2
2
1
1
0
1
1
2
1
2
1
2
0
0
1
0
1
1
1
1
1
1
1
2
1
2
1
2
1
2
1
3
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
2
0
1
1
1
1
2
2
0
1
2
1
1
1
0
0
0
3
2
1
1
2
0
1
2
2
0
1
1
1
1
2
2
1
0
1
1
2
0
1
1
2
1
2
0
0
1
2
1
2
1
1
2
1
1
1
1
2
1
2
1
0
1
2
0
1
1
0
1
1
1
1
1
1
1
2
1
0
1
2
1
1
2
1
1
0
1
2
2
0
1
2
1
1
1
2
0
1
0
2
1
1
1
0
0
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
2
2
0
1
1
0
1
0
2
1
1
1
2
2
1
1
0
1
1
2
1
1
2
0
2
0
1
2
1
1
0
1
1
1
1
1
1
1
1
1
2
1
1
0
1
1
1
1
0
1
1
1
0
1
0
2
1
1
2
0
2
1
1
1
0
1
0
1
1
1
1
1
0
2
0
1
2
2
0
1
1
0
1
0
1
0
1
1
2
1
1
1
0
0
1
0
1
2
1
2
1
1
0
2
0
1
1
1
1
4
1
1
1
2
1
1
2
1
1
0
1
1
1
0
1
1
1
1
0
1
2
1
2
2
2
0
2
1
1
0
1
2
2
1
2
2
1
0
0
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
0
2
0
1
2
1
1
1
2
1
0
1
1
1
1
1
1
2
1
0
1
1
0
1
1
1
1
1
1
2
1
1
3
2
1
2
1
1
2
0
1
1
1
1
0
2
0
2
0
2
1
1
2
1
0
1
1
2
2
0
1
1
2
1
1
2
2
2
1
1
1
2
1
1
0
1
1
0
1
1
1
2
1
0
0
1
2
1
0
1
0
1
1
0
1
1
1
1
1
0
1
1
1
2
1
2
1
1
1
0
1
1
2
0
1
1
1
1
1
1
2
1
2
2
1
1
1
0
1
1
1
1
1
1
2
1
1
0
1
0
2
1
1
2
2
0
1
1
1
1
1
0
2
1
0
1
0
1
1
1
1
0
1
1
1
1
1
2
1
2
1
1
1
0
1
1
2
1
2
2
0
1
1
0
0
2
1
0
2
1
1
1
2
1
1
1
2
2
2
1
0
0
1
1
1
1
1
2
1
0
1
1
1
1
0
0
0
1
0
2
1
2
2
2
2
1
1
2
2
1
1
1
2
1
1
2
1
1
2
2
1
2
2
2
1
0
1
1
0
0
1
1
1
1
1
1
1
1
0
2
1
1
1
1
2
1
1
2
1
1
0
1
0
1
2
1
1
0
1
1
1
1
0
0
0
0
0
1
1
1
1
2
2
1
0
2
1
2
1
1
0
0
0
1
2
2
1
0
1
1
1
1
1
0
1
2
1
1
1
1
2
1
1
2
0
0
1
1
0
1
2
1
0
1
1
1
0
2
4
1
1
2
1
1
1
1
0
1
1
1
0
2
1
1
1
1
0
2
2
2
2
1
1
1
2
1
1
1
1
1
0
1
0
1
0
1
1
2
1
1
1
1
1
0
2
0
1
2
0
1
1
0
1
0
2
2
2
2
2
0
1
2
0
2
1
1
2
3
1
2
2
1
2
1
1
1
2
1
1
1
1
1
0
2
1
1
2
1
1
0
0
2
1
4
1
2
1
1
0
0
2
2
0
0
2
1
2
1
0
1
1
2
0
1
2
1
1
0
1
1
0
2
1
1
1
2
1
2
1
0
1
2
0
1
1
0
1
0
1
1
2
0
1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
2
1
0
1
1
2
1
2
1
1
1
2
2
2
1
0
1
1
2
1
1
1
2
0
0
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
0
1
2
2
1
1
1
1
1
0
2
1
0
1
2
1
2
2
1
2
1
2
1
1
3
1
2
2
2
1
0
1
1
1
0
0
1
1
1
2
1
0
0
1
0
2
0
1
0
1
2
2
1
1
0
1
1
1
1
2
0
1
1
1
1
1
1
1
1
2
2
1
2
1
2
1
1
2
1
1
1
1
0
1
0
0
2
2
1
2
1
1
0
1
0
1
0
0
1
2
0
2
1
0
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
0
1
2
1
1
1
2
0
2
1
4
1
1
0
0
1
1
0
2
1
1
1
0
1
1
1
1
1
1
1
1
1
2
1
2
1
0
0
1
2
2
1
1
1
3
2
1
2
1
0
1
1
1
1
2
1
0
1
1
0
0
1
1
2
2
0
1
2
1
0
1
0
2
1
1
0
1
0
1
1
0
1
1
1
1
0
1
1
1
1
1
1
1
0
1
2
1
0
2
2
1
1
1
1
1
1
1
1
0
1
2
1
1
1
0
0
1
2
1
1
2
1
1
1
0
1
1
2
1
1
0
2
2
1
2
1
1
1
0
0
1
2
1
1
2
1
1
1
1
2
0
1
2
1
1
1
1
1
2
0
1
0
2
1
2
2
1
1
1
1
1
0
1
1
2
1
2
1
2
0
2
1
1
1
1
1
1
1
1
1
0
2
1
2
0
1
1
0
1
2
1
0
1
0
2
1
1
0
1
1
2
0
1
1
1
1
2
1
0
1
1
1
2
1
2
2
1
1
1
1
0
2
1
2
1
1
1
1
1
2
1
2
1
1
2
2
1
0
2
2
1
1
0
1
2
1
0
2
1
2
1
1
0
2
1
2
1
1
0
1
1
1
2
1
1
0
1
0
0
1
2
1
0
2
1
1
1
2
0
1
2
0
1
2
1
0
1
2
0
0
2
1
1
2
2
2
2
1
1
2
1
1
2
1
0
1
1
1
1
1
1
0
1
0
1
1
1
2
1
1
0
1
1
1
1
1
1
1
0
2
1
1
0
1
1
1
1
1
2
2
0
1
1
0
2
1
1
1
1
1
2
1
1
1
0
2
1
1
1
2
2
0
1
1
0
1
2
0
1
1
1
1
2
5
0
2
1
0
1
1
1
2
2
1
1
1
1
1
0
2
2
1
1
0
1
1
1
1
0
1
1
1
1
2
0
2
1
0
1
2
1
1
2
1
1
2
2
2
1
1
1
1
2
1
0
1
1
2
1
1
1
0
1
7
1
1
1
0
0
2
1
1
1
0
1
0
1
0
2
0
0
2
1
2
2
1
0
1
1
2
1
1
1
1
1
3
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
0
2
1
1
1
0
1
2
0
1
1
0
1
1
1
1
1
1
0
2
1
1
0
1
1
0
1
1
1
0
0
2
1
1
2
0
1
0
2
1
2
3
2
1
0
0
1
1
1
1
2
1
0
1
1
0
1
1
1
1
1
2
1
0
1
1
0
1
1
1
2
2
1
1
1
0
0
2
2
2
0
1
1
3
0
0
0
2
0
1
0
2
2
1
1
1
0
1
1
1
1
1
1
1
1
0
1
0
3
1
2
1
1
1
2
0
1
1
2
0
0
1
1
1
1
1
1
2
0
2
1
1
1
1
1
1
2
1
1
1
4
1
1
1
2
2
0
2
1
1
0
1
1
0
0
1
0
1
1
3
0
1
1
1
1
1
0
2
2
1
2
0
2
1
1
2
2
1
1
2
1
1
0
1
1
6
1
1
0
1
0
1
0
2
1
1
1
1
1
0
0
1
2
1
1
2
1
1
1
1
1
1
1
1
3
2
1
2
1
2
1
0
2
1
0
1
2
2
1
0
0
1
1
1
1
1
1
2
1
1
1
1
2
1
2
1
2
1
1
1
2
2
1
2
1
0
1
1
2
1
2
1
2
0
2
1
1
2
1
1
1
0
1
1
1
2
0
1
2
1
2
1
1
1
1
1
1
1
2
0
2
0
0
0
1
0
1
1
1
0
1
1
1
1
1
0
0
1
1
2
2
1
1
1
2
1
2
1
2
2
2
1
1
2
2
3
1
1
1
1
2
1
2
2
1
2
1
1
2
1
1
0
1
1
1
1
0
2
2
2
1
0
0
1
1
1
0
2
1
1
1
1
2
2
2
2
2
1
0
1
1
1
0
2
2
2
1
1
1
2
1
0
2
1
2
1
1
2
1
1
1
0
1
1
2
0
2
1
1
0
1
1
1
3
1
1
2
1
1
0
1
1
1
1
1
1
1
2
2
1
1
1
2
0
1
1
1
1
1
2
0
1
2
0
2
2
2
1
1
1
0
1
1
2
1
2
1
1
2
1
1
1
1
1
5
1
0
1
2
2
1
2
0
1
0
2
1
1
1
1
1
1
0
2
0
0
1
0
0
1
1
1
1
1
0
1
1
1
1
1
2
1
1
2
1
1
2
1
2
0
1
0
1
1
1
1
1
0
0
2
1
1
2
1
1
1
0
1
1
0
1
1
2
1
0
1
1
1
1
2
1
1
1
2
1
1
0
1
1
1
2
2
2
1
1
2
0
2
1
1
1
1
1
1
1
1
1
2
1
2
2
1
0
1
1
0
1
2
1
1
1
0
1
1
1
0
1
1
1
2
1
1
0
2
1
2
1
2
1
1
1
1
1
2
1
1
1
1
3
1
1
1
1
1
1
2
0
1
1
2
1
1
1
0
1
1
1
2
1
2
0
1
1
0
1
2
1
0
1
0
2
1
1
2
2
1
1
1
1
2
2
2
1
2
1
1
1
1
1
0
1
1
1
1
1
1
2
1
1
2
3
2
1
1
0
2
1
0
1
2
2
2
0
1
2
0
0
2
1
1
2
1
1
1
1
2
2
1
2
1
1
0
2
1
0
1
0
2
1
1
1
1
1
1
1
1
1
0
2
1
2
1
1
1
2
1
0
1
1
1
0
2
1
1
1
0
1
2
1
1
1
0
2
1
0
1
1
2
1
1
1
1
1
1
0
1
1
2
0
2
2
2
2
1
1
1
0
2
0
2
1
2
0
1
2
2
1
1
0
1
1
1
0
1
1
1
1
2
1
0
2
1
1
1
2
2
0
1
2
1
1
1
1
2
2
1
1
1
1
1
1
1
0
1
1
1
0
1
2
1
0
1
1
2
1
0
0
1
1
0
1
1
1
1
1
1
1
1
2
2
1
1
0
2
2
2
1
1
1
2
1
0
2
1
1
0
1
1
1
0
2
2
1
1
1
1
0
1
1
0
1
1
0
0
1
1
0
2
2
1
1
1
2
2
1
1
2
1
2
0
0
1
1
2
1
2
1
1
1
1
1
1
1
0
1
1
0
2
1
1
0
1
1
1
2
1
1
2
0
0
1
1
2
1
0
0
1
1
0
1
0
2
1
1
1
2
1
1
2
1
0
1
1
1
0
1
2
1
2
1
0
0
1
0
1
1
2
1
0
2
1
1
2
1
2
2
1
1
2
2
0
1
1
1
1
0
1
1
1
1
0
1
1
1
1
0
1
1
1
2
1
0
1
4
2
0
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
2
1
0
1
1
0
3
0
0
0
1
1
1
1
2
1
1
1
1
1
0
2
0
2
0
1
1
0
1
0
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
2
1
0
2
1
1
1
0
1
1
2
1
1
1
1
2
1
0
0
2
2
3
1
1
1
0
1
2
1
1
1
2
2
0
0
2
2
1
2
1
1
0
1
2
2
2
0
0
1
0
1
1
0
1
0
2
1
1
1
1
1
2
3
0
1
1
1
0
1
1
2
1
1
1
2
0
1
0
1
0
2
1
0
1
2
1
1
1
1
1
1
1
2
0
1
2
2
0
1
0
1
1
1
2
1
2
1
1
0
0
1
1
0
1
1
2
3
2
2
0
0
1
2
1
2
2
2
1
0
1
1
0
2
1
1
2
2
1
2
2
1
1
1
2
2
2
1
1
1
0
1
0
2
1
1
0
2
2
1
2
0
1
0
2
0
2
0
0
1
3
1
0
0
0
1
0
1
0
1
1
2
2
1
2
0
4
1
2
0
2
2
1
1
0
0
1
0
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
0
1
2
1
1
0
1
1
2
2
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
0
1
1
2
1
1
1
1
1
1
1
2
1
0
1
0
1
1
1
6
1
1
1
2
1
2
1
1
1
1
1
1
1
2
0
2
1
2
1
2
2
2
2
2
2
0
1
1
0
2
1
0
1
1
2
1
1
1
1
1
1
1
0
0
2
0
0
1
1
1
0
1
0
2
1
1
2
1
2
2
1
1
2
1
0
0
2
1
0
2
1
1
2
0
0
2
1
1
1
1
2
0
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
2
1
2
2
1
1
1
1
1
1
4
2
0
0
1
2
1
2
2
1
1
1
2
1
1
2
1
1
1
1
0
1
2
0
2
1
1
2
2
1
1
2
2
1
1
1
2
1
1
2
0
1
1
0
0
1
1
1
1
1
1
1
2
2
0
1
1
2
2
1
1
2
2
2
1
1
1
2
1
0
0
1
1
1
0
2
2
0
1
0
1
1
1
1
1
1
1
2
2
1
1
1
1
1
3
3
1
1
1
3
2
1
0
1
1
1
1
1
0
0
2
2
1
2
2
1
0
0
0
1
0
1
1
1
1
1
0
1
2
1
2
1
0
0
0
2
1
2
1
1
1
2
0
1
1
2
2
1
2
2
0
2
2
0
2
1
0
1
1
1
1
2
2
2
1
1
1
1
1
0
1
1
1
0
0
2
0
1
2
1
1
0
1
2
0
1
1
0
2
1
1
2
1
0
0
0
2
0
0
2
0
1
0
1
1
0
1
1
1
1
0
1
2
0
1
1
0
1
1
0
2
1
1
1
0
1
1
1
2
0
2
2
0
1
1
1
1
1
0
1
1
2
1
1
1
1
1
1
1
0
1
2
1
0
1
1
1
1
1
1
1
1
1
0
1
1
1
2
1
2
0
0
1
1
1
2
1
1
1
2
1
0
2
1
2
0
1
0
1
1
1
1
1
2
1
2
1
2
0
0
1
1
2
1
1
1
1
1
2
2
1
0
1
1
1
1
1
2
0
1
0
1
1
2
0
0
1
2
1
2
1
1
1
1
1
2
0
1
0
0
1
2
2
2
2
2
1
0
2
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
2
1
0
1
1
1
1
2
1
1
1
2
1
0
1
1
1
2
1
0
1
2
1
2
1
0
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
2
1
1
1
0
1
1
1
1
0
1
2
1
1
1
2
2
0
0
2
0
2
1
1
1
0
1
1
2
1
1
0
1
1
1
1
1
1
0
1
1
1
1
2
2
0
1
1
0
0
1
2
1
0
1
1
1
1
0
1
1
1
2
0
1
1
1
1
0
1
2
2
1
0
1
1
1
1
1
1
2
1
0
0
1
1
0
1
2
1
0
0
2
0
1
2
2
1
0
0
2
0
1
0
1
1
0
1
1
2
1
2
1
1
1
1
1
1
1
1
2
1
1
1
0
0
1
3
1
1
0
0
1
0
1
1
1
1
1
1
1
1
2
1
1
2
0
1
1
1
0
2
1
1
0
1
2
1
1
3
2
1
1
1
1
0
1
2
1
1
1
0
0
1
0
1
0
1
2
1
2
2
1
1
1
2
1
1
1
1
1
0
2
1
0
1
0
1
1
2
1
2
2
0
1
1
1
1
1
1
1
1
2
1
1
2
1
0
0
2
1
1
1
1
2
1
2
2
1
1
1
1
1
1
0
1
1
0
2
1
0
1
2
1
0
2
0
1
1
2
1
1
1
1
1
0
1
1
2
0
1
1
2
2
1
0
1
2
0
1
1
0
1
1
1
0
1
1
0
1
1
1
1
1
1
2
1
2
2
1
1
2
1
1
2
1
1
2
1
1
1
1
0
1
1
0
1
1
0
2
1
0
1
1
2
1
1
1
0
1
0
1
2
1
2
1
0
2
2
1
2
1
2
1
1
1
1
2
2
1
0
2
2
0
1
0
2
1
0
0
1
0
1
1
1
1
1
1
2
0
0
2
2
2
1
1
1
0
0
1
1
2
1
1
2
2
1
1
1
2
0
1
2
2
1
2
2
0
1
2
1
2
1
1
1
1
2
1
1
0
2
1
2
1
0
0
0
1
1
2
0
0
1
2
2
2
0
1
2
1
1
0
2
1
1
2
1
0
1
2
1
0
1
1
2
1
1
1
1
2
0
1
1
1
0
2
1
2
2
1
2
1
2
2
0
0
1
1
1
1
0
1
1
1
2
0
1
1
2
1
2
3
1
0
1
2
2
2
1
2
1
1
0
0
0
2
1
1
2
1
1
2
2
0
0
1
1
2
1
0
2
1
1
2
1
1
0
0
1
1
1
2
1
1
1
1
2
1
1
1
1
1
2
2
0
2
1
1
1
1
1
2
2
1
2
1
2
0
2
1
1
2
1
1
1
1
2
1
0
1
0
2
0
0
1
1
1
2
2
1
1
2
1
1
1
1
1
0
0
2
2
1
1
1
1
1
1
1
1
1
0
0
0
1
1
2
1
2
1
0
1
2
1
1
2
2
1
1
1
2
1
1
1
0
1
1
0
1
1
1
1
1
1
0
2
2
1
1
1
1
1
0
1
2
0
1
2
1
1
1
1
1
1
1
2
1
2
2
1
1
4
2
1
1
2
2
1
3
1
1
1
1
1
2
1
1
0
1
1
2
1
0
1
2
0
1
1
2
2
0
2
0
0
0
1
2
2
1
0
1
2
1
0
0
1
1
1
1
2
1
2
2
1
1
1
1
2
1
1
0
2
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
0
1
1
1
1
1
1
1
0
1
2
2
1
1
0
1
2
2
1
1
1
1
2
2
1
2
1
0
2
2
2
1
1
0
0
2
1
2
1
1
2
2
1
1
0
0
1
1
1
1
2
0
2
7
2
0
1
0
2
1
1
1
0
1
2
1
1
1
1
2
1
2
0
2
0
1
0
1
1
1
1
1
1
2
2
2
1
0
1
1
1
1
1
1
2
1
0
2
1
1
1
1
1
1
1
1
0
1
1
2
1
3
0
1
1
1
1
0
2
2
1
1
1
1
1
2
0
2
1
1
1
1
0
1
2
2
0
1
1
1
0
0
2
2
2
1
2
1
2
2
1
2
1
2
1
2
1
2
2
3
1
2
0
2
1
2
1
0
1
1
1
0
1
2
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
2
1
3
1
1
1
1
1
1
1
0
2
1
0
1
1
1
1
1
2
1
0
2
1
1
1
1
1
1
2
0
1
2
0
1
0
1
2
1
2
1
0
1
1
1
1
0
1
1
1
1
2
1
2
1
1
1
1
2
2
1
0
0
1
2
1
1
0
0
1
2
2
0
2
1
1
1
0
1
1
2
2
1
1
2
1
1
1
1
0
0
1
1
1
1
0
0
1
1
2
1
0
1
0
1
1
1
0
0
1
0
2
2
1
1
1
1
2
1
1
1
0
1
1
2
1
0
1
0
0
1
0
1
3
0
1
0
1
0
2
1
2
2
1
0
1
2
1
0
2
1
1
0
2
0
0
0
0
1
0
1
0
1
1
1
1
2
0
2
1
1
2
1
1
2
1
1
1
0
2
1
0
1
2
2
2
1
0
1
1
1
0
2
1
0
1
1
2
1
2
1
1
2
1
2
1
0
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
2
1
0
1
1
1
0
0
1
1
2
0
0
1
1
1
1
1
1
1
2
1
2
0
0
1
1
0
2
1
1
1
2
1
2
0
1
1
0
1
1
1
1
1
1
2
2
1
1
0
1
2
1
2
1
1
0
1
2
1
1
1
1
1
1
1
2
0
2
2
1
1
2
1
2
1
1
1
2
2
1
2
1
0
1
1
1
2
1
2
0
1
1
1
0
1
0
1
1
0
2
1
2
1
0
1
0
2
2
1
1
1
1
1
1
1
0
2
1
1
2
2
1
1
1
1
0
1
2
1
2
1
1
1
0
1
1
1
2
1
2
1
2
2
0
0
0
2
0
1
1
1
2
0
1
1
1
1
1
1
0
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
2
3
1
2
1
2
0
1
2
1
1
1
1
1
0
1
1
1
1
1
1
0
2
1
1
0
1
1
0
1
1
2
2
1
2
1
1
2
0
0
1
1
1
2
1
0
2
2
1
1
2
1
1
2
0
1
2
1
2
2
1
1
1
1
2
1
1
1
1
1
2
1
1
2
1
1
1
0
1
1
1
2
0
1
1
1
2
1
2
1
1
2
1
1
0
1
1
1
1
1
2
1
0
2
1
1
1
2
2
1
2
1
1
1
1
0
2
2
1
1
2
1
1
1
1
1
1
2
0
1
2
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
0
2
1
1
0
1
3
1
2
0
0
1
2
0
2
2
1
1
1
0
1
1
1
2
1
2
1
1
1
1
1
0
1
1
2
2
0
0
2
1
1
0
0
1
1
1
2
1
0
2
1
1
1
2
1
1
2
1
1
1
1
2
2
1
2
1
1
1
1
1
1
2
2
1
0
1
1
1
2
0
1
1
2
2
2
1
1
2
1
1
1
2
1
1
1
1
0
1
0
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
0
0
1
2
2
1
1
2
1
1
1
0
1
0
1
1
1
2
2
1
2
1
2
1
1
1
1
1
2
1
1
1
1
2
2
1
2
2
1
2
2
0
2
1
2
1
2
1
2
0
1
1
0
0
0
1
1
1
1
2
2
1
0
1
2
2
1
1
2
0
1
1
1
0
1
1
1
2
1
1
1
1
0
1
2
1
2
2
2
1
1
2
2
1
1
0
1
1
2
2
2
1
1
1
2
1
1
1
2
1
1
1
2
2
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
2
0
1
0
1
2
2
1
2
2
1
1
0
1
2
1
1
2
2
1
0
3
0
1
1
1
0
1
2
2
2
0
2
1
2
2
1
0
1
1
1
1
1
1
1
2
2
1
1
1
1
0
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
4
0
0
0
1
1
2
1
2
1
2
1
1
0
1
0
2
1
2
1
0
0
1
2
1
1
1
2
1
0
0
1
1
1
2
2
1
2
1
1
1
1
1
1
1
2
2
1
1
1
1
2
1
0
2
2
1
1
2
1
1
1
1
1
1
0
2
1
1
1
1
2
2
1
1
2
1
0
0
0
2
1
1
2
1
1
2
0
2
2
2
1
0
1
0
2
0
1
1
2
1
1
0
1
3
1
1
2
1
0
1
1
1
1
2
0
1
1
2
1
2
2
1
1
1
1
2
2
1
0
2
1
1
2
1
1
2
1
0
1
1
2
1
1
8
1
1
1
2
1
1
2
1
1
1
0
1
1
1
1
1
1
1
1
0
1
1
0
1
2
1
0
2
0
1
2
1
1
1
1
1
2
1
3
1
4
0
1
2
2
1
1
2
2
1
1
0
1
1
1
2
2
2
1
1
1
0
1
2
1
0
0
1
1
0
2
1
1
0
1
1
1
0
1
1
0
0
1
0
1
1
1
1
1
1
1
0
2
2
2
2
1
1
0
0
0
1
1
1
1
1
2
1
1
0
2
0
1
0
2
1
2
2
2
1
1
1
1
1
1
1
2
2
2
2
0
0
1
2
1
1
1
1
1
0
1
1
1
0
2
1
2
1
2
1
1
1
1
2
0
2
1
0
1
2
2
1
0
1
2
1
2
1
1
1
1
1
1
1
2
0
1
1
2
0
0
1
1
2
2
0
1
1
1
1
2
1
2
0
1
0
1
0
1
1
2
1
1
1
2
1
1
1
2
1
2
1
0
0
1
2
2
1
1
1
2
0
1
1
1
2
1
1
1
3
3
1
1
1
2
1
1
0
1
1
1
1
2
0
4
1
2
4
0
1
2
0
0
1
0
1
1
1
2
1
0
1
1
2
1
0
0
1
1
2
1
0
2
1
1
1
1
1
0
2
0
0
2
2
2
1
1
0
1
2
2
1
2
0
2
1
2
1
1
1
1
0
1
1
1
2
1
2
0
1
1
1
1
1
0
0
1
1
2
1
0
1
0
1
2
1
0
0
1
2
1
3
0
0
2
2
1
1
1
1
1
1
1
2
1
1
0
2
1
0
1
2
0
2
1
1
1
0
1
1
2
1
1
0
1
1
2
1
1
2
2
2
1
1
2
0
1
1
2
3
1
1
1
2
1
1
2
1
1
2
2
0
1
0
0
1
1
1
1
0
1
2
0
2
1
1
0
1
0
1
1
1
1
2
2
1
1
0
1
1
0
1
1
1
2
2
2
1
0
2
1
1
2
2
1
0
0
0
1
2
1
2
2
0
1
1
1
1
2
0
1
2
0
1
1
1
1
1
2
1
1
1
2
2
1
0
1
1
1
1
0
1
1
1
0
1
0
1
2
0
1
1
0
1
0
2
1
1
0
1
2
1
2
2
1
2
1
2
1
1
0
1
1
0
1
0
0
0
1
0
0
2
2
1
1
1
2
1
2
2
1
1
1
1
1
1
0
1
1
2
0
1
1
2
1
1
2
0
2
1
2
2
0
1
2
1
1
1
1
2
1
1
2
0
1
2
1
1
0
1
1
2
1
1
2
1
1
1
2
1
1
1
1
0
1
2
1
1
1
1
2
0
2
0
0
2
1
1
1
1
1
2
0
0
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
0
0
1
2
1
2
2
2
1
0
1
2
2
1
2
1
0
0
1
1
2
1
1
2
1
1
1
3
0
2
1
1
2
1
0
0
2
1
1
2
1
1
1
1
1
1
2
2
1
1
3
0
1
2
1
0
1
0
2
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
0
1
1
1
0
0
1
2
1
0
1
1
1
1
1
2
2
0
1
1
1
2
1
1
1
1
1
1
1
1
2
0
1
1
1
2
1
2
2
0
0
1
1
1
1
1
1
1
2
1
1
1
1
0
1
2
2
2
0
0
2
2
2
1
2
0
2
1
2
1
1
1
2
1
1
2
1
0
2
2
1
1
2
0
1
0
1
1
1
1
2
1
2
1
2
1
1
1
1
1
0
0
0
1
2
2
1
1
0
0
2
0
1
2
1
1
2
1
1
2
1
1
2
1
0
1
1
0
1
2
1
2
0
1
1
2
1
0
2
1
0
2
1
1
1
0
1
0
1
1
1
2
0
1
1
2
1
0
1
0
1
0
1
2
1
2
1
1
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
0
2
1
2
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
0
3
1
1
2
0
1
1
1
1
0
1
0
1
1
1
1
1
0
1
0
1
0
1
0
1
1
2
1
2
2
1
1
1
2
1
2
1
0
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
2
0
1
1
2
1
2
0
1
1
1
1
1
0
1
1
1
1
0
1
2
2
2
1
2
1
2
1
1
2
0
0
1
2
3
1
2
0
0
0
2
0
2
1
2
2
0
1
1
2
0
1
0
0
1
2
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
2
2
1
1
1
1
1
2
1
1
0
0
1
1
1
2
1
2
0
2
2
2
0
1
0
1
1
1
1
2
1
0
1
1
1
2
1
0
2
0
7
2
1
1
2
0
1
1
1
0
1
2
1
1
1
1
1
2
2
1
1
1
2
2
1
1
1
1
2
2
2
2
1
0
1
2
1
0
2
1
1
0
1
2
1
1
1
0
0
0
1
0
2
2
1
1
1
0
1
1
0
1
1
2
0
1
1
1
1
2
1
1
1
1
0
1
1
2
1
1
2
1
1
1
0
2
2
1
1
0
1
1
1
1
2
1
2
2
0
0
2
0
1
1
1
1
3
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
0
0
2
1
1
2
1
1
1
1
0
1
0
1
2
1
1
0
1
1
1
2
0
1
1
2
1
1
1
2
2
1
1
0
1
2
0
2
2
1
2
2
1
0
1
1
1
1
0
1
1
1
1
1
0
1
1
1
3
2
1
0
2
1
2
2
1
1
2
1
0
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
0
1
1
1
1
2
1
2
1
1
0
1
0
1
0
2
1
1
1
1
1
1
0
2
0
1
1
1
1
1
2
2
1
1
2
2
0
0
0
1
0
1
2
1
1
2
1
1
1
0
1
1
2
0
2
1
1
1
1
1
2
1
1
1
0
1
1
1
1
1
1
0
1
1
0
1
1
0
2
2
2
1
1
1
2
2
1
1
1
1
1
1
0
1
0
1
1
1
1
1
0
2
2
1
1
1
1
1
1
1
0
1
2
1
1
1
2
1
1
0
1
1
1
2
1
0
2
1
0
0
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
2
2
1
2
1
2
2
2
2
1
1
1
2
0
2
0
1
0
1
1
1
1
1
2
1
1
1
1
0
1
2
1
1
1
0
0
1
1
1
1
2
0
1
2
2
1
0
2
1
1
0
1
2
1
1
1
1
1
1
1
1
1
0
1
1
1
1
0
2
1
0
1
0
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
0
1
1
2
2
1
1
2
0
1
1
1
1
0
2
1
0
2
1
2
0
0
0
0
1
2
1
1
1
1
1
1
0
2
1
1
2
1
0
2
2
0
2
0
0
1
1
2
1
1
3
1
1
1
1
0
0
1
1
1
1
2
1
2
2
1
1
0
2
2
1
1
2
0
1
2
0
1
2
2
1
1
2
2
1
2
1
1
2
0
2
0
1
1
1
2
1
1
2
2
0
2
1
1
1
0
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
0
1
1
0
2
0
1
1
1
0
1
1
0
2
1
1
1
1
1
0
2
1
1
2
1
1
1
1
1
1
0
1
2
1
1
0
1
1
2
0
2
1
1
1
0
1
0
2
1
2
1
1
1
0
2
0
1
1
1
0
1
1
1
1
0
1
2
2
1
1
1
1
1
2
1
2
1
2
2
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
2
2
0
1
0
1
0
2
0
1
1
2
2
2
1
0
1
0
1
2
1
1
2
2
0
1
1
0
1
1
1
1
0
0
1
1
1
1
1
2
0
2
1
1
1
1
1
1
1
1
2
1
0
1
1
1
2
0
1
1
2
1
0
0
2
1
1
0
2
3
0
1
1
1
1
1
1
1
0
1
1
1
1
2
1
0
0
2
1
1
0
1
2
1
1
0
1
1
0
0
1
1
1
0
0
2
1
0
1
1
1
1
2
0
1
2
0
2
1
0
0
1
1
0
1
1
2
1
2
1
1
2
2
1
0
0
0
1
1
1
1
1
1
1
1
2
1
0
2
1
1
1
1
2
1
1
1
1
1
2
1
2
1
1
0
1
0
1
1
2
2
1
1
1
1
2
1
1
1
2
1
2
0
1
0
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
2
0
2
0
1
1
2
1
0
1
2
0
1
1
1
1
1
1
1
2
1
2
2
2
1
2
2
2
2
0
1
1
2
0
1
1
1
1
0
2
1
0
1
2
2
1
1
2
2
1
1
2
0
0
1
0
2
1
0
1
1
2
1
1
1
1
0
1
0
1
1
1
2
1
0
1
1
1
2
1
1
1
1
1
0
1
3
2
1
2
2
1
0
1
1
2
1
2
1
1
1
1
1
1
2
2
2
0
1
1
1
1
2
1
1
1
1
0
1
1
1
2
1
2
1
1
2
1
1
0
0
2
2
1
2
1
1
0
1
1
2
1
1
1
1
2
2
2
1
0
1
0
0
2
1
0
1
1
1
1
2
1
1
1
1
2
1
1
0
2
2
1
0
0
1
1
2
0
1
1
2
0
2
1
1
1
2
0
1
2
1
1
2
0
1
1
2
1
1
1
2
1
1
1
2
2
1
1
2
2
0
2
1
2
1
0
0
2
1
1
0
0
1
2
1
2
1
2
1
1
1
2
1
1
1
1
2
1
2
2
0
1
0
2
1
1
2
1
2
0
1
1
1
1
2
1
1
2
2
7
1
1
2
2
1
0
2
1
1
1
2
1
1
1
1
1
1
2
0
1
0
2
1
1
2
1
0
2
2
1
1
1
2
3
1
1
0
2
1
1
0
1
2
1
1
1
2
1
1
0
2
1
0
1
0
1
1
2
1
0
0
1
2
1
1
1
1
0
0
2
2
1
1
1
1
1
2
1
1
1
2
1
0
1
1
1
1
1
0
2
0
1
1
1
2
2
1
0
2
1
1
0
1
2
0
0
1
1
1
1
0
0
2
0
1
1
1
0
1
2
2
0
1
1
0
1
2
1
2
1
2
1
2
2
1
1
0
1
1
1
0
2
2
1
2
1
1
2
2
1
1
0
1
1
2
0
1
0
1
1
1
1
1
1
1
0
2
0
1
1
1
0
0
1
2
2
1
0
1
1
1
1
1
2
2
2
0
2
1
1
0
0
2
1
1
1
0
1
1
2
1
1
2
1
1
1
1
2
1
0
1
1
0
0
0
2
1
0
1
1
1
1
2
1
0
1
0
2
1
1
1
1
2
2
1
1
1
2
2
1
0
2
1
1
1
2
1
2
1
1
2
2
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
2
0
1
1
1
1
2
1
1
1
1
1
1
1
0
2
1
1
1
1
1
0
2
2
0
1
0
1
1
1
1
1
2
1
2
1
2
1
2
1
1
1
2
0
2
1
1
1
1
1
1
1
1
2
2
1
1
1
0
1
0
1
1
1
1
2
2
1
0
2
2
0
2
2
1
1
0
0
1
1
2
1
1
1
1
1
1
1
0
1
1
2
1
1
1
2
1
1
1
0
1
1
1
2
2
1
1
1
1
1
2
1
1
2
1
1
1
2
1
1
1
0
0
0
2
1
2
1
1
1
1
2
1
1
0
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
0
1
2
1
1
2
1
2
1
1
2
2
1
2
1
1
2
1
2
0
2
1
3
1
1
1
1
0
1
2
1
2
0
2
1
1
1
1
0
1
0
1
2
2
1
1
0
2
1
1
2
0
0
1
0
1
1
1
1
1
2
0
1
1
1
1
0
2
2
2
1
1
0
1
1
1
1
2
2
1
1
1
1
1
0
0
2
2
1
1
2
0
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
2
0
0
2
1
1
0
2
1
2
0
1
1
0
2
1
2
2
0
2
1
1
1
1
2
1
1
1
1
1
2
1
1
0
1
0
2
0
1
2
1
1
2
2
2
1
1
1
1
0
2
0
1
2
2
0
2
1
2
0
1
1
1
0
1
1
1
1
2
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
0
2
2
1
0
1
2
0
2
1
1
1
1
1
1
1
1
1
1
1
0
1
0
1
1
0
1
1
2
0
1
1
1
1
2
2
0
1
1
1
1
2
1
0
2
1
2
1
0
1
1
2
1
1
1
0
1
0
1
1
1
1
1
1
0
1
1
1
2
0
1
1
2
1
2
1
0
0
2
1
0
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
0
1
2
1
1
0
1
0
1
2
2
0
1
1
1
1
0
1
1
0
1
2
2
1
2
1
1
1
2
0
1
1
2
1
2
1
1
0
0
2
0
1
0
0
1
1
1
0
2
1
1
2
1
2
2
1
1
1
2
1
1
2
2
2
1
2
1
0
1
2
2
2
1
1
0
3
1
2
0
1
1
2
1
1
1
0
0
2
2
1
0
1
2
2
0
0
1
0
1
0
2
1
1
2
0
1
1
1
2
1
1
1
1
1
0
2
2
2
1
1
2
0
2
1
1
0
0
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
0
2
2
1
1
1
1
1
1
0
1
0
3
1
2
0
0
1
1
1
0
0
2
2
0
2
0
1
1
0
0
1
1
1
2
2
1
1
2
1
1
3
2
1
1
2
1
1
0
1
2
1
1
2
1
1
1
0
1
1
1
0
1
2
2
3
1
1
2
1
0
1
1
2
1
2
1
2
0
1
1
1
1
1
1
1
0
0
1
1
1
2
1
1
1
0
0
0
1
1
2
1
2
2
1
1
1
2
1
2
1
1
1
0
1
2
1
1
2
1
1
1
1
1
0
2
0
1
1
1
0
2
2
1
1
1
1
1
1
1
1
2
1
1
0
1
0
1
1
2
1
1
0
2
1
1
0
0
1
1
1
0
2
2
2
1
2
2
0
0
2
1
0
0
2
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
0
1
1
0
1
2
0
2
1
0
1
1
1
0
0
2
0
1
1
1
0
2
0
1
0
0
1
2
2
1
0
2
1
2
1
2
2
1
1
2
1
2
1
2
1
1
2
1
1
1
1
2
0
0
1
1
0
2
1
1
0
0
0
1
2
2
2
1
1
0
2
2
1
2
1
1
1
0
1
2
0
2
1
1
1
0
2
2
0
1
0
1
1
1
2
1
1
0
1
1
1
0
1
2
1
1
0
1
1
1
1
1
1
0
1
1
1
0
2
1
0
1
2
0
1
0
2
1
1
1
2
0
0
1
1
1
1
2
1
1
1
2
1
1
1
2
1
0
1
2
2
2
1
1
1
0
1
0
0
1
1
1
2
2
1
0
1
1
0
2
1
2
1
1
1
1
1
1
1
2
1
1
1
2
0
2
1
1
2
1
1
0
1
2
1
0
0
1
1
0
0
0
1
2
2
2
2
1
2
1
3
0
1
1
1
1
2
1
2
1
1
2
1
0
2
1
1
0
2
1
1
2
0
2
0
1
1
2
3
2
2
1
0
1
0
0
1
1
1
2
0
1
1
1
2
1
1
1
2
0
1
1
1
1
1
2
0
0
1
2
1
1
1
1
1
0
0
0
1
1
2
1
0
1
1
1
1
1
1
1
1
2
1
1
1
0
1
0
0
1
1
2
1
0
1
1
1
0
2
0
1
1
0
1
1
0
2
1
1
1
0
1
1
2
1
1
0
1
1
1
2
2
2
0
1
0
1
1
1
0
2
1
1
1
1
0
2
1
1
2
1
1
1
1
0
0
0
1
1
1
1
2
1
1
1
1
0
1
1
0
2
1
2
0
2
2
1
1
1
1
1
0
0
1
1
1
2
1
2
1
2
1
0
1
2
2
1
0
1
2
1
1
1
1
1
1
0
1
1
2
2
1
1
0
0
1
1
1
1
0
0
1
0
2
1
1
1
1
0
1
0
0
1
2
2
1
2
2
1
1
0
1
2
1
1
2
0
2
1
2
1
1
1
1
0
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
0
0
0
1
1
2
0
1
0
1
1
1
1
1
1
1
1
2
0
2
1
1
2
1
2
1
0
1
2
1
2
1
1
0
1
1
2
2
1
0
1
1
0
0
0
1
1
1
0
1
2
2
1
1
0
1
2
1
0
2
1
1
1
1
1
1
1
0
1
0
1
0
0
1
0
2
1
1
1
1
1
0
1
2
1
1
0
1
1
1
0
2
1
1
1
2
0
2
1
0
1
2
1
1
0
1
0
0
1
1
1
1
1
1
0
1
1
1
0
1
2
2
1
0
2
2
1
1
2
1
2
1
1
0
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
0
1
1
2
2
0
1
2
1
2
1
1
1
1
1
1
1
2
1
2
0
1
1
2
1
2
2
1
2
0
0
0
1
1
2
1
1
1
1
2
1
0
3
2
0
1
0
1
1
2
1
2
1
1
1
1
1
2
1
2
2
2
1
1
2
2
2
2
1
1
1
1
1
0
2
1
0
1
1
2
1
2
2
1
1
1
1
2
1
2
0
2
1
2
2
1
1
1
1
2
1
1
0
1
2
2
1
1
0
1
1
1
0
1
2
2
2
1
1
1
2
0
1
0
0
2
1
1
1
2
0
1
2
1
2
2
1
1
1
1
1
2
1
1
1
1
1
1
3
0
2
2
1
2
1
1
1
1
2
1
2
1
2
2
0
1
0
0
0
1
0
0
1
0
1
1
1
1
1
1
1
0
1
0
1
1
2
2
1
2
1
2
1
1
0
1
2
1
2
2
1
1
1
1
1
1
3
1
1
1
2
2
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
0
2
1
1
1
2
1
2
1
1
0
2
2
2
2
0
0
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
0
0
1
1
0
2
1
1
2
2
1
2
1
1
1
2
0
1
1
2
2
1
1
0
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
2
2
1
1
2
1
2
2
1
1
1
1
1
1
1
1
1
2
0
2
1
1
1
1
0
0
1
1
1
1
0
2
1
3
1
0
0
1
1
1
1
1
1
1
1
1
2
0
1
1
2
2
1
1
1
1
1
1
1
1
2
1
0
1
2
1
1
1
1
1
2
2
1
1
0
1
1
2
2
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
0
1
0
1
0
2
1
1
1
2
2
0
1
1
2
1
0
1
2
1
2
0
1
0
2
1
1
2
2
2
1
1
1
0
2
0
0
2
0
1
0
1
1
1
1
1
1
1
1
0
2
1
0
1
1
1
1
2
1
1
2
1
1
0
1
1
2
1
2
1
2
0
2
1
2
2
2
1
1
1
1
0
1
1
0
1
2
1
0
1
1
2
1
2
1
1
1
0
2
1
1
2
2
1
1
2
1
1
1
1
1
2
0
1
1
1
0
2
2
1
1
2
1
2
0
2
2
1
1
1
4
1
2
1
1
1
0
1
1
0
1
1
1
0
2
1
1
1
1
2
1
1
1
2
1
0
0
1
1
1
2
0
1
1
0
1
1
0
1
0
1
1
1
1
2
1
1
2
1
1
1
0
0
2
0
1
1
1
0
1
1
2
1
0
1
2
1
1
1
0
0
1
1
2
1
1
1
1
1
1
1
2
0
1
1
1
2
0
1
1
1
2
1
1
1
2
1
1
1
1
2
1
2
1
1
2
2
1
0
2
1
1
0
2
1
1
0
1
2
1
2
1
1
1
1
1
1
1
1
1
1
2
1
0
1
1
1
2
2
1
1
1
1
1
0
0
1
1
1
2
2
1
1
1
1
1
2
1
0
1
1
1
2
1
1
2
1
1
1
1
1
1
0
0
1
1
1
1
2
0
2
2
1
1
1
0
2
1
2
1
1
2
1
1
1
0
1
2
1
0
1
1
2
1
0
2
0
1
1
1
1
2
2
1
0
1
1
1
1
1
1
0
2
1
1
4
2
2
2
1
2
1
1
1
1
1
0
1
1
1
0
2
1
1
0
1
1
1
2
1
2
2
1
1
2
1
1
1
0
2
2
1
0
1
1
1
1
1
1
1
1
0
1
1
1
2
1
0
0
0
0
1
2
1
1
1
2
2
1
1
1
1
1
1
2
1
2
0
1
1
1
1
2
1
1
2
0
1
1
0
2
2
1
1
1
1
0
0
0
1
1
1
1
2
1
2
1
1
1
3
1
2
1
1
0
2
2
2
1
0
2
1
1
1
1
0
0
2
1
1
1
2
1
1
0
1
1
1
1
1
2
1
2
1
1
1
0
2
0
1
2
0
1
2
1
1
1
1
1
1
2
2
1
2
1
0
1
1
2
1
1
1
2
0
2
1
0
1
1
2
1
0
1
1
1
1
2
2
1
1
1
1
1
0
1
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
1
0
0
2
1
1
1
2
1
1
2
0
1
2
2
1
1
0
1
1
1
1
1
1
1
1
0
2
0
1
2
1
2
1
1
0
0
1
0
1
1
2
2
2
1
2
1
1
0
1
2
2
2
1
0
1
1
0
2
0
2
2
2
1
1
1
2
1
2
1
1
0
1
1
1
1
0
1
1
2
1
0
1
1
0
2
0
0
1
1
1
2
1
0
3
1
2
0
2
1
0
1
2
1
1
1
1
1
2
1
2
1
2
1
2
1
1
1
0
1
1
1
2
2
1
0
0
1
2
1
1
1
1
0
2
1
2
0
2
1
1
0
1
1
1
1
1
0
1
1
0
2
1
2
1
2
2
0
1
2
0
1
2
2
1
0
1
1
2
2
1
1
1
1
0
2
1
1
1
0
2
1
2
1
1
1
0
1
1
1
0
1
0
1
1
1
1
2
1
2
0
0
1
1
1
1
1
1
0
2
0
2
0
1
2
2
1
0
2
2
1
1
1
1
2
1
0
2
2
2
1
2
0
1
1
1
0
1
1
2
1
1
1
1
0
1
1
1
1
2
2
1
1
1
0
1
1
1
1
1
2
1
1
1
2
2
1
2
1
2
1
1
1
1
0
1
0
0
1
2
1
2
1
2
2
2
1
0
1
0
0
2
2
2
0
0
1
1
1
1
2
1
1
0
1
1
1
1
0
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
0
1
1
1
1
1
2
1
1
1
1
1
2
0
0
0
1
1
2
1
0
1
1
1
2
1
1
1
0
1
1
2
2
2
2
1
2
1
1
2
1
0
2
1
1
1
2
0
1
1
0
2
1
1
1
1
1
0
2
1
0
1
2
2
1
0
0
1
1
1
1
1
0
1
1
1
2
1
2
2
2
1
0
2
2
1
3
0
0
1
0
2
1
1
2
2
1
2
1
1
1
2
1
1
1
1
1
2
0
0
1
1
2
1
0
1
0
0
1
1
0
1
1
2
1
1
0
2
1
2
1
1
2
1
2
2
1
1
1
2
0
1
1
1
2
1
1
1
0
1
1
0
0
0
0
1
1
1
1
1
1
1
2
1
2
1
1
0
0
2
1
1
1
0
1
1
1
1
2
2
2
2
1
2
2
0
1
2
1
1
1
1
2
1
0
1
1
1
1
1
1
1
2
1
1
1
0
0
1
2
1
0
2
1
3
0
0
1
1
0
1
2
1
1
1
0
1
1
2
1
2
1
1
1
2
0
2
0
1
1
1
1
1
0
1
2
1
1
1
2
1
1
0
1
1
2
1
1
1
1
1
1
1
1
1
0
1
2
1
1
0
2
2
1
0
0
1
1
1
2
2
1
1
1
2
2
2
2
1
0
2
0
1
1
1
2
1
1
0
1
0
1
1
2
1
2
1
1
2
1
1
1
1
1
2
1
1
1
0
2
1
1
1
2
1
1
0
2
2
1
1
1
2
2
0
2
1
0
1
1
1
0
1
1
1
1
0
2
1
1
0
1
1
0
1
1
0
2
1
1
0
1
1
1
2
2
0
0
1
2
1
1
2
2
2
1
0
1
1
1
1
1
2
1
1
2
1
0
1
0
1
2
2
0
1
1
1
1
1
1
0
2
0
0
1
1
0
2
0
2
2
1
1
1
2
0
1
0
1
1
2
1
1
1
1
1
0
1
2
2
0
2
1
1
1
2
2
1
1
1
1
0
1
0
0
0
2
2
0
2
1
2
1
0
1
2
1
1
0
1
2
0
0
0
2
2
1
1
2
1
0
1
1
0
0
1
2
2
0
1
0
0
1
1
0
2
1
1
1
1
1
0
1
2
1
2
1
0
1
0
0
2
0
0
1
0
1
2
1
1
0
1
1
1
0
1
1
2
1
1
1
1
2
2
1
2
2
1
1
2
1
1
1
0
2
1
0
2
1
1
0
1
1
2
0
2
0
1
1
0
1
1
0
0
1
1
8
1
1
0
1
1
1
0
2
1
1
1
1
1
1
1
1
2
0
2
1
2
1
1
0
0
1
0
1
1
2
2
1
0
0
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
2
1
2
1
2
2
1
1
1
2
2
1
1
1
0
2
2
1
1
1
0
2
1
0
0
1
2
1
1
3
1
1
1
0
2
2
1
2
0
1
1
1
2
0
1
1
0
1
1
1
1
1
1
2
0
1
2
1
2
1
1
1
1
2
1
1
1
2
1
1
1
2
0
2
1
1
1
0
2
0
1
2
0
2
1
1
2
1
1
1
1
2
1
0
1
0
0
2
2
2
2
1
1
1
1
2
0
1
1
2
2
1
2
2
1
2
1
0
0
0
1
5
2
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
2
2
1
1
1
2
1
2
1
1
1
2
1
0
2
1
0
1
1
2
1
1
1
2
1
2
1
1
0
1
0
1
2
2
0
2
1
1
1
1
1
1
0
1
1
2
2
1
1
1
1
0
1
2
2
2
1
2
1
1
2
1
1
1
2
2
0
0
1
1
0
1
2
1
1
2
1
1
1
1
1
1
2
1
2
1
1
2
2
1
0
1
1
1
2
1
0
1
1
1
2
2
1
1
1
1
1
1
3
1
2
1
1
1
2
1
0
2
1
0
1
2
1
1
1
1
0
1
1
0
1
1
1
1
2
1
2
0
1
1
1
1
2
2
2
2
2
1
0
2
1
1
1
0
1
2
1
0
1
1
1
2
1
2
1
1
0
1
2
1
2
1
1
1
1
1
0
1
2
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
0
2
1
0
2
2
1
1
1
2
1
1
1
1
2
1
1
0
0
2
2
1
0
1
2
1
2
1
1
1
1
2
2
1
2
1
0
1
1
1
1
2
1
1
1
1
1
2
1
2
2
0
2
2
1
0
0
1
2
1
1
1
1
1
2
1
2
2
1
2
0
1
0
1
2
1
1
1
2
1
1
2
1
1
1
1
1
0
0
0
2
1
2
0
1
0
0
2
0
2
1
1
1
0
1
1
1
1
1
1
2
1
1
0
1
2
1
0
1
2
0
1
1
1
2
0
1
1
1
1
2
2
1
1
2
2
0
1
2
1
2
0
1
1
2
2
1
0
1
1
0
1
0
0
2
1
0
1
1
2
1
1
1
6
2
0
0
0
3
1
2
1
1
1
0
1
1
2
1
1
2
1
1
1
0
0
1
1
2
0
2
2
2
2
0
2
1
1
0
1
2
1
0
2
1
1
0
1
1
1
0
1
1
1
0
1
0
1
1
2
2
1
2
1
0
1
1
1
1
1
1
1
2
0
1
1
2
2
2
0
1
1
1
2
0
2
2
1
1
0
2
0
1
0
2
2
0
1
2
1
1
1
1
1
1
1
2
2
1
2
0
2
1
1
1
2
1
0
2
1
1
3
1
1
1
1
1
1
1
1
1
1
1
1
2
0
1
1
2
1
0
0
1
2
2
1
2
1
1
1
1
0
1
1
1
0
2
0
1
1
1
1
1
0
1
1
1
1
0
0
1
1
1
2
2
2
1
1
2
0
1
1
1
0
1
1
1
1
2
0
1
1
1
0
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
2
1
1
0
2
2
0
1
1
1
0
1
0
1
2
1
2
0
1
1
1
1
1
2
1
1
1
1
0
2
1
1
1
1
2
2
2
1
1
0
1
1
1
2
2
2
1
1
2
1
2
1
1
1
2
2
2
1
2
1
1
0
1
1
2
0
1
1
0
1
1
0
2
2
1
2
2
0
1
1
1
1
1
1
2
2
1
2
1
0
1
1
0
1
0
2
0
1
2
3
0
1
1
1
3
0
1
0
1
1
1
1
1
1
1
0
1
2
2
1
1
1
1
1
0
1
2
1
2
2
0
1
1
2
1
1
0
1
1
2
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
2
0
1
1
1
1
1
1
1
0
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
2
1
1
2
2
1
1
1
1
0
1
1
1
0
1
1
0
0
1
1
1
2
1
1
1
2
1
0
1
2
0
1
1
1
1
2
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
2
1
1
2
2
0
2
1
2
0
0
1
0
1
4
2
1
0
2
1
1
1
1
1
1
1
3
1
1
2
1
1
1
2
2
2
1
2
1
0
1
1
1
1
1
0
2
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
2
1
2
2
1
2
1
1
0
1
1
1
1
1
1
2
1
1
1
1
1
0
1
1
2
1
0
1
1
2
2
1
1
1
1
1
1
2
1
2
1
0
1
1
2
1
1
2
1
2
1
1
1
1
0
1
0
0
1
1
1
1
1
2
0
1
2
1
1
2
2
1
2
2
0
1
1
1
2
1
2
1
0
0
1
1
1
1
0
2
0
2
2
0
1
0
2
2
1
1
0
1
2
0
0
1
1
1
2
1
0
2
2
1
2
1
1
1
1
1
1
2
1
1
2
0
1
1
1
1
2
2
1
1
3
1
0
1
1
2
1
1
1
0
1
0
1
1
1
0
1
0
1
1
2
2
1
2
1
2
2
1
1
1
0
0
1
0
1
1
1
0
1
2
2
1
0
2
1
1
0
0
1
2
3
1
1
0
1
1
1
2
1
1
1
0
0
1
2
1
1
1
1
0
1
0
2
1
1
1
1
2
1
2
2
0
0
1
1
1
1
1
2
1
1
1
2
0
2
1
1
1
0
2
0
1
0
0
3
1
1
2
1
1
1
2
2
0
1
2
2
0
2
1
1
1
1
1
1
1
0
0
0
1
1
0
2
2
0
1
1
1
0
1
2
1
1
1
1
1
1
2
2
1
2
1
1
1
2
3
0
1
2
0
1
1
1
1
1
1
1
0
1
1
2
0
1
1
0
1
0
1
2
2
1
1
1
1
0
1
0
2
1
2
1
2
1
1
1
1
2
1
1
1
2
2
0
1
1
2
1
0
2
0
1
1
1
1
2
0
1
2
2
2
0
2
0
1
1
1
1
0
1
1
1
2
2
1
1
1
2
1
1
1
1
1
0
1
2
1
2
1
1
1
1
1
0
1
1
2
0
2
0
1
1
0
1
1
1
1
1
2
0
0
1
0
2
1
1
2
1
0
1
1
1
0
1
1
0
1
1
0
1
2
2
1
2
1
1
1
1
2
2
2
1
2
1
1
2
1
1
1
1
1
2
0
1
0
0
2
1
1
2
2
1
1
1
1
1
1
2
9
1
1
1
2
1
1
0
2
2
2
1
0
0
1
2
0
1
1
2
1
1
1
2
1
1
1
1
1
1
1
0
1
1
1
2
2
1
2
1
2
1
1
2
1
1
1
1
1
3
1
0
1
0
1
0
0
2
0
0
2
0
2
2
1
1
1
0
0
0
1
1
2
0
1
0
1
1
1
1
0
1
1
2
0
1
1
1
0
2
1
2
1
0
1
1
1
0
1
2
1
1
1
1
1
0
1
1
1
1
2
1
1
1
0
1
3
1
0
1
2
1
2
2
1
1
2
1
2
1
2
2
1
1
1
1
1
0
0
0
2
1
1
0
0
2
1
1
1
1
2
1
1
1
1
2
2
1
2
2
0
0
0
0
2
0
0
2
2
1
1
1
3
1
1
0
1
1
1
1
1
0
2
1
1
2
0
1
1
2
1
1
0
1
1
1
0
2
1
1
0
1
1
1
1
1
0
1
1
1
1
1
1
1
1
0
1
0
1
1
1
3
0
1
2
1
1
1
1
1
0
1
2
1
2
1
1
1
2
2
0
1
1
1
1
1
1
1
1
2
2
0
1
1
1
1
1
1
1
1
0
1
1
1
2
0
1
0
1
2
2
1
1
1
1
2
2
0
2
2
1
2
1
1
1
1
1
1
2
1
1
2
1
0
2
1
2
1
1
2
1
1
0
1
2
0
0
2
0
2
2
2
0
1
1
0
0
2
2
1
1
2
2
1
1
2
1
1
3
0
2
0
1
1
0
0
2
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
2
0
1
1
0
1
1
1
0
1
1
2
1
1
1
0
1
1
2
0
0
1
1
1
2
1
1
1
1
2
1
2
1
0
1
1
1
1
2
0
1
2
1
0
0
2
1
0
1
1
2
1
2
1
1
3
1
1
1
1
2
2
1
1
1
1
0
1
2
1
2
1
2
1
0
1
2
1
0
1
1
3
1
1
2
1
1
0
1
1
2
0
2
1
1
1
1
1
1
2
1
1
1
1
1
1
0
1
1
1
1
1
0
2
1
1
1
0
1
1
2
1
1
1
2
1
1
1
2
1
1
2
1
1
1
1
1
0
1
2
2
2
1
0
2
1
1
1
1
1
1
1
1
2
0
0
1
2
2
0
1
1
1
2
1
1
1
1
1
2
1
2
2
0
0
0
1
1
1
2
0
2
1
1
1
0
1
2
1
2
1
1
1
1
1
1
1
1
0
1
1
2
0
2
1
1
1
1
1
0
0
0
1
2
2
2
1
1
2
1
1
2
1
1
2
2
1
0
1
2
0
1
1
1
0
2
1
1
0
1
1
2
1
0
1
1
1
1
2
4
1
1
2
1
0
1
1
1
1
1
1
2
1
2
0
0
0
1
2
0
1
0
0
1
0
0
0
0
1
0
0
1
1
2
2
1
1
1
1
1
1
2
2
1
1
1
2
2
1
1
1
1
1
1
1
2
0
1
1
1
2
1
1
1
1
2
1
1
1
1
0
1
1
0
2
1
2
1
0
2
2
2
1
2
1
0
2
1
2
3
1
1
0
1
2
2
1
0
1
0
1
0
2
1
2
0
1
1
1
0
1
1
1
0
2
1
2
1
2
1
1
1
1
1
2
1
2
2
1
0
1
1
1
2
1
0
0
0
1
1
1
1
2
1
0
0
0
1
1
1
1
2
1
0
2
0
0
0
1
1
2
2
1
1
1
0
1
0
1
2
2
1
1
1
1
0
1
1
2
1
1
1
2
2
1
1
2
1
2
1
2
2
1
2
1
0
1
0
1
1
1
2
1
1
1
1
2
1
1
1
0
2
1
1
2
1
1
0
0
1
1
0
1
1
1
0
1
1
1
1
1
2
2
2
0
1
1
2
3
1
2
1
1
1
1
1
1
2
1
2
2
1
1
0
2
1
1
1
1
0
0
1
2
1
3
2
0
2
1
1
1
0
1
1
2
2
1
1
1
1
1
0
1
2
1
2
2
0
1
3
1
2
1
2
2
1
0
2
0
1
1
1
1
1
2
1
0
1
1
1
2
1
2
2
1
1
0
1
1
0
0
1
1
1
1
1
0
2
0
1
1
1
1
1
2
2
1
1
0
2
1
1
1
2
1
1
1
0
1
1
1
2
2
1
1
1
2
1
2
1
1
1
2
2
1
1
1
2
1
0
0
1
1
2
1
0
0
1
1
0
2
2
2
1
1
1
2
2
1
1
2
1
1
1
0
1
2
2
0
2
1
1
0
2
0
2
1
0
1
1
2
2
2
1
1
1
2
1
2
2
1
1
1
1
1
0
2
2
2
1
2
1
0
1
1
1
1
1
2
1
0
1
0
0
1
1
1
1
1
1
1
1
1
1
0
0
1
2
1
0
2
0
2
1
0
1
1
1
2
0
1
1
1
1
1
1
1
0
1
1
2
2
1
1
1
2
1
2
1
1
1
2
0
2
2
2
0
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
0
1
1
2
3
0
0
0
2
1
1
2
2
1
2
2
2
2
1
0
2
1
0
1
1
1
0
1
1
1
1
0
1
2
2
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
2
1
0
1
2
0
2
1
1
1
0
1
1
1
1
2
2
1
1
0
1
1
2
2
1
0
1
1
0
2
2
1
2
1
1
1
0
0
0
1
0
2
1
1
0
2
1
1
1
1
0
1
1
2
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
0
1
1
1
0
1
1
1
1
1
1
0
1
1
1
1
1
2
1
1
1
1
2
1
1
1
0
2
2
2
1
1
1
2
2
1
1
0
2
1
1
0
2
1
1
1
2
1
1
1
1
2
0
0
2
1
1
1
0
1
1
1
1
2
1
2
2
2
1
1
1
1
1
1
0
2
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
0
0
1
1
1
1
1
2
1
1
1
2
2
1
0
1
1
1
0
1
0
1
1
0
1
1
1
1
1
1
1
2
1
1
0
1
1
1
2
1
1
1
2
1
1
0
1
1
1
0
1
1
2
2
1
0
1
2
2
1
1
0
0
2
2
1
0
1
0
2
1
1
1
1
1
1
2
2
1
2
0
2
1
1
1
0
0
0
2
2
1
2
2
1
1
2
1
1
1
1
2
2
1
1
1
1
1
2
2
2
1
1
0
1
2
1
1
1
2
0
0
1
2
0
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
0
1
1
2
1
2
2
2
1
1
0
1
0
1
2
2
0
1
2
0
1
1
0
0
0
2
1
1
2
1
0
2
2
0
1
2
1
1
2
1
1
1
0
0
1
1
2
1
0
2
1
0
1
1
1
1
0
0
1
1
1
0
1
0
1
2
1
1
1
1
1
2
1
2
1
1
2
1
2
2
1
1
2
1
1
2
2
0
0
1
1
1
0
1
0
1
1
0
1
1
2
0
1
2
1
1
1
1
0
1
1
1
0
1
2
0
1
0
1
2
0
2
1
1
1
0
0
1
2
1
2
2
1
1
1
2
1
1
2
2
0
1
0
2
1
1
1
0
2
2
0
1
1
1
0
1
1
1
2
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
0
1
2
1
1
1
0
1
1
0
2
1
1
2
2
0
2
2
1
2
1
1
2
1
1
1
0
1
1
1
1
1
1
1
2
2
1
1
2
1
0
2
1
1
1
1
2
1
2
0
1
1
1
1
1
1
1
1
2
1
0
2
1
1
1
2
1
1
1
1
1
0
1
1
1
1
1
1
1
0
1
2
0
2
1
0
1
1
1
1
0
1
2
1
1
1
1
2
1
1
2
1
1
3
1
2
1
1
0
2
2
1
1
1
2
1
2
1
0
1
2
0
1
1
2
1
1
1
1
1
0
2
1
1
1
0
1
1
2
0
1
1
1
0
1
0
1
2
1
1
1
1
2
1
0
1
2
1
0
1
1
2
0
1
1
1
1
0
1
2
1
2
2
0
1
1
2
2
0
1
1
2
1
0
0
1
1
1
1
1
1
1
2
1
2
0
2
2
2
1
1
1
2
2
2
1
1
0
2
1
2
0
1
0
2
2
2
1
1
1
1
0
1
2
1
1
1
1
2
1
1
1
1
0
1
0
1
1
1
1
1
0
2
0
1
1
0
2
4
1
1
2
1
1
0
1
2
1
0
1
0
1
1
2
2
2
2
2
1
2
1
1
1
0
1
0
1
2
1
0
1
1
2
0
0
1
2
2
1
1
1
1
0
1
1
1
0
1
1
1
1
2
0
2
1
1
2
1
1
1
1
1
1
1
2
1
0
2
1
0
1
1
2
1
1
2
1
1
1
1
2
1
1
2
1
1
0
1
1
1
2
2
0
1
2
0
2
1
1
1
1
0
2
1
1
1
0
1
1
1
1
1
1
2
2
0
0
1
1
2
1
1
0
2
1
2
1
1
1
0
0
1
1
1
1
1
1
0
1
1
2
1
1
1
2
1
0
2
2
2
1
0
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
2
0
1
1
1
1
2
1
1
0
2
2
0
1
1
1
1
1
2
1
1
2
1
1
2
1
2
2
1
0
0
1
1
1
1
1
2
1
1
0
2
1
1
0
0
2
2
2
1
0
1
1
0
1
1
0
0
1
1
1
1
1
2
0
1
2
1
2
1
1
2
1
0
0
1
0
1
0
1
1
0
1
1
1
2
0
1
1
2
1
0
2
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
2
2
1
2
2
2
0
0
1
1
2
1
1
1
1
1
2
1
0
1
0
1
2
2
1
2
1
1
1
1
0
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
2
0
1
1
1
1
2
4
2
1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
1
1
0
1
0
1
0
1
1
0
0
1
2
1
1
2
1
2
1
1
0
2
2
1
1
1
2
0
1
1
1
0
0
1
1
1
2
1
1
1
1
2
2
1
1
1
1
1
0
1
1
2
1
2
1
1
1
2
1
2
1
1
2
1
1
0
1
0
1
1
0
0
0
1
1
1
2
1
1
1
2
1
0
2
1
1
0
1
2
1
0
1
1
2
0
1
2
1
2
1
2
0
0
1
2
1
0
1
1
2
0
1
3
1
2
2
0
0
1
1
1
1
2
0
2
1
1
1
1
1
0
1
0
1
1
1
0
1
1
1
2
1
1
1
1
1
1
1
1
0
0
1
1
1
1
2
1
1
1
1
1
1
0
1
2
2
1
1
0
2
0
2
1
2
0
1
1
1
0
1
1
1
2
2
1
1
0
2
2
1
1
1
0
2
1
1
2
2
1
1
2
0
1
1
1
1
0
1
2
2
2
1
0
1
1
0
2
1
1
1
1
1
3
2
1
2
1
1
1
1
1
1
2
1
1
0
2
1
2
2
2
0
1
2
2
2
2
1
1
0
1
1
1
2
2
2
2
1
1
1
2
1
2
1
1
2
2
0
1
1
1
1
1
2
2
1
1
1
2
0
1
1
0
1
1
1
3
1
1
1
0
1
1
1
2
2
1
1
1
2
0
0
0
1
1
1
3
2
1
2
0
2
2
0
1
0
1
2
1
1
1
1
2
1
2
1
1
2
1
1
1
1
0
0
1
1
1
1
0
2
1
1
1
1
1
2
1
1
1
1
1
1
0
1
2
1
0
1
2
1
1
1
1
0
1
1
1
2
1
1
1
1
1
1
1
1
2
1
0
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
0
2
1
2
1
10
1
0
0
1
1
2
1
1
1
0
2
1
2
2
0
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
0
1
1
0
1
1
1
2
0
2
1
2
2
1
1
2
2
1
0
2
0
0
1
1
1
1
1
1
0
1
1
2
1
1
1
2
1
1
2
1
2
0
0
1
1
1
2
0
1
1
2
1
1
1
2
0
2
1
1
1
2
1
1
1
0
1
2
2
0
1
1
2
1
1
1
1
1
2
2
1
1
0
1
2
2
1
1
1
1
1
1
1
1
0
2
1
0
2
0
2
1
1
1
2
0
2
0
1
3
1
0
1
1
2
0
1
1
2
1
2
0
1
1
1
1
0
0
2
1
0
1
1
1
2
1
1
0
2
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
2
1
0
1
1
2
2
2
1
1
1
1
0
1
1
2
2
2
1
1
1
2
1
2
1
1
2
2
1
1
0
1
2
1
1
1
1
0
1
1
1
1
1
1
1
1
2
2
1
1
1
2
1
2
1
0
2
2
1
1
0
1
1
2
2
2
1
1
1
0
2
1
0
2
2
1
1
1
0
0
1
1
1
1
0
2
1
1
0
2
1
1
1
2
1
2
1
1
1
1
1
2
1
0
0
2
2
2
0
1
1
1
1
2
1
1
2
2
0
4
1
1
2
1
2
0
2
0
1
2
2
1
2
1
1
1
1
1
1
2
2
1
1
1
1
2
1
1
2
1
1
1
0
0
1
0
1
0
0
1
1
2
1
2
1
2
1
1
0
1
1
1
1
2
2
1
1
2
1
0
1
1
1
1
1
2
0
1
0
1
2
1
1
1
1
0
0
1
1
2
1
1
0
0
2
0
1
2
2
1
1
1
1
1
1
2
2
1
2
1
0
1
1
0
1
1
1
1
1
1
1
1
2
2
0
0
2
1
2
0
1
2
1
0
1
1
1
2
1
1
1
0
0
1
2
1
1
1
1
1
2
1
1
1
1
1
2
2
0
0
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
2
1
1
2
1
0
1
1
2
0
0
1
0
1
1
1
1
2
1
1
2
1
1
1
1
3
1
2
1
1
2
1
2
2
2
1
1
2
2
1
1
1
1
2
2
1
0
2
1
1
2
1
1
1
0
0
1
2
0
5
1
1
0
2
1
1
1
1
0
1
1
1
1
0
1
1
2
1
1
2
1
1
1
1
1
1
1
2
2
1
0
1
2
1
0
0
1
0
2
2
1
1
1
1
5
0
1
0
1
2
1
1
1
2
1
1
1
2
1
0
1
2
2
0
2
1
2
1
0
0
1
0
1
2
2
1
2
1
2
1
1
2
1
2
1
2
1
2
1
2
1
2
1
2
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
3
1
1
1
0
1
1
1
0
2
0
2
2
1
1
2
2
1
0
1
1
2
1
1
1
1
1
2
1
1
0
1
1
1
2
0
2
1
1
0
1
2
0
0
2
1
2
1
1
1
4
2
1
2
0
0
2
1
1
2
1
1
2
2
1
1
5
1
1
3
2
1
1
0
1
1
0
1
1
1
1
1
0
1
1
1
1
1
1
1
0
1
2
2
1
1
2
1
1
1
0
1
1
1
2
1
0
0
1
1
1
0
2
1
0
1
1
1
0
2
2
2
0
1
2
1
2
0
1
1
0
1
1
1
1
0
1
1
1
0
2
2
1
0
1
0
0
2
2
1
1
1
1
1
0
1
2
1
2
1
2
1
1
1
2
1
1
0
2
1
1
1
1
1
1
0
1
1
2
1
1
1
1
2
1
1
0
1
1
1
2
1
1
1
2
1
1
2
1
1
0
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
0
1
1
1
0
2
1
2
2
1
1
2
2
1
1
2
1
0
1
1
1
0
0
0
2
0
2
1
1
1
1
1
1
2
1
1
1
0
2
2
1
1
2
1
2
2
0
2
0
1
1
1
1
0
1
0
1
1
1
1
1
1
1
1
1
2
1
1
2
2
1
1
1
1
2
0
1
0
0
1
2
1
0
2
1
1
2
2
1
1
2
0
1
0
2
1
1
1
0
1
2
2
2
1
1
1
1
2
0
1
1
0
0
0
2
1
1
2
1
1
1
1
2
1
2
1
2
1
1
1
0
1
0
1
0
1
2
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
2
0
2
1
1
1
1
0
2
2
1
2
2
2
1
2
1
2
1
1
1
1
2
3
2
0
1
1
0
2
1
1
1
1
1
1
2
1
0
1
1
2
0
1
1
1
1
1
1
2
1
2
1
2
0
1
0
2
2
1
1
1
1
1
1
1
2
1
1
1
1
0
1
1
1
2
1
1
2
2
1
1
2
1
1
1
0
2
1
2
1
1
0
1
1
2
1
0
1
1
1
0
1
1
1
1
1
2
1
0
0
0
0
0
0
1
2
1
1
2
1
1
1
2
1
1
0
1
1
1
1
1
0
0
0
1
1
1
1
2
0
1
0
1
0
1
1
1
1
1
1
2
1
1
0
2
1
1
0
2
0
1
2
2
1
0
1
1
2
2
1
1
2
1
1
1
1
2
1
1
1
1
0
1
1
1
0
1
1
1
1
1
2
0
0
2
2
2
1
1
2
0
1
2
0
1
1
1
2
2
1
2
0
1
1
1
2
0
0
2
1
1
1
1
1
2
2
1
1
1
0
1
2
2
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
0
1
2
0
0
2
1
1
0
1
1
1
0
1
0
2
2
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
0
1
1
2
0
0
1
2
2
1
1
0
1
1
1
2
2
2
0
1
1
1
0
1
0
1
1
0
1
0
0
1
0
1
1
1
1
1
0
1
1
0
0
1
1
2
1
1
1
1
2
0
1
0
1
1
1
0
2
0
0
1
1
0
1
1
1
1
1
1
0
0
1
1
1
1
3
1
1
2
0
1
1
0
1
0
2
2
2
0
1
1
1
1
1
0
2
1
2
1
1
2
2
1
1
1
1
1
1
1
1
2
0
2
0
1
1
2
1
1
1
1
0
1
1
1
0
1
2
0
0
0
1
1
1
1
1
1
1
1
1
0
1
2
0
2
1
1
0
1
2
1
0
2
2
0
0
1
2
2
2
1
1
1
1
1
2
0
0
1
0
1
1
1
1
1
1
2
1
1
1
1
0
1
1
1
0
1
1
1
1
1
2
0
1
0
1
1
1
1
1
1
0
1
1
1
1
1
1
2
3
2
1
2
0
1
1
0
1
1
2
2
1
0
2
0
1
0
1
1
0
1
2
1
0
2
0
1
1
1
1
1
2
1
1
1
1
0
1
1
2
1
2
2
1
1
1
5
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
0
1
0
1
1
1
0
1
1
1
0
1
0
2
0
0
0
1
1
1
1
2
2
1
0
1
2
2
1
0
2
1
1
0
1
1
0
1
1
1
1
2
1
0
1
2
0
1
2
1
1
1
1
2
1
2
1
1
1
0
0
1
0
2
1
0
1
1
2
0
0
1
1
2
1
1
1
0
0
1
2
1
0
1
1
1
1
2
1
1
1
2
1
1
1
2
1
1
2
0
2
1
1
2
1
1
1
2
2
1
1
2
1
1
1
0
2
1
1
1
1
1
1
2
0
1
3
1
1
0
0
2
0
2
1
0
1
2
1
1
1
1
1
1
1
1
1
1
2
0
1
2
2
1
1
0
2
1
2
1
2
2
1
1
1
0
2
1
1
2
0
1
2
0
1
1
1
1
1
0
0
0
1
1
0
2
1
1
3
1
2
2
1
3
0
2
1
1
1
2
1
1
1
1
2
1
1
0
1
1
0
1
1
0
0
1
0
1
1
0
1
2
1
2
1
1
0
1
2
0
1
0
0
1
1
2
2
1
2
0
1
1
2
2
1
2
0
1
1
0
1
1
0
0
0
1
1
2
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
0
1
1
0
2
2
2
1
1
2
2
1
2
1
1
0
1
2
2
1
1
2
2
2
1
0
2
2
1
0
1
1
1
2
1
1
1
1
2
2
1
1
2
1
2
0
1
1
1
1
1
1
1
0
1
4
1
1
1
2
1
0
1
1
2
1
0
0
1
1
2
1
1
0
1
2
2
1
1
2
1
1
2
1
1
2
0
1
3
1
1
2
1
0
1
0
1
1
1
1
1
1
0
2
1
0
2
2
2
1
1
2
1
1
2
1
1
1
0
3
4
1
1
0
1
1
1
1
0
1
1
2
1
1
2
1
2
1
2
1
1
1
2
1
2
1
2
0
1
0
0
1
1
1
1
0
0
1
1
1
1
1
1
2
0
1
1
2
2
1
1
1
0
2
1
1
1
0
1
0
1
0
1
1
0
1
1
2
1
2
22
2
1
1
1
1
2
1
1
1
1
1
1
2
1
0
2
2
0
1
1
1
1
0
1
1
1
2
1
1
2
2
1
1
1
0
2
1
1
1
1
1
2
1
1
0
1
2
2
1
1
1
0
1
1
1
1
0
1
2
1
1
1
0
2
0
1
0
1
1
0
0
1
1
1
1
1
2
1
2
2
2
1
2
1
1
1
1
1
1
1
2
0
1
0
0
2
1
1
0
1
1
1
1
1
2
2
0
1
1
1
1
1
1
0
0
2
2
2
0
0
1
1
2
0
1
0
1
1
1
2
1
1
0
2
2
1
1
2
2
1
1
0
2
0
1
1
1
1
1
1
1
1
1
0
0
2
1
2
2
0
2
0
1
1
1
1
1
1
1
2
2
1
0
0
1
1
1
2
1
1
2
2
1
0
1
0
2
0
1
2
1
1
1
2
1
2
1
1
1
2
1
1
0
2
2
2
1
1
1
1
1
1
0
2
1
1
2
0
4
0
1
1
2
1
2
1
0
2
1
1
1
1
2
1
2
2
1
1
2
1
2
1
1
1
1
1
0
1
2
2
2
0
1
1
2
1
1
2
1
1
1
1
1
2
1
1
2
1
1
1
1
0
1
1
1
2
1
1
1
1
0
1
0
2
1
0
0
2
0
0
2
1
2
1
0
0
2
2
1
0
2
1
1
2
1
1
2
2
1
2
2
0
1
1
1
5
2
1
1
1
1
1
1
0
1
1
0
1
1
1
1
0
1
1
0
1
0
1
1
1
1
0
0
1
1
2
2
1
0
2
1
1
1
1
1
2
1
1
3
1
2
0
2
0
0
2
0
2
2
1
2
1
2
2
2
1
1
0
1
1
1
0
1
1
0
1
1
0
1
1
1
1
1
0
0
2
1
1
1
2
1
1
1
2
1
1
3
1
1
1
2
1
1
3
2
2
2
2
1
1
1
1
1
1
1
1
1
1
2
2
2
1
0
1
2
0
1
1
1
1
2
1
1
1
1
1
1
2
2
1
2
3
0
1
2
1
1
1
1
1
1
1
0
1
1
1
1
2
2
1
2
1
0
1
2
1
1
1
2
0
2
1
1
1
1
1
2
0
1
2
0
2
1
1
1
1
2
0
1
1
1
1
1
1
0
1
1
1
1
1
1
2
1
1
1
0
0
0
1
1
1
0
1
2
2
1
2
2
1
0
1
2
0
1
2
2
0
1
1
2
1
0
2
1
1
1
2
1
2
2
1
2
1
1
1
2
1
1
1
1
1
2
1
1
0
1
1
2
2
1
2
1
2
1
1
2
1
1
3
1
2
1
1
1
2
1
1
2
2
1
1
2
1
1
2
1
2
1
1
2
1
2
3
2
0
2
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
2
1
0
1
1
1
1
1
0
1
0
0
2
1
1
1
2
2
1
2
1
2
2
2
1
2
1
1
1
1
2
2
2
1
2
0
1
2
1
1
2
1
2
1
1
0
1
1
1
1
2
1
2
1
2
1
1
1
0
2
0
0
2
2
1
1
2
1
1
1
2
1
1
1
1
1
0
1
2
2
1
2
1
0
1
2
1
1
2
1
1
1
1
0
1
1
1
0
1
2
2
1
1
2
1
0
2
2
1
1
2
1
1
1
1
1
1
0
1
0
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
0
1
1
1
2
1
0
2
1
2
0
2
0
1
1
1
1
1
1
2
1
1
1
0
1
0
2
1
1
1
2
0
1
0
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
0
2
2
1
2
2
0
2
2
1
2
1
2
1
1
0
1
0
1
2
1
0
2
1
2
1
1
0
1
2
1
1
0
2
2
2
1
1
1
0
2
1
1
1
0
1
0
1
2
2
1
1
1
1
2
2
1
1
1
1
1
1
1
0
1
1
0
1
0
0
1
1
1
0
1
2
1
1
0
2
1
1
1
1
0
1
2
1
0
1
2
1
1
0
2
1
1
0
0
1
1
0
1
1
1
1
1
1
2
2
1
1
1
1
0
2
1
1
2
2
1
1
2
2
2
2
1
2
0
2
1
2
2
1
1
1
1
1
0
2
1
1
1
2
1
2
1
0
1
2
0
2
2
2
2
1
1
2
1
1
1
1
1
2
1
2
2
0
1
2
0
1
0
1
1
0
0
0
2
0
2
1
1
1
1
1
1
1
2
2
0
1
1
1
1
1
1
2
0
2
1
2
0
1
1
1
2
2
2
1
1
1
1
1
0
1
1
1
1
1
0
1
1
2
1
1
1
1
1
2
1
1
1
0
0
1
1
1
0
1
0
1
0
0
1
1
1
2
1
1
2
0
1
0
0
2
0
1
1
1
0
1
0
0
0
0
2
1
1
2
1
2
1
2
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
3
1
1
1
1
1
1
0
1
1
1
0
1
1
2
2
0
1
1
1
1
0
0
1
0
2
0
1
1
1
1
0
1
1
1
1
1
0
1
0
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
0
1
2
1
2
2
2
2
1
0
2
1
1
2
1
1
1
1
1
0
2
1
1
2
0
1
2
2
2
1
1
1
1
0
2
0
1
1
2
1
1
1
1
1
0
1
0
1
0
2
1
2
1
2
1
2
2
1
0
1
1
1
1
2
1
1
0
1
1
1
0
1
0
2
2
2
0
1
0
2
1
0
1
0
1
0
2
1
2
1
1
2
2
1
1
1
1
0
1
1
2
1
1
1
1
0
1
1
1
1
2
2
1
1
1
1
0
1
0
1
2
1
0
2
2
1
1
1
1
1
0
1
1
0
2
1
1
0
2
1
1
1
1
1
1
1
2
2
1
1
0
1
1
2
1
0
1
1
1
1
0
1
1
0
1
1
0
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
2
2
2
1
1
1
1
3
2
1
1
1
2
1
0
1
1
1
2
1
2
2
0
1
2
1
2
1
2
0
0
1
1
1
1
1
1
0
1
1
2
1
1
1
1
0
1
1
1
1
1
0
1
1
2
2
1
2
1
1
1
2
1
1
1
1
1
1
1
2
0
1
1
1
2
1
1
1
0
1
0
2
1
1
0
2
1
0
1
0
1
1
2
0
1
1
1
0
0
1
1
0
2
2
1
2
2
2
1
1
2
1
1
1
1
0
1
0
2
1
0
1
1
0
0
1
1
1
1
0
2
1
1
0
0
1
2
2
1
0
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
0
2
1
1
2
1
1
0
1
1
2
1
2
1
2
2
2
2
1
1
1
2
2
1
2
2
0
0
1
1
0
2
1
2
0
1
0
1
2
2
1
2
2
0
1
1
2
0
1
1
0
1
0
1
1
1
1
1
1
1
1
2
1
1
2
0
0
0
1
2
1
2
1
1
1
1
0
2
1
1
0
1
1
1
2
0
1
4
1
2
0
1
1
0
2
1
1
1
2
0
1
1
0
0
1
0
2
0
0
1
1
1
0
1
1
1
1
0
1
1
1
0
1
1
1
0
2
1
0
1
1
1
1
1
1
1
0
0
1
0
1
1
1
1
1
2
2
0
2
1
1
1
2
2
1
1
1
1
0
1
1
2
1
2
1
2
1
2
1
1
1
2
1
1
1
0
2
0
0
1
1
1
1
2
1
1
1
1
2
1
2
1
1
1
1
0
1
1
0
1
1
1
2
2
1
2
2
1
1
0
1
1
1
0
0
1
1
2
1
2
1
1
1
0
1
1
1
1
1
1
1
0
1
1
0
1
0
0
1
1
1
2
1
1
1
1
2
2
1
1
2
2
1
1
2
1
1
1
0
5
1
1
1
0
1
1
1
1
1
1
1
2
2
1
1
1
1
2
0
2
1
2
1
2
1
0
0
2
0
1
2
2
2
1
1
2
2
1
2
0
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
0
1
1
2
2
2
1
1
1
1
1
1
1
1
1
1
0
1
1
0
1
1
1
2
2
1
1
0
1
2
1
1
0
1
1
0
2
2
0
1
0
1
0
1
0
2
2
1
1
2
2
1
2
1
1
1
1
1
1
1
1
0
1
0
2
1
2
1
1
2
1
1
1
1
0
1
1
1
1
1
0
2
3
2
0
2
1
0
0
1
1
3
0
1
1
2
1
2
0
2
0
2
1
1
1
0
0
1
1
1
1
2
0
0
1
1
1
1
1
2
2
0
1
1
1
1
1
1
2
2
0
1
1
1
2
1
1
1
1
0
1
3
1
1
1
1
1
0
1
2
1
1
1
2
1
1
1
2
0
2
1
1
0
1
1
1
1
2
0
2
1
1
1
1
1
0
2
2
1
0
1
0
0
1
1
0
1
1
1
2
2
0
0
0
2
1
1
3
2
2
1
1
1
2
1
1
1
1
1
1
1
1
0
1
1
1
1
2
1
2
1
1
0
1
1
1
0
1
1
0
1
0
1
1
1
1
0
1
1
1
1
0
2
1
1
1
1
1
1
2
2
2
1
2
1
1
1
2
1
0
2
0
2
1
0
2
2
1
1
1
2
2
2
0
1
2
0
0
1
2
1
1
0
1
1
1
1
2
2
1
1
0
0
2
1
2
1
1
1
2
1
0
2
1
1
2
2
2
0
1
0
1
0
2
5
1
1
1
0
2
1
1
1
1
2
1
0
1
0
1
1
1
2
1
1
1
0
1
1
1
1
2
2
0
1
1
1
1
1
1
1
1
1
2
2
0
0
0
1
1
1
2
2
0
1
2
0
1
2
0
1
0
0
3
0
1
1
1
2
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
0
1
2
1
1
1
0
1
0
1
0
1
1
2
1
0
1
0
0
2
1
0
2
1
0
2
0
1
1
1
1
1
2
2
1
1
1
1
1
1
0
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
0
1
1
1
1
1
1
1
0
2
1
2
1
2
1
1
0
2
1
1
1
1
0
0
1
1
1
0
0
1
2
1
0
1
1
0
1
1
1
1
1
2
1
2
2
1
1
1
1
1
2
2
1
2
1
1
1
1
1
0
0
1
1
1
1
0
1
1
1
1
1
1
0
1
2
2
1
2
0
0
1
0
2
2
0
1
0
1
1
1
1
1
1
2
0
0
1
0
1
1
2
1
2
1
2
1
0
0
1
1
1
2
1
0
1
1
1
1
1
0
5
1
1
2
2
1
0
0
1
1
1
0
2
1
2
1
1
1
0
1
1
0
1
1
1
0
1
2
0
2
1
1
1
2
1
1
1
0
1
2
1
1
1
2
1
0
1
2
2
1
2
1
2
2
1
1
1
1
0
1
1
0
1
2
1
1
0
1
0
1
1
0
0
1
1
1
2
2
1
1
2
1
2
1
1
0
1
0
2
1
1
1
0
0
0
2
1
1
1
0
1
1
0
1
2
1
0
1
2
2
0
1
1
0
1
1
2
1
1
1
2
0
2
0
1
1
1
1
1
1
2
0
0
1
1
2
1
0
1
1
2
1
0
1
1
2
1
2
1
2
1
3
1
1
1
1
1
1
2
2
1
1
2
0
2
1
1
1
1
0
0
1
1
2
0
0
2
1
0
0
1
1
2
2
1
2
0
1
1
1
1
1
1
0
1
1
2
1
2
2
2
1
2
1
1
1
1
1
1
1
2
0
1
1
2
1
1
0
0
1
1
1
1
0
2
0
1
2
0
1
1
2
2
1
1
1
0
1
1
1
2
1
2
1
1
1
0
2
1
1
1
2
0
1
1
1
1
1
1
1
1
1
1
2
0
1
1
1
1
1
1
0
1
0
1
1
1
1
0
1
1
0
0
1
0
1
2
1
0
2
2
1
1
0
0
2
0
1
2
1
2
1
2
0
1
0
2
2
1
1
0
1
1
1
1
1
1
1
2
2
1
1
1
2
0
1
1
1
1
1
0
2
1
1
1
1
1
1
1
0
1
0
2
2
1
1
2
1
0
0
2
0
1
1
1
1
1
1
2
2
1
1
2
1
2
1
0
2
0
1
0
0
1
2
1
1
3
1
2
0
1
0
2
2
1
0
0
1
1
1
2
1
1
2
1
1
0
2
2
1
1
1
1
2
0
2
2
2
1
1
2
2
1
1
1
2
1
1
1
0
1
2
1
2
1
1
1
1
1
1
2
2
2
1
2
1
2
0
1
2
0
1
2
1
4
1
1
1
2
2
1
0
1
1
0
1
1
1
1
2
2
1
1
1
0
1
0
2
1
1
1
2
1
2
1
1
1
1
1
1
1
0
2
2
1
1
2
0
2
1
2
1
2
1
0
1
1
0
1
0
1
2
0
1
1
1
2
2
2
0
2
1
1
2
1
1
2
1
1
1
2
0
1
1
2
0
1
1
2
1
2
1
1
1
1
0
1
1
1
1
2
1
1
0
2
2
1
2
1
1
1
2
0
2
1
1
2
1
1
2
0
1
1
1
1
1
1
1
0
1
1
2
0
1
1
0
1
0
0
2
2
0
1
1
1
2
1
2
1
1
1
2
1
0
0
0
0
1
1
1
1
2
1
2
1
3
1
1
1
1
0
1
1
0
2
1
1
2
1
1
1
2
2
1
1
2
0
2
2
1
1
1
2
2
1
1
0
0
0
1
2
0
1
0
1
1
2
1
2
1
1
2
2
1
1
2
2
1
2
1
1
1
2
1
1
1
2
1
0
2
1
1
1
1
2
1
1
1
1
1
2
1
1
3
1
2
1
1
1
1
2
1
2
1
0
2
4
2
1
2
1
2
1
1
1
2
2
1
1
1
1
2
1
2
1
0
0
2
0
1
1
1
1
1
1
1
0
2
1
2
1
0
1
1
0
2
1
1
1
0
0
1
1
2
1
1
2
3
1
0
1
1
1
0
1
1
1
2
1
2
1
1
1
1
1
1
1
2
2
0
1
1
0
1
1
1
1
1
1
2
1
0
1
1
2
0
0
0
1
1
1
5
1
2
1
1
1
2
2
2
1
2
1
1
2
1
2
1
1
2
1
1
1
2
1
1
2
1
2
0
0
1
0
1
2
1
1
1
1
1
1
1
2
1
1
0
1
1
1
1
1
1
0
1
0
0
1
0
1
0
0
1
0
1
1
1
0
1
1
0
2
1
2
1
2
0
2
2
2
0
1
1
2
3
0
2
1
2
1
1
0
3
1
2
1
1
1
1
2
1
2
1
1
0
1
0
1
1
1
2
0
1
1
1
0
1
2
2
1
1
0
1
1
1
1
2
1
2
1
1
1
1
1
1
2
0
1
2
1
2
2
2
1
1
1
2
2
1
0
1
2
2
2
1
2
2
1
1
2
2
2
1
1
1
2
1
1
1
2
1
2
2
1
1
0
1
2
1
1
2
1
0
0
1
1
1
1
0
2
0
1
1
1
1
1
2
1
1
1
1
1
2
1
0
1
2
1
1
1
1
2
1
0
1
1
0
1
1
2
2
1
2
2
0
1
1
1
0
1
2
2
0
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
2
2
1
2
1
1
1
0
0
2
1
1
0
1
0
0
1
0
1
1
1
1
1
2
1
0
1
2
1
1
2
1
1
1
0
0
1
1
2
1
2
1
2
1
0
0
0
1
1
1
0
3
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
0
1
0
1
2
2
0
1
2
1
0
1
0
0
0
1
0
1
1
1
1
1
1
1
2
1
2
1
1
2
1
2
1
1
0
1
2
1
0
1
2
1
2
0
1
2
2
1
2
1
1
0
1
1
1
0
1
2
1
1
3
1
0
1
1
1
0
0
1
2
1
1
1
1
2
0
1
1
1
1
1
2
2
1
2
2
1
1
0
1
0
0
2
1
2
1
1
1
1
1
0
1
1
2
1
1
0
1
2
1
1
1
1
1
0
1
1
1
2
2
1
1
1
0
2
2
1
0
1
2
1
0
1
1
1
1
1
1
1
0
2
1
0
0
2
1
2
1
2
0
1
0
0
1
1
2
1
2
1
1
1
2
1
1
2
3
1
1
1
0
1
1
1
1
2
1
1
2
1
1
1
1
0
1
2
1
1
1
1
1
0
2
1
1
1
2
1
1
0
1
1
1
1
2
1
2
2
1
2
2
4
0
1
2
0
1
1
1
0
1
1
1
1
1
1
0
1
1
2
0
1
2
1
0
1
1
1
1
1
1
1
1
1
1
0
0
1
1
1
0
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
0
1
2
1
0
0
1
1
1
0
1
0
0
1
0
2
0
1
2
1
1
0
2
2
0
1
1
1
1
0
2
2
0
2
1
1
1
1
0
1
2
1
1
2
1
1
1
1
0
2
2
2
1
1
1
1
1
1
2
1
2
1
1
1
1
0
1
2
1
0
1
1
2
0
2
1
0
2
2
1
1
3
1
0
1
2
2
1
1
2
1
0
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
0
1
1
0
2
2
1
1
3
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
0
1
1
1
2
1
1
1
2
2
2
1
1
2
2
3
2
1
1
1
2
1
1
1
1
1
0
2
1
1
2
1
2
1
2
2
1
2
1
2
1
0
0
1
1
0
1
1
2
1
4
2
2
2
0
1
1
1
2
1
2
1
2
1
1
1
1
1
1
1
2
2
1
1
1
2
1
2
1
1
1
2
1
1
1
1
1
0
2
1
1
1
1
2
0
1
2
0
2
1
1
2
1
1
1
0
2
1
1
1
2
1
1
1
1
2
1
1
0
1
2
1
1
0
0
1
1
1
1
1
0
2
2
2
1
0
1
2
2
1
1
2
1
1
1
1
0
1
2
1
1
1
1
2
2
2
1
1
1
1
1
2
2
1
2
1
2
2
1
1
1
1
1
1
1
1
1
2
1
2
1
2
1
1
1
1
2
1
1
1
0
0
1
1
0
1
1
2
2
2
0
1
2
2
2
3
1
2
1
1
1
2
1
1
2
0
1
1
0
2
1
1
1
1
0
2
0
0
1
0
2
1
1
1
1
0
1
1
1
0
2
2
0
2
1
2
2
1
2
1
2
0
0
2
1
1
1
1
6
0
0
1
0
1
1
2
1
1
0
1
1
1
1
1
1
0
2
1
1
0
1
1
2
1
1
1
1
1
0
2
1
3
0
1
1
1
0
1
1
1
1
2
1
1
2
1
0
0
1
0
1
1
1
1
1
2
1
0
1
0
1
0
2
1
1
1
1
1
1
1
0
1
1
1
0
1
1
1
2
0
1
1
2
2
0
2
1
2
2
0
1
1
1
2
2
1
1
0
1
1
1
2
1
1
1
2
2
1
2
2
1
2
2
1
2
1
1
2
1
0
1
0
1
1
2
1
1
1
0
0
1
1
1
1
1
1
2
1
2
1
2
1
1
1
1
2
1
2
2
1
1
1
0
3
1
1
1
1
1
1
2
1
1
1
1
1
1
0
0
1
0
2
1
2
1
1
1
0
1
1
1
1
2
1
1
1
1
3
1
1
2
2
2
1
1
2
1
2
2
2
1
1
0
2
1
0
1
1
1
1
1
1
1
0
0
1
2
0
1
2
1
1
1
0
2
1
1
1
1
1
2
1
1
1
1
12
1
0
0
1
0
0
1
2
1
1
2
2
1
1
4
1
1
1
1
1
0
2
2
1
2
1
0
1
1
1
1
1
1
0
1
2
0
1
3
1
1
1
0
1
1
1
1
1
1
1
1
1
2
1
1
1
0
2
1
1
2
1
1
2
1
0
2
1
2
1
2
2
1
2
1
2
0
1
1
1
1
0
2
0
1
1
0
1
0
1
3
1
0
2
1
1
1
1
1
1
0
1
1
1
1
1
2
0
1
1
0
1
1
0
1
1
2
1
1
1
2
2
1
1
1
2
0
2
2
3
1
2
1
1
1
1
1
1
2
1
1
1
1
2
0
1
2
0
0
1
1
2
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
1
1
0
1
1
1
1
2
1
1
1
1
0
2
0
1
1
2
1
1
1
1
1
1
2
0
1
1
1
2
1
1
1
1
1
1
1
2
0
1
1
2
1
1
2
2
1
2
1
1
1
1
1
2
2
1
1
1
2
2
1
2
1
1
2
0
1
0
1
1
1
1
2
1
1
1
1
1
1
2
1
1
2
1
1
1
1
2
1
2
0
1
1
2
1
1
1
1
1
1
1
2
1
4
3
2
1
0
1
1
1
1
0
2
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
2
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
2
2
1
1
1
2
0
2
0
1
1
2
0
1
1
2
2
2
1
1
1
2
0
0
2
1
2
1
2
1
1
1
1
1
2
0
1
2
2
1
1
1
1
0
1
1
1
1
0
1
0
1
0
1
1
0
1
2
1
3
1
1
0
1
1
0
2
1
2
0
3
0
1
2
2
2
1
1
1
1
2
1
2
1
1
1
1
3
2
1
2
1
0
1
1
2
1
0
0
0
1
1
1
0
1
1
2
1
0
1
1
1
1
1
2
0
0
2
2
1
1
0
1
1
2
2
0
2
2
2
1
1
1
1
1
1
1
1
1
1
1
0
1
0
1
1
0
1
1
2
1
0
2
0
1
2
0
1
1
0
1
0
2
1
2
0
2
1
2
2
1
1
1
1
1
1
1
2
0
1
1
2
2
1
1
0
1
1
1
1
2
2
0
2
2
1
1
1
1
1
2
2
2
0
2
1
1
1
2
1
1
2
2
1
1
2
1
1
1
1
2
1
1
1
2
3
2
5
1
1
0
1
2
2
1
2
2
2
3
1
1
1
2
1
1
1
2
1
2
2
2
0
1
1
0
2
1
2
1
1
1
2
2
1
0
0
0
1
1
1
0
0
2
0
1
0
1
0
0
2
1
1
2
1
0
1
1
2
0
1
1
0
1
1
0
1
0
1
1
2
1
1
1
1
1
2
0
0
0
1
1
1
0
1
1
0
1
2
2
1
0
1
1
1
2
0
2
1
1
1
1
2
1
2
0
1
0
1
0
2
0
0
1
0
1
1
2
2
2
1
2
1
1
2
1
2
1
1
2
1
1
1
1
0
2
1
0
2
1
1
1
2
1
1
0
2
1
1
1
1
0
3
1
0
1
1
1
1
2
1
0
1
0
1
1
1
0
1
1
0
1
1
1
1
0
0
0
2
2
1
2
1
2
1
1
0
1
1
2
1
1
0
2
1
0
1
1
2
1
0
2
2
1
0
1
1
2
1
1
1
1
1
2
1
0
1
2
0
1
2
0
2
0
2
1
1
2
1
1
5
2
1
1
1
1
1
2
0
1
0
2
2
1
1
1
1
1
2
1
2
1
1
1
1
0
0
1
0
2
1
0
2
1
1
2
1
1
2
0
1
1
0
1
0
1
1
2
0
1
1
1
2
0
1
1
1
0
0
1
1
1
0
1
0
0
2
2
0
1
1
1
0
1
2
1
2
1
2
1
1
1
0
1
1
1
1
1
3
1
0
1
1
1
1
0
0
2
1
2
2
1
2
1
2
1
1
0
1
1
1
1
1
1
1
0
2
1
0
1
0
0
1
1
1
1
2
1
2
1
2
2
1
1
1
1
0
1
2
2
2
1
1
1
0
1
2
0
2
1
2
1
1
2
2
1
1
2
1
1
0
2
1
2
1
0
3
1
1
1
1
1
2
1
1
1
1
2
1
2
1
0
1
2
1
1
1
1
2
2
1
1
2
2
2
1
1
1
1
1
1
1
0
1
1
1
1
1
2
1
2
2
1
1
1
1
0
1
2
1
1
1
1
0
1
0
1
2
1
2
0
1
1
1
1
1
2
1
1
2
1
1
1
1
0
1
2
3
2
2
2
1
1
0
1
1
1
8
1
1
0
2
2
1
2
1
8
0
1
1
1
2
1
1
2
1
2
1
1
0
1
1
2
2
1
2
1
1
0
1
2
1
1
0
0
0
1
1
1
1
1
1
0
1
1
1
2
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
3
1
2
1
1
2
1
1
1
1
1
1
0
1
1
1
1
1
0
1
1
1
0
1
2
1
1
2
0
1
2
2
2
1
1
1
1
0
1
1
1
0
1
1
2
1
1
1
1
1
0
2
1
1
0
2
2
1
1
1
1
2
1
1
2
1
2
2
1
2
1
3
1
1
2
1
0
0
1
1
2
2
1
1
0
2
2
2
2
2
2
0
2
0
1
2
1
1
1
0
1
1
1
1
2
2
1
1
1
2
1
1
1
1
2
2
0
0
2
1
1
1
1
2
2
2
1
0
1
1
1
1
1
0
2
2
1
1
1
2
1
0
1
1
1
0
1
1
1
2
1
0
2
2
2
2
0
1
1
2
3
1
1
1
1
1
1
2
2
1
1
1
2
1
1
1
2
2
0
1
1
1
1
0
1
0
1
2
2
2
1
2
1
1
1
0
0
1
1
1
1
2
1
1
0
1
1
1
3
0
1
1
1
2
1
1
1
1
1
1
0
0
1
0
1
1
1
1
1
1
1
1
0
1
1
2
1
1
1
1
1
2
1
1
2
0
1
1
1
1
1
0
1
1
1
1
1
2
0
2
1
2
1
0
1
1
1
1
1
0
1
1
2
2
1
0
1
1
1
1
1
2
1
1
1
1
1
1
0
1
1
1
1
1
2
0
1
1
2
2
0
1
1
0
2
2
1
1
1
1
1
2
1
1
2
1
1
1
1
1
0
0
2
1
1
1
2
1
2
4
2
0
1
2
2
2
0
3
1
1
2
1
1
2
1
1
1
1
1
1
2
2
2
0
1
2
2
2
1
1
1
1
2
1
1
2
1
1
2
1
2
2
1
1
2
0
1
0
2
1
1
1
0
1
1
0
1
1
1
1
2
1
2
0
2
1
1
0
1
1
2
2
1
1
1
1
2
0
0
1
2
2
1
2
1
0
1
1
0
2
1
2
1
2
1
2
2
1
2
3
1
2
1
2
1
2
2
1
0
0
1
2
0
2
2
1
2
1
1
1
1
1
2
0
2
1
1
1
1
1
1
1
0
1
2
1
0
2
0
1
1
0
1
2
1
0
2
2
0
1
0
0
0
1
1
1
1
1
2
1
1
2
1
1
1
1
0
1
0
0
2
1
1
1
1
2
1
2
0
2
1
2
2
1
2
1
1
1
2
0
1
0
1
1
1
1
1
1
1
1
1
1
2
1
1
0
1
1
2
1
0
0
0
1
1
1
1
3
1
2
0
1
0
0
1
1
1
2
2
2
2
0
1
2
2
0
1
1
2
0
1
1
0
1
2
2
1
1
2
1
2
1
2
1
0
1
1
1
1
1
2
1
1
0
0
2
0
1
1
1
2
1
1
1
1
0
1
1
1
0
0
2
0
1
2
1
1
2
1
1
0
2
1
1
1
0
1
1
2
1
1
1
1
0
1
1
1
1
2
1
1
1
1
1
2
1
2
0
1
1
2
2
1
1
1
0
1
6
1
0
1
1
2
1
1
1
1
1
2
0
1
1
2
1
1
1
1
1
1
1
0
0
2
1
0
0
1
1
2
1
2
1
2
2
1
2
1
1
1
1
0
6
1
1
1
1
1
2
2
0
1
1
1
2
1
1
2
1
1
0
0
1
2
2
1
2
2
1
1
0
1
0
1
0
1
1
1
2
0
1
1
2
1
1
1
1
1
2
1
2
1
2
1
1
1
1
1
1
1
2
1
1
4
1
0
1
0
1
2
1
2
2
1
1
2
1
1
1
1
2
2
1
2
1
0
0
0
1
0
1
1
2
0
1
0
0
0
1
1
2
1
1
1
1
1
1
1
1
1
2
2
2
1
2
1
2
1
2
2
1
1
0
1
2
0
1
1
1
1
1
1
1
2
2
0
2
1
2
1
0
1
1
2
2
2
1
1
0
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
0
2
2
1
1
2
1
1
1
1
2
2
0
2
2
1
1
1
0
1
2
0
2
2
1
2
1
1
1
1
0
0
0
1
1
1
1
2
1
0
2
1
2
1
3
1
1
0
1
1
1
1
1
2
0
1
1
1
2
1
1
2
1
2
1
0
2
2
1
2
1
0
1
2
1
1
1
1
2
1
2
2
1
1
1
1
0
2
2
1
1
2
1
1
0
1
1
1
2
0
1
1
0
1
1
1
1
1
2
2
2
1
0
1
1
1
0
1
1
1
2
2
1
1
2
0
1
1
1
0
1
1
0
2
2
1
1
0
1
1
1
2
2
2
1
2
1
1
1
1
1
1
1
1
1
1
0
1
1
1
2
0
1
1
1
1
1
0
1
1
0
1
2
1
1
1
2
1
2
2
1
0
1
1
0
5
1
1
4
2
0
1
1
1
1
1
1
0
1
1
1
1
2
1
1
1
2
1
1
0
2
1
1
2
2
1
1
1
2
0
1
0
1
0
0
1
1
2
2
2
1
1
2
1
1
1
2
1
1
1
1
0
1
1
0
1
2
2
1
2
0
2
1
1
1
1
2
1
1
2
1
1
1
6
1
0
0
2
2
1
1
0
1
2
1
2
2
2
1
2
0
1
2
2
2
1
1
1
1
1
4
1
1
1
2
1
1
1
1
1
1
2
2
1
1
2
1
1
1
0
1
2
1
2
1
1
0
2
2
2
1
2
1
0
2
1
0
2
1
0
2
0
0
0
1
0
2
0
1
2
2
0
1
1
1
1
1
2
2
2
1
0
0
0
1
1
1
1
1
2
1
2
1
1
1
1
1
0
1
1
1
0
2
1
2
1
2
1
1
0
1
1
1
1
1
1
2
2
1
1
0
1
1
1
1
0
0
2
0
1
1
1
1
0
0
1
2
2
0
2
2
0
1
2
2
1
1
1
0
1
2
1
2
1
1
1
1
0
1
2
1
1
0
2
2
1
1
1
0
1
0
2
0
1
1
0
1
0
2
0
0
1
1
1
1
1
1
1
1
0
2
2
1
3
1
1
2
0
1
1
1
1
1
0
0
2
1
2
1
1
2
1
1
2
1
1
2
1
0
1
1
1
2
1
1
1
1
2
1
0
1
1
1
1
1
1
1
3
1
2
2
2
1
2
1
2
0
1
1
2
1
2
1
1
1
2
1
1
1
1
1
2
1
1
0
1
1
1
1
0
1
2
0
1
1
1
2
2
1
1
1
2
2
1
1
2
1
1
2
1
1
1
1
2
1
1
1
2
2
1
1
1
0
2
2
1
2
1
1
2
2
0
1
1
1
0
1
1
0
2
1
2
1
1
2
1
1
0
2
2
1
1
0
1
1
1
1
1
2
2
1
1
1
2
0
2
0
0
1
3
1
0
1
0
0
1
0
2
1
1
1
0
1
1
0
2
1
1
1
2
1
2
1
2
1
1
2
3
0
1
2
2
1
2
1
0
1
2
1
0
2
2
1
2
1
1
0
1
1
1
1
1
2
1
2
2
1
1
0
0
2
1
1
1
1
1
1
1
0
1
1
0
1
2
2
1
1
1
1
2
0
2
2
1
1
1
2
1
1
1
1
3
1
1
2
1
0
1
1
1
2
1
1
2
2
0
1
1
1
1
2
0
1
1
1
1
1
2
2
1
1
0
3
0
2
2
1
2
2
1
0
0
1
1
1
1
1
1
0
1
1
1
1
1
2
1
1
1
1
1
0
1
0
0
1
1
0
0
1
2
1
2
1
1
1
0
1
2
1
0
1
2
1
0
1
0
0
1
0
1
1
1
0
0
2
0
2
2
0
1
2
2
2
1
2
1
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
0
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
2
1
1
1
1
0
1
2
1
1
2
1
2
1
1
1
1
1
0
1
1
1
2
0
0
1
1
1
1
0
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
0
2
2
1
1
1
0
1
1
2
2
4
2
1
1
2
1
2
1
0
1
1
1
1
1
1
2
1
1
1
1
1
1
0
1
0
2
1
2
1
0
2
1
0
1
2
0
1
1
2
1
1
1
0
1
1
1
0
1
0
2
2
1
1
1
2
1
0
0
2
1
1
1
2
1
0
0
1
1
1
1
1
0
0
1
0
2
1
1
1
2
1
1
2
1
2
1
1
0
0
1
2
1
1
1
2
0
1
1
1
1
1
1
1
1
1
2
2
1
1
0
0
1
2
0
1
1
1
1
0
1
2
1
2
2
2
1
1
0
1
1
1
1
1
1
1
1
1
2
2
0
0
1
1
1
0
2
1
1
2
1
1
2
0
1
2
1
1
0
1
1
2
1
1
2
2
1
1
1
2
0
1
2
1
2
0
0
2
2
0
1
1
0
1
1
2
1
1
2
3
0
1
1
1
2
1
2
1
1
0
0
1
2
0
1
1
2
1
1
0
1
1
2
1
1
1
2
1
0
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
2
1
1
2
1
1
1
1
0
2
1
0
0
1
1
1
2
0
1
1
1
1
1
1
2
0
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
4
2
1
2
1
1
1
2
2
1
1
0
1
1
1
1
2
1
1
0
1
2
1
1
1
1
3
0
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
1
2
1
0
2
1
0
1
1
0
1
1
1
2
2
2
1
1
0
2
2
1
2
1
1
1
0
0
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
0
2
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
3
2
1
2
1
1
2
1
1
1
0
1
0
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
0
1
1
1
1
2
1
1
1
0
1
1
1
2
1
2
1
0
0
0
1
1
2
0
0
1
1
1
1
1
2
1
0
0
2
1
1
0
1
0
2
0
2
2
1
1
1
1
2
1
2
0
1
2
2
2
2
1
1
1
0
1
2
1
1
2
0
2
2
1
2
1
2
1
1
0
2
2
1
1
1
1
1
1
3
1
2
2
1
1
1
1
2
1
1
0
2
1
2
1
1
1
1
0
2
1
1
1
1
0
1
1
1
0
0
0
2
2
0
1
1
0
0
1
1
2
1
1
1
1
2
2
1
0
1
1
1
2
2
1
1
2
2
1
1
0
1
0
1
1
2
0
1
1
2
0
2
2
1
2
1
2
1
2
1
1
1
1
1
2
0
1
2
2
2
1
1
1
1
1
2
1
0
1
2
1
0
0
1
1
1
2
1
2
2
1
1
0
1
1
2
2
1
2
1
1
2
0
1
2
0
1
0
2
1
2
2
1
1
1
2
2
0
1
1
2
1
1
0
2
1
2
2
1
0
1
1
1
0
1
0
2
1
1
1
1
2
2
1
1
0
0
1
0
0
1
2
1
1
1
2
2
2
1
1
0
2
1
1
3
1
1
1
1
1
2
1
1
2
1
1
0
1
0
0
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
2
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
2
1
1
1
1
0
1
2
1
1
2
1
1
0
2
0
1
2
1
1
1
1
1
2
3
1
1
1
2
2
0
0
1
1
2
0
2
1
0
1
1
1
1
2
1
1
1
0
1
0
1
2
0
2
1
1
1
1
0
2
1
0
1
1
2
1
1
1
2
2
1
1
1
1
1
2
1
2
1
1
2
1
2
0
1
0
0
0
0
1
2
1
2
1
2
1
1
0
2
1
1
1
1
1
2
0
0
1
0
1
0
1
1
0
1
1
0
1
1
1
1
2
2
1
1
1
2
1
2
2
2
1
1
1
2
1
1
2
1
2
1
1
1
1
2
0
2
0
1
1
1
2
1
2
0
1
2
1
0
1
2
2
2
1
2
1
0
2
1
0
0
0
1
0
2
1
1
1
2
1
0
1
1
1
2
1
2
2
2
1
1
1
1
0
2
1
1
1
1
0
2
2
1
1
0
1
0
1
2
1
0
1
0
1
1
1
1
0
0
0
1
1
0
0
1
1
0
1
2
1
1
1
1
1
0
1
1
1
2
0
0
1
1
1
1
2
2
2
1
2
2
1
1
2
1
2
1
0
1
0
1
1
2
0
1
1
2
1
1
2
2
2
1
0
1
2
2
0
1
1
1
1
2
1
2
1
0
1
1
1
0
2
1
2
1
1
0
1
1
1
0
0
1
1
0
1
1
0
0
1
0
2
1
1
1
2
1
2
0
2
1
1
1
1
2
1
1
1
0
1
1
1
1
1
1
0
2
1
1
1
1
2
1
2
1
1
2
1
0
1
0
1
3
1
1
2
2
1
1
0
1
0
0
1
0
0
1
1
0
1
0
1
2
2
1
1
0
1
3
1
1
1
1
2
0
1
1
2
0
1
1
2
0
1
1
1
0
0
1
2
1
2
0
1
0
1
1
0
0
0
1
1
1
2
2
0
1
1
2
1
1
1
1
1
1
0
2
1
0
1
2
1
1
1
0
1
1
1
0
1
1
1
1
2
1
0
2
1
1
1
1
2
1
1
1
1
1
1
1
2
0
2
1
1
1
1
2
1
1
0
1
1
2
0
2
2
2
1
0
1
1
1
1
1
0
1
1
1
0
1
0
1
0
2
1
1
0
2
1
1
2
1
2
2
2
3
1
1
1
0
1
2
1
1
2
2
2
1
2
0
1
1
2
1
0
1
1
1
1
1
2
0
1
1
2
1
1
0
1
1
1
2
1
1
1
2
1
2
1
1
2
2
1
1
1
1
2
1
1
0
1
1
1
1
1
0
1
1
2
0
1
2
1
1
2
1
1
2
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
0
1
1
1
1
2
1
2
1
2
1
1
1
1
0
3
1
1
0
1
1
2
0
0
2
1
1
1
1
1
1
2
0
1
1
1
1
1
2
2
0
1
1
0
1
1
1
1
1
1
0
2
1
1
2
2
2
0
1
1
1
0
0
1
0
1
1
2
1
2
2
1
0
2
1
2
2
1
1
1
0
1
1
1
1
0
1
2
1
1
1
2
2
1
2
0
2
1
1
1
1
2
1
0
1
0
1
2
1
1
2
0
2
1
1
0
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
3
1
1
2
1
0
1
1
1
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
2
2
1
0
1
1
1
1
0
0
0
1
1
1
1
1
1
1
1
1
1
3
1
2
1
2
1
1
0
2
1
1
0
1
2
1
1
1
2
1
1
1
0
0
1
2
1
0
2
0
1
1
0
2
2
2
1
1
1
1
1
2
1
1
1
2
1
1
2
0
2
1
1
1
1
0
1
1
1
1
1
0
1
1
2
1
2
1
2
2
2
2
0
1
0
1
1
0
1
1
1
1
2
1
1
0
1
0
1
1
1
2
1
1
1
2
2
1
1
1
1
0
2
2
0
2
1
0
2
1
3
0
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
0
1
1
1
1
0
1
1
0
2
0
2
1
2
2
0
1
1
0
1
0
1
1
1
1
2
0
1
1
1
0
1
1
1
0
1
1
1
1
1
1
2
1
1
1
0
1
0
1
2
2
1
1
1
1
0
2
1
2
2
1
1
1
2
2
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
0
2
1
2
1
2
1
2
1
1
1
1
1
1
3
1
1
1
2
2
1
1
1
2
1
2
2
1
2
2
1
1
0
1
1
1
2
1
1
1
0
0
1
1
0
1
2
1
1
0
2
1
2
1
0
2
1
1
1
0
1
1
0
1
2
3
0
2
1
2
0
1
1
1
1
1
1
1
1
2
1
0
1
0
2
0
2
2
2
2
1
1
1
1
0
1
1
1
2
1
2
1
2
0
1
0
1
1
0
2
0
2
0
0
1
1
0
2
1
2
1
1
2
1
2
1
1
2
1
0
0
1
1
1
1
0
0
1
1
1
1
1
1
0
2
0
2
2
2
0
2
1
1
0
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
0
1
1
2
0
2
1
1
0
2
1
1
1
1
2
2
0
1
2
2
1
1
1
1
1
0
1
2
2
2
1
1
1
1
1
1
1
0
2
1
0
1
1
0
1
1
1
3
1
2
2
0
1
1
2
1
2
2
1
1
1
2
1
2
0
2
2
2
0
1
1
1
2
2
2
1
1
1
2
0
1
2
0
0
1
2
0
1
1
2
2
2
1
2
2
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
2
1
1
1
1
0
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
2
2
1
1
2
1
1
2
1
1
1
0
0
1
2
2
2
2
1
2
0
2
1
1
1
1
1
2
0
2
1
1
2
0
2
2
1
1
1
2
2
2
1
1
0
1
2
2
2
0
1
1
1
1
1
2
1
1
2
1
2
2
1
2
2
1
1
2
1
0
0
1
2
1
1
2
2
1
1
2
1
1
0
5
2
1
1
2
1
0
0
3
2
1
1
1
1
2
0
1
2
2
2
2
0
1
2
1
2
0
2
1
2
2
1
3
1
1
2
2
2
1
2
0
1
1
1
0
2
0
1
2
2
0
0
1
1
1
2
0
1
1
0
1
1
1
2
1
2
1
1
0
2
1
1
1
1
1
2
1
1
1
1
2
1
0
0
1
1
2
1
2
2
1
1
5
1
2
1
0
1
1
1
1
0
1
0
2
1
0
1
1
1
0
2
3
1
0
1
1
1
2
1
1
1
2
1
2
1
1
3
1
1
1
1
1
2
2
1
1
0
1
1
2
0
1
2
0
1
1
0
0
1
1
1
2
1
1
1
0
1
1
1
1
1
2
1
2
1
1
2
1
2
1
2
2
1
1
1
0
2
1
1
1
0
1
2
1
1
2
1
2
1
1
1
1
0
1
0
2
0
2
1
1
1
0
1
1
1
2
2
1
1
2
1
0
1
1
0
0
1
2
1
1
1
2
2
1
1
2
2
1
1
0
2
1
2
1
1
1
2
1
2
1
1
0
1
0
1
1
1
1
1
0
1
0
0
1
2
2
1
2
2
2
1
1
1
2
1
1
1
2
1
1
2
1
1
0
2
1
1
2
1
1
2
0
2
1
0
1
1
1
0
1
0
2
1
0
0
1
1
1
1
1
1
1
1
1
2
1
0
1
1
1
1
1
1
0
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
2
1
2
1
2
0
1
0
1
0
1
0
1
1
1
2
2
2
1
2
1
1
1
0
2
0
2
0
2
1
1
1
1
1
1
1
2
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
0
2
0
0
1
1
0
0
1
0
1
2
1
1
2
1
2
1
1
0
1
2
0
0
0
1
1
0
1
1
1
1
1
0
1
1
1
1
1
1
1
2
1
2
0
1
0
1
0
2
1
1
1
2
1
1
1
1
2
2
1
1
1
1
1
2
1
1
1
1
2
2
1
1
2
1
1
1
1
2
2
1
1
1
2
1
1
2
1
1
0
1
1
1
1
1
1
1
2
1
1
2
1
1
1
0
1
1
1
1
2
0
1
1
1
2
1
1
1
1
1
1
0
1
0
2
0
1
1
1
1
0
1
0
0
1
0
1
2
2
0
2
1
1
1
0
1
0
2
2
2
1
1
1
1
2
1
2
2
1
0
1
0
1
1
1
1
1
1
1
1
1
2
0
1
1
0
2
2
1
1
1
1
1
2
1
1
1
2
1
2
0
0
1
1
1
2
1
0
2
1
3
0
1
2
2
1
1
0
0
1
2
1
2
2
1
1
1
1
1
2
2
1
1
1
1
1
0
2
1
1
1
1
1
2
1
1
1
0
1
1
1
0
1
2
1
1
1
1
1
1
2
2
1
1
2
2
0
1
1
1
2
1
1
1
2
0
2
2
1
1
1
0
1
2
2
3
0
1
1
1
2
1
0
2
0
1
0
1
2
1
0
0
1
1
1
1
2
1
0
2
1
1
1
1
2
1
1
2
0
2
2
2
0
1
1
0
2
1
1
0
0
2
1
1
3
1
1
1
2
1
1
1
2
1
1
1
1
0
1
1
1
1
1
1
0
1
1
2
2
1
1
1
2
1
1
1
1
1
2
0
1
1
2
1
1
1
2
1
1
1
1
2
1
1
0
1
1
1
2
1
1
1
0
1
0
0
1
0
2
2
2
1
0
1
1
1
2
1
0
1
1
1
2
1
1
1
2
1
2
2
1
1
1
0
2
0
1
1
1
1
2
0
1
1
1
2
1
1
1
1
1
1
1
2
1
1
2
0
2
0
2
0
1
2
1
2
1
2
2
1
1
2
2
1
1
1
1
2
2
1
2
1
1
1
1
1
0
2
1
1
2
1
2
0
2
2
0
1
1
1
1
1
1
2
1
1
0
1
0
1
2
2
2
1
0
1
1
1
2
0
1
1
1
1
2
1
1
2
1
0
1
1
2
1
2
0
2
0
1
1
2
1
1
1
1
2
1
1
1
0
1
0
1
2
1
1
1
0
2
0
2
1
1
2
2
0
1
1
1
1
1
2
1
0
0
1
2
1
1
1
1
1
0
1
1
0
2
1
1
1
1
2
2
1
1
2
1
0
1
2
2
2
1
1
1
1
1
0
1
1
1
1
3
1
1
0
2
1
1
1
1
2
1
1
0
0
0
1
1
0
0
1
2
1
0
2
1
1
0
1
1
1
1
0
1
1
1
1
2
2
1
0
2
1
1
2
1
1
1
1
1
1
3
1
1
0
0
1
1
1
1
1
0
2
0
0
1
1
2
0
0
1
1
0
1
2
1
2
1
1
1
1
2
1
2
1
1
2
2
1
1
1
2
2
0
0
1
1
2
2
1
0
1
1
1
2
0
1
1
2
2
1
2
3
1
1
1
1
1
1
1
0
0
0
1
1
2
2
1
2
1
0
0
1
1
0
1
2
2
2
1
2
1
2
2
0
2
2
1
0
1
1
1
1
1
1
0
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
0
1
1
1
1
1
2
2
1
1
2
1
1
1
1
0
1
0
1
1
1
2
3
1
1
1
0
2
1
1
0
1
1
1
0
1
1
1
1
3
2
1
1
1
1
2
1
2
2
1
0
0
2
2
1
1
2
1
1
1
1
1
0
1
1
2
1
1
1
2
1
1
1
2
2
1
2
0
2
3
1
1
2
1
0
2
1
1
2
1
3
1
2
1
1
2
1
1
2
2
2
1
1
1
1
0
1
1
2
3
1
0
1
1
2
2
2
1
2
0
1
1
1
2
1
1
2
0
1
2
2
1
1
0
1
0
2
2
2
1
1
1
1
1
1
1
2
2
2
1
2
1
1
2
2
2
1
2
0
0
1
1
1
1
0
0
1
1
2
1
2
1
1
2
0
2
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
2
1
1
0
1
2
1
1
1
1
1
1
2
2
1
2
1
2
1
1
1
2
1
1
1
2
1
1
2
1
0
2
1
1
0
2
2
1
1
2
1
1
1
1
1
1
1
0
2
1
2
1
1
1
2
1
1
1
1
1
1
1
0
2
1
0
1
1
1
1
1
0
2
3
0
1
1
1
2
1
1
0
1
1
1
2
0
2
1
1
1
1
5
1
1
2
0
1
2
0
1
2
1
0
0
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
2
1
1
0
1
1
3
1
0
0
1
1
0
1
1
1
2
2
0
2
2
1
0
1
0
1
1
1
1
1
2
1
1
0
0
1
1
2
0
2
1
1
2
0
2
1
1
1
2
1
1
3
0
1
1
1
1
1
1
1
2
1
2
1
1
1
2
0
1
1
1
2
2
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
5
1
1
1
1
1
0
2
2
1
1
1
1
2
1
1
2
2
0
2
1
0
1
2
1
1
1
2
2
1
2
4
1
1
1
1
2
1
1
1
1
2
1
0
2
1
1
0
1
1
1
2
1
1
1
1
1
1
1
0
1
0
1
1
1
1
1
1
0
1
1
1
1
0
0
1
1
1
1
1
1
0
2
2
1
2
1
2
2
2
1
0
2
1
1
1
0
2
1
2
1
1
1
2
1
1
2
1
0
2
1
0
1
2
3
1
1
1
2
1
2
1
1
1
1
1
1
3
1
1
0
1
1
2
1
1
0
1
1
1
0
1
1
1
2
2
1
2
1
0
1
1
2
1
1
0
1
2
1
1
1
1
1
1
1
1
2
0
2
2
1
1
1
1
1
2
1
1
0
1
1
1
2
1
1
1
0
0
2
0
1
1
1
1
2
2
1
1
1
1
1
2
1
1
1
3
2
1
0
1
0
0
0
1
1
2
1
1
1
3
2
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
0
2
1
0
1
1
2
2
1
1
2
1
1
1
0
1
1
2
1
1
1
1
1
1
1
2
1
0
0
1
1
0
0
1
2
0
1
0
1
2
1
0
0
2
0
0
1
0
1
1
2
2
1
1
1
1
1
1
2
2
1
1
2
1
1
1
1
0
1
0
2
1
2
1
2
1
2
1
1
1
1
1
1
0
1
1
2
1
1
1
1
2
0
1
1
0
1
2
0
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
2
1
0
1
1
0
1
0
0
3
1
1
1
2
1
2
1
1
2
2
2
1
1
1
2
1
0
0
1
2
0
1
2
1
2
1
0
3
1
0
1
1
1
0
1
0
2
0
1
1
1
2
1
1
2
1
1
1
0
0
1
1
1
1
1
2
1
2
1
2
1
1
0
1
1
2
1
1
1
2
1
0
1
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
2
1
1
1
2
0
1
1
0
2
2
2
1
2
1
1
2
1
2
1
1
1
2
0
1
1
1
1
2
1
2
1
1
0
2
1
3
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
4
0
0
1
1
2
1
2
2
1
1
2
1
0
1
1
1
1
1
1
2
1
0
2
0
1
1
1
1
0
0
1
1
2
1
1
1
1
1
0
2
2
1
0
2
1
0
1
0
1
2
1
1
1
1
1
1
3
1
1
3
1
1
1
1
1
0
0
1
2
1
1
2
0
0
2
1
1
1
1
2
2
1
2
2
1
0
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
2
1
1
0
2
0
1
1
0
0
1
1
2
0
1
1
0
1
0
1
1
1
0
1
2
1
2
1
1
2
1
1
1
1
1
3
1
2
1
1
2
1
2
0
2
1
0
0
1
1
2
2
1
1
1
1
0
1
1
1
1
1
1
0
2
0
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
0
2
2
0
2
0
0
0
0
1
1
1
0
0
1
0
0
0
1
1
0
1
1
0
1
1
1
1
1
1
1
1
1
1
2
0
3
1
1
1
1
1
1
1
1
1
1
1
2
2
1
0
2
2
2
0
2
1
0
2
1
1
0
2
1
1
3
0
0
2
1
1
0
2
1
2
1
2
6
1
2
2
1
2
1
1
1
0
0
1
2
1
1
1
1
0
0
0
2
2
0
1
1
1
1
1
0
0
1
2
1
1
1
1
1
1
1
1
2
0
0
1
2
1
1
2
0
1
0
0
2
1
0
1
2
1
1
1
1
1
1
1
0
1
2
1
1
1
1
1
0
2
1
0
1
1
0
1
1
1
1
0
1
0
0
0
1
2
1
2
1
1
2
0
1
7
1
1
1
0
0
0
2
1
0
0
0
1
1
1
0
1
2
1
1
1
1
1
1
1
1
0
1
2
0
2
1
1
0
2
0
2
1
2
1
2
4
2
2
1
1
0
1
1
1
2
1
1
1
1
1
1
0
1
2
1
1
2
1
1
0
2
1
0
1
1
1
2
1
3
1
1
2
1
2
0
1
1
2
1
1
1
1
2
2
1
1
1
2
2
0
1
0
1
2
0
0
1
1
1
1
2
1
1
2
1
1
2
2
1
1
1
1
1
0
1
2
1
1
1
1
1
1
1
1
1
2
2
1
1
1
2
1
2
0
1
1
1
1
2
2
1
1
0
1
1
1
0
2
1
0
2
2
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
0
1
1
2
1
2
1
1
1
2
2
1
1
2
0
1
2
1
0
1
2
0
1
1
1
1
1
1
1
1
1
0
1
2
2
1
1
1
0
1
1
1
0
2
1
1
2
1
1
0
1
1
1
2
2
2
0
0
0
1
0
2
1
0
0
1
1
1
0
1
0
2
1
1
1
0
1
0
2
1
0
1
1
2
0
1
1
1
1
1
1
1
0
1
1
0
1
1
2
1
1
1
1
0
1
1
1
1
1
0
1
1
1
1
2
0
1
0
0
2
0
1
1
1
1
0
2
0
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
0
2
1
2
1
1
2
2
1
1
1
0
0
1
1
1
1
2
1
1
1
1
2
0
1
1
2
1
2
1
1
1
1
1
1
0
0
1
0
2
1
1
1
1
2
0
0
1
1
1
1
1
1
2
2
4
1
0
1
1
3
1
1
2
1
0
2
1
1
0
0
1
1
1
1
1
1
2
1
1
1
2
1
0
1
2
1
1
2
1
2
1
2
0
0
1
1
1
2
1
1
2
1
1
2
1
2
2
1
2
0
2
1
2
1
1
2
2
1
1
2
1
2
1
2
1
2
0
1
1
2
1
1
1
2
2
1
1
0
2
1
1
2
0
1
2
0
0
2
1
0
2
1
1
1
1
2
1
1
2
2
1
2
1
1
0
1
1
1
1
1
1
1
1
1
1
0
2
0
1
2
0
1
2
0
1
1
1
0
2
1
2
0
0
1
1
0
1
1
0
1
0
1
1
2
0
1
1
0
1
0
1
1
2
2
1
2
1
1
2
3
1
1
0
0
1
2
0
2
2
2
0
2
1
0
2
1
2
2
1
1
0
0
1
1
2
1
1
0
1
1
1
1
1
1
1
1
1
0
1
1
2
1
1
2
1
1
0
0
1
2
0
0
1
1
1
1
2
0
1
1
2
0
1
1
1
1
0
1
1
0
1
1
1
0
1
1
1
2
1
1
1
1
1
2
1
1
2
0
1
1
1
2
1
2
0
2
0
1
0
2
0
1
1
1
1
1
1
1
0
2
0
1
1
2
1
1
1
1
1
2
2
0
1
1
2
1
0
1
1
1
1
2
2
1
2
5
0
0
2
1
1
0
2
2
1
1
2
1
1
1
1
0
1
1
1
2
1
0
1
1
1
1
1
1
1
1
2
0
1
1
1
2
2
2
1
1
1
0
2
1
1
1
0
2
0
1
1
1
1
1
0
1
2
1
2
2
1
0
0
1
2
0
0
2
2
1
2
1
1
1
1
2
1
0
2
1
2
2
1
0
1
1
2
2
0
1
0
2
2
0
0
1
2
2
1
1
1
2
0
2
2
1
1
1
0
1
1
2
2
1
0
1
1
1
2
1
3
0
1
1
1
1
1
1
2
1
1
1
1
1
0
2
2
2
1
1
1
1
0
1
2
1
1
1
1
2
1
0
2
1
1
1
1
0
2
1
1
1
2
1
1
0
0
1
1
1
0
1
1
2
2
1
0
2
2
0
1
0
1
0
2
0
0
1
2
1
1
0
1
1
1
2
1
1
2
1
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
0
1
1
1
0
1
1
2
0
1
1
0
1
2
1
1
1
1
2
2
0
0
1
0
1
1
1
0
1
1
1
2
2
0
1
2
2
2
1
2
1
0
1
1
2
1
2
1
1
0
1
2
0
1
1
2
1
2
1
2
1
1
0
1
1
1
2
1
2
1
0
0
1
1
2
1
2
2
1
1
0
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
0
0
2
1
2
2
1
1
1
2
0
1
0
1
2
2
2
1
1
1
1
0
1
0
1
1
2
0
1
1
2
1
0
0
1
2
1
2
0
1
1
1
1
1
1
2
1
1
1
2
2
0
1
2
1
0
1
2
0
1
1
1
0
2
1
1
2
1
1
1
2
0
1
0
0
1
1
1
2
2
1
1
1
1
2
1
1
2
2
1
1
1
4
0
3
1
0
2
1
1
1
2
1
1
2
0
0
1
0
1
1
0
1
0
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
0
0
1
2
0
1
1
2
1
2
0
1
1
1
2
1
1
1
1
2
0
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
3
0
0
1
1
0
3
1
2
1
1
1
1
0
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
0
1
1
1
1
1
1
0
4
2
0
1
1
1
1
2
2
2
1
2
2
2
0
1
1
0
0
3
1
1
2
1
1
1
2
1
2
1
1
0
1
1
1
1
2
1
2
2
2
1
2
2
1
2
0
0
0
1
1
0
2
1
1
1
0
2
1
1
1
0
1
1
0
1
1
1
1
0
3
0
1
1
1
2
0
1
1
1
2
1
2
2
1
1
2
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
2
0
1
1
1
1
3
1
1
0
1
2
2
2
1
0
1
1
1
1
2
2
0
1
2
0
2
1
1
1
1
1
1
0
2
2
2
1
2
2
1
2
1
1
2
1
0
1
1
1
1
1
2
1
0
2
1
1
2
0
1
0
0
1
2
1
1
1
2
1
2
1
1
1
0
2
1
1
1
2
2
1
0
1
0
0
1
0
1
1
1
0
1
1
1
1
1
1
2
1
1
1
1
1
0
1
1
2
1
2
1
1
0
0
0
2
1
0
2
0
2
1
1
0
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
2
1
0
1
1
1
1
2
2
1
2
1
1
1
2
0
1
1
0
0
0
1
0
0
0
1
3
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
2
1
1
2
1
1
0
1
2
2
0
1
1
2
1
1
2
2
0
1
0
2
1
1
2
0
0
1
1
1
1
0
0
0
1
1
0
1
0
1
2
2
0
2
2
1
2
1
1
1
0
0
1
1
1
0
0
1
2
1
1
0
1
1
0
1
2
1
2
1
2
1
2
1
2
2
1
2
0
1
1
2
1
1
0
2
1
1
1
1
0
1
0
1
0
0
2
1
2
2
0
2
1
2
0
2
1
1
0
1
0
2
1
1
0
2
1
1
1
2
1
0
2
1
1
1
1
0
1
1
1
1
1
0
2
1
1
1
1
0
1
2
1
0
1
1
0
1
1
0
1
1
1
1
0
1
2
1
2
1
1
1
1
1
0
1
1
2
1
1
1
2
2
1
1
1
1
1
1
1
1
0
1
0
0
1
1
1
1
2
1
1
1
1
1
2
1
2
1
2
2
1
2
1
1
1
1
1
1
0
1
1
2
1
0
2
1
2
1
1
1
1
1
1
1
1
1
1
0
1
3
1
1
0
1
1
1
1
1
0
0
0
1
0
1
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
2
0
2
1
0
0
1
0
1
1
1
2
2
0
1
1
1
0
0
1
1
1
1
1
2
1
0
2
1
1
2
0
1
1
2
1
1
2
2
1
1
0
1
1
2
1
1
1
2
0
1
2
0
1
0
0
1
1
0
1
1
1
1
1
0
2
2
1
1
1
1
1
1
1
1
1
2
2
2
0
1
1
1
0
1
2
1
1
1
1
1
0
1
1
2
1
2
2
1
0
2
2
2
1
1
2
1
2
2
1
1
1
1
0
1
0
0
1
2
0
2
0
2
1
2
0
1
1
1
1
2
0
2
1
1
1
0
1
1
1
2
1
2
2
1
1
1
0
1
0
1
1
1
1
1
1
2
1
2
1
1
1
0
2
1
0
2
1
2
2
2
1
1
1
1
1
2
2
2
1
1
2
2
1
1
1
1
1
1
0
1
1
1
2
2
1
0
1
1
0
0
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
0
2
2
1
1
1
2
1
2
1
1
1
2
1
0
2
0
1
2
0
0
1
1
1
1
1
1
1
1
2
2
0
2
1
1
2
1
2
2
0
3
1
2
1
1
1
1
2
0
1
1
1
1
2
0
1
2
1
1
0
1
1
1
0
1
1
1
0
1
1
0
1
0
0
2
2
1
1
0
1
1
2
0
1
2
1
0
1
1
1
2
2
1
0
0
1
0
1
2
2
2
1
1
1
1
2
1
2
1
0
1
2
1
0
1
2
2
3
0
1
1
1
1
2
1
2
1
2
1
1
2
0
1
1
2
1
1
1
2
2
2
1
2
1
1
1
1
1
1
2
1
1
1
1
0
1
1
1
1
0
1
1
1
3
1
0
2
1
0
2
1
2
1
2
1
1
1
2
1
2
1
1
2
0
1
1
2
0
2
1
1
1
2
2
1
1
1
1
1
1
1
1
2
1
2
1
1
1
2
1
1
0
1
1
2
1
1
2
2
2
0
1
2
2
1
1
1
1
2
0
1
0
1
2
2
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
0
0
1
1
1
2
1
1
1
0
1
0
0
1
0
2
1
2
1
1
1
1
2
1
2
1
0
1
1
2
1
1
1
2
1
1
1
2
1
2
0
1
2
1
1
0
1
1
2
1
0
1
1
1
1
2
1
1
0
1
2
1
1
1
1
1
2
1
1
2
0
1
1
0
1
2
1
0
1
1
0
1
1
1
1
1
1
3
1
1
1
1
1
2
0
2
0
0
0
1
1
1
1
2
1
1
2
2
0
1
0
1
1
1
0
1
1
1
2
0
2
1
0
1
1
1
2
1
1
0
1
0
2
1
0
0
0
1
1
1
1
1
0
1
0
1
2
2
1
1
0
1
2
1
1
1
2
0
2
1
1
1
1
2
1
1
2
1
1
1
0
1
1
1
1
1
0
0
2
1
1
1
1
1
1
1
1
1
1
1
1
3
1
1
0
0
0
1
0
1
1
1
1
1
2
0
2
0
1
0
1
0
1
1
1
1
1
1
0
0
1
0
2
2
1
1
0
1
1
1
1
1
1
0
1
1
2
1
2
1
1
1
1
1
1
0
0
1
1
1
1
1
2
2
2
1
1
0
0
1
1
1
0
1
1
2
1
2
1
2
1
0
1
1
1
2
2
1
0
0
4
1
0
1
1
1
1
1
2
1
1
1
2
1
2
1
1
0
1
1
2
1
1
2
1
2
1
2
1
0
1
2
1
2
1
0
2
1
2
1
1
2
2
1
2
1
1
1
2
1
1
1
0
1
1
1
2
0
1
1
1
1
1
0
2
1
1
1
2
2
1
1
4
2
1
1
1
1
0
2
2
1
2
2
1
1
2
0
1
2
1
1
1
1
1
2
1
1
1
2
0
0
2
1
1
1
2
2
2
1
1
0
1
1
0
0
1
1
1
1
1
2
2
2
0
2
1
0
2
1
0
1
1
2
2
2
1
1
1
1
1
1
1
2
1
1
0
0
1
1
1
1
0
1
1
1
0
2
1
1
1
1
1
1
1
1
0
1
2
2
1
0
1
2
0
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
2
2
1
1
1
2
1
1
2
1
1
1
5
1
1
1
0
0
1
1
2
1
0
1
1
1
0
2
2
1
1
1
1
2
1
2
2
1
1
1
1
1
0
1
2
0
1
1
1
2
1
0
0
1
1
1
1
1
2
0
1
1
2
2
1
1
2
1
0
1
0
1
1
2
2
1
0
0
1
2
1
1
2
2
2
2
1
1
2
0
2
1
1
2
1
0
1
1
1
1
1
2
1
1
2
1
1
1
0
1
0
2
1
1
1
0
1
1
1
2
1
1
0
0
1
1
1
2
2
0
2
1
1
0
1
1
2
1
1
1
1
1
2
2
1
0
2
1
1
0
1
1
1
2
1
1
2
2
1
1
2
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
2
1
1
0
1
0
1
1
1
1
0
1
1
0
2
1
0
1
0
1
1
1
1
1
1
1
1
1
2
1
1
0
2
1
2
1
1
2
0
2
0
0
2
1
1
1
2
1
0
1
1
1
1
1
2
0
2
0
1
1
1
1
1
1
1
1
1
2
1
2
2
1
2
1
1
1
2
1
0
1
3
2
1
2
1
1
1
1
1
1
1
0
2
1
0
1
1
2
1
2
1
2
0
2
1
1
1
1
1
5
1
1
1
1
1
1
1
1
0
1
1
1
1
2
1
1
0
0
2
0
0
1
1
2
1
2
0
1
2
1
1
2
1
1
1
2
1
2
0
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
0
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
2
1
0
0
1
1
1
2
2
2
1
2
1
0
1
2
1
1
1
2
0
0
1
0
1
2
2
0
0
1
0
2
1
1
1
2
0
0
2
1
0
2
1
0
1
1
1
1
2
1
1
3
1
1
2
1
2
1
1
1
1
1
1
1
0
1
1
1
3
1
1
2
1
2
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
0
0
0
0
0
1
0
2
2
1
1
0
1
1
2
2
1
2
2
0
1
0
1
0
0
1
2
1
1
2
1
2
0
1
0
1
1
1
2
1
1
3
2
2
1
1
1
1
1
1
1
2
0
1
1
0
1
1
2
1
1
1
1
1
1
1
2
1
2
0
1
0
1
1
1
2
1
0
2
1
1
1
1
1
1
1
0
1
2
1
1
1
1
2
0
0
1
1
1
1
0
1
1
2
2
1
0
1
0
1
1
0
1
0
2
2
2
2
1
0
1
1
1
1
1
2
2
2
1
1
1
2
1
1
0
0
2
2
1
1
0
0
2
2
0
1
0
1
1
3
1
1
1
1
1
1
2
1
1
0
1
1
1
1
1
0
0
2
1
1
1
1
1
1
1
0
2
1
2
0
1
1
1
2
2
1
1
1
1
0
1
0
2
0
1
1
0
1
1
0
1
1
0
2
1
3
1
1
1
1
1
0
2
3
1
2
2
1
1
1
2
1
2
1
1
2
1
1
1
2
2
2
2
2
1
1
0
1
1
1
1
0
1
0
1
1
2
0
1
2
0
1
1
1
1
1
2
1
2
2
2
0
1
2
0
1
1
0
2
1
1
1
1
2
2
0
1
1
1
0
1
2
1
0
0
0
0
1
2
2
1
0
2
1
0
1
0
1
2
1
1
2
1
2
1
1
1
2
1
1
1
1
1
2
0
1
1
0
2
2
0
0
1
1
1
1
2
2
2
2
1
1
1
0
0
2
0
1
0
1
2
1
1
2
1
2
2
0
2
1
1
2
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
2
0
0
1
0
1
2
1
2
1
1
1
1
0
2
0
0
0
1
2
1
2
0
0
1
1
1
0
0
1
1
1
1
1
2
1
1
1
1
1
2
0
1
1
0
2
1
0
1
2
2
1
2
1
1
1
1
1
2
1
0
0
1
1
1
0
2
1
1
1
1
2
1
1
2
2
1
1
1
0
2
2
1
1
1
3
2
1
1
1
1
1
1
0
1
1
1
1
1
0
1
1
1
1
1
0
2
2
0
1
1
2
1
1
2
3
1
0
1
0
1
1
1
2
1
1
1
2
2
2
1
1
1
2
0
1
1
2
1
1
1
0
1
1
1
1
3
2
1
0
2
1
1
2
1
1
0
1
0
2
2
1
1
0
2
2
0
1
1
1
0
1
1
1
1
1
2
1
1
1
1
2
2
2
3
1
0
1
0
1
1
0
2
2
2
3
1
1
1
1
1
0
1
0
0
2
0
1
1
1
1
2
1
1
0
1
0
2
1
1
1
1
2
0
1
1
1
1
2
1
1
1
1
0
0
1
0
2
2
1
2
1
1
1
1
1
1
1
1
1
2
1
0
0
0
1
0
2
1
1
1
1
1
0
2
1
1
1
1
0
2
2
2
1
1
0
1
2
2
1
1
2
2
1
0
0
1
1
1
1
1
1
1
1
0
1
2
1
1
0
1
1
2
1
1
1
1
1
1
1
1
5
1
2
1
1
1
1
0
2
3
1
1
1
0
1
2
1
1
2
0
2
1
0
0
1
2
1
2
2
1
1
2
1
1
2
1
1
1
1
1
2
2
1
1
0
1
0
1
0
1
1
0
1
2
1
1
1
2
0
2
2
2
1
0
1
1
1
1
0
1
1
1
1
1
1
1
2
1
2
1
1
1
2
0
1
2
1
1
1
2
1
1
1
1
0
1
1
1
1
1
2
1
1
0
0
1
2
1
1
2
1
1
1
2
0
1
2
2
1
2
1
1
1
1
1
2
0
2
1
2
1
1
1
1
1
3
1
0
1
0
1
1
2
1
1
2
2
0
1
2
2
0
2
1
1
1
2
0
1
1
1
1
1
0
1
2
1
1
2
2
1
1
1
1
0
1
0
1
1
1
2
0
1
1
1
1
1
2
2
0
0
1
1
1
2
1
1
0
1
1
2
1
2
1
2
2
1
1
1
1
1
1
0
1
2
1
1
2
1
1
1
1
2
1
1
2
1
2
0
1
1
1
1
1
1
1
1
0
1
2
1
1
1
2
2
1
1
1
1
1
2
1
1
1
3
1
1
1
1
0
1
1
1
1
0
1
2
2
1
1
2
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
2
0
1
2
1
2
1
1
1
0
2
1
1
1
2
1
1
1
2
2
1
0
1
1
0
1
1
1
1
0
1
1
2
1
0
1
1
2
1
2
0
1
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
0
2
2
1
2
0
2
0
1
1
1
1
2
2
2
1
1
0
2
1
1
1
1
1
1
2
1
1
0
1
0
1
2
2
1
2
2
1
1
0
1
1
2
1
0
1
1
1
1
0
1
1
1
2
1
1
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
0
0
1
0
2
1
0
2
2
1
2
1
1
1
1
1
1
0
2
2
1
1
1
1
1
3
0
2
1
2
2
1
3
1
1
1
2
0
0
2
2
1
1
2
2
1
1
1
0
1
0
1
2
1
2
2
1
1
1
1
1
2
1
0
0
1
2
1
1
1
0
1
1
1
1
1
1
1
2
1
2
1
0
1
1
1
2
1
0
1
1
1
1
2
1
1
1
2
0
1
1
1
2
1
1
0
2
2
1
0
1
1
2
2
1
1
0
2
1
1
2
1
2
0
2
0
1
2
0
1
1
2
0
1
1
1
1
1
1
2
0
1
0
1
1
1
1
1
1
1
2
1
1
1
2
1
1
0
1
0
1
1
1
2
1
1
1
2
1
1
1
1
0
0
1
2
1
1
2
1
1
1
2
0
1
1
1
1
2
1
1
2
1
0
2
1
1
0
1
0
0
3
1
1
1
1
0
2
0
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
1
1
2
1
0
2
0
1
1
1
1
2
2
1
1
2
2
2
1
1
1
1
1
1
0
2
0
1
2
2
1
1
1
1
0
1
1
1
1
1
2
0
1
1
1
2
1
1
2
1
2
2
1
0
2
1
2
0
1
1
2
1
2
2
1
2
1
1
1
1
2
1
2
0
2
2
2
2
1
1
1
1
2
1
1
1
2
1
0
2
2
2
0
1
1
2
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
0
2
1
1
1
1
1
1
1
1
0
2
1
2
1
1
1
1
3
1
1
1
1
1
1
2
1
1
1
2
0
2
0
1
1
1
1
1
0
1
2
1
0
1
2
0
1
0
1
2
1
0
1
0
2
1
1
1
2
1
1
0
1
1
0
0
2
0
1
1
1
1
0
1
0
1
0
0
1
1
2
1
0
1
1
1
1
1
1
1
1
0
1
1
0
1
1
1
1
0
1
2
2
1
2
0
1
0
1
1
2
1
1
1
2
2
1
1
2
0
1
1
1
1
2
1
1
1
1
2
2
1
2
1
2
1
1
2
0
0
1
2
1
1
1
1
1
0
1
2
2
1
2
1
1
1
1
1
1
1
1
1
0
1
2
2
1
1
2
2
0
2
1
0
1
1
1
1
1
2
1
1
3
1
0
1
1
1
1
1
2
2
0
0
2
1
3
2
1
2
1
1
1
1
1
0
1
0
1
1
1
2
2
1
2
2
1
2
2
1
2
0
1
2
1
1
1
0
2
0
2
0
1
1
2
2
1
1
1
0
0
0
1
1
1
1
1
1
0
1
1
1
2
0
2
2
1
1
1
1
0
1
1
1
1
1
0
1
1
1
2
1
1
1
1
0
0
1
1
2
1
1
2
2
2
1
1
2
1
1
1
0
0
1
1
1
1
1
1
1
1
1
1
2
0
1
1
0
1
0
0
1
0
0
0
1
2
1
1
1
3
2
2
1
0
0
1
2
2
1
1
1
0
0
2
0
3
1
0
1
1
2
0
2
1
1
1
2
2
2
1
1
1
1
0
1
1
1
0
1
1
2
1
1
2
0
1
1
1
1
1
2
1
2
0
1
2
1
1
2
2
1
2
2
2
0
1
3
1
1
1
1
1
0
1
2
1
1
2
2
0
2
1
0
0
1
1
1
0
2
0
1
1
1
2
0
1
2
2
1
1
1
1
1
2
1
1
0
1
0
0
1
1
1
1
1
1
0
1
1
2
0
1
0
1
2
2
2
1
1
2
1
1
1
1
0
1
1
1
1
1
2
1
1
2
1
2
1
1
2
1
1
1
1
1
2
3
1
0
1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
2
1
1
2
1
1
1
1
1
0
1
1
1
2
1
1
2
1
2
1
2
1
2
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
0
1
1
2
1
1
1
2
1
1
3
2
0
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
2
2
1
1
1
0
1
1
1
2
0
1
2
1
1
3
1
1
1
1
2
0
0
2
1
1
2
1
2
1
1
0
2
1
3
2
1
1
1
2
1
2
1
1
0
1
1
0
1
0
0
1
2
1
1
1
2
0
1
2
1
2
0
1
1
1
0
1
1
1
2
1
1
3
2
1
1
1
1
0
2
1
2
1
2
1
1
1
0
1
1
0
1
1
1
2
1
1
1
1
2
1
2
1
2
1
1
1
0
0
2
1
1
1
1
2
0
2
2
1
1
1
1
2
1
0
1
0
1
2
2
1
1
1
1
1
1
1
0
2
1
1
2
1
2
1
1
2
1
1
2
1
1
0
1
0
1
0
2
0
1
1
1
1
1
1
2
2
1
2
1
2
1
0
1
2
2
0
2
0
2
1
1
1
1
1
0
0
2
1
1
2
2
1
2
0
0
1
1
0
2
1
1
1
1
2
2
0
1
2
2
0
1
1
1
2
1
2
2
0
1
0
1
0
2
0
1
1
1
2
0
1
2
2
0
1
2
2
1
1
2
1
1
1
2
1
1
1
1
0
2
1
2
1
1
1
1
1
0
1
1
1
1
0
5
1
1
1
0
1
1
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
0
0
1
1
1
2
2
1
1
0
1
1
1
1
1
0
1
1
2
2
1
1
1
2
1
1
1
2
0
1
1
2
2
2
1
1
2
1
0
1
1
2
1
1
1
2
1
2
1
0
0
0
1
1
0
1
1
1
1
1
1
2
1
2
1
1
0
0
1
2
1
0
1
0
1
1
0
2
1
1
1
1
2
1
2
1
0
1
2
1
1
0
1
2
2
0
1
1
2
1
0
2
1
1
1
1
2
2
3
0
1
1
1
1
1
1
1
2
2
1
1
1
0
1
2
1
5
2
1
0
1
1
0
1
1
2
0
1
1
1
2
1
1
1
1
0
1
1
1
0
1
0
1
0
1
2
0
1
1
1
1
2
1
1
1
0
1
1
1
1
0
1
1
1
1
1
2
1
1
1
1
1
0
0
1
1
1
1
2
0
0
1
0
1
1
0
1
2
1
0
1
0
1
1
1
2
0
2
3
2
1
1
1
1
0
1
2
2
1
2
0
1
1
1
2
1
2
2
1
1
1
1
0
1
1
2
1
2
0
1
1
1
1
0
1
1
1
2
1
1
1
1
2
0
1
1
0
1
0
1
0
1
1
2
2
1
2
0
1
1
2
0
1
1
1
1
2
1
1
2
1
2
1
1
1
2
1
1
1
0
1
0
2
1
1
1
1
2
0
1
1
1
1
1
0
1
2
2
1
1
1
1
2
2
1
1
1
0
0
1
1
1
1
1
2
1
2
2
3
2
1
0
1
1
1
1
1
0
2
2
1
1
1
1
2
2
2
2
2
1
1
2
1
2
1
2
0
2
1
1
1
1
2
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
2
1
1
1
3
1
1
1
0
1
1
2
1
2
2
1
0
1
2
1
0
1
2
1
1
0
1
1
1
0
2
0
1
0
1
1
0
1
2
1
0
0
1
1
2
1
1
1
2
1
1
1
2
2
2
2
0
1
2
2
1
2
1
2
1
0
1
1
2
1
1
1
1
1
2
2
1
1
1
0
0
1
2
1
0
2
1
2
1
0
1
0
1
1
1
1
1
1
2
3
1
1
5
2
2
1
0
0
1
2
1
1
0
0
1
0
1
2
0
1
1
1
1
1
1
0
0
1
0
2
1
1
1
1
0
1
1
1
1
1
2
1
0
2
0
1
1
1
1
1
1
0
1
1
1
1
0
2
1
1
1
1
0
1
1
2
1
1
1
2
1
1
1
2
1
1
1
0
1
1
1
1
0
1
0
1
0
2
1
1
1
1
1
3
2
1
1
2
1
1
1
1
2
1
1
0
1
1
0
1
1
0
1
1
1
2
2
1
1
2
0
1
1
1
2
1
1
1
1
0
1
1
2
2
2
1
2
2
0
1
2
1
2
0
1
1
1
1
1
0
1
1
1
1
1
1
2
1
2
0
0
1
2
1
1
1
1
1
0
1
0
2
2
2
2
1
1
1
1
2
1
1
1
1
0
1
1
1
2
2
1
1
1
1
0
1
2
1
1
1
2
0
2
1
2
1
1
1
1
0
2
1
2
1
2
1
1
1
2
0
1
1
1
1
1
1
1
1
1
0
1
2
1
1
0
2
0
1
3
1
2
2
1
0
1
0
1
0
1
1
0
0
0
0
2
1
2
1
1
2
1
2
0
1
1
0
0
2
1
2
1
2
1
1
1
1
1
0
0
1
2
2
1
0
0
1
1
0
2
1
2
2
1
1
2
1
1
1
0
1
0
0
1
1
1
2
0
1
1
2
1
1
1
2
1
2
0
2
2
1
1
2
1
2
1
1
1
2
1
1
1
1
2
1
1
2
1
2
2
1
2
1
0
1
2
1
2
2
1
1
1
2
1
1
1
2
0
1
1
0
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
0
0
1
2
1
1
0
2
1
2
2
1
2
0
1
1
0
1
1
1
1
2
0
1
1
1
1
0
1
1
0
1
1
1
2
1
1
1
1
1
0
1
0
1
4
2
1
1
2
1
1
1
1
1
2
0
1
1
1
0
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
0
1
2
1
0
0
0
1
1
1
1
1
1
1
1
1
2
0
1
1
1
1
2
2
1
1
0
1
1
1
3
1
0
2
0
1
1
2
1
1
0
2
1
1
0
0
1
1
0
2
1
1
1
1
2
1
2
2
2
1
0
1
0
2
1
1
2
0
1
1
2
2
1
2
1
2
1
0
1
2
1
1
2
1
1
0
1
2
1
2
1
1
1
0
1
1
1
1
2
1
2
1
2
1
0
1
1
2
0
0
1
1
1
1
1
1
0
1
2
0
1
0
1
1
1
1
1
2
1
2
1
1
1
3
2
2
1
1
1
0
1
1
0
1
1
1
1
1
2
1
2
1
1
2
1
0
1
2
1
1
1
1
0
0
1
1
2
0
1
2
1
1
2
2
1
1
2
0
1
1
1
1
2
2
1
1
1
1
1
1
2
1
1
0
0
1
1
2
1
1
2
1
1
1
1
0
2
2
1
2
2
1
0
0
1
0
2
1
1
0
1
2
0
0
2
2
1
0
0
1
1
1
2
2
1
1
1
1
1
1
1
2
2
2
2
2
1
1
1
0
2
0
1
0
2
1
0
1
1
1
2
0
2
1
1
2
1
0
1
0
2
1
1
1
1
2
1
1
0
1
1
2
1
1
2
1
2
1
1
1
0
1
1
0
1
1
2
1
1
1
1
1
3
1
1
0
1
2
1
2
1
0
1
1
1
2
1
1
1
1
1
1
0
1
1
1
1
2
1
1
1
2
2
2
1
1
1
1
1
2
2
1
2
1
1
0
1
2
1
2
0
2
0
0
0
1
1
1
1
1
2
1
0
1
2
2
2
1
2
1
1
1
0
1
1
0
2
0
2
1
0
1
0
1
2
2
1
1
2
0
1
1
1
1
0
2
1
1
1
1
1
1
0
1
0
1
1
1
1
0
2
2
0
1
1
1
1
0
1
0
1
0
1
2
2
2
4
1
2
0
2
2
1
1
2
1
1
0
1
1
2
2
2
1
2
1
2
0
0
1
0
0
0
1
2
2
1
2
0
0
1
1
0
1
1
1
1
1
1
1
1
1
1
2
2
1
0
1
1
2
1
1
1
1
1
2
1
0
1
1
1
1
1
1
1
1
0
1
0
2
1
0
2
1
1
1
1
1
2
2
1
0
0
1
2
0
1
2
1
0
1
0
0
1
1
1
2
1
1
1
2
2
2
1
1
3
2
1
1
1
1
1
1
0
0
1
2
1
2
1
2
2
2
2
2
2
1
2
2
2
2
1
1
1
0
0
1
3
0
1
1
1
1
2
0
1
1
2
2
2
2
1
0
1
2
1
1
1
1
2
0
1
1
2
1
0
0
1
1
1
0
1
1
1
2
1
1
0
0
1
0
1
1
0
2
2
0
1
0
1
1
1
1
1
1
2
2
1
1
0
1
1
1
0
1
0
1
1
0
2
1
2
1
1
1
1
1
1
2
2
0
2
1
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
0
2
2
1
1
1
1
1
2
2
1
1
1
0
1
0
1
2
1
0
1
0
1
0
1
2
0
1
1
1
0
3
2
0
0
0
1
1
1
0
1
0
1
1
1
2
0
1
1
0
1
1
2
1
1
1
1
1
1
0
2
1
2
2
1
0
2
1
1
1
2
1
0
2
1
1
1
0
2
1
2
1
1
1
2
1
0
1
0
2
2
0
0
2
1
2
0
2
2
1
1
0
1
1
1
0
2
0
1
1
0
2
1
2
1
1
2
2
1
1
1
1
2
1
1
1
0
2
1
1
0
1
1
1
2
0
1
1
1
2
1
1
1
1
2
1
1
1
1
0
2
2
2
1
1
2
1
1
1
0
1
1
1
0
1
1
1
1
2
2
1
1
1
1
1
1
2
2
1
0
1
1
1
1
1
2
0
2
1
2
2
1
1
1
1
1
2
2
2
2
1
1
1
2
1
1
0
2
1
1
1
0
0
1
1
2
2
1
0
1
2
1
1
1
1
2
2
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
1
0
1
1
2
2
1
0
1
1
1
1
1
1
2
2
1
2
1
1
1
1
2
2
1
2
1
2
0
2
2
1
1
1
1
1
2
1
1
1
1
1
2
1
0
0
1
0
1
2
0
2
2
1
1
1
1
1
1
0
0
1
1
1
1
1
0
0
1
2
1
1
1
2
1
1
1
1
0
2
1
0
1
1
1
1
0
1
1
1
1
1
2
1
1
0
2
1
2
2
1
0
0
2
0
2
0
1
1
1
1
1
0
0
1
0
1
1
1
2
2
1
1
0
1
1
0
1
0
1
1
1
1
1
2
1
1
2
2
0
1
0
1
2
1
2
0
2
2
0
0
1
1
1
1
0
0
1
1
1
1
1
1
2
1
1
1
1
1
1
1
0
1
2
1
1
1
1
0
2
1
1
0
1
1
1
1
0
1
1
1
1
1
1
1
2
1
1
1
0
3
2
1
0
1
2
0
1
1
1
1
0
0
2
0
1
1
2
1
1
1
2
2
2
1
2
1
1
1
1
1
1
1
0
1
0
1
1
1
1
1
1
0
0
2
2
1
1
1
1
2
2
0
0
2
2
2
1
1
1
1
2
3
1
2
1
1
1
1
0
1
0
2
1
1
1
1
2
1
2
1
1
1
1
2
0
0
0
1
2
1
2
1
1
1
1
2
1
1
2
2
2
0
1
0
2
2
1
2
2
1
2
1
1
2
0
1
1
1
2
2
1
0
1
1
1
1
1
3
1
2
1
1
2
2
0
2
2
1
1
1
1
1
1
0
1
1
0
0
1
1
1
1
0
1
0
0
2
1
0
1
0
1
2
2
2
2
1
0
0
1
2
0
1
1
2
2
2
2
1
0
1
1
1
1
0
1
1
1
0
1
1
1
1
2
0
1
1
1
2
1
0
1
2
1
0
1
1
2
0
1
1
1
0
1
1
1
1
1
0
1
1
1
2
1
2
1
1
1
2
2
2
1
2
2
1
1
2
1
0
2
2
0
1
1
1
1
1
1
0
1
1
1
0
1
0
0
1
2
1
1
1
1
1
0
1
1
2
1
1
1
2
0
2
0
1
0
2
1
2
1
1
1
1
1
1
1
1
1
1
1
2
0
2
1
1
2
1
2
1
0
1
1
1
1
2
2
2
2
0
2
2
0
3
0
2
1
2
0
1
0
1
0
0
2
1
2
2
1
0
2
1
2
1
1
0
1
2
1
1
1
0
1
1
2
2
1
2
0
1
0
0
2
0
1
0
1
2
1
1
2
1
1
0
2
1
1
1
0
1
1
1
1
1
1
0
1
1
1
2
1
1
1
0
2
1
0
1
1
1
0
1
1
0
1
1
2
1
2
2
1
2
1
1
2
2
1
2
1
1
2
1
1
1
0
1
1
1
1
1
1
1
2
0
1
2
0
1
1
0
2
0
2
2
1
2
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
2
2
1
0
0
1
3
1
2
0
1
0
1
1
1
0
1
1
1
1
1
1
1
1
2
0
1
1
1
1
1
3
0
2
0
1
2
1
1
1
0
1
1
1
2
1
2
1
0
3
1
2
1
1
1
1
1
1
1
2
1
2
2
1
0
1
0
2
2
1
2
1
3
1
2
2
1
1
2
1
2
2
1
1
1
2
1
1
2
1
1
0
0
1
1
1
1
1
2
2
1
1
1
0
2
1
1
1
1
2
0
0
1
1
1
1
1
1
1
1
1
0
1
2
2
1
1
1
3
1
1
2
1
0
0
2
2
1
1
1
1
1
1
2
1
1
0
0
1
0
2
2
0
1
1
2
2
2
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
0
2
1
2
1
1
0
1
1
1
1
0
2
1
2
1
2
0
2
0
2
1
1
1
2
1
1
1
1
2
1
1
2
0
2
1
2
1
1
1
1
1
0
2
2
2
1
1
2
2
2
1
1
0
1
1
2
0
1
2
2
1
1
1
1
2
1
1
1
2
1
1
1
1
1
2
1
0
1
2
0
2
1
1
1
1
1
1
1
1
1
2
1
1
1
0
0
1
1
1
1
1
2
2
2
1
0
1
1
1
1
1
2
1
1
1
1
0
1
0
2
0
1
2
1
1
1
2
1
1
0
1
2
2
1
2
1
2
1
1
1
1
0
1
1
1
1
1
1
1
1
0
1
1
1
1
1
0
1
2
2
1
1
2
2
1
1
1
0
1
1
2
1
2
2
2
1
1
1
2
1
1
1
0
0
1
3
0
1
1
1
1
1
2
0
2
1
1
1
2
0
1
1
1
1
2
1
1
0
1
2
1
1
2
1
1
1
0
1
1
2
1
1
1
1
1
0
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
2
1
1
2
2
0
2
1
1
1
2
2
1
1
1
0
0
1
1
1
2
1
1
0
1
1
1
1
1
0
1
1
1
1
2
2
1
1
1
2
2
1
1
2
2
1
2
1
2
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
0
2
0
1
2
1
1
0
0
2
1
1
1
1
2
1
1
1
1
1
1
0
1
0
2
1
2
1
0
1
1
1
1
1
2
2
1
1
1
2
1
1
1
1
1
1
2
1
1
0
1
1
1
2
2
1
2
1
0
1
1
0
1
2
2
1
1
2
2
2
0
1
1
2
0
1
2
0
1
0
0
1
1
1
2
0
2
2
2
1
2
1
1
1
1
0
1
1
2
1
1
1
1
2
2
2
2
1
1
0
1
1
1
1
0
1
0
1
1
0
1
1
2
1
2
1
2
2
1
1
1
2
0
0
2
1
0
1
1
0
0
3
2
2
0
1
1
1
1
1
0
1
1
1
1
1
1
0
1
2
1
2
1
0
1
1
1
1
1
2
1
1
1
2
1
1
1
1
2
2
0
1
1
1
1
1
1
1
1
0
1
1
0
1
1
1
2
1
1
2
1
1
1
2
1
1
1
1
1
4
0
1
0
1
1
1
0
1
1
0
2
1
1
1
0
1
1
1
1
1
1
0
0
1
1
1
1
1
1
1
1
1
1
0
1
1
0
0
2
2
1
1
1
0
1
1
1
1
2
1
1
1
1
1
1
0
1
1
1
2
1
2
1
1
1
1
0
0
1
1
1
1
1
1
1
1
0
0
2
2
1
0
2
1
2
1
1
1
1
1
1
1
1
1
0
2
1
0
2
0
1
1
0
1
0
1
2
1
0
2
1
3
1
2
0
1
1
1
1
0
1
1
0
1
2
1
1
2
0
1
0
1
1
1
0
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
1
0
2
1
1
0
2
1
1
1
1
1
1
1
1
0
2
1
3
0
1
1
1
2
2
1
0
1
2
1
0
2
1
2
2
0
1
2
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
0
1
1
1
1
0
0
3
2
1
1
2
1
2
1
1
2
0
1
0
1
1
2
2
0
1
1
1
2
2
1
1
1
1
2
1
1
2
1
1
1
2
1
1
1
1
2
0
2
2
1
0
2
1
1
2
1
1
2
1
2
2
2
1
0
2
2
2
1
2
2
2
1
1
1
1
2
2
1
2
1
2
0
1
0
1
1
2
1
2
2
2
1
2
2
1
1
1
0
1
1
1
1
1
0
1
2
1
1
1
1
1
1
0
1
1
2
3
1
1
1
2
1
1
2
2
0
2
2
1
2
2
1
0
4
1
1
1
1
1
1
0
1
0
1
0
2
4
1
1
1
2
2
0
0
1
2
1
0
1
1
1
2
1
1
1
1
1
1
1
1
0
2
1
2
0
2
1
1
1
2
1
2
1
0
0
2
1
1
2
1
1
1
1
2
1
2
2
2
1
2
1
1
1
1
2
0
0
0
1
1
2
1
1
0
0
2
1
2
1
1
3
0
1
0
1
0
2
1
2
1
1
2
2
1
1
1
0
1
0
0
1
1
1
1
1
1
2
1
1
2
2
1
1
1
1
2
2
1
1
1
2
2
1
1
1
0
1
1
2
1
0
1
1
1
1
1
1
1
2
2
1
2
0
0
1
2
2
1
1
1
1
2
2
0
1
2
1
1
1
1
1
1
1
1
1
0
1
2
0
1
2
1
1
2
1
2
0
1
1
1
1
1
1
1
2
1
1
2
0
0
1
1
1
2
1
2
2
0
1
1
1
1
1
1
2
1
0
1
0
0
0
1
2
1
2
1
1
1
1
1
1
1
0
1
1
2
1
1
0
2
2
1
2
2
1
2
0
1
0
1
1
2
1
1
1
1
1
1
1
1
0
2
0
2
1
1
1
1
1
2
1
3
6
0
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
2
2
1
1
3
1
2
1
1
0
1
2
1
0
1
2
1
2
0
1
1
2
2
1
1
0
1
0
1
0
2
1
2
1
0
2
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
2
1
1
0
2
1
1
0
0
0
1
2
1
2
1
1
1
0
1
1
1
1
2
1
0
1
0
1
0
0
1
0
1
0
1
0
1
2
0
1
1
2
2
1
2
2
0
1
2
2
1
0
0
1
0
0
2
1
1
1
1
1
1
1
1
0
1
1
2
2
1
1
1
1
2
1
0
2
1
2
1
2
1
1
0
2
1
2
0
1
1
1
1
1
1
1
2
2
0
1
0
3
1
1
1
1
1
1
1
1
1
2
2
1
1
0
1
1
1
1
1
0
1
2
1
2
0
1
1
1
0
1
1
0
1
2
1
1
2
2
0
1
1
1
1
0
1
1
2
1
1
2
1
0
1
1
1
2
0
2
2
1
1
2
1
2
1
1
2
0
0
1
0
1
2
2
1
2
1
2
2
1
2
2
1
1
1
0
1
1
0
1
1
1
1
0
1
1
0
1
2
1
1
2
2
2
1
1
2
0
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
0
0
2
2
1
1
1
1
1
1
1
0
1
1
2
1
2
2
1
1
3
2
0
1
1
1
2
1
1
1
1
3
1
1
1
2
1
1
0
0
1
1
1
2
1
1
1
1
1
1
0
1
2
1
1
1
2
1
0
3
2
1
1
1
0
1
1
2
0
2
0
2
1
1
2
1
1
1
1
2
0
1
1
0
1
2
2
1
2
2
0
2
0
0
1
2
1
2
1
1
1
1
1
1
1
1
1
0
1
1
1
0
1
1
2
1
1
0
0
2
1
0
1
1
1
0
0
1
1
1
0
0
3
1
0
2
1
1
2
2
0
1
1
1
0
1
2
1
1
1
1
1
1
0
1
2
1
1
2
1
0
1
2
0
1
0
1
1
1
1
1
1
1
2
1
0
1
1
2
0
1
1
0
1
2
1
1
0
1
1
2
1
1
1
1
2
1
1
2
1
1
2
1
1
1
2
1
1
1
0
2
1
2
1
1
1
0
0
1
2
1
1
1
0
1
1
2
2
2
1
1
1
1
0
2
2
1
1
1
0
0
0
2
1
1
1
2
1
1
2
1
1
0
0
1
1
0
2
2
1
1
1
2
2
0
3
1
1
2
2
1
1
2
1
2
1
2
1
2
1
0
1
0
1
2
1
1
0
1
1
0
1
1
2
1
1
1
1
1
1
1
2
1
1
2
1
0
1
1
1
1
1
2
1
1
1
1
0
2
1
1
1
1
2
1
1
0
0
1
1
1
1
1
1
1
1
0
1
2
1
1
0
0
1
2
1
1
1
1
2
1
2
1
0
1
1
2
1
0
2
3
1
1
2
1
0
1
0
0
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
0
0
2
1
0
1
1
2
1
2
1
1
1
0
1
1
0
1
1
2
0
2
1
1
2
1
2
1
1
1
1
1
2
2
1
3
1
1
0
1
0
2
0
2
1
1
1
1
1
1
1
1
0
1
1
1
2
2
2
2
0
0
1
2
0
1
0
1
2
1
2
1
2
1
1
1
0
2
1
1
2
2
2
5
2
1
0
1
1
2
1
1
1
1
1
1
1
2
2
0
1
1
1
1
1
1
0
1
1
1
0
2
1
1
1
1
1
2
2
0
0
1
1
2
0
1
1
2
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
0
1
0
2
1
1
1
2
1
1
1
1
2
1
1
1
0
2
1
1
1
2
0
1
1
1
1
1
1
1
1
1
2
0
1
1
1
2
1
1
1
1
2
1
1
0
1
1
0
1
1
2
1
0
1
2
1
2
1
1
1
1
0
2
1
1
2
1
1
1
0
2
1
1
1
1
1
2
1
1
1
2
1
0
1
0
0
1
2
1
1
1
1
1
2
1
1
2
1
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
2
0
1
1
1
1
2
2
2
1
2
2
1
1
1
2
1
0
2
1
2
2
2
1
2
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
0
1
1
1
1
0
1
0
0
1
2
1
2
1
1
1
1
1
0
0
1
1
1
1
1
1
0
2
0
1
2
2
2
0
0
2
2
1
1
1
2
1
3
0
2
0
1
2
1
2
2
1
2
1
1
1
1
1
1
2
1
1
1
1
0
2
2
1
1
1
1
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
3
0
2
0
1
1
1
2
1
2
1
1
1
0
0
1
0
2
1
2
1
2
2
1
1
0
0
1
0
0
1
0
1
1
1
1
0
2
2
1
2
2
1
1
1
1
1
1
1
0
2
0
2
0
1
1
1
1
1
1
1
1
1
1
1
0
1
2
2
1
1
1
1
2
1
0
1
2
1
1
1
2
0
1
1
1
0
1
1
5
1
2
1
1
1
1
1
1
1
1
1
1
0
1
2
0
0
1
1
0
1
1
1
0
1
1
0
1
2
1
1
1
2
0
1
1
1
1
0
0
1
1
2
1
0
2
2
1
2
0
1
1
1
1
0
2
1
1
3
2
1
0
0
1
0
1
2
1
1
2
1
1
0
1
2
1
2
1
0
0
2
1
1
1
2
0
0
1
2
1
1
1
1
2
2
1
2
2
1
1
1
2
2
1
1
0
2
1
1
2
1
2
1
0
2
1
2
1
0
2
2
0
0
2
1
1
1
2
1
1
1
1
0
0
1
1
1
1
1
2
1
1
0
2
1
1
1
1
1
2
2
0
1
2
0
1
2
1
0
0
1
1
2
0
2
0
2
0
0
2
1
1
1
1
1
0
1
2
2
2
1
2
1
0
1
1
1
2
2
1
1
1
1
1
2
2
1
1
2
1
2
1
1
1
0
1
1
1
1
1
1
1
2
1
0
2
2
1
2
1
2
2
2
2
1
1
0
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
0
0
2
2
1
2
1
2
0
2
1
2
1
1
2
1
1
0
1
1
1
2
1
1
2
1
2
1
2
0
3
0
1
1
1
1
2
1
1
1
0
2
0
1
2
1
1
1
2
1
2
1
2
1
1
1
1
0
1
2
1
0
2
1
1
0
1
2
1
1
1
2
1
1
1
2
1
1
2
1
2
1
1
1
1
2
1
2
1
1
0
1
2
1
0
2
1
1
1
2
0
1
1
2
2
1
2
0
1
1
2
1
1
1
2
1
0
0
2
0
2
2
2
1
2
1
1
1
0
1
1
0
1
1
1
0
0
0
0
1
2
2
2
0
1
2
2
2
1
1
0
1
1
1
1
1
1
1
2
1
1
0
2
2
3
1
1
1
1
1
1
1
2
1
1
2
1
1
1
2
0
1
1
1
1
1
2
1
1
1
0
1
1
1
1
2
0
1
0
1
2
1
2
1
2
1
1
2
2
0
1
0
1
0
1
1
2
1
2
2
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
0
1
1
1
1
1
1
0
1
1
1
0
1
0
0
2
2
2
1
1
1
1
0
2
1
3
1
1
2
2
1
1
1
1
1
1
0
1
2
2
1
0
1
1
2
0
1
1
2
1
1
1
0
1
1
0
1
1
1
1
1
1
1
0
1
1
1
2
1
2
2
2
2
1
2
1
1
1
2
0
1
2
2
1
1
0
1
2
1
0
1
1
0
2
1
1
2
1
1
2
1
1
1
1
2
2
1
0
1
1
1
0
1
1
1
2
1
2
0
0
1
1
1
1
1
1
1
1
2
2
1
2
1
1
0
1
0
1
1
1
2
1
1
1
1
1
0
1
1
1
1
1
1
1
2
0
1
1
1
1
1
1
1
1
2
2
2
1
2
1
1
2
0
0
2
1
1
1
1
1
1
1
0
2
1
2
2
1
1
0
1
2
1
2
1
1
1
2
2
2
1
2
0
2
1
2
1
0
0
1
1
0
1
0
2
1
1
0
2
1
1
2
1
1
1
1
1
1
1
2
1
1
2
2
1
2
1
1
1
1
1
1
1
1
2
2
0
1
1
1
1
2
1
2
1
1
2
1
2
2
1
0
1
1
1
2
0
1
0
1
2
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
0
1
1
2
2
1
2
1
2
0
1
2
2
1
0
1
1
2
1
2
1
1
2
1
1
2
1
2
1
2
1
1
1
1
1
1
2
1
1
2
1
2
1
1
1
1
1
1
0
2
2
3
0
2
1
2
0
1
1
1
1
0
2
1
0
2
1
1
1
1
1
1
2
1
2
1
0
0
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
0
1
1
2
1
2
2
2
2
2
3
1
0
1
0
1
2
1
1
1
0
1
1
2
2
1
2
2
1
2
1
2
1
2
1
1
2
1
2
1
1
0
0
1
3
2
1
1
0
1
1
2
1
2
1
2
1
2
1
2
1
2
1
1
0
1
1
2
1
0
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
0
2
1
0
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
0
0
1
0
1
1
0
1
3
1
1
1
2
1
1
1
1
0
0
1
2
2
0
1
0
1
2
1
0
1
2
0
1
1
2
1
1
2
1
1
0
2
1
2
1
1
1
1
1
1
1
1
0
1
2
0
1
2
1
2
1
1
1
1
0
0
1
1
1
2
1
2
1
0
0
1
0
2
1
1
2
0
1
1
1
1
0
2
0
2
0
1
1
0
1
1
0
1
2
0
1
1
0
1
1
1
0
2
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
0
1
1
1
0
1
1
1
0
1
1
1
2
2
2
1
1
1
2
2
0
2
1
1
1
1
1
0
1
1
0
1
2
1
0
1
1
1
1
0
1
0
2
1
0
1
1
1
0
2
1
1
1
0
1
1
2
2
1
1
0
2
0
1
2
0
0
1
1
0
0
1
2
2
0
2
2
2
0
2
2
2
0
0
1
1
0
1
1
2
2
0
1
1
1
1
0
1
2
2
1
1
1
1
1
0
2
1
1
1
1
1
1
1
1
2
0
1
2
1
1
2
2
0
1
1
2
1
1
1
1
1
0
1
2
2
1
1
2
1
1
1
2
1
0
1
2
1
2
1
1
3
1
0
1
1
1
1
1
2
1
1
2
1
2
1
0
2
1
0
1
1
1
1
2
0
1
1
1
1
1
1
1
1
0
0
1
2
3
2
1
0
0
1
1
2
2
0
1
2
1
2
1
1
1
1
1
2
0
1
2
2
1
1
0
2
3
1
1
1
1
1
2
0
1
1
1
1
1
2
1
0
2
2
4
1
0
1
2
1
1
0
2
2
1
2
3
2
1
0
1
2
2
2
2
2
1
0
2
2
0
2
1
1
0
2
2
0
2
0
0
1
2
1
0
1
1
0
3
1
1
0
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
0
1
1
1
1
2
0
2
1
1
2
2
2
2
2
2
1
1
0
2
1
2
2
0
1
1
1
2
0
2
0
0
2
0
1
0
2
1
2
0
2
0
1
1
1
2
1
0
1
2
1
1
2
0
2
0
0
1
1
1
0
1
2
1
1
1
1
2
4
1
1
0
2
1
1
1
2
1
4
2
0
1
1
0
1
1
0
1
2
1
0
1
1
1
1
2
2
2
2
1
1
1
1
0
2
1
0
2
1
1
1
2
1
2
0
3
1
1
1
1
1
2
1
1
2
1
2
2
2
1
1
0
2
0
1
1
1
1
2
2
1
1
1
2
1
2
1
2
1
2
1
2
1
2
2
1
1
1
0
1
1
1
2
1
2
1
1
1
1
0
1
1
1
1
1
0
1
1
1
1
0
0
2
1
2
1
1
1
2
1
1
1
1
1
1
2
1
1
2
1
1
2
1
1
1
0
1
2
1
2
1
1
0
1
1
1
1
1
1
1
2
2
1
0
2
1
1
1
1
1
1
1
1
1
2
1
0
0
2
2
1
1
2
0
1
0
1
1
1
3
1
1
1
1
2
0
2
1
2
2
1
2
2
1
3
0
1
1
0
0
0
1
1
2
0
2
1
1
2
1
1
1
1
1
0
2
1
2
2
1
0
1
2
0
2
3
1
1
1
2
1
1
1
1
1
2
2
1
2
1
2
2
1
0
1
2
2
1
1
1
1
2
1
1
1
1
1
1
2
2
0
0
1
1
0
2
1
1
1
1
1
1
1
2
1
0
1
2
2
1
0
2
2
1
1
1
1
2
1
2
1
2
1
1
1
2
1
2
1
0
2
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
0
1
1
2
2
1
2
1
1
2
1
1
3
2
1
0
1
1
1
1
1
1
1
1
1
3
2
0
1
1
0
2
2
1
1
1
0
1
1
2
1
1
1
1
1
2
1
2
0
1
1
1
0
1
0
1
1
1
2
1
1
1
1
1
0
1
0
1
1
1
1
1
0
0
1
1
1
1
1
0
1
1
1
2
1
5
1
2
1
2
1
1
1
1
1
1
1
0
2
1
0
2
2
1
1
1
1
0
1
1
2
1
1
0
2
1
1
0
1
2
1
1
1
1
1
0
1
0
1
1
1
2
0
1
1
1
2
1
1
0
1
1
1
1
0
0
2
2
1
1
1
1
1
1
1
1
0
1
1
1
0
1
1
2
0
1
1
1
1
1
1
0
2
3
1
1
2
1
0
2
1
1
1
2
2
1
2
1
0
2
1
1
1
1
1
2
0
1
1
1
1
1
1
0
2
1
0
2
1
0
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
0
1
0
2
1
1
0
1
1
3
1
2
1
1
1
1
2
1
1
1
0
2
0
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
0
2
1
0
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
0
1
1
2
1
0
2
1
1
0
0
1
1
2
2
1
0
1
1
1
2
2
1
2
1
2
2
2
2
2
1
1
1
4
2
1
1
1
2
2
2
2
1
1
2
1
2
2
1
1
1
0
1
1
1
2
1
1
2
0
2
3
1
0
1
1
0
1
2
0
1
1
1
1
1
2
1
2
1
1
0
1
1
1
0
2
1
1
0
1
1
0
0
1
2
0
1
1
1
1
1
1
2
0
1
2
2
1
1
1
1
2
0
0
1
0
1
1
1
1
2
1
2
1
1
1
1
2
2
1
0
1
1
1
1
1
0
1
2
1
1
2
1
1
2
1
1
1
1
1
0
1
2
1
2
1
1
1
2
1
1
1
1
1
1
0
2
2
0
1
2
2
2
2
1
2
2
1
2
1
1
0
0
1
2
1
2
1
1
2
1
2
1
0
2
0
0
2
2
2
1
0
1
1
1
0
1
1
1
1
8
1
2
1
1
2
1
1
1
1
2
1
2
0
2
1
1
1
1
2
1
2
2
0
1
1
2
1
2
1
2
1
1
1
2
1
1
1
1
2
1
1
2
2
1
1
1
0
1
1
1
1
1
1
1
1
0
2
1
1
2
1
1
2
1
1
2
2
2
1
0
2
2
2
2
1
1
2
1
1
0
1
2
2
0
1
0
0
1
1
1
1
1
0
0
1
2
0
0
1
1
1
1
0
1
1
1
0
2
1
1
0
2
2
2
1
3
0
1
1
4
1
2
0
1
2
1
1
2
2
0
1
2
1
2
2
0
0
1
1
1
1
2
2
2
2
0
1
0
0
1
1
0
0
1
2
1
1
1
1
0
1
1
2
1
1
1
0
0
1
2
2
0
2
1
1
1
0
1
1
1
2
2
1
1
1
1
1
1
0
1
0
1
1
1
1
1
2
1
2
1
2
1
1
2
2
2
0
1
0
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
1
0
1
1
1
2
1
1
1
2
1
2
0
1
1
1
1
1
2
1
1
2
1
2
1
1
1
2
2
2
1
1
1
1
2
1
2
0
1
1
2
1
2
2
1
1
1
1
1
2
1
0
1
1
0
1
1
0
1
1
0
0
0
1
0
1
2
2
1
1
1
1
1
1
1
1
2
0
2
0
0
1
2
1
0
1
1
1
2
2
1
1
1
1
0
1
1
1
1
1
1
1
0
0
2
1
1
0
1
1
2
1
1
0
1
1
1
1
1
1
0
2
1
1
1
0
1
1
2
1
1
2
1
1
0
1
1
1
2
1
2
2
1
0
2
0
2
1
1
1
1
1
1
1
2
2
0
1
1
1
2
1
2
1
1
1
1
0
1
2
1
1
0
0
2
1
0
1
1
1
2
1
1
2
0
0
1
1
1
1
1
2
1
1
1
1
1
0
2
1
0
0
1
2
1
1
0
0
1
2
1
1
2
1
1
2
2
1
1
1
1
0
0
0
0
0
1
1
1
2
2
2
1
1
1
0
1
1
2
1
1
0
1
1
2
1
0
1
1
2
2
2
1
0
1
1
2
1
2
2
1
1
1
1
1
1
2
1
2
1
2
1
2
1
0
0
1
0
1
1
1
1
2
2
0
1
1
1
0
1
3
1
1
0
1
3
0
1
1
2
1
2
1
0
1
1
2
2
1
1
1
0
2
1
0
1
1
1
1
2
2
2
1
2
0
1
1
1
1
0
0
1
3
2
2
1
2
1
2
1
1
1
1
2
1
2
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
2
1
1
1
1
2
1
2
1
1
2
2
1
1
2
1
1
0
1
1
1
0
0
1
2
2
1
1
1
1
0
1
2
2
1
1
0
1
2
1
1
1
2
1
1
1
2
0
1
2
2
2
2
1
1
1
1
1
1
2
0
1
1
2
1
2
1
2
0
1
1
1
2
0
1
2
1
2
1
0
1
1
2
1
1
1
1
0
1
0
1
2
1
1
1
1
1
2
1
1
0
1
2
2
1
1
2
1
2
1
2
0
1
1
1
1
1
1
1
0
2
1
2
2
0
0
2
0
1
1
2
2
1
1
2
1
1
2
1
2
0
1
2
2
0
2
1
1
1
1
1
1
0
2
1
2
1
1
1
1
2
0
1
2
1
2
2
2
1
2
1
1
1
1
2
1
1
2
1
1
2
1
2
1
1
1
1
0
2
2
0
2
1
2
1
2
1
2
1
0
0
0
1
1
1
1
0
2
1
2
1
1
1
1
1
0
2
2
1
1
1
1
2
2
1
2
0
2
1
2
2
1
0
2
1
0
1
0
1
0
2
0
2
2
1
2
1
1
2
1
0
1
2
1
1
2
1
1
1
1
1
2
1
1
1
1
2
2
1
1
1
1
1
1
0
1
3
2
0
2
1
1
2
2
1
2
1
1
0
1
1
1
0
1
1
1
1
2
1
1
1
1
1
1
1
0
2
1
1
2
2
1
1
2
0
2
1
0
2
1
1
1
1
1
2
1
0
1
2
1
1
1
1
1
2
2
1
1
1
0
2
1
1
1
1
0
2
2
0
0
1
2
2
1
1
0
0
1
2
1
1
1
2
2
1
1
1
2
1
1
0
0
1
0
1
0
1
1
1
1
1
0
1
1
1
1
0
0
1
1
1
1
1
2
2
1
0
2
1
1
1
1
0
2
1
1
0
0
1
1
2
1
1
1
1
1
1
1
0
0
1
1
1
1
2
1
0
1
1
1
1
1
0
1
0
0
2
2
0
1
1
2
1
1
1
0
0
1
1
2
1
1
2
2
2
0
1
0
1
1
2
2
2
1
2
2
1
1
2
1
1
0
1
0
1
0
1
2
1
2
1
1
2
1
2
1
1
2
0
0
1
2
2
1
1
1
1
1
0
1
1
1
1
1
0
1
0
1
1
1
2
0
2
1
2
1
1
0
1
1
0
1
1
1
1
1
1
0
2
1
2
1
2
2
1
1
1
2
1
1
1
1
1
0
2
2
2
2
2
1
2
0
1
1
1
1
1
1
1
1
1
2
2
1
1
1
2
1
2
0
1
1
1
1
0
1
1
2
1
1
2
1
1
2
1
1
2
1
1
0
0
1
0
1
1
0
1
2
2
2
1
1
1
0
0
1
1
2
2
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
1
0
0
1
1
3
1
1
1
1
0
1
1
1
1
2
1
2
0
1
1
2
1
0
2
1
2
1
2
1
1
2
0
2
2
1
1
2
1
2
2
1
0
2
1
1
1
1
2
0
1
1
1
1
1
1
1
2
1
0
2
1
2
1
2
1
1
1
1
2
2
2
1
2
1
1
0
0
2
1
1
1
0
1
2
0
1
1
1
2
0
1
0
1
2
0
1
1
0
1
1
2
1
1
0
1
0
1
1
1
1
2
1
1
1
0
2
2
1
1
2
2
1
1
1
2
1
1
1
2
2
1
1
2
2
1
1
1
1
4
0
0
2
1
1
1
1
0
1
0
1
1
2
1
1
1
1
1
1
1
1
0
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
0
1
2
1
1
3
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
0
1
1
2
2
3
1
1
1
1
1
1
2
0
0
2
1
2
1
1
1
1
2
1
1
1
0
0
1
0
0
0
1
1
1
0
1
1
1
2
0
1
1
0
4
2
1
1
2
2
1
1
1
2
2
1
1
1
0
1
1
1
1
1
1
1
2
1
1
1
3
0
1
1
2
1
0
1
0
2
1
1
2
1
1
1
1
1
0
1
1
1
1
0
1
0
1
0
2
0
2
1
2
1
1
1
1
0
0
1
0
2
2
1
1
0
0
2
1
1
2
1
1
1
2
0
2
1
1
0
0
0
2
2
1
2
2
1
2
1
1
3
1
0
1
1
0
1
1
2
0
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
2
0
1
1
1
1
1
2
2
0
1
2
1
1
1
2
1
0
1
1
1
1
3
2
0
1
1
2
1
1
0
2
2
0
2
1
1
1
1
1
2
2
1
0
3
1
2
1
1
0
0
1
0
1
0
1
2
1
0
0
1
2
2
0
0
1
1
2
1
1
2
3
2
1
2
0
1
0
2
1
1
1
1
1
1
1
1
2
1
1
2
2
1
1
2
1
2
1
1
2
2
5
1
0
1
1
1
2
1
1
1
0
2
1
0
1
0
1
2
1
1
1
1
0
2
1
2
2
1
1
1
0
1
2
1
2
1
1
1
0
1
0
2
1
1
1
2
1
2
1
0
1
1
1
0
0
2
1
2
1
1
0
1
1
1
0
2
1
0
2
1
2
0
0
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
0
1
1
2
1
1
2
1
2
2
1
2
1
2
2
0
1
0
1
1
1
1
2
2
1
0
2
0
2
1
0
2
1
1
1
1
0
1
0
2
0
2
1
2
1
1
2
1
2
1
1
1
1
1
0
1
1
1
0
0
1
2
0
2
0
1
2
2
1
1
0
2
1
1
1
2
1
1
2
2
1
1
1
1
2
0
1
0
1
1
1
1
1
0
1
1
1
0
0
0
1
1
2
0
1
2
0
1
2
1
2
0
1
1
2
2
2
1
2
2
1
0
1
1
2
0
0
1
1
1
1
2
1
2
1
1
0
2
2
1
0
1
0
1
0
1
1
1
2
1
0
1
1
1
0
1
2
2
1
1
1
1
2
1
2
1
1
2
1
1
4
2
1
0
1
0
1
1
1
2
2
1
0
0
1
2
0
1
1
1
2
1
1
1
1
2
0
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
4
1
0
2
0
1
2
2
3
1
1
1
1
1
0
0
1
1
1
1
1
1
1
0
0
2
1
1
1
2
1
2
1
1
2
3
1
2
1
0
1
1
1
2
1
0
2
1
1
1
2
1
1
1
0
2
1
1
1
1
2
1
0
0
1
0
2
0
2
2
1
2
2
2
2
1
1
1
2
0
1
1
1
1
1
1
1
2
1
1
0
1
1
1
1
1
1
1
0
2
1
1
1
2
1
1
2
1
0
0
1
1
2
1
1
1
0
1
1
2
2
2
1
1
0
1
1
1
3
0
1
2
1
0
1
1
1
1
1
1
1
2
2
0
1
0
1
1
0
2
1
1
2
1
1
0
1
2
1
2
1
2
0
1
1
2
1
0
1
1
1
2
1
1
2
2
1
1
1
1
1
1
2
0
1
1
0
1
2
1
1
1
2
1
2
2
0
2
1
1
1
1
1
1
0
1
1
1
0
1
1
2
2
1
1
2
2
1
1
1
1
1
1
1
2
2
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
2
1
0
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
0
0
0
1
1
1
3
1
1
1
1
1
1
1
1
1
0
1
1
2
1
1
1
1
2
3
1
1
1
1
1
0
1
1
2
1
2
1
1
2
2
0
1
2
0
2
0
1
0
2
0
1
1
1
1
1
1
1
2
1
1
1
2
1
0
1
1
2
1
0
0
2
1
0
1
0
1
3
1
1
2
1
2
1
1
2
1
1
2
2
0
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
1
2
0
1
1
1
0
1
1
1
1
0
2
0
1
0
1
1
0
0
1
1
2
2
2
1
1
1
0
1
1
0
2
1
1
1
1
1
2
1
1
1
1
1
0
3
2
1
1
1
1
1
1
1
0
4
0
0
1
1
0
1
1
1
1
0
2
2
2
1
2
1
1
1
1
0
1
1
1
0
2
1
1
1
2
0
2
0
2
1
1
2
1
2
1
1
1
1
1
0
2
2
1
1
2
0
0
1
2
1
1
1
2
2
2
2
2
1
2
1
1
2
2
1
0
1
1
0
1
0
1
0
1
2
1
1
1
2
0
1
2
2
1
1
0
1
1
2
1
1
2
1
2
1
1
1
0
2
1
1
2
2
2
0
1
0
0
2
1
1
1
0
0
1
1
2
1
2
1
1
1
1
1
1
1
0
2
0
1
2
1
1
1
0
1
2
1
0
1
2
0
1
0
0
0
1
1
1
1
1
0
0
2
2
1
0
1
1
1
1
1
0
0
1
1
0
2
1
0
0
0
1
0
1
0
1
2
1
2
1
1
0
1
1
2
0
2
1
1
1
1
1
1
2
2
1
2
2
2
1
1
1
1
1
0
2
0
1
2
1
1
2
1
2
0
1
1
1
2
2
1
2
0
1
1
1
2
2
1
1
2
0
1
2
1
1
0
1
1
1
1
1
2
1
2
1
2
2
1
2
2
2
1
1
1
1
2
1
0
2
2
1
1
1
1
2
1
1
1
0
1
1
2
2
2
1
0
0
2
1
1
0
1
1
1
1
2
2
2
1
0
1
1
1
1
0
1
1
1
0
0
2
1
1
1
0
0
1
1
2
1
1
1
0
1
1
1
0
1
1
1
2
1
2
2
1
1
0
1
1
1
2
2
1
1
1
1
1
1
1
1
0
1
0
1
1
1
0
2
1
1
1
1
1
2
1
1
1
1
1
2
1
0
1
1
2
1
0
1
1
2
0
1
1
0
2
0
0
2
1
2
1
1
2
2
1
1
2
1
2
2
0
1
2
1
2
1
2
1
1
1
2
1
1
1
2
1
1
6
1
2
1
1
1
2
1
1
1
0
1
1
1
1
1
0
0
2
1
2
2
1
0
2
1
1
1
1
0
2
3
0
1
1
1
2
2
0
1
1
2
1
1
1
1
1
0
1
0
1
1
1
1
1
0
0
1
1
1
1
1
0
1
1
1
1
2
0
1
0
1
1
1
0
1
0
1
2
1
2
1
1
1
1
0
1
2
1
1
2
1
2
1
1
0
2
2
1
2
1
0
2
1
2
0
1
1
1
1
1
1
0
1
1
2
0
1
2
1
1
2
1
2
0
0
1
0
2
1
1
1
2
2
1
0
0
1
1
2
1
1
0
1
2
1
2
1
1
1
2
2
1
1
1
2
1
2
0
1
2
2
1
0
2
1
1
2
1
0
2
0
2
1
2
2
1
0
1
1
1
1
0
1
0
1
1
1
1
1
1
0
2
0
0
2
1
2
1
1
1
1
1
1
1
5
2
1
1
1
2
1
1
1
0
0
1
2
2
2
2
2
1
0
2
1
0
1
2
1
2
1
1
0
1
1
0
1
1
2
1
0
1
2
0
1
2
1
2
1
1
2
2
1
1
2
2
1
1
1
2
1
2
1
1
1
1
2
0
1
1
1
1
1
2
1
0
2
1
0
2
1
1
0
2
1
1
1
1
2
0
1
2
1
1
2
1
1
2
1
1
1
0
1
1
2
2
2
2
1
2
0
1
0
2
2
1
3
2
0
1
2
1
0
1
1
1
2
1
1
1
1
1
0
1
1
1
1
2
2
2
1
2
0
2
2
2
2
1
2
0
1
1
0
0
1
0
1
0
1
1
1
1
1
1
2
0
1
1
1
1
0
2
1
1
1
1
1
1
1
1
1
2
1
1
0
1
2
1
0
1
1
2
1
1
2
0
3
4
2
1
1
1
1
1
2
1
1
2
1
0
1
1
1
1
1
2
1
1
2
2
0
2
1
1
1
2
1
1
1
1
3
0
0
0
2
1
2
1
1
1
1
0
1
0
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
0
2
3
1
1
0
0
1
0
1
1
0
2
1
1
1
1
1
0
2
1
3
1
1
1
1
1
1
0
0
1
1
1
2
1
0
2
1
1
2
1
0
1
1
1
1
1
1
2
0
1
1
1
1
0
1
1
2
3
1
1
1
1
2
2
1
1
1
2
2
1
1
2
2
1
2
1
0
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
2
1
1
1
1
2
1
2
0
2
1
1
1
1
1
1
2
2
1
0
1
1
2
1
1
2
1
2
1
2
0
0
1
2
2
1
1
1
1
1
1
2
0
0
1
1
0
0
1
0
0
2
1
1
1
2
1
0
1
1
0
0
1
1
1
2
2
1
1
1
2
1
1
1
1
0
1
1
2
2
0
0
2
1
1
1
2
0
1
1
0
2
2
1
0
1
1
1
0
1
1
1
1
1
0
1
2
1
1
2
0
1
1
1
0
1
1
1
1
2
1
0
1
0
2
1
1
1
0
1
1
4
0
1
0
1
1
2
0
1
1
1
2
2
1
1
1
1
2
1
1
2
1
2
1
1
0
1
1
0
2
2
1
0
0
1
0
1
1
1
1
1
1
1
1
2
1
0
2
2
1
1
1
1
1
1
2
1
1
1
1
2
1
0
1
1
2
2
0
1
0
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
0
0
1
0
1
1
2
0
1
0
1
1
2
1
0
1
1
0
1
1
1
1
2
1
0
1
2
3
1
0
1
1
0
1
1
1
2
0
1
1
1
1
1
0
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
3
1
1
2
0
2
2
1
2
1
0
2
1
1
0
2
1
1
1
1
2
1
1
2
1
1
1
1
0
0
1
0
1
0
0
0
3
1
0
1
0
1
2
1
1
2
1
0
1
1
1
2
2
1
2
1
1
1
0
1
1
1
0
0
2
1
1
1
1
2
1
0
2
2
1
1
1
1
2
0
1
1
1
2
1
1
1
1
0
1
1
1
2
1
2
2
1
0
0
2
1
1
1
1
0
1
1
1
2
1
1
1
2
2
1
1
1
1
0
1
0
2
1
1
1
2
2
1
2
2
0
1
2
2
1
1
0
1
1
0
1
1
0
2
0
0
1
2
0
1
2
2
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
0
2
1
1
2
1
1
1
2
1
2
1
1
2
1
2
2
1
1
1
1
1
2
0
1
1
1
1
2
1
1
1
0
1
1
1
1
0
1
1
2
1
1
2
1
1
1
1
0
2
0
1
2
1
2
0
1
2
1
1
2
1
2
2
1
2
0
2
1
2
2
0
0
1
0
1
0
2
1
0
1
0
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
0
1
2
1
1
1
1
2
0
1
1
4
1
1
0
2
1
1
2
1
1
0
1
1
2
2
1
1
2
0
1
2
2
1
1
1
2
0
2
2
1
1
1
1
1
1
1
1
0
1
1
1
1
1
2
0
1
2
1
2
2
0
1
2
0
1
1
1
0
1
0
1
2
2
1
1
1
1
1
1
1
0
2
2
1
1
1
1
1
1
0
2
1
1
2
1
1
1
1
1
1
1
1
0
2
0
1
1
2
1
1
2
1
1
1
2
1
2
1
1
1
2
2
1
0
1
1
2
2
1
1
1
2
1
1
1
0
2
1
0
0
1
1
1
1
1
1
2
1
0
1
1
1
0
2
1
1
2
1
2
0
0
1
0
2
1
1
2
1
1
1
2
1
1
1
1
1
1
2
1
2
1
1
0
1
1
1
2
1
1
0
0
0
2
2
1
2
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
2
1
1
0
0
2
0
2
1
1
1
1
1
1
2
2
1
2
1
1
2
1
2
1
2
1
1
1
1
0
2
1
1
1
1
0
1
2
2
1
1
1
1
2
0
1
1
2
1
0
1
0
2
1
2
1
1
1
1
2
1
1
2
2
1
1
2
2
1
2
1
1
2
1
1
1
2
1
1
2
2
1
1
1
0
1
1
0
1
1
1
1
1
0
0
0
1
1
0
1
1
2
1
1
1
1
1
1
2
2
2
2
2
1
1
0
2
1
0
1
0
0
1
1
2
1
1
0
2
2
1
2
1
0
1
1
0
1
1
2
1
2
2
0
1
1
2
0
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
0
1
2
1
2
1
1
2
2
1
1
2
1
2
1
1
1
1
1
1
2
1
2
1
1
2
1
2
0
0
1
1
1
1
3
1
2
2
2
0
2
2
2
2
1
2
2
1
1
1
1
2
2
1
1
2
2
1
2
0
2
2
1
1
1
1
1
0
1
1
0
1
2
4
1
0
0
1
1
2
0
2
1
1
2
0
1
1
0
1
2
1
1
1
1
2
1
2
1
0
2
0
1
1
1
2
0
1
2
1
0
1
1
1
1
1
0
1
1
0
1
2
1
1
1
0
1
2
2
1
0
1
1
1
1
1
2
1
1
2
1
2
0
1
1
1
1
0
1
2
1
1
2
1
0
1
1
3
1
3
0
0
1
1
0
0
1
2
1
3
2
1
2
1
1
1
0
1
1
1
1
1
2
1
1
1
0
1
1
2
0
1
1
1
1
2
0
1
1
0
1
1
1
2
1
1
2
2
0
1
1
1
1
2
1
0
1
2
1
1
1
1
1
2
2
1
1
0
1
0
0
2
1
1
1
1
0
1
1
1
2
1
0
2
1
1
1
1
3
1
3
0
1
1
1
1
1
1
2
2
2
1
2
1
2
0
2
1
0
0
1
1
1
1
1
2
1
2
1
0
2
2
1
1
0
1
2
1
1
2
0
1
1
1
2
1
1
1
2
1
1
1
0
1
2
1
0
2
2
0
0
1
1
1
2
2
1
1
1
1
2
0
1
1
1
1
1
2
1
0
1
0
1
1
1
1
1
1
1
1
2
2
1
1
0
0
2
1
1
0
2
2
1
1
1
1
0
1
1
0
1
1
2
1
2
2
2
1
1
0
1
1
1
2
1
1
0
1
1
2
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
2
2
1
2
1
0
0
1
2
1
2
1
1
0
1
2
1
1
0
1
1
2
2
1
0
1
1
2
1
2
1
2
1
1
0
2
2
2
1
0
0
1
1
2
0
1
1
1
1
2
1
0
1
1
1
1
2
1
1
1
2
0
1
2
1
1
2
1
0
2
1
1
2
2
2
2
0
0
1
2
2
0
0
1
1
0
1
1
3
0
1
1
1
0
1
2
1
1
1
1
1
2
1
2
1
2
1
1
2
2
4
1
0
1
1
2
1
0
0
0
0
1
1
1
2
0
2
1
2
1
1
2
0
2
1
1
1
2
1
2
0
1
2
2
2
2
1
2
1
2
0
2
1
2
0
2
2
1
2
1
1
2
0
1
1
1
1
1
1
1
1
1
2
1
1
1
1
0
1
2
0
1
1
1
1
2
1
1
1
2
1
2
2
1
2
0
1
2
1
1
1
2
0
1
2
2
2
1
1
1
0
2
1
1
1
1
1
2
1
1
1
0
1
2
1
1
1
3
1
0
1
0
1
0
1
1
1
1
2
1
2
1
1
2
1
0
1
2
1
1
1
1
1
1
1
1
2
2
0
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
0
2
1
2
0
1
1
1
2
2
1
1
1
2
2
1
1
0
0
0
1
1
1
1
2
0
1
1
1
1
2
2
1
1
1
1
0
1
1
1
1
1
1
1
1
1
4
1
2
1
1
1
2
1
1
1
2
0
2
1
1
1
3
0
1
1
1
2
2
2
2
1
1
1
1
1
0
1
1
3
2
2
1
0
1
2
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
0
2
1
1
1
0
1
1
0
1
0
1
1
1
2
2
0
1
1
0
1
1
1
0
2
1
0
1
2
1
1
0
1
0
1
2
2
1
1
1
0
0
1
1
2
2
1
2
2
0
2
1
1
2
1
1
2
0
1
1
1
1
1
0
0
1
1
2
0
1
1
1
2
2
1
1
1
1
1
1
1
1
1
2
2
1
2
1
1
0
1
0
1
2
1
1
1
1
1
1
0
0
2
1
1
2
1
2
2
0
2
2
0
0
2
1
1
1
1
1
0
1
1
1
1
2
0
1
1
0
2
2
2
1
1
1
1
2
1
1
2
2
2
1
1
1
2
0
1
1
0
1
1
1
1
2
1
1
0
1
1
1
1
0
1
1
1
0
2
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
0
1
2
2
1
1
1
1
1
0
2
2
2
1
1
1
2
1
2
0
1
1
1
0
3
1
1
2
1
2
0
1
2
1
0
2
0
0
1
1
2
1
1
1
2
1
1
1
2
1
1
2
1
1
1
2
1
2
1
0
0
1
1
1
0
1
1
2
0
1
1
1
4
1
1
2
1
0
1
1
1
1
0
2
1
1
1
0
1
0
1
1
1
1
1
1
2
0
2
1
1
1
1
2
1
1
1
0
1
1
1
0
1
1
1
2
0
0
1
1
1
1
2
2
2
1
1
1
2
1
1
1
1
2
1
2
1
1
1
2
1
0
1
2
1
1
1
1
1
1
1
1
1
2
0
1
2
0
2
0
1
1
1
2
1
1
1
1
1
1
1
2
1
2
2
0
1
1
2
3
0
1
2
2
0
0
1
1
1
1
1
2
1
1
0
2
1
0
1
1
1
2
1
1
0
0
1
1
0
1
1
1
0
0
1
1
1
1
0
1
1
1
1
0
1
2
2
1
2
2
1
1
0
1
2
1
0
1
1
1
1
1
1
1
1
1
0
2
2
2
1
0
0
1
0
1
0
1
1
1
0
2
1
1
1
2
1
2
2
1
0
0
1
0
1
0
2
0
2
1
2
1
2
1
0
0
1
1
0
1
1
1
1
0
0
1
2
0
1
1
2
1
0
0
1
1
1
2
1
1
1
1
1
1
3
1
2
1
1
1
0
1
2
1
2
1
1
1
0
1
1
1
1
0
1
1
1
0
2
1
2
0
1
1
1
0
2
0
2
0
1
0
2
1
2
1
1
1
2
1
2
2
1
1
1
0
1
1
1
2
1
2
1
1
1
1
2
0
1
1
1
1
2
0
0
1
2
1
2
0
2
0
0
0
1
1
1
1
1
1
1
1
1
2
1
2
2
1
1
2
1
0
0
1
0
1
1
0
2
3
2
0
1
0
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
2
2
1
1
0
1
1
0
1
1
1
1
2
1
1
1
0
1
0
0
1
0
2
1
1
1
1
2
2
2
1
1
1
0
1
0
1
1
0
1
2
1
1
2
1
1
1
0
2
1
1
1
2
0
1
1
2
2
1
2
1
1
1
2
1
2
0
1
1
1
2
2
2
1
1
1
1
1
2
2
1
1
1
1
1
2
2
0
1
0
1
2
1
0
2
1
2
1
1
1
1
1
1
0
1
1
1
0
1
1
1
1
1
1
0
1
1
1
1
1
0
2
2
1
2
2
2
1
0
1
1
0
1
2
2
2
1
0
1
2
0
2
1
1
1
0
2
2
1
1
1
0
1
1
1
1
1
2
0
1
1
2
1
2
1
1
1
3
0
2
1
2
1
1
2
1
1
0
1
1
1
1
2
2
0
1
2
1
0
1
1
2
1
2
1
1
1
2
1
1
2
1
1
0
2
1
2
1
0
1
1
1
1
2
1
1
2
1
1
0
1
1
2
0
0
2
1
2
1
1
2
0
2
0
2
0
0
1
1
1
1
2
1
0
1
0
0
1
1
1
1
1
1
1
2
0
1
0
1
2
1
1
1
0
1
1
2
1
1
1
1
1
1
1
1
0
0
1
0
2
3
1
1
2
2
2
2
2
0
1
1
0
2
0
2
1
1
1
1
1
1
1
2
2
2
1
0
0
0
2
1
0
1
0
1
1
1
1
1
0
0
1
1
1
1
2
2
1
2
2
1
1
1
1
2
1
0
1
1
1
1
1
1
1
1
2
2
2
2
0
3
1
2
1
1
1
0
0
2
2
0
2
1
0
0
1
1
1
1
1
1
1
0
1
0
1
2
1
1
0
2
1
2
1
2
1
0
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
2
2
0
0
3
1
0
1
1
2
1
1
1
2
1
2
1
0
3
2
0
0
0
1
1
1
0
2
1
0
1
1
2
1
1
1
1
2
1
1
2
1
1
2
1
0
2
1
1
1
1
1
2
1
1
2
2
1
2
1
1
2
0
2
1
2
1
2
0
0
1
1
0
2
1
1
1
2
2
2
2
1
1
1
3
1
1
1
1
0
2
1
1
1
1
1
1
1
1
1
2
1
2
2
1
0
1
2
0
1
1
1
1
1
1
1
2
1
1
2
1
0
1
1
0
1
1
0
1
2
2
0
1
1
1
1
1
1
1
1
0
1
0
2
0
2
2
2
1
0
1
1
1
0
0
3
0
0
1
2
2
1
0
2
2
2
0
1
1
2
2
1
0
0
0
2
2
1
1
2
1
0
1
1
2
1
0
1
1
2
1
2
1
0
0
1
1
1
0
1
1
1
0
1
2
1
2
1
0
0
1
2
1
1
1
1
0
1
0
1
0
2
1
1
0
1
0
2
2
2
1
1
1
1
1
1
1
1
1
0
2
0
2
1
1
1
1
1
1
0
0
1
2
1
0
1
1
1
1
0
2
2
1
0
1
3
1
1
1
1
1
0
1
2
1
2
1
2
1
1
1
1
1
2
2
3
1
1
1
1
1
1
2
1
1
1
1
0
2
2
1
0
0
1
2
1
1
1
1
1
2
0
2
1
1
2
1
1
2
2
1
2
1
0
5
1
1
1
0
1
1
1
0
1
1
2
2
0
1
1
0
1
2
1
0
2
1
2
2
1
1
1
2
0
1
1
1
2
3
1
1
0
0
2
1
1
0
1
0
1
0
0
1
1
1
0
1
0
1
1
1
2
1
0
2
1
1
1
1
1
2
1
0
2
2
0
1
2
0
1
1
1
1
0
1
1
2
2
0
1
1
1
0
0
2
1
1
1
2
2
2
1
1
0
1
2
1
1
0
1
1
0
2
1
1
1
1
1
1
2
0
0
1
1
2
1
1
1
2
1
1
1
2
0
0
1
2
1
1
1
1
0
1
2
0
0
1
1
1
1
0
1
0
0
1
2
0
1
1
1
1
1
2
1
2
2
0
0
2
2
0
1
2
0
1
1
0
1
2
1
1
2
1
1
1
1
1
3
2
1
1
0
1
2
2
1
1
1
2
2
1
0
1
1
1
0
2
1
1
1
1
1
1
1
1
3
1
1
1
1
2
0
2
1
1
1
1
0
2
2
1
1
1
0
2
1
2
0
0
1
2
2
1
2
1
1
0
1
2
0
0
2
1
1
0
2
2
0
0
1
1
0
1
2
1
1
2
2
1
1
1
1
1
1
1
1
2
2
0
1
1
1
0
1
1
2
2
1
1
3
2
1
1
1
1
1
1
1
1
3
0
1
0
2
1
1
1
1
0
0
2
0
1
0
1
1
0
2
0
1
1
3
1
2
0
1
0
0
0
1
1
1
1
1
2
1
2
1
1
1
1
0
1
2
1
1
1
1
1
1
1
1
1
0
2
1
1
1
0
0
1
1
1
1
0
0
1
1
1
0
0
2
2
0
1
1
1
1
1
2
2
0
2
1
0
0
1
1
1
1
0
2
1
1
2
0
1
2
1
2
2
1
1
1
1
1
0
2
2
1
1
2
1
1
1
1
2
1
2
1
0
1
2
2
1
1
2
2
1
1
1
1
0
1
0
2
1
2
1
1
2
1
1
0
1
1
1
0
1
1
1
1
1
1
2
0
2
1
0
1
1
1
2
0
1
2
0
1
1
1
1
1
1
1
1
0
2
1
2
1
1
1
1
1
1
1
1
1
1
2
0
1
2
1
1
0
1
1
0
0
1
1
1
1
0
2
1
1
0
1
2
2
2
1
0
1
1
1
2
2
1
2
2
1
1
2
1
0
0
2
2
1
2
1
1
2
1
2
2
3
2
0
0
2
1
0
1
1
1
1
1
2
1
1
2
1
0
1
1
1
1
2
2
0
1
0
1
1
1
1
1
2
1
1
1
2
0
1
1
2
0
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
2
4
1
2
1
1
0
1
0
1
2
1
0
1
1
0
1
0
1
2
1
1
1
1
1
1
1
1
0
0
1
1
1
1
1
2
0
1
0
2
1
2
1
1
2
1
1
2
1
1
0
2
2
1
1
2
1
1
1
0
2
0
2
2
1
1
2
1
2
5
1
1
0
1
1
1
1
0
0
1
0
1
4
1
1
1
1
0
2
1
2
1
1
1
2
3
2
0
0
1
1
0
1
1
1
1
2
1
1
1
0
1
1
1
2
1
1
1
2
1
2
1
1
1
2
1
1
2
1
1
2
1
0
0
1
1
1
2
0
1
0
7
2
1
1
1
1
2
2
0
1
1
2
1
1
1
0
2
1
1
1
2
0
2
1
1
1
1
1
1
1
2
1
1
1
1
0
1
1
2
1
1
2
0
1
1
0
2
0
1
2
2
1
1
1
1
2
1
1
1
1
1
2
2
1
2
2
1
1
1
1
0
1
1
1
2
1
2
1
0
2
1
1
1
1
2
1
1
1
1
2
0
0
1
0
1
0
0
1
1
0
1
0
1
0
0
1
2
0
2
0
1
1
0
1
1
1
0
3
1
1
1
0
0
0
1
1
2
1
1
2
1
2
1
0
1
1
1
1
1
0
2
1
0
2
1
1
1
0
1
1
0
1
1
1
0
1
1
2
1
3
1
1
2
1
1
1
2
1
1
1
1
0
1
1
1
2
1
2
1
1
0
1
1
1
1
2
1
1
1
1
1
1
1
0
2
2
2
1
0
1
0
1
2
1
1
1
1
2
1
1
2
2
2
0
1
1
1
1
1
1
1
2
2
0
1
1
1
1
2
1
1
1
0
2
0
1
2
1
0
1
2
1
2
1
1
1
2
2
1
1
1
1
0
1
1
0
1
0
2
0
2
2
2
2
2
0
2
0
0
2
1
1
1
1
2
1
0
1
1
1
1
0
2
1
1
1
2
2
1
1
1
0
1
1
1
0
1
2
1
1
1
1
1
0
1
0
2
0
1
1
1
1
1
1
1
1
1
1
2
1
0
1
1
0
1
2
1
0
1
1
1
1
1
2
1
1
1
2
1
1
2
0
2
1
1
0
1
1
2
1
2
2
2
1
2
2
1
0
2
1
1
1
2
1
2
4
1
1
2
2
1
0
1
1
0
2
0
2
1
1
1
1
1
1
3
1
1
1
1
1
1
1
1
1
2
1
0
1
0
1
2
1
1
1
0
0
0
2
1
1
1
1
2
1
2
1
1
1
1
1
1
1
2
0
2
1
1
0
1
1
2
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
0
1
2
1
1
0
1
0
1
2
2
1
2
0
1
1
1
1
2
1
3
1
1
1
2
2
1
0
1
1
3
1
1
1
1
0
0
1
0
0
2
1
1
1
1
0
2
1
0
2
2
1
2
1
1
1
1
0
1
2
0
0
1
0
1
2
2
1
2
1
1
1
2
1
1
1
2
2
0
1
0
1
1
1
0
2
2
1
1
1
2
1
1
2
1
2
1
1
2
2
1
0
0
1
0
1
1
1
1
2
1
1
1
1
1
1
1
0
2
2
0
0
0
1
1
1
0
1
1
2
1
0
1
2
2
0
1
1
2
1
1
1
1
1
2
0
0
1
1
1
2
1
1
0
1
1
2
2
1
1
2
2
2
0
2
2
1
0
1
2
0
1
0
2
1
2
0
2
0
2
1
0
1
0
1
2
0
1
1
1
1
1
1
1
0
1
1
1
0
3
1
1
1
0
1
1
2
1
2
2
1
1
1
1
1
1
0
1
0
1
1
0
1
1
1
1
1
1
0
2
1
2
1
1
2
1
0
1
2
1
0
1
1
2
2
0
1
2
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
0
1
1
1
2
1
2
2
2
0
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
2
1
2
1
2
1
0
1
2
1
1
2
1
4
2
2
0
1
0
1
0
1
1
1
1
1
1
2
2
1
1
1
0
0
1
2
2
1
1
1
1
2
2
1
1
0
2
0
1
2
1
1
1
1
16
1
0
1
0
2
1
1
1
2
1
0
1
0
2
2
1
1
0
0
1
1
1
1
0
2
1
2
3
0
2
0
0
1
1
1
0
1
2
1
1
1
0
1
0
1
1
1
1
2
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
2
2
1
0
2
0
2
2
1
2
1
1
2
2
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
1
1
2
0
2
1
1
1
1
2
1
1
1
1
1
0
2
1
1
1
1
2
1
1
1
1
0
1
2
1
1
1
1
0
2
1
1
1
1
1
2
1
1
1
2
2
1
0
2
1
1
1
1
1
0
1
1
0
1
2
0
1
1
1
2
1
2
1
0
0
1
2
1
2
2
2
1
2
2
2
1
2
1
1
1
0
1
0
1
1
1
1
0
0
1
1
1
1
1
1
1
2
1
1
1
0
1
0
2
1
0
1
1
1
0
1
2
1
2
1
0
1
1
1
0
0
2
2
2
1
0
1
0
0
2
0
1
1
1
1
2
1
1
1
1
1
2
1
0
1
1
2
2
1
2
0
1
2
0
1
1
2
1
1
1
1
1
2
2
1
1
1
1
0
1
1
0
2
2
0
0
4
1
1
1
2
1
1
1
1
2
1
2
0
2
0
1
1
1
0
1
0
2
0
1
0
1
1
1
2
1
2
2
2
2
1
1
2
0
0
0
1
1
1
1
1
2
0
2
1
2
0
0
2
1
2
1
0
1
1
1
2
1
1
0
0
1
1
1
0
1
1
1
0
0
1
2
2
2
1
1
1
0
2
1
0
1
1
1
1
0
1
2
1
1
1
1
1
0
1
0
2
1
1
1
1
0
1
1
1
1
1
1
1
1
1
0
0
2
2
0
1
2
2
0
1
0
1
1
2
1
0
1
0
1
1
1
1
1
0
1
1
1
1
1
2
1
1
2
2
0
0
1
2
1
1
1
2
2
1
1
1
2
1
2
2
1
1
0
1
1
2
0
1
1
2
1
1
0
1
1
0
1
0
2
1
1
1
1
1
2
1
2
2
1
1
1
0
2
1
2
1
2
1
1
1
2
0
2
1
1
0
1
1
1
1
1
1
1
1
1
1
2
1
0
2
1
0
1
1
1
1
0
2
1
0
1
1
1
2
2
0
1
1
2
2
1
0
2
0
2
1
0
1
1
1
0
2
1
2
0
2
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
1
1
2
1
2
0
0
1
1
2
2
2
1
2
2
1
1
2
2
1
1
2
1
2
1
1
1
2
3
2
2
1
1
2
1
1
1
1
2
1
1
0
0
1
2
2
1
1
2
1
2
1
1
1
1
0
1
1
1
1
1
2
1
1
1
0
2
1
1
1
1
0
1
1
1
0
2
0
1
1
0
1
1
1
1
1
1
1
0
1
1
1
1
2
3
0
2
0
2
1
0
2
0
2
2
2
1
1
0
2
2
1
0
0
2
1
1
1
1
1
1
2
1
1
1
1
1
1
0
2
1
2
1
1
2
2
2
0
1
2
1
2
1
0
1
1
2
2
2
2
1
0
0
0
1
2
2
2
2
2
1
1
1
2
1
1
2
1
1
1
1
1
2
0
1
1
2
1
1
0
1
0
0
1
2
0
1
0
2
1
1
1
1
1
1
1
1
1
0
1
1
1
0
0
0
1
1
0
1
1
1
0
2
0
0
1
2
0
2
1
3
1
2
1
1
1
1
0
0
1
1
1
0
1
2
0
1
3
2
1
1
1
0
1
1
1
0
0
1
1
1
2
2
1
1
1
1
0
2
1
0
1
1
2
0
1
0
1
2
1
1
1
2
1
0
1
0
2
1
2
2
2
1
1
0
1
0
1
4
1
1
1
0
1
1
2
2
2
0
1
1
2
1
0
1
1
2
1
1
0
1
2
2
1
0
1
2
1
0
1
1
1
1
2
0
1
1
1
1
1
0
0
1
1
1
2
1
1
1
1
1
2
1
1
1
2
2
1
1
2
1
2
2
3
1
1
2
1
0
1
1
0
1
1
0
1
1
1
2
1
1
2
1
2
1
1
1
2
1
0
1
1
1
1
0
1
2
1
1
1
1
0
1
1
1
1
1
1
1
0
1
1
1
3
1
1
1
1
1
1
2
1
1
2
0
1
2
2
0
1
1
0
1
1
0
2
1
0
2
2
1
1
1
2
1
1
2
1
1
1
1
0
4
1
1
1
2
0
1
1
1
1
1
1
1
1
1
0
2
2
0
1
1
2
1
1
2
1
1
0
1
2
1
1
1
1
2
1
1
0
1
2
1
1
2
1
0
1
0
2
1
1
1
0
1
2
2
1
1
1
1
1
0
1
2
2
1
1
1
1
1
0
1
2
2
2
1
1
1
2
1
1
0
2
0
2
1
0
1
1
0
0
2
1
1
1
1
0
1
1
2
1
2
1
1
1
1
0
0
1
1
1
2
1
2
2
1
1
1
1
1
2
1
0
2
2
1
1
1
2
1
1
2
0
1
1
1
1
1
1
2
1
1
1
1
1
2
0
0
1
0
0
0
1
1
0
2
1
1
1
1
1
1
1
2
2
1
1
1
1
2
1
2
1
0
1
0
1
1
1
1
2
1
1
2
1
0
0
1
1
1
1
2
1
3
1
2
1
1
0
2
2
1
1
0
1
1
1
1
0
0
1
1
2
0
1
2
1
1
0
1
1
1
1
2
1
2
1
0
2
1
1
1
1
1
1
1
1
0
2
2
0
2
1
1
1
2
2
0
1
1
1
2
0
1
1
1
1
1
0
1
1
1
2
1
0
1
2
1
1
0
1
0
1
1
0
1
1
2
1
1
0
1
1
2
2
1
2
1
1
1
1
1
1
0
1
1
1
1
1
0
1
1
2
2
2
2
1
2
2
2
1
1
0
2
2
2
2
1
2
1
2
2
1
1
1
1
6
1
2
0
2
1
0
1
1
1
0
2
0
1
1
1
2
2
0
2
1
1
2
0
3
0
1
0
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
2
1
0
0
0
1
2
1
1
2
2
1
1
1
2
2
0
1
0
1
1
1
0
0
0
0
1
1
2
1
1
1
2
1
1
1
0
1
1
1
2
1
1
1
1
1
1
2
1
1
1
0
2
1
0
0
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
0
0
1
2
2
2
1
0
0
1
1
1
0
1
2
1
1
2
2
1
1
1
1
1
1
2
2
1
0
0
1
0
1
2
1
1
1
1
1
1
1
2
0
2
1
1
1
1
1
2
0
2
1
2
1
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
0
1
1
1
1
1
2
1
1
0
1
0
1
2
2
2
1
0
1
0
1
1
2
2
2
2
1
0
0
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
0
1
1
2
1
2
0
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
2
1
2
0
2
1
1
1
0
0
2
1
2
1
1
1
0
1
1
2
2
1
1
1
2
2
1
2
0
1
1
1
1
1
1
2
0
0
0
1
1
2
1
1
1
0
1
1
1
1
1
0
1
1
1
1
1
0
1
1
0
1
1
1
1
1
0
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
1
0
2
1
0
2
2
1
1
0
1
1
2
1
2
1
2
2
2
1
1
1
1
1
2
1
2
1
1
1
2
3
2
2
1
1
1
1
1
1
2
2
1
1
1
2
1
0
2
1
1
2
2
0
1
0
1
1
1
1
1
1
1
2
0
1
1
2
1
1
0
1
0
1
1
0
2
1
1
0
1
2
0
2
2
1
0
1
3
1
1
1
1
0
1
2
1
1
0
1
1
1
1
0
1
1
1
0
2
2
2
2
0
2
1
1
1
2
0
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
0
0
2
1
1
1
1
1
1
0
1
0
1
1
1
1
0
0
2
1
1
1
2
1
1
1
0
1
0
2
1
1
1
1
0
1
2
0
1
1
1
1
0
1
2
0
1
1
2
1
1
1
2
0
1
1
1
0
0
1
1
0
2
1
2
2
2
1
1
1
0
2
1
2
2
1
1
2
1
2
1
1
1
1
2
2
1
1
1
1
1
3
0
1
1
0
2
1
1
0
0
1
1
2
2
1
1
1
2
2
0
0
0
1
2
3
1
1
2
1
2
1
1
1
1
2
2
1
1
1
3
1
2
1
0
1
2
0
1
1
1
1
1
0
1
2
2
1
1
1
1
1
2
1
2
2
0
1
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
0
0
2
1
0
2
1
1
2
1
1
2
0
0
1
2
0
1
2
1
1
1
2
1
2
1
1
1
1
2
0
1
1
1
2
1
1
1
1
1
0
1
1
1
0
1
2
1
0
1
1
1
1
1
0
1
1
2
2
0
1
1
1
2
1
1
1
1
2
1
1
0
1
0
2
1
1
1
0
2
2
1
1
2
1
2
1
1
1
2
1
0
1
1
1
2
1
0
1
1
2
1
1
1
1
1
0
1
1
2
1
1
1
2
2
1
1
1
0
1
1
1
0
0
1
1
0
1
2
2
1
1
1
0
1
2
2
1
1
0
0
1
0
1
1
1
1
1
0
1
2
1
2
1
0
0
2
1
1
2
0
1
2
0
1
1
2
1
1
2
1
1
0
1
1
2
2
1
0
1
1
1
0
0
0
1
3
2
1
1
1
1
1
1
2
2
1
1
0
0
0
0
0
1
2
2
2
2
1
1
1
1
2
1
1
2
1
2
1
2
1
1
1
1
1
1
1
2
1
1
2
1
0
1
1
1
1
1
0
1
2
1
1
1
0
1
0
0
0
0
1
0
1
1
1
1
1
2
0
1
1
0
1
2
0
1
0
2
0
1
2
1
1
1
1
2
0
2
0
0
0
2
1
1
1
1
1
1
1
1
0
2
1
0
1
0
2
1
1
1
0
1
1
0
1
1
1
2
1
1
1
1
1
1
0
0
0
1
1
1
1
2
0
2
2
3
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
2
2
1
1
0
1
0
0
1
2
1
0
1
1
3
1
0
1
1
2
1
1
1
2
1
2
1
0
1
1
1
0
1
1
0
1
2
2
1
1
1
2
1
1
1
1
1
1
0
1
1
2
1
2
3
2
2
2
1
1
1
2
0
2
1
1
1
2
2
2
1
2
1
1
1
2
1
1
0
1
2
1
2
1
2
1
1
1
2
2
1
0
1
2
1
1
2
2
1
1
1
1
2
1
2
0
2
0
2
1
2
0
2
0
0
0
1
0
2
2
2
1
1
1
1
1
2
1
0
1
1
1
2
2
1
1
2
0
3
0
0
1
1
1
1
1
1
0
0
1
2
0
1
2
0
2
1
2
1
1
0
0
1
2
2
1
2
2
1
1
0
1
0
2
0
0
0
1
1
2
2
0
1
1
1
0
1
1
1
2
1
2
1
1
1
1
1
1
1
1
2
1
0
1
1
1
1
1
2
1
2
1
1
1
2
2
2
1
2
1
2
1
2
1
2
1
1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
2
2
1
1
1
2
2
1
1
1
1
1
0
0
0
1
1
1
0
1
0
1
1
1
0
1
1
1
1
1
3
1
2
2
0
1
1
0
0
0
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
2
1
2
0
1
1
1
1
1
1
1
1
2
2
1
0
1
1
1
2
1
0
1
1
1
1
1
1
1
0
2
1
0
1
0
2
2
1
2
2
0
0
1
1
1
2
1
1
2
2
2
1
0
1
2
1
0
0
1
1
1
1
1
1
1
2
1
1
2
1
0
2
2
2
1
2
3
1
1
1
0
0
1
2
1
1
1
1
2
1
1
2
1
0
1
0
0
1
1
1
1
0
0
2
1
0
1
2
1
1
1
1
1
2
0
1
0
1
0
1
2
2
0
0
2
2
0
0
2
1
0
0
0
1
2
1
1
1
1
0
0
1
1
0
0
1
2
0
1
0
0
1
1
1
1
1
0
0
0
2
1
0
2
1
1
1
2
1
0
2
1
1
0
1
1
1
1
1
1
2
2
1
1
1
1
1
0
1
0
1
1
2
1
1
1
1
1
1
0
1
1
1
0
1
0
2
1
0
0
1
0
2
1
1
1
3
1
1
1
2
1
2
1
2
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
0
0
2
1
0
1
0
1
1
1
1
1
1
1
1
0
1
1
1
1
0
2
1
0
0
1
1
1
1
1
1
2
1
1
1
1
0
1
0
1
0
1
2
0
2
1
1
2
1
0
1
0
1
0
1
1
1
1
0
2
0
0
1
1
2
1
1
0
2
1
1
1
1
1
2
2
1
1
1
0
1
1
2
1
1
1
1
1
1
1
2
2
2
2
0
1
1
2
1
1
2
1
1
0
1
1
1
2
1
1
0
1
0
0
1
0
1
1
2
1
0
1
1
1
1
1
0
1
1
1
1
2
0
1
1
1
1
2
2
0
1
0
0
1
0
1
2
2
1
1
1
2
2
2
1
1
1
0
3
1
1
0
2
2
1
0
2
1
0
1
2
1
1
1
1
1
1
2
1
2
1
1
0
0
1
0
1
2
2
1
1
2
1
1
0
0
1
0
1
1
1
1
0
1
1
1
2
1
2
1
1
1
1
1
0
1
1
0
2
1
1
1
1
1
2
1
1
0
0
0
0
0
2
1
1
1
1
1
2
2
2
1
2
1
2
0
1
1
1
1
2
0
1
1
1
1
0
0
0
1
1
1
2
1
1
1
0
1
0
1
1
0
2
1
1
0
1
1
1
2
2
1
1
1
2
2
0
1
2
1
2
1
0
1
0
2
2
2
2
1
1
0
1
2
2
1
1
1
1
1
1
2
2
1
1
0
1
1
0
1
1
1
1
2
1
0
1
3
3
0
2
1
2
1
0
1
0
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
0
0
1
2
1
1
2
1
0
0
1
1
0
1
1
1
0
1
2
1
2
2
2
0
0
1
1
1
0
2
0
2
1
0
1
1
1
1
1
2
0
1
1
0
1
1
2
1
1
1
1
1
2
1
1
1
1
0
2
2
1
0
1
2
1
1
0
0
1
1
1
1
1
1
2
2
1
1
2
1
0
2
0
0
2
1
1
2
1
1
1
1
1
2
1
0
1
0
1
1
0
0
1
1
1
2
2
2
1
2
1
1
2
1
1
1
1
1
1
0
0
0
0
0
1
0
0
1
1
1
1
1
1
0
0
1
2
1
1
0
2
1
2
1
1
1
0
0
1
1
2
1
0
1
1
0
1
1
1
1
2
0
0
1
1
0
1
1
0
1
1
1
2
2
1
1
0
1
0
0
2
1
0
1
2
1
1
2
1
1
1
2
0
0
1
1
1
1
1
1
0
2
2
0
0
2
0
1
0
1
0
1
1
1
2
1
2
2
1
1
1
2
2
1
1
1
1
2
1
1
1
0
1
1
1
2
1
1
1
2
1
1
1
2
1
2
2
2
0
1
1
1
1
1
1
1
1
0
0
1
0
1
2
0
1
1
1
0
1
1
1
1
1
2
1
1
0
1
1
1
1
1
1
0
1
1
1
1
4
1
1
2
2
2
1
1
1
1
3
1
2
1
1
2
1
1
1
0
3
0
2
2
1
2
1
1
1
2
2
1
1
1
0
1
1
2
2
2
0
1
2
0
2
1
1
2
1
2
1
1
0
1
1
2
2
1
2
2
1
1
2
1
1
0
2
2
2
0
1
1
1
2
0
1
1
2
1
2
1
1
2
1
2
1
1
1
1
1
2
1
1
2
2
1
2
0
0
0
2
2
3
1
1
1
1
1
1
1
0
1
2
1
1
1
1
1
2
1
2
1
1
1
1
2
1
2
1
2
2
1
0
1
0
0
0
1
2
0
1
1
2
1
1
2
0
1
1
2
1
1
2
1
2
1
0
2
1
1
2
1
2
1
1
1
0
1
1
2
1
1
1
1
2
3
1
1
2
0
1
1
1
1
1
0
1
1
1
2
1
0
0
1
2
1
1
2
2
2
2
1
0
1
0
2
2
1
1
1
0
0
1
1
1
1
2
1
1
1
1
0
1
1
2
1
2
1
1
1
1
1
1
1
0
0
1
1
1
1
0
2
1
1
2
1
1
1
2
1
1
1
2
0
0
1
1
1
2
0
2
2
1
1
1
2
1
0
1
2
2
1
1
1
0
1
0
1
1
2
1
3
1
0
1
2
0
1
2
1
2
1
1
2
0
2
2
1
1
1
1
1
0
0
1
2
1
2
0
2
2
1
1
1
2
1
1
1
1
0
2
1
1
1
1
1
2
0
2
1
1
2
1
1
1
2
1
2
1
1
0
1
1
1
1
0
1
1
0
0
1
1
2
1
1
1
1
1
3
1
0
0
1
2
1
1
2
0
1
1
1
1
1
1
1
2
0
2
1
1
1
1
0
1
2
1
1
2
1
2
1
1
0
2
0
1
1
1
1
0
2
1
1
2
0
1
0
2
1
1
1
1
1
1
2
1
2
0
1
0
1
0
1
1
2
1
1
1
1
0
1
1
1
1
1
0
1
1
1
1
1
1
1
1
0
1
2
1
2
1
0
2
2
1
1
2
1
2
2
1
1
1
4
2
1
1
1
1
1
1
1
1
1
1
1
2
0
2
2
1
2
1
1
1
3
1
1
0
0
1
1
1
2
0
0
1
0
2
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
2
2
1
1
1
1
2
2
1
2
1
2
2
1
1
1
0
1
0
1
1
1
1
1
0
1
2
1
2
1
1
2
2
0
1
2
1
1
2
1
1
1
2
1
0
1
1
2
2
1
1
1
0
1
1
0
1
1
0
2
0
1
2
0
1
0
1
2
1
2
1
1
2
0
1
2
1
1
1
1
1
0
0
1
0
1
0
2
1
2
0
1
0
1
1
2
1
0
1
1
1
2
2
2
1
1
0
3
1
1
0
1
2
2
1
3
0
1
1
2
2
1
0
0
2
1
2
2
1
1
7
2
2
2
1
0
1
0
1
1
1
2
1
1
0
1
0
1
0
0
1
0
0
0
1
1
1
1
1
1
1
1
0
2
2
2
0
2
1
1
1
1
1
1
0
2
1
1
1
2
1
2
2
1
2
1
2
1
1
2
1
2
0
1
2
1
2
1
1
1
1
1
1
0
1
0
1
2
1
1
1
0
1
2
1
1
2
1
0
1
1
0
1
1
0
2
1
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
0
2
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
0
1
2
2
2
1
1
0
0
1
3
1
2
0
1
2
1
1
1
2
1
0
2
1
1
1
1
0
2
1
1
2
2
1
1
1
1
0
1
1
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
2
2
1
1
1
1
0
1
1
2
1
1
2
1
1
1
1
2
3
0
2
1
1
0
1
1
1
1
1
0
0
1
3
1
0
0
1
1
2
2
1
1
0
1
2
1
2
2
1
1
1
1
2
1
1
1
2
1
1
0
2
2
2
1
0
0
0
2
1
1
1
1
1
1
0
1
1
1
1
2
1
1
1
1
0
3
1
2
1
1
1
0
1
2
1
2
0
0
1
0
1
1
2
1
1
1
1
1
0
1
2
1
2
0
1
1
1
1
1
0
0
2
2
1
1
1
0
1
1
2
2
2
1
1
1
2
0
2
1
2
2
2
1
2
2
1
1
1
2
1
1
1
1
1
2
2
3
2
1
0
1
1
1
1
0
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
2
2
2
0
2
1
0
0
0
2
1
1
2
1
2
0
0
2
2
1
1
1
1
1
2
1
1
1
1
2
2
1
1
1
2
1
2
1
1
1
2
2
2
1
1
1
1
2
1
2
1
0
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
1
2
2
1
2
0
2
1
1
1
1
2
2
0
1
1
1
0
1
2
0
2
1
1
1
1
0
0
1
1
1
2
2
1
0
2
0
1
1
1
2
1
0
0
0
0
1
1
2
1
1
1
1
1
1
1
0
2
1
1
1
1
3
1
1
1
2
1
1
0
2
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
0
0
1
2
0
1
1
2
1
1
1
1
1
0
0
1
2
2
2
2
0
2
1
0
1
1
1
1
2
1
1
2
1
0
1
1
1
1
1
1
1
0
0
1
2
0
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
0
1
1
0
1
0
1
2
1
0
2
2
1
1
1
1
1
2
1
2
2
0
2
2
1
1
1
2
2
1
1
1
1
2
1
2
2
2
1
1
2
1
1
1
2
0
2
1
2
2
1
1
1
1
1
0
1
1
0
0
1
1
2
1
1
2
2
1
1
2
1
1
2
1
1
1
0
1
1
1
1
0
2
1
2
0
1
1
2
1
1
0
0
2
0
0
1
1
1
1
2
0
1
2
1
1
2
2
1
1
0
1
1
2
1
2
1
2
1
0
1
1
1
2
1
1
1
2
1
1
1
1
1
1
0
1
1
1
0
1
1
1
2
1
0
0
1
2
1
1
1
2
1
1
1
1
0
1
1
1
2
1
0
1
0
1
0
1
1
2
1
1
1
1
1
1
1
0
1
1
3
0
1
1
0
1
1
1
2
1
2
1
0
0
2
2
1
1
1
2
1
3
1
1
2
1
1
0
2
1
2
1
1
1
1
1
0
0
1
2
0
1
1
0
2
1
1
0
1
1
2
1
1
1
1
1
1
1
5
1
1
1
2
2
1
1
1
2
2
0
1
2
1
2
2
0
2
2
0
0
1
1
1
2
1
2
2
1
1
1
1
0
1
1
2
2
7
1
0
1
2
2
1
1
2
2
2
1
2
1
1
1
2
0
2
1
0
1
1
0
0
1
2
1
1
1
1
2
1
1
0
1
1
1
1
1
2
2
2
2
2
1
2
1
1
1
0
1
1
2
1
1
1
2
2
1
1
2
1
1
1
3
1
2
2
1
2
1
1
1
1
0
2
0
1
0
1
1
0
1
1
1
2
1
2
0
2
1
1
1
1
1
1
1
1
2
2
1
1
1
0
2
1
2
1
1
1
0
1
2
2
1
1
2
1
2
2
0
2
0
1
0
1
1
0
1
1
1
2
0
1
1
1
1
1
2
1
2
1
1
0
1
1
1
1
2
0
0
1
2
2
2
0
1
1
1
0
2
1
1
1
1
2
1
1
2
1
2
0
1
1
1
1
1
1
1
2
1
0
1
1
2
1
0
1
0
0
1
1
1
1
1
0
1
1
0
1
1
1
1
1
1
1
2
0
2
1
1
3
1
0
2
2
2
0
2
2
2
1
2
0
1
1
1
1
1
1
2
1
0
1
1
0
0
2
1
0
1
1
1
1
1
0
2
2
0
1
2
2
0
1
1
1
2
1
2
2
2
0
1
2
1
1
1
0
1
0
2
2
1
1
1
0
0
1
1
2
1
0
1
1
1
1
1
1
1
1
2
1
2
1
2
1
1
1
0
1
2
1
0
1
1
1
1
1
1
0
2
2
2
2
2
1
2
0
0
0
1
1
0
1
1
1
1
1
1
2
1
0
1
1
1
1
2
1
1
1
2
3
1
1
1
1
2
1
0
1
0
0
1
2
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
0
0
2
1
1
2
1
0
1
0
1
2
3
1
2
0
2
1
1
0
1
1
0
1
1
1
1
1
1
1
1
2
0
1
2
1
1
2
1
0
2
1
0
2
2
2
1
1
2
2
1
1
1
1
2
0
1
1
1
1
1
0
2
2
1
2
1
2
1
1
1
1
1
1
0
2
1
1
2
1
1
1
0
2
2
0
1
1
0
1
1
1
1
1
1
1
1
0
1
1
2
1
1
1
1
1
2
1
2
0
0
2
1
2
1
0
0
1
1
1
2
0
1
1
1
1
1
2
2
1
1
1
1
1
0
0
1
1
2
1
1
2
2
1
1
2
2
0
0
2
1
1
0
1
0
1
0
1
1
2
2
1
1
1
2
0
1
0
1
0
1
1
1
1
1
2
1
0
2
2
2
1
1
0
0
1
2
2
0
2
0
2
0
0
1
1
1
1
1
1
2
1
0
0
2
0
2
2
9
1
0
2
1
2
1
1
1
1
1
1
1
0
1
1
1
1
2
1
0
2
1
1
0
2
0
1
1
1
2
1
1
1
2
1
2
1
2
1
2
0
2
1
0
1
1
1
1
1
1
0
2
1
2
0
1
1
1
0
4
1
1
1
2
1
1
2
2
1
0
0
2
2
1
2
1
1
2
1
2
2
0
2
1
0
2
1
1
1
0
1
1
1
1
2
1
0
1
1
1
1
0
0
0
1
2
2
1
0
1
2
1
1
2
1
1
1
2
0
2
1
1
1
1
1
2
1
2
1
1
2
6
2
2
1
1
1
0
2
3
1
1
2
1
1
2
2
1
1
1
1
2
2
1
2
1
0
2
1
2
1
1
1
1
0
0
2
0
1
0
1
1
1
1
1
1
0
1
1
2
1
1
1
2
1
1
1
1
1
2
2
1
0
1
1
1
0
1
1
1
2
1
1
1
1
0
0
1
2
1
0
0
4
1
1
0
0
1
2
2
2
1
1
2
1
1
1
1
0
1
2
2
1
1
1
1
1
1
2
1
0
2
0
1
2
2
1
2
0
2
1
1
1
0
2
1
2
1
0
1
1
0
2
1
0
1
2
1
1
1
0
1
2
1
1
0
0
1
2
1
1
2
2
2
1
0
2
0
1
0
1
0
1
1
1
0
2
0
1
2
0
2
1
2
1
1
1
0
1
0
2
1
1
5
0
1
1
1
1
1
2
2
2
1
1
3
1
1
2
0
1
2
2
0
2
0
2
1
0
1
0
1
2
0
1
0
1
2
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
0
1
1
2
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
2
1
2
1
2
2
2
1
1
1
0
0
1
2
0
2
1
1
1
2
1
1
1
2
0
1
1
0
2
1
1
2
1
0
1
1
1
1
1
0
1
2
1
1
0
2
1
1
1
1
0
2
2
1
1
1
2
1
1
2
1
1
1
1
1
2
1
2
2
1
1
1
2
1
0
1
0
0
0
1
1
0
1
1
0
1
1
2
1
1
1
1
0
0
1
1
2
1
0
1
1
2
1
2
0
0
0
1
0
2
1
1
0
1
1
0
1
1
1
2
2
1
1
1
1
1
2
2
1
2
1
1
1
1
2
1
1
1
1
1
2
1
1
0
1
2
1
1
1
1
2
1
2
1
2
2
2
1
1
2
1
1
3
1
1
0
0
1
1
2
1
1
1
1
2
2
1
0
1
1
1
1
1
2
1
1
2
1
1
1
1
1
0
2
1
2
2
2
1
1
1
0
1
1
1
0
2
1
1
1
2
2
1
1
1
1
1
1
2
1
0
1
1
1
1
1
1
1
1
1
1
1
1
0
1
0
1
3
1
2
0
1
1
1
1
1
2
1
1
1
1
2
1
1
0
1
1
1
1
1
2
1
0
1
1
1
1
2
2
1
1
1
2
1
2
0
1
1
2
1
2
1
0
1
2
1
0
2
0
1
1
2
2
1
0
0
1
1
1
1
1
1
1
2
1
1
1
0
0
1
1
2
2
1
1
1
0
0
2
0
2
2
1
1
1
2
0
1
2
0
0
2
2
1
2
1
1
1
1
1
1
1
1
2
1
1
0
0
0
0
1
1
1
1
0
1
1
1
0
2
0
2
2
1
1
2
1
0
1
1
1
0
1
0
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
0
2
1
0
0
1
1
1
2
0
1
0
1
0
1
1
1
2
0
1
1
1
1
1
2
0
2
0
2
1
1
2
1
1
2
1
2
1
1
2
0
1
1
1
0
2
2
2
1
2
0
2
0
2
1
1
1
1
1
1
0
1
0
1
1
1
1
2
1
1
0
1
1
1
1
1
1
0
1
0
1
1
1
0
1
0
2
2
1
1
1
2
1
1
1
1
1
2
1
1
1
2
0
2
1
1
2
1
1
1
0
3
1
0
1
2
2
1
1
2
2
1
1
0
1
1
0
1
1
0
1
1
1
1
2
1
2
1
1
1
1
0
2
1
1
1
2
2
2
0
1
1
0
1
1
1
2
2
2
1
1
2
1
0
1
1
2
2
1
0
2
1
1
1
1
1
1
1
0
0
0
1
1
1
1
1
1
1
1
2
1
1
1
0
1
0
1
1
1
1
1
0
1
0
2
2
0
1
1
2
0
1
1
1
1
2
1
1
0
1
1
1
0
2
1
0
1
1
2
1
1
1
2
1
1
0
2
1
0
2
2
2
1
1
1
0
1
0
1
1
1
1
1
1
1
2
0
2
1
2
1
1
1
1
1
0
1
2
0
1
1
0
2
1
1
1
2
0
1
0
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
0
1
1
3
0
0
1
0
1
0
1
1
0
1
1
2
2
2
1
2
0
0
2
1
1
1
1
1
2
0
2
0
1
1
2
1
1
0
1
0
0
2
0
0
1
2
2
2
2
2
1
0
1
2
2
1
0
0
2
0
1
2
1
1
1
0
1
2
0
1
1
1
1
1
1
2
1
0
1
2
1
1
1
2
0
1
2
2
0
1
0
2
0
1
1
1
1
1
1
1
0
1
2
1
1
1
2
1
2
1
1
2
2
2
1
1
3
2
0
1
1
1
1
1
1
1
2
1
2
2
2
1
1
1
1
2
1
1
1
2
1
1
2
1
1
2
0
1
0
1
1
1
1
1
1
1
0
0
1
1
0
1
1
1
2
1
1
0
1
1
0
1
1
0
1
1
1
0
1
0
1
2
1
2
1
0
1
2
1
2
1
2
1
1
1
2
1
1
1
1
1
1
0
1
1
1
0
1
0
1
0
1
0
1
2
1
0
2
1
2
1
2
2
0
1
0
1
1
1
1
1
0
1
1
1
1
1
1
1
1
2
1
2
2
1
2
2
1
1
0
0
2
2
0
0
0
1
1
1
1
2
1
1
1
1
2
1
2
2
2
0
1
1
0
0
1
1
2
1
1
1
2
2
2
1
1
1
0
1
2
1
1
0
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
2
1
2
1
1
1
2
0
2
1
1
2
1
1
2
1
1
2
1
1
0
0
2
3
1
1
2
1
1
0
1
1
2
2
0
1
1
1
0
1
2
2
2
2
1
2
2
1
1
1
0
2
1
0
1
1
1
1
2
1
1
0
1
1
0
1
2
0
1
1
1
1
1
0
1
0
1
1
1
1
1
0
1
1
2
2
2
1
1
1
1
1
1
0
1
0
1
1
1
1
3
2
1
2
1
2
1
1
1
0
1
2
2
0
1
1
1
1
1
1
3
0
1
1
1
0
2
1
1
1
0
1
2
2
0
0
1
2
1
1
1
1
1
1
1
3
1
1
1
1
1
1
2
1
1
2
1
1
1
1
0
1
1
0
0
0
1
0
1
1
2
1
1
1
2
0
1
1
1
0
0
2
1
1
1
2
0
2
2
1
1
2
2
1
2
0
1
1
2
1
1
1
0
1
0
1
1
1
0
0
2
1
1
1
2
1
2
0
0
1
1
2
1
2
2
1
2
1
1
0
1
0
2
1
1
2
0
1
1
1
1
2
2
1
2
1
0
1
1
2
1
0
1
1
1
0
2
1
2
2
1
2
1
1
0
1
1
1
1
2
2
2
0
1
1
2
1
1
1
2
0
0
1
1
1
1
2
2
1
1
2
1
1
1
2
0
0
1
1
1
2
1
1
2
2
0
1
1
0
0
0
1
1
1
1
1
1
1
1
1
2
2
2
0
2
0
1
2
0
2
2
0
0
1
1
0
1
2
1
3
0
1
1
1
1
0
2
0
1
1
2
2
1
2
1
1
1
1
1
0
1
3
2
1
1
1
0
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
0
2
1
2
2
1
0
2
2
2
2
1
1
2
1
0
2
1
1
1
1
0
1
2
1
1
1
1
1
1
0
1
2
1
1
2
2
1
0
1
0
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
1
4
1
0
1
0
1
2
1
2
1
1
1
1
2
1
0
1
2
2
0
2
0
1
0
1
2
2
1
1
2
2
1
2
0
1
0
2
0
1
2
1
2
0
0
2
1
2
1
1
0
1
1
0
1
1
2
2
1
1
2
1
1
1
0
1
2
1
1
0
1
1
1
1
1
0
0
1
1
2
0
1
1
0
0
1
2
1
2
2
0
1
1
2
2
1
0
2
2
1
1
1
1
1
1
0
1
1
1
1
1
0
1
0
1
1
1
1
1
1
1
1
1
0
1
2
1
1
2
1
1
1
0
2
1
1
1
1
0
1
2
1
1
1
1
1
1
1
0
1
0
1
0
2
1
1
1
1
2
0
2
1
2
0
1
2
1
2
2
0
1
1
1
1
2
0
2
2
2
1
2
1
1
1
0
1
1
1
0
1
1
1
1
1
0
0
1
1
0
2
1
2
1
2
2
1
1
1
0
2
1
1
1
2
1
1
0
0
1
1
1
2
0
1
2
1
1
1
2
1
1
1
0
2
1
1
1
1
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
0
1
1
0
1
2
1
0
1
1
2
1
2
0
1
1
2
2
1
0
1
1
0
0
2
1
1
1
1
1
2
1
1
1
2
2
0
1
0
1
1
1
0
1
2
1
1
1
1
0
2
2
0
1
2
1
2
2
1
1
1
2
2
1
0
1
1
2
0
2
1
1
1
1
1
1
1
2
2
1
1
1
0
1
1
0
1
1
1
1
1
2
2
2
1
1
2
0
1
1
0
0
2
1
0
0
1
1
1
1
1
2
1
1
2
1
1
1
2
2
1
1
0
1
1
1
1
1
0
1
0
1
1
2
0
1
0
2
2
1
1
0
1
1
1
1
1
2
0
1
2
1
1
1
2
1
2
1
1
2
1
1
1
1
1
1
1
0
0
0
1
1
1
1
2
1
1
1
1
1
1
0
0
0
2
0
1
0
1
1
1
0
2
1
1
2
1
2
1
1
1
0
2
2
1
1
1
1
0
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
0
0
1
1
2
1
2
2
1
1
2
2
1
1
2
1
1
1
1
2
1
1
1
1
1
1
0
0
1
1
0
1
1
1
2
0
0
1
2
1
1
0
1
2
2
0
1
2
1
1
1
1
0
1
0
1
1
2
0
1
1
1
0
1
2
1
2
1
1
1
2
1
1
2
3
2
1
0
1
1
2
1
2
2
2
2
0
1
2
1
1
0
1
1
1
0
0
0
1
2
2
2
1
2
1
1
1
2
1
2
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
2
1
2
1
0
1
2
1
1
1
0
1
2
2
2
1
2
0
2
1
1
1
1
2
1
1
1
2
0
0
2
1
1
0
2
0
1
1
1
1
3
1
1
1
1
1
1
0
1
1
1
1
1
1
0
2
0
0
2
1
1
2
1
1
1
2
1
3
2
2
1
2
2
1
1
1
0
3
1
0
0
1
0
1
0
2
2
1
0
1
2
1
0
2
1
0
1
1
0
0
3
1
1
1
1
1
2
2
2
1
2
1
1
2
1
1
1
1
2
0
2
1
2
0
1
1
1
1
1
1
1
0
2
1
1
1
1
2
1
1
2
1
1
2
1
2
1
1
1
1
1
0
0
1
1
1
1
2
1
1
2
1
2
1
1
1
1
0
1
2
0
1
1
2
1
1
2
0
2
1
1
1
0
1
1
1
2
0
1
0
1
1
1
1
1
1
2
2
1
2
1
0
0
1
1
1
2
2
1
1
2
1
2
0
0
1
0
1
1
1
2
2
0
1
2
2
1
1
1
1
1
2
1
2
1
2
1
1
0
1
1
2
1
1
1
1
1
1
0
2
1
1
1
1
1
3
1
1
1
2
1
1
0
1
1
2
1
1
0
0
1
2
0
1
1
1
1
2
0
2
2
1
1
1
0
0
2
1
1
0
1
1
2
0
1
1
0
0
2
1
2
1
1
1
0
1
1
0
0
0
1
2
3
1
1
2
1
0
1
1
2
2
0
1
1
1
1
2
1
2
1
1
0
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
2
2
0
1
1
1
1
1
1
1
2
2
2
2
1
2
1
1
1
2
3
2
2
1
1
2
1
0
1
1
1
1
1
2
2
1
1
2
0
1
1
2
1
0
0
0
1
1
1
2
1
1
0
0
0
0
0
1
1
1
1
1
2
1
2
0
2
1
1
2
1
1
0
2
1
1
0
2
1
2
1
0
2
1
2
2
1
1
1
0
1
1
0
2
2
1
1
1
2
1
2
2
1
1
2
2
1
1
1
1
2
1
1
1
0
1
1
0
1
0
1
1
1
1
1
1
1
0
1
1
1
0
1
1
1
1
1
1
2
2
1
1
0
1
2
1
1
1
1
1
1
2
1
1
2
1
1
2
2
0
1
0
0
1
1
1
1
3
2
2
2
1
1
1
0
1
2
1
1
1
1
1
0
2
1
1
2
2
0
1
1
0
1
1
2
1
1
2
2
1
1
1
1
2
2
1
0
1
1
1
0
2
1
1
2
0
0
1
1
1
1
1
2
0
1
1
1
2
1
1
2
2
2
2
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
0
1
1
1
1
0
1
1
1
0
0
1
1
1
1
0
1
2
1
0
1
0
1
2
2
1
1
2
2
1
1
1
1
3
1
1
1
1
1
2
0
1
1
1
0
1
1
1
2
1
2
0
1
1
1
1
0
0
0
2
1
2
0
1
1
0
2
1
2
2
1
1
1
1
0
1
1
0
1
0
1
1
1
0
0
1
2
0
1
1
2
2
1
1
2
1
1
1
2
1
2
0
1
1
1
1
0
2
1
1
2
1
1
1
1
1
1
1
1
2
1
2
1
1
1
2
0
2
0
1
2
1
2
2
1
1
1
2
1
0
1
1
1
2
0
1
1
2
1
1
2
0
2
2
1
1
2
0
1
0
2
0
1
0
1
2
1
2
2
1
1
1
1
1
1
1
1
0
2
0
1
2
0
1
2
2
2
1
0
1
1
1
2
1
1
1
1
1
1
1
0
1
1
1
2
1
2
1
1
1
0
1
0
2
2
1
1
1
1
0
1
2
1
1
1
1
1
0
1
2
2
1
1
0
1
1
1
1
1
2
0
2
1
1
2
1
2
1
1
1
1
2
0
2
1
1
2
1
0
2
2
1
1
1
1
1
2
1
1
0
1
2
1
2
1
1
1
2
1
1
1
1
1
1
2
0
0
2
1
2
1
1
2
1
2
2
1
0
0
1
2
4
1
1
1
1
2
1
1
2
0
1
1
1
1
1
1
1
2
1
1
0
2
0
1
2
1
0
1
1
1
1
1
1
1
1
0
1
3
1
1
2
1
1
1
1
1
1
0
1
1
2
2
0
0
1
1
1
0
1
1
1
1
1
0
1
1
1
1
2
1
2
2
1
1
1
1
0
2
1
1
1
2
1
1
0
1
2
2
0
1
1
1
1
2
1
1
1
1
1
0
1
2
1
1
0
1
1
1
1
1
1
2
0
0
1
1
2
1
1
1
1
2
1
2
1
2
1
2
2
0
1
2
0
1
1
2
1
1
2
1
2
1
2
2
1
2
1
0
1
0
0
0
1
1
1
1
2
2
2
1
2
1
2
1
2
1
1
1
1
1
1
1
1
2
2
1
0
1
2
1
0
1
2
2
0
2
1
1
1
2
0
1
1
0
0
1
0
0
1
1
1
1
1
2
2
1
1
2
1
0
2
0
0
1
1
1
2
2
0
1
1
1
0
1
1
1
0
1
1
0
0
1
2
0
1
1
1
2
2
2
1
2
1
1
1
1
1
2
2
1
1
1
1
0
1
2
2
1
0
0
7
1
1
1
0
2
1
2
2
2
1
1
1
1
1
1
2
0
1
1
2
1
2
0
1
2
1
0
1
1
0
0
2
1
2
2
1
1
2
2
0
1
2
0
1
1
1
1
1
0
1
1
1
1
2
2
2
1
1
0
1
1
1
1
2
1
1
2
2
1
1
1
0
1
1
1
2
1
2
1
1
1
1
1
0
2
1
3
1
1
2
1
1
1
1
1
1
0
2
1
1
2
1
1
1
2
0
0
0
1
0
1
2
1
1
2
2
2
2
1
2
2
0
0
1
1
2
1
1
1
2
1
1
2
0
2
1
2
2
1
2
1
2
1
2
1
0
2
0
1
0
0
1
1
1
2
0
1
2
2
2
1
2
2
1
1
1
2
1
1
2
2
2
2
1
2
1
0
1
1
1
1
1
2
0
2
0
0
1
0
1
2
2
2
2
2
1
1
1
2
1
2
1
0
1
1
1
2
2
0
1
0
1
0
2
1
1
2
0
0
2
1
1
2
2
0
1
2
3
1
0
1
2
1
1
1
2
1
1
0
2
1
1
1
2
1
0
2
0
0
1
1
1
1
0
1
2
1
1
1
2
0
0
2
1
1
1
1
1
1
1
1
2
0
2
2
0
0
1
2
2
0
1
2
0
1
1
1
1
1
2
0
1
1
1
0
1
2
1
2
1
1
1
0
1
2
1
1
0
1
1
2
0
1
2
1
1
1
0
1
1
0
1
1
1
2
1
1
1
1
2
1
2
2
1
1
0
1
1
1
1
1
1
0
1
2
0
1
0
1
1
1
2
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
1
2
0
1
1
3
1
1
1
2
1
1
2
1
1
1
1
0
1
1
1
2
1
0
1
1
1
0
1
1
1
2
1
1
2
2
0
1
1
0
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
2
1
2
1
0
2
1
0
1
1
0
1
2
1
2
1
2
1
1
1
2
1
0
0
2
0
1
0
2
1
0
1
1
1
0
0
0
1
1
2
2
1
1
1
1
1
1
2
1
1
1
0
0
2
1
1
2
1
2
0
2
1
0
1
1
1
1
0
2
0
1
2
1
1
1
1
2
2
1
1
1
1
2
0
1
1
1
1
1
1
0
1
1
1
1
2
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
2
0
2
0
1
1
1
1
1
1
1
2
0
0
0
1
1
1
1
1
1
2
2
1
1
1
1
0
2
2
1
0
1
2
1
0
2
1
1
0
1
1
2
1
2
1
0
0
1
0
1
1
1
0
0
1
2
1
2
1
1
0
1
1
1
1
1
1
0
2
1
1
1
1
2
2
1
1
2
0
1
1
1
0
0
1
0
2
2
1
1
1
1
0
1
1
1
1
1
1
1
1
1
0
0
2
2
2
1
1
1
2
0
1
1
2
2
2
1
1
0
1
0
2
1
1
1
1
2
1
1
2
2
1
2
2
1
2
1
1
2
1
1
1
0
2
1
2
1
1
0
0
0
2
1
0
1
2
1
1
1
1
1
2
2
0
2
2
1
2
0
1
0
0
1
1
3
2
2
0
2
1
2
1
0
1
1
1
1
1
1
1
3
1
0
2
1
1
2
2
1
1
1
2
2
1
1
1
1
1
0
1
0
1
0
2
1
1
1
1
1
1
2
2
0
1
1
1
1
1
2
1
2
1
2
0
0
1
1
2
1
1
1
0
1
1
2
1
1
2
1
2
0
0
1
1
1
1
1
1
1
0
2
0
1
3
1
1
0
1
1
1
1
1
0
1
1
0
1
1
1
1
2
1
1
2
1
1
2
2
3
1
2
2
1
1
1
2
1
0
1
1
1
1
1
1
1
0
2
1
1
1
1
3
2
1
1
0
2
2
2
0
2
0
1
1
1
1
0
1
2
1
2
1
1
1
0
0
1
2
0
1
1
1
1
1
2
2
2
1
1
2
3
0
1
1
2
0
1
1
2
1
0
0
2
2
2
2
1
1
1
1
1
2
1
0
0
2
1
1
2
0
2
1
1
0
1
1
0
0
1
2
1
1
2
1
1
1
2
0
2
0
1
2
2
1
1
1
0
2
1
2
2
1
1
2
1
4
1
1
2
1
0
2
2
2
2
1
0
1
1
1
1
1
1
2
2
1
1
0
1
0
2
1
2
1
2
2
1
0
1
1
2
2
1
3
0
2
1
1
2
1
1
2
1
2
1
2
2
1
1
1
1
1
1
1
1
0
0
1
1
2
2
1
2
1
2
1
1
0
1
1
1
1
1
1
1
1
1
0
1
0
1
1
2
2
1
1
0
2
2
2
2
1
1
2
1
1
2
0
2
0
1
2
1
2
2
1
0
1
1
1
1
2
1
1
1
2
1
1
1
0
1
1
1
2
2
1
1
0
1
1
1
1
1
0
0
1
1
2
1
1
1
0
2
1
1
1
1
1
2
0
1
0
1
2
1
0
1
1
2
1
1
1
2
2
2
1
1
0
2
1
1
0
1
2
1
1
0
1
2
1
0
0
2
1
1
1
0
2
2
1
0
1
1
2
0
1
2
0
0
1
1
1
1
1
1
1
1
3
1
0
1
0
1
1
2
1
1
2
0
0
2
2
1
0
1
0
1
1
1
0
0
2
0
2
1
2
1
2
1
2
1
1
1
1
1
1
1
1
0
0
1
0
1
0
1
1
2
1
1
2
2
1
2
1
2
2
1
1
2
2
1
1
1
1
0
1
1
1
1
2
1
1
1
1
0
1
2
2
1
0
1
0
1
2
4
1
2
1
1
0
0
1
1
2
1
2
2
2
1
1
1
1
1
0
0
2
0
1
2
1
1
0
1
0
2
1
1
0
0
1
0
1
1
2
2
1
1
0
1
2
1
3
2
1
1
1
1
1
1
0
0
1
2
0
1
2
1
1
2
2
2
1
2
0
1
1
2
1
2
0
1
1
1
1
1
2
1
1
1
2
0
2
2
1
1
2
1
0
0
1
1
1
1
1
1
2
1
2
0
0
1
1
2
2
1
2
1
2
2
0
2
1
1
1
2
1
2
1
1
1
1
1
1
2
1
2
2
1
1
2
1
1
0
1
2
2
1
1
1
1
1
1
0
1
2
1
2
1
1
0
1
2
1
1
1
0
1
1
1
0
1
2
0
1
1
2
1
1
0
0
1
2
1
2
1
1
2
1
1
1
1
2
2
1
1
1
2
1
1
0
0
1
2
0
1
2
0
1
1
2
1
0
1
1
2
2
1
1
0
1
0
0
1
1
1
3
1
1
1
1
1
1
2
1
3
1
2
0
0
0
1
2
2
0
2
1
2
1
1
1
2
0
0
1
1
1
1
1
0
1
1
0
1
1
1
0
1
2
1
2
1
2
1
0
5
2
0
1
1
2
3
1
1
1
2
0
1
1
1
1
1
0
1
1
1
1
2
1
2
1
1
1
1
1
0
0
1
2
1
1
0
2
0
0
1
1
2
1
1
5
1
1
1
2
1
0
1
2
2
1
2
3
1
2
0
0
2
2
0
1
1
1
1
1
1
1
1
1
1
2
1
1
0
0
1
1
1
1
1
1
1
1
1
1
2
1
1
0
1
1
2
1
2
1
2
1
0
1
1
1
1
1
1
1
1
1
2
2
2
2
1
1
1
1
2
2
0
2
1
1
1
0
0
1
0
1
1
1
2
1
1
1
1
0
1
2
1
0
1
0
2
1
2
1
0
1
0
2
0
1
2
2
1
1
0
1
1
1
1
2
2
0
1
1
1
0
2
2
2
2
1
1
1
2
2
2
1
2
2
1
1
1
2
1
1
0
2
1
1
2
1
1
2
0
1
1
1
0
2
1
2
1
0
1
2
1
1
4
1
2
1
0
2
1
2
1
2
1
1
1
1
1
1
1
2
0
2
1
1
2
0
1
1
2
1
2
1
1
1
1
0
0
0
1
2
1
1
1
1
1
2
1
1
1
0
1
1
2
1
2
1
0
0
0
0
2
1
2
2
1
1
1
2
2
1
2
2
1
1
2
0
2
2
1
1
2
1
1
0
0
1
0
1
1
0
2
0
0
2
0
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
0
2
1
1
0
0
1
1
2
2
2
0
1
1
1
0
1
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
2
2
1
1
1
0
1
1
1
0
2
2
1
1
0
1
0
1
1
1
1
1
2
1
2
2
1
1
2
1
1
1
2
1
2
2
1
1
0
1
0
1
2
1
1
0
1
1
1
0
2
1
1
1
2
1
1
1
1
2
1
1
1
1
1
2
0
1
1
0
2
1
2
1
0
0
2
2
0
0
1
1
1
1
2
2
0
1
2
1
0
2
2
2
1
1
2
1
0
1
1
1
1
2
2
1
1
1
1
2
1
1
2
0
1
1
1
1
1
1
1
1
2
0
1
1
1
1
1
1
1
1
1
0
1
0
1
2
0
2
1
0
2
1
0
2
1
0
1
0
1
1
1
1
1
0
0
1
2
0
0
1
1
1
1
2
1
0
1
2
2
0
1
0
2
1
1
1
1
1
2
0
0
1
2
1
1
1
1
1
2
1
0
2
2
0
1
1
1
1
1
2
0
2
1
1
1
1
2
1
1
1
2
1
0
2
2
1
1
1
1
1
1
2
1
2
1
1
1
1
2
1
2
0
1
1
0
1
2
1
1
0
2
2
1
1
1
2
1
1
1
1
1
1
2
1
1
2
1
1
0
1
2
1
2
2
2
1
2
1
1
1
1
0
0
0
1
1
1
2
2
2
0
1
2
2
1
2
0
0
1
1
1
1
1
1
1
1
0
1
2
1
1
2
0
1
1
1
2
2
1
1
1
1
1
0
2
1
1
0
1
2
2
1
0
1
0
0
1
2
1
1
1
2
2
1
1
2
2
2
1
1
2
0
1
1
1
1
0
1
1
0
1
0
0
0
1
1
0
1
1
1
1
1
1
1
2
2
1
1
3
1
1
2
1
0
1
1
1
2
1
1
1
2
1
1
1
3
1
0
1
2
1
0
2
2
1
1
1
0
1
2
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
2
1
0
0
1
1
2
1
2
1
1
0
1
0
2
3
2
1
1
1
0
0
2
0
2
0
1
0
1
2
1
1
1
1
1
2
1
2
2
2
1
1
1
1
1
1
1
1
1
3
0
2
0
0
2
2
2
1
1
1
1
1
2
1
1
1
1
1
2
2
1
2
1
2
2
0
0
2
1
1
1
2
1
1
0
1
1
2
2
0
2
2
1
1
1
0
2
1
2
1
1
1
2
0
2
1
1
1
2
1
0
2
0
1
2
0
2
1
1
1
1
1
1
1
1
2
1
0
2
1
1
1
1
2
0
1
1
1
1
0
2
1
2
2
1
0
1
1
2
0
0
1
2
1
1
1
2
1
0
2
2
2
1
1
0
1
0
0
2
2
1
1
1
0
0
1
1
1
1
1
2
1
1
2
1
0
1
1
1
2
2
2
2
2
2
2
1
1
0
1
0
1
1
1
1
1
2
1
1
1
2
2
1
2
2
2
1
1
1
2
2
1
1
1
2
1
1
0
0
1
1
1
0
1
2
1
1
1
2
2
1
1
1
1
1
2
1
0
1
1
1
0
2
1
1
0
1
1
1
1
1
1
0
2
2
1
1
0
2
1
1
1
1
1
0
0
2
1
1
1
2
0
2
1
0
2
1
1
2
1
0
1
1
0
2
1
1
0
2
1
1
0
1
1
0
0
2
2
1
0
2
2
1
0
0
1
1
2
1
1
2
2
1
2
1
1
1
1
1
1
2
1
1
1
0
2
2
1
1
1
0
2
0
1
1
2
1
1
1
1
1
2
1
1
1
2
1
2
2
1
0
1
1
1
1
1
1
0
2
1
0
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
1
0
1
0
0
0
1
2
2
2
1
1
0
1
2
1
1
1
1
2
1
0
1
1
1
2
1
1
1
2
2
1
1
1
2
1
2
1
0
1
1
1
0
2
1
0
1
1
1
1
0
0
2
0
2
2
2
1
1
2
2
1
0
1
0
2
2
0
1
0
2
1
1
1
1
1
1
1
1
2
2
2
1
2
1
1
1
1
2
1
0
1
2
0
2
1
1
1
1
0
1
1
1
1
1
1
1
0
1
0
1
1
1
2
1
1
1
1
0
1
1
1
2
1
1
1
1
1
0
1
2
1
2
1
0
1
0
0
1
2
1
1
1
1
1
2
0
1
1
1
1
1
1
3
2
3
2
1
1
2
1
1
2
2
1
1
2
2
0
1
2
1
2
1
1
1
2
1
0
2
2
2
1
1
1
0
1
1
0
1
1
0
0
1
1
1
0
3
1
0
0
1
1
1
0
1
1
1
1
1
1
0
1
1
0
4
1
1
2
1
1
1
1
2
0
2
2
2
1
0
1
2
2
1
1
2
1
1
0
1
0
1
0
1
1
1
1
1
1
2
1
0
2
1
1
2
2
1
2
0
2
1
2
1
1
1
1
2
1
1
0
2
1
1
1
0
1
2
2
1
0
1
1
2
0
0
1
1
2
1
1
1
1
2
1
2
1
0
1
2
2
1
0
0
2
1
1
2
1
1
1
1
1
1
2
2
2
1
1
2
2
1
1
1
2
1
1
2
1
0
1
1
2
0
0
1
0
1
2
0
0
2
1
1
0
1
1
1
1
2
1
1
1
1
1
2
2
1
1
0
1
1
1
1
2
2
2
0
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
0
2
2
2
1
2
1
1
2
1
1
1
0
1
2
2
1
1
1
1
1
0
1
1
1
1
1
1
0
1
2
1
0
1
2
2
0
1
1
1
0
1
1
0
1
2
1
1
2
2
0
1
1
2
0
1
1
1
1
1
1
1
1
2
1
1
0
3
1
1
1
1
1
2
1
2
2
1
1
1
1
0
1
1
2
0
2
2
1
2
1
1
1
1
2
1
2
1
2
0
0
1
1
1
1
1
1
0
1
2
1
1
1
1
0
0
2
1
1
1
0
2
0
1
1
0
2
1
2
1
2
0
1
1
0
2
1
1
1
1
0
2
1
2
2
1
1
1
1
2
2
1
1
0
2
1
0
2
1
1
1
1
2
1
1
1
2
1
1
1
2
0
2
0
1
0
0
2
2
1
1
0
1
1
1
1
2
2
0
2
1
1
2
1
2
1
1
1
1
1
1
1
1
1
2
2
0
1
2
0
1
0
0
2
1
2
0
1
2
1
1
2
0
1
2
1
1
0
3
2
1
0
1
1
2
1
0
1
1
0
1
1
1
2
2
0
1
1
1
1
1
1
2
1
1
2
1
1
1
0
1
2
2
1
2
2
1
1
1
1
1
0
2
0
1
2
0
1
0
0
4
2
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
2
2
1
1
1
1
2
0
1
2
0
1
1
1
1
1
1
1
1
0
1
2
1
1
1
0
1
0
1
1
1
2
1
0
2
1
1
1
1
1
1
1
2
1
2
1
1
2
1
2
1
2
1
0
2
1
0
1
0
1
1
1
0
2
1
1
2
0
1
1
0
1
2
2
1
1
2
1
1
0
1
1
1
0
0
2
1
1
1
1
1
1
0
1
1
2
2
1
1
1
1
1
1
4
1
2
2
1
1
2
1
1
1
0
1
2
2
1
1
0
1
0
1
0
1
1
1
1
1
0
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
0
2
1
1
1
2
1
1
0
1
0
1
1
2
1
1
1
0
2
1
2
1
2
1
2
1
1
1
2
1
1
1
2
1
1
2
2
0
1
1
1
1
1
1
2
1
1
1
3
2
2
1
2
1
0
1
0
0
2
2
2
2
1
2
0
1
1
0
1
2
0
1
1
1
1
2
1
1
1
1
2
2
1
0
2
0
1
0
2
1
1
1
0
2
2
1
1
2
0
2
2
0
2
0
1
1
2
1
0
1
2
0
1
1
2
1
1
2
1
1
0
1
1
1
2
1
1
2
0
1
1
2
1
1
2
1
2
1
1
1
2
1
1
1
2
2
0
1
2
0
0
0
2
0
0
1
1
1
1
1
1
1
0
2
1
1
1
1
2
1
2
1
1
2
1
0
0
2
1
2
1
1
1
1
1
0
2
1
1
1
1
1
2
1
1
1
1
2
1
0
1
2
0
1
1
0
1
2
1
1
3
0
2
1
0
0
1
0
0
1
0
1
1
1
2
1
1
1
1
1
2
1
2
2
1
0
1
0
1
1
1
1
2
1
0
2
1
0
0
2
1
0
2
0
1
2
0
1
2
1
1
1
2
0
1
0
1
1
1
1
2
1
1
1
0
1
1
0
0
0
1
1
3
2
1
2
1
0
1
1
1
1
2
0
1
1
0
1
0
0
1
1
2
0
1
1
1
2
0
1
1
0
1
1
1
2
1
1
1
1
3
1
1
1
1
1
0
1
2
2
2
1
1
1
2
3
0
1
2
2
0
2
1
1
2
1
1
2
0
1
1
1
1
2
2
1
1
1
0
1
0
0
1
0
1
1
0
1
1
1
1
2
1
2
1
1
2
2
1
0
0
2
2
1
0
2
2
2
1
0
2
1
1
2
1
0
1
1
1
1
0
1
1
1
2
1
3
2
2
2
0
2
1
1
2
1
1
1
0
2
0
2
1
1
1
1
2
2
0
2
1
2
0
3
1
1
0
0
2
2
3
0
1
2
0
1
2
1
2
1
2
2
1
1
1
2
1
1
1
1
0
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
2
1
1
1
1
2
1
0
2
0
2
0
2
2
0
1
1
2
1
1
1
1
0
0
0
1
0
2
1
0
1
0
2
1
1
2
2
1
1
1
1
0
0
2
1
1
1
1
1
1
1
1
1
1
1
0
2
0
1
1
2
1
1
1
0
2
0
2
2
2
1
0
2
1
2
1
0
1
1
0
2
2
2
2
1
1
2
1
2
1
0
2
1
2
2
2
2
0
1
1
0
2
0
0
2
1
2
2
1
1
1
2
1
0
1
1
2
1
0
1
1
1
1
1
2
1
1
1
0
1
2
1
1
1
0
1
0
1
1
1
1
0
1
1
1
1
1
2
1
1
2
1
2
2
1
1
1
1
1
1
1
2
1
1
1
0
2
2
1
1
1
2
1
2
2
1
2
2
2
0
1
2
0
1
2
2
2
1
2
2
1
2
2
2
0
1
1
1
1
0
1
2
1
1
1
1
0
0
1
2
1
1
0
1
1
1
1
0
1
0
1
0
2
0
2
2
0
2
1
4
0
1
3
1
0
1
1
2
0
1
1
2
1
1
1
1
1
0
0
1
1
1
2
2
1
1
1
1
1
1
1
2
2
1
1
0
1
0
1
2
2
1
0
1
0
2
2
2
1
1
1
1
2
1
1
1
1
0
1
1
2
1
1
1
2
2
1
1
1
1
0
1
2
1
1
2
0
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
2
2
1
1
1
0
2
2
1
1
2
2
1
1
1
0
2
0
1
1
0
1
1
1
1
1
1
2
1
1
1
0
1
1
1
1
1
2
1
1
0
1
1
1
1
1
0
1
1
1
1
1
1
1
0
0
1
1
2
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
0
1
0
0
1
2
2
1
1
2
0
2
1
0
0
1
0
2
1
2
1
2
1
1
1
2
1
2
0
1
1
2
1
2
0
1
1
1
2
0
1
1
0
1
1
1
0
1
0
1
1
2
2
1
1
1
0
1
1
0
1
2
1
2
1
1
2
2
2
1
0
1
2
1
2
1
1
1
0
1
1
1
1
1
1
2
3
1
0
1
1
1
1
1
1
1
1
1
2
1
4
0
1
1
2
1
1
1
1
1
2
2
2
1
1
2
2
1
1
2
1
2
1
1
1
1
1
0
1
2
1
0
1
1
1
2
1
1
1
2
2
0
1
1
1
2
1
2
0
1
1
1
1
1
1
1
1
0
1
2
1
1
1
1
1
1
1
1
1
2
1
2
1
2
0
2
0
1
1
2
0
2
0
2
2
0
2
1
1
1
2
1
2
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
0
0
1
1
0
2
0
1
1
1
0
1
1
2
1
1
2
1
1
0
0
1
1
1
0
2
2
2
1
1
2
0
0
1
1
1
1
1
1
1
1
1
2
1
1
1
1
0
1
1
1
2
1
1
2
1
1
2
1
2
1
2
2
0
1
2
1
1
1
1
1
1
2
1
1
2
2
1
2
1
2
1
1
1
2
1
2
1
1
2
1
0
1
1
1
1
2
2
1
1
2
2
1
1
1
2
0
1
0
1
1
1
0
1
1
2
1
2
1
1
2
2
1
1
3
1
1
2
1
1
1
2
1
2
2
2
1
1
1
1
2
1
0
1
2
0
1
1
1
1
1
0
0
1
1
1
1
2
1
1
1
2
0
2
2
0
1
2
2
1
0
1
1
2
1
2
1
1
1
1
2
1
1
1
2
1
0
2
2
1
2
1
1
0
1
0
1
1
1
1
0
1
1
0
2
1
2
1
1
1
1
1
2
1
1
0
0
2
2
0
1
0
1
1
1
1
1
2
2
0
1
1
1
1
1
1
0
2
2
2
0
0
2
2
1
0
1
3
2
2
0
2
1
1
1
0
0
2
2
1
1
0
1
2
2
1
1
0
0
1
2
1
1
0
1
1
1
1
2
1
2
2
2
1
1
1
0
1
1
1
2
1
2
0
2
1
1
1
2
0
1
0
1
2
1
2
0
1
1
1
0
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
2
0
1
1
1
1
1
0
2
0
0
2
1
0
1
0
2
1
2
2
0
1
1
1
1
2
2
1
0
2
1
1
1
1
0
1
1
1
1
1
1
1
0
1
1
0
1
1
0
1
1
1
0
1
0
1
1
0
0
1
2
2
2
1
2
2
1
1
2
0
0
1
0
1
1
0
0
1
1
0
1
1
2
1
1
1
1
1
1
1
1
1
4
2
1
1
1
1
1
1
1
1
1
0
1
2
2
0
1
2
2
1
1
1
1
1
2
1
1
1
1
1
1
2
2
1
2
0
1
1
0
0
1
0
0
0
1
1
1
1
2
1
0
1
2
2
1
1
1
1
1
1
2
2
0
1
0
1
1
1
0
1
0
0
1
2
1
2
1
0
1
2
0
1
1
0
1
2
2
1
1
1
1
1
2
1
0
1
1
1
2
0
1
2
1
0
1
1
2
1
1
1
1
1
1
5
0
1
1
0
1
2
2
1
1
1
2
1
1
1
1
1
2
2
1
2
1
1
1
1
2
1
1
1
0
0
1
1
1
0
2
1
1
1
1
2
1
2
2
1
1
1
2
1
2
0
1
0
1
2
2
5
1
1
2
1
1
4
1
1
1
1
0
1
1
1
1
1
2
1
1
0
3
0
2
0
0
1
0
1
1
1
2
1
1
2
1
1
1
1
2
1
1
1
1
3
0
1
1
0
0
1
2
1
2
1
2
5
1
2
1
1
0
1
0
1
2
1
2
1
0
1
2
1
2
1
1
1
1
1
0
2
2
0
1
1
1
1
2
1
2
1
1
2
1
2
1
1
1
0
1
2
1
1
1
2
1
1
2
2
1
1
2
2
0
2
2
1
1
1
0
1
1
1
2
1
2
0
2
1
1
1
1
2
2
1
0
1
2
1
1
1
1
2
0
1
1
0
1
2
1
2
2
1
1
1
2
1
1
1
1
1
0
1
1
1
1
3
1
1
1
1
1
0
0
0
1
1
2
1
2
1
2
2
2
1
1
0
0
1
1
1
2
2
2
2
1
1
0
1
1
1
1
0
2
1
1
1
1
1
1
1
2
0
2
1
1
2
1
2
0
0
1
1
1
1
1
1
0
1
0
0
2
2
1
1
1
2
2
1
2
1
0
1
1
1
0
1
1
1
1
0
1
2
0
0
1
0
3
3
1
1
1
1
2
2
0
2
0
1
1
2
1
1
1
2
1
0
1
1
2
0
2
1
1
1
1
2
1
2
2
0
2
1
1
1
2
2
1
2
2
2
1
1
1
2
1
1
1
2
1
1
2
1
2
1
1
1
1
2
2
2
1
2
1
0
2
2
0
0
0
1
1
1
0
1
1
1
4
1
0
1
2
2
2
1
1
0
1
3
1
2
1
2
1
1
1
0
1
2
0
0
1
1
1
0
2
1
1
2
1
1
1
1
0
2
1
1
1
1
1
1
1
2
1
3
2
0
1
0
0
1
2
2
1
1
2
0
2
1
1
2
1
3
2
1
1
0
2
0
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
2
2
1
1
1
1
0
1
1
2
1
0
2
1
0
1
1
1
1
2
1
2
1
1
1
2
1
0
1
1
1
1
1
1
1
0
1
1
2
2
2
2
2
1
2
1
0
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
0
2
1
0
1
2
1
1
0
1
1
1
2
2
2
2
2
1
2
1
1
2
1
1
1
1
1
2
1
1
0
1
0
1
1
1
0
2
1
1
2
0
0
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
0
1
0
1
1
2
1
2
0
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
0
1
1
1
1
1
1
1
2
1
0
2
1
1
2
1
1
1
1
1
2
1
1
1
1
0
1
0
1
1
1
2
2
2
2
0
0
2
2
1
1
1
2
1
1
2
1
1
2
1
1
2
0
1
1
1
1
0
1
0
1
1
2
1
0
1
1
1
1
1
1
2
1
1
1
1
0
1
1
2
1
0
2
1
2
1
0
1
1
1
2
2
1
1
1
1
1
1
0
1
1
1
1
0
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
2
1
1
2
1
2
2
2
1
1
1
2
1
2
1
0
1
1
1
1
1
1
1
2
1
2
1
0
2
1
2
1
1
2
0
2
2
1
2
2
1
1
1
0
2
0
0
0
1
0
0
1
0
1
1
1
1
2
1
2
2
2
0
2
1
2
1
2
1
0
2
1
2
1
2
3
0
1
1
1
0
1
1
1
0
2
1
1
0
2
1
1
2
1
1
2
1
1
0
1
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
0
2
1
1
1
1
1
0
1
1
1
3
1
0
1
1
1
2
1
1
1
0
0
0
0
1
0
1
2
1
1
1
0
1
1
0
2
2
1
0
1
1
1
1
1
2
2
1
1
2
1
2
1
0
1
2
2
1
2
2
1
1
1
0
0
1
2
2
1
1
2
1
2
1
1
1
2
1
0
1
1
1
1
1
1
1
1
2
1
2
1
2
1
1
1
2
1
1
1
2
1
2
1
2
1
1
1
2
0
1
1
1
0
2
2
1
2
1
1
2
1
1
2
2
2
1
2
1
2
1
1
2
1
0
2
1
1
0
1
1
1
1
1
0
1
2
3
1
0
0
1
1
1
1
1
1
2
1
1
1
2
1
0
1
1
2
0
1
1
1
1
1
2
0
1
1
1
1
1
1
1
2
1
0
1
1
1
1
1
1
1
1
0
1
1
2
2
0
1
1
1
1
0
1
1
0
1
1
1
1
1
1
1
0
1
1
1
1
1
0
0
1
2
1
0
0
1
1
1
2
1
0
1
0
1
0
1
0
2
2
1
1
1
2
1
2
0
1
1
1
1
1
0
1
1
0
1
2
0
1
2
1
1
1
2
2
1
1
2
1
1
2
1
1
0
1
2
1
1
1
2
1
2
2
2
1
1
1
1
1
1
1
1
2
1
2
1
2
1
0
1
1
0
1
1
1
1
2
0
2
2
0
1
1
1
1
1
1
1
0
2
2
0
1
2
2
2
1
1
1
1
1
2
0
1
1
0
1
1
1
1
1
1
0
2
0
1
1
1
2
0
2
1
1
2
1
1
1
1
2
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
2
2
2
1
0
1
2
1
1
2
2
2
0
1
2
0
1
0
0
1
0
0
1
1
1
0
1
1
1
1
2
2
1
1
2
1
2
1
1
1
1
1
2
0
1
1
1
1
1
1
0
1
2
1
0
2
1
1
0
1
0
1
0
1
2
1
1
2
1
1
1
1
1
1
2
0
1
1
1
1
1
1
1
1
1
1
2
0
2
1
2
0
1
1
1
1
1
0
0
1
2
4
1
0
1
1
2
1
1
1
0
1
1
1
1
0
0
1
1
1
0
2
1
2
0
2
1
0
2
1
1
2
1
1
1
0
1
3
1
2
1
1
2
0
1
1
1
1
1
1
1
2
1
1
0
2
0
1
0
2
2
2
2
0
1
1
1
1
0
1
0
1
1
0
0
1
1
1
2
2
0
0
1
1
1
1
2
1
2
1
1
2
2
2
2
1
1
2
1
2
0
2
1
1
1
1
1
1
1
2
1
2
2
2
0
1
1
1
1
0
2
1
1
1
0
1
1
1
1
0
1
2
2
1
1
1
0
1
0
1
0
1
1
0
1
2
1
2
1
1
1
0
0
1
2
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
1
0
2
1
1
1
1
0
1
2
1
0
1
2
1
2
0
1
1
2
0
1
1
1
1
0
1
1
1
0
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
0
2
2
1
1
0
1
1
1
2
1
2
1
1
1
0
0
1
0
1
1
2
1
1
1
0
0
1
1
1
1
1
1
1
2
1
2
1
2
1
2
1
1
2
1
1
2
1
2
1
1
2
1
0
1
2
1
1
2
1
1
2
1
1
1
1
1
1
1
2
2
0
0
0
1
1
1
0
1
2
1
1
2
1
1
2
2
0
0
1
1
1
0
1
1
1
1
1
0
1
1
1
1
1
0
2
2
0
1
2
1
1
0
2
1
0
1
1
1
1
1
1
2
1
1
0
2
1
2
0
2
1
2
1
1
2
1
2
0
1
3
1
1
1
1
1
0
1
1
1
0
1
0
1
1
1
1
1
0
1
1
0
2
1
3
1
1
1
0
1
1
1
1
1
1
1
2
2
2
2
1
1
1
0
2
1
1
2
1
1
1
2
1
1
0
1
1
0
0
0
1
1
0
1
1
1
3
1
2
1
2
0
2
1
1
0
1
1
1
1
1
1
2
1
1
2
0
2
1
0
1
2
1
1
1
1
1
1
1
1
2
1
1
1
0
1
1
2
1
1
1
1
1
1
1
2
0
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
0
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
2
2
1
0
1
3
1
2
1
1
2
2
1
1
1
1
1
1
1
1
1
2
2
1
1
0
1
2
1
2
2
2
0
0
1
1
1
1
2
1
0
2
2
1
2
2
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
1
2
1
2
0
2
2
1
0
1
0
2
2
0
1
2
0
1
1
1
1
1
1
1
1
1
2
1
0
1
1
1
2
2
2
2
0
1
1
0
1
0
2
2
1
1
2
1
1
1
2
1
3
1
1
2
2
2
1
1
0
1
1
2
1
1
0
1
1
1
1
1
1
1
0
0
1
1
1
1
1
1
1
1
1
0
1
2
1
1
1
0
2
1
1
2
2
1
0
0
1
1
1
1
1
1
0
2
0
2
1
0
1
1
1
1
0
1
0
0
1
1
0
1
2
1
2
1
2
2
1
2
1
0
1
0
1
0
0
1
0
0
1
2
1
2
1
2
1
0
1
1
1
1
1
0
1
1
1
1
2
1
0
0
1
1
1
1
1
2
1
1
1
1
0
1
1
1
1
1
0
1
1
1
0
1
1
0
2
0
0
2
1
1
1
0
1
2
1
1
2
0
1
1
1
1
1
0
0
1
1
1
2
0
1
1
1
1
2
1
0
1
1
1
1
1
1
1
2
1
2
1
1
1
1
0
0
3
1
0
1
0
1
1
1
2
0
1
1
0
1
2
2
1
2
0
1
1
1
2
2
0
1
1
1
2
1
1
0
3
2
1
0
1
1
0
0
2
1
0
0
1
1
0
2
1
1
1
1
0
4
1
1
2
1
0
1
2
2
2
2
1
2
2
1
1
1
2
2
1
1
1
0
1
1
1
2
1
1
1
1
1
1
2
2
1
2
1
1
1
1
2
0
0
0
1
0
0
1
2
1
1
1
1
0
1
1
1
1
0
2
0
2
1
1
1
1
0
1
1
2
1
2
0
1
2
1
1
1
2
2
2
1
0
1
2
1
1
1
1
2
2
1
1
0
1
1
1
1
1
1
1
1
0
0
1
1
2
2
1
1
1
1
1
2
1
2
1
1
2
1
1
0
1
1
0
0
1
1
1
1
0
1
1
1
2
2
1
1
1
1
1
2
1
2
1
0
0
0
1
1
0
1
1
1
2
2
2
1
0
1
2
3
1
1
2
0
1
1
2
1
1
1
1
2
1
1
1
0
1
2
1
1
2
2
1
1
1
1
1
1
0
0
0
2
2
1
1
4
1
0
1
1
2
0
1
1
1
1
0
0
0
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
2
1
0
1
2
0
1
1
2
1
1
0
0
1
1
0
1
1
1
1
1
1
1
2
1
1
0
1
2
2
2
0
3
1
1
2
1
1
1
1
0
1
1
2
1
2
1
0
0
1
2
2
2
2
2
1
0
1
1
0
1
1
0
1
0
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
0
1
2
0
1
1
2
1
1
1
0
1
0
1
2
0
1
2
1
2
1
2
0
0
2
0
1
1
0
2
3
2
1
0
1
1
1
2
1
1
1
1
1
1
1
1
1
2
0
2
0
1
2
1
1
1
0
1
1
0
2
0
2
0
2
1
1
1
1
1
1
1
2
1
1
1
1
2
0
1
1
1
1
1
2
2
1
2
1
2
1
1
1
2
1
1
1
1
1
0
2
1
0
1
1
0
1
1
2
2
1
1
2
0
1
0
1
0
2
0
2
1
1
1
1
1
1
2
1
1
2
1
2
1
1
2
1
1
0
1
2
1
2
1
1
1
1
2
1
1
0
1
1
1
1
1
0
1
2
1
1
1
2
1
0
1
1
1
2
1
0
2
2
0
1
2
1
1
1
1
1
0
2
2
1
1
1
1
2
2
1
0
0
1
0
0
1
1
0
1
1
0
1
2
1
1
1
1
2
1
0
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
2
2
2
1
1
2
1
1
1
1
1
0
1
0
1
1
2
1
1
1
1
1
1
1
2
1
1
2
2
1
3
1
0
1
1
2
0
1
2
1
1
1
1
2
1
2
1
0
2
1
0
0
0
1
2
1
0
1
1
1
2
1
1
1
1
1
1
2
2
2
0
1
1
1
2
1
1
1
1
1
2
1
1
2
1
1
2
1
2
3
1
0
1
0
1
1
1
2
1
1
1
2
0
1
1
1
1
1
1
1
2
1
2
1
1
2
1
2
1
2
2
2
1
1
4
1
1
1
1
1
1
1
1
1
1
2
2
1
1
0
0
2
0
0
1
0
1
2
1
2
1
1
1
2
2
1
2
2
2
2
1
2
0
1
1
1
2
1
2
0
1
1
1
0
0
0
1
1
1
2
0
1
1
1
1
0
1
0
2
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
2
1
1
1
0
2
1
1
1
2
0
0
1
1
0
1
1
0
0
1
2
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
2
1
0
3
1
1
2
1
2
0
1
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
2
0
1
2
1
3
2
1
2
3
2
0
0
2
2
1
1
1
1
0
1
1
1
0
1
1
1
0
1
1
1
1
2
2
1
2
1
1
1
2
1
2
0
0
0
1
2
1
1
2
2
2
1
0
1
2
0
1
1
2
1
0
1
0
2
1
0
2
1
1
1
1
0
2
1
1
1
1
1
1
1
2
1
1
1
2
1
0
1
1
1
1
1
1
0
1
0
0
1
0
0
2
0
1
0
2
2
1
1
1
0
2
2
1
1
1
1
1
5
2
1
2
0
1
1
2
2
1
2
2
1
1
2
1
1
0
2
1
2
0
1
0
1
0
0
1
2
0
3
1
1
0
0
0
1
2
2
1
2
1
1
1
1
0
1
1
1
2
1
0
2
1
1
1
0
1
1
4
1
2
2
1
1
2
2
1
1
1
1
1
2
1
1
2
1
0
1
2
1
1
1
1
1
2
2
1
2
1
1
1
0
1
0
1
1
0
1
1
1
1
1
1
2
2
1
1
1
0
2
1
1
2
1
1
1
1
0
2
2
1
0
2
1
1
2
2
1
0
2
2
1
1
1
1
1
0
1
1
2
0
0
1
3
2
1
1
1
1
1
2
1
1
3
2
1
1
1
2
1
1
1
1
1
1
0
1
1
0
2
1
1
0
1
1
1
1
1
1
1
1
0
1
2
1
0
2
2
3
2
1
1
0
1
1
0
2
1
2
2
1
2
1
2
1
1
3
2
1
0
1
1
1
1
2
1
2
1
1
2
1
0
1
1
1
2
0
2
0
2
1
1
2
2
1
1
1
1
0
1
1
1
0
0
0
2
0
1
1
1
1
1
1
1
1
1
3
2
1
1
2
2
1
0
2
1
0
1
1
0
1
2
1
0
0
1
1
2
1
1
1
2
1
0
1
1
1
1
1
0
1
1
1
1
1
2
1
1
1
0
1
0
1
1
1
1
2
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
0
0
1
2
2
1
0
1
1
1
0
1
1
2
1
1
1
1
0
1
2
1
1
1
2
1
2
1
1
1
2
1
1
1
0
1
1
0
1
1
2
1
1
1
1
1
0
2
0
1
0
1
1
1
2
1
1
1
0
1
1
0
2
2
1
0
1
1
0
1
1
1
1
1
1
1
0
1
1
1
2
1
0
2
1
1
1
0
1
1
1
0
1
1
1
1
2
2
1
1
2
2
0
2
1
1
1
2
1
0
2
1
1
1
2
1
0
1
1
1
2
2
0
1
1
1
0
2
1
1
0
1
1
2
1
1
2
1
2
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
3
1
1
1
2
1
2
0
1
0
1
1
2
1
1
1
1
2
0
1
2
1
0
1
1
1
1
0
1
0
1
1
0
0
1
1
1
2
0
1
0
1
1
1
1
1
2
1
0
1
2
2
1
2
1
0
2
1
1
1
0
1
1
1
1
2
1
0
1
2
1
1
0
1
1
1
1
1
1
1
1
2
2
0
1
1
1
1
1
0
1
1
1
1
2
1
1
1
0
0
2
1
1
1
1
2
1
1
0
3
1
1
0
1
3
1
1
1
1
2
1
1
0
1
2
1
0
1
2
1
1
1
2
2
1
1
1
2
1
1
1
1
1
0
2
0
1
1
1
0
2
1
2
2
0
1
2
1
0
2
1
1
1
2
2
1
1
1
1
1
2
1
1
2
1
1
1
1
1
2
2
1
1
1
1
2
1
0
1
1
1
1
0
1
1
1
1
1
0
1
1
2
2
1
2
0
1
1
0
1
1
1
1
2
1
1
1
1
2
1
1
0
0
1
0
1
1
1
1
1
2
0
2
1
1
1
1
2
1
1
1
1
2
2
1
1
0
1
1
1
1
1
1
1
2
1
0
1
1
1
1
2
1
2
1
1
1
1
2
1
2
1
1
3
2
2
2
1
1
1
1
4
1
2
0
1
1
1
1
1
1
2
2
1
1
2
0
2
0
1
1
1
3
2
1
1
0
1
1
1
0
1
1
2
1
1
2
1
1
1
1
1
1
1
2
2
2
2
1
1
2
1
0
1
0
1
1
2
2
2
1
1
2
1
1
1
1
1
2
1
1
2
2
1
1
3
1
1
1
2
1
2
0
1
1
2
1
1
1
1
1
2
2
3
1
2
2
2
1
1
1
2
0
1
1
1
0
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
0
2
1
1
1
1
2
2
1
1
1
2
1
1
0
1
2
1
1
2
2
1
0
2
1
2
2
2
0
2
1
1
1
1
1
1
0
1
1
1
1
0
1
2
1
1
1
1
0
1
1
1
2
2
2
1
2
0
0
1
1
1
1
0
1
2
1
0
1
1
2
2
1
2
1
1
2
1
2
2
2
1
1
1
1
1
0
1
1
2
1
1
1
1
1
1
2
1
2
1
2
0
1
2
3
1
2
1
1
2
0
1
2
0
1
1
1
1
1
0
1
2
0
1
0
1
1
1
0
2
1
2
2
2
0
1
1
2
2
0
1
1
2
1
2
1
0
0
0
1
1
1
0
1
1
1
1
2
0
0
1
1
2
1
1
1
1
0
1
1
1
0
2
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
2
1
2
1
0
1
0
2
1
0
1
1
1
2
0
2
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
2
1
2
1
2
1
2
1
1
1
0
1
2
2
0
0
2
2
1
1
1
1
1
2
1
1
2
2
1
2
1
1
2
1
2
1
1
0
2
1
1
0
1
0
1
1
2
1
3
0
1
0
1
1
0
1
1
1
0
1
0
1
1
1
1
1
2
1
0
0
1
5
1
1
0
1
1
1
2
1
1
1
1
2
2
1
2
0
2
1
2
1
1
1
2
1
2
1
2
2
1
2
2
0
1
1
3
2
2
1
1
1
2
1
0
1
1
0
1
0
1
2
1
1
2
2
0
2
1
2
1
0
1
2
1
0
2
1
2
1
2
0
1
2
5
2
2
1
1
1
2
1
2
0
1
1
1
2
0
1
0
2
2
2
0
2
2
1
1
1
0
2
2
1
1
1
2
1
1
1
0
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
0
0
1
2
1
1
1
2
2
1
2
2
2
1
2
1
1
1
0
2
1
1
2
2
1
0
0
2
0
2
1
2
1
1
0
1
1
1
1
1
2
0
1
1
1
1
1
1
1
0
2
1
1
1
1
1
0
1
1
1
1
1
0
1
1
1
0
1
1
1
1
2
1
1
0
0
1
1
1
0
2
1
1
1
2
1
2
1
1
1
1
1
1
1
0
1
1
2
1
1
1
1
2
1
0
1
1
0
1
1
2
1
1
0
1
1
2
1
1
0
1
1
0
2
0
1
1
0
1
1
1
2
2
1
0
1
1
1
1
1
2
0
1
1
1
1
0
1
1
1
2
1
1
1
0
0
2
0
1
0
1
1
1
0
2
1
1
1
2
1
1
1
1
2
0
1
0
1
2
1
0
0
2
2
0
1
1
2
2
1
1
1
1
1
2
0
2
0
2
0
0
1
2
1
1
1
0
1
2
1
1
1
1
1
1
2
1
2
2
3
2
1
2
1
1
1
2
1
0
1
0
1
2
0
2
1
1
0
1
1
2
2
2
1
1
2
1
1
2
2
1
1
1
0
1
1
1
1
3
1
0
1
2
1
0
3
1
1
1
1
2
1
1
0
0
1
1
1
1
1
2
0
1
0
1
0
2
1
1
0
1
1
1
1
1
2
1
0
1
1
2
1
1
1
1
1
2
2
1
1
1
0
1
1
2
1
1
1
2
1
0
2
0
1
1
1
1
1
0
1
0
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
0
1
2
1
2
2
1
1
1
0
1
2
1
1
1
1
1
1
2
2
1
0
1
2
1
2
1
0
1
1
2
1
1
1
1
1
2
1
0
2
1
2
2
1
1
0
0
2
1
1
0
1
2
1
2
0
0
0
1
0
0
1
0
0
0
0
1
1
2
0
1
0
2
1
1
2
1
1
1
1
1
2
0
1
0
1
0
2
2
2
0
1
1
1
1
1
1
0
1
1
1
1
2
0
1
2
2
1
1
0
0
1
2
1
0
2
1
1
1
2
1
1
1
1
1
0
0
1
2
1
2
1
1
1
2
1
1
1
0
1
1
1
0
1
0
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
0
2
2
2
2
1
2
1
0
2
1
1
1
1
0
1
0
1
2
0
2
2
1
1
2
0
1
1
1
1
1
2
1
1
1
1
0
1
1
1
1
2
1
2
0
2
2
2
2
1
1
1
2
1
1
1
1
1
1
1
1
0
1
1
1
0
1
2
1
2
0
2
1
2
2
1
0
2
1
1
1
1
1
2
2
2
2
2
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
0
0
0
1
0
1
0
1
3
1
1
2
0
0
1
1
1
0
1
1
1
1
1
1
0
0
1
1
1
1
2
1
2
2
1
2
2
2
0
2
1
1
1
1
0
1
2
2
1
1
2
1
1
0
2
0
1
1
0
1
2
1
0
1
1
0
2
0
1
1
2
1
1
0
3
1
1
2
1
0
1
1
1
0
0
1
2
1
1
2
1
0
1
1
1
1
2
1
2
1
1
0
1
1
1
2
1
1
1
1
1
1
0
0
2
0
1
2
1
1
1
2
2
0
1
1
1
2
0
1
1
2
1
0
1
1
2
1
0
1
1
1
1
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
0
0
0
1
1
1
1
0
1
2
1
1
2
0
2
0
1
1
0
2
0
0
1
0
0
1
1
2
1
1
2
1
1
1
1
0
2
2
0
1
2
1
1
1
1
1
1
1
1
1
1
1
1
0
0
2
1
2
1
1
1
1
1
1
1
2
2
2
0
1
2
1
2
0
2
2
2
2
0
1
1
2
1
0
2
3
2
2
2
1
1
2
1
1
2
1
0
1
0
1
1
0
1
2
1
1
1
3
1
2
1
2
1
2
1
1
1
0
1
1
0
2
2
1
1
2
2
1
1
1
2
1
1
1
1
1
0
0
1
1
0
1
1
1
0
0
3
1
0
1
1
1
1
1
0
1
1
1
1
2
2
0
1
0
1
1
2
1
1
1
0
1
1
1
1
0
1
2
1
2
0
2
1
1
1
2
2
2
2
1
0
1
1
1
1
2
1
0
2
1
1
2
2
2
1
1
2
0
2
0
1
1
0
1
1
1
2
1
1
2
1
1
1
2
2
0
1
2
1
1
2
2
1
1
1
1
1
0
2
1
1
1
2
0
1
1
1
1
2
1
0
2
3
1
1
1
1
1
0
0
1
1
1
1
1
1
1
1
1
1
1
0
1
0
2
1
1
1
1
2
1
0
1
1
1
1
1
1
0
2
0
2
2
2
1
1
2
1
1
1
1
0
1
1
2
1
0
1
0
0
0
1
1
0
2
0
1
1
1
1
1
1
1
1
0
1
1
1
1
1
2
1
0
2
1
1
1
0
1
1
1
2
1
2
1
1
2
1
1
0
1
0
2
2
2
1
2
1
2
2
0
1
0
2
1
1
1
2
1
1
2
1
1
2
0
2
1
1
1
2
1
0
1
0
1
1
1
1
1
1
1
0
2
2
1
1
1
2
1
1
1
1
2
1
1
2
1
2
1
1
1
1
2
2
2
2
2
1
1
0
1
1
1
2
1
1
1
2
1
1
1
0
2
2
2
1
1
0
1
1
2
0
2
2
0
1
2
2
0
0
2
1
1
2
1
0
0
1
1
1
1
1
1
1
1
0
0
2
1
1
1
1
1
1
2
0
2
1
4
3
2
1
0
0
0
1
2
1
1
1
1
1
1
1
2
2
1
2
0
1
1
0
1
1
1
2
1
0
0
1
0
1
1
1
0
0
1
0
1
2
1
1
0
1
2
1
1
1
2
1
1
3
1
1
1
2
1
1
2
1
1
2
0
2
1
1
1
0
1
1
2
2
1
0
1
1
1
1
2
0
0
1
1
2
2
0
1
1
0
0
1
0
1
1
1
1
1
2
2
0
1
1
1
2
2
0
1
0
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
2
1
2
0
1
1
2
1
1
1
0
0
1
1
1
1
2
2
2
2
3
1
1
1
2
1
2
1
1
0
1
1
2
2
0
2
0
0
1
1
2
2
1
1
1
0
2
2
2
2
1
1
1
2
1
1
1
0
0
2
1
0
0
1
2
1
0
1
1
1
2
0
2
1
1
2
2
1
1
2
0
1
2
1
1
1
1
1
1
1
0
1
0
2
1
0
3
1
1
1
1
2
1
1
2
1
2
1
2
0
1
1
0
0
0
2
2
1
1
1
1
1
1
1
1
1
2
2
1
0
1
1
2
1
1
2
1
1
1
2
2
2
1
2
1
0
1
2
1
1
0
1
1
1
1
1
1
1
1
2
2
1
1
0
1
0
0
1
2
1
1
1
1
0
1
2
2
0
1
0
1
1
0
1
1
2
1
1
1
2
1
1
1
1
1
0
1
2
1
1
0
1
1
1
0
2
1
1
2
0
2
1
0
1
1
0
1
2
1
0
1
0
1
1
1
1
1
1
1
0
1
1
1
0
0
0
1
1
2
1
1
1
0
2
1
1
2
0
1
1
1
1
0
0
0
1
2
2
1
1
2
1
2
2
2
2
2
1
2
1
2
2
1
1
2
0
1
0
0
1
2
0
0
1
2
1
2
0
1
1
1
1
1
1
0
0
1
1
1
1
2
2
1
1
2
1
2
2
1
1
1
2
1
1
1
2
0
1
0
1
2
2
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
1
2
1
2
0
0
1
1
2
1
2
1
1
1
2
0
1
2
1
0
0
1
1
2
2
1
0
1
0
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
0
1
1
1
1
1
0
2
1
2
1
1
1
2
0
1
0
1
2
1
2
1
2
0
1
2
0
0
1
1
0
2
0
1
2
1
1
1
1
2
2
1
1
1
1
0
1
1
0
0
0
0
1
1
2
1
2
1
2
1
1
0
1
1
1
1
1
1
1
2
1
0
0
1
1
2
0
2
1
2
1
1
1
1
1
1
0
2
2
1
0
2
2
1
0
1
1
1
1
1
1
0
2
1
0
1
1
1
1
1
2
1
1
2
2
1
2
2
0
1
1
0
1
1
1
1
1
1
1
2
2
1
1
0
1
1
2
1
1
0
1
2
1
2
2
0
1
1
1
1
1
2
1
2
1
3
2
0
1
2
2
1
2
1
1
2
1
1
1
1
0
1
1
0
1
1
2
0
0
1
1
1
1
1
0
1
1
2
0
1
2
0
2
0
1
1
1
1
2
1
1
1
1
1
2
1
1
2
0
2
1
2
1
2
1
1
1
1
2
1
0
1
1
0
2
0
1
1
1
0
1
2
1
2
2
0
1
1
0
0
2
0
0
0
1
1
1
0
2
1
1
1
1
1
1
2
1
1
1
0
1
0
2
2
1
1
2
1
2
2
1
2
1
0
1
1
3
1
1
1
2
2
0
1
0
1
2
1
0
1
2
2
1
2
2
1
1
2
2
1
1
1
1
2
1
2
2
1
0
0
1
0
1
2
1
0
1
1
2
1
0
2
1
1
5
2
2
1
0
2
1
0
1
1
0
1
1
1
1
0
1
1
1
2
1
1
1
1
1
0
1
1
2
2
2
2
0
2
1
2
1
2
1
2
1
1
2
2
1
2
1
2
1
1
0
1
1
1
2
1
0
1
1
1
1
1
2
0
1
2
0
1
1
1
1
1
1
1
3
1
2
1
1
2
1
2
2
1
2
2
1
2
1
1
1
1
1
2
1
1
1
1
0
2
2
1
1
1
1
1
2
2
0
1
0
1
1
1
1
0
1
2
2
1
0
1
1
2
0
1
0
2
1
0
1
1
2
0
2
1
0
1
1
1
1
1
1
2
1
1
1
0
1
0
2
1
1
1
1
1
2
1
1
1
1
1
2
0
1
1
1
0
0
1
2
1
1
1
1
1
1
2
1
1
1
1
2
0
2
2
1
0
1
0
0
1
2
2
2
1
1
2
1
0
0
1
1
1
1
1
1
1
0
0
2
0
2
0
2
1
2
1
1
1
2
0
0
1
0
0
1
1
1
0
0
2
1
2
2
1
0
2
2
1
0
1
2
1
0
1
2
2
2
2
2
1
0
1
1
1
1
3
1
2
1
1
0
1
1
0
1
2
2
3
1
2
1
1
1
0
0
2
2
1
1
1
2
1
1
1
2
2
2
1
2
2
1
1
1
1
1
1
1
2
1
2
1
2
1
1
0
1
1
1
2
1
1
1
1
1
0
1
1
0
2
1
1
1
1
1
2
1
1
1
1
2
0
1
1
0
1
1
0
1
1
1
0
1
1
1
1
2
0
1
2
2
2
1
1
2
1
1
0
1
2
1
2
1
0
0
1
1
1
2
2
1
2
1
2
1
1
1
1
1
1
1
0
1
0
1
0
2
1
0
1
1
1
1
1
1
1
2
2
1
1
0
2
1
2
1
2
1
1
1
1
0
0
1
0
0
1
1
2
0
2
0
2
1
2
1
0
2
1
1
1
1
2
0
0
1
2
1
1
1
2
2
1
1
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
0
2
1
1
1
1
1
1
0
0
1
1
0
1
1
0
2
1
0
1
2
5
2
1
2
2
2
1
1
2
0
1
2
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
2
1
1
1
1
2
1
1
1
1
1
0
1
0
3
2
1
1
1
2
1
0
0
1
1
1
1
1
1
1
1
1
1
2
0
2
1
1
1
1
0
1
0
0
0
1
1
2
0
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
0
0
1
1
1
1
0
0
1
2
1
2
2
1
0
0
0
1
2
1
2
2
1
3
0
2
1
2
1
0
0
0
0
0
2
1
1
0
1
1
0
1
1
1
0
1
2
1
1
2
2
1
2
1
1
2
1
1
1
1
1
1
1
1
1
0
1
0
2
2
1
1
1
1
1
0
2
1
2
0
2
2
1
1
0
1
0
1
1
0
1
1
1
2
1
2
2
1
1
1
2
2
1
2
0
1
1
1
1
1
1
0
1
1
1
1
1
1
1
3
2
1
1
1
1
1
0
0
1
0
1
1
2
1
1
2
2
1
2
1
1
1
2
1
0
1
0
1
0
0
1
2
3
0
1
0
1
2
1
1
2
1
1
1
1
2
1
1
1
1
0
1
0
1
2
1
0
2
1
1
0
1
1
1
1
1
1
2
1
1
2
1
1
0
1
1
0
1
2
0
1
1
2
2
1
1
1
1
2
0
1
1
2
0
0
1
2
2
1
2
1
1
2
1
1
1
1
1
1
0
1
2
1
2
1
1
0
1
0
0
0
0
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
4
1
0
1
0
2
0
1
2
1
2
1
2
2
2
1
1
2
1
1
0
1
1
1
1
2
1
1
0
0
1
2
2
2
1
1
1
2
2
2
2
2
1
1
2
2
0
1
1
0
0
1
1
2
0
0
1
2
1
2
1
1
1
1
2
2
1
1
1
2
1
1
2
1
1
0
1
0
1
0
0
0
2
1
1
2
2
0
2
1
0
2
1
1
0
1
1
0
2
1
0
2
1
1
2
1
1
2
2
1
0
1
1
1
1
1
1
0
1
0
0
1
1
1
0
1
1
1
1
1
0
2
1
0
0
1
1
2
1
0
2
1
1
1
3
0
1
1
1
1
1
1
1
2
2
1
0
2
2
1
1
2
1
1
2
1
0
1
0
1
1
1
1
1
1
0
1
0
2
2
1
1
1
0
1
2
1
1
2
0
2
0
1
0
0
2
0
1
0
0
2
0
1
1
1
2
1
1
2
1
1
0
1
1
1
3
0
0
1
2
2
1
1
1
1
1
1
2
1
0
2
1
0
1
1
1
1
1
0
1
3
1
1
2
1
1
1
1
1
1
1
1
0
1
1
1
1
1
2
1
1
2
2
0
1
2
1
1
3
0
2
1
1
1
1
2
2
1
0
1
1
1
2
2
1
0
1
1
1
1
2
0
1
1
1
1
1
1
1
1
0
1
1
1
1
2
1
2
2
1
0
2
1
0
1
1
1
1
2
1
0
1
0
0
1
1
2
1
2
1
2
1
1
1
0
2
1
1
1
1
2
1
3
1
1
2
2
2
0
0
1
1
2
1
1
1
0
1
1
1
1
2
0
1
0
1
1
1
1
2
1
1
2
1
2
2
1
0
1
1
1
1
2
1
0
2
1
2
1
1
1
0
2
1
2
0
1
1
2
1
2
0
2
1
1
1
0
1
0
1
1
1
2
0
1
1
0
1
1
1
2
2
0
2
1
2
1
2
0
2
2
1
0
1
2
1
1
3
1
0
1
1
1
0
1
1
2
2
0
3
1
1
1
1
2
1
1
1
1
1
1
0
2
0
1
1
0
1
1
1
2
1
1
1
1
2
0
3
1
1
1
1
1
2
1
2
1
1
0
1
2
0
1
2
1
1
1
0
1
1
1
0
2
1
1
1
1
1
1
2
1
1
0
1
1
1
2
3
1
1
1
1
1
2
1
1
0
1
1
2
2
1
2
2
1
1
1
1
2
0
1
0
1
2
0
0
4
2
1
1
1
1
2
1
1
1
1
1
0
0
2
1
1
1
1
1
1
0
1
1
1
1
1
0
0
2
1
1
1
1
1
1
1
1
1
2
1
0
1
0
1
2
1
2
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
0
2
2
2
1
0
0
2
1
2
1
0
2
2
1
2
1
1
0
1
1
2
0
1
1
2
2
1
2
1
1
1
1
1
1
0
1
1
1
2
2
1
1
1
2
0
1
1
1
1
1
2
1
1
2
1
1
1
1
0
1
0
2
1
1
2
1
2
0
0
1
2
1
1
1
0
2
1
0
1
1
0
2
1
2
1
0
2
2
0
0
1
1
1
2
1
1
1
0
0
3
1
1
1
0
1
1
1
1
1
2
1
1
0
1
0
1
0
1
0
0
2
2
1
1
1
1
1
2
1
2
1
1
2
2
1
1
2
1
1
1
1
0
1
2
1
2
1
1
2
1
1
2
2
0
1
1
1
2
1
0
0
1
1
1
1
2
1
1
2
1
1
1
1
0
1
1
1
2
0
1
1
1
0
0
0
0
1
1
2
1
1
2
0
1
0
1
0
1
0
0
1
1
2
1
1
1
0
3
1
0
1
1
1
1
2
2
0
2
2
2
1
1
1
1
0
0
1
0
2
1
1
1
1
1
0
1
2
2
1
2
2
1
1
0
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
2
2
1
0
1
1
1
1
1
1
1
1
1
2
1
2
0
0
1
2
1
1
2
1
1
2
1
1
1
2
1
1
0
2
1
0
1
0
1
1
0
0
2
2
0
0
2
0
1
1
0
2
2
1
2
0
1
1
1
1
1
2
1
2
0
0
1
2
1
1
1
1
2
1
1
1
2
2
1
1
1
1
2
2
1
0
2
1
1
2
0
2
2
1
1
1
1
0
1
1
2
0
0
0
2
1
1
0
0
0
0
0
1
1
0
1
2
1
1
2
1
1
2
0
2
1
1
0
1
1
2
0
1
2
0
1
1
2
1
2
2
1
1
2
1
2
1
1
0
2
0
0
1
2
1
1
0
0
2
1
1
0
0
1
1
1
1
0
1
1
2
1
1
1
2
1
1
1
0
0
1
1
1
2
1
1
1
2
2
2
1
2
1
1
2
1
0
2
0
1
1
0
1
0
1
1
2
1
1
2
1
1
1
1
1
0
1
2
1
1
1
0
0
2
1
1
2
0
2
2
1
1
0
2
0
2
0
1
2
1
1
1
1
1
1
1
2
0
0
1
1
0
2
1
2
2
0
2
3
1
1
2
0
2
0
0
1
1
1
1
1
2
1
1
1
0
2
2
0
2
0
1
2
1
0
1
2
1
0
1
2
1
2
1
1
0
1
1
0
0
1
0
0
2
0
0
2
1
1
1
1
2
1
1
1
1
0
1
1
1
1
1
0
2
1
1
0
0
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
0
1
1
2
1
1
1
0
2
0
1
0
1
1
1
2
2
1
1
1
2
0
1
3
2
1
2
0
1
2
1
0
1
1
1
1
1
1
0
1
1
1
2
0
0
1
0
1
1
1
1
1
1
0
2
1
1
1
1
0
1
1
1
1
1
1
1
1
1
2
2
1
0
1
0
1
1
1
1
1
2
1
2
2
2
1
0
2
1
1
2
1
0
1
1
1
1
0
1
1
1
2
1
0
1
2
1
1
1
1
1
1
1
0
1
2
1
1
2
1
1
1
1
0
1
0
1
1
1
1
1
2
1
2
1
1
1
0
1
1
1
2
0
2
2
0
2
1
1
1
1
1
1
1
1
1
0
1
1
2
1
1
1
0
2
0
0
0
0
1
1
3
1
0
1
1
1
1
2
1
1
0
0
1
2
0
1
1
0
1
1
0
1
2
1
2
2
1
2
1
1
1
1
1
2
2
2
0
2
1
1
1
1
1
2
2
1
1
0
1
1
0
1
1
1
2
1
1
0
1
2
2
1
1
1
0
1
1
2
1
1
1
1
1
2
2
1
2
1
2
1
1
0
1
1
2
2
1
1
1
1
1
1
1
1
0
2
2
2
0
1
1
2
0
0
1
1
1
2
1
1
1
0
2
1
2
1
1
2
2
1
1
2
0
2
2
1
2
0
1
2
1
1
1
1
2
2
0
2
1
1
0
1
1
1
1
1
1
0
1
1
1
2
1
1
1
2
2
2
1
1
2
1
1
1
1
1
0
2
1
1
1
1
2
1
1
2
1
2
2
0
0
1
1
2
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
1
0
1
0
1
2
1
1
1
1
1
1
2
2
1
0
2
1
2
1
1
0
1
1
2
1
0
1
1
2
1
0
1
2
2
1
1
1
0
2
1
1
1
1
1
0
1
0
1
1
1
1
1
1
2
1
1
1
0
2
0
1
2
1
2
1
1
1
1
2
1
2
1
2
1
0
2
1
0
0
1
0
1
1
2
1
1
1
2
1
0
2
1
1
2
3
0
1
1
2
2
1
1
2
0
2
1
1
1
1
1
1
1
1
1
0
1
1
1
2
2
1
1
2
2
1
1
0
2
2
0
1
2
2
1
1
1
1
0
1
1
1
0
1
1
1
1
1
1
2
0
1
1
2
0
1
1
1
1
1
1
1
1
0
1
0
1
1
1
1
1
1
2
1
1
1
0
0
1
1
1
2
0
1
1
1
1
1
1
2
0
1
0
1
0
2
1
1
1
2
1
2
1
2
2
1
1
1
1
1
1
1
0
0
2
2
1
0
1
1
2
2
2
1
1
1
0
1
1
3
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
2
1
2
1
0
2
1
0
2
1
2
0
1
2
1
1
1
1
2
0
1
2
1
1
0
2
1
0
1
0
1
1
1
1
2
0
0
2
1
2
1
1
1
1
1
1
1
0
1
1
0
1
0
1
0
0
1
1
1
1
1
2
1
1
1
1
1
2
0
1
1
2
1
2
2
1
1
2
1
1
1
1
1
1
1
0
1
1
0
0
1
1
1
1
1
1
1
0
1
1
2
1
1
0
1
1
2
1
2
1
1
1
1
1
2
0
2
1
0
1
2
1
0
1
0
1
0
1
1
3
2
2
1
0
0
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
0
1
1
2
0
1
1
0
1
0
1
1
2
0
1
1
0
1
1
1
1
1
1
1
0
1
0
1
1
0
1
0
1
0
0
2
1
1
2
1
1
2
1
1
1
1
1
1
0
0
0
2
1
2
1
1
1
1
0
1
0
1
1
0
1
1
0
2
1
1
1
1
1
1
0
1
1
1
1
0
1
1
1
1
1
1
0
1
1
1
1
0
1
1
1
0
1
0
1
0
1
0
1
0
2
2
1
2
0
0
0
2
0
1
2
2
1
1
1
2
2
1
1
1
0
2
1
1
2
2
2
1
0
2
2
1
1
0
0
1
1
0
2
1
2
1
2
1
1
2
1
1
2
0
1
1
0
0
2
2
1
2
2
0
2
1
2
2
0
1
1
1
1
1
1
3
1
0
2
1
1
2
1
2
1
1
0
2
1
1
0
1
2
2
0
2
1
0
1
1
1
0
2
2
1
0
2
1
1
1
1
1
2
1
1
0
0
1
1
3
1
1
1
1
1
1
0
0
2
0
1
1
0
0
1
1
2
2
1
0
1
0
3
1
0
1
1
0
1
1
1
1
0
1
1
0
1
2
1
0
0
2
0
2
3
2
0
1
0
1
0
1
0
0
1
1
0
2
0
1
2
1
2
2
0
0
1
0
1
1
1
1
2
0
1
0
0
1
0
1
0
2
1
1
0
1
1
2
1
1
1
2
1
1
1
0
0
1
1
0
1
1
1
2
1
0
2
1
1
1
0
1
1
1
1
1
1
1
1
1
2
1
1
1
1
0
0
1
1
1
0
0
2
2
1
0
1
1
1
2
1
1
1
1
2
1
1
1
0
1
1
0
1
0
1
0
1
1
0
2
1
1
0
1
1
1
1
1
0
0
2
0
1
1
0
1
1
1
1
1
1
1
1
2
1
0
1
1
1
1
2
1
1
0
0
0
1
3
2
1
1
1
0
2
1
1
1
0
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
2
2
1
1
0
1
2
0
1
0
1
2
1
2
2
0
1
0
1
1
1
0
0
1
1
1
0
0
2
2
1
1
1
0
0
0
1
1
1
1
0
1
1
2
1
1
1
1
1
2
1
1
0
0
1
1
1
1
0
1
1
1
0
2
0
1
0
1
1
0
0
1
2
2
2
1
1
0
1
1
1
1
2
1
1
0
1
0
1
1
1
1
1
1
0
2
0
1
1
1
1
1
2
1
1
2
1
2
1
1
1
2
2
1
2
1
1
2
2
1
1
0
0
1
2
1
1
1
1
0
1
1
1
1
1
1
2
0
1
2
1
0
1
1
1
1
0
1
1
2
0
0
1
1
1
1
2
3
1
2
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
0
1
1
1
2
1
0
2
2
1
1
1
0
2
1
2
1
2
2
2
1
0
2
1
1
0
0
2
0
2
1
1
1
2
1
2
1
1
1
2
1
1
1
0
1
0
2
2
1
2
1
1
1
2
1
2
2
1
1
1
1
2
1
0
1
1
1
2
1
1
1
2
1
2
2
2
1
2
1
2
0
1
2
1
1
1
2
1
0
1
1
0
1
2
1
0
1
1
2
2
1
0
1
1
1
3
1
2
0
1
0
1
0
1
1
2
1
1
1
2
1
0
1
0
0
1
1
1
1
1
2
0
1
1
1
1
1
1
0
0
2
1
1
2
1
2
1
1
1
2
0
1
2
1
1
1
0
1
1
0
1
2
2
0
1
1
1
1
1
1
2
1
1
0
1
2
2
1
0
2
0
1
1
1
2
0
0
0
0
2
1
2
2
1
0
1
1
2
0
1
0
1
0
3
1
1
1
1
1
1
0
2
2
1
1
1
1
1
2
0
2
2
1
1
1
2
1
0
1
2
2
2
2
0
2
2
0
2
0
1
1
2
1
2
2
2
2
1
1
2
1
3
1
0
2
0
1
1
0
0
1
1
2
1
1
2
2
1
0
1
0
1
1
1
1
2
2
2
1
0
1
1
1
1
1
1
0
1
0
1
1
2
0
2
2
1
1
1
1
0
0
2
1
0
1
1
1
1
0
2
1
1
1
2
1
0
1
2
2
1
2
1
1
1
1
2
1
1
0
1
1
1
0
1
1
1
2
1
2
1
1
2
0
0
1
1
0
2
0
1
1
1
1
2
1
1
0
0
2
2
1
0
0
1
0
1
2
2
1
2
1
0
0
1
1
2
1
1
1
0
1
1
2
2
1
1
0
0
0
0
1
1
0
2
1
1
1
1
1
1
2
1
1
0
2
1
1
1
0
1
2
1
1
1
1
1
1
1
2
2
0
1
0
2
1
1
1
2
1
1
2
1
1
1
2
2
1
1
1
1
0
2
1
1
1
1
2
2
2
0
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
0
1
2
1
2
0
1
1
2
1
1
0
1
2
1
1
2
1
0
1
1
1
1
1
1
2
1
1
1
1
1
2
1
0
2
1
2
2
1
1
2
2
2
1
0
1
0
1
2
1
1
0
1
1
1
1
1
2
0
1
1
1
2
1
1
0
0
2
1
0
1
2
1
1
0
1
1
0
0
1
2
1
1
0
1
1
1
1
0
1
2
2
1
1
2
1
1
0
1
0
1
0
0
1
1
1
1
4
2
0
2
1
1
1
1
1
1
1
1
1
1
1
0
1
1
2
0
1
2
1
1
0
2
1
1
1
2
1
0
1
2
0
1
1
0
1
1
1
1
1
1
1
1
0
2
2
2
0
1
2
1
1
2
1
0
1
1
1
1
1
0
1
2
1
1
1
1
1
1
2
1
1
0
1
2
0
1
1
2
2
2
1
0
1
1
0
1
1
1
2
1
0
2
1
1
1
1
0
0
1
1
1
1
2
1
1
2
2
1
2
1
0
1
2
1
1
1
1
1
1
2
2
0
1
1
1
1
1
0
2
1
0
2
1
1
1
0
1
0
1
1
2
1
1
2
1
0
3
1
2
1
1
1
0
1
0
2
1
1
2
0
2
0
1
2
1
0
1
1
2
1
2
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
2
1
2
1
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
0
2
0
0
1
1
1
0
0
2
1
1
0
1
1
2
2
1
2
1
1
2
1
1
1
1
2
1
1
0
1
2
2
0
1
1
1
1
2
0
1
0
1
1
1
1
1
1
1
0
1
1
1
1
1
1
2
2
1
0
2
1
1
2
1
1
1
1
2
2
1
1
1
2
1
0
1
2
1
1
1
1
0
1
1
2
2
1
1
2
2
1
0
1
0
1
1
1
1
1
1
0
2
1
0
1
0
2
0
1
1
1
1
2
0
1
1
2
2
1
1
0
1
0
1
1
0
1
1
1
1
0
0
2
1
2
0
1
1
2
1
0
1
1
2
0
1
1
0
2
2
2
0
1
1
1
1
2
1
0
1
1
1
1
1
2
2
1
1
2
2
1
2
2
1
0
1
0
1
2
1
1
0
1
1
0
0
2
1
1
1
0
0
1
0
1
1
2
1
1
0
2
0
1
2
2
1
1
1
2
1
0
1
1
1
0
2
1
1
1
0
1
1
0
1
1
1
1
0
2
2
1
1
2
0
3
1
1
2
1
1
1
1
2
2
1
1
1
2
1
1
1
1
1
2
1
1
0
1
0
1
2
1
1
1
1
2
0
1
2
1
1
1
1
0
0
0
2
1
1
2
4
1
2
0
1
1
0
1
1
1
2
1
1
0
0
1
1
2
1
1
1
1
1
0
0
1
2
2
1
2
2
0
1
1
0
0
0
1
1
1
2
1
1
2
1
2
1
0
1
5
2
0
1
1
2
1
0
1
1
2
0
2
2
1
1
1
1
1
2
1
2
1
1
0
2
1
2
1
0
0
0
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
0
0
0
2
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
2
2
2
2
1
1
0
2
1
1
1
1
2
1
2
2
1
2
2
2
1
1
0
1
1
1
0
1
1
2
2
1
2
2
1
0
1
2
1
0
2
1
1
2
2
0
1
0
2
0
0
2
1
1
1
0
1
0
1
1
0
1
2
2
2
1
1
2
1
1
1
1
0
1
0
1
0
2
1
2
2
1
1
1
1
0
0
1
0
1
1
2
0
0
1
2
2
2
1
1
1
1
1
2
1
1
1
1
0
1
2
2
1
1
1
1
0
2
1
1
2
2
1
0
1
0
1
2
1
1
1
1
1
0
1
1
2
0
0
1
2
1
0
1
0
2
1
0
2
1
1
2
1
1
0
0
1
0
1
1
0
1
0
1
1
2
1
3
1
0
1
1
1
2
1
1
2
1
2
0
1
1
1
1
1
1
1
0
0
0
1
1
1
1
0
1
1
1
1
1
0
2
1
1
1
1
2
2
2
1
0
1
2
1
1
1
0
1
1
1
1
2
2
1
1
1
1
0
2
2
1
1
1
2
2
2
1
2
0
1
2
0
1
1
1
1
2
0
1
2
2
2
1
1
0
1
1
1
1
1
1
0
1
2
1
2
2
1
0
2
2
1
1
0
1
1
1
1
1
2
1
1
1
1
1
0
1
0
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
2
0
2
1
1
1
1
1
1
1
1
1
1
0
2
1
1
2
2
1
2
1
0
0
2
1
1
1
1
1
2
2
0
1
1
1
1
0
1
1
1
2
1
1
1
0
1
2
1
2
1
1
2
2
0
2
0
2
0
1
3
2
2
2
1
2
1
1
1
1
0
1
1
1
1
0
1
1
1
0
2
1
1
1
2
1
1
1
1
1
1
1
2
0
1
1
3
2
2
1
2
1
1
2
2
2
1
1
0
2
2
2
0
1
1
1
2
1
1
1
1
2
2
1
1
1
1
1
2
1
1
1
1
0
1
2
1
1
1
1
1
2
1
0
1
2
1
1
1
1
1
1
2
0
1
2
2
2
0
2
0
1
2
1
1
1
2
0
1
0
1
1
2
1
1
1
1
1
1
1
1
1
1
2
0
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
0
2
1
2
1
0
0
1
0
0
2
1
2
1
1
1
2
1
2
1
1
2
2
0
1
1
1
2
1
1
1
1
0
0
2
2
0
2
1
0
1
1
0
2
1
1
2
1
1
0
0
2
1
2
0
1
1
1
2
0
2
0
1
2
2
1
1
2
2
1
3
2
1
2
1
1
1
2
1
1
1
1
2
2
2
1
1
1
0
1
2
0
1
1
1
1
1
0
1
1
2
2
1
1
1
2
1
2
2
1
2
1
1
1
1
1
1
1
0
1
1
1
1
1
1
0
2
0
2
2
0
1
2
1
2
2
1
1
1
1
1
1
1
1
2
0
2
1
2
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
0
1
1
1
1
0
1
0
1
1
1
1
1
1
1
0
1
1
1
1
0
0
0
0
1
2
1
1
1
1
0
2
1
1
0
1
1
1
2
2
2
1
1
1
2
0
2
1
1
1
1
1
1
2
1
1
2
1
2
1
0
1
1
1
2
2
1
2
1
1
2
1
0
2
0
1
1
0
2
1
2
1
1
1
1
1
1
1
1
0
1
1
2
0
1
2
2
0
2
1
2
1
1
1
0
2
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
2
1
1
1
2
1
1
1
0
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
0
1
1
2
0
2
0
1
2
1
0
1
2
0
1
1
1
1
1
1
0
0
2
1
2
1
1
0
0
1
3
2
1
2
0
1
1
1
1
1
2
1
1
0
0
1
2
1
1
0
2
1
1
0
1
1
0
1
1
0
2
1
1
2
1
1
1
1
1
2
1
1
2
1
1
0
0
1
1
1
1
1
1
1
1
2
2
1
0
0
2
1
0
1
1
1
0
1
3
1
1
1
1
1
1
2
0
1
2
1
1
1
2
1
1
2
1
2
1
0
1
1
2
2
2
1
1
1
2
0
2
1
1
1
1
1
0
1
1
1
1
1
0
1
0
2
1
1
1
1
1
1
2
1
1
1
0
3
0
2
1
0
2
1
1
1
2
2
2
2
2
0
1
2
1
2
1
1
1
1
1
2
1
0
1
1
2
2
2
1
2
1
0
2
1
1
0
1
0
0
1
1
1
1
1
1
1
1
2
1
1
1
0
1
0
1
1
1
2
2
2
0
3
1
1
1
2
1
1
1
1
0
0
0
1
1
1
0
1
1
1
1
2
2
1
1
1
1
0
1
1
0
1
1
1
2
0
0
4
2
0
1
1
2
2
1
2
1
1
2
0
2
1
0
1
1
2
1
2
1
1
2
1
1
2
1
1
1
2
1
1
1
2
0
0
1
1
1
1
2
1
1
1
2
0
0
1
1
0
1
1
2
1
1
1
1
1
0
0
1
1
1
1
0
2
1
1
1
1
1
0
0
0
0
0
1
1
1
5
1
1
1
2
1
1
2
1
1
1
1
1
1
0
1
1
2
2
1
1
1
0
2
1
1
0
1
0
1
1
2
1
1
2
1
0
1
0
0
1
1
0
1
1
1
0
1
1
2
0
2
0
1
2
0
2
0
1
1
1
2
1
1
1
0
1
1
1
1
1
1
0
1
0
1
1
2
2
1
1
1
1
1
1
1
0
1
1
1
1
1
2
2
1
1
2
1
2
0
2
1
1
2
2
2
0
1
1
1
1
0
1
1
1
0
1
1
2
3
1
2
1
1
1
1
0
1
1
1
1
0
1
0
1
1
1
1
1
1
1
0
1
2
1
1
1
0
1
1
2
1
2
1
2
2
0
0
2
1
2
1
2
1
1
2
1
2
0
1
1
1
2
1
2
2
2
1
2
0
1
0
1
1
1
2
1
1
1
2
1
2
1
1
1
0
2
0
1
2
2
2
1
1
1
1
0
0
1
1
1
2
1
3
0
1
2
1
0
1
1
1
2
0
2
2
1
1
2
2
1
2
0
1
1
0
0
1
0
1
2
1
1
1
1
0
1
1
0
2
1
0
1
2
1
0
1
1
1
1
1
2
2
0
1
1
1
1
0
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
0
0
2
1
0
1
2
1
1
0
0
2
1
1
1
1
1
1
3
2
1
0
1
3
1
2
0
1
1
2
2
2
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
0
1
1
1
1
2
1
1
1
2
1
1
1
2
1
1
2
2
1
1
1
1
1
1
1
0
2
1
2
2
1
1
0
1
1
0
1
0
0
1
2
2
2
2
0
2
0
1
1
0
2
1
1
1
2
0
1
1
1
1
1
1
1
0
1
1
0
2
1
1
1
1
1
1
1
0
0
2
0
1
1
0
1
0
1
2
1
1
2
2
1
0
1
0
2
2
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
2
1
0
2
0
2
1
1
1
2
0
1
1
1
1
4
1
1
1
1
1
1
2
1
1
0
1
1
0
2
1
1
1
0
1
2
1
0
1
1
0
0
2
1
1
1
0
0
1
1
0
1
2
1
1
1
1
1
2
1
0
0
0
0
2
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
2
1
1
1
0
1
1
1
2
0
0
1
1
0
1
1
0
0
2
2
1
0
0
1
1
1
1
1
5
1
1
0
1
1
1
1
2
0
1
1
2
1
2
1
2
2
0
2
1
2
2
0
1
1
0
1
1
1
0
1
2
1
1
1
1
0
1
1
2
1
0
1
0
0
2
1
1
0
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
0
1
2
1
2
0
0
1
2
1
0
1
2
1
2
1
2
2
1
1
0
1
1
1
1
1
1
1
0
2
2
0
1
1
1
2
1
1
1
2
2
0
1
2
2
1
1
2
1
2
2
1
2
2
1
1
0
1
1
0
1
1
0
1
1
1
1
1
0
1
1
1
1
1
2
1
2
1
1
2
1
1
1
0
0
1
1
1
1
1
1
2
1
1
1
0
2
0
2
0
2
0
0
1
2
2
2
2
1
1
1
2
1
0
1
1
2
1
0
0
2
0
0
0
1
1
1
1
0
2
1
1
1
1
0
2
1
1
1
1
1
0
0
1
0
1
1
1
1
1
1
1
1
1
1
0
2
1
2
1
1
1
2
1
1
0
1
1
0
2
0
0
1
1
2
1
0
1
1
1
0
0
1
0
0
2
2
0
1
2
2
2
1
2
0
2
1
1
0
1
1
1
0
1
1
2
3
2
0
1
2
2
1
1
1
1
2
2
2
1
2
1
0
2
0
2
2
1
1
1
0
2
0
1
1
1
2
1
0
0
0
1
1
1
1
0
1
1
1
1
0
1
1
1
1
2
1
1
1
0
1
0
1
1
0
1
0
1
1
2
1
2
2
2
1
1
0
1
1
2
1
0
1
0
2
0
2
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
2
2
3
2
1
1
1
0
1
1
1
1
2
2
1
1
1
0
0
1
1
1
1
1
0
0
0
1
1
1
0
1
1
2
1
1
1
0
1
0
1
3
1
1
3
2
2
1
1
0
1
2
1
0
4
2
1
1
1
1
2
0
1
1
1
1
1
1
1
1
1
2
2
1
0
1
1
1
1
1
2
1
0
1
2
1
0
0
1
2
1
0
0
1
0
0
2
2
1
1
0
1
1
1
1
1
1
1
0
2
0
2
2
1
1
2
1
1
1
0
1
2
2
1
1
1
0
0
1
0
1
1
1
1
0
1
1
1
0
1
1
1
2
2
0
2
1
1
1
1
0
1
1
0
1
1
2
2
1
0
0
1
1
1
1
2
2
1
2
1
0
1
1
0
1
1
2
0
1
0
1
1
2
1
0
1
0
1
1
1
1
1
2
1
1
1
1
1
2
1
0
1
1
2
1
2
0
2
1
1
1
1
1
1
1
1
1
2
1
2
1
0
0
1
1
2
0
2
1
1
1
1
2
1
2
1
2
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
2
1
1
1
2
2
1
1
1
1
1
2
0
0
1
1
1
2
1
1
2
0
2
2
1
1
0
1
1
1
2
0
2
1
2
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
2
0
2
1
1
1
2
1
1
2
2
1
1
2
0
1
1
0
1
2
2
1
0
1
1
2
0
1
1
1
1
2
1
0
1
0
2
1
1
1
1
1
0
1
0
1
1
1
1
1
1
1
2
1
0
0
0
0
1
1
2
1
2
1
0
1
1
2
1
0
1
2
1
1
2
1
1
0
1
0
1
1
2
3
1
1
0
2
2
1
2
1
1
1
2
1
1
2
1
0
1
2
1
1
1
0
1
1
1
1
0
1
1
0
1
2
1
1
2
2
2
1
1
2
1
0
2
1
1
2
1
1
2
2
2
2
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
2
1
2
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
0
1
1
2
1
1
1
1
0
1
1
0
1
1
2
1
1
1
1
1
1
1
1
1
1
1
0
2
1
1
1
1
1
1
1
2
1
1
0
2
1
2
0
1
1
1
1
0
1
1
1
1
1
1
1
4
1
1
2
1
1
2
5
1
1
2
1
1
0
1
1
0
2
1
1
1
1
1
1
0
1
1
1
1
1
1
3
1
2
2
0
1
1
1
1
0
1
1
1
2
1
1
2
1
0
0
3
0
0
1
2
1
1
1
1
1
1
2
1
0
2
0
1
1
1
1
2
0
1
0
1
0
1
1
2
1
1
1
0
1
2
1
1
1
1
0
2
1
1
1
1
0
1
3
1
1
2
2
1
1
2
0
1
1
1
1
1
1
1
1
2
1
2
1
2
1
0
2
0
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
0
1
2
0
1
1
1
1
1
1
1
1
1
1
1
0
2
1
1
1
2
1
0
0
1
2
1
1
0
0
1
2
0
1
1
2
1
0
0
2
3
1
1
1
2
1
2
0
0
2
3
2
1
1
1
1
0
0
2
1
1
1
1
1
1
2
1
1
1
1
1
1
0
1
2
1
3
1
1
1
0
1
1
1
1
3
2
1
1
1
1
2
1
1
2
1
1
2
0
2
2
2
1
1
1
1
0
1
2
2
2
1
2
1
1
1
1
1
0
1
2
1
2
0
1
1
2
0
2
0
1
2
2
0
1
1
1
1
1
1
3
1
1
2
0
1
0
2
1
2
1
1
1
1
2
1
0
0
2
1
2
2
0
1
1
2
1
1
1
1
1
1
2
0
1
0
0
1
1
2
1
1
2
2
1
1
1
1
1
2
1
1
1
2
1
2
1
1
2
1
1
1
1
1
2
1
1
1
2
2
0
1
0
2
0
0
3
2
2
1
1
1
1
2
1
0
2
1
1
1
2
0
2
1
3
1
0
2
1
2
2
0
1
1
1
1
1
1
2
1
2
1
1
0
1
1
2
0
1
1
0
1
1
1
2
2
2
1
1
1
2
1
1
2
1
0
1
0
1
1
1
1
0
1
1
1
2
2
2
1
0
1
1
1
0
1
1
0
1
2
0
2
0
2
2
1
2
1
2
1
1
1
1
2
0
1
1
0
0
1
0
1
0
2
1
1
2
1
1
2
1
2
1
2
1
0
1
1
1
1
1
1
0
2
1
1
2
1
1
2
1
1
1
0
2
1
1
1
1
1
0
1
2
1
1
1
2
0
1
1
0
1
1
2
1
1
2
2
1
1
1
1
0
1
2
1
1
2
1
1
1
2
0
1
2
1
1
1
1
0
0
0
5
1
0
1
1
2
1
1
1
0
2
1
1
2
0
2
1
1
0
1
1
1
0
2
2
1
1
3
1
2
0
1
2
2
1
1
1
0
2
0
0
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
2
0
1
1
1
1
2
1
0
1
1
1
0
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
0
1
0
1
2
0
1
2
1
0
1
1
1
1
1
1
1
0
1
0
2
1
2
1
1
2
1
1
1
2
0
1
1
0
1
2
1
1
1
1
1
2
1
1
2
2
1
2
1
1
0
0
2
2
1
1
1
2
0
1
2
1
1
0
1
0
1
1
0
1
2
1
0
1
1
1
1
2
2
1
0
1
3
1
0
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
0
1
0
1
1
1
1
1
1
2
2
2
1
0
2
1
1
1
1
0
1
0
0
1
1
1
1
0
1
0
1
0
1
1
1
2
1
1
1
2
2
1
3
0
1
1
0
1
1
1
1
2
0
0
2
2
1
1
1
1
0
1
1
0
1
2
1
2
0
1
2
1
1
2
1
1
1
1
0
1
1
2
1
0
1
0
0
2
2
1
2
1
1
2
1
1
0
2
2
1
1
1
1
1
1
1
1
1
1
1
0
2
2
1
1
0
2
1
1
0
1
1
1
2
1
2
0
1
0
1
1
0
1
2
1
1
1
1
1
2
0
1
1
1
0
1
1
1
1
1
1
1
2
1
1
1
0
0
0
1
2
1
2
1
1
1
0
1
0
1
1
1
2
1
0
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
0
1
2
1
2
2
1
1
1
0
1
2
2
1
1
1
1
0
1
1
1
0
2
2
0
1
2
1
1
0
1
1
1
1
1
2
1
2
1
1
2
1
1
2
1
1
1
3
2
2
1
1
2
1
1
1
0
0
1
1
1
1
0
1
1
1
1
1
0
1
1
1
0
1
1
1
0
2
0
2
1
2
1
1
0
0
1
2
0
1
1
1
1
2
1
1
0
1
1
1
1
2
1
1
0
1
1
2
2
1
2
1
1
0
1
1
2
2
0
2
2
2
2
1
1
0
1
1
1
1
1
0
1
1
1
1
0
1
1
2
2
1
1
1
1
1
2
1
0
0
1
0
2
0
1
1
0
0
1
0
0
0
0
0
0
1
2
1
1
1
1
1
1
1
2
1
1
0
0
3
2
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
0
1
1
1
0
0
1
2
0
1
1
2
1
1
1
1
1
1
1
1
1
0
1
1
1
2
2
1
1
2
1
2
1
0
1
2
1
1
1
1
1
1
1
1
2
1
2
2
1
1
2
1
1
0
1
1
1
1
1
2
1
1
1
0
2
1
2
1
0
2
2
1
2
1
1
1
1
0
1
1
1
2
1
1
2
0
1
2
1
1
1
2
2
1
1
1
1
1
2
1
1
1
1
1
1
0
1
1
0
0
3
1
1
1
0
2
0
1
1
0
1
2
1
1
1
1
1
1
2
0
1
1
0
2
1
1
2
1
0
1
2
2
1
1
2
0
0
1
1
1
1
1
2
1
1
2
2
2
1
0
1
1
1
0
1
0
1
1
0
1
1
1
2
1
1
1
1
1
0
1
1
1
2
0
0
1
1
1
1
1
1
1
2
0
2
1
0
1
1
2
2
0
0
1
1
0
0
2
0
2
1
1
2
1
1
1
1
2
1
1
1
2
0
1
1
1
1
2
0
0
2
0
1
0
1
3
1
2
1
2
0
1
1
1
1
2
3
2
1
1
1
1
2
1
2
1
0
1
1
0
1
0
1
1
0
1
1
2
1
1
1
0
1
2
1
2
1
2
1
2
2
2
1
1
1
0
1
1
2
1
1
1
0
1
0
1
1
1
1
1
0
1
1
2
1
0
0
2
1
2
1
1
1
1
1
1
0
1
1
1
1
1
1
1
0
0
0
1
0
1
0
1
1
0
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
0
2
1
2
1
0
1
1
4
1
1
1
2
1
1
0
2
1
1
1
2
0
2
1
1
2
1
2
2
2
1
1
2
1
1
0
1
0
1
1
1
1
2
0
1
1
1
2
1
0
1
1
1
1
0
0
0
1
1
2
1
2
1
1
0
1
0
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
0
1
1
2
0
1
2
0
1
1
2
1
1
1
2
2
1
1
1
1
2
2
2
0
1
2
2
0
1
2
1
1
2
1
1
1
1
1
0
1
0
1
0
1
1
1
2
1
1
2
1
1
1
1
0
2
1
1
1
1
1
2
0
1
0
1
1
1
1
1
0
1
0
1
0
2
0
1
1
0
2
1
2
1
2
1
2
1
1
1
1
1
1
1
2
0
1
1
1
2
0
2
1
1
1
3
0
2
0
1
1
0
1
1
1
1
1
1
1
1
0
0
1
1
2
0
2
1
1
1
2
2
1
2
2
2
1
1
2
2
1
1
0
2
0
2
0
1
0
1
1
1
2
0
0
1
1
1
1
2
0
0
0
1
2
2
2
2
1
1
1
1
1
1
1
1
2
1
1
0
2
2
1
2
2
1
1
1
0
0
2
1
1
2
1
2
1
1
1
2
3
2
1
2
2
1
1
1
1
0
1
1
2
1
1
1
1
0
1
1
1
1
1
1
2
1
1
1
0
0
1
0
1
1
1
0
2
0
0
2
1
1
1
0
1
1
2
2
2
2
2
0
3
2
0
1
2
1
0
1
1
1
1
1
1
1
0
1
2
0
0
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
0
1
1
2
1
2
2
1
1
2
1
2
1
0
1
1
1
2
0
1
1
1
1
1
1
1
0
1
1
2
1
1
0
0
2
1
1
2
2
1
2
0
1
2
1
0
2
1
1
1
1
1
1
2
1
1
0
2
2
1
1
1
0
1
1
0
0
2
1
1
1
1
1
1
1
1
1
1
1
2
2
0
1
1
1
1
1
1
2
1
1
1
1
1
2
1
0
1
2
2
1
2
1
1
1
1
1
0
1
2
1
1
1
0
1
1
1
0
1
1
1
1
1
1
1
1
2
2
1
2
1
0
2
2
1
0
1
0
2
1
1
0
2
1
3
1
1
1
1
2
1
2
1
2
1
1
1
1
1
1
0
1
1
1
1
1
2
1
1
1
2
1
2
2
0
2
2
0
1
2
1
0
1
2
1
2
0
1
1
1
2
1
1
1
1
0
0
0
0
1
0
1
1
1
0
1
0
1
1
1
1
1
1
1
1
0
1
1
3
2
1
0
1
2
2
0
1
1
2
2
1
1
1
1
2
0
1
1
1
0
2
1
1
1
1
1
2
1
2
1
2
1
1
0
1
2
1
1
1
1
1
1
1
2
1
1
1
2
1
2
0
2
1
1
1
1
2
1
2
1
1
2
0
1
0
0
1
1
2
1
1
1
2
0
1
0
0
2
1
1
0
1
0
1
0
1
2
1
1
2
2
1
1
0
1
1
1
1
2
1
0
2
2
1
1
1
1
1
1
0
1
0
2
1
2
2
1
0
0
2
1
1
0
1
1
2
1
1
0
2
2
1
1
1
1
1
1
2
1
1
0
1
1
1
1
2
2
1
1
0
2
0
1
1
1
0
0
2
1
1
1
0
2
1
1
2
2
1
1
1
1
2
1
2
1
0
2
2
1
1
2
1
2
1
1
0
1
1
1
1
1
1
1
1
1
0
1
2
1
0
1
1
1
1
1
1
1
2
1
0
0
1
1
1
1
1
2
0
0
1
0
0
1
1
2
2
2
1
1
1
0
2
1
2
0
2
2
2
0
2
1
2
0
1
2
1
1
2
1
0
0
1
1
1
0
1
1
0
2
0
2
1
0
1
1
1
1
1
1
1
1
1
0
2
1
2
1
1
1
0
1
2
1
1
0
2
1
1
1
0
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
2
1
0
1
1
2
1
1
1
1
1
0
1
1
2
1
1
1
1
1
1
1
0
1
1
0
1
2
0
1
2
1
1
1
2
0
2
1
1
1
1
2
2
2
1
1
2
1
2
1
1
2
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
0
0
1
0
0
2
0
1
2
0
2
1
1
1
1
1
1
0
0
2
2
2
0
1
1
0
1
1
0
2
2
1
0
1
2
1
2
0
1
1
1
1
2
0
2
0
1
1
2
1
1
1
1
0
0
1
1
1
1
2
2
0
0
1
1
2
1
1
0
0
1
2
2
3
2
1
1
2
0
1
1
1
1
0
0
1
1
1
1
1
1
1
0
1
1
0
0
1
2
0
1
2
2
0
1
1
1
1
2
2
1
2
1
1
1
0
2
1
1
1
1
2
2
1
1
2
1
2
1
2
1
1
2
1
1
2
1
1
0
1
1
0
1
1
1
1
1
2
2
1
2
0
2
1
1
1
0
1
2
1
1
1
2
1
1
2
1
2
1
2
1
0
1
3
1
2
1
2
1
2
1
3
1
2
1
1
0
2
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
1
2
1
0
1
1
2
0
1
1
1
1
2
0
1
2
0
2
2
0
1
1
1
2
1
0
0
0
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
0
1
1
2
1
1
2
1
1
2
2
1
2
1
0
2
2
1
1
1
0
2
1
1
1
1
1
0
2
1
2
1
1
1
2
1
1
0
1
1
1
1
2
2
1
1
2
2
0
2
2
1
2
2
2
2
2
1
1
1
1
1
0
0
1
2
1
1
0
1
0
2
2
1
1
2
0
1
1
1
1
1
1
0
0
1
2
1
2
0
1
2
1
2
1
0
1
2
2
1
2
1
2
1
0
1
1
1
1
2
1
1
2
2
1
0
1
1
2
1
0
2
1
1
0
0
1
2
1
1
1
1
1
2
1
1
1
0
2
1
1
2
0
2
0
1
1
1
1
1
1
1
1
1
1
1
2
0
0
1
2
2
2
1
0
1
1
0
1
1
0
1
2
1
2
1
1
1
0
1
1
3
0
0
1
0
0
0
1
2
1
1
1
1
1
1
1
1
1
1
2
0
2
1
1
1
1
1
1
1
1
2
1
0
1
2
2
0
0
1
2
1
2
1
1
1
0
0
1
2
2
1
1
2
2
2
1
0
1
2
1
1
2
2
1
1
1
0
0
2
2
0
1
0
2
1
1
0
1
2
1
1
2
1
1
2
1
1
0
0
1
0
2
2
1
2
1
2
0
0
1
2
2
1
1
1
2
1
2
1
1
2
0
1
0
1
2
1
1
1
2
1
2
2
0
1
2
2
2
2
1
1
2
1
0
2
1
1
2
1
1
1
0
1
1
1
0
2
1
1
2
0
2
2
2
1
2
1
1
1
2
1
1
2
1
2
1
1
1
1
1
1
0
1
1
1
1
2
2
1
1
0
1
1
0
1
1
1
1
1
1
1
1
2
1
1
0
0
0
0
1
1
1
0
1
2
2
1
1
0
1
1
2
2
1
1
2
1
0
1
1
1
0
2
0
1
0
2
1
0
0
0
1
1
1
1
0
1
1
1
1
2
1
1
2
0
0
1
1
1
1
1
0
0
0
1
1
2
1
1
0
1
1
2
1
2
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
2
2
2
2
2
0
1
2
1
0
1
1
1
0
0
1
1
1
1
1
2
1
0
2
1
1
1
0
0
1
1
2
1
5
2
1
1
2
0
2
1
2
1
1
1
2
1
2
2
1
0
1
1
1
1
0
1
1
1
2
1
0
2
1
1
2
2
0
1
0
0
0
1
2
1
2
1
1
2
2
1
1
0
2
0
1
0
1
2
1
1
2
1
1
1
1
1
2
1
1
2
2
1
1
2
2
1
2
1
2
2
1
1
0
1
1
1
1
1
1
2
1
1
1
1
2
2
2
1
2
2
1
1
1
2
1
1
1
1
3
0
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
0
2
1
1
0
1
2
1
2
1
2
1
1
1
0
1
1
1
2
2
1
1
0
1
1
1
1
1
2
0
1
1
1
0
1
1
1
1
1
2
0
1
2
1
2
2
1
1
0
2
0
2
2
1
1
1
1
2
2
1
1
2
2
1
1
1
1
1
1
1
1
0
2
0
1
1
1
2
1
1
1
1
1
2
1
0
1
0
1
1
1
2
1
2
0
1
0
1
1
0
0
0
1
1
1
1
2
1
1
1
1
2
2
1
2
3
0
2
1
0
1
2
2
2
0
0
2
1
0
0
1
1
2
2
1
1
1
1
0
1
2
0
2
1
1
1
1
0
1
2
0
2
1
0
1
1
0
1
2
1
1
0
0
1
1
2
1
1
1
1
2
1
2
1
1
1
0
2
0
2
1
0
0
2
1
0
0
2
1
2
1
1
2
1
2
2
2
2
1
1
1
0
1
2
2
1
0
1
1
1
0
2
1
1
2
2
2
1
1
1
1
1
1
2
3
0
2
1
1
1
2
3
2
1
1
1
2
1
1
2
0
2
2
1
1
1
1
0
1
1
2
1
1
2
1
2
4
0
0
0
0
0
0
1
1
1
2
1
2
1
1
0
1
1
0
1
1
2
1
1
1
2
2
1
1
0
1
2
1
2
1
1
2
1
2
2
1
1
0
2
1
1
1
1
1
0
1
1
1
1
1
1
1
0
2
1
0
1
2
1
0
0
1
1
1
2
1
1
1
1
1
2
0
1
1
1
3
1
0
1
1
1
0
1
0
0
1
1
1
1
2
1
1
1
2
0
0
1
1
2
0
2
1
1
1
2
1
2
1
0
1
1
0
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
3
1
1
2
1
1
1
1
0
1
1
1
2
2
1
1
1
1
0
0
0
3
0
1
1
1
1
2
1
1
1
1
0
0
0
4
1
1
2
1
2
1
0
0
1
1
2
1
1
1
0
0
1
1
0
2
1
1
2
1
1
1
1
1
2
1
1
0
0
1
3
1
0
1
1
1
0
1
2
0
1
1
0
1
1
1
1
2
1
2
1
2
1
1
0
0
3
1
2
1
1
1
1
2
2
1
2
1
1
0
0
2
0
0
0
0
1
2
2
2
1
1
1
2
1
0
2
0
1
1
0
1
1
0
1
1
2
1
1
1
2
0
1
0
1
1
2
2
1
2
1
1
0
2
1
2
1
1
1
1
0
1
1
2
2
1
1
1
2
1
0
1
0
1
1
1
1
0
3
1
0
0
1
1
2
1
1
2
1
1
0
2
1
0
1
2
1
0
0
1
1
1
1
0
0
1
1
1
2
2
2
1
1
1
0
1
1
2
1
1
0
1
0
0
1
1
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
2
1
0
1
0
1
2
0
1
5
1
1
1
1
2
2
1
0
1
1
2
0
1
2
1
1
2
1
1
1
1
1
1
1
1
0
1
1
1
0
1
1
1
2
1
2
0
2
1
1
1
1
1
0
1
2
2
1
2
1
0
1
2
1
2
0
0
0
0
2
0
1
2
0
0
1
1
1
1
1
0
2
1
1
0
1
1
1
2
1
1
0
0
1
1
1
3
1
1
0
1
1
1
2
1
2
1
1
1
2
1
0
1
1
0
2
2
1
0
1
1
0
1
0
1
2
1
1
1
2
1
1
1
1
1
1
2
0
1
2
2
1
2
1
2
1
1
1
1
2
0
0
0
2
1
0
1
2
1
1
1
1
2
1
2
1
1
0
1
1
1
0
2
1
0
0
1
1
1
1
2
0
2
1
1
0
2
0
1
1
1
0
2
2
1
1
1
1
2
1
1
1
0
2
0
1
0
1
1
0
1
2
1
2
2
1
2
1
1
1
1
0
1
1
0
1
1
2
0
0
1
1
2
1
1
0
0
0
1
1
1
1
2
1
0
0
2
1
2
1
1
1
1
2
0
0
1
1
0
1
2
1
1
1
0
0
0
0
1
1
1
1
0
1
0
1
1
1
0
0
1
3
0
1
1
1
0
2
1
1
0
1
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
2
2
2
1
2
1
2
1
1
1
1
1
1
1
1
0
1
1
1
1
1
0
1
2
1
1
1
1
0
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
0
0
0
1
0
1
1
1
2
1
1
1
0
0
1
1
1
1
1
2
2
1
1
1
0
0
2
1
2
1
2
1
1
1
0
1
1
1
1
2
1
2
1
1
0
2
1
1
1
0
0
0
0
1
2
2
1
2
1
2
1
1
1
1
2
2
2
2
0
1
2
2
1
1
1
1
1
1
2
1
0
1
2
2
1
2
0
0
1
1
1
0
0
2
1
0
1
2
1
0
1
1
1
2
1
0
2
2
2
1
1
1
1
2
1
1
0
1
1
2
0
1
1
0
0
1
2
0
2
0
0
0
1
1
1
0
2
1
1
1
2
1
1
2
2
0
1
1
0
0
0
1
1
2
1
2
1
1
2
1
1
1
4
1
1
1
0
1
2
2
0
0
0
0
2
1
0
1
1
2
2
1
1
2
2
2
1
1
2
1
2
1
1
1
1
2
1
1
1
2
2
2
3
1
0
2
1
1
1
0
1
1
1
1
2
2
1
1
0
1
0
1
1
0
2
2
1
1
2
1
1
0
1
2
1
1
0
1
1
1
1
1
1
2
1
1
1
2
1
1
2
1
2
1
2
2
1
1
1
1
2
1
1
0
2
0
1
1
2
1
2
1
1
1
1
1
0
1
1
2
1
1
2
1
2
0
0
1
1
1
1
1
1
1
0
1
2
1
2
1
1
1
1
1
1
1
1
2
1
1
2
2
0
1
1
1
0
1
1
1
1
1
1
1
1
1
0
0
1
1
1
2
2
0
1
1
1
2
1
1
2
2
1
2
1
1
1
0
2
2
1
1
1
1
1
0
1
1
0
2
0
1
1
2
0
1
1
1
0
1
1
1
1
1
2
1
0
1
1
3
1
1
2
0
2
0
1
1
1
2
0
1
2
0
2
1
1
0
2
2
2
1
1
1
1
1
0
1
2
1
1
1
1
2
0
1
1
2
2
1
2
1
1
1
2
1
2
1
1
1
2
1
1
0
2
1
2
1
1
1
3
1
1
1
2
1
2
1
1
1
2
1
1
1
1
0
2
1
1
0
1
0
1
3
2
1
1
2
1
0
1
1
2
2
1
1
1
0
2
1
1
2
2
1
1
2
1
1
1
2
1
0
2
1
0
1
1
2
1
1
1
1
1
1
2
2
2
1
2
1
0
0
0
1
1
2
2
2
3
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
0
2
1
2
1
2
2
1
1
1
0
2
1
1
1
1
1
1
2
1
1
1
2
2
0
1
1
1
2
1
1
1
1
1
0
2
1
1
0
0
2
1
1
1
2
2
1
0
2
2
1
1
1
1
2
1
2
1
1
0
0
2
2
1
1
1
1
1
0
2
0
2
0
1
2
1
1
2
0
1
1
1
0
1
1
2
2
1
2
2
2
2
1
1
1
1
2
2
1
2
2
2
0
0
1
0
2
1
1
2
1
0
1
2
2
2
1
1
1
1
2
1
2
1
1
1
2
0
1
1
1
1
0
1
2
0
2
1
2
0
1
1
1
1
0
1
1
1
2
2
0
2
1
2
0
2
0
2
1
1
1
1
0
1
2
0
1
1
2
2
1
1
0
1
0
2
1
0
1
0
1
1
1
2
1
1
1
1
2
2
0
1
1
0
2
1
0
2
1
3
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
0
1
0
0
1
0
1
1
1
3
0
2
2
2
1
0
2
1
1
1
1
1
1
0
0
0
2
0
1
1
2
1
1
1
2
2
1
0
1
1
2
1
1
1
2
0
1
1
1
2
0
1
2
1
2
1
0
1
2
0
2
1
2
1
1
1
1
0
1
2
1
2
1
0
0
1
0
0
1
1
1
0
1
1
1
0
1
1
1
1
1
2
1
2
0
0
2
2
0
0
1
0
2
1
0
1
2
0
1
1
0
1
2
2
1
2
2
2
1
1
0
2
0
2
0
1
2
0
0
1
2
2
1
2
1
0
2
1
1
0
2
2
1
1
1
1
1
1
2
2
1
2
2
1
1
1
2
1
1
1
0
1
2
2
0
1
0
0
3
1
2
1
2
1
0
1
2
1
1
1
1
1
1
1
3
1
1
1
10
0
0
1
1
1
1
1
1
1
1
0
2
1
1
1
1
2
1
0
0
1
2
2
0
1
2
2
1
0
0
1
1
1
3
1
3
0
1
1
1
0
2
1
1
1
1
0
1
1
2
2
1
2
2
2
2
1
2
1
1
1
1
1
1
1
0
2
1
1
1
1
0
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
2
0
1
2
1
0
1
1
0
1
0
1
2
1
1
1
1
1
0
0
1
1
2
2
1
1
1
1
1
1
0
1
2
1
1
1
2
1
0
1
1
1
1
1
1
1
0
1
2
2
2
1
2
0
1
0
1
1
1
2
0
1
2
1
1
1
1
1
1
0
2
2
0
1
2
2
1
1
0
1
1
1
1
2
1
1
1
0
2
1
1
1
2
2
1
1
1
1
1
1
1
0
1
1
0
1
1
1
1
1
1
2
0
0
2
1
2
2
1
1
2
1
1
1
0
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
1
0
1
2
2
1
2
0
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
2
0
1
2
1
1
1
1
1
1
2
0
0
1
1
1
1
1
0
1
2
1
1
1
2
2
1
0
0
1
0
1
2
0
1
0
1
1
1
0
1
1
1
1
1
1
0
1
1
0
1
1
1
1
0
1
1
0
1
2
2
1
1
1
1
1
0
2
0
1
1
1
1
1
1
2
0
2
1
2
1
1
1
1
1
0
1
2
0
1
1
1
1
0
1
1
0
2
1
1
1
0
1
1
1
1
1
1
1
0
2
1
2
0
2
2
2
1
0
1
1
1
0
2
2
1
2
2
1
2
2
0
0
2
1
2
0
1
1
1
1
0
1
1
1
0
2
0
2
2
1
1
1
2
0
1
1
1
1
1
1
3
1
1
1
2
2
1
0
2
1
2
1
1
4
0
1
1
2
1
1
1
1
1
1
0
0
2
0
1
0
2
0
1
2
1
1
1
2
2
3
1
2
2
2
0
2
0
1
2
1
1
1
1
1
1
1
1
0
1
1
2
1
1
1
1
0
2
1
1
1
0
1
2
1
2
1
2
1
0
2
1
2
1
1
0
0
1
1
1
1
2
0
1
1
1
1
1
2
1
0
1
1
1
1
1
0
1
2
0
1
1
1
1
2
1
2
0
0
1
1
1
1
1
1
1
1
1
1
1
2
2
2
0
2
2
0
2
1
1
2
1
1
1
2
1
0
1
1
1
1
1
2
0
2
1
1
1
1
1
2
1
1
2
1
3
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
2
1
1
1
1
1
1
1
2
2
1
0
1
1
1
1
1
1
1
2
0
1
2
2
1
1
1
1
1
1
1
1
1
0
1
1
0
1
2
1
2
1
2
2
1
1
1
1
2
2
2
1
1
1
1
1
2
1
0
0
1
1
0
1
1
0
1
2
2
1
1
1
2
1
2
0
0
1
1
1
2
0
1
2
1
0
1
0
2
1
1
2
0
1
1
1
3
1
0
1
1
2
0
1
1
2
2
0
1
1
2
1
0
1
2
2
2
1
0
0
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
2
1
3
1
0
1
1
1
1
2
0
1
1
0
2
1
0
2
1
1
1
2
1
1
2
0
0
1
1
1
0
2
1
1
0
1
0
1
1
2
2
1
1
2
1
2
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
2
1
0
0
1
2
2
2
0
1
2
1
1
2
2
1
1
1
1
0
1
0
1
1
1
1
1
1
2
1
1
1
2
2
1
2
0
2
1
2
0
1
1
2
2
1
0
1
0
2
2
0
1
0
1
1
2
1
1
2
1
0
1
1
2
2
3
1
1
0
1
0
1
1
0
0
0
0
2
0
1
1
0
0
2
2
3
1
1
2
2
2
1
1
0
1
0
2
2
0
1
2
1
1
1
1
2
2
1
1
1
1
2
0
0
0
0
1
0
2
2
1
1
0
2
1
1
1
0
1
1
1
1
1
1
1
2
1
1
0
0
1
2
2
2
1
1
2
2
1
1
0
1
0
1
1
1
1
2
0
0
0
1
1
1
2
1
1
1
1
1
1
2
0
1
1
2
0
0
2
1
1
2
1
0
2
1
1
1
0
1
2
1
1
1
1
1
1
0
0
1
1
1
1
1
1
2
0
1
0
1
1
0
1
2
1
1
1
1
0
1
2
0
2
1
1
2
2
0
1
0
0
0
1
0
1
0
2
1
2
0
1
2
1
1
2
1
0
1
1
3
2
1
1
1
1
2
2
1
1
0
2
1
0
1
2
1
0
1
1
1
1
2
1
1
1
1
1
1
1
2
0
0
2
1
1
0
1
2
0
1
2
1
1
2
0
1
1
1
1
1
2
1
2
1
1
2
0
0
0
0
0
1
1
1
2
1
1
1
0
1
1
1
1
1
1
1
1
2
1
1
1
2
1
0
2
0
2
1
1
0
2
0
1
1
2
0
2
1
1
1
1
1
1
1
2
0
1
1
1
2
1
0
0
1
2
0
2
1
1
1
2
2
1
0
1
0
1
1
1
0
1
2
1
1
0
1
2
1
2
0
2
1
2
1
1
1
1
1
1
1
1
1
0
2
1
1
2
1
1
2
1
2
2
1
1
0
0
1
1
1
1
1
1
2
1
2
1
1
2
2
1
1
0
1
1
1
1
1
1
0
2
2
1
1
1
2
1
2
2
0
1
2
1
1
1
2
0
2
2
2
0
1
2
2
2
1
1
1
0
2
1
0
1
1
2
1
0
2
0
1
2
0
1
1
1
1
2
1
2
1
1
2
1
1
2
1
1
2
1
1
1
2
1
0
1
2
1
0
0
2
2
0
2
1
1
1
3
0
1
0
1
0
1
0
1
1
1
2
0
1
1
1
0
2
1
1
2
1
1
1
0
2
1
1
1
2
0
1
1
1
1
1
0
1
2
1
1
0
1
0
1
1
0
1
1
2
2
1
0
1
0
2
1
2
1
1
0
1
0
1
1
2
1
1
1
1
2
0
0
2
1
0
1
1
2
1
1
4
1
1
2
1
1
1
1
0
2
2
2
1
2
1
1
0
1
1
1
0
0
1
2
1
1
0
2
0
1
1
1
1
1
2
2
0
1
1
2
1
1
1
0
1
2
1
1
1
1
2
2
1
1
1
1
0
2
1
1
1
1
1
1
1
2
2
0
0
1
1
1
1
1
1
1
0
0
1
1
1
2
0
2
0
1
1
1
2
1
2
1
0
1
3
1
2
2
1
1
1
1
1
0
1
1
2
0
1
2
1
1
2
2
2
2
0
1
1
1
2
1
2
1
1
1
1
0
2
1
2
1
1
2
0
2
1
1
1
1
2
1
0
2
0
1
2
2
1
1
2
1
2
2
2
1
1
1
2
1
2
1
2
1
3
2
1
1
1
0
1
1
1
0
1
0
1
1
2
1
2
0
1
2
2
2
0
1
1
1
1
2
0
0
1
2
0
1
2
3
1
0
1
2
1
1
1
2
2
1
0
2
1
1
1
1
1
1
0
1
1
1
0
0
1
0
2
2
1
1
0
1
1
1
1
5
2
1
2
1
2
1
1
1
1
0
1
2
2
0
1
1
1
0
2
1
1
1
2
2
1
0
1
2
1
0
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
0
2
1
2
1
1
1
1
0
1
0
2
0
1
2
1
2
2
1
1
2
0
1
2
2
2
0
2
0
0
1
2
1
2
2
1
0
4
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
0
1
1
2
1
1
1
0
2
1
2
0
1
1
1
1
1
1
1
1
2
0
0
2
2
0
0
1
2
1
1
2
1
2
1
1
1
2
2
1
0
1
1
1
2
1
0
2
1
2
1
1
1
0
0
2
0
1
1
1
2
1
1
3
2
3
1
2
1
1
1
1
1
1
2
2
1
2
1
1
1
1
2
0
0
0
2
1
1
1
1
1
1
0
1
1
2
2
2
0
0
1
1
0
0
2
1
1
1
0
1
1
1
2
1
0
2
1
2
1
0
1
1
0
1
0
2
2
2
1
1
2
0
1
1
0
1
0
1
0
1
1
1
1
2
1
1
1
2
2
2
2
0
1
1
3
1
1
1
0
2
1
0
1
2
1
1
1
1
1
1
0
1
0
1
1
2
2
1
1
1
1
2
1
1
1
1
1
2
2
0
1
2
2
1
1
1
1
0
1
1
3
0
1
1
0
2
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
0
1
2
1
1
1
1
2
2
2
1
1
1
1
2
2
0
2
0
1
2
1
2
2
2
2
2
2
0
2
1
1
1
1
2
1
1
1
2
1
1
2
1
1
2
1
0
1
1
1
1
1
1
1
1
1
1
0
0
1
1
1
1
2
2
1
2
0
1
1
3
1
1
2
1
0
0
1
2
1
0
1
0
1
0
1
1
1
0
1
0
1
2
1
1
1
2
1
1
2
2
1
1
1
0
0
1
1
1
1
0
0
0
5
3
1
1
0
1
1
1
1
1
2
1
1
1
2
1
2
1
1
2
0
1
1
2
1
1
0
0
1
1
1
0
1
1
1
1
1
1
1
0
2
0
1
1
0
2
2
1
1
1
2
1
1
1
1
2
1
0
2
1
2
1
0
2
0
2
2
2
2
1
1
0
0
1
1
0
1
1
1
1
1
1
1
2
1
1
0
0
1
1
1
1
1
1
1
2
2
1
4
2
1
1
1
1
1
0
1
2
2
1
1
1
1
1
1
0
1
1
2
1
1
0
2
1
2
2
2
1
1
2
1
2
1
1
1
0
1
1
2
1
1
2
1
2
1
0
1
1
0
3
0
1
0
2
1
1
2
1
2
1
1
2
1
2
1
1
1
1
0
1
2
2
1
0
1
1
1
1
1
1
0
1
1
0
0
1
2
1
1
0
1
1
1
1
1
1
3
0
2
1
1
0
2
2
2
2
1
1
2
1
1
2
1
1
1
0
0
0
2
0
2
2
1
1
1
1
2
2
0
1
2
2
0
0
2
1
1
1
2
1
2
0
1
1
1
0
3
0
1
1
0
1
1
0
2
1
1
1
0
2
2
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
2
1
1
0
1
1
2
2
1
0
1
1
2
1
2
1
1
0
0
0
2
1
2
1
1
2
1
2
2
2
2
0
1
2
1
2
0
1
1
1
0
0
1
2
0
0
2
1
1
1
1
1
1
1
2
1
0
1
2
2
2
1
0
1
1
1
1
1
1
1
1
1
2
2
1
1
2
2
1
0
0
1
1
1
1
0
2
1
1
1
1
2
0
1
2
1
1
1
2
1
1
1
1
2
2
1
2
1
1
1
1
2
2
2
2
1
3
2
1
2
1
1
1
1
2
1
0
1
1
1
1
0
1
2
1
1
1
1
1
0
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
0
0
1
1
0
0
0
2
1
2
2
1
3
1
2
2
3
0
1
1
2
0
1
1
1
1
1
1
1
2
1
0
0
1
1
2
2
1
1
0
2
1
1
0
1
1
0
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
0
1
1
1
2
1
1
2
1
1
0
1
1
1
1
1
2
2
1
1
1
1
1
0
2
2
1
1
1
2
2
1
2
0
1
1
1
1
0
1
0
2
1
3
1
1
1
0
1
1
1
2
1
2
1
1
1
0
1
1
0
1
2
2
0
1
3
0
1
0
1
1
1
2
1
0
2
1
2
1
2
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
1
1
0
2
2
1
1
0
2
1
1
2
2
0
0
2
1
1
0
2
1
2
1
2
2
1
1
1
2
1
1
2
1
1
2
1
2
1
1
1
1
1
2
1
1
0
1
2
2
0
1
2
0
3
0
0
0
1
2
1
2
2
1
2
1
1
1
1
1
2
1
1
0
1
0
0
1
0
0
1
1
2
1
2
1
1
1
1
1
1
2
2
0
1
0
2
1
1
1
2
1
0
1
0
2
2
2
1
2
5
2
1
0
1
0
0
1
1
0
2
1
0
2
1
2
1
2
1
1
1
0
1
0
1
2
1
0
0
1
1
2
1
2
1
1
2
0
1
1
0
1
2
1
0
2
1
0
1
2
0
1
1
2
1
2
1
1
2
2
0
0
1
1
2
2
1
1
1
2
1
0
1
1
0
1
2
1
2
1
1
0
1
1
1
0
1
2
0
2
1
1
1
1
1
1
1
1
2
1
2
2
2
1
1
1
1
2
1
2
1
1
1
0
2
0
1
1
1
1
1
1
1
1
0
1
1
1
2
0
1
2
2
2
1
2
1
0
2
2
0
1
0
1
0
0
2
1
1
1
1
1
2
1
1
1
1
2
2
1
2
1
0
3
0
1
1
1
0
1
1
1
1
1
1
2
0
1
1
1
1
1
4
1
0
1
2
1
2
0
1
1
1
1
1
1
2
0
1
0
2
2
1
2
0
1
1
1
1
1
0
1
1
0
1
1
1
1
1
1
1
1
1
2
0
0
1
0
1
0
1
1
2
2
1
0
2
2
2
2
1
1
1
1
1
2
2
2
1
1
1
1
2
1
1
2
2
2
1
1
1
1
1
2
1
1
2
1
1
2
3
2
2
2
1
1
0
1
0
1
0
2
1
2
2
1
1
2
0
1
0
1
1
1
2
1
1
1
1
0
1
2
1
1
1
1
2
1
0
1
1
0
1
2
1
2
0
1
1
0
1
1
2
2
1
1
1
1
0
1
0
2
0
1
1
1
1
1
1
1
1
1
1
1
2
1
2
0
0
1
1
0
1
0
1
1
1
1
1
1
1
2
0
0
1
2
1
0
1
1
1
2
1
1
2
1
1
0
1
1
1
1
2
1
2
1
1
0
0
2
0
1
1
0
1
2
1
2
1
1
0
1
1
2
1
1
3
1
0
1
1
30
1
1
1
1
1
1
3
1
1
1
1
1
1
2
1
1
0
1
1
1
2
1
1
1
1
1
1
2
1
1
0
0
1
1
1
1
2
0
1
0
1
1
0
1
2
1
1
0
2
0
2
1
3
1
1
2
0
1
2
2
1
1
1
2
1
2
2
0
1
1
0
1
1
1
1
1
1
2
2
2
1
1
1
2
1
2
1
1
2
0
1
2
0
1
0
0
1
2
1
0
1
1
0
1
1
1
1
1
0
1
2
1
1
1
1
0
1
2
1
1
1
0
1
0
1
1
1
1
2
1
2
2
2
1
1
0
1
1
0
1
2
1
1
0
2
0
1
1
0
1
2
1
0
1
2
1
1
1
1
1
2
2
1
1
0
1
2
1
1
1
2
0
1
0
1
0
2
2
1
1
3
1
1
1
1
1
1
1
1
1
2
1
1
1
0
1
2
2
1
1
0
1
2
1
1
1
2
1
0
1
0
1
2
1
1
2
2
1
1
2
0
1
1
1
1
1
1
0
1
1
1
2
1
1
2
1
1
1
2
1
1
1
2
1
0
1
2
1
0
0
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
2
1
1
2
2
1
1
1
2
0
0
2
0
1
1
2
2
1
1
1
1
1
1
1
1
1
0
1
1
1
2
2
0
0
2
1
2
1
1
1
0
0
2
1
1
0
1
2
0
1
1
1
1
1
2
1
0
1
1
1
1
1
0
0
1
1
0
0
1
1
2
1
1
1
2
2
2
2
1
2
1
2
1
0
1
2
0
1
0
1
2
0
1
1
2
1
1
1
1
2
0
0
2
1
1
1
1
1
0
1
2
1
1
2
2
1
2
2
1
1
2
2
0
0
1
1
1
0
1
1
2
1
1
0
1
2
0
1
1
1
2
2
1
1
2
1
2
2
2
0
1
0
1
1
1
2
1
2
1
1
1
1
2
1
2
0
1
1
2
2
2
1
0
2
1
1
1
1
1
2
2
0
1
2
2
0
1
3
1
1
2
2
1
1
0
1
0
1
1
1
1
1
1
2
0
1
2
1
1
1
1
2
0
1
1
2
1
0
1
1
2
1
0
0
0
1
1
0
1
1
1
0
0
0
2
2
2
1
2
1
0
1
2
0
2
1
1
0
0
0
1
2
2
1
0
2
1
1
2
1
1
2
3
2
1
1
0
1
2
1
2
0
1
0
1
0
1
2
1
1
1
0
1
2
1
1
2
1
1
1
2
1
1
2
0
1
1
1
1
1
2
1
1
1
2
2
1
0
1
2
1
2
1
1
0
1
0
1
1
1
1
0
1
1
2
1
1
1
2
2
1
1
0
2
1
2
1
1
1
2
1
1
2
1
2
1
2
2
2
1
1
1
1
2
1
1
1
1
1
2
0
1
1
1
1
1
0
0
1
0
0
0
1
1
2
1
2
1
1
0
1
1
2
2
1
2
1
1
1
1
1
0
0
1
1
1
1
1
1
1
1
0
1
1
1
0
2
0
1
1
1
1
0
1
2
2
1
2
1
2
1
0
1
1
2
2
1
0
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
2
1
2
1
2
2
0
1
2
1
2
0
1
1
1
1
0
1
1
1
2
1
1
2
2
1
2
0
1
1
1
1
1
2
1
1
2
1
1
1
2
0
0
2
1
1
1
1
2
1
0
1
1
2
2
0
2
1
1
2
2
2
2
2
2
2
1
1
1
0
0
0
1
1
1
1
1
1
1
1
1
2
0
0
0
1
1
0
2
1
0
1
0
1
3
1
2
1
2
1
1
1
1
0
1
0
1
1
1
2
1
0
1
1
1
0
1
1
1
0
2
2
1
1
2
3
1
1
2
1
2
1
2
1
1
1
1
2
1
0
2
0
1
2
1
0
1
1
1
2
1
2
1
1
1
1
1
0
1
1
1
2
1
1
1
3
1
1
1
0
0
1
2
2
1
1
0
0
1
2
1
1
1
2
0
1
1
1
1
1
1
1
1
2
1
2
0
1
0
1
2
0
1
2
1
0
1
1
2
2
1
1
1
0
1
1
2
2
0
1
2
2
1
2
1
1
2
1
2
1
2
0
2
1
1
1
2
2
0
1
1
1
1
2
1
2
1
1
2
2
1
2
1
1
3
2
1
1
2
1
1
1
1
1
2
0
1
1
1
1
1
2
1
2
0
3
2
2
2
1
1
2
2
1
2
1
0
1
1
1
2
1
2
1
1
1
1
1
1
2
2
0
1
0
2
1
1
1
1
2
1
1
1
1
2
2
1
1
0
1
1
0
2
1
3
1
1
2
1
2
1
1
1
1
1
1
1
1
0
2
1
0
1
1
2
1
1
0
1
1
2
1
1
1
1
1
2
1
0
1
1
0
2
1
2
1
1
0
1
2
1
2
2
1
0
3
0
0
1
1
1
1
1
2
2
2
2
0
2
1
2
1
1
0
2
1
1
1
2
1
1
0
2
1
1
1
0
0
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
1
1
2
2
2
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
0
1
1
2
2
1
1
2
2
1
0
1
1
1
2
2
0
1
2
1
1
1
2
1
2
2
2
1
2
0
1
1
2
2
1
0
1
1
2
1
2
1
2
1
0
1
1
0
1
0
0
2
1
1
0
1
0
2
1
1
1
2
2
1
2
2
2
1
1
2
2
1
1
1
0
0
2
2
1
1
0
0
1
1
1
1
1
0
1
1
1
2
1
2
1
2
0
1
1
1
2
2
3
2
1
2
1
2
2
0
1
1
2
0
1
0
1
2
2
1
1
1
2
0
1
1
0
2
1
0
1
2
3
2
0
1
0
2
1
2
1
2
1
0
1
1
2
2
1
2
2
1
0
2
0
2
1
2
1
2
1
1
2
2
1
2
2
1
2
0
0
1
1
1
1
1
2
0
1
1
2
0
2
1
1
1
1
1
1
2
0
1
2
1
1
2
2
1
0
1
1
1
5
2
1
1
2
2
0
0
2
2
1
1
1
0
1
1
0
0
2
2
0
0
1
1
2
1
2
0
1
1
1
2
0
2
1
1
1
2
2
1
2
2
1
2
2
0
0
1
1
1
1
1
1
1
1
1
0
1
1
1
0
1
1
1
2
2
1
1
0
1
2
2
1
2
1
0
3
2
1
1
2
1
2
0
1
2
1
2
2
0
2
1
2
1
1
1
2
2
1
1
1
0
1
2
1
1
1
1
1
0
0
1
1
1
1
0
2
0
1
2
2
2
1
1
1
1
2
1
2
0
1
1
1
1
1
1
1
0
1
1
1
1
1
1
2
0
2
1
1
0
1
1
2
2
1
1
2
1
1
0
1
1
1
2
1
1
1
1
1
1
4
0
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
0
1
2
2
1
0
1
1
1
1
1
1
1
1
1
2
1
2
2
1
2
1
2
1
1
1
1
1
2
1
0
1
2
1
3
1
1
2
1
1
1
2
0
0
1
2
1
1
1
2
2
0
1
1
1
1
1
1
1
1
1
2
1
0
2
1
1
1
2
0
1
0
1
1
0
1
2
2
1
1
1
0
1
1
1
1
0
1
1
1
0
1
1
1
1
0
2
1
2
0
1
1
1
2
2
2
1
0
0
2
0
1
1
0
1
2
2
1
2
1
1
1
1
2
1
2
0
1
1
1
0
0
2
1
1
1
0
1
2
1
0
1
1
1
1
1
2
1
2
1
0
1
2
1
1
0
1
1
2
1
1
1
1
2
1
2
2
1
2
1
1
1
1
1
1
1
1
0
1
0
0
0
1
1
2
2
1
2
1
1
0
1
1
1
0
0
1
0
0
1
1
1
0
1
0
0
1
2
2
1
1
1
2
2
2
1
0
1
2
0
0
1
1
2
0
0
1
1
2
1
1
1
2
1
2
1
1
0
1
0
1
1
1
1
1
1
0
0
1
1
1
0
2
0
2
1
2
1
1
0
1
1
0
0
1
1
0
1
2
1
0
1
1
1
1
2
0
0
1
1
1
1
2
0
2
1
1
1
1
2
3
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
0
0
1
1
2
1
2
2
0
1
1
2
2
1
1
1
1
1
3
2
0
0
1
2
1
1
1
2
1
1
1
1
2
1
1
1
2
0
1
1
2
1
1
2
1
2
1
1
1
0
1
1
1
1
2
0
1
2
2
0
1
0
1
1
2
1
1
1
1
0
2
1
1
2
1
1
2
1
1
0
2
1
2
1
2
2
1
1
1
1
1
1
0
1
2
1
2
0
1
1
2
1
2
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
2
0
0
1
1
2
1
0
1
1
1
1
2
1
1
2
0
0
1
1
1
0
2
1
0
2
1
1
1
1
2
2
2
1
1
1
2
1
2
1
2
2
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
0
1
2
1
1
2
2
1
0
1
2
1
2
1
1
1
0
1
2
2
0
1
2
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
0
1
1
0
0
1
2
1
1
2
1
2
1
0
1
1
2
1
0
2
1
2
1
1
0
1
1
1
1
2
1
1
0
1
2
1
1
1
2
1
1
1
2
1
1
2
1
1
0
1
3
1
2
2
1
0
1
1
1
2
2
2
1
2
1
2
0
1
2
2
1
2
0
1
0
2
1
1
2
0
1
1
0
1
2
1
0
1
0
1
0
1
1
1
0
0
2
1
3
1
2
2
1
2
0
1
2
2
0
1
0
2
0
0
2
1
0
1
0
2
2
1
0
2
1
2
1
2
0
0
2
1
0
1
1
1
1
1
3
1
2
1
2
1
2
1
1
2
1
2
1
1
1
0
0
1
0
2
1
1
2
1
2
1
1
1
0
1
1
1
1
1
0
1
1
1
0
1
2
2
1
1
2
1
1
1
1
2
0
2
1
2
1
2
2
0
1
1
1
0
2
1
1
1
2
1
2
3
2
2
1
1
1
2
1
2
0
1
1
0
1
1
2
1
0
2
1
2
2
2
1
1
1
1
1
2
1
2
2
1
1
1
2
1
0
0
1
0
2
1
1
0
1
1
2
1
1
1
0
0
1
2
2
0
1
1
1
1
1
1
1
0
1
2
1
2
1
1
1
0
1
1
1
2
2
1
2
0
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
4
2
1
1
0
2
0
0
1
2
1
0
2
1
0
1
1
2
0
2
1
0
1
2
1
0
1
1
1
1
1
1
1
1
1
2
0
1
2
2
2
1
2
2
2
2
1
1
1
0
1
1
0
1
10
0
0
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
0
1
1
0
2
1
0
1
1
0
1
2
1
1
1
1
0
1
1
2
0
1
1
2
0
1
1
1
2
1
0
1
2
2
2
2
1
2
1
1
1
1
0
3
1
1
1
2
2
1
0
2
3
2
2
1
1
0
1
2
2
1
2
1
1
0
1
2
1
2
1
1
1
1
1
1
1
0
2
1
0
1
1
2
1
0
1
2
2
1
1
0
2
2
1
0
1
1
1
1
1
0
4
2
1
2
1
1
1
1
2
2
1
1
1
1
2
1
1
2
1
1
0
1
1
0
1
1
0
1
1
1
2
1
1
1
1
2
2
1
1
2
2
2
0
0
1
1
2
2
1
2
0
1
1
1
1
2
1
0
1
1
2
1
1
0
2
1
2
0
1
2
0
1
2
2
0
1
1
1
2
2
2
0
1
1
2
1
2
1
1
1
2
0
2
0
1
2
0
1
2
0
1
1
2
1
1
2
1
2
2
1
1
1
1
0
0
1
1
3
0
1
0
1
2
1
2
0
0
1
0
1
1
0
1
2
1
1
1
1
2
2
2
2
1
1
2
1
0
1
1
1
2
0
1
2
1
1
1
1
1
0
2
1
1
1
0
0
1
1
2
0
2
1
1
0
0
2
2
1
1
1
2
1
1
2
1
1
1
1
1
1
0
1
0
2
0
1
1
1
2
1
1
0
1
1
1
1
3
1
1
0
1
0
1
1
1
1
2
1
1
1
2
1
1
2
1
0
1
2
1
1
1
1
1
1
1
1
0
1
1
0
1
1
1
1
1
0
2
1
3
0
1
1
1
0
1
0
0
0
1
1
0
1
1
0
1
2
1
0
1
1
2
1
0
1
0
1
1
1
1
1
1
1
1
0
1
2
0
1
1
0
0
1
2
1
2
1
1
1
2
1
0
0
2
0
0
1
1
1
1
1
1
1
2
0
1
1
2
0
3
2
1
2
1
2
2
1
1
2
1
1
1
2
1
1
2
2
1
1
1
1
2
1
1
2
0
0
1
2
1
1
1
2
1
1
1
1
1
1
1
0
1
1
1
0
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
2
1
0
0
1
1
1
1
2
2
0
1
1
1
1
1
1
0
1
2
3
1
1
2
0
1
1
1
2
1
1
0
1
2
2
0
0
1
1
1
0
0
1
1
1
1
2
0
0
0
1
1
1
1
2
1
1
1
1
1
1
0
1
0
1
0
0
0
0
1
2
1
2
1
2
2
1
1
2
1
1
1
1
2
1
1
1
0
1
2
1
2
0
1
1
1
1
3
1
2
2
1
0
1
0
2
1
2
1
1
1
1
2
2
1
1
1
2
0
0
2
1
1
1
2
1
1
2
1
1
0
2
1
1
1
0
2
2
1
1
1
2
1
0
0
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
0
1
1
2
1
0
1
1
0
1
1
1
2
0
1
1
1
1
2
1
2
1
1
2
2
2
1
1
2
1
1
3
2
1
0
0
1
1
2
2
2
1
1
0
1
1
1
0
1
0
1
2
0
1
1
0
1
1
1
1
1
1
1
0
1
0
1
2
1
1
2
0
0
1
1
1
1
1
1
2
1
1
1
1
2
2
1
2
1
1
1
1
0
1
1
2
1
2
1
0
1
1
1
2
1
0
2
2
1
0
2
1
2
2
1
1
1
2
1
2
1
1
2
1
2
1
1
1
2
2
0
1
1
1
2
1
1
1
1
0
0
1
1
1
3
0
1
1
2
1
1
1
1
2
2
1
0
0
1
2
1
1
1
0
2
1
1
1
1
0
1
0
1
1
1
1
1
1
0
0
2
0
1
1
1
1
1
1
1
2
2
0
1
1
0
0
1
2
2
0
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
2
1
1
2
1
1
1
1
2
2
1
0
1
1
2
0
0
2
2
1
1
1
1
1
1
1
1
2
2
1
1
1
1
0
1
1
1
0
2
2
2
2
1
1
1
2
0
2
1
1
1
2
0
1
0
1
0
0
1
2
2
2
1
2
1
1
2
2
1
1
2
0
1
2
0
0
1
2
1
1
1
1
0
1
1
1
1
2
0
2
1
1
0
2
1
1
1
2
1
2
0
1
1
0
1
2
1
1
1
2
1
0
2
2
0
2
1
0
1
1
1
1
1
1
2
1
1
1
0
1
1
2
2
1
1
2
1
1
2
1
1
1
2
0
1
2
0
0
1
2
1
1
1
1
2
1
0
1
2
2
1
2
1
1
0
2
0
2
2
1
1
1
2
0
0
2
1
1
2
1
0
1
2
1
1
2
1
2
1
1
1
1
0
1
1
1
1
0
2
1
1
0
2
0
1
1
0
1
1
1
1
2
2
1
1
1
3
0
1
2
1
2
2
1
0
0
1
1
2
1
1
0
1
1
1
0
1
1
1
1
1
1
0
1
2
1
3
1
1
0
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
0
1
1
1
1
2
1
1
1
2
1
1
2
2
2
1
1
0
1
1
2
0
2
0
1
2
1
1
1
0
1
1
0
2
2
1
1
1
1
1
1
0
1
1
1
2
0
0
2
1
2
0
1
1
1
2
1
1
1
2
2
1
2
2
2
1
1
1
1
1
2
1
0
2
1
1
1
2
1
0
0
0
2
1
0
0
2
1
1
1
0
1
2
1
1
1
1
1
2
1
1
1
3
1
3
2
1
0
0
2
0
1
1
1
1
1
1
0
2
2
0
1
2
0
1
0
1
1
1
2
0
1
1
1
2
1
0
0
1
1
1
1
1
2
1
0
1
1
1
1
1
1
1
1
1
2
2
0
2
1
0
2
2
1
1
0
2
0
2
1
1
1
1
0
2
1
1
1
1
1
1
2
1
2
1
1
0
0
1
2
0
0
2
1
2
1
2
1
1
2
1
2
1
1
0
1
1
5
1
1
1
1
1
1
2
1
1
0
2
1
1
1
2
1
1
1
2
2
1
1
2
1
2
0
1
0
1
1
2
1
0
0
1
2
2
0
2
1
1
1
1
0
1
2
1
1
1
1
1
0
1
2
1
1
2
1
1
1
0
2
2
1
1
1
0
1
1
1
2
2
1
1
1
1
0
2
0
1
1
1
1
2
1
1
0
1
1
1
1
0
2
1
2
0
2
1
1
1
1
2
1
0
2
1
1
1
1
1
2
1
1
2
1
2
2
2
1
1
0
2
1
1
1
1
0
1
2
1
0
1
1
2
1
1
0
1
1
2
1
1
0
0
0
2
1
1
1
1
2
1
0
1
2
1
2
2
1
1
1
0
1
1
1
1
1
2
2
2
1
1
2
1
1
0
1
1
1
2
2
1
2
1
0
1
2
2
0
0
1
1
0
1
2
1
2
1
1
1
0
0
1
1
1
1
2
2
1
2
1
1
1
2
0
0
0
1
2
0
2
1
2
2
0
1
1
2
1
2
1
2
1
2
1
2
1
1
1
1
1
0
1
1
1
2
2
2
1
2
2
1
2
0
1
0
1
1
1
1
1
1
1
1
1
2
2
2
0
1
0
2
2
1
1
1
1
1
1
2
2
2
2
2
1
1
2
0
1
0
1
2
2
2
1
1
1
1
2
0
1
2
1
1
2
0
1
1
1
1
1
2
2
2
2
0
5
0
1
2
1
0
0
1
1
1
1
0
2
1
2
2
1
3
2
1
1
1
1
1
2
0
2
2
0
1
1
1
1
1
1
1
1
1
2
1
2
0
1
1
2
1
1
1
1
1
0
0
1
2
0
1
0
1
2
1
1
1
1
1
2
1
2
1
0
1
0
1
1
1
2
0
0
1
1
1
1
0
2
1
1
0
1
2
2
1
2
1
1
1
1
1
1
2
1
0
2
1
1
1
2
1
1
2
1
2
0
1
0
2
2
1
1
1
1
2
1
1
0
1
0
1
2
1
1
1
2
3
1
2
0
0
2
0
0
1
1
2
1
0
0
0
1
2
2
0
1
1
1
0
1
2
2
1
2
1
0
2
2
1
1
1
2
2
1
1
0
1
0
1
1
1
2
1
1
0
0
1
0
1
2
0
1
2
1
2
1
3
1
1
1
1
2
0
0
2
2
0
1
2
1
0
1
1
1
1
0
0
0
1
2
2
1
2
2
1
1
0
2
1
1
1
0
1
1
2
2
1
2
2
1
0
0
1
2
1
2
1
2
1
1
1
1
2
1
2
1
1
2
2
0
1
2
0
1
2
1
2
2
1
1
1
2
2
2
2
1
1
2
1
2
0
0
1
0
1
1
1
1
2
1
2
1
1
2
1
0
1
1
2
1
0
2
1
1
0
1
1
1
1
2
1
2
1
2
1
1
0
2
1
0
1
1
2
1
1
1
3
1
1
1
2
0
1
0
1
1
0
1
1
1
1
2
0
1
2
2
1
1
1
2
1
1
2
2
1
1
1
2
1
0
0
0
1
0
1
1
1
1
0
1
2
1
2
0
0
2
1
1
1
2
0
0
1
2
1
1
1
0
0
1
0
1
1
2
2
1
1
1
1
1
1
1
1
0
0
1
1
0
3
1
2
0
1
1
1
2
1
1
1
2
1
1
0
2
0
1
1
0
2
1
1
1
1
2
1
2
1
2
0
1
1
1
1
1
1
2
1
1
1
0
2
1
1
0
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
0
1
1
1
2
1
1
1
2
2
1
1
2
1
0
4
2
1
1
1
2
1
1
1
0
1
0
1
2
2
1
1
0
2
1
1
1
1
1
0
2
0
0
2
1
1
1
0
1
1
1
0
2
1
1
2
2
1
1
1
1
2
1
1
0
1
1
1
2
2
2
1
2
1
2
2
2
2
1
2
1
1
2
1
1
1
1
0
1
2
1
1
2
1
2
1
1
1
0
1
1
1
1
2
0
1
0
0
1
0
1
1
1
1
1
0
0
1
1
2
1
1
2
2
1
1
1
1
1
1
1
1
2
1
2
0
1
1
1
1
2
2
2
1
1
1
1
0
2
2
1
1
2
1
1
5
2
1
2
1
1
2
2
1
1
0
1
2
0
1
1
2
1
2
2
1
1
1
1
0
1
2
1
2
1
1
1
2
1
0
1
0
0
2
1
1
1
1
1
2
1
1
0
1
6
1
1
1
2
2
1
0
2
0
2
1
1
0
1
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
1
0
1
0
0
1
1
1
0
2
0
1
1
1
1
1
0
1
1
0
1
1
1
2
1
1
0
2
2
1
0
2
1
1
1
1
1
1
0
1
1
0
0
1
1
1
1
1
2
1
1
2
1
1
0
1
1
1
2
0
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
2
0
1
2
3
1
2
1
0
1
1
1
2
1
1
1
1
1
1
2
1
0
2
1
1
1
1
0
0
0
1
1
2
1
1
1
2
2
1
0
0
1
2
1
1
1
2
2
2
1
1
1
1
2
1
1
1
1
1
1
1
2
2
2
1
1
0
2
3
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
2
0
2
2
1
0
1
1
1
0
1
1
2
1
1
1
1
1
0
1
1
2
1
2
2
1
2
2
1
1
2
1
1
3
1
1
1
1
1
1
0
2
0
1
1
1
6
1
1
0
1
2
2
2
0
1
1
2
1
1
1
1
2
1
1
2
1
1
1
2
1
0
2
0
1
1
1
0
2
1
1
2
1
1
1
1
0
1
0
1
0
1
0
1
1
2
1
1
1
1
0
1
1
1
1
1
2
1
2
1
1
1
1
0
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
2
1
1
1
1
0
0
1
2
1
0
0
0
1
1
1
1
2
1
1
0
1
0
2
1
2
1
0
2
1
1
2
1
1
2
1
1
1
1
0
2
2
1
2
2
0
1
1
0
2
1
1
1
1
0
1
1
2
1
0
1
0
1
2
1
2
2
1
0
2
1
1
1
1
1
1
0
1
1
1
0
0
1
0
1
1
1
0
1
0
1
2
1
1
0
0
2
2
2
0
2
1
1
1
1
1
2
2
1
1
1
2
1
1
1
1
1
1
1
0
1
2
0
1
0
1
1
1
1
1
1
1
1
0
1
1
1
1
1
2
0
1
1
1
1
2
0
2
0
1
1
2
2
1
1
0
0
2
1
1
0
1
1
1
1
1
1
0
2
1
0
2
1
2
2
2
2
0
2
1
0
1
0
1
2
2
1
1
0
2
2
1
0
0
2
2
2
1
2
0
1
1
1
0
0
1
2
1
1
1
2
1
1
1
2
1
0
1
1
1
2
1
1
0
1
1
1
1
1
1
1
0
1
2
1
1
1
1
1
1
1
1
1
1
2
1
0
1
2
2
1
1
1
2
0
2
1
1
2
2
2
1
0
2
0
2
1
1
1
2
2
1
2
2
2
1
2
1
1
1
0
0
1
1
1
0
1
2
1
1
2
1
1
1
1
2
1
2
1
2
1
1
1
1
1
2
1
2
0
1
0
1
1
1
1
1
1
1
1
0
1
2
1
1
0
1
0
1
1
1
2
1
1
2
1
1
0
2
1
1
1
1
2
1
2
1
1
2
1
2
1
0
1
1
1
2
1
1
1
0
1
1
1
1
1
1
1
1
0
1
1
2
1
1
1
0
2
1
1
1
1
2
1
1
2
0
0
2
1
1
0
0
1
1
1
1
0
2
1
1
2
1
2
1
1
2
1
1
1
1
1
0
1
0
2
2
1
1
2
2
1
0
1
1
1
1
1
2
1
0
2
1
1
2
1
1
0
2
1
1
0
1
1
1
0
1
1
2
1
0
1
1
1
1
0
1
2
2
1
0
0
1
1
2
1
2
2
1
0
2
2
1
2
0
1
1
1
1
2
2
1
1
2
1
1
1
0
2
1
1
1
2
2
0
1
0
2
0
2
2
1
2
6
1
1
1
1
0
2
1
2
0
1
2
1
1
0
1
1
2
1
1
1
0
1
0
1
2
0
1
0
1
1
1
1
0
1
1
2
1
0
2
1
1
1
2
2
1
1
1
1
2
1
2
2
0
1
1
1
0
1
2
2
2
1
1
2
2
1
1
0
1
1
1
2
1
1
1
2
1
1
0
1
1
1
1
1
1
1
0
1
1
1
0
1
1
2
1
1
1
0
2
1
2
2
1
1
0
1
2
1
1
1
0
1
1
0
1
0
1
1
3
2
1
0
0
1
2
1
1
1
1
2
1
2
0
1
1
1
3
2
1
1
2
1
2
0
0
1
1
0
0
2
1
1
2
4
2
2
1
1
2
1
2
1
0
1
2
2
2
0
0
1
2
2
2
1
1
0
1
1
1
1
1
1
2
1
1
2
1
3
1
2
1
2
1
2
2
2
1
2
1
2
2
0
2
0
1
0
1
0
1
1
1
2
1
1
2
1
0
1
1
1
1
1
1
1
1
1
1
1
1
2
3
1
1
0
1
2
2
1
0
2
1
2
1
2
2
1
0
2
1
0
0
1
1
2
1
0
2
1
1
1
1
1
1
0
0
1
1
1
2
1
0
0
2
1
2
1
2
1
0
1
0
0
1
2
1
2
1
2
1
1
1
0
0
1
0
1
1
3
0
1
1
1
0
2
1
0
2
2
1
2
1
1
0
0
1
1
2
2
0
0
0
1
2
1
0
1
0
1
1
0
2
1
1
2
0
0
2
1
0
2
1
1
2
1
1
1
1
1
0
0
0
1
2
1
0
2
2
0
1
2
2
0
0
1
1
2
2
2
1
1
1
1
0
0
2
1
1
0
1
1
2
1
0
1
1
0
1
1
1
0
1
2
1
1
1
0
2
1
0
1
0
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
3
1
2
1
1
1
1
0
1
1
1
1
2
1
1
1
0
0
1
1
1
1
1
1
1
1
0
2
0
2
1
1
0
0
1
1
2
0
2
1
1
0
2
1
2
1
1
0
1
1
1
2
1
1
1
0
1
1
1
1
1
1
1
0
1
0
1
1
2
0
1
2
2
2
0
1
2
1
1
0
1
1
1
1
1
1
0
0
2
1
0
1
0
0
1
2
1
0
2
1
0
1
0
1
1
2
1
1
0
2
1
2
0
0
1
1
0
1
1
1
0
2
2
1
1
1
1
1
2
1
1
1
0
1
2
1
1
1
2
1
3
1
1
1
1
1
1
2
1
0
1
1
1
1
1
0
0
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
2
0
0
1
1
2
1
0
0
1
1
1
1
1
1
1
2
1
1
1
1
2
2
1
1
2
2
1
2
1
1
0
1
2
1
0
1
2
1
2
1
2
2
1
1
2
2
1
2
2
1
1
1
2
1
1
1
1
0
2
1
2
2
1
1
2
1
0
1
1
0
1
0
1
1
1
2
1
1
1
1
1
1
1
2
1
1
0
0
1
1
1
0
1
0
1
1
1
1
1
0
1
1
1
1
1
1
0
1
1
1
1
2
2
2
1
1
0
2
1
0
1
2
1
1
1
1
1
0
0
2
1
1
2
0
1
3
1
2
2
1
2
1
1
2
1
1
1
2
2
1
1
3
1
1
0
1
1
1
0
2
2
1
1
1
2
0
1
1
1
1
1
1
0
1
1
2
1
1
2
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
0
1
1
1
1
0
1
1
1
0
2
1
2
1
2
0
0
1
2
1
1
0
1
2
1
2
1
2
2
2
1
2
1
2
1
1
2
1
1
1
1
1
0
1
1
2
2
0
0
2
1
1
1
1
2
2
1
1
1
0
1
1
2
1
2
1
0
1
2
1
0
2
1
1
1
2
1
2
0
0
2
2
1
1
2
1
2
2
1
1
1
1
1
2
0
1
1
0
2
1
1
2
1
1
2
1
1
1
1
2
2
2
1
1
1
2
1
1
2
1
1
1
1
1
1
2
0
1
0
1
1
0
1
2
0
2
1
1
2
1
1
0
1
0
2
1
2
1
1
0
1
2
1
1
1
1
1
2
0
1
2
1
2
1
1
2
1
0
0
1
1
1
1
2
1
1
0
2
0
1
1
2
1
1
1
2
1
1
1
2
1
2
1
1
0
1
1
0
1
0
1
1
1
0
0
1
2
2
2
1
1
1
1
1
2
1
1
2
1
0
2
2
1
1
1
1
1
1
1
2
0
0
1
2
0
0
1
2
1
2
2
1
1
1
0
1
0
1
2
2
1
1
1
1
1
1
1
2
2
1
1
1
0
1
1
1
1
2
2
2
2
2
0
1
2
1
0
2
1
1
1
1
1
2
1
1
1
1
2
2
1
1
1
1
1
2
1
0
1
1
2
1
2
1
1
1
1
0
1
1
2
1
1
1
1
0
0
1
1
0
2
2
3
2
2
1
1
1
1
1
1
1
1
1
1
0
2
1
1
1
1
0
2
0
1
1
2
1
2
2
0
1
2
1
1
1
2
0
1
1
2
2
0
0
1
0
0
1
1
1
2
1
2
2
1
1
2
1
1
2
1
3
1
1
1
1
0
1
2
2
1
2
1
2
2
1
2
1
2
1
0
0
1
1
2
1
0
0
2
2
2
1
1
1
1
0
2
2
1
1
1
0
1
0
2
0
1
2
2
2
1
1
2
1
1
0
1
1
1
1
1
2
1
1
1
1
1
1
2
1
0
1
1
0
2
1
1
1
2
1
0
1
1
1
2
2
2
1
1
5
1
0
2
0
2
1
2
2
2
1
0
2
1
1
2
2
2
1
0
1
1
3
1
1
2
1
1
2
1
1
1
1
0
1
0
1
2
2
1
1
2
1
1
0
2
0
1
1
1
1
1
2
0
0
2
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
2
0
1
2
1
2
1
1
1
1
1
2
1
1
1
0
1
1
0
1
2
1
2
1
1
0
1
0
1
0
1
0
3
1
1
2
1
1
1
1
2
1
0
1
1
1
1
0
2
2
1
2
1
1
0
3
1
1
1
2
1
2
1
1
1
0
0
1
1
0
1
2
1
1
1
2
1
1
1
0
2
0
0
1
2
2
0
2
3
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
0
1
1
2
0
1
1
1
0
2
1
2
0
1
1
1
1
1
1
1
2
2
1
2
1
1
2
2
2
0
1
1
1
1
1
1
1
0
0
1
1
1
1
1
2
1
1
1
2
1
1
0
2
2
1
2
1
0
1
1
2
0
1
2
1
1
1
2
1
1
1
0
2
1
1
1
0
1
1
1
2
1
1
2
0
1
1
1
1
1
1
1
1
0
2
2
1
2
2
1
0
2
1
1
2
2
1
2
2
1
1
1
1
2
0
1
2
1
0
2
1
1
7
1
1
0
2
0
2
1
1
1
0
1
1
2
0
1
1
0
0
2
1
1
0
2
2
2
1
1
1
1
2
2
0
0
1
2
1
2
1
1
2
1
1
2
1
1
0
0
1
1
1
0
1
2
1
1
1
1
2
1
1
1
1
0
1
1
3
1
1
2
1
1
2
0
1
1
2
2
0
1
1
0
2
1
0
2
1
2
1
1
1
0
1
2
1
0
1
1
1
1
1
1
1
1
1
1
1
1
0
2
1
2
1
0
1
2
1
1
1
1
2
0
1
1
1
0
2
1
1
2
2
1
0
1
1
1
2
5
1
1
0
1
1
1
2
1
1
1
0
1
0
1
1
2
1
1
1
1
1
2
2
1
1
1
1
1
1
0
2
2
1
1
1
1
2
0
1
0
1
2
2
1
1
0
1
1
0
0
1
1
0
0
1
0
0
1
1
1
1
1
1
0
1
0
1
2
1
1
1
1
1
1
1
1
0
2
1
1
1
2
1
1
0
1
2
1
0
1
1
2
1
1
0
0
0
1
3
2
1
1
1
1
1
2
2
1
2
1
1
1
2
1
1
1
1
1
1
0
2
1
1
2
2
1
2
0
2
1
1
0
1
2
1
1
0
0
1
1
2
2
1
1
1
1
1
2
1
0
2
2
1
1
1
1
0
2
2
2
1
1
1
2
2
1
1
2
1
2
1
1
1
1
1
2
2
1
1
1
1
1
0
1
1
1
2
0
1
2
1
1
1
1
2
1
2
0
2
0
0
1
2
0
1
1
1
1
3
0
1
2
1
1
1
1
2
1
1
1
1
1
0
1
1
2
0
2
1
1
2
1
2
1
1
2
0
2
0
1
2
0
1
2
1
1
1
1
2
1
1
1
2
1
1
1
1
1
0
2
2
1
1
1
2
1
1
1
1
1
1
2
2
2
2
1
0
2
1
1
2
1
0
1
1
2
2
1
1
2
1
2
0
1
2
1
1
1
1
1
1
0
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
0
1
1
1
2
0
1
0
1
1
1
1
0
0
1
1
1
1
1
2
2
1
0
1
1
3
1
1
0
0
2
1
1
1
1
2
0
2
1
1
2
1
2
2
1
1
1
2
1
2
0
2
1
1
1
2
2
1
1
2
2
2
1
1
1
0
0
1
1
0
2
1
2
1
0
1
1
1
1
1
2
1
2
2
1
1
1
0
2
1
1
2
2
0
1
2
1
1
1
2
1
1
1
0
0
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
0
2
1
1
1
0
2
1
1
1
1
1
0
2
1
1
0
0
1
1
1
0
2
1
0
3
2
1
1
1
2
0
1
2
1
1
1
2
1
1
1
0
1
1
2
2
2
1
1
1
0
2
1
2
1
0
1
1
0
2
1
2
0
2
1
2
2
1
1
2
1
1
1
0
1
0
1
1
0
2
2
1
1
2
1
0
1
0
0
1
1
1
2
1
0
1
2
1
1
1
0
1
1
0
1
1
2
1
1
2
1
1
1
1
1
1
1
1
2
0
1
1
2
2
2
1
1
1
1
2
1
1
1
1
1
1
0
2
1
2
1
0
0
0
1
1
2
1
1
2
0
2
2
2
1
1
1
1
2
2
1
2
1
1
2
1
1
1
1
1
1
1
4
2
2
0
1
1
0
0
2
1
1
1
2
2
0
2
2
0
0
1
1
1
2
1
0
2
2
1
0
1
1
2
1
1
1
0
2
1
2
1
1
1
1
1
0
0
0
1
1
1
1
1
2
2
0
2
1
1
1
2
1
1
1
1
1
1
1
0
1
0
1
1
1
2
2
1
1
2
1
1
1
1
1
2
0
1
1
0
1
2
0
1
2
1
1
2
1
1
1
2
0
1
2
2
2
2
1
1
2
0
1
1
0
2
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
0
1
1
1
1
2
1
1
2
2
1
2
1
2
1
1
1
1
1
1
0
1
0
1
2
1
1
0
2
1
1
1
3
0
0
1
1
1
1
2
1
1
0
1
0
0
2
1
2
0
2
1
1
1
1
0
1
1
0
1
0
1
1
1
0
2
1
1
1
1
1
1
1
1
0
1
1
2
2
1
1
1
2
1
1
1
1
2
0
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
0
1
2
2
3
1
1
1
0
2
1
1
2
2
0
0
0
1
1
1
1
2
2
2
1
1
0
0
1
11
1
1
1
1
2
2
1
1
2
0
1
1
1
1
1
1
1
2
2
2
1
2
1
1
0
1
1
1
1
1
1
1
1
1
1
2
0
0
1
1
1
1
1
1
2
0
0
2
2
0
1
0
2
2
1
2
1
1
1
0
2
1
1
1
1
2
1
0
1
2
1
1
1
2
1
1
0
1
1
2
2
1
1
1
2
1
1
2
1
1
1
1
1
0
1
0
0
1
1
1
1
2
2
0
0
1
2
2
1
2
2
0
1
3
2
1
2
2
2
1
2
1
1
2
2
1
0
1
2
1
0
1
1
1
1
1
0
1
1
0
2
1
1
1
1
2
1
2
2
1
2
1
1
1
2
2
2
1
1
0
1
1
2
2
2
1
1
1
0
1
1
1
1
1
2
1
0
0
0
2
1
2
0
1
1
1
1
0
2
1
1
1
1
1
1
1
1
1
1
0
2
2
1
2
2
2
1
2
1
2
1
1
1
2
1
1
1
0
1
1
1
0
3
1
1
1
2
1
0
1
0
1
1
1
0
2
1
1
1
1
2
1
0
1
0
2
2
1
0
1
0
1
2
2
1
0
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
0
1
0
1
2
1
1
0
1
1
1
0
1
2
1
0
2
1
1
1
1
1
1
1
0
0
1
1
0
2
1
2
1
2
0
2
2
1
1
1
2
1
1
0
1
1
0
0
1
0
1
1
0
1
1
1
2
1
1
1
1
1
1
0
1
1
1
1
1
2
2
1
0
2
1
1
2
2
1
1
0
1
1
0
2
1
2
0
0
2
1
1
1
2
1
2
1
0
1
1
1
0
2
0
0
0
1
1
2
3
1
1
1
1
2
2
1
1
2
1
1
1
1
1
0
1
2
1
1
1
0
2
2
2
0
2
1
3
1
1
1
1
2
1
0
1
1
1
1
0
2
1
1
1
1
2
1
1
1
1
1
1
1
1
2
0
1
1
1
1
1
2
1
2
0
2
2
2
2
1
1
1
2
1
2
1
1
1
1
0
2
1
1
1
0
2
1
1
2
0
1
1
0
0
1
1
0
1
1
1
2
0
1
1
2
2
2
1
0
1
1
0
0
1
0
2
1
2
0
2
1
1
1
1
0
1
1
1
1
0
1
0
1
1
1
1
0
1
1
1
1
2
0
1
1
0
1
2
2
1
2
1
1
2
1
1
1
2
1
0
2
2
0
0
1
1
0
1
1
1
1
2
0
2
2
2
0
1
0
1
3
1
1
2
0
1
0
2
0
1
0
1
1
1
1
1
2
1
0
1
1
1
1
1
2
0
2
0
0
0
1
1
1
0
1
0
1
0
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
0
1
0
0
0
2
2
1
1
2
2
0
2
1
0
1
1
2
1
2
1
2
1
1
1
1
1
1
2
1
1
0
1
2
2
2
1
2
2
1
1
2
0
1
2
0
0
2
1
1
2
1
1
1
0
1
1
1
1
1
2
2
1
1
2
1
0
1
1
2
1
1
1
1
1
1
0
2
1
1
2
1
1
2
1
0
2
1
1
1
0
0
1
1
0
1
1
0
2
1
1
2
1
1
2
1
1
1
1
1
1
0
1
1
1
0
1
1
1
1
2
1
0
1
1
0
0
0
1
1
2
1
1
1
1
1
1
1
1
1
0
2
1
1
1
2
0
1
1
0
1
2
0
1
1
2
2
0
0
1
1
1
0
1
2
1
1
1
2
2
1
1
1
1
1
0
1
2
2
1
1
1
0
1
2
1
1
1
1
1
1
1
1
1
0
1
1
1
2
2
1
2
1
0
1
1
3
1
1
1
1
1
1
2
1
0
1
0
2
1
2
1
2
1
1
1
1
2
0
1
1
1
1
1
0
1
0
1
1
2
2
1
0
0
4
1
1
2
2
0
0
1
0
1
2
1
1
2
0
1
1
1
1
1
1
1
0
1
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
1
1
1
0
2
3
2
1
2
1
1
2
0
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
0
2
2
0
0
0
1
1
2
1
2
1
1
0
1
1
2
2
1
1
1
1
0
1
1
1
1
0
2
0
1
0
1
0
1
2
1
2
1
1
1
0
1
1
2
0
1
0
1
0
1
0
2
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
2
0
1
1
1
2
0
1
1
0
1
1
2
2
0
1
1
1
1
1
2
1
1
1
1
0
1
1
0
2
0
2
0
1
1
1
1
2
2
2
1
2
0
0
2
0
1
0
1
1
1
1
2
1
0
0
1
2
1
0
0
1
1
1
1
1
0
1
1
1
2
1
0
1
1
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
2
2
2
2
1
1
2
1
1
2
1
1
1
0
1
2
1
2
10
1
2
2
0
0
2
1
2
0
1
2
1
1
1
2
1
1
0
2
1
1
2
1
1
0
1
0
2
2
2
4
2
1
0
1
2
2
1
1
1
1
1
1
0
2
1
2
1
1
1
1
0
2
0
1
1
1
2
1
0
0
2
1
1
0
1
2
1
2
1
2
1
0
1
1
1
1
0
1
0
1
1
1
1
1
0
0
2
1
1
1
2
2
2
1
2
2
1
1
0
1
1
2
1
1
1
2
2
1
1
0
0
1
1
2
1
1
2
2
1
2
0
1
1
1
1
1
2
1
2
2
2
1
1
1
2
2
3
1
0
1
1
1
1
1
0
1
1
1
2
1
1
2
1
0
1
1
1
0
1
1
2
1
1
0
1
0
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
0
1
1
1
0
2
1
2
0
1
1
1
1
0
1
1
1
0
1
1
1
0
0
1
0
0
1
2
0
1
1
1
1
1
1
1
0
0
1
1
2
2
1
1
1
1
1
1
1
0
2
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
2
1
2
1
1
0
1
0
1
0
1
2
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
0
1
1
1
2
0
2
1
1
1
0
1
1
1
2
1
2
1
1
1
1
2
1
1
1
2
2
1
1
2
1
2
0
1
1
0
2
0
0
1
1
2
1
0
1
1
1
1
2
2
1
1
1
1
1
1
0
0
1
1
2
1
1
0
2
2
1
1
1
1
1
1
0
2
1
1
1
2
1
0
1
1
0
2
2
1
0
1
1
2
1
1
0
0
1
2
1
1
3
2
0
1
2
1
1
0
2
2
2
0
1
1
0
2
0
1
1
1
1
1
1
1
1
2
2
0
0
0
1
1
1
1
1
0
1
1
0
2
1
1
2
1
1
2
1
0
1
1
0
2
1
2
1
0
0
1
2
1
1
2
1
0
2
0
1
1
2
0
1
0
0
0
1
3
1
1
1
1
1
1
0
2
2
2
0
2
1
1
1
1
0
1
1
1
0
1
0
1
1
0
1
1
1
2
1
1
1
2
1
1
1
1
1
0
2
1
1
2
1
1
2
2
0
1
1
1
1
0
1
0
1
1
1
1
1
1
1
2
2
1
2
1
1
0
2
1
1
1
2
2
1
0
1
2
2
2
0
1
1
0
0
0
1
0
1
1
2
1
1
1
0
1
1
1
2
2
2
2
0
1
1
1
2
2
1
1
1
2
2
1
2
2
1
2
0
2
1
1
2
1
0
1
1
0
0
1
1
2
1
2
1
2
1
1
0
1
0
0
2
2
2
0
1
2
0
1
1
1
1
1
1
1
0
0
1
1
2
2
1
0
2
1
2
1
1
1
1
1
1
2
1
1
1
3
1
0
1
1
1
1
0
1
1
3
1
1
2
2
1
2
1
0
1
1
2
1
0
1
1
0
1
2
1
1
1
2
0
1
1
0
2
1
1
1
1
1
1
2
1
1
1
2
3
1
1
2
0
1
1
1
0
1
1
2
1
1
1
2
1
1
2
1
2
2
1
0
1
2
1
1
1
1
0
1
2
2
2
2
1
0
2
2
1
1
1
1
1
2
1
1
2
2
2
1
1
2
1
2
1
1
1
1
2
1
1
0
1
1
1
2
1
1
2
0
2
1
0
1
0
2
0
1
1
1
2
0
2
0
2
2
1
1
1
2
1
2
1
1
0
0
1
1
1
2
1
0
0
0
2
1
1
1
0
2
1
2
1
2
1
2
2
1
1
0
2
1
1
1
1
1
1
2
1
0
1
0
1
1
0
2
1
1
2
2
1
1
1
1
2
1
1
2
1
1
2
1
1
0
1
0
1
1
1
1
3
2
2
1
2
1
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
0
2
0
1
2
1
0
1
1
1
1
0
0
1
0
1
1
1
2
2
1
1
0
1
1
1
1
2
0
2
1
0
1
1
1
2
1
2
1
2
2
0
1
1
1
0
1
1
1
1
1
0
0
1
1
1
2
0
1
2
1
1
1
1
2
1
0
1
0
2
1
0
1
1
0
1
0
1
0
2
0
0
1
1
1
1
1
1
2
1
1
1
2
2
1
2
1
1
0
1
1
2
3
0
1
1
1
1
2
2
1
2
1
1
0
1
2
0
2
1
1
1
1
2
2
1
2
2
1
1
1
1
0
0
1
1
1
1
0
1
0
1
1
0
1
1
1
1
0
1
2
2
1
0
1
2
0
2
2
1
1
2
0
1
2
1
1
0
0
0
1
1
0
1
1
1
1
1
1
1
2
1
2
1
0
1
1
0
2
0
0
1
0
0
2
1
1
1
2
0
2
2
1
0
1
1
1
2
0
1
2
2
1
1
1
1
0
1
1
1
1
0
1
0
1
1
1
2
1
1
1
1
1
2
1
1
2
1
1
1
2
1
1
2
0
1
2
1
0
2
1
1
1
1
1
2
2
0
1
1
1
1
2
1
1
2
1
1
2
1
2
0
1
1
1
1
1
1
0
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
0
1
1
2
2
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
0
1
2
0
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
2
2
1
1
1
2
0
2
1
2
2
2
2
1
1
0
2
2
1
0
0
1
2
1
1
1
1
0
2
1
1
0
0
1
0
1
1
0
1
1
0
1
2
1
1
2
1
2
3
1
2
1
2
2
0
1
0
1
0
1
2
1
2
1
2
2
1
0
1
0
2
1
2
1
2
3
1
1
1
1
1
1
2
0
2
1
1
1
1
1
2
2
1
1
1
0
1
1
2
1
1
1
2
1
0
0
2
1
1
0
2
2
1
2
1
1
1
1
1
1
1
2
2
1
1
2
1
0
0
2
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
1
0
2
1
0
1
3
2
0
1
1
1
1
1
1
1
0
1
0
1
1
1
1
0
1
1
2
2
2
1
2
2
2
2
1
0
1
1
0
0
1
1
0
0
0
1
2
2
1
2
1
1
1
1
1
2
1
2
2
1
1
1
2
1
0
0
1
1
2
0
1
1
1
1
1
1
0
1
1
1
1
2
1
1
1
0
1
0
1
1
2
1
1
2
1
2
2
1
0
2
1
2
2
1
1
1
0
2
1
2
1
1
0
1
0
1
1
0
1
0
0
1
1
1
1
0
0
1
1
1
1
1
2
1
1
1
2
1
1
1
1
2
0
2
1
1
0
1
1
1
0
0
1
1
1
0
1
2
1
1
2
1
1
1
2
2
2
0
1
1
1
2
2
1
1
1
1
0
1
0
0
1
2
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
1
1
2
0
2
1
1
0
1
1
1
0
1
1
1
0
1
2
0
1
1
1
1
1
2
0
1
1
0
1
1
2
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
0
1
1
1
1
1
1
1
0
1
1
1
0
1
2
1
1
0
0
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
0
1
3
1
1
1
1
2
1
1
1
1
1
2
0
2
1
0
1
1
1
3
1
2
1
1
1
2
1
1
1
1
1
0
2
1
0
2
2
1
2
2
2
1
1
1
1
0
2
0
0
2
2
1
1
0
2
1
1
1
1
1
2
1
0
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
0
2
2
1
1
1
2
1
0
1
1
1
1
1
2
1
0
0
1
1
2
0
1
1
1
1
1
1
1
1
2
1
1
1
1
4
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
2
1
0
1
0
2
1
2
2
0
1
0
1
1
1
2
1
0
1
0
0
0
2
1
1
2
1
2
1
2
1
1
2
1
1
1
1
1
1
1
1
0
1
2
1
2
2
1
1
1
1
0
1
1
1
1
1
1
3
1
1
1
2
1
2
1
0
1
2
1
0
1
2
0
1
0
1
2
1
0
2
2
1
1
1
1
1
0
0
1
1
2
2
1
1
2
1
0
1
1
1
1
2
1
1
2
1
1
1
1
2
1
1
1
1
1
2
1
2
2
1
0
2
1
1
1
1
0
1
2
0
1
1
0
0
2
2
2
1
1
0
1
1
1
1
2
1
2
1
1
2
0
1
1
1
2
1
1
1
4
1
1
2
1
2
1
1
1
1
0
0
1
1
1
0
0
2
1
1
1
1
1
1
1
1
1
1
0
1
1
1
2
1
1
0
1
2
0
1
1
2
0
1
1
1
1
0
2
1
2
1
3
0
0
3
1
1
1
1
1
1
1
1
0
1
1
2
1
2
2
1
1
2
1
0
2
2
0
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
2
0
1
1
2
2
2
2
0
0
1
1
2
2
0
1
1
2
1
1
2
1
1
0
1
0
2
0
2
1
1
1
0
1
2
1
1
1
1
1
0
1
1
1
1
1
2
2
1
1
2
2
2
1
2
2
2
1
2
2
1
0
1
1
1
0
1
0
2
2
1
1
1
0
2
1
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
2
1
1
0
1
2
1
2
0
0
2
0
1
3
1
0
0
1
1
1
1
2
1
1
0
1
2
1
1
1
0
1
1
1
1
2
1
1
1
1
1
1
1
0
1
1
1
0
2
2
1
1
0
1
1
1
1
2
0
1
0
0
0
1
1
1
1
0
0
2
2
1
1
2
2
0
1
2
1
1
0
1
2
2
1
1
2
1
0
1
1
1
2
1
1
2
2
1
1
1
1
1
2
1
0
2
1
1
1
2
1
0
2
1
1
1
1
1
1
2
1
1
1
2
0
1
0
1
1
1
2
0
1
2
1
0
0
1
2
0
1
2
1
1
1
1
1
1
2
2
0
1
1
4
1
1
2
1
2
1
1
0
1
2
2
2
1
1
3
0
1
1
1
1
1
1
0
2
1
1
1
1
1
2
1
2
0
0
1
1
1
2
1
0
1
1
1
1
0
1
0
1
1
1
1
0
1
0
1
1
1
1
2
1
0
2
1
2
2
1
1
2
1
1
0
1
1
0
1
0
1
0
2
2
1
1
1
1
1
2
1
1
1
0
1
0
1
2
2
1
1
1
1
2
0
1
1
0
2
1
1
2
2
1
1
1
1
1
1
1
4
0
1
1
2
0
0
1
0
1
1
2
1
1
2
1
2
2
1
1
1
1
0
1
2
0
1
1
2
1
1
1
1
1
1
1
0
2
1
1
2
1
0
1
2
1
2
2
1
1
1
1
1
1
2
1
1
3
1
2
1
1
2
1
2
1
1
0
0
1
2
0
1
1
1
1
0
1
0
0
2
2
1
1
2
1
2
1
1
2
2
1
4
1
1
3
2
1
1
0
1
0
2
2
1
0
2
2
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
0
2
2
1
2
1
1
1
1
0
1
1
1
1
0
2
1
1
1
1
1
1
1
1
0
0
1
2
0
1
1
0
2
1
0
2
1
1
0
1
1
1
0
1
1
0
1
1
1
1
2
1
1
1
1
1
0
1
1
1
2
0
0
1
1
1
2
2
0
0
0
2
2
2
0
1
2
1
0
1
1
2
1
0
1
1
1
2
1
1
2
1
1
0
2
2
2
2
1
1
1
1
0
1
1
1
2
1
1
1
1
1
1
0
1
1
2
1
2
1
1
1
1
1
1
1
2
2
2
0
1
1
0
1
1
1
1
1
2
1
1
1
1
0
2
1
2
0
1
2
1
2
1
1
2
1
1
1
1
1
0
1
1
0
1
1
1
1
2
2
1
2
2
1
0
1
1
2
2
0
1
1
0
2
1
1
1
1
1
0
1
1
0
1
1
1
1
2
1
1
2
0
2
2
2
1
1
2
2
1
1
2
1
1
2
0
1
1
1
1
1
2
1
1
1
1
1
0
1
1
1
2
2
1
2
1
1
0
0
1
1
1
0
1
2
0
2
2
1
1
2
1
1
2
1
1
0
1
1
1
0
2
0
1
2
2
2
2
0
1
2
1
0
2
0
1
1
1
1
1
1
1
2
1
2
1
0
1
1
0
0
1
0
2
2
2
1
2
1
2
2
1
2
2
1
0
0
1
0
1
1
0
2
0
2
1
1
1
2
2
1
1
2
2
0
1
1
0
2
2
2
1
0
0
1
2
2
1
0
0
1
2
1
1
0
1
1
1
1
2
1
1
2
2
2
1
1
1
1
1
2
1
1
1
1
1
1
1
0
0
1
1
0
1
1
1
0
0
1
0
1
1
1
2
1
1
1
1
0
1
2
1
1
1
2
2
1
1
2
1
1
1
1
2
1
1
2
2
1
0
1
2
1
1
1
1
1
1
0
2
1
2
1
1
0
2
1
1
1
0
1
1
1
2
2
2
1
2
1
3
2
1
1
2
1
1
1
1
0
1
1
1
0
1
1
0
1
1
1
2
1
0
2
1
2
0
2
1
1
1
1
1
0
1
1
1
2
2
1
0
2
0
0
0
1
1
1
1
1
2
2
1
1
1
1
3
1
1
2
0
1
0
1
0
0
2
1
1
0
1
2
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
2
1
1
2
0
3
1
0
1
1
2
1
2
1
1
0
1
1
1
2
1
2
1
1
1
2
1
0
1
1
0
1
1
1
1
1
1
1
1
1
0
1
1
2
1
0
1
1
0
1
1
1
1
1
1
1
1
1
1
0
1
2
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
0
1
0
0
1
0
0
2
1
2
2
1
1
1
1
1
0
1
0
0
1
1
1
2
1
2
2
2
4
1
1
2
1
2
0
2
2
1
1
0
0
1
2
0
1
1
1
1
2
1
1
2
1
1
1
2
0
1
1
1
1
2
1
0
0
1
2
1
1
1
0
0
1
2
2
1
2
0
2
1
1
1
0
1
1
1
1
1
2
1
1
2
1
1
1
2
2
0
0
2
1
2
2
2
1
1
2
1
0
1
1
1
1
1
0
0
1
1
0
2
1
1
1
2
1
2
1
2
1
1
0
1
1
1
1
0
1
1
1
2
2
1
0
1
1
0
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
2
1
1
1
0
1
1
1
1
2
0
1
1
2
1
1
1
1
2
1
0
0
1
1
2
2
1
1
0
0
2
0
0
1
1
2
0
1
1
1
1
1
2
2
0
0
1
2
1
1
1
2
1
1
0
1
0
1
1
1
0
0
1
2
0
0
0
1
0
0
1
1
0
1
2
1
1
1
1
0
2
1
1
2
1
0
1
1
1
1
0
1
1
2
0
2
1
0
1
1
2
1
1
0
2
1
2
1
1
0
1
0
0
2
1
1
1
2
1
2
1
2
1
2
2
1
1
1
1
0
1
2
1
2
1
2
2
1
2
1
1
1
1
1
2
2
1
1
1
1
1
2
2
2
1
1
1
1
0
2
2
2
2
1
1
2
2
1
1
1
2
1
0
1
1
1
1
2
1
2
1
1
2
1
0
1
1
1
0
1
1
1
0
2
1
1
0
1
1
2
2
1
0
1
1
1
2
1
0
1
1
2
0
1
0
0
1
1
1
2
1
3
2
1
1
1
1
2
2
1
1
1
0
0
1
1
2
1
2
1
0
0
1
1
1
0
1
1
1
1
2
1
1
1
1
2
0
1
2
0
2
0
1
1
0
1
1
1
2
1
1
1
1
1
0
1
1
1
2
1
2
1
1
1
2
1
1
1
2
1
1
0
1
2
1
0
1
1
1
1
1
1
1
1
0
0
1
1
2
1
1
3
1
1
4
2
1
1
0
0
0
1
0
1
1
1
1
0
1
0
1
1
1
1
2
1
1
2
0
1
1
1
1
1
2
2
2
0
1
1
1
1
1
0
2
1
1
1
0
2
1
2
1
0
2
0
1
1
2
2
0
1
1
2
2
2
1
2
0
0
1
1
2
1
1
2
1
1
2
1
1
1
1
2
2
2
2
1
2
1
2
0
2
0
1
1
1
2
2
1
1
0
1
1
1
0
1
1
1
1
1
1
1
0
1
2
0
1
2
2
2
2
1
1
3
2
1
1
0
0
2
2
1
1
1
1
1
1
0
1
2
1
1
1
0
1
1
2
1
1
1
1
1
1
1
0
1
0
0
1
1
1
1
2
1
1
1
1
0
1
1
2
1
1
1
2
0
1
1
2
1
1
1
2
1
1
1
0
1
0
1
2
0
1
0
2
1
1
0
1
1
1
2
1
1
0
1
1
2
2
1
1
2
0
1
1
1
0
0
1
2
1
1
1
2
1
2
2
2
1
1
2
1
1
1
2
0
2
1
1
3
2
0
3
2
1
2
1
1
1
0
1
1
1
1
0
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
0
2
1
0
2
2
1
1
0
2
1
2
1
1
2
1
4
2
1
2
1
1
2
1
1
2
1
0
0
1
0
2
0
0
2
1
1
1
1
1
1
2
2
1
2
1
2
0
1
0
0
1
1
2
2
2
0
2
2
1
1
0
2
1
1
2
1
1
0
1
1
1
2
0
1
2
1
1
1
2
1
1
1
2
0
2
1
1
1
1
0
1
2
2
1
0
0
0
1
0
0
1
0
2
0
1
1
0
1
1
1
1
1
1
2
0
1
1
1
1
1
1
1
1
2
1
1
0
1
1
1
1
2
1
1
0
2
2
1
1
1
1
1
1
2
1
0
1
1
1
1
1
2
1
1
0
0
1
1
1
2
1
0
1
2
2
1
0
1
1
1
1
2
1
1
2
2
1
2
0
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
2
0
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
0
4
1
2
1
2
0
1
1
1
1
0
0
1
1
1
1
1
1
2
2
0
0
0
1
1
0
1
1
0
1
1
2
2
1
0
2
1
0
0
1
1
1
1
0
1
1
1
1
1
1
1
0
2
1
2
0
1
2
1
1
1
1
1
1
0
1
1
2
2
1
1
0
0
2
0
1
0
0
1
1
1
2
1
2
0
1
1
2
1
1
1
1
1
1
2
1
1
1
1
0
1
1
2
1
1
2
1
1
0
0
1
0
1
2
3
1
2
1
1
0
0
1
1
0
2
2
1
3
1
2
1
1
1
0
2
2
1
2
1
1
1
2
1
2
0
0
0
1
1
1
2
1
2
0
0
1
1
1
0
2
1
2
2
1
2
1
1
2
0
1
2
0
0
1
1
2
0
1
2
1
0
0
1
1
1
1
1
0
2
1
2
1
1
0
3
2
1
1
2
1
1
1
1
1
0
0
2
0
1
0
1
1
1
2
1
1
2
0
1
0
1
1
1
0
2
2
1
1
0
1
0
2
0
2
1
0
1
1
1
0
1
1
1
2
1
0
1
2
2
1
1
2
2
0
1
1
1
1
1
2
1
1
0
1
0
1
1
1
0
1
1
1
0
2
1
1
2
0
1
2
0
2
2
1
2
2
1
1
1
1
1
1
1
2
0
1
0
1
1
1
2
1
2
2
1
0
1
1
1
1
1
1
1
2
0
1
1
2
2
1
1
0
2
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
2
1
1
2
1
0
1
0
2
2
0
1
2
1
1
1
2
0
1
1
2
2
1
3
1
1
0
0
0
1
1
1
1
2
1
1
1
1
2
0
1
0
0
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
0
2
1
1
1
1
2
1
2
1
2
0
1
0
1
1
1
1
1
0
1
1
1
2
1
1
1
2
1
0
1
1
1
0
2
1
1
2
1
1
1
0
1
1
1
1
2
2
1
2
0
1
2
1
1
1
1
1
0
2
1
0
0
0
1
2
1
0
1
0
1
1
1
1
1
1
0
0
1
1
2
1
1
1
2
1
1
0
1
2
2
1
2
1
1
1
0
2
1
1
0
1
2
1
1
1
1
1
1
1
1
0
0
1
1
2
2
2
2
1
2
1
1
1
1
1
1
1
1
0
1
1
1
1
1
0
2
2
1
1
1
2
1
2
0
1
1
0
2
1
1
2
1
1
2
4
3
1
1
2
1
1
1
2
1
1
2
1
2
1
2
1
2
1
1
2
0
1
0
1
2
0
1
1
1
1
0
1
2
0
1
1
1
2
1
1
0
0
1
2
2
1
2
1
1
2
1
2
1
0
1
2
1
1
0
0
0
2
1
0
1
1
1
1
1
1
1
2
0
1
1
1
2
0
0
0
2
1
1
0
2
1
2
1
2
1
1
1
2
2
1
1
1
0
1
1
0
1
0
2
1
1
1
1
0
1
0
2
2
0
0
2
0
1
2
0
1
1
1
0
1
1
1
1
2
2
0
1
1
2
1
1
1
1
1
0
2
1
1
1
1
0
2
1
0
1
1
1
0
1
1
1
0
1
1
1
1
2
1
1
0
1
2
3
2
1
1
0
1
0
2
1
1
0
2
1
0
1
0
2
2
1
1
2
1
0
0
3
0
1
1
0
1
2
0
2
1
1
1
1
2
1
1
1
1
1
1
1
0
1
2
0
0
1
2
0
1
2
0
1
1
1
1
1
1
1
1
1
2
2
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
0
2
0
0
1
0
1
0
0
2
1
2
1
2
1
1
1
2
0
0
2
1
2
1
2
0
2
1
0
1
1
1
0
1
1
0
0
1
2
2
1
0
1
0
1
2
0
2
1
0
0
0
1
2
3
1
1
0
2
1
1
1
0
1
1
1
2
2
2
1
0
2
0
1
1
1
1
0
0
1
1
1
0
2
1
0
1
0
1
2
3
1
1
1
0
1
0
1
3
1
2
2
1
2
1
2
2
0
1
0
2
1
1
1
1
1
3
1
1
1
2
1
1
0
1
0
2
2
2
1
1
1
1
1
3
1
1
0
1
1
1
1
0
2
2
2
2
1
1
2
2
1
2
0
1
1
0
2
0
1
1
1
0
1
0
0
1
2
1
1
1
1
1
0
0
2
2
1
1
1
1
2
0
0
1
1
2
1
1
2
1
1
1
1
1
1
1
2
1
2
2
2
1
1
0
0
2
2
1
1
1
1
2
1
0
1
1
2
1
0
1
1
2
1
2
1
1
1
1
1
0
1
0
2
2
1
1
2
1
2
1
0
2
1
0
1
1
1
1
1
2
1
1
1
0
1
1
1
1
1
2
0
1
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
0
0
1
0
2
1
1
2
1
0
2
1
0
1
1
1
1
2
1
1
1
2
2
0
0
1
2
1
2
2
2
1
1
2
0
1
1
0
2
1
0
2
0
1
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
3
1
1
0
0
1
2
0
2
0
1
0
2
2
1
1
1
2
1
1
0
1
1
0
1
1
1
1
1
1
2
2
2
0
1
0
2
1
1
1
0
0
1
1
1
1
0
0
3
1
1
1
0
2
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
0
1
1
1
1
0
1
1
1
0
0
1
2
2
1
1
1
1
0
1
0
1
1
1
0
0
2
1
1
1
1
2
0
1
2
1
2
0
1
1
2
1
1
1
0
0
2
1
1
3
1
1
2
0
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
2
1
1
1
0
1
1
2
1
1
1
2
1
1
1
0
1
1
1
2
2
1
1
1
1
1
0
0
1
2
2
2
0
1
1
1
1
2
1
0
1
1
1
1
1
2
1
2
1
1
1
2
1
0
1
1
1
1
0
1
2
1
2
1
1
2
1
0
1
1
2
1
1
1
1
1
1
1
0
1
1
1
1
2
1
1
2
1
2
0
0
0
1
2
0
1
1
0
1
1
1
2
2
1
2
1
1
1
1
1
2
1
1
2
2
2
1
0
0
1
0
2
1
2
1
1
0
2
1
1
0
0
0
1
2
2
1
2
0
1
2
1
2
1
0
1
1
1
2
0
2
0
1
2
1
0
1
2
1
1
1
1
2
2
1
1
2
1
0
2
1
0
1
1
2
2
2
1
1
1
2
1
1
1
1
1
2
1
2
1
0
1
0
1
1
0
0
0
1
2
0
1
2
2
2
0
2
1
2
1
1
1
2
0
1
1
2
0
1
1
1
1
1
1
1
0
2
1
1
1
1
1
1
2
1
1
2
0
1
2
1
0
1
1
2
1
2
1
1
1
1
1
1
0
2
0
2
1
2
1
1
1
1
1
2
1
1
1
1
1
0
2
1
2
1
1
2
1
1
2
2
1
1
0
0
1
2
2
0
1
0
0
1
1
1
1
0
1
1
2
1
1
2
2
1
1
2
1
1
1
1
2
2
1
1
1
0
1
2
1
1
0
1
1
2
1
0
2
1
1
0
1
2
1
1
1
1
2
0
2
2
1
1
1
1
1
0
1
1
1
1
2
1
1
0
1
2
1
0
1
1
2
1
0
2
2
0
1
2
1
1
1
3
1
1
1
0
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
2
1
2
3
1
1
1
2
0
1
1
1
1
1
2
1
1
1
1
0
0
1
1
2
0
1
2
1
1
1
2
0
0
2
1
1
1
2
1
1
1
2
0
1
1
0
1
1
1
1
1
2
0
1
2
2
1
1
2
0
2
1
1
1
1
1
1
1
0
2
1
0
0
1
1
1
1
1
1
3
1
0
2
1
1
1
2
1
1
2
1
1
1
0
1
1
1
0
0
1
2
1
2
1
2
2
1
0
2
1
2
1
2
1
2
0
1
1
1
1
0
1
1
2
2
2
1
2
1
1
1
1
1
0
1
1
1
2
1
2
2
1
3
1
0
2
1
1
1
0
0
1
2
1
1
1
2
2
1
1
1
1
1
1
1
0
1
0
0
0
1
0
1
1
2
1
0
1
2
1
2
1
2
1
1
2
1
0
2
1
2
1
1
2
1
1
1
1
0
2
2
1
1
1
2
0
1
1
1
1
1
2
2
0
1
1
1
0
1
0
2
1
1
1
1
1
1
1
1
0
1
0
1
2
1
1
1
0
1
1
2
1
1
1
1
1
1
0
1
2
2
2
1
2
1
1
1
1
2
1
1
1
0
2
1
1
1
2
2
1
2
1
1
1
1
0
2
1
2
0
1
1
2
1
2
1
2
1
1
2
1
1
1
1
2
1
1
0
0
1
2
1
1
1
0
0
0
1
0
1
1
1
2
2
1
0
0
1
2
1
0
2
1
1
2
0
1
1
2
2
1
1
2
0
1
1
1
2
1
2
2
2
2
2
1
2
1
1
1
1
2
1
1
1
1
2
2
2
1
1
1
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
2
0
1
2
0
0
1
1
1
0
1
0
1
2
1
1
1
1
0
1
1
1
0
1
1
1
1
1
1
2
1
1
1
2
0
1
1
1
1
1
1
1
1
1
1
0
0
2
1
1
1
1
2
1
1
1
2
1
1
3
0
0
1
1
1
2
1
1
0
1
0
1
2
0
2
1
0
1
1
1
1
2
0
1
1
0
0
1
1
1
1
0
1
1
1
0
1
1
1
1
0
2
1
0
1
1
1
1
0
0
1
1
2
1
1
1
1
1
2
1
2
1
0
1
2
1
2
2
0
1
1
1
1
2
2
2
2
2
1
2
1
1
0
1
0
2
1
2
1
2
1
2
1
1
2
0
2
0
2
1
1
2
0
1
0
1
0
1
1
1
1
1
0
1
1
2
1
1
0
1
0
1
1
1
0
0
2
1
1
1
2
1
1
2
1
1
1
1
1
1
0
2
3
2
2
0
1
1
0
2
1
1
1
0
0
2
1
2
0
1
1
1
1
1
1
2
1
1
2
3
0
1
1
1
1
1
1
1
0
1
2
1
1
0
1
2
1
2
1
2
1
1
1
1
2
1
2
2
0
1
2
2
1
2
2
1
1
1
2
2
2
1
1
1
1
0
1
1
1
3
2
1
1
1
1
1
0
1
1
1
1
1
1
2
1
0
0
1
0
1
1
1
3
1
0
1
0
1
2
1
1
2
1
2
2
2
1
2
1
1
2
1
1
2
2
0
0
2
1
2
1
1
0
2
1
3
1
0
2
1
1
2
2
1
2
0
2
2
1
1
0
2
1
1
0
1
2
2
1
2
2
0
1
1
1
0
2
2
2
1
1
0
2
0
0
1
0
1
1
1
0
1
1
0
1
1
1
1
2
1
2
1
1
2
1
1
1
1
2
1
1
1
2
2
1
1
1
1
2
2
1
1
1
1
1
0
1
0
2
1
3
0
2
1
1
1
0
1
1
1
1
2
1
1
1
0
1
0
0
2
1
1
2
2
2
2
1
2
2
2
2
1
2
1
1
0
1
2
1
2
1
2
2
1
2
1
2
1
0
2
2
1
1
1
2
0
2
0
1
1
2
2
1
2
2
1
2
2
1
2
1
1
2
1
1
2
2
1
1
1
1
2
1
1
1
0
1
1
1
1
0
1
0
0
2
1
2
1
1
0
2
2
1
0
1
0
1
2
2
0
0
1
0
0
1
2
0
1
1
0
0
1
2
1
1
2
1
1
1
1
1
2
1
0
1
2
2
1
2
1
1
2
1
2
1
2
1
1
0
1
1
1
1
1
0
0
1
0
3
2
1
1
1
0
0
1
1
2
2
2
2
1
1
2
0
1
1
0
1
2
2
2
2
2
2
1
1
1
2
2
1
0
1
1
1
0
0
3
0
1
1
1
1
2
2
1
2
1
2
0
1
1
1
0
2
1
0
2
0
1
2
2
1
1
1
0
1
1
0
1
1
1
2
0
2
2
2
1
2
1
1
0
1
1
1
1
2
1
1
1
2
1
1
1
0
1
1
2
2
2
2
1
2
2
1
0
1
1
2
1
1
1
1
1
1
0
1
1
1
1
1
2
1
2
2
1
0
1
2
1
1
0
1
1
1
1
2
1
1
1
0
2
1
2
1
1
2
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
1
2
2
0
1
1
2
2
1
1
1
0
2
1
1
2
1
1
1
1
2
2
1
1
2
1
1
0
1
1
0
1
1
0
1
2
1
1
1
0
1
1
0
0
2
1
1
1
1
2
1
2
1
1
1
0
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
0
1
0
1
1
2
2
2
1
1
1
0
1
2
2
2
1
1
0
1
1
0
0
2
1
1
0
2
0
1
1
0
1
1
2
4
1
1
0
2
1
2
1
1
0
3
0
1
2
2
1
1
1
1
1
0
1
1
2
2
1
1
1
1
1
2
2
1
0
0
1
0
1
1
1
2
1
0
1
0
1
2
2
1
1
0
1
1
1
0
0
1
2
1
1
0
2
1
2
0
2
1
3
3
1
2
0
2
2
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
0
1
1
1
0
1
0
0
2
2
0
2
2
0
0
2
1
0
1
2
1
2
1
0
1
0
1
1
1
2
0
1
1
1
1
0
2
0
1
2
0
1
2
2
1
1
2
2
0
2
1
1
0
1
1
1
1
1
1
1
0
2
1
2
1
2
0
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
0
1
2
1
1
0
2
2
1
2
1
1
2
1
2
1
1
1
1
0
1
1
2
0
0
1
1
1
1
1
2
1
1
1
0
0
0
0
1
1
2
1
0
1
2
0
0
1
1
2
1
1
1
0
1
1
4
2
2
2
0
0
1
1
1
2
1
1
1
0
3
2
1
2
1
1
1
1
1
2
1
2
1
1
0
1
1
1
2
0
0
1
1
0
1
2
1
2
1
1
1
1
1
1
0
1
2
2
1
1
0
1
1
1
1
2
1
1
0
1
2
1
2
1
1
1
0
1
1
1
1
1
0
0
1
1
1
1
1
2
0
2
2
1
0
1
1
2
1
1
2
1
0
0
1
1
1
1
1
1
0
1
0
1
1
0
2
2
1
2
2
0
1
2
0
1
1
2
1
1
2
1
1
2
2
0
1
1
1
1
1
1
1
2
2
1
2
3
1
1
0
2
1
1
1
1
0
0
1
1
1
2
1
2
1
1
2
2
1
1
2
2
1
0
0
1
2
1
0
1
1
1
1
2
1
1
1
1
0
2
1
2
1
1
2
1
1
1
1
1
0
1
1
1
2
0
0
2
2
1
1
1
2
0
1
1
2
1
0
1
0
2
0
1
1
2
2
1
2
1
1
1
0
1
1
1
1
1
1
0
1
0
0
2
1
2
1
1
1
1
1
1
1
0
1
1
1
0
1
2
1
1
0
1
1
0
1
0
0
2
1
1
1
1
1
2
1
1
1
0
0
1
1
1
1
1
1
0
1
0
2
1
2
1
1
1
0
1
2
1
0
2
2
4
0
1
2
0
2
0
1
1
2
1
2
1
1
1
2
1
1
1
0
1
1
1
2
2
1
0
1
2
1
2
2
0
2
1
0
1
1
2
1
1
1
1
1
2
0
1
2
1
2
1
1
1
1
2
3
2
1
2
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
1
0
1
2
1
1
1
1
0
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
0
1
0
0
1
2
0
2
0
1
1
2
2
0
2
0
2
1
1
1
1
1
0
2
0
1
1
1
1
1
1
1
1
1
2
1
1
1
0
2
1
1
1
2
1
2
1
2
1
2
1
2
1
2
2
1
1
2
1
0
2
1
1
0
2
1
0
2
2
1
2
1
1
0
1
2
1
1
2
2
2
2
0
1
1
0
1
0
2
1
1
1
0
1
1
1
1
0
1
1
1
0
1
0
1
1
1
1
2
1
1
2
0
2
0
1
2
0
0
1
1
0
0
2
1
2
1
0
2
1
1
2
2
1
1
1
1
2
2
1
2
1
2
1
1
2
1
1
2
2
1
1
2
0
1
1
0
1
1
1
1
1
2
0
0
1
2
1
0
2
1
1
1
2
0
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
2
1
1
2
2
1
1
1
1
1
0
0
1
2
1
0
2
1
1
1
2
1
0
2
0
2
1
2
1
1
2
1
1
0
2
1
0
1
0
0
2
0
2
1
2
1
1
1
2
1
1
0
2
1
1
2
1
1
1
1
0
1
2
1
2
1
0
1
1
1
1
1
2
2
0
1
1
1
2
0
0
1
1
1
1
2
1
2
1
1
0
1
1
1
1
1
0
2
2
2
0
1
1
1
1
1
1
2
1
1
1
0
1
2
2
2
0
0
0
1
2
1
1
1
2
2
2
0
1
2
1
1
0
0
1
1
0
1
1
2
0
1
1
1
1
2
1
0
1
1
2
0
1
1
1
0
0
2
0
1
1
1
0
1
2
1
1
2
0
2
1
1
0
2
2
1
2
0
2
0
1
1
1
1
1
1
1
2
2
0
1
1
1
2
1
0
1
0
1
1
1
1
1
1
1
2
1
1
1
0
1
0
0
0
1
1
2
2
1
1
1
1
1
2
2
2
1
2
2
1
2
0
1
1
0
1
2
1
1
2
1
1
1
1
1
2
0
1
1
1
1
1
1
2
1
1
1
1
2
1
2
0
2
1
2
1
1
1
2
1
1
1
1
0
1
1
1
0
1
2
2
0
1
2
1
0
1
2
1
1
1
1
2
2
1
2
2
1
2
2
2
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
0
1
2
3
2
1
0
1
1
2
1
2
0
1
1
0
1
2
0
2
1
2
1
0
0
1
1
1
2
2
0
1
1
1
1
1
1
1
0
1
2
1
0
2
1
1
2
1
0
1
0
2
2
0
1
2
2
1
0
1
1
2
1
1
1
0
2
0
2
0
1
2
1
2
0
1
1
1
1
1
1
0
1
4
2
1
1
1
1
0
1
1
2
1
1
1
1
2
1
2
1
1
1
2
0
1
2
1
2
1
1
1
1
1
1
1
0
0
1
2
2
0
2
1
2
1
1
0
1
2
2
2
1
1
1
1
1
1
0
1
1
1
1
2
1
2
2
2
1
2
1
1
1
0
0
1
0
2
1
0
2
0
2
1
1
1
1
2
2
0
1
0
1
0
1
0
1
1
1
1
1
2
1
1
1
1
5
1
2
2
1
0
1
1
1
1
1
1
1
2
2
1
0
0
1
2
1
1
1
1
1
1
2
1
1
2
1
0
1
1
1
1
1
1
1
0
2
2
1
1
1
1
0
1
2
0
1
2
0
2
2
1
2
2
1
2
2
1
1
2
1
1
1
0
1
2
1
1
0
1
1
2
1
1
1
1
2
1
0
2
1
2
2
1
1
1
2
1
1
1
0
1
2
1
1
0
1
1
0
1
2
1
2
1
1
1
1
1
1
0
1
1
2
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
0
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
0
1
1
0
1
2
2
0
1
1
1
2
1
0
2
1
0
2
1
0
1
0
1
1
1
2
1
2
0
2
1
2
1
1
1
0
2
0
1
1
0
1
1
0
1
1
2
2
2
1
1
1
1
1
0
1
2
2
2
2
1
1
1
0
1
1
2
2
1
2
2
0
1
3
2
0
1
2
1
0
1
0
0
1
1
2
0
1
1
2
1
1
1
1
2
2
1
1
2
1
1
0
2
1
1
2
1
2
0
1
1
1
0
1
0
1
1
1
2
1
1
1
1
2
0
1
1
1
1
1
1
2
1
1
0
2
1
1
0
1
1
1
1
2
1
1
1
1
1
1
1
0
1
1
1
0
1
2
2
0
1
1
1
2
0
2
1
2
2
1
0
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
0
1
1
1
1
1
1
2
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
2
1
2
0
0
0
2
1
1
1
0
0
0
1
1
1
1
2
2
2
0
1
2
2
0
1
1
0
0
1
2
1
1
1
2
1
2
1
2
1
2
1
1
1
1
0
1
0
0
1
0
2
0
2
1
1
1
1
1
3
3
1
2
1
1
1
0
1
1
2
0
1
2
1
2
2
1
2
1
1
1
1
0
1
1
1
0
0
2
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
0
2
0
1
1
1
0
0
1
1
1
0
2
0
1
1
1
1
1
1
1
2
1
1
1
0
1
1
0
1
1
2
1
2
1
1
1
0
1
1
1
2
1
2
3
0
1
1
1
1
2
2
1
2
1
2
2
1
2
1
1
2
1
1
1
1
1
2
1
1
1
2
0
1
1
0
1
0
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
0
0
1
1
0
1
1
0
1
1
1
0
1
2
0
2
1
3
0
1
1
0
2
1
1
0
1
0
2
0
1
1
1
1
1
0
1
1
1
1
0
2
1
0
1
1
1
1
2
2
0
1
0
1
1
0
1
1
1
0
2
2
1
2
1
0
1
1
2
1
2
1
1
1
1
1
2
1
1
1
4
1
2
2
0
0
0
1
4
1
0
1
0
1
2
1
0
1
1
2
2
1
1
1
0
1
2
1
2
2
1
0
1
0
2
0
1
1
2
1
1
0
2
1
0
2
1
2
1
0
1
0
2
0
1
2
1
2
0
2
1
1
1
2
1
1
1
0
1
1
0
1
2
2
0
1
2
2
1
1
1
1
2
2
0
1
1
1
1
1
2
1
1
0
2
1
1
2
1
1
0
1
1
1
2
2
1
2
1
1
1
0
1
2
2
2
2
2
0
1
2
1
1
2
1
0
2
1
1
0
0
2
0
1
2
1
1
1
1
1
2
1
1
2
2
2
2
1
1
0
1
1
1
1
1
1
1
1
1
0
1
1
1
1
2
1
2
1
2
2
2
2
1
1
1
2
1
1
2
1
0
1
1
1
1
1
0
2
1
0
1
1
1
0
1
2
1
1
1
1
1
1
1
1
0
1
0
1
1
1
1
1
1
1
2
1
1
1
1
2
1
2
2
2
1
2
1
0
1
1
1
1
0
1
1
2
2
0
1
1
2
0
1
1
1
2
2
3
1
1
1
1
1
2
0
1
1
1
1
1
0
1
1
0
2
0
1
1
2
1
1
0
0
1
2
1
2
2
2
2
2
1
1
2
0
1
1
1
1
1
1
0
1
1
2
1
1
1
2
1
2
0
1
1
1
1
1
1
1
2
1
0
1
0
1
1
2
2
0
2
1
1
2
1
2
1
2
1
0
0
0
2
0
1
2
1
1
1
1
3
1
0
0
1
1
1
0
2
1
2
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
1
0
1
1
1
1
1
1
0
1
1
2
2
2
1
2
1
1
1
0
0
1
0
1
1
0
2
0
1
1
2
2
1
0
1
2
0
0
1
2
1
1
2
0
0
1
1
1
1
1
0
2
1
0
1
1
1
2
1
1
0
1
2
1
1
3
1
1
1
1
1
0
1
0
0
1
2
0
2
1
1
0
1
1
2
1
1
1
1
1
1
0
1
1
0
1
2
1
1
1
1
2
1
1
0
1
0
0
1
3
1
0
1
1
1
1
0
1
1
0
1
1
2
1
1
2
2
2
1
2
1
1
1
2
2
2
1
1
1
1
0
2
1
2
2
0
1
1
2
2
1
1
1
1
2
1
1
1
2
0
1
1
1
1
1
1
1
0
1
0
0
1
1
1
2
2
1
2
1
2
1
2
1
1
0
1
1
0
1
1
0
1
0
0
1
1
1
1
0
1
0
1
1
1
1
0
1
0
2
0
2
2
1
1
1
0
2
1
2
1
1
0
2
3
1
1
0
1
0
1
1
1
2
1
2
2
1
1
1
0
0
2
3
1
1
0
1
1
1
0
2
1
1
2
2
2
1
1
2
1
1
1
1
1
1
1
1
1
0
1
1
0
1
1
2
2
1
1
2
1
2
2
1
1
1
1
2
0
2
0
1
1
1
2
1
2
1
1
1
2
1
1
2
1
1
2
0
2
0
1
2
1
1
1
2
0
1
0
2
0
1
1
2
1
1
2
1
1
1
2
1
0
0
0
1
1
1
0
1
1
1
0
1
2
1
2
1
2
1
2
1
1
1
1
2
2
1
1
2
0
0
1
1
0
1
1
1
1
0
0
2
0
1
1
1
0
0
1
0
1
2
1
1
2
1
1
1
2
2
1
1
0
1
2
1
2
1
3
0
2
2
1
1
1
1
3
1
1
1
1
0
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
0
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
0
2
2
1
1
1
1
2
1
1
0
0
1
1
0
2
1
1
2
0
2
2
0
0
1
0
1
2
2
1
2
2
1
1
1
2
1
1
2
1
0
1
0
1
1
2
1
1
2
0
2
2
2
1
1
2
1
1
1
1
0
2
1
1
2
1
0
2
1
1
1
0
2
1
1
0
1
0
1
1
0
1
1
1
1
1
2
1
2
0
1
0
3
2
2
2
1
0
1
2
1
0
2
0
1
0
1
2
1
0
2
1
1
1
1
1
2
0
1
1
0
2
2
1
2
2
1
0
1
1
2
2
1
2
2
1
1
1
1
1
1
2
2
2
1
2
0
2
1
1
1
2
1
1
1
1
1
1
1
1
1
0
1
2
2
1
0
1
1
2
1
1
1
1
1
2
1
1
1
0
0
2
1
0
1
0
1
2
1
1
1
2
2
1
0
2
1
2
0
2
1
2
1
0
1
1
2
1
0
1
1
2
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
2
1
1
1
2
2
1
1
1
1
1
1
3
2
2
1
1
1
1
0
1
0
1
1
1
1
0
2
1
1
1
2
0
1
0
2
1
1
1
0
0
1
1
1
1
1
0
1
1
1
1
1
2
1
0
1
0
1
1
1
1
2
1
0
1
1
0
0
1
0
1
0
0
1
2
0
2
1
1
1
0
2
0
1
0
2
0
2
1
1
2
1
0
1
3
1
0
0
2
1
1
3
0
2
1
2
2
2
1
1
1
0
0
0
1
1
0
1
0
1
1
1
1
1
1
1
1
1
1
0
1
2
0
0
1
2
0
0
1
1
0
1
1
4
1
2
1
2
1
0
2
3
0
1
0
0
1
2
1
2
1
1
0
1
1
1
2
2
1
0
0
3
1
0
0
1
1
1
1
2
1
1
1
1
0
0
2
1
1
1
0
1
1
1
2
1
1
2
1
1
1
2
1
1
2
1
1
2
1
1
2
1
2
1
0
2
2
1
1
1
0
2
0
1
0
1
1
0
1
1
1
2
0
0
2
1
1
1
2
1
0
1
1
1
1
1
0
0
0
1
1
1
0
2
2
1
2
0
2
1
2
1
1
1
1
2
2
1
1
0
1
0
2
1
2
1
2
0
1
2
1
1
1
1
1
2
1
0
1
1
2
1
2
1
1
2
1
0
2
1
0
1
1
2
1
0
2
1
1
0
1
1
1
2
2
0
1
0
0
1
1
1
1
1
1
1
1
1
1
1
1
2
1
0
2
1
2
0
1
1
0
1
2
1
1
1
1
1
1
2
2
1
0
2
1
1
2
0
1
1
2
0
2
0
1
1
1
1
1
1
0
1
1
1
0
1
1
1
1
1
0
1
1
1
2
1
2
1
1
1
1
2
1
1
2
1
2
2
0
0
0
2
1
1
1
0
2
0
1
0
1
2
1
0
2
2
2
1
1
1
2
1
1
1
2
1
1
2
1
2
2
1
1
1
1
0
0
2
2
0
2
1
1
1
0
2
2
1
1
1
2
1
1
1
2
1
1
1
2
1
1
0
1
2
1
2
2
1
2
1
2
1
1
2
0
1
1
0
1
1
0
1
1
0
1
1
1
0
1
1
1
1
2
2
2
1
2
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
2
2
3
1
1
2
1
1
1
1
1
0
2
1
1
2
2
1
2
2
1
2
1
1
1
0
1
1
2
0
1
2
1
3
0
0
1
2
2
2
1
0
2
1
1
1
1
1
0
1
1
1
1
2
1
1
1
1
0
1
2
0
1
2
0
1
1
1
2
1
0
2
1
1
1
1
2
0
1
1
1
1
1
2
1
2
1
0
0
1
1
1
1
1
2
1
1
1
1
1
2
2
0
1
1
1
1
1
2
1
1
1
1
1
2
1
2
0
0
2
1
1
1
1
2
1
2
0
0
1
1
1
1
1
2
2
1
0
2
0
2
2
1
1
1
1
2
2
1
1
0
2
0
1
2
0
2
2
1
1
1
1
0
1
0
2
2
0
1
1
1
2
1
1
1
1
1
1
1
2
0
0
2
0
2
1
1
1
2
2
1
0
0
1
0
1
1
1
2
0
1
2
1
1
0
1
2
2
1
1
2
1
0
2
0
2
1
0
0
2
1
1
1
2
0
1
1
1
1
1
1
1
1
1
1
2
1
1
1
0
2
1
0
2
1
1
1
1
2
0
2
1
0
1
0
1
0
2
1
1
2
2
1
1
1
0
2
1
1
1
1
1
2
1
0
2
1
2
1
0
1
1
1
2
1
1
1
1
1
2
1
1
0
0
0
1
2
2
1
1
1
0
1
1
0
1
0
1
1
2
1
0
2
1
0
1
1
2
0
0
0
0
1
0
0
1
2
1
1
0
2
1
2
1
1
1
1
1
2
1
1
0
1
1
2
0
2
1
2
1
1
1
2
2
0
0
1
1
1
1
1
2
1
0
1
0
2
1
2
1
2
0
2
1
0
1
1
1
1
1
1
0
1
1
1
0
0
1
1
1
0
1
0
0
1
2
1
0
1
0
1
1
1
2
3
1
1
1
1
2
0
2
1
1
1
1
1
0
1
1
1
1
1
1
0
1
0
0
2
1
1
1
1
1
1
1
1
0
2
1
1
2
1
1
0
2
1
1
2
1
1
4
1
1
0
0
1
1
1
1
1
0
2
1
2
2
2
1
1
1
4
1
1
2
0
2
1
1
1
1
0
2
1
1
1
1
2
1
1
2
0
2
2
1
1
1
1
0
1
1
0
0
1
1
2
0
1
0
1
2
2
1
0
1
1
0
2
1
1
1
2
1
2
2
1
1
2
1
1
1
1
1
1
0
2
0
1
2
2
2
0
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
0
0
1
1
0
1
1
1
1
2
2
2
2
1
1
1
1
0
1
1
2
1
0
1
1
0
2
1
2
2
2
1
2
1
1
2
2
1
1
1
1
0
1
0
1
1
1
1
1
1
1
1
2
1
0
1
2
0
2
2
0
2
1
2
1
1
1
0
0
1
1
1
1
0
1
1
0
2
1
2
0
2
2
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
0
0
2
1
1
1
5
1
2
1
2
1
1
2
0
1
2
2
1
0
1
2
2
1
0
1
1
1
1
0
2
0
0
1
0
1
0
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
2
1
1
0
1
2
2
0
1
0
2
0
2
0
1
2
1
2
2
1
2
1
1
2
2
1
0
0
1
0
1
1
2
1
2
0
0
2
1
0
0
1
0
0
0
2
1
2
2
0
2
0
1
1
1
1
1
0
1
1
2
2
0
1
0
2
2
1
2
1
1
1
2
1
1
0
1
1
2
1
2
1
1
0
1
1
2
1
2
1
1
2
2
2
0
1
2
1
1
2
1
1
1
1
0
2
0
1
1
1
1
0
2
1
0
2
0
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
0
1
1
2
0
0
1
1
1
1
1
1
1
1
1
1
0
0
1
1
1
1
0
1
2
1
2
2
1
1
0
2
2
1
1
2
1
0
1
1
1
0
0
1
1
1
1
0
0
0
1
1
1
1
1
2
1
1
0
1
1
2
1
1
1
1
1
0
1
1
2
2
1
0
0
1
3
1
0
0
1
2
2
0
1
1
1
1
1
2
1
2
1
2
1
0
2
1
1
1
2
1
1
2
0
0
1
1
1
1
1
0
1
1
2
0
0
1
1
0
0
1
1
1
1
2
1
3
2
2
1
2
1
0
2
1
1
0
1
1
0
2
2
1
1
1
2
1
2
1
1
1
1
2
2
0
1
0
0
0
0
1
0
1
0
0
2
2
1
1
1
2
3
1
1
2
1
1
1
1
0
0
1
1
1
1
0
1
0
1
1
1
2
2
2
2
1
1
3
1
1
1
0
1
1
1
1
0
1
1
0
1
1
1
0
2
1
2
2
2
1
1
0
1
1
1
0
0
2
1
0
1
1
1
1
1
1
3
1
0
1
1
1
1
0
1
2
2
0
1
2
1
1
0
1
1
1
1
1
1
1
1
2
1
1
1
1
1
3
1
0
1
3
1
2
1
1
2
1
1
1
1
1
1
2
2
0
2
2
2
2
1
2
1
1
1
1
1
2
2
2
1
1
1
2
0
1
1
1
1
1
2
1
0
1
0
1
0
1
0
2
1
1
1
1
1
2
2
1
1
2
1
1
2
2
1
1
1
0
1
1
1
2
1
0
1
2
1
1
0
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
0
0
2
1
1
1
1
1
1
1
2
2
1
0
1
1
2
0
1
2
1
1
1
1
0
2
1
1
1
1
1
1
1
2
1
1
0
2
0
2
1
1
1
1
1
1
2
1
1
1
1
1
0
0
1
0
1
0
0
1
0
1
1
1
0
1
0
2
0
2
1
1
2
1
2
1
1
2
1
1
1
0
1
1
2
1
1
1
1
2
2
2
1
3
2
2
1
2
2
1
2
1
2
2
2
1
1
1
1
2
1
1
2
2
2
1
0
1
2
2
0
0
2
1
1
2
1
1
1
3
1
1
1
0
1
1
0
0
0
2
2
1
1
2
1
2
2
0
1
1
1
1
2
1
1
1
0
1
1
1
2
0
1
1
1
1
2
1
2
2
1
1
1
0
0
1
1
1
2
1
2
2
2
0
0
1
1
0
1
1
1
1
1
1
2
2
1
1
1
0
1
1
1
0
2
4
0
1
2
3
2
1
0
1
0
0
2
1
1
0
1
1
2
1
1
1
1
1
1
1
1
1
2
1
2
1
2
0
1
2
1
2
1
2
1
2
1
0
1
0
1
1
2
1
2
0
1
0
0
2
1
2
1
1
2
1
1
0
2
2
1
1
2
1
1
1
1
2
1
2
1
2
1
1
0
2
2
1
1
0
1
1
2
2
2
0
1
2
0
1
1
0
1
0
1
1
2
1
2
1
1
1
0
1
1
1
1
1
1
1
1
1
1
0
1
0
1
1
1
0
1
1
0
1
1
2
1
1
1
2
1
0
2
0
1
1
2
1
2
2
1
1
1
1
2
1
1
1
1
1
1
1
2
0
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
2
1
0
1
1
2
2
1
0
1
1
1
1
0
1
1
0
0
0
0
1
1
0
2
1
1
2
1
1
2
0
1
1
1
2
1
0
1
1
2
1
2
1
1
1
2
1
2
1
2
1
1
2
2
1
3
1
0
1
0
1
2
1
1
1
1
1
2
1
2
0
2
0
2
0
2
1
2
1
0
1
1
0
1
1
1
1
1
1
0
1
1
2
1
2
1
1
1
1
2
2
2
1
1
1
1
2
0
1
0
1
1
1
2
2
1
1
0
1
0
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
0
0
1
0
0
1
2
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
0
0
1
1
0
2
1
1
2
2
1
1
1
1
2
1
0
2
1
0
1
1
1
1
1
2
1
2
1
2
1
2
2
1
2
2
2
1
0
1
0
0
1
1
2
2
1
1
0
1
1
1
2
1
1
1
0
1
1
2
1
1
0
0
1
1
1
1
4
1
1
2
1
1
1
2
2
1
1
2
1
0
1
0
0
1
1
0
1
1
0
1
1
1
2
1
1
1
1
1
1
1
0
1
2
1
1
1
1
1
1
0
0
1
2
1
1
1
0
1
1
1
1
1
1
1
1
2
0
1
3
2
1
2
1
1
1
1
1
1
1
2
1
1
0
2
1
1
1
0
0
1
1
1
1
1
1
1
1
0
1
1
1
1
0
1
1
0
0
1
1
1
1
0
0
3
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
0
1
0
2
1
0
1
2
2
1
1
1
2
1
1
2
1
1
2
1
1
1
2
1
0
4
1
1
1
1
1
1
2
0
1
1
1
1
1
1
0
1
1
1
0
1
2
2
1
2
1
1
2
2
2
2
0
2
1
1
2
1
1
1
0
1
1
0
1
1
0
1
2
2
1
1
1
1
1
1
1
1
1
0
1
1
2
1
1
0
2
2
2
1
1
2
2
1
1
0
2
1
1
0
2
0
1
2
2
3
1
3
0
2
1
1
2
1
1
0
1
1
1
2
1
1
1
1
1
1
1
1
0
1
1
1
2
1
3
2
1
0
2
2
1
2
1
2
1
1
0
1
0
1
2
2
1
2
1
1
1
1
1
1
2
1
1
1
1
0
1
0
1
1
2
0
1
2
1
0
1
2
1
1
2
2
1
1
1
0
2
0
1
1
1
1
1
1
0
1
1
1
1
2
1
1
1
2
0
1
2
2
2
2
2
2
2
1
1
1
1
2
0
1
1
1
1
1
2
1
1
1
1
2
2
2
2
2
1
3
1
1
2
1
1
1
2
0
1
2
2
2
1
1
1
1
2
0
1
1
1
1
1
1
1
2
2
2
1
2
1
1
1
1
2
2
2
0
0
1
1
0
1
0
1
0
1
2
1
2
2
2
1
0
2
1
1
1
1
1
1
1
0
0
1
1
1
1
1
1
2
0
2
1
1
1
2
2
0
2
1
0
1
1
2
1
1
1
3
1
1
0
1
1
3
2
1
0
1
0
0
1
1
1
2
0
2
1
1
2
1
1
1
1
1
1
1
1
0
1
0
0
2
1
1
1
1
1
0
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
0
1
1
1
1
2
1
1
0
2
1
1
1
1
1
1
2
2
2
1
1
2
1
1
1
2
2
0
0
1
2
2
1
1
1
1
1
2
1
2
1
1
0
0
2
0
1
2
1
1
1
1
0
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
0
1
0
1
1
0
1
1
0
1
2
1
0
2
0
0
2
2
1
1
1
1
1
0
1
2
1
2
0
2
0
0
1
1
2
1
1
1
1
1
1
1
0
1
2
1
2
0
2
2
1
0
1
1
2
1
1
1
1
2
0
1
1
1
0
1
2
1
1
1
1
1
0
1
1
1
1
1
2
1
1
1
1
1
0
1
2
2
1
2
1
1
0
0
1
1
0
2
1
1
1
2
2
1
2
2
0
1
1
1
2
1
0
1
1
1
2
1
1
2
1
0
2
1
1
1
1
2
0
1
1
1
2
2
1
1
1
1
1
0
0
1
0
2
1
2
1
1
1
2
1
0
1
0
1
1
1
2
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
2
1
2
1
2
2
1
2
1
1
3
1
2
1
0
0
2
1
1
1
1
0
2
1
2
1
1
1
1
1
1
1
1
2
2
0
0
1
2
1
1
1
2
1
1
2
1
1
1
1
1
0
1
1
1
1
1
2
1
1
1
3
1
1
2
1
2
1
1
0
1
1
1
1
1
2
1
1
1
0
1
2
1
2
1
2
1
2
0
1
0
2
2
2
1
2
1
1
2
1
0
1
1
2
1
0
0
1
2
1
1
1
1
3
2
1
2
2
1
1
1
1
0
1
2
1
2
0
1
1
1
2
1
2
2
1
1
0
0
1
1
0
2
1
3
1
1
1
2
1
1
1
1
3
0
1
1
1
0
1
1
2
2
2
2
2
1
2
1
1
1
7
2
2
1
0
1
1
1
2
2
1
0
2
1
2
1
0
1
1
0
1
1
2
2
1
0
1
0
0
2
2
2
1
1
2
1
1
2
2
0
1
0
1
1
0
2
1
2
1
0
2
2
1
1
1
0
2
1
1
1
1
0
1
1
2
0
0
2
1
1
2
1
2
2
1
1
1
2
1
2
1
1
1
1
1
2
1
1
0
1
1
2
1
1
2
0
1
1
1
1
1
1
1
2
0
2
2
1
1
1
0
2
0
1
1
1
1
1
1
2
2
1
1
1
1
2
1
1
0
1
2
2
1
0
2
1
1
1
2
2
0
0
0
2
2
2
1
0
2
1
1
2
1
1
1
0
1
1
2
1
0
1
2
2
0
0
2
3
1
1
1
1
0
1
1
0
1
1
2
1
2
1
1
1
1
1
1
1
1
1
0
0
0
0
0
1
0
1
0
0
2
2
2
2
1
1
1
2
1
1
1
0
1
1
1
1
1
1
2
1
0
2
1
1
0
0
0
0
1
2
1
1
1
1
1
1
1
0
1
1
1
2
0
2
2
1
0
1
1
2
1
2
1
1
1
1
1
1
2
0
1
1
1
1
2
0
1
1
1
1
1
1
0
1
2
0
1
1
1
1
2
1
1
2
2
0
1
1
0
1
1
1
2
0
1
1
0
1
1
2
1
2
1
1
1
1
0
1
2
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
2
1
1
1
0
1
2
1
0
1
1
1
1
1
1
1
1
1
2
1
0
1
1
1
0
2
1
0
1
1
0
2
2
1
0
2
1
1
0
0
1
1
3
1
1
2
2
1
1
1
0
1
1
1
2
0
2
1
1
1
1
1
1
1
1
1
1
1
3
1
1
1
2
1
1
1
1
2
1
0
1
2
2
2
2
1
1
2
1
1
2
1
0
1
1
1
1
1
1
2
3
2
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
0
2
1
1
2
2
1
1
1
0
1
2
2
2
1
1
2
1
2
1
2
1
1
1
1
1
1
2
1
1
1
2
3
2
2
1
1
1
2
1
1
1
2
0
1
0
1
1
1
2
2
1
1
1
1
1
1
1
1
0
1
0
0
2
1
1
1
5
1
1
1
1
1
1
1
1
2
0
1
1
1
1
1
1
1
2
2
2
2
2
2
0
1
1
1
0
1
1
2
1
2
1
1
2
2
0
1
1
1
1
0
1
2
2
1
2
0
1
1
0
1
1
1
1
2
2
1
2
1
1
0
1
1
1
0
1
2
1
1
2
2
1
1
0
1
1
1
1
1
2
1
1
2
1
1
0
2
1
1
1
1
1
1
1
1
3
1
1
1
3
2
0
2
1
2
1
1
1
1
1
2
0
1
2
2
1
0
2
2
0
2
2
1
1
0
1
0
1
2
0
1
1
1
0
0
1
2
1
2
0
1
1
0
1
1
1
1
1
2
2
2
0
2
1
1
0
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
0
1
1
0
1
0
2
0
2
1
0
1
2
2
0
1
1
1
1
0
1
1
2
1
1
1
1
1
1
0
2
1
2
1
1
2
1
0
2
1
2
2
2
1
1
1
1
0
1
0
2
3
1
1
0
1
2
2
1
2
1
0
1
1
1
0
1
0
2
2
1
2
2
1
0
1
1
0
1
1
1
1
2
0
4
0
1
1
1
1
1
3
2
2
1
0
1
1
1
1
0
1
2
1
1
2
1
1
1
1
0
1
1
2
0
2
0
1
1
2
1
1
1
2
2
0
1
1
1
2
1
1
1
1
2
2
1
1
1
1
2
1
0
1
1
2
1
1
0
1
0
0
1
1
1
1
0
1
1
0
1
2
1
2
0
1
2
1
2
2
1
2
2
0
1
1
2
1
0
1
2
0
2
1
0
1
1
1
2
1
1
1
1
1
1
0
1
1
1
1
1
1
2
1
2
0
1
1
2
1
1
2
1
1
0
2
0
1
1
1
1
1
0
1
1
1
1
0
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
0
1
3
1
1
5
1
2
0
2
2
1
2
1
2
1
1
1
1
1
1
1
2
1
0
2
1
0
1
1
1
1
2
1
0
2
2
1
2
0
0
1
1
1
2
1
0
1
1
0
2
1
0
1
0
1
1
1
1
1
3
1
1
2
1
1
1
1
1
1
2
0
1
0
1
1
1
0
0
2
2
2
2
0
1
0
2
1
2
1
1
1
0
1
1
1
0
1
1
2
0
0
1
1
1
1
1
0
1
1
0
0
1
2
2
3
1
1
1
1
1
1
2
0
1
1
2
1
1
2
1
2
1
2
1
1
0
2
1
2
0
1
2
2
1
1
2
1
0
2
1
2
1
1
1
1
1
0
1
2
1
2
1
3
1
1
1
1
1
0
1
2
1
1
1
1
2
1
1
2
1
0
0
2
1
1
1
0
2
1
1
1
0
1
1
0
1
1
0
1
1
1
2
1
1
1
1
2
1
1
1
1
2
3
1
0
0
2
1
2
1
1
0
0
1
1
1
0
2
1
1
3
1
0
2
2
1
2
1
1
1
1
1
0
2
1
2
1
1
1
1
0
1
1
0
2
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
1
2
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
1
2
3
1
1
1
1
0
2
2
1
2
1
1
1
1
2
0
2
2
1
0
1
0
1
2
1
0
1
2
2
1
1
0
1
0
2
2
1
1
1
2
2
1
1
2
0
2
2
1
1
0
2
1
1
0
1
1
1
0
2
1
1
1
1
1
0
1
2
0
2
1
1
0
2
2
1
1
2
2
2
1
2
1
2
2
1
1
0
1
1
0
1
1
2
2
1
2
0
1
0
1
1
0
0
3
2
1
1
1
2
1
0
0
1
2
1
1
1
1
2
1
0
1
1
1
1
1
1
2
2
0
1
1
1
1
2
2
1
1
0
2
2
0
1
1
2
2
1
1
3
1
2
2
2
1
1
1
1
1
2
1
1
1
1
2
2
1
0
2
0
1
1
1
3
2
1
2
1
1
2
2
1
1
3
1
1
2
1
1
1
1
1
1
0
1
1
0
0
1
1
1
0
0
0
0
1
1
1
0
0
2
1
2
1
1
1
0
1
0
0
1
1
2
1
1
1
0
0
2
1
0
0
1
2
0
1
1
2
1
0
2
0
1
1
2
1
1
0
1
1
1
1
1
0
2
2
0
2
2
0
2
2
1
1
2
1
2
1
1
0
1
3
1
1
1
1
0
1
2
1
2
0
1
0
2
1
1
2
1
0
1
2
1
1
0
1
2
2
1
1
1
1
0
2
2
1
1
2
1
1
1
1
1
2
1
2
2
1
1
0
1
1
1
2
2
1
1
1
1
1
0
1
1
1
1
1
0
2
2
2
0
1
1
2
2
1
1
1
1
1
1
2
1
1
0
1
1
1
1
1
1
1
2
1
0
0
0
1
1
1
1
1
2
1
1
1
1
1
2
2
2
1
0
1
2
3
1
1
1
2
1
1
2
1
1
0
1
2
1
1
0
1
1
1
1
1
1
1
2
0
0
2
1
0
1
1
2
1
2
1
1
1
1
1
1
1
2
2
0
0
1
1
1
2
0
1
1
1
1
0
1
0
2
1
1
2
1
1
1
1
0
1
0
1
2
1
1
0
1
2
1
0
1
0
1
1
2
1
1
2
1
0
1
2
0
0
2
1
0
1
1
1
1
2
1
1
1
1
0
2
0
2
1
1
2
0
1
0
2
1
1
2
1
2
1
2
1
2
1
1
2
2
1
1
0
1
1
0
1
0
2
1
2
2
1
0
0
1
1
0
1
1
1
1
1
1
0
1
1
0
1
1
0
2
1
2
0
0
0
1
0
0
0
2
1
2
0
1
1
1
1
1
1
1
1
1
1
1
2
0
1
1
1
1
1
0
1
1
1
1
2
2
1
0
1
1
1
1
0
1
2
1
2
1
0
2
1
1
1
1
2
2
2
1
2
2
1
2
1
1
1
1
2
1
0
2
1
2
1
1
1
2
1
1
1
0
1
1
1
1
1
0
1
2
1
2
0
1
0
1
1
1
1
1
2
2
1
0
1
1
1
2
1
0
1
2
1
1
0
1
1
0
1
2
2
0
1
1
3
1
1
1
1
1
2
0
1
1
1
2
0
1
1
2
1
1
0
1
1
2
1
1
1
1
0
0
1
1
0
1
1
1
1
2
1
1
1
1
0
1
0
3
1
1
0
1
2
1
1
1
1
1
1
1
0
1
1
2
0
0
0
1
2
1
0
0
1
2
1
1
1
1
1
0
1
0
1
0
0
2
1
2
1
1
1
2
1
2
1
1
2
2
1
0
2
1
1
2
2
2
1
1
2
1
1
1
1
1
1
0
1
1
1
1
2
1
1
0
1
1
1
1
0
2
1
2
1
1
2
1
2
1
1
2
1
1
2
2
1
0
2
0
1
2
1
1
1
1
1
0
1
0
0
0
1
1
1
2
1
0
2
2
1
2
2
0
1
2
1
1
0
1
2
1
0
2
1
1
1
1
1
1
1
1
2
1
1
2
2
0
0
0
1
1
1
1
2
1
1
1
2
1
1
0
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
2
0
2
1
1
1
1
1
1
1
1
1
0
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
2
2
1
1
1
1
0
1
1
1
2
1
0
1
1
1
1
1
1
1
1
1
2
0
0
0
1
2
0
1
1
2
1
1
2
1
1
1
1
1
0
1
1
0
2
2
1
2
1
1
1
2
0
0
1
1
1
2
1
1
1
2
1
2
0
1
0
0
1
1
1
1
1
1
1
0
2
1
1
2
1
1
0
1
0
2
0
1
0
1
1
0
1
2
1
0
1
1
1
0
1
2
1
1
1
2
1
0
0
1
1
1
1
2
1
2
0
2
1
0
4
0
1
0
2
0
1
1
1
0
1
0
1
1
0
1
1
2
1
2
2
1
0
1
2
1
0
1
1
1
1
2
1
2
1
2
1
0
1
1
1
0
0
2
1
1
3
1
1
1
0
0
1
1
1
1
2
2
1
0
2
1
1
1
1
3
2
2
2
1
1
1
2
1
1
1
1
2
1
1
0
2
0
2
2
0
2
3
1
0
2
0
1
2
2
1
2
2
1
2
1
1
1
2
2
1
2
1
1
1
0
2
0
1
1
1
1
0
1
1
1
2
2
1
0
2
2
2
2
1
1
2
1
1
1
0
1
1
1
2
1
1
1
2
0
0
1
1
2
1
1
1
1
1
3
2
1
1
1
3
1
1
1
2
0
1
0
1
1
1
2
1
2
1
2
1
0
0
1
1
2
1
1
1
0
1
0
1
1
0
1
0
1
1
1
1
2
2
0
2
1
2
1
1
1
1
1
1
1
1
1
1
1
0
2
2
1
2
2
1
1
1
1
1
2
1
1
2
1
0
1
2
1
1
1
1
1
2
1
1
2
1
2
2
1
1
1
0
2
1
1
2
1
6
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
2
1
1
2
1
0
2
2
2
0
0
3
2
1
1
1
1
1
0
2
1
1
1
2
0
0
1
0
0
1
1
1
1
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
2
1
2
6
4
1
1
1
1
1
0
2
1
1
1
1
0
2
0
2
1
0
1
2
0
1
1
0
2
0
2
1
2
1
0
1
1
2
1
1
2
1
2
1
2
1
1
2
1
0
1
1
1
2
1
2
0
1
0
1
0
2
2
2
2
1
2
1
1
1
2
0
0
1
0
1
1
1
2
0
0
0
1
1
1
1
1
1
1
0
1
1
2
0
1
1
2
2
2
2
0
1
1
1
1
1
1
0
1
1
1
1
2
1
1
1
2
1
1
2
1
2
1
2
0
0
1
1
1
1
1
1
1
1
1
2
2
0
1
1
1
1
1
1
0
1
1
2
2
1
2
1
2
1
1
1
1
2
1
1
1
1
2
0
1
0
2
1
1
4
1
2
1
0
1
2
1
1
0
0
0
1
1
0
0
2
1
0
1
1
2
0
1
2
2
1
1
1
2
1
1
0
1
0
1
1
1
1
1
1
0
1
0
1
1
1
2
2
1
0
2
0
1
2
1
2
1
2
0
2
2
0
1
1
1
1
3
1
1
1
1
2
1
1
2
1
2
0
1
0
0
2
0
1
2
1
1
1
1
1
1
2
0
2
2
1
1
1
0
1
1
0
1
0
0
1
1
1
1
0
1
0
1
1
1
0
1
2
1
0
2
1
1
1
1
2
1
2
1
2
1
1
0
1
1
1
1
2
1
1
2
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
0
1
1
1
1
2
1
1
1
0
1
1
1
0
1
1
1
1
1
1
2
1
0
1
1
2
1
1
1
1
2
0
1
2
1
1
1
2
3
1
0
1
2
1
1
0
2
1
1
1
2
2
2
1
1
1
1
1
0
2
1
2
1
1
0
2
2
0
1
1
1
2
0
2
2
1
1
1
2
4
2
2
2
1
0
0
2
1
1
2
0
1
0
1
2
1
1
0
1
1
0
1
1
1
2
1
1
1
2
1
0
2
2
1
0
1
0
1
1
1
1
4
1
2
1
2
2
2
1
1
1
1
2
1
2
1
0
1
2
1
1
2
1
1
1
1
1
2
1
1
1
1
2
3
0
1
2
1
1
1
2
1
2
0
2
1
1
1
2
1
2
1
1
0
0
1
1
2
2
1
0
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
0
1
1
1
2
2
1
1
1
1
1
1
1
1
1
0
1
2
2
1
1
1
2
1
0
1
1
1
2
0
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
2
1
2
1
1
1
1
2
2
1
1
1
0
1
1
1
0
2
1
1
1
2
1
2
2
1
1
1
1
0
1
1
1
1
2
2
2
1
1
1
1
3
1
2
1
0
1
1
1
1
1
1
1
1
1
2
2
2
1
2
0
1
0
1
1
1
1
1
1
0
1
2
0
1
1
0
2
1
1
1
0
2
1
1
1
0
2
1
0
0
1
1
1
1
1
1
2
1
1
1
1
2
1
1
3
1
1
2
2
1
1
1
2
1
1
0
1
1
2
1
2
1
2
2
2
1
1
1
1
1
1
1
0
1
0
1
2
0
0
1
2
2
2
2
2
1
0
1
2
1
0
2
0
0
0
1
2
1
1
2
1
2
1
0
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
3
1
0
2
1
0
1
2
0
1
3
1
2
1
1
1
1
0
0
2
1
2
1
2
1
2
2
1
1
2
2
1
2
1
0
0
1
1
1
1
1
0
1
2
1
1
1
1
2
0
2
1
2
1
1
0
1
0
0
1
1
1
1
1
2
1
1
0
1
1
1
2
1
2
1
0
0
2
1
2
2
1
1
2
2
0
2
1
0
1
0
1
1
1
2
1
1
1
1
1
0
2
1
2
1
2
1
1
1
0
2
1
1
1
1
1
2
1
2
1
1
0
1
1
2
0
1
2
0
2
1
1
2
1
1
2
1
2
0
2
1
2
1
2
0
0
1
1
1
1
2
1
0
1
1
1
2
0
1
1
1
1
1
2
1
1
2
1
1
0
1
0
1
1
2
2
1
1
1
2
1
2
1
1
2
1
1
1
2
1
1
1
0
1
1
2
2
0
1
1
1
1
2
0
2
0
0
0
1
1
0
1
0
0
1
1
0
2
0
5
1
0
1
1
2
1
2
0
2
0
1
1
2
2
0
1
1
1
1
2
2
1
1
1
2
2
1
1
0
1
0
2
0
1
1
1
1
2
2
2
1
1
2
1
1
1
0
1
1
1
2
0
1
1
1
1
1
1
1
1
1
0
1
1
1
1
2
1
1
1
1
1
1
2
1
2
2
2
1
0
1
1
1
1
1
1
2
0
1
1
1
1
1
0
0
1
2
0
0
1
0
0
1
1
1
2
2
1
0
1
1
0
1
1
1
2
1
1
1
1
0
0
0
0
0
0
1
1
2
1
1
0
1
2
2
1
1
1
1
1
1
1
1
1
1
1
2
0
1
1
1
1
1
2
0
2
1
1
1
2
2
1
1
0
1
0
2
1
1
1
1
1
1
1
2
1
1
2
0
1
2
1
1
1
1
1
1
1
2
1
0
1
2
1
2
1
0
0
1
2
2
2
1
1
1
1
2
1
0
1
2
1
1
0
2
1
2
2
1
1
1
0
2
0
1
0
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
2
2
1
1
1
1
2
2
1
1
1
1
1
1
2
2
1
0
2
1
0
1
2
1
0
1
0
2
1
0
2
1
2
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
0
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
2
1
0
0
2
0
0
1
1
1
1
0
0
1
2
1
2
2
2
1
1
1
1
2
1
1
0
2
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
0
1
1
1
3
1
1
0
2
2
1
0
2
0
1
0
1
1
1
2
2
0
3
1
2
2
2
1
1
0
0
1
1
2
1
0
1
1
0
2
1
0
0
2
0
2
2
2
0
1
1
2
0
1
1
0
1
2
0
1
2
1
1
2
1
1
2
2
2
1
1
1
1
1
1
1
0
2
0
1
1
1
0
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
0
2
1
0
2
1
1
0
1
1
0
1
1
2
0
2
2
3
1
1
0
2
0
1
2
3
2
0
1
2
2
1
0
2
1
1
1
1
2
2
1
0
1
2
1
1
1
1
1
1
1
1
1
2
2
1
2
1
2
2
1
0
1
2
1
1
2
1
0
1
1
1
1
1
0
0
1
0
0
1
2
1
2
1
2
2
2
1
1
1
1
0
1
2
2
2
2
0
0
0
1
1
0
1
1
2
2
1
1
0
1
0
1
2
2
1
1
1
1
1
1
2
2
2
2
1
0
2
1
1
1
2
2
1
0
1
1
2
2
1
2
1
2
1
1
0
1
1
0
1
1
1
1
0
1
2
2
1
1
2
1
0
1
0
2
0
2
2
1
2
3
2
0
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
5
1
0
0
2
2
1
2
1
1
1
2
2
1
0
0
1
1
1
1
1
1
1
1
0
1
1
1
1
0
0
0
1
1
1
1
1
0
2
2
0
1
1
1
1
1
1
1
2
1
1
0
2
1
1
2
0
2
1
2
1
1
0
1
1
3
1
1
1
2
1
2
1
2
0
2
0
1
2
1
1
1
2
2
2
1
1
2
1
0
2
1
1
1
1
2
0
1
2
1
2
0
1
0
1
0
1
2
1
0
1
0
0
1
2
2
1
1
1
1
1
1
2
1
1
1
0
1
1
2
0
2
1
1
2
1
1
1
2
1
2
1
0
1
1
2
1
1
0
1
0
2
1
0
1
1
0
1
0
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
2
1
0
1
1
0
1
2
0
1
1
1
2
1
0
1
2
1
2
1
2
1
1
1
1
1
1
0
2
1
2
1
1
1
0
1
1
2
2
0
1
1
1
2
1
0
1
1
2
1
2
1
1
0
1
1
1
2
1
0
1
1
2
4
2
1
1
2
1
0
2
0
1
2
1
1
0
2
1
1
2
2
1
1
1
1
0
0
0
1
1
0
1
1
1
1
1
1
1
1
1
0
1
2
1
0
1
0
0
2
1
1
2
1
1
1
2
0
1
2
1
2
2
0
0
0
1
1
1
0
1
0
1
2
1
0
1
1
1
0
1
1
1
2
2
1
1
1
1
2
1
2
0
1
1
1
2
1
1
1
0
2
1
1
2
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
0
1
0
2
1
0
2
0
2
1
1
1
2
1
1
1
4
1
0
1
0
2
1
1
1
1
1
2
0
1
1
1
2
1
1
0
2
1
0
1
1
1
1
1
0
1
1
1
1
2
0
2
1
0
2
0
1
1
1
0
1
1
1
1
1
2
1
0
1
1
1
1
2
1
1
0
0
1
0
1
2
1
1
2
1
1
0
1
1
0
2
1
0
0
1
0
1
1
0
2
3
1
0
1
0
0
1
1
1
2
0
1
1
2
2
1
1
1
2
2
2
1
1
0
1
1
2
0
2
1
1
2
1
2
1
1
1
1
1
2
0
1
0
1
2
1
2
2
1
1
2
1
1
1
1
1
0
1
2
0
1
1
0
2
2
2
2
1
1
0
1
1
3
1
0
1
2
2
1
1
1
2
1
2
1
2
1
1
0
1
0
3
1
2
2
1
2
2
1
2
2
2
2
0
1
1
1
1
1
2
3
1
1
2
1
1
1
2
1
1
1
1
0
2
2
2
1
2
0
1
2
0
1
1
1
1
0
1
1
1
1
0
1
1
2
2
2
2
1
1
1
1
1
2
1
1
1
0
1
1
1
1
0
1
1
0
0
1
1
0
1
1
0
1
1
1
1
1
1
0
1
0
0
1
2
0
1
1
1
1
1
1
1
2
1
2
1
3
1
2
0
1
1
1
2
2
1
0
1
1
1
2
0
1
2
0
1
2
0
1
1
0
1
1
2
0
0
0
2
0
1
2
0
2
1
2
1
1
1
2
1
1
2
1
0
1
2
1
1
1
2
2
1
2
1
2
1
1
2
1
1
1
2
1
2
2
0
0
0
1
2
2
1
2
0
2
0
1
1
2
2
1
1
1
1
2
0
1
1
1
1
2
0
0
1
1
1
0
1
1
1
1
2
1
2
2
0
1
1
1
1
1
1
1
0
2
1
1
2
1
1
1
1
1
1
0
1
1
3
2
2
1
1
2
1
1
0
0
0
2
1
2
3
0
2
1
1
1
1
2
1
2
1
1
2
1
1
1
0
2
1
1
1
1
1
1
0
1
1
2
0
2
0
1
1
1
1
1
1
1
1
1
2
2
2
0
1
1
2
1
0
2
1
1
1
2
1
2
1
1
1
3
1
1
0
1
2
2
1
2
1
1
1
2
1
2
0
1
2
1
1
0
0
1
2
1
2
1
1
1
1
1
1
1
0
2
0
1
1
1
0
1
0
1
1
1
2
0
1
1
2
1
3
0
2
1
2
1
1
2
2
1
1
1
0
1
0
1
1
2
0
1
0
1
2
0
1
1
1
1
1
1
0
1
1
1
2
1
1
2
2
1
0
1
0
1
1
1
1
2
1
2
1
1
1
1
1
2
2
2
2
1
1
1
1
1
1
1
1
1
0
1
2
2
1
2
1
2
1
1
2
2
1
0
1
1
2
1
0
1
1
0
0
2
2
1
1
2
1
2
1
1
1
1
2
3
0
1
2
1
1
0
2
0
1
1
1
1
1
0
1
2
0
2
1
0
0
1
0
1
2
2
1
0
1
1
1
0
1
1
1
2
1
1
1
1
0
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
1
1
2
0
2
1
2
0
1
0
1
0
2
1
1
0
1
0
1
2
1
1
2
1
1
0
1
1
1
1
2
1
1
1
1
1
0
2
1
1
0
1
1
1
1
2
0
2
0
1
1
1
0
1
0
2
2
2
1
0
0
1
1
0
1
1
1
1
2
1
1
1
1
1
2
1
2
1
2
2
2
1
2
1
1
1
0
2
1
1
1
1
2
1
1
2
1
2
1
1
1
1
1
2
2
2
1
1
2
1
0
0
2
2
4
1
1
2
0
2
1
0
0
1
0
0
1
1
0
2
2
1
1
1
0
0
1
1
1
0
1
2
1
1
0
1
0
1
0
2
1
1
2
0
0
1
2
1
1
2
1
1
0
2
0
1
2
1
2
2
1
2
1
1
1
1
1
1
2
1
1
0
1
1
2
1
1
1
2
1
2
0
1
0
2
2
1
2
1
2
1
2
1
1
2
1
0
2
2
1
1
2
1
1
1
1
1
2
1
1
1
1
2
2
1
0
1
2
1
1
2
1
0
1
2
1
1
2
1
1
1
1
1
0
2
1
1
1
2
1
1
2
2
1
1
0
2
2
1
1
1
2
0
1
2
2
1
1
1
1
1
1
1
0
0
2
1
2
0
1
0
0
1
1
2
2
1
1
1
2
1
2
0
2
0
0
2
1
0
2
1
0
2
2
1
0
2
0
1
1
1
1
1
1
1
2
2
1
1
0
1
1
2
1
1
1
1
1
1
2
0
2
1
2
1
2
3
1
2
1
0
0
1
1
0
1
1
1
1
2
1
2
2
1
1
2
1
1
2
1
1
3
1
2
1
0
1
3
2
1
0
2
1
1
1
0
1
2
1
3
1
1
1
1
0
2
3
0
1
2
1
1
1
1
1
2
2
1
1
0
1
1
1
1
1
0
1
0
2
1
0
1
1
1
2
1
2
1
1
0
1
1
1
2
1
2
1
1
0
1
0
1
2
1
1
1
2
1
1
1
1
2
0
0
1
1
1
2
1
1
1
0
0
2
1
2
1
1
0
1
2
1
2
1
2
1
1
0
1
2
2
1
1
1
1
1
2
1
0
1
2
1
1
0
2
1
1
2
1
0
1
1
1
1
1
2
1
1
1
2
1
2
1
2
1
1
1
2
0
1
1
0
2
0
2
1
2
1
1
0
2
2
1
0
2
1
1
1
1
2
1
0
1
0
1
2
1
1
2
1
1
1
1
0
1
1
0
4
1
2
1
1
1
1
2
0
1
2
1
1
1
1
0
2
1
0
1
1
1
1
1
2
1
1
0
1
1
1
0
2
1
1
0
1
1
0
1
1
0
1
2
1
1
1
1
1
1
0
2
1
1
1
2
0
1
1
1
1
1
0
1
1
1
1
1
1
2
1
1
1
1
1
0
1
1
1
0
0
1
1
1
1
2
1
1
1
2
0
2
1
1
1
0
1
1
1
2
1
1
1
0
0
1
2
2
1
0
1
1
1
1
0
0
1
1
1
2
1
2
1
1
1
1
0
1
1
1
1
0
1
2
0
1
1
1
0
1
2
1
0
1
1
2
1
1
1
1
1
1
2
0
1
1
2
1
1
1
0
1
1
0
3
1
1
1
2
1
1
1
0
1
1
1
1
1
1
1
2
1
0
0
2
1
1
1
1
2
2
1
2
1
2
3
1
0
0
1
2
0
2
1
2
3
1
2
1
1
2
2
0
1
3
1
2
1
1
1
2
0
0
1
1
1
1
2
1
1
2
2
0
1
1
2
1
1
2
1
2
1
2
0
2
1
1
2
1
1
0
2
1
1
1
1
1
1
1
0
1
1
1
2
2
0
0
2
1
1
1
0
1
1
2
1
0
1
0
3
1
1
1
2
1
1
2
1
2
0
1
1
0
1
1
1
1
1
1
1
2
1
1
1
1
2
2
1
0
0
1
1
1
2
1
1
0
0
1
0
1
1
1
1
0
1
1
2
1
1
1
1
1
1
1
2
1
1
1
0
2
1
2
2
0
1
0
0
1
1
2
1
0
1
1
0
1
1
1
1
2
1
1
2
0
2
1
0
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
0
0
1
2
1
1
2
2
1
0
1
1
0
1
1
1
1
0
1
1
1
2
0
2
1
0
1
0
1
1
1
1
1
0
0
2
2
1
1
2
2
1
1
1
1
1
1
0
1
0
2
1
1
1
1
1
2
2
2
2
1
1
0
2
1
2
1
2
0
2
1
2
0
1
1
0
1
2
2
2
2
1
1
1
0
1
1
0
1
1
0
1
1
1
2
1
1
1
1
1
0
0
1
2
1
1
1
1
0
1
1
1
0
1
2
1
1
1
2
1
1
0
2
0
2
1
0
1
1
0
1
1
1
1
0
1
2
1
1
1
1
2
1
1
1
2
0
1
2
1
1
1
2
1
2
2
1
1
2
1
2
1
0
2
0
0
1
1
1
1
1
2
2
0
2
1
1
1
2
2
1
2
0
2
1
2
1
1
1
1
1
1
1
2
1
1
0
2
0
2
0
1
0
1
2
1
0
0
2
0
1
1
0
1
1
0
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
0
2
1
2
1
2
1
0
1
2
1
1
1
1
1
0
0
0
1
1
2
1
1
1
0
1
2
1
1
1
1
0
2
0
1
0
2
1
1
0
0
0
2
1
0
0
2
1
0
1
1
1
0
2
1
1
1
3
1
0
1
1
8
2
0
1
0
0
1
1
1
1
0
1
0
1
2
0
1
1
1
1
1
1
0
1
1
2
1
2
0
1
2
2
1
1
1
1
1
0
1
0
2
2
1
1
1
0
1
2
0
1
0
1
1
1
0
1
1
1
1
2
0
2
1
2
0
1
0
1
0
1
1
1
2
1
2
1
1
1
2
0
2
0
1
2
0
1
0
1
1
1
1
2
2
1
2
1
0
2
0
1
1
1
1
1
0
0
1
2
1
1
2
1
2
1
0
1
1
0
2
0
1
0
1
2
2
2
1
1
1
1
1
2
1
1
2
2
1
0
1
0
1
1
1
1
1
1
1
1
0
1
0
1
1
1
3
0
2
2
1
2
1
1
0
2
1
1
1
1
1
1
0
1
1
1
1
1
1
2
1
2
2
1
2
1
2
1
1
1
1
1
1
1
1
1
0
1
1
1
0
1
1
1
0
2
1
2
1
0
1
2
0
2
0
2
1
2
1
2
1
1
2
0
1
1
1
2
1
1
1
2
1
1
1
1
1
2
2
1
2
1
1
0
1
1
1
2
1
2
1
1
1
1
1
2
0
2
1
2
3
1
1
1
0
0
2
1
2
2
2
1
0
0
1
2
1
2
1
1
1
1
0
1
0
1
1
1
2
0
1
1
2
2
3
2
1
2
0
2
1
1
2
2
2
2
0
1
1
2
1
2
1
0
1
2
0
1
1
2
0
4
1
2
1
1
1
1
1
1
2
2
1
1
1
2
1
1
1
1
2
2
1
1
1
1
2
1
0
0
1
1
2
1
1
0
1
1
1
0
2
1
1
0
2
1
1
1
2
1
1
1
0
0
0
1
0
1
1
0
2
0
1
0
2
2
0
1
1
1
2
1
1
2
0
1
2
1
1
2
1
1
2
1
1
1
2
0
1
0
1
2
2
0
1
2
1
1
1
0
2
1
1
1
2
2
1
1
1
2
2
1
0
1
1
1
1
2
2
1
1
1
1
1
2
1
1
0
2
2
1
1
1
1
1
2
1
2
1
1
0
1
1
2
2
1
1
0
1
0
0
2
0
1
1
1
0
1
1
1
1
1
2
1
1
0
1
1
2
2
1
0
1
1
1
1
1
2
1
1
1
1
1
1
3
1
1
2
1
0
1
0
1
1
1
2
2
1
2
0
2
0
2
1
2
1
2
0
2
1
1
0
2
1
2
1
0
1
2
0
1
0
2
1
1
0
0
2
1
2
1
2
0
1
1
1
1
1
0
2
1
1
1
1
2
2
1
1
1
2
0
0
1
4
2
0
1
0
2
1
0
1
1
1
2
1
1
1
2
1
2
0
1
1
0
1
1
2
1
1
1
1
0
1
2
1
1
2
1
2
1
1
0
0
2
1
2
0
1
1
1
2
0
2
0
1
2
1
1
1
1
2
1
0
0
1
0
1
1
1
1
1
1
0
1
2
2
0
0
2
1
2
2
1
2
0
0
1
1
1
1
1
0
1
1
0
1
1
2
2
1
1
1
1
1
2
0
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
1
2
2
1
1
1
1
2
1
2
1
0
0
1
2
1
2
1
1
2
0
1
1
1
1
1
1
1
1
2
1
1
1
2
0
1
0
2
1
0
1
1
1
2
1
1
2
1
1
1
2
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
0
0
2
1
1
2
0
1
1
1
1
1
2
2
0
1
1
1
0
2
1
2
1
1
1
1
1
2
0
1
2
1
1
1
1
2
2
1
0
2
1
1
0
3
2
1
1
0
1
1
2
1
1
2
1
1
1
2
1
1
2
1
1
1
2
1
1
1
0
1
1
2
1
2
1
1
0
1
0
1
2
1
1
1
2
0
1
1
2
1
1
1
1
1
2
1
1
0
1
0
1
0
1
1
1
2
2
1
0
2
1
1
2
1
1
0
1
1
2
1
0
1
1
1
1
1
1
2
1
2
2
1
1
2
2
1
1
1
0
2
1
1
1
2
2
1
1
0
1
0
1
1
1
1
1
2
1
1
2
0
2
1
2
1
0
0
0
0
0
1
1
1
1
1
1
1
2
1
1
1
0
3
1
2
0
1
1
1
1
2
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
0
0
2
1
1
1
1
2
1
1
2
1
1
0
1
1
2
2
2
2
1
1
1
1
0
0
1
2
2
1
1
0
0
1
0
2
0
1
2
1
0
2
1
2
1
2
1
1
0
2
2
0
1
0
2
1
2
0
1
0
0
0
0
0
1
1
2
1
0
1
0
1
1
2
1
0
1
0
1
2
0
1
1
2
1
0
0
1
1
1
2
1
1
1
1
1
1
0
1
1
2
1
1
1
1
1
1
1
1
1
1
1
0
2
1
0
2
1
1
0
1
0
1
1
1
1
2
1
3
1
2
1
0
2
1
1
2
2
2
1
2
1
0
1
2
1
1
1
0
0
1
1
0
1
1
1
2
1
2
0
1
2
1
1
2
1
1
1
1
0
1
2
1
0
2
1
0
2
0
0
1
2
1
1
2
1
0
1
1
0
2
0
1
1
1
2
2
1
2
1
0
1
1
1
2
2
2
1
1
1
1
2
1
1
1
1
1
1
0
1
1
1
0
1
2
0
1
1
1
0
1
1
1
0
1
1
2
1
2
1
1
1
1
1
1
0
2
1
2
1
2
0
2
1
2
2
1
2
2
0
1
0
2
1
2
1
2
2
1
0
1
1
0
1
0
2
1
0
1
1
2
2
1
1
3
1
2
0
1
1
2
2
1
2
1
0
0
2
1
1
1
0
0
2
0
2
0
1
1
1
2
1
0
0
0
1
2
1
2
1
1
2
2
1
2
1
0
0
1
2
1
2
1
1
2
1
0
1
1
1
2
1
2
1
2
0
1
1
0
0
0
1
1
0
0
1
0
2
0
1
1
2
1
2
1
1
1
1
1
0
1
0
1
2
0
0
1
1
1
1
2
1
0
1
1
1
0
1
2
0
1
1
0
0
2
1
1
1
1
0
2
2
1
1
1
2
0
2
0
2
0
2
2
1
3
2
0
0
2
1
1
1
2
1
2
3
2
0
2
1
1
1
1
1
0
1
1
1
1
0
2
1
1
2
1
1
2
1
1
2
1
0
2
1
1
0
0
0
2
2
2
1
1
1
2
1
3
1
0
1
1
2
2
1
0
0
1
1
1
1
2
1
2
1
1
2
2
2
0
2
2
2
1
1
0
2
0
2
0
2
0
2
1
2
2
1
2
1
1
1
2
2
2
1
1
2
1
1
1
1
1
0
1
1
1
2
0
2
0
0
1
0
1
1
1
2
2
1
1
1
2
1
0
1
1
1
1
2
0
1
1
1
1
1
0
1
1
2
1
2
1
1
1
1
0
1
1
1
1
1
2
1
1
1
0
1
1
1
1
2
2
1
1
1
2
0
1
1
2
1
1
2
2
1
1
1
0
1
0
1
0
1
1
1
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
2
0
1
0
1
1
2
1
2
1
1
0
1
2
3
1
1
0
0
2
2
2
1
1
0
1
1
1
0
2
1
1
1
2
2
1
1
1
0
1
1
1
2
2
1
2
1
1
1
1
1
2
1
1
1
2
1
0
2
1
0
2
1
2
0
2
1
0
1
1
1
0
1
2
1
1
2
1
0
1
1
3
2
1
0
1
0
1
0
2
0
0
2
1
1
2
1
1
1
1
0
0
1
0
0
2
2
1
1
2
0
1
1
2
2
0
1
0
1
1
1
1
1
1
2
1
1
1
2
0
1
1
1
0
2
1
0
1
2
1
1
2
1
2
1
1
1
1
0
0
2
0
1
1
2
1
0
1
1
1
2
2
1
1
1
0
1
1
1
0
1
2
1
2
1
1
1
0
2
0
0
2
1
1
0
1
2
1
1
1
2
1
2
2
1
1
1
1
2
1
2
1
1
0
2
1
1
0
1
0
1
1
1
1
1
0
1
2
1
1
1
1
0
2
2
1
2
3
1
0
2
2
1
1
1
1
1
1
1
1
1
3
0
2
0
1
2
1
0
1
1
0
1
2
2
2
2
1
2
2
1
0
1
2
1
1
0
1
1
0
1
2
1
2
2
0
1
2
1
1
1
2
1
1
2
1
2
1
0
0
1
1
2
1
1
1
2
1
2
1
1
2
1
1
2
2
1
1
1
0
1
1
0
1
1
2
2
1
1
1
2
2
0
1
1
1
0
1
0
0
2
1
1
2
1
1
0
1
2
1
2
1
2
1
2
2
0
2
1
2
0
1
1
1
1
1
1
2
1
1
2
2
0
1
2
1
1
0
1
1
2
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
0
1
2
2
0
1
1
1
0
0
1
2
1
1
0
2
1
2
1
1
2
2
1
1
1
0
1
1
1
1
1
0
1
0
1
2
1
1
1
0
1
1
0
3
2
1
1
1
0
1
1
1
1
2
2
0
2
2
0
0
0
1
2
1
0
1
1
1
2
1
1
1
1
1
0
1
1
2
1
1
1
0
1
1
2
2
1
0
1
0
1
1
2
1
2
0
1
1
0
1
1
1
1
1
1
2
1
1
2
1
1
1
1
0
1
1
0
1
2
2
3
2
1
1
0
1
1
2
1
2
2
2
1
1
0
1
0
0
1
0
1
2
0
1
2
2
0
1
1
0
1
1
2
1
1
2
0
2
1
1
1
1
1
0
0
1
1
1
2
2
1
1
0
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
0
2
1
2
1
1
1
2
1
2
1
1
0
1
1
1
1
1
2
1
0
0
1
1
2
1
1
1
1
2
0
2
0
0
1
1
1
1
1
2
0
1
2
1
1
1
1
0
2
1
2
1
1
1
0
2
2
0
2
1
2
1
2
1
1
1
2
2
1
1
0
1
2
2
1
1
2
1
0
1
1
2
1
2
2
2
1
0
2
1
0
0
0
1
1
2
1
0
1
2
1
1
1
1
2
2
1
0
0
1
2
0
1
1
1
2
2
2
1
1
1
2
1
1
1
0
0
0
1
1
1
1
1
1
0
1
1
0
1
0
0
0
2
1
1
0
1
1
1
1
0
0
0
2
1
1
1
1
2
1
1
2
2
1
0
0
0
2
1
1
2
2
1
0
1
2
1
0
1
2
0
0
2
2
2
0
1
1
1
1
1
1
1
0
1
2
1
1
1
1
2
1
1
0
1
1
2
1
1
1
1
1
1
2
1
1
0
2
0
2
1
2
0
0
1
1
1
1
1
2
0
2
1
2
3
0
1
1
0
1
1
1
3
1
1
1
0
2
1
1
1
2
2
2
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
0
2
2
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
2
1
1
0
2
1
1
3
0
1
2
1
2
1
1
1
1
1
2
1
1
3
1
2
1
1
1
1
1
0
1
1
1
1
2
2
1
0
1
0
1
1
1
1
1
0
1
2
1
1
0
1
1
1
2
2
1
0
1
0
3
1
2
0
1
0
1
0
1
1
1
0
2
1
1
1
1
2
1
0
1
1
1
1
1
1
2
0
1
2
1
1
2
0
1
1
1
0
0
1
1
1
1
1
0
1
1
1
1
2
2
1
2
1
1
1
1
0
1
2
2
2
0
2
2
1
1
1
1
3
1
1
1
0
1
2
2
1
2
2
1
1
1
0
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
2
0
1
2
1
1
1
1
1
1
1
5
1
1
1
1
1
1
1
0
1
1
0
1
0
0
2
1
1
3
1
1
0
2
0
1
1
1
1
1
0
0
1
1
1
1
1
0
2
1
1
2
2
1
2
0
1
1
1
1
1
0
1
1
2
1
2
2
1
1
2
2
1
1
0
1
2
1
0
2
2
1
1
2
2
2
1
1
0
1
0
1
1
1
2
0
1
1
0
2
1
1
1
2
1
1
0
1
2
2
2
0
1
0
1
0
1
1
1
0
1
0
1
2
1
1
0
2
1
1
1
1
1
1
0
1
1
1
1
1
2
1
1
1
0
1
0
2
2
2
2
0
1
1
1
1
0
0
0
2
0
1
1
2
1
2
1
2
0
1
1
1
2
1
0
0
1
1
1
2
0
2
1
0
0
1
1
1
1
1
1
0
2
2
2
1
1
1
0
1
1
1
1
3
1
1
0
1
0
1
1
2
1
2
2
1
1
1
2
0
1
2
2
1
1
1
1
1
1
0
1
0
0
1
2
1
1
1
2
0
1
2
2
0
1
1
0
0
1
1
1
1
1
1
1
2
2
1
1
1
0
1
2
1
1
2
2
1
1
2
1
1
1
1
0
1
1
2
2
1
1
2
1
1
2
3
1
0
1
1
1
1
1
1
0
1
2
1
1
1
0
1
0
1
1
1
2
2
1
1
1
0
1
1
1
1
1
1
1
1
2
1
0
2
1
1
1
1
0
1
1
1
2
2
1
1
2
1
2
1
1
2
1
1
0
1
0
2
0
2
2
1
1
0
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
0
2
1
1
1
1
2
2
0
1
1
2
0
0
1
1
1
1
0
2
1
1
1
0
1
0
2
1
2
2
0
0
1
1
1
1
2
1
1
1
2
1
1
0
1
1
1
1
2
1
1
2
1
1
1
2
1
1
2
2
0
2
0
1
0
0
1
2
1
1
2
2
1
1
1
1
1
0
1
1
2
1
1
1
2
2
1
1
1
1
2
1
1
0
1
1
2
1
1
1
1
2
1
1
0
0
1
2
1
1
0
1
2
2
1
1
0
2
1
1
0
2
0
2
0
1
1
1
1
2
0
1
1
1
0
1
2
1
2
1
2
1
2
1
2
3
1
1
2
1
1
0
0
2
2
2
2
1
0
1
1
0
2
1
0
1
0
1
2
1
1
0
0
1
1
1
0
1
1
0
2
1
1
1
1
2
0
2
0
1
1
2
2
1
1
1
1
1
1
1
2
1
1
0
1
1
2
0
1
2
1
1
1
1
1
1
2
2
1
1
1
1
2
2
1
1
0
2
2
1
2
1
1
0
1
1
0
1
1
1
1
1
0
1
1
1
0
0
0
1
2
1
2
1
3
1
2
2
1
1
1
1
1
1
0
1
0
0
2
1
1
1
0
2
2
1
0
0
1
2
2
2
2
1
1
0
2
1
2
2
0
1
2
1
1
2
1
2
1
1
1
1
0
1
0
2
1
1
2
2
1
1
2
1
1
2
1
1
0
1
0
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
0
2
1
1
1
1
1
1
2
1
0
2
1
0
2
2
1
1
1
2
1
0
1
0
1
2
1
1
1
1
1
1
2
1
2
0
2
2
2
1
1
1
2
1
1
1
1
1
0
3
2
2
1
1
1
2
1
0
1
1
0
1
1
1
0
1
2
0
1
0
2
1
1
1
1
2
1
0
1
0
1
0
1
1
1
1
1
2
1
1
2
1
1
1
1
2
0
2
2
1
1
1
1
0
2
2
1
2
2
1
1
0
0
1
2
2
2
1
1
1
0
1
2
0
1
2
3
1
0
2
1
0
2
2
2
0
0
1
2
1
1
2
0
2
2
1
1
2
0
1
1
1
2
1
0
1
0
2
1
2
0
2
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
1
2
2
1
0
1
1
1
2
1
2
1
2
1
1
2
2
1
1
1
1
1
1
1
1
2
2
2
2
2
2
1
1
1
1
1
1
2
0
0
1
0
1
1
1
1
2
1
0
2
0
0
1
0
1
1
1
1
2
1
1
1
1
2
0
1
1
0
0
1
0
2
2
1
0
0
2
2
1
1
0
3
2
2
1
2
2
1
2
0
0
1
1
1
1
1
1
1
1
0
2
2
0
1
2
1
1
1
1
0
1
2
0
0
1
2
1
1
0
1
1
2
1
2
1
1
2
1
0
1
2
1
1
2
1
1
1
0
1
1
1
1
1
1
2
1
2
0
2
1
0
1
0
1
2
1
0
1
1
1
1
2
1
1
2
2
2
0
1
0
1
1
1
2
1
4
1
1
1
0
1
1
1
1
1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
0
0
1
1
2
1
0
1
1
1
1
1
1
0
1
1
1
0
1
1
1
1
1
1
2
1
1
2
2
2
1
1
1
1
1
1
1
1
1
1
2
2
1
2
0
1
2
1
1
1
0
2
1
1
1
1
1
1
1
0
1
2
2
1
1
2
1
2
0
1
1
1
1
0
1
2
1
0
1
1
2
1
1
1
0
1
2
0
1
1
1
1
3
0
1
1
0
1
2
1
1
2
1
2
1
1
1
1
0
2
0
2
1
3
1
1
0
1
0
1
1
1
2
1
0
1
2
1
1
0
0
2
2
1
2
0
0
1
0
1
1
2
1
0
1
1
0
1
1
2
1
2
1
1
0
2
1
2
1
1
1
1
2
0
1
1
1
2
1
1
1
1
0
1
0
0
0
1
0
2
1
1
1
2
1
1
2
2
0
1
1
0
1
1
1
0
1
1
0
1
1
1
1
1
2
0
1
0
2
2
2
1
2
1
1
1
0
1
1
2
0
1
0
3
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
0
1
1
2
2
2
1
1
0
1
1
1
1
1
1
1
0
1
1
0
1
1
1
0
2
1
0
2
0
2
1
1
1
1
1
1
0
1
2
2
1
2
1
1
0
2
1
0
3
0
0
1
1
2
2
0
2
1
2
1
1
2
3
2
1
1
2
1
2
1
1
1
2
2
1
1
1
2
1
1
1
2
1
1
2
2
0
1
2
1
1
1
1
1
2
1
1
3
1
1
2
0
1
0
2
1
1
2
1
1
0
2
1
1
1
1
1
1
1
1
0
0
1
0
1
2
2
1
1
1
1
1
2
1
1
0
1
1
1
2
1
2
2
0
1
0
1
2
1
2
1
0
0
2
0
1
1
1
1
2
2
1
2
0
1
1
0
1
1
1
2
0
1
1
1
1
1
1
1
1
1
0
1
2
2
1
1
2
1
2
1
1
2
1
1
1
1
1
2
1
1
1
1
0
2
1
0
1
1
2
2
2
0
1
1
1
3
1
1
0
2
0
1
2
1
2
1
1
1
1
2
0
1
2
0
1
1
2
2
1
1
0
1
0
2
1
2
0
1
2
1
2
1
1
0
1
0
2
1
1
1
2
1
1
2
2
1
1
1
1
2
1
1
1
2
2
1
1
1
1
2
1
0
2
1
2
0
0
1
1
1
2
0
1
0
2
1
1
1
1
1
1
3
1
0
1
2
2
2
1
1
1
1
1
2
0
1
0
2
1
1
1
1
1
2
2
0
1
1
2
1
1
1
0
2
1
2
1
1
1
0
1
1
2
1
0
1
1
1
0
1
0
1
1
1
2
2
2
1
1
0
1
1
1
0
1
0
1
2
1
0
1
1
1
2
1
1
2
1
1
0
2
1
1
0
2
1
1
1
1
2
2
1
0
1
0
0
1
0
0
1
1
2
2
0
0
2
1
1
2
2
1
1
1
1
1
1
1
0
1
1
1
4
0
1
1
1
1
0
1
0
1
2
1
2
1
0
1
1
2
1
1
2
1
2
0
1
1
1
0
2
1
1
1
0
1
1
1
1
0
1
1
0
2
0
1
2
1
1
1
1
1
1
1
2
2
1
2
1
1
1
1
1
2
2
2
0
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
2
1
1
1
1
0
0
0
1
0
0
0
2
1
1
2
2
1
1
0
1
0
1
1
1
1
0
2
1
0
1
1
1
1
1
0
2
2
1
1
2
1
2
1
1
2
2
2
2
2
2
1
1
1
1
2
1
1
2
1
0
1
2
1
0
2
1
1
0
1
1
2
1
1
2
1
2
2
1
1
1
1
1
3
1
2
3
1
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
2
1
1
1
1
1
1
1
0
0
1
1
2
1
2
0
1
2
1
2
0
2
2
1
1
1
1
0
1
0
1
1
0
1
2
2
1
1
1
1
2
1
1
1
0
1
0
1
2
2
1
1
2
1
0
1
2
2
2
2
1
2
1
1
0
1
1
1
1
1
2
1
1
0
1
1
1
0
1
1
1
2
1
1
1
1
0
1
2
1
1
1
1
1
2
1
1
2
0
1
1
2
1
1
0
2
2
0
1
0
0
1
2
1
1
1
0
2
3
1
1
2
0
0
1
1
2
1
1
1
1
0
1
1
1
1
1
1
1
2
0
1
0
1
1
2
1
1
1
0
2
2
1
1
2
1
1
2
2
1
1
2
1
2
1
1
1
1
2
1
1
0
2
1
2
1
1
1
1
1
2
1
1
1
2
0
2
1
2
1
0
1
1
1
2
3
2
1
1
0
1
1
1
1
2
1
2
1
1
2
1
0
2
0
1
2
1
0
1
0
2
2
1
1
1
2
2
2
1
1
1
1
1
1
2
0
1
1
1
1
1
1
2
2
0
1
1
2
0
2
1
1
3
2
0
0
2
1
1
1
1
2
1
2
1
0
1
1
1
3
0
0
2
2
1
1
2
1
1
1
0
2
0
0
2
1
1
2
1
0
0
0
1
1
1
1
1
1
1
1
1
1
2
2
1
1
0
1
0
1
0
3
0
1
1
1
0
1
2
1
1
0
1
1
2
1
2
1
2
1
1
2
2
2
1
1
2
1
1
1
2
2
1
1
3
1
1
0
1
1
2
2
1
1
2
0
1
1
1
1
1
3
2
1
2
2
0
2
2
2
0
1
1
1
1
1
1
1
0
0
1
1
1
1
1
1
1
1
0
2
1
2
1
2
0
1
0
0
0
1
1
2
2
0
0
2
2
0
0
1
1
2
1
1
2
2
1
1
1
1
1
1
0
2
1
1
1
0
0
1
1
2
1
1
2
2
1
1
0
0
1
1
2
1
0
0
2
0
0
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
2
2
1
2
1
2
1
1
1
2
1
1
1
1
2
1
0
1
2
1
1
1
0
1
1
1
2
2
1
1
2
2
1
2
1
0
2
1
1
1
2
0
0
1
2
0
2
1
2
1
2
1
1
1
1
1
1
2
0
1
1
1
1
2
1
1
1
1
0
0
0
0
2
1
1
2
0
0
1
1
1
1
2
1
1
2
1
0
2
2
1
1
1
0
2
1
0
0
0
2
1
2
0
1
0
2
1
0
1
1
0
1
1
1
1
0
1
1
0
2
1
1
2
1
2
1
0
1
1
2
1
1
1
1
0
1
1
1
1
0
1
2
0
1
2
1
1
2
1
1
1
1
0
2
1
1
2
1
2
1
1
1
1
0
1
2
1
1
1
1
2
0
1
1
2
0
0
1
1
2
1
1
2
1
1
1
1
1
0
1
1
1
1
1
1
1
0
1
2
2
2
2
1
1
1
1
3
1
1
0
1
0
2
2
2
1
0
2
2
1
2
1
2
1
1
2
1
1
1
1
0
1
1
1
0
1
1
0
2
1
0
1
2
2
1
4
0
0
0
2
1
2
1
1
1
2
0
1
1
1
2
2
0
1
1
1
0
1
1
2
0
1
0
1
0
0
2
1
1
1
1
2
1
0
0
1
1
1
1
0
2
1
0
0
1
2
1
2
0
2
0
0
2
2
2
1
1
0
1
1
2
2
2
1
1
2
1
1
1
1
1
1
0
1
1
0
1
2
2
1
1
1
1
0
1
2
1
0
1
0
0
2
2
2
1
2
1
0
1
0
1
1
1
8
1
1
1
1
1
0
0
1
1
1
1
0
2
2
3
1
1
1
1
1
1
0
1
1
0
1
2
0
1
2
1
1
1
0
1
1
1
0
1
2
1
1
1
0
1
1
1
1
0
2
1
1
2
2
3
1
0
1
0
2
1
1
1
0
0
2
2
2
2
1
1
2
4
2
2
0
1
1
1
1
1
1
1
0
1
0
1
1
1
2
1
2
1
1
1
0
0
1
1
1
1
1
1
2
2
2
1
2
0
1
1
2
0
0
1
1
1
1
1
0
1
2
1
0
1
0
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
0
2
1
1
1
1
2
2
2
1
1
1
0
0
1
1
1
1
1
1
2
1
2
1
0
1
0
0
2
1
1
1
0
2
0
2
1
1
0
0
2
1
0
1
2
1
1
1
0
1
2
1
0
1
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
0
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
2
2
0
0
1
1
0
2
1
1
0
1
2
0
2
1
1
2
1
1
1
2
0
2
2
2
1
0
1
1
1
1
1
0
2
1
2
1
1
1
2
1
1
2
1
1
1
2
1
1
2
2
0
0
1
0
2
1
1
1
1
1
0
2
1
0
2
1
1
1
2
1
1
1
2
1
1
1
2
1
1
1
0
1
2
1
0
1
1
1
1
1
2
1
1
1
1
2
2
1
1
0
1
0
1
1
0
1
1
1
1
2
0
1
1
1
1
2
2
2
2
2
2
1
1
1
0
1
1
1
2
1
1
2
1
2
1
1
2
2
2
1
1
1
1
1
1
1
2
1
1
2
1
2
0
2
0
0
2
1
0
0
0
2
1
0
1
2
0
1
2
1
2
1
0
0
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
2
2
1
2
0
3
1
1
1
2
0
1
0
0
0
1
1
0
0
1
1
2
0
1
2
2
2
1
1
1
1
1
1
0
0
1
1
1
0
1
2
0
1
1
1
0
1
1
0
1
1
1
1
2
1
1
1
2
2
0
1
1
0
2
1
2
2
1
1
1
2
1
0
1
1
1
1
1
0
1
1
1
1
2
2
3
2
1
1
0
1
1
1
0
2
2
0
1
0
1
1
2
1
1
0
2
1
1
1
1
0
2
0
2
2
1
2
1
1
2
2
0
0
1
0
1
1
1
0
1
1
1
1
0
1
1
1
0
2
1
1
0
2
1
1
1
1
1
2
0
1
0
1
2
1
1
1
2
0
1
1
2
2
2
1
0
2
0
1
1
0
0
1
1
1
2
1
1
1
2
0
2
1
1
2
1
1
0
2
0
1
1
2
0
1
1
2
2
0
2
0
1
0
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
2
2
2
0
2
1
1
1
1
1
2
0
1
1
1
0
1
2
1
0
2
1
1
1
2
1
1
2
1
1
2
0
1
0
0
1
1
2
1
2
2
1
1
2
1
1
0
2
1
0
0
1
1
1
2
1
1
0
0
1
0
1
0
1
1
2
1
1
2
0
2
2
2
1
0
2
1
0
1
1
1
1
1
2
0
3
2
1
2
1
0
1
1
2
1
1
1
1
2
1
2
1
0
1
1
0
0
2
2
2
1
1
1
2
1
1
1
1
1
1
1
1
1
0
1
1
0
1
3
1
2
1
0
1
1
2
1
1
1
2
0
1
1
0
1
1
1
1
1
1
1
0
1
1
0
1
0
1
2
1
1
1
1
1
1
1
1
0
1
2
0
1
1
2
1
1
1
1
0
1
1
2
0
1
1
1
2
1
0
1
1
2
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
0
0
1
0
0
0
1
1
1
1
2
1
1
4
0
1
2
1
1
0
1
1
0
0
0
0
1
2
5
1
2
0
2
1
2
0
1
0
1
0
1
1
0
2
0
1
2
1
1
1
2
0
2
0
1
1
1
2
0
1
1
1
2
2
1
3
1
1
0
1
0
2
2
1
1
1
0
1
2
1
1
2
0
1
2
0
2
1
0
1
1
2
1
1
1
1
1
1
1
2
0
1
1
1
1
1
1
0
1
1
2
0
2
0
2
1
1
1
1
2
2
1
2
2
1
1
1
0
1
1
2
2
1
1
1
1
0
1
1
1
0
2
0
0
0
0
0
1
2
2
1
2
0
0
2
1
0
0
0
1
1
2
2
1
1
0
2
1
1
1
2
1
1
1
2
1
1
1
0
1
0
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
0
2
1
1
0
1
2
1
1
2
1
0
1
0
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
0
1
1
0
1
1
1
2
2
0
2
1
1
1
1
1
1
0
1
1
1
1
1
0
2
0
2
1
1
2
2
1
1
1
1
0
1
0
0
2
0
2
1
1
0
1
1
1
1
1
1
1
2
1
1
1
1
2
0
1
1
1
2
2
2
1
1
1
0
1
1
1
1
2
1
1
1
2
2
0
2
1
2
2
1
1
2
1
1
1
0
2
2
1
0
1
1
0
1
1
2
2
2
1
1
1
1
1
1
0
0
0
1
0
0
1
1
1
1
1
1
1
1
1
1
1
0
0
1
2
1
1
1
1
1
0
1
2
2
2
1
2
2
1
2
2
1
2
1
1
2
1
1
2
1
3
0
2
1
0
0
1
2
1
2
1
1
1
0
1
2
2
1
1
1
1
0
1
2
1
1
0
1
0
1
1
2
2
2
1
2
1
2
2
2
2
1
1
2
0
1
2
1
2
0
1
1
0
1
0
0
1
1
1
0
0
1
1
0
1
1
1
1
2
2
2
1
0
1
2
1
1
0
2
1
1
1
1
2
1
1
1
1
1
1
2
1
4
2
1
1
1
1
2
0
1
1
1
2
2
1
1
2
0
0
2
1
2
1
1
1
2
1
1
1
1
1
2
1
1
1
0
1
1
1
1
2
1
2
1
1
0
1
1
1
1
1
1
1
1
0
0
0
2
1
1
0
1
1
2
1
1
0
2
0
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
0
1
0
2
1
1
1
1
1
1
1
0
1
1
2
1
1
1
0
1
1
1
1
0
0
2
1
0
1
2
1
2
2
0
1
2
1
1
1
1
1
1
1
1
0
1
1
0
1
1
2
1
2
2
1
0
1
1
1
2
0
2
1
2
1
1
1
1
2
1
1
2
0
1
1
1
1
1
1
2
0
0
1
1
0
0
1
1
2
1
1
1
1
1
0
0
1
1
2
2
2
1
1
6
0
1
2
1
1
1
1
1
0
1
1
1
0
2
1
1
1
0
1
2
2
1
2
1
2
2
1
2
0
1
0
1
0
1
1
2
0
1
2
2
1
0
1
2
2
1
1
1
0
0
1
0
0
2
1
1
1
2
0
1
1
1
1
1
1
1
1
1
1
1
0
0
0
1
1
1
1
0
1
0
1
1
1
1
0
1
1
2
2
2
0
2
1
2
1
1
1
2
1
1
0
2
1
0
1
1
2
1
0
2
1
0
2
1
0
1
1
1
1
2
0
1
1
2
1
0
1
1
2
0
0
2
1
1
1
1
3
3
1
1
0
2
1
1
0
1
2
2
0
0
1
1
1
0
1
0
1
2
0
1
1
2
1
1
1
1
0
1
1
1
2
1
2
2
0
2
1
1
1
0
2
2
0
1
1
1
0
1
0
2
1
1
0
1
1
1
2
2
1
1
0
1
1
1
1
2
1
0
1
0
0
0
1
1
2
1
1
0
1
1
2
2
2
0
2
2
1
1
1
2
2
2
1
1
2
1
2
2
1
2
1
1
1
2
1
0
2
2
1
1
1
0
1
2
1
2
1
0
1
0
2
1
1
2
1
1
1
1
2
2
1
1
1
2
0
1
1
1
1
1
2
1
1
2
0
1
2
1
0
0
0
1
1
2
1
2
1
1
1
1
1
1
2
2
2
0
2
2
1
0
1
1
0
1
1
1
1
1
1
1
1
0
2
4
1
1
1
1
0
0
2
1
0
0
1
2
1
0
1
1
2
1
1
1
1
1
1
0
1
2
1
1
2
1
1
1
1
1
2
1
1
0
1
0
0
2
2
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
0
0
2
2
1
1
0
1
2
1
2
1
1
1
0
1
1
1
1
2
2
1
1
0
1
1
1
4
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
2
1
1
1
1
1
1
1
2
2
2
1
0
1
1
2
2
2
2
1
2
0
1
1
0
1
1
2
1
1
1
1
0
1
2
0
2
2
1
1
1
0
1
1
2
2
1
1
2
0
2
2
2
1
1
1
1
1
1
2
2
2
1
2
2
1
1
0
1
0
3
2
2
2
1
1
1
1
1
0
0
1
1
1
1
1
1
2
2
0
0
2
1
1
0
0
2
1
0
1
1
1
1
1
1
1
0
1
2
2
1
0
1
2
2
1
1
2
1
1
1
1
1
0
2
1
1
1
1
0
1
1
1
1
1
1
2
2
1
0
1
1
0
1
2
2
1
2
1
1
1
0
1
2
1
1
2
1
1
1
1
1
2
2
1
1
1
2
2
0
1
2
1
1
1
1
1
0
2
2
1
2
1
1
1
1
1
0
1
1
0
2
1
1
1
2
2
2
1
0
1
2
1
1
2
0
1
1
0
2
0
1
2
1
0
1
1
2
1
2
2
1
0
1
2
1
2
2
1
1
2
1
2
2
2
1
2
2
1
1
1
2
1
0
2
0
0
1
1
1
1
2
0
0
3
1
2
1
0
1
0
1
1
2
1
1
0
1
1
1
1
1
1
1
2
1
0
0
1
0
2
2
2
1
1
2
1
2
0
0
0
1
2
2
0
2
0
2
1
0
2
2
1
2
1
1
1
2
2
1
1
1
1
1
1
2
0
1
1
1
2
1
0
1
0
0
1
2
2
1
0
2
0
1
1
0
1
2
1
2
2
1
0
1
1
2
0
0
1
1
2
2
0
2
2
1
1
1
2
2
1
1
1
2
2
2
2
2
1
0
0
0
1
1
1
4
1
1
1
1
1
0
1
1
0
1
1
1
2
0
1
1
1
1
1
1
1
2
1
1
0
1
0
1
1
1
1
1
1
2
1
1
1
2
0
1
1
2
1
1
2
2
1
0
1
1
0
2
1
1
0
2
2
2
1
1
2
1
0
2
1
1
1
1
1
1
2
1
1
0
1
1
2
0
1
1
1
1
1
1
1
2
2
2
2
2
1
1
1
1
1
1
1
1
1
1
1
0
1
1
2
0
1
1
1
1
1
2
1
2
1
1
2
2
1
2
1
1
0
2
1
2
1
1
1
2
2
1
0
1
0
1
0
2
0
1
1
1
0
1
1
1
2
2
1
1
0
0
1
1
1
1
2
1
2
1
1
2
1
0
1
1
2
1
1
1
0
0
2
1
0
1
1
1
2
1
1
1
0
2
1
0
1
0
1
2
1
3
1
2
1
1
2
1
0
0
2
2
2
2
1
1
1
2
0
1
0
1
2
1
2
1
2
1
1
2
1
0
1
1
1
0
0
1
1
1
1
1
1
1
2
3
2
1
1
1
1
1
1
1
1
1
0
5
1
1
1
1
0
1
1
0
1
1
1
1
1
1
1
1
1
2
1
1
1
2
0
2
1
1
2
1
1
2
1
2
2
0
1
1
1
1
1
1
1
1
1
0
1
0
0
0
1
1
1
0
2
1
1
1
1
2
1
1
1
1
1
1
1
1
0
2
0
2
1
1
2
2
1
2
1
1
1
1
1
0
2
1
1
0
0
1
0
1
1
1
2
1
1
1
2
1
2
2
1
1
1
2
2
1
0
2
2
1
1
1
1
3
1
1
1
1
2
1
1
0
1
1
1
1
1
1
2
2
2
1
1
1
0
2
2
1
1
1
0
1
5
1
1
0
0
0
0
1
2
1
2
1
1
0
0
1
0
1
1
0
0
2
2
1
1
2
1
1
1
1
1
0
1
1
0
2
0
1
1
0
1
0
2
0
1
2
1
1
0
1
1
1
1
1
1
0
1
1
2
2
2
1
2
2
2
1
1
2
1
0
1
0
1
0
1
2
1
2
1
1
1
1
1
1
0
1
2
0
2
1
1
1
0
0
0
1
1
1
1
0
1
1
1
1
0
1
1
0
1
1
1
2
1
1
2
0
1
1
2
0
1
1
1
2
0
1
1
1
1
1
1
1
1
1
0
1
2
0
1
1
1
1
1
2
0
1
0
0
1
1
0
1
1
2
1
2
0
2
1
2
2
1
1
1
1
2
1
1
1
0
2
0
1
1
1
2
1
2
1
0
0
1
1
1
0
1
1
1
1
0
2
1
1
1
1
1
1
0
1
2
1
1
1
0
0
2
1
2
2
1
1
3
1
0
2
2
2
1
1
2
1
1
1
1
1
1
1
2
2
1
0
1
1
1
0
1
0
1
2
1
2
1
2
0
1
2
2
2
2
1
0
2
2
1
0
1
1
1
1
1
1
1
2
1
1
0
1
1
1
1
0
1
1
0
1
1
2
1
1
1
1
1
2
2
1
3
0
1
1
0
2
1
2
1
0
1
1
2
1
2
0
1
1
2
1
1
2
1
0
1
2
1
1
2
2
0
2
2
1
1
2
1
2
0
0
0
1
1
1
1
2
1
2
1
2
2
1
2
0
1
2
1
1
1
2
1
1
2
0
0
1
3
2
1
0
2
1
1
1
0
1
2
1
1
1
2
2
1
1
1
0
1
2
1
0
1
2
1
1
2
1
1
1
3
0
2
1
0
2
1
1
1
0
1
1
1
2
1
2
1
1
1
1
1
0
1
1
1
1
0
1
1
1
1
1
2
0
1
1
1
0
1
2
2
1
1
1
2
1
2
1
0
1
1
0
2
2
0
2
1
0
1
2
2
1
0
2
1
1
0
2
1
1
2
1
1
1
1
1
1
1
1
0
2
1
1
1
1
1
0
1
1
1
1
1
0
2
1
1
3
1
1
1
1
2
1
1
1
1
1
1
0
2
2
2
2
3
1
1
1
1
1
1
0
2
1
0
1
0
2
1
1
1
1
1
1
2
1
1
1
2
2
1
1
1
0
1
2
2
1
2
1
2
0
1
1
0
2
1
2
2
2
0
1
1
1
2
2
0
1
1
2
1
1
0
0
1
1
1
0
2
1
1
1
1
1
1
1
1
0
0
1
1
2
1
1
1
2
2
1
1
1
1
1
0
0
2
0
1
1
2
0
1
0
1
1
1
2
1
1
2
1
1
0
2
1
1
2
1
0
1
2
1
1
1
1
2
1
1
2
1
2
2
1
1
1
1
2
1
2
1
2
0
2
0
2
0
1
1
2
1
1
1
2
1
0
1
2
1
2
2
1
2
1
0
1
2
2
1
1
1
1
2
1
1
1
2
1
2
1
0
1
2
1
1
2
1
1
2
1
2
0
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
0
0
1
0
0
0
2
1
2
1
1
1
1
1
1
1
1
1
3
2
2
1
1
2
1
1
1
0
0
1
2
1
2
2
1
0
0
1
1
1
2
1
1
2
2
0
1
1
1
1
2
0
0
2
2
1
1
1
0
1
0
2
0
1
1
2
1
1
2
1
1
1
1
2
1
0
2
2
1
0
2
1
1
1
1
1
2
2
2
2
1
2
1
1
1
1
1
1
1
2
0
1
1
1
1
2
1
1
1
0
0
1
2
1
1
0
1
1
1
2
1
1
0
2
0
2
0
1
1
2
1
0
0
0
0
1
1
0
2
1
1
2
2
3
1
1
1
1
2
1
1
0
1
1
0
2
1
1
2
0
1
1
2
1
0
1
1
2
1
1
1
0
2
2
1
1
0
1
0
1
1
2
1
0
1
2
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
2
2
2
2
1
1
2
1
1
1
1
1
1
1
0
1
1
1
1
0
0
1
0
1
1
2
2
1
1
1
1
1
1
0
1
1
1
2
0
0
2
2
1
0
2
1
1
1
1
0
0
1
0
2
1
2
1
2
1
0
1
0
0
2
1
1
1
1
1
0
1
2
0
2
1
1
0
0
1
2
1
1
1
1
1
1
0
1
1
0
2
0
0
1
1
2
2
2
2
1
0
1
2
1
1
0
1
1
0
1
2
1
1
0
1
1
1
2
0
2
1
0
1
2
4
1
1
2
1
1
1
2
0
1
2
1
5
1
1
2
1
1
1
1
2
2
1
1
2
1
1
1
2
1
1
1
1
1
1
0
1
1
1
2
1
1
1
1
1
0
0
1
2
1
0
1
1
2
1
0
1
1
2
1
1
1
1
0
1
1
2
0
1
1
2
2
1
1
1
0
2
2
0
4
1
1
1
1
0
1
0
2
1
0
2
1
0
0
1
1
1
1
0
0
2
0
1
1
1
1
0
1
1
0
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
0
1
1
0
2
0
1
2
1
0
2
1
2
1
2
1
1
1
2
1
1
1
1
1
1
0
2
1
2
1
0
1
1
1
2
1
1
0
1
2
2
1
2
2
1
1
2
2
1
1
2
1
0
0
2
1
2
1
1
1
1
0
0
2
1
1
1
1
2
0
0
2
2
1
1
1
1
1
2
2
1
1
2
1
2
0
1
1
0
1
0
0
2
1
2
1
1
2
0
0
1
1
2
1
2
1
1
2
0
1
2
1
2
0
1
3
1
1
1
1
1
2
1
0
0
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
0
1
1
2
1
1
1
1
1
1
1
0
1
1
2
1
0
1
0
1
1
2
2
1
1
1
2
1
1
2
1
1
1
1
2
2
2
1
1
0
3
0
0
1
1
2
2
2
0
2
1
0
1
1
1
2
0
0
1
2
2
1
1
1
1
0
2
1
2
1
0
2
1
3
0
0
0
0
2
2
1
1
1
0
1
1
1
1
1
2
0
2
1
1
2
1
1
2
1
1
1
1
1
1
0
2
2
2
2
1
1
2
2
1
2
0
1
2
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
0
1
1
2
2
0
2
1
1
1
1
2
1
0
0
1
4
1
2
1
0
1
5
0
1
1
1
1
2
2
2
1
1
2
1
1
0
2
2
2
1
1
1
1
0
1
2
0
1
1
1
1
2
1
1
2
2
1
1
2
0
1
1
2
1
2
0
2
0
1
2
0
1
0
1
1
1
1
2
1
1
0
2
2
1
1
2
1
2
2
0
1
2
1
0
2
1
0
2
2
1
2
1
2
0
1
0
1
2
1
1
1
2
1
1
1
0
0
1
2
1
1
1
2
1
1
2
1
1
1
1
2
1
1
2
1
0
2
1
1
1
0
2
0
2
0
1
1
1
2
2
1
1
1
0
0
1
2
2
0
1
2
1
1
1
2
0
0
1
0
1
1
2
1
2
1
2
1
1
2
2
2
0
2
1
2
1
1
2
1
1
2
1
2
1
2
1
1
2
0
1
0
1
2
1
1
0
1
1
1
1
1
2
2
1
1
2
0
0
2
1
1
1
1
1
1
1
1
1
1
2
1
1
3
1
0
2
2
1
1
1
2
1
2
2
2
1
2
2
1
1
1
1
1
2
1
1
0
2
1
1
1
0
0
1
2
0
1
1
1
1
1
1
1
2
2
1
1
0
2
2
1
1
1
1
1
2
2
1
1
2
0
1
1
1
1
1
1
1
0
1
1
2
1
0
1
0
0
1
0
1
1
1
1
1
1
0
2
1
1
1
1
1
1
1
1
2
0
2
1
2
0
0
1
2
1
0
1
1
1
2
3
1
1
1
2
1
2
1
1
1
2
1
1
0
2
2
0
1
0
0
1
0
2
1
1
0
2
0
2
1
1
1
1
2
1
1
1
2
1
1
2
1
1
1
1
0
1
1
1
1
1
1
1
2
1
0
1
0
1
2
1
1
1
1
1
2
1
2
2
2
0
1
2
1
1
1
1
0
1
0
1
1
0
2
1
1
2
1
0
2
1
2
1
2
1
0
1
2
2
1
0
0
1
1
2
0
0
1
4
1
0
1
0
2
2
0
0
0
1
2
2
2
1
1
1
2
1
0
0
1
2
2
2
1
0
2
1
0
1
0
1
0
2
2
1
1
1
1
2
1
1
0
0
1
1
0
1
0
2
3
0
2
3
1
0
2
0
2
1
1
2
1
1
2
1
0
2
0
2
0
1
1
2
1
1
1
1
0
2
1
2
1
1
1
2
1
3
1
0
1
1
1
1
2
1
2
2
2
1
1
1
1
1
2
1
1
1
1
2
0
1
1
0
1
1
1
1
2
1
1
1
0
2
0
1
2
1
1
0
1
1
2
1
1
2
1
2
2
1
1
1
1
0
1
1
1
1
2
2
0
1
1
2
1
1
0
1
1
1
2
0
1
1
1
2
1
1
2
1
2
2
2
2
1
2
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
0
2
1
1
1
0
1
1
1
1
0
1
2
2
2
1
1
3
2
2
1
1
2
1
1
1
0
1
2
1
1
1
1
1
1
1
1
1
2
2
1
1
1
0
2
0
2
1
2
2
1
2
1
1
1
1
1
2
2
2
1
1
1
0
0
1
1
1
1
1
2
1
2
1
1
1
2
1
1
1
0
1
1
1
1
1
2
1
1
1
1
2
1
0
1
1
1
2
2
1
1
1
1
2
0
0
1
1
1
2
0
1
1
2
1
2
1
0
1
1
2
1
1
0
1
1
1
0
1
2
1
1
1
1
0
1
2
1
1
0
1
2
0
3
1
1
1
0
1
0
1
2
0
1
1
2
1
1
2
2
2
1
1
1
1
1
2
1
1
1
1
1
0
1
2
0
1
1
1
0
1
2
0
0
1
1
1
1
1
1
1
1
1
2
2
0
1
1
2
0
1
1
2
0
1
2
0
1
1
1
1
1
1
1
2
2
1
2
0
1
1
1
2
1
1
1
1
1
0
0
2
2
2
2
1
1
1
2
1
1
1
1
2
1
0
2
1
1
2
1
1
1
1
2
1
1
1
2
6
1
1
1
2
2
1
1
1
1
1
2
1
0
1
0
0
1
1
1
2
2
1
2
2
1
1
1
1
1
1
1
2
1
2
1
0
1
2
1
0
3
1
1
1
3
2
1
1
0
1
1
1
1
2
1
1
1
0
1
1
1
0
1
2
1
1
1
1
2
1
1
1
2
1
2
1
0
1
2
1
0
2
3
1
1
2
1
1
2
2
1
0
0
0
1
0
1
0
2
3
1
2
1
1
1
0
0
2
0
0
1
1
0
2
1
1
1
1
0
1
1
1
0
0
1
0
1
0
0
2
1
2
1
1
1
1
1
2
0
1
2
1
1
1
0
1
1
1
1
1
1
1
1
0
0
1
1
2
0
0
1
1
1
1
1
1
1
0
1
1
1
0
2
3
1
0
2
2
1
1
2
1
2
1
0
0
2
1
2
1
1
1
1
1
0
1
1
0
1
1
2
0
1
1
1
1
1
2
2
1
1
1
2
1
2
2
2
0
1
1
1
1
1
0
1
1
1
1
2
1
0
2
1
2
1
2
0
1
1
2
0
1
0
1
1
2
2
0
1
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
2
0
1
0
1
0
1
1
1
2
1
2
1
1
2
1
1
1
1
2
2
1
1
0
1
2
2
1
1
2
2
3
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
2
2
0
1
2
1
2
0
2
1
1
1
1
1
1
1
1
0
2
1
1
1
1
1
1
1
2
0
1
2
2
2
1
0
1
2
2
0
1
1
0
1
1
1
1
2
2
2
1
1
2
2
1
2
0
1
3
0
1
1
0
2
1
1
1
2
1
2
1
1
2
1
2
1
1
2
2
2
1
1
1
1
1
0
1
1
2
1
0
1
1
1
1
1
1
1
0
0
1
2
1
2
1
1
0
0
1
1
0
2
1
1
1
0
1
2
1
1
1
1
2
1
1
1
0
0
1
2
3
1
1
0
2
2
1
1
1
1
1
1
1
1
2
1
1
1
0
1
2
1
1
2
1
1
1
1
1
1
1
2
1
1
0
2
0
1
2
0
0
2
1
1
1
0
1
1
1
1
0
2
2
1
1
1
1
2
1
1
1
2
0
0
2
1
1
1
1
1
2
4
2
2
1
0
2
1
1
1
1
3
0
1
1
1
0
1
1
1
0
1
1
1
1
1
0
1
2
2
1
1
1
1
1
1
1
1
1
1
1
0
1
1
0
1
1
1
2
1
1
0
1
2
1
1
2
2
1
2
1
0
0
1
2
0
1
3
1
1
1
1
1
1
1
2
2
1
1
1
2
0
2
2
1
0
2
2
0
2
1
1
1
1
1
1
1
0
2
1
1
2
2
1
0
1
1
1
1
0
0
1
0
1
1
0
2
1
1
0
1
0
1
1
0
0
2
2
2
0
0
1
1
1
0
2
2
1
1
1
2
1
1
0
2
1
1
1
1
2
1
1
1
1
1
2
1
2
2
2
1
0
1
2
2
1
0
2
2
1
1
1
3
1
0
1
2
1
1
2
1
1
1
1
3
1
1
0
2
1
1
0
1
1
1
2
0
2
1
1
1
1
1
1
0
1
1
1
2
1
1
1
0
1
1
2
1
1
1
0
0
1
2
1
2
2
0
2
2
1
1
1
2
1
2
1
1
2
1
1
1
1
1
1
1
1
1
0
1
1
0
0
1
1
1
0
2
1
1
1
0
1
2
1
1
1
0
1
0
1
1
0
2
1
1
0
2
2
1
1
0
1
1
0
2
2
1
1
2
1
2
2
1
1
1
1
2
1
1
0
0
1
1
1
2
1
1
0
1
1
1
2
1
1
2
5
0
1
1
0
2
2
1
2
1
1
3
0
2
1
3
0
1
1
1
0
0
2
1
1
1
1
1
2
1
1
1
2
0
2
1
1
2
1
1
0
0
1
0
1
1
1
1
1
2
1
1
1
1
0
1
0
1
1
1
0
1
1
2
0
1
2
1
2
1
1
1
1
1
1
1
1
0
0
0
1
1
1
1
1
2
0
2
0
2
0
1
2
1
1
1
1
2
1
1
1
0
0
0
1
1
1
2
1
2
2
2
1
1
1
1
1
0
1
0
2
0
1
0
1
2
1
0
1
1
2
1
0
2
1
1
1
2
2
1
2
2
1
1
1
2
0
1
1
1
2
1
1
1
1
1
0
1
1
1
2
1
1
2
1
2
0
1
1
1
1
1
0
2
0
2
1
1
2
1
1
2
1
2
1
2
2
1
1
0
2
1
0
1
1
1
1
1
2
1
1
1
2
1
2
2
2
0
1
0
2
1
1
1
2
1
0
1
1
1
1
1
0
1
0
2
1
1
1
1
1
1
0
0
1
2
1
2
0
1
1
1
2
1
1
1
2
1
2
2
1
1
1
1
1
1
1
0
1
1
1
2
2
0
1
1
1
1
1
1
1
2
1
1
0
2
1
3
1
1
0
2
1
1
1
1
1
2
0
1
1
0
2
1
1
0
0
1
1
3
0
2
2
0
0
2
1
1
2
1
2
1
0
1
1
1
2
2
1
1
1
2
1
1
1
1
1
0
1
1
1
1
2
1
1
1
2
1
0
1
1
1
2
0
1
1
0
0
1
1
1
1
1
1
1
1
1
0
1
1
0
1
0
1
1
1
1
1
2
1
0
2
1
0
2
1
1
1
1
0
2
2
0
1
1
1
1
2
1
1
1
1
1
0
2
1
1
1
2
1
1
2
1
1
2
1
1
1
2
0
1
2
1
1
1
2
2
1
1
2
0
2
2
1
1
1
2
1
1
2
1
1
1
1
1
1
2
0
1
0
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
0
2
1
1
1
1
1
1
2
2
2
1
1
1
0
1
1
1
1
1
1
1
1
0
2
1
2
1
1
1
1
2
2
1
2
1
1
2
1
2
1
1
2
0
1
1
1
0
1
2
1
1
1
1
0
1
1
0
1
2
2
1
1
1
1
1
2
2
0
2
1
1
2
0
4
1
2
1
0
2
1
1
1
1
1
2
1
2
1
2
0
1
2
1
0
1
0
1
1
1
2
1
3
2
1
2
1
1
1
1
2
1
2
4
2
2
2
1
1
3
1
1
0
1
1
2
1
1
1
2
1
1
0
1
1
2
0
1
1
1
1
1
1
2
1
1
1
1
2
2
1
1
1
1
1
1
0
2
0
1
2
1
2
3
1
2
1
1
1
3
1
2
0
1
2
1
1
1
1
1
1
2
2
0
1
2
2
1
2
0
1
0
0
1
1
0
0
0
1
1
1
1
1
2
1
0
2
2
2
1
1
1
1
1
2
2
1
1
1
2
2
1
2
1
1
1
0
0
0
1
1
1
0
1
1
1
1
0
0
0
0
2
0
1
2
0
1
2
1
1
1
2
1
2
1
2
0
2
0
0
1
1
2
1
1
1
1
1
2
2
1
1
1
0
2
0
0
1
1
1
2
2
1
2
1
0
2
1
1
2
1
0
0
1
1
1
1
2
2
0
1
2
1
0
1
0
2
1
1
1
1
2
2
1
1
1
1
0
1
1
1
2
0
2
2
2
2
2
0
1
1
1
1
2
1
2
2
1
1
1
1
1
1
1
2
2
1
1
0
1
1
0
0
0
1
2
1
1
1
1
1
1
2
2
1
1
1
1
2
1
1
0
1
1
2
1
2
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
2
1
0
2
2
0
0
0
2
1
3
1
0
3
2
1
0
1
1
1
0
2
2
2
1
1
0
0
1
0
1
1
0
0
0
1
1
1
1
1
1
1
1
1
1
0
1
1
0
2
1
0
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
0
1
0
2
0
1
0
1
1
1
1
1
1
1
1
1
0
1
1
0
1
1
1
1
1
1
1
1
0
1
2
1
1
1
2
2
1
0
1
0
1
1
0
1
1
1
1
1
1
0
1
1
1
1
0
2
1
2
0
2
1
1
1
1
1
2
2
1
1
0
2
1
1
2
1
1
1
2
2
2
0
1
2
1
0
2
1
1
2
1
1
1
2
0
0
0
1
1
1
1
2
2
1
1
1
2
2
1
2
1
1
1
1
1
0
1
2
1
1
2
1
1
2
1
1
2
1
0
1
1
1
1
1
2
2
0
1
1
1
1
1
2
1
1
1
2
1
1
1
2
2
1
2
1
2
1
1
2
0
1
1
1
1
2
2
1
1
0
1
1
1
1
1
1
0
1
2
0
2
2
0
0
1
1
2
2
0
1
1
2
1
1
1
0
0
2
1
1
2
0
2
2
1
1
1
0
1
1
1
0
1
1
1
1
1
0
0
1
1
1
0
1
2
1
1
1
0
1
0
0
2
2
1
0
0
1
0
3
1
1
2
2
1
2
1
1
1
1
0
1
2
2
2
1
1
1
1
1
0
1
2
1
2
1
1
1
2
1
0
3
1
2
1
0
1
0
2
1
0
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
0
1
2
2
1
1
2
1
1
1
1
0
2
2
1
0
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
0
0
0
1
2
1
1
0
1
2
1
1
1
1
2
1
1
1
1
1
2
0
2
1
2
1
1
2
1
1
1
2
2
0
1
1
1
1
1
1
1
1
3
2
0
1
2
1
1
2
1
2
1
1
1
2
1
0
2
1
1
1
1
2
1
1
1
1
1
2
1
2
2
2
1
1
1
1
1
1
1
0
1
1
2
2
1
2
1
1
0
1
1
0
1
0
1
1
2
1
0
1
1
0
1
1
0
1
2
1
0
0
0
0
2
1
1
1
0
4
1
0
0
2
2
2
1
1
2
2
1
1
1
1
1
1
2
0
1
1
0
1
1
1
1
1
2
2
1
0
1
1
1
1
1
1
1
1
1
1
2
3
1
0
1
1
1
1
1
2
1
1
0
1
1
1
1
2
2
1
1
2
3
1
1
0
1
1
1
1
1
1
1
1
1
1
1
4
1
2
1
1
0
1
2
2
1
1
2
2
1
1
1
2
1
2
1
1
1
0
1
1
1
1
0
1
2
0
1
1
1
1
2
1
1
1
1
1
1
3
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
2
1
2
1
1
1
1
1
2
0
2
2
2
2
0
0
1
2
1
1
0
0
1
1
1
1
1
1
1
4
1
1
0
1
1
1
1
2
1
1
0
2
0
2
0
1
1
2
1
1
0
1
1
2
1
0
1
1
1
2
0
1
1
1
2
1
1
2
0
1
0
1
4
1
3
2
1
1
0
1
1
1
2
1
0
2
0
0
1
1
2
0
2
1
2
0
1
1
1
1
1
1
2
0
0
1
1
1
1
1
1
1
1
0
1
2
2
1
0
1
1
1
2
0
0
1
1
3
0
1
1
1
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
2
0
2
1
0
1
1
1
0
2
1
1
0
0
1
1
1
1
1
1
1
1
2
1
1
0
1
1
0
2
0
0
2
1
2
1
2
1
1
1
1
0
1
2
0
1
1
2
1
1
1
1
1
1
1
0
2
1
2
1
1
2
0
0
2
0
1
2
1
1
2
1
2
1
2
1
1
1
1
1
2
0
1
1
1
0
1
1
1
1
2
4
2
0
0
0
1
1
1
2
1
0
0
0
1
1
0
1
0
1
0
1
1
1
1
0
1
1
0
1
1
2
2
1
1
1
0
1
1
2
2
2
2
1
1
1
2
2
1
0
2
1
1
1
1
1
2
2
3
1
1
1
1
1
0
0
1
3
1
1
0
0
0
1
2
2
1
1
1
2
1
1
0
0
1
1
1
0
1
2
2
2
1
0
1
1
1
1
1
0
1
1
1
1
0
0
1
1
1
1
2
1
2
1
2
1
1
1
1
1
1
1
2
0
2
2
1
0
1
1
1
1
2
1
1
2
0
2
0
0
1
0
1
1
2
1
1
0
2
2
1
1
1
1
2
2
2
2
2
1
2
0
1
2
2
1
0
2
1
2
1
1
2
1
2
1
1
1
1
0
0
1
1
1
2
1
1
1
0
2
2
1
2
1
1
1
1
0
0
2
1
2
0
2
1
1
0
1
2
2
1
2
1
1
1
2
1
1
1
2
1
1
0
2
1
1
2
1
2
1
1
2
2
3
1
0
2
2
2
0
1
0
2
1
0
1
1
0
2
1
0
2
1
0
0
1
1
1
2
2
1
1
1
1
0
2
1
0
2
1
1
2
2
1
2
0
1
1
2
1
1
1
2
0
1
1
1
3
1
2
1
1
3
1
1
0
0
1
1
2
0
2
1
1
1
1
1
0
1
2
0
1
2
1
0
1
1
2
1
1
1
2
1
0
1
0
2
0
1
0
1
0
0
2
1
1
2
0
1
0
1
0
2
2
1
2
2
1
1
1
0
2
1
1
1
1
2
1
0
1
1
1
1
1
2
1
0
2
1
2
1
1
2
1
2
0
1
2
0
1
0
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
0
1
1
1
0
1
1
0
0
1
0
1
1
0
1
1
1
2
2
1
0
0
0
1
1
1
1
0
1
1
0
1
2
1
2
1
2
1
2
1
2
0
1
0
2
2
2
2
1
2
1
2
1
1
1
1
2
0
0
2
1
1
1
2
1
0
1
2
2
1
2
1
1
1
0
1
1
1
2
2
1
1
1
1
1
1
1
2
0
1
1
1
1
1
1
1
2
2
4
2
1
1
1
1
1
1
0
1
1
1
0
0
1
1
1
1
1
1
2
2
1
1
1
1
0
2
1
1
1
1
1
1
1
0
1
1
2
2
1
0
1
1
2
1
1
1
1
0
2
2
3
2
0
1
1
1
0
1
2
2
2
1
1
0
0
2
1
1
2
3
0
1
1
1
1
1
0
1
1
2
1
2
1
1
1
1
1
1
2
2
2
2
1
1
2
1
3
1
1
1
1
1
1
2
2
2
2
1
2
1
4
1
1
1
1
1
1
2
3
2
1
1
1
1
1
0
2
1
0
0
2
0
2
1
1
1
2
1
1
2
2
2
0
1
1
0
1
1
1
1
0
1
1
2
1
0
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
0
1
1
2
1
0
1
0
1
1
0
1
0
0
1
1
1
2
0
0
2
1
0
1
0
0
0
0
2
1
2
1
1
1
1
1
1
1
0
2
0
1
1
1
1
1
0
2
1
1
1
2
1
1
1
1
1
1
0
1
2
0
1
1
1
1
2
1
1
2
1
1
1
1
2
2
1
1
1
1
0
2
2
1
1
1
1
0
0
0
1
0
1
2
1
1
2
1
1
2
0
0
2
1
0
1
1
1
2
1
1
0
1
2
2
2
1
2
1
1
1
0
1
0
2
1
0
2
1
1
2
1
0
0
2
2
2
1
1
2
0
1
1
1
2
0
2
2
0
2
0
0
2
1
1
1
1
1
2
1
1
1
1
2
2
1
0
1
0
2
2
1
2
0
1
1
0
1
1
1
2
0
1
1
1
1
1
1
2
0
1
1
1
1
0
1
1
1
1
1
0
1
2
0
1
1
2
1
1
2
1
1
1
1
2
1
1
0
2
1
1
1
1
0
0
0
2
1
1
0
0
1
1
1
2
1
1
1
0
2
1
2
1
1
1
0
1
1
2
1
0
2
1
2
1
1
1
2
2
1
2
1
1
1
1
1
0
0
1
1
1
0
2
1
2
1
0
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
1
1
2
1
0
1
3
1
1
1
1
1
2
1
1
1
1
2
0
1
0
1
1
1
1
1
2
1
1
1
2
2
2
1
1
1
1
1
2
2
2
1
1
1
2
1
1
1
2
1
2
1
1
2
1
1
2
1
2
1
1
3
1
0
1
1
1
1
1
1
1
1
2
1
2
0
1
1
1
0
2
1
1
1
2
1
1
2
1
1
3
1
1
1
1
1
1
1
1
2
1
1
1
1
2
0
2
1
1
1
1
2
2
2
1
1
0
1
1
1
0
1
1
1
1
1
2
2
1
0
0
1
1
1
2
1
1
2
1
1
1
1
2
2
0
1
0
1
1
0
1
1
0
0
1
2
0
1
2
1
2
1
2
2
1
1
2
1
0
1
2
0
2
2
1
2
1
1
1
1
1
1
2
2
1
2
1
0
1
1
1
2
0
1
2
2
1
1
2
1
1
1
2
1
1
1
0
2
3
0
1
1
1
1
0
1
1
0
1
1
2
1
2
1
1
1
1
0
1
0
2
2
1
2
1
1
2
1
2
2
1
2
1
2
1
1
1
1
0
2
0
1
1
0
1
1
1
1
1
1
1
2
1
2
1
1
1
2
1
1
2
1
2
1
0
2
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
0
1
2
2
1
2
2
1
1
0
1
1
2
2
1
1
2
1
1
0
1
0
2
2
1
2
2
2
3
1
1
1
1
1
1
2
1
1
1
2
0
0
1
1
1
1
0
1
1
2
1
1
1
1
1
0
2
0
2
2
1
1
2
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
2
1
1
1
1
1
1
2
2
1
2
2
2
1
0
0
2
1
2
0
0
0
1
1
1
1
1
1
1
2
0
2
2
1
1
1
1
2
0
2
1
1
1
1
1
0
1
0
3
1
1
1
1
1
1
1
2
1
1
1
1
1
1
0
3
0
1
1
2
2
1
2
2
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
1
2
1
0
2
1
1
1
2
1
2
1
1
1
1
1
0
1
1
0
1
2
1
2
1
2
2
1
2
2
2
0
1
1
1
2
1
1
0
1
1
0
1
2
1
1
2
1
2
1
2
1
2
2
1
2
1
1
0
0
0
1
1
2
2
1
0
1
0
1
0
1
2
2
1
1
2
1
1
1
1
1
2
2
1
1
2
1
1
1
1
1
1
0
2
1
0
1
1
1
1
2
1
1
2
1
2
1
0
0
1
2
1
1
1
1
1
1
1
1
1
1
0
1
0
1
2
3
1
1
1
1
1
1
1
1
1
0
2
0
0
1
1
2
1
1
1
2
1
0
3
2
1
0
1
1
1
1
1
1
1
1
2
0
2
1
1
1
2
1
2
0
1
2
1
1
1
0
1
2
1
3
0
1
1
0
1
1
1
1
1
0
1
1
2
1
1
0
1
1
2
0
2
2
0
1
1
2
1
2
2
1
2
1
0
1
2
1
0
1
1
1
2
0
2
1
0
1
1
1
0
1
1
2
1
1
2
1
1
1
1
1
2
1
1
0
0
1
1
1
0
2
1
2
0
1
2
1
1
1
0
1
1
1
1
1
2
1
0
2
1
2
0
0
1
1
2
1
1
1
0
2
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
0
2
0
2
1
0
1
0
1
1
1
1
2
0
1
1
1
1
1
1
1
0
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
2
2
1
2
2
1
2
2
1
1
2
1
0
0
1
1
1
1
1
1
1
1
0
2
1
2
1
2
1
2
2
1
2
1
1
1
2
1
1
0
1
1
1
2
1
1
2
1
1
0
1
1
1
2
1
1
0
1
1
1
1
0
2
1
1
1
1
0
0
1
1
2
1
1
2
1
1
1
1
2
1
1
1
1
0
2
1
1
2
0
1
2
1
1
0
1
0
0
2
1
1
1
2
0
1
2
1
0
2
0
2
1
1
0
0
1
1
1
2
1
2
1
0
0
2
1
1
1
0
1
1
1
1
0
1
0
0
2
2
0
0
1
1
2
1
1
1
1
2
1
2
1
2
1
2
2
0
1
1
1
2
1
1
1
2
1
0
1
1
2
2
1
1
1
1
2
0
1
1
2
1
2
0
0
1
0
1
1
1
2
1
1
0
1
2
1
1
1
1
3
1
1
2
1
0
2
2
0
0
0
1
1
0
1
0
1
2
1
0
1
1
2
1
1
1
1
2
1
1
2
1
1
1
2
1
0
1
1
1
0
1
1
1
1
0
1
0
2
2
2
2
2
1
2
0
2
1
1
1
1
2
1
2
5
0
1
1
1
1
1
1
2
4
0
1
1
1
0
2
1
1
1
0
0
1
1
0
1
1
2
2
1
0
1
2
1
0
2
1
1
2
0
2
2
2
1
1
1
2
1
0
1
2
2
1
0
2
1
1
2
2
1
1
1
1
2
1
1
1
0
2
2
1
2
1
0
0
1
1
2
1
0
1
2
1
1
1
1
2
1
1
0
0
1
1
1
0
2
0
2
1
1
1
1
1
2
1
2
1
1
2
1
1
1
2
0
2
1
1
1
1
0
1
1
2
1
1
1
1
1
1
2
2
0
3
1
2
1
2
1
0
0
1
1
1
1
1
1
1
2
1
1
1
1
0
0
1
1
1
1
1
1
1
0
1
1
1
2
1
1
1
0
1
0
1
1
2
1
1
1
1
2
2
1
1
2
1
1
0
1
0
1
2
1
2
0
2
2
1
0
1
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
2
1
1
2
2
2
2
1
1
2
1
2
2
1
2
1
1
1
1
1
2
1
0
1
1
1
0
1
1
1
1
1
2
1
1
2
2
1
1
1
1
0
1
1
1
2
0
3
0
0
1
1
2
2
1
1
0
1
2
2
1
1
1
1
1
0
2
1
0
2
1
2
1
1
1
1
0
1
1
1
1
1
1
1
2
1
2
0
1
2
1
1
1
1
1
1
1
2
0
1
2
1
1
1
2
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
2
1
1
2
1
0
1
0
1
1
1
1
1
1
2
1
2
1
0
0
2
0
1
0
1
1
0
2
1
1
1
1
2
1
2
2
1
0
1
1
1
1
1
1
1
0
0
1
2
0
1
1
1
1
2
1
1
0
2
1
1
2
0
2
0
1
1
1
1
1
1
1
1
0
1
1
0
1
2
0
0
2
2
0
1
1
2
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
0
1
2
1
1
1
0
1
1
0
1
1
2
1
1
2
1
1
0
1
1
1
1
0
0
2
2
1
2
2
1
1
1
2
2
1
1
0
0
2
1
1
1
1
0
1
1
0
1
1
1
2
1
1
1
2
0
1
2
2
2
0
1
1
1
1
2
2
0
1
2
2
1
1
2
2
1
1
0
2
3
1
0
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
0
1
2
2
1
1
1
0
1
1
1
2
1
1
1
1
1
0
1
1
1
2
1
0
1
0
1
2
2
1
1
1
0
1
0
1
0
1
1
1
0
1
0
2
2
0
0
1
2
1
1
1
2
2
0
1
1
1
2
1
2
2
1
2
2
2
2
2
0
2
2
1
1
1
2
2
2
1
1
1
1
1
0
0
1
0
2
1
0
0
1
1
1
1
2
1
1
2
0
1
2
1
2
1
1
1
1
1
1
1
2
1
3
0
2
1
1
2
1
2
3
1
0
1
1
1
1
1
1
0
1
1
2
1
2
1
1
2
2
1
1
1
2
2
1
1
1
1
1
1
0
0
0
0
2
1
1
1
2
1
1
2
1
2
2
2
1
0
2
2
0
1
0
2
1
1
0
1
1
1
1
0
1
2
1
0
1
0
2
1
1
2
1
2
1
1
1
0
1
2
2
1
1
2
1
1
0
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
0
2
2
2
0
0
1
1
1
1
1
1
0
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
1
1
1
2
0
1
2
2
1
1
1
0
1
2
1
1
1
2
1
0
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
0
2
0
2
0
2
1
1
0
1
0
1
1
1
0
1
2
1
2
0
1
3
1
1
2
1
1
1
2
2
1
1
1
1
2
3
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
2
0
1
1
1
0
1
1
2
1
2
2
1
1
1
1
0
0
1
2
2
2
1
2
1
0
2
2
0
1
2
1
0
0
1
1
1
0
0
2
2
1
1
0
1
2
0
2
2
2
1
2
1
2
1
1
2
2
1
0
0
1
1
1
0
1
1
1
1
1
1
1
2
0
1
4
1
1
1
1
1
1
0
1
2
1
1
0
1
1
1
2
1
2
1
2
1
1
1
1
0
2
1
1
1
1
1
0
1
1
1
1
0
2
1
1
2
2
2
1
0
1
1
1
1
2
2
1
2
1
1
1
0
1
1
1
2
1
0
3
2
0
0
1
1
2
2
1
1
1
1
0
0
0
1
2
0
1
2
1
0
1
2
3
2
1
2
1
1
1
0
1
1
2
1
1
1
2
1
1
2
2
1
2
1
2
1
2
2
0
1
2
1
1
1
1
0
1
2
1
1
1
1
1
0
0
1
1
1
1
2
1
0
1
1
0
1
2
1
2
1
2
0
2
1
2
2
0
2
0
1
0
2
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
0
0
1
2
1
1
1
1
2
0
1
2
1
0
1
0
1
1
1
0
1
1
1
0
1
1
1
1
0
1
1
0
1
1
1
1
1
2
1
2
2
1
1
1
1
1
1
1
0
1
1
0
1
1
1
2
1
0
1
1
3
1
1
0
0
1
0
1
1
2
1
3
2
0
1
1
1
0
2
1
1
0
1
2
1
1
0
1
1
2
1
1
0
1
2
0
1
1
0
1
2
1
2
1
2
1
1
1
2
1
1
0
1
2
0
1
1
1
1
3
1
2
0
0
2
1
1
2
1
1
1
1
1
2
1
2
0
1
2
1
2
1
1
2
0
1
0
1
0
1
0
1
0
2
1
1
1
1
2
2
1
1
1
2
0
1
2
1
1
1
0
1
1
1
1
0
1
1
2
0
1
1
2
2
2
1
2
0
0
1
1
0
1
1
4
0
1
0
1
2
1
1
1
2
1
2
1
1
1
1
2
1
1
1
1
1
2
2
2
0
1
1
1
1
1
0
2
1
0
1
1
1
1
2
1
1
2
1
2
0
0
0
1
1
1
2
0
0
1
2
2
2
1
2
2
1
5
2
1
0
2
1
1
0
2
1
1
2
2
1
1
0
1
2
3
0
1
1
1
1
0
0
1
1
1
0
0
1
1
0
2
1
0
2
1
0
1
2
1
1
1
1
0
2
1
2
1
1
1
1
2
1
1
1
1
1
4
1
0
1
0
0
1
1
2
1
1
0
2
1
1
0
0
1
1
1
1
0
1
1
1
0
1
1
1
2
1
1
1
1
1
0
1
2
1
1
1
1
0
1
2
1
1
0
1
1
0
0
1
2
1
2
1
1
1
2
0
1
1
2
0
2
1
1
1
2
2
1
0
2
1
1
1
0
0
2
0
0
1
1
0
1
0
2
2
2
1
1
0
2
0
1
0
1
0
1
0
2
1
0
1
1
2
1
2
1
1
1
1
2
1
0
2
1
1
0
1
1
1
1
1
1
0
1
1
1
0
1
1
1
1
0
1
0
2
1
1
2
1
1
2
1
1
1
0
1
1
1
1
1
0
0
1
1
2
1
1
1
2
2
0
1
1
2
1
1
2
1
1
0
1
1
3
1
3
0
0
1
1
2
1
2
1
1
1
1
1
0
2
1
1
0
1
1
2
2
1
1
1
1
0
2
2
2
1
1
2
1
0
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
2
0
2
0
1
2
1
2
1
0
2
1
1
2
0
1
1
2
1
0
0
1
2
1
2
4
1
1
1
1
1
0
0
1
1
0
1
1
0
1
2
1
2
1
0
1
0
1
1
1
2
0
0
2
0
0
2
0
2
1
1
1
1
2
2
0
1
2
0
1
2
1
0
1
1
2
1
1
2
1
1
0
1
2
1
1
1
2
0
1
1
1
1
1
0
1
1
2
1
0
1
1
1
2
2
1
2
0
1
2
1
2
1
1
0
2
2
1
1
1
2
1
1
1
1
0
1
1
1
0
2
0
1
0
2
1
1
1
0
1
1
2
1
0
1
0
2
1
0
0
2
1
1
2
1
0
1
1
1
2
0
2
2
2
0
1
1
2
1
1
1
2
1
2
1
2
1
0
2
1
1
1
0
1
0
2
1
2
1
1
2
1
2
0
2
1
1
2
1
0
0
1
0
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
0
2
1
1
1
1
1
0
2
0
1
0
1
0
1
1
1
0
1
2
0
1
0
0
0
1
2
1
0
1
2
1
1
1
1
1
1
0
1
0
2
1
1
1
2
3
1
1
1
2
1
1
1
1
2
1
2
1
2
1
1
1
2
1
1
1
2
0
2
2
1
1
1
2
1
1
0
0
1
2
1
1
0
3
1
1
2
1
0
1
1
2
2
1
1
0
0
1
1
1
2
2
2
1
0
1
1
1
1
1
1
2
0
1
1
1
2
1
2
1
1
1
0
3
0
1
1
1
1
2
1
1
2
0
1
2
2
1
2
0
2
3
2
1
2
1
1
1
1
2
1
0
1
2
1
0
2
2
1
2
1
1
1
2
0
1
1
1
0
1
2
2
1
1
1
1
1
1
1
0
1
0
0
2
1
1
2
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
0
0
2
1
1
1
0
1
1
1
1
2
1
0
2
0
1
2
0
0
1
1
1
1
2
1
1
1
0
1
1
0
1
1
1
2
2
1
0
2
0
1
2
1
0
2
1
2
1
2
0
1
1
1
4
1
2
0
1
1
0
1
0
2
0
1
1
2
1
1
1
1
1
1
1
2
1
1
2
0
1
1
0
0
1
1
1
1
2
1
0
1
1
2
1
1
2
1
2
1
1
0
1
1
1
1
1
1
1
2
1
1
0
1
1
1
1
1
2
1
1
1
1
1
2
1
1
2
2
1
0
1
2
1
0
0
1
2
1
1
1
1
0
1
2
1
2
0
1
0
2
0
1
1
1
1
1
1
1
1
2
2
2
1
1
1
0
1
2
0
1
2
0
0
1
1
1
1
2
2
2
1
0
1
1
2
0
1
2
0
2
1
1
0
1
1
1
0
0
1
1
0
1
0
1
2
1
1
1
2
1
2
2
0
1
2
2
0
1
1
1
2
1
0
2
1
1
1
1
1
2
0
2
1
2
1
1
1
1
1
1
2
1
0
0
0
1
2
1
2
2
1
0
2
1
1
1
1
1
1
1
1
0
2
1
1
1
2
2
1
2
2
2
1
2
1
1
2
1
1
1
1
1
1
0
1
2
1
1
0
1
1
0
2
1
1
1
1
0
1
1
1
1
1
1
1
1
1
2
0
2
2
1
1
1
0
1
0
1
1
0
0
1
1
0
1
1
1
1
1
1
1
1
2
1
1
1
0
1
2
1
2
0
2
1
1
1
1
1
0
1
1
2
2
1
1
1
1
0
0
1
2
1
2
2
2
1
1
2
1
0
0
0
1
1
0
1
1
0
1
2
1
0
0
2
1
0
1
2
0
2
1
1
1
1
1
1
1
3
2
2
1
1
1
2
2
1
1
1
1
1
2
1
1
1
0
1
2
1
1
1
2
0
1
1
0
1
2
1
1
1
1
1
1
0
2
0
1
2
1
1
2
1
2
1
2
0
1
1
2
1
0
1
0
0
1
2
2
1
1
0
0
1
1
2
1
2
2
1
2
1
1
2
2
2
1
1
1
1
0
2
2
1
0
1
1
1
0
0
0
1
0
0
1
2
1
2
1
4
1
1
1
1
1
1
0
0
1
1
1
2
0
0
2
2
1
1
0
1
1
1
0
1
1
1
1
1
1
2
1
1
2
0
1
1
1
1
1
2
2
0
1
1
1
2
1
2
2
0
2
1
1
1
1
1
1
1
1
2
2
0
1
2
1
1
1
1
1
1
1
0
2
1
0
2
1
1
1
2
2
1
2
2
1
2
1
2
1
0
0
3
2
1
1
1
1
1
1
1
1
1
0
1
1
0
2
2
2
0
1
0
2
1
0
1
1
2
2
1
1
0
3
1
0
1
1
2
1
0
2
1
1
1
1
0
0
1
1
1
1
1
2
1
2
2
1
1
1
2
1
1
1
1
1
0
2
2
1
2
1
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
0
2
2
2
1
2
2
2
1
1
0
2
1
2
1
1
1
0
0
2
1
0
1
2
2
1
2
2
1
1
1
1
1
1
1
1
3
1
1
1
1
1
0
1
0
1
2
1
2
0
0
2
1
1
2
1
1
0
1
2
1
1
1
2
1
0
2
2
1
1
2
0
1
1
1
2
1
2
2
1
1
0
1
1
0
1
1
0
0
0
1
3
2
2
1
1
1
1
1
1
1
0
1
1
2
0
1
2
1
2
2
0
1
2
2
1
2
1
2
1
0
1
0
1
1
0
2
1
2
2
0
1
0
1
1
1
1
1
1
1
0
0
1
1
2
2
2
1
2
0
2
2
1
2
2
0
1
1
1
1
1
2
0
1
1
2
1
2
1
1
2
0
0
1
1
2
2
1
1
0
0
1
1
2
1
1
0
2
2
2
1
2
1
1
1
1
1
1
2
2
2
2
2
0
0
1
0
1
2
1
1
1
1
1
2
1
0
1
0
1
1
2
0
0
1
2
1
1
2
1
2
0
0
1
0
1
2
2
0
1
1
0
1
1
1
2
2
1
0
1
2
2
1
1
1
1
2
0
1
0
1
1
2
1
0
1
0
2
1
2
1
0
2
2
1
1
2
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
0
2
1
1
1
1
2
2
1
1
1
1
1
1
1
1
2
0
2
1
1
1
0
0
0
1
1
1
1
1
1
1
1
1
0
2
2
0
2
1
0
1
0
2
0
1
1
0
0
0
0
1
1
0
1
1
0
1
1
2
1
2
2
1
2
1
0
0
2
1
2
2
1
1
2
1
1
2
1
1
1
1
0
1
2
1
1
0
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
0
1
1
1
2
0
0
2
0
1
1
1
1
1
2
1
1
1
2
2
0
1
1
1
1
1
1
1
0
1
1
1
0
2
1
2
1
2
2
1
2
0
1
1
2
1
0
2
1
1
1
1
0
2
0
2
0
2
1
2
1
1
1
2
1
1
0
1
1
1
0
0
2
1
1
1
1
2
0
2
1
1
2
2
2
1
1
1
1
0
0
1
1
2
0
0
1
1
1
1
1
1
2
0
1
1
1
1
0
1
2
2
0
1
1
0
0
1
2
2
2
1
1
0
0
2
1
0
1
1
1
1
1
1
1
1
1
2
0
1
1
2
2
2
1
1
2
0
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
0
2
1
2
1
1
1
1
2
0
1
1
1
0
1
1
2
2
1
1
1
1
1
1
2
0
0
1
0
1
1
1
2
1
1
1
1
2
2
1
1
3
1
2
1
1
1
1
1
0
1
0
1
1
1
1
0
1
2
2
1
2
1
1
1
2
1
0
1
0
1
1
1
1
1
0
2
2
0
0
0
1
1
1
2
1
1
0
1
1
1
2
1
2
1
1
1
2
0
1
0
1
1
1
1
1
2
1
1
0
1
2
1
1
1
2
0
2
1
1
1
0
1
1
1
2
1
1
0
0
2
1
1
0
1
2
0
1
2
0
1
1
0
1
1
1
1
2
2
1
1
1
0
1
1
2
2
1
2
2
1
1
0
2
2
2
2
1
1
1
2
1
1
2
0
1
1
1
1
1
1
2
2
2
1
2
1
0
1
1
1
1
1
0
1
0
1
1
1
1
1
0
2
1
0
1
2
0
1
1
2
1
1
1
1
1
1
2
1
1
1
2
0
2
1
1
1
2
0
1
0
1
1
1
1
2
0
0
2
0
1
2
1
0
1
2
1
0
2
1
1
2
2
1
2
1
1
0
1
1
1
1
0
0
1
1
1
1
2
2
0
0
1
1
1
1
1
1
1
1
2
1
0
0
1
1
2
1
2
1
0
1
1
3
1
1
1
2
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
1
2
0
1
1
2
1
1
1
2
1
1
1
0
1
1
1
1
1
1
1
2
1
1
2
2
2
1
0
2
2
1
1
1
2
0
3
2
0
2
2
1
1
2
1
1
1
2
1
1
1
2
1
0
1
1
1
0
1
1
1
0
1
1
1
1
0
1
1
2
0
0
1
2
0
1
1
1
0
1
2
1
1
1
1
1
2
1
0
0
0
1
2
1
0
2
2
0
0
1
1
1
3
2
0
2
1
1
0
2
1
4
1
1
1
1
2
1
1
2
1
1
2
0
6
0
1
1
1
0
2
1
0
0
0
2
1
0
1
1
0
0
3
1
0
2
1
1
1
1
1
1
1
1
1
2
0
1
0
2
1
1
2
0
0
2
2
1
2
1
1
1
1
2
1
1
0
0
1
0
1
1
1
1
1
2
2
2
1
0
1
0
1
1
1
2
2
1
1
1
1
1
2
2
0
1
1
0
2
2
1
2
1
1
1
1
2
1
1
2
1
1
0
1
1
1
0
2
1
1
2
2
2
2
2
2
1
1
0
1
2
1
1
1
1
1
2
2
2
2
4
2
1
2
0
1
2
1
2
1
2
2
2
2
1
1
3
0
1
1
1
1
1
1
2
1
2
2
0
1
1
1
2
2
2
3
0
2
1
2
0
1
1
1
1
1
0
2
2
2
0
0
1
1
1
1
2
1
2
2
1
1
2
1
0
1
1
1
1
2
1
1
2
1
0
1
2
0
0
2
1
2
2
1
1
1
1
1
2
1
0
1
1
1
1
0
2
1
1
1
1
2
1
1
3
0
1
1
1
1
1
2
1
1
1
0
0
0
0
1
2
0
2
1
1
2
0
2
1
2
1
4
1
1
1
2
1
3
1
1
1
0
1
1
1
2
1
1
1
2
1
1
1
1
2
1
2
1
2
2
1
0
1
1
2
1
1
1
1
2
0
2
1
1
2
1
1
1
1
1
3
1
1
1
0
1
1
0
0
2
0
1
2
1
2
2
2
1
1
1
1
2
2
1
1
1
2
0
1
1
1
1
0
1
1
1
1
2
1
1
1
1
2
1
1
0
1
1
0
1
0
1
1
1
0
1
1
1
0
0
1
0
0
1
0
2
1
1
1
2
0
0
1
2
0
2
1
0
2
1
1
1
0
2
2
1
2
1
2
1
1
1
1
2
1
1
2
0
2
2
1
2
1
1
1
1
1
0
1
1
1
1
2
1
0
2
1
2
1
1
1
1
1
1
1
1
1
3
1
1
1
1
1
1
1
0
1
1
2
1
1
2
1
1
0
1
1
2
1
1
1
1
1
1
0
1
1
0
1
1
0
2
1
0
1
0
1
0
1
1
1
0
1
1
2
1
2
1
2
0
2
2
2
1
1
1
0
1
1
1
1
1
2
0
1
0
2
1
1
3
1
1
1
2
0
1
1
1
1
1
1
2
1
0
1
1
1
0
1
1
0
1
2
0
2
1
1
0
1
2
1
1
2
1
1
0
1
1
1
0
2
1
1
0
0
2
3
2
2
1
0
1
1
3
2
1
0
2
2
2
1
2
0
1
2
0
2
1
2
1
2
1
0
0
1
1
1
1
1
1
1
1
1
2
1
2
2
2
1
1
2
1
2
1
1
1
1
0
1
2
2
2
1
2
2
1
2
1
1
2
1
2
1
1
1
2
1
1
1
2
0
1
1
1
1
2
1
3
0
2
1
0
1
1
1
2
1
1
1
1
0
2
2
1
1
2
1
1
1
1
1
0
1
1
0
2
1
1
1
2
0
1
2
1
1
0
0
1
1
2
2
2
1
2
2
1
2
2
2
0
1
1
2
0
0
1
1
1
1
1
1
1
1
2
1
0
1
2
1
0
1
1
1
1
1
1
2
0
0
0
1
2
0
1
0
0
2
3
1
1
3
2
2
1
0
1
2
1
0
2
1
1
3
1
0
2
0
1
1
1
2
1
1
0
1
0
2
1
1
1
2
1
1
2
0
1
1
1
1
2
1
2
1
2
1
1
1
2
1
0
0
1
1
0
1
1
0
0
2
0
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
0
1
1
1
0
1
1
2
1
1
1
1
0
1
2
0
1
0
1
1
2
1
2
1
2
1
0
2
1
1
2
0
0
1
1
2
0
1
1
1
1
3
0
2
2
1
1
2
2
1
1
0
1
1
2
1
0
0
1
2
1
2
1
1
1
3
1
1
2
2
0
1
0
1
1
1
0
1
1
1
0
2
2
1
1
1
1
1
1
1
1
1
2
1
1
1
0
2
0
2
0
2
1
2
0
0
0
1
0
2
1
1
2
1
1
2
1
0
1
1
2
2
2
1
1
1
1
1
1
0
1
2
1
2
2
1
2
1
1
2
1
1
1
1
2
1
2
2
1
0
1
2
1
0
1
1
1
0
1
1
0
2
1
1
1
1
1
1
1
1
0
1
0
2
2
1
2
1
1
1
2
1
1
1
2
2
1
2
1
1
1
1
2
1
2
0
1
1
1
2
1
1
1
0
1
0
1
1
2
1
0
0
1
1
1
1
1
1
1
1
0
0
1
1
1
2
1
1
0
0
1
1
2
1
2
2
0
0
0
1
1
1
0
2
1
2
2
0
1
1
1
2
1
1
1
2
1
2
1
1
2
1
1
1
1
2
1
1
1
0
1
0
1
1
1
2
1
0
2
1
1
1
0
1
0
2
1
1
1
0
2
1
1
2
1
1
1
0
1
2
1
1
0
1
1
1
1
1
2
1
2
0
0
2
1
2
1
1
1
1
1
2
1
2
1
1
2
1
0
1
1
1
2
2
2
0
1
1
0
1
0
2
2
1
1
1
1
1
1
0
2
2
1
2
1
1
1
1
1
3
1
1
0
2
2
1
1
0
2
2
1
2
1
0
1
1
1
0
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
2
1
1
2
0
1
1
1
1
1
1
2
2
2
1
1
0
2
1
1
1
1
1
2
1
1
2
0
1
1
0
1
0
1
1
1
1
1
2
1
1
2
1
1
1
1
1
0
2
2
1
0
0
1
2
2
1
2
1
2
1
1
1
2
0
1
3
1
0
1
0
0
1
2
2
2
1
1
2
1
1
0
2
1
0
1
1
2
0
1
1
2
0
1
1
2
1
2
0
1
0
1
2
2
1
1
1
2
0
0
2
1
2
1
1
0
1
1
1
0
1
1
0
1
2
1
1
1
1
1
1
1
0
2
3
2
1
2
1
1
2
1
0
1
2
0
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
0
1
2
1
1
0
2
0
1
1
2
1
1
2
2
2
1
2
1
1
1
1
1
1
1
0
1
1
1
1
1
2
1
1
3
0
2
2
1
1
1
2
0
1
2
1
2
1
2
1
1
2
1
0
2
1
1
0
1
2
1
1
2
1
0
1
1
0
1
2
2
1
1
1
1
2
1
1
1
1
1
0
2
1
1
2
2
2
1
1
1
1
2
0
2
1
1
3
1
2
1
2
1
1
1
2
2
1
3
2
2
1
0
1
1
2
2
3
0
0
2
0
2
1
2
1
1
1
2
2
1
1
0
0
2
1
1
2
1
1
1
1
0
2
2
1
2
1
1
1
1
0
0
1
0
1
2
0
0
1
1
1
2
1
2
1
1
1
1
1
2
0
1
1
1
0
1
2
0
1
1
3
1
2
1
0
2
1
2
1
3
1
1
2
2
1
1
1
1
0
2
2
2
1
2
2
2
1
1
1
2
1
0
0
0
2
0
1
2
2
1
1
1
0
1
1
1
0
2
1
1
1
1
1
0
1
0
1
1
2
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
0
1
1
1
2
1
0
0
1
1
1
1
1
1
2
1
1
1
1
0
1
1
1
2
1
0
2
0
1
2
1
2
0
2
1
1
1
1
2
1
1
1
2
0
0
1
0
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
1
1
2
2
1
2
1
0
1
2
2
1
2
1
2
1
2
1
1
1
1
1
1
1
1
2
1
1
1
0
2
1
0
1
1
0
2
1
0
2
2
1
1
0
1
0
1
1
1
0
0
1
1
2
1
1
1
1
2
0
1
1
1
1
1
1
0
2
1
1
2
2
2
2
2
1
1
1
1
1
2
1
2
0
1
2
1
2
1
1
1
1
1
1
1
0
1
1
1
2
1
1
1
1
2
1
2
1
2
2
1
0
0
0
0
0
2
1
1
0
2
1
1
1
2
2
1
2
2
1
0
1
2
1
1
2
2
1
1
1
2
2
2
2
2
0
1
1
1
1
1
1
0
1
1
2
1
1
2
1
1
1
1
1
0
0
1
1
1
0
2
1
1
1
1
2
1
1
1
1
1
2
2
1
0
1
1
0
1
1
2
0
1
0
2
1
2
2
2
1
0
0
2
1
1
2
1
1
1
2
2
2
2
1
1
1
0
0
3
1
2
1
1
2
1
1
1
2
0
2
1
1
1
1
1
0
1
3
2
1
1
2
1
1
1
2
2
2
1
1
2
1
1
0
2
1
1
1
1
0
0
1
1
1
2
2
1
1
1
1
1
0
1
0
1
0
0
0
0
2
1
2
2
1
1
0
0
1
1
1
1
1
0
1
1
0
1
2
1
1
1
1
2
1
1
1
1
1
2
1
2
2
1
1
1
0
2
2
1
1
1
2
0
1
1
1
2
1
1
1
0
0
1
2
2
1
1
1
0
1
2
0
2
0
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
0
0
1
2
1
1
0
1
0
1
1
2
1
1
2
1
1
0
1
1
1
1
1
2
1
1
1
1
1
2
2
1
0
1
2
1
1
2
1
2
2
1
0
1
2
0
1
1
0
0
1
2
1
2
0
1
0
0
2
2
1
1
2
1
1
0
1
1
0
1
0
0
0
0
1
0
1
1
1
1
0
2
1
1
0
1
1
2
1
1
0
0
1
1
2
0
2
0
1
1
1
1
2
1
1
0
1
1
2
1
2
1
2
2
3
2
1
1
0
0
2
1
1
1
1
0
2
2
2
0
1
1
0
1
1
2
0
2
1
1
1
2
0
1
1
2
1
1
2
1
1
1
0
0
1
1
1
1
1
1
8
1
1
1
2
0
1
2
0
0
1
2
1
1
1
0
0
1
1
0
1
0
2
2
0
0
2
1
2
2
1
1
2
1
2
1
0
1
2
0
1
1
1
0
1
1
1
1
1
1
1
2
0
1
2
0
1
0
0
0
2
2
2
1
0
0
1
2
1
1
0
0
2
1
0
2
1
1
1
0
2
0
1
0
1
1
1
1
1
1
2
0
1
2
0
1
1
1
1
1
0
1
1
3
2
1
1
1
1
0
1
2
2
1
1
0
1
2
2
1
1
1
1
2
1
0
1
1
1
1
0
1
2
1
1
2
2
1
0
1
0
0
1
2
1
1
1
1
1
3
1
2
2
2
0
1
2
2
2
2
1
1
1
2
2
1
2
1
1
2
1
1
1
1
1
1
1
2
0
2
1
2
2
0
1
1
1
1
1
1
2
1
2
1
0
1
1
0
0
2
2
1
1
1
2
1
2
2
1
0
1
2
2
2
1
2
1
2
2
0
2
2
2
1
1
1
1
1
0
0
2
2
1
0
2
0
1
0
2
0
1
0
0
1
2
1
0
1
0
1
2
2
2
2
2
2
1
2
0
1
1
1
1
0
1
1
1
2
2
3
1
1
0
0
0
0
1
1
1
1
1
1
0
2
1
3
2
1
1
2
0
1
1
0
1
1
1
2
2
1
0
1
1
1
1
2
1
1
1
1
0
1
1
0
2
2
3
2
1
2
1
2
14
2
1
1
1
1
1
2
2
1
1
1
1
2
2
1
2
1
2
1
1
1
0
0
0
1
1
1
1
1
0
1
1
1
0
1
3
1
0
1
1
1
1
1
1
1
1
1
1
2
2
0
2
1
1
0
1
1
1
2
1
1
1
1
1
1
2
2
1
1
0
1
1
2
0
1
1
1
0
0
1
2
1
2
0
2
2
1
1
2
0
0
1
2
1
1
1
1
1
0
1
1
1
1
0
0
1
2
2
1
1
1
1
1
2
2
1
2
1
1
2
0
1
1
1
2
1
1
1
1
0
2
2
1
1
2
2
0
1
1
1
1
1
1
1
1
1
0
2
1
1
2
1
1
1
2
2
0
1
1
1
1
2
1
2
1
1
0
0
0
0
2
1
0
0
1
0
1
1
1
1
0
1
4
2
1
2
2
1
2
1
2
1
1
0
1
1
1
0
3
2
1
0
1
0
1
1
0
0
1
2
0
2
2
0
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
0
2
1
1
1
1
1
2
1
2
0
1
1
0
0
2
2
2
1
2
1
1
2
1
2
2
1
1
2
2
2
1
2
1
2
2
2
1
1
1
1
1
1
1
1
1
0
1
1
0
0
1
2
1
1
1
0
1
1
1
2
1
0
1
0
1
1
0
1
1
1
2
2
0
0
0
1
2
2
1
1
1
1
2
1
1
1
3
2
1
1
1
1
1
1
1
0
0
0
1
2
2
1
0
2
1
1
1
2
2
0
1
0
1
1
1
1
0
1
0
1
1
1
0
1
2
1
2
1
1
0
1
2
0
1
2
1
1
0
0
1
2
0
1
0
2
0
1
0
1
1
0
3
0
1
2
1
1
0
2
2
1
0
1
0
1
2
1
1
1
2
2
2
1
2
1
1
2
2
1
1
1
1
2
0
3
1
2
1
2
1
1
0
2
1
2
1
2
0
1
1
1
0
2
1
0
0
1
0
1
1
1
2
1
0
0
1
1
1
2
0
2
1
0
2
1
0
1
1
0
1
1
1
1
1
1
1
1
1
2
1
0
1
2
1
2
1
1
1
1
1
1
2
1
0
1
1
1
1
1
2
1
1
1
1
2
0
2
1
1
2
1
1
2
2
0
2
2
2
1
1
1
1
2
1
2
2
1
1
2
1
2
1
1
1
1
1
2
1
1
0
1
1
2
1
1
1
1
1
1
1
0
1
1
0
1
0
1
1
1
1
1
1
1
1
0
1
2
0
1
0
1
2
1
2
1
0
1
1
1
1
1
2
1
2
1
1
1
1
0
1
2
1
1
2
1
1
1
2
1
1
1
2
2
2
0
0
2
2
2
2
1
1
1
1
2
1
0
1
1
0
1
2
2
1
2
1
1
0
1
1
1
0
1
1
1
1
1
2
1
2
0
1
1
1
0
1
2
1
0
2
2
2
1
1
1
2
2
1
2
1
2
1
1
2
2
1
0
2
0
2
1
1
1
2
2
1
1
1
1
0
1
0
1
1
1
1
1
1
1
2
2
1
1
2
1
0
1
2
2
1
1
2
2
1
1
1
0
1
0
1
1
1
1
1
1
0
0
2
1
2
1
1
2
1
2
1
1
2
0
2
1
0
0
1
1
1
1
1
1
2
1
1
1
2
1
0
0
3
1
1
1
2
1
2
1
2
1
2
0
1
1
1
1
1
2
1
1
0
1
2
2
2
1
1
1
1
1
1
1
2
1
1
3
1
1
1
1
2
2
2
1
1
1
2
2
1
2
1
1
1
2
1
1
2
1
0
0
1
1
1
1
1
2
1
0
1
1
1
2
1
2
1
0
1
0
2
1
2
2
1
1
1
1
0
0
0
1
1
0
1
2
1
2
1
2
2
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
0
2
1
1
1
2
0
2
0
1
2
1
1
1
1
2
1
0
1
1
2
1
0
1
1
2
0
1
1
2
1
1
2
1
1
4
2
1
1
2
2
0
3
0
0
1
2
1
1
1
1
0
0
1
1
1
1
2
1
0
1
0
1
1
2
1
1
1
1
1
1
1
1
2
1
0
1
1
0
2
0
1
1
1
1
1
1
1
2
0
2
1
2
0
1
3
1
1
2
2
0
2
1
1
2
1
1
1
1
2
3
1
1
0
2
1
1
0
1
1
1
0
2
2
0
0
1
2
1
1
2
0
1
2
1
2
1
1
1
1
2
1
0
0
1
2
0
1
2
0
2
1
1
1
0
2
2
1
2
1
2
2
1
1
1
1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
0
2
1
0
1
1
1
0
1
1
0
1
2
1
2
2
2
2
1
1
1
1
2
1
2
1
0
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
2
1
1
0
2
1
1
0
1
1
2
1
1
1
0
0
2
0
1
2
1
1
0
0
2
2
0
3
1
3
1
2
1
1
1
2
0
2
1
2
1
1
1
1
0
1
1
1
0
1
1
1
0
1
2
0
1
1
1
2
2
0
2
1
0
2
1
1
2
1
0
2
0
2
2
1
1
1
1
0
1
2
0
1
1
1
0
3
2
2
1
1
1
2
2
1
1
1
1
0
1
0
2
1
0
1
1
2
1
1
1
1
0
1
1
1
1
1
1
1
1
1
2
1
1
6
1
0
1
2
0
0
0
2
2
1
1
1
1
0
2
1
0
2
2
1
0
0
1
1
0
1
1
2
3
0
1
0
1
2
2
1
1
1
1
0
0
1
1
1
0
2
1
1
2
1
1
2
2
1
1
2
1
1
1
1
2
0
0
0
1
2
1
1
2
1
2
1
1
1
1
0
1
2
0
1
1
1
2
1
2
1
1
1
1
1
1
2
1
3
1
0
2
1
1
0
0
1
0
0
1
2
1
1
2
1
1
0
1
1
0
1
2
1
1
2
1
1
1
2
1
1
0
1
2
1
1
2
1
1
1
2
1
1
2
2
2
2
1
1
1
0
1
1
1
1
0
1
1
1
1
1
1
1
2
1
1
1
1
0
0
0
1
2
1
0
1
1
4
2
0
1
0
1
2
1
1
1
1
1
2
0
1
0
0
1
1
1
1
1
1
0
1
0
0
1
2
1
1
1
1
1
1
0
1
1
1
1
2
1
2
1
1
2
1
1
1
2
0
1
2
1
1
1
1
0
1
2
1
1
1
0
0
0
1
0
2
0
2
1
0
0
1
2
0
1
1
1
1
1
1
2
0
1
0
1
1
1
1
2
0
0
2
0
1
2
2
2
1
0
1
1
1
1
1
0
1
1
1
1
1
1
0
1
1
1
1
2
1
0
1
2
2
2
1
2
2
0
0
2
1
2
2
1
1
1
1
1
1
1
0
2
2
1
1
1
1
1
2
1
1
0
2
1
1
1
2
3
0
2
2
0
1
0
2
1
0
2
1
2
2
1
0
1
1
1
2
1
1
1
1
2
1
1
0
2
2
1
1
2
2
1
1
1
1
1
1
1
1
1
0
1
1
2
1
1
1
1
2
1
1
2
1
2
2
2
1
0
1
2
0
2
1
2
2
1
1
2
1
1
1
1
2
1
1
1
1
0
2
2
1
2
2
0
2
2
1
1
2
2
1
1
1
0
1
1
1
1
2
1
1
1
1
1
1
2
1
0
2
2
2
2
1
1
1
1
0
0
1
1
1
1
1
1
2
1
0
1
1
1
1
1
0
1
2
0
1
0
0
2
1
2
1
1
1
1
0
1
1
1
1
1
2
1
2
0
0
0
1
1
1
1
1
2
1
1
1
1
2
4
1
1
0
2
1
1
1
0
1
2
1
1
2
1
1
0
1
2
1
1
2
1
2
1
1
0
0
1
2
1
0
1
1
1
2
1
2
1
1
0
1
1
2
1
1
1
1
0
2
0
0
1
1
2
2
1
1
2
0
0
1
1
1
1
1
1
1
3
0
1
2
0
1
1
0
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
2
0
2
1
0
1
1
1
2
1
1
1
2
1
1
1
0
1
2
2
0
0
1
1
1
1
1
0
0
1
1
1
1
1
2
1
1
0
2
2
0
3
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
0
1
2
1
1
2
0
1
2
1
2
1
2
1
0
1
1
1
2
1
1
0
2
1
0
0
1
0
1
1
0
1
1
0
1
0
1
2
1
1
1
1
2
1
1
2
1
0
1
2
1
1
1
1
2
1
2
1
1
0
0
2
1
1
1
2
1
2
0
1
1
1
1
1
1
1
1
1
2
1
1
2
2
2
1
0
1
1
0
1
2
1
1
1
1
2
1
2
2
1
2
1
1
2
1
1
1
2
1
1
2
0
1
1
2
0
1
2
2
1
1
0
1
1
1
1
2
1
0
1
0
2
1
2
1
2
1
2
1
1
1
0
0
2
0
1
1
1
0
0
4
1
1
1
1
2
2
0
1
1
1
1
1
2
1
2
1
0
2
2
1
0
0
0
1
1
1
2
1
1
1
1
2
0
1
1
1
0
1
3
2
1
1
1
1
1
1
1
1
1
2
0
1
1
1
1
1
2
2
1
0
2
1
1
1
2
2
1
1
1
1
1
1
2
2
2
1
1
2
1
1
0
0
1
1
1
1
2
2
1
1
2
2
1
0
1
1
1
2
1
0
1
2
1
1
1
1
2
0
1
0
1
2
1
1
2
0
1
2
1
0
1
1
1
1
1
1
1
1
2
2
2
2
0
0
2
1
1
1
2
1
1
2
1
1
1
1
1
1
1
2
0
0
1
1
2
1
0
2
1
1
1
2
1
0
1
1
1
1
2
1
1
0
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
0
1
1
1
1
1
0
1
0
1
1
2
0
1
1
0
0
1
1
1
1
0
1
2
0
1
1
0
0
2
1
1
1
1
2
1
0
1
1
1
0
1
2
2
0
1
2
1
1
0
2
1
1
0
1
2
1
1
0
1
1
1
1
1
2
1
1
0
1
1
1
1
1
1
1
1
2
2
1
1
1
1
0
1
1
1
1
1
1
2
1
2
2
1
1
0
0
2
2
1
1
1
1
1
2
0
1
0
0
2
1
0
1
1
1
2
1
1
1
2
1
2
1
1
2
1
1
0
2
1
1
2
0
2
2
0
2
2
1
1
1
0
1
1
1
0
1
0
2
0
1
1
1
2
1
1
0
1
1
1
1
1
0
0
1
1
2
1
2
1
0
1
1
2
1
0
1
0
1
1
1
2
2
1
1
1
1
0
0
2
1
1
1
1
2
2
1
2
1
0
1
1
1
1
1
0
1
2
2
1
0
1
1
1
0
1
0
1
1
1
0
0
2
0
1
0
1
1
1
2
0
0
1
0
0
1
1
2
0
1
1
1
1
1
1
1
2
1
1
1
1
2
1
2
1
1
1
1
2
1
1
0
1
0
1
0
1
1
2
1
0
1
1
0
1
2
1
0
1
0
0
2
0
2
1
2
0
1
1
0
1
0
1
2
2
1
1
1
2
0
1
2
1
2
2
1
1
1
2
1
1
0
1
1
1
2
1
1
2
2
2
2
1
2
1
0
1
1
1
0
2
2
1
1
2
1
2
2
0
0
0
1
0
1
2
2
0
2
0
1
2
1
1
1
2
1
2
1
1
0
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
0
1
2
1
2
1
1
1
1
0
1
0
1
0
1
1
1
0
1
1
1
2
1
1
2
2
1
2
1
1
0
1
1
1
1
0
2
1
1
2
1
2
0
1
1
2
1
1
1
1
2
0
2
0
1
0
0
2
1
1
1
1
0
1
1
0
1
1
2
1
1
0
1
1
1
2
1
1
2
1
1
1
0
1
2
1
0
2
1
1
2
0
1
2
1
1
1
2
2
1
1
2
1
0
1
1
0
2
1
0
1
1
1
1
1
1
1
2
1
2
1
2
2
1
1
0
2
2
1
1
0
1
0
1
2
3
1
1
2
2
2
1
0
1
1
2
1
1
0
1
1
1
1
0
1
1
2
1
2
0
1
1
1
2
1
1
1
0
1
2
1
1
1
1
2
1
0
1
2
1
2
1
1
1
1
2
1
1
1
1
2
1
2
2
1
1
0
1
0
1
0
1
1
1
0
2
2
0
1
1
1
2
1
0
1
1
1
1
2
1
1
0
2
0
0
1
2
2
1
1
1
2
2
2
1
1
1
0
2
1
2
2
1
2
1
2
1
1
1
1
2
2
1
2
1
2
2
3
1
1
1
0
1
2
1
1
1
2
1
1
1
0
2
1
2
1
1
2
1
0
1
1
0
1
1
1
2
2
1
1
1
1
1
6
0
1
2
2
1
1
1
1
1
1
1
1
0
1
2
1
1
1
2
1
1
0
1
1
1
1
1
0
0
2
0
2
1
2
1
2
1
1
0
1
2
0
1
1
1
2
1
2
1
2
1
1
2
1
1
1
1
2
2
1
1
2
1
0
1
0
0
0
1
0
0
1
2
1
2
1
1
0
1
1
3
2
1
1
1
1
1
2
2
2
1
1
1
2
0
1
2
1
1
1
2
0
2
1
2
2
1
1
0
1
1
1
2
1
1
2
3
2
1
1
2
2
1
1
1
1
1
1
0
0
1
1
0
2
2
0
1
1
1
0
0
1
1
2
2
1
1
1
1
1
1
0
0
1
1
2
1
1
0
3
1
2
1
1
1
1
2
1
2
1
2
1
1
1
1
1
1
1
2
0
1
1
0
0
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
2
1
1
0
2
1
2
1
0
1
1
1
0
0
2
1
1
0
0
1
1
0
1
1
1
2
1
1
0
0
1
2
3
1
1
0
1
1
1
1
2
1
1
1
1
1
1
2
1
2
1
1
2
1
1
2
1
0
2
1
2
2
1
1
1
1
1
1
1
1
1
2
4
1
0
1
1
1
0
2
1
1
1
1
2
0
1
1
1
1
1
1
1
1
1
1
1
1
0
1
2
1
1
0
1
0
1
1
1
2
1
2
1
0
2
1
1
1
1
1
2
2
2
1
0
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
0
2
2
1
4
1
0
0
0
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
2
1
1
1
1
2
2
1
1
2
1
1
1
0
1
2
1
1
1
1
1
2
0
2
1
0
1
0
3
0
1
1
2
1
2
1
0
1
1
1
0
1
2
2
1
1
1
1
2
3
2
2
1
0
1
1
0
1
2
1
0
1
1
1
1
2
1
1
2
2
1
2
1
2
1
1
2
1
2
1
1
1
0
1
1
0
1
0
1
1
1
0
1
1
1
1
1
0
1
1
2
1
0
0
0
1
1
0
1
1
0
1
1
1
1
2
1
1
2
2
2
0
1
2
2
1
1
1
1
1
3
2
0
1
3
0
1
1
1
1
1
0
2
2
1
0
2
1
0
2
1
1
2
1
2
1
2
0
1
1
1
2
2
0
1
1
1
1
1
1
1
1
3
2
1
1
2
2
1
1
1
1
0
1
3
1
1
0
1
2
1
2
1
2
1
2
0
3
0
1
2
2
0
0
1
1
2
1
0
1
1
1
2
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
0
2
2
2
2
1
1
1
0
1
1
2
1
0
1
1
2
2
1
0
0
0
0
0
1
1
2
2
1
1
2
1
1
2
2
1
2
2
1
2
1
0
1
1
1
1
1
1
2
1
1
1
1
1
0
2
1
2
1
0
1
1
1
1
1
2
1
1
1
0
1
1
2
1
1
1
1
1
1
0
3
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
2
2
2
1
0
2
2
1
2
1
1
2
2
0
0
2
1
1
1
1
1
1
0
0
2
1
2
1
2
2
0
1
0
1
2
2
0
2
0
1
1
1
1
1
2
0
1
1
0
2
1
1
1
1
2
0
2
1
3
1
0
0
1
3
1
1
1
1
1
1
1
1
1
2
1
4
1
1
1
2
0
1
1
2
2
2
0
1
2
1
1
2
1
2
0
1
2
0
1
1
1
0
0
2
1
1
1
1
1
0
0
1
1
1
2
1
2
2
2
1
1
1
1
1
1
1
0
1
2
0
1
2
1
1
1
0
2
1
2
2
1
1
1
2
1
0
1
1
1
1
1
1
1
2
0
0
2
1
2
1
1
2
1
1
1
1
0
1
2
1
1
0
0
1
1
1
1
2
2
0
1
2
2
1
2
1
1
2
1
1
0
1
1
1
1
2
2
0
1
1
1
1
1
0
1
1
2
1
0
0
1
1
1
2
0
1
1
1
2
1
1
1
1
1
0
0
1
1
1
2
1
0
2
1
0
0
1
1
1
1
1
1
1
1
1
2
1
0
1
1
1
1
1
1
0
2
2
1
1
1
2
1
1
2
2
1
1
1
0
1
0
2
1
1
2
1
1
1
1
1
2
0
2
0
1
0
1
2
0
1
1
1
3
0
0
1
1
1
1
1
1
1
2
1
0
0
1
1
1
0
2
2
2
1
1
1
2
1
2
2
2
1
5
1
2
1
1
1
1
1
1
0
1
2
2
1
1
1
0
0
1
2
1
1
2
1
1
2
1
1
1
2
1
2
1
2
1
2
1
1
2
2
0
2
1
2
0
1
1
2
2
1
0
2
2
1
1
0
1
1
4
2
1
0
1
1
2
0
1
1
1
0
1
1
0
1
0
1
0
0
2
2
0
2
1
2
2
1
1
3
2
0
2
1
1
1
1
1
0
1
1
2
1
1
0
0
2
1
1
0
2
0
1
1
2
1
1
0
2
2
1
1
1
1
1
1
0
0
1
1
2
1
1
1
1
0
0
1
1
1
2
0
1
1
1
2
1
2
1
0
2
1
1
1
1
1
2
1
1
0
0
1
2
0
1
1
2
2
1
1
2
1
0
2
1
1
1
1
1
1
0
1
2
1
1
0
0
2
1
1
1
1
0
1
2
0
2
1
1
1
2
1
1
1
1
0
1
0
1
1
2
1
1
1
1
1
2
1
1
2
1
1
1
1
2
1
1
1
1
1
2
1
1
0
1
1
0
2
2
2
0
0
1
1
1
1
1
2
2
1
1
1
1
1
0
1
1
1
0
2
1
1
0
2
2
1
1
1
2
1
1
2
1
2
1
2
2
2
1
1
2
2
1
0
1
1
2
2
1
1
1
1
1
1
0
1
1
1
2
2
1
1
2
1
1
1
2
1
1
1
1
1
2
2
0
1
1
1
1
1
2
1
2
2
1
2
2
1
1
0
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
3
0
1
0
2
1
1
1
1
0
1
2
1
1
1
2
0
1
1
1
1
1
1
2
0
2
1
2
1
0
5
1
1
1
1
0
1
1
1
1
2
1
2
0
1
2
1
2
1
1
2
1
2
1
0
0
1
1
2
2
2
0
2
0
1
1
1
0
2
1
1
1
1
1
1
2
2
1
2
0
0
1
1
1
0
1
1
1
2
1
2
1
0
2
1
2
1
1
2
1
1
2
0
1
0
1
2
0
1
1
0
0
0
1
1
1
1
0
1
0
0
1
2
1
2
2
0
3
0
1
1
2
0
0
2
1
1
1
1
0
1
2
2
1
0
2
2
1
2
0
1
1
2
1
1
0
2
1
0
2
1
1
1
0
0
1
1
2
1
1
1
2
1
2
0
1
1
1
1
1
1
1
1
0
0
2
0
1
1
1
2
0
0
1
2
1
2
1
1
2
2
1
1
1
2
1
1
2
2
2
1
2
1
1
0
0
2
1
2
2
1
1
0
1
1
0
1
2
1
1
2
2
1
2
1
1
1
1
1
1
0
0
0
1
2
1
1
0
1
2
1
1
0
1
1
2
1
2
2
2
2
1
1
0
1
1
1
1
1
1
2
2
1
1
2
1
1
1
1
2
1
1
1
1
1
0
0
1
1
3
0
1
1
1
1
2
1
0
0
1
0
1
3
0
1
2
0
1
2
2
1
1
1
1
0
1
2
1
0
0
1
0
1
2
2
1
1
2
1
1
0
2
1
1
0
2
1
1
0
1
1
2
2
0
1
1
0
1
1
0
2
2
2
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
0
2
1
2
1
1
2
1
1
1
1
1
2
1
0
1
1
1
1
2
1
1
1
0
2
1
0
2
0
1
1
1
1
1
1
1
1
0
1
1
2
1
1
1
1
1
1
1
1
2
2
2
0
1
1
1
1
2
1
0
1
1
2
2
1
1
0
2
1
1
1
1
2
1
2
1
1
0
1
1
1
2
2
2
1
1
1
1
1
1
1
1
2
2
1
1
1
1
0
2
1
1
2
1
1
1
1
1
1
1
2
0
1
2
1
1
2
1
1
0
1
1
2
2
1
2
1
1
0
0
0
1
2
0
0
1
1
1
0
0
2
0
2
2
1
2
1
1
2
2
2
1
1
1
1
1
2
2
1
2
1
1
1
1
1
2
1
2
1
1
2
1
3
2
1
1
1
1
1
0
1
1
1
1
1
2
1
1
2
1
0
1
2
1
1
1
1
2
1
2
0
1
2
1
1
2
2
1
0
0
0
2
1
1
1
2
1
0
2
1
1
2
1
0
2
1
1
1
1
2
1
1
1
0
1
0
0
2
1
2
1
1
1
0
1
1
0
1
2
1
2
1
1
1
1
1
1
1
0
1
1
0
1
2
1
1
1
0
1
1
1
1
2
1
1
1
0
1
2
2
1
1
0
0
1
1
1
0
1
0
1
1
1
0
2
1
2
1
1
2
1
2
1
1
1
1
1
1
1
3
1
2
2
1
2
2
1
1
2
2
1
1
1
2
1
2
1
2
3
1
2
1
1
0
0
2
1
2
2
2
1
2
2
0
0
1
1
1
1
1
1
0
1
1
1
0
1
2
1
2
2
1
2
0
0
1
2
1
1
1
1
0
2
1
1
1
1
1
2
1
1
0
2
2
1
0
0
2
1
1
1
1
1
0
1
1
1
1
1
1
1
2
0
1
1
1
1
0
0
0
2
1
1
2
0
0
2
1
1
1
1
1
1
1
1
1
2
2
1
2
1
2
1
2
1
2
1
1
1
1
0
1
0
2
2
1
1
1
1
0
2
2
1
1
2
1
1
2
2
1
0
2
1
1
1
0
0
1
3
0
2
2
2
2
3
2
1
0
0
1
1
1
0
1
1
1
2
1
1
1
2
0
1
1
1
1
0
0
1
1
1
1
1
1
2
1
0
1
1
2
0
1
0
1
2
1
1
1
1
1
1
1
1
2
2
0
0
2
1
2
0
1
1
1
1
0
1
2
1
1
2
0
2
1
2
1
2
0
1
1
2
1
1
2
0
1
1
1
2
0
0
0
0
2
1
2
1
1
1
1
0
1
1
1
2
1
0
1
0
2
1
2
1
1
1
2
1
1
2
0
1
2
0
1
1
1
1
0
0
2
0
2
1
1
1
0
2
1
2
1
1
1
0
1
0
1
1
1
1
1
1
1
0
1
1
1
2
1
1
1
1
1
1
2
0
1
1
0
2
1
2
2
1
1
1
0
1
2
1
1
1
0
0
1
1
0
1
1
1
2
3
1
2
2
1
2
0
1
0
1
1
2
1
1
0
1
0
1
2
1
1
0
1
2
1
2
1
2
1
1
2
1
1
1
2
0
1
0
0
1
1
1
1
2
0
1
1
0
0
1
1
2
0
1
1
1
0
2
2
1
0
1
1
1
1
1
1
1
1
1
1
0
1
1
0
1
1
2
2
2
1
1
0
1
1
0
1
1
0
1
1
1
1
1
2
1
1
1
2
1
2
1
0
1
1
2
2
1
1
1
2
0
1
1
2
0
1
1
1
1
1
0
1
1
1
0
1
1
0
1
1
1
1
1
2
0
1
2
2
2
1
0
1
1
2
2
0
1
1
0
2
1
1
1
1
2
1
0
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
0
1
1
0
2
1
1
1
1
0
1
1
1
0
2
1
1
0
2
1
0
2
0
2
1
1
1
1
1
1
1
1
0
0
0
1
1
1
1
1
2
1
0
1
0
1
1
2
2
1
0
0
1
1
1
2
0
1
1
0
1
1
1
2
1
1
1
2
0
1
1
2
1
0
1
1
1
2
1
1
2
1
1
1
1
0
0
1
0
0
1
1
1
0
1
1
1
2
1
2
0
2
2
1
1
1
2
0
1
2
2
1
1
1
1
1
1
1
1
1
2
1
2
1
2
1
1
0
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
2
1
1
2
1
1
2
1
1
2
1
2
0
1
1
2
1
1
2
0
1
1
2
1
1
1
1
2
1
2
1
0
2
1
1
1
0
2
0
1
2
1
1
1
0
1
2
1
1
1
1
1
1
1
2
2
2
1
0
2
0
1
1
0
1
1
1
1
1
1
2
1
0
1
1
0
1
1
1
1
2
2
1
1
1
1
1
1
1
1
0
0
0
1
1
1
1
2
1
2
1
1
0
1
1
0
2
1
1
2
1
2
1
2
1
1
2
1
1
2
0
1
0
1
1
1
0
0
1
1
0
1
1
2
0
1
1
0
1
1
1
1
2
0
0
1
2
1
0
1
1
0
1
0
3
1
1
1
1
3
0
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
0
1
1
2
1
1
1
1
2
0
1
3
0
2
2
0
1
0
2
0
2
0
1
1
1
1
1
2
1
1
1
0
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
2
0
2
1
0
2
1
0
1
2
2
2
1
2
0
1
1
1
1
2
1
1
0
1
2
0
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
2
2
1
1
0
1
1
1
1
0
0
2
1
0
1
1
0
1
1
0
2
1
0
0
1
1
0
2
0
1
1
1
1
1
1
0
2
2
1
2
0
2
1
1
0
2
2
2
1
1
0
1
1
0
2
2
1
2
2
1
1
1
1
2
0
1
1
0
1
2
0
1
6
1
1
2
0
1
1
1
1
0
1
2
1
8
3
1
2
1
1
0
2
2
1
1
0
1
2
0
1
1
1
0
1
2
2
2
1
2
1
1
1
1
1
0
0
1
2
0
1
0
1
2
1
0
2
2
0
0
0
1
1
0
1
1
2
1
0
0
2
2
1
1
1
1
2
2
1
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
0
1
1
2
2
1
1
1
1
1
2
1
1
0
1
2
1
2
2
1
0
0
2
1
1
1
2
1
1
2
0
1
2
0
1
1
1
2
1
2
2
1
1
0
0
2
1
0
2
1
1
2
1
1
1
1
2
1
1
0
1
1
1
2
0
2
2
0
1
1
1
2
1
1
0
1
2
1
1
1
2
0
2
1
2
2
1
0
2
1
2
1
2
1
2
0
1
2
1
2
2
0
1
1
1
1
1
1
1
1
1
2
1
2
2
1
0
2
0
0
0
1
1
1
1
1
2
1
2
0
0
1
1
0
2
1
1
1
1
1
1
1
1
2
1
2
1
2
2
1
0
1
1
1
0
0
1
1
1
1
1
1
2
1
1
1
1
0
2
2
1
1
1
1
1
1
2
1
1
1
2
2
1
1
2
1
1
2
1
1
1
2
2
1
0
1
0
2
1
2
1
1
1
2
1
0
1
1
2
1
2
1
2
1
0
1
0
1
0
1
1
1
1
2
1
1
1
1
1
2
1
0
1
2
1
1
1
0
1
1
0
1
1
2
2
1
2
1
1
2
1
3
1
2
2
1
2
1
1
0
1
0
1
2
1
1
1
1
0
0
2
1
1
2
1
1
0
2
1
2
1
1
2
1
1
1
2
2
1
2
0
1
2
1
2
2
2
2
0
1
1
1
1
1
1
1
1
1
2
3
1
0
1
2
1
1
1
0
1
0
2
2
1
1
2
0
2
1
0
1
0
2
1
1
1
2
2
1
1
1
0
0
2
0
0
1
1
2
1
1
0
1
1
2
1
1
2
0
1
0
1
2
0
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
0
1
1
2
0
2
2
2
2
1
1
1
2
0
0
1
1
1
1
8
2
1
0
2
2
1
2
1
2
1
2
2
1
0
0
0
1
1
2
2
2
1
1
1
2
1
2
1
0
2
1
1
4
1
1
0
1
1
1
1
1
1
2
2
1
1
2
2
1
0
2
1
1
0
2
0
0
2
1
2
1
1
1
1
1
0
1
2
1
0
1
1
1
0
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
2
2
2
1
1
1
2
1
2
1
1
2
1
0
0
1
1
2
2
1
0
2
2
1
2
1
1
1
1
2
2
2
0
1
0
1
1
1
0
2
2
1
2
1
1
1
1
1
0
2
1
2
2
1
1
1
1
2
1
2
2
1
0
1
1
1
1
2
1
1
1
0
1
1
1
0
0
1
1
0
1
2
2
2
1
1
1
1
1
1
0
1
1
1
2
1
1
1
1
1
1
0
1
1
1
2
2
1
0
0
2
1
2
0
1
0
1
1
1
1
0
2
1
1
1
2
1
0
1
1
1
2
0
0
1
0
2
0
0
1
1
1
1
0
2
1
0
1
1
1
1
0
2
1
1
1
0
0
1
1
2
1
2
1
1
1
0
1
0
0
1
1
2
0
2
2
2
0
1
2
2
1
1
0
2
2
2
1
0
2
1
1
2
1
1
1
0
1
0
1
1
1
0
2
1
1
2
1
2
1
1
2
1
1
1
1
1
1
1
1
0
2
1
1
1
1
1
1
1
1
1
1
0
0
1
1
1
1
2
0
1
2
0
1
1
1
1
1
1
2
1
1
0
2
1
1
0
1
1
1
1
1
1
1
1
1
0
1
1
1
2
2
0
0
1
2
1
1
1
0
1
2
1
2
2
1
0
1
0
2
1
1
1
1
2
1
1
2
2
1
1
0
0
1
1
0
1
2
2
1
0
1
2
2
1
2
2
0
0
1
1
1
1
1
0
1
0
1
1
2
1
1
0
1
1
2
1
1
0
0
1
1
1
1
0
0
2
1
0
1
1
1
1
2
2
1
0
1
1
0
0
0
0
2
2
2
1
2
0
1
2
1
1
1
2
1
1
1
2
1
3
2
2
2
1
0
0
0
2
1
0
1
2
2
2
2
2
1
1
2
1
2
1
3
1
0
1
1
1
1
1
1
2
2
1
1
1
0
1
1
1
1
2
1
1
1
0
0
1
1
1
1
1
2
1
1
1
2
1
1
0
1
1
1
1
0
1
1
1
1
0
0
2
1
2
0
1
2
1
1
2
2
1
2
1
1
1
2
2
1
0
4
1
1
0
2
1
0
2
1
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
2
1
2
2
1
1
1
2
1
1
1
0
2
1
1
1
1
2
2
1
0
2
2
1
1
1
2
0
1
2
2
2
1
1
1
1
1
2
1
1
2
0
1
1
0
0
1
1
1
1
1
1
2
0
1
1
0
1
1
1
2
1
1
2
2
2
0
0
0
1
0
1
2
1
1
1
1
1
1
0
1
1
2
1
2
2
0
2
1
1
1
2
1
2
1
1
2
1
1
2
1
0
1
1
2
1
0
1
1
1
2
1
1
1
0
1
0
1
2
1
1
1
2
2
1
1
1
2
0
1
1
1
1
1
2
1
0
1
2
1
1
1
3
1
1
1
1
2
1
1
2
2
1
1
0
0
2
3
2
1
1
1
0
2
1
1
1
0
1
2
2
1
1
1
2
1
2
1
2
1
1
1
1
1
1
1
2
2
1
1
1
1
0
1
1
2
1
2
1
1
1
1
1
1
2
2
1
2
2
0
1
0
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
0
1
1
1
1
1
1
1
2
2
0
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
2
1
2
2
1
1
1
0
0
2
1
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
2
1
0
1
1
1
0
1
0
1
1
1
0
1
1
1
0
0
0
2
1
0
1
1
1
2
1
1
1
0
1
1
0
1
2
1
2
1
1
1
2
1
0
0
1
1
1
1
1
0
2
2
2
2
0
1
1
1
1
0
2
2
0
0
2
2
1
2
3
1
1
2
1
0
1
1
1
2
1
1
2
2
1
0
1
1
0
2
1
1
1
1
1
3
1
2
1
1
2
1
0
1
1
2
2
1
1
1
1
2
1
1
2
1
1
1
1
1
0
1
1
2
1
0
0
1
1
2
1
0
1
1
1
1
0
2
1
1
1
1
0
0
1
0
1
1
1
2
2
0
1
0
3
1
1
4
1
1
0
1
1
1
2
1
1
1
1
2
0
1
2
1
1
1
1
1
1
0
2
1
1
1
1
1
1
1
1
1
2
1
1
1
0
0
0
1
1
1
1
1
1
2
0
1
1
1
2
1
2
1
0
1
0
1
2
1
1
1
1
3
1
1
1
2
1
1
1
2
0
1
0
0
1
2
0
1
1
1
1
1
1
0
2
1
1
2
1
1
1
2
1
2
2
1
1
1
0
0
0
1
2
1
1
0
1
2
1
0
1
2
0
1
1
2
1
1
2
1
1
1
1
2
0
1
1
1
0
1
2
1
2
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
2
1
1
0
1
1
1
1
1
2
2
1
1
1
1
2
1
1
2
2
1
0
1
0
1
1
2
1
1
3
1
1
1
1
0
1
1
1
1
1
0
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
2
0
1
1
2
1
1
1
2
1
2
1
0
1
1
2
2
1
1
0
1
0
1
0
1
1
2
1
1
2
1
1
1
1
1
1
1
2
1
2
0
1
1
1
3
2
1
1
1
0
1
1
0
2
1
0
0
1
0
1
1
1
0
1
0
1
1
1
1
1
1
2
1
2
1
2
1
1
1
0
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
0
1
0
1
1
2
1
1
1
1
0
1
1
1
2
3
1
2
1
2
1
1
0
1
2
2
1
0
1
1
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
2
1
0
1
1
0
2
1
2
1
2
1
1
1
0
1
1
1
1
0
1
1
1
1
2
0
2
2
2
0
1
1
2
3
0
0
2
1
2
2
1
1
2
0
1
1
1
1
1
1
1
1
2
1
1
2
2
2
2
1
1
1
0
1
0
1
1
3
2
1
1
2
0
1
2
1
1
1
1
2
1
1
0
0
2
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
2
2
0
3
1
1
2
0
1
1
0
1
2
1
1
2
1
0
1
1
1
0
1
1
1
1
1
1
1
1
2
2
2
0
1
2
1
0
2
2
1
1
1
0
2
2
0
1
2
0
0
1
1
2
1
1
1
1
1
2
1
2
1
0
1
1
1
1
1
2
1
1
1
1
1
2
2
1
1
0
1
1
1
1
0
2
2
1
0
2
1
2
1
1
0
1
1
1
1
0
2
1
1
1
1
1
1
2
0
1
2
2
1
1
4
1
0
1
1
2
1
1
0
0
0
1
1
1
1
1
1
1
2
0
1
1
2
0
1
1
1
1
2
1
1
1
2
1
2
1
1
1
2
1
1
1
1
0
1
1
1
1
0
0
2
2
1
1
1
1
1
0
1
2
0
2
1
1
1
0
0
1
3
1
2
1
2
1
1
1
1
1
1
1
1
0
1
1
2
2
2
1
0
0
1
1
1
0
1
2
1
1
1
1
0
1
1
1
0
1
0
1
2
0
1
1
1
0
1
1
1
0
2
2
0
1
2
1
2
1
2
0
2
1
0
2
1
1
2
1
1
1
2
1
1
2
0
1
2
1
1
1
0
1
2
1
1
1
2
2
1
2
1
2
1
1
0
2
2
1
2
0
0
3
1
1
1
0
1
1
2
1
1
1
2
1
2
2
1
0
2
1
1
1
1
0
1
0
1
2
1
0
0
2
1
1
1
1
1
1
1
1
1
1
0
1
1
1
0
0
1
2
0
2
1
0
1
1
0
1
2
0
1
1
0
1
2
1
2
2
1
1
1
1
1
0
2
1
1
1
1
0
1
1
0
0
1
1
2
2
1
1
1
2
2
2
1
2
1
2
0
1
0
1
1
1
0
1
1
1
2
1
1
2
0
1
1
0
1
0
0
1
2
0
2
1
0
0
0
1
1
2
2
2
1
2
1
1
0
1
1
1
1
0
1
1
1
2
1
1
1
2
0
2
0
2
1
1
2
2
1
1
1
1
1
1
1
0
1
1
1
1
1
0
0
1
1
1
1
2
1
2
2
0
1
1
1
2
1
1
1
0
1
1
1
2
2
1
1
1
1
0
1
2
1
2
0
1
2
1
1
2
1
2
1
0
1
2
1
0
2
0
3
2
0
2
1
1
1
0
2
2
2
1
1
2
1
2
2
0
1
1
2
1
2
1
2
0
1
1
1
0
1
2
0
2
1
0
0
0
1
1
1
1
1
1
2
1
1
0
2
1
2
1
2
1
1
1
0
1
1
1
1
1
1
2
0
1
1
2
1
1
0
1
1
1
1
1
1
1
1
1
2
1
2
1
1
0
1
1
1
1
0
1
1
1
1
0
0
2
1
1
1
3
1
1
1
1
1
1
2
1
1
2
1
1
1
1
2
1
1
2
2
1
2
1
0
1
1
0
0
1
1
2
1
1
0
1
1
0
1
2
1
1
1
0
1
1
1
0
1
0
0
1
1
1
0
2
1
0
0
2
1
1
1
1
1
1
0
1
0
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
0
1
0
1
1
1
0
2
1
1
1
1
1
1
1
0
0
1
0
2
1
2
0
2
1
2
2
1
0
2
1
1
2
0
1
2
1
2
0
1
1
1
1
1
0
1
2
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
1
3
1
2
2
1
1
2
1
1
1
2
1
1
0
1
0
1
2
1
4
1
1
0
2
2
1
0
1
1
1
1
2
1
0
1
1
1
1
1
1
0
1
1
1
1
0
2
3
1
1
1
2
1
0
0
1
1
1
0
1
2
2
1
2
0
0
1
2
1
1
2
2
1
0
1
1
1
1
0
1
2
1
1
2
0
0
1
1
1
1
2
0
2
1
1
1
2
1
0
1
1
1
1
2
1
1
2
0
1
2
1
0
1
2
2
2
1
1
0
2
1
1
1
1
1
1
1
1
1
2
0
1
1
3
1
1
1
1
1
1
1
1
1
1
0
0
2
2
0
0
1
0
1
1
3
1
1
1
1
1
1
0
2
1
2
1
1
1
2
1
1
2
2
1
1
1
2
1
1
2
1
3
0
0
1
1
2
1
3
2
0
2
1
0
1
1
1
0
1
1
0
1
1
1
1
2
1
1
2
1
1
2
0
1
1
1
1
1
1
1
1
2
1
2
1
0
1
1
1
2
2
1
0
1
0
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
2
2
1
1
2
1
0
2
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
0
1
2
2
1
1
2
3
1
1
2
1
1
2
2
1
1
0
1
2
1
1
2
1
1
2
1
1
2
2
1
2
1
3
1
2
1
0
1
1
1
1
0
1
1
0
1
1
2
0
2
1
1
0
1
1
1
0
0
1
0
0
1
1
1
2
1
1
1
0
1
2
0
1
1
1
0
2
0
1
2
0
1
0
1
0
1
1
1
0
2
1
1
1
1
1
2
0
1
2
0
0
1
0
0
1
1
0
1
2
1
1
2
1
1
1
2
1
1
2
1
1
1
1
1
1
1
2
0
1
2
1
0
2
1
1
2
2
0
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
0
1
1
3
2
0
2
1
1
6
1
2
1
2
1
1
2
1
1
1
2
2
1
1
1
1
2
1
1
1
0
0
2
1
1
1
0
2
1
1
2
2
2
0
1
1
2
1
1
0
1
2
1
1
0
1
1
1
1
1
1
1
1
1
2
0
2
2
1
1
2
1
2
0
0
2
1
1
1
2
0
0
1
1
2
1
1
0
1
0
1
2
1
1
1
1
1
1
1
1
1
0
1
2
1
1
2
2
1
2
1
1
1
0
1
1
1
1
1
1
1
0
1
0
0
2
0
0
0
1
1
1
1
1
1
1
0
1
1
1
7
1
1
0
1
1
1
0
2
0
1
2
2
2
2
1
1
1
1
1
1
0
2
2
2
0
1
1
1
1
1
0
0
2
2
1
2
0
0
1
2
1
1
0
0
2
1
2
0
2
2
2
0
2
1
2
1
1
1
1
2
1
2
1
1
1
0
0
1
1
2
1
1
1
1
1
1
2
1
1
1
0
1
1
1
0
1
2
1
1
1
2
1
0
2
0
1
1
1
1
1
0
2
1
2
1
0
0
1
2
1
2
1
1
1
1
1
1
0
2
0
1
0
1
1
2
0
0
0
2
2
1
1
2
0
2
2
1
1
2
1
0
1
1
1
0
1
1
1
2
1
1
1
1
0
1
2
1
1
4
2
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
0
1
1
0
0
0
1
1
2
1
1
1
1
2
1
2
0
1
0
0
2
0
0
0
2
2
0
2
1
1
2
2
1
2
1
0
1
1
1
2
3
1
1
1
2
1
1
2
1
0
1
2
2
0
0
1
0
1
1
0
1
1
1
2
0
2
1
2
1
1
1
1
0
1
0
1
0
1
0
1
2
1
1
1
1
1
1
0
1
1
1
1
0
0
2
1
2
0
1
2
1
1
1
1
1
0
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
2
1
2
1
1
1
1
2
1
1
2
2
2
0
0
1
1
1
1
1
1
1
2
0
1
1
1
1
2
1
1
1
0
0
1
2
1
1
1
2
2
2
1
2
2
1
1
2
1
1
0
1
2
1
0
2
2
2
0
2
1
1
1
0
2
2
0
2
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
0
1
2
0
0
1
1
2
2
1
0
1
1
2
0
1
1
1
1
0
1
1
2
1
1
1
1
1
0
2
2
2
1
0
1
2
0
0
1
1
1
1
1
0
0
1
2
1
1
1
2
1
1
2
1
0
5
1
2
2
1
1
1
1
1
2
1
1
1
1
1
4
2
1
1
1
0
2
2
0
1
2
1
1
2
2
1
2
0
1
1
1
0
0
1
2
1
1
1
1
1
2
2
1
2
0
1
0
1
1
1
0
2
1
1
5
1
1
1
1
1
1
2
2
1
1
1
1
1
2
0
0
1
2
0
1
0
1
1
1
2
1
1
1
2
1
1
1
2
2
1
1
2
2
1
1
0
1
2
0
1
2
1
1
1
1
0
1
1
1
1
1
0
0
0
2
1
1
2
1
1
1
1
1
2
2
1
0
1
1
2
1
2
0
2
2
2
2
1
0
1
1
1
1
0
2
2
0
1
1
1
0
1
1
0
2
1
1
2
0
1
2
2
1
0
1
2
1
1
1
0
2
1
1
2
1
0
2
1
1
2
0
1
1
1
1
1
0
0
2
2
0
1
1
2
1
0
1
1
1
1
0
0
0
2
1
1
1
0
1
2
2
1
1
0
1
1
0
2
2
2
1
1
2
2
1
1
1
2
1
2
0
1
0
1
1
2
2
1
1
2
2
1
2
2
1
1
1
2
1
2
0
1
0
1
1
0
0
2
2
1
2
1
2
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
0
1
1
1
1
0
1
1
1
0
1
1
1
2
2
1
1
1
2
1
2
1
1
0
1
1
2
1
1
3
1
1
1
2
1
1
1
0
2
2
2
0
2
0
1
0
1
1
1
1
2
2
1
2
1
1
1
1
1
2
0
1
1
1
1
2
2
1
1
0
0
2
1
1
2
2
1
2
1
1
0
1
1
0
2
1
1
1
1
1
1
1
1
1
2
0
2
1
1
1
1
1
2
1
1
2
0
1
0
0
1
1
0
1
2
1
1
1
2
1
2
1
2
2
1
1
1
1
2
1
1
0
1
0
1
1
1
1
1
1
1
2
0
1
1
2
1
1
1
1
0
2
1
1
0
1
1
1
2
1
1
1
1
1
1
1
1
1
2
0
2
1
1
1
0
1
2
1
1
0
1
2
1
1
1
1
2
1
0
1
1
1
1
1
2
1
0
2
1
1
1
1
1
2
1
2
1
1
0
0
1
1
1
1
0
2
0
0
1
0
1
1
1
2
0
1
1
1
1
1
1
0
1
1
1
1
1
0
1
2
1
1
1
0
2
2
1
1
1
1
2
1
1
1
1
1
2
1
0
1
2
2
1
1
1
1
1
1
1
1
1
2
1
0
1
1
2
1
2
2
1
2
1
1
0
1
1
1
1
0
0
2
1
1
1
1
2
0
1
1
1
2
0
1
1
1
1
1
2
0
0
1
2
2
2
1
0
1
1
1
1
1
0
1
2
2
1
1
2
2
1
1
2
0
2
2
2
1
0
2
1
2
1
2
1
2
1
1
1
1
1
2
0
2
1
1
1
1
1
1
1
2
2
2
3
1
1
1
1
1
2
2
3
1
1
3
1
2
0
1
2
1
0
2
1
1
2
1
1
2
1
1
2
1
1
0
1
1
0
1
1
2
2
1
2
0
0
2
1
2
1
1
1
1
1
2
1
0
2
2
2
1
1
2
0
1
1
0
2
0
1
1
1
1
1
1
0
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
2
2
1
1
1
0
1
1
2
2
2
0
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
0
1
1
1
1
1
1
1
1
4
0
1
2
0
1
1
0
2
1
2
0
1
2
1
1
1
0
1
2
2
1
1
2
2
2
0
0
0
2
0
2
1
1
1
1
1
0
2
2
1
1
0
2
0
1
1
0
2
3
1
1
1
0
2
1
1
1
1
1
1
0
1
0
1
1
0
2
0
2
1
1
1
1
1
2
2
0
1
1
1
1
5
2
1
0
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
0
2
2
1
1
1
2
1
0
1
1
1
2
0
2
1
2
1
1
0
1
1
2
1
2
1
2
1
1
2
1
1
1
0
1
2
2
2
0
2
1
1
0
1
1
1
0
2
0
1
2
1
1
2
1
1
0
2
1
0
1
2
2
1
1
1
1
1
2
1
0
1
1
2
1
0
2
1
1
2
0
3
1
1
1
1
2
0
3
0
0
2
1
2
2
1
1
1
1
1
0
1
0
1
2
1
1
1
2
2
1
1
2
2
2
1
1
1
2
0
1
1
0
1
1
1
1
2
2
2
2
2
1
1
1
1
1
2
1
1
1
1
2
2
2
0
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
0
1
1
1
0
1
2
2
1
0
1
0
2
1
1
2
1
1
1
2
2
2
1
1
1
1
1
0
2
1
0
1
1
1
2
1
1
1
2
2
1
1
2
1
2
1
1
1
1
1
1
1
2
2
2
2
1
1
2
1
1
1
1
2
2
0
1
1
0
2
1
2
1
1
0
1
1
1
1
1
0
1
2
1
1
2
1
1
1
1
1
1
1
1
1
0
1
1
1
0
1
2
1
1
1
2
2
2
1
1
1
1
0
2
2
1
2
2
2
1
1
1
2
1
1
1
1
1
0
1
1
1
1
2
1
2
2
2
1
1
0
1
1
1
1
2
1
3
1
1
2
0
2
1
1
2
2
1
1
1
1
1
0
1
1
2
1
1
0
2
1
0
1
1
1
1
1
2
1
0
1
2
1
1
1
1
2
1
1
1
0
0
1
1
2
1
1
1
2
1
1
2
1
0
1
0
2
0
1
1
2
1
0
2
2
1
0
1
2
2
1
1
1
1
1
0
0
1
1
2
1
2
2
2
1
0
1
0
2
2
1
2
2
2
1
2
1
2
1
0
1
2
0
1
2
2
1
0
1
2
1
2
1
1
1
1
1
1
1
2
0
1
0
2
0
1
2
1
1
1
1
1
0
1
1
0
2
1
1
1
0
2
2
1
1
2
2
2
1
1
1
1
0
0
0
1
2
1
1
0
1
2
1
0
2
1
1
2
1
0
1
1
2
1
1
1
2
1
1
1
1
1
1
1
0
0
3
1
1
1
0
1
0
1
0
1
0
2
2
1
2
2
1
0
3
1
1
2
2
0
1
3
1
0
1
1
3
1
0
1
1
2
1
0
1
1
1
2
0
0
1
1
1
1
1
2
1
0
2
2
1
2
1
1
0
1
0
1
2
1
1
2
1
2
1
1
1
1
1
0
0
1
1
1
0
1
1
2
0
1
1
2
1
2
2
1
1
1
0
1
2
0
2
1
1
1
1
1
1
1
0
1
1
2
2
1
1
1
1
1
2
2
1
2
1
2
0
1
2
0
2
1
0
1
2
1
2
0
2
1
0
1
2
2
1
1
1
1
1
0
1
2
0
2
1
2
0
0
1
1
2
1
2
2
1
1
0
2
1
1
1
1
2
1
1
1
1
1
1
1
2
0
1
0
1
3
1
1
1
1
1
1
1
1
2
1
2
0
0
1
1
0
0
0
1
1
2
2
0
1
1
1
2
2
0
1
0
0
1
1
1
2
2
1
2
1
1
0
1
0
1
0
2
1
2
2
1
1
1
1
0
1
0
0
0
1
1
1
1
1
2
0
4
0
1
1
1
1
1
1
0
1
1
1
1
1
1
2
0
2
0
1
0
0
1
2
1
1
2
1
1
2
1
2
1
1
1
1
0
2
0
1
1
1
2
1
0
1
2
1
1
1
0
1
1
1
2
1
0
1
2
2
1
1
1
2
0
1
0
1
1
1
1
1
1
1
2
1
2
1
1
0
0
1
2
2
1
1
0
0
2
0
0
1
0
1
0
1
1
1
1
1
2
1
2
2
1
2
2
1
2
1
1
0
0
1
1
2
1
1
0
1
1
1
1
1
1
1
1
2
2
1
1
4
1
1
2
1
1
1
0
1
1
1
2
1
1
2
1
1
0
1
1
2
1
0
2
1
2
0
1
0
1
2
1
0
2
2
2
1
1
1
1
1
1
1
0
2
1
0
1
2
1
1
0
2
1
1
1
1
2
1
1
1
1
4
0
0
0
2
0
2
2
2
2
0
1
1
1
0
0
1
1
1
1
2
1
3
1
2
2
1
2
2
1
2
0
1
1
1
1
1
1
1
2
0
1
1
1
1
1
0
1
2
0
1
1
0
2
1
1
1
1
2
1
1
1
1
2
1
1
0
2
1
0
1
2
1
1
0
0
1
2
1
0
1
1
1
1
1
0
2
1
1
1
2
1
2
1
0
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
0
0
1
3
0
2
0
1
2
1
1
0
0
1
1
1
1
1
0
1
1
0
1
1
1
1
2
1
1
0
1
2
1
2
0
2
0
1
1
1
2
1
1
1
2
0
2
1
2
1
2
1
2
2
0
0
0
1
0
1
1
1
1
1
2
1
0
1
1
1
1
1
1
3
0
2
1
1
3
1
1
1
1
3
1
1
1
0
1
1
1
0
1
1
1
2
0
1
2
1
1
2
0
1
1
1
1
1
2
1
0
1
0
0
0
2
1
0
1
2
1
1
2
0
1
2
1
1
2
0
2
2
0
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
0
0
1
1
2
1
0
0
1
2
0
1
1
2
2
0
0
1
1
1
1
1
2
1
1
0
0
0
1
1
1
1
1
0
1
1
1
1
1
0
1
0
2
0
2
1
2
1
2
1
1
2
2
1
1
2
1
0
1
0
0
2
1
1
1
1
2
1
1
1
2
0
1
2
2
1
1
1
2
2
1
1
2
1
0
1
1
1
1
1
1
2
1
1
2
1
1
0
1
1
1
1
0
1
1
0
1
0
2
1
1
1
2
2
1
2
1
1
2
0
0
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
0
1
1
0
2
1
1
3
0
1
1
1
1
1
2
1
2
0
1
2
2
1
1
0
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
0
1
0
1
1
1
1
0
1
1
1
1
1
2
1
2
0
0
0
1
2
1
0
1
1
0
0
1
1
2
1
0
1
1
1
0
1
1
2
2
2
2
1
1
1
0
1
0
1
2
2
1
1
1
0
1
1
0
1
1
0
1
2
2
0
2
1
0
1
1
2
1
2
2
0
1
1
1
1
1
1
0
1
0
1
2
0
2
3
1
2
1
2
1
1
1
2
2
1
1
1
2
1
0
1
2
1
2
2
2
2
2
1
0
1
1
1
1
2
2
2
0
1
2
2
1
0
0
0
2
2
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
1
1
0
1
0
2
2
2
1
1
1
1
2
1
0
1
1
1
2
1
1
1
0
2
1
1
1
1
2
1
0
1
2
2
2
0
1
2
1
1
1
1
3
2
1
1
2
2
1
1
1
1
0
1
0
0
1
1
0
0
1
0
1
1
0
2
1
2
1
1
2
1
0
0
1
2
1
0
1
1
2
1
0
2
2
1
1
2
1
2
1
1
1
3
1
2
2
2
1
2
1
0
2
2
1
1
1
1
1
2
0
1
0
1
2
1
2
2
1
2
0
0
2
2
1
1
2
2
1
1
0
1
2
0
2
1
1
2
1
2
0
1
1
1
2
1
1
1
1
1
2
1
1
0
1
1
1
1
2
0
0
0
1
1
2
1
1
2
1
2
1
1
0
1
0
2
1
2
1
1
0
2
1
1
0
1
2
2
1
1
1
2
1
1
1
1
2
1
3
1
1
0
2
1
1
1
1
0
2
1
1
1
1
2
2
2
1
1
1
1
1
1
2
1
1
2
2
1
0
0
1
0
1
1
1
1
1
1
1
2
1
1
2
1
1
1
2
1
0
1
1
3
0
0
1
2
1
1
2
1
1
1
1
1
1
2
0
2
1
1
2
4
2
1
1
0
0
1
0
1
2
1
1
1
1
0
1
2
0
1
2
1
1
1
1
0
1
0
1
2
0
0
1
1
2
1
1
1
1
2
1
0
1
0
1
1
0
1
1
1
1
3
2
1
0
1
1
2
1
1
1
1
1
0
1
2
1
1
0
1
0
1
1
0
2
1
1
2
1
1
1
1
1
2
1
0
2
1
2
1
0
2
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
0
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
0
1
1
5
1
2
1
1
0
1
1
1
1
1
0
1
1
2
1
2
1
1
0
1
1
2
1
1
2
1
0
1
0
2
1
1
0
0
1
1
2
2
1
2
1
1
2
1
1
1
1
1
1
0
1
2
2
2
1
0
1
1
1
1
1
0
1
1
1
1
0
1
2
0
1
1
8
1
1
1
0
1
1
1
0
2
1
0
1
1
1
1
1
1
1
1
1
0
2
1
1
1
2
1
1
1
1
2
1
0
2
1
2
1
0
2
1
1
1
1
1
1
1
0
0
1
0
1
2
1
1
2
1
1
2
2
1
1
2
1
1
1
0
1
0
1
2
1
1
1
1
1
1
2
0
1
1
2
2
2
1
0
1
2
1
1
2
0
0
1
0
1
1
1
1
0
0
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
0
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
0
1
1
2
1
1
1
1
2
1
1
0
0
2
1
1
1
2
1
1
2
1
1
0
0
2
1
2
0
0
1
1
2
0
1
0
1
1
1
1
1
0
0
1
2
0
2
0
2
1
2
1
1
2
1
0
2
1
2
0
2
2
1
1
1
0
2
1
1
2
0
1
1
1
1
0
0
2
1
0
1
0
3
2
1
0
2
1
2
2
2
1
0
0
1
0
1
1
1
1
2
1
0
2
1
1
1
1
0
1
1
2
1
1
2
0
2
0
1
2
0
0
1
2
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
2
2
1
1
1
1
1
2
2
1
1
1
0
1
1
2
1
2
2
1
1
1
2
1
0
1
2
2
1
1
1
1
0
0
1
1
0
2
1
1
1
1
0
1
0
2
0
0
0
1
1
1
2
2
2
2
1
1
1
1
2
2
1
1
2
1
0
0
2
1
1
1
1
0
1
2
2
0
1
0
2
1
1
1
1
2
1
1
0
2
1
2
2
1
1
1
1
1
1
0
2
1
1
1
1
1
1
1
1
0
1
1
1
1
2
1
1
1
2
1
2
1
2
2
1
2
0
1
2
1
2
1
1
1
2
2
1
1
1
0
1
2
2
1
0
1
1
0
2
1
1
2
2
1
0
2
1
2
2
1
1
0
1
0
1
1
1
1
1
2
1
0
1
0
2
1
2
1
0
2
1
1
0
1
0
2
1
1
1
1
1
1
0
2
1
3
1
0
1
1
1
1
2
2
0
2
1
1
1
2
1
1
1
2
1
0
1
2
1
1
1
1
1
0
1
2
2
1
1
0
1
1
0
2
2
1
2
1
0
1
1
1
1
0
1
1
1
1
0
2
1
1
1
2
1
0
2
1
1
0
0
0
0
2
2
1
1
1
0
1
0
1
1
1
2
2
1
2
2
1
2
1
1
1
2
1
1
0
0
0
1
1
1
1
1
0
1
1
1
1
1
0
1
0
0
1
1
0
0
2
2
1
1
1
2
1
1
0
2
2
1
1
2
1
1
1
0
1
1
1
1
1
2
2
1
1
1
1
1
1
0
1
1
1
1
2
2
1
2
2
1
1
1
1
1
1
2
0
1
1
1
2
1
0
1
1
1
1
1
1
2
2
1
2
1
0
2
0
1
1
1
1
2
0
1
1
0
2
2
1
1
1
1
0
0
1
1
1
2
0
1
1
1
2
1
1
1
2
1
1
2
1
0
1
1
0
1
0
2
0
0
1
2
1
2
0
1
1
1
2
0
2
1
0
1
1
1
2
2
1
1
2
1
2
1
1
1
1
2
1
2
1
0
1
0
0
1
1
0
2
1
1
1
1
1
2
6
1
1
1
1
2
1
1
1
1
1
1
1
1
0
1
2
1
1
1
1
1
1
1
1
1
1
0
2
2
1
1
1
1
2
1
1
1
1
1
2
2
2
1
1
1
1
0
1
2
2
1
1
1
2
1
2
2
1
2
2
1
1
2
1
0
1
1
1
1
1
1
0
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
0
1
2
1
1
1
2
1
1
0
1
2
2
0
2
1
2
1
2
1
2
2
0
1
0
1
1
2
2
0
0
1
1
0
1
0
1
1
1
2
1
1
2
1
0
2
1
2
1
1
2
1
1
1
2
2
1
2
1
1
0
1
2
2
1
0
2
2
0
1
2
1
1
1
0
1
2
1
2
1
1
1
1
0
1
1
2
1
1
0
1
2
1
1
1
0
2
1
2
1
1
2
1
1
1
2
1
0
1
1
1
2
1
1
1
1
1
2
1
1
2
3
1
0
2
1
2
2
1
1
1
0
0
1
1
1
1
1
1
2
1
1
1
1
1
2
0
2
1
2
1
1
1
1
0
1
1
1
1
2
1
1
1
2
2
1
2
0
1
1
1
1
2
1
1
1
1
1
1
1
0
1
1
2
1
1
1
2
1
1
1
0
1
1
2
0
1
0
0
0
1
2
1
1
1
2
2
2
0
0
1
1
0
1
1
1
1
2
2
0
1
2
0
1
1
2
2
0
1
1
1
1
0
1
1
0
1
1
1
1
2
1
0
2
1
1
1
2
2
1
1
2
2
1
1
2
1
2
1
1
0
1
1
1
1
0
2
1
1
1
1
0
1
1
2
2
2
1
1
1
1
0
3
1
1
1
1
2
1
1
1
2
1
2
1
1
1
2
1
1
1
0
0
1
1
1
2
1
1
0
2
1
1
1
1
1
2
2
1
0
2
1
2
1
2
2
0
0
1
1
2
0
1
1
1
1
2
1
1
2
2
1
2
2
6
2
2
2
1
1
1
0
2
1
1
1
0
1
1
2
1
1
2
1
1
2
1
2
1
2
1
0
1
1
0
1
1
2
1
0
1
1
2
1
1
2
1
1
1
1
1
2
2
1
1
2
2
1
2
2
1
1
1
0
0
1
2
2
2
1
2
0
2
2
1
1
2
1
1
1
1
0
0
1
1
2
1
1
1
1
1
1
1
2
1
2
2
1
2
2
2
2
2
2
1
1
1
1
1
1
0
1
2
0
1
1
0
1
1
2
2
0
2
1
1
1
1
1
2
1
1
1
1
0
0
1
0
1
1
2
2
1
1
1
2
1
2
1
1
1
0
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
0
2
1
1
1
1
1
2
0
2
2
1
1
2
0
2
1
2
1
1
1
1
0
1
1
1
1
1
2
2
0
1
1
1
0
0
1
1
0
0
2
0
1
0
2
2
0
1
2
1
0
0
1
2
2
1
1
0
1
1
1
2
0
1
1
1
1
0
1
0
0
1
0
1
0
1
0
0
1
1
1
1
2
1
1
0
0
1
2
1
0
1
2
1
3
1
1
2
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
1
0
0
1
2
1
2
1
1
2
0
1
0
1
1
1
2
1
2
2
2
1
1
0
1
1
0
1
1
1
2
0
2
1
1
1
1
1
2
1
0
1
1
1
1
1
2
1
1
2
1
0
0
1
1
1
1
1
2
0
2
1
0
0
0
2
1
1
1
1
2
1
1
1
2
1
1
0
1
1
1
1
0
2
2
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
1
0
2
2
1
1
2
2
1
1
1
1
2
1
1
3
2
1
1
1
1
1
1
2
1
2
0
1
1
1
2
1
1
1
2
1
0
2
0
2
1
1
1
2
1
1
2
0
1
1
1
1
0
2
1
1
0
1
2
0
1
1
1
1
1
0
2
2
1
1
2
2
0
1
1
1
2
2
1
1
1
1
1
1
1
2
1
0
2
1
2
1
1
1
2
0
1
1
1
1
0
2
2
1
1
1
1
2
0
2
1
1
1
1
2
1
1
1
1
1
1
2
1
0
1
2
0
2
2
2
1
1
1
0
2
1
1
2
0
1
1
1
1
1
1
2
1
0
2
1
1
1
1
1
1
0
1
1
1
0
1
1
1
1
1
2
2
1
1
1
2
1
1
1
2
2
1
1
1
1
0
1
1
2
1
2
2
0
1
1
1
1
1
1
2
1
1
0
2
1
1
0
1
2
1
1
2
2
1
2
2
0
1
0
1
0
1
1
0
0
2
1
1
1
1
0
2
1
1
0
1
1
1
1
2
2
1
1
1
1
2
1
2
0
1
0
1
1
1
1
1
2
1
2
2
2
1
0
1
1
2
2
1
1
1
0
0
0
1
1
1
2
1
0
0
1
0
1
1
0
2
1
0
2
1
1
1
2
1
1
1
2
0
1
1
1
1
1
2
2
0
1
0
1
2
1
2
2
1
1
1
1
2
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
2
0
1
1
2
1
1
2
2
1
2
1
2
2
2
0
2
1
2
0
0
1
3
2
1
1
1
1
1
0
2
1
1
2
0
0
0
1
0
1
2
0
1
0
1
0
2
2
1
1
1
0
2
0
2
1
2
1
1
1
1
0
2
2
2
0
1
1
1
1
0
1
1
1
2
2
2
0
1
0
0
1
0
1
2
1
0
1
1
1
0
1
1
1
0
1
2
0
1
0
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
0
0
1
2
1
1
2
0
2
1
2
2
1
1
2
0
1
0
1
1
0
2
2
2
1
1
1
1
1
2
1
1
1
0
1
2
1
1
1
1
0
2
2
2
1
1
1
1
0
1
2
1
1
1
3
0
0
1
0
0
0
0
1
1
2
1
0
1
1
0
1
2
1
2
2
1
1
0
0
0
1
1
1
1
3
1
2
0
1
1
1
1
1
0
0
1
0
0
1
1
1
2
2
2
1
1
0
1
1
1
1
2
1
0
1
0
2
2
0
1
1
1
1
1
1
0
0
2
2
1
1
1
2
2
0
1
1
1
1
0
1
1
2
1
1
1
2
2
2
1
1
0
2
0
1
1
1
1
2
1
2
1
1
1
2
2
2
1
1
1
1
1
1
2
2
2
1
1
1
1
0
2
1
1
1
1
1
1
2
2
1
1
1
2
1
0
1
2
1
1
1
1
0
1
1
1
2
2
0
2
2
1
2
1
2
1
1
1
1
1
0
1
1
1
0
1
0
2
0
2
1
1
0
2
1
2
2
1
1
0
1
2
1
1
2
2
1
1
2
1
1
1
1
1
0
1
1
1
0
0
1
3
1
1
1
1
2
1
1
1
1
2
2
1
2
1
0
1
1
1
1
2
1
1
1
0
1
0
0
2
1
2
2
0
1
1
0
0
1
1
1
0
1
2
1
1
2
0
1
0
1
1
1
1
0
0
1
1
1
1
2
0
1
1
2
0
2
1
2
1
2
1
2
2
0
0
1
0
1
1
1
2
0
1
1
1
0
1
1
0
1
0
1
1
2
1
2
1
2
1
2
1
1
2
0
2
0
0
2
2
1
0
1
1
1
1
1
0
1
1
0
1
2
1
1
0
2
2
2
0
2
2
1
1
1
1
1
0
0
1
2
1
1
1
1
1
1
0
1
1
0
1
1
2
1
2
1
1
1
0
1
2
1
0
0
2
1
1
1
2
2
1
0
1
2
1
2
1
1
0
1
1
2
1
1
0
1
2
1
2
0
1
0
1
2
0
2
1
2
1
2
2
0
0
1
2
2
1
0
1
2
2
2
0
0
1
2
2
1
0
1
0
2
0
1
2
1
1
1
2
0
1
1
0
2
1
2
2
2
0
1
2
2
1
1
1
1
1
2
2
1
3
0
1
0
1
1
1
1
0
1
2
1
0
1
1
0
1
1
0
1
1
0
0
1
2
2
1
1
2
2
0
0
1
2
2
0
2
1
2
1
1
2
1
1
0
2
2
0
2
0
2
0
1
0
1
2
1
1
2
1
1
2
1
1
1
2
2
1
1
0
2
1
2
1
1
0
1
1
1
2
2
1
0
1
0
1
0
1
1
1
1
1
1
1
0
0
1
1
2
1
1
1
1
1
0
1
2
1
1
1
1
2
1
1
1
2
2
1
1
1
2
2
1
2
1
1
1
0
3
1
0
2
1
1
1
1
1
1
0
1
0
1
0
0
1
1
2
0
0
1
0
2
0
2
2
1
2
2
1
1
1
2
1
0
0
2
1
2
2
1
2
2
1
1
0
1
1
1
2
2
1
1
1
2
2
2
0
1
1
1
2
1
1
1
1
2
1
1
1
1
0
1
1
2
0
1
1
2
1
1
2
0
1
0
1
1
1
2
1
2
1
1
1
0
0
1
2
1
2
1
2
1
1
2
1
0
0
1
1
0
1
0
1
1
0
1
1
1
2
1
1
2
1
2
1
1
1
1
0
1
0
1
1
1
2
2
2
1
2
0
2
1
1
0
1
0
2
0
1
0
1
1
0
0
1
1
1
1
0
1
1
1
1
2
1
2
0
2
0
1
1
1
0
0
1
2
2
0
1
1
0
1
0
2
2
1
1
1
0
0
1
1
1
1
2
2
2
2
1
1
1
2
2
1
1
1
2
1
1
2
0
1
1
1
1
1
1
2
1
2
2
2
2
1
1
2
1
2
2
2
1
0
1
1
1
1
1
0
1
2
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
2
1
1
1
0
2
1
1
0
1
1
1
0
1
1
0
1
1
0
0
1
1
1
1
2
1
1
1
1
1
1
2
1
1
2
3
0
1
1
2
0
2
0
2
1
1
1
0
2
0
0
1
1
2
2
1
1
2
1
1
1
1
2
1
1
1
1
1
1
0
1
1
4
1
0
1
1
0
1
0
1
2
1
1
2
1
1
1
0
0
2
1
1
2
1
1
1
2
0
1
1
1
0
1
1
1
2
1
1
1
2
2
1
0
0
1
1
1
1
1
1
1
1
1
1
0
1
1
2
1
1
1
2
1
5
1
1
1
2
1
1
0
1
1
0
1
1
1
1
1
1
2
1
0
2
0
2
1
2
1
2
1
1
1
2
1
2
1
1
0
0
2
2
1
0
1
1
1
0
2
1
0
2
1
1
2
1
2
1
2
1
0
0
1
1
1
1
1
1
1
1
0
1
2
1
1
2
1
2
1
1
2
1
2
1
2
1
1
0
2
2
1
1
1
1
1
1
1
1
0
1
1
1
0
1
1
2
1
1
1
0
0
0
2
1
1
1
1
1
3
0
2
1
0
1
0
0
0
1
1
1
2
2
2
1
1
1
2
0
1
1
1
1
1
2
1
2
1
1
2
1
1
2
1
2
0
0
2
2
2
1
1
2
1
1
1
2
1
1
2
0
1
1
1
2
2
0
1
1
0
1
1
2
1
1
1
2
1
1
1
0
1
1
0
1
1
1
1
0
1
1
1
1
1
2
0
1
2
2
1
2
0
2
1
1
1
1
1
1
1
1
1
1
0
1
0
1
1
2
0
2
2
1
0
2
1
0
2
2
1
2
1
1
2
1
2
1
1
1
2
0
0
0
1
1
2
0
0
1
1
1
1
2
1
2
1
1
2
1
2
1
0
1
1
2
1
1
3
1
2
1
0
1
1
1
1
1
1
1
1
1
1
1
2
1
3
0
1
0
2
2
2
0
0
2
0
1
0
1
2
1
2
1
3
1
1
1
1
1
0
2
1
1
1
1
1
2
1
0
1
1
1
2
2
1
1
1
0
1
1
1
1
2
1
1
1
2
2
1
2
2
0
1
1
1
0
0
1
2
1
2
2
1
1
1
0
1
0
2
2
1
0
1
2
1
1
1
1
2
0
1
1
1
1
1
3
1
1
1
2
1
2
0
2
1
2
2
0
1
1
0
1
1
1
1
0
1
0
1
1
1
1
0
0
1
1
1
2
1
1
0
0
1
2
2
0
1
0
2
1
1
1
3
1
1
2
0
1
1
0
1
0
2
1
0
0
2
1
1
0
1
1
1
0
1
1
2
1
1
2
1
2
1
0
0
0
2
0
2
1
2
2
2
1
2
1
2
2
1
1
0
0
2
2
1
2
2
1
1
1
2
1
1
0
0
1
1
2
1
0
0
0
0
1
0
1
0
1
1
0
2
2
2
2
1
2
1
1
2
1
2
0
2
2
1
0
1
2
1
1
2
2
1
1
1
2
2
0
1
1
1
2
1
0
3
1
2
2
2
1
1
0
1
2
0
2
1
2
1
1
1
2
0
1
0
1
2
1
1
3
2
1
2
0
1
1
1
1
0
1
2
2
1
1
1
1
1
2
1
1
0
1
1
2
1
2
1
2
1
1
1
2
1
0
1
1
1
2
1
1
1
1
2
2
1
0
2
3
1
2
1
1
0
2
1
2
1
1
2
2
2
2
1
0
0
2
2
1
1
1
1
0
1
2
1
0
1
0
1
2
1
1
0
1
1
2
1
1
0
1
2
1
1
1
0
0
0
1
1
2
3
1
2
0
2
1
1
0
2
1
0
2
1
1
0
1
0
2
1
1
1
2
1
1
1
1
2
1
0
1
1
1
1
0
1
2
1
0
2
2
1
1
1
1
2
1
2
1
2
1
2
0
1
1
2
1
1
0
1
1
0
2
2
1
2
1
1
1
2
0
1
0
1
1
1
1
1
2
1
1
1
2
2
3
1
1
0
0
1
2
1
1
2
2
2
1
1
2
1
1
2
1
1
1
2
1
1
1
1
0
1
1
1
1
1
2
0
0
1
1
1
1
1
1
0
0
2
1
1
1
0
1
2
2
1
0
2
2
1
1
0
0
1
2
1
1
2
1
1
1
1
1
0
1
1
1
0
1
2
2
0
1
0
0
2
0
0
1
2
1
0
0
1
1
1
2
2
1
1
1
2
2
1
1
1
1
2
1
1
1
0
1
0
1
1
1
0
2
2
1
2
0
1
1
1
2
1
0
1
0
0
3
0
3
1
0
2
1
1
2
1
2
1
1
1
2
1
1
2
1
1
2
1
0
1
1
2
1
1
2
1
1
1
1
1
0
1
2
2
2
1
1
2
1
1
1
2
1
0
1
1
1
1
0
1
2
0
2
1
1
1
1
1
2
1
2
1
1
1
1
1
0
2
1
2
2
0
0
1
2
2
2
0
2
2
1
1
1
1
1
0
0
0
1
1
3
0
1
1
1
2
1
1
1
1
2
2
1
0
2
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
0
0
0
0
1
0
2
1
1
1
1
1
2
0
1
1
0
2
1
0
1
1
2
1
1
1
1
1
1
1
1
1
0
0
1
1
1
1
1
1
0
1
0
1
1
2
0
1
2
1
0
0
2
2
1
1
2
1
1
1
0
0
1
1
1
2
0
1
2
2
2
0
2
1
0
1
1
1
2
1
1
1
0
1
1
2
1
2
1
2
1
0
1
1
2
0
1
0
1
0
1
1
1
0
1
1
2
1
1
1
1
0
1
0
1
2
1
0
2
0
2
1
1
0
1
1
1
1
0
1
0
1
1
2
1
1
1
0
1
1
2
2
1
2
1
1
0
1
2
1
1
1
1
1
0
1
2
0
1
1
1
0
2
0
0
1
0
1
0
2
2
2
2
1
1
1
1
1
1
2
2
1
1
1
0
1
1
0
1
0
1
2
1
1
1
2
1
1
3
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
2
1
1
0
1
1
1
1
1
1
1
1
2
1
2
1
2
1
2
0
2
1
1
0
2
2
2
1
1
1
2
2
1
1
1
1
1
2
1
1
1
2
1
1
0
0
2
1
2
2
1
1
1
1
0
1
1
2
1
1
1
1
1
1
1
1
0
3
2
0
1
1
1
0
1
1
2
1
1
0
2
1
1
1
1
2
0
1
2
1
2
0
1
1
1
1
0
0
1
0
0
1
0
1
1
2
0
1
1
1
1
2
1
1
2
1
1
0
0
1
1
1
1
1
1
0
1
1
1
1
1
2
1
1
1
1
1
2
2
3
1
1
2
1
1
1
1
2
1
3
1
0
1
2
2
1
1
1
1
1
0
1
2
1
1
0
1
2
1
1
1
2
1
0
1
1
2
1
1
2
2
1
1
1
1
2
1
1
1
1
2
0
2
1
1
2
0
1
2
0
0
1
2
1
2
2
3
1
1
1
1
2
1
1
1
1
0
2
0
1
1
1
0
1
1
2
2
2
2
0
1
1
2
1
2
0
1
1
2
1
1
1
2
2
0
1
1
0
1
1
2
2
2
2
2
1
1
0
1
1
1
0
0
2
1
1
2
1
1
2
1
2
1
1
2
1
0
1
1
1
1
1
1
1
2
2
2
2
0
2
0
2
0
1
1
0
1
1
2
1
1
1
1
0
1
1
2
1
1
0
1
1
1
1
1
1
2
1
1
1
2
1
1
1
2
2
2
0
2
1
1
1
1
0
1
1
1
0
2
2
1
0
1
1
1
1
2
2
2
0
1
1
1
1
0
1
1
1
1
1
1
2
2
0
1
1
1
1
2
2
3
2
2
1
1
1
1
3
2
1
1
1
2
0
1
1
0
1
1
0
0
1
2
2
1
1
1
1
1
1
1
1
1
0
2
1
2
2
1
1
1
1
2
1
2
1
0
1
2
0
1
1
1
0
1
1
1
2
1
1
2
1
1
2
0
2
2
2
1
1
0
1
0
1
1
1
2
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
0
2
1
2
1
1
0
1
3
1
0
0
0
1
0
0
1
1
1
0
1
1
0
0
1
1
2
0
2
2
2
1
1
1
1
1
1
1
1
0
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
5
1
1
3
1
0
0
0
1
1
2
1
1
2
0
2
0
1
2
2
0
2
0
0
2
1
1
1
2
1
1
2
2
0
1
2
0
1
0
2
2
2
1
1
1
1
1
1
1
1
1
1
1
3
1
1
0
2
1
1
1
1
1
1
0
2
1
1
2
2
0
1
0
0
1
1
2
2
2
1
1
1
1
3
1
0
0
1
0
0
1
1
1
1
0
2
1
0
0
0
2
1
1
1
1
1
2
0
1
1
1
1
2
0
1
1
1
2
0
1
2
1
1
1
1
1
1
1
2
1
1
1
2
2
2
1
1
1
2
2
1
1
1
1
0
0
1
2
2
1
0
1
0
0
1
2
2
1
1
1
1
1
1
2
2
0
0
2
2
1
1
2
1
0
1
2
0
1
1
1
0
1
2
1
1
1
1
1
2
2
2
0
1
1
0
1
2
2
1
0
2
1
1
2
1
1
1
1
1
0
2
1
3
1
1
0
1
1
1
1
1
2
1
1
2
1
2
1
2
2
0
0
2
2
1
2
2
1
0
1
2
1
2
1
1
1
2
2
2
0
2
1
2
1
0
2
1
1
1
1
1
2
0
2
0
0
2
1
2
1
0
0
0
1
0
2
0
1
0
1
1
1
0
1
0
2
1
1
2
1
0
1
1
2
1
1
2
1
2
4
0
1
0
1
2
0
1
1
1
0
0
2
1
1
2
1
1
1
1
0
1
2
1
1
1
2
1
1
1
1
1
2
0
1
2
1
1
1
1
4
2
1
1
0
1
1
1
1
1
3
0
0
2
1
2
0
0
2
1
0
1
1
1
1
1
1
1
2
0
1
1
0
1
1
2
2
0
1
1
0
1
2
2
2
1
1
5
1
0
1
1
1
2
0
1
1
2
2
1
1
1
1
1
0
0
0
1
2
1
1
1
2
0
0
0
1
1
1
1
1
1
1
2
1
1
1
0
1
0
0
1
0
1
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
2
0
0
1
2
2
1
0
0
2
1
2
1
0
0
1
1
2
1
1
2
1
1
2
1
1
1
2
2
1
2
0
1
0
2
0
1
1
0
2
1
1
0
1
1
2
0
1
1
1
1
1
1
1
2
1
1
2
2
1
1
1
1
1
0
2
3
1
1
0
1
1
1
1
1
1
2
1
1
1
2
1
2
1
2
1
1
1
1
1
1
1
1
0
1
2
1
1
0
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
0
2
2
1
1
1
1
1
1
2
0
1
1
2
1
2
0
1
1
2
2
0
2
2
2
0
1
1
1
2
2
0
1
1
0
1
1
2
1
0
2
1
2
1
1
2
1
0
1
2
2
1
1
0
1
1
0
2
2
1
0
0
1
1
2
2
0
1
1
1
0
2
2
1
2
1
1
1
2
1
0
3
1
1
1
2
0
0
2
1
1
1
2
1
1
0
1
1
1
0
1
1
1
1
0
2
1
1
1
1
1
2
1
2
2
1
1
3
0
1
1
0
1
2
1
2
1
2
1
0
2
1
2
2
2
1
2
2
0
2
1
2
2
1
2
1
0
1
1
2
2
0
1
2
2
0
4
2
2
1
1
2
1
1
1
0
1
1
1
0
2
2
1
0
1
1
1
2
1
2
1
1
1
1
2
1
2
1
1
1
1
0
1
1
1
3
2
1
1
1
1
0
2
1
1
1
1
1
2
1
1
1
1
0
1
1
1
0
1
1
2
1
1
2
1
0
1
1
0
1
2
0
1
0
0
2
0
1
2
0
0
2
1
2
1
2
2
1
2
0
1
0
1
1
1
1
0
1
2
2
2
1
1
1
2
1
1
1
1
1
1
0
1
2
2
2
2
2
2
2
1
0
1
0
1
2
0
2
1
1
2
1
1
1
1
0
1
2
1
1
1
1
1
1
0
0
1
0
2
1
0
1
1
2
2
1
1
1
1
0
1
2
2
0
1
2
2
1
0
0
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
2
2
1
1
2
1
2
1
1
0
0
2
1
2
0
2
1
2
1
1
1
2
0
0
1
1
1
1
0
0
1
2
1
1
1
1
2
2
1
0
1
1
1
0
3
2
1
1
2
1
0
1
1
1
0
0
1
0
2
1
1
1
0
1
2
1
0
1
2
2
2
1
0
1
1
1
0
1
1
0
0
0
1
1
1
1
2
1
2
2
2
1
1
4
1
2
2
2
2
0
1
1
1
0
1
1
1
1
1
1
1
1
3
1
0
1
1
1
2
0
1
2
0
1
1
1
0
0
1
2
1
0
0
1
1
1
1
1
2
2
0
2
1
2
1
2
1
1
1
1
2
1
2
3
2
1
1
0
0
1
1
2
2
2
0
2
0
1
1
0
2
1
1
0
1
2
1
0
1
1
1
2
2
1
1
1
1
2
0
1
1
2
1
1
1
1
1
1
2
2
0
2
0
1
1
1
1
1
0
1
0
2
2
1
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
0
1
1
1
1
0
1
1
1
2
2
2
2
1
1
1
0
2
0
1
1
2
1
1
1
2
0
1
2
2
2
1
0
0
1
1
2
1
0
1
2
1
1
1
1
2
1
0
1
2
1
2
1
0
1
1
1
1
0
2
1
1
2
2
0
1
2
1
1
2
1
2
2
1
1
2
1
1
1
1
1
2
2
2
1
2
0
1
0
1
1
0
1
0
1
2
2
2
1
3
1
2
0
1
1
2
1
0
0
0
0
1
0
1
1
1
1
2
2
0
1
1
0
1
1
2
0
0
1
1
1
1
2
2
1
1
3
0
1
1
2
1
2
1
2
1
0
1
1
1
1
2
1
1
0
1
1
2
1
1
1
1
1
1
1
1
1
0
1
1
1
2
1
2
0
2
1
2
1
1
2
1
1
1
2
1
0
1
1
0
0
1
2
0
2
1
1
1
1
1
0
2
0
2
0
0
1
1
1
1
1
0
2
1
1
1
1
2
1
3
2
2
0
1
1
1
1
1
3
0
1
2
1
1
2
1
0
1
2
0
1
1
2
2
1
1
0
1
2
1
1
1
2
0
2
0
2
2
2
0
1
1
2
0
2
1
1
1
1
0
0
1
1
2
0
1
0
1
2
0
1
0
0
0
1
2
0
2
1
1
1
1
1
1
1
0
1
1
1
0
1
1
1
1
1
0
1
0
1
2
1
1
1
2
1
0
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
5
1
0
1
2
1
1
0
0
2
1
1
1
1
1
2
1
2
2
0
2
1
2
0
1
1
1
1
1
1
0
2
2
0
2
1
1
1
0
1
0
1
0
1
1
1
2
1
1
0
2
2
0
1
1
1
1
1
1
2
0
1
2
2
2
1
0
1
1
0
1
2
1
1
0
1
1
0
2
0
2
1
1
1
1
1
1
1
2
1
1
1
1
0
2
1
1
1
2
2
1
1
2
0
0
1
1
1
2
0
2
0
1
2
1
2
0
1
1
0
1
1
1
1
1
2
2
1
1
0
1
0
1
1
1
1
2
1
3
0
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
0
2
0
1
1
1
1
2
1
2
2
1
0
2
1
1
1
1
1
1
1
2
0
1
0
2
1
0
1
0
2
1
1
2
1
1
1
2
1
1
1
0
1
0
0
1
1
0
1
1
1
0
0
1
1
1
1
1
1
1
0
0
1
2
1
2
1
1
1
1
1
1
1
1
1
1
0
1
1
0
1
1
1
1
2
0
1
1
1
0
2
1
1
0
1
0
1
0
2
2
1
1
1
1
1
1
0
0
1
1
0
0
0
2
1
1
0
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
0
0
1
0
1
1
2
0
1
0
2
1
1
1
2
1
1
1
2
2
1
3
2
1
1
1
1
1
1
2
0
0
2
0
0
1
0
1
1
0
1
2
1
1
1
1
0
0
1
1
1
1
2
2
1
2
1
1
1
2
2
0
1
2
1
1
0
2
1
2
1
0
1
2
0
1
2
1
2
1
1
1
2
1
1
1
1
2
2
0
2
4
2
1
6
1
1
1
3
1
1
1
0
1
1
2
0
1
1
1
1
0
1
2
1
0
1
1
1
1
2
1
1
1
1
1
0
1
0
2
1
2
1
1
0
1
1
1
2
1
1
1
1
2
5
1
1
1
1
1
0
2
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
2
1
1
2
1
1
0
1
1
0
1
1
1
1
1
2
1
1
2
1
0
1
1
0
0
2
1
1
1
2
1
0
1
2
2
2
0
2
1
1
1
2
2
0
0
1
0
1
1
0
1
2
2
2
0
1
2
0
2
1
1
2
2
1
1
0
1
0
0
1
1
2
0
2
1
2
2
2
1
1
2
2
0
1
1
2
1
1
2
1
2
1
1
2
1
0
2
0
1
1
1
2
2
2
2
0
1
1
1
1
2
0
2
1
1
2
1
1
1
1
1
1
6
0
1
1
1
1
1
1
1
1
1
2
1
0
0
0
1
1
2
1
1
1
1
0
1
1
1
0
1
1
0
1
2
2
1
1
0
1
2
2
1
1
0
1
1
0
2
1
2
0
2
1
1
1
1
1
1
1
2
1
2
2
0
1
1
1
1
1
1
1
1
1
1
0
1
0
1
2
0
1
1
0
1
2
1
1
1
2
1
1
0
0
1
1
2
0
0
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
0
0
2
2
0
1
1
0
1
1
1
1
1
1
2
1
2
2
2
1
1
1
2
1
0
2
0
2
2
1
1
2
0
1
1
2
1
1
1
1
1
1
1
1
1
1
1
0
2
1
2
1
1
0
2
0
1
1
1
2
1
1
1
1
1
1
1
0
1
1
2
2
0
0
2
1
2
1
0
2
2
0
0
1
1
1
2
1
3
2
0
2
2
2
0
1
1
1
1
2
2
2
1
1
1
0
1
1
1
2
1
1
1
2
1
1
2
0
1
1
1
0
1
1
2
1
2
1
0
1
0
1
1
2
1
1
2
1
2
1
2
1
1
1
2
2
1
0
0
1
2
1
1
1
0
1
1
0
1
1
2
1
1
1
3
2
1
2
1
1
2
1
1
0
1
1
1
2
1
1
1
1
0
2
1
1
2
1
1
2
1
2
1
2
1
2
1
2
2
1
0
1
0
1
1
2
2
1
1
2
1
1
1
0
0
2
1
1
1
1
2
1
1
0
1
1
1
1
1
1
0
0
1
1
1
1
0
1
1
1
0
1
1
1
1
1
1
2
1
2
1
1
0
1
1
2
1
2
1
1
0
0
1
1
1
1
2
0
2
1
1
1
1
1
2
2
1
1
1
1
1
1
1
0
2
1
1
1
2
2
1
1
1
1
1
2
1
2
1
1
1
2
1
1
0
1
1
5
1
1
1
1
1
1
1
1
1
2
1
0
1
2
2
2
2
1
1
1
2
1
2
1
1
1
0
2
1
0
1
0
1
1
1
1
1
0
1
1
1
1
0
1
1
1
1
0
1
0
1
1
1
1
0
2
1
2
1
1
1
2
0
1
1
2
1
2
0
0
1
2
1
1
1
2
0
2
1
1
1
1
1
1
1
2
1
0
1
0
1
2
2
1
2
2
2
2
2
2
1
0
1
0
0
1
0
1
1
1
1
1
2
0
2
1
2
0
0
2
2
2
1
0
2
1
2
2
2
0
1
1
2
1
1
2
2
2
1
1
0
1
1
1
0
1
2
1
1
2
2
1
1
0
1
1
2
1
0
0
2
1
0
1
2
1
1
1
2
2
1
0
2
1
1
2
1
1
2
1
1
2
2
1
1
0
1
0
1
0
1
0
1
2
1
1
1
2
2
1
1
0
1
0
2
1
2
3
1
1
2
1
0
2
1
1
1
1
2
2
1
1
1
2
1
1
1
0
2
0
1
2
1
2
0
1
1
1
2
2
0
0
1
0
1
0
1
0
1
2
2
0
1
1
0
1
1
1
0
1
0
1
1
2
1
2
0
2
1
1
6
2
1
0
1
0
1
2
0
0
1
1
2
1
1
2
1
1
1
1
0
2
1
0
1
1
1
0
1
0
1
1
1
2
2
1
1
1
0
2
1
1
1
2
1
2
1
1
3
0
1
1
1
1
2
0
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
2
2
1
1
3
1
1
1
1
1
0
1
2
1
1
1
0
0
0
1
0
1
1
2
0
2
1
1
2
0
1
3
2
1
1
0
1
2
2
1
1
0
0
2
1
1
1
2
1
0
1
1
1
1
3
1
1
2
1
0
2
0
1
1
1
1
1
1
2
0
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
1
1
2
1
2
2
2
2
1
1
1
1
1
2
1
1
1
0
0
1
0
2
2
2
2
1
1
2
1
0
2
0
0
1
1
1
1
1
0
1
1
1
0
2
2
1
0
1
2
0
1
1
1
1
2
1
1
1
0
1
0
2
1
1
2
1
1
2
1
2
2
2
1
1
0
0
2
2
0
2
1
1
1
1
1
1
1
2
0
1
0
2
0
0
1
1
2
1
1
0
1
0
0
0
2
1
0
1
1
1
0
2
1
2
1
0
1
1
0
1
1
2
0
1
1
2
2
1
1
1
1
2
1
1
0
1
1
1
0
0
0
2
1
1
1
1
2
1
1
0
1
1
2
1
1
0
2
1
2
0
0
1
1
1
1
7
1
1
1
1
2
1
1
1
0
1
2
1
0
1
0
3
2
1
0
0
2
1
1
1
1
1
2
1
2
1
1
1
1
2
0
2
2
1
2
1
1
0
2
1
2
1
1
1
1
1
0
1
2
1
2
2
1
2
1
1
1
2
2
1
1
2
1
0
1
0
1
1
2
1
1
1
2
0
1
1
1
0
1
1
1
2
1
0
2
1
0
1
1
2
1
2
1
0
2
2
1
2
0
0
2
1
1
1
1
1
0
1
1
0
2
0
1
1
2
1
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
0
1
1
1
2
2
1
2
1
1
1
2
2
1
1
2
2
1
1
1
1
0
1
2
1
1
2
2
0
1
1
2
2
0
1
1
1
1
1
0
1
1
1
0
1
1
0
2
0
1
2
1
1
1
1
1
1
1
2
2
1
0
1
0
1
1
0
1
1
1
1
1
2
2
1
2
2
1
0
0
2
1
1
1
1
1
1
0
1
1
1
1
0
2
2
2
0
1
0
1
1
4
2
2
1
0
1
1
0
1
2
1
0
1
2
2
2
2
2
0
2
0
0
2
1
1
0
2
1
2
1
2
0
0
0
1
1
0
1
1
2
2
1
2
1
1
1
1
0
2
1
1
1
1
1
1
2
1
1
2
0
2
0
1
0
1
1
1
2
1
2
1
2
1
1
1
1
1
1
0
2
0
2
2
1
2
0
0
2
1
1
2
1
1
2
0
1
1
1
0
1
1
1
1
1
2
2
1
1
1
2
3
2
1
0
2
1
1
1
0
1
3
1
2
1
1
1
1
0
0
0
2
0
0
1
2
1
0
1
1
1
0
2
1
1
1
0
2
1
1
1
1
1
0
0
1
1
1
1
1
0
1
1
1
1
1
1
1
0
2
0
1
1
1
0
1
2
1
1
1
1
1
1
2
0
1
2
2
2
2
1
2
1
1
1
1
2
2
1
1
1
3
1
1
1
2
1
1
1
1
1
0
1
1
1
0
1
2
1
2
0
1
1
1
1
1
0
0
2
1
1
1
1
2
1
2
2
2
1
2
2
2
1
1
1
0
2
1
1
2
0
2
1
1
2
2
2
1
1
2
1
1
0
1
0
1
2
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
2
2
2
0
1
1
2
0
2
1
0
1
1
1
0
1
1
2
2
1
0
1
1
1
1
2
1
1
2
1
0
0
1
1
1
0
2
0
2
1
1
1
1
0
2
1
1
1
1
1
0
1
1
1
2
2
0
1
3
1
2
1
2
3
1
1
1
2
2
1
2
2
0
1
1
0
0
0
0
0
1
2
1
2
1
1
2
0
1
2
1
0
1
1
1
1
1
0
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
2
1
2
1
1
0
1
2
1
2
1
2
1
1
2
1
1
1
1
1
0
1
2
1
2
1
1
2
1
0
1
1
1
1
1
1
1
0
1
1
2
2
2
1
2
2
1
2
1
2
1
1
1
0
1
1
1
2
0
1
2
0
1
0
0
1
1
0
2
1
0
1
1
2
1
0
0
2
1
0
2
1
0
0
1
2
1
1
1
0
1
2
1
1
1
2
1
1
1
1
1
2
2
1
1
0
1
1
1
0
2
2
1
1
1
2
1
0
2
2
1
1
1
2
1
2
1
2
0
1
0
1
1
1
1
0
3
0
2
1
1
1
0
2
2
1
0
2
2
0
1
1
1
1
1
2
2
2
1
1
1
2
1
0
1
1
2
1
0
1
0
1
0
1
0
2
0
1
0
1
2
2
2
1
1
1
1
1
2
1
1
1
0
1
2
1
1
1
0
1
1
2
0
0
2
2
2
2
1
1
1
1
1
1
1
1
1
1
0
2
2
1
1
0
1
1
1
1
0
0
1
2
1
1
2
1
2
0
2
2
0
2
1
1
1
1
2
3
0
1
2
0
2
1
1
2
1
1
1
1
1
3
1
1
1
1
0
0
2
1
1
2
0
0
4
2
1
1
1
0
2
1
0
2
1
1
1
0
1
1
0
1
1
0
0
1
1
1
2
0
1
1
2
1
1
1
1
1
1
1
1
2
1
3
2
1
4
3
1
1
1
1
0
1
0
2
1
0
2
1
2
1
2
0
1
1
1
0
2
1
1
0
1
1
2
1
1
2
2
1
1
1
1
1
2
1
0
2
3
1
2
2
1
1
0
1
1
1
0
1
2
1
1
1
1
2
1
1
2
0
2
1
0
2
2
0
0
1
0
2
0
1
1
0
1
1
2
1
1
2
1
0
1
2
2
1
2
1
1
1
2
2
1
1
2
1
1
1
2
0
1
2
1
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
2
1
1
2
2
1
1
1
1
0
2
1
2
1
1
2
1
1
1
0
1
2
1
2
2
1
0
0
0
1
1
1
2
1
1
1
2
1
1
2
2
0
1
1
2
0
0
0
0
1
2
1
1
1
2
2
1
1
2
1
1
1
1
0
2
1
1
0
0
1
1
2
1
2
1
2
0
1
2
1
1
1
1
1
1
1
2
1
0
0
1
0
2
1
1
1
1
2
1
1
2
1
1
2
1
2
2
1
1
2
1
1
1
1
2
1
2
2
1
2
1
1
1
0
2
2
1
1
1
0
1
1
0
1
2
1
1
1
2
1
1
2
1
0
2
1
2
1
1
2
1
2
1
2
2
1
1
4
0
1
1
2
1
1
0
1
2
0
2
0
2
1
0
2
0
2
1
1
0
2
1
1
2
3
2
1
1
1
2
2
2
0
1
1
2
1
1
2
1
1
1
1
1
1
2
2
1
1
2
1
1
1
1
1
0
1
1
1
1
1
0
2
2
1
2
1
1
0
1
2
1
2
2
2
1
1
1
2
1
1
0
2
0
2
1
2
3
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
2
1
1
1
1
2
1
1
2
2
1
1
2
2
1
2
1
0
1
1
0
2
2
1
1
2
1
2
2
0
1
0
0
0
2
1
2
1
0
2
2
1
0
1
1
1
1
0
2
0
1
1
1
1
0
1
0
2
1
0
1
2
2
1
2
1
1
1
2
1
1
1
2
1
2
0
2
1
1
2
1
1
1
2
2
1
2
0
1
1
1
2
1
1
1
1
1
1
1
0
1
1
2
2
1
1
2
1
2
1
2
1
1
1
1
1
1
1
1
0
1
2
2
1
2
1
1
1
1
2
1
1
2
0
1
1
2
0
1
2
2
1
2
1
1
0
1
2
1
1
1
1
0
1
1
0
1
1
2
1
1
0
1
2
1
1
0
2
0
1
1
1
1
1
1
1
1
1
1
1
1
0
2
0
1
1
2
2
0
2
0
2
2
1
1
1
2
1
1
2
1
2
0
1
2
1
1
2
2
1
2
0
1
1
2
1
0
1
1
1
1
1
2
1
2
1
0
1
0
1
1
1
2
2
1
2
1
1
1
2
1
1
0
2
1
2
0
0
1
2
1
2
1
1
2
1
1
2
1
2
1
1
1
1
1
2
0
0
1
1
1
1
1
1
2
1
1
1
3
1
1
2
1
2
1
2
1
0
1
1
1
1
0
3
1
1
2
1
1
1
1
1
1
1
1
2
1
0
0
0
2
1
0
0
1
1
0
2
1
0
2
1
1
1
1
4
2
1
2
1
2
0
1
0
2
0
1
2
2
1
1
2
1
0
1
1
2
0
0
2
0
2
1
0
1
1
1
2
0
3
1
2
1
0
0
1
0
2
1
1
2
1
2
2
1
1
0
1
2
1
2
1
1
0
1
2
1
2
1
2
2
0
0
1
2
1
1
1
0
1
0
1
1
2
0
0
1
1
2
1
1
1
2
1
1
2
1
2
1
1
1
1
1
0
0
0
0
1
1
0
1
1
1
1
2
1
1
1
1
0
1
1
2
1
1
2
1
1
1
1
4
0
1
2
1
0
1
1
0
1
2
1
0
1
1
1
1
1
2
0
1
1
1
2
0
0
1
1
1
1
2
0
2
1
0
2
1
2
2
1
1
1
2
1
2
2
2
0
0
2
1
1
1
0
2
1
1
2
2
1
1
1
0
1
1
1
1
0
1
2
0
1
1
1
2
2
1
2
1
2
1
0
1
2
2
1
2
1
0
1
0
1
1
1
0
1
0
2
2
0
1
0
0
2
0
2
0
2
1
1
2
1
1
2
2
1
1
2
0
2
2
1
1
1
1
1
1
1
1
1
2
2
2
1
2
2
1
2
1
0
1
0
1
1
1
1
1
1
1
1
0
0
2
2
2
1
1
2
2
1
1
2
0
1
2
1
2
2
1
1
1
1
2
2
1
1
1
0
2
2
0
1
1
0
1
0
1
1
1
1
1
0
0
1
0
1
1
1
1
1
1
1
2
0
2
1
0
2
2
1
1
2
2
1
1
2
1
1
1
1
1
1
0
0
1
0
1
2
1
1
1
1
2
1
2
1
2
1
2
1
1
0
1
2
1
2
1
1
1
1
2
1
0
1
0
1
1
1
2
1
0
1
1
0
2
1
1
1
1
0
2
0
1
0
2
0
1
1
1
1
2
1
0
1
0
1
0
1
1
1
2
1
1
1
2
1
1
0
1
1
1
1
2
1
1
2
1
2
1
1
0
1
1
0
0
1
2
1
2
2
1
0
1
1
2
1
1
0
2
0
1
1
2
1
1
1
1
1
1
2
1
2
1
1
1
2
1
1
0
2
1
2
1
1
2
2
2
1
0
1
1
0
0
2
1
1
1
2
1
2
1
2
0
0
0
2
1
1
2
1
0
1
1
2
0
1
1
0
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
2
1
2
2
1
1
0
1
2
1
1
0
1
1
0
1
2
1
1
0
2
0
1
1
2
1
1
0
1
1
1
1
2
0
1
2
1
1
0
0
1
2
1
1
1
2
2
1
0
1
1
1
2
2
2
1
1
1
0
2
1
1
1
1
0
1
1
1
1
1
0
1
0
0
1
1
1
1
0
1
2
2
2
1
0
2
1
2
2
1
1
0
2
1
2
2
1
1
1
1
2
2
1
0
1
1
1
2
1
2
2
1
1
0
1
2
1
0
0
1
1
1
2
1
1
1
1
1
0
0
1
1
0
4
2
1
1
2
1
0
1
1
1
1
2
1
1
1
0
1
1
1
1
1
0
1
0
2
1
1
0
1
2
2
1
1
1
1
2
0
1
1
2
1
2
1
2
2
1
1
1
1
1
1
1
1
1
2
1
1
2
0
1
1
2
2
2
1
1
0
1
1
2
2
2
0
2
1
0
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
0
0
2
1
1
1
2
1
1
1
1
1
1
2
0
1
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
2
2
2
2
1
2
1
1
1
0
2
2
1
1
0
2
1
1
1
1
0
2
1
2
0
1
0
1
1
1
1
0
0
0
1
3
1
1
2
2
2
2
1
1
2
0
1
2
1
0
0
1
1
2
1
1
1
1
1
2
2
0
1
2
1
1
1
1
1
1
1
1
1
2
1
1
2
1
0
1
1
1
1
2
2
2
1
2
1
1
2
1
0
1
0
0
1
1
1
1
0
1
1
1
0
2
1
2
1
1
2
1
1
1
0
1
1
0
2
1
1
1
1
1
1
2
2
0
1
1
1
1
1
1
1
1
2
3
2
1
2
1
1
1
0
2
1
1
2
0
1
2
1
2
1
0
0
1
0
1
0
1
1
0
1
2
2
1
1
1
1
0
2
1
1
1
0
0
2
0
1
0
0
1
1
2
2
1
1
0
1
1
1
1
1
2
2
1
2
2
0
1
2
2
0
2
0
1
0
0
1
1
1
2
1
1
2
2
2
1
1
1
1
1
1
2
1
1
2
1
2
2
2
2
2
2
2
1
1
2
1
1
2
2
1
2
1
0
1
1
1
2
1
0
2
1
2
1
1
2
1
2
1
0
0
1
2
2
1
1
0
0
1
2
1
1
1
1
1
1
2
2
2
2
2
2
1
1
2
1
1
0
1
0
0
1
2
1
2
1
0
2
2
1
2
0
1
6
1
1
2
2
0
1
1
1
1
2
1
1
1
2
1
1
1
2
0
2
1
1
1
2
2
1
2
1
1
1
1
2
1
1
1
1
1
2
2
0
0
3
1
1
0
1
1
2
0
1
1
1
0
1
1
1
1
1
1
2
2
1
1
1
0
1
1
1
0
1
0
0
0
1
2
2
1
0
0
2
1
1
0
1
1
0
0
0
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
2
0
2
2
0
1
1
1
1
2
0
1
2
1
2
1
1
1
0
1
1
1
1
1
1
2
1
1
1
1
3
1
0
0
2
0
1
0
1
1
1
0
0
2
2
1
1
2
1
0
1
2
1
1
2
0
1
2
2
2
1
0
0
2
1
1
2
1
1
1
1
1
1
1
0
2
1
2
1
1
1
0
0
3
1
0
2
1
1
2
1
1
0
2
1
1
1
1
1
1
2
1
1
2
0
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
0
1
1
0
1
0
1
1
0
1
1
1
1
2
0
1
1
1
3
1
0
0
1
1
1
1
1
1
1
1
1
2
2
1
0
2
1
1
2
0
1
0
1
1
1
0
1
0
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
0
1
1
1
1
1
1
2
0
2
2
2
1
3
1
0
1
1
2
0
1
2
0
1
1
1
2
1
0
1
1
0
1
2
1
1
1
1
0
1
1
1
1
1
1
2
2
1
1
0
1
6
1
1
1
2
1
1
1
1
1
1
0
1
1
1
2
1
1
0
1
1
2
1
0
0
0
0
2
1
1
1
1
2
2
0
1
1
1
1
1
1
1
0
1
1
1
1
1
0
1
1
1
1
1
2
2
2
2
2
1
1
1
1
1
2
1
0
2
1
1
1
0
2
0
0
1
1
0
2
3
0
2
1
1
0
3
2
1
1
0
1
2
2
1
1
2
1
0
1
1
0
2
0
1
0
2
1
1
0
1
0
1
1
1
1
1
0
1
2
1
4
2
1
0
1
2
2
1
1
1
2
1
0
0
1
1
1
0
1
1
1
1
0
2
0
1
0
1
1
0
2
1
2
0
1
1
2
1
1
0
1
1
1
1
0
1
0
0
1
2
2
1
1
1
1
1
1
0
1
1
1
1
2
1
2
1
1
1
1
2
2
1
1
2
1
1
1
2
1
1
1
1
1
2
0
1
2
1
1
1
1
1
2
2
1
0
2
1
2
1
3
1
1
1
2
1
2
1
2
1
1
3
1
2
1
1
1
0
0
1
2
1
2
2
1
2
1
0
1
0
0
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
0
0
2
2
1
1
2
1
1
1
2
0
1
2
2
0
2
2
0
1
2
2
2
1
1
1
1
1
1
2
1
1
0
1
2
0
1
1
1
2
1
0
1
0
1
0
1
0
2
0
1
1
2
0
0
1
2
2
2
1
2
0
1
1
1
1
2
1
2
1
1
1
0
1
1
2
1
1
1
1
1
1
1
2
2
2
0
0
1
1
1
0
1
1
2
0
2
2
1
1
1
1
1
1
2
0
2
1
1
1
2
1
2
1
1
0
1
2
1
0
1
1
1
2
1
1
1
1
0
2
1
1
1
1
1
2
1
2
1
0
1
2
1
2
1
1
1
0
1
0
1
1
1
2
1
2
1
0
2
0
1
0
0
2
1
1
1
2
0
1
1
0
2
2
2
1
1
2
1
0
1
1
1
0
1
1
0
1
1
2
0
1
1
0
1
1
0
1
1
0
0
1
1
0
1
1
1
2
1
1
1
0
1
1
1
2
0
1
2
1
2
2
4
1
0
2
0
2
1
1
1
1
1
0
0
2
2
2
1
1
1
1
0
1
1
1
1
2
2
2
1
1
1
1
0
0
2
0
1
0
0
0
1
2
1
1
0
1
1
1
1
2
1
1
0
0
1
1
1
0
1
0
2
1
1
1
1
1
1
1
2
1
1
1
1
2
0
0
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
0
1
0
1
1
1
1
0
0
2
1
1
0
0
1
1
0
1
1
1
1
1
1
2
1
0
2
0
0
1
1
0
0
1
1
1
2
1
0
0
1
1
1
1
4
2
1
2
2
1
0
1
1
0
2
0
0
0
1
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
0
1
2
1
2
1
1
1
2
2
2
1
1
2
1
1
2
1
1
0
1
1
1
1
2
1
1
1
1
3
2
1
2
2
2
1
1
7
1
2
2
2
2
2
1
1
1
1
1
2
1
1
1
2
1
1
0
1
1
1
2
1
1
2
1
1
1
1
1
1
1
2
1
1
2
2
1
2
2
1
1
1
1
0
1
1
1
2
1
0
1
1
2
1
1
1
1
2
1
1
1
2
1
0
2
1
2
1
1
1
1
1
2
1
2
1
1
1
0
2
0
1
1
0
2
1
1
1
1
1
0
1
1
2
1
1
1
2
0
1
0
1
1
1
2
1
2
2
1
1
1
0
1
1
1
1
1
1
1
1
2
0
1
1
1
1
1
1
1
1
2
2
1
2
1
1
0
0
1
1
2
2
2
1
1
1
0
1
2
1
1
1
1
2
1
2
1
2
1
1
3
2
1
1
2
0
0
2
1
1
1
2
1
0
2
4
1
1
0
1
1
0
2
1
1
1
1
1
1
1
1
2
0
1
1
0
1
0
1
0
1
1
2
2
0
1
1
1
0
1
1
2
1
1
1
1
2
1
0
0
2
2
0
1
1
2
1
1
1
0
0
2
0
2
0
1
0
1
2
2
1
1
1
0
1
0
1
1
1
1
0
2
2
2
1
1
1
0
1
1
1
2
1
1
0
2
0
1
1
1
1
1
0
1
1
1
1
0
1
0
1
1
1
2
2
1
2
1
2
1
1
0
1
0
1
1
1
2
2
1
1
0
1
0
0
1
1
1
1
2
0
1
1
1
2
1
1
1
1
1
0
2
1
0
0
1
1
0
2
1
0
1
1
1
1
2
1
0
2
1
2
1
0
1
0
1
1
1
0
2
1
1
0
1
0
2
1
1
0
1
0
1
2
1
1
2
2
1
1
1
2
1
1
1
2
2
1
2
2
1
0
1
1
3
2
1
1
0
0
1
0
1
2
1
1
1
2
1
0
2
1
0
0
2
2
1
0
0
1
1
2
1
0
1
1
1
1
2
0
1
2
0
1
1
1
0
0
1
0
1
1
0
1
1
1
2
1
1
0
2
1
2
2
1
0
1
2
1
2
1
1
0
1
1
1
2
2
2
0
1
1
2
1
1
1
1
2
1
1
0
1
0
2
1
1
0
1
1
0
2
2
2
1
1
1
2
1
0
1
1
1
2
0
1
2
1
1
1
2
1
1
1
0
2
2
2
2
1
0
4
1
2
2
2
1
0
0
1
0
1
1
0
1
1
0
2
1
1
0
1
0
0
1
2
1
0
1
0
1
0
0
1
1
2
1
1
2
2
0
2
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
2
0
2
1
1
2
2
0
1
1
1
1
1
1
1
1
1
2
2
2
1
2
2
1
0
1
0
1
1
2
2
1
1
2
3
1
0
1
1
1
1
2
1
1
2
1
2
0
1
2
2
1
1
1
2
0
2
1
2
0
2
1
2
0
1
1
1
1
1
1
2
1
1
2
1
1
0
1
1
2
1
1
1
1
2
1
1
0
1
1
1
1
1
1
0
1
1
1
2
1
1
1
1
1
0
1
1
0
1
1
1
1
2
2
1
1
1
1
1
2
4
2
1
1
0
1
1
1
0
1
1
1
2
1
1
1
1
1
1
0
2
1
1
1
1
0
0
0
1
2
2
1
0
1
1
2
1
0
1
1
1
2
0
1
2
1
1
1
2
0
2
1
2
1
1
0
1
2
2
1
2
1
1
2
2
1
1
2
2
1
1
1
1
1
2
1
0
1
0
1
1
1
1
2
1
1
1
1
1
0
3
1
0
1
0
2
1
1
1
1
1
1
1
0
2
1
1
1
2
1
1
1
1
0
1
1
0
1
1
1
2
1
1
1
2
1
1
0
2
2
1
1
0
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
0
1
2
1
1
2
1
0
2
1
0
1
1
1
2
1
0
1
0
1
1
2
2
1
1
1
1
2
0
0
0
0
1
1
2
1
2
2
1
1
1
2
1
1
1
0
2
2
1
2
1
1
2
1
1
0
1
1
1
0
0
1
2
0
1
1
1
1
1
1
2
2
1
1
0
1
1
1
0
2
1
2
2
1
1
2
1
2
2
1
1
2
0
1
0
1
1
2
1
1
1
1
1
0
1
2
2
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
0
2
1
2
0
1
2
1
1
1
1
1
0
1
2
1
0
1
2
2
1
1
1
1
1
1
2
1
1
1
0
2
1
0
2
2
1
2
2
2
2
1
2
1
1
0
3
1
2
2
3
2
1
2
0
1
1
1
1
1
2
2
1
2
1
2
1
1
1
2
1
2
1
0
1
1
0
1
1
1
0
1
1
2
1
0
1
2
0
0
1
1
0
1
0
1
1
2
0
2
1
2
1
0
2
1
2
0
1
1
1
1
1
1
0
2
1
1
2
1
0
1
1
1
1
1
2
2
0
0
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
2
0
0
1
0
1
1
1
2
1
0
1
1
2
2
0
1
1
2
1
1
1
2
1
2
1
1
0
1
0
2
1
1
2
0
2
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
2
2
0
1
1
2
0
1
1
1
2
1
0
1
1
1
1
2
1
0
0
1
1
2
1
2
0
1
2
0
1
1
2
1
1
1
1
0
0
1
1
1
1
1
0
2
1
0
1
1
1
2
1
2
2
2
2
0
1
1
1
2
1
2
3
1
1
2
2
1
2
2
3
0
1
1
2
2
2
1
1
1
0
1
0
1
2
1
1
1
2
2
2
2
1
2
1
2
1
1
1
1
0
1
1
1
1
1
1
0
1
0
2
1
1
0
2
3
1
2
0
1
1
0
1
2
0
0
2
1
2
0
1
2
2
0
2
2
0
2
2
1
1
1
0
1
2
0
0
1
1
1
1
0
1
1
1
1
2
1
1
1
1
0
2
1
1
2
0
1
0
0
1
2
0
1
1
1
1
1
1
2
1
1
0
1
1
2
1
1
1
1
1
0
1
1
1
1
1
0
2
0
1
1
2
0
0
1
1
0
1
1
2
0
0
0
1
1
1
0
0
1
1
3
1
0
2
0
1
1
1
1
2
0
1
1
1
0
1
2
1
1
1
1
1
0
2
1
2
1
1
1
1
1
1
1
1
1
0
0
1
1
1
0
1
2
0
0
1
0
1
0
1
1
1
1
1
0
2
0
0
1
1
2
2
1
2
1
1
2
2
0
0
2
1
1
1
1
2
1
0
1
2
0
1
0
0
1
1
1
0
1
0
1
1
0
1
1
2
2
1
0
0
1
1
2
2
0
1
1
1
1
1
1
1
1
0
0
0
2
1
1
1
1
1
2
1
0
2
0
1
2
2
1
1
1
1
0
1
1
1
2
1
1
2
1
0
2
0
2
1
1
1
1
1
1
0
0
1
1
1
0
1
0
1
0
2
0
2
1
1
2
1
1
0
2
0
2
1
1
0
2
1
1
1
1
2
2
1
2
1
1
2
2
2
2
1
0
2
0
1
1
1
1
0
1
1
1
1
2
1
0
1
1
1
1
1
1
0
1
1
1
2
2
1
2
1
1
1
1
2
2
0
1
1
1
2
2
1
2
0
1
1
1
2
1
1
0
2
2
1
1
1
1
1
0
1
1
1
2
1
1
2
2
1
1
2
1
0
2
0
2
1
1
1
1
1
2
2
1
1
1
1
2
0
2
1
1
2
1
2
1
2
1
1
1
1
1
0
1
1
1
1
2
1
1
1
1
2
0
1
1
0
1
2
1
0
0
1
2
1
0
2
1
1
1
0
0
1
2
2
1
2
4
1
0
2
1
0
2
2
1
1
1
1
1
1
1
1
0
1
2
1
1
1
1
1
1
1
1
0
0
0
1
1
1
2
1
4
1
2
1
0
1
0
2
2
2
1
1
1
1
2
1
1
1
1
0
1
1
1
2
1
1
1
1
0
0
0
1
1
2
2
0
2
1
1
1
1
1
1
1
1
1
2
1
1
0
1
0
1
2
1
0
1
0
1
1
1
1
1
1
1
0
2
3
1
0
1
2
1
1
1
1
1
1
0
2
0
1
2
1
0
1
1
1
2
1
1
1
0
1
1
0
1
0
2
1
1
1
2
1
2
1
1
1
0
0
1
1
1
2
1
0
0
1
2
1
1
1
1
1
2
2
1
2
2
1
0
1
1
2
1
0
0
0
1
0
1
2
0
2
1
2
1
0
1
1
0
1
0
1
1
1
0
1
1
0
2
1
2
1
1
1
1
1
1
2
1
1
1
0
0
0
0
1
0
2
1
1
2
1
1
0
1
2
2
1
1
1
2
2
0
1
1
1
1
1
2
1
1
1
0
1
2
0
0
1
1
2
1
2
2
1
2
2
1
1
1
2
1
1
2
1
1
1
1
2
1
1
1
1
1
0
1
0
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
2
1
1
1
1
1
0
1
1
0
1
2
1
2
1
1
0
2
0
1
1
0
1
1
1
1
2
2
1
1
1
1
1
0
1
1
1
0
1
2
1
1
2
1
0
2
1
0
2
0
2
2
1
0
2
2
0
1
2
0
1
1
1
2
1
1
2
1
0
0
1
1
1
0
0
1
2
1
1
1
1
1
1
2
2
2
1
2
2
0
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
0
0
1
1
1
2
2
1
2
2
1
0
1
0
0
2
1
1
0
1
1
1
0
1
2
1
0
2
0
1
1
1
2
1
1
2
1
0
1
1
1
2
1
1
1
2
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
2
2
1
1
2
1
2
2
1
1
2
1
2
1
2
2
1
1
1
1
0
1
1
0
1
1
1
1
0
1
1
0
2
0
1
1
1
1
1
2
1
0
1
2
2
2
2
1
2
1
2
1
0
0
1
1
2
1
1
2
2
1
1
1
1
1
1
2
2
2
0
0
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
0
2
1
1
1
0
2
2
1
1
1
1
2
1
1
1
2
0
2
0
0
1
0
2
1
2
0
1
2
2
0
1
1
1
0
1
2
0
1
1
1
1
1
1
1
1
1
1
2
1
1
0
2
2
2
1
2
2
2
1
1
1
2
1
1
1
2
1
0
0
2
2
0
1
0
2
2
1
1
1
0
1
2
1
1
2
0
2
1
2
1
1
1
1
0
1
1
1
1
1
1
1
1
2
1
2
2
0
1
1
2
1
1
1
1
1
2
1
1
2
1
1
0
1
1
1
1
2
1
2
1
1
0
1
1
1
1
1
1
2
1
0
1
1
2
1
1
0
1
1
1
1
2
0
1
1
0
0
0
1
2
1
1
1
1
1
1
1
2
1
0
1
1
2
0
1
1
1
1
1
1
1
1
1
2
1
1
1
2
0
1
2
2
1
1
1
0
1
2
1
1
2
2
2
1
2
2
2
1
1
2
1
1
2
2
2
1
0
2
0
1
1
2
1
0
1
0
0
1
2
1
1
2
0
0
2
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
0
1
0
0
0
1
1
2
0
1
2
2
1
2
1
2
0
1
1
1
1
1
1
0
1
0
1
1
1
1
0
1
1
1
2
0
0
1
0
1
1
1
1
1
1
1
2
2
1
1
2
2
1
2
1
1
2
1
1
1
1
1
0
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
2
1
1
0
1
1
1
1
1
1
1
1
2
1
1
1
1
1
0
1
1
2
1
1
0
0
1
2
0
1
1
1
1
0
2
0
1
1
0
2
0
1
1
0
1
1
2
2
1
1
2
0
0
1
1
0
0
0
2
2
4
1
1
0
1
1
3
0
1
1
0
1
1
2
1
1
2
2
1
2
1
1
1
1
1
2
1
1
1
2
0
2
0
1
0
1
1
2
0
1
1
2
1
1
1
2
2
2
0
1
1
2
1
1
1
1
0
1
0
1
0
1
1
1
1
1
1
1
2
1
1
1
1
2
1
2
2
2
1
1
1
1
1
1
2
0
0
1
1
1
1
1
0
1
1
2
1
0
1
1
0
1
0
1
0
1
1
1
0
1
0
1
2
0
1
2
1
1
1
1
0
1
1
1
2
1
1
0
1
1
1
2
2
1
1
0
0
1
2
1
1
1
1
1
1
2
1
2
2
1
2
0
0
2
1
1
0
2
1
1
0
1
1
1
1
1
0
2
1
1
2
1
1
1
3
0
1
1
0
2
0
1
2
2
0
0
0
1
1
0
2
1
1
0
1
2
1
1
1
2
1
2
1
1
1
1
1
0
1
0
1
0
1
2
2
1
1
2
0
2
1
0
1
1
1
1
1
0
2
2
0
1
1
1
1
1
1
0
1
1
0
1
1
1
0
0
1
1
2
1
1
2
1
1
0
1
0
1
1
1
1
1
2
1
3
1
1
2
2
4
1
1
1
1
2
1
1
1
1
1
3
2
1
0
1
2
2
1
1
1
1
1
1
0
0
1
0
1
1
3
0
1
2
0
2
1
2
1
2
0
0
1
1
2
1
2
1
0
1
0
1
1
1
1
2
2
0
0
1
2
2
1
2
0
0
1
2
1
2
1
1
1
0
0
1
1
1
0
1
1
1
0
2
1
0
2
1
1
1
1
2
0
1
2
0
2
2
1
1
1
0
1
2
0
1
2
1
1
1
1
1
1
1
0
1
0
1
1
1
0
1
1
2
0
2
1
1
0
2
1
0
1
2
0
1
2
1
1
1
1
1
1
0
1
0
1
1
2
1
0
1
0
1
0
1
1
2
1
1
1
1
1
1
2
1
2
1
2
1
1
2
1
2
2
1
0
1
1
1
2
0
1
1
1
2
1
1
0
1
1
0
1
1
1
2
1
1
1
0
2
2
1
2
2
1
1
1
1
1
1
0
1
1
1
2
1
0
2
0
2
2
1
1
1
1
1
1
1
2
2
1
1
2
1
0
1
2
2
2
0
2
2
1
2
0
2
1
1
1
1
1
1
6
0
2
1
2
1
0
1
1
1
1
1
0
1
0
1
1
0
1
2
2
2
2
2
1
1
0
1
1
2
1
1
0
2
1
2
1
1
1
1
2
2
1
1
0
0
1
1
0
1
0
1
2
1
1
1
2
0
1
0
1
1
1
1
0
1
1
0
1
2
1
2
1
1
1
1
1
1
1
1
1
2
2
2
1
2
2
0
2
1
1
2
2
1
0
1
1
1
2
0
1
1
1
1
1
2
1
0
1
1
1
2
1
2
1
1
1
1
2
1
1
1
1
0
2
1
1
1
2
2
1
1
1
1
1
1
2
2
1
2
2
1
1
2
1
1
0
2
0
1
0
1
1
1
1
0
0
0
1
1
1
1
1
0
0
1
2
2
2
1
2
1
2
2
1
1
1
2
1
1
1
1
1
1
0
1
0
2
1
1
1
0
1
1
2
2
1
1
1
0
1
1
1
1
1
2
1
1
2
0
1
0
1
1
0
2
2
2
1
1
0
1
1
1
1
0
2
1
1
2
2
1
1
0
1
2
2
1
2
2
0
0
2
2
1
0
1
1
1
2
2
1
0
1
1
1
1
1
0
1
1
0
0
1
1
1
1
2
1
0
1
1
2
1
2
0
2
1
1
2
0
1
2
1
1
1
0
2
0
2
1
0
1
0
1
0
1
2
2
0
0
1
1
0
1
1
0
1
1
1
1
1
0
1
0
0
0
1
1
1
1
1
1
3
1
1
1
1
2
1
0
0
1
1
1
2
2
1
1
1
1
1
1
1
1
0
1
0
0
1
1
1
1
1
1
1
2
2
2
1
2
2
1
1
1
2
1
1
1
1
1
1
2
1
0
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
0
1
2
2
1
1
1
1
1
1
2
2
1
2
1
2
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
0
2
2
1
2
1
1
2
1
1
1
1
1
2
1
0
1
1
2
1
1
1
1
0
1
2
1
1
2
1
1
2
1
2
1
1
1
0
0
1
0
1
2
1
0
0
0
1
2
1
2
1
2
0
0
0
1
1
1
1
2
2
1
2
1
1
1
1
1
0
1
1
1
1
1
2
0
0
1
1
1
1
1
1
1
1
1
1
0
2
2
0
2
1
1
0
1
2
0
1
1
1
2
1
1
0
1
0
1
1
2
2
1
2
1
1
2
2
1
1
1
0
2
1
1
1
2
1
2
0
1
1
0
1
0
1
1
1
0
1
1
0
1
0
1
1
1
0
1
1
2
1
1
0
1
1
2
2
0
1
3
2
2
1
1
2
1
1
1
1
1
1
1
1
2
0
2
0
1
1
1
1
2
1
0
0
0
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
2
0
2
1
0
1
1
0
1
0
1
1
0
1
1
2
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
2
2
1
2
1
0
1
0
1
1
2
1
2
1
1
1
0
2
0
1
0
1
1
0
0
1
0
1
1
0
0
1
0
1
1
2
0
1
1
2
2
1
1
2
2
2
0
1
1
2
1
1
1
1
2
1
1
2
2
2
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
1
2
1
1
1
0
1
1
1
1
1
0
2
0
0
1
1
1
0
1
2
0
2
1
2
1
1
1
1
1
1
1
2
2
2
2
2
1
1
1
2
2
1
1
1
1
2
1
1
2
1
2
1
1
1
1
1
0
1
1
1
2
1
1
1
1
1
2
1
1
2
1
0
0
1
2
1
0
1
1
0
1
0
1
2
1
0
1
0
1
2
1
0
0
2
1
1
1
2
1
0
1
0
1
1
1
1
1
1
2
0
2
1
0
0
1
1
1
1
0
1
1
0
0
1
1
0
1
1
1
1
1
1
1
0
2
1
2
1
2
1
1
1
1
1
0
1
1
1
0
1
1
1
1
0
2
1
1
1
1
2
2
1
0
2
1
1
0
1
1
1
0
1
2
1
1
1
0
0
2
1
0
1
1
1
1
1
2
1
1
0
1
2
1
1
1
1
2
2
1
1
0
1
2
1
1
0
1
0
1
2
2
0
0
1
0
1
1
0
1
1
1
1
1
1
1
1
1
1
0
0
1
2
1
1
1
2
1
1
1
0
2
2
2
0
1
2
2
1
1
0
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
0
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
2
1
1
0
1
1
1
1
1
1
1
1
2
2
0
1
2
1
1
1
1
1
1
1
3
2
2
1
1
1
0
1
1
1
1
0
1
1
1
1
0
2
4
0
1
1
2
1
0
1
1
2
0
2
1
2
1
1
1
0
1
2
1
1
1
1
0
2
0
2
1
2
1
0
1
1
2
1
1
1
0
0
0
3
1
2
1
1
1
1
1
2
1
2
1
1
1
0
2
1
1
1
1
1
2
1
2
1
2
1
0
1
0
1
2
2
2
0
1
1
1
0
2
1
1
0
1
2
1
2
2
1
1
1
1
2
1
1
0
0
1
1
1
1
1
2
2
1
1
1
1
1
0
1
1
2
1
1
2
1
1
1
1
1
1
2
1
1
2
1
2
1
1
0
0
0
2
0
1
1
1
1
0
2
0
1
1
1
2
0
1
1
1
2
1
1
1
1
1
1
1
1
0
1
1
1
1
1
0
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
1
3
1
0
1
1
1
0
2
2
0
1
1
1
1
0
1
0
1
1
2
1
1
1
1
1
1
0
0
0
2
3
1
1
1
0
2
2
1
1
1
1
1
1
2
1
2
1
1
1
2
1
0
1
1
3
0
1
1
1
1
1
1
1
2
1
1
1
1
0
1
1
1
1
2
2
1
1
2
1
2
1
1
2
2
2
1
2
2
1
1
1
1
2
2
1
1
0
1
0
2
1
1
0
1
2
0
2
2
2
2
1
1
1
0
0
2
1
1
1
3
1
1
2
3
2
2
1
1
0
1
1
1
1
1
1
2
2
0
0
1
2
1
2
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
0
1
1
2
1
1
1
1
0
1
1
1
1
1
2
1
1
1
1
2
1
1
1
0
1
1
0
1
1
1
1
1
1
2
1
1
1
3
1
1
2
2
0
0
2
1
1
2
2
1
1
2
1
2
1
1
0
1
1
1
1
1
2
2
2
2
1
1
0
1
2
2
1
1
0
1
1
1
0
2
1
1
1
1
0
1
2
2
2
1
1
1
7
0
1
0
1
1
1
1
2
1
1
0
1
1
0
1
1
0
1
0
1
0
1
1
1
2
1
1
1
1
2
2
1
2
1
1
1
1
2
2
1
1
1
0
1
1
1
2
2
2
2
1
1
1
0
0
2
1
1
1
0
2
1
1
2
1
2
1
1
1
2
1
1
2
1
1
1
1
2
1
1
1
0
2
1
2
0
2
2
1
1
2
1
2
2
0
1
1
1
0
1
2
1
1
2
2
1
2
1
2
1
1
0
1
1
1
1
1
1
2
1
2
2
1
1
1
2
2
3
1
1
0
0
1
1
1
1
1
1
2
0
1
1
2
2
1
2
0
2
1
0
2
2
1
1
1
1
4
2
1
2
1
1
2
2
1
0
1
1
1
0
0
2
0
1
0
1
2
0
0
1
1
1
1
2
1
0
1
1
2
2
0
1
0
0
0
0
1
1
1
1
1
0
2
1
2
0
0
1
2
1
1
2
1
1
1
1
3
0
1
1
1
1
1
1
0
2
1
0
1
1
1
1
2
0
1
1
1
2
1
0
2
1
1
2
1
2
1
2
2
1
0
1
2
1
1
1
1
1
2
2
1
1
2
2
2
1
1
1
1
1
1
1
0
1
1
1
2
0
2
1
1
2
3
1
1
1
2
1
1
2
2
2
2
1
2
0
2
1
2
1
0
2
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
0
1
1
1
1
1
1
0
1
0
1
2
3
1
1
1
2
1
1
1
1
2
0
1
1
1
1
0
1
1
0
1
2
2
0
2
0
2
1
1
0
0
1
1
1
1
1
1
2
1
2
1
2
3
0
1
0
1
1
2
2
1
1
2
2
2
1
0
2
1
2
0
0
0
1
1
0
1
2
2
0
2
1
1
0
0
1
1
1
0
0
1
0
1
1
1
1
1
1
0
2
1
1
1
1
1
1
2
2
2
1
0
0
1
1
1
0
1
2
1
1
2
0
1
0
2
1
1
1
2
1
1
1
0
1
2
2
2
3
1
1
1
0
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
0
1
1
1
2
1
1
1
1
1
1
2
0
2
2
1
1
0
1
0
1
1
1
1
2
1
1
1
1
0
1
0
2
1
1
0
0
1
4
1
1
1
0
1
1
1
1
0
0
2
2
1
0
1
1
1
1
1
1
1
1
0
2
2
0
1
1
1
1
0
1
1
1
2
1
3
1
1
1
1
2
1
1
0
0
0
1
1
0
1
1
1
2
1
2
1
1
1
2
1
1
0
1
1
2
1
0
1
1
1
2
1
1
1
1
0
1
2
2
1
1
2
1
0
1
1
2
1
0
1
1
1
1
1
0
2
1
1
1
1
2
2
1
1
1
1
1
0
1
1
0
2
0
2
2
2
0
2
2
2
0
1
2
1
0
2
2
1
1
1
1
1
2
1
0
1
0
2
1
1
1
1
1
1
1
1
0
0
1
2
1
0
1
1
1
1
2
2
0
1
0
1
1
2
2
1
1
2
1
0
0
1
2
2
1
1
1
1
1
2
0
1
1
1
2
1
2
1
1
4
1
2
0
0
1
1
1
2
2
1
1
2
0
1
0
1
2
0
1
0
1
1
1
1
1
2
0
1
1
2
0
1
1
1
1
1
0
1
2
1
1
0
1
1
2
1
2
2
0
1
0
1
1
0
1
0
1
0
1
1
1
2
0
1
1
1
1
1
2
1
1
1
0
1
2
1
1
2
1
2
1
0
2
1
1
2
1
2
1
1
0
1
1
1
1
1
1
0
1
1
2
1
1
0
2
1
1
1
2
1
1
2
0
0
0
2
1
0
1
1
2
0
2
0
2
3
1
1
2
1
1
2
2
1
1
1
2
1
1
1
1
1
1
0
1
0
0
1
1
1
2
1
1
1
1
1
0
1
2
1
1
2
1
1
1
1
1
2
2
1
1
0
1
1
2
1
2
1
1
1
2
2
1
0
1
0
1
1
1
1
1
2
1
1
0
1
1
2
1
1
0
2
0
0
2
1
1
0
1
2
1
1
1
0
1
1
1
1
0
0
1
1
1
0
0
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
2
0
1
2
2
0
0
1
2
2
2
1
1
1
1
1
2
0
2
2
1
1
2
1
2
1
1
1
1
1
0
0
1
1
1
2
1
1
2
1
2
1
1
2
1
0
2
1
1
1
1
1
1
1
0
2
1
1
2
0
1
2
2
1
1
2
2
0
1
1
3
2
2
1
1
2
0
1
1
0
0
2
2
2
1
2
0
0
1
1
1
1
1
2
1
1
1
1
1
1
1
2
0
1
1
1
2
2
1
1
1
0
1
1
0
2
3
1
2
1
1
1
0
1
1
1
1
2
1
0
1
0
1
0
1
2
0
1
2
0
1
1
1
0
2
2
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
2
2
2
1
1
1
0
1
1
1
2
2
1
0
1
1
2
1
1
1
1
1
0
1
1
2
1
1
1
0
1
1
1
1
1
1
2
2
2
0
0
1
2
0
1
2
3
1
2
1
1
1
5
2
1
0
0
2
1
2
1
1
0
1
0
2
1
2
1
1
1
2
2
1
1
1
2
0
1
2
1
2
1
1
1
1
2
0
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
2
1
2
1
0
1
1
1
1
1
1
1
1
2
0
2
0
1
1
1
0
0
1
2
0
1
0
2
1
2
1
1
1
2
2
2
0
0
1
2
1
1
1
1
0
1
2
1
2
1
2
0
1
1
1
1
1
1
1
1
0
1
1
1
1
0
0
0
1
2
0
0
0
0
2
0
2
1
1
0
1
1
1
0
1
2
1
1
1
2
1
1
1
1
1
0
1
1
2
1
1
1
1
1
1
1
1
1
0
0
1
0
0
1
1
0
1
2
1
1
0
0
1
0
1
1
1
0
1
2
2
1
0
0
1
0
0
0
1
1
1
3
1
0
2
5
2
2
1
0
1
2
1
0
2
2
0
2
2
2
1
1
1
2
1
1
1
1
1
1
2
2
2
1
2
1
1
1
2
1
1
0
1
1
1
1
1
1
1
1
1
1
1
0
1
0
1
0
1
1
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
0
2
1
1
1
1
1
1
0
1
2
1
1
1
1
1
0
2
1
2
1
1
2
1
1
1
0
1
0
0
1
1
1
1
2
0
2
0
0
1
0
0
1
1
1
2
1
0
1
0
0
2
1
1
1
1
1
1
2
2
2
1
1
1
0
1
1
2
1
2
1
1
1
1
0
0
0
1
0
0
1
1
1
1
1
1
1
1
1
2
2
2
1
2
1
1
1
1
1
1
1
1
0
0
2
1
1
1
1
1
2
0
2
1
2
2
2
1
1
1
1
1
1
1
1
1
0
0
1
0
1
0
1
0
1
1
1
1
1
1
2
1
1
1
1
1
0
3
1
1
1
2
0
1
1
1
0
1
1
2
2
1
0
1
1
1
2
2
1
1
0
1
2
1
2
1
2
1
0
1
1
0
1
1
1
1
0
0
1
2
2
1
1
0
1
2
1
1
0
1
1
1
1
0
2
1
1
0
1
1
2
1
1
2
1
1
1
2
1
1
2
1
1
2
1
2
1
2
2
1
2
2
1
1
1
1
1
1
2
1
0
0
1
2
1
2
1
2
1
0
0
1
2
1
2
2
1
1
1
0
2
0
1
2
2
1
0
1
1
1
1
1
1
1
1
1
2
0
2
2
1
1
1
0
1
0
1
1
2
2
1
0
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
0
0
1
1
1
1
1
2
1
1
1
1
1
2
1
0
2
1
1
2
1
1
0
1
1
1
1
1
2
2
2
0
2
1
1
1
1
1
1
1
2
1
1
1
2
2
1
2
2
0
1
0
2
1
0
1
1
1
1
2
1
2
0
1
2
2
1
0
1
1
2
2
1
2
2
1
2
2
1
2
1
1
1
1
2
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
0
0
1
0
2
2
2
1
0
2
1
1
1
1
1
1
1
2
1
2
2
1
1
1
0
1
2
1
1
1
1
2
1
0
1
1
2
1
1
1
1
1
1
0
1
2
2
1
1
2
1
1
0
1
0
2
0
0
2
1
0
0
1
2
2
0
2
2
1
1
1
2
1
1
0
1
1
1
2
1
3
1
1
2
0
0
1
0
2
1
0
1
1
1
0
0
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
2
1
1
1
0
0
1
1
0
1
1
1
1
1
2
2
1
1
0
1
1
2
2
0
1
0
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
0
1
1
0
1
1
0
2
1
0
0
2
1
1
1
1
0
1
1
1
4
1
1
1
0
1
1
1
0
1
1
1
1
2
1
1
2
1
2
2
1
0
2
1
1
1
1
0
1
2
1
1
2
0
1
0
2
1
2
0
0
1
0
2
1
1
1
0
2
1
1
1
1
1
1
1
1
2
1
2
2
2
1
0
1
1
2
0
1
1
1
1
1
0
1
1
1
1
2
1
2
2
2
1
1
2
2
0
1
2
1
0
1
2
2
1
1
2
1
1
1
1
2
1
0
1
2
1
1
2
0
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
2
1
2
1
1
0
1
1
2
1
1
0
2
1
2
2
1
1
2
1
1
1
1
1
0
0
1
1
1
1
0
1
2
2
0
1
1
1
0
1
1
1
1
1
1
1
1
1
2
1
0
0
0
0
2
1
1
1
1
1
1
1
0
1
0
0
1
2
2
0
0
1
0
1
1
1
1
1
1
1
0
1
1
1
0
1
1
2
2
1
1
1
2
2
2
1
1
1
2
0
0
2
0
1
0
1
1
1
1
1
0
2
2
1
1
0
2
1
1
1
0
1
1
1
1
2
0
1
1
1
1
2
1
1
1
1
1
1
0
1
0
2
2
1
1
1
2
1
1
1
0
1
2
1
0
1
2
1
0
1
1
1
1
0
0
1
1
1
0
0
1
0
1
1
1
1
1
1
1
2
1
1
0
1
1
1
1
1
1
1
1
1
0
2
2
2
1
2
1
1
1
1
0
0
0
1
2
1
1
1
1
1
1
0
1
2
1
1
2
1
1
1
0
2
0
1
1
1
1
2
1
1
1
1
0
1
1
0
0
1
2
1
1
2
1
1
1
2
1
1
1
1
0
0
1
1
0
0
1
1
0
1
0
2
2
0
1
1
1
2
1
2
0
0
2
0
2
1
5
0
1
1
2
0
1
1
1
1
1
2
1
2
1
3
1
1
2
1
1
1
1
1
1
1
1
2
1
0
2
1
1
1
1
1
2
1
0
1
1
2
0
1
0
1
1
1
1
0
1
1
0
0
0
1
1
2
1
2
1
1
1
0
1
1
1
2
2
1
1
1
1
2
1
2
1
0
0
0
1
1
0
1
2
2
1
1
0
1
0
2
2
0
2
2
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
2
2
0
2
1
1
0
3
2
0
0
1
1
2
1
1
1
1
2
1
1
1
2
0
2
1
2
1
2
1
2
1
1
0
0
1
1
0
1
1
1
2
1
0
1
1
1
1
1
1
1
0
0
1
1
0
1
1
0
1
1
1
1
2
1
2
0
2
2
1
1
1
2
1
2
2
2
1
1
1
0
2
1
1
2
1
1
2
1
1
0
2
0
1
0
1
0
1
1
2
1
1
1
1
1
0
1
0
1
0
1
2
1
1
1
1
2
1
1
1
2
2
2
1
2
2
1
1
1
1
1
1
1
1
2
1
2
0
1
0
1
2
3
3
1
2
1
0
2
1
1
1
1
1
1
0
1
1
0
0
0
1
2
1
1
0
1
2
0
1
0
0
2
1
0
1
2
2
1
0
0
0
1
0
1
1
0
1
1
0
1
2
0
1
0
1
1
1
2
1
1
1
1
1
1
0
2
1
1
1
1
1
1
0
1
1
1
2
1
1
1
1
2
1
2
2
2
0
1
2
1
2
2
0
1
1
1
2
1
2
1
0
1
0
0
1
1
3
1
1
0
1
1
2
1
4
1
2
1
1
1
2
1
2
1
3
1
1
2
2
1
2
1
1
2
1
0
1
1
1
1
1
2
0
1
1
1
0
1
2
0
1
1
1
0
1
2
1
2
1
0
1
1
1
1
0
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
2
1
3
1
2
2
2
1
2
1
1
1
2
1
1
1
1
0
1
1
1
2
1
1
1
1
0
2
1
1
0
1
1
2
0
0
1
2
0
1
1
0
1
1
1
1
1
1
1
0
1
2
1
1
1
2
1
1
1
1
2
2
1
1
1
1
1
1
1
2
3
2
0
0
0
2
0
1
1
1
1
1
1
1
1
0
2
2
1
2
2
0
1
1
1
2
2
1
1
1
1
1
1
1
0
1
1
1
1
2
0
1
1
2
2
2
2
1
1
1
1
2
0
1
0
0
1
0
1
2
2
1
1
1
1
1
0
2
0
1
1
1
1
1
1
1
3
0
1
2
1
2
1
2
1
0
1
1
1
1
2
2
0
1
1
3
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
0
1
0
1
1
1
1
1
3
0
0
1
1
1
1
1
0
2
1
2
0
1
1
2
0
1
2
2
0
0
2
2
1
1
0
2
0
1
1
1
1
1
1
1
0
1
1
2
0
2
1
2
1
1
2
2
2
1
0
0
0
1
0
2
2
1
1
0
1
2
2
1
1
0
1
1
1
2
0
1
0
1
0
1
1
1
1
2
1
1
1
0
3
2
1
1
1
2
1
1
1
0
1
1
1
2
2
1
1
1
2
1
1
1
1
2
0
1
2
2
2
1
1
0
1
1
2
1
0
1
0
1
0
0
2
1
1
2
1
2
2
1
1
0
2
1
1
2
1
1
0
2
0
1
1
1
1
1
0
0
1
2
1
1
1
1
0
1
1
1
1
0
1
1
1
0
2
1
1
1
2
2
1
1
1
1
1
1
2
1
0
1
1
1
0
1
0
2
2
1
0
1
1
2
2
0
1
2
1
1
1
1
1
2
2
0
2
0
1
1
1
2
1
2
1
1
1
1
2
2
2
1
1
1
2
1
2
1
1
2
1
0
1
1
2
1
1
1
0
2
1
1
1
1
0
1
1
1
1
2
2
2
1
1
1
2
1
0
1
1
0
1
0
1
2
1
0
1
1
0
1
1
1
0
1
1
1
1
1
0
1
0
1
1
1
0
1
1
1
2
2
1
1
2
0
0
1
0
1
2
0
0
1
2
1
0
2
1
2
2
1
1
2
1
3
0
1
1
0
1
1
0
1
2
0
0
0
1
2
1
1
1
1
1
1
1
0
2
0
1
2
1
2
1
1
1
2
1
2
1
1
1
1
2
1
1
2
2
1
0
0
1
1
2
1
1
1
1
0
1
1
2
0
1
1
0
1
1
0
1
1
1
1
2
2
0
1
0
2
1
1
0
1
2
0
0
1
0
1
1
1
1
1
1
1
1
1
2
2
2
2
1
1
1
1
1
1
2
2
2
2
0
1
1
1
1
2
1
1
0
1
1
0
1
1
1
1
1
2
0
0
1
2
1
1
1
1
2
1
0
1
2
2
1
1
1
1
1
1
0
1
0
1
1
1
1
1
0
2
1
1
2
1
0
1
1
2
2
1
0
1
1
0
2
1
1
2
1
1
2
2
1
1
1
1
1
1
1
1
1
2
1
2
2
1
1
0
2
1
1
1
1
2
1
0
1
1
1
2
0
2
1
0
2
1
1
2
2
1
1
2
1
0
1
2
0
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
2
0
1
1
0
1
2
1
0
2
1
1
1
0
1
1
1
0
1
1
1
2
0
2
1
1
2
1
1
1
2
0
0
1
1
2
0
1
0
1
1
0
1
0
0
0
1
2
2
2
1
1
1
2
2
0
1
1
1
2
2
2
1
0
1
0
1
1
1
2
0
1
1
1
1
0
2
1
1
1
1
2
2
2
1
1
0
1
1
1
1
2
0
2
2
1
0
2
1
2
0
1
1
1
1
2
2
2
0
2
2
1
1
1
1
1
1
2
2
0
1
2
0
2
0
1
1
2
1
2
1
0
0
1
2
2
1
2
1
1
2
2
1
1
1
0
1
1
1
2
0
1
2
1
1
2
1
1
0
0
2
1
1
2
1
0
1
1
1
2
2
0
0
1
2
2
2
0
2
2
1
2
2
1
2
2
0
1
2
2
2
1
1
2
1
1
0
1
2
1
1
2
1
1
1
1
1
2
1
1
2
1
0
0
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
2
1
3
1
2
1
2
1
1
0
1
0
1
1
1
1
1
2
1
1
1
1
1
1
2
1
2
1
0
0
1
1
0
2
0
0
1
1
1
1
1
2
1
1
2
1
0
0
2
2
1
1
1
1
2
2
0
1
1
1
2
1
0
2
1
2
2
0
0
1
1
1
0
1
1
2
1
1
1
2
1
2
1
0
1
1
1
2
1
0
2
2
1
1
1
1
2
1
1
0
1
2
2
1
2
2
2
1
1
2
0
2
2
1
1
1
1
2
1
1
1
0
0
1
1
0
2
1
2
1
0
1
2
1
1
1
0
1
1
1
1
1
1
1
1
1
2
1
2
1
0
0
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
0
2
1
1
1
2
1
2
0
1
2
1
1
2
1
1
0
2
1
0
1
2
2
1
1
0
2
1
2
1
0
0
2
2
1
1
2
1
2
1
0
1
2
1
0
2
1
1
1
2
2
1
1
0
2
1
1
1
2
1
2
1
1
1
1
2
1
1
1
2
0
1
1
2
0
2
0
1
2
1
0
1
1
1
1
3
1
2
1
0
0
1
1
0
1
1
1
2
0
0
1
2
2
1
1
1
1
2
2
1
1
0
1
1
1
1
0
1
0
1
1
0
1
1
0
1
1
1
0
1
1
2
1
2
1
1
1
1
1
1
1
2
0
2
2
2
1
1
1
2
2
0
1
2
1
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
2
1
2
2
1
1
1
0
0
1
2
0
2
1
1
2
1
1
1
1
1
0
0
0
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
0
1
1
2
1
1
0
1
2
0
2
1
1
1
1
2
1
1
1
0
1
1
1
1
1
2
1
2
2
2
2
1
0
1
1
0
1
0
1
0
1
2
0
1
1
1
1
1
1
2
2
1
1
0
1
1
1
2
1
2
2
1
2
1
0
2
2
1
1
0
2
0
1
0
2
0
2
2
1
1
1
1
1
2
1
2
1
2
2
1
1
2
1
1
2
2
1
1
1
0
1
1
1
1
2
1
1
3
0
3
1
1
1
1
2
1
0
1
2
1
1
1
1
0
1
2
2
1
1
1
2
1
1
1
1
1
0
2
0
1
1
1
2
0
2
1
1
2
1
2
0
1
0
1
1
1
1
2
2
1
1
2
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
0
0
1
2
1
0
1
1
1
1
1
1
2
0
0
2
1
1
1
0
1
0
1
0
0
4
2
1
1
0
1
0
1
2
1
0
2
0
2
1
1
1
2
0
2
2
1
1
1
1
1
1
0
1
1
0
1
1
2
2
1
1
2
1
2
2
1
1
1
2
2
2
0
1
1
1
1
0
2
1
1
1
1
1
1
1
2
2
0
1
1
2
0
1
1
1
1
1
2
1
1
1
1
1
1
1
1
3
2
1
0
1
2
2
0
1
0
2
1
0
1
1
2
2
0
2
1
2
1
2
1
1
1
1
1
1
1
2
1
2
0
1
1
1
2
0
2
2
0
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
0
1
1
1
1
0
1
1
1
1
0
0
1
1
1
0
1
1
1
1
1
1
1
1
1
2
2
0
1
0
0
1
1
1
1
1
1
1
0
1
1
1
2
2
1
0
0
1
2
1
2
1
2
1
1
0
1
1
1
1
1
1
2
1
2
2
2
1
1
1
2
1
1
1
1
1
1
1
1
0
1
1
1
1
1
0
1
1
0
2
0
1
1
1
1
1
0
1
3
1
2
1
1
1
0
1
1
1
1
1
2
2
1
1
1
2
1
2
1
1
1
2
1
2
1
3
1
2
2
1
1
0
1
1
0
0
1
2
1
1
1
1
0
1
1
0
1
2
1
0
2
2
0
1
1
1
1
2
1
0
1
2
2
2
1
1
1
1
2
2
2
1
1
1
2
0
2
1
1
2
2
0
1
1
0
1
2
1
2
0
1
3
2
1
1
2
1
1
1
1
1
1
2
1
2
0
1
0
2
1
1
0
1
1
1
1
1
0
2
1
2
2
2
1
2
1
1
2
1
1
1
2
0
2
2
1
1
0
2
1
2
1
1
1
1
0
0
2
1
1
1
1
2
1
1
2
1
0
1
2
1
1
0
1
2
1
2
1
1
1
1
0
0
1
2
1
2
2
2
1
0
0
0
2
2
0
1
0
1
1
1
1
1
1
1
1
1
2
1
2
0
1
1
0
2
1
1
1
1
1
1
1
0
1
1
1
1
1
1
2
1
2
1
1
1
0
1
2
1
1
1
2
1
2
1
1
3
2
1
0
1
1
1
1
1
2
1
2
1
0
1
0
2
1
2
3
1
1
1
0
2
1
1
0
1
0
1
1
1
0
2
1
1
0
0
1
2
2
1
1
1
1
1
0
1
1
1
1
1
0
1
1
2
2
0
1
1
0
2
1
0
1
1
2
1
1
1
1
1
1
1
1
1
2
1
2
1
1
0
0
1
1
1
1
2
1
1
0
2
2
1
2
0
1
1
2
1
1
2
0
0
1
2
2
1
0
0
1
1
1
1
0
1
1
0
0
1
2
1
1
1
1
2
1
2
2
1
0
1
1
1
0
1
1
0
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
2
2
1
0
1
2
2
2
0
0
1
1
1
1
0
1
1
2
1
2
0
1
1
1
1
1
1
1
1
1
0
2
1
2
0
2
1
2
0
0
2
1
1
1
1
0
2
1
1
1
1
1
1
0
2
2
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
2
1
2
1
0
2
0
0
1
1
1
0
1
2
1
2
1
1
1
1
1
0
1
1
1
1
1
1
2
1
1
1
2
0
1
1
3
1
1
1
1
1
2
1
1
0
0
1
0
1
0
1
1
1
2
1
1
0
1
1
0
1
1
2
1
1
0
2
1
2
0
0
1
1
1
1
1
1
1
1
0
0
2
1
1
0
2
1
1
2
1
1
1
0
0
1
1
1
1
1
1
1
1
2
1
0
1
2
1
0
1
1
0
2
1
2
2
2
1
1
2
1
1
1
1
1
1
0
2
1
1
0
1
1
1
1
2
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
0
1
1
1
1
0
1
2
1
2
1
2
1
0
1
2
2
0
1
2
3
1
2
1
1
2
1
1
1
1
0
2
2
0
1
1
2
1
1
0
0
2
2
0
1
1
1
1
2
1
1
1
0
0
1
1
2
1
1
0
2
1
1
1
1
1
1
1
1
0
1
1
2
0
1
1
2
0
0
1
2
2
2
1
0
2
2
0
1
0
2
2
0
1
0
1
2
2
1
2
2
1
0
2
1
2
2
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
3
2
0
0
1
0
1
2
1
1
0
2
1
2
1
3
0
0
1
0
1
0
2
2
0
1
0
1
1
2
1
1
0
1
1
1
1
2
1
0
1
2
0
2
2
0
1
2
1
0
1
0
2
1
0
1
1
0
2
1
2
1
1
1
2
2
1
1
1
1
1
1
2
1
1
1
2
2
1
1
1
0
1
1
0
2
2
0
1
1
1
2
1
0
2
2
1
2
1
1
1
2
2
1
1
0
1
0
1
3
1
1
1
0
2
1
0
1
2
2
1
1
1
2
1
1
0
0
1
1
0
1
0
1
2
0
1
0
0
2
1
1
1
2
1
2
1
0
1
0
1
1
0
2
1
0
1
1
0
2
0
2
1
1
0
2
0
0
0
1
2
2
1
1
1
2
1
1
1
1
1
1
0
1
0
1
2
1
0
1
1
2
2
1
1
1
1
1
1
1
0
1
2
1
0
1
2
1
2
1
2
2
1
1
2
1
1
1
1
1
1
1
1
0
0
1
1
0
1
0
2
1
1
2
1
1
0
0
0
2
1
2
1
2
1
0
1
0
1
2
1
1
2
1
1
1
1
2
1
1
1
0
0
2
0
0
1
1
1
2
0
2
1
0
2
2
1
2
0
1
1
0
1
2
5
1
1
0
2
1
1
0
0
2
1
0
1
0
0
1
2
2
1
1
1
1
1
1
2
0
1
1
1
1
2
1
1
1
1
1
1
0
2
1
0
1
2
0
2
1
0
1
1
1
0
1
0
0
1
1
1
2
1
0
1
1
1
2
1
0
0
1
2
2
1
1
1
1
1
2
2
2
1
0
0
1
0
1
1
0
2
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
0
1
1
2
1
0
0
0
0
0
1
1
2
1
1
1
1
1
2
2
1
0
2
2
1
1
1
2
1
1
1
1
2
1
1
0
1
1
1
1
0
1
3
1
1
2
1
1
1
1
0
1
0
0
0
1
1
1
1
2
0
1
2
0
1
2
1
1
1
2
1
0
2
2
2
2
0
1
0
1
1
1
0
0
0
1
2
0
1
1
1
1
1
1
1
0
0
2
1
2
0
2
2
1
1
0
1
2
2
1
1
1
1
1
0
1
0
1
1
2
1
1
1
1
1
0
1
0
1
2
1
0
1
1
2
0
1
2
0
1
1
2
0
1
2
1
1
2
0
1
1
0
0
1
1
1
1
1
1
2
1
1
0
1
1
1
2
2
0
1
0
2
2
1
2
2
1
2
1
0
1
1
2
1
1
2
2
1
0
1
1
2
1
0
1
1
1
1
1
2
1
0
1
1
1
1
1
1
0
1
1
3
2
2
1
0
1
1
1
2
2
1
0
1
1
1
2
1
1
1
1
1
1
2
1
1
0
0
1
1
1
1
1
2
2
0
1
1
1
1
1
0
1
0
2
2
1
1
2
1
0
1
2
1
1
0
1
1
0
2
1
2
0
1
2
0
2
1
1
1
0
0
2
1
1
1
1
1
2
1
1
0
1
2
1
1
2
1
1
2
1
1
1
1
1
2
2
2
1
1
0
1
2
1
2
1
1
1
1
0
0
1
1
0
1
0
1
0
0
1
2
1
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
2
1
2
1
2
1
0
1
1
2
0
2
1
2
1
1
1
1
0
1
0
1
1
1
1
2
0
1
0
1
1
4
1
0
2
1
1
1
1
0
1
2
1
0
1
1
0
1
1
3
1
1
0
1
2
1
1
1
0
2
2
1
2
1
1
2
1
1
1
1
1
1
2
2
1
1
2
1
0
2
2
2
1
2
1
2
1
1
1
0
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
0
2
1
0
1
0
1
2
1
1
2
0
1
1
2
1
2
1
2
2
0
1
1
1
0
1
2
1
2
2
2
2
1
1
2
1
1
1
1
1
2
1
1
1
0
1
2
0
0
1
2
1
2
1
1
1
1
0
2
1
2
1
0
2
1
1
1
1
0
2
1
1
1
1
0
1
1
2
1
2
1
1
1
1
0
0
1
0
1
1
0
0
1
2
1
1
1
1
1
0
1
0
1
0
2
0
1
1
1
1
2
2
2
0
0
2
1
0
1
1
2
2
0
1
0
2
2
0
2
1
1
1
1
2
1
1
1
0
2
1
1
0
2
2
1
1
1
2
1
1
1
1
0
2
1
1
1
1
1
1
0
1
1
2
0
1
2
1
2
1
1
1
0
1
1
0
1
0
1
1
1
1
1
1
0
1
0
2
1
3
1
1
1
1
1
2
0
1
1
0
2
1
1
2
1
1
1
1
0
1
1
1
2
1
1
1
0
1
1
2
1
1
1
0
1
1
1
1
1
1
1
0
1
1
1
1
0
1
2
1
1
0
1
0
1
1
1
0
1
1
2
2
1
2
0
0
1
0
1
1
1
1
2
2
0
1
1
1
1
1
1
1
1
1
0
2
1
0
1
1
1
1
1
1
0
1
2
1
1
2
2
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
0
1
1
1
3
1
0
1
1
1
1
2
0
1
2
1
0
0
1
1
1
1
1
1
2
2
1
2
1
2
1
0
2
2
1
1
1
1
2
2
1
1
1
2
1
2
2
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
2
1
1
0
1
2
1
1
0
2
2
0
1
1
1
1
2
0
1
1
1
1
1
1
1
0
1
1
1
2
1
1
1
0
1
1
3
1
1
1
1
1
1
1
1
1
1
2
0
2
1
2
1
1
1
1
1
0
0
1
2
1
2
1
1
1
0
1
2
2
1
2
2
1
1
2
1
2
2
1
3
0
1
1
1
1
1
1
1
2
0
1
1
0
1
1
1
2
0
1
2
0
1
1
1
0
1
1
2
1
1
2
0
2
0
1
1
0
1
0
1
1
1
1
1
2
2
1
1
1
2
1
1
1
1
1
2
1
0
1
2
1
1
1
1
1
1
1
1
1
0
0
2
1
1
1
2
1
2
1
1
2
1
0
2
2
1
1
1
1
1
2
0
0
1
2
1
2
1
2
1
1
1
1
1
1
1
1
1
2
1
0
1
1
1
1
2
1
1
1
0
2
2
0
0
2
0
1
0
1
1
1
0
1
2
1
2
1
1
2
1
2
1
0
2
0
1
1
2
1
1
1
1
2
1
0
1
0
1
1
2
1
1
1
1
2
1
1
2
0
1
1
1
2
1
0
2
2
0
1
1
1
1
0
1
1
1
2
1
1
1
0
1
1
1
0
0
2
1
1
2
0
1
1
1
1
1
1
1
1
0
1
1
1
2
2
2
0
1
1
2
1
1
0
1
2
1
1
1
1
2
1
2
2
1
2
2
1
1
1
1
0
1
2
2
1
1
1
2
1
1
0
1
3
1
1
1
1
0
2
2
0
1
1
0
1
2
0
0
1
0
2
1
2
2
1
1
2
1
1
1
1
0
2
0
0
1
1
0
2
1
1
1
5
0
1
2
1
1
1
1
1
1
1
0
0
1
1
1
1
2
0
3
2
2
2
2
0
2
2
1
0
1
2
0
1
2
0
0
1
0
0
1
0
0
1
1
2
1
1
1
1
0
0
1
2
1
1
1
2
1
1
1
2
2
1
1
1
1
2
0
1
1
1
1
1
1
1
1
2
0
0
1
1
1
1
1
0
1
2
0
2
2
1
1
0
1
1
1
1
1
4
2
2
1
1
2
1
0
2
0
2
0
2
2
1
1
1
1
1
2
2
1
1
0
2
2
1
1
1
1
1
1
1
1
2
2
1
2
0
2
1
2
1
2
2
1
1
1
1
1
1
1
1
1
2
0
1
1
1
2
1
1
0
1
0
0
2
1
1
1
1
1
0
2
0
1
1
2
1
1
1
0
1
1
1
1
1
1
2
2
2
1
1
2
0
2
2
1
2
0
1
1
2
1
1
0
1
1
1
2
1
1
0
2
0
1
2
1
1
2
1
2
1
1
1
1
0
0
2
0
2
1
1
1
2
1
0
1
0
0
1
2
2
1
1
2
1
2
1
1
2
1
1
0
1
1
2
2
1
1
1
1
2
1
1
1
1
1
0
2
1
0
1
2
1
2
2
3
1
3
1
2
0
1
1
1
1
1
1
0
1
1
1
2
2
2
2
2
0
1
1
1
1
1
1
0
2
2
1
1
1
1
0
0
1
1
2
1
2
2
1
1
1
3
0
2
1
0
1
0
1
0
0
2
1
2
2
1
0
1
1
1
1
0
1
2
1
2
1
1
0
2
2
1
1
2
0
1
1
1
1
2
1
1
2
2
1
0
1
1
1
2
2
2
0
1
1
1
1
2
0
1
0
1
1
1
1
2
1
1
1
1
0
2
1
3
1
0
2
1
1
1
1
0
2
2
0
2
1
2
0
1
1
1
1
2
2
1
1
2
2
1
1
2
0
1
1
1
1
2
1
1
1
0
2
1
1
1
0
1
1
0
1
1
1
2
1
1
2
1
0
1
1
0
2
1
1
2
2
2
1
2
1
2
2
1
0
1
0
2
1
1
1
2
0
1
1
0
2
2
1
1
1
1
1
1
1
3
1
2
2
1
1
1
1
1
1
1
1
0
2
2
1
0
1
1
2
0
0
1
1
1
1
2
1
2
0
0
1
1
0
2
1
1
0
0
1
2
2
2
1
2
0
1
1
0
2
1
1
1
1
1
1
2
1
1
1
2
0
2
2
0
2
1
0
1
0
1
2
1
2
2
2
1
1
1
1
1
1
1
2
2
2
0
2
1
1
0
1
1
2
1
1
1
0
1
1
0
1
2
1
1
0
1
0
0
2
0
1
2
1
1
1
2
2
2
1
0
1
1
1
0
3
1
1
1
1
1
0
1
1
0
1
1
1
0
1
0
1
1
1
1
2
1
1
2
1
0
0
1
2
1
1
2
2
1
1
2
2
1
1
0
1
1
1
1
0
1
2
1
2
2
1
1
2
0
1
1
1
2
2
2
2
1
1
1
2
0
0
2
2
2
1
2
1
0
1
1
1
1
1
1
1
1
0
0
1
1
1
0
1
1
1
4
1
1
1
1
1
1
1
1
1
1
2
1
2
2
2
3
1
2
2
1
1
2
0
2
1
1
0
1
1
1
1
1
2
1
0
1
2
1
1
1
0
1
2
0
0
0
0
1
0
1
0
2
1
1
1
2
2
1
0
1
1
1
3
1
1
1
1
0
1
1
0
3
1
2
1
1
1
1
1
1
1
0
0
0
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
0
1
1
2
0
1
2
2
1
0
0
1
2
1
1
1
1
1
1
2
1
0
1
0
1
1
4
1
2
2
1
1
1
1
1
0
0
1
1
1
1
1
1
2
1
0
1
1
2
0
1
0
1
0
2
1
2
1
0
1
0
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
0
2
1
1
1
1
2
1
0
1
0
1
1
1
1
1
0
1
1
1
1
1
0
1
0
1
2
1
1
2
1
0
1
1
2
2
1
1
1
1
1
0
1
1
1
1
1
1
1
2
1
1
1
0
1
2
2
1
2
0
2
2
2
1
0
0
3
0
1
1
0
1
2
1
1
2
4
0
2
1
1
2
2
1
2
0
0
2
1
1
0
0
1
2
1
1
2
1
0
1
1
1
1
0
0
2
0
1
0
2
0
0
1
1
2
1
1
2
1
1
1
2
2
1
0
0
1
1
1
2
1
1
2
1
2
0
1
1
1
2
1
0
1
1
0
2
1
2
3
0
1
2
2
1
1
1
1
1
1
1
1
1
5
2
2
1
1
1
0
1
1
1
1
2
0
1
1
2
1
1
2
1
1
0
1
2
1
0
2
1
1
1
1
0
2
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
0
1
2
2
1
1
1
1
1
1
1
1
0
1
2
2
1
1
1
2
1
1
1
1
0
1
1
2
2
2
1
1
1
2
1
2
1
1
0
1
1
2
1
2
1
1
0
0
0
1
2
1
2
2
1
1
2
1
1
1
1
1
1
1
1
0
2
0
1
1
2
1
1
0
2
1
2
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
0
1
1
0
1
1
1
0
2
2
1
1
0
1
1
1
2
1
0
1
0
1
1
0
0
2
1
1
0
2
1
1
1
0
0
1
3
1
2
0
1
2
2
1
1
2
0
1
0
1
1
0
2
1
1
1
1
1
2
1
1
1
1
1
2
2
1
1
1
1
0
1
1
0
1
1
1
1
1
1
1
1
0
1
1
2
2
1
1
2
1
1
0
1
2
0
1
1
1
2
1
1
1
1
1
0
1
1
1
0
1
2
1
1
1
0
0
1
1
1
1
1
1
1
1
1
2
0
1
1
1
2
1
1
1
1
1
1
0
1
1
1
0
1
3
1
1
1
0
0
1
2
1
1
1
1
2
1
2
2
0
1
1
0
2
2
1
1
1
0
2
2
1
0
1
1
1
2
1
1
1
1
0
1
2
1
0
1
2
1
2
1
1
1
1
1
0
2
0
1
1
1
2
2
1
1
1
1
2
1
1
0
1
1
1
1
2
1
1
0
2
0
1
1
1
1
0
2
1
0
0
1
1
4
2
1
1
1
0
0
1
1
1
0
1
2
0
1
2
0
1
1
2
2
1
1
2
1
0
1
1
2
0
2
1
1
0
2
1
2
1
0
2
2
1
2
2
1
0
2
1
1
1
0
1
2
1
1
0
1
1
1
2
1
1
1
1
1
1
0
2
1
2
2
0
1
2
0
2
2
1
1
2
1
0
0
1
2
1
1
1
2
1
0
1
1
1
1
1
0
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
0
2
0
2
2
1
2
0
2
0
2
1
2
2
2
1
1
2
2
0
1
1
0
1
1
1
1
0
1
0
1
1
2
0
1
1
1
1
1
1
0
0
1
1
2
1
2
1
1
1
1
0
1
0
0
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
2
1
0
3
1
1
1
1
0
1
1
1
0
2
1
1
1
2
2
0
2
0
1
2
2
1
0
1
1
1
1
1
1
2
1
1
1
1
0
0
1
0
1
1
1
1
1
1
1
1
1
1
1
1
0
1
0
1
1
2
1
0
1
1
1
1
1
0
0
1
2
1
0
2
1
1
2
1
2
1
2
2
1
2
1
1
1
0
1
1
1
1
2
1
1
1
1
0
1
1
1
1
1
0
2
0
1
1
0
1
1
2
1
1
0
2
1
0
0
1
1
1
1
1
9
1
2
1
1
1
1
1
0
1
1
2
1
1
1
1
1
1
1
1
2
1
2
1
1
1
0
0
1
2
1
2
1
2
1
1
1
2
0
1
3
1
1
2
0
2
0
1
0
1
1
1
1
1
1
2
1
1
1
2
1
0
1
0
1
2
1
1
1
2
1
1
2
2
2
1
0
0
1
1
1
1
1
1
2
1
2
1
0
2
2
1
0
0
2
1
2
1
1
0
1
1
1
1
1
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
2
1
1
0
1
1
2
2
1
1
0
1
2
0
1
1
1
2
1
1
1
1
1
1
0
1
2
2
1
2
1
1
1
1
1
2
1
0
2
2
1
0
1
1
1
1
1
2
1
0
1
2
1
1
0
1
1
1
1
1
2
0
0
1
1
1
0
1
2
1
1
1
2
1
1
0
2
1
0
1
2
1
1
2
0
2
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
0
2
0
2
2
1
1
2
1
2
1
2
2
0
2
2
2
2
2
1
1
0
2
1
1
2
1
2
0
2
1
1
1
2
0
1
2
1
0
0
1
1
0
1
1
0
0
1
1
2
1
1
0
1
2
0
1
0
1
1
1
1
1
2
2
1
0
0
2
1
2
0
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
2
0
1
2
2
1
0
1
1
1
2
1
1
2
1
1
1
1
1
2
1
2
1
1
1
2
1
0
0
0
1
2
1
2
0
1
0
1
0
1
1
1
1
1
1
0
0
1
2
1
1
2
1
2
1
0
1
1
1
1
0
0
2
1
1
1
1
1
1
1
2
2
1
1
0
2
1
2
0
2
0
2
1
1
1
2
2
1
1
0
0
1
1
1
1
1
1
1
1
2
0
2
2
1
1
0
0
2
2
2
1
2
1
0
1
1
2
0
2
2
0
1
0
1
2
1
1
1
1
1
1
1
1
2
2
1
0
1
2
1
1
2
1
2
1
1
1
2
2
1
2
0
1
1
2
1
0
1
2
2
0
1
2
1
2
1
1
1
1
1
1
1
2
1
0
2
2
1
1
1
0
2
1
2
1
1
1
0
0
1
0
2
1
1
2
2
1
1
0
1
2
2
1
1
0
1
1
1
2
2
0
1
2
0
1
1
0
2
1
1
2
2
1
1
1
2
1
1
1
1
1
1
2
0
3
1
0
1
2
0
2
1
1
1
1
2
2
2
1
1
1
2
1
1
1
1
1
2
1
0
2
0
1
2
2
2
2
2
2
0
1
2
1
0
0
1
1
2
2
2
1
0
1
1
0
1
1
1
1
1
0
1
2
2
2
1
1
1
1
1
1
2
1
0
0
2
1
1
0
0
0
0
2
1
2
1
0
2
1
2
1
1
1
0
0
2
1
1
0
0
2
1
1
2
0
1
1
1
1
2
1
2
1
2
1
2
0
2
4
1
1
2
2
1
1
2
1
1
2
1
1
1
1
1
1
0
1
1
1
0
1
1
1
1
0
1
1
0
1
2
2
2
0
1
1
1
2
2
2
1
1
0
1
2
1
0
1
1
2
1
2
0
1
1
2
0
1
1
1
1
1
1
1
1
1
2
2
1
1
0
1
1
1
1
2
0
1
2
2
1
1
1
2
1
1
2
2
1
2
1
1
0
2
1
1
1
1
0
2
0
0
2
1
1
2
1
2
0
1
0
1
1
2
0
1
0
0
1
0
0
1
1
2
0
2
1
1
0
1
2
1
1
1
1
0
1
2
1
1
1
2
3
1
1
1
2
1
1
1
1
0
1
1
0
0
1
1
1
1
1
2
2
1
1
0
0
2
0
2
1
2
0
2
1
1
1
1
1
1
0
1
0
1
1
1
2
1
0
1
1
1
1
0
2
2
2
1
1
1
1
1
0
2
1
1
1
1
2
2
1
0
1
1
2
0
0
1
1
2
1
0
0
0
1
2
1
2
1
1
1
2
1
1
0
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
1
1
2
1
1
0
2
1
1
1
1
1
1
1
1
1
1
1
0
2
1
1
0
1
1
1
2
1
0
2
1
1
1
1
0
0
0
1
1
2
1
0
1
0
2
0
2
1
1
3
1
1
1
1
0
1
3
2
2
2
0
3
2
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
0
1
2
1
1
1
1
1
0
2
1
1
0
2
1
2
1
0
1
1
2
1
0
0
1
1
0
1
2
1
2
1
1
0
0
1
1
1
1
1
1
1
0
1
1
2
0
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
0
1
1
1
1
1
2
0
1
2
2
0
1
0
1
2
1
0
0
1
1
1
1
0
1
1
1
1
0
0
1
1
3
2
0
1
1
1
1
0
0
1
1
1
0
3
1
0
0
1
0
1
0
1
2
1
1
2
1
1
1
1
2
0
1
2
1
1
1
1
2
1
2
1
0
1
2
0
2
1
1
0
1
0
1
1
1
1
2
0
1
1
1
2
1
1
1
2
2
1
2
0
1
1
1
0
0
2
1
0
1
0
2
1
1
1
1
0
0
1
2
1
1
2
2
1
1
1
1
1
1
0
1
1
0
2
1
1
0
2
2
1
1
1
2
1
1
0
1
1
1
0
1
2
2
1
1
1
1
2
1
1
1
2
1
0
2
1
2
2
2
2
0
0
2
0
2
1
1
1
1
1
1
1
2
2
1
1
1
1
2
1
2
1
2
2
1
2
1
2
0
0
0
2
0
1
0
2
1
2
1
1
1
0
0
2
2
2
2
0
1
1
1
1
0
2
2
0
1
2
1
1
0
1
0
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
0
2
1
1
0
2
1
1
1
1
1
2
1
0
1
1
2
1
1
0
1
1
1
2
1
0
2
0
1
2
0
2
2
2
1
1
1
2
1
1
1
0
1
1
0
1
3
0
1
2
1
1
1
2
0
2
2
1
0
0
1
1
1
0
1
2
1
1
1
2
1
1
2
2
1
2
2
0
2
1
1
0
2
1
2
0
2
2
1
2
1
1
1
1
0
1
0
1
1
1
0
1
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
0
1
1
0
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
2
2
1
2
0
2
1
2
1
2
1
1
0
1
3
0
2
2
0
1
2
0
1
2
2
1
1
1
2
1
0
0
1
1
0
3
1
1
2
1
1
1
1
1
0
1
1
0
1
1
1
1
0
2
1
1
2
1
1
0
1
1
1
0
2
0
1
0
1
2
2
2
2
0
2
2
0
1
1
0
1
1
1
1
0
1
1
1
0
1
2
0
1
1
0
1
2
1
1
1
1
1
0
0
0
3
1
0
1
1
2
1
1
1
0
1
1
1
2
0
1
2
1
0
1
0
1
1
1
1
2
1
0
0
2
1
1
1
1
1
1
2
1
1
1
0
0
1
1
1
1
1
2
1
1
0
0
2
1
0
0
1
1
1
0
1
1
1
1
1
0
1
2
2
1
2
2
1
1
2
2
2
2
1
1
0
2
2
1
2
1
2
2
2
1
2
1
1
1
1
2
0
1
1
0
2
2
0
1
3
1
1
0
1
1
2
0
2
1
2
2
1
1
1
1
2
1
1
1
1
2
0
1
1
1
1
1
0
0
1
2
1
1
2
1
5
2
1
1
2
1
2
1
1
2
0
1
1
1
1
0
1
1
1
1
1
1
1
0
2
1
1
1
1
1
1
1
1
1
1
2
1
0
0
1
1
1
2
1
1
1
0
2
0
0
1
1
1
1
0
1
2
1
1
1
1
2
1
0
2
2
2
1
1
1
1
2
1
1
2
2
1
0
1
0
1
1
1
7
1
1
1
2
2
1
1
1
0
2
2
2
0
2
1
0
2
2
1
2
2
1
1
1
1
2
2
1
1
0
0
1
2
2
1
1
1
1
1
1
1
1
0
2
0
1
0
1
1
2
1
1
1
2
1
1
2
2
1
1
1
1
1
2
0
0
1
2
1
0
2
1
1
1
2
1
1
1
0
1
1
1
1
2
1
2
2
2
1
2
1
2
1
2
1
1
1
2
2
1
1
2
1
2
1
1
0
2
1
0
1
1
0
1
1
2
1
1
1
2
1
0
1
1
1
1
0
1
3
1
1
0
1
1
2
2
1
1
0
1
1
0
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
2
0
1
1
2
1
0
1
1
1
1
2
1
1
1
2
0
2
1
1
1
1
0
2
2
2
1
1
1
1
2
0
2
1
1
1
2
0
2
1
1
1
1
1
2
1
1
2
1
0
1
0
1
2
2
0
3
0
1
1
0
1
1
1
1
2
1
2
1
1
1
1
0
1
1
1
1
0
1
1
0
0
1
2
1
1
1
1
0
1
0
1
2
2
1
1
0
2
1
1
1
1
1
1
2
2
0
0
1
1
1
2
1
1
1
1
1
1
1
0
0
2
1
2
1
1
1
1
1
1
2
2
1
2
2
1
1
0
0
1
1
1
0
1
1
1
1
1
1
0
1
1
2
1
0
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
0
1
0
0
1
0
1
1
2
2
0
0
2
0
2
0
1
0
2
1
1
2
2
1
2
0
0
1
1
2
1
2
0
2
0
0
1
1
1
1
1
1
2
0
0
1
0
0
2
2
1
1
1
2
1
2
1
1
2
1
1
1
3
0
1
1
2
1
1
1
0
1
1
2
0
1
0
1
2
1
1
0
2
1
2
1
2
0
1
2
0
1
0
1
1
1
1
1
1
2
0
1
2
1
1
1
1
1
2
2
2
1
1
2
2
1
1
1
1
1
1
2
1
2
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
0
0
1
0
1
0
0
1
0
0
2
1
1
2
1
1
1
1
2
2
0
1
0
0
1
2
1
1
2
2
1
1
1
2
1
0
1
2
1
1
0
2
1
1
1
1
1
0
1
1
2
2
1
1
1
0
2
2
1
2
0
1
0
0
2
1
1
2
1
1
0
1
1
1
1
0
1
2
0
2
1
5
0
2
0
0
1
1
1
3
1
2
2
1
1
1
1
1
1
1
1
1
2
1
2
0
2
1
1
1
2
1
1
1
2
0
1
1
1
1
1
0
1
1
2
1
1
0
2
1
1
0
0
1
1
0
2
0
1
1
1
1
0
2
2
2
2
1
1
1
1
1
1
2
1
2
1
0
1
1
1
1
1
2
1
2
1
1
1
0
2
1
2
0
1
1
1
1
1
1
1
1
2
2
2
0
2
2
0
1
1
0
2
3
1
0
2
1
1
1
1
0
1
2
1
3
0
2
2
1
2
1
1
2
1
1
1
2
2
1
0
1
2
2
0
0
1
0
1
1
1
0
1
1
2
1
1
1
1
2
0
2
2
1
1
2
1
1
2
1
0
1
0
1
1
2
1
1
0
1
1
2
1
2
2
1
0
1
0
1
1
0
2
1
1
3
1
1
1
1
0
1
2
1
1
1
0
0
2
0
1
1
0
0
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
0
2
1
1
2
0
1
0
2
1
0
2
1
1
1
1
2
2
0
2
1
0
1
1
1
1
0
1
0
1
1
2
0
1
1
1
1
2
1
1
1
1
1
2
0
2
2
1
1
0
2
2
1
1
2
1
1
0
1
1
1
0
1
0
0
1
2
0
1
1
1
1
2
0
1
0
2
1
2
0
0
1
1
1
2
1
1
1
1
2
1
2
2
2
1
2
2
0
1
1
1
1
0
2
2
0
1
1
0
0
1
1
1
1
0
2
1
1
2
0
0
1
1
1
1
0
2
1
2
1
1
0
1
1
1
1
1
0
2
1
2
1
2
0
1
1
1
1
1
1
1
1
0
1
1
2
1
2
0
0
1
2
1
0
0
1
1
2
0
2
1
1
1
0
0
1
0
0
1
2
1
1
0
2
1
1
2
1
3
0
1
1
1
1
1
1
1
1
0
0
2
1
1
1
1
2
1
1
1
1
0
2
1
2
1
1
2
2
3
1
0
1
1
1
1
1
3
2
1
1
1
0
0
1
1
1
0
0
0
2
1
0
1
2
1
2
1
2
2
1
1
1
1
1
2
1
1
1
2
2
2
2
1
0
1
1
2
2
1
1
2
1
0
2
2
1
2
1
1
0
1
1
2
1
1
0
2
2
1
1
1
2
2
1
1
2
1
1
2
1
2
2
2
0
1
2
0
1
1
1
1
1
0
0
2
0
2
1
1
2
1
2
1
1
0
1
2
1
0
0
1
2
1
1
1
1
1
1
1
2
2
1
3
1
1
1
1
1
0
1
2
1
2
0
2
1
1
2
0
1
1
2
0
1
1
0
1
1
1
2
1
2
1
2
2
1
1
1
0
1
2
2
1
1
1
2
1
1
2
1
1
2
1
1
1
1
1
2
1
1
1
5
2
2
0
1
1
1
1
1
1
0
1
1
2
1
0
1
2
1
1
2
1
0
0
1
1
2
1
2
1
0
0
1
1
2
1
0
1
1
1
1
1
1
0
1
0
1
2
1
0
2
1
1
0
2
1
1
1
1
1
2
1
1
2
2
1
1
1
0
1
1
2
0
1
1
1
1
2
1
1
1
1
1
2
2
0
2
2
1
1
0
1
1
1
0
1
1
1
1
1
1
2
1
1
1
0
1
1
2
1
1
1
2
1
1
0
0
0
2
2
1
1
0
1
2
1
2
0
1
0
1
1
1
0
1
1
1
0
1
1
1
2
0
2
1
2
1
1
1
1
1
1
1
0
1
1
1
2
1
1
1
1
1
2
2
1
0
1
1
2
1
1
1
1
1
1
1
2
1
2
0
1
0
1
2
2
1
0
1
1
2
0
2
0
1
2
2
1
1
1
1
2
2
1
2
1
0
1
1
1
1
1
0
1
0
1
1
1
1
0
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
0
3
1
1
0
0
1
2
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
0
1
2
1
1
2
0
11
1
1
1
1
0
1
2
1
1
2
2
1
0
1
1
0
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
0
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
3
1
2
2
1
2
1
1
0
1
1
1
1
1
1
1
1
2
2
2
1
0
1
2
1
1
0
1
2
1
1
0
2
0
1
2
2
1
1
0
2
1
1
1
1
0
1
2
1
0
1
1
1
0
2
1
0
1
0
0
1
0
2
0
1
1
1
1
2
0
4
1
0
1
1
2
1
0
2
1
1
0
1
1
0
2
2
1
1
0
3
0
1
1
2
2
1
1
1
0
2
1
0
1
0
1
1
1
1
1
1
1
0
1
2
1
2
1
1
1
0
1
1
1
0
0
1
1
2
0
2
1
1
2
1
2
1
0
1
1
0
0
1
1
0
1
1
1
1
0
1
0
3
2
1
2
2
1
1
1
2
1
0
1
0
2
1
2
0
0
1
1
0
2
1
1
1
1
1
0
1
1
0
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
0
1
1
1
1
1
0
2
0
1
2
2
1
2
1
2
2
0
1
0
2
1
2
1
0
0
1
1
1
0
2
2
1
1
0
2
2
1
1
1
2
1
2
0
1
0
1
0
1
2
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
0
1
2
1
1
3
1
1
1
1
1
0
1
2
0
1
1
2
1
1
2
1
1
1
0
1
1
2
2
1
1
6
1
1
1
1
2
1
2
1
2
2
1
0
1
1
1
1
1
0
1
1
0
1
1
2
0
2
1
1
1
1
0
1
2
1
1
1
1
1
1
0
1
2
1
1
1
2
1
0
2
1
2
2
1
0
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
2
1
1
2
2
0
1
2
2
1
2
1
2
1
1
1
1
2
1
2
1
2
0
1
1
1
2
1
2
1
2
2
0
1
1
1
2
1
0
3
2
1
1
1
2
2
1
1
2
1
2
1
1
0
2
1
1
1
1
1
1
1
1
1
2
1
1
0
1
0
1
1
1
1
1
0
1
0
1
1
1
0
1
1
0
1
0
2
1
1
2
1
1
2
1
1
2
1
0
1
1
2
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
3
1
0
1
1
1
1
0
2
2
1
1
1
1
0
1
1
1
1
1
1
1
2
0
2
1
1
1
2
1
1
1
2
0
2
1
1
1
1
1
1
1
1
0
1
0
0
2
1
1
1
3
0
1
1
1
1
0
1
1
1
1
4
1
1
0
2
0
1
2
1
1
1
1
1
1
0
0
1
2
0
2
1
3
0
1
1
2
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
2
1
1
1
1
0
1
1
1
1
1
2
2
0
1
2
1
1
1
1
2
2
1
0
1
0
1
2
1
1
1
1
4
0
1
0
1
1
0
1
2
2
1
2
2
1
2
1
0
1
1
1
1
1
1
1
2
0
1
2
2
1
1
1
1
1
2
1
2
2
1
1
1
0
1
1
0
1
1
1
1
2
1
2
2
2
1
1
1
1
0
1
1
2
1
0
0
2
1
1
1
1
1
1
1
1
2
1
1
0
2
0
1
1
1
1
1
0
1
2
2
1
2
1
1
1
1
2
1
1
1
1
0
1
1
0
1
1
1
1
1
0
2
1
1
2
2
1
1
1
1
1
1
0
2
2
1
1
1
1
0
0
1
1
1
2
2
2
2
1
0
1
1
0
2
1
1
2
1
1
0
2
2
1
2
1
1
2
1
0
2
0
1
1
1
1
2
1
1
1
1
0
1
1
1
3
0
1
1
1
0
1
1
2
1
1
1
1
1
1
1
2
2
1
2
1
2
1
1
1
2
1
1
1
2
2
1
2
1
2
1
1
1
1
1
1
1
1
0
1
1
2
0
2
1
1
1
1
1
1
1
2
0
2
1
0
2
0
2
2
2
1
2
1
0
1
1
1
1
1
0
1
1
2
1
1
1
0
0
1
2
1
2
1
0
2
1
1
2
1
1
1
1
0
0
1
1
1
1
0
1
0
1
1
1
1
2
1
1
0
2
1
1
0
1
1
1
1
1
1
2
1
1
1
1
1
2
2
1
1
0
0
1
0
1
1
2
2
1
1
0
1
2
2
1
2
1
0
1
2
0
1
0
1
1
1
2
1
0
1
2
2
2
1
1
2
1
1
0
1
0
0
1
2
2
1
1
1
0
2
2
0
1
1
1
1
2
0
0
0
2
1
0
1
1
1
1
0
1
1
1
0
2
2
2
1
1
1
1
1
1
1
0
2
1
1
0
2
1
2
1
1
1
1
0
2
2
1
0
2
0
1
1
1
2
2
1
1
2
2
2
1
0
2
1
1
1
1
1
1
0
0
2
0
0
1
0
1
1
2
2
1
2
2
1
1
0
0
2
1
1
1
2
1
0
2
1
0
1
0
0
1
0
1
1
1
1
2
1
1
1
0
2
2
1
1
2
1
0
2
1
1
2
0
1
1
0
1
1
2
0
1
2
1
1
1
1
0
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
0
0
1
1
1
0
1
2
2
2
1
1
1
2
2
2
1
2
1
1
0
1
1
1
0
2
2
1
2
1
2
2
2
1
2
1
0
1
2
2
2
1
1
0
0
1
1
1
2
1
2
1
1
1
1
1
2
1
1
0
2
1
1
2
0
1
1
1
1
0
2
1
1
1
2
1
0
2
2
1
0
1
0
1
2
1
1
0
2
1
0
0
1
1
1
2
1
1
1
2
1
0
1
1
1
2
2
1
1
1
1
1
0
2
1
1
1
2
1
1
1
3
1
1
1
0
1
2
1
0
1
0
2
1
0
1
1
1
1
1
0
1
1
2
1
1
0
0
1
2
1
1
1
1
1
1
0
1
1
0
0
2
1
0
1
2
1
2
0
1
1
2
2
2
1
1
2
2
1
1
2
1
1
0
0
1
1
2
0
1
2
0
0
1
2
1
1
2
0
0
0
1
1
1
1
1
2
1
1
1
2
0
2
1
1
3
0
1
2
1
1
1
0
1
2
1
1
0
0
1
1
0
2
0
1
1
1
1
1
0
2
1
0
1
1
0
2
1
0
1
1
2
1
1
1
2
2
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
0
1
1
1
0
2
1
2
1
2
1
2
0
0
2
1
1
0
2
0
2
1
1
1
0
0
2
2
1
2
1
2
2
2
1
2
1
2
1
1
0
2
0
2
1
0
0
1
2
0
2
2
2
1
2
0
1
1
1
1
2
0
1
2
2
1
1
1
2
2
1
1
0
2
0
1
1
1
1
1
2
0
1
2
1
1
7
1
1
1
0
1
2
0
1
1
1
1
1
0
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
2
0
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
0
1
1
0
2
1
0
1
2
0
1
2
1
1
0
1
0
1
1
2
1
2
2
2
1
1
1
1
2
2
0
1
1
1
1
0
0
2
1
1
1
0
2
2
1
2
1
2
0
1
1
1
1
1
2
2
0
1
1
1
1
1
3
1
1
1
2
0
1
1
1
1
1
1
0
1
2
1
2
0
1
1
0
1
0
2
1
1
1
0
1
1
0
1
1
1
1
1
1
0
1
1
2
0
1
0
1
2
1
0
1
1
1
1
1
1
1
1
0
1
2
1
1
1
1
1
1
2
1
1
1
1
0
1
2
1
2
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
0
2
2
1
0
1
1
2
1
0
1
2
2
1
1
2
1
0
1
1
2
1
0
0
1
1
2
0
1
1
0
1
0
2
1
1
1
2
2
0
1
1
1
0
1
2
1
2
2
0
2
2
0
1
2
0
1
1
1
1
1
1
1
0
0
0
1
1
1
1
1
1
2
1
1
1
0
2
1
0
1
2
2
1
1
1
1
1
2
0
1
2
1
1
1
1
1
1
1
0
0
1
1
2
2
1
0
2
1
2
1
1
1
1
1
0
1
2
1
0
2
2
1
1
1
2
0
1
1
1
0
2
0
2
1
1
1
0
1
1
2
1
2
1
1
1
1
1
0
1
1
1
2
1
1
1
0
2
0
1
0
0
2
1
2
1
1
2
0
1
1
1
1
1
1
0
1
2
4
1
2
1
0
1
0
1
2
1
2
0
1
0
0
2
0
2
1
1
1
1
2
0
0
0
0
1
1
1
1
1
0
2
1
1
1
2
2
0
1
2
2
1
0
1
1
2
1
1
2
1
2
1
2
2
1
1
1
1
1
1
2
0
1
1
2
2
0
1
2
1
1
1
3
1
1
1
2
1
0
1
1
0
1
1
1
2
0
1
1
0
2
2
1
2
1
1
1
1
0
2
1
1
0
0
1
1
1
1
1
1
1
1
2
1
1
1
1
0
2
2
0
2
1
2
1
1
2
1
2
0
1
1
0
0
0
1
2
1
1
1
1
0
1
1
1
1
1
1
1
2
1
1
2
2
0
0
1
0
0
1
1
1
1
1
1
2
1
1
1
1
1
2
2
1
0
0
1
0
1
1
2
1
2
1
0
1
1
1
0
1
0
1
2
1
2
1
1
0
1
1
2
1
1
2
1
2
1
2
1
1
2
1
2
1
1
1
0
0
0
1
1
1
1
1
1
2
1
1
1
1
1
1
1
0
1
1
1
2
1
1
1
1
2
1
1
1
2
2
1
1
2
1
0
1
1
0
1
1
1
0
1
1
0
1
1
2
2
2
1
1
1
1
1
1
1
1
1
0
1
0
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
2
1
2
1
1
2
1
1
0
0
1
1
0
1
1
2
0
1
1
0
0
0
1
2
1
2
0
2
0
2
1
1
1
1
2
2
2
1
1
1
1
0
2
1
1
1
1
2
0
1
1
1
0
2
2
1
0
2
0
1
1
1
1
0
0
0
2
0
1
1
2
0
1
1
1
1
1
1
1
2
0
1
1
0
1
1
0
2
1
1
3
0
2
1
1
1
2
1
0
0
1
1
1
0
0
2
1
1
1
2
0
0
2
1
1
1
1
1
1
2
1
1
1
1
0
1
1
1
0
1
2
2
1
1
2
2
0
0
0
1
0
0
2
1
1
1
2
1
1
0
1
1
1
1
1
1
1
2
1
1
2
2
1
0
2
2
0
0
1
1
2
1
1
2
1
1
2
1
1
1
1
1
2
1
1
0
1
1
1
1
0
1
1
1
2
2
1
1
1
1
0
0
1
1
2
1
1
1
1
0
2
1
0
2
0
0
1
1
1
1
1
2
0
2
1
2
1
2
0
1
1
0
0
0
0
1
2
1
2
0
1
0
0
2
0
1
1
1
1
0
1
2
1
3
1
1
1
2
2
1
1
2
2
1
1
1
1
1
2
1
1
2
1
1
2
2
2
0
1
2
2
1
0
2
1
1
1
1
1
1
1
2
1
1
1
1
1
0
1
2
2
0
2
1
1
1
1
1
2
2
1
1
1
2
1
0
1
0
0
1
1
2
1
0
1
2
1
1
1
1
1
1
2
1
1
1
1
0
2
1
0
1
1
1
1
1
1
1
2
2
1
1
2
2
0
1
2
2
1
2
2
2
2
1
1
1
1
2
2
1
2
1
0
1
1
1
1
0
1
1
0
1
2
0
0
2
2
1
1
1
2
1
0
1
1
2
1
0
1
1
1
1
2
1
2
2
1
0
0
1
1
1
1
1
2
1
2
1
0
2
2
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
4
1
1
2
0
1
1
1
1
0
1
1
1
1
2
2
1
2
0
1
0
1
0
1
0
1
1
1
0
2
1
2
1
1
0
1
1
1
1
0
1
0
1
0
1
0
2
1
1
0
1
2
1
0
2
2
1
1
1
1
0
1
1
1
1
1
1
0
0
2
1
1
1
1
1
2
1
2
2
2
2
1
1
1
2
1
0
1
1
2
0
2
1
2
2
1
0
0
1
0
0
1
1
1
1
1
1
1
2
2
1
1
1
0
1
2
2
1
1
1
2
1
1
0
1
1
1
1
1
2
1
1
2
2
2
1
2
1
0
1
2
2
1
1
1
2
0
1
1
2
1
1
1
1
0
2
2
1
1
1
1
2
1
2
2
1
1
1
1
2
0
0
1
2
1
1
0
2
1
1
0
1
2
1
1
1
1
3
0
1
2
1
1
1
2
0
1
2
2
2
1
1
2
1
1
1
2
2
1
1
0
0
2
1
1
2
1
1
0
1
2
1
1
1
1
2
1
2
2
2
0
1
1
1
2
1
1
1
1
0
1
2
1
2
1
1
1
1
2
1
0
1
1
0
2
1
0
1
1
1
1
2
2
1
2
1
2
1
1
1
0
2
1
2
1
2
0
1
2
2
1
0
1
1
0
1
1
1
1
1
0
1
1
1
1
1
1
0
2
1
1
2
0
1
1
2
0
1
1
1
1
1
1
0
2
1
1
1
2
0
0
1
1
2
1
0
2
2
1
0
1
1
1
2
0
2
0
2
1
2
2
1
2
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
1
0
2
1
1
2
1
1
1
0
1
2
2
1
1
3
0
1
2
0
0
2
1
1
1
0
1
1
0
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
2
1
1
2
1
1
2
1
2
0
1
2
1
1
2
0
0
1
1
1
1
0
0
1
2
1
1
1
1
0
1
2
1
1
1
1
1
1
2
2
2
1
1
2
1
0
0
1
2
0
0
2
2
1
1
1
1
0
2
1
1
1
2
0
1
1
1
2
1
1
1
2
1
1
1
1
0
1
2
2
1
1
1
1
1
1
2
2
0
1
0
2
1
1
3
0
2
1
0
1
1
1
1
1
1
0
1
1
1
1
0
1
1
0
2
1
0
2
2
1
0
2
1
0
1
2
2
1
1
1
1
2
1
2
1
1
2
1
1
2
2
2
0
2
1
2
1
1
2
1
1
1
2
1
1
2
0
1
2
2
1
1
2
2
1
1
2
0
1
0
1
1
2
1
1
2
1
1
1
1
2
1
0
1
1
2
1
1
1
1
0
1
2
1
1
2
1
1
2
0
2
2
2
2
0
1
1
4
1
2
0
1
0
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
0
0
0
2
0
1
1
1
1
1
1
1
2
0
2
2
1
2
2
1
1
1
1
2
1
1
0
0
1
1
1
1
2
1
0
2
2
2
1
2
2
1
2
2
0
1
0
1
1
1
2
1
1
1
1
1
1
1
1
2
2
1
2
1
2
2
1
2
2
2
2
1
1
1
2
1
0
1
0
1
1
1
0
2
2
1
1
0
1
1
1
1
1
2
2
2
1
1
2
1
1
1
2
0
1
2
1
0
1
1
2
1
1
1
1
2
1
2
1
1
2
1
0
1
1
1
1
1
1
3
1
1
2
1
1
3
1
0
0
1
2
2
2
0
1
1
1
1
1
1
1
1
1
1
2
1
0
1
2
2
2
1
0
2
2
1
1
2
1
1
0
0
0
0
1
1
0
1
1
0
1
1
1
1
1
1
2
2
1
1
1
0
1
1
2
2
0
1
2
2
1
1
1
1
2
1
1
2
1
0
0
1
1
1
0
0
0
1
1
0
1
0
1
1
1
1
1
2
1
2
0
1
0
1
1
1
0
1
1
1
0
0
0
1
1
1
0
1
0
0
1
1
0
1
1
2
1
2
1
0
0
2
1
1
0
2
1
0
2
2
1
1
0
1
1
2
0
1
1
0
0
0
1
3
2
1
2
2
1
1
1
1
2
2
1
1
2
0
2
1
1
0
1
0
1
1
1
2
2
1
1
2
2
1
1
1
2
1
1
1
1
1
1
1
0
1
1
2
0
0
1
0
1
1
0
1
0
1
1
0
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
2
0
2
2
1
1
1
1
2
1
1
1
0
1
1
0
1
0
1
1
0
1
1
1
1
1
0
1
2
2
1
0
1
1
1
2
2
1
1
0
1
0
1
1
0
1
1
1
1
2
1
1
1
1
1
1
2
2
2
2
2
1
2
2
1
1
2
1
1
2
1
0
1
1
1
1
1
0
1
2
1
1
0
1
1
1
1
1
1
1
1
0
0
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
1
0
1
0
1
0
2
1
1
1
2
1
0
1
2
1
1
0
1
1
1
0
1
1
1
1
1
1
1
0
1
2
2
1
1
1
2
2
0
1
1
2
1
1
2
1
1
0
2
1
0
1
1
2
1
1
2
1
1
1
2
1
2
1
1
2
0
1
1
0
1
0
1
2
1
1
1
1
2
1
0
1
2
1
0
1
2
1
1
0
1
0
1
1
2
1
2
1
2
2
1
1
1
0
1
2
1
1
1
1
0
1
1
1
1
1
2
0
1
0
1
0
1
2
1
2
1
1
2
2
0
1
1
1
1
2
1
1
2
1
1
1
1
2
1
0
1
1
2
1
0
1
1
1
1
1
1
1
0
2
0
1
1
0
1
1
2
2
3
0
1
3
1
2
1
2
1
1
1
1
1
1
1
1
0
1
1
1
2
2
1
1
1
1
1
2
2
1
0
1
1
1
1
1
2
1
1
1
1
0
1
0
2
1
2
1
1
0
1
1
1
1
1
0
2
1
1
1
1
2
1
1
1
2
0
1
1
1
2
1
0
2
1
1
1
0
1
2
1
1
1
1
0
1
1
2
1
2
1
0
1
1
1
2
0
1
0
1
2
1
2
0
1
2
1
1
1
2
1
1
2
1
1
1
3
2
1
2
1
2
1
2
1
1
1
1
1
2
1
0
2
2
0
1
1
1
1
2
1
1
1
1
2
0
2
1
1
1
1
2
2
0
2
1
1
1
2
1
1
2
1
2
0
1
1
2
1
1
0
1
1
1
0
1
2
1
1
1
2
0
2
1
1
0
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
0
0
1
1
0
2
1
2
0
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
2
2
1
2
1
1
1
1
2
2
2
1
1
0
1
1
0
0
1
0
2
2
2
1
1
2
1
1
1
2
2
1
2
2
1
2
1
1
1
1
1
1
2
1
1
1
2
0
2
0
1
1
1
1
1
0
0
2
1
1
1
1
0
1
0
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
0
1
1
3
0
2
0
2
0
0
1
1
1
1
1
1
0
1
2
2
1
2
1
0
1
1
1
0
1
0
5
0
0
1
1
2
1
1
1
0
0
2
0
1
1
1
1
0
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
0
2
1
1
1
1
2
1
1
1
1
1
1
1
1
0
0
1
0
4
1
2
0
1
1
1
0
2
1
1
1
1
0
0
2
1
2
1
2
2
1
1
1
1
0
2
1
1
1
1
0
1
1
0
1
0
1
1
1
0
1
1
0
0
1
2
2
2
2
2
1
1
1
0
1
2
1
1
2
1
2
2
2
2
1
1
1
1
2
0
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
0
1
2
2
1
1
0
0
2
2
1
2
1
2
0
0
1
2
2
2
1
2
2
1
0
2
2
1
2
1
1
1
2
2
1
2
0
1
1
1
1
1
0
0
0
0
0
1
1
1
1
1
0
1
1
1
2
0
1
0
1
1
1
1
1
1
1
2
2
2
1
2
2
1
1
2
1
2
2
2
1
2
1
0
0
1
0
2
0
0
0
0
2
1
1
1
1
0
2
1
1
1
1
1
2
1
1
1
2
2
1
2
2
1
1
2
1
1
1
2
0
0
2
1
2
0
1
2
1
0
1
1
1
1
1
0
2
1
1
0
1
1
1
1
2
0
0
1
1
1
1
1
1
2
1
2
1
1
0
2
0
2
1
0
2
1
1
1
1
1
1
1
1
2
1
2
1
0
1
2
1
2
1
1
1
1
1
2
1
1
0
2
1
1
1
1
1
2
1
1
0
1
1
1
1
0
1
1
1
1
2
1
2
1
1
1
2
1
1
1
2
2
1
2
2
1
1
0
1
0
1
1
1
0
1
2
1
2
1
2
1
2
0
0
2
1
1
0
1
2
1
2
1
2
1
2
0
0
1
1
1
0
1
1
3
2
1
1
1
1
1
1
1
1
2
2
1
2
0
0
1
1
2
1
0
1
2
1
1
1
1
1
0
0
1
1
0
1
1
0
1
1
0
2
0
2
1
2
0
1
2
1
0
1
2
0
1
1
2
1
2
0
2
1
2
0
1
0
1
1
0
2
1
1
1
0
1
1
2
2
1
2
0
1
1
1
1
1
1
1
1
1
1
0
1
2
0
1
2
2
1
0
1
1
1
1
1
1
1
1
2
1
0
1
1
1
2
1
1
1
2
2
2
0
2
1
0
1
1
2
0
2
0
1
0
0
0
1
1
1
1
1
2
0
1
1
0
1
1
1
1
0
1
2
1
1
0
1
2
2
0
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
0
1
1
0
1
0
1
1
1
2
1
1
2
1
1
1
1
1
2
2
1
0
1
1
2
1
1
1
0
2
2
1
1
2
1
2
1
1
0
1
0
2
1
2
1
1
2
0
1
1
1
0
2
0
2
2
2
2
1
1
2
1
1
1
1
1
1
2
1
2
0
1
0
1
2
1
1
2
2
0
1
1
2
1
0
1
0
1
0
1
2
0
1
2
1
0
2
1
1
1
2
1
1
0
2
1
1
2
1
1
2
1
1
1
1
2
2
0
1
0
2
1
1
1
1
2
0
2
1
1
0
0
1
1
1
0
0
2
1
1
2
1
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
2
1
2
1
1
1
2
2
1
1
1
2
2
1
1
1
2
2
1
1
2
0
1
1
0
1
2
1
1
1
1
2
1
1
1
1
1
1
1
0
2
0
1
1
0
1
1
0
2
2
1
1
0
1
0
1
2
1
1
1
0
1
2
1
1
1
1
2
1
1
1
0
0
1
1
1
1
1
1
1
1
1
2
1
1
0
2
1
2
1
0
2
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
0
0
1
0
1
1
2
1
0
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
0
0
1
0
0
0
2
2
2
2
2
2
1
1
1
1
0
0
1
1
0
2
1
2
1
2
0
0
1
2
1
1
2
1
0
0
0
0
1
3
1
1
0
1
1
1
2
1
1
2
1
1
0
2
1
2
1
1
1
1
1
2
1
1
1
2
1
2
2
1
1
1
1
1
1
1
2
0
2
1
0
2
1
0
0
1
2
1
1
2
1
0
0
1
1
1
1
1
1
2
1
0
1
0
1
1
0
1
1
1
1
1
1
1
0
1
2
0
1
2
1
1
2
2
1
1
1
0
0
2
1
1
1
1
1
1
1
1
1
1
2
1
0
2
0
1
2
2
1
1
2
1
1
1
0
2
1
1
0
0
0
0
0
3
1
1
1
0
1
2
1
0
1
1
3
0
0
2
1
1
0
2
1
1
1
1
1
1
1
0
0
0
1
1
2
0
0
1
0
2
1
2
1
1
0
1
1
1
0
1
2
0
0
1
0
2
1
2
1
1
1
1
1
1
1
0
5
1
1
1
2
1
1
2
1
1
0
1
1
1
1
1
2
1
1
1
0
1
1
1
1
1
1
2
0
1
1
0
2
2
2
1
1
0
1
1
1
2
1
2
1
1
1
0
0
1
2
2
1
2
1
1
1
1
0
1
1
0
1
0
2
1
0
0
1
0
0
1
0
1
2
1
0
1
2
2
1
1
1
1
2
0
1
2
1
1
1
1
1
2
1
1
0
2
1
0
1
1
1
1
3
0
2
2
2
1
1
2
2
2
1
0
1
1
3
2
1
1
2
1
2
0
1
1
1
0
1
1
0
1
1
2
1
2
0
2
0
0
2
0
1
1
0
0
0
1
0
1
2
1
1
1
1
2
0
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
2
1
1
2
2
2
1
1
1
1
1
1
1
2
0
2
2
1
1
2
2
1
2
1
0
0
2
2
1
2
2
0
1
1
1
1
1
1
2
1
2
2
1
1
1
1
0
1
0
2
1
1
1
1
1
0
2
2
1
1
0
1
1
0
0
2
0
1
0
1
1
2
0
0
1
0
2
2
1
2
0
1
2
2
2
0
2
1
1
2
3
1
1
1
1
1
0
0
1
2
1
0
2
0
1
2
1
2
1
2
1
1
1
0
1
1
0
2
0
1
1
0
2
1
1
1
1
1
0
2
1
2
1
0
0
2
1
1
1
2
1
0
2
0
0
2
1
1
1
1
1
2
1
1
1
1
0
2
2
2
1
2
1
0
0
2
1
1
1
1
2
1
1
1
1
2
2
0
1
0
0
1
1
1
1
1
2
1
1
1
1
2
1
1
0
2
1
1
2
0
1
1
1
1
3
2
1
2
2
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
2
1
2
0
1
2
1
1
2
1
1
0
2
1
1
1
0
1
2
1
2
2
1
1
1
1
0
1
0
0
1
2
1
1
1
1
1
2
1
1
1
1
0
1
2
2
2
0
2
2
1
0
1
0
1
1
3
0
1
0
1
1
0
1
0
1
1
1
0
1
2
1
1
2
1
2
2
1
1
1
0
0
1
1
0
1
1
1
2
0
1
1
1
2
1
1
1
1
2
0
1
2
0
1
2
0
2
1
1
0
1
1
1
1
2
2
1
0
1
1
1
1
0
1
1
0
1
1
1
2
2
0
1
2
1
2
1
1
1
1
2
1
2
2
1
1
2
1
1
1
2
2
1
1
0
1
1
0
1
1
2
1
1
1
1
0
1
1
1
0
2
0
2
1
1
2
1
1
1
1
3
1
0
1
0
1
1
2
2
2
1
1
1
1
1
0
1
1
1
2
2
0
1
1
2
0
2
1
1
2
1
1
1
1
1
1
1
0
1
1
1
2
1
1
1
1
1
1
0
0
1
1
0
1
2
2
1
1
1
2
1
0
1
2
1
1
1
1
2
1
1
1
1
2
1
2
1
1
3
1
2
2
0
1
2
0
2
1
2
3
2
0
1
1
2
1
1
1
2
0
1
1
0
1
0
2
2
2
1
1
2
1
0
2
2
1
1
3
2
1
2
1
1
2
1
1
1
1
1
1
2
1
1
2
1
1
2
1
1
2
0
1
2
0
1
1
1
1
0
2
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
2
2
2
1
1
1
2
0
2
2
0
2
1
1
1
0
0
1
0
1
1
1
1
2
1
1
0
1
1
0
0
1
1
1
0
2
2
2
1
1
1
1
1
2
2
2
0
0
1
3
1
1
1
2
2
2
1
0
1
1
1
2
2
4
1
1
2
0
3
2
1
1
2
0
1
2
1
2
1
1
1
1
1
1
1
0
1
1
2
0
1
3
1
1
0
1
1
3
2
1
2
1
1
1
1
1
1
0
1
2
2
5
1
0
1
2
1
1
1
2
2
1
1
2
2
0
2
2
0
1
1
2
1
1
1
1
1
1
1
1
2
2
1
1
2
2
1
0
2
1
1
1
0
1
0
0
1
0
1
1
1
0
2
1
1
2
1
1
2
1
2
1
2
2
1
2
1
1
1
1
2
0
1
1
1
1
2
0
1
1
0
1
2
1
2
1
1
2
1
1
1
0
1
0
1
1
2
1
1
3
2
1
1
1
1
0
1
1
2
2
2
2
2
1
0
2
2
0
3
1
0
1
1
3
1
1
0
2
1
1
1
1
1
1
1
1
1
1
2
1
0
2
1
2
1
1
2
1
1
2
2
1
1
1
0
1
1
1
2
1
1
1
1
1
0
1
1
0
2
1
2
1
0
1
1
1
1
2
2
1
1
3
2
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
3
3
1
1
1
0
1
1
2
2
1
0
2
1
0
1
1
1
1
0
1
0
1
1
1
3
1
0
1
1
1
1
0
2
2
1
1
1
1
1
2
1
1
1
1
1
2
2
2
1
1
0
1
2
1
1
0
2
0
1
2
0
2
1
0
1
1
1
0
2
2
1
2
1
1
1
2
1
1
1
2
1
1
1
2
2
2
1
1
1
2
1
1
0
2
1
0
1
1
0
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
0
1
1
1
1
0
1
2
1
2
1
1
1
1
2
2
1
1
2
1
2
2
1
1
4
1
1
1
1
0
1
1
1
1
1
2
1
1
1
0
2
1
2
1
2
0
0
1
1
2
1
1
3
1
1
2
1
0
1
0
1
2
2
1
0
1
1
2
2
1
2
0
1
2
1
2
1
1
1
1
1
0
0
2
1
1
1
2
1
1
1
0
1
1
1
2
1
1
0
1
2
2
0
1
1
1
0
1
2
1
1
2
1
1
1
0
1
1
1
1
2
1
2
1
1
1
1
2
1
1
1
2
0
1
1
1
2
1
1
2
1
1
2
1
1
0
1
0
1
2
1
1
1
2
2
1
1
0
2
1
2
1
1
1
1
1
1
0
1
1
1
2
0
1
1
2
1
1
1
2
1
2
1
1
1
0
1
0
1
2
1
0
2
1
1
1
1
1
3
1
2
2
1
1
2
2
1
2
1
1
0
1
2
3
0
0
0
1
2
2
2
1
0
1
1
1
0
1
1
1
2
1
2
1
0
1
2
1
2
1
1
2
0
1
1
2
1
2
1
1
1
2
0
1
1
1
1
1
1
2
0
0
1
1
1
2
1
1
0
1
0
1
2
2
2
1
1
1
0
1
1
1
1
1
1
1
0
1
2
0
2
1
1
1
2
2
1
0
1
1
0
2
1
2
0
1
2
2
1
1
1
1
1
2
2
1
1
1
2
0
0
1
2
1
0
0
1
2
1
0
1
1
0
1
1
0
1
1
1
0
1
2
1
2
2
1
1
1
0
0
1
1
1
1
0
2
0
1
0
1
1
1
1
1
2
0
1
0
1
0
0
2
1
1
1
1
1
1
0
2
2
2
1
1
2
1
2
1
1
1
2
0
2
1
1
1
2
2
1
0
1
1
1
1
2
1
1
1
0
1
2
1
0
4
2
2
1
1
1
0
1
2
2
1
2
1
0
0
2
2
0
1
2
0
1
2
1
2
1
1
1
1
0
0
0
1
2
1
0
1
1
3
2
1
1
2
1
2
1
0
1
3
2
2
0
1
1
1
0
0
0
2
1
1
0
1
1
0
0
1
2
1
1
2
2
1
1
0
1
0
1
1
1
1
2
1
1
1
1
1
2
1
0
1
2
2
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
0
1
2
1
1
0
2
2
2
1
0
1
0
1
2
1
1
1
1
2
2
2
1
1
2
1
1
2
2
1
1
1
2
0
1
2
1
2
1
2
2
2
2
1
1
1
2
2
2
0
1
1
1
1
0
1
1
1
0
2
1
0
2
1
1
2
2
1
2
1
2
1
2
2
1
1
1
2
1
0
1
0
2
1
2
1
0
1
1
1
1
1
2
0
2
1
1
1
1
2
2
2
0
1
1
1
2
1
2
1
1
2
2
0
0
1
1
2
2
1
1
2
1
2
1
2
0
1
1
2
0
1
0
1
0
1
1
1
0
1
2
1
0
1
1
0
0
2
1
1
0
2
1
1
1
2
0
1
1
1
1
1
2
1
2
1
1
0
2
1
1
2
2
1
0
1
1
2
2
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
2
2
0
2
0
1
2
0
1
1
0
2
1
1
1
2
2
2
1
1
2
1
2
0
1
1
1
1
2
2
1
0
1
2
1
1
1
2
1
2
2
2
1
2
1
2
1
1
1
1
1
2
1
1
1
1
1
1
0
1
1
0
1
0
2
1
1
1
0
0
2
2
0
1
1
2
1
1
1
2
1
2
2
1
1
0
0
1
2
1
2
1
1
1
1
2
1
1
1
2
1
2
1
1
1
2
2
1
2
1
1
1
0
2
1
1
1
1
2
0
0
1
2
1
0
1
1
1
1
1
1
1
0
1
2
0
1
1
2
0
0
1
2
2
1
0
1
1
1
2
2
0
1
2
1
1
1
1
1
1
2
2
1
1
1
0
2
1
2
1
1
0
1
0
1
0
1
1
1
1
2
1
0
1
1
0
0
2
1
1
2
0
1
2
2
1
1
2
1
1
1
2
1
1
2
1
1
0
1
0
2
1
1
1
1
1
1
1
2
2
1
2
1
0
1
1
2
1
0
0
3
0
1
1
1
1
1
2
2
1
1
0
0
1
2
1
1
1
1
0
1
0
1
1
1
1
2
0
1
2
2
2
1
1
1
2
1
1
1
0
1
1
1
2
1
1
1
0
1
0
0
1
2
0
1
1
2
1
1
2
1
0
1
1
0
1
2
1
2
1
2
1
1
2
2
2
1
1
1
0
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
0
0
1
0
1
1
1
0
3
1
2
0
2
1
1
1
1
0
1
0
1
0
1
0
2
2
1
1
1
2
1
0
1
2
2
1
2
1
1
1
1
2
1
0
1
2
1
0
0
1
0
1
0
1
0
1
1
1
0
2
2
2
1
1
1
2
1
1
1
1
1
2
1
1
2
1
1
1
2
1
2
1
1
2
0
1
1
2
1
1
1
1
1
1
1
1
0
0
2
1
2
1
1
1
1
1
1
2
1
2
1
2
0
2
1
0
2
1
0
1
1
1
2
1
0
1
1
1
2
2
1
2
2
0
1
0
1
1
1
0
2
2
1
2
0
1
2
0
1
1
1
1
2
0
2
2
0
1
1
0
2
0
1
1
2
0
0
1
1
2
1
1
1
0
1
2
1
2
2
1
2
1
0
1
1
2
1
2
0
0
1
2
2
0
2
0
0
1
1
1
0
2
2
0
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
2
2
1
1
2
0
1
2
1
1
1
1
0
1
1
1
1
1
2
1
1
1
2
2
0
2
1
0
2
0
1
1
1
0
1
2
1
2
1
1
1
2
1
1
0
2
1
2
0
0
2
1
0
1
1
2
2
1
1
1
1
1
1
1
1
1
0
0
0
0
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
0
1
1
1
0
1
2
1
1
1
1
1
1
1
0
1
1
2
1
1
1
1
1
1
1
1
2
1
2
0
1
1
2
1
2
1
0
2
0
1
2
1
1
2
0
0
1
2
1
2
2
3
1
2
1
1
1
2
1
1
2
2
0
2
2
1
2
0
2
1
1
0
1
0
0
2
1
1
1
2
2
1
1
1
2
2
1
1
0
1
0
1
2
1
1
0
1
0
1
1
1
1
1
1
1
3
1
2
2
1
2
1
1
2
1
0
2
1
1
1
1
1
1
1
1
2
2
2
2
0
1
2
0
2
1
1
0
1
1
1
2
2
1
1
1
1
1
2
2
1
0
1
1
1
1
1
2
1
1
1
2
1
2
1
2
2
2
2
1
1
1
2
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
0
1
1
1
1
2
2
1
3
2
1
1
0
1
1
1
1
0
0
1
2
1
1
1
2
0
0
2
1
1
0
1
1
0
1
1
1
2
1
1
2
2
1
0
1
2
2
2
0
1
1
1
0
2
2
2
1
1
1
2
1
1
1
0
1
1
0
2
2
0
0
1
1
1
0
0
2
2
1
1
2
2
1
2
2
0
2
0
1
1
1
1
0
1
1
0
2
1
1
2
2
1
1
2
1
1
1
1
0
1
1
2
1
1
2
1
1
1
2
0
1
1
1
0
1
2
2
1
2
0
1
1
0
1
3
1
0
1
2
0
1
1
2
1
1
0
2
2
1
1
1
1
1
1
1
1
1
1
0
1
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
0
1
2
1
1
1
1
1
1
1
0
1
1
0
0
0
0
1
1
1
0
2
1
1
1
2
1
0
2
0
1
2
1
0
1
1
1
0
1
1
2
1
1
1
0
1
2
1
1
0
0
2
1
1
1
1
2
0
1
1
2
0
1
1
1
0
2
1
1
1
1
0
0
0
0
0
1
1
1
1
1
0
1
2
1
1
0
1
2
1
1
1
1
1
1
1
1
2
1
2
1
0
1
2
0
1
0
2
1
0
0
1
0
1
1
1
2
1
1
2
0
1
2
1
1
2
1
0
1
2
1
1
2
3
1
1
1
1
2
0
1
1
2
2
1
2
1
2
1
1
1
3
1
1
1
0
0
0
0
1
1
2
1
1
1
1
2
1
1
0
1
1
1
1
1
1
2
2
0
0
1
1
1
2
1
1
1
0
1
1
0
2
0
1
1
2
1
1
1
1
1
1
0
2
0
1
3
0
0
1
2
1
0
1
2
1
0
1
0
1
1
1
1
1
1
1
2
2
2
2
2
1
1
2
2
1
0
2
3
1
0
1
2
1
1
2
1
1
1
2
2
2
1
1
0
1
2
1
1
1
1
0
1
0
1
2
2
2
1
1
2
1
2
1
1
1
1
0
2
1
1
2
1
1
1
1
2
0
1
0
2
1
1
1
1
1
1
1
1
1
1
0
1
0
1
2
1
0
1
0
1
2
1
2
1
1
0
1
1
2
1
2
1
1
1
1
0
0
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
0
1
2
1
1
1
2
1
2
2
1
1
1
0
0
1
1
2
1
1
2
1
2
2
0
1
0
1
2
2
1
2
0
1
1
1
0
2
1
0
2
1
1
0
1
1
1
0
2
2
1
1
1
2
1
1
1
1
0
1
1
0
0
2
1
1
1
1
1
1
1
2
1
0
0
2
0
0
1
1
1
0
1
1
1
0
1
1
2
1
1
1
2
1
1
1
0
0
1
1
1
1
2
0
2
2
0
1
2
2
1
2
0
1
1
1
2
1
1
1
1
1
1
1
1
2
1
2
1
2
2
1
1
1
1
2
1
1
1
1
1
1
0
2
1
1
1
1
0
1
2
0
2
1
1
1
1
2
1
0
1
0
0
2
0
2
1
1
2
1
1
1
1
0
1
1
1
1
2
0
0
2
1
1
1
2
1
1
1
2
2
1
1
1
2
1
0
2
2
2
1
1
1
3
1
1
1
1
2
1
1
1
1
2
1
4
1
2
1
2
1
2
1
2
0
1
2
2
2
1
1
1
1
2
1
1
0
1
1
1
2
2
1
2
1
2
1
1
0
0
1
1
1
1
1
0
0
2
1
2
2
1
1
0
2
1
1
0
1
1
1
2
1
1
1
2
1
2
1
0
1
1
0
1
2
0
0
1
2
1
1
1
1
2
0
0
0
1
1
0
2
0
0
2
1
2
2
1
0
1
2
1
1
2
0
2
1
1
1
2
1
2
1
1
1
1
1
2
1
2
1
0
1
0
1
1
2
0
1
1
1
1
1
1
1
3
0
1
2
1
1
1
1
1
2
1
1
1
1
0
1
1
1
1
1
1
1
1
1
0
1
1
1
0
0
1
1
1
2
0
1
2
1
0
0
1
0
2
0
1
1
1
1
1
1
0
0
1
0
0
1
2
1
1
1
0
1
0
2
1
0
0
1
1
1
2
1
0
1
1
1
1
2
1
0
1
0
2
2
1
1
2
1
1
0
1
1
2
1
1
1
0
1
1
2
0
1
1
1
1
1
1
2
1
0
1
1
1
1
2
1
1
0
1
1
1
1
1
2
2
1
2
1
2
1
1
2
1
1
1
0
1
1
0
1
1
0
0
0
1
0
1
1
1
2
1
1
0
2
1
2
1
0
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
0
0
1
1
1
1
2
1
2
1
1
1
2
1
2
2
1
0
1
0
0
1
1
1
1
1
1
1
2
1
0
1
0
1
1
0
1
1
1
1
1
1
1
2
1
0
1
1
0
1
0
0
1
2
2
1
1
1
1
2
1
1
2
1
1
1
1
2
1
1
2
2
2
1
1
1
2
0
1
1
1
0
0
2
1
1
2
1
1
0
1
1
1
1
1
0
0
2
1
0
1
1
2
0
2
1
0
0
1
2
2
2
1
1
2
1
0
0
2
0
1
1
2
1
1
0
2
1
1
1
1
1
2
1
1
1
0
1
1
1
2
0
2
1
1
1
1
1
1
1
2
0
0
1
0
2
1
1
2
1
1
0
0
1
1
0
1
0
1
2
1
2
1
0
1
1
2
1
2
1
1
1
1
1
2
1
1
1
2
0
0
1
1
0
0
1
1
1
2
1
2
1
2
0
1
1
0
1
1
2
1
1
0
2
0
1
1
2
0
1
1
1
1
1
1
1
1
1
1
2
1
1
2
2
2
1
2
0
1
3
0
2
1
1
1
1
1
1
1
0
1
1
0
1
1
1
0
3
2
1
1
1
1
2
1
1
3
3
0
1
1
1
1
1
1
1
2
2
1
1
1
2
1
2
0
2
0
1
2
1
1
1
1
1
1
2
1
0
1
1
0
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
2
2
1
1
0
1
1
1
1
1
1
1
1
1
2
0
2
2
1
1
1
1
1
1
1
1
1
2
2
1
1
1
0
1
1
1
2
1
2
1
1
2
1
2
1
1
1
1
2
2
1
0
1
0
2
0
0
1
1
0
2
1
0
1
1
1
2
1
2
2
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
0
1
2
1
1
1
1
1
1
1
1
0
0
2
0
1
1
2
2
1
1
1
2
2
2
1
1
1
0
2
2
4
1
1
2
2
1
1
1
2
0
0
2
2
1
1
1
1
1
0
2
0
0
0
1
0
1
1
1
1
2
1
1
0
0
1
2
0
0
1
1
1
2
0
2
2
1
2
1
2
1
2
0
0
1
2
1
1
0
0
0
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
2
0
0
2
2
0
2
1
1
1
1
1
1
1
1
0
1
0
0
2
0
2
1
1
1
0
1
1
1
0
1
0
2
2
1
1
2
1
2
1
1
1
1
2
1
1
1
0
1
1
0
1
2
1
1
0
2
1
2
2
2
2
0
0
1
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
0
1
2
1
0
1
1
1
0
1
2
1
1
4
1
1
1
0
1
2
1
1
0
1
1
1
1
1
1
2
2
2
1
2
1
2
2
2
0
1
2
1
1
1
2
1
2
0
1
2
1
2
3
2
1
0
1
1
0
2
1
2
2
1
0
0
0
1
2
1
1
1
2
2
1
3
1
1
0
1
2
0
2
2
0
0
1
1
0
1
2
1
0
1
2
1
0
0
1
1
1
1
2
1
0
2
1
0
1
1
2
1
0
1
0
0
1
1
1
2
1
0
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
2
0
1
1
0
0
1
0
0
2
2
1
1
0
1
1
1
2
2
0
2
1
2
1
2
0
2
1
1
1
2
1
1
2
1
2
1
0
1
1
1
2
1
1
2
1
1
1
0
1
2
2
2
1
2
2
2
1
2
2
2
1
1
1
1
0
2
1
2
1
0
1
0
1
2
0
1
2
1
1
1
1
1
0
2
1
1
1
1
1
2
1
2
1
0
1
1
1
1
1
1
2
0
1
0
1
1
1
0
1
2
1
1
1
1
1
1
0
1
0
1
1
1
1
1
2
1
2
2
1
2
1
2
1
1
1
0
2
1
1
1
2
0
2
1
1
2
2
1
2
1
1
0
1
0
1
0
1
0
1
0
1
1
0
1
1
1
1
0
1
1
0
1
1
3
0
1
1
2
2
1
0
2
0
2
1
0
1
1
2
2
2
1
1
1
1
0
1
0
1
1
2
0
2
2
0
1
1
0
1
0
1
1
1
1
1
2
0
2
2
2
2
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
2
1
0
1
1
0
1
1
1
1
1
2
1
0
1
1
2
1
1
1
1
2
2
1
1
0
0
1
1
6
3
1
1
2
1
3
1
0
1
1
1
1
1
2
1
1
1
1
0
1
2
1
1
0
1
1
1
2
1
0
1
2
0
1
1
1
1
0
1
0
1
2
0
1
1
2
0
1
0
2
2
1
0
2
1
3
1
2
1
1
1
1
2
2
1
1
1
1
0
1
2
1
2
1
2
1
1
1
0
2
1
1
2
1
2
1
1
1
1
2
1
1
0
0
1
1
1
1
0
0
1
1
1
2
2
1
2
1
0
2
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
0
1
1
1
1
0
1
0
1
1
0
1
0
1
0
1
2
1
1
1
1
2
1
1
1
1
1
0
1
1
0
1
1
1
2
2
0
2
1
0
1
3
2
0
2
1
1
1
2
1
0
0
1
1
1
2
1
1
2
0
0
1
1
0
1
0
1
1
1
1
2
0
2
0
1
2
1
1
1
0
1
2
1
0
1
1
1
2
2
2
1
2
1
0
1
1
1
1
1
3
1
1
0
1
1
0
0
2
1
1
1
1
1
2
2
1
1
1
0
1
2
1
1
2
1
1
1
2
2
1
0
1
1
1
1
1
1
1
1
1
2
1
2
0
1
2
1
2
1
0
1
1
2
1
1
1
2
1
2
2
1
0
1
1
2
1
1
2
1
1
0
1
0
1
0
2
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
0
2
2
1
1
1
0
1
0
2
2
1
1
1
2
1
1
1
0
1
2
1
0
0
1
1
2
1
1
1
2
1
1
1
0
0
1
1
0
1
1
0
3
0
1
1
1
0
2
1
0
2
1
1
2
0
1
0
0
0
1
0
2
1
2
1
1
0
2
1
0
1
1
1
0
1
2
2
1
1
1
1
2
2
1
1
0
1
1
1
2
1
1
1
1
1
0
1
2
1
2
1
1
1
1
1
1
1
1
1
0
1
0
2
1
1
1
0
2
1
2
1
1
1
1
1
2
2
1
1
1
1
2
1
1
2
2
2
1
1
1
1
1
1
1
2
1
0
0
0
1
0
1
2
0
1
0
2
2
2
1
0
0
0
0
1
2
2
2
1
2
1
1
1
2
0
1
1
1
1
2
1
1
1
1
0
2
1
2
1
1
1
1
2
1
1
0
1
2
1
0
1
1
1
1
0
0
1
1
1
2
2
1
1
0
1
1
2
1
0
2
1
0
2
0
2
1
0
1
1
1
0
0
1
2
2
2
0
1
1
1
0
1
0
1
1
1
1
1
0
1
1
1
2
1
1
1
1
1
0
2
2
0
0
1
1
1
0
1
1
2
1
2
1
1
1
0
1
1
2
2
1
1
2
1
1
1
1
2
2
0
1
1
0
1
0
1
1
1
1
1
2
2
0
1
0
0
2
2
1
1
1
1
1
0
2
2
1
1
1
2
2
1
1
2
1
0
2
1
1
1
0
0
0
2
0
1
1
1
2
1
0
1
1
1
2
2
1
1
0
1
1
1
1
1
1
1
1
0
2
1
1
0
0
2
1
1
2
1
1
0
1
0
2
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
0
0
0
1
2
1
0
2
2
1
2
1
2
1
1
1
0
1
1
0
1
0
0
1
1
1
2
1
1
1
1
1
0
1
1
1
1
0
2
0
2
0
1
0
1
1
2
1
1
1
1
1
2
1
2
0
0
2
1
2
1
1
1
2
2
1
1
2
1
2
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
2
1
1
0
1
1
1
2
2
1
2
1
1
2
1
0
1
2
1
1
1
1
1
0
1
1
1
3
2
1
1
2
1
1
0
1
1
0
1
0
2
1
1
2
0
1
1
2
1
1
2
3
0
2
1
2
1
0
2
2
0
2
2
2
2
2
2
2
0
1
1
0
2
1
1
2
0
1
1
1
0
1
1
0
2
1
1
1
1
1
0
0
2
1
1
3
1
2
0
1
3
2
0
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
0
2
2
1
1
0
1
2
1
0
1
0
0
2
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
0
1
1
2
1
1
0
1
1
1
0
2
2
2
0
0
1
1
1
2
2
1
1
2
1
1
1
0
1
1
1
1
1
2
1
2
2
1
1
1
1
1
1
1
2
2
2
1
1
2
1
0
1
1
1
1
1
0
0
2
2
2
1
1
1
0
2
2
0
0
0
1
1
1
1
2
1
1
1
2
1
1
2
1
1
1
0
2
1
2
1
1
1
1
1
0
1
2
1
2
2
0
1
1
0
1
1
1
1
1
2
1
1
1
1
1
3
2
1
2
1
1
1
0
2
1
1
1
0
2
1
0
1
3
0
0
1
1
7
2
1
1
1
2
2
0
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
1
0
1
2
1
1
1
2
2
1
0
2
2
1
0
1
1
3
2
0
1
2
2
2
0
2
1
1
1
1
0
1
1
1
1
0
1
0
2
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
0
1
1
0
0
2
1
1
0
1
1
1
1
1
0
1
2
1
0
2
1
1
2
2
2
2
0
2
1
2
1
2
1
2
1
1
1
2
1
1
2
2
1
1
2
1
0
1
1
2
0
0
2
1
2
1
1
1
1
2
1
1
1
1
1
1
0
1
1
1
3
1
2
0
1
1
1
1
2
1
0
1
1
2
1
0
1
2
2
1
2
2
0
0
1
1
0
2
2
1
0
2
2
1
2
1
0
2
1
1
1
1
2
1
2
1
1
1
1
0
1
0
1
2
1
1
2
1
1
1
1
1
0
0
0
2
2
1
0
2
3
0
1
2
0
1
0
2
1
1
1
2
2
1
0
2
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
0
0
1
1
1
1
0
2
1
1
1
1
0
2
1
1
2
0
1
2
2
0
1
1
2
0
1
1
1
1
1
0
1
1
1
2
1
0
1
0
2
1
1
1
1
0
1
2
0
1
1
1
1
2
2
0
2
1
0
1
1
1
1
1
1
1
2
1
2
2
1
0
2
1
1
2
1
2
2
0
2
2
0
2
1
1
1
1
1
1
1
0
0
1
1
1
1
1
2
0
1
1
1
1
2
1
0
1
0
0
1
2
0
2
1
1
1
2
0
0
2
1
1
0
2
4
1
1
1
2
0
2
1
1
1
1
1
0
1
1
1
0
0
1
2
1
1
0
1
1
2
2
0
3
1
1
1
1
1
1
1
1
2
1
0
2
1
1
2
1
0
2
0
1
1
1
2
1
1
2
0
0
2
2
2
1
1
1
0
2
0
2
0
0
3
2
1
0
2
2
1
2
1
1
1
1
2
1
1
1
2
2
1
1
1
2
0
1
1
0
0
0
1
2
0
1
1
3
1
2
1
1
1
1
0
1
1
1
2
2
1
0
1
1
2
1
1
0
1
2
1
2
1
1
1
1
1
0
0
2
2
1
1
1
2
1
1
1
1
2
0
2
0
0
0
0
0
2
2
1
2
1
2
1
0
1
1
0
1
1
3
1
2
1
1
0
1
1
0
2
2
0
2
1
0
0
0
1
1
0
1
1
1
1
2
1
1
2
1
1
2
1
1
2
2
1
1
1
1
1
1
1
2
0
0
0
1
0
1
0
1
1
1
1
2
0
1
1
1
0
2
1
2
1
0
1
1
1
1
0
0
0
1
1
1
1
1
2
1
0
0
0
1
1
2
1
1
1
1
1
0
1
0
1
1
1
1
2
1
2
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
3
1
2
1
1
1
0
1
1
2
1
0
1
1
1
2
2
1
2
1
2
2
1
1
2
1
1
1
1
1
0
1
1
1
1
1
2
2
2
2
0
1
2
1
0
2
2
1
2
1
2
1
1
1
0
1
0
1
2
0
1
2
2
1
0
1
0
1
1
1
2
1
0
2
0
2
1
1
1
1
0
0
0
2
0
1
1
1
1
1
2
1
2
0
0
0
2
0
1
1
1
2
1
0
2
1
1
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
2
1
1
2
1
1
1
1
0
1
1
1
2
1
1
2
0
1
2
2
1
1
2
0
2
1
2
2
1
1
1
1
1
1
0
1
1
0
2
1
1
2
1
1
0
2
1
1
1
2
2
1
1
2
1
0
1
1
1
1
0
1
1
2
1
1
1
0
1
0
1
1
0
2
0
1
1
1
1
1
0
1
1
1
0
1
1
2
2
1
1
2
2
2
1
1
1
2
1
1
2
0
1
2
0
1
1
2
0
0
0
1
1
1
1
2
1
2
1
1
1
1
0
0
2
1
1
1
0
1
1
0
1
1
0
1
2
2
1
0
1
1
2
1
1
0
3
1
1
2
0
1
2
1
1
0
1
2
0
1
1
1
1
0
1
2
2
1
1
1
1
0
1
0
1
1
2
0
1
0
1
1
0
1
2
2
1
1
1
2
2
1
2
1
0
1
1
2
1
0
1
1
0
2
2
1
1
0
1
1
0
2
2
1
1
0
2
1
2
1
1
1
1
1
1
1
2
2
0
2
1
0
0
1
0
0
1
2
1
0
2
0
2
1
1
2
1
1
1
0
1
2
0
1
1
1
1
1
1
2
1
2
1
1
0
1
1
0
1
1
0
1
1
1
1
1
2
1
1
0
0
0
0
0
0
1
0
2
2
2
0
1
1
1
1
1
0
1
1
1
0
1
3
1
0
0
0
1
1
0
0
1
2
1
1
1
1
1
1
1
1
1
1
1
2
0
2
1
1
1
1
1
1
1
1
1
1
2
0
0
1
1
2
1
1
1
1
1
1
2
1
1
0
0
0
2
1
0
1
1
3
2
1
2
1
2
0
1
0
1
0
1
2
4
1
1
1
0
1
1
1
1
1
1
2
1
2
1
1
1
3
2
1
1
3
1
1
1
2
1
0
1
1
1
1
1
1
2
1
1
0
1
1
1
1
2
1
1
1
1
1
2
1
1
1
0
1
0
0
0
2
1
0
1
2
0
0
1
2
1
2
1
0
0
1
0
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
0
1
1
0
0
1
1
2
2
1
0
0
1
1
1
1
2
1
2
1
2
0
0
1
1
1
1
2
1
2
1
1
0
1
1
2
2
4
1
2
0
2
1
1
0
2
2
1
1
1
2
0
1
1
1
1
1
1
1
1
1
0
1
0
0
1
1
1
1
1
1
4
1
2
0
1
1
2
1
2
2
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
0
1
1
1
1
0
1
1
1
2
1
1
2
1
0
1
1
2
1
0
2
1
1
1
0
0
0
1
2
1
1
2
1
2
1
1
1
0
0
0
2
1
2
1
2
2
0
1
2
1
2
1
1
1
2
2
2
2
0
1
0
2
1
1
2
1
1
1
2
1
1
0
2
1
1
1
0
1
1
1
1
0
1
1
1
1
1
1
0
1
2
0
0
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
0
2
1
1
2
1
1
1
1
0
1
0
0
0
2
0
1
2
1
1
2
2
2
1
2
1
1
2
0
1
0
0
1
2
2
1
1
0
2
1
0
1
2
1
1
0
2
1
0
1
0
0
1
0
3
1
2
1
1
0
1
2
1
1
1
2
1
1
1
1
1
1
0
2
0
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
2
0
1
1
0
1
2
1
1
1
1
2
1
0
1
1
1
0
1
1
2
1
1
2
1
2
2
1
1
1
1
1
1
1
0
1
2
1
1
1
1
0
0
1
1
2
1
0
1
2
2
1
1
1
1
0
1
1
2
1
2
2
0
0
1
2
1
1
1
1
2
1
1
0
1
1
1
1
1
1
1
1
1
0
1
2
1
0
1
1
2
2
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
4
2
1
1
0
0
2
2
3
1
1
0
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
2
2
2
1
0
2
2
1
0
1
1
0
1
2
1
0
0
1
1
2
1
0
1
1
2
1
1
2
1
1
1
1
1
2
1
1
0
1
1
1
1
2
1
1
1
2
1
1
0
1
1
2
0
1
2
1
3
1
1
1
0
2
1
1
1
0
1
2
1
1
0
1
0
2
0
1
1
0
2
1
1
1
1
1
0
1
2
1
1
1
0
2
0
2
2
0
1
1
1
1
1
1
1
2
2
2
2
1
1
1
2
1
0
1
1
1
2
0
0
1
1
0
1
1
1
0
1
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
0
1
1
0
2
1
0
2
1
0
1
4
2
1
2
1
1
1
1
1
0
1
1
0
1
1
0
0
1
1
2
1
1
2
1
0
1
1
2
0
1
1
2
2
0
0
2
0
1
1
1
1
0
1
1
2
1
1
1
1
2
1
1
2
1
1
2
2
1
1
1
0
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
2
2
2
1
1
2
2
2
1
1
1
1
1
0
1
2
1
2
1
1
0
0
2
1
0
0
1
2
1
1
1
1
1
0
1
1
2
1
1
2
1
1
0
1
1
2
0
1
1
1
0
1
1
0
1
0
2
1
0
1
1
2
0
1
1
2
1
1
1
1
0
1
1
0
1
0
1
1
0
1
2
2
1
2
0
1
0
1
2
1
1
1
2
1
0
1
1
1
1
1
1
1
0
0
0
1
0
2
2
1
1
1
2
1
2
1
2
1
2
1
1
1
2
2
1
2
1
1
1
2
1
0
2
1
1
2
0
0
1
1
2
0
1
1
1
0
2
1
1
4
2
1
1
2
0
1
1
2
2
0
1
1
1
2
1
1
0
2
2
3
0
1
2
0
1
2
1
1
3
1
0
1
2
1
1
1
1
0
1
1
1
1
0
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
0
1
0
2
1
1
1
2
2
2
2
1
1
1
0
1
1
1
1
1
1
1
2
0
0
0
2
1
1
0
1
0
2
1
2
1
1
1
1
0
2
0
2
0
1
2
3
0
2
0
1
0
1
1
1
0
1
0
0
2
2
1
1
0
2
1
0
6
0
1
2
0
0
2
2
2
1
1
1
2
0
2
2
0
2
2
1
1
2
0
1
0
1
2
1
1
1
1
1
0
1
1
0
2
0
1
1
1
2
1
1
2
2
1
2
1
1
1
0
2
1
2
1
1
2
1
0
1
1
1
3
1
2
1
0
1
1
2
1
1
2
2
1
0
1
1
0
2
2
0
2
0
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
2
1
1
1
1
2
2
1
2
2
1
2
1
1
1
3
1
1
2
1
1
1
1
1
0
1
0
1
1
1
1
1
1
1
1
2
1
0
1
2
2
2
1
0
1
0
1
2
1
1
1
2
1
1
1
1
1
0
2
1
2
1
6
1
1
0
1
1
1
1
1
1
1
1
0
0
1
1
1
1
0
1
1
1
1
1
1
1
1
1
0
1
1
2
1
2
1
1
0
1
0
1
3
2
1
2
1
1
2
2
1
1
0
1
1
2
1
1
1
2
1
1
1
1
2
1
1
0
1
1
1
1
2
1
1
1
0
1
1
1
1
1
2
2
0
1
2
1
1
2
0
0
2
0
1
1
1
1
0
0
2
1
1
1
1
2
1
2
2
1
1
1
1
2
2
1
1
1
1
2
1
0
1
1
1
1
2
1
1
1
0
1
1
1
1
0
3
1
2
2
1
3
1
1
1
1
1
1
1
1
1
2
1
1
1
0
3
0
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
3
1
1
1
1
0
2
1
2
1
2
2
1
2
2
2
1
1
1
1
1
2
1
2
2
1
0
0
1
0
1
1
2
1
1
0
2
1
1
1
1
1
1
1
1
2
1
1
0
1
1
2
0
2
2
1
2
1
1
1
1
0
2
1
1
1
2
2
2
1
1
2
2
1
2
1
1
1
1
2
1
1
1
2
1
0
1
2
1
2
2
2
0
1
1
1
1
1
1
1
1
0
1
2
1
2
0
2
1
1
1
1
2
1
1
2
2
0
1
1
1
1
1
1
1
1
2
2
2
2
1
1
1
2
1
1
0
1
1
0
1
1
2
1
1
2
2
1
1
2
1
1
2
2
1
1
0
1
2
0
1
1
1
1
1
1
1
0
1
1
1
2
1
1
1
1
1
2
4
2
2
1
2
2
1
1
1
1
1
2
2
2
2
1
1
1
1
1
0
1
2
2
1
2
2
2
0
1
1
1
0
2
2
0
1
2
1
1
1
1
1
2
1
1
0
1
2
1
1
1
1
2
1
2
1
1
1
0
0
1
1
1
1
1
2
1
1
1
1
1
1
1
1
0
1
2
0
1
2
1
2
1
1
1
0
1
1
2
1
1
0
1
2
1
0
1
1
2
1
1
0
1
1
1
1
0
1
2
1
0
1
1
5
3
0
1
0
1
2
1
2
0
0
0
1
1
1
1
1
0
1
1
1
2
1
0
2
1
0
1
1
2
1
2
1
1
1
1
1
0
1
1
1
1
1
0
1
1
2
1
1
0
1
2
2
1
1
2
0
1
2
1
1
0
1
0
2
2
3
0
2
2
1
0
2
1
1
1
2
1
2
2
1
2
1
0
1
1
2
1
0
1
1
0
2
1
2
2
1
2
1
1
2
1
1
2
1
0
2
2
1
1
2
0
1
1
1
0
1
1
0
1
0
2
2
1
1
0
2
1
2
2
0
2
1
0
2
0
2
1
2
0
2
1
0
2
1
1
1
0
0
1
2
0
2
2
0
0
0
1
1
3
1
1
0
1
1
1
1
1
1
2
1
1
2
1
1
0
0
1
1
2
1
1
1
2
1
1
1
1
2
1
1
0
1
1
2
1
1
2
1
1
0
1
1
1
1
1
2
1
1
1
2
1
2
0
1
1
1
1
1
1
2
2
1
1
1
1
1
1
0
2
0
2
2
1
2
1
1
0
1
2
1
1
2
0
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
2
2
1
2
1
1
1
0
1
1
1
1
0
1
2
1
2
0
2
0
1
1
0
1
0
1
1
1
1
1
1
2
1
1
2
1
1
1
1
0
1
1
1
0
3
1
1
2
0
1
2
1
2
0
1
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
1
2
2
0
1
1
0
0
2
1
1
2
1
1
1
1
1
2
0
2
1
1
0
1
1
1
4
1
1
1
1
1
2
2
2
1
1
1
1
1
1
2
1
1
1
0
1
0
1
1
1
1
1
1
1
2
1
1
2
2
1
0
0
1
2
2
1
2
0
1
1
1
0
1
1
0
2
1
1
1
0
1
1
1
1
0
2
0
1
0
1
0
0
1
1
1
0
1
1
0
1
0
1
1
2
1
0
1
1
1
1
1
1
1
2
0
0
1
0
1
1
2
1
0
1
1
0
0
1
1
0
1
2
0
0
1
1
1
1
1
1
2
1
2
2
1
1
1
0
2
1
0
2
2
1
1
0
1
2
1
1
0
1
0
0
1
1
0
1
2
2
0
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
0
1
1
2
1
2
2
2
0
2
1
1
5
2
1
0
1
0
1
2
0
0
0
1
1
1
1
1
1
1
0
1
2
1
1
2
2
1
2
1
2
0
1
1
0
1
1
2
1
1
1
1
1
1
2
0
2
1
1
1
1
1
0
2
2
0
1
1
2
1
2
1
1
1
1
1
1
0
1
2
0
1
1
2
1
1
1
2
1
1
1
1
0
1
2
1
1
2
2
1
1
1
2
0
1
1
1
2
2
2
2
1
2
1
2
0
1
1
0
1
1
1
2
2
2
0
1
1
1
1
1
0
2
2
2
1
1
1
2
2
1
1
1
1
1
1
0
1
2
2
1
1
1
2
2
0
2
1
0
1
1
0
1
2
0
0
1
1
1
1
1
1
2
1
1
0
0
1
1
2
1
0
1
1
2
1
2
0
1
1
2
1
1
0
1
3
2
1
0
0
2
0
1
0
2
1
2
0
1
2
2
1
1
1
0
1
0
1
2
2
0
1
1
0
1
1
0
1
1
1
1
0
2
2
1
2
1
1
0
1
2
0
0
2
2
1
2
1
1
0
2
1
0
1
0
0
1
1
3
2
0
1
1
1
0
2
1
1
2
0
1
1
1
1
0
2
1
1
0
0
1
1
1
2
1
1
1
1
3
2
1
1
1
0
1
1
1
2
1
1
2
1
4
1
1
1
1
2
1
1
2
2
1
1
0
0
2
1
1
2
1
1
2
1
1
0
1
1
0
1
2
2
2
1
1
1
1
1
1
0
1
0
1
1
1
1
1
2
1
1
1
2
1
1
1
0
0
0
1
1
1
1
2
1
0
2
1
3
1
1
1
1
0
0
1
3
2
0
0
1
1
2
2
1
0
2
1
1
1
2
1
2
1
1
1
1
0
1
1
1
2
1
2
1
2
2
1
1
0
1
0
2
1
0
1
1
2
3
1
0
1
1
2
2
0
2
2
1
1
0
2
2
1
0
2
1
2
1
0
1
2
1
1
1
2
1
1
3
1
1
1
2
1
1
1
1
0
0
1
1
2
1
2
0
2
0
0
1
1
1
1
1
1
1
1
1
0
2
2
1
0
1
1
2
1
1
1
2
1
1
1
0
2
1
1
1
1
1
2
1
0
1
3
1
1
1
1
0
1
2
1
1
1
2
1
2
0
0
1
1
2
0
2
1
2
1
0
1
1
1
0
1
1
2
1
2
1
1
1
1
1
1
1
1
1
0
0
1
1
1
2
0
1
1
1
1
1
1
1
2
1
2
2
2
2
1
4
1
0
0
1
1
1
1
2
1
1
1
1
2
1
1
0
1
2
1
1
1
1
1
1
2
2
2
2
2
2
1
0
1
1
1
2
2
1
2
2
2
1
1
1
2
1
1
0
1
1
1
0
1
1
1
2
1
0
1
1
1
1
1
0
1
0
0
1
1
2
2
1
1
1
1
2
0
1
1
2
2
1
0
1
1
1
1
1
0
2
1
1
1
1
2
0
2
1
1
2
1
1
0
1
1
1
2
2
2
1
2
1
2
1
1
2
1
1
1
0
0
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
1
2
1
2
1
2
1
2
2
4
1
1
2
1
1
1
1
0
1
1
0
2
1
1
0
1
1
1
1
1
1
1
1
1
1
0
1
1
1
0
0
1
0
2
1
0
1
1
1
1
1
1
1
1
0
1
1
1
1
1
2
1
1
1
2
1
0
1
1
2
1
2
2
1
2
1
0
1
1
0
3
2
1
2
1
2
1
0
1
1
1
1
2
5
1
0
2
0
1
1
0
1
1
1
2
0
0
0
2
1
2
1
0
1
1
1
0
0
1
1
1
1
0
0
0
1
2
1
1
1
1
2
1
0
1
2
1
1
1
1
1
2
1
1
1
1
2
1
2
1
1
1
2
2
1
1
1
2
2
1
1
1
1
2
1
1
1
1
2
1
0
1
0
1
0
1
1
1
1
2
2
1
0
1
2
1
2
1
1
1
2
2
2
0
1
2
2
1
0
1
1
1
1
1
1
1
1
2
1
1
1
0
0
2
1
2
1
1
0
0
0
2
1
1
1
0
1
0
2
2
0
0
2
1
1
1
1
1
2
0
0
1
2
2
1
0
2
1
0
1
2
1
0
2
1
2
1
1
2
1
0
2
1
0
1
1
0
1
1
1
0
0
0
1
1
1
1
2
1
1
2
1
2
1
1
1
0
2
4
0
1
1
0
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
0
1
2
1
1
1
3
2
1
1
1
1
2
2
1
1
0
1
1
1
1
1
1
0
1
1
2
2
1
1
2
1
1
0
1
1
1
2
1
1
1
0
1
1
2
1
2
1
1
1
1
2
1
1
0
1
1
2
2
2
2
2
0
1
1
1
1
0
0
1
1
1
0
1
1
1
1
1
0
2
1
1
0
1
1
1
1
1
2
1
1
1
2
1
0
0
2
1
6
2
0
1
1
0
1
2
2
2
2
1
1
2
1
1
0
1
1
0
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
0
0
2
0
1
1
1
1
1
1
0
2
2
1
1
1
2
0
1
1
2
1
0
2
1
1
2
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
2
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
0
1
1
0
1
1
1
1
1
1
0
0
2
2
2
0
1
1
0
2
2
1
1
1
2
2
1
1
1
1
1
0
0
3
2
0
0
1
1
1
1
1
1
1
1
1
1
2
1
1
0
1
1
0
1
1
1
0
1
1
1
2
1
2
0
1
1
1
1
0
2
2
1
2
2
1
1
1
0
1
0
0
1
2
1
2
2
1
2
2
1
1
2
1
2
1
1
2
1
1
1
1
2
0
1
2
1
1
1
1
1
1
0
1
2
1
1
1
1
1
1
1
2
0
0
1
2
1
1
1
0
1
1
1
1
2
0
0
0
2
2
1
1
2
2
0
1
0
2
2
1
1
2
1
2
1
2
1
0
1
1
2
1
1
1
2
1
2
0
1
1
0
0
1
1
1
0
1
1
2
1
2
1
1
1
1
1
2
1
2
1
2
2
1
1
2
2
0
1
1
0
0
1
0
1
1
0
0
0
1
1
1
0
1
2
2
2
2
0
1
1
2
1
0
1
2
1
2
2
1
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
1
0
0
1
2
2
2
0
1
1
2
1
1
2
1
2
1
1
0
2
0
1
1
1
3
1
0
1
1
0
1
1
1
0
1
0
1
1
1
1
1
1
0
1
2
0
1
1
2
2
1
1
2
0
1
0
1
1
1
1
1
1
1
2
2
1
2
1
1
1
0
2
1
1
2
1
2
1
1
1
1
2
1
3
2
2
0
0
0
0
2
0
1
1
1
1
1
3
1
1
1
0
2
2
0
1
2
1
1
1
1
0
1
1
0
1
1
2
1
1
2
1
2
2
0
1
1
1
0
2
1
1
0
1
0
0
1
1
1
1
1
1
1
2
2
0
2
2
1
1
0
1
2
1
1
0
1
1
1
0
1
1
1
1
1
1
1
1
1
0
2
2
1
1
1
1
1
0
1
1
1
1
2
1
1
1
1
1
2
0
0
1
1
1
2
1
1
2
1
2
2
1
1
1
1
1
1
1
1
2
0
1
1
0
0
1
1
1
1
0
1
1
2
2
1
2
6
1
1
2
1
1
1
1
1
1
0
1
1
1
2
1
1
1
0
2
2
2
1
1
2
1
1
1
2
1
1
2
1
1
1
1
1
1
1
2
1
0
1
1
1
1
2
0
1
1
1
2
1
1
1
2
1
1
2
1
1
2
1
0
0
2
1
1
2
2
1
0
1
1
2
0
2
0
2
1
0
1
1
2
2
1
1
1
1
4
2
1
1
1
1
2
1
1
1
0
1
1
2
0
1
1
1
1
0
2
0
1
0
0
0
1
1
1
1
0
1
1
2
2
1
1
0
1
1
0
2
2
1
2
1
1
1
0
2
2
1
1
1
1
3
0
1
1
2
0
2
1
1
1
0
1
1
1
1
0
2
0
1
1
2
1
0
0
1
1
1
1
2
2
0
1
1
1
2
2
1
2
2
1
0
1
1
2
1
1
1
1
1
2
0
1
2
1
1
1
0
0
1
1
1
0
1
0
1
0
1
1
1
2
0
2
1
0
1
1
0
1
1
2
1
0
1
1
1
1
1
0
1
1
1
2
2
1
1
1
1
1
1
1
0
0
1
0
0
1
0
1
2
1
1
0
1
1
1
1
0
1
1
1
2
0
0
1
1
1
3
1
0
0
2
1
1
1
1
1
1
0
1
2
1
1
1
1
1
2
1
2
1
1
1
1
2
2
1
1
0
1
1
2
1
0
0
1
1
1
1
1
2
1
1
1
2
1
1
0
0
1
0
1
1
1
2
1
2
1
1
1
1
1
2
2
1
1
1
1
0
1
1
1
1
2
2
2
2
1
0
1
0
2
0
1
1
0
2
2
1
2
1
1
1
0
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
1
0
1
2
1
2
1
1
2
2
1
1
1
1
2
2
1
1
1
1
2
0
2
0
1
2
1
1
1
1
1
1
1
1
1
2
3
1
1
1
1
1
0
1
0
1
1
2
1
2
0
1
0
1
2
1
2
1
1
1
0
2
1
1
1
3
1
1
1
1
1
1
1
1
0
1
3
0
0
1
1
1
0
2
2
0
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
2
1
1
2
1
2
2
1
1
2
1
1
2
1
1
1
1
1
1
1
1
0
1
0
1
1
1
2
1
1
0
1
1
1
0
1
1
2
2
1
1
2
1
1
1
1
1
2
0
1
0
1
1
0
0
1
2
1
1
2
0
2
1
1
1
1
1
0
1
1
3
0
1
0
2
1
1
1
1
1
1
1
2
1
1
2
2
2
1
1
1
1
1
0
2
2
1
2
1
2
1
1
2
1
1
1
0
1
1
1
2
1
1
2
1
0
1
2
1
2
0
1
2
0
1
1
2
1
0
2
2
1
0
0
1
1
1
1
1
0
1
1
1
1
2
1
2
1
1
1
1
2
1
1
1
2
2
2
1
2
1
1
1
1
1
2
2
0
1
1
1
2
1
0
1
2
2
1
1
2
2
1
1
1
0
1
0
1
2
1
2
2
0
1
1
0
1
0
1
1
1
1
0
2
0
0
0
0
1
1
1
1
1
1
0
1
2
0
1
1
1
0
1
1
1
1
1
1
2
2
2
1
2
1
1
2
2
1
2
1
2
2
1
1
1
0
1
1
1
1
0
1
1
1
1
0
1
1
1
1
2
0
1
1
1
2
1
1
1
2
1
2
1
0
2
1
0
1
1
1
1
1
1
0
1
0
1
1
0
0
2
1
1
0
1
0
1
1
2
1
1
1
1
2
1
1
2
1
2
2
1
1
0
2
1
2
2
1
1
1
2
0
1
2
2
0
0
2
0
1
2
2
0
2
2
0
1
2
2
1
1
2
1
1
1
0
2
2
1
1
1
2
1
2
2
1
1
1
2
1
1
2
2
1
1
1
1
0
1
2
0
0
2
1
1
2
1
1
2
1
0
0
1
1
2
0
1
0
2
1
1
1
1
2
0
1
0
1
2
1
0
1
1
2
1
0
2
0
2
2
1
2
1
0
2
1
1
1
1
1
2
2
1
1
0
1
1
2
1
1
1
0
0
1
1
1
2
3
1
1
1
2
2
1
1
2
1
2
1
0
2
1
1
1
2
2
1
2
1
1
1
2
2
1
1
1
1
1
1
1
2
2
0
0
0
1
1
1
2
0
1
2
1
2
1
2
1
1
1
1
0
1
2
1
1
1
1
2
1
1
1
1
0
1
1
1
0
1
2
2
1
1
0
2
2
1
1
2
1
1
1
1
2
1
0
1
1
2
0
2
2
2
0
0
1
0
1
1
1
1
2
1
1
1
0
1
1
0
1
1
2
1
1
1
1
2
1
1
2
2
1
1
1
0
1
1
1
2
0
1
3
1
2
1
2
1
0
2
2
1
1
2
1
0
1
2
0
1
0
1
2
1
1
1
1
0
1
1
2
2
2
1
2
2
1
1
1
2
3
2
2
2
1
0
1
1
0
1
1
2
1
1
1
0
1
2
0
1
1
2
3
1
1
0
2
0
2
1
1
0
1
0
1
1
2
1
1
0
2
1
2
2
1
1
1
0
1
1
0
1
0
2
2
1
1
1
2
1
1
0
1
1
1
2
1
1
1
2
1
1
0
1
1
0
1
2
1
2
1
0
2
1
1
1
1
1
1
1
2
1
2
1
2
1
1
1
1
1
2
1
1
1
1
0
1
1
1
1
1
0
1
1
1
1
2
2
1
1
1
1
0
1
2
1
1
1
1
1
1
0
1
1
1
2
2
1
1
1
1
1
1
2
2
2
1
1
1
0
1
1
0
1
1
0
1
0
1
1
3
1
2
0
1
1
1
1
2
0
2
1
1
2
0
0
0
2
1
2
0
0
0
1
2
0
1
1
1
1
1
0
1
2
2
1
1
0
0
2
0
1
1
1
2
1
1
0
1
1
0
1
1
1
2
2
0
1
1
1
1
2
1
0
2
1
1
0
1
2
2
0
2
1
1
0
0
0
1
0
1
2
0
1
1
1
0
1
1
0
1
1
2
0
1
1
2
1
2
1
2
0
0
2
1
1
1
2
1
0
1
1
1
0
1
1
1
1
2
2
1
0
2
1
1
1
2
1
2
1
1
1
2
2
1
0
1
0
1
2
1
1
1
1
0
1
1
1
0
0
1
1
0
1
1
1
1
2
1
1
2
0
1
1
1
0
1
1
1
2
1
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
2
2
2
2
1
1
2
0
2
1
1
1
0
1
1
2
1
0
2
2
2
1
1
0
1
1
2
2
1
1
1
0
1
1
2
1
0
1
2
2
1
1
1
1
1
2
3
1
1
2
2
2
1
2
2
1
1
0
2
0
2
2
2
2
1
1
1
2
0
1
1
0
1
1
1
0
1
1
1
0
0
2
1
1
2
2
1
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
2
1
1
5
0
0
1
1
2
1
1
2
1
1
1
0
1
3
1
2
1
2
0
1
2
1
1
1
0
1
1
1
2
0
1
1
1
0
1
1
1
2
1
1
1
1
0
1
1
2
0
0
1
0
0
0
1
2
1
0
1
1
0
1
1
1
1
1
1
1
0
1
2
1
1
2
1
1
0
1
0
0
1
1
0
1
1
2
2
1
2
0
1
1
0
1
1
2
0
1
1
1
1
2
0
0
2
1
1
2
1
0
1
1
0
2
0
1
2
2
0
2
2
1
1
2
1
0
1
2
1
1
0
2
0
1
1
2
1
1
1
1
1
2
0
1
2
1
2
1
1
2
1
1
2
1
1
2
2
0
0
2
1
1
1
2
1
2
1
2
1
1
1
1
2
1
1
0
1
1
0
1
1
1
2
1
1
0
0
0
1
1
2
0
1
1
1
2
1
1
0
1
1
1
0
2
0
1
0
1
1
1
1
0
1
1
1
2
1
1
2
0
1
1
1
2
1
1
2
1
1
1
1
2
1
0
0
1
0
1
1
1
1
1
2
1
1
1
1
1
1
2
0
2
1
1
0
3
1
2
1
1
1
1
0
0
2
1
0
2
0
2
1
2
1
1
2
2
1
1
1
1
1
2
0
1
4
1
1
1
1
1
1
0
1
0
1
0
2
0
1
1
2
2
0
0
2
1
0
0
0
1
1
2
1
1
0
1
1
1
1
1
1
1
1
1
1
1
2
0
1
1
0
2
1
2
1
2
1
1
1
2
2
1
0
1
1
1
2
2
1
0
1
0
1
1
2
1
1
1
1
1
1
0
0
0
1
1
1
0
1
1
2
2
2
2
0
1
1
0
1
0
2
3
1
0
2
1
1
1
1
1
2
2
1
1
1
1
1
1
0
0
2
1
1
1
2
1
1
0
0
0
0
1
0
2
2
1
1
1
1
1
1
1
1
3
2
2
1
0
1
1
1
2
2
1
1
1
2
3
2
2
1
1
1
1
1
1
2
2
0
1
1
0
1
2
0
1
0
0
0
0
2
2
2
2
2
2
1
1
1
1
1
2
2
2
1
1
0
0
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
2
0
0
1
1
1
2
2
1
1
1
2
0
1
1
1
1
1
1
2
2
1
1
1
2
0
2
1
0
2
1
1
1
1
0
1
1
2
1
2
1
2
2
1
0
3
1
1
2
1
0
1
0
1
2
2
1
2
2
2
1
1
1
1
2
2
2
0
0
1
0
1
2
1
2
2
1
2
0
1
2
1
1
2
1
2
1
1
1
2
1
0
1
1
0
2
1
0
2
2
0
2
0
0
0
2
0
1
2
0
1
2
1
1
2
0
1
1
1
1
4
1
1
1
0
1
0
1
0
1
0
2
2
1
1
1
0
1
1
1
0
1
1
1
2
0
1
0
1
1
1
0
2
0
1
2
2
1
2
0
2
0
1
2
1
1
2
2
1
1
1
2
1
1
2
1
1
1
2
1
0
1
1
0
1
1
2
1
1
1
2
1
2
1
1
2
1
1
2
1
1
1
1
1
1
1
2
0
2
2
2
2
2
2
1
1
2
2
2
2
2
1
2
1
2
1
2
0
0
1
1
1
1
0
1
1
0
1
2
1
1
1
2
1
2
1
2
1
1
1
2
1
0
1
2
2
0
1
1
0
0
2
2
1
1
1
0
2
1
1
1
1
0
1
0
1
2
0
1
0
1
1
1
1
0
2
0
0
0
1
1
1
0
1
2
1
1
1
1
1
2
1
1
1
0
1
1
0
1
1
2
2
2
1
1
1
2
1
0
1
1
2
1
1
1
2
1
1
1
1
1
0
1
1
1
1
2
1
2
1
2
1
1
1
1
1
2
1
2
2
2
2
1
1
2
3
2
1
1
1
1
2
1
1
1
1
1
1
1
1
3
0
2
2
1
1
2
1
0
3
1
1
0
1
2
1
2
2
0
1
1
0
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
0
1
1
1
2
1
1
2
1
1
2
1
1
1
1
2
1
0
2
1
2
1
2
1
1
1
1
1
1
1
1
1
2
2
1
1
1
2
1
1
1
1
1
0
1
1
2
0
1
0
1
1
2
2
2
0
1
1
1
1
1
2
3
2
2
2
0
1
2
1
1
1
1
1
2
2
0
1
3
2
1
1
2
1
1
1
1
1
1
2
1
2
0
1
2
1
2
1
0
1
1
1
1
1
1
0
2
2
1
1
1
0
2
1
1
1
1
2
1
0
1
1
0
0
1
1
1
2
1
0
1
1
2
0
2
1
1
2
1
1
2
1
1
2
2
2
1
3
2
1
1
1
1
2
1
2
0
1
1
0
1
1
1
1
1
2
2
1
1
0
1
0
1
2
1
2
1
1
1
1
1
0
0
2
1
1
1
2
2
1
1
0
2
1
0
1
1
0
1
1
2
1
1
2
1
1
1
1
1
1
2
2
2
1
1
0
0
2
1
1
2
1
0
2
0
1
1
1
2
0
1
1
2
1
1
1
0
2
1
1
1
1
0
1
1
1
1
0
2
1
1
1
1
0
0
1
1
1
1
1
1
1
1
0
2
1
0
1
2
1
1
1
1
2
2
1
2
3
0
1
1
1
0
2
0
1
1
2
2
1
1
1
1
1
1
0
1
2
2
2
0
1
1
2
1
1
2
2
1
1
2
2
1
2
2
1
1
1
0
1
1
1
1
0
1
1
1
2
10
1
1
0
1
1
1
2
1
1
2
1
1
1
0
1
0
2
0
1
1
0
1
1
1
1
1
2
0
1
0
0
0
1
1
1
1
0
3
1
0
1
2
1
1
1
0
1
0
2
1
1
1
1
1
0
1
2
2
1
1
1
1
1
1
0
1
2
1
0
1
1
1
1
1
2
0
0
2
1
1
1
1
2
1
1
0
1
0
1
0
1
2
2
1
1
1
1
2
1
2
1
0
2
1
0
2
1
0
0
1
1
1
2
0
1
2
1
1
1
1
1
1
2
0
1
1
1
1
1
1
0
2
1
2
2
1
0
1
2
1
0
1
1
1
1
1
1
1
2
2
1
1
2
2
1
0
0
1
1
1
2
2
0
0
1
1
2
1
2
1
1
1
2
1
2
1
2
1
1
1
1
1
1
1
1
2
1
1
0
0
2
1
0
1
2
2
2
2
1
1
2
1
2
1
1
1
1
2
1
0
2
3
3
1
0
1
1
1
1
1
1
0
1
1
0
1
2
2
2
1
1
1
2
1
0
1
0
2
1
0
1
2
1
1
1
1
1
1
0
1
1
1
1
1
1
1
0
1
1
1
3
0
1
1
0
1
1
1
1
1
1
1
1
1
1
2
2
0
1
1
1
1
1
2
2
2
2
1
2
1
1
2
0
1
1
1
1
0
2
2
2
2
2
2
1
1
0
1
1
1
1
1
2
1
1
1
0
0
1
1
0
2
2
1
1
0
0
1
0
2
1
1
1
1
1
0
2
0
0
2
1
1
1
1
1
1
0
1
1
0
2
0
1
1
1
2
1
0
2
1
2
0
0
1
0
1
1
2
1
2
2
1
0
1
1
1
2
2
1
0
1
1
0
3
1
0
1
1
2
1
2
1
0
1
0
1
1
1
1
2
1
1
0
2
1
1
2
2
1
2
1
1
3
1
1
1
1
0
1
2
1
1
2
1
1
1
1
2
0
1
2
1
2
0
1
1
1
0
1
0
0
0
0
2
1
1
1
0
2
1
2
1
1
2
0
1
2
9
1
1
0
0
4
1
1
1
1
1
1
0
0
1
1
0
1
2
1
2
0
2
1
1
1
2
1
1
1
1
1
1
2
2
1
1
2
2
1
1
1
1
2
1
0
1
1
1
1
1
1
1
1
1
2
1
2
2
2
1
1
2
1
1
2
1
1
1
2
1
0
2
0
2
1
0
0
1
1
2
1
1
0
2
2
0
1
1
2
1
5
1
1
1
1
2
1
2
2
1
2
1
2
2
1
1
1
1
1
2
1
2
1
0
0
2
3
1
1
2
1
1
1
1
0
1
0
1
0
1
1
0
2
0
1
1
1
1
1
0
2
1
1
0
1
1
1
1
1
2
1
1
1
0
1
1
2
0
1
0
0
1
2
2
0
2
0
0
3
0
1
1
1
2
1
1
1
1
0
0
1
1
2
0
1
1
1
1
1
1
2
0
0
0
0
1
0
1
2
1
2
2
1
2
1
2
1
1
1
1
1
1
1
0
1
0
1
2
0
1
3
1
2
1
1
1
1
0
2
0
1
0
1
2
0
1
2
1
2
2
0
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
0
1
1
1
1
1
2
1
1
2
0
1
0
1
2
1
0
2
1
1
0
2
2
1
1
1
0
1
0
1
1
0
2
0
1
0
2
1
0
1
2
3
0
2
2
1
0
1
1
1
3
1
1
1
1
1
1
1
0
1
2
1
1
2
2
1
1
1
0
1
2
2
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
0
0
1
0
1
1
2
1
0
1
1
0
1
1
2
1
2
1
1
1
0
1
1
1
2
4
1
2
1
1
0
0
2
2
1
2
1
1
1
1
1
1
0
1
1
1
0
3
1
0
1
0
2
1
2
2
2
2
2
2
1
2
1
1
2
1
0
1
0
1
1
1
1
1
1
1
1
1
0
1
1
1
2
2
1
1
1
1
2
1
1
0
1
1
0
2
1
2
1
1
2
1
0
1
1
0
0
2
1
1
0
2
2
2
2
1
2
1
1
1
2
0
1
2
1
0
0
1
2
1
1
2
2
0
1
0
2
1
1
1
1
0
3
0
2
1
1
1
1
1
1
1
0
1
1
0
1
2
2
1
0
1
0
0
1
1
1
0
1
1
0
0
1
1
0
1
1
1
0
2
2
0
1
0
0
0
2
1
0
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
0
1
1
2
0
1
1
1
1
0
1
2
1
0
0
1
1
1
1
1
2
2
1
2
1
1
0
2
0
2
1
1
2
1
1
1
1
1
2
3
1
1
1
1
1
2
0
0
2
1
1
0
0
1
1
1
1
2
1
1
1
0
1
2
0
1
0
2
1
1
2
1
1
1
0
1
0
2
1
0
1
2
2
0
1
2
1
0
1
1
1
1
2
1
1
2
1
2
1
1
1
2
2
2
1
1
1
2
0
2
1
1
1
2
1
1
0
1
1
1
1
1
1
1
1
0
2
1
1
2
0
2
1
1
1
1
1
2
1
2
0
1
1
2
4
0
1
1
0
1
1
1
1
1
2
2
0
1
1
1
1
1
1
1
1
1
0
2
1
2
0
1
0
2
1
2
1
1
1
1
1
0
0
1
1
1
0
1
1
2
0
0
1
0
1
2
1
1
1
1
0
2
0
0
1
2
1
1
1
1
2
1
1
2
1
0
2
2
2
1
1
0
1
2
1
1
1
2
0
0
2
0
1
1
2
0
0
1
2
0
2
1
1
0
1
1
1
1
2
0
2
1
1
1
1
0
1
1
1
2
0
2
1
1
1
0
1
2
0
2
1
2
2
2
2
0
1
1
1
0
1
1
1
1
1
1
2
0
2
1
0
1
1
1
1
2
1
2
2
2
1
0
2
1
1
0
2
2
0
1
3
1
1
2
1
1
1
2
1
1
1
0
0
2
1
1
2
0
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
4
1
2
1
1
1
0
0
1
2
0
0
1
1
2
1
1
2
1
0
1
0
1
0
1
0
1
1
0
1
1
1
1
2
1
0
1
1
2
0
0
2
1
1
0
2
2
2
1
1
1
1
0
0
2
2
0
0
2
1
1
2
1
1
2
1
1
1
1
0
1
1
1
1
1
1
2
1
2
0
1
1
2
1
1
2
1
1
1
2
0
1
1
1
1
1
0
1
1
1
2
0
0
1
1
2
0
0
0
1
1
1
1
2
1
1
1
1
1
0
2
2
1
2
2
0
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
0
1
0
1
1
1
1
1
0
0
1
2
1
2
1
0
0
1
1
0
1
1
2
0
0
1
0
3
2
0
2
1
3
0
0
2
0
2
1
1
0
1
2
1
2
0
1
2
2
1
0
1
0
1
0
1
1
2
1
2
2
2
1
2
1
1
0
1
1
1
1
1
0
2
1
1
1
1
1
2
1
2
1
1
2
1
1
1
0
1
1
2
1
0
0
0
1
1
1
1
1
2
0
1
1
2
2
1
2
2
0
1
1
1
1
2
1
2
0
2
0
1
1
0
0
1
0
2
1
1
1
1
1
0
1
1
2
1
1
2
1
2
1
0
2
2
4
1
1
2
0
1
1
0
2
1
0
1
1
0
1
1
1
2
2
0
1
2
1
2
0
0
1
2
1
1
0
1
1
0
1
2
0
1
1
0
2
1
1
1
1
0
1
1
2
1
1
2
1
1
1
0
0
1
1
0
1
2
1
0
1
1
2
1
1
1
1
2
2
1
1
0
1
1
1
1
1
1
1
1
1
0
0
2
1
1
1
1
1
1
0
1
2
1
1
0
2
1
1
1
1
2
1
2
1
2
1
1
0
1
0
1
1
2
1
0
2
1
0
1
0
1
1
2
1
1
1
0
3
2
2
1
0
1
0
1
2
2
2
1
1
1
2
1
1
1
2
1
1
1
1
1
0
1
1
1
1
1
1
1
1
0
2
0
0
2
2
1
2
1
2
2
1
2
1
0
0
1
2
2
0
1
1
1
0
1
1
1
0
1
1
1
2
0
0
1
2
1
1
0
2
1
2
1
1
0
0
2
1
1
1
0
2
1
1
1
2
1
0
1
1
0
1
1
1
0
1
1
0
1
1
2
1
1
1
1
1
2
1
1
1
2
1
2
0
2
1
1
2
1
1
2
1
1
0
1
0
2
1
1
1
2
0
2
1
0
1
1
1
2
1
1
2
0
0
1
1
2
1
1
1
0
1
1
2
2
1
1
2
2
1
1
0
2
1
1
1
1
0
2
0
0
1
0
2
1
1
2
1
0
0
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
2
1
2
1
2
2
0
1
3
1
2
1
0
2
0
2
1
1
1
1
2
2
1
1
0
2
1
1
1
1
1
1
2
1
1
0
1
1
1
2
1
1
2
1
2
1
1
1
2
1
1
2
0
1
2
1
1
2
1
1
1
2
0
1
2
1
2
0
1
2
2
1
1
1
1
1
1
2
0
1
2
1
1
1
1
0
1
2
1
0
1
1
1
2
1
1
1
0
2
0
1
1
1
1
1
1
1
1
2
1
2
1
0
2
0
1
1
2
1
2
1
1
0
0
1
1
0
2
2
1
1
1
0
2
1
2
1
2
0
1
1
1
1
1
1
0
1
1
2
1
0
1
1
1
2
1
2
1
1
1
1
2
1
1
2
2
1
1
1
2
0
1
0
1
0
1
2
2
1
1
2
1
0
2
1
0
1
1
0
2
1
1
0
1
1
0
1
1
2
0
1
1
1
2
1
1
1
2
1
1
2
1
1
1
0
2
0
1
1
1
0
2
2
1
2
2
2
1
2
2
2
1
1
1
1
1
1
1
1
1
0
1
1
2
1
1
1
2
1
1
1
1
0
2
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
0
2
1
2
1
2
1
1
0
2
1
1
0
1
2
1
1
1
1
1
1
2
1
0
1
0
1
1
0
1
2
2
1
1
1
1
1
1
1
1
2
1
0
2
1
1
1
2
0
1
2
2
1
1
2
1
1
1
1
2
2
1
1
1
2
1
2
2
1
1
2
1
1
1
0
1
1
1
0
1
1
1
1
1
1
0
1
1
2
2
1
0
0
0
1
1
0
0
2
0
2
1
1
2
0
1
1
1
1
1
1
0
1
1
1
1
0
2
1
1
1
2
1
1
2
2
2
0
1
0
1
1
2
1
2
1
1
1
2
2
0
1
0
1
2
2
0
1
1
1
1
1
2
0
1
1
2
1
0
2
0
1
1
1
1
2
1
1
1
2
1
0
1
0
0
1
0
1
1
1
1
1
2
1
1
0
1
2
1
1
1
1
2
1
1
1
0
1
1
1
1
1
1
0
1
1
1
2
0
2
2
1
2
1
0
2
1
1
1
1
1
1
1
2
0
2
1
1
2
2
1
1
2
2
2
2
2
1
1
0
0
1
1
0
1
1
1
2
2
1
1
1
0
1
2
2
0
2
2
1
0
0
2
1
0
1
1
1
1
1
1
2
2
1
1
1
1
1
0
2
0
1
0
0
2
1
1
0
0
1
2
1
1
1
1
1
1
1
1
1
2
2
1
1
2
2
1
0
1
1
2
2
1
1
1
1
1
2
1
2
1
1
0
1
1
1
1
2
2
0
2
1
1
1
0
0
1
0
0
0
1
0
0
0
2
2
0
1
1
0
1
2
2
0
1
1
2
1
0
0
2
1
2
1
0
1
1
2
1
2
2
2
1
0
1
1
1
1
2
2
1
1
1
0
2
0
1
1
1
1
2
1
1
2
1
1
1
2
2
1
1
1
0
0
1
1
0
1
0
0
0
1
1
1
2
2
1
2
1
1
1
0
1
2
1
1
2
1
0
2
2
0
1
1
1
2
1
1
0
0
1
1
1
2
0
1
2
0
2
1
2
2
1
1
2
1
1
1
0
2
1
2
1
1
2
1
1
1
2
1
2
2
1
1
1
1
2
1
1
1
0
0
1
1
2
1
1
2
0
2
0
0
0
2
1
1
2
0
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
2
1
1
1
1
1
2
2
1
2
2
0
2
1
2
1
1
2
1
1
0
1
1
1
2
1
1
2
1
2
1
0
0
0
1
0
1
2
0
1
0
2
1
2
1
1
1
2
1
0
1
1
2
1
4
1
2
1
1
1
2
1
2
1
2
2
0
1
1
2
0
1
1
0
0
1
2
1
1
1
0
1
0
1
1
4
1
1
0
2
0
1
1
0
1
1
1
1
1
1
1
1
2
2
1
2
0
1
2
1
0
1
1
2
3
0
1
0
1
1
0
2
1
1
2
1
0
2
2
1
2
2
1
1
1
1
1
0
0
0
2
1
1
1
0
1
1
1
1
1
1
1
0
1
1
1
1
0
2
0
1
2
1
1
2
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
2
0
0
2
1
1
1
2
1
1
1
2
1
2
1
1
2
1
1
2
0
2
2
2
2
0
2
1
1
2
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
2
1
2
0
0
1
1
1
1
1
2
2
0
1
0
1
0
1
1
0
2
2
1
2
2
1
1
1
1
1
1
2
3
2
1
1
0
1
2
0
1
2
1
1
1
0
2
2
0
1
2
1
1
2
1
2
1
1
2
1
1
1
1
2
2
1
2
1
0
1
1
2
1
0
1
1
1
1
1
1
1
1
1
1
1
2
1
0
1
2
0
2
0
2
1
0
2
1
2
1
1
2
1
1
1
1
2
0
1
2
1
2
1
0
2
1
0
1
1
1
2
0
1
1
0
0
1
0
1
1
2
1
1
1
1
1
2
2
1
0
1
2
2
2
1
1
1
1
2
1
1
1
2
1
1
2
1
2
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
0
1
2
2
1
1
1
1
1
1
2
1
2
1
1
1
2
2
1
0
0
2
1
2
1
0
1
1
1
1
1
1
0
2
1
1
1
2
1
1
0
0
1
1
0
1
1
2
1
1
2
1
1
1
0
3
1
0
1
2
0
3
1
2
1
1
1
1
2
1
0
3
1
2
2
1
1
0
1
1
2
1
1
1
0
1
1
2
1
2
1
1
0
0
2
0
1
1
0
1
1
0
1
0
1
1
2
1
1
2
1
2
2
1
1
0
0
0
0
1
1
1
0
2
0
1
2
1
2
0
1
1
1
1
0
1
1
2
1
1
2
1
1
0
0
1
2
0
1
1
2
0
2
1
1
2
2
1
1
1
2
2
1
2
1
0
2
1
1
1
1
1
0
1
1
2
2
1
2
2
1
2
1
0
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
2
1
2
1
1
1
1
0
1
1
2
1
1
0
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
2
2
1
1
0
1
1
2
1
1
2
2
1
1
1
0
0
2
1
1
0
1
1
0
2
2
1
2
2
0
1
1
1
1
2
1
1
2
1
1
0
1
1
1
1
0
1
1
1
2
1
1
1
1
0
2
1
1
0
2
1
1
1
2
1
1
0
1
2
1
0
1
1
2
2
1
0
2
1
1
2
1
0
1
1
2
1
1
2
2
1
1
1
1
1
1
1
0
1
1
0
1
2
0
1
2
1
2
0
2
1
1
2
1
1
1
0
0
1
1
0
0
1
1
1
1
1
1
1
1
2
1
0
1
2
0
2
2
1
2
1
1
1
0
0
1
1
0
0
1
1
1
0
1
1
2
1
2
2
6
0
1
1
1
2
1
0
2
1
1
1
1
0
2
1
1
0
0
1
1
1
1
1
1
1
1
1
1
2
1
1
0
1
1
0
2
2
3
1
0
1
1
2
0
0
1
1
0
1
1
0
2
1
1
0
0
1
1
1
2
1
1
1
1
2
1
0
1
0
1
1
2
1
2
1
1
1
1
0
1
1
1
1
1
1
0
1
0
2
1
0
1
2
1
1
1
2
1
1
1
2
0
2
2
0
0
0
2
1
1
1
1
1
1
1
2
3
2
1
1
1
0
2
1
3
1
2
1
1
1
1
1
1
1
2
0
0
1
1
1
2
1
1
0
2
0
1
1
1
1
1
2
1
1
0
1
0
1
0
2
1
1
1
1
2
1
1
2
2
0
1
0
1
0
0
1
1
1
1
1
2
1
1
1
3
1
2
2
1
1
1
1
3
0
1
1
2
2
0
2
1
2
1
0
0
2
1
0
1
1
1
2
1
2
1
0
1
0
1
1
1
2
1
1
1
0
0
1
1
1
1
2
1
1
1
1
1
1
2
1
1
2
0
1
1
1
1
1
2
1
2
0
0
1
2
1
1
0
2
1
0
1
1
2
2
1
0
1
2
0
1
1
0
0
2
1
1
1
1
0
0
0
1
2
1
0
2
0
1
2
1
0
0
1
2
1
1
1
1
1
1
0
1
0
1
1
2
1
1
0
1
1
1
1
1
2
1
1
0
0
1
2
0
1
1
1
1
1
0
1
0
1
1
2
2
2
0
1
2
0
1
0
1
2
1
0
1
2
0
2
1
1
0
1
1
2
0
1
1
1
1
2
1
1
1
1
1
1
0
1
0
2
2
1
2
2
2
1
1
2
1
1
0
0
0
0
1
1
1
1
1
2
1
0
1
1
2
1
1
1
1
1
0
1
1
1
1
1
1
1
2
1
0
2
1
0
1
1
1
1
1
2
1
1
0
2
1
2
1
2
0
1
1
1
0
1
1
1
2
1
0
1
1
1
1
2
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
2
1
0
2
1
2
1
2
1
0
2
1
1
3
1
1
0
2
1
2
1
1
1
2
0
1
2
2
0
1
2
1
0
1
0
1
2
1
1
2
2
0
1
1
0
1
1
0
1
1
0
1
1
2
1
2
1
1
1
2
2
1
0
1
2
1
1
1
1
1
1
1
0
0
1
1
2
2
1
2
2
1
2
1
1
1
0
1
2
1
1
0
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
0
1
2
2
1
1
1
0
1
1
2
0
1
2
1
1
1
1
1
0
2
1
1
1
1
1
1
2
2
0
2
2
1
0
1
1
2
1
1
1
2
1
1
1
1
1
2
1
1
1
0
1
1
0
2
0
1
1
1
1
0
0
1
1
2
1
1
1
1
1
1
1
1
1
2
0
1
0
1
1
1
1
1
2
1
1
1
1
2
0
1
1
2
1
1
1
1
1
2
2
1
2
1
1
0
2
4
1
1
1
0
1
1
2
2
1
1
1
1
2
1
1
1
1
0
0
1
1
1
2
2
1
1
1
1
0
0
0
2
0
0
2
2
1
1
1
1
1
2
1
0
1
1
1
1
0
1
2
0
1
1
1
0
1
0
0
1
1
1
1
1
1
0
0
1
2
1
2
1
0
1
1
2
1
2
0
0
1
1
2
1
2
0
1
2
1
2
1
1
1
1
1
0
3
1
1
1
0
2
2
1
0
1
0
1
1
2
1
1
0
2
0
2
1
0
2
1
0
2
1
1
1
2
1
1
1
1
0
1
1
2
2
1
1
2
1
1
1
1
1
1
2
1
1
2
2
1
0
1
1
0
1
1
1
1
1
1
1
1
1
2
2
1
2
0
1
1
0
1
1
1
1
1
0
1
1
2
1
2
1
0
2
1
1
1
1
2
2
1
1
0
2
1
1
0
0
2
1
1
2
1
2
1
1
1
1
1
0
2
1
2
1
2
0
0
1
1
2
2
2
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
2
2
1
1
1
2
1
1
1
0
1
1
1
1
1
1
1
2
0
1
1
2
1
2
0
2
4
1
1
2
1
1
1
0
1
1
0
1
1
0
1
2
1
0
2
2
1
1
1
2
1
2
1
0
1
1
1
1
1
0
1
1
1
2
2
0
1
2
1
1
1
2
1
1
1
2
1
1
1
1
1
2
1
1
0
1
0
0
0
1
2
1
1
1
0
1
2
1
2
2
1
3
1
1
0
1
0
2
1
2
1
1
1
1
1
2
1
1
0
1
1
2
1
1
1
1
1
0
1
0
1
1
0
0
2
2
1
1
0
2
0
0
2
0
2
2
2
1
2
1
1
1
0
1
0
1
1
2
0
1
0
0
1
1
1
1
2
0
1
1
1
1
1
0
1
2
1
1
1
1
0
1
1
0
1
2
1
0
1
0
1
1
2
2
1
1
0
0
0
1
1
1
2
1
1
2
0
1
0
1
2
2
1
1
1
1
2
2
0
1
2
1
1
1
1
3
0
1
0
2
1
2
1
1
1
1
0
1
2
1
1
1
2
2
0
0
1
1
0
1
1
0
1
0
1
1
1
2
1
1
2
1
1
1
2
1
1
2
1
1
1
1
0
1
1
1
0
0
2
1
1
1
0
0
0
1
1
1
2
1
1
1
2
2
2
2
2
1
1
2
1
0
2
1
0
2
0
1
2
2
2
0
2
1
0
1
2
2
1
0
2
0
1
1
2
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
2
0
2
2
1
2
1
1
0
1
1
1
2
0
1
2
1
1
1
1
1
1
1
1
1
1
1
0
1
0
1
1
1
2
1
1
2
1
1
2
1
2
0
0
1
0
0
1
1
1
1
1
1
1
0
0
0
2
3
0
1
1
2
1
1
0
2
1
1
1
1
1
2
0
1
2
1
1
1
2
1
2
1
2
2
1
1
2
1
2
1
2
2
2
1
1
2
2
0
1
2
1
1
0
1
1
1
0
1
0
2
2
1
1
1
1
1
2
0
1
1
2
0
1
1
1
2
1
0
4
1
1
2
1
0
0
1
1
1
0
1
1
1
1
2
0
2
0
1
2
3
1
1
1
1
1
1
1
2
1
0
1
1
0
1
0
1
1
2
1
2
1
3
2
0
1
1
2
2
2
0
1
1
1
1
1
0
2
1
1
2
2
1
1
1
1
1
2
0
1
2
1
1
1
0
1
1
1
1
2
1
1
1
1
0
2
1
0
1
1
1
1
1
1
2
1
1
1
1
1
1
1
0
0
1
1
2
1
1
0
0
1
1
1
2
2
0
1
1
1
1
2
1
1
1
2
1
0
1
1
1
2
2
2
1
1
2
0
0
0
1
1
2
2
2
1
1
1
1
1
1
1
0
2
1
1
0
1
0
2
2
1
0
0
1
2
2
2
1
3
2
0
0
1
1
1
1
1
1
1
1
1
2
1
1
0
0
2
1
0
1
0
0
0
0
2
1
1
1
1
2
2
1
1
0
2
1
1
0
1
1
0
2
0
1
2
1
2
1
1
1
1
0
1
0
0
0
1
2
1
1
1
2
0
2
1
1
1
2
1
1
2
1
1
0
0
1
2
1
1
1
2
1
0
1
0
0
2
4
1
2
1
0
0
1
0
1
1
2
0
1
2
1
0
2
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
0
2
1
1
1
2
1
1
2
2
4
1
1
1
0
1
1
0
2
0
0
1
1
1
2
1
1
2
1
1
1
2
2
1
2
1
0
0
1
2
1
2
1
1
1
2
1
1
1
1
1
1
1
1
0
1
1
1
1
1
0
1
1
0
2
1
1
1
1
3
1
1
1
1
1
1
1
1
2
0
1
0
1
1
1
1
2
2
1
0
1
1
1
1
0
2
1
2
1
0
1
1
1
2
1
0
2
1
1
0
2
2
1
1
1
1
2
1
2
1
1
1
1
0
0
1
1
0
0
1
1
2
1
2
1
1
2
2
0
0
0
1
1
1
1
1
1
2
1
0
0
2
1
0
0
1
1
2
1
0
1
1
0
1
1
1
0
0
1
2
1
1
1
1
1
0
1
1
1
1
1
1
0
1
2
0
1
2
2
2
1
1
1
2
0
1
0
0
1
0
1
1
1
1
1
0
0
2
2
2
0
1
1
2
2
1
1
2
1
2
1
0
0
1
2
2
1
1
2
1
1
2
2
1
2
2
1
1
1
1
1
1
0
1
1
1
2
1
1
2
1
2
1
2
2
1
1
1
1
2
2
2
1
1
0
1
1
1
0
0
0
2
1
1
2
4
1
2
1
1
1
1
0
2
2
2
2
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
0
1
1
2
1
2
2
1
2
1
1
1
1
1
1
1
0
1
2
1
1
1
2
1
1
1
0
2
1
1
1
2
2
1
2
1
1
1
1
2
0
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
2
1
3
1
0
0
1
1
1
0
1
1
1
2
0
0
0
1
1
1
0
0
1
1
0
1
2
1
1
0
0
2
0
1
1
1
0
2
2
1
0
1
0
1
1
0
1
1
1
1
2
1
1
2
1
1
2
1
2
0
2
1
1
1
0
0
1
1
2
1
2
1
1
1
1
1
1
0
2
0
2
1
1
2
0
2
1
1
2
3
1
1
1
1
1
0
2
0
2
2
2
1
2
0
1
2
2
1
2
2
1
1
1
0
1
0
2
1
1
1
2
1
0
1
1
2
2
1
0
1
1
1
1
1
2
1
1
1
2
1
2
0
2
1
2
2
0
1
0
1
1
0
0
2
1
1
1
1
0
2
1
0
0
1
6
1
1
1
0
0
1
0
0
1
1
1
1
1
1
1
1
1
2
0
2
2
1
1
2
0
2
0
1
0
1
1
2
1
1
0
0
1
1
1
0
1
1
1
0
1
0
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
0
1
0
1
1
2
2
2
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
1
0
0
0
1
0
0
1
1
2
1
2
1
2
0
1
1
1
1
1
1
1
1
0
2
2
1
2
1
0
1
2
2
0
1
1
1
1
1
1
2
0
1
1
1
1
1
1
1
1
1
1
1
1
2
1
0
1
0
1
1
0
1
2
0
1
0
0
1
2
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
1
1
2
0
2
2
2
2
1
1
2
0
1
1
2
1
0
0
2
2
2
2
0
2
2
2
1
1
2
0
0
2
1
1
2
1
1
2
1
2
1
0
1
2
1
1
1
0
1
1
1
2
2
1
1
0
1
2
1
1
3
1
2
1
2
2
1
0
1
2
1
2
1
1
0
1
1
2
0
0
2
1
2
1
1
0
2
2
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
0
2
1
1
1
1
1
0
1
1
1
1
0
1
1
1
2
2
1
1
2
2
1
0
0
1
1
1
1
1
2
2
1
0
1
2
1
2
2
1
0
1
0
2
1
0
2
1
1
0
1
0
0
1
1
2
1
0
1
2
2
0
2
0
0
1
1
0
1
0
0
2
2
1
1
2
1
1
0
1
0
0
0
2
1
0
1
1
1
1
1
2
0
1
0
1
2
1
1
0
1
1
2
1
1
1
1
1
1
1
0
1
1
1
1
2
2
1
2
1
1
1
1
1
1
0
1
0
0
1
2
1
1
0
1
1
2
1
0
2
1
1
1
1
1
2
1
0
0
2
1
0
1
1
1
0
1
1
1
0
1
1
1
1
1
1
2
2
1
2
1
1
1
0
1
1
2
1
0
1
1
2
1
0
1
1
1
1
1
1
1
2
2
2
0
2
1
1
2
1
2
1
1
2
1
2
1
2
1
2
1
0
0
0
0
1
1
1
2
1
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
0
2
0
1
1
1
1
1
1
2
2
2
1
0
1
1
1
2
1
0
3
1
1
1
0
2
1
0
2
1
1
2
1
1
0
1
1
0
2
1
2
1
1
1
1
1
1
1
1
2
1
1
2
2
1
2
1
1
1
1
2
0
1
0
1
0
2
1
1
1
0
1
1
2
1
1
3
0
0
2
1
1
1
0
1
2
0
1
1
0
1
1
1
1
2
1
1
3
1
2
0
3
1
1
1
0
1
1
1
1
1
0
1
0
1
1
0
1
1
1
1
2
1
1
1
1
1
1
1
0
1
2
1
1
1
1
1
0
1
2
1
2
2
2
1
0
1
2
2
1
1
2
1
2
1
1
1
1
1
0
1
1
0
2
2
1
1
1
0
1
1
1
1
2
1
1
1
2
1
2
0
0
1
2
1
1
1
1
0
1
1
0
2
1
1
1
1
0
0
1
0
1
2
1
1
1
0
0
0
2
1
1
1
1
1
1
1
1
1
1
2
0
1
2
1
2
1
2
1
0
0
1
2
0
2
1
2
3
2
1
2
1
2
1
2
1
1
2
1
1
1
0
1
1
2
1
0
1
2
0
0
1
1
1
2
0
1
1
1
2
1
2
1
2
0
1
1
1
1
0
1
1
1
1
0
1
1
1
0
1
1
2
2
1
1
1
1
1
1
1
1
0
2
1
2
1
2
1
2
2
1
2
1
0
1
0
0
1
1
1
1
1
1
1
1
0
1
2
2
1
1
1
1
2
1
2
2
1
1
2
2
0
1
1
1
1
2
2
0
1
2
0
1
1
1
1
1
0
1
1
1
1
2
0
2
0
2
0
2
2
2
1
1
0
1
1
2
1
0
0
0
1
0
1
1
1
1
2
1
1
2
2
2
2
1
2
2
0
1
1
2
0
1
1
1
0
1
2
1
1
1
1
1
0
1
0
1
0
1
0
1
2
1
2
1
1
1
1
1
2
0
1
2
1
1
1
1
2
2
0
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
1
1
0
2
1
0
1
2
1
0
0
1
1
1
1
1
1
2
1
1
2
0
2
1
0
1
1
2
1
0
1
2
1
0
0
0
0
1
1
0
0
2
1
1
1
2
2
0
1
2
0
1
0
2
1
2
1
2
1
2
1
2
1
1
1
0
1
1
0
1
2
2
1
2
1
1
0
1
1
1
1
1
1
3
1
1
1
0
2
1
2
1
1
2
2
1
0
2
1
2
1
0
0
1
1
1
0
1
2
1
0
1
2
0
0
1
2
1
0
2
1
1
1
1
1
2
1
1
1
1
1
0
1
2
1
0
1
0
2
1
1
2
2
0
1
1
1
1
0
1
0
0
1
1
1
1
1
1
1
1
1
1
1
2
0
1
1
1
0
2
1
1
1
1
1
0
2
2
1
1
1
1
2
0
2
1
2
1
1
1
0
2
2
2
2
0
0
2
1
1
2
2
1
0
1
1
2
1
2
2
1
0
1
1
0
1
1
1
2
2
1
1
1
2
2
1
2
2
1
1
1
0
1
1
2
0
1
1
1
0
2
1
2
1
1
1
1
1
0
0
1
1
1
2
0
1
1
2
1
1
1
1
1
1
1
1
1
0
1
2
0
0
2
1
0
1
0
1
0
1
1
2
1
0
1
2
1
2
2
1
1
2
1
0
0
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
0
1
2
1
1
2
2
1
1
1
2
1
1
1
1
2
1
2
0
1
0
2
2
2
1
2
1
2
2
1
1
1
1
1
1
2
1
1
1
2
1
2
0
0
0
2
1
1
0
1
2
1
2
1
1
2
1
2
1
0
0
1
1
1
1
1
0
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
0
1
2
1
1
2
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
0
1
1
1
1
1
0
1
1
1
2
1
1
1
1
1
0
1
1
1
2
2
1
1
1
2
2
1
2
1
1
2
1
0
2
2
2
1
1
1
2
1
1
1
1
1
1
1
1
0
0
2
1
1
0
1
2
2
0
2
1
1
2
1
1
1
2
1
1
0
1
1
2
2
1
1
1
1
2
1
0
1
1
1
0
1
0
1
2
1
2
0
0
1
2
1
1
2
1
1
2
1
1
0
1
1
1
0
2
1
0
2
2
1
1
1
1
0
2
1
1
2
2
1
1
1
0
1
2
1
1
2
0
2
2
0
1
0
1
0
1
1
0
2
2
2
2
0
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
2
2
2
0
1
1
2
0
1
3
1
2
2
0
2
1
2
1
0
1
0
1
1
0
1
2
1
2
0
1
2
1
0
2
1
1
1
1
1
0
0
1
0
1
1
1
1
1
0
0
2
1
0
1
1
1
0
1
2
0
1
1
1
0
1
2
1
1
1
1
0
1
2
1
1
1
1
2
1
1
0
1
2
0
2
0
1
2
1
2
0
1
1
1
1
2
1
0
1
1
1
1
1
1
1
1
1
0
2
2
1
1
1
2
1
0
1
1
1
1
0
2
1
1
0
0
1
1
1
0
1
1
2
2
0
1
1
2
1
2
1
1
1
2
1
1
0
2
1
0
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
0
1
2
0
0
0
1
2
2
1
1
0
1
1
1
2
2
1
1
1
2
1
1
1
1
0
1
1
2
2
1
1
1
1
1
2
1
1
2
1
1
2
1
1
2
1
1
1
1
1
1
1
4
1
0
1
0
1
2
1
1
2
1
2
1
0
1
0
1
0
2
1
2
2
0
0
0
1
2
1
2
2
1
0
1
0
1
0
1
1
2
1
1
2
1
2
2
1
1
1
1
2
1
1
0
2
2
2
1
1
1
1
1
1
0
1
0
1
0
2
1
2
1
1
1
1
1
1
1
0
0
1
1
1
1
1
1
2
1
1
1
2
0
1
1
1
1
1
1
1
2
1
1
0
1
2
2
1
2
1
1
1
2
2
1
1
2
2
1
1
1
1
1
3
2
1
1
1
2
1
0
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
2
2
2
1
1
0
0
2
1
2
1
2
1
1
3
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
1
1
2
1
1
1
2
3
1
0
0
1
1
1
2
1
1
1
1
2
0
1
1
1
2
2
0
0
2
3
1
0
1
1
2
2
1
0
0
0
1
1
1
1
1
0
1
1
1
2
1
1
0
1
1
1
1
1
1
1
0
1
1
1
0
1
1
1
1
1
2
0
1
2
1
2
2
4
1
1
0
1
0
1
1
0
1
1
2
2
1
1
1
1
0
3
1
1
1
1
1
4
2
0
2
1
1
2
1
1
0
0
1
1
0
1
1
1
1
2
2
1
1
2
1
1
0
2
0
2
1
1
1
2
0
1
2
1
1
1
1
1
2
1
1
1
2
2
1
2
1
1
0
2
1
1
1
0
1
1
0
1
1
1
1
1
2
2
1
1
1
0
0
1
1
2
2
1
2
2
1
1
1
1
2
0
3
1
2
0
2
1
2
0
0
1
1
1
2
2
2
1
0
1
0
2
1
0
1
1
1
1
1
1
1
2
1
2
0
1
0
2
1
1
1
0
1
1
0
2
1
2
1
1
1
1
1
0
2
1
1
1
2
0
2
1
1
1
1
1
1
1
1
2
2
0
1
1
1
1
0
0
1
1
2
1
1
0
2
2
1
2
1
0
0
1
0
1
0
1
1
1
0
2
1
1
1
0
1
0
2
1
1
1
1
0
0
1
1
0
1
1
1
1
1
1
0
1
0
1
2
1
1
1
0
2
2
1
1
0
1
1
2
2
1
1
1
1
1
1
1
1
1
2
0
1
1
2
0
1
2
1
1
0
2
2
2
1
1
1
2
1
1
0
0
1
2
1
1
1
1
1
2
0
0
1
1
1
1
0
2
1
1
1
1
0
1
0
2
1
2
1
1
1
1
0
0
1
1
2
1
1
0
0
1
3
2
0
1
2
2
1
1
3
2
2
1
1
2
1
1
1
1
1
2
1
1
0
1
0
0
1
1
1
1
1
1
2
1
1
1
1
1
1
0
1
0
2
1
1
1
2
1
0
1
1
1
2
1
1
1
1
2
0
1
1
1
1
0
1
1
2
2
1
2
1
2
1
2
2
1
1
1
0
1
0
1
1
1
1
2
2
1
1
1
1
0
1
1
1
0
1
0
1
1
1
1
0
0
2
0
1
1
1
2
1
1
0
0
1
0
1
0
1
1
2
1
1
1
1
2
0
1
1
1
2
2
1
1
1
1
1
1
0
1
0
0
2
0
1
1
1
1
1
2
1
0
2
2
2
2
0
1
2
1
3
1
1
1
1
2
1
1
2
1
1
2
1
2
0
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
0
1
1
1
1
1
0
1
0
0
1
2
1
3
2
2
1
1
2
2
1
2
1
1
2
1
2
2
0
1
1
2
1
2
2
2
2
0
1
2
2
1
2
2
0
1
0
1
1
1
1
1
0
1
1
1
1
1
1
1
0
0
1
1
0
1
2
2
0
1
2
0
1
1
1
0
0
1
1
2
1
2
1
0
1
1
0
1
0
0
0
2
2
2
1
2
2
0
1
0
1
1
0
2
1
1
2
1
1
2
1
2
1
0
1
1
1
1
0
0
1
1
1
1
1
2
1
1
2
1
1
0
0
0
1
2
0
1
1
0
1
2
1
3
1
1
0
2
2
1
1
1
1
2
2
2
1
1
1
1
1
2
1
1
2
1
1
1
1
1
2
2
2
0
1
1
1
1
2
1
1
1
2
1
1
0
1
1
1
2
1
1
2
1
1
2
2
2
0
1
2
1
2
0
2
1
1
1
1
1
2
1
1
1
1
1
1
2
2
1
0
1
1
2
2
0
0
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
0
1
0
1
1
1
1
1
2
0
2
1
2
2
1
1
0
1
2
1
1
2
0
2
1
0
0
1
1
1
3
2
1
1
1
1
0
1
0
1
0
2
8
1
1
0
1
0
0
1
1
2
1
2
2
0
1
1
1
0
0
1
1
1
2
1
0
1
1
1
1
2
1
2
1
0
1
2
1
1
1
1
1
1
2
2
1
1
0
1
0
1
0
0
1
1
0
1
1
1
1
1
1
0
2
2
1
1
1
0
0
1
1
2
1
0
2
1
1
1
1
2
2
1
1
1
1
1
1
1
1
0
1
1
0
1
2
1
2
3
2
2
1
1
2
1
0
2
1
1
2
0
0
1
1
1
1
0
2
0
2
2
1
1
0
2
1
1
1
1
1
2
0
2
1
0
1
1
1
2
2
1
3
1
2
3
2
1
2
0
1
1
2
1
1
1
2
1
1
0
0
2
2
0
1
2
1
1
1
1
2
1
1
1
0
2
0
2
1
1
2
2
1
1
1
1
0
1
1
1
2
2
1
0
1
1
1
1
1
1
1
1
0
2
0
2
1
1
6
0
1
0
1
2
1
1
0
1
1
0
3
1
1
0
1
2
2
1
0
0
0
2
0
1
2
2
0
1
1
0
1
1
0
1
1
1
0
2
1
1
1
1
1
2
2
1
1
0
0
1
1
2
1
3
2
0
1
2
1
2
2
1
1
0
2
1
1
2
1
1
1
1
2
1
0
1
2
2
3
1
1
1
1
0
1
2
0
1
2
1
1
1
1
1
2
2
1
1
1
1
2
2
1
1
1
0
0
0
1
1
0
2
2
2
2
1
1
1
1
0
2
2
1
2
0
2
1
1
1
1
1
1
0
2
1
1
0
1
1
0
1
2
1
1
1
1
0
0
1
1
2
2
0
2
1
1
0
0
2
1
1
1
1
1
0
1
0
1
0
2
1
1
2
0
2
1
1
2
2
1
2
1
1
1
2
2
1
2
0
1
2
1
1
1
1
3
2
1
0
1
2
1
2
1
0
1
0
3
1
0
1
2
1
0
0
0
1
1
2
1
0
1
1
1
0
0
1
0
0
1
0
2
1
2
1
1
1
1
1
1
1
2
1
0
0
0
0
1
1
1
1
1
1
1
1
0
1
2
1
1
1
2
1
1
2
0
0
2
2
1
1
1
1
1
0
2
1
1
1
1
2
0
1
2
2
1
1
2
2
2
0
1
1
2
1
0
1
1
2
0
0
1
1
2
1
2
0
0
1
1
1
1
1
1
1
1
1
0
2
1
2
1
1
1
2
2
1
2
2
0
1
1
1
1
1
2
2
1
1
2
1
1
0
2
2
0
2
1
0
1
2
1
1
0
1
1
2
2
1
1
1
1
0
1
1
0
2
1
2
2
1
1
1
1
1
2
1
2
1
2
1
1
1
2
2
2
0
1
2
1
0
2
1
2
2
0
1
1
1
0
2
1
1
2
1
1
1
1
2
1
1
2
0
1
0
1
3
2
1
1
2
2
2
2
1
1
2
1
1
1
2
1
1
2
0
1
1
1
0
2
1
1
2
2
1
1
1
1
2
2
2
1
1
1
1
1
3
1
0
1
1
0
0
1
1
1
1
2
1
2
2
4
1
1
2
1
1
0
0
1
1
2
2
1
1
0
0
0
1
1
0
1
2
0
0
4
0
0
1
0
1
0
1
0
1
1
1
2
0
1
0
1
0
2
0
0
1
1
2
2
2
1
2
1
1
0
1
1
1
1
1
2
0
1
1
0
1
0
0
1
1
1
1
2
2
1
1
0
1
0
1
1
1
1
1
2
0
1
0
0
1
1
1
1
1
2
1
2
1
2
1
1
1
1
1
2
0
1
1
0
2
0
1
0
1
1
0
1
1
1
2
1
2
0
0
0
1
1
2
1
1
1
2
2
1
0
2
1
1
1
0
0
0
2
1
2
1
1
1
2
1
1
1
1
0
2
1
2
1
0
3
1
1
2
1
1
1
2
0
1
0
1
2
1
0
1
2
2
1
1
2
2
1
0
1
2
2
0
1
1
2
1
0
0
1
1
2
2
1
0
2
4
2
2
2
1
1
2
2
0
1
1
1
1
1
1
1
2
0
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
0
2
1
1
1
2
1
1
1
0
2
1
0
2
1
1
1
1
1
2
0
0
0
1
2
1
1
0
1
2
0
1
2
2
1
1
0
1
1
2
1
1
1
1
1
1
1
0
1
1
0
2
0
1
2
1
1
1
1
2
1
0
0
1
0
1
1
2
2
2
1
2
1
0
1
0
1
0
2
0
0
1
2
1
2
2
0
1
1
0
1
1
2
0
1
1
2
2
2
2
1
1
1
1
1
1
0
2
1
2
2
1
2
1
1
0
1
1
0
1
2
1
0
1
1
1
0
1
0
2
1
1
1
1
1
2
1
0
1
1
1
0
2
0
1
2
1
1
1
1
1
1
1
1
2
2
1
2
0
1
1
1
1
2
1
1
0
1
1
2
1
1
1
2
1
0
1
2
1
2
1
2
1
2
0
1
1
4
1
1
1
1
1
0
1
0
1
1
1
1
1
1
1
2
1
0
2
1
0
1
1
4
2
1
0
1
1
1
1
1
2
0
0
0
1
1
2
0
1
0
0
1
1
1
2
1
1
2
0
2
1
2
1
2
2
1
1
0
1
2
1
1
2
1
3
1
1
1
0
1
0
2
1
1
1
0
1
2
1
0
2
1
2
1
1
1
1
2
1
2
1
1
0
1
2
2
0
2
1
0
0
1
1
0
0
2
0
1
1
1
2
2
2
2
2
1
1
1
1
1
1
0
1
1
1
1
2
2
2
0
1
1
1
2
1
2
1
1
2
1
1
0
0
2
1
2
2
1
2
1
1
2
2
1
1
1
2
2
3
1
1
1
1
0
1
1
1
1
3
1
2
1
1
0
1
3
1
0
1
1
2
1
0
1
1
1
1
2
2
2
0
1
1
2
2
1
2
1
2
1
0
1
1
1
1
2
1
2
1
1
1
0
1
2
1
1
1
0
0
1
1
1
2
1
1
2
1
1
1
2
2
1
2
1
1
1
1
1
2
2
0
1
0
1
2
1
3
2
1
1
1
1
1
1
1
0
2
1
1
1
1
1
1
1
1
2
2
1
0
1
0
1
2
1
2
1
1
0
0
0
2
1
2
1
0
0
0
0
1
1
2
1
1
2
1
1
1
1
1
2
1
2
0
1
1
1
1
1
2
1
1
2
1
2
0
1
1
0
2
2
1
2
1
1
1
1
1
1
0
2
1
1
1
2
1
2
2
0
0
1
1
1
1
0
1
1
1
1
1
2
1
1
1
2
1
0
2
1
1
0
1
1
1
2
1
1
1
1
1
2
1
2
1
1
3
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
3
2
1
1
1
2
1
0
1
1
0
1
2
1
1
1
2
1
0
1
1
1
1
1
1
1
1
1
2
0
1
0
1
1
1
2
1
1
1
1
1
0
1
1
0
0
1
0
1
2
2
1
1
2
1
1
0
1
1
1
1
1
0
2
1
1
1
0
1
1
1
3
0
1
1
1
0
1
2
1
1
1
1
1
1
2
1
1
0
2
1
0
0
1
1
2
1
1
0
1
1
0
1
1
1
2
2
2
2
0
2
1
1
1
2
1
1
1
1
1
0
0
2
1
0
0
1
2
0
0
2
0
1
1
1
1
0
2
1
1
2
1
2
3
0
1
1
0
1
1
2
1
1
1
0
2
1
1
2
0
1
1
2
1
1
2
1
2
1
1
2
0
1
1
1
2
1
1
1
2
1
0
1
2
1
0
1
1
0
2
2
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
0
1
1
0
1
1
1
1
0
2
2
2
1
0
1
1
1
0
0
0
1
1
1
2
0
1
1
2
0
1
1
1
1
2
1
1
0
0
1
1
1
1
1
0
0
2
0
1
2
0
1
1
1
2
2
2
1
2
1
1
1
2
1
0
1
1
1
2
2
0
2
1
1
1
1
1
2
1
1
1
0
3
1
2
1
1
1
1
2
2
2
1
1
1
1
0
1
1
1
0
1
2
1
0
2
1
1
0
0
1
1
0
1
1
0
1
1
2
2
2
1
1
2
1
1
2
1
1
0
1
2
3
1
2
1
1
1
2
2
1
1
2
1
2
1
1
1
0
2
1
2
1
0
0
1
0
1
1
2
2
1
1
0
1
1
0
1
2
1
1
2
1
2
1
1
1
0
1
1
1
2
1
1
0
1
1
0
2
2
2
1
1
2
1
0
1
1
0
1
0
3
1
1
1
1
0
1
1
2
2
2
2
2
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
2
2
1
2
1
2
0
1
1
1
2
1
0
1
1
1
1
1
1
2
2
0
0
1
1
2
1
2
1
1
0
1
2
1
1
2
0
0
1
1
1
1
0
1
0
2
2
2
1
0
0
1
2
0
2
1
1
2
2
0
1
2
1
1
1
1
1
2
1
2
1
2
2
1
0
1
1
0
1
2
0
0
2
1
1
2
2
1
2
0
2
2
2
0
1
0
1
0
1
1
1
1
1
1
1
1
3
2
1
0
3
1
1
1
2
0
2
1
1
1
1
1
1
0
1
1
1
0
0
1
2
2
1
2
2
1
1
1
0
2
0
1
2
1
2
2
1
2
1
1
1
1
2
1
0
1
1
0
1
2
1
2
1
0
1
1
1
2
0
1
1
2
2
1
0
1
1
1
1
2
2
1
1
2
1
2
1
2
1
2
1
1
2
0
1
1
0
2
1
1
0
2
1
2
1
1
0
0
1
1
2
2
1
0
1
0
0
1
1
1
2
0
0
0
1
0
1
2
0
1
2
1
1
1
1
1
1
0
1
1
1
2
2
0
1
0
1
2
1
1
1
1
1
2
0
0
2
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
0
1
0
2
1
1
1
1
1
1
1
0
1
1
1
1
1
2
0
1
2
2
2
2
0
1
2
1
1
0
0
1
2
2
2
0
2
1
1
1
2
2
1
1
2
0
2
1
1
1
1
1
1
1
1
2
1
1
0
1
1
1
0
2
0
1
1
0
1
1
1
1
2
0
1
1
1
2
2
2
0
1
2
1
2
1
1
1
0
2
1
1
1
1
1
1
0
1
0
0
0
1
1
2
0
2
1
1
0
1
1
2
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
0
1
1
2
1
1
2
0
1
2
2
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
0
2
1
1
1
0
2
0
0
0
1
1
0
2
0
1
1
1
2
2
1
1
0
1
1
1
1
0
1
0
2
1
1
1
1
1
1
1
1
1
0
1
2
1
1
1
0
2
0
1
1
1
1
2
2
0
1
3
1
2
1
1
1
1
1
1
1
1
1
2
0
1
0
1
1
1
0
1
1
1
1
1
2
0
2
1
0
0
1
2
2
1
1
1
2
0
2
1
1
1
1
1
1
0
1
2
1
2
0
1
2
1
0
2
0
0
1
0
2
1
2
1
1
1
2
0
2
1
2
2
0
0
1
1
2
1
0
2
1
1
1
2
1
3
2
0
2
1
3
1
1
1
1
1
1
0
2
1
1
1
1
1
1
1
1
1
2
1
2
0
1
2
1
1
2
1
1
1
1
1
0
2
2
1
2
1
2
1
2
1
1
1
1
3
1
0
2
1
1
1
0
1
1
2
1
1
1
2
2
1
1
1
1
1
1
1
0
1
1
0
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
0
0
2
1
0
1
2
1
2
1
0
2
1
2
1
1
2
1
1
1
1
0
2
2
1
0
0
1
1
0
2
2
1
0
2
0
0
0
1
1
1
1
2
1
2
2
1
0
0
1
2
1
1
1
1
0
0
1
1
1
2
2
0
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
2
2
2
1
0
1
0
2
1
1
1
0
1
0
1
2
1
1
0
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
0
1
2
1
2
2
1
1
2
0
0
2
2
1
1
1
1
1
1
0
1
1
0
0
1
0
1
1
1
1
0
1
0
1
1
1
2
1
2
2
2
0
2
2
3
0
1
1
2
0
0
0
1
2
0
1
0
1
1
2
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
0
1
1
0
1
2
1
0
0
2
2
1
0
1
2
0
2
0
1
2
0
1
2
0
1
2
1
0
0
0
2
1
1
1
2
2
1
2
0
1
1
1
1
2
1
2
1
1
1
2
0
1
1
0
2
1
2
2
1
0
1
1
1
1
1
1
1
0
0
2
2
0
1
2
2
0
0
1
0
0
1
1
1
1
0
0
0
0
1
1
0
2
2
1
2
1
1
1
1
1
2
1
0
1
1
1
0
1
1
1
2
1
1
2
0
1
1
1
1
2
1
0
0
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
3
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
0
2
1
2
0
1
1
1
1
1
1
0
1
2
1
1
1
1
1
0
0
4
1
1
1
0
1
1
0
1
1
2
2
1
1
0
2
0
2
0
0
1
2
0
1
2
1
1
0
2
2
4
2
0
1
1
0
1
1
1
1
2
2
0
1
0
1
1
1
1
0
1
0
1
1
1
0
1
0
2
2
2
1
3
0
2
1
1
1
2
2
4
1
1
2
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
2
1
0
1
0
1
2
0
2
1
2
1
1
1
0
0
2
0
2
0
0
1
2
2
1
2
0
2
0
0
1
1
1
0
0
2
0
2
1
1
0
1
1
0
0
0
1
0
1
1
2
1
1
2
1
1
1
1
1
1
2
1
2
0
1
2
2
1
4
0
1
1
1
2
1
1
1
0
1
0
1
1
1
1
0
2
1
1
1
1
1
1
1
1
0
1
0
1
1
1
1
1
1
1
2
0
1
1
1
1
1
1
0
2
1
1
2
1
1
2
0
0
1
1
2
1
0
1
1
1
1
1
1
1
1
1
0
1
0
1
1
2
0
2
2
1
1
1
1
0
2
0
1
2
2
2
1
0
1
2
1
2
1
1
1
2
2
2
0
1
2
1
1
2
0
2
0
1
1
2
1
1
1
0
2
1
1
1
1
2
1
1
2
2
1
2
2
2
1
2
1
1
0
1
0
2
1
1
2
0
1
1
2
2
1
1
2
1
2
1
3
1
1
0
1
1
1
1
1
1
1
1
1
1
2
2
1
0
1
2
1
1
2
0
2
1
1
1
1
1
1
1
1
3
1
0
1
2
1
0
1
2
2
1
3
0
3
1
2
1
1
1
0
1
0
1
1
2
2
0
2
0
0
1
2
1
1
1
1
0
0
2
1
1
0
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
2
2
2
1
0
1
0
2
1
0
1
1
1
2
1
0
1
1
0
1
1
2
1
1
1
1
1
1
0
1
1
1
1
2
0
2
1
0
0
1
1
1
1
2
2
1
0
1
1
2
0
1
2
0
0
0
2
1
1
1
2
1
2
0
1
1
1
1
2
2
0
1
0
2
1
1
0
2
0
2
1
1
1
1
1
1
2
0
1
1
1
1
1
1
1
2
1
1
1
1
2
1
3
2
1
1
1
1
1
0
1
1
1
2
0
1
1
0
2
1
1
2
1
2
1
0
0
3
1
2
1
1
1
2
1
1
2
2
2
1
2
2
1
1
2
0
2
1
1
1
2
1
1
0
0
1
1
2
1
1
1
1
0
2
1
0
1
2
0
1
2
1
1
2
2
1
1
0
0
2
1
1
1
1
2
1
2
1
1
1
1
0
2
1
1
1
1
0
2
2
2
1
2
2
1
1
0
0
1
1
2
1
1
1
2
1
0
1
1
1
1
2
1
1
1
2
1
1
2
2
1
2
1
2
1
1
1
1
2
2
0
1
2
2
2
1
1
0
1
2
0
2
2
0
2
2
0
1
1
1
0
1
1
2
1
2
1
1
1
1
1
0
1
2
1
1
2
2
1
2
1
0
0
1
2
1
1
0
0
2
1
0
1
1
1
1
2
2
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
0
2
1
0
1
0
1
0
2
2
2
1
1
2
1
1
2
1
0
1
1
1
0
2
1
0
0
1
2
2
0
1
1
1
1
1
1
0
1
1
0
1
2
2
1
1
2
1
1
1
2
2
0
0
1
1
1
1
1
1
2
1
1
1
1
1
0
0
1
1
7
0
1
2
2
1
1
2
1
0
1
1
2
0
1
2
1
1
1
1
1
1
0
1
1
1
0
1
2
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
0
0
1
1
1
0
0
2
1
1
1
1
1
1
1
1
1
1
2
1
0
1
1
1
1
1
0
2
2
1
1
2
2
3
1
0
2
1
2
1
2
2
0
1
1
1
1
1
1
1
1
0
2
2
2
2
1
1
2
1
0
0
1
1
1
1
2
2
0
0
1
2
2
1
1
1
1
1
1
1
1
0
2
2
1
1
1
0
1
0
2
1
2
1
1
2
2
0
3
0
0
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
0
0
1
2
2
1
1
1
1
1
0
1
1
1
0
1
1
1
1
1
1
1
1
0
1
1
2
1
1
1
1
0
1
1
1
1
0
1
1
0
1
2
1
2
0
1
1
0
1
0
0
2
1
2
1
0
1
0
2
2
1
1
1
2
1
2
2
1
1
1
2
1
3
1
0
2
1
1
1
1
2
1
0
1
2
1
0
1
1
1
1
1
1
1
2
1
1
1
2
2
1
0
1
1
1
1
1
1
1
2
2
2
0
2
1
1
0
1
1
1
1
1
1
1
1
1
2
0
1
2
0
1
2
1
1
2
1
1
1
2
0
1
1
2
1
1
1
0
0
1
1
1
1
1
1
1
0
1
1
1
1
0
2
1
1
1
1
2
2
1
1
1
2
1
1
1
2
1
0
2
1
1
2
0
0
0
1
2
2
2
0
0
1
2
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
1
0
1
1
1
1
1
2
1
1
2
1
1
1
2
1
1
2
1
2
1
1
1
2
1
2
1
3
2
0
1
1
1
2
1
1
1
1
1
1
2
1
2
1
1
2
1
2
0
1
2
2
1
1
1
0
1
1
1
1
1
2
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
2
1
2
1
1
1
1
1
0
0
1
0
1
4
1
1
1
1
1
2
0
1
2
1
1
2
2
1
1
2
1
1
1
0
0
1
1
1
1
1
1
2
1
2
3
2
0
0
1
1
0
2
1
3
1
2
1
1
1
1
1
2
1
1
1
0
1
1
2
1
2
1
1
1
0
1
1
1
0
1
1
0
1
2
1
2
2
1
2
1
2
1
1
1
2
1
2
0
1
0
0
1
2
0
1
1
1
1
2
1
0
2
0
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
2
1
2
1
0
1
2
1
0
1
0
0
0
1
0
2
2
1
1
1
0
1
1
2
1
1
1
0
1
1
1
1
1
0
1
1
0
1
1
1
2
1
0
1
2
1
0
1
2
1
2
1
2
1
1
2
1
0
2
1
0
1
1
1
2
1
0
1
2
1
0
1
1
2
1
2
1
1
1
0
1
2
0
2
2
1
0
1
2
2
0
0
1
2
1
1
2
0
2
0
1
2
0
2
0
0
1
1
2
0
2
2
1
1
1
1
2
3
1
1
0
2
1
0
1
1
1
2
2
1
1
2
1
3
1
2
1
0
1
2
1
2
0
1
1
0
1
1
1
1
2
1
2
0
1
1
2
1
0
0
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
0
1
2
0
0
1
0
1
1
1
2
0
1
1
1
2
1
0
1
2
1
1
1
0
2
1
1
1
1
1
0
5
1
2
1
2
1
0
0
1
0
0
2
1
1
0
1
1
2
2
0
1
1
1
2
1
1
1
1
2
2
1
1
0
2
1
1
1
2
1
0
1
0
1
0
1
0
0
2
2
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
0
3
1
2
1
0
1
2
1
1
2
1
2
2
1
2
1
1
1
1
2
0
1
0
2
0
1
1
1
1
1
1
1
2
2
1
1
1
3
2
1
0
1
2
1
1
1
1
1
1
1
2
2
2
1
1
1
2
1
3
1
1
1
0
1
1
1
1
1
2
0
1
1
1
2
1
2
2
1
0
0
1
1
2
2
1
1
1
1
1
1
2
0
0
1
2
1
2
1
1
2
1
0
1
1
0
1
1
1
1
2
1
0
1
2
1
0
1
1
0
1
1
1
1
1
2
2
1
1
1
2
2
0
1
1
2
1
1
0
1
1
1
1
0
0
1
1
1
1
2
1
1
0
1
2
1
2
2
1
1
1
1
1
0
1
1
1
1
0
1
0
1
1
2
1
1
2
1
1
2
1
0
1
1
2
1
1
1
2
2
0
1
1
0
2
2
1
1
2
1
1
2
2
0
1
1
1
1
0
2
2
1
1
2
1
2
2
1
1
0
1
0
1
1
2
1
2
1
1
1
1
2
2
1
1
1
1
2
1
0
2
1
1
0
1
2
1
2
1
2
1
1
1
1
2
2
1
1
0
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
1
2
1
2
1
2
1
0
2
0
2
2
1
2
1
2
0
2
1
1
0
2
1
1
1
2
1
1
1
2
0
0
0
0
1
0
2
2
1
1
1
0
0
0
1
1
0
2
2
0
1
2
1
1
1
1
0
1
0
1
2
1
2
1
1
1
2
1
1
0
0
1
0
1
1
1
1
1
0
1
1
2
1
2
1
2
2
2
0
0
2
1
1
2
2
0
1
0
2
1
1
1
1
1
1
1
3
1
1
1
1
2
1
2
1
1
3
0
1
2
0
2
1
1
2
1
2
1
1
0
1
1
1
2
1
2
1
1
2
1
2
0
1
2
1
1
2
1
2
0
2
1
1
1
1
1
2
2
0
0
1
1
1
0
1
1
1
2
0
2
2
0
0
0
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
0
1
1
2
2
2
1
1
1
2
1
1
0
1
0
1
1
0
1
0
2
2
1
0
2
0
1
1
1
0
1
1
0
1
1
2
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
0
1
1
1
1
1
0
0
2
1
2
2
2
1
0
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
1
2
0
1
0
1
1
1
1
1
1
2
1
1
1
1
0
1
2
0
1
2
1
1
1
2
1
0
1
1
1
1
1
0
2
1
0
1
2
1
3
1
1
1
1
1
1
2
1
0
1
1
1
1
1
1
0
2
1
1
2
0
1
1
1
2
2
0
2
0
1
0
0
2
1
1
1
1
0
1
0
2
1
2
1
0
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
0
2
2
1
0
1
2
0
1
1
1
2
2
1
0
2
1
1
1
1
1
2
0
1
1
2
0
1
1
2
1
1
1
2
1
1
2
4
1
1
1
1
1
2
1
2
1
2
1
1
0
2
0
1
1
2
0
2
2
2
2
1
1
1
2
1
1
0
1
1
1
0
1
1
1
0
0
1
1
1
0
1
1
1
2
2
1
1
2
1
1
1
1
0
1
0
0
1
1
0
2
2
1
2
0
1
1
1
0
2
1
2
1
2
2
1
0
1
1
2
1
0
1
1
1
1
1
2
2
2
2
1
2
1
1
2
1
2
2
1
1
0
1
1
1
0
1
1
1
0
1
1
1
1
2
2
0
1
1
1
1
1
1
1
0
1
1
1
1
1
0
0
1
0
1
1
1
1
2
1
0
1
0
1
1
1
2
1
0
1
0
0
2
0
1
1
1
0
1
0
0
2
1
0
2
1
2
1
0
0
0
1
1
1
1
2
1
2
2
2
1
0
2
2
1
2
1
1
0
1
2
2
1
0
1
2
1
0
1
1
1
1
2
2
0
2
1
1
2
0
1
1
2
2
1
2
1
2
1
1
1
2
2
1
3
1
1
2
0
1
1
0
0
0
0
1
1
1
1
1
1
1
0
1
0
1
1
1
2
2
0
0
1
1
1
1
2
1
2
1
0
1
1
1
0
1
1
1
1
1
1
2
1
0
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
0
0
2
2
1
1
2
2
1
2
1
0
1
0
1
0
1
2
1
0
0
3
1
0
2
0
1
1
0
1
1
1
2
1
0
1
2
1
2
1
1
1
0
1
1
1
0
1
1
1
2
2
1
1
2
4
0
1
1
0
2
1
0
1
2
0
1
2
1
2
1
1
2
2
1
2
2
1
1
1
1
1
1
1
2
1
0
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
2
2
0
1
1
2
2
0
1
1
2
1
0
2
0
2
0
1
1
1
0
1
1
2
1
1
1
1
1
1
2
1
0
2
0
2
0
1
0
2
1
2
1
1
1
2
1
2
1
1
1
1
2
1
1
0
1
2
1
1
1
0
2
1
1
1
1
1
1
0
0
2
1
0
1
1
2
1
1
1
0
1
1
2
1
1
0
1
0
2
1
0
1
0
1
1
2
0
1
1
1
1
2
2
1
1
0
1
1
1
1
0
1
1
1
1
0
1
1
0
1
2
2
0
1
0
0
0
0
1
1
2
1
2
2
1
2
1
1
1
1
1
2
1
2
1
2
2
0
1
0
1
1
1
1
1
1
1
2
1
1
2
2
1
2
1
2
1
1
1
1
1
2
1
1
1
1
2
1
1
0
1
1
1
0
0
2
2
1
1
1
2
1
0
1
0
2
2
1
2
2
2
0
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
2
2
1
0
0
1
1
1
1
2
0
1
1
1
0
1
2
1
1
1
0
2
1
1
2
0
1
1
1
1
1
1
2
1
0
1
2
1
1
1
2
0
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
0
1
1
1
1
2
2
1
1
0
1
1
2
0
2
1
2
1
1
2
1
1
0
1
2
1
1
1
0
1
2
0
1
1
2
1
1
0
1
1
1
1
0
2
1
2
1
0
2
1
0
1
1
2
0
0
1
1
2
1
1
2
1
0
1
1
2
1
0
2
1
1
1
1
1
2
2
1
0
2
1
2
1
2
0
0
2
0
2
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
2
0
1
1
1
0
1
2
1
1
1
0
2
1
1
1
1
2
1
1
2
2
0
2
1
1
1
1
2
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
0
2
1
2
2
1
1
1
0
0
2
2
2
2
2
2
1
1
1
1
2
0
1
0
0
1
1
1
1
1
1
0
2
1
2
1
1
1
0
1
2
1
1
1
1
1
1
0
1
1
0
2
1
0
1
1
1
1
0
2
1
0
1
2
2
2
0
2
2
1
2
2
1
1
1
1
1
0
1
0
1
1
1
1
1
2
1
1
2
1
1
2
0
1
1
1
1
2
1
2
2
0
1
1
1
1
1
1
1
1
1
1
2
1
0
1
1
2
1
0
1
0
1
1
0
1
0
0
0
2
1
1
0
1
1
1
1
2
1
2
0
0
1
1
1
1
0
1
0
0
2
1
0
2
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
2
1
1
0
2
1
2
1
0
1
1
0
0
1
2
0
1
1
2
0
2
2
0
1
1
2
1
1
0
1
1
1
1
1
1
1
1
1
1
2
0
1
1
1
1
1
1
2
1
2
1
2
0
1
1
1
1
2
1
1
1
2
1
0
1
2
1
2
3
2
2
1
1
0
1
1
1
1
0
1
1
1
1
1
1
2
1
2
2
2
1
1
1
1
1
2
1
0
0
1
1
2
0
1
1
1
2
1
1
1
1
1
0
0
0
0
1
1
2
1
2
2
0
1
1
2
1
0
0
2
1
1
1
2
1
1
1
1
4
1
1
1
1
1
1
1
1
1
0
1
1
1
1
2
1
1
1
1
0
1
1
1
2
1
1
2
2
1
2
1
1
1
2
1
0
1
2
1
1
2
1
1
1
2
1
1
1
2
3
1
0
2
1
1
1
2
1
0
1
0
1
1
1
1
1
1
1
1
2
0
2
2
2
1
1
1
2
1
2
1
1
1
0
1
2
1
2
2
1
2
0
1
1
2
1
0
0
1
1
2
2
2
1
0
1
0
1
1
0
1
1
2
1
0
2
1
1
1
1
1
1
2
1
0
0
2
1
1
1
0
1
1
0
1
1
1
0
1
0
2
2
1
1
0
0
1
1
2
1
2
2
0
1
1
1
1
1
2
0
1
1
2
1
2
2
1
1
2
1
1
1
1
1
1
2
1
1
1
0
2
1
1
0
2
0
2
0
0
1
2
1
1
2
2
1
1
2
1
2
1
1
1
1
1
1
1
1
2
2
1
1
0
2
1
1
2
1
1
3
1
2
0
0
1
2
2
1
2
1
2
1
1
2
1
1
1
0
0
1
2
2
2
2
1
2
1
1
2
0
2
1
0
1
1
0
2
2
1
0
1
1
1
2
1
1
1
0
2
1
0
1
2
2
0
2
1
1
1
1
1
2
1
1
0
1
2
1
1
2
1
2
1
1
1
4
0
0
1
1
2
1
1
2
1
1
1
1
1
1
1
1
3
1
1
1
1
2
2
1
1
1
0
0
1
0
2
1
2
2
0
1
2
1
1
1
0
2
1
1
1
2
1
1
0
1
1
0
1
1
0
0
1
1
1
1
0
0
1
1
0
2
1
0
2
1
0
0
0
0
0
1
0
1
2
2
0
0
2
1
2
1
1
0
1
0
2
1
1
0
0
1
2
1
1
1
1
1
1
2
1
2
1
1
2
1
0
1
1
0
1
1
1
1
1
0
1
1
1
1
0
2
0
1
1
2
1
0
1
1
1
1
1
0
2
1
1
2
1
1
1
0
0
1
0
2
2
1
0
2
1
1
0
1
1
2
1
1
1
0
0
1
1
2
2
1
1
1
1
1
1
0
1
1
1
0
0
1
1
1
1
1
2
1
4
0
1
1
0
0
0
0
1
1
1
2
2
1
1
1
0
2
1
1
1
0
0
1
2
2
2
1
1
1
1
1
1
0
1
1
1
1
2
1
2
5
1
0
1
1
2
0
1
0
1
1
1
1
1
2
1
0
2
1
0
0
0
3
1
1
0
2
1
2
1
1
0
2
2
1
1
1
1
2
2
0
1
0
1
2
1
2
0
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
0
2
2
1
2
1
2
1
2
6
1
2
0
2
0
0
1
2
2
2
2
1
0
1
1
1
2
0
1
1
0
0
1
1
2
2
0
0
1
0
1
1
1
1
2
0
1
0
1
1
0
1
1
1
1
2
1
1
1
0
1
2
1
0
1
1
0
0
1
1
2
1
1
0
1
1
1
1
2
1
0
1
1
0
1
2
2
1
2
2
1
2
2
1
1
1
1
1
0
1
0
1
1
1
1
1
2
2
2
1
0
2
1
2
0
1
1
0
2
1
1
0
1
0
1
1
1
0
2
1
3
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
0
1
2
0
1
1
1
1
2
0
0
1
1
0
1
1
2
2
2
0
0
1
1
0
2
1
1
1
1
1
1
1
1
1
2
0
1
1
1
2
1
1
2
1
1
1
2
1
0
1
2
1
0
1
1
0
1
1
1
1
0
1
0
0
2
2
1
1
0
1
2
2
1
1
1
1
1
0
0
1
0
2
1
1
0
1
1
1
1
1
2
2
1
1
1
1
2
1
2
1
1
2
1
1
0
1
0
1
2
1
2
2
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
1
1
2
0
2
0
2
2
1
1
0
1
1
0
1
1
1
0
0
1
1
1
1
1
0
1
1
0
1
2
1
1
1
1
2
0
1
2
2
1
1
0
0
1
2
0
1
1
1
3
1
0
1
1
1
2
1
2
0
1
1
2
2
1
1
0
1
1
1
2
1
1
1
2
1
1
1
1
3
1
2
1
2
1
1
1
2
2
1
1
2
1
3
0
1
1
1
1
1
1
1
0
1
1
2
0
2
1
2
0
1
0
2
0
2
1
0
0
1
1
1
1
1
1
1
1
1
0
2
2
1
1
1
0
1
1
1
0
1
1
0
1
1
1
1
2
1
1
2
4
1
2
2
1
1
2
1
2
1
1
1
1
1
2
1
2
2
2
1
2
1
1
1
1
1
1
0
1
1
2
1
1
1
0
0
2
0
1
0
1
1
2
1
1
1
1
1
2
1
2
0
1
2
1
2
1
1
1
1
2
1
1
2
2
1
2
1
0
1
1
1
2
2
2
1
1
1
0
2
2
0
0
1
2
0
2
1
1
1
2
0
1
2
1
1
2
1
0
1
2
1
1
2
0
1
1
1
2
0
1
0
1
2
1
1
2
2
1
0
2
0
1
1
1
0
1
1
1
0
2
1
1
2
1
3
1
2
0
1
1
1
1
1
1
1
1
1
0
1
1
0
1
1
1
1
2
1
0
1
1
1
2
1
0
2
0
1
2
1
3
1
1
1
1
1
0
1
1
1
2
1
1
1
1
1
1
2
2
2
1
1
1
1
0
1
1
1
1
1
2
1
1
0
1
2
1
1
1
1
1
1
1
1
2
0
1
1
0
1
1
1
2
1
1
1
1
1
2
2
1
1
1
0
1
0
2
1
1
1
0
2
0
1
0
1
1
1
2
2
2
2
1
1
1
1
1
2
1
0
1
0
0
1
1
1
1
0
1
1
1
0
2
1
0
0
1
0
3
1
2
2
1
2
1
1
1
1
1
2
1
1
1
1
2
2
2
0
0
2
0
1
0
1
1
1
1
2
1
0
2
1
0
2
1
1
1
1
2
1
1
2
1
0
1
2
1
1
2
0
2
1
1
0
1
1
2
1
1
0
1
1
0
0
2
0
1
1
1
1
2
0
0
0
2
1
2
1
2
0
1
2
1
0
2
1
1
1
0
1
1
2
2
2
0
1
0
2
0
2
2
2
0
2
1
1
1
2
1
1
1
1
0
1
1
2
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
0
0
0
2
1
1
1
2
1
0
0
1
0
1
2
1
2
1
1
1
2
0
2
2
1
1
1
1
2
2
1
0
1
1
0
1
1
2
1
1
1
2
0
1
1
0
2
2
2
1
1
1
1
1
1
2
1
1
0
0
1
0
0
2
0
0
1
1
2
2
2
0
1
1
2
1
1
1
1
0
1
1
2
1
1
1
0
2
1
2
1
1
2
1
2
1
2
1
1
0
1
1
1
2
0
0
1
0
1
0
0
2
1
1
1
0
1
2
1
1
2
1
2
1
0
1
1
1
1
1
0
1
0
0
1
2
1
2
1
1
1
1
1
2
1
0
0
2
1
1
1
1
1
2
0
0
1
0
1
1
0
1
1
1
1
1
2
0
0
1
1
1
2
0
1
2
1
1
0
2
2
1
1
1
2
2
1
1
1
1
1
1
2
1
2
1
0
0
3
2
1
1
1
1
2
0
1
1
1
2
2
1
1
1
2
1
0
1
2
1
1
1
2
1
0
1
2
0
1
0
1
2
1
2
2
0
2
1
0
1
1
1
1
1
2
1
0
1
1
1
1
0
1
2
0
1
1
2
1
1
1
2
2
2
1
2
1
1
0
1
1
2
1
1
1
1
1
0
1
0
1
2
1
1
1
1
2
1
1
1
1
2
0
1
0
2
1
1
1
2
1
0
2
1
0
0
1
0
1
0
1
2
1
1
2
2
1
1
0
1
2
1
1
1
1
2
0
0
1
1
1
0
1
1
1
0
2
1
1
1
2
1
2
1
1
0
1
1
2
2
1
1
2
1
2
1
0
1
1
1
0
2
0
1
1
0
0
2
1
0
1
1
1
2
1
1
2
1
0
2
1
1
1
1
1
1
1
1
1
3
1
2
1
1
1
1
2
2
1
1
1
1
2
2
1
1
2
1
1
2
3
1
1
1
0
1
2
1
2
1
1
3
1
1
2
1
1
0
0
1
1
1
2
0
1
1
2
0
1
1
2
1
1
2
0
0
1
0
1
2
2
0
1
2
1
1
0
1
1
1
1
1
1
2
1
1
1
1
1
2
2
0
1
2
1
1
0
1
2
1
1
2
1
1
1
2
0
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
0
0
0
2
1
0
1
1
2
0
2
2
1
0
1
1
1
1
2
1
0
1
0
1
1
0
1
0
2
1
1
0
1
2
3
0
1
0
1
0
1
1
1
1
0
1
1
1
1
1
1
2
1
0
1
1
1
2
1
1
2
0
1
2
2
1
1
2
1
1
1
0
2
2
2
2
1
2
2
1
1
2
0
1
2
2
1
1
2
0
2
2
1
4
2
1
1
0
1
1
1
1
2
1
2
1
1
2
1
1
1
1
3
1
1
1
1
1
2
1
2
1
0
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
2
2
3
2
1
2
0
1
1
2
1
1
1
1
2
2
0
0
2
1
1
2
2
0
2
1
1
1
2
0
0
0
2
0
3
1
1
1
0
1
1
1
0
1
2
0
1
1
1
1
1
0
2
1
2
2
0
1
1
1
2
1
1
0
1
1
1
1
2
1
0
0
0
1
1
1
1
1
3
2
2
1
0
2
1
1
1
0
1
0
2
0
2
0
1
0
1
1
0
1
0
1
1
1
0
0
1
2
0
2
1
1
1
1
2
1
0
1
0
1
2
1
2
1
1
1
2
2
1
0
1
1
1
0
2
1
1
2
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
2
1
1
1
2
2
1
1
1
1
3
1
1
2
1
1
1
1
2
2
1
1
1
0
1
2
1
1
1
1
0
1
0
1
1
1
2
2
2
2
0
0
0
1
2
1
1
2
1
1
1
2
1
1
1
1
1
1
2
1
1
2
1
1
1
2
2
1
1
1
2
0
2
0
0
2
1
0
1
0
1
1
1
2
1
1
2
2
2
2
1
2
1
0
0
1
1
0
1
0
0
1
1
1
1
1
1
0
1
1
2
2
0
1
1
0
2
1
1
2
1
1
1
1
0
1
1
0
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
2
0
1
1
1
1
1
2
1
1
0
1
1
1
1
2
0
1
2
2
1
2
1
1
0
2
0
2
1
0
0
1
1
1
1
1
1
1
0
1
2
2
2
1
1
1
1
2
0
1
1
2
1
1
1
1
0
1
2
1
1
1
1
1
1
2
0
1
2
1
1
0
1
0
0
0
0
1
1
1
1
1
1
1
1
2
1
1
2
1
1
2
1
1
2
1
1
2
1
1
2
2
2
1
1
2
1
1
1
2
1
1
0
6
1
1
1
1
1
1
1
0
1
2
2
0
1
1
1
1
1
2
1
1
2
1
1
1
2
1
2
1
0
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
0
1
1
2
1
0
1
2
1
2
0
1
1
1
1
1
2
1
1
1
2
1
2
2
2
1
0
1
1
1
1
1
0
0
0
2
1
1
0
1
2
0
0
1
0
0
2
0
1
1
1
0
0
2
1
2
1
1
2
1
2
0
1
0
2
2
1
1
1
0
2
0
1
1
2
2
1
1
1
0
0
3
0
3
0
1
0
1
2
2
0
1
1
0
1
2
1
1
1
1
1
1
1
1
2
0
2
1
2
1
2
1
1
1
1
1
1
1
1
2
2
1
0
0
1
1
1
1
2
1
2
0
2
1
2
1
1
1
1
0
0
0
1
0
0
1
1
1
1
0
0
1
1
1
1
1
1
1
1
1
2
0
1
4
1
2
2
2
1
2
2
1
1
1
0
1
2
3
1
1
2
2
3
1
2
2
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
0
1
0
2
1
1
1
2
1
1
1
1
2
2
2
0
2
1
2
1
0
2
3
1
2
1
1
1
0
0
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
2
1
1
0
1
0
2
0
1
2
2
2
0
1
1
2
1
0
2
1
1
2
0
1
1
2
1
2
1
0
0
1
1
1
2
1
1
0
2
1
1
1
1
2
2
0
1
1
2
0
1
1
0
2
1
1
1
2
1
2
1
0
1
1
1
1
2
2
1
1
0
1
1
1
0
1
1
0
1
1
1
2
1
2
4
1
0
1
2
1
1
1
2
1
0
0
2
2
1
1
1
1
2
1
1
1
1
2
1
1
1
2
0
1
2
2
0
0
2
1
1
1
1
1
1
2
1
1
0
0
2
0
0
2
1
2
2
2
2
1
1
1
1
1
1
1
1
0
1
1
1
1
1
0
1
0
2
2
1
1
2
2
1
1
1
1
1
2
2
2
2
1
2
1
1
1
2
0
1
2
2
1
0
2
1
1
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
0
1
1
2
1
2
1
1
0
1
1
0
1
2
0
1
2
1
2
1
1
0
2
1
1
1
1
1
0
1
1
1
2
0
1
1
1
1
1
0
1
1
0
1
0
1
1
1
1
0
1
1
2
1
1
0
1
2
2
1
1
1
1
2
1
1
2
1
1
1
1
2
0
0
0
2
1
0
1
0
1
1
1
2
1
1
1
1
1
2
2
2
2
1
0
1
1
1
1
3
1
0
2
2
0
1
1
1
1
1
1
1
2
1
2
1
1
2
1
2
2
0
1
2
1
1
1
1
0
2
1
1
0
1
1
1
2
1
1
1
2
2
2
2
2
1
1
1
1
0
1
2
1
0
1
0
1
0
0
1
1
1
1
2
2
2
1
1
1
1
1
1
2
2
1
1
1
2
0
0
1
1
2
2
1
1
1
1
1
3
2
1
1
1
1
0
1
2
1
1
1
3
1
1
2
0
1
2
3
1
2
0
2
1
1
0
1
1
1
1
2
1
2
0
0
1
0
1
2
1
1
1
1
2
0
2
1
3
1
2
0
1
2
2
1
1
1
1
1
2
1
2
2
1
0
0
0
1
1
2
2
1
1
1
1
1
1
1
2
1
2
1
2
1
2
1
1
1
2
0
1
1
2
1
1
1
0
1
0
1
1
2
1
1
1
2
1
0
2
1
1
1
1
0
1
1
2
0
0
1
1
0
2
1
1
1
2
1
2
1
1
1
1
1
1
1
0
1
0
1
2
2
1
1
0
2
1
1
2
1
0
1
0
1
2
1
1
1
2
1
1
1
1
2
1
1
1
0
2
1
1
1
0
1
0
1
0
1
2
1
0
2
3
1
2
0
2
0
1
3
0
2
1
1
2
1
1
1
1
0
2
0
2
1
2
1
1
0
0
0
1
1
1
1
1
1
0
3
0
1
1
0
1
1
1
1
1
3
0
2
3
0
1
0
0
2
1
1
1
2
1
2
1
1
0
1
1
0
0
1
0
2
1
2
1
1
1
2
1
1
1
2
1
1
1
2
1
0
1
2
1
2
0
1
2
1
1
2
1
1
1
1
2
2
0
1
1
1
0
2
1
1
1
2
0
1
2
1
0
1
1
1
2
2
1
2
0
1
1
1
1
1
2
1
1
3
1
2
1
1
1
1
1
0
1
0
2
2
1
1
1
1
2
1
0
2
1
2
1
0
1
1
1
2
2
0
1
1
0
0
2
0
1
0
1
0
2
0
1
0
2
1
1
0
0
1
1
2
1
1
1
0
1
1
2
2
0
1
3
0
1
1
1
2
2
1
1
1
2
1
1
2
1
1
1
3
2
0
1
1
2
1
2
1
1
1
1
1
1
1
1
2
0
2
1
1
1
0
1
1
1
1
0
0
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
2
0
1
1
1
2
1
0
0
1
2
1
1
2
2
2
2
1
1
1
1
1
1
1
2
1
2
1
0
1
1
0
1
1
1
1
1
0
1
1
1
1
1
1
0
1
1
2
0
2
1
1
0
1
2
0
1
0
1
1
1
1
1
1
2
1
1
0
0
0
1
1
2
2
1
2
1
2
1
2
0
1
1
1
1
0
3
1
1
1
1
2
1
1
1
1
1
1
1
0
2
1
1
2
1
0
0
1
2
1
1
1
1
0
1
2
2
2
1
0
1
1
1
1
1
2
0
2
1
0
1
2
0
1
2
1
2
1
1
1
0
2
2
1
1
1
0
1
1
0
1
1
0
1
1
2
0
2
1
1
0
1
0
2
1
1
2
1
1
0
1
1
1
1
2
0
1
1
1
0
2
2
1
0
1
1
1
1
2
2
0
1
1
1
2
0
0
1
2
1
2
0
0
1
1
1
2
1
1
1
1
2
1
1
1
1
1
2
2
0
1
2
1
1
1
1
0
1
1
1
1
2
1
1
1
0
2
1
2
1
2
1
1
1
1
0
1
1
1
2
2
1
1
1
1
1
1
1
1
1
0
1
1
2
2
2
1
1
0
1
1
2
1
0
2
1
1
0
2
2
1
1
1
1
1
1
1
0
1
1
0
2
1
1
1
0
0
1
1
1
1
0
1
1
1
0
1
2
1
2
1
1
1
1
1
0
2
1
2
1
1
1
1
2
1
1
1
1
2
2
2
2
1
2
2
1
1
2
1
0
2
1
3
1
0
1
1
0
1
1
2
1
0
2
1
0
1
1
1
1
1
0
1
2
2
0
2
2
1
1
2
1
1
1
1
2
1
1
1
1
0
0
1
0
2
1
1
2
2
2
0
1
2
1
2
1
2
1
1
2
2
2
0
1
1
1
1
2
0
0
1
1
1
1
1
2
2
2
0
2
2
1
1
1
2
1
0
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
0
0
0
1
1
1
0
1
2
1
1
2
0
1
1
0
0
2
1
2
1
0
1
1
1
2
0
1
1
1
1
2
1
1
2
0
2
2
1
0
1
2
1
1
1
0
1
2
1
0
3
1
1
2
0
2
1
1
0
1
1
0
1
2
1
2
1
1
2
1
1
1
1
0
2
0
0
1
1
1
1
1
2
1
1
1
2
2
0
1
2
1
1
2
1
1
2
1
1
1
1
2
4
0
1
1
1
2
2
0
1
1
1
1
1
2
1
1
0
2
1
0
1
1
1
2
2
2
1
1
1
0
1
2
1
0
0
0
2
2
2
0
1
2
2
0
0
1
0
2
0
1
1
1
2
0
0
1
2
2
1
2
2
0
1
0
1
2
0
2
2
2
1
2
1
0
1
1
2
1
1
2
1
1
1
1
3
1
1
1
1
0
2
1
1
2
1
1
0
0
1
1
1
0
1
1
1
0
1
0
0
2
0
2
2
1
2
0
1
1
1
1
1
1
0
1
0
1
0
1
1
1
0
1
1
0
0
0
1
1
0
1
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
0
1
1
1
1
0
2
0
1
1
2
2
2
0
1
1
2
1
2
2
1
1
2
1
1
1
1
1
1
2
0
2
0
1
1
1
0
1
1
1
1
1
1
4
1
1
2
1
1
1
0
2
1
0
1
1
1
1
1
1
2
0
1
1
1
1
2
2
3
1
1
1
1
1
2
1
0
2
2
1
1
1
1
1
2
1
1
1
1
1
0
0
1
3
1
1
1
1
1
1
0
2
2
1
0
1
1
1
1
2
1
1
0
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
2
2
2
1
1
1
1
2
1
2
2
2
1
1
1
1
1
1
1
0
0
1
1
0
1
1
1
2
1
1
1
1
1
1
2
1
2
1
2
1
1
1
0
1
1
1
3
2
0
0
1
1
1
0
1
0
1
1
1
2
1
2
1
1
0
0
2
1
0
1
2
2
2
1
2
1
2
2
1
1
1
1
1
2
0
1
1
2
2
2
1
1
1
1
0
0
1
0
1
1
1
1
2
1
1
1
1
1
1
1
0
2
1
2
1
1
1
2
2
2
2
0
0
1
1
1
1
1
0
2
1
2
2
1
1
0
1
1
0
1
1
0
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
0
1
2
0
2
2
2
2
1
1
2
1
2
1
0
1
2
2
1
2
1
0
1
1
2
1
1
1
1
1
0
4
1
1
1
0
1
2
1
1
0
1
1
1
1
1
1
1
2
2
1
1
0
1
1
0
1
1
2
2
1
1
1
2
0
1
1
1
2
1
2
1
1
0
1
1
1
1
0
1
0
1
2
1
2
2
2
1
0
1
1
0
0
1
2
1
1
2
1
0
0
1
0
1
2
1
2
1
1
0
2
2
1
2
1
1
2
1
0
0
2
1
1
1
1
1
1
2
1
0
1
2
1
2
2
1
2
2
1
1
1
2
0
1
1
1
1
1
1
0
1
1
1
1
1
0
1
1
1
1
2
1
1
1
1
0
2
1
1
2
1
1
1
1
2
2
1
2
2
2
1
1
1
2
0
1
1
1
1
0
1
1
0
0
1
1
1
2
1
1
1
2
1
1
0
1
2
1
1
1
1
0
0
1
2
2
1
0
0
1
0
1
1
2
1
1
0
2
1
2
1
0
1
0
1
1
2
2
1
1
1
0
2
1
1
1
1
1
1
1
1
2
1
2
1
0
1
1
1
1
3
0
1
0
1
0
1
1
1
1
1
1
3
1
1
1
1
1
1
1
0
1
0
0
1
1
2
1
2
2
1
1
2
1
1
1
2
1
1
2
1
2
2
1
0
2
2
1
1
1
0
2
2
1
1
1
2
2
1
0
1
2
0
1
2
1
1
2
3
2
1
1
1
2
2
2
1
0
1
0
2
2
1
1
1
1
1
2
2
2
2
2
0
1
1
1
2
1
2
0
2
2
1
1
2
1
0
3
1
1
1
2
1
2
2
1
2
2
1
2
1
1
0
1
1
0
2
1
0
0
2
1
2
0
1
2
1
1
1
2
1
1
1
0
2
0
2
1
2
2
0
1
1
1
1
1
2
0
1
1
1
0
1
1
1
1
0
1
1
1
1
2
1
1
1
2
0
1
1
1
0
1
1
0
0
1
1
2
1
1
1
0
0
2
1
2
1
2
1
2
1
1
1
1
1
1
1
1
2
1
0
1
0
2
1
1
0
1
0
1
1
0
1
2
1
0
1
1
1
2
1
1
0
0
2
2
1
1
0
0
1
0
0
1
1
1
1
1
1
2
2
1
1
1
2
1
0
0
2
1
1
1
1
0
1
2
2
2
0
1
2
1
1
0
1
2
2
1
0
1
2
1
1
1
0
1
1
1
1
1
1
2
2
1
1
1
1
1
2
0
1
1
1
2
1
0
0
0
1
2
0
1
1
2
3
1
1
0
1
0
1
1
1
1
1
4
1
2
0
2
1
1
1
2
2
1
2
1
1
2
1
2
0
2
1
1
0
2
1
1
1
1
1
0
1
1
2
1
1
1
1
1
1
2
1
0
1
1
1
1
3
0
1
2
1
2
1
0
2
1
1
2
1
1
2
1
1
1
1
1
1
1
0
1
2
2
2
1
1
0
2
1
1
0
1
2
1
1
0
0
1
1
0
0
1
1
1
1
2
0
3
2
1
1
1
2
1
1
0
1
2
1
2
2
1
1
0
2
1
0
1
1
2
2
1
1
0
1
0
1
0
1
0
1
2
1
1
0
2
0
1
0
2
1
1
2
0
1
2
2
1
1
1
0
2
1
1
2
0
2
2
2
2
1
2
1
2
1
1
1
2
1
2
1
0
1
2
1
1
2
0
1
2
2
1
1
1
1
1
1
0
1
1
1
0
1
1
2
1
1
3
0
1
1
2
2
1
2
1
1
1
2
1
2
1
2
1
2
1
1
2
2
1
2
2
1
1
1
1
1
1
1
2
1
0
1
1
1
1
1
1
1
2
1
1
1
1
2
2
1
0
1
2
3
0
2
1
1
0
1
1
1
1
2
0
1
2
1
0
1
2
0
1
0
2
1
7
0
1
1
1
0
2
2
1
1
0
2
1
1
0
1
1
1
0
1
2
2
2
1
1
0
2
1
2
0
1
1
1
2
0
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
0
0
1
1
1
1
2
0
2
1
1
2
2
0
1
0
1
2
2
1
1
1
1
1
2
1
1
1
0
1
1
1
1
1
1
1
0
1
1
0
1
1
1
1
2
0
2
1
0
1
1
2
0
1
1
1
1
2
1
1
2
2
2
1
1
1
0
0
1
0
0
1
2
1
1
1
2
1
1
2
1
1
1
2
2
3
1
1
1
1
2
1
1
2
2
1
1
1
1
2
1
1
1
1
2
1
2
1
1
0
0
1
1
2
1
0
1
1
2
1
2
2
1
1
2
1
1
1
0
0
1
1
1
1
1
2
2
0
1
1
1
0
1
1
2
2
1
2
1
0
1
0
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
0
2
1
2
1
1
1
1
2
1
0
2
1
1
1
0
2
1
1
2
1
0
0
1
0
1
1
1
2
2
1
1
1
2
1
0
1
1
2
1
1
2
1
1
0
1
2
2
2
0
2
0
1
2
1
1
0
1
2
1
1
1
2
1
2
0
1
2
1
1
1
1
0
1
1
1
1
1
2
1
1
1
1
1
0
1
0
1
0
0
1
1
1
1
1
0
1
1
1
1
1
0
1
2
1
2
1
1
0
0
1
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
0
2
1
2
2
1
0
1
1
1
0
1
1
1
1
1
1
1
2
1
0
1
1
0
2
1
0
2
1
2
1
0
1
1
0
0
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
0
1
1
1
0
2
0
2
2
1
2
1
1
1
2
1
2
1
1
0
1
1
2
1
1
1
1
1
1
2
1
1
2
1
1
1
0
2
2
1
0
2
2
1
1
1
0
1
1
1
2
1
1
1
1
2
1
1
1
2
1
1
1
0
0
2
0
1
1
2
1
1
0
2
2
1
0
3
1
1
1
2
2
1
0
1
2
0
1
1
1
1
1
2
1
1
0
1
1
1
0
0
0
1
1
1
1
1
0
2
2
1
1
2
1
1
1
0
1
2
2
1
1
1
0
1
2
2
1
1
1
2
1
2
1
1
1
1
1
1
0
2
2
1
1
0
0
1
1
2
0
3
1
1
1
1
2
1
0
0
1
2
1
0
1
0
2
2
1
2
1
1
1
2
1
0
1
1
2
1
2
1
1
1
2
1
1
2
1
0
1
1
1
2
2
2
2
1
1
1
1
2
1
1
2
1
1
1
0
1
1
2
1
1
2
2
0
2
1
2
1
1
2
1
1
1
1
2
2
0
0
1
0
1
0
1
2
0
0
1
1
1
1
3
1
2
2
1
1
0
1
0
2
2
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
2
0
1
3
1
2
1
1
1
1
0
1
1
2
1
1
1
2
1
0
1
2
1
2
2
6
1
1
1
0
2
1
1
0
2
1
2
1
0
1
1
1
1
1
1
1
1
1
1
2
1
0
2
1
2
2
1
2
2
2
1
0
0
1
0
1
0
1
1
2
0
1
1
2
0
0
2
1
1
1
2
1
1
0
1
1
1
1
1
0
0
2
1
0
0
1
1
1
1
0
2
0
0
1
1
2
1
2
0
1
2
1
1
1
1
0
2
1
2
1
0
1
1
1
1
1
2
1
1
1
1
1
0
1
1
2
1
2
1
1
1
2
1
0
1
2
1
1
1
1
0
1
1
1
0
3
2
0
0
2
1
2
2
1
1
1
1
1
2
0
1
1
1
1
2
1
2
0
1
1
1
2
0
1
0
1
1
1
1
1
0
2
1
0
0
1
1
1
0
2
2
0
2
2
0
1
1
1
0
0
0
1
1
1
0
0
0
1
1
0
0
1
0
1
1
1
2
1
1
0
2
1
2
2
1
1
1
1
2
1
2
1
0
0
2
1
2
1
2
1
1
2
1
0
1
0
2
1
1
0
1
2
0
1
1
1
1
1
0
1
1
0
1
0
1
2
1
0
1
0
1
0
1
0
2
1
2
1
1
0
2
1
1
1
2
1
1
2
2
1
1
2
1
0
1
2
1
1
1
0
0
2
1
3
1
1
0
2
2
1
0
2
2
1
2
0
2
1
1
0
1
1
0
2
1
1
2
1
1
1
0
2
1
0
1
0
1
1
1
2
2
2
1
2
2
2
1
1
2
1
1
2
1
2
1
1
2
1
1
0
1
1
1
1
1
1
1
1
1
1
1
0
1
1
0
1
1
0
1
1
2
1
1
1
1
1
1
0
0
2
2
1
1
1
1
1
1
0
1
1
1
1
2
1
1
0
2
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
2
0
0
1
2
0
1
1
1
0
1
1
1
1
1
1
1
0
1
1
1
0
1
1
1
1
1
1
1
1
0
1
1
2
1
1
0
1
1
0
0
1
1
1
1
1
2
1
0
1
2
1
2
1
1
1
0
1
0
1
0
1
2
0
0
1
1
2
2
1
0
1
1
1
1
2
1
2
1
1
1
1
1
2
1
2
0
2
1
0
1
0
0
0
1
3
1
0
2
1
1
2
0
1
2
1
1
1
1
1
1
1
2
1
0
2
1
1
1
1
2
0
0
2
2
1
2
1
2
0
0
2
2
0
2
1
2
1
1
1
2
1
1
1
1
2
1
1
1
2
1
0
0
1
1
2
1
1
0
2
1
0
1
1
1
0
0
1
2
0
2
1
2
0
0
1
1
1
0
2
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
2
0
1
1
2
2
2
2
1
0
0
2
1
1
0
1
0
1
1
4
1
2
2
0
1
1
1
1
1
1
1
2
2
2
2
0
1
1
1
2
1
1
1
0
1
2
1
1
0
1
1
0
1
1
1
1
1
1
2
0
1
1
1
2
2
2
2
0
2
1
0
1
1
1
1
1
0
1
1
0
1
1
2
1
1
1
1
2
0
1
1
1
2
1
1
1
1
1
1
0
1
1
2
2
1
2
2
1
1
1
1
1
1
2
0
0
1
1
0
2
1
1
1
0
1
2
1
1
1
1
2
2
1
0
1
1
2
1
0
0
0
0
2
1
1
0
1
1
1
1
2
2
1
1
2
1
0
0
3
1
1
1
1
1
1
1
1
1
1
2
1
2
0
1
2
1
1
1
1
1
0
0
4
0
1
0
1
1
2
1
1
1
1
1
1
2
1
1
2
2
1
1
1
0
2
2
1
0
1
1
2
1
1
2
0
1
1
0
2
1
1
1
2
1
1
0
2
2
1
1
0
1
1
1
1
1
1
1
1
1
0
1
1
0
1
1
0
1
1
2
0
1
2
1
1
1
1
1
2
0
1
1
0
1
1
0
1
1
0
1
1
1
1
1
2
2
2
2
1
2
5
2
2
0
1
1
1
1
1
0
1
2
1
1
1
1
0
0
1
0
1
1
0
1
1
6
1
1
1
1
2
1
1
1
1
2
1
1
0
2
1
1
1
2
1
1
1
1
2
2
1
1
1
1
0
1
1
1
2
2
2
1
1
0
1
1
2
0
2
1
0
1
1
1
2
2
1
0
1
1
0
1
1
1
2
1
1
0
2
1
0
1
1
1
2
1
1
0
1
2
1
2
1
1
2
2
2
0
0
1
1
1
0
1
1
0
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
0
1
2
2
2
1
2
3
1
2
0
2
1
1
1
2
1
0
1
1
0
1
0
0
2
0
1
0
0
1
0
1
1
1
0
1
0
2
1
1
1
2
1
1
0
2
0
2
1
1
2
1
3
1
1
1
1
1
1
1
1
0
1
1
2
2
1
0
2
0
1
0
1
1
2
0
2
2
1
1
2
2
2
2
1
2
0
2
2
1
1
1
1
1
2
2
2
1
0
2
2
1
2
1
0
1
0
1
0
1
1
1
2
1
1
1
0
2
1
0
1
0
0
1
2
2
1
1
2
1
1
0
1
1
1
2
1
0
0
1
2
1
2
2
2
0
1
1
2
1
1
0
1
0
1
1
1
1
1
1
0
1
1
1
2
2
1
2
1
2
1
0
2
2
1
0
1
0
2
2
0
2
1
1
2
1
1
0
0
2
2
1
1
1
1
2
0
1
1
1
1
0
0
1
1
1
1
2
2
2
1
2
1
1
1
1
1
1
2
1
1
1
2
2
1
1
2
0
1
1
1
0
1
2
0
1
2
1
2
0
2
2
1
2
1
1
1
1
1
1
1
1
3
2
2
1
1
0
0
1
2
2
1
2
0
1
1
1
1
2
1
1
1
0
2
2
1
0
0
1
2
1
0
1
0
1
2
1
0
0
1
1
0
0
2
2
2
2
1
1
1
2
2
2
1
0
1
2
1
0
1
1
1
1
1
1
2
2
1
1
0
0
1
1
2
0
0
2
1
2
1
1
1
2
1
2
1
1
0
1
2
2
0
1
2
0
1
2
1
1
1
1
1
1
1
2
1
0
1
1
1
0
2
2
2
1
1
1
1
1
1
2
1
2
1
1
1
1
2
1
2
1
0
1
3
0
2
1
2
1
1
1
2
1
0
2
0
2
1
1
1
0
1
1
0
1
1
0
2
0
0
1
1
1
2
1
1
1
0
1
1
1
1
1
2
1
1
0
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
2
1
1
1
1
1
1
1
1
2
1
0
1
1
1
0
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
2
1
1
1
1
1
1
2
0
1
1
1
2
1
1
2
0
2
1
1
1
1
2
1
1
1
1
2
1
1
1
3
1
1
1
1
0
1
1
2
1
1
2
1
1
0
2
1
1
1
1
2
1
2
0
1
1
1
1
1
1
1
1
1
0
1
1
1
1
0
2
2
2
1
1
1
1
0
2
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
0
1
1
2
2
1
2
1
0
2
0
1
1
1
0
1
2
1
0
1
2
1
1
1
1
1
1
1
1
2
2
2
0
1
0
1
1
0
1
1
2
1
1
2
1
0
0
1
1
1
2
2
1
1
1
1
2
1
2
1
2
0
1
2
2
1
0
2
1
0
0
2
1
2
1
1
0
0
0
2
1
2
2
0
1
1
2
1
1
2
0
0
0
2
1
2
1
1
1
1
1
0
1
1
0
2
2
1
1
1
1
1
1
2
1
2
1
1
0
2
2
1
1
2
1
1
1
0
1
4
1
1
1
1
0
0
1
1
4
1
1
1
2
1
1
1
1
2
1
0
1
0
0
1
1
1
2
1
2
1
5
2
2
1
2
1
1
2
1
1
1
0
1
1
1
1
2
1
1
1
2
2
2
1
1
0
2
2
1
0
2
1
0
1
0
0
2
2
1
1
2
1
2
2
1
0
1
1
1
1
1
2
2
1
0
1
0
0
2
2
1
1
1
1
1
0
0
0
1
2
0
1
2
2
1
1
2
0
2
1
2
1
0
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
2
2
1
2
0
1
1
0
1
1
1
0
0
1
0
1
1
2
0
0
1
1
1
2
2
1
0
0
1
1
2
1
1
1
1
1
0
1
2
0
0
1
1
1
2
1
1
2
0
1
1
0
2
0
1
0
0
1
1
1
0
1
2
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
0
2
1
1
1
1
1
2
0
1
1
1
2
1
1
1
1
1
1
1
2
0
1
1
2
1
1
1
2
2
1
1
0
1
2
1
1
2
1
1
2
2
1
0
2
1
0
1
1
0
2
1
0
1
1
1
0
0
1
1
1
1
1
1
1
1
2
2
2
1
0
1
2
1
2
0
1
1
2
2
1
1
2
1
2
1
1
1
1
2
2
1
1
0
2
1
1
1
1
2
2
0
1
0
2
1
1
0
0
1
0
1
1
1
1
1
1
0
0
0
0
2
2
1
2
1
2
1
1
1
1
1
1
2
1
2
1
0
1
0
1
1
2
1
0
1
0
2
1
1
2
2
0
0
2
1
1
1
2
1
2
2
0
1
1
2
0
0
0
2
1
1
3
1
0
1
1
1
2
1
2
2
1
1
0
1
2
2
1
0
0
2
2
1
2
2
1
2
0
0
2
2
1
1
2
1
1
0
1
2
2
1
1
1
1
1
0
2
1
1
2
0
0
1
1
1
0
0
1
1
0
2
1
1
1
1
1
5
1
2
0
1
1
1
0
1
1
1
1
1
2
2
0
1
2
1
2
1
1
2
1
1
1
2
0
2
1
1
1
1
2
1
1
1
1
2
1
0
1
1
1
2
1
2
1
0
2
0
1
1
0
0
2
2
2
2
1
1
1
1
1
2
1
1
1
1
2
2
2
0
1
2
2
1
2
3
2
1
2
1
12
2
1
0
1
1
2
0
1
1
1
1
1
0
1
1
1
3
1
1
1
0
1
2
1
2
1
1
1
2
1
1
0
1
1
1
1
2
1
1
1
1
2
1
1
0
1
1
1
1
0
2
1
1
2
0
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
2
2
1
1
2
1
2
0
0
1
0
2
1
1
2
1
2
0
1
2
1
1
1
1
1
1
1
1
1
1
0
1
1
5
2
2
1
1
2
1
1
0
2
1
1
2
1
1
1
1
1
1
1
1
1
0
1
1
0
1
2
0
0
1
2
1
1
2
0
1
1
0
2
0
2
0
1
1
2
1
1
1
2
0
1
1
0
2
0
1
1
0
2
2
1
0
2
1
2
1
0
1
1
1
1
1
0
2
1
1
1
1
2
2
1
1
1
1
1
2
1
1
1
1
1
2
1
2
0
2
1
1
1
0
1
2
1
2
1
1
1
0
0
2
2
2
2
2
1
1
1
2
0
1
1
2
0
1
1
0
1
2
1
2
0
0
0
1
2
2
1
2
2
1
1
1
2
0
1
1
1
2
2
1
1
2
2
1
0
0
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
2
0
1
1
1
1
1
1
1
1
1
1
0
1
0
2
0
2
0
1
2
2
1
0
2
1
1
1
1
0
0
1
2
1
1
0
1
1
1
2
2
1
0
1
0
2
1
1
0
1
2
2
1
1
2
1
1
1
0
1
1
2
1
1
1
1
0
1
1
2
1
1
2
1
2
1
2
1
0
1
2
1
2
1
2
1
0
1
2
2
1
1
1
0
0
1
1
1
0
1
1
1
0
1
1
1
2
2
1
1
1
1
0
0
1
1
0
1
2
1
2
0
1
1
2
1
0
1
1
1
1
1
1
2
1
1
1
0
2
1
1
1
0
1
1
1
1
1
0
1
2
2
1
2
3
1
2
1
1
1
1
1
0
1
1
1
1
1
1
3
1
1
1
1
2
0
1
2
1
0
3
0
2
0
1
2
0
2
1
1
1
1
0
0
2
1
0
0
1
2
1
1
1
1
1
2
1
1
2
1
1
0
2
1
0
0
0
1
1
1
2
1
0
1
0
0
1
0
1
2
2
1
1
1
1
1
1
2
2
2
2
0
2
1
1
2
0
2
1
1
2
1
2
1
1
1
0
0
1
1
2
1
1
1
2
2
1
0
2
1
5
1
1
1
1
1
2
1
1
2
1
1
1
1
2
1
1
0
1
1
1
1
1
1
2
1
1
2
2
1
2
1
1
1
1
1
1
1
0
1
1
1
2
2
0
0
0
1
2
2
1
2
2
2
1
1
1
1
1
0
2
0
1
1
1
1
1
1
2
1
1
0
1
1
1
1
1
1
1
2
1
0
1
1
2
1
1
1
0
0
1
2
1
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
2
1
0
1
2
2
0
1
2
0
2
2
0
0
1
1
1
0
1
1
1
0
2
1
1
1
1
1
1
1
1
0
1
1
2
2
1
0
1
2
1
1
1
1
1
0
2
2
1
1
1
0
2
1
1
2
0
2
1
2
1
0
1
1
1
1
2
2
1
1
1
0
1
1
2
1
2
0
2
1
1
1
1
0
2
1
2
1
2
0
0
1
3
1
0
2
1
1
2
1
1
1
1
3
0
2
2
1
2
2
2
1
1
0
1
1
1
2
2
2
1
0
1
0
1
2
0
0
1
1
2
1
1
1
1
2
1
2
1
0
1
1
1
0
2
2
0
2
0
1
1
2
1
1
1
1
3
1
1
2
2
1
2
2
1
1
1
1
1
1
2
2
1
0
2
2
1
0
1
1
1
1
1
0
1
1
1
2
2
0
2
2
2
1
0
1
1
2
1
2
2
1
1
2
1
1
1
1
2
0
0
1
1
2
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
0
1
1
1
2
1
2
2
1
1
1
2
2
2
2
1
1
1
1
1
2
1
2
1
0
0
1
0
2
0
0
0
2
0
1
0
1
1
1
1
1
1
1
2
1
1
1
1
0
0
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
2
0
1
2
1
2
1
2
1
1
0
0
1
0
0
1
2
1
2
2
0
2
1
2
1
1
1
1
1
1
0
2
1
1
1
1
1
0
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
2
0
1
1
1
0
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
1
1
0
0
1
1
1
1
1
2
2
2
1
1
1
1
2
2
1
1
1
1
1
1
1
0
2
1
0
2
1
1
1
1
1
1
1
0
0
1
1
1
0
1
2
1
1
1
0
1
0
0
1
1
2
1
0
1
2
1
2
0
2
3
2
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
1
1
1
1
2
2
2
2
1
0
0
2
2
1
1
1
2
1
1
1
2
1
1
2
3
2
1
1
2
0
1
1
1
1
0
0
1
1
2
1
1
2
2
1
2
1
2
2
2
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
0
0
1
1
1
1
2
0
2
1
2
0
1
2
1
2
1
1
2
5
1
2
2
2
1
1
1
1
1
2
1
2
2
1
1
1
2
2
1
1
1
1
2
2
1
1
1
1
0
1
1
1
1
0
0
1
1
1
2
1
0
1
2
1
1
0
1
0
1
1
1
1
1
1
1
0
1
1
1
2
0
0
0
1
2
2
1
1
0
1
2
1
0
2
1
1
1
2
1
2
1
2
2
1
1
1
1
2
1
1
1
1
1
2
2
1
2
1
1
0
0
1
1
2
1
2
1
1
1
2
2
1
2
0
1
1
0
1
1
1
1
1
1
0
0
0
1
2
1
0
1
1
1
2
0
1
1
1
0
2
1
0
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
0
2
1
1
2
1
1
2
1
0
1
3
1
1
1
2
0
1
1
2
1
1
1
1
1
1
1
0
2
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
2
0
2
0
1
1
1
0
0
2
1
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
0
1
1
1
0
1
1
1
0
2
2
0
1
1
2
1
2
1
2
1
1
0
2
1
2
1
1
1
2
0
1
0
1
2
1
1
2
2
1
3
1
1
1
2
1
1
1
2
2
0
2
2
1
1
2
2
1
2
0
0
1
0
2
1
0
0
0
1
1
1
3
1
1
0
2
1
1
1
1
2
1
1
1
2
1
1
1
1
2
2
2
1
2
2
1
0
1
2
1
1
0
1
0
1
1
2
1
1
1
1
3
2
2
0
0
2
1
2
0
1
1
0
2
1
2
1
2
2
0
1
2
1
1
2
4
1
0
1
2
1
1
1
0
1
1
1
0
1
1
2
1
1
1
1
1
0
2
2
1
0
1
1
2
0
0
1
2
2
0
1
2
1
2
2
0
0
1
2
2
1
1
1
2
0
2
0
1
1
1
1
1
1
1
0
2
0
2
1
1
2
1
2
1
0
1
1
1
1
0
1
0
0
0
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
0
2
1
0
0
1
1
0
1
1
1
0
1
1
2
1
1
1
1
1
2
1
2
1
2
1
0
1
2
1
2
2
1
2
1
2
1
3
1
1
2
1
1
2
0
1
1
1
1
1
2
2
0
1
1
1
1
2
0
0
2
0
0
1
2
2
0
1
1
2
2
2
1
0
1
1
1
1
1
1
0
2
0
0
1
2
2
0
2
2
2
2
1
2
2
1
1
0
1
1
1
1
0
2
1
1
1
1
1
1
1
1
0
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
2
2
0
1
1
1
0
2
1
1
1
1
0
1
2
2
1
0
1
1
1
0
0
1
1
0
1
1
1
2
2
2
1
1
1
3
0
0
1
2
1
1
0
0
1
0
1
1
2
0
1
1
1
1
1
2
2
1
2
1
0
1
2
0
3
1
4
1
2
1
1
2
1
1
1
2
2
1
1
2
1
1
1
1
1
0
1
1
1
2
1
4
1
1
1
1
1
1
1
1
2
2
1
1
1
0
1
1
2
1
1
1
1
1
2
2
2
1
2
1
1
1
1
1
1
1
2
1
2
0
1
0
2
1
2
1
1
1
2
1
1
1
1
1
2
2
1
1
1
0
1
1
1
1
0
1
2
2
1
1
1
0
2
1
2
2
1
2
0
1
0
1
1
2
1
1
2
0
1
2
0
1
1
1
0
0
0
1
1
1
2
0
2
1
2
1
1
2
1
1
1
0
2
1
1
1
0
1
0
0
1
0
0
1
1
2
2
1
0
1
1
2
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
1
2
1
1
0
2
0
1
1
1
1
1
2
2
1
1
1
0
0
1
1
0
1
1
1
0
0
1
1
1
0
1
0
1
0
1
1
1
0
1
2
1
1
2
1
1
1
1
2
1
0
2
0
1
3
1
2
1
1
1
0
1
1
1
2
1
1
2
0
1
1
1
1
0
1
1
2
1
2
1
2
1
1
0
0
1
0
1
1
1
1
1
1
1
2
2
1
2
1
1
1
0
1
1
1
1
1
1
0
1
1
2
1
2
2
1
1
1
0
5
1
1
0
2
0
1
1
1
1
1
2
1
3
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
0
1
0
1
1
1
1
2
3
1
2
1
2
1
1
2
0
1
3
0
1
0
0
1
1
1
1
1
1
0
1
0
1
1
0
1
1
2
0
2
1
1
2
2
0
0
2
1
2
1
1
1
1
2
0
1
0
2
0
1
1
2
1
1
2
2
2
0
1
1
1
1
1
2
0
0
1
1
1
1
1
1
2
1
0
1
0
1
1
1
0
0
1
2
0
2
1
2
2
3
1
1
2
1
1
0
2
1
1
0
0
2
2
1
1
3
2
1
1
1
0
1
0
1
1
1
0
1
0
1
0
1
2
1
0
0
2
1
0
1
1
2
1
2
1
1
2
1
2
1
1
2
2
1
1
0
2
1
0
1
1
1
0
2
2
2
1
1
1
1
2
1
0
1
1
0
0
0
2
1
1
1
1
1
1
1
1
1
1
0
0
2
1
1
1
0
2
2
0
1
1
1
1
2
0
2
1
1
1
1
1
2
1
1
1
1
2
2
1
0
2
1
2
1
1
1
1
2
4
1
1
2
2
1
1
1
2
1
0
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
0
1
1
2
1
1
0
0
2
1
1
1
2
2
2
1
2
1
1
1
1
2
1
1
1
2
1
2
0
1
1
0
3
1
1
1
2
1
0
0
1
2
1
2
2
1
1
1
1
1
2
1
2
1
1
1
1
1
4
1
0
1
1
0
1
2
1
1
2
2
0
0
0
1
2
1
0
1
1
1
1
1
1
1
2
1
1
1
0
1
2
1
0
1
0
1
2
1
0
1
2
2
1
1
1
2
1
0
2
0
1
1
1
1
1
1
1
0
0
1
2
0
1
1
4
1
1
1
1
1
1
1
2
1
1
1
2
2
2
1
2
0
1
0
1
2
1
1
2
1
2
0
2
1
0
2
1
0
1
0
0
1
1
2
2
2
1
2
0
1
0
2
1
1
1
1
1
2
0
2
0
1
1
0
2
1
1
1
2
1
2
0
0
0
1
1
1
1
2
2
1
0
2
1
0
2
1
0
2
1
1
1
1
2
2
1
2
1
1
2
1
1
0
1
0
1
1
2
2
1
1
2
1
1
2
1
1
2
1
1
1
1
0
1
2
2
1
1
1
1
1
1
2
1
1
0
1
2
1
1
1
1
1
1
2
1
1
2
0
1
1
0
0
1
1
1
1
0
1
1
1
1
1
0
2
1
3
1
1
1
1
0
1
1
1
1
1
0
0
0
0
1
1
2
1
1
0
2
0
0
1
2
3
1
1
0
0
0
2
1
1
2
0
2
2
0
0
1
1
1
0
1
2
1
1
1
3
1
1
1
2
0
2
1
1
1
2
1
2
2
2
2
1
1
2
1
0
1
1
1
1
1
1
1
2
1
1
2
0
1
2
1
0
1
1
1
0
1
2
1
1
1
1
0
1
2
1
1
1
1
1
1
1
2
1
1
1
2
2
1
0
1
2
0
1
2
0
0
1
1
1
1
2
1
2
0
2
1
1
1
1
1
1
1
2
1
1
1
0
0
0
1
0
1
1
1
1
0
1
1
1
1
0
0
0
1
1
2
3
2
1
1
2
0
1
0
0
1
1
1
1
1
0
1
1
0
1
1
1
0
1
1
0
0
2
1
1
1
1
0
1
0
1
1
2
0
1
1
1
1
1
0
1
1
0
2
0
1
2
1
1
2
2
1
1
0
1
1
0
1
0
2
1
2
1
1
2
1
1
2
2
1
2
2
0
1
2
2
1
1
2
1
1
2
1
1
1
0
2
1
2
2
2
1
1
2
1
2
0
1
1
1
1
1
2
1
1
0
2
1
2
1
0
1
1
2
1
1
1
1
1
1
1
2
1
1
2
1
0
1
0
0
2
1
1
1
1
1
1
2
2
1
1
1
0
2
0
1
1
1
1
1
2
0
1
1
1
2
2
1
1
2
1
1
2
1
1
0
1
1
1
2
2
1
1
0
1
2
1
0
0
2
2
1
1
1
1
2
1
0
0
0
1
2
1
2
1
1
2
2
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
0
1
1
1
1
1
2
1
0
2
1
1
1
4
2
1
1
1
1
0
2
2
1
1
1
0
1
2
1
1
2
1
1
1
1
1
0
2
1
1
0
1
1
0
1
1
1
0
1
1
1
2
1
0
2
1
1
2
2
0
1
1
1
1
1
2
2
1
0
1
2
1
1
2
2
1
1
3
1
1
0
2
1
2
0
2
1
1
2
2
1
1
0
1
1
0
1
1
0
1
1
1
0
1
1
2
1
1
2
1
0
1
1
2
1
1
1
2
0
1
2
1
1
0
0
2
1
2
1
0
1
2
1
2
1
1
1
1
2
1
1
1
1
2
1
1
2
2
1
1
1
0
0
1
1
1
0
1
1
2
1
0
1
1
2
0
1
0
1
1
1
2
1
2
1
2
1
1
1
1
0
1
1
1
2
1
1
2
1
1
0
2
1
1
2
1
0
1
2
1
2
2
1
1
0
1
1
2
2
1
1
1
1
0
2
1
1
2
2
0
1
0
0
1
1
1
1
0
1
2
1
1
1
3
1
0
1
2
1
2
2
0
0
2
1
1
0
1
0
1
1
1
1
1
2
2
2
1
2
0
1
2
1
0
1
1
1
1
0
2
1
0
2
1
2
2
0
1
1
2
1
0
0
2
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
0
1
2
1
1
0
1
1
1
2
1
0
2
1
1
0
1
0
1
1
1
2
0
2
1
1
1
2
2
1
1
2
2
0
1
1
1
1
0
2
2
1
1
1
1
2
1
1
1
0
2
1
2
2
1
0
1
1
2
1
0
1
1
0
1
0
2
1
0
1
1
0
1
1
1
1
2
1
2
1
1
1
1
3
3
1
2
1
0
1
1
1
1
2
2
1
1
2
1
1
1
0
1
1
1
2
1
1
2
1
2
2
1
2
2
2
1
1
0
1
1
1
2
1
2
1
1
0
1
1
1
2
0
2
1
0
0
2
1
1
1
1
1
1
3
1
2
1
1
1
1
2
1
1
2
0
1
1
1
1
2
2
0
1
0
1
0
1
1
0
1
1
1
0
1
2
1
0
0
1
2
1
2
1
1
1
2
1
2
1
2
1
1
1
1
1
1
0
1
1
1
2
0
1
2
1
1
2
0
1
0
1
2
1
2
1
2
1
1
1
0
1
2
2
2
1
1
1
1
1
1
1
1
1
2
1
0
1
1
1
0
2
2
1
1
1
1
1
3
1
1
0
1
1
1
1
1
0
2
3
1
1
1
3
0
0
2
0
1
0
1
2
1
1
0
1
1
2
0
1
1
1
1
1
1
1
1
2
0
2
1
1
1
1
0
0
1
0
2
0
1
0
1
1
0
1
1
0
0
2
1
1
1
2
0
2
1
2
1
2
0
1
1
0
0
2
1
2
1
1
1
1
1
1
2
1
1
0
2
0
1
1
1
0
1
0
1
1
2
0
1
1
1
2
1
0
1
2
2
1
0
2
2
2
1
2
1
1
1
1
2
1
0
1
1
1
0
1
2
2
0
1
2
0
1
2
1
1
1
1
2
0
2
1
2
2
1
1
1
1
1
0
2
1
1
1
1
0
0
1
1
0
1
1
1
1
1
2
1
1
0
3
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
0
2
2
2
2
0
1
2
0
0
1
1
1
1
2
1
1
0
2
1
0
1
1
2
1
1
2
1
1
1
1
1
2
1
1
1
1
2
2
1
1
1
1
0
0
0
2
1
0
0
2
2
2
1
1
0
1
1
1
1
1
1
1
2
1
0
1
1
1
1
1
1
1
1
1
1
2
1
1
0
1
0
1
2
1
1
1
1
1
1
1
0
2
2
1
1
0
0
2
2
1
0
0
1
1
1
0
0
2
1
0
1
0
2
1
1
2
2
1
1
1
1
0
1
1
2
1
2
2
1
2
5
2
1
1
2
1
1
1
0
2
2
1
0
2
2
2
1
1
1
2
1
1
1
1
1
2
1
0
1
1
2
0
0
2
0
2
2
1
0
2
2
1
0
1
0
0
3
1
0
2
1
2
1
1
1
2
0
1
1
1
0
0
0
2
2
1
1
1
2
2
1
1
1
2
1
1
0
1
0
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
0
1
1
2
1
1
1
1
0
2
1
0
1
0
1
1
1
1
0
1
1
1
1
2
1
1
1
1
1
2
0
1
2
2
1
1
2
1
1
1
1
1
1
1
2
2
1
1
0
1
1
2
0
2
2
2
0
0
2
0
1
1
0
1
2
1
1
1
1
1
1
2
2
1
1
2
1
2
2
1
0
2
1
1
2
2
1
2
0
2
2
1
1
2
2
1
0
1
1
2
2
1
1
0
1
0
0
2
2
2
2
1
1
1
1
1
1
2
1
1
0
1
1
1
2
0
1
1
1
1
0
2
1
2
0
0
2
0
1
2
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
5
1
1
1
1
0
1
1
0
2
1
1
0
0
0
0
3
2
2
2
2
0
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
0
1
1
1
2
1
1
2
0
1
0
1
1
1
1
2
1
1
2
1
2
1
1
1
1
2
1
2
2
2
1
2
0
1
0
2
1
1
2
0
2
1
1
0
2
0
1
2
0
1
2
2
1
2
2
1
2
0
1
0
1
1
2
2
1
1
1
0
2
0
1
0
2
2
1
0
1
1
1
2
1
2
2
1
1
1
2
1
1
1
3
0
3
1
0
2
0
2
1
2
1
2
0
2
2
0
1
1
1
1
2
2
1
1
2
2
1
0
0
2
1
1
1
1
1
1
1
1
0
0
1
1
2
1
1
1
0
0
1
0
1
1
1
1
1
2
0
2
1
0
1
1
1
1
1
0
2
2
2
0
1
1
1
3
0
0
2
1
1
1
1
1
0
0
1
2
1
2
1
1
1
2
1
1
1
1
1
2
1
1
0
2
1
1
0
1
0
0
1
1
1
2
1
1
1
2
2
0
1
1
1
2
1
1
0
1
1
0
2
1
2
1
2
1
1
1
1
1
1
1
2
2
0
1
1
0
1
1
2
1
1
1
2
0
1
1
1
0
2
1
1
1
1
1
1
1
1
1
1
1
1
0
1
2
1
1
1
1
1
1
1
1
2
1
3
1
1
1
1
2
2
1
1
1
1
0
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
0
1
2
0
0
1
1
1
1
2
2
2
1
1
2
1
0
1
1
1
0
1
1
0
1
1
1
1
1
1
1
2
2
2
0
1
1
2
2
1
0
0
2
2
0
2
1
0
0
1
0
1
2
1
2
1
1
2
1
1
2
0
1
1
2
1
0
0
0
1
1
1
0
1
0
1
1
0
1
1
1
1
1
1
1
2
2
1
2
0
2
2
1
0
1
1
1
0
1
0
1
2
1
0
1
1
1
2
2
2
1
1
0
3
1
2
3
1
1
1
2
1
2
1
2
2
0
1
2
2
1
2
2
1
1
1
0
1
3
0
1
2
2
1
0
2
1
2
2
1
1
1
1
1
0
1
1
2
1
2
2
0
1
1
1
1
1
1
0
0
1
1
2
0
1
1
2
2
2
1
1
2
2
1
1
2
1
1
1
0
1
1
1
1
1
2
2
1
1
0
0
1
1
2
0
1
0
1
1
1
1
2
1
2
0
2
1
0
1
1
2
2
1
0
0
1
2
2
2
1
2
0
2
0
1
2
1
2
1
1
0
0
1
2
1
1
1
0
1
1
1
1
1
1
2
1
1
1
1
0
1
1
1
2
1
0
0
2
1
2
0
2
2
1
2
1
1
1
2
1
2
2
0
2
1
2
1
0
1
0
1
1
1
1
1
1
1
0
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
2
1
1
1
0
0
1
1
0
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
2
2
1
1
0
1
1
2
2
1
1
1
1
0
1
1
1
1
1
0
1
1
1
1
1
1
1
2
1
1
0
2
2
1
2
2
1
1
1
1
1
1
1
1
2
1
2
1
0
2
2
2
1
0
2
1
1
1
1
1
1
1
2
0
1
1
1
1
2
1
2
1
1
0
1
2
1
0
0
2
1
1
1
1
1
1
2
0
2
1
2
2
1
1
1
1
1
0
1
0
1
1
1
1
1
2
1
1
1
0
2
1
1
2
2
1
1
3
0
1
1
1
2
2
1
1
2
1
1
0
1
1
1
2
1
1
2
0
1
1
1
1
2
1
2
0
2
1
1
0
1
1
1
1
2
1
2
1
1
2
1
1
0
2
1
0
1
1
1
1
1
1
0
1
2
0
1
0
0
1
1
1
2
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
2
1
1
2
1
1
1
1
0
0
1
1
2
1
1
1
1
1
1
1
1
0
1
1
1
0
1
2
1
1
1
0
1
2
1
2
1
1
1
1
1
1
2
1
0
1
2
1
1
2
1
0
1
1
1
1
1
1
1
2
0
1
3
1
0
1
1
1
2
1
1
1
0
2
2
1
1
1
0
2
2
1
2
0
2
2
1
0
1
0
1
1
1
0
0
3
1
2
0
1
0
1
1
0
1
1
1
1
2
1
1
1
2
2
2
1
1
0
0
0
0
1
0
1
2
1
1
1
0
1
1
1
1
1
2
1
0
1
1
1
2
1
1
1
1
0
1
1
1
2
1
1
1
2
1
1
1
0
1
1
0
3
2
1
2
1
0
2
2
1
1
1
2
2
1
1
1
0
2
1
2
1
2
1
1
1
2
1
1
2
1
1
1
1
0
1
2
0
1
2
2
1
1
1
1
2
1
1
1
2
0
1
2
1
1
2
1
1
1
1
0
2
1
0
1
1
1
1
1
0
0
2
1
2
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
0
1
1
1
1
2
1
2
0
2
2
2
2
2
1
3
1
2
2
2
1
1
0
2
1
2
1
2
1
2
0
2
2
1
0
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
2
1
1
2
2
0
1
1
1
1
1
0
1
1
1
1
1
1
1
0
1
1
0
1
0
2
0
0
0
1
2
1
1
3
1
3
1
1
1
0
2
1
0
2
1
0
0
2
1
1
1
1
0
1
1
2
3
1
2
2
1
1
1
1
2
0
2
1
2
2
2
2
2
1
1
1
1
1
0
1
1
0
1
1
0
2
1
0
0
2
1
2
0
2
1
1
1
1
0
1
1
1
2
1
1
1
1
2
1
1
1
2
2
1
1
0
1
1
1
1
2
2
1
1
2
0
0
1
1
1
0
1
1
0
1
1
2
2
0
2
1
1
2
0
1
0
1
0
1
1
0
2
0
1
0
2
1
1
3
1
2
2
1
1
1
2
1
0
1
2
2
1
1
0
2
1
1
0
2
1
1
0
2
2
0
2
3
1
1
1
1
1
1
2
0
1
1
1
0
1
1
1
1
2
0
1
0
1
2
2
1
0
1
2
1
0
1
2
2
0
2
1
1
0
2
0
1
1
1
1
0
1
1
0
2
0
1
1
1
0
0
1
1
0
1
1
1
1
1
1
1
1
1
0
1
2
0
1
1
2
1
4
1
1
1
1
1
2
0
1
1
1
1
1
2
0
1
2
0
0
1
1
1
1
1
1
1
1
1
1
1
0
2
1
2
1
0
0
1
2
2
1
1
1
2
0
0
1
1
2
1
0
2
1
1
1
2
0
2
0
1
1
2
1
0
1
2
1
1
1
1
1
2
0
0
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
0
1
1
0
1
0
1
1
1
1
1
1
0
1
1
0
1
2
1
1
2
0
1
2
0
2
1
2
2
1
1
1
1
0
2
0
1
1
1
1
1
2
2
1
1
2
2
2
2
2
0
1
1
1
1
2
1
0
1
2
1
1
1
1
1
1
0
1
1
0
2
1
0
2
0
0
1
1
1
2
1
1
1
1
1
1
3
2
2
1
1
0
1
0
1
1
2
2
1
1
1
2
1
3
0
1
1
1
1
1
1
0
1
1
2
1
0
1
2
1
1
2
2
0
0
2
0
0
1
2
2
1
1
2
1
0
1
2
3
1
1
1
1
2
0
2
1
1
2
1
0
1
1
1
0
1
1
0
1
0
0
1
1
1
1
1
1
1
1
1
1
1
2
0
1
2
2
0
2
1
1
1
1
1
1
1
2
1
0
2
0
2
0
0
0
1
1
1
1
0
0
2
0
1
1
1
2
1
0
1
2
1
1
1
0
1
1
1
0
2
2
0
1
0
1
1
1
1
0
2
1
1
0
1
1
0
1
1
1
1
2
1
2
2
1
1
1
2
1
2
0
1
1
1
0
1
1
0
0
0
0
2
3
0
0
0
1
1
1
0
0
1
2
1
2
0
1
1
2
0
0
1
2
1
1
1
1
1
2
1
1
0
0
0
1
0
1
1
1
0
0
2
1
2
1
1
1
2
1
1
1
0
2
1
0
1
1
1
0
2
1
1
0
2
0
1
1
1
1
1
2
0
1
1
1
2
1
2
1
1
2
3
1
1
1
0
0
1
2
1
2
0
1
1
1
1
1
2
1
1
1
2
2
1
0
1
1
1
1
1
1
1
0
1
2
2
1
3
2
1
1
2
1
2
1
2
2
1
0
1
2
2
2
0
1
1
1
2
0
2
1
1
1
2
2
1
1
0
1
1
1
0
1
1
1
1
1
2
1
1
2
0
0
2
2
2
2
0
1
2
1
0
1
0
1
0
2
0
1
2
2
1
1
0
2
1
2
2
1
1
1
1
2
2
0
2
0
2
0
1
0
1
2
1
1
0
1
1
1
2
2
0
1
1
2
1
1
1
2
2
1
1
1
1
1
2
1
2
0
2
1
1
1
1
2
0
0
1
1
2
1
2
2
2
1
2
1
1
1
1
2
1
2
2
1
2
1
1
2
1
3
2
2
1
0
2
1
1
0
1
0
1
1
1
1
1
1
0
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
2
1
0
1
1
1
2
1
2
1
1
1
1
2
1
1
2
1
1
1
0
1
2
1
2
1
1
2
0
1
2
1
1
1
0
1
2
1
2
0
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
2
1
2
1
2
1
0
0
1
1
2
1
3
3
1
1
0
1
1
1
1
1
2
1
1
1
1
0
1
2
1
0
1
0
2
1
1
2
1
2
0
0
0
1
1
2
1
1
1
0
1
1
1
1
0
0
2
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
0
2
1
1
1
1
1
1
1
2
1
2
0
1
1
1
1
1
1
0
0
1
1
1
2
1
2
1
1
3
2
1
1
1
2
1
1
2
1
1
1
1
1
2
2
0
1
1
2
1
1
0
0
2
0
2
1
0
2
2
1
1
1
1
0
0
1
2
2
2
1
1
1
1
0
1
1
2
1
1
0
0
1
1
1
2
2
1
1
2
1
1
2
1
1
1
2
1
1
2
1
0
1
1
2
0
3
0
0
1
2
2
1
1
1
0
1
1
1
0
1
1
1
0
1
1
1
1
2
1
1
2
1
1
0
2
1
1
1
1
0
1
1
2
1
1
0
1
1
2
2
2
1
1
1
1
2
0
1
1
0
0
1
0
0
1
0
0
2
1
0
2
1
0
2
1
1
2
1
2
2
2
1
1
1
3
2
3
1
0
1
0
0
2
1
0
1
1
1
2
1
1
1
0
2
0
1
2
1
1
1
0
1
1
1
0
2
0
2
1
2
1
0
2
0
2
2
1
1
1
1
2
2
1
1
1
1
2
0
1
0
0
2
2
2
1
2
2
2
1
1
2
1
2
1
0
2
1
2
1
1
1
1
1
0
1
1
0
1
1
0
1
1
1
0
1
1
1
0
1
1
0
1
1
2
1
2
1
1
1
0
1
1
1
1
1
1
0
1
2
2
2
0
1
0
1
1
1
1
0
1
1
1
1
1
2
1
1
1
0
2
2
2
1
2
1
2
1
0
1
1
2
1
1
1
2
0
1
1
0
1
1
0
1
2
1
1
2
1
1
2
1
1
1
2
2
1
1
1
1
1
2
1
1
1
3
0
1
1
2
1
1
2
1
1
2
2
0
1
2
1
1
2
1
1
1
1
1
1
1
0
0
1
1
1
0
0
2
1
1
1
0
0
1
1
0
1
1
1
0
0
1
1
1
1
1
1
2
1
1
2
2
1
1
1
1
0
0
3
1
1
6
1
2
1
1
1
0
2
1
1
1
1
1
1
1
0
1
1
0
0
1
2
1
0
1
2
2
1
1
1
1
1
1
2
0
1
0
1
1
0
1
0
1
1
1
2
2
1
2
2
2
0
1
2
1
2
1
2
1
2
1
1
1
1
2
1
1
1
0
1
1
2
2
1
0
2
1
0
1
1
2
1
0
0
2
1
2
2
1
1
1
2
1
1
0
1
1
1
0
1
0
1
2
1
2
1
1
0
2
0
1
2
1
1
1
1
2
1
2
0
0
1
1
1
1
1
0
1
1
2
0
2
1
1
2
2
1
1
1
1
1
2
2
0
1
0
2
2
1
1
1
2
1
0
1
1
1
1
1
2
1
1
1
2
1
0
1
1
1
1
2
2
4
1
2
1
2
1
0
1
1
1
1
1
4
1
0
2
2
1
1
0
1
1
1
0
1
1
1
1
0
1
0
0
0
1
1
1
0
1
1
0
1
0
0
1
1
1
1
0
3
2
0
2
0
1
1
2
0
0
1
1
1
3
1
1
2
2
1
1
0
0
2
1
1
1
0
1
1
2
0
1
2
2
1
1
1
1
0
1
1
1
1
0
1
2
0
1
1
1
1
2
2
2
1
0
0
2
2
1
2
1
2
0
1
1
1
1
1
1
0
1
1
2
1
2
1
0
0
2
0
1
0
2
2
1
1
0
0
1
0
0
1
1
1
1
1
1
1
2
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
2
1
2
2
1
2
0
1
2
0
1
0
2
2
2
1
2
0
1
1
1
0
1
1
0
0
1
2
1
0
2
1
1
1
1
1
2
3
1
1
0
1
1
1
0
0
2
2
0
0
2
1
0
1
0
2
1
0
1
2
1
2
1
2
0
1
1
3
2
0
2
1
1
0
1
1
0
0
1
0
1
1
1
1
0
2
1
1
0
2
1
1
1
1
1
1
0
1
2
0
1
1
4
1
1
1
0
2
2
1
1
1
1
1
0
1
1
2
1
2
1
0
2
2
1
2
1
2
2
0
1
1
1
2
0
2
2
2
2
1
1
1
1
0
1
2
0
2
1
1
1
2
1
1
2
1
1
0
1
1
1
1
0
1
1
1
2
1
1
1
0
1
1
2
1
1
1
1
1
1
2
1
1
2
1
1
2
0
2
1
0
3
2
1
2
1
1
0
1
0
1
2
0
1
1
0
1
1
1
2
2
1
2
2
0
1
0
0
1
1
1
2
2
1
1
1
1
1
0
1
1
1
2
2
0
0
0
1
1
1
1
0
0
1
0
1
0
1
1
1
0
2
1
1
2
2
1
0
1
1
1
2
1
2
1
1
2
1
1
2
1
1
1
2
1
2
0
1
1
1
1
1
1
0
1
2
2
0
0
2
1
1
2
0
2
1
1
2
0
1
0
0
0
1
1
1
1
1
1
0
1
1
1
1
1
1
1
2
2
1
6
1
1
2
2
1
2
0
1
2
0
2
1
2
2
1
2
2
0
2
0
2
1
1
1
0
1
1
1
1
1
2
0
2
1
0
2
1
0
1
2
1
0
1
1
0
0
1
1
0
1
0
1
1
1
1
1
0
0
0
2
1
0
1
0
1
1
1
1
1
1
1
1
1
0
1
1
1
2
1
2
1
2
1
1
1
0
1
0
1
2
1
1
1
0
0
1
0
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
0
1
0
0
2
1
1
1
1
0
1
1
1
1
1
0
1
1
2
1
0
1
2
1
2
1
1
0
1
1
2
0
1
1
0
1
1
1
2
2
1
1
2
1
1
1
2
0
1
2
1
1
2
1
1
2
1
0
1
1
1
1
1
1
1
1
2
0
0
2
0
0
1
2
1
0
1
0
1
1
2
2
2
1
2
0
0
1
1
1
0
0
1
1
1
1
0
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
0
2
1
1
0
1
1
1
2
1
1
1
0
0
1
1
0
1
1
2
1
2
1
0
1
1
1
1
1
2
2
1
1
2
1
0
2
1
1
0
1
0
1
1
1
0
1
1
2
1
2
1
0
0
1
1
1
2
2
2
1
1
2
0
0
1
1
2
1
2
1
1
2
1
1
1
0
0
2
2
0
0
1
1
2
1
0
2
1
0
1
2
0
0
1
1
2
2
1
2
2
1
1
1
0
1
1
1
2
2
1
0
0
1
0
2
2
1
1
1
2
2
2
1
2
1
0
1
1
1
0
1
1
2
0
1
0
1
1
0
1
1
1
1
2
0
2
2
1
2
2
0
1
1
1
1
1
2
1
0
0
2
1
1
0
1
1
1
1
2
1
2
1
1
1
0
1
1
1
1
0
1
1
1
1
1
1
2
1
2
2
1
2
0
2
0
1
1
1
1
1
0
1
1
2
0
1
0
1
1
1
1
1
1
1
1
1
1
1
0
5
2
2
2
0
1
3
2
1
1
1
0
2
1
1
2
2
1
2
2
1
1
2
1
0
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
0
2
1
1
1
1
1
1
2
2
1
0
1
1
1
3
1
1
0
2
2
1
1
1
1
2
2
1
0
1
1
2
0
1
0
2
1
1
1
2
1
2
1
0
1
0
1
2
1
1
1
2
0
1
0
1
1
2
1
7
2
2
1
2
1
1
2
2
1
2
1
0
2
1
2
1
0
1
0
1
2
1
1
1
0
1
1
2
2
1
1
0
1
1
1
1
1
1
2
1
2
2
0
2
1
2
1
1
2
2
2
1
1
2
1
2
1
1
0
2
0
2
1
0
0
3
2
2
1
2
2
1
2
1
1
2
1
2
0
2
1
1
1
0
2
3
1
2
1
0
0
0
0
1
0
2
1
2
1
0
0
1
2
1
1
1
2
1
1
1
0
0
1
1
0
1
1
2
1
2
2
1
1
1
1
1
0
2
1
2
2
2
0
2
1
1
1
0
1
1
1
1
2
0
0
2
1
1
0
2
0
1
1
1
0
2
2
0
0
3
2
0
1
0
2
1
1
1
1
2
1
1
1
1
2
2
2
1
1
0
1
1
1
2
1
2
0
2
2
0
0
2
1
0
2
0
0
1
1
1
0
1
1
1
1
2
2
1
1
1
1
0
1
1
1
1
0
1
2
1
0
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
0
2
0
1
2
1
1
0
2
1
0
1
2
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
1
1
0
2
2
2
1
1
1
1
1
2
1
1
1
2
2
1
1
1
0
2
1
0
0
1
2
1
0
1
1
0
1
2
1
1
1
1
0
0
1
1
0
2
1
2
1
1
1
1
1
1
1
2
1
0
0
1
1
2
1
2
1
2
0
1
2
1
2
1
1
1
2
1
1
2
2
1
2
1
2
0
2
1
1
0
1
1
1
1
1
2
0
0
0
1
1
1
2
1
1
2
1
1
1
1
1
1
1
2
1
0
0
2
0
1
1
0
1
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
2
2
6
2
0
2
2
1
1
0
2
1
1
1
1
1
2
0
0
1
1
1
1
1
1
1
1
0
1
1
1
1
2
1
0
2
1
1
1
1
0
1
1
1
1
0
2
0
1
1
2
1
1
2
1
1
1
1
1
2
2
1
1
2
1
0
1
1
1
2
1
1
1
1
2
1
1
1
1
1
2
2
1
1
1
0
1
2
2
1
1
4
1
1
1
1
2
1
1
1
2
1
1
0
1
1
1
4
0
1
1
0
1
2
0
0
2
2
1
2
1
1
1
1
1
1
1
0
0
1
1
1
1
0
1
1
2
0
2
1
2
1
1
0
1
1
1
1
2
1
1
0
1
2
2
1
1
1
1
2
1
2
1
1
1
1
0
1
0
2
2
1
1
1
1
1
2
2
1
1
0
2
1
1
0
2
2
1
1
1
1
2
2
1
1
1
1
1
0
0
0
0
2
0
1
1
1
2
1
2
1
1
1
0
1
2
1
0
1
1
1
1
1
1
1
1
0
0
1
0
1
1
1
2
1
1
1
1
0
1
0
2
1
2
1
1
2
0
1
1
3
1
2
1
1
1
0
3
2
2
1
0
1
1
1
0
1
2
1
1
1
0
1
2
1
2
2
0
2
2
2
2
1
1
1
0
1
1
1
1
2
0
2
0
1
2
1
1
1
1
1
0
1
1
1
2
0
2
0
0
3
1
1
1
1
1
1
1
2
1
2
1
1
0
0
0
2
0
1
2
1
1
1
2
1
1
1
1
0
2
1
2
2
2
1
2
3
1
1
2
1
1
0
1
1
1
1
3
0
1
1
1
2
2
2
1
0
0
2
1
1
1
0
1
1
1
1
1
1
1
1
1
1
3
1
1
1
1
0
0
0
1
1
0
1
1
0
2
1
2
1
2
1
1
0
2
1
0
1
1
1
0
2
2
1
0
1
1
2
2
1
1
2
2
1
2
2
2
1
1
2
1
1
9
1
1
1
0
1
0
2
1
1
2
1
2
1
1
1
1
1
2
1
1
2
2
1
1
1
1
2
1
2
1
1
2
1
2
0
1
1
1
1
0
2
1
1
1
1
0
2
1
1
0
2
1
2
1
1
2
2
1
2
1
1
2
2
1
1
0
1
0
2
1
2
2
1
1
0
1
0
2
2
1
1
1
0
1
1
1
1
1
2
0
2
1
0
1
1
0
2
1
2
2
1
0
1
1
2
0
1
0
1
3
1
1
1
1
0
1
1
1
1
1
1
1
0
2
1
0
1
2
1
1
1
2
1
0
1
0
0
2
1
2
1
1
1
1
0
0
1
2
1
1
4
1
1
1
1
2
1
2
1
1
0
1
1
0
2
0
1
1
0
0
0
0
0
1
1
0
0
2
1
1
1
0
1
1
2
1
1
1
1
1
1
1
1
0
1
1
0
1
2
2
2
1
0
1
1
1
1
1
1
1
1
1
1
1
0
1
0
1
1
1
1
1
2
1
2
2
2
0
1
1
1
1
1
2
1
2
1
1
1
2
2
0
2
1
0
0
1
1
0
1
1
0
0
2
1
1
2
1
1
2
2
2
2
3
1
2
1
2
1
0
1
1
1
1
1
2
1
0
2
0
1
1
1
0
2
0
0
2
1
1
0
1
2
1
2
2
2
2
0
1
1
2
1
2
0
1
1
1
1
2
1
0
1
1
0
1
1
1
2
1
1
0
1
2
2
1
2
2
2
1
0
1
2
1
1
1
1
0
1
0
2
1
0
2
0
2
2
2
2
2
1
0
1
1
1
1
0
1
1
1
1
1
2
2
0
1
0
1
2
1
0
1
1
1
1
0
1
1
0
1
1
0
2
1
1
1
1
1
1
2
1
1
0
2
2
0
1
0
1
1
1
2
1
2
1
3
2
2
1
1
1
1
2
1
0
1
0
1
2
1
2
2
1
0
1
1
0
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
0
1
0
1
2
2
1
1
1
0
2
1
1
2
0
0
2
2
1
2
1
1
1
2
1
1
1
1
0
1
1
1
1
0
1
1
2
0
1
1
1
1
1
0
2
0
1
1
1
4
1
1
0
1
0
0
1
1
2
1
0
2
2
1
1
1
2
2
2
2
0
1
0
1
2
1
2
1
2
0
1
2
1
1
1
1
0
1
0
2
1
1
1
2
2
1
1
0
0
1
1
1
2
1
2
2
1
1
0
1
1
2
1
1
0
0
0
2
1
1
0
1
1
1
0
1
1
3
1
1
2
1
1
2
1
2
2
2
1
0
0
1
1
1
1
2
1
2
2
0
2
1
1
2
2
2
1
2
2
1
2
1
1
2
0
2
1
1
0
0
0
1
1
1
0
1
1
1
1
1
2
1
1
0
2
2
1
1
2
2
1
1
2
1
2
2
0
2
0
1
1
1
1
2
1
1
2
1
1
1
1
1
0
2
2
0
2
0
1
0
0
0
1
1
1
2
1
3
2
2
2
1
1
1
1
1
1
0
0
1
2
1
0
2
1
1
0
1
1
1
2
1
1
2
0
1
1
1
0
1
1
2
1
1
0
1
2
1
1
1
1
1
2
2
1
1
2
0
1
1
1
1
1
2
1
2
1
1
2
1
1
1
2
2
1
1
1
1
1
1
2
0
1
0
0
2
2
2
1
1
0
1
1
1
1
2
1
1
1
0
1
1
0
0
1
1
2
1
1
1
1
1
1
2
2
1
1
1
0
1
1
1
1
1
1
0
1
1
2
1
1
1
1
2
1
2
2
1
1
0
1
1
1
0
0
1
1
1
0
1
2
1
1
1
2
1
0
1
1
3
1
1
1
2
2
1
0
2
1
1
0
1
0
2
2
1
1
0
0
2
1
0
0
1
1
2
2
0
1
1
2
1
2
1
1
2
1
2
2
0
0
0
1
1
0
1
1
1
1
1
1
2
0
1
2
1
1
1
0
0
1
1
0
1
0
1
0
1
1
2
1
1
2
2
1
1
2
2
1
1
0
0
1
1
2
1
1
1
1
1
1
0
1
1
0
1
1
1
0
2
1
1
0
1
0
0
1
1
1
2
1
1
1
1
1
0
2
1
1
2
2
1
2
2
0
2
2
1
1
0
1
1
1
1
1
1
1
2
1
0
2
0
1
2
0
1
0
1
1
2
0
1
2
1
2
2
1
1
2
0
1
0
1
2
1
2
3
2
1
2
1
1
1
1
1
0
0
2
2
2
2
1
0
1
1
1
1
0
1
2
1
2
0
2
2
1
1
2
0
1
1
1
1
1
2
1
2
0
0
0
0
2
1
1
1
1
1
1
1
1
1
2
2
0
1
1
1
2
1
1
2
1
1
1
0
1
0
1
2
1
1
1
2
1
1
0
1
1
1
0
0
1
0
1
1
3
1
1
1
0
1
1
1
2
2
0
1
1
1
2
2
1
1
2
1
1
1
1
1
1
2
2
2
0
1
1
1
1
2
1
1
1
1
2
1
1
1
1
0
1
0
1
1
1
0
2
2
1
1
1
1
1
0
2
2
1
0
1
1
0
1
0
1
0
1
1
1
1
2
0
1
1
1
1
1
1
1
2
2
0
2
0
2
1
1
1
1
1
1
2
0
1
2
0
2
1
1
2
1
1
0
2
2
1
1
1
2
2
1
1
2
1
0
0
1
0
0
0
1
1
1
1
1
2
2
1
1
2
1
1
1
1
1
1
2
1
0
0
1
1
1
1
1
2
1
1
1
1
1
1
0
1
0
1
1
2
1
1
1
1
2
1
2
1
1
1
1
2
1
0
1
1
2
1
1
0
1
1
0
2
1
1
1
2
1
1
1
0
2
1
1
1
0
1
1
1
1
1
1
0
1
0
1
1
1
1
1
0
1
1
0
2
0
2
0
1
2
3
1
1
0
1
0
1
0
3
2
1
0
1
1
2
1
0
2
2
1
0
0
1
1
0
2
2
1
2
1
0
1
1
2
1
1
2
2
1
1
2
1
1
0
2
1
1
0
1
2
1
0
1
1
2
0
1
1
1
1
0
1
1
0
1
1
2
0
1
1
1
1
1
1
2
2
0
2
1
1
2
0
0
1
2
2
2
0
1
2
1
1
1
0
1
2
0
1
1
2
0
0
1
0
2
1
2
1
2
1
1
1
1
1
1
2
0
1
1
1
1
1
1
0
2
2
0
1
1
1
1
2
1
1
1
1
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
2
0
1
1
1
1
1
1
1
1
0
2
0
1
1
2
2
1
1
1
1
1
1
1
1
1
0
1
1
1
0
2
2
2
1
2
1
1
1
2
2
0
1
1
0
1
1
1
1
2
2
0
1
0
1
2
1
0
2
1
1
1
1
2
0
1
2
2
1
0
1
1
1
2
1
1
1
1
2
2
0
1
0
1
1
0
1
1
0
1
1
1
2
1
1
1
1
1
1
1
0
0
1
1
1
0
2
2
0
1
2
1
1
1
1
1
1
1
1
1
3
1
0
0
2
1
0
2
1
2
1
1
0
2
0
2
0
1
1
0
1
1
1
1
2
2
1
1
1
1
0
0
1
1
0
0
0
2
1
1
1
1
2
1
2
1
1
1
1
1
2
2
0
1
2
1
2
1
0
2
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
1
0
1
0
2
1
1
1
1
1
2
2
1
1
1
2
1
1
1
1
0
0
1
1
1
0
2
1
1
1
1
0
0
1
1
2
1
0
2
1
1
1
1
1
2
1
1
0
1
0
2
2
1
1
2
1
1
1
1
1
2
1
1
2
1
2
0
0
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
0
1
0
1
1
1
1
1
0
1
1
1
1
0
1
2
2
0
1
2
2
0
3
0
1
1
0
1
1
2
0
1
1
0
0
1
1
2
2
1
2
1
1
2
1
0
1
1
2
1
1
0
1
1
2
2
1
0
2
2
0
1
1
1
2
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
0
0
0
1
1
0
2
1
2
1
0
2
1
2
2
0
1
0
1
1
0
1
1
1
1
1
0
1
1
3
1
2
1
2
1
1
1
1
1
2
1
1
2
1
1
2
1
0
1
0
2
1
2
1
2
1
2
1
2
2
1
1
1
1
2
1
1
1
1
2
0
1
2
1
1
1
1
1
1
1
2
0
1
1
2
0
2
1
0
1
1
1
2
1
1
1
2
0
1
1
1
1
1
1
1
2
1
2
1
1
1
2
1
1
2
1
1
0
1
1
0
0
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
2
2
1
0
1
1
0
1
2
0
2
1
0
1
1
2
1
1
1
2
1
2
1
0
1
2
1
0
0
1
1
1
2
0
1
1
1
1
0
2
1
1
2
0
1
1
1
1
0
0
1
1
1
1
1
1
1
0
1
1
0
1
0
2
1
0
1
1
0
3
2
2
0
1
2
1
2
1
1
1
0
2
0
1
0
2
2
1
1
1
1
1
2
2
2
2
2
1
2
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
2
1
2
1
1
2
0
1
1
1
1
2
1
1
1
0
2
1
2
2
2
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
0
0
1
1
1
1
2
1
1
1
2
1
0
1
1
0
2
2
1
1
2
1
1
1
2
1
2
1
0
1
1
2
0
1
0
2
1
1
2
2
1
1
1
2
1
1
2
1
1
1
0
1
2
2
1
1
1
2
1
1
1
0
1
2
1
2
1
2
1
2
1
2
0
0
2
0
0
1
1
1
1
0
1
2
0
1
0
1
2
2
1
1
1
1
0
1
1
1
0
1
1
2
2
1
2
2
2
0
0
1
1
1
1
1
0
1
1
1
1
1
1
1
0
1
1
1
4
2
2
0
2
1
1
1
1
1
1
1
0
1
2
2
1
1
2
2
1
0
1
1
1
1
2
2
1
1
1
1
0
2
0
0
0
1
2
2
2
1
1
2
1
1
0
2
1
2
1
1
1
1
1
2
2
1
1
1
1
1
1
1
3
2
1
1
1
1
0
2
2
1
2
0
1
0
0
2
1
0
1
1
2
1
1
2
1
1
1
1
1
1
1
0
2
1
2
0
1
1
1
1
2
2
2
2
1
1
2
1
0
0
0
2
0
1
1
0
2
1
1
0
1
1
1
3
1
0
1
0
1
2
1
1
1
1
1
1
0
2
2
1
1
0
1
1
1
1
0
2
2
2
2
1
2
1
1
1
2
1
2
1
1
0
1
1
0
2
1
0
1
1
3
2
2
0
0
1
1
1
1
1
2
2
1
0
0
0
2
1
1
1
1
1
0
0
0
1
2
0
1
1
2
1
1
1
1
1
0
2
2
2
0
0
0
1
1
1
2
1
1
1
1
0
1
1
2
1
1
1
1
2
2
1
1
1
1
0
2
2
0
0
1
1
2
1
1
1
1
0
1
2
2
1
2
1
1
0
1
2
1
1
1
2
1
1
2
1
1
1
3
2
2
0
0
2
1
0
1
1
1
1
1
1
0
0
1
1
1
0
1
2
2
1
2
2
1
1
1
2
1
3
2
1
1
1
1
1
2
1
1
0
0
1
2
1
1
1
1
1
2
1
1
2
1
2
1
2
1
1
1
1
1
2
1
0
2
1
0
1
1
0
1
1
1
1
1
1
2
1
1
1
1
1
2
1
2
1
1
2
0
2
1
1
0
2
1
1
0
1
1
2
1
0
0
1
1
1
1
0
1
1
1
1
0
0
1
1
2
0
2
1
1
1
0
1
2
1
1
2
1
2
2
2
0
1
1
1
2
0
0
0
1
1
0
1
1
0
1
0
0
0
1
2
2
1
0
0
0
1
0
1
2
1
1
1
1
1
1
2
2
2
2
1
2
1
2
0
1
0
1
1
1
2
0
2
2
1
2
2
1
2
2
1
1
0
1
2
1
2
0
2
1
1
5
0
2
0
1
1
2
1
1
1
1
0
0
2
1
1
2
0
1
1
1
0
2
1
2
0
1
0
1
1
0
0
1
1
1
3
1
2
1
2
0
1
2
2
0
1
1
1
1
1
2
0
0
1
0
1
2
1
1
1
2
1
0
1
1
1
2
2
2
1
1
2
0
1
0
2
2
1
1
1
1
2
1
1
2
1
1
1
1
1
2
0
1
2
1
2
1
1
2
2
1
2
0
0
0
0
2
2
1
0
0
2
1
1
1
2
1
2
2
1
1
1
1
0
1
1
0
1
2
1
2
1
1
2
3
0
1
1
1
2
2
2
1
0
0
2
1
0
1
1
2
0
1
1
2
2
2
1
2
1
0
1
1
1
0
1
0
1
1
1
1
1
1
2
1
2
1
1
0
2
1
1
2
2
1
1
0
2
0
2
2
1
0
2
1
0
1
1
2
1
1
1
1
2
1
0
1
1
1
1
0
2
1
1
0
1
0
1
1
2
2
1
1
2
1
0
0
1
1
2
1
0
0
2
1
2
1
1
2
1
1
1
1
1
1
1
0
2
1
2
1
2
1
1
1
1
1
1
1
1
0
1
1
0
1
1
2
0
2
2
1
0
0
1
1
1
1
0
1
1
0
2
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
2
1
0
1
0
2
1
1
1
1
0
1
2
2
1
1
1
1
1
1
2
2
1
2
2
0
2
1
0
0
1
1
2
1
1
1
1
0
2
1
2
0
1
2
0
2
1
1
0
2
2
1
1
1
1
0
1
1
2
0
1
1
1
1
1
1
1
1
0
2
2
1
2
1
0
1
1
1
1
1
0
1
1
2
1
1
2
0
2
1
1
1
1
0
1
1
1
1
1
1
1
1
2
1
0
2
1
1
0
1
1
1
2
1
2
0
1
1
0
1
1
1
2
1
0
1
1
1
2
1
1
1
1
0
1
2
2
2
1
1
0
0
0
1
1
4
2
1
1
0
0
1
1
2
1
2
2
1
1
0
1
2
1
1
2
0
2
0
0
0
1
1
2
1
1
1
1
2
1
1
4
1
1
2
1
1
2
1
2
0
1
2
1
0
2
0
1
0
2
2
0
0
1
1
2
0
0
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
0
1
1
2
1
1
1
2
2
1
1
1
1
1
1
0
1
2
0
1
1
2
1
1
1
1
1
1
1
0
0
2
1
1
2
1
1
1
1
0
0
1
0
1
2
1
2
1
1
0
1
2
1
1
0
2
1
0
1
1
1
1
1
1
2
3
2
0
1
0
1
1
1
1
1
2
1
1
0
1
1
0
1
1
2
2
1
0
1
1
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
0
0
2
2
1
2
1
1
1
2
1
1
1
2
1
1
1
1
2
1
0
0
1
1
1
1
1
2
1
1
1
2
0
1
1
1
1
3
2
1
1
2
1
1
0
2
3
0
1
1
2
1
1
0
1
0
1
2
1
2
1
1
1
1
1
1
0
0
2
0
0
1
1
1
1
2
1
1
2
0
1
1
1
2
1
2
2
2
1
2
0
2
1
0
1
1
2
1
3
1
0
2
1
1
1
1
1
1
0
1
2
1
2
1
0
2
2
1
1
1
1
1
1
1
1
3
0
1
2
0
2
1
1
2
1
1
2
1
1
1
1
0
1
1
1
1
5
1
2
1
0
1
0
0
1
0
2
1
0
1
1
1
1
1
1
1
0
1
1
0
2
1
1
0
2
1
1
2
0
1
2
1
1
1
2
1
1
0
2
1
1
2
1
0
0
1
2
1
1
2
1
1
1
2
1
1
1
2
0
1
2
1
2
1
0
2
2
0
1
2
2
0
2
1
0
0
0
1
1
1
1
1
0
1
1
1
1
0
2
0
1
1
2
1
2
1
1
1
1
1
1
0
2
1
0
1
0
2
1
1
1
1
0
1
0
0
1
1
1
1
0
1
0
0
1
1
2
0
1
1
1
2
1
1
1
1
2
1
1
1
2
1
0
1
1
1
0
2
1
1
1
1
1
1
1
1
1
1
1
2
0
2
2
1
2
2
2
2
1
0
1
1
1
2
0
2
1
0
1
2
0
1
0
1
1
2
2
1
1
1
1
1
2
0
2
0
0
1
1
0
2
2
1
1
1
0
0
2
1
3
1
2
2
1
0
2
0
1
1
2
1
1
1
2
1
2
1
1
0
0
2
1
1
2
1
1
0
0
0
1
1
1
0
1
1
1
0
1
0
1
1
2
1
1
2
2
2
1
2
2
1
1
2
1
2
2
1
1
1
0
1
1
1
2
1
2
3
1
1
1
1
1
1
1
1
1
0
1
1
1
1
2
1
0
1
1
1
1
2
1
2
1
2
1
0
2
1
2
3
1
1
1
0
1
1
1
1
1
1
1
1
0
1
1
1
1
1
2
1
2
2
1
1
0
1
1
1
0
0
1
2
1
1
0
2
1
1
1
2
1
3
1
1
0
0
1
1
1
0
0
1
1
1
0
2
0
2
0
2
0
1
0
1
1
2
1
1
1
0
0
0
0
0
2
1
2
2
0
1
2
1
1
1
1
0
0
0
0
1
2
0
0
1
1
2
1
4
1
1
1
2
2
1
0
2
4
1
0
2
0
2
1
2
1
1
2
0
1
2
2
2
2
1
2
1
1
0
0
1
1
2
1
2
2
0
1
2
0
1
1
0
2
1
1
2
0
0
2
1
1
0
1
0
1
0
1
0
0
2
1
1
0
1
1
0
1
2
0
0
0
1
0
2
2
1
0
2
1
1
1
1
2
1
1
0
0
1
4
2
2
1
2
1
2
1
0
1
1
1
1
2
0
1
1
1
2
1
1
1
1
0
1
1
1
0
1
2
1
0
1
1
3
1
1
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
2
0
1
1
1
1
2
2
1
1
1
0
1
0
1
1
1
0
1
1
0
2
2
1
1
1
1
1
2
1
0
1
2
1
1
1
1
1
1
1
0
2
2
1
2
2
1
1
1
1
1
1
1
0
2
1
0
1
1
1
1
0
1
1
1
0
2
0
1
1
1
1
1
1
2
1
3
1
2
1
1
1
0
0
1
1
1
1
0
1
1
1
2
1
2
1
1
2
0
0
0
1
1
1
0
2
3
1
1
2
2
1
2
1
2
1
1
1
1
0
2
1
1
1
2
1
2
1
2
1
1
0
2
1
1
1
0
1
1
0
1
1
1
1
2
0
2
1
1
1
1
1
1
1
1
1
1
1
0
2
1
2
1
1
0
1
1
1
1
0
1
1
1
1
1
1
1
1
1
0
1
3
0
2
1
2
1
1
0
0
1
2
1
1
2
1
0
1
2
1
1
0
2
2
0
0
1
1
1
1
1
0
1
1
2
0
1
0
1
1
0
2
2
0
1
1
2
1
1
1
1
1
2
1
1
0
0
0
1
2
2
1
2
2
1
2
1
2
1
1
1
2
1
1
1
1
1
1
1
2
0
2
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
1
2
2
2
1
1
1
2
2
1
1
1
0
1
1
1
0
1
0
1
0
1
1
1
0
1
1
1
1
0
0
0
1
2
0
1
1
0
1
2
1
1
1
2
1
1
1
1
1
2
1
1
0
1
1
1
0
1
3
1
1
0
0
1
1
1
0
2
2
1
2
1
0
0
1
1
1
0
0
0
2
1
1
1
1
0
1
2
1
1
1
3
2
1
2
2
2
1
1
1
0
1
1
0
1
1
1
1
2
2
1
1
1
1
1
2
1
1
2
2
1
2
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
2
2
2
1
1
1
1
0
1
1
2
2
2
2
0
1
1
0
2
0
2
1
1
2
2
0
1
2
1
1
1
1
2
1
2
1
0
1
0
1
1
0
1
1
1
1
0
1
1
1
1
2
1
1
1
1
1
0
1
2
2
1
1
2
2
2
1
1
1
1
2
1
1
2
1
0
1
1
2
0
2
0
2
1
2
4
2
1
2
0
1
0
0
2
2
0
1
0
1
1
1
1
1
1
0
1
1
2
1
0
1
2
2
1
1
2
2
1
1
1
1
1
1
1
1
0
1
1
3
0
1
1
1
1
2
1
1
1
0
1
1
1
2
0
1
2
2
1
1
1
1
1
1
1
0
2
2
0
1
2
1
1
1
1
1
1
1
1
2
2
0
0
1
2
2
1
1
0
2
2
1
1
0
2
2
2
0
1
1
1
2
2
0
2
1
2
1
0
2
1
1
2
0
1
0
2
2
0
1
1
1
1
1
1
2
2
2
2
0
1
2
1
1
1
0
1
1
1
2
0
1
1
1
1
1
2
1
0
1
2
1
1
0
1
3
1
1
1
1
2
1
1
1
1
2
2
1
1
0
2
1
1
2
1
1
2
0
0
0
0
1
2
0
0
1
2
3
1
1
2
2
2
1
1
2
1
1
2
1
0
1
0
1
1
1
0
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
2
1
0
2
2
1
1
2
1
1
1
1
2
0
0
2
1
1
1
1
2
2
1
1
2
1
1
0
1
2
0
1
0
1
1
1
1
2
2
1
1
2
1
0
5
1
0
1
1
1
1
1
1
1
2
2
2
1
2
2
1
0
1
2
2
1
1
2
0
1
1
1
1
2
1
1
2
1
1
0
1
1
1
0
0
2
1
1
0
1
0
1
1
1
2
1
1
1
1
1
0
1
1
2
0
1
1
1
1
1
0
2
0
2
1
2
1
2
0
2
1
0
1
2
2
2
1
1
2
0
2
2
2
1
1
2
1
1
0
2
1
1
0
2
1
1
0
1
1
1
1
2
1
0
1
1
1
2
2
2
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
0
1
0
2
1
1
1
2
1
1
1
1
0
1
2
0
2
1
0
1
1
1
1
1
2
2
2
1
0
2
2
1
1
2
1
1
1
1
0
0
1
2
1
1
1
0
2
1
1
2
1
0
0
3
1
1
0
0
1
1
1
1
1
1
0
2
1
1
1
1
1
2
1
0
0
1
1
2
1
2
0
2
1
1
0
2
1
1
1
0
2
1
2
1
2
1
2
1
2
0
2
1
1
1
1
2
2
2
1
1
0
1
0
1
2
0
2
0
1
1
2
2
1
1
2
2
2
0
1
2
0
1
1
0
1
2
1
0
0
1
2
2
2
1
1
1
2
1
1
2
1
0
1
1
1
1
1
2
2
0
1
0
1
2
0
0
1
1
0
2
1
1
0
1
1
1
2
1
1
0
1
1
2
1
1
1
0
1
1
2
1
0
1
1
1
1
1
1
2
1
1
1
1
3
2
1
0
2
1
1
0
1
1
1
1
2
1
1
1
1
0
1
2
2
1
2
1
1
1
1
1
1
1
0
1
1
1
1
1
1
0
1
1
1
1
1
1
2
1
2
1
2
1
1
0
0
0
2
0
1
1
2
2
1
2
2
1
2
1
1
0
1
1
2
0
2
1
1
1
1
1
1
2
2
1
1
3
1
0
1
0
2
1
2
2
1
1
2
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
0
0
0
1
1
1
1
0
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
2
0
1
1
1
1
2
1
3
1
2
2
2
1
1
1
2
1
1
1
1
1
2
0
2
1
1
2
1
0
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
0
1
1
1
1
1
1
2
1
1
0
1
1
1
2
2
2
0
1
2
1
1
0
0
1
1
1
1
1
2
0
1
1
2
1
2
0
2
1
1
1
2
1
1
0
2
2
1
2
2
0
2
0
0
2
2
1
1
2
1
1
0
2
1
0
1
0
0
1
2
1
1
0
1
1
1
2
1
1
1
2
1
0
1
1
0
1
1
1
1
1
0
1
2
1
2
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
0
1
0
1
1
0
1
2
1
2
1
1
1
1
0
1
1
1
1
1
0
1
1
1
0
1
1
2
1
1
1
2
0
2
2
2
0
1
1
1
1
2
2
1
2
1
1
1
2
1
1
1
1
2
2
1
1
1
1
1
0
1
2
2
1
0
0
1
1
1
1
2
1
2
0
1
1
1
1
0
0
2
1
1
1
1
1
0
2
1
1
1
1
0
1
1
2
1
1
2
0
1
2
0
1
2
1
1
0
0
1
1
2
2
2
2
0
2
1
2
1
0
1
1
0
1
1
1
1
2
2
0
1
1
0
0
1
2
1
0
1
2
1
1
1
1
1
1
1
1
2
1
2
0
0
1
1
1
1
1
2
2
0
2
1
1
1
2
1
1
1
1
1
3
1
1
0
1
1
2
1
2
1
2
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
0
1
2
2
1
1
2
1
0
2
1
1
2
1
1
2
2
2
2
1
1
1
1
1
0
1
1
2
0
2
1
1
1
1
0
1
2
2
1
1
1
2
1
1
0
2
1
1
2
1
0
0
1
2
2
1
0
1
0
1
2
1
0
1
1
1
1
1
1
2
1
2
1
1
1
2
2
0
2
2
1
2
1
1
1
1
2
1
1
1
1
1
1
2
0
1
1
2
0
0
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
2
2
1
1
1
2
1
2
1
0
0
1
1
1
1
1
0
1
2
1
1
0
1
1
2
2
1
2
2
1
0
2
1
1
1
1
0
1
1
1
2
1
2
2
1
1
1
4
1
0
1
1
1
1
1
2
1
1
1
2
2
1
3
0
0
2
1
2
1
0
0
2
0
1
1
0
1
1
2
1
0
2
0
1
1
1
0
1
2
1
0
2
1
1
0
0
1
1
1
1
2
1
1
1
1
1
1
2
1
1
2
2
1
1
0
2
1
1
0
2
1
2
1
1
1
1
1
2
2
1
1
2
1
1
2
1
1
0
2
0
1
0
1
1
2
1
1
1
0
1
1
1
1
1
1
1
2
3
0
1
2
0
1
1
2
1
2
1
1
1
2
1
1
1
1
1
2
0
1
2
0
1
0
0
2
1
0
1
2
1
1
1
0
0
1
1
0
1
1
0
1
0
1
1
1
1
2
1
0
1
1
1
1
2
3
1
2
2
1
1
1
2
1
1
1
2
1
1
2
1
2
1
1
2
0
0
1
1
0
2
2
0
1
1
1
1
2
1
2
1
1
1
2
0
1
2
0
2
1
0
1
1
0
1
1
1
0
1
1
0
1
1
1
0
1
1
0
1
1
2
2
1
2
2
1
1
2
1
1
2
1
1
2
1
0
1
1
0
1
0
2
2
1
2
1
1
2
1
0
1
0
1
1
1
0
1
2
1
1
2
2
1
3
1
1
1
1
2
1
2
2
1
1
0
1
2
1
2
2
1
1
1
2
1
0
1
0
2
2
1
1
1
1
1
1
1
1
0
1
1
2
2
1
1
2
2
0
2
1
2
1
3
1
1
1
2
0
2
1
0
2
1
2
1
0
1
2
0
0
2
1
1
0
2
1
1
2
1
1
0
2
1
1
0
1
1
2
1
2
1
1
1
1
0
1
1
0
1
1
1
0
1
2
1
1
2
1
0
1
0
1
1
1
3
1
1
1
0
1
1
1
1
1
2
0
1
2
1
0
1
1
2
1
2
1
3
2
1
0
0
0
1
1
1
0
0
1
1
2
1
2
1
1
1
1
1
2
2
2
1
1
1
0
1
0
1
2
1
1
0
1
2
1
1
2
1
1
0
0
1
0
1
1
0
1
0
1
1
1
1
1
1
1
1
2
1
0
1
2
1
3
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
2
2
1
1
1
2
0
0
1
2
0
1
1
1
1
2
1
1
0
0
1
1
2
1
1
0
2
1
1
1
1
0
0
2
3
0
2
0
0
1
0
2
1
0
1
1
0
1
1
2
1
1
0
1
1
2
1
0
1
1
1
2
2
0
0
1
1
1
0
2
2
1
1
1
1
0
0
1
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
2
1
1
0
1
1
2
2
2
0
1
1
0
2
0
0
1
1
1
1
1
0
0
1
1
0
1
2
0
1
1
2
1
2
0
1
3
1
2
0
1
1
2
1
0
0
1
1
0
4
1
1
1
1
1
1
2
1
1
0
2
1
2
1
0
1
1
1
1
2
0
2
1
1
1
1
1
2
1
2
1
1
0
1
1
1
1
0
1
0
0
1
1
0
2
1
1
1
1
0
1
2
2
2
1
1
2
2
1
1
1
1
0
1
1
0
2
1
1
2
1
2
1
1
0
2
1
1
1
2
1
2
2
3
2
1
1
1
1
0
1
1
1
2
2
2
4
0
1
2
2
2
2
0
1
1
1
1
1
1
1
0
2
2
2
1
2
1
1
1
2
0
0
1
0
1
0
0
1
1
2
2
2
1
1
1
1
1
1
2
1
2
2
0
2
1
1
1
2
2
1
2
1
1
1
1
1
2
2
3
0
1
1
1
1
1
0
2
1
1
0
0
1
2
1
1
2
1
0
1
2
2
2
0
1
0
1
1
1
1
0
2
1
1
1
0
1
1
1
1
0
1
2
1
1
2
0
1
1
2
2
2
1
1
1
1
0
2
2
1
1
1
0
1
1
0
2
1
1
1
0
2
1
1
2
1
2
0
1
1
1
1
1
1
2
1
1
1
1
1
1
1
3
1
1
2
1
1
1
1
0
1
2
1
0
1
1
1
1
1
1
1
1
1
1
1
2
1
0
1
2
0
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
2
2
1
0
1
1
1
0
0
1
1
1
2
1
2
1
1
1
1
1
2
2
2
1
0
1
3
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
2
0
2
0
0
0
1
2
1
2
1
1
1
1
1
1
1
0
4
1
0
1
0
1
0
0
1
1
1
1
1
1
3
0
1
2
1
2
0
1
1
1
1
1
2
1
2
1
0
1
1
2
1
1
2
0
2
1
1
0
1
1
1
0
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
2
2
2
1
1
1
1
2
1
2
0
2
0
1
1
1
1
1
0
0
2
1
2
0
1
0
1
1
1
1
1
1
1
2
0
0
3
1
1
1
1
1
0
1
0
1
1
1
1
1
1
1
0
1
1
2
0
2
1
1
0
0
1
2
2
1
1
1
2
1
1
1
1
0
1
1
1
2
1
1
2
1
0
1
1
1
0
1
1
1
1
2
0
1
2
1
1
1
1
1
2
1
2
2
2
3
1
1
2
1
2
1
1
1
2
1
2
2
2
1
1
6
1
1
1
1
1
1
2
0
1
0
2
1
1
1
1
1
1
1
1
0
1
1
0
1
2
2
1
1
1
2
2
2
1
1
0
1
1
1
2
2
2
0
3
1
0
0
1
2
1
1
1
1
1
2
1
2
1
2
2
1
3
2
0
2
1
1
1
1
1
0
1
0
1
1
1
1
1
1
1
1
2
2
0
2
1
1
0
1
1
0
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
1
1
0
1
2
2
0
0
1
1
1
1
0
2
1
1
1
1
2
2
1
2
1
1
0
1
1
1
2
2
0
1
2
2
0
2
1
2
1
1
1
1
2
1
1
1
1
2
0
2
2
1
1
2
1
0
1
0
1
2
1
1
2
2
1
1
1
1
0
1
1
1
2
1
1
1
0
0
1
0
1
1
1
1
1
1
2
1
1
0
0
0
2
1
2
0
0
1
1
1
1
1
2
1
1
2
2
0
1
2
1
1
2
1
1
1
1
2
1
2
0
1
2
1
1
0
1
2
2
1
2
1
1
1
1
1
0
0
1
2
1
1
0
0
1
1
1
0
1
2
1
1
2
1
2
2
2
2
1
2
1
1
0
0
2
1
1
1
1
1
1
0
1
1
3
1
1
1
1
1
0
0
2
1
0
1
2
1
1
1
2
1
1
0
1
0
1
0
1
1
1
1
1
1
0
1
1
0
2
1
1
1
1
2
0
1
1
1
1
1
2
0
1
1
1
2
2
1
2
2
1
1
1
1
2
1
2
0
1
1
1
1
2
1
2
1
1
1
1
0
2
1
1
1
1
2
0
1
2
2
1
1
0
1
1
1
2
1
1
0
0
1
1
1
0
1
0
0
2
0
1
1
2
2
2
1
1
1
0
0
1
1
0
0
2
1
1
0
2
1
1
1
1
2
2
2
1
0
1
1
1
0
1
2
3
2
1
2
1
1
1
2
3
0
2
1
1
0
2
1
2
2
1
2
2
1
1
1
1
1
1
1
1
1
1
2
0
2
1
1
1
1
2
0
1
1
0
2
2
1
1
1
0
1
0
1
1
1
2
1
2
1
1
0
1
0
1
1
1
0
1
1
1
0
0
1
1
1
0
1
2
0
1
1
1
1
2
0
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
0
1
1
1
1
4
0
1
1
2
1
1
1
2
1
1
0
3
2
1
2
0
1
0
1
1
0
1
1
1
0
2
1
0
2
0
1
2
2
0
1
1
2
2
1
1
1
1
1
1
2
1
1
1
0
1
1
0
1
2
1
2
1
2
1
1
2
0
1
2
1
1
1
0
2
1
0
0
1
0
1
2
0
1
0
1
1
1
1
0
2
2
1
0
2
0
2
0
1
1
2
2
2
1
2
2
1
1
0
1
2
1
1
1
2
0
2
1
1
2
1
1
1
1
0
0
1
1
1
1
1
1
1
0
4
2
1
1
2
1
1
1
2
1
1
1
1
0
0
0
1
0
1
1
1
1
2
0
1
2
2
1
1
1
1
1
1
1
0
1
1
1
1
2
2
0
1
0
2
1
2
1
0
1
1
1
1
1
1
1
1
1
0
0
2
0
1
2
1
1
2
2
0
0
0
1
1
1
0
1
1
1
1
0
1
1
1
0
2
1
1
1
1
1
1
1
0
1
0
1
1
1
0
1
1
1
3
1
1
0
1
1
1
0
1
1
1
2
2
0
0
1
1
2
1
1
1
2
1
1
3
1
2
1
1
1
1
0
2
1
2
1
1
2
0
1
0
0
1
1
1
2
1
1
1
1
2
1
1
1
1
1
2
0
0
1
1
2
1
1
1
1
0
1
0
0
1
1
0
1
0
1
2
2
1
1
1
1
1
0
2
0
1
1
1
1
1
2
2
2
1
1
1
2
1
1
2
0
2
1
1
1
1
1
1
1
0
0
1
2
2
1
1
3
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
0
2
1
0
1
1
1
1
1
0
1
1
1
0
1
1
0
1
1
2
2
1
1
1
2
1
1
1
2
2
0
2
2
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
2
1
1
1
1
1
2
1
0
0
1
0
1
1
1
2
2
1
1
1
1
2
1
2
1
2
1
0
0
1
0
0
1
1
1
1
1
0
2
1
1
0
1
1
1
1
1
0
0
2
2
1
1
0
2
1
0
1
2
2
1
1
2
1
1
0
0
2
1
1
2
2
1
2
2
0
0
2
1
0
1
1
1
0
0
1
1
0
1
2
1
0
1
1
1
2
1
1
2
0
2
1
1
2
1
0
1
1
2
1
1
2
1
1
1
1
1
2
1
2
2
0
0
1
0
1
1
1
1
2
0
0
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
2
2
1
1
1
1
1
0
1
2
1
2
1
1
2
0
1
1
1
1
0
0
1
0
2
1
0
1
0
2
2
0
1
2
1
1
1
1
1
1
1
0
1
1
2
1
1
1
1
1
1
0
1
2
1
0
2
1
2
1
2
2
1
2
0
0
1
1
0
1
1
2
1
1
1
2
1
1
0
0
1
2
0
2
2
1
0
2
1
1
1
1
2
1
1
1
2
1
1
1
0
2
2
0
2
2
1
2
1
0
1
2
1
1
1
1
1
0
0
1
1
1
1
1
1
2
1
1
1
0
1
2
1
1
1
1
1
1
1
0
1
2
1
2
1
1
1
1
2
1
1
0
1
2
2
1
2
2
1
1
1
0
2
1
0
1
0
2
1
1
0
1
1
1
1
1
1
2
1
2
1
1
0
1
1
1
1
1
1
2
2
1
0
1
2
1
1
0
1
1
1
2
1
1
2
2
0
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
0
1
0
0
2
1
2
1
2
1
1
1
1
1
0
1
1
1
1
1
1
2
0
1
1
0
1
0
1
2
1
0
1
1
2
1
1
1
2
1
2
1
2
1
2
1
0
2
1
2
2
1
0
2
1
1
1
1
1
1
1
0
0
1
1
2
1
1
1
0
0
1
1
2
0
1
2
2
2
0
1
0
1
0
2
1
1
1
0
1
1
0
1
1
2
1
1
1
0
0
1
1
1
2
1
1
0
1
1
2
1
1
1
1
2
1
1
1
1
1
2
3
1
2
0
1
1
1
2
0
1
2
0
1
0
1
1
0
0
2
0
0
1
1
1
0
0
1
1
1
1
1
1
1
1
1
1
1
2
1
0
1
1
2
1
1
1
1
1
2
2
0
0
2
0
1
1
1
1
0
0
1
3
2
2
1
1
1
0
1
2
0
1
1
1
2
1
0
0
0
1
1
1
1
0
1
1
3
1
2
0
1
2
2
1
2
0
1
0
0
0
1
2
1
1
1
1
1
1
1
1
1
1
0
1
2
1
0
1
1
0
2
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
1
2
2
1
2
1
1
0
1
2
1
2
0
1
0
0
1
1
1
2
0
2
1
2
1
2
2
1
1
0
2
0
1
2
2
1
1
1
1
1
1
1
2
1
2
2
1
2
2
1
1
1
1
2
2
2
1
1
1
1
2
1
0
1
1
1
1
2
1
1
1
0
2
2
1
0
0
1
3
1
1
1
1
0
0
1
2
1
1
0
1
1
1
2
1
1
1
0
1
2
2
1
2
2
1
2
1
1
2
2
1
1
1
2
1
0
2
0
2
2
2
0
2
2
1
2
1
1
1
1
1
1
1
0
0
1
2
0
1
0
1
1
1
0
0
0
1
0
1
1
1
1
1
1
1
1
1
2
0
1
2
1
1
2
1
1
1
2
2
2
0
1
1
0
1
2
1
1
1
1
1
0
1
1
2
0
1
0
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
0
0
1
0
0
1
1
2
1
1
1
1
2
2
0
1
1
1
2
1
0
0
2
2
1
2
2
1
2
1
1
2
1
2
1
0
1
1
1
1
0
2
1
2
1
1
1
1
1
1
1
1
0
1
1
1
2
2
1
1
1
0
0
1
1
1
1
1
1
1
0
2
1
0
2
0
1
1
1
0
1
1
1
1
1
1
1
0
2
1
0
0
1
1
1
1
1
1
1
0
1
2
1
1
2
1
1
1
2
1
0
1
0
2
2
0
2
2
2
1
1
1
0
1
1
2
1
2
1
1
1
1
1
1
1
0
1
1
1
0
2
2
1
2
1
1
2
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
0
0
1
1
2
2
1
1
2
2
0
1
1
1
2
1
2
1
0
1
2
2
1
1
1
1
2
1
0
0
0
1
1
1
2
1
1
1
1
2
1
0
0
2
1
1
1
2
0
0
2
1
2
0
2
3
2
1
1
1
1
1
2
2
1
1
1
2
0
0
0
1
1
1
1
1
1
0
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
0
2
1
1
1
1
1
1
2
1
1
0
1
1
1
2
2
1
2
1
0
1
2
2
1
1
1
1
0
2
0
1
2
1
1
2
1
1
1
1
1
2
0
1
0
2
0
2
2
2
1
1
1
1
0
0
1
1
1
1
1
1
0
2
1
2
2
0
0
1
0
1
1
2
1
1
2
1
1
1
0
1
2
1
2
1
2
1
2
1
1
1
1
2
2
2
1
1
1
0
2
1
1
1
1
2
2
1
2
0
0
1
1
1
1
2
0
1
1
2
0
1
1
1
1
1
0
2
1
0
1
2
1
1
1
1
1
1
0
0
0
1
1
1
1
2
1
1
2
0
1
1
0
1
2
1
2
1
0
1
1
0
1
1
3
1
1
0
1
2
0
1
1
0
1
1
1
1
2
1
1
1
1
1
1
2
5
1
4
0
1
1
1
0
4
1
2
1
1
1
2
2
2
0
0
1
1
2
1
2
1
2
1
0
2
1
1
1
1
1
1
1
1
2
2
3
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
0
1
2
1
1
0
1
1
1
1
2
1
1
1
2
0
1
0
1
1
2
1
2
1
1
1
2
1
2
1
1
1
1
1
2
1
1
2
1
2
1
1
1
1
0
1
2
1
1
0
1
1
2
1
1
1
1
1
1
2
1
2
0
1
0
1
1
1
2
2
0
1
1
1
0
1
1
1
2
1
1
1
0
2
0
2
1
1
2
1
1
1
1
1
1
2
0
2
1
1
2
1
1
1
0
1
0
1
2
0
1
1
1
1
1
0
0
1
1
1
2
2
0
2
2
1
1
2
0
1
2
0
1
1
2
2
1
1
0
2
1
1
2
0
0
1
2
0
1
2
0
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
0
2
1
1
1
0
1
2
1
1
0
1
1
2
1
0
2
1
1
0
1
1
1
0
1
1
1
1
1
0
2
1
1
2
2
1
0
1
1
1
1
1
0
1
0
1
2
2
1
0
1
1
0
2
0
2
0
1
1
1
2
1
1
1
0
2
1
1
1
1
1
1
0
0
1
1
1
2
1
1
1
2
2
1
1
1
1
0
1
4
1
2
1
2
1
0
1
1
1
1
1
0
1
0
1
1
1
1
1
1
1
1
1
0
1
1
1
2
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
4
1
0
0
2
0
2
2
1
1
2
1
1
1
1
1
2
2
1
1
1
0
2
2
1
1
0
1
1
1
1
1
2
2
0
2
1
2
1
1
0
2
2
2
0
0
1
1
1
1
1
0
0
0
1
1
2
1
2
1
1
1
1
1
2
1
0
1
1
1
2
1
2
1
2
1
3
1
1
1
2
0
1
1
1
1
1
0
0
2
0
2
1
1
0
2
0
1
1
1
2
2
0
1
1
0
1
1
2
1
0
1
1
1
2
1
1
0
2
2
1
1
2
1
1
1
0
1
1
2
1
1
1
1
2
1
1
1
1
1
2
0
0
2
1
1
1
1
2
2
0
1
1
1
2
1
1
1
2
0
1
1
0
0
2
0
0
1
1
1
1
0
1
0
1
0
1
2
2
1
2
2
0
1
0
1
1
1
2
1
1
1
1
1
2
2
2
1
1
2
0
1
2
1
1
1
1
2
1
2
1
0
0
1
1
1
1
1
1
1
2
1
0
2
1
1
1
2
1
1
2
1
1
1
0
0
1
1
0
1
1
1
0
1
1
1
1
0
1
2
2
1
1
1
1
1
0
2
1
2
1
1
2
1
1
0
1
2
2
2
2
0
1
1
2
2
1
1
1
0
0
2
1
1
1
2
1
2
1
0
2
1
1
1
2
1
1
2
1
2
1
1
0
0
1
2
1
0
2
0
1
1
2
1
0
1
0
2
2
1
0
2
2
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
0
2
2
1
1
1
1
0
1
1
2
2
1
2
0
1
1
3
1
2
2
1
2
1
0
0
1
0
0
2
1
2
1
1
1
5
1
1
2
1
1
0
1
2
1
2
1
0
1
1
0
0
1
0
0
0
2
1
2
2
1
1
1
1
0
1
1
2
1
1
1
1
1
1
1
1
1
1
3
2
1
1
1
2
1
1
2
0
2
2
1
1
1
2
2
1
1
1
1
1
2
1
1
1
2
2
2
1
2
2
2
0
1
0
0
1
1
0
1
1
1
1
1
0
1
1
1
0
1
2
1
1
1
2
1
1
1
0
1
0
2
1
2
2
1
0
1
2
1
0
2
2
0
1
1
2
3
1
0
2
1
1
0
1
2
3
1
1
2
1
1
1
1
1
2
1
2
1
0
0
1
2
2
2
1
1
0
0
1
1
1
2
1
1
3
2
1
0
2
0
1
3
1
1
0
1
1
0
1
2
2
1
1
1
0
1
1
1
0
1
0
1
1
1
0
1
1
1
1
2
1
1
0
2
1
1
0
0
1
0
2
1
1
2
1
2
1
0
0
1
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
0
1
1
2
1
1
1
0
1
1
1
1
1
2
1
1
1
1
2
2
1
1
2
2
1
0
1
1
1
2
1
1
0
2
1
1
2
1
0
1
1
1
1
1
1
1
1
0
2
2
1
1
1
0
0
1
1
1
1
2
1
1
0
1
2
1
1
2
1
1
1
2
0
2
0
2
2
1
0
1
1
1
1
1
1
1
1
1
2
1
1
1
0
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
0
1
0
0
1
1
2
1
2
1
1
1
1
2
2
0
1
1
0
0
2
1
1
1
1
1
1
1
1
2
1
2
1
2
1
1
1
1
0
0
0
0
2
1
1
1
0
1
1
2
1
0
0
1
2
1
2
2
1
1
1
2
2
1
1
2
2
1
1
2
1
2
0
2
0
0
2
1
0
1
1
0
0
2
2
0
0
2
2
0
1
1
0
1
1
1
2
0
2
2
1
1
5
2
0
1
1
1
1
0
2
1
2
1
2
2
0
1
1
1
2
2
2
1
1
2
2
2
1
1
0
1
1
1
0
0
1
1
1
1
0
1
2
1
1
2
1
2
1
2
1
2
2
1
1
0
1
1
1
2
2
1
1
3
0
0
2
2
1
2
1
1
1
1
2
2
1
1
1
3
0
1
1
1
2
1
0
2
1
1
1
2
2
1
2
1
1
1
0
1
1
1
1
1
0
1
1
1
1
1
2
2
1
2
1
2
1
0
1
1
1
1
1
1
2
0
1
1
0
2
1
1
1
2
1
2
1
2
1
2
1
1
1
1
1
1
1
1
2
0
2
1
2
1
2
1
1
0
1
0
1
0
1
2
0
1
1
2
1
1
1
1
1
1
1
1
2
2
1
2
1
0
2
2
2
0
1
0
0
1
1
1
1
1
2
1
0
1
0
1
4
1
2
1
1
0
1
2
1
0
1
1
1
2
1
0
1
1
0
2
1
2
0
2
1
1
1
0
0
3
2
2
1
1
1
0
0
1
1
0
1
1
1
0
1
1
1
1
0
2
1
2
2
0
0
2
2
1
1
0
0
2
1
1
1
1
0
2
1
1
1
1
1
0
1
1
1
2
0
1
2
1
0
1
1
1
1
1
1
1
2
2
1
0
0
0
1
0
1
1
3
2
2
1
2
0
2
0
2
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
0
0
1
0
1
1
1
1
1
0
2
2
1
1
0
2
1
1
1
0
1
1
0
1
1
2
1
1
1
2
1
1
1
1
1
2
1
2
2
1
2
0
1
0
1
2
1
0
1
1
0
1
2
1
0
2
2
1
1
1
2
1
1
1
1
0
1
0
1
1
1
1
1
1
1
1
0
0
1
0
1
1
1
1
1
0
1
1
2
3
1
1
2
2
1
1
1
2
0
1
1
1
2
1
0
1
0
0
1
1
0
1
2
1
0
1
1
0
0
1
0
2
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
1
1
2
1
1
2
1
2
1
0
4
0
0
1
1
1
1
1
1
0
2
0
2
1
1
1
0
2
2
0
2
0
2
1
0
1
1
2
2
2
1
0
1
0
0
1
1
0
1
1
0
2
1
2
1
0
2
1
1
1
1
1
1
2
0
2
1
0
2
1
2
1
2
1
0
0
1
1
2
2
1
1
1
2
0
1
1
2
2
1
1
0
1
1
1
0
1
1
2
0
0
1
1
1
1
1
1
2
1
2
1
1
0
1
1
1
1
2
1
1
2
1
1
0
1
2
1
1
1
0
1
2
0
0
1
1
1
1
2
0
0
1
1
0
0
1
1
2
0
1
1
1
1
1
1
2
1
1
0
0
0
0
0
1
1
1
2
1
0
1
1
2
1
1
2
1
1
0
1
0
1
2
0
1
2
2
2
2
1
1
0
2
1
0
1
1
2
1
0
2
1
1
2
1
1
2
1
2
1
1
1
1
2
1
1
2
0
1
1
1
2
1
1
1
1
0
1
1
1
1
1
0
1
2
2
0
1
1
0
1
1
1
1
2
1
1
1
1
1
2
0
1
2
3
1
1
1
1
1
0
0
1
0
2
1
2
1
2
1
1
2
2
1
1
1
2
0
0
0
2
0
1
1
1
1
1
1
1
2
0
2
2
1
1
1
1
1
2
2
0
1
1
1
1
1
1
1
1
1
2
1
2
1
2
1
2
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
0
0
2
1
0
1
2
0
1
2
2
1
1
1
2
0
1
0
1
2
1
1
1
1
0
2
1
1
1
1
2
1
2
1
2
1
1
1
1
1
0
1
1
1
1
0
1
2
1
1
1
1
1
2
1
0
1
2
1
1
1
1
1
1
1
2
2
0
1
1
1
2
2
1
1
1
1
1
0
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
0
1
1
2
2
1
1
2
2
2
0
0
1
2
1
1
2
1
0
2
1
2
1
0
1
2
1
1
1
0
1
1
3
1
2
0
2
1
2
1
1
1
1
1
1
1
1
2
1
0
1
1
1
1
1
2
2
1
1
1
1
2
0
1
1
1
2
1
1
2
0
1
2
1
0
1
1
2
2
0
2
0
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
0
0
1
1
1
1
0
2
1
2
1
1
2
1
0
1
1
2
2
1
2
1
1
1
2
1
1
1
1
0
1
1
1
2
2
2
0
2
0
1
1
1
1
2
0
2
0
1
1
2
3
1
1
1
2
0
1
1
2
1
2
1
1
1
1
1
1
1
1
2
2
2
2
1
1
0
2
1
2
1
2
2
1
0
1
0
1
1
1
1
1
2
2
2
0
0
1
1
0
2
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
0
1
1
2
1
1
2
2
1
1
2
1
2
1
2
1
1
1
2
2
1
1
1
1
1
1
1
1
2
0
2
0
1
1
2
2
2
3
1
1
1
1
2
0
2
1
1
1
2
0
1
2
1
1
1
1
2
2
0
1
1
1
2
1
1
2
1
0
1
0
1
1
2
1
2
1
2
2
1
1
1
1
1
0
2
2
2
1
2
1
2
2
2
0
1
1
0
1
1
1
0
1
1
2
2
2
1
1
1
1
1
1
1
2
3
1
1
1
3
2
2
2
1
1
0
2
1
1
2
1
1
1
0
0
1
0
2
1
1
1
1
1
1
1
2
0
1
1
2
1
1
1
1
1
1
0
1
0
1
1
0
0
1
0
0
2
1
2
1
0
2
1
0
1
1
1
1
0
0
2
2
1
1
0
1
2
0
2
0
1
1
1
1
1
1
1
2
1
1
1
2
0
1
2
1
1
1
1
1
1
1
2
2
0
1
2
0
1
1
1
0
1
2
1
1
1
0
0
1
1
1
2
1
1
1
2
1
2
0
1
0
1
1
1
2
2
0
0
1
1
1
1
0
1
1
1
1
2
0
1
1
1
1
1
1
2
0
1
1
1
1
1
2
2
0
0
2
1
1
0
1
1
1
2
0
2
1
1
0
0
1
1
2
1
2
2
1
1
2
1
1
0
2
1
2
0
1
1
1
2
0
1
1
2
1
1
2
1
1
2
1
2
1
0
1
1
1
0
1
1
1
1
0
1
0
1
2
2
1
2
2
3
2
1
1
1
1
0
1
1
2
1
1
1
0
0
1
2
1
1
1
2
0
0
2
0
1
0
0
1
1
0
1
2
1
0
1
2
1
1
1
1
1
2
0
1
2
1
2
1
1
1
0
2
1
1
1
1
2
1
1
1
0
1
1
2
1
2
1
1
1
1
1
2
1
2
0
1
2
2
1
1
1
1
1
1
0
1
1
1
1
1
0
1
1
1
0
1
1
2
1
0
1
1
1
2
1
2
1
2
2
1
2
1
1
2
1
1
1
1
2
2
2
1
0
1
1
0
2
2
1
2
1
0
2
1
1
2
0
1
1
1
1
0
1
1
0
2
1
1
1
0
2
0
1
1
1
2
0
1
1
2
0
2
2
2
0
1
2
2
0
1
1
2
1
1
0
1
2
0
1
1
1
2
1
1
0
2
1
1
2
2
2
2
2
1
1
1
1
2
1
2
1
1
2
1
0
2
0
2
1
2
1
1
2
1
1
1
0
0
1
2
1
2
0
1
1
2
2
1
0
1
2
1
1
1
1
2
0
2
1
1
0
0
0
1
2
1
1
1
0
1
1
1
0
0
1
1
1
1
1
2
2
0
2
0
1
0
1
1
0
2
2
2
1
1
2
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
0
1
1
0
1
2
0
1
1
0
2
1
1
1
1
1
1
2
0
1
2
0
0
1
2
1
2
1
1
2
1
2
1
1
1
2
1
1
1
0
2
2
1
2
1
1
1
0
1
1
0
1
2
1
0
0
0
1
2
2
1
1
0
1
1
1
0
1
1
1
1
0
0
1
2
1
0
0
3
1
1
2
1
1
1
1
0
0
4
1
0
2
0
1
2
0
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
0
1
1
1
1
2
1
2
1
0
0
1
1
1
0
1
1
1
3
2
1
2
0
0
1
2
0
1
1
1
1
0
1
1
1
2
2
1
1
1
1
2
2
1
1
1
1
2
1
1
0
1
1
1
1
0
2
1
2
1
4
1
1
2
1
2
2
1
1
1
0
0
1
2
0
2
1
0
1
0
1
0
1
1
0
1
1
1
1
2
1
1
2
1
2
0
3
1
1
0
1
1
0
0
1
2
1
1
1
1
1
2
2
2
1
2
1
0
1
1
1
1
1
1
1
1
1
0
1
1
1
0
1
1
1
1
0
1
0
2
1
1
1
2
1
2
1
0
1
1
2
1
1
1
1
0
1
0
0
1
1
0
2
1
1
0
2
2
1
1
1
1
2
0
2
1
1
2
1
1
1
0
0
0
2
2
2
0
1
0
0
0
1
1
2
0
2
0
2
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
0
1
1
1
1
1
1
1
1
2
1
1
1
0
2
1
1
0
2
1
0
2
0
1
0
1
0
0
2
1
1
1
2
2
1
2
0
1
1
1
1
1
2
1
1
1
2
1
1
2
1
1
1
1
1
2
0
1
2
2
1
1
1
0
0
2
1
1
1
1
0
2
2
1
1
2
0
1
1
2
1
0
2
0
2
0
0
1
1
1
0
1
0
1
2
1
2
0
1
0
0
2
1
0
1
1
0
2
1
1
2
1
0
1
0
2
2
1
0
0
2
2
1
0
1
3
1
1
1
1
1
1
1
0
1
1
1
1
2
1
0
2
2
1
0
1
1
1
1
2
0
2
1
1
2
1
1
2
2
2
1
1
1
1
1
2
1
1
0
1
2
2
1
1
1
1
1
0
1
1
2
1
0
2
2
1
3
1
1
1
0
1
1
0
0
1
1
1
2
1
1
1
1
2
1
0
0
1
1
1
1
1
0
2
0
1
2
1
1
0
1
0
1
2
1
0
1
1
2
1
2
1
2
0
2
0
1
1
1
2
1
1
1
1
1
1
1
0
2
1
1
0
1
0
2
2
1
1
1
1
2
1
2
0
0
1
2
1
2
2
1
0
1
1
2
1
2
1
2
1
1
2
1
1
1
1
0
1
0
1
1
1
0
2
2
2
1
3
0
1
1
0
1
2
2
1
1
1
1
1
1
0
1
0
1
0
1
1
0
1
1
1
2
1
2
1
2
1
0
2
0
1
2
1
1
0
2
2
1
1
1
2
1
1
1
0
1
4
1
1
2
2
1
1
2
1
1
2
1
0
1
1
1
3
1
1
2
1
1
2
2
0
3
1
2
1
1
1
1
0
2
1
1
1
2
1
1
2
1
2
2
1
1
2
1
0
0
1
2
0
1
2
0
1
1
2
2
1
1
1
1
1
1
0
0
1
0
1
1
1
1
0
0
2
2
1
1
1
1
2
0
1
2
1
1
0
1
1
2
1
0
1
2
1
2
2
1
2
0
2
1
1
1
1
1
2
1
1
1
1
1
1
1
0
1
2
1
1
2
1
0
1
2
1
1
0
2
1
1
0
2
1
1
1
1
1
2
1
1
1
1
2
1
2
2
2
0
1
0
1
2
1
0
1
1
1
2
1
0
1
2
2
1
1
1
1
2
1
1
1
2
1
3
1
1
0
1
0
1
1
2
2
1
0
2
1
1
1
1
1
1
1
2
1
1
2
0
1
0
1
1
1
2
2
2
1
0
0
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
0
2
4
2
0
1
1
2
1
2
1
1
1
0
2
2
2
2
2
1
0
2
1
1
0
1
0
1
1
2
1
1
2
1
1
1
0
2
2
1
0
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
1
2
1
2
1
0
2
0
1
2
0
1
0
2
1
2
1
1
0
1
1
1
2
1
1
0
2
1
1
1
1
1
2
1
1
0
0
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
0
1
2
1
1
1
1
1
1
1
2
1
0
1
1
1
1
1
2
1
2
1
2
1
1
5
1
2
2
1
1
0
0
1
2
1
2
1
1
2
2
1
2
1
0
1
0
0
6
0
2
1
0
0
0
1
2
1
1
1
2
1
2
1
2
2
2
2
1
1
1
2
1
2
1
1
0
1
0
2
1
1
1
1
1
0
0
1
1
0
1
1
1
2
2
0
1
0
1
2
2
0
1
1
2
2
1
1
2
0
2
1
0
1
1
1
1
0
2
0
1
1
0
1
1
0
2
1
1
0
0
2
2
0
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
0
1
2
1
0
0
1
1
1
1
2
0
1
0
0
0
1
0
2
0
1
2
2
1
0
1
2
1
0
2
2
1
1
0
0
2
1
1
1
1
1
1
1
1
0
1
1
1
3
1
0
1
1
1
1
0
1
1
1
0
1
1
1
1
0
2
1
1
0
0
3
0
1
1
2
1
1
1
2
1
2
1
2
1
2
1
1
2
1
1
1
2
2
0
1
0
1
0
1
2
1
2
0
1
1
1
0
2
0
1
1
1
1
2
1
0
0
1
1
3
1
1
0
1
1
1
1
2
1
1
1
2
1
0
0
1
1
1
0
1
1
2
1
1
1
1
1
2
0
0
1
0
1
2
0
1
1
1
1
1
1
2
2
1
2
1
1
1
1
2
1
0
0
1
0
1
2
2
1
0
2
0
0
2
0
1
1
1
1
2
1
1
1
2
1
1
0
1
1
5
1
2
1
1
2
1
1
0
0
2
1
1
0
0
1
1
3
1
2
1
1
1
1
0
1
1
1
2
2
1
1
1
2
1
2
2
1
1
1
0
2
2
1
1
0
0
0
0
1
1
1
0
1
1
1
1
2
1
1
1
1
0
0
0
1
0
3
1
2
1
1
1
1
1
1
1
3
0
1
2
2
1
2
2
2
1
0
2
1
1
1
1
1
1
1
1
1
2
1
0
2
1
2
2
1
2
2
1
1
1
2
1
2
2
1
1
0
1
2
1
2
1
0
1
1
1
1
1
1
1
2
2
1
1
0
3
1
1
0
1
1
2
2
2
1
2
1
1
1
1
2
1
0
2
0
1
1
1
2
1
2
1
2
1
1
1
1
0
1
2
0
1
1
1
2
1
2
2
1
2
2
1
1
1
1
1
1
1
1
2
1
2
1
1
1
2
1
2
1
1
2
2
2
1
2
1
2
1
1
1
2
2
2
1
2
1
2
1
2
2
0
1
0
1
0
1
1
1
1
1
1
1
2
2
2
1
0
1
1
0
0
1
1
1
0
0
2
1
2
2
2
1
2
0
0
1
2
1
2
1
1
0
2
2
1
1
2
0
1
1
1
1
1
1
1
1
1
0
1
1
2
1
1
1
0
1
2
2
1
2
1
1
1
1
0
1
1
2
1
1
1
0
1
2
0
0
2
1
1
0
0
0
1
1
1
1
1
0
1
2
0
1
1
2
1
0
1
0
0
1
0
1
2
0
1
1
3
0
1
1
2
0
0
0
0
2
2
1
1
1
2
1
1
0
1
0
2
1
1
1
1
1
1
1
2
0
2
1
1
0
0
1
1
1
1
1
1
1
2
1
0
1
1
1
2
1
1
1
0
1
0
0
1
1
1
1
1
0
2
1
0
1
1
2
1
1
0
0
0
2
1
1
1
0
1
1
0
1
1
1
1
2
2
1
1
1
1
1
2
1
2
1
1
1
0
2
1
1
1
0
2
1
0
0
1
0
1
1
1
0
0
1
1
0
2
1
2
0
0
1
0
0
1
1
0
1
1
1
1
2
0
1
1
1
1
0
2
1
2
0
1
2
1
1
1
1
1
0
1
1
1
1
1
1
0
1
1
1
2
1
2
2
2
1
2
1
1
1
2
1
0
0
1
0
1
2
2
2
1
0
1
1
1
1
2
1
1
1
2
1
1
1
1
1
2
1
2
0
1
1
2
1
0
0
2
1
1
1
1
2
1
1
0
1
2
1
1
1
1
0
1
0
2
1
1
2
2
2
1
0
1
2
1
1
1
1
2
0
1
1
1
1
0
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
3
1
1
2
0
2
1
1
0
0
1
0
1
2
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
0
1
1
0
1
2
1
1
0
2
1
2
2
1
3
2
0
2
2
1
1
1
2
1
2
1
0
1
1
1
0
0
1
1
1
0
1
1
1
0
1
2
1
1
0
2
1
0
1
1
1
1
2
1
1
1
2
1
1
1
0
1
0
2
2
2
1
2
0
1
2
1
1
1
2
1
1
1
0
1
2
2
1
1
1
1
2
2
1
2
1
2
0
1
0
1
1
2
1
0
0
2
2
1
1
0
1
1
1
0
1
1
1
0
1
0
1
0
1
0
1
1
1
1
1
1
1
1
1
1
2
1
1
2
0
2
1
1
2
2
1
0
0
0
1
1
2
1
1
2
1
2
1
0
1
2
1
2
2
1
2
2
1
1
2
1
1
1
1
2
1
1
1
1
1
2
1
1
3
1
2
2
1
0
1
2
1
2
1
0
0
1
2
2
0
1
1
1
2
1
0
3
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
0
1
1
1
1
1
0
2
2
2
1
2
0
0
2
1
3
1
0
0
1
1
2
1
2
0
1
1
1
2
1
2
1
1
2
0
1
1
2
0
1
1
1
2
1
1
1
1
2
1
1
2
1
2
2
1
0
1
1
0
2
2
1
1
1
1
2
1
1
1
2
0
1
0
2
3
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
0
0
2
1
1
1
0
2
0
1
1
1
2
1
1
1
1
1
1
1
2
0
2
1
0
2
1
1
0
1
2
1
2
1
1
1
1
1
0
1
0
1
2
1
1
1
0
1
0
1
1
1
1
0
1
0
1
0
1
1
1
2
0
1
1
0
3
1
2
0
2
0
0
1
0
1
1
2
1
1
0
0
2
1
2
2
2
1
1
2
1
1
1
1
0
1
2
1
0
1
0
2
2
1
2
1
0
2
1
1
1
1
1
1
1
2
1
2
1
1
1
2
0
0
1
1
2
0
1
1
0
1
1
2
2
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
2
0
1
0
0
1
1
2
1
1
1
1
1
1
1
2
1
1
0
2
1
1
0
1
1
1
2
1
2
0
1
1
1
2
0
1
1
1
1
0
0
1
1
1
1
0
2
1
2
2
2
0
1
1
2
0
1
1
1
1
1
0
1
3
1
1
1
0
1
1
1
2
1
1
1
1
1
0
2
1
1
1
0
1
2
1
1
1
1
1
2
1
1
1
1
2
1
1
0
1
0
2
2
0
1
1
0
1
1
2
1
2
2
1
1
1
0
1
1
1
1
1
1
1
1
0
1
1
1
0
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
3
1
2
1
1
0
1
0
0
2
0
1
0
0
1
2
1
2
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
2
1
2
1
2
1
1
2
1
2
1
0
2
1
1
2
2
2
0
1
1
1
2
1
0
1
0
1
0
2
1
1
1
2
1
1
1
1
0
1
1
0
1
2
0
1
1
1
2
1
0
1
1
1
1
1
2
1
2
1
1
0
1
1
1
1
2
2
2
2
1
1
1
2
1
0
1
1
1
1
1
2
0
2
1
1
2
1
1
1
2
2
1
0
1
1
0
1
1
1
0
2
2
1
1
0
1
0
1
1
1
0
1
1
1
2
2
1
1
0
1
2
1
1
1
1
0
1
2
1
0
1
3
2
2
1
0
2
1
1
2
1
2
0
1
1
1
0
1
1
2
1
1
1
1
1
1
2
0
2
1
2
1
1
0
1
0
1
1
1
2
0
1
2
1
2
2
0
1
1
2
1
1
1
2
0
0
2
2
1
0
1
1
1
2
2
2
2
1
1
1
2
1
1
2
2
0
1
1
1
1
1
1
1
0
1
1
1
1
2
1
1
2
0
0
2
2
1
1
1
1
1
2
2
1
1
1
2
1
1
0
1
1
0
1
1
2
1
1
2
2
1
1
1
1
0
2
1
1
2
1
1
1
1
1
2
1
1
1
1
0
1
1
1
1
0
0
1
2
2
1
1
1
1
1
2
0
2
1
1
0
2
2
1
1
0
1
0
1
1
2
1
0
1
0
1
3
0
0
2
2
2
1
1
1
1
2
2
1
1
0
1
0
1
1
2
2
2
1
1
0
1
1
0
1
0
1
0
0
1
2
1
1
2
1
0
1
1
1
1
0
2
0
1
2
1
1
2
2
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
0
1
2
0
1
1
2
2
1
1
1
1
0
1
2
1
2
1
1
1
0
2
1
1
1
1
1
2
1
1
1
1
2
1
2
1
2
1
2
1
1
0
1
0
1
0
2
1
1
2
2
0
1
2
0
1
1
1
0
1
1
0
0
1
1
2
3
1
1
1
1
1
2
2
1
1
1
1
1
2
0
2
2
2
1
1
2
1
1
1
1
1
1
1
2
2
1
1
3
1
1
1
0
1
1
1
1
0
1
0
1
1
1
2
0
1
1
2
1
0
2
2
1
1
1
2
1
0
2
1
2
1
2
1
1
1
1
1
1
1
1
0
2
1
2
1
0
1
0
1
1
1
1
1
1
0
2
0
1
2
2
1
1
2
1
1
1
1
1
1
1
1
0
1
2
2
1
1
0
1
1
1
3
0
1
2
1
1
0
0
1
0
1
1
1
1
1
1
1
0
2
1
0
1
1
1
1
1
0
2
1
2
1
1
0
0
1
1
1
2
2
2
1
1
1
1
1
1
1
1
1
1
1
2
0
0
1
1
2
2
2
1
0
1
1
0
1
2
1
1
1
1
0
1
0
0
1
1
2
0
1
1
1
1
1
1
1
1
1
0
1
1
2
2
1
2
0
2
1
1
1
1
1
1
2
2
2
1
0
1
1
2
2
1
1
0
1
1
1
0
1
1
2
1
1
1
1
1
1
1
1
1
1
0
1
1
1
2
1
1
1
2
1
1
2
1
2
1
1
0
2
0
1
1
1
1
1
1
1
2
1
1
1
1
2
0
1
0
2
1
1
1
1
0
1
1
1
1
0
2
2
0
2
2
2
1
1
0
1
1
2
2
1
2
1
1
1
1
2
0
1
1
2
1
2
2
1
1
2
2
2
1
1
0
2
1
1
0
1
2
0
1
2
1
1
2
0
2
1
1
1
2
1
2
2
1
1
1
1
0
1
2
2
1
1
0
1
2
1
0
1
1
2
1
2
1
1
2
0
1
1
1
1
1
1
1
1
1
0
1
1
0
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
2
1
0
1
2
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
2
0
1
1
1
1
1
1
1
1
1
1
0
2
1
1
1
0
1
0
1
1
1
1
1
1
1
0
2
1
1
0
1
2
1
2
1
1
0
1
2
1
0
1
2
1
1
1
1
1
0
1
2
1
0
2
1
1
1
2
0
2
2
1
2
2
0
0
2
2
1
1
1
0
2
1
2
1
1
1
1
2
1
1
2
2
1
0
1
0
2
1
1
0
1
1
2
0
2
2
1
1
2
1
1
1
1
1
2
1
2
1
2
1
0
1
1
0
0
1
1
1
2
1
1
1
0
2
0
1
1
2
1
1
2
2
1
1
1
0
1
0
1
1
1
1
1
0
1
1
1
2
0
2
1
1
1
0
1
1
1
1
1
1
0
1
1
2
1
1
2
1
1
1
1
1
1
2
1
2
2
0
2
0
1
2
0
1
1
0
1
2
0
1
2
2
2
0
2
0
1
0
1
0
2
1
1
1
2
2
1
1
1
1
2
1
1
0
1
1
2
0
1
1
1
1
2
1
2
2
1
0
0
2
1
1
1
1
1
2
1
1
2
2
1
0
1
1
1
2
1
0
1
2
1
1
1
1
2
2
1
1
1
1
1
0
2
2
2
1
2
1
0
1
0
1
1
0
1
2
2
1
2
1
2
1
0
1
1
1
1
2
1
1
2
1
1
1
0
1
1
0
1
1
1
2
1
1
0
1
2
2
0
2
1
1
0
2
2
1
2
2
1
0
1
2
2
2
1
0
2
0
1
1
1
1
1
2
0
2
1
2
1
0
4
1
1
1
1
2
1
1
2
0
1
1
1
1
1
1
0
1
2
1
1
2
1
2
1
1
1
2
2
2
1
1
1
1
1
0
2
0
0
1
1
1
1
1
1
2
1
0
1
1
2
0
1
1
2
3
2
2
2
1
1
1
1
1
1
0
1
0
0
0
1
2
2
1
1
1
2
1
1
2
1
1
0
2
1
1
1
1
1
2
2
1
1
1
1
1
0
1
1
1
2
1
1
2
2
1
1
1
1
0
1
1
1
0
1
0
1
1
0
1
1
2
0
2
1
1
1
1
1
1
1
0
1
1
2
1
2
1
0
1
1
1
0
2
1
2
1
1
2
0
2
0
1
1
1
1
0
1
1
1
2
2
1
2
1
2
1
1
0
0
1
1
2
2
1
0
0
1
1
0
1
1
0
2
1
1
1
1
0
0
1
0
0
1
1
2
1
1
2
1
2
1
2
3
1
0
1
1
1
2
0
1
1
1
2
1
1
1
2
1
1
1
1
1
0
2
1
0
1
1
2
1
2
1
1
1
0
1
1
0
1
0
1
0
2
2
1
1
1
1
2
2
0
1
1
1
0
1
2
0
1
1
1
2
2
2
1
3
1
1
0
1
2
1
1
0
1
0
0
2
1
1
1
1
1
0
2
0
1
1
1
1
1
1
2
1
1
2
2
2
2
1
2
2
1
2
2
2
0
1
2
1
1
1
2
1
1
1
2
1
1
1
0
2
1
1
2
2
1
1
1
1
1
1
1
1
2
2
0
0
1
1
0
0
1
2
1
1
1
1
1
2
1
1
2
1
1
2
1
1
2
1
2
1
1
0
1
2
1
1
1
2
0
1
1
2
0
1
1
1
1
1
1
1
0
1
1
1
0
1
1
1
2
2
2
1
1
2
1
2
1
1
1
1
2
0
1
1
1
2
1
1
0
2
0
1
0
2
2
1
2
0
1
0
1
1
0
1
1
1
1
2
3
2
0
1
1
2
1
1
1
0
2
0
1
1
1
1
2
1
0
1
0
1
0
1
1
1
1
2
0
1
0
1
1
1
1
2
1
2
2
1
2
1
1
2
0
1
0
0
1
0
1
1
1
1
1
0
1
1
1
2
2
2
0
1
1
2
0
1
2
1
0
2
1
0
1
1
1
0
1
2
2
0
0
2
1
2
0
2
1
0
1
2
2
2
1
1
2
2
0
2
1
1
1
1
1
1
0
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
0
2
2
1
2
1
1
2
1
1
1
1
1
0
1
2
1
1
1
1
1
0
0
2
1
1
1
1
1
2
1
1
2
1
2
1
1
1
1
2
1
3
2
1
1
2
1
1
0
1
1
2
1
1
1
2
0
0
2
1
0
0
1
1
0
1
1
1
0
2
1
1
1
2
1
2
1
1
1
1
1
2
1
0
1
1
1
2
2
0
1
2
2
0
2
2
0
2
1
2
0
1
0
1
2
1
1
1
1
2
2
1
1
2
1
1
0
2
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
2
1
1
2
1
1
2
1
1
0
1
0
1
2
1
1
1
2
1
1
2
1
1
1
0
1
1
0
2
2
1
2
0
0
1
0
1
1
2
1
1
0
1
2
1
2
1
2
1
0
1
1
2
1
1
2
1
1
1
1
2
1
1
0
1
1
1
1
2
2
1
1
1
4
0
1
2
1
0
1
1
2
1
2
0
2
1
1
1
1
1
1
3
2
1
1
2
1
1
1
1
0
1
1
1
2
1
1
0
2
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
0
2
1
1
1
1
0
1
1
1
2
1
2
1
1
1
0
1
0
2
0
2
1
1
1
2
1
0
1
1
1
1
1
1
1
1
1
1
0
2
1
1
0
2
2
1
1
1
1
0
2
2
0
1
1
1
1
1
1
2
0
1
0
1
1
1
1
1
0
1
1
1
1
2
2
2
1
2
2
1
2
0
1
1
0
1
2
1
0
1
2
1
1
2
1
1
2
1
2
1
0
1
1
2
1
0
2
1
1
2
2
2
0
1
1
2
1
1
1
2
1
1
2
1
1
1
1
0
2
2
3
2
1
2
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
0
2
1
2
1
1
1
1
1
1
0
1
2
1
2
2
1
2
1
1
1
3
0
2
1
1
2
1
0
1
1
1
1
0
1
1
2
0
1
1
1
1
1
1
1
1
2
0
0
2
1
0
0
1
0
2
0
1
1
1
1
1
1
0
0
1
1
2
2
0
1
1
0
1
1
1
1
0
2
1
1
1
1
0
2
1
1
1
1
0
0
1
1
0
1
0
2
2
1
2
1
2
0
2
0
1
1
1
1
1
0
0
1
1
1
1
1
2
1
1
2
2
2
1
2
2
1
1
2
2
1
2
1
1
0
1
2
1
4
2
1
2
3
1
2
2
1
1
2
2
1
0
1
2
2
1
1
1
2
2
1
1
2
0
0
2
0
1
2
2
2
0
1
2
3
1
1
1
2
1
1
1
1
2
1
2
1
0
1
1
0
1
1
2
1
0
2
0
2
1
0
1
1
1
1
0
1
1
1
1
1
0
1
0
0
1
2
1
1
1
2
1
1
3
1
2
0
1
1
1
1
1
1
2
1
1
1
0
0
1
1
0
0
0
1
0
1
1
0
1
1
0
1
2
0
0
1
2
0
2
1
1
1
1
2
1
0
0
2
1
1
0
1
1
1
1
0
1
2
0
2
0
1
2
1
0
1
1
1
1
1
2
1
0
1
1
1
2
1
1
0
1
1
1
1
2
0
0
1
1
1
1
1
1
1
1
1
2
1
1
0
2
1
1
2
2
1
2
1
1
1
0
1
1
1
1
2
1
1
1
1
2
2
1
1
1
1
1
0
1
2
0
1
1
1
0
1
2
1
3
2
1
1
2
2
1
1
1
0
0
2
2
1
2
0
2
0
1
1
1
0
1
1
1
1
2
1
1
2
1
1
1
3
1
2
0
1
2
1
1
1
1
1
1
1
0
1
1
0
1
0
1
1
1
1
1
1
1
2
1
2
0
1
2
1
0
1
1
1
0
1
1
2
0
1
0
1
1
1
0
0
1
1
1
1
2
1
2
1
1
1
0
2
1
1
0
1
1
2
1
1
2
0
1
1
1
2
2
1
2
6
1
2
1
1
1
1
2
1
1
1
0
0
1
1
1
1
1
1
1
0
1
0
1
1
1
1
0
2
1
1
1
1
1
2
1
2
2
2
0
1
2
1
1
1
2
1
0
0
2
0
1
1
0
1
1
0
1
1
1
1
1
2
2
2
1
1
1
1
0
2
1
1
1
1
1
1
4
1
2
1
1
1
1
0
2
1
1
1
2
1
2
1
1
3
1
2
1
1
2
1
2
1
0
1
2
1
0
1
0
2
2
1
1
2
2
0
1
0
2
1
2
1
1
2
1
1
1
1
2
1
0
2
2
1
1
1
1
0
2
1
2
2
1
1
2
1
1
2
1
1
2
0
1
1
2
1
1
0
1
0
1
1
1
1
2
1
2
1
1
1
1
1
0
1
2
1
1
1
2
1
2
2
0
1
1
1
1
1
2
2
1
1
1
1
2
1
2
0
1
2
1
2
1
1
1
2
1
1
2
0
1
2
1
0
2
0
1
2
1
1
1
2
2
1
2
0
1
0
1
1
1
1
0
0
2
3
0
0
1
1
2
0
1
0
1
2
1
2
0
2
2
1
1
0
1
1
1
1
1
1
1
1
0
1
2
1
1
2
1
0
1
2
2
1
2
1
1
1
2
1
1
0
0
1
2
2
1
0
4
1
1
2
1
1
2
0
0
1
1
0
1
1
1
2
1
0
1
1
0
0
2
2
2
1
0
2
2
2
1
1
0
1
2
1
1
2
2
2
1
0
2
1
0
0
1
2
1
2
1
1
0
2
0
2
2
1
1
1
1
1
2
1
0
1
0
1
1
2
1
1
1
1
1
1
1
1
0
1
2
1
1
1
1
0
0
0
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
0
2
2
1
1
2
2
1
2
1
2
1
0
1
0
0
0
1
0
2
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
2
1
1
1
2
0
1
2
0
1
0
1
1
1
1
1
1
2
1
0
1
0
2
1
0
1
1
0
1
2
1
1
1
1
1
2
1
1
1
1
0
1
1
1
1
0
1
1
2
1
2
1
0
1
2
1
0
1
3
0
1
0
1
0
2
2
2
0
2
0
1
2
1
2
1
1
0
0
1
1
1
0
0
1
2
1
2
0
1
2
1
2
1
0
2
1
0
1
1
2
1
2
1
2
1
2
2
2
0
1
1
0
1
1
1
0
2
2
2
1
1
1
1
0
1
2
1
1
0
2
1
1
2
0
0
2
0
0
2
2
1
2
1
3
1
1
0
2
1
0
1
1
2
1
1
1
2
1
1
1
1
0
2
0
1
1
2
1
1
0
1
1
1
1
1
0
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
2
1
2
1
1
0
0
0
0
0
2
1
1
0
0
1
2
0
0
0
2
1
1
1
0
0
1
0
1
1
1
0
2
1
1
1
2
1
0
0
2
1
1
1
0
1
1
1
1
1
2
2
1
2
1
0
1
0
1
1
0
2
1
2
2
1
2
1
1
2
2
2
1
0
2
0
1
1
1
4
0
1
1
1
1
0
1
2
0
2
2
1
0
0
1
1
2
2
0
1
2
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
3
0
1
1
1
1
1
2
1
1
1
2
1
1
1
1
2
1
0
1
0
1
1
1
0
1
1
0
1
0
0
1
2
1
2
1
1
1
2
0
0
1
2
1
2
1
1
1
1
2
1
1
1
0
1
1
2
0
2
1
2
1
1
1
2
0
1
0
1
2
2
1
2
1
1
1
2
2
1
2
2
1
0
3
1
2
1
1
1
1
1
2
2
1
1
0
2
1
1
1
2
1
1
1
1
1
2
2
0
1
1
1
0
2
2
1
0
0
1
1
2
2
1
1
1
0
2
1
3
1
2
0
1
2
0
1
1
1
2
2
1
1
0
2
1
1
0
1
1
1
1
0
0
1
1
2
2
1
2
0
1
1
0
1
2
1
2
0
1
0
2
1
2
0
2
1
1
0
2
2
1
2
1
1
1
1
1
2
0
1
1
2
3
0
1
1
2
1
1
1
0
2
1
1
2
2
1
2
1
1
1
1
2
1
1
0
2
1
1
1
1
1
1
2
1
0
1
1
2
0
1
2
1
2
2
0
0
1
0
1
2
1
1
1
1
1
1
0
1
1
1
1
0
1
2
0
1
0
0
1
1
1
1
1
2
1
1
1
2
0
1
0
1
1
2
2
1
1
0
2
1
2
2
2
1
2
1
0
1
2
0
1
2
1
0
0
0
2
2
2
2
2
1
1
2
1
2
1
2
2
1
3
1
0
2
1
1
1
2
0
2
0
1
2
1
1
2
2
2
1
1
1
0
1
1
0
1
1
1
1
0
2
2
1
1
0
0
1
1
1
1
1
1
0
1
1
2
0
1
0
0
0
1
1
1
1
1
0
1
0
1
2
1
1
1
2
0
1
1
0
1
0
1
1
2
0
0
1
1
1
1
0
0
2
2
0
1
1
0
1
1
0
2
0
1
1
0
2
0
0
2
0
2
1
1
1
1
1
0
1
1
1
0
2
2
2
1
2
1
1
1
0
1
0
2
2
1
1
1
1
1
1
0
1
1
1
2
1
0
1
2
2
1
1
1
1
0
1
4
1
0
0
1
0
2
1
0
0
1
1
1
2
1
2
1
1
1
1
2
1
1
0
1
0
0
1
2
2
1
1
0
0
2
2
2
1
2
1
2
2
1
0
1
0
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
0
1
0
1
1
1
1
2
2
2
1
2
2
1
1
2
1
1
1
1
1
0
1
2
1
3
1
1
1
1
2
1
2
0
1
1
1
1
1
0
0
1
1
2
1
1
1
1
1
1
1
0
1
1
1
2
0
2
0
1
2
0
2
1
1
2
1
0
1
1
0
2
0
1
1
2
2
0
1
1
1
1
2
2
1
2
1
2
1
2
0
2
1
1
1
1
1
0
1
1
2
1
0
1
1
1
2
0
1
2
2
1
2
1
1
1
1
0
1
2
2
0
1
1
2
1
1
1
1
1
0
0
0
2
1
1
1
1
1
0
1
1
2
0
1
0
0
1
2
1
1
2
1
1
0
0
1
1
0
2
0
2
1
2
1
1
0
1
0
1
1
0
1
1
1
2
1
1
1
1
1
1
1
0
0
1
1
2
1
0
1
1
2
2
1
0
1
1
1
2
0
1
1
1
4
2
2
2
0
1
1
2
1
1
1
1
1
1
0
1
2
1
1
2
1
2
2
2
1
1
0
1
0
0
2
1
1
1
1
0
0
1
1
1
1
1
2
1
1
0
3
1
0
0
2
1
1
0
0
1
1
2
1
2
1
1
1
2
1
1
1
2
2
1
1
0
2
0
1
1
1
1
1
1
2
0
2
2
1
1
1
1
2
0
1
1
1
1
0
1
1
0
0
1
1
2
1
0
1
1
2
2
0
0
0
1
1
0
1
1
2
1
1
1
2
1
1
1
1
2
1
2
1
1
1
2
1
0
2
1
2
2
1
1
1
1
2
1
1
1
0
1
1
0
1
2
1
1
2
0
0
1
2
0
1
1
1
2
1
2
0
0
0
1
1
2
0
1
1
1
1
0
1
1
1
2
3
1
1
1
2
1
1
1
1
0
1
1
0
1
2
1
0
0
1
0
1
2
1
1
1
0
1
1
1
2
1
1
1
1
0
2
0
0
1
1
1
1
1
2
1
1
1
1
0
3
1
2
0
2
1
1
2
1
1
1
2
1
1
1
2
2
2
0
1
1
2
1
1
0
1
2
2
1
0
1
1
2
2
0
0
2
1
1
1
2
1
1
1
0
1
1
3
0
1
2
2
0
0
2
1
0
1
0
1
1
1
1
1
1
1
1
2
0
1
0
2
2
0
2
2
0
1
2
1
2
1
2
2
2
2
0
1
1
2
1
1
1
1
1
1
1
2
1
0
1
1
2
1
1
2
1
0
1
1
1
1
1
1
2
1
1
1
1
2
1
0
1
1
0
1
0
0
0
1
0
1
1
2
0
1
1
1
1
0
1
1
1
2
1
1
1
0
1
1
2
1
0
2
0
1
1
0
1
2
1
2
1
1
0
1
0
1
2
1
1
1
1
1
1
1
1
1
2
0
1
0
1
1
1
2
0
1
1
1
0
1
1
1
1
2
2
0
1
1
1
3
2
2
0
1
1
2
1
1
1
1
0
1
3
0
1
1
1
1
2
2
2
0
2
0
1
2
1
1
1
1
1
0
1
1
1
1
2
0
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
0
1
1
0
0
1
1
1
1
2
0
2
1
0
2
2
1
1
1
0
1
1
1
0
0
0
0
1
1
2
1
2
2
1
2
1
1
2
2
2
1
1
0
1
2
2
1
0
2
1
1
1
1
1
1
0
2
1
1
0
2
1
1
2
0
2
0
0
2
0
1
1
2
2
1
1
1
1
1
5
1
0
1
2
1
2
2
1
2
2
1
1
1
2
2
1
1
1
2
2
0
1
2
0
1
1
1
1
1
1
1
2
2
2
0
1
0
1
2
2
0
0
0
1
1
2
1
1
1
2
1
2
1
2
0
1
2
2
1
1
1
1
2
2
1
0
1
1
1
1
2
1
0
2
2
1
1
1
1
1
1
0
1
1
2
0
1
1
1
1
0
1
1
1
1
1
1
2
1
1
1
1
1
1
0
2
0
0
0
1
2
2
0
2
1
1
2
1
2
1
1
1
2
2
1
1
1
2
0
0
2
0
1
1
0
2
1
0
1
1
1
0
2
1
1
1
0
2
0
2
1
0
1
0
2
1
1
3
1
0
1
1
0
1
1
0
1
2
1
1
1
0
0
0
0
2
0
1
1
1
2
1
1
0
0
1
1
0
2
1
1
1
1
1
1
0
2
0
0
0
1
1
2
1
1
2
0
0
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
2
1
1
2
1
1
1
2
1
1
2
1
1
0
2
2
1
2
0
1
1
1
1
3
1
1
1
1
1
0
1
2
3
1
1
0
1
1
0
2
1
0
1
0
1
0
1
1
1
2
1
1
2
1
1
0
2
1
1
1
2
1
0
2
1
2
1
1
2
2
1
1
0
1
1
2
1
0
1
1
1
2
1
1
0
1
0
2
2
1
1
0
1
0
1
1
2
1
0
1
1
1
1
1
1
1
2
1
0
0
1
1
1
2
1
1
1
1
1
1
1
0
2
1
1
1
0
1
0
1
1
1
1
1
1
1
1
1
2
0
1
1
1
1
1
1
0
1
0
1
2
0
1
1
2
1
1
1
1
0
1
1
1
1
2
1
2
1
1
0
1
2
1
1
1
1
1
1
2
2
0
1
1
1
1
0
2
2
1
1
1
1
1
0
1
1
1
1
0
1
2
1
2
2
2
1
2
1
0
1
1
2
1
1
1
1
2
1
1
0
1
1
2
2
0
1
2
1
1
2
4
1
5
7
1
1
1
0
1
1
0
2
0
0
1
1
1
1
1
2
1
1
1
1
2
0
1
2
1
1
2
0
1
1
1
1
1
0
1
2
1
2
1
0
1
2
1
0
2
1
1
0
0
1
1
2
2
1
1
2
1
1
2
1
2
0
1
1
2
2
1
1
0
1
1
1
1
1
0
1
0
1
1
1
1
2
1
1
2
1
2
2
1
1
1
2
1
1
1
1
2
1
0
0
1
2
1
1
1
0
0
1
0
1
0
0
2
1
0
1
1
2
2
1
1
1
2
2
1
2
0
1
1
1
2
1
0
0
1
1
1
2
1
1
1
0
2
0
1
2
2
0
0
1
1
0
2
2
2
1
1
1
0
1
1
1
1
1
2
1
1
1
0
1
1
1
1
2
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
2
4
1
2
1
1
1
1
0
2
1
2
1
0
1
2
2
1
2
1
1
0
2
1
2
1
2
0
1
1
1
1
1
1
0
1
1
2
0
0
2
1
1
1
1
1
2
1
1
2
1
1
1
2
1
0
2
0
3
1
2
2
1
1
0
0
1
1
3
1
1
1
2
0
1
2
1
1
1
0
0
2
2
2
1
0
0
2
1
1
1
1
2
1
2
1
1
2
6
1
1
1
1
1
0
0
1
1
2
0
2
1
0
1
0
1
1
2
1
1
1
1
1
1
1
0
0
2
0
2
1
1
1
1
2
0
0
1
1
1
0
1
1
1
1
1
2
1
1
2
2
2
1
1
0
1
1
1
0
0
0
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
0
2
0
1
1
1
1
1
1
1
1
1
2
0
2
1
2
1
2
2
0
3
1
4
0
0
1
1
2
1
1
1
1
0
1
2
0
1
1
1
2
2
0
1
1
1
1
1
1
0
1
2
2
0
1
1
0
2
1
1
1
0
2
2
2
1
1
0
1
2
1
1
1
2
0
2
1
1
1
2
1
0
0
1
0
1
1
1
1
0
1
1
2
2
1
2
1
1
1
2
0
1
1
1
2
1
1
0
0
2
1
2
1
2
1
2
1
1
1
1
1
0
1
2
0
1
1
1
0
0
2
1
1
2
1
0
2
1
1
1
2
0
1
2
1
2
1
1
1
2
1
2
1
1
2
2
2
1
1
1
0
1
1
1
1
1
0
1
1
2
1
1
1
2
1
1
2
2
0
1
0
2
1
2
2
1
0
1
1
1
1
2
1
1
1
1
1
1
0
1
2
1
0
1
1
1
1
0
2
0
1
1
0
2
1
1
1
1
0
1
1
1
1
1
2
1
2
0
1
1
1
0
1
2
0
0
0
1
1
0
1
2
0
2
0
1
1
1
1
1
1
1
2
1
1
1
1
0
1
2
1
2
0
0
2
1
2
1
1
1
0
1
1
0
0
1
1
1
0
1
0
0
2
1
1
2
1
1
0
1
2
3
2
0
1
1
1
1
0
0
1
0
2
1
1
0
1
1
1
2
1
2
2
1
1
1
1
1
0
2
1
2
1
2
1
2
2
2
2
1
2
1
2
1
2
1
0
2
1
2
0
2
2
1
1
2
1
2
1
0
1
2
1
1
2
1
2
2
2
1
2
1
0
1
1
2
0
1
2
2
1
1
2
1
1
1
2
2
2
2
1
1
1
1
2
0
1
2
1
1
0
0
1
1
0
1
1
1
1
1
2
1
2
0
1
1
1
2
1
1
1
1
1
2
0
1
2
1
1
0
1
1
0
2
0
1
2
1
1
1
1
3
1
1
1
0
1
1
0
0
1
1
1
2
1
1
1
2
2
1
0
1
1
1
1
1
2
2
2
1
2
2
2
2
2
2
1
1
2
1
2
1
0
2
1
1
1
1
1
1
0
1
1
0
1
0
1
0
0
1
1
1
2
1
1
1
1
1
0
0
0
2
1
1
1
1
2
0
1
1
2
3
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
0
1
2
0
1
1
1
1
1
1
1
1
2
1
0
2
2
1
2
1
2
2
1
1
1
1
1
2
1
2
1
1
1
1
2
0
2
1
2
0
2
0
2
1
2
1
1
0
0
1
1
1
5
1
0
2
1
1
2
0
1
2
1
1
2
2
1
1
1
1
2
0
0
1
0
1
1
1
1
1
1
0
2
1
1
0
1
2
1
2
1
1
1
0
1
1
0
1
1
1
0
0
1
2
1
1
2
2
1
1
1
1
1
2
0
2
2
1
1
0
1
0
1
0
1
1
1
1
2
1
2
1
1
1
0
1
1
1
0
0
1
0
2
1
0
0
2
2
0
2
1
2
1
0
1
2
1
1
1
1
1
2
1
1
1
2
1
2
2
1
2
0
1
1
1
1
2
1
2
3
1
1
1
1
1
1
1
2
1
0
2
1
0
1
0
2
1
1
1
2
2
1
1
2
1
1
1
1
1
2
1
0
1
1
1
0
2
1
1
2
1
2
2
2
1
1
1
1
2
2
0
1
1
1
2
1
1
1
1
2
2
1
1
1
1
1
1
1
1
2
0
0
1
0
2
1
2
1
1
1
1
1
2
1
2
2
1
0
0
3
2
0
1
0
1
3
1
1
2
1
1
2
1
1
1
2
2
1
4
2
1
2
2
2
2
2
2
0
1
1
1
2
0
1
0
0
0
2
1
1
1
1
2
2
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
0
1
2
0
1
1
1
1
1
1
1
1
0
1
0
0
1
1
1
2
2
1
0
1
2
1
1
1
0
0
1
1
2
2
2
0
1
1
1
2
0
1
0
1
1
1
2
1
0
2
0
1
1
1
1
0
2
2
0
2
1
2
1
2
1
0
1
0
1
0
2
1
1
1
2
0
2
1
1
2
1
0
0
2
1
1
2
1
2
0
1
2
1
0
1
2
1
1
1
0
1
3
1
1
2
0
2
1
1
0
0
1
0
2
1
6
1
2
2
0
1
1
1
1
1
0
2
1
2
0
1
1
1
2
1
2
1
1
2
1
1
1
2
1
2
1
1
1
2
1
1
1
1
0
1
0
2
2
1
1
1
2
2
2
0
1
1
2
0
1
3
1
1
1
1
1
2
1
2
2
2
2
1
1
1
1
2
0
1
1
0
1
1
1
2
1
1
1
2
1
2
1
1
1
2
1
1
1
1
2
1
1
2
1
0
2
1
0
1
0
2
2
1
1
2
0
1
1
1
2
1
3
0
1
2
1
1
1
1
2
1
0
2
0
1
0
2
1
1
1
1
1
0
0
1
2
2
1
1
2
1
2
0
1
1
0
0
1
1
1
1
1
2
0
2
1
0
1
1
2
1
1
1
1
0
1
1
1
2
1
0
1
1
2
2
1
1
1
1
1
0
0
2
2
2
1
2
2
1
1
2
1
2
2
0
2
1
1
1
0
2
2
1
1
2
1
2
1
1
1
1
1
1
0
1
2
2
1
0
1
2
1
2
2
0
0
1
1
1
1
1
1
2
2
0
1
1
0
1
2
2
1
1
1
1
1
0
1
1
1
2
0
2
1
2
0
1
1
0
0
1
0
2
1
1
0
1
1
0
2
0
2
2
1
1
1
0
1
1
1
1
2
0
1
0
1
1
1
1
0
2
1
1
1
2
2
0
0
1
2
1
1
2
1
2
1
1
0
1
2
2
1
1
1
1
2
1
2
1
1
1
1
2
0
1
1
1
1
1
1
1
0
2
1
1
1
0
1
1
1
1
0
1
1
1
3
1
0
2
2
1
1
1
1
2
0
1
1
0
1
2
2
2
1
1
1
1
1
2
1
1
2
2
1
1
1
1
2
2
1
1
1
0
1
1
1
1
1
2
1
1
0
1
1
1
1
0
0
1
0
1
0
2
2
1
1
1
1
2
2
1
1
2
2
1
2
1
1
1
1
0
2
2
1
2
1
1
2
2
1
1
1
1
1
1
1
0
1
2
1
1
1
0
1
1
2
1
0
1
1
4
1
1
1
1
1
2
1
0
2
1
1
1
1
2
1
0
2
1
1
1
2
1
2
2
2
1
1
2
1
1
1
0
0
2
1
3
1
1
1
1
2
0
2
1
1
1
2
1
1
1
2
0
2
2
1
1
0
1
1
1
1
2
1
1
1
1
2
2
1
1
1
1
1
0
1
0
1
1
0
1
1
1
0
1
0
1
1
1
1
1
1
1
0
2
0
1
1
1
1
1
2
1
0
1
1
1
1
1
2
2
2
1
0
1
1
1
0
1
2
1
1
1
1
2
0
0
1
1
2
0
1
1
2
1
1
1
1
3
1
1
1
1
1
1
1
2
1
1
1
1
1
0
2
2
2
0
2
2
1
2
2
0
1
1
1
4
1
0
2
1
0
2
1
1
2
1
1
1
2
1
2
1
0
2
1
2
1
1
1
2
2
1
1
1
1
1
2
1
1
1
1
2
0
2
1
1
2
1
2
2
2
2
1
1
1
1
0
1
2
1
1
1
1
1
1
0
1
1
0
1
0
1
1
1
1
1
0
2
1
1
1
1
2
0
1
1
1
1
2
1
2
0
0
1
1
1
2
1
1
1
1
0
1
2
0
1
2
1
2
2
1
2
1
0
0
1
1
2
1
1
1
1
1
0
1
2
1
0
2
2
1
1
1
2
0
2
2
1
0
2
1
1
1
1
1
1
1
1
2
2
0
0
0
1
1
1
1
1
1
2
0
0
0
0
2
1
2
1
1
2
1
1
1
1
1
1
0
1
0
0
2
2
1
1
2
0
1
0
0
1
1
1
2
1
1
0
1
1
0
1
1
1
1
2
2
0
0
1
1
2
1
1
1
1
1
0
1
0
1
3
2
0
0
1
0
1
1
0
1
1
2
1
1
3
2
0
1
1
1
2
0
1
1
1
2
1
1
2
1
0
1
1
1
2
3
1
1
1
1
1
1
2
1
0
1
1
1
2
1
1
1
2
2
1
1
1
1
2
0
2
1
0
1
1
2
2
0
0
0
0
1
1
2
0
1
1
1
2
1
1
2
1
1
0
2
1
2
1
2
1
0
2
2
2
1
1
2
0
1
0
1
2
2
1
1
2
1
1
2
1
1
1
2
1
1
1
1
0
2
1
1
1
2
1
1
2
1
0
2
1
2
1
2
0
2
1
1
2
2
1
1
1
1
1
1
2
2
2
1
1
2
2
2
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
0
1
1
1
2
2
1
1
1
2
1
0
1
2
1
1
0
1
2
2
0
0
2
0
2
1
1
1
1
1
0
1
0
1
1
1
1
2
2
2
1
0
1
2
1
0
1
1
2
2
0
1
1
1
0
2
2
1
2
0
1
1
1
1
0
1
0
0
2
2
1
0
1
1
1
0
1
1
2
0
1
1
1
2
2
1
1
1
1
1
0
1
2
1
1
1
1
1
1
0
1
1
2
1
1
2
0
1
0
1
1
1
1
1
1
1
2
0
2
2
2
2
0
2
1
2
0
2
1
2
1
2
2
1
1
1
0
1
0
1
1
1
2
1
0
1
1
1
1
1
1
1
1
2
1
2
1
2
2
1
1
1
2
1
2
2
1
1
1
0
2
0
3
1
2
0
2
2
1
0
1
1
2
0
1
2
1
0
2
1
1
1
1
1
1
1
0
0
0
1
1
1
2
1
0
1
2
1
2
1
1
1
0
1
1
0
1
2
1
1
0
1
2
2
1
2
1
1
1
2
2
2
1
2
2
1
0
1
2
1
1
1
1
1
1
1
1
1
2
1
1
0
0
1
2
0
2
1
1
1
1
1
1
1
0
0
2
2
1
0
1
0
2
2
1
1
2
1
1
2
2
1
1
1
1
1
2
1
0
1
1
1
0
1
1
1
1
1
2
1
1
1
2
1
1
2
1
0
0
0
1
0
0
1
2
1
1
1
1
1
1
1
1
1
0
1
1
2
1
1
1
1
2
1
2
1
2
1
1
1
2
1
2
1
1
0
2
1
1
1
2
1
1
0
2
1
2
1
2
1
2
1
2
1
1
2
1
0
0
1
2
0
2
1
1
2
1
1
1
1
2
2
1
1
2
1
1
1
0
1
1
1
1
2
2
1
2
0
1
1
1
1
2
1
2
1
2
1
2
1
1
1
2
1
1
1
2
0
1
0
1
0
1
0
0
1
1
1
1
0
1
1
0
1
2
1
0
1
2
0
1
0
0
1
1
1
2
1
0
1
1
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
0
2
2
1
1
1
0
2
1
1
0
0
2
2
0
1
0
1
1
1
1
1
2
1
0
1
0
2
1
2
1
2
0
0
1
0
1
0
1
1
2
2
2
0
1
1
1
1
0
2
1
1
1
1
1
1
2
1
2
0
2
0
1
1
1
2
1
0
1
1
2
0
2
1
2
1
1
1
1
2
1
2
1
2
0
0
1
1
1
1
2
2
2
1
1
1
2
1
2
0
1
2
1
0
1
0
0
2
0
2
1
1
1
1
1
0
1
1
2
2
1
2
2
1
1
1
0
3
1
1
0
0
2
1
0
2
1
1
1
2
0
1
0
2
1
0
1
1
1
0
1
2
1
0
0
1
1
1
1
1
0
0
0
1
2
1
1
2
1
1
2
1
1
1
1
2
1
1
1
2
0
1
1
8
0
1
1
2
1
1
0
1
4
1
1
1
1
0
1
1
1
2
1
0
1
1
0
0
1
1
1
1
1
1
4
3
2
1
2
2
1
2
2
1
0
5
1
1
1
0
2
0
1
1
0
2
1
2
2
0
1
1
2
1
1
2
1
2
2
2
1
2
0
1
1
1
1
2
1
1
1
1
1
2
1
2
1
2
1
1
0
1
1
2
1
1
2
1
0
1
1
1
1
1
1
0
2
1
1
0
1
1
1
1
1
0
1
0
0
2
2
1
1
0
2
2
0
1
1
2
1
1
2
2
1
1
0
1
1
0
1
1
1
2
1
2
1
0
2
2
1
0
1
0
1
1
1
2
1
1
2
0
1
1
0
1
1
2
0
1
1
0
1
2
1
1
1
0
1
1
2
1
1
1
0
0
2
0
1
0
1
1
0
1
0
1
1
1
2
1
1
2
1
1
1
1
1
0
2
1
2
1
1
2
1
1
1
1
2
0
0
2
2
0
1
1
0
2
2
2
2
1
2
1
1
1
0
1
1
0
1
0
1
2
0
1
2
2
0
0
1
0
2
0
0
1
2
1
0
2
1
1
2
1
1
1
0
1
2
1
1
1
0
1
2
2
1
1
1
0
1
1
1
1
1
2
1
1
1
1
0
1
1
2
1
1
0
2
2
1
1
1
1
1
2
2
2
2
2
0
1
0
2
1
1
0
2
1
2
2
1
1
0
1
0
0
2
2
2
1
1
0
1
1
0
1
1
1
1
1
2
1
0
2
0
0
0
1
2
0
1
1
2
2
1
1
1
0
1
1
2
0
1
0
1
1
2
0
0
1
1
1
1
2
1
0
1
2
0
2
1
0
1
1
1
0
2
1
0
1
1
1
3
2
0
1
1
1
1
1
2
1
1
1
2
0
0
1
2
0
1
1
1
0
2
1
2
1
2
1
1
0
7
0
2
0
1
2
2
1
0
1
1
2
1
1
1
1
1
2
2
2
0
0
0
1
0
1
1
1
0
0
1
1
1
1
1
1
2
1
0
1
1
1
3
2
3
1
0
2
1
1
1
1
2
1
1
1
2
0
1
2
0
0
2
2
2
1
1
1
1
1
1
2
2
1
1
0
1
1
1
1
2
1
1
0
1
0
1
0
0
1
1
1
1
1
0
1
1
1
1
2
0
1
2
0
1
1
1
1
1
0
0
1
1
0
0
0
0
2
0
1
1
1
1
1
0
1
2
1
1
1
2
1
0
2
0
0
0
2
2
2
1
1
0
0
1
1
1
1
1
2
1
1
0
1
0
1
2
2
1
2
0
2
2
2
2
1
1
1
1
2
0
2
1
1
1
1
2
0
1
1
1
1
1
1
1
1
1
1
1
2
1
2
0
1
1
3
1
1
1
1
1
1
1
1
2
1
0
1
1
3
1
1
0
1
0
1
1
1
0
0
2
1
1
1
1
1
2
1
2
2
0
1
0
1
1
0
1
0
1
1
2
1
1
1
2
1
0
0
2
0
1
0
0
2
2
1
0
0
1
2
1
1
1
1
1
2
1
1
2
1
1
1
2
1
0
0
0
1
1
1
1
1
1
2
2
2
1
3
0
2
1
0
1
1
1
1
1
1
0
2
1
2
1
1
2
2
1
1
2
1
2
2
1
2
0
1
1
1
1
2
0
1
1
1
2
1
1
2
1
1
1
0
2
0
2
1
1
1
0
0
1
2
1
0
1
1
0
2
1
2
2
0
1
1
2
0
2
1
1
2
1
1
2
1
1
2
1
0
2
1
2
1
0
2
1
0
1
1
0
2
1
1
1
1
1
1
1
1
0
3
0
1
1
2
1
1
0
2
0
2
2
1
1
1
1
1
1
1
1
2
1
1
2
1
2
2
1
2
1
1
2
0
1
1
1
1
1
2
1
0
1
0
0
1
0
0
1
2
2
1
2
2
2
1
0
1
1
2
1
0
2
1
2
2
0
1
1
1
1
2
1
1
0
1
1
1
1
1
1
2
2
2
1
1
0
1
1
1
2
1
1
2
1
1
1
2
1
1
2
1
0
2
2
1
1
2
1
1
2
2
1
0
1
1
1
0
1
1
0
1
1
2
2
0
1
0
2
1
0
1
1
1
1
2
1
2
1
1
1
1
0
1
2
0
1
2
0
1
1
2
1
1
0
2
2
1
0
2
0
1
1
1
0
0
1
0
2
1
2
1
1
1
0
2
1
2
1
2
2
2
2
2
0
1
2
2
0
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
0
0
1
2
1
1
1
0
2
1
1
2
1
0
1
1
1
2
0
2
0
1
1
1
2
0
0
1
2
1
1
0
1
1
2
2
2
2
1
1
1
0
0
1
2
1
1
2
3
1
1
1
1
1
0
1
2
2
1
1
1
2
1
2
0
1
1
1
0
2
1
0
2
2
0
1
1
1
1
1
2
2
1
1
1
2
1
2
1
2
2
1
1
1
2
1
1
1
1
1
0
2
2
0
2
2
1
1
2
1
0
1
1
1
0
1
1
1
1
2
1
1
1
1
2
0
2
1
1
1
1
2
1
0
1
1
1
0
1
1
1
0
1
2
4
1
1
0
1
1
1
1
1
1
2
1
1
1
1
0
1
0
1
1
1
1
0
2
0
1
2
1
0
1
2
1
1
2
1
2
1
2
2
2
1
0
1
0
1
1
1
0
0
1
0
2
1
0
2
1
2
2
2
1
1
2
0
1
1
1
1
1
2
1
1
2
1
2
1
1
0
2
2
1
2
2
0
1
1
0
1
2
2
1
1
0
2
0
1
1
2
1
1
0
1
0
1
1
1
2
1
0
1
1
1
1
1
2
0
1
1
1
1
2
1
0
1
0
1
0
0
3
2
2
1
1
1
2
1
1
1
1
0
1
0
2
1
1
0
2
1
2
1
1
2
2
1
1
2
2
1
1
1
2
0
2
2
1
1
0
2
0
1
1
1
1
2
2
1
2
0
1
1
1
2
2
2
1
1
0
1
2
1
1
1
1
1
2
1
2
1
0
0
1
2
1
1
1
2
1
2
1
2
1
1
2
2
1
2
1
0
2
2
1
1
2
1
1
2
0
1
1
2
1
2
1
1
2
1
2
1
1
2
2
1
2
1
1
1
1
2
1
1
1
1
0
1
2
1
1
2
1
1
1
1
0
2
1
2
2
0
1
0
2
1
2
1
1
0
1
0
1
2
0
1
1
1
1
1
1
1
0
1
0
0
2
0
1
2
2
1
1
0
1
0
1
2
1
0
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
0
2
1
1
1
1
2
1
2
0
1
2
1
1
1
0
2
1
1
0
1
0
0
1
1
0
1
2
1
1
1
1
1
1
1
1
0
0
1
2
0
1
0
1
2
2
2
1
2
1
1
1
1
1
1
1
2
0
1
0
0
1
2
2
0
1
0
1
1
1
1
1
0
1
1
1
0
1
0
2
0
2
1
1
1
0
1
1
1
0
1
2
1
1
2
0
1
1
1
0
1
1
1
1
1
0
1
0
1
1
1
1
2
2
2
1
1
1
1
2
0
1
1
1
1
2
1
2
2
1
1
1
2
1
1
0
1
1
0
1
2
2
2
1
1
0
1
1
1
1
1
0
1
1
1
0
0
2
1
4
1
0
2
1
1
1
1
1
1
1
2
2
2
0
1
2
1
0
2
1
1
1
2
1
1
1
0
2
1
1
1
2
1
1
2
1
2
2
0
0
0
1
1
1
1
2
2
1
2
1
1
1
1
1
0
1
1
2
1
1
1
0
2
2
0
1
2
1
1
1
2
1
1
0
2
2
1
1
1
1
1
1
1
2
2
0
2
2
1
1
0
1
2
1
1
2
0
1
2
1
1
2
1
1
0
1
2
1
0
0
1
1
1
1
1
3
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
0
0
1
0
2
1
1
1
1
1
0
0
2
0
1
2
2
1
1
1
0
2
2
0
0
2
1
1
1
2
2
0
1
1
1
2
1
1
1
1
1
0
1
0
1
1
1
1
1
0
1
0
2
0
0
0
2
2
2
1
2
1
1
1
1
0
1
1
1
1
1
1
1
1
1
0
1
1
1
1
0
0
1
1
1
2
0
1
2
2
2
1
1
2
0
1
2
1
1
1
1
1
0
1
1
2
0
1
1
1
2
1
1
2
1
2
0
1
2
1
0
2
2
2
2
1
0
0
2
1
0
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
0
1
0
1
0
1
2
1
0
1
0
2
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
1
2
1
1
0
1
1
0
1
0
0
1
1
1
1
1
0
1
0
0
0
0
1
0
1
1
1
0
0
1
3
0
1
1
1
1
0
1
1
1
2
1
1
2
1
1
2
1
1
0
1
1
1
1
2
1
0
2
2
1
0
1
1
0
0
2
2
1
0
1
2
2
2
1
2
1
3
2
1
1
1
1
1
1
2
1
2
1
2
1
2
1
1
0
1
1
2
2
1
1
0
1
1
1
2
2
1
1
1
1
0
2
1
0
2
0
2
1
1
1
1
1
1
1
2
1
1
0
1
0
0
0
1
1
0
0
1
2
1
1
2
1
2
2
0
2
1
0
0
1
1
1
1
1
1
1
1
2
0
1
0
1
1
1
2
1
1
1
0
1
1
1
1
2
1
0
1
0
1
2
1
0
1
1
2
1
2
1
3
2
1
0
1
1
0
1
1
1
2
1
1
1
1
1
1
0
2
0
1
0
0
0
1
0
2
1
1
1
1
2
1
0
1
2
1
1
0
1
2
2
0
2
1
1
2
1
0
1
1
1
1
1
1
2
0
1
1
1
2
2
1
0
2
2
1
1
1
0
1
0
0
0
2
2
1
1
1
2
1
1
2
1
1
1
1
1
1
2
2
0
2
2
1
0
0
1
2
2
1
1
2
0
1
1
0
0
1
1
1
0
1
3
1
2
1
0
0
1
0
1
1
0
1
2
2
1
0
2
1
0
2
1
1
1
1
1
1
2
1
1
1
1
2
0
0
0
2
3
2
1
0
2
2
0
1
1
1
2
0
1
2
1
0
1
1
2
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
1
2
1
1
0
1
1
2
1
0
0
1
0
2
1
0
2
1
1
1
1
1
1
1
1
1
2
1
1
2
0
1
1
0
1
2
1
0
1
0
1
1
0
1
2
1
0
1
1
1
1
1
2
1
1
0
1
1
2
1
1
2
0
2
1
2
1
2
0
1
2
1
1
1
1
2
1
2
1
2
1
2
2
0
0
0
0
1
1
1
2
1
1
1
1
1
0
1
1
3
0
1
0
0
1
1
1
1
1
2
1
1
0
2
1
1
0
2
1
1
0
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
0
2
2
1
2
2
1
0
1
0
2
1
0
1
2
1
1
2
0
1
0
1
1
0
2
1
2
2
1
1
1
2
1
3
2
2
0
2
1
1
1
1
2
1
1
1
1
2
0
1
1
1
1
0
1
1
2
1
1
0
0
1
1
1
1
1
1
1
1
0
2
1
1
2
1
1
0
2
0
1
1
2
0
1
1
2
1
1
1
1
0
1
2
2
1
0
1
0
2
1
0
1
1
1
1
2
0
2
0
1
0
1
1
2
1
1
0
0
1
2
2
1
1
2
1
2
2
1
1
1
1
2
0
0
1
1
1
1
1
1
2
1
2
1
0
1
1
1
1
4
0
1
0
2
0
2
1
1
0
1
1
0
0
1
1
1
0
2
1
0
2
2
1
2
1
1
2
0
1
2
1
1
1
1
1
1
1
2
1
1
1
1
0
0
0
1
1
1
1
1
1
1
0
0
0
4
2
0
1
1
2
1
0
2
2
1
0
1
1
1
1
1
2
0
1
1
1
1
1
1
1
2
1
3
0
0
1
0
1
1
2
2
1
1
1
0
1
2
1
1
1
2
1
0
2
3
1
1
1
2
2
1
1
1
2
1
0
1
1
1
0
1
1
1
1
1
1
1
1
0
1
1
0
1
1
2
1
0
1
0
2
1
2
1
1
1
0
1
1
0
1
1
1
1
0
1
1
1
1
0
0
2
2
2
1
2
1
1
1
2
1
1
0
1
2
1
2
1
2
1
0
1
2
1
2
0
0
1
1
1
1
0
0
1
2
0
2
1
0
1
2
2
1
1
1
1
2
2
1
1
1
0
1
0
1
1
2
1
2
0
0
0
1
2
2
1
1
0
1
2
1
3
2
2
1
2
1
1
3
1
1
1
1
1
1
0
0
0
0
1
2
0
2
2
1
0
2
0
1
1
1
2
0
2
2
2
2
2
1
1
0
1
1
1
1
2
1
1
1
1
1
2
1
2
1
2
1
0
0
1
2
1
1
2
1
0
1
0
0
1
1
1
2
1
0
1
1
1
0
2
1
1
1
1
1
1
1
0
0
1
2
2
0
1
1
0
1
1
1
1
1
1
2
1
1
2
2
1
1
2
1
1
1
2
1
1
1
0
1
1
2
1
1
1
2
2
2
2
2
1
2
2
1
2
0
2
1
1
1
1
1
0
1
0
1
0
0
1
2
2
1
0
1
2
0
1
1
1
1
1
0
1
0
1
0
5
1
0
1
1
2
1
1
1
1
1
1
0
0
3
1
1
2
1
2
1
0
1
1
1
2
2
1
2
0
2
2
1
0
1
1
2
0
1
1
1
2
1
1
1
0
1
1
1
1
1
2
2
1
2
1
1
0
0
1
1
1
0
1
2
1
2
1
2
1
1
2
2
2
0
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
0
0
2
1
1
0
0
1
2
1
1
1
1
1
0
1
0
1
2
1
1
2
2
1
2
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
0
1
2
1
2
0
2
2
1
1
1
1
1
1
2
2
1
0
1
1
1
1
2
1
1
1
0
1
1
1
1
2
0
1
1
1
2
1
1
1
2
0
0
1
1
2
1
2
1
1
2
1
2
2
2
1
2
1
1
1
1
2
1
0
2
0
1
1
1
2
1
0
0
1
1
1
0
0
1
1
2
2
1
1
1
1
2
0
2
2
1
1
1
1
0
1
2
0
0
2
2
1
1
2
1
1
1
2
2
1
2
0
1
1
1
1
3
1
0
1
1
2
1
1
1
2
1
1
0
1
2
1
1
1
1
1
0
0
2
1
1
2
0
1
2
2
2
1
2
1
1
2
1
2
1
1
1
0
0
2
1
1
2
2
1
2
1
1
1
1
1
0
0
1
1
2
1
1
1
1
2
0
1
1
0
1
1
2
1
0
1
1
0
1
2
1
2
1
0
1
1
2
1
1
1
2
2
2
1
1
1
2
1
1
1
0
1
1
2
1
1
1
2
2
1
2
0
1
1
1
0
1
1
1
0
0
0
1
2
1
1
1
1
1
2
0
2
2
1
2
2
1
2
0
2
1
1
1
2
0
1
2
1
1
1
1
1
0
2
1
1
1
2
1
2
1
1
1
1
1
1
0
2
2
1
2
0
1
0
1
1
0
1
2
1
2
1
1
1
1
0
0
0
1
1
0
1
2
1
0
3
2
1
4
1
1
1
0
2
1
2
1
1
1
2
2
3
1
0
1
2
2
1
2
1
1
2
1
2
2
0
0
1
1
0
2
1
1
2
1
2
1
1
1
0
2
1
2
1
1
2
1
1
1
1
1
1
0
0
2
2
1
1
2
1
1
0
1
1
0
0
0
1
0
1
2
1
2
2
2
2
1
1
2
1
0
1
1
2
2
1
1
0
1
1
1
2
1
1
1
1
2
1
0
1
1
2
0
2
1
0
1
1
2
1
0
1
1
1
1
1
1
1
1
2
1
0
3
1
1
1
2
1
1
1
1
1
2
0
1
1
2
1
1
1
2
2
1
2
2
0
0
2
1
2
1
1
1
2
1
2
1
1
1
1
1
0
2
0
2
2
1
2
2
0
1
2
1
2
2
1
1
1
1
2
2
1
1
1
2
2
1
1
2
1
1
0
2
1
1
1
2
1
1
1
1
0
1
1
2
2
2
1
1
1
1
0
1
1
1
1
1
2
1
1
2
1
1
1
1
0
1
1
1
1
1
2
1
1
0
1
1
1
2
1
2
1
1
0
1
2
2
1
2
2
2
1
1
1
1
1
0
2
2
1
1
1
1
0
1
1
2
1
0
0
0
2
0
2
0
1
1
0
1
1
1
1
2
2
1
2
1
1
1
1
1
1
1
0
1
3
1
0
1
1
2
0
1
1
1
1
1
1
2
1
1
1
0
2
2
2
1
2
1
2
1
1
0
0
0
1
0
1
1
1
3
2
1
1
0
1
2
1
0
0
1
1
0
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
0
1
1
2
1
1
2
1
0
1
1
0
2
1
1
2
1
1
1
1
1
1
0
1
1
2
1
1
0
1
1
1
2
1
2
1
1
1
2
1
2
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
2
1
0
1
2
0
1
1
1
1
2
1
0
2
2
1
1
2
0
0
1
0
1
1
1
0
1
0
1
2
1
1
2
1
1
1
1
1
1
1
0
0
1
0
2
0
2
1
1
2
1
1
1
1
0
1
2
1
2
2
0
0
3
1
2
1
1
1
1
1
1
2
0
0
2
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
0
1
0
2
1
1
1
2
1
1
1
0
0
1
2
2
1
0
1
1
0
1
2
1
0
2
2
1
2
1
1
0
1
2
1
2
2
1
1
1
1
2
0
1
1
1
1
1
0
1
1
1
1
2
1
2
1
2
2
0
1
0
1
1
1
0
0
2
1
1
2
2
0
1
1
1
1
1
1
2
2
1
0
1
1
0
1
0
1
1
1
2
1
3
1
0
2
1
0
1
1
0
1
1
2
1
1
1
2
2
1
0
1
2
1
2
1
1
1
1
1
2
0
1
1
1
2
0
1
1
1
1
1
1
1
1
3
0
0
1
0
2
2
2
1
2
2
1
1
2
1
2
1
2
1
1
1
1
2
1
1
1
1
0
1
1
1
0
0
1
1
0
0
2
1
1
1
1
0
2
1
2
1
2
1
1
1
0
0
0
2
1
1
1
2
2
1
1
0
1
1
1
0
1
1
1
2
2
0
2
1
0
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
2
1
1
1
1
1
1
1
0
1
1
2
1
0
0
1
1
1
2
1
0
1
2
2
1
1
1
0
0
1
1
2
1
1
0
0
1
1
1
1
1
2
0
1
1
1
1
2
1
1
2
1
1
1
1
2
1
1
1
2
1
0
1
1
1
0
0
1
1
2
1
0
1
2
1
1
2
1
1
1
1
0
1
1
1
1
1
1
3
1
1
1
1
1
0
1
1
1
2
1
1
1
1
2
1
0
1
1
1
2
0
1
2
0
1
1
0
1
1
1
1
1
1
2
0
2
0
1
1
2
0
1
1
1
1
1
2
1
1
0
1
0
1
0
2
2
0
1
2
1
1
2
1
0
2
0
1
0
1
1
1
1
1
1
1
1
1
2
1
1
0
1
0
0
1
1
1
2
1
2
1
2
0
0
2
1
1
1
1
1
3
1
1
1
1
0
2
1
0
0
1
1
1
1
1
1
2
2
2
1
1
2
1
1
1
0
1
1
1
0
1
1
1
1
1
0
1
0
1
1
0
0
0
1
1
1
2
1
2
1
2
1
1
1
2
1
2
0
2
1
1
1
2
2
2
2
1
2
1
1
2
1
1
1
1
1
2
2
1
2
2
1
1
1
1
2
1
1
1
2
1
1
2
1
1
1
1
2
2
2
0
1
1
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
0
0
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
0
2
0
2
1
1
0
1
1
1
1
1
1
1
1
0
1
1
0
2
1
2
1
0
1
1
1
2
2
2
1
1
0
2
1
1
1
0
1
1
2
2
1
2
1
1
1
1
1
1
0
2
0
1
2
1
1
1
1
2
1
2
2
1
2
1
1
1
1
2
1
1
3
1
2
1
1
1
1
2
1
0
2
0
1
2
1
2
1
0
2
0
0
1
2
1
1
0
1
1
1
1
1
1
2
1
2
0
1
1
0
0
1
2
2
1
1
1
2
1
1
2
0
1
1
2
1
1
1
1
1
1
1
2
1
1
0
1
1
2
1
1
1
0
1
1
1
1
1
1
0
2
1
2
2
2
2
1
2
0
0
1
2
0
1
0
1
1
1
1
1
0
1
2
2
2
0
1
1
2
1
0
0
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
2
2
2
0
1
1
2
1
1
1
1
2
2
1
2
1
0
2
2
1
2
2
0
1
1
1
1
0
0
1
1
1
2
1
2
2
1
1
1
1
1
1
0
1
1
2
1
1
0
1
2
2
0
1
0
0
0
1
2
2
0
2
1
1
1
2
1
1
2
1
1
0
1
2
5
1
2
1
1
1
0
1
0
1
0
1
0
2
1
2
1
1
0
1
1
2
3
0
0
1
1
2
1
2
2
2
1
1
1
0
0
1
1
1
1
1
1
1
0
1
0
0
0
1
1
2
0
1
1
0
1
1
1
1
2
1
1
2
1
0
1
1
0
2
0
1
2
1
2
1
2
1
1
1
2
1
1
1
2
1
1
0
2
2
2
1
1
0
2
2
0
2
2
1
2
2
0
0
0
1
1
0
1
1
2
1
2
0
0
1
0
1
1
1
2
1
1
2
1
1
2
1
2
2
2
2
0
1
0
0
1
1
2
0
0
1
1
2
1
1
1
2
2
1
1
1
2
1
1
2
1
1
1
2
3
0
0
0
0
0
1
0
0
2
2
1
2
1
2
1
0
1
2
2
2
1
1
1
2
1
1
2
1
0
0
1
2
1
1
10
1
1
1
0
1
1
1
1
1
1
1
1
2
0
0
3
2
1
0
1
0
1
1
2
1
1
0
1
1
2
1
1
1
2
2
1
1
1
1
2
0
1
0
0
1
1
0
1
1
1
0
2
2
0
1
1
1
1
0
1
0
0
1
1
2
1
1
1
0
1
2
0
1
0
2
2
1
2
1
1
2
1
1
0
0
1
1
0
1
0
2
2
1
1
1
2
1
1
1
1
1
1
1
1
1
0
1
1
2
0
1
0
0
1
1
1
1
0
1
2
1
1
1
2
1
1
2
2
0
4
2
1
1
2
1
1
2
2
2
1
2
1
1
2
1
1
1
1
1
1
0
2
0
1
1
1
0
2
2
2
2
1
2
0
2
1
0
2
1
1
0
0
2
1
2
1
1
1
2
2
1
1
0
1
1
0
2
1
1
1
1
1
0
2
1
1
1
2
0
0
2
0
1
0
1
1
2
1
1
0
1
0
0
1
2
1
1
0
1
0
2
0
2
2
1
1
1
0
2
1
1
1
1
1
1
1
1
0
2
1
1
2
2
2
1
1
1
1
0
2
1
1
1
8
1
0
0
1
2
1
1
1
1
1
2
1
1
2
0
1
2
1
2
0
2
2
0
1
2
1
2
2
0
0
1
1
1
1
2
1
2
2
1
2
1
1
1
1
1
2
1
1
1
1
0
1
0
2
0
0
1
1
1
1
0
1
0
1
2
1
1
1
1
2
2
1
2
0
1
1
1
2
1
2
0
2
1
0
1
0
3
1
0
1
0
1
1
0
1
1
1
1
1
1
1
2
1
1
0
1
1
0
0
1
0
1
1
2
1
0
1
3
2
1
1
2
0
1
2
1
1
1
1
1
0
1
1
2
2
1
1
1
2
1
1
1
2
2
2
0
1
0
1
1
1
1
1
2
1
1
2
0
1
1
1
1
2
1
1
2
1
0
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
0
1
1
0
0
2
1
1
3
0
0
2
1
1
1
1
1
1
1
1
2
0
1
1
1
1
1
1
1
0
2
1
1
1
1
2
1
1
1
1
1
0
2
1
1
2
1
1
1
1
0
0
1
2
1
1
1
2
0
2
1
1
1
1
1
1
1
0
1
1
1
1
2
1
0
1
1
1
1
2
2
1
1
2
2
1
0
0
1
1
1
1
1
0
1
1
1
1
1
2
0
1
3
1
1
1
1
1
2
1
2
1
1
1
1
0
1
0
1
2
1
1
0
1
2
1
0
2
1
1
1
2
2
1
2
0
0
1
1
1
1
1
1
1
1
2
1
0
0
0
2
0
1
1
0
0
1
1
1
0
2
1
1
1
1
2
1
1
1
0
2
2
1
1
0
1
1
1
0
2
2
1
1
1
1
1
1
1
0
1
0
2
2
1
2
1
1
2
0
0
1
0
1
1
2
1
1
1
2
0
1
1
1
1
1
1
2
1
0
0
2
0
1
3
1
1
2
2
2
2
1
1
2
0
1
2
0
0
1
1
0
0
0
1
1
1
1
1
2
2
1
1
0
1
1
1
0
1
1
1
1
1
2
1
0
2
1
0
1
1
1
3
1
1
1
2
1
0
1
2
1
1
1
1
1
1
1
1
2
2
2
2
1
2
1
0
1
1
1
2
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
0
1
1
1
1
2
1
0
2
1
2
1
1
2
2
2
0
0
0
2
2
1
2
1
0
2
0
1
2
2
2
1
2
1
0
2
0
0
1
1
1
1
1
0
1
0
1
1
1
1
2
1
1
1
1
0
1
1
2
2
1
1
1
0
0
1
1
1
1
2
1
1
0
1
1
1
2
1
1
1
0
1
0
0
2
1
1
1
1
2
1
0
1
1
0
0
0
2
1
1
0
0
0
1
1
2
2
0
1
1
1
0
2
1
1
1
2
1
1
0
1
1
1
1
0
1
0
1
2
1
1
1
1
1
1
2
1
0
1
1
0
0
1
1
1
1
2
2
2
1
0
1
1
2
2
1
1
0
1
0
1
1
1
1
0
1
1
0
1
1
1
1
1
1
0
1
1
1
1
1
0
1
2
2
1
0
0
1
1
3
2
1
1
2
1
1
1
0
2
1
1
2
1
1
1
2
1
0
1
1
0
1
1
1
1
0
1
1
2
1
0
1
1
1
0
1
1
1
2
2
0
1
2
1
2
1
1
1
2
2
2
1
0
2
2
1
0
0
0
1
3
1
2
1
1
0
1
1
1
1
1
2
1
0
1
2
1
2
1
0
1
1
1
1
1
2
0
1
2
0
1
0
0
1
2
1
1
0
1
1
2
2
1
1
1
1
2
2
1
1
1
1
1
0
0
2
2
0
1
0
0
2
0
1
1
1
2
1
0
1
1
1
1
2
1
2
1
0
1
1
1
1
2
1
2
1
2
1
1
1
1
1
2
2
2
1
2
1
2
1
1
1
0
1
2
1
1
0
1
1
1
0
1
1
1
0
0
1
1
2
2
1
0
2
0
3
2
1
1
2
2
1
1
0
1
0
1
1
1
0
1
1
2
1
2
2
1
1
1
2
1
1
2
1
1
1
1
1
2
2
2
2
1
2
2
2
2
1
1
2
2
2
1
0
2
1
0
1
2
1
1
0
2
1
0
2
0
1
1
1
0
1
1
2
1
1
1
1
0
1
1
1
1
0
1
0
2
1
1
0
1
1
1
1
0
1
1
2
0
1
1
1
1
1
1
1
1
0
0
1
1
1
1
2
1
1
0
0
1
1
2
2
2
2
1
0
2
1
1
1
1
1
0
1
1
1
1
0
0
2
1
1
2
2
0
1
0
2
2
2
1
1
1
1
2
2
1
1
1
2
0
1
1
1
1
1
0
1
0
2
2
1
1
1
1
1
1
1
1
0
0
0
1
2
2
2
1
1
1
1
1
1
1
2
0
1
0
1
1
0
1
0
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
0
1
1
1
0
1
1
1
1
0
2
2
1
2
2
2
1
0
1
1
2
0
0
2
1
1
2
0
1
2
2
1
3
0
1
1
0
1
1
1
1
1
1
1
0
1
1
1
0
0
0
1
0
1
2
1
1
2
1
1
2
1
0
0
0
0
1
1
1
1
1
1
1
1
2
2
1
1
0
2
1
2
1
1
2
1
1
1
2
1
2
2
2
0
2
1
1
2
1
1
1
1
1
0
1
1
1
1
1
1
1
0
1
0
1
1
1
2
1
1
1
1
2
1
2
2
2
2
1
0
0
1
2
2
1
1
1
1
1
1
2
2
2
1
1
0
0
1
2
1
0
1
2
2
1
1
1
1
1
1
1
1
1
1
1
0
2
2
0
1
2
1
1
1
1
0
1
1
1
2
1
1
0
1
1
1
3
1
1
2
2
2
2
0
0
0
1
0
1
1
2
0
2
1
1
1
0
2
1
1
1
1
1
0
1
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
2
0
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
2
1
2
2
1
1
1
2
1
1
0
1
1
0
2
0
0
2
1
2
1
1
1
1
2
1
1
1
1
2
2
0
2
1
1
1
1
0
0
2
1
1
1
0
2
1
2
1
1
1
1
1
0
2
0
0
1
0
1
1
1
1
0
1
1
0
0
0
2
0
2
2
1
2
2
1
0
2
2
1
0
2
1
1
2
1
1
0
2
1
2
1
0
1
1
1
1
0
0
1
1
1
1
0
1
0
2
1
1
2
1
1
2
1
1
1
2
0
1
2
1
1
1
1
2
1
2
1
1
1
1
2
1
3
1
1
1
2
2
1
1
1
2
1
1
1
1
1
1
0
1
0
1
0
1
1
1
1
1
1
2
0
1
2
0
1
1
2
0
0
1
1
0
1
0
1
1
0
2
2
1
2
1
1
1
1
2
0
1
1
2
0
0
1
1
2
1
1
2
1
0
1
2
0
1
1
2
1
2
1
0
1
1
0
1
1
1
1
0
1
1
1
1
2
1
0
1
1
1
2
2
2
1
1
1
2
1
2
2
2
4
1
1
0
1
1
2
1
2
2
2
2
1
1
0
1
0
1
1
1
3
1
0
2
2
2
1
1
2
2
2
0
1
0
2
0
2
2
2
1
1
2
2
0
1
2
1
1
1
1
1
0
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
2
1
1
2
2
2
2
2
1
1
1
0
0
1
0
1
1
1
1
1
1
1
2
1
1
2
2
2
1
1
1
1
0
1
1
1
1
1
0
1
1
1
1
2
1
1
1
1
1
1
0
1
1
0
1
1
1
2
0
1
0
1
1
3
1
1
1
1
1
2
0
1
1
2
0
1
1
1
1
1
1
2
1
0
1
2
1
2
1
2
2
1
1
1
2
1
2
0
1
0
1
2
0
2
2
1
0
2
1
1
2
1
1
1
0
1
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
0
0
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
0
0
1
1
2
8
2
1
1
1
1
1
2
0
3
1
1
1
0
1
2
0
0
0
2
0
1
1
1
1
1
1
1
1
2
1
1
0
1
1
1
1
0
2
2
0
1
1
2
1
2
2
1
1
1
1
2
1
2
1
1
1
0
1
2
1
1
1
0
1
1
1
1
2
0
1
0
2
1
1
1
0
1
0
2
2
1
1
1
0
0
2
0
1
1
2
1
2
0
1
1
1
1
0
1
1
1
1
1
1
1
2
0
0
2
2
1
1
2
1
1
1
1
2
1
2
0
1
0
2
1
1
1
1
1
2
0
1
1
1
1
1
1
1
2
1
1
1
1
0
1
1
1
1
1
2
1
2
1
1
2
1
2
1
1
0
1
1
0
1
1
1
1
0
0
1
1
2
2
2
0
1
2
2
1
1
0
0
1
0
1
1
0
1
0
1
2
1
1
1
1
0
1
1
1
2
1
1
1
0
3
1
1
1
1
1
1
2
2
1
2
1
0
1
1
0
2
1
1
2
1
0
3
1
1
1
1
1
1
0
1
1
1
1
3
2
2
1
0
2
1
1
1
0
0
5
2
1
1
0
2
2
1
1
2
1
2
2
2
1
2
1
1
1
1
1
1
2
2
0
1
1
2
1
1
1
2
1
1
1
1
1
1
3
1
1
1
1
1
2
1
2
2
0
1
1
1
0
1
1
0
0
2
2
0
1
1
2
2
1
2
2
1
0
2
1
1
1
1
1
1
0
1
2
2
1
1
2
0
1
2
2
1
1
1
1
1
1
1
2
0
2
0
4
3
2
1
1
0
1
1
2
2
0
2
1
2
2
1
1
2
1
1
1
2
1
1
3
1
1
1
1
2
1
1
1
1
2
1
2
1
2
1
2
1
1
1
1
1
1
2
1
1
2
1
1
1
1
2
2
2
2
2
1
2
2
0
2
1
1
1
2
2
1
1
1
0
1
1
1
2
2
1
2
1
1
1
1
2
2
2
1
1
2
2
1
2
1
0
2
0
0
1
1
1
0
0
1
2
1
2
2
1
1
0
1
1
0
2
0
1
2
1
2
1
1
1
0
1
2
1
1
1
1
1
1
2
0
1
1
0
0
0
0
2
2
1
0
1
1
2
1
1
2
1
1
1
1
1
0
1
0
2
2
0
1
0
1
1
1
2
1
0
0
2
1
1
1
2
1
0
1
1
1
2
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
0
1
2
1
1
1
1
0
1
1
1
0
0
1
2
0
1
2
1
2
1
1
1
2
2
0
2
1
2
1
1
0
1
2
2
0
1
0
1
1
1
1
1
1
1
2
1
0
0
1
1
1
1
2
1
1
1
2
1
0
0
0
1
2
1
1
2
1
0
2
1
2
0
2
1
1
1
1
1
1
1
2
1
1
0
0
1
0
1
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
0
1
0
1
0
1
2
2
1
1
1
2
3
2
1
0
0
2
1
0
1
0
0
1
1
2
1
2
1
2
2
1
2
1
2
1
1
1
2
1
1
2
1
1
2
1
1
1
0
1
1
2
0
2
1
1
1
0
0
0
1
2
1
0
2
0
2
2
0
1
1
1
1
2
0
1
1
0
1
0
1
2
1
1
1
2
1
1
2
1
1
1
1
2
2
0
1
0
0
2
1
1
1
1
1
2
1
2
1
2
1
1
0
2
1
2
1
1
1
0
1
1
0
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
0
1
2
1
2
0
0
2
1
1
2
2
1
0
0
1
0
2
1
2
3
1
0
0
1
1
1
1
1
0
2
1
0
1
1
2
1
0
2
1
1
2
1
0
0
2
2
1
1
1
0
1
2
0
2
2
1
0
1
1
1
2
1
2
0
0
1
2
1
1
1
2
1
1
1
2
0
1
1
1
2
1
1
1
0
2
1
1
1
1
0
2
0
1
1
1
1
1
1
1
2
0
1
0
1
1
1
1
1
1
1
1
1
0
1
0
1
2
1
1
0
2
1
0
1
1
2
1
0
1
2
0
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
2
2
1
2
2
2
1
1
2
0
2
1
1
1
2
1
2
1
2
1
1
1
0
1
1
2
1
2
1
2
1
2
1
3
1
1
2
1
0
1
0
2
1
1
1
1
2
1
2
2
2
0
0
2
1
1
1
3
1
0
2
2
2
0
1
1
1
0
1
1
1
1
1
0
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
1
1
0
1
1
1
2
0
1
1
2
1
0
1
1
1
1
1
1
0
1
1
1
0
2
2
1
2
1
1
1
1
1
1
2
0
1
2
1
1
1
0
2
1
2
1
2
1
0
1
1
1
1
2
1
2
3
2
1
2
1
1
1
2
1
0
1
1
2
2
1
0
1
1
1
1
1
1
0
0
1
1
2
0
0
1
1
2
1
1
1
1
0
2
1
0
1
1
1
2
1
1
1
1
2
1
1
1
2
0
1
1
1
1
0
1
0
2
1
0
1
0
1
2
1
1
0
0
2
0
0
2
0
2
1
0
0
0
1
0
1
2
1
2
1
1
1
1
1
2
1
2
2
2
0
1
2
1
1
1
1
1
2
1
0
1
1
1
1
1
1
1
1
3
0
0
1
2
2
1
0
1
2
1
2
0
1
2
0
1
1
1
1
1
0
1
1
0
0
1
2
1
1
1
1
1
2
2
0
1
1
1
0
0
0
2
1
0
2
1
1
1
1
2
2
1
1
1
1
1
1
1
0
1
1
2
1
0
2
1
1
1
1
2
2
0
1
2
1
1
1
1
1
2
1
1
2
1
2
0
1
2
2
1
1
1
1
1
1
2
0
2
1
2
1
0
1
0
2
2
0
2
1
1
2
2
1
2
1
1
0
1
0
1
1
1
0
0
1
2
0
1
1
1
1
0
2
0
1
1
1
1
1
1
1
1
1
0
1
2
2
1
1
1
2
1
2
1
1
0
2
1
2
1
1
1
1
2
1
1
1
1
2
0
1
2
2
1
3
1
2
1
1
1
0
1
2
1
1
1
1
1
1
1
2
2
2
1
1
1
2
1
1
0
1
2
1
0
1
1
0
1
1
1
1
2
2
2
1
1
2
1
1
1
1
1
1
0
0
1
2
0
1
0
3
2
0
1
1
1
2
0
1
2
1
2
0
1
2
2
1
1
1
2
1
1
2
1
1
2
0
0
0
1
1
1
0
1
1
2
0
1
1
1
1
2
1
1
0
1
1
1
1
1
2
1
1
2
1
1
1
1
2
1
2
1
0
0
1
2
0
1
0
1
1
1
0
2
2
1
1
0
1
0
2
1
1
1
1
1
2
1
1
0
2
1
0
1
0
1
0
0
0
2
1
1
1
1
2
1
2
2
1
0
1
0
1
1
1
2
1
1
1
1
0
1
1
2
1
0
0
0
2
1
2
1
1
2
1
0
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
2
2
2
1
2
1
1
1
1
2
1
1
1
2
2
1
1
0
1
2
1
0
0
1
1
1
1
1
1
0
0
0
3
2
1
1
1
0
0
1
1
0
1
1
0
0
1
1
1
2
1
0
1
1
2
1
1
0
2
1
0
1
1
0
0
1
2
1
2
1
2
1
1
0
1
3
1
1
0
1
1
2
2
1
0
1
0
2
1
1
0
0
2
2
0
1
1
0
2
2
0
1
1
2
2
1
2
1
1
1
2
2
2
2
1
1
2
2
1
0
1
0
1
0
1
2
1
2
2
1
2
1
0
1
0
1
1
1
1
1
2
1
1
1
2
2
1
1
1
2
1
2
1
1
1
0
0
1
1
1
0
1
2
2
0
1
1
2
0
2
1
1
1
1
1
1
1
1
0
1
2
0
2
1
0
1
1
1
1
1
1
2
1
0
2
1
1
1
2
1
0
1
2
0
0
1
1
0
1
2
2
0
0
2
0
1
1
1
1
0
0
1
1
1
2
1
1
0
2
0
0
2
1
0
1
2
1
2
2
2
1
1
2
1
1
1
1
2
0
1
0
1
1
2
1
1
1
2
1
1
1
1
1
2
2
2
0
0
2
0
1
2
1
1
1
2
2
1
0
0
1
1
1
1
1
2
1
2
1
2
1
0
2
2
2
1
0
2
1
2
1
0
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
2
0
2
1
1
0
2
1
1
2
0
1
1
1
2
1
1
1
1
2
1
1
1
0
2
2
1
1
1
0
1
1
1
1
1
0
0
2
2
0
1
0
0
2
1
1
1
1
1
0
2
1
1
1
1
2
1
1
1
1
1
1
1
1
0
1
1
2
1
0
1
1
2
2
1
1
2
0
0
0
1
1
1
2
2
1
1
2
1
1
1
1
1
0
1
1
1
2
2
1
1
1
2
1
1
1
3
2
1
1
1
1
1
1
1
1
0
1
2
1
1
1
2
1
2
1
1
0
0
1
1
1
1
1
0
1
1
1
0
2
1
0
2
1
1
1
1
0
0
1
1
1
1
0
1
1
2
1
1
1
1
1
0
0
2
1
0
1
0
2
1
0
1
0
3
1
1
2
1
1
0
1
2
1
0
2
0
1
0
1
1
1
1
2
1
0
1
0
1
2
0
0
0
1
2
1
1
1
1
1
1
2
0
1
1
1
2
2
1
0
0
1
0
0
1
1
1
2
1
1
1
0
1
1
1
1
0
1
1
1
1
1
1
2
0
2
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
0
0
2
1
1
1
1
1
0
1
1
1
1
0
1
2
2
1
1
0
1
2
0
1
2
1
1
1
1
1
2
2
0
0
1
2
1
1
2
1
1
0
1
1
1
1
2
2
1
2
1
2
0
0
1
1
1
1
2
0
1
1
2
1
1
1
1
1
1
1
1
1
1
1
0
1
2
1
2
0
1
1
1
0
1
1
2
1
1
1
1
0
1
1
1
0
1
1
1
1
1
1
1
0
1
0
1
1
1
1
1
1
2
1
1
2
0
0
1
1
0
1
0
1
1
1
2
1
1
1
2
0
1
1
1
1
1
0
4
0
2
1
1
1
1
2
0
2
1
1
2
1
1
1
1
1
0
1
1
2
1
1
2
1
2
1
1
1
1
1
2
5
1
2
1
2
2
2
1
1
1
0
2
2
1
1
0
1
1
1
1
1
2
2
2
1
1
1
2
2
1
1
1
2
1
1
1
1
1
1
1
1
0
1
1
2
0
1
0
1
1
1
1
0
0
1
1
1
2
2
1
1
1
0
0
1
2
1
1
2
1
1
0
2
2
1
2
1
1
2
1
0
1
1
2
1
2
0
1
0
0
1
1
1
2
1
1
2
1
2
1
1
0
1
1
1
2
0
0
1
1
0
2
2
1
2
1
0
1
0
0
0
0
1
1
2
2
1
1
1
1
0
1
1
1
1
1
1
1
2
0
1
2
2
1
2
2
1
2
1
0
1
1
2
1
2
2
1
0
1
1
1
2
1
1
2
1
1
1
1
0
1
1
1
1
0
2
1
2
0
1
2
1
0
1
1
1
1
2
1
0
1
1
2
1
0
2
1
2
1
1
1
1
2
1
0
1
1
1
1
2
2
1
1
0
0
1
2
2
1
0
1
2
1
1
0
1
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
1
3
1
1
2
1
1
1
0
1
1
0
1
1
3
2
1
2
2
1
1
1
1
1
1
0
1
1
0
3
1
1
1
1
1
1
1
1
2
1
1
0
1
1
2
1
2
1
1
0
2
1
2
1
1
1
6
2
2
1
1
2
1
1
1
1
1
0
0
2
2
1
2
1
1
0
2
1
2
1
1
2
2
2
3
1
1
0
0
1
1
0
2
1
0
1
0
1
2
1
1
1
1
1
1
0
1
0
1
1
1
1
1
1
1
2
1
1
2
1
1
1
0
2
2
1
2
2
2
1
1
0
1
1
3
2
1
2
1
1
1
1
1
1
2
1
0
1
1
0
1
0
2
1
2
1
0
2
2
1
0
1
2
1
2
0
2
1
1
2
2
2
0
0
0
2
2
1
2
0
1
1
1
2
2
0
3
1
1
1
0
2
1
1
1
1
0
1
1
1
1
1
1
1
2
1
1
1
2
1
1
0
1
1
1
1
1
0
2
1
1
0
0
1
0
1
2
2
0
1
1
1
1
2
1
0
4
0
2
0
0
1
0
1
2
0
1
1
1
2
1
2
1
0
2
1
1
1
2
2
1
1
1
2
2
1
1
1
1
2
1
2
1
1
1
2
2
1
1
0
1
2
1
1
2
0
2
1
0
2
2
1
1
2
1
2
1
2
0
1
2
1
1
1
2
1
1
1
0
1
1
2
2
1
1
0
0
3
1
0
0
2
0
1
1
2
0
1
1
1
1
2
1
2
1
1
0
2
2
1
2
2
2
1
1
0
1
2
1
0
1
2
1
1
1
1
2
0
0
1
2
0
1
1
1
2
2
1
1
1
2
2
1
1
2
1
0
1
2
1
1
1
2
1
2
0
2
1
1
1
0
2
0
2
1
2
2
1
1
1
0
1
2
1
1
2
1
0
1
1
2
1
1
2
1
1
2
1
1
1
2
1
0
1
1
1
2
1
2
2
1
1
2
1
1
1
1
1
1
0
1
0
1
0
1
1
1
0
0
1
0
1
1
1
1
1
1
1
1
1
2
2
1
1
2
0
1
2
0
2
1
0
3
1
1
1
2
1
1
1
2
1
1
1
0
1
1
0
0
1
1
1
1
1
2
0
1
0
4
0
1
1
1
3
0
0
2
0
1
1
1
0
0
1
2
2
0
2
1
1
1
1
1
2
1
1
0
0
1
1
1
0
1
1
1
1
1
2
0
1
1
0
0
1
0
1
2
1
1
1
2
1
2
2
1
1
2
0
1
0
1
2
0
2
1
1
1
1
1
2
1
0
2
0
1
1
1
1
1
1
1
2
1
1
2
2
1
1
2
1
1
0
1
1
1
2
1
1
1
1
2
2
1
0
1
0
0
1
2
1
1
2
1
1
1
0
1
1
2
2
2
0
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
2
2
1
1
1
0
1
1
1
1
1
1
2
1
2
0
1
2
1
1
1
1
1
1
2
2
2
1
1
1
0
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
0
1
1
2
0
0
1
1
1
2
1
1
1
0
1
2
2
1
1
2
1
0
1
1
0
1
1
0
1
0
2
1
2
2
1
0
1
1
1
1
1
1
2
3
1
1
1
1
1
2
1
1
1
0
1
2
2
2
2
1
1
0
1
1
1
1
1
1
2
1
1
2
0
1
1
2
0
2
1
0
1
1
1
1
1
2
1
1
1
1
1
2
1
1
0
1
2
1
1
3
2
0
0
1
0
1
2
2
0
3
1
2
0
2
0
2
2
1
1
0
2
1
1
1
1
1
1
2
1
1
1
1
1
2
2
1
0
0
1
1
1
1
2
1
1
0
1
1
0
2
2
2
1
1
1
1
2
0
1
1
1
0
1
1
1
2
1
3
1
2
1
0
0
2
2
1
2
0
1
1
1
2
1
1
1
1
0
1
2
2
2
0
1
1
2
2
1
1
1
2
0
2
1
2
1
1
0
2
1
2
1
2
1
0
1
2
0
0
1
2
1
0
1
1
1
1
0
0
1
1
1
1
1
1
2
0
1
2
0
1
1
1
2
1
0
1
0
0
0
2
1
2
1
2
1
1
1
0
1
1
1
2
0
1
2
2
1
1
1
1
1
0
1
2
0
1
2
1
2
2
1
1
1
2
2
1
1
1
2
1
2
0
2
2
2
1
1
0
1
2
0
2
1
2
1
1
1
2
0
1
0
2
1
1
1
2
2
1
0
1
1
1
1
1
1
2
2
2
1
1
0
1
0
0
2
0
0
1
0
0
3
1
1
1
0
0
2
1
1
2
1
1
1
1
0
2
1
1
1
2
0
2
0
2
2
1
1
0
1
1
2
2
2
1
3
2
2
2
1
1
2
1
1
1
0
1
1
1
1
2
1
1
1
1
1
1
0
1
2
1
0
3
1
2
1
1
2
1
2
1
0
1
1
1
2
2
2
1
1
2
1
1
2
1
2
0
1
1
2
1
1
1
2
1
2
0
1
1
2
1
1
2
1
2
1
1
1
0
0
1
0
1
0
1
1
1
1
1
0
1
1
1
1
2
2
0
1
1
1
1
1
2
2
1
1
0
2
0
2
0
1
1
1
2
1
2
2
1
1
2
1
1
1
1
0
1
1
1
1
1
0
2
0
1
1
1
1
0
0
2
1
1
1
1
2
1
2
1
1
1
1
1
1
3
1
1
1
2
1
2
2
2
0
1
0
2
1
1
2
2
1
1
1
1
0
1
1
0
1
1
1
0
1
0
0
1
1
0
2
1
1
1
2
1
0
0
2
0
0
1
1
2
1
2
1
1
0
1
3
1
1
2
2
1
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
0
2
1
0
2
1
1
0
2
2
1
1
2
2
0
0
1
1
1
1
1
2
0
1
1
2
1
1
1
2
1
0
1
2
1
1
1
0
1
1
2
1
0
1
1
1
1
1
1
2
1
1
1
1
0
1
1
1
2
1
1
1
1
1
0
1
1
1
0
2
1
1
0
0
1
1
1
0
1
1
1
1
1
1
2
1
2
0
1
1
1
0
2
0
1
0
2
0
1
1
1
1
1
0
1
2
0
1
1
2
1
1
0
1
1
2
1
1
2
1
1
1
0
1
0
0
2
1
0
1
2
2
1
2
1
1
3
1
1
1
1
1
0
1
2
1
2
0
1
1
0
2
1
1
3
2
2
1
1
2
3
0
2
1
0
1
0
1
1
1
2
1
1
1
0
2
1
0
1
0
0
0
1
1
2
0
0
1
1
2
1
0
1
1
1
1
0
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
2
1
2
2
0
1
0
1
1
1
1
0
1
2
1
2
2
1
1
2
1
1
0
1
1
2
1
2
0
2
1
1
2
1
2
2
0
2
1
0
2
1
1
1
0
1
1
1
1
1
0
1
2
0
2
1
1
2
1
1
0
1
2
1
1
1
1
0
1
2
2
2
1
1
1
1
0
1
0
1
2
1
2
1
1
0
2
0
0
1
1
1
0
1
1
0
1
2
2
1
1
2
0
1
1
1
2
2
1
1
1
1
1
1
1
2
1
2
1
1
1
0
0
0
0
1
1
0
0
1
1
2
1
1
1
1
2
0
0
1
1
1
1
1
1
1
2
2
1
2
1
1
2
0
2
1
1
1
1
1
1
2
2
0
1
1
1
1
0
1
1
1
1
1
0
1
1
1
1
2
1
1
1
1
2
0
1
1
1
1
1
1
0
1
1
0
1
2
1
1
2
1
1
2
1
0
2
1
1
1
1
1
0
0
1
1
0
2
0
2
1
1
1
2
0
1
1
0
1
1
0
2
2
1
1
0
2
3
1
1
2
1
0
1
1
0
1
1
0
2
1
1
1
1
0
2
1
1
2
1
1
1
1
0
2
1
0
1
0
1
1
2
2
2
0
0
1
2
1
1
1
0
0
1
2
1
1
1
1
1
1
1
1
1
1
2
0
2
1
1
1
2
0
0
0
1
0
2
1
0
1
0
1
1
1
0
2
1
0
1
1
1
3
1
1
1
1
1
1
1
1
0
1
1
1
2
0
1
0
0
2
1
2
1
2
1
1
1
1
0
2
0
2
2
1
0
4
2
2
1
2
1
1
0
1
1
0
1
1
0
1
0
2
1
2
1
0
1
1
2
1
1
1
1
1
2
1
1
2
1
1
1
2
2
2
2
2
1
2
2
1
1
1
2
1
1
1
1
1
1
2
1
2
1
2
1
1
2
2
0
0
2
1
1
2
1
1
1
2
2
0
1
0
2
1
2
2
1
0
2
1
1
1
1
2
2
2
1
1
2
2
2
0
2
0
1
1
1
1
2
1
1
2
2
0
1
2
1
0
1
0
0
1
2
1
0
1
0
1
1
2
1
2
1
2
1
1
2
1
2
2
2
1
2
1
1
1
2
0
0
1
0
1
2
2
2
1
1
1
1
1
2
0
2
2
2
1
1
1
0
1
2
1
2
2
1
0
0
2
2
0
0
2
1
1
1
0
0
1
1
1
1
1
2
1
0
2
1
1
1
1
1
2
2
1
1
0
2
0
1
1
1
1
2
2
2
1
1
2
1
1
1
0
2
1
1
1
1
1
0
1
1
0
2
2
1
2
0
0
0
1
1
0
1
1
1
0
1
1
2
1
1
1
2
1
2
0
2
1
1
1
1
1
1
1
1
2
1
1
0
1
1
1
1
0
1
1
1
1
1
1
1
1
2
1
1
1
2
0
2
1
2
1
0
1
1
2
1
2
1
2
1
0
2
1
1
1
0
1
0
1
0
1
1
2
1
1
0
2
1
1
0
1
2
0
0
0
2
1
1
1
0
2
2
1
1
1
1
0
1
1
2
2
1
2
1
1
2
0
0
1
1
1
2
2
1
1
2
0
2
2
2
2
1
1
1
0
1
1
1
2
1
1
1
1
0
0
0
1
0
2
1
1
1
1
1
1
1
2
1
2
1
0
1
1
1
0
1
1
0
1
0
1
1
0
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
2
2
2
0
2
0
2
0
0
0
1
1
0
1
1
1
1
1
1
1
1
2
0
0
1
2
1
1
2
1
2
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
0
1
1
2
1
3
1
1
1
1
0
0
1
2
1
1
1
1
1
0
2
2
0
2
1
1
1
2
1
0
1
0
0
2
0
2
0
1
1
1
0
3
2
1
1
1
1
0
1
1
0
1
1
0
2
1
1
1
1
2
1
1
0
1
1
1
1
1
1
1
2
1
2
1
0
2
1
1
1
0
1
1
2
2
0
2
2
1
1
2
0
1
1
1
1
1
2
1
1
1
0
1
1
2
1
0
0
1
1
2
1
0
0
1
1
0
0
1
0
1
1
0
1
1
1
1
1
1
1
1
1
2
2
2
2
0
1
1
2
1
0
1
1
2
2
1
2
1
0
0
1
1
1
0
0
1
2
1
1
0
0
1
1
1
2
1
2
2
1
2
1
1
1
1
1
1
1
1
1
0
1
1
0
1
1
1
0
1
1
2
1
1
0
1
2
1
2
0
1
0
1
1
1
2
0
1
1
2
1
2
1
1
1
0
0
1
1
0
1
0
0
1
1
1
2
2
1
1
1
0
1
1
1
1
1
0
1
1
1
1
2
2
1
1
1
0
0
2
1
1
1
2
2
2
1
2
1
1
1
2
1
2
0
2
1
1
2
0
1
1
2
2
1
1
1
1
2
1
1
2
0
2
1
2
2
0
1
1
1
2
1
1
1
1
0
1
1
1
0
2
1
0
1
1
1
1
1
1
0
1
1
1
1
0
1
1
0
1
1
3
0
2
2
1
1
2
1
1
1
2
1
1
1
2
1
1
2
1
0
0
3
1
0
1
2
0
1
2
0
1
1
1
2
1
0
1
1
0
1
1
1
1
1
1
1
1
1
0
1
1
2
1
2
1
1
1
1
0
1
1
1
1
0
0
1
1
0
2
1
1
1
2
2
2
1
1
1
1
1
1
1
2
1
1
0
1
1
1
0
1
2
1
1
1
2
1
1
2
2
1
0
0
1
1
1
0
1
2
2
2
1
3
1
1
2
1
1
1
1
1
2
0
1
0
1
0
1
2
2
1
1
1
1
1
1
1
2
1
2
2
1
1
2
3
0
2
2
2
2
0
1
0
1
0
1
2
2
2
1
2
1
1
1
1
1
1
0
0
1
2
1
0
1
1
2
0
1
1
1
1
1
0
1
1
1
1
1
1
1
2
0
1
2
2
1
2
0
2
1
1
2
1
1
2
0
1
1
0
1
1
1
1
1
1
2
0
1
1
1
1
2
1
1
1
1
0
1
0
1
0
1
1
1
2
1
1
1
1
0
1
1
1
1
1
1
1
1
0
1
1
1
3
2
1
2
1
1
0
2
0
1
0
0
2
1
1
0
2
1
1
1
1
2
1
1
1
1
1
0
2
1
2
1
1
1
1
1
1
1
1
2
1
2
2
0
1
2
1
1
1
2
2
0
0
2
1
0
3
1
1
0
1
1
1
1
4
1
0
0
1
2
1
0
0
2
1
1
1
1
1
1
3
2
2
1
2
0
2
2
1
0
1
0
1
0
0
3
1
1
2
2
1
1
0
0
1
0
1
1
1
2
1
1
2
1
2
0
1
1
2
1
1
0
1
0
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
0
2
1
1
1
1
0
1
1
1
1
1
1
0
1
0
1
0
1
1
2
2
1
0
0
1
0
1
1
0
0
2
2
1
1
2
1
0
1
2
1
2
0
1
1
1
1
2
1
1
1
2
2
1
2
1
1
2
2
2
2
1
2
2
2
2
2
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
2
4
1
1
0
1
1
1
0
1
1
2
2
2
2
1
2
2
1
1
1
1
0
0
0
1
0
1
0
1
1
1
0
1
1
1
0
1
0
2
0
1
1
2
1
1
1
1
1
0
1
0
1
2
0
0
1
2
0
1
1
0
2
1
1
1
0
1
1
1
1
2
0
1
1
2
2
1
1
0
2
1
1
2
1
1
0
2
1
2
2
0
1
1
1
0
1
2
1
1
1
2
2
1
1
0
1
2
0
1
1
1
1
1
0
1
0
1
1
1
1
1
1
2
1
0
1
0
0
1
0
2
1
2
2
2
0
1
1
2
1
1
1
1
1
2
2
1
1
0
1
1
1
1
1
1
1
2
1
2
2
1
1
0
1
0
1
2
1
1
0
1
1
0
1
1
1
0
2
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
2
1
1
1
2
0
1
1
1
1
1
1
1
0
0
1
0
0
1
1
1
1
2
2
1
1
1
1
1
2
2
1
0
1
2
0
2
1
2
2
1
1
1
0
2
0
1
1
1
1
1
1
1
1
1
2
3
1
1
1
1
1
1
1
2
1
2
0
3
2
2
1
1
1
0
1
1
1
1
0
1
1
1
1
2
1
1
1
1
1
1
1
0
1
1
1
2
1
1
2
2
1
2
1
0
1
1
1
1
1
0
1
1
1
2
1
2
0
0
1
1
2
1
2
2
1
1
0
1
1
1
1
0
2
1
1
2
1
2
1
2
2
2
2
1
1
1
1
1
0
1
1
0
1
1
1
1
1
1
1
2
2
3
1
1
1
0
0
0
0
1
1
1
1
1
2
2
0
0
1
1
0
1
0
1
1
1
2
1
1
2
1
1
1
0
1
1
2
1
1
2
1
1
1
0
2
2
1
0
1
1
1
1
2
2
0
1
0
1
2
1
1
2
2
1
1
2
1
1
2
1
2
2
2
1
1
1
0
1
1
1
1
1
1
1
0
0
2
2
1
1
1
1
1
2
1
0
2
1
2
1
0
1
1
2
0
2
1
1
2
0
1
2
1
2
1
2
1
2
1
2
1
1
1
0
1
0
2
1
2
2
1
1
2
2
1
0
1
1
2
1
1
4
2
0
2
1
1
1
0
2
1
1
1
1
1
1
1
2
1
0
2
1
1
0
1
1
1
1
1
1
0
1
1
2
1
1
1
1
1
2
1
1
3
2
1
1
1
2
2
2
2
0
2
0
0
0
0
0
1
0
1
1
2
2
1
1
1
1
0
0
0
1
1
2
1
2
2
1
1
2
1
1
1
0
1
0
0
1
1
2
2
1
0
1
1
1
1
0
1
1
1
1
1
1
1
2
0
1
1
2
0
1
1
1
1
1
1
0
0
1
2
2
2
1
1
1
0
0
1
1
0
1
2
2
1
1
1
2
0
1
1
0
1
2
1
2
1
1
1
2
2
0
2
1
0
1
0
1
1
2
1
2
1
2
2
1
1
1
0
1
1
2
1
1
2
1
2
1
4
1
1
0
2
1
1
1
1
1
2
1
2
2
2
0
1
0
0
0
1
2
1
1
0
0
1
1
1
2
1
1
2
1
1
1
2
1
0
1
2
1
0
0
2
1
1
2
1
1
1
1
1
1
1
2
0
1
2
1
0
1
1
1
1
1
2
1
0
1
1
3
1
2
2
1
1
1
2
2
1
1
0
2
1
1
1
1
1
1
1
1
1
1
2
2
2
1
2
0
1
1
1
0
1
1
1
1
0
1
1
1
1
1
0
1
1
0
1
2
2
1
1
1
1
1
2
0
1
0
2
1
1
1
2
1
1
1
2
0
1
1
1
1
2
1
1
0
1
2
1
1
2
0
1
1
1
2
1
2
0
2
1
2
1
1
1
0
2
2
1
2
1
0
1
0
2
2
1
1
2
0
0
2
1
1
2
2
0
2
0
2
1
1
7
2
1
1
1
1
1
1
0
1
1
1
1
2
0
0
1
2
1
1
1
0
0
2
2
1
1
0
1
1
1
0
1
1
2
2
2
1
1
0
0
0
2
1
0
1
1
2
1
2
1
1
1
1
1
1
1
0
0
1
2
1
2
0
0
1
1
0
2
2
1
1
1
0
1
1
1
0
2
1
1
1
1
1
1
1
1
1
0
1
1
1
2
2
1
2
2
0
2
1
1
1
1
1
1
0
1
2
1
1
1
0
1
0
1
1
0
1
1
0
1
1
2
2
1
1
1
2
2
2
1
1
1
2
2
1
1
1
0
2
1
1
1
1
1
2
1
1
1
2
1
2
1
1
2
2
1
2
1
1
1
2
0
0
1
0
0
1
1
1
1
2
2
0
1
2
0
1
0
0
1
1
1
0
1
1
1
0
1
0
1
0
1
2
2
1
0
2
2
0
1
1
2
2
2
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
2
2
2
1
1
1
1
0
1
1
1
2
1
2
0
1
1
1
1
1
1
2
1
2
4
1
2
1
1
1
2
0
1
1
1
2
0
0
1
1
1
1
0
1
1
1
2
0
2
0
1
1
0
1
1
1
0
1
1
1
1
2
0
1
2
1
1
1
1
0
0
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
2
2
1
0
1
0
2
2
1
2
1
0
0
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
0
1
0
1
1
1
1
2
0
0
2
0
3
0
0
1
2
1
0
1
1
1
1
1
1
2
1
1
1
2
2
1
1
0
2
0
1
1
0
1
1
1
1
3
1
1
0
0
1
1
0
0
1
1
1
1
1
1
0
1
1
1
0
0
2
1
3
0
2
1
0
0
1
1
1
0
1
0
2
1
0
1
1
1
0
2
2
2
2
0
1
1
1
1
1
2
2
1
2
1
1
1
0
1
2
1
2
2
1
2
1
1
1
1
2
0
1
2
2
1
2
1
1
2
1
1
2
1
1
2
1
1
1
1
1
1
1
0
0
1
2
1
2
0
1
1
2
2
1
1
1
1
0
1
2
1
2
1
2
1
1
2
0
0
1
1
1
2
1
1
1
0
2
1
1
1
1
1
2
0
1
2
0
2
2
1
2
1
5
1
1
1
0
0
0
0
1
2
1
1
0
1
1
1
2
2
1
1
1
0
0
1
1
1
1
1
2
1
5
1
0
1
0
2
1
1
2
1
2
2
0
1
1
0
1
1
1
1
2
2
2
1
1
1
0
1
2
1
1
0
1
2
1
1
1
2
1
1
2
1
0
1
2
0
1
0
2
1
2
1
2
1
0
1
2
1
1
1
0
1
1
1
0
1
2
1
1
1
0
1
1
2
1
0
2
1
1
1
1
1
1
1
2
2
0
2
1
0
1
1
1
1
1
1
1
1
1
1
0
2
1
2
0
1
1
2
1
1
1
2
0
0
0
0
2
1
1
1
1
2
1
1
1
0
1
2
1
1
1
0
2
0
2
1
0
1
1
2
2
1
0
2
1
2
1
1
1
2
1
1
1
0
2
2
1
1
0
1
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
0
1
2
0
1
1
1
2
1
1
0
1
0
1
2
2
2
0
1
1
2
1
1
1
1
2
2
0
1
1
2
1
1
1
1
0
1
1
2
2
1
2
1
0
0
1
1
1
1
0
0
0
3
1
1
2
0
1
1
0
1
2
1
2
1
2
1
1
0
2
2
1
1
1
2
1
2
2
1
2
0
1
0
0
1
1
1
1
1
1
0
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
2
0
1
3
1
1
0
0
2
2
1
1
1
1
1
1
1
1
1
0
1
1
1
1
0
1
1
1
2
1
1
2
1
1
2
1
2
2
1
2
2
0
1
2
1
1
1
1
1
1
0
1
0
0
1
1
1
1
1
1
1
1
1
1
2
1
0
1
1
1
2
0
2
2
1
1
2
1
0
1
1
2
0
4
1
0
1
1
2
1
1
0
2
0
0
1
1
2
1
1
1
1
1
1
2
2
2
2
0
1
1
1
2
1
0
1
0
0
2
1
1
2
0
1
2
1
2
1
1
2
1
2
1
1
2
1
2
1
1
1
1
0
2
1
0
1
1
1
2
2
1
1
3
1
1
1
1
1
1
1
3
2
2
1
1
1
1
1
2
1
0
2
1
0
1
1
1
1
1
2
2
1
1
1
2
2
1
1
1
1
2
1
1
1
2
0
2
1
1
1
1
0
1
1
1
1
2
1
2
1
0
1
1
2
2
2
2
1
0
1
1
1
0
1
1
1
1
0
4
0
2
1
1
2
1
2
2
2
1
1
1
1
2
1
0
1
1
1
0
0
2
1
1
0
2
2
1
2
0
1
1
1
0
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
0
2
1
1
2
1
0
2
1
0
1
2
1
1
1
0
1
2
1
2
1
2
0
2
1
2
1
2
1
1
2
0
1
2
0
1
1
0
1
4
1
1
2
2
1
1
1
2
1
1
1
0
2
1
0
1
1
1
0
0
0
1
1
1
1
4
2
1
1
1
1
2
1
2
1
1
1
2
2
2
1
2
2
1
1
1
0
2
1
0
1
2
2
1
2
1
2
2
2
1
2
1
0
2
1
0
1
1
1
1
2
1
0
1
3
3
1
2
1
1
1
1
0
1
1
1
0
0
1
2
1
1
1
1
1
1
2
1
2
0
2
1
0
1
2
1
1
1
0
1
2
1
1
1
1
1
2
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
0
2
1
2
1
2
1
1
1
1
2
0
2
1
0
1
1
1
0
1
2
1
2
1
1
2
1
0
1
1
1
2
1
1
2
1
1
1
1
2
0
2
2
1
2
1
1
1
2
2
1
0
0
1
2
2
0
0
1
1
1
1
2
0
1
2
0
1
1
1
0
0
0
1
0
2
2
2
1
1
0
1
1
1
0
0
1
2
1
2
2
2
2
2
2
1
0
0
1
0
2
1
1
1
1
1
1
1
1
1
0
1
1
2
1
1
0
1
2
1
2
0
2
0
1
1
1
1
1
0
2
1
2
0
2
1
0
1
2
2
0
1
1
2
1
2
0
2
2
1
1
4
2
1
2
0
1
0
1
0
2
1
1
0
1
1
0
1
1
0
2
1
1
1
1
1
2
2
1
0
1
1
2
2
2
0
1
1
2
2
2
1
0
2
2
1
1
1
0
0
1
2
1
2
4
2
1
2
0
1
2
0
2
2
0
1
0
1
2
1
0
1
0
1
0
0
1
1
1
2
1
2
1
1
2
2
0
0
0
0
1
1
1
0
1
1
0
1
2
1
2
0
1
2
1
0
1
1
1
1
0
1
1
1
1
1
1
0
0
1
1
1
3
1
0
1
1
1
1
1
0
1
1
1
1
1
1
2
1
0
1
2
0
0
0
1
0
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
2
1
0
0
1
1
1
2
1
0
1
2
1
1
1
0
0
2
2
0
1
1
1
2
0
2
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
0
2
0
2
2
0
1
1
0
1
2
2
0
2
1
1
1
2
2
1
5
0
1
0
2
1
2
2
1
1
1
1
2
2
2
2
1
1
1
1
1
1
2
0
1
2
2
1
1
3
1
2
0
1
1
1
2
1
1
0
0
1
2
1
1
1
1
1
0
1
0
1
1
2
1
2
2
2
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
2
2
0
1
2
1
1
1
1
0
2
1
2
1
1
1
0
0
1
0
0
2
2
2
2
1
1
0
1
2
0
0
0
1
1
1
1
1
2
0
1
2
0
0
1
1
1
2
1
1
1
1
1
1
1
2
2
2
1
1
1
1
0
2
2
1
0
1
1
1
1
1
0
2
2
0
2
1
0
1
2
1
1
1
1
2
1
1
0
1
2
1
0
2
1
4
1
1
1
1
1
1
2
1
3
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
2
1
0
1
1
1
1
2
0
0
1
1
1
1
1
1
0
2
2
1
1
1
1
1
0
1
2
2
1
1
0
1
1
1
0
2
2
1
2
0
2
2
1
1
1
1
1
1
1
0
2
1
1
1
2
1
1
2
1
2
2
1
0
2
0
1
1
2
1
2
0
1
2
1
1
1
2
2
0
1
1
1
0
0
2
2
1
0
2
1
0
1
2
2
2
1
1
2
2
2
1
1
2
2
1
1
2
1
1
1
2
1
1
1
1
0
1
1
0
0
1
1
1
1
1
1
2
1
3
1
2
1
2
2
2
1
1
1
1
1
1
1
0
1
0
1
1
1
0
1
2
2
0
0
2
1
2
1
1
1
1
2
1
0
1
1
2
1
1
2
1
1
2
2
1
2
1
1
2
2
0
2
1
0
2
1
1
1
2
2
1
0
1
1
1
2
2
1
2
1
1
2
1
1
0
1
1
1
1
1
1
1
1
1
1
3
1
2
1
1
1
1
1
1
1
0
1
2
0
2
2
2
0
2
1
1
1
1
1
1
1
0
2
1
1
1
0
0
1
1
1
0
1
2
2
3
1
1
1
2
1
0
2
1
1
1
2
2
1
0
2
2
0
0
1
1
2
1
2
1
2
2
1
2
0
1
1
2
2
1
0
1
1
1
1
1
0
1
2
2
0
1
1
0
2
4
0
2
2
2
1
1
2
2
2
1
1
0
0
1
0
1
2
1
1
2
1
0
0
1
1
0
1
1
0
2
0
1
1
1
0
1
2
1
1
1
1
2
1
2
1
2
2
2
1
1
2
2
1
1
1
1
2
1
0
0
2
0
1
2
1
0
1
1
0
1
0
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
0
1
1
2
0
0
1
0
1
0
1
2
1
1
1
1
0
2
0
2
1
1
1
1
1
1
2
1
1
1
2
1
1
0
1
1
2
1
1
1
2
0
0
1
1
1
1
1
1
0
1
2
1
1
2
2
1
1
0
1
2
1
1
2
1
1
1
2
2
1
1
2
1
1
1
1
2
2
0
1
0
1
2
2
1
1
1
2
1
1
1
1
0
1
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
2
1
2
2
0
1
1
2
2
0
1
2
1
1
1
1
1
0
1
0
1
1
0
1
0
2
0
0
1
2
1
1
2
1
1
1
1
0
1
2
1
1
1
1
2
1
1
2
1
1
0
1
2
1
0
0
1
1
1
0
0
0
2
0
0
0
0
1
1
1
1
1
0
1
1
1
0
1
1
1
0
0
2
1
0
2
2
1
0
1
1
1
1
1
1
1
2
2
2
1
1
0
1
1
1
0
2
2
1
1
2
1
0
0
2
1
2
0
0
2
0
1
0
1
1
2
1
2
1
0
1
1
1
1
3
1
1
0
1
0
0
2
1
1
2
1
2
2
0
2
1
2
0
2
3
3
0
1
1
1
1
1
1
2
0
1
2
1
2
1
1
0
1
1
2
2
2
2
1
1
0
1
2
2
3
2
1
1
0
1
1
1
1
1
0
1
1
2
0
1
2
1
1
1
2
1
1
1
1
1
1
0
1
1
2
1
1
2
0
0
1
1
2
1
1
1
1
2
2
2
1
1
1
0
1
0
1
1
2
1
1
1
1
1
2
2
2
2
2
0
1
1
1
2
1
1
1
1
1
2
1
2
1
2
0
1
1
1
1
1
0
2
1
2
1
0
1
0
0
0
1
2
1
0
1
0
2
0
1
1
2
1
2
1
2
2
1
1
2
1
0
0
1
1
1
1
2
1
1
1
1
1
1
1
0
1
2
1
1
0
2
1
1
1
2
1
1
1
0
2
1
1
1
0
2
2
1
0
1
2
2
0
1
0
1
0
2
1
2
1
1
1
0
1
2
2
2
1
1
1
1
1
2
2
2
2
1
1
2
2
0
0
1
1
0
2
1
0
1
1
2
1
1
0
2
1
2
2
0
2
1
0
2
1
1
1
1
1
1
1
1
2
2
0
0
1
0
1
1
1
0
1
1
2
1
2
1
1
1
2
2
1
2
1
1
1
0
2
1
1
1
2
2
1
1
2
0
0
2
1
2
1
0
2
1
1
1
0
0
1
0
1
0
2
0
0
3
1
1
0
0
2
1
1
0
1
1
0
0
1
0
0
1
2
0
1
1
1
0
2
1
1
0
2
1
2
0
0
2
1
2
1
1
0
2
1
2
1
0
2
2
2
1
1
1
0
1
2
0
1
1
1
1
2
1
1
0
1
2
1
1
1
0
2
2
0
0
2
1
1
1
0
0
1
0
2
1
1
0
0
3
2
1
0
2
2
1
1
1
1
0
0
1
2
1
1
1
1
1
2
1
2
0
1
1
2
1
1
1
1
0
1
1
1
2
1
1
1
1
1
1
1
3
1
0
1
1
1
0
0
0
1
1
1
1
2
2
2
1
1
2
2
0
1
0
1
0
0
2
1
0
0
1
1
2
1
1
0
1
2
0
1
2
1
1
0
0
1
1
1
2
1
1
1
1
1
0
1
1
1
0
0
2
2
1
1
1
2
2
0
1
2
1
0
2
0
1
0
2
1
1
1
2
2
1
2
2
1
1
2
1
1
2
1
2
1
1
0
0
1
2
1
2
0
0
0
1
0
1
1
0
1
2
1
0
0
1
1
1
1
1
1
2
1
2
1
0
1
1
1
0
2
1
2
0
1
1
1
2
1
2
1
1
0
1
1
1
2
1
1
1
2
2
1
2
1
1
2
1
0
2
1
1
1
2
1
0
0
0
1
2
1
1
1
1
2
0
1
2
1
2
1
2
1
0
1
1
2
1
1
2
1
1
1
2
1
1
1
2
1
0
2
0
1
0
1
1
1
2
0
2
1
1
1
0
2
1
0
1
2
1
1
1
1
1
1
1
0
0
1
2
1
1
1
2
1
1
1
1
0
1
1
1
1
1
2
1
1
2
1
1
1
1
2
1
2
2
2
1
1
1
2
2
1
1
1
1
1
1
0
0
2
0
2
1
1
0
1
0
1
2
0
1
2
1
2
1
2
1
1
1
1
2
1
0
0
1
1
1
0
2
2
1
1
2
1
0
1
0
0
1
1
2
1
1
0
1
1
1
1
1
2
1
0
1
1
1
1
0
1
2
0
1
4
1
2
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
0
0
1
1
0
1
1
0
1
0
0
1
1
1
1
1
1
1
1
0
1
1
1
0
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
0
1
1
1
2
2
1
1
2
1
1
2
2
2
1
2
2
0
0
0
1
0
1
1
1
0
1
0
1
1
2
1
2
1
1
2
1
1
2
1
1
0
1
1
1
2
1
2
2
1
1
1
1
1
1
2
0
2
1
1
1
1
1
1
1
1
1
1
1
0
2
0
2
1
1
2
1
1
1
1
1
1
2
2
1
2
2
1
1
2
1
1
2
1
1
2
1
2
2
1
1
1
1
2
2
0
1
1
1
1
1
2
2
1
2
1
1
2
1
1
1
0
1
0
1
1
2
1
1
1
1
2
1
1
2
0
0
2
1
1
2
2
1
1
0
3
1
0
2
1
0
1
0
1
2
1
1
1
1
1
2
0
1
2
1
1
0
0
1
0
2
1
1
0
2
1
1
0
4
1
1
2
2
1
1
2
2
1
1
0
1
1
2
1
1
2
1
2
1
0
2
1
1
1
2
2
2
0
1
1
2
2
1
1
2
1
1
1
2
2
2
1
0
2
1
1
2
1
0
2
1
1
1
1
1
1
0
3
0
1
1
1
1
0
1
1
1
1
1
2
0
1
0
1
2
2
1
1
1
2
1
1
1
1
1
2
0
2
1
2
1
1
0
1
1
2
2
0
1
1
1
1
0
2
6
2
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
0
1
2
1
1
1
0
1
0
1
0
2
1
1
0
2
1
1
2
2
2
1
2
0
1
2
1
0
1
0
1
1
2
1
1
1
1
0
1
1
1
0
1
2
2
2
1
1
0
1
1
2
1
0
2
1
1
0
0
1
1
1
2
1
2
1
0
1
0
0
1
0
2
1
1
0
1
1
1
1
1
1
2
1
1
1
1
1
1
0
1
1
3
1
1
1
2
2
1
1
2
2
2
0
2
1
1
1
2
1
2
1
1
2
1
2
1
1
1
1
0
0
0
1
1
0
1
2
0
1
0
1
3
1
0
0
2
2
1
1
0
1
1
1
1
1
0
1
2
1
1
0
1
0
1
2
0
1
2
1
1
1
1
1
0
0
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
2
1
0
1
1
2
1
0
2
1
1
1
2
1
1
1
1
1
1
0
0
2
1
1
0
1
2
0
1
1
1
1
1
1
1
1
0
1
1
0
1
1
2
1
1
1
1
1
1
1
2
0
2
2
0
1
1
1
1
2
1
1
2
0
0
1
2
0
1
0
1
1
1
2
0
2
1
1
1
1
0
2
1
1
2
0
1
1
2
2
1
1
1
0
1
1
1
1
0
2
1
1
1
1
1
1
2
1
1
0
2
2
2
1
0
0
1
1
0
1
0
2
2
2
2
1
2
2
2
1
1
0
1
0
2
3
1
1
1
2
1
1
1
1
1
0
1
2
0
0
1
1
1
2
1
1
1
0
0
2
1
1
2
2
1
1
1
1
0
1
2
2
1
0
2
1
1
2
1
1
0
1
1
1
1
2
1
1
2
1
1
2
2
2
1
0
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
2
1
1
1
1
1
0
1
1
1
2
2
1
2
3
1
1
1
1
2
1
0
0
1
1
1
1
0
1
1
2
1
1
1
2
1
1
1
2
0
0
0
2
2
1
1
1
2
2
1
1
1
1
1
2
1
1
0
1
1
1
0
0
1
1
2
1
0
0
1
2
1
1
1
2
0
0
1
2
1
1
1
1
2
1
0
1
1
1
0
2
2
2
1
1
1
1
1
1
2
1
2
2
0
0
1
1
1
1
1
1
2
1
2
0
0
1
0
1
1
1
2
1
2
2
1
2
1
1
1
1
1
0
1
1
1
1
1
2
1
2
0
1
1
1
1
0
1
0
1
1
1
0
1
0
1
1
1
0
1
0
1
1
1
1
1
1
1
1
0
2
1
0
2
1
0
1
1
1
1
1
1
1
0
2
1
1
1
2
2
0
1
1
1
1
1
1
1
1
0
1
1
0
0
0
2
1
2
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
0
1
1
1
1
2
1
2
0
2
1
1
2
1
3
1
2
1
1
1
2
1
1
1
1
0
1
1
1
1
1
1
2
0
1
1
0
2
1
1
1
1
1
2
1
0
1
4
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
0
2
1
1
2
1
1
1
0
1
2
2
1
1
1
1
1
1
0
1
1
2
1
0
0
1
2
0
2
2
2
0
0
0
0
1
1
1
1
1
1
0
2
1
1
0
1
1
1
1
0
1
1
1
2
0
1
0
2
2
1
1
2
2
1
2
0
1
0
0
2
2
1
2
2
1
1
0
2
3
2
1
1
2
2
1
2
1
1
2
1
2
2
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
0
1
2
1
1
1
1
0
1
0
1
2
1
0
1
1
2
2
0
2
1
0
1
1
1
1
1
1
2
1
1
0
0
1
2
2
2
1
1
0
1
1
2
1
0
0
1
1
0
0
0
0
1
1
1
1
0
1
1
1
1
2
1
1
1
0
1
1
0
2
1
0
2
0
2
1
1
1
1
0
1
0
1
2
1
1
1
4
0
2
2
2
2
1
1
0
2
2
2
1
0
1
1
0
1
1
0
2
0
0
1
0
2
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
0
2
2
1
1
1
1
1
1
1
0
0
1
1
2
0
1
0
1
2
1
1
1
2
2
1
1
2
2
1
1
1
1
1
2
1
2
1
1
0
0
2
1
1
2
1
0
2
1
1
2
0
1
0
2
1
0
1
1
1
2
1
1
1
1
1
1
2
1
2
1
0
1
1
0
1
2
0
2
0
2
1
1
1
1
1
1
0
1
2
2
1
0
1
2
1
1
1
0
1
0
1
1
1
1
2
0
2
1
2
1
0
1
2
1
1
2
1
1
1
2
1
1
1
0
2
1
2
1
1
2
1
0
2
1
2
2
1
2
0
1
1
1
1
2
1
2
2
1
1
2
1
2
0
1
1
1
0
2
2
1
1
2
2
1
0
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
0
1
1
1
1
1
1
0
1
2
0
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
0
1
1
0
1
1
0
1
1
2
2
1
1
1
1
2
2
1
1
1
1
0
2
1
2
2
1
1
1
2
1
2
0
1
0
0
1
1
1
0
1
1
1
0
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
0
1
3
0
1
1
2
1
1
1
2
1
2
0
1
0
1
0
2
1
0
1
0
1
1
2
1
1
2
1
2
2
1
2
1
1
1
2
1
2
1
1
2
1
1
2
0
1
1
1
1
0
1
1
2
1
1
1
1
1
0
2
1
1
1
1
1
1
1
0
2
2
0
0
1
1
0
1
1
1
1
1
0
0
2
2
2
1
1
1
0
2
1
1
2
1
2
1
1
1
0
2
2
1
3
1
2
1
2
3
2
1
2
1
2
2
1
0
1
0
1
2
0
1
2
0
2
1
1
1
0
2
1
2
1
6
2
1
2
1
1
0
1
2
1
0
1
1
0
1
0
1
1
1
1
1
1
0
1
2
2
1
2
2
2
1
1
0
1
1
1
1
2
1
2
1
2
1
0
1
1
2
1
1
1
1
1
1
1
0
1
2
2
0
1
0
0
1
1
1
1
1
1
1
0
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
3
1
2
2
1
0
1
1
0
0
2
1
0
1
2
2
2
0
2
2
1
1
3
2
2
1
2
1
1
0
1
1
2
0
1
0
1
1
1
1
1
1
2
0
1
1
1
2
1
0
1
2
0
0
1
0
1
0
1
1
3
1
2
1
1
0
0
2
1
2
2
0
0
1
1
2
1
0
0
1
0
1
1
1
2
1
0
1
1
1
1
1
1
0
1
1
0
1
1
1
0
1
1
1
2
1
1
1
1
1
0
1
0
1
1
1
0
1
1
1
1
1
2
2
0
2
2
1
0
1
1
1
1
2
2
0
2
0
1
1
1
1
1
0
1
1
1
2
1
1
0
2
0
0
0
1
2
1
0
2
0
2
1
0
0
0
1
1
0
2
2
1
2
2
1
2
1
2
1
2
1
1
1
1
0
2
2
1
1
2
1
1
1
1
2
0
0
0
2
2
1
1
0
1
1
0
2
1
1
2
1
1
1
1
1
0
0
1
1
1
1
2
0
1
2
1
0
0
1
0
2
1
1
1
1
0
1
1
1
1
1
2
2
1
0
1
1
2
2
1
1
1
1
1
1
1
0
0
2
1
0
1
1
0
0
1
1
0
1
0
1
1
0
1
1
1
1
1
2
0
1
1
0
1
1
1
1
1
1
1
1
2
2
2
1
1
0
0
1
1
1
1
0
0
2
1
2
1
1
1
1
0
1
2
2
2
1
2
1
0
1
1
2
1
0
1
1
1
0
1
1
2
2
1
1
1
1
2
0
1
1
0
2
1
1
1
2
2
1
0
1
1
2
1
1
1
1
0
4
0
1
0
1
1
0
1
4
1
1
1
2
2
1
1
2
1
1
10
1
2
1
1
1
0
1
2
1
0
1
1
2
2
0
1
1
1
1
0
1
2
2
1
1
0
1
1
1
1
1
0
2
2
1
0
1
0
1
2
0
1
1
2
2
1
1
1
2
1
0
2
0
1
1
1
1
1
1
2
1
0
1
1
1
1
1
1
1
1
2
1
4
1
1
1
0
1
1
1
1
1
1
2
1
1
1
1
1
2
2
0
1
0
2
1
2
1
1
0
0
2
2
1
0
1
2
0
1
2
2
2
0
1
0
1
0
1
1
2
1
0
0
0
1
1
1
1
2
1
1
1
2
1
1
0
0
1
0
2
0
1
1
1
0
2
2
0
1
1
2
0
1
0
1
0
1
0
1
1
1
2
4
1
3
1
2
1
2
0
1
1
2
1
1
0
0
2
1
0
2
0
0
1
0
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
0
1
1
1
1
1
2
1
0
2
2
2
1
0
1
1
1
1
0
2
1
1
1
1
2
2
2
0
0
0
1
2
1
1
2
2
1
1
1
1
1
1
2
0
0
1
2
1
1
1
1
1
1
1
0
1
1
1
2
1
2
2
0
2
1
1
0
2
2
2
0
1
2
1
1
2
2
0
1
0
2
1
0
2
2
2
2
1
1
0
1
1
1
1
1
1
1
1
2
0
1
1
1
1
0
1
0
1
1
2
0
0
1
1
1
0
2
3
0
0
0
0
1
0
2
1
1
0
1
0
2
2
1
2
1
2
1
2
0
1
0
1
1
1
1
2
2
1
1
3
2
2
1
1
1
0
1
2
1
1
1
3
0
2
1
2
2
0
1
1
1
1
0
1
1
1
1
1
2
2
1
1
1
1
1
1
2
2
2
1
0
2
2
1
1
1
1
1
3
1
3
2
1
1
0
1
1
1
1
1
1
2
0
1
1
1
2
1
1
1
1
1
1
1
0
1
0
1
2
2
1
1
0
1
2
1
2
1
2
1
1
1
1
0
2
2
1
1
1
1
2
1
1
2
0
2
2
1
2
0
1
0
1
1
0
1
1
0
2
1
1
1
1
0
2
0
1
1
2
0
2
2
1
0
1
0
2
1
2
1
1
1
1
0
2
1
1
1
0
1
2
1
0
2
1
1
1
2
1
1
1
2
2
2
3
1
1
1
0
1
2
0
1
0
1
1
2
1
1
1
1
1
1
1
1
1
1
0
2
1
1
1
1
2
2
1
2
1
1
1
0
2
1
1
1
1
1
1
1
1
0
2
1
1
2
3
1
1
2
0
1
2
2
1
1
0
2
1
0
1
1
0
1
1
0
0
2
1
1
0
2
1
2
1
2
1
1
1
8
1
0
1
0
1
3
1
1
0
2
2
1
1
1
0
0
1
2
1
0
2
2
0
1
1
1
0
1
1
1
1
1
1
1
0
0
1
1
2
1
2
2
1
1
0
1
2
1
1
1
0
2
0
1
1
1
2
2
1
1
1
1
1
1
1
1
2
1
1
0
1
2
1
1
0
0
2
1
1
1
2
1
2
1
0
2
1
0
1
2
1
1
0
2
1
1
2
1
0
1
1
2
2
1
0
1
1
2
0
1
1
1
1
1
0
1
1
1
1
2
2
1
1
0
0
1
1
0
1
1
1
1
2
1
1
0
0
1
0
1
1
1
1
2
1
1
2
1
1
2
0
1
1
1
1
1
2
0
2
1
2
1
2
1
1
2
1
2
0
1
1
2
0
1
2
1
2
2
2
1
1
0
1
1
1
1
1
1
1
1
0
1
0
1
3
1
1
0
1
1
1
1
2
1
0
0
1
1
1
1
1
1
2
1
1
2
1
2
2
2
1
1
2
1
1
1
1
2
2
1
0
0
1
1
0
1
1
1
0
1
1
1
2
1
2
1
1
1
1
0
1
1
2
1
1
2
2
1
0
2
1
1
1
0
2
0
2
1
1
1
2
2
1
1
1
0
0
2
1
1
0
1
1
2
0
1
1
0
0
1
1
1
1
1
1
1
2
1
1
1
1
0
2
0
2
0
1
1
2
0
0
1
2
2
1
1
1
1
0
1
1
1
1
1
2
2
2
0
1
1
1
2
1
1
1
1
2
2
0
2
0
1
1
0
0
2
1
2
1
1
0
1
2
1
1
2
1
0
0
0
2
1
1
0
0
0
3
1
1
0
1
2
1
1
0
1
2
0
1
2
1
0
1
2
1
1
1
1
1
2
1
0
1
1
2
2
0
0
2
1
1
2
0
1
1
2
1
1
1
0
3
1
1
0
2
1
1
0
1
1
1
1
1
2
1
1
1
0
2
1
0
2
1
1
1
1
2
0
1
2
0
1
2
1
2
2
1
0
1
1
0
1
1
1
0
2
1
2
0
2
0
1
0
1
1
1
2
1
0
1
1
1
1
1
2
1
1
1
2
2
2
2
2
0
1
0
0
2
4
2
1
1
0
1
1
1
0
1
0
0
0
1
1
1
1
1
2
2
0
1
1
1
1
2
1
1
2
1
1
2
1
2
0
1
2
2
2
1
2
1
1
2
1
0
1
1
2
1
1
2
0
1
2
1
0
2
0
1
1
0
2
1
0
2
0
1
2
0
0
1
1
1
1
1
1
0
1
2
1
1
1
2
2
1
1
0
1
2
2
1
1
3
1
2
1
0
1
2
2
1
2
1
1
2
1
0
0
2
1
2
2
1
1
1
0
2
1
0
1
1
1
2
0
2
1
0
1
0
1
0
0
2
2
1
0
0
1
1
1
2
1
1
1
1
1
1
1
3
1
1
1
0
1
0
2
2
0
1
0
0
2
1
1
2
0
1
0
2
1
1
1
1
4
1
1
1
1
1
0
0
0
2
1
2
0
1
1
1
1
2
1
2
0
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
3
0
0
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
0
2
1
1
1
1
1
2
1
1
1
2
1
1
2
2
2
2
0
1
0
2
3
2
1
1
1
1
2
2
2
1
2
1
2
0
1
1
0
1
1
2
1
0
2
0
2
0
1
1
1
2
1
2
2
1
1
1
1
0
1
1
2
1
2
1
1
1
1
0
2
2
2
1
2
1
0
1
3
1
1
1
1
2
2
1
1
1
1
1
2
1
0
1
1
2
1
2
1
1
2
0
1
1
2
2
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
2
3
2
1
1
1
2
6
1
0
1
0
1
1
2
4
2
1
1
2
2
2
1
1
2
2
1
0
1
2
1
0
0
2
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
2
1
1
2
1
2
2
0
1
1
2
1
2
1
1
1
2
0
2
2
0
1
1
0
1
0
1
0
1
2
1
1
1
2
2
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
0
1
1
2
1
1
4
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
2
2
1
1
0
0
2
1
1
1
1
1
2
0
1
1
1
1
2
1
0
2
0
1
1
1
0
2
2
2
2
0
1
1
1
3
2
2
1
1
2
1
1
1
1
2
1
2
1
0
1
0
1
2
2
2
0
2
0
1
2
0
1
0
1
1
0
1
1
1
3
1
1
1
1
2
1
1
1
1
1
0
0
1
2
1
1
2
1
2
1
1
1
0
2
0
1
2
1
0
1
0
1
1
0
2
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
2
1
1
2
1
1
1
1
2
1
0
1
1
2
1
1
2
1
1
1
1
0
1
2
2
0
0
0
1
1
2
1
1
2
1
0
1
1
1
0
1
0
2
1
2
1
0
0
1
1
2
0
1
2
1
1
2
0
1
2
1
2
2
1
1
1
0
1
2
2
1
1
1
0
1
1
1
2
2
2
2
2
2
3
2
0
1
2
2
1
1
1
1
1
0
1
1
1
0
1
1
1
2
2
2
1
2
0
1
2
1
1
1
1
2
2
2
1
0
0
2
1
1
1
1
1
1
2
1
0
1
1
1
1
1
2
0
1
2
1
0
1
2
1
2
0
2
2
0
1
2
1
2
1
1
1
4
2
1
0
2
1
2
1
1
1
1
1
1
1
1
2
0
1
1
1
2
1
1
2
1
1
1
2
1
1
1
1
2
1
1
0
1
2
2
2
1
1
0
1
1
1
1
0
1
0
1
0
1
1
3
0
0
1
1
2
1
0
0
1
2
1
2
0
1
1
1
0
1
1
1
1
1
1
0
2
2
2
0
2
1
1
0
1
1
2
1
1
2
1
0
2
1
1
1
2
1
1
0
2
0
0
1
2
0
0
1
0
1
2
1
1
2
1
2
2
1
0
0
0
1
1
1
1
1
2
0
1
1
1
0
1
2
1
1
1
0
2
0
1
1
1
1
1
1
0
0
1
2
1
1
1
2
2
2
1
2
0
1
0
1
1
1
2
1
1
1
0
2
0
2
1
0
1
0
1
1
1
2
1
1
1
1
1
2
1
2
0
1
1
1
1
1
1
1
1
1
1
2
2
1
1
0
1
1
2
1
1
1
2
1
2
1
0
1
0
1
1
2
2
1
1
1
0
2
2
1
1
1
1
1
1
0
0
1
1
2
2
1
1
2
2
1
2
0
1
0
0
1
1
1
1
1
1
1
2
0
1
1
1
1
1
1
2
2
1
2
2
1
2
1
1
1
0
1
2
1
1
2
0
1
1
2
1
2
1
1
1
1
1
2
2
2
1
1
1
1
2
0
1
2
0
3
1
0
1
1
2
1
0
2
2
1
1
2
1
1
1
1
1
2
2
1
2
1
1
2
2
1
1
0
1
2
1
0
1
1
1
1
1
0
0
1
1
0
2
2
2
1
1
7
2
0
0
1
2
2
1
2
2
2
1
2
1
2
0
1
2
1
1
1
0
1
1
1
1
1
0
1
1
1
1
1
1
0
1
1
0
1
1
1
1
1
0
1
1
1
1
1
1
1
1
0
1
0
1
0
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
0
1
1
2
0
2
1
2
1
1
1
2
2
1
1
1
0
1
0
1
0
1
1
1
1
2
0
1
1
2
1
0
1
1
1
0
0
1
1
2
1
2
2
1
0
1
1
2
1
0
2
3
1
2
1
0
1
1
2
2
2
2
0
2
0
2
2
1
1
1
2
1
2
1
2
1
1
2
1
1
1
1
1
1
1
2
2
2
2
2
1
1
1
1
0
1
1
0
0
2
1
1
1
0
1
2
1
0
2
2
2
2
1
1
0
2
1
1
2
1
2
1
2
1
1
2
1
0
1
2
1
0
1
2
1
1
1
1
2
1
2
2
2
1
1
1
2
2
0
2
1
1
1
2
2
0
1
1
2
1
1
1
0
1
2
2
2
2
1
1
1
2
1
0
1
2
0
1
2
0
2
0
2
0
1
0
0
1
1
1
1
2
1
0
2
1
1
1
1
2
1
0
2
2
1
1
1
0
2
1
1
1
1
1
2
0
2
1
2
1
1
0
1
2
1
2
2
1
1
1
2
1
1
0
2
1
1
1
1
1
2
1
2
1
1
1
2
2
1
2
1
0
1
1
1
1
1
1
2
2
0
2
2
1
2
1
1
1
2
1
1
1
2
1
1
2
2
1
0
2
0
2
1
2
0
1
0
1
1
0
1
2
1
0
2
2
1
1
1
1
1
1
0
2
1
1
2
1
2
1
0
1
1
1
1
1
2
1
1
1
1
0
1
2
0
1
1
1
1
1
1
2
1
0
1
1
1
2
1
1
2
2
1
1
0
1
2
1
1
1
2
0
1
2
1
1
0
1
1
1
1
2
1
1
1
1
1
1
0
1
1
1
1
0
1
0
1
2
1
1
1
1
2
0
0
2
1
2
0
1
0
1
2
1
1
1
0
0
2
1
0
1
2
3
1
1
1
0
0
1
0
0
1
2
2
1
0
0
1
1
1
2
1
1
1
0
2
2
1
1
1
0
0
1
1
1
1
1
1
1
1
1
1
2
1
0
1
0
1
1
1
1
2
1
1
1
1
0
2
1
2
2
1
1
2
1
0
1
0
2
1
1
2
0
1
2
1
0
2
0
0
1
0
1
2
0
1
2
2
1
1
0
1
2
0
1
1
1
0
0
1
1
0
2
2
2
0
1
2
2
1
0
1
0
1
0
1
2
0
1
1
0
2
1
0
1
2
1
1
0
1
1
2
2
0
1
1
1
1
1
2
0
1
1
2
1
1
0
1
1
3
2
1
1
0
1
1
1
1
1
1
1
2
3
1
1
2
1
0
0
2
1
1
1
0
1
1
1
1
2
2
1
0
1
0
1
1
0
1
1
1
1
1
1
1
1
1
0
1
2
0
1
0
1
2
1
2
0
1
1
0
1
0
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
2
0
2
1
1
2
1
1
0
1
0
1
1
2
0
2
2
0
1
1
0
1
1
1
0
1
3
1
1
0
1
0
0
1
2
1
0
1
1
1
1
1
1
1
0
1
1
2
1
0
1
2
2
2
1
2
2
1
1
0
1
1
1
1
0
1
0
0
1
1
2
1
1
1
1
1
0
1
1
1
1
1
1
0
1
2
1
1
2
1
2
1
1
2
1
1
1
2
1
1
1
1
0
1
1
0
1
1
2
2
0
2
1
0
1
1
1
0
2
1
1
1
0
2
0
1
2
1
1
2
1
1
1
1
1
0
1
1
1
1
1
1
1
1
2
1
3
1
1
0
0
1
2
0
1
2
1
2
1
2
1
0
1
2
2
2
1
2
1
1
1
0
2
1
0
1
1
1
0
1
0
1
2
0
1
0
1
1
1
1
1
1
2
2
0
1
1
1
1
2
0
1
1
1
2
1
1
1
1
1
2
1
1
2
1
1
1
1
1
2
2
2
1
2
0
1
2
1
1
2
1
1
1
1
1
0
1
1
1
1
3
1
2
1
2
1
1
0
1
0
2
1
0
2
2
0
1
1
1
2
1
2
2
2
1
2
1
1
1
1
2
1
1
2
0
1
1
2
2
1
1
2
1
1
1
0
1
1
2
1
1
1
1
1
2
1
2
1
1
0
1
1
0
0
1
1
0
0
2
1
1
1
1
0
1
1
1
1
2
3
1
0
0
1
1
0
0
1
1
0
2
0
1
0
1
0
1
1
1
1
1
0
1
0
1
2
1
1
1
1
2
3
2
1
1
2
1
1
1
1
1
1
2
0
0
2
1
2
1
2
1
2
0
1
1
1
2
1
1
1
0
1
1
2
3
2
1
1
2
1
1
2
2
1
1
2
1
2
1
1
1
1
2
0
1
2
0
1
2
0
0
1
2
2
1
0
2
1
1
1
2
1
1
2
1
1
0
2
1
1
0
1
1
0
1
1
1
1
1
0
2
2
0
2
0
2
1
1
1
1
2
1
1
0
1
2
1
0
0
0
1
0
1
1
1
1
2
1
0
2
1
1
2
1
1
2
1
1
1
0
1
1
1
0
2
1
0
1
0
1
0
2
1
1
1
2
1
1
1
2
0
1
2
1
2
2
2
1
1
1
2
1
0
1
1
1
2
1
0
1
1
1
1
1
1
1
0
1
2
0
1
1
1
1
1
1
1
1
0
0
2
1
2
1
1
2
1
2
0
0
2
0
1
1
1
1
1
1
1
2
2
1
0
2
2
1
2
2
2
1
1
1
1
0
2
1
2
2
2
1
0
1
0
1
2
1
0
1
2
1
1
1
1
1
2
2
1
1
1
1
1
0
1
1
2
1
1
0
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
0
1
2
2
2
1
2
0
1
2
1
0
1
1
0
0
1
1
1
0
2
0
2
2
1
1
2
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
0
0
3
1
1
1
1
0
0
1
1
1
1
0
0
2
0
0
1
1
2
2
2
1
2
1
1
0
1
2
1
1
2
2
0
1
1
2
1
1
0
2
0
1
1
1
1
0
1
1
1
1
0
1
0
1
1
1
1
2
1
2
2
1
0
2
0
2
2
1
1
2
1
0
0
0
1
2
1
1
0
1
1
1
1
3
2
2
1
2
0
1
1
0
1
2
1
1
2
2
1
2
1
1
1
1
1
1
1
2
1
1
1
0
1
1
1
3
1
1
1
1
2
0
2
0
0
2
1
2
2
1
1
1
2
2
2
0
0
1
1
1
0
1
2
0
0
2
2
1
1
1
0
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
2
0
1
1
2
1
1
0
0
2
1
1
1
1
0
1
0
1
1
1
0
1
0
1
2
1
1
1
0
1
2
0
1
1
2
1
1
1
1
1
1
1
0
1
2
0
1
1
2
1
0
1
1
1
2
1
2
1
0
0
1
1
1
1
1
1
1
1
8
0
1
1
1
1
3
1
0
1
1
2
1
4
1
1
1
1
1
2
2
2
1
1
1
1
1
2
1
1
1
2
1
1
1
0
0
0
2
1
0
0
1
1
1
1
1
1
1
1
1
1
1
0
1
1
2
0
1
0
1
1
1
1
0
2
0
1
1
2
2
1
1
1
0
1
1
1
0
2
2
2
0
3
1
1
2
1
1
1
0
1
1
1
1
1
2
2
1
2
1
1
0
1
2
1
2
0
2
0
1
0
1
2
2
1
1
1
2
1
1
2
0
0
1
2
0
2
1
2
1
2
1
0
1
1
2
1
1
1
1
1
0
2
0
0
1
2
1
1
2
2
0
2
1
1
1
2
0
1
0
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
0
1
2
1
1
1
1
0
1
0
2
1
1
0
1
2
0
2
2
3
1
0
1
1
1
2
0
1
0
2
1
1
0
1
2
1
2
1
2
1
2
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
0
2
0
2
1
1
1
3
1
1
0
1
1
0
1
1
1
1
2
2
1
1
1
1
2
1
1
8
1
2
3
1
2
2
1
1
2
1
1
2
1
1
2
2
0
1
1
1
1
0
2
2
2
1
2
1
1
1
1
2
0
0
0
2
2
1
1
0
2
2
1
1
1
1
1
1
1
0
3
1
3
1
2
1
1
2
1
1
1
1
0
2
0
1
1
2
2
1
2
2
1
2
1
2
0
1
2
1
1
1
2
1
2
2
1
1
1
1
1
2
1
1
1
1
1
1
0
1
3
2
1
2
1
0
2
1
1
2
2
1
2
1
1
2
3
0
2
2
2
1
2
1
0
1
1
2
1
0
2
1
2
1
0
1
0
1
1
1
1
2
1
2
1
2
2
1
1
1
1
0
0
2
1
2
1
1
0
0
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
0
1
1
1
2
0
1
0
1
0
1
2
2
2
0
1
1
2
1
0
2
3
2
1
2
0
0
2
1
2
1
0
1
0
2
1
1
1
0
1
0
1
1
2
2
1
1
1
1
1
1
1
1
2
2
1
3
2
1
1
3
0
0
2
1
0
2
2
0
2
1
0
2
1
1
1
0
2
1
2
1
0
2
2
1
2
1
1
2
1
1
1
0
1
1
1
1
1
1
1
1
0
1
1
0
1
2
2
2
1
1
2
1
1
0
1
1
1
2
1
1
3
0
1
1
1
1
1
0
1
1
1
1
1
0
1
0
1
0
1
1
0
2
2
2
1
1
1
1
2
2
0
2
1
2
1
2
1
1
1
0
1
0
1
2
0
0
0
1
0
1
1
1
1
1
2
1
1
1
1
2
2
1
1
1
0
1
0
0
1
1
1
1
1
0
2
1
1
0
2
2
1
2
1
0
1
0
1
0
0
2
1
1
2
1
1
1
1
0
0
0
2
1
1
1
2
1
1
0
1
2
0
1
1
1
1
2
1
2
0
1
1
2
0
2
1
2
1
1
1
1
1
1
1
1
2
1
2
0
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
0
1
0
2
1
1
3
1
0
1
1
2
1
0
3
1
1
2
1
1
0
2
1
0
1
1
2
1
1
1
1
2
2
0
5
0
1
1
1
2
1
0
1
0
1
1
1
2
1
1
2
2
0
2
1
0
1
1
1
2
1
1
1
1
1
1
2
2
0
2
1
0
2
2
2
1
1
1
1
2
1
1
1
1
2
0
2
1
1
2
2
1
2
2
1
1
1
1
1
1
2
1
0
0
1
1
1
1
1
1
1
1
1
1
2
2
1
2
1
1
1
0
0
0
2
1
2
2
1
1
1
0
1
2
2
1
1
1
1
0
1
1
1
1
0
1
1
1
0
1
1
1
1
2
1
1
1
1
1
1
4
0
2
0
1
1
1
1
2
2
1
2
0
2
1
1
0
1
0
1
1
1
1
2
1
1
1
1
1
0
1
2
2
1
2
2
2
1
1
3
1
1
2
1
0
2
1
1
0
2
1
2
2
1
1
1
1
1
2
2
2
2
2
1
2
1
1
2
0
1
1
2
0
0
1
1
0
1
1
1
0
2
2
1
1
0
2
2
0
2
0
0
1
1
1
1
2
1
0
1
2
1
1
1
1
2
1
1
1
2
1
2
1
1
0
1
0
1
0
1
1
0
1
0
3
1
1
1
1
2
2
1
0
1
2
1
1
2
1
2
1
1
2
1
1
0
1
1
2
1
1
2
2
2
2
1
1
1
2
1
1
1
1
2
0
1
1
1
1
0
2
1
1
1
2
1
2
0
0
1
1
1
1
1
2
0
1
1
1
1
2
1
1
1
1
1
0
2
1
1
1
2
2
1
1
1
2
1
1
1
2
1
1
1
2
1
1
1
0
2
4
1
1
0
1
0
0
1
1
1
1
2
1
2
1
0
0
2
1
0
2
1
0
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
2
1
2
2
1
1
0
1
2
0
2
2
2
2
1
1
1
1
3
0
1
1
1
1
1
1
1
1
2
2
1
0
0
0
0
1
1
1
1
1
2
1
2
1
0
1
1
2
1
0
0
2
1
1
1
0
0
1
1
0
1
1
2
1
2
2
1
1
0
1
1
1
1
1
1
1
1
2
2
1
1
2
2
2
1
2
1
1
2
1
2
0
1
2
1
1
1
1
0
1
1
1
2
1
2
2
1
1
1
1
0
1
1
1
1
0
1
1
1
1
1
1
0
2
1
1
2
2
0
2
1
1
1
2
1
1
0
1
2
0
0
1
0
1
2
0
1
1
1
2
0
1
2
1
2
1
2
2
1
1
1
2
1
0
0
1
1
2
0
0
0
1
1
1
1
1
2
0
1
1
1
1
0
1
1
2
2
2
1
2
2
2
1
1
1
2
1
2
2
0
2
1
2
1
2
1
1
1
2
1
1
1
1
0
2
1
1
1
2
0
2
2
1
0
0
1
1
1
2
3
1
1
1
1
0
1
1
1
0
0
1
0
2
1
0
2
2
0
1
1
2
1
0
0
0
0
1
2
1
1
0
1
0
2
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
2
0
0
0
2
1
1
0
1
1
1
0
1
1
1
1
2
2
1
1
1
1
2
2
1
0
0
0
1
1
2
0
2
1
2
2
1
1
1
1
1
2
2
2
1
2
0
1
0
0
1
1
1
0
1
2
3
1
1
1
2
1
1
1
1
0
1
1
2
1
2
1
1
0
1
1
1
1
1
2
1
1
1
2
0
1
1
0
1
1
1
1
1
2
1
1
1
1
0
1
2
0
2
1
1
0
1
1
2
1
1
1
1
1
2
0
0
1
1
1
1
0
1
1
0
2
2
1
1
1
0
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
0
2
2
1
1
1
1
1
1
1
0
1
0
1
1
1
1
2
1
1
1
1
1
0
1
1
1
1
1
1
2
1
1
1
0
1
2
0
2
0
0
1
1
0
0
1
2
0
1
0
1
2
1
1
2
2
0
1
1
2
0
1
2
1
1
1
1
1
1
1
2
0
1
0
3
0
1
0
2
1
0
1
1
1
1
2
1
1
2
1
1
1
0
0
2
1
1
0
1
1
1
1
1
2
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
0
0
1
1
1
2
1
1
0
1
2
0
1
2
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
0
1
2
1
2
2
1
2
1
1
2
1
1
1
1
0
1
1
0
1
2
1
1
2
1
1
0
2
1
1
2
1
1
1
1
1
2
2
2
1
1
2
2
1
1
1
2
2
1
2
1
1
1
1
1
1
1
0
2
1
1
1
1
2
0
1
2
0
2
1
2
2
2
0
1
2
2
1
1
2
1
1
1
1
1
1
1
1
2
1
0
2
2
1
1
2
1
0
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
0
1
2
1
1
1
1
1
1
0
2
1
2
1
1
2
0
0
0
2
0
1
1
1
2
0
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
0
1
2
1
1
2
1
1
2
1
1
0
1
2
0
1
1
2
1
2
3
0
2
0
0
2
1
1
1
3
0
1
0
1
1
2
0
1
1
2
1
0
1
1
1
1
0
1
0
1
1
1
2
1
2
1
1
1
0
2
2
1
2
1
1
1
2
1
1
2
1
2
1
1
1
2
2
1
0
2
2
0
1
1
2
1
0
1
1
1
1
2
2
1
2
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
2
3
0
1
1
2
1
1
1
0
0
1
2
1
1
1
1
1
2
1
0
1
1
1
2
1
1
1
0
0
0
1
1
1
1
1
2
2
0
1
0
2
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
0
3
2
1
2
0
1
2
1
0
1
2
2
1
0
1
0
1
1
0
1
0
1
1
0
1
0
0
1
1
1
0
2
1
0
1
1
0
0
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
0
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
2
0
2
1
1
1
1
1
1
1
1
2
2
1
2
0
1
1
2
2
1
1
1
2
0
2
0
1
2
1
1
0
0
2
0
0
1
2
1
1
0
1
2
1
2
0
1
1
1
1
0
1
0
1
1
0
5
1
1
1
0
1
1
1
0
1
1
0
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
0
1
0
1
1
0
1
2
2
1
2
0
1
0
0
1
1
1
1
1
0
2
1
0
0
1
1
2
0
1
0
1
2
2
1
1
1
0
1
0
1
0
1
1
1
1
1
0
1
1
0
0
1
1
1
1
2
2
2
2
1
1
2
0
1
1
2
1
0
0
1
2
1
2
0
1
1
0
0
2
1
1
0
1
1
1
1
1
1
0
0
1
1
0
1
1
1
2
1
1
1
1
0
1
1
1
1
1
1
1
1
2
2
0
2
1
2
2
2
1
0
1
1
1
2
1
2
1
1
1
1
1
1
1
1
2
0
1
1
1
0
1
2
1
1
2
2
0
1
2
1
1
1
1
1
1
1
1
1
0
0
1
2
1
2
2
1
1
1
1
1
1
2
2
2
1
1
1
1
0
2
0
1
1
2
1
1
2
2
2
0
0
1
2
1
1
2
1
1
1
0
1
0
0
1
0
0
1
1
2
1
1
2
1
1
1
1
0
1
1
1
1
0
1
0
2
1
0
1
0
0
1
2
1
0
1
1
1
1
2
0
2
2
1
1
0
0
1
2
1
0
2
1
1
1
1
1
0
0
1
2
1
1
0
1
0
1
1
1
0
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
0
1
1
2
1
0
1
0
1
2
1
1
1
0
1
0
0
1
1
1
2
2
1
1
2
1
1
0
1
1
1
1
1
1
1
2
1
1
0
1
2
2
1
1
2
1
1
1
0
1
2
1
1
1
1
1
2
2
2
2
0
1
2
2
1
2
1
1
1
0
2
1
0
0
1
1
1
2
2
2
0
1
1
1
2
1
1
1
1
2
1
3
1
1
1
1
0
1
0
0
1
1
2
1
0
1
1
1
1
0
1
1
1
0
0
0
1
1
0
0
1
1
2
1
1
2
0
0
0
1
1
1
1
2
1
1
0
1
0
1
2
2
1
0
1
0
0
1
1
2
1
1
1
0
1
2
0
0
2
1
0
2
0
0
2
2
1
1
1
1
2
1
1
1
2
2
1
2
1
0
1
1
2
1
1
4
1
2
2
1
1
2
1
2
2
1
1
1
1
0
1
1
1
2
1
1
0
1
1
1
1
1
1
0
1
0
0
1
1
0
0
1
2
1
1
1
2
2
2
1
0
2
1
1
2
0
1
1
1
0
1
0
1
1
1
1
0
2
1
1
1
1
0
1
1
2
1
1
0
1
2
1
0
1
1
2
2
2
1
2
1
0
0
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
0
2
2
0
1
1
1
0
1
2
1
2
0
1
2
1
1
1
1
1
1
2
0
0
1
0
2
2
2
1
2
1
1
2
1
1
0
1
2
0
2
1
2
1
1
2
0
1
0
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
2
1
1
0
1
1
1
1
1
1
2
1
1
2
1
0
0
1
1
1
0
2
0
1
2
1
1
2
2
1
0
1
0
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
2
1
2
1
1
0
0
1
1
1
2
1
2
1
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
2
1
1
0
1
1
1
0
1
1
0
1
2
3
0
1
1
2
2
0
1
1
2
1
1
1
1
2
1
0
1
1
0
2
2
1
1
2
1
2
2
1
1
1
2
0
0
1
1
1
1
1
0
2
1
1
1
0
2
1
1
2
2
1
0
1
1
1
1
1
1
1
1
0
0
2
1
1
2
0
2
0
2
1
1
1
1
1
0
1
1
1
1
2
1
1
1
0
2
1
1
1
1
1
0
1
1
0
0
0
2
2
0
1
2
2
0
1
2
1
1
2
1
1
1
1
2
1
0
2
3
2
1
2
1
1
2
1
0
1
1
1
2
1
1
2
1
1
0
1
0
0
0
0
1
1
1
1
1
2
0
1
1
1
1
1
1
0
2
1
0
2
1
1
0
1
2
1
1
0
1
0
1
2
1
2
1
1
2
1
1
0
1
2
2
1
1
1
1
1
2
0
1
2
1
2
2
1
1
2
1
2
2
1
1
2
2
1
2
0
1
1
0
1
2
1
1
0
2
1
1
0
2
1
1
1
1
1
2
1
1
2
3
2
2
1
1
2
2
0
1
1
1
2
2
1
2
2
1
2
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
0
2
0
2
2
1
0
1
2
0
0
2
0
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
0
1
1
0
1
1
1
1
1
1
1
2
1
1
0
1
1
0
0
1
0
1
2
2
1
2
1
1
1
1
1
1
2
1
2
0
1
0
2
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
2
1
2
2
1
2
0
2
1
0
1
2
1
1
1
1
1
0
1
1
2
2
1
1
0
1
1
1
1
1
2
2
1
2
1
0
1
1
1
1
1
2
1
1
2
1
1
1
0
1
0
2
1
1
2
1
0
1
1
2
2
1
1
1
1
2
2
1
1
1
2
1
1
1
2
1
1
6
0
2
2
0
2
0
2
0
1
1
1
0
0
0
1
2
0
1
1
2
0
1
1
1
1
0
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
1
0
1
1
2
0
1
1
2
1
0
1
2
1
0
1
1
1
1
2
0
0
0
0
0
1
0
2
1
2
2
1
0
1
1
0
2
0
1
1
1
1
1
1
2
0
2
2
2
0
2
1
1
1
1
1
0
1
1
1
0
1
1
2
1
1
1
0
0
1
1
1
1
2
2
1
1
1
0
1
1
1
1
0
2
1
0
0
0
2
1
2
1
1
1
3
1
0
2
1
1
1
1
1
2
1
1
1
0
1
1
2
1
1
1
0
1
1
2
2
1
1
0
0
0
1
1
1
1
2
1
2
1
0
1
1
0
2
1
1
1
1
1
1
2
0
1
1
0
1
0
2
1
2
1
2
1
0
1
1
2
2
0
2
2
1
1
1
1
1
1
2
0
0
1
1
1
2
1
3
2
1
0
1
1
1
1
2
1
1
2
1
1
2
0
1
0
1
2
2
2
1
0
0
1
1
1
0
0
1
1
0
1
2
2
1
1
0
1
2
3
2
1
1
1
1
1
1
1
1
1
1
0
0
1
0
2
1
0
2
1
1
1
0
1
0
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
2
0
2
1
0
2
1
1
0
2
2
1
2
1
0
1
0
2
1
1
0
1
1
2
1
1
1
1
2
0
0
1
1
1
0
1
2
1
0
1
2
1
1
1
1
2
2
1
1
1
2
0
1
2
1
1
1
2
1
2
0
0
0
1
1
2
1
1
2
1
2
1
1
2
2
1
1
3
1
1
2
0
2
2
2
2
1
1
1
1
0
2
0
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
0
2
2
1
2
1
2
2
1
0
1
2
2
0
1
1
1
1
1
1
2
1
1
1
1
1
0
0
1
0
1
1
1
1
2
1
1
1
1
1
1
1
0
0
0
0
1
0
1
2
0
1
1
0
1
0
1
2
1
0
1
2
0
1
2
1
1
0
0
1
1
1
1
0
2
1
2
2
1
0
0
2
1
1
1
2
2
1
1
0
1
1
1
1
1
1
1
1
1
0
2
1
1
2
1
2
0
0
0
1
2
2
1
1
0
2
2
1
1
1
1
1
1
2
0
2
1
0
0
0
2
1
1
1
2
0
1
1
0
1
1
1
2
1
1
2
1
1
1
1
2
0
1
0
1
0
2
1
2
0
1
0
0
1
1
1
2
1
1
1
0
0
0
2
2
0
1
1
1
1
0
1
1
2
1
2
0
0
1
0
1
2
1
1
2
1
2
2
2
1
1
3
3
1
2
2
1
2
2
1
1
1
1
1
0
1
1
2
2
1
2
1
1
1
1
2
0
1
1
1
2
0
1
0
2
1
0
0
0
1
2
2
1
2
2
1
1
2
2
1
1
1
1
0
1
1
1
1
1
1
1
2
1
1
2
1
1
1
2
1
1
1
0
2
0
0
1
1
1
1
1
1
2
0
2
1
1
1
1
1
2
1
1
1
1
0
1
2
2
2
1
1
2
1
1
1
0
2
1
1
1
1
1
1
1
1
2
2
0
3
1
1
0
1
2
1
2
1
1
1
0
2
1
1
1
1
1
2
1
2
1
1
1
1
2
2
1
0
1
2
2
1
1
1
2
1
0
2
2
2
2
2
1
2
1
1
1
0
2
1
1
1
1
1
1
1
1
1
0
2
1
0
2
1
0
2
2
1
2
2
0
1
2
1
0
2
1
1
2
3
1
1
2
1
1
3
1
1
1
2
2
2
1
1
1
1
1
0
1
0
2
1
1
1
0
1
1
1
1
1
4
2
1
1
2
1
1
1
1
1
1
1
0
1
2
1
1
0
1
0
1
1
1
1
1
2
0
1
0
1
2
2
0
1
2
1
1
0
1
2
1
2
1
1
0
1
0
1
1
1
1
1
1
2
0
2
2
2
1
1
1
2
0
1
1
2
2
1
0
1
1
0
1
1
2
2
1
1
0
1
1
0
4
2
2
1
2
2
1
1
2
1
1
1
1
1
1
2
1
3
0
1
1
0
0
1
2
1
1
0
1
2
0
2
1
0
1
1
1
0
2
1
1
1
0
1
1
1
0
1
1
2
1
1
1
0
1
2
1
1
2
1
1
0
2
1
1
2
1
2
1
0
1
1
1
0
1
1
1
1
1
3
1
0
2
2
1
1
1
1
0
1
1
1
1
2
2
0
0
2
2
2
0
1
2
1
0
0
2
0
2
2
1
1
1
1
2
1
0
1
1
0
2
0
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
0
1
1
1
0
0
1
2
2
1
1
1
1
1
0
0
1
0
1
0
1
1
0
0
1
1
2
1
2
1
1
2
1
1
1
1
1
0
1
1
1
1
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
0
1
2
2
2
1
2
1
2
1
1
1
0
1
1
2
1
0
0
1
0
2
0
2
0
1
2
0
0
1
0
0
2
1
1
1
3
1
0
1
1
2
2
0
0
1
1
1
1
1
0
1
2
1
2
1
3
1
1
1
1
1
1
1
0
1
0
1
1
0
1
2
2
1
1
0
0
2
0
1
1
1
1
0
1
1
0
1
1
1
2
1
1
1
1
1
3
1
1
4
1
1
2
1
1
1
1
2
2
1
1
0
0
1
0
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
2
0
2
0
1
1
1
1
1
1
2
1
1
1
0
1
1
2
1
2
1
1
2
2
0
2
1
0
1
1
1
0
1
1
0
1
1
1
1
1
1
3
1
1
2
0
1
1
1
0
1
2
2
1
1
1
1
1
1
2
1
1
1
2
2
1
1
2
1
2
1
1
1
1
1
1
1
2
2
1
1
1
1
2
2
2
2
1
2
1
3
3
1
1
1
2
0
2
0
1
3
2
0
2
1
1
1
0
1
1
1
1
2
1
1
1
0
0
1
1
2
1
1
0
0
1
1
0
2
1
1
0
1
0
2
1
0
1
2
2
2
1
1
1
1
2
1
1
0
1
1
1
0
1
1
1
2
2
2
1
1
0
1
0
1
1
2
2
1
1
0
0
2
0
2
1
1
0
0
1
0
1
1
1
1
1
0
0
2
0
0
1
1
1
1
1
1
2
2
1
2
2
2
1
2
2
1
2
1
0
0
0
2
0
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
0
0
1
2
1
1
1
1
1
2
0
1
2
2
2
2
1
1
1
2
1
2
1
2
1
2
2
0
1
1
2
2
1
1
2
1
1
1
2
1
1
2
1
1
1
1
1
2
1
1
0
1
1
1
1
1
0
2
2
1
1
1
1
1
0
1
1
1
1
0
1
1
0
0
1
1
1
2
1
1
1
1
2
1
0
2
1
2
1
1
0
2
1
2
1
1
1
1
0
1
2
1
1
1
0
1
1
1
2
1
1
1
1
0
0
0
0
1
2
0
2
0
1
0
1
1
1
2
1
2
1
1
1
2
1
2
0
1
1
2
2
2
0
1
1
2
1
1
2
1
3
2
1
1
2
1
1
2
2
1
1
0
2
1
2
1
1
1
1
1
1
1
1
2
3
1
1
1
1
0
2
2
1
1
1
1
1
0
2
1
1
1
0
0
0
1
2
1
2
1
1
1
0
1
1
1
2
1
1
1
1
3
2
1
2
1
2
1
1
1
1
1
0
2
1
1
1
1
0
1
1
2
0
2
1
1
1
0
1
1
1
2
1
1
1
1
1
0
2
1
1
1
2
1
2
1
2
1
2
2
2
1
1
1
0
2
1
0
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
2
0
1
1
1
1
1
0
1
1
2
1
1
2
0
2
1
2
0
2
1
1
1
0
1
1
1
1
1
3
1
1
1
2
1
1
1
0
1
1
1
0
1
1
0
1
4
1
1
1
0
5
1
1
1
3
2
1
2
2
1
0
0
1
1
2
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
2
1
0
0
0
1
1
2
1
1
1
1
0
2
1
0
1
1
2
1
2
0
1
1
1
0
0
2
1
2
1
1
1
0
1
2
2
2
2
1
4
1
1
1
1
1
2
2
1
2
1
1
2
2
2
1
2
1
1
2
1
1
2
0
0
0
1
1
0
1
1
1
1
0
2
0
2
1
2
2
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
2
3
1
2
1
1
0
1
1
2
1
2
1
1
1
1
0
2
1
1
0
0
1
1
0
1
2
1
2
1
1
2
1
2
1
1
2
0
0
1
1
1
1
5
1
1
1
1
1
1
0
1
1
1
2
1
1
2
2
0
1
0
1
1
2
1
1
2
1
0
1
2
0
1
2
1
2
0
2
1
2
1
1
2
1
0
2
0
1
2
1
1
0
1
2
0
1
1
1
1
0
1
1
1
1
1
0
1
3
1
1
1
0
1
1
2
1
0
1
0
1
0
1
1
0
2
1
1
1
1
1
1
1
0
1
1
1
2
1
0
1
1
1
1
2
2
0
2
1
1
1
3
1
1
1
1
2
1
0
1
0
1
1
0
1
2
1
1
1
2
1
2
1
1
0
0
1
0
1
0
2
1
1
0
1
2
1
1
2
1
1
1
1
1
1
0
0
1
1
0
2
1
1
1
0
1
2
1
1
0
1
1
1
0
2
2
2
2
1
1
0
2
1
1
2
1
1
2
3
3
3
1
0
1
0
1
2
1
0
1
2
0
1
2
1
1
1
0
1
0
1
1
2
1
2
2
2
1
1
1
1
1
2
1
1
2
2
1
0
0
0
1
1
1
0
1
2
0
2
2
0
2
1
2
0
0
1
2
0
1
1
1
2
0
2
0
1
0
2
1
0
0
2
2
1
0
2
1
0
1
1
2
1
0
0
1
1
1
1
1
1
3
1
1
1
1
1
2
1
1
1
0
1
1
1
2
1
2
2
0
1
2
1
1
0
2
1
1
1
1
0
2
3
2
0
1
1
2
2
1
0
2
0
1
1
1
1
1
2
1
2
1
1
0
2
2
0
2
3
1
2
6
1
1
2
1
1
1
2
1
1
1
0
2
1
1
1
1
1
0
2
2
2
2
2
0
2
3
1
1
2
0
0
1
2
1
1
2
1
1
1
1
0
1
2
0
1
1
1
1
1
1
2
0
2
1
2
2
1
1
0
1
0
1
1
1
0
0
1
1
1
1
1
1
1
0
2
0
1
1
0
1
2
0
2
1
1
0
0
1
2
1
1
1
2
0
1
1
0
0
1
1
2
1
0
2
1
1
0
1
2
1
1
1
2
1
1
1
0
1
1
2
1
1
2
2
1
1
0
0
1
1
0
1
2
2
1
0
2
1
0
1
1
0
1
1
1
0
1
0
2
1
1
1
2
1
1
1
2
1
2
2
1
1
1
1
0
1
0
2
0
1
2
1
1
1
0
1
2
1
1
1
1
1
0
0
1
2
1
1
2
1
2
2
1
1
1
2
2
1
1
1
1
1
0
1
1
1
1
1
1
1
0
1
2
1
1
0
1
0
1
1
0
0
2
1
2
1
1
2
1
1
1
1
1
1
0
1
2
1
1
1
0
2
2
2
1
2
2
0
0
2
1
1
2
1
1
2
2
1
1
2
1
2
2
1
0
1
1
2
1
1
1
0
1
2
1
1
1
1
1
2
2
1
1
0
1
1
1
1
1
1
2
1
1
2
2
1
2
1
1
1
2
0
0
0
1
1
1
2
2
1
2
1
1
2
1
1
1
1
1
2
1
1
0
2
1
0
1
2
1
1
1
2
1
1
2
1
1
0
0
1
1
1
1
1
0
1
1
2
2
1
1
1
1
0
0
1
2
2
1
2
1
0
2
2
1
1
2
0
1
1
0
1
2
1
2
1
1
1
2
1
0
1
1
1
2
1
2
2
1
1
2
0
0
0
2
1
2
1
0
1
2
1
1
1
1
1
1
1
0
1
2
2
0
0
1
1
2
2
1
2
1
1
0
1
1
1
1
2
1
2
1
2
1
2
1
0
2
2
1
1
0
0
0
0
1
1
1
1
0
1
1
2
0
2
1
1
2
1
2
1
1
2
1
1
2
1
1
0
0
1
0
2
1
2
0
1
2
2
1
1
1
2
1
1
1
2
1
1
1
1
0
1
1
1
1
1
1
1
2
1
1
0
2
1
2
1
0
2
1
1
1
2
2
2
0
1
1
1
1
1
1
2
1
1
2
1
1
1
2
0
1
2
1
1
1
2
0
0
2
1
1
2
2
1
1
1
2
1
2
1
2
1
0
2
2
1
0
0
1
1
1
0
1
1
2
1
0
2
1
2
1
1
1
0
1
1
1
1
0
2
1
1
1
2
1
1
1
1
2
2
1
1
1
1
1
2
2
1
0
2
0
1
2
0
1
1
1
2
2
1
1
1
1
1
2
1
1
1
2
1
2
1
0
2
1
1
1
1
1
1
1
1
0
1
1
1
2
1
1
1
1
0
1
1
2
1
3
1
1
1
1
2
1
1
2
2
1
1
0
1
1
0
1
1
0
1
1
1
2
1
2
1
2
1
1
1
1
1
2
1
1
2
2
0
1
1
1
2
1
1
2
2
1
3
2
1
1
1
1
2
2
2
1
0
0
1
1
0
1
1
0
0
0
2
1
1
2
1
1
1
2
1
2
1
1
2
1
1
2
2
1
1
1
0
1
1
1
1
1
1
2
1
1
1
1
0
0
0
1
1
0
0
1
2
2
1
2
1
1
1
2
1
1
0
1
1
1
1
1
1
1
1
1
1
1
2
2
1
0
2
1
1
2
1
1
1
1
1
1
0
2
1
1
2
1
1
1
1
2
1
1
1
0
1
1
2
2
2
0
1
0
1
1
2
2
1
1
4
1
2
1
1
2
0
1
2
1
2
1
1
2
1
0
1
0
3
0
1
0
2
1
2
2
1
1
2
1
1
2
0
2
1
1
1
1
3
0
1
0
1
1
1
1
2
1
1
1
1
1
2
0
2
1
0
1
2
1
1
2
1
0
1
1
1
2
1
1
1
1
1
1
1
0
2
2
2
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
0
0
2
0
0
2
1
1
2
1
2
1
2
2
2
1
1
0
2
1
2
2
1
0
2
1
2
0
1
1
1
1
1
1
1
2
1
1
2
2
2
1
1
1
2
1
2
1
0
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
2
0
1
2
1
1
1
0
2
1
1
1
1
2
1
1
2
1
1
0
0
0
1
2
1
2
1
2
0
1
1
2
1
1
1
2
0
1
0
1
0
2
1
1
2
1
0
2
1
1
1
0
1
2
1
2
1
2
1
1
1
0
1
1
1
0
1
1
1
2
0
1
2
1
0
2
1
1
1
2
0
0
1
0
0
0
2
1
0
1
1
1
1
1
1
2
1
1
2
2
1
2
0
1
2
2
1
1
1
1
0
1
1
1
1
0
2
1
2
2
1
1
1
1
0
0
1
2
1
1
1
1
1
4
1
0
1
2
1
0
1
2
1
0
0
1
1
1
1
0
2
1
1
2
1
0
0
0
1
0
2
1
1
2
1
0
1
0
1
2
1
1
2
0
1
1
0
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
0
0
0
0
1
1
1
1
1
1
2
2
0
1
1
1
3
1
0
2
1
0
1
1
1
1
0
1
1
1
2
1
2
2
1
1
1
1
1
1
2
0
2
2
1
1
2
2
2
2
1
1
1
1
2
1
2
1
1
1
2
1
0
1
0
1
1
1
1
1
2
1
1
1
1
2
2
1
1
2
1
1
1
1
2
1
2
2
2
1
1
1
1
1
1
0
2
1
1
1
1
1
1
0
1
1
2
1
1
2
2
2
1
1
2
1
1
2
1
1
1
1
2
0
1
1
1
0
2
0
1
1
2
2
1
1
2
1
1
0
1
1
0
0
0
2
2
2
2
2
0
0
1
1
0
1
1
1
1
1
0
1
0
2
0
1
2
1
1
1
0
2
1
1
0
1
2
0
1
2
1
0
0
0
1
1
1
1
0
1
1
1
1
0
1
0
1
2
1
1
1
0
2
1
0
1
1
1
2
2
1
0
1
1
0
1
1
1
1
2
1
1
1
2
0
1
1
1
2
0
1
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
1
2
2
0
1
1
1
1
1
1
0
1
0
1
1
0
1
2
2
0
1
1
0
0
1
1
1
1
1
0
1
1
1
1
0
0
1
2
1
1
2
2
2
2
2
0
0
1
0
1
1
2
1
0
2
1
2
1
1
1
1
1
2
1
1
1
0
2
0
0
1
1
2
1
1
1
2
1
1
1
1
1
1
0
1
1
1
1
0
1
1
1
2
1
0
1
1
1
0
1
2
1
1
2
1
1
0
1
1
2
1
1
1
1
0
2
1
0
1
1
1
1
1
0
1
1
1
1
1
1
1
2
1
0
0
2
1
1
1
1
0
0
1
1
1
0
1
1
0
1
1
0
0
1
2
2
0
1
1
0
2
2
0
1
1
0
0
0
1
2
1
2
1
1
1
2
0
0
0
1
1
2
1
1
0
0
1
2
0
1
1
1
1
1
0
1
2
1
1
1
2
0
2
1
3
0
2
0
1
0
0
1
0
1
1
1
1
1
0
1
1
1
1
1
2
1
1
1
1
1
1
1
0
0
2
0
2
0
1
1
0
2
1
1
1
2
1
1
1
1
0
2
2
1
1
1
1
1
1
1
1
1
2
1
0
1
0
1
1
1
1
1
1
0
1
1
2
1
2
2
1
0
1
1
2
2
1
1
1
0
2
0
2
1
0
1
0
0
1
2
0
0
2
2
1
1
1
1
1
1
2
2
2
1
1
0
1
1
1
0
1
1
1
1
2
1
1
0
0
1
1
2
1
1
1
1
2
0
2
1
1
1
1
0
1
1
1
2
1
1
2
2
1
0
1
2
1
1
1
1
1
0
1
0
2
1
1
1
0
1
1
1
1
1
1
1
1
2
1
2
1
2
2
1
0
2
1
2
2
1
0
1
2
1
0
0
0
1
2
2
1
2
1
1
1
1
0
0
1
1
0
1
0
0
1
1
1
1
3
1
0
2
1
3
2
1
1
1
2
1
1
1
0
2
2
2
1
1
2
1
2
2
1
1
1
2
0
1
0
0
1
1
1
1
1
2
1
1
1
2
2
1
1
1
2
1
1
1
0
2
1
2
1
2
2
1
0
0
1
2
1
2
1
2
1
1
1
1
0
0
2
1
1
2
2
1
1
1
1
1
2
0
1
1
1
2
1
1
1
1
1
1
1
1
2
0
0
1
1
1
1
1
1
1
2
1
2
0
1
1
1
1
1
2
0
0
1
1
1
1
0
1
1
2
1
1
1
2
0
2
2
1
1
2
2
1
1
0
1
0
2
1
0
2
1
2
1
1
1
1
0
1
0
1
3
1
2
1
2
2
2
1
0
0
1
2
1
1
1
2
0
2
3
2
2
2
1
2
1
0
2
1
1
1
2
2
1
2
2
1
0
1
1
1
1
0
1
0
1
1
0
0
1
1
1
1
1
1
1
2
2
2
2
1
2
1
1
1
0
1
1
2
1
2
1
2
1
1
1
1
0
2
2
2
1
1
1
2
0
1
0
1
0
1
0
2
1
0
1
1
1
1
1
0
2
1
1
2
0
1
1
0
1
1
0
1
1
0
0
1
1
1
1
1
1
2
0
1
1
1
1
2
1
1
1
1
2
1
1
1
1
0
1
1
0
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
0
2
2
1
1
1
1
1
2
0
3
1
1
0
1
2
1
1
1
0
1
1
0
2
0
1
0
2
1
1
0
1
1
2
1
2
1
1
1
2
1
1
1
1
1
2
2
1
0
1
0
1
1
2
0
2
1
1
1
1
0
2
1
0
1
1
2
1
1
1
1
0
2
1
0
2
1
1
1
1
1
1
2
2
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
0
1
2
0
1
1
1
1
1
1
0
2
1
0
1
1
1
1
1
0
1
1
0
1
0
1
1
1
1
0
1
0
0
3
1
0
1
0
2
3
1
2
1
1
1
2
1
0
1
1
1
1
1
1
1
2
2
0
0
1
1
1
1
0
2
0
1
1
1
1
1
1
1
1
0
2
1
1
1
0
0
2
1
0
2
1
0
2
1
0
1
1
0
2
3
2
1
2
3
1
1
2
0
2
0
2
1
2
1
0
0
1
1
0
2
1
1
0
1
0
0
1
2
1
1
2
0
1
1
1
2
2
1
2
0
0
0
1
1
1
2
1
1
0
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
0
1
1
0
1
1
0
0
0
2
1
0
1
0
2
1
1
2
1
2
0
1
2
1
1
1
2
1
1
0
2
1
1
1
1
2
2
0
0
1
1
1
1
2
0
1
2
1
2
1
0
1
1
1
2
1
1
1
0
1
1
1
2
2
2
0
1
1
1
1
1
1
0
1
1
2
2
2
0
1
2
1
1
1
2
0
1
2
2
0
1
2
1
1
1
1
0
1
1
3
1
1
0
1
1
0
1
1
1
2
1
2
1
1
0
1
1
0
0
1
1
1
1
1
1
1
1
1
2
0
2
0
0
2
1
2
1
1
1
1
0
1
1
1
2
1
1
3
2
1
1
2
0
1
1
0
1
2
1
1
1
1
0
2
1
1
0
1
1
0
1
1
0
1
1
0
1
2
1
1
1
1
1
1
2
0
1
1
1
0
1
1
1
2
2
2
1
1
1
1
0
1
1
0
0
1
2
1
1
1
1
0
0
1
2
1
2
1
1
1
2
2
1
1
1
1
2
1
2
0
1
1
1
1
2
1
2
2
1
1
1
0
1
0
2
2
1
1
2
1
1
1
0
2
1
1
1
1
0
1
0
1
0
2
1
2
1
1
1
2
1
2
1
2
1
1
0
1
2
1
0
0
1
4
2
1
1
1
2
1
1
0
1
1
1
1
2
1
1
1
1
1
1
1
1
0
0
1
1
1
1
0
2
1
1
2
2
1
1
1
1
1
1
1
1
1
1
0
1
0
2
0
1
0
1
2
1
1
1
1
1
1
1
1
2
0
1
1
1
2
2
0
1
1
0
1
1
1
2
1
1
2
0
1
0
0
1
1
1
1
1
1
2
1
1
1
2
2
1
1
1
2
1
1
1
2
0
1
1
1
1
2
1
2
1
0
2
1
1
0
1
0
0
1
1
0
2
1
1
0
2
2
1
1
2
1
2
0
1
0
1
2
1
1
0
1
1
2
1
2
1
2
1
0
1
1
1
1
0
0
1
1
2
1
1
0
1
1
1
1
2
1
2
1
2
2
1
2
1
2
2
1
1
1
1
0
2
0
2
1
1
1
2
1
2
0
1
0
0
1
1
2
2
2
2
2
1
2
2
2
2
1
1
1
1
0
2
0
0
1
2
1
1
1
1
2
1
1
0
1
1
0
0
1
1
0
1
1
1
2
1
1
1
0
0
1
1
1
0
0
1
2
2
0
0
1
2
1
0
2
1
0
2
1
2
2
1
1
1
2
3
0
1
1
1
1
1
1
1
2
0
2
2
2
2
1
1
1
1
0
1
1
1
1
0
1
2
1
2
0
0
2
0
2
2
1
2
0
1
1
2
1
2
2
1
2
2
1
2
1
1
2
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
0
1
1
2
2
1
2
0
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
0
0
1
1
1
1
1
1
1
1
1
1
1
0
1
1
2
1
1
1
1
0
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
2
0
1
1
1
1
1
1
2
2
1
0
2
0
2
2
2
1
1
0
1
1
2
1
2
2
2
2
2
2
1
2
1
1
0
1
1
0
1
1
1
1
1
2
0
1
2
1
2
1
0
1
1
1
0
1
0
2
1
0
2
1
2
1
1
1
1
0
1
1
1
0
1
1
2
1
1
1
1
1
1
3
1
1
1
2
2
1
1
0
1
1
2
1
0
1
1
0
2
1
1
1
0
1
2
1
1
1
2
1
0
1
1
1
0
1
0
2
2
1
2
1
2
2
1
2
0
1
1
1
1
1
0
1
0
1
0
2
1
1
1
0
0
0
1
1
0
1
3
1
0
1
0
1
1
2
1
1
3
1
2
4
1
1
0
2
2
0
2
2
1
1
0
2
1
1
1
2
2
2
0
1
1
1
2
3
1
1
0
1
2
1
1
2
0
1
1
2
1
1
1
1
2
2
1
2
1
1
1
0
2
0
1
0
2
0
1
1
1
2
2
0
1
1
1
1
1
1
1
1
0
1
1
1
1
2
1
1
1
0
2
1
1
0
0
1
1
1
2
1
0
2
1
1
0
1
0
2
1
2
0
1
1
2
2
0
1
1
2
2
1
1
0
1
1
1
1
1
2
2
1
0
0
1
1
2
1
0
2
1
0
1
0
1
1
2
1
1
0
2
1
0
0
1
0
1
1
0
1
1
0
0
1
1
1
2
1
1
1
1
2
2
2
1
1
1
1
0
1
1
1
2
1
0
1
1
1
1
1
1
0
0
2
1
0
1
1
0
2
1
0
1
1
2
1
2
1
1
1
2
1
1
2
1
2
2
0
1
0
1
0
1
1
1
1
0
1
1
2
2
0
1
1
1
1
0
1
1
1
0
1
1
1
1
0
1
2
2
2
0
1
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
2
2
3
1
1
0
2
2
0
1
1
0
1
2
2
1
1
1
2
0
2
1
1
1
1
2
0
2
1
1
2
2
0
0
3
1
1
3
2
1
1
1
1
1
2
1
1
1
0
1
0
1
1
1
2
1
1
1
1
1
0
1
1
2
1
1
0
1
1
0
1
2
2
2
1
1
1
1
1
0
2
1
0
1
1
2
1
1
1
1
1
1
2
2
2
1
1
1
2
1
2
1
2
1
1
2
0
0
2
1
1
1
1
0
1
1
2
2
2
1
0
1
0
2
0
2
2
0
1
0
1
0
2
2
0
2
1
1
1
1
1
1
0
2
2
0
0
2
1
1
1
1
1
2
0
1
2
0
1
1
2
2
0
1
1
2
1
1
2
2
1
1
2
2
1
2
1
1
1
1
1
2
1
1
0
1
2
1
0
1
2
1
2
2
1
1
2
1
1
2
0
0
2
0
2
2
1
1
1
1
1
0
0
1
2
1
0
0
1
2
0
2
1
1
1
1
1
1
0
0
0
1
1
0
1
2
1
1
2
2
1
1
0
0
2
1
1
1
1
0
1
1
2
1
10
2
1
2
2
2
0
2
1
1
1
2
1
0
1
1
0
1
2
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
2
1
2
0
0
1
1
1
3
1
2
1
0
2
2
2
1
1
1
2
2
1
1
2
1
1
1
1
0
1
2
1
1
1
0
1
1
2
2
0
0
0
1
1
1
2
1
2
1
0
1
2
1
1
2
1
0
2
1
1
1
1
1
0
1
1
2
1
1
0
1
1
2
1
0
1
3
1
1
1
1
1
2
2
1
2
2
0
1
1
2
2
2
1
0
1
1
1
1
1
1
1
1
2
1
1
0
0
1
2
1
2
1
2
1
1
1
1
1
1
2
2
0
2
2
2
1
0
1
1
1
0
1
1
1
1
2
2
1
2
1
1
1
2
1
0
0
0
2
0
0
1
2
2
1
1
0
1
0
0
1
1
1
1
1
0
1
1
1
1
1
1
1
1
2
1
1
1
1
2
0
1
2
0
1
2
1
1
1
0
1
0
1
2
2
1
2
1
1
1
2
2
1
2
1
1
2
1
1
2
2
2
1
1
1
0
1
1
1
0
0
1
1
1
1
2
1
1
1
0
0
1
1
1
2
0
2
1
1
1
1
1
1
0
2
0
2
0
1
1
0
1
1
1
2
1
2
1
1
1
0
0
1
1
1
1
1
1
1
1
2
1
1
0
0
2
1
0
1
1
0
2
1
1
1
1
1
1
0
1
1
1
2
1
1
2
1
2
1
2
1
1
1
1
2
2
2
1
1
1
2
1
1
1
1
1
1
1
1
0
1
1
1
2
1
2
1
1
0
1
1
1
1
1
1
1
2
1
1
1
2
1
0
1
2
0
1
2
1
2
1
1
1
2
2
1
0
2
0
2
1
1
2
1
0
1
1
0
1
1
0
2
2
1
1
0
2
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
1
1
1
0
2
1
2
0
1
0
2
1
1
1
2
1
0
1
1
1
2
1
1
1
1
0
0
1
2
1
1
1
1
0
1
1
1
1
2
2
1
2
2
1
2
1
1
0
1
0
1
0
1
2
2
2
1
1
0
1
1
1
1
1
0
2
1
2
2
1
1
0
1
2
0
1
1
1
0
1
1
1
1
1
1
0
1
1
2
2
0
1
2
1
2
2
0
1
0
2
1
0
1
2
1
2
2
1
1
1
1
2
1
0
1
1
1
1
0
1
1
0
1
0
2
1
1
1
2
1
1
2
1
0
1
0
1
1
0
1
1
2
2
1
1
1
2
1
1
2
2
2
1
1
0
1
1
0
1
2
1
0
1
0
1
1
1
2
2
2
1
1
2
1
1
1
1
1
1
0
1
1
0
0
1
2
1
2
2
2
1
1
1
1
1
0
0
0
1
2
2
1
1
0
2
1
1
2
0
2
0
1
2
1
0
1
2
0
2
1
1
2
1
1
0
1
1
1
1
0
2
2
1
1
0
2
2
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
0
1
1
1
0
1
1
2
1
1
1
0
2
0
1
2
2
1
1
1
1
1
1
2
1
0
1
1
2
1
1
0
0
1
1
1
1
0
1
2
2
1
0
0
0
1
1
1
1
1
0
1
2
1
0
2
1
0
1
0
0
1
2
1
1
0
1
2
0
1
1
1
1
1
1
1
2
1
1
2
0
2
1
2
2
2
1
3
2
1
1
1
1
0
1
1
1
2
1
1
1
2
2
1
1
0
1
1
1
2
1
0
0
1
0
2
0
1
2
1
0
1
1
1
2
0
1
2
1
1
1
0
2
1
1
0
1
1
1
2
0
0
2
2
0
1
1
1
1
1
1
1
1
1
1
1
2
0
1
1
2
1
2
2
2
1
0
2
1
0
1
1
1
2
1
2
2
1
1
1
1
1
1
1
2
1
1
1
2
0
1
1
1
0
2
2
1
2
1
0
2
1
3
1
1
2
2
2
2
1
1
1
1
2
1
0
0
1
1
1
2
1
2
0
2
1
0
1
0
0
1
2
1
1
2
0
1
0
1
1
2
1
2
0
1
2
2
1
1
1
0
1
1
1
2
1
0
1
2
0
1
1
1
1
1
2
1
0
2
1
1
2
1
1
1
0
1
1
2
0
2
2
1
1
0
0
1
2
2
1
1
1
2
0
1
1
0
1
0
1
2
1
1
1
1
2
0
2
2
1
1
1
2
0
2
1
1
0
0
2
1
1
1
0
2
1
1
2
0
0
0
0
1
2
1
1
1
2
1
1
0
1
2
2
0
0
1
1
0
1
1
2
1
0
1
1
1
1
2
1
1
0
2
1
1
1
1
1
1
0
1
2
1
1
0
1
1
1
1
2
2
0
1
1
0
1
4
2
1
0
0
1
2
1
1
0
1
1
2
1
0
1
1
1
2
0
1
1
1
1
2
1
1
0
1
1
3
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
0
2
2
0
0
1
1
1
1
1
1
1
0
1
1
1
1
1
1
2
2
2
2
0
2
1
2
1
2
1
3
1
1
2
1
1
1
1
1
2
2
1
2
1
2
1
1
1
0
1
1
2
1
1
1
2
2
0
2
1
2
1
1
1
1
1
1
0
0
0
1
1
2
1
2
1
1
1
2
1
1
2
2
2
1
1
1
2
1
1
1
0
1
1
1
1
2
2
2
1
0
2
1
1
2
1
1
0
1
0
1
2
1
0
0
1
0
1
0
0
2
1
1
1
1
1
2
1
1
2
0
2
1
1
1
1
0
0
0
1
1
2
1
2
1
1
1
0
1
1
1
1
1
2
1
2
0
2
2
1
1
2
0
1
2
0
2
1
1
0
0
1
0
2
1
2
1
1
1
1
1
2
0
0
1
1
1
1
1
2
1
1
1
1
2
2
1
0
0
1
1
1
1
1
1
1
1
2
0
1
1
1
1
1
1
0
0
1
1
1
2
2
1
1
1
1
1
0
2
1
1
1
1
0
2
0
1
2
2
1
1
1
2
2
0
2
1
1
0
1
2
1
1
1
1
1
2
1
0
2
1
1
2
1
2
1
1
2
4
2
0
1
1
1
2
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
0
1
1
1
1
1
2
0
0
0
1
1
1
0
1
1
1
1
2
2
1
0
0
1
1
2
1
2
1
1
1
1
0
2
1
1
1
1
1
1
2
0
1
1
1
2
0
2
1
2
0
1
0
1
2
1
1
1
1
1
1
1
2
1
1
2
2
1
1
1
1
2
1
1
2
2
1
1
1
0
1
2
1
2
1
1
2
1
1
2
1
1
1
1
2
1
1
2
1
1
2
1
2
1
1
1
1
0
0
1
0
1
1
1
1
1
2
0
1
2
1
3
2
1
1
0
1
2
1
1
1
1
0
0
1
1
1
0
1
1
1
2
1
1
0
0
0
1
2
1
1
1
1
2
2
0
2
0
1
1
1
2
1
0
2
2
1
1
1
1
1
1
1
1
1
1
2
2
1
2
1
1
2
0
1
1
1
1
1
0
1
1
0
0
2
0
1
1
1
0
1
0
1
2
1
1
2
2
1
0
1
1
3
3
1
0
2
0
0
2
1
2
2
1
1
1
1
1
0
1
1
2
2
0
1
1
1
1
1
2
1
2
1
1
1
1
0
2
1
1
1
1
1
0
1
1
1
1
1
0
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
0
0
2
1
0
1
2
1
0
2
1
1
1
1
1
1
2
1
1
1
1
1
1
0
1
0
0
1
1
1
1
2
2
1
1
1
1
0
1
1
0
1
1
2
1
1
0
1
1
1
2
1
1
1
2
1
1
1
0
0
1
2
1
5
5
1
1
1
2
1
1
0
1
2
1
1
1
4
1
1
1
1
0
0
2
0
2
1
0
1
1
1
3
2
1
0
2
0
0
0
1
1
1
0
2
0
2
1
1
2
1
1
0
1
1
1
1
1
0
1
1
2
2
0
2
0
1
1
1
2
1
0
0
2
1
2
1
2
0
1
1
1
2
1
0
1
1
0
0
1
1
0
3
2
1
2
0
0
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
0
0
2
1
1
1
1
1
1
1
2
0
1
1
1
0
1
1
1
1
1
1
1
2
2
0
0
1
0
0
1
1
0
1
1
1
2
1
1
0
1
1
1
0
1
2
0
1
1
1
0
1
2
1
2
2
1
2
3
1
0
1
2
0
1
1
1
1
1
0
2
1
1
1
1
1
2
0
1
2
1
1
1
1
2
1
0
1
2
1
0
1
0
1
1
1
1
1
1
1
1
1
2
2
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
2
0
1
1
2
1
1
2
0
1
0
1
2
0
0
1
1
0
1
1
2
1
1
2
2
0
2
2
2
0
0
1
1
1
1
2
0
0
1
1
0
1
2
1
1
1
1
2
2
2
1
1
1
2
2
1
0
2
1
1
1
1
1
1
1
1
2
1
1
1
0
1
1
1
1
1
2
1
1
1
2
0
0
0
1
2
1
0
1
1
1
2
2
0
3
0
1
2
0
1
2
0
1
1
1
2
1
1
0
1
1
1
1
0
1
1
1
0
0
2
2
0
1
1
0
0
2
1
1
1
2
1
1
2
1
2
1
0
1
2
1
1
1
1
1
1
1
0
2
1
1
1
1
1
2
1
2
1
2
1
0
1
1
2
1
2
2
1
1
1
1
2
2
0
2
2
1
1
1
2
1
0
0
1
1
1
2
1
1
2
0
2
1
1
1
0
1
1
0
1
1
1
2
2
2
0
2
1
1
1
0
2
1
0
2
1
1
2
1
1
2
1
2
1
1
1
0
2
1
2
3
1
1
2
2
1
1
1
1
1
1
1
2
1
0
0
1
1
0
1
1
0
1
1
1
0
1
2
1
1
0
1
1
1
1
1
1
2
1
0
1
1
1
1
0
1
1
0
1
1
1
0
1
1
1
1
1
1
1
1
1
1
2
1
0
1
2
1
0
1
0
1
1
1
1
0
1
2
1
1
1
1
1
1
0
1
0
1
1
2
1
1
1
1
0
1
2
2
1
1
2
1
1
1
2
2
0
0
1
0
0
1
1
0
2
1
2
1
1
1
0
1
3
1
1
1
1
0
1
1
1
1
1
1
0
1
1
1
1
0
0
0
1
1
1
1
2
2
1
1
1
1
1
1
2
1
1
2
1
0
1
1
2
1
1
1
1
2
2
2
1
1
0
1
1
1
1
1
1
3
2
2
1
2
1
1
1
1
2
1
1
0
1
0
1
1
0
2
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
0
1
2
1
1
1
0
1
1
2
0
1
1
1
1
1
2
1
1
1
1
1
2
1
2
1
2
2
1
1
1
2
1
1
2
2
1
2
0
2
2
1
1
1
0
1
1
2
1
1
1
1
1
2
1
2
1
2
2
2
1
2
1
1
1
1
1
2
2
1
1
1
2
2
1
1
1
0
1
0
1
1
1
0
1
2
2
2
1
1
1
1
1
2
1
1
1
1
1
2
2
1
1
1
0
0
2
1
1
0
1
1
1
1
2
0
1
0
2
1
1
1
0
1
1
0
2
2
1
2
2
1
2
1
1
1
1
1
1
1
1
2
0
1
1
1
2
1
1
1
1
0
1
1
1
0
2
2
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
0
0
2
1
2
0
1
1
2
2
1
1
1
2
0
1
1
0
2
2
2
1
1
2
1
1
1
2
2
1
1
0
1
2
0
1
1
1
1
1
1
2
1
1
1
0
1
1
1
2
1
2
1
1
2
1
1
1
1
2
1
2
1
2
2
1
0
2
1
1
1
1
0
1
2
2
1
1
2
0
1
1
2
1
0
1
0
2
0
1
1
2
1
1
1
1
1
1
0
1
2
1
1
2
2
2
1
0
0
1
2
1
1
0
2
3
1
1
0
2
0
0
2
1
1
2
1
1
1
0
1
1
1
1
1
1
1
0
1
1
1
1
2
1
0
1
1
0
1
1
1
1
0
2
2
2
1
2
2
0
1
2
1
1
0
1
1
1
1
1
1
2
2
0
1
2
1
1
0
1
1
2
1
1
1
0
0
1
2
1
1
2
1
1
0
0
1
2
0
1
1
1
1
1
1
2
1
1
0
0
1
1
2
2
1
1
2
1
1
1
1
1
1
2
1
1
2
0
1
1
2
1
1
0
2
1
0
0
1
2
4
1
0
1
1
0
1
1
0
1
1
1
1
1
1
2
1
1
1
1
0
0
2
0
1
2
1
1
1
1
2
1
2
0
1
0
1
0
2
1
1
0
0
1
2
1
1
1
1
1
0
2
0
2
2
0
1
0
1
2
1
1
1
0
0
1
1
0
0
1
1
1
0
2
1
1
1
2
1
1
2
1
1
1
0
1
0
1
1
0
0
1
2
1
2
2
1
0
1
1
1
1
1
2
0
1
1
1
1
1
2
1
0
2
1
1
1
1
1
2
1
0
2
1
0
1
1
1
2
1
1
0
1
2
1
2
0
1
0
1
0
1
1
1
0
2
1
1
1
0
0
2
1
2
1
1
2
0
1
0
1
1
1
1
1
2
1
1
1
1
0
0
1
0
1
1
0
1
0
1
1
1
1
1
0
1
2
1
1
1
1
1
0
0
1
1
1
1
2
1
1
1
1
1
1
3
1
0
1
1
1
1
0
2
0
2
1
1
0
2
2
2
1
1
1
2
1
2
2
1
0
2
1
1
1
2
2
1
1
1
2
2
2
1
2
1
0
0
2
2
1
0
1
1
0
2
1
1
2
1
2
1
1
1
0
1
1
1
1
2
2
1
1
1
0
1
1
2
0
1
1
2
1
1
3
1
1
0
1
0
1
0
1
2
1
1
1
2
0
1
1
0
0
0
1
1
1
0
1
1
1
2
1
2
2
1
2
1
1
2
0
1
2
1
1
0
2
1
1
1
0
2
1
0
1
1
1
2
1
0
1
1
1
2
1
1
1
1
0
0
1
1
2
1
2
1
1
1
0
0
0
0
1
1
1
0
1
0
1
1
2
1
1
1
0
1
2
0
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
0
0
0
1
2
1
1
2
1
1
1
1
1
0
0
1
1
1
2
1
2
2
1
2
1
0
0
1
1
2
0
1
0
2
1
1
2
0
2
0
2
1
1
1
1
1
1
2
0
0
1
2
0
1
2
1
2
1
1
1
1
1
0
1
2
1
1
1
2
1
1
2
1
1
1
1
1
1
1
2
1
1
1
0
1
1
1
1
1
1
2
1
1
0
1
2
1
2
1
1
1
0
1
2
0
2
1
0
1
2
1
2
2
0
1
2
1
1
2
1
1
2
1
2
1
2
1
1
0
1
1
1
1
2
1
0
1
1
1
0
1
1
2
1
1
1
0
1
1
2
0
2
1
1
1
1
0
1
2
1
1
1
1
1
0
1
1
0
0
0
2
1
0
2
0
1
1
0
1
1
1
1
0
1
2
1
0
2
1
0
2
1
1
1
2
1
1
1
1
0
2
1
1
0
1
1
1
1
2
1
2
1
1
2
1
1
2
0
3
1
0
1
0
0
3
1
1
2
1
0
1
1
0
1
2
0
1
2
2
1
0
1
1
2
0
1
1
1
1
1
1
1
2
1
1
1
1
2
1
0
2
1
0
1
0
2
1
0
1
1
1
1
0
2
2
1
1
0
2
1
1
1
1
4
1
0
0
1
3
1
1
1
2
0
2
1
2
0
2
1
1
2
1
1
1
0
1
1
0
1
0
2
1
1
1
2
1
1
2
2
1
2
1
2
1
1
2
1
3
2
2
0
1
1
1
1
1
2
0
0
2
1
1
2
1
1
1
0
1
0
0
1
1
2
1
0
1
2
2
1
1
1
2
0
0
0
0
1
1
1
2
1
0
1
1
1
1
1
1
1
1
1
0
0
1
2
1
2
1
1
1
0
1
2
0
1
2
1
1
1
1
2
1
0
1
1
1
2
1
2
1
1
1
2
2
1
2
0
1
0
2
1
1
2
1
1
1
1
0
2
1
0
2
1
2
0
2
0
2
1
1
1
0
1
1
1
1
1
0
1
2
1
2
0
0
1
2
1
2
1
1
1
2
1
1
1
1
2
0
1
2
1
1
1
0
1
0
1
4
1
1
1
0
3
2
1
1
1
1
1
1
1
1
2
1
1
2
0
1
0
2
1
1
1
1
1
1
1
1
2
0
1
2
2
1
0
1
1
1
1
0
2
0
2
2
2
1
1
2
1
1
1
1
1
2
2
1
2
1
0
1
2
2
1
1
2
2
0
2
1
1
1
1
0
1
0
0
1
1
1
2
1
3
1
1
1
1
1
1
2
1
1
1
1
1
1
0
1
2
0
1
0
3
1
1
2
1
2
1
1
2
2
1
1
1
1
1
2
1
2
1
1
0
0
1
2
2
0
1
1
2
0
0
2
1
0
1
1
2
1
1
2
1
2
1
2
0
1
1
1
0
1
2
1
1
2
1
1
1
0
1
1
0
1
1
1
3
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
0
1
1
1
2
1
2
1
1
1
1
0
1
1
0
0
2
0
0
2
1
1
0
2
1
1
1
0
2
0
1
1
2
2
1
0
1
2
0
1
1
1
1
2
1
2
1
0
2
1
1
1
1
1
1
1
0
1
2
1
1
1
1
2
1
3
1
1
1
1
2
1
2
2
1
1
0
2
1
2
1
2
1
1
1
0
1
1
1
2
2
1
1
2
0
0
0
1
1
1
2
1
1
0
1
2
1
1
1
2
2
1
1
2
1
2
0
1
1
0
1
1
2
1
2
1
0
1
2
1
2
2
1
1
1
1
1
1
2
0
1
2
1
2
1
0
1
0
2
2
0
1
1
1
1
1
1
2
1
0
1
2
1
2
1
2
1
1
2
1
2
1
1
1
1
0
1
1
1
1
2
0
1
2
0
1
1
3
2
1
2
0
0
1
2
0
1
2
1
3
1
2
1
1
1
2
2
2
1
1
1
0
1
1
0
0
2
1
2
1
2
0
1
1
1
2
1
1
2
1
2
2
1
1
1
1
1
1
1
1
1
2
2
1
1
0
1
2
1
1
1
2
0
2
2
1
1
1
1
0
2
2
1
1
2
1
1
1
1
1
0
1
1
1
0
0
1
1
0
2
0
0
1
2
0
3
1
1
1
1
1
1
1
2
2
2
1
1
1
0
2
1
1
1
0
1
1
2
0
1
2
0
1
1
1
1
1
2
2
2
1
1
1
0
1
1
1
1
0
2
2
1
1
1
1
0
1
0
0
2
1
1
1
0
2
1
0
1
1
4
2
1
1
1
1
1
2
1
2
2
2
1
1
0
1
0
2
0
2
2
1
0
1
2
0
1
1
1
1
0
2
1
1
1
1
1
1
1
2
0
1
2
2
1
1
1
1
1
1
1
1
1
2
1
2
0
1
0
2
1
1
1
2
0
1
1
1
2
1
1
2
1
1
0
2
0
1
1
2
1
1
1
1
0
1
1
1
1
1
2
0
1
1
0
1
0
0
1
1
1
1
1
0
1
1
0
0
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
5
1
1
1
1
1
1
1
2
1
1
1
1
2
2
1
0
1
2
1
1
1
1
2
0
1
2
1
1
1
2
1
1
1
0
1
0
1
2
1
1
2
0
1
0
2
1
0
0
0
2
2
1
1
1
1
0
1
1
2
1
1
0
1
1
1
0
1
1
0
1
1
0
0
1
2
1
2
2
0
0
1
1
1
0
2
1
1
1
1
1
1
1
1
2
1
2
2
1
1
2
1
1
1
0
1
1
1
1
2
1
0
2
2
1
1
1
2
1
1
1
0
1
3
1
1
1
2
2
0
1
1
0
1
2
1
2
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
2
1
2
1
1
0
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
0
1
0
2
0
2
1
0
2
1
1
1
1
1
1
1
3
1
2
0
1
1
1
2
1
1
1
1
2
1
1
2
1
2
1
2
1
1
2
1
1
1
1
2
1
1
1
2
2
2
1
0
0
2
1
1
2
2
1
2
2
1
1
0
1
2
1
1
1
1
1
1
0
0
1
1
0
1
2
1
1
1
1
0
2
1
1
2
1
2
1
2
2
1
1
0
1
1
1
1
1
1
0
1
1
2
2
2
1
2
1
1
1
1
0
1
2
1
2
1
2
0
0
2
2
2
2
1
1
1
2
1
2
1
2
1
2
0
1
2
2
1
1
1
1
0
1
1
1
0
3
1
1
1
1
1
1
3
1
2
2
1
1
2
2
1
1
1
0
1
2
1
1
1
1
2
1
1
0
1
0
1
1
1
2
2
2
1
2
1
0
1
2
1
1
2
2
1
1
0
1
1
2
1
0
1
0
2
1
0
0
1
1
1
1
0
1
6
1
1
3
2
1
0
1
0
1
2
1
0
1
0
1
2
0
2
2
1
1
0
1
2
1
1
1
1
0
0
2
0
1
1
1
1
2
1
1
2
1
2
2
2
0
1
0
0
1
2
1
2
1
1
1
0
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
2
0
1
1
1
1
1
1
1
2
2
1
1
1
1
0
0
0
0
1
0
2
1
1
1
1
1
1
2
1
0
1
2
0
2
1
1
2
2
1
1
1
0
0
1
1
1
0
1
2
1
2
1
1
1
1
1
2
0
1
2
1
1
0
2
2
1
1
2
1
2
1
1
0
1
1
1
1
1
2
1
0
1
1
2
0
1
1
1
1
1
1
1
2
1
2
1
1
0
1
1
1
1
1
1
1
1
2
1
2
2
1
2
1
2
0
2
1
1
0
1
2
2
1
1
2
1
1
0
1
1
1
2
1
2
1
2
0
1
1
1
1
1
0
2
1
1
1
2
1
1
2
1
0
0
2
1
1
2
1
1
1
1
0
1
2
2
0
3
2
1
0
0
1
1
1
1
1
1
2
2
1
2
1
1
2
1
1
1
1
2
1
0
0
1
2
1
3
1
0
1
2
0
2
1
2
1
0
1
1
1
0
2
2
1
1
0
2
0
2
0
1
1
2
1
0
2
1
0
1
1
1
1
2
2
2
1
1
1
1
1
1
2
2
1
0
0
1
2
1
2
1
0
1
1
1
1
1
0
1
2
0
1
1
2
1
0
0
1
1
0
0
1
2
1
0
1
1
1
1
1
0
1
1
1
2
1
0
0
1
2
0
1
1
1
1
2
2
2
2
0
2
1
2
1
1
1
1
1
1
1
2
2
1
1
1
1
2
0
1
1
1
0
1
1
1
0
1
1
1
0
1
1
1
1
1
1
1
2
0
2
0
1
1
1
2
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
2
1
0
0
1
2
1
1
3
1
1
2
1
1
1
0
2
2
1
0
2
1
1
1
2
0
1
2
0
2
0
0
1
0
0
2
2
1
1
1
0
2
0
1
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
2
2
0
2
0
0
0
1
0
0
1
1
0
1
1
2
0
1
3
2
1
1
1
1
0
2
1
1
1
1
1
0
1
1
2
1
2
1
1
1
1
1
3
1
1
1
2
1
0
2
1
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
3
1
0
1
1
1
2
1
3
0
1
2
0
0
1
0
2
2
1
1
1
1
1
1
2
2
2
1
1
2
1
1
1
2
2
1
1
1
1
1
0
0
0
3
1
1
1
2
1
2
2
1
1
2
1
1
1
1
1
1
2
1
1
1
3
2
1
1
2
0
1
2
1
2
1
1
0
2
1
1
2
2
1
2
1
2
1
1
2
0
0
0
2
1
2
0
1
0
1
1
2
1
2
1
1
0
1
1
0
0
1
1
2
0
1
1
0
2
0
0
2
1
1
0
1
1
2
2
1
1
1
2
0
1
1
2
2
2
1
0
2
1
1
1
0
2
2
0
2
1
1
1
1
1
0
1
1
0
1
1
0
1
1
1
1
1
1
1
1
1
1
0
0
1
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
2
2
1
1
2
1
2
1
1
1
1
1
0
0
1
1
1
1
2
2
0
0
2
0
1
1
1
1
1
1
0
1
2
1
1
2
1
2
0
1
1
0
0
2
0
0
2
1
1
0
1
0
1
1
1
1
1
0
1
0
1
2
0
1
1
1
1
2
1
1
1
2
1
2
1
3
2
1
1
0
2
1
0
2
1
2
0
1
1
4
1
1
2
2
1
2
0
0
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
2
1
1
2
2
0
0
1
0
0
0
1
1
2
0
1
1
1
0
1
1
1
0
0
1
2
1
1
1
2
1
1
1
1
1
2
1
0
1
1
1
1
1
2
2
0
2
0
1
0
1
1
2
2
2
2
0
1
2
1
1
1
0
1
1
1
0
0
1
1
1
1
1
2
0
1
2
1
2
2
0
0
1
1
0
1
1
1
1
1
2
1
2
1
1
1
1
2
0
0
1
0
1
1
1
1
1
1
1
0
1
1
1
1
2
2
1
1
1
2
1
0
0
1
2
1
1
1
1
1
2
1
1
1
1
1
2
0
0
1
2
2
2
1
1
2
0
1
1
2
2
2
2
1
0
1
1
1
2
1
1
1
3
1
0
1
1
1
0
1
2
1
0
2
1
1
1
1
2
0
0
2
1
1
1
0
2
0
0
1
1
3
1
1
2
1
1
2
2
0
1
1
1
2
1
0
1
0
0
1
0
1
1
1
1
1
1
1
1
1
1
2
1
0
2
1
2
1
1
1
1
2
1
1
1
1
0
1
1
1
1
1
1
0
1
1
1
1
1
0
2
1
2
1
2
0
1
2
2
2
1
2
1
1
1
2
1
1
0
1
1
2
2
1
1
1
2
0
1
0
1
1
0
2
1
1
1
1
1
2
1
1
1
2
0
0
1
2
0
0
1
2
2
1
1
2
0
2
1
1
1
1
0
2
1
2
2
1
0
2
1
2
2
1
1
0
0
2
2
1
2
1
1
0
1
1
2
1
1
1
1
1
2
2
2
1
1
0
1
1
0
0
1
0
1
1
2
1
1
1
2
1
1
1
1
2
2
1
0
0
0
2
1
2
1
2
1
1
1
2
0
1
1
1
1
1
1
2
1
1
0
1
1
1
2
1
1
1
1
1
1
0
0
1
1
1
1
1
1
1
0
1
1
1
1
0
3
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
2
1
1
1
2
1
1
0
1
0
1
1
1
2
1
1
1
1
2
0
1
0
1
0
2
0
0
0
2
1
2
1
1
0
1
1
0
0
1
1
2
1
1
2
1
1
0
1
1
1
1
1
1
1
0
1
2
2
1
0
1
0
1
2
1
1
2
1
1
1
1
0
1
1
1
2
1
1
1
1
1
1
1
0
2
2
1
1
1
1
2
1
2
1
0
2
1
2
1
1
2
1
2
1
3
0
0
2
1
1
1
1
2
1
2
1
1
1
0
1
1
1
3
1
0
1
1
1
1
1
1
1
1
1
0
1
2
1
0
1
1
1
1
1
1
1
1
1
0
2
0
1
1
1
2
2
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
2
0
1
1
3
2
1
0
2
1
1
1
1
2
1
1
0
1
1
2
1
1
2
1
0
1
1
1
2
1
1
1
0
1
1
1
1
1
1
2
1
0
1
1
1
1
3
1
0
1
0
1
1
2
0
1
2
1
1
2
1
2
1
1
1
1
2
1
0
0
2
2
1
1
1
1
1
1
1
1
2
0
1
0
2
1
1
1
0
0
0
1
0
1
1
1
2
1
1
5
1
0
1
0
1
1
2
2
1
1
1
0
1
2
2
1
1
2
1
2
0
1
2
1
1
1
1
0
0
1
0
0
0
1
0
1
0
2
1
2
1
0
0
1
1
1
1
1
1
0
0
1
1
1
0
1
1
1
1
2
1
1
1
0
2
0
0
1
1
2
2
1
1
1
1
1
1
1
0
2
0
1
1
1
2
1
1
1
2
1
0
1
0
1
1
1
0
1
2
2
2
2
1
2
0
1
1
2
1
1
1
2
0
1
0
1
1
1
0
1
2
1
1
1
0
0
1
0
2
2
2
0
1
1
1
1
2
2
3
1
0
1
2
1
2
1
1
2
1
2
1
2
1
2
1
1
2
1
2
2
1
1
1
2
1
1
2
1
1
1
1
2
1
0
2
2
1
0
2
1
0
2
7
3
2
1
0
1
1
2
2
2
0
1
1
1
0
0
1
1
1
1
1
0
1
0
2
0
1
1
1
1
2
1
2
0
2
2
1
3
2
1
0
2
1
1
2
0
1
2
0
2
1
2
0
1
0
1
0
2
1
1
2
1
0
1
0
1
1
1
2
2
2
1
1
0
1
1
2
2
1
1
1
2
3
2
1
1
2
1
1
0
1
1
1
1
0
1
2
2
2
0
2
1
2
0
1
1
1
2
0
1
0
1
2
1
1
1
1
1
1
0
1
1
2
1
1
2
1
2
1
2
2
1
2
1
0
1
0
1
2
1
1
1
1
1
3
0
1
0
2
1
1
0
1
2
1
2
2
1
1
0
1
1
1
2
1
2
1
1
1
2
1
0
0
2
0
0
1
1
0
2
2
1
1
0
2
2
1
2
0
1
0
0
1
2
2
1
1
0
3
1
0
1
0
1
0
1
2
1
2
1
1
1
2
0
1
0
2
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
0
1
0
2
0
2
1
1
1
1
0
1
1
2
2
1
1
0
2
1
1
1
0
1
2
1
1
2
0
1
0
0
2
2
1
1
1
2
0
1
1
1
2
1
1
2
1
1
1
0
0
1
1
1
1
2
1
3
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
2
4
0
1
0
2
1
1
1
0
1
1
1
0
1
1
1
1
0
2
1
2
0
0
1
1
2
1
1
1
1
0
1
1
1
2
0
1
2
1
1
1
2
1
1
1
1
1
1
2
0
0
1
0
1
1
1
1
2
0
1
1
1
0
2
0
1
1
1
0
0
2
1
1
1
2
2
1
1
1
1
1
2
0
1
1
1
0
1
1
0
2
2
1
1
1
0
1
1
1
1
1
1
1
1
0
2
2
1
1
1
0
1
1
1
2
2
2
2
1
1
1
1
2
1
2
1
2
1
0
0
1
1
1
1
0
1
2
1
2
1
1
2
1
2
0
1
1
0
1
1
1
2
2
2
2
2
1
1
3
0
1
2
1
1
1
1
1
1
2
2
0
2
1
1
1
0
1
1
1
2
1
0
2
1
2
2
1
1
0
1
1
1
2
2
2
2
0
1
1
1
2
1
0
2
1
1
1
1
1
1
1
1
0
2
1
1
1
1
1
2
1
2
0
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
0
1
0
1
1
1
1
3
1
2
1
1
2
2
1
1
0
1
0
1
2
1
1
1
1
2
1
1
2
1
3
1
0
2
2
2
1
1
1
1
1
1
1
0
2
1
1
1
0
1
0
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
2
0
1
4
2
1
0
1
1
2
1
0
2
1
3
1
1
1
1
2
1
1
1
2
1
1
2
1
2
1
1
2
1
0
1
1
1
0
0
0
1
0
2
1
3
1
2
1
0
1
1
2
2
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
0
0
0
0
1
1
1
1
0
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
2
1
3
1
1
2
0
2
1
2
1
2
1
1
0
2
1
2
1
1
1
2
1
1
1
1
1
1
1
0
2
0
0
1
1
2
1
1
0
0
1
2
0
1
1
1
1
1
1
1
1
2
2
0
1
1
1
2
0
1
2
1
1
1
1
1
0
1
0
2
2
2
1
2
2
2
0
1
2
1
2
2
0
1
1
2
1
0
1
1
0
1
1
0
1
1
0
1
1
0
0
1
1
1
1
1
0
0
1
2
1
1
1
1
1
1
1
2
1
2
1
2
2
1
2
2
1
1
1
1
1
2
1
2
1
0
0
2
1
0
1
1
1
2
1
0
1
2
1
1
1
2
0
2
1
3
1
2
1
2
1
1
0
2
1
0
2
1
1
1
3
1
1
1
1
0
2
1
2
2
1
2
0
1
1
1
1
0
2
1
1
2
1
1
0
2
1
1
1
1
2
1
1
1
1
1
0
1
1
2
1
2
0
1
2
1
1
1
0
2
0
1
1
2
1
0
1
1
1
2
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
0
1
2
2
2
1
2
2
0
1
1
1
1
1
1
1
1
1
0
1
1
1
2
2
1
2
1
1
1
0
2
1
1
1
1
0
1
2
1
1
1
0
1
0
2
1
1
2
1
1
1
0
2
3
2
0
1
0
1
0
1
1
1
1
1
4
1
2
0
1
2
1
0
0
0
1
0
1
1
1
1
1
1
0
1
1
1
0
1
1
1
1
1
2
1
1
1
1
2
0
2
1
1
1
1
1
0
2
1
1
2
1
0
1
0
1
2
1
1
1
1
2
1
2
1
1
0
1
2
2
1
1
1
1
2
1
0
1
1
1
2
1
1
1
1
1
0
0
1
0
3
1
1
1
1
1
2
1
0
0
1
1
1
2
2
1
0
0
1
2
0
1
1
1
0
2
1
1
1
0
2
1
2
1
1
1
1
1
1
1
1
1
1
0
1
1
1
2
1
1
1
1
1
2
1
2
0
0
1
1
0
1
1
2
2
1
1
1
2
1
0
1
2
2
1
2
2
1
0
2
2
1
0
1
1
1
2
1
2
2
1
2
0
1
1
2
1
1
1
1
2
2
1
1
0
1
1
0
2
1
0
1
2
0
0
2
0
1
2
2
1
2
1
1
2
2
2
2
2
2
1
1
0
0
1
1
1
0
1
1
1
0
1
1
1
1
1
2
2
1
1
1
0
1
1
1
1
2
1
1
1
2
1
1
1
0
2
1
1
1
2
1
2
1
1
0
2
1
1
1
2
1
1
0
0
2
1
2
1
1
1
1
1
2
1
1
0
1
0
1
0
1
1
0
2
1
1
1
0
0
0
1
0
1
1
1
2
1
3
1
1
0
0
0
2
1
2
2
1
0
1
1
1
0
2
1
1
1
0
1
1
0
1
2
2
1
2
0
1
2
2
2
2
1
1
1
0
2
1
1
1
0
1
2
1
1
0
1
2
1
2
1
1
1
1
2
1
2
2
2
2
1
1
1
2
1
3
1
1
1
2
0
1
1
1
0
1
1
1
0
1
1
2
1
2
1
1
2
2
2
2
1
1
2
3
2
2
2
1
1
1
2
1
1
2
1
1
1
2
1
1
0
1
1
1
1
1
1
2
1
1
1
1
1
0
1
1
1
1
1
0
0
2
1
2
2
1
1
0
1
1
0
2
1
0
2
0
1
2
1
1
0
2
1
2
1
1
1
2
1
1
2
1
2
2
1
3
1
2
2
2
1
1
2
1
1
2
1
1
1
1
2
1
1
2
0
0
2
1
1
1
1
2
1
0
1
0
1
1
1
1
2
1
1
1
1
0
0
1
0
1
1
1
0
1
2
0
1
2
1
1
1
1
1
1
1
0
1
0
1
1
2
1
1
1
1
4
1
0
0
2
1
1
1
2
1
1
1
3
1
1
1
0
1
2
1
1
1
2
0
1
3
1
2
1
1
2
1
1
1
2
0
1
0
1
2
1
1
1
1
1
2
1
1
1
2
0
1
1
1
1
1
1
2
1
2
1
1
1
0
2
0
1
2
2
1
0
2
2
1
1
2
1
2
1
1
1
1
1
2
2
1
1
1
0
1
0
0
0
0
1
1
1
1
0
1
1
1
1
1
1
1
1
1
2
0
1
1
0
1
2
1
1
0
1
1
2
1
2
1
1
2
0
1
2
1
2
1
1
1
1
1
1
1
1
2
1
1
0
2
2
4
0
1
1
0
1
0
1
1
1
0
0
1
2
1
1
1
1
1
1
0
2
1
2
1
1
2
1
0
3
1
0
1
2
2
1
2
1
0
1
1
0
0
1
2
1
2
1
2
0
1
1
1
1
2
0
1
2
1
1
1
2
0
2
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
2
1
1
2
2
2
1
1
0
1
1
2
1
1
1
1
1
2
2
2
2
1
2
1
1
0
2
2
1
2
1
0
2
1
1
1
2
0
1
2
0
1
1
1
1
1
0
1
1
1
1
1
1
0
1
1
1
1
1
2
1
1
1
2
1
1
2
1
1
1
1
1
0
1
1
1
1
1
1
2
1
0
1
1
2
1
0
1
1
1
0
1
2
1
1
1
1
2
0
1
1
1
1
1
2
1
2
2
2
2
1
2
2
1
2
1
0
2
1
1
1
1
0
1
1
1
0
0
1
1
2
2
2
0
1
1
0
1
2
2
1
1
1
1
1
0
1
1
1
2
2
2
1
1
2
2
1
1
1
1
1
2
2
1
2
1
1
1
1
0
1
0
0
1
0
3
2
0
1
1
0
0
1
1
1
1
1
1
0
0
0
1
0
2
1
1
2
0
1
1
1
1
1
1
1
0
1
1
0
1
1
2
0
2
1
1
1
2
2
1
1
1
1
1
2
1
1
1
2
1
2
2
0
2
0
0
3
1
0
0
1
1
2
2
3
2
1
1
1
1
1
1
0
2
0
2
0
1
1
1
1
2
0
1
1
1
1
1
2
0
1
1
1
0
1
2
1
2
0
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
3
2
1
1
1
0
2
1
1
1
0
0
1
1
1
1
1
0
2
1
1
1
1
1
2
2
1
1
0
1
1
4
1
1
2
2
2
2
2
1
1
1
1
1
1
1
1
1
2
0
1
1
0
0
2
0
1
0
0
1
1
0
1
1
1
0
1
1
2
1
1
0
1
1
2
1
2
1
1
2
1
2
1
2
0
1
3
1
1
2
2
1
1
1
1
2
2
0
1
1
1
1
2
1
1
1
1
1
1
1
2
0
1
1
2
1
1
2
1
1
1
1
0
2
1
0
1
1
1
1
1
0
2
1
1
1
1
2
1
1
2
2
2
1
1
2
1
1
1
2
2
0
1
2
1
2
1
2
1
2
1
1
2
1
1
1
0
3
0
1
1
1
1
1
2
1
1
0
1
1
0
2
1
0
1
1
1
2
0
2
1
1
2
1
1
1
1
1
1
1
0
0
2
1
1
1
0
2
0
1
1
2
0
1
1
2
1
2
1
0
2
2
2
1
0
2
2
0
1
1
1
1
1
2
1
1
1
2
1
1
0
1
2
2
1
1
1
2
1
2
1
0
2
1
1
1
1
2
2
1
2
1
0
1
0
0
1
2
0
1
1
0
0
1
1
1
1
2
1
0
2
0
1
1
1
2
1
2
1
1
2
2
1
0
1
2
1
2
2
1
1
1
1
1
2
2
1
0
0
1
1
1
1
1
1
2
1
1
2
2
1
1
0
1
2
1
1
1
0
2
1
2
1
0
1
1
1
1
1
1
1
1
0
1
1
2
5
1
1
1
2
1
1
1
1
1
2
1
0
1
1
1
2
1
1
1
1
2
1
2
1
1
1
2
2
1
1
1
2
1
2
4
1
1
2
2
2
1
1
1
1
1
0
2
1
2
2
1
2
2
1
2
0
1
0
1
1
1
1
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
0
1
1
0
1
1
0
1
1
1
1
1
2
1
1
0
1
1
0
2
1
1
1
1
2
2
1
2
3
2
1
2
2
0
2
2
2
1
1
2
1
0
1
1
1
0
1
2
1
0
1
1
0
1
1
0
0
1
2
0
1
1
0
1
1
0
2
1
1
1
1
1
2
1
1
2
2
1
1
1
1
2
1
1
2
2
1
1
1
1
0
0
1
1
0
1
1
1
1
2
0
1
1
1
1
0
0
1
1
1
0
2
1
1
2
2
2
1
1
1
0
2
1
1
2
1
2
1
0
1
2
0
1
2
1
0
1
2
1
1
3
1
1
2
1
2
1
2
0
0
1
1
2
1
0
2
1
1
0
1
1
2
1
3
2
2
1
1
1
2
1
2
0
2
1
1
1
1
1
1
0
1
1
1
1
0
2
1
0
1
0
0
1
1
2
2
1
0
1
0
0
1
0
2
1
2
1
0
1
0
1
0
1
1
2
2
1
0
1
2
0
1
0
1
1
0
1
0
1
1
0
0
0
2
0
1
0
0
1
2
2
2
2
3
1
2
1
0
0
1
1
1
2
2
1
1
1
1
1
1
2
1
0
0
2
2
1
1
0
1
0
0
1
0
1
1
2
1
0
1
2
1
0
1
1
1
1
1
1
0
1
1
0
1
0
2
1
0
1
1
2
1
1
0
1
2
2
1
0
0
2
1
1
1
0
2
1
1
1
1
2
1
2
1
2
2
1
1
0
1
0
2
1
0
2
1
0
1
0
0
0
0
1
1
2
0
0
1
1
2
1
0
1
2
0
2
0
1
2
2
1
2
1
0
1
1
1
2
1
1
1
1
1
0
1
0
0
2
0
1
0
0
1
2
0
1
3
1
2
1
1
1
2
1
1
1
1
1
1
0
1
0
1
2
1
1
0
1
2
1
2
2
2
2
2
2
0
0
1
0
1
1
2
2
1
1
0
1
1
1
2
1
2
1
1
1
1
0
2
1
1
1
1
2
1
1
1
1
0
1
0
2
0
1
1
1
1
1
1
1
1
2
0
2
1
2
1
1
2
1
1
1
1
1
1
1
0
0
1
0
1
1
1
1
1
1
0
1
0
1
1
1
1
1
1
1
1
1
0
1
1
1
1
2
2
1
0
0
2
1
2
0
2
2
1
1
1
0
0
0
1
1
1
1
1
1
2
1
2
1
0
2
2
2
1
2
0
2
1
1
1
1
1
0
1
1
2
2
1
1
1
1
0
1
2
1
1
1
1
0
1
1
1
1
2
2
1
1
1
1
0
0
0
0
1
2
1
1
2
6
1
1
2
1
1
2
1
2
2
1
1
1
1
2
2
1
1
2
2
1
0
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
2
1
1
3
2
1
2
2
1
2
2
1
1
1
1
1
1
0
1
1
0
1
2
1
0
0
1
1
1
0
1
1
1
1
1
1
2
0
0
0
1
1
2
1
1
0
1
1
1
1
1
1
1
1
2
1
1
1
0
1
2
1
0
1
1
2
1
1
1
1
1
1
2
1
0
1
0
0
1
2
1
0
1
1
0
2
0
1
1
2
1
1
1
1
4
2
1
2
2
1
2
1
1
0
1
1
1
0
0
2
0
1
2
0
0
1
1
1
1
1
1
2
1
1
1
1
1
1
0
0
1
1
1
1
1
0
2
2
0
1
2
2
0
5
0
0
1
0
1
1
1
1
1
1
1
1
1
2
1
0
1
1
0
1
1
0
1
2
1
2
1
1
1
0
1
1
2
0
2
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
0
1
1
1
2
1
1
0
2
2
1
2
1
2
2
2
0
0
0
1
1
1
1
1
1
0
1
1
1
1
1
1
1
0
0
1
2
1
1
1
0
0
1
2
2
0
2
2
1
0
2
2
2
2
1
1
1
2
0
1
1
2
1
1
1
1
0
1
1
2
1
1
1
0
1
1
2
1
2
1
0
0
1
1
1
1
1
2
1
1
1
2
1
1
1
2
2
2
0
1
2
1
1
0
1
2
2
1
2
1
0
0
1
1
1
2
1
1
1
0
1
1
1
1
1
1
1
2
0
1
2
1
0
1
2
1
1
1
0
2
2
1
0
2
1
2
1
1
2
2
1
2
1
2
1
1
1
2
0
1
1
0
0
1
1
0
0
0
2
1
1
1
0
2
0
1
0
1
1
0
2
1
1
1
0
2
1
2
1
2
1
1
2
1
2
1
1
2
1
1
2
1
0
2
1
1
1
2
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
0
2
2
1
0
1
0
2
2
1
0
1
1
1
0
0
1
0
1
1
1
1
2
1
1
2
1
1
1
1
0
0
2
2
1
1
1
0
2
0
1
1
1
0
1
1
1
1
1
2
1
1
1
1
2
0
2
1
1
1
2
1
2
1
1
2
1
2
0
1
1
1
1
2
1
2
1
1
0
0
1
0
0
1
1
2
1
2
2
1
1
1
1
2
1
1
1
2
2
1
1
2
1
0
1
1
2
0
1
1
0
0
1
1
1
1
1
1
2
1
1
1
0
1
2
1
0
2
2
1
1
1
1
1
1
0
1
1
2
1
2
0
1
1
2
1
0
1
2
2
1
2
1
1
2
2
1
0
0
1
2
1
0
1
1
0
0
1
2
1
0
0
1
1
1
2
2
1
1
1
2
2
1
1
1
1
1
2
1
1
2
1
4
1
1
0
1
1
0
2
1
1
1
1
1
0
2
1
2
0
2
1
0
0
1
1
0
1
2
2
1
1
1
1
2
2
1
1
1
2
0
0
0
1
2
0
2
0
1
1
1
1
1
1
1
1
0
1
2
1
1
2
1
0
1
0
0
1
0
1
2
2
1
1
1
2
1
1
1
1
1
1
0
1
1
1
0
2
1
1
1
1
1
0
1
2
1
1
1
1
1
1
1
1
1
1
1
0
2
1
1
1
1
0
2
1
1
1
1
1
1
1
1
1
1
0
1
1
2
2
1
1
1
2
2
0
1
1
1
2
1
2
1
1
2
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
2
1
1
2
1
2
1
1
0
1
2
2
1
2
2
0
0
1
2
1
2
1
1
2
0
2
1
1
1
2
1
1
1
0
2
0
2
1
1
1
1
1
1
1
2
0
1
2
1
2
0
2
1
2
0
2
1
0
1
1
1
3
1
0
1
1
1
0
1
1
1
1
0
2
1
2
1
2
0
2
1
1
1
1
0
1
2
1
1
1
0
1
1
2
1
1
0
2
1
0
1
0
1
1
0
0
1
1
1
1
1
1
1
1
0
1
0
1
1
1
1
1
0
1
1
3
2
1
2
1
1
2
2
1
4
1
1
1
0
1
1
2
1
2
1
1
1
1
2
1
1
0
1
1
8
0
1
1
0
1
0
1
0
2
1
4
2
2
1
0
1
1
1
1
1
1
0
1
2
1
0
1
0
1
1
1
1
0
1
1
1
3
1
1
1
2
2
1
1
1
1
1
1
0
1
2
2
2
1
2
1
2
2
0
2
0
2
1
1
1
1
1
0
0
2
2
1
0
1
1
0
1
1
1
0
1
1
1
2
2
0
2
1
1
2
3
2
0
1
2
1
1
2
0
1
1
1
1
1
1
2
2
1
2
1
1
1
0
1
2
2
0
2
0
1
1
1
1
1
2
1
1
0
1
0
1
0
1
2
1
1
1
1
2
2
1
1
1
1
1
2
1
2
1
0
1
1
1
0
1
0
0
2
0
1
2
1
1
0
1
1
1
0
0
1
2
1
1
1
1
2
1
1
1
1
1
1
0
0
1
0
0
0
1
1
0
1
1
1
1
0
0
2
1
1
2
0
1
2
0
1
1
1
0
1
1
1
1
1
1
2
2
0
2
0
2
1
1
1
2
1
1
2
1
0
1
1
1
0
1
1
1
2
1
1
1
1
1
1
0
0
2
1
1
1
2
1
2
1
1
1
1
0
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
0
0
2
1
0
1
1
1
2
0
1
0
1
1
1
1
1
0
0
2
2
1
1
0
2
1
1
2
1
0
2
2
2
0
0
2
1
1
0
2
0
2
1
1
0
1
1
1
0
2
1
1
1
1
1
0
2
1
1
0
1
1
2
2
1
2
2
1
0
1
1
1
1
0
1
1
1
2
1
1
2
1
1
0
2
2
1
1
0
0
1
2
1
2
1
1
1
1
1
1
1
2
2
0
2
2
2
2
2
1
3
2
2
1
2
1
0
0
2
1
1
2
0
1
1
1
1
1
2
2
2
1
1
1
1
2
1
2
1
1
1
1
1
0
1
1
1
2
2
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
2
0
0
1
1
1
1
2
1
1
2
1
0
2
0
2
1
1
1
2
1
1
5
2
1
1
1
1
2
1
1
2
2
1
0
1
1
2
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
0
2
0
1
0
1
1
1
1
1
0
1
2
2
1
1
0
2
2
1
0
0
0
1
2
1
0
0
1
1
1
1
1
0
2
2
1
1
1
1
2
1
2
1
1
2
1
1
1
1
2
0
0
0
2
0
1
1
0
1
2
3
1
1
2
1
1
2
2
0
0
1
1
1
2
1
2
0
0
1
0
2
1
1
2
0
1
1
2
1
0
2
0
2
0
1
2
1
2
1
2
1
2
0
1
1
1
2
1
2
0
2
0
1
0
2
2
1
1
1
1
1
1
2
1
1
1
0
1
2
2
1
1
2
1
1
0
1
1
0
1
1
1
1
1
2
2
1
3
0
1
1
1
1
1
1
1
2
0
3
2
1
1
2
2
1
0
1
0
2
1
0
1
1
1
1
2
2
2
1
1
1
1
1
2
2
1
1
1
1
2
1
1
0
1
1
1
1
1
2
1
1
1
1
0
1
1
1
0
1
1
1
0
1
0
1
1
1
1
1
1
2
0
1
1
0
1
0
1
1
1
2
1
2
2
1
1
1
1
1
1
3
2
2
1
1
1
2
2
0
3
0
1
1
1
1
0
1
1
0
1
1
1
1
2
0
1
1
1
1
0
1
1
1
1
1
2
1
1
1
0
2
1
1
0
1
1
2
1
1
1
1
2
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
0
1
1
1
1
1
1
2
1
0
2
2
1
1
1
1
1
1
0
0
2
1
0
2
1
1
0
2
0
0
0
1
1
1
0
2
1
2
2
1
1
2
1
0
1
2
2
2
1
1
1
1
2
1
2
1
1
1
1
2
0
1
1
1
2
2
0
1
1
1
1
2
1
0
1
2
1
2
1
0
2
2
1
2
1
2
1
0
0
0
0
1
2
1
1
1
1
1
1
0
2
2
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
2
1
0
1
1
1
1
1
1
1
2
1
1
1
0
1
0
2
1
0
2
0
1
1
1
1
1
0
1
1
2
1
2
1
1
1
0
1
2
1
2
1
2
1
5
0
1
1
2
2
1
2
1
1
1
1
1
2
1
0
2
1
1
2
1
1
0
1
0
2
1
1
1
1
2
1
1
1
1
1
1
0
2
1
1
1
2
1
1
1
0
1
1
0
1
2
1
1
1
0
2
1
2
2
0
0
1
1
1
1
1
0
2
1
0
1
0
2
1
1
1
1
2
1
1
1
0
1
2
0
2
2
0
1
0
0
0
1
1
1
2
2
1
2
2
2
1
1
0
1
2
0
0
1
2
1
1
2
2
1
2
0
0
2
1
1
1
2
1
1
1
1
0
1
0
2
1
1
1
1
1
1
1
2
0
2
0
1
2
1
1
0
2
1
1
2
0
2
0
1
2
1
0
2
1
2
2
1
2
1
1
2
1
1
1
1
0
0
1
0
0
2
0
0
1
1
3
1
1
1
2
1
3
1
1
0
1
1
0
2
0
0
1
1
0
1
1
1
1
3
2
1
2
0
0
0
1
1
2
2
1
2
2
0
2
2
2
1
1
2
1
2
0
1
0
1
2
0
0
1
0
1
1
2
1
0
1
1
0
0
1
1
1
1
1
0
0
2
1
1
1
1
2
2
2
1
1
1
1
0
1
2
1
2
1
1
0
1
1
1
2
1
0
1
2
0
0
1
1
1
1
1
2
1
1
1
2
1
2
2
1
2
1
2
1
1
2
1
1
2
0
2
1
0
1
2
1
1
1
1
1
1
2
2
2
1
2
1
1
0
0
1
1
1
1
0
1
1
1
1
2
1
1
0
1
1
2
2
0
2
2
2
0
1
0
1
0
1
0
1
1
2
0
1
0
1
1
1
0
2
0
2
1
1
1
0
0
2
1
2
2
2
1
0
2
1
1
2
2
1
1
2
1
1
0
0
1
1
1
2
2
1
1
1
1
1
2
1
0
1
1
0
2
2
0
0
1
2
1
2
1
0
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
2
1
2
1
1
0
0
1
1
1
1
1
0
1
1
0
2
1
2
1
1
1
1
2
2
0
0
2
1
1
2
1
2
1
1
0
2
0
0
2
1
1
1
1
2
2
1
1
1
3
2
1
2
0
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
1
1
2
1
0
1
1
1
0
1
0
1
1
1
2
1
1
2
1
1
1
2
0
1
1
1
2
1
1
0
2
0
1
0
1
2
1
2
2
2
1
2
2
1
0
2
1
1
1
2
1
2
1
2
2
1
0
2
0
1
0
1
1
1
1
1
1
1
2
1
1
1
1
2
1
0
0
2
1
1
1
1
2
1
1
2
1
2
1
1
0
2
1
1
1
0
1
2
2
1
1
1
0
1
1
0
2
1
1
1
1
1
1
2
2
2
1
2
2
0
2
1
0
1
0
1
1
1
1
2
2
2
1
2
1
1
1
0
1
2
1
1
1
1
1
1
2
0
1
1
1
0
1
1
0
1
1
1
0
3
1
0
0
0
0
2
1
1
2
1
1
1
0
1
2
0
1
1
0
2
1
0
1
2
1
1
1
1
1
0
0
1
1
0
2
1
0
1
2
1
0
1
1
2
0
1
1
2
1
1
0
1
2
1
1
2
1
1
1
1
1
1
0
1
1
1
0
1
1
1
1
0
0
1
0
0
1
1
1
1
0
2
0
1
1
0
1
1
1
0
0
1
1
1
0
1
0
2
2
1
2
1
0
5
1
1
0
1
1
1
1
1
0
1
4
1
1
1
1
2
1
1
1
1
0
1
1
1
1
1
1
0
2
1
2
0
2
1
1
2
1
0
0
1
1
2
1
1
2
1
2
1
0
1
0
2
1
2
1
0
2
2
1
1
1
1
0
1
0
1
0
1
0
1
0
1
3
2
1
1
2
1
0
1
1
2
1
2
1
2
1
0
2
1
1
0
1
0
2
1
2
2
0
1
1
1
0
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
2
1
2
1
0
0
1
2
0
0
0
0
0
1
1
1
2
1
1
0
2
1
1
1
1
2
2
0
0
0
2
1
1
2
1
1
1
1
2
1
2
1
0
2
0
1
1
2
1
1
2
1
1
2
1
1
2
0
1
1
1
2
1
1
0
1
0
1
2
1
3
0
1
1
1
0
2
1
1
1
0
0
1
1
2
0
1
1
0
2
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
2
2
1
2
1
1
0
2
2
1
1
1
1
2
1
2
1
1
2
0
1
1
1
1
3
2
1
1
0
1
2
1
1
1
0
1
1
2
2
2
2
2
1
0
1
2
2
1
1
1
2
1
1
1
0
2
1
1
0
1
1
1
1
0
2
0
1
1
1
0
2
1
0
1
1
1
1
1
1
1
1
0
2
0
1
2
1
2
1
1
2
1
2
2
2
2
1
1
1
1
1
2
2
1
2
1
1
2
2
2
1
1
1
1
2
2
1
2
1
0
1
2
1
0
3
1
1
1
0
1
0
0
1
1
2
1
1
0
1
1
0
0
1
2
1
1
1
2
1
1
1
1
0
1
1
0
0
1
2
1
1
1
1
2
1
2
1
1
2
1
1
3
1
1
1
1
2
1
1
2
1
0
0
1
2
1
1
2
2
1
1
0
2
0
1
1
1
0
1
1
1
1
0
1
0
2
1
3
2
2
1
1
1
1
2
2
1
1
1
1
1
2
1
1
1
1
1
1
0
1
1
2
1
2
0
1
1
1
1
1
2
1
1
1
1
1
1
0
1
1
1
1
1
1
0
1
1
1
1
1
1
2
0
1
1
1
0
1
2
1
2
1
2
1
1
0
2
1
2
0
1
1
1
1
2
2
1
1
2
2
1
1
1
1
1
0
2
2
0
2
0
2
2
0
1
1
1
1
1
1
2
1
0
2
2
1
0
1
2
1
0
0
1
1
1
1
0
1
1
1
2
1
1
0
1
1
1
2
1
0
1
1
2
1
2
1
1
0
1
2
0
1
1
3
3
2
0
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
2
0
1
2
1
1
1
0
0
1
1
0
1
0
2
1
1
1
1
2
2
2
2
0
2
2
0
1
2
2
1
1
0
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
0
1
2
1
1
1
1
1
2
1
1
1
0
2
1
1
0
1
0
1
2
1
1
2
0
1
0
1
0
2
1
0
1
1
2
0
1
1
2
1
1
1
1
2
0
1
0
0
1
1
1
0
1
2
1
0
1
2
1
1
1
0
1
1
2
2
2
0
2
0
1
1
1
1
1
2
1
0
2
1
0
0
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
2
1
1
0
1
0
1
1
0
1
1
1
2
1
1
1
2
0
0
2
1
1
1
1
2
1
1
1
1
1
0
1
2
0
0
0
2
1
1
0
2
1
1
0
1
1
2
1
1
2
2
2
0
0
1
1
0
1
2
1
1
1
1
0
0
0
2
0
1
1
2
1
1
1
0
1
1
1
2
0
1
0
1
1
1
1
1
1
1
1
1
2
1
1
0
0
1
2
1
1
1
2
1
0
1
0
0
1
1
0
0
1
2
1
1
0
0
1
1
1
1
0
2
1
1
2
1
2
1
2
2
0
0
2
1
2
2
1
1
1
2
1
1
1
0
1
1
2
2
1
2
1
1
0
1
1
1
0
2
0
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
2
2
0
1
1
0
1
1
0
1
0
1
1
1
1
1
1
1
0
1
2
1
1
0
2
1
1
1
2
1
2
1
2
1
2
1
2
2
1
0
2
1
1
1
0
1
1
0
2
1
2
1
1
2
1
2
1
1
0
1
1
1
2
1
1
1
0
1
0
1
1
0
1
1
1
0
1
0
2
1
1
1
0
1
1
1
1
0
0
1
1
1
1
2
1
2
0
2
1
1
1
1
1
2
0
0
2
1
2
1
1
2
1
0
1
1
2
1
0
1
0
1
1
1
1
1
0
2
2
0
2
0
1
2
0
1
1
1
2
0
1
1
1
1
2
1
0
1
1
2
1
2
1
1
1
2
0
0
2
2
0
1
1
1
2
2
1
0
1
1
0
2
1
1
1
0
1
4
2
1
3
1
0
1
1
0
2
2
1
1
4
1
2
0
2
2
1
1
1
0
1
1
2
0
1
0
1
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
0
1
1
3
2
0
1
2
2
1
1
2
0
1
1
1
1
2
0
2
1
0
0
1
2
2
0
1
1
1
2
2
1
1
1
0
1
1
1
1
0
2
2
1
1
1
1
1
2
1
0
1
0
1
2
1
0
1
1
1
1
1
2
1
1
2
1
1
1
2
0
1
1
2
1
0
1
1
2
2
1
1
1
1
1
1
1
1
1
0
1
1
3
1
0
2
1
2
0
2
1
1
1
1
1
2
0
1
1
2
1
1
2
1
1
1
2
1
1
1
0
1
2
0
0
1
0
0
1
1
2
1
1
1
1
1
1
2
0
1
1
1
2
1
1
1
2
1
1
2
1
2
0
1
1
1
1
0
1
1
2
2
2
0
1
1
1
1
0
0
2
1
1
2
2
2
1
1
1
1
1
2
1
2
2
1
1
1
0
1
1
1
1
1
1
1
2
1
0
1
1
2
2
1
1
1
1
2
2
2
1
2
1
1
2
1
0
1
1
0
1
0
2
2
1
0
2
1
2
1
3
0
1
1
1
2
2
1
1
1
1
1
1
1
1
2
1
1
1
3
1
1
1
1
0
2
1
0
1
1
1
0
2
2
0
2
1
1
2
1
0
2
0
1
2
1
2
1
1
1
0
2
1
2
2
2
1
1
2
1
1
3
1
1
1
1
1
2
1
1
1
2
1
2
0
0
2
4
2
0
2
1
2
1
1
0
1
1
1
1
0
2
0
0
0
1
1
1
0
1
3
1
2
1
1
2
2
2
1
0
1
0
1
0
1
1
2
1
0
2
2
2
2
4
0
1
0
1
1
1
1
0
0
1
1
0
1
0
0
2
2
0
4
1
0
1
1
2
1
1
1
1
1
1
0
1
2
1
1
0
1
1
2
2
1
0
2
1
0
1
2
2
1
1
1
0
1
0
1
1
1
0
1
1
1
2
1
2
0
1
1
1
2
1
1
1
1
0
1
2
1
2
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
2
2
1
1
1
0
1
1
1
1
0
0
1
1
1
1
0
1
1
1
2
0
2
2
2
0
1
1
1
1
1
3
0
1
1
1
2
1
0
2
1
1
1
1
1
2
1
0
1
1
1
2
1
1
0
0
1
0
1
2
2
1
1
1
1
1
1
1
1
2
1
1
1
1
0
2
0
1
2
2
1
0
1
1
1
0
1
1
1
1
1
1
1
1
0
2
0
0
1
1
0
1
1
1
1
1
1
1
1
0
1
0
2
0
2
0
2
0
0
1
1
2
0
1
1
1
1
1
1
1
0
0
1
1
1
1
2
0
2
0
1
1
2
2
1
1
1
0
1
1
1
1
1
2
1
2
0
1
1
2
1
2
0
1
1
1
2
2
2
2
2
1
1
1
2
0
1
1
1
1
1
1
3
0
2
1
2
0
0
1
0
1
1
1
1
1
1
1
0
1
1
3
2
1
2
1
0
1
1
0
2
1
1
2
1
1
1
1
2
2
0
1
1
1
2
2
1
1
1
1
1
1
1
0
0
1
1
1
0
1
1
0
2
2
0
2
0
1
0
1
1
2
1
1
0
2
1
1
1
0
1
1
1
1
0
2
1
1
0
1
1
2
1
2
0
1
1
2
2
1
1
1
1
1
2
1
1
2
1
1
2
2
2
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
2
2
1
1
0
1
1
2
1
2
1
4
2
1
2
1
2
1
1
0
1
2
0
1
2
1
2
2
0
0
2
2
1
0
1
1
1
1
0
1
1
0
1
1
1
1
1
0
2
0
1
1
1
1
1
2
2
1
0
1
0
1
1
1
1
1
2
0
0
1
0
1
1
2
1
2
1
2
1
1
1
3
1
1
1
1
1
1
0
2
0
1
0
0
1
2
0
1
1
1
1
1
1
1
1
2
0
1
1
2
1
2
2
0
1
0
0
0
1
0
0
1
2
1
1
2
0
1
2
1
0
1
2
2
0
1
0
1
2
1
1
1
0
2
1
1
1
2
1
1
1
2
1
1
1
1
1
2
0
1
1
1
2
1
2
1
1
1
1
1
0
2
1
0
0
2
1
1
1
1
1
2
1
1
2
1
1
1
2
1
0
1
0
1
1
1
1
1
1
1
1
1
0
1
1
5
1
1
1
1
1
1
1
1
0
1
0
1
3
2
1
1
1
0
1
1
1
1
1
2
0
1
1
2
2
0
2
2
2
2
1
1
1
1
0
2
0
1
2
1
1
2
1
1
1
0
1
1
2
1
0
1
1
1
0
1
1
2
2
1
1
1
2
2
2
1
0
0
1
1
1
1
1
1
0
1
1
0
1
5
1
1
1
2
1
0
1
1
1
1
2
1
1
0
1
1
1
1
0
0
2
1
1
0
1
2
0
1
1
1
0
0
1
1
1
1
1
1
1
1
1
2
2
2
2
1
1
2
1
0
1
1
1
0
1
2
2
1
1
1
2
0
1
1
2
1
0
2
1
1
2
1
0
1
1
2
1
1
0
1
2
1
1
2
0
1
1
1
2
1
0
2
1
1
1
0
1
1
1
1
1
0
1
2
8
1
2
2
0
0
1
1
1
1
1
2
2
1
0
1
2
1
1
1
1
0
1
2
0
1
1
1
1
2
1
1
2
4
2
2
0
1
1
2
1
1
2
0
1
1
0
0
1
2
1
0
2
0
1
2
1
2
1
2
0
1
0
0
1
1
1
0
1
1
1
1
0
2
1
2
2
1
1
0
1
3
1
0
1
2
2
0
0
2
1
1
0
0
2
0
1
1
1
2
2
1
1
2
2
1
2
0
1
1
1
1
1
1
2
1
2
1
1
0
1
1
1
1
1
0
1
1
1
1
2
1
1
1
1
2
1
0
1
1
1
0
1
1
3
2
1
1
0
1
0
2
1
1
1
1
1
1
1
1
2
1
2
1
1
2
0
0
1
1
0
1
2
2
1
1
1
1
1
1
1
2
0
0
1
2
0
1
1
2
2
1
0
1
3
1
1
1
1
0
0
2
1
1
2
2
1
1
2
2
0
1
1
1
0
1
2
0
0
2
0
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
2
2
1
2
1
2
1
0
1
0
0
1
0
1
1
1
2
1
2
1
1
1
3
1
2
2
1
1
2
1
2
1
2
1
2
2
1
1
1
1
1
1
1
1
2
2
1
1
0
0
1
2
1
2
0
2
0
1
1
1
0
1
1
0
2
2
0
2
2
1
1
2
2
1
1
1
1
1
1
1
1
1
0
1
1
2
1
2
0
2
1
2
2
1
1
1
1
1
1
1
1
0
2
0
2
1
0
1
1
1
2
0
0
0
2
0
1
1
0
2
0
1
1
0
1
1
0
1
1
2
2
0
0
2
1
2
1
0
0
2
0
2
1
1
2
0
2
1
2
1
1
1
1
1
1
1
0
1
2
0
1
1
0
2
1
2
1
2
1
1
1
1
1
3
1
1
1
0
2
1
2
1
1
2
1
0
2
2
1
1
3
0
2
1
1
0
1
2
1
1
0
1
1
0
0
1
1
1
1
0
2
1
1
1
1
1
2
1
0
1
1
1
1
1
0
2
1
0
0
1
1
3
1
2
1
1
1
1
0
1
1
1
0
1
1
0
1
1
1
2
0
1
1
1
2
1
1
2
1
2
2
0
1
2
0
1
1
1
1
1
2
0
1
1
2
1
0
1
2
0
1
1
1
1
1
1
2
1
1
1
1
2
1
2
1
1
1
1
0
1
1
1
1
1
2
2
1
1
1
2
1
1
2
1
1
0
1
2
2
1
2
2
1
0
1
1
1
0
2
0
1
0
1
0
1
0
1
2
1
2
1
0
1
2
2
0
1
0
2
2
2
2
0
1
2
1
0
1
2
0
2
1
0
1
2
1
1
1
2
1
2
2
0
1
1
1
2
1
1
1
1
1
1
1
0
1
1
0
1
2
2
0
2
2
1
2
1
2
2
1
2
1
1
1
2
0
1
1
1
1
1
1
1
2
1
0
0
1
1
1
1
2
0
0
1
3
1
2
2
2
2
0
2
1
0
1
0
2
1
0
1
1
1
1
1
1
0
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
3
1
1
0
1
1
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
0
1
0
1
1
0
1
2
1
1
2
2
2
1
1
2
2
1
1
1
1
1
0
2
1
0
1
1
1
1
1
1
1
1
2
1
2
0
1
1
2
2
2
0
0
2
1
0
1
0
2
0
1
1
2
1
0
1
0
0
2
1
1
1
0
2
1
1
1
1
1
1
0
0
2
2
2
2
0
1
2
1
1
1
1
1
0
1
1
1
2
2
1
0
1
2
1
1
1
1
2
1
0
3
1
1
0
1
0
1
1
1
2
2
1
1
1
2
1
2
2
1
1
2
4
1
2
1
1
1
1
2
1
1
1
0
1
1
1
0
0
1
1
0
0
1
0
2
2
1
1
2
0
1
0
1
0
1
1
0
1
1
1
1
1
0
1
2
1
2
2
1
1
1
1
1
0
1
1
1
1
1
3
1
0
0
1
2
1
1
1
1
2
2
1
1
1
2
2
0
0
0
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
0
0
2
1
2
0
2
1
0
2
2
1
1
1
1
1
1
2
0
0
1
1
2
1
1
1
0
1
2
2
2
1
1
2
2
2
2
2
0
1
0
1
1
1
1
2
1
1
1
1
1
0
1
0
1
1
2
1
1
1
1
1
1
1
1
1
0
1
2
1
1
1
1
2
1
1
2
2
1
0
0
2
2
1
2
1
2
0
1
0
2
0
1
1
1
1
1
2
2
2
2
1
1
0
1
2
1
1
1
1
1
2
1
1
1
0
1
1
1
0
2
0
1
0
1
0
2
0
1
0
1
1
0
1
2
1
1
2
1
1
1
1
1
1
1
1
3
1
1
1
1
2
0
1
0
1
1
0
2
1
1
0
1
1
0
2
1
1
2
1
1
1
1
1
1
0
2
1
1
2
0
1
1
1
2
0
1
2
0
1
1
2
0
0
0
1
1
0
1
2
2
1
0
0
1
1
1
0
2
2
1
1
1
1
1
2
2
1
0
1
1
1
1
1
1
2
2
1
1
1
0
0
0
2
2
1
1
2
2
0
1
1
2
1
0
1
1
1
0
1
1
1
1
0
0
1
1
2
1
1
0
1
2
1
2
1
1
1
2
1
1
1
2
1
0
2
1
2
1
0
0
1
1
2
0
2
1
1
1
1
1
1
2
1
0
1
2
1
0
2
0
2
1
1
2
2
1
2
1
1
0
1
1
2
1
1
0
1
2
2
2
2
1
0
2
2
2
1
1
1
2
1
2
0
1
2
1
1
1
1
1
1
0
1
0
2
1
1
1
1
1
0
1
1
1
1
2
2
1
0
0
1
1
1
1
1
0
2
2
2
0
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
0
1
1
0
1
1
1
0
2
1
2
1
2
2
1
1
1
1
2
2
2
1
0
1
1
1
0
2
1
0
2
1
0
1
1
3
2
1
0
1
1
0
2
0
0
2
2
2
2
2
2
0
1
1
1
1
2
1
2
2
1
1
2
0
1
1
2
1
2
1
2
0
2
1
0
2
1
2
1
2
1
0
1
3
0
1
1
2
2
0
1
1
0
2
1
2
1
1
1
1
2
1
1
1
2
0
2
1
1
1
0
0
1
2
1
1
1
1
2
1
1
2
0
2
1
1
2
2
0
1
1
1
2
4
1
0
1
1
1
1
1
1
0
1
1
2
1
1
1
0
0
1
1
2
1
1
1
3
2
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
2
2
1
1
3
2
0
3
2
0
1
1
1
1
0
2
3
2
1
1
1
1
0
1
2
0
0
2
2
0
2
1
2
1
1
1
2
1
1
2
2
1
1
2
1
0
1
2
1
2
1
0
2
1
1
1
1
2
0
0
1
1
1
1
1
1
1
0
1
1
2
1
1
1
1
2
2
1
0
2
1
1
1
1
1
1
2
1
2
0
2
0
1
1
1
0
1
1
1
1
1
1
2
2
3
1
1
2
2
1
1
2
1
1
0
0
1
1
1
0
1
1
1
0
1
0
1
1
1
1
1
2
2
1
0
0
0
1
2
1
2
2
2
1
2
1
1
1
1
1
1
1
1
0
1
1
1
0
2
1
0
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
2
2
3
1
1
1
1
2
0
1
1
0
0
1
1
2
2
0
1
1
0
1
2
1
2
0
2
1
1
1
1
1
1
1
1
1
2
2
1
0
2
1
2
2
2
1
1
1
1
0
1
1
0
1
1
1
0
1
1
1
0
1
2
1
1
0
0
1
2
0
1
2
2
1
1
1
0
1
2
1
1
1
2
2
0
0
0
1
1
0
1
1
2
1
0
1
2
2
1
1
0
2
1
1
1
1
0
1
0
2
2
1
1
1
1
2
2
0
1
1
0
1
1
2
1
1
1
0
2
1
1
0
1
1
2
2
1
1
2
0
1
1
1
1
1
1
1
1
1
0
1
2
2
1
1
1
1
0
1
2
1
2
1
2
1
0
0
2
11
2
1
0
1
0
1
1
2
1
1
1
1
3
0
1
1
2
0
0
1
0
1
1
1
1
2
0
1
2
1
0
1
1
0
2
1
2
1
0
1
1
0
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
0
1
0
1
1
1
1
2
1
1
1
1
1
2
2
0
0
1
1
2
2
1
2
1
2
0
1
1
1
1
2
1
1
2
1
1
0
1
1
1
0
1
1
1
2
2
4
1
2
1
2
1
3
1
1
1
1
1
0
2
0
1
1
0
0
1
1
1
1
1
1
2
1
2
1
1
2
2
1
1
1
2
1
0
1
1
0
1
1
1
0
2
1
0
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
1
0
0
1
1
1
1
2
1
1
0
0
2
2
1
0
1
2
1
1
1
1
2
2
1
2
1
1
1
1
0
1
1
0
1
1
0
2
1
2
1
1
1
0
1
2
0
2
2
1
2
1
1
1
1
1
3
2
2
1
1
1
0
1
1
1
1
9
0
2
1
2
0
1
0
1
1
1
0
1
2
1
1
1
1
1
2
1
0
2
1
0
0
1
1
0
0
1
1
2
1
1
0
1
1
1
0
2
2
1
1
2
1
1
1
0
1
2
0
2
0
0
1
0
0
0
1
1
1
2
1
0
2
2
0
0
1
1
2
2
2
1
2
2
1
1
1
1
2
1
6
1
1
1
1
1
1
1
0
1
1
1
1
2
1
1
1
1
2
0
2
1
1
1
1
1
1
0
1
2
2
1
1
2
2
0
0
1
1
0
0
2
2
1
2
0
1
1
1
2
1
1
1
2
1
1
2
1
1
1
2
0
1
1
1
1
2
0
1
1
2
1
1
2
0
1
1
0
1
2
2
1
0
1
1
1
1
1
1
2
0
1
0
1
1
1
1
1
0
0
1
2
1
2
2
0
1
1
0
0
0
2
1
2
2
1
2
1
1
1
0
1
2
1
0
1
0
1
1
2
0
1
0
0
1
0
2
2
1
2
1
1
2
1
2
1
2
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
0
2
0
0
1
1
1
2
1
0
0
1
2
1
1
1
3
1
1
1
0
1
1
0
2
1
1
1
1
1
0
1
1
3
1
2
1
0
1
1
1
0
1
1
0
1
1
2
0
0
0
0
0
2
1
2
1
1
2
1
2
1
1
2
0
1
0
2
1
1
2
1
2
1
1
1
1
2
1
2
1
1
1
2
0
0
1
1
1
2
1
1
1
0
2
1
2
0
2
1
1
0
1
1
1
2
1
1
0
1
1
1
1
0
1
2
1
2
1
1
2
1
1
2
1
1
1
2
0
1
0
2
1
2
1
1
1
2
1
1
2
1
1
1
1
2
2
1
2
2
1
1
2
1
0
1
0
2
1
1
1
2
0
0
1
1
1
1
2
1
1
2
1
2
1
1
2
1
1
0
1
1
1
1
0
1
1
9
1
1
1
0
1
1
0
2
1
2
2
1
1
1
1
2
4
1
2
4
2
1
0
2
2
2
1
1
2
2
2
1
1
0
0
0
1
1
0
1
0
0
1
2
1
1
1
2
1
1
0
1
1
1
1
2
1
1
2
0
1
1
2
2
0
1
1
2
2
1
1
1
2
1
1
1
1
1
1
0
1
1
1
2
1
0
0
1
1
1
2
1
1
2
2
2
2
1
2
1
1
1
2
1
2
0
1
2
1
1
1
1
1
0
1
1
1
1
1
1
1
1
0
1
2
0
1
2
1
2
2
0
1
1
1
1
1
2
2
1
2
0
1
1
1
1
1
1
1
0
1
1
1
1
0
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
0
2
1
0
0
1
1
0
1
1
2
1
1
2
2
0
0
2
1
1
0
2
0
1
1
1
1
2
1
1
1
2
1
1
0
2
2
1
0
0
1
2
2
1
1
2
2
2
0
1
1
1
0
2
1
1
1
1
0
2
1
1
1
2
2
1
1
1
1
1
1
2
2
1
0
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
0
2
1
1
2
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
0
1
2
1
1
1
0
1
1
0
1
0
2
1
1
1
1
0
1
1
1
1
1
1
0
2
1
1
1
1
0
1
1
0
2
1
2
1
1
2
1
1
1
0
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
0
1
0
0
0
1
1
1
0
1
0
0
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
0
1
0
1
1
2
1
1
1
1
1
1
2
0
2
1
1
0
1
2
2
1
0
2
1
1
0
1
1
0
1
1
1
2
1
1
1
0
1
1
1
2
5
1
1
1
1
0
0
1
1
1
1
1
0
2
1
1
1
2
2
2
2
2
2
1
2
2
1
1
1
1
1
1
2
0
1
2
1
1
1
1
1
1
2
1
1
2
1
1
1
0
1
1
0
1
1
1
1
1
1
0
1
0
1
2
1
1
1
1
0
0
2
1
1
1
1
1
2
1
0
2
1
2
0
1
1
1
0
1
2
1
1
1
2
1
0
1
1
2
1
1
1
2
1
2
1
1
1
1
1
2
0
2
1
0
1
1
2
1
0
1
0
0
0
1
1
1
1
1
1
2
2
1
2
1
1
1
2
0
2
0
2
0
2
1
1
0
2
1
1
0
1
2
1
1
1
1
1
2
1
1
1
1
1
0
1
1
1
1
2
1
1
1
2
2
2
1
2
0
2
0
1
2
1
1
1
1
1
1
2
1
1
1
1
0
1
2
1
0
1
2
1
0
2
2
1
1
1
1
1
1
0
2
1
1
1
1
1
1
1
0
1
1
1
2
2
1
1
1
0
0
1
0
2
0
1
2
1
1
1
0
1
1
1
1
1
0
2
1
2
1
2
0
1
1
1
1
2
1
0
0
1
2
1
2
1
1
1
1
2
1
1
1
0
1
1
1
1
1
1
1
2
0
2
2
2
0
1
1
1
2
1
2
1
1
1
1
0
1
1
1
1
2
0
2
2
2
2
1
1
2
0
2
1
0
1
1
1
2
2
1
1
1
2
0
2
1
2
2
1
1
1
2
2
2
1
1
1
1
1
1
1
1
1
1
0
2
1
2
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
0
3
2
1
2
0
0
1
1
0
1
1
1
2
1
1
1
1
0
0
1
1
1
1
2
1
1
1
1
2
2
1
1
2
0
1
1
1
1
1
2
0
1
1
0
1
2
2
1
1
1
1
1
2
0
2
2
2
2
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
0
1
1
1
1
1
0
1
1
2
1
2
2
1
2
1
2
0
2
1
1
0
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
2
0
1
1
1
2
1
1
1
1
0
1
1
1
1
0
0
1
2
0
2
1
1
1
0
1
1
1
2
2
1
1
2
0
0
3
1
1
0
2
1
2
1
1
1
1
1
1
2
1
0
2
1
2
2
1
1
0
1
1
2
1
2
1
1
1
1
0
0
2
1
2
1
2
1
2
2
0
1
2
2
1
0
1
1
0
1
2
1
2
0
1
1
2
1
1
1
2
1
0
2
1
1
1
1
2
0
1
1
2
1
3
0
1
1
2
0
2
1
2
2
1
1
1
1
1
1
0
0
0
1
2
1
1
1
1
1
1
1
2
2
2
2
1
1
1
2
1
2
2
1
0
1
0
0
0
0
1
1
1
1
1
2
1
1
1
1
1
2
1
1
2
2
1
1
1
2
1
1
2
1
2
1
0
2
1
2
1
2
0
1
2
1
1
1
1
0
2
1
0
1
1
2
0
1
1
1
3
0
1
1
1
1
1
2
0
1
0
1
1
0
1
1
1
0
1
1
0
2
0
0
2
1
0
2
1
1
2
1
0
1
2
2
1
0
2
2
1
1
1
1
1
0
0
2
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
0
1
2
1
1
1
1
1
2
1
1
0
2
2
0
1
0
1
1
1
1
2
1
1
1
1
0
1
1
2
1
1
1
0
2
1
1
0
0
1
1
1
1
1
0
1
0
1
3
0
0
3
2
1
1
2
2
0
1
1
1
1
1
1
2
2
1
2
1
0
1
1
2
1
1
1
1
1
2
2
2
0
1
1
1
1
1
0
1
0
2
1
0
1
1
1
1
0
2
2
0
2
0
0
1
1
0
2
2
1
0
2
1
1
1
2
0
1
1
2
1
0
2
1
2
1
0
0
0
2
0
1
2
2
1
2
1
1
1
1
1
1
1
1
1
1
2
0
1
1
0
1
1
1
1
1
1
2
1
0
1
2
0
1
3
1
2
1
1
2
1
1
2
1
0
1
1
2
1
1
1
1
2
1
1
1
2
0
1
2
1
1
2
1
1
0
2
0
1
1
1
1
2
0
1
1
0
2
2
0
1
1
1
0
2
1
1
1
0
0
1
1
1
1
1
1
1
1
1
2
0
2
1
1
1
1
2
1
0
2
1
2
0
2
1
1
2
2
1
1
1
2
2
1
1
1
1
1
2
2
1
0
1
2
0
1
2
1
2
1
1
1
1
1
2
2
1
1
1
1
1
1
3
0
1
1
2
0
1
1
1
1
0
0
1
1
2
1
1
1
1
2
0
1
1
1
1
2
1
1
0
2
0
1
0
1
0
1
2
1
1
1
0
0
1
0
1
1
0
2
1
1
0
2
1
1
0
1
1
2
1
0
1
2
1
1
0
2
2
2
2
0
2
0
1
4
1
1
2
2
1
1
0
2
0
1
2
2
1
1
2
1
2
2
1
1
1
1
1
1
1
0
1
1
1
1
1
1
2
3
2
1
0
2
1
1
1
1
0
1
2
2
1
1
1
2
2
0
0
0
1
1
2
0
2
1
1
1
2
1
1
1
0
1
0
1
0
1
0
1
2
1
1
1
1
1
1
2
1
2
2
2
1
1
1
1
2
2
2
2
0
1
1
0
1
1
1
1
2
0
2
1
0
2
1
2
1
2
1
0
0
2
2
0
2
1
2
1
1
1
1
3
2
1
1
1
2
1
1
1
2
1
2
1
1
1
1
0
0
0
1
1
2
1
2
3
3
0
2
1
2
1
1
1
1
1
2
1
1
1
1
2
1
1
1
0
1
0
1
1
2
1
1
1
1
1
1
2
2
1
2
2
0
0
1
0
1
1
1
0
2
2
1
0
0
1
2
1
2
1
1
1
1
1
0
2
0
1
1
1
2
1
1
2
2
2
1
2
1
2
1
1
1
0
1
2
0
0
0
1
2
1
1
1
1
2
2
2
1
1
1
1
2
0
1
1
1
1
0
1
1
0
0
2
1
1
1
0
1
0
0
1
1
1
1
1
1
1
0
0
1
1
1
1
0
2
2
1
1
2
1
2
1
1
2
0
1
1
1
0
0
2
1
2
1
2
1
0
1
1
1
2
1
0
1
2
0
1
1
1
1
1
0
1
1
1
2
1
2
0
2
1
0
2
2
2
0
2
2
1
1
0
1
2
1
1
2
1
2
1
0
0
0
1
1
1
2
1
1
1
1
2
1
1
0
2
1
1
1
1
1
1
1
0
1
0
2
1
1
1
2
2
1
0
2
2
0
1
1
1
0
1
1
1
1
2
1
1
1
2
1
0
1
0
2
2
1
2
1
2
1
1
2
1
1
1
1
1
1
1
2
1
0
2
1
1
1
2
1
1
1
2
0
1
1
1
1
2
1
1
2
1
1
1
1
1
0
1
1
2
1
1
3
0
1
1
2
1
2
1
1
2
1
1
2
1
1
1
1
1
0
1
0
1
1
2
1
2
1
0
1
1
2
1
1
1
2
1
2
1
1
0
1
1
1
2
0
1
2
1
1
2
1
2
1
1
1
1
0
0
1
1
1
1
1
1
1
0
1
0
1
1
1
1
0
1
1
0
1
1
2
1
1
1
1
1
0
1
2
0
1
1
1
0
1
0
0
1
1
1
2
1
0
1
0
1
2
2
0
1
1
1
0
0
0
1
0
0
1
1
2
1
1
2
1
1
1
0
0
2
1
0
1
1
2
0
1
2
2
0
1
2
0
1
1
0
2
2
2
2
1
1
1
1
1
1
1
2
1
2
0
1
0
2
0
0
0
1
1
2
0
1
1
1
2
2
1
1
0
1
1
0
1
1
1
2
1
1
0
1
0
2
1
1
0
1
2
1
1
1
2
2
2
1
1
1
4
0
1
2
1
1
0
1
2
1
1
2
1
2
1
2
0
1
0
2
1
1
1
1
1
0
2
1
2
1
0
2
2
1
1
1
0
1
1
1
2
1
2
1
1
1
1
2
1
1
1
0
1
1
1
1
2
1
2
1
2
1
0
1
0
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
2
0
0
0
1
1
1
0
1
1
1
1
3
0
2
2
1
1
2
2
1
1
1
0
0
1
0
1
2
2
1
1
1
0
2
0
0
1
0
2
1
1
1
1
1
1
1
2
0
1
0
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
2
0
1
1
0
0
2
1
1
1
1
2
0
2
1
1
1
1
0
1
1
0
1
1
1
0
1
1
1
1
1
1
2
1
0
2
1
1
0
1
1
2
2
2
1
1
1
2
1
2
0
0
1
1
1
1
1
2
1
1
2
0
0
2
2
1
0
2
1
1
0
0
1
1
1
1
1
2
1
1
2
2
2
0
1
0
1
2
2
2
1
0
1
2
2
1
2
1
1
2
1
0
2
1
0
1
1
1
2
2
2
0
1
2
1
2
1
1
1
1
0
2
1
1
1
1
1
1
1
1
1
1
2
2
1
2
2
1
1
1
2
1
1
0
1
1
0
2
1
0
2
1
0
1
2
0
2
1
1
0
0
2
1
1
1
2
2
1
2
1
0
1
2
2
2
2
1
0
2
1
1
2
1
0
1
1
0
2
1
1
1
0
1
1
0
1
1
2
0
2
1
1
2
3
1
2
0
2
2
1
1
0
2
1
2
2
1
1
0
0
2
1
2
2
1
1
2
0
2
2
1
1
1
1
0
1
1
0
1
2
2
1
2
1
1
1
1
1
0
1
1
2
1
1
2
1
1
1
1
2
1
2
1
2
2
0
1
1
0
0
2
0
0
1
0
0
1
2
0
2
1
1
1
3
1
0
0
0
1
1
1
1
0
0
3
1
2
1
1
1
1
0
0
1
1
1
1
1
0
1
2
1
2
2
0
2
0
2
0
2
2
0
0
1
0
1
1
2
1
1
2
0
2
2
1
0
1
1
0
2
0
1
1
1
2
1
1
2
1
2
0
1
1
0
1
1
2
1
1
1
1
1
1
2
0
1
2
1
2
1
0
1
1
1
0
1
2
2
0
1
1
1
1
2
1
1
2
2
1
1
0
0
1
1
1
1
1
2
2
0
1
2
1
0
1
2
2
1
0
2
1
2
1
0
1
1
0
0
2
1
2
1
0
1
1
0
1
1
2
1
3
1
1
0
2
1
0
1
1
1
1
2
1
1
1
2
1
0
0
1
2
1
1
1
1
1
1
1
1
2
0
1
1
0
1
1
1
1
1
0
0
0
1
2
2
1
1
1
1
1
2
1
0
1
1
2
2
1
1
1
0
1
1
1
0
1
1
2
0
0
2
1
1
0
1
0
1
2
0
1
1
1
0
1
1
1
0
1
2
0
1
1
0
1
1
0
0
2
1
0
1
1
1
1
1
1
1
1
0
0
2
1
1
1
3
0
2
1
2
1
1
2
4
1
1
1
2
1
1
0
0
1
2
2
2
1
0
2
1
1
1
2
0
1
2
1
1
1
2
1
1
1
1
1
1
1
2
2
2
1
1
1
1
0
0
1
1
1
2
1
2
1
0
2
0
0
0
0
1
1
0
2
0
1
2
0
1
1
1
0
1
1
0
1
2
2
1
0
2
2
1
1
2
1
1
0
1
2
1
1
1
2
1
2
1
1
1
1
0
1
1
2
2
1
2
2
0
1
1
2
1
1
2
2
1
0
1
1
2
2
0
0
2
1
1
1
1
1
0
2
0
2
2
1
1
0
1
0
1
1
2
1
1
1
2
2
1
1
1
0
0
1
1
0
0
2
1
1
1
1
2
1
1
2
0
1
1
1
1
2
0
1
1
0
2
1
1
2
1
1
1
2
2
1
1
0
2
1
2
2
1
1
1
2
2
0
1
1
1
2
0
0
1
1
1
1
0
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
0
2
1
1
2
0
1
1
2
1
0
1
2
1
1
1
2
1
1
0
1
1
1
1
1
0
0
0
1
1
1
1
1
1
1
0
0
0
1
1
2
1
1
2
1
1
1
2
2
1
1
2
1
1
1
1
2
0
2
2
2
1
1
2
1
1
2
0
1
1
1
1
1
1
0
1
0
1
1
1
0
1
1
0
2
2
2
0
2
1
0
2
2
2
0
1
2
2
0
1
1
1
1
2
0
1
1
0
1
0
0
2
1
2
1
4
0
2
2
2
1
1
0
1
2
1
1
2
1
1
0
1
1
1
0
4
0
2
1
2
0
1
1
2
1
1
1
0
1
1
1
1
2
1
1
1
1
1
1
0
2
2
1
1
2
1
1
1
1
0
1
1
2
1
2
2
0
1
2
0
0
1
1
1
4
2
1
1
1
1
1
1
1
1
1
2
1
0
2
1
2
0
2
1
0
1
2
3
2
2
1
1
1
1
1
1
0
2
1
1
0
1
2
2
1
1
1
1
1
2
1
0
2
0
1
1
1
0
1
1
1
1
2
0
2
0
0
1
2
2
1
2
1
1
0
1
1
2
4
0
2
1
2
1
1
0
1
0
0
1
1
0
1
1
2
1
2
1
2
1
0
2
0
2
0
0
1
2
1
2
1
1
2
1
0
1
1
1
1
1
2
0
1
1
0
1
0
2
2
1
1
1
1
2
1
2
1
0
1
1
2
2
4
1
1
1
1
1
1
1
1
1
0
1
0
1
1
1
0
1
2
1
1
1
1
2
2
1
1
1
0
0
2
1
1
1
1
0
1
1
2
1
1
0
1
2
1
1
1
2
1
1
2
1
1
1
2
0
1
2
1
1
1
1
1
1
2
0
1
2
1
1
2
2
2
0
2
2
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
0
1
1
2
1
2
2
2
2
1
1
1
1
2
1
2
1
1
1
1
1
0
0
1
2
1
1
1
0
1
1
1
2
2
0
0
1
1
1
1
1
0
1
2
1
1
2
1
2
1
2
1
1
1
1
1
1
0
1
1
2
0
2
1
2
1
0
1
1
0
2
1
1
2
1
2
0
1
1
1
1
2
2
2
1
1
2
1
1
1
1
1
1
1
1
1
0
1
1
0
0
1
2
0
1
1
1
0
0
2
1
1
1
2
0
1
0
2
2
0
1
1
1
1
2
1
2
1
0
0
1
1
1
1
1
2
0
2
1
1
1
1
2
2
2
0
2
2
1
1
2
1
1
1
1
2
2
2
0
1
2
1
1
1
1
1
1
2
0
1
1
1
1
2
1
1
1
0
0
0
1
0
1
0
2
2
1
0
2
2
1
2
1
2
1
2
1
1
0
1
1
1
2
1
1
2
2
0
1
1
1
2
1
1
0
2
1
2
0
1
1
0
1
0
1
1
2
2
1
2
1
2
1
1
1
1
1
1
1
2
1
2
0
2
1
2
0
1
1
2
1
2
1
1
1
1
1
1
1
1
1
2
2
0
1
1
0
1
2
1
1
2
1
1
0
1
0
2
2
2
0
0
0
1
1
0
1
1
2
1
2
2
2
0
0
2
1
0
2
1
2
1
2
1
0
1
3
1
1
1
1
2
0
1
0
1
1
1
0
1
1
1
1
0
0
0
1
2
2
2
1
1
2
1
2
2
2
1
1
1
1
1
2
2
2
2
1
2
0
2
0
2
1
2
1
0
1
1
1
1
0
1
1
1
1
2
1
1
1
2
1
1
0
1
1
0
1
1
1
2
1
0
1
1
1
0
2
0
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
0
1
2
2
1
1
2
2
2
2
2
1
1
1
1
1
2
1
0
1
1
0
2
1
1
1
1
1
2
1
0
2
1
1
2
1
1
1
1
1
1
2
2
1
1
2
1
0
2
0
1
1
1
1
1
1
2
0
1
1
0
1
1
1
1
1
2
1
0
1
1
1
1
0
2
1
0
0
2
1
1
2
1
1
1
1
1
1
1
1
1
1
0
0
0
2
1
1
1
0
0
2
1
1
1
1
0
1
1
0
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
2
2
2
1
2
0
1
2
1
1
1
1
1
1
1
0
1
1
1
0
0
2
1
0
1
1
2
0
1
1
1
1
2
1
1
1
1
2
1
2
1
1
0
1
1
2
1
2
1
2
1
1
0
1
1
1
1
2
1
1
1
2
0
2
1
1
1
0
1
0
1
1
0
1
2
0
1
2
1
2
1
0
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
0
1
1
0
2
2
2
0
0
1
1
1
0
2
1
1
1
1
2
0
5
1
1
0
2
1
1
0
0
0
0
1
1
1
2
1
1
0
1
0
2
2
1
1
0
2
1
2
1
1
2
1
1
1
1
3
0
2
1
1
2
1
1
1
2
1
0
1
2
1
1
1
2
1
0
1
1
1
0
1
1
1
1
0
2
1
1
1
1
2
1
1
1
2
0
0
2
0
0
1
2
1
1
2
1
0
1
2
2
2
0
1
2
0
2
2
3
1
2
1
2
0
0
1
1
2
1
1
1
1
2
1
1
1
1
0
1
1
1
1
1
1
1
1
2
1
0
1
1
0
1
1
1
1
2
0
1
1
1
2
2
2
2
1
1
0
1
1
2
1
2
2
1
1
1
2
1
2
2
2
1
1
1
2
0
1
0
2
0
1
1
2
0
1
0
0
1
1
1
1
0
1
1
1
1
1
1
1
1
1
0
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
0
0
1
1
1
0
2
2
1
2
0
1
1
1
1
1
1
2
1
2
1
1
0
1
3
1
0
1
1
0
0
2
2
1
0
0
1
2
2
1
1
2
1
2
0
0
1
1
0
2
1
0
1
2
0
1
1
0
1
1
1
1
2
1
2
0
1
2
1
1
1
0
1
0
1
2
1
1
2
1
1
0
2
1
2
0
1
2
1
2
2
2
0
1
1
1
0
1
1
1
1
1
0
1
1
1
2
2
1
2
0
1
1
1
0
2
1
1
1
1
2
2
1
1
1
0
1
2
2
1
1
1
2
1
2
1
1
1
1
2
2
1
1
0
2
1
1
1
1
1
1
0
1
0
0
1
1
1
0
1
0
0
2
1
0
0
2
2
1
2
0
1
1
1
3
1
0
1
2
1
1
1
0
1
1
0
1
1
1
0
2
2
2
1
0
1
1
2
2
1
1
2
1
1
2
2
0
1
1
1
0
2
0
2
3
1
0
2
0
2
1
1
1
2
1
1
1
1
1
2
2
1
1
1
1
2
2
1
2
0
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
0
0
2
1
1
1
2
1
1
1
2
0
1
1
1
1
1
1
1
0
0
1
6
1
0
0
1
1
1
2
0
0
2
1
1
1
1
0
1
0
1
1
0
1
1
1
1
1
1
1
0
1
1
1
0
1
1
1
0
0
0
1
2
2
2
1
0
2
2
2
1
1
1
0
2
2
1
1
1
0
2
1
2
1
1
1
2
2
2
2
1
1
1
0
1
1
0
1
1
1
0
1
1
0
1
1
1
0
1
0
0
1
2
1
1
1
1
2
2
1
1
1
1
0
1
1
2
1
2
1
1
2
2
1
1
0
1
0
0
1
1
1
1
1
1
0
1
1
0
1
0
1
2
0
0
1
0
1
2
2
2
2
1
1
2
1
2
0
1
1
2
0
0
1
2
2
2
2
2
1
1
1
1
1
1
1
2
2
2
1
0
2
1
0
1
0
1
0
1
0
1
1
1
1
1
1
2
0
0
2
1
1
1
1
2
1
1
2
0
0
1
1
1
1
2
1
0
0
2
1
1
2
1
0
1
1
1
1
2
1
1
1
1
2
1
1
1
0
2
2
0
1
1
2
1
2
2
2
1
0
1
2
1
0
0
1
1
1
2
1
0
1
1
1
1
1
1
1
1
1
1
1
1
0
0
1
1
1
1
1
0
1
1
2
2
1
1
2
2
1
1
2
1
1
1
0
2
1
1
2
1
1
1
1
1
1
1
0
2
0
1
1
1
1
1
0
1
1
2
0
1
1
1
2
1
1
1
1
2
1
1
2
1
2
2
1
0
0
1
1
1
0
1
1
1
1
1
1
2
0
1
1
2
0
0
1
1
2
2
1
2
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
2
0
2
1
1
1
1
1
1
1
1
0
1
1
1
2
0
2
0
1
2
0
1
1
2
0
2
1
1
1
1
2
1
1
1
2
1
2
2
2
2
1
1
0
0
0
0
1
1
0
1
1
1
2
1
1
0
1
1
2
1
2
2
0
2
1
1
1
1
2
0
1
1
2
1
1
0
0
0
1
1
2
1
1
2
1
2
0
1
1
0
1
2
1
1
2
0
3
1
0
2
0
2
0
1
2
1
2
2
0
1
1
2
1
1
1
0
1
2
1
1
1
1
1
1
1
2
2
2
1
0
2
1
2
0
2
1
2
1
2
3
2
2
2
1
3
2
1
0
1
2
1
0
1
1
0
1
0
1
1
0
1
2
2
1
0
1
2
2
1
1
1
1
0
1
0
2
0
1
1
1
1
1
1
2
2
0
1
2
2
1
2
0
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
0
2
2
1
1
1
3
1
0
1
1
1
2
2
1
2
0
1
3
1
0
2
1
2
2
0
1
1
0
2
2
1
2
1
2
1
1
1
2
0
1
1
0
1
0
1
2
2
1
2
0
0
0
1
0
1
1
1
0
2
1
1
1
1
2
0
2
1
1
1
2
1
1
1
0
1
0
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
0
1
1
2
1
1
1
2
1
1
0
1
1
1
1
2
2
1
1
0
1
1
1
1
1
1
1
1
2
0
1
2
2
1
1
1
1
0
2
1
0
1
1
1
0
1
1
0
1
2
1
2
3
0
1
1
1
0
0
0
1
1
2
2
1
0
1
2
1
0
0
1
1
1
2
1
1
1
1
0
0
1
1
1
1
1
1
2
1
1
0
2
1
1
1
2
2
1
0
0
1
1
2
1
1
1
1
1
1
1
1
1
2
0
2
1
2
2
1
0
2
2
1
1
1
0
1
2
1
2
1
2
1
2
1
1
1
1
1
1
2
2
0
2
1
1
0
1
2
1
1
1
1
2
1
1
0
1
0
0
1
1
1
1
1
1
1
0
1
1
1
2
1
2
2
0
1
1
1
2
1
0
0
0
2
2
2
1
2
2
0
0
1
0
2
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
0
2
1
1
1
0
1
1
1
1
2
2
1
0
0
2
1
2
1
1
2
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
2
2
1
1
1
1
1
0
1
1
1
1
2
1
0
1
1
0
1
1
2
1
2
1
2
0
2
1
0
0
1
1
1
1
1
1
2
2
1
1
1
1
1
1
0
1
1
2
1
0
0
2
0
1
1
0
1
1
0
1
1
1
0
2
2
1
0
0
1
1
1
0
1
1
1
1
1
1
2
1
1
2
0
2
1
1
1
1
2
1
0
1
1
2
1
2
2
1
2
1
2
0
1
0
0
1
2
1
1
0
1
2
1
1
0
0
1
0
1
0
1
1
1
2
1
1
2
1
1
0
1
1
2
1
1
1
2
2
1
1
1
2
1
1
2
0
1
2
1
2
1
0
1
2
2
1
1
1
1
1
2
0
1
1
1
1
1
1
2
0
2
1
1
1
2
2
2
1
1
1
1
1
3
1
0
1
1
1
1
1
2
2
2
1
2
1
0
0
0
1
1
1
1
0
2
1
2
1
1
2
1
0
0
2
1
0
1
1
1
1
1
3
1
2
1
1
1
1
1
2
1
2
4
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
0
1
1
1
0
0
1
2
3
1
1
1
1
2
0
2
2
0
1
0
1
1
1
0
1
2
1
1
2
2
1
1
1
1
2
1
1
1
0
1
2
1
1
1
2
1
0
1
1
1
1
2
1
2
1
1
0
1
0
1
2
0
2
0
1
3
2
2
1
1
1
1
2
2
0
0
2
2
1
3
1
2
0
1
1
1
2
1
2
0
2
1
2
1
1
1
1
2
2
0
0
2
1
1
1
1
2
0
1
1
2
1
1
1
2
1
0
2
2
0
0
1
1
0
0
2
2
2
1
1
1
0
1
0
1
1
0
0
1
0
0
2
0
1
0
1
1
1
1
1
1
1
1
2
1
1
2
0
2
0
2
1
1
0
2
2
1
1
1
0
1
1
1
0
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
0
1
1
0
2
0
2
1
1
2
1
1
1
1
1
0
2
1
1
1
1
2
1
0
0
0
1
2
1
1
1
1
2
0
2
1
1
1
2
1
1
1
1
2
1
0
1
0
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
2
1
1
1
2
0
0
1
1
1
1
2
2
1
1
1
3
1
1
2
1
1
1
2
2
0
1
1
1
1
1
2
2
2
0
1
1
1
2
1
1
1
0
1
2
1
1
1
1
1
1
2
0
0
1
1
1
0
2
1
1
1
2
0
1
1
2
2
2
1
0
1
1
1
1
0
1
1
0
1
1
2
2
2
0
1
0
1
0
2
0
1
0
0
1
1
1
2
1
0
1
1
2
2
2
1
0
0
0
0
1
1
1
1
0
1
1
1
2
1
1
2
0
1
1
0
1
1
1
1
1
1
1
2
1
1
0
1
1
1
1
2
0
2
0
1
1
2
1
0
0
1
2
2
1
0
0
1
0
1
1
2
1
1
1
1
1
1
2
1
2
1
2
1
1
0
1
2
2
2
2
0
1
1
2
0
1
1
2
1
1
1
1
1
1
1
2
0
0
1
1
1
1
1
1
0
2
2
0
0
1
2
0
1
1
1
1
0
1
2
1
1
1
1
2
1
2
0
2
2
1
1
1
1
1
2
1
1
0
0
2
1
0
0
1
2
1
1
1
0
2
2
0
1
1
1
1
1
1
1
0
0
1
2
1
2
1
1
1
2
2
1
2
2
2
1
1
1
2
1
1
1
1
1
1
1
0
1
0
1
1
1
1
0
2
0
1
1
0
1
1
1
2
2
1
1
1
2
3
1
1
1
0
0
1
1
1
1
1
1
0
1
1
1
0
1
0
1
2
2
0
1
1
0
1
1
1
1
1
2
1
3
1
0
1
1
2
1
1
0
1
1
1
2
0
2
1
1
1
1
1
0
1
2
2
1
1
1
1
0
1
1
2
1
1
1
1
1
1
1
1
1
1
0
1
2
1
0
0
2
1
1
1
1
1
2
0
1
0
0
0
1
1
1
2
1
1
1
2
1
1
0
2
1
1
1
1
1
1
0
2
2
1
0
1
1
0
1
1
2
0
1
2
1
1
1
1
2
2
2
1
0
0
1
2
1
1
1
1
1
1
3
0
2
1
1
1
1
2
1
1
1
1
0
2
0
0
1
1
2
1
1
1
1
1
1
2
0
2
1
1
1
2
2
1
1
0
1
0
1
2
0
1
1
2
2
1
2
2
1
1
2
1
0
1
1
1
1
1
1
1
0
2
2
2
1
2
1
1
1
1
1
2
1
2
2
1
1
1
1
1
1
2
1
1
0
1
1
0
1
1
1
1
1
2
0
1
0
1
1
1
1
2
1
0
1
1
1
1
1
2
1
1
1
2
2
0
2
1
1
1
0
2
1
1
1
1
2
1
0
1
0
1
1
1
2
1
0
2
0
1
1
1
2
1
1
1
2
1
2
0
1
1
1
1
2
1
2
1
1
2
1
1
1
0
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
0
1
1
1
1
2
2
2
0
2
1
0
2
1
1
0
1
1
0
2
1
1
0
2
1
0
0
1
1
1
1
2
0
2
1
2
2
0
0
1
1
1
1
1
2
2
1
1
1
2
1
1
1
2
1
0
1
1
2
1
1
1
1
0
0
2
0
2
1
2
0
1
1
0
1
1
1
1
2
1
1
2
0
1
1
2
1
1
0
2
1
1
2
1
1
0
0
1
1
1
1
1
2
1
1
2
1
1
0
1
1
1
1
1
1
0
1
1
1
1
2
0
0
2
2
1
2
1
1
0
0
2
1
0
0
0
1
2
1
0
2
1
1
1
0
1
2
1
0
2
2
1
0
1
1
2
2
1
0
1
1
2
2
2
0
1
1
2
1
2
1
0
3
1
0
1
0
1
1
2
1
1
1
0
0
0
2
2
1
1
1
1
2
2
1
0
1
1
0
1
2
1
2
1
0
2
1
2
1
0
1
2
1
2
0
1
1
2
6
1
1
1
2
2
1
1
2
2
2
1
1
0
0
1
1
1
2
2
1
1
1
0
0
0
0
1
1
1
1
2
1
1
0
1
0
1
0
1
1
1
1
1
1
2
0
2
1
1
0
1
1
1
1
0
1
0
1
2
1
0
1
1
1
1
2
2
1
1
2
1
1
1
3
1
1
1
1
2
1
1
1
2
2
2
0
2
1
1
2
0
1
1
1
2
1
1
2
1
1
1
0
0
1
0
1
2
1
1
0
2
1
2
0
0
2
2
0
0
2
1
1
1
2
0
2
1
0
1
1
2
1
1
1
0
2
2
1
1
1
1
1
1
1
2
0
2
2
0
1
2
1
1
1
0
1
2
1
1
1
1
1
1
3
0
1
1
1
1
1
1
2
2
1
1
2
2
1
0
1
2
1
1
1
1
1
0
1
2
2
1
1
1
1
1
1
1
2
2
1
1
2
1
1
2
2
1
1
2
0
2
0
1
0
1
1
2
1
2
1
2
1
1
1
1
1
1
1
1
1
2
2
1
1
1
2
2
2
0
1
1
1
2
0
1
2
1
1
1
1
0
1
1
0
1
1
2
2
1
1
1
1
1
1
0
1
0
1
1
1
1
2
2
2
1
1
0
1
2
2
1
1
1
1
0
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
0
1
1
1
1
1
0
1
2
1
1
2
1
2
1
1
0
1
1
0
1
0
1
1
1
2
1
1
1
0
1
1
1
2
2
0
2
2
1
1
1
1
2
1
1
1
1
0
2
1
0
1
2
1
2
1
1
1
1
2
1
1
1
1
1
2
2
1
1
1
1
1
2
1
0
2
1
0
1
2
1
1
0
0
1
1
2
0
2
1
2
1
2
1
1
1
1
2
2
1
1
1
1
2
0
2
1
1
1
1
0
0
1
1
1
2
1
2
2
1
1
1
2
1
1
1
1
2
1
1
1
2
0
1
1
0
1
0
1
0
2
0
1
1
0
0
1
2
1
1
2
1
2
1
1
1
2
2
2
3
1
1
0
1
1
0
0
1
0
0
1
1
0
1
2
1
1
1
0
1
1
2
1
1
1
1
1
1
1
1
0
1
1
0
1
0
1
1
1
1
1
2
1
2
1
1
1
1
1
1
2
1
0
1
1
1
1
1
2
1
1
1
1
2
0
2
1
1
2
0
1
1
2
1
1
2
1
0
0
1
1
1
1
2
1
0
0
1
2
1
11
0
1
1
0
1
1
1
0
0
2
2
1
0
0
2
1
1
1
1
1
1
0
1
1
1
1
2
0
1
1
2
1
1
1
2
1
1
1
1
1
0
1
1
0
1
1
2
1
2
1
2
0
0
0
2
2
1
1
1
0
1
1
2
2
0
1
0
2
1
1
1
1
2
2
0
1
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
0
1
0
1
2
0
1
2
1
2
2
1
1
1
1
1
1
1
1
2
1
1
1
2
0
1
0
1
2
1
0
2
1
1
0
1
2
0
1
1
1
1
2
1
0
2
1
0
0
2
1
0
1
0
1
1
1
1
2
2
0
1
1
1
1
1
2
1
2
1
1
0
2
0
2
1
2
2
0
1
1
1
1
1
1
1
1
2
1
0
1
2
2
2
1
1
0
1
1
1
1
0
0
4
0
2
0
1
1
1
1
2
0
0
1
1
1
0
1
2
0
1
2
1
1
1
1
1
2
1
1
0
2
3
2
1
2
1
1
2
0
1
1
0
1
1
2
1
1
0
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
2
1
2
2
2
1
2
1
1
1
1
1
1
0
1
2
0
2
1
1
1
0
1
1
1
1
1
1
1
1
1
0
1
1
2
1
2
1
1
1
1
1
2
1
1
1
0
1
1
0
2
1
0
1
0
0
1
2
1
0
1
0
1
2
2
1
1
2
3
2
1
1
1
0
1
2
2
1
2
1
0
1
0
1
1
0
1
0
1
1
1
1
1
1
0
0
1
1
0
1
1
4
2
0
2
2
1
2
1
2
2
2
1
0
2
1
1
1
2
1
1
1
0
1
1
1
1
1
1
1
1
1
1
2
2
1
0
0
2
0
1
1
0
1
2
1
1
0
1
1
1
2
1
2
1
0
1
2
2
0
2
2
1
1
1
1
1
2
2
1
1
1
1
1
0
1
2
1
0
1
1
2
1
0
1
0
1
0
1
1
1
2
2
1
0
0
1
1
1
0
3
2
1
0
1
1
1
2
2
1
1
1
1
1
1
0
2
1
2
1
1
1
0
2
2
2
0
2
2
1
1
2
1
2
1
1
1
2
2
2
1
1
2
2
1
1
1
1
2
0
1
1
0
1
0
0
1
1
1
1
1
2
1
1
2
1
1
0
2
1
2
1
0
1
5
2
1
2
1
0
2
1
2
1
1
2
1
1
1
2
2
1
2
0
1
1
2
1
1
0
0
1
1
1
2
1
1
2
2
2
1
1
2
1
2
2
1
1
1
1
1
1
2
1
2
1
2
2
1
1
1
2
2
2
2
2
0
1
1
0
1
2
1
1
1
0
1
1
1
1
2
0
1
0
2
1
1
0
0
0
1
2
2
0
2
1
1
2
1
1
1
2
1
2
1
1
0
1
1
2
1
1
1
2
2
0
0
0
2
1
1
1
0
1
2
1
2
0
1
0
1
2
0
2
0
1
1
1
2
1
2
1
2
0
1
3
1
0
2
1
1
2
1
1
1
2
0
1
2
0
1
1
2
1
0
1
2
1
0
1
0
2
1
1
2
2
1
2
1
0
0
1
1
1
1
1
1
1
1
0
0
1
2
2
0
1
1
1
2
1
1
0
2
2
1
0
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
2
1
2
1
0
1
2
1
1
1
0
1
1
2
1
1
1
2
3
2
2
0
2
1
1
0
0
0
0
3
1
1
2
0
1
1
1
1
0
0
2
1
1
2
1
1
2
1
2
0
1
1
1
2
1
1
2
1
2
0
1
1
2
1
1
0
2
0
1
1
1
0
0
1
2
2
2
0
1
1
1
1
1
0
1
1
1
1
0
1
1
0
0
1
1
1
1
2
0
1
0
1
1
0
1
1
1
2
2
1
2
0
1
1
1
1
2
1
1
1
1
1
2
1
1
0
1
0
2
1
1
2
2
2
2
0
2
1
2
1
1
1
1
1
1
0
2
1
1
2
1
1
1
1
2
1
1
0
2
1
0
1
1
1
0
1
0
1
2
1
2
1
2
0
2
0
1
1
0
1
2
1
1
1
2
1
1
0
0
2
1
1
1
2
1
1
1
1
0
1
2
1
1
1
1
1
1
0
1
2
2
1
1
1
1
1
0
1
0
2
0
1
1
1
1
1
2
2
2
2
1
1
1
2
2
1
1
1
2
1
2
1
1
1
3
1
2
2
1
2
1
1
1
0
1
0
1
1
1
2
2
1
2
2
2
0
2
0
1
1
1
0
1
0
1
2
1
1
0
1
1
1
3
1
1
1
0
1
0
1
1
1
2
1
0
2
0
2
2
1
0
1
1
1
1
2
2
1
1
1
2
1
0
1
2
1
1
2
0
1
1
1
1
1
1
1
1
2
0
2
1
1
1
1
1
3
2
1
0
1
0
1
1
1
2
2
1
2
0
1
1
2
1
1
0
1
2
1
0
1
1
1
1
0
0
0
1
1
1
0
1
1
0
2
1
1
1
1
1
2
1
1
1
2
2
1
1
1
0
1
2
0
1
1
0
1
2
1
0
1
1
1
1
1
2
1
1
2
0
0
1
1
0
1
1
1
2
1
1
1
1
2
1
2
1
1
0
1
2
0
1
1
1
2
1
1
1
1
0
1
1
5
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
0
2
1
0
1
1
1
1
1
2
1
1
0
2
2
1
1
0
2
0
2
1
2
1
0
0
2
1
1
2
2
1
1
0
0
1
1
2
1
2
0
1
2
0
1
2
1
1
0
2
1
0
1
2
2
1
1
1
1
1
1
1
1
1
1
0
2
1
1
1
1
2
1
1
1
1
2
2
1
1
2
1
1
1
1
2
1
1
0
2
1
1
1
1
1
1
1
0
1
0
1
0
1
1
0
0
1
0
1
2
1
2
1
1
1
2
2
1
2
1
1
1
0
0
2
0
1
3
1
0
2
1
0
1
0
1
0
1
1
1
2
2
1
2
1
1
0
2
1
0
1
1
1
1
2
1
1
6
2
2
1
1
1
2
0
2
1
0
2
1
3
0
1
1
1
2
1
1
2
0
1
1
0
1
2
1
2
0
0
2
2
2
1
0
1
1
2
2
1
1
1
0
0
2
1
2
0
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
0
2
0
0
1
0
1
2
3
1
0
2
2
1
1
2
0
1
2
2
1
2
1
1
1
1
2
1
2
2
1
1
2
1
1
1
1
1
1
0
2
1
1
1
1
1
1
1
0
11
2
1
1
1
0
1
0
1
0
1
2
2
2
1
1
1
1
2
1
0
2
1
2
1
1
2
1
0
1
2
1
1
2
1
1
1
0
1
0
0
1
1
1
2
0
2
0
1
1
1
1
1
1
1
1
2
2
2
1
0
1
0
2
1
2
1
0
1
1
1
2
1
1
1
1
1
2
1
1
1
0
1
1
0
1
1
1
2
2
0
2
1
1
1
2
1
1
0
0
1
2
2
2
1
2
0
1
1
1
1
0
1
0
1
1
0
2
1
0
1
1
0
1
0
1
2
1
1
2
2
1
1
1
1
0
0
1
1
0
0
2
1
1
2
1
2
1
1
0
1
1
1
2
1
1
2
2
2
1
0
0
0
1
1
1
0
0
1
1
2
1
2
2
0
1
0
1
2
0
1
1
1
2
1
1
0
1
0
0
2
1
1
1
0
1
1
1
1
2
2
1
0
1
1
1
1
2
0
0
1
2
1
0
1
2
1
1
1
1
0
2
1
2
0
2
2
4
2
2
1
0
1
1
1
1
1
0
1
1
1
1
2
1
2
1
2
1
2
1
1
1
0
1
1
3
0
1
1
1
2
1
1
0
1
1
1
0
0
0
1
0
0
1
1
0
2
1
0
1
1
1
0
2
0
1
1
2
0
2
1
0
1
1
1
1
1
1
2
0
2
0
1
1
0
1
1
1
0
1
1
2
1
2
0
0
1
1
1
1
1
1
0
1
1
1
1
0
1
2
1
1
1
1
2
1
1
1
0
1
1
1
1
1
0
1
1
2
2
2
1
1
0
2
1
1
0
1
1
0
1
1
2
1
0
0
2
1
0
0
1
1
0
0
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
1
1
1
1
0
2
2
2
1
0
2
1
0
2
0
1
2
0
2
2
1
1
2
1
1
0
1
0
1
0
0
1
2
1
1
1
2
1
1
2
1
1
2
1
1
2
1
1
2
1
2
1
0
2
1
1
2
2
1
1
0
1
2
3
2
0
2
1
2
0
2
0
0
2
2
1
0
1
0
2
1
1
2
1
1
1
1
2
0
2
0
1
1
0
2
2
1
2
1
1
1
2
1
2
1
0
0
1
2
1
2
1
1
0
1
1
1
1
1
1
1
1
1
1
2
1
1
2
0
2
1
0
0
1
1
1
1
1
2
1
1
1
0
0
1
1
0
1
1
2
1
1
2
1
1
1
1
1
0
0
4
1
1
1
1
1
0
1
2
1
1
1
0
2
1
2
0
1
1
1
1
1
1
1
1
1
2
1
1
0
3
1
1
0
2
1
0
0
1
1
0
1
0
0
0
2
0
1
2
1
1
1
1
1
2
1
0
1
2
1
2
2
2
1
2
1
0
1
2
2
0
1
2
2
1
1
1
2
2
1
1
1
0
0
1
0
1
1
1
1
0
1
1
2
0
2
0
1
1
1
1
1
2
1
1
1
2
1
0
1
1
1
0
4
0
1
1
1
2
2
1
2
1
1
1
0
2
2
1
0
2
1
2
2
0
1
1
1
1
1
2
1
1
0
1
2
1
1
1
1
0
1
1
1
1
1
1
1
1
0
0
1
1
1
1
2
1
1
0
0
0
2
1
1
0
1
0
1
2
1
1
1
1
1
2
1
1
1
0
1
0
1
2
2
0
1
1
0
1
1
1
2
1
0
3
1
1
2
1
1
1
1
1
1
2
1
0
1
1
0
1
2
0
1
1
0
0
1
2
0
1
1
1
3
1
1
1
1
1
2
1
0
0
1
1
2
1
0
1
2
1
1
1
0
1
0
1
1
2
1
2
1
0
1
0
1
2
1
1
1
1
2
2
3
2
1
1
1
1
1
2
0
0
1
1
1
0
2
1
0
1
1
0
0
1
1
1
1
0
2
1
2
0
1
0
1
1
1
7
1
1
2
0
1
1
1
0
1
0
1
2
1
1
1
1
1
2
2
1
1
1
1
1
0
2
0
1
1
1
0
2
1
0
2
2
1
1
0
0
0
0
2
1
1
1
1
1
1
1
0
2
1
1
1
2
2
2
2
1
1
1
0
1
1
1
1
2
2
0
2
1
1
2
2
1
1
1
0
1
0
0
1
1
2
0
0
1
2
1
1
2
2
1
2
1
1
1
1
2
0
1
1
1
0
0
0
1
1
2
0
1
0
1
1
0
1
1
2
1
2
2
1
1
1
1
2
2
0
1
1
2
1
1
1
1
1
2
1
1
2
2
1
2
0
1
1
2
1
0
1
1
1
3
0
1
1
1
0
1
1
2
1
2
2
0
1
2
1
1
1
1
1
1
2
1
1
1
2
2
1
1
2
1
1
0
0
0
1
1
1
2
1
0
1
1
2
2
1
1
0
0
1
0
1
2
0
0
1
1
1
1
1
1
2
1
1
1
0
1
1
1
1
1
1
2
2
2
1
1
1
1
2
0
0
1
1
1
2
1
2
1
1
2
2
1
0
2
2
0
0
1
1
1
2
0
1
2
2
0
2
0
1
0
0
1
1
2
1
1
2
1
0
1
1
2
0
0
0
2
0
1
2
2
2
2
2
0
2
1
1
1
2
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
0
0
2
2
0
1
0
1
0
2
2
1
1
1
1
0
1
1
1
1
1
1
0
1
1
2
1
0
1
1
1
1
0
0
2
0
1
0
1
1
2
1
0
0
2
2
1
0
0
2
2
0
1
1
1
0
1
3
1
2
1
1
2
0
1
0
2
1
1
1
1
0
1
1
1
1
2
0
2
1
1
1
2
1
1
1
2
2
1
0
1
1
0
2
0
2
2
1
1
2
2
1
1
1
1
1
1
1
1
2
1
4
1
1
0
1
0
1
1
1
0
1
2
2
0
1
0
1
1
1
1
2
1
3
2
1
0
2
0
2
1
2
2
1
2
2
0
2
2
2
1
0
1
2
1
1
2
1
1
1
0
0
1
0
1
0
0
1
1
1
2
2
1
0
2
1
1
0
1
0
1
1
1
1
1
1
2
1
0
2
2
0
2
2
1
2
1
1
1
2
2
2
1
1
1
1
0
1
1
0
2
1
1
0
2
1
2
1
1
0
1
1
2
2
1
1
2
2
1
2
1
1
1
1
2
1
1
1
1
1
1
2
1
2
2
0
1
1
0
2
1
1
0
0
0
1
1
1
1
1
1
1
1
1
2
1
1
1
0
1
0
1
2
1
1
1
1
0
1
0
2
1
2
1
0
3
1
1
1
1
1
0
1
1
1
1
1
1
3
1
1
1
0
1
2
1
2
1
0
2
2
1
1
2
1
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
1
0
1
2
0
2
0
2
1
0
0
1
1
0
1
2
1
1
0
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
0
1
1
1
3
1
1
1
2
1
2
0
1
2
1
1
2
1
1
1
2
1
1
0
1
1
2
1
1
1
0
0
2
1
2
3
1
0
2
2
1
0
1
2
1
1
1
1
1
0
1
1
2
1
0
1
1
2
2
2
1
1
1
1
1
1
1
1
1
1
0
1
1
1
2
2
1
1
1
1
0
2
0
1
1
2
1
1
1
5
2
1
2
0
1
1
1
1
1
2
1
2
0
1
2
1
2
1
1
2
1
0
1
1
1
1
2
2
1
1
1
1
2
1
1
1
2
1
1
0
0
1
2
1
0
2
2
1
1
1
0
2
1
0
0
0
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
0
1
1
2
1
1
1
1
2
1
0
1
2
1
1
0
0
2
2
1
1
1
1
1
1
0
1
1
1
1
0
1
2
2
0
2
1
0
1
1
1
1
1
2
0
1
1
2
1
0
2
1
0
2
1
1
1
0
1
1
0
2
2
0
1
1
2
1
1
0
1
2
2
2
1
2
1
1
2
1
1
1
1
2
1
0
2
1
2
1
0
1
0
0
1
1
1
2
2
1
2
1
0
1
1
2
1
2
1
2
1
2
2
1
2
1
2
2
0
1
2
1
2
1
1
1
1
1
1
1
1
0
1
0
2
2
1
1
1
1
1
1
0
1
2
1
1
1
2
1
1
2
1
2
2
2
1
1
2
0
1
1
1
1
0
0
1
1
2
2
2
1
1
1
0
2
1
2
1
2
2
1
1
3
1
0
1
1
2
1
1
1
1
1
1
2
1
2
1
1
2
2
1
0
1
1
1
2
2
0
1
1
1
1
1
1
1
0
1
1
1
1
1
2
1
2
1
1
0
1
1
1
1
0
1
1
1
2
1
1
2
2
2
2
0
1
0
2
0
2
2
2
1
1
2
1
1
1
1
1
2
1
1
2
1
0
2
1
0
1
1
0
1
2
1
0
1
1
1
1
2
1
1
1
1
1
1
0
2
0
1
1
1
1
1
1
1
1
1
1
2
1
1
0
1
1
3
2
1
2
0
1
1
2
2
1
1
1
2
2
1
1
1
1
1
1
2
2
0
1
1
2
2
1
2
0
2
1
1
2
1
1
1
2
1
1
1
1
1
2
1
1
1
0
2
2
1
2
0
1
2
1
1
0
2
1
1
1
0
2
2
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
2
1
0
2
1
0
2
2
0
1
2
0
1
2
1
1
2
1
2
1
1
1
1
1
1
2
0
1
0
1
1
2
1
0
1
1
1
1
0
1
2
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
0
2
2
1
0
0
2
0
0
0
1
2
1
1
2
0
2
0
2
1
1
0
1
0
1
2
1
1
1
1
1
1
2
1
1
0
1
1
3
2
1
1
1
1
1
1
1
1
2
1
0
1
1
2
1
1
1
2
1
0
1
1
1
1
1
0
1
1
1
1
1
1
1
1
0
2
1
2
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
2
0
1
0
1
2
1
1
1
2
1
1
0
1
1
1
0
1
1
1
0
1
2
1
2
0
1
0
0
2
2
1
1
1
1
2
1
0
1
1
1
1
1
1
1
1
1
2
2
2
0
1
1
1
0
2
1
0
2
1
0
1
1
2
1
1
2
2
1
1
2
1
0
1
1
0
2
1
1
1
2
1
0
0
1
1
1
0
1
1
0
1
0
1
2
1
1
3
1
1
2
2
1
2
2
2
0
2
1
1
3
1
0
2
2
2
1
0
1
1
2
0
1
1
0
1
1
1
1
2
1
1
1
2
1
2
1
0
1
2
0
1
2
0
1
2
1
1
1
0
0
1
1
1
0
1
1
1
2
2
1
1
1
2
2
2
1
1
1
2
1
1
0
1
1
0
1
1
0
1
1
2
1
1
2
2
2
2
1
1
2
1
2
1
0
1
1
2
1
1
1
0
1
1
2
1
1
1
1
1
0
1
1
0
1
0
1
1
1
1
0
1
0
1
2
2
2
2
0
0
1
0
2
1
1
0
1
1
1
1
1
1
0
1
1
1
1
1
0
1
2
1
3
1
1
2
1
1
1
0
1
2
2
0
0
0
0
1
1
1
2
1
0
1
1
1
1
2
1
1
1
1
1
0
1
1
2
0
0
1
2
1
1
1
1
1
2
1
1
1
2
1
2
1
2
2
1
1
2
1
1
1
1
1
2
1
2
1
1
1
0
2
2
1
1
1
1
0
0
1
2
1
0
1
1
1
1
1
1
2
1
1
2
1
2
2
0
2
1
2
1
1
1
1
1
2
1
1
1
1
1
1
0
0
0
1
0
0
2
1
2
1
2
1
2
0
2
1
2
2
1
2
2
1
1
0
1
0
1
2
1
1
1
1
2
0
1
0
1
1
2
1
0
0
1
0
1
1
0
1
0
1
1
0
1
1
1
1
1
2
1
1
1
1
1
1
1
0
1
1
0
2
1
1
0
1
1
1
1
1
1
1
1
1
0
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
0
2
1
1
1
0
1
1
1
4
1
0
1
1
0
0
1
1
1
2
1
1
0
0
1
2
0
0
0
1
1
2
1
1
1
1
0
1
1
0
1
1
1
1
0
1
1
1
1
2
1
1
2
2
1
1
2
1
1
0
1
2
0
1
1
1
1
2
1
2
1
0
1
1
1
1
1
0
0
0
2
0
2
2
0
2
0
1
1
1
2
1
2
1
1
2
2
0
1
0
0
1
1
0
1
2
0
1
1
1
0
2
1
1
1
2
0
2
1
3
1
0
2
1
0
2
1
1
2
1
2
0
1
1
1
0
1
2
1
1
1
1
2
0
1
1
1
0
1
2
1
2
0
2
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
2
1
2
1
1
0
1
0
1
2
1
0
1
1
1
1
0
1
1
2
0
1
1
1
0
2
2
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
2
1
2
2
0
1
1
1
2
1
2
1
2
1
0
1
1
1
1
2
0
1
2
1
1
0
1
1
1
1
1
0
1
2
1
1
1
2
1
1
1
1
1
2
2
1
1
1
2
1
0
2
2
2
1
0
2
1
1
0
1
2
0
1
1
1
1
1
1
1
2
1
2
2
2
2
1
2
0
1
1
1
2
1
2
2
1
1
0
1
1
0
1
1
1
1
1
2
1
2
2
2
1
2
2
1
1
1
1
0
0
0
1
1
1
1
1
2
2
0
1
2
1
1
0
2
0
4
1
0
2
2
3
2
0
1
2
1
1
0
1
2
2
1
1
2
0
1
1
1
1
2
0
2
2
1
1
1
2
0
0
1
1
1
1
2
1
2
1
1
1
2
0
1
1
2
1
1
1
2
1
1
1
0
1
1
1
0
1
3
1
1
2
1
1
1
2
2
0
0
2
2
1
1
0
1
1
2
1
2
1
1
1
2
1
1
1
1
2
0
1
2
2
2
1
2
2
1
0
1
0
1
2
0
1
0
1
1
1
2
1
1
0
0
2
3
1
0
1
1
1
1
1
0
1
1
0
2
2
0
1
2
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
2
1
1
1
1
1
0
0
2
1
1
1
1
0
1
1
2
0
1
1
0
2
1
1
1
1
2
1
2
1
1
1
1
2
2
1
1
1
1
2
1
0
1
2
0
1
0
1
1
2
2
2
0
1
2
1
2
0
2
1
2
1
0
2
1
1
1
2
1
2
0
1
1
2
1
0
1
1
1
0
0
1
2
1
1
1
1
1
0
1
1
2
1
1
2
2
2
0
2
2
1
1
2
1
1
0
1
1
1
1
0
1
2
0
2
3
1
2
1
1
1
1
2
1
1
1
2
1
1
1
2
0
1
1
1
1
1
0
2
0
2
1
1
0
1
1
1
1
0
0
2
1
0
1
1
1
1
0
0
2
1
1
0
1
2
0
2
0
0
1
2
1
1
0
0
1
1
1
1
1
1
3
1
1
2
0
0
2
0
1
2
0
2
1
1
2
1
1
2
1
1
2
1
1
0
1
0
2
2
1
1
2
0
0
1
1
1
1
3
0
1
1
0
0
0
0
2
1
2
2
1
2
2
1
2
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
2
2
0
1
1
0
2
1
1
1
0
2
1
2
2
1
1
1
0
2
1
1
2
1
1
1
1
1
0
2
0
1
2
1
1
1
2
1
1
1
1
0
2
1
2
1
1
1
1
1
0
1
1
1
1
2
1
1
1
2
0
1
1
2
0
2
1
1
1
2
2
1
1
0
1
1
1
1
2
1
0
1
2
1
1
1
1
1
2
2
1
1
2
1
1
3
2
2
1
1
0
2
1
2
1
1
2
1
1
1
1
1
1
0
1
1
0
1
2
1
0
1
2
1
0
1
1
1
2
1
2
1
1
0
3
0
1
2
1
0
1
1
2
1
1
1
2
0
0
2
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
1
2
0
0
0
2
1
1
1
0
2
1
1
1
1
2
1
0
2
1
0
1
1
1
1
0
1
1
1
1
2
2
1
0
1
1
1
2
0
2
0
1
2
1
1
1
1
2
2
2
2
0
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
0
2
0
1
1
1
0
1
2
1
1
1
2
1
1
2
1
1
2
1
1
1
1
2
2
2
1
1
2
1
1
0
2
1
1
0
1
2
0
0
1
2
1
1
1
1
0
0
1
1
0
0
2
0
1
1
0
0
1
1
1
1
0
2
1
2
0
0
0
1
1
1
1
1
2
1
1
1
1
0
1
1
1
1
0
1
2
0
1
1
0
1
2
1
1
1
0
1
2
2
1
2
0
1
1
1
1
1
2
1
3
1
2
1
1
3
0
1
1
2
2
2
1
2
1
2
1
1
1
1
2
0
0
1
1
1
1
1
1
0
1
2
3
1
1
1
2
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
0
0
1
0
2
1
0
1
0
2
1
1
1
2
1
1
1
2
2
1
3
1
0
1
1
0
0
0
0
1
1
2
1
1
2
1
1
1
1
1
1
1
0
2
1
1
1
1
1
2
1
2
1
2
1
1
1
0
2
1
1
1
0
1
2
1
2
1
1
1
0
3
1
1
1
1
2
2
1
2
1
1
2
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
2
1
0
1
1
0
1
2
1
1
1
2
1
1
2
1
1
2
1
0
1
1
2
1
1
0
1
2
1
1
1
1
1
1
1
3
1
0
1
1
1
0
2
1
2
1
0
1
1
2
2
0
1
1
2
1
1
3
1
1
2
1
0
1
0
1
0
1
1
1
0
0
1
2
1
2
0
0
0
0
1
1
1
2
1
2
1
2
1
0
0
1
1
1
0
0
1
1
1
2
2
2
1
1
0
0
0
2
1
1
1
1
0
1
1
1
1
2
1
1
0
0
2
1
1
1
1
1
1
1
1
2
1
1
1
1
3
1
0
2
1
1
1
1
1
1
3
2
1
1
0
1
1
1
1
0
1
2
1
1
1
1
0
2
1
0
1
1
1
1
1
1
1
1
2
1
2
0
1
1
2
0
1
1
2
0
1
2
0
1
1
1
1
0
0
1
0
2
1
2
1
0
2
1
5
1
1
2
1
1
1
1
2
1
1
1
2
1
1
2
0
1
0
1
2
1
0
0
2
1
2
1
1
1
1
2
2
1
2
1
0
1
1
0
1
1
0
2
1
2
1
1
0
1
1
1
1
0
1
0
0
1
1
1
1
1
1
0
0
2
1
1
1
2
1
1
2
0
1
1
1
1
1
1
1
1
1
0
0
2
2
0
2
1
1
2
1
1
0
1
1
1
1
1
0
3
1
1
2
2
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
1
2
1
1
0
1
0
1
2
1
1
2
2
1
0
0
1
1
2
1
1
2
1
0
1
1
1
1
1
1
2
2
0
2
1
1
1
1
1
1
1
1
2
0
1
0
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
0
1
1
1
2
2
0
0
1
0
1
2
0
2
1
1
3
1
2
1
1
1
1
1
0
1
1
2
0
1
0
2
0
1
1
0
1
2
0
0
2
2
2
1
1
2
1
1
1
2
0
1
1
2
1
1
1
1
1
1
1
0
1
2
2
2
1
1
0
0
1
3
1
1
1
2
1
1
2
0
0
1
1
1
1
0
1
1
1
0
1
1
2
1
2
1
1
2
1
1
1
2
1
1
1
0
1
1
0
1
1
0
1
3
2
0
1
0
1
1
1
1
0
1
2
1
1
2
1
2
1
0
1
2
1
0
1
2
1
1
1
1
0
1
1
1
1
1
1
2
1
1
1
2
2
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
0
2
1
2
1
1
1
0
2
1
1
2
1
0
0
1
2
1
1
1
1
0
2
1
1
0
0
0
1
2
1
1
1
0
1
0
2
0
1
0
1
1
1
1
2
2
1
1
1
0
0
2
0
1
2
1
1
1
0
2
1
1
0
2
0
1
1
1
0
1
1
1
0
1
2
1
1
0
1
2
1
1
1
2
1
1
1
1
2
1
0
1
2
0
1
1
1
1
1
1
0
0
2
2
2
0
1
2
1
1
1
1
0
1
1
1
1
0
2
1
2
1
1
1
0
1
1
1
1
1
1
2
2
1
2
2
1
1
1
2
0
1
1
1
2
3
1
1
1
2
1
1
1
1
1
1
1
2
1
1
2
0
1
1
1
1
0
1
2
0
1
1
1
2
0
1
1
0
1
0
2
0
0
3
0
0
1
1
1
1
0
1
2
1
2
1
1
0
0
2
2
1
1
2
1
2
2
1
2
1
1
1
2
2
0
0
1
1
0
1
1
1
0
1
1
1
1
1
2
1
2
1
0
1
1
2
1
1
0
1
0
0
1
1
2
0
1
2
1
2
1
0
3
1
2
1
1
0
0
1
0
1
2
2
1
3
2
2
2
2
2
0
2
2
1
2
0
0
2
1
1
2
1
2
1
1
1
1
1
2
1
1
1
0
1
1
0
2
2
1
0
0
2
2
1
1
1
2
2
1
1
2
1
0
1
1
1
1
0
1
2
1
0
0
1
1
1
1
1
1
2
1
1
1
0
2
1
0
1
1
1
2
1
1
1
0
2
1
1
1
1
1
1
1
1
1
2
2
1
1
0
0
1
1
1
1
0
0
0
0
1
2
1
2
2
2
1
1
0
0
1
0
1
1
1
2
0
1
2
0
0
2
2
2
1
0
0
2
1
1
0
1
1
1
2
1
1
1
0
1
1
1
2
2
2
1
0
1
2
1
2
2
0
1
2
1
1
2
1
0
1
1
0
2
1
1
0
1
1
2
1
1
1
1
1
1
0
1
0
2
1
1
0
1
1
0
1
1
1
1
1
1
1
2
1
1
1
0
1
2
1
1
2
0
1
0
1
1
1
1
1
1
2
2
1
0
0
1
2
2
0
1
2
1
1
1
1
0
1
2
2
1
0
0
1
0
2
1
1
2
0
1
1
2
1
1
0
1
2
1
2
0
1
1
2
1
2
1
1
1
2
1
0
2
2
1
1
0
1
1
1
2
2
1
1
2
1
1
1
1
1
2
1
1
1
1
2
0
1
0
2
1
1
1
1
1
0
1
1
2
0
0
0
1
1
1
2
2
2
2
1
1
1
1
1
2
0
0
3
1
1
0
1
1
1
1
2
1
1
1
1
0
2
1
1
1
1
1
2
2
1
1
0
2
1
2
1
1
0
1
2
1
1
2
1
2
1
1
2
1
2
2
1
1
0
2
1
1
1
1
1
1
0
2
1
0
2
1
0
1
1
2
1
0
1
1
1
2
1
1
2
1
1
1
1
2
0
2
0
2
0
2
1
1
1
2
1
0
2
1
1
2
3
1
1
1
0
1
1
1
0
0
2
2
1
1
2
2
1
1
2
1
1
0
0
4
1
1
1
1
2
1
1
1
1
2
6
1
1
1
1
0
1
1
2
2
1
1
2
1
1
0
0
0
1
0
2
2
2
2
1
2
1
1
0
1
2
2
2
1
1
2
1
1
2
1
1
1
2
0
2
1
0
1
2
2
1
1
2
1
1
1
1
2
2
1
1
0
1
0
2
1
2
0
2
1
0
1
2
1
1
2
1
2
1
1
1
0
0
2
1
1
2
1
3
2
1
1
1
1
2
0
0
1
2
2
0
1
1
0
2
1
1
0
1
1
1
2
1
2
0
3
2
2
1
1
0
2
2
1
0
2
2
1
1
0
1
1
1
1
1
1
1
1
2
1
1
2
0
0
1
1
4
0
1
0
2
2
1
0
0
1
1
0
1
1
2
2
0
1
1
1
1
1
2
0
0
1
0
2
1
1
1
2
1
2
1
1
1
1
1
1
1
1
0
2
0
1
1
1
2
1
1
1
2
0
1
0
1
2
1
1
1
0
0
1
1
1
1
1
0
0
0
2
2
0
1
0
1
2
1
1
0
1
1
1
2
1
2
1
0
1
1
2
1
2
1
2
0
1
1
1
2
2
2
2
1
1
0
1
1
1
1
0
1
1
2
1
2
1
0
1
1
1
1
0
0
0
1
1
1
2
1
1
1
1
2
1
1
1
2
2
1
1
0
1
1
0
0
1
1
1
2
0
2
1
0
1
0
1
0
1
1
2
2
1
0
1
0
2
0
2
1
2
1
1
1
2
2
1
1
0
1
0
1
1
1
2
1
0
1
1
1
1
2
1
2
3
1
2
0
1
1
0
2
1
1
1
0
2
1
1
2
0
1
2
0
0
2
1
1
1
1
2
2
0
1
1
0
1
2
0
1
1
2
1
2
2
1
1
1
2
1
0
0
1
1
2
2
0
1
1
2
1
1
1
1
1
1
1
1
0
2
2
1
1
1
1
2
1
1
1
0
2
1
1
1
3
1
1
2
1
1
1
1
1
1
2
0
0
1
2
1
1
1
1
1
2
2
2
1
1
0
1
1
0
1
1
1
1
1
0
2
2
1
0
1
1
1
1
1
1
2
1
1
2
1
2
2
1
1
1
1
2
2
1
2
1
1
1
2
2
0
0
0
2
0
1
2
1
1
1
1
2
1
2
2
1
1
1
0
1
2
0
1
2
1
1
1
1
1
1
1
1
1
2
1
1
0
2
1
2
0
1
1
2
1
2
2
1
1
1
1
1
1
1
2
1
1
0
0
1
1
1
1
2
0
1
1
1
2
0
1
1
1
2
1
1
0
2
1
0
1
2
1
1
1
0
1
0
0
2
1
1
2
2
1
1
1
3
1
1
1
1
1
0
1
2
1
2
0
0
1
1
1
2
1
1
1
1
2
2
1
1
0
2
2
1
2
0
1
0
2
1
2
2
1
1
1
1
0
1
1
2
2
1
1
1
1
1
1
1
1
2
1
0
1
0
1
0
1
2
0
0
1
1
1
2
2
1
1
0
1
1
1
2
2
1
1
0
0
0
0
2
2
1
1
2
1
2
1
1
2
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
0
1
1
2
2
1
1
1
1
0
1
1
2
0
1
1
0
1
0
1
2
1
2
1
1
2
1
2
2
1
1
0
2
0
1
1
1
1
1
0
1
2
1
1
0
2
1
1
2
0
1
1
1
2
1
1
1
1
1
1
0
2
1
1
2
1
2
1
1
2
1
1
1
0
1
2
1
0
1
2
1
0
1
1
1
0
2
1
2
1
1
1
0
0
2
1
1
1
1
1
0
1
2
1
1
1
2
1
1
1
1
1
2
1
1
1
0
1
1
2
1
1
5
1
1
2
1
2
2
1
2
1
1
1
1
1
1
1
1
2
2
1
2
1
2
1
1
0
1
1
1
1
1
0
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
0
0
2
0
0
2
2
1
2
2
1
2
2
1
1
1
0
1
1
1
2
2
0
1
0
0
2
2
0
1
1
1
1
2
0
1
1
1
2
1
2
0
0
1
1
2
2
1
2
2
0
2
1
1
2
3
0
1
1
1
1
2
2
1
1
1
1
0
1
0
1
2
1
0
1
0
1
0
1
0
1
2
2
2
1
0
2
1
1
1
2
1
2
2
1
1
2
1
1
1
0
1
1
1
1
2
2
1
2
2
1
0
2
1
3
2
1
1
2
0
1
1
1
0
1
1
2
1
1
0
1
1
1
2
3
1
2
1
1
3
1
0
1
2
2
0
1
1
0
1
0
2
2
0
1
1
0
1
2
0
2
2
1
2
1
0
0
0
0
1
0
1
1
2
2
1
0
3
1
1
0
0
3
1
2
2
3
1
2
0
2
1
1
0
2
1
1
1
1
1
2
2
1
1
1
1
1
2
1
0
2
1
2
1
0
1
1
0
1
2
1
1
0
1
0
2
1
0
1
1
1
1
2
1
1
2
1
0
1
1
0
1
0
1
2
1
0
1
0
1
1
1
1
0
2
2
6
1
0
1
0
1
2
2
1
1
1
1
0
1
4
0
1
2
1
2
0
1
0
1
1
2
2
1
1
2
2
2
0
1
0
2
1
1
0
0
1
1
3
1
0
1
1
1
1
1
1
1
2
1
1
1
1
0
1
1
1
1
2
1
0
1
2
1
0
1
1
0
2
1
1
1
1
0
2
2
1
1
1
0
1
1
0
2
1
0
1
1
0
1
1
2
1
0
1
2
2
1
2
1
2
1
1
1
0
2
1
0
1
1
1
2
2
2
0
1
1
1
1
1
1
2
0
1
1
1
1
0
1
0
1
2
0
2
2
1
1
1
1
1
1
0
0
1
0
1
1
1
2
1
2
1
2
1
1
0
1
0
1
2
0
2
3
2
1
1
1
1
1
2
2
1
1
1
1
1
2
2
1
2
0
1
1
1
1
0
2
2
2
1
1
0
1
1
0
1
0
1
1
1
3
2
1
1
0
2
1
1
1
1
0
1
1
1
1
1
1
2
0
1
2
2
1
2
2
1
1
1
2
0
2
2
1
0
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
0
1
1
1
1
0
2
1
0
1
1
1
1
1
0
2
2
1
1
1
0
1
2
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
2
2
1
1
1
1
2
1
1
2
2
1
0
2
0
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
1
1
0
1
1
1
1
1
1
0
0
1
1
2
0
0
1
1
2
1
1
2
1
2
2
2
2
1
0
2
1
2
1
2
1
1
2
0
1
1
2
1
1
1
1
1
0
1
1
2
1
1
1
0
2
1
0
0
1
1
1
1
1
2
1
0
1
1
1
0
1
2
0
2
2
2
1
1
2
2
2
1
2
1
1
1
2
1
2
1
2
0
1
1
0
1
1
1
2
2
1
0
0
2
1
1
0
1
1
1
1
1
1
1
1
0
1
1
1
2
1
0
2
2
1
1
0
1
1
2
1
1
1
2
1
2
1
0
2
1
1
0
1
1
1
1
1
1
1
0
2
1
1
0
1
1
1
1
1
10
1
0
2
1
1
1
2
1
0
1
1
1
2
2
1
0
1
1
1
0
1
1
1
1
1
1
1
1
1
0
2
0
1
0
3
1
2
0
1
1
2
1
0
1
1
1
0
2
2
2
2
1
2
1
0
1
1
0
1
2
1
1
0
0
0
1
2
2
0
1
1
1
1
0
0
1
0
1
1
2
0
1
2
1
1
1
0
1
1
1
1
0
1
1
2
2
0
1
1
1
2
2
1
0
1
1
1
1
1
1
0
1
1
1
1
2
1
2
2
1
2
1
1
2
1
2
2
1
1
0
2
1
1
1
1
1
1
2
0
1
1
2
2
1
1
0
2
0
1
1
1
1
1
1
1
1
1
0
0
0
0
1
0
1
1
1
1
2
2
0
1
1
2
1
1
2
0
2
0
1
1
1
3
1
0
1
0
0
1
1
1
2
2
1
2
1
0
1
1
1
1
0
0
0
0
1
0
1
1
0
1
0
2
1
2
1
2
0
0
1
1
1
1
0
2
0
0
1
0
1
2
2
1
2
1
1
0
1
0
1
2
2
1
2
1
1
2
1
0
2
1
1
0
2
2
1
1
1
0
0
1
1
0
1
0
2
1
1
2
1
3
1
2
1
2
2
1
2
1
0
1
2
1
0
1
0
1
0
0
1
1
1
1
1
1
0
1
1
0
1
2
0
1
2
1
0
1
1
1
1
0
1
2
1
0
1
1
1
0
1
2
0
1
0
0
2
2
2
1
1
1
1
2
0
1
1
1
1
0
1
1
2
2
0
0
0
2
2
1
1
0
0
1
1
1
1
2
1
1
2
1
2
1
0
1
1
2
1
1
1
1
1
1
1
0
1
2
0
3
1
1
2
1
1
1
1
1
2
1
2
1
1
1
2
1
0
2
1
2
1
2
1
1
2
1
0
2
2
1
1
2
1
2
1
0
1
1
1
1
1
1
2
1
1
1
0
2
1
1
1
1
1
1
0
1
1
1
0
0
2
1
0
1
1
1
1
1
0
2
0
1
1
2
1
2
1
0
2
2
1
1
1
1
1
2
1
0
1
1
2
0
1
0
0
2
0
1
0
1
1
0
1
0
1
1
1
1
1
1
2
1
1
1
1
1
0
1
1
1
1
2
0
2
1
0
0
1
1
2
1
0
2
0
1
0
2
1
1
1
1
1
1
1
1
1
1
2
2
1
0
0
2
1
1
0
1
1
1
1
0
0
1
2
0
2
1
1
1
1
1
1
0
1
1
1
1
0
1
1
2
2
0
1
1
0
0
1
2
0
2
1
1
1
1
1
1
0
1
2
1
0
0
2
0
1
2
1
2
1
1
1
1
2
2
1
1
1
1
1
1
1
1
0
1
1
1
2
1
2
1
2
1
1
0
0
2
1
2
1
2
2
1
1
1
0
2
2
1
2
1
3
2
1
1
0
0
2
1
1
1
0
0
2
2
0
2
2
2
1
2
2
1
0
1
1
1
2
2
0
2
1
0
0
1
2
2
0
2
0
1
1
1
1
1
0
0
2
2
1
1
1
1
1
1
0
1
1
1
1
1
1
1
0
2
1
1
1
1
2
1
1
1
1
1
0
1
2
1
2
1
1
2
1
1
2
2
1
0
0
1
1
2
0
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
0
0
1
2
2
1
1
0
2
1
1
1
0
0
1
1
1
0
0
1
1
1
0
1
2
1
1
0
2
1
2
1
1
0
1
1
1
2
1
0
1
1
0
1
0
1
1
2
0
1
2
0
1
0
1
1
2
0
1
2
2
1
0
2
1
0
0
0
1
1
2
1
1
1
1
1
1
2
1
1
2
2
1
1
0
1
2
1
2
2
1
1
1
1
0
2
0
1
1
0
1
1
1
1
0
1
2
1
1
1
2
1
2
0
2
1
0
1
1
1
2
0
2
0
1
0
1
2
1
1
1
2
2
1
1
1
2
1
2
1
1
1
1
1
1
2
2
1
2
1
1
1
1
0
1
0
1
17
2
1
1
2
0
1
1
1
1
1
1
1
0
1
1
2
2
2
1
1
1
1
1
2
1
1
1
2
0
3
1
1
1
0
1
0
1
0
1
1
1
0
2
1
0
1
1
2
1
2
1
1
2
1
1
1
2
1
0
1
0
1
1
2
0
2
1
1
1
1
1
2
1
2
1
1
2
1
2
1
0
1
2
1
2
0
1
1
2
1
0
1
2
1
1
1
1
1
0
0
1
1
1
2
2
1
0
1
0
1
1
1
2
1
1
1
0
2
1
0
1
1
1
0
2
1
1
1
1
0
1
2
2
1
0
1
1
1
1
0
1
1
1
1
1
1
1
0
2
1
1
1
0
1
1
2
1
1
1
1
2
2
2
1
1
1
0
1
2
1
1
1
0
2
2
1
1
0
1
1
0
2
1
2
1
0
0
1
1
1
1
1
0
1
1
2
1
2
1
0
2
1
2
0
1
2
1
0
1
2
1
2
2
0
1
2
2
2
1
0
2
1
1
1
1
2
2
2
2
1
0
1
0
1
2
1
1
2
0
1
2
2
1
2
1
0
1
1
2
2
1
1
1
1
1
1
0
0
1
1
1
1
1
1
1
2
1
0
1
2
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
1
0
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
0
1
1
1
1
1
1
1
1
1
0
1
0
1
2
1
0
2
0
0
0
1
1
2
2
2
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
2
1
1
2
1
0
1
1
2
2
0
0
1
1
1
1
1
1
1
2
1
1
1
2
1
1
0
0
2
0
0
2
0
1
1
1
1
0
1
1
1
2
0
0
1
0
1
2
2
2
1
0
1
2
1
0
2
0
1
1
1
2
2
2
1
0
2
2
2
2
2
0
0
0
1
1
1
1
1
1
2
1
1
2
1
1
2
1
1
0
2
0
1
1
1
2
1
3
1
1
1
1
2
1
1
2
1
1
1
0
1
1
0
1
0
0
1
1
1
1
2
1
2
1
1
2
2
2
1
0
1
1
1
1
2
1
1
1
1
1
1
2
1
1
2
0
1
1
1
2
1
1
0
1
1
2
2
1
2
1
1
0
2
1
1
1
2
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
0
1
2
1
0
1
2
1
1
2
1
0
1
1
1
1
0
2
2
1
1
1
0
1
1
1
1
1
1
0
1
2
1
0
2
1
2
1
0
2
2
1
0
0
1
2
1
2
2
1
1
1
1
2
0
1
2
2
1
2
1
2
1
1
3
3
1
0
2
1
1
2
1
1
1
2
1
2
1
1
1
1
1
2
0
0
1
1
1
1
2
2
0
1
0
1
1
1
2
1
0
2
1
1
2
1
1
2
2
1
1
1
2
1
1
1
0
1
0
1
0
2
0
1
2
1
1
1
2
1
2
1
1
1
1
0
1
1
1
1
1
2
1
2
1
1
2
2
2
0
1
1
1
1
1
1
2
1
1
2
1
0
2
1
1
1
1
1
2
4
2
1
1
1
2
1
0
1
1
1
2
1
1
1
1
2
1
0
2
1
1
1
2
1
1
1
1
2
0
1
2
1
0
2
1
1
1
1
1
1
1
4
0
1
1
2
1
0
1
1
2
1
2
1
0
1
1
1
0
1
1
1
0
0
1
2
2
1
2
1
0
1
2
0
1
2
2
1
2
1
0
1
0
1
0
1
1
2
1
1
1
0
2
1
1
2
2
1
1
0
2
1
2
2
1
1
1
0
2
1
1
2
1
1
2
2
1
1
1
2
1
1
1
1
1
0
0
2
1
0
1
2
1
2
1
1
0
2
1
1
1
1
1
2
0
1
1
2
0
1
1
1
4
0
0
1
1
0
0
1
1
2
1
2
0
1
2
1
1
1
1
1
1
1
1
2
1
1
0
2
2
2
0
1
2
1
2
1
0
1
1
1
2
1
1
1
1
0
1
1
1
1
0
1
1
1
2
0
1
2
1
2
1
2
1
1
0
1
2
2
2
1
1
1
1
1
0
1
1
1
1
1
2
1
2
1
0
1
1
0
2
1
2
0
1
0
2
0
1
1
2
2
1
2
2
1
0
1
1
1
2
1
3
1
2
2
1
1
1
0
1
1
1
3
1
1
1
1
2
1
0
1
1
1
1
1
1
1
1
2
1
1
0
1
0
0
2
1
1
1
2
1
2
2
1
1
1
1
2
0
0
1
0
1
1
1
0
0
1
1
1
1
1
1
1
1
2
4
2
2
1
1
1
0
1
2
1
1
1
0
1
2
1
1
1
1
0
1
1
1
1
2
2
1
0
1
1
1
1
1
0
2
2
0
1
1
1
1
0
0
0
0
0
0
2
1
1
0
1
0
1
1
1
1
2
0
3
0
1
1
2
1
1
1
1
1
1
0
1
1
2
1
0
1
1
0
0
1
1
1
1
2
1
2
2
1
1
0
1
1
2
1
2
2
1
1
1
2
2
1
1
1
2
1
0
0
1
1
1
1
0
0
1
0
1
0
1
1
2
1
2
2
1
1
1
2
1
1
2
2
1
0
0
2
2
1
2
0
1
1
1
1
1
0
1
1
1
1
0
1
2
1
1
1
1
1
2
1
0
1
1
1
1
2
1
0
1
2
1
0
2
0
1
1
2
0
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
1
1
0
1
0
1
1
2
1
1
1
1
0
1
0
1
1
3
1
1
1
1
1
2
2
1
1
2
1
2
1
2
2
1
1
2
1
1
1
0
0
2
2
1
1
2
2
1
1
0
1
0
2
1
1
1
2
0
2
0
1
1
0
1
1
1
2
1
0
0
1
1
1
1
1
1
0
2
1
2
1
2
1
1
2
1
1
2
0
1
1
1
0
1
1
1
0
1
1
2
2
2
1
1
1
1
0
0
1
1
1
1
1
2
0
0
2
1
1
1
1
1
1
1
2
1
0
1
1
1
1
3
1
2
1
0
1
1
1
0
0
2
1
2
2
1
1
1
1
1
1
2
0
1
2
1
1
0
1
2
1
1
0
1
2
1
0
1
1
1
0
1
2
2
1
1
1
1
1
0
1
2
0
1
1
0
0
1
1
1
0
1
1
1
1
1
1
2
1
0
1
1
2
1
1
1
0
2
2
2
1
1
1
1
1
1
2
1
0
1
0
2
1
1
1
0
1
2
2
2
0
1
1
1
1
2
1
2
1
0
2
2
2
1
1
1
1
1
0
1
1
1
2
0
1
1
1
1
1
2
1
1
1
1
1
2
2
1
0
1
1
1
2
0
0
1
0
1
1
1
1
0
1
0
0
1
1
1
2
1
1
1
1
1
1
0
1
2
0
1
2
1
1
1
1
0
1
2
0
1
2
1
0
1
2
1
1
0
0
1
1
1
2
2
1
1
1
2
2
1
1
0
0
1
1
1
1
0
0
0
2
2
1
1
1
0
1
2
2
1
0
1
1
2
2
2
1
1
0
1
0
1
2
1
1
0
2
0
1
2
2
1
0
1
1
0
1
1
1
1
1
0
1
2
2
1
1
1
1
0
2
1
0
1
2
1
2
2
1
0
1
2
1
1
1
0
2
1
1
2
0
1
1
1
1
1
2
1
0
2
1
2
1
0
0
2
2
2
1
2
2
1
1
2
2
2
1
1
1
1
0
2
1
1
1
1
2
2
1
0
0
1
1
1
1
1
2
0
1
0
1
2
1
1
2
1
1
1
2
1
2
0
0
1
1
1
0
2
1
1
1
1
0
2
2
1
1
0
0
3
1
1
0
1
2
2
0
1
2
1
1
1
1
1
2
1
1
2
2
1
1
1
1
2
1
1
1
0
1
2
0
1
2
1
2
2
1
1
0
2
1
1
1
1
2
1
2
2
1
3
1
2
1
2
1
0
2
1
0
1
0
0
1
0
2
0
2
2
0
1
1
1
0
1
2
0
2
2
1
1
1
2
0
2
1
2
0
2
1
0
0
2
1
1
1
1
1
2
1
1
0
2
1
1
3
1
2
0
1
1
2
1
1
1
1
1
2
1
1
0
1
1
0
1
2
1
1
0
0
1
2
2
2
1
1
2
1
1
1
1
1
0
1
1
1
0
1
1
1
1
0
2
1
0
0
1
2
0
1
3
0
1
1
3
1
1
2
1
2
1
1
1
1
0
1
1
2
1
1
0
2
1
1
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
0
0
1
2
2
1
2
0
1
1
0
1
1
1
0
2
0
1
1
1
1
2
1
2
2
2
1
1
2
0
1
0
1
1
1
1
1
1
1
1
2
1
2
1
3
0
1
2
2
0
2
1
1
1
0
2
2
2
1
1
1
1
0
1
2
1
1
1
1
1
1
2
1
1
2
1
1
1
2
0
1
1
2
0
3
1
1
1
1
1
1
1
1
2
1
0
2
0
0
2
0
1
1
1
1
2
2
2
1
1
1
2
2
1
0
0
1
1
2
1
1
0
0
1
1
2
1
1
2
1
2
2
1
1
3
1
0
1
1
2
2
0
1
1
1
0
1
0
1
3
2
2
1
1
1
0
2
1
0
0
1
1
1
0
1
0
1
1
2
1
1
1
1
2
1
2
1
0
1
1
1
1
1
1
2
2
0
1
1
1
2
2
1
0
2
1
2
2
2
2
1
1
0
3
2
1
2
0
1
1
0
0
2
2
1
1
2
2
1
0
1
1
1
2
1
2
1
1
1
0
1
2
0
1
1
1
1
1
3
0
1
2
1
1
1
0
2
0
2
1
1
2
3
1
1
1
1
1
0
0
1
2
1
1
1
1
0
1
3
2
1
2
1
2
2
1
1
2
1
2
1
1
2
2
1
1
2
2
1
2
1
1
0
2
1
1
1
1
2
1
2
1
2
1
1
2
0
2
1
0
1
1
1
0
1
2
1
1
2
2
2
0
1
2
1
2
1
2
4
1
0
1
1
1
1
1
1
2
0
2
1
2
1
1
1
1
1
1
2
1
1
2
1
1
1
1
0
1
1
1
1
0
2
0
1
1
1
1
1
1
1
1
1
1
3
0
0
2
1
1
1
2
1
0
2
0
2
1
2
1
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
0
2
1
0
1
1
2
1
2
1
1
1
1
2
1
1
2
2
2
2
1
0
1
2
1
1
1
1
1
2
1
1
2
1
3
0
0
1
1
1
1
1
1
0
1
1
1
1
2
1
1
1
1
1
1
1
1
2
2
1
1
1
0
1
1
1
0
1
1
1
1
2
1
1
2
11
0
2
1
2
2
1
1
1
1
1
1
2
1
1
2
1
2
0
1
1
3
2
1
1
1
1
2
0
1
0
1
2
1
0
1
0
1
0
1
0
1
2
1
1
0
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
0
2
1
0
1
2
1
2
1
1
4
2
0
0
1
1
1
1
2
0
1
1
0
1
0
1
0
2
1
1
1
0
1
1
0
1
0
2
1
0
1
1
2
2
1
0
1
0
1
2
2
1
1
0
2
1
1
2
2
0
3
1
1
1
2
1
1
1
1
1
0
1
1
2
0
1
1
1
1
0
1
1
1
2
1
1
0
1
1
2
2
1
2
1
0
0
1
2
1
1
1
1
2
2
1
1
1
2
2
0
2
1
1
2
1
1
1
1
1
1
2
2
1
1
0
1
1
1
0
2
1
2
1
1
2
1
1
1
2
0
0
2
1
0
1
2
0
1
1
1
1
1
2
2
1
1
1
1
2
1
0
2
2
2
2
1
0
1
2
1
1
0
1
1
2
2
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
2
1
2
2
2
1
1
1
1
1
1
1
1
0
1
1
1
2
2
2
2
1
1
1
1
2
1
0
0
0
2
1
1
2
1
1
1
0
1
2
3
1
1
1
1
2
2
0
2
0
1
1
0
1
1
1
0
1
1
2
1
1
1
0
1
2
1
1
1
2
1
1
0
1
1
0
2
1
1
0
1
1
1
1
1
2
1
1
1
1
0
1
2
1
1
0
1
0
0
0
1
1
1
0
1
2
1
1
1
2
2
1
3
2
2
2
1
1
2
0
1
1
1
1
1
0
0
1
1
1
2
0
2
1
2
1
2
1
0
0
2
1
0
0
1
1
2
0
1
0
2
2
1
1
1
0
1
2
0
2
1
0
1
1
2
0
1
0
1
1
1
1
0
1
1
1
1
1
1
2
1
2
0
1
0
0
1
1
0
1
3
1
1
0
2
0
2
1
1
2
2
2
1
1
2
1
1
2
2
1
2
0
0
2
2
1
1
1
1
2
1
1
2
2
0
1
1
1
1
1
1
2
1
1
2
1
0
1
1
2
1
0
1
1
2
2
1
2
2
0
1
0
1
1
1
1
0
1
1
2
1
1
1
2
0
1
1
0
1
1
0
1
0
1
0
0
1
1
2
2
2
2
1
1
1
2
0
1
0
2
0
1
0
1
0
1
0
1
1
2
0
0
2
1
1
1
2
0
1
1
2
2
1
1
1
1
1
2
2
1
1
1
1
2
1
3
0
1
1
0
0
1
1
1
1
2
2
1
0
0
0
0
2
0
1
2
2
1
1
0
2
1
0
1
1
1
2
1
0
0
0
1
2
0
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
2
0
1
1
0
0
1
1
1
1
1
1
2
1
1
2
0
1
1
2
1
0
1
1
1
1
1
1
1
0
0
1
2
2
1
0
2
0
0
2
2
1
1
1
2
0
1
1
1
0
1
0
1
1
1
1
1
2
1
1
0
2
2
1
1
2
2
1
2
1
1
2
2
1
1
1
1
1
0
1
1
1
1
1
1
0
1
1
2
0
1
1
2
1
2
1
1
1
0
1
1
1
2
1
1
2
2
0
1
1
0
1
2
1
1
1
2
1
0
1
0
1
2
1
1
0
1
1
0
2
1
0
2
1
1
1
1
1
1
1
1
0
0
1
1
1
2
1
1
1
1
1
1
1
1
2
1
2
1
2
1
1
1
0
1
1
1
2
1
2
1
1
2
1
1
1
1
1
1
2
2
1
1
0
1
2
1
2
1
1
1
2
1
2
1
2
0
1
2
0
1
0
1
1
1
0
1
0
0
2
1
2
2
0
1
0
0
1
2
1
2
2
2
1
1
1
0
0
1
1
0
1
1
1
2
1
1
1
1
1
1
2
1
2
2
0
1
1
2
1
2
0
1
1
1
1
0
2
1
1
0
1
1
1
1
2
1
1
1
1
0
1
2
0
1
1
1
0
2
1
1
1
2
1
1
1
1
2
0
1
2
2
0
2
2
0
1
1
2
1
2
1
3
2
0
1
2
1
2
1
1
1
1
1
1
1
2
0
3
0
2
0
0
1
0
1
1
0
1
1
1
1
0
1
1
1
2
1
1
0
1
1
0
1
1
1
1
1
0
1
2
1
0
1
1
1
1
0
0
2
1
1
1
1
1
2
2
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
0
2
1
1
1
0
0
1
1
1
1
4
0
1
1
1
2
1
1
1
1
1
1
1
2
2
2
0
1
1
1
1
1
1
0
2
1
1
0
1
1
2
2
1
1
2
2
1
0
1
0
1
1
1
0
1
1
0
2
2
2
0
0
1
1
1
1
1
1
1
1
1
1
2
1
0
1
1
1
0
0
2
1
1
1
2
1
1
1
1
1
1
1
1
1
0
0
2
0
1
1
1
1
2
0
1
3
2
0
0
1
2
0
1
1
1
2
2
1
1
0
1
0
2
1
0
1
2
0
0
1
2
1
1
2
1
0
1
2
1
0
1
1
2
1
1
1
1
1
0
2
1
1
2
2
2
1
0
1
1
1
0
2
2
1
1
1
1
3
1
1
2
1
1
1
0
2
1
1
1
1
2
1
1
1
0
1
1
1
1
2
1
1
1
1
1
1
2
2
1
1
0
1
0
0
1
1
2
1
1
1
1
1
1
0
0
1
1
1
1
1
2
1
2
2
2
1
3
0
1
2
0
0
1
1
2
1
1
1
1
2
0
1
0
0
1
1
1
2
2
2
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
1
2
1
2
1
1
2
0
1
2
0
1
1
1
0
1
1
0
1
0
0
2
0
2
1
2
1
0
1
2
1
2
1
1
1
1
2
0
0
1
2
2
1
2
2
1
1
1
1
0
1
1
0
1
1
1
1
1
1
0
2
2
1
1
1
1
0
0
1
1
2
1
1
3
1
1
1
1
2
0
0
1
1
1
1
1
2
1
0
1
1
1
1
1
1
1
2
2
0
0
0
1
1
1
2
1
2
1
1
1
0
2
0
1
6
1
1
1
2
2
1
1
2
2
1
1
1
0
1
0
1
2
2
1
1
1
0
1
2
1
1
2
1
1
1
1
2
1
1
1
0
1
1
0
1
1
1
1
2
0
1
2
1
2
1
0
1
0
1
1
1
1
2
1
1
0
2
0
1
1
0
1
1
1
2
2
2
1
1
0
0
2
1
2
1
0
2
1
1
1
2
2
3
1
2
1
1
1
1
1
1
1
1
1
1
1
0
2
0
2
0
2
1
1
1
1
1
1
0
1
2
1
2
0
1
1
0
1
1
0
1
1
1
2
1
1
2
1
1
1
1
0
1
0
1
0
1
1
0
1
1
1
0
1
1
1
0
1
1
1
1
1
1
1
1
1
2
2
0
2
2
1
2
2
0
1
1
1
0
1
1
1
1
1
5
1
0
1
0
2
1
1
2
1
1
1
1
0
2
0
0
2
1
2
1
2
1
0
0
0
1
1
0
1
0
1
2
1
2
1
1
1
0
1
2
1
1
2
1
1
1
1
1
2
1
2
2
1
1
2
2
2
2
2
1
1
2
1
1
1
1
2
1
0
1
1
1
1
1
1
1
1
1
0
1
0
2
0
1
1
2
2
2
0
2
0
1
1
1
0
1
2
0
1
2
1
2
1
1
0
1
1
1
1
0
1
2
0
0
1
1
0
1
2
1
1
0
0
1
1
0
1
1
2
1
1
1
1
1
1
1
0
1
2
1
2
2
2
1
1
1
2
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
2
1
1
1
2
0
1
2
1
2
0
2
1
1
3
2
3
0
1
1
1
1
1
2
2
0
1
1
1
2
1
0
1
1
1
1
1
1
1
0
1
1
1
0
2
2
1
2
1
1
2
1
1
1
0
1
1
1
1
1
0
1
2
0
2
2
1
1
1
1
0
1
1
2
1
2
1
1
1
1
0
1
2
1
1
2
1
2
1
1
0
0
2
1
1
1
2
1
0
1
1
1
1
1
1
1
1
1
1
2
1
2
1
0
2
2
2
1
2
1
2
1
1
0
1
2
0
1
1
2
1
0
1
1
1
2
1
0
1
0
2
0
1
2
1
1
1
1
1
1
0
0
0
1
1
0
1
0
1
1
2
1
2
0
1
2
1
2
2
1
2
1
2
1
2
0
1
1
2
1
1
1
1
0
1
1
1
1
1
1
0
1
1
1
0
0
1
2
1
2
1
4
0
1
2
2
0
1
1
2
0
2
1
0
1
1
1
2
0
0
2
1
0
2
0
3
1
1
1
1
0
1
2
1
0
1
1
1
2
1
1
1
0
1
0
1
0
1
1
1
2
1
1
3
0
1
1
2
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
0
0
1
1
0
0
2
1
1
0
0
1
1
0
1
1
1
0
1
1
1
2
1
0
1
1
2
2
2
1
2
2
2
1
0
0
1
1
2
1
0
1
2
0
1
2
1
1
2
2
2
1
1
0
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
0
1
2
2
0
2
0
1
2
1
1
1
1
1
1
1
1
1
1
0
5
1
1
0
2
0
1
3
1
1
1
1
1
1
1
0
1
3
2
1
1
0
0
2
2
2
0
2
1
0
1
2
2
1
2
1
1
1
1
1
1
0
1
0
2
2
2
1
1
1
1
1
1
0
1
2
1
1
1
1
2
1
1
1
2
1
1
1
1
0
2
2
0
2
1
1
1
1
0
1
2
0
2
1
1
0
2
1
1
1
2
1
1
1
1
1
0
1
1
1
1
1
0
0
2
1
0
0
2
2
1
1
1
2
1
2
1
1
0
0
1
2
1
1
1
2
1
2
1
2
2
1
0
0
1
1
2
1
1
1
0
1
1
2
2
0
1
1
1
1
1
1
2
0
1
0
2
1
1
2
1
1
1
1
1
1
1
1
1
2
0
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
1
2
0
0
0
2
1
2
0
0
2
2
2
0
0
1
0
1
1
1
1
2
1
2
1
1
2
1
1
2
1
5
1
0
1
0
1
2
1
1
1
2
1
1
1
1
1
1
2
2
2
0
1
0
2
1
0
1
2
2
2
2
0
1
2
2
2
1
1
0
2
1
1
2
1
1
1
1
1
1
1
2
2
0
0
1
1
2
1
1
2
1
1
1
0
2
2
0
0
1
1
2
1
1
2
1
0
1
1
1
1
1
1
1
1
2
1
1
1
0
1
1
1
0
1
2
1
1
1
2
1
0
1
1
0
2
0
2
0
1
2
1
2
1
0
1
1
1
0
1
1
0
1
0
0
1
0
1
1
1
2
0
0
1
1
0
2
1
1
1
1
1
1
2
1
1
1
2
1
0
1
1
2
1
2
1
1
1
0
1
1
1
2
1
1
1
1
1
2
3
0
1
0
2
2
0
1
1
2
2
2
1
1
1
2
1
2
2
2
2
1
0
1
0
1
2
1
1
2
1
1
1
1
0
1
0
0
1
0
2
1
1
2
1
1
1
1
1
2
0
3
0
1
2
0
0
0
1
2
1
1
1
2
0
2
2
1
2
2
2
1
2
1
2
0
1
1
0
1
1
2
1
2
2
1
1
1
1
2
1
1
0
0
1
1
1
0
0
2
1
1
2
1
1
1
0
1
1
1
1
1
1
1
2
1
1
1
4
2
1
2
1
1
1
2
0
1
0
1
1
1
2
1
2
0
1
0
2
1
2
2
1
1
1
1
0
1
1
1
1
1
1
2
1
0
2
0
2
1
1
0
1
0
2
1
1
0
1
2
1
0
1
0
1
0
1
2
1
1
0
2
2
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
3
1
1
1
1
1
0
2
0
2
1
0
2
1
2
1
0
1
1
1
1
1
1
0
2
2
1
0
0
1
1
1
0
2
1
0
0
1
0
0
1
1
0
1
1
1
0
2
1
1
1
1
1
1
2
1
0
1
0
2
1
1
0
1
1
2
1
1
1
1
1
0
1
1
1
2
1
1
1
1
1
0
1
2
2
1
0
2
1
1
0
2
1
0
2
2
2
1
2
1
3
2
2
0
1
0
0
0
1
1
2
1
2
2
1
0
1
2
2
1
1
1
4
2
1
1
1
2
1
1
0
1
2
1
2
1
1
1
1
0
3
2
1
1
1
1
0
1
1
1
1
1
1
2
2
1
1
2
1
2
1
1
1
1
1
0
1
2
1
1
1
2
1
2
1
2
1
1
1
1
1
2
1
1
9
1
1
1
0
2
1
0
1
1
2
0
1
1
1
1
1
1
2
1
1
2
1
0
2
1
1
1
2
0
2
0
0
0
1
2
1
1
1
1
2
2
0
2
2
1
1
0
0
1
0
2
0
1
2
2
2
1
1
2
1
1
1
2
1
2
1
1
2
1
2
1
1
0
1
1
1
2
2
1
1
1
1
2
1
0
1
2
1
1
1
2
1
2
2
1
0
3
1
2
2
1
1
1
1
2
1
1
1
2
1
2
1
2
0
2
1
1
1
2
1
0
0
1
1
2
1
1
2
0
1
1
0
2
1
2
1
1
1
1
1
2
1
1
2
1
2
1
0
1
1
1
1
1
1
1
1
0
1
1
0
2
0
1
2
2
1
0
1
1
1
1
1
0
1
0
1
1
0
2
2
0
1
1
1
2
2
2
0
1
1
1
0
1
1
1
1
1
1
0
2
1
1
1
0
1
0
2
2
1
1
1
1
1
2
1
1
1
2
2
2
1
1
2
1
1
2
1
0
2
1
2
1
0
2
1
2
1
1
0
0
1
1
2
1
1
1
1
1
1
2
0
1
0
2
4
3
1
0
0
1
1
1
0
2
1
1
1
2
1
1
1
0
0
2
1
1
1
0
2
0
2
1
1
1
2
1
0
1
1
0
1
2
0
0
1
0
1
1
1
1
1
1
1
1
0
2
0
1
1
0
0
1
1
0
2
2
0
2
1
1
2
0
2
0
0
1
1
0
0
0
1
0
1
2
0
1
2
2
0
1
1
1
1
1
1
1
2
0
1
2
1
1
2
2
1
0
1
1
2
0
4
1
2
0
1
0
0
1
1
1
1
1
1
1
1
1
1
1
2
3
0
1
2
1
0
0
1
0
1
0
1
2
1
1
0
1
1
1
1
2
2
1
1
2
1
0
1
1
1
2
1
0
1
1
1
1
1
1
1
0
1
0
1
1
2
1
1
1
1
0
1
1
1
2
1
2
2
1
0
1
0
1
1
1
1
1
1
2
0
2
2
0
1
1
1
1
2
1
2
1
1
2
1
1
1
1
0
1
1
2
1
1
1
1
1
1
1
3
1
1
0
2
0
1
0
2
2
0
1
1
1
1
1
2
0
1
2
1
1
1
1
1
2
1
0
1
2
1
1
1
2
1
1
1
2
1
1
1
0
2
0
3
1
1
0
1
2
1
1
1
1
2
1
2
2
1
0
2
2
2
2
1
2
1
1
1
2
2
0
2
2
1
0
1
1
2
0
1
1
2
1
0
0
0
1
0
1
1
1
1
1
1
1
1
0
1
2
2
0
0
0
1
1
1
2
0
1
0
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
2
0
1
2
1
1
2
2
1
2
1
0
1
1
1
1
0
1
1
1
2
1
2
1
1
1
1
1
1
1
0
2
2
0
1
3
1
1
1
2
0
1
0
1
1
1
1
1
1
1
1
1
0
0
0
1
0
1
1
1
0
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
1
0
2
1
1
1
1
1
1
2
0
1
2
1
1
2
2
2
2
0
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
2
2
1
2
2
2
1
1
1
2
1
1
0
2
1
1
2
2
1
1
2
3
0
2
1
1
1
1
2
1
2
2
2
1
1
1
1
1
1
1
1
0
1
0
1
1
1
1
0
1
1
1
1
1
2
1
2
1
0
1
0
1
0
1
1
1
1
1
1
1
1
1
2
1
1
2
0
1
2
0
1
1
2
1
0
2
1
1
1
1
2
0
2
2
1
1
1
1
2
0
1
0
2
2
0
0
2
1
2
2
1
1
1
2
1
1
2
2
1
1
2
0
0
1
1
1
1
0
1
1
0
1
2
2
2
0
1
1
1
0
0
0
0
1
1
1
1
2
1
1
0
1
1
0
1
1
2
0
1
1
2
1
1
2
1
1
1
1
2
0
1
2
2
1
1
0
1
1
2
2
2
1
1
1
1
0
1
0
2
1
0
1
1
1
0
1
2
1
2
1
1
0
1
1
1
0
1
1
1
1
3
0
1
0
2
1
1
2
1
1
1
1
1
1
1
1
2
2
0
1
0
2
0
1
1
1
2
2
1
1
0
2
1
1
2
2
1
2
1
1
1
1
1
0
1
1
1
1
1
1
0
0
1
1
0
2
0
1
1
0
2
1
0
2
0
1
1
1
2
2
1
1
2
2
2
1
1
0
1
1
1
1
1
2
1
0
3
2
1
1
1
1
0
0
1
2
1
1
2
1
1
0
1
1
2
1
0
0
1
0
0
2
0
1
1
1
1
1
1
0
1
1
1
0
2
0
1
2
1
1
1
2
2
1
1
1
1
1
1
1
0
1
1
1
0
1
0
2
0
1
1
0
1
1
1
1
1
1
1
1
1
1
0
0
2
1
1
1
1
2
0
1
1
1
1
2
1
0
2
0
1
2
1
2
1
0
1
0
0
1
2
1
1
1
1
0
1
1
1
0
2
1
1
1
2
2
2
0
2
1
1
1
2
1
1
1
0
1
2
1
1
2
1
0
0
1
0
1
0
1
1
1
1
1
2
1
1
1
1
1
1
1
0
1
2
1
0
1
1
0
1
2
0
2
1
1
2
1
1
1
0
1
1
0
2
0
2
2
0
0
2
2
1
1
0
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
2
1
1
0
2
1
2
1
0
1
1
0
0
2
1
2
1
0
2
1
2
0
0
2
2
2
1
1
2
1
2
1
1
0
1
1
2
1
1
1
2
1
2
0
1
2
1
1
1
1
0
1
2
1
1
1
1
1
2
1
1
1
1
0
2
1
1
1
1
1
1
1
1
0
2
1
2
1
1
1
1
1
2
2
1
1
1
0
1
1
1
1
0
0
0
0
1
0
1
2
1
1
1
1
1
1
2
2
4
1
1
0
1
2
1
1
1
1
1
0
0
2
0
1
1
2
2
1
1
1
2
1
1
4
1
1
1
1
0
2
0
1
0
0
1
1
2
1
1
0
2
0
2
1
1
1
1
2
1
0
0
1
1
1
1
1
1
1
2
1
1
0
2
2
1
1
2
2
2
1
1
0
1
2
1
0
1
2
1
0
1
1
0
2
0
2
1
1
1
1
1
0
1
2
1
0
0
1
1
1
1
1
0
1
1
1
1
2
1
1
1
0
2
1
1
1
2
1
0
0
1
0
2
1
0
0
1
1
1
1
1
1
0
1
1
1
0
0
1
2
3
2
0
1
1
2
2
0
1
1
2
0
2
1
0
1
0
0
0
1
1
2
2
1
2
1
1
2
2
1
1
1
0
1
0
0
1
0
1
1
2
1
2
1
2
1
1
1
1
2
1
1
1
2
1
1
0
1
1
1
1
1
2
1
2
2
2
1
1
1
1
0
2
1
1
1
1
1
1
1
0
1
2
1
1
2
2
1
0
2
1
2
2
0
2
1
3
0
0
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
5
1
2
2
2
1
1
1
0
1
1
0
0
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
2
2
1
0
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
2
1
1
2
1
1
1
2
1
0
0
1
2
0
1
1
1
1
2
0
1
1
1
1
1
0
2
0
2
1
1
1
2
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
2
1
0
1
1
1
0
2
2
1
2
1
0
1
2
1
1
2
1
2
1
1
1
1
2
1
0
1
1
1
2
1
1
2
1
1
1
1
1
1
1
2
1
1
1
0
2
0
1
2
1
2
1
2
1
1
1
0
1
1
1
1
2
1
1
0
1
2
1
2
2
1
1
1
1
2
2
2
0
1
2
2
0
1
1
1
1
1
2
2
2
2
1
1
2
0
1
1
2
1
1
1
2
1
1
0
0
1
0
0
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
2
0
1
2
1
0
1
1
0
1
2
2
2
0
0
1
1
0
1
1
0
1
1
1
1
1
1
2
2
2
2
1
2
2
0
1
2
2
1
1
1
1
1
0
0
1
1
2
1
1
1
1
2
0
1
1
1
0
2
2
1
1
0
0
1
1
1
1
2
2
1
1
0
0
0
0
1
1
2
0
2
2
1
0
0
1
1
2
1
1
2
1
1
0
0
1
1
1
0
1
2
1
0
2
3
1
2
0
2
1
0
0
0
1
1
2
2
1
2
1
1
1
1
1
1
1
2
1
0
0
1
1
1
2
2
2
2
0
1
2
1
1
1
0
1
2
0
0
0
2
1
1
2
0
1
2
1
0
1
0
0
2
1
1
1
1
1
1
0
2
2
1
0
0
1
1
1
1
0
1
2
1
2
1
2
0
0
1
1
1
1
2
0
1
1
2
1
0
1
1
0
1
2
2
2
1
1
0
1
1
1
1
0
0
2
1
1
0
1
2
1
0
0
1
2
2
1
1
1
1
0
0
1
1
1
1
0
0
1
3
1
1
2
0
1
2
1
1
0
0
0
1
2
1
1
2
1
0
0
2
1
2
1
1
0
0
1
1
1
1
2
2
2
1
1
1
1
0
1
0
2
1
1
1
1
0
1
1
2
1
0
1
0
1
0
2
2
2
0
1
1
1
1
1
1
2
1
0
1
0
1
2
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
0
1
1
1
0
1
3
2
1
1
2
1
0
1
2
1
1
2
2
2
1
2
2
2
2
2
1
1
2
1
1
1
0
1
1
2
2
1
1
0
1
1
2
1
1
1
1
1
2
1
1
1
0
2
1
1
1
2
1
1
0
2
2
1
1
1
0
1
2
1
2
1
2
1
2
1
1
2
1
0
1
1
0
0
1
1
1
2
2
1
2
1
1
2
0
2
0
0
2
0
1
1
0
2
2
1
1
2
1
1
0
1
2
2
2
0
1
1
0
2
2
2
2
2
1
1
1
2
1
2
1
1
0
1
1
2
2
5
0
2
1
2
0
1
0
2
1
1
0
1
1
1
1
2
1
1
0
2
0
1
1
1
2
1
1
1
2
2
0
0
2
1
0
1
1
0
2
1
0
1
2
1
1
2
1
1
1
0
1
0
0
1
1
1
1
1
1
1
2
2
2
1
2
2
2
1
2
1
1
1
1
1
1
1
0
2
2
0
2
1
2
1
1
1
1
1
1
3
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
2
1
1
0
2
0
2
0
2
1
1
1
1
1
1
2
1
1
2
2
0
1
1
1
1
1
0
2
1
0
1
0
2
2
1
1
1
2
1
1
1
2
0
0
1
1
0
2
1
1
1
1
0
1
1
0
1
1
1
0
1
1
2
2
2
0
2
1
0
2
2
1
0
1
1
2
0
1
1
2
2
1
2
1
1
2
1
2
1
1
0
2
2
0
1
0
0
1
0
1
2
1
2
2
1
2
2
2
1
0
1
2
0
1
0
1
1
1
2
1
1
2
1
1
1
2
2
0
1
1
1
1
2
2
1
2
2
0
0
2
1
0
1
1
0
4
1
1
2
2
0
1
1
1
1
0
1
2
0
1
2
1
0
1
2
2
1
1
2
0
0
1
2
2
2
2
0
1
1
0
1
1
1
2
2
1
0
1
2
1
2
0
1
1
2
1
1
2
0
1
1
2
1
0
2
2
1
1
1
1
0
0
2
1
1
1
1
3
2
2
1
2
1
2
0
1
1
2
2
1
1
1
2
2
0
0
1
1
1
1
2
1
1
1
1
1
1
1
0
1
2
1
1
0
2
1
1
0
1
0
2
1
1
1
0
0
1
0
2
1
2
0
2
2
0
1
1
0
2
1
1
2
1
1
0
1
1
1
1
1
0
2
1
1
1
1
2
1
1
1
1
1
1
1
0
1
1
2
2
0
1
0
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
0
2
1
1
1
1
1
1
2
1
0
1
0
1
1
0
0
1
1
2
2
1
1
1
1
1
0
1
1
1
0
1
1
0
0
2
1
1
1
0
1
1
1
1
0
0
1
0
1
1
2
0
1
1
0
1
1
1
0
2
0
1
2
1
1
1
1
0
1
2
1
1
3
2
1
2
0
2
0
1
1
2
1
1
1
1
1
0
2
0
1
1
2
1
1
1
0
1
2
1
1
0
2
2
2
1
1
1
1
1
2
1
2
1
2
1
1
1
1
0
0
1
2
0
1
1
1
0
1
1
0
1
2
2
2
1
1
0
1
1
1
1
1
0
1
2
1
2
2
1
1
1
0
1
0
1
1
1
2
1
2
0
1
1
0
1
0
2
1
0
1
2
2
1
1
1
2
1
2
1
1
1
1
0
1
1
2
2
1
1
1
0
0
2
1
1
1
1
1
2
1
0
1
1
3
1
1
1
1
0
1
1
0
0
1
1
0
0
1
2
4
0
0
2
1
0
1
1
1
1
1
1
2
2
1
1
1
0
1
2
2
1
0
1
1
1
0
1
1
2
1
2
1
1
1
0
1
1
2
1
1
0
1
0
1
1
0
1
1
1
1
1
2
2
1
1
2
1
1
1
1
1
2
0
1
2
1
1
1
3
2
0
2
1
0
1
1
2
1
0
2
2
1
0
2
0
0
1
2
0
1
0
0
1
1
0
2
0
1
1
2
1
1
2
1
1
1
1
0
2
1
0
1
2
1
1
0
1
1
2
1
1
1
1
0
2
1
1
0
2
1
1
1
2
1
1
1
1
2
0
1
1
2
1
1
2
2
0
1
1
1
1
0
2
1
0
2
1
1
1
3
2
1
1
2
1
2
1
1
0
2
2
2
2
2
1
1
2
0
0
0
2
2
2
1
1
1
0
1
1
2
1
1
1
2
1
2
1
1
2
0
1
1
1
2
1
0
1
1
1
1
2
2
1
1
1
1
0
2
2
2
1
1
1
1
0
1
2
1
2
1
2
1
1
2
0
2
2
2
1
1
1
1
1
2
1
1
1
0
1
1
2
1
1
1
1
0
1
1
1
2
2
1
1
1
1
1
1
1
1
0
2
1
1
1
1
1
1
1
1
1
0
2
1
1
2
1
0
1
2
0
0
1
1
2
1
1
1
1
1
1
1
1
1
2
2
0
1
2
1
1
2
2
1
1
0
2
1
2
1
1
1
1
1
1
1
1
1
1
0
1
0
2
0
2
1
1
0
1
1
1
1
1
1
1
1
1
2
2
1
1
1
2
1
0
2
1
1
1
1
2
0
1
0
0
1
0
1
2
0
1
2
1
1
0
2
1
1
1
1
2
1
1
0
1
1
0
0
1
1
1
1
1
1
0
1
0
0
1
1
2
2
1
1
1
1
1
0
1
0
2
1
1
1
2
2
0
1
1
1
1
1
1
2
1
1
1
1
0
1
0
1
2
0
1
1
1
1
1
1
1
0
1
1
0
2
2
1
2
2
2
2
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
0
0
2
0
2
1
1
1
0
2
1
2
1
0
1
0
2
2
1
1
0
2
1
1
1
1
0
1
0
0
1
2
1
1
1
0
1
1
2
2
1
1
1
2
2
2
4
1
1
2
1
1
1
1
1
2
2
0
1
2
1
0
0
1
1
1
1
2
1
0
0
1
2
2
0
0
2
2
2
1
0
1
1
1
0
1
2
1
2
1
1
0
1
1
1
1
1
3
1
1
2
1
0
1
1
1
1
0
0
1
2
1
1
2
2
2
2
2
1
1
0
1
1
1
2
1
0
2
0
2
1
1
1
1
1
1
1
1
1
0
1
2
1
1
1
1
1
1
1
0
0
0
2
1
3
0
2
1
1
1
1
2
1
1
1
0
1
1
2
1
0
2
1
1
2
2
1
1
1
1
0
1
1
2
1
2
0
1
1
1
1
1
2
1
1
1
1
0
2
1
1
2
1
1
1
1
1
1
2
0
2
2
2
1
2
0
1
1
1
0
1
2
2
0
1
1
2
1
1
2
1
2
1
1
1
1
1
1
2
2
1
2
2
2
0
1
0
1
1
2
1
1
1
1
1
2
1
1
2
1
0
2
1
2
1
1
1
0
1
2
1
2
0
2
1
2
0
1
2
2
2
1
2
2
1
1
0
2
1
0
1
1
2
1
1
0
2
1
2
1
2
1
1
2
1
2
1
1
1
1
1
1
0
1
1
0
2
0
1
1
2
1
1
1
1
2
1
2
1
0
2
1
2
1
0
2
1
0
1
1
1
1
0
1
2
0
2
1
0
0
2
2
1
1
1
2
2
0
1
2
0
2
0
1
1
2
1
1
1
1
0
2
1
1
1
1
1
1
0
0
0
1
1
2
1
0
1
1
1
1
1
0
1
0
1
0
0
1
0
1
1
1
1
1
1
0
1
1
0
1
0
1
1
0
1
1
2
1
0
1
1
1
1
1
2
0
2
1
0
0
1
1
2
1
1
1
0
1
1
1
1
1
2
0
1
0
1
1
1
2
2
0
0
1
1
1
1
1
3
1
1
2
1
1
1
1
2
1
2
0
2
2
1
5
1
1
1
1
1
1
1
1
2
0
2
0
1
0
1
1
1
2
0
1
2
1
1
2
2
2
1
1
1
2
1
2
1
0
1
1
1
1
1
1
0
0
1
1
1
1
1
1
1
1
2
1
1
0
1
2
2
2
0
2
1
5
1
2
1
1
1
1
1
0
1
1
1
1
1
1
2
1
1
0
1
1
2
0
2
0
1
0
0
1
1
1
3
1
1
0
0
1
2
1
1
1
2
2
1
1
1
2
1
2
1
1
1
1
1
1
0
1
1
0
2
1
1
0
1
2
1
0
1
1
0
1
1
1
2
1
2
1
2
1
0
1
1
1
2
1
1
2
0
1
0
1
2
1
0
1
0
1
0
2
1
1
2
1
1
1
1
1
2
1
1
2
2
1
2
2
1
1
1
1
1
2
2
0
1
2
0
1
0
1
2
1
0
1
1
0
1
2
1
2
1
1
2
1
1
1
0
1
2
2
1
1
1
1
1
1
2
1
1
0
1
0
1
1
2
1
1
1
1
2
1
1
0
1
2
0
0
2
1
0
1
2
1
1
1
1
1
0
1
0
0
0
1
0
2
1
1
1
2
1
1
1
2
0
1
0
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
2
1
1
2
1
0
1
0
1
2
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
0
0
1
1
1
2
1
3
1
2
2
1
1
0
1
1
2
1
2
1
1
1
0
1
1
1
2
1
0
1
1
2
2
2
2
1
1
1
2
1
0
1
1
1
1
0
1
1
0
1
1
1
1
1
0
2
1
1
1
2
1
1
0
1
1
0
2
1
1
1
1
2
1
0
1
2
1
1
1
0
1
2
1
0
1
1
1
0
1
0
0
1
1
1
1
0
0
1
1
2
1
1
1
2
1
1
2
1
1
1
1
1
1
0
1
1
1
2
1
2
0
1
0
2
1
0
1
1
1
2
1
1
0
1
1
2
0
1
2
1
1
1
1
1
3
2
1
0
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
2
1
2
3
1
1
1
1
1
2
1
1
2
0
2
1
1
0
1
1
2
2
1
1
0
1
2
1
1
0
1
1
0
0
1
2
0
0
1
1
1
2
2
1
1
2
1
1
0
0
0
0
2
0
1
2
0
1
1
2
1
1
0
1
1
2
1
1
0
0
0
1
1
1
1
0
0
1
1
2
0
1
1
1
1
1
1
2
1
3
2
2
0
1
1
1
2
1
0
2
1
1
1
0
2
1
1
1
0
1
2
1
1
1
1
1
0
1
0
1
1
2
1
1
2
1
1
2
1
1
1
1
1
1
0
1
1
1
1
2
1
1
1
0
1
1
1
2
1
0
1
1
1
0
1
2
2
2
0
1
2
2
1
2
1
0
1
2
1
0
0
2
1
1
1
1
2
1
0
0
1
2
1
1
4
1
1
1
1
1
1
0
2
1
1
1
2
1
1
2
0
2
1
1
1
1
2
1
1
1
1
1
2
2
2
2
2
2
0
1
2
2
1
1
1
2
0
0
2
1
0
0
1
2
0
2
1
1
1
1
2
1
0
2
1
2
1
0
1
2
1
1
2
2
1
2
2
1
1
1
2
1
2
1
2
1
1
1
2
1
1
1
1
0
1
2
0
1
1
1
1
1
2
1
2
2
4
1
1
1
2
2
1
2
1
0
0
1
1
1
2
1
0
2
0
2
1
2
2
0
1
1
1
1
2
0
1
1
1
1
0
1
1
2
2
1
0
1
1
1
1
1
1
1
0
1
1
2
1
0
1
2
1
2
1
2
0
1
1
0
1
1
2
2
0
1
1
1
0
1
0
0
1
0
1
1
4
2
1
2
1
0
2
1
2
1
0
1
1
1
2
1
1
2
1
0
2
1
2
2
1
0
1
2
1
1
0
1
0
1
1
1
2
2
1
1
1
2
2
1
1
0
1
1
1
1
0
1
4
2
2
1
0
1
1
2
2
0
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
0
1
2
0
1
1
2
1
1
0
2
1
0
1
2
1
2
1
0
1
1
0
1
1
2
0
1
2
1
1
1
1
1
1
1
2
2
1
1
1
0
1
2
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
0
1
1
1
1
2
1
1
1
1
1
0
2
1
2
1
2
0
0
2
2
1
0
1
1
2
2
0
2
1
0
1
2
0
2
2
2
1
2
2
2
1
1
1
2
1
1
2
0
2
2
1
1
0
2
1
0
1
0
1
1
1
2
2
0
0
0
1
2
0
2
2
2
1
2
1
0
1
2
1
1
1
1
1
0
1
1
1
1
2
2
0
2
1
1
0
0
1
1
0
1
1
0
1
1
2
1
1
1
2
1
0
1
1
2
1
1
2
1
0
1
1
1
1
1
1
0
1
1
1
2
0
0
1
1
1
2
1
1
0
2
2
1
1
0
1
1
1
1
0
1
1
2
1
1
1
1
2
1
1
0
1
1
1
2
2
1
2
1
1
1
1
2
1
0
1
1
1
1
2
1
0
1
0
1
1
1
1
0
2
0
1
2
1
1
0
0
1
1
0
1
0
1
0
1
0
0
0
0
1
2
2
2
1
1
1
1
2
1
1
0
1
1
2
1
2
1
1
0
0
0
2
1
2
1
1
2
2
1
1
1
0
2
2
1
1
1
0
1
0
0
2
1
2
0
2
2
2
1
1
2
0
1
2
1
0
1
2
2
1
1
1
1
1
0
1
0
1
0
1
2
1
1
0
1
1
1
1
1
1
1
2
2
1
0
1
2
1
1
1
1
1
0
1
1
1
1
0
1
0
1
0
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
0
0
1
2
1
1
1
1
2
1
1
2
1
1
1
2
2
1
1
0
2
1
1
2
1
1
1
2
2
1
1
2
2
0
1
0
0
1
2
1
2
0
2
1
0
1
1
2
0
1
2
1
1
2
1
1
1
2
1
0
1
1
1
1
0
0
1
1
2
1
1
1
0
1
1
1
1
0
2
1
2
1
2
1
1
1
1
1
1
0
1
1
1
1
0
0
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
2
2
1
2
1
0
1
1
1
1
2
2
0
1
1
2
2
0
2
1
1
1
1
1
1
0
0
0
0
0
2
0
0
2
2
1
2
1
1
2
2
1
1
1
0
2
1
1
1
1
2
0
2
1
2
0
1
0
0
2
1
0
1
1
2
1
2
1
1
1
1
2
1
2
1
1
2
1
1
1
1
2
1
1
2
1
0
2
1
1
1
1
2
1
2
1
2
1
0
1
2
1
1
1
1
1
1
0
2
1
1
1
1
0
0
3
0
1
2
1
1
1
1
1
1
1
0
2
1
2
2
1
1
1
1
1
0
2
2
0
1
1
1
2
1
0
1
1
1
1
2
1
1
1
0
1
0
2
1
2
1
0
1
1
2
1
1
1
1
2
1
1
0
1
0
1
0
0
2
1
0
1
1
1
1
1
2
1
1
0
1
1
1
1
2
1
1
0
0
1
0
0
2
1
1
0
1
1
1
1
1
1
0
0
2
1
1
1
1
2
2
1
3
1
1
1
1
1
1
1
1
0
1
1
1
1
2
0
1
1
2
1
2
1
0
1
1
1
0
1
1
2
1
0
1
1
2
1
1
1
1
0
2
1
1
1
2
1
1
1
2
0
1
2
1
2
1
1
1
1
1
1
1
1
2
1
0
1
1
1
1
1
1
1
1
1
1
0
2
1
1
1
2
2
1
1
1
1
1
0
1
1
2
2
1
2
1
2
1
1
0
1
1
0
1
1
2
2
2
2
2
0
0
0
0
1
2
0
1
1
1
0
0
1
1
1
1
2
1
2
1
2
1
0
0
2
1
1
3
2
0
1
1
2
2
1
1
1
1
0
1
1
1
2
0
1
1
2
1
1
2
1
2
2
0
0
1
0
2
1
2
1
2
2
3
2
1
1
2
2
0
1
1
1
0
1
0
2
2
1
2
1
1
0
1
2
2
1
0
0
0
0
1
1
1
1
2
1
1
1
1
0
0
1
1
1
2
1
1
2
2
0
1
1
1
1
2
1
0
1
1
1
2
1
1
1
2
1
0
1
1
1
1
2
1
2
1
1
1
2
0
1
1
0
1
2
1
1
1
1
1
2
1
1
1
1
0
2
1
1
0
2
1
1
2
1
1
1
2
2
1
1
1
1
1
1
2
1
0
1
1
2
1
2
1
1
1
2
1
1
1
2
1
1
0
2
2
0
2
1
1
2
2
1
0
1
1
1
3
1
1
1
0
1
1
0
2
1
1
0
2
1
1
1
1
0
1
1
2
2
0
0
2
1
1
2
1
1
1
1
2
2
2
1
2
1
0
2
1
1
1
2
0
2
1
1
1
1
1
1
1
0
2
2
1
2
1
1
0
1
2
2
1
0
1
1
1
2
1
1
1
0
1
0
1
1
0
1
0
2
1
1
1
1
1
1
2
1
0
1
2
1
0
1
2
1
1
1
1
0
1
0
1
2
0
1
1
1
1
0
1
1
1
1
0
1
2
1
0
1
1
1
1
0
0
1
0
1
2
1
0
2
1
1
2
0
1
1
1
2
1
2
2
0
1
1
0
2
1
0
1
1
1
2
1
0
1
2
2
1
1
1
1
1
1
1
1
2
1
1
2
0
1
0
2
1
1
2
0
1
1
1
1
1
2
2
1
1
2
1
1
1
1
1
2
1
1
2
2
1
1
1
1
0
0
1
1
1
1
1
2
0
1
0
0
1
2
1
0
2
0
1
2
2
2
1
0
1
1
2
1
0
1
0
1
2
1
1
0
2
1
1
1
1
1
1
2
1
2
0
1
1
2
2
1
2
2
1
0
1
0
0
2
1
1
0
0
1
2
1
1
1
1
1
1
0
1
2
1
0
1
1
1
2
1
0
2
1
1
1
1
1
2
1
1
0
1
0
1
1
1
1
2
1
0
1
1
2
2
1
2
1
1
1
1
1
1
1
2
2
0
1
0
0
1
2
1
0
0
1
1
2
0
1
1
1
2
1
1
2
1
2
2
2
1
2
1
1
2
1
1
1
1
2
1
1
1
2
1
2
0
1
0
1
1
1
1
1
1
0
0
0
0
1
1
1
1
1
0
1
2
0
2
1
1
1
1
1
1
2
1
1
1
2
0
2
2
2
2
2
1
1
0
2
1
1
2
1
2
2
1
1
0
0
1
1
1
2
0
1
1
1
1
0
1
1
0
1
0
1
1
2
2
2
1
1
2
0
2
0
1
1
2
0
1
1
1
2
1
1
1
1
1
2
2
1
2
1
2
1
0
2
2
1
2
2
0
2
0
1
1
1
2
1
2
2
0
1
1
1
1
2
1
1
1
1
1
1
0
2
1
1
2
2
0
2
1
2
2
1
0
1
1
1
2
2
1
1
0
0
1
0
2
1
0
1
1
1
2
1
1
1
1
1
2
1
2
0
0
1
1
1
0
1
1
2
1
1
1
2
1
1
1
2
0
1
1
1
0
1
0
1
0
1
1
1
1
1
2
2
1
1
1
0
1
1
0
0
2
1
1
1
2
2
1
1
2
2
2
1
1
1
1
2
2
1
1
0
2
2
1
1
1
2
0
1
1
1
1
1
1
1
1
1
1
0
2
1
0
1
2
1
1
2
1
1
2
2
1
2
2
1
1
0
1
1
0
0
1
2
1
1
1
2
0
1
1
2
0
1
1
0
0
2
1
1
0
2
1
1
2
1
1
0
0
1
1
1
1
0
0
2
1
2
0
1
0
1
2
1
1
0
1
1
2
1
1
0
1
1
1
1
1
1
1
2
1
2
1
2
1
1
1
0
0
0
0
1
1
0
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
0
2
1
1
1
1
0
2
2
1
1
0
2
0
2
1
1
1
0
1
2
1
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
2
2
0
1
0
1
0
0
1
2
1
1
1
1
2
2
2
1
2
0
0
2
1
1
2
0
0
1
2
1
1
1
1
1
1
1
2
1
1
0
1
1
1
2
1
1
2
1
1
1
1
1
2
1
1
0
1
1
1
1
1
0
1
2
1
1
2
1
0
2
0
2
1
2
1
1
1
1
1
1
0
2
0
2
1
2
1
1
1
2
1
0
1
1
0
1
1
1
1
1
0
1
0
1
0
1
2
2
1
1
1
2
2
0
1
2
2
1
2
0
1
1
1
1
1
2
0
1
2
0
0
1
2
1
1
3
1
2
1
0
2
1
1
0
1
1
1
3
1
1
1
2
1
2
0
0
0
1
0
2
1
2
1
2
1
0
1
1
1
2
1
0
1
1
0
1
1
1
1
1
1
1
0
2
1
0
0
1
1
1
1
1
1
1
1
0
0
1
2
2
1
1
1
1
1
2
1
2
1
2
2
1
2
1
1
0
1
2
1
2
1
2
1
1
2
1
1
2
1
1
1
1
1
1
2
1
1
2
0
1
0
1
1
0
2
1
1
1
1
2
1
1
1
1
1
2
2
0
1
2
2
0
1
1
1
1
1
1
2
2
0
1
2
1
2
1
0
1
1
0
1
1
0
1
1
1
2
1
2
2
1
1
1
1
1
2
2
2
1
1
0
1
1
2
0
1
0
2
1
1
1
0
1
1
0
2
2
1
0
1
1
1
1
0
2
1
0
1
1
2
1
1
1
0
2
1
1
1
0
0
1
1
1
2
3
1
1
0
1
1
1
1
1
2
1
1
1
0
0
1
0
2
1
1
0
1
2
0
2
1
2
0
1
3
1
1
1
1
2
1
1
1
2
1
2
1
1
2
1
0
2
2
1
1
1
0
2
1
2
1
1
2
1
2
1
1
1
1
2
2
2
2
1
2
0
0
2
0
0
1
2
2
1
1
1
1
1
2
1
2
1
0
0
3
1
1
1
0
0
1
0
1
1
1
1
1
1
1
0
1
2
1
1
1
1
1
1
1
1
1
2
1
0
1
1
1
1
1
1
1
2
2
1
1
1
1
2
1
2
2
0
1
1
2
2
2
1
1
3
0
0
1
0
0
2
1
1
1
1
0
1
0
1
1
0
1
2
4
1
2
1
2
1
1
2
1
1
1
1
0
0
1
1
1
0
1
1
1
0
1
0
0
2
1
1
0
0
1
2
1
3
1
1
1
1
1
0
1
0
1
1
2
1
0
1
1
1
1
0
1
0
2
1
1
2
1
1
1
1
2
0
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
0
1
1
1
2
1
2
2
2
1
1
1
1
2
1
0
1
1
3
1
1
1
1
2
2
1
1
1
1
2
0
2
1
1
0
1
0
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
3
2
2
1
2
1
1
1
0
2
1
0
0
0
1
1
1
1
2
2
1
2
1
0
2
1
1
1
1
1
1
1
1
1
0
2
0
1
2
1
1
1
0
0
1
1
1
0
1
1
2
1
1
1
1
2
1
1
1
1
1
1
2
0
2
1
1
1
1
0
1
2
2
0
2
2
2
0
2
1
1
1
1
0
2
2
1
1
0
0
2
1
2
1
2
0
2
0
2
2
1
1
1
2
1
2
1
1
1
2
1
1
1
2
0
0
2
2
1
1
1
1
1
1
1
0
1
2
1
1
1
0
1
1
0
1
0
0
2
3
1
0
2
1
1
2
1
0
1
0
1
1
1
3
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
2
1
1
1
2
3
2
0
2
2
0
0
1
1
2
1
1
2
1
2
1
0
0
1
0
1
2
1
2
1
1
2
2
0
1
0
0
2
2
2
1
2
1
1
1
1
1
1
1
2
0
1
1
1
0
1
1
1
1
2
1
1
0
1
2
1
1
0
2
1
1
1
1
2
2
2
1
0
1
1
1
1
0
1
1
1
2
0
1
1
1
1
3
2
1
1
1
1
1
0
1
1
1
0
1
0
1
1
0
1
1
2
0
1
0
0
1
0
1
1
1
1
0
1
1
0
1
1
1
1
1
0
2
0
1
2
2
2
1
2
1
1
1
1
1
1
2
2
0
1
1
2
1
1
1
1
2
0
1
0
1
0
1
2
1
0
1
2
2
1
2
2
0
2
2
1
1
1
1
2
1
1
1
1
0
2
1
2
1
2
1
0
1
0
2
1
1
1
2
0
1
0
1
1
1
0
1
1
1
0
1
1
2
1
1
2
0
2
1
4
0
1
2
2
2
2
1
1
1
1
2
0
2
2
1
1
2
0
2
1
1
1
1
1
1
2
1
1
1
1
1
0
2
2
1
1
1
1
1
1
1
2
1
1
3
1
1
1
1
0
1
1
1
1
1
0
1
1
1
1
1
1
2
1
2
1
1
1
0
0
2
1
1
0
0
2
0
0
1
1
4
1
1
1
1
2
0
1
2
1
1
1
1
0
1
1
0
0
1
1
0
1
0
2
0
1
1
1
2
1
2
1
1
2
1
1
2
1
1
0
0
1
1
2
0
3
1
2
1
1
0
1
1
1
2
1
2
1
1
2
1
2
1
2
2
2
1
1
2
1
1
1
1
1
1
1
1
0
2
2
1
2
1
1
1
1
2
0
1
0
2
2
1
1
1
1
2
1
0
1
1
2
1
2
0
2
1
2
2
2
1
1
0
2
2
0
2
1
1
1
0
1
1
2
2
2
0
1
1
1
3
2
2
1
1
2
1
1
1
2
1
1
1
1
2
1
1
2
1
2
1
0
1
1
1
1
2
1
0
1
1
2
1
0
1
1
1
1
1
1
1
1
1
2
1
1
0
1
0
1
1
0
3
1
0
0
1
1
1
1
1
1
1
0
2
1
1
1
2
2
0
1
0
1
1
1
1
1
2
1
1
1
2
0
1
2
2
1
1
0
1
1
0
1
1
1
1
1
0
0
1
1
2
1
1
1
1
2
0
0
0
0
0
1
0
1
2
1
2
2
1
1
1
1
2
0
1
1
0
1
1
1
0
1
1
1
1
0
3
2
0
1
2
1
1
1
1
2
0
2
0
1
0
1
2
2
0
1
1
0
1
1
0
1
2
1
1
1
1
1
1
1
2
2
2
1
2
0
1
1
1
2
1
0
1
1
1
1
1
0
1
1
2
1
1
0
1
1
1
0
2
0
1
1
0
1
2
0
1
2
1
1
2
0
2
1
2
2
0
0
1
1
0
1
1
0
2
2
1
1
1
0
1
2
1
1
1
1
1
1
2
1
2
1
2
1
1
1
1
1
0
0
2
1
1
1
1
1
1
0
1
1
1
1
1
2
0
2
1
1
1
0
2
1
0
2
0
0
1
1
0
1
1
2
2
1
2
1
1
2
2
1
1
2
1
1
0
1
1
2
1
2
0
0
1
1
1
0
1
1
1
1
1
1
1
1
2
0
1
1
1
0
1
2
0
1
1
0
1
1
1
0
1
1
1
1
1
1
1
1
1
2
2
2
0
1
2
0
1
1
2
1
2
1
1
0
2
1
2
1
1
1
1
2
0
1
2
1
1
1
1
1
1
1
0
1
1
2
1
0
1
1
1
1
1
0
2
1
1
1
1
0
2
1
2
2
1
1
2
2
2
1
1
2
1
0
2
1
1
1
2
3
2
1
0
0
0
1
2
1
1
2
0
1
1
2
0
1
1
1
2
2
1
1
1
1
1
1
1
2
1
0
1
1
1
2
1
1
1
1
0
0
1
2
0
2
2
1
1
1
0
1
1
1
0
1
1
1
2
1
2
2
1
0
2
0
2
1
1
1
0
1
2
2
2
1
2
0
1
0
0
1
1
1
1
1
0
1
2
2
1
1
1
1
2
1
2
1
1
2
1
1
1
1
2
2
1
1
2
1
1
2
1
1
2
1
2
1
2
0
0
2
1
0
0
1
1
1
0
2
1
2
1
0
1
1
1
1
1
1
2
2
0
1
1
0
0
0
1
1
0
1
1
0
2
1
1
1
1
1
1
1
1
1
0
0
1
1
3
0
1
0
1
1
1
1
1
0
0
2
0
1
1
2
0
2
2
2
0
0
1
1
1
1
0
1
2
1
0
2
1
0
1
0
0
1
1
2
2
3
2
1
1
1
1
1
2
1
2
0
0
2
2
1
0
1
1
0
1
2
0
1
1
1
0
1
0
1
0
1
1
2
1
1
0
0
1
0
1
0
1
0
1
2
1
0
1
2
0
2
1
0
1
2
2
2
1
0
1
0
0
0
1
1
1
1
1
1
0
2
1
1
1
1
1
1
1
1
0
2
1
2
1
1
2
0
1
1
1
1
2
0
2
1
2
1
0
2
2
1
3
2
2
0
0
2
1
2
2
1
2
1
1
1
1
1
2
2
1
0
2
2
2
1
1
1
2
1
1
1
0
1
1
2
0
1
1
0
1
1
2
1
0
2
1
1
0
1
1
1
1
1
1
3
0
1
1
1
0
1
1
1
0
1
0
0
1
0
1
1
1
1
1
2
1
0
0
1
2
1
0
1
1
1
1
1
1
0
1
2
1
1
1
1
1
1
1
1
1
1
7
1
1
1
1
1
1
1
2
1
2
0
0
1
1
0
2
2
1
1
2
1
1
1
0
1
1
1
0
0
1
0
2
1
1
1
2
1
2
1
1
0
0
1
1
1
1
1
0
1
1
2
0
1
1
1
1
1
1
2
0
1
1
0
1
2
1
1
2
1
1
1
2
0
1
1
0
0
1
1
1
0
2
1
1
1
1
2
1
0
2
2
2
1
1
2
1
2
2
1
1
0
1
2
1
0
1
2
1
1
2
1
1
1
1
0
1
1
2
2
2
1
1
0
0
3
2
1
1
2
0
2
1
0
2
0
1
1
1
2
1
2
2
1
1
1
2
1
1
0
2
1
1
1
1
1
1
1
2
2
0
1
1
1
1
1
1
2
0
2
0
1
2
2
1
2
1
1
0
1
2
1
0
0
2
1
1
0
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
2
1
1
0
1
0
2
2
1
1
2
1
0
2
1
1
1
1
2
1
2
1
2
2
1
1
2
1
1
1
1
1
1
2
0
0
1
1
0
1
0
1
1
1
2
1
2
1
2
1
2
1
1
0
1
1
2
2
1
1
1
1
1
1
2
1
1
0
2
1
1
0
2
2
0
1
0
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
2
2
1
1
1
1
1
1
0
1
1
1
1
1
2
1
0
2
0
1
1
1
2
1
0
2
0
1
1
1
0
1
2
0
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
2
2
1
1
1
0
1
1
1
2
0
2
1
0
2
2
1
2
0
1
1
1
1
0
1
0
0
2
2
1
1
1
1
1
0
1
2
1
1
1
2
0
1
1
2
2
0
1
2
1
0
2
0
1
1
1
1
1
0
1
1
2
2
2
1
1
1
1
0
0
0
3
0
1
1
2
2
1
2
3
1
1
1
0
1
2
1
1
1
2
2
0
1
0
1
1
1
1
1
3
2
1
2
0
1
1
0
1
1
1
1
2
1
0
2
1
1
0
1
0
1
0
1
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
0
0
2
1
0
1
0
1
1
1
0
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
0
2
0
1
2
1
2
1
2
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
0
0
2
1
2
1
1
1
2
0
0
0
2
2
1
0
1
1
2
1
0
2
0
1
0
1
1
1
1
2
1
0
1
1
2
1
2
2
1
1
1
0
1
1
2
1
2
0
3
2
0
0
0
0
2
1
2
1
1
2
1
1
3
1
0
1
1
2
1
0
1
1
1
0
0
1
1
2
2
2
1
0
2
1
1
2
2
1
1
2
1
0
1
1
0
2
1
1
2
1
0
0
1
1
2
1
1
2
2
1
1
2
1
0
3
0
1
1
2
1
1
2
2
1
2
1
1
2
2
2
1
1
1
1
2
1
2
1
2
1
1
1
1
1
0
2
2
1
1
1
1
1
1
1
2
0
1
1
1
1
1
1
2
1
2
2
1
0
0
2
0
0
2
0
0
0
2
0
2
2
2
2
0
1
1
1
2
1
1
0
2
2
1
2
1
1
2
2
0
1
2
1
2
0
2
1
2
1
2
1
0
0
1
1
1
1
2
1
0
2
0
1
2
1
1
2
0
1
1
1
1
1
2
0
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
2
2
1
0
1
1
0
1
1
2
0
1
2
1
0
0
0
2
2
1
2
2
1
1
1
0
1
1
0
1
0
1
1
1
1
1
2
1
1
0
1
2
1
1
2
1
1
1
1
0
1
2
1
2
1
0
1
2
2
1
0
2
1
1
1
1
2
1
0
2
2
2
1
1
1
1
1
0
1
0
1
1
2
1
1
2
1
2
2
1
1
2
0
2
2
0
1
1
2
2
1
2
1
1
1
1
0
1
0
1
1
0
1
1
2
1
1
1
1
2
1
0
2
0
0
1
1
2
0
1
1
1
0
2
2
1
2
2
2
1
2
1
1
1
1
1
0
2
1
1
2
0
1
1
1
1
1
1
1
1
1
2
2
2
1
1
0
1
2
1
1
2
1
0
1
1
0
1
1
1
1
1
0
1
1
1
2
1
2
2
3
2
1
1
2
1
1
1
1
0
1
1
1
0
1
1
2
0
1
2
0
1
2
1
2
1
2
1
1
0
1
1
0
1
1
1
1
2
1
1
2
0
1
1
1
1
2
1
0
0
1
0
1
1
0
2
1
1
1
0
1
1
1
0
1
2
1
1
1
0
0
1
2
1
2
1
0
1
2
1
2
1
1
1
1
1
0
1
1
1
1
0
1
2
0
1
1
1
1
1
1
2
1
1
1
2
1
0
1
1
2
1
1
1
0
2
1
1
1
1
1
2
1
2
1
1
1
2
2
1
1
2
2
2
1
1
2
0
1
1
1
1
1
0
1
1
1
2
1
2
1
2
1
1
1
0
1
2
1
2
1
1
1
0
0
1
1
1
1
1
0
0
1
1
1
1
1
2
1
0
2
1
2
2
1
1
1
2
1
1
0
0
2
0
1
0
1
2
0
1
1
0
2
2
0
1
1
0
1
1
1
0
0
1
2
2
2
1
2
2
1
1
1
1
0
2
1
2
1
0
1
1
0
0
1
2
2
1
1
1
1
0
1
1
1
1
1
1
1
1
2
0
0
1
1
1
2
1
1
1
0
2
1
2
1
1
1
1
0
1
1
1
1
1
2
1
0
0
0
2
1
2
1
0
1
1
2
1
2
2
0
1
2
3
0
1
1
0
1
1
1
0
0
1
1
2
2
1
1
2
2
2
2
1
0
2
0
0
1
1
1
1
1
0
1
1
0
1
0
1
1
2
2
1
1
1
1
1
1
1
0
1
1
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
0
2
2
1
1
1
1
2
0
0
1
2
1
2
2
1
2
1
1
1
1
1
0
1
0
1
1
1
0
0
3
1
1
0
2
2
2
1
1
1
1
0
1
1
1
1
1
2
2
1
2
1
1
1
1
1
2
0
1
1
1
2
1
1
1
1
2
1
1
1
0
0
1
0
0
1
2
1
2
1
0
1
1
0
1
1
1
0
0
1
2
1
1
1
1
1
2
1
1
1
0
1
1
0
0
2
1
1
1
0
1
0
1
1
2
1
1
0
1
1
1
1
1
1
1
0
1
0
2
0
1
1
1
1
1
0
2
1
0
1
2
1
0
0
1
2
1
1
0
1
2
0
1
5
0
1
0
1
2
2
0
1
0
0
1
1
1
2
1
2
2
1
0
1
1
1
2
1
0
1
2
2
1
2
1
2
1
0
2
1
0
0
1
0
1
2
1
3
1
0
0
2
1
0
0
1
1
1
0
1
1
1
0
3
1
1
2
1
1
1
1
2
1
2
0
0
2
2
1
0
1
1
0
1
1
1
1
0
0
1
2
1
1
0
2
1
1
1
1
1
0
0
1
0
1
2
1
0
0
1
0
1
1
1
1
1
2
2
1
0
0
2
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
2
0
1
1
0
0
0
1
1
1
2
1
1
2
1
0
2
1
1
1
1
2
1
1
0
1
1
2
2
2
2
0
1
1
1
1
2
2
1
1
1
1
0
1
1
0
1
2
0
2
2
1
0
0
1
1
2
2
1
1
1
2
1
2
1
2
2
1
1
1
0
1
0
1
1
2
2
2
1
1
1
1
2
0
0
1
1
2
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
0
1
2
1
0
1
2
2
2
1
0
2
1
1
0
1
1
1
2
1
1
0
2
1
2
1
1
0
1
1
2
1
2
1
2
1
2
2
0
1
1
1
1
0
2
2
1
1
0
1
1
1
2
1
1
1
0
2
2
1
0
1
2
2
1
2
2
1
1
2
2
1
1
2
1
0
0
1
2
1
1
0
2
1
1
1
1
2
1
2
2
1
0
1
1
0
2
1
0
1
1
0
1
1
1
1
2
2
2
1
2
2
1
0
1
1
1
2
2
1
1
1
1
1
0
1
1
1
1
2
1
2
1
1
1
2
1
1
1
1
0
1
0
1
1
0
1
0
2
2
0
1
1
2
1
2
2
2
2
1
0
2
1
1
2
0
1
1
1
1
1
1
2
1
1
1
0
1
1
2
1
2
1
2
1
1
1
1
1
1
1
2
1
1
0
1
1
1
1
2
1
1
1
1
1
1
1
0
2
1
1
0
2
1
1
0
0
2
2
1
0
2
0
1
2
1
1
1
2
2
2
0
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
0
0
1
1
1
0
0
2
1
1
1
0
2
0
2
0
2
1
2
1
1
0
0
1
0
2
1
1
1
2
1
0
1
1
1
2
2
1
1
0
0
1
1
1
1
0
1
1
1
2
2
0
1
2
1
1
1
1
1
2
1
1
1
1
2
2
0
1
1
1
2
1
1
0
2
0
1
0
2
2
1
1
1
1
2
1
1
0
0
2
2
1
1
1
1
2
1
0
1
1
2
1
1
2
1
1
2
0
2
1
2
2
2
2
0
1
1
1
2
1
1
1
1
1
0
1
2
1
0
2
1
2
1
1
1
2
1
2
0
1
1
1
1
1
1
2
0
0
2
1
1
2
0
0
2
1
1
0
2
0
1
1
0
1
1
1
2
1
0
1
1
1
2
2
1
1
1
1
2
1
1
2
1
2
0
1
1
0
1
1
0
3
1
0
0
1
0
1
1
1
1
1
1
1
0
2
0
1
0
0
1
0
0
1
0
0
1
2
0
0
1
2
1
1
2
0
3
0
1
2
1
2
1
1
2
2
1
2
1
2
2
2
1
2
2
2
1
1
1
0
1
1
1
1
0
2
1
1
1
1
2
2
2
1
1
2
0
1
1
2
1
1
1
1
2
0
0
1
0
0
2
1
1
2
1
1
1
1
2
0
1
1
1
1
1
1
2
2
1
2
1
2
1
2
0
1
2
0
1
2
1
1
2
0
1
2
1
1
0
1
0
1
1
1
2
1
1
2
1
1
1
1
1
2
1
1
1
2
0
1
1
0
1
3
1
2
0
1
2
1
2
1
1
1
1
1
1
0
2
2
1
1
2
2
1
1
2
0
1
1
2
1
2
1
1
2
1
0
2
2
0
0
0
1
1
1
1
1
2
1
2
0
2
1
1
1
0
1
1
1
0
1
0
1
2
1
0
2
0
1
2
1
1
1
1
0
1
1
2
1
0
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
0
0
1
1
0
1
0
1
0
1
0
1
0
1
1
1
0
1
1
1
1
2
2
1
2
1
0
2
1
2
2
3
1
2
1
0
1
1
1
2
1
2
2
1
1
1
5
2
1
2
1
2
2
1
1
1
1
1
0
1
1
0
1
0
1
0
2
1
0
1
5
2
0
1
0
0
1
2
1
2
1
1
1
1
0
2
0
1
2
2
0
2
1
1
2
0
0
2
1
1
2
2
1
2
2
2
1
2
2
1
1
1
2
1
2
1
1
1
1
0
0
1
2
2
1
1
1
1
2
0
1
1
3
1
1
1
1
1
2
2
4
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
2
1
2
1
2
0
0
1
1
2
0
1
1
1
1
1
1
1
2
1
0
1
0
1
1
1
1
0
1
1
1
1
0
0
1
2
1
1
0
1
0
1
2
1
1
1
1
2
2
2
1
1
3
1
2
1
2
1
1
0
0
2
1
1
2
2
2
2
2
1
0
2
1
0
2
0
1
1
0
1
0
1
0
1
2
1
1
2
1
1
1
2
2
2
1
1
0
1
1
1
1
1
1
0
0
1
0
1
0
1
0
1
1
1
1
1
1
2
2
1
0
1
2
2
1
0
1
2
1
1
1
0
1
0
1
1
2
2
1
2
0
2
1
2
2
0
2
1
2
1
1
0
1
1
1
2
1
0
1
2
0
0
3
1
1
1
1
1
2
2
0
0
0
1
1
1
1
2
1
1
2
1
0
1
3
1
2
0
1
2
1
1
2
1
0
1
1
1
0
1
0
2
1
1
1
1
0
1
1
1
2
1
1
1
0
2
2
0
1
2
1
1
2
0
2
0
1
0
0
1
1
1
0
1
2
1
0
2
1
1
1
2
1
2
1
3
1
1
1
1
1
0
1
1
1
1
1
1
2
0
1
1
2
1
1
1
1
2
0
1
2
2
0
0
0
1
1
1
2
1
2
1
1
1
2
2
1
1
2
1
0
1
1
2
2
0
1
1
0
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
1
0
1
1
1
1
0
1
1
1
2
1
1
1
1
0
0
2
1
0
0
1
1
1
1
0
1
2
2
1
2
1
1
0
1
2
1
5
2
1
1
1
0
2
2
1
1
2
0
1
2
1
1
1
1
2
1
2
2
0
1
2
1
1
1
1
2
1
2
0
2
1
1
0
1
2
1
1
2
0
2
1
1
1
1
0
0
2
1
2
2
1
1
0
1
0
2
0
1
0
1
2
1
1
1
1
1
1
1
2
1
1
1
1
2
1
2
0
1
2
1
2
0
1
0
1
2
1
1
0
1
1
5
1
0
1
1
2
1
1
0
1
1
1
1
1
2
0
1
1
0
1
0
1
0
1
1
0
1
0
1
1
1
2
1
2
2
2
1
1
1
1
2
2
1
1
1
1
2
1
1
1
2
2
1
1
1
2
1
1
1
1
1
0
1
2
1
1
0
1
0
0
1
1
2
1
2
2
1
0
1
2
1
2
1
2
1
1
2
2
0
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
0
2
1
1
1
1
1
1
1
2
2
1
1
1
1
2
1
2
1
1
1
1
1
0
2
1
2
1
1
1
1
2
1
1
1
1
1
1
2
1
2
2
0
0
2
1
2
1
1
2
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
2
2
1
0
0
1
1
1
1
1
1
1
0
1
1
1
2
1
1
1
1
0
1
1
1
2
1
1
1
1
1
1
2
1
1
2
1
0
2
1
1
1
1
1
1
2
0
1
2
2
1
1
1
0
1
1
1
1
2
1
1
1
0
0
1
1
0
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
0
0
1
1
1
0
2
1
2
1
1
1
1
0
1
2
2
1
0
1
2
0
1
1
1
1
0
2
1
1
0
1
0
1
1
2
1
1
1
0
2
1
2
1
1
1
2
1
1
1
1
1
1
1
0
0
1
1
2
1
1
1
2
1
2
2
1
2
2
1
2
2
1
2
1
2
0
1
2
1
0
0
1
0
0
1
1
2
1
1
1
1
0
1
2
0
2
1
1
0
1
2
0
1
1
2
1
0
2
2
0
0
1
1
1
1
0
1
1
1
1
2
2
0
2
0
1
1
1
1
1
0
1
1
1
0
1
2
0
2
0
1
1
1
1
1
0
1
1
2
1
1
1
0
1
1
1
2
1
1
0
2
2
1
1
1
2
1
0
2
1
2
2
2
0
0
1
1
0
1
2
1
2
1
1
1
1
1
1
1
0
1
1
1
1
1
0
4
0
0
1
3
0
2
0
1
1
0
0
4
0
0
1
1
1
1
1
1
0
1
0
1
0
2
2
1
1
1
1
1
2
1
2
2
1
2
0
1
1
1
0
0
2
0
1
1
2
0
1
1
0
1
1
2
4
1
1
1
1
2
1
2
1
0
1
1
1
2
1
1
1
1
1
1
3
1
0
1
0
1
1
1
2
1
0
0
1
2
1
1
2
1
1
1
1
1
0
1
2
1
0
1
2
0
2
2
2
1
1
0
1
3
2
1
1
1
1
1
1
1
1
1
1
0
1
0
1
1
1
0
2
0
0
1
1
1
1
1
1
1
2
1
2
0
0
1
2
2
2
2
1
1
2
1
1
1
1
1
1
1
1
1
2
4
0
2
2
1
1
1
0
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
2
0
1
1
2
2
1
0
1
1
1
2
1
0
1
1
1
0
0
1
1
1
1
2
2
0
1
1
1
2
1
1
1
0
0
2
2
0
2
0
1
1
0
1
2
1
2
1
0
0
0
2
1
1
1
0
0
2
2
2
0
2
0
2
1
0
2
0
2
1
0
1
1
1
1
0
1
1
0
2
1
1
1
0
0
1
2
0
2
1
1
1
2
0
2
2
1
1
1
1
0
2
1
0
1
0
1
0
1
1
1
1
1
0
1
2
2
0
1
1
2
0
1
1
0
0
0
0
1
1
2
1
1
1
1
2
1
2
2
1
1
0
0
1
0
1
2
1
2
0
2
0
2
1
0
1
1
1
1
0
0
1
1
1
1
3
0
2
1
1
1
2
1
1
1
1
2
0
0
1
0
2
1
2
1
0
2
1
1
1
2
1
1
1
1
1
1
1
0
1
1
0
1
2
1
2
2
2
1
1
1
1
1
2
2
1
1
1
2
1
2
0
1
3
1
3
1
0
0
0
1
0
1
0
0
1
0
0
1
2
1
1
1
1
2
1
1
2
1
1
1
1
2
2
0
3
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
0
1
0
0
1
1
2
1
1
2
1
2
1
0
0
1
1
1
1
2
2
2
2
1
1
1
2
1
2
1
1
2
2
2
2
1
0
2
1
0
1
1
2
2
1
1
1
2
2
1
1
0
1
1
2
1
2
1
1
1
2
0
1
1
0
0
1
2
2
0
0
2
1
0
2
1
2
1
2
0
0
1
2
2
0
1
1
0
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
0
1
1
2
1
1
2
1
1
1
2
2
0
0
2
1
2
0
1
0
1
1
0
1
1
2
1
2
0
2
1
1
2
1
1
1
1
1
0
1
1
1
1
0
0
0
0
4
1
0
1
2
1
0
0
2
2
1
1
1
0
1
0
1
0
1
1
1
1
1
1
1
1
2
1
0
1
0
1
1
0
1
1
1
1
2
2
1
1
1
1
0
1
1
1
0
1
1
2
1
1
0
1
2
1
2
2
1
1
2
2
1
0
1
1
0
2
1
2
1
2
1
1
1
1
1
0
1
2
1
0
2
1
2
1
2
0
1
1
1
0
1
1
0
1
1
1
1
1
1
0
2
1
0
1
0
2
2
2
0
1
1
1
1
0
0
0
1
1
2
1
1
0
1
2
0
1
1
1
1
1
1
1
0
1
0
1
2
2
2
1
1
1
1
1
0
1
2
2
2
1
0
1
1
1
1
1
0
2
1
2
0
1
1
2
1
1
2
0
2
1
1
1
1
0
1
1
2
0
2
1
1
1
0
2
1
1
1
1
1
1
1
0
0
2
1
2
1
2
2
1
0
1
1
1
0
1
0
1
2
1
2
1
1
0
1
1
1
2
1
1
1
1
1
1
2
0
3
2
1
1
2
2
1
1
2
2
2
2
1
1
1
1
2
2
0
2
1
1
0
2
2
1
1
2
1
2
2
2
1
0
1
2
1
1
2
0
2
1
0
0
2
1
1
1
1
1
3
1
0
1
1
1
1
1
2
0
1
1
1
1
1
1
1
0
0
1
3
1
2
1
1
1
2
1
2
1
1
1
2
2
1
1
0
2
2
1
0
1
0
1
2
1
1
2
1
1
1
1
0
0
1
0
1
1
1
2
1
1
1
1
0
0
0
1
2
1
2
2
1
2
1
2
1
2
1
0
1
1
1
2
2
2
0
1
1
2
0
1
0
1
1
1
1
2
1
1
0
2
2
0
1
2
1
1
2
1
2
1
0
0
1
2
1
0
1
2
0
2
1
2
1
2
0
2
0
2
1
1
1
0
2
2
2
1
1
2
0
1
1
1
1
2
0
1
1
2
1
2
0
1
1
1
0
1
0
1
1
0
1
0
1
1
0
2
1
1
2
0
1
2
1
1
1
1
3
1
1
1
2
0
1
0
0
0
1
2
1
0
0
1
1
1
1
2
1
0
1
1
2
2
0
2
1
2
1
1
2
2
1
1
1
1
2
2
2
1
1
2
1
1
1
2
1
0
1
1
1
1
2
1
2
2
1
1
1
2
1
0
2
1
1
1
2
1
1
1
1
1
1
1
0
0
1
1
0
1
1
2
1
2
1
2
1
1
0
1
1
2
0
0
2
1
2
1
2
1
0
1
1
2
1
2
1
2
2
2
1
2
2
1
2
1
1
2
1
1
1
0
1
1
1
2
1
1
1
1
1
1
1
2
1
1
2
2
2
1
0
1
2
2
1
1
2
1
1
1
1
1
1
1
0
0
1
1
1
1
0
0
1
2
1
1
0
1
0
1
1
1
2
0
0
1
0
1
2
0
0
2
1
1
0
1
2
1
0
0
0
2
1
0
1
1
1
1
1
1
1
1
1
0
1
1
2
2
0
2
1
1
2
2
1
1
2
1
2
2
2
1
1
1
0
2
1
2
0
1
1
1
1
1
1
0
1
2
1
1
2
2
2
1
1
1
2
1
0
2
1
0
0
0
2
1
0
0
2
2
1
1
0
1
1
1
1
1
0
2
2
1
2
2
0
2
1
1
0
1
0
1
1
1
0
1
1
2
1
0
1
1
1
0
1
1
2
1
2
2
1
2
1
1
1
0
0
2
2
1
1
1
0
2
0
1
1
1
1
2
1
1
2
2
1
2
0
2
1
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
2
1
1
2
1
2
2
1
2
1
2
1
1
0
1
1
1
1
0
1
1
2
2
1
1
1
1
1
1
1
2
2
0
1
1
0
1
2
1
1
1
1
2
2
1
0
0
2
2
1
1
1
1
1
1
1
1
1
1
2
2
1
0
2
2
2
1
2
1
1
0
0
2
2
1
1
0
1
0
1
1
1
1
0
2
1
1
0
0
0
1
2
0
1
2
2
1
2
0
1
1
1
1
1
0
1
1
1
1
2
0
2
4
0
2
2
2
1
1
1
1
1
1
2
1
2
2
2
1
2
1
3
1
0
1
1
0
0
1
2
1
1
1
1
1
1
1
1
2
2
0
1
1
1
1
1
1
1
1
2
2
1
1
2
1
2
0
2
1
2
1
2
1
1
1
1
2
0
2
0
1
1
0
2
0
2
1
1
1
2
0
1
1
0
2
0
1
2
0
1
1
1
1
0
2
1
1
1
2
0
1
1
1
1
2
0
1
2
1
1
1
1
1
1
0
0
1
1
1
2
1
1
1
0
1
2
0
2
2
2
2
1
2
1
0
1
1
0
1
1
0
1
1
1
1
1
0
1
1
1
1
1
2
1
2
0
1
2
1
0
1
2
1
2
2
1
2
1
1
2
1
1
2
1
1
1
1
2
0
1
2
0
1
1
1
1
1
1
2
1
2
1
4
1
2
1
1
1
1
0
0
1
0
1
2
1
0
0
1
1
1
2
1
0
1
0
2
1
1
2
1
1
1
1
1
1
1
2
0
0
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
0
1
0
0
1
1
1
2
1
1
1
0
2
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
2
3
1
0
1
0
1
2
1
1
3
1
1
1
1
1
1
2
2
2
1
1
1
0
1
1
1
0
0
2
3
0
1
1
0
2
1
2
1
3
2
2
1
0
0
1
0
1
1
2
0
2
1
2
2
1
2
1
1
1
1
0
2
0
1
1
2
1
1
2
3
1
1
1
1
1
1
2
0
1
1
2
1
2
0
1
1
0
1
2
2
1
1
1
1
0
1
0
1
1
1
1
1
0
1
2
1
1
2
1
1
1
1
0
1
1
1
2
1
1
1
1
2
0
1
1
1
0
1
2
1
0
0
1
1
1
1
1
1
2
1
1
1
0
2
2
1
1
2
1
0
2
0
0
2
1
1
2
0
1
2
1
2
0
1
1
1
1
1
1
1
1
1
2
1
0
1
1
1
0
1
1
2
1
1
1
2
0
1
1
1
2
0
1
1
2
1
0
0
1
1
1
1
1
1
3
2
2
2
1
2
1
0
0
1
0
1
2
0
1
1
2
1
0
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
0
1
1
0
1
1
1
1
1
1
2
2
1
2
1
2
2
1
2
1
1
1
1
1
1
2
2
1
1
1
2
1
0
0
0
2
1
2
0
1
1
1
1
2
2
0
1
1
2
1
0
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
2
0
2
0
2
0
1
2
1
2
2
0
2
0
1
0
1
1
2
1
1
3
1
2
1
2
0
1
1
0
2
1
1
1
0
0
1
1
2
1
0
1
1
1
1
1
1
1
1
2
1
2
1
2
1
1
0
1
2
3
1
2
1
0
1
1
1
1
1
1
2
0
0
1
2
1
1
0
0
0
2
1
1
1
2
1
2
3
1
1
1
0
2
1
0
1
1
2
0
1
1
1
1
1
2
2
1
0
1
0
2
1
0
1
1
1
2
1
1
1
1
1
1
0
1
1
2
1
2
1
1
2
0
2
1
1
0
0
1
1
0
1
0
1
2
1
1
2
1
1
1
1
1
1
2
0
0
2
0
1
3
0
3
1
1
1
1
0
1
1
1
2
2
1
0
1
1
2
2
1
1
2
1
0
2
0
1
2
1
2
2
1
2
1
1
1
0
1
1
2
1
1
0
2
1
2
1
0
0
2
0
1
2
0
1
2
0
1
0
1
1
2
1
2
0
1
1
2
2
1
2
0
1
1
1
1
1
1
1
1
2
2
1
1
0
0
0
2
1
1
2
0
1
1
1
1
1
1
1
0
1
1
0
1
1
2
2
2
1
0
1
2
0
1
2
2
2
1
1
1
1
0
1
1
2
0
1
0
1
1
0
1
0
1
1
1
1
1
2
1
1
1
2
1
1
1
0
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
0
0
1
1
1
1
0
1
1
1
0
1
2
1
1
2
0
1
2
1
1
2
1
1
3
0
0
1
1
2
2
1
0
2
0
1
2
1
1
2
2
1
1
2
2
0
1
1
1
0
1
1
1
1
2
1
0
1
1
1
0
0
2
2
2
1
0
1
2
2
0
1
1
2
1
1
2
2
1
1
0
1
1
1
1
1
3
1
1
0
0
1
1
0
2
1
1
2
1
2
1
0
2
1
1
1
1
0
1
1
2
1
2
1
2
1
1
1
1
0
2
2
1
1
1
2
1
1
1
2
1
0
1
0
1
1
1
0
2
1
1
1
0
2
1
2
1
2
1
1
1
0
1
0
1
0
1
1
1
2
1
1
1
2
1
1
0
1
1
0
0
2
0
0
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
2
1
1
1
1
2
0
1
1
0
1
1
2
1
2
2
0
2
1
1
1
0
0
0
2
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
0
1
0
2
1
1
1
2
0
1
0
0
1
1
1
2
2
1
0
1
1
1
0
1
1
1
2
0
1
1
1
2
2
2
1
2
1
1
0
1
1
2
1
1
1
2
1
0
1
0
2
2
0
1
1
1
0
1
1
0
1
1
1
0
1
1
2
1
1
2
1
0
1
0
1
2
1
1
1
2
1
1
1
2
2
1
2
1
0
2
2
2
2
1
0
0
1
0
1
0
0
1
1
1
1
2
2
0
2
1
1
1
1
1
2
1
0
0
1
0
1
2
2
1
1
1
2
1
1
0
2
2
0
1
1
2
1
1
2
2
1
1
0
1
1
2
1
2
0
1
1
1
1
1
2
0
1
2
1
1
0
1
1
3
2
2
0
1
1
1
1
2
1
1
1
1
1
0
0
1
2
1
1
1
1
1
2
1
1
2
1
1
0
1
2
1
1
0
0
1
1
1
2
1
1
1
2
0
1
2
1
1
1
1
1
1
2
0
1
1
1
0
1
1
1
1
0
2
1
1
1
3
0
1
1
1
1
1
1
0
1
1
1
0
0
1
1
2
1
1
0
0
2
1
1
2
2
2
2
1
1
1
0
1
0
2
1
1
1
2
1
1
1
0
1
2
1
1
0
1
0
2
1
0
1
2
0
1
0
1
1
1
1
0
1
1
0
1
2
1
2
1
2
0
1
0
1
1
1
1
0
2
0
2
0
0
1
1
0
1
0
0
1
1
2
0
1
3
1
2
0
1
1
2
0
0
1
1
1
1
1
1
0
1
0
1
0
2
2
1
1
2
1
1
1
0
0
1
2
2
1
2
2
1
1
1
1
1
1
1
1
2
1
0
1
1
1
0
2
1
0
1
1
1
1
2
1
3
1
2
2
2
1
1
0
0
2
2
1
0
2
1
1
1
2
2
0
2
2
2
0
1
1
1
2
2
0
2
1
0
2
1
1
0
1
1
1
1
1
1
0
1
1
1
0
1
1
1
1
1
0
1
2
0
0
1
1
2
0
2
0
1
1
1
1
0
1
1
1
2
1
0
1
2
0
0
1
0
1
1
1
1
0
1
1
2
1
1
2
3
2
1
1
0
2
1
1
0
1
2
1
1
1
1
1
2
1
0
1
1
2
1
1
1
1
1
1
0
1
1
1
2
0
2
2
1
2
1
1
1
1
1
1
1
2
2
1
2
1
1
2
1
1
1
1
2
1
1
1
0
0
1
1
1
1
0
1
1
1
1
1
1
1
1
2
1
1
2
0
1
1
1
1
1
1
1
2
3
0
2
2
1
2
0
2
0
2
2
1
1
1
1
2
1
1
2
1
2
2
1
2
1
1
0
1
1
1
2
1
2
1
1
2
0
3
1
1
2
1
3
1
1
1
1
0
1
1
1
1
1
1
0
1
1
3
0
1
0
0
0
1
1
2
1
0
0
1
1
1
1
1
1
1
1
1
2
1
1
2
3
2
2
0
1
1
1
1
1
1
1
2
2
2
0
1
1
1
1
1
2
1
0
1
0
1
2
0
2
1
1
1
0
1
0
0
1
1
1
1
1
1
2
1
2
1
1
1
0
1
1
1
2
1
1
1
1
2
0
0
2
1
1
1
2
1
0
0
2
0
1
1
1
1
2
1
1
1
1
2
1
1
0
0
1
1
1
1
2
2
2
1
1
0
1
0
1
1
0
0
0
0
1
1
2
1
1
2
1
2
1
2
0
1
1
2
1
1
1
1
0
1
1
2
2
1
1
1
0
1
1
1
1
1
1
1
0
2
2
1
1
0
1
2
2
0
1
1
1
2
1
2
1
1
2
0
1
1
2
1
2
0
1
1
1
0
0
1
1
0
1
1
2
1
2
3
1
0
1
1
1
2
0
0
1
1
2
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
2
0
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
2
0
1
1
1
1
4
1
1
0
2
1
1
1
1
2
0
1
2
1
1
1
0
1
1
1
2
2
2
1
1
2
0
1
1
1
1
0
1
1
1
1
1
1
2
1
1
2
2
1
0
2
1
2
2
1
1
0
1
1
1
1
0
0
0
1
0
0
0
2
0
0
2
1
1
1
1
0
1
1
1
0
1
0
1
2
2
1
0
2
1
1
1
2
1
1
1
1
1
1
1
1
0
1
1
1
1
1
0
0
1
0
1
1
1
0
1
1
2
2
1
1
1
0
1
2
2
2
2
0
1
1
2
1
1
1
1
2
0
1
0
1
1
1
1
2
1
1
1
1
1
1
1
0
1
2
1
1
1
1
2
1
2
1
2
2
1
1
0
2
0
0
2
1
2
1
1
2
2
1
1
1
1
1
0
2
0
0
1
0
0
0
2
2
0
0
1
2
0
0
1
0
1
1
1
0
2
6
2
1
1
2
2
1
1
0
0
1
0
1
1
1
1
2
1
0
0
0
2
1
1
2
2
2
2
1
1
2
1
2
2
1
1
0
1
1
0
1
1
1
0
2
0
1
0
2
0
1
2
2
2
1
1
1
0
0
1
2
1
2
0
1
2
1
0
0
3
1
2
1
1
2
1
2
0
1
1
1
1
1
2
1
1
1
3
1
1
1
1
2
1
1
1
1
3
2
2
1
2
2
1
0
1
1
1
1
1
0
1
2
0
1
1
2
2
0
1
2
1
2
2
1
1
1
1
1
0
0
1
1
2
1
1
1
1
1
2
1
1
1
1
2
2
2
1
2
1
0
2
1
1
1
2
1
1
1
1
2
1
1
1
0
2
2
1
1
1
1
1
0
0
1
1
1
0
1
1
1
1
1
1
1
2
2
2
1
2
2
1
1
1
1
1
1
1
2
1
1
2
1
2
0
1
2
0
2
0
1
1
1
1
1
0
1
1
2
0
2
2
1
1
2
0
0
0
4
2
2
0
2
1
2
1
1
1
0
1
1
1
0
1
1
1
1
2
4
1
1
1
0
1
1
1
2
1
1
1
0
2
1
1
2
1
1
2
1
1
0
1
1
2
2
1
0
2
1
1
0
1
1
2
0
1
2
1
1
1
0
0
1
1
1
0
1
1
2
1
1
2
1
0
0
1
1
1
1
1
0
2
1
2
0
1
0
1
2
1
1
0
1
1
0
1
1
1
1
1
1
2
1
1
2
1
1
2
0
0
1
1
1
2
0
1
1
1
1
0
1
2
0
1
1
0
0
1
0
0
0
0
1
0
0
0
1
1
1
0
1
1
1
1
1
2
0
1
1
1
1
1
1
2
1
1
2
1
1
1
1
2
0
1
1
2
2
0
0
1
0
1
0
1
1
2
1
0
1
1
2
1
2
1
2
1
1
1
0
1
2
0
2
2
0
0
1
0
1
1
2
2
1
1
1
0
0
2
1
2
1
1
0
0
1
1
0
1
1
1
1
0
0
1
0
1
0
1
1
1
0
0
2
1
2
1
1
1
1
0
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
0
1
1
2
1
2
0
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
0
1
0
1
1
1
0
1
1
2
2
1
2
1
1
1
1
1
1
0
0
0
1
0
1
2
2
2
1
1
1
1
0
1
2
1
5
2
1
1
2
1
2
1
1
0
1
2
0
2
1
2
2
2
1
3
1
2
1
1
2
1
1
2
1
0
2
2
1
0
2
1
1
1
1
1
1
1
1
1
2
1
0
0
1
1
1
1
0
2
2
2
0
1
2
0
1
2
0
1
0
1
2
1
2
0
1
0
1
0
2
1
1
1
2
1
1
2
0
1
1
1
0
2
1
1
1
1
0
2
1
0
1
1
1
1
2
0
1
1
2
1
1
1
0
1
1
1
0
1
2
0
1
2
1
0
0
2
1
1
1
1
0
2
1
1
1
2
2
2
1
1
1
1
1
0
1
1
0
2
0
1
1
1
1
1
0
0
1
1
1
1
1
1
0
1
1
1
1
0
0
1
0
0
2
1
1
2
1
1
0
1
1
0
2
1
1
1
1
1
1
1
2
1
1
0
0
2
1
1
0
1
1
0
1
0
1
2
1
2
2
1
0
1
1
1
0
2
1
0
1
2
2
1
1
1
1
3
1
1
1
1
1
1
0
1
0
1
0
3
1
1
1
2
2
2
2
1
0
0
1
2
1
1
0
2
0
2
1
1
1
1
2
1
1
0
1
2
1
1
1
2
1
1
1
3
1
1
1
1
2
1
2
0
0
1
1
1
1
1
1
1
0
1
1
1
1
1
2
1
1
0
1
1
1
2
0
2
2
1
1
1
1
1
0
1
1
1
0
1
3
1
1
1
0
1
2
1
1
1
2
0
2
1
1
0
1
1
2
1
1
1
1
2
1
2
1
2
0
1
0
1
1
1
1
2
0
2
1
1
0
2
2
2
1
2
1
1
1
1
1
1
2
1
1
3
1
1
2
1
2
1
2
1
1
1
0
1
1
2
0
1
1
2
1
1
1
1
2
1
1
0
3
0
2
1
1
1
1
2
0
1
1
1
1
1
2
2
1
1
2
1
1
1
1
1
2
1
2
1
0
1
1
2
1
1
2
2
1
0
1
1
1
1
1
1
2
2
2
2
0
1
1
0
1
2
1
1
0
1
1
1
0
1
0
0
2
1
1
2
1
0
1
1
0
1
0
1
1
2
2
2
1
0
2
2
1
1
0
1
0
2
1
1
1
1
1
2
1
0
1
0
1
1
1
1
0
2
1
1
1
2
0
2
1
1
0
1
0
0
0
0
1
1
1
0
1
1
2
2
1
0
1
1
1
0
1
1
2
1
2
2
1
1
0
1
1
1
1
2
2
1
0
1
0
2
1
1
1
1
1
1
0
1
1
1
2
1
1
1
1
1
1
2
0
1
2
0
2
1
1
1
1
1
2
0
1
2
0
2
1
2
1
2
1
1
1
0
1
3
2
2
1
0
1
1
2
1
1
1
1
1
2
0
2
0
1
1
2
1
1
1
1
1
0
2
2
0
1
2
1
0
2
2
0
2
3
2
2
1
1
2
0
2
1
0
1
1
0
1
2
2
1
1
2
3
1
2
1
1
1
2
1
1
0
2
2
2
2
2
1
2
1
0
1
2
2
1
1
1
2
0
2
1
1
1
2
1
1
1
4
1
0
2
1
0
1
1
0
1
0
1
1
1
1
1
0
2
2
0
1
2
0
1
1
1
0
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
0
1
1
1
1
2
1
1
0
2
1
0
0
1
2
0
2
1
1
2
1
1
1
1
1
1
1
2
2
2
2
1
1
1
0
2
0
1
2
1
1
1
1
1
2
2
1
1
0
1
2
1
1
1
1
2
2
1
0
1
1
1
0
1
0
1
1
1
1
1
2
2
1
2
0
0
0
1
0
2
0
1
1
1
1
1
1
2
1
1
2
1
0
1
1
2
1
1
1
0
1
1
1
2
2
2
1
1
1
0
1
1
0
0
1
0
1
1
2
1
2
1
0
0
0
0
0
1
1
1
1
2
0
1
0
2
1
1
1
2
1
2
1
1
1
1
2
1
5
0
2
1
1
1
2
1
1
1
1
2
2
1
2
1
1
0
1
1
0
2
1
0
2
0
1
1
0
0
1
1
1
2
0
2
1
1
1
1
0
1
2
1
0
1
0
2
0
1
0
1
2
1
1
0
1
2
1
1
2
0
2
1
1
0
1
1
1
2
2
1
2
2
1
2
1
0
1
1
1
1
1
0
2
1
2
0
2
1
1
2
1
1
1
2
0
1
2
1
1
1
2
1
1
0
1
1
1
1
1
1
1
1
0
1
2
2
0
1
0
1
0
1
2
2
2
1
1
0
2
1
2
2
1
0
1
0
0
1
1
0
0
1
0
1
1
1
0
1
0
1
3
1
0
1
1
1
1
2
2
1
1
1
1
1
1
2
1
1
0
3
2
0
0
1
2
1
2
2
1
1
0
2
0
2
2
1
1
2
1
1
1
1
0
1
0
1
1
2
1
1
1
1
2
1
1
1
2
2
1
1
2
1
2
2
1
1
1
1
2
0
1
1
0
1
1
1
1
2
0
1
2
2
1
2
1
0
2
1
0
2
1
1
1
1
1
2
1
1
0
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
0
2
2
1
0
6
1
2
1
2
2
0
1
1
0
1
2
1
0
1
1
0
2
1
1
1
0
1
2
1
1
1
2
1
0
2
1
1
2
0
1
1
1
0
1
1
1
1
0
2
0
2
1
0
1
1
0
1
0
1
2
2
1
1
0
1
2
1
3
1
2
1
3
2
2
1
1
0
0
1
1
1
2
1
2
0
1
2
1
1
1
2
1
1
2
2
1
2
1
0
1
1
1
2
1
0
1
2
1
2
1
1
0
1
1
1
1
1
1
1
0
1
2
1
2
2
1
1
2
1
2
1
1
0
1
0
1
1
1
0
1
1
0
1
2
1
1
1
1
1
1
0
1
1
1
1
0
2
2
1
1
2
1
0
1
1
1
2
1
2
2
1
1
1
0
1
1
4
1
2
1
1
0
1
0
1
1
0
1
1
1
1
2
0
1
1
0
2
1
1
1
1
1
1
1
2
1
2
2
2
0
2
1
1
0
0
1
1
1
0
1
1
1
1
1
1
1
2
1
0
0
1
0
1
1
1
1
1
1
1
1
0
0
1
1
1
2
2
1
1
0
0
0
0
1
2
2
1
1
2
1
0
1
2
1
2
1
2
1
2
2
1
2
2
1
0
1
1
1
1
2
0
1
1
2
1
0
0
1
1
2
2
1
0
1
1
2
1
1
2
0
1
0
0
1
1
1
1
1
1
1
1
2
1
1
0
1
2
1
1
1
1
1
2
2
1
2
1
1
0
2
1
1
0
1
1
0
1
1
1
0
0
0
1
1
1
1
2
1
2
1
2
1
2
1
2
2
0
0
1
1
0
1
2
0
1
1
2
1
0
1
2
0
1
2
2
2
0
1
1
1
0
1
1
1
2
1
2
2
1
1
2
1
1
1
1
2
0
0
1
2
1
1
1
2
1
1
1
2
2
1
0
1
1
1
0
1
1
1
2
1
1
1
1
0
1
2
0
1
1
1
2
1
1
2
2
1
0
1
0
0
2
1
1
2
1
1
0
2
1
1
0
1
2
1
2
1
1
1
0
1
1
1
1
0
2
1
0
1
1
2
1
2
2
0
1
2
1
2
1
1
1
1
0
0
0
0
1
2
1
1
1
1
2
2
0
1
1
2
0
2
2
0
2
1
1
2
1
1
1
1
1
0
0
1
2
2
0
2
2
2
0
1
0
1
2
1
1
1
1
1
0
1
2
0
1
0
2
1
2
2
1
2
1
0
2
1
1
1
2
1
2
0
1
1
2
0
2
2
0
2
0
2
1
2
1
1
1
2
1
0
0
1
1
1
1
0
2
2
0
1
1
1
1
3
2
1
2
0
2
2
1
1
1
2
0
0
1
1
1
0
1
0
1
1
1
1
2
2
3
1
0
0
0
2
1
1
2
2
0
1
2
0
1
2
0
2
1
0
2
1
0
3
1
1
0
1
2
2
1
1
1
1
1
2
1
2
1
1
1
2
2
1
1
2
0
1
1
0
0
2
1
1
2
1
1
2
0
1
1
2
1
1
2
1
0
1
1
0
1
0
1
1
2
1
1
2
1
1
2
1
1
2
0
1
2
1
1
1
1
1
0
0
1
2
1
0
0
2
1
0
1
2
0
1
0
1
1
1
1
0
1
1
2
1
2
1
1
1
1
1
2
1
2
1
1
1
0
2
0
1
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
2
0
0
1
0
2
0
1
1
1
0
1
1
2
2
1
2
0
1
1
1
2
1
0
2
1
1
1
0
1
2
2
1
2
2
2
1
2
0
1
1
0
0
2
1
1
1
0
1
0
2
1
1
1
1
0
1
1
1
1
1
0
1
1
2
1
1
0
2
1
1
1
1
1
3
1
1
0
2
1
0
0
2
0
2
1
1
0
2
1
1
1
1
1
4
1
1
2
2
1
2
1
1
1
0
1
1
0
2
1
0
1
1
1
1
1
0
1
1
1
1
2
1
1
1
1
1
1
0
1
1
1
1
0
1
2
2
2
1
0
1
1
0
2
0
2
1
2
1
1
1
1
0
1
1
1
0
2
1
1
2
0
2
1
1
0
1
0
0
1
1
0
1
1
1
1
2
1
1
1
1
2
0
1
0
2
1
1
1
1
0
1
0
2
0
2
1
2
1
1
1
1
1
0
1
1
0
0
2
1
2
1
1
2
1
1
1
2
0
1
1
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
0
1
0
2
1
2
1
2
1
2
1
1
0
1
0
2
0
1
0
0
0
1
1
1
2
2
2
1
2
1
2
1
0
2
1
2
1
1
1
1
1
1
1
0
1
1
2
1
0
0
1
1
1
1
1
1
1
1
0
1
1
2
2
1
2
1
1
0
1
2
2
1
1
0
1
2
1
1
1
0
1
1
1
1
2
2
1
1
2
2
2
1
2
1
1
1
1
1
0
0
1
1
1
3
2
0
1
2
2
2
1
0
1
1
0
1
1
0
0
1
1
2
1
1
2
1
1
2
1
1
0
2
1
2
3
1
2
2
2
2
1
0
0
1
0
1
0
1
1
1
1
2
1
1
0
1
2
1
0
1
2
2
2
0
1
1
1
1
2
1
0
1
2
0
0
0
1
1
1
2
1
2
1
1
1
1
2
1
0
1
1
1
2
2
2
1
0
1
1
1
1
0
0
1
3
1
2
0
1
1
0
0
1
2
1
1
0
0
0
0
1
2
1
1
4
1
1
0
2
1
1
1
1
1
1
1
2
2
1
0
0
1
2
1
0
1
0
1
1
1
2
1
2
1
1
2
0
1
1
1
1
1
1
1
0
2
0
0
1
2
1
1
1
2
1
0
0
1
2
1
2
1
2
1
1
2
2
1
1
0
0
1
2
1
1
2
1
1
2
0
0
1
1
2
2
2
2
1
2
1
1
1
1
2
1
2
1
1
1
2
1
2
1
0
1
0
1
1
0
1
0
2
2
1
2
2
3
1
0
2
1
1
1
1
1
1
1
1
0
1
0
2
2
1
0
2
2
1
0
1
2
2
1
0
0
0
1
2
0
1
2
2
1
1
2
1
1
1
2
1
1
1
0
0
2
1
2
1
0
1
2
1
1
1
1
0
1
2
1
0
1
0
1
1
1
1
1
1
2
1
1
1
1
0
2
0
2
1
1
1
1
1
1
0
1
2
1
1
2
1
1
1
2
1
0
2
1
1
2
1
2
0
1
1
2
1
1
2
0
1
1
1
1
1
2
1
1
1
1
1
0
0
1
1
0
2
1
0
1
1
1
0
0
1
2
1
1
0
1
1
1
1
0
0
1
0
1
2
1
1
1
0
1
2
1
2
1
0
1
0
1
1
0
0
1
2
2
2
0
1
2
1
1
2
1
1
0
1
1
2
0
0
0
1
0
2
2
1
1
1
1
1
0
0
0
2
1
1
2
0
1
1
0
1
1
1
0
2
1
1
1
1
1
2
1
2
2
1
1
1
1
0
1
1
1
2
1
0
1
2
1
1
1
1
1
1
1
1
2
1
0
1
1
1
1
0
0
1
1
0
1
0
0
1
2
0
2
1
1
0
1
2
1
1
1
1
2
2
1
1
2
1
2
0
1
1
0
1
1
1
0
0
1
2
1
1
1
1
1
1
1
1
0
1
1
3
1
2
0
0
1
1
1
1
2
1
1
2
2
1
1
0
0
1
2
0
1
1
0
2
2
1
0
1
1
1
1
1
1
0
1
0
1
2
1
1
1
0
1
1
0
1
1
1
2
2
1
1
0
1
1
1
1
1
1
0
0
2
1
2
2
2
1
1
0
1
1
3
1
2
0
2
2
1
1
0
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
0
1
1
2
1
2
1
0
0
1
0
0
1
2
1
2
1
0
1
0
1
2
2
0
1
2
1
2
1
0
2
2
1
1
1
1
1
1
2
1
2
1
1
1
2
0
0
1
1
1
2
0
1
1
2
1
2
1
2
1
0
1
1
2
0
1
0
1
1
1
1
2
1
1
1
0
1
2
1
2
0
1
1
1
1
1
1
2
1
1
2
1
2
1
2
1
0
1
2
0
1
1
1
2
1
1
2
1
2
2
1
1
2
1
0
1
1
1
1
1
2
0
1
1
1
1
2
0
1
1
1
1
0
2
1
1
2
3
1
1
0
1
2
2
0
2
1
0
1
1
0
0
2
1
1
1
0
2
2
2
1
1
1
1
0
1
1
1
1
1
1
1
1
2
2
3
0
1
2
0
1
0
1
1
0
2
1
2
1
1
1
2
2
1
1
2
1
2
0
1
1
1
1
0
1
2
1
1
1
1
1
2
1
1
0
0
1
2
2
0
1
1
1
2
1
1
1
2
1
2
1
2
0
2
0
2
2
2
2
1
1
1
1
1
1
2
1
1
2
1
1
0
2
2
1
2
2
1
1
1
1
2
1
1
2
1
2
0
1
1
2
1
1
1
2
1
1
2
1
2
3
1
2
2
2
1
1
0
1
1
2
2
1
2
1
1
1
1
0
0
2
1
2
1
1
2
1
0
1
2
0
1
1
2
1
1
2
1
1
0
1
1
2
0
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
0
0
2
2
1
1
1
1
1
2
1
0
1
2
2
1
0
0
1
1
1
0
1
2
1
2
0
1
1
1
2
0
1
2
0
1
1
1
2
1
1
1
1
1
2
1
1
0
0
1
1
1
1
1
2
0
1
1
0
1
1
2
1
2
2
7
1
2
0
1
1
2
1
0
3
1
1
1
2
2
2
2
2
1
1
0
2
1
0
0
2
1
2
2
1
1
1
1
0
1
2
2
1
1
1
2
1
1
0
1
1
1
2
2
0
1
1
1
1
1
1
2
0
2
2
1
2
2
2
1
1
1
1
1
1
1
1
2
1
0
1
1
1
1
1
0
1
1
0
2
1
1
2
1
0
0
1
1
1
1
1
1
1
1
1
0
2
1
0
1
1
2
1
2
1
0
1
2
1
0
2
0
2
0
1
0
0
1
1
1
2
2
2
1
1
2
1
0
1
0
1
1
2
0
0
0
1
2
2
1
1
2
0
2
1
0
1
1
1
2
2
1
2
2
2
1
2
1
2
1
1
2
1
1
1
1
0
1
0
2
1
1
0
1
1
1
0
0
2
1
1
1
1
0
1
1
1
2
2
2
1
2
1
2
0
2
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
1
1
0
1
0
1
1
2
1
1
1
2
2
1
1
2
2
2
0
5
2
1
0
1
1
2
1
0
1
2
2
0
1
0
2
1
1
2
1
1
2
0
0
1
0
1
1
1
1
1
2
2
1
2
1
2
2
1
1
2
1
2
1
0
2
0
0
2
0
1
2
1
1
2
1
1
0
0
1
1
1
1
1
2
1
1
0
1
1
1
1
2
1
2
1
0
1
1
2
1
2
1
1
0
0
1
1
1
1
1
1
1
2
2
1
1
1
2
3
0
1
1
2
2
2
2
1
1
2
2
1
1
2
1
2
2
1
1
1
0
2
1
0
1
2
2
1
1
1
0
1
1
0
2
0
0
0
1
1
0
2
1
1
2
1
1
1
2
1
1
2
1
1
0
0
2
0
2
0
1
1
1
1
1
0
1
1
1
0
1
0
1
2
1
1
1
1
0
2
1
1
2
1
1
0
1
1
2
2
1
1
1
0
1
1
2
1
0
2
1
2
1
2
0
0
1
1
1
0
1
1
2
1
1
0
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
2
0
1
1
0
1
2
1
1
0
0
1
1
0
0
2
1
1
1
0
1
0
1
1
1
2
1
0
0
2
2
2
1
0
1
2
2
1
0
1
3
1
1
1
0
1
1
1
1
1
2
2
0
1
2
2
1
2
0
1
1
1
0
1
1
0
0
1
0
1
1
2
1
1
1
1
1
2
0
2
1
0
1
1
0
1
1
2
1
1
0
1
3
1
0
1
1
1
0
2
1
0
1
1
1
2
1
0
1
0
2
2
1
0
2
2
0
1
2
2
1
0
1
2
2
1
1
2
1
1
1
1
1
0
1
2
1
1
0
1
1
1
0
1
0
0
1
0
2
1
1
0
2
0
2
1
2
0
1
0
2
1
1
1
2
2
1
1
0
1
0
2
1
1
3
2
1
1
1
0
1
1
2
1
2
1
1
1
2
1
1
0
1
2
0
0
1
1
3
2
1
0
1
0
2
1
2
0
0
1
0
1
2
1
2
1
1
1
1
1
2
2
2
1
0
1
1
1
1
1
2
2
0
0
2
1
0
2
2
1
1
1
0
1
2
1
0
0
1
1
0
2
2
2
1
2
1
0
1
2
2
1
1
1
1
2
1
2
0
1
1
0
1
1
1
1
1
1
1
1
1
2
1
1
0
0
2
1
0
1
1
2
1
2
1
0
1
2
1
1
2
1
1
1
0
0
2
2
1
2
2
2
2
0
1
2
0
1
2
2
1
1
1
1
0
1
0
2
1
1
1
1
1
0
1
2
1
0
1
1
1
0
2
2
1
0
1
3
1
1
1
1
2
0
0
2
1
1
1
1
2
2
2
1
1
1
3
2
1
1
1
1
1
1
1
0
0
2
1
1
0
2
1
1
1
1
1
1
2
2
1
1
0
1
1
1
2
1
1
1
2
0
1
1
0
1
1
2
0
1
1
1
2
0
0
1
1
1
2
1
0
2
2
0
2
2
2
1
2
1
2
1
1
0
2
2
1
1
2
1
1
2
1
1
2
2
1
2
1
1
0
2
1
1
1
1
2
2
2
2
0
1
1
1
2
2
2
1
2
2
1
2
3
1
1
1
2
0
1
1
1
1
2
1
1
1
0
1
1
1
1
1
1
1
0
1
1
1
1
1
0
1
1
1
1
3
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
0
1
1
2
1
2
1
1
1
1
0
1
1
1
1
0
2
1
1
1
2
1
1
2
2
1
1
0
1
1
1
1
1
0
2
1
1
1
1
1
1
1
0
1
0
1
1
1
1
1
1
2
1
2
1
2
2
1
2
1
1
1
1
2
0
1
0
1
1
2
2
3
1
2
0
1
2
1
1
2
1
2
2
2
2
1
2
2
1
2
1
1
1
1
2
2
2
2
0
1
1
1
1
1
0
1
1
1
1
1
1
1
1
0
0
0
1
1
1
1
1
1
1
1
2
1
2
0
1
0
2
1
1
1
1
1
1
2
0
1
1
2
0
2
0
1
1
1
1
0
1
1
2
1
2
1
2
1
1
1
0
1
2
1
1
1
2
1
1
2
0
0
1
1
1
1
2
1
1
1
1
0
1
1
0
0
2
2
1
2
1
2
1
1
1
0
1
1
1
1
1
1
2
1
1
1
2
2
1
1
2
1
1
1
0
1
1
2
1
1
1
1
1
0
1
0
1
1
1
2
2
2
1
1
1
1
1
3
2
2
2
1
1
1
0
1
0
1
2
0
1
1
1
1
1
1
2
0
1
0
0
1
1
1
2
1
1
0
2
0
0
1
0
1
1
1
1
1
1
2
1
1
1
0
1
1
1
1
1
0
1
2
2
1
1
1
2
1
0
0
2
0
2
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
2
1
1
1
0
0
2
1
1
2
2
2
2
1
0
2
1
1
1
1
1
0
2
1
2
0
1
2
2
1
0
1
1
1
1
1
1
2
1
1
1
1
1
2
2
1
2
2
1
1
2
1
3
0
1
2
1
1
1
1
0
1
1
1
1
0
1
1
0
1
0
2
1
1
1
2
1
1
2
1
1
1
1
1
1
1
2
2
0
2
2
1
2
0
2
1
1
1
1
1
1
0
1
2
1
1
1
1
1
0
1
1
1
1
0
2
2
1
0
1
8
1
2
1
1
1
1
1
2
1
1
2
2
0
1
1
1
1
2
0
2
2
1
1
1
2
1
1
1
0
0
1
1
2
1
1
1
2
2
1
1
2
1
1
1
1
1
1
2
2
2
1
0
0
2
2
3
3
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
4
1
1
1
1
1
1
1
1
1
1
0
1
1
2
1
1
2
2
2
2
1
2
1
0
1
1
1
1
3
1
1
1
1
1
0
1
1
2
1
1
0
1
0
1
1
1
2
0
1
1
0
1
1
2
1
2
0
2
2
1
1
2
0
2
0
1
1
1
2
1
1
1
1
0
2
1
1
0
1
1
1
1
1
2
1
1
1
1
0
2
1
2
0
0
1
1
0
2
1
2
0
0
1
1
1
1
1
1
1
1
1
0
1
1
0
0
2
1
0
1
1
2
2
2
2
1
1
0
1
1
1
1
0
0
1
1
1
0
1
1
0
0
1
1
1
1
1
1
1
1
1
0
1
2
2
1
1
0
1
0
1
1
1
3
1
3
1
1
1
2
0
1
2
1
1
2
1
1
1
1
1
1
0
1
0
8
2
1
1
0
1
2
0
1
1
0
1
0
1
0
1
2
1
1
1
1
0
1
2
1
1
1
0
0
1
1
1
2
2
2
1
2
1
0
1
1
2
1
0
1
1
1
1
2
1
2
2
1
1
1
1
2
1
1
2
1
1
0
2
2
1
1
0
0
1
1
1
1
2
0
1
1
1
1
2
2
1
0
1
1
0
1
2
1
2
0
1
3
0
0
1
1
1
2
2
2
1
1
1
1
1
1
2
1
1
1
1
1
2
2
1
0
1
0
1
0
2
1
0
2
1
1
1
2
1
0
1
1
1
2
0
1
1
2
2
1
1
1
1
0
0
1
1
1
1
1
1
1
2
2
2
2
0
1
0
1
1
1
1
1
1
2
1
0
1
1
1
1
0
1
0
1
1
1
0
1
1
1
1
2
2
1
2
1
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
0
2
1
2
1
1
0
2
0
2
1
2
2
0
0
1
1
2
2
2
0
1
2
1
1
2
2
2
2
1
1
2
1
0
2
0
1
1
2
1
0
1
1
1
1
1
0
1
0
1
1
2
1
1
1
1
1
1
2
1
2
1
1
0
2
1
1
1
1
0
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
2
2
1
1
0
0
0
2
2
2
2
1
0
1
1
1
2
1
1
2
1
0
1
2
2
2
1
1
1
2
2
1
1
0
0
1
1
2
1
2
2
0
1
1
1
1
1
2
2
1
1
2
2
1
0
0
2
1
0
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
0
1
1
1
2
1
1
1
1
1
2
2
1
1
2
2
1
1
1
1
0
0
0
0
1
1
1
1
1
1
0
0
0
1
2
1
0
0
2
2
1
1
1
1
0
2
2
1
3
2
2
0
3
2
0
1
1
0
2
2
2
5
0
1
0
1
1
1
1
1
1
2
1
1
1
1
2
2
1
2
1
1
2
2
0
1
0
1
1
0
0
0
0
2
1
2
0
0
2
1
0
1
0
1
0
0
2
1
1
2
1
2
2
2
1
0
1
1
0
1
1
1
1
2
2
1
1
0
0
2
1
0
1
0
1
0
0
2
2
1
1
0
2
1
1
1
0
2
1
0
2
1
0
1
0
2
2
0
2
1
2
1
1
0
2
1
1
0
1
1
0
0
2
1
1
1
1
1
2
2
2
1
3
1
1
1
1
0
1
2
1
1
1
1
0
1
1
1
2
1
2
1
2
2
1
1
0
1
2
0
1
1
1
1
1
1
1
2
1
1
2
0
2
1
1
2
1
2
0
1
2
1
0
1
1
2
1
1
1
0
2
1
1
1
1
1
1
1
1
2
1
2
0
2
0
1
1
2
2
1
0
1
1
2
1
1
3
1
1
2
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
2
0
1
2
1
2
1
1
0
1
1
1
2
1
3
1
1
1
2
0
1
1
1
0
1
1
2
1
0
1
1
1
1
1
1
1
1
1
2
1
1
2
2
0
1
1
0
1
0
2
1
2
1
0
1
2
4
0
1
1
2
2
1
0
0
0
2
1
1
0
0
2
1
1
1
2
1
1
0
2
1
2
2
2
1
2
1
1
1
1
1
0
1
2
2
0
1
1
1
2
0
0
1
0
1
1
1
2
0
1
2
1
1
2
1
2
1
1
1
2
1
1
0
1
0
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
0
2
1
2
2
2
1
1
1
1
0
1
0
2
1
2
2
1
1
1
2
3
2
0
1
0
1
2
0
1
1
1
2
0
1
1
1
1
0
0
1
2
2
0
2
1
1
1
1
1
1
1
0
1
1
1
1
1
2
1
1
0
0
0
1
1
2
1
2
1
2
0
1
1
1
1
1
2
2
1
2
1
2
0
1
2
2
1
0
2
1
1
1
0
0
1
0
2
1
0
2
0
0
2
1
2
0
3
2
0
1
1
0
0
0
0
1
1
0
1
0
1
1
1
1
0
0
2
1
1
2
1
1
1
2
1
2
1
1
0
1
0
1
1
2
2
1
1
0
3
2
1
1
2
1
1
0
1
1
2
1
1
1
0
1
1
1
2
0
2
0
1
1
1
1
1
0
1
1
1
0
2
1
1
1
1
0
1
1
2
0
1
1
1
0
2
1
1
1
1
1
1
0
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
0
1
1
0
1
0
1
0
1
0
2
1
0
1
1
2
1
2
0
0
1
1
1
2
2
0
2
1
2
1
1
1
2
2
1
1
2
1
1
1
1
2
1
1
2
2
1
1
0
2
1
1
1
1
1
2
0
3
1
1
1
1
2
2
1
1
0
1
0
2
2
1
1
1
1
1
1
1
0
1
1
2
1
1
0
1
0
1
1
2
1
1
2
1
1
1
2
2
1
0
1
1
1
0
1
1
2
1
1
1
0
0
1
0
2
1
1
1
0
0
1
0
1
1
2
1
0
1
1
1
1
1
2
2
1
1
1
1
2
0
1
1
1
0
1
1
1
1
2
1
2
2
0
0
0
3
1
2
1
2
1
1
1
1
1
1
1
0
1
0
1
1
1
2
2
1
1
0
1
2
1
1
1
0
1
1
1
1
1
1
1
1
1
0
1
1
2
1
2
2
1
2
2
0
1
1
2
0
0
1
0
1
1
2
1
1
1
1
1
1
0
1
1
1
0
0
2
0
1
1
2
0
2
1
1
1
1
3
1
1
1
1
1
2
2
1
0
1
1
1
0
1
1
2
1
1
1
2
2
0
0
2
1
1
1
1
2
1
0
1
2
1
0
1
1
1
1
1
1
1
1
2
2
0
1
1
1
1
0
1
2
1
2
2
0
2
1
0
2
1
2
0
1
1
0
2
1
1
1
1
1
1
1
2
1
1
0
2
1
1
2
1
1
2
1
0
2
1
1
4
0
1
0
2
1
0
0
1
1
1
1
2
1
1
2
2
1
0
2
2
1
0
1
2
1
2
2
0
0
1
1
1
0
1
1
1
1
2
2
1
1
1
1
2
0
1
1
2
3
1
1
1
1
1
0
2
1
1
2
1
4
1
1
3
1
1
1
0
1
1
1
1
1
1
0
2
2
0
1
3
1
1
1
2
2
2
3
0
0
0
3
1
2
2
2
0
1
2
3
0
1
0
1
2
1
1
1
0
2
1
0
1
1
1
0
0
1
1
0
2
1
1
2
0
2
0
1
1
1
2
2
2
1
2
1
1
1
1
1
1
0
1
2
1
1
1
1
2
2
2
1
2
1
1
3
0
1
0
2
2
1
1
1
0
1
1
0
1
2
1
1
1
0
1
1
1
2
0
2
1
0
2
0
1
1
1
1
1
1
1
1
1
1
1
1
0
2
1
1
1
1
0
1
1
2
1
2
1
1
2
2
1
2
0
0
1
2
0
1
0
2
1
0
0
1
1
0
1
0
1
1
0
0
2
1
1
1
1
1
1
1
2
1
1
3
1
1
2
1
1
2
1
0
0
1
1
1
1
0
1
1
0
2
2
1
1
1
0
1
0
1
1
1
1
1
1
1
1
0
0
0
1
1
1
1
0
2
1
2
0
2
1
2
1
1
1
1
0
1
1
1
2
2
1
1
0
1
2
1
0
0
2
2
2
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
2
2
0
1
0
2
2
1
0
0
2
1
0
1
2
2
1
2
1
1
0
1
1
1
2
2
1
1
0
2
1
1
0
1
0
2
1
2
0
1
1
1
0
1
1
1
2
2
2
1
1
1
1
1
2
2
1
1
0
1
0
0
1
2
2
1
0
1
1
1
1
2
1
2
1
1
1
1
1
1
1
0
1
1
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
2
1
0
1
2
1
1
1
1
1
2
1
1
1
0
1
1
2
1
2
1
1
2
0
2
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
2
1
1
1
1
0
1
0
1
0
1
1
0
0
0
1
1
0
1
1
2
1
2
2
1
3
2
0
0
1
1
2
1
1
0
1
1
0
0
1
1
2
1
1
1
1
0
0
2
0
1
1
1
1
0
1
2
1
0
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
0
1
1
1
2
2
1
1
1
0
2
1
1
2
0
1
0
1
2
1
1
1
1
1
1
1
2
1
1
2
2
1
1
1
2
1
2
2
2
0
1
2
1
2
1
3
1
1
1
1
1
2
1
1
1
0
1
1
1
2
2
0
1
1
1
1
1
2
1
0
0
0
1
1
0
1
1
2
1
1
1
0
2
2
1
1
5
1
2
1
1
1
0
1
1
0
1
1
3
1
1
1
1
1
1
2
0
1
1
2
1
2
2
1
0
1
1
0
2
0
2
1
0
0
1
2
1
2
2
1
1
1
2
1
2
1
1
1
0
1
2
0
1
1
1
1
1
1
1
0
1
2
0
1
1
1
0
1
3
1
1
1
1
1
2
1
2
1
2
1
2
1
1
1
0
0
1
1
1
0
1
1
0
1
1
2
2
1
1
2
0
1
2
1
1
0
1
0
1
1
2
1
2
0
1
0
0
1
2
0
2
1
1
2
0
0
1
1
2
2
0
2
1
1
1
1
0
2
0
1
1
2
1
1
2
1
1
1
2
2
0
2
1
2
0
1
0
2
2
2
0
1
1
1
0
2
1
0
1
1
1
1
1
2
0
1
1
0
0
1
1
2
1
1
1
1
3
0
0
2
2
0
1
0
0
1
0
1
1
0
1
0
1
2
2
2
1
2
0
1
1
0
0
1
0
1
0
1
1
2
2
1
1
2
2
2
2
2
2
1
1
1
2
1
1
2
0
2
3
2
0
1
1
1
2
0
1
1
2
1
0
1
1
0
2
2
1
1
1
1
1
0
2
1
0
1
1
1
2
0
0
1
1
1
1
2
1
1
2
1
2
1
0
0
0
1
0
1
0
1
1
1
2
1
1
1
0
1
1
1
1
1
0
1
1
2
2
1
0
1
2
1
2
2
1
1
1
1
0
1
1
1
1
1
0
1
1
1
0
1
1
2
1
1
1
1
1
1
0
1
1
0
1
2
1
1
0
0
0
1
1
1
1
1
1
1
2
0
1
1
2
1
1
1
1
2
2
1
1
0
1
2
1
0
0
1
0
1
1
0
1
2
1
2
1
2
2
1
0
1
0
1
2
2
1
0
1
2
2
0
2
1
1
2
2
1
1
2
1
2
1
0
1
1
1
1
1
1
1
1
1
1
3
2
0
1
2
1
2
2
1
1
1
1
0
1
2
1
2
1
0
1
1
0
2
1
1
0
1
0
0
1
0
0
1
1
1
1
1
0
1
1
0
1
2
1
1
1
1
1
1
1
1
1
0
1
1
0
0
0
0
0
0
1
0
1
1
1
1
2
0
1
1
2
1
0
1
1
1
2
0
1
1
1
2
1
1
0
1
2
1
1
2
0
1
3
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
2
1
2
0
1
1
1
1
2
1
1
0
1
1
2
1
1
0
0
1
2
1
1
1
1
0
2
2
1
1
1
1
1
1
2
2
0
0
1
1
1
1
1
0
1
1
0
1
2
1
1
2
1
1
3
2
0
1
1
1
2
0
1
2
1
0
1
3
0
2
1
1
1
2
1
2
1
0
1
2
0
1
0
2
0
1
1
1
0
1
1
1
1
3
1
1
0
1
1
1
1
2
1
1
0
1
0
1
1
2
1
1
1
2
2
2
0
3
0
1
1
1
2
0
2
0
0
1
0
2
0
1
1
2
1
0
2
2
1
1
0
0
1
1
1
0
1
0
2
0
1
1
1
2
2
1
0
2
2
2
1
1
2
1
2
2
0
0
1
3
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
1
0
1
1
1
1
1
0
0
1
1
1
1
0
0
1
2
0
1
0
0
1
0
1
1
2
2
1
1
1
1
0
1
1
1
2
1
1
1
2
1
1
1
0
1
1
1
1
1
2
1
2
1
1
1
0
0
1
1
2
1
2
1
1
0
1
1
1
0
1
0
1
1
1
0
2
0
0
2
3
1
1
0
1
1
1
1
2
1
1
2
1
1
0
1
0
0
0
1
1
1
2
0
1
0
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
0
1
1
1
1
0
0
0
2
1
2
1
1
1
1
1
2
0
1
1
1
1
0
1
1
2
1
2
2
0
1
2
3
0
1
2
1
0
0
1
1
1
1
1
2
1
1
2
0
2
0
2
0
2
1
2
2
2
2
0
1
1
1
1
0
1
0
1
2
1
0
0
0
1
1
0
2
0
2
2
0
1
2
1
2
0
0
1
1
1
0
1
1
1
2
1
2
2
1
2
2
0
1
1
1
1
2
1
1
0
2
1
2
1
2
0
1
2
2
1
0
1
1
2
1
1
2
1
1
1
0
2
1
0
1
1
1
1
0
2
0
1
1
2
1
2
2
2
1
2
1
1
1
0
1
2
0
2
1
0
1
1
1
1
2
2
1
1
1
0
0
1
0
1
1
2
1
1
2
0
1
2
1
2
1
0
2
0
1
1
2
2
1
1
1
1
0
2
1
1
2
1
1
1
1
2
0
1
1
1
1
2
0
1
1
1
2
1
0
1
2
2
0
0
2
1
0
2
1
0
1
1
3
2
1
0
2
1
1
1
0
1
1
1
2
0
1
0
1
0
1
1
1
1
1
1
1
1
2
1
1
2
2
0
1
1
2
1
1
2
1
0
0
2
1
1
1
0
1
2
1
1
0
1
0
2
2
1
2
1
1
1
0
1
1
0
2
1
1
1
1
2
0
1
0
1
0
0
1
0
1
1
1
2
1
0
0
1
1
1
1
0
0
1
0
1
1
0
1
2
2
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
2
1
2
1
0
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
1
2
2
1
2
1
0
2
1
1
1
1
0
0
1
0
1
0
1
2
1
1
0
1
1
2
1
1
2
0
1
1
1
1
1
1
1
1
0
2
2
1
2
0
1
1
0
1
1
1
1
0
1
2
0
2
0
2
1
1
0
1
1
0
2
1
1
1
1
1
2
1
1
0
1
1
2
2
1
0
1
3
2
1
1
0
0
2
2
1
1
0
1
1
1
1
1
1
0
2
0
1
1
0
2
1
2
0
2
1
1
0
1
1
1
1
0
2
2
1
0
1
2
1
0
1
2
1
0
1
0
1
2
0
0
0
1
1
0
1
2
1
0
1
1
2
1
2
0
1
2
1
2
1
2
1
1
1
2
0
3
1
2
1
2
1
1
1
1
2
1
2
0
1
2
0
1
1
1
2
1
0
1
1
0
1
2
2
1
1
1
1
2
1
1
2
2
2
0
1
1
1
2
1
1
1
1
1
0
1
1
0
1
1
2
2
1
1
2
1
0
1
1
0
1
1
1
1
3
3
2
2
1
1
0
1
1
1
1
1
1
2
1
0
1
1
0
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
2
0
2
2
1
0
1
2
0
2
2
0
1
1
2
2
2
1
1
2
1
2
1
2
1
1
1
1
1
2
1
1
0
0
1
1
1
1
2
0
1
1
0
1
1
1
0
1
2
1
1
1
1
2
1
0
1
2
0
0
2
0
1
1
2
2
1
2
0
0
1
1
1
1
1
1
1
1
1
1
2
0
2
1
1
1
1
1
2
2
1
2
1
0
1
0
0
0
0
1
2
1
1
1
1
0
1
1
1
1
0
2
1
0
1
1
1
1
2
2
1
1
1
2
2
1
0
1
1
1
0
1
0
0
1
0
1
0
2
1
1
1
1
1
0
2
2
2
1
2
2
1
2
1
0
2
1
1
0
1
2
1
2
1
0
0
1
1
1
1
1
0
2
1
0
1
1
0
2
0
1
1
0
1
0
1
2
1
0
1
2
2
1
1
2
1
1
1
2
1
2
0
2
0
0
1
2
2
0
2
1
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
1
1
2
1
2
1
0
1
2
1
0
1
0
1
1
1
0
1
1
1
1
1
0
3
2
1
2
2
1
1
2
0
0
2
1
0
1
2
1
1
2
0
1
1
1
2
0
1
0
0
1
0
2
0
2
1
1
0
1
1
2
1
1
1
1
1
1
0
2
0
1
2
0
1
2
0
1
2
0
1
1
2
1
0
1
2
2
1
2
2
2
1
0
0
1
2
2
1
1
2
1
1
1
1
1
0
1
0
1
1
2
2
1
1
1
1
2
2
1
1
1
0
0
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
2
1
1
1
1
2
2
1
1
1
2
1
1
0
1
2
1
2
0
1
0
0
1
1
0
1
2
1
2
1
2
1
2
2
1
0
0
2
2
1
1
2
2
2
0
1
1
0
0
2
1
1
2
1
1
2
1
1
1
2
1
1
2
0
1
1
0
0
2
1
1
1
1
1
1
0
2
2
1
1
1
2
0
2
1
2
2
0
2
0
0
0
0
0
1
2
2
0
0
1
1
1
0
2
0
0
0
1
2
1
2
1
1
0
2
0
2
2
0
1
2
0
1
2
1
2
1
0
3
1
0
2
0
1
2
2
0
0
1
1
1
2
1
0
1
1
0
1
1
2
1
2
2
1
1
1
1
2
1
2
1
2
1
1
0
1
2
2
1
2
2
2
1
1
1
1
1
1
2
2
0
2
0
1
1
1
1
1
2
0
1
1
0
2
2
1
1
1
0
1
1
2
0
1
1
0
1
1
0
2
2
1
2
1
1
2
1
2
2
1
0
1
1
0
1
1
0
0
1
1
1
1
2
2
2
1
0
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
0
1
1
1
0
0
0
2
2
0
0
1
0
1
2
1
2
1
1
1
1
2
1
0
1
1
0
0
1
2
1
1
2
2
2
0
1
2
1
0
2
1
2
1
1
1
0
1
1
1
1
1
2
1
2
2
0
1
1
1
1
0
1
1
1
1
0
1
1
1
1
1
2
1
0
2
2
0
2
2
2
0
1
1
1
1
1
1
1
1
1
2
0
1
1
1
1
1
1
2
0
1
1
2
0
1
1
1
1
0
1
1
2
1
0
0
1
2
1
2
0
0
0
1
0
1
1
1
2
1
1
1
1
2
3
2
2
1
2
0
1
1
1
2
1
2
1
1
0
1
1
2
2
2
1
2
1
1
1
1
1
1
0
2
1
1
1
1
2
2
1
0
0
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
0
0
1
1
1
1
2
1
0
2
1
1
2
2
1
1
0
1
1
0
2
2
2
1
1
1
1
2
2
2
0
0
1
0
2
1
1
1
2
2
0
0
1
1
1
2
1
1
2
1
2
1
1
1
0
2
2
1
2
1
1
1
1
1
1
2
1
1
1
0
0
2
2
1
1
1
1
2
1
1
2
1
0
2
1
1
1
1
1
0
1
2
1
1
1
1
1
0
0
1
2
1
1
2
2
1
1
1
0
1
1
2
1
1
1
1
1
1
2
1
1
1
0
1
0
1
2
1
1
1
1
2
1
0
1
2
1
1
1
1
1
1
2
1
1
2
1
1
1
1
2
0
0
1
2
1
1
0
1
1
0
1
1
1
2
1
1
2
0
1
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
0
2
2
0
1
1
2
1
1
1
1
0
1
0
0
2
1
2
0
2
1
1
1
1
2
2
1
1
1
0
1
1
2
1
1
1
0
1
1
1
1
1
0
1
2
1
1
1
2
1
2
1
0
1
1
2
1
1
1
1
2
0
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
2
1
1
2
0
0
1
2
2
2
1
1
2
1
2
1
1
1
1
1
1
0
1
1
1
1
0
2
1
2
2
2
0
2
0
2
0
1
2
3
1
2
0
1
2
1
2
1
1
1
0
2
1
1
3
2
1
0
2
1
1
1
0
0
2
1
1
2
1
1
0
1
1
1
2
1
1
1
2
1
2
1
1
2
1
2
1
1
1
2
1
1
2
1
1
2
2
1
2
1
1
1
1
1
1
2
2
1
2
1
1
1
2
1
0
1
2
1
0
1
2
1
1
1
1
1
2
1
1
2
1
0
1
0
2
1
1
1
2
2
2
2
0
1
1
1
2
1
1
3
1
0
1
1
2
0
1
1
1
2
2
0
1
0
2
2
0
2
0
1
1
0
1
1
1
1
1
1
1
1
1
2
0
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
2
0
1
0
1
2
2
1
1
0
1
1
1
1
2
1
1
1
0
1
1
1
1
1
2
1
1
1
0
2
1
1
1
1
0
1
1
2
2
1
0
1
0
2
1
1
2
0
1
2
1
0
1
1
2
1
0
1
1
2
1
2
1
1
1
1
1
0
1
1
2
2
0
2
1
1
0
2
0
1
1
1
1
1
2
0
0
0
2
2
2
0
1
1
2
2
0
1
0
1
0
1
0
2
1
1
0
1
1
1
2
0
1
1
1
1
1
1
0
2
1
1
2
1
0
1
0
0
3
1
0
1
1
0
2
1
2
2
1
1
1
1
2
2
1
0
1
1
1
2
1
0
1
1
1
0
1
1
1
1
1
2
1
1
1
2
2
1
1
2
2
0
0
1
1
0
1
2
1
1
2
2
1
1
0
1
2
2
1
1
2
1
1
1
1
1
1
2
1
1
2
1
2
0
1
1
2
1
1
1
1
1
1
1
1
0
1
1
2
2
1
1
2
0
1
1
1
2
1
1
1
1
1
0
1
1
1
1
1
1
1
1
2
1
1
1
1
0
2
2
1
0
2
0
1
1
1
0
1
1
1
1
2
2
1
0
1
2
1
1
0
1
0
1
1
1
0
1
0
2
1
1
1
1
1
1
1
1
1
1
1
0
1
2
1
1
2
2
0
1
1
1
1
0
1
2
1
1
2
1
1
1
2
1
1
1
1
1
1
2
0
1
2
1
0
2
1
0
2
1
2
1
2
1
2
0
2
2
2
1
2
1
1
0
1
1
1
1
0
2
1
1
0
2
2
1
1
0
1
2
1
2
2
1
1
2
1
2
1
1
2
0
1
1
1
2
1
0
1
1
0
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
0
1
2
1
1
2
2
1
1
1
1
1
1
1
2
1
2
1
1
1
0
1
2
1
1
1
1
2
1
1
1
1
1
2
2
1
2
1
2
0
2
2
2
1
1
0
1
1
0
1
1
0
0
1
0
0
1
1
1
1
0
1
1
1
0
1
1
1
1
1
1
2
1
1
2
1
1
1
0
1
1
0
0
1
1
1
1
1
1
1
1
1
1
1
0
1
0
1
1
1
0
1
1
0
0
0
2
2
1
1
1
1
0
1
2
1
1
2
2
1
1
2
1
2
1
3
1
1
2
2
0
1
0
1
1
1
1
0
1
0
1
1
1
2
1
2
1
1
1
1
1
1
0
1
1
1
1
1
1
1
0
1
1
0
0
0
1
1
1
2
1
1
1
1
1
1
2
1
1
2
1
1
0
1
1
2
1
0
1
1
2
1
1
1
1
2
1
1
2
1
2
2
2
1
1
1
1
0
1
1
1
1
1
1
2
2
0
2
1
2
1
2
0
1
1
1
2
0
1
0
1
1
1
0
1
3
2
1
2
1
0
1
0
0
1
1
0
1
1
0
0
1
1
1
0
0
1
1
1
1
1
1
1
1
0
1
1
2
2
1
1
1
0
1
1
1
2
0
2
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
0
1
1
1
2
1
1
1
1
0
2
2
1
2
1
1
1
0
1
1
1
1
2
0
2
1
2
1
2
0
2
1
1
1
1
1
1
1
2
1
1
1
1
1
0
0
0
1
2
1
1
1
2
2
0
2
1
1
2
0
2
1
2
1
1
0
1
2
0
1
1
0
0
1
2
2
2
1
1
1
1
1
1
2
2
3
2
1
1
0
0
1
2
1
1
0
2
2
1
0
0
1
0
2
1
1
0
2
1
2
1
2
1
2
0
1
1
1
1
1
1
1
0
2
0
1
1
0
1
1
1
1
1
1
3
2
1
2
2
1
1
0
0
1
1
1
1
1
1
1
2
1
2
1
1
1
2
2
1
1
1
2
0
0
2
2
2
1
1
1
1
1
0
1
1
2
1
0
1
1
1
1
1
1
2
1
1
1
0
1
1
0
1
1
1
0
1
1
1
1
2
1
1
1
1
0
1
1
2
0
2
1
1
0
0
2
1
1
0
1
1
1
1
1
1
0
0
1
2
2
1
1
2
0
1
1
2
1
1
1
1
1
0
0
1
1
1
1
2
1
2
1
2
1
1
2
1
1
0
1
2
1
1
2
1
1
1
2
1
2
0
1
0
1
1
1
1
1
2
0
2
0
0
1
1
1
0
0
1
1
1
0
2
2
1
2
1
0
1
1
2
1
1
1
2
1
0
1
1
0
1
0
1
1
1
1
1
1
1
1
1
1
0
1
2
1
2
1
1
1
1
2
2
1
2
0
0
2
2
0
1
1
1
2
1
1
1
1
1
0
1
1
1
1
0
2
1
1
2
1
1
0
1
2
0
1
0
2
1
2
1
1
2
2
1
1
0
0
1
1
1
1
0
1
1
1
1
2
1
1
1
0
0
2
1
0
1
1
1
2
1
0
1
0
1
1
1
2
1
2
0
1
0
1
1
1
2
1
2
1
0
0
2
1
1
2
2
1
0
2
2
1
2
1
0
2
1
1
2
1
1
1
0
2
2
2
0
1
2
1
0
0
1
1
1
1
1
3
1
1
1
2
1
1
2
1
1
0
1
1
2
2
1
1
1
0
0
2
0
1
2
1
0
2
1
2
1
2
2
0
0
0
2
1
1
1
1
1
1
1
1
0
2
2
1
0
1
2
1
1
1
1
0
2
1
2
0
2
0
2
0
2
2
1
2
1
2
1
1
1
1
2
1
1
2
0
0
0
1
0
0
0
2
2
0
2
0
1
1
3
1
1
1
1
0
1
1
1
1
2
1
2
1
2
1
2
0
1
1
1
1
1
2
2
1
1
1
1
1
2
1
2
0
2
1
0
0
1
1
1
1
1
1
1
1
1
1
2
2
1
2
2
1
2
1
1
1
1
2
1
2
0
0
0
1
1
0
1
1
2
1
0
0
0
0
1
1
2
1
1
1
2
0
0
1
1
1
2
0
1
1
0
2
1
1
2
1
1
0
0
1
1
2
1
1
0
1
1
0
1
0
1
1
1
2
1
2
2
1
1
1
2
1
1
2
0
1
0
2
1
1
0
0
1
1
0
1
2
1
0
1
1
0
2
2
1
0
1
1
1
1
1
0
1
2
1
1
1
1
2
0
1
1
1
2
0
2
0
0
0
1
0
5
2
1
0
0
0
1
1
1
0
1
1
1
2
1
1
1
2
2
2
1
1
1
2
2
1
1
1
1
1
1
2
2
0
2
3
1
2
2
1
2
0
2
2
2
1
1
1
2
1
2
0
0
1
2
0
1
1
0
1
1
0
1
1
1
2
1
3
0
2
2
1
1
1
1
1
2
1
1
0
1
1
2
1
3
1
1
1
1
1
2
1
1
1
0
1
1
1
1
0
1
1
1
1
0
1
1
1
1
0
1
1
1
2
2
2
1
1
0
2
1
0
1
1
2
0
2
1
1
1
2
2
0
1
1
2
2
1
2
1
2
1
1
3
2
1
1
1
1
1
2
1
1
0
1
1
1
1
1
0
1
0
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
0
1
1
1
0
1
1
1
0
1
1
1
1
1
1
0
0
1
1
1
1
2
1
1
1
0
0
1
2
1
1
1
1
0
2
0
0
1
1
2
1
1
2
2
1
1
1
1
1
2
2
1
2
1
1
1
2
0
1
1
1
1
1
2
1
1
1
1
2
1
2
2
1
1
1
1
1
0
0
1
1
1
1
1
0
1
1
1
1
1
1
2
1
2
1
2
1
2
1
1
1
2
2
1
2
0
0
2
2
1
1
0
0
2
1
1
1
1
2
3
0
1
1
1
1
1
0
2
2
1
1
1
1
1
2
1
1
1
1
3
0
2
2
1
2
1
2
0
1
1
1
1
1
2
1
1
2
2
1
1
2
1
2
2
1
1
0
1
1
0
2
1
1
1
0
2
2
1
0
1
1
1
1
0
1
1
2
0
1
1
0
0
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
2
2
1
1
0
1
2
1
1
1
2
0
2
2
1
0
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
2
1
2
2
1
1
1
1
1
1
2
1
1
2
1
1
2
1
1
1
2
1
1
2
1
2
1
2
1
1
1
1
0
1
1
1
2
0
1
1
2
1
1
1
2
1
1
2
1
1
1
2
1
0
1
1
1
2
0
1
2
0
2
1
1
1
1
1
2
1
0
2
2
1
1
2
1
1
2
1
1
1
1
1
0
2
2
1
0
1
0
1
2
1
1
1
1
2
1
1
1
2
1
1
1
2
2
2
2
1
2
1
2
2
1
1
1
0
1
0
1
1
1
0
1
2
0
1
2
1
1
1
0
1
2
1
1
1
1
1
1
1
1
0
1
1
1
1
2
2
1
2
2
1
0
1
1
0
1
2
2
2
0
1
1
1
1
2
0
1
0
2
2
0
1
1
1
1
1
1
1
1
1
2
2
1
0
1
2
1
1
2
2
2
2
2
2
1
1
1
2
0
1
1
1
0
1
1
2
2
2
0
1
1
1
1
2
1
1
1
1
1
1
1
1
4
1
0
2
2
1
1
1
2
2
1
2
1
1
1
1
2
1
1
0
1
1
1
2
1
1
1
1
1
1
1
1
0
0
0
1
0
0
2
1
0
0
1
2
1
1
0
1
1
1
2
1
1
2
0
1
1
2
1
1
1
1
1
1
1
2
0
1
1
1
2
1
1
1
1
1
1
0
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
0
1
1
1
0
1
1
0
2
1
1
1
1
0
1
1
3
2
1
1
1
1
1
0
0
1
0
0
0
1
1
0
1
1
0
1
1
1
3
1
0
1
2
2
0
0
1
1
0
2
2
1
2
1
1
0
1
1
1
2
1
2
2
1
0
2
1
0
1
1
2
1
1
1
2
1
0
1
2
2
1
0
1
2
2
2
1
1
1
2
1
0
1
1
2
2
1
0
0
0
1
0
1
0
1
1
1
2
1
0
0
1
1
2
0
2
1
2
1
2
1
1
1
1
0
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
0
2
0
1
1
1
3
0
0
2
2
1
1
1
1
2
0
2
2
1
1
1
1
0
2
1
2
1
1
1
1
2
2
2
2
1
1
2
1
2
1
2
2
1
1
0
0
1
0
1
2
1
1
1
2
1
0
1
2
2
2
1
1
2
0
1
1
1
1
2
1
2
2
1
1
2
0
1
1
0
0
1
2
2
1
1
1
1
2
2
0
0
1
0
1
0
1
1
1
0
1
0
2
1
1
1
1
0
1
1
0
2
1
1
1
1
2
1
1
2
0
1
0
1
1
2
2
1
1
1
0
0
1
1
0
1
2
1
1
0
1
1
1
1
1
1
1
0
2
1
2
2
1
0
1
0
1
1
1
1
1
1
1
2
2
2
2
1
1
2
1
1
2
1
1
1
0
1
1
1
1
2
1
2
2
1
0
1
2
1
1
1
2
0
1
1
1
1
1
2
0
1
2
0
1
1
1
1
1
1
1
1
1
1
1
1
0
0
1
1
1
1
0
2
1
0
0
1
1
0
1
1
2
0
0
2
1
1
1
1
1
1
1
2
1
1
1
1
2
2
0
1
1
1
1
0
1
1
2
0
2
1
1
1
1
1
0
1
2
0
1
2
1
1
2
0
1
1
1
1
1
0
1
0
1
1
2
1
2
2
1
0
1
1
2
2
2
2
1
2
1
1
1
4
1
2
1
1
2
1
1
2
0
1
1
1
1
1
0
0
1
1
0
2
1
1
1
1
2
2
1
0
1
1
0
1
1
1
1
1
1
1
0
1
0
1
1
1
1
1
2
0
1
1
1
1
1
1
0
1
2
2
1
0
1
1
1
1
2
1
1
1
1
2
1
1
0
2
0
1
1
0
1
0
0
1
1
0
2
1
2
1
1
0
1
1
1
0
0
2
2
1
1
1
1
1
2
2
1
2
1
1
1
2
2
1
1
0
0
0
2
0
1
0
1
2
1
1
1
0
1
1
1
0
2
1
1
1
1
1
2
0
1
1
1
1
2
1
0
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
0
0
0
1
2
2
1
0
1
0
0
2
0
1
2
2
0
2
1
1
1
1
2
1
0
0
2
2
0
1
2
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
0
0
1
1
0
1
1
0
1
1
1
1
1
1
1
1
1
1
2
1
2
1
2
1
1
0
1
0
1
1
1
1
2
1
0
2
1
1
0
2
1
1
1
1
1
1
1
0
2
2
1
1
2
1
1
1
1
1
1
1
1
2
2
1
0
2
0
1
1
1
2
0
1
0
2
1
1
0
0
1
1
1
1
1
1
1
1
1
0
2
1
1
1
0
2
1
1
2
0
1
1
1
1
1
1
1
1
2
1
2
1
2
1
1
1
2
2
3
4
1
1
2
0
2
1
2
2
0
1
1
1
0
1
1
0
1
2
3
0
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
0
2
1
0
1
1
2
1
2
1
1
0
1
2
2
0
1
1
1
2
1
1
1
1
1
1
1
0
1
2
1
0
0
1
1
0
1
1
2
1
0
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
2
1
0
1
1
1
1
2
1
0
2
1
1
2
1
1
2
1
1
3
1
0
1
1
1
2
1
1
2
3
1
1
1
2
1
3
0
2
1
1
1
1
1
2
2
1
2
1
1
1
1
1
0
1
0
1
0
1
1
0
1
1
1
1
1
0
2
0
2
1
2
1
1
1
1
0
0
1
1
1
1
2
1
1
1
2
2
0
0
1
1
1
1
1
2
2
1
2
1
2
1
2
1
1
0
1
2
2
2
0
2
1
0
2
3
2
0
2
1
1
2
2
0
1
1
1
1
1
0
1
1
0
1
2
1
1
2
2
1
1
0
2
0
1
1
2
1
2
0
1
1
1
1
2
1
2
2
1
1
1
0
1
1
1
1
0
1
2
1
1
1
2
1
1
1
1
1
0
1
1
0
1
0
1
0
0
2
1
2
1
1
2
1
1
1
0
1
1
1
2
1
1
1
1
3
0
0
2
2
1
1
1
2
1
1
1
0
1
1
1
2
1
1
1
1
0
0
0
1
1
1
2
2
0
1
0
0
1
1
1
2
1
0
1
1
3
2
1
1
1
0
2
1
0
2
1
1
0
1
1
1
0
1
1
1
0
1
2
2
1
1
1
1
1
1
0
1
1
0
1
0
2
0
0
1
1
2
0
1
1
1
1
1
1
1
2
2
1
1
3
2
1
0
2
1
2
2
2
0
1
1
1
1
2
1
1
2
1
1
1
0
1
0
2
0
0
2
2
2
1
1
1
0
2
3
2
2
0
1
1
1
1
1
1
2
1
1
0
1
2
1
1
1
1
1
1
2
1
1
1
2
2
2
1
1
1
2
1
1
1
0
1
2
0
0
2
0
1
1
2
1
1
0
1
0
2
0
1
1
0
0
1
0
0
0
1
2
0
3
2
1
1
2
2
1
2
1
1
0
0
1
0
1
4
2
2
0
1
1
2
1
1
1
1
1
2
1
0
1
2
1
0
2
0
0
0
2
1
2
1
0
1
1
2
2
1
2
1
2
0
1
0
2
1
2
1
1
1
1
1
0
1
3
1
0
1
2
0
1
0
0
1
1
2
1
1
0
1
1
1
2
1
1
1
2
1
2
1
1
1
0
1
1
0
1
1
1
2
2
1
0
1
1
1
2
1
1
1
1
1
0
1
0
2
1
1
2
0
1
1
0
0
0
1
0
1
0
1
1
1
0
0
1
2
1
1
1
2
0
1
1
0
1
1
0
1
0
1
1
1
1
1
1
1
1
1
0
2
2
2
0
1
1
1
1
2
0
0
1
0
1
0
1
2
0
1
1
1
0
1
0
1
1
0
1
1
1
1
0
1
1
1
1
1
0
2
1
2
1
2
2
1
1
1
1
1
2
1
1
2
0
1
2
0
1
1
1
2
0
1
2
0
2
1
2
2
0
1
0
2
2
0
1
0
2
1
2
2
1
0
1
0
2
3
0
2
0
0
1
0
1
1
1
1
1
1
1
2
1
1
0
0
1
2
1
1
1
1
2
0
2
2
0
1
1
1
1
2
0
1
1
2
2
2
2
1
2
2
2
1
0
0
1
1
2
1
1
0
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
0
1
1
1
1
1
1
1
2
1
2
1
1
0
2
1
1
1
0
1
1
1
1
2
2
1
0
1
1
1
1
2
1
1
2
1
1
2
1
0
1
1
1
2
1
0
1
2
1
0
0
1
1
0
1
1
1
1
1
2
1
1
1
1
2
2
2
1
0
1
1
1
2
1
2
1
1
2
1
1
0
1
2
1
0
1
1
1
0
2
1
1
2
1
1
1
1
1
2
1
0
1
1
2
1
2
0
1
1
2
1
1
1
0
1
3
1
2
2
0
1
1
2
1
1
2
1
1
1
0
2
1
1
2
1
1
1
1
1
1
1
0
1
1
1
1
2
1
1
1
1
2
1
2
1
1
2
1
1
1
1
0
1
2
2
1
2
1
1
1
1
1
1
2
1
2
0
0
2
2
1
1
2
1
1
1
2
1
0
1
2
1
1
1
1
1
1
1
2
1
2
2
1
0
1
3
0
2
1
1
2
1
0
1
1
0
2
1
1
1
2
1
1
1
2
0
2
2
1
1
0
1
1
1
2
1
2
0
2
2
1
2
1
0
1
1
2
2
2
1
1
2
1
1
0
1
1
1
0
0
0
2
1
1
0
0
1
2
2
2
0
1
2
2
1
1
1
1
0
0
1
0
2
0
2
2
0
1
1
1
1
2
1
1
1
1
2
1
1
2
2
1
1
0
2
1
2
0
1
1
1
1
1
2
1
1
0
0
1
2
1
1
3
2
1
1
1
1
0
2
1
1
0
1
1
2
1
1
0
1
2
1
0
1
1
0
0
0
1
1
1
1
1
1
1
0
1
1
2
1
1
1
1
2
2
1
0
1
1
1
2
0
2
0
1
1
1
0
0
1
2
0
0
1
1
0
0
1
1
1
2
1
0
2
0
2
1
2
1
2
0
2
1
2
1
2
0
2
1
2
2
1
0
1
2
1
1
1
1
0
1
1
2
3
1
0
1
2
0
0
0
3
1
1
4
2
2
1
1
2
1
1
2
2
1
0
1
0
1
0
1
1
1
1
1
0
2
2
1
0
2
0
2
1
1
1
1
0
1
1
1
0
1
1
1
2
1
3
3
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
0
1
1
1
2
1
1
0
1
1
1
2
1
0
4
1
2
2
1
1
2
0
2
2
1
1
0
0
1
1
1
2
1
0
1
2
1
3
0
1
1
1
0
1
2
2
1
1
2
1
1
0
1
1
1
1
0
1
1
1
1
1
1
1
1
1
2
0
2
2
1
1
1
1
0
2
1
2
1
1
1
1
4
1
1
1
2
2
2
1
1
1
0
1
1
0
1
1
1
1
1
2
1
1
0
1
1
1
1
1
0
1
1
1
1
1
1
2
1
2
1
0
1
1
0
1
1
2
2
1
1
1
2
2
1
2
1
0
0
0
1
0
1
1
2
1
1
2
1
6
1
2
2
1
1
0
1
2
1
2
1
1
1
1
1
1
1
1
2
1
1
1
0
2
1
1
2
1
1
2
1
1
1
1
0
2
2
0
1
0
0
0
1
1
2
1
0
1
1
1
1
0
1
2
1
1
2
1
0
1
1
1
2
1
1
2
1
1
2
2
3
1
1
1
1
1
2
1
1
1
1
2
1
1
3
1
2
1
1
0
1
2
2
2
1
0
2
1
1
0
2
1
1
2
1
1
0
1
1
2
1
1
1
1
1
1
1
2
2
2
1
0
1
1
0
1
1
2
0
1
0
0
1
1
1
1
2
1
1
3
1
2
1
1
0
0
0
0
0
1
0
1
1
0
1
1
1
1
1
1
1
1
1
2
0
1
0
3
2
2
1
1
1
1
2
1
1
1
1
2
1
3
1
1
1
0
1
2
1
2
2
2
1
2
1
0
0
0
0
1
1
1
2
2
1
1
1
0
2
2
2
0
1
1
2
2
1
2
2
2
1
0
0
1
2
1
1
2
0
1
1
0
0
1
1
2
0
1
1
0
1
1
1
0
1
1
0
0
0
2
0
1
2
1
2
2
1
2
1
2
2
0
1
0
0
1
2
1
1
0
1
1
2
1
1
1
2
2
1
0
1
0
0
1
1
1
1
1
0
2
1
1
1
1
2
1
2
1
1
1
2
0
2
0
1
2
0
2
1
2
1
1
1
1
1
0
2
1
1
1
1
0
1
0
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
0
1
0
0
2
2
1
2
1
0
1
1
1
2
1
2
1
2
1
0
1
2
1
2
1
2
0
0
1
1
1
0
1
1
0
1
1
0
1
1
1
2
2
2
1
1
2
1
1
0
0
2
1
2
1
1
0
1
1
1
0
2
1
2
1
1
1
1
1
0
1
1
2
1
1
2
1
1
1
2
2
1
1
0
1
0
0
1
1
0
1
1
1
0
1
1
1
1
1
2
0
2
0
2
0
1
1
2
1
1
1
1
1
2
2
1
1
1
1
1
2
1
2
2
0
1
1
1
1
1
0
1
1
1
0
0
1
1
1
2
0
1
0
1
1
1
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
0
0
2
2
0
1
2
1
1
2
1
1
1
1
0
1
1
2
0
1
1
1
2
2
0
1
1
0
0
1
1
1
1
0
2
1
0
1
1
1
1
1
2
0
3
1
1
2
2
1
0
1
1
1
1
3
1
2
1
1
2
1
2
2
1
1
1
1
0
1
0
2
1
0
1
2
1
1
1
0
0
5
1
1
1
1
1
1
3
1
1
0
1
1
1
3
1
2
1
1
2
0
1
2
1
1
2
1
2
1
1
1
0
0
2
1
1
1
1
1
2
1
1
0
1
2
1
2
1
1
1
1
0
1
1
1
0
0
1
2
2
0
0
1
1
1
0
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
0
1
1
1
2
1
1
2
1
2
1
2
1
1
1
1
0
1
2
3
1
2
1
1
2
1
1
2
1
1
1
1
1
1
2
2
1
0
1
2
1
1
1
2
0
2
2
1
1
1
1
1
0
2
1
1
1
0
1
1
1
1
1
1
0
1
1
1
1
1
0
1
0
1
1
1
1
0
1
0
1
2
2
0
1
1
0
1
1
1
1
2
1
0
1
0
2
0
1
1
0
1
1
2
1
1
1
0
1
2
0
2
0
0
2
2
1
1
1
2
0
2
0
2
1
1
2
1
1
2
1
2
2
1
1
1
0
1
1
1
1
2
1
2
2
0
1
1
1
1
1
1
2
1
0
0
2
1
1
1
0
1
1
1
0
2
1
1
2
1
1
2
2
1
1
1
2
2
1
1
2
1
0
1
1
1
2
1
0
0
0
2
1
1
0
1
0
1
1
0
0
0
1
1
2
1
0
2
1
2
1
2
2
1
1
1
2
1
1
0
1
1
1
1
1
1
1
1
1
2
1
1
0
1
1
2
0
1
1
1
1
1
0
1
2
0
1
0
2
0
1
1
1
0
0
2
1
1
0
3
2
0
1
0
1
1
1
2
0
1
1
1
0
1
1
0
2
2
1
2
1
1
0
0
0
1
0
0
0
2
1
1
1
1
2
1
2
1
2
1
1
2
1
2
1
1
1
1
1
0
1
2
2
1
0
1
1
1
1
1
1
1
0
0
1
0
1
2
1
1
3
1
1
1
1
1
1
2
1
1
1
1
2
0
0
1
0
1
0
1
2
1
1
1
0
1
1
0
1
1
1
0
1
1
2
0
1
1
0
0
2
1
1
1
1
1
0
0
0
1
2
1
1
1
1
1
0
1
1
1
1
2
2
1
1
1
2
1
0
2
1
1
1
1
0
3
2
1
0
1
1
2
2
0
1
1
1
1
1
2
1
1
1
2
0
2
2
1
1
2
2
0
0
0
1
2
1
1
1
1
1
0
1
1
1
1
1
1
1
1
2
1
2
3
1
1
0
1
1
0
1
1
0
1
1
0
1
1
1
1
2
0
1
0
1
1
1
1
0
1
1
2
1
2
1
0
1
1
2
0
1
1
1
1
1
0
0
0
2
1
1
1
2
2
1
1
2
1
0
1
1
0
1
1
1
1
0
1
1
1
0
2
1
1
1
0
2
0
1
2
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
0
1
1
1
2
0
1
0
0
0
1
1
1
1
1
2
1
1
0
0
1
2
1
0
1
1
1
2
1
2
1
0
0
0
2
2
1
0
1
1
1
0
0
1
1
1
0
2
2
3
1
2
1
2
1
1
0
2
1
0
1
0
0
0
1
1
1
1
1
1
2
1
1
1
1
1
1
0
2
1
1
2
2
1
1
1
1
1
2
2
1
0
2
1
1
2
1
1
1
1
0
0
3
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
2
2
1
1
0
1
1
1
1
1
1
2
1
0
2
0
1
1
0
1
1
1
0
1
1
0
0
2
1
2
1
1
1
1
1
0
2
1
1
1
1
1
1
0
3
1
2
1
1
1
1
0
1
2
1
2
1
0
1
1
1
1
1
1
1
2
1
2
1
0
1
1
2
1
1
1
1
1
0
1
1
1
1
1
2
1
1
2
1
2
6
1
0
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
0
0
1
1
1
1
1
1
1
1
1
1
1
2
2
1
0
0
2
1
1
1
1
0
1
1
0
2
2
1
1
1
1
2
2
1
1
0
1
1
0
2
2
1
1
1
2
1
1
1
1
2
0
1
1
1
1
1
0
2
1
1
2
2
1
1
1
2
1
1
1
1
0
1
1
1
1
0
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
2
1
0
0
1
2
1
0
1
2
1
1
1
1
1
1
1
2
2
1
1
2
0
1
2
0
0
2
2
1
1
1
1
1
0
0
1
0
1
1
0
1
1
3
1
1
1
1
2
1
2
1
0
0
1
0
1
1
1
0
1
1
1
1
2
2
1
0
2
2
2
1
1
2
2
2
0
2
0
2
1
1
1
1
1
0
0
1
2
0
1
1
1
1
2
1
1
1
1
1
0
1
2
0
2
2
2
1
1
2
1
2
2
0
2
1
1
2
1
2
1
1
1
1
0
2
2
2
2
2
1
1
1
1
1
1
0
1
2
0
1
1
1
0
0
1
1
0
1
1
1
1
1
1
1
0
0
2
2
2
1
2
2
2
1
1
0
1
2
1
0
1
1
1
2
1
0
1
1
1
1
0
1
1
1
1
1
1
1
1
1
0
2
2
2
2
0
2
0
1
2
2
1
1
1
1
2
1
1
0
2
1
1
0
1
2
1
1
2
0
2
1
1
1
1
1
1
2
1
1
2
0
1
2
1
1
0
1
0
0
3
3
0
1
1
1
2
1
2
0
1
3
1
2
1
1
2
2
2
1
0
0
1
2
0
1
1
1
0
0
2
2
1
0
2
1
0
1
1
1
3
2
1
1
1
0
1
2
0
1
1
0
1
1
2
1
1
2
1
1
0
0
1
0
2
2
1
0
2
2
0
1
0
1
1
0
1
0
3
1
0
2
2
0
1
3
1
1
1
1
1
0
2
1
1
3
1
1
1
1
0
2
2
1
1
1
1
1
1
1
2
1
2
1
1
2
0
1
1
1
1
2
0
0
0
1
1
1
3
1
1
0
1
1
1
2
2
1
1
2
1
1
2
2
1
1
0
1
0
0
1
1
1
0
1
2
1
4
2
2
1
2
1
1
2
2
2
2
0
1
0
3
0
1
0
1
1
1
1
1
1
0
2
0
0
1
2
1
1
1
1
0
1
1
1
1
2
2
1
1
0
1
0
2
0
1
1
1
1
1
1
1
2
1
1
2
1
0
0
2
1
0
1
1
2
0
1
1
0
1
0
0
1
1
1
1
1
2
1
1
1
0
1
1
0
1
1
1
1
2
1
1
1
0
1
2
1
2
2
1
1
2
1
1
1
0
1
2
2
1
1
1
2
2
1
1
1
1
1
1
2
2
1
1
1
1
1
1
0
2
1
0
0
1
2
2
1
1
2
2
1
1
0
0
1
1
1
1
1
0
1
2
1
2
1
0
1
1
1
1
1
1
0
1
1
1
2
1
1
1
0
1
1
1
1
1
3
0
0
1
1
2
1
0
1
0
1
1
1
1
0
2
1
1
0
1
1
1
2
0
2
2
1
1
1
1
0
1
2
2
1
1
1
0
2
1
1
2
0
1
2
2
1
2
2
1
1
2
0
1
2
0
1
1
2
1
1
1
2
1
1
1
0
0
1
1
1
1
2
2
1
2
0
1
1
1
1
1
1
1
1
1
0
1
2
1
0
2
1
1
1
1
1
1
2
1
1
1
2
0
2
2
1
1
2
2
1
1
2
1
0
2
2
2
1
1
2
2
2
1
1
2
0
2
1
1
1
1
0
1
0
2
0
2
2
1
1
2
0
1
2
1
1
1
2
0
1
2
1
0
3
0
2
1
1
2
0
2
1
2
1
0
2
1
2
0
1
0
0
1
2
1
1
1
2
1
2
1
1
1
1
2
1
0
0
1
1
1
1
1
1
1
1
0
2
1
1
1
1
2
1
1
0
1
1
1
2
0
0
2
0
1
1
1
2
0
0
2
0
1
0
1
0
1
2
0
1
1
1
1
1
1
2
1
0
1
1
1
0
2
0
1
1
0
1
1
0
1
2
2
1
1
0
1
1
2
1
2
1
1
1
1
2
0
1
2
0
1
0
2
1
2
2
1
1
1
2
1
2
1
1
1
1
2
1
1
1
1
0
1
0
1
1
1
1
1
1
0
1
2
1
2
2
2
1
0
0
2
1
2
1
1
2
0
2
1
1
1
1
2
1
1
1
1
1
1
2
1
1
0
2
1
2
1
0
1
0
0
1
1
2
1
1
2
2
1
1
2
1
1
1
1
2
1
1
1
0
0
1
0
2
1
0
1
0
2
2
0
1
1
1
1
1
1
1
1
2
1
1
2
0
1
0
2
0
1
2
1
1
2
1
1
1
1
1
0
1
1
2
1
1
1
3
1
2
2
0
1
0
2
2
1
1
1
1
1
0
1
1
1
1
2
1
1
1
2
1
1
1
1
2
2
2
1
1
0
1
1
1
1
0
0
1
2
1
1
1
1
2
2
2
0
1
1
2
0
2
1
1
2
1
1
3
1
1
0
0
1
0
0
1
1
1
1
1
2
1
1
0
1
1
1
1
0
2
1
1
1
1
1
1
1
0
0
1
2
1
2
1
1
1
0
1
1
0
1
2
0
1
0
2
1
2
1
2
1
1
1
2
1
1
0
2
0
1
1
0
0
1
0
1
1
2
0
0
1
2
1
0
2
0
0
1
1
2
0
2
2
2
0
1
1
1
1
1
2
0
1
1
1
1
0
1
1
1
1
1
1
0
1
2
1
0
1
2
2
1
2
2
2
2
0
2
1
2
0
1
1
2
2
1
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
0
1
2
1
1
2
0
1
3
1
1
0
0
1
1
1
2
1
2
1
0
1
0
2
1
1
1
1
1
1
1
1
1
1
1
2
0
1
1
1
1
1
0
1
1
0
1
0
1
0
0
2
2
0
1
1
1
2
2
1
1
1
2
1
1
2
1
1
1
2
2
0
0
1
1
1
2
1
1
1
1
1
1
1
2
1
1
2
2
1
1
2
2
2
1
1
0
1
1
0
1
1
2
2
0
1
2
1
1
1
1
0
1
1
1
1
2
1
2
2
0
1
1
0
2
0
1
2
0
1
2
1
2
2
2
1
1
1
1
0
2
0
1
2
1
1
1
1
1
0
1
0
1
0
1
2
1
2
0
0
1
1
0
1
1
1
1
1
1
1
0
1
1
1
2
2
0
2
1
2
1
1
2
0
1
1
0
1
1
2
2
2
1
2
1
1
2
1
1
2
1
1
1
0
1
1
1
0
2
2
2
1
1
1
1
1
2
1
1
0
0
2
0
1
1
1
0
1
1
1
1
1
1
2
0
1
2
1
1
1
1
2
2
1
1
2
2
0
0
1
0
0
1
2
1
1
0
1
1
1
2
2
1
2
1
2
1
1
1
0
2
2
2
2
1
1
2
0
2
0
2
1
0
2
1
2
1
1
1
1
1
2
1
1
1
1
0
2
1
1
2
0
0
2
1
2
1
1
1
1
1
1
1
3
1
2
0
1
0
2
1
1
1
1
0
1
2
0
1
2
0
1
1
0
1
1
2
1
2
1
2
0
1
1
2
2
2
1
1
1
1
1
1
1
1
2
1
0
0
1
0
1
1
0
1
1
2
1
1
2
2
1
1
1
2
1
1
1
1
2
2
0
1
1
0
1
1
1
0
1
1
0
1
0
1
2
1
2
1
1
2
2
1
1
1
1
2
0
0
0
1
1
0
1
2
2
1
1
1
1
1
1
2
2
1
2
2
0
1
2
1
2
0
1
0
2
0
0
1
1
0
1
0
1
1
1
2
0
1
2
2
2
1
0
1
1
1
2
0
1
1
0
1
1
2
1
1
2
2
0
1
0
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
2
1
2
1
1
0
1
1
1
2
2
0
3
1
1
2
1
1
1
2
1
2
0
2
1
1
2
2
0
1
1
0
2
2
0
1
1
2
1
1
1
1
1
1
0
1
0
1
2
0
0
2
1
1
1
2
0
0
1
1
1
0
2
2
2
1
2
1
1
1
3
2
1
0
2
1
2
2
0
2
1
0
0
1
0
0
1
1
1
1
2
2
1
1
2
1
1
1
1
1
0
1
1
1
1
0
1
2
0
1
0
1
0
1
2
2
1
1
1
2
2
2
1
1
2
1
3
1
1
1
0
0
1
2
2
1
0
2
2
2
1
1
1
1
1
1
1
0
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
0
2
1
0
1
2
1
0
1
0
1
1
1
0
1
1
1
1
1
0
2
1
1
1
2
1
2
1
1
1
2
1
2
2
1
2
1
1
1
2
1
0
1
1
1
0
2
2
2
1
0
1
1
1
2
1
2
1
1
0
2
2
1
2
1
1
0
1
1
1
1
1
1
1
2
1
0
1
1
1
1
2
2
1
2
2
1
1
1
1
0
2
0
1
1
2
2
1
2
1
1
2
1
1
1
1
2
1
1
2
1
2
1
0
2
1
2
1
1
1
1
0
1
1
1
1
1
1
2
1
1
1
2
1
2
2
1
1
1
2
1
1
2
1
1
1
2
1
0
1
1
1
1
1
0
0
0
1
1
1
0
2
0
2
1
1
1
0
2
2
2
0
1
1
1
1
1
2
2
1
2
1
1
0
1
1
0
0
0
1
0
1
0
0
2
1
1
1
0
2
2
1
1
1
1
0
1
1
1
0
0
1
2
1
1
1
1
0
2
1
1
1
2
0
1
1
2
1
1
2
1
0
1
1
1
1
1
1
1
0
2
1
1
1
0
1
1
0
1
1
2
2
1
1
0
0
1
1
0
0
2
0
1
1
1
1
1
1
1
1
0
2
1
0
1
1
2
0
1
3
0
1
1
1
1
2
1
1
2
0
0
1
0
1
2
1
1
0
1
0
2
0
1
0
2
1
0
1
2
1
2
0
1
1
1
1
0
0
2
2
1
1
0
0
1
1
1
0
1
0
1
2
0
1
2
0
1
1
2
1
2
1
0
2
0
1
1
0
0
2
2
1
1
0
1
2
1
1
2
2
2
2
2
1
1
1
2
1
2
2
2
1
3
1
0
0
0
1
1
1
1
2
2
0
1
1
0
1
2
2
1
1
1
2
0
1
2
1
3
1
1
2
1
1
2
2
2
1
1
2
0
2
1
0
1
1
2
1
1
1
0
1
1
1
2
2
0
0
1
1
0
2
1
1
1
1
1
1
1
0
0
1
3
1
1
1
7
1
0
1
1
2
1
1
1
2
1
2
0
2
1
2
1
1
0
1
1
1
1
1
0
1
0
1
0
1
1
2
0
2
2
2
1
0
1
2
1
1
1
2
1
1
2
1
2
1
1
2
2
2
0
1
1
1
1
2
1
2
2
2
1
1
2
1
1
1
0
0
2
2
1
2
1
2
2
2
0
1
1
1
1
1
2
2
0
1
0
1
2
1
1
1
1
2
1
0
1
0
2
0
1
1
2
1
0
0
0
1
1
0
0
1
2
2
0
0
1
1
1
1
1
1
2
3
2
1
1
2
1
2
1
1
1
0
0
0
0
0
1
1
2
2
0
0
1
1
2
0
0
2
2
1
1
1
1
0
0
1
1
0
1
1
0
1
1
1
2
1
1
1
0
1
2
1
1
1
1
1
0
1
1
0
1
2
2
2
0
1
2
1
1
1
1
2
1
0
0
2
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
0
2
1
1
1
2
1
2
1
2
3
1
1
1
1
1
0
0
1
1
1
0
2
1
0
2
1
1
1
1
0
1
0
3
1
0
2
1
0
0
1
2
2
2
1
1
1
0
1
1
1
2
1
1
0
1
0
1
2
1
0
2
1
1
2
1
2
1
1
1
2
2
1
2
2
1
1
1
0
1
2
1
1
1
1
0
6
0
1
2
1
1
1
1
2
1
2
2
1
1
0
2
1
1
1
2
1
1
2
2
1
1
1
1
1
1
1
1
0
2
1
1
2
1
0
1
1
1
0
0
1
1
1
2
1
1
1
1
2
1
1
1
1
0
1
1
1
1
0
1
1
2
1
1
1
0
1
1
2
1
1
1
2
2
1
1
0
1
2
2
0
0
2
1
1
2
2
0
0
1
2
2
1
1
1
2
1
2
0
1
1
0
0
2
1
0
1
1
2
1
1
1
1
1
2
1
0
1
2
0
1
1
0
1
0
0
1
1
0
2
1
1
1
1
2
0
0
2
1
1
0
0
0
1
1
1
1
2
1
1
4
2
1
2
2
0
1
1
1
1
2
1
1
1
0
0
2
1
0
1
1
2
1
1
1
0
0
2
2
1
1
2
1
2
1
1
2
1
1
2
1
1
0
0
1
0
2
1
1
0
2
2
1
0
1
1
1
0
1
0
1
2
0
1
0
13
1
2
2
2
1
2
1
2
1
2
1
1
1
2
2
0
2
1
2
1
1
1
1
1
2
1
1
2
1
1
0
2
2
1
1
2
0
2
2
0
0
1
2
1
1
1
1
1
1
1
0
0
1
1
5
1
1
2
1
1
0
1
0
2
1
0
1
0
1
1
1
2
0
1
2
1
1
1
1
2
2
1
0
1
2
1
1
2
1
0
1
1
1
1
2
2
1
2
1
2
2
1
0
2
2
1
1
2
0
1
1
2
1
1
1
0
1
1
1
2
1
1
1
1
1
1
0
1
2
1
1
1
1
2
1
1
1
1
2
2
1
2
1
0
1
1
1
1
1
0
1
1
1
0
1
1
1
2
1
1
1
0
2
1
1
2
2
1
1
0
1
2
1
2
1
0
1
2
0
2
1
1
3
1
2
1
1
1
1
1
0
0
2
2
2
1
2
1
1
0
2
1
2
1
0
1
1
2
1
1
2
2
0
2
1
1
0
1
1
1
1
1
2
1
1
1
1
0
1
2
1
0
2
0
1
1
2
0
1
1
0
1
0
1
1
1
2
1
1
0
1
2
2
0
0
1
2
2
2
4
2
1
1
2
2
1
1
1
1
1
1
2
1
0
1
1
1
2
1
0
1
0
2
1
1
1
0
2
1
2
2
2
1
1
1
2
2
1
1
0
2
0
2
2
1
1
1
1
2
1
2
2
1
1
1
0
1
0
1
1
1
1
2
2
1
2
0
0
1
1
2
2
1
2
1
2
2
1
1
1
2
2
0
0
1
2
1
2
0
1
2
1
1
1
1
2
1
1
0
2
2
1
2
1
1
0
2
2
1
1
1
0
0
1
0
1
2
1
1
2
1
2
1
1
0
2
0
1
1
1
1
1
1
2
0
1
0
1
1
1
2
1
1
2
0
1
2
1
1
1
1
1
2
1
1
1
1
0
2
1
1
1
1
2
1
1
1
1
2
0
1
1
2
1
2
0
2
2
1
0
1
2
2
1
1
1
1
1
0
2
1
1
1
1
1
1
2
2
1
1
1
1
0
1
1
2
1
1
1
0
1
2
1
1
2
1
2
1
1
0
1
2
1
3
1
1
1
1
1
1
0
0
1
1
1
2
1
1
2
1
2
0
1
1
1
1
1
1
1
1
1
1
1
1
0
2
2
0
2
1
0
2
1
1
0
0
2
1
0
0
1
0
2
1
1
1
2
2
2
1
0
1
0
2
1
2
1
2
1
1
1
1
0
2
0
1
2
1
2
1
2
1
2
1
0
1
1
2
2
2
0
1
2
2
1
1
2
0
1
1
2
2
1
1
0
0
2
1
1
2
1
2
1
1
2
1
2
0
1
1
1
1
2
0
1
1
1
2
1
1
1
1
1
1
1
1
1
0
2
2
2
2
0
2
1
1
1
1
0
1
2
1
1
0
1
1
1
1
1
1
2
1
1
1
2
0
0
1
1
0
2
0
1
0
1
1
1
2
0
1
1
1
0
1
1
1
1
1
1
1
2
1
1
0
0
2
2
1
2
1
1
1
1
1
1
3
1
0
1
1
1
1
1
1
1
0
0
1
1
0
1
1
1
1
1
0
0
0
1
1
1
2
2
1
1
2
2
1
1
1
2
1
1
1
1
0
0
1
2
0
2
1
1
1
1
1
1
0
1
1
0
1
1
1
2
0
1
1
1
1
2
1
1
1
1
1
1
2
1
1
0
0
1
1
2
1
1
2
2
1
1
1
1
1
1
2
2
0
0
2
2
1
1
1
0
0
2
1
2
2
2
1
2
1
0
1
1
1
2
2
1
1
1
1
2
0
0
2
2
1
1
2
2
1
1
1
0
1
1
1
1
1
2
1
1
1
1
1
1
2
2
0
1
2
2
1
2
0
1
2
1
0
1
1
1
0
2
1
1
1
1
0
1
2
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
1
1
1
0
0
1
1
1
1
0
1
1
1
1
0
1
1
1
0
2
1
0
0
1
0
3
2
2
0
1
0
0
1
0
1
2
1
1
2
0
1
1
1
1
1
0
1
0
0
1
1
0
2
2
1
2
1
1
1
2
1
1
2
1
1
1
1
0
0
1
0
1
0
2
1
1
1
1
1
1
1
1
1
0
1
2
1
2
2
2
1
1
2
1
0
4
2
1
1
2
2
1
1
1
0
1
0
1
1
1
2
1
2
1
1
1
1
0
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
2
1
1
1
2
1
1
1
2
0
2
2
1
1
2
1
1
1
0
1
2
1
2
2
1
1
0
0
2
1
1
1
1
1
1
1
1
1
1
1
0
1
1
2
2
1
1
2
1
1
0
1
1
1
0
1
2
1
1
1
1
0
1
1
0
1
1
0
2
1
2
2
1
1
2
1
1
0
1
1
0
2
1
1
2
1
1
2
1
1
1
0
0
1
1
0
2
1
1
3
1
1
0
1
0
2
1
1
1
1
1
0
1
1
1
1
1
2
1
1
2
1
2
2
1
2
2
1
1
1
1
2
2
1
1
2
1
1
2
0
1
1
0
1
0
1
0
2
1
0
2
0
1
1
1
1
1
2
1
0
0
2
0
1
1
0
1
2
2
0
2
2
1
1
0
0
0
1
0
1
1
2
2
2
0
1
1
1
1
2
0
2
2
1
1
1
1
1
1
2
1
0
2
1
2
2
2
1
2
2
1
0
0
2
1
0
1
1
1
1
1
3
1
2
1
1
1
1
1
1
1
0
0
1
1
2
6
2
1
0
1
2
1
0
1
3
1
1
0
1
2
1
1
1
1
1
2
1
0
1
1
0
1
1
1
1
1
1
1
1
1
1
0
1
1
1
2
1
0
0
1
1
1
0
1
1
2
1
2
2
2
2
2
1
1
1
1
2
1
1
1
3
1
2
1
2
1
0
1
1
1
1
0
1
1
1
0
1
1
1
1
1
1
2
1
1
0
1
1
1
2
0
2
2
2
1
2
2
0
1
2
1
1
2
1
0
1
0
1
2
1
0
2
2
0
2
1
1
1
1
1
2
1
1
2
0
2
1
0
1
0
2
1
1
2
1
1
0
2
1
1
2
0
1
2
0
1
0
2
1
1
0
0
0
1
0
3
1
1
1
1
1
3
2
1
1
1
1
2
1
1
2
0
1
2
1
1
2
1
1
2
2
1
1
2
2
2
1
1
1
2
2
1
2
1
2
1
1
1
1
1
0
1
1
2
1
2
2
0
1
2
1
2
1
1
0
1
1
2
1
0
1
1
1
1
2
1
2
2
1
2
0
1
2
1
0
0
0
0
1
1
2
1
1
1
1
2
1
2
1
0
1
1
1
1
1
0
2
1
1
1
0
2
0
1
1
1
2
1
1
2
1
1
2
1
0
1
0
1
0
1
2
1
1
1
3
1
1
2
2
1
1
2
1
0
3
1
2
1
1
1
1
1
1
2
1
2
0
0
2
1
1
1
1
1
2
0
0
1
1
1
0
1
1
0
0
2
1
1
1
1
3
1
0
2
1
1
0
2
1
1
0
0
1
2
1
0
0
1
1
1
1
0
1
1
0
1
0
1
1
2
2
2
1
0
0
1
1
2
1
1
2
1
1
2
1
0
1
1
1
1
2
1
1
3
1
2
0
1
1
1
0
2
0
1
1
0
1
2
2
2
1
0
1
1
1
1
1
1
2
2
0
2
1
0
1
1
1
2
2
1
2
1
2
2
1
1
1
2
1
0
1
0
1
1
1
2
1
1
2
1
2
1
2
2
2
1
1
1
1
0
1
1
1
1
2
1
2
1
1
1
1
2
1
1
1
0
1
1
0
0
1
0
1
2
1
1
2
1
2
1
1
1
2
1
1
1
2
0
0
1
1
1
1
0
1
1
1
2
1
2
2
0
1
1
1
0
2
2
0
2
1
1
0
1
1
1
2
0
1
0
0
0
1
1
1
1
0
0
1
1
1
1
2
1
0
1
2
1
1
0
1
1
1
1
0
1
1
1
2
1
1
1
0
0
1
1
1
0
1
1
1
2
1
1
2
1
1
1
2
1
2
1
3
0
1
0
1
1
0
1
0
1
1
1
1
2
1
1
0
2
0
1
0
1
1
1
2
1
1
0
1
0
0
1
1
1
2
0
1
0
1
2
1
2
1
1
1
2
0
0
1
1
1
0
1
1
2
1
1
2
1
1
2
0
1
2
2
1
1
0
0
1
0
1
1
1
2
0
1
1
1
2
1
1
1
1
1
1
0
1
1
0
1
2
1
0
1
1
1
1
2
1
1
1
2
1
0
1
1
0
1
1
0
1
1
1
1
0
1
2
0
1
2
1
1
1
0
1
1
1
0
0
1
2
2
1
1
1
1
1
1
0
0
2
1
3
1
1
0
1
1
1
2
1
2
2
2
2
1
1
2
1
1
1
1
1
2
2
0
1
2
1
2
2
1
1
1
1
2
2
2
0
1
1
0
1
1
1
1
1
0
2
0
1
1
1
2
0
1
1
1
2
1
2
1
3
2
0
0
1
2
2
0
2
2
2
1
2
1
1
1
2
2
2
0
1
1
1
0
1
1
1
1
1
2
2
1
1
0
1
1
1
1
1
0
2
0
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
0
0
1
1
1
1
1
0
1
1
1
2
0
1
0
1
1
1
1
2
1
1
1
0
0
1
2
2
1
1
2
2
2
1
0
2
0
1
1
1
1
2
1
1
0
2
0
1
1
1
0
2
1
0
1
0
4
1
1
1
3
1
1
0
1
1
0
1
0
0
1
2
1
0
1
1
1
0
1
2
1
0
1
1
1
1
0
2
2
1
2
1
1
0
1
2
2
2
0
1
1
3
1
0
1
1
1
1
1
0
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
2
0
1
0
1
1
2
2
0
3
1
0
1
1
2
1
0
0
2
1
1
2
0
2
1
0
0
2
1
1
1
1
1
2
0
0
2
0
1
2
1
1
2
2
0
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
3
1
1
0
0
1
2
1
0
0
2
1
0
1
1
1
1
0
0
2
0
1
0
1
2
1
1
1
3
2
0
2
2
1
1
2
2
0
1
1
2
1
2
2
1
1
1
2
1
2
2
1
1
2
1
1
2
2
1
2
1
2
1
1
1
1
2
1
1
1
1
1
2
1
0
1
1
1
1
2
1
1
1
1
1
1
1
0
0
1
1
0
1
1
0
1
1
2
0
0
1
0
1
1
1
2
0
1
1
2
1
1
2
1
1
0
3
1
1
1
2
2
1
0
1
1
1
1
2
1
1
1
2
1
2
1
1
0
2
0
1
2
1
2
2
1
0
2
2
1
1
2
1
1
2
1
1
1
1
2
0
2
2
1
0
1
0
2
1
2
1
1
1
2
2
1
1
2
2
1
1
2
2
0
1
1
1
2
1
1
0
1
1
2
2
2
1
1
1
0
0
2
1
0
0
0
1
1
1
0
0
2
0
1
2
1
2
1
0
1
1
0
0
1
1
1
1
1
1
1
1
2
2
1
1
2
0
0
2
0
2
1
1
1
0
1
0
0
1
1
1
1
1
1
2
0
1
1
2
2
1
2
0
1
2
0
1
1
0
2
0
1
0
0
1
1
2
2
1
1
1
2
1
1
2
1
1
0
0
1
1
2
1
2
2
1
1
2
2
1
2
0
2
1
0
1
1
2
0
1
1
1
1
1
1
0
2
2
1
1
2
2
1
1
1
1
0
1
1
2
2
1
2
1
1
1
1
0
2
1
2
2
2
1
0
0
0
1
2
2
1
1
1
0
1
1
1
1
1
2
1
1
0
0
0
0
1
2
1
2
1
1
1
2
1
1
1
1
2
1
0
1
1
1
1
2
1
1
0
0
2
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
2
1
0
1
1
0
1
1
2
0
0
1
1
1
2
1
1
1
1
2
0
1
1
2
2
0
1
2
2
0
2
1
1
1
0
0
0
1
1
1
1
1
1
2
1
2
2
0
1
1
1
0
1
1
1
2
1
1
0
0
1
1
1
0
1
2
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
2
1
1
0
0
2
2
1
3
2
2
1
0
0
0
1
1
1
0
1
1
1
1
1
2
0
1
1
1
1
2
0
1
1
1
0
2
1
1
1
0
1
1
1
2
1
1
1
1
2
0
1
2
1
1
0
1
0
1
1
1
1
1
0
0
0
1
0
1
2
1
2
1
1
1
0
0
1
1
1
2
1
1
1
1
1
2
1
0
1
2
2
2
1
2
1
0
1
0
1
1
1
1
1
2
1
1
2
1
1
1
0
2
2
2
1
1
0
1
1
1
0
1
0
0
1
1
1
2
1
1
1
1
2
2
1
1
2
2
1
0
2
1
2
1
2
2
2
1
1
1
0
2
0
0
1
2
0
1
1
0
1
0
1
1
0
0
1
1
1
1
0
1
1
1
0
1
1
1
1
1
0
1
2
1
1
1
1
1
2
1
2
0
1
1
0
2
1
2
1
1
0
1
1
0
0
2
1
1
0
1
1
1
1
2
1
2
2
0
1
1
1
0
2
1
1
2
2
1
2
2
1
1
1
2
1
1
2
1
1
1
0
1
0
1
1
1
1
1
1
1
0
2
1
1
1
2
0
1
1
1
1
1
0
1
1
2
1
1
2
0
2
1
1
2
1
1
2
0
1
2
2
0
2
1
1
1
1
0
1
1
2
2
1
1
1
2
0
0
1
1
2
2
1
1
1
2
1
1
0
2
1
2
1
1
0
2
0
2
1
1
0
2
2
2
1
1
1
1
0
1
1
2
2
1
1
1
0
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
0
1
1
1
2
3
1
1
2
1
1
1
0
1
1
2
1
1
1
0
1
2
1
1
2
1
2
1
0
2
1
1
1
1
2
1
1
2
3
1
1
1
2
2
0
1
1
1
1
1
2
2
1
1
2
2
1
0
2
1
1
2
0
2
1
0
1
1
0
1
1
1
1
1
0
2
1
0
1
1
1
1
1
0
1
2
1
0
1
1
0
1
1
1
1
2
0
2
2
1
2
1
1
1
2
1
2
1
1
0
2
1
1
1
1
1
1
2
1
1
0
1
1
0
2
0
1
2
0
2
1
1
1
2
2
1
0
1
2
0
1
0
1
0
1
1
1
1
2
1
1
1
1
2
1
0
0
1
1
1
2
2
2
1
1
0
2
0
1
0
1
2
2
2
1
1
1
1
0
2
0
1
1
1
2
2
1
0
2
1
2
1
0
1
1
1
1
0
2
1
1
0
2
1
1
0
1
1
2
0
1
2
0
0
0
2
2
1
1
1
1
1
1
1
1
1
1
1
2
0
1
1
2
1
1
0
2
0
1
1
2
0
1
1
1
2
1
0
1
0
1
1
1
1
1
1
1
1
1
1
1
2
2
0
1
1
2
0
1
1
1
1
1
1
1
0
1
1
1
1
2
1
1
1
2
1
1
2
1
1
2
1
0
1
0
1
1
1
1
1
1
2
1
1
1
0
0
2
0
2
1
1
0
1
2
0
1
1
2
0
1
2
2
1
1
0
0
1
1
1
1
1
1
2
1
1
1
0
1
1
2
1
2
1
0
2
0
1
2
1
1
2
2
1
1
1
1
2
1
1
1
1
1
0
2
1
2
1
1
1
1
2
2
2
1
1
0
2
1
1
0
1
2
2
2
1
2
0
1
2
2
1
0
1
1
0
4
1
1
1
1
0
0
2
2
1
2
1
0
3
1
1
1
1
0
1
1
0
0
1
2
1
1
1
1
1
1
2
0
0
1
2
1
1
0
2
2
1
2
1
2
1
1
0
2
1
1
2
0
1
1
1
0
0
1
1
1
3
2
2
1
0
0
1
1
1
1
2
0
1
0
0
0
1
1
1
2
1
1
2
1
1
0
2
1
1
1
0
0
1
1
1
1
2
1
1
2
1
2
2
0
1
1
1
2
0
2
1
1
1
1
2
1
1
1
1
1
2
1
1
0
1
2
1
1
0
1
1
1
1
1
2
1
0
1
0
1
1
0
2
2
1
2
2
1
0
2
1
1
0
1
0
0
1
2
1
1
0
1
1
1
1
1
0
0
0
1
1
1
1
1
1
1
1
1
2
2
2
1
2
2
0
1
2
1
2
1
2
2
1
1
1
2
2
0
1
1
1
0
1
2
2
1
2
1
1
1
2
2
2
1
2
0
0
1
2
1
1
1
1
1
1
0
2
1
1
0
1
2
1
0
1
1
1
2
1
1
1
1
1
0
1
1
0
1
2
0
0
2
1
1
1
1
0
1
1
0
2
1
1
0
2
1
1
2
1
2
1
1
1
1
2
0
1
1
1
0
2
1
1
2
0
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
0
0
1
1
2
1
1
0
1
1
0
1
1
1
2
2
2
0
1
1
1
1
1
1
1
0
1
1
1
0
2
2
1
1
2
1
2
3
2
1
1
2
1
1
1
1
1
2
1
2
1
2
1
1
0
1
3
1
1
1
1
2
2
2
1
1
2
1
0
0
2
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
2
2
1
2
1
2
1
2
2
0
1
0
1
1
2
0
0
0
1
1
1
1
2
1
1
1
1
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
2
2
2
1
1
1
0
1
1
0
1
1
0
0
2
1
2
1
1
0
2
1
0
2
1
2
1
0
1
0
1
1
1
2
1
2
1
2
1
1
2
3
1
2
0
0
0
1
2
1
1
1
1
1
2
0
1
2
1
1
1
1
1
1
1
2
2
2
2
1
1
2
1
1
1
1
1
1
2
1
0
2
1
0
0
1
0
1
1
0
1
2
2
1
0
1
1
3
1
1
1
2
2
1
0
1
1
1
1
0
0
2
2
1
1
1
0
1
1
1
0
2
1
1
1
2
1
2
1
1
2
1
1
1
1
1
1
2
1
1
2
1
1
1
2
1
1
0
1
1
2
2
1
2
1
1
1
1
1
1
0
1
1
1
1
1
0
2
1
1
2
1
2
1
1
2
2
1
2
2
2
1
1
1
0
0
1
1
1
1
1
1
1
1
1
1
0
0
1
0
0
2
2
2
1
1
2
1
1
1
2
1
0
1
1
1
1
0
1
1
0
0
0
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
0
0
0
1
0
1
1
1
2
0
1
1
1
2
1
1
0
1
1
0
1
0
1
1
0
2
1
2
1
0
2
0
0
1
1
1
1
1
0
0
1
1
0
1
0
2
1
2
2
1
0
0
1
2
1
2
0
1
1
0
1
2
1
2
2
0
0
1
1
1
1
0
2
2
1
1
2
3
1
1
2
1
0
1
1
1
2
1
2
0
1
2
2
1
2
1
1
1
1
1
1
1
1
1
0
1
0
0
3
1
2
1
1
1
1
1
1
0
1
1
2
1
1
2
1
0
1
1
0
2
1
1
1
1
2
1
0
9
1
2
2
1
1
0
0
2
1
1
0
1
1
1
1
0
0
2
1
1
1
2
1
1
1
1
2
1
0
1
1
1
1
1
1
0
1
1
1
2
1
2
1
1
0
1
1
1
0
1
1
2
1
1
1
1
1
1
1
1
0
2
1
1
0
1
0
2
1
1
1
1
1
0
1
1
1
1
0
2
1
0
1
1
1
2
1
2
1
1
1
2
0
1
0
2
1
0
1
2
1
2
1
2
0
0
0
0
0
1
1
2
1
0
0
1
2
1
1
1
1
1
2
1
1
1
0
1
1
1
0
1
1
1
2
1
2
0
1
0
2
2
1
1
1
0
1
2
1
2
1
1
1
2
1
0
2
1
2
1
3
2
0
0
0
1
2
1
1
0
2
1
2
2
2
0
1
1
1
0
0
1
2
1
2
1
1
1
2
0
0
1
0
1
0
2
2
0
1
1
2
1
1
0
0
1
1
0
1
1
0
0
1
0
1
1
0
1
1
1
2
1
2
1
2
1
1
1
0
1
1
2
1
1
0
1
1
1
0
1
2
1
0
1
1
2
1
0
1
0
1
1
1
2
0
2
1
1
1
1
2
2
1
1
2
0
2
1
0
1
1
1
1
2
0
2
1
0
1
1
0
1
0
1
1
2
1
0
1
2
0
2
1
1
2
2
1
1
1
0
0
1
1
1
2
0
0
1
1
1
1
0
2
1
1
1
2
1
0
1
1
1
0
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
0
0
1
2
2
0
1
1
1
2
1
1
0
1
2
2
0
1
2
2
2
1
2
1
1
1
1
1
1
2
2
1
1
0
0
0
1
2
0
2
1
0
1
2
1
0
1
1
2
2
2
1
2
2
2
2
1
1
0
1
2
1
1
1
0
1
1
1
1
0
1
0
1
0
1
0
0
1
1
1
2
1
1
0
1
1
2
1
2
1
0
4
1
1
1
1
2
1
1
1
2
1
1
1
2
1
1
2
1
1
1
1
2
0
0
1
2
0
2
0
2
1
1
0
2
0
0
1
0
1
1
0
1
2
0
0
0
2
1
0
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
0
1
1
1
1
0
0
0
1
2
2
1
1
2
1
1
2
2
1
2
1
1
1
1
9
1
0
1
2
1
2
1
2
1
1
2
1
1
0
0
1
1
0
1
2
2
1
1
0
2
0
1
1
1
1
1
1
2
1
1
1
2
0
2
1
1
1
1
1
1
2
0
2
1
1
2
1
1
2
1
2
0
2
2
1
1
2
1
0
2
1
0
2
2
0
1
1
0
1
0
1
1
1
2
1
1
1
1
0
0
1
1
1
2
0
2
1
1
0
1
0
0
1
1
1
0
1
2
2
0
2
1
1
1
1
1
1
1
1
1
1
1
1
0
2
2
0
1
1
1
1
1
0
1
0
1
1
0
2
1
1
2
2
1
1
1
1
1
2
1
1
2
2
1
1
1
1
0
1
1
1
2
0
1
0
2
0
0
1
2
1
1
0
2
1
0
1
1
0
1
1
1
0
1
1
0
1
1
1
1
3
2
1
1
1
1
2
1
1
1
2
2
1
1
1
1
2
0
1
1
0
1
1
1
2
0
2
1
2
1
0
1
2
1
1
0
1
1
2
2
2
1
1
1
2
1
1
1
0
1
2
0
1
2
1
1
1
1
1
1
1
1
2
2
2
1
1
1
0
1
0
1
2
1
1
1
2
2
0
2
1
0
0
1
1
1
1
1
0
1
1
0
1
1
1
1
0
2
1
1
1
3
1
1
2
1
2
1
2
1
1
2
0
2
1
2
1
1
1
1
2
0
2
2
2
1
1
2
1
1
1
1
1
1
1
1
1
0
1
3
0
1
0
2
1
2
0
2
0
1
1
1
1
0
1
2
1
2
0
2
1
2
1
1
2
1
1
1
2
1
2
1
1
0
1
1
1
1
1
0
1
2
2
1
2
1
2
0
1
1
1
1
1
2
1
1
1
1
1
2
2
1
2
1
1
0
1
2
1
1
2
1
2
1
1
1
1
1
1
2
1
1
0
0
2
1
0
1
2
0
2
0
0
0
1
1
1
1
0
1
1
2
1
2
2
2
1
2
1
1
0
1
1
1
2
2
1
1
1
2
1
2
1
0
2
1
1
0
1
0
2
2
1
1
1
2
2
1
2
1
1
2
2
0
1
1
1
0
1
2
3
1
1
1
2
2
0
1
1
1
1
1
2
1
1
0
2
1
1
2
0
1
1
1
0
1
0
1
0
1
1
1
0
1
1
0
1
1
1
1
1
0
0
1
1
1
1
1
1
0
1
2
2
1
1
2
0
1
1
0
3
3
1
1
0
1
1
2
1
2
2
1
1
0
0
0
1
2
0
2
2
1
1
2
0
2
1
1
1
0
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
2
1
1
2
1
0
1
0
2
2
0
2
2
0
1
0
1
1
1
2
0
0
0
1
1
0
1
0
1
2
1
0
0
1
2
1
1
0
0
0
2
1
2
2
1
2
1
0
1
2
0
1
0
2
1
2
1
1
0
2
2
1
2
1
1
2
1
1
1
1
1
1
1
1
0
0
1
1
4
1
1
2
1
1
1
0
1
2
1
1
3
1
1
1
1
0
1
1
1
1
1
1
2
0
2
2
1
0
2
1
1
2
2
2
2
1
2
1
1
1
1
1
2
0
1
1
1
1
0
1
2
0
1
1
2
0
2
1
1
1
1
2
1
1
0
1
0
1
2
2
1
1
1
1
0
0
1
2
1
1
2
2
0
1
2
1
1
1
1
1
2
0
1
0
1
1
0
1
2
0
1
2
0
1
1
1
1
2
2
2
0
2
2
1
1
1
1
0
0
0
1
1
1
2
1
2
1
1
0
1
2
1
2
2
1
1
0
2
1
0
1
2
1
2
1
2
1
0
1
1
2
0
2
1
1
1
1
0
1
1
2
1
2
1
1
0
2
2
1
0
0
1
1
1
1
1
0
1
1
1
0
0
2
0
1
2
0
1
0
2
0
2
1
1
1
1
0
1
2
1
2
1
1
0
0
1
0
0
1
2
2
1
1
1
1
2
1
2
1
0
1
1
2
1
1
1
1
1
2
2
2
1
1
1
2
2
1
1
2
0
2
1
2
1
2
1
0
3
0
1
1
1
2
0
0
0
0
0
1
1
1
1
2
1
0
1
2
2
1
2
2
1
1
1
2
1
1
1
2
2
1
1
2
2
1
1
1
1
1
1
0
1
1
1
2
1
1
0
1
1
1
1
2
0
3
2
1
1
1
1
1
1
2
1
2
1
2
1
2
2
0
1
3
1
2
2
0
2
0
1
0
0
1
0
0
0
2
1
8
1
1
0
1
2
1
0
1
1
1
1
0
1
1
1
1
2
2
1
1
1
0
2
1
2
1
0
2
2
1
1
2
1
1
2
2
0
1
0
1
1
2
0
2
1
1
0
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
0
0
1
1
0
0
1
1
1
1
1
1
1
0
0
1
1
2
2
1
1
0
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
0
1
0
0
1
2
0
2
1
1
1
1
1
1
2
1
1
2
1
0
1
1
0
0
1
1
2
1
1
1
2
1
1
1
2
0
1
1
1
1
1
0
2
0
2
1
1
1
1
2
3
1
1
2
2
1
0
1
1
0
1
2
1
2
1
2
2
1
1
3
2
1
0
1
1
2
1
2
2
2
1
1
1
1
2
2
1
2
1
1
1
1
2
1
1
2
0
0
2
2
1
0
1
1
1
0
2
0
0
1
2
2
1
1
1
0
0
0
1
0
1
0
1
1
2
2
1
0
1
1
1
1
2
1
1
1
0
1
1
1
1
0
1
1
2
1
0
0
1
1
2
1
1
1
1
0
1
2
1
1
1
3
2
1
2
1
1
1
1
1
1
2
2
1
1
0
0
2
2
1
0
1
1
1
1
1
1
0
1
1
2
1
0
0
2
1
2
2
0
1
1
1
1
2
1
1
1
0
1
1
1
1
0
0
2
1
2
1
0
2
2
2
1
1
3
2
1
1
2
1
1
1
2
1
1
1
1
2
1
1
0
2
2
2
1
1
0
1
1
0
0
2
1
2
2
2
0
1
1
1
1
0
1
0
1
2
1
1
1
0
1
0
0
1
1
0
3
0
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
0
2
1
1
0
2
1
2
2
1
1
1
0
1
2
1
1
1
0
0
1
1
2
2
2
2
1
1
0
0
1
3
1
1
0
1
1
1
2
0
1
1
1
1
0
0
1
1
2
1
1
0
1
0
1
1
1
1
2
1
1
1
0
2
0
1
0
1
0
1
1
1
0
2
1
1
1
1
2
0
0
1
1
1
1
1
1
1
1
2
2
0
1
1
1
1
2
2
0
1
1
2
1
1
0
1
2
1
2
1
1
1
1
1
1
1
1
2
0
1
1
0
2
1
0
0
0
2
2
0
1
1
1
1
2
1
1
1
1
1
2
1
0
1
2
2
1
3
1
1
1
0
0
1
1
1
1
1
2
0
1
1
2
3
2
1
2
1
1
2
1
1
0
0
1
1
0
1
2
2
1
1
0
0
1
1
1
1
2
3
1
1
1
1
2
1
2
0
1
2
2
1
1
1
2
1
2
1
1
1
1
2
0
2
2
1
2
2
0
1
1
1
1
1
2
1
1
2
1
1
2
2
1
1
0
1
1
1
1
1
1
1
1
1
1
0
1
1
0
1
1
1
0
2
1
2
2
1
2
1
1
0
1
1
1
1
0
1
0
1
0
0
2
2
1
1
1
1
0
1
0
2
0
1
1
1
0
1
1
2
2
2
2
1
1
1
1
1
1
1
1
0
1
1
1
2
0
1
1
1
0
1
1
1
0
2
1
0
1
2
0
2
1
1
1
0
1
1
2
0
1
0
1
1
1
2
1
2
1
3
1
1
1
2
3
2
0
1
1
1
1
1
1
1
1
1
2
2
1
0
1
2
1
1
2
0
1
1
1
2
1
0
0
1
1
2
3
0
0
2
1
1
1
1
1
1
0
2
1
0
0
0
1
1
1
1
0
0
0
2
1
1
2
1
1
1
0
2
2
1
1
1
1
1
1
1
1
1
1
2
0
0
1
2
0
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
2
2
1
1
1
1
1
0
2
0
1
1
1
0
2
2
1
1
0
0
0
1
1
1
1
1
1
1
2
0
2
0
0
2
1
2
2
1
1
1
1
1
1
0
0
2
1
0
1
1
1
1
1
1
1
2
1
1
1
0
1
0
2
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
3
2
1
1
1
1
1
2
1
2
1
2
1
1
1
2
0
1
0
1
1
0
2
1
0
3
0
1
1
1
1
2
2
2
2
1
1
0
1
1
0
1
1
1
2
1
1
1
1
1
1
1
2
0
1
1
2
1
1
2
1
0
1
1
2
0
1
1
2
2
1
2
1
1
1
1
1
2
1
1
1
2
2
0
2
2
1
0
1
1
0
1
1
1
1
1
1
1
1
1
2
2
1
2
1
1
1
1
2
1
1
0
1
1
1
0
2
0
0
2
1
0
0
2
1
1
2
1
1
1
1
1
1
1
0
1
1
0
1
1
1
0
2
1
1
1
0
0
1
1
2
1
1
2
1
1
1
1
0
2
0
2
2
1
1
1
1
1
1
0
1
1
1
1
1
2
2
1
1
2
1
2
2
2
2
0
2
1
2
1
1
1
2
0
0
2
1
2
1
1
1
0
1
1
1
1
2
1
1
1
2
0
1
1
3
2
2
1
1
2
1
2
2
2
1
0
3
0
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
2
0
0
1
1
1
1
1
1
2
1
1
0
1
1
2
0
1
2
1
1
0
1
1
1
1
1
0
0
0
1
0
1
1
0
2
1
0
1
1
1
1
1
2
2
1
0
1
2
1
1
0
1
1
2
2
2
1
1
2
1
0
3
1
2
0
2
1
1
1
1
1
1
1
1
1
0
1
2
1
1
2
1
1
2
0
2
0
1
2
1
0
0
1
1
1
1
2
1
1
1
2
1
2
1
2
1
1
0
2
1
0
0
0
1
2
2
1
2
1
0
2
1
2
1
2
1
1
1
1
0
1
0
1
1
0
1
1
1
0
1
2
1
0
1
0
1
2
1
1
0
1
2
1
2
0
1
2
0
1
1
2
0
1
2
2
2
0
1
1
1
2
1
1
1
1
1
1
0
1
1
0
1
1
5
1
1
1
1
1
2
2
0
1
1
2
1
2
1
0
1
1
1
2
1
1
1
1
2
0
0
1
1
1
1
2
2
1
0
3
1
1
1
1
1
1
3
0
2
2
1
0
0
1
1
1
1
1
3
1
1
0
2
1
2
0
2
1
1
1
0
2
1
1
0
1
1
0
0
1
0
2
2
2
1
1
1
0
1
1
1
0
2
1
1
1
2
1
2
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
0
1
1
1
1
2
1
1
0
1
0
1
1
1
1
1
0
2
1
1
2
1
1
1
2
1
2
2
1
0
0
1
1
1
1
0
1
1
0
1
2
2
1
1
1
1
0
0
2
1
2
2
1
1
2
1
1
1
1
1
2
1
0
1
0
2
2
1
2
1
1
1
2
2
0
1
1
1
1
2
2
2
1
1
1
1
0
1
0
1
1
1
0
1
1
1
1
1
2
1
1
0
2
1
1
1
1
1
1
2
1
1
2
1
1
1
1
2
2
2
0
2
0
1
2
0
1
1
0
1
2
3
1
0
1
1
1
1
1
2
1
1
1
1
2
1
1
1
0
1
2
1
0
1
1
1
2
1
0
1
2
0
2
2
1
1
1
0
1
2
1
0
1
0
1
1
1
0
1
0
0
0
1
0
1
1
2
1
1
1
1
1
2
1
1
1
1
1
0
1
1
1
0
2
1
1
1
1
0
0
1
1
1
1
2
1
2
1
1
1
1
2
2
1
1
1
1
1
0
1
1
1
1
1
1
0
1
1
0
2
2
1
1
1
1
1
1
1
1
2
3
0
1
0
2
1
0
0
1
0
0
1
1
1
1
1
1
1
2
2
1
1
1
2
0
2
2
1
1
2
0
1
1
0
1
1
1
2
2
1
0
1
1
1
0
1
1
0
0
2
1
2
1
1
1
1
2
2
0
2
1
1
1
1
1
1
0
0
0
1
1
1
2
1
1
1
1
1
1
1
0
2
2
2
0
1
1
1
1
1
1
1
2
0
1
2
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
1
0
1
1
2
1
2
1
0
1
1
1
2
1
1
2
1
1
3
1
0
1
1
1
1
1
1
2
2
2
0
1
1
1
1
1
1
1
2
1
2
0
1
1
1
0
2
2
2
2
1
0
1
1
1
2
1
1
2
1
1
2
0
1
1
7
1
1
1
2
1
2
1
0
0
1
1
2
1
1
1
2
1
2
1
1
0
1
0
1
1
2
1
0
1
1
1
2
0
0
2
3
1
0
1
1
1
1
1
1
2
1
1
0
0
1
1
1
0
1
1
1
1
1
0
1
1
0
1
2
1
2
2
1
1
1
1
1
1
1
1
0
0
0
1
1
1
1
1
1
1
2
1
1
0
1
1
1
1
2
6
1
1
1
2
1
2
1
1
1
1
2
1
1
2
1
2
1
0
0
1
2
1
1
2
1
0
1
2
1
1
1
0
1
1
2
2
1
1
1
1
0
0
2
1
1
2
1
2
2
1
1
1
1
0
2
0
0
1
1
1
0
1
2
1
0
2
0
1
2
2
1
1
0
2
1
1
2
1
0
2
1
1
1
0
1
1
1
1
2
1
1
2
0
1
1
1
1
1
1
1
1
1
1
2
0
2
2
1
2
2
2
0
1
1
0
2
2
1
1
1
1
0
2
2
0
2
1
1
0
1
1
2
0
2
1
1
1
1
1
1
1
2
1
1
2
2
1
2
1
2
1
0
1
1
2
2
2
1
0
1
1
1
1
1
0
1
1
0
0
2
1
2
1
0
1
1
2
2
1
0
1
1
1
1
2
1
0
2
1
2
1
0
1
1
1
1
1
1
1
2
2
0
1
1
1
2
2
1
1
1
1
1
3
1
1
2
1
1
0
1
2
1
1
1
1
1
1
0
1
1
1
1
1
0
1
1
2
2
1
2
1
1
0
0
2
1
0
1
1
1
2
2
1
2
1
1
1
1
2
1
0
0
1
1
1
1
1
1
2
1
2
1
1
1
0
0
2
2
2
1
1
1
2
1
1
1
2
1
1
1
1
0
1
2
0
2
0
1
1
1
1
1
1
0
0
1
2
0
1
1
1
0
1
1
0
0
1
0
2
2
1
1
0
1
1
2
2
0
2
1
1
2
1
1
1
1
1
1
2
0
1
0
2
1
0
2
1
0
1
1
0
2
1
0
1
0
2
1
0
0
0
1
1
0
1
2
1
1
1
1
1
2
2
1
0
1
1
2
1
0
1
2
0
2
1
0
1
1
2
2
2
1
1
1
1
1
2
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
1
1
1
2
1
1
0
2
1
1
3
1
1
1
0
1
2
2
2
0
1
1
1
1
1
2
2
1
2
1
1
2
0
2
1
0
2
1
0
2
0
2
2
1
2
0
2
1
2
0
2
0
0
2
0
1
1
0
2
1
1
2
2
2
0
1
2
1
1
1
1
2
1
0
1
1
1
2
2
1
1
0
2
0
0
2
1
0
0
1
0
1
0
2
0
1
1
0
2
2
1
2
1
2
0
2
1
0
0
1
0
2
1
0
0
1
2
1
1
1
1
1
2
2
0
1
1
2
0
1
1
1
2
1
1
1
1
2
2
0
1
1
1
1
0
1
2
1
0
2
1
0
0
1
2
1
1
1
1
0
1
2
1
0
2
1
2
2
1
2
2
1
1
1
1
1
0
0
0
2
1
1
1
1
0
1
0
2
2
1
1
1
1
4
1
2
0
1
1
3
1
1
2
0
0
1
1
1
1
1
0
0
2
1
0
3
1
1
2
1
1
2
1
0
0
2
1
1
1
2
1
1
3
0
1
0
2
1
0
1
0
2
1
1
2
1
0
1
1
1
1
0
1
1
1
0
1
1
2
1
1
1
1
1
1
1
1
1
2
2
0
1
1
1
1
0
2
0
0
1
1
1
0
1
1
1
1
1
1
0
1
1
1
1
1
2
2
1
1
2
1
1
1
1
1
2
1
0
0
1
1
1
1
2
2
0
0
1
2
1
2
1
2
1
1
2
0
2
0
1
1
1
1
1
2
0
0
2
1
1
1
1
1
1
1
0
0
2
1
1
2
1
2
1
0
0
1
0
1
1
1
1
1
0
1
1
1
2
1
2
1
0
1
1
0
1
1
2
0
1
0
1
1
2
1
1
1
0
2
0
2
1
0
1
1
1
1
1
1
1
2
2
1
0
1
2
1
1
1
1
0
1
0
1
1
1
1
1
1
2
1
1
1
1
2
1
2
0
1
1
1
2
1
0
0
1
1
1
2
2
2
2
1
1
1
2
0
2
1
1
1
1
1
2
1
1
1
1
1
2
1
0
2
1
0
0
1
1
1
2
2
2
1
0
1
0
1
1
1
1
1
1
2
2
1
1
1
2
0
2
1
1
1
1
1
2
0
2
1
2
1
1
2
2
1
0
1
1
1
0
2
1
1
1
1
0
1
1
1
1
0
1
1
2
1
0
1
1
2
1
1
0
1
2
0
1
0
1
1
3
1
1
1
1
1
1
2
2
2
1
1
2
1
0
1
1
1
1
2
1
2
2
0
1
1
1
1
0
0
0
1
1
1
1
2
1
0
0
1
2
1
0
2
2
0
0
1
1
2
2
2
1
0
2
2
1
1
1
2
1
2
1
0
0
2
1
1
3
1
1
1
2
1
1
0
0
0
2
1
1
2
1
0
2
1
2
1
0
0
1
2
1
1
0
1
1
2
1
1
0
1
1
2
2
1
2
1
1
1
2
1
2
1
0
1
1
0
0
1
2
2
2
1
1
1
1
2
1
2
0
2
1
2
2
2
1
1
0
1
2
1
1
1
2
1
1
0
0
1
2
2
1
1
1
0
2
0
1
1
2
0
2
1
1
1
1
0
2
1
1
1
1
1
2
1
1
1
0
1
2
0
0
1
1
2
1
0
1
2
1
2
1
1
1
2
0
1
0
0
2
1
1
2
0
1
0
1
2
1
2
1
0
2
1
2
0
2
1
1
1
2
0
0
2
1
1
1
1
1
1
1
0
0
1
1
1
1
1
1
0
1
2
1
1
1
1
0
2
1
1
1
0
1
1
1
2
1
1
1
0
1
2
1
1
2
1
2
2
0
1
0
1
1
1
0
1
0
1
1
0
0
1
1
0
1
1
1
2
1
1
1
1
2
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
2
1
1
1
1
0
1
2
1
2
2
1
2
1
1
1
2
1
0
0
1
2
2
2
1
1
2
1
1
1
1
1
2
1
2
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
0
2
1
1
1
0
2
1
1
1
2
1
1
1
0
4
2
1
2
2
1
2
2
2
1
0
2
0
1
2
2
1
2
0
1
2
0
1
1
1
1
1
1
1
1
1
1
0
2
2
0
1
0
1
1
1
0
2
1
1
1
1
1
2
2
1
0
3
0
2
1
2
1
1
1
1
1
1
0
0
1
2
0
0
1
1
2
0
2
1
2
1
1
0
1
1
2
1
0
1
2
1
2
0
1
1
2
2
0
1
1
1
0
1
2
1
1
2
0
1
1
1
1
1
1
1
1
0
2
1
2
1
1
1
2
1
1
0
1
1
2
1
2
0
0
1
2
0
1
1
1
1
2
1
0
1
2
1
1
1
2
1
0
1
0
1
1
1
1
1
0
1
2
1
1
1
1
1
0
1
2
0
2
1
0
1
1
1
1
1
0
2
2
1
1
1
1
0
1
1
1
1
0
0
1
2
0
2
1
0
1
2
1
0
2
1
1
1
1
1
0
0
0
2
1
2
1
0
1
1
2
1
0
1
1
0
1
1
0
1
1
1
1
1
2
1
1
1
1
5
1
1
2
1
1
1
1
1
0
0
1
2
1
2
2
0
2
1
0
2
2
1
2
2
0
0
1
1
2
1
1
0
1
2
1
1
1
1
1
2
1
2
1
2
0
2
1
1
2
1
1
1
1
1
2
0
0
1
1
1
0
3
1
0
0
1
1
0
1
1
0
1
2
1
0
0
1
1
1
1
0
3
1
1
1
1
1
1
1
0
1
1
0
1
1
2
2
1
1
0
1
0
1
2
0
1
2
1
2
2
1
1
1
2
1
1
0
0
0
2
2
1
2
1
1
2
2
0
1
0
2
1
1
1
2
1
2
1
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
2
1
1
1
0
1
3
2
1
2
1
0
2
1
2
1
2
0
1
1
1
0
1
0
2
0
1
1
1
1
1
1
2
1
1
2
1
1
1
2
2
1
1
2
0
2
1
1
1
0
1
1
1
1
1
1
1
0
0
1
2
1
2
1
1
1
1
1
1
0
1
1
1
2
2
3
1
1
2
0
1
2
1
1
1
1
1
2
1
0
1
1
2
0
2
2
0
1
2
2
2
1
1
1
1
1
1
2
0
1
0
0
1
1
1
1
1
1
2
1
2
2
1
0
0
1
1
1
2
2
1
2
1
1
1
1
0
1
1
1
1
0
2
1
2
1
1
2
2
2
1
2
2
2
0
2
1
2
1
2
1
0
1
1
1
1
0
1
2
2
1
1
2
2
1
1
0
1
0
1
1
0
1
1
2
1
2
2
0
1
2
1
1
1
2
1
1
1
1
1
1
1
1
3
1
1
1
1
0
1
1
0
0
1
1
2
1
0
0
1
2
1
1
0
2
1
1
2
1
2
2
1
0
2
0
0
1
1
2
0
1
2
2
0
2
3
2
2
2
2
1
0
1
1
2
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
0
2
1
2
1
1
0
1
2
3
2
2
1
1
2
1
1
0
2
1
1
1
1
1
1
1
2
2
1
0
1
2
0
3
1
1
1
0
1
1
0
2
1
2
0
0
2
1
1
1
2
0
1
0
1
1
1
1
2
1
0
0
1
1
1
1
0
1
1
1
1
1
2
1
1
1
1
3
2
1
2
1
2
2
1
1
3
1
1
2
0
0
1
1
1
1
0
1
1
1
1
1
1
2
1
0
1
1
1
0
1
1
1
2
1
2
1
2
1
2
1
1
1
1
1
1
2
1
1
2
1
0
1
1
2
1
1
1
2
1
2
0
1
1
2
0
1
1
1
2
1
1
1
1
2
2
1
1
1
1
1
2
3
1
0
2
0
0
1
2
2
2
2
2
0
2
1
1
2
1
2
1
1
1
2
1
1
2
1
1
2
0
1
1
1
2
1
0
1
1
1
2
0
0
1
2
0
0
2
1
1
2
1
1
1
1
1
0
1
2
1
0
1
0
2
0
1
0
0
1
2
2
1
1
1
0
0
3
1
1
2
1
1
2
1
1
2
1
2
1
1
2
1
2
1
1
1
0
1
1
1
2
1
1
1
2
1
1
1
0
1
1
0
2
1
1
1
1
1
0
1
1
1
2
1
1
2
1
1
0
1
1
1
1
2
2
2
1
1
2
1
1
0
1
0
2
1
1
1
1
2
0
2
2
0
0
1
0
1
1
1
1
1
0
1
2
1
0
1
1
1
2
2
1
1
2
1
1
1
1
1
1
2
1
1
3
0
0
1
2
1
2
3
2
1
1
0
1
2
0
1
1
1
1
2
1
3
1
2
2
1
2
2
0
1
2
2
2
2
2
2
1
0
2
1
2
2
1
1
0
2
2
0
1
2
1
1
1
1
0
1
1
1
3
1
2
0
1
1
2
2
1
1
1
0
1
2
0
2
1
1
1
2
0
1
1
1
1
1
1
1
0
1
2
1
1
1
2
1
1
0
1
1
1
1
2
1
0
2
2
0
2
1
1
1
0
2
0
2
1
1
0
1
1
2
2
0
1
1
1
0
2
1
2
0
2
0
1
1
1
0
0
2
1
0
2
1
1
1
1
0
1
1
1
1
1
1
1
1
0
1
2
1
2
2
2
2
0
2
1
1
0
2
2
1
1
2
0
0
2
2
1
1
2
0
2
2
2
0
2
2
1
1
1
1
1
0
1
2
1
2
2
2
2
0
2
0
0
2
1
1
1
1
1
1
1
1
2
1
1
1
2
0
0
0
2
1
1
1
1
1
0
1
0
2
1
0
1
2
1
2
1
2
1
2
3
1
1
2
1
1
1
1
0
1
1
1
1
2
1
1
1
2
1
1
1
1
0
1
2
1
0
1
2
1
1
2
1
1
1
1
1
1
1
0
1
0
1
2
1
1
0
2
1
0
1
1
1
1
1
1
0
0
1
1
1
2
1
2
0
0
1
1
2
1
1
1
2
1
3
1
1
1
1
2
1
1
1
0
0
1
1
1
1
1
1
1
1
0
1
2
2
1
1
1
1
2
1
1
2
1
0
2
2
1
2
1
2
1
2
0
1
1
1
1
1
1
1
2
1
1
1
1
1
1
0
2
0
0
1
2
1
0
0
0
1
1
1
0
0
1
1
0
0
1
2
1
0
0
2
0
1
0
1
1
1
0
1
0
1
1
0
1
1
2
2
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
0
0
1
1
1
1
0
0
2
1
1
5
1
5
3
0
1
0
1
2
1
2
0
2
0
2
2
1
1
1
1
1
1
2
1
1
2
1
2
1
1
0
1
1
1
1
1
2
2
2
2
0
2
2
1
1
1
1
1
0
1
2
0
2
0
1
1
1
2
0
1
1
2
1
1
1
1
3
1
1
1
1
1
3
1
0
1
2
1
1
1
1
1
0
1
1
1
1
1
1
0
1
0
1
1
0
1
1
0
2
2
1
1
1
2
0
1
2
1
1
1
2
1
1
2
0
2
2
0
1
1
2
1
0
2
1
4
1
1
1
1
2
1
2
0
1
0
1
1
1
2
0
2
2
2
1
1
1
1
1
1
1
0
2
1
1
0
0
1
0
1
1
2
2
1
2
1
1
1
1
1
1
2
2
1
2
1
1
2
2
1
2
1
1
2
1
1
1
2
1
1
1
2
2
1
1
0
1
1
0
0
1
2
2
1
1
2
1
1
2
1
2
1
1
2
2
1
1
0
0
1
3
0
1
1
0
2
1
1
1
0
0
1
1
0
0
1
2
1
1
2
1
2
2
0
1
0
0
1
1
1
1
2
1
1
1
1
2
1
0
2
1
1
1
2
1
2
2
1
1
2
1
2
2
1
1
1
1
2
1
1
1
1
1
0
0
0
2
1
1
2
2
0
1
1
0
2
1
0
1
1
0
1
3
1
1
1
2
0
1
1
2
1
2
2
0
0
0
0
0
1
2
1
1
2
0
1
1
0
1
1
1
1
1
1
2
1
1
3
1
0
1
1
1
1
1
1
1
1
0
0
0
2
1
2
1
0
0
0
0
1
0
2
0
2
2
2
1
1
2
2
2
1
1
1
1
2
1
1
1
1
1
0
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
0
1
1
2
2
1
0
1
1
0
4
1
2
1
1
1
0
1
1
1
1
1
1
2
1
1
1
0
1
1
2
1
1
0
2
1
1
1
0
1
1
2
2
2
0
2
0
2
2
1
1
0
1
3
1
1
1
1
0
1
1
1
2
0
1
2
1
0
1
1
1
2
1
1
2
2
0
0
1
1
1
1
1
1
1
1
1
2
2
1
0
1
2
0
2
1
1
1
2
2
1
1
2
2
1
1
0
2
1
1
1
0
2
2
1
0
1
0
1
2
1
1
1
1
0
0
1
1
0
2
1
1
0
2
1
1
1
2
1
1
1
1
1
1
2
1
1
0
1
2
1
1
1
1
2
1
2
1
1
1
1
2
1
1
0
2
1
2
1
1
2
2
2
0
2
1
3
1
2
1
1
0
1
1
1
0
1
2
1
2
0
1
0
1
0
1
1
1
1
2
0
1
1
1
0
1
0
1
1
1
1
0
1
1
1
1
1
1
1
1
0
2
0
1
1
1
1
1
0
0
0
0
2
1
1
1
0
1
1
1
1
0
2
1
2
1
2
1
0
0
1
1
2
1
1
1
2
2
0
1
1
1
1
1
1
0
1
0
1
1
1
1
0
0
2
1
1
0
1
1
3
2
2
1
2
1
1
1
0
0
1
1
1
0
2
1
1
1
1
1
1
1
1
0
0
0
0
1
1
1
1
0
0
1
1
1
1
1
1
1
0
2
2
2
0
0
1
0
1
1
2
1
1
1
0
1
1
2
1
0
1
1
1
1
1
2
1
0
0
1
1
2
2
1
2
2
1
1
1
1
1
1
0
2
1
1
0
2
1
2
1
0
0
0
3
1
2
1
1
2
1
0
1
1
1
1
0
0
2
2
1
1
2
0
1
1
2
1
1
0
1
1
2
1
1
1
1
0
2
1
1
1
1
1
1
1
1
2
0
1
2
1
2
0
1
1
1
2
1
1
1
2
0
0
2
1
2
0
1
1
1
2
1
1
1
1
2
1
3
1
2
1
2
1
1
1
1
2
2
1
0
0
1
1
2
0
1
1
1
1
1
2
1
2
2
0
2
2
1
1
1
0
1
1
2
1
1
1
0
1
0
1
1
0
1
1
2
2
1
2
1
1
1
1
2
1
1
1
1
1
1
0
1
2
2
0
1
1
0
1
2
1
1
1
1
1
4
2
1
2
0
0
1
2
1
2
1
1
1
1
1
1
0
1
1
1
0
0
1
2
1
1
1
0
0
1
1
1
0
0
2
1
0
1
1
1
1
1
2
1
1
1
1
0
0
1
1
1
1
2
2
1
1
1
1
1
0
0
2
2
0
1
2
0
1
2
2
1
2
2
2
1
1
2
0
2
1
1
2
0
1
1
1
2
2
1
1
2
1
1
1
0
2
1
2
0
1
1
2
1
0
1
1
1
3
0
2
1
1
2
1
1
1
1
2
0
2
2
2
2
2
1
2
0
0
1
1
0
2
1
2
0
1
1
1
0
2
2
1
1
0
2
1
1
1
1
2
2
2
1
1
1
2
0
1
0
2
2
1
1
0
1
1
1
1
1
0
1
1
1
2
1
1
2
1
1
1
1
1
2
0
1
1
0
0
1
1
1
1
1
1
2
1
1
1
1
2
0
1
2
1
1
1
1
0
2
2
2
2
1
3
1
1
0
2
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
2
2
2
2
1
1
1
0
1
1
1
0
1
1
2
0
3
2
2
2
0
1
1
0
2
0
1
0
0
1
1
2
1
1
1
1
0
1
2
1
1
0
0
2
2
2
1
0
1
0
1
0
1
1
2
1
2
0
2
1
0
1
2
1
0
0
1
0
1
2
1
0
1
2
1
1
0
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
0
1
1
2
0
2
1
0
2
0
1
0
2
1
0
1
3
1
1
1
1
0
1
2
1
0
0
1
1
0
2
1
1
2
2
0
2
1
1
1
2
1
2
2
1
2
1
1
1
2
0
2
1
0
2
0
0
2
1
1
0
2
0
2
1
1
1
2
1
2
1
1
0
0
0
1
1
1
1
1
1
0
1
1
1
1
1
0
1
0
2
1
1
0
1
1
1
1
1
1
1
2
1
1
0
0
1
1
1
1
2
2
1
1
1
1
1
1
1
1
3
1
1
1
1
2
1
0
0
2
1
2
1
0
2
1
2
2
1
0
1
1
1
0
1
1
1
0
2
1
1
0
1
1
2
2
2
1
1
2
0
2
0
1
1
2
2
2
1
1
1
0
1
1
1
1
0
1
1
2
1
1
1
1
1
0
0
2
1
0
1
0
1
1
1
2
1
1
2
0
1
1
2
2
1
1
1
2
1
1
2
1
2
1
1
2
1
2
2
1
1
0
2
1
1
1
1
0
2
2
1
1
2
1
0
1
2
2
0
1
1
1
1
0
1
1
2
2
1
0
1
1
2
1
1
0
0
0
2
1
1
0
1
1
1
0
1
0
0
2
2
2
1
1
1
1
1
2
0
2
1
1
1
1
1
0
2
2
1
1
1
1
0
1
2
1
0
1
0
1
1
0
2
1
2
1
1
0
2
1
2
1
2
2
1
3
2
0
2
0
1
1
0
1
1
2
3
0
1
2
2
1
1
1
2
2
0
1
1
1
0
1
1
1
2
2
0
2
1
2
2
1
1
1
1
0
0
2
1
2
2
1
2
0
1
1
2
1
0
1
1
0
2
1
2
1
1
0
1
1
1
0
1
2
1
1
0
0
0
2
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
2
1
1
2
2
2
1
0
2
2
2
1
1
2
1
1
1
2
1
0
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
2
2
1
0
2
1
2
1
1
0
2
1
0
1
1
1
1
0
1
2
0
1
0
1
2
1
0
0
1
1
1
2
1
1
2
1
1
1
1
1
2
1
1
2
1
2
2
2
1
2
1
2
0
2
1
1
2
1
1
0
0
2
1
1
0
1
0
2
2
0
1
2
2
1
1
0
1
1
1
1
1
2
1
1
2
2
2
1
1
1
1
1
1
2
1
0
1
1
0
1
1
1
1
1
3
1
1
1
1
1
1
1
0
1
0
0
0
2
1
1
1
1
1
0
0
2
1
1
0
2
1
1
1
0
1
0
1
0
2
0
1
0
0
1
1
2
2
1
1
1
2
1
2
1
1
1
1
1
1
1
2
1
0
1
1
0
1
1
1
2
1
1
1
2
2
1
2
1
1
2
2
2
1
1
1
1
1
1
2
0
1
2
0
1
1
1
1
1
1
1
1
0
1
2
1
1
1
1
2
1
2
2
1
1
0
0
1
1
1
1
2
2
1
0
1
1
0
0
1
1
1
1
1
1
1
2
2
1
1
1
2
2
1
1
1
1
1
1
0
1
0
1
0
1
2
2
0
1
1
2
1
1
1
0
2
2
1
2
1
2
1
0
0
1
2
2
0
1
1
0
1
2
1
0
0
2
1
0
1
1
0
1
0
0
1
2
1
1
2
1
2
1
0
1
0
2
1
0
1
0
1
0
1
0
1
1
1
1
1
1
1
1
0
1
1
1
2
2
1
1
1
2
1
1
1
0
2
1
1
1
1
1
0
0
1
1
0
2
1
1
0
1
1
2
1
2
0
0
2
1
1
1
1
1
1
0
2
1
2
2
1
1
1
1
1
2
1
1
0
1
1
1
1
2
1
0
2
2
0
1
2
0
1
1
2
0
2
1
1
1
2
2
2
1
0
1
1
1
1
1
1
1
2
1
1
1
1
0
1
1
2
0
1
0
1
0
2
1
1
1
2
1
1
1
1
2
0
0
1
1
1
1
0
1
1
0
1
2
1
0
1
1
1
1
1
1
1
1
1
0
2
1
1
0
1
1
2
1
1
1
2
1
1
1
0
1
0
1
1
1
1
0
1
1
2
1
1
1
1
1
1
0
1
2
2
1
0
0
0
2
2
1
1
1
3
0
1
0
1
1
1
0
1
1
2
1
2
1
2
2
1
1
1
2
2
0
1
1
1
1
1
1
0
2
1
1
1
2
2
2
1
1
1
2
1
0
1
1
1
1
1
2
1
1
1
1
2
1
2
1
2
1
0
1
0
1
1
2
1
0
0
0
1
1
2
1
1
2
0
0
0
2
1
2
0
0
1
1
1
2
2
1
2
1
2
1
0
0
2
1
1
1
0
1
0
1
1
1
1
1
1
1
2
2
1
1
2
1
2
1
1
1
1
1
1
0
2
1
1
2
1
1
2
1
1
2
1
2
0
1
2
2
2
2
1
1
0
2
0
1
2
2
0
1
2
0
2
2
1
0
0
1
1
0
0
0
2
1
1
0
1
2
1
1
1
0
1
1
1
1
1
0
1
2
1
1
1
1
3
1
1
1
1
1
2
1
2
1
2
1
1
2
1
2
1
1
1
3
1
2
1
1
1
2
2
1
1
0
1
1
1
1
1
1
1
2
1
1
1
1
2
3
0
1
1
2
1
0
0
2
0
1
2
3
1
1
2
2
1
1
1
1
1
2
1
2
1
1
1
0
1
2
1
0
2
1
0
0
1
1
1
1
1
1
1
2
1
1
0
1
0
0
2
1
1
2
0
2
1
2
0
2
1
0
1
1
1
1
0
0
2
2
1
0
1
1
0
2
1
2
0
2
1
1
1
2
2
2
1
1
1
3
0
1
0
1
0
2
0
2
2
2
2
1
1
1
2
2
1
1
2
1
1
0
1
2
1
2
0
1
1
1
1
2
0
1
3
0
0
2
2
1
1
1
1
2
0
1
1
0
1
1
1
1
1
2
0
1
1
1
0
2
1
1
1
1
1
1
1
1
2
0
1
1
0
1
1
1
0
2
2
1
0
1
1
1
1
1
1
2
2
2
1
2
0
2
1
0
1
0
1
1
1
0
1
1
1
2
1
1
2
1
2
2
1
2
1
1
1
2
0
2
1
0
1
1
2
1
2
2
1
1
2
1
2
0
1
1
2
2
2
2
1
1
1
2
1
1
1
1
1
2
0
2
3
2
1
2
1
1
2
2
1
1
1
2
1
2
1
1
0
1
0
2
1
1
1
0
0
1
1
1
1
2
1
1
2
1
1
2
1
1
2
1
1
1
0
1
1
1
1
1
1
1
1
2
1
1
1
0
2
1
1
1
1
2
1
0
2
1
1
1
2
1
1
1
1
1
1
1
5
1
2
1
1
0
0
1
2
1
0
2
2
1
0
1
1
1
1
2
1
0
0
1
1
0
2
1
2
1
2
2
1
1
0
0
0
1
2
1
0
1
2
0
1
2
0
2
0
2
1
1
0
1
1
1
2
1
0
1
0
0
1
1
1
1
1
2
2
1
1
1
0
1
1
0
2
1
1
0
1
0
1
1
0
0
2
1
0
1
0
1
2
0
1
1
1
2
2
2
1
1
2
1
1
0
2
1
0
0
2
1
1
1
2
1
0
1
2
2
1
1
1
0
2
1
0
1
1
1
2
1
1
2
2
1
1
2
0
1
1
0
1
1
1
0
1
0
0
1
1
1
0
1
2
1
1
1
1
1
1
1
2
1
1
1
0
1
2
2
0
0
1
2
2
1
2
1
1
1
2
2
2
1
1
0
2
1
1
1
1
1
1
2
1
1
1
1
2
3
2
1
2
0
1
1
1
2
1
0
1
1
2
0
1
2
1
2
1
0
1
2
1
3
1
1
2
1
1
1
2
1
1
1
2
1
1
2
1
0
2
1
1
0
2
0
0
1
1
1
0
1
2
1
1
1
1
1
2
1
1
0
2
2
0
0
1
2
1
2
2
1
2
1
1
0
1
1
1
1
1
0
1
0
2
1
1
1
1
2
2
1
1
0
2
2
1
0
1
0
2
1
1
1
1
1
1
1
1
0
2
1
1
0
1
0
1
2
0
2
1
0
2
1
2
1
1
1
2
0
1
2
1
2
0
2
2
0
1
1
1
2
2
1
2
1
1
0
2
1
1
1
2
1
1
2
1
1
2
1
0
2
1
1
0
2
1
1
1
1
1
2
1
2
0
2
1
0
1
1
0
2
2
2
0
2
1
1
2
0
0
1
1
1
2
1
1
2
2
2
0
1
1
1
1
1
2
1
1
1
1
1
1
1
1
0
0
0
2
2
1
2
1
1
1
1
1
0
1
1
1
2
0
1
1
1
0
1
1
2
0
0
1
1
2
1
1
0
0
2
1
2
2
1
1
1
0
1
0
1
1
0
2
0
1
1
1
1
2
0
0
2
0
1
0
2
0
1
1
2
1
1
1
1
1
1
2
1
1
0
2
2
1
2
0
0
1
0
1
1
1
1
1
1
2
1
1
0
1
2
1
2
2
2
1
2
2
1
1
2
2
2
1
2
1
1
0
2
1
2
1
1
1
1
0
1
0
0
1
1
1
1
1
0
0
0
1
2
1
2
0
0
2
0
1
1
1
1
0
0
3
1
2
1
2
1
1
2
1
2
1
1
0
1
1
1
1
1
0
1
1
1
0
1
1
3
1
1
2
2
2
1
1
1
0
0
0
2
0
0
1
1
1
1
2
1
1
1
0
1
1
1
2
1
1
2
1
1
1
1
1
0
1
1
1
0
1
1
1
0
0
2
0
1
1
1
1
2
2
1
1
2
0
1
2
1
1
0
1
2
1
1
1
1
1
1
2
0
2
1
1
1
0
1
1
1
5
1
2
2
0
2
1
0
2
0
1
1
1
1
2
0
1
1
0
1
1
1
1
1
2
1
2
1
0
0
0
1
1
2
2
0
2
0
2
2
2
1
1
3
1
1
2
1
2
1
2
0
0
1
2
1
0
1
1
1
1
2
1
2
1
1
1
1
1
2
2
2
1
0
1
2
2
2
1
1
1
1
2
1
0
0
1
0
1
1
0
1
1
0
1
2
2
2
0
0
1
2
0
0
1
0
2
2
1
1
1
1
1
2
1
0
1
1
1
1
2
1
0
2
1
1
1
2
1
1
1
5
1
1
1
1
2
1
2
2
1
2
2
2
1
1
1
2
1
1
2
0
0
1
1
1
1
2
1
1
1
1
2
1
1
1
0
1
0
0
1
0
1
1
0
1
2
1
2
0
1
1
0
1
0
1
1
1
0
1
1
1
1
1
1
2
1
1
1
1
1
2
2
1
1
1
1
1
1
0
1
0
2
1
1
1
0
1
1
2
1
1
1
1
1
1
1
2
1
2
2
1
2
0
1
1
1
1
1
1
1
1
1
1
2
2
1
0
2
1
0
0
2
0
1
1
1
2
1
2
0
1
1
0
1
1
1
2
0
1
0
0
2
1
1
1
1
2
2
1
1
1
1
1
2
1
1
1
1
1
1
0
1
1
1
1
0
1
1
1
1
1
2
1
1
1
1
1
1
2
0
1
0
1
1
1
1
1
2
1
2
0
2
0
1
1
2
1
1
2
1
1
1
2
1
2
0
3
1
1
1
1
1
3
1
1
1
1
2
1
0
2
1
1
1
1
0
1
2
1
1
0
1
1
2
1
2
1
1
0
1
1
2
2
1
1
1
1
0
2
0
1
1
1
0
1
1
0
0
1
0
0
1
1
1
1
0
0
1
1
1
3
2
0
0
1
1
1
2
1
1
1
0
1
1
1
2
2
1
2
2
1
1
1
1
1
2
1
1
1
1
0
1
0
2
2
2
1
0
1
0
0
1
1
2
1
0
2
1
0
0
1
0
0
1
1
1
2
0
1
1
0
2
2
2
1
2
1
0
0
1
1
1
1
1
1
1
1
2
0
1
1
1
2
1
0
1
3
1
3
1
1
2
1
1
1
2
1
1
1
0
2
1
1
1
3
0
1
1
1
1
2
1
2
1
1
1
1
2
1
1
2
0
0
1
1
0
2
1
1
2
1
1
1
0
1
1
1
1
1
1
2
0
1
1
1
2
1
2
1
1
1
1
0
2
1
1
1
1
1
1
1
0
1
0
2
1
1
2
1
1
1
2
1
1
2
4
0
1
1
1
0
1
0
2
1
2
1
2
1
2
0
0
2
2
1
1
1
1
2
1
0
2
1
1
1
0
1
1
0
1
0
1
2
1
2
0
0
1
1
2
1
1
1
1
2
1
1
1
1
0
1
1
1
1
1
1
1
2
1
2
0
0
1
1
2
3
2
1
1
1
1
2
1
1
0
1
1
2
1
1
2
1
1
1
1
0
2
1
2
1
1
1
2
1
1
2
2
2
1
1
1
1
1
1
2
2
1
0
2
1
1
1
2
0
1
1
0
1
1
1
2
0
0
1
2
0
0
1
1
2
2
1
1
2
1
1
1
2
1
1
1
1
1
1
2
2
0
1
2
2
1
0
1
1
1
1
1
0
0
2
2
1
1
0
1
2
1
1
0
2
1
1
1
1
2
2
2
0
1
1
1
0
2
1
1
2
0
1
1
0
0
1
1
2
0
2
1
1
1
0
1
1
2
1
0
1
1
1
0
1
1
2
2
1
2
1
2
2
2
0
1
1
2
1
0
2
2
0
2
1
1
2
2
1
1
1
2
1
2
2
1
1
0
0
1
0
1
2
0
0
1
2
2
1
1
1
2
2
1
0
0
2
2
1
1
1
2
1
1
2
0
0
1
2
1
1
0
1
1
1
2
0
2
1
1
2
0
1
1
0
1
1
0
2
1
1
1
1
1
2
0
1
2
3
1
1
1
1
0
2
2
1
1
1
0
0
2
1
1
1
1
0
0
0
2
0
0
2
1
1
1
1
1
1
1
1
1
1
1
0
1
2
2
2
1
2
1
1
2
1
0
1
1
1
1
1
0
1
1
1
1
0
2
1
0
1
2
1
2
0
1
1
2
1
1
2
0
1
2
2
1
1
0
1
0
1
0
3
1
1
1
2
1
1
1
2
1
0
2
1
2
2
1
0
1
2
0
0
0
1
1
1
1
0
1
1
2
1
2
1
1
2
1
2
1
1
1
2
0
1
1
1
2
1
1
1
1
1
1
0
1
1
1
1
2
1
1
1
2
0
1
1
1
0
2
2
1
1
0
1
0
2
2
1
1
0
1
0
1
0
1
0
0
1
2
1
2
1
1
1
1
1
1
2
0
1
1
1
1
0
1
0
1
0
1
1
2
2
1
2
2
1
1
1
2
1
0
1
1
1
1
1
1
1
2
1
1
1
1
2
0
1
1
1
2
1
1
0
2
1
1
1
2
1
0
1
1
1
2
2
1
0
1
1
1
0
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
2
0
2
1
1
0
2
1
0
1
1
1
0
1
1
1
1
1
2
1
1
1
1
2
1
1
0
0
1
1
2
1
2
1
0
1
3
1
2
2
0
1
1
1
2
0
1
1
0
0
1
1
2
2
1
1
1
1
1
2
1
1
2
2
1
1
1
1
2
2
2
2
1
1
0
0
1
1
0
1
1
1
2
1
0
0
1
1
0
2
1
2
2
2
1
1
0
1
1
2
1
1
1
2
2
0
1
1
1
1
1
1
1
1
1
1
3
1
1
1
2
1
2
2
1
0
1
0
0
1
0
0
1
1
2
1
1
1
2
2
1
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
0
1
2
1
2
1
2
1
0
3
0
1
2
2
0
0
1
1
1
1
1
2
1
1
1
0
1
2
0
1
2
1
2
2
1
1
2
1
1
1
1
2
0
0
1
1
1
1
2
1
1
2
1
1
1
2
0
1
0
1
1
0
1
2
1
1
1
0
2
1
1
1
0
2
0
1
1
1
1
1
1
1
2
1
1
2
2
1
1
2
1
1
1
2
0
2
1
1
2
1
2
2
1
1
0
2
1
1
2
1
0
1
1
2
0
2
1
1
2
2
1
1
1
2
1
1
1
2
1
1
0
1
0
1
1
2
1
0
1
1
2
2
1
0
1
1
2
2
1
1
0
0
2
1
2
1
2
1
1
1
1
1
2
1
2
1
1
1
1
0
1
2
3
0
1
2
1
1
0
1
2
2
1
2
0
0
1
1
2
1
0
1
1
0
1
1
0
1
1
1
1
2
1
2
1
2
1
1
1
2
0
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
3
1
2
1
1
1
1
0
1
1
1
1
1
1
2
1
1
0
0
1
2
1
2
2
1
0
1
0
1
1
1
1
2
2
2
1
1
1
1
2
0
0
1
2
1
1
2
1
1
1
1
1
1
0
2
2
1
2
1
4
1
1
1
1
2
2
0
1
1
0
2
1
1
3
0
0
1
1
0
1
1
1
1
1
1
0
1
1
2
1
1
1
0
1
1
1
0
2
1
1
1
2
0
1
2
0
2
1
1
1
0
1
1
2
1
2
1
1
3
1
1
0
1
2
1
0
2
2
2
1
1
1
1
2
1
2
1
2
1
1
0
0
0
1
2
1
0
2
1
1
1
1
1
1
1
2
1
0
0
1
2
2
0
1
2
1
2
1
0
0
1
2
1
1
1
1
0
2
1
1
1
0
0
1
1
1
1
0
1
1
1
1
0
0
0
0
1
2
2
1
1
3
1
2
1
2
1
1
0
1
2
1
1
0
2
1
1
1
2
1
0
2
2
1
1
1
1
2
1
1
1
1
0
1
1
1
0
0
2
1
0
2
1
2
0
1
2
1
1
2
1
1
1
1
1
1
2
2
2
1
1
3
1
1
1
2
2
1
1
3
1
2
1
1
2
1
1
1
1
1
0
1
2
0
1
1
1
1
2
1
1
1
0
0
1
1
1
0
3
1
0
1
0
1
1
1
0
2
1
1
1
1
1
1
0
1
2
1
1
1
2
1
1
2
1
0
1
1
0
0
0
2
2
2
1
1
1
2
1
1
1
1
2
2
2
2
1
1
1
1
1
2
2
2
1
1
1
2
1
1
1
0
2
1
1
1
1
1
0
1
1
0
1
1
2
1
1
1
1
2
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
2
1
1
1
2
1
2
1
1
1
1
1
1
0
0
1
1
1
1
0
1
0
1
0
1
2
0
0
2
0
1
1
2
1
0
1
1
1
1
0
2
2
0
2
2
2
1
3
0
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
2
1
1
2
0
1
2
1
1
0
2
1
2
2
1
1
1
1
1
1
0
1
2
1
0
1
1
1
2
2
0
1
2
0
0
0
1
2
1
1
2
1
1
0
1
1
2
1
1
1
0
1
1
2
0
0
2
0
2
0
1
1
0
2
0
2
0
1
1
0
1
1
1
2
1
0
1
0
1
2
1
2
1
2
1
1
0
0
0
0
1
1
1
0
0
1
1
1
1
1
0
1
1
1
0
1
1
2
2
1
1
2
1
1
2
1
1
0
1
1
2
1
1
1
1
1
0
1
1
0
1
1
1
1
1
2
0
1
2
2
2
2
2
2
2
1
2
1
1
1
0
1
0
0
1
1
0
1
2
2
0
0
1
1
0
1
0
1
0
1
1
2
1
1
0
1
1
0
2
2
0
1
2
2
0
1
0
0
2
1
2
1
1
0
1
1
2
1
1
0
0
0
1
1
0
1
1
1
2
0
2
1
1
1
0
2
2
2
1
1
1
2
1
1
0
1
1
1
1
1
0
1
1
2
2
2
0
1
1
1
0
1
1
0
1
1
1
1
1
1
0
1
1
0
2
0
2
1
1
1
0
2
1
0
1
2
2
1
1
0
1
1
2
1
1
2
1
2
1
1
1
1
2
1
0
2
0
1
0
2
1
1
1
1
1
1
0
1
1
1
1
1
1
0
3
1
1
1
1
2
1
2
0
2
0
0
2
1
1
1
1
2
1
1
2
2
2
0
1
2
0
1
0
0
0
0
1
0
2
0
1
1
2
1
2
0
1
1
2
0
1
2
1
1
1
2
2
1
2
0
1
2
0
2
0
2
0
0
2
2
1
2
1
1
1
1
0
1
2
2
1
1
2
1
1
1
0
1
2
0
0
1
2
0
2
1
2
0
2
0
1
1
1
1
1
1
1
1
2
1
1
1
2
0
2
0
1
1
1
2
1
1
1
0
1
1
1
1
1
1
1
2
1
0
1
0
1
1
0
0
1
1
1
2
1
1
1
1
1
0
1
2
1
1
1
0
1
2
1
0
1
1
1
1
1
0
1
1
2
1
1
1
1
1
2
0
2
2
1
2
2
0
1
2
1
1
1
2
2
1
0
1
1
2
1
1
1
2
1
0
4
1
0
2
1
1
0
1
1
2
0
1
0
1
1
0
2
1
2
0
1
1
1
0
2
1
0
1
1
1
2
1
0
1
2
1
2
1
1
2
1
2
0
0
1
1
2
0
2
0
2
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
2
0
2
1
1
2
1
0
2
0
1
1
1
2
1
1
1
1
0
1
1
0
1
2
2
1
1
1
1
0
1
1
1
1
2
1
1
1
1
2
2
1
1
1
2
2
1
0
2
0
0
1
1
0
2
0
3
1
2
1
2
2
3
1
1
1
1
0
1
2
1
1
1
1
2
1
2
0
1
0
1
1
2
3
1
1
1
2
1
1
2
1
2
1
1
2
1
1
0
2
1
0
1
0
1
1
3
1
1
1
0
1
0
1
2
2
1
1
1
2
0
1
0
2
1
1
1
1
1
2
1
2
1
2
1
1
1
1
1
2
2
0
2
0
1
1
1
1
2
2
2
1
0
2
0
1
2
2
2
0
0
1
2
1
2
0
1
2
1
0
0
1
2
1
1
1
2
1
2
1
1
2
0
1
1
2
2
0
2
1
1
1
1
1
0
1
2
1
0
1
1
0
2
1
1
1
1
1
1
2
2
0
1
1
0
2
2
2
1
2
1
0
1
2
1
0
2
2
0
2
1
1
2
0
2
0
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
0
1
1
1
1
2
2
2
1
0
1
0
0
1
1
2
2
1
1
0
2
0
1
1
0
3
1
0
1
0
1
1
0
1
2
2
2
1
1
1
0
0
0
1
0
2
1
1
1
1
1
1
1
1
1
0
1
1
1
0
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
0
0
1
1
1
0
1
2
2
1
0
1
1
0
1
1
2
2
2
1
1
1
1
1
2
0
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
0
1
1
0
1
1
1
2
1
1
0
1
0
1
2
2
1
2
0
1
1
1
2
1
0
2
2
2
2
0
0
1
1
1
0
0
1
1
1
0
1
0
2
1
2
2
1
1
1
4
1
0
1
1
1
1
1
2
0
2
0
0
2
0
1
2
0
0
2
2
1
2
1
2
2
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
0
0
1
1
1
1
2
2
1
1
1
0
1
1
0
1
1
1
2
1
1
1
3
1
1
1
1
2
1
1
1
0
1
2
0
1
1
2
1
2
1
1
1
1
0
1
2
0
1
1
2
0
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
0
1
2
1
1
1
0
0
2
0
0
1
2
1
0
1
1
1
1
0
2
1
1
0
2
1
1
2
0
1
1
1
1
0
1
1
1
1
0
1
1
1
2
1
2
1
1
0
1
1
0
1
1
1
1
1
1
2
1
1
3
1
2
1
0
1
1
0
1
1
0
2
2
1
1
1
2
1
2
1
2
1
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
0
1
0
1
1
1
1
1
1
1
1
1
1
1
2
2
0
1
1
1
0
0
1
0
2
2
1
1
2
1
0
2
1
2
0
0
1
1
2
2
1
1
1
0
1
1
1
1
1
0
1
2
0
1
1
1
2
2
1
2
0
2
1
2
1
2
1
0
1
1
1
1
1
1
1
1
0
1
1
0
1
1
1
2
1
1
2
2
1
1
2
2
2
1
10
1
1
0
2
1
1
1
1
2
1
0
1
1
2
1
3
0
0
1
1
1
0
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
3
2
1
1
2
1
1
1
1
0
1
0
1
1
1
1
2
1
2
1
2
1
2
1
2
0
2
2
1
1
1
0
1
1
0
1
1
1
1
2
1
1
1
2
0
1
1
2
0
1
0
0
0
1
2
1
1
1
1
2
1
1
2
1
1
1
2
1
1
0
1
1
1
2
2
2
2
2
1
0
1
1
2
2
1
1
2
1
0
1
1
1
0
2
2
0
1
1
0
1
1
1
1
1
1
1
2
1
1
1
0
1
1
2
0
1
0
1
1
2
1
1
1
0
1
3
2
1
2
1
1
1
1
0
0
0
0
1
2
1
0
1
1
1
0
0
1
1
2
0
2
1
1
1
1
1
1
1
1
0
1
1
0
0
0
2
0
2
1
2
2
0
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
2
2
1
1
1
2
1
1
2
1
1
1
0
0
1
2
1
2
1
0
1
0
1
1
2
1
1
1
1
0
1
1
1
1
1
1
2
0
1
0
1
1
1
1
1
2
1
0
0
1
1
0
1
1
0
0
1
1
1
1
2
1
0
1
1
2
1
0
1
2
1
1
1
1
0
2
1
2
2
1
1
2
1
1
1
1
2
0
1
1
0
2
2
1
2
1
0
1
2
0
1
0
2
0
1
0
1
2
1
2
2
1
2
1
2
1
1
1
1
1
1
1
2
1
2
2
1
0
0
1
2
1
1
1
0
1
1
1
1
2
1
1
1
0
1
1
1
1
0
1
1
2
1
1
1
0
1
1
1
1
0
2
2
1
1
2
1
1
2
1
1
2
0
1
1
2
0
0
1
0
0
1
0
1
1
1
2
0
1
1
2
1
1
2
1
0
0
1
1
2
2
1
1
1
0
0
1
1
1
2
0
2
0
1
2
1
1
1
2
1
1
2
1
1
1
1
2
0
1
2
2
1
1
2
1
1
2
1
0
0
0
2
1
2
0
1
0
1
1
1
1
0
0
2
2
1
1
2
2
1
2
1
1
1
1
2
2
1
0
0
2
0
1
1
1
1
0
2
1
2
1
1
1
0
1
2
2
1
2
1
1
1
1
1
1
1
2
0
1
1
0
1
2
1
1
1
1
2
2
2
2
1
2
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
2
1
2
2
0
1
1
2
1
1
2
2
0
1
1
0
2
1
2
0
1
1
1
1
0
2
1
1
0
1
1
1
1
2
1
0
2
1
2
1
2
1
1
1
1
0
2
0
1
1
1
1
2
2
1
1
1
0
0
1
1
0
2
0
1
1
1
1
1
1
1
2
0
1
1
0
2
1
2
1
1
0
1
1
1
2
1
1
1
1
2
1
2
1
2
2
1
0
1
1
2
2
1
1
0
1
1
0
0
1
1
1
1
1
1
1
2
1
1
0
1
1
2
1
2
1
1
0
2
2
1
0
1
1
2
0
0
2
1
1
1
0
1
1
1
1
1
2
1
1
1
2
0
1
1
1
1
2
1
1
1
1
1
1
0
2
1
1
1
0
1
1
1
0
0
0
2
0
1
1
1
2
1
0
1
1
1
1
0
1
2
0
2
1
2
1
1
0
0
1
2
1
2
2
2
1
1
1
2
1
1
1
2
3
1
1
1
1
1
0
2
1
1
1
2
1
1
1
2
2
0
2
0
2
2
0
0
0
0
1
1
2
1
2
1
0
1
1
0
1
1
1
1
2
0
1
1
1
1
1
1
0
0
1
2
1
1
1
0
2
1
2
0
0
0
2
1
1
0
0
0
1
1
2
1
1
1
2
0
1
2
1
2
1
2
1
1
0
2
0
2
2
1
0
1
0
2
1
0
2
1
1
0
2
1
2
1
2
1
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
3
3
0
1
0
1
2
1
1
1
0
2
1
2
3
1
1
1
1
1
2
1
2
1
0
2
0
1
1
1
0
1
1
2
1
1
0
1
2
1
2
1
2
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
0
1
0
0
1
1
1
1
1
4
2
0
1
1
1
0
1
1
1
1
1
1
1
1
2
2
1
1
0
1
2
1
1
1
2
2
0
1
1
0
1
2
1
0
2
1
0
0
1
1
1
0
1
1
2
1
0
2
2
2
1
1
2
1
2
2
0
0
1
2
1
0
2
1
2
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
2
1
1
2
2
1
1
2
1
1
1
1
2
0
1
1
1
2
1
2
2
2
1
1
1
1
1
1
2
1
0
1
0
2
2
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
0
1
1
2
1
1
1
1
1
0
0
2
1
2
1
2
2
2
1
1
1
1
1
2
1
1
1
2
1
1
2
1
2
2
0
1
0
2
0
1
1
0
2
1
2
1
0
1
0
3
2
0
2
1
1
1
0
1
1
0
0
2
0
2
1
0
0
2
1
1
1
0
1
2
1
2
1
2
2
1
2
0
1
1
1
1
1
1
2
2
1
1
0
1
2
2
1
4
2
1
1
0
0
2
1
1
2
1
2
0
2
1
2
2
2
1
2
0
2
0
1
1
1
1
0
1
2
0
1
1
1
1
1
1
1
2
1
5
1
2
2
1
1
3
1
1
1
0
2
2
2
1
0
0
1
1
0
1
2
2
1
2
1
1
2
0
1
2
1
1
2
1
1
1
1
1
1
2
1
2
1
2
1
0
0
2
1
2
1
2
1
1
0
1
1
1
1
1
1
2
2
0
2
2
2
1
1
0
1
2
0
1
1
1
0
1
0
2
1
0
2
1
2
1
1
1
1
2
2
2
0
1
1
1
1
0
0
1
2
0
1
1
2
1
1
1
0
1
1
1
1
1
1
1
0
2
1
0
1
1
1
2
2
2
0
1
1
1
1
1
1
2
1
1
0
2
0
2
2
0
1
2
1
1
2
1
1
1
1
0
1
1
1
1
2
1
1
0
1
0
1
2
1
1
1
1
2
2
2
2
2
1
1
2
1
1
1
1
2
1
2
2
2
1
1
2
1
1
1
1
1
3
1
2
0
2
2
2
1
1
1
2
1
0
1
1
1
1
0
2
2
2
1
1
1
0
1
2
0
2
1
2
1
0
2
2
1
1
0
0
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
0
1
2
1
1
2
2
0
1
2
1
1
1
2
1
1
0
1
2
1
2
1
3
1
1
1
2
1
1
2
0
1
0
1
2
2
1
1
1
1
1
2
1
1
0
0
1
1
2
1
0
1
1
1
1
1
1
1
0
1
1
2
1
1
1
2
1
1
2
1
2
2
0
1
1
0
1
0
5
1
1
0
1
0
0
2
1
1
2
1
2
1
1
1
1
1
1
1
1
0
1
0
1
0
2
2
0
3
1
1
0
2
1
1
1
1
2
2
1
1
2
1
1
1
1
2
1
0
0
2
1
1
2
2
1
1
0
2
0
1
1
1
2
2
1
2
1
0
2
1
2
1
0
1
2
0
1
1
2
0
1
1
0
1
1
1
2
2
1
0
0
1
1
1
1
2
1
2
2
1
1
1
1
0
1
1
2
1
1
2
2
1
1
2
1
1
1
2
2
2
1
1
2
2
1
1
1
1
1
1
1
0
0
2
1
1
1
1
0
2
1
0
0
1
1
0
2
1
0
1
1
0
1
2
1
1
0
1
1
2
1
1
2
2
0
3
2
0
1
0
1
1
1
1
1
0
0
1
1
1
2
1
0
1
1
1
0
0
0
3
1
1
1
1
1
4
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
2
2
1
1
1
2
1
2
2
0
0
1
1
2
1
0
1
1
1
1
2
1
1
1
1
1
1
2
0
1
1
1
2
2
2
1
1
1
2
2
1
1
1
1
2
0
1
2
1
2
1
0
2
1
1
1
1
1
0
2
0
1
1
1
2
1
2
1
1
1
1
1
0
2
2
1
1
1
1
0
1
2
2
0
2
1
0
2
1
2
3
1
2
2
2
1
1
0
2
1
1
0
2
1
2
1
0
1
0
1
1
1
0
1
1
0
0
1
1
2
0
2
2
1
2
1
1
1
2
1
1
1
1
1
1
2
1
0
1
1
2
2
1
0
0
1
2
2
0
2
2
1
0
2
1
1
2
1
1
2
1
1
1
1
1
1
1
2
0
1
1
2
2
1
0
0
1
1
0
2
1
0
1
1
2
2
1
1
1
2
1
0
1
2
2
0
2
1
2
2
2
1
2
2
1
1
1
1
1
1
1
1
2
1
0
1
1
1
2
0
1
1
0
1
2
2
1
1
1
1
1
0
0
0
2
1
1
1
2
1
2
2
2
2
2
1
1
1
1
1
0
2
0
0
2
1
1
1
3
0
2
2
1
1
2
1
0
2
2
0
1
0
0
2
2
2
0
1
1
1
0
2
1
1
1
2
1
1
1
2
1
1
2
0
2
2
1
0
1
0
2
1
1
1
1
1
1
1
2
1
2
1
2
1
0
2
1
2
1
1
1
0
0
0
0
2
2
2
0
0
1
0
1
1
1
1
1
1
1
1
0
0
1
0
1
1
2
0
0
1
1
1
1
1
1
1
1
2
0
2
0
1
0
1
2
1
1
1
3
1
1
2
1
0
0
1
1
1
1
1
2
2
2
1
0
0
1
1
1
0
0
1
1
1
2
0
1
1
2
0
1
1
2
1
1
2
1
0
1
1
2
1
1
2
1
1
2
1
1
1
1
1
0
2
2
1
1
1
2
0
2
2
2
2
0
0
0
0
1
2
0
2
2
1
1
1
2
2
2
1
1
0
1
2
1
1
0
1
1
1
1
1
1
1
1
1
0
0
1
2
2
1
0
1
1
2
2
1
3
1
0
2
1
1
1
2
2
0
1
1
1
1
1
2
1
0
0
1
1
1
2
1
1
1
2
2
1
2
1
1
1
0
2
1
1
1
1
2
1
1
1
2
1
0
1
1
1
1
2
1
0
2
1
0
1
0
0
2
1
1
1
2
1
1
0
1
1
1
1
0
2
1
2
1
0
0
1
2
2
1
1
1
1
2
1
2
1
1
0
1
1
0
1
1
0
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
0
1
0
2
2
0
0
2
4
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
2
1
2
1
1
2
1
1
2
1
1
1
1
2
0
1
2
0
0
0
1
1
1
1
1
0
1
2
2
0
1
0
1
1
1
2
1
1
2
1
2
2
1
1
1
1
2
1
2
1
1
2
1
1
3
1
1
1
0
2
1
1
1
0
1
1
0
2
1
1
0
1
4
1
0
1
1
1
2
0
2
0
1
1
2
1
0
1
1
1
1
1
1
1
0
0
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
2
2
1
2
1
1
2
1
1
2
1
0
1
1
1
2
1
1
2
0
1
1
1
2
1
2
2
1
0
1
0
0
1
1
1
1
1
0
0
0
1
2
1
1
2
1
0
2
1
1
2
2
1
1
0
0
2
1
0
1
1
1
1
1
2
1
2
1
1
2
1
2
2
2
0
0
1
2
1
2
1
0
0
1
2
1
0
1
2
0
1
1
1
2
1
1
0
1
1
1
0
2
2
2
1
0
3
1
1
1
2
1
1
1
1
0
1
1
2
2
2
1
2
1
0
2
0
1
0
2
2
1
1
2
1
2
1
1
1
0
0
2
1
1
1
1
2
2
1
1
1
0
1
2
1
0
1
2
1
2
2
1
1
2
1
0
1
2
1
1
1
1
1
1
1
2
2
2
0
0
1
2
2
2
2
1
1
1
1
1
1
0
0
0
1
1
2
0
0
1
0
1
2
1
1
1
1
1
2
1
1
1
0
1
0
2
1
1
1
1
0
1
3
2
1
2
1
2
2
0
1
4
0
2
2
0
1
2
2
0
1
0
2
1
1
2
1
1
1
1
1
0
0
1
2
2
1
0
1
1
2
2
0
2
1
0
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
0
2
1
1
0
1
1
1
1
2
1
1
1
1
2
1
2
3
2
1
1
1
0
1
3
2
1
0
1
2
1
0
2
0
1
1
2
2
2
0
1
1
1
1
1
1
1
2
1
1
0
2
2
0
1
1
1
2
2
1
2
1
0
0
0
0
2
2
1
2
0
2
0
1
0
2
0
0
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
3
1
0
1
0
1
0
1
1
0
1
1
1
1
1
2
2
1
0
1
1
1
2
2
1
1
2
2
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
0
1
1
2
2
2
0
2
1
0
2
0
0
1
1
0
1
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
1
2
1
0
0
0
1
1
2
2
1
2
0
1
1
0
1
1
0
1
2
2
1
0
1
2
2
2
1
1
2
2
0
1
2
0
2
1
1
1
2
0
1
1
1
1
1
0
0
2
2
1
0
0
1
1
2
1
1
1
2
1
1
1
1
1
1
2
0
1
1
1
2
1
2
0
1
1
1
1
2
0
1
1
2
1
1
2
2
0
1
1
2
1
2
1
1
0
2
2
2
0
2
1
2
2
0
1
1
0
2
2
2
1
1
1
0
1
0
1
1
1
1
1
1
1
1
2
1
1
0
1
1
1
0
1
1
1
1
1
1
1
0
1
1
1
2
1
1
2
1
2
1
1
1
1
2
1
2
1
0
2
2
1
1
1
0
2
1
1
1
1
2
1
0
1
1
1
1
1
1
1
1
1
1
1
0
0
0
2
0
1
1
0
1
1
1
2
1
1
1
1
0
1
2
1
2
1
1
1
1
2
2
1
1
1
2
1
2
1
1
1
2
2
2
2
1
1
1
1
1
0
1
1
1
1
2
1
1
1
1
2
1
0
0
2
1
0
2
2
1
2
0
1
1
1
1
1
1
1
1
1
2
1
2
1
2
1
1
1
2
1
1
1
1
1
0
1
2
0
1
1
1
1
1
1
2
2
1
1
1
2
1
0
0
1
0
2
1
1
1
2
1
2
0
1
0
0
0
1
2
1
1
1
1
2
1
1
1
2
1
2
2
1
1
1
1
1
2
0
1
1
1
0
2
0
0
1
1
0
1
3
1
1
0
1
1
1
0
1
2
1
0
1
0
2
1
2
1
2
2
1
2
0
0
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
0
1
0
0
1
0
1
1
0
1
1
1
1
1
2
2
0
1
1
1
1
1
1
1
1
1
1
1
0
2
1
1
1
1
1
2
2
1
2
1
1
1
0
1
0
1
1
1
1
1
1
1
1
2
1
1
1
0
2
1
1
2
1
1
1
1
1
2
2
1
1
0
1
2
1
1
1
0
0
1
0
1
1
2
0
0
2
2
0
2
2
1
0
0
1
1
1
0
1
0
2
0
1
2
1
1
1
1
1
1
1
0
1
0
2
1
1
1
1
2
1
2
2
1
1
1
1
1
0
1
1
1
1
0
2
1
0
2
1
1
2
1
1
2
1
1
1
1
0
1
1
1
2
1
2
1
1
1
1
2
1
0
1
1
1
1
2
1
0
1
1
1
1
0
1
1
1
0
1
1
1
1
2
1
0
0
1
1
2
1
2
1
0
1
2
2
1
1
1
1
1
2
2
2
1
1
2
2
1
0
0
2
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
0
2
1
1
2
1
0
0
1
1
0
0
1
1
0
1
1
1
1
1
1
2
0
1
1
1
1
2
2
1
3
2
2
1
2
0
2
0
1
1
0
0
2
1
0
2
1
1
1
2
3
1
1
1
1
1
1
1
2
1
1
0
1
1
2
1
2
2
1
1
2
1
2
1
0
1
2
0
1
0
1
1
1
2
1
1
2
1
0
2
3
1
1
1
1
1
0
2
2
1
1
1
2
1
1
1
1
1
2
1
1
1
2
2
1
1
2
1
0
2
2
2
1
0
1
1
1
1
2
1
1
1
1
1
1
0
1
0
1
1
1
1
2
1
1
0
1
1
1
0
1
1
1
1
1
1
2
1
0
1
1
2
1
2
1
2
1
1
1
1
1
1
2
1
1
1
2
0
1
1
1
1
0
0
2
0
1
0
1
1
1
1
2
0
2
2
2
0
0
2
2
1
1
1
1
0
1
0
1
0
1
4
1
1
0
1
3
1
0
2
1
1
1
2
0
2
1
2
3
2
1
2
0
1
2
1
1
2
1
1
2
2
1
0
1
1
1
1
1
0
2
1
2
3
0
1
2
0
2
1
2
0
1
1
1
1
0
1
2
1
1
0
2
0
1
1
1
1
1
1
1
2
1
1
0
1
0
1
2
1
2
1
2
1
2
1
0
2
1
1
1
2
2
2
1
0
1
2
1
1
2
1
2
1
1
0
0
1
0
2
1
1
0
1
1
0
0
2
0
1
1
2
1
2
1
0
0
1
1
1
1
0
1
0
2
2
0
1
2
2
1
1
1
2
1
2
1
2
0
1
2
1
1
1
0
1
0
2
1
1
1
2
1
0
1
1
1
0
0
1
1
2
0
2
0
0
2
1
2
2
2
1
0
2
2
1
2
1
2
1
1
1
1
1
1
1
0
0
1
2
1
2
1
2
1
2
2
1
1
2
1
2
1
1
0
2
1
2
2
2
1
2
1
1
0
1
2
0
1
0
1
2
0
2
1
1
1
0
1
1
2
0
1
2
1
0
2
1
0
1
1
2
1
1
2
1
1
1
1
1
1
1
2
1
0
1
1
0
1
1
1
1
2
1
0
1
2
1
1
0
1
1
1
1
1
4
1
2
1
1
2
1
1
1
0
2
1
1
1
2
1
2
2
1
1
0
2
1
1
0
1
1
1
1
1
1
1
2
0
0
1
1
0
1
1
1
1
1
1
1
1
0
1
1
1
0
1
2
2
1
2
2
2
2
0
1
1
1
2
1
2
1
0
2
1
1
0
1
1
1
2
0
2
1
2
0
2
2
1
0
0
2
1
1
1
1
2
1
1
1
1
0
2
0
2
0
1
1
1
1
2
1
3
1
1
1
1
2
1
0
1
1
1
1
1
2
1
1
2
2
0
1
1
1
0
0
2
1
1
1
1
1
1
0
1
1
1
0
1
0
0
0
1
3
0
1
1
1
1
1
1
1
0
1
0
1
1
1
2
1
2
1
1
2
0
2
2
2
2
0
0
2
1
2
1
1
1
1
1
2
2
1
1
2
0
3
1
0
1
1
0
1
1
0
1
1
1
1
2
1
0
1
1
1
2
1
2
1
1
1
0
0
1
1
0
1
1
2
2
2
1
1
1
2
1
1
2
0
0
0
2
1
1
1
1
1
2
2
1
1
2
1
1
1
2
0
1
1
1
2
1
0
2
1
1
1
0
0
1
0
1
0
1
1
3
1
0
1
1
1
1
1
1
1
1
0
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
2
1
2
2
1
0
1
1
1
1
0
1
1
1
0
1
1
2
1
2
1
0
2
3
1
2
1
2
1
0
1
2
1
0
2
1
1
2
1
1
1
1
1
1
0
1
1
0
1
0
1
1
1
0
1
1
1
1
2
1
1
1
0
1
1
1
2
1
1
1
5
2
1
1
1
2
1
1
1
1
2
1
2
0
2
1
4
2
1
1
1
0
1
2
0
0
2
2
0
1
1
1
1
0
2
1
1
2
1
2
2
2
1
1
0
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
2
1
1
1
1
2
0
1
1
1
1
1
2
1
0
1
1
1
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
0
0
1
1
0
1
1
1
1
1
0
3
1
1
3
2
2
1
1
0
1
1
1
2
1
1
1
1
1
1
2
2
1
2
2
1
1
1
2
1
2
1
1
0
1
1
1
1
2
1
1
1
2
1
0
1
2
1
1
1
1
0
1
1
1
1
1
0
1
1
1
2
0
1
2
1
1
1
2
1
1
1
1
2
1
1
0
1
1
1
0
0
0
1
1
1
0
1
2
2
1
1
1
1
1
0
1
1
0
2
0
2
1
1
0
3
2
1
1
2
2
1
1
1
1
1
2
1
2
1
1
0
1
1
1
1
3
1
1
2
0
0
1
0
0
0
3
1
1
2
0
2
2
1
1
1
1
2
0
1
1
1
1
1
1
1
0
1
2
1
1
2
1
1
1
0
1
2
1
1
1
1
2
2
1
1
2
0
1
1
1
2
1
3
0
1
2
1
1
1
2
2
2
2
2
1
1
1
2
1
2
1
1
1
1
1
1
1
1
0
1
1
1
0
0
2
1
0
1
0
2
0
0
2
2
1
1
1
1
1
1
2
2
1
0
1
2
1
1
2
1
2
1
2
1
0
2
2
1
9
0
2
1
2
1
0
0
0
1
0
1
1
1
1
1
2
1
2
0
2
2
1
1
1
1
1
2
1
2
1
0
1
1
2
2
0
0
1
1
1
1
1
1
2
1
0
2
2
1
1
1
0
0
0
1
1
1
1
2
2
0
1
1
1
1
1
1
2
2
1
1
1
1
1
2
2
1
1
0
1
2
1
1
1
1
0
2
1
1
0
2
2
0
0
1
1
1
1
1
0
1
2
1
1
1
1
0
2
1
0
0
0
1
0
1
2
2
1
1
2
0
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
0
0
2
0
0
2
0
1
1
2
2
1
1
1
2
0
2
2
2
1
1
2
1
2
1
1
0
0
1
1
0
1
1
1
0
1
1
2
1
1
1
1
0
1
0
1
1
2
2
1
1
0
1
0
1
0
2
2
1
1
0
1
1
1
0
1
0
2
1
0
1
0
1
1
2
2
0
1
2
0
1
1
2
1
1
2
1
0
1
1
1
2
1
1
2
1
1
2
1
1
1
1
0
0
1
1
1
2
1
1
2
1
0
2
2
2
2
1
1
2
1
1
1
0
1
2
2
1
1
2
0
1
1
1
0
1
1
2
1
1
1
2
1
1
1
0
1
1
1
2
1
1
1
0
1
4
1
1
2
2
2
1
2
0
1
1
0
0
1
0
0
1
1
1
2
0
1
2
1
1
2
1
1
0
1
0
1
1
2
0
1
1
1
1
1
0
0
1
1
2
0
2
1
2
2
3
2
1
1
1
2
1
1
1
2
1
1
0
1
1
1
2
1
0
1
1
1
1
1
1
0
2
1
2
0
2
1
2
1
1
2
2
0
2
0
1
0
1
3
1
1
0
1
2
2
1
1
2
1
2
0
0
1
1
2
1
1
1
2
1
1
2
1
1
1
1
2
2
1
0
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
5
1
1
2
1
1
2
1
0
1
1
1
0
0
1
0
0
1
1
0
2
0
2
1
1
1
1
1
1
1
0
1
2
1
1
1
2
1
1
2
2
1
1
1
2
1
1
0
0
1
2
1
2
1
1
2
1
1
1
1
1
0
2
1
1
1
1
1
2
2
1
1
1
1
1
1
1
0
1
1
1
1
0
2
2
1
1
2
1
0
1
1
1
1
1
1
1
3
0
1
1
1
1
2
2
1
1
0
1
2
1
2
1
1
1
2
1
2
1
1
1
0
1
1
2
2
1
1
2
0
2
0
1
1
1
2
2
1
1
1
0
0
2
1
1
1
2
2
1
1
1
4
0
1
0
2
0
2
1
1
1
1
1
1
1
2
1
1
0
1
0
2
1
1
2
1
0
0
0
1
1
2
1
0
2
1
1
0
2
0
2
1
1
2
1
0
1
1
0
1
1
1
1
1
2
2
2
1
1
0
1
1
1
0
1
1
0
1
1
0
0
0
1
0
2
1
1
0
1
1
2
2
1
1
1
2
1
0
1
2
1
0
1
2
1
1
0
0
1
2
1
0
1
0
1
1
1
1
1
1
1
2
1
0
1
1
2
1
1
1
2
2
1
1
1
0
1
0
1
2
1
2
2
2
1
1
0
1
1
1
0
0
1
1
0
1
0
1
1
1
1
1
2
0
1
2
1
3
2
0
0
0
1
1
1
1
1
0
0
0
1
0
1
1
1
1
1
0
2
1
0
1
2
2
1
2
1
1
1
1
1
2
1
2
1
1
1
0
2
0
1
1
2
0
1
0
1
1
1
1
1
1
1
1
1
0
2
1
1
1
2
0
1
1
2
1
2
0
0
1
1
1
0
1
1
4
1
2
0
1
1
2
2
1
1
0
2
1
1
1
1
0
1
1
1
1
0
1
1
3
1
1
2
1
1
1
1
1
2
0
2
0
1
1
1
0
1
1
1
2
1
2
2
1
2
1
2
2
0
0
1
1
1
1
1
2
1
1
0
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
2
2
1
1
0
1
1
2
2
2
1
1
2
1
0
1
1
1
1
1
1
1
2
2
2
1
1
1
1
2
1
2
1
1
2
1
1
1
2
1
0
1
1
2
1
1
2
1
1
1
2
0
1
1
1
0
1
0
0
2
1
1
2
2
1
1
1
2
2
0
1
0
1
2
1
1
0
0
1
1
2
1
0
0
1
0
0
1
0
2
1
1
2
1
2
1
0
1
1
1
1
1
1
1
1
0
2
2
1
1
1
1
2
1
1
2
2
1
2
1
2
2
1
1
2
1
1
1
2
0
1
1
2
0
1
1
0
2
2
2
2
1
1
1
2
0
0
0
1
1
0
1
1
1
0
0
1
1
1
0
2
0
1
1
1
1
0
1
1
0
1
1
1
1
2
1
0
2
2
0
0
0
1
1
1
1
2
2
1
0
1
1
1
1
1
1
1
1
2
0
1
1
1
2
0
1
1
2
2
0
0
1
2
0
1
1
1
1
1
1
0
1
1
1
1
1
2
1
1
0
0
2
1
1
0
2
1
2
1
1
2
1
1
2
1
0
1
1
2
2
0
1
1
4
1
1
1
1
2
1
2
0
1
1
1
1
0
1
0
0
2
2
1
2
2
0
0
0
1
2
0
1
1
1
1
0
1
1
1
0
1
0
1
1
1
0
1
1
1
1
1
1
1
2
2
2
2
1
1
0
1
1
1
1
1
0
1
0
0
1
2
1
1
1
1
1
2
1
1
1
0
3
0
0
1
1
1
1
1
1
1
1
2
0
0
3
1
1
1
0
2
1
1
1
1
1
1
0
1
1
2
2
1
0
1
1
1
1
1
1
2
1
1
2
1
2
1
2
1
1
1
0
1
0
2
1
1
0
1
0
2
0
1
2
2
1
1
1
0
0
1
0
2
1
1
2
2
1
1
1
1
1
0
0
1
1
1
1
1
1
1
2
1
0
1
1
1
1
1
1
0
0
0
1
0
1
2
1
1
2
0
1
2
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
0
0
1
1
1
1
0
1
1
0
1
1
1
1
1
0
2
2
1
2
1
0
1
1
0
2
1
0
1
1
2
1
1
2
0
1
1
1
1
1
2
1
1
1
2
0
1
1
2
1
1
1
1
3
1
0
0
2
0
1
1
2
1
1
2
1
1
0
1
0
0
1
1
1
1
1
1
1
1
2
1
2
1
1
0
2
0
0
1
2
1
1
1
2
1
2
1
1
1
2
2
1
0
2
1
1
0
1
3
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
0
2
0
1
1
0
1
1
0
0
1
0
1
3
0
2
1
0
1
1
1
1
2
1
2
2
1
0
0
2
2
1
1
1
1
1
2
1
1
1
2
0
1
1
1
1
0
1
2
1
1
1
0
2
2
1
1
0
0
0
0
0
0
1
1
2
2
0
0
0
1
1
1
1
2
1
2
1
0
2
0
0
1
2
2
0
2
1
0
0
1
1
1
1
1
1
1
0
1
1
2
1
1
1
0
1
0
1
0
1
2
1
1
1
1
1
2
1
1
1
1
3
2
1
1
0
1
2
1
1
1
2
2
0
1
0
0
2
1
1
0
1
2
1
1
1
1
1
1
0
1
2
2
1
2
1
1
0
2
1
1
1
0
2
1
2
2
2
1
2
1
1
1
1
2
1
1
1
1
1
2
0
1
1
2
3
1
1
1
1
0
1
1
2
0
1
0
3
1
1
1
1
1
2
0
0
0
1
2
1
1
1
1
1
1
2
1
0
1
1
0
2
2
2
1
1
2
1
1
1
1
1
1
2
1
2
1
1
0
0
1
1
1
2
0
1
1
1
2
1
2
1
1
1
0
1
0
1
0
0
1
1
2
1
1
1
2
2
1
1
1
1
0
0
1
1
1
0
1
1
1
1
1
1
1
0
1
1
0
2
2
0
1
1
2
0
1
1
0
1
1
1
2
2
0
2
1
2
1
1
1
2
2
1
2
1
0
1
1
0
2
1
1
0
1
2
1
0
3
1
2
0
1
0
0
0
1
1
2
0
0
1
1
2
0
0
1
0
1
1
1
0
1
1
2
1
1
0
1
2
0
1
2
1
1
2
1
1
2
1
1
0
1
0
2
1
1
2
2
0
2
0
2
2
1
1
1
2
2
1
1
1
1
2
2
2
0
2
1
1
2
0
1
0
1
3
2
2
1
2
1
1
1
2
1
2
1
1
1
1
1
2
2
1
0
1
0
1
1
0
2
2
2
1
1
1
1
1
2
1
0
1
0
0
1
1
1
1
0
1
1
1
1
1
2
1
1
2
1
0
1
1
1
0
1
1
0
1
1
1
1
0
1
1
1
2
1
2
0
1
1
1
1
0
1
1
1
1
1
1
0
1
0
2
2
1
1
1
2
1
2
0
0
0
1
1
1
1
0
2
1
1
0
1
2
1
2
1
2
1
1
1
2
1
2
1
1
1
1
0
2
1
2
1
0
1
2
1
1
2
2
2
1
1
2
1
2
1
2
1
2
1
1
0
2
0
0
2
1
1
1
0
2
0
0
2
1
1
1
1
1
1
1
1
3
1
2
2
1
2
0
0
2
1
1
0
1
1
1
1
0
1
1
1
1
2
1
2
0
0
1
2
2
1
2
2
1
2
0
1
1
1
1
1
2
1
1
2
1
1
1
1
2
1
1
1
1
1
2
1
1
0
0
1
2
1
1
1
1
2
1
0
2
1
3
1
1
0
1
1
0
0
2
1
2
1
1
1
1
1
1
1
1
1
1
2
3
1
2
1
1
0
2
1
1
0
1
2
1
0
1
1
0
1
2
1
1
1
1
2
0
2
1
0
2
1
1
1
1
2
1
1
1
1
2
1
3
1
2
0
2
1
2
1
1
4
1
1
2
0
2
1
1
0
0
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
2
1
2
2
1
1
1
2
1
2
0
1
0
1
2
1
1
1
1
0
1
1
1
1
2
2
0
1
1
1
0
1
0
1
1
1
0
1
1
1
0
1
1
2
1
2
1
2
0
1
1
0
2
2
0
0
1
2
2
1
0
2
2
1
1
2
2
0
2
1
0
1
1
1
1
1
1
0
1
2
0
1
0
1
1
0
1
2
1
1
1
1
1
0
0
0
1
1
2
2
1
1
1
1
2
1
2
2
0
1
1
2
0
0
1
1
1
2
1
0
0
2
1
1
2
1
1
0
1
0
1
2
0
0
1
1
1
1
1
1
0
0
1
2
1
1
1
0
1
2
0
0
0
1
1
0
1
2
2
1
0
0
1
1
1
1
1
0
1
0
0
1
2
1
2
0
2
1
1
0
2
1
2
0
0
1
0
1
1
1
0
1
1
1
1
1
1
1
1
0
0
1
1
0
1
1
0
0
1
1
2
1
1
1
0
1
1
1
0
1
1
1
1
1
2
1
2
2
2
1
2
2
1
1
1
0
2
2
1
1
2
2
1
1
1
2
0
0
1
1
2
1
2
1
1
2
1
1
1
1
1
1
0
1
2
2
1
1
1
1
0
2
2
1
2
1
0
0
0
2
0
5
0
2
0
1
0
0
2
1
0
1
1
1
0
1
2
2
1
2
2
0
0
2
1
1
1
1
0
0
1
2
1
0
1
1
0
0
2
1
2
1
1
1
1
1
1
1
1
0
1
0
1
0
0
1
1
1
0
1
1
2
1
0
2
2
2
0
0
2
2
0
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
0
1
1
0
1
0
0
1
2
1
0
0
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
0
2
1
2
1
0
2
1
0
1
1
3
2
2
1
2
1
2
1
1
2
1
0
1
1
1
1
2
2
1
2
0
1
1
1
0
0
1
1
1
1
1
1
2
1
0
1
1
1
1
1
1
1
2
1
1
1
0
1
1
1
1
1
1
0
1
2
1
1
1
1
1
1
1
1
0
1
1
1
1
2
0
2
0
1
0
2
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
2
0
0
0
1
0
1
1
1
0
1
1
1
1
1
1
1
2
0
1
1
2
2
2
2
1
0
1
2
1
2
1
1
1
1
2
1
0
1
1
1
1
2
1
1
2
1
1
1
1
2
1
2
2
2
2
1
0
0
0
0
1
1
1
1
1
1
1
1
2
1
1
1
2
0
1
1
1
1
0
1
3
1
1
1
1
1
2
1
1
1
1
1
1
1
0
0
2
1
2
1
0
1
0
0
1
1
1
0
1
1
1
1
1
2
1
1
1
0
2
0
0
1
2
1
1
1
1
1
0
1
1
0
2
0
2
2
1
0
2
2
1
0
1
1
0
1
2
1
2
2
1
0
1
1
0
2
1
1
2
1
0
2
0
1
1
1
1
2
1
1
2
1
1
0
2
1
2
1
1
1
2
2
0
1
1
1
0
1
0
1
1
1
0
1
1
2
1
2
0
1
2
2
2
1
1
2
1
1
0
0
1
0
1
2
0
1
1
1
1
1
1
1
0
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
2
0
1
1
1
1
1
1
2
1
1
1
1
0
1
2
2
2
1
1
0
1
1
2
1
2
1
1
1
1
0
1
1
1
0
0
1
1
2
1
1
2
1
2
1
2
1
1
1
2
1
1
2
1
1
2
2
0
1
1
2
2
1
1
1
2
1
1
2
1
0
0
1
1
0
2
1
1
2
2
0
2
2
1
2
1
2
1
1
1
2
2
0
1
1
1
2
2
2
2
0
2
2
1
1
1
1
0
1
2
2
0
1
1
1
1
2
1
0
1
2
2
1
0
0
1
1
2
0
1
2
2
1
0
1
1
2
1
1
1
2
1
1
1
0
1
1
1
0
2
1
1
1
1
1
0
0
1
1
1
0
2
0
2
2
2
1
1
2
1
1
0
2
1
1
1
1
1
0
1
0
1
1
1
1
1
3
0
1
2
0
2
1
1
2
2
1
0
2
2
0
1
1
1
1
1
0
1
1
1
2
1
1
2
2
1
1
0
1
2
1
0
1
0
2
1
2
2
0
1
2
2
1
1
1
0
1
2
0
2
2
1
0
0
1
1
1
1
0
2
2
1
1
2
0
0
2
1
1
2
0
0
2
1
2
1
1
2
0
0
1
2
1
1
1
1
0
2
1
2
1
2
1
1
2
0
1
1
1
0
0
1
1
0
1
1
2
1
0
1
1
1
2
1
1
1
1
1
1
1
2
2
2
2
1
0
1
1
0
1
2
0
1
1
2
1
0
1
1
2
1
1
1
1
2
1
1
1
1
2
0
1
1
2
2
0
4
1
1
2
2
1
2
1
2
2
1
2
1
2
2
1
1
1
0
2
1
1
2
2
2
1
1
1
2
1
1
2
1
1
2
1
1
0
1
1
1
2
0
1
1
2
1
1
1
2
2
1
1
1
2
1
0
1
1
1
1
1
1
2
1
1
1
1
0
2
1
1
1
1
1
3
0
2
1
2
2
1
1
1
2
2
1
1
2
1
1
2
1
1
1
2
2
0
0
0
1
1
1
1
2
1
1
0
1
1
0
1
1
0
2
1
1
1
2
2
1
2
2
2
1
0
1
1
2
1
1
1
1
2
0
0
1
1
0
1
2
2
1
1
1
2
1
1
1
2
1
1
1
0
1
2
1
1
1
0
2
1
0
2
0
2
1
1
2
2
1
1
2
1
1
1
0
1
0
1
2
0
1
0
1
2
0
2
2
1
2
1
1
1
0
1
1
1
0
1
1
1
1
1
0
0
1
2
1
2
1
1
0
2
2
0
1
0
1
2
0
1
2
2
2
2
1
0
1
0
1
1
0
0
1
0
1
1
1
2
2
1
1
1
1
2
0
0
1
1
1
1
1
1
0
1
1
1
1
0
0
2
2
1
1
0
0
2
1
2
0
1
2
1
0
2
1
1
2
1
2
1
1
2
0
1
2
0
2
1
1
2
0
0
2
1
2
1
1
2
0
2
1
1
0
1
1
0
1
0
2
1
1
1
1
0
1
2
1
2
1
1
1
2
2
1
2
0
1
0
1
1
2
1
2
2
1
2
2
1
1
1
2
1
1
2
1
1
2
2
0
1
1
0
0
0
1
2
2
2
2
1
1
0
1
0
1
2
1
1
2
1
1
1
0
0
1
1
2
1
1
1
2
2
1
1
0
2
0
1
1
2
1
1
0
1
0
0
2
1
1
1
1
2
1
0
1
1
2
0
1
1
0
1
1
1
0
1
1
1
1
0
1
2
4
1
1
3
0
2
1
1
1
1
0
1
2
0
1
2
0
1
1
1
0
1
2
2
0
1
2
1
2
1
0
1
1
1
0
1
1
2
2
2
2
1
1
1
1
0
1
1
0
2
0
1
1
1
0
1
2
0
0
1
2
1
1
1
0
1
1
1
0
1
1
1
2
1
1
1
1
1
1
1
0
2
2
1
1
1
1
0
1
1
1
0
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
0
1
1
2
1
1
0
1
1
1
1
1
0
1
0
1
0
1
2
2
0
1
1
1
1
1
1
1
1
1
0
1
0
1
1
1
0
0
0
1
1
1
1
1
1
0
1
1
2
0
1
0
2
1
0
1
1
1
1
1
2
2
2
0
0
2
1
1
1
2
1
1
2
1
1
2
2
0
1
1
0
1
0
1
2
1
0
2
1
0
2
0
1
1
1
0
1
2
0
1
0
1
0
1
1
1
2
1
1
1
2
1
1
2
1
1
0
1
1
1
0
0
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
3
1
1
3
1
1
1
1
1
1
0
0
2
0
0
2
1
1
1
1
1
0
0
0
1
2
2
0
2
2
1
2
1
1
3
1
1
0
0
1
1
1
1
2
2
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
0
1
0
1
1
1
2
0
2
2
2
2
1
2
0
1
2
2
1
1
2
1
1
1
1
2
1
1
1
2
2
1
2
2
1
0
2
1
1
1
1
1
1
1
1
2
0
1
0
2
0
0
1
2
1
1
1
1
1
0
0
2
2
1
1
0
1
1
1
1
1
1
2
1
1
2
1
0
2
3
1
0
0
1
1
1
0
1
0
0
1
1
1
1
1
0
1
2
1
2
1
1
1
1
1
0
2
1
0
1
2
0
0
0
1
1
0
1
1
1
1
2
2
0
2
0
0
1
2
3
0
2
1
1
1
1
1
2
1
1
1
1
2
2
1
1
2
0
2
1
2
1
2
1
1
1
1
1
0
1
2
2
2
2
1
1
2
2
1
1
1
2
2
1
1
1
1
0
2
1
5
2
1
1
1
1
2
1
3
1
1
1
1
1
2
0
1
0
2
2
1
1
2
1
1
2
1
2
1
1
0
2
1
1
1
1
1
1
1
1
0
2
2
1
1
2
1
2
1
1
1
2
1
0
0
1
0
1
1
1
1
1
1
0
2
0
2
2
0
0
2
0
3
1
2
1
1
2
1
1
1
1
1
1
0
1
1
1
2
1
1
2
1
1
2
1
1
2
1
1
0
1
1
1
1
1
2
1
0
2
1
1
2
0
2
0
2
1
1
1
1
2
1
1
1
0
1
1
2
1
1
1
1
1
1
1
0
1
1
1
2
1
1
0
1
1
1
1
1
1
1
1
2
2
0
0
1
1
1
1
1
1
1
2
0
1
1
0
1
1
1
0
1
1
2
1
2
1
2
0
1
0
1
1
0
1
0
2
2
2
1
2
1
2
1
1
1
0
1
2
2
1
0
1
2
0
1
0
2
0
0
1
1
1
2
0
1
2
2
1
2
1
3
1
1
2
2
1
1
2
2
1
1
1
1
1
1
2
1
2
1
1
1
0
0
1
0
1
2
1
1
1
1
2
2
2
1
1
1
1
2
1
2
1
1
2
1
0
2
2
0
0
1
1
2
0
1
1
0
0
1
1
1
1
1
2
1
1
2
0
2
0
0
0
1
1
1
1
0
2
2
1
1
1
1
2
1
2
1
2
2
0
0
1
1
1
1
1
2
1
2
1
0
0
1
1
2
2
2
1
2
1
1
2
0
1
1
1
1
1
1
1
2
1
2
2
1
1
1
0
0
0
2
2
0
1
2
0
2
1
1
1
0
1
2
2
2
1
2
2
2
1
1
2
1
0
1
2
2
2
1
1
2
2
1
0
1
0
1
1
0
0
0
1
1
2
0
1
1
0
0
1
2
1
0
2
1
1
1
0
0
1
1
1
2
2
1
1
1
0
1
1
2
3
0
0
0
0
1
2
2
1
0
1
2
1
1
0
2
1
2
1
2
1
1
1
1
0
1
1
0
1
1
1
1
1
1
1
1
1
0
0
1
2
0
1
1
2
1
1
2
1
1
0
1
1
2
1
2
0
1
1
2
1
1
1
1
1
1
2
1
0
1
1
1
1
1
2
1
0
1
1
2
1
0
1
1
1
2
1
2
2
1
1
2
1
0
1
2
0
1
0
2
1
1
2
2
1
1
1
1
1
0
1
1
2
1
0
15
1
0
0
2
0
1
1
1
1
2
0
1
0
1
3
1
1
0
2
1
0
1
0
1
1
0
2
2
2
1
0
1
2
1
1
3
1
1
1
2
2
1
1
2
1
2
3
0
1
0
1
2
1
1
1
0
0
2
2
1
1
0
1
1
1
2
1
1
1
1
1
1
0
2
0
2
0
2
1
2
5
0
2
1
1
1
0
0
0
1
1
0
0
2
1
2
2
2
2
0
1
2
1
1
1
1
0
1
0
1
1
2
2
0
2
2
2
1
0
1
1
1
0
0
1
1
2
1
2
2
1
1
1
2
2
0
1
0
1
1
0
1
1
1
0
2
1
2
2
1
1
1
1
1
1
0
1
1
2
1
2
0
1
1
2
1
3
1
2
2
0
1
2
1
2
1
0
1
2
1
0
2
0
0
1
2
1
1
1
0
2
2
0
2
1
1
1
1
2
0
0
0
1
2
1
1
1
0
1
1
1
1
1
1
1
1
2
2
1
1
1
0
2
2
1
1
1
2
1
1
4
1
1
1
0
2
1
1
1
0
0
1
1
2
1
1
1
1
2
1
1
1
1
2
2
2
0
2
1
1
1
2
1
1
1
0
1
1
1
1
1
0
2
1
1
1
2
1
1
0
1
1
1
0
0
1
2
1
1
2
1
0
0
2
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
2
0
1
2
1
1
0
1
2
1
1
1
1
1
1
2
2
1
0
1
0
1
1
1
1
1
0
1
0
1
2
1
0
1
2
1
1
1
1
1
1
1
0
2
1
2
1
1
1
1
2
1
1
0
1
0
1
1
0
2
1
1
3
1
2
1
1
2
1
2
1
1
1
1
1
1
2
1
0
1
0
1
2
1
2
2
1
2
1
2
2
1
0
0
1
1
2
1
2
0
1
2
1
1
1
2
0
1
0
1
0
2
0
2
1
1
1
2
0
0
1
0
3
0
2
0
2
2
1
1
1
1
2
1
0
1
2
0
0
2
1
1
1
1
0
1
1
1
1
1
1
1
0
1
1
2
1
1
0
1
0
3
2
0
0
1
1
1
1
1
1
2
1
1
1
1
2
1
1
0
1
1
2
1
1
0
0
1
1
1
1
1
1
2
0
2
1
0
0
1
1
1
1
1
2
1
1
1
1
0
0
1
0
2
2
1
1
1
2
2
1
1
1
0
1
1
3
1
0
1
1
1
0
2
2
1
0
1
1
2
2
1
1
1
2
1
1
1
1
1
1
1
2
0
1
0
1
1
1
2
0
2
1
1
1
2
1
2
1
2
2
1
0
1
1
1
1
1
1
1
1
1
1
0
2
1
2
0
2
1
1
1
1
1
2
1
1
0
1
2
1
2
2
1
0
1
1
1
1
1
2
1
1
1
2
1
1
2
0
1
1
1
1
2
1
2
2
1
0
0
1
2
1
2
1
0
1
0
1
1
0
1
2
2
1
2
1
1
2
0
2
2
2
0
2
1
2
2
0
1
0
1
2
1
1
0
1
1
2
0
1
1
2
2
0
2
1
2
1
1
1
1
1
2
1
2
1
1
2
0
0
1
1
0
4
1
1
0
0
1
1
1
2
1
2
0
1
0
1
1
1
0
1
1
2
2
1
1
1
0
2
0
1
1
1
1
1
1
1
2
1
0
0
1
0
1
1
0
2
1
2
0
0
2
2
1
1
1
1
2
0
1
1
1
1
2
2
2
0
1
1
1
0
1
1
2
2
1
0
1
0
2
1
0
2
1
1
1
0
2
1
2
2
0
0
1
0
2
1
1
0
1
0
2
0
2
0
1
1
2
1
0
1
2
0
1
1
2
1
2
1
1
1
2
1
1
1
1
2
1
0
1
1
1
1
1
1
2
1
0
1
1
0
2
0
3
1
1
1
2
1
1
3
2
2
1
1
2
1
1
1
1
1
2
1
1
1
2
1
0
1
2
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
0
1
0
1
0
2
2
1
1
1
1
1
1
3
1
1
1
1
1
1
1
1
1
1
0
1
0
0
1
1
1
0
1
1
0
1
0
1
1
1
1
2
2
1
1
2
1
1
2
1
1
1
1
0
1
1
1
2
2
1
1
1
0
1
1
1
0
1
1
2
0
2
2
1
1
2
1
0
1
1
0
1
0
2
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
0
2
2
0
1
1
2
1
0
0
1
2
0
1
1
1
1
0
0
2
0
2
1
1
2
2
1
1
1
2
1
1
1
1
0
2
2
1
0
1
0
0
0
1
1
1
1
1
1
1
1
1
1
2
1
1
2
0
1
2
1
1
0
2
1
1
1
2
1
0
2
1
0
0
1
1
2
1
0
0
1
0
1
2
1
0
1
1
1
1
0
0
2
2
1
1
1
0
1
2
1
2
0
2
2
0
0
1
2
0
1
1
1
2
1
1
1
2
1
1
2
0
1
2
1
1
1
1
1
2
2
1
2
1
1
1
2
2
1
1
1
1
0
1
2
1
0
1
2
2
1
1
1
1
2
0
2
1
0
2
1
1
0
2
2
2
1
1
1
1
2
1
1
0
1
1
1
1
1
1
1
0
1
1
2
1
0
1
1
0
2
2
1
0
1
1
3
1
0
1
0
1
2
1
1
0
1
1
1
1
1
0
1
1
2
1
2
0
1
2
1
2
1
0
1
2
0
1
1
1
0
1
1
2
0
1
1
0
0
1
1
0
1
2
1
1
2
2
1
2
1
2
1
2
1
1
0
1
0
2
0
0
1
0
0
3
0
1
2
2
1
1
1
0
2
2
1
1
2
1
1
1
1
1
5
1
1
1
0
1
1
1
1
1
1
0
1
1
1
1
0
2
1
1
1
1
2
1
0
2
1
2
2
0
1
0
1
1
1
1
0
2
1
1
1
0
1
2
1
0
1
1
1
1
2
2
1
0
2
2
1
1
0
1
0
1
1
1
1
1
2
2
1
0
1
1
0
1
1
1
1
1
2
2
1
1
0
2
0
1
2
1
1
1
1
1
2
2
0
1
2
0
1
1
1
1
1
2
1
0
1
1
2
2
1
1
1
2
1
1
2
2
1
2
2
1
0
2
1
1
1
1
2
1
1
1
0
1
1
2
1
1
2
1
2
2
2
0
1
0
1
1
0
0
0
1
1
1
1
1
1
1
0
2
0
2
1
0
1
1
1
1
1
1
1
1
1
0
1
1
1
2
1
0
1
1
1
2
0
2
2
2
1
2
1
0
1
1
1
1
1
2
0
1
3
0
1
2
0
0
1
1
1
2
1
1
1
1
1
1
1
2
0
1
4
1
1
1
2
1
1
2
2
1
1
2
1
1
1
1
2
1
1
0
1
0
1
0
1
1
1
2
2
1
1
2
3
1
1
1
1
1
1
1
1
1
2
1
1
0
1
1
1
1
0
1
1
2
1
1
2
1
1
1
0
1
1
0
2
1
1
0
1
0
1
1
1
2
2
0
1
1
2
0
0
1
0
1
2
1
1
1
1
2
2
2
1
0
2
1
1
0
1
1
1
2
2
1
1
1
1
1
1
1
1
1
2
1
0
2
1
1
1
1
0
0
1
2
0
0
0
2
1
0
1
2
2
1
2
2
1
1
1
1
0
1
1
1
1
2
0
1
2
2
1
0
2
0
1
0
2
2
1
1
2
2
0
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
3
1
1
1
1
2
2
1
1
1
2
0
1
2
1
0
0
1
0
1
1
1
0
1
0
1
1
1
1
1
1
1
0
0
1
1
1
1
0
2
1
2
2
1
1
1
1
1
2
0
2
1
1
1
1
1
1
0
1
1
0
3
0
0
1
0
1
1
0
1
2
1
0
1
1
0
1
0
1
2
0
1
0
1
1
0
1
2
1
0
0
3
1
2
2
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
0
2
1
1
0
1
1
1
0
1
1
2
2
2
1
2
1
1
1
2
2
1
0
1
2
2
2
0
1
1
1
1
1
2
2
2
1
1
1
1
1
2
1
1
1
1
1
2
1
0
1
1
1
0
1
0
1
0
2
1
1
1
1
1
1
0
0
1
1
0
2
0
0
2
0
1
2
1
1
2
1
1
2
1
2
1
1
1
1
1
2
0
1
2
2
1
0
1
2
1
1
1
1
1
2
0
1
1
1
1
2
1
1
1
1
3
1
1
1
0
0
0
1
1
1
1
0
2
1
2
0
2
1
1
2
1
1
1
0
1
0
1
1
1
1
1
1
1
1
1
2
1
0
2
1
1
1
1
0
1
2
2
1
2
2
2
2
0
0
1
2
1
1
0
1
1
1
1
0
1
1
2
1
1
1
2
1
1
0
1
0
2
2
1
1
1
0
2
1
2
1
1
1
0
2
1
3
1
1
2
1
1
1
1
1
1
1
2
1
1
1
0
1
0
0
1
0
1
1
0
2
0
2
1
5
1
2
1
2
2
0
1
1
1
0
1
1
0
0
1
1
0
1
1
1
2
2
0
1
1
1
0
1
1
1
1
1
1
1
1
0
2
1
0
1
1
1
1
1
1
1
1
1
1
1
3
1
0
2
2
1
1
0
1
1
2
1
1
1
0
2
1
1
0
1
1
2
1
2
1
2
1
1
1
0
1
0
2
0
0
2
1
2
1
2
2
2
1
1
1
1
1
1
1
1
1
0
1
1
1
2
1
1
1
1
1
2
1
1
2
1
1
2
0
1
0
1
1
1
1
1
1
0
1
1
2
1
1
1
1
1
1
1
1
4
0
1
2
1
0
1
0
1
1
2
1
0
1
1
1
0
1
1
1
2
1
2
3
0
2
0
0
1
1
1
0
0
2
2
1
1
2
2
1
1
1
1
1
1
2
1
1
2
2
1
1
1
2
2
1
0
1
2
0
1
0
2
1
2
2
1
2
1
1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
1
1
1
0
2
2
2
0
1
2
1
1
2
1
1
1
0
1
1
1
1
1
1
1
2
2
2
1
2
1
2
0
0
1
2
1
1
1
0
1
2
1
1
1
1
0
1
1
1
1
2
2
2
0
1
1
1
1
1
2
1
1
0
1
1
1
1
1
1
2
1
2
2
1
1
0
1
2
2
1
1
2
2
0
1
1
1
1
1
1
2
1
2
1
1
0
0
0
0
1
0
1
1
1
1
0
0
1
2
1
1
2
2
1
1
0
1
1
1
0
2
1
1
0
0
1
1
1
1
1
1
2
2
0
2
0
1
1
3
2
1
1
1
2
1
1
0
0
0
1
0
2
1
1
2
1
1
1
1
1
1
2
1
1
2
1
0
1
1
1
1
2
1
2
0
1
1
2
1
2
1
1
1
2
1
0
1
1
2
1
1
0
0
2
1
1
1
1
1
2
0
1
1
1
1
1
2
1
1
0
1
1
1
2
1
2
1
1
1
1
1
1
1
1
2
2
1
2
0
1
1
2
2
1
1
1
2
0
1
1
1
1
0
0
0
1
2
1
1
1
1
2
2
0
1
2
0
2
2
1
1
2
2
2
2
2
2
1
5
1
1
1
2
2
0
1
1
3
2
0
1
1
1
1
1
2
2
0
0
0
1
0
1
1
0
0
1
1
1
0
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
2
0
0
1
0
1
1
1
1
0
2
1
0
1
1
1
1
1
1
1
1
2
1
2
0
1
1
1
0
3
2
1
1
3
1
1
0
0
1
1
1
1
1
0
1
2
1
1
1
1
1
1
0
2
1
1
1
1
0
2
2
2
1
0
1
1
1
1
2
1
2
1
1
2
0
0
1
1
0
1
0
1
2
0
1
2
0
1
2
0
1
0
2
1
1
2
1
0
0
1
1
2
1
0
1
1
1
4
1
2
1
0
1
1
1
1
1
1
1
2
1
1
1
1
0
1
1
1
1
2
1
1
0
1
0
1
1
2
2
1
1
2
2
1
1
1
3
1
2
2
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
0
1
1
1
1
2
0
1
1
2
1
1
1
2
0
1
2
2
1
0
0
2
1
1
1
1
1
0
1
1
2
2
1
2
0
0
1
1
1
0
2
0
1
0
2
2
2
1
2
2
2
1
1
0
2
0
0
1
1
1
0
0
1
2
1
1
1
2
1
1
0
1
1
1
2
1
1
0
1
2
1
1
2
2
0
1
1
1
1
1
1
0
2
1
2
1
1
0
1
2
2
2
1
2
2
1
1
1
0
1
2
1
2
2
0
2
0
0
1
1
1
1
1
1
1
1
2
2
0
1
0
1
2
2
1
2
2
2
1
2
1
1
2
1
1
1
1
1
1
1
0
2
1
0
0
1
1
1
2
1
0
0
2
1
1
0
1
1
0
1
1
1
1
0
0
1
1
0
1
1
1
1
2
1
0
0
0
0
1
1
2
1
1
1
1
1
1
1
1
0
1
1
1
0
2
0
1
1
1
2
0
1
1
1
1
0
1
2
1
0
1
1
0
1
1
0
0
2
1
1
0
1
1
1
0
2
1
1
1
1
1
0
0
1
1
2
2
1
2
0
1
1
1
1
2
1
0
0
1
1
1
0
2
1
1
0
2
1
1
1
1
1
1
2
2
1
0
1
1
2
0
1
1
1
2
0
2
1
1
1
1
2
1
1
2
2
1
2
1
2
0
1
2
1
2
2
1
0
1
0
2
0
1
1
1
2
1
1
2
1
1
0
1
1
1
1
2
2
1
2
1
1
1
1
0
2
1
1
1
2
2
1
2
1
1
1
2
1
1
2
1
1
0
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
0
1
2
1
1
1
1
2
2
1
2
0
2
1
1
1
1
1
1
1
2
1
1
1
2
1
1
2
2
1
1
1
1
1
1
0
1
1
2
1
1
1
2
1
0
1
2
1
1
1
1
0
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
3
1
1
0
1
2
0
2
2
0
1
2
1
0
0
1
0
0
1
0
0
1
1
0
0
1
1
1
1
2
0
1
2
0
0
1
1
0
1
2
0
2
2
1
1
2
1
1
0
1
2
2
1
1
1
1
1
2
1
1
0
1
1
2
1
2
1
2
2
2
0
1
2
1
1
1
1
1
1
1
1
1
0
0
2
1
2
1
2
1
1
2
1
1
1
1
1
1
0
1
1
0
1
1
2
0
1
1
2
1
1
1
1
1
0
2
1
0
1
1
1
2
1
2
2
1
0
1
2
2
1
1
1
1
0
2
2
1
0
1
0
2
1
1
0
0
1
0
1
1
1
1
1
1
0
1
1
1
1
2
1
1
1
2
1
1
1
1
0
1
2
0
1
0
0
0
0
0
1
0
1
1
1
0
2
2
1
1
2
2
0
1
1
2
1
0
1
2
1
1
0
1
1
1
1
1
1
0
1
0
1
2
0
2
1
1
1
3
2
1
2
2
0
1
0
0
1
0
2
2
2
0
0
2
1
2
2
1
2
1
1
2
1
1
1
1
0
1
1
1
1
0
1
1
1
1
1
1
0
0
1
1
1
1
0
0
1
0
2
0
0
1
1
0
1
1
2
2
1
2
1
0
2
2
3
1
0
1
1
1
1
2
1
1
2
1
2
2
1
2
2
2
1
1
1
1
0
1
2
0
0
1
1
1
0
1
2
0
1
2
0
1
1
1
0
1
2
2
0
0
1
2
1
1
2
1
1
1
1
1
0
2
1
2
1
1
0
1
1
1
1
1
1
2
0
1
2
1
2
1
2
1
1
0
0
0
1
1
1
2
1
2
1
1
3
1
1
1
1
1
1
0
1
0
1
1
1
2
1
1
1
0
2
1
1
2
0
1
1
2
1
1
1
1
1
2
2
1
1
1
2
1
0
1
1
1
0
1
0
2
1
2
1
1
1
0
1
2
2
1
2
1
0
1
1
1
1
2
1
0
2
2
1
2
1
0
1
2
1
1
1
0
0
1
1
1
1
1
1
2
0
2
0
2
1
1
1
2
1
1
0
1
1
3
0
1
3
2
0
1
2
1
1
1
0
1
0
1
1
1
1
2
2
1
0
0
1
1
1
0
2
1
1
2
0
1
2
2
0
1
2
1
0
2
1
2
1
0
1
0
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
2
1
1
1
0
1
2
2
1
0
2
0
1
1
1
1
1
1
0
1
1
2
1
2
2
0
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
0
2
0
1
1
1
1
1
1
1
2
0
2
2
1
1
0
1
1
0
1
0
2
1
1
1
1
2
1
1
1
1
1
0
2
0
1
0
0
1
0
0
1
1
2
2
0
0
0
1
1
2
1
0
1
1
1
1
1
1
1
3
0
0
1
0
2
1
1
1
1
2
0
0
0
2
1
1
1
2
0
1
1
1
0
1
1
1
0
1
0
1
1
2
0
1
1
1
2
0
1
1
1
1
2
1
1
2
2
1
2
1
0
1
1
2
1
0
1
0
1
1
0
1
0
2
0
0
1
2
1
0
0
0
1
1
1
0
2
1
1
1
0
1
0
2
1
1
2
1
1
1
1
1
1
2
2
0
0
0
2
1
1
1
0
1
1
1
1
0
2
1
2
1
2
1
0
2
0
1
1
0
2
1
1
1
1
1
0
1
1
2
2
2
2
0
1
2
1
1
1
2
1
0
0
0
1
1
2
1
2
1
1
0
2
2
0
0
2
0
0
1
2
1
0
0
2
0
1
2
2
1
1
1
1
1
2
1
0
1
1
1
1
0
1
2
1
1
1
1
1
1
1
2
0
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
0
2
2
1
0
1
1
1
0
1
1
2
0
2
1
0
1
0
1
1
1
0
0
0
0
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
2
1
1
1
0
1
1
1
0
1
1
0
1
1
2
1
2
1
2
1
1
2
2
1
1
1
1
1
1
0
1
1
1
1
2
1
1
1
1
1
0
1
0
1
2
1
0
1
1
0
0
1
1
1
2
0
2
1
2
1
1
1
1
0
1
2
3
2
1
2
0
1
2
2
0
1
1
1
0
0
1
0
2
1
2
2
1
0
1
1
2
0
1
1
1
2
2
0
0
0
1
2
2
1
1
2
0
1
1
1
1
1
1
1
1
2
1
0
1
1
0
1
1
1
1
2
0
1
1
2
2
2
0
1
1
1
2
1
1
1
1
1
2
1
1
0
1
1
0
0
1
0
1
2
1
1
1
1
0
0
1
1
2
1
1
1
1
2
1
2
1
2
1
1
1
1
1
2
1
1
0
2
1
1
1
1
0
1
0
2
1
2
1
2
1
1
0
1
1
2
1
1
1
1
0
1
1
1
1
0
0
0
2
1
1
1
0
1
1
0
1
1
0
0
0
1
0
1
1
1
1
0
1
2
1
2
2
0
1
1
1
2
2
1
1
1
1
1
1
0
2
1
1
1
2
2
1
1
1
1
1
0
1
1
0
1
1
1
1
1
1
1
1
1
2
1
2
2
1
2
1
2
1
1
2
1
1
2
1
1
1
2
1
2
1
2
1
2
1
2
0
0
0
1
2
1
2
1
1
2
3
1
1
1
0
1
2
2
2
1
1
2
0
0
1
2
0
2
1
1
1
2
0
1
1
2
0
1
0
0
2
1
0
2
0
1
0
2
2
2
1
1
1
1
1
1
1
0
1
1
1
1
0
2
0
1
0
0
1
1
0
1
0
2
1
1
1
1
2
0
0
1
1
0
1
1
2
2
1
1
1
2
2
1
0
2
2
2
2
1
1
1
1
0
0
2
1
0
1
0
2
2
2
1
2
2
1
1
1
1
1
2
1
2
2
1
0
0
0
1
0
1
1
2
0
1
1
1
1
0
2
2
1
2
0
1
1
2
2
1
2
2
1
1
1
1
2
2
1
1
1
2
1
1
0
0
1
1
1
2
0
0
2
1
1
2
1
1
1
0
1
1
2
1
2
2
1
1
1
1
1
1
2
1
0
1
0
2
0
0
2
2
1
2
0
0
1
2
0
0
1
1
1
1
0
0
0
0
0
2
2
1
2
2
1
2
1
1
0
2
1
1
1
1
1
1
1
0
1
1
0
1
2
0
2
1
1
1
1
3
1
1
1
5
0
1
0
1
1
2
1
0
2
2
1
0
1
2
0
1
1
1
1
1
1
1
1
1
1
0
0
2
0
2
1
0
2
0
1
1
2
1
2
2
1
1
1
1
0
1
2
0
1
1
1
0
1
0
1
2
1
2
0
2
2
0
1
2
1
2
1
1
2
1
2
2
1
1
2
1
2
0
1
2
1
0
1
1
1
1
1
0
1
1
1
0
1
2
1
0
1
1
1
2
1
2
1
2
2
0
1
2
1
2
1
0
1
1
1
1
1
2
2
1
1
2
1
2
1
1
2
1
0
1
0
1
2
1
2
1
2
2
2
0
1
1
1
0
1
1
1
2
2
1
2
0
1
1
0
1
1
1
2
1
0
1
1
2
1
2
1
1
1
1
1
1
0
1
1
1
1
1
1
1
2
1
1
1
1
1
0
1
1
2
1
1
2
1
1
1
1
2
2
2
1
2
2
2
0
1
1
0
2
1
1
1
1
1
0
0
0
1
1
1
1
2
1
1
0
0
1
1
0
1
0
0
0
1
0
1
1
1
2
1
1
1
1
1
0
0
1
0
1
1
0
0
1
0
1
1
4
1
1
1
1
1
1
1
1
0
2
2
2
2
3
0
1
0
0
1
1
1
2
1
1
1
1
2
1
1
1
2
0
1
0
1
1
0
2
2
2
2
1
1
0
1
1
1
2
1
1
0
1
1
0
1
2
1
0
2
1
1
1
1
0
1
0
2
1
0
2
1
0
1
2
1
1
1
2
0
1
0
0
1
1
2
1
1
1
1
1
1
2
1
2
0
1
2
1
1
1
2
1
2
1
2
1
2
1
1
0
1
2
2
2
1
1
1
1
0
1
1
1
2
1
2
0
2
1
1
1
1
1
2
0
1
1
2
0
1
1
0
1
2
1
1
1
2
1
2
1
1
2
2
1
0
2
1
1
2
1
0
1
2
1
1
2
1
1
2
2
2
2
1
0
1
0
0
1
2
0
2
1
1
0
1
0
1
2
1
2
2
1
1
1
2
1
2
1
2
2
2
0
2
0
2
1
1
1
0
1
0
1
1
1
1
1
0
0
0
1
2
3
1
0
2
0
1
1
0
0
0
1
1
1
1
1
2
1
0
0
2
1
1
1
1
1
1
1
0
1
2
1
1
0
1
2
1
2
1
2
1
1
0
2
1
2
1
1
0
2
1
1
1
0
1
0
1
2
2
1
2
1
1
1
1
1
1
2
0
1
1
1
1
2
1
1
1
1
0
1
2
1
1
0
1
1
1
1
0
0
0
2
1
1
1
1
1
2
1
2
2
0
0
1
1
0
1
0
1
1
2
2
1
1
1
2
0
2
2
0
1
1
1
2
2
1
2
0
1
2
2
2
1
2
1
1
2
0
1
1
2
0
1
0
1
2
1
1
0
1
1
1
1
1
1
0
1
1
1
2
1
0
0
0
1
1
0
0
1
1
1
2
1
1
1
1
2
1
0
1
0
2
2
1
1
2
1
1
2
2
1
1
0
1
1
2
0
2
2
1
2
1
1
2
1
0
1
2
0
2
2
1
2
0
1
1
1
1
1
1
2
1
2
1
1
1
0
1
1
1
1
1
1
1
1
1
1
0
1
2
1
0
1
1
1
1
0
1
1
0
1
2
1
1
1
1
1
1
2
0
0
1
1
0
1
1
1
0
0
1
1
0
1
2
0
1
1
1
2
1
1
1
2
1
0
1
2
1
1
1
0
1
2
1
1
1
1
0
1
1
0
1
1
0
1
1
0
2
1
7
2
0
1
2
1
1
2
0
1
0
2
1
1
2
0
0
2
1
1
1
0
1
1
1
0
2
1
1
0
1
21
1
2
1
0
1
1
1
0
1
2
0
1
0
1
1
1
0
1
1
1
1
1
1
2
1
1
0
1
1
0
1
2
1
2
0
0
1
1
2
1
1
1
1
0
2
1
1
0
2
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
0
0
1
1
1
1
2
1
1
1
1
0
1
0
1
1
2
1
2
2
2
1
1
1
2
1
1
0
1
0
1
1
2
1
2
2
1
2
1
2
2
1
1
1
1
1
1
2
1
1
1
1
0
1
2
1
1
0
1
2
2
2
1
0
1
2
1
0
1
1
1
0
0
1
2
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
0
2
1
1
0
0
2
2
1
1
1
1
2
2
1
0
2
1
1
2
1
1
1
2
1
1
0
2
2
1
1
2
1
0
1
0
2
2
0
1
1
1
0
2
1
1
0
0
1
0
1
1
2
1
1
2
1
1
2
1
1
1
2
2
1
1
1
1
1
0
1
1
1
1
0
1
1
1
1
0
1
0
2
1
1
1
0
0
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
2
1
0
1
1
3
0
1
1
1
1
2
2
2
1
1
0
2
2
0
1
0
2
0
1
2
1
2
1
1
1
2
0
2
1
1
2
1
1
1
0
1
1
1
1
2
1
1
2
0
1
1
1
1
0
2
1
0
2
2
2
1
0
0
2
0
2
0
1
1
2
3
1
0
2
1
2
2
0
0
1
1
0
2
1
3
2
3
0
1
1
0
1
1
2
1
2
1
1
1
3
1
1
2
2
1
1
2
1
1
0
1
1
2
1
1
1
2
0
1
2
1
1
1
1
1
1
2
2
3
1
1
1
1
1
1
1
1
1
2
1
0
0
1
0
2
1
1
1
2
1
1
1
2
2
0
1
2
1
1
0
1
1
1
1
1
1
1
0
1
1
1
1
0
0
1
2
1
1
1
1
0
1
1
1
1
1
2
1
1
2
1
2
1
1
3
0
2
1
1
0
1
0
1
1
1
1
2
1
1
1
1
2
0
1
2
1
1
1
1
0
1
2
1
1
1
2
2
1
2
2
2
1
1
1
1
1
1
0
2
1
0
0
2
1
1
1
2
1
0
1
2
0
1
1
2
1
0
1
2
1
0
0
1
1
1
1
0
1
0
0
1
0
1
0
0
1
1
2
1
0
0
1
1
2
1
0
1
2
1
1
1
2
1
0
1
1
0
1
1
1
2
0
1
1
1
1
1
1
2
0
1
1
0
1
2
1
1
0
1
1
1
0
1
2
1
0
1
1
0
1
1
1
0
1
3
2
1
1
2
1
1
0
0
1
1
1
1
1
1
1
0
1
1
1
0
0
2
1
0
1
1
1
1
1
1
1
1
2
1
2
2
1
1
0
1
2
1
1
1
1
1
2
1
1
2
1
1
1
2
1
2
0
1
0
2
1
1
1
1
2
1
1
2
2
1
1
1
0
0
1
1
1
1
0
2
1
2
1
1
2
1
1
1
1
1
1
1
0
0
1
0
1
1
1
1
0
1
2
1
1
0
2
0
1
1
2
1
2
2
1
2
1
1
0
2
2
2
0
1
2
0
0
1
1
0
1
2
1
1
1
0
1
0
1
2
1
1
1
1
1
1
1
1
1
1
1
0
0
1
1
1
0
0
0
2
1
1
0
2
2
2
2
1
1
0
0
1
1
1
1
1
1
0
1
1
1
1
1
1
2
1
1
0
2
1
1
0
2
1
1
2
1
2
1
1
0
2
1
1
1
1
1
3
0
0
1
0
2
1
0
1
1
2
0
1
0
1
1
1
1
1
2
1
2
2
0
0
1
0
1
1
2
1
1
2
1
2
2
2
1
1
2
2
0
1
2
1
1
1
1
1
1
0
2
2
1
2
1
2
1
1
1
1
2
2
2
2
1
1
0
1
1
1
1
0
0
1
1
2
0
2
1
1
1
2
1
2
1
1
1
1
1
0
1
1
2
2
0
1
2
2
1
1
1
1
1
2
1
1
2
0
1
1
0
1
1
2
1
3
1
0
0
2
1
2
1
1
0
1
1
1
0
0
2
1
1
1
1
2
1
1
2
1
2
1
0
1
1
1
0
1
2
0
2
2
1
1
1
1
0
1
1
1
1
0
1
2
1
2
1
1
1
1
1
1
1
1
1
0
1
1
1
1
0
2
1
2
1
2
2
1
1
1
1
0
2
1
1
1
1
1
1
1
0
0
1
1
2
2
2
1
1
0
1
1
1
1
1
1
2
1
0
1
1
0
1
1
2
2
0
0
1
1
0
1
1
1
1
2
1
1
0
1
1
1
3
1
0
0
0
0
2
2
2
1
1
1
1
0
1
1
0
1
1
1
2
2
1
1
2
1
1
1
0
1
2
1
2
1
1
1
1
0
2
1
2
0
1
2
2
0
1
1
1
0
2
1
1
0
2
0
1
2
1
1
1
1
1
1
1
1
2
2
0
2
2
1
0
1
2
1
2
0
2
1
0
2
0
2
2
2
1
2
0
1
2
1
2
1
0
0
1
0
1
1
1
1
1
1
1
1
0
1
1
1
1
1
0
0
1
3
1
1
1
2
2
0
2
1
1
1
2
2
1
0
2
1
1
1
1
0
2
1
1
0
1
1
2
1
0
1
1
1
1
1
1
1
1
1
2
1
0
2
1
0
1
1
2
1
1
0
2
1
1
2
1
1
0
1
0
1
1
1
1
1
2
2
2
1
1
0
1
2
1
2
2
1
1
0
1
1
0
0
3
0
1
1
0
1
0
1
1
2
1
1
1
2
1
1
1
2
2
1
1
0
1
1
1
1
1
1
1
1
1
2
1
1
0
1
1
1
2
1
1
2
1
2
1
2
0
1
2
1
1
2
2
2
2
2
0
0
1
0
2
1
1
1
1
1
0
1
0
1
1
1
0
0
2
1
1
0
0
1
1
1
1
2
1
1
1
2
1
1
2
0
2
0
2
1
1
1
1
1
0
0
1
1
1
0
0
0
1
1
1
1
0
2
2
1
2
1
1
2
1
1
1
1
1
2
1
1
1
2
0
1
1
0
1
2
1
1
2
1
2
1
1
0
1
1
0
2
1
0
2
1
2
2
1
1
2
1
1
1
1
1
1
0
1
1
0
1
2
1
1
1
2
2
0
0
1
2
1
1
0
1
1
1
2
0
0
1
1
1
2
0
0
1
1
1
1
0
1
1
2
1
2
1
2
1
2
1
2
1
1
0
1
2
1
1
1
1
0
1
2
0
2
1
1
1
0
2
1
1
0
1
1
1
1
1
1
1
1
0
0
2
1
1
1
2
2
1
0
0
1
2
1
1
1
1
1
2
1
1
0
1
0
2
1
1
2
1
1
1
1
1
1
0
2
0
1
1
1
1
1
1
0
1
1
1
1
1
0
2
1
1
1
1
1
1
1
2
1
1
2
1
2
2
2
1
1
1
2
2
1
1
1
2
1
3
1
1
1
0
2
1
2
1
1
0
2
1
1
2
2
1
2
0
0
1
1
1
2
1
1
1
2
1
0
2
1
0
0
0
1
0
1
2
2
1
0
2
1
2
2
0
2
0
1
0
1
1
1
0
1
2
1
1
1
1
0
2
0
0
1
0
1
1
1
2
1
1
1
1
0
1
1
2
0
2
2
1
1
0
2
2
1
0
2
1
2
2
1
3
1
2
1
2
1
0
2
1
0
0
1
1
1
2
2
2
1
0
1
1
1
0
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
4
1
1
2
1
1
2
1
1
1
1
0
1
3
2
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
0
1
0
0
1
1
1
0
2
1
0
0
1
2
1
2
1
1
0
1
1
1
2
0
2
1
2
1
1
1
2
0
1
0
1
1
1
1
0
1
0
0
0
1
1
0
1
0
1
1
1
2
0
2
1
1
0
1
1
1
2
1
1
2
1
0
1
1
1
0
0
1
1
0
1
2
1
1
2
1
1
1
2
0
1
2
0
1
2
0
2
1
1
2
0
1
1
2
1
1
0
1
2
2
1
1
2
1
1
2
0
1
2
1
1
1
1
0
1
1
1
1
1
2
1
1
2
1
2
0
1
0
1
0
1
2
2
1
1
0
1
2
1
2
1
1
2
1
1
2
1
0
2
1
1
1
1
0
1
1
1
2
1
1
1
1
2
1
1
1
2
1
1
1
2
0
0
1
1
1
0
2
2
2
0
2
0
2
0
2
1
1
1
2
1
1
1
0
1
0
1
2
2
1
1
1
2
2
0
0
1
2
2
2
1
1
1
1
2
1
1
1
2
1
1
0
1
1
2
1
1
1
2
1
1
1
2
1
1
0
1
1
0
1
1
2
1
0
1
1
2
1
1
2
1
1
1
1
1
1
2
12
0
1
1
0
1
0
1
1
0
0
1
1
1
1
2
1
2
2
2
1
1
2
1
0
2
1
2
2
1
2
0
1
1
1
2
0
1
2
2
2
0
2
1
1
1
1
0
1
1
1
1
1
2
1
2
1
1
1
1
1
1
0
1
1
1
2
1
0
1
1
1
0
1
1
2
0
1
0
1
1
1
0
2
1
1
1
1
1
1
1
2
1
1
1
1
0
2
0
1
1
1
1
1
2
2
1
2
1
0
1
1
1
1
1
1
1
0
2
1
2
1
1
1
0
1
1
1
0
2
2
0
2
1
1
1
1
1
0
1
2
1
1
0
0
1
0
0
0
1
2
1
2
1
2
0
1
1
0
0
1
0
2
0
1
2
1
1
1
1
0
0
1
2
2
1
1
1
1
1
2
1
0
0
0
1
2
1
1
1
1
2
1
2
1
1
2
1
2
0
2
1
1
2
1
1
0
1
0
2
1
1
2
1
1
2
1
3
0
2
1
1
1
1
1
1
2
1
2
1
1
0
1
2
1
2
1
1
2
1
1
2
2
1
1
1
0
2
1
1
1
0
1
2
1
2
0
1
2
2
1
1
2
1
0
0
1
1
1
2
1
1
1
1
1
1
1
2
0
1
1
1
1
0
1
2
1
2
1
1
2
0
1
2
1
2
1
1
1
2
1
2
2
1
0
0
1
1
0
1
2
1
1
2
2
1
1
1
1
1
0
1
1
1
1
1
1
2
1
1
0
2
1
2
1
1
0
1
1
2
1
2
1
1
1
1
1
1
0
2
2
1
1
2
2
2
1
1
0
2
1
1
0
1
1
1
1
1
1
1
1
1
2
1
1
1
1
0
2
1
1
0
4
2
2
1
0
1
1
1
1
2
2
1
1
2
1
2
1
1
0
0
0
1
1
1
2
1
1
1
1
0
1
2
2
1
2
2
1
1
0
2
1
2
1
1
1
1
2
1
2
2
1
1
1
1
1
1
2
2
1
1
1
1
0
1
1
1
2
1
2
1
1
1
1
2
2
1
1
1
1
1
2
2
0
1
1
0
1
1
2
1
2
1
2
2
1
1
2
1
1
0
2
1
1
1
1
1
1
0
2
4
1
1
1
1
2
2
0
0
1
2
1
1
1
0
1
1
1
2
1
3
1
1
2
0
1
2
0
0
2
0
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
0
0
0
1
1
2
1
1
1
2
1
1
2
1
2
1
1
1
1
1
2
1
1
2
0
0
0
2
1
0
1
1
2
1
0
1
2
0
1
1
0
1
1
2
0
1
2
2
1
1
1
2
1
1
0
0
1
1
1
1
0
0
1
1
1
1
1
2
2
2
1
0
1
1
0
1
1
0
2
1
1
0
1
2
1
1
1
1
2
1
1
2
0
1
1
1
1
2
0
1
1
1
1
1
0
2
1
2
2
2
0
1
1
2
1
0
1
1
1
1
0
1
1
1
1
1
2
1
1
2
0
1
2
1
0
1
1
0
0
0
2
0
1
0
1
1
1
1
0
1
1
2
1
2
2
1
1
1
0
0
2
1
0
2
1
1
1
1
2
1
1
0
0
1
0
0
0
1
1
0
1
1
1
1
1
2
1
2
1
1
1
0
1
2
2
2
2
2
1
0
1
1
1
1
0
2
0
1
1
1
1
0
1
1
1
0
1
1
0
1
2
1
2
1
1
1
1
2
1
1
1
1
2
2
2
2
2
1
2
2
1
1
1
1
1
2
0
2
2
2
2
2
0
1
1
1
2
1
2
1
1
2
1
1
0
1
0
0
2
1
1
0
1
1
1
0
2
0
1
1
1
2
2
1
0
1
1
1
0
1
1
2
2
1
1
0
1
2
1
1
1
1
1
1
1
2
1
0
1
2
1
2
1
0
1
1
1
1
0
2
3
1
1
2
1
0
1
1
1
2
1
0
1
2
1
1
1
1
1
0
1
0
1
0
1
2
0
2
1
1
0
1
1
1
1
1
1
1
1
1
1
0
1
1
2
0
2
0
1
1
0
2
2
1
1
1
1
0
2
1
2
1
2
0
2
1
0
0
2
1
1
1
2
2
1
1
2
1
0
1
0
2
0
0
1
1
1
0
1
2
1
1
2
2
2
0
1
1
1
1
2
1
0
1
1
2
0
0
1
0
1
1
0
1
1
1
2
2
1
2
1
1
1
0
1
0
1
1
1
1
1
1
0
1
0
1
1
1
2
1
1
1
1
2
2
2
2
1
1
1
1
2
1
1
1
1
1
1
0
2
2
0
1
1
1
1
1
1
0
1
1
0
2
2
2
1
1
1
0
1
0
1
1
1
2
1
0
1
2
1
2
1
1
1
1
1
0
0
2
0
1
0
2
1
2
1
2
0
2
1
1
2
2
1
2
1
0
1
2
0
1
1
1
2
1
2
1
1
1
1
1
1
0
1
2
1
2
1
1
2
1
1
0
1
1
0
0
1
1
2
1
1
1
0
1
2
1
1
1
3
1
1
1
1
0
1
1
2
1
1
1
1
6
0
2
1
1
1
1
0
2
1
2
0
1
1
1
2
1
1
0
3
1
1
1
1
1
1
1
1
2
3
0
1
1
1
1
1
2
1
1
1
3
0
1
1
0
1
0
1
1
0
1
0
1
1
3
3
0
1
2
1
0
1
1
2
1
2
0
1
3
2
0
2
1
1
1
1
2
0
2
0
0
1
1
0
1
1
1
2
2
1
1
0
1
1
1
0
0
0
1
0
1
2
1
1
1
2
1
1
1
1
0
0
0
2
1
1
2
1
1
0
1
1
2
1
0
1
2
2
1
1
0
1
1
2
2
1
1
2
1
2
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
2
1
2
1
0
1
1
1
1
2
2
1
1
1
0
1
1
0
0
1
1
1
1
1
1
1
2
1
1
1
2
0
0
1
2
1
2
1
1
1
2
2
1
2
2
0
1
1
0
0
2
2
2
2
2
0
1
2
1
1
2
2
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
2
1
1
0
1
1
1
0
1
1
1
1
2
1
1
1
1
1
1
1
2
1
0
1
2
1
1
1
2
1
1
1
1
1
2
1
4
1
2
1
1
0
2
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
0
2
1
1
1
1
2
1
1
1
2
1
0
1
1
1
4
0
0
2
4
0
1
2
1
1
1
2
1
0
2
1
1
1
1
1
1
1
2
1
1
0
1
1
1
2
2
1
0
2
1
2
1
2
1
1
2
1
2
1
1
2
1
1
1
0
0
1
1
1
2
2
1
2
1
0
1
0
2
2
1
1
1
1
1
2
1
2
0
1
1
1
2
1
1
0
1
1
1
0
2
0
0
1
1
1
1
0
1
0
1
1
0
2
2
1
1
1
1
1
2
0
0
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
3
0
1
0
1
2
0
1
2
0
1
2
1
1
1
1
1
1
0
2
1
2
1
0
1
1
2
1
2
1
0
1
1
2
1
0
1
2
0
1
0
1
1
0
1
1
0
0
0
0
2
2
0
2
0
1
1
1
2
2
1
1
1
2
2
0
0
1
2
1
0
1
1
1
2
1
0
1
1
1
1
2
2
1
4
2
2
1
2
1
1
1
0
1
2
1
1
2
1
1
1
1
1
1
2
1
0
1
1
0
1
1
1
1
1
1
0
1
2
0
1
2
0
1
1
2
1
2
0
1
1
1
2
2
0
2
1
0
1
0
1
1
1
0
1
1
1
2
2
1
1
0
0
3
0
2
1
1
0
1
1
0
2
2
1
0
2
1
2
1
1
0
0
2
1
2
1
1
1
1
1
2
2
1
1
1
1
0
1
1
1
0
1
2
1
1
0
2
1
1
1
0
1
1
0
0
1
1
2
1
1
1
1
1
1
2
1
0
1
1
1
2
0
1
1
2
1
0
1
1
1
2
2
0
1
1
1
1
1
1
1
1
2
2
2
0
1
1
1
1
1
1
0
2
0
1
1
1
1
1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
1
0
1
1
0
0
2
0
1
1
1
2
0
0
2
1
2
1
1
1
1
0
1
1
1
0
2
1
2
1
0
2
1
0
1
2
2
0
1
1
1
0
2
1
2
2
1
1
0
3
1
1
2
1
1
2
0
1
2
1
1
1
1
2
1
1
2
2
2
1
0
1
0
1
1
1
1
0
1
1
1
1
1
0
1
1
1
1
1
2
2
1
1
1
2
1
1
1
1
1
1
1
0
0
2
2
0
2
2
1
1
2
0
1
1
0
1
1
1
0
2
0
0
1
1
2
1
1
2
1
2
0
1
1
0
1
2
1
1
2
1
1
2
0
0
0
2
1
1
1
1
2
1
1
1
1
1
0
1
1
0
1
1
1
1
0
1
0
1
0
1
1
1
2
1
1
1
2
1
2
1
1
1
0
1
1
1
1
1
2
1
0
1
1
1
1
1
2
1
1
1
1
2
2
1
2
2
2
2
1
2
1
1
2
1
2
1
1
1
0
1
1
1
2
1
2
1
0
1
1
1
1
1
1
2
2
1
2
1
1
1
0
2
1
1
2
1
2
1
1
1
1
1
1
1
0
2
1
1
2
1
2
1
2
1
2
1
1
1
1
1
1
1
0
1
2
0
1
1
1
2
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
0
0
0
1
1
1
1
1
2
1
1
0
1
2
1
2
0
0
1
1
1
1
1
1
1
1
2
1
1
2
1
0
1
2
1
1
1
1
2
1
1
1
2
0
0
1
0
2
1
2
1
0
1
1
1
0
1
0
1
0
1
1
2
1
2
2
0
2
1
1
1
1
2
2
2
1
1
1
2
1
1
1
1
2
0
2
1
1
2
1
2
1
1
2
1
2
0
0
2
1
2
1
2
1
1
2
2
0
2
1
1
0
0
2
0
1
1
1
0
1
1
1
1
1
0
2
2
1
2
2
1
1
1
0
2
1
1
1
2
0
1
0
0
1
0
1
1
1
1
2
2
1
1
2
2
0
0
1
1
0
1
0
3
0
2
1
0
1
1
0
1
1
1
1
1
1
1
1
3
1
1
0
1
0
1
1
1
0
1
1
1
1
1
2
0
2
1
2
1
1
0
2
1
2
1
1
2
1
0
1
2
1
1
1
1
1
1
0
1
1
1
1
1
2
0
1
1
1
0
2
2
1
1
1
1
1
0
2
2
1
1
0
1
1
1
1
0
2
0
1
0
0
0
1
1
1
1
1
1
1
2
1
1
1
0
1
0
1
2
0
1
2
0
1
0
0
1
0
1
2
1
0
0
1
1
0
3
1
1
2
1
1
1
2
1
2
3
0
0
1
2
1
0
1
1
1
1
1
2
0
1
1
1
1
2
1
0
2
1
2
2
0
1
1
1
0
1
1
1
2
1
0
2
0
1
1
1
2
1
2
2
2
0
0
1
1
1
2
1
0
2
1
1
1
1
1
0
1
1
1
2
2
1
1
0
1
1
2
0
1
3
0
1
1
1
2
0
1
2
1
1
0
1
0
0
2
1
1
1
0
1
0
2
2
0
1
2
1
2
1
1
0
1
1
0
1
1
2
1
1
1
1
1
1
1
2
2
1
1
0
1
0
1
2
0
0
1
1
1
1
0
2
1
0
1
0
2
1
2
1
0
0
0
1
1
1
1
2
1
0
1
2
1
1
1
0
1
2
2
1
0
1
1
1
2
2
2
2
1
2
1
1
1
1
0
1
2
1
1
1
1
1
1
1
2
1
1
0
3
1
1
1
1
1
1
1
2
2
1
0
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
2
1
2
1
2
2
1
0
1
2
1
1
2
1
1
1
2
1
1
0
1
1
1
1
1
0
2
0
2
1
2
2
1
1
0
2
1
1
0
1
1
2
0
0
1
0
0
2
2
1
1
2
2
1
1
2
1
1
0
1
1
2
1
1
1
1
1
0
2
2
0
1
1
1
2
1
1
2
0
1
2
1
2
2
2
1
0
1
1
1
1
2
1
1
1
1
1
1
2
1
0
2
0
0
1
1
0
2
1
1
2
1
1
1
1
2
2
2
1
2
1
1
2
1
1
1
3
2
1
1
1
0
1
1
1
1
0
2
1
1
1
2
1
0
2
1
2
1
1
0
1
1
1
1
2
0
1
1
1
2
1
1
2
2
0
1
0
2
3
1
1
1
0
1
1
0
1
0
1
2
0
1
3
2
1
1
1
2
0
2
1
0
0
1
1
1
2
2
2
1
1
1
1
2
1
2
0
4
1
0
2
1
0
1
1
2
2
2
1
1
1
0
1
1
1
0
2
1
1
1
2
1
1
0
1
1
1
1
2
0
1
1
0
1
0
1
1
1
0
1
1
1
1
1
1
1
2
1
4
1
1
1
2
1
1
1
2
1
0
0
1
0
1
1
1
0
1
1
1
1
1
1
2
1
0
1
1
1
1
1
0
2
1
2
1
1
1
0
0
1
1
1
0
1
1
1
1
0
1
1
0
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
0
1
0
1
1
1
1
1
2
1
1
0
2
3
1
1
1
2
1
1
2
1
2
2
1
1
1
1
1
0
1
1
1
1
0
0
1
1
1
1
1
1
0
1
1
0
2
2
2
2
1
1
2
2
1
2
1
1
1
1
0
1
0
1
1
1
1
2
1
1
1
1
1
1
0
1
2
1
1
3
1
1
3
0
0
2
2
1
0
1
1
0
2
0
0
2
1
1
1
0
1
1
1
1
2
1
1
0
1
1
2
2
1
1
1
1
1
0
1
1
0
1
1
1
0
1
1
2
1
0
2
1
1
1
1
1
1
1
2
1
1
0
0
0
2
2
1
1
0
1
1
0
0
1
1
1
0
1
2
1
1
1
1
0
0
2
1
1
1
1
1
1
1
2
0
1
1
1
1
1
1
1
1
0
2
1
1
1
2
0
1
1
2
1
1
2
1
1
2
2
1
1
2
0
2
2
1
2
0
1
1
1
1
1
2
0
1
1
2
1
1
0
1
1
0
1
1
2
1
2
1
1
0
1
1
2
3
0
1
1
1
2
1
1
2
0
1
1
1
1
1
2
1
2
2
1
2
0
0
1
2
1
1
0
1
2
2
0
2
2
1
1
0
2
1
1
1
2
0
0
0
1
1
1
1
1
0
2
0
0
0
1
1
0
2
1
1
1
1
2
0
1
2
1
2
2
1
1
1
1
2
2
0
1
1
0
0
1
0
1
1
1
1
1
1
2
2
2
0
0
2
1
1
1
1
1
1
1
1
0
1
1
1
2
0
0
0
2
1
0
1
1
2
1
2
1
1
1
1
0
2
2
1
1
1
1
0
1
0
0
2
1
0
1
1
1
0
2
2
1
1
1
2
1
1
2
1
0
3
1
1
1
2
1
2
1
1
2
2
1
1
1
0
0
1
2
0
1
2
0
1
1
1
0
2
2
0
0
2
1
1
2
1
1
0
1
0
1
2
2
2
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
2
1
2
1
0
0
1
0
1
1
2
1
1
2
1
1
3
1
1
1
1
1
2
1
0
0
2
0
2
1
1
2
1
1
1
1
0
1
1
2
1
0
1
0
1
1
1
1
1
1
1
1
2
1
2
2
1
2
1
0
1
1
2
0
2
1
1
0
1
2
1
2
2
1
2
1
2
1
2
1
2
1
2
0
4
2
1
0
0
1
0
1
1
1
0
1
1
1
0
0
0
1
1
1
2
1
2
1
1
1
1
0
0
0
1
2
1
0
1
1
1
1
1
1
2
0
1
1
1
1
1
2
2
1
1
1
1
1
2
2
2
0
0
1
0
0
1
1
1
1
1
0
1
1
1
1
1
1
2
2
2
1
2
1
2
1
2
1
1
0
0
1
1
1
2
1
1
2
1
0
2
2
2
0
1
0
0
2
0
1
2
0
1
1
1
0
2
1
1
2
1
1
1
0
1
1
1
1
0
1
2
0
1
1
1
1
0
1
2
1
1
2
2
2
1
1
1
1
1
0
1
1
2
1
1
2
1
1
1
2
1
1
1
1
1
1
2
1
0
0
1
1
1
2
2
1
0
1
2
1
1
0
1
2
1
1
2
2
1
1
1
1
2
1
0
1
0
2
1
2
0
1
0
1
2
2
1
1
1
1
2
1
1
0
1
1
0
1
0
1
1
0
1
1
1
1
1
0
2
1
1
1
2
1
1
1
1
1
0
3
1
1
1
1
1
1
2
0
0
1
0
2
1
1
1
2
1
1
2
1
2
0
1
2
0
1
0
2
2
1
0
1
1
1
2
1
2
1
2
3
1
1
2
1
0
1
2
0
1
1
1
2
0
1
1
0
2
1
1
2
2
0
0
1
1
0
1
1
1
1
1
2
0
1
0
1
2
1
2
2
0
1
2
1
2
1
0
2
2
3
2
1
2
0
1
2
2
0
2
1
0
2
1
1
2
0
1
2
1
2
0
1
0
1
1
2
1
2
1
0
2
1
1
1
1
1
1
1
1
2
1
1
0
2
1
2
1
1
2
2
1
1
1
1
1
1
1
1
0
1
1
1
1
0
1
0
0
1
2
1
2
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
2
0
1
1
2
1
0
1
1
1
2
1
1
2
3
1
1
1
1
1
1
1
2
0
1
1
0
0
1
2
1
2
2
0
1
1
1
0
2
0
1
0
1
1
0
1
1
1
1
0
1
1
1
0
1
1
0
1
1
1
1
0
2
1
0
0
1
0
2
1
0
0
2
2
1
1
1
1
2
1
2
1
0
2
2
2
1
1
1
2
2
1
1
1
1
1
1
0
1
0
1
1
1
1
0
1
0
1
1
1
2
0
1
1
1
1
1
1
1
1
1
1
1
1
0
0
1
1
1
2
1
2
1
2
1
0
2
0
1
1
2
1
1
0
2
0
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
0
2
1
1
2
1
1
1
2
2
2
1
2
1
1
0
1
1
0
1
1
2
1
2
2
1
1
2
0
2
3
1
1
1
1
1
1
0
1
1
1
2
1
1
1
1
0
1
1
1
1
1
0
2
0
0
1
1
0
2
1
1
1
1
1
1
1
2
1
1
1
0
0
1
2
1
1
2
0
1
2
0
1
1
1
1
1
1
1
0
1
1
2
1
1
1
1
0
0
1
1
1
2
1
1
2
1
1
1
2
2
1
1
2
1
1
1
1
1
1
2
2
0
1
0
1
0
1
0
1
1
2
1
1
1
1
1
1
2
1
1
0
1
2
1
1
1
1
0
1
0
0
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
0
1
1
1
2
2
1
1
1
2
1
1
1
1
0
1
2
2
1
0
2
0
1
0
1
0
2
2
0
2
1
2
1
0
2
1
3
1
2
1
2
1
2
2
0
2
0
2
1
1
1
0
2
2
2
1
1
1
0
2
1
2
1
1
1
0
1
0
0
1
1
0
0
2
1
2
1
2
2
0
0
1
1
1
1
1
0
0
1
0
1
2
1
2
1
2
2
2
1
1
1
1
1
1
1
1
2
2
1
1
0
2
1
1
1
1
1
3
2
1
1
0
1
1
1
1
2
1
1
1
1
0
2
2
1
1
1
1
1
2
0
1
1
0
1
1
1
2
2
1
1
0
1
1
1
2
1
1
1
2
1
1
2
0
1
2
2
1
2
1
1
1
0
1
1
2
1
2
1
1
0
1
0
0
1
1
1
1
1
0
1
1
1
1
1
1
2
1
2
1
0
2
1
0
1
1
0
0
1
0
2
1
0
0
1
1
1
2
1
0
1
1
1
1
1
1
1
1
1
1
2
1
2
1
0
0
1
2
1
2
2
2
1
1
1
2
0
1
1
0
1
2
2
1
0
2
1
1
2
1
0
1
1
0
1
0
1
1
1
1
0
2
0
2
1
2
1
0
1
1
0
2
1
2
0
0
1
0
2
2
0
0
2
2
0
1
2
0
1
1
2
0
2
1
1
1
2
1
1
2
1
0
2
2
0
3
0
1
1
0
1
2
0
1
1
1
1
1
1
1
0
1
1
0
0
1
1
1
1
1
1
1
1
1
1
1
0
1
1
0
1
0
1
1
1
2
2
0
1
1
0
2
2
2
0
1
1
1
2
1
1
0
1
1
1
1
1
2
1
1
2
1
1
1
1
2
2
0
1
1
1
1
1
2
2
0
2
0
2
1
1
1
1
1
1
1
1
2
2
0
1
2
1
1
2
2
1
1
1
1
2
0
0
2
0
1
1
1
1
2
1
1
2
1
0
1
1
0
1
1
0
1
2
1
0
1
1
1
2
0
1
1
0
0
1
2
1
0
1
1
0
0
1
1
1
1
1
1
1
2
2
1
2
1
2
2
2
2
1
0
1
1
1
1
1
2
1
1
0
0
1
1
0
2
2
1
1
1
1
1
1
2
2
1
0
1
1
2
1
1
1
0
1
0
1
1
2
1
1
0
1
1
2
1
1
1
1
2
1
2
1
2
1
2
0
1
1
2
2
1
1
0
2
1
0
1
1
2
1
1
1
1
2
1
0
2
1
1
2
0
2
0
2
1
1
1
0
1
1
1
0
0
1
2
2
0
2
2
1
1
1
2
2
2
2
1
1
1
2
1
2
1
1
2
0
1
1
2
1
0
1
0
1
1
1
1
1
0
1
2
1
2
0
0
2
2
2
1
1
0
1
1
2
1
2
2
1
0
0
1
0
1
1
2
1
0
1
7
2
0
1
0
2
2
1
2
1
1
1
1
1
0
1
1
0
1
1
1
0
2
1
0
1
2
0
2
3
1
2
2
1
2
2
0
1
1
1
0
1
0
1
2
2
0
1
1
1
1
1
1
1
1
1
1
2
3
0
2
1
0
1
1
1
2
2
1
2
1
2
2
1
1
1
2
3
1
1
2
1
1
0
0
1
1
1
0
1
2
2
1
1
1
2
2
1
1
1
1
3
1
1
1
2
1
1
2
1
1
1
1
1
2
1
1
2
1
2
0
0
1
1
2
2
0
2
2
2
2
0
0
1
0
0
1
1
1
1
2
0
1
0
2
1
1
0
1
0
1
0
1
2
1
1
2
1
1
0
2
1
2
1
1
2
1
2
2
0
1
1
0
2
1
1
1
1
1
1
1
2
1
1
2
1
2
0
1
1
1
1
2
0
1
3
2
0
1
2
2
2
2
1
0
1
1
2
1
2
1
2
0
0
0
1
1
1
1
1
1
1
1
2
1
2
0
2
2
1
1
2
1
1
1
1
1
0
2
2
1
1
2
2
0
2
1
2
1
1
0
1
1
1
1
2
1
0
1
1
1
2
2
1
1
0
1
2
2
1
0
2
2
1
1
1
2
2
1
0
1
1
1
1
0
1
1
1
1
0
2
2
1
0
1
1
2
0
2
1
0
1
0
1
1
2
0
4
1
2
1
1
1
0
0
1
1
1
2
0
2
2
1
1
1
1
1
2
0
2
2
0
1
1
0
2
0
0
1
2
2
2
1
0
1
0
1
1
1
1
2
0
1
1
2
1
2
1
1
2
1
1
3
0
1
2
0
1
1
0
0
2
0
0
1
1
1
1
2
1
1
1
1
0
1
1
1
1
1
2
1
0
1
0
1
0
1
2
1
1
1
1
2
2
1
1
2
1
1
0
1
2
1
1
2
2
0
1
1
2
0
1
1
1
0
0
2
1
1
2
1
2
1
0
1
0
0
0
1
1
1
0
1
2
1
0
2
0
3
1
1
0
2
1
0
2
1
2
1
2
2
0
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
0
2
2
1
1
0
0
1
0
1
1
2
1
1
1
0
0
0
1
0
1
2
1
0
2
1
2
2
0
1
1
1
1
2
0
1
1
1
2
2
1
1
0
1
0
2
1
0
1
1
2
2
1
1
2
1
2
1
1
1
1
2
1
0
1
2
1
2
2
0
1
1
1
1
2
1
1
1
1
1
2
2
2
2
2
2
2
1
0
1
1
2
1
0
1
1
2
1
1
0
2
2
0
1
1
2
1
0
1
2
2
1
1
1
1
0
1
1
1
0
1
1
1
0
0
2
2
1
1
0
2
1
2
1
1
0
1
2
1
2
2
2
2
0
2
1
1
1
2
1
1
2
2
2
0
1
0
1
1
1
1
1
1
2
1
1
0
1
0
1
0
1
2
1
1
1
0
2
1
1
1
2
1
0
1
0
0
2
1
2
1
0
0
2
1
1
1
2
1
1
1
3
1
3
2
1
1
2
1
2
0
2
2
1
2
0
1
1
2
0
1
1
0
1
1
2
0
1
2
2
1
0
1
1
2
1
1
1
1
0
1
1
1
1
1
1
1
0
1
1
1
1
0
0
1
8
2
2
1
2
1
0
0
1
2
1
0
0
1
1
2
1
1
1
1
1
2
2
2
1
1
1
2
1
0
1
2
2
2
2
1
0
1
0
1
2
2
1
2
2
0
1
0
1
2
1
1
1
2
1
2
1
2
0
1
2
2
0
2
1
3
8
1
2
1
2
1
2
1
1
1
1
1
1
1
0
1
1
2
2
1
1
1
2
0
1
0
0
2
1
0
1
1
1
1
2
1
2
1
1
1
1
1
0
2
1
2
2
2
1
1
1
1
1
1
1
1
1
1
0
1
1
1
3
1
1
1
0
2
1
0
1
0
1
0
1
1
2
2
1
1
1
2
0
1
0
1
1
1
1
2
1
1
0
1
1
0
1
1
0
1
1
1
1
2
2
1
1
2
2
1
1
2
2
2
1
2
2
0
1
1
2
1
1
1
1
2
2
1
1
1
1
0
3
1
1
0
1
2
1
1
1
1
2
1
1
1
3
1
1
2
1
1
0
0
1
1
1
1
2
1
2
1
1
1
1
2
2
1
1
0
1
1
1
2
0
2
1
2
2
0
2
0
0
0
0
0
1
2
1
0
2
1
1
0
0
2
2
1
2
1
1
1
1
1
1
3
0
1
1
1
1
1
2
1
2
1
0
2
1
0
1
0
1
1
2
0
2
1
1
1
1
0
0
0
0
1
3
2
1
1
1
2
0
1
2
1
1
1
0
1
1
2
1
2
0
2
2
0
1
2
1
1
1
1
1
2
2
1
1
0
1
2
1
0
3
1
1
0
0
1
1
0
0
1
2
1
1
1
1
1
1
2
1
1
0
1
1
1
1
1
1
0
1
0
0
1
2
1
1
2
2
1
2
1
1
1
1
0
2
1
1
1
2
0
0
2
1
0
2
1
1
1
1
0
1
1
1
2
2
1
2
1
1
1
1
0
1
2
2
2
1
1
1
1
2
0
1
1
0
2
1
1
1
1
1
1
2
1
2
0
1
1
1
1
1
1
1
0
1
1
1
1
1
2
1
1
1
0
1
0
0
1
1
1
1
1
1
2
0
1
1
1
1
0
2
2
2
1
0
0
1
1
1
1
0
1
1
0
2
1
0
1
1
1
2
1
1
1
0
2
1
1
1
1
0
2
0
1
1
0
1
1
0
2
1
2
2
1
0
1
0
1
1
1
1
1
1
0
2
0
1
2
1
0
1
2
1
2
1
1
1
1
1
1
0
0
1
1
0
1
1
1
1
1
1
0
1
0
2
1
2
1
0
1
2
1
0
0
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
0
1
0
1
1
0
2
1
1
1
1
1
1
2
2
2
0
0
1
0
2
0
1
2
0
1
2
1
1
0
2
1
1
1
2
1
1
1
1
1
0
0
1
3
1
1
1
1
0
1
1
2
2
1
1
2
2
1
1
2
1
1
0
1
2
0
2
1
1
1
0
1
1
1
0
1
1
3
1
2
1
0
1
0
2
0
1
1
1
0
0
0
2
1
0
1
2
1
0
2
2
1
1
1
1
2
1
1
1
2
0
0
1
1
1
1
1
1
0
1
0
0
0
1
2
1
0
2
1
2
1
2
1
1
1
0
2
1
2
1
2
2
1
0
2
0
2
1
1
1
1
1
0
1
1
2
2
1
1
2
1
1
1
2
2
1
0
1
2
2
2
1
0
0
2
2
2
0
1
0
1
1
2
1
1
1
1
1
0
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
0
0
2
1
2
2
1
1
0
1
4
1
1
1
1
2
1
2
1
1
1
0
1
1
2
1
2
1
1
1
1
1
1
1
1
2
2
1
1
0
1
1
1
1
1
2
0
2
2
2
1
1
2
1
0
1
1
1
2
1
0
1
1
1
1
0
2
1
0
2
1
1
0
1
2
2
1
1
0
2
0
1
1
1
1
1
2
1
1
1
2
1
1
1
2
0
1
1
0
1
0
1
0
1
1
1
2
1
2
1
0
2
1
0
3
1
0
0
0
1
1
0
1
1
1
1
2
0
1
2
1
1
1
1
1
1
2
0
1
2
2
1
1
2
0
1
3
1
0
1
2
1
1
1
0
1
1
1
2
0
1
2
1
1
1
1
2
2
2
1
1
1
4
0
1
0
1
2
1
2
0
0
1
1
1
1
0
2
0
1
2
1
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
2
0
1
1
1
2
1
1
1
1
1
1
1
2
1
0
2
1
2
1
1
1
1
0
2
1
0
0
1
1
2
1
1
1
1
1
1
1
2
0
1
1
1
1
0
2
0
1
1
1
1
1
1
0
0
0
1
0
1
0
1
1
1
1
1
1
1
1
1
1
1
1
2
0
0
1
2
0
0
0
1
2
1
1
1
1
3
0
1
1
1
1
0
1
2
1
1
1
1
2
0
1
1
2
1
1
0
1
2
2
1
1
1
1
2
1
2
1
1
0
1
2
2
1
1
2
1
1
0
1
1
1
1
1
1
1
2
1
1
1
2
0
1
1
2
1
0
1
1
1
1
1
0
1
1
1
0
1
1
0
2
1
2
1
0
0
1
0
1
2
2
2
1
1
2
0
1
1
3
1
1
0
0
0
0
1
0
0
1
2
1
1
1
1
0
3
1
1
1
0
1
1
1
1
1
1
1
1
1
1
2
2
1
2
2
0
1
2
1
1
2
1
1
1
1
2
2
2
2
1
2
1
1
1
2
1
1
1
0
1
1
2
1
2
1
1
1
1
1
1
1
1
0
1
0
1
0
0
2
2
1
2
1
1
0
1
1
1
2
1
1
2
0
2
0
2
1
1
0
2
1
0
1
2
0
1
2
1
1
0
1
1
1
1
1
2
1
1
2
1
1
1
1
0
1
2
1
2
1
1
0
1
1
1
1
2
0
1
1
1
1
1
1
2
2
2
1
2
2
1
0
1
0
1
0
1
0
0
0
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
0
0
1
1
0
2
1
2
1
1
1
2
1
1
2
1
0
1
0
1
1
2
0
1
1
0
2
1
2
1
1
1
2
2
1
2
1
0
2
0
1
0
1
1
2
1
1
2
0
1
1
2
2
1
1
0
1
1
1
1
2
0
1
1
2
1
1
2
1
2
1
2
1
2
1
1
1
0
0
2
0
2
1
1
2
0
1
0
2
1
1
1
1
0
1
1
1
1
2
2
1
1
2
2
0
1
1
1
1
1
1
0
0
2
1
2
0
1
1
2
1
0
2
2
1
0
1
0
1
2
1
2
1
1
1
1
0
1
1
1
2
2
1
1
1
0
1
1
0
0
1
2
1
1
1
1
1
0
1
2
0
2
1
1
2
1
1
1
2
1
4
2
1
1
1
1
1
1
1
0
1
1
1
2
0
0
1
1
1
1
2
2
0
2
2
1
1
1
0
0
0
1
1
1
1
0
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
0
1
1
2
1
0
1
2
1
1
1
1
2
2
0
0
1
1
2
1
1
1
1
2
1
1
2
1
2
1
1
1
2
2
1
1
1
1
0
0
0
1
1
1
0
1
1
0
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
0
1
0
2
0
0
0
2
1
1
2
0
1
1
1
2
2
2
2
2
0
1
0
1
2
1
1
0
1
1
2
1
2
1
2
2
2
0
2
1
1
1
2
2
0
0
1
1
1
1
1
2
2
2
1
0
1
1
2
1
1
1
1
1
1
0
1
1
1
2
1
1
0
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
0
0
1
1
0
1
1
1
1
1
1
1
1
1
2
0
1
1
0
1
1
1
1
0
5
2
1
0
1
1
1
0
0
2
0
1
0
1
0
1
1
1
1
2
2
1
1
1
2
1
2
1
0
2
2
2
1
1
1
0
0
0
0
0
1
1
1
0
1
1
1
1
0
1
1
1
0
2
2
1
0
1
0
1
1
2
0
0
2
1
2
1
1
1
1
0
1
2
1
2
1
1
1
2
2
0
2
2
2
1
1
0
1
2
0
1
1
0
1
0
2
1
1
1
2
1
1
1
1
1
2
0
1
1
0
1
1
0
1
0
1
1
1
1
1
1
1
0
2
0
2
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
0
1
1
2
1
1
2
2
1
1
2
0
0
1
0
1
2
2
1
1
1
1
0
1
1
1
1
2
1
2
1
2
1
1
2
2
1
2
1
1
2
2
1
1
0
2
2
1
0
1
1
1
7
1
1
1
1
0
2
1
1
2
2
2
1
1
1
2
1
0
1
2
1
2
0
1
2
0
0
2
0
2
0
0
2
1
1
1
2
1
4
1
2
2
1
2
1
1
0
1
1
1
1
1
1
1
1
0
2
2
1
2
1
0
1
1
0
1
1
2
1
2
1
1
2
2
1
2
2
1
2
1
1
1
1
1
1
1
0
2
1
1
0
1
0
1
1
1
1
1
1
1
1
1
3
1
2
0
1
0
1
2
1
1
1
0
0
2
2
1
2
1
1
2
1
3
2
1
1
1
0
1
1
2
0
1
1
1
1
1
1
1
1
2
0
1
2
1
2
1
0
1
2
1
1
1
1
1
2
1
2
1
0
2
2
1
0
1
1
0
1
1
1
1
1
0
1
0
1
1
1
1
1
1
2
1
2
1
1
0
0
1
2
3
2
1
1
1
0
2
1
1
2
1
1
0
1
1
1
1
0
1
0
1
1
1
1
1
2
1
1
0
0
1
2
0
1
1
1
2
1
1
1
1
1
1
1
1
0
2
1
0
1
1
1
1
2
1
1
1
1
1
1
0
1
2
1
2
0
0
1
1
1
0
1
2
1
1
1
1
1
1
1
2
0
0
1
2
1
2
1
1
2
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
0
1
1
3
0
1
2
3
1
0
1
1
1
2
1
0
1
1
0
0
1
2
1
0
1
0
2
2
1
2
1
2
2
1
0
0
1
0
0
0
2
1
2
1
0
1
1
2
0
1
1
1
1
1
0
1
0
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
2
2
2
0
0
1
2
1
2
1
0
2
1
1
1
1
0
0
1
1
0
2
1
1
1
1
0
1
0
2
1
0
0
1
1
1
1
2
2
1
2
1
0
2
2
0
2
1
1
0
2
0
1
1
1
0
1
0
0
0
1
2
1
1
2
1
0
1
0
0
2
2
0
1
1
1
1
0
1
1
2
1
1
0
2
0
1
1
1
1
1
0
1
1
1
1
1
1
1
2
0
1
1
1
0
1
2
1
1
0
1
2
0
1
0
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
0
0
2
1
2
1
1
2
1
0
1
2
1
1
0
1
1
2
0
1
3
1
1
0
1
1
2
1
1
1
1
1
1
2
2
2
1
1
2
1
2
1
1
0
1
2
1
1
1
2
2
3
1
1
0
1
0
2
1
1
2
1
1
1
1
0
1
2
1
1
1
2
1
2
2
0
1
1
0
0
0
1
1
1
2
0
1
1
3
2
3
1
1
2
0
1
1
1
1
0
0
2
0
1
1
2
1
1
1
1
1
0
1
0
1
1
1
2
1
1
0
1
1
1
1
1
1
0
1
2
1
1
2
1
2
1
1
1
2
1
1
1
0
1
0
0
1
2
2
1
1
1
2
1
1
1
2
2
1
2
1
1
0
1
0
1
2
0
1
1
1
0
2
2
2
2
1
1
1
1
0
1
2
2
1
1
0
2
1
4
2
1
0
1
1
1
1
1
1
1
1
0
2
1
1
2
2
1
2
0
1
0
0
1
1
1
1
0
2
1
2
1
1
2
1
1
2
1
1
0
2
2
1
2
2
0
1
1
1
2
1
1
1
2
1
1
1
4
0
2
1
1
1
2
0
1
1
3
2
1
1
2
2
0
0
1
1
0
0
1
1
0
1
1
2
1
1
1
1
1
1
2
1
0
1
0
2
1
2
1
1
2
0
4
1
2
0
2
1
1
1
1
2
2
0
0
1
1
2
0
1
2
2
1
2
1
1
2
1
1
1
1
2
1
2
2
2
2
2
0
0
1
1
2
0
1
1
1
2
0
1
1
1
0
2
0
1
0
2
1
0
0
2
2
1
1
2
1
2
0
0
0
1
1
1
1
0
2
1
1
1
1
0
2
0
2
2
2
0
1
0
1
2
1
1
0
2
1
1
0
1
2
1
1
0
1
0
2
2
1
1
0
2
0
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
0
1
0
1
1
2
1
0
1
1
1
1
0
0
2
1
2
2
1
0
2
1
1
2
1
1
1
0
1
1
2
1
2
1
1
0
0
1
1
1
1
1
1
1
1
0
1
1
1
0
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
0
0
1
0
0
0
1
2
2
0
1
0
2
1
1
1
1
1
1
1
0
1
1
1
2
0
2
1
2
2
2
1
1
0
1
1
0
0
1
1
1
1
1
1
2
1
2
0
0
2
2
0
2
1
1
2
0
0
0
1
1
1
1
0
2
0
1
1
0
2
1
1
1
1
2
1
1
1
0
2
1
0
0
1
0
1
1
1
3
1
2
2
1
2
0
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
0
1
2
0
2
0
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
2
1
2
1
1
0
0
1
1
1
1
1
1
2
1
0
2
2
1
0
1
2
1
1
1
1
2
1
2
2
1
0
1
1
0
1
1
0
1
1
1
1
1
1
2
2
2
1
1
1
0
1
2
2
2
2
1
1
1
0
1
2
1
0
0
1
1
1
0
0
2
1
1
1
0
1
2
1
1
2
2
2
0
1
2
1
1
1
1
2
1
2
1
1
1
2
1
1
0
1
0
1
1
0
2
1
1
0
1
2
1
1
2
2
0
2
1
0
1
0
1
1
1
1
2
1
1
0
1
1
0
2
1
1
1
1
1
1
1
2
0
1
1
2
1
1
2
0
2
2
0
1
1
0
1
1
1
1
1
2
0
1
2
1
1
0
1
2
1
0
1
1
1
0
0
0
2
1
1
1
0
2
1
1
1
1
1
1
1
0
1
1
1
1
1
0
0
1
1
2
2
1
1
0
1
2
2
1
1
0
1
1
2
1
2
1
2
2
0
2
0
2
1
1
0
2
1
1
1
1
0
1
1
1
2
1
1
1
0
1
1
1
2
2
1
1
1
1
1
1
2
1
2
1
1
1
2
2
2
0
1
1
1
1
1
2
1
2
2
1
1
1
1
1
0
2
0
1
1
2
1
0
2
1
1
2
0
2
1
1
1
0
0
1
1
0
0
1
1
1
2
1
2
2
1
1
1
1
1
0
0
0
2
0
1
1
1
0
0
1
1
1
2
1
1
0
0
1
0
0
1
0
1
2
1
1
1
2
1
2
1
2
1
1
1
1
1
2
1
1
1
1
1
0
2
2
1
0
1
1
1
2
2
1
1
0
1
2
2
2
1
1
1
0
2
1
1
2
2
2
0
1
3
2
1
2
0
1
1
1
1
1
0
2
1
1
1
1
1
1
1
2
1
1
1
2
0
2
1
2
1
2
1
1
1
1
2
1
1
1
1
1
2
1
1
2
2
3
1
0
1
1
1
1
2
1
1
0
1
0
1
1
2
2
0
1
0
0
1
0
0
1
1
1
1
0
1
1
0
1
0
2
1
0
1
1
1
1
1
2
1
3
1
1
2
1
1
1
2
1
1
1
1
0
1
1
1
0
1
1
0
1
1
1
2
1
1
2
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
0
2
1
2
1
1
1
0
1
2
1
1
2
0
1
2
2
0
2
2
1
0
1
1
2
1
2
0
1
1
2
1
1
1
2
1
0
1
2
1
1
1
3
1
0
1
2
1
1
2
1
2
2
1
1
0
0
1
1
1
2
2
1
1
1
2
1
1
1
1
1
1
1
0
1
1
2
0
1
1
1
2
1
2
1
2
1
2
1
0
1
1
1
2
2
1
2
1
2
1
1
0
0
1
1
1
1
2
2
1
1
1
1
0
1
1
1
1
2
0
0
1
1
1
2
3
1
1
2
1
2
1
1
1
2
2
0
1
1
0
1
0
1
1
1
1
1
1
1
1
1
1
1
0
2
0
0
1
1
2
0
0
2
1
2
2
1
2
0
1
2
1
1
1
2
1
0
2
1
1
1
0
1
1
1
1
1
2
1
1
2
0
1
1
1
1
1
2
1
1
2
1
1
2
1
1
0
1
1
2
0
1
0
1
1
1
1
1
1
1
1
2
0
1
1
1
1
0
1
1
1
1
0
0
0
1
2
5
0
0
1
2
1
2
0
1
1
1
1
1
1
0
1
1
1
2
1
1
1
1
2
1
1
1
2
2
1
2
1
1
1
1
1
0
1
1
2
2
1
1
0
0
0
1
1
1
3
2
1
2
2
1
0
1
1
1
2
1
2
1
1
2
2
2
1
1
1
0
1
1
2
1
2
1
2
1
2
1
0
0
2
1
0
1
1
1
1
1
2
1
1
0
1
1
0
1
0
0
2
2
2
1
1
0
1
0
1
0
0
1
1
1
1
1
2
1
2
1
2
1
1
1
1
2
0
0
2
0
7
1
2
0
2
2
1
1
1
1
2
1
2
1
2
1
0
2
2
1
2
1
1
2
1
1
1
2
2
2
1
2
1
2
2
1
1
0
0
0
1
0
1
1
1
1
1
0
2
2
1
2
1
2
1
1
1
1
1
1
2
1
0
1
1
0
0
1
2
2
1
1
1
1
1
1
0
2
1
1
2
1
2
1
2
1
0
0
0
1
2
2
1
1
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
0
2
1
1
1
0
1
1
1
1
1
2
2
1
1
0
2
1
3
1
2
1
0
0
1
1
1
0
1
1
1
1
1
1
2
1
1
1
2
2
1
0
1
1
1
1
2
2
2
1
1
1
1
2
2
2
1
1
2
0
2
1
1
1
2
0
1
1
2
1
1
0
1
1
1
2
2
2
1
1
0
2
2
0
1
0
0
1
0
1
1
2
1
0
2
2
1
2
2
1
1
1
2
1
2
1
1
1
0
1
0
0
1
1
0
0
0
0
1
1
1
1
1
2
1
1
1
1
0
1
1
1
0
1
1
0
1
1
2
0
1
1
2
2
1
1
1
0
1
0
2
1
1
0
1
1
0
1
1
2
2
1
0
2
1
1
2
1
1
2
0
1
1
2
0
1
1
0
2
2
1
1
3
0
2
1
1
2
1
2
2
2
0
1
1
2
1
1
1
1
1
2
1
2
1
3
1
1
1
2
2
1
1
1
1
1
2
2
1
1
1
1
1
0
1
1
1
1
1
0
2
1
0
0
0
1
1
2
1
1
0
0
1
1
1
3
2
0
2
2
1
0
1
2
1
1
0
1
1
1
2
1
1
2
1
1
2
1
0
1
1
0
1
2
1
2
2
1
1
1
1
2
2
0
2
1
2
1
1
1
1
1
1
0
1
1
1
0
2
1
1
1
0
1
2
0
1
1
2
0
1
3
1
2
1
1
0
2
1
0
2
1
2
2
1
1
1
0
0
1
1
0
0
1
1
1
0
2
0
1
3
1
2
0
1
1
1
1
2
1
2
0
1
1
1
1
1
1
1
1
1
0
1
1
1
2
1
0
1
1
1
2
1
1
1
2
1
0
1
1
1
0
2
1
2
1
2
1
1
0
1
2
1
1
2
1
0
2
2
1
1
0
1
1
1
1
1
1
2
1
2
1
3
2
2
2
2
1
1
2
1
2
1
0
1
2
1
2
1
1
1
1
2
1
2
2
2
2
2
1
1
2
1
1
0
1
1
1
1
1
1
1
1
1
1
2
0
2
1
0
1
1
2
2
0
1
1
2
2
0
2
2
0
1
1
2
2
2
2
1
2
1
1
2
1
0
2
1
2
1
2
0
1
1
1
2
1
2
0
1
0
2
0
1
1
2
1
1
0
1
2
1
2
1
1
2
1
1
2
1
0
0
0
1
0
1
0
2
2
1
2
2
0
1
2
1
1
1
2
1
1
1
2
1
1
2
1
1
2
0
1
1
1
1
2
1
0
2
2
0
1
1
0
1
1
1
1
1
1
1
2
0
1
1
1
3
2
1
1
2
0
1
1
1
2
1
1
1
1
2
1
1
2
2
1
1
2
1
1
1
1
1
0
1
1
2
1
0
1
1
2
0
1
1
2
0
1
1
0
0
1
1
1
0
1
1
1
0
1
1
0
0
1
2
2
1
1
1
2
2
2
1
1
2
3
2
0
1
1
1
0
0
1
0
1
1
1
1
0
1
1
1
1
0
0
1
1
1
2
1
1
1
1
2
2
1
1
1
1
2
0
1
0
1
0
2
0
2
2
1
1
0
1
1
0
2
1
1
1
1
1
1
1
2
0
2
2
0
2
2
1
1
2
2
0
1
1
1
1
1
2
1
2
0
1
2
1
2
0
2
2
2
2
1
1
1
2
1
1
0
0
1
1
1
0
2
0
2
1
2
1
1
1
1
0
2
1
1
0
1
1
2
2
1
2
1
1
1
2
0
1
2
0
2
0
1
2
2
0
1
2
1
0
2
1
0
1
0
1
1
0
1
1
1
1
2
1
1
2
1
3
1
1
1
1
0
2
1
1
1
3
1
1
1
0
1
2
2
2
1
1
1
1
1
1
1
0
0
3
0
1
1
1
0
2
1
1
2
1
1
2
1
1
1
0
1
0
2
1
2
1
1
2
1
0
1
1
1
0
1
2
1
1
2
1
1
0
1
1
1
1
1
0
2
1
1
1
2
2
1
1
2
1
2
2
0
2
1
1
1
2
1
1
1
0
1
2
1
1
0
1
0
1
2
1
1
0
2
2
1
2
2
1
0
1
1
2
2
0
1
2
1
1
1
0
2
1
1
1
1
1
2
1
1
1
1
1
1
1
0
1
2
1
1
1
1
2
2
1
2
1
1
0
1
1
1
2
1
0
1
1
0
0
1
1
0
1
0
1
1
1
2
2
1
0
1
1
2
1
1
2
1
1
1
2
0
0
1
2
1
1
1
1
1
1
2
2
1
2
1
1
2
1
2
1
2
1
0
1
1
2
1
2
0
1
2
1
1
1
1
0
2
1
2
1
3
2
1
1
2
1
2
0
0
0
0
1
2
1
1
1
1
1
2
0
1
2
1
0
1
0
2
1
2
2
0
0
0
0
1
1
1
1
1
1
2
1
1
1
2
0
1
2
2
2
1
0
0
0
1
0
2
0
1
1
1
1
1
1
1
0
1
2
1
2
1
3
1
1
1
2
1
1
1
1
1
0
1
1
1
0
2
1
2
1
1
2
1
1
0
1
1
1
2
1
0
1
1
1
1
1
2
2
1
1
2
1
2
1
2
1
0
1
2
0
1
1
1
0
1
1
1
1
1
1
2
1
1
1
0
1
3
0
1
2
1
1
2
1
1
0
2
0
1
0
0
0
2
1
1
1
2
2
2
1
1
1
2
1
1
1
1
2
2
2
1
1
1
1
2
1
1
0
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
2
1
2
1
0
2
1
0
1
2
0
1
1
2
1
1
1
0
2
1
0
1
0
1
1
1
1
1
0
1
1
1
1
0
0
1
0
2
1
1
2
2
1
1
1
2
2
1
2
2
1
1
2
1
1
2
1
1
1
1
1
1
0
1
1
1
1
2
1
2
1
2
0
1
1
0
1
0
1
2
1
1
1
1
1
1
1
1
0
1
1
1
2
1
2
1
1
1
1
0
2
1
0
1
1
1
1
1
1
1
2
0
1
1
2
2
1
1
1
2
1
2
0
1
2
2
2
1
2
1
1
1
1
0
0
0
2
1
1
1
1
0
1
2
1
2
1
0
1
1
1
1
1
1
2
0
0
1
2
3
0
2
2
1
1
0
0
1
1
2
2
2
1
1
1
1
0
0
1
1
1
1
1
1
1
2
1
0
2
1
0
0
2
1
1
0
1
2
1
2
1
1
0
1
1
1
2
1
2
1
1
1
2
1
2
1
2
0
1
0
1
2
2
1
1
2
0
1
1
1
1
1
2
1
1
1
0
1
2
1
1
1
0
2
0
0
1
1
1
2
0
1
0
1
1
1
1
0
2
1
1
1
0
2
1
2
1
2
1
1
2
1
1
1
1
1
0
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
0
1
4
2
1
2
2
1
2
1
2
2
1
1
1
1
1
0
1
2
2
1
0
1
1
1
1
0
0
1
1
0
1
2
0
0
0
2
2
1
2
1
0
1
1
0
1
2
1
0
1
2
0
0
1
1
1
0
1
1
1
1
2
1
1
3
1
1
1
2
1
1
0
1
1
2
1
2
1
2
2
1
0
2
1
1
1
0
0
1
2
2
1
1
0
1
1
0
1
1
2
2
1
2
1
1
1
1
1
1
2
1
1
0
2
2
2
1
1
1
1
1
0
0
1
0
1
0
0
0
1
1
1
0
2
1
1
1
1
2
1
2
1
0
1
1
0
3
2
2
1
1
2
1
2
1
2
0
2
1
2
1
1
1
1
2
1
1
1
1
2
0
0
2
1
1
1
1
1
2
1
1
2
1
1
1
1
0
2
1
0
2
1
1
2
1
0
2
0
1
1
1
2
1
0
0
1
2
2
1
1
1
1
1
1
1
2
0
0
1
0
1
0
1
2
1
1
1
1
1
1
1
1
0
2
0
1
1
1
0
0
0
2
1
1
1
1
1
1
1
1
1
2
1
1
1
0
1
1
2
1
1
1
1
1
0
1
1
1
1
0
2
2
1
1
1
0
1
0
0
1
1
0
1
0
1
2
1
1
1
0
1
0
1
2
1
1
1
1
1
1
1
2
0
1
2
3
1
1
3
1
1
1
1
1
1
1
0
2
1
1
1
2
1
1
2
1
0
2
0
1
1
2
0
1
2
2
1
3
0
1
2
1
1
1
2
1
0
0
1
1
1
2
1
3
1
0
1
1
2
2
0
1
1
1
1
1
2
1
1
2
1
2
1
1
2
1
2
1
2
1
1
4
1
1
1
0
2
1
1
1
1
0
1
1
2
1
0
1
0
2
0
0
1
1
1
1
1
1
0
2
0
1
1
2
0
1
2
1
0
1
1
1
2
1
1
1
1
1
1
1
1
1
0
2
1
0
1
2
1
1
2
0
1
2
1
0
2
1
1
1
1
0
1
2
1
1
1
1
2
2
1
2
1
1
0
1
1
2
2
1
1
1
2
1
1
1
1
1
1
2
1
0
2
1
1
1
0
1
1
1
1
1
0
1
2
2
1
1
2
0
1
1
1
1
1
1
1
1
1
2
2
1
2
1
1
1
0
1
1
0
1
1
1
1
1
0
1
1
1
1
1
1
2
2
2
1
2
1
2
1
1
0
2
1
1
1
0
1
2
1
1
1
0
1
1
0
2
2
0
1
1
1
0
1
1
2
1
1
2
1
1
1
0
2
0
1
2
2
1
2
1
1
1
0
1
0
0
2
2
1
1
1
1
2
2
1
3
0
2
1
1
1
1
1
1
1
2
2
1
1
2
1
2
1
2
1
0
0
0
1
1
2
2
0
1
1
1
0
0
1
1
2
1
1
1
2
1
1
1
1
0
0
3
2
1
1
1
1
2
1
1
1
1
1
1
2
2
1
2
2
2
0
2
2
0
0
1
1
1
1
0
2
2
1
1
0
1
1
2
1
1
2
1
1
1
1
2
1
1
1
0
1
0
0
2
4
2
1
1
2
2
1
1
1
0
1
0
1
1
1
1
1
2
0
2
1
0
1
2
1
2
1
0
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
0
0
0
1
0
1
1
2
1
1
2
2
1
1
2
1
2
1
2
2
1
2
1
2
1
1
1
1
2
2
2
1
1
1
1
1
2
0
0
2
1
0
0
0
2
2
1
1
0
0
1
2
1
1
0
0
1
1
2
2
1
1
1
2
1
1
1
2
1
1
0
2
2
1
1
1
1
1
0
2
1
1
1
1
1
1
2
0
1
1
0
1
1
2
1
1
0
0
2
1
1
1
1
0
1
1
1
1
2
1
1
1
0
1
2
2
1
1
1
1
1
0
1
1
1
0
3
1
0
1
1
1
1
2
1
1
1
1
0
1
1
1
1
2
1
0
0
1
0
1
1
1
0
2
1
1
1
1
2
2
1
1
1
2
0
1
3
0
1
0
1
1
1
2
0
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
2
1
2
1
2
1
2
2
2
1
1
2
1
1
2
0
2
1
2
1
1
0
0
1
0
1
1
0
1
2
1
2
1
2
1
0
2
2
2
0
1
0
1
1
1
1
2
1
1
1
1
2
1
1
2
3
0
2
1
1
0
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
0
0
0
1
0
1
2
1
1
1
0
1
2
0
1
1
1
1
1
3
1
1
1
2
1
0
1
1
1
0
0
1
2
1
1
1
1
1
2
2
1
0
1
0
2
1
1
1
1
0
1
1
1
1
0
2
2
1
2
2
1
1
1
2
1
1
1
1
2
0
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
0
1
1
1
2
1
2
2
0
1
1
0
1
2
2
1
1
2
0
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
2
1
1
2
1
1
1
1
2
1
1
0
1
2
2
0
0
1
1
1
1
1
1
2
0
2
1
2
2
1
1
0
0
1
1
2
0
1
1
2
1
1
1
1
0
1
1
1
1
1
0
1
1
2
1
1
0
2
0
1
1
1
1
1
1
1
2
1
1
0
1
0
1
2
1
0
1
1
2
0
0
1
1
3
0
1
1
2
1
1
1
1
1
1
1
0
2
0
0
1
0
2
1
2
0
1
2
0
1
1
3
1
1
1
2
1
1
1
2
0
1
1
1
1
0
1
1
1
1
1
1
1
2
1
1
2
0
0
1
0
1
2
1
1
0
1
1
2
1
1
0
2
0
0
2
1
0
2
1
1
1
2
1
1
1
1
2
1
0
1
1
1
0
0
1
2
2
3
0
1
1
2
1
1
2
1
1
1
1
2
1
1
1
3
0
2
1
1
1
2
1
1
2
0
2
2
2
2
1
1
1
1
1
2
2
1
2
1
1
2
1
2
2
0
0
1
2
0
2
1
1
2
1
0
0
1
2
1
1
2
1
1
0
0
0
1
2
5
2
1
2
0
1
0
1
0
2
1
0
2
1
1
0
1
1
2
1
2
0
4
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
0
1
2
2
1
0
1
2
0
1
1
2
1
1
2
0
1
1
1
2
1
1
2
1
1
0
1
0
1
1
1
1
2
1
2
2
1
2
0
2
1
1
1
1
1
0
2
1
2
2
0
1
1
0
1
0
2
1
1
1
1
3
1
1
1
1
1
2
1
1
2
1
2
1
1
1
1
1
1
2
2
0
2
0
1
2
1
2
0
1
1
1
2
1
1
1
1
1
1
0
0
1
2
1
2
1
1
1
1
2
1
1
0
1
0
2
2
1
1
1
2
2
2
1
1
2
1
2
1
1
2
2
1
1
1
1
0
2
1
0
1
1
2
0
1
1
1
1
0
1
0
2
1
1
1
1
1
1
1
0
1
1
1
1
1
1
2
0
1
1
1
1
2
2
2
1
3
0
1
0
2
0
0
1
0
0
2
0
1
2
1
1
0
1
2
0
2
2
1
1
1
2
1
1
0
0
0
0
1
1
1
2
0
1
1
1
2
1
2
0
0
1
1
0
0
1
1
1
1
0
1
0
1
2
2
1
2
1
1
1
1
1
1
1
2
2
2
2
1
2
2
0
1
0
1
2
1
1
1
3
0
0
2
2
2
2
1
2
1
2
1
1
1
1
2
1
0
1
0
0
1
1
1
1
1
1
0
0
2
2
2
3
1
0
0
1
2
1
2
1
0
2
1
1
0
2
1
2
2
1
1
2
2
2
2
2
1
1
1
1
0
1
1
1
1
1
1
2
1
2
1
0
0
2
0
0
0
1
0
1
0
0
2
1
1
2
0
1
1
2
0
0
1
2
1
1
0
1
1
2
1
1
1
0
2
2
1
1
1
1
1
1
0
1
2
2
1
2
1
2
1
2
0
1
2
0
1
1
1
0
2
1
1
1
2
1
2
1
1
1
0
1
1
1
2
2
4
0
1
1
1
1
2
0
1
0
1
2
0
1
1
3
1
1
0
0
1
1
0
2
1
2
2
3
0
0
1
1
1
2
1
1
1
1
2
2
0
2
0
1
1
1
1
1
1
1
0
1
1
2
1
2
2
1
0
1
0
2
1
1
1
2
0
1
1
1
1
2
2
1
0
1
1
0
1
1
1
1
2
1
1
1
0
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
0
1
2
0
0
1
1
1
2
1
1
1
0
0
1
1
1
1
1
2
1
2
1
2
1
1
7
2
0
1
1
1
2
1
2
0
1
2
1
0
1
1
1
1
2
0
2
1
1
2
1
0
0
2
2
1
2
2
1
1
1
2
2
1
0
1
1
1
1
2
0
1
1
0
1
1
1
1
1
2
1
3
2
1
2
2
2
0
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
1
0
0
1
1
2
0
0
0
0
2
1
1
2
1
1
1
1
2
0
2
1
1
0
1
1
1
1
2
2
0
1
1
1
1
1
1
1
1
2
1
1
2
1
2
0
1
2
2
1
2
1
1
2
0
2
1
0
1
1
2
2
2
1
2
1
1
0
1
1
1
1
2
2
0
2
1
0
1
2
0
1
1
1
2
1
0
1
1
2
0
2
1
0
2
1
1
2
1
0
2
2
0
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
2
2
1
2
1
1
2
2
1
1
0
1
1
1
1
0
1
2
1
1
0
2
1
0
2
1
1
2
0
1
1
1
1
1
0
1
0
0
1
2
2
0
1
0
0
2
0
2
1
1
1
1
1
1
1
0
0
2
0
2
1
0
2
2
1
1
1
1
2
1
1
1
1
2
0
1
1
2
1
1
0
1
0
0
0
2
1
1
1
1
1
1
0
1
2
0
2
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
0
1
2
2
0
1
2
1
1
0
2
1
1
0
2
1
1
1
1
0
1
1
1
2
1
1
1
1
1
1
0
2
2
1
0
1
2
2
1
1
1
1
2
1
0
0
1
1
2
1
2
1
1
0
2
1
1
1
0
0
1
1
1
1
2
1
1
2
2
0
1
0
1
1
1
1
2
1
2
2
1
6
1
1
0
1
1
1
0
1
1
1
2
1
2
1
0
2
1
2
1
1
1
1
1
3
1
1
1
1
0
2
0
2
1
0
1
2
0
1
2
1
1
0
1
0
1
1
1
1
1
0
1
1
2
2
1
1
0
1
1
0
3
0
0
2
1
1
0
0
0
3
1
2
2
1
1
1
1
2
2
0
1
0
1
1
0
2
1
2
3
1
1
1
2
0
0
1
0
1
1
1
1
1
0
1
0
0
1
1
1
2
1
1
1
1
1
1
1
1
0
1
1
1
0
1
2
1
1
0
1
2
1
1
2
2
1
0
1
1
0
1
2
1
1
2
1
1
1
2
1
2
1
0
1
2
1
1
1
1
1
1
0
0
1
1
2
1
1
0
1
1
2
2
0
2
1
1
1
1
2
1
1
0
1
0
1
1
1
1
1
1
2
1
1
1
1
2
0
1
1
1
1
2
1
1
0
0
1
2
2
0
1
2
1
2
2
1
1
1
2
1
2
1
1
1
0
1
1
1
1
1
1
2
1
1
2
1
2
2
1
1
1
1
0
2
0
0
1
1
0
1
0
1
1
1
3
0
1
1
2
0
0
0
1
2
1
1
1
1
2
1
2
1
2
1
1
0
1
0
1
0
2
1
1
1
2
0
2
0
1
1
1
1
1
1
2
1
1
0
1
1
0
0
1
2
2
2
1
0
1
1
0
1
0
0
0
2
2
2
2
2
2
0
2
1
0
1
1
1
2
0
1
1
1
0
2
1
2
0
1
1
2
1
2
1
2
1
1
1
2
1
1
2
2
0
2
0
1
1
1
1
1
1
1
1
0
1
1
0
2
2
0
1
1
0
0
3
2
1
0
2
1
1
0
1
0
0
2
0
2
1
1
1
1
1
1
2
1
1
1
0
2
2
1
0
0
3
1
1
1
1
1
2
1
1
1
2
1
2
2
1
2
1
1
1
2
1
2
1
0
1
0
1
2
1
1
0
1
1
1
0
1
2
1
1
2
1
1
1
2
1
1
0
0
2
0
3
1
1
1
1
1
1
2
2
1
1
0
0
1
1
1
0
1
1
1
1
2
1
2
1
0
0
2
1
0
1
1
1
2
0
2
1
1
2
2
2
1
1
1
1
1
1
0
2
1
2
2
2
1
2
1
1
1
1
2
0
1
1
1
1
1
1
0
1
1
1
0
1
1
0
0
0
0
0
1
0
1
1
1
0
1
2
1
1
0
0
1
0
1
1
1
1
1
1
2
2
1
0
1
0
0
1
2
1
1
1
0
0
1
0
2
1
0
1
2
1
1
0
1
2
2
1
1
1
1
1
0
0
1
1
1
0
1
1
2
0
1
2
1
1
0
1
1
0
1
1
1
1
1
0
2
1
2
0
2
1
0
0
1
2
1
2
1
1
2
2
1
2
1
1
2
0
0
1
2
1
1
2
2
1
0
1
3
2
2
1
1
0
1
0
0
1
1
1
2
1
1
1
1
1
1
1
0
3
1
1
1
2
0
1
1
1
1
1
3
0
1
1
1
2
1
1
1
1
2
1
2
1
1
0
1
1
2
1
1
1
2
1
1
1
1
1
1
0
1
2
0
1
1
1
1
1
1
1
0
0
1
1
1
0
1
2
2
1
1
0
1
1
1
1
2
2
2
2
1
1
0
2
1
2
1
2
0
1
0
1
0
0
2
1
1
1
1
1
1
0
2
1
1
3
0
1
1
0
1
1
0
2
1
0
1
0
1
2
1
2
1
2
0
2
2
0
2
2
1
1
1
2
1
0
1
1
1
1
1
1
1
2
1
0
2
1
1
3
0
1
2
1
2
1
0
2
0
2
1
1
1
1
2
1
2
1
1
1
2
1
1
0
1
2
2
1
2
3
2
1
1
2
1
0
2
1
1
1
1
1
0
2
1
0
2
1
1
1
1
1
1
1
1
1
2
0
1
1
1
2
0
1
1
1
1
2
0
1
0
1
1
1
1
1
1
2
1
2
1
2
2
3
1
0
1
1
1
2
2
1
0
2
0
0
1
0
0
1
2
2
0
2
1
1
1
0
1
0
1
1
1
2
1
0
2
2
2
1
1
0
1
1
1
2
1
0
1
1
1
2
2
2
2
1
2
1
0
2
2
1
2
1
1
1
2
0
1
1
1
2
1
1
1
1
1
0
1
0
1
1
2
2
1
2
1
1
1
1
2
1
2
1
2
1
0
1
0
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
2
2
1
0
1
1
2
1
1
1
1
0
0
1
1
1
2
1
1
0
1
1
1
0
1
1
0
1
1
0
1
1
2
1
0
2
1
1
1
2
1
0
1
1
0
0
1
1
1
1
1
1
0
1
1
2
0
0
1
0
1
1
1
0
1
1
0
1
2
2
2
1
1
1
1
1
0
1
2
2
2
1
2
2
1
1
1
1
1
0
2
1
1
2
1
2
0
0
1
1
1
2
2
2
1
0
1
1
1
2
1
1
0
2
1
1
1
2
1
1
2
1
1
1
1
0
2
1
1
1
1
0
1
1
0
1
0
1
2
2
1
2
1
1
2
2
2
0
1
0
1
3
2
1
1
1
0
2
1
1
2
2
0
1
1
1
0
1
0
1
1
1
1
1
1
1
0
1
1
2
0
2
1
1
2
1
2
0
1
0
2
1
2
2
1
1
1
0
2
1
0
1
1
1
1
1
0
1
0
1
0
1
0
1
2
1
1
2
2
0
1
1
0
1
1
2
1
1
2
1
1
1
2
2
2
2
2
1
1
0
2
2
1
0
1
0
0
0
1
2
1
1
1
0
1
1
0
2
1
1
1
1
1
0
1
1
2
2
2
0
1
1
1
1
1
1
1
0
2
1
1
1
1
2
1
1
2
1
1
2
2
1
2
1
1
1
1
1
2
2
2
1
2
0
1
1
1
1
1
1
0
1
1
1
1
2
1
1
1
2
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
2
2
1
2
1
0
0
2
2
0
1
0
1
1
0
1
2
1
0
1
1
1
0
1
1
2
0
1
1
1
1
1
2
1
1
1
1
2
0
0
1
1
0
1
2
1
2
2
1
1
2
2
2
2
0
1
2
2
2
1
1
1
2
1
0
0
1
1
1
0
2
1
0
2
1
1
0
1
0
2
0
2
3
0
1
1
1
1
1
0
1
2
2
1
0
0
1
0
1
2
0
1
1
1
1
2
0
2
0
0
1
1
1
2
1
1
0
0
1
1
2
1
1
1
1
1
1
2
2
1
1
2
2
0
1
1
0
1
1
1
1
1
1
0
1
0
1
1
0
1
1
2
1
1
1
1
2
0
1
0
1
1
0
1
1
1
1
2
0
1
1
2
1
1
1
0
2
0
1
2
1
2
0
0
1
1
1
0
2
1
1
0
1
2
1
1
1
2
1
1
2
1
1
0
1
2
1
2
1
0
1
1
2
1
1
1
0
2
2
1
1
2
1
2
2
1
1
1
1
1
2
2
2
1
1
1
2
2
1
1
1
1
2
2
1
2
1
1
1
2
1
2
1
2
1
2
1
1
3
1
1
2
1
2
1
0
1
1
0
0
1
1
1
0
1
1
2
1
1
1
1
0
2
1
1
1
2
2
1
1
1
0
1
2
0
2
1
1
1
1
1
2
1
1
1
1
1
1
0
1
2
0
1
1
0
0
1
0
0
1
1
1
2
1
1
1
1
1
1
0
1
0
2
1
1
2
2
1
1
0
1
2
0
1
1
1
0
0
1
1
2
1
1
1
0
1
2
0
2
0
0
0
1
0
0
0
2
2
0
1
1
1
1
2
1
1
1
1
0
2
1
1
1
2
2
0
1
1
1
0
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
2
1
0
2
1
1
3
2
1
0
1
1
1
1
2
1
0
1
2
1
2
1
2
1
0
1
1
1
1
1
1
0
1
0
0
1
1
1
1
1
1
1
0
1
2
1
1
1
2
2
1
0
1
1
2
1
2
2
1
2
1
1
1
3
1
1
0
1
1
2
1
1
1
2
2
0
0
1
1
1
2
1
1
1
1
2
0
1
2
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
4
1
1
1
1
1
0
1
0
1
1
0
2
1
1
1
0
0
0
2
0
1
1
1
0
1
0
1
1
1
1
0
1
1
0
0
0
1
2
1
1
0
1
1
1
1
1
0
2
1
1
1
1
2
0
1
2
2
1
1
2
1
1
0
1
0
2
1
1
1
0
1
1
1
1
1
0
1
1
1
1
1
0
0
2
2
1
0
1
2
1
1
1
1
2
2
1
2
1
2
2
2
1
0
2
1
2
1
1
2
2
0
1
1
1
0
1
1
0
2
1
2
1
1
1
1
2
1
2
0
1
2
3
2
1
0
0
1
2
1
1
1
2
1
0
2
2
1
2
1
1
2
1
1
1
0
2
1
0
0
0
1
1
1
2
0
1
0
3
1
1
1
1
2
1
2
2
0
0
2
1
1
1
1
5
1
2
1
0
1
1
0
1
1
1
2
1
0
1
2
0
2
2
0
0
1
2
2
1
1
1
2
1
1
0
1
0
1
1
1
0
1
1
1
1
1
1
1
1
1
2
2
0
0
1
1
1
1
0
2
2
1
1
1
1
1
0
1
0
1
1
1
1
1
2
0
1
0
1
1
1
1
0
0
2
1
1
1
1
1
1
1
1
0
0
1
2
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
2
2
2
2
0
1
1
2
2
1
1
2
2
1
1
2
1
0
0
1
2
1
1
2
2
1
1
1
2
1
1
1
1
0
1
1
0
2
1
0
0
0
1
1
2
1
2
1
0
1
1
0
1
1
0
2
2
1
2
1
1
1
2
1
2
1
2
0
0
2
1
1
2
1
1
0
2
1
1
0
2
0
1
1
1
1
1
0
0
2
1
0
2
1
1
1
1
1
1
1
0
2
0
1
1
0
1
1
1
1
2
2
1
1
1
2
1
1
1
1
3
3
1
1
1
1
0
2
0
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
2
0
1
2
1
1
1
0
1
1
1
1
1
2
2
0
1
1
1
1
2
1
1
1
1
2
1
1
2
0
1
1
1
1
1
2
1
2
2
1
1
2
2
1
1
1
0
2
2
1
1
2
1
0
0
2
1
1
1
1
1
0
1
0
1
1
1
1
1
2
1
1
1
0
1
0
2
1
0
2
0
2
0
0
2
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
1
2
1
1
0
1
1
1
2
1
1
1
1
0
1
1
2
0
2
1
1
2
1
1
1
1
1
2
1
1
0
2
1
1
1
1
1
1
1
2
2
1
1
1
2
1
0
1
0
2
1
3
1
2
1
2
1
2
1
1
1
1
1
1
1
1
0
1
1
1
0
2
3
1
1
1
2
1
1
0
0
2
0
1
1
0
0
2
2
0
1
1
0
0
1
1
2
1
2
0
3
2
0
1
1
1
2
1
1
1
2
2
1
1
2
3
1
2
1
2
2
4
1
1
1
1
1
1
1
2
2
2
2
1
1
1
2
2
0
1
1
1
1
2
1
1
2
1
0
1
1
1
1
2
1
3
2
1
0
1
0
2
2
1
2
3
1
1
2
2
1
1
2
2
1
2
1
1
2
2
1
1
2
0
0
1
1
2
1
1
1
1
1
1
0
1
1
1
0
1
1
1
1
1
1
0
1
1
1
1
1
0
1
1
0
1
1
0
2
1
1
4
0
1
0
1
2
1
1
2
0
1
1
1
0
1
1
1
1
1
1
0
1
1
1
1
1
1
2
2
0
1
2
1
5
1
1
2
0
2
1
1
2
2
1
2
1
1
0
1
2
1
1
1
0
0
2
1
1
1
1
1
2
0
1
1
1
2
1
1
1
1
1
1
0
0
0
1
1
0
1
1
1
1
2
0
1
1
2
1
2
1
1
1
2
0
1
2
0
1
2
0
1
1
1
1
1
2
2
0
2
1
1
1
0
1
0
0
2
1
0
1
1
2
0
2
1
1
1
0
1
0
1
1
1
1
1
0
0
1
0
2
2
1
1
0
1
2
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
2
1
0
1
1
1
1
1
1
2
0
1
2
1
1
0
1
3
1
0
1
1
1
1
1
1
2
1
1
1
1
1
1
2
0
1
1
1
1
1
0
1
1
0
2
1
1
1
2
1
1
1
1
2
1
1
1
2
1
1
0
1
1
1
1
1
1
2
0
2
2
2
1
1
0
1
2
1
1
1
1
1
0
1
1
1
1
0
0
2
1
2
2
0
1
1
0
0
2
0
1
1
1
0
1
0
1
0
1
2
1
2
0
1
1
1
1
0
1
1
1
1
0
2
1
1
2
1
2
1
1
2
1
1
2
0
1
2
0
0
1
2
1
0
2
2
1
0
2
1
2
2
1
1
2
1
1
1
0
1
1
1
0
1
1
1
0
0
1
1
1
1
1
2
2
2
1
1
2
1
2
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
2
1
1
1
2
1
1
1
2
1
1
0
0
1
1
1
1
1
2
1
1
0
1
1
2
1
2
1
1
1
0
2
2
1
1
1
1
1
1
1
2
1
0
0
1
1
1
2
1
2
0
2
1
2
1
1
0
0
2
0
2
2
0
2
2
2
1
2
1
1
1
1
1
0
1
1
2
1
1
1
1
2
1
1
2
1
0
1
1
1
2
2
1
1
2
1
1
1
2
1
2
2
1
1
1
0
2
1
1
1
1
1
0
1
1
1
2
0
1
1
1
0
0
1
1
1
1
1
1
2
0
0
0
2
2
2
1
2
2
1
1
1
1
1
1
1
2
1
0
2
1
1
2
1
0
1
2
0
2
2
1
1
1
1
1
1
0
1
0
1
0
2
0
2
1
1
1
1
1
0
1
0
1
1
2
2
1
1
1
2
1
2
1
1
1
1
0
1
1
1
1
1
2
1
1
1
1
2
1
2
0
1
2
2
1
1
1
1
1
1
1
0
0
1
1
1
2
1
1
2
1
1
1
1
0
1
1
2
2
0
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
2
1
1
1
0
1
1
2
1
0
1
2
3
2
1
1
1
1
1
2
0
0
1
1
1
1
1
2
1
1
1
1
0
1
1
1
0
1
2
1
1
0
1
1
1
1
2
0
0
1
0
1
1
1
2
1
1
1
1
1
0
1
2
0
1
2
0
1
1
1
0
0
1
1
1
1
1
1
0
1
1
0
1
1
2
1
2
1
2
1
1
0
1
0
1
1
1
0
0
0
2
0
0
1
0
0
1
2
2
0
1
2
1
1
1
0
1
2
1
1
2
0
0
0
2
1
1
0
2
1
1
2
0
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
0
1
0
1
0
1
1
0
2
2
1
2
1
0
2
1
1
1
1
1
0
0
0
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
0
1
2
1
1
1
3
1
2
0
0
1
2
1
0
2
0
2
0
1
1
1
0
2
1
2
1
1
1
1
1
0
2
1
2
1
1
0
2
2
0
1
1
1
0
1
2
1
1
1
1
1
2
1
0
1
1
2
1
1
1
0
0
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
0
0
1
0
1
1
2
1
4
1
1
1
0
1
1
1
2
1
1
2
2
1
2
1
0
2
1
2
1
0
1
2
1
1
1
1
0
0
1
2
1
2
1
1
2
1
1
1
1
3
0
1
2
0
0
0
0
2
2
0
1
1
1
0
1
2
1
1
2
0
1
1
2
1
2
2
1
2
1
2
0
1
1
2
0
1
1
1
1
2
2
1
1
1
1
1
2
1
1
0
1
2
1
2
1
2
2
2
1
0
2
1
0
0
1
1
1
1
2
1
1
0
1
1
1
1
1
1
1
0
0
1
3
2
1
2
1
2
2
1
1
1
0
1
1
4
1
1
1
0
1
1
2
1
0
2
0
1
1
1
1
2
1
0
1
1
0
2
2
2
1
1
2
1
0
1
1
1
1
2
1
1
0
1
2
2
2
2
1
1
1
1
2
0
2
1
1
1
1
1
1
2
1
1
2
1
1
2
1
0
1
1
1
0
1
0
0
0
2
2
1
1
1
1
2
2
0
1
1
1
2
1
2
1
0
1
0
1
1
2
1
2
0
2
2
2
0
2
1
1
1
1
0
1
1
2
1
1
2
0
2
1
0
0
0
0
1
1
1
1
1
1
1
1
0
1
1
2
1
1
1
1
2
0
1
1
2
1
1
1
1
1
1
2
2
1
3
1
1
2
2
0
0
0
1
0
1
1
0
1
1
1
1
1
1
1
2
2
2
0
2
0
2
2
1
1
0
1
1
0
1
0
2
9
7
2
1
1
2
1
1
1
0
1
0
1
1
1
2
0
1
1
2
2
0
0
1
2
0
2
1
3
2
2
2
1
0
1
1
1
1
2
1
2
1
1
1
2
0
2
2
1
1
1
1
1
1
0
1
0
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
2
0
1
0
0
1
2
1
1
2
2
1
6
1
1
1
1
1
1
0
2
2
2
2
0
1
1
1
2
1
1
1
2
1
2
2
0
1
1
2
2
2
2
2
1
1
1
1
0
0
1
1
1
1
2
1
1
0
0
1
0
0
1
1
1
1
1
2
1
1
1
1
1
0
0
1
3
1
2
0
2
0
2
1
0
2
1
2
2
2
1
0
1
0
1
1
1
1
2
2
1
1
0
0
1
0
2
1
1
1
1
2
0
1
1
1
2
1
2
2
2
1
1
2
1
0
3
2
1
2
1
0
1
1
0
1
1
1
2
0
1
1
1
0
1
1
1
2
0
1
1
0
1
0
1
1
1
0
1
1
1
0
0
1
1
0
0
2
1
2
1
1
0
1
1
0
0
1
1
1
0
1
1
0
1
1
1
1
1
0
1
1
2
1
1
1
1
0
1
2
1
0
2
1
1
1
1
0
0
0
1
0
2
1
0
2
1
0
0
1
1
1
1
1
2
1
1
0
1
1
1
1
2
1
1
1
1
1
1
2
2
0
1
1
0
2
1
0
1
2
0
1
1
0
1
0
1
1
1
0
1
1
2
1
2
1
1
1
1
1
0
1
1
2
2
2
0
1
2
3
0
2
1
0
1
1
1
1
1
0
0
0
1
2
1
0
2
1
1
2
0
1
1
1
0
1
1
2
0
0
2
1
2
1
1
1
1
1
1
1
2
2
1
1
0
0
2
1
1
1
1
2
2
1
2
2
1
1
1
2
2
0
0
2
0
0
1
1
2
1
2
1
2
1
1
0
1
1
1
2
0
2
1
0
1
2
1
0
0
1
1
2
1
2
1
1
2
1
1
1
2
1
0
1
1
1
2
1
1
2
2
1
4
2
2
1
2
0
1
2
2
1
0
1
1
2
0
1
1
1
1
0
1
2
2
1
1
1
1
0
1
1
1
1
1
1
1
1
0
1
2
0
0
0
1
1
1
1
0
1
1
1
0
1
1
1
1
1
1
0
1
1
2
2
1
1
1
1
0
1
1
0
2
0
1
0
1
1
1
1
1
1
0
1
1
1
1
0
0
1
0
1
2
1
1
1
1
1
1
2
1
1
2
1
0
1
1
1
2
1
1
0
2
2
1
1
2
2
2
1
0
1
1
1
1
1
1
1
2
2
0
1
1
2
0
1
1
1
1
2
1
1
2
0
2
1
2
2
1
2
2
0
0
1
1
1
1
1
1
1
1
1
1
1
1
0
1
2
2
1
2
0
1
1
1
1
1
1
2
1
0
2
2
2
1
1
1
2
1
0
1
1
1
0
2
1
1
2
1
1
0
0
1
1
2
1
0
0
1
0
2
2
2
2
1
1
2
1
2
1
2
1
0
1
1
1
1
1
2
1
1
2
1
2
2
1
1
1
1
1
1
1
2
1
1
1
3
2
1
0
1
0
1
1
1
1
1
1
1
0
1
2
1
1
1
1
1
1
1
1
1
1
1
0
1
0
0
1
1
1
2
2
1
1
0
1
0
1
1
1
1
2
2
0
1
2
0
2
0
1
1
0
1
1
1
2
1
1
2
1
1
2
1
1
0
1
0
1
1
0
1
1
0
1
1
1
1
1
1
1
1
1
2
0
2
2
1
1
0
1
2
0
2
2
0
1
0
1
1
2
1
0
1
1
0
0
1
0
0
1
2
1
1
1
0
2
1
1
1
1
1
1
1
1
0
1
0
1
1
0
1
1
2
1
1
2
0
2
1
1
1
1
1
1
1
0
1
1
0
1
0
1
0
2
1
1
1
1
1
1
2
0
2
2
0
1
0
1
1
1
1
1
1
2
1
1
0
1
1
2
1
1
1
0
2
1
1
2
1
2
1
1
1
2
1
1
1
1
1
2
2
1
1
1
2
2
1
1
1
1
2
1
1
1
1
2
1
1
1
0
0
1
0
1
0
1
1
2
1
2
2
1
1
1
1
1
2
0
1
1
0
1
1
2
1
1
1
2
2
1
2
2
1
1
1
1
1
0
2
1
1
0
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
3
0
0
2
1
1
2
1
1
0
2
0
2
1
1
0
1
1
1
0
1
1
1
0
2
1
2
2
1
2
1
2
2
0
0
1
1
1
1
1
0
2
1
1
2
1
2
1
2
1
1
1
0
1
1
1
2
2
1
0
2
1
0
1
1
1
1
0
0
1
1
0
1
1
1
2
0
1
0
0
1
2
0
2
2
1
1
0
1
1
0
1
1
0
1
1
1
1
1
1
2
0
2
2
1
1
0
1
1
1
1
2
1
2
2
1
0
1
0
1
2
2
1
1
1
1
1
2
1
0
1
0
0
1
1
0
1
0
1
0
0
2
1
0
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
0
0
1
1
0
0
1
1
1
1
1
0
1
1
1
0
0
1
2
1
1
1
0
2
2
0
1
2
1
1
2
0
1
1
1
1
0
1
5
0
0
1
1
0
2
1
0
0
1
1
2
1
1
1
1
2
1
1
2
1
0
2
0
1
0
2
1
0
2
1
1
2
5
2
1
2
0
1
1
1
2
1
1
1
0
0
0
1
2
2
1
1
1
1
1
1
1
1
1
1
0
3
2
1
0
1
1
1
0
1
2
1
0
1
2
1
4
1
2
1
1
2
2
2
1
1
1
1
1
1
1
1
2
2
0
1
1
0
0
1
1
1
2
0
1
0
1
0
1
1
1
2
1
1
1
1
1
0
1
0
1
1
2
1
2
1
1
0
2
1
1
1
0
2
1
1
0
2
1
1
0
1
1
2
1
1
1
1
1
2
1
1
0
1
0
0
1
2
1
2
1
2
2
1
2
1
0
1
0
1
1
0
2
1
1
1
1
2
1
1
1
1
0
1
2
2
1
1
1
0
1
1
2
1
1
4
1
0
1
2
1
1
1
0
2
1
1
1
2
2
2
1
1
1
2
2
1
0
1
0
1
1
0
1
1
1
0
2
2
2
1
1
1
2
1
0
0
2
1
0
0
0
0
2
1
1
2
1
1
1
2
1
2
2
0
1
1
1
0
2
1
1
0
0
1
1
2
1
0
1
2
1
1
1
1
1
1
1
1
2
0
1
1
1
1
2
0
0
2
1
2
2
1
0
2
2
2
1
0
1
1
1
2
1
1
2
1
1
2
2
1
1
2
2
0
1
1
1
1
2
1
1
0
0
1
1
1
3
1
1
1
1
1
1
2
2
2
1
1
1
1
2
1
1
2
1
1
2
1
1
1
3
1
1
2
1
0
0
1
1
1
1
1
0
1
1
1
1
2
1
2
1
2
2
2
2
1
2
0
1
1
2
1
1
1
1
1
1
2
1
1
1
0
1
1
2
1
2
0
1
0
0
1
0
2
0
1
0
2
1
1
2
1
1
1
2
2
1
1
1
1
2
1
2
1
2
1
1
1
1
1
0
0
1
2
0
0
2
1
1
1
2
1
2
1
1
1
2
0
1
1
1
3
1
1
0
1
1
1
1
1
1
1
0
2
1
1
1
5
1
1
1
1
1
2
0
1
1
1
1
2
1
2
2
1
0
1
2
1
1
1
1
1
0
1
1
1
2
1
1
1
1
2
0
1
1
1
1
1
2
1
1
0
0
2
1
1
2
1
1
1
2
1
2
1
0
1
0
2
1
0
2
2
0
0
0
1
1
1
2
2
1
1
1
1
2
2
1
1
1
1
0
1
1
1
0
1
0
0
1
1
0
2
2
1
1
1
1
1
1
1
1
1
2
0
1
1
1
1
1
1
1
1
1
1
1
1
1
2
4
0
0
2
1
1
1
1
1
1
0
1
0
1
0
1
1
1
1
1
1
3
0
1
1
1
1
1
2
1
1
1
1
1
0
0
1
1
1
2
1
0
2
1
1
2
1
2
1
1
1
0
1
0
1
0
1
1
1
1
1
1
0
1
2
1
0
1
1
1
0
2
0
1
0
1
1
0
1
0
1
1
1
1
2
1
1
1
1
2
1
2
1
1
0
2
2
2
1
1
1
0
1
2
1
1
1
1
1
1
2
0
1
0
1
1
1
1
1
1
1
1
2
1
2
2
1
1
0
2
0
1
1
0
1
2
1
2
1
1
0
0
1
0
1
2
2
1
0
2
1
1
2
2
2
1
0
2
0
1
1
0
0
0
1
1
1
1
2
2
1
1
1
1
1
1
2
1
1
1
0
1
1
1
1
1
1
2
2
1
1
1
0
1
0
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
0
0
1
2
1
2
1
2
1
1
0
0
1
0
1
1
2
1
1
1
2
1
2
0
0
1
0
0
0
2
1
1
1
0
1
1
2
0
1
1
1
1
1
1
1
1
1
0
1
1
0
1
1
1
0
1
1
1
1
1
0
1
1
0
1
1
2
2
1
2
1
3
1
2
0
0
1
0
1
0
2
1
1
1
1
1
2
1
2
1
1
0
1
0
2
1
1
1
1
2
1
2
0
2
2
0
1
2
3
1
2
1
1
2
1
2
2
1
0
1
2
1
1
1
1
2
1
1
2
0
1
0
2
1
2
1
1
2
1
3
1
0
0
1
0
1
1
1
0
1
1
2
0
2
1
0
2
1
1
2
1
2
2
1
1
2
1
2
0
2
2
1
1
2
1
1
1
1
1
1
1
0
0
1
1
1
2
1
1
1
1
2
1
1
1
0
2
2
2
0
0
1
1
2
0
0
1
1
1
0
1
1
0
1
1
1
1
1
0
1
1
0
1
1
0
0
1
2
0
1
1
2
1
1
1
0
0
0
1
1
2
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
0
0
0
2
1
2
1
1
0
0
0
0
3
2
1
1
1
2
0
2
0
1
1
1
1
1
0
3
1
1
1
2
1
2
1
1
2
2
1
1
2
1
2
1
2
2
1
0
2
1
1
0
1
2
2
2
0
2
2
1
1
0
1
0
1
1
0
1
1
1
1
1
2
3
2
1
1
0
0
1
2
0
1
2
0
2
1
0
1
1
1
2
0
1
0
1
1
1
2
2
2
1
0
1
1
1
1
2
1
1
1
1
1
1
0
0
2
1
1
1
1
1
1
2
1
1
1
0
0
0
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
2
1
1
2
0
1
2
1
1
1
1
0
1
1
0
3
2
2
0
0
1
2
1
0
2
1
1
0
1
0
0
1
0
1
0
2
0
0
1
0
1
1
2
1
2
1
1
0
2
1
0
1
2
2
1
1
1
1
2
1
1
2
1
2
1
0
4
1
1
2
1
2
1
2
0
1
0
1
2
1
1
2
1
1
1
0
2
1
1
1
1
0
2
1
1
2
1
1
2
1
1
1
1
1
0
1
1
1
0
1
1
1
0
1
1
2
1
1
2
1
0
0
1
1
0
1
2
1
1
0
1
1
1
2
1
0
2
2
2
0
1
1
0
1
1
1
0
1
1
1
1
2
2
1
1
1
0
1
0
0
2
1
1
0
1
2
1
0
1
1
1
0
1
2
1
2
1
1
2
2
1
0
1
0
1
1
1
1
1
1
2
1
2
1
2
2
2
1
1
2
2
1
1
1
1
2
1
2
1
2
1
1
1
1
2
0
1
1
2
1
3
1
1
1
0
1
0
1
1
1
1
1
1
0
1
2
2
1
1
0
2
1
1
0
1
1
0
2
1
2
1
1
2
0
2
1
2
1
0
1
1
2
3
0
1
1
1
2
1
2
2
0
0
2
0
2
2
1
1
2
2
0
1
1
1
2
1
1
1
1
0
2
1
1
1
1
1
2
2
1
2
2
2
2
2
1
1
1
2
1
1
3
1
1
1
1
1
0
1
1
1
1
1
2
0
0
1
1
1
1
0
1
1
1
1
0
1
1
1
1
1
2
2
1
0
1
1
0
2
1
1
3
1
1
1
1
1
0
1
1
1
1
1
2
1
1
1
1
1
0
1
2
2
1
1
0
0
1
0
1
0
1
0
0
1
0
2
2
1
0
2
2
1
2
1
1
2
1
1
1
1
0
0
2
2
1
1
2
0
1
2
1
1
1
2
2
1
2
1
1
1
1
1
1
1
2
2
1
1
1
2
1
0
1
1
1
1
1
1
1
0
1
1
1
2
1
1
1
1
1
2
1
0
1
1
1
1
1
1
1
1
0
1
1
0
1
2
0
1
1
1
2
2
1
2
0
1
1
1
2
1
0
1
1
1
2
1
3
0
1
1
1
1
2
1
1
3
0
1
1
1
1
1
1
2
1
1
1
2
1
1
0
1
1
1
2
2
1
0
1
2
2
2
1
2
1
2
2
1
0
1
1
2
2
1
2
1
1
2
1
1
2
1
0
2
0
1
1
1
0
1
0
0
1
1
1
1
1
1
0
0
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
2
1
1
0
2
2
2
2
1
0
1
1
2
2
0
1
1
0
1
1
0
0
1
1
1
2
1
1
1
1
3
2
1
1
1
1
0
0
0
1
1
3
2
2
2
2
0
1
1
1
0
1
2
0
2
1
1
1
1
1
1
2
1
1
1
1
2
2
0
1
1
2
1
1
1
0
1
1
1
1
0
2
1
1
1
1
1
2
0
1
1
1
2
2
2
2
0
0
1
1
1
2
1
1
2
2
1
1
2
2
1
1
1
2
1
0
1
1
1
0
1
0
1
0
2
1
1
1
0
1
1
0
1
1
2
1
2
1
2
1
2
1
1
1
2
0
2
1
2
1
1
2
1
1
2
1
1
3
2
0
2
1
0
1
1
1
2
2
1
1
1
0
1
1
1
1
2
1
1
3
2
1
1
0
2
2
1
1
2
2
0
1
0
1
1
1
1
0
1
2
1
1
1
0
1
2
1
1
1
1
2
2
1
1
1
1
1
2
1
1
2
2
0
1
2
2
1
1
2
1
0
0
1
1
1
1
1
2
2
1
1
1
1
2
0
0
1
1
1
1
2
1
0
0
1
2
1
1
1
1
1
2
2
1
1
2
1
1
1
2
1
1
0
2
1
1
0
1
1
1
1
0
1
0
1
1
1
1
1
1
0
0
2
2
1
2
1
1
1
1
1
1
1
1
1
2
1
2
0
1
1
1
2
1
1
1
2
1
0
1
1
2
2
1
1
2
2
1
1
2
1
1
2
1
2
2
1
1
2
1
1
0
1
1
2
1
1
2
2
1
1
1
1
1
0
2
2
1
1
1
2
2
0
1
1
0
1
1
1
2
1
1
1
2
1
1
1
2
2
1
0
1
1
0
1
1
1
1
1
2
1
0
2
1
0
1
1
0
0
1
1
1
1
0
4
2
2
1
2
1
1
1
1
1
0
1
2
0
0
2
2
1
1
2
1
2
1
2
1
1
3
0
2
2
1
1
2
1
1
1
2
2
1
1
1
1
2
0
1
1
1
0
1
0
1
1
2
1
2
2
1
1
1
1
1
1
2
2
1
0
1
1
1
1
1
1
2
1
0
1
1
1
1
1
0
2
2
1
1
1
2
0
1
1
1
1
2
1
1
1
1
1
1
1
0
2
1
1
2
2
1
1
1
1
1
2
0
1
1
1
1
1
1
0
1
1
1
1
1
2
1
3
1
1
0
1
1
1
1
1
0
1
2
1
0
1
1
1
1
0
1
1
1
1
1
2
1
1
0
1
2
2
1
2
2
2
1
1
0
1
0
1
2
1
0
1
0
1
1
2
2
1
0
1
1
2
1
0
1
2
0
0
0
0
1
0
0
2
1
1
1
0
2
2
0
1
0
1
1
1
1
2
0
0
2
1
1
0
1
0
0
0
1
1
2
1
1
1
2
2
1
1
2
1
1
0
2
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
0
1
1
0
1
0
1
1
1
0
2
1
1
1
1
1
1
1
2
1
0
3
1
2
1
1
1
1
1
0
1
2
1
0
1
2
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
0
1
1
0
2
1
0
1
2
1
0
1
1
0
0
1
1
0
0
0
1
0
2
1
0
1
2
2
1
1
1
1
1
1
2
0
0
1
2
0
0
1
0
1
1
0
0
2
2
1
0
1
1
1
0
1
2
1
1
1
1
0
0
1
2
1
1
1
1
1
1
0
1
2
2
1
0
0
1
2
1
1
1
1
2
1
0
1
1
0
1
1
2
0
2
1
2
1
0
2
2
2
1
1
1
2
1
1
1
2
2
0
1
0
1
0
1
1
2
1
1
1
1
1
0
1
1
2
1
1
1
1
1
0
1
1
1
2
0
2
1
2
1
2
2
1
1
1
1
1
1
1
0
1
1
2
1
2
1
2
2
0
1
1
1
0
2
1
2
0
2
1
1
1
1
0
0
2
2
1
0
1
1
1
4
0
2
1
1
0
1
1
2
1
1
1
1
1
2
2
1
2
1
0
2
2
0
1
2
1
0
0
1
0
1
1
1
1
1
1
0
1
1
2
1
1
0
0
1
2
1
2
2
1
1
1
1
1
1
1
1
2
0
1
0
1
1
1
1
2
1
2
1
1
2
2
2
1
1
1
1
0
1
0
1
2
1
1
2
1
1
2
0
2
0
1
1
3
1
1
2
0
1
1
1
2
2
0
1
2
2
1
1
2
1
2
0
2
1
0
2
0
0
1
1
1
0
1
0
1
0
1
1
0
1
2
1
0
2
0
0
1
1
2
0
3
0
2
1
0
1
1
1
1
1
2
0
2
1
2
0
1
1
1
0
2
1
1
2
1
1
1
0
1
1
1
1
0
1
0
3
1
2
1
0
1
1
2
1
1
1
2
0
0
1
1
1
2
2
2
1
0
2
2
2
1
1
1
1
1
1
1
1
2
0
1
2
1
1
1
2
1
0
1
0
2
1
0
1
0
1
1
1
1
1
3
1
1
1
0
1
1
1
0
1
2
0
2
1
2
2
1
1
2
1
1
1
0
0
1
1
1
2
1
1
1
1
0
2
1
1
2
1
1
1
0
3
1
2
0
3
1
2
1
1
0
1
1
1
0
1
1
1
1
2
0
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
0
2
2
1
1
0
2
1
0
2
1
2
1
2
2
0
0
1
1
1
1
2
2
1
2
1
1
0
2
1
1
0
2
0
0
1
1
1
2
0
2
1
0
1
1
2
2
2
1
1
1
0
1
2
1
1
0
1
1
0
2
0
1
1
1
0
1
1
0
0
0
2
1
1
1
1
2
1
0
1
2
0
1
1
1
1
1
2
2
2
1
0
2
1
2
1
0
1
0
2
0
1
1
1
2
1
0
1
1
1
2
1
1
2
1
1
1
2
1
1
2
1
2
1
1
1
1
0
1
1
1
0
0
0
2
2
1
1
0
1
2
1
2
2
0
1
1
1
0
0
2
2
1
1
1
1
2
2
1
1
1
0
1
2
1
0
1
1
1
1
1
0
1
2
2
0
1
1
1
2
1
0
1
1
1
2
1
2
2
1
2
1
1
1
2
0
1
1
1
1
1
0
0
1
2
1
0
2
1
0
1
2
1
1
1
2
1
0
2
1
1
0
1
1
2
2
1
0
1
1
2
1
0
2
1
0
1
1
3
1
0
1
0
1
2
1
0
1
1
2
1
1
1
1
2
1
1
1
1
1
0
1
1
1
1
1
1
0
1
1
1
1
1
0
0
1
1
2
1
1
1
3
1
2
1
1
1
1
1
1
1
1
2
0
0
0
1
2
2
1
1
1
1
2
1
1
1
2
1
1
1
2
1
1
0
1
0
1
2
3
1
1
1
0
0
1
1
1
0
2
1
2
1
1
1
1
1
0
2
1
1
2
1
1
2
2
2
0
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
0
2
2
1
1
1
0
1
0
2
2
2
1
2
2
1
2
1
0
1
0
2
1
1
1
1
1
2
2
0
1
0
2
1
2
1
2
0
2
1
2
1
1
0
0
2
1
2
1
1
0
2
1
2
2
1
0
1
2
2
2
0
0
1
1
1
1
1
0
1
1
0
1
1
1
2
0
0
1
1
1
2
1
1
1
1
1
1
1
2
1
1
2
2
1
3
2
1
1
1
1
1
1
3
1
1
1
2
1
1
2
1
2
1
0
1
1
1
2
0
2
0
2
2
1
0
1
1
1
1
2
1
0
1
2
1
1
2
0
1
1
1
0
1
1
0
0
0
1
0
1
1
1
1
0
1
2
1
1
1
1
1
1
0
1
0
0
1
0
1
1
0
2
1
0
1
2
0
2
1
2
2
1
1
1
1
2
1
0
0
1
1
1
0
1
1
1
2
1
2
2
1
1
1
0
1
2
2
1
1
1
0
2
1
1
1
1
1
1
1
1
0
1
2
1
2
1
1
1
0
2
2
1
1
1
1
1
2
0
2
0
1
2
1
1
1
1
1
1
2
0
2
0
1
1
1
0
1
1
1
1
1
1
2
3
0
0
1
1
1
1
1
2
1
2
1
1
0
1
0
0
0
1
1
1
1
0
1
2
0
0
2
2
0
0
0
1
2
0
2
0
2
0
0
2
2
1
1
1
1
1
1
2
1
1
1
1
1
1
0
2
1
2
2
1
1
1
2
0
0
1
1
0
1
1
0
4
1
1
2
0
1
1
1
1
1
0
1
1
1
1
0
1
1
1
1
1
1
1
8
1
2
2
1
1
1
1
1
0
1
2
2
1
1
2
1
1
2
0
2
2
8
1
1
1
2
2
1
2
1
1
1
2
2
1
2
0
2
0
2
1
1
1
1
0
2
0
1
1
1
1
1
0
1
1
2
1
1
1
1
1
0
2
1
1
1
2
0
1
1
1
1
1
1
2
1
0
0
2
1
0
0
2
1
1
0
0
1
2
1
1
1
1
0
1
1
1
1
2
1
2
2
2
0
2
0
1
1
0
2
1
1
2
1
1
1
2
1
1
2
1
2
1
1
1
1
1
0
0
1
0
1
2
0
1
2
0
1
0
2
2
1
2
0
2
2
1
1
1
2
1
1
2
1
2
1
1
1
0
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
0
2
1
0
2
1
2
2
0
1
1
0
2
1
0
0
1
2
1
2
1
1
1
2
2
1
1
2
1
1
1
2
2
2
1
1
1
2
1
0
2
2
2
2
1
2
0
0
1
2
2
1
2
2
2
1
2
1
2
2
2
1
1
1
2
2
1
1
1
1
2
1
1
2
0
2
1
0
0
2
1
1
1
0
1
1
1
1
0
1
2
1
3
2
2
0
1
2
1
1
2
2
1
1
1
0
1
1
0
1
1
0
1
1
1
1
2
2
1
0
1
1
1
1
1
1
1
1
1
0
1
1
2
1
0
1
1
2
0
1
1
0
2
0
1
1
2
1
2
2
0
1
1
0
1
1
1
1
1
1
1
1
2
2
1
2
1
1
3
2
1
1
0
1
0
0
2
0
1
1
1
1
1
1
1
1
1
2
1
1
1
0
2
0
0
2
1
1
1
1
2
2
1
1
2
2
1
1
1
2
1
1
1
1
1
0
1
1
0
0
1
0
0
2
0
1
1
1
1
1
1
2
2
0
1
2
2
0
1
1
1
1
1
0
0
1
3
0
2
1
1
1
1
2
1
1
0
1
0
1
0
1
1
1
1
1
1
2
2
1
2
0
2
2
0
1
1
1
1
0
2
3
1
1
1
1
1
2
0
1
1
2
0
1
1
0
1
2
1
1
2
2
0
1
1
2
2
1
2
2
2
1
0
1
1
1
1
1
1
1
1
1
1
2
1
2
3
1
1
0
1
1
2
2
1
3
1
1
2
0
1
1
1
0
4
0
0
2
1
1
2
1
1
2
1
1
1
1
0
1
2
2
1
1
1
1
1
1
0
1
2
0
1
2
1
1
2
1
1
1
1
2
1
0
2
1
1
1
1
1
2
2
2
1
2
1
1
1
1
1
1
2
1
1
0
2
1
1
0
1
1
1
1
1
2
0
1
1
2
1
1
1
2
2
1
1
0
1
2
1
2
0
1
1
2
2
1
1
2
0
1
1
1
1
0
0
1
1
0
1
2
1
0
1
2
1
1
0
0
1
1
1
2
2
1
0
1
0
1
3
1
1
2
2
1
1
1
0
1
2
1
1
1
1
1
1
2
0
2
1
2
1
2
2
2
1
0
1
2
0
1
2
1
0
1
1
1
1
1
1
1
1
2
1
2
2
2
1
1
1
0
1
1
2
1
1
1
1
1
0
1
0
1
1
2
2
1
1
1
1
1
1
1
2
1
2
0
1
1
0
2
0
0
0
1
2
1
2
1
1
2
0
0
0
0
0
1
1
1
2
0
1
2
1
2
1
0
1
1
0
1
1
1
1
2
1
0
2
2
0
2
1
2
2
1
1
2
1
1
0
1
1
2
1
2
1
1
0
1
2
1
2
1
2
1
0
2
1
1
1
0
1
0
0
0
1
1
1
0
0
0
1
1
2
1
2
1
1
1
1
1
2
2
2
1
1
1
2
1
1
1
0
1
1
1
1
1
1
2
2
1
0
1
1
1
1
2
0
0
1
1
1
0
1
0
1
2
1
1
0
2
1
2
1
0
1
1
2
1
1
1
1
0
2
1
1
1
1
2
0
2
2
1
2
1
1
1
1
0
1
3
1
1
1
0
2
1
2
1
1
1
1
1
1
0
1
0
1
1
0
1
1
0
2
0
1
1
1
1
0
2
2
1
1
1
0
1
1
2
2
1
0
2
2
2
1
1
1
2
1
1
2
2
2
1
2
0
1
1
0
0
0
1
1
1
0
1
2
1
1
0
2
1
2
0
1
1
0
3
1
2
1
2
1
1
2
1
2
1
1
0
1
1
1
0
0
2
0
1
1
2
1
1
1
1
0
0
1
1
1
1
2
2
1
1
1
0
1
1
0
2
1
0
2
2
1
2
1
0
1
1
2
2
2
1
1
1
2
1
2
2
1
2
2
0
1
1
1
1
1
1
1
1
1
0
2
1
1
1
1
0
1
1
1
1
1
2
1
0
1
1
2
1
1
1
2
1
1
0
2
2
1
1
1
1
1
0
0
0
1
1
2
1
2
1
1
1
2
1
2
1
1
2
0
2
0
0
1
2
1
1
1
1
1
2
1
1
0
1
0
2
1
2
1
1
1
2
1
2
2
0
0
1
0
2
0
1
2
0
0
2
0
2
2
2
0
1
1
1
1
1
1
1
1
0
1
2
2
2
0
2
2
1
1
1
0
2
1
1
1
2
1
2
1
1
1
1
0
2
0
1
1
1
1
2
1
2
1
1
1
0
1
1
1
1
1
0
3
0
1
2
1
0
2
0
2
0
1
1
2
1
2
0
1
1
1
2
0
1
2
1
0
2
1
1
0
1
2
1
1
2
1
1
0
1
1
1
2
1
2
0
1
0
1
1
0
2
1
1
1
1
1
0
0
2
2
1
1
2
1
1
1
1
0
1
1
2
2
0
0
1
1
1
1
1
0
1
3
1
0
1
1
1
1
1
1
1
2
2
0
2
1
1
1
1
0
1
1
0
2
1
1
1
1
1
1
2
1
0
2
1
1
2
2
1
0
1
1
1
1
1
2
1
2
0
0
2
1
1
0
1
1
1
1
0
0
2
1
0
0
1
0
1
0
1
0
1
1
1
2
1
1
1
1
1
1
0
2
1
1
1
1
0
1
2
1
2
2
1
2
1
0
2
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
2
1
2
1
1
2
1
2
2
1
0
1
1
0
1
1
2
1
2
0
0
1
1
1
1
1
1
2
1
1
0
0
1
2
0
0
2
1
1
0
1
1
1
1
1
1
1
1
1
0
2
1
2
1
0
1
1
1
1
2
2
1
1
1
1
1
2
1
1
1
0
1
1
0
0
1
1
1
1
1
3
1
1
1
0
2
0
1
2
1
2
1
2
0
2
5
1
0
1
2
0
1
0
1
1
0
1
1
1
0
1
2
2
1
2
1
0
1
1
0
0
1
1
2
1
2
1
2
0
0
2
0
2
0
0
1
1
1
2
1
1
2
4
1
1
2
0
0
0
1
2
1
2
0
1
1
2
1
2
2
1
2
1
0
2
0
1
1
1
1
1
2
2
2
0
1
0
2
2
2
1
0
0
1
1
1
0
2
1
2
2
1
0
2
1
1
1
0
2
1
0
2
0
1
1
2
0
1
2
1
1
1
1
1
0
1
4
1
1
0
1
0
1
1
1
1
0
2
0
1
2
1
1
1
2
2
1
0
0
1
1
1
1
1
1
2
2
2
2
2
1
0
1
1
0
1
2
0
1
1
1
0
0
1
1
1
1
0
1
0
1
1
1
1
2
1
0
2
2
1
1
1
2
4
0
2
0
1
0
1
0
2
1
1
1
1
2
1
1
1
2
1
0
2
2
1
1
2
0
1
0
2
2
2
2
1
2
2
1
2
1
0
1
1
2
1
1
2
2
2
2
0
1
0
1
2
1
1
1
2
2
1
1
1
0
1
1
1
0
2
1
2
1
2
0
1
1
1
2
1
1
2
2
1
1
1
0
0
0
1
1
1
1
0
2
1
1
1
1
1
1
1
1
0
0
0
2
0
1
0
0
2
1
0
1
2
1
2
1
1
1
0
0
2
1
0
2
1
1
1
1
1
0
1
1
1
2
1
2
1
1
1
2
0
2
1
1
0
1
1
1
1
1
0
1
0
1
2
1
1
1
1
0
1
2
2
0
0
1
1
0
2
1
1
1
1
1
1
0
0
2
1
1
2
2
0
1
1
1
1
1
1
0
1
1
1
2
1
0
0
0
2
2
1
1
0
1
1
1
0
1
2
1
1
1
1
1
1
1
1
2
1
1
1
0
2
1
0
1
2
1
3
1
0
1
2
0
0
1
1
1
1
0
2
0
1
0
1
1
1
2
1
1
0
1
0
1
1
1
2
1
1
1
1
1
2
0
2
1
1
0
1
2
1
1
4
2
0
1
1
0
0
1
0
2
1
1
0
0
2
1
1
2
1
1
0
2
1
1
0
1
0
1
1
0
1
1
1
1
2
1
0
1
0
1
2
1
1
1
0
1
2
1
1
1
1
1
1
1
1
0
0
2
2
1
1
1
1
0
1
1
1
1
1
1
1
1
0
1
0
1
0
1
6
1
1
1
2
0
2
1
1
1
1
1
1
1
0
0
1
1
0
2
1
1
1
2
1
1
1
1
2
0
1
1
7
1
1
2
2
1
1
1
0
1
1
1
1
1
0
1
0
1
0
1
1
0
1
1
1
0
1
2
2
2
2
1
1
1
0
1
1
1
2
0
2
2
0
0
1
1
2
1
1
1
2
1
2
1
1
1
2
0
1
2
1
2
2
2
1
1
1
1
1
1
1
1
1
2
1
2
2
1
1
0
2
1
1
0
0
1
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
0
1
1
1
1
2
1
1
0
1
2
1
0
1
1
2
1
1
3
1
1
1
0
0
0
0
0
1
1
1
2
1
1
1
2
2
0
1
0
2
2
2
2
1
1
2
1
2
1
1
2
1
1
2
0
1
1
1
1
3
1
1
1
1
1
2
2
1
1
2
0
1
1
0
0
2
1
1
1
0
1
0
3
1
1
1
1
1
0
2
1
1
1
1
1
2
1
1
0
1
2
1
2
1
2
1
1
1
2
1
1
1
1
0
1
2
1
2
0
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
2
2
1
1
2
0
1
1
0
1
1
0
1
1
1
1
2
1
1
1
0
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
0
1
2
1
1
1
2
0
1
1
1
2
1
1
1
1
1
1
1
0
2
2
2
1
1
1
1
1
0
1
1
1
1
2
0
2
1
1
1
1
0
3
2
2
1
2
1
1
1
0
2
2
0
1
1
2
2
1
2
1
0
0
0
0
1
1
1
0
0
0
1
1
0
1
1
2
2
1
1
0
0
2
2
1
1
1
1
1
0
1
1
1
1
2
1
1
1
1
1
2
2
1
1
1
1
1
2
1
2
2
1
0
2
1
1
1
1
2
1
1
2
1
2
2
1
1
1
2
1
1
1
1
1
1
0
0
1
1
1
2
3
2
2
2
0
0
1
2
1
2
1
1
1
1
1
1
1
0
1
3
2
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
0
1
2
1
1
1
0
2
1
2
1
1
1
0
1
1
1
2
2
1
0
1
1
0
3
2
0
1
2
1
1
1
2
1
1
2
1
2
0
1
1
2
2
1
1
1
1
2
1
1
2
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
0
1
1
2
0
2
1
0
1
1
1
0
1
1
0
1
1
0
0
1
1
1
2
1
1
2
0
1
1
0
2
1
2
1
2
0
1
1
1
4
0
2
1
0
1
2
1
2
0
2
2
0
2
0
2
1
0
1
0
0
1
1
2
0
1
1
1
1
2
2
0
0
2
2
0
1
2
0
2
0
1
1
1
2
0
1
2
2
1
2
2
1
2
2
2
2
1
1
0
1
1
0
0
2
1
1
1
1
1
2
0
1
1
1
1
1
2
1
0
1
1
1
1
2
1
0
1
0
0
1
1
1
0
1
1
1
2
1
2
1
1
1
1
0
2
2
2
0
1
2
1
1
0
2
1
0
0
0
1
2
1
1
2
1
1
1
1
1
2
1
2
2
0
1
1
1
2
1
2
1
1
0
0
1
2
1
2
2
1
0
1
1
1
1
1
2
0
0
1
2
0
1
2
2
0
1
2
1
1
1
1
1
2
1
1
2
0
2
1
0
1
2
1
2
1
1
1
2
1
1
0
2
2
1
2
1
1
2
1
1
1
0
2
1
1
1
2
1
0
1
2
1
1
1
1
1
1
1
2
0
1
1
1
2
1
2
0
2
1
2
0
1
1
1
2
3
0
0
2
0
1
0
1
1
2
0
1
2
1
0
2
0
1
1
2
1
1
2
1
0
0
0
0
1
1
0
1
1
2
2
1
1
1
0
1
0
1
1
0
1
1
1
1
1
2
0
2
1
1
1
1
2
0
1
1
1
1
2
0
1
1
1
1
2
0
1
1
1
1
1
1
0
2
0
1
1
1
2
2
1
1
0
2
1
1
1
1
1
0
2
1
0
2
1
1
0
1
0
0
0
1
0
1
1
1
2
0
1
1
1
2
2
1
1
1
1
0
0
1
1
2
1
1
2
0
1
1
2
2
1
0
1
0
1
2
0
1
1
1
1
1
2
1
1
1
0
2
1
1
1
1
2
1
1
1
1
1
2
1
1
1
0
1
1
2
1
1
2
1
1
2
3
1
0
1
2
1
1
1
0
0
0
1
1
1
2
1
1
1
2
0
2
2
1
2
1
2
1
1
1
2
0
2
2
0
2
1
1
2
2
2
1
2
2
1
2
1
2
0
1
2
2
1
0
2
1
1
0
2
2
1
1
1
2
1
1
1
2
1
1
0
2
2
1
2
1
1
1
1
1
1
2
0
1
1
1
1
1
2
1
1
1
0
1
1
0
2
1
0
1
1
1
2
1
1
1
0
1
2
1
1
1
1
2
2
0
1
0
1
1
1
1
1
1
0
0
1
0
1
1
0
0
1
1
1
1
2
0
0
1
2
1
1
1
1
1
1
1
1
1
1
1
0
1
2
1
2
0
0
1
1
1
0
1
2
1
1
1
0
1
2
0
1
1
2
1
0
1
1
1
1
1
1
1
1
1
1
1
0
4
1
1
1
2
1
2
1
1
1
1
1
2
2
1
2
1
2
1
2
2
1
0
1
1
1
2
2
0
0
1
2
1
0
1
1
1
2
1
2
2
2
1
1
1
0
1
1
1
2
0
0
1
1
1
1
2
2
1
1
1
1
1
0
1
1
1
0
2
2
2
1
1
2
2
1
1
1
1
1
1
1
1
1
0
2
1
1
2
1
1
1
2
0
0
1
2
1
1
1
1
1
2
1
1
1
1
2
1
1
2
2
2
0
1
1
0
2
0
2
0
1
1
0
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
3
0
1
1
1
0
0
1
2
2
2
2
2
1
0
2
0
1
1
2
1
0
0
2
1
2
0
1
0
1
1
0
1
2
2
0
2
2
0
1
1
2
1
0
1
1
1
2
2
2
0
1
0
1
2
1
1
1
2
1
1
1
0
2
1
1
2
2
1
0
0
1
1
3
1
2
0
0
1
1
1
1
0
0
0
1
0
1
2
1
1
0
2
0
2
1
2
1
2
1
0
1
2
1
1
2
0
2
0
0
1
2
2
1
1
1
2
1
1
1
1
2
1
0
1
0
2
1
1
2
1
1
1
1
1
1
1
0
1
2
1
1
1
1
2
1
1
2
1
1
1
1
0
0
2
1
1
1
1
1
2
1
1
1
1
1
2
0
0
1
1
1
2
1
0
0
2
1
1
2
2
1
2
2
0
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
0
2
1
1
1
0
1
0
1
0
2
2
0
2
1
2
0
1
1
1
2
1
0
0
1
0
0
0
0
2
1
1
1
1
1
1
0
2
0
0
2
1
1
1
1
0
1
1
0
1
1
0
1
1
0
0
1
1
1
3
2
1
1
0
1
0
1
0
0
2
2
1
1
2
1
1
1
1
1
1
2
1
1
0
1
2
0
1
0
0
2
2
2
1
1
2
2
1
1
1
2
0
2
0
0
2
1
1
1
0
2
1
1
1
1
1
0
2
0
1
1
1
0
1
2
0
0
1
2
0
1
1
2
2
1
1
2
1
1
0
1
1
1
1
1
1
2
1
1
1
1
0
2
1
1
1
1
1
2
1
1
1
2
2
1
0
4
0
0
3
0
2
1
0
0
1
1
1
0
1
1
1
1
0
0
1
1
2
0
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
2
0
2
1
1
1
0
2
1
2
0
1
0
1
1
1
1
1
1
2
1
2
2
1
0
1
1
0
2
0
2
1
1
1
2
0
1
0
1
1
2
2
2
1
0
2
1
1
1
1
1
2
1
1
2
0
2
1
1
1
2
1
1
1
0
1
1
2
2
1
2
0
1
2
0
1
1
1
1
1
2
1
0
1
1
1
1
1
2
1
1
1
1
1
1
0
1
0
1
2
1
0
2
0
1
2
0
1
1
0
2
1
1
1
2
1
1
2
1
1
1
0
1
2
1
2
0
0
1
1
0
1
1
1
0
1
2
1
1
1
0
0
2
2
1
1
1
2
2
0
2
2
0
2
2
2
1
1
1
1
1
0
0
1
1
1
2
2
0
1
1
0
0
1
1
1
1
4
1
1
2
1
2
1
1
0
2
0
2
1
1
2
0
4
3
0
1
1
1
0
1
1
1
2
2
0
1
1
2
2
1
2
2
1
1
1
1
1
1
1
0
2
1
0
2
2
1
1
0
2
1
2
1
1
1
1
1
1
1
2
1
2
1
1
2
0
1
1
0
2
2
0
1
1
0
2
0
1
0
1
1
2
2
0
0
0
1
1
0
0
2
2
0
1
0
1
1
1
1
1
1
1
2
1
1
2
0
1
2
1
1
1
0
2
1
1
1
1
0
0
4
1
1
2
2
1
2
0
1
3
1
1
1
1
2
1
1
1
2
1
1
1
1
2
2
1
2
1
1
0
2
1
1
2
2
1
0
0
0
1
2
0
2
2
1
1
1
0
1
1
1
2
2
2
1
0
2
1
1
0
1
5
1
0
0
1
1
2
1
3
0
2
2
1
0
1
0
1
0
1
1
1
1
1
2
2
1
1
1
2
1
1
2
1
1
1
1
2
0
1
1
2
1
1
0
2
0
1
1
0
1
2
1
2
1
1
1
1
1
1
1
2
2
0
1
0
2
2
1
2
1
2
1
1
0
1
0
1
1
2
1
1
2
0
2
0
1
1
2
1
0
1
0
1
1
1
2
0
2
2
1
1
2
1
1
2
1
1
2
0
1
0
1
1
1
1
0
2
1
2
1
1
1
2
0
0
0
0
2
2
0
1
1
2
1
2
0
1
2
0
1
1
1
2
2
1
2
2
1
0
1
2
1
1
1
1
1
1
1
0
1
1
1
1
1
0
1
1
2
1
1
2
2
1
0
1
1
0
1
1
1
1
1
1
1
1
2
1
1
1
1
0
1
1
1
1
1
1
2
2
1
0
1
1
2
1
1
0
0
1
1
1
1
1
1
2
0
1
1
1
1
1
1
1
2
1
2
2
0
1
1
1
0
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
2
1
1
2
1
1
0
1
1
0
1
1
2
1
2
0
1
1
1
0
1
1
2
1
0
1
1
1
1
1
1
1
2
1
2
1
1
0
1
2
1
1
0
1
1
1
2
2
1
1
0
1
1
1
2
2
2
1
2
1
1
1
2
2
1
0
1
1
0
1
1
0
0
0
1
1
0
0
2
1
1
0
1
1
1
1
1
2
2
1
2
1
2
2
1
1
1
0
1
0
2
2
1
1
2
1
1
0
1
1
1
0
1
1
1
2
2
0
1
1
0
0
3
1
1
1
1
1
0
0
1
1
2
1
1
0
2
1
1
2
1
1
2
1
1
1
2
1
2
1
1
0
1
2
0
0
2
1
0
2
1
0
1
0
1
1
2
2
9
1
2
1
0
1
2
1
1
1
2
2
1
1
1
2
0
1
1
1
1
1
1
2
0
1
1
1
1
1
0
0
1
1
2
1
2
1
0
2
0
1
2
1
0
1
1
1
1
2
2
1
1
1
2
1
0
1
1
1
1
1
0
2
0
1
2
1
0
2
1
2
1
0
1
1
2
0
2
1
2
1
1
1
1
2
1
2
1
2
1
0
1
2
2
1
0
2
1
1
2
1
1
1
2
0
0
2
0
1
1
1
1
1
1
1
1
1
2
0
1
2
1
1
1
1
0
2
1
2
2
1
0
1
0
1
1
0
1
2
0
1
1
1
1
2
0
1
2
1
0
1
0
0
1
1
1
1
0
1
1
0
0
1
0
1
0
1
1
2
1
1
2
1
1
1
1
2
1
1
0
2
0
1
2
2
1
2
1
1
1
1
1
0
1
5
2
1
1
1
2
2
1
1
1
1
1
1
1
2
2
1
1
1
2
1
1
1
0
0
0
0
1
1
1
1
0
1
1
2
1
1
0
0
0
1
1
1
0
1
1
0
0
2
1
2
0
1
0
2
0
0
1
1
1
1
2
1
1
2
1
1
0
4
0
0
1
1
2
0
1
1
1
1
1
1
0
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
2
1
1
1
2
2
2
2
1
2
0
1
0
2
1
1
0
2
0
1
0
1
1
0
2
2
1
2
2
1
0
1
2
1
1
2
1
1
1
1
1
2
4
1
2
0
1
0
1
2
2
1
2
1
2
1
0
2
0
1
1
2
0
1
0
1
0
1
0
1
2
1
2
2
2
1
2
1
1
1
1
1
0
1
2
1
0
0
1
1
1
0
1
1
2
1
0
1
1
2
1
1
1
1
2
2
1
1
0
2
0
2
0
1
1
0
0
0
1
1
0
1
1
2
0
1
0
0
1
1
1
1
1
1
2
2
1
1
1
1
1
0
2
1
1
0
2
1
1
0
2
0
0
1
2
1
1
1
1
0
3
2
1
0
2
1
1
2
1
1
1
2
1
0
1
0
1
1
1
0
1
1
0
0
1
1
1
1
1
2
1
2
0
0
1
2
1
1
0
1
2
2
1
1
2
1
0
1
2
1
1
0
1
1
1
1
1
1
1
1
2
1
0
1
0
2
1
1
1
1
2
1
1
1
2
1
2
1
0
1
1
1
1
0
0
1
2
1
1
1
1
2
1
2
2
0
1
1
2
2
1
1
1
2
2
1
1
1
1
1
1
0
0
1
1
1
1
2
2
1
2
1
2
2
0
1
2
0
1
2
1
0
1
1
1
1
1
1
1
1
1
1
0
1
2
1
0
1
1
1
1
1
2
1
2
1
1
1
0
1
1
1
0
2
1
1
1
1
1
1
1
1
1
1
1
0
2
2
0
0
1
1
0
1
1
0
2
2
1
1
2
1
0
1
1
2
0
2
1
1
1
1
0
2
1
2
2
1
1
1
2
1
1
1
0
1
0
1
1
2
1
2
0
0
0
2
2
1
0
0
0
1
1
0
1
2
1
2
0
1
2
1
1
2
1
2
1
0
1
3
2
1
1
1
2
1
1
1
0
0
1
2
1
1
0
1
2
2
1
1
1
0
1
1
1
1
1
1
2
1
1
0
1
0
0
1
2
2
2
2
1
1
2
1
1
0
2
1
1
1
3
1
2
2
1
0
1
2
1
2
2
1
0
0
0
1
1
1
1
2
1
1
2
2
2
1
1
0
1
1
1
1
1
1
1
1
1
1
1
0
1
1
0
1
1
1
0
1
1
1
1
0
1
2
0
2
2
0
1
0
2
2
1
0
1
1
0
1
0
0
1
1
1
2
2
1
1
2
0
2
1
1
1
1
1
0
1
1
1
1
1
0
1
1
1
0
1
1
1
0
0
1
1
1
2
2
0
1
2
0
1
1
1
2
1
0
1
0
1
1
1
0
1
0
1
1
2
2
1
1
1
1
1
5
1
1
1
0
1
1
1
1
1
2
1
2
0
1
1
0
2
1
0
2
2
0
2
1
2
0
1
1
1
0
0
1
1
1
1
1
0
1
1
1
0
1
1
1
1
1
1
1
1
0
1
1
0
1
1
1
0
3
1
0
1
0
0
1
2
1
6
0
1
2
1
0
1
0
1
1
1
1
2
2
2
0
0
1
2
0
1
1
2
1
1
2
1
1
1
2
0
1
0
0
2
1
2
2
1
1
2
0
0
1
0
2
1
1
1
1
2
1
2
1
1
1
1
1
1
1
2
2
1
1
1
1
2
1
1
2
1
1
1
2
1
0
2
1
1
1
2
1
1
1
0
2
1
2
1
1
1
0
2
1
1
1
1
0
1
1
0
1
0
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
0
1
1
1
0
2
1
1
0
1
2
0
1
1
0
0
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
0
2
1
1
1
0
0
1
1
0
0
2
1
1
1
1
1
1
2
0
0
1
2
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
2
2
0
1
1
2
2
2
1
2
2
0
2
2
2
1
0
2
1
3
1
0
0
2
1
1
1
1
1
0
1
2
1
1
2
1
2
1
2
1
2
0
1
1
2
2
0
1
1
1
2
0
1
1
1
2
1
1
2
1
1
2
1
2
0
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
3
2
2
2
2
1
1
0
1
1
2
1
2
0
1
0
0
1
1
1
2
1
1
0
1
2
2
0
2
1
1
0
1
0
0
0
2
0
1
1
0
1
1
0
2
1
0
2
0
1
0
1
0
1
0
2
1
0
2
1
1
1
1
2
1
2
1
1
0
1
2
2
0
2
1
2
2
2
1
1
1
1
1
0
2
1
1
1
1
1
2
0
0
1
1
1
1
2
1
1
2
1
2
2
1
2
2
2
1
1
2
1
1
0
0
2
2
1
1
2
1
2
1
2
1
1
2
2
2
0
3
1
1
2
1
1
1
1
1
1
0
1
2
1
1
2
2
1
2
1
0
1
1
1
2
1
1
2
1
1
1
1
1
1
1
0
1
3
0
1
0
1
2
1
2
1
2
2
1
1
1
1
2
0
1
2
0
1
1
1
2
2
1
2
1
0
1
1
1
2
0
0
0
1
1
1
1
1
1
2
1
0
1
2
1
1
0
0
0
1
2
1
1
1
1
1
1
1
1
1
2
1
1
2
3
1
0
1
1
1
2
2
1
0
1
0
1
2
1
1
1
1
2
2
0
1
1
1
0
3
1
1
2
2
1
1
1
1
2
1
0
1
1
1
1
0
1
1
1
2
1
1
0
2
1
2
1
0
2
2
1
1
1
0
2
1
1
1
0
1
1
2
2
2
2
0
1
2
0
1
1
1
4
1
2
1
2
1
0
1
2
1
1
2
2
1
1
1
1
2
1
2
0
1
1
1
0
1
1
1
1
1
1
1
1
1
1
2
2
1
0
1
1
1
1
0
1
0
1
0
0
1
1
1
2
1
2
0
1
2
3
1
2
1
2
1
2
1
1
2
1
2
1
1
0
1
1
1
1
1
2
1
2
1
2
1
1
1
2
2
0
1
1
1
2
1
2
1
1
0
0
1
1
1
1
0
2
1
2
2
1
0
1
1
1
1
1
1
2
1
2
0
0
2
1
1
4
1
1
0
1
0
1
2
1
1
2
2
1
1
2
0
2
1
1
1
0
1
1
1
1
0
1
1
0
1
1
0
0
1
1
1
0
1
2
1
1
2
1
1
1
1
1
2
0
1
1
1
1
1
1
2
2
1
1
2
1
0
1
1
2
1
1
2
0
1
1
1
0
1
1
1
1
0
1
0
2
1
1
0
1
1
0
0
2
2
1
1
1
0
1
0
0
1
1
0
1
1
1
0
2
2
1
0
1
1
1
1
1
2
1
1
1
0
1
1
2
0
1
2
1
1
1
2
0
1
1
1
2
2
1
1
2
0
2
1
1
1
0
0
0
1
1
1
1
1
1
0
1
1
1
1
0
1
1
0
1
1
1
1
0
1
0
1
0
1
1
2
0
1
0
2
1
0
2
2
1
1
1
1
1
2
0
1
1
1
1
1
1
0
1
1
1
2
0
1
2
1
0
1
1
2
1
1
1
2
1
1
0
1
1
1
1
1
0
1
2
0
1
1
1
1
1
1
1
1
1
2
0
1
1
1
1
0
1
1
2
1
1
0
1
1
2
1
1
1
0
2
1
2
1
1
0
1
1
1
1
1
1
1
1
2
0
1
0
1
2
1
1
0
1
0
1
0
1
1
3
0
2
0
0
1
1
1
0
1
1
3
0
1
1
0
1
1
1
1
2
1
2
1
2
1
2
1
2
2
1
1
1
1
1
1
2
1
0
2
1
1
1
2
2
1
2
0
1
1
1
1
2
2
1
1
1
1
1
1
2
0
1
0
1
0
0
1
1
0
2
1
1
2
2
0
1
1
0
1
0
1
1
2
1
0
1
1
2
1
1
2
1
1
1
1
1
0
2
0
1
1
2
1
1
1
2
1
2
1
1
1
2
1
0
0
2
2
0
2
0
1
1
0
1
0
1
0
2
1
2
1
1
1
1
0
1
0
1
1
1
2
1
1
1
1
1
1
1
0
2
2
2
2
1
1
2
1
2
0
1
1
1
2
1
1
1
1
0
2
0
2
1
2
1
2
1
1
0
1
0
1
1
2
1
1
0
1
1
0
1
1
1
1
1
1
1
2
2
1
1
0
3
1
1
0
0
2
0
1
1
1
0
1
1
0
0
2
2
2
1
1
1
1
0
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
2
1
1
2
1
1
1
2
2
2
1
0
2
2
0
1
1
0
1
1
2
5
1
4
1
0
2
1
1
0
1
1
1
1
1
1
1
1
0
1
2
1
1
1
1
1
1
1
1
1
1
2
2
1
1
0
1
0
1
1
1
2
3
1
3
0
1
2
1
1
1
4
1
0
2
0
1
0
0
0
0
0
1
1
1
1
2
2
1
1
2
0
1
2
2
1
0
1
1
1
1
1
1
2
1
1
1
2
1
1
2
1
1
0
2
1
1
1
1
1
1
1
1
1
2
0
2
1
1
2
1
2
1
1
0
1
2
1
1
0
1
1
1
1
1
2
2
1
2
1
2
1
1
1
1
1
1
2
2
1
2
1
0
1
2
0
1
1
0
1
2
1
1
0
1
0
1
1
1
0
0
1
1
4
2
0
0
1
3
2
1
2
0
1
1
1
1
1
2
1
2
1
0
1
0
2
1
1
1
2
1
1
1
0
2
1
1
1
1
0
1
2
1
1
0
1
1
1
1
1
1
2
1
1
1
2
1
0
0
1
2
0
1
2
1
1
0
1
1
1
1
1
0
0
2
1
1
0
2
2
0
1
1
0
1
1
1
0
1
1
1
2
1
1
2
0
1
1
2
0
1
2
1
2
1
0
2
1
1
0
0
1
1
0
0
0
1
1
0
2
1
2
1
1
1
2
2
1
1
1
2
1
0
1
1
1
1
1
1
1
1
1
2
1
0
1
0
1
1
2
1
1
2
1
0
1
0
1
1
2
2
2
1
2
1
2
1
0
1
2
1
1
2
2
1
1
2
2
1
1
1
0
0
1
0
1
1
1
1
1
0
1
1
1
1
1
2
0
1
1
1
2
1
1
1
1
1
1
0
1
1
1
1
0
1
2
1
1
1
0
0
2
1
1
2
2
0
1
1
2
0
1
2
1
1
1
1
1
1
1
1
1
1
0
1
0
1
0
1
1
2
1
0
2
1
1
1
1
0
2
1
2
2
1
2
1
2
1
0
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
2
0
1
1
1
0
1
1
1
2
2
0
2
0
1
2
1
2
1
2
1
2
1
1
1
1
2
1
2
0
0
2
1
0
1
1
1
0
1
1
0
1
1
1
1
1
1
0
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
1
0
1
1
1
2
1
0
2
2
1
1
1
2
0
1
2
1
1
1
1
0
1
1
0
2
1
2
1
2
1
2
0
2
1
1
1
1
2
1
1
0
0
1
1
1
1
0
1
0
1
1
0
1
1
1
0
2
1
2
1
1
1
2
1
0
1
1
1
1
1
3
2
1
1
1
1
0
2
2
0
0
0
2
0
1
1
1
0
1
1
2
1
1
1
0
1
2
2
0
1
1
1
1
2
0
1
2
1
2
1
2
1
1
1
2
1
1
1
1
1
2
1
1
1
1
0
1
1
2
1
1
0
1
2
1
1
1
2
3
2
0
2
1
1
1
2
0
2
1
1
1
0
2
1
1
1
1
1
1
2
2
2
0
0
1
1
1
0
2
1
0
1
2
0
1
1
0
1
2
2
2
1
0
0
1
0
1
2
1
1
1
1
1
2
1
2
0
1
2
0
1
1
2
1
1
1
2
1
0
0
1
1
1
2
1
2
1
1
2
2
1
1
1
2
1
0
0
1
1
1
2
0
1
1
1
1
0
1
2
2
2
1
1
1
1
0
1
0
0
2
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
2
0
1
1
1
2
2
0
1
1
1
1
0
1
1
1
1
1
3
1
1
1
2
0
1
1
1
1
1
2
0
0
1
0
1
1
1
2
2
1
1
1
1
0
1
1
1
1
1
2
1
0
1
0
0
1
1
1
0
2
1
1
1
2
1
0
1
1
2
1
0
0
1
1
0
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
0
0
0
0
2
1
1
0
2
2
0
0
1
1
1
1
1
0
0
1
2
1
1
1
2
1
1
1
1
1
2
0
1
1
1
2
1
0
1
1
1
1
1
1
1
2
0
1
2
1
2
1
1
2
0
1
1
1
1
1
2
1
1
1
2
1
1
0
1
1
2
2
1
1
1
1
1
2
1
1
0
1
2
1
0
1
1
2
0
1
0
3
1
2
1
1
1
1
1
1
0
0
1
1
0
2
2
1
1
1
2
0
2
0
0
1
1
1
1
1
1
1
0
1
1
1
1
1
1
2
1
2
1
1
0
1
1
1
1
2
0
1
2
0
2
1
0
1
0
1
1
1
1
1
0
1
0
1
1
0
1
1
1
0
2
2
1
1
1
1
1
0
1
1
1
1
2
2
1
2
0
0
1
1
1
1
1
1
1
2
1
0
1
2
2
1
1
1
0
1
2
1
2
1
1
0
1
1
1
2
2
1
1
1
2
1
1
1
1
1
0
1
2
2
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
0
2
0
1
1
2
1
1
0
1
1
1
1
1
2
1
0
1
1
1
1
1
1
1
0
1
1
1
1
1
1
0
1
2
1
1
2
1
1
1
1
1
1
1
2
1
1
2
2
1
1
0
0
1
2
2
0
1
1
2
1
1
2
2
1
2
1
2
2
2
0
2
1
1
2
1
1
1
1
1
1
0
2
1
1
1
1
1
1
1
0
1
0
1
2
2
1
1
1
1
2
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
3
2
1
2
0
1
2
1
1
0
1
2
1
2
1
1
1
0
0
0
2
0
2
2
2
1
1
0
0
1
1
1
2
0
2
1
0
1
1
1
2
4
2
2
1
1
1
2
1
1
1
1
1
2
2
2
0
2
2
0
1
1
1
0
0
1
1
2
0
2
1
1
0
1
0
2
1
2
1
2
1
1
1
1
2
0
2
1
1
1
0
2
0
1
0
2
1
1
1
0
1
1
2
1
2
1
1
1
1
1
1
1
2
1
2
1
2
1
4
1
1
1
1
1
2
1
2
1
1
1
0
0
1
1
1
2
0
0
1
0
2
1
0
0
1
1
1
1
1
1
1
2
1
1
2
0
2
1
1
1
1
1
1
2
2
1
1
0
0
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
0
1
2
1
1
0
2
1
2
0
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
0
1
1
1
0
1
1
1
1
1
1
1
0
0
1
2
2
1
1
1
2
1
2
1
1
1
1
1
2
1
2
1
1
2
1
1
0
1
1
1
1
1
1
2
2
2
1
1
2
3
1
2
1
1
2
0
1
0
2
1
0
1
1
1
1
2
1
1
1
0
1
1
1
1
1
2
2
1
1
1
1
0
1
2
1
2
1
0
1
1
1
1
1
1
1
1
2
1
0
1
0
0
1
2
2
1
1
1
1
1
2
2
1
1
1
1
2
2
1
0
0
1
1
0
2
0
1
0
1
1
2
2
1
1
1
2
1
2
1
0
0
1
1
1
1
1
0
1
0
2
0
1
0
1
1
0
0
1
2
1
2
1
1
2
2
1
1
2
1
1
1
2
1
2
0
2
1
1
1
1
2
1
0
1
2
1
1
2
2
1
0
1
2
0
1
1
1
1
1
1
1
1
2
1
2
1
2
0
2
4
0
2
2
1
0
2
1
1
0
2
1
1
1
1
0
1
2
2
2
1
1
1
2
0
1
0
1
1
0
1
1
1
1
1
0
1
2
1
2
0
0
1
1
1
0
1
0
1
2
0
1
2
2
1
1
1
0
1
1
2
1
1
0
1
1
1
1
1
1
1
1
1
0
0
1
0
0
0
1
4
1
2
0
1
1
0
2
1
2
1
2
1
1
1
1
0
1
0
1
1
2
1
2
1
1
1
1
1
2
1
2
2
1
0
1
2
1
2
1
1
1
1
1
1
0
0
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
2
0
0
1
1
2
1
0
1
2
1
0
2
1
1
1
1
1
2
1
0
1
2
0
1
2
2
0
1
2
2
0
1
2
1
1
0
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
2
1
2
1
1
1
1
1
1
2
0
1
0
0
2
0
2
1
1
0
1
0
0
2
0
1
2
1
1
1
1
1
1
2
0
1
0
2
1
1
2
1
1
1
1
1
1
0
2
0
2
1
0
1
2
2
1
1
1
0
2
1
1
1
1
1
1
2
2
1
1
0
0
1
1
0
0
0
0
1
1
1
1
2
2
1
2
1
1
0
1
1
1
2
1
1
1
0
2
0
1
0
1
1
2
2
1
1
1
1
1
2
2
2
1
0
1
2
0
0
1
0
1
2
1
0
2
2
1
1
0
2
2
1
2
1
0
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
0
1
2
0
1
1
0
0
1
1
0
1
2
1
0
1
1
1
1
0
1
1
0
1
1
1
4
1
0
0
1
2
2
1
1
0
1
1
1
2
1
0
2
1
2
1
1
1
1
2
1
0
1
1
2
1
1
1
1
1
1
1
1
0
1
0
1
2
1
1
1
1
1
1
2
0
2
1
1
0
1
2
0
1
1
2
2
1
1
1
1
1
0
0
2
1
0
1
0
2
1
0
2
1
0
1
2
1
1
1
2
0
1
1
2
2
0
0
0
1
1
1
1
2
0
2
1
1
2
1
1
1
1
1
2
1
0
1
1
1
1
2
1
1
0
1
2
3
2
1
1
1
1
2
1
1
2
0
2
1
1
1
0
1
1
1
3
1
1
1
2
1
1
1
1
1
1
0
1
0
0
0
2
0
2
2
1
2
1
2
1
2
0
2
1
1
2
1
0
1
1
1
1
2
2
1
1
1
2
0
1
0
2
1
2
1
2
2
1
1
1
1
2
2
1
0
1
2
1
1
1
2
2
1
2
2
1
1
0
1
1
2
1
3
1
1
1
1
1
2
1
2
0
2
1
1
1
0
1
1
2
1
1
0
0
1
2
1
1
1
2
1
1
2
1
2
1
1
2
0
0
1
1
1
2
2
1
1
1
2
0
1
1
1
1
0
2
1
1
0
2
1
1
1
0
1
0
1
1
1
0
0
1
1
2
1
2
0
1
1
2
1
2
1
0
2
2
2
1
0
1
1
1
2
1
2
1
1
2
1
0
1
2
2
1
2
1
1
0
1
2
1
1
0
1
1
1
2
3
1
1
1
1
1
1
0
1
1
0
0
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
0
0
2
1
1
1
0
1
1
0
2
1
2
2
0
2
1
1
2
2
2
1
1
1
1
1
1
0
1
0
1
1
2
1
2
1
1
1
1
0
0
2
0
1
1
2
0
1
0
0
2
0
1
1
0
1
1
1
2
1
0
2
2
2
0
1
2
1
1
1
2
1
2
2
1
2
1
1
1
1
1
1
2
2
2
1
2
1
1
2
1
1
1
2
1
1
1
2
1
0
1
2
1
2
2
1
1
1
2
1
2
3
2
1
1
1
1
1
1
1
1
2
1
0
1
1
0
1
2
1
2
2
1
2
1
1
1
1
2
1
1
0
0
1
2
1
1
2
0
2
1
1
2
1
1
0
0
0
1
2
1
1
0
1
0
0
0
1
2
1
1
1
2
0
1
0
2
1
1
0
1
1
1
2
2
2
0
1
1
1
1
1
1
1
0
2
1
2
1
3
1
0
1
1
1
1
1
2
1
1
1
1
0
1
0
0
1
1
1
2
2
1
1
3
1
1
1
1
0
0
1
1
1
2
1
1
1
1
1
2
2
1
0
1
0
2
1
1
2
1
1
0
2
1
0
1
1
1
1
1
2
1
1
2
1
1
1
0
0
1
1
1
1
1
3
1
1
1
2
1
0
2
1
2
0
0
2
1
1
1
1
0
1
1
0
1
1
1
0
1
1
1
0
1
1
0
1
1
0
2
1
2
2
1
1
1
1
0
1
2
0
0
0
1
1
1
1
1
1
0
1
0
1
1
1
2
0
0
1
1
1
0
1
1
2
1
2
1
2
1
2
1
1
1
0
0
1
1
1
2
1
2
0
2
1
0
1
1
0
2
1
1
1
0
2
2
2
1
2
1
1
1
1
1
1
1
2
4
1
2
2
1
1
1
1
2
1
1
2
2
0
1
2
1
0
4
1
0
0
1
1
1
0
2
1
2
1
0
2
2
1
1
1
0
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
0
1
2
2
1
1
1
1
1
1
1
1
1
1
0
3
0
2
2
1
2
1
1
2
1
1
0
2
2
2
1
2
0
0
2
1
1
2
1
2
0
1
1
1
1
1
0
1
1
1
1
2
1
1
2
2
1
2
1
1
0
2
0
1
0
0
1
1
1
1
2
0
0
1
1
5
2
2
1
1
1
1
2
1
2
2
1
1
0
1
0
1
0
2
1
1
1
2
0
2
2
2
1
1
0
1
1
1
1
1
0
1
1
1
0
1
2
1
1
1
1
1
1
1
1
1
0
1
1
3
2
1
1
2
2
1
1
1
1
1
1
0
1
1
1
2
2
1
0
1
0
1
1
1
2
1
2
0
1
2
1
1
0
2
1
2
2
2
1
1
1
1
2
1
1
0
0
0
2
0
2
3
1
1
2
2
2
1
0
0
2
2
1
1
2
1
1
1
2
1
1
1
1
0
1
0
1
1
0
0
0
2
1
2
1
1
0
1
0
1
1
1
2
1
1
2
0
2
1
1
0
1
2
1
1
1
0
0
1
1
2
1
1
2
1
1
1
1
1
1
1
0
1
1
1
1
1
4
1
2
1
2
1
0
0
1
1
0
2
1
1
0
1
1
1
1
2
1
1
2
2
0
1
0
1
2
1
1
1
1
2
1
1
3
1
1
0
1
1
0
1
2
1
1
0
0
1
2
2
1
1
1
2
2
1
1
1
1
1
1
1
2
2
1
2
1
0
2
1
1
0
1
1
1
1
2
2
1
1
1
0
0
1
1
2
1
1
1
1
0
0
1
1
1
1
0
0
1
1
1
2
2
1
1
1
1
1
2
1
1
1
2
0
0
2
0
2
0
2
1
1
1
1
1
2
1
1
1
2
1
2
0
0
1
1
1
1
0
1
1
1
1
1
0
1
2
1
2
1
2
1
1
1
2
1
1
1
1
1
0
2
1
1
1
1
1
1
1
1
0
0
2
1
0
1
1
0
0
1
2
2
2
2
1
1
1
1
0
2
1
1
0
0
0
1
1
1
1
0
1
0
1
2
2
1
1
1
1
0
1
1
1
1
1
1
1
1
2
1
0
1
2
0
1
1
1
0
1
1
2
1
1
1
1
1
0
2
2
2
1
1
2
1
1
1
1
1
1
2
2
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
2
1
2
2
3
2
1
1
2
1
2
1
1
1
0
1
1
2
1
1
1
2
3
1
1
1
1
0
0
1
2
1
0
0
1
1
1
1
1
0
0
1
1
1
2
0
2
1
2
1
1
0
3
1
1
1
1
0
1
1
1
1
1
1
1
2
2
0
1
1
2
2
1
1
2
1
2
2
2
1
2
1
1
2
0
1
1
0
1
1
1
2
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
0
1
2
1
1
1
0
1
1
2
1
4
1
1
1
1
2
1
0
2
1
0
1
1
1
2
1
0
1
1
2
2
1
2
1
1
2
2
2
1
2
1
1
1
1
1
1
1
0
1
1
1
2
0
1
1
1
3
2
1
1
2
1
1
2
0
1
1
1
1
1
1
1
1
1
1
2
0
2
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
0
1
1
1
1
1
1
2
0
1
1
1
0
0
1
1
1
2
2
1
0
2
2
2
2
1
1
2
2
2
1
2
1
1
1
2
2
1
2
2
1
1
1
2
1
1
1
1
1
0
1
0
1
1
1
1
1
2
1
1
1
0
1
0
0
0
0
0
1
2
2
1
1
2
0
1
1
0
1
0
0
1
1
1
2
2
1
3
2
1
0
0
1
2
2
2
1
2
2
1
0
2
0
0
1
2
1
1
1
1
0
2
1
2
1
0
0
1
1
1
2
1
1
1
1
1
1
2
0
2
1
0
1
2
2
1
1
1
0
2
2
2
1
1
1
1
2
0
0
0
2
1
2
1
2
1
1
2
1
1
1
1
3
1
1
2
0
1
2
0
2
2
0
2
2
1
1
0
0
1
2
2
0
1
1
2
2
1
1
0
1
1
0
1
0
0
1
2
0
2
1
2
1
0
1
1
1
2
0
1
0
2
1
1
1
1
0
1
0
0
1
0
1
2
1
2
2
3
1
0
2
0
1
2
1
0
1
0
2
2
2
0
1
1
0
1
1
0
1
0
1
2
1
1
1
1
0
1
1
1
1
1
1
1
1
2
1
1
1
0
1
0
1
1
0
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
2
1
0
1
2
2
1
0
1
2
0
0
2
1
1
2
1
2
1
1
1
2
2
1
0
2
1
1
0
1
0
1
0
1
2
1
1
0
1
1
1
0
1
1
0
1
2
1
2
0
1
1
1
2
2
0
2
1
1
1
1
1
2
2
1
0
1
1
0
1
1
3
2
2
3
0
1
1
1
1
1
2
1
0
2
1
1
1
1
1
0
1
1
0
1
1
2
1
0
2
1
2
0
0
1
0
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
2
1
2
0
1
1
1
1
1
0
2
2
1
0
2
1
1
0
1
2
1
1
1
1
0
1
2
3
0
1
1
2
1
1
2
2
0
1
1
1
1
2
2
1
0
1
1
1
2
1
1
1
1
2
1
2
2
1
0
0
1
1
1
1
0
1
0
1
1
0
1
1
1
1
1
1
2
2
1
1
1
1
0
2
2
2
1
2
1
2
0
0
0
1
2
1
2
1
1
2
1
2
2
1
0
2
1
0
1
1
1
2
1
0
2
1
1
1
1
2
0
0
1
1
0
0
2
1
1
1
1
1
1
2
2
1
1
1
1
2
1
2
0
2
1
1
2
2
0
1
1
1
1
1
2
2
1
1
0
3
1
2
0
1
0
1
0
1
0
1
2
1
1
1
1
2
0
1
0
2
1
1
1
2
1
1
2
2
2
1
1
2
1
1
1
0
1
0
2
1
0
2
0
1
1
1
2
1
1
1
1
1
2
0
1
1
1
1
0
1
1
0
1
1
1
1
2
1
0
4
1
2
1
2
1
1
0
2
1
1
1
2
2
1
2
2
1
2
1
1
2
1
0
1
0
2
2
1
2
1
1
1
0
0
1
0
1
1
1
0
1
1
2
1
1
2
0
1
1
1
2
2
1
1
2
1
2
2
1
1
2
0
2
1
1
2
2
1
2
1
0
1
1
1
2
1
0
2
1
1
1
1
1
0
1
2
1
1
2
0
0
1
1
1
1
1
1
2
2
0
1
0
0
2
0
1
1
1
2
2
2
1
2
2
1
0
2
1
1
1
2
1
2
2
2
1
1
1
0
2
1
0
1
2
1
0
1
1
2
2
1
1
2
0
1
1
2
2
1
1
1
1
1
2
1
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
0
1
0
1
1
0
0
1
1
1
2
1
1
1
0
2
1
1
0
1
1
1
1
1
2
1
2
1
2
1
1
0
0
1
0
1
2
1
0
1
2
1
0
1
0
0
0
1
0
1
1
1
2
1
1
1
1
2
3
2
0
1
3
1
1
1
1
1
0
1
1
1
2
0
2
2
1
3
1
1
1
1
1
2
0
1
0
1
0
1
0
2
0
2
1
0
2
2
0
1
2
2
1
1
0
1
0
2
2
1
1
1
1
2
1
0
1
0
1
0
2
1
0
2
1
1
2
1
0
1
0
2
2
1
1
0
1
2
1
1
0
1
1
2
0
1
0
1
2
2
2
2
1
0
1
2
0
0
1
1
2
1
1
0
1
1
1
0
1
0
0
1
1
0
0
1
1
2
0
1
2
1
1
1
2
2
1
1
2
1
2
0
1
1
1
1
1
1
2
1
2
1
1
2
2
1
0
3
1
1
1
1
1
1
0
1
1
1
1
2
1
1
1
1
2
1
1
0
2
2
1
2
1
1
0
1
2
1
1
2
1
2
1
0
1
0
0
2
1
1
1
1
1
1
1
1
1
0
2
2
2
0
1
2
1
0
2
0
1
1
1
0
1
0
1
1
2
2
1
1
1
1
1
2
2
0
2
1
2
1
1
1
1
1
0
1
0
2
2
2
1
1
1
2
0
1
2
1
1
2
1
2
2
1
0
0
2
2
2
1
1
2
1
2
1
1
2
1
2
1
0
2
2
1
0
1
0
1
1
3
0
0
2
1
2
1
1
1
1
1
2
1
1
1
2
2
1
1
1
0
0
1
1
1
0
1
1
1
2
0
1
1
1
1
1
1
0
2
0
0
2
1
1
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
3
1
1
2
0
1
0
2
0
1
2
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
2
0
1
2
1
2
0
0
2
1
2
2
1
2
1
1
2
2
2
1
1
1
1
1
1
1
2
2
1
2
1
0
0
0
1
0
0
2
1
1
1
1
2
1
1
2
2
1
1
1
1
0
0
1
10
0
0
0
1
1
2
0
1
1
2
2
0
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
2
0
1
1
0
1
1
1
1
1
2
1
1
2
1
1
1
0
1
2
1
2
0
0
1
1
1
2
1
1
1
0
1
1
1
2
1
1
0
1
0
1
1
1
1
2
2
1
2
1
1
2
0
0
0
2
1
0
0
1
2
2
2
1
1
0
2
2
1
2
1
1
2
1
1
1
2
1
1
2
1
1
2
1
3
2
2
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
2
0
2
1
1
1
1
2
1
1
3
1
1
1
2
2
1
1
0
1
1
0
2
1
1
1
0
1
1
2
0
1
1
1
0
1
1
1
0
1
0
0
1
1
1
2
2
0
2
0
1
2
2
1
2
0
2
1
1
0
1
0
3
2
2
0
0
1
1
1
0
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
0
1
0
1
1
1
1
2
1
1
1
1
1
2
1
2
2
2
1
1
2
1
1
1
1
1
2
1
2
0
0
1
2
1
1
0
1
1
2
0
1
1
0
2
2
1
2
1
2
0
0
0
1
1
2
2
1
0
0
1
1
2
1
2
2
1
1
1
1
1
1
0
1
1
1
1
1
0
0
0
1
2
1
1
1
1
1
1
1
1
1
0
0
1
1
1
1
1
0
1
1
0
1
1
1
1
1
1
2
0
1
1
1
1
0
0
1
2
1
1
2
1
2
1
2
1
1
1
1
0
2
2
1
2
1
1
1
1
0
1
0
1
2
0
1
0
1
1
3
1
1
1
1
1
1
1
1
2
0
1
2
1
1
1
0
1
2
3
2
0
1
2
2
2
1
1
1
1
1
3
2
2
1
1
0
1
1
1
1
1
1
1
1
1
1
1
2
2
4
1
2
0
0
3
1
0
2
3
1
1
0
1
0
0
0
0
0
1
1
1
1
1
1
1
0
1
0
1
0
2
1
2
0
1
2
1
1
1
0
0
2
0
1
2
0
1
1
1
0
1
1
1
2
1
0
3
1
1
0
1
1
1
1
1
1
2
1
2
1
1
1
2
1
1
2
3
1
1
2
2
0
2
2
1
2
0
1
1
0
0
1
2
1
2
0
1
2
1
1
1
0
1
1
1
2
1
1
2
2
1
1
1
2
1
0
1
1
1
1
2
0
1
1
2
3
0
2
1
1
1
1
2
1
0
0
2
1
1
1
1
1
2
2
1
1
1
0
2
1
1
1
1
2
1
0
1
1
1
0
1
1
1
1
1
1
1
0
1
1
1
1
0
1
0
2
0
2
1
1
1
1
2
0
1
1
1
1
1
1
2
1
1
0
1
1
2
2
1
0
1
2
1
2
2
1
1
1
0
1
0
0
1
2
1
0
1
1
1
0
2
0
1
1
0
2
0
2
1
1
0
2
1
1
2
1
2
1
0
1
1
2
0
2
1
1
2
1
0
1
1
0
1
0
1
1
1
2
0
0
1
0
2
1
2
1
1
1
1
1
2
2
2
1
1
1
0
1
1
2
2
1
0
0
1
0
1
1
1
0
0
1
2
2
1
1
2
0
2
1
1
1
2
1
2
0
1
3
0
1
2
1
0
2
0
1
2
2
1
0
1
0
2
0
1
1
0
2
0
1
1
1
0
1
0
1
1
1
0
1
1
0
1
1
1
1
0
1
1
1
1
2
1
1
1
1
2
1
1
0
2
1
2
1
1
2
1
1
1
1
1
0
1
2
2
1
1
0
1
1
1
2
1
0
1
1
1
1
0
1
1
1
1
2
1
1
2
2
1
1
0
1
1
0
3
0
1
1
1
2
1
0
1
1
1
1
2
1
2
2
1
1
1
1
1
0
0
2
1
1
0
2
1
2
2
1
1
1
2
2
1
2
2
1
2
1
2
1
1
2
0
0
0
1
1
1
0
1
1
1
1
0
1
0
1
0
1
0
1
2
2
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
0
1
0
0
2
0
0
1
1
1
1
1
1
1
0
2
1
2
1
1
1
1
1
2
0
1
1
1
0
1
1
2
2
0
2
2
2
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
0
0
1
2
1
2
0
2
1
0
1
1
0
1
1
1
1
2
1
2
1
1
2
1
1
2
1
0
1
1
2
0
0
2
1
1
2
1
0
1
2
1
1
1
0
1
2
2
1
1
1
1
2
2
1
2
0
1
1
1
1
1
1
1
0
1
2
2
1
1
2
2
1
1
2
1
0
1
2
1
2
1
0
1
2
1
1
1
1
2
1
0
1
1
2
2
1
1
0
2
1
0
1
1
1
2
1
1
1
1
1
1
2
1
6
0
2
1
2
1
2
2
0
1
1
2
1
2
1
1
0
0
1
2
0
0
0
2
1
0
1
0
1
2
0
1
1
2
2
2
1
1
0
1
1
2
1
1
2
0
1
2
0
1
1
2
2
1
2
2
1
2
0
1
1
1
1
1
1
1
0
1
2
1
1
0
1
1
1
0
1
0
1
1
1
1
1
2
1
2
1
2
2
1
1
0
1
1
2
1
1
1
1
1
1
2
2
0
2
1
1
1
2
1
1
1
2
2
1
0
1
0
1
1
0
1
1
2
1
1
1
2
2
1
1
1
1
1
1
2
0
0
2
1
1
1
0
1
0
1
1
2
1
1
2
1
0
1
1
0
0
1
2
1
1
0
1
3
0
1
2
1
2
1
1
1
0
0
1
1
2
1
2
1
1
1
1
2
1
1
1
2
0
1
2
3
2
0
1
0
1
1
2
0
2
1
1
1
1
2
0
2
2
1
1
1
1
1
0
2
1
1
1
1
1
0
0
1
1
1
1
2
2
1
1
2
1
2
0
1
1
1
1
1
1
2
1
0
2
1
0
2
1
0
0
1
1
2
1
1
1
1
0
0
0
2
0
1
3
2
1
1
2
0
2
1
0
1
2
1
1
1
1
1
0
1
1
1
2
1
1
1
0
1
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
2
2
1
0
0
1
1
1
1
0
0
1
1
1
1
1
1
0
1
0
1
1
0
1
2
1
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
2
1
1
1
1
0
1
3
0
1
1
1
0
1
0
0
1
1
1
0
1
2
2
1
1
2
0
1
1
0
1
0
2
2
1
1
1
1
0
2
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
0
0
0
1
1
1
2
0
3
1
1
1
1
1
0
1
2
0
0
1
2
1
1
1
1
1
2
1
2
1
2
2
0
0
1
0
1
0
2
0
1
1
1
1
1
1
1
2
0
2
2
1
2
1
1
1
0
2
2
2
0
2
0
1
0
2
0
0
1
1
1
2
1
1
0
2
1
1
2
1
0
2
1
0
1
1
1
1
1
1
1
1
2
0
0
2
0
1
1
1
1
2
1
1
1
2
2
1
1
2
0
1
1
2
2
1
1
1
1
1
1
2
2
2
1
1
1
0
2
1
1
1
0
2
1
0
1
1
2
1
0
1
1
0
1
1
0
1
2
2
1
2
2
1
1
1
1
1
1
0
0
3
2
2
2
1
1
1
1
2
2
1
0
2
1
1
1
1
2
2
1
1
1
1
1
1
1
0
2
1
1
2
3
1
2
2
0
0
1
1
1
1
1
1
1
1
1
1
1
1
0
1
2
1
0
1
2
1
1
2
1
1
1
1
2
1
0
2
2
1
2
2
2
1
1
1
1
2
1
1
0
0
2
2
1
1
1
1
1
0
1
0
2
1
1
1
1
2
1
1
1
2
1
2
0
1
2
2
1
0
2
1
1
1
2
1
1
1
0
0
0
0
1
1
1
2
1
1
1
1
1
1
1
2
0
2
2
0
1
1
1
2
1
1
2
1
1
1
2
1
1
0
2
0
0
2
0
1
0
1
1
1
0
1
1
1
0
1
2
2
1
1
1
1
1
0
0
1
1
2
1
0
1
0
1
1
1
2
1
1
2
1
0
1
1
0
1
1
1
1
1
1
0
1
0
1
1
1
0
1
2
1
1
0
1
1
1
1
1
0
1
2
1
2
1
2
1
2
2
2
1
0
1
0
1
1
1
2
1
2
2
1
2
2
0
1
0
1
1
1
1
2
0
1
2
0
1
1
2
1
0
1
3
0
1
1
0
2
1
1
2
1
2
1
2
1
2
1
2
2
2
1
2
2
1
1
0
0
1
2
1
1
1
1
2
1
1
1
1
2
1
2
1
1
2
1
2
2
0
2
1
1
0
1
3
0
1
1
1
1
1
1
0
0
0
1
1
1
1
0
1
1
2
1
1
1
2
0
1
2
0
2
0
0
1
1
0
2
1
1
2
1
0
0
2
1
2
2
0
1
2
0
1
0
1
1
1
2
1
1
1
1
1
0
0
2
1
1
0
1
1
1
2
1
0
1
2
1
1
1
0
1
1
2
2
1
1
2
2
1
2
1
2
4
1
1
1
2
1
0
2
0
3
1
1
3
2
2
0
0
0
2
0
1
0
2
1
1
2
1
0
2
0
2
1
1
2
0
1
1
3
1
1
1
2
1
0
1
1
1
1
2
2
2
0
1
2
1
1
1
0
1
0
1
2
1
0
1
1
0
0
0
0
2
1
2
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
0
1
2
1
1
2
1
1
1
1
1
1
1
0
1
2
1
2
0
1
0
2
0
1
0
1
0
1
1
1
1
1
4
2
2
2
1
1
1
1
2
2
1
1
1
0
1
1
1
1
2
1
0
1
1
1
1
0
1
2
1
1
1
1
1
0
0
2
1
1
0
0
1
2
1
0
1
1
1
1
0
0
0
1
1
0
1
0
1
1
1
0
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
2
2
0
1
0
1
2
1
0
0
1
1
1
1
1
2
0
2
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
1
1
1
0
1
1
1
2
2
1
2
1
1
2
1
1
1
1
2
2
2
1
1
1
1
1
2
2
1
1
2
2
0
1
1
2
2
0
1
2
1
1
1
0
1
1
0
0
1
1
1
2
1
1
1
0
1
0
0
1
1
1
1
1
1
2
1
1
2
1
1
2
0
0
1
1
1
1
2
2
2
2
1
1
1
0
2
1
2
1
1
2
0
2
1
1
0
1
1
1
1
2
1
2
1
1
1
0
1
1
2
0
1
2
1
0
1
2
1
1
1
1
0
2
2
1
5
0
1
2
1
1
0
1
1
1
2
1
1
0
1
2
1
1
1
1
1
2
1
1
1
0
1
2
2
0
1
1
2
1
2
2
1
1
0
1
1
0
1
1
1
1
0
1
2
1
2
1
0
2
1
1
0
1
1
1
1
2
1
2
1
1
1
2
0
0
1
2
1
0
1
2
1
1
1
1
1
0
2
2
1
2
0
2
2
0
0
1
0
1
0
0
1
0
1
1
1
1
1
1
2
1
1
1
2
1
1
2
0
0
1
0
1
0
2
1
1
0
1
1
1
1
2
1
0
1
2
1
1
1
1
1
1
2
1
1
1
1
1
0
1
1
1
1
2
2
1
1
2
1
1
1
1
0
2
0
1
1
0
1
1
2
1
1
3
1
2
2
1
3
1
0
2
1
1
0
1
1
1
2
0
2
0
2
1
1
2
2
3
2
2
1
2
2
2
1
1
1
2
1
1
0
0
0
1
0
1
2
1
1
1
2
2
1
2
1
2
0
1
0
1
1
0
1
1
1
1
2
1
2
1
0
1
2
2
1
0
1
1
1
1
2
0
1
0
1
1
2
0
0
1
1
2
1
1
1
2
1
1
2
0
0
0
0
0
0
0
2
1
0
1
1
1
1
2
1
1
1
1
1
1
0
1
2
1
1
1
1
1
1
3
1
1
1
1
0
2
1
2
2
1
1
1
2
1
1
1
2
2
1
0
1
1
2
2
0
0
1
0
1
2
1
1
1
1
1
2
1
1
1
1
1
2
2
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
0
0
1
0
2
1
1
1
2
1
1
1
1
2
2
0
1
1
2
1
1
1
2
0
1
1
2
2
1
1
2
2
1
1
0
1
1
1
0
1
1
2
0
2
1
2
1
1
1
1
1
2
2
1
2
1
1
1
1
0
1
1
1
1
0
2
2
0
2
2
1
0
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
0
0
1
0
2
1
1
1
1
1
0
4
1
1
1
0
1
0
1
1
2
2
1
1
1
0
1
1
2
0
0
0
2
1
1
1
1
2
2
1
1
0
1
1
1
1
2
2
2
1
0
1
0
1
0
1
1
1
0
1
1
2
0
1
0
1
1
1
1
2
1
1
2
1
1
2
1
2
1
2
1
0
0
1
1
1
1
0
1
1
0
1
0
2
1
1
2
1
2
1
1
1
1
1
0
1
1
2
1
1
2
0
1
1
1
1
1
1
1
1
1
1
1
2
1
0
1
1
2
1
1
1
1
1
1
1
0
1
2
1
1
1
1
0
1
2
1
0
0
1
1
1
1
1
1
1
1
2
2
0
1
1
0
0
1
0
1
2
0
2
0
1
1
1
0
0
1
2
2
0
2
1
1
0
2
1
1
0
1
2
2
1
2
1
0
2
2
2
1
1
2
2
2
0
0
1
1
2
2
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
0
2
0
1
1
1
0
0
1
1
1
1
1
2
2
1
1
1
1
2
1
1
1
2
2
1
1
1
0
1
1
0
1
2
1
2
1
1
1
1
0
2
2
1
1
1
1
1
0
0
0
1
0
2
2
1
2
0
1
0
0
2
0
1
0
1
1
0
1
1
1
2
1
0
2
0
1
1
2
1
0
1
0
1
1
2
1
2
2
1
0
2
0
1
2
1
1
0
0
1
1
2
0
1
0
0
0
1
1
1
2
2
1
2
1
1
1
1
1
2
1
1
1
0
1
1
2
1
1
1
1
2
0
1
0
2
2
2
1
2
1
1
0
1
2
1
1
1
0
1
2
1
1
0
1
1
1
1
0
1
2
2
1
2
2
0
1
2
1
1
1
3
1
1
1
1
2
1
2
1
1
0
0
2
0
1
1
0
1
1
0
1
2
1
2
2
0
1
2
0
2
1
1
1
1
1
2
1
1
0
0
1
1
2
0
1
1
2
0
1
2
1
2
1
1
2
1
1
2
1
0
1
1
1
1
2
1
0
0
1
0
1
1
1
1
1
1
0
1
1
1
1
0
0
0
1
0
1
1
1
2
2
2
2
0
2
0
1
1
0
2
1
1
2
2
0
2
1
1
0
0
1
2
0
1
1
1
2
1
2
0
1
0
1
2
0
0
1
1
1
2
1
2
1
2
0
0
1
1
0
1
0
1
1
1
2
2
2
2
2
0
1
2
2
0
1
2
0
1
1
0
1
1
2
2
0
1
1
3
1
2
1
2
2
1
1
2
0
1
1
1
1
1
1
1
1
2
1
0
1
0
1
1
1
1
0
1
0
1
2
1
1
2
2
2
2
0
0
2
2
2
1
2
1
2
1
0
0
1
2
0
1
0
1
1
1
1
0
2
1
1
1
2
1
2
1
2
1
0
1
1
1
1
0
2
2
1
1
2
2
2
1
2
2
1
1
1
1
0
1
1
0
2
1
1
1
1
0
2
1
1
1
1
2
2
1
2
1
3
2
1
1
1
1
1
1
1
1
1
2
1
0
1
1
1
0
2
0
0
1
1
1
1
1
1
2
1
1
2
1
0
0
0
0
2
1
2
1
1
2
2
2
1
1
0
0
2
2
1
1
1
0
0
1
1
0
1
1
2
0
1
1
2
1
0
2
1
2
1
0
0
1
1
1
1
2
1
1
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
0
1
1
2
2
2
0
1
0
1
1
10
1
2
0
2
1
2
2
1
2
1
1
1
1
1
1
1
1
2
1
0
0
1
1
1
1
1
1
1
2
1
1
2
2
1
2
0
1
1
1
0
2
1
2
2
1
2
1
1
0
0
0
0
2
1
0
1
3
1
1
1
1
2
1
2
1
0
1
0
1
1
2
1
1
0
1
2
0
2
1
0
2
3
1
1
1
1
1
2
1
1
0
1
1
2
2
0
0
1
1
1
1
0
1
0
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
0
2
0
1
1
1
1
1
2
0
1
0
0
2
1
0
2
1
2
1
2
1
2
0
1
2
1
1
1
1
1
1
2
2
1
1
1
0
1
1
1
1
0
0
2
0
0
1
1
2
1
2
0
1
1
0
2
0
0
0
2
0
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
2
1
0
2
2
1
1
0
1
2
1
0
1
1
1
1
1
2
1
0
0
0
2
1
1
1
0
1
0
1
1
1
1
2
0
1
2
0
1
0
0
1
1
2
1
1
1
1
1
1
1
0
1
1
0
1
1
1
1
1
0
2
2
1
2
1
0
2
1
1
1
2
1
1
2
1
1
1
2
2
0
0
0
0
1
1
1
1
2
1
0
1
0
1
2
1
1
1
1
2
1
0
0
0
2
2
1
1
1
2
1
1
3
1
0
1
1
1
2
2
1
2
1
0
1
0
1
2
3
2
1
2
1
3
1
0
1
1
1
2
1
1
1
0
3
1
1
2
1
1
1
0
1
1
1
0
0
1
0
1
1
1
1
2
2
0
0
1
1
2
1
1
1
0
1
2
2
1
1
2
1
2
1
1
0
1
2
1
1
1
1
1
1
2
2
1
2
1
1
0
2
2
1
1
0
1
1
1
0
2
2
0
2
0
2
0
2
0
1
0
0
0
1
1
1
2
1
2
1
0
2
1
2
0
1
2
2
1
0
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
1
1
0
2
0
0
0
0
2
1
2
1
1
1
1
1
1
0
1
1
2
1
0
1
2
2
5
1
2
1
1
2
1
1
2
2
0
3
1
0
1
1
1
1
1
2
1
2
0
0
1
1
2
1
1
1
0
2
1
1
2
2
0
2
1
2
1
1
1
1
2
1
0
1
1
1
1
1
1
1
1
1
1
1
2
3
2
1
1
1
1
1
1
2
2
1
0
1
1
1
1
1
1
1
1
1
0
1
2
1
1
2
1
2
1
1
1
1
0
1
1
1
0
2
1
2
2
1
1
0
1
0
1
2
1
1
1
2
2
1
2
1
0
1
1
2
0
1
0
0
2
2
1
1
1
0
0
0
1
2
1
1
1
2
1
1
1
2
1
0
0
0
1
1
1
1
1
0
0
1
1
1
1
1
2
0
2
0
1
0
1
2
2
0
2
0
2
0
2
1
1
1
1
1
0
2
1
1
1
0
0
1
1
1
1
1
1
0
1
1
1
0
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
0
0
2
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
0
1
2
1
2
1
1
2
1
2
1
1
0
1
0
2
1
0
1
2
1
1
1
1
1
1
0
1
1
1
2
1
1
2
0
2
0
1
0
1
0
1
2
0
1
0
1
2
1
1
1
1
2
2
1
1
1
1
1
1
1
0
1
2
2
2
2
0
1
1
1
1
1
2
1
0
1
2
2
2
2
2
0
1
1
1
1
1
0
2
1
1
1
2
2
1
1
1
1
2
2
1
0
1
1
0
0
2
1
0
1
1
2
1
0
1
1
2
1
0
1
0
1
2
2
0
0
1
0
2
0
1
1
1
1
1
1
1
1
1
0
1
1
0
0
2
2
1
1
1
2
0
2
1
0
1
2
2
1
2
1
2
1
1
1
1
2
2
1
1
1
2
1
0
0
0
1
1
0
1
1
1
1
0
2
2
2
1
0
2
2
2
2
2
1
2
1
1
2
1
2
1
2
2
1
1
1
2
2
0
1
1
2
2
1
1
1
0
1
0
0
2
2
1
1
1
1
1
2
0
0
1
0
2
2
2
1
2
2
1
1
0
1
2
1
0
0
0
1
3
0
1
1
1
1
0
2
1
1
1
0
2
1
1
1
1
1
1
0
1
2
0
2
1
2
0
2
1
0
2
1
2
2
2
1
1
1
0
1
1
1
1
1
0
1
1
0
2
1
2
1
0
1
0
1
0
1
0
2
1
1
1
1
1
0
0
2
0
2
1
1
0
1
1
1
2
1
1
0
1
0
1
1
0
1
1
0
0
0
0
1
1
1
2
0
1
1
1
1
1
0
1
1
2
1
1
1
0
1
2
1
2
2
0
1
1
1
1
2
1
1
1
2
1
1
0
0
2
1
1
1
1
0
1
0
0
2
1
2
2
1
1
2
2
1
1
1
1
1
0
1
1
1
1
2
1
1
2
2
2
1
1
1
1
2
2
2
1
1
2
1
1
1
1
1
1
0
1
1
2
1
1
1
1
0
2
0
1
1
0
2
1
1
1
1
0
2
1
2
1
1
2
1
1
1
1
1
1
0
1
1
1
1
1
2
1
0
2
1
2
1
2
1
1
2
1
0
2
1
1
1
1
1
1
1
1
1
1
1
3
1
1
1
0
1
1
1
2
1
1
2
1
1
0
0
1
1
2
1
0
1
1
3
2
1
1
1
1
2
0
1
1
0
2
1
1
1
1
1
1
1
1
2
0
2
1
1
1
0
2
1
1
1
1
1
1
1
1
0
2
0
1
0
2
0
4
2
1
2
1
0
2
1
1
1
3
1
1
2
1
2
2
1
2
1
2
2
2
1
0
1
0
2
1
2
2
1
1
1
1
2
2
0
1
1
1
1
1
1
0
0
1
0
1
1
1
0
1
1
1
1
2
1
0
1
0
0
1
2
2
2
1
2
1
2
1
1
1
2
2
1
1
0
1
2
1
2
1
1
1
1
1
2
1
1
2
0
1
1
1
1
1
1
2
1
1
1
0
0
1
1
1
2
0
1
0
1
1
1
1
0
2
2
1
1
2
1
1
0
1
1
1
1
2
1
1
2
2
2
1
1
2
1
1
1
1
2
2
1
1
2
2
1
1
2
1
1
1
2
1
1
1
1
0
2
2
1
2
2
0
1
0
1
1
2
1
2
2
0
2
1
0
1
2
2
1
2
1
0
1
1
0
0
1
2
0
1
0
1
1
1
0
0
1
2
0
1
2
1
0
1
1
1
2
0
0
0
2
1
0
1
1
0
2
1
1
2
1
2
1
1
2
2
2
3
2
2
3
1
2
2
2
1
2
2
1
1
2
2
1
1
1
0
2
0
2
0
1
1
1
0
1
1
1
0
1
2
1
2
1
1
0
1
1
1
1
1
1
1
1
1
1
1
2
0
0
1
1
1
2
0
0
1
1
2
1
1
2
1
2
0
2
1
3
1
2
2
1
1
2
1
2
1
1
1
1
1
1
1
1
0
0
1
1
1
1
1
0
2
1
2
1
2
2
2
2
1
1
1
2
2
1
1
1
1
1
1
1
1
1
2
1
2
2
0
0
0
1
1
2
1
1
2
1
1
1
1
0
1
1
2
1
0
0
2
2
1
1
1
2
2
1
2
1
1
1
0
1
1
1
2
1
2
1
0
2
1
1
1
1
1
2
1
1
0
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
0
1
0
1
1
1
2
1
1
2
1
1
2
1
1
1
2
1
2
1
1
1
1
0
1
1
1
1
1
1
1
1
2
0
1
2
1
2
1
1
1
0
1
1
5
1
2
1
0
2
2
2
2
1
1
1
1
1
0
0
2
0
1
1
1
1
2
1
1
0
1
2
2
0
2
1
0
2
0
1
1
1
0
0
0
0
1
1
1
2
2
0
1
1
0
1
2
0
2
1
2
1
1
1
1
1
1
2
2
0
1
1
1
0
0
2
1
1
2
2
1
1
1
1
0
1
1
1
2
2
0
1
1
2
1
2
0
1
1
1
0
1
0
1
2
1
2
2
0
2
1
1
1
1
0
2
1
2
1
1
2
1
2
1
2
0
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
2
1
2
0
2
1
1
2
2
2
1
1
0
1
1
2
1
0
0
2
1
1
1
1
0
2
1
1
2
1
1
2
1
0
1
1
2
0
1
1
1
0
2
1
1
1
1
1
1
2
0
0
1
1
2
1
0
1
1
1
2
1
2
0
1
1
1
0
1
1
2
1
2
1
1
2
1
0
1
1
2
0
1
1
2
0
1
2
2
1
1
1
1
1
1
1
1
1
0
1
0
0
2
1
1
0
1
2
1
1
1
2
1
0
1
2
1
1
2
1
0
2
1
1
1
2
2
1
1
1
1
1
2
0
0
1
1
1
1
1
2
1
1
1
2
1
1
0
1
1
1
1
2
2
1
2
1
0
1
1
1
2
1
1
1
2
1
1
1
1
1
2
0
0
0
0
1
2
1
0
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
2
1
1
1
1
2
1
0
1
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
2
2
2
0
1
2
0
1
2
1
2
1
2
2
2
2
1
0
1
1
0
0
0
1
1
1
1
0
1
1
1
0
1
0
1
1
1
1
2
0
2
1
2
0
1
0
2
0
1
1
1
1
1
0
0
1
1
1
2
2
2
0
0
1
1
1
1
2
2
2
2
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
2
1
1
0
1
1
2
0
0
0
0
1
2
0
1
1
0
2
2
1
1
0
0
0
1
1
1
1
1
1
0
1
2
2
1
2
0
1
2
2
2
0
1
0
1
2
8
0
0
2
1
1
1
1
3
1
3
1
1
1
1
0
2
1
1
0
3
1
0
1
1
1
1
0
1
1
1
0
1
1
2
2
0
2
0
2
1
1
1
1
0
0
0
1
1
0
2
1
2
2
1
1
0
2
1
1
2
1
1
2
1
1
0
1
1
1
1
1
1
0
1
0
1
1
2
2
1
1
1
1
1
2
0
2
1
1
1
2
1
2
1
1
1
0
0
1
0
1
1
0
1
2
1
2
1
1
1
1
1
0
1
1
2
1
2
1
1
1
0
1
0
1
1
1
1
1
1
1
1
0
2
1
1
2
1
1
1
0
1
1
1
0
1
0
2
1
1
2
1
1
1
2
0
1
1
1
1
1
2
1
1
1
1
1
1
0
1
2
2
1
2
1
2
1
1
1
2
0
1
1
1
1
0
2
1
1
1
0
0
1
1
1
1
2
1
1
1
1
1
1
2
2
1
2
1
0
1
1
1
1
1
2
1
1
0
0
1
1
1
1
1
1
0
1
1
0
1
0
0
1
3
0
2
1
1
1
1
1
2
1
1
1
1
2
2
1
1
1
1
0
2
0
1
1
1
1
1
2
2
1
1
1
2
1
1
1
1
0
1
1
0
1
1
1
1
2
1
1
1
0
1
1
1
0
1
0
1
0
2
1
2
2
1
1
2
2
1
1
2
2
0
2
1
2
0
2
0
0
1
1
1
0
1
1
1
1
1
1
1
1
0
1
1
1
2
1
1
1
1
1
1
1
1
0
0
1
1
1
0
2
1
1
2
2
2
2
1
0
0
1
1
1
0
1
2
1
2
1
0
1
1
0
1
1
1
1
1
1
0
2
2
1
2
2
0
1
1
2
2
2
2
0
1
0
0
0
1
2
1
0
1
0
1
1
1
1
0
2
2
1
1
1
0
1
0
0
1
2
0
2
1
1
1
3
0
0
1
0
0
1
1
1
1
0
1
1
3
1
1
1
1
1
0
2
2
1
1
1
2
1
1
1
2
0
1
1
1
1
1
1
1
2
1
0
2
1
1
1
1
1
1
1
0
2
1
3
1
0
1
0
1
0
1
1
0
1
1
2
2
1
1
1
1
2
3
1
2
1
2
1
1
1
1
2
2
2
1
1
3
1
2
1
1
1
2
0
1
1
0
1
1
0
1
1
1
1
2
1
1
1
1
2
0
0
1
2
2
2
1
2
1
2
1
2
1
1
1
1
0
1
2
1
1
1
1
2
2
1
2
1
1
2
1
2
1
1
1
1
1
0
1
0
1
2
1
0
2
1
1
1
1
1
0
1
1
1
1
2
1
0
2
1
0
2
1
1
1
1
1
0
0
1
0
1
4
0
1
0
1
1
2
0
1
1
1
1
1
1
1
1
1
0
0
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
2
1
2
0
1
2
5
2
1
1
0
2
1
2
1
2
2
2
2
2
1
0
1
1
1
1
0
1
0
2
1
1
2
0
1
1
1
2
0
1
0
0
2
2
1
1
1
1
0
1
1
1
0
1
0
2
0
0
0
1
0
1
1
1
1
2
2
1
0
3
2
0
2
2
1
1
1
0
1
0
1
1
0
0
1
0
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
0
1
2
1
2
1
1
1
2
2
2
1
1
1
1
2
1
1
1
1
2
2
0
1
0
2
1
1
1
0
1
1
1
1
2
0
1
2
1
1
0
2
1
2
1
1
1
0
1
2
1
1
1
1
1
2
1
0
1
1
2
1
1
2
1
1
2
1
0
1
1
1
1
1
1
1
1
1
0
2
2
1
1
1
0
1
1
1
1
0
1
2
2
2
0
1
2
2
2
1
0
1
0
1
0
1
0
1
1
0
1
2
1
0
1
2
1
1
3
2
2
1
1
1
0
1
1
1
1
2
2
1
2
2
1
2
2
1
2
1
1
0
1
1
1
1
0
0
1
1
0
1
1
3
2
0
0
2
2
1
1
1
1
1
0
2
1
1
1
1
3
1
1
2
1
1
2
1
0
2
1
1
2
1
1
2
1
2
1
2
2
1
1
2
3
1
1
1
2
0
1
1
1
1
1
1
1
1
1
0
1
2
2
2
1
1
2
2
0
1
0
1
2
1
2
2
0
2
1
1
2
3
1
1
3
1
2
1
2
0
0
1
1
1
2
1
1
1
2
2
0
1
1
0
1
2
1
2
1
0
2
1
1
2
2
0
1
1
0
1
0
0
0
0
2
2
2
1
1
2
1
2
1
0
1
1
1
1
1
1
1
0
2
2
1
1
2
2
1
2
3
2
1
2
2
0
1
1
1
1
0
1
0
1
1
1
1
1
2
1
0
2
0
0
1
1
1
2
0
1
1
1
1
0
1
2
1
1
1
1
2
1
1
1
1
0
1
2
0
0
2
2
0
1
1
1
2
1
0
1
2
2
0
1
2
3
1
1
2
1
1
1
1
0
2
2
2
1
1
0
2
1
1
1
2
1
1
1
1
1
1
1
0
0
2
1
1
1
1
1
1
1
1
0
0
1
1
1
0
2
0
0
1
1
1
1
1
0
0
0
1
1
1
1
1
1
1
2
2
1
2
2
1
0
2
0
0
2
0
1
1
1
1
2
1
2
0
1
0
1
2
1
1
1
1
1
2
1
1
2
1
1
0
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
0
1
1
2
1
2
1
2
1
2
2
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
0
1
0
1
1
1
2
0
2
0
0
2
2
1
1
1
1
2
1
1
2
1
1
1
2
1
0
2
0
1
0
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
0
1
1
1
0
2
2
1
2
1
1
1
1
1
2
1
0
1
2
1
2
2
1
2
1
1
2
2
2
2
2
1
2
1
1
1
1
1
0
1
1
0
2
1
2
2
1
0
2
2
2
0
2
2
1
1
0
1
1
0
1
2
2
0
0
1
1
0
1
0
1
1
1
2
1
1
2
2
1
1
2
1
1
0
1
1
1
2
1
0
1
1
1
1
1
2
1
0
0
1
2
1
1
1
1
2
0
2
2
1
1
1
2
0
1
1
2
1
1
1
1
1
1
0
1
2
2
2
1
3
2
2
0
6
1
1
1
1
1
2
1
1
2
2
1
1
1
1
2
2
0
1
0
1
0
0
1
0
0
1
1
1
1
1
1
1
1
1
1
2
2
1
1
0
1
1
1
0
0
1
1
1
1
4
1
2
1
0
0
1
1
1
1
1
2
0
1
1
0
1
0
1
2
1
1
1
1
2
1
1
1
2
0
1
1
1
0
2
0
1
1
1
1
0
1
1
1
1
0
2
3
1
1
2
0
2
2
1
1
2
1
1
1
1
0
1
2
2
1
1
1
1
1
1
1
1
0
1
1
0
1
2
2
1
1
0
1
2
1
0
0
1
1
1
2
2
1
0
2
1
1
1
0
1
0
1
1
2
1
2
0
2
1
1
1
0
0
4
1
1
1
0
1
1
1
1
0
0
1
1
0
1
2
0
0
0
1
1
1
1
0
1
2
1
1
1
0
1
1
0
1
2
0
1
2
1
2
2
1
1
1
1
1
1
0
2
1
1
1
1
2
1
1
1
1
1
1
2
1
2
2
1
1
2
2
1
1
1
0
0
2
1
1
2
1
1
2
2
1
2
1
2
2
1
1
0
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
0
0
2
1
1
1
0
0
0
0
2
2
1
1
1
0
1
1
0
1
1
1
1
0
1
1
1
0
0
1
2
2
1
1
1
1
1
2
1
1
2
1
2
2
1
2
1
0
1
0
1
1
1
1
1
0
1
2
2
0
1
0
1
1
1
1
1
1
1
0
0
1
0
1
1
1
1
1
1
2
2
2
1
2
0
1
1
1
1
1
0
2
1
0
2
2
2
1
1
0
2
1
1
1
0
1
1
0
1
1
1
1
1
1
0
1
1
1
1
1
0
1
2
1
2
2
0
0
1
2
0
1
2
1
0
1
1
0
1
1
1
2
1
1
1
0
0
2
0
1
2
0
0
1
1
1
0
1
1
1
1
1
2
1
1
0
1
1
2
2
1
1
1
0
2
1
2
1
0
1
2
1
1
1
1
1
2
1
1
2
2
0
0
1
1
1
1
2
2
2
0
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
0
1
0
0
1
2
0
0
2
2
1
2
1
2
2
0
2
1
1
0
1
2
1
2
1
1
1
2
1
1
2
0
1
0
1
1
2
2
0
1
2
1
1
2
0
1
1
2
1
0
1
1
1
0
1
2
0
0
2
1
1
0
1
2
1
0
1
1
1
1
1
1
1
0
1
1
1
0
0
3
1
2
3
2
1
2
1
0
1
2
1
1
0
1
1
0
1
1
0
1
2
2
2
1
1
1
1
1
0
2
1
0
1
1
0
0
2
2
2
1
1
2
1
2
1
1
2
1
0
2
1
2
1
1
0
1
1
2
1
2
0
1
1
2
1
2
0
3
0
2
2
1
1
0
0
1
1
1
2
2
2
1
0
0
1
2
1
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
0
1
2
0
0
1
1
2
1
1
2
1
1
1
2
2
1
2
1
1
1
1
1
1
2
0
1
1
0
1
1
1
1
1
1
0
1
2
2
1
1
2
0
2
1
1
1
1
1
1
1
1
1
0
1
2
2
0
2
0
0
2
2
0
1
1
1
0
1
1
1
0
2
2
0
1
2
1
1
1
1
1
2
1
1
1
0
1
1
2
2
1
0
2
1
1
1
2
0
1
1
1
1
0
1
1
0
1
1
0
2
0
1
1
2
0
1
1
1
0
1
2
2
1
1
1
1
1
1
2
1
2
1
3
3
1
1
0
1
1
1
0
0
2
0
2
1
1
1
1
2
2
2
1
1
1
2
0
1
0
1
1
1
1
1
2
1
2
1
1
0
1
1
1
2
2
2
1
1
1
0
1
2
1
2
1
1
1
1
1
2
2
1
2
1
0
0
2
1
1
1
1
1
1
0
2
1
1
0
1
2
1
2
1
1
2
1
1
2
1
0
2
1
0
1
1
2
1
2
2
1
1
2
1
2
2
1
1
2
2
2
1
0
1
1
2
0
1
0
2
1
1
1
1
1
1
1
0
1
0
1
0
1
1
1
1
1
2
1
1
1
1
1
1
0
0
1
1
1
2
2
2
1
1
0
0
0
2
2
2
2
1
2
1
1
2
0
0
1
0
1
0
0
1
1
1
1
1
1
1
1
1
2
2
0
1
0
1
1
0
0
1
2
1
2
1
2
1
1
1
2
1
0
2
1
1
2
1
1
1
0
1
2
3
1
1
0
0
2
1
2
1
2
1
1
0
1
1
0
1
1
1
2
1
0
1
1
2
0
1
1
2
0
1
2
1
1
2
0
1
0
1
0
1
0
0
0
2
0
0
1
0
0
0
1
1
4
1
1
1
1
2
0
1
0
2
1
2
2
2
0
1
1
0
1
0
1
1
1
1
1
2
1
0
0
1
1
1
1
2
1
1
0
2
0
1
0
1
0
1
2
1
1
1
2
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
2
1
1
1
1
0
0
1
0
1
1
1
1
1
1
1
0
1
1
1
0
1
1
2
1
1
2
1
2
1
1
2
1
1
2
1
1
3
2
1
1
1
1
0
1
0
1
1
2
1
0
1
2
1
1
2
2
0
1
2
1
0
1
2
1
2
1
2
1
0
0
2
1
1
2
2
1
0
1
2
2
1
1
1
0
1
0
1
1
1
1
1
0
0
1
2
1
1
2
2
1
1
1
2
1
1
0
1
1
2
4
2
1
1
1
2
1
1
0
1
1
1
1
0
2
1
0
2
1
1
1
2
1
2
1
1
2
1
1
1
1
2
1
0
1
2
1
0
1
1
1
1
2
1
0
1
1
2
1
0
1
0
0
1
0
1
1
0
2
1
1
1
2
1
0
0
1
1
1
0
2
1
0
0
1
1
1
1
0
2
2
1
2
1
2
1
2
1
1
2
1
1
1
2
1
0
1
1
1
0
1
1
1
0
1
1
1
1
2
1
1
0
2
1
2
1
0
1
1
2
2
1
1
1
0
1
1
1
1
1
0
1
1
1
1
2
1
1
1
1
1
1
1
2
0
1
2
1
1
0
2
2
2
1
1
1
1
2
1
1
0
1
1
1
1
1
0
1
1
1
1
1
2
1
2
1
2
1
1
0
0
1
1
2
1
0
2
1
1
2
2
1
1
2
1
1
1
2
0
2
2
1
1
1
2
0
1
1
2
0
1
1
1
0
0
2
1
1
1
1
2
1
1
1
2
2
1
1
1
1
0
0
1
1
1
0
1
0
1
1
1
1
1
0
1
1
3
1
2
1
1
1
2
1
1
1
2
1
1
0
0
1
1
1
1
1
1
1
1
0
1
0
1
2
1
0
1
2
1
0
0
0
1
2
1
1
1
1
2
1
1
1
2
2
1
2
1
0
1
1
2
2
0
1
1
1
1
2
1
1
0
1
1
1
0
1
1
1
1
1
1
2
1
2
1
1
2
1
0
2
0
2
1
2
1
1
1
1
1
0
1
1
0
1
1
1
0
0
0
1
1
1
1
1
2
1
1
0
1
2
0
2
1
1
2
1
2
2
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
2
2
0
1
1
1
1
0
0
1
0
2
1
1
1
1
0
1
1
0
1
1
2
1
1
1
1
0
1
1
1
0
1
1
1
1
1
1
1
2
1
2
0
1
1
2
1
1
1
0
1
2
0
2
1
1
1
1
0
1
1
1
1
1
1
1
2
0
0
1
2
0
1
2
2
0
1
1
0
2
0
1
1
1
1
0
1
0
0
1
1
1
0
1
1
1
2
2
0
1
2
1
1
2
1
1
0
1
0
1
1
1
1
1
0
1
2
1
2
3
1
1
1
1
2
1
0
0
3
1
2
1
2
1
1
1
0
0
1
1
0
1
1
1
1
1
1
1
2
1
0
1
1
1
1
1
1
1
1
0
1
0
0
1
1
1
1
1
1
1
1
0
1
1
0
1
2
1
1
0
1
0
1
2
0
1
1
0
2
0
1
2
2
1
0
1
0
1
1
1
1
2
0
1
0
2
1
1
1
1
1
1
1
2
1
0
0
2
1
2
1
1
1
2
1
3
1
0
0
1
2
2
2
3
1
2
2
1
2
2
2
1
1
1
1
2
1
1
2
1
1
2
0
0
1
0
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
2
0
1
1
0
1
0
1
2
1
1
0
0
1
1
2
1
2
1
1
1
2
1
2
1
1
1
1
1
2
0
1
1
0
2
1
1
0
0
0
1
2
0
0
1
1
0
0
2
2
1
1
2
1
2
2
1
0
2
1
0
1
1
1
2
0
2
1
1
1
1
0
1
1
2
1
2
1
1
1
0
1
1
1
1
1
1
2
2
2
1
0
1
1
1
2
1
1
0
1
1
0
1
1
0
1
2
2
0
2
2
1
1
1
1
1
4
0
1
1
2
1
1
1
0
1
1
1
1
0
0
0
1
1
0
1
1
1
1
2
0
0
1
2
2
2
2
1
1
1
1
1
0
2
0
1
2
1
1
1
0
2
2
1
3
1
1
1
2
1
0
1
0
1
1
1
1
0
1
1
1
1
1
1
1
0
1
1
1
2
1
1
1
1
1
1
0
1
0
2
1
2
1
1
2
1
0
0
1
2
2
2
1
1
1
0
1
0
1
2
1
0
1
1
0
1
2
1
1
1
2
0
3
2
1
1
2
1
0
1
1
1
1
1
1
1
1
0
1
0
1
1
1
1
1
1
1
1
0
2
0
0
0
1
1
1
0
2
0
2
1
2
1
2
1
1
0
1
0
1
0
1
1
1
2
2
0
1
0
1
1
2
1
0
1
0
2
0
1
2
2
1
0
0
1
1
2
1
0
1
1
2
2
1
1
0
0
2
1
1
1
1
1
1
0
2
2
2
2
3
2
2
1
1
1
1
1
1
0
1
2
1
0
1
1
0
1
2
0
1
1
1
1
0
0
2
0
1
2
2
1
1
1
1
2
1
0
2
1
0
2
1
2
1
1
1
1
1
1
0
2
1
1
0
2
1
1
2
1
1
0
0
1
0
0
0
0
0
1
0
2
2
2
2
1
2
1
1
1
2
1
1
1
0
2
2
1
2
1
1
1
1
1
0
2
1
1
2
1
2
2
0
1
0
2
1
2
2
1
1
2
1
1
0
1
1
1
1
1
1
2
1
1
0
1
0
1
0
2
1
1
2
2
1
1
1
2
1
1
2
2
0
1
1
1
1
1
2
0
1
2
1
1
2
0
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
0
1
1
0
0
1
1
0
1
2
1
1
1
1
1
1
0
2
0
1
1
2
2
0
1
1
1
1
2
1
0
1
2
0
2
1
0
2
2
1
4
2
2
1
1
1
2
1
0
1
1
2
1
0
1
2
0
2
0
1
2
2
2
2
1
1
3
1
1
2
2
0
1
2
1
2
1
2
1
1
1
1
1
1
1
0
1
2
1
0
0
1
0
2
1
1
2
2
1
2
2
1
1
1
1
1
1
1
1
1
1
2
0
1
1
2
1
1
1
2
1
2
2
1
1
2
2
1
0
0
1
0
2
0
1
1
2
0
1
1
0
1
1
0
2
2
0
1
1
1
1
0
1
1
0
2
1
1
2
1
0
0
1
1
0
1
0
0
1
0
0
1
0
2
1
0
1
6
1
1
1
1
1
3
1
1
0
2
2
1
1
1
1
1
0
0
0
0
2
1
1
2
2
1
1
1
2
1
1
1
2
2
0
1
2
0
1
1
2
1
2
0
1
1
1
0
0
2
2
1
0
1
0
1
2
1
2
1
1
2
1
1
0
1
1
1
1
1
1
1
1
2
1
2
0
1
0
2
2
1
2
1
2
2
1
2
2
1
0
2
0
0
1
1
1
0
1
2
1
2
0
2
1
1
1
2
2
1
0
0
2
2
2
1
1
0
2
1
1
1
0
1
1
1
0
2
0
2
2
1
0
0
1
1
2
1
1
1
1
2
0
1
2
0
1
0
0
1
1
1
2
1
0
1
1
1
1
1
1
1
2
1
1
1
1
1
1
0
2
2
2
1
0
1
2
1
1
1
1
1
1
1
1
0
1
1
1
1
2
1
2
1
2
1
4
1
1
0
1
0
1
1
1
2
1
1
0
0
1
1
1
2
1
2
2
1
1
1
1
0
1
1
0
1
1
1
2
1
1
1
1
0
1
1
1
1
2
1
1
0
1
0
2
1
1
1
2
0
0
1
1
1
2
1
2
4
1
1
0
1
1
2
2
2
1
0
0
1
2
1
0
1
2
0
1
1
0
1
1
1
1
2
1
2
2
1
2
1
2
1
0
1
1
1
1
2
1
0
1
1
2
0
1
0
1
2
1
1
1
1
2
1
1
1
2
1
2
1
1
0
1
1
1
1
2
1
1
1
2
1
2
2
1
2
1
1
1
2
1
0
2
0
1
0
2
1
1
1
1
1
2
1
0
1
1
2
1
1
1
1
2
0
1
1
1
1
1
1
1
1
0
1
2
0
2
0
0
1
0
2
1
1
2
2
2
1
2
1
0
2
0
2
1
1
1
1
2
1
2
0
1
1
1
1
1
1
2
1
2
0
1
0
1
1
1
2
0
2
1
1
2
0
1
2
0
1
2
1
2
1
0
1
1
2
3
0
1
0
0
1
1
2
1
1
1
1
1
1
1
1
0
2
1
1
0
0
2
0
0
1
0
2
0
0
1
1
0
2
1
2
1
0
1
1
0
0
2
1
0
1
1
1
1
1
1
1
1
1
1
0
1
2
1
1
2
0
1
4
1
1
2
0
2
0
0
1
1
2
1
1
1
0
1
1
2
2
1
1
1
1
1
1
2
1
1
1
2
1
1
0
2
2
2
1
0
2
2
1
1
0
1
2
2
2
2
1
1
1
0
1
2
1
2
2
2
3
1
1
1
1
1
2
0
0
1
1
1
2
1
1
1
0
1
1
1
0
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
1
2
0
1
1
1
2
1
1
1
0
0
2
1
1
1
1
1
1
2
0
2
1
1
2
1
1
1
1
1
0
1
0
2
1
2
1
2
0
1
1
1
0
1
0
1
2
1
2
0
1
1
3
1
1
0
0
1
1
1
1
0
1
2
1
3
0
2
1
0
1
2
1
2
1
1
1
1
2
1
2
1
3
1
2
1
2
1
3
1
1
1
1
1
0
1
0
0
1
2
1
2
1
1
0
1
0
0
2
2
3
2
1
1
0
0
0
0
0
1
1
1
1
1
2
2
1
2
1
1
1
0
1
1
1
1
1
0
1
1
1
1
1
1
0
1
2
1
1
2
1
1
1
1
0
0
0
1
2
1
1
0
1
1
2
1
1
2
1
2
2
1
1
2
0
1
1
1
0
1
1
0
2
0
0
2
1
1
0
1
1
2
1
2
0
1
2
2
0
1
0
1
0
1
2
1
2
0
1
0
2
1
3
1
1
2
1
1
0
1
1
0
1
0
1
1
0
0
0
0
2
2
2
1
0
2
1
1
1
2
0
2
0
2
1
1
0
2
0
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
0
1
0
2
0
2
1
1
1
1
0
1
2
0
2
1
1
0
1
1
1
2
1
2
1
1
1
1
2
2
2
2
1
2
0
1
1
1
1
1
1
1
1
1
1
1
0
2
2
1
2
1
1
1
0
1
0
2
1
1
0
1
2
1
1
1
1
1
1
0
1
1
1
1
1
0
1
2
2
1
3
0
1
2
1
3
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
0
2
1
1
0
2
0
4
0
1
0
2
1
1
1
1
2
0
1
1
1
0
1
1
1
1
1
2
2
1
1
1
0
1
1
1
1
1
1
2
1
2
1
1
1
1
2
0
1
2
2
1
2
0
2
1
1
1
1
0
2
0
1
1
1
2
1
2
1
1
1
0
1
1
1
1
1
1
2
2
2
0
1
1
1
1
2
1
2
2
0
2
2
0
0
2
1
1
1
1
0
1
1
1
0
1
1
1
1
1
1
1
2
1
2
1
2
0
1
1
1
1
1
0
0
2
1
0
1
0
1
0
1
0
1
0
1
2
1
2
1
1
2
1
1
2
1
1
1
1
1
0
1
2
0
3
1
1
1
2
1
2
1
0
1
1
1
1
1
2
1
0
1
0
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
0
1
1
2
0
1
1
2
1
1
0
1
2
3
2
0
1
1
1
1
1
1
0
1
1
1
1
1
2
1
1
1
1
1
0
1
1
2
1
2
2
0
2
1
0
0
1
1
1
2
0
2
2
1
0
1
1
1
1
0
1
0
0
0
0
2
1
0
1
1
1
1
1
2
1
1
1
2
1
1
1
1
0
0
1
1
1
1
1
1
2
2
0
1
1
1
1
0
1
1
1
1
1
1
0
1
1
1
2
1
0
1
0
2
1
1
1
2
1
1
1
2
1
1
1
2
2
0
1
1
1
1
1
1
1
1
1
1
1
0
1
2
2
1
1
1
1
1
1
0
1
1
2
1
2
0
1
1
2
1
0
1
0
1
0
2
0
1
2
2
1
1
3
1
1
1
1
0
0
1
1
2
1
0
1
2
0
1
1
2
1
1
1
1
1
1
1
1
2
2
0
1
1
1
1
0
1
1
1
1
1
2
1
2
1
1
0
2
1
1
1
1
2
1
2
1
0
2
1
1
2
1
1
0
1
1
2
2
1
1
1
0
1
2
0
1
1
2
1
1
0
0
1
1
1
0
1
2
1
2
1
1
0
1
0
1
1
1
1
1
0
1
1
0
1
0
1
1
1
1
0
1
1
1
1
1
2
2
0
1
1
1
1
2
1
1
1
1
2
1
1
1
1
0
2
1
1
1
2
1
1
1
0
0
1
1
0
0
1
1
1
1
1
1
2
2
1
0
2
0
1
1
1
2
1
2
0
1
1
2
2
1
2
2
0
2
1
2
2
1
1
2
1
1
2
1
0
1
1
2
1
1
2
1
2
1
1
2
1
1
0
1
0
2
1
0
0
2
1
2
2
1
1
1
2
1
1
0
1
2
1
1
1
1
1
1
1
2
2
2
2
1
1
2
1
0
1
2
0
1
0
1
1
0
2
1
2
1
1
1
1
1
2
2
2
1
1
2
1
1
2
1
0
0
1
1
2
1
1
0
1
0
1
2
1
0
1
2
1
1
1
0
1
2
0
1
2
2
1
1
0
1
0
2
1
1
1
1
1
1
1
0
1
0
2
0
0
0
1
1
2
1
0
2
1
1
1
1
1
1
0
1
1
0
2
1
1
1
2
1
1
1
1
0
0
1
1
1
1
2
1
0
0
2
2
1
1
2
1
1
1
0
2
0
2
2
1
0
1
0
1
1
0
1
1
1
2
1
1
0
2
2
0
2
1
1
2
1
0
2
1
2
2
2
1
0
1
1
2
1
2
1
2
2
1
2
1
1
4
1
1
2
1
1
2
1
0
2
1
1
2
2
0
1
0
2
1
1
2
1
1
1
1
0
1
2
0
0
1
2
1
1
1
1
0
2
1
1
1
1
1
3
1
0
1
1
0
1
1
2
1
1
2
1
0
1
2
1
0
1
1
1
1
2
2
1
2
1
1
1
2
1
1
1
2
0
1
1
1
1
2
2
2
1
1
1
1
1
2
0
1
2
0
2
0
2
0
2
2
2
1
1
0
1
1
0
1
1
1
1
2
0
1
0
2
0
1
1
0
1
1
1
1
0
2
0
0
1
1
2
1
0
1
1
0
2
1
1
2
1
1
2
1
0
1
1
0
2
2
1
0
1
0
1
1
0
1
1
2
1
1
1
1
1
0
1
1
1
2
1
1
1
2
1
0
2
1
0
1
1
1
2
1
1
0
2
0
1
1
1
1
2
2
0
0
1
2
2
1
1
1
1
1
2
1
2
1
1
0
1
0
1
1
1
1
1
1
0
0
2
1
0
0
1
1
1
0
0
2
1
1
1
1
2
1
2
1
0
1
2
0
1
0
1
1
1
2
1
1
1
1
2
1
0
1
2
0
1
1
2
1
2
1
0
1
0
1
1
1
2
1
2
1
2
0
1
1
0
2
0
1
1
1
0
2
0
1
1
0
2
1
2
1
1
1
0
2
0
1
2
2
1
1
1
1
1
1
0
1
1
2
2
2
0
0
1
1
1
0
2
1
1
2
1
0
1
1
1
2
0
1
0
1
1
1
0
1
1
2
1
2
0
1
0
1
2
1
1
1
0
2
2
1
1
1
0
2
0
1
2
0
1
1
1
1
1
2
2
1
1
1
1
1
2
2
0
2
1
1
1
0
1
1
1
1
0
1
1
2
1
1
1
0
0
2
1
2
1
1
1
1
1
1
1
1
2
1
2
1
2
1
0
1
1
2
1
0
1
2
2
2
1
2
1
2
2
2
0
1
0
0
2
1
1
1
2
1
1
1
2
0
2
0
1
2
1
1
1
1
1
0
1
2
1
0
2
2
1
1
1
1
1
1
1
2
2
1
1
1
0
2
2
2
2
1
2
1
2
1
1
2
0
2
1
0
1
0
2
0
1
2
1
0
2
0
1
2
1
1
0
2
1
0
1
2
1
0
0
1
2
2
0
2
1
0
0
2
2
4
1
1
0
1
2
2
1
1
1
0
0
1
1
1
0
1
1
1
1
1
1
1
0
0
1
0
1
1
1
2
0
0
1
0
1
2
2
0
1
2
0
0
0
1
1
1
2
1
2
1
0
0
1
0
0
1
1
1
1
1
1
0
1
1
1
0
0
1
1
1
2
2
1
1
0
1
1
1
1
1
1
1
1
1
0
2
0
1
1
2
1
2
1
1
1
1
2
1
1
0
2
1
0
1
1
1
2
1
1
1
0
1
1
2
0
2
2
0
1
1
0
1
1
0
2
1
1
1
1
1
1
1
0
1
1
0
1
2
1
0
1
1
1
0
1
1
2
2
1
1
0
1
2
1
2
1
1
2
1
1
1
1
1
1
0
2
1
1
1
2
1
0
2
2
2
1
1
1
1
1
1
1
1
1
1
1
3
1
2
0
2
1
1
1
1
1
1
0
2
1
0
1
1
1
1
0
0
1
2
0
1
1
1
1
1
1
2
2
1
0
1
1
1
1
1
0
0
3
1
0
1
1
0
0
2
0
0
2
0
1
2
1
1
0
1
1
1
1
1
1
2
1
0
1
0
1
0
1
2
3
1
1
2
0
0
0
2
1
1
1
0
0
2
2
2
2
1
1
0
2
1
0
2
2
0
0
1
1
3
1
2
0
1
0
1
2
1
1
0
0
1
1
1
1
1
1
1
1
2
1
0
1
2
1
2
0
1
2
1
1
1
1
1
1
0
0
1
2
2
1
1
1
2
1
2
1
2
1
2
1
1
1
2
2
1
1
1
1
1
1
1
1
0
1
1
2
1
1
1
2
1
1
0
2
1
0
1
1
0
1
1
2
0
1
1
2
1
1
1
1
2
1
0
0
2
1
1
1
1
2
1
0
2
0
1
1
1
1
0
1
1
0
2
3
1
2
0
0
1
1
0
2
1
1
1
1
1
0
1
2
1
0
1
1
2
1
1
2
1
2
1
0
2
0
1
1
1
1
2
1
2
0
1
1
1
1
1
0
2
2
1
2
1
1
1
1
1
0
2
0
0
1
1
1
1
1
1
1
0
0
2
2
1
1
1
1
1
1
1
2
1
1
1
1
0
1
1
0
1
1
1
1
0
1
2
1
0
2
1
1
1
2
1
0
1
1
1
1
1
0
1
2
1
1
1
1
1
1
2
0
2
1
1
1
1
2
0
0
2
2
1
1
1
0
1
1
0
2
0
1
1
1
0
1
1
1
1
1
0
1
1
1
2
1
1
2
2
1
1
1
1
1
2
1
0
1
1
1
1
1
1
2
1
1
2
0
1
1
1
1
0
2
0
1
2
2
1
0
1
1
1
1
1
0
2
1
1
1
1
0
1
1
2
0
1
2
0
1
1
1
2
1
1
2
1
1
2
2
1
1
2
1
0
1
1
1
0
0
1
1
1
1
2
2
1
0
0
1
1
1
0
2
1
0
2
1
2
1
1
1
1
0
0
0
1
1
1
2
0
1
1
1
2
1
2
1
1
1
1
2
1
1
1
3
1
2
1
1
0
2
2
0
1
1
1
1
1
1
0
1
1
2
1
1
2
1
1
2
1
0
2
1
1
1
0
1
1
2
1
2
1
1
1
2
1
2
1
0
1
1
2
0
1
2
1
0
2
2
1
0
1
2
1
1
1
1
1
1
2
1
1
2
1
2
1
1
1
2
1
2
2
1
1
1
0
1
0
0
1
2
1
1
2
0
0
1
2
1
1
0
1
1
1
0
0
2
2
1
1
2
1
1
2
0
1
2
1
0
1
1
1
1
2
1
0
1
1
0
1
2
1
2
1
0
0
0
0
1
2
1
1
1
1
1
1
1
1
0
1
1
1
1
1
0
1
2
0
1
1
0
1
1
2
1
2
1
0
1
2
2
2
1
2
1
2
1
1
2
1
1
0
2
2
1
0
0
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
0
1
1
2
0
1
1
1
2
1
1
0
1
2
1
0
1
1
1
0
1
1
1
1
2
1
0
2
0
1
2
1
0
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
2
2
0
1
1
1
1
2
2
1
1
1
2
1
1
1
1
1
0
1
1
2
1
2
4
0
1
2
0
1
2
1
1
1
1
1
2
0
0
0
1
0
1
0
1
0
1
0
0
0
2
0
1
1
2
0
2
1
1
2
1
1
1
4
0
0
1
1
2
2
1
1
1
2
1
1
0
1
1
1
0
0
2
1
1
0
2
1
1
0
1
1
1
1
1
1
2
2
2
1
0
2
0
1
1
2
1
2
0
2
2
2
1
0
1
0
1
1
2
1
0
2
2
1
1
1
2
1
1
2
2
2
0
1
1
1
1
0
1
1
1
1
2
0
1
1
1
1
1
1
2
1
0
1
1
1
1
1
0
1
1
1
0
1
0
1
2
1
2
0
1
2
1
0
2
1
2
0
1
1
1
1
1
3
1
3
0
2
1
0
3
1
1
1
2
2
1
1
1
1
0
0
2
0
1
1
1
1
1
2
1
1
1
1
1
2
0
2
1
1
1
1
1
1
2
1
1
1
0
1
1
0
1
1
1
1
2
1
0
4
1
1
0
1
0
1
1
1
1
1
1
1
1
1
0
1
1
0
2
1
0
1
1
1
0
0
2
2
0
1
1
1
1
1
1
1
1
1
0
2
1
1
1
1
1
1
0
1
1
1
2
1
2
1
1
1
2
0
0
0
1
2
0
1
1
1
0
2
1
2
0
2
1
1
2
2
0
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
0
2
2
1
2
3
2
1
2
2
2
1
1
1
1
0
1
1
1
0
1
1
0
0
2
0
1
1
2
0
1
1
1
0
1
0
1
1
1
0
1
1
1
1
1
1
1
2
1
2
1
0
0
1
2
2
2
1
1
1
2
1
1
1
0
0
1
1
0
0
1
2
1
1
1
0
2
1
1
1
1
0
1
1
1
2
1
2
2
1
1
0
0
1
1
1
2
2
0
1
0
2
0
1
2
1
2
1
0
0
1
1
0
0
1
0
1
1
0
1
2
2
1
1
2
0
2
0
0
1
1
1
0
1
1
1
1
0
1
1
1
1
1
2
1
1
2
0
1
1
1
2
0
2
0
1
0
1
2
1
1
1
0
2
1
2
1
2
1
1
1
2
1
1
1
1
2
0
1
1
1
1
2
0
1
2
1
1
1
1
1
1
0
1
1
0
1
1
2
2
2
1
0
1
1
1
1
0
0
0
0
1
1
1
1
2
1
1
2
1
1
1
1
2
1
0
2
0
1
1
2
1
1
0
1
1
1
1
1
2
1
2
1
0
1
1
1
0
1
2
3
1
2
2
1
2
2
1
2
1
0
0
1
1
1
1
0
1
2
1
1
1
1
1
1
2
1
0
1
1
1
1
0
2
1
1
0
0
0
1
0
0
0
2
2
1
2
1
2
1
2
1
1
1
2
1
1
1
1
1
2
0
0
1
2
1
2
1
1
1
0
1
1
1
2
1
1
1
1
1
1
1
1
2
0
1
0
1
0
1
1
1
0
0
1
1
0
1
2
0
1
1
1
0
1
3
1
1
1
1
1
1
1
0
1
0
2
1
2
0
2
1
1
2
2
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
0
2
2
1
1
0
2
1
1
1
3
1
1
1
0
1
1
1
2
1
2
1
1
1
1
1
1
2
2
1
1
2
1
1
2
0
2
0
2
1
1
1
1
0
2
1
0
1
1
1
2
1
1
2
1
0
1
1
1
0
1
1
2
1
1
1
1
2
2
0
1
2
1
2
1
1
1
2
2
1
1
0
2
1
1
2
1
1
1
0
1
1
3
0
2
1
1
1
1
1
1
1
1
1
0
0
1
0
1
1
0
1
1
2
2
1
2
1
1
1
1
1
2
1
2
1
1
0
0
2
2
1
1
0
1
2
2
0
1
2
1
2
1
0
1
2
0
1
1
1
2
1
1
2
1
1
1
1
1
1
1
0
1
0
3
2
0
2
1
3
0
1
1
0
1
1
2
2
2
1
1
1
1
0
2
1
1
1
1
2
0
1
1
1
1
1
2
0
0
2
2
0
1
3
0
0
1
0
1
1
0
0
1
1
1
1
1
0
0
1
1
1
2
0
1
2
1
1
2
2
0
2
1
1
1
2
1
1
1
0
1
2
2
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
2
2
1
1
1
0
2
1
0
0
1
0
1
0
0
1
1
1
2
1
1
0
0
1
2
0
1
0
1
1
2
1
2
1
0
3
2
1
0
2
1
0
0
1
1
2
1
0
2
0
1
1
1
2
1
1
0
2
0
2
1
1
0
1
2
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
0
0
2
2
2
1
1
1
1
1
1
2
1
0
1
1
1
0
0
1
2
1
0
1
1
1
1
1
1
0
1
1
1
2
0
1
1
3
2
2
0
1
2
1
1
1
1
1
1
2
0
1
1
2
2
1
1
1
0
1
1
1
2
2
1
0
2
1
0
1
1
2
1
2
1
1
1
1
1
2
1
2
1
1
1
1
2
2
1
1
1
0
1
1
1
1
0
0
2
1
1
1
1
1
1
0
1
1
0
0
1
2
1
2
1
2
1
0
1
1
1
0
1
2
1
2
1
2
2
1
1
2
1
1
0
2
1
1
1
1
0
1
2
1
2
2
1
1
0
1
0
1
1
1
1
1
0
1
1
0
1
2
1
0
1
1
1
1
1
1
3
1
1
1
2
1
2
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
1
1
3
1
2
1
1
2
1
1
1
0
1
1
1
2
1
3
1
1
1
1
1
2
0
1
0
1
1
1
0
1
0
1
2
1
1
1
2
2
2
1
0
2
0
1
1
1
2
1
1
0
1
1
1
1
1
1
1
1
1
0
1
1
1
0
1
2
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
0
0
1
2
1
1
1
1
1
0
1
1
2
1
2
2
1
1
1
1
1
1
1
1
0
1
1
1
2
2
1
1
1
0
1
2
2
1
1
1
0
1
1
1
1
1
1
2
2
2
1
2
0
2
1
0
1
1
1
2
1
1
1
1
1
2
1
1
0
2
1
2
1
1
1
1
2
1
0
1
0
1
1
1
1
1
1
3
1
2
1
2
1
2
2
1
2
1
1
2
1
1
1
1
1
2
2
1
0
1
0
0
1
2
1
1
2
2
2
1
1
1
1
1
1
1
1
1
0
1
1
1
2
2
0
1
1
2
2
2
0
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
2
2
2
1
0
1
1
1
1
1
2
1
1
3
1
1
2
1
0
1
1
0
1
1
2
2
1
1
0
0
2
1
1
1
2
1
1
2
1
2
2
0
0
0
2
1
1
1
1
1
1
1
0
1
2
1
2
1
1
1
1
0
2
1
1
2
2
1
2
0
1
1
1
2
2
2
1
1
1
1
1
1
2
2
1
1
1
1
0
1
2
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
2
0
1
1
1
1
2
0
2
1
1
0
1
1
1
1
1
3
2
1
1
1
2
2
1
1
0
0
1
1
0
1
2
1
1
2
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
2
1
1
2
0
1
1
1
2
0
1
1
0
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
1
0
1
0
1
1
1
1
2
1
1
1
1
1
1
1
1
2
2
1
0
1
1
2
1
1
1
1
1
1
0
1
2
2
1
0
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
0
1
1
1
1
1
1
1
2
2
1
1
1
0
1
1
3
1
1
1
2
1
1
1
1
1
2
1
1
0
2
1
1
1
1
0
1
0
2
1
1
3
3
1
1
1
3
2
1
0
1
2
1
1
1
2
1
1
2
1
2
2
1
1
1
1
2
0
1
0
2
2
1
1
2
1
1
0
0
0
2
2
1
1
2
1
2
0
1
2
2
0
0
1
1
1
1
1
2
1
1
1
1
0
2
0
1
0
1
1
1
2
1
2
1
1
1
1
0
1
2
2
2
0
1
0
1
2
1
1
0
0
2
1
1
1
0
1
1
0
0
2
1
2
1
2
1
2
0
1
1
1
0
1
1
1
1
1
2
1
2
0
0
4
0
1
0
2
1
2
1
2
1
2
0
1
1
2
1
0
0
6
0
2
1
1
1
1
1
1
0
2
1
1
1
1
1
2
2
0
2
1
1
1
1
2
2
0
0
1
2
1
1
0
1
1
2
1
1
1
1
1
0
0
2
1
1
1
1
0
0
1
1
0
1
1
1
1
1
1
1
1
2
1
1
0
1
2
2
1
2
0
2
0
0
1
1
2
1
1
2
1
2
0
2
1
2
3
1
0
2
1
1
2
1
1
1
0
1
1
1
0
1
0
1
1
1
1
0
1
1
0
1
1
0
1
1
2
2
1
0
1
1
0
2
1
2
2
2
1
0
0
1
1
0
1
2
0
1
2
2
1
1
0
1
1
1
2
2
4
2
2
1
1
1
1
1
1
1
1
0
2
2
1
1
2
0
1
2
1
2
2
2
2
1
1
0
2
2
1
1
1
1
1
1
1
2
2
1
1
2
0
1
3
1
1
1
0
1
1
1
1
1
0
1
0
1
1
2
0
2
1
1
2
0
1
1
0
2
0
1
0
2
0
0
1
1
1
1
1
1
1
1
0
0
2
1
2
1
1
1
0
0
1
1
1
1
1
0
1
2
1
1
2
1
1
1
2
0
0
2
2
1
2
1
0
1
1
1
0
2
1
0
0
1
1
1
2
1
1
1
1
1
1
1
1
1
0
1
1
3
2
2
1
0
0
1
1
2
1
0
1
0
2
2
0
2
0
2
1
2
1
2
1
1
0
1
0
2
1
1
2
1
1
2
0
1
1
2
1
1
1
1
1
1
0
2
1
1
1
1
2
2
2
1
0
1
1
2
1
2
2
2
1
2
0
1
1
2
0
1
1
2
1
2
1
1
0
2
1
1
0
1
1
1
1
0
1
0
0
1
2
1
2
1
1
2
1
1
1
1
1
1
0
0
1
1
1
2
2
1
1
0
1
0
1
1
2
1
2
1
0
1
2
1
1
1
0
0
1
2
1
1
1
1
0
1
0
1
1
2
2
0
1
1
1
1
1
1
1
1
0
2
1
2
2
1
2
1
2
0
1
1
3
1
1
0
1
2
0
2
0
1
2
1
1
1
1
1
2
1
1
2
2
1
1
1
2
2
1
1
1
0
2
0
1
2
2
1
2
1
1
2
1
1
1
2
1
0
0
2
1
2
2
2
0
1
1
1
3
0
1
1
2
0
2
0
0
1
1
1
0
0
2
1
1
0
2
1
1
1
2
1
1
1
1
1
1
1
1
1
0
0
0
2
1
0
2
1
2
1
1
1
1
2
0
1
1
1
0
2
2
1
1
1
1
2
0
1
2
1
1
1
1
1
1
2
2
2
1
1
1
1
1
0
1
0
1
2
1
1
2
1
1
2
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
0
1
2
2
0
0
0
1
1
2
1
2
0
2
1
1
3
1
1
2
1
0
0
1
0
0
0
1
2
0
2
2
1
1
1
1
1
2
1
1
1
1
2
1
2
1
1
1
3
2
1
1
1
0
2
1
1
2
1
1
1
1
2
1
1
1
2
2
1
1
1
2
2
1
1
1
1
0
2
1
1
1
0
2
1
1
1
1
1
0
0
1
1
1
1
1
0
1
1
1
2
1
2
1
0
1
2
1
2
2
1
1
1
0
2
1
1
2
1
1
1
1
2
2
1
1
1
1
1
0
1
2
2
1
1
2
2
1
2
2
1
1
1
1
1
2
2
1
2
0
2
1
1
2
0
1
2
1
1
1
1
1
0
2
2
2
1
0
0
0
2
0
2
1
1
2
1
1
0
1
1
1
0
1
1
1
0
1
0
1
2
1
0
1
1
1
1
1
1
2
6
2
2
1
1
3
1
1
0
2
2
1
2
2
1
1
1
1
2
1
1
1
2
1
1
1
1
0
1
0
1
1
1
0
1
1
1
0
1
2
2
2
0
1
1
1
1
2
1
1
2
1
2
1
0
1
2
2
0
1
2
1
1
1
0
1
1
1
2
2
1
1
0
1
1
2
1
2
1
0
1
0
1
0
2
2
2
0
1
1
1
1
1
1
2
2
2
2
1
1
1
1
1
1
1
1
1
2
0
0
2
1
2
1
1
0
1
0
2
1
2
1
1
2
5
0
2
1
1
1
2
1
1
1
1
1
1
1
0
1
2
1
1
1
1
1
2
0
2
1
1
2
1
2
1
1
1
2
1
2
2
1
1
1
2
1
1
2
1
1
0
1
1
2
1
0
1
2
2
1
1
0
0
0
2
0
1
1
1
1
2
1
0
0
1
2
2
1
1
1
2
1
1
1
1
2
1
1
1
2
2
1
2
0
1
1
1
1
1
1
1
0
1
1
1
1
2
1
0
1
1
1
2
2
1
2
0
1
1
0
1
2
1
1
2
1
1
0
1
1
1
1
1
0
0
1
1
1
1
2
0
1
0
0
1
1
2
1
1
1
2
1
2
1
1
1
0
0
1
2
2
0
0
1
3
1
1
2
0
1
2
1
1
1
1
0
2
1
1
2
1
1
1
2
1
2
0
0
1
2
0
1
1
1
0
1
1
2
0
2
1
1
1
1
0
2
0
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
2
0
1
1
1
0
1
1
1
2
1
1
1
2
1
1
2
1
1
0
0
1
1
0
1
2
1
2
3
2
1
1
1
1
1
2
1
2
2
0
0
2
1
0
0
2
1
0
1
1
2
1
1
0
0
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
2
1
1
2
1
0
0
1
1
1
1
1
0
1
1
2
0
0
1
0
2
0
0
1
0
1
2
1
1
1
2
0
0
1
2
1
2
1
1
1
1
2
2
1
1
1
3
1
1
1
1
1
3
1
2
1
1
2
1
1
1
1
0
1
0
0
0
1
1
1
0
0
1
1
2
1
1
0
1
1
1
1
1
1
1
2
1
1
0
2
1
1
2
1
0
1
0
0
1
1
2
1
1
1
0
1
2
1
1
1
2
2
1
2
0
1
1
1
0
0
2
1
1
1
2
0
1
0
1
1
3
2
1
1
2
1
1
1
0
0
1
1
1
0
1
1
1
1
1
4
2
1
1
0
2
0
1
1
2
2
1
1
2
1
0
2
1
1
0
1
2
1
4
2
2
2
1
2
1
1
1
0
1
1
1
2
1
1
1
1
1
2
1
2
1
1
1
2
2
1
1
1
1
2
1
2
1
1
0
1
1
1
1
1
1
1
0
1
2
1
1
1
1
1
2
1
1
1
2
1
1
0
1
1
1
1
1
0
1
0
1
0
3
1
1
2
1
1
1
1
0
0
0
0
1
2
1
2
0
0
0
2
1
0
2
0
1
2
2
0
2
2
2
2
1
1
1
1
1
1
1
0
2
2
2
1
2
2
2
0
1
0
2
1
2
1
0
0
1
1
2
1
1
0
0
1
2
1
2
1
2
2
0
1
1
1
0
2
1
1
2
1
1
1
1
1
0
0
0
0
2
0
1
1
2
1
1
1
1
1
2
1
1
2
0
1
1
0
0
1
1
1
0
2
2
0
2
2
2
2
2
2
1
1
2
1
1
1
0
0
2
0
1
0
1
1
1
0
1
1
1
1
1
0
2
2
0
2
1
1
0
1
2
1
1
1
1
1
1
2
2
1
1
1
0
0
1
1
1
2
0
1
1
1
1
0
2
0
1
1
2
0
1
1
1
2
1
1
2
2
0
0
1
3
1
0
1
1
2
0
1
1
1
1
1
1
1
2
1
4
2
1
1
2
1
1
1
2
1
1
1
1
1
0
1
1
2
1
2
1
2
1
1
0
1
2
0
2
1
2
1
0
1
2
2
2
2
1
2
0
0
0
1
0
1
2
1
2
3
1
2
1
1
1
1
1
2
0
1
1
1
1
1
0
0
1
1
0
1
2
1
1
1
1
1
1
2
1
0
0
1
1
1
1
2
1
2
1
2
1
1
1
1
1
2
2
1
1
0
2
1
1
1
0
1
1
0
1
1
2
2
0
0
2
2
2
0
1
1
1
2
1
1
2
1
1
1
1
2
1
0
1
2
2
1
0
1
1
0
1
1
1
0
0
2
2
1
1
2
1
0
1
2
0
1
1
0
1
1
1
1
1
1
1
1
1
1
0
0
1
1
1
1
2
1
1
0
0
1
1
0
2
1
1
1
1
1
1
0
1
1
0
1
1
1
0
3
0
0
0
0
1
1
0
1
1
1
1
1
1
1
0
1
0
1
1
1
2
2
1
1
2
1
2
1
1
1
1
0
1
2
1
1
1
0
2
0
1
1
1
0
1
2
1
1
2
0
1
2
1
2
1
1
1
0
3
2
1
1
0
0
1
0
2
1
0
2
2
1
2
2
1
2
2
1
2
1
1
3
0
2
1
0
1
2
1
1
1
1
0
1
3
2
3
1
1
1
1
1
1
1
1
1
1
1
1
3
1
1
1
1
0
1
1
0
1
1
1
1
0
1
1
0
1
2
1
1
2
1
1
0
1
1
2
1
1
0
1
0
0
1
1
1
1
0
0
2
1
1
0
1
1
1
2
1
2
0
1
1
2
1
2
2
2
0
0
0
1
1
1
1
1
1
2
1
2
0
2
1
0
1
1
1
0
2
1
0
1
2
1
1
1
1
1
1
0
1
1
1
2
0
1
1
2
2
2
1
1
0
1
2
2
1
2
1
1
1
0
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
0
1
1
1
1
0
0
1
1
1
0
1
2
2
2
1
1
1
1
1
0
2
2
2
2
3
2
1
1
1
0
0
2
1
1
1
2
1
1
2
0
1
1
1
0
0
1
1
1
1
1
1
2
1
1
0
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
0
0
0
2
2
1
1
1
1
1
1
1
2
1
0
2
0
1
1
1
3
1
2
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
0
1
2
2
2
1
1
1
1
1
2
1
2
2
0
0
1
1
0
1
1
0
1
1
0
1
1
1
1
1
0
0
0
2
1
2
1
0
0
1
1
1
1
0
1
2
0
1
1
2
2
1
1
1
1
1
1
2
1
1
0
1
0
1
1
2
1
1
2
1
1
0
1
1
2
1
0
1
1
2
1
2
2
1
2
1
1
1
1
2
2
2
0
1
1
0
1
1
1
0
1
0
1
1
0
1
2
1
1
1
1
1
3
1
1
2
1
0
0
1
3
2
0
2
1
2
1
1
2
2
0
1
2
2
1
2
1
0
0
1
1
1
1
1
1
1
1
2
1
1
1
0
1
1
1
1
1
0
2
1
1
1
2
2
2
1
0
0
2
0
2
1
1
1
1
0
2
0
0
1
2
1
1
1
1
2
0
0
2
1
1
1
1
1
1
0
2
2
2
1
2
1
1
0
1
1
2
1
1
1
1
1
2
1
2
0
1
0
0
1
1
1
1
1
3
2
1
2
3
1
2
1
1
1
1
1
0
2
0
1
0
1
2
0
1
2
1
2
1
1
1
1
2
2
1
1
1
1
0
2
0
1
2
1
2
0
0
2
1
0
2
0
1
1
2
0
1
3
1
2
0
2
1
1
1
1
1
2
1
2
0
2
1
2
2
2
0
2
1
1
1
2
0
0
1
1
1
1
2
1
1
1
1
1
2
1
0
1
1
2
2
2
1
1
2
2
2
1
0
1
1
1
1
0
1
2
1
1
1
1
1
1
1
0
2
1
0
1
2
2
1
1
1
1
1
0
2
0
2
1
1
0
0
1
1
1
2
1
1
0
1
2
1
1
1
2
1
2
0
0
2
1
1
1
1
1
0
0
2
1
1
1
2
2
1
1
1
0
1
2
1
0
1
1
2
1
1
2
2
1
1
1
1
3
2
1
2
1
0
2
1
2
2
1
1
0
1
2
1
0
0
1
1
1
0
1
1
1
1
1
1
1
1
2
0
0
1
2
1
2
1
2
0
1
0
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
0
1
1
1
1
2
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
0
2
1
2
1
2
1
1
1
0
2
1
1
0
1
0
1
1
1
1
2
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
2
1
1
1
2
1
1
1
1
1
0
3
1
1
1
1
1
2
2
1
1
0
1
2
1
1
2
1
0
1
1
1
0
1
0
0
1
1
0
1
1
0
1
1
2
0
1
0
0
1
0
2
1
0
1
2
2
1
1
1
1
1
0
1
0
0
0
1
0
0
1
2
0
2
1
1
2
1
0
1
2
0
1
1
1
1
1
0
1
2
1
2
1
0
1
0
2
0
1
1
2
1
1
1
0
2
0
0
2
1
2
1
1
1
1
0
1
1
2
1
1
1
1
0
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
2
1
2
1
0
2
0
2
1
1
1
1
1
1
1
2
0
1
1
1
2
1
1
2
1
0
1
1
0
1
1
0
0
0
1
1
0
1
1
1
2
1
1
1
2
1
2
2
1
0
1
2
0
1
1
0
2
0
0
2
1
0
0
2
1
1
1
2
1
2
2
1
0
0
1
2
0
2
2
1
1
1
1
1
1
1
2
2
1
2
1
2
2
0
1
0
1
0
1
1
1
2
1
1
2
1
2
2
0
1
0
1
1
1
1
1
1
1
1
1
0
0
7
0
1
1
2
0
2
2
2
1
1
1
1
0
1
0
0
0
1
1
1
0
0
0
1
1
1
0
1
1
1
1
0
1
1
2
0
1
0
1
3
1
1
1
1
2
0
1
1
1
1
1
1
1
1
0
2
1
1
2
1
0
2
1
1
2
1
1
1
0
1
1
2
2
1
1
1
1
1
1
0
0
0
1
2
1
0
0
0
2
1
1
0
1
0
1
1
2
0
1
1
1
1
2
1
1
1
1
0
1
2
1
0
1
0
1
0
1
1
1
1
1
1
1
2
4
1
1
1
0
0
1
1
1
2
1
0
1
1
2
0
2
2
0
1
0
1
1
0
1
1
1
0
2
1
0
2
1
2
2
0
1
0
1
0
1
1
1
0
2
1
1
2
2
1
1
1
1
2
1
0
1
2
2
1
2
0
1
1
1
2
1
1
1
0
1
1
1
0
1
2
1
1
1
1
2
1
1
1
1
2
0
1
1
1
2
1
0
1
2
0
1
0
2
1
1
1
2
0
3
2
1
2
1
2
1
0
1
2
1
1
0
0
0
1
1
3
2
0
2
1
1
1
1
1
2
1
2
1
0
1
1
2
1
1
3
1
1
1
1
2
1
1
0
1
1
1
2
1
0
1
3
1
2
0
1
1
2
1
0
0
1
2
1
0
1
2
1
1
2
2
1
2
1
1
1
1
2
1
2
0
1
1
6
1
2
1
0
0
1
1
2
1
2
0
1
1
0
2
1
2
1
1
1
0
1
2
1
2
2
1
1
1
2
1
0
1
1
1
1
1
1
1
0
1
1
1
0
0
0
1
0
1
1
1
0
2
1
2
1
1
1
1
2
0
2
2
1
3
2
0
1
1
1
0
1
0
1
0
2
1
2
2
1
2
1
0
1
1
1
1
0
1
1
0
1
1
1
1
0
1
1
1
1
0
1
2
1
2
1
1
1
0
1
1
1
2
2
2
0
1
1
1
1
0
1
1
2
2
1
0
1
1
2
1
2
2
1
0
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
4
2
0
0
1
1
1
1
2
2
1
0
1
1
1
1
1
2
1
1
1
0
1
1
1
0
1
1
2
1
0
2
1
1
2
0
0
0
1
1
0
1
1
0
4
1
1
1
2
1
1
0
1
1
1
1
0
1
1
0
1
1
1
0
2
3
1
1
0
1
0
1
1
0
0
0
2
1
2
1
1
1
2
1
0
1
1
0
1
0
1
1
0
0
1
2
1
0
2
1
2
5
2
2
2
1
2
0
2
1
2
1
2
2
1
1
0
1
1
2
2
1
1
2
1
1
2
1
0
1
1
2
1
2
1
1
1
1
0
0
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
2
0
2
1
1
1
1
0
1
1
2
2
1
1
1
1
1
1
0
0
1
2
1
1
1
2
1
1
1
1
0
1
1
1
1
1
2
1
2
1
1
0
0
0
2
3
0
0
1
2
1
1
2
2
1
2
1
0
2
2
2
1
1
2
2
0
1
1
0
1
1
1
1
2
1
1
0
1
2
2
1
2
1
1
1
0
0
1
1
1
2
1
2
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
4
0
1
1
0
1
1
1
1
1
1
1
1
1
2
1
1
3
2
1
1
1
1
0
1
1
3
3
1
0
0
2
1
1
1
1
1
0
1
1
1
1
0
2
1
1
1
1
1
1
1
0
1
1
1
1
1
2
1
1
0
1
1
0
1
1
1
2
0
2
1
0
1
2
0
1
1
1
2
1
1
2
1
0
2
1
1
0
0
1
1
0
2
1
1
1
2
1
2
2
0
1
0
1
0
1
2
1
1
1
1
1
1
2
1
2
1
2
2
2
0
2
2
0
1
0
2
1
1
1
2
1
1
2
1
0
1
1
1
1
1
2
2
1
2
1
1
1
2
1
1
0
2
2
0
2
1
1
1
1
1
1
2
2
2
1
0
1
1
1
2
0
1
2
2
2
1
0
1
1
0
2
2
2
0
0
1
1
1
1
2
1
2
1
2
1
2
2
1
1
1
2
2
1
1
1
0
2
1
2
2
1
1
2
1
2
1
0
2
1
1
0
1
1
2
0
2
0
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
0
1
1
2
1
1
1
1
2
1
1
1
2
0
0
2
1
2
1
0
1
0
0
1
1
1
1
2
0
1
1
1
2
0
1
1
1
1
0
2
0
0
1
2
2
1
1
2
0
0
1
1
2
0
1
1
1
1
2
1
1
2
2
1
1
1
2
1
1
1
0
2
2
2
1
5
1
0
1
1
1
0
2
2
0
1
0
0
1
2
1
0
0
1
1
0
1
0
1
1
2
0
1
1
2
1
1
2
1
0
1
1
1
1
1
2
1
1
1
2
0
1
1
1
1
0
0
0
1
1
1
1
1
1
2
1
0
1
1
1
1
1
0
1
1
1
2
2
1
1
1
2
2
0
1
0
0
1
0
1
0
1
2
0
1
1
2
1
1
1
0
1
1
1
0
0
2
0
0
1
0
1
1
1
0
0
1
1
1
0
1
0
1
1
1
2
1
1
1
1
0
1
0
0
1
1
1
2
0
1
1
1
2
0
1
0
1
2
0
1
2
1
1
1
1
0
1
1
0
0
2
1
1
1
0
1
1
2
1
1
0
1
1
1
1
1
0
2
2
1
2
1
1
0
2
2
2
1
2
1
2
1
1
0
1
1
1
1
0
1
0
0
1
1
0
1
0
2
1
2
1
2
1
1
1
1
2
1
0
1
0
0
0
1
1
1
0
0
1
1
1
2
2
2
0
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
0
1
0
1
1
2
0
1
1
1
1
2
2
1
1
2
2
2
1
2
2
1
1
1
1
2
0
2
1
0
1
2
1
1
2
0
0
1
1
2
1
1
4
1
1
3
1
1
0
2
1
1
2
1
1
0
0
1
1
2
1
1
1
1
1
1
2
1
1
1
0
2
1
0
2
1
1
2
1
0
1
2
1
2
2
1
1
0
1
1
2
0
1
0
0
0
1
0
1
0
2
0
0
0
1
1
1
1
1
2
2
0
1
2
2
0
1
1
0
0
2
1
1
1
2
1
1
1
0
1
0
1
1
1
0
1
1
1
0
1
2
2
2
1
1
0
1
2
2
1
1
1
1
1
1
2
1
2
1
0
1
1
1
2
1
1
1
2
1
0
0
1
0
1
0
1
2
1
1
0
2
1
0
2
1
1
2
1
1
2
2
0
2
1
1
1
1
0
2
0
2
2
1
0
1
1
1
1
1
0
1
1
1
1
0
1
1
2
1
1
2
1
2
1
0
1
2
0
0
2
1
1
2
1
1
1
1
1
0
2
2
0
2
0
1
1
1
2
2
1
1
1
1
1
1
0
1
1
2
0
1
2
1
1
2
2
1
1
2
1
1
2
1
0
0
0
1
1
1
2
0
2
1
1
1
1
2
1
2
1
0
1
0
1
1
1
1
2
2
0
0
2
1
0
1
2
1
2
1
0
1
1
0
1
1
1
1
1
0
1
2
0
2
1
1
2
1
1
1
2
2
2
1
1
0
2
1
2
1
0
1
1
2
1
1
2
0
1
0
1
1
1
2
2
2
1
1
0
0
2
1
2
1
0
0
1
1
1
2
1
1
2
1
1
1
2
1
2
1
1
0
0
1
2
1
0
0
1
1
2
2
1
1
2
2
2
1
2
2
0
1
1
0
1
1
1
1
0
1
1
1
1
0
1
2
1
1
0
1
0
1
1
0
2
2
0
1
0
1
0
0
0
1
0
1
1
1
2
1
1
1
1
0
2
2
1
1
1
2
2
1
0
0
1
0
2
0
1
1
0
1
1
2
1
2
0
1
1
1
1
2
1
2
1
1
1
2
1
2
2
2
1
2
1
2
1
2
1
1
1
1
0
1
1
2
1
1
1
0
1
1
2
1
1
2
1
2
1
1
1
0
0
1
0
2
0
1
0
1
1
1
1
1
0
1
0
1
1
2
2
1
1
1
1
2
1
2
2
0
0
1
0
2
1
1
1
1
1
1
1
1
2
1
1
0
1
3
1
0
1
1
2
2
1
1
2
2
2
0
1
0
0
2
1
2
1
0
1
1
1
1
1
1
1
1
1
2
1
1
0
1
1
2
0
1
0
0
1
0
1
2
1
1
2
1
2
2
2
2
0
2
1
1
1
1
1
0
0
1
1
1
1
0
2
0
1
1
1
1
2
1
0
2
0
2
1
1
1
1
2
2
1
1
0
1
1
1
1
0
1
1
1
1
1
1
1
1
2
1
0
2
1
1
2
2
1
0
1
2
2
1
1
1
0
1
1
0
0
2
0
0
2
1
2
2
1
1
1
1
2
0
1
1
2
1
2
2
2
2
2
1
1
2
2
2
1
1
2
1
1
0
2
1
1
2
2
2
0
2
2
1
2
0
1
2
0
0
2
0
1
2
1
1
0
2
0
1
2
2
1
0
1
1
2
2
1
1
0
1
2
2
0
0
2
1
1
1
1
1
1
1
1
0
2
2
1
2
1
1
2
0
1
1
1
2
1
1
2
1
1
0
2
0
1
1
1
1
1
1
2
0
2
1
0
1
1
2
1
2
1
0
0
0
2
2
1
1
2
2
1
1
0
0
0
0
1
1
1
0
1
1
1
0
1
1
1
2
1
1
0
2
0
1
1
2
2
1
1
2
1
1
1
0
1
2
0
1
2
3
0
2
1
1
1
2
1
1
1
1
0
0
2
1
1
2
1
0
0
0
0
1
1
3
1
0
0
1
1
1
0
2
1
1
1
1
1
1
3
1
1
0
8
2
1
2
1
1
1
2
0
1
1
1
2
3
1
1
0
2
2
1
0
1
2
2
0
1
0
1
1
2
1
1
0
1
1
1
1
1
1
1
0
1
1
1
2
0
0
1
1
0
2
1
0
1
0
1
1
1
2
0
1
1
2
1
1
1
1
0
1
0
2
1
0
1
1
1
1
1
1
2
1
1
1
1
1
2
1
2
0
1
2
5
1
2
1
1
2
0
1
1
1
1
3
2
1
2
2
1
1
1
0
1
0
1
2
1
1
1
1
1
1
1
1
2
1
2
0
1
2
1
0
1
2
2
0
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
2
1
0
1
1
1
2
1
1
1
1
1
0
1
1
1
0
2
1
2
1
0
1
1
0
1
1
0
2
1
1
0
1
1
2
2
1
2
1
1
0
0
0
2
1
1
0
1
2
0
1
1
0
1
1
1
1
1
1
0
2
0
2
1
1
1
0
2
2
2
0
2
2
1
0
1
1
1
1
2
1
2
2
1
0
2
1
1
1
2
2
1
2
0
0
5
0
1
2
1
1
0
2
0
1
1
1
2
1
1
1
1
1
1
2
0
1
1
1
0
1
0
0
1
2
1
2
2
1
0
2
2
1
2
1
1
2
2
2
1
1
1
1
1
1
0
0
1
1
1
1
2
1
1
1
0
1
2
1
1
1
0
1
1
0
1
1
1
1
1
1
1
2
2
1
1
0
0
1
1
1
1
1
0
1
1
2
1
0
0
1
1
1
1
0
1
0
0
1
2
1
1
1
1
1
2
1
0
2
2
0
1
2
1
1
1
1
0
1
1
1
2
1
2
2
0
0
1
1
2
2
0
0
1
0
2
1
2
1
2
1
1
1
1
1
2
1
1
1
0
1
1
1
1
1
2
2
1
1
0
2
0
2
1
1
1
0
0
0
2
2
1
0
1
1
1
1
0
1
2
1
2
1
0
1
1
2
1
2
1
2
2
1
1
2
1
1
1
1
0
1
0
2
0
1
1
0
2
2
1
0
1
1
1
2
1
1
2
1
0
2
2
3
1
0
2
1
1
0
1
2
0
1
2
1
2
1
1
2
2
0
1
1
1
0
2
1
1
1
2
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
0
1
1
1
0
1
1
1
1
1
1
2
0
1
1
1
1
2
1
1
2
1
0
2
2
0
1
0
0
1
2
1
1
1
1
1
1
2
1
1
0
2
2
1
1
0
0
1
1
0
1
0
0
1
1
1
2
1
0
1
1
1
1
1
1
2
1
1
1
2
2
1
1
2
0
0
1
1
1
0
1
2
1
1
1
1
1
1
1
0
2
2
0
2
2
1
1
2
2
0
1
1
1
1
1
2
0
1
0
1
1
1
1
1
1
2
1
0
2
1
2
0
1
1
1
0
1
1
1
1
2
2
1
2
1
1
0
1
0
0
1
1
2
0
2
1
1
1
0
2
1
1
1
2
2
0
2
2
2
1
2
1
1
1
1
2
0
0
1
1
2
1
1
1
0
0
0
1
0
1
0
0
0
2
1
1
1
3
2
2
2
1
1
1
1
1
1
1
1
1
0
0
1
2
1
2
1
1
2
2
1
2
2
2
1
2
1
0
0
1
2
1
1
1
2
2
2
1
1
1
1
2
1
1
0
0
1
0
0
2
1
0
1
0
1
2
1
1
0
2
2
0
1
1
2
1
1
1
1
1
1
1
1
0
0
1
1
1
1
2
0
1
1
0
1
0
2
0
2
1
1
1
1
1
1
1
1
1
1
2
1
2
0
2
1
1
1
1
1
1
1
0
1
1
1
1
2
1
1
1
2
0
1
1
0
0
1
2
0
5
1
1
1
2
1
2
0
2
1
0
1
1
1
2
1
2
0
1
1
0
1
1
2
2
1
2
2
1
2
1
2
2
1
1
1
1
2
1
2
1
1
1
1
1
1
2
0
2
1
1
1
0
0
1
2
2
1
1
1
0
1
1
0
1
2
1
0
1
1
1
2
1
2
1
2
1
1
2
0
0
1
1
1
0
1
1
1
1
1
2
1
1
1
1
2
1
2
0
1
2
1
2
2
1
1
1
0
2
1
1
1
0
1
1
1
1
1
1
1
1
2
0
1
1
0
1
0
2
2
1
1
1
1
1
1
1
1
1
2
1
2
1
2
1
1
1
1
0
1
2
0
1
1
0
0
2
2
1
0
1
1
1
1
1
1
1
1
1
2
1
0
0
1
1
1
1
1
2
1
1
1
0
2
1
1
1
1
1
2
2
1
1
1
0
1
1
1
0
1
1
1
1
2
0
2
3
1
2
1
1
2
2
2
1
1
1
1
1
0
2
2
0
2
1
1
1
1
2
1
0
0
0
1
2
1
1
2
0
1
1
1
1
1
1
2
6
1
1
2
1
1
2
2
1
1
1
1
1
1
1
1
0
1
1
1
2
1
2
1
1
2
1
0
2
1
1
2
0
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
0
2
0
1
2
0
0
1
2
1
1
1
1
1
0
1
1
0
0
2
0
1
1
2
1
0
1
1
1
2
1
2
1
1
1
0
2
1
1
1
0
2
1
2
1
1
2
1
0
0
1
1
1
1
1
2
1
1
1
1
1
2
0
0
2
2
2
1
1
1
0
1
0
1
0
2
0
1
1
1
3
1
2
1
1
1
0
2
0
1
0
1
0
1
1
1
1
2
1
1
0
1
1
1
2
0
2
1
1
2
1
2
1
2
1
2
1
0
1
0
1
2
0
2
2
1
1
0
1
1
1
1
2
1
0
1
0
0
0
2
2
1
2
1
1
1
1
1
0
1
1
1
1
2
2
1
1
2
1
2
0
1
0
2
1
2
0
1
0
2
1
1
1
2
1
2
1
1
2
0
0
1
2
2
1
1
1
2
1
2
1
1
2
2
0
2
2
0
1
1
1
2
2
2
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
0
0
1
1
1
2
2
1
1
1
2
0
2
2
1
1
1
2
0
2
1
2
1
2
1
1
1
1
2
0
2
1
2
0
1
1
2
0
2
2
1
1
1
2
2
0
1
0
1
1
1
1
1
1
2
0
2
1
2
1
1
1
1
2
2
2
2
0
1
1
2
1
1
1
0
1
1
0
2
0
1
1
2
1
1
2
1
1
0
2
1
0
1
0
2
1
1
0
0
2
1
1
0
1
1
2
0
2
1
2
2
1
0
0
2
2
2
1
0
1
2
1
1
1
2
3
1
2
1
1
2
1
2
1
1
2
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
2
2
0
1
1
1
1
0
0
1
0
2
1
1
2
1
1
1
0
1
2
1
1
1
1
0
1
1
2
1
1
3
1
1
1
1
1
1
1
2
1
1
1
0
1
1
1
0
0
1
1
1
2
2
1
2
2
1
1
2
1
0
2
1
1
1
2
1
2
1
2
0
1
2
2
1
1
0
1
1
1
0
1
0
2
1
1
2
1
2
1
1
2
0
0
1
1
0
1
2
0
1
2
1
2
0
1
1
2
0
1
0
2
1
3
1
0
1
2
3
1
2
1
1
1
1
1
1
2
1
1
1
2
2
2
2
1
0
2
1
1
2
1
1
2
2
0
1
2
0
1
1
2
1
0
1
1
0
1
1
2
0
1
1
1
0
4
2
1
2
1
1
1
1
1
0
1
1
2
1
0
1
2
1
1
1
2
1
2
0
1
2
1
2
1
2
1
0
1
1
2
2
1
0
1
2
0
1
0
1
2
2
1
1
1
1
2
1
1
0
2
1
0
1
1
1
0
0
2
2
0
0
1
1
2
0
1
0
1
2
1
2
2
1
1
1
1
1
0
0
2
1
2
0
1
1
0
1
1
1
1
2
1
2
0
1
1
3
1
0
2
1
1
1
0
1
1
1
1
1
2
2
1
2
1
1
1
1
1
2
1
0
2
1
1
2
0
0
0
1
1
3
1
2
1
1
1
1
2
2
1
1
1
2
1
1
1
1
1
0
2
2
0
2
1
0
1
1
1
2
2
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
2
0
1
1
1
0
1
2
1
1
1
1
1
2
5
1
0
1
1
1
1
0
2
2
1
2
1
0
2
2
1
0
1
1
2
1
1
1
1
1
1
2
1
1
0
2
1
1
1
1
1
2
0
1
1
1
0
1
1
2
1
1
0
1
2
2
0
1
0
1
1
0
1
2
2
1
1
1
1
1
1
1
1
1
1
2
0
0
0
1
1
1
2
1
1
1
1
1
1
2
1
0
1
1
1
1
1
1
1
1
2
1
1
0
2
1
1
1
1
0
1
0
2
2
1
2
1
2
1
1
1
1
0
1
2
0
1
1
1
1
2
0
2
2
1
1
1
1
1
1
2
2
1
1
0
1
2
2
2
1
0
1
1
2
2
2
1
1
1
1
1
2
1
1
0
1
2
1
1
0
1
1
1
1
1
1
1
0
2
1
2
1
1
2
0
2
1
1
0
1
2
1
1
0
2
1
1
1
0
2
0
2
0
0
1
2
1
1
1
2
1
1
0
4
2
1
0
1
1
0
1
2
1
1
0
1
1
0
1
0
2
1
2
2
2
1
1
2
2
2
1
2
0
1
0
1
1
1
2
1
1
1
0
2
1
0
1
1
2
2
2
1
0
2
1
1
1
2
1
0
1
1
1
0
0
2
1
2
1
1
0
1
0
1
1
1
2
0
2
1
1
2
2
2
1
1
1
2
1
1
1
2
1
1
0
1
0
1
1
1
1
1
2
0
1
2
0
2
1
1
1
1
2
1
2
1
1
0
1
1
2
1
2
1
0
1
1
0
0
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
1
0
1
1
2
1
1
1
1
1
1
1
1
1
1
2
2
1
2
0
2
1
2
0
2
1
2
1
1
2
1
2
0
1
1
0
0
1
2
0
0
2
1
0
0
2
1
1
1
0
2
1
2
2
1
1
2
2
0
2
2
1
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
2
1
0
2
1
2
1
1
1
1
2
1
0
0
1
1
1
1
0
1
1
1
1
0
1
1
2
2
2
2
1
1
0
1
1
2
2
1
1
1
0
1
2
1
1
1
2
1
1
1
1
2
0
2
0
1
1
2
1
1
1
2
1
0
1
1
2
2
1
2
1
1
1
2
1
1
0
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
0
1
2
1
1
2
1
0
1
0
1
1
0
2
1
1
0
2
1
0
1
1
1
1
2
0
1
0
1
1
2
1
1
1
1
1
1
2
0
1
0
1
1
0
1
2
1
0
2
2
2
1
1
1
0
1
0
1
2
1
1
1
0
2
2
1
1
1
1
0
0
1
1
1
1
1
2
0
2
2
1
0
1
1
2
0
1
1
2
1
1
1
0
2
1
2
2
1
1
1
2
2
2
2
1
1
2
2
0
1
0
1
0
1
2
1
1
2
1
1
1
1
1
1
1
1
0
1
1
1
0
1
1
2
2
5
1
0
0
1
0
2
2
1
0
0
2
1
1
1
2
1
0
0
1
1
1
0
1
1
1
1
1
2
1
1
1
1
0
0
2
1
0
1
2
0
1
2
1
1
0
1
1
1
1
0
1
1
2
1
1
0
1
1
2
2
1
1
2
1
0
1
1
1
1
0
2
2
2
2
1
1
2
1
1
1
2
2
0
1
1
1
2
0
0
1
1
1
1
1
1
1
1
1
0
0
1
0
0
0
1
1
1
0
1
0
0
0
2
1
1
1
2
1
1
0
0
2
1
2
1
1
1
0
1
2
2
1
1
1
1
1
1
2
0
1
0
1
0
1
1
1
2
1
1
1
2
1
0
1
2
1
2
1
0
2
1
1
1
0
3
2
1
1
1
1
1
1
1
1
0
1
1
1
1
2
1
1
2
1
1
1
3
1
2
1
1
1
2
0
1
1
1
0
1
1
2
0
0
1
0
1
1
0
2
1
0
1
0
2
2
1
1
1
2
1
0
1
2
1
0
0
1
1
0
3
1
1
1
1
0
0
2
2
1
1
0
1
1
1
1
1
1
3
1
0
1
0
1
1
1
1
0
1
2
1
2
1
1
0
1
1
1
1
0
1
1
2
2
1
1
0
0
2
1
1
0
1
1
0
1
1
1
0
1
1
0
2
2
0
2
2
1
1
1
1
1
1
0
0
0
1
1
2
1
1
0
1
2
1
2
2
1
1
2
2
2
0
2
1
2
1
0
1
1
1
1
0
1
0
2
1
1
2
1
0
1
2
0
2
1
1
1
2
0
0
0
0
2
0
1
1
1
2
0
1
1
1
1
0
1
2
0
1
1
1
1
2
1
1
1
1
0
0
0
2
1
0
0
1
2
1
1
1
2
1
0
2
1
1
0
2
1
1
0
1
2
1
0
0
2
0
1
1
2
0
0
2
0
1
1
0
0
2
0
0
1
0
1
1
1
1
1
0
2
1
1
1
1
0
1
1
2
1
0
0
1
2
3
1
1
2
1
1
2
1
1
1
0
0
1
1
1
1
1
2
2
1
1
2
0
1
2
1
1
1
2
1
1
1
0
0
1
2
0
1
1
1
1
1
1
1
0
2
1
1
1
2
1
1
0
2
1
1
1
2
2
2
1
1
1
1
1
1
3
2
1
1
2
1
0
0
1
0
0
1
0
1
2
1
1
1
0
2
1
1
2
2
2
0
1
1
1
1
1
1
2
1
1
2
0
1
1
2
0
1
1
1
1
1
0
1
1
2
1
1
1
2
0
1
0
0
2
0
1
1
1
1
1
0
0
1
1
0
2
2
2
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
2
0
0
2
2
1
1
1
1
1
1
1
0
1
0
1
1
0
0
2
1
2
1
0
5
2
1
1
1
2
1
1
1
2
1
1
1
2
1
2
1
0
2
2
1
1
0
1
0
2
1
1
1
2
1
1
1
2
2
1
1
1
1
2
1
1
1
2
2
1
0
1
1
2
1
2
0
0
1
1
2
2
1
0
1
2
1
0
2
0
2
2
0
1
2
1
1
1
0
1
2
1
1
2
1
1
0
1
0
1
2
1
1
2
0
1
2
1
1
1
1
1
1
2
2
1
2
1
0
1
1
0
1
1
1
2
1
2
1
2
1
0
2
2
0
1
0
1
1
1
2
2
1
1
1
1
0
0
1
0
1
1
0
1
1
2
1
1
1
1
2
1
2
2
0
1
2
0
1
0
1
1
1
1
2
0
1
2
0
1
1
1
2
0
1
2
1
2
2
0
2
1
1
1
1
0
2
2
2
2
2
1
2
1
2
0
1
1
1
2
1
2
2
1
1
2
2
1
3
2
1
1
0
0
2
0
1
1
2
1
1
1
1
1
1
0
2
2
1
1
1
0
1
0
2
0
1
1
1
1
2
1
1
1
0
1
1
0
1
1
1
2
1
1
1
1
1
1
1
1
0
3
1
0
2
1
1
2
1
2
1
2
0
2
0
1
2
1
1
2
2
0
1
0
1
1
1
0
1
1
2
1
1
2
1
0
1
2
1
2
1
2
1
1
1
0
1
1
1
2
1
1
0
0
1
1
1
1
0
2
1
2
1
1
2
0
1
1
2
0
0
0
2
1
1
1
0
1
2
1
2
2
1
1
0
0
2
0
1
1
2
2
1
1
2
1
1
1
2
1
1
1
1
1
0
1
1
1
1
0
1
1
2
1
2
1
1
1
1
1
0
2
1
1
1
1
1
1
1
0
4
2
1
2
1
1
1
1
1
2
1
1
1
1
0
1
1
1
1
2
1
1
0
1
1
1
2
2
3
2
0
2
1
0
1
2
0
2
2
1
2
2
1
2
1
0
2
1
1
1
2
0
0
2
1
1
2
1
0
1
1
0
1
0
1
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
2
1
2
2
1
1
2
1
0
2
1
2
1
2
2
1
2
1
1
2
3
2
1
2
2
1
1
1
1
0
1
0
0
1
0
1
1
1
1
1
2
3
1
1
2
0
3
2
1
1
0
1
1
1
2
0
1
0
1
1
2
0
1
1
0
2
2
1
1
0
1
1
1
2
2
0
1
1
1
1
1
1
0
2
2
1
1
0
1
1
2
1
1
1
1
1
2
0
1
1
1
2
1
1
0
2
1
1
1
2
1
2
1
0
1
0
2
1
0
1
2
1
1
1
0
0
1
2
1
1
2
2
1
1
1
1
1
1
2
1
1
1
0
2
1
1
0
2
1
2
1
0
2
1
1
1
1
0
1
1
2
1
1
1
1
1
2
1
0
1
0
1
1
1
2
1
1
2
2
1
1
1
0
1
1
0
1
1
1
1
0
0
1
1
4
1
2
0
2
1
1
1
2
1
0
1
1
1
1
2
0
1
1
1
1
0
1
1
1
1
1
1
1
0
1
0
2
0
1
1
1
1
1
1
2
1
1
1
2
1
3
1
2
1
1
1
2
2
2
1
2
0
0
1
1
1
1
1
2
1
2
1
2
2
1
0
1
2
2
1
1
2
1
1
1
0
1
1
1
2
0
1
1
2
0
2
1
1
0
7
2
0
1
1
1
2
2
1
1
1
0
3
1
1
1
2
2
1
1
0
1
2
1
1
1
0
1
1
2
0
1
1
1
1
2
0
1
0
1
2
1
1
2
1
2
1
1
2
1
1
1
2
2
2
1
0
2
0
1
2
1
1
2
2
2
0
1
2
1
1
1
1
2
1
1
1
1
0
1
1
1
2
0
0
2
1
1
1
2
0
1
2
1
0
0
1
1
1
0
0
0
1
2
0
0
0
1
1
1
1
2
1
1
1
0
1
1
1
2
2
2
1
2
0
1
0
1
1
1
1
2
1
0
1
2
1
2
1
1
1
1
0
1
1
1
0
0
1
1
1
1
2
0
2
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
3
0
2
1
2
1
1
1
1
1
0
1
2
1
1
1
1
1
2
1
0
0
1
2
0
1
1
2
1
0
1
2
0
1
1
0
1
1
1
1
2
2
1
1
1
2
1
0
1
1
0
1
1
1
1
0
1
2
2
1
2
2
1
1
1
1
1
1
1
2
0
1
0
2
1
1
1
1
2
2
2
1
2
2
1
1
1
1
0
2
1
1
2
2
1
0
0
1
1
0
1
2
1
2
1
1
2
0
1
1
0
0
1
0
0
1
0
2
1
2
2
2
0
2
1
2
0
0
1
0
1
2
1
1
2
1
1
0
1
2
1
1
2
0
0
1
2
1
0
1
1
1
2
2
0
2
1
0
0
1
1
1
1
0
0
1
1
1
1
0
2
1
1
1
1
1
1
1
1
0
2
1
1
0
2
1
1
0
0
1
1
1
2
2
2
1
1
1
0
1
2
0
1
1
0
1
1
2
0
0
2
1
1
0
1
1
0
0
1
1
1
2
1
1
1
2
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
0
1
2
1
1
2
1
1
2
1
2
1
2
1
2
0
2
0
2
2
0
1
1
1
1
1
1
2
1
1
1
1
0
1
0
1
2
1
1
1
1
1
1
2
0
4
2
2
1
0
0
1
1
0
1
1
1
2
1
1
1
4
2
1
2
2
1
1
0
1
1
2
0
0
1
0
2
1
1
1
0
1
3
1
2
1
1
0
2
1
0
0
1
1
1
0
1
1
2
1
0
1
2
1
0
0
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
0
1
1
1
1
1
1
1
0
1
1
1
0
2
1
0
1
1
1
1
1
2
1
1
0
1
1
2
1
1
1
0
0
1
2
0
1
0
2
2
1
1
1
1
2
0
1
1
1
1
1
0
1
1
1
2
1
0
1
1
1
2
2
1
1
1
2
0
1
0
2
1
2
1
1
1
0
2
1
1
1
2
1
2
1
0
1
1
1
1
1
1
1
1
0
1
1
2
1
0
1
1
1
1
1
0
1
1
0
1
1
1
1
1
1
1
0
1
1
1
1
1
1
2
0
2
0
1
1
1
0
0
1
0
1
1
1
1
2
1
2
1
1
0
1
0
1
2
1
2
1
1
2
2
1
1
1
0
1
1
1
0
1
0
1
2
2
1
2
0
1
1
0
0
2
1
3
1
1
2
1
1
1
2
2
1
2
1
1
1
3
1
1
1
1
3
1
0
1
1
1
1
1
1
0
1
1
1
0
2
1
2
1
1
1
1
1
1
0
0
0
2
1
0
1
0
2
2
1
2
1
1
2
1
2
1
1
1
1
2
2
1
1
1
2
0
1
2
1
2
2
2
2
2
1
2
0
1
1
1
1
0
1
1
0
2
0
1
2
1
2
2
1
1
1
1
1
1
1
1
0
0
2
1
0
1
2
2
1
1
0
0
1
1
1
1
2
1
1
0
1
1
1
1
1
1
2
1
1
2
1
0
1
2
0
1
1
1
0
1
0
0
1
2
1
1
1
1
1
0
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
2
2
2
1
1
1
0
2
1
0
1
1
1
1
2
1
1
2
2
0
0
2
2
1
1
1
1
1
1
1
1
3
1
1
1
1
1
1
1
1
2
2
1
0
1
2
0
0
0
0
1
1
1
1
2
2
1
1
1
1
1
1
2
0
1
1
1
1
0
3
1
1
1
1
1
2
1
1
0
1
0
1
2
2
1
0
2
1
1
0
1
0
3
1
1
2
1
1
0
2
2
1
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
2
1
1
1
1
1
1
1
2
0
0
1
5
0
0
1
3
2
2
2
1
1
2
1
2
1
0
1
1
1
1
1
1
1
1
1
1
2
1
1
1
0
1
0
0
1
2
1
1
1
0
1
1
1
0
1
1
1
1
1
2
2
2
2
1
1
2
1
1
1
1
2
2
2
1
1
1
0
2
0
2
1
1
2
1
0
1
0
1
1
1
1
1
2
0
2
1
2
1
1
2
0
1
1
1
0
0
0
2
2
1
2
1
2
1
1
1
2
0
1
1
1
2
1
2
1
0
3
1
1
2
2
2
1
2
2
1
1
1
1
2
1
1
1
2
1
1
1
0
0
1
0
0
1
1
3
0
1
1
1
1
2
2
1
1
1
2
0
1
2
1
1
0
1
1
2
0
1
0
1
0
1
2
1
2
1
2
1
2
2
2
2
0
1
0
2
1
0
0
1
1
1
0
2
2
1
1
0
0
1
1
1
1
1
2
1
2
1
2
1
0
1
1
2
1
1
1
1
1
1
2
1
0
2
1
1
1
1
1
1
1
2
1
0
1
1
2
1
2
2
1
1
1
0
1
2
1
2
0
0
0
1
1
2
2
0
2
1
1
1
1
0
1
1
1
0
2
2
1
1
2
1
1
1
1
2
2
0
0
1
2
1
1
2
1
1
1
0
1
1
1
2
2
1
0
1
1
1
2
2
1
1
1
0
0
2
1
0
1
2
1
1
1
1
2
1
1
0
1
0
1
2
1
1
1
0
2
0
0
0
2
0
2
1
1
2
1
0
2
1
1
1
1
2
0
1
1
1
1
1
2
1
2
2
1
2
1
1
1
0
1
1
0
0
1
2
0
0
0
1
1
0
2
1
1
1
0
2
2
1
2
2
2
1
2
2
1
2
1
2
0
1
1
1
1
2
2
1
1
1
0
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
0
2
1
1
2
2
2
1
2
2
1
0
1
1
1
1
1
1
0
1
1
1
0
1
0
0
1
1
0
1
1
0
1
1
2
1
0
1
1
1
0
1
1
0
2
1
1
1
2
1
2
1
1
0
1
0
0
0
0
1
0
1
1
1
1
1
0
1
2
2
0
0
1
0
2
1
0
1
2
2
1
1
1
2
1
0
2
0
1
2
2
1
1
0
1
2
1
1
1
1
0
1
2
0
1
1
1
1
4
1
1
1
2
1
1
1
1
0
0
0
2
1
1
0
1
1
2
2
0
0
0
1
1
2
1
1
2
1
0
1
1
1
1
1
1
1
1
2
1
2
2
1
2
1
2
1
0
2
1
0
1
1
3
1
1
2
2
0
1
2
1
2
1
1
1
1
1
2
1
1
2
1
0
2
1
1
1
0
1
0
1
2
0
1
1
1
2
1
2
1
1
1
2
1
1
1
1
0
1
2
2
2
1
1
2
0
0
0
1
0
1
1
1
1
1
1
2
2
2
0
0
1
0
1
2
1
2
0
1
1
1
1
0
2
1
0
0
1
1
2
1
1
1
2
0
1
2
1
2
1
0
0
1
2
1
1
1
1
2
2
2
1
1
2
1
1
1
0
1
2
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
0
1
1
1
1
1
0
1
2
1
0
2
1
1
2
0
1
1
1
2
0
1
1
2
1
1
1
0
1
0
1
1
2
0
3
1
1
1
0
0
1
2
1
1
1
1
0
1
2
1
0
0
1
1
1
1
0
2
1
1
0
0
2
1
2
1
1
1
1
0
1
1
0
1
2
2
1
2
1
1
1
1
1
0
0
1
0
0
1
1
0
1
1
1
1
0
0
1
3
1
3
1
2
1
2
2
0
0
1
1
1
1
1
2
1
1
0
2
1
1
1
0
0
1
0
0
2
1
2
2
3
1
1
0
1
0
2
3
2
1
2
0
1
1
1
1
2
1
2
1
1
1
1
0
1
1
1
1
2
1
1
1
1
0
1
2
2
2
0
1
2
0
1
1
0
0
0
1
0
2
1
1
2
1
0
1
1
1
2
0
1
2
1
1
2
1
1
1
1
2
0
0
1
2
0
1
1
1
1
1
2
0
1
1
2
2
2
1
1
2
1
0
0
1
1
1
1
0
1
1
1
2
0
1
1
1
2
0
0
2
2
1
1
1
1
1
1
1
1
0
0
2
1
1
2
2
1
1
1
2
1
0
2
1
2
1
3
1
0
0
2
1
1
2
1
1
1
0
2
2
0
2
2
1
0
2
1
1
2
0
2
1
1
2
1
1
0
0
1
2
2
1
0
1
1
2
2
0
1
1
1
1
1
1
1
1
2
1
1
2
1
0
1
2
1
2
1
1
0
1
1
2
1
1
1
1
1
1
1
1
2
0
0
0
0
2
2
1
1
2
0
1
2
2
2
1
1
3
1
0
2
2
1
1
1
0
1
1
0
1
1
2
1
1
1
0
2
0
1
0
1
2
1
2
2
1
1
2
1
1
2
0
1
1
0
1
2
1
1
1
4
0
0
0
1
1
1
2
2
1
0
1
0
1
2
1
2
1
1
1
1
1
2
1
0
2
1
1
0
1
0
1
1
1
2
1
2
1
1
2
0
1
0
1
1
1
2
1
1
0
1
2
0
1
1
1
1
0
2
0
1
2
1
2
0
0
1
0
3
1
2
1
0
2
1
2
0
1
2
0
1
1
0
3
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
0
1
2
0
1
0
1
2
1
1
1
2
2
2
2
1
1
2
2
1
1
2
1
2
1
0
1
0
1
0
2
0
1
0
1
1
1
1
1
1
1
1
1
0
0
2
1
2
1
1
1
1
0
0
1
1
0
1
2
0
2
1
2
1
2
0
1
0
1
1
1
1
1
1
1
1
1
0
1
0
1
1
1
1
2
1
1
0
2
2
1
1
0
1
1
1
2
1
1
1
1
1
2
1
2
0
1
1
2
2
1
1
1
2
1
1
2
2
2
0
1
3
1
1
1
0
2
0
1
1
1
1
1
1
1
2
1
0
1
1
0
1
2
1
1
0
1
2
1
2
1
1
0
1
1
2
1
1
1
1
0
1
1
1
1
2
0
2
0
2
1
1
1
2
2
2
2
1
1
1
1
1
1
1
1
0
1
1
0
0
1
1
2
2
1
2
1
0
0
0
1
1
0
1
0
2
0
1
2
1
0
1
2
2
1
1
1
1
1
0
2
1
3
2
0
1
1
1
1
1
0
9
1
2
1
1
1
1
0
0
2
1
1
1
2
1
1
2
1
1
1
1
1
1
3
1
1
1
1
1
1
1
2
1
1
2
1
2
1
2
0
1
2
1
1
1
2
1
1
1
1
0
1
0
1
2
0
1
1
2
2
1
1
1
1
1
0
2
1
2
1
0
1
0
0
1
2
0
1
1
1
1
1
1
1
1
1
1
1
2
1
0
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
1
4
2
0
1
1
1
1
1
2
0
2
2
2
1
1
0
0
1
0
2
1
1
1
1
0
1
1
0
1
1
1
2
1
1
1
2
2
1
1
1
1
1
2
1
1
1
1
0
2
0
0
0
2
1
0
0
1
1
1
1
2
1
0
1
0
1
1
2
0
0
2
1
0
1
2
2
1
0
2
1
1
0
1
0
0
1
1
1
1
1
0
1
2
2
1
1
1
1
1
0
1
0
2
1
1
1
0
0
2
0
2
2
1
1
1
0
2
2
1
0
1
0
2
1
1
1
0
2
1
1
0
1
2
0
2
1
1
1
2
2
2
1
1
1
2
2
2
2
0
1
0
0
2
0
2
1
2
2
0
1
1
1
1
0
0
1
2
1
1
1
2
1
1
0
1
1
0
2
1
1
1
2
0
1
0
1
2
1
1
1
1
0
2
1
1
1
2
2
1
2
1
1
2
1
1
1
1
1
0
1
1
1
1
1
3
1
2
1
0
1
2
1
0
2
2
2
2
2
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
0
1
1
0
1
0
1
2
1
1
0
1
1
1
2
1
1
1
1
1
0
1
1
1
2
1
2
1
1
0
2
2
1
1
2
1
0
1
2
2
0
2
1
0
1
1
1
1
2
1
2
2
1
2
3
1
2
1
1
1
1
2
1
1
2
1
1
1
1
0
2
1
1
2
0
0
0
1
2
0
1
1
1
1
1
1
0
1
0
1
0
1
2
1
2
1
2
0
1
2
1
1
2
1
1
2
2
1
1
2
1
1
1
2
1
1
2
1
1
2
0
1
2
1
2
1
2
1
0
2
1
2
1
0
2
1
0
1
1
0
2
0
1
1
0
2
1
2
1
1
2
1
1
1
2
1
2
1
2
1
0
1
1
0
1
1
1
1
2
1
1
2
0
1
1
0
0
1
0
0
2
1
2
1
1
0
1
0
0
1
1
1
2
1
3
0
0
1
1
0
2
1
1
0
2
1
1
0
1
1
1
1
1
2
1
2
2
1
1
1
1
0
1
2
2
2
2
2
1
1
0
1
0
0
1
1
1
2
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
0
1
1
1
1
1
1
1
1
1
0
0
1
2
1
1
2
1
1
1
1
1
0
1
2
2
2
2
1
2
0
2
2
0
1
2
0
1
1
0
1
0
0
0
1
3
1
1
0
1
2
1
2
1
1
1
1
0
2
1
0
1
0
0
1
1
2
1
1
1
1
1
0
1
1
0
1
2
0
1
1
2
1
1
0
1
2
0
0
1
0
1
0
0
1
1
0
1
2
1
2
1
1
1
1
1
2
2
1
1
1
0
0
2
1
1
1
1
0
1
0
1
0
1
1
1
0
0
1
1
1
1
1
1
2
2
0
2
0
3
0
1
2
0
1
1
0
0
1
0
1
1
2
1
1
0
2
1
1
1
0
1
2
2
1
1
2
1
1
1
2
2
0
1
1
0
0
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
1
0
1
1
1
1
1
2
2
0
0
1
0
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
0
1
1
2
1
0
0
1
1
1
0
1
1
2
2
0
0
0
1
2
1
1
1
0
1
1
1
1
0
1
1
1
0
1
1
1
2
1
0
1
2
1
2
0
2
0
1
1
2
2
1
1
1
1
1
0
1
1
1
1
0
1
0
2
1
1
1
1
0
2
1
1
1
1
0
1
1
2
2
0
0
1
2
1
2
1
1
0
1
1
4
1
1
1
1
1
1
1
0
1
1
1
1
0
2
0
0
1
1
1
1
2
1
2
1
1
1
1
1
0
2
1
1
2
2
1
0
0
0
2
1
2
1
2
1
2
1
0
1
2
1
0
0
1
2
1
1
2
1
2
0
1
1
0
1
1
2
1
0
1
1
2
1
2
1
1
1
1
1
1
0
1
1
1
0
0
1
2
1
1
2
2
1
1
2
1
1
1
1
2
1
0
1
2
1
1
0
1
1
1
1
1
0
1
1
3
2
1
0
1
0
1
1
1
1
2
1
0
1
2
2
1
1
1
2
2
1
1
1
1
1
1
0
1
1
2
0
0
2
1
3
0
0
1
1
2
1
1
1
1
1
2
1
1
0
1
2
1
2
0
2
1
1
1
1
2
2
2
0
1
1
1
2
1
2
1
1
1
2
2
1
2
1
2
7
1
2
1
1
0
1
1
1
0
1
1
1
1
4
1
2
2
1
3
1
0
1
1
1
2
2
3
0
1
1
2
0
0
0
1
1
1
1
1
2
2
0
0
1
1
1
0
1
1
0
2
1
1
2
0
0
1
1
1
1
1
1
1
0
1
0
1
2
2
1
1
2
2
3
1
1
0
1
1
1
2
0
1
1
1
1
0
0
1
1
2
1
1
2
1
1
2
2
0
1
0
1
0
2
1
2
1
0
2
2
1
1
1
1
1
1
1
2
1
4
1
1
2
1
2
1
0
1
1
1
0
1
0
1
2
2
2
1
1
1
1
1
0
0
2
1
0
0
2
0
1
0
0
3
1
1
0
2
1
0
1
0
1
2
1
1
0
2
0
1
0
2
1
2
1
1
1
1
2
1
2
1
1
2
0
1
1
1
1
0
1
1
2
0
1
1
0
0
1
1
1
1
0
2
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
0
0
0
0
0
1
2
0
1
1
1
0
2
0
1
0
2
1
2
1
2
1
1
2
1
1
1
0
2
1
1
1
1
1
1
1
1
1
0
1
2
1
1
1
1
1
1
1
1
1
2
1
1
0
0
1
1
1
0
0
2
0
1
0
0
2
1
1
1
2
2
1
1
1
1
0
1
1
1
1
1
1
2
2
5
1
0
2
1
1
2
1
1
1
1
0
1
1
0
0
1
2
1
1
1
2
2
1
2
2
1
1
2
1
0
1
1
1
0
1
0
0
1
1
2
1
1
1
1
2
1
0
2
0
1
2
1
1
0
1
1
2
1
1
1
0
1
1
2
1
0
1
1
1
1
0
1
2
1
1
1
1
0
2
0
1
0
0
0
0
2
2
1
1
1
0
1
1
2
2
1
1
1
0
0
1
1
1
1
0
1
1
0
1
1
1
1
0
1
1
0
1
1
2
1
0
1
1
0
1
1
0
1
1
1
1
1
1
1
1
1
0
1
2
0
0
1
0
1
2
0
3
1
2
1
2
1
2
0
0
2
1
2
1
1
0
1
0
1
1
1
2
1
2
1
0
0
0
1
2
2
0
0
1
2
2
1
1
2
1
1
2
1
1
0
1
2
2
1
1
2
2
0
1
1
0
1
1
1
0
1
1
2
2
1
1
0
1
1
2
1
1
1
1
2
1
1
2
1
1
1
0
1
1
1
1
1
1
1
1
0
1
1
2
1
1
1
1
2
0
1
1
0
1
1
0
2
1
2
1
1
1
0
2
2
1
2
1
0
1
1
1
2
1
1
1
0
1
1
2
1
2
1
2
1
1
1
1
1
2
1
1
1
1
2
0
2
1
2
1
1
1
1
2
1
1
1
1
1
2
0
1
2
1
0
1
1
1
2
0
1
0
1
0
0
2
0
1
1
0
1
1
1
1
2
2
2
0
1
0
1
1
1
1
2
0
0
1
1
2
2
2
1
2
0
2
2
1
2
1
2
1
1
1
2
2
2
1
0
0
0
2
1
1
2
1
2
1
1
0
0
1
1
0
1
1
0
3
1
0
1
0
1
1
0
1
1
2
1
1
0
2
1
1
1
2
1
0
1
1
1
2
1
1
1
0
1
2
1
2
2
0
1
1
1
1
1
1
2
1
1
1
0
1
1
1
2
0
1
0
1
1
0
2
2
2
1
0
1
1
0
1
1
0
0
1
0
1
1
0
0
0
1
1
2
2
1
1
1
1
1
1
2
0
1
1
0
2
1
0
1
2
2
1
1
1
1
2
0
0
1
1
1
2
2
1
1
0
1
0
2
1
1
1
0
2
1
1
1
2
1
0
1
1
1
1
1
1
0
4
1
1
2
1
1
0
1
1
1
2
1
2
1
1
2
0
2
0
1
2
0
1
0
2
1
1
2
1
1
2
0
0
0
0
2
1
1
0
2
1
1
0
1
1
1
2
1
0
1
1
2
1
1
1
1
1
2
1
1
1
1
1
0
1
1
0
1
1
0
1
2
2
1
0
1
0
2
1
1
2
0
2
2
0
2
2
1
0
1
2
1
1
0
0
1
1
0
1
1
2
1
1
1
1
1
0
2
0
2
0
1
1
1
3
1
1
1
2
1
1
1
0
1
1
2
0
1
1
1
2
2
1
2
2
0
2
2
2
1
2
0
1
1
1
2
1
1
1
2
1
1
1
1
2
2
2
2
1
1
1
2
2
1
1
0
0
1
1
1
2
1
1
1
0
1
1
0
1
1
0
1
2
2
1
1
1
1
2
3
1
0
2
1
1
1
0
0
1
1
2
1
1
1
1
2
1
1
1
1
2
0
1
2
1
1
1
1
0
1
1
1
1
0
1
2
1
1
2
1
1
1
0
2
1
4
1
1
0
0
1
1
1
1
1
1
1
0
1
0
1
1
0
0
1
1
1
1
0
0
2
1
0
1
1
2
1
1
2
1
0
2
1
2
1
1
0
1
1
1
2
2
1
1
2
3
0
1
1
0
1
1
2
0
1
2
1
1
3
2
2
1
2
1
1
2
1
0
1
1
0
1
1
0
1
0
0
2
1
1
2
1
1
2
0
0
2
0
0
1
3
1
2
1
2
0
0
1
0
1
1
1
2
1
1
0
1
0
1
2
1
0
2
1
0
1
2
1
1
1
2
2
1
0
2
1
1
0
1
2
2
1
1
1
0
2
1
3
2
2
0
1
1
2
0
0
0
1
2
1
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
2
0
2
1
1
1
2
1
1
1
1
1
2
1
1
3
1
1
0
1
0
1
1
0
0
0
1
0
2
1
0
2
1
1
0
0
1
1
1
2
2
1
0
1
0
1
2
1
1
0
2
2
1
0
1
0
1
1
1
1
1
1
2
1
0
1
1
1
1
1
1
1
1
2
1
4
1
1
2
1
0
2
2
2
1
1
1
1
1
0
2
2
2
1
2
1
2
1
0
1
2
0
1
0
2
1
0
1
1
1
1
1
1
1
2
1
1
1
1
2
1
0
1
1
1
1
2
1
1
1
1
1
2
1
1
1
0
1
1
0
2
1
0
1
2
1
1
0
1
2
2
1
1
0
1
1
1
1
1
1
0
2
1
1
1
2
1
0
2
0
1
2
1
1
0
1
1
1
2
0
1
1
2
2
2
1
2
0
0
1
0
2
2
2
0
2
2
1
2
1
1
1
1
0
0
1
2
1
1
1
1
2
1
0
1
1
1
1
1
2
1
1
2
0
2
1
2
1
2
2
2
0
0
2
2
1
1
1
0
1
0
3
2
1
1
1
2
1
2
0
1
0
0
1
1
0
2
1
2
2
2
1
1
0
2
0
2
1
1
1
2
1
1
1
2
1
0
1
0
1
1
0
1
1
1
1
1
1
1
0
1
2
2
1
2
1
0
1
2
1
1
1
0
1
2
1
1
1
0
2
1
2
1
1
2
2
0
2
1
1
1
1
2
2
1
2
2
1
1
0
0
2
1
1
1
1
1
1
1
1
2
1
0
2
1
1
2
2
0
2
1
0
1
1
1
1
1
1
1
0
1
2
1
0
2
1
1
1
1
1
1
0
2
1
1
1
0
1
1
2
1
1
1
1
1
2
0
0
1
2
0
1
0
0
2
2
0
1
1
2
0
4
1
1
1
1
1
1
1
1
1
2
2
2
1
1
2
1
1
0
1
1
1
2
1
2
1
2
2
1
0
1
1
0
0
1
1
2
1
2
2
1
2
1
2
2
2
0
1
1
2
1
2
1
1
1
1
2
1
1
1
0
1
1
1
1
1
1
0
1
2
0
1
1
1
1
2
1
2
2
1
1
0
1
2
1
1
0
2
2
0
1
0
2
0
1
1
1
0
1
0
1
1
1
1
2
1
1
2
1
1
2
1
1
2
2
2
2
1
2
1
2
2
1
1
0
2
1
2
1
0
2
1
2
1
2
1
2
1
1
1
1
0
2
1
1
1
1
2
2
2
2
1
0
1
1
0
0
2
1
1
2
0
1
2
0
1
2
1
1
0
1
1
2
2
2
1
2
0
3
0
2
2
1
1
2
1
1
1
2
1
2
1
1
2
2
1
0
1
1
1
1
0
1
0
1
1
1
0
2
1
1
0
1
2
2
0
1
0
1
2
1
2
1
0
2
2
0
1
1
1
2
1
2
1
3
1
2
2
0
0
2
1
1
1
0
0
1
1
1
1
0
0
1
1
1
0
1
3
1
1
1
0
2
2
1
1
1
1
2
0
1
1
2
1
1
1
1
1
1
2
1
0
1
1
1
1
1
0
2
1
1
1
1
0
0
2
1
0
1
1
1
1
1
1
1
0
2
1
1
0
2
1
1
1
0
1
1
1
1
2
1
1
1
1
1
0
1
1
0
1
1
1
2
1
2
1
2
1
2
1
0
0
1
1
1
1
0
1
1
1
0
0
0
1
1
2
0
2
0
1
1
1
0
2
2
1
2
1
1
1
3
1
1
1
1
1
1
1
0
2
2
1
2
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
0
1
2
1
1
1
0
1
0
1
1
1
1
2
1
1
2
1
0
1
1
1
2
0
1
1
1
1
1
0
2
1
2
1
1
3
2
0
1
1
2
2
0
1
0
0
1
0
0
1
1
1
1
0
1
1
1
1
2
2
1
1
1
1
2
1
0
0
2
1
1
2
1
0
1
1
1
1
1
1
2
0
1
1
2
1
2
1
1
0
2
1
1
2
1
0
1
0
2
1
1
1
2
0
2
2
1
0
2
0
2
2
1
2
1
2
2
1
1
1
0
1
1
0
1
0
2
1
0
2
0
1
0
1
1
1
2
4
1
2
0
1
1
1
1
1
2
1
0
1
1
1
1
1
2
1
1
1
0
0
1
1
2
1
1
1
0
2
1
1
2
2
1
1
2
2
1
1
1
1
2
0
1
0
1
1
1
1
1
1
1
1
1
2
0
1
1
1
1
2
1
1
2
2
2
1
1
2
1
2
1
0
1
2
1
1
1
1
1
1
1
1
2
1
2
2
0
1
2
1
2
1
1
2
2
2
1
2
2
0
2
3
1
1
2
2
2
0
1
0
1
2
2
1
1
0
1
1
0
1
1
1
2
1
0
1
2
1
0
0
0
1
1
1
1
0
2
2
1
2
0
1
2
0
1
1
0
2
1
1
2
1
1
0
2
2
0
1
2
2
1
2
1
1
2
1
1
2
1
0
2
2
0
1
1
0
1
2
1
0
1
1
1
2
0
0
2
1
1
0
2
2
1
1
1
1
1
2
1
1
1
2
1
1
0
2
1
2
1
1
2
0
0
0
1
1
1
1
2
1
1
1
0
2
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
2
1
0
1
1
1
1
1
2
2
1
2
1
1
1
1
1
2
0
1
1
2
0
0
0
1
1
1
1
0
0
1
1
2
0
2
1
2
0
2
1
0
1
0
0
0
1
1
1
1
0
2
1
1
1
0
2
0
1
1
1
1
0
1
0
0
0
1
1
0
2
1
0
2
1
1
1
1
1
2
1
1
1
2
1
1
2
1
1
1
2
1
2
1
0
2
2
1
2
1
1
1
1
2
0
1
1
2
1
0
1
1
0
1
1
0
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
0
2
0
1
1
2
2
2
2
1
0
1
1
2
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
0
1
2
1
0
1
1
0
0
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
2
3
1
1
2
1
1
1
1
1
1
1
2
0
1
2
1
2
0
2
2
2
1
0
1
2
1
1
0
1
1
0
1
0
2
1
1
0
1
1
2
1
1
0
2
1
2
1
0
1
1
0
2
1
1
1
1
2
1
1
1
2
1
2
1
2
1
1
0
1
2
1
1
1
1
0
1
2
2
0
2
2
1
1
2
1
2
0
1
1
1
1
1
1
1
0
2
1
2
1
1
1
1
1
1
1
1
3
2
1
1
0
2
1
0
0
1
2
1
0
0
1
1
1
0
2
1
1
0
1
2
1
1
0
1
0
2
1
0
1
1
2
1
1
1
2
1
1
1
1
2
1
2
1
0
1
1
1
2
2
2
1
1
1
1
1
0
2
0
1
2
1
1
1
1
1
2
1
1
2
2
1
1
1
0
1
1
1
0
0
2
0
0
1
1
1
1
1
2
1
1
1
1
1
1
2
0
1
2
2
1
2
1
0
1
2
0
1
2
2
1
2
1
1
1
0
1
1
0
3
1
1
1
2
1
1
1
1
1
3
1
1
1
1
1
1
2
1
0
1
0
1
1
2
2
2
0
1
3
1
2
2
2
1
2
2
1
1
1
0
1
1
1
1
1
1
0
1
2
0
1
1
2
1
1
0
1
1
1
1
0
2
1
2
1
2
1
1
1
0
1
2
2
1
1
2
1
1
1
1
2
0
2
1
1
2
1
0
1
1
1
1
0
1
1
0
1
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
0
1
1
4
1
1
0
0
1
2
1
1
1
1
1
0
0
1
1
2
1
0
1
0
2
0
2
1
1
1
2
0
1
1
0
1
1
1
0
1
2
1
0
1
1
3
0
0
2
1
1
0
1
1
1
1
1
0
0
1
1
1
1
0
1
1
1
3
1
1
1
2
1
1
0
0
0
1
1
1
0
1
2
0
1
0
1
1
1
0
1
1
1
1
1
2
2
1
2
1
2
2
0
0
1
1
0
1
1
1
1
1
1
1
2
2
1
1
1
1
1
0
1
1
2
2
2
2
1
1
2
0
0
2
1
1
0
1
1
1
1
0
1
1
2
1
1
2
1
1
1
2
1
2
1
1
0
2
2
1
1
1
2
2
1
1
1
2
1
2
1
0
1
1
1
1
1
1
1
1
1
0
1
0
1
2
1
1
1
1
2
1
1
0
1
1
1
1
2
2
0
1
0
1
1
1
1
0
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
2
1
1
0
2
1
0
1
2
2
4
1
1
2
2
1
2
1
0
2
0
1
1
2
1
1
2
1
0
2
1
1
0
2
1
1
1
2
1
0
2
1
1
1
0
1
1
2
2
2
1
1
2
0
1
2
1
1
0
1
1
1
1
2
1
1
0
1
1
1
2
2
1
1
1
0
1
0
1
2
0
1
1
1
1
2
1
2
0
1
2
0
1
2
1
1
0
0
1
1
1
1
1
1
1
2
2
2
1
0
1
1
1
1
1
0
1
1
1
1
2
1
1
2
1
0
0
1
1
2
1
0
1
2
1
1
0
1
1
1
0
1
0
1
1
1
1
1
0
1
1
2
1
1
1
1
2
0
1
1
1
1
1
1
1
1
0
0
2
2
0
0
1
1
1
0
1
1
3
0
1
1
0
1
1
2
1
1
1
1
1
1
2
1
1
1
2
0
2
0
1
1
1
1
1
1
1
1
2
3
1
2
1
2
2
1
1
1
2
0
0
2
1
1
0
1
0
3
2
2
2
1
1
0
1
1
3
1
1
1
1
1
1
0
1
1
1
2
1
1
0
1
2
1
0
1
1
1
1
0
1
2
1
1
2
1
1
1
1
1
1
2
0
1
0
1
1
1
1
1
2
1
1
0
1
1
1
1
1
1
1
2
1
0
0
1
1
1
1
0
1
1
2
1
0
2
2
1
1
1
1
1
0
2
2
1
1
1
2
1
1
1
0
2
1
1
0
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
0
1
2
1
1
1
1
1
2
1
1
2
1
1
0
1
2
2
0
0
1
0
1
1
1
1
1
1
1
2
1
1
1
1
1
2
2
2
1
2
1
0
1
1
1
1
1
1
1
2
0
1
1
1
1
1
1
2
2
1
1
0
0
2
1
0
1
1
0
1
1
2
1
1
1
0
2
1
1
1
1
2
1
1
0
1
2
1
1
0
0
3
1
1
2
1
1
2
1
1
1
1
0
1
1
1
2
1
2
1
2
1
2
1
0
1
2
2
1
0
2
2
2
0
2
2
2
1
1
1
1
1
1
0
2
1
2
1
2
0
1
1
2
1
2
2
0
1
2
1
1
1
1
1
1
0
1
2
0
2
1
1
2
1
2
2
1
1
0
2
2
1
2
1
0
0
1
1
1
2
1
2
0
0
3
1
1
2
2
1
1
1
1
4
0
1
1
1
0
1
0
1
1
2
1
1
1
2
2
1
1
1
1
1
1
1
1
2
2
2
1
1
1
0
2
1
1
1
1
0
1
1
1
1
2
0
1
1
1
1
1
1
0
0
1
1
1
1
1
0
1
0
2
1
1
0
1
0
1
0
2
1
0
0
1
2
1
1
0
0
1
1
0
1
1
1
2
1
1
3
1
1
1
1
1
0
1
2
2
1
0
2
0
1
1
1
2
2
1
1
0
1
0
2
0
0
0
1
1
1
1
1
2
1
2
1
1
0
1
1
2
1
2
1
2
1
1
1
1
1
1
2
1
1
1
2
0
2
1
2
1
2
1
1
1
1
0
1
2
1
0
1
1
2
1
1
1
0
1
1
1
1
2
2
1
1
2
0
0
2
2
0
1
0
2
2
1
2
0
1
1
1
1
1
1
1
1
0
0
2
1
1
1
1
2
1
0
1
1
0
1
1
0
0
2
1
2
1
1
2
1
2
0
1
1
1
2
0
1
1
1
0
1
0
0
1
0
2
1
1
1
1
1
1
2
1
2
1
1
1
1
0
1
2
2
2
1
2
1
0
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
0
2
2
0
1
1
1
2
1
1
1
0
2
1
1
0
1
2
0
2
2
1
2
1
1
2
3
1
1
0
1
1
1
2
0
0
0
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
2
1
1
2
0
0
2
1
1
1
1
1
1
0
2
1
1
1
0
1
1
1
0
2
1
1
1
1
1
1
2
2
0
1
1
0
1
1
1
1
2
1
0
2
2
1
1
1
1
1
2
0
0
2
1
1
2
1
2
1
1
0
1
0
1
1
0
1
0
1
1
0
1
0
2
1
1
0
2
2
1
1
2
2
0
2
1
1
0
0
1
1
1
1
2
1
1
0
0
1
1
0
1
2
1
1
1
1
0
1
0
1
1
1
2
2
1
3
2
2
0
2
1
1
2
2
1
0
2
1
2
1
2
1
0
2
2
1
1
0
2
1
1
1
1
1
2
1
1
2
1
1
2
2
0
0
1
2
2
0
1
1
0
2
2
0
1
1
6
1
2
2
1
1
1
1
1
1
1
1
3
2
1
1
0
1
1
3
0
0
2
1
1
1
1
2
1
1
2
0
0
0
1
1
1
1
1
1
1
2
0
1
2
2
0
0
1
1
1
1
1
1
1
2
0
1
2
1
1
2
1
1
1
1
0
2
2
2
1
1
1
2
1
1
2
1
1
2
1
1
1
0
1
1
1
0
2
2
1
1
0
1
1
1
1
1
1
2
0
0
1
1
1
0
0
1
1
1
1
1
1
1
1
2
2
2
1
2
2
1
1
1
0
1
1
1
2
1
1
2
2
0
0
0
1
1
1
0
0
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
0
1
1
1
0
1
1
1
1
1
2
1
1
0
1
1
2
1
0
1
1
2
1
0
1
0
1
1
2
1
1
1
1
1
2
0
0
2
1
1
1
0
2
1
0
1
2
1
1
1
1
1
1
2
2
0
0
1
1
2
1
1
1
2
1
0
1
2
1
1
0
2
1
2
1
1
1
1
1
0
0
2
1
2
2
0
0
1
1
2
1
1
1
0
1
2
1
0
1
1
2
2
0
1
2
1
2
3
2
2
1
2
1
1
2
1
1
0
1
1
1
2
1
4
1
2
1
1
1
1
1
1
1
0
1
2
1
1
0
1
0
1
1
1
1
2
0
1
1
1
1
2
0
1
1
2
1
1
1
2
0
2
1
1
1
0
0
1
0
2
1
0
1
0
1
1
1
1
0
0
1
0
1
2
2
1
1
1
1
1
0
1
1
1
0
2
0
1
1
0
2
1
1
1
1
0
1
0
0
1
1
2
1
1
1
0
1
1
1
2
2
2
2
1
1
2
0
1
1
2
1
2
1
0
1
2
1
0
1
1
1
2
1
3
2
2
0
2
0
1
2
2
1
2
2
1
1
1
1
1
1
1
2
0
1
2
1
2
1
1
0
0
0
1
0
0
1
1
0
0
1
0
1
2
1
2
0
1
0
1
1
1
0
0
2
0
1
2
0
2
1
1
3
1
1
0
1
1
0
1
1
1
2
2
1
0
1
1
0
1
1
3
1
1
1
1
1
1
1
1
2
0
1
1
1
1
2
1
0
2
1
2
1
0
1
1
1
1
1
1
0
1
2
2
1
1
0
1
1
0
0
2
2
0
1
0
1
1
0
1
1
1
1
1
0
0
1
2
0
0
1
1
0
1
0
1
1
2
0
2
0
0
2
1
1
2
1
1
0
2
2
2
1
1
0
2
2
2
1
2
2
2
1
1
2
1
2
2
1
2
0
2
1
1
1
1
1
1
1
2
0
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
1
1
1
1
0
2
1
1
1
1
1
2
1
2
1
2
1
1
2
2
1
1
0
1
1
1
1
1
1
1
1
1
2
1
2
1
2
1
3
2
1
1
1
0
2
2
1
2
2
1
1
1
1
1
1
2
1
0
1
1
1
1
1
1
1
0
1
0
1
2
1
1
0
1
0
2
1
0
2
1
1
2
1
2
1
2
1
0
1
1
0
1
1
0
2
1
1
0
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
2
2
1
1
1
1
1
2
1
1
1
0
1
1
2
1
1
1
1
0
2
0
0
1
1
1
1
1
0
1
2
1
1
2
1
1
1
1
1
1
2
1
0
1
2
1
0
2
1
2
0
1
1
0
1
0
0
1
2
1
1
0
0
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
1
1
0
2
0
2
1
1
0
1
2
1
2
1
2
2
2
0
0
1
1
1
1
0
0
1
2
1
1
2
0
3
1
0
1
0
2
2
2
1
1
2
1
1
1
1
2
1
2
1
1
2
1
0
0
1
0
0
1
0
1
1
1
2
1
1
1
1
0
3
0
2
2
1
1
0
2
1
0
1
1
2
2
0
1
1
1
1
2
1
1
1
1
1
1
1
1
2
0
0
2
2
0
1
2
1
2
0
1
0
1
0
1
1
0
2
1
2
2
2
2
2
1
1
1
1
1
2
1
1
1
0
1
0
2
1
0
1
1
1
1
2
2
1
2
1
1
0
0
1
0
1
1
2
1
2
2
0
0
2
2
0
1
0
1
0
1
2
1
1
1
1
1
1
0
2
0
1
1
1
2
0
1
1
1
2
1
2
2
0
0
1
2
1
1
2
2
2
2
0
1
2
2
2
2
7
0
0
1
2
2
2
2
0
1
1
2
2
2
1
0
2
1
2
1
1
1
2
0
0
2
2
2
2
0
1
0
2
0
0
2
1
1
1
2
1
2
1
0
3
1
2
1
0
1
1
1
1
2
1
1
1
2
1
1
2
1
1
0
0
1
0
1
1
2
1
1
0
1
1
1
1
1
1
1
1
2
1
2
1
0
0
1
0
1
1
0
1
1
0
1
1
1
1
2
0
1
1
1
2
0
1
2
1
2
1
1
1
1
0
1
2
2
1
1
2
0
0
1
0
0
1
0
2
2
1
1
1
1
1
1
1
1
2
1
1
2
1
0
1
1
0
1
2
0
2
0
1
1
2
0
1
1
0
1
0
2
0
1
1
2
0
2
0
0
2
1
1
1
1
0
0
1
0
2
1
0
2
0
1
2
1
1
0
2
1
0
1
1
1
1
1
2
1
2
2
1
2
1
1
1
1
0
2
2
0
1
2
1
1
0
0
1
1
1
1
2
1
0
1
1
0
1
1
1
1
0
1
0
1
1
2
1
1
0
1
1
1
0
1
1
1
1
1
0
0
1
1
2
2
0
1
2
1
0
1
0
2
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
2
1
1
1
0
1
1
1
1
2
1
2
1
1
0
1
0
0
0
1
1
1
2
1
1
2
1
2
1
1
1
2
1
0
1
1
1
2
1
1
1
2
2
3
2
1
1
0
1
1
2
1
1
1
1
2
1
1
1
2
2
1
1
2
1
0
1
1
0
2
1
1
1
1
2
1
1
2
0
1
1
1
1
1
2
2
2
1
1
1
2
2
2
2
2
1
1
1
1
1
1
2
0
1
1
1
1
1
1
1
0
1
1
1
2
1
1
1
1
1
1
2
1
2
1
1
1
0
1
1
2
1
0
2
1
2
1
0
0
1
1
1
0
1
2
2
1
1
0
1
1
1
2
1
2
0
1
1
1
0
1
0
1
2
1
2
1
2
2
1
1
0
2
2
1
1
2
0
1
1
2
1
0
2
1
1
0
1
2
0
1
2
1
1
1
1
3
1
1
1
1
1
1
0
1
1
2
1
1
0
2
1
2
1
1
0
0
2
2
1
2
1
0
0
2
1
2
2
0
1
1
0
1
0
1
0
1
1
1
0
1
1
1
1
1
0
1
2
1
2
0
2
1
1
1
1
1
0
0
0
2
1
1
1
0
1
1
1
1
2
1
0
1
1
0
1
0
0
1
1
2
2
2
1
2
2
1
1
1
1
1
1
1
0
1
2
0
2
1
2
1
2
1
0
1
1
0
2
2
0
1
1
2
2
1
1
2
1
1
0
2
1
2
1
1
2
2
1
1
1
1
2
1
1
1
0
1
2
0
1
0
1
2
2
1
0
1
2
1
1
0
1
1
1
2
0
1
0
1
1
1
1
0
2
1
0
1
1
1
1
2
1
1
0
0
1
2
2
2
1
1
0
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
0
1
1
2
0
1
1
2
1
1
1
0
1
0
1
1
0
1
1
1
1
2
1
2
0
1
1
0
1
0
1
2
1
1
1
1
0
2
2
0
1
0
1
0
1
1
0
1
2
0
1
1
1
1
2
1
2
1
1
2
1
1
0
1
1
0
1
1
2
1
2
1
1
1
1
2
1
1
1
1
0
2
2
0
1
1
1
0
1
2
0
1
1
2
1
2
0
1
1
1
2
0
1
1
2
2
0
1
1
0
2
0
2
0
1
1
1
1
1
1
0
1
1
1
1
2
1
1
1
1
2
1
1
1
0
2
1
1
1
1
1
1
0
1
1
1
2
1
1
1
1
1
1
0
2
1
1
1
3
2
1
2
1
2
0
2
1
1
2
1
1
1
1
0
2
2
1
1
2
0
2
0
1
2
1
1
2
2
1
2
1
1
1
2
3
1
1
0
0
1
2
1
1
1
1
0
1
1
1
1
2
1
1
1
2
1
1
1
1
0
2
2
1
2
2
1
0
1
1
1
0
2
0
1
1
0
2
1
1
2
1
2
1
1
1
0
1
2
1
1
2
1
1
1
1
1
2
1
1
2
1
0
1
0
1
2
1
1
2
1
1
1
2
1
1
2
0
0
1
1
2
0
1
1
1
3
1
1
1
1
1
1
1
1
2
1
2
1
0
1
1
2
0
1
1
2
0
0
2
2
2
2
1
2
0
1
0
1
1
2
1
1
1
2
1
0
1
1
2
1
1
1
2
1
1
1
1
1
1
2
0
2
0
1
1
0
1
1
2
1
1
1
2
1
1
0
1
1
1
1
1
2
1
1
0
1
1
1
1
2
1
0
1
2
1
0
0
1
1
1
1
1
1
1
1
2
1
2
0
0
2
1
0
2
1
1
1
2
1
1
1
0
2
1
0
2
1
1
3
2
2
1
0
1
1
2
0
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
0
1
1
1
1
1
2
1
1
2
2
1
1
2
1
1
1
1
2
1
2
2
1
1
2
0
0
0
1
1
1
1
2
1
1
1
1
0
1
2
1
2
1
1
1
1
0
1
1
1
2
0
1
1
0
1
0
1
1
2
1
2
0
0
0
2
1
1
1
1
2
0
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
0
0
1
1
2
0
2
1
0
2
2
0
1
1
1
1
1
1
2
2
1
1
1
1
2
1
0
1
2
1
2
1
2
0
1
1
2
0
1
1
1
2
1
1
1
1
0
1
0
1
1
1
1
1
1
1
2
2
1
2
0
1
1
0
1
1
1
2
1
1
0
2
1
1
3
1
0
0
2
1
1
0
1
0
2
1
1
0
0
2
0
0
1
1
0
0
1
1
0
0
2
0
1
1
1
1
1
0
1
1
0
2
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
2
0
2
2
1
1
1
1
0
1
1
1
1
1
0
2
0
1
2
2
1
1
1
1
0
4
1
1
1
1
1
1
1
1
1
2
0
1
1
1
1
2
1
1
1
1
0
1
1
0
0
1
2
1
2
1
1
1
2
1
0
0
2
1
2
2
1
2
1
0
1
1
1
0
2
1
1
2
2
1
1
1
1
1
1
2
1
1
1
2
2
2
1
0
1
2
2
2
1
1
1
2
1
1
1
1
1
2
1
1
1
0
2
1
2
2
1
2
1
0
0
2
1
2
2
1
1
1
1
0
1
1
1
0
1
2
0
2
0
1
1
1
1
0
2
1
1
1
1
2
2
0
2
1
1
0
1
1
1
2
1
0
2
1
2
0
0
1
1
2
0
2
1
1
2
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
0
1
2
1
1
1
1
0
1
0
0
2
1
1
1
0
0
1
1
0
1
0
0
1
0
1
2
0
0
0
2
1
0
0
1
1
1
1
1
1
1
2
0
1
2
2
1
2
2
1
2
1
1
1
1
1
2
2
2
1
1
1
2
1
1
1
1
1
1
1
2
1
0
1
0
1
1
1
1
1
2
2
1
1
1
1
1
0
0
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
0
1
1
2
0
2
0
2
1
0
1
1
0
1
1
0
1
1
0
1
1
1
2
1
0
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
0
1
2
2
2
1
2
0
1
1
1
1
1
0
0
2
2
0
1
2
2
0
2
2
0
1
1
1
0
1
0
1
2
1
2
1
2
1
2
0
1
2
1
1
1
2
1
1
1
1
0
2
1
0
2
1
1
0
1
1
1
1
1
1
0
1
2
0
2
1
2
1
1
2
1
2
1
2
1
1
1
0
0
1
2
1
0
2
1
2
1
1
0
1
2
1
1
1
0
1
1
0
1
1
0
2
1
0
2
1
2
1
0
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
0
2
1
1
1
1
1
4
1
2
0
1
1
2
1
2
0
2
2
1
1
2
1
1
1
2
1
2
0
1
1
2
1
1
2
1
1
1
2
1
1
0
2
2
1
1
1
2
1
1
1
1
2
1
1
0
0
1
1
2
3
1
1
2
0
1
1
0
1
0
2
1
2
1
2
1
1
1
1
1
0
2
1
1
1
1
1
2
2
0
0
1
2
2
1
2
1
2
0
0
1
1
2
1
1
1
0
2
0
1
1
2
3
2
1
1
1
0
0
2
1
2
0
1
1
1
1
1
1
2
1
1
0
2
1
1
1
1
1
2
2
1
1
2
1
2
1
2
1
1
1
1
1
1
1
0
1
1
1
0
1
1
1
1
1
1
1
1
2
1
1
1
1
0
1
1
1
1
1
1
1
0
1
1
0
1
1
0
0
1
1
1
2
0
0
0
1
1
1
1
1
2
2
1
0
1
0
1
2
1
1
1
0
1
1
1
1
1
1
1
2
0
2
1
1
0
1
2
1
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
0
0
2
1
1
2
1
1
2
2
1
1
1
1
0
1
1
1
1
1
1
1
1
0
0
1
1
1
1
1
1
1
0
0
0
0
1
0
1
2
1
2
2
1
0
2
1
1
0
1
2
1
1
2
1
2
2
1
1
1
1
2
0
1
1
1
1
1
2
1
0
0
2
1
0
1
2
1
0
0
2
2
1
2
1
1
1
2
1
1
1
2
1
0
2
2
1
1
3
0
1
1
0
1
1
1
2
2
1
1
1
1
2
1
0
1
2
1
1
1
0
1
1
1
1
2
1
1
1
1
2
1
0
0
1
1
1
2
2
2
1
1
1
1
1
1
1
2
0
1
2
1
2
1
1
1
0
1
1
1
1
1
1
1
1
2
1
1
2
1
0
1
1
1
1
2
1
2
2
2
2
2
1
1
2
2
2
1
1
1
1
2
1
1
0
2
1
1
1
2
3
0
2
2
2
2
1
1
0
1
4
1
2
1
1
1
1
1
1
0
1
0
1
1
0
1
1
1
1
1
1
1
1
2
2
0
1
2
3
1
2
0
2
0
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
0
0
1
2
2
1
2
1
1
0
1
1
1
0
1
1
0
1
1
0
2
2
0
1
0
2
1
0
2
2
1
1
2
1
2
1
1
0
1
1
1
1
0
2
1
2
1
2
2
0
1
0
0
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
0
2
0
2
2
2
2
1
1
0
1
1
2
1
1
1
0
2
0
1
1
1
1
1
2
2
1
1
2
1
1
0
1
0
1
1
0
1
1
1
3
1
2
2
0
2
1
1
1
1
1
1
1
1
1
2
0
1
2
1
2
2
1
1
1
0
2
2
1
2
2
2
0
1
1
0
0
1
1
1
1
1
1
1
2
2
1
0
0
0
2
2
1
1
0
1
0
2
1
0
0
2
2
1
1
1
1
1
0
1
2
1
0
0
2
1
1
0
1
1
1
1
2
1
1
0
1
2
2
1
1
1
1
1
1
1
2
1
1
0
1
1
1
1
0
1
0
1
1
1
2
1
1
1
2
2
2
0
2
0
1
1
0
1
1
2
2
1
2
1
2
0
1
1
1
2
1
1
1
1
1
2
1
2
1
0
1
2
2
0
1
2
0
1
1
1
1
1
2
2
1
2
1
2
1
1
2
1
1
0
1
1
2
1
1
1
1
2
2
2
1
1
1
2
1
1
1
1
1
1
2
0
2
1
0
1
2
0
2
1
1
0
0
2
1
1
2
1
1
1
2
2
1
2
1
2
1
1
1
3
1
1
1
2
1
1
1
0
0
2
1
1
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
0
1
2
0
1
1
0
1
1
2
2
1
0
1
1
2
1
0
1
0
0
1
1
1
1
2
2
2
1
0
1
1
2
2
2
1
1
1
0
1
1
1
0
1
0
1
1
1
1
1
1
0
1
0
1
1
1
1
1
2
1
1
0
1
0
1
0
1
1
0
1
1
1
1
0
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
2
1
1
1
2
1
0
1
0
1
1
1
1
1
1
1
0
1
1
2
1
0
1
1
2
2
1
1
2
2
0
2
0
0
1
1
0
1
2
1
1
1
1
1
2
0
1
0
1
1
1
1
1
1
1
1
1
2
2
2
0
1
0
0
1
1
1
0
0
1
2
1
1
1
1
1
0
2
2
0
1
1
1
1
1
0
2
0
1
1
1
2
1
2
2
0
1
1
1
1
0
1
0
1
0
0
1
1
0
2
1
0
1
1
1
1
1
1
2
1
1
1
1
2
0
0
1
0
0
0
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
0
1
0
1
1
2
2
1
1
1
0
1
2
0
0
1
1
0
2
1
1
1
1
1
1
1
0
2
0
2
1
1
0
1
1
2
1
1
2
0
1
1
0
2
1
1
1
1
1
2
0
2
2
1
1
2
0
1
1
1
1
1
0
1
2
1
2
1
1
1
2
2
1
0
1
0
1
2
0
2
0
0
1
0
1
1
1
1
1
1
2
1
1
1
1
1
1
0
0
2
1
1
1
1
1
2
0
1
1
2
1
1
1
1
1
1
2
0
1
1
2
2
1
1
1
1
1
1
1
1
2
1
0
2
1
1
0
1
1
1
0
1
1
1
2
2
0
1
1
1
1
1
2
1
1
1
1
0
2
1
1
1
0
1
0
0
2
1
1
1
2
1
1
1
1
1
1
1
0
0
1
1
1
0
1
1
2
1
2
2
1
1
1
2
2
1
1
1
0
0
0
1
1
1
1
1
1
1
0
2
1
1
1
0
1
1
1
0
1
1
0
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
1
0
0
1
1
1
0
0
3
1
1
1
0
1
0
0
1
2
0
2
0
0
0
2
1
1
1
1
1
1
1
1
0
0
1
2
2
2
2
0
2
0
0
1
1
1
0
1
1
0
1
2
1
1
2
1
1
1
1
0
1
2
2
2
1
1
0
2
1
1
1
2
1
0
0
2
2
1
1
1
2
1
1
2
2
1
1
2
1
0
0
2
1
1
1
2
1
1
1
0
0
2
1
1
1
1
1
2
1
1
0
2
2
1
2
1
0
2
1
1
1
1
2
2
1
1
3
1
0
1
1
2
1
0
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
2
1
2
1
1
0
0
1
2
2
1
1
1
0
1
2
1
2
1
1
0
2
2
1
2
0
2
1
1
1
1
2
2
2
1
1
1
1
0
0
1
1
2
1
2
1
1
1
1
2
2
1
1
1
1
1
1
1
1
2
1
2
0
1
0
1
0
0
1
1
1
1
1
1
1
2
1
1
1
1
1
1
0
1
1
0
1
2
0
2
1
0
0
1
1
2
0
2
1
1
1
1
0
2
0
0
0
1
2
2
0
0
0
0
0
0
1
1
2
2
0
1
1
1
1
0
1
1
1
0
1
0
1
1
1
2
2
1
1
0
0
1
1
1
2
1
2
1
0
1
0
0
2
1
1
2
1
2
1
1
1
1
0
0
2
0
0
1
1
1
1
1
2
2
1
2
0
1
1
2
1
1
1
0
1
1
2
1
1
1
1
1
2
1
1
1
1
1
0
1
1
0
0
1
1
2
0
1
1
0
1
0
1
1
2
1
0
1
3
1
1
2
1
2
0
2
1
2
1
2
0
2
0
1
0
0
1
1
2
1
2
2
0
1
1
1
2
1
1
2
1
2
0
2
0
2
2
1
0
2
2
0
1
0
0
2
1
3
0
0
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
0
2
1
1
1
1
1
1
1
0
2
2
1
1
0
1
1
0
1
1
0
2
1
0
1
1
2
2
2
1
0
0
1
2
0
1
1
2
1
1
1
1
2
2
0
1
2
1
1
0
1
1
0
0
1
2
2
0
1
1
0
0
0
2
1
1
2
2
2
1
1
1
3
1
1
3
1
1
0
1
1
0
2
1
1
2
1
2
1
0
1
0
0
1
0
0
1
1
0
1
2
1
1
0
0
1
0
2
1
1
1
1
1
1
1
1
2
1
1
2
1
0
2
0
1
1
0
1
2
3
0
1
2
1
1
1
1
0
1
1
2
0
1
2
1
0
1
3
1
1
2
1
1
1
1
0
1
2
0
2
0
1
2
1
2
1
1
1
2
0
1
1
1
2
1
1
2
2
1
2
1
2
2
3
0
1
1
1
2
1
2
0
1
1
1
0
1
2
1
1
2
1
2
0
1
1
1
0
0
2
2
1
2
2
1
2
2
1
2
1
0
1
2
1
1
1
1
2
1
0
2
1
2
1
1
0
1
2
2
0
1
1
0
1
0
1
1
2
1
1
0
3
1
2
2
2
1
2
1
1
2
2
1
1
0
2
0
0
1
1
2
2
1
2
1
1
3
1
1
2
1
2
1
0
1
1
2
1
1
1
2
1
1
1
1
1
0
2
1
0
0
2
1
2
0
1
1
1
1
0
2
1
1
0
2
1
1
1
1
2
1
1
1
1
2
1
2
1
2
1
2
1
0
1
1
1
2
1
2
1
0
1
1
0
1
1
1
1
1
1
1
2
0
0
1
1
1
1
1
1
1
1
2
1
1
1
2
1
0
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
2
1
1
1
2
0
1
1
1
1
1
1
3
1
1
1
1
1
1
1
1
1
1
2
0
1
1
1
1
0
1
1
1
1
1
2
1
2
1
1
5
1
1
1
2
1
1
2
0
1
2
1
1
1
1
2
1
1
2
2
1
1
1
2
2
2
3
0
1
2
0
0
1
2
1
0
2
2
1
1
2
1
1
2
1
2
1
2
2
0
2
1
1
1
1
2
1
3
0
0
1
1
2
1
1
1
1
2
1
0
1
1
1
2
1
0
0
0
2
2
1
1
1
1
1
1
1
2
1
1
2
2
1
2
2
2
1
0
1
2
0
2
1
0
1
1
0
1
1
1
0
1
1
0
1
1
2
0
3
1
2
1
2
1
2
1
2
2
2
1
1
1
1
1
1
1
1
0
1
1
1
2
0
1
1
2
1
2
2
1
1
1
1
1
0
1
2
1
1
0
1
1
1
0
2
2
0
0
1
2
1
1
0
2
1
1
1
1
2
0
1
2
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
1
2
0
1
2
1
0
2
1
1
2
1
1
1
2
2
1
1
2
1
3
0
1
1
0
1
1
1
1
1
1
1
1
1
1
2
2
0
1
1
1
1
1
2
1
1
2
0
2
1
1
0
1
1
0
1
0
1
1
1
1
1
1
2
1
0
1
0
1
1
1
2
2
1
2
0
2
0
1
1
0
2
1
1
2
0
1
1
2
1
1
2
0
2
3
1
1
0
1
2
1
0
1
1
1
1
1
1
1
0
1
0
2
0
2
1
1
2
1
0
1
2
1
1
1
1
1
1
1
1
2
0
1
0
2
2
1
1
1
1
1
2
2
0
1
0
1
0
1
0
2
2
1
1
3
2
1
1
1
1
2
2
0
2
2
1
1
2
1
2
1
1
2
2
1
1
1
1
1
2
2
1
1
1
1
2
2
1
2
0
0
1
2
1
0
1
0
0
0
0
2
1
2
2
2
1
1
2
1
1
0
1
3
1
1
2
1
1
1
1
1
9
1
1
1
3
1
2
1
1
1
1
1
0
1
2
1
1
1
1
1
1
1
1
1
0
0
1
1
2
1
1
1
1
2
0
2
1
1
1
1
1
2
2
1
1
1
1
2
1
0
2
0
2
0
1
1
1
1
2
1
2
2
1
1
1
1
1
1
2
1
1
0
1
1
1
2
0
1
1
0
1
2
1
1
1
1
1
1
0
3
0
2
1
1
2
2
1
2
1
1
2
1
1
1
2
1
1
2
1
1
0
2
1
1
1
1
1
1
1
1
1
1
0
2
0
2
2
2
1
2
1
1
1
2
1
1
3
2
0
2
0
2
1
1
0
2
1
0
0
2
2
1
2
2
1
2
1
1
0
1
1
1
0
1
1
1
1
1
2
0
1
1
1
1
1
2
1
1
0
2
1
1
0
3
1
2
2
2
2
1
1
0
2
0
1
0
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
0
1
2
1
2
2
1
1
1
1
1
0
1
1
2
1
0
1
2
1
1
1
0
0
2
0
2
1
1
1
1
1
1
1
1
1
1
3
1
1
1
2
1
1
2
1
1
1
0
0
1
1
2
2
1
2
2
0
2
1
1
1
2
0
0
2
1
1
1
0
2
2
1
1
1
1
1
2
0
0
0
1
1
1
2
1
2
1
1
1
1
0
1
1
1
1
1
2
1
0
1
1
1
1
1
1
0
2
2
1
0
2
1
0
1
1
2
1
2
1
1
1
1
0
1
1
1
1
2
2
1
1
2
2
0
1
2
2
0
1
1
1
1
2
1
1
2
2
1
1
2
0
1
0
1
1
1
1
2
1
2
1
1
1
1
2
2
1
1
1
1
1
0
1
0
1
1
1
1
1
1
1
2
1
1
2
2
0
1
2
2
1
1
0
1
1
1
1
2
1
2
1
0
2
1
2
0
1
1
1
0
2
0
2
0
0
1
0
1
0
1
0
1
1
2
1
2
1
2
1
1
1
1
2
1
1
2
1
2
2
1
1
1
1
1
1
2
2
1
1
2
2
0
1
0
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
0
1
0
0
0
1
1
2
2
1
1
1
1
2
1
0
2
2
2
1
1
1
2
1
1
1
2
0
1
1
1
2
2
1
1
0
2
1
0
1
0
1
2
1
0
1
1
1
0
1
1
1
1
1
2
1
2
1
1
1
1
0
1
1
1
2
1
2
0
0
0
1
2
1
1
1
2
1
1
5
0
1
2
1
1
1
0
1
2
1
2
2
1
2
0
1
1
1
2
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
1
0
2
0
1
0
0
1
1
1
1
1
2
0
1
3
2
0
1
2
1
0
1
1
1
1
2
2
1
1
0
1
1
2
1
0
1
0
1
1
0
0
1
1
1
0
1
2
1
1
1
1
1
1
2
1
2
1
1
0
2
0
2
1
1
1
2
2
1
2
0
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
0
1
0
1
3
2
1
1
2
1
2
0
0
1
1
0
0
1
1
0
1
1
1
1
1
1
2
1
0
1
1
1
2
1
1
2
1
2
1
2
2
2
1
1
1
1
0
1
2
1
1
2
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
2
1
1
1
1
0
1
0
2
0
1
1
1
1
2
1
1
0
1
1
2
1
1
0
2
2
1
1
2
1
1
0
1
1
1
2
0
1
1
1
0
2
2
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
2
1
2
2
2
1
2
0
1
2
1
1
0
1
0
2
1
3
2
1
1
1
1
1
1
2
1
1
1
1
1
0
2
3
2
2
1
0
1
1
2
1
1
0
1
2
1
2
1
1
1
1
2
1
0
1
1
2
1
2
1
1
1
0
0
1
1
0
0
0
0
1
1
2
2
1
0
1
0
1
1
1
1
2
1
1
1
1
0
1
2
2
1
1
1
0
2
0
1
1
2
1
1
1
1
2
2
1
1
2
1
0
1
0
1
1
1
1
1
0
0
1
1
1
0
2
2
1
2
0
1
0
1
1
1
2
1
0
2
1
1
2
1
2
2
0
1
0
1
0
1
1
1
1
2
2
1
2
2
1
1
1
1
1
1
1
2
1
1
0
1
0
1
1
0
1
1
2
2
2
1
1
1
1
2
1
1
0
1
0
2
1
1
0
1
2
1
2
2
1
1
0
1
2
1
0
0
3
1
1
1
0
2
1
1
0
1
2
1
0
1
1
1
2
1
2
1
2
2
2
1
1
1
0
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
0
1
2
1
0
1
0
2
1
2
1
0
2
0
1
1
1
1
1
1
1
3
1
0
1
1
0
2
1
0
2
0
3
1
1
0
1
1
1
1
0
1
1
1
1
2
0
1
1
1
0
1
1
1
1
3
1
1
0
1
1
4
1
0
2
0
1
1
0
2
0
0
2
1
1
2
1
1
0
2
1
0
1
2
2
1
2
1
2
2
1
1
1
0
2
2
2
0
1
1
2
1
0
2
1
0
2
1
2
1
2
0
1
0
3
2
2
1
2
2
1
2
1
2
1
1
0
2
1
0
2
1
1
0
1
2
1
0
1
2
2
1
1
1
0
1
1
0
1
1
1
1
1
1
2
1
0
1
1
1
1
1
0
1
1
1
1
1
1
1
2
1
1
1
1
0
1
1
0
1
1
1
1
2
1
1
1
0
1
1
2
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
2
1
0
1
1
0
1
1
1
1
1
0
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
0
1
1
1
1
1
2
1
1
1
1
1
1
0
0
2
3
1
2
2
2
1
1
1
1
1
0
1
2
0
1
1
1
2
1
1
2
1
2
2
1
0
2
1
1
1
1
0
1
2
2
1
1
1
1
1
2
1
1
2
1
2
1
1
1
2
0
1
0
1
2
0
1
1
1
0
1
3
1
1
0
1
1
1
0
0
2
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
0
1
1
2
1
2
2
1
1
2
1
0
1
0
1
2
2
1
2
1
1
2
1
2
1
1
1
2
1
1
1
0
1
1
1
0
0
0
1
1
1
0
0
1
1
1
1
1
1
1
2
1
1
1
1
0
2
1
2
2
1
1
2
1
0
0
1
1
1
1
1
1
1
1
2
1
0
0
0
1
0
2
1
1
1
1
2
1
1
1
1
0
1
1
1
1
1
1
1
0
1
1
1
1
0
1
1
2
1
2
3
1
1
2
2
2
2
2
0
1
1
1
2
2
2
1
2
1
1
2
0
1
1
1
1
1
1
1
1
1
0
1
1
0
1
1
1
1
1
2
0
0
2
1
1
1
1
1
0
0
2
1
1
1
1
1
0
1
2
0
0
1
1
2
2
2
1
0
2
1
2
1
1
2
2
1
1
0
0
0
2
2
2
2
1
0
1
1
0
3
1
1
0
1
0
1
2
1
1
1
1
1
1
2
1
2
1
2
0
1
0
2
0
1
2
1
0
0
1
1
1
0
2
1
0
2
1
1
1
2
1
1
1
1
2
2
2
3
2
1
1
2
1
1
0
1
1
1
0
1
1
1
2
1
1
1
1
1
1
2
1
2
0
0
2
2
2
1
0
1
1
1
1
2
0
1
1
1
2
1
1
0
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
1
0
1
1
2
1
1
1
0
1
1
1
1
1
1
1
0
0
1
2
1
1
0
1
2
1
1
1
2
1
1
0
0
1
2
2
1
0
0
1
2
1
1
1
1
1
1
0
1
1
1
2
2
1
1
1
0
1
1
1
1
1
2
1
1
1
1
1
1
1
1
0
1
1
1
0
1
2
1
1
0
2
0
0
5
1
0
1
1
2
2
1
1
1
1
1
0
2
1
1
2
1
0
1
1
1
1
2
1
0
2
1
1
1
1
1
1
1
1
0
0
1
1
0
0
0
1
0
2
0
1
1
0
2
1
1
2
1
2
1
1
1
1
0
1
1
1
1
0
1
1
1
1
1
1
1
0
1
1
0
1
1
1
1
0
1
1
3
0
1
0
1
2
1
1
1
1
1
1
1
1
0
1
2
1
1
0
1
2
0
2
0
2
0
2
2
2
2
0
1
2
1
1
1
1
0
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
2
0
2
0
2
1
1
1
1
1
1
1
1
0
0
1
1
2
2
1
2
0
1
2
1
1
0
0
2
2
1
1
1
2
1
0
1
1
1
1
1
1
2
2
1
2
2
1
1
1
1
1
2
2
0
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
0
0
1
1
2
2
0
0
0
0
1
1
0
2
1
1
1
1
1
2
0
1
1
1
1
1
0
1
1
1
2
1
1
1
2
1
2
2
1
1
0
2
0
1
1
0
0
2
1
1
1
1
0
1
1
1
2
1
1
1
1
1
0
2
2
1
1
0
1
1
2
1
1
1
1
1
2
1
1
2
1
2
1
2
0
0
0
2
1
1
2
0
2
1
1
2
2
1
2
0
1
1
0
2
1
1
1
1
0
2
1
1
3
0
0
1
1
2
1
1
2
0
1
2
1
1
0
1
2
2
2
0
1
0
2
1
2
1
2
1
0
1
0
1
1
1
2
2
2
1
1
1
2
1
1
0
1
1
2
1
1
0
1
1
1
1
2
0
2
0
1
0
1
0
1
1
1
1
1
0
1
1
0
2
1
2
1
2
0
1
2
1
1
1
1
1
1
2
1
2
2
1
2
1
1
0
1
1
1
1
2
0
1
1
1
1
0
0
2
1
1
0
0
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
0
2
1
1
2
0
1
1
2
1
1
2
1
1
2
1
0
2
1
1
4
1
1
1
1
1
1
2
1
2
2
2
2
1
1
1
2
1
1
1
1
1
1
1
0
0
2
1
2
1
2
1
1
0
1
1
1
7
1
2
2
1
1
1
1
1
0
2
1
2
2
2
1
1
1
2
1
2
0
1
1
1
0
0
1
1
2
1
0
2
1
2
1
0
2
1
1
2
2
0
1
1
3
0
1
1
2
2
2
4
1
1
1
1
2
2
1
1
2
1
2
1
2
1
1
1
0
1
0
1
1
1
1
1
2
1
2
2
1
2
1
1
1
1
2
1
1
0
1
2
2
0
1
1
1
1
2
1
1
0
1
2
2
1
0
1
1
1
0
0
1
0
0
1
1
1
0
2
1
1
1
1
1
0
2
0
2
2
1
0
1
1
1
1
0
1
0
1
1
1
0
1
0
0
2
1
2
0
0
2
1
1
1
1
3
1
1
1
2
0
1
1
0
1
1
0
0
0
2
2
1
1
1
0
2
1
1
1
1
1
2
1
1
1
1
0
2
1
0
2
0
2
2
1
1
0
1
2
1
1
1
0
2
0
2
1
0
1
2
0
1
1
2
1
1
1
2
1
2
2
1
1
0
0
2
2
1
0
3
2
2
2
1
1
1
1
2
1
1
0
2
2
0
0
1
1
1
2
1
1
1
1
2
1
1
1
2
1
0
1
1
0
0
1
1
1
1
1
1
2
1
1
0
1
0
1
0
1
2
1
1
1
0
0
1
1
1
1
1
1
2
0
1
1
1
2
1
2
3
1
1
2
0
0
1
1
1
1
1
1
1
1
1
2
1
0
2
3
1
1
1
1
1
2
1
1
1
1
0
0
2
0
0
1
1
1
2
0
1
0
1
0
1
2
0
0
0
0
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
0
1
1
0
2
1
2
0
1
1
1
2
1
1
1
2
1
1
0
2
1
2
1
1
0
0
0
0
1
1
1
2
2
2
1
0
0
0
1
1
2
1
0
0
1
0
1
1
1
0
1
1
0
0
0
2
1
2
1
2
1
1
0
0
2
1
2
1
0
2
1
2
1
1
1
1
1
2
1
1
1
0
0
0
0
1
1
1
2
1
1
0
2
1
0
1
1
1
0
0
2
1
0
0
2
1
1
0
2
1
8
1
1
1
1
1
1
2
0
2
0
1
2
1
1
1
2
1
1
2
1
1
2
2
1
2
1
1
1
1
1
1
0
1
1
0
1
2
1
2
1
2
1
1
1
1
0
1
2
1
1
1
2
1
1
1
1
1
1
0
1
1
2
1
1
0
1
1
2
0
1
1
1
0
1
1
2
1
2
1
2
1
2
1
0
1
1
1
1
1
2
2
1
0
1
2
1
1
1
1
1
1
0
0
1
1
0
1
1
2
0
1
1
2
1
2
1
1
1
0
1
2
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
0
1
1
1
0
2
1
1
1
0
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
1
1
2
1
0
1
2
1
1
0
1
1
1
2
2
2
0
1
1
1
1
1
1
2
1
0
1
1
1
1
2
1
1
2
2
1
2
0
0
3
2
1
2
1
1
1
1
0
1
1
1
1
1
1
0
2
1
0
1
1
2
0
1
2
2
3
1
2
0
1
1
2
1
1
2
1
1
1
1
1
1
0
0
1
1
1
1
1
1
4
1
2
2
2
0
0
1
1
2
2
1
0
2
2
1
1
0
2
0
0
1
0
1
1
1
2
0
0
1
0
1
0
2
1
1
1
1
1
1
1
1
0
0
1
1
1
1
1
1
0
0
1
1
1
1
1
0
2
3
1
2
1
2
1
0
1
2
2
0
1
1
2
2
1
2
2
1
2
1
1
1
2
1
1
1
1
1
1
2
1
1
2
1
1
2
1
2
2
0
0
2
1
2
1
1
1
1
1
1
1
2
1
2
1
0
0
0
2
1
0
0
1
1
1
2
1
1
1
0
1
0
1
1
1
1
1
1
1
1
1
1
0
0
1
2
2
2
2
0
1
0
2
1
1
1
2
2
1
0
1
1
0
2
1
1
2
0
1
1
1
0
1
2
2
1
2
1
1
1
0
1
0
0
1
2
0
1
1
2
1
0
1
2
1
0
1
2
1
0
1
1
1
1
2
0
1
2
1
0
1
1
1
0
1
1
0
1
1
1
2
2
1
2
2
1
0
1
2
0
2
2
3
1
2
0
1
0
0
1
2
2
0
1
1
1
2
1
1
2
1
0
2
1
0
2
2
1
1
1
2
1
1
1
1
2
0
0
0
1
2
1
1
2
1
0
2
1
2
1
1
1
1
1
1
1
2
1
2
1
1
0
1
2
1
2
1
2
1
1
1
1
1
1
1
1
0
0
1
0
1
2
1
1
2
1
2
2
1
1
2
1
1
0
2
2
2
0
1
1
1
2
0
0
0
1
1
1
1
1
1
1
1
1
1
0
1
1
1
2
1
1
1
1
2
0
0
1
2
1
2
1
1
2
0
1
1
1
1
2
1
1
1
2
0
1
2
1
1
0
1
1
2
1
1
0
2
0
1
2
1
1
1
1
2
1
0
1
1
3
1
2
2
1
2
2
1
1
2
2
1
0
1
2
2
0
1
1
2
0
1
1
1
0
2
1
1
1
1
0
1
0
1
2
1
1
0
1
1
0
1
1
1
2
2
1
1
1
1
1
1
1
0
1
1
0
2
1
2
1
1
1
1
0
1
0
1
2
0
2
1
1
1
1
1
1
1
1
1
1
0
1
0
1
1
1
1
1
2
1
2
1
2
1
1
2
1
0
1
1
1
1
1
0
1
2
1
2
1
1
1
1
1
1
1
0
1
1
1
1
2
1
2
1
1
2
0
1
1
1
1
1
1
1
0
1
1
2
1
0
1
1
2
1
1
1
1
2
2
2
1
0
1
0
1
2
2
1
1
1
1
1
0
0
1
1
0
1
1
2
1
1
1
1
1
1
0
1
1
3
0
2
2
1
0
0
1
0
1
0
1
1
1
1
1
0
1
1
0
0
0
1
0
1
1
1
0
1
1
1
1
5
0
2
1
1
2
1
0
1
1
1
3
1
2
1
1
0
1
1
2
0
1
0
2
7
2
2
1
2
2
0
2
2
1
1
0
1
1
1
0
2
1
1
1
1
2
2
0
2
1
2
1
1
1
0
1
1
1
5
1
1
1
2
1
2
2
2
1
2
1
2
1
1
1
0
1
1
1
0
2
0
1
1
0
1
2
1
2
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
0
1
1
1
1
1
0
2
1
1
2
1
2
1
0
2
1
0
1
1
2
1
1
2
0
1
1
1
1
0
0
1
1
2
1
1
1
1
0
1
2
2
0
1
1
1
1
2
2
2
2
2
1
1
2
2
1
1
1
2
1
1
1
1
1
1
1
1
0
1
1
1
0
1
0
0
0
1
1
2
0
0
0
0
1
1
0
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
0
0
2
2
1
0
1
1
1
1
1
0
1
1
0
1
0
1
2
1
1
1
1
1
2
0
0
1
1
1
1
1
2
1
2
1
2
1
1
0
0
0
2
1
2
0
1
1
2
0
1
0
0
1
0
2
1
2
1
1
1
0
2
1
1
1
2
0
1
1
2
2
1
1
1
1
1
0
0
0
2
1
1
1
1
2
1
1
1
2
1
1
0
1
2
0
1
1
1
1
1
1
1
1
0
1
2
1
1
1
1
1
1
1
1
0
1
1
1
2
1
0
1
1
1
1
1
1
1
1
2
2
1
2
1
1
2
1
1
1
1
0
0
1
2
1
1
1
1
0
2
1
1
2
0
0
2
1
1
1
0
1
1
1
2
1
0
1
1
1
1
1
1
0
1
2
1
1
2
2
2
2
1
1
2
2
2
0
1
1
1
1
0
0
0
0
2
1
0
1
2
1
1
2
1
0
2
3
1
1
2
1
2
1
1
1
1
1
2
0
1
1
1
1
0
2
1
1
0
1
1
1
1
0
0
2
1
1
1
1
1
2
1
1
1
0
0
0
0
0
2
2
2
1
1
1
1
2
2
1
2
1
1
1
1
2
0
1
0
1
1
0
1
2
2
1
1
1
1
2
2
1
0
0
2
0
1
2
1
1
1
1
2
0
1
1
1
1
2
1
1
1
1
3
2
2
0
1
1
2
1
1
2
1
1
2
1
0
2
1
0
2
1
1
0
0
2
1
1
1
1
1
1
1
0
1
0
1
1
1
1
2
2
2
1
2
2
1
1
1
0
1
1
1
1
1
2
0
2
2
0
1
1
0
0
1
1
0
1
1
2
1
0
2
0
1
2
2
1
1
1
1
0
1
2
1
1
2
1
1
1
0
1
1
1
0
1
2
2
1
1
1
0
1
2
1
1
1
0
1
0
1
0
2
1
1
0
1
1
1
1
1
1
1
1
1
1
2
2
1
0
2
0
1
0
1
0
2
2
2
1
2
2
1
1
1
2
0
1
1
1
1
2
1
1
2
1
0
2
1
1
1
1
1
1
0
1
0
2
0
0
2
1
0
0
1
1
2
2
1
1
2
1
1
0
1
2
2
1
2
3
2
1
0
1
0
2
2
0
1
0
1
1
1
2
3
1
1
1
1
1
1
1
1
1
1
1
3
0
2
1
1
1
0
0
0
2
0
0
1
1
0
1
1
1
2
1
2
1
0
1
1
1
2
1
1
1
2
1
0
1
1
1
0
1
2
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
0
1
1
1
1
0
1
2
1
1
1
1
1
2
2
1
2
2
1
1
2
0
1
2
1
0
1
2
2
1
1
1
1
1
2
0
2
0
0
1
2
1
1
2
0
1
1
1
1
1
0
1
0
1
1
1
1
1
0
1
1
2
2
0
1
1
0
0
1
0
1
1
1
1
2
1
0
1
2
1
0
1
1
1
1
1
1
0
1
2
1
2
2
2
0
2
1
1
1
1
0
0
1
2
0
2
1
1
3
2
1
0
2
1
2
1
1
2
0
1
2
2
1
1
2
1
2
2
1
1
1
1
1
1
2
1
2
2
1
0
1
1
1
1
1
2
1
1
2
2
1
1
1
1
2
1
1
0
1
1
2
0
1
2
1
1
1
1
1
1
1
1
0
1
1
0
2
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
0
2
1
1
1
0
1
1
1
1
2
1
1
0
0
2
1
1
1
1
1
0
2
2
1
0
1
1
1
1
2
0
1
1
0
2
2
0
2
1
2
1
1
1
1
2
1
1
2
1
0
1
1
1
1
1
1
1
1
0
1
1
1
2
1
2
2
1
2
1
1
2
2
1
1
2
1
2
1
2
1
1
1
1
0
1
1
0
1
2
0
1
2
0
2
2
1
1
1
1
2
0
2
1
1
1
1
2
2
1
0
2
0
1
2
1
2
2
1
1
0
1
1
1
1
1
2
2
1
0
1
0
1
1
0
1
2
1
2
1
1
1
1
0
1
1
1
2
2
1
1
0
2
1
2
0
1
1
2
2
0
2
2
2
0
2
1
1
1
2
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
0
1
1
1
2
2
1
2
0
1
2
1
1
2
1
2
1
1
1
1
1
0
1
2
2
1
1
1
2
2
1
1
1
1
2
1
2
2
1
2
1
1
1
0
1
2
3
1
1
1
1
1
1
2
0
2
1
2
1
2
1
0
1
1
2
0
1
1
1
2
0
2
1
2
2
2
2
1
1
1
2
2
1
1
1
0
2
1
1
1
1
1
2
2
2
0
1
1
1
1
1
1
2
2
1
0
0
2
0
1
0
0
1
1
1
1
1
2
0
1
1
2
1
1
1
1
1
1
0
1
0
2
1
1
0
1
0
0
1
0
1
2
2
1
1
1
0
2
2
1
0
1
2
1
2
1
1
1
2
1
1
6
1
1
1
0
2
2
2
0
1
1
2
2
0
1
1
1
1
1
1
0
0
1
0
1
1
1
0
1
2
1
2
2
1
0
2
2
1
2
1
2
1
1
1
0
1
1
1
1
1
1
1
1
1
0
0
1
1
0
1
2
2
1
2
1
1
0
2
1
1
2
0
1
2
1
1
2
1
1
1
1
2
2
2
1
1
2
2
0
1
1
2
1
1
1
1
1
0
2
2
1
3
0
2
1
2
1
1
1
1
2
1
1
1
1
1
0
1
2
1
1
1
1
1
1
1
1
1
0
1
1
2
1
1
1
0
1
1
2
1
1
1
2
0
1
1
1
0
1
2
2
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
0
2
0
1
1
0
1
0
1
2
2
0
1
2
1
1
1
1
2
1
2
1
2
1
2
0
1
1
1
1
1
0
2
2
1
2
2
1
2
1
1
1
2
1
1
2
1
1
1
0
1
1
0
2
1
0
1
1
1
1
1
1
2
1
2
1
0
1
1
1
1
1
2
1
1
1
1
0
2
2
1
2
1
0
2
1
1
1
2
1
1
1
0
0
1
0
1
1
1
0
1
0
1
0
1
0
1
0
1
0
1
0
0
1
1
1
0
0
0
2
2
1
0
1
0
2
0
0
0
1
2
2
1
0
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
0
1
0
1
0
1
0
1
2
1
1
2
2
0
0
2
1
0
0
2
2
1
1
0
1
2
0
2
1
2
1
1
2
2
2
0
2
1
0
0
1
1
2
1
0
2
2
2
2
2
1
1
1
1
1
2
0
1
1
1
1
1
1
2
1
2
1
2
1
1
1
1
1
0
1
2
1
1
2
2
1
2
1
1
0
0
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
0
0
1
2
2
1
1
2
2
2
1
1
1
1
1
0
1
2
0
2
1
2
1
1
2
0
1
1
2
0
2
2
1
2
2
1
1
1
0
1
1
1
0
2
1
2
1
0
0
2
1
0
2
0
2
1
0
1
0
1
0
1
1
1
2
1
1
0
0
2
2
1
1
1
1
1
0
0
1
1
1
0
0
1
2
0
1
1
2
2
2
1
2
1
1
1
1
1
1
2
0
1
1
2
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
0
2
2
1
1
0
1
0
2
2
1
2
2
1
1
0
0
1
1
1
1
1
2
1
1
0
2
1
0
2
2
1
0
1
1
2
1
1
1
1
1
0
1
1
1
0
1
2
0
1
1
0
1
2
0
2
0
1
1
1
1
2
1
0
2
0
2
2
1
1
1
2
1
1
2
1
1
0
2
0
1
2
1
1
0
1
1
1
0
1
1
0
0
4
1
2
1
1
1
1
1
1
0
1
1
2
0
1
1
2
0
1
1
1
1
2
2
2
1
1
2
1
2
2
1
0
1
1
2
1
0
1
1
1
0
1
0
1
2
2
0
1
1
1
2
1
1
0
2
1
0
2
1
1
1
1
1
2
1
1
1
0
1
2
2
1
1
1
1
2
1
1
2
1
2
1
0
1
1
0
1
1
1
1
1
2
1
1
0
0
1
1
2
1
0
2
0
0
1
1
2
1
1
2
1
2
0
1
1
2
2
0
1
1
0
0
1
2
0
1
1
1
1
1
0
1
2
3
1
1
1
1
1
1
0
0
0
2
2
1
0
0
1
2
0
2
1
1
2
1
1
1
1
1
0
1
1
2
2
2
1
1
1
0
2
1
1
1
1
1
1
1
1
0
2
1
1
1
2
1
1
0
1
2
1
1
1
2
0
1
1
1
1
2
1
1
1
1
2
1
1
2
0
1
1
0
1
0
0
1
1
0
1
2
1
1
2
2
1
2
0
1
1
1
0
1
1
2
0
0
0
1
1
2
2
1
2
1
2
1
1
0
1
1
2
1
1
0
1
1
1
2
1
2
0
1
1
0
1
2
2
1
1
1
1
1
2
1
3
0
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
2
1
0
1
0
1
1
1
1
0
1
0
0
0
1
1
1
2
2
2
1
1
0
1
2
1
1
1
1
1
2
1
1
1
1
2
2
1
1
2
2
0
0
1
1
2
1
1
2
1
1
0
2
1
0
1
0
2
1
0
2
2
1
1
1
2
1
1
0
1
1
1
1
1
2
1
1
0
2
2
0
1
0
0
0
1
1
0
1
0
1
2
2
1
0
1
2
0
2
1
3
1
1
2
2
2
1
2
1
1
1
0
1
2
1
0
2
1
1
1
2
0
1
2
2
1
2
1
1
1
1
0
2
0
2
0
2
1
1
0
0
1
0
1
2
1
2
1
1
1
1
2
0
0
1
1
0
1
0
1
1
2
1
2
1
1
1
0
1
1
1
1
2
1
3
1
1
1
1
1
1
1
2
1
2
1
2
0
1
2
2
2
2
1
2
1
1
2
2
1
0
2
0
1
3
1
1
0
0
0
2
0
1
1
0
0
2
1
2
0
0
1
1
1
1
1
2
1
1
2
1
2
1
1
1
1
1
0
2
0
1
1
1
1
2
1
1
2
0
2
2
1
0
1
1
1
1
1
1
1
1
2
1
1
1
2
0
1
0
2
2
2
0
2
0
1
1
0
2
1
1
1
1
2
0
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
0
1
1
1
1
1
1
1
1
1
1
0
1
2
0
1
0
0
1
1
1
2
1
1
2
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
0
1
2
2
1
1
1
1
0
0
1
1
1
1
2
1
2
1
2
1
1
1
1
0
2
1
0
1
1
1
1
1
1
1
0
0
0
0
1
1
1
1
1
2
1
1
1
2
2
1
1
2
2
0
1
1
1
0
0
1
1
2
0
1
0
0
2
1
1
2
1
0
2
1
0
1
0
1
1
0
1
1
1
1
0
1
1
1
1
1
1
2
1
1
0
2
1
0
0
1
1
0
2
1
1
1
2
1
1
1
1
1
2
2
0
0
1
1
1
1
2
2
2
3
0
1
2
1
1
1
2
1
1
0
1
1
0
1
1
0
1
2
0
1
1
1
2
1
2
2
2
1
1
2
2
1
1
1
0
2
2
0
1
1
6
0
2
0
0
1
2
1
2
2
2
0
1
2
2
1
1
0
1
2
1
2
2
1
1
1
1
1
2
1
1
1
1
0
1
0
1
1
1
0
1
1
1
0
2
1
2
0
2
1
1
1
2
0
2
1
2
1
1
2
1
1
1
2
1
1
1
2
2
1
1
1
0
1
1
1
1
2
1
2
0
2
1
1
2
1
1
0
0
1
1
3
1
1
1
1
0
1
2
1
1
1
1
1
1
1
1
2
0
2
0
1
2
3
1
0
1
0
2
2
1
1
0
1
0
0
0
1
0
1
1
1
0
0
1
1
0
0
2
1
1
0
2
1
1
2
2
1
1
1
2
1
2
1
2
3
2
1
0
1
1
2
0
1
1
0
1
2
0
0
1
2
1
1
2
1
1
1
2
1
2
1
1
1
2
2
1
1
2
1
2
1
1
1
1
2
7
0
2
1
2
1
2
1
0
1
1
2
0
1
4
1
2
1
1
1
1
1
1
0
1
1
2
1
0
1
1
0
1
2
1
1
2
1
1
1
1
1
0
1
0
1
1
0
2
1
2
1
1
1
1
1
0
2
0
1
1
1
0
1
2
0
1
1
2
1
2
2
1
2
1
2
0
1
1
2
2
2
0
0
2
1
1
1
1
2
1
2
1
1
1
0
0
2
2
2
1
2
1
2
1
0
1
0
1
1
1
1
1
0
2
2
1
2
2
1
1
1
1
0
2
1
1
1
1
1
1
2
2
1
0
2
0
1
1
1
1
1
1
1
1
0
1
1
2
0
1
2
1
2
1
1
1
2
1
1
1
2
1
2
2
1
2
2
1
2
0
2
1
1
1
1
2
0
0
1
1
1
2
1
1
1
2
0
0
1
2
2
1
0
0
1
1
1
1
1
0
1
0
1
2
1
1
2
1
1
0
2
1
1
2
1
1
1
1
2
1
1
2
1
1
2
0
2
0
1
1
2
2
0
1
1
1
1
2
1
1
1
1
1
1
1
0
1
2
2
1
1
0
2
1
2
2
1
2
1
1
2
2
2
2
2
2
1
1
2
1
2
1
2
0
0
1
1
1
1
1
1
1
1
2
1
3
1
1
2
2
2
0
2
1
1
2
2
1
1
1
2
1
1
1
2
2
2
0
2
2
2
1
1
1
1
1
1
1
2
2
2
1
1
1
1
2
1
1
2
2
1
1
1
1
0
1
1
0
1
0
0
0
1
4
1
1
1
1
1
1
1
1
2
2
2
1
1
2
1
1
0
1
1
1
0
1
1
1
2
1
1
1
0
0
1
1
2
1
1
0
1
0
1
1
0
0
0
1
1
1
2
1
1
1
1
1
0
1
1
1
1
0
1
2
0
1
0
2
2
2
1
2
1
1
1
1
1
0
1
0
1
0
1
1
1
1
1
0
2
1
1
0
2
2
1
1
0
1
1
1
3
2
1
1
0
2
1
1
0
1
1
1
1
1
0
1
1
1
1
1
0
1
1
1
0
0
0
1
1
2
2
2
1
1
1
0
2
2
1
0
0
1
1
1
0
2
0
0
1
0
2
1
1
0
1
0
3
0
1
3
1
2
1
1
1
3
1
1
1
0
1
1
2
0
1
2
1
2
1
1
0
1
1
2
2
0
2
1
2
1
1
2
2
2
2
1
1
1
1
1
1
2
1
2
0
1
1
1
0
2
2
1
1
1
6
2
1
1
1
1
1
1
0
2
1
1
1
1
1
2
1
0
1
1
2
0
1
0
0
1
2
1
0
1
0
1
1
1
1
1
2
2
1
0
0
1
2
1
2
0
1
2
1
1
2
1
3
1
1
2
2
1
1
1
0
1
2
0
1
1
0
1
2
0
0
1
1
0
2
0
2
1
2
1
1
1
1
2
1
1
0
0
0
2
2
0
1
0
0
2
0
1
1
1
2
1
2
2
0
1
1
1
2
1
1
2
2
1
2
1
2
2
1
1
2
0
0
2
1
1
1
1
1
1
1
1
2
2
0
1
1
1
2
2
0
2
0
1
1
0
2
2
1
1
1
1
2
1
0
1
0
1
1
1
2
1
1
1
1
1
1
2
1
1
2
1
1
0
0
1
1
1
1
1
2
2
0
2
1
1
1
1
1
0
1
2
1
2
1
0
1
2
1
1
1
2
0
1
1
1
1
1
2
0
1
1
2
1
1
1
2
2
0
1
1
0
2
1
1
1
1
1
1
1
1
0
1
1
1
0
1
1
2
3
1
2
1
1
0
1
1
1
1
1
2
1
1
1
1
2
2
0
1
0
2
1
2
1
1
1
1
1
2
1
1
1
1
2
0
2
2
1
0
1
1
0
1
2
0
4
1
1
0
2
1
1
1
1
1
1
2
2
1
1
0
1
1
0
0
2
1
2
1
1
4
2
0
2
1
0
1
2
1
0
2
1
2
2
1
0
1
0
1
1
0
1
1
1
1
2
2
1
1
1
1
0
1
1
2
1
1
1
1
2
2
0
1
0
1
1
2
0
0
0
1
1
1
1
1
1
1
1
1
2
0
1
1
2
1
0
1
1
1
2
2
1
1
1
0
0
1
1
1
2
1
1
1
1
0
1
1
1
2
2
1
2
1
0
1
1
1
1
0
2
1
2
1
1
0
1
1
0
1
1
1
1
0
0
1
2
2
2
1
0
1
1
1
0
1
1
1
1
1
1
0
1
2
2
0
1
1
2
2
1
2
0
0
0
1
2
1
0
2
3
1
0
2
0
1
2
1
1
2
0
1
1
1
0
1
0
1
0
2
1
1
1
1
0
1
1
1
1
1
1
1
0
0
2
2
0
0
1
0
1
0
0
2
2
1
1
2
2
1
0
1
0
1
0
2
2
1
2
1
1
1
2
2
2
1
1
2
1
1
3
1
2
0
1
1
2
1
1
0
2
2
2
2
2
1
2
2
1
1
1
1
0
0
1
2
1
0
1
0
0
1
0
3
1
1
1
2
1
1
2
1
2
1
2
1
0
0
1
1
1
0
1
1
1
1
2
1
1
1
1
0
2
2
1
1
1
1
0
1
2
1
1
1
1
2
1
0
0
2
0
0
0
1
1
2
1
1
2
1
2
1
1
2
2
1
1
2
1
1
2
1
1
1
1
2
1
1
1
2
2
1
2
0
1
1
1
1
0
1
1
1
1
1
0
1
0
0
1
1
1
2
0
0
0
2
2
1
1
2
1
2
1
2
0
1
1
2
1
0
1
1
1
1
2
2
2
1
1
0
1
2
0
1
2
1
1
1
1
2
1
2
0
0
2
1
1
0
2
0
1
1
0
1
2
0
1
3
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
0
1
0
1
1
1
2
0
1
1
1
1
1
1
1
1
0
2
1
2
1
2
1
1
1
1
1
0
1
1
1
1
1
2
2
1
2
2
1
1
2
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
0
2
1
1
1
1
1
0
2
0
2
1
1
2
1
1
2
2
2
1
2
1
0
2
1
1
1
1
1
1
0
1
1
1
1
1
1
0
2
0
0
1
2
2
1
2
1
1
1
1
1
1
2
1
2
1
2
1
1
1
1
2
0
1
1
1
3
2
1
1
2
1
0
0
1
2
0
0
2
0
2
1
1
2
1
1
1
2
1
1
0
1
1
1
1
2
0
0
1
2
1
0
1
1
0
1
1
1
1
1
0
2
1
0
0
1
2
0
1
2
3
0
1
1
1
1
1
0
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
2
2
0
2
0
1
2
1
1
1
1
1
2
1
1
2
1
2
1
1
2
1
2
0
1
1
1
2
1
1
2
2
1
1
2
1
0
1
1
1
1
1
1
2
1
0
1
1
2
1
1
4
1
2
2
1
1
1
1
0
1
0
1
2
1
1
2
1
1
1
0
2
1
1
1
1
0
1
1
1
1
1
1
0
2
1
2
2
2
1
0
1
1
1
0
2
1
1
2
1
2
1
0
1
2
1
1
2
1
0
1
2
1
1
2
2
2
0
1
1
2
1
2
1
0
2
1
1
1
1
1
2
2
3
2
1
1
1
1
2
1
3
1
1
3
1
1
1
1
0
1
1
1
0
1
0
1
1
1
1
2
1
1
0
2
1
0
1
1
1
1
1
1
2
2
1
2
2
1
1
2
0
1
0
0
2
2
1
1
0
1
1
0
2
1
1
1
1
1
2
2
1
1
2
1
2
1
2
1
0
1
1
0
2
1
1
0
1
1
1
2
0
0
2
1
1
2
1
1
1
1
1
1
1
1
2
0
1
1
1
1
1
1
1
0
1
1
1
2
2
1
1
1
3
1
1
1
1
1
1
2
1
2
2
1
1
2
0
2
0
1
2
1
0
2
1
2
2
1
1
1
0
1
2
1
0
1
0
1
2
2
1
1
1
1
1
1
1
2
1
1
2
1
1
2
0
2
1
1
2
1
2
0
1
1
0
1
0
1
0
1
2
1
1
1
2
2
1
0
2
1
0
1
1
2
0
2
0
1
1
0
0
2
0
1
2
1
1
2
0
2
1
1
1
1
1
1
1
2
0
1
2
2
2
2
2
1
1
1
2
2
1
2
2
2
2
1
4
1
2
2
0
1
1
2
2
2
1
2
2
0
1
0
1
1
1
2
1
1
1
1
1
2
2
2
2
1
2
1
0
0
0
1
2
1
1
0
1
1
2
1
2
0
1
0
2
0
1
1
1
2
1
1
2
2
0
0
2
2
1
2
1
2
1
1
0
0
1
0
1
1
1
1
0
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
0
1
2
1
1
1
1
1
2
2
1
1
0
1
1
1
1
1
0
1
0
1
0
1
0
2
1
1
0
1
2
1
2
2
1
2
1
0
2
1
1
0
1
2
1
2
0
1
1
0
1
0
2
0
2
1
1
1
1
1
1
1
0
2
2
1
1
1
1
1
1
1
0
0
1
0
2
1
1
1
1
0
1
2
1
2
1
1
2
1
1
0
1
2
2
0
1
1
1
0
1
2
1
1
1
2
0
0
2
1
1
3
2
2
1
0
2
2
2
1
1
2
1
1
1
1
0
2
0
1
2
0
1
2
1
2
1
1
0
2
2
1
1
1
0
1
1
1
1
2
1
1
1
2
1
1
1
3
1
1
1
1
0
1
2
1
2
2
2
1
1
2
1
1
2
1
1
1
1
2
1
1
0
1
1
1
1
2
1
0
1
3
0
1
3
0
1
1
2
1
1
2
1
0
2
0
1
1
2
2
1
1
0
1
1
1
1
2
1
1
1
1
1
0
1
1
2
1
1
1
0
1
2
1
1
2
1
1
1
0
1
1
1
0
1
1
1
0
1
1
0
0
2
2
0
0
2
0
1
1
1
2
1
1
1
0
0
1
1
1
2
0
0
1
1
4
0
2
2
1
1
1
0
1
1
1
1
1
0
1
1
0
1
0
1
1
1
0
1
1
1
1
1
2
1
1
1
1
1
1
0
1
1
1
1
1
1
1
0
1
1
2
2
1
1
1
1
1
1
1
2
1
0
1
1
0
0
0
1
1
0
1
1
1
0
0
1
0
1
2
0
1
2
1
1
1
0
2
1
1
1
1
0
1
2
1
0
1
1
1
2
1
2
0
2
1
2
0
2
2
2
0
2
0
2
0
1
2
0
0
1
2
0
2
1
1
0
0
2
2
2
0
1
1
1
1
1
3
1
1
2
1
1
1
1
2
0
1
1
1
1
2
1
4
0
2
2
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
0
2
1
2
2
0
0
0
1
0
2
0
1
1
1
1
0
1
1
0
1
1
2
1
1
2
0
1
2
1
0
2
0
0
1
0
0
1
0
1
1
1
2
0
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
1
1
1
2
2
0
2
2
1
1
1
1
0
1
1
1
0
1
2
1
1
1
0
1
1
2
1
1
2
1
2
2
1
1
0
2
0
1
0
1
1
1
1
2
1
1
1
1
2
0
1
2
2
1
1
2
1
1
1
1
0
1
0
1
1
0
2
0
1
1
1
0
1
3
1
1
1
1
1
0
1
1
0
0
1
1
1
1
1
1
0
1
1
0
1
1
1
0
1
2
0
0
1
1
0
2
0
0
1
2
1
0
2
1
1
0
1
2
0
2
3
0
1
0
1
1
2
1
1
0
1
1
1
1
1
2
1
1
0
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
0
2
1
0
1
2
1
1
1
1
0
2
1
1
0
2
1
1
1
1
0
1
1
2
2
0
0
3
2
2
0
1
1
0
1
2
2
1
1
1
1
1
0
1
2
0
1
1
2
1
1
0
2
1
0
1
1
2
1
1
1
1
0
1
1
1
1
1
1
0
1
1
2
1
0
1
0
2
0
1
1
2
2
2
0
0
1
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
1
1
0
1
2
1
0
1
0
1
1
0
1
1
0
2
1
1
1
1
1
1
2
1
0
0
1
2
0
2
1
0
1
2
1
1
1
1
2
1
1
2
2
1
0
1
2
1
1
2
2
0
1
0
2
2
1
0
1
1
1
2
0
0
2
0
1
1
1
1
1
1
1
1
2
0
1
0
1
1
1
1
1
0
2
2
1
2
1
1
1
0
2
1
2
1
2
2
1
1
1
0
1
0
2
0
2
1
0
1
1
1
1
0
0
1
1
1
2
1
2
0
0
1
0
2
1
1
1
0
1
2
1
1
1
2
0
2
1
1
1
1
1
0
2
1
1
2
1
0
1
1
1
1
2
0
2
2
2
1
1
1
0
1
1
1
1
2
3
1
1
0
1
2
2
2
1
1
1
1
1
0
1
1
2
2
1
2
0
2
1
2
2
1
1
2
1
2
1
3
0
1
1
1
1
1
1
1
1
1
2
2
1
2
1
1
1
0
1
1
2
1
1
0
1
1
1
0
1
1
0
2
1
2
1
1
1
1
1
0
2
1
1
1
1
1
1
1
1
1
0
2
1
1
1
1
2
2
1
0
0
1
2
2
1
0
1
1
1
1
1
1
2
0
0
1
1
1
0
1
1
1
1
1
1
0
0
1
2
1
3
1
2
2
0
1
0
3
1
2
0
0
0
1
1
1
1
1
1
0
1
2
1
1
1
0
2
0
2
1
1
1
1
1
0
2
0
3
0
1
1
1
0
1
1
1
1
2
1
1
0
0
1
1
0
1
0
1
0
0
1
0
1
1
1
2
1
3
0
2
1
1
1
1
1
1
1
1
0
1
1
1
0
1
2
0
2
1
1
1
1
3
0
1
1
1
2
0
0
1
1
1
2
2
2
1
0
0
2
1
1
2
2
1
1
1
1
1
0
1
1
1
1
1
2
0
1
1
2
1
2
1
1
0
1
1
1
1
1
1
1
1
0
0
2
2
1
1
1
1
1
1
1
2
0
1
2
2
1
1
2
1
1
2
2
1
2
1
2
1
1
1
0
1
2
0
2
2
1
3
1
1
2
0
0
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
0
0
1
1
2
0
2
0
1
1
1
1
1
1
1
0
1
2
1
1
0
2
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
1
2
2
0
2
1
1
1
2
2
1
0
0
1
1
2
1
1
1
1
1
1
0
1
1
1
1
1
2
1
1
0
1
1
0
1
0
1
2
1
0
2
1
3
1
1
1
1
1
0
1
1
2
1
1
1
1
2
0
1
1
1
1
2
1
1
0
1
1
2
0
1
1
1
1
1
1
1
1
1
1
1
0
2
1
2
1
1
2
1
1
0
1
0
2
1
2
0
1
2
0
1
1
2
1
0
0
1
1
0
0
1
1
1
1
2
2
2
0
1
6
1
2
2
1
2
2
1
2
1
1
1
2
1
1
0
1
1
1
0
1
1
1
2
2
1
1
0
1
2
1
1
1
1
2
0
2
2
1
0
1
2
1
0
1
1
1
2
1
1
1
2
1
0
1
1
1
2
1
1
2
2
1
1
2
1
2
1
1
2
1
0
0
1
1
1
2
1
2
0
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
0
2
1
1
0
2
1
0
1
1
3
1
1
1
2
1
1
1
1
1
1
1
2
2
2
1
1
2
1
0
1
1
1
2
2
0
2
2
1
1
1
2
1
2
1
0
2
1
1
2
1
1
1
1
1
2
1
1
0
0
2
1
1
1
2
1
1
1
1
1
1
2
2
1
2
0
1
1
1
0
1
1
0
2
1
1
0
1
1
0
1
1
1
0
1
0
1
2
0
0
1
0
1
3
0
0
1
1
2
1
3
1
2
1
1
1
1
1
1
0
1
2
1
2
1
1
1
1
1
1
2
2
2
1
1
1
2
2
1
1
0
1
1
1
1
1
1
2
0
1
2
2
1
1
2
2
1
0
1
0
2
1
1
1
0
2
0
1
2
1
0
2
1
1
0
2
0
1
1
1
1
1
0
0
1
1
1
1
0
0
1
2
0
0
2
1
1
1
1
2
2
0
1
1
1
1
1
1
1
0
1
1
1
1
1
2
2
1
1
1
1
1
0
0
0
0
1
1
1
1
1
1
2
1
2
2
1
0
1
0
1
1
2
1
2
1
1
0
1
1
0
0
0
1
1
1
1
0
1
0
1
1
1
1
1
1
1
2
2
0
1
1
1
0
1
1
0
1
2
1
1
1
1
0
1
0
1
1
1
1
1
1
1
1
0
0
1
1
1
1
1
1
1
1
2
0
2
1
1
1
1
1
1
2
0
1
1
1
0
2
1
0
0
1
2
0
2
1
1
1
1
1
2
0
1
1
0
1
1
2
1
0
2
1
1
1
1
1
1
1
0
1
1
1
0
1
1
1
1
1
1
1
1
1
0
0
1
2
0
2
1
0
3
1
1
1
1
1
0
2
1
2
1
1
2
2
1
3
1
2
1
1
2
1
1
2
1
0
2
2
1
0
2
2
0
1
1
1
2
2
1
1
1
1
1
2
1
1
1
1
1
1
0
1
0
1
1
1
1
1
1
1
1
0
0
2
2
2
2
1
1
1
2
0
0
0
1
1
1
2
1
1
0
1
0
1
2
1
1
1
2
0
2
1
1
1
0
0
0
1
2
0
1
1
1
2
1
1
0
0
1
2
1
1
1
1
1
2
1
2
1
2
1
2
0
1
1
3
1
1
1
1
1
1
0
1
1
0
1
2
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
0
2
1
2
1
0
1
1
1
1
2
1
0
0
1
1
1
1
2
2
0
2
1
0
1
1
1
1
0
1
1
1
2
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
0
2
1
1
1
1
3
2
1
1
0
0
2
1
1
1
1
1
1
1
1
0
1
1
1
2
1
2
0
2
2
1
1
1
0
2
1
1
1
2
2
1
1
1
1
2
1
0
1
2
1
2
0
1
1
0
1
1
1
1
1
1
0
1
0
1
1
2
1
1
1
2
2
1
0
1
2
1
1
2
2
0
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
0
0
0
1
0
2
0
1
1
2
0
2
1
1
1
0
1
1
2
0
2
1
1
0
0
1
1
1
0
0
1
1
1
1
1
2
0
0
0
0
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
2
2
0
1
1
2
2
1
1
1
2
1
2
1
1
1
0
2
1
1
1
1
0
1
1
0
1
1
0
0
2
1
1
1
0
1
1
1
1
2
1
1
1
1
1
0
0
1
2
2
2
1
2
1
1
1
3
0
0
1
1
1
1
1
1
1
1
1
1
1
0
0
1
1
1
0
2
0
1
1
1
1
1
2
1
1
2
1
0
1
2
2
0
1
2
0
1
1
1
1
1
2
1
0
0
0
2
2
1
1
0
1
1
0
2
1
1
0
1
0
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
2
0
1
2
0
5
1
2
2
2
0
2
0
2
1
4
1
1
1
2
1
1
2
2
1
1
1
0
0
1
0
0
1
1
0
1
0
2
1
3
1
2
1
1
0
2
0
2
2
0
0
0
1
1
1
2
1
1
1
0
1
1
2
1
2
0
2
1
0
1
1
1
2
1
1
2
2
2
1
1
1
2
1
1
0
1
1
1
1
0
1
1
1
2
2
2
2
1
1
1
1
0
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
0
1
1
2
2
2
1
0
2
2
1
1
1
1
1
1
1
1
1
2
1
1
0
1
0
1
1
1
1
1
1
1
1
1
0
2
1
1
1
1
1
1
0
1
1
0
1
0
1
1
1
2
2
1
1
1
0
1
1
0
1
2
1
1
0
2
1
2
0
1
2
1
1
1
1
2
1
1
1
1
1
2
1
1
0
1
2
0
3
2
1
0
1
1
1
1
0
1
0
1
1
1
1
1
1
1
0
1
0
1
1
0
0
2
1
1
0
1
1
2
1
1
1
0
1
1
0
0
1
0
0
1
1
2
1
1
2
1
2
2
0
0
1
2
1
1
1
2
0
1
0
0
2
1
2
1
0
0
1
1
1
0
1
1
0
2
3
2
0
2
1
2
2
1
1
2
1
1
2
2
0
1
1
2
2
2
1
0
2
1
1
2
2
1
0
2
1
0
2
1
1
1
1
1
2
1
1
0
2
2
1
1
1
0
2
1
1
1
0
0
1
0
1
2
1
1
1
1
2
0
0
1
1
2
1
1
1
0
1
1
1
1
0
1
1
1
0
0
2
1
2
2
1
0
1
2
2
2
2
1
2
2
1
1
1
1
1
2
0
1
2
1
1
1
1
1
1
0
1
2
2
1
2
1
1
2
1
2
2
1
1
0
0
1
1
2
1
2
1
1
1
2
1
0
1
1
2
1
2
2
2
1
0
1
0
1
1
1
1
2
2
0
2
0
1
0
1
2
1
1
1
0
1
0
1
1
1
1
2
1
1
1
0
1
0
2
1
3
1
1
1
1
1
1
1
1
2
1
1
1
0
1
2
2
2
1
1
1
2
1
1
0
1
1
2
1
1
1
1
1
0
2
1
2
1
2
0
1
0
1
2
1
2
1
2
1
2
1
1
0
1
1
2
0
1
1
1
1
1
1
1
1
1
0
1
2
2
1
1
0
1
1
0
1
0
1
0
2
1
1
0
1
1
0
1
1
1
2
0
1
0
2
1
3
1
2
2
2
0
1
0
2
1
1
0
1
1
1
2
1
1
1
2
1
2
2
0
0
1
1
2
1
1
0
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
2
2
2
2
0
1
1
1
1
1
2
1
0
1
1
1
1
1
1
1
1
1
1
2
1
0
1
2
2
2
1
2
3
1
1
0
1
2
1
2
1
0
1
2
1
2
2
1
3
1
1
1
1
2
1
2
1
0
0
2
1
1
0
0
2
0
1
0
2
1
2
1
1
1
1
0
1
0
1
1
2
1
2
0
1
2
2
1
2
3
1
1
2
0
1
0
1
1
1
1
1
4
1
2
2
0
0
2
1
1
1
1
1
1
0
1
0
1
1
0
0
1
1
1
0
2
1
1
2
0
1
1
3
0
2
0
0
0
2
2
1
1
1
1
2
2
1
2
1
1
2
2
1
2
0
0
1
1
2
1
1
2
2
2
2
1
1
1
0
1
2
2
2
1
1
2
0
0
2
1
1
1
2
2
1
1
1
1
0
2
1
0
1
1
1
1
1
1
2
1
1
1
1
1
2
1
2
2
1
2
1
1
1
1
1
2
1
0
0
1
1
1
1
1
2
0
1
1
1
2
1
1
1
1
2
2
1
0
2
0
1
0
1
0
1
1
1
1
0
0
0
0
1
1
1
2
1
1
1
3
2
2
2
0
1
1
1
0
0
1
0
1
1
1
0
1
1
2
2
2
1
2
1
1
2
1
1
0
2
0
0
1
1
1
2
2
2
1
1
1
2
1
2
1
1
2
1
1
1
1
0
1
2
1
0
1
2
1
1
1
2
2
1
2
1
1
1
2
2
2
1
1
1
2
1
2
2
2
0
0
1
1
0
0
2
1
1
1
1
2
1
1
1
2
1
1
2
1
1
2
2
1
0
1
1
2
1
1
1
1
1
1
1
0
1
1
2
3
1
1
1
1
2
1
1
0
0
0
1
2
1
0
2
1
0
2
2
2
1
0
1
0
1
1
0
1
1
1
1
0
1
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
0
1
1
1
1
0
1
1
0
1
1
2
2
1
1
1
1
2
1
1
2
2
2
1
1
0
0
1
1
1
2
1
0
1
2
0
1
2
1
2
0
0
1
2
1
1
1
1
0
1
1
0
2
1
1
2
0
0
0
2
0
0
0
2
2
1
1
2
1
1
1
1
0
1
1
2
0
1
2
1
1
1
1
1
2
1
1
2
1
1
1
1
1
2
0
2
2
1
1
0
2
1
1
2
4
2
1
0
1
2
1
0
2
0
2
0
2
0
1
2
2
1
1
1
1
1
2
1
0
1
0
0
2
0
1
1
1
1
2
0
2
1
1
2
1
0
0
1
1
1
0
0
1
2
1
1
1
1
1
2
2
0
1
2
1
1
1
0
0
1
0
2
1
1
2
1
0
1
1
1
0
2
1
1
1
1
2
1
2
2
2
1
1
1
2
1
1
0
1
0
1
0
1
1
2
0
2
2
1
2
1
1
2
1
2
1
2
1
1
0
2
1
1
1
1
0
0
2
1
1
1
1
2
1
1
1
0
1
1
1
1
1
1
1
1
2
1
1
2
0
2
1
2
2
1
1
1
2
2
0
0
1
1
2
1
0
2
1
0
1
2
2
2
1
1
0
0
1
1
2
1
2
1
0
0
1
2
1
1
2
1
1
1
2
1
1
1
2
0
1
1
0
0
1
2
1
1
1
1
2
1
1
2
1
2
2
0
2
1
1
1
2
0
0
1
0
1
1
1
1
2
2
1
1
1
0
2
2
0
0
1
0
1
0
1
1
1
2
1
1
1
1
1
1
1
1
2
0
2
0
1
1
2
1
2
1
0
0
2
1
1
0
1
0
1
0
1
0
1
1
1
0
2
1
2
2
0
1
1
1
1
0
2
1
1
0
2
1
0
0
1
2
2
0
1
0
1
1
0
1
1
2
2
1
2
2
1
0
1
0
1
1
2
0
2
2
2
1
1
1
0
2
0
2
1
0
1
2
1
0
2
0
0
2
2
1
1
2
1
1
0
1
1
1
1
0
2
1
1
1
2
0
1
1
1
2
1
1
1
1
1
1
0
0
1
1
1
0
1
1
1
0
0
2
1
1
1
1
1
0
2
2
1
1
1
1
3
0
0
0
1
1
1
1
0
1
1
0
0
1
1
1
1
2
1
1
0
1
2
2
2
2
1
2
1
2
2
0
1
1
2
1
1
1
1
1
1
0
7
2
1
1
1
2
1
2
1
1
1
1
2
1
2
2
2
0
0
0
1
1
0
1
0
1
0
1
1
2
0
2
1
1
0
1
0
1
1
0
0
1
2
1
1
0
2
1
1
0
1
1
1
1
1
0
1
1
1
0
1
1
1
0
0
0
2
0
1
2
2
1
0
1
2
1
2
1
0
0
1
1
2
2
1
2
0
0
1
0
2
1
1
2
0
1
1
2
0
1
1
1
2
1
1
0
1
2
1
1
1
1
0
2
1
1
3
1
2
2
1
2
0
1
1
1
0
1
1
1
2
1
2
1
1
0
0
1
1
2
0
2
0
1
1
1
1
2
2
1
0
1
1
0
1
1
1
1
2
0
2
1
1
1
1
1
1
1
2
1
0
1
1
1
1
2
2
1
1
1
3
0
2
1
1
0
1
1
1
2
1
1
1
1
2
2
1
1
1
1
1
1
2
0
0
0
1
1
2
0
2
0
1
1
0
0
1
1
0
1
1
0
2
1
2
1
1
1
1
1
2
0
1
1
1
1
1
0
2
0
2
1
1
1
0
1
2
1
2
1
0
1
1
1
1
0
0
1
1
1
0
2
1
2
1
1
0
2
1
1
0
1
1
2
1
1
1
0
2
3
1
2
0
0
1
1
1
1
0
2
2
2
3
2
1
1
1
2
1
1
1
1
0
1
2
1
1
1
1
1
1
2
2
2
1
2
1
1
0
0
0
0
0
1
2
1
2
1
0
1
1
1
2
2
0
1
1
0
2
1
2
2
1
1
1
1
2
1
1
1
1
1
1
0
1
2
1
1
1
1
1
2
1
2
1
1
0
1
1
2
0
1
1
1
2
1
1
1
4
0
1
1
1
0
1
0
1
0
1
1
1
1
1
1
2
1
2
1
1
1
3
1
1
1
1
1
2
0
1
1
0
1
1
1
1
1
2
1
2
2
1
0
0
1
2
2
2
2
1
1
0
1
1
1
1
1
1
1
1
2
1
2
0
1
1
1
1
1
0
1
2
1
1
1
1
2
1
1
2
2
1
1
1
1
2
1
0
1
1
1
1
1
1
1
3
1
1
1
0
0
0
2
1
1
1
1
1
1
2
0
1
1
1
1
1
1
1
0
1
1
1
0
2
1
1
1
1
1
2
0
1
2
1
1
0
1
1
1
2
2
1
2
1
3
1
0
1
1
2
2
1
1
1
1
1
2
1
2
1
2
1
1
1
2
2
2
1
1
1
2
0
0
2
0
1
1
1
0
1
1
0
1
1
2
1
1
1
1
0
2
1
1
1
2
1
1
0
1
1
1
1
1
1
0
1
1
1
0
0
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
0
2
0
1
0
1
2
1
2
1
2
1
1
2
0
1
1
1
1
1
1
1
1
2
1
0
1
2
1
1
1
0
2
1
1
0
1
2
1
0
2
1
2
1
1
0
1
1
1
2
1
1
0
1
2
1
2
1
1
1
0
2
0
1
0
0
2
1
0
2
5
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
2
1
0
1
0
0
1
0
1
2
1
2
1
0
2
2
1
0
1
1
1
0
0
2
1
1
0
2
2
1
0
3
1
1
1
1
0
1
1
2
1
2
1
2
1
1
1
0
1
1
1
1
2
2
1
1
2
1
0
1
1
1
1
1
2
0
1
2
1
1
1
1
1
0
1
1
1
2
2
2
0
0
1
1
1
2
1
1
1
2
2
1
1
0
0
2
1
1
1
2
1
2
2
2
1
1
1
1
1
0
1
1
0
0
2
1
1
1
1
1
1
2
0
0
1
2
1
2
1
1
3
1
1
1
0
1
1
1
1
1
1
0
2
1
1
1
0
1
1
1
2
1
1
0
2
0
1
1
1
1
1
0
1
1
1
1
1
1
2
1
1
0
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
2
3
2
0
0
1
0
1
1
1
1
1
1
1
1
2
1
1
0
0
1
1
1
2
1
1
2
1
2
0
1
1
1
1
2
0
2
1
1
2
2
0
0
1
1
1
2
1
2
2
1
1
2
0
1
0
0
3
1
2
2
1
1
1
2
0
1
1
1
2
1
1
1
1
1
0
1
2
0
1
2
1
2
2
1
0
1
1
1
1
1
1
1
2
1
2
0
0
1
1
0
2
1
0
0
1
1
1
1
0
2
2
1
2
1
1
1
2
1
1
1
0
1
1
2
1
2
2
0
1
0
1
0
1
0
2
1
2
1
0
2
1
1
2
2
1
1
1
1
2
0
1
2
1
1
1
1
2
1
1
1
0
0
1
0
1
1
1
1
2
0
2
1
1
3
1
1
0
2
1
1
2
1
1
1
2
1
1
0
1
1
1
2
2
1
0
1
2
1
2
1
1
1
2
1
1
1
0
2
2
1
1
2
1
1
2
1
2
1
1
2
1
1
2
1
1
1
1
1
0
2
1
0
0
1
2
1
2
1
1
1
2
2
1
2
0
1
1
1
0
2
2
2
0
1
1
1
1
1
0
0
1
2
1
3
2
1
2
1
1
2
1
1
1
0
1
2
1
0
2
1
2
0
0
1
2
2
1
2
1
1
1
2
2
1
1
2
0
2
0
2
1
1
1
0
2
1
0
2
0
1
1
2
1
1
1
0
1
1
1
2
1
1
0
1
1
1
1
0
1
1
1
1
2
2
1
0
2
1
1
1
1
1
1
0
2
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
0
1
2
2
1
2
1
0
2
1
0
1
1
1
2
2
0
1
2
1
1
1
2
1
0
1
2
1
2
0
0
2
2
0
2
2
0
1
1
2
0
1
1
1
0
0
1
1
1
1
2
1
1
1
2
2
1
1
2
1
2
2
1
1
0
1
1
2
2
2
1
1
1
2
1
1
1
1
1
2
2
0
2
0
1
1
3
1
1
1
1
0
1
1
1
2
1
1
2
1
0
2
2
1
1
0
0
1
1
1
2
2
2
0
0
1
1
1
2
1
2
1
2
1
0
2
1
1
1
0
1
1
1
1
1
1
0
1
1
1
0
1
0
1
2
0
1
1
1
0
1
2
2
0
2
0
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
2
2
0
1
0
1
1
2
1
1
1
1
1
1
1
0
1
0
1
0
0
1
1
1
2
0
2
2
0
1
1
0
2
1
2
2
1
1
2
1
2
1
1
0
3
1
1
1
0
1
1
1
1
1
0
2
0
1
1
0
2
1
0
2
1
2
1
1
1
2
1
1
2
2
0
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
0
1
1
1
0
1
1
2
1
1
0
0
2
1
2
1
2
2
0
1
1
1
0
1
2
2
1
1
1
1
1
0
1
1
0
2
1
0
2
0
0
1
0
1
1
2
1
2
1
1
2
1
1
0
1
1
2
1
1
1
1
1
1
1
2
1
0
0
0
1
1
0
1
1
0
1
2
0
1
0
1
2
0
1
0
1
1
1
1
1
0
1
1
4
1
1
2
1
3
1
1
2
1
1
1
1
2
0
1
1
1
2
1
1
1
2
2
0
1
2
2
0
0
1
1
2
1
1
0
1
0
1
1
2
2
1
1
1
2
1
1
1
2
2
1
1
1
1
0
1
1
0
2
1
2
1
1
1
1
1
1
2
1
1
0
1
0
2
1
2
1
0
1
2
2
1
1
0
1
1
1
1
1
1
1
1
0
1
1
1
1
1
0
0
0
2
2
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
0
1
0
1
1
0
1
2
2
1
2
1
1
0
1
1
0
2
1
1
0
1
1
0
0
0
2
1
1
4
0
1
1
1
1
2
1
1
0
2
1
1
1
1
0
0
1
0
2
1
1
1
0
1
1
1
1
0
1
1
1
1
1
0
1
1
1
2
1
1
0
0
1
1
1
1
1
1
1
2
1
1
1
1
2
1
0
2
2
1
1
1
1
1
1
2
0
1
2
2
1
2
2
1
0
0
1
1
0
1
1
2
1
1
0
1
1
2
1
0
1
2
1
0
1
1
1
1
0
1
2
1
1
1
1
0
1
5
1
1
1
0
2
2
1
1
0
2
2
1
1
0
1
1
1
0
2
1
1
1
0
0
1
1
1
1
1
2
1
1
1
1
0
1
1
1
1
1
1
1
1
3
1
1
1
1
1
1
2
0
1
3
1
0
2
2
0
1
0
1
1
2
2
1
0
1
2
1
1
2
1
1
2
1
1
0
1
1
1
1
1
2
2
1
0
0
1
2
1
1
1
1
0
1
1
2
2
1
0
1
0
1
1
1
2
0
0
1
1
0
2
2
2
1
1
1
2
2
1
1
0
0
1
1
1
1
1
1
1
0
1
1
2
1
2
1
1
2
2
1
0
1
2
1
1
0
1
1
1
3
1
2
1
2
1
1
1
1
1
0
0
1
1
0
1
1
2
1
1
1
2
0
1
2
2
1
2
1
1
1
1
2
1
0
1
2
2
2
0
1
0
1
0
0
0
1
2
1
1
1
2
2
1
2
1
2
3
0
0
1
0
1
2
1
2
2
2
1
0
2
1
1
1
1
1
1
1
0
1
1
2
1
1
0
1
0
1
1
1
2
1
2
0
1
1
0
1
1
1
2
1
2
0
1
1
2
2
1
1
0
2
1
2
1
2
2
0
1
0
1
0
1
1
1
2
1
0
1
1
1
1
1
2
2
1
1
2
1
1
2
1
1
2
2
1
1
1
1
1
2
1
1
2
2
0
2
2
1
1
0
2
1
1
0
1
2
1
1
2
2
1
1
1
0
1
0
1
1
1
1
1
1
2
1
2
0
1
1
1
0
0
2
2
1
1
2
1
1
0
1
2
1
0
2
0
2
1
1
1
2
1
1
1
1
1
1
0
1
1
1
1
2
0
1
1
1
1
0
1
0
1
2
1
2
0
1
1
1
1
1
0
1
1
2
0
1
1
1
1
1
2
3
0
1
1
2
1
1
0
0
2
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
3
2
1
2
2
1
2
1
2
1
1
1
2
1
1
0
1
1
0
0
1
2
2
2
1
1
1
2
0
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
2
0
1
0
1
3
2
1
0
1
1
2
2
1
1
2
1
1
1
0
1
1
1
1
0
0
2
0
1
0
2
2
1
0
1
1
0
1
1
1
0
0
0
0
0
1
2
2
1
1
2
1
1
1
1
0
0
1
1
1
3
0
0
1
1
1
1
1
0
2
0
2
2
1
2
2
0
1
0
2
0
1
0
1
0
2
2
1
2
2
1
2
0
0
1
1
2
1
0
0
0
1
1
0
1
1
2
1
1
1
1
1
2
1
1
2
0
1
0
1
1
0
1
1
1
0
1
2
0
1
0
1
2
0
1
1
2
1
1
1
0
2
1
1
1
1
1
2
2
2
2
0
1
1
1
1
2
1
1
1
1
1
1
2
2
2
2
2
1
0
1
1
1
0
1
1
1
1
0
1
2
1
0
1
1
0
2
1
1
0
1
0
2
1
1
0
2
0
2
1
1
1
1
1
1
1
1
0
1
1
2
1
1
0
3
2
1
1
1
0
1
1
1
1
1
1
2
2
2
2
2
2
2
2
0
0
2
1
1
1
1
1
2
2
1
2
1
2
2
0
0
1
3
2
0
0
1
1
2
1
2
1
1
1
2
0
1
1
2
2
1
0
1
2
0
1
0
1
1
1
0
0
2
0
0
1
1
1
1
1
2
0
1
1
2
0
1
2
1
1
0
1
2
0
2
1
2
1
1
1
1
0
2
1
1
0
2
2
1
0
1
1
1
1
1
2
1
1
0
1
1
0
2
1
1
2
2
1
1
0
0
1
2
2
1
1
0
0
1
1
0
2
2
2
1
1
1
1
1
1
2
1
1
1
1
0
2
0
1
0
1
1
2
0
1
2
2
1
1
1
1
1
1
0
1
3
0
1
0
2
1
2
2
1
1
1
0
2
1
2
2
1
0
1
1
0
1
0
0
1
2
2
2
2
2
1
0
1
2
1
2
1
0
0
2
1
1
0
1
0
1
2
1
1
2
1
1
0
1
0
1
1
2
0
0
1
1
0
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
0
1
1
1
1
0
1
0
1
0
1
0
0
2
2
1
1
1
1
1
1
1
1
2
0
1
3
0
2
2
1
0
1
1
2
1
0
1
0
1
1
3
2
1
1
0
1
2
0
1
2
1
2
1
2
2
1
1
0
1
0
0
2
1
1
0
2
0
0
0
1
2
1
1
1
2
1
2
0
1
0
2
2
2
2
2
2
0
0
1
1
0
0
2
1
1
1
2
0
1
1
2
1
0
1
2
2
0
1
0
1
2
2
1
1
1
1
0
1
1
3
1
0
2
1
1
2
1
1
1
2
1
1
1
1
2
1
2
2
0
1
1
1
1
3
2
1
1
2
1
2
0
0
1
1
0
2
2
1
1
1
1
1
1
0
0
1
2
0
2
2
2
1
2
1
0
1
2
2
1
1
1
1
1
2
2
1
2
0
1
1
1
1
0
0
1
1
1
1
1
1
1
1
0
1
2
2
0
1
2
1
2
1
0
1
1
1
2
1
1
1
2
2
2
0
1
1
1
0
2
1
1
1
1
1
1
0
2
2
1
0
2
1
2
1
1
0
1
1
2
0
1
1
0
1
0
1
2
1
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
2
1
2
1
0
1
2
1
0
1
1
2
0
1
1
1
1
1
2
1
1
2
0
1
1
1
1
1
1
0
0
2
0
0
1
0
1
1
2
1
2
1
1
2
1
0
1
1
1
2
2
0
2
0
1
1
2
1
1
1
0
2
1
1
1
1
1
0
1
0
1
1
0
2
1
0
2
1
2
0
2
1
1
0
1
1
2
0
1
1
2
0
1
1
1
2
2
1
1
2
1
2
2
1
1
2
0
2
1
2
1
2
1
2
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
2
1
1
0
1
3
0
1
1
2
1
2
2
1
0
1
2
1
1
1
1
2
1
1
0
2
1
0
1
1
1
0
2
1
2
2
1
1
1
0
0
1
7
0
1
1
1
0
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
0
2
1
2
1
0
1
2
1
2
1
2
1
1
0
2
1
2
1
1
0
1
1
0
1
1
2
1
1
0
2
0
0
1
0
1
1
1
0
2
1
1
2
1
0
1
1
0
2
1
0
1
1
2
0
0
2
0
1
2
0
1
1
1
1
1
1
1
2
1
1
2
2
1
1
1
1
3
1
2
1
0
1
1
1
3
2
1
0
1
2
0
1
1
1
3
1
1
1
2
2
1
2
1
0
2
1
2
1
2
1
2
1
2
1
1
1
2
0
1
1
1
0
1
1
4
1
2
1
2
2
1
2
1
2
0
2
1
0
1
1
2
2
1
0
0
2
0
0
1
1
1
2
1
1
2
2
1
1
0
1
1
1
1
0
0
1
1
1
1
2
0
1
2
1
1
1
1
0
0
1
1
1
1
1
1
1
0
1
2
2
1
0
1
2
1
0
2
1
0
1
1
1
1
1
2
2
1
1
2
1
1
2
1
1
2
1
2
1
0
1
1
2
2
2
1
1
2
0
0
0
1
1
1
0
1
2
1
1
0
1
1
2
1
1
1
1
1
1
2
1
0
1
1
1
0
1
2
0
1
1
1
1
1
0
2
2
2
1
2
2
1
1
1
0
1
0
2
1
1
1
1
1
1
1
2
1
0
2
0
1
2
0
0
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
1
2
0
1
1
1
2
0
2
1
1
1
2
1
0
1
2
0
0
1
1
1
1
1
1
2
0
2
1
1
1
1
2
1
2
1
0
1
0
1
2
1
2
1
2
1
1
1
0
2
1
1
1
0
2
0
0
2
1
1
1
1
1
1
2
1
3
0
2
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
0
2
1
1
2
2
1
1
1
0
1
0
1
1
2
1
0
1
1
2
1
1
2
1
2
1
2
1
1
2
1
2
2
1
1
1
2
1
1
1
1
2
1
1
1
0
1
1
1
1
2
1
1
1
1
1
2
1
2
0
1
1
2
1
2
1
1
1
0
1
2
2
1
1
1
1
0
2
0
1
2
0
1
1
2
1
1
1
0
0
1
1
1
2
1
1
2
0
1
1
1
1
0
2
3
1
1
1
2
2
1
1
1
1
0
1
1
1
1
1
0
2
1
1
1
1
1
1
1
2
0
2
0
2
2
1
1
1
2
2
3
1
2
1
1
2
1
1
1
1
1
0
2
2
2
0
1
1
1
1
1
1
2
2
0
1
1
1
0
0
2
1
0
1
0
1
1
1
2
1
1
2
0
0
0
1
0
0
1
1
1
2
1
1
2
1
1
1
2
0
1
2
2
1
1
2
1
0
1
1
2
0
2
1
2
2
1
1
1
1
2
2
1
2
2
1
1
1
1
1
2
1
0
2
1
0
2
2
0
1
0
1
2
1
0
1
1
1
0
1
2
1
1
1
0
1
1
4
1
1
1
2
1
0
1
2
1
1
2
0
1
1
1
1
1
0
1
1
0
1
0
2
2
0
1
2
0
0
1
1
1
1
1
1
1
1
1
1
1
1
0
2
1
2
2
1
1
1
1
1
2
1
1
0
3
1
2
1
1
1
1
1
1
1
1
1
0
0
1
2
2
1
1
1
2
1
1
2
0
1
0
1
1
1
1
1
1
1
1
2
1
2
1
1
0
1
1
1
0
2
1
1
2
1
1
0
1
1
1
0
1
1
1
1
1
0
2
1
1
1
1
1
1
1
1
3
1
1
2
1
1
1
1
1
0
1
0
1
1
0
1
1
1
0
1
1
0
1
1
0
1
2
1
1
1
2
2
2
1
1
0
1
1
1
0
0
1
2
1
0
0
0
1
0
1
0
1
1
1
2
1
1
2
1
1
1
1
1
1
1
0
0
0
1
1
2
1
2
0
2
1
2
1
1
1
0
1
2
1
2
0
1
1
2
1
0
1
1
2
1
1
2
1
2
1
0
1
1
1
1
2
2
0
0
1
1
2
2
2
2
1
0
1
0
2
0
2
1
2
1
1
0
1
1
1
1
1
1
0
1
1
1
1
1
2
1
1
2
0
1
1
0
0
1
0
2
2
1
1
0
1
1
1
1
1
0
1
1
1
1
1
0
2
1
1
0
0
2
1
1
2
2
1
1
2
1
1
1
1
1
1
2
1
2
1
2
1
0
1
0
1
3
1
1
1
2
2
1
2
1
1
0
1
2
2
1
0
1
1
1
3
0
1
2
1
1
1
1
1
1
0
2
1
3
0
1
2
2
2
0
1
1
1
0
1
2
1
1
2
1
1
1
0
1
1
1
2
2
2
1
1
0
1
0
2
0
1
1
1
2
1
2
1
0
2
2
1
1
1
1
1
1
1
2
1
1
1
1
2
2
2
0
2
1
1
0
2
1
1
2
1
1
1
1
1
0
1
2
1
0
1
2
2
1
0
1
1
2
1
1
1
2
1
0
1
1
1
1
1
2
2
1
2
2
2
2
1
0
2
0
0
1
1
1
1
1
1
0
1
1
1
2
2
1
2
2
2
1
2
1
1
2
1
1
2
1
1
2
1
1
1
2
1
1
0
0
1
1
0
1
2
0
1
1
1
1
1
2
0
2
1
1
2
2
1
0
2
1
0
1
1
2
2
2
1
1
1
1
1
1
1
1
1
2
1
1
2
1
0
1
0
3
1
2
2
1
2
2
0
0
1
2
1
1
1
1
0
1
1
2
0
2
1
1
1
1
1
1
2
1
1
0
2
1
1
2
0
2
2
1
0
1
1
2
1
1
2
2
2
2
1
0
1
1
1
1
2
1
1
2
1
2
0
1
1
1
1
0
2
2
1
1
1
0
1
0
1
2
0
1
1
2
1
2
1
3
0
2
1
1
2
2
1
1
1
1
2
1
1
1
2
1
1
0
1
0
0
1
2
1
1
1
1
0
2
1
1
0
0
2
2
2
1
1
1
1
2
2
2
1
2
2
1
2
1
1
0
0
0
2
2
2
0
1
1
0
1
1
1
1
1
2
2
2
2
2
1
2
1
2
1
1
2
1
0
1
1
1
1
2
0
1
1
1
1
1
1
1
2
2
2
0
1
2
0
1
0
2
1
2
1
1
1
1
1
1
1
2
1
3
1
0
1
2
1
1
1
1
0
2
0
2
1
0
0
1
1
1
0
0
1
1
0
2
1
1
1
1
2
2
1
1
1
1
2
3
0
2
0
3
2
1
1
1
1
0
1
1
0
1
1
1
1
1
1
1
1
0
1
2
1
2
1
0
2
2
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
2
1
1
2
2
0
0
1
2
1
2
2
1
1
1
1
1
0
2
1
1
1
0
0
1
1
1
1
2
0
1
1
0
2
2
0
1
2
1
0
1
1
0
0
2
1
1
0
2
0
2
2
1
1
1
0
3
1
1
1
1
1
1
1
2
1
2
1
1
0
1
1
1
1
1
1
1
1
2
1
1
1
0
1
1
0
1
2
2
0
0
1
2
1
1
2
0
1
1
2
2
1
0
2
0
1
1
1
1
1
1
1
1
1
1
1
2
0
1
1
1
1
0
0
0
1
1
0
0
2
0
1
2
1
2
1
1
1
1
1
2
1
0
1
2
1
1
0
0
2
1
1
1
1
1
0
0
1
2
2
1
2
0
0
2
2
0
2
1
2
2
0
1
2
1
1
2
2
2
1
0
1
2
1
0
2
1
2
0
0
0
0
1
1
1
1
1
1
2
2
1
1
3
1
1
0
2
0
2
1
0
1
2
2
1
0
1
1
0
2
1
2
1
0
1
0
1
1
1
1
1
2
1
1
0
2
1
2
0
0
1
1
2
1
1
1
2
1
1
0
1
1
2
0
2
0
1
1
2
1
1
1
2
1
7
2
1
1
1
0
0
1
2
0
1
1
1
0
1
2
0
2
2
1
1
1
2
1
1
2
1
2
5
0
1
2
0
2
1
1
1
0
1
1
2
1
1
1
1
2
1
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
0
1
1
1
2
1
1
0
1
1
2
1
2
1
0
0
1
1
1
1
1
2
2
2
2
2
1
0
2
1
1
1
1
1
1
4
2
0
0
1
2
1
1
2
1
0
0
1
1
3
0
2
1
2
1
2
1
1
2
2
1
2
1
1
1
0
0
1
1
0
0
1
1
2
2
0
2
1
1
1
2
1
0
1
1
1
1
1
1
0
0
1
1
1
2
0
1
1
2
0
0
1
1
2
1
1
1
2
1
1
0
1
1
0
2
2
1
1
2
1
0
2
1
1
1
2
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
2
0
1
1
1
2
1
1
2
0
1
1
1
1
2
2
0
1
2
1
1
1
0
1
2
1
1
1
1
2
2
1
0
0
0
2
2
2
0
1
1
2
1
1
2
0
1
1
1
1
2
0
0
2
0
2
1
1
1
1
1
2
1
1
1
0
1
1
1
2
1
1
2
1
2
1
1
1
1
1
1
2
2
1
1
1
0
0
2
2
2
1
1
2
2
1
0
1
2
0
1
2
2
1
0
0
0
2
1
1
1
1
1
1
2
1
1
1
2
2
2
0
0
1
2
1
0
0
1
2
1
1
0
2
1
1
1
1
2
2
0
1
1
2
2
0
1
1
1
2
2
1
2
2
2
1
0
1
1
1
2
1
1
2
1
2
1
0
1
1
1
2
1
0
2
1
1
2
2
0
1
2
2
0
1
2
0
1
1
1
2
2
1
1
1
3
2
1
0
1
1
1
1
0
1
2
1
1
1
1
0
2
1
0
2
2
2
0
2
1
2
2
2
1
1
2
1
1
1
1
1
1
0
1
1
1
1
1
1
1
2
0
1
1
0
1
0
1
0
2
1
1
1
1
0
1
1
1
1
0
0
1
0
1
1
2
1
2
1
1
1
1
1
2
1
1
2
1
1
0
1
1
0
0
1
1
1
1
2
2
2
1
0
1
0
1
5
1
2
2
1
1
0
1
2
2
2
1
1
0
1
1
1
1
1
1
1
0
0
1
1
1
1
2
0
1
1
2
2
1
2
0
1
1
1
1
1
0
2
0
1
1
0
0
1
0
1
0
0
2
0
1
1
2
1
1
2
0
1
2
0
1
1
1
1
1
0
2
1
1
0
0
2
1
0
2
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
2
2
2
1
1
1
2
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
0
1
1
1
1
1
1
1
1
1
2
2
2
2
2
2
1
1
1
1
1
1
0
0
1
1
0
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
2
1
2
2
2
1
1
0
1
2
1
2
1
0
1
0
2
1
1
2
1
1
1
2
0
1
2
1
1
0
2
0
0
1
1
2
1
1
0
1
1
2
1
0
1
3
1
2
2
1
1
2
1
0
1
2
1
1
2
0
0
1
1
0
0
0
2
0
1
0
1
1
1
1
1
1
2
1
1
1
1
1
1
2
0
1
1
0
1
0
1
1
0
1
1
1
1
2
2
1
0
0
0
1
1
0
1
1
1
1
1
2
2
1
1
1
1
3
0
1
1
1
0
1
1
1
1
1
0
2
0
1
1
1
2
2
1
1
2
2
1
1
1
2
1
0
1
0
2
1
2
1
1
2
2
1
1
1
1
1
1
1
2
0
1
2
2
1
1
1
1
2
1
0
2
1
1
1
1
1
1
1
2
2
1
2
1
0
0
1
0
2
2
1
1
1
1
1
0
1
1
2
0
1
0
1
2
1
1
1
1
0
1
0
1
1
1
1
1
2
1
1
1
1
0
1
1
2
1
2
1
1
3
1
1
1
2
2
1
2
0
2
1
0
2
1
0
0
1
1
2
2
1
1
1
1
1
1
1
3
1
2
0
2
2
2
1
1
0
1
1
1
1
1
2
1
0
2
1
0
0
1
1
1
1
1
1
0
1
2
1
2
2
1
1
1
1
1
1
1
1
2
1
1
2
2
0
1
1
1
1
2
0
1
2
1
2
1
1
0
3
1
2
0
1
0
1
1
0
1
1
1
1
0
1
0
1
1
1
1
2
1
1
1
2
1
1
2
2
2
3
1
2
2
1
1
1
2
0
1
1
1
0
2
2
1
1
1
1
1
0
1
0
0
1
1
1
2
1
1
0
1
0
0
1
0
1
0
2
1
0
0
2
1
2
1
1
2
2
2
0
1
2
2
1
0
1
1
1
1
1
1
1
0
1
0
2
2
1
2
0
1
1
1
1
0
1
1
1
0
1
1
1
0
0
1
1
0
1
0
2
1
0
1
0
1
3
0
1
1
1
1
1
2
1
1
1
0
2
1
1
1
1
1
1
2
0
0
3
0
2
1
0
2
1
1
0
1
1
1
1
1
0
1
0
1
1
0
0
0
2
0
2
5
2
2
1
2
1
2
1
0
0
1
1
1
1
1
1
0
2
1
2
1
1
0
1
1
0
1
1
2
2
2
1
1
1
2
0
2
2
1
1
1
1
0
1
2
1
2
1
1
2
1
1
0
0
1
2
0
2
1
2
1
1
0
0
1
2
1
1
1
1
1
1
1
1
2
2
2
1
0
1
1
1
1
1
2
1
0
2
1
2
0
1
1
1
0
2
0
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
0
1
2
0
0
0
1
1
1
1
0
1
1
1
1
0
1
2
1
1
0
1
2
1
1
0
1
2
1
2
1
2
0
2
2
1
1
1
1
0
2
2
0
1
0
0
0
1
1
1
2
1
1
1
0
1
1
1
0
2
1
2
1
0
0
2
2
1
1
1
2
0
0
1
1
2
0
3
2
1
2
0
0
1
0
2
1
1
2
0
1
2
0
1
0
1
1
0
1
1
1
1
1
2
1
1
1
2
0
1
0
1
1
1
0
1
1
1
1
1
0
2
1
2
2
2
2
1
2
2
2
1
1
0
2
1
4
2
2
1
1
1
1
1
1
1
0
0
1
1
1
2
1
1
0
1
1
1
1
1
1
0
1
1
2
1
1
1
1
2
2
1
1
1
0
1
1
1
0
0
2
2
1
1
1
1
2
2
2
1
0
1
0
1
1
1
1
1
1
0
1
0
1
0
1
0
0
0
1
1
1
1
1
0
1
0
1
0
2
1
2
0
1
1
0
2
0
1
2
0
1
1
1
2
1
2
0
0
1
1
1
0
2
2
2
1
1
0
0
0
2
1
3
1
3
2
0
1
1
1
1
0
1
1
1
1
0
1
1
2
0
0
2
2
2
1
2
1
1
0
3
1
1
2
0
2
0
0
2
1
1
2
1
1
1
1
2
1
0
1
1
2
1
2
1
1
1
0
1
1
1
2
2
1
1
2
1
2
1
2
1
1
2
1
1
1
1
1
1
2
1
1
0
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
2
1
0
1
2
0
1
1
1
1
1
1
2
2
0
2
1
2
2
1
1
1
1
2
2
0
1
2
1
1
2
1
1
2
1
0
0
1
2
2
1
2
0
1
2
1
1
2
1
1
1
1
1
1
1
0
1
2
1
2
0
1
1
1
1
1
2
1
1
1
1
2
1
0
1
1
0
1
0
0
1
1
1
0
1
1
1
0
2
1
1
1
1
1
0
1
0
1
1
1
2
2
1
1
1
0
0
2
1
1
0
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
0
1
1
0
2
2
2
1
1
1
1
1
1
1
0
1
1
0
0
2
2
1
1
1
1
2
1
1
1
1
1
1
0
2
2
1
0
1
1
1
1
2
1
1
1
0
2
1
1
2
2
2
2
2
0
1
0
2
1
1
0
1
0
2
0
1
2
2
1
0
1
1
2
1
1
1
2
1
1
0
2
1
1
2
2
0
1
1
2
2
1
0
0
0
1
0
2
1
1
2
0
1
0
2
1
2
1
1
1
1
1
1
1
2
0
1
0
1
1
2
0
1
1
1
1
1
2
1
1
1
1
1
0
2
2
2
0
1
2
1
0
2
1
2
1
2
1
1
1
0
1
2
0
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
0
1
1
1
1
2
1
0
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
4
1
2
1
1
1
1
2
2
2
0
2
1
1
0
2
2
2
1
1
1
2
1
1
2
2
1
0
2
0
1
0
1
0
1
1
1
0
1
2
1
2
2
1
2
1
1
2
2
1
0
1
2
1
0
2
1
1
0
1
1
1
0
1
0
1
2
1
1
1
1
1
0
0
1
0
1
0
0
2
0
1
2
1
1
0
1
2
1
0
1
0
1
1
1
1
1
1
1
2
1
1
2
1
1
2
1
1
1
2
2
1
0
1
1
0
0
1
0
1
0
2
1
1
1
1
1
1
0
0
1
0
1
1
0
2
1
1
0
2
1
1
2
1
1
0
2
0
2
0
1
2
2
2
0
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
0
0
1
2
1
1
1
0
1
0
2
1
1
2
2
1
0
1
2
1
1
2
1
1
2
0
1
2
2
1
1
1
1
1
2
2
2
1
1
0
1
2
1
2
1
2
0
1
1
2
1
2
1
1
1
1
2
2
1
1
1
1
0
2
2
2
1
2
2
0
3
2
0
0
2
0
1
1
1
1
2
1
1
0
1
1
2
1
7
1
2
2
2
1
1
2
0
1
2
1
0
0
0
1
1
1
2
1
1
0
1
2
2
1
1
2
1
3
3
0
1
1
1
0
1
1
2
1
0
1
1
0
2
1
2
1
0
1
0
2
1
0
1
1
1
2
1
2
1
2
1
1
1
3
1
1
0
0
1
1
1
1
2
2
0
0
2
2
2
1
0
1
1
1
1
1
2
1
0
1
1
2
1
1
2
1
0
2
7
0
2
1
1
2
1
1
0
2
1
1
2
0
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
0
2
0
1
0
2
1
1
2
1
0
0
1
0
1
1
0
0
1
1
0
0
1
1
0
1
1
1
1
1
1
2
1
1
1
0
2
2
2
1
2
0
2
0
0
0
1
1
1
1
1
0
0
0
1
2
1
1
1
1
1
0
2
0
1
2
0
1
2
2
2
2
1
1
1
1
1
1
1
1
1
1
0
0
2
1
2
2
0
1
1
2
0
1
3
1
1
2
2
0
1
0
2
1
0
1
0
1
2
1
1
1
1
1
1
1
2
2
1
1
1
0
1
1
1
2
0
0
1
0
0
2
3
1
0
2
1
1
1
0
2
2
1
2
0
1
1
0
1
0
1
0
1
1
1
2
1
0
1
1
1
2
1
1
0
1
1
0
1
1
1
0
1
1
0
1
1
0
3
2
1
1
0
2
2
2
1
1
1
0
1
0
2
1
1
1
1
1
1
1
1
0
2
0
1
1
1
1
4
2
1
1
1
0
2
1
0
2
1
0
1
0
2
1
1
1
0
0
1
1
2
2
2
1
1
0
1
1
1
0
0
1
1
0
0
2
1
0
0
1
0
1
1
1
1
1
1
1
0
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
2
2
0
1
0
2
1
1
1
1
1
1
2
1
1
1
2
1
3
0
1
1
1
0
1
2
1
1
1
0
2
1
1
1
1
2
1
1
1
2
1
0
1
1
0
1
2
1
1
1
1
0
0
1
2
1
2
2
1
0
2
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
0
1
2
1
2
2
1
0
1
1
0
1
2
1
1
2
0
2
1
0
1
2
1
3
1
1
1
1
2
1
1
1
2
0
0
1
1
1
1
1
2
1
2
1
1
1
2
0
2
1
1
1
2
3
1
1
1
1
1
0
0
2
2
2
1
2
2
2
0
1
2
1
1
1
2
1
0
2
0
1
2
1
2
2
2
2
1
1
2
0
0
2
0
1
0
0
0
1
0
1
1
1
1
0
1
1
1
2
1
1
1
2
1
1
2
1
1
1
1
1
2
1
2
1
2
1
2
1
1
1
2
1
1
0
1
2
2
1
1
1
0
2
1
1
0
1
1
1
1
0
2
1
2
2
1
1
1
2
1
1
1
1
1
2
2
0
1
0
1
1
2
2
1
0
1
1
2
0
1
2
1
0
0
2
0
1
1
1
1
1
0
1
1
2
2
1
1
0
0
1
1
1
1
2
0
0
3
1
2
1
1
1
0
1
1
1
1
1
0
0
1
2
2
2
1
2
2
1
0
0
2
1
2
1
1
1
0
2
2
1
1
2
2
1
2
1
0
2
1
2
1
1
0
1
0
1
1
2
1
1
1
1
1
1
1
1
2
2
1
0
0
2
1
1
1
0
1
0
1
1
2
0
2
1
1
1
1
1
1
1
1
2
1
2
4
0
1
1
1
1
2
0
2
2
0
2
1
2
2
2
1
1
1
1
1
1
0
1
1
1
1
1
1
1
0
1
1
1
1
2
1
1
1
1
1
1
2
1
0
1
1
1
2
1
1
1
1
0
2
1
1
1
2
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
2
0
1
1
1
1
0
0
0
2
2
1
1
1
1
1
1
2
0
2
0
0
2
1
1
1
1
1
1
1
0
1
1
1
1
1
0
1
2
1
1
1
2
1
2
1
1
1
1
1
1
0
0
2
0
1
2
1
1
0
1
1
2
1
0
2
1
0
1
1
2
1
1
1
0
2
1
1
0
1
1
2
0
0
2
1
1
0
1
1
1
1
1
1
1
1
0
2
0
2
2
1
1
0
2
0
1
1
0
2
1
2
1
2
1
1
1
0
1
2
2
1
1
1
1
1
1
0
1
1
2
2
2
0
1
1
1
2
1
1
1
2
1
0
1
0
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
0
1
1
2
1
1
2
2
1
1
0
0
1
1
1
1
2
1
1
2
0
2
1
1
1
2
0
0
1
1
2
1
1
1
1
0
1
0
2
1
1
1
1
2
1
1
0
1
0
1
0
1
2
0
1
1
0
0
0
2
1
1
1
1
1
1
2
2
1
2
0
1
2
1
1
1
1
1
0
2
1
2
0
2
0
1
0
2
1
1
1
0
0
0
1
1
1
1
2
2
1
0
1
1
2
2
1
1
1
1
2
1
0
1
1
1
2
1
1
1
2
2
1
1
1
1
0
2
1
1
1
1
1
1
0
2
2
1
2
1
0
0
1
1
0
0
1
2
0
1
0
2
0
0
2
1
1
1
2
1
3
0
0
1
1
0
1
1
1
1
0
0
0
1
2
2
1
1
2
1
1
1
0
1
3
0
1
0
1
1
1
1
1
1
2
0
1
1
0
2
1
1
1
1
1
1
1
2
2
0
1
2
2
0
2
1
1
2
0
1
1
1
0
1
1
3
0
1
2
1
1
2
1
1
2
0
1
1
1
1
0
1
1
1
1
1
2
1
0
1
1
2
1
1
1
2
0
1
1
2
1
0
1
1
1
2
1
1
1
1
1
3
1
1
1
1
1
1
0
0
2
1
0
1
1
1
2
0
1
0
1
2
2
1
2
0
1
2
1
2
1
1
0
1
1
1
2
2
1
1
1
0
3
0
0
2
1
1
1
0
2
1
0
2
1
0
0
2
1
1
1
0
2
1
0
0
2
2
2
0
1
1
1
0
0
1
0
2
1
2
1
2
2
1
2
2
1
0
1
1
1
2
0
1
1
1
2
1
0
0
1
1
1
1
0
1
0
2
1
1
0
1
1
1
1
1
1
1
1
0
1
1
2
1
0
1
1
2
1
0
2
0
1
0
2
2
0
0
2
1
1
0
1
1
2
1
1
1
1
0
1
0
2
1
2
1
2
1
1
1
1
2
0
1
2
2
2
0
1
1
2
0
2
1
2
0
1
1
1
1
2
1
1
0
1
1
0
1
2
2
1
1
2
1
1
3
1
1
1
1
1
0
0
1
2
1
1
1
2
0
1
1
2
1
2
1
2
1
1
1
1
2
1
1
2
1
1
0
1
2
0
2
0
2
1
1
2
2
2
0
1
1
1
1
2
1
2
1
2
1
1
1
1
1
1
2
1
1
2
1
1
0
1
1
2
1
2
1
3
1
0
1
0
2
1
1
0
1
1
1
1
1
0
1
1
1
1
2
1
0
2
1
1
1
3
2
2
1
1
1
0
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
3
2
0
1
2
1
1
0
1
1
1
0
1
2
1
1
1
1
2
2
0
2
0
2
0
2
2
1
2
1
1
0
1
2
0
1
1
0
1
0
1
2
2
2
1
2
0
1
0
0
0
1
1
2
2
1
1
1
2
1
1
1
1
1
1
1
2
1
0
0
3
1
0
1
1
1
1
0
2
2
1
0
1
1
1
1
1
2
2
1
1
1
1
0
0
1
2
1
0
0
2
2
0
2
1
1
1
0
2
0
0
1
2
1
2
1
1
1
1
2
0
1
1
2
1
0
1
2
1
2
3
1
3
1
0
2
1
0
2
1
1
1
1
1
1
1
1
2
1
0
1
0
2
1
2
1
2
1
2
2
1
0
2
0
0
1
1
1
0
0
0
2
1
1
1
1
0
1
1
2
1
1
1
1
1
2
0
1
1
1
2
1
2
2
1
0
1
0
1
2
1
1
1
1
2
1
1
2
2
2
1
1
1
1
1
1
1
1
0
0
1
2
2
2
1
1
2
1
3
1
1
1
2
2
0
1
1
2
2
1
2
2
1
1
1
0
1
1
1
1
2
1
0
1
2
1
1
1
0
1
1
0
2
0
2
2
0
1
0
1
2
1
0
1
1
2
1
1
1
2
1
1
0
1
1
1
1
1
1
1
0
1
1
2
1
1
1
1
0
0
1
1
1
1
0
3
1
1
1
0
1
1
1
1
1
1
1
1
1
1
2
1
2
0
1
0
1
1
1
0
0
1
1
1
2
0
4
2
0
1
2
0
1
1
1
1
1
2
2
1
2
1
0
1
1
1
1
0
2
1
1
1
2
1
1
1
0
2
2
1
1
1
0
1
2
1
2
1
1
1
1
2
0
1
1
1
1
2
1
1
2
1
0
1
2
1
1
1
0
1
1
2
1
1
2
0
1
2
2
1
2
0
2
1
0
1
1
1
1
2
0
1
0
0
1
1
1
1
1
0
1
0
1
1
2
0
0
1
0
1
0
2
2
0
1
1
1
1
1
1
1
1
1
1
1
0
0
1
1
2
1
1
1
1
0
2
6
2
1
0
1
1
1
1
1
2
1
1
2
0
2
1
1
1
1
0
2
1
1
0
0
1
1
1
1
2
1
0
1
1
2
2
1
1
0
1
2
1
1
0
1
2
1
1
1
3
3
2
1
2
1
0
1
1
1
1
2
2
1
1
1
2
1
1
2
2
2
1
0
1
0
1
1
2
0
2
1
0
1
1
2
1
2
2
1
1
3
0
1
1
1
2
1
1
2
2
2
2
0
2
1
0
1
1
1
0
1
2
1
0
1
1
2
1
1
2
1
1
1
1
1
0
0
1
0
1
1
1
1
1
3
1
2
2
1
1
2
1
1
1
1
1
0
1
0
2
1
1
2
2
1
0
1
0
0
1
1
1
2
1
1
1
1
0
1
3
0
2
2
1
0
0
0
0
2
0
1
1
1
2
1
1
1
1
2
2
1
2
1
1
1
1
2
2
1
1
2
1
2
1
0
0
1
0
1
2
1
1
1
1
1
1
1
1
0
0
2
0
1
1
0
1
2
0
1
1
0
0
2
1
1
1
1
1
2
3
2
1
1
1
1
1
1
1
2
1
0
0
1
1
2
1
1
1
1
0
1
1
0
0
1
1
2
1
1
2
1
2
2
1
1
0
2
1
0
2
1
1
2
2
2
2
0
0
1
1
1
1
1
1
2
0
1
1
0
2
2
1
1
2
1
1
2
1
1
2
1
0
0
2
2
1
2
1
1
2
1
1
1
1
1
0
1
2
2
1
1
2
0
2
0
1
2
2
0
1
1
2
1
0
2
2
1
2
2
1
1
1
1
2
0
1
1
1
1
1
1
1
0
1
1
2
2
2
1
1
2
2
1
2
0
1
1
1
1
1
1
1
1
1
0
0
1
1
1
0
1
1
0
1
1
1
0
2
1
0
2
1
1
1
1
2
1
1
1
2
1
2
1
1
0
1
0
2
1
2
1
1
0
0
0
1
1
1
1
0
1
1
2
2
0
0
1
0
2
1
0
0
1
1
1
1
1
0
1
1
1
1
1
1
1
2
1
1
1
0
1
0
2
0
1
0
1
0
2
0
1
2
2
2
1
1
2
1
1
1
1
1
0
2
0
0
1
2
2
0
1
1
0
0
1
1
0
1
1
1
2
1
1
1
1
1
1
0
1
1
1
2
1
1
2
1
2
0
1
1
0
1
1
1
1
1
2
0
1
2
2
0
0
1
0
1
1
0
2
3
2
1
1
1
0
1
1
0
1
2
1
1
0
1
1
1
1
1
1
0
2
2
1
0
2
0
1
1
1
1
1
0
0
2
0
1
1
1
2
2
2
2
0
1
2
0
1
1
1
1
1
1
1
1
1
1
0
2
1
2
1
2
2
2
1
1
2
1
1
1
1
1
1
0
2
1
0
0
1
2
1
1
1
1
1
2
0
1
2
1
1
1
2
1
2
1
1
1
1
1
2
1
1
0
1
1
1
3
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
0
1
1
1
1
0
1
2
2
1
0
1
2
1
1
1
0
1
0
1
2
1
2
1
0
2
2
1
1
0
1
2
0
1
1
1
0
1
2
1
1
1
2
2
1
1
1
2
2
2
0
1
2
1
2
1
1
1
1
2
2
2
2
1
1
2
0
1
1
0
1
1
1
2
1
0
1
1
1
2
2
0
1
1
2
1
1
0
2
1
2
1
1
1
0
2
2
1
1
1
2
1
1
0
1
2
0
1
2
1
3
1
1
2
1
1
0
2
1
2
2
1
1
0
0
1
2
0
0
0
0
1
0
2
1
0
1
2
1
1
1
0
2
0
2
1
1
2
0
1
0
1
1
2
1
1
1
2
1
1
1
0
1
1
2
1
1
0
1
1
1
1
1
3
2
1
2
0
1
1
2
1
2
0
1
1
1
1
1
1
1
2
1
1
0
0
2
1
1
1
1
1
1
2
1
0
1
2
1
0
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
2
1
0
1
1
1
2
0
1
1
1
0
2
1
0
1
1
0
0
2
1
2
1
0
1
2
1
1
1
1
1
2
0
1
1
1
1
1
2
1
1
0
0
0
1
0
1
1
1
1
1
1
1
2
1
1
2
0
1
2
0
1
0
1
1
1
2
1
1
0
0
2
1
0
1
1
1
1
0
1
1
2
0
1
2
2
0
1
2
0
1
1
0
1
1
1
1
0
1
1
1
2
1
1
2
1
0
0
1
0
1
1
1
1
0
1
2
1
1
2
2
1
1
1
1
1
1
1
1
0
1
1
1
1
1
0
1
2
1
0
1
1
1
1
1
1
2
0
2
2
0
0
1
1
2
0
2
1
1
1
0
2
1
0
2
2
1
2
1
1
2
1
0
1
1
2
0
1
2
0
1
1
1
0
2
0
2
1
1
1
0
2
2
1
1
0
1
1
0
1
1
1
1
1
1
2
1
1
2
1
2
0
1
1
1
1
1
1
1
1
0
1
2
1
0
2
1
2
1
1
1
1
1
2
2
0
1
2
2
1
1
1
3
1
1
2
1
1
1
1
0
1
0
1
0
0
1
1
1
0
1
0
1
0
2
2
0
1
1
1
1
0
1
1
1
1
0
0
1
1
1
1
0
1
1
1
1
2
0
1
2
1
1
1
2
1
1
1
1
2
0
2
2
1
1
1
1
2
1
1
1
2
0
0
1
0
2
2
2
1
2
1
2
1
1
2
2
2
1
1
1
1
1
1
0
2
1
2
1
1
1
1
1
2
2
2
2
2
1
2
1
2
0
0
0
1
2
0
1
1
1
2
1
1
2
0
1
1
1
2
0
1
0
2
1
1
0
2
0
1
2
2
1
2
1
1
2
1
1
1
1
1
0
1
1
1
2
2
1
1
0
0
0
0
1
2
2
1
0
1
1
2
1
1
2
1
2
1
1
2
1
0
2
2
2
1
1
0
1
2
1
1
1
0
1
1
2
0
1
1
2
2
2
1
1
1
2
2
1
0
1
1
2
1
0
1
0
1
1
1
2
0
1
1
1
1
1
2
2
1
1
1
2
1
2
1
0
2
1
1
1
0
2
1
1
2
0
1
2
1
1
1
2
1
1
0
2
2
3
1
1
1
1
2
1
2
1
2
0
1
1
1
2
2
2
1
1
1
0
0
0
1
1
1
1
1
1
0
0
1
1
1
1
2
0
1
2
1
1
0
2
1
1
2
1
2
1
1
1
1
1
2
0
2
1
0
0
1
1
2
2
4
0
1
1
0
2
2
1
1
0
2
1
1
2
0
2
1
2
1
0
1
1
1
1
0
1
1
1
1
1
1
0
0
1
2
1
2
1
1
1
1
0
0
1
1
1
1
1
1
0
1
0
0
1
1
2
1
1
2
1
1
1
0
2
2
1
0
0
1
1
0
1
0
0
2
1
1
1
0
0
0
2
0
1
1
2
0
1
1
2
1
1
0
0
0
2
0
2
2
1
1
1
1
1
0
0
1
1
1
2
0
1
0
1
1
2
1
1
0
1
1
0
0
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
2
1
0
1
0
1
1
1
2
1
1
1
0
2
0
0
2
2
1
0
1
2
0
1
2
1
1
1
1
2
1
0
2
1
1
1
0
2
1
2
1
1
1
2
2
1
1
0
1
1
1
2
1
2
1
2
1
1
1
1
0
1
1
1
1
0
1
2
1
1
1
0
1
2
2
1
1
1
2
1
2
1
1
1
2
3
1
1
0
1
0
1
2
1
0
1
2
1
1
1
1
1
2
1
0
1
1
1
2
1
2
1
2
2
1
2
1
1
1
2
1
2
2
2
1
1
1
2
1
1
1
1
1
0
1
1
2
1
1
1
0
1
1
1
1
1
2
0
2
2
2
1
1
1
0
1
1
1
1
1
1
0
1
1
1
1
1
2
1
1
1
2
1
2
2
0
2
1
1
1
2
0
0
0
1
1
1
1
1
1
1
2
1
1
2
1
2
2
1
0
0
1
2
0
6
1
2
1
0
1
2
1
1
1
1
1
0
2
1
2
1
1
2
2
0
2
1
1
2
1
2
1
1
0
2
0
0
1
2
0
0
2
1
0
1
1
0
1
2
0
1
2
1
1
2
1
1
1
1
0
1
1
1
0
1
2
0
1
2
1
1
0
2
2
1
1
1
1
2
1
1
2
1
1
2
1
1
1
0
1
1
3
2
1
2
1
1
2
1
1
1
2
1
1
3
1
2
2
1
2
1
1
1
1
1
1
2
1
2
1
1
2
1
1
2
0
0
1
1
1
1
3
0
1
0
2
1
0
1
1
0
0
1
1
1
1
1
1
1
0
1
2
2
1
2
0
1
1
0
1
1
1
1
1
2
1
1
2
1
1
1
2
0
1
1
2
2
1
1
1
2
2
1
1
1
0
2
1
1
2
0
1
0
1
2
1
3
1
1
1
1
2
0
1
1
0
1
1
1
1
0
2
1
1
1
1
0
2
2
2
0
1
1
2
1
1
0
0
1
1
1
2
1
1
0
1
0
1
2
2
2
1
2
2
0
1
1
2
1
1
1
1
0
0
1
1
1
2
1
1
1
2
1
1
4
0
1
1
2
2
1
2
1
1
0
0
2
1
1
0
0
1
1
1
0
2
1
0
1
2
0
0
1
1
1
1
1
1
1
2
0
1
1
1
2
2
1
1
1
1
2
2
0
2
1
2
1
0
1
1
0
1
2
1
2
2
0
1
2
1
1
1
1
0
3
1
2
0
2
1
1
1
1
1
2
1
2
1
2
1
0
2
1
0
1
1
1
1
1
1
1
1
0
0
1
1
1
1
0
0
1
1
0
1
1
1
0
2
1
1
1
1
1
0
2
1
2
2
1
2
1
1
2
3
1
1
1
2
5
1
1
1
1
1
1
1
0
1
2
0
1
1
1
1
2
2
3
1
1
1
1
0
2
1
1
0
0
1
2
0
2
2
1
0
1
1
1
1
1
1
0
1
1
0
2
1
2
1
0
1
1
1
0
2
1
1
1
3
1
2
0
1
1
0
0
1
0
1
1
2
1
1
1
1
2
0
1
1
1
0
1
2
0
2
1
1
1
2
1
1
1
1
1
2
1
1
0
1
2
0
1
1
0
2
2
1
2
0
0
1
1
1
1
2
0
1
1
1
1
1
2
2
1
1
0
1
2
1
2
1
1
2
0
1
1
1
2
0
1
1
2
1
1
2
1
1
1
1
2
2
2
4
0
1
2
1
1
1
2
2
1
1
0
1
1
0
1
1
0
2
1
1
1
1
1
1
0
1
1
1
1
1
0
0
1
1
1
1
1
1
1
1
1
1
1
0
2
2
1
1
0
2
1
1
1
2
1
1
1
0
1
0
2
0
1
1
1
2
2
2
0
1
1
1
1
1
2
1
4
0
1
0
1
0
2
1
1
1
2
1
1
1
1
1
2
0
1
1
1
0
1
1
1
1
2
1
0
1
1
1
1
0
1
0
1
1
1
2
2
2
1
1
2
1
0
2
0
2
0
0
2
1
1
1
1
2
1
0
1
1
0
2
1
0
1
1
1
1
1
2
1
1
1
1
1
0
1
2
1
1
1
1
2
2
1
2
1
1
1
1
1
0
1
0
1
1
1
0
2
0
1
1
1
2
1
1
2
1
1
0
1
2
1
1
1
1
1
1
1
2
2
1
0
2
1
1
1
1
1
2
2
1
1
2
1
2
2
1
1
2
1
1
0
1
1
1
1
1
1
0
1
1
0
1
1
1
2
0
2
1
1
2
2
1
2
0
1
1
1
0
1
0
1
2
1
0
1
1
0
0
1
2
1
1
1
1
1
0
1
1
1
5
1
0
1
1
1
1
2
1
1
2
1
2
0
1
0
2
0
1
1
1
3
1
0
2
1
1
1
3
1
1
2
0
2
1
3
0
1
2
1
1
2
1
2
1
1
1
0
1
1
0
1
1
1
0
0
1
2
1
1
0
1
2
1
1
1
0
0
1
1
1
2
2
0
1
1
3
1
2
0
1
2
1
2
1
1
2
0
2
1
0
1
1
0
0
0
1
1
1
2
1
1
1
0
0
1
2
1
1
2
2
1
1
1
1
1
1
1
1
0
1
0
1
1
2
0
1
0
1
1
0
1
1
1
1
1
2
0
1
0
2
1
2
0
2
1
1
1
1
1
2
0
1
2
1
1
1
2
3
0
1
0
1
2
1
2
5
2
0
1
1
1
1
1
1
1
1
1
1
1
1
1
0
2
2
1
0
1
1
1
1
1
0
0
1
1
1
0
2
1
1
1
1
1
2
1
1
2
2
1
2
2
1
2
1
2
1
1
1
0
2
2
0
2
2
1
1
2
2
1
1
1
1
1
2
1
1
2
0
2
0
0
2
1
2
0
1
1
1
1
1
2
1
1
1
1
0
1
1
2
0
1
1
0
1
0
0
0
1
1
2
2
0
1
1
1
1
2
2
0
0
1
0
1
1
1
2
3
1
1
1
0
1
1
2
2
1
1
1
1
0
1
0
1
2
1
2
1
1
1
2
1
2
1
1
0
1
1
0
0
1
2
1
1
1
0
1
1
1
1
1
0
2
1
2
2
1
1
0
0
0
1
0
1
3
2
1
1
1
1
2
1
2
1
1
0
1
1
2
1
2
2
1
2
1
0
0
1
1
2
0
0
2
2
1
2
1
1
0
0
1
2
1
2
0
1
0
2
0
0
2
1
1
1
1
2
1
0
1
1
1
1
1
3
2
0
1
1
0
2
0
1
1
1
1
2
2
1
0
2
2
2
1
1
1
2
1
1
1
1
1
0
2
1
0
2
2
0
1
1
1
1
1
1
0
1
0
1
1
1
1
1
1
1
0
2
1
1
1
2
0
0
2
0
1
1
1
2
2
1
1
2
0
2
0
0
1
1
1
2
2
1
1
0
2
2
1
1
0
1
1
1
1
2
2
1
1
1
1
0
2
0
1
1
2
1
1
2
0
2
2
1
2
0
0
2
2
2
1
1
2
1
1
0
0
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
0
0
2
2
0
1
1
0
1
1
2
1
1
2
1
0
1
1
1
0
1
1
0
1
1
1
1
1
0
0
0
2
2
1
0
2
2
2
1
0
1
1
1
0
2
2
2
1
0
0
1
0
1
0
0
2
2
1
1
1
1
2
1
1
1
1
1
2
1
0
1
0
1
0
1
1
2
1
0
0
1
2
1
2
2
1
2
1
1
1
0
1
1
1
2
1
1
0
2
1
1
2
1
1
1
1
1
2
0
1
2
1
0
3
1
1
1
0
0
1
1
1
1
1
1
2
1
1
2
2
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
2
2
2
2
1
1
1
2
1
2
1
2
1
1
0
1
2
1
1
1
2
1
1
1
1
0
0
2
0
1
1
0
1
1
1
2
0
1
2
0
1
1
2
3
1
1
1
1
1
1
1
1
0
1
1
0
1
2
1
0
1
1
1
1
0
1
1
0
1
1
0
1
1
1
2
1
1
1
1
1
0
2
2
2
1
1
3
1
1
1
1
1
1
2
1
0
1
2
1
1
0
1
1
0
1
1
0
2
0
2
1
2
1
1
1
0
1
2
2
1
0
1
1
0
1
1
2
0
1
1
1
2
2
1
2
1
6
1
1
2
2
2
0
1
1
2
0
1
0
2
0
0
0
2
1
0
1
2
1
1
1
0
1
0
0
1
1
0
1
2
1
1
0
2
1
1
1
1
1
2
1
1
2
1
2
1
1
0
1
0
1
0
1
2
1
1
1
0
1
1
2
0
1
0
1
0
2
1
1
1
2
1
2
1
2
1
1
0
1
1
1
1
1
2
1
1
1
2
2
1
2
1
2
0
1
1
0
2
1
0
1
2
2
2
1
2
0
0
0
0
2
2
2
1
1
2
0
1
1
0
1
1
1
2
2
0
0
2
1
1
1
0
2
1
1
2
0
1
0
1
2
1
1
1
0
1
1
2
1
0
2
0
0
0
1
1
0
0
1
0
2
1
2
1
1
2
1
1
1
0
2
0
0
2
1
1
2
2
1
0
1
1
1
1
1
1
1
0
2
0
1
1
2
0
2
2
0
2
0
1
1
1
1
4
1
1
1
1
2
2
0
2
2
1
1
2
1
1
1
2
1
1
1
1
0
1
1
1
1
2
1
2
3
1
0
1
2
1
2
1
0
2
0
1
1
1
2
1
1
1
1
0
1
1
1
0
1
1
1
1
1
1
1
2
1
1
0
2
2
0
0
1
2
1
1
0
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
0
2
1
1
0
0
1
1
0
1
0
1
1
1
2
0
1
2
1
1
1
1
1
1
1
0
1
2
1
0
0
1
0
1
1
1
0
0
2
2
0
1
2
1
1
1
1
1
2
0
1
1
0
2
1
2
2
1
1
0
1
2
1
1
1
2
0
1
0
2
0
1
2
0
1
1
0
0
1
2
2
1
1
2
2
0
2
1
1
0
1
2
1
1
2
1
1
2
0
1
0
1
1
1
1
1
1
2
2
2
1
2
1
0
1
2
1
1
1
1
2
1
1
0
1
1
0
0
0
1
2
1
0
1
2
1
2
2
1
0
1
1
0
1
2
1
1
1
0
1
1
2
1
1
1
0
1
1
2
1
0
2
0
1
2
1
1
1
0
2
1
2
2
1
2
1
1
1
1
3
0
2
1
0
1
1
0
0
1
0
1
1
1
2
0
0
0
0
1
1
2
1
1
0
1
1
1
1
1
2
2
2
1
2
0
1
0
0
1
1
2
1
1
2
1
2
1
2
1
1
2
2
2
0
2
2
0
0
1
1
0
1
0
1
1
1
1
1
0
2
0
2
0
2
1
1
1
1
1
2
2
1
1
1
1
1
1
0
0
1
1
1
2
4
2
1
2
2
1
1
0
1
1
2
1
2
1
1
1
2
1
1
1
2
1
1
1
2
0
1
1
1
1
2
2
1
0
1
0
1
0
1
1
1
1
1
0
1
1
1
1
1
1
1
1
0
1
0
1
2
1
1
0
2
1
2
1
2
1
1
1
2
1
1
1
1
2
1
0
1
1
1
0
0
1
1
0
1
1
2
2
1
0
0
1
1
1
2
1
2
1
1
2
1
1
2
2
1
0
2
1
2
1
1
0
1
2
0
1
1
1
1
1
1
0
2
0
1
0
1
1
1
0
1
1
1
2
1
1
1
3
1
0
0
1
1
1
1
2
2
1
1
1
1
2
0
2
1
1
1
1
0
1
2
1
1
0
1
1
2
1
2
1
1
1
1
1
1
1
2
1
0
2
1
0
0
1
1
1
1
2
1
0
0
0
1
2
0
1
1
1
2
1
1
2
0
0
2
2
1
1
2
1
2
0
1
0
5
1
2
0
1
0
1
0
1
1
0
2
1
2
1
1
2
1
1
2
2
2
1
1
1
0
1
0
1
1
0
2
1
1
0
1
1
1
2
2
1
1
2
2
0
1
2
2
1
2
1
2
2
2
1
1
0
0
0
2
2
0
2
1
1
0
1
0
2
0
1
1
1
1
2
1
1
1
0
1
2
2
1
1
1
0
1
0
1
2
1
2
2
1
1
1
1
2
1
1
1
0
0
0
1
7
0
0
0
1
1
0
1
1
2
1
0
0
1
1
2
1
2
0
2
2
2
1
0
2
2
1
1
1
0
2
1
3
0
1
1
1
1
1
1
1
1
2
1
2
1
1
0
1
1
1
1
1
1
2
0
1
0
1
0
1
1
1
2
1
1
1
1
1
1
2
2
1
2
1
2
0
2
2
1
0
0
1
1
2
1
1
1
1
1
2
0
2
1
1
1
0
2
2
1
1
1
2
0
2
0
1
1
0
1
1
1
2
2
1
0
1
1
1
1
0
1
1
1
1
2
1
1
2
1
0
0
1
1
0
1
1
1
1
1
2
2
0
1
1
1
2
1
1
1
0
2
1
1
1
0
1
2
1
1
2
1
3
0
1
1
2
1
1
1
1
1
1
0
2
1
2
1
1
2
0
2
1
1
1
1
1
0
2
1
1
1
2
1
1
1
1
0
1
2
0
1
1
1
2
1
2
1
1
0
1
1
1
0
1
2
1
1
1
0
0
3
1
1
0
1
1
1
0
1
1
1
2
1
0
1
1
1
1
1
1
2
1
2
2
2
0
1
1
2
1
1
1
1
1
1
1
2
2
0
1
1
0
1
0
1
1
1
1
1
1
1
0
2
1
2
1
0
1
1
1
1
2
2
1
1
2
1
1
0
1
2
0
1
1
0
0
1
0
1
1
2
1
1
3
1
1
0
1
0
0
1
0
2
1
1
2
1
2
1
0
2
1
2
1
1
0
1
1
1
2
2
1
2
1
0
1
2
2
1
2
0
2
3
2
1
1
0
1
1
2
0
0
2
2
2
0
1
1
1
1
1
1
1
1
1
2
0
2
1
2
0
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
0
0
2
0
0
1
2
1
1
1
1
2
1
1
1
0
2
3
0
0
1
0
2
2
0
2
1
1
2
2
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
2
1
2
1
2
1
1
2
1
1
1
1
1
1
1
1
1
0
1
2
2
1
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
0
0
1
2
1
1
1
1
2
0
2
1
1
1
2
0
1
1
1
1
1
1
0
0
1
1
1
3
1
1
1
1
1
2
2
2
0
1
1
0
2
1
0
1
1
1
1
2
0
2
1
1
2
0
2
0
1
2
2
1
0
2
0
2
2
1
1
1
1
2
2
1
1
2
1
1
2
1
1
1
0
1
1
0
2
1
0
1
0
1
1
1
0
0
0
1
1
2
0
1
1
2
1
1
1
2
2
2
0
1
0
0
1
0
0
1
1
1
1
1
0
2
1
2
1
1
0
2
1
1
2
1
2
1
1
1
1
2
2
0
1
1
1
1
2
1
1
1
1
0
2
1
1
2
1
1
1
1
1
2
1
0
1
1
2
2
1
0
1
1
2
1
1
2
1
0
1
1
2
2
1
2
4
0
0
1
1
1
1
2
1
2
1
1
1
1
1
1
0
1
1
1
1
1
1
1
0
0
2
2
1
2
0
0
0
2
1
1
2
1
1
0
0
2
1
1
1
1
0
1
2
2
2
0
1
1
0
1
2
0
1
1
1
2
1
1
1
2
1
2
0
1
1
1
1
1
1
1
2
0
2
0
2
1
2
1
0
1
1
1
1
0
1
2
2
1
0
1
1
1
1
2
2
1
1
2
1
2
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
0
2
2
1
1
1
0
1
0
1
1
1
2
1
2
0
0
1
1
1
2
1
0
1
2
2
2
1
2
0
1
1
2
0
1
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
0
0
2
0
1
0
1
2
1
0
2
1
2
0
1
2
1
0
1
1
1
0
1
2
1
0
1
2
1
1
2
1
2
0
1
1
1
2
2
1
1
2
1
0
1
0
1
2
0
1
1
1
1
1
1
0
0
1
2
0
1
0
1
1
1
1
1
2
0
1
1
2
2
0
1
2
1
1
0
1
2
2
0
0
1
1
1
1
2
2
2
1
0
0
0
2
4
1
1
1
1
0
0
2
1
1
0
1
1
1
1
1
1
1
1
1
0
0
2
1
2
2
1
2
1
1
0
1
1
1
2
1
0
1
2
0
2
0
1
1
0
1
2
2
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
2
2
0
1
1
1
2
1
1
1
1
2
1
2
1
2
2
1
1
1
1
1
1
1
1
1
0
1
1
0
2
2
0
1
1
1
1
0
2
2
1
2
1
0
0
2
2
1
1
1
2
0
1
2
1
1
1
1
1
1
2
1
2
2
0
1
0
2
2
0
2
1
1
0
1
0
0
1
1
1
1
1
2
2
1
0
1
1
1
0
1
1
2
1
1
2
1
1
1
2
1
1
1
1
0
1
1
2
1
1
1
1
0
0
1
2
0
2
1
1
1
1
5
1
0
1
1
2
2
1
2
0
0
1
1
2
2
1
2
2
1
1
2
1
0
0
1
0
2
2
1
0
1
1
1
2
1
1
1
2
1
1
1
1
1
2
1
0
1
1
1
1
1
1
1
2
1
0
2
2
2
2
1
0
1
0
2
1
1
1
1
1
1
1
2
2
1
1
2
2
1
1
1
1
0
1
1
1
1
1
0
1
1
1
1
0
1
1
1
1
2
1
1
0
1
1
1
1
1
1
1
2
0
0
2
1
1
1
1
1
1
0
1
0
1
1
2
2
2
1
2
1
0
1
1
1
2
1
1
0
0
1
2
1
1
2
0
1
1
1
1
2
2
1
1
1
1
0
1
0
2
2
0
1
1
0
1
2
1
1
1
1
2
1
2
1
1
0
2
2
1
1
1
0
1
1
2
0
0
2
1
1
1
1
1
0
0
1
4
0
1
1
1
1
1
2
2
1
0
1
1
2
1
1
1
1
2
1
2
1
1
1
0
2
1
0
1
1
1
2
1
1
2
1
0
1
1
1
1
1
0
0
1
1
1
1
1
1
1
1
2
1
2
1
0
0
1
2
2
2
0
1
1
1
0
1
1
1
1
1
1
1
0
0
0
1
2
1
2
1
1
0
1
1
0
1
1
1
1
2
0
1
1
2
1
2
1
0
0
1
1
2
0
1
2
1
2
1
1
0
2
1
1
1
1
1
1
2
1
2
0
1
1
1
1
0
2
1
1
1
1
0
0
0
0
0
1
1
1
1
1
2
1
0
0
0
0
1
2
0
2
2
1
0
0
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
2
2
2
1
1
1
1
2
2
2
2
1
0
0
1
1
2
1
1
0
0
0
2
1
0
1
2
1
1
1
2
1
1
1
2
1
2
1
0
0
2
0
1
1
2
2
1
1
1
1
2
2
1
0
1
1
1
1
0
1
1
2
2
0
1
0
1
1
1
2
1
2
2
2
1
1
1
2
2
3
1
1
1
0
2
1
1
2
1
1
2
1
1
1
2
1
1
1
0
1
1
0
1
1
1
1
1
1
1
2
2
1
2
1
1
0
2
2
2
1
1
0
2
2
2
1
1
0
1
0
2
2
2
1
0
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
2
2
0
1
1
2
0
2
0
1
2
1
1
1
1
2
2
1
2
1
2
1
1
2
1
1
1
2
1
1
1
2
0
1
0
2
1
1
1
0
2
2
1
1
0
1
1
2
2
1
1
1
2
2
2
2
0
1
0
1
0
1
1
0
1
1
1
2
2
2
2
0
2
2
1
2
0
1
2
2
0
2
2
1
1
1
1
1
2
2
0
3
2
1
1
2
1
1
1
1
2
2
1
0
1
1
1
1
2
1
1
1
0
0
2
2
1
1
1
1
1
2
2
1
1
1
0
2
1
2
1
3
1
1
0
1
2
1
0
0
1
1
1
1
1
0
2
2
3
1
1
2
1
1
1
1
3
1
1
0
1
1
1
2
1
1
1
2
2
1
0
0
2
1
1
1
2
1
1
0
2
1
2
1
0
1
1
1
2
1
1
0
1
1
1
1
2
1
1
1
1
0
1
1
2
2
0
2
1
0
1
1
1
1
1
2
1
0
1
1
1
2
2
2
1
2
0
2
0
2
1
1
1
1
2
1
2
2
0
0
1
0
0
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
2
0
1
0
1
1
1
1
1
0
1
2
1
0
1
1
2
1
0
1
1
0
1
1
1
1
1
0
2
2
1
1
1
2
1
1
0
1
1
2
1
1
1
0
0
1
1
0
1
0
1
2
0
0
1
2
1
1
1
2
1
1
2
2
3
1
0
1
2
1
1
1
1
0
1
1
1
1
0
1
1
2
1
2
0
1
0
1
1
1
2
0
1
1
2
1
1
0
0
1
2
1
1
2
1
1
1
0
1
1
0
1
2
1
1
1
1
2
2
0
3
0
2
0
1
1
1
2
0
1
1
1
1
1
1
1
2
1
1
1
1
0
0
1
1
1
1
1
1
1
1
2
1
1
2
2
1
1
2
1
1
2
1
3
1
0
0
2
0
2
0
0
2
0
0
1
2
0
2
1
1
2
2
2
1
1
1
1
1
1
2
1
0
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
2
1
1
2
2
1
1
1
1
1
2
2
2
2
1
1
1
1
1
0
1
0
1
0
1
1
1
0
1
1
1
2
2
0
0
1
1
2
0
2
2
1
1
0
1
1
2
1
1
2
1
2
1
0
1
1
1
1
0
1
1
2
2
2
2
1
2
1
1
0
0
1
1
1
1
1
0
1
1
1
1
0
1
0
1
0
0
1
1
2
2
1
1
2
1
2
1
1
0
1
2
2
2
1
1
1
2
1
2
2
2
0
1
0
1
1
2
1
1
1
1
1
1
2
0
0
1
1
2
1
0
1
1
1
1
0
2
0
1
2
0
0
0
2
1
1
2
1
1
0
0
0
1
0
1
2
2
0
1
1
1
1
0
1
0
2
0
1
1
1
2
0
1
1
2
1
1
1
0
1
1
2
1
2
0
1
1
1
1
1
1
0
1
1
1
1
1
2
1
2
1
2
1
1
2
1
2
2
1
2
0
2
0
0
1
1
0
1
1
2
1
0
0
1
1
0
1
1
1
0
2
1
2
2
1
2
1
2
2
1
1
1
1
2
0
2
1
2
1
1
2
1
2
2
2
0
1
1
2
1
1
1
1
1
1
2
1
0
1
1
1
1
2
0
0
1
1
1
1
0
1
0
4
1
2
1
2
2
1
0
2
1
1
0
1
1
1
2
1
2
1
1
0
2
1
2
0
1
1
0
1
1
1
1
1
1
2
1
0
1
1
2
1
0
1
0
1
1
2
1
2
1
2
0
2
2
1
2
2
1
0
1
1
0
2
1
1
2
1
1
0
2
1
1
1
1
1
1
2
1
0
2
2
1
0
0
2
1
2
2
2
1
1
1
2
1
1
1
1
2
2
2
2
1
1
3
2
2
0
1
1
1
1
1
4
0
1
1
2
0
1
1
2
1
0
1
2
1
2
1
1
2
1
1
1
1
1
1
2
1
1
0
1
2
2
2
2
2
0
0
1
1
2
0
1
2
2
1
1
1
2
0
1
2
2
1
1
2
0
1
1
1
2
1
1
1
2
0
1
2
1
2
2
1
1
1
1
1
2
1
1
1
0
1
2
2
1
0
1
0
1
1
2
0
1
2
0
1
2
2
2
1
1
1
1
0
1
2
2
1
2
1
2
1
0
1
1
2
4
1
1
2
2
1
0
1
1
1
2
2
1
1
1
1
1
0
2
2
1
1
1
2
1
1
1
1
2
1
2
2
1
0
1
1
2
1
1
2
0
1
1
1
1
1
0
1
1
0
1
1
1
2
1
1
0
1
0
1
2
1
0
1
0
2
1
2
1
1
0
0
1
1
0
2
1
2
2
1
1
1
1
1
0
2
1
1
1
1
0
1
1
1
1
2
1
1
1
1
1
1
0
2
1
1
1
1
0
2
1
0
1
1
2
0
0
1
1
2
1
1
0
1
1
0
2
1
2
0
1
1
2
2
2
0
2
0
2
2
1
3
2
2
2
2
1
2
0
1
1
1
1
1
2
2
1
1
0
1
1
2
2
0
1
1
0
2
1
0
1
1
1
0
2
0
1
1
1
0
1
1
1
2
1
2
1
2
1
2
1
2
0
1
1
2
2
1
1
1
0
0
1
0
1
1
1
1
1
2
2
1
1
2
0
1
1
1
1
1
2
1
0
1
1
1
2
1
2
2
1
0
1
0
1
0
1
1
2
0
0
1
0
2
1
0
1
2
0
1
1
1
1
0
1
1
1
1
1
1
1
1
0
2
1
2
1
0
2
2
0
1
2
1
2
1
1
1
1
1
1
2
1
2
1
0
0
1
2
1
2
1
1
0
0
1
2
1
1
1
1
1
0
1
1
1
2
0
2
1
0
2
2
1
1
1
1
1
0
1
1
1
1
2
0
0
0
0
1
0
0
1
1
1
2
2
1
2
2
1
2
0
1
1
2
1
0
2
1
0
2
1
1
0
2
1
2
1
0
1
2
2
0
1
2
1
1
1
0
2
0
0
2
1
1
0
2
1
2
1
2
1
1
2
1
1
1
1
1
0
0
0
1
1
0
0
2
1
1
2
1
2
0
0
1
0
1
1
1
1
1
0
1
0
0
1
1
1
2
0
1
1
1
1
1
2
1
1
1
1
1
2
0
2
1
1
0
2
1
1
2
1
2
2
1
1
2
1
1
1
1
2
1
1
1
1
1
1
2
0
1
1
2
2
2
1
2
1
1
1
1
1
2
0
0
1
1
1
1
1
2
1
0
1
1
1
1
1
1
2
1
1
1
0
0
1
2
1
2
2
2
1
2
1
1
1
1
0
1
1
0
2
1
1
1
0
0
1
1
1
2
1
2
1
1
1
1
1
2
2
1
1
0
1
1
1
1
0
4
1
2
1
1
1
0
1
1
1
1
2
1
1
1
1
2
1
1
2
1
0
0
2
1
2
2
1
0
1
1
0
1
0
1
2
2
1
2
1
1
2
1
1
1
2
0
0
1
0
1
2
1
1
1
0
2
0
1
1
1
1
1
1
0
1
0
1
1
2
1
2
2
1
1
1
2
0
2
2
0
1
1
0
2
1
1
2
0
0
1
1
1
0
2
1
1
1
1
1
1
1
1
1
1
1
3
1
1
2
2
1
2
1
1
1
1
1
1
1
0
1
1
1
1
2
1
5
1
1
2
1
0
1
1
3
2
0
2
1
0
2
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
1
0
2
1
1
2
0
1
1
2
1
2
1
2
4
2
2
1
1
1
1
2
1
2
1
2
2
2
0
1
0
1
0
1
3
0
1
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
0
1
2
1
1
1
0
1
1
2
1
1
1
1
1
2
0
2
1
1
1
1
2
1
0
2
0
1
2
2
0
2
1
0
2
1
1
1
1
2
1
1
2
0
2
2
0
1
2
0
1
1
1
2
2
0
1
1
1
1
2
0
2
1
0
1
3
1
0
1
3
0
1
1
1
2
1
1
1
1
1
2
0
1
1
1
1
2
0
2
1
2
1
0
2
1
1
1
1
1
1
2
1
1
2
2
1
2
2
1
2
2
0
1
1
2
1
0
1
1
0
2
1
1
0
1
1
2
0
1
2
0
1
2
2
1
2
2
1
1
1
0
1
1
1
1
1
1
1
1
1
0
1
0
2
1
0
1
2
1
1
1
1
0
1
1
1
1
1
1
1
0
1
1
1
1
0
1
2
0
2
0
0
1
1
1
2
1
1
1
2
2
1
1
1
1
0
2
0
2
1
0
1
1
1
1
1
2
1
1
1
2
1
2
2
0
1
1
2
1
0
1
1
1
1
1
1
1
1
1
1
0
2
1
2
1
2
1
1
1
1
0
1
2
0
1
1
1
1
1
5
2
1
1
2
2
2
0
1
1
2
0
1
1
1
1
1
2
2
1
1
1
1
1
2
1
4
2
1
1
1
1
2
1
0
2
1
1
0
1
0
1
2
1
0
2
2
0
1
1
1
2
1
1
2
1
2
1
1
1
2
2
0
2
0
1
2
2
2
1
1
2
1
1
0
2
2
1
0
0
2
2
1
0
1
2
1
1
1
0
2
0
1
1
1
1
2
1
1
1
0
2
2
1
2
0
1
1
1
1
2
1
0
2
1
1
1
2
0
1
2
1
1
0
2
1
1
0
1
0
1
1
0
1
2
0
2
1
1
1
2
1
0
0
1
2
1
2
2
1
0
0
2
1
3
0
1
0
2
1
1
0
1
0
0
1
1
1
2
2
0
1
2
2
1
1
1
0
1
0
1
1
1
0
1
1
0
1
2
1
1
1
1
1
2
1
3
1
2
1
1
1
0
1
1
2
2
1
0
2
2
2
1
1
0
1
2
2
1
1
0
1
0
1
1
4
0
2
1
1
2
1
0
2
1
1
0
3
2
2
0
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
0
2
1
0
0
1
0
1
1
1
1
1
2
1
2
1
2
0
0
1
1
0
1
0
2
1
1
1
0
2
1
2
2
1
2
0
2
1
1
1
0
0
1
1
0
2
1
2
0
2
1
2
2
1
1
1
0
0
1
1
2
0
1
0
1
1
2
1
2
2
1
2
1
2
1
2
1
1
1
0
2
3
2
0
1
1
1
1
2
2
1
2
0
2
2
1
0
1
1
1
1
1
1
0
1
1
1
1
0
0
2
1
0
2
1
1
2
1
1
1
1
2
1
1
1
0
1
1
1
0
1
1
1
0
1
1
1
1
1
1
1
1
2
1
1
0
1
1
1
0
0
1
0
1
2
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
0
1
1
1
1
1
5
1
1
2
2
0
2
2
1
1
1
1
1
1
1
1
2
1
1
2
2
1
1
1
2
1
1
0
0
1
0
2
0
1
2
1
5
1
1
1
1
0
0
1
1
0
1
2
1
1
1
1
1
1
1
0
2
0
1
1
1
2
1
1
1
2
0
0
1
1
0
1
1
0
1
1
1
0
1
1
2
0
2
2
1
1
2
2
1
1
1
0
1
1
2
1
1
0
1
1
0
2
1
1
1
0
1
2
1
1
2
1
0
1
1
2
2
1
0
0
4
1
1
1
2
1
0
0
0
1
1
1
1
1
1
1
2
2
2
1
2
1
0
0
1
2
1
1
2
3
1
0
1
1
1
1
2
1
0
1
1
1
0
1
0
2
2
1
0
2
0
0
0
0
1
1
1
1
0
1
2
0
1
1
0
1
2
2
2
3
1
1
1
1
0
1
2
2
1
1
1
1
2
0
1
1
1
1
0
1
2
1
1
1
0
1
0
1
0
1
2
1
2
2
1
2
1
2
1
1
1
2
2
1
1
0
1
2
0
0
1
1
1
1
1
1
1
1
1
1
0
0
2
2
1
1
0
1
1
2
1
0
1
1
2
1
2
0
1
2
1
2
1
1
2
1
2
1
1
1
0
1
1
2
1
1
2
1
2
1
2
1
1
1
2
4
2
0
1
1
2
0
0
2
2
1
1
2
2
0
0
2
2
2
1
1
2
1
0
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
0
2
3
1
1
0
2
1
2
1
1
2
0
1
0
1
1
0
1
0
2
1
1
1
1
1
2
1
1
2
1
2
0
2
1
1
1
1
1
2
1
0
2
1
2
0
1
1
1
1
1
1
0
0
1
0
1
1
1
1
2
2
1
1
0
1
1
2
1
2
1
1
1
1
1
1
2
1
0
1
0
1
1
1
1
1
1
1
2
2
1
0
1
0
1
1
2
1
2
2
1
1
1
2
1
2
1
0
1
1
1
1
2
1
1
2
1
2
1
2
1
1
0
1
1
2
0
1
1
1
0
2
0
0
2
1
1
1
1
1
0
1
1
1
1
0
2
1
1
0
1
0
0
0
1
1
0
1
0
1
1
2
1
1
0
1
1
1
1
1
0
1
1
1
1
1
1
1
1
2
2
2
1
1
1
2
0
1
0
1
0
1
1
1
0
0
0
3
1
1
1
1
1
2
1
0
2
2
1
2
2
1
0
1
3
1
1
0
0
1
2
2
1
0
2
1
1
1
1
1
1
1
1
2
0
1
1
1
2
1
2
1
1
1
1
1
2
0
2
1
1
1
1
1
1
1
1
2
2
2
2
1
1
1
0
2
1
1
1
1
0
1
1
1
1
1
0
1
1
1
1
1
2
0
1
1
0
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
0
2
1
1
1
1
0
2
0
1
1
1
1
1
2
0
2
2
1
1
0
0
1
1
2
1
1
1
2
1
2
1
1
1
0
1
2
2
1
0
2
2
0
0
1
1
0
1
2
3
2
1
1
1
2
1
1
2
2
1
1
2
1
1
0
1
0
1
1
1
0
2
1
0
2
0
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
0
1
0
0
1
1
0
1
2
4
1
0
1
1
1
1
0
1
0
1
1
2
1
1
1
1
2
1
0
1
1
1
0
1
1
1
0
4
0
1
0
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
0
0
0
1
1
0
0
1
1
2
1
1
1
0
1
2
1
2
1
1
1
1
2
1
1
1
1
1
0
1
2
1
1
1
1
2
2
1
2
1
1
2
0
1
2
2
1
1
1
0
0
1
0
2
1
1
1
1
0
1
1
1
1
2
1
2
2
1
1
2
1
1
1
1
1
1
1
1
2
2
2
2
1
1
1
1
1
2
2
1
2
1
0
2
1
2
1
1
0
1
2
2
0
2
1
2
1
2
2
1
1
1
0
0
1
1
1
0
3
2
1
1
2
1
1
1
1
2
2
1
1
1
1
2
2
1
1
1
0
1
1
1
2
1
1
0
0
2
1
1
1
1
1
2
1
1
0
2
1
0
2
2
1
6
2
2
1
1
2
1
1
0
1
1
1
1
2
1
1
0
1
2
2
0
1
1
2
3
1
1
2
1
1
0
2
1
0
1
1
1
0
1
2
2
0
2
1
1
1
1
2
1
2
1
1
2
0
1
2
0
2
1
1
1
1
1
1
1
1
2
1
0
1
2
1
1
1
1
1
1
1
1
3
2
0
2
1
2
2
1
0
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
0
1
1
1
1
0
2
1
2
1
1
1
0
1
1
1
0
1
1
2
1
1
1
1
1
1
1
1
1
2
0
1
1
0
1
1
1
0
1
1
0
2
1
1
1
1
2
0
0
1
2
2
1
1
2
1
2
1
2
1
1
1
0
1
1
1
1
2
1
1
0
2
1
1
1
2
2
0
1
1
0
0
1
1
1
2
1
2
1
2
1
1
1
1
0
1
1
0
1
1
1
2
1
2
1
2
2
1
2
1
1
1
1
1
1
1
0
1
1
2
2
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
0
1
1
1
1
1
1
2
1
0
1
1
1
2
1
1
2
2
1
1
0
1
2
1
1
1
1
2
0
1
1
1
1
1
1
1
1
1
2
1
2
1
1
0
1
2
2
0
1
1
1
1
1
1
1
0
1
2
1
1
0
1
1
1
1
2
1
2
1
1
1
1
2
1
1
0
1
1
2
0
1
1
1
1
1
2
0
1
1
2
0
1
1
1
1
1
1
1
1
1
0
1
2
0
1
1
3
1
0
1
1
1
0
1
1
1
0
1
0
1
1
2
1
1
2
1
1
0
2
1
1
1
2
0
0
1
1
1
1
1
1
1
2
1
2
0
0
0
1
1
0
1
1
1
0
1
1
2
1
0
2
1
1
2
2
2
1
1
1
1
1
1
0
1
1
2
1
1
0
1
2
1
1
2
0
1
2
1
1
2
2
2
1
1
1
0
1
2
2
2
1
0
1
1
1
1
2
0
2
1
0
1
1
1
1
1
1
1
2
0
2
2
1
1
1
1
2
1
1
3
1
1
2
1
1
1
0
2
2
1
1
1
1
4
1
1
1
1
1
1
2
1
1
1
2
0
0
1
1
1
1
2
2
1
1
2
2
1
1
1
1
1
1
1
1
1
2
0
1
2
2
2
2
2
1
1
2
0
1
1
1
1
2
1
2
1
1
1
1
0
1
1
1
1
1
1
2
1
2
1
1
2
1
1
0
1
1
1
1
1
1
1
1
0
2
1
1
1
1
2
2
1
1
1
0
2
1
1
0
0
2
0
1
1
2
1
1
1
2
1
1
1
1
2
2
1
1
0
1
1
1
1
2
1
1
1
1
2
1
1
2
2
0
1
1
2
1
1
1
2
1
1
1
1
0
1
1
1
2
2
1
0
1
0
1
2
1
0
2
1
1
1
1
0
0
1
0
1
0
1
0
1
1
2
2
1
0
0
2
2
1
2
1
1
1
1
1
2
1
1
1
1
1
2
3
1
0
1
2
2
1
1
1
4
1
1
0
1
1
1
1
0
2
2
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
2
0
1
1
0
1
1
1
2
0
1
1
2
2
1
1
2
2
1
1
1
0
1
1
1
1
1
1
1
1
1
1
2
1
0
1
2
1
1
1
1
1
1
2
1
1
0
1
2
1
1
1
1
1
0
0
1
1
1
1
1
1
1
2
1
2
1
0
2
1
1
2
1
2
1
0
1
1
2
1
1
2
1
2
2
1
0
1
1
1
1
1
1
1
1
0
0
2
0
0
1
1
1
1
1
1
0
0
0
0
1
1
0
1
1
0
1
1
1
1
1
1
1
2
1
1
2
0
1
1
2
1
1
1
0
1
1
1
1
2
1
1
0
2
2
1
2
1
1
1
1
0
1
1
0
1
1
2
1
1
1
1
1
1
1
3
1
2
1
1
1
2
2
2
0
2
2
1
1
0
2
1
1
2
1
4
2
0
0
2
1
1
0
1
1
1
2
1
1
2
2
2
0
1
2
1
1
2
1
1
1
2
1
1
1
1
1
0
0
0
1
1
1
1
1
1
1
2
1
2
0
2
0
2
1
1
1
1
0
1
1
1
0
0
1
2
1
1
1
1
1
1
2
2
1
1
0
1
2
2
2
1
0
1
1
1
2
1
1
1
1
3
2
1
1
1
0
0
0
0
2
0
2
1
2
0
1
1
1
1
0
0
0
0
0
2
1
0
1
1
1
2
1
1
0
2
1
2
1
2
1
1
1
1
1
2
1
1
1
2
2
0
2
1
1
2
2
1
0
2
2
1
1
1
1
1
1
1
0
1
2
1
1
2
1
0
1
2
0
1
1
1
4
1
1
1
1
4
0
1
3
2
1
1
2
1
1
1
1
1
2
2
1
0
1
1
0
1
2
1
1
2
2
1
1
1
1
1
1
1
2
1
1
0
1
1
2
1
1
1
1
1
1
2
1
1
0
1
1
0
4
1
1
2
1
0
2
1
1
1
1
0
2
1
2
0
0
1
2
2
1
1
1
2
0
0
2
1
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
2
0
2
1
1
1
2
1
0
1
1
0
2
1
2
1
1
2
2
2
0
0
2
1
1
1
2
1
1
1
0
0
2
0
1
1
2
0
0
1
2
1
1
1
1
1
2
2
0
2
1
2
1
0
1
1
1
1
0
1
2
0
0
1
0
2
1
1
1
1
1
1
1
1
2
1
0
1
1
1
1
0
1
1
2
2
0
1
0
0
0
1
2
1
1
1
1
1
1
0
1
0
2
1
1
1
2
1
1
1
1
1
1
0
2
2
1
1
1
1
1
1
1
1
1
0
0
0
2
1
0
2
2
1
2
0
1
1
1
1
2
1
1
1
1
0
2
1
2
0
2
1
1
2
2
0
0
0
1
1
1
2
2
0
1
1
0
2
2
0
1
1
0
0
0
1
2
2
1
1
1
1
1
2
2
0
1
2
1
1
1
0
1
0
2
0
1
1
1
1
1
0
0
1
1
1
1
2
1
1
1
0
0
1
1
1
1
2
1
2
2
1
2
1
1
2
1
2
0
2
1
1
0
1
2
1
1
1
2
2
2
2
2
1
1
2
1
0
1
1
0
1
0
2
1
2
2
1
2
1
1
2
2
1
1
1
0
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
0
1
1
1
1
1
1
0
0
0
1
0
1
2
1
0
0
0
1
1
1
0
1
1
2
1
1
1
1
2
0
1
2
0
1
2
1
1
1
0
0
0
2
1
1
2
2
1
2
1
1
0
1
2
0
1
2
3
1
1
1
0
1
1
2
2
1
4
1
2
2
2
1
2
1
2
1
1
2
0
1
2
0
2
1
1
0
1
2
0
1
1
1
0
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
2
2
2
1
0
1
1
2
1
0
1
1
1
1
2
0
0
2
0
1
0
1
2
2
1
2
1
1
1
1
1
1
2
1
1
2
2
2
3
2
2
0
2
1
1
2
1
1
1
2
0
0
1
1
2
1
1
0
0
1
1
0
2
1
0
2
1
1
2
2
1
1
0
1
2
1
1
1
2
0
1
1
0
1
1
2
1
2
2
0
1
2
2
1
1
2
1
2
0
2
1
1
2
1
1
1
1
1
1
0
2
2
1
2
1
2
1
2
0
0
2
2
1
1
1
1
0
1
0
0
1
1
2
2
0
2
1
0
1
1
2
1
0
0
1
1
1
1
1
1
1
2
1
1
0
1
0
1
1
0
1
0
3
1
1
2
2
1
0
0
1
1
1
1
1
2
0
1
2
0
1
1
1
2
1
1
2
1
0
0
1
1
0
1
1
1
0
1
1
1
0
1
2
1
1
0
1
2
2
3
1
2
1
1
1
1
1
1
2
2
1
1
2
2
0
0
3
0
0
1
1
2
0
0
0
2
0
2
0
2
0
2
0
1
0
1
2
0
2
1
1
1
1
1
4
1
0
1
2
1
1
1
2
1
2
1
0
1
1
1
1
2
1
1
1
1
0
1
0
0
0
3
1
0
1
2
2
1
1
1
0
1
1
0
2
1
2
2
2
1
0
2
1
1
1
1
1
0
1
2
0
2
2
1
1
0
2
1
1
2
2
0
1
0
2
2
2
1
2
1
1
2
2
1
2
1
1
2
1
0
1
0
0
1
1
1
0
1
1
1
1
1
2
0
2
1
2
2
1
4
2
1
2
0
2
0
1
1
1
1
1
1
1
0
0
1
3
1
1
0
2
0
0
2
1
1
1
2
1
2
1
2
2
1
2
2
1
0
1
1
0
1
1
2
1
2
0
2
0
0
1
0
1
1
2
1
0
2
0
1
1
2
1
1
1
2
1
1
1
1
2
2
1
1
1
2
0
3
1
1
1
1
2
0
1
2
1
1
1
2
0
1
1
1
1
1
1
1
1
1
0
2
1
2
0
1
1
2
0
1
1
1
1
1
1
1
2
1
2
2
1
1
1
0
2
2
0
2
2
1
2
0
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
0
1
0
2
2
2
1
2
0
0
1
1
0
0
2
0
1
1
1
1
1
1
2
1
1
0
1
1
1
1
1
1
1
0
2
2
1
2
1
1
2
1
0
1
0
0
0
1
1
2
1
1
0
1
0
0
1
2
1
2
1
1
1
0
0
1
0
1
1
2
1
1
1
2
2
1
1
1
1
1
1
2
0
1
1
1
2
1
2
3
0
2
1
2
0
1
2
1
1
1
2
2
0
1
2
2
1
1
1
2
2
1
1
1
2
3
1
1
1
1
2
0
0
1
2
0
1
1
1
1
1
2
1
1
2
1
1
2
1
1
2
0
0
1
2
1
1
1
1
1
2
1
2
0
1
1
1
2
0
2
1
1
2
1
1
1
1
1
2
1
1
1
0
1
0
1
1
1
1
0
1
2
0
1
1
1
1
0
2
2
2
1
0
1
1
2
1
0
0
2
1
3
3
1
2
1
1
2
2
2
0
1
1
0
2
0
9
2
2
2
1
1
0
1
1
1
1
1
1
2
1
0
0
1
1
0
1
1
1
1
1
1
1
0
0
2
1
0
1
1
1
1
2
1
2
1
2
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
1
2
1
1
0
1
2
1
1
2
1
1
1
1
0
0
1
1
2
0
1
0
0
1
0
2
2
1
1
2
1
2
1
3
2
1
2
2
2
0
2
2
2
1
2
0
1
1
1
1
1
2
1
2
2
1
2
1
1
1
2
1
0
2
1
2
3
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
0
1
1
1
2
2
1
1
1
1
1
1
1
2
1
3
2
1
1
3
1
1
1
1
1
1
1
1
2
2
0
1
1
2
1
1
1
1
1
0
1
1
1
2
0
1
2
8
2
0
0
1
1
1
1
0
1
1
1
0
1
1
2
1
1
1
0
1
1
1
2
0
1
0
0
1
0
1
0
2
2
1
2
2
1
1
0
1
0
1
0
0
1
0
0
1
1
1
1
1
1
1
0
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
2
1
2
2
2
0
1
0
1
1
2
0
1
1
2
1
0
1
2
1
2
1
1
1
1
1
0
0
2
0
1
1
1
2
2
1
0
2
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
2
0
1
1
0
2
1
0
2
1
1
1
1
2
2
1
1
1
1
0
1
1
0
2
0
1
0
2
2
0
1
0
1
1
1
0
1
1
1
1
0
0
2
1
0
2
1
1
2
1
1
0
3
1
2
1
1
0
2
1
1
1
2
1
1
1
1
3
2
1
0
1
2
2
1
2
1
1
0
0
1
1
0
2
1
1
1
1
1
2
0
3
0
1
0
1
1
1
0
2
0
1
2
1
1
1
1
2
0
1
1
1
0
1
1
1
1
1
1
1
1
1
2
0
0
1
1
1
1
1
0
1
1
0
1
3
1
1
1
0
1
2
1
0
1
1
2
1
2
0
0
1
2
0
1
0
1
1
0
2
1
1
1
1
1
2
1
1
1
1
1
2
2
1
1
0
1
1
1
0
1
1
1
1
1
1
0
1
1
1
2
1
1
2
0
1
0
1
0
1
1
2
1
0
2
0
0
1
1
1
1
2
1
1
2
1
1
2
0
1
0
2
0
1
2
2
0
0
2
1
1
0
0
2
1
0
0
0
2
1
1
1
2
1
1
1
0
1
2
1
1
0
0
0
1
1
1
1
1
2
1
1
1
1
1
1
0
0
0
1
1
1
1
0
1
2
1
0
1
1
1
2
2
2
2
1
2
0
2
0
2
1
1
0
1
1
1
1
1
2
1
2
3
1
2
1
2
1
1
2
1
0
1
1
1
2
0
1
1
1
0
1
1
1
1
1
2
1
0
1
2
0
1
0
2
1
1
1
0
0
1
1
1
3
1
1
1
2
1
0
2
1
2
2
2
1
2
2
1
0
1
1
1
2
1
1
2
0
1
1
1
0
2
1
1
1
2
1
1
1
0
0
1
1
0
1
1
1
1
1
1
1
1
1
0
1
1
1
2
1
1
1
1
1
1
0
1
2
1
0
0
1
1
2
1
0
1
2
2
2
1
2
0
2
2
1
1
1
1
1
1
2
1
0
1
1
1
2
1
1
1
1
1
1
2
1
1
0
2
0
1
2
1
2
0
2
2
1
0
1
2
1
0
0
0
2
1
0
2
1
1
0
1
0
0
1
1
1
2
1
1
1
1
1
1
1
1
1
2
0
0
1
2
1
2
1
1
1
1
2
0
0
1
1
2
1
2
2
0
1
1
2
2
1
2
2
1
1
1
0
1
1
1
0
1
0
1
1
1
0
2
0
1
1
1
1
2
1
1
1
2
1
1
2
2
1
1
2
2
2
2
0
1
1
1
1
1
2
1
2
0
1
0
1
1
1
0
1
1
0
2
1
2
1
0
1
2
0
2
2
1
0
1
2
0
1
1
1
2
1
2
1
2
1
1
1
1
1
1
1
1
0
1
1
3
1
0
2
0
1
1
1
1
1
1
2
1
1
0
1
0
1
1
2
1
1
1
1
3
2
2
3
1
2
2
2
1
1
2
1
1
1
0
2
2
1
2
2
2
1
1
1
1
0
1
1
1
0
1
1
1
2
2
1
2
1
1
0
1
1
1
1
2
1
0
0
0
1
0
1
2
2
2
1
2
1
2
1
1
2
0
1
1
2
1
2
1
1
1
1
2
0
1
2
1
1
2
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
0
1
0
1
1
0
1
2
1
2
1
0
1
1
1
0
1
1
2
0
4
2
1
0
1
2
1
2
1
2
2
1
1
1
2
1
0
1
1
1
0
1
0
0
2
0
1
1
1
1
1
0
2
1
2
1
1
1
2
2
1
1
1
1
2
2
0
1
0
2
1
0
1
2
1
1
2
1
1
1
1
1
1
1
1
0
1
0
1
2
2
2
1
1
1
1
1
1
0
1
1
2
0
2
1
1
1
2
1
1
1
1
1
1
1
0
3
2
2
1
1
2
2
0
0
2
1
1
0
1
1
2
1
0
1
0
2
1
1
1
1
0
2
2
2
1
1
2
1
1
1
0
1
1
1
1
1
1
2
1
1
0
0
1
1
2
1
0
1
0
2
1
2
1
1
1
1
1
1
1
2
0
1
1
1
1
1
0
1
1
0
1
1
0
0
0
1
1
1
1
3
1
1
1
1
1
2
1
1
1
0
2
2
1
1
2
1
1
1
1
1
1
2
1
0
1
2
2
2
1
2
1
1
0
1
1
1
1
1
1
2
2
1
2
2
1
1
2
2
1
1
0
0
0
0
2
1
1
1
1
1
0
0
2
1
3
1
0
0
1
1
1
1
2
1
2
0
0
1
1
1
0
0
1
1
0
1
1
0
0
3
1
0
1
1
0
0
1
1
2
1
1
0
1
2
1
1
0
0
2
2
1
1
1
1
2
2
1
2
2
1
1
1
1
1
0
2
1
1
3
1
1
0
2
1
1
1
1
0
0
1
2
1
1
1
1
1
2
1
1
1
1
1
0
1
1
1
0
1
0
1
1
1
2
2
0
1
1
0
0
1
2
1
1
1
2
1
1
1
2
1
2
2
1
1
1
1
2
0
2
0
3
1
0
0
1
1
0
2
1
0
1
1
2
1
1
0
1
1
1
1
1
0
2
1
2
1
0
1
1
1
0
1
2
1
0
1
0
2
1
0
0
1
2
1
2
4
2
1
1
2
1
2
0
1
0
1
1
1
3
2
1
1
1
0
1
0
1
0
2
1
2
1
1
2
1
1
2
1
1
0
0
0
1
1
1
2
2
2
0
1
0
1
1
1
1
2
0
1
2
1
1
1
0
1
2
1
2
2
1
1
2
1
0
1
2
0
2
0
0
2
2
0
1
1
1
2
1
0
0
2
1
0
1
1
1
1
2
1
2
2
1
1
2
1
2
0
1
2
1
1
1
0
1
2
1
0
1
1
1
2
0
3
2
1
2
2
1
1
0
1
1
1
2
1
0
1
1
1
0
1
1
1
1
0
2
0
1
2
0
1
2
1
1
2
1
1
2
1
1
2
2
2
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
0
0
0
0
1
0
1
1
4
1
2
2
1
2
2
2
1
1
1
0
2
1
1
1
0
2
0
1
2
2
1
0
1
2
0
0
1
0
2
0
2
1
2
0
0
1
1
2
1
1
0
2
1
1
1
2
2
1
1
0
2
2
2
0
1
1
1
0
2
0
2
1
1
0
2
2
1
1
2
1
1
1
1
0
1
0
0
1
2
1
0
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
2
2
1
0
1
1
2
1
1
1
0
0
1
4
1
3
1
1
0
1
1
1
2
1
1
1
0
1
2
1
0
1
1
1
0
1
1
1
1
1
2
2
2
1
1
1
1
1
0
1
1
2
2
1
1
1
1
1
1
0
1
1
1
0
2
1
1
1
1
0
2
0
1
1
1
1
0
1
2
1
1
1
0
1
0
1
1
2
0
1
0
1
1
1
2
1
1
1
2
1
2
1
0
1
1
1
1
1
1
0
1
1
2
0
0
1
1
1
1
1
2
0
1
1
0
1
0
1
2
1
1
0
2
2
2
2
1
1
1
1
0
2
0
2
0
1
2
2
1
2
2
0
1
0
2
1
1
1
1
2
2
1
1
1
1
0
0
0
1
2
0
1
0
2
1
0
1
1
1
1
2
0
1
1
1
1
2
1
2
2
1
0
1
2
0
2
0
1
1
1
1
0
1
2
0
1
1
1
2
0
0
2
1
1
1
1
1
2
1
1
1
2
2
0
2
1
2
2
2
1
1
1
1
0
1
2
2
0
1
2
1
1
2
1
1
2
0
1
0
2
1
1
1
1
1
1
1
1
0
1
2
0
0
1
1
1
1
1
0
2
1
1
0
1
1
2
0
1
2
0
1
1
0
1
1
1
2
1
2
2
1
1
2
1
0
1
1
1
1
2
1
1
1
1
1
1
1
1
0
1
2
1
1
1
1
0
2
0
1
1
2
1
0
0
1
0
1
1
2
2
1
1
2
1
2
1
0
2
1
0
1
2
1
2
2
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
2
1
0
1
0
1
1
1
1
1
0
1
1
0
1
2
1
1
1
1
1
2
1
2
2
1
1
1
0
1
0
1
2
2
2
1
2
1
2
2
1
2
0
2
1
2
2
1
1
1
2
1
1
2
1
1
1
1
1
2
0
1
1
2
2
1
1
1
1
2
1
2
1
1
1
2
0
0
0
1
1
1
2
1
2
2
1
1
1
1
1
1
1
2
0
1
1
0
1
1
2
0
1
0
0
1
2
0
1
0
1
1
0
0
1
2
1
2
2
1
1
2
1
2
1
1
2
2
0
1
0
1
1
0
2
0
0
2
1
1
1
2
1
1
1
0
2
1
0
1
2
1
1
1
1
2
1
1
1
2
0
1
0
1
1
1
2
0
2
0
1
2
2
1
1
1
1
1
0
1
1
1
0
1
1
0
2
1
1
2
0
1
1
1
1
1
1
1
1
2
0
1
1
1
1
1
1
2
1
1
2
0
1
1
1
1
0
0
1
0
1
1
2
1
1
1
1
2
1
1
2
1
0
1
0
0
1
1
1
0
1
0
2
0
2
0
1
2
1
1
2
1
1
1
0
1
1
2
1
0
2
0
2
2
2
2
1
1
1
2
1
0
0
2
2
1
1
1
1
0
2
1
2
1
1
2
1
1
2
1
1
1
1
2
2
0
2
2
1
0
1
1
1
0
0
2
2
2
1
1
1
2
0
1
2
2
0
2
1
1
1
1
1
3
1
2
1
1
1
1
1
1
1
0
2
3
0
1
2
2
2
1
1
1
1
1
0
1
2
1
2
1
0
0
1
1
1
0
1
1
1
1
2
2
1
2
2
1
1
1
0
2
0
2
1
2
0
2
1
3
1
1
2
2
1
1
1
1
0
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
0
1
2
1
1
1
0
2
1
1
1
1
1
3
1
1
1
1
0
1
1
2
2
1
1
1
1
2
2
1
1
0
1
1
2
1
1
1
0
1
0
2
1
2
1
2
0
1
0
2
2
1
1
1
1
1
1
2
0
1
1
1
2
0
1
1
0
2
1
2
1
1
0
1
1
1
0
1
1
2
1
1
2
1
1
2
1
2
0
1
1
2
1
1
2
1
1
0
0
2
1
0
1
0
1
1
1
0
1
1
1
1
0
2
2
1
1
1
1
1
1
1
1
1
2
1
1
2
2
0
1
0
0
1
1
1
1
0
1
1
0
1
1
1
2
1
1
9
0
1
1
1
0
1
1
0
1
0
0
2
1
0
0
1
0
1
1
1
0
0
1
2
2
1
0
1
2
1
0
1
1
1
2
1
1
2
1
2
0
0
1
0
1
1
1
1
1
1
2
0
1
1
1
1
3
1
1
1
2
0
0
2
1
1
2
2
0
1
1
0
1
1
1
1
1
1
1
1
1
0
2
1
2
1
1
1
0
2
1
1
1
0
2
1
1
1
1
1
1
1
1
1
2
1
0
2
1
0
1
2
1
1
2
0
2
1
0
1
0
1
1
1
1
2
0
0
1
1
1
0
1
1
0
1
1
0
2
0
2
0
2
1
0
1
0
0
1
0
3
1
0
1
1
1
1
1
1
2
1
1
2
1
1
0
1
1
0
1
1
2
1
1
2
1
3
0
1
2
1
2
0
1
2
0
0
2
2
1
2
1
1
1
2
0
1
1
2
1
1
1
1
2
1
1
2
0
1
1
0
1
1
2
0
1
2
1
1
2
2
1
2
2
1
1
0
2
1
1
0
1
1
2
1
1
1
1
1
1
2
1
2
0
1
1
1
1
2
1
2
1
0
2
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
0
0
1
2
2
0
1
0
2
1
2
1
2
2
1
0
1
2
1
0
0
1
1
3
0
2
2
0
1
2
2
1
1
1
1
1
0
1
2
1
1
1
1
2
1
0
1
1
2
0
0
1
1
1
0
1
1
1
0
0
1
1
1
1
1
1
0
1
0
1
2
1
0
1
2
1
2
1
1
1
1
1
1
1
0
0
2
1
0
1
2
2
2
1
1
1
1
1
2
2
1
2
1
2
2
1
0
1
2
1
1
1
1
0
0
2
2
1
1
1
1
1
1
1
2
2
1
1
2
1
2
1
2
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
2
1
2
1
0
1
2
1
1
0
0
1
2
2
1
2
1
2
2
2
2
1
1
1
0
2
2
2
2
3
1
1
1
0
1
1
2
2
1
2
1
0
0
1
1
1
1
1
1
1
1
2
0
0
1
2
1
0
0
2
1
2
2
1
2
1
2
0
2
1
1
0
1
1
2
2
0
0
1
1
0
1
0
1
0
2
0
1
1
1
1
1
1
1
0
1
2
1
0
2
1
1
1
3
1
2
0
1
1
0
1
1
2
1
0
0
1
1
2
1
1
0
1
1
0
1
1
1
1
5
1
1
0
0
2
1
0
1
0
1
1
1
1
1
1
0
1
0
3
2
2
2
2
1
2
1
1
1
1
1
1
2
2
2
1
1
1
2
2
1
1
0
0
2
0
1
1
0
0
1
1
2
0
1
1
1
1
1
0
1
1
1
1
2
1
1
1
1
0
1
2
0
1
1
2
1
2
1
1
1
1
2
2
2
0
1
2
1
2
0
2
1
1
1
1
2
0
1
1
0
0
1
1
1
1
1
0
0
2
2
2
0
2
2
1
1
1
0
1
2
1
3
3
2
3
1
1
2
1
1
2
1
1
1
2
0
0
1
0
2
1
0
1
2
2
1
1
1
1
1
1
2
0
0
1
1
1
1
1
1
1
0
1
1
0
0
1
2
0
1
1
2
2
0
1
0
2
0
0
0
0
2
0
1
2
0
1
2
2
1
1
1
2
0
1
2
1
1
1
2
3
0
2
1
0
1
1
2
1
2
0
1
1
1
2
1
1
1
1
0
2
0
1
1
2
0
0
1
0
3
1
1
0
2
1
1
1
1
1
1
1
0
1
1
2
1
0
2
1
3
1
1
2
2
0
1
0
2
1
1
2
1
3
1
1
1
0
2
1
2
0
1
0
0
1
1
0
2
1
0
2
1
1
2
1
0
1
1
1
2
1
2
1
1
1
3
1
0
1
2
1
1
1
0
1
0
1
1
1
1
0
2
0
1
2
0
1
1
1
1
0
1
0
1
0
1
2
1
1
3
1
1
1
1
1
1
1
0
1
0
2
1
2
2
1
1
1
0
0
1
1
2
0
1
0
2
2
1
2
0
1
1
2
1
1
2
1
0
1
2
1
2
1
2
0
1
2
1
1
0
1
1
1
2
1
2
2
1
2
2
2
2
1
1
2
1
0
1
1
1
1
1
1
2
1
1
2
1
1
1
2
1
2
0
1
1
0
1
1
2
1
1
0
2
1
1
1
1
2
1
1
2
1
0
0
1
1
1
1
0
2
2
2
0
1
0
2
0
1
1
2
2
1
1
2
1
1
2
1
0
2
0
1
0
1
1
1
1
1
1
1
0
0
1
1
1
2
1
1
1
2
0
2
3
1
0
2
1
0
1
1
2
2
1
1
2
1
1
1
1
0
2
1
1
1
1
1
0
1
1
0
1
1
1
2
0
1
1
1
0
0
1
1
2
1
2
1
1
1
1
1
2
1
1
1
1
0
1
1
0
0
2
1
1
1
0
1
1
1
1
1
2
1
1
1
1
2
1
2
1
1
2
1
1
1
0
2
1
1
1
2
1
0
0
1
1
1
2
1
1
0
0
1
2
1
2
2
2
2
1
2
0
1
0
0
1
1
1
1
1
0
1
1
0
1
0
0
1
1
0
0
0
1
2
1
1
1
1
1
1
1
1
0
2
1
0
2
2
1
2
2
1
1
2
1
2
2
0
1
1
1
1
2
2
0
2
1
2
2
0
2
1
1
1
0
1
2
0
2
1
1
1
1
1
1
2
0
1
1
1
0
0
1
1
2
1
2
0
0
1
1
1
1
1
1
1
1
1
1
0
1
1
1
0
2
2
1
3
2
0
2
2
1
0
1
1
1
1
1
0
1
0
0
2
1
1
0
1
1
2
1
1
1
2
0
2
1
2
0
1
1
0
1
2
0
2
1
2
1
2
0
0
2
1
1
1
1
1
2
2
2
1
2
1
1
1
1
1
1
0
1
1
2
1
2
2
2
2
0
0
1
1
1
1
1
1
2
1
0
1
1
2
1
0
2
1
0
0
0
1
1
2
0
1
2
1
1
1
1
2
1
1
1
1
1
1
1
0
1
1
1
1
1
0
2
2
1
1
1
1
1
0
1
2
1
1
1
1
1
1
1
2
1
1
0
1
1
1
0
1
1
1
1
1
1
4
1
1
0
1
1
1
1
1
0
3
1
2
1
2
0
1
1
1
1
1
1
1
1
1
1
1
0
1
2
1
0
1
1
1
1
0
1
3
2
1
1
1
1
1
0
1
1
0
1
1
2
4
1
1
0
1
0
1
2
2
1
2
2
2
1
1
1
1
0
1
0
1
0
1
2
1
0
0
1
1
1
0
1
1
1
1
2
0
1
1
1
0
2
0
2
0
2
1
2
1
1
1
0
1
2
1
1
1
2
1
0
1
0
1
1
1
1
1
0
1
2
1
0
0
2
1
1
1
1
2
2
1
1
1
1
1
2
2
0
0
1
3
2
1
0
0
2
2
1
0
1
2
1
0
1
2
1
0
0
1
1
1
2
1
1
1
1
2
1
2
1
1
1
1
2
1
1
1
0
1
0
1
2
1
1
1
2
0
1
1
1
1
1
2
1
1
1
2
2
2
0
1
1
1
1
0
1
1
1
1
1
1
1
0
1
2
1
1
0
2
0
0
1
2
1
1
0
1
1
2
1
2
1
1
3
1
1
1
1
1
1
2
1
1
2
2
2
1
1
1
1
0
2
1
1
2
1
1
0
1
1
0
1
1
0
1
1
0
2
1
1
0
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
1
0
1
2
1
2
1
0
2
1
1
0
0
2
1
1
1
2
0
2
1
1
0
2
1
1
1
2
1
1
0
1
1
1
1
2
1
1
1
1
0
1
2
0
0
1
1
1
0
1
1
0
2
2
1
3
0
2
1
1
2
2
1
1
1
0
1
2
1
0
0
1
0
0
1
1
1
1
1
1
1
2
2
0
0
1
2
1
2
1
1
1
2
2
2
1
2
0
1
1
1
2
1
1
1
2
1
2
1
0
2
1
0
1
0
1
1
1
2
1
1
0
2
1
3
1
1
1
1
0
1
1
1
0
0
0
1
2
2
1
1
1
2
1
0
1
1
1
1
2
2
1
2
2
1
0
1
2
1
2
2
1
0
0
1
1
1
2
1
0
2
1
1
0
2
1
1
1
1
1
1
1
2
2
5
0
1
1
1
2
2
1
0
1
0
2
2
1
0
1
0
0
1
1
1
0
2
1
0
1
2
0
1
0
1
2
1
0
1
0
2
1
1
0
1
1
2
1
1
1
1
2
2
1
1
1
1
1
0
0
2
2
0
1
2
2
0
0
2
0
2
1
2
1
1
0
0
1
0
1
1
0
1
1
2
0
1
1
1
1
1
1
1
1
1
1
1
1
1
2
0
1
0
1
1
0
1
2
1
2
2
1
1
0
1
0
2
0
1
2
2
0
2
1
1
0
2
1
0
1
1
1
1
1
1
2
2
1
1
1
0
1
1
1
1
1
1
0
2
2
1
1
0
1
1
2
1
1
1
1
1
1
1
0
1
0
0
0
2
1
1
0
0
1
1
0
1
1
1
2
2
2
1
1
0
1
1
1
1
1
1
1
1
1
0
0
0
1
1
0
1
1
1
1
1
1
2
0
0
2
1
1
2
1
2
1
1
0
1
0
1
0
1
1
1
1
1
2
1
1
0
1
0
1
2
1
1
2
4
0
2
1
2
2
0
1
1
1
2
1
0
1
2
2
1
2
0
2
1
1
1
2
1
2
1
2
1
1
1
0
1
1
1
1
1
1
0
2
1
1
1
1
2
1
1
0
1
2
2
1
1
2
1
2
1
2
0
0
2
1
1
1
1
1
1
1
0
1
1
1
2
2
1
1
0
0
1
0
0
1
1
1
1
0
1
0
2
1
2
2
2
1
0
2
1
1
1
1
2
1
1
2
1
2
1
1
2
0
0
1
2
1
2
1
0
0
0
1
2
2
1
1
1
1
1
1
0
1
1
0
2
1
0
1
1
1
1
1
1
1
2
0
1
1
1
1
1
1
1
1
1
2
1
2
1
2
0
1
0
2
1
1
1
2
0
1
1
2
1
1
1
0
2
2
1
0
2
0
1
1
1
1
1
1
2
1
2
2
1
1
1
2
1
1
1
0
1
2
2
2
2
1
1
1
0
1
1
1
1
1
0
1
2
0
1
1
1
1
1
1
2
2
3
1
1
1
1
1
1
1
1
1
2
1
1
0
2
1
1
1
1
1
1
1
1
1
0
0
1
1
2
2
0
1
2
1
1
1
1
2
1
1
1
2
1
2
1
0
1
1
2
1
1
1
1
2
0
1
1
1
0
2
0
1
1
0
1
1
1
0
0
0
2
1
2
2
2
1
0
0
0
1
1
1
1
2
1
0
1
1
1
1
0
0
1
2
0
1
1
1
1
1
1
1
1
0
1
1
1
1
1
0
1
1
1
2
1
0
0
0
0
2
1
1
1
1
1
1
1
1
2
1
2
1
1
2
1
0
2
0
1
1
1
2
1
2
1
1
2
1
1
0
1
1
1
2
1
2
0
1
1
1
2
0
0
0
1
2
2
0
2
0
1
1
0
2
2
1
1
2
2
2
1
1
0
2
1
1
1
1
1
0
1
1
1
1
1
0
2
1
0
1
0
0
1
1
1
1
2
2
1
1
1
1
1
2
0
1
1
1
1
2
1
1
0
0
1
1
2
1
4
2
0
2
1
1
1
1
1
1
1
0
1
1
2
0
1
1
1
1
1
1
1
1
2
1
1
2
0
1
0
1
0
1
1
1
2
1
1
1
1
2
0
0
1
2
1
1
0
1
0
2
1
2
1
0
1
0
1
1
0
1
0
1
0
1
2
0
0
1
1
0
1
1
1
4
0
0
1
0
0
2
1
1
2
0
1
2
1
1
2
0
1
0
1
2
0
2
1
2
2
1
2
1
2
1
1
1
2
1
2
1
0
0
1
1
1
1
0
1
1
0
1
1
1
2
2
1
0
1
1
1
0
1
1
2
1
1
1
2
1
0
1
1
2
1
2
1
0
1
1
1
1
1
1
1
1
1
0
1
1
1
2
1
1
1
2
2
1
0
2
1
1
1
1
1
0
0
1
0
1
0
1
1
1
2
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
3
1
1
2
2
1
2
2
0
1
0
0
1
1
2
2
2
2
1
1
1
2
1
1
1
0
1
0
1
0
1
2
1
2
0
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
0
0
1
1
2
0
1
1
2
1
1
2
0
1
1
0
1
1
0
0
2
1
1
2
3
1
1
2
1
1
2
2
2
0
2
1
1
0
1
1
1
1
1
0
1
0
1
1
2
1
2
1
2
2
2
0
1
2
0
1
1
1
1
1
1
2
1
1
1
1
1
2
0
1
0
1
1
5
1
0
2
0
3
2
0
1
0
1
1
2
0
2
1
1
1
1
1
1
1
0
2
2
1
1
1
0
2
1
1
2
0
0
2
1
1
0
1
0
2
0
1
2
1
1
2
1
0
1
2
1
2
1
2
1
2
0
1
1
0
1
2
0
1
2
1
0
1
1
0
0
1
1
1
2
1
0
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
0
1
2
1
1
2
1
2
1
2
1
1
1
1
2
1
0
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
0
2
1
1
0
2
1
2
2
1
1
3
0
1
1
1
1
1
0
0
1
1
0
1
1
0
0
2
1
0
1
2
2
0
1
2
1
1
0
1
1
1
3
1
2
1
0
1
1
2
0
2
0
2
0
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
1
2
0
1
1
2
2
1
1
1
1
2
2
1
0
1
1
0
2
0
1
0
1
1
1
0
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
2
0
1
1
1
2
3
0
1
0
1
2
0
1
2
1
1
1
1
2
2
2
1
1
1
1
1
0
1
1
2
0
1
0
2
1
1
1
1
2
1
1
0
1
0
2
2
2
0
2
1
1
1
2
2
1
1
1
1
0
1
0
1
0
1
2
1
2
0
1
1
1
0
1
1
2
1
0
1
2
0
2
0
1
1
2
1
1
1
1
1
2
1
1
1
1
1
0
2
3
0
1
1
1
2
1
1
0
2
0
1
1
2
1
2
0
2
0
2
0
1
2
1
0
1
0
1
1
2
2
2
1
1
0
2
2
1
0
2
1
1
2
1
1
1
1
1
0
1
0
1
1
1
1
1
1
1
0
1
1
2
1
1
1
1
1
0
0
1
1
0
1
1
1
1
0
2
0
1
1
2
1
1
2
1
2
1
1
1
1
1
2
2
2
1
1
0
1
2
3
2
1
1
2
2
1
1
0
2
0
1
1
0
1
2
1
2
1
2
1
2
1
3
2
0
1
2
2
1
2
1
2
1
1
0
0
1
2
2
1
1
1
0
1
0
1
1
1
1
0
0
2
1
1
2
1
0
1
2
1
0
2
2
4
1
0
2
0
1
2
1
2
1
2
2
2
1
2
2
1
2
1
1
1
1
1
1
1
1
2
2
1
0
1
2
2
1
1
1
1
2
1
2
1
1
1
2
2
2
2
0
1
2
1
1
1
8
0
1
1
0
0
1
1
0
0
1
1
1
1
1
1
1
1
1
2
0
0
0
1
2
1
0
1
0
0
2
2
1
2
1
1
0
1
1
1
1
1
1
0
1
2
1
1
0
2
1
1
1
2
1
2
1
1
2
1
0
3
0
1
1
2
1
1
1
1
2
1
1
2
1
1
2
1
0
1
1
1
1
1
1
1
2
1
1
0
1
0
1
1
0
0
1
0
1
1
0
2
2
2
2
1
1
1
1
1
2
2
0
0
2
1
1
1
2
1
0
1
2
2
0
1
1
2
1
1
1
1
2
2
3
1
0
1
2
2
1
1
2
1
2
2
0
2
1
1
0
1
0
2
2
1
1
1
0
1
2
1
1
2
1
1
0
1
0
1
0
1
1
2
1
2
1
0
2
2
1
1
1
0
1
1
1
1
1
1
1
0
1
1
2
0
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
2
0
1
2
1
1
1
1
1
1
1
0
1
2
0
1
1
1
1
0
2
1
2
1
2
1
2
0
1
0
1
2
1
1
1
5
1
1
1
2
0
2
1
1
0
1
0
1
1
1
0
0
2
2
1
1
0
1
1
0
0
2
1
2
1
1
1
1
2
1
2
1
1
2
1
1
0
1
1
1
1
1
2
0
0
2
3
1
2
1
0
1
1
1
1
1
1
0
1
1
2
1
2
1
1
1
1
1
1
1
0
1
0
1
1
1
1
2
2
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
0
1
1
1
2
1
1
1
1
0
0
2
0
2
1
1
2
1
2
1
2
1
1
0
2
0
1
0
1
1
0
1
2
1
2
2
1
1
0
1
1
2
1
1
1
2
0
1
1
1
2
1
0
0
1
2
1
1
1
1
2
1
0
1
0
1
1
1
1
1
1
2
2
1
0
1
1
0
1
0
1
0
0
2
1
2
1
1
1
2
1
0
1
1
1
1
1
0
2
2
1
0
0
2
2
0
1
1
1
1
1
2
2
1
1
0
1
0
0
1
0
2
1
2
1
1
0
1
1
1
1
1
1
1
2
0
0
1
1
2
1
1
0
1
1
0
2
1
3
1
1
2
1
1
1
1
0
0
2
1
2
1
2
1
2
1
2
0
2
1
1
1
1
0
2
2
1
0
1
1
1
2
1
1
1
1
1
1
1
2
1
0
1
1
2
1
2
1
0
1
1
1
1
0
1
2
1
1
1
1
2
1
1
1
1
1
0
1
1
1
2
1
2
0
1
2
2
1
0
1
2
1
1
0
1
2
0
2
0
0
1
2
3
1
0
1
2
2
1
0
1
2
1
1
2
0
1
1
1
2
1
1
2
1
2
1
1
0
1
1
1
1
2
1
2
3
2
2
1
1
1
1
0
0
2
1
1
2
1
1
1
1
0
1
1
2
1
1
1
2
0
0
1
1
2
2
0
1
0
1
1
0
1
0
1
0
1
0
0
1
0
2
1
0
1
2
1
0
1
1
1
1
1
0
2
1
1
1
1
2
1
2
1
2
1
1
0
1
1
0
1
1
1
0
0
1
1
1
2
1
0
1
1
2
1
2
1
2
1
2
1
2
1
1
1
1
2
0
2
1
1
1
1
2
1
2
1
0
0
1
0
1
2
0
2
0
1
1
1
1
0
1
1
1
2
2
0
2
2
1
2
1
1
0
0
0
1
0
1
2
2
0
2
0
1
1
2
0
1
2
1
0
1
0
0
2
1
1
1
0
1
0
0
1
1
1
2
1
1
1
1
1
0
0
2
2
1
1
2
1
0
1
1
1
1
2
1
1
1
1
2
2
1
1
1
3
2
1
2
0
0
1
0
2
1
0
0
1
1
2
1
1
2
1
2
1
2
1
1
1
2
1
2
1
2
0
1
1
0
2
2
1
1
1
1
2
1
2
2
1
2
1
0
2
1
0
1
1
1
1
1
1
1
1
1
1
1
0
1
0
1
1
1
0
1
1
2
1
2
0
2
0
1
2
0
1
2
1
2
1
1
1
1
1
1
1
1
1
0
1
0
1
1
0
1
2
1
1
5
1
1
1
1
1
1
2
2
1
1
0
1
0
1
1
1
0
1
1
1
1
2
0
0
1
1
1
2
1
1
1
1
1
2
1
1
1
2
2
1
1
1
0
1
1
1
1
0
1
1
1
1
2
1
0
0
0
1
2
0
0
2
1
1
1
1
2
1
2
1
0
0
2
1
2
2
2
1
2
2
0
1
2
1
1
2
1
0
2
2
1
2
1
1
2
1
1
1
0
0
1
1
1
1
1
1
1
1
0
1
3
1
0
1
2
1
1
1
1
0
2
0
0
2
1
0
1
2
1
2
0
2
1
1
1
0
1
2
2
1
0
2
1
1
2
0
1
1
1
2
2
1
2
2
0
0
2
1
1
0
2
0
2
0
0
1
1
1
1
0
0
0
2
0
1
1
1
1
1
0
0
1
1
1
0
0
1
0
1
0
1
1
0
2
2
2
0
2
1
1
2
1
0
1
1
1
1
0
1
1
2
1
2
1
2
1
1
0
1
1
1
1
1
1
1
1
2
0
1
1
1
0
2
1
1
1
2
0
0
1
0
1
1
0
2
1
0
0
0
1
1
0
1
1
2
2
1
1
1
2
1
0
1
3
1
1
1
2
1
1
1
1
2
2
2
1
1
2
0
1
1
1
2
1
0
1
1
2
1
2
1
1
1
2
1
1
2
1
2
1
2
2
0
1
1
1
1
2
2
1
1
1
2
2
2
2
2
1
1
0
1
2
1
1
1
1
1
1
2
1
2
1
1
2
0
0
0
2
1
1
1
1
1
0
1
1
2
1
1
2
2
1
1
0
0
0
2
2
2
0
0
0
2
1
1
0
2
0
1
1
1
2
0
1
1
2
1
1
1
1
1
1
2
1
1
0
2
2
1
1
1
1
0
1
2
1
1
1
2
2
2
2
0
1
1
1
1
1
0
1
2
0
1
0
1
2
1
1
1
2
2
2
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
0
1
1
0
1
1
2
1
1
0
2
1
0
0
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
0
2
0
2
1
1
2
1
0
2
0
1
0
1
1
0
0
1
0
0
0
0
1
1
1
1
1
1
1
0
1
2
0
1
0
1
0
1
1
2
1
0
1
0
1
2
2
2
0
1
1
0
1
1
4
2
0
1
2
2
1
1
1
1
0
0
1
2
0
2
1
0
0
1
1
1
1
1
1
3
1
1
2
1
1
1
1
0
0
0
2
1
1
1
1
1
1
1
0
1
1
1
2
1
2
1
1
0
0
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
2
0
0
1
1
2
1
2
1
0
1
1
0
0
1
2
0
1
1
2
1
2
1
1
1
1
1
1
1
1
1
0
1
1
1
2
1
1
1
0
1
0
2
1
0
1
1
1
2
1
1
3
1
2
2
1
1
1
1
2
2
1
1
1
1
0
1
2
1
1
1
2
0
1
1
1
2
2
1
2
1
0
2
2
1
2
1
2
1
1
1
2
1
1
2
1
2
1
1
1
1
1
1
0
1
1
1
0
2
1
1
2
2
0
0
0
2
2
1
1
2
2
2
1
0
2
0
1
1
1
1
1
1
2
0
1
1
1
0
1
2
2
1
0
1
1
1
1
2
1
1
1
1
1
1
2
1
1
0
1
0
2
1
1
1
1
2
1
2
2
2
1
2
1
0
0
1
2
1
1
1
1
1
2
2
2
0
1
2
1
2
1
1
2
1
2
0
1
1
1
1
2
1
0
1
1
1
2
0
1
1
1
2
1
0
2
1
1
1
0
2
1
1
2
1
2
1
2
1
0
1
1
2
1
1
2
1
1
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
3
1
2
1
1
1
0
0
1
1
1
2
1
0
1
1
1
0
1
2
2
2
1
1
1
1
1
2
1
1
1
0
1
1
2
1
1
1
1
1
1
1
2
1
2
1
0
1
1
1
0
2
0
1
1
0
1
2
1
2
1
1
0
2
1
1
2
1
1
1
2
1
1
1
2
1
2
0
1
1
1
1
0
2
1
1
0
1
1
1
1
1
1
1
2
0
0
1
2
1
1
1
2
1
2
2
2
1
1
1
2
1
1
1
2
1
1
0
1
0
1
0
1
0
1
1
1
0
2
0
2
0
2
2
1
2
1
0
0
2
1
2
1
0
0
2
0
1
0
1
1
0
1
1
1
1
0
0
2
1
1
1
2
1
1
0
0
1
0
2
1
2
2
1
2
0
1
1
1
1
2
4
1
2
1
2
0
2
1
0
2
1
1
1
1
1
2
1
1
1
2
1
2
0
1
0
1
1
0
1
0
0
1
1
1
1
1
1
1
1
0
1
2
1
2
2
1
1
1
2
1
1
2
1
1
0
1
2
1
1
1
1
0
1
1
0
1
1
0
1
1
1
1
0
1
1
1
2
2
1
0
0
1
0
1
1
1
2
1
1
0
2
1
1
2
2
0
2
2
2
1
0
1
2
2
1
1
1
3
2
2
1
1
2
1
2
2
0
1
1
1
2
1
1
2
1
2
0
0
1
1
1
1
1
1
2
2
1
1
1
2
1
1
1
1
2
1
2
1
2
1
1
0
1
1
2
0
0
2
2
0
2
1
0
0
0
2
1
1
2
1
0
0
2
1
0
0
1
1
2
2
1
1
1
1
1
1
2
2
1
2
1
2
1
1
1
2
0
1
0
1
1
2
1
1
1
1
2
1
2
1
1
1
0
1
1
1
0
2
1
1
1
1
1
0
2
1
1
1
1
2
0
1
1
0
1
1
1
2
1
1
1
2
1
1
0
2
1
2
1
2
1
1
1
0
2
1
2
1
0
1
2
1
0
1
2
1
2
2
0
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
2
1
0
2
0
1
1
1
1
1
2
1
1
1
1
1
0
2
1
1
1
1
2
1
1
1
2
1
2
1
1
0
1
0
1
2
1
0
1
1
1
1
2
2
0
1
1
1
2
1
2
0
1
1
2
1
0
1
1
0
1
2
1
1
1
0
2
2
1
0
0
2
1
2
1
1
1
0
1
1
2
1
2
2
1
0
1
1
1
0
1
0
1
1
1
1
1
1
1
1
1
1
0
0
0
1
2
1
3
1
1
0
1
1
1
0
1
2
0
1
1
2
2
3
1
1
1
2
2
1
1
1
1
1
1
2
1
2
1
0
1
1
2
2
1
1
1
1
0
1
1
1
2
2
2
2
1
1
0
3
2
1
1
2
0
2
1
1
2
0
2
1
1
1
1
1
1
1
1
1
0
1
2
1
2
1
1
1
2
0
1
2
1
1
2
1
1
2
1
0
1
0
2
1
0
1
1
1
2
1
1
1
1
1
1
0
1
1
0
1
2
2
0
1
1
1
2
1
0
1
1
1
2
1
0
1
2
0
0
1
1
3
0
1
2
2
2
0
2
2
2
1
2
1
0
1
2
0
2
1
1
2
1
1
0
0
1
1
1
0
1
2
2
0
1
2
0
1
1
1
1
1
2
0
0
0
1
0
0
2
0
1
1
1
1
0
0
4
1
1
2
1
0
1
0
1
0
0
2
0
0
0
1
0
2
1
1
1
1
1
0
1
1
2
0
2
1
0
2
0
1
1
1
2
1
1
1
0
2
2
1
1
1
1
1
1
1
2
1
1
1
0
1
2
0
2
0
2
1
1
1
1
1
2
2
1
2
1
1
2
1
1
1
1
0
1
0
1
1
1
0
1
0
0
1
1
1
2
1
3
2
2
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
2
1
1
1
0
1
1
2
1
2
0
1
1
2
1
1
1
1
1
1
0
1
1
1
2
1
0
1
0
2
1
0
1
2
1
2
2
1
1
1
1
0
0
1
1
1
0
1
1
1
2
0
1
2
1
1
1
2
1
1
2
1
1
1
0
1
1
0
2
2
1
1
2
1
1
1
1
2
2
1
1
1
1
2
1
1
2
0
0
0
1
1
2
1
0
1
2
2
1
2
2
0
0
2
1
1
2
0
2
3
1
1
1
1
0
2
1
2
1
2
2
1
1
2
0
1
0
0
0
1
1
1
2
2
2
1
0
1
1
0
2
1
2
0
0
1
1
1
1
0
1
2
1
1
2
1
1
1
1
1
1
0
0
0
0
1
1
0
1
1
1
1
1
1
1
1
0
1
2
3
1
1
1
0
1
2
1
0
1
1
1
1
1
1
1
0
1
2
1
1
2
1
1
1
1
1
0
2
0
1
1
1
1
0
2
0
2
1
1
1
0
0
1
1
2
2
1
1
1
1
1
0
1
1
1
0
0
1
1
1
2
2
1
1
1
1
0
1
0
1
1
1
0
1
2
1
2
1
1
1
1
2
1
1
1
1
1
0
2
1
0
1
1
1
1
1
1
1
1
2
2
1
0
2
0
2
0
1
1
2
1
1
2
2
1
2
0
1
1
0
2
1
0
1
1
1
0
0
1
1
0
1
0
1
2
0
1
1
0
1
1
0
2
1
1
1
2
0
0
0
1
1
1
0
0
1
0
1
1
1
1
2
1
2
0
1
2
2
1
0
1
2
2
1
0
2
1
1
1
1
1
0
2
0
3
1
1
1
1
1
1
1
1
1
1
2
2
2
0
0
2
2
2
1
2
1
1
2
1
1
1
0
0
1
2
1
1
0
1
0
0
1
1
2
2
0
1
1
0
0
1
1
0
2
2
0
1
1
1
1
1
1
1
1
2
1
2
1
1
2
0
0
1
1
0
0
0
0
1
1
1
0
2
1
1
1
1
1
1
0
2
1
1
1
1
0
2
0
1
1
1
0
2
1
1
0
1
2
1
1
1
0
1
1
1
1
1
0
1
1
2
1
1
2
1
1
0
0
0
2
1
1
2
1
2
1
1
1
2
0
2
1
1
0
1
1
1
1
0
2
2
1
1
0
0
1
2
1
1
2
1
0
1
2
0
1
1
2
1
0
1
2
0
0
1
0
0
2
1
2
2
1
2
2
1
1
0
1
2
0
2
0
1
0
1
0
1
1
1
1
1
0
1
0
2
1
1
1
1
2
1
1
6
2
1
2
2
1
2
0
2
0
0
1
1
1
1
2
2
1
1
2
2
0
0
2
1
1
1
2
2
1
2
0
1
1
1
0
1
1
2
0
2
1
2
0
2
1
2
2
1
1
1
1
1
0
1
1
2
1
2
1
0
1
0
0
1
1
0
1
2
1
1
1
1
2
2
1
1
0
1
1
2
1
1
1
1
0
1
2
1
0
0
2
1
1
2
1
1
0
0
1
1
2
1
1
1
2
1
2
0
1
0
1
2
2
2
2
1
1
1
0
1
1
1
1
1
2
1
1
0
1
2
1
0
1
1
1
1
1
1
1
1
2
0
1
1
2
1
1
1
0
0
2
2
0
1
2
1
1
1
1
1
1
2
1
2
1
1
0
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
1
1
2
0
1
1
1
0
1
1
2
1
1
0
0
2
2
0
0
2
1
1
2
1
1
1
2
1
1
1
2
2
1
1
2
0
1
1
1
1
1
1
1
1
0
1
1
1
2
1
1
1
0
1
2
1
1
2
1
0
1
1
2
1
0
1
1
1
1
3
1
1
1
1
1
1
1
0
1
1
1
2
1
1
1
2
0
0
1
1
2
2
1
1
2
1
1
1
2
1
1
1
1
1
0
1
1
2
1
1
2
2
0
1
1
0
1
0
2
0
1
2
1
2
2
0
0
1
0
1
1
1
1
1
1
0
0
1
1
1
2
1
1
1
1
1
2
1
1
0
1
2
0
2
1
1
1
1
1
1
1
2
0
2
2
1
0
2
0
2
3
1
1
1
0
0
1
0
0
1
1
2
1
1
1
1
2
1
0
0
1
2
1
0
2
1
2
1
1
1
1
1
2
0
1
0
2
1
0
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
0
0
0
1
1
2
1
0
1
4
0
1
2
2
1
1
1
1
7
2
0
0
1
1
0
1
2
1
2
0
1
0
1
0
1
0
0
1
1
1
1
1
1
0
1
1
2
1
1
0
2
0
0
0
0
1
1
1
1
1
0
1
1
1
0
2
2
2
0
1
2
2
1
0
1
1
0
1
2
0
1
1
2
2
2
1
2
2
1
1
1
2
2
0
1
1
2
2
2
0
0
1
1
1
1
1
1
1
1
0
1
1
2
2
1
1
0
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
2
0
1
2
2
1
2
1
2
2
0
1
0
1
1
1
2
1
1
1
1
1
1
1
2
0
0
1
0
2
1
0
0
0
1
2
1
1
1
1
1
1
1
0
2
1
1
1
1
2
0
1
1
2
1
1
1
1
0
2
2
1
0
1
1
0
1
1
1
0
1
2
0
1
1
2
0
2
0
1
1
1
1
1
2
1
0
3
2
1
0
1
2
1
1
0
1
1
1
1
2
1
1
1
0
1
1
0
0
1
2
2
1
1
1
1
1
1
1
2
1
1
3
1
1
0
1
1
0
1
2
1
2
0
1
2
1
1
1
1
2
1
1
2
0
1
1
0
1
1
1
0
1
2
1
0
1
2
2
2
1
0
1
1
1
2
1
0
1
2
0
1
0
1
1
5
2
0
1
1
1
0
1
1
1
2
2
0
1
2
0
2
1
1
1
1
2
1
1
1
2
0
1
1
0
2
2
0
1
1
0
1
1
0
1
1
1
0
1
1
2
0
1
2
1
0
2
1
1
1
1
1
2
1
1
2
0
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
2
1
0
1
0
1
2
1
0
1
1
0
2
1
0
1
0
3
2
0
2
1
1
1
1
0
2
1
1
0
1
2
1
1
2
1
2
2
2
1
1
1
1
1
1
1
1
1
0
1
1
1
1
0
1
0
1
1
1
1
1
1
2
2
1
1
1
1
0
1
1
2
1
1
0
1
1
0
1
2
2
0
0
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
0
0
0
1
0
1
1
1
2
1
0
1
1
1
1
0
2
1
2
1
1
2
1
2
1
1
1
2
0
1
1
2
1
1
2
2
1
2
0
1
1
0
1
1
0
1
1
1
1
2
1
0
1
1
1
1
0
2
1
0
1
2
0
2
1
1
1
2
2
2
2
2
1
1
1
1
1
1
2
1
1
2
1
1
0
1
1
1
1
0
0
2
2
0
1
1
1
1
0
1
1
1
1
0
1
1
2
1
0
0
2
1
1
1
1
1
1
2
1
0
2
1
1
2
2
0
1
2
2
1
2
0
2
1
0
0
3
1
0
1
1
0
0
2
1
1
1
0
1
0
1
0
4
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
1
1
1
1
1
2
0
2
1
2
0
2
2
1
1
1
1
1
2
1
1
1
1
2
2
0
0
2
2
2
1
2
1
2
1
0
0
1
0
1
1
0
2
2
1
2
2
1
2
1
1
1
2
1
2
1
1
1
1
1
1
2
1
0
0
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
0
1
2
1
1
1
0
2
0
1
1
1
1
1
0
1
1
1
2
1
2
0
1
1
2
1
2
1
1
1
2
2
1
0
0
1
1
2
2
0
2
0
2
2
1
1
1
1
1
2
1
1
1
1
1
1
0
2
1
0
2
0
2
2
1
1
2
1
1
2
2
1
2
2
5
2
1
1
0
1
0
3
1
1
1
1
1
0
1
1
0
1
1
2
0
1
2
2
0
1
1
1
1
0
2
2
1
1
2
0
2
0
2
1
1
0
1
0
2
1
1
2
1
1
1
2
0
1
0
2
1
1
1
0
2
1
1
1
1
1
1
0
1
1
0
2
0
0
1
2
1
1
2
0
0
2
3
2
1
2
1
0
0
0
1
0
1
2
0
0
2
0
1
2
1
1
1
1
1
2
1
1
1
0
1
1
1
2
1
1
2
1
2
0
2
0
1
2
1
0
2
1
3
0
0
1
0
0
2
0
1
1
2
0
1
2
1
0
1
1
1
1
1
1
2
1
0
1
0
1
2
0
1
1
1
1
1
2
1
1
0
1
2
2
1
1
0
2
1
0
2
1
2
2
1
1
0
1
2
1
2
1
2
1
2
0
1
0
1
1
0
0
0
1
2
1
1
1
2
1
1
2
1
0
2
2
1
1
2
2
1
1
1
2
1
2
1
1
1
1
1
1
0
2
1
1
1
1
1
0
1
2
1
1
1
1
1
2
1
2
1
2
1
1
1
0
1
1
1
2
2
1
1
0
2
0
1
1
2
0
1
1
1
2
1
2
0
1
2
2
1
2
0
1
0
1
0
1
1
0
1
1
1
1
1
1
1
1
2
2
1
2
0
1
0
1
0
2
2
1
2
1
0
1
2
2
1
1
1
0
2
1
0
1
1
1
1
2
1
1
1
1
2
1
1
2
2
2
0
2
0
1
1
1
1
0
1
1
2
1
1
1
0
1
0
1
1
1
1
1
2
1
1
1
2
0
1
0
1
0
1
1
0
0
1
0
1
1
2
1
2
0
0
2
2
1
1
1
2
1
1
2
0
2
1
2
0
2
2
1
0
1
2
1
1
1
1
1
1
1
1
2
1
2
1
2
0
1
1
1
0
1
1
1
0
0
1
2
1
1
1
0
1
1
1
0
2
1
0
0
0
1
0
1
1
1
1
2
1
1
1
2
1
1
2
1
2
1
1
1
2
2
0
1
0
1
1
2
1
0
1
1
2
1
0
1
2
1
0
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
0
2
1
2
0
2
2
0
1
0
1
1
1
0
1
2
1
1
2
0
2
1
1
0
1
1
1
2
1
2
1
0
1
1
2
0
0
1
1
0
1
1
0
1
1
1
0
1
1
0
1
1
1
1
1
0
1
1
0
0
2
0
2
1
2
0
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
0
0
1
1
1
1
1
1
0
1
1
1
1
0
1
1
1
1
0
0
0
1
1
1
0
1
1
0
1
0
1
2
1
2
1
0
0
1
2
0
0
1
2
1
0
2
1
1
2
1
0
1
2
1
1
2
0
0
3
1
1
0
1
1
1
2
1
1
1
1
1
1
1
1
1
2
0
0
1
1
1
1
2
1
1
0
0
1
0
0
1
1
1
1
0
2
1
1
1
1
1
1
0
0
1
1
1
1
2
1
2
1
1
0
1
1
1
1
1
1
1
0
1
1
2
0
1
1
1
1
1
1
0
1
2
0
1
1
2
0
1
1
3
2
1
2
1
1
1
1
0
1
1
1
2
0
1
0
4
2
2
2
0
1
1
1
2
0
1
2
1
0
2
1
1
2
1
1
1
1
0
1
1
1
0
1
0
1
1
1
1
0
2
1
1
0
0
1
1
2
1
1
1
1
2
0
0
1
0
0
1
1
1
1
2
1
1
1
1
1
3
1
0
1
0
1
2
1
1
1
1
1
2
2
1
0
1
2
1
1
0
2
0
0
2
1
0
1
2
2
1
2
1
2
1
0
2
2
1
1
0
2
1
0
0
1
2
2
0
1
2
1
1
2
1
1
2
1
1
1
1
1
2
1
1
1
3
0
2
1
1
1
1
1
0
2
1
1
0
3
1
1
1
2
1
1
1
1
1
1
1
0
1
1
1
2
1
1
1
1
0
1
1
0
1
1
1
1
2
0
2
3
1
0
1
2
1
1
1
0
1
1
1
1
1
1
1
0
1
0
1
1
1
1
1
1
0
1
1
1
1
1
2
0
0
1
1
1
1
1
1
1
1
1
1
0
1
0
0
1
2
2
1
1
0
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
2
0
1
1
1
2
2
0
2
2
1
1
2
1
1
1
3
3
1
2
1
0
0
0
1
0
2
2
1
2
0
2
1
1
0
2
0
1
1
2
0
2
1
1
2
2
1
1
1
2
1
1
1
1
2
1
1
1
2
1
0
1
0
1
1
1
0
0
0
1
2
1
2
3
2
1
0
1
1
0
0
1
1
1
2
1
1
0
2
2
1
1
2
0
2
1
1
0
0
1
1
1
1
1
1
1
1
1
1
1
1
0
2
1
1
2
1
0
2
1
1
0
2
0
1
1
1
1
1
0
1
1
0
2
2
1
2
1
0
1
0
1
2
1
2
2
2
1
2
1
1
1
0
1
1
0
1
0
2
1
1
1
0
1
2
2
1
1
1
1
2
0
1
1
1
0
0
1
1
1
1
1
2
1
0
1
2
1
2
2
2
1
1
0
0
1
2
2
1
0
2
0
0
1
1
0
1
2
2
1
2
1
1
1
2
2
1
2
1
1
1
2
1
2
0
1
2
2
2
1
1
1
0
1
1
2
2
1
1
1
1
2
1
2
1
1
1
1
1
0
2
2
1
1
1
1
1
1
2
1
2
2
1
1
0
1
2
0
3
1
1
2
1
1
2
2
1
2
0
2
0
2
1
0
1
1
1
0
2
1
1
1
2
0
1
1
1
1
1
2
1
1
1
2
1
2
1
0
1
1
1
0
1
1
2
2
0
1
1
1
1
1
1
1
1
1
1
0
1
2
1
1
0
0
0
1
1
1
2
1
0
0
1
1
3
1
0
1
1
1
0
1
2
0
0
1
2
1
1
1
1
0
1
2
1
2
1
1
1
1
1
1
1
0
0
2
1
2
1
3
1
2
1
2
0
0
1
0
1
0
1
0
1
1
1
1
2
4
1
1
1
2
1
0
1
1
0
1
2
2
1
2
0
0
1
2
2
0
0
1
1
1
2
2
1
2
1
1
1
2
0
2
3
0
2
1
1
1
2
1
2
1
1
1
1
2
0
1
1
1
0
0
2
1
1
1
2
1
2
1
1
0
1
1
1
1
2
1
0
1
2
1
1
0
0
1
2
0
1
0
2
2
2
1
2
0
1
0
2
1
2
1
1
0
1
2
2
2
1
1
1
1
1
1
1
1
1
1
1
2
0
1
1
1
2
1
2
2
2
2
1
2
1
1
0
2
2
1
1
0
1
0
2
1
2
1
2
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
1
1
1
1
0
2
2
0
2
1
1
1
1
1
2
1
0
2
1
1
0
2
1
1
1
1
1
1
1
0
1
2
0
1
0
1
1
1
2
0
1
2
0
2
1
2
1
1
0
1
1
1
1
1
2
1
1
2
1
1
2
1
1
2
1
0
2
0
2
1
0
0
1
0
1
1
1
2
1
3
1
0
0
1
1
0
1
1
0
1
1
2
1
1
0
1
1
1
0
2
1
1
0
0
2
1
1
1
1
1
0
2
1
2
1
1
1
0
1
1
1
1
2
0
2
2
2
1
2
1
0
0
2
0
0
0
0
1
0
1
0
1
1
2
1
1
1
1
1
2
2
1
2
1
1
1
0
1
0
0
1
2
1
2
2
2
1
0
1
1
1
2
1
1
1
1
1
1
1
0
1
1
0
2
1
0
0
1
2
1
1
1
1
2
1
0
2
2
0
1
2
0
0
0
2
1
1
2
1
1
1
0
1
0
2
1
2
0
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
4
1
2
1
1
0
0
1
1
1
1
1
1
0
2
0
2
1
1
1
1
1
1
1
1
3
1
0
3
2
1
0
1
1
1
1
2
0
0
2
1
2
1
0
2
0
2
2
0
1
2
1
1
0
0
2
2
1
1
1
1
3
0
2
0
0
1
1
0
1
2
1
2
1
2
1
1
1
1
2
2
1
1
1
0
1
1
2
1
2
1
1
1
0
1
1
1
2
0
2
2
1
1
1
1
2
0
2
1
1
0
1
2
2
1
0
0
0
3
1
2
1
0
2
2
2
1
2
2
1
1
2
1
1
0
1
1
1
7
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
2
2
1
1
1
2
0
1
1
1
2
1
1
1
1
1
2
1
0
1
0
1
1
2
1
1
1
1
2
5
1
1
0
1
0
1
1
1
1
1
1
1
1
1
1
0
1
1
1
2
1
1
1
2
1
2
2
1
1
2
2
0
2
3
0
0
1
1
1
1
1
1
2
1
1
1
2
2
1
2
1
1
2
2
1
1
1
2
0
0
2
1
2
2
1
1
1
1
0
1
0
0
2
1
1
0
2
1
1
1
1
1
0
1
0
1
1
0
1
1
1
1
1
1
1
1
0
0
2
1
1
2
1
1
1
0
1
2
1
1
1
1
2
1
1
1
1
1
0
0
2
2
1
1
1
1
2
2
1
0
1
1
1
1
2
0
0
1
1
1
0
2
1
1
0
1
0
1
2
2
0
1
2
2
1
1
2
2
1
1
1
2
1
1
2
1
1
1
2
1
1
1
1
1
2
1
1
1
1
2
2
2
2
2
0
2
2
1
1
1
2
1
1
1
1
2
1
2
0
1
1
1
1
1
3
1
1
0
1
1
1
1
1
1
1
1
1
0
2
1
2
1
1
0
0
1
1
2
1
2
1
1
0
2
2
1
2
1
1
1
2
2
1
1
2
1
0
1
0
1
0
1
1
1
1
2
1
1
2
0
1
1
1
1
1
2
2
0
1
1
1
1
0
1
1
1
1
0
2
1
1
1
1
1
0
0
1
0
2
1
0
1
0
1
1
1
1
1
2
1
1
1
1
0
1
1
0
1
1
2
2
0
2
1
0
2
1
1
1
2
1
1
2
1
1
1
0
0
1
1
1
2
1
2
0
7
2
1
1
2
2
2
1
0
1
1
0
3
1
1
0
0
1
2
1
1
1
0
2
2
2
1
0
1
0
1
1
1
0
2
2
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
0
0
2
2
1
2
2
1
2
1
1
2
1
1
1
1
1
2
1
1
2
0
0
0
1
0
1
2
0
1
0
0
0
0
1
1
2
1
1
0
1
1
1
1
0
1
1
1
1
1
2
1
0
2
1
1
1
1
0
1
1
1
1
2
1
1
0
1
0
1
0
1
2
1
2
1
1
2
1
0
0
0
1
1
2
1
0
1
1
0
1
2
2
1
1
0
0
2
1
1
0
1
1
1
1
2
1
1
2
1
1
0
0
1
2
0
2
1
2
1
1
2
1
2
2
1
2
1
1
1
0
2
0
2
2
1
1
1
1
2
1
1
0
2
1
0
1
0
1
0
0
1
1
0
1
1
2
1
1
1
0
2
1
0
2
0
2
1
2
2
1
0
2
2
0
0
2
2
2
2
1
1
1
2
2
1
2
0
0
1
1
1
1
1
0
1
1
1
0
1
1
1
1
0
1
1
1
1
0
0
0
0
2
1
2
1
1
0
0
1
1
1
2
2
0
1
2
3
1
1
2
0
1
0
1
1
0
1
2
1
0
1
2
1
0
1
1
1
1
1
1
2
0
1
0
1
2
1
1
2
1
2
1
1
1
0
2
1
1
2
1
1
0
1
1
2
2
2
1
0
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
0
2
0
1
2
1
1
1
1
1
1
0
0
2
2
0
2
2
2
0
2
0
1
1
1
2
2
2
1
1
1
1
1
2
0
2
1
1
1
2
2
1
1
1
1
1
1
1
1
0
1
1
1
0
2
0
1
2
1
0
1
2
1
1
0
1
1
0
1
0
1
1
1
1
1
2
1
1
1
2
1
0
1
1
1
1
2
1
1
1
2
1
1
0
1
0
2
2
1
1
1
1
2
1
0
1
2
1
0
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
0
1
1
3
1
1
1
2
0
1
1
1
1
2
1
1
1
1
2
2
1
1
1
0
2
2
1
2
2
1
1
1
1
0
1
1
1
1
1
1
2
3
1
1
0
1
1
2
1
2
2
0
1
1
1
1
0
1
2
1
0
2
1
1
1
1
2
2
1
0
1
2
1
1
1
1
1
2
1
1
2
1
0
2
2
0
1
2
1
2
1
1
1
0
1
1
1
1
0
2
2
1
0
0
1
3
2
1
1
1
2
1
2
0
2
1
1
1
2
2
2
1
1
1
0
0
1
1
1
1
1
1
1
1
0
0
0
2
1
1
1
2
1
1
1
2
1
1
2
0
1
1
0
2
1
1
2
0
1
0
1
0
1
1
1
2
0
1
1
2
1
1
0
2
2
1
1
0
1
2
1
2
0
2
2
0
2
1
0
0
1
1
1
1
1
1
1
0
1
2
1
1
0
0
1
1
1
1
1
2
0
1
2
2
2
1
2
1
2
1
1
1
1
2
1
1
1
1
1
2
1
0
1
2
1
0
5
1
0
0
1
1
1
1
1
0
1
1
2
1
2
2
1
1
1
1
1
2
1
0
0
1
1
1
2
1
0
0
1
2
1
1
1
0
2
1
1
2
0
0
0
2
1
1
1
1
1
1
1
0
1
0
2
1
1
2
0
1
2
1
1
1
2
0
2
0
1
2
0
1
1
1
2
2
2
1
1
1
2
1
1
1
2
1
2
1
1
2
1
1
0
2
1
0
2
1
1
0
0
0
2
1
1
1
2
1
0
1
1
1
2
1
1
0
1
2
1
1
0
2
1
1
1
1
2
1
2
2
0
2
0
1
0
1
1
1
1
1
1
1
1
1
0
1
1
2
1
0
2
1
0
0
1
1
2
2
1
1
1
2
1
1
1
1
0
1
0
1
1
1
0
1
1
1
1
2
2
0
1
1
1
0
1
1
1
1
1
2
2
1
1
0
1
0
1
1
1
1
0
2
1
0
1
1
1
1
2
2
1
1
2
1
1
2
1
1
1
2
2
1
1
1
1
1
1
2
2
1
1
0
1
0
0
1
1
0
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
0
2
0
1
1
0
0
1
2
1
0
2
2
1
2
1
2
1
2
0
1
1
0
1
2
0
1
1
0
2
1
1
1
2
0
2
1
0
2
2
1
1
1
1
1
1
2
2
0
1
1
2
2
0
2
1
1
1
2
2
1
1
1
1
2
0
1
1
0
1
1
2
2
1
1
1
1
1
1
0
1
3
1
0
1
1
2
1
1
0
1
1
1
1
1
1
0
2
0
1
2
1
1
1
1
1
1
0
2
1
1
0
0
0
1
0
1
1
1
1
1
1
1
2
1
1
1
1
2
2
2
1
1
1
1
1
1
2
1
0
1
1
1
1
1
1
2
1
1
1
1
3
1
1
1
0
2
0
1
1
0
2
0
2
1
1
1
1
1
1
1
2
0
1
2
1
1
1
2
1
2
0
1
1
0
1
0
1
2
2
1
1
0
0
0
2
2
2
1
0
0
2
2
2
0
1
1
1
1
1
0
2
1
1
1
0
2
2
1
2
2
1
1
2
1
0
1
2
0
0
0
0
0
1
1
1
1
1
0
2
2
1
0
1
1
0
1
1
2
1
1
2
1
1
2
2
0
0
1
1
1
1
2
1
2
1
2
3
1
0
1
1
1
1
2
0
1
1
1
1
2
1
1
4
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
0
1
1
1
1
1
0
1
1
1
1
1
0
1
2
1
1
1
0
1
0
1
1
1
1
0
2
1
1
1
2
1
3
1
1
2
1
1
1
1
0
2
2
1
1
1
1
0
1
1
1
1
1
0
1
1
1
1
1
1
1
2
1
1
0
1
0
1
0
1
1
1
0
1
1
1
1
1
1
1
1
1
1
2
2
0
1
0
0
2
2
1
1
1
1
0
2
1
2
1
0
0
2
0
1
1
2
1
1
1
0
1
1
1
1
2
2
1
1
1
0
0
0
1
1
1
0
1
1
0
1
1
1
1
1
0
1
1
1
1
0
1
0
2
2
1
2
1
2
0
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
2
0
2
1
2
1
1
0
1
0
1
1
1
2
0
1
1
2
1
1
1
2
2
2
1
1
2
1
0
1
1
1
0
2
1
1
1
1
2
1
1
2
2
0
1
2
2
1
1
1
0
1
1
1
1
1
1
2
0
0
2
1
2
2
0
2
1
0
0
2
1
1
2
1
0
0
1
1
0
1
1
0
1
1
1
2
0
1
2
1
1
0
1
2
1
1
2
2
2
2
1
1
1
2
1
1
1
1
2
1
2
0
1
0
1
1
0
2
1
1
0
0
1
2
1
0
1
0
2
0
1
2
1
1
0
2
3
1
0
1
0
1
0
2
1
1
1
2
2
1
2
1
2
1
1
1
0
1
1
1
0
1
1
1
0
2
1
2
1
1
0
0
2
2
1
0
2
1
1
3
1
2
1
2
2
1
0
1
2
0
1
0
1
0
1
1
0
1
1
1
2
1
1
1
0
0
0
1
2
0
1
0
0
1
1
1
1
1
1
1
2
1
0
0
1
1
1
0
1
2
2
2
0
1
2
0
0
1
1
2
1
0
1
2
1
1
0
2
1
1
1
1
1
1
0
1
1
0
2
1
0
1
1
0
2
1
1
2
0
1
2
1
0
1
2
1
1
1
1
1
1
1
2
1
0
1
1
0
1
1
1
1
2
2
2
2
1
2
1
1
0
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
0
1
1
1
0
1
1
0
1
1
1
1
1
1
2
1
1
1
1
1
1
1
0
1
1
1
0
2
0
2
1
1
1
0
2
1
0
2
1
1
1
2
1
1
1
1
1
0
2
2
1
2
2
1
1
1
0
1
1
1
2
1
1
0
0
0
0
0
2
0
1
0
2
0
1
0
1
1
1
1
1
2
1
2
1
2
1
5
1
1
1
2
2
1
0
2
2
1
3
1
2
2
1
1
1
2
2
2
0
2
1
0
1
1
0
2
2
1
1
1
1
1
0
1
1
0
2
1
1
0
1
0
1
0
1
1
1
2
0
2
1
1
2
2
2
1
1
1
1
1
2
1
1
2
1
1
1
1
0
0
0
2
0
2
1
1
1
2
1
1
2
1
1
1
1
1
0
1
0
0
2
0
1
1
2
0
0
1
1
1
1
1
1
2
0
0
1
1
1
1
0
1
2
1
1
1
2
0
1
1
2
0
2
2
2
1
1
1
1
1
2
0
0
1
1
1
0
1
1
2
1
2
1
1
1
2
1
1
1
2
1
0
2
1
1
2
1
1
0
1
1
1
1
1
1
0
1
1
0
1
1
0
1
0
2
2
1
1
2
1
1
1
1
1
1
1
0
0
1
1
1
1
1
1
1
2
1
1
1
2
2
2
0
2
1
1
1
1
1
1
2
0
0
0
1
2
2
2
1
1
1
1
1
1
2
0
1
2
0
1
0
1
1
2
0
2
1
0
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
1
1
0
1
2
1
1
1
1
0
2
1
1
1
2
1
1
2
2
0
1
2
1
2
0
1
0
2
2
0
0
2
1
1
2
2
2
1
1
0
1
2
1
1
0
0
1
1
1
1
1
2
1
0
1
1
0
1
1
1
0
1
1
2
2
0
1
1
1
0
1
0
1
2
1
1
0
1
1
1
0
2
0
0
1
1
2
0
1
1
2
1
1
2
2
2
1
1
1
1
1
2
2
0
2
2
1
1
1
1
2
1
0
2
2
2
1
2
1
0
2
1
1
1
1
1
1
2
0
1
0
1
1
0
0
1
2
1
1
0
1
0
0
2
0
1
1
0
1
2
1
0
2
2
1
2
1
0
0
1
1
1
2
2
0
1
1
0
1
1
1
1
1
1
1
1
1
2
1
1
3
1
0
1
1
1
1
1
1
2
1
1
1
0
0
0
1
1
1
2
1
1
1
2
1
0
2
1
1
1
1
2
0
1
1
1
1
1
2
3
1
0
2
1
1
1
2
3
1
2
2
1
1
1
1
1
1
1
2
1
2
0
2
1
2
1
2
1
2
1
0
1
1
2
0
1
0
0
0
1
1
0
1
2
1
0
2
0
2
2
1
0
1
2
0
1
2
1
1
2
2
0
2
2
0
1
2
2
1
1
1
2
1
1
1
2
1
2
1
1
2
1
2
2
1
2
1
1
1
1
1
1
2
0
1
0
1
0
2
1
1
1
1
2
2
1
0
1
2
1
3
1
1
1
1
1
2
1
1
2
1
1
1
1
1
2
2
2
2
1
2
1
2
2
2
1
1
2
2
1
1
2
0
1
2
2
1
1
1
2
0
1
1
1
2
1
1
2
2
1
1
1
1
1
0
0
1
2
1
1
1
1
1
1
1
1
1
0
1
1
1
1
0
0
0
2
2
0
2
0
2
2
2
0
2
1
0
1
2
1
0
1
1
1
1
2
1
1
1
2
1
1
0
1
1
2
2
0
0
1
1
1
1
3
0
1
1
1
1
1
0
0
1
0
1
0
1
2
2
2
1
2
1
1
0
1
1
2
1
1
1
1
1
2
1
2
2
1
0
1
1
2
0
1
2
1
2
1
1
1
0
0
1
2
0
1
1
1
1
1
1
1
0
1
1
0
1
1
2
1
1
0
1
2
1
1
0
1
1
1
1
1
1
2
1
2
1
1
1
1
1
2
2
1
0
1
1
2
0
2
1
1
2
1
1
2
1
1
1
1
0
1
2
2
1
0
1
1
1
1
1
0
2
1
1
1
0
1
1
1
1
1
0
1
0
1
1
1
2
1
2
0
1
0
2
1
1
0
1
1
1
1
1
1
0
1
0
2
2
1
1
1
1
1
1
1
2
0
2
0
2
1
2
1
0
2
1
4
0
1
1
0
1
1
1
2
1
0
2
1
0
2
2
0
2
2
1
2
1
0
1
1
0
1
2
1
1
1
0
2
0
2
1
1
1
2
0
1
1
1
1
2
0
1
2
2
1
1
0
1
1
1
2
1
1
0
1
1
1
0
1
1
0
1
0
0
0
1
1
1
0
0
2
1
2
2
1
2
1
1
2
1
1
0
2
2
1
2
2
1
1
0
2
0
2
1
2
2
1
1
2
2
1
0
1
0
2
2
1
1
1
1
1
0
1
1
1
1
1
1
1
2
1
2
1
1
1
1
0
2
0
1
1
2
0
1
1
1
1
2
1
1
1
1
1
0
1
1
0
2
0
2
0
1
0
1
1
1
1
1
1
1
1
1
2
2
0
1
1
1
1
0
1
2
2
1
1
1
1
1
1
2
0
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
0
0
1
1
2
1
1
1
0
1
1
1
1
1
1
2
2
1
2
1
2
1
1
1
1
1
1
1
1
2
0
2
1
1
1
1
2
1
1
2
1
3
2
0
2
1
0
1
1
1
1
1
1
2
2
0
0
1
1
1
1
2
2
2
1
1
1
0
1
1
2
0
0
1
2
0
1
2
1
1
0
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
0
2
1
0
1
1
0
1
1
1
1
1
0
1
1
1
1
3
1
1
1
2
0
0
1
0
1
0
0
1
1
1
0
2
1
1
1
2
1
1
2
1
0
1
2
1
1
2
0
0
0
1
0
1
1
0
1
1
0
1
0
1
1
1
1
1
2
1
1
1
1
1
2
2
1
1
0
2
1
1
1
1
0
0
1
1
1
0
2
1
2
1
1
1
2
0
1
1
0
2
1
0
1
1
2
0
3
1
0
1
0
1
1
1
1
1
1
2
1
1
0
2
1
1
1
1
1
0
1
1
1
1
1
1
0
1
2
0
2
1
1
2
1
1
1
0
1
1
1
1
2
2
1
1
1
0
0
0
0
2
1
2
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
2
0
2
0
2
2
0
0
1
2
1
1
2
1
1
2
1
2
0
1
2
1
2
1
2
1
2
1
2
1
0
2
0
0
1
2
0
0
1
1
0
1
1
1
1
1
1
2
2
2
1
1
2
1
2
0
0
1
1
2
0
1
1
1
2
0
1
1
0
2
1
0
2
1
0
0
1
1
1
2
2
0
1
2
2
1
1
1
0
0
2
1
1
1
1
2
2
0
0
1
0
2
0
1
1
1
0
1
0
0
1
1
1
1
1
2
1
0
1
0
2
1
2
2
1
1
2
2
0
1
1
2
1
1
0
1
2
1
1
1
1
1
3
2
2
0
2
3
0
1
1
2
1
1
1
3
1
1
2
0
0
1
1
2
0
1
1
1
0
0
2
1
1
0
2
0
1
0
1
0
0
0
2
2
1
1
1
1
1
0
0
1
1
0
1
1
2
0
2
1
0
1
1
2
1
2
1
2
1
1
2
1
0
2
1
2
2
0
1
1
2
2
1
0
2
0
1
1
1
1
1
1
1
0
0
1
1
1
0
2
1
1
0
1
1
2
0
2
1
2
1
1
2
2
2
1
0
2
1
1
2
1
1
1
1
1
0
1
1
1
0
1
0
2
4
2
2
1
2
1
1
1
1
1
0
1
1
0
0
2
2
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
1
2
1
1
1
2
0
1
1
1
2
1
1
2
1
1
1
1
1
2
2
0
2
0
1
1
2
2
1
1
1
0
2
1
1
2
1
2
0
2
2
1
2
1
2
2
2
1
1
2
1
1
0
1
2
0
1
2
2
1
1
1
1
0
2
0
0
0
2
2
1
1
1
0
1
0
0
1
0
1
2
2
1
1
1
1
0
2
2
1
1
1
1
1
2
1
1
1
1
0
1
1
1
1
2
1
0
1
2
2
1
0
1
1
0
1
1
1
0
2
2
1
1
2
1
1
0
2
1
0
1
1
1
1
0
1
2
1
1
0
0
1
1
1
1
1
1
1
1
2
1
2
1
1
2
1
2
0
2
0
1
0
0
1
0
1
1
1
2
0
1
2
1
1
1
1
1
0
2
2
0
1
1
1
2
0
1
1
0
2
0
1
2
2
2
0
2
0
1
1
1
0
1
2
2
2
1
0
0
1
2
2
0
1
1
2
1
0
1
1
1
0
1
2
1
1
1
1
0
1
1
1
2
2
0
1
2
0
1
2
1
1
1
0
1
1
0
1
1
0
2
2
1
1
2
2
0
2
0
1
1
2
2
1
2
0
0
2
1
1
1
1
1
0
2
1
0
0
1
1
1
1
1
2
2
2
2
1
1
1
0
1
2
0
1
1
1
2
1
1
1
1
2
1
1
2
1
0
1
2
1
2
2
0
0
1
2
2
1
2
1
1
1
2
1
2
1
0
2
1
2
1
1
1
1
2
1
0
1
0
0
0
1
1
2
2
1
2
1
3
0
1
2
1
2
1
1
1
1
0
1
2
1
0
1
0
1
2
1
0
1
1
1
1
0
1
1
0
1
1
1
0
2
2
1
2
0
2
1
2
1
1
0
2
1
1
1
1
1
0
1
2
1
0
0
2
1
1
1
0
0
2
0
1
2
1
1
1
1
0
0
1
1
1
1
1
0
2
1
2
1
0
1
0
1
2
1
0
0
0
1
2
1
0
2
2
0
2
1
0
1
1
0
1
2
1
1
1
1
3
1
0
2
0
1
2
1
0
0
0
2
1
1
0
1
1
1
2
2
1
0
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
0
0
0
2
1
1
1
2
1
1
1
1
0
1
1
1
1
1
1
1
1
2
1
2
0
2
0
1
1
1
2
0
1
0
0
2
1
1
0
1
1
1
2
1
1
2
1
0
1
1
1
2
2
1
1
1
1
1
2
2
1
2
2
0
1
0
2
1
1
1
1
1
2
1
2
2
2
1
0
2
0
2
1
1
1
0
1
1
2
1
2
0
0
0
1
2
0
1
1
0
0
0
0
1
0
2
2
2
1
1
2
2
1
1
1
1
2
2
1
1
2
1
2
1
1
0
1
1
2
1
1
1
3
0
2
1
2
2
2
1
2
1
1
1
0
0
1
1
1
2
1
1
1
1
2
1
2
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
0
1
2
1
2
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
0
1
2
2
0
1
1
2
2
1
2
0
2
1
1
0
0
1
1
0
1
2
0
1
1
1
1
1
2
0
2
1
1
1
1
2
2
0
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
2
0
12
1
0
2
2
1
1
1
2
1
1
1
1
0
2
1
1
1
1
1
2
2
2
1
1
0
1
1
0
1
1
1
1
0
2
2
0
1
0
1
1
2
1
1
1
0
1
1
2
0
2
1
1
1
0
1
1
1
1
1
1
2
2
2
1
1
1
2
0
1
1
0
2
1
2
0
1
1
1
0
2
0
1
1
0
1
2
0
1
1
0
1
1
0
1
1
2
1
2
2
1
1
1
1
1
2
1
1
1
0
1
2
2
1
1
1
2
1
1
1
1
0
1
1
1
2
0
1
1
1
2
0
1
1
1
2
1
0
0
1
1
1
1
0
1
0
1
2
2
1
0
1
1
1
1
1
2
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
0
1
1
1
1
1
1
2
1
0
2
1
1
1
1
1
4
2
2
1
2
0
1
1
1
0
1
1
0
1
2
1
0
1
1
1
1
1
1
0
1
0
0
2
1
1
1
2
2
1
2
0
1
1
1
1
1
0
1
1
1
1
1
1
2
1
0
1
0
1
1
1
1
0
1
0
1
2
2
1
2
1
2
1
1
2
0
1
1
1
0
1
0
2
2
1
2
2
1
1
1
0
1
1
1
2
1
1
1
1
3
0
1
2
1
0
1
1
1
1
2
1
1
1
1
2
1
1
1
1
0
2
1
2
0
1
0
1
2
1
1
0
0
1
1
0
2
2
2
1
2
0
1
2
1
1
1
0
2
0
1
1
1
0
1
2
1
1
1
1
1
2
1
1
2
1
1
0
1
0
1
2
1
2
1
1
2
2
1
1
1
1
1
1
2
1
1
2
0
1
2
1
1
1
1
0
1
2
1
1
1
2
1
1
0
1
1
1
0
0
1
2
1
1
1
2
0
1
1
2
2
1
1
1
1
1
1
2
2
2
2
0
2
1
2
0
1
1
1
2
1
1
0
1
1
1
1
2
2
1
1
1
1
1
2
0
2
1
0
1
1
2
1
1
1
1
1
1
1
1
1
0
1
2
1
1
1
1
1
0
1
1
1
1
2
1
1
1
2
2
1
0
1
1
1
1
1
2
1
1
0
1
3
0
1
1
2
2
1
0
1
0
1
2
0
1
1
2
1
1
1
1
1
0
1
1
0
2
0
2
2
1
1
1
1
1
1
1
0
2
1
1
1
2
2
1
0
2
0
2
1
1
1
0
1
1
1
0
1
0
1
1
1
1
1
2
2
1
2
0
1
1
1
2
1
2
0
1
6
2
1
1
1
2
0
2
0
0
1
0
2
1
0
1
1
1
1
2
1
1
1
1
0
1
1
0
0
1
2
1
2
0
2
2
2
1
1
2
2
1
1
1
1
1
1
0
0
0
1
1
1
1
1
1
0
0
1
1
1
2
0
1
1
1
0
1
0
1
0
1
2
3
1
1
1
1
1
1
0
1
2
1
1
1
1
2
2
1
0
2
0
2
2
1
1
2
0
2
1
1
1
1
0
0
2
2
0
1
2
2
2
0
1
0
3
0
2
0
1
0
1
1
1
0
2
1
5
1
1
0
2
2
2
1
1
2
1
2
1
1
1
0
2
1
2
1
1
0
1
0
1
1
1
1
2
0
0
2
1
1
1
2
1
1
2
2
2
1
1
2
0
2
2
2
2
1
2
2
0
1
1
1
0
2
0
1
2
0
1
1
2
1
1
2
1
2
1
2
0
1
1
1
2
1
1
1
2
0
1
1
0
1
1
0
1
1
2
1
1
0
0
1
0
2
0
2
1
1
2
1
1
1
1
1
0
1
0
1
1
1
1
0
0
1
1
1
1
2
1
2
2
1
1
2
1
1
2
0
2
1
1
0
1
1
1
0
2
0
1
1
2
1
1
1
1
1
1
2
1
0
2
1
1
1
1
0
0
2
1
0
2
1
1
1
1
1
0
0
0
1
1
2
0
1
1
1
1
1
0
2
1
1
0
1
1
1
2
1
2
1
0
1
1
0
0
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
2
1
2
1
1
1
1
0
1
2
0
1
1
1
2
1
1
1
1
1
2
1
2
0
1
1
2
2
1
1
1
0
1
2
1
0
1
1
0
1
2
0
0
1
0
2
1
1
0
3
1
2
1
0
1
2
1
2
9
1
1
2
1
2
1
1
2
1
1
2
1
1
0
1
1
1
1
1
2
1
1
0
1
1
2
0
1
0
1
0
1
1
1
1
0
2
1
1
1
1
0
3
1
1
1
0
1
1
2
1
1
1
2
1
1
1
0
1
2
1
2
1
1
2
1
1
1
2
1
1
1
1
1
0
1
2
1
0
1
1
0
1
1
1
2
1
1
1
2
1
2
1
2
1
1
0
1
2
1
0
1
1
1
3
0
1
1
6
2
1
0
1
2
1
1
0
2
0
1
1
1
1
1
1
2
0
0
2
1
2
1
1
2
1
1
1
0
2
1
1
0
1
1
2
1
0
1
1
1
2
1
1
1
1
2
2
2
1
1
1
1
0
1
0
2
0
1
1
1
1
1
2
1
1
1
2
1
1
2
1
0
2
0
2
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
2
2
1
1
0
2
2
0
1
0
0
1
0
1
1
1
1
1
2
2
1
2
2
1
2
2
1
2
1
1
2
1
1
2
0
3
0
1
1
1
0
1
1
1
3
2
1
2
2
2
2
3
0
1
2
1
1
1
0
2
1
0
1
1
2
2
1
0
2
1
1
1
0
2
2
1
3
1
0
2
2
1
1
1
1
5
2
1
1
1
1
1
1
1
0
1
2
0
1
1
1
1
0
2
2
1
2
2
1
0
2
0
0
1
2
1
1
1
0
1
0
1
1
1
1
0
0
1
1
1
1
1
1
0
1
1
1
0
2
2
0
1
1
2
2
1
0
1
1
2
1
1
1
2
1
2
1
1
0
1
1
0
1
1
2
2
1
1
1
1
1
2
1
1
1
1
1
1
2
2
1
0
1
1
1
1
0
1
1
2
1
1
1
1
0
1
2
1
1
1
0
2
1
1
1
1
1
2
1
1
1
1
1
3
0
2
0
1
1
2
1
2
2
1
2
2
2
1
0
0
1
2
1
2
2
1
1
1
1
1
3
1
1
0
1
2
1
1
1
1
0
2
2
1
2
1
0
0
2
1
1
2
1
2
1
1
1
1
1
1
2
1
1
2
1
1
2
1
1
2
2
0
1
2
2
1
1
1
1
1
1
1
0
1
0
2
2
1
1
1
1
0
0
1
2
1
0
2
1
1
1
1
0
1
1
1
2
1
1
1
1
1
2
2
0
2
1
2
0
1
2
2
1
0
1
0
1
1
1
1
1
1
1
0
1
0
0
0
0
1
1
2
1
1
2
1
1
2
2
2
1
2
1
2
1
0
0
2
2
0
1
1
1
0
1
1
0
1
1
1
0
1
1
1
0
1
1
0
0
2
1
0
1
2
1
1
1
1
1
1
1
1
1
1
2
0
2
0
0
1
0
1
0
0
1
2
0
1
2
2
0
2
2
1
2
2
1
2
1
1
1
1
1
1
2
2
1
1
1
2
1
1
1
1
0
1
1
2
0
1
2
1
0
1
0
2
2
1
1
0
1
2
1
2
1
1
1
2
1
0
1
1
1
0
2
1
1
1
1
2
0
1
0
1
1
1
2
2
2
1
2
0
2
0
1
0
1
1
1
1
1
1
2
0
1
1
1
1
0
2
2
0
1
2
1
0
1
1
2
1
0
1
1
1
1
0
1
1
1
1
0
2
2
2
1
0
1
1
1
0
1
1
1
2
0
1
2
0
0
1
0
1
1
0
0
0
1
2
2
2
1
1
2
1
2
2
0
1
1
1
1
1
2
0
2
1
1
1
2
1
1
2
1
0
0
0
2
1
1
1
0
2
1
1
0
1
2
1
2
0
1
0
1
0
0
2
4
2
1
2
2
1
1
2
1
1
1
2
1
2
1
0
0
1
1
1
1
1
1
1
1
2
1
1
2
2
1
2
1
1
1
2
1
0
2
0
2
2
1
1
1
2
1
0
2
2
1
1
2
2
1
1
1
2
1
1
0
2
1
1
2
0
1
1
2
1
2
1
1
1
1
1
0
1
0
2
1
2
0
0
1
2
1
0
1
1
0
2
1
1
1
2
0
2
1
2
1
1
0
2
2
1
0
2
2
2
0
1
1
2
2
1
2
1
0
1
0
1
2
2
2
0
2
2
1
0
0
2
0
1
0
0
2
1
0
0
1
1
2
2
0
1
2
1
1
1
1
1
1
2
1
1
1
1
0
1
1
2
2
1
2
2
1
1
1
1
1
1
1
1
1
1
2
0
1
1
2
2
2
1
0
1
1
1
2
1
1
0
1
1
1
1
1
2
0
2
1
1
1
2
1
2
1
1
2
2
1
1
1
2
0
1
2
0
1
0
1
0
0
1
1
0
2
2
1
0
1
1
0
1
2
1
1
1
2
0
0
1
1
1
2
0
0
1
1
0
1
0
2
1
0
0
1
0
1
1
1
2
1
0
2
1
0
1
2
0
2
2
4
0
1
1
1
0
2
1
0
1
1
2
2
0
0
1
1
2
1
1
1
1
2
1
2
1
0
1
2
2
1
1
2
1
1
1
0
2
2
1
1
1
1
1
1
1
1
0
0
1
1
1
1
0
2
1
2
1
1
2
2
0
1
1
1
1
2
2
1
1
1
1
1
1
1
0
1
2
1
1
0
1
1
2
0
2
0
2
1
1
0
1
2
0
1
2
1
1
2
1
1
1
1
1
1
2
2
1
0
2
1
0
1
0
1
1
1
0
0
0
1
1
1
0
1
1
1
0
1
0
1
1
1
1
2
1
2
1
1
1
2
1
1
1
1
1
2
1
2
2
1
1
1
1
2
1
1
2
1
1
1
1
1
0
0
1
1
0
0
1
0
1
2
1
1
0
1
1
1
1
0
0
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
0
1
1
1
1
1
1
0
1
0
0
1
2
0
2
1
2
1
2
1
1
1
1
1
1
1
1
0
2
0
2
1
1
1
2
2
1
1
2
1
0
1
0
0
1
0
1
1
2
1
2
1
1
1
1
0
1
1
1
3
0
0
3
2
1
1
1
0
1
1
2
1
2
2
1
1
0
1
1
1
1
1
1
2
1
2
0
1
1
2
2
2
1
1
1
0
1
2
2
1
1
1
0
1
2
2
1
2
1
2
0
1
0
2
2
0
1
0
2
1
1
0
0
1
2
1
1
0
1
2
2
1
0
0
1
1
0
0
2
2
1
1
1
2
0
1
1
1
1
6
1
1
2
1
0
1
1
1
2
2
1
0
0
1
2
1
1
1
1
0
1
1
1
0
2
1
0
2
1
1
1
1
2
1
2
1
1
1
2
1
1
0
1
0
1
0
1
1
1
0
1
1
1
1
2
2
2
1
0
1
2
2
1
1
0
0
1
2
1
0
1
1
0
0
1
0
1
2
1
0
1
1
1
2
1
1
1
1
0
1
1
1
0
1
1
1
1
1
1
1
1
2
0
1
2
1
2
2
1
1
1
1
1
1
2
1
1
2
1
1
1
2
1
1
0
1
1
0
1
2
1
1
0
1
1
2
0
1
1
2
1
1
1
1
1
1
3
1
1
1
2
3
0
2
1
1
1
1
1
1
1
0
0
1
1
2
1
1
2
1
1
1
1
1
1
1
1
0
2
0
1
2
1
0
1
1
0
0
0
0
1
2
0
1
1
2
1
1
1
0
0
0
1
1
1
1
1
1
2
0
1
2
1
1
1
0
5
0
2
1
1
1
0
2
1
1
0
1
2
2
2
0
1
1
0
1
2
2
1
0
1
1
1
1
0
1
1
2
1
1
1
1
1
0
2
2
2
1
1
1
1
0
0
1
1
1
0
1
1
1
1
2
2
1
1
1
1
1
0
0
1
1
1
1
2
1
1
0
1
0
1
1
1
1
0
2
1
1
1
0
2
2
2
1
1
1
1
0
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
0
1
0
1
0
1
1
0
2
2
1
0
1
1
0
2
1
2
2
1
0
0
0
2
0
1
2
1
1
2
1
1
1
0
1
1
2
1
2
0
2
1
2
2
1
1
2
2
1
1
0
0
1
1
2
1
1
2
1
2
1
0
0
0
1
1
1
1
1
1
0
0
2
1
2
1
1
1
1
2
1
1
1
0
2
1
1
2
3
1
2
0
1
1
1
2
3
1
2
2
1
2
1
0
0
1
1
1
1
0
1
2
1
0
2
2
0
1
1
1
1
0
1
1
2
2
1
1
1
0
1
0
2
0
1
1
1
1
0
2
1
1
2
2
1
1
1
0
1
0
1
1
0
1
1
0
1
2
2
1
0
1
2
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
2
1
1
0
0
2
1
0
1
1
2
1
1
0
2
1
3
1
3
2
1
1
1
1
1
1
1
1
1
1
0
1
1
2
1
1
0
1
1
1
2
2
1
1
3
1
1
2
2
1
1
1
1
2
0
2
1
1
1
2
2
2
2
1
1
2
0
1
1
1
0
2
1
0
2
2
0
1
1
1
1
2
2
0
2
2
2
1
1
1
1
1
1
1
1
2
2
1
1
1
1
2
1
0
1
2
1
0
2
1
0
2
0
0
2
1
0
0
0
0
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
0
1
2
1
3
0
1
0
1
2
1
2
1
1
1
1
2
1
0
2
1
1
1
1
1
2
1
0
1
0
1
1
1
1
1
1
2
2
1
1
1
1
0
1
0
0
1
1
1
0
0
1
1
1
2
0
1
1
2
1
0
1
2
0
2
0
1
1
1
1
1
2
1
0
0
1
1
2
2
2
0
1
1
1
1
1
1
1
1
0
0
1
1
2
1
1
1
0
1
1
1
1
2
1
0
1
1
1
2
2
0
1
2
1
1
2
1
1
1
2
1
1
1
1
0
0
2
1
2
0
0
0
1
2
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
0
1
2
1
1
1
2
0
1
1
0
0
1
1
0
1
1
1
1
1
2
0
2
1
1
1
1
1
2
1
0
1
1
2
0
1
0
0
1
1
1
1
1
1
0
1
1
0
2
1
1
0
1
2
2
0
1
1
1
1
1
1
0
2
2
1
1
1
1
2
1
1
0
1
1
1
1
2
0
0
0
1
0
1
2
1
0
1
1
1
1
2
1
0
0
1
1
0
2
1
1
1
2
2
0
0
1
0
1
1
1
0
2
1
0
1
1
1
1
2
0
2
1
2
0
1
2
1
1
0
2
2
1
1
1
1
2
1
1
1
2
0
2
1
2
1
1
1
0
1
1
2
1
0
2
2
2
1
1
2
1
1
2
1
0
2
0
1
2
1
2
1
1
1
1
1
0
0
1
1
1
0
2
2
1
2
1
1
1
1
0
1
1
1
1
0
0
1
1
1
1
1
0
0
2
1
1
1
1
1
0
1
1
1
0
2
1
2
1
1
1
1
2
1
2
0
1
1
0
1
2
1
2
1
1
4
0
1
1
2
2
0
2
0
1
0
0
1
1
2
1
1
1
0
2
1
2
2
1
0
1
1
1
1
0
2
1
1
1
1
1
2
3
2
1
1
1
2
2
1
2
1
1
1
1
0
2
1
0
2
2
1
0
1
0
0
1
0
2
1
2
2
1
2
1
1
1
1
1
0
1
1
1
1
1
1
2
1
1
2
2
2
1
3
1
2
2
2
1
2
2
2
2
1
2
1
1
2
2
0
1
2
1
1
1
1
2
1
2
0
2
1
1
2
1
1
0
1
1
1
0
0
1
1
1
1
1
1
0
1
0
1
1
1
0
1
2
1
0
1
1
0
1
1
1
1
1
1
0
2
1
1
1
0
2
1
1
1
2
1
2
2
2
1
1
1
0
1
1
1
1
1
1
1
1
2
2
2
1
1
1
0
2
2
2
1
0
1
0
1
1
2
0
0
1
0
0
2
1
1
2
0
1
0
1
1
2
2
1
2
0
1
1
1
1
1
2
1
1
2
1
1
1
2
2
2
2
2
1
0
0
1
0
1
0
2
0
0
1
2
1
0
1
1
2
2
0
0
2
1
2
2
3
2
2
2
1
0
10
0
2
2
1
2
0
1
1
0
2
1
1
1
2
1
1
1
0
1
1
2
0
0
1
1
1
1
2
1
2
1
1
1
1
1
1
2
2
1
0
1
1
1
1
0
1
1
1
2
1
1
2
1
1
1
1
0
1
1
1
1
2
1
0
1
2
1
1
2
1
1
1
0
2
2
1
0
0
0
1
1
1
1
2
1
0
1
2
1
2
1
1
1
1
1
1
0
0
1
1
2
2
0
1
2
1
1
2
2
1
1
0
1
1
0
1
2
1
1
2
1
0
1
0
2
2
1
1
2
0
1
0
0
0
0
0
0
0
1
1
1
1
1
1
1
2
0
0
0
1
0
1
0
1
0
1
1
1
1
2
1
1
1
1
1
0
0
1
1
0
1
2
2
1
1
0
0
2
1
0
1
1
2
1
2
1
1
2
0
1
1
0
1
0
1
1
0
1
1
3
1
1
2
1
1
1
1
0
0
1
2
2
0
0
1
2
1
1
1
2
0
0
0
1
0
1
1
1
2
2
2
2
1
1
2
0
1
1
0
0
1
1
1
1
2
1
2
1
1
1
1
2
2
1
0
0
1
2
2
4
1
1
2
1
1
1
2
0
0
0
1
0
1
1
1
1
1
1
2
1
1
2
0
1
0
0
0
0
1
1
2
1
0
1
0
1
1
2
0
2
0
2
1
1
0
1
2
1
1
1
1
2
2
1
2
1
1
1
1
1
1
0
1
1
2
1
1
1
1
1
1
0
2
2
2
2
1
0
1
2
0
2
1
0
1
2
2
1
2
0
2
1
1
1
1
1
1
2
1
1
2
1
1
0
1
1
2
1
0
1
0
1
1
0
1
2
0
2
2
0
1
1
1
0
1
1
1
2
2
1
2
2
1
1
0
2
1
0
1
2
0
2
2
1
0
0
1
2
1
2
1
0
1
2
1
1
1
1
1
1
2
2
1
1
2
2
1
1
0
2
2
2
2
1
0
0
1
0
1
1
1
0
1
0
1
1
0
2
1
0
1
2
1
1
1
1
0
1
0
1
1
1
2
0
1
1
1
0
1
2
0
1
2
2
1
1
1
0
2
2
2
1
1
1
1
1
1
1
2
0
1
1
1
1
2
2
1
0
1
1
1
1
2
1
0
2
2
1
0
1
1
2
2
2
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
2
0
2
2
1
0
1
0
0
0
0
1
2
1
1
3
2
1
1
1
1
0
2
1
1
2
0
1
1
1
1
1
1
1
2
0
1
2
1
1
0
2
0
1
1
2
1
1
1
1
2
1
0
1
1
1
2
1
1
1
1
1
1
1
0
3
1
1
1
1
1
2
1
2
1
1
1
0
1
1
2
2
2
0
1
1
2
1
1
0
1
1
1
2
0
1
2
0
1
1
0
1
1
1
1
1
2
2
1
0
0
1
2
1
1
1
1
2
2
1
0
1
1
0
1
1
0
1
2
1
2
0
1
2
2
2
1
1
1
1
1
2
0
1
2
1
2
1
0
0
0
4
2
2
0
0
1
1
2
1
1
1
1
1
1
0
3
1
1
1
1
0
2
0
1
0
1
2
1
1
0
0
0
1
0
1
1
2
2
1
0
2
1
2
0
1
0
2
1
1
1
1
1
1
1
1
2
1
1
1
1
2
2
0
1
0
1
0
1
1
1
1
1
1
1
1
2
1
2
2
1
0
2
1
1
1
1
1
2
1
1
0
0
1
0
0
1
2
1
0
1
0
1
2
1
0
1
2
1
1
1
1
2
0
1
1
1
1
1
0
2
1
1
1
2
1
1
1
0
2
2
0
1
1
2
1
1
0
2
2
1
1
1
2
1
1
2
1
3
2
2
1
2
0
3
2
1
2
1
0
1
1
1
2
2
0
1
2
1
1
0
1
2
1
2
1
1
2
1
1
1
0
2
0
1
2
4
2
1
1
1
1
1
0
0
2
1
1
0
0
2
0
2
1
1
2
1
2
1
1
0
1
1
1
1
2
1
1
1
1
1
1
1
1
0
1
0
2
1
1
1
2
2
1
1
2
0
2
2
1
1
1
0
1
1
3
1
2
1
1
1
2
1
2
0
1
1
1
1
1
1
0
2
0
1
1
1
2
2
1
2
2
0
3
2
1
1
1
1
1
1
1
1
0
2
1
1
1
1
1
1
2
2
2
1
1
1
1
1
2
1
1
1
0
2
2
1
2
1
0
1
0
0
1
1
1
1
2
1
0
2
2
1
1
0
1
2
0
1
1
3
1
1
2
1
2
1
1
2
0
3
1
0
1
2
1
1
1
1
2
1
2
1
1
0
2
2
1
0
1
0
1
2
2
1
1
1
1
2
1
0
1
1
2
0
1
1
1
2
2
1
2
1
1
1
1
1
1
0
1
1
0
2
1
1
1
1
0
3
1
1
0
2
1
3
1
1
3
1
1
1
1
0
1
1
0
0
0
1
1
2
1
2
2
0
2
1
1
2
2
1
2
0
2
1
2
1
1
0
1
1
1
1
1
0
1
0
1
0
1
2
0
1
1
1
1
2
0
1
1
1
1
2
1
0
2
1
0
1
1
1
1
0
2
2
2
1
1
1
1
1
1
2
1
0
1
1
1
1
0
1
0
2
0
1
2
1
2
2
2
1
1
1
1
1
1
0
1
0
1
1
1
1
2
2
1
1
2
1
0
0
2
2
1
2
0
1
2
1
0
1
2
1
0
1
0
1
1
0
1
0
1
0
2
2
2
0
1
1
1
2
1
1
0
1
1
1
1
2
1
0
0
2
1
0
0
1
1
0
2
2
1
2
2
1
2
2
0
2
2
2
1
1
0
1
1
1
1
1
1
0
1
1
1
0
2
1
1
2
0
0
2
0
1
2
2
1
0
1
1
1
2
2
2
1
1
1
0
1
0
2
1
1
1
1
1
1
1
1
1
0
1
1
1
1
0
0
0
0
2
2
0
1
1
1
1
2
2
1
0
1
1
1
0
1
1
1
0
1
2
0
2
2
1
1
1
1
1
0
1
1
1
2
1
1
2
1
3
1
0
1
0
1
1
1
2
1
0
1
1
0
2
1
1
1
1
0
2
1
1
1
1
0
0
2
2
1
2
1
0
1
1
1
1
1
1
2
1
1
0
2
0
1
1
1
0
1
2
1
3
1
1
0
0
1
1
1
4
0
1
1
0
1
1
1
1
1
1
1
2
0
1
0
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
0
1
1
2
1
2
2
1
1
1
1
0
1
2
2
1
0
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
0
1
1
1
0
2
0
1
1
0
1
1
1
1
1
1
1
1
1
0
1
0
2
0
1
0
1
0
0
1
1
1
1
2
0
0
1
1
2
2
1
2
2
1
0
1
1
1
2
2
1
1
1
1
1
0
1
2
2
1
2
2
2
1
1
1
1
1
2
2
2
0
1
2
2
3
0
0
1
1
1
0
1
0
0
1
1
0
1
0
1
0
1
2
0
1
0
1
1
0
1
2
1
1
1
0
1
1
2
1
1
0
1
0
1
1
1
1
1
2
1
0
2
2
0
2
2
2
1
2
2
1
0
2
1
1
2
1
2
1
0
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
0
2
0
0
1
1
1
2
0
2
1
1
1
1
1
2
2
2
0
1
1
0
1
1
0
1
1
1
1
1
0
1
1
0
1
2
2
0
1
0
0
0
1
2
1
1
1
2
2
1
0
0
1
0
2
0
1
1
1
1
0
0
1
0
0
2
0
1
1
2
1
0
1
1
1
0
1
3
1
1
0
2
1
2
0
2
1
1
1
1
0
1
1
0
1
1
1
0
1
0
0
0
1
0
0
0
0
0
1
2
1
1
1
2
1
1
0
1
1
1
1
1
1
2
1
1
2
1
1
0
1
1
2
2
2
1
1
1
0
2
1
1
1
0
1
2
1
1
1
1
0
2
2
1
2
0
1
2
1
1
1
0
1
0
1
3
1
2
2
2
1
1
1
0
1
0
1
1
1
1
1
1
0
0
1
0
0
0
1
0
0
1
1
0
1
2
2
2
2
1
1
0
2
1
1
0
2
1
1
0
2
1
1
1
1
2
1
0
2
0
1
1
1
2
1
2
2
2
1
1
1
2
1
1
1
1
2
0
2
2
1
0
2
1
1
2
0
1
1
0
1
2
2
2
1
0
0
1
2
1
2
1
1
0
1
1
2
0
1
1
1
1
1
2
0
1
3
0
1
1
1
1
1
1
1
0
1
0
0
2
2
2
1
2
2
1
1
1
0
1
2
1
1
1
2
0
2
0
1
0
0
1
1
1
0
1
1
0
0
0
1
1
0
1
1
2
1
2
1
1
1
0
1
1
1
1
1
1
1
1
0
2
1
1
1
0
2
1
1
2
2
0
1
1
1
1
1
1
1
1
1
0
1
1
2
1
2
2
2
2
3
2
2
1
1
0
1
1
1
0
1
2
1
1
2
0
0
1
1
0
1
2
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
0
2
1
1
2
1
0
0
1
0
1
2
1
1
1
1
1
1
1
1
0
1
2
1
1
0
1
1
2
1
2
1
2
1
1
1
0
0
1
2
1
0
2
1
1
1
0
1
2
2
1
1
1
1
1
1
1
1
1
1
1
2
0
1
2
2
1
1
2
1
4
1
0
1
1
2
0
1
2
2
2
1
1
1
2
1
0
1
1
1
0
1
1
2
1
2
2
0
1
1
0
2
2
1
1
2
1
1
1
1
1
1
1
1
0
1
0
0
2
2
0
1
0
1
1
1
0
1
1
1
1
1
1
1
2
1
1
1
1
1
3
2
1
1
1
1
2
1
0
1
1
2
1
2
2
1
1
1
1
1
0
2
2
1
1
0
1
1
5
1
1
0
1
1
0
2
2
2
0
0
1
2
0
2
0
2
0
1
1
2
2
1
0
2
2
2
1
1
2
1
1
0
0
0
1
1
4
1
1
2
1
1
2
1
1
5
1
2
0
1
1
1
2
1
2
1
0
1
1
1
1
3
0
2
1
0
1
2
1
0
1
1
0
1
0
0
0
1
1
1
2
1
2
0
0
1
1
0
1
0
1
2
1
1
1
2
1
2
1
1
1
1
2
2
2
0
2
1
1
1
0
0
0
1
1
1
1
1
1
2
3
1
1
2
1
1
1
1
2
2
1
1
0
0
0
1
1
2
1
0
1
1
2
1
1
2
1
2
1
1
1
1
0
0
1
1
0
1
0
0
1
2
1
1
1
1
1
1
2
2
1
2
1
1
2
1
1
2
1
1
2
1
1
1
1
1
1
2
2
1
0
2
2
1
0
2
1
2
2
2
2
2
2
1
2
0
0
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
0
2
1
1
1
0
1
1
1
2
2
0
2
1
2
2
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
0
0
1
0
1
0
1
1
1
1
1
1
0
1
2
0
2
1
1
1
2
2
2
2
1
2
1
0
1
1
1
0
1
0
0
1
1
0
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
2
0
2
1
1
1
0
1
1
0
1
2
2
1
1
1
2
1
1
1
2
1
3
1
0
2
0
1
1
2
1
1
0
1
1
1
1
0
1
1
0
1
1
1
1
4
1
1
3
2
5
1
2
0
1
1
1
1
1
1
1
1
1
1
1
1
2
0
1
1
0
1
1
1
2
1
1
1
0
1
0
0
1
1
1
0
0
2
1
1
2
1
0
1
1
2
1
0
0
1
1
1
2
1
2
1
0
1
1
2
1
1
1
2
1
1
1
2
2
2
1
1
2
1
2
2
1
0
1
0
1
0
2
0
1
2
2
1
1
1
1
1
1
1
0
0
1
0
1
1
0
2
1
0
2
1
1
1
1
0
0
2
1
2
1
1
1
1
1
2
5
1
1
1
1
0
0
1
0
1
1
1
2
0
1
1
1
2
1
1
1
1
2
1
2
1
0
0
0
2
1
0
1
0
2
1
2
1
0
2
1
0
0
1
1
2
2
0
1
2
0
0
2
1
1
2
0
0
1
1
1
1
0
1
2
1
1
1
1
1
1
1
1
0
1
1
0
1
0
1
2
1
3
1
2
0
1
1
1
1
1
1
0
1
2
1
0
1
1
2
1
0
1
1
1
2
3
0
2
2
1
0
1
0
2
1
1
0
2
2
1
1
2
1
0
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
0
2
1
1
1
0
1
1
1
2
1
1
0
1
1
0
1
2
2
1
0
0
2
1
1
1
1
1
1
1
2
2
0
2
1
2
1
1
1
0
1
1
1
2
1
1
2
1
1
3
0
2
2
2
1
1
1
1
0
1
2
0
2
1
1
2
2
0
1
1
1
2
1
1
0
1
1
1
1
2
1
1
1
1
1
2
2
1
1
2
1
0
1
1
1
0
0
1
1
1
1
1
0
2
0
1
1
1
1
1
2
1
2
0
1
1
0
1
1
1
2
2
1
0
0
1
2
0
2
1
1
2
1
2
0
1
2
1
1
1
1
1
1
0
2
2
1
2
1
0
2
2
1
1
1
2
0
1
1
1
1
1
0
1
1
0
0
1
1
0
2
4
1
2
0
0
1
2
2
1
2
1
1
0
1
1
1
2
1
1
2
1
0
1
2
0
1
1
1
1
1
0
1
1
2
1
0
2
2
1
2
1
1
1
1
1
1
0
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
0
1
1
2
2
1
1
0
2
1
1
1
1
1
0
1
0
2
0
1
2
0
0
0
2
0
2
2
2
1
1
0
1
1
1
0
0
0
2
1
1
0
0
2
2
1
1
0
0
1
0
1
0
1
1
0
2
1
1
1
1
0
1
0
1
1
1
1
1
0
1
1
1
1
1
1
0
1
3
0
2
1
1
0
0
1
1
2
1
2
1
2
1
0
1
0
1
2
0
1
1
2
1
1
2
2
1
2
2
2
1
1
0
1
1
1
1
0
1
0
2
2
2
1
1
1
1
1
0
1
1
4
2
0
2
1
2
1
2
1
0
1
1
2
1
1
2
1
0
0
1
0
1
0
1
2
2
1
2
1
2
0
0
1
2
1
2
1
1
1
2
2
1
1
2
1
1
1
0
0
2
0
0
1
1
0
1
0
2
0
2
1
1
2
0
0
0
1
1
0
2
1
0
3
1
0
2
1
1
0
1
1
1
1
1
1
0
1
2
1
0
0
0
2
1
1
0
1
1
1
2
0
0
1
1
2
1
1
1
0
2
1
1
1
2
2
1
1
2
0
1
2
2
2
1
1
2
2
1
1
1
2
1
0
1
0
1
1
1
2
1
2
1
1
1
1
0
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
3
1
2
1
2
1
1
0
1
1
1
1
2
0
0
0
1
1
0
2
2
2
2
1
3
1
1
1
1
2
1
1
1
1
2
0
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
0
2
1
1
1
1
1
0
1
1
1
2
1
1
0
1
0
1
0
1
0
0
1
1
2
0
1
1
1
1
0
1
1
1
1
0
0
2
2
1
1
1
1
1
0
1
3
1
2
3
2
1
0
0
0
1
1
2
0
1
0
1
1
2
2
1
1
1
0
1
1
2
0
1
1
0
2
2
1
0
1
1
1
2
1
2
1
1
1
0
2
1
3
0
1
0
2
0
1
1
2
2
2
1
0
2
1
2
2
2
1
0
1
1
0
1
1
0
1
1
1
1
1
2
1
1
1
2
1
2
2
2
1
1
2
2
2
1
1
0
1
2
2
2
1
1
2
0
0
3
1
1
2
0
1
1
1
1
0
1
1
0
1
1
2
0
0
0
2
0
1
1
1
1
1
1
1
2
1
0
2
2
1
0
2
1
1
2
1
1
1
2
0
0
1
1
1
1
1
2
1
2
1
2
1
1
2
1
1
0
1
2
1
2
1
1
1
1
0
1
1
1
1
2
1
1
1
0
1
1
1
1
1
1
1
0
2
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
2
0
1
1
1
0
1
1
1
1
2
1
1
1
1
2
1
2
2
1
1
2
1
1
1
0
1
1
2
1
1
1
1
0
2
2
1
0
1
1
1
0
1
1
2
2
0
1
1
2
2
1
1
0
0
1
0
1
2
0
2
1
0
1
1
1
1
1
0
0
1
3
0
2
1
1
2
1
2
1
1
2
1
1
2
2
1
1
2
1
1
2
2
1
2
1
2
1
1
1
2
1
2
1
1
1
2
2
0
1
1
1
1
2
2
1
1
1
2
1
1
2
1
1
1
1
2
1
1
1
2
1
1
0
1
2
0
0
1
1
1
0
1
1
1
1
2
0
1
1
2
1
1
1
0
0
2
1
0
0
1
1
1
2
1
1
1
1
1
0
2
1
2
1
1
1
1
0
0
1
1
1
1
1
2
1
1
1
1
1
1
2
2
1
1
2
1
1
2
1
1
1
0
1
1
2
2
0
0
2
1
1
2
0
1
1
3
0
1
1
1
1
1
2
0
1
1
1
0
1
1
1
1
2
2
0
2
1
1
1
2
1
2
1
1
0
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
0
1
1
1
0
0
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
0
1
1
0
1
1
1
1
2
2
1
2
1
1
0
1
1
1
0
2
0
1
1
1
1
1
2
0
2
1
1
2
2
1
2
2
1
1
1
0
2
1
1
1
2
1
2
0
2
2
1
2
0
0
0
0
1
1
1
1
0
1
2
3
1
0
1
1
2
0
1
1
1
1
2
2
3
1
0
0
1
1
1
1
0
1
2
1
2
1
1
1
0
1
1
2
2
2
2
1
1
1
1
2
2
1
1
1
1
2
0
2
2
2
1
1
2
4
2
1
1
1
1
1
2
2
1
2
2
2
1
0
2
2
1
2
1
0
2
1
2
1
2
1
0
1
0
0
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
0
2
2
0
0
1
1
0
0
2
1
0
0
1
0
1
4
1
1
2
0
1
0
1
2
1
1
1
1
1
0
1
0
1
1
1
1
1
1
1
1
0
1
0
1
1
2
1
1
0
1
1
1
1
0
0
2
1
0
1
0
0
1
2
2
1
1
2
1
2
1
1
0
1
1
0
0
1
1
1
1
2
1
2
1
1
1
0
1
1
1
1
2
0
1
1
1
2
2
0
1
1
2
1
1
1
1
2
1
2
2
1
0
2
1
2
0
1
2
1
1
1
1
1
1
2
1
1
1
2
0
2
2
2
1
1
1
1
1
1
1
2
1
1
0
1
1
0
0
1
0
1
1
2
1
1
1
1
1
1
1
2
2
0
2
1
1
0
0
1
2
0
1
2
1
2
1
1
1
1
0
0
1
1
1
0
1
1
1
1
0
1
1
1
2
2
1
0
1
1
0
0
2
0
0
1
1
1
1
1
2
1
2
1
2
4
0
0
1
0
1
2
1
1
1
1
1
1
2
1
1
2
1
1
1
0
0
1
2
2
1
0
1
1
1
1
1
2
1
1
0
2
1
1
0
1
1
1
0
0
2
1
2
0
1
1
1
2
1
1
1
0
1
0
1
1
1
0
1
1
0
0
1
1
1
1
0
0
2
0
0
2
1
0
0
2
2
2
1
2
1
0
1
0
1
1
2
1
1
2
1
1
0
2
0
2
1
1
1
2
0
2
1
1
1
1
1
2
0
1
1
1
1
1
1
1
1
1
1
1
2
1
1
0
1
1
1
0
0
1
1
2
1
1
1
2
1
1
1
1
1
1
0
2
1
0
1
0
1
0
1
2
1
2
0
1
0
1
1
2
1
2
1
2
0
1
0
1
1
2
0
1
3
1
2
0
1
0
1
1
1
1
1
1
2
1
1
2
0
1
0
2
2
5
1
2
1
1
0
1
1
2
2
0
2
1
1
1
1
2
1
1
2
1
2
1
1
1
1
2
1
2
1
0
0
0
1
1
2
1
1
2
0
1
2
1
0
1
0
0
1
1
1
0
1
1
0
0
1
2
1
1
1
1
1
2
1
0
2
2
2
1
2
1
2
2
0
2
1
1
2
0
1
0
1
1
1
1
1
1
0
2
0
2
2
1
2
0
1
1
1
0
0
1
0
1
2
2
1
1
1
2
1
0
1
1
0
1
2
0
0
1
1
0
1
2
1
1
1
1
2
1
2
1
1
2
2
0
0
1
1
1
2
1
1
0
1
2
1
0
2
1
0
1
0
1
2
0
2
1
1
2
1
0
1
1
1
1
1
1
0
1
1
0
1
1
1
1
2
1
0
0
1
0
1
1
0
1
1
1
1
1
2
1
0
1
1
2
1
1
1
1
2
1
1
1
2
1
1
2
0
4
0
1
1
1
0
2
1
2
2
2
2
1
0
1
1
2
0
2
1
1
2
2
1
1
1
0
0
1
0
1
1
2
1
2
2
1
0
2
1
1
1
2
1
1
1
1
1
1
2
1
2
0
2
1
2
2
1
2
0
0
1
2
2
3
1
1
1
1
1
2
0
2
1
0
1
1
2
1
2
1
1
1
0
0
1
1
0
1
2
1
1
1
1
1
1
1
1
1
0
2
1
1
2
1
1
1
2
1
2
2
1
2
0
1
1
1
2
1
1
2
0
2
1
1
1
0
1
1
0
2
1
2
1
2
2
1
2
1
1
2
1
1
1
1
0
2
1
2
0
1
2
2
1
2
1
1
2
1
1
2
1
2
2
0
1
1
1
1
0
1
1
2
1
2
0
0
0
2
1
2
0
1
1
0
2
1
2
1
0
2
2
1
1
0
2
1
1
2
0
2
0
1
1
1
1
2
1
1
2
0
2
1
1
1
0
1
2
1
0
2
2
1
2
2
2
1
1
1
0
1
1
1
1
1
1
1
2
2
1
1
2
0
1
2
1
1
0
1
2
1
1
0
0
1
2
1
2
1
2
2
1
0
1
2
1
3
1
2
0
1
2
0
2
1
2
1
1
1
1
1
2
1
1
0
0
2
0
2
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
1
1
0
2
1
1
1
2
1
0
1
0
1
1
0
2
0
1
2
1
1
2
1
1
1
1
1
0
1
1
1
2
0
0
1
1
1
1
1
0
1
2
1
1
1
1
0
2
2
1
1
1
1
0
1
0
1
1
1
1
2
1
1
1
2
0
1
0
0
1
0
1
2
0
1
1
2
1
1
0
1
2
2
2
0
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
0
0
1
1
2
1
1
0
1
2
1
1
1
0
1
0
2
0
1
2
1
1
0
2
1
1
0
1
2
4
1
1
1
1
0
1
2
2
1
1
1
1
1
0
0
1
2
1
3
2
1
0
0
2
1
2
1
0
1
1
1
1
1
0
0
1
1
2
2
2
1
1
0
1
1
0
2
2
1
2
1
0
2
0
1
1
1
0
2
1
1
2
1
0
1
1
1
2
1
0
2
2
2
1
1
1
1
1
1
1
1
1
2
2
0
1
1
3
1
1
0
2
1
1
1
1
0
1
1
0
2
1
1
0
2
0
1
1
0
2
2
1
2
0
0
2
0
1
1
2
0
1
0
1
1
2
1
2
2
1
2
1
2
0
2
0
2
2
2
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
0
1
2
1
2
1
1
1
1
2
2
1
1
2
1
2
0
1
1
0
2
1
2
2
1
1
0
1
2
1
2
1
1
2
1
2
3
1
1
1
1
1
1
2
1
2
2
2
1
1
1
1
1
0
0
1
2
1
1
1
1
0
1
1
1
0
1
1
0
1
0
1
2
1
1
2
2
2
2
1
1
1
1
0
1
0
1
2
0
1
2
1
1
1
0
1
1
2
2
2
1
1
0
2
1
2
1
1
1
1
1
2
0
1
0
0
0
1
1
1
1
1
0
1
0
2
1
1
1
2
2
0
1
1
2
2
1
1
1
1
2
1
1
2
1
1
1
2
1
1
2
1
1
0
2
3
1
1
0
1
1
2
1
1
0
0
2
1
1
0
1
1
1
1
2
1
1
1
2
1
1
2
1
1
1
1
1
1
1
2
1
1
2
0
2
1
1
2
0
2
1
1
1
1
1
1
1
1
1
0
2
0
1
1
0
1
2
2
2
1
1
0
2
1
0
1
1
1
2
1
1
1
0
1
2
1
1
2
2
0
1
1
1
0
1
1
0
0
1
1
1
1
2
1
1
2
1
1
1
2
1
2
1
1
0
2
2
1
1
0
2
2
1
2
0
2
1
1
0
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
2
2
1
1
2
2
1
2
1
2
1
1
1
2
0
0
1
0
1
1
2
1
2
1
2
2
1
2
1
1
2
0
0
0
2
1
1
1
1
0
1
2
1
1
1
1
1
2
2
1
1
0
1
1
1
2
0
1
1
1
1
1
2
1
1
1
2
0
0
2
1
0
1
1
1
1
0
0
2
0
1
1
1
2
1
0
2
0
1
1
1
1
1
3
0
2
1
1
2
2
1
1
1
1
1
2
1
2
1
1
1
1
1
0
2
1
1
1
1
1
0
0
2
1
2
0
2
0
1
1
1
1
0
2
2
1
2
1
2
2
1
1
1
2
2
0
0
1
1
1
1
0
1
2
1
1
2
1
1
1
1
1
1
1
0
1
1
0
1
2
2
1
1
1
2
2
1
1
1
1
1
2
2
1
2
1
0
2
0
2
0
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
2
0
2
1
1
1
2
1
1
2
1
2
1
0
1
2
1
1
0
1
1
0
2
2
2
2
1
1
1
1
1
1
1
1
1
0
1
1
0
1
2
1
2
1
3
0
2
1
0
1
2
0
1
2
1
1
1
1
2
0
2
1
1
1
1
1
3
1
1
2
1
0
1
1
2
1
1
2
1
1
0
1
2
0
1
2
1
1
2
0
1
0
1
1
2
2
1
1
1
0
1
1
0
0
1
2
1
1
1
0
1
1
0
1
2
1
2
0
2
1
1
2
0
2
1
0
2
0
1
1
1
1
1
1
0
1
1
1
1
2
0
0
1
0
1
1
0
2
2
1
1
1
1
1
1
1
1
1
0
2
2
2
2
1
1
1
1
0
1
1
1
1
0
0
1
2
1
2
1
0
1
2
1
1
1
1
0
1
0
2
1
1
0
1
1
1
2
1
2
1
1
0
2
0
1
0
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
0
0
1
1
2
2
1
1
1
1
1
1
0
2
1
0
1
1
1
0
1
1
1
1
2
1
1
2
1
1
1
2
1
1
0
2
1
0
1
1
2
1
2
1
1
1
1
0
2
1
1
1
0
1
1
0
1
1
1
2
2
0
0
1
1
1
1
0
1
0
2
1
1
1
1
1
1
2
0
0
1
1
1
1
1
1
1
1
2
2
2
1
1
0
0
1
1
1
0
1
1
2
1
1
1
1
1
1
0
1
1
1
2
1
1
1
2
1
2
2
2
1
1
0
1
0
1
1
0
3
1
1
0
0
1
1
1
0
1
2
1
1
0
2
1
1
1
2
0
0
1
0
1
1
0
1
2
1
1
2
1
1
2
0
2
2
0
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
0
0
1
2
2
0
1
1
0
2
1
1
1
2
2
1
1
2
1
0
1
1
2
0
0
1
0
1
1
1
1
0
1
2
1
1
2
2
1
1
1
1
1
0
1
1
1
1
1
1
2
1
1
1
1
1
0
1
2
0
1
2
1
1
1
1
0
0
1
1
2
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
0
1
0
1
1
1
0
1
1
1
2
2
2
0
2
2
1
2
1
1
0
1
1
1
2
0
0
2
2
1
1
2
2
0
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
0
1
2
1
2
0
1
1
0
1
1
1
1
0
1
0
2
1
2
2
0
1
1
0
1
2
1
0
2
1
2
1
2
2
1
1
1
1
1
1
0
0
2
0
0
1
2
1
1
1
1
1
0
2
2
1
0
1
1
0
1
0
1
1
4
1
0
1
1
2
1
1
1
2
1
1
1
0
1
1
1
1
2
2
1
1
2
1
2
2
2
1
1
1
0
0
1
1
0
0
1
1
1
0
1
2
1
1
0
1
2
1
1
1
2
2
2
1
1
1
0
2
1
1
2
1
2
1
2
1
2
2
2
1
2
0
0
1
1
1
1
1
1
2
1
1
1
2
1
2
0
2
1
1
1
0
2
1
1
1
2
1
1
1
1
1
0
2
1
3
1
2
2
1
2
1
0
3
1
1
1
1
1
3
1
1
2
1
1
2
1
2
1
2
1
0
0
1
1
1
0
1
1
1
1
1
1
2
1
2
1
0
0
1
1
0
0
2
1
0
1
1
1
2
1
1
1
0
2
1
1
2
2
1
2
2
0
1
1
1
2
1
0
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
0
1
0
1
2
2
1
1
1
1
0
2
0
1
1
0
1
1
0
0
1
1
0
0
2
2
0
1
1
1
1
0
1
1
0
0
1
1
0
1
1
1
1
1
1
1
0
2
1
2
1
1
1
0
2
2
2
1
1
2
1
1
0
2
0
1
2
2
2
1
1
0
1
2
0
0
2
2
2
1
0
1
3
2
2
1
2
1
1
2
1
1
2
1
0
0
1
2
0
1
0
1
1
1
1
0
1
0
0
1
0
1
1
3
2
0
1
1
0
2
1
1
2
1
1
1
2
0
0
1
1
1
2
1
1
1
1
1
0
0
2
2
0
0
1
1
0
2
1
1
1
2
1
1
2
1
0
1
1
0
1
1
3
0
1
1
1
1
1
1
2
1
1
0
2
2
1
1
2
2
0
1
2
2
1
2
1
1
1
0
2
1
2
1
1
1
1
2
1
2
2
0
0
2
0
1
0
1
1
2
1
0
1
1
2
2
1
1
2
2
2
1
0
1
0
1
1
1
0
1
2
2
2
1
1
2
2
1
0
1
0
2
2
2
1
2
1
1
1
1
1
0
1
2
2
2
2
2
1
2
1
1
0
2
0
0
1
1
1
2
1
1
1
1
0
1
1
1
1
0
0
0
1
1
1
2
1
0
0
2
2
1
2
1
1
2
0
0
2
1
1
2
0
1
1
2
1
2
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
3
0
0
2
2
0
0
1
1
2
1
1
1
1
1
0
1
1
1
2
2
4
2
2
1
0
1
1
1
0
1
0
1
1
1
1
1
2
1
2
1
2
2
1
1
1
2
1
0
1
1
1
1
2
0
1
1
1
2
1
1
1
0
1
1
0
1
1
0
0
1
1
1
0
0
1
1
1
1
2
0
0
2
1
1
1
0
1
1
1
2
2
1
0
2
1
1
2
1
1
0
1
2
1
0
1
2
0
1
0
2
2
1
4
1
1
2
1
0
1
1
2
1
1
1
2
1
2
2
1
1
0
2
1
1
1
1
2
1
0
1
1
0
0
2
0
1
1
1
1
1
0
1
1
1
1
2
2
1
1
2
1
1
0
1
1
1
0
1
2
2
0
1
1
1
1
2
1
0
2
0
0
1
1
1
2
1
1
2
1
1
1
0
2
1
1
0
2
1
0
2
2
1
1
1
1
1
2
2
1
1
2
1
1
2
2
2
0
1
0
1
2
1
1
0
2
0
1
0
1
1
1
2
0
0
2
0
1
2
1
1
2
0
1
1
1
1
1
0
1
1
0
2
1
0
0
1
1
2
1
0
2
1
1
2
2
2
1
1
1
2
1
1
1
1
1
3
2
1
0
1
2
2
1
1
1
2
1
2
1
1
1
1
1
2
2
1
1
1
2
2
0
0
1
0
1
1
1
2
1
1
1
0
0
0
1
1
1
1
1
1
1
2
1
2
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
2
2
1
0
1
1
1
1
1
1
0
2
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
0
1
1
2
2
1
1
2
1
1
2
1
1
1
2
1
2
0
1
0
1
1
1
1
1
0
1
1
1
2
1
1
0
0
1
1
0
1
2
0
1
2
1
1
0
1
0
1
1
1
1
0
0
2
1
1
0
0
1
1
0
1
1
1
0
1
2
0
1
1
1
1
1
1
0
1
2
1
2
1
1
0
1
0
1
0
2
2
1
1
2
2
1
1
1
2
1
0
1
2
0
1
2
1
2
1
1
2
1
0
1
1
1
0
1
2
2
0
1
1
2
1
1
1
0
1
1
0
1
1
0
1
1
1
2
0
2
2
2
1
1
0
1
1
1
1
1
2
1
2
1
0
1
0
1
1
0
1
1
1
2
0
2
1
1
1
1
1
1
2
1
2
1
1
0
2
0
1
1
1
1
0
0
2
1
1
1
1
2
1
1
1
1
2
0
0
1
1
0
0
1
1
1
2
0
1
1
3
1
0
2
1
1
1
1
1
1
2
2
2
1
1
1
0
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
0
1
1
1
0
0
2
1
1
1
2
1
1
1
1
1
1
0
0
1
1
2
1
1
2
1
1
1
0
1
4
2
1
1
1
1
2
2
1
1
1
2
1
1
1
1
2
2
1
1
1
1
1
1
1
2
3
1
1
1
1
0
1
2
2
1
1
1
1
2
0
1
2
2
1
2
1
1
1
0
1
1
0
1
1
2
1
2
1
1
1
1
1
2
1
2
1
1
1
1
1
0
0
1
0
1
0
1
0
1
2
2
0
1
2
0
0
1
1
2
2
0
1
0
1
1
1
0
0
2
1
0
0
1
1
0
0
2
1
1
2
1
1
0
1
1
1
0
0
1
1
1
1
0
1
1
1
1
1
2
1
2
1
1
0
0
0
1
1
2
2
1
0
1
1
1
1
1
1
2
2
0
2
2
2
1
2
2
1
2
1
2
1
0
1
1
0
1
1
0
2
1
1
1
0
1
2
1
1
2
1
1
2
1
2
2
2
0
2
1
1
1
2
2
1
0
1
1
1
1
2
2
2
3
2
2
1
1
1
1
2
1
1
1
2
2
1
2
1
0
1
2
1
1
1
0
2
1
1
2
1
0
1
0
2
1
2
2
0
1
1
0
1
1
1
1
0
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
2
1
1
1
2
1
1
0
1
2
1
0
0
1
1
1
1
0
1
1
1
1
0
0
2
0
2
1
1
1
2
0
1
1
2
2
2
1
1
2
2
1
0
1
1
2
1
0
2
0
0
1
1
1
1
1
1
0
1
1
1
2
0
1
1
2
2
1
2
2
1
1
1
1
1
1
1
2
2
2
1
0
2
2
1
1
1
2
1
2
0
0
0
1
1
1
0
2
0
2
1
2
1
2
1
0
1
0
1
2
2
1
1
1
1
2
2
0
1
1
1
1
1
1
2
1
1
2
0
2
2
1
1
1
1
0
0
1
1
1
1
2
0
2
2
2
2
1
0
1
1
2
2
0
2
1
1
0
1
1
1
1
1
1
1
1
1
1
2
2
1
0
2
0
0
0
2
1
1
0
1
0
3
1
0
1
1
2
2
2
1
1
1
1
1
0
0
1
1
1
2
2
1
2
1
2
1
2
2
1
0
0
1
1
1
0
2
0
1
1
2
1
1
1
2
1
2
0
2
1
0
1
1
0
1
1
2
1
1
2
1
2
0
0
0
2
0
1
1
2
1
2
1
1
2
1
0
2
1
1
1
1
1
1
2
0
1
0
2
2
0
0
1
1
1
1
1
1
1
1
1
2
0
1
2
1
2
2
1
1
0
1
2
2
1
1
1
1
0
1
2
1
2
1
2
1
2
1
1
0
0
1
1
2
1
2
1
1
0
2
1
1
1
0
2
0
1
0
4
1
2
1
2
2
1
1
2
0
1
1
1
2
1
2
1
1
1
1
1
0
1
1
2
0
1
0
1
1
2
2
1
2
0
0
0
2
0
2
2
1
1
1
2
1
2
1
0
1
0
0
1
1
1
2
1
1
0
1
1
2
0
2
1
0
1
1
0
0
2
1
0
1
1
1
0
2
2
1
1
1
1
2
1
1
2
1
2
1
0
2
2
1
0
2
0
1
0
1
1
1
0
1
1
0
1
1
0
1
2
1
1
1
0
1
0
1
1
1
0
0
1
0
1
2
2
1
1
2
2
0
1
1
0
1
1
0
2
1
1
1
1
1
1
1
2
0
1
2
1
0
0
1
0
1
1
1
0
2
2
2
0
1
1
1
0
1
1
0
1
2
1
2
1
2
1
1
0
1
1
1
2
2
2
1
2
2
2
1
0
1
3
1
1
2
2
1
1
1
1
0
1
0
2
0
3
2
1
1
1
0
1
1
1
0
1
1
1
1
2
2
1
1
2
1
0
1
1
2
1
2
1
0
0
2
2
1
0
2
1
1
1
1
1
2
1
1
2
1
0
0
1
2
1
0
1
1
1
1
2
0
1
1
1
2
1
2
1
1
2
1
1
1
1
1
2
1
2
2
1
1
0
2
1
1
0
1
1
1
0
1
2
0
1
1
2
0
1
2
1
1
0
1
1
1
1
2
1
0
1
1
1
2
1
2
1
1
1
2
1
1
0
1
1
1
0
1
1
1
1
0
1
0
0
1
1
1
2
1
0
1
0
1
1
1
2
2
1
1
1
0
2
1
2
1
0
0
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
2
1
1
1
1
1
2
1
2
0
2
0
1
0
0
0
1
1
0
2
1
1
1
1
0
1
2
2
1
1
2
1
3
1
1
1
0
1
1
0
1
0
1
1
4
2
1
2
1
0
0
1
3
2
1
0
0
2
1
2
1
1
1
2
0
2
1
1
1
2
1
1
1
2
1
1
2
2
1
1
2
1
1
1
1
0
1
1
0
1
1
0
2
0
1
1
2
1
1
1
1
2
1
2
2
0
1
2
1
1
1
2
2
1
2
0
2
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
0
0
0
1
2
2
1
2
1
1
0
1
1
2
2
1
2
1
2
0
1
1
1
1
0
1
1
2
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
0
0
0
1
0
2
1
0
2
2
0
2
1
1
1
1
1
0
1
1
1
2
1
1
1
0
2
0
2
0
1
1
0
1
1
1
1
1
1
1
2
1
1
2
0
1
1
2
1
0
1
1
2
1
2
0
0
3
0
1
1
2
1
1
2
0
1
1
2
0
2
1
0
1
1
2
1
1
2
2
1
1
1
2
1
1
2
0
1
1
1
0
1
0
1
1
1
1
1
0
1
1
0
0
1
1
1
1
2
1
2
1
1
0
1
2
1
2
0
0
1
1
1
0
1
1
1
0
1
0
1
1
1
2
1
1
2
2
1
2
0
0
1
1
0
1
1
1
1
0
1
0
1
1
1
1
1
0
1
1
0
1
1
0
1
1
1
0
1
1
2
1
0
0
2
2
0
0
1
1
1
1
0
1
2
3
2
1
2
1
1
0
0
2
1
0
2
1
1
0
1
2
2
2
1
1
2
1
1
1
1
1
1
1
3
1
1
1
1
0
1
2
1
1
1
1
1
1
1
1
0
1
0
0
1
2
1
2
1
1
2
1
2
0
1
0
1
2
1
1
1
1
1
2
0
1
1
1
1
1
1
1
2
0
1
2
2
2
1
1
0
0
2
2
1
1
1
1
1
1
1
2
0
0
0
1
2
1
0
1
1
2
1
2
1
1
1
0
0
0
2
1
1
2
2
1
2
2
2
1
2
1
2
1
0
1
2
1
1
1
1
1
0
1
0
1
0
1
2
1
0
0
0
1
1
2
2
0
1
1
1
1
7
1
1
0
2
2
1
1
1
1
2
1
2
2
0
2
2
1
1
2
2
1
1
2
1
2
1
1
1
1
2
1
1
0
1
1
0
0
2
1
0
1
1
0
1
1
1
1
1
2
1
1
1
1
4
1
1
1
2
1
2
1
2
1
0
1
2
2
0
1
1
1
1
0
1
1
2
1
1
0
1
0
1
2
1
1
1
1
2
1
0
0
1
2
1
1
0
1
0
2
1
1
0
2
0
0
1
1
0
1
2
0
2
1
1
1
2
1
2
1
1
1
1
1
1
2
2
1
2
1
1
2
1
1
1
1
0
1
1
1
2
1
1
1
1
2
0
1
0
0
1
1
2
1
1
1
1
1
1
2
1
0
1
2
0
1
1
1
0
1
1
2
1
1
1
1
2
1
1
2
0
2
1
1
2
1
1
1
1
2
2
0
1
1
0
0
0
2
1
1
0
1
1
1
2
1
2
2
2
1
1
1
1
2
1
2
1
1
1
1
1
1
0
2
1
0
1
1
0
1
1
2
2
2
1
2
1
1
1
0
2
1
0
2
2
1
2
2
2
1
1
1
1
2
1
1
1
2
0
2
1
1
0
1
1
1
2
3
2
0
1
1
1
1
2
2
1
0
1
1
1
1
1
1
2
1
1
0
1
2
0
0
1
0
2
1
0
0
1
1
2
1
0
1
1
1
1
2
1
0
1
1
1
2
0
1
1
1
1
2
1
1
2
1
0
2
1
1
1
2
1
1
1
0
0
2
1
1
1
1
1
2
1
1
2
2
1
2
2
1
2
1
2
2
1
0
0
1
1
0
0
1
1
1
1
2
2
1
1
1
2
1
2
1
2
1
1
2
2
2
1
0
1
1
2
0
1
2
1
0
1
0
1
1
2
1
2
0
0
1
1
0
0
1
1
1
1
1
1
2
1
0
1
1
0
1
1
0
1
1
1
0
0
2
1
2
1
2
2
0
1
1
2
3
2
1
1
1
2
1
2
0
2
2
1
1
2
1
1
1
1
2
1
0
1
2
1
1
1
0
1
1
2
0
1
0
2
1
2
2
0
0
1
0
0
0
2
1
1
1
1
1
1
2
1
1
2
0
2
1
1
2
0
0
1
0
2
1
1
0
0
2
2
2
1
1
2
1
1
1
1
0
0
0
2
1
0
1
1
2
2
1
0
1
1
1
2
1
1
2
1
0
1
2
0
1
0
1
1
0
2
0
0
1
1
1
0
1
1
1
0
1
0
1
1
2
0
1
2
1
0
0
2
3
1
1
0
1
2
1
2
1
0
0
0
0
1
2
2
2
1
1
1
0
3
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
0
1
1
0
1
0
0
1
1
0
1
1
2
0
0
1
1
1
0
1
1
1
1
2
0
1
2
1
1
0
0
1
1
1
1
0
1
0
1
2
2
1
1
0
0
2
2
0
1
2
1
1
0
2
1
1
1
1
1
1
2
1
1
1
2
0
1
1
1
2
2
0
1
1
0
1
1
0
1
0
1
0
1
0
1
1
2
2
2
1
1
2
1
2
1
1
1
2
1
0
2
1
0
0
1
1
1
2
2
1
1
1
0
1
1
1
0
1
0
2
0
1
2
2
0
1
2
1
0
1
0
2
2
1
2
2
1
1
2
2
1
1
1
2
1
0
0
1
2
1
1
2
0
0
1
1
1
0
1
1
2
2
1
0
1
1
0
0
1
1
1
2
1
1
1
0
1
2
1
0
2
0
1
1
1
2
1
0
0
1
0
1
1
1
1
1
1
1
2
1
2
1
2
0
2
1
1
1
0
1
0
1
1
1
1
0
1
1
1
2
1
1
0
1
1
2
1
2
1
1
2
2
1
2
2
1
0
0
1
2
1
1
2
2
1
1
1
1
2
0
2
0
0
0
0
1
1
2
1
1
1
2
1
1
2
2
0
1
1
0
2
2
0
1
0
1
1
1
1
1
1
2
1
2
2
2
1
1
1
2
1
1
1
1
1
1
2
1
2
2
1
1
1
2
1
1
2
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
0
1
1
1
2
2
1
2
2
1
1
1
2
1
2
2
2
2
2
0
2
1
1
1
1
2
1
2
1
1
2
2
1
1
0
0
1
1
1
0
2
1
2
1
0
2
2
0
2
1
0
1
1
1
1
2
2
1
1
1
1
1
1
0
1
1
1
1
2
2
1
2
2
1
0
1
1
1
0
0
1
1
0
2
1
1
1
1
2
1
2
1
1
2
1
1
0
1
2
1
0
2
1
1
2
0
2
1
1
1
0
2
1
0
1
2
1
1
2
1
1
1
1
2
2
1
2
1
2
1
1
1
1
1
3
1
1
1
1
1
1
2
1
2
2
1
2
1
2
1
1
2
1
1
1
0
0
0
1
2
1
2
2
0
1
1
1
1
0
1
1
1
1
0
1
1
0
1
1
3
1
0
1
1
0
2
2
1
2
1
0
1
1
1
2
1
2
1
1
1
1
3
2
2
2
1
2
0
1
1
1
1
1
1
0
1
0
1
2
0
2
1
1
1
2
2
1
0
1
1
0
1
2
2
1
1
1
1
2
2
0
1
1
2
1
1
0
1
2
2
1
1
1
0
2
1
1
1
2
1
2
2
1
2
1
1
1
1
2
0
1
0
2
1
0
1
1
1
3
1
2
1
2
0
1
1
2
2
1
1
1
1
1
0
2
1
1
1
2
2
2
1
1
1
2
5
1
2
1
1
1
1
0
2
2
1
1
1
0
1
1
2
1
1
1
0
2
1
2
2
0
2
0
1
1
0
1
1
1
2
1
0
1
1
2
1
1
1
1
1
1
1
0
1
1
2
1
0
1
1
2
1
1
1
1
0
2
2
1
1
1
1
0
1
2
1
0
1
1
1
0
1
1
0
1
1
1
1
2
2
1
2
0
0
2
2
0
1
1
2
1
1
0
0
2
1
0
2
1
1
2
1
0
1
1
1
1
1
1
0
0
0
1
0
0
0
1
2
1
1
1
0
1
2
0
2
2
1
1
1
1
1
0
2
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
0
1
2
1
1
0
1
0
2
1
1
2
3
0
1
1
1
1
2
1
1
1
1
2
1
1
0
1
1
1
1
1
1
2
1
1
1
1
1
2
2
1
2
2
0
0
2
1
1
1
1
0
2
1
1
1
1
1
1
1
1
0
0
1
0
0
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
0
0
1
1
1
2
2
1
2
0
1
2
4
0
1
1
1
1
1
1
2
0
1
2
0
1
1
2
1
0
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
0
2
1
0
1
1
1
2
1
2
0
1
1
0
2
1
1
1
0
1
1
1
1
1
1
1
2
1
0
1
2
1
2
2
1
1
0
1
2
1
1
2
1
0
1
2
1
1
2
1
2
2
1
2
2
2
2
2
1
1
1
2
1
2
1
1
1
1
1
1
0
1
1
1
2
2
2
0
0
2
1
2
1
2
1
1
2
1
2
1
1
1
0
0
0
1
0
1
0
1
0
0
1
1
0
1
2
0
0
1
0
1
0
2
3
2
1
0
1
1
1
1
1
1
0
1
1
1
1
1
2
2
2
2
0
1
0
1
1
1
2
0
1
0
0
1
1
1
0
2
0
1
2
2
1
1
2
1
0
0
1
2
1
1
1
1
1
1
2
2
0
1
2
0
1
1
1
2
2
1
1
1
2
1
1
1
0
2
0
1
2
1
1
0
1
0
2
0
1
1
1
2
1
1
1
0
2
0
1
1
1
1
1
1
1
1
1
0
0
1
1
1
1
1
2
1
1
1
2
1
2
2
2
1
1
2
1
1
2
1
1
2
1
0
1
2
2
1
2
1
2
1
2
1
1
1
2
2
2
1
2
3
1
1
1
2
1
1
0
1
1
1
2
1
2
1
0
1
2
1
0
1
0
1
2
0
0
1
1
2
0
1
2
1
1
1
0
0
1
0
2
2
1
0
0
0
2
1
1
0
2
0
0
2
1
0
1
1
1
0
1
1
2
0
1
1
1
0
1
2
0
0
1
1
2
1
2
2
0
2
1
2
1
2
0
0
1
2
1
1
0
1
2
1
1
2
1
2
2
0
1
1
0
1
1
1
1
1
1
2
5
0
1
1
1
0
0
0
2
1
0
2
1
1
1
1
0
2
1
1
0
2
1
1
1
1
1
1
1
1
2
0
1
1
2
2
1
1
1
1
1
1
1
1
0
2
2
0
1
1
2
1
0
1
1
2
1
1
0
2
2
1
2
1
2
1
1
2
1
1
0
0
1
0
1
1
1
1
1
1
1
0
1
2
1
0
2
1
2
1
2
1
1
1
2
1
1
1
2
1
0
1
0
1
1
0
0
1
1
1
2
2
1
0
2
1
0
2
1
2
2
1
0
0
1
1
1
1
3
2
1
2
2
1
1
1
1
1
2
2
2
1
1
2
1
1
1
2
2
0
1
1
1
1
1
1
1
1
1
1
1
2
0
2
1
1
1
2
1
1
1
1
0
1
1
2
0
2
1
1
1
1
0
1
2
1
0
2
0
2
2
0
1
2
1
1
2
0
0
1
2
0
1
2
1
1
1
1
1
1
2
0
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
0
1
2
0
1
2
2
1
3
0
2
2
1
1
1
1
1
1
1
2
0
2
2
0
1
1
0
1
2
1
1
1
1
0
1
1
1
1
2
1
1
1
1
1
2
1
0
1
2
1
2
0
1
1
1
0
1
1
0
1
1
2
1
1
1
1
0
1
2
1
1
2
2
0
2
1
1
2
1
1
1
2
0
1
2
1
1
2
1
1
0
0
1
1
1
1
1
0
1
1
1
1
2
1
1
0
1
1
1
1
2
1
1
1
1
1
0
2
1
0
0
0
1
1
2
1
1
0
0
0
1
2
1
0
0
2
2
2
1
0
1
1
1
2
1
2
0
0
1
0
1
1
0
1
1
2
0
1
1
1
2
1
1
2
0
0
1
0
2
0
0
2
1
1
2
2
2
1
1
0
1
0
1
1
1
1
2
2
1
2
1
0
1
1
0
0
1
0
2
2
0
1
1
2
0
2
1
1
1
1
1
1
1
1
3
3
1
0
0
2
1
2
2
0
2
1
1
1
1
1
1
0
2
2
3
1
1
2
1
1
1
1
1
2
1
1
1
1
0
1
1
2
1
2
2
1
2
2
1
2
1
1
1
1
1
1
1
2
2
1
3
1
1
0
1
0
0
0
1
1
1
2
1
2
1
1
1
1
0
1
1
1
1
0
1
2
1
2
0
1
2
1
1
0
1
2
2
0
1
1
1
1
0
1
0
1
2
1
2
1
0
1
1
1
1
1
1
2
0
1
1
1
0
1
1
0
1
1
2
1
1
0
1
1
2
1
2
0
2
2
1
4
0
2
2
0
1
1
0
1
1
1
2
1
2
2
0
1
2
2
0
1
1
1
1
1
2
2
1
1
2
0
0
1
1
0
1
2
0
0
0
2
1
2
1
1
1
1
1
2
0
1
0
1
2
2
1
1
1
0
1
2
1
2
1
1
2
1
2
0
1
2
1
2
1
1
2
1
0
2
2
1
1
1
0
2
1
0
1
2
0
1
1
1
4
1
1
1
1
2
1
1
1
0
1
1
1
1
1
3
1
1
0
0
2
1
1
0
3
2
1
1
1
1
0
2
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
0
2
1
2
1
0
1
0
0
1
1
0
1
2
1
3
1
1
1
4
1
1
4
0
1
0
1
2
2
1
1
1
1
1
1
0
0
1
2
1
1
2
2
0
0
0
0
1
0
1
1
0
0
0
1
1
1
1
1
2
1
1
1
1
2
1
1
1
0
1
1
0
1
1
1
0
0
2
2
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
0
0
2
1
0
1
0
2
0
1
0
2
1
1
1
1
1
1
2
1
1
1
1
0
2
2
1
2
2
1
2
1
2
0
1
1
1
2
1
1
2
1
0
0
1
0
2
1
2
2
1
0
1
0
1
1
1
1
1
1
1
1
1
2
0
1
0
1
2
1
0
0
1
0
0
1
1
2
0
1
2
1
2
1
0
1
1
2
1
1
1
1
1
1
0
1
1
1
1
1
1
2
2
0
2
2
2
1
2
1
1
2
0
1
1
2
1
1
1
1
2
2
1
0
1
1
1
1
1
1
1
0
2
2
1
1
0
1
2
1
1
1
1
1
1
2
2
0
1
2
2
1
1
1
0
2
1
1
1
0
1
1
2
2
1
1
1
1
0
1
1
1
1
1
2
1
0
1
1
1
1
1
2
2
1
1
1
2
0
1
2
0
3
2
2
2
1
1
1
2
1
2
1
1
0
1
0
1
1
1
1
1
1
0
2
1
1
1
1
0
1
2
0
1
1
2
2
1
1
1
1
1
1
2
1
2
1
1
0
1
0
1
1
1
2
2
2
1
2
2
1
1
1
1
1
0
2
2
1
1
0
1
2
1
2
1
1
1
2
2
1
1
1
1
2
1
0
1
2
1
1
0
1
2
1
0
0
2
1
1
0
2
1
0
1
1
0
0
1
1
2
1
0
1
0
0
1
0
2
2
1
2
1
1
0
1
1
0
2
1
1
1
1
1
1
1
1
1
0
1
2
0
0
1
1
2
1
2
0
1
1
0
2
0
2
1
2
1
0
1
0
1
0
2
2
1
1
1
2
1
1
1
0
1
1
1
0
1
0
2
0
1
1
1
0
1
1
1
0
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
0
0
1
1
0
2
1
1
1
2
1
2
0
1
1
1
2
0
1
1
1
1
1
0
1
2
1
1
2
1
1
2
1
1
0
1
1
1
0
1
1
1
1
1
0
1
3
1
1
1
1
0
1
0
1
1
1
2
1
2
1
1
0
1
1
1
2
0
0
1
1
2
2
2
0
1
1
1
0
1
1
0
1
1
1
1
1
0
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
0
1
1
1
1
2
1
1
1
1
0
1
0
0
2
1
1
1
1
1
2
1
2
0
2
2
0
2
1
1
1
0
2
1
0
1
1
0
1
2
2
2
1
2
1
2
1
1
3
2
2
0
1
2
1
1
2
2
2
1
2
0
0
1
1
1
1
2
0
1
1
1
1
1
1
0
1
2
0
0
0
1
1
2
1
1
1
1
0
2
1
1
1
2
1
2
1
2
1
1
1
1
2
1
1
0
0
1
1
2
1
1
1
0
2
1
0
1
1
2
1
1
0
1
1
1
0
1
2
2
2
0
2
2
1
0
1
0
1
0
1
1
1
0
0
2
0
0
1
1
0
2
1
1
1
1
0
2
0
1
2
1
2
1
2
1
1
0
2
2
0
2
1
0
1
0
2
2
1
0
1
1
1
1
1
0
0
1
2
1
3
0
1
1
1
1
0
1
1
1
0
1
0
1
2
1
1
0
1
1
1
1
1
0
1
0
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
0
2
0
0
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
0
1
1
1
1
2
1
2
1
1
1
1
2
1
1
1
0
1
1
1
1
1
0
1
1
2
1
2
1
1
1
0
1
2
1
1
1
2
2
1
1
0
2
0
2
1
0
1
2
0
0
1
2
1
1
1
1
2
1
1
2
1
1
1
1
2
1
2
1
1
1
1
4
2
0
1
2
2
1
1
1
0
2
0
0
2
0
1
0
2
0
2
1
1
1
0
2
1
1
2
2
1
1
1
1
1
1
1
0
2
1
1
1
0
2
1
1
2
1
1
2
0
1
2
0
1
1
1
1
2
0
1
1
2
1
2
1
3
1
1
1
2
1
1
1
2
2
2
2
0
0
1
1
0
0
2
0
1
1
1
2
0
1
1
1
2
1
0
1
1
0
1
1
1
1
2
1
0
1
0
2
1
1
1
0
2
0
4
2
1
2
1
0
0
1
1
1
1
1
0
1
0
2
1
1
1
0
2
1
1
1
1
0
1
1
1
1
1
1
0
2
0
2
1
1
1
1
1
1
1
1
1
1
1
1
0
1
0
2
1
0
2
1
1
1
0
1
1
1
1
1
1
2
2
1
1
1
2
2
0
0
2
1
2
1
1
1
2
2
1
1
1
1
2
1
2
1
1
2
2
2
0
2
1
2
0
1
1
1
1
1
2
1
1
0
2
0
2
2
1
3
1
0
1
1
1
1
2
2
0
0
1
1
1
0
0
2
1
1
1
1
2
1
1
2
1
0
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
0
2
1
1
2
1
1
0
0
1
1
1
0
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
0
0
1
0
0
2
1
1
1
1
2
3
1
1
1
1
0
2
1
1
1
1
1
1
1
0
1
3
1
1
2
1
1
1
1
1
1
1
1
1
1
0
1
0
1
2
1
2
1
1
1
1
1
1
2
2
1
2
1
1
2
1
1
1
2
1
1
1
1
1
0
1
2
1
2
2
1
2
1
2
1
1
1
1
1
1
2
1
1
0
2
1
1
1
2
1
2
1
1
1
1
1
1
2
0
1
1
1
1
1
1
0
1
1
1
2
2
1
1
1
1
1
1
1
3
1
1
2
2
1
1
2
2
0
1
1
2
1
2
1
1
0
2
1
2
1
1
1
2
1
0
0
1
1
1
1
2
2
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
0
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
2
1
2
1
1
1
0
1
1
1
0
1
1
2
1
1
0
2
1
1
1
1
1
1
0
0
0
2
1
2
2
0
2
1
2
1
1
1
1
1
0
1
0
2
0
1
3
0
2
2
1
2
1
2
2
1
1
1
0
1
0
1
1
0
1
1
1
1
2
1
1
1
0
1
1
1
2
1
1
1
1
1
0
0
1
2
0
1
1
1
0
0
1
1
2
2
0
1
0
0
0
2
1
2
1
1
0
1
2
2
1
1
1
1
2
1
2
2
1
2
2
0
2
1
1
1
0
1
3
0
1
2
1
2
1
0
1
1
2
1
2
1
2
0
1
1
1
1
1
2
2
0
1
1
1
1
1
0
1
1
1
2
0
1
2
2
1
2
1
0
1
0
1
2
1
2
1
1
1
1
1
0
0
1
0
1
1
1
0
1
1
0
1
0
1
1
1
2
2
1
0
1
0
2
1
2
2
1
2
1
1
2
2
2
1
2
1
1
0
1
1
0
0
1
1
1
1
1
1
2
1
1
0
1
1
2
1
1
1
2
2
0
1
0
2
0
2
0
1
1
1
2
1
2
1
1
1
1
4
1
0
2
0
2
1
1
0
2
2
1
2
0
1
1
1
2
0
1
1
2
2
2
1
0
2
2
2
1
1
2
2
1
2
0
1
1
0
2
2
0
1
0
1
1
1
1
1
2
3
2
0
2
1
0
0
1
1
2
1
0
2
2
1
0
0
2
1
1
1
0
2
1
1
2
1
0
1
1
2
0
0
0
1
1
1
1
1
2
0
2
1
1
1
1
0
1
2
1
3
1
1
1
2
0
1
1
1
2
1
1
1
1
2
0
1
0
2
1
2
2
1
1
1
0
1
1
0
1
0
0
1
1
1
2
0
1
1
1
1
0
1
1
2
1
1
0
1
1
1
1
2
1
1
0
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
0
1
1
1
1
0
2
1
0
2
1
2
2
1
0
0
2
1
1
2
1
2
1
1
1
1
0
0
2
1
1
1
2
1
2
1
1
1
1
2
1
2
1
0
1
1
0
1
2
1
0
1
1
2
0
1
1
2
1
2
2
1
1
1
1
1
1
2
1
1
0
0
1
0
1
0
1
1
1
1
1
1
1
2
1
1
1
0
2
1
2
4
1
1
0
1
1
2
1
2
0
2
2
2
1
1
1
0
1
2
1
1
1
2
0
1
1
1
1
0
0
2
2
0
2
1
2
1
0
2
2
1
2
2
1
1
1
1
2
0
1
1
2
1
0
1
1
0
1
1
3
1
2
1
0
2
1
0
1
1
1
0
0
2
2
1
0
1
1
1
2
1
1
2
1
2
1
0
1
1
2
2
0
2
1
2
2
1
0
2
0
2
0
1
1
0
2
2
1
2
1
0
1
1
0
1
1
2
1
1
1
1
2
1
1
1
0
1
1
1
1
1
0
1
1
1
1
0
1
2
1
1
1
2
1
2
2
1
0
2
1
0
3
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
2
1
1
2
1
1
0
0
2
1
1
1
0
1
1
1
1
1
1
1
1
1
1
3
1
2
1
5
2
1
1
0
0
1
1
2
1
1
2
1
2
1
1
1
1
1
2
1
1
0
0
1
1
2
1
2
0
1
1
1
1
1
2
1
1
2
1
2
1
2
0
0
1
0
2
2
1
0
1
1
1
0
0
2
1
1
1
0
1
0
0
2
1
1
1
1
1
1
0
2
1
1
1
0
2
1
2
1
2
1
0
1
1
2
1
2
1
1
2
1
2
1
2
1
2
1
1
1
1
1
1
1
1
2
0
1
1
0
2
2
1
1
1
0
2
1
0
1
1
1
0
2
1
0
1
1
1
1
1
1
1
2
2
1
0
0
1
1
0
1
1
1
1
0
1
2
1
1
2
2
0
3
1
1
2
1
1
1
1
0
0
1
1
0
0
2
1
1
1
2
1
0
1
1
0
1
0
3
0
2
1
0
1
2
2
1
2
1
2
5
2
1
1
2
2
2
1
1
0
1
1
2
1
2
1
0
1
2
2
0
0
0
1
2
1
0
1
0
1
1
1
1
1
1
1
1
0
1
1
1
2
1
1
1
1
1
1
1
2
1
0
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
1
1
1
0
0
0
0
1
0
2
2
1
1
1
2
0
2
1
0
2
1
0
1
1
2
1
1
2
2
2
1
1
1
1
1
2
1
0
2
1
1
1
2
0
1
1
1
1
1
0
1
2
0
1
4
1
1
2
1
1
2
2
2
1
2
0
2
1
2
1
0
0
1
2
1
0
1
2
1
2
2
1
1
0
1
1
1
1
2
1
1
0
1
0
1
1
1
2
1
0
2
1
1
1
1
2
2
0
1
2
1
2
1
2
0
0
0
1
1
1
2
1
2
1
1
0
2
2
1
0
1
1
1
2
1
1
1
1
2
1
1
2
2
0
0
0
1
1
2
1
1
1
1
1
1
2
1
2
1
0
1
1
1
2
1
2
0
1
1
2
1
0
2
1
1
1
1
3
1
1
1
1
1
0
1
1
0
1
1
1
2
0
1
4
1
1
1
1
1
0
1
0
1
4
1
1
1
1
1
2
1
1
2
1
1
1
1
2
2
1
1
1
1
1
1
2
0
1
1
1
0
2
2
1
2
1
0
0
0
0
1
2
1
0
2
0
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
0
2
1
2
1
1
1
1
0
0
0
1
2
1
0
0
1
2
2
3
1
1
1
2
1
4
1
1
1
1
1
1
1
0
1
1
1
2
1
1
1
0
2
2
2
2
1
1
1
2
1
2
1
1
1
1
1
2
1
1
2
2
1
1
0
2
2
2
1
2
2
0
2
1
2
1
1
0
0
1
2
1
1
2
2
2
1
1
1
1
1
1
2
1
0
1
2
1
1
1
1
2
2
1
0
1
1
1
0
2
1
0
1
1
1
1
1
1
0
1
0
0
1
1
1
1
1
1
1
0
1
2
0
2
2
1
1
0
1
1
2
0
2
1
2
1
1
2
1
1
2
1
1
2
1
1
0
1
1
2
2
0
1
0
1
1
0
1
0
1
2
1
1
0
1
1
1
1
1
2
1
1
1
1
1
0
1
1
1
2
0
2
2
0
2
1
2
4
2
1
1
1
1
2
1
1
1
2
0
2
1
0
1
1
2
1
0
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
0
0
1
1
2
1
0
0
1
1
0
2
1
1
1
0
1
0
1
2
1
1
1
0
2
2
2
2
1
1
2
1
2
1
1
1
2
1
0
2
1
1
1
2
1
1
1
1
0
1
1
1
1
1
0
0
1
1
1
0
1
2
1
1
1
1
1
1
1
1
0
1
1
0
1
1
1
2
1
0
3
6
0
1
1
1
1
1
1
1
1
1
0
1
2
1
1
1
0
1
1
1
2
1
2
0
2
1
1
2
2
0
1
1
0
0
1
1
2
1
2
1
1
1
1
1
0
1
1
1
0
1
2
0
2
1
1
1
0
2
2
1
1
1
1
1
1
1
1
1
0
3
2
0
1
1
1
1
1
0
0
2
1
0
1
1
1
2
1
1
1
1
1
1
1
1
2
0
1
1
0
1
1
1
1
1
1
2
2
1
1
2
2
1
1
1
2
1
0
1
2
1
2
0
1
1
1
1
2
1
0
2
1
1
1
1
1
0
0
1
2
1
1
2
1
0
1
2
1
1
1
1
1
1
0
2
2
1
0
0
0
1
1
2
0
1
2
1
1
0
2
1
1
1
2
0
1
0
1
1
2
1
2
1
1
1
2
2
1
1
2
1
2
0
2
2
1
2
0
2
1
1
1
1
1
1
1
2
1
2
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
2
2
1
2
0
1
1
2
1
0
0
1
1
0
1
3
0
1
0
2
1
1
0
2
5
1
1
1
2
1
1
1
2
0
2
1
1
2
1
2
2
1
1
1
1
2
1
1
0
1
0
1
1
2
1
1
1
1
1
1
2
2
0
1
1
1
2
0
1
1
2
2
1
1
0
1
2
1
1
1
1
2
1
1
1
2
2
1
0
1
0
1
1
1
1
0
1
0
0
1
1
1
2
1
1
1
0
2
1
0
1
1
0
2
0
1
2
1
2
1
1
1
1
0
1
2
1
1
0
1
0
1
2
0
2
1
0
1
1
0
5
1
1
1
1
1
1
1
1
1
0
1
1
2
1
0
1
1
1
2
1
1
1
0
1
1
1
2
1
1
1
2
1
2
1
1
1
2
0
1
2
0
1
2
1
1
1
2
1
0
1
1
2
2
1
1
1
0
1
1
1
1
0
0
2
2
1
1
0
1
1
1
1
2
2
1
1
1
0
0
1
2
1
1
1
1
1
2
2
2
1
2
1
1
1
0
2
1
0
1
1
1
1
0
2
1
1
1
2
1
0
2
1
2
0
1
1
1
1
2
1
2
1
1
1
2
1
2
1
1
1
1
0
0
1
0
1
1
1
1
1
0
0
1
1
2
2
1
1
2
1
1
1
1
1
2
1
1
0
1
1
0
2
1
2
1
1
0
1
2
2
1
1
2
2
2
2
1
1
0
1
1
2
0
2
0
0
1
1
2
1
1
1
1
1
1
1
1
0
1
2
1
2
1
1
1
1
1
1
1
1
1
2
2
1
1
1
2
1
1
1
0
2
0
2
1
2
1
1
1
1
1
1
1
1
0
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
0
0
0
0
1
1
2
1
2
1
2
1
1
1
1
1
1
1
3
1
1
2
1
3
1
1
0
2
1
0
1
2
1
1
0
0
2
1
1
1
0
1
2
0
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
2
1
1
1
0
0
2
1
0
1
1
1
1
0
1
1
1
1
0
1
1
1
1
0
1
1
1
2
1
1
0
1
1
1
1
1
2
0
0
1
1
1
2
2
1
1
0
2
1
1
2
1
0
1
1
2
1
2
1
1
1
1
1
2
2
2
2
2
1
1
2
1
1
1
0
1
1
1
1
0
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
1
0
1
2
1
1
1
0
1
0
0
2
1
1
1
1
0
0
2
0
2
1
2
1
1
1
2
0
1
0
2
1
1
1
1
2
0
0
0
2
2
2
1
0
1
1
2
1
0
0
0
0
1
1
0
1
1
1
1
1
1
0
2
1
2
2
1
2
0
0
1
1
1
0
1
1
0
0
2
2
2
1
1
0
2
1
1
2
0
1
1
1
2
1
0
1
1
0
1
2
0
2
1
1
1
1
1
1
1
0
2
2
1
1
1
1
1
2
0
1
2
2
1
2
1
1
2
1
0
1
1
1
1
2
2
1
1
1
1
1
1
0
0
1
1
2
0
1
1
1
1
0
0
2
2
1
1
2
4
1
1
0
1
1
1
2
1
1
1
2
1
1
1
2
2
2
1
1
2
1
1
3
1
1
1
2
0
1
1
2
1
1
1
1
1
1
0
0
0
0
0
1
2
2
2
0
1
1
1
1
1
2
1
1
2
0
2
0
0
1
0
1
1
2
2
1
1
1
1
1
1
0
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
0
1
0
1
1
2
2
1
1
2
1
2
2
1
1
1
2
1
2
1
1
1
1
1
1
1
0
1
1
2
1
2
0
2
2
1
0
1
2
0
1
2
1
0
1
1
1
1
1
1
1
1
1
1
1
1
0
1
0
1
0
0
1
1
2
1
1
1
2
1
1
1
2
2
2
1
2
1
1
2
2
0
1
1
2
1
1
0
0
0
1
2
0
1
1
1
1
2
0
1
1
1
0
1
0
0
0
1
1
0
1
2
0
1
1
1
2
0
2
0
2
1
1
1
0
2
1
1
2
2
0
0
1
0
1
1
1
1
1
1
2
1
1
0
0
1
0
0
0
3
2
1
1
1
2
2
1
2
1
2
2
0
1
0
1
2
1
2
1
1
2
0
1
0
0
1
2
2
1
1
1
0
1
0
0
1
2
2
1
2
1
2
1
0
0
2
1
2
1
1
2
2
1
0
2
2
1
1
2
1
1
1
1
2
0
1
1
2
0
1
2
1
0
1
2
1
1
0
1
1
1
1
0
0
1
1
1
2
2
1
2
1
1
1
0
2
1
1
1
1
1
2
1
1
1
0
0
0
1
0
1
2
3
1
2
2
0
1
2
0
1
0
2
1
1
1
1
1
1
0
0
0
1
1
1
1
2
1
2
0
0
2
2
2
0
1
1
1
2
1
2
1
1
3
2
1
1
0
1
1
1
1
1
0
2
2
1
2
1
0
1
2
1
0
1
1
1
1
1
0
1
2
1
1
1
1
1
1
1
1
0
1
0
1
0
1
1
1
1
2
1
1
0
1
0
1
1
1
1
1
1
1
1
1
2
1
0
1
3
0
1
1
1
1
1
0
1
0
2
2
0
0
2
1
2
0
1
0
0
1
2
2
1
1
1
0
2
1
1
3
1
1
1
1
0
2
2
2
2
1
0
3
2
2
2
1
2
1
1
0
2
0
0
0
0
1
1
2
1
1
2
1
2
1
1
1
1
1
0
0
1
0
0
1
1
1
1
1
1
1
1
1
0
1
0
2
1
1
1
1
0
1
1
1
2
0
1
0
1
0
0
0
0
1
1
1
1
2
2
1
1
1
1
2
1
1
1
2
0
1
0
1
1
1
1
2
2
2
1
1
1
2
0
0
1
1
2
1
2
1
2
1
0
0
2
1
1
2
0
0
0
2
1
0
2
0
1
2
1
2
1
1
2
1
1
1
2
1
1
2
2
2
2
1
1
1
1
1
1
0
0
0
1
1
1
1
0
1
1
2
1
1
1
1
2
1
1
1
0
1
2
1
1
2
0
1
1
0
1
1
0
1
2
1
2
0
1
2
1
1
0
0
1
2
1
0
1
1
2
1
2
1
1
1
0
1
1
0
2
1
1
2
1
0
2
1
1
1
2
1
2
1
1
1
1
0
0
2
1
0
0
2
1
0
1
0
1
0
2
2
2
1
1
1
1
0
0
1
1
2
1
0
0
1
0
1
1
1
1
2
1
2
1
1
2
0
1
1
1
2
3
1
1
2
1
2
2
2
2
1
1
2
1
0
2
2
1
2
1
2
1
1
1
1
1
2
1
2
1
2
0
1
1
2
1
1
1
2
1
1
0
1
0
2
1
0
1
1
1
2
2
1
1
2
2
1
1
1
1
1
0
1
0
2
1
1
1
2
0
1
0
2
1
0
1
0
0
2
1
0
2
1
0
2
1
2
1
1
1
0
2
1
1
2
1
1
0
1
2
2
0
1
1
1
1
1
1
1
1
1
3
2
1
0
1
1
0
1
1
0
2
1
1
1
1
1
1
1
2
1
0
0
2
0
0
1
2
1
1
1
0
1
2
2
1
2
0
1
0
2
1
1
1
1
2
0
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
0
2
3
1
0
2
1
1
1
2
1
1
0
2
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
2
2
0
0
2
1
2
1
1
1
1
2
2
0
1
1
1
1
2
1
1
0
2
0
2
1
0
2
1
1
2
0
1
2
1
1
0
1
0
1
2
2
0
2
2
1
1
2
0
2
1
1
1
0
0
0
1
0
1
1
1
0
1
0
1
1
1
2
0
1
1
1
0
1
2
1
2
1
2
0
1
1
1
0
1
1
2
2
2
1
1
1
1
1
2
1
2
1
2
1
2
1
2
2
2
1
1
2
2
1
1
2
0
1
1
1
0
2
2
0
2
2
2
1
1
1
1
0
0
1
0
1
1
1
1
1
4
2
1
4
1
2
0
1
2
1
2
1
1
1
0
2
1
1
2
0
1
1
0
1
1
0
0
2
1
1
2
2
2
1
1
0
1
1
2
1
1
1
1
1
1
2
1
2
2
2
2
1
1
1
2
2
2
1
1
2
3
1
2
2
1
0
1
0
2
1
0
1
1
1
0
1
1
2
1
1
1
1
0
2
0
1
0
1
2
1
0
1
2
2
0
1
1
1
0
0
1
1
1
2
1
1
1
1
1
3
2
0
1
1
1
0
1
0
2
1
1
1
1
2
1
0
1
0
1
1
1
1
2
1
1
0
2
1
1
1
1
1
0
1
1
1
1
1
2
0
1
1
1
1
1
1
1
1
2
0
1
2
1
1
1
2
0
1
1
1
0
1
1
0
1
1
1
0
0
1
1
1
1
2
1
1
1
2
1
1
0
1
1
0
0
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
2
1
0
1
2
2
1
2
1
2
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
0
1
0
0
1
1
0
1
0
0
1
1
1
1
1
0
1
2
2
1
1
0
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
0
1
1
1
1
0
2
1
2
1
1
1
0
0
1
1
1
1
1
1
1
1
1
1
1
2
1
2
0
0
1
1
1
0
1
1
1
1
2
1
1
1
1
1
0
1
1
2
2
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
2
0
3
1
1
2
1
2
1
1
1
1
0
1
1
0
0
1
3
0
1
0
2
0
1
1
1
1
1
1
0
1
2
2
2
0
0
2
1
1
2
0
1
2
1
0
1
1
1
1
2
1
2
1
1
1
1
2
1
1
1
2
2
2
2
1
1
0
1
1
1
0
0
2
1
0
0
0
2
1
1
1
2
0
2
1
2
1
1
1
0
1
2
1
0
1
2
1
1
1
1
1
1
0
2
1
1
1
1
1
0
0
2
1
2
0
1
1
0
1
2
1
0
2
1
1
2
1
1
2
0
1
1
1
2
2
1
2
2
2
1
2
1
0
0
1
1
0
1
0
1
1
1
1
2
1
0
2
1
1
0
1
2
2
2
1
1
1
1
1
1
0
2
0
1
1
2
1
0
2
2
0
1
1
1
1
2
1
1
2
2
1
1
1
0
0
2
2
1
0
0
0
1
0
2
1
0
1
1
1
2
0
2
1
1
1
0
0
1
1
1
1
2
1
1
1
1
2
1
2
1
2
2
1
1
2
1
1
2
2
0
1
2
1
1
1
0
2
2
0
0
1
2
1
0
2
0
1
1
2
1
1
2
5
0
1
1
0
1
1
2
2
2
2
2
1
1
1
0
1
1
1
1
0
2
2
1
0
1
0
1
2
0
2
1
2
0
0
2
2
1
1
2
2
1
1
2
1
0
1
1
1
1
1
2
1
1
1
2
2
2
1
2
1
0
1
1
2
1
2
2
2
2
1
2
2
1
1
1
0
1
1
1
1
1
1
1
1
0
1
2
0
1
1
1
1
1
2
2
1
2
0
1
1
1
2
2
1
0
1
0
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
2
0
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
0
2
1
1
1
1
0
0
1
0
1
1
1
1
1
1
0
1
1
0
1
3
1
1
1
1
2
2
1
0
1
0
1
1
0
0
1
2
1
1
2
0
1
1
2
1
1
2
2
1
2
1
1
1
1
2
1
2
1
1
0
1
1
1
0
3
1
1
1
1
1
0
0
2
2
0
0
1
1
2
1
1
1
2
1
1
0
2
1
1
1
2
0
1
1
1
0
1
1
0
1
1
1
1
0
1
0
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
2
2
1
0
2
1
1
1
1
2
1
0
1
2
2
1
1
0
0
2
2
1
2
1
2
0
2
1
1
1
1
1
1
1
0
1
1
1
1
1
1
2
1
3
2
1
1
1
1
1
1
1
1
1
2
0
2
2
1
1
1
1
1
1
2
0
0
2
3
1
1
0
0
1
2
1
1
1
1
3
2
1
0
1
1
1
2
1
2
0
1
2
0
1
0
0
0
1
0
1
3
1
2
2
1
1
1
2
1
1
1
1
3
1
2
3
1
1
2
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
0
1
1
1
1
2
1
1
2
1
1
1
0
0
2
1
0
2
0
2
1
1
2
2
0
1
1
1
1
2
2
1
0
0
1
1
2
1
0
1
1
1
1
1
1
2
1
0
2
1
1
1
1
1
5
1
1
1
1
2
2
2
0
0
2
2
2
1
2
2
0
2
1
2
1
1
1
1
0
1
1
2
2
1
0
1
2
2
1
2
1
1
1
2
1
1
1
2
2
2
1
1
2
0
2
1
1
1
1
1
1
3
2
0
1
0
1
1
0
1
0
1
0
1
1
0
1
2
1
2
2
1
0
2
1
0
1
1
0
1
1
1
2
1
1
1
1
2
0
2
2
1
1
0
2
1
2
3
1
1
0
1
0
2
1
1
1
1
1
1
1
2
0
1
1
1
1
2
2
1
1
2
1
1
1
2
1
0
1
0
1
1
1
2
2
1
1
1
1
2
2
1
1
1
1
1
1
0
0
1
3
1
2
0
2
2
1
1
1
0
0
2
0
1
1
1
0
0
1
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
1
2
1
2
1
2
0
1
1
1
1
1
0
2
1
1
1
1
0
1
0
0
1
1
2
1
0
1
0
1
1
1
4
1
1
0
1
2
2
1
1
1
2
1
1
0
1
1
1
1
1
2
1
1
1
1
2
1
0
1
1
2
1
1
2
1
0
0
2
1
2
0
1
1
1
1
1
1
1
1
0
0
1
0
1
0
1
1
1
8
0
1
0
1
1
1
2
1
2
0
1
0
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
0
4
2
1
1
1
0
1
1
1
1
1
1
1
1
1
0
1
2
2
1
2
1
1
1
2
0
1
1
2
1
0
1
1
1
1
1
1
0
0
0
0
0
2
2
1
0
1
2
1
2
1
1
0
1
0
1
1
2
0
1
1
2
2
0
0
1
1
1
0
0
1
1
1
1
1
2
2
0
1
1
2
1
1
1
1
1
2
1
2
3
1
1
1
1
1
1
1
2
0
1
1
1
2
1
1
2
1
1
0
1
3
1
2
1
2
0
1
1
1
1
0
0
1
0
0
3
1
1
1
1
0
0
1
1
2
0
2
1
1
1
0
0
1
1
1
1
1
2
2
1
1
1
0
2
1
2
1
2
1
1
2
1
1
0
1
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
0
2
2
0
0
1
1
2
2
1
0
1
1
1
0
1
1
1
1
0
0
1
1
1
5
1
0
2
2
0
2
0
2
0
2
0
1
1
1
1
2
1
1
2
0
2
1
1
0
1
0
0
1
0
1
0
2
1
0
0
1
1
2
1
1
1
1
1
2
1
1
2
0
2
1
0
2
2
1
0
1
1
2
1
1
2
1
1
2
1
0
1
1
1
1
1
2
1
2
1
1
1
0
1
2
2
0
0
1
2
1
1
1
1
1
1
1
2
1
2
2
0
0
1
1
2
1
0
2
1
2
2
1
1
1
2
0
1
2
1
1
1
1
1
1
1
2
2
1
0
2
2
1
1
0
2
2
1
1
1
1
2
1
1
0
0
2
0
1
1
1
1
2
0
1
1
1
0
1
2
0
2
4
2
1
0
1
3
1
0
0
1
1
2
1
1
2
1
3
2
1
1
1
2
1
0
2
1
2
1
1
0
0
1
0
0
1
1
1
1
1
1
1
0
1
1
1
2
2
2
1
1
0
1
1
0
1
1
2
1
2
2
1
1
2
1
1
0
1
1
0
0
1
1
2
2
1
1
1
1
0
2
1
3
2
1
2
1
2
0
2
1
2
1
1
1
0
1
1
3
0
1
1
0
2
1
1
1
2
1
1
2
1
0
1
1
0
1
1
1
2
1
0
1
0
0
1
1
0
1
1
0
2
1
1
1
1
1
1
1
1
1
0
1
2
1
1
1
0
1
1
2
2
1
0
1
1
1
0
0
1
2
0
1
0
1
2
1
0
2
2
1
2
1
1
2
2
0
2
1
0
2
1
1
0
1
1
1
1
0
2
2
2
1
0
1
1
1
1
1
2
1
1
2
1
0
1
2
1
1
0
1
0
0
0
1
0
1
0
2
2
2
2
0
1
1
2
1
0
1
1
2
1
1
1
1
2
1
0
0
0
2
1
0
1
1
1
1
2
3
2
1
1
1
2
0
2
1
1
2
1
0
1
2
2
1
1
2
0
2
1
1
1
1
1
1
1
1
1
1
10
1
2
1
1
1
2
0
2
0
0
1
1
2
0
1
2
1
2
1
0
0
2
1
0
1
0
0
1
1
1
2
1
2
1
1
2
1
1
1
1
2
1
2
2
2
1
0
1
2
1
1
1
1
1
1
1
2
1
1
1
2
1
1
2
1
2
2
1
0
1
1
1
1
2
1
2
1
1
2
2
2
0
2
0
1
1
1
1
1
1
1
1
0
1
2
1
1
2
1
1
2
1
2
1
1
0
2
0
2
1
1
1
1
2
2
1
2
0
0
2
1
1
0
1
0
1
1
1
1
1
2
1
1
2
2
1
1
1
1
2
0
2
1
1
2
1
1
0
1
1
2
2
1
2
0
0
2
1
0
1
1
1
1
1
0
2
1
2
2
2
2
0
1
1
2
1
1
0
1
1
1
2
2
1
2
1
1
0
1
1
0
1
1
2
1
1
1
1
2
0
1
0
2
1
1
2
1
1
1
1
3
2
1
1
0
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
2
2
0
1
1
1
1
0
0
1
1
2
2
0
0
2
1
0
1
1
1
1
1
1
2
1
1
2
1
1
1
2
1
1
1
0
0
1
2
1
0
0
1
2
2
1
1
1
1
0
1
1
2
1
1
1
1
1
1
1
2
0
0
0
1
2
1
4
2
1
0
1
2
0
1
2
0
1
1
1
1
2
1
1
1
2
1
1
1
1
1
0
1
1
1
1
1
0
1
1
1
0
1
1
0
2
1
1
1
1
2
1
2
1
1
0
1
1
0
1
2
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
0
0
1
2
1
1
0
1
1
0
1
1
1
0
1
0
0
1
2
0
1
1
2
0
1
1
2
1
0
0
1
2
1
2
1
2
1
1
2
1
0
1
1
1
0
1
1
1
2
1
2
1
0
2
1
1
1
1
1
1
0
2
1
1
1
1
1
1
1
1
2
2
1
0
2
2
2
0
0
1
2
2
1
1
1
1
1
2
1
2
2
1
0
1
1
2
0
2
0
2
0
1
0
2
1
1
1
1
2
1
1
1
0
2
1
0
1
1
3
0
1
0
1
2
0
1
1
1
1
1
0
1
2
1
2
2
2
2
0
0
0
1
0
0
1
1
1
1
1
0
2
1
2
2
2
0
0
0
1
0
1
2
2
0
2
0
1
2
1
0
1
0
1
2
0
1
1
1
1
2
0
1
1
1
1
1
1
1
1
2
1
2
1
1
0
1
1
1
2
1
1
1
1
1
2
0
1
1
1
2
1
1
1
0
1
1
0
1
1
0
2
0
0
0
3
1
2
1
1
1
1
1
0
2
0
1
1
0
1
2
1
1
1
0
1
0
1
2
0
1
2
0
1
2
1
2
1
1
3
0
1
1
1
0
1
1
2
4
2
1
1
1
1
1
0
2
2
1
1
2
2
1
1
2
0
0
1
2
1
1
1
0
1
2
2
1
2
1
1
2
1
1
1
2
1
1
1
2
1
0
3
1
1
1
2
1
1
1
1
0
2
1
1
1
1
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
2
0
1
1
1
1
1
2
0
0
2
1
1
1
1
1
1
0
1
0
0
0
1
1
1
1
1
2
2
0
1
2
0
1
2
2
2
1
2
0
1
1
0
1
1
2
2
0
0
2
3
1
2
1
0
1
1
1
1
1
1
1
0
1
2
0
2
0
2
1
1
1
1
1
0
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
0
1
1
1
0
0
2
1
3
0
1
1
1
0
2
0
0
1
1
1
1
1
1
2
2
1
1
2
2
2
1
0
2
2
1
1
1
0
1
2
0
1
2
0
1
1
2
2
0
1
1
0
1
2
1
0
1
1
2
0
1
0
2
1
1
1
0
1
0
1
0
0
1
2
1
2
1
1
1
1
1
1
0
1
1
2
1
1
0
1
1
1
1
1
1
1
1
0
1
0
1
1
0
1
1
2
0
2
1
2
1
1
1
1
1
2
1
1
2
1
1
1
1
2
1
1
2
2
1
2
2
0
1
1
0
1
2
1
1
1
1
2
0
1
0
2
2
2
2
0
1
1
0
1
1
1
2
0
1
1
1
0
1
1
1
2
2
0
1
1
2
0
0
1
1
1
1
0
2
1
1
1
1
1
0
2
2
2
1
1
1
2
0
2
1
1
2
1
0
1
2
1
1
2
1
1
1
1
0
1
1
0
1
2
1
1
2
2
2
2
0
1
1
2
0
1
1
2
1
0
0
2
1
1
1
1
1
2
1
1
1
0
1
1
1
1
1
1
2
0
0
1
1
0
0
0
1
1
1
1
1
2
2
2
2
1
1
0
1
1
1
1
1
1
1
1
1
2
1
2
1
2
1
1
1
1
1
0
0
1
1
1
1
0
2
2
1
1
1
1
1
2
1
0
1
1
2
1
1
1
0
1
1
1
1
2
1
1
1
1
2
0
1
1
1
1
0
2
1
2
1
0
1
1
3
1
2
2
2
1
1
1
2
0
1
2
1
1
0
0
1
2
2
1
2
1
1
1
0
1
2
0
0
1
1
1
1
1
2
1
1
1
1
1
0
2
1
1
1
0
0
0
1
1
1
2
2
1
1
2
2
1
2
2
1
1
1
0
2
1
1
1
2
1
1
1
1
1
2
1
1
2
1
2
1
0
1
1
0
1
1
2
2
1
2
2
1
0
2
1
2
0
1
1
1
2
2
1
1
0
1
0
1
1
2
2
1
0
0
1
2
1
1
2
1
1
0
2
2
1
1
1
1
1
1
1
0
1
1
2
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
0
2
1
1
1
3
2
1
0
2
1
2
2
0
1
2
1
2
1
1
2
2
1
1
1
1
1
0
1
2
1
1
0
1
1
1
0
0
1
1
2
0
2
1
1
1
1
2
0
2
1
1
0
1
0
1
2
2
1
1
2
1
2
2
0
1
1
2
1
2
1
2
1
1
0
1
1
1
1
1
1
1
0
0
2
1
2
1
0
2
2
1
0
2
0
1
0
1
1
0
1
1
1
1
2
1
1
1
1
2
0
1
0
2
1
1
1
1
1
1
0
1
1
1
0
1
1
0
1
1
1
0
1
2
1
0
1
1
2
2
1
0
0
0
0
0
0
0
1
1
2
1
2
1
2
0
3
2
0
2
1
1
2
1
0
1
2
1
0
1
1
0
0
1
0
1
1
2
0
1
1
0
1
0
1
1
1
1
1
0
1
1
0
0
1
1
1
1
2
1
1
1
1
2
1
1
1
0
1
1
1
1
2
1
1
1
1
1
0
1
2
1
1
1
1
1
1
2
1
1
1
2
0
1
0
1
0
0
0
0
1
1
3
1
2
1
1
1
1
1
1
2
1
1
1
0
1
1
1
1
1
2
1
1
1
1
0
2
2
1
2
2
1
2
2
1
1
1
1
1
1
0
1
0
0
1
0
1
1
0
1
1
1
1
1
0
2
1
2
0
1
0
0
2
2
0
0
3
1
1
2
1
2
1
1
0
1
1
1
2
1
3
1
0
1
1
2
0
1
1
1
2
1
2
2
1
1
2
2
1
1
0
1
1
0
0
0
1
1
1
0
0
1
2
1
1
0
1
1
1
0
1
1
1
1
1
2
1
0
1
0
2
1
0
1
1
2
2
1
1
1
1
1
2
1
1
1
1
1
1
5
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
0
1
1
1
1
1
0
1
2
2
1
1
1
1
1
1
2
1
2
1
0
2
1
1
2
2
1
1
1
0
2
2
0
2
0
1
0
1
1
1
1
1
1
0
0
1
2
2
0
1
0
1
1
2
0
2
1
1
1
2
0
2
2
0
1
0
2
2
1
2
1
2
6
1
1
1
1
1
0
3
2
0
1
0
1
2
1
2
2
1
0
1
1
1
1
1
1
1
1
1
1
1
1
0
0
1
2
0
1
2
0
1
1
0
1
2
1
1
2
0
1
3
0
1
1
0
1
1
1
1
2
1
1
1
0
2
1
1
1
2
0
2
1
1
2
1
2
2
1
1
1
0
2
1
1
0
0
1
0
0
1
2
1
1
0
0
2
2
2
1
2
1
1
0
0
1
1
1
1
1
1
1
2
1
1
2
0
1
1
1
1
0
2
1
1
2
2
1
1
0
2
2
1
1
2
1
1
1
1
2
1
0
2
1
0
2
1
1
0
1
2
1
1
1
1
1
1
1
1
0
2
1
1
1
1
2
1
1
2
0
2
1
0
1
1
0
1
1
2
2
1
1
1
2
2
1
1
1
1
2
0
1
0
1
1
1
2
1
1
2
1
0
0
2
0
0
1
1
2
1
2
1
2
1
0
1
1
1
2
2
2
1
1
1
2
1
1
1
1
0
0
1
1
1
2
1
1
1
1
1
1
1
1
2
0
2
1
0
1
1
0
1
0
0
1
0
2
2
0
1
1
1
0
0
1
0
0
1
1
1
1
1
1
2
2
1
1
1
1
0
1
1
1
1
1
0
1
0
0
1
1
1
1
0
2
0
2
2
1
1
1
0
1
2
2
0
1
1
1
1
1
1
1
0
1
1
1
1
2
1
1
1
2
0
1
1
2
1
0
0
1
0
1
1
2
5
1
1
2
1
1
1
0
2
1
1
1
2
1
2
1
1
1
0
1
1
1
1
1
2
2
2
1
1
1
1
0
1
0
1
1
0
1
1
1
1
2
1
0
1
0
2
2
2
1
1
2
2
1
2
1
1
1
0
2
1
1
2
1
1
1
0
1
1
2
1
0
2
1
2
2
1
1
1
0
1
1
0
1
2
1
1
2
1
2
2
1
1
1
1
1
3
1
2
2
2
1
1
1
1
1
0
2
1
2
1
1
0
1
0
1
2
2
1
1
1
0
1
2
1
1
1
0
1
1
1
2
2
1
2
1
1
1
1
0
2
1
1
0
0
1
1
1
2
1
2
0
0
1
1
0
0
0
1
0
1
1
0
1
2
2
0
1
1
1
1
2
2
1
1
0
0
1
0
1
1
2
0
1
1
2
2
1
2
1
1
2
1
1
0
0
1
1
1
2
1
1
0
1
1
1
2
1
1
0
1
2
1
1
2
2
0
1
1
1
1
3
1
1
2
1
2
1
1
0
0
1
0
1
1
2
1
2
1
1
0
0
2
1
1
1
2
1
1
2
0
1
1
1
2
1
1
1
1
1
2
2
1
1
1
1
2
1
2
1
1
2
2
0
2
2
1
1
1
1
2
0
1
0
2
2
1
0
0
1
1
1
0
1
1
1
1
2
1
2
2
0
1
1
1
0
1
1
1
1
0
5
1
1
1
1
1
1
1
2
1
2
1
0
1
2
1
1
1
1
1
4
1
0
0
0
0
1
1
0
2
1
1
1
1
2
1
2
1
2
1
0
0
0
2
1
2
1
2
1
2
1
0
1
1
1
2
2
1
1
1
0
1
1
1
1
1
1
0
1
1
0
1
1
1
1
2
1
2
2
1
1
1
1
1
1
2
0
0
0
0
1
0
2
1
1
2
0
2
1
0
2
2
0
2
2
2
1
2
1
1
2
1
1
0
2
1
1
2
1
1
2
0
1
2
0
2
4
1
2
1
1
1
1
1
1
2
0
2
2
2
1
0
0
0
2
1
1
1
2
0
1
0
2
2
1
1
1
0
1
0
0
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
1
0
1
2
1
0
1
1
0
1
1
0
2
2
1
2
1
1
1
1
1
0
1
2
1
1
1
1
0
2
0
0
2
1
1
1
1
1
2
2
1
0
1
2
2
2
1
0
2
1
1
2
2
2
3
2
0
1
1
0
1
0
2
0
1
0
2
1
0
1
1
0
1
2
1
1
1
0
2
1
1
0
1
1
0
1
1
1
1
0
1
2
1
2
1
1
1
1
1
1
1
1
1
0
0
2
0
1
1
0
1
1
2
2
2
1
1
1
1
0
4
2
1
2
2
1
0
0
0
1
0
1
2
1
0
0
1
1
1
1
1
1
1
0
1
1
1
2
1
1
1
2
0
1
1
2
2
1
1
1
1
0
2
1
1
2
1
1
1
0
1
0
1
1
1
1
0
2
2
0
2
1
0
1
1
0
0
2
1
3
2
1
0
1
1
1
2
1
2
2
0
0
2
1
1
0
2
2
1
1
1
0
1
1
1
1
2
0
1
0
0
1
0
2
1
1
1
1
1
4
2
2
0
1
1
1
0
1
2
1
2
1
1
1
0
1
2
1
1
1
1
2
1
1
1
1
1
1
0
1
1
1
2
0
0
1
2
1
1
0
1
0
1
1
1
1
2
1
1
1
0
1
0
1
1
2
0
2
1
1
1
1
2
2
2
0
1
1
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
1
1
4
0
2
2
1
1
1
0
1
2
2
2
1
1
1
1
1
0
1
0
1
1
0
0
2
2
2
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
2
1
2
2
1
1
1
1
1
0
1
1
1
0
1
1
0
1
1
1
3
1
1
0
0
2
1
1
0
1
1
2
1
0
1
2
1
1
0
2
1
1
0
2
0
1
0
0
0
2
1
1
2
1
1
2
2
0
0
2
1
1
0
1
2
1
0
1
1
1
2
1
2
1
1
1
1
2
1
1
2
1
1
1
0
2
1
1
0
0
1
1
1
1
2
1
1
1
1
1
1
2
0
1
1
1
2
2
1
1
1
1
1
1
1
0
0
1
2
1
0
2
1
1
1
1
2
1
0
1
2
2
2
0
1
0
1
1
1
2
1
0
1
1
2
1
1
2
2
1
2
1
1
1
1
1
0
1
1
2
2
2
2
1
1
2
2
2
0
2
0
1
1
0
1
1
1
1
1
2
3
1
1
1
1
1
1
1
2
1
1
1
1
2
0
1
2
1
1
0
1
1
1
0
0
1
0
1
0
2
1
2
1
1
0
0
1
2
0
1
3
2
1
2
2
1
1
0
1
1
2
0
1
1
1
0
2
2
1
1
1
2
1
1
1
1
1
1
1
1
2
0
0
2
1
0
2
0
0
1
1
1
2
2
1
2
1
1
2
2
1
2
1
1
1
0
1
1
1
1
0
2
2
0
0
1
1
0
0
1
1
1
2
2
1
1
1
1
2
1
2
2
1
0
2
2
1
1
1
2
1
2
1
2
2
0
1
0
1
2
1
0
0
2
2
1
2
0
1
2
1
2
1
0
0
2
1
1
2
1
0
0
1
2
2
1
1
1
1
1
5
1
2
0
1
2
2
0
1
1
1
1
0
1
2
1
1
1
1
1
2
1
0
0
1
0
1
0
1
1
1
1
1
2
1
2
1
1
1
1
1
0
2
1
1
1
1
2
3
1
0
1
1
1
1
0
1
0
1
1
2
2
1
1
1
1
1
0
1
1
1
1
1
1
1
2
2
1
2
1
1
1
2
1
2
1
1
2
2
0
1
2
1
2
1
1
1
1
0
2
1
1
2
1
1
2
1
1
1
1
0
1
2
0
2
1
1
2
2
2
2
1
1
0
2
1
0
2
1
2
1
0
1
1
1
1
1
1
1
2
1
1
1
1
2
1
0
0
1
0
0
1
1
1
0
2
1
0
1
0
2
1
2
0
1
1
0
1
1
1
1
2
1
0
1
1
1
2
1
1
2
1
1
1
2
1
0
1
1
1
1
1
1
1
0
0
0
0
1
1
0
0
2
1
2
1
1
2
1
2
1
0
1
1
1
0
1
0
2
2
1
1
2
2
1
2
0
2
1
2
1
1
1
0
1
1
2
1
1
2
1
2
1
1
2
0
2
0
0
0
1
4
0
1
1
1
0
2
0
1
1
1
0
0
2
2
1
1
2
2
1
1
1
2
1
2
1
1
2
1
1
2
2
1
1
0
1
2
0
0
1
1
1
0
2
1
0
1
2
0
1
1
1
1
1
1
1
1
0
0
2
2
1
0
0
1
1
1
2
1
2
2
1
2
0
1
1
1
1
0
2
1
2
1
1
1
2
1
1
2
0
0
2
1
1
1
2
1
1
1
1
1
2
1
1
0
1
1
2
2
2
3
1
2
1
1
2
2
0
1
2
2
1
2
1
0
1
2
0
1
2
2
0
0
1
2
1
1
1
0
2
1
1
0
0
1
0
1
1
2
0
1
2
2
2
2
2
1
1
1
0
1
1
0
1
2
0
1
2
1
2
1
1
1
2
0
2
1
0
1
2
1
1
0
1
2
1
1
0
0
1
1
1
1
0
2
1
0
1
1
1
1
2
1
0
1
1
1
1
2
1
1
2
1
0
1
1
0
2
0
0
1
1
0
0
0
1
1
1
1
1
2
0
2
2
1
1
1
2
2
0
0
0
1
1
0
1
2
1
0
1
1
1
1
0
1
2
1
0
1
1
1
1
0
2
1
1
1
0
0
1
1
1
1
2
2
1
0
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
0
1
1
1
1
1
1
2
1
0
1
1
1
1
1
1
1
2
0
1
1
2
2
1
1
2
0
1
1
1
0
0
2
1
1
1
1
0
1
2
1
2
0
1
1
2
2
1
2
1
3
0
1
2
0
0
1
2
1
1
0
1
1
2
2
2
2
1
2
1
1
0
1
2
2
1
1
1
1
1
1
1
0
0
1
0
1
2
0
2
2
2
2
1
2
2
1
1
2
1
1
2
1
1
1
0
1
1
1
0
2
1
1
1
1
1
2
2
2
2
2
1
0
1
1
0
1
0
1
0
2
1
1
1
1
1
0
2
1
2
1
1
1
1
1
2
1
0
0
0
1
1
1
1
0
0
1
1
1
1
1
1
2
1
1
3
0
2
2
1
1
0
2
1
0
2
1
1
0
2
1
2
1
1
2
0
1
0
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
0
0
0
0
2
1
1
1
2
1
2
1
1
2
0
0
1
1
1
1
1
1
2
2
1
0
1
1
0
0
0
2
0
1
3
2
2
1
1
1
1
2
1
1
1
0
1
2
1
1
1
1
1
3
2
1
0
1
0
1
0
2
1
1
2
1
2
0
0
1
2
1
1
1
0
0
0
2
2
1
2
1
0
2
1
1
0
1
1
1
1
1
1
1
1
1
2
1
0
1
1
1
0
1
0
1
1
0
1
0
1
1
1
1
1
2
1
0
1
1
1
1
1
2
2
2
2
1
1
2
1
2
1
1
1
0
2
1
1
1
2
4
0
1
1
1
1
1
0
1
1
1
2
1
1
1
1
2
1
1
1
2
2
1
0
1
1
1
2
0
0
1
1
1
1
2
1
1
2
1
1
1
1
1
0
0
0
1
1
1
1
1
1
0
1
0
1
1
2
0
0
0
0
1
1
1
1
1
0
0
0
1
1
1
1
2
1
1
0
0
1
1
1
0
1
2
1
0
2
2
1
1
1
0
1
1
0
1
1
1
1
1
2
1
0
1
1
1
0
2
1
1
1
1
1
0
1
2
2
1
1
0
1
1
2
1
1
2
0
1
0
1
1
1
1
1
2
1
1
2
0
1
1
2
1
0
2
2
0
1
2
0
1
1
0
1
1
1
2
1
1
1
0
1
0
1
1
1
1
1
1
1
1
1
2
2
0
1
0
1
3
1
1
1
1
1
1
2
2
1
1
2
0
0
1
1
2
0
0
2
1
2
2
1
1
1
1
0
1
1
0
2
0
2
2
1
1
2
1
1
1
3
1
1
1
2
1
1
2
1
1
2
1
2
1
2
1
1
1
1
1
1
2
0
2
1
1
1
1
1
1
1
1
2
2
1
0
2
1
2
0
2
1
1
0
1
0
1
1
2
1
1
2
1
1
1
1
1
1
3
2
1
1
1
1
0
2
2
1
1
1
1
1
1
0
1
2
1
2
1
0
2
2
2
2
1
0
1
0
1
2
0
1
2
1
0
1
1
1
2
1
0
2
1
2
1
1
1
1
2
2
2
2
1
1
2
1
1
2
1
1
2
2
2
1
0
1
2
1
1
3
1
0
1
2
2
0
1
1
1
0
1
3
1
1
1
0
1
1
2
1
1
1
2
2
1
2
0
2
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
2
0
2
1
2
1
1
2
2
2
1
1
2
2
1
1
2
0
1
2
2
1
2
2
0
2
0
2
1
1
1
2
2
0
1
0
2
2
7
1
0
1
2
2
1
1
2
0
1
1
1
1
2
0
0
1
0
1
2
1
2
1
1
2
2
1
1
1
2
2
1
2
2
3
1
2
1
1
1
1
1
1
1
0
0
2
1
1
1
2
1
1
1
2
1
1
1
0
2
1
0
1
1
1
1
1
2
1
2
1
2
1
1
1
1
1
1
1
1
2
1
0
2
0
0
1
1
1
1
1
1
2
2
1
0
2
1
1
1
1
1
1
1
1
1
1
1
0
1
1
3
1
0
1
1
1
1
1
1
0
1
1
1
1
1
1
2
2
1
1
0
1
1
2
2
0
1
1
1
1
0
0
0
1
1
2
0
2
2
1
2
0
2
0
1
2
1
1
1
2
2
1
2
2
1
3
1
1
1
4
1
2
0
0
2
2
0
1
1
2
1
0
1
1
1
2
1
1
2
1
2
2
1
1
1
1
2
1
2
2
2
1
1
2
1
1
1
0
1
1
0
3
0
1
2
2
0
1
1
1
2
2
2
0
1
1
2
0
1
2
1
1
1
1
0
0
0
2
1
0
1
0
2
2
2
2
0
2
1
1
1
0
2
1
1
1
1
1
0
1
1
0
2
1
1
1
2
1
1
1
2
1
0
1
1
1
0
1
2
2
1
0
1
2
0
1
1
1
2
1
1
1
0
0
1
2
1
2
1
1
1
4
1
1
1
1
2
1
2
0
2
1
0
1
0
2
0
0
1
1
1
2
1
1
2
1
1
1
1
0
2
1
1
1
1
1
2
2
1
0
1
2
0
2
2
1
2
1
1
1
2
1
1
1
2
1
0
1
1
1
2
2
1
1
1
0
1
2
1
1
1
1
0
1
1
1
1
1
0
2
1
1
1
0
1
1
1
2
1
1
0
1
1
1
1
1
0
1
2
0
2
1
1
1
0
1
0
1
2
1
0
2
2
0
0
0
1
1
0
4
2
0
1
2
0
1
2
1
0
0
0
0
1
0
1
0
1
1
1
1
1
2
1
1
1
0
1
1
1
0
0
1
2
2
0
2
1
2
1
1
1
2
1
1
0
1
0
1
2
2
2
1
1
2
1
2
1
2
1
2
2
1
1
1
1
0
1
2
1
2
2
1
1
2
0
1
1
1
2
1
1
1
1
1
1
0
0
1
1
2
0
0
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
0
1
1
0
1
1
1
1
1
2
1
0
0
1
1
1
1
4
1
2
1
2
1
1
1
1
1
1
2
0
2
2
1
1
1
1
2
3
1
1
1
3
2
1
0
1
2
1
0
2
0
1
1
1
2
1
1
1
1
0
1
1
1
1
1
1
1
1
0
1
1
1
1
1
2
1
2
0
0
1
2
2
0
2
1
1
2
1
0
1
2
1
0
0
2
0
1
1
1
1
1
1
1
1
2
1
2
0
2
1
1
2
1
1
2
1
0
1
1
2
1
0
1
1
1
0
0
0
1
0
2
2
2
2
2
2
1
3
1
2
2
2
1
1
0
0
0
2
1
1
0
1
1
1
1
1
1
2
0
1
1
1
2
2
1
1
1
1
1
1
1
1
2
2
1
1
1
2
1
0
1
2
0
2
1
0
1
1
0
1
1
1
2
1
1
0
2
1
1
0
1
0
2
2
1
1
2
1
0
2
1
1
1
1
1
2
1
1
1
0
1
1
1
1
1
0
1
2
0
0
1
1
1
0
1
1
1
2
1
0
0
0
1
1
2
2
1
0
2
1
1
2
1
1
0
1
2
1
1
2
1
3
1
0
0
1
1
3
2
0
0
1
1
2
0
1
0
2
1
1
1
1
0
1
2
2
1
0
0
2
1
2
1
1
2
1
1
1
1
2
0
1
1
0
0
2
1
2
1
0
0
1
1
1
1
2
1
2
1
2
2
2
1
0
1
1
1
1
1
1
1
1
1
1
0
0
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
1
2
2
2
0
1
2
2
1
1
2
1
1
1
1
1
2
1
2
1
1
2
2
0
1
1
1
0
1
2
0
1
1
1
1
2
1
0
2
1
2
1
0
2
1
1
2
1
0
1
1
1
1
1
1
1
2
2
1
0
1
1
0
0
0
1
1
1
1
2
1
0
2
0
2
1
1
1
1
1
1
1
2
0
1
1
1
0
1
2
0
2
0
1
1
0
2
1
3
1
2
1
0
1
1
1
1
1
1
1
1
0
1
1
2
0
2
0
0
1
1
1
2
1
1
1
2
1
2
0
1
1
1
0
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
2
0
1
1
2
1
0
1
0
1
1
2
1
1
2
0
1
2
1
1
1
2
1
1
1
2
1
1
1
1
1
0
1
0
1
1
1
2
1
1
0
1
1
2
1
1
1
1
2
1
0
0
1
0
1
1
0
1
2
2
1
2
1
1
2
1
0
0
1
1
1
2
0
2
0
1
1
1
1
1
1
1
1
1
2
2
2
1
1
0
2
1
1
2
0
2
1
1
1
1
1
1
2
2
1
2
1
2
0
0
1
1
1
1
2
1
1
1
0
2
1
0
0
1
1
1
1
1
2
1
2
0
1
2
1
1
0
1
1
1
1
1
0
2
1
0
1
1
1
0
2
1
1
1
1
0
2
4
2
1
1
1
1
0
3
1
2
0
1
2
1
0
1
1
1
1
2
0
1
1
0
0
0
2
1
1
2
1
0
1
1
1
1
1
0
0
1
1
2
1
1
3
1
1
1
1
2
1
1
0
0
1
1
2
2
1
1
1
1
1
0
0
1
1
1
1
1
1
0
2
2
2
2
1
1
1
1
1
2
2
1
2
1
0
2
1
1
2
2
1
3
2
2
1
1
0
1
1
2
2
0
0
2
1
1
1
2
2
1
1
1
1
1
0
1
0
1
0
1
1
1
1
1
2
1
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
1
0
1
2
1
1
1
1
1
2
1
1
2
2
0
1
1
1
2
2
1
1
3
0
2
1
2
2
0
2
0
2
2
1
1
1
2
1
1
1
1
0
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
0
0
0
0
2
1
1
1
1
0
2
2
2
1
2
1
2
1
0
1
2
2
1
0
1
1
0
1
2
1
1
2
0
1
0
1
0
2
1
0
1
1
2
1
2
1
0
0
1
2
0
2
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
1
0
1
2
0
2
0
2
1
1
0
1
0
2
1
1
1
0
1
0
2
2
0
1
1
2
1
1
1
1
2
1
2
1
1
0
1
1
0
1
1
2
2
1
1
2
1
2
1
2
1
1
1
1
2
1
1
2
1
1
2
0
2
1
0
0
1
0
1
1
1
2
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
0
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
0
1
1
1
1
1
2
2
2
2
2
1
2
1
0
0
1
1
1
1
1
1
2
1
1
1
0
1
0
1
1
2
1
0
1
1
1
0
2
0
1
2
1
2
1
1
1
0
1
1
0
2
1
0
2
2
2
2
1
2
1
1
1
1
1
1
1
1
2
1
1
1
0
1
2
1
0
2
1
1
2
1
1
1
1
0
1
2
0
1
2
1
1
2
2
1
2
1
0
2
1
1
2
1
1
0
1
0
1
0
0
1
1
1
2
1
0
2
1
2
0
1
1
1
1
0
2
0
0
2
1
2
1
1
0
2
1
1
2
1
1
1
1
1
1
0
1
0
1
1
1
1
2
1
0
1
2
0
0
1
1
1
1
2
1
1
2
2
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
2
2
1
1
1
2
1
1
2
1
1
1
1
0
1
2
2
2
1
2
0
1
1
2
1
1
1
2
1
1
0
2
1
1
0
2
2
1
0
1
1
1
2
1
1
1
0
1
2
1
1
1
2
0
1
1
3
1
1
2
1
1
1
1
2
1
0
0
0
1
1
1
2
2
1
2
2
1
2
0
2
1
1
1
2
1
1
0
1
2
0
1
2
0
0
1
1
0
1
1
1
2
1
1
1
0
2
1
0
1
1
2
2
1
1
1
1
1
1
2
1
0
1
1
1
0
0
1
2
1
1
1
0
2
1
0
2
0
2
1
1
1
1
1
1
0
1
1
2
1
1
1
2
2
2
1
0
1
2
2
1
1
1
5
1
1
2
1
2
1
0
1
1
2
1
0
1
2
1
1
0
2
1
0
1
0
2
1
1
2
1
0
1
1
1
1
1
1
1
1
2
1
1
0
1
1
1
2
1
1
1
0
1
1
2
1
1
0
1
1
1
2
1
1
0
1
1
1
0
2
1
0
0
1
1
1
0
1
2
1
2
1
1
2
1
1
1
0
1
1
2
1
1
1
3
1
1
1
1
0
1
1
1
1
1
1
2
0
2
1
1
1
0
1
2
1
0
2
0
1
1
0
2
1
1
1
1
0
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
2
1
0
1
2
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
0
1
2
1
1
1
1
1
1
1
1
0
0
2
1
1
1
1
0
2
0
1
1
2
0
0
1
2
1
1
2
2
2
1
0
2
0
0
0
0
1
1
0
1
2
1
0
2
1
1
0
2
1
0
1
0
1
1
0
1
2
1
1
1
0
1
1
2
1
1
1
1
1
1
1
0
1
0
2
1
0
0
1
1
1
1
1
2
1
1
1
2
1
2
0
1
1
2
1
1
1
3
0
0
1
1
1
0
2
0
1
1
0
2
1
2
1
1
1
0
1
1
0
1
1
2
0
1
1
2
3
1
2
2
1
2
1
1
0
1
1
0
2
0
0
1
0
1
2
0
1
1
1
0
0
1
1
1
1
0
1
2
1
1
1
1
0
1
0
2
1
1
2
1
1
0
1
2
1
1
1
0
0
1
2
1
1
0
1
0
0
1
2
0
1
0
1
1
1
1
1
0
1
1
2
1
2
1
1
1
1
1
1
2
0
0
1
1
0
2
1
2
0
0
1
1
1
1
1
2
0
1
0
1
1
2
1
2
1
2
1
2
1
0
0
2
1
0
0
2
0
2
2
2
2
1
1
1
0
2
1
1
1
1
1
0
1
0
1
1
1
0
2
1
2
0
2
1
1
1
1
1
1
0
0
1
2
1
1
1
1
1
2
0
1
1
1
1
1
1
1
0
1
2
2
1
1
1
1
2
2
1
1
1
0
1
1
2
0
1
1
2
1
1
1
1
0
2
1
1
1
0
0
1
1
0
2
1
2
2
1
2
0
1
1
0
1
2
2
2
1
1
2
1
2
1
1
1
2
2
2
1
0
1
1
1
1
1
1
1
0
1
1
2
0
1
1
1
2
1
1
0
1
1
2
0
2
1
1
0
1
2
2
1
2
1
2
1
1
1
0
1
1
1
1
2
2
1
2
0
2
1
1
1
1
0
2
2
1
2
2
1
1
1
2
2
0
2
1
1
0
0
1
0
0
1
2
1
2
0
1
1
2
2
1
1
1
0
2
1
2
1
1
2
1
1
2
2
2
1
1
2
0
4
1
1
1
1
1
2
0
2
2
1
1
1
1
1
0
1
1
1
2
0
1
1
1
2
0
1
0
1
1
1
1
1
2
2
1
0
1
1
2
1
1
0
0
1
1
1
1
0
2
1
1
0
0
2
1
2
1
2
2
2
1
2
1
0
1
2
1
2
1
1
2
1
2
0
0
2
1
1
2
0
0
2
1
2
1
2
1
1
2
1
2
1
0
1
2
1
0
2
0
0
2
1
1
2
0
2
0
2
0
1
1
1
1
0
0
2
1
1
1
1
1
0
2
1
1
2
1
1
1
2
2
1
2
1
2
1
0
1
1
1
2
1
0
1
1
0
1
1
2
1
1
0
0
0
1
1
2
2
1
0
1
0
1
0
1
1
1
1
1
1
1
2
0
1
1
2
1
0
1
0
2
1
1
1
1
0
1
1
1
1
1
2
1
0
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
2
2
2
0
1
1
2
1
0
1
1
1
0
1
0
1
2
1
2
1
1
1
1
0
1
0
2
1
1
0
1
0
1
2
1
1
1
2
2
1
1
1
0
2
1
2
2
1
2
1
0
1
1
1
1
1
1
0
2
2
0
1
1
2
2
2
1
2
1
2
0
2
1
0
1
2
1
2
1
1
1
1
1
2
1
2
0
1
1
1
1
1
1
2
2
1
0
1
1
1
1
0
0
0
1
1
0
1
1
0
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
2
0
3
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
0
0
1
1
1
1
0
2
1
1
2
0
2
1
1
1
1
1
0
2
1
2
1
1
1
0
1
2
2
1
2
1
0
2
0
1
0
0
1
1
2
0
1
1
2
2
1
0
2
0
1
2
1
1
2
0
1
1
0
1
1
1
2
1
1
3
1
2
1
2
1
1
1
0
0
1
1
1
1
1
1
1
0
1
1
1
1
1
2
1
1
4
0
1
2
0
1
2
0
0
1
2
1
1
1
2
1
1
0
1
3
1
1
2
1
1
0
1
0
1
1
1
0
2
1
1
2
1
0
1
2
2
2
1
1
2
0
0
1
1
1
1
2
1
1
2
0
2
1
0
1
1
1
1
1
2
2
1
0
2
1
1
1
0
1
0
1
1
1
2
1
2
0
1
2
2
1
2
0
1
2
0
1
0
1
1
2
1
1
2
2
1
1
0
1
2
2
1
1
2
2
2
1
1
1
1
2
1
1
1
0
1
1
1
0
3
1
1
1
1
1
1
1
1
1
3
0
1
3
1
1
1
1
1
2
1
2
2
1
2
2
2
2
2
1
0
1
2
1
1
1
1
0
2
2
0
1
1
1
0
1
1
1
1
1
2
1
1
1
0
2
1
2
1
1
1
1
1
1
0
1
1
1
1
0
1
1
2
1
1
1
1
2
2
2
0
1
1
1
1
1
2
1
1
1
2
1
2
2
2
1
1
0
1
1
1
1
2
2
1
1
1
2
1
1
2
2
1
0
1
1
1
1
1
0
1
2
1
1
2
2
0
1
1
2
1
1
1
0
1
1
1
2
1
2
1
2
0
1
2
0
2
1
2
2
1
1
2
1
0
1
1
0
1
1
1
0
1
2
1
2
0
1
1
2
0
0
2
1
1
2
1
2
1
1
1
1
1
1
2
2
1
1
1
1
2
0
0
1
2
1
0
2
0
1
2
1
0
1
2
2
1
1
1
1
2
2
1
2
1
0
0
1
1
0
1
1
2
1
1
1
1
2
0
1
0
0
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
2
1
1
0
3
2
2
0
1
1
1
0
1
2
0
1
1
2
1
1
1
2
4
0
1
1
1
0
1
0
2
2
1
1
1
1
1
1
2
2
0
0
1
0
0
1
3
2
1
1
2
2
2
1
1
0
1
1
2
1
1
1
0
2
1
0
0
1
0
1
1
2
1
1
2
2
1
0
0
1
1
2
2
2
1
2
1
2
1
1
2
2
0
0
2
1
1
2
1
0
1
2
1
1
1
0
1
2
1
2
1
2
0
0
2
1
1
0
1
1
0
0
2
2
1
1
1
1
1
2
1
1
0
2
1
2
1
0
1
2
2
0
1
1
2
1
1
2
1
1
2
0
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
0
0
1
1
2
2
1
2
0
1
0
2
1
1
1
0
1
0
2
1
1
2
1
0
1
1
1
1
0
1
1
2
1
1
2
1
1
0
0
0
2
2
1
1
1
2
2
0
1
0
2
2
0
0
0
0
1
1
1
0
1
1
1
1
1
0
0
0
2
1
1
0
1
2
1
0
1
1
2
0
1
1
1
1
1
1
2
1
1
2
4
2
0
0
2
1
2
2
1
1
1
1
0
0
2
1
2
1
2
1
0
1
2
0
1
1
1
1
2
1
1
0
1
1
0
1
1
2
0
2
1
2
0
2
2
1
1
1
0
2
0
1
2
1
1
1
2
0
2
0
1
1
0
0
0
0
2
0
1
1
1
2
1
1
1
1
1
0
1
2
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
0
2
2
0
1
1
2
1
2
1
1
2
2
1
1
3
1
2
1
1
3
1
0
2
2
2
3
1
1
0
0
2
2
2
1
1
1
2
1
1
1
0
1
1
2
1
1
1
1
1
1
0
1
1
2
2
0
1
2
2
1
2
2
1
3
0
0
0
1
0
1
0
1
1
1
1
2
1
0
0
2
1
1
1
0
0
1
1
0
1
2
1
1
2
1
1
2
1
1
1
1
1
1
1
0
1
1
1
1
1
2
0
2
2
1
2
1
1
1
1
2
0
1
2
1
1
1
2
1
1
2
1
1
2
0
1
2
1
0
1
1
1
2
0
1
0
2
1
2
1
1
3
0
2
2
3
2
1
1
1
1
0
0
1
1
2
1
1
1
1
0
1
0
0
2
2
0
1
2
1
2
1
0
0
1
0
1
1
0
0
1
1
0
1
1
1
1
0
1
1
2
1
1
1
1
1
0
1
1
0
0
1
2
0
0
0
1
2
2
2
0
0
1
1
1
0
1
1
1
1
1
0
1
0
1
2
0
1
1
1
1
2
0
1
0
0
1
1
1
1
2
2
2
1
1
1
1
0
2
1
0
1
0
1
1
2
1
2
2
1
0
1
1
1
2
2
1
1
1
1
2
2
2
1
1
2
0
1
2
0
0
1
2
2
1
1
1
1
1
1
2
1
2
1
0
2
1
1
2
1
2
1
1
4
1
1
1
1
1
0
2
1
1
2
0
1
1
1
2
1
1
1
2
1
2
0
1
2
1
1
2
0
1
1
1
1
0
2
2
1
1
0
1
1
1
1
1
1
1
2
0
2
0
1
1
2
1
1
2
2
1
2
0
1
1
1
1
1
2
1
1
2
1
1
1
1
2
1
1
1
1
1
2
0
1
0
2
1
1
1
0
1
1
1
1
1
1
2
1
0
2
1
3
0
1
1
2
1
1
2
2
2
2
1
1
0
1
1
0
0
0
1
1
2
0
1
2
1
1
0
1
0
1
1
0
2
1
0
1
1
2
1
1
2
1
1
0
0
0
2
1
1
0
1
2
0
1
1
0
2
1
1
0
0
2
0
2
1
4
1
3
1
0
1
1
1
1
1
1
0
1
1
1
0
0
0
2
1
1
2
1
1
1
1
0
1
2
1
1
2
1
1
1
1
0
0
1
1
0
1
2
0
0
2
1
1
1
1
0
2
0
1
0
3
1
1
1
1
2
1
0
1
2
1
1
0
1
0
0
1
0
1
2
2
0
2
1
0
2
2
1
0
0
0
2
2
2
1
0
1
1
1
1
1
3
0
1
1
0
1
1
0
1
2
1
1
0
1
1
3
0
1
3
2
0
2
1
1
1
2
1
1
1
1
1
2
0
1
1
0
1
1
0
0
1
1
1
1
1
1
0
2
1
1
1
1
2
1
0
1
1
2
1
0
2
1
1
2
2
1
0
1
1
1
1
1
2
0
2
1
1
1
1
1
1
1
1
1
1
0
1
1
0
1
2
1
2
2
0
1
1
0
2
1
0
1
0
1
1
1
1
0
1
1
2
1
0
1
0
1
1
1
1
2
1
1
1
2
2
2
1
2
2
1
0
1
1
0
0
1
1
1
2
1
0
2
2
1
0
1
1
1
1
0
1
1
1
2
1
1
1
2
2
1
2
1
2
2
2
2
1
0
1
3
0
1
1
1
1
1
0
1
1
0
1
0
1
0
1
2
1
1
1
1
1
1
1
2
1
2
1
1
2
1
2
1
0
1
0
2
1
0
1
1
3
0
0
0
1
0
2
1
1
3
1
1
4
2
0
0
2
1
1
2
2
2
1
1
1
1
1
1
1
0
1
1
2
1
2
2
2
1
2
1
0
1
1
1
1
1
1
2
1
0
0
1
2
0
2
1
2
0
2
0
1
0
1
0
0
1
0
2
1
1
2
2
2
1
0
2
1
1
1
0
2
0
1
1
1
1
2
2
1
1
0
1
1
1
0
1
0
1
2
2
2
1
1
1
1
1
1
1
1
1
1
2
1
0
1
1
1
2
2
2
1
2
1
1
1
1
2
1
2
1
1
1
0
2
1
1
2
0
2
2
0
0
3
2
0
2
1
2
1
1
1
1
2
2
1
1
2
1
0
2
1
2
1
1
1
1
1
1
1
2
1
1
1
3
1
0
1
2
2
1
1
1
1
0
1
2
1
0
1
0
2
1
0
1
1
2
1
0
0
1
1
0
2
2
1
1
1
1
1
1
4
2
2
1
2
2
2
2
1
1
0
1
2
1
1
1
1
1
1
0
0
2
0
2
2
1
1
0
1
1
2
1
1
1
1
0
1
0
2
2
1
1
1
1
1
1
1
2
0
1
1
1
1
3
1
0
0
1
1
1
2
2
1
1
1
1
0
2
2
1
0
1
0
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
0
1
2
1
1
2
0
1
1
1
2
2
2
1
0
2
1
1
1
1
1
2
1
1
0
1
1
1
2
1
0
1
1
1
2
0
2
2
1
0
1
2
1
1
2
2
1
1
0
1
1
2
1
1
1
1
0
1
2
1
2
1
1
1
1
0
1
1
1
1
2
0
1
1
0
2
1
1
2
1
1
1
0
1
0
1
3
2
0
2
1
1
2
0
1
1
1
2
1
2
2
0
2
1
2
2
1
2
1
1
0
0
1
1
1
1
1
1
1
0
1
2
2
0
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
0
2
2
1
1
0
2
2
0
1
0
2
2
1
1
1
2
0
1
2
1
0
1
2
1
2
1
0
2
1
1
1
0
1
1
1
1
2
2
1
1
1
0
1
1
0
0
1
3
0
1
1
1
2
0
1
1
1
1
1
1
0
1
1
1
0
2
2
2
1
1
0
1
2
0
1
1
1
1
1
1
1
1
1
3
1
1
1
1
1
2
1
0
1
2
1
1
1
1
0
2
1
1
2
0
1
2
1
2
0
0
1
2
1
2
1
1
1
0
1
2
1
2
1
1
1
0
1
2
3
1
1
1
1
2
2
0
1
1
1
3
2
1
1
1
1
1
3
1
1
1
0
0
0
1
1
1
2
1
1
1
3
1
2
1
0
2
0
1
0
1
2
1
1
1
1
1
1
1
0
1
0
0
1
1
1
2
1
0
1
3
2
2
1
1
0
0
1
2
2
1
1
1
1
2
1
0
1
1
1
0
0
0
1
1
2
1
1
1
2
2
1
3
0
3
0
2
0
0
2
1
0
0
1
2
2
1
2
0
1
1
1
1
2
1
1
1
2
1
1
0
1
1
2
1
1
1
1
0
1
1
1
1
1
1
1
3
1
1
1
1
2
1
1
2
2
0
1
1
1
0
1
2
0
1
1
0
1
0
1
2
1
1
0
1
1
2
1
1
1
2
2
1
1
1
2
1
0
2
1
1
0
2
1
1
2
0
2
1
0
1
0
1
1
1
2
1
2
1
1
1
2
2
1
1
1
1
1
1
0
0
1
1
1
1
0
0
1
2
1
1
1
1
1
1
1
0
1
1
1
1
1
2
1
1
2
1
1
0
1
2
0
1
2
2
2
2
0
0
1
1
1
2
1
1
1
1
1
0
2
2
2
0
1
0
0
2
2
2
1
2
2
1
0
1
1
0
1
2
1
2
1
1
1
2
1
1
2
0
0
1
2
1
0
3
1
1
3
1
1
2
2
2
1
1
2
1
2
1
1
1
2
1
1
0
2
2
1
1
2
1
2
2
2
0
0
1
1
1
1
0
0
2
2
0
1
1
1
1
0
1
2
2
2
1
0
2
0
0
1
1
0
1
1
1
0
1
2
2
1
0
0
1
1
1
0
0
1
1
1
1
0
1
1
1
1
1
1
1
1
0
1
1
2
1
1
0
1
1
1
2
1
0
1
1
0
1
1
1
1
1
2
2
1
1
1
1
0
0
1
2
1
1
0
0
1
2
1
1
2
1
2
1
2
1
1
1
0
2
1
1
1
0
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
2
2
1
1
2
1
2
1
1
0
2
2
2
1
1
2
2
1
0
1
1
2
0
1
0
0
0
2
2
1
1
2
3
1
2
2
1
1
0
1
1
1
1
1
1
1
2
1
1
0
1
1
1
0
2
2
1
2
1
1
1
0
1
1
2
0
1
0
1
2
2
1
1
2
1
0
1
1
0
0
1
1
1
1
1
1
1
1
0
1
2
0
2
2
1
1
1
2
2
1
0
1
2
1
1
2
1
1
2
2
1
1
0
1
2
1
1
1
1
1
1
1
1
1
1
0
2
1
0
1
2
1
1
1
1
1
0
1
1
1
1
1
0
2
2
1
1
2
1
2
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
0
1
1
1
0
1
0
1
1
1
2
2
2
0
1
1
1
1
1
1
1
1
0
0
2
1
1
1
1
1
1
0
1
1
2
1
2
1
1
1
1
1
1
2
1
0
1
0
1
0
1
2
1
1
1
1
1
1
1
0
2
1
2
0
1
1
1
1
0
1
0
0
1
2
2
1
2
2
2
2
1
0
2
1
1
0
0
1
1
0
1
1
1
1
1
1
2
0
0
1
1
1
1
1
1
0
0
2
0
1
1
0
1
2
1
1
0
2
1
1
1
0
1
1
2
1
0
1
1
0
1
1
0
1
2
1
1
2
1
1
2
1
2
1
1
1
0
1
1
1
1
2
1
0
1
2
1
0
1
3
1
1
1
1
0
0
1
2
1
2
2
1
1
1
0
1
1
0
2
2
1
1
1
0
2
2
1
1
1
1
1
0
1
1
2
2
1
0
1
1
1
1
0
0
1
1
1
0
0
1
1
2
2
0
0
1
1
2
1
1
2
2
2
1
2
0
1
1
2
2
1
1
2
1
1
1
2
2
0
2
1
1
1
2
0
1
1
1
0
2
1
2
1
1
0
1
0
0
1
1
1
1
1
1
1
2
1
1
0
1
0
0
0
1
1
1
2
1
1
2
1
1
1
0
2
1
2
1
2
1
2
0
1
1
1
0
1
1
1
1
1
1
1
1
0
0
1
2
1
1
1
0
1
2
2
0
0
2
1
2
2
1
2
0
2
0
1
2
1
0
1
1
1
1
0
0
1
3
1
0
2
2
1
1
1
2
1
0
0
3
0
1
1
1
2
1
2
1
0
1
0
0
0
1
1
1
1
1
1
2
1
1
2
1
0
2
1
1
1
2
2
1
1
1
0
1
2
0
1
1
0
1
2
0
2
2
1
0
0
0
1
1
1
2
2
1
1
1
1
1
0
1
1
1
1
2
1
1
1
1
2
0
1
1
1
0
2
1
1
1
1
2
1
1
1
2
2
0
2
1
2
0
0
1
1
1
1
1
3
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
0
1
1
1
2
2
1
0
1
1
1
0
0
0
3
1
0
1
2
2
1
2
1
1
2
2
1
1
2
1
2
1
0
0
0
2
2
1
1
0
2
1
1
0
2
0
2
1
1
1
1
0
1
1
1
2
0
2
1
0
2
1
1
1
2
1
1
0
0
3
1
0
1
2
0
0
0
0
2
2
1
1
1
1
2
1
1
1
0
2
1
1
1
0
1
1
0
2
2
1
1
1
1
1
2
2
0
1
0
1
1
1
0
1
0
2
1
1
0
2
2
1
1
2
1
0
0
0
1
1
1
1
2
2
1
1
0
1
0
2
1
3
1
2
1
2
2
1
2
1
1
0
1
1
2
0
1
0
1
1
1
1
1
1
0
2
0
2
2
0
2
0
0
1
1
2
1
0
1
2
1
1
1
2
1
0
2
1
2
1
1
0
1
1
2
1
1
1
1
1
1
2
1
1
1
1
0
1
0
1
1
1
2
2
1
2
1
1
1
2
0
0
2
1
1
1
2
2
1
0
1
1
1
2
2
2
2
1
1
1
1
2
1
1
1
1
2
2
1
1
1
1
1
2
1
1
1
1
2
1
2
2
0
1
1
1
0
1
1
1
1
0
1
1
0
1
0
2
1
0
1
1
0
0
1
1
1
1
1
1
2
1
2
1
1
1
1
1
0
2
1
1
0
0
1
1
1
2
1
2
1
2
3
2
0
1
0
2
0
1
1
1
2
1
1
1
0
1
1
1
2
1
2
1
0
1
3
0
2
1
1
1
1
1
1
2
2
0
1
1
1
1
1
1
2
1
0
1
2
1
1
2
1
0
1
0
2
2
0
1
1
0
0
2
1
1
1
2
1
2
0
1
0
1
2
0
1
1
1
1
2
1
0
2
1
0
1
1
1
1
0
0
1
1
2
1
2
1
1
0
1
2
1
0
2
1
1
1
1
1
1
1
2
2
2
1
1
2
2
0
1
2
1
0
2
0
2
0
1
1
1
1
1
0
2
1
2
1
1
2
1
1
3
1
1
1
2
1
2
1
1
1
1
1
1
0
0
1
0
1
1
1
0
2
1
1
0
2
0
1
1
1
2
0
1
1
1
2
0
0
1
1
1
1
1
1
1
5
1
2
1
1
2
2
2
1
0
1
1
2
1
2
1
1
0
2
2
1
1
2
1
2
1
1
1
1
1
0
0
1
2
1
0
0
1
2
2
0
0
1
0
0
1
1
1
1
2
1
2
1
1
1
2
0
1
1
1
1
2
2
2
1
1
1
1
1
2
1
0
1
2
1
2
1
1
2
1
1
1
1
1
2
2
2
1
0
2
1
1
2
3
1
1
0
1
0
0
1
1
2
1
1
3
1
2
3
2
0
3
2
1
1
2
1
2
0
1
1
2
2
1
2
2
1
2
1
0
1
0
2
0
0
1
2
1
0
1
0
2
0
1
2
1
1
1
1
1
0
1
1
3
1
2
0
0
1
1
2
0
2
1
1
1
0
1
2
1
1
1
1
1
0
1
1
1
1
3
1
1
0
0
0
1
1
1
0
0
1
1
1
1
0
1
1
1
2
1
2
2
2
0
1
2
1
1
0
1
1
0
1
0
1
0
1
0
2
2
2
1
1
2
1
2
0
2
0
1
1
1
1
0
1
2
0
1
1
1
2
0
1
1
1
1
3
1
2
1
1
0
1
0
1
2
1
1
1
1
2
1
0
2
0
0
2
1
0
1
1
0
1
0
2
2
1
2
1
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
1
1
2
2
1
0
0
1
1
1
1
1
1
0
0
1
2
2
2
2
1
2
0
1
1
1
1
1
1
0
2
1
2
1
1
1
0
1
1
1
0
1
1
1
0
1
1
1
1
1
2
1
1
1
1
0
1
0
2
1
2
0
0
0
0
2
2
2
0
2
1
1
2
1
1
2
0
0
2
0
2
1
0
1
1
1
0
1
1
1
2
2
2
1
1
0
1
1
1
2
1
1
1
1
1
2
1
2
1
1
2
1
1
1
2
1
2
0
2
1
1
0
0
0
2
2
1
0
1
0
2
1
2
1
1
1
1
1
1
2
0
1
0
0
2
1
2
0
0
0
1
1
1
0
1
1
1
1
1
1
1
1
1
1
0
1
0
2
1
0
2
1
1
1
1
1
0
2
1
0
1
1
1
1
1
1
1
1
1
0
1
1
1
2
0
1
1
1
1
1
2
1
0
1
2
1
1
1
2
1
1
1
0
1
1
2
0
1
1
1
1
1
1
1
1
0
1
2
1
1
1
2
1
2
0
1
1
0
1
1
1
1
1
1
1
1
1
2
0
1
1
1
1
0
0
1
1
2
1
1
0
2
1
1
1
2
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
2
0
2
1
1
1
1
2
1
1
2
0
1
1
2
0
0
1
0
1
2
0
0
2
1
1
0
1
1
1
1
1
2
2
0
1
1
1
1
1
1
0
1
2
1
1
1
0
1
1
1
3
1
1
1
1
1
1
0
1
2
1
2
1
1
1
2
1
1
2
1
2
2
2
1
2
1
2
1
1
0
2
1
1
0
2
1
1
1
2
1
1
0
2
2
0
0
1
2
1
1
1
1
2
0
2
2
3
1
1
1
1
1
2
0
1
1
1
2
1
3
1
0
1
1
0
1
0
1
1
0
0
0
2
1
1
1
1
1
1
2
3
1
0
1
0
1
0
0
1
0
2
1
2
2
1
1
1
2
1
2
1
1
2
2
1
1
2
1
0
2
0
0
1
1
1
1
0
1
1
2
0
0
1
2
1
1
2
0
1
0
0
2
1
1
2
0
2
1
0
1
2
1
0
0
0
1
1
1
2
1
1
2
1
1
1
0
1
0
0
1
0
0
1
2
2
1
1
1
2
2
1
2
2
1
2
2
1
2
0
0
2
1
1
1
2
1
0
1
1
1
1
1
2
1
0
3
1
0
1
2
2
1
1
1
0
1
0
1
1
2
0
1
0
1
0
0
2
0
1
2
1
1
0
1
0
1
1
1
1
1
1
1
1
4
1
2
0
1
1
1
2
2
0
1
2
1
2
1
2
1
2
1
2
1
1
0
0
1
0
1
1
0
1
1
0
1
1
2
0
0
1
0
1
1
1
0
1
2
1
1
0
1
1
1
1
0
1
2
2
1
1
0
1
1
1
1
2
1
1
2
1
1
0
1
1
1
1
1
1
1
1
2
1
2
1
1
1
2
0
1
1
0
1
1
1
2
0
1
2
1
1
1
0
1
3
2
1
0
1
1
1
2
1
1
2
1
0
2
0
2
0
1
1
1
2
1
2
1
1
1
2
1
2
1
0
1
1
1
1
2
0
1
0
1
2
2
1
1
0
1
1
1
0
1
0
1
1
2
1
2
1
1
1
2
2
1
1
0
1
1
2
1
1
0
0
1
1
1
1
1
2
1
1
0
1
2
1
0
2
0
1
1
1
0
1
0
0
1
2
1
1
0
1
2
0
0
1
0
1
0
1
1
1
2
2
0
1
1
1
1
1
2
1
1
1
1
1
0
1
1
1
2
1
1
1
1
1
2
2
1
1
0
1
1
1
1
1
1
2
0
1
1
1
1
1
0
1
2
1
1
1
1
1
1
2
2
1
1
2
1
1
1
2
1
0
2
1
2
2
2
2
0
1
1
1
1
2
1
1
2
2
2
2
2
0
2
1
2
1
0
0
0
2
2
1
1
0
1
1
1
0
1
0
1
2
1
1
1
2
0
1
2
1
1
1
1
1
1
0
0
0
1
0
0
1
0
2
1
0
1
2
1
2
1
1
1
1
1
1
0
1
0
2
2
1
2
1
1
1
0
1
1
1
1
1
1
1
1
1
1
0
0
2
2
1
2
1
1
2
1
1
1
2
2
2
1
1
2
1
0
2
1
1
0
2
1
2
2
0
1
1
0
2
1
1
2
1
1
2
1
1
1
1
0
0
1
2
1
1
0
1
1
1
1
1
1
1
1
1
1
0
2
2
2
1
0
1
1
1
1
1
3
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
0
1
1
4
2
1
1
1
2
1
0
4
1
0
2
1
1
2
2
1
2
2
1
1
1
0
1
1
0
1
1
1
2
2
2
1
1
0
2
0
1
1
1
1
0
2
0
1
0
1
1
0
2
0
1
1
1
0
1
1
1
1
1
1
2
1
1
2
1
2
1
1
2
1
0
2
0
2
0
2
2
3
0
1
1
1
2
1
1
2
0
2
1
1
1
1
1
0
2
1
1
1
1
0
0
0
1
1
1
1
1
1
1
2
1
2
2
1
1
0
0
2
1
1
1
1
0
1
2
1
1
0
1
1
2
0
1
2
2
2
2
1
1
0
1
1
2
4
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
0
1
2
2
1
1
1
1
1
0
2
1
0
1
1
0
1
1
0
1
1
3
0
1
2
1
2
0
0
0
1
1
1
0
1
1
2
0
2
2
1
2
1
1
1
1
1
1
1
1
1
2
2
2
1
2
2
1
1
1
2
1
1
1
1
1
1
1
2
2
0
1
2
1
2
1
0
1
0
0
1
1
1
2
0
1
1
2
1
2
1
1
1
1
1
0
2
2
2
1
1
1
2
1
1
0
0
1
1
1
0
1
2
1
2
1
0
1
2
1
1
1
1
0
2
2
0
1
1
1
0
1
2
1
1
1
1
0
0
2
1
2
2
1
2
1
2
1
1
2
1
2
1
0
1
1
1
1
2
0
0
1
2
1
1
1
0
2
2
2
1
1
1
1
2
1
1
1
1
2
2
0
2
2
1
2
1
1
1
2
2
1
2
1
1
1
1
1
0
1
2
1
1
1
2
1
1
1
2
2
2
2
2
1
2
0
2
1
1
1
1
1
2
1
1
1
0
1
2
2
2
1
1
1
1
1
2
2
0
0
1
1
1
0
1
2
2
1
0
1
1
1
1
2
2
1
1
1
1
3
1
2
0
2
1
1
1
1
1
2
1
0
1
0
0
2
1
0
2
1
1
0
0
2
1
0
1
0
3
1
1
2
1
2
1
2
1
2
2
2
1
1
1
1
1
1
0
1
1
1
1
1
0
2
2
1
1
1
1
1
2
1
2
2
1
2
1
0
1
1
2
0
1
0
1
2
0
1
0
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
2
1
0
1
2
2
1
0
1
1
3
0
1
2
2
1
1
1
1
1
1
1
0
1
0
1
1
0
1
1
1
1
1
1
1
1
1
4
2
1
1
1
1
0
2
2
1
1
1
1
1
1
1
1
2
2
1
2
2
0
0
2
2
1
1
1
1
1
0
1
2
0
1
1
1
1
2
1
2
1
1
2
1
1
1
0
2
0
0
0
1
0
2
1
1
1
0
0
1
0
2
0
2
0
1
2
2
1
1
1
1
1
2
2
1
1
0
0
2
1
1
1
2
2
1
2
1
0
1
0
0
1
1
2
0
1
1
0
1
2
2
1
1
1
2
2
1
1
1
2
0
2
1
3
2
1
0
2
1
1
2
1
1
1
1
1
0
1
2
0
2
1
2
0
1
1
2
0
1
1
2
1
1
1
2
1
1
2
1
1
2
1
1
0
1
1
1
0
0
1
0
0
1
0
0
1
0
1
1
0
1
0
1
1
1
1
1
0
1
0
2
0
1
1
1
0
1
1
1
1
2
1
2
1
0
1
0
1
1
2
2
1
1
2
2
0
2
2
0
1
1
1
1
0
2
2
2
1
1
1
1
2
1
2
2
1
1
1
2
1
2
2
1
2
0
1
1
2
1
1
0
1
1
2
1
1
2
1
2
2
2
1
2
1
2
1
2
1
2
2
2
2
2
1
1
1
1
0
1
2
1
1
1
2
1
2
2
1
0
0
0
0
1
1
0
2
2
1
1
1
2
2
2
2
2
1
2
2
2
1
0
0
1
2
2
1
1
1
1
2
1
0
1
1
1
1
0
2
1
1
1
1
0
1
1
0
1
1
1
1
0
1
1
1
0
2
1
2
2
2
1
1
0
1
1
0
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
1
1
2
1
0
0
0
1
2
2
2
1
1
0
2
1
2
1
2
0
1
1
1
1
0
2
2
0
2
1
1
0
2
0
2
0
0
2
1
1
0
1
1
2
2
2
1
1
0
0
1
0
1
1
0
1
1
1
1
2
0
2
2
1
1
2
1
1
0
0
2
1
0
1
2
2
2
1
1
1
2
2
1
1
1
1
1
2
2
1
0
1
1
0
1
1
1
0
1
2
3
1
1
2
1
2
1
1
1
2
0
1
1
2
0
0
1
0
1
1
1
0
1
0
1
1
1
1
0
0
1
0
1
1
2
1
5
1
1
0
1
1
0
0
1
1
0
1
0
2
2
1
1
2
1
0
0
3
2
3
2
2
1
0
0
1
2
1
1
1
1
1
1
1
1
0
0
1
1
1
1
1
0
1
1
2
1
1
2
2
1
1
1
2
1
0
1
2
1
2
1
1
0
1
1
1
0
2
0
1
1
1
1
1
2
0
1
0
1
2
1
2
1
1
1
1
1
1
1
1
2
0
2
1
1
1
1
2
2
1
2
1
1
1
1
1
0
1
2
1
0
1
2
2
1
1
1
1
1
1
1
1
0
1
1
0
1
3
1
2
0
1
1
0
1
1
1
0
1
1
1
1
2
1
1
0
1
1
1
1
2
1
2
1
0
0
2
2
2
1
1
1
0
2
2
2
0
0
2
0
2
2
1
1
1
2
0
1
0
1
1
2
2
0
1
0
2
1
2
2
1
1
2
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
0
1
0
1
1
1
2
1
2
1
0
1
1
2
2
1
0
0
3
0
0
2
1
1
1
1
0
0
1
1
1
0
1
0
1
1
1
1
1
2
1
0
1
0
1
1
1
2
1
0
1
1
0
0
1
2
1
1
2
0
1
2
1
1
0
2
0
1
2
1
1
1
1
0
1
1
1
0
1
1
0
1
2
2
1
1
1
1
0
4
1
2
1
1
1
2
2
1
0
2
1
1
1
2
1
0
2
2
2
0
1
1
2
0
1
1
1
1
1
1
0
1
1
1
1
2
1
1
1
1
0
1
0
1
1
1
2
0
1
1
2
1
2
1
1
1
0
1
2
1
2
1
1
1
1
2
2
1
2
1
0
1
0
1
0
0
1
1
1
1
0
1
2
0
2
1
0
2
1
1
2
1
2
2
1
2
1
1
1
1
1
1
0
0
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
0
1
1
0
1
1
0
1
2
1
0
1
1
1
1
0
1
1
1
1
2
1
0
1
1
0
1
1
0
1
1
1
2
1
2
1
1
2
1
2
1
1
2
0
1
1
1
1
1
1
1
0
2
2
1
2
1
1
1
1
1
1
0
0
1
1
1
0
0
1
2
1
1
2
1
1
1
2
0
1
1
1
1
1
1
1
1
1
1
1
2
2
1
0
1
2
0
0
0
2
1
1
2
0
1
2
1
0
2
1
1
1
1
1
1
2
1
2
1
1
0
1
2
1
1
1
1
2
0
1
1
1
2
1
1
2
2
1
0
2
2
2
1
0
1
1
1
0
2
1
1
2
1
1
1
0
1
1
2
1
1
1
1
0
1
1
1
2
1
1
0
1
0
1
1
0
1
1
1
1
2
3
1
1
2
1
1
1
0
2
2
0
0
2
2
2
2
1
1
2
1
1
1
0
2
1
3
1
0
2
0
1
0
1
1
1
1
0
1
1
1
0
2
0
0
2
2
1
2
1
1
0
1
2
1
0
1
1
1
2
1
1
2
0
2
2
2
1
0
1
1
0
0
0
0
0
1
1
1
1
1
1
0
2
2
0
1
1
1
1
1
1
1
1
2
1
1
1
0
0
2
1
0
1
2
0
0
3
0
1
1
0
1
1
1
1
0
2
1
2
2
1
1
0
0
1
0
1
2
0
1
1
1
1
1
1
1
1
3
1
1
2
1
0
1
1
1
1
1
0
1
1
1
1
1
1
1
2
1
1
2
1
1
0
0
1
1
1
2
0
1
1
2
1
1
2
1
0
2
2
1
0
2
0
2
1
2
1
1
1
1
2
1
2
1
1
2
1
1
2
1
1
0
0
0
2
1
2
0
1
1
2
1
1
0
2
1
2
1
1
1
0
0
1
1
2
1
1
2
2
1
1
1
1
1
0
1
1
1
1
0
0
1
2
1
1
0
2
1
1
1
2
2
2
1
1
0
2
2
2
2
1
2
1
0
0
2
2
0
0
1
0
1
1
0
0
1
0
0
1
1
1
0
1
2
2
1
1
1
1
2
1
0
2
1
1
0
1
1
2
0
1
1
1
0
1
1
1
1
2
1
0
1
2
1
1
1
0
2
1
2
1
1
1
2
0
2
0
0
1
0
2
1
1
2
1
2
1
2
0
1
1
1
2
1
1
1
2
1
2
1
2
2
1
2
4
0
1
1
1
1
1
0
1
0
1
2
2
1
2
2
1
1
1
1
3
1
1
0
1
2
1
1
1
1
2
1
1
0
1
1
1
1
2
1
0
2
2
1
1
1
0
0
1
1
1
1
0
1
1
2
1
0
2
1
0
1
1
0
1
1
1
2
1
2
1
1
2
0
2
2
0
2
1
1
1
2
0
1
0
1
2
1
1
1
0
1
1
1
1
1
1
2
2
1
1
2
0
0
0
1
1
0
1
1
2
1
1
2
0
1
1
1
6
0
1
1
1
1
2
1
2
1
1
2
0
0
0
2
2
1
0
0
1
2
1
1
1
0
1
1
0
1
1
1
1
1
0
0
0
1
1
1
1
1
1
1
0
2
1
1
0
2
2
3
2
0
1
1
1
0
0
0
1
1
1
2
1
0
1
2
1
1
2
1
1
2
1
2
0
0
1
1
1
0
2
2
2
1
2
1
0
1
2
1
1
1
1
1
1
1
2
1
2
2
0
1
1
1
2
1
2
2
1
0
2
1
0
1
2
0
0
1
1
0
1
1
2
0
1
1
0
0
2
0
0
2
1
1
1
2
1
1
1
1
1
2
3
1
1
1
1
2
1
1
1
1
1
1
2
1
1
2
1
0
1
0
2
1
1
1
0
1
1
1
2
1
0
2
1
1
0
1
1
1
2
2
2
0
1
1
2
1
2
1
1
1
0
1
0
1
0
0
0
0
0
1
1
0
1
1
1
2
1
1
1
1
1
0
0
1
1
1
1
1
0
1
1
1
0
1
1
1
1
2
1
0
1
1
1
1
1
1
2
1
1
1
1
2
2
1
0
1
1
1
2
1
0
1
2
1
1
1
2
1
0
1
1
1
1
1
0
1
1
0
1
2
1
1
2
0
1
0
0
1
1
2
2
0
1
1
2
1
1
1
1
1
0
1
1
2
1
1
2
2
1
1
2
2
1
0
1
1
0
0
1
2
1
0
0
1
1
0
2
0
1
1
1
1
1
1
0
1
0
2
0
0
1
2
0
2
1
1
1
0
2
1
1
1
2
0
2
1
1
0
2
1
1
1
1
0
0
2
1
1
1
1
2
1
2
0
1
2
1
1
0
1
1
3
1
1
2
1
1
1
1
1
2
0
1
0
1
1
2
0
1
2
2
1
2
0
2
1
2
2
0
2
1
0
2
1
0
1
2
0
1
1
0
1
1
1
3
0
0
1
0
1
0
2
1
2
2
1
2
0
2
2
1
1
2
2
1
0
2
2
1
2
1
2
1
1
1
1
0
1
1
1
0
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
0
2
1
0
2
2
0
1
2
1
2
1
0
1
2
1
2
1
1
0
1
2
1
1
1
1
1
1
2
1
1
2
0
0
3
1
1
1
2
2
1
9
1
2
1
0
2
2
1
1
1
2
3
2
1
1
1
2
1
1
1
0
1
2
1
1
1
2
1
1
1
1
2
2
1
1
0
2
0
1
1
1
1
2
1
1
1
0
1
0
1
2
1
2
1
1
1
1
1
1
0
1
0
1
0
1
0
1
2
2
3
0
2
1
1
0
2
0
2
1
1
1
2
1
1
2
1
2
1
1
1
2
1
1
2
1
1
2
0
1
1
0
2
2
1
2
2
0
1
1
1
1
9
1
1
0
1
1
1
1
2
1
1
0
1
0
0
1
1
0
2
2
1
2
0
1
1
1
1
1
1
1
0
1
2
0
2
1
2
1
1
0
1
1
2
1
2
1
1
1
2
0
1
1
2
1
0
1
1
0
1
2
1
2
0
0
2
1
1
1
1
1
0
1
1
2
2
1
2
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
1
1
1
1
2
0
1
2
2
0
1
0
1
1
2
1
0
0
1
1
1
1
2
2
1
2
0
1
0
1
1
2
2
2
2
1
1
2
1
0
0
1
1
0
1
1
1
2
2
2
1
0
1
1
1
2
1
1
2
1
0
2
1
1
3
0
2
1
1
1
1
2
0
2
0
1
1
1
0
2
2
2
1
2
1
1
1
1
1
1
1
0
3
0
1
1
1
1
1
0
1
2
2
0
2
2
0
1
1
0
2
1
1
1
2
1
1
0
0
2
1
1
1
2
2
1
1
2
1
1
0
1
0
1
1
1
0
2
2
2
1
1
1
1
1
1
1
0
0
1
1
1
1
1
1
0
0
2
1
1
1
1
0
1
0
1
1
1
1
1
3
1
0
0
2
1
1
1
1
1
1
1
1
0
1
1
1
1
3
2
1
1
2
1
3
1
1
2
0
2
1
2
1
1
0
1
1
0
2
1
1
1
2
2
2
1
1
1
2
1
0
1
2
1
0
1
1
1
0
1
1
1
1
1
1
1
2
2
2
2
0
1
3
2
1
1
2
0
2
0
0
0
1
2
1
0
2
1
1
0
0
0
0
1
2
0
1
2
1
1
0
1
0
2
1
1
1
1
1
2
2
1
1
1
1
2
0
1
1
1
2
0
2
1
1
1
2
1
1
1
1
1
2
1
0
1
1
1
1
1
2
1
1
1
1
0
2
2
0
2
1
2
2
1
0
2
2
1
1
1
1
1
1
1
2
1
1
1
0
0
1
1
1
1
1
1
2
1
1
1
6
2
1
1
2
2
2
1
1
2
1
1
2
2
1
0
1
2
2
1
1
1
1
1
1
0
2
2
0
1
1
0
1
1
1
2
1
1
1
1
1
1
1
1
1
1
0
1
0
1
0
2
1
1
1
1
1
2
1
2
2
1
1
0
1
1
0
1
2
1
2
2
0
3
2
0
1
1
1
1
0
1
4
2
0
1
0
1
2
2
2
2
1
0
1
2
0
1
1
1
2
0
2
1
2
2
1
1
1
1
2
0
1
1
2
2
0
1
1
1
1
1
2
1
1
2
1
3
1
0
0
1
2
2
1
0
2
0
1
2
1
1
1
1
0
1
1
1
1
2
2
2
0
0
2
3
1
0
1
0
1
1
1
0
1
1
2
1
1
1
1
1
2
1
1
1
0
1
2
1
0
2
2
1
2
1
0
1
0
2
0
0
2
0
0
2
1
3
1
1
0
0
1
1
2
2
1
1
0
1
1
1
0
1
1
1
1
1
1
1
2
0
1
1
2
1
2
0
1
0
1
1
0
1
1
1
1
1
2
0
1
2
1
2
0
1
1
2
1
1
1
1
0
1
1
1
1
1
2
1
0
1
1
1
2
1
1
0
2
2
1
2
0
0
1
1
0
1
2
1
1
1
0
0
1
2
1
1
1
2
2
1
2
2
1
0
1
1
1
1
1
1
0
1
1
1
1
1
2
1
1
0
2
2
1
2
1
0
1
1
2
1
1
2
1
2
1
1
1
2
2
0
2
1
3
0
0
1
1
1
2
0
2
1
0
0
1
1
1
1
1
1
1
1
1
1
1
2
1
0
0
1
1
1
0
1
1
0
1
1
1
2
0
0
1
1
2
0
0
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
2
1
0
0
2
0
1
2
1
1
0
2
1
1
2
1
2
3
1
2
2
0
1
0
2
2
1
1
2
2
1
1
0
1
1
2
0
1
2
2
0
2
1
1
1
1
1
2
2
1
0
1
0
1
1
1
0
1
1
1
1
0
1
1
1
1
2
1
1
1
3
1
1
2
1
0
1
1
1
1
1
0
2
0
1
1
1
0
1
1
3
1
1
2
1
3
1
1
1
2
1
0
1
3
1
1
2
1
1
2
2
2
0
1
0
0
1
1
2
2
0
1
1
1
1
1
0
0
2
0
1
1
0
1
2
0
2
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
2
1
1
2
2
1
2
2
1
1
2
0
1
1
2
2
1
1
1
1
1
1
1
2
0
1
1
1
1
1
1
1
0
1
2
1
2
1
0
1
2
1
1
1
0
2
0
1
0
2
1
1
1
1
1
2
1
1
1
1
1
0
1
1
0
1
0
0
1
1
1
1
1
1
1
0
0
1
1
5
1
2
1
2
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
0
2
1
1
2
0
2
2
1
1
2
1
1
1
1
1
1
0
1
2
0
1
1
1
2
1
1
3
2
3
1
0
0
1
2
2
2
1
2
1
1
2
1
1
2
2
1
0
1
1
1
0
1
1
2
1
2
0
1
2
2
0
1
1
2
1
2
1
1
0
1
1
0
1
0
1
1
1
1
0
1
0
0
2
1
1
1
2
1
1
1
2
1
1
1
2
1
0
1
1
1
0
0
1
1
1
2
1
2
1
1
3
0
1
1
0
2
1
2
1
0
1
1
1
1
1
0
1
2
2
3
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
0
1
2
1
0
2
1
1
1
1
2
1
1
1
1
1
2
1
1
0
1
1
1
1
1
0
0
2
2
1
0
1
3
0
1
2
2
2
0
1
1
1
2
1
0
2
1
1
0
2
2
0
0
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
2
0
1
1
0
1
1
0
2
1
2
1
0
2
1
0
2
2
2
1
1
0
1
2
1
2
0
1
1
1
2
2
1
1
1
2
1
1
1
1
1
1
0
1
1
1
0
0
1
1
0
1
1
0
1
0
2
1
0
0
1
1
2
1
0
1
2
2
2
1
1
0
1
1
2
1
1
1
1
1
1
1
1
2
0
0
1
0
1
1
0
2
1
2
0
0
2
1
2
2
1
1
1
1
2
0
2
1
1
1
2
0
1
2
1
1
2
1
2
0
1
2
1
1
1
1
1
2
1
0
1
1
1
1
2
1
1
1
1
1
1
1
1
0
0
2
2
1
0
1
1
1
0
2
1
1
1
0
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
2
0
1
1
1
1
1
2
1
0
1
2
2
2
4
1
0
1
1
1
1
1
1
1
1
1
1
0
1
1
2
1
1
1
1
2
1
1
1
1
1
2
0
1
1
2
2
2
1
0
1
2
1
2
1
2
0
1
1
1
1
1
1
1
1
1
2
1
1
2
0
1
0
2
1
1
1
0
2
1
1
0
1
2
1
2
1
1
1
2
2
1
2
1
1
2
1
1
2
2
1
2
2
0
1
1
1
0
1
0
2
1
1
1
1
1
0
2
1
1
1
1
2
1
0
0
1
1
0
2
1
1
2
2
1
1
0
1
1
2
1
1
1
0
1
1
1
0
2
1
0
1
1
1
2
1
1
2
0
2
1
1
1
1
2
2
2
1
2
1
1
1
1
1
2
1
0
1
1
1
2
1
1
1
1
1
2
0
0
1
0
1
2
1
2
1
1
2
2
1
0
0
1
1
2
2
1
1
1
1
1
0
2
0
1
1
0
2
2
1
1
1
2
1
1
1
1
2
1
1
1
1
0
0
1
1
2
0
1
0
1
2
2
2
1
1
1
1
2
2
1
1
1
1
1
1
0
1
1
1
0
0
1
1
1
1
1
1
1
0
2
0
1
2
0
1
2
1
0
1
0
2
2
1
1
1
2
0
1
1
1
1
2
2
1
1
1
0
1
3
1
1
1
1
1
0
1
2
1
0
0
1
1
1
1
0
2
2
0
2
1
1
1
1
2
1
1
1
1
1
1
0
0
1
1
1
2
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
1
0
1
1
1
0
1
0
1
1
0
1
1
1
1
1
1
1
1
1
2
2
1
1
1
2
2
0
1
0
0
2
2
1
1
1
0
1
2
0
1
1
2
0
0
2
0
0
0
0
0
2
2
1
2
1
1
1
1
0
1
1
1
1
2
0
1
1
1
1
0
1
1
2
1
1
1
1
2
1
0
0
1
0
1
0
0
1
2
1
2
2
1
1
1
2
1
2
1
1
0
2
1
1
0
1
1
0
1
1
2
1
0
1
2
1
0
0
2
1
2
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
2
0
1
2
0
1
0
1
1
1
0
1
0
1
0
0
0
1
0
1
1
1
1
2
1
1
2
1
2
1
2
1
1
1
1
1
2
2
0
1
2
1
1
0
1
1
2
1
1
0
1
1
2
1
1
2
1
2
0
1
0
1
1
1
1
1
1
1
2
1
2
1
0
1
2
1
1
1
1
0
1
0
1
2
1
0
1
1
1
1
1
1
1
2
0
1
1
1
1
1
1
1
1
0
1
1
0
1
0
2
2
2
1
1
1
0
2
1
1
1
0
1
2
1
1
0
2
1
0
2
0
2
1
2
1
1
1
0
1
1
2
1
1
2
2
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
0
1
1
1
1
0
2
1
1
1
1
2
1
1
2
2
0
2
1
2
1
1
2
1
0
2
1
1
1
1
1
1
2
1
2
1
2
1
0
0
1
1
1
0
1
0
1
1
1
2
0
2
2
0
1
1
2
1
2
0
1
2
1
0
2
2
1
1
1
1
1
1
1
0
2
0
2
1
1
2
0
1
1
1
1
1
1
1
2
1
1
2
2
2
1
2
2
1
1
1
0
0
1
0
1
1
2
0
0
0
1
1
1
0
2
0
1
2
2
0
1
1
1
1
2
1
2
1
1
0
1
2
1
0
2
1
2
2
2
1
0
1
1
2
1
1
1
1
2
0
1
1
2
0
1
0
1
1
0
2
1
1
2
1
1
1
3
1
0
2
2
0
1
1
1
2
1
1
1
0
1
2
0
1
1
1
0
1
1
1
1
1
1
1
0
2
0
1
0
0
1
2
0
1
0
0
1
2
0
0
2
2
1
0
0
2
0
2
1
1
1
2
1
1
1
0
1
2
1
2
2
1
1
0
1
1
1
1
1
1
1
1
1
0
1
1
2
1
0
0
1
1
1
0
1
2
0
1
1
1
1
1
1
1
1
1
1
1
0
0
1
2
1
0
1
1
1
0
1
2
1
2
1
1
1
1
0
1
0
3
2
1
1
2
2
1
1
1
1
1
1
1
0
1
2
1
1
1
1
0
1
1
1
1
0
1
0
1
0
1
2
1
1
0
1
1
1
2
0
1
1
1
2
0
1
1
1
1
1
1
1
1
2
2
2
0
1
0
2
0
2
0
1
1
1
1
1
0
2
1
1
1
1
0
1
0
1
0
2
1
1
1
1
2
1
0
1
0
0
0
2
1
2
1
1
0
2
1
1
2
1
2
0
1
1
0
1
1
1
1
2
1
0
1
1
0
1
1
1
1
1
2
1
1
1
1
1
0
1
1
2
1
0
1
1
1
1
0
1
1
1
1
2
1
2
1
0
0
0
2
1
1
1
1
2
2
1
1
1
1
1
0
2
0
0
1
1
1
1
1
1
1
1
1
1
2
0
1
1
2
5
2
2
1
1
1
1
1
0
1
1
2
1
2
1
2
0
2
1
1
1
0
2
2
0
1
1
0
2
1
1
1
1
1
1
0
3
1
1
1
0
2
1
2
0
2
0
1
2
1
1
0
0
2
1
2
2
1
1
1
1
1
2
1
0
0
0
1
2
1
2
2
2
2
2
2
1
1
2
0
2
2
2
1
0
1
1
1
1
1
2
1
0
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
0
2
1
1
0
0
2
1
1
1
1
2
1
1
1
1
1
2
0
1
2
4
1
1
1
1
1
2
1
0
2
1
0
1
2
3
2
1
1
0
2
1
1
1
0
1
1
0
0
1
1
1
1
0
1
1
2
2
1
2
0
0
1
1
1
0
1
1
0
0
1
1
1
0
1
1
1
1
1
1
2
2
1
3
0
2
0
0
1
1
1
1
1
2
0
1
1
1
2
1
0
1
1
0
1
2
2
2
2
2
0
2
2
2
1
1
2
1
4
1
1
0
2
0
2
1
1
1
1
1
1
1
0
2
1
1
2
1
1
1
1
1
1
1
0
1
1
2
0
2
1
0
2
1
2
1
2
1
1
0
1
1
1
1
3
1
1
0
1
0
2
0
1
0
1
1
1
0
1
0
1
1
1
1
1
1
1
0
1
1
1
2
1
2
1
0
0
0
1
2
1
1
2
1
1
1
1
1
2
1
2
1
1
1
0
1
1
0
1
1
1
1
2
1
1
1
1
0
2
2
0
0
3
1
0
2
1
1
1
2
1
0
2
1
1
1
3
0
1
1
2
0
2
2
0
1
1
1
1
1
1
1
2
2
0
0
1
2
1
1
1
1
1
1
2
2
0
0
2
1
0
1
0
1
1
1
1
1
2
1
1
1
0
1
2
1
0
0
1
2
2
0
1
1
1
0
1
1
1
2
1
1
0
1
1
1
0
1
2
2
1
1
1
1
1
1
1
1
1
2
2
2
0
2
1
1
1
2
0
1
1
0
1
0
1
1
0
2
2
1
1
2
2
0
0
1
6
2
1
2
2
0
2
2
2
1
1
1
2
2
0
2
2
1
0
1
1
0
1
1
0
1
1
2
1
0
0
2
1
0
2
1
1
0
0
1
1
1
0
1
1
1
1
1
1
1
2
1
1
1
1
0
2
1
2
2
2
1
1
1
1
3
1
1
0
1
1
1
2
0
1
2
1
1
1
1
1
1
2
1
0
1
2
1
1
1
1
0
1
2
1
1
1
1
0
1
1
1
1
2
1
2
0
2
1
0
2
1
1
1
1
0
1
1
1
1
2
1
1
2
2
1
0
1
0
6
0
1
1
0
1
1
0
0
1
2
1
1
1
1
1
1
1
1
1
1
0
2
0
0
2
0
2
1
0
1
1
0
2
2
1
1
2
1
2
1
2
2
1
2
1
1
1
1
0
1
1
1
1
1
2
1
1
1
0
1
1
1
1
1
1
2
0
2
2
1
0
1
2
0
1
0
1
2
1
0
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
2
2
1
1
0
1
1
0
2
2
1
1
1
0
0
1
1
2
1
1
1
0
2
2
0
1
1
1
1
2
2
1
0
1
2
1
1
2
0
2
1
1
1
1
1
0
0
1
0
0
2
2
1
1
0
1
2
1
1
2
2
1
1
2
1
0
0
1
2
1
1
2
2
1
0
2
0
1
2
0
1
1
1
1
0
0
1
2
1
1
1
0
0
0
2
0
1
2
2
2
0
1
1
2
0
1
1
1
1
1
2
1
1
3
1
1
1
2
1
2
1
1
1
0
1
1
1
1
0
1
2
2
0
1
1
0
2
2
2
1
1
1
1
1
1
2
2
2
2
1
1
1
0
1
1
0
1
1
2
2
0
0
0
1
0
1
0
1
2
1
2
1
1
1
1
1
2
1
1
1
1
0
2
0
1
0
2
1
1
1
1
2
1
1
0
0
1
0
2
2
2
2
0
0
1
1
1
2
0
1
0
1
1
2
1
0
2
2
0
1
1
1
1
1
1
2
0
2
1
1
0
0
1
2
1
2
1
1
1
2
2
0
1
1
0
2
1
1
1
1
1
1
2
2
1
1
2
1
1
1
2
1
0
1
0
0
0
1
1
1
1
0
0
1
2
1
1
2
0
1
1
0
2
1
0
2
1
1
2
3
1
1
1
0
2
0
1
1
2
1
0
0
1
1
2
1
0
2
1
1
1
2
1
1
1
2
1
1
2
0
1
1
1
1
1
0
0
1
1
3
0
1
1
2
2
1
0
2
2
0
1
0
1
1
1
1
0
1
1
1
2
0
2
2
1
1
1
0
1
2
2
1
2
2
2
1
2
2
2
0
1
2
1
1
1
0
1
1
1
1
0
0
1
1
1
1
1
1
1
1
2
1
2
1
0
1
1
1
1
2
1
0
1
1
1
1
2
1
2
1
2
1
2
0
1
1
2
0
1
1
0
2
2
2
2
0
5
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
0
1
1
1
2
2
2
1
1
1
0
1
1
1
2
1
2
2
2
0
1
1
2
2
2
2
1
1
0
0
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
1
1
0
1
2
1
2
0
0
1
1
1
2
1
1
0
1
1
1
2
0
0
1
1
2
0
2
1
0
1
2
0
2
2
0
1
1
1
1
1
1
1
0
2
1
2
1
2
2
1
0
1
1
1
0
2
1
1
0
2
1
0
1
2
1
1
0
0
2
1
0
1
1
0
2
2
1
1
0
0
0
1
2
2
1
1
1
2
2
2
2
1
1
1
1
2
2
1
1
0
1
2
3
0
2
1
2
1
1
2
1
1
2
1
2
0
1
0
9
1
1
1
1
1
0
1
0
1
1
1
1
1
2
2
1
1
1
1
1
1
0
0
1
1
0
1
1
0
0
2
2
1
1
0
0
1
1
1
1
1
0
0
0
1
1
0
2
2
1
0
1
2
0
1
1
0
1
2
1
1
1
1
1
1
1
1
2
1
0
0
2
1
1
2
1
2
0
1
1
1
1
1
1
1
2
0
0
0
1
1
0
2
0
0
1
2
1
1
1
1
2
1
2
1
1
1
1
0
1
1
0
1
1
1
1
1
1
1
1
0
0
0
0
1
1
1
2
2
1
2
2
0
1
2
1
0
0
0
1
0
0
1
2
1
2
1
1
0
2
2
1
2
1
1
1
1
2
1
1
2
1
1
1
1
0
1
2
1
0
0
1
0
0
1
2
1
1
1
1
4
0
1
1
0
2
1
2
1
2
1
0
1
0
2
1
1
1
2
0
1
2
1
1
1
1
1
1
2
1
1
2
1
2
1
1
1
1
2
1
0
1
0
1
2
0
1
2
1
2
1
1
2
0
1
2
1
2
0
0
1
1
1
1
1
0
0
1
2
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
2
0
1
1
0
0
2
1
0
0
0
1
2
2
1
0
1
1
1
1
2
1
2
1
0
1
1
1
1
2
2
1
1
0
1
1
2
2
2
2
2
1
1
2
2
1
1
2
1
1
2
1
1
1
1
2
1
1
1
0
0
2
1
0
0
1
1
1
1
5
2
1
0
1
1
1
1
3
1
0
1
1
2
3
0
1
1
2
1
1
1
1
1
1
2
1
0
0
1
1
3
2
2
2
2
0
1
1
0
1
1
0
1
1
1
2
1
0
1
1
1
1
1
1
1
0
1
1
1
1
2
1
2
2
1
1
0
1
1
1
2
1
1
1
0
2
2
1
2
0
1
1
1
2
1
1
1
0
2
2
1
1
1
1
1
2
1
1
1
1
2
0
1
2
2
1
0
2
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
2
0
1
0
1
2
0
2
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
2
1
1
2
2
1
1
1
1
2
1
1
1
0
2
1
1
0
1
1
1
0
0
1
1
1
1
0
0
0
0
1
3
1
2
2
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
0
1
1
2
1
0
1
0
1
2
2
1
1
0
1
2
1
1
2
0
1
0
2
2
1
1
2
1
1
1
1
1
0
2
0
1
2
1
1
1
1
1
0
1
1
1
0
3
1
1
2
2
1
1
0
1
1
2
1
1
1
0
1
0
1
2
1
2
1
2
0
0
2
0
1
2
2
1
1
1
2
2
1
1
0
1
2
1
2
1
1
2
1
2
2
1
1
1
2
0
1
1
1
2
1
2
1
0
1
1
0
1
2
1
1
1
1
2
1
0
0
3
2
2
0
1
1
1
0
0
1
1
1
2
0
0
1
1
1
1
1
1
1
0
1
2
0
1
1
2
2
1
1
1
2
0
0
2
1
1
1
2
0
1
1
1
1
2
2
2
0
1
0
0
0
1
1
0
1
0
1
0
0
1
2
0
0
1
0
1
0
1
1
0
1
2
1
1
1
2
2
1
2
1
2
1
1
1
1
1
1
1
1
1
0
1
2
3
2
1
1
2
1
1
1
1
0
2
0
1
0
1
0
0
1
2
2
0
2
1
0
1
2
1
2
0
2
1
1
0
2
2
1
1
1
1
0
1
0
0
1
1
1
1
2
0
1
2
1
1
0
0
2
1
0
2
1
1
1
1
2
0
0
1
2
2
1
2
0
1
2
0
1
2
1
1
2
2
2
1
2
2
1
1
1
1
1
1
1
1
0
2
3
1
2
2
1
1
1
2
1
1
1
1
0
1
1
2
1
1
2
1
0
1
1
1
1
0
2
0
1
1
2
0
1
2
1
2
1
1
1
1
1
1
0
0
0
1
1
0
1
1
0
1
1
1
1
2
1
1
2
1
1
2
1
1
1
2
0
2
1
2
1
1
1
1
0
1
1
2
1
1
0
1
0
0
1
2
1
0
2
1
2
0
1
2
1
1
0
1
1
2
1
1
1
0
0
0
1
1
1
2
2
2
0
2
2
1
1
1
1
2
1
2
1
1
1
1
0
2
1
1
2
1
2
0
2
2
1
1
1
1
2
2
1
2
1
1
2
1
1
1
1
1
2
2
1
2
1
0
1
0
2
1
2
1
1
1
0
0
1
2
1
0
0
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
2
1
1
1
1
1
0
1
0
0
1
1
0
1
1
1
1
2
1
1
1
1
1
2
0
1
0
1
1
0
1
1
2
2
1
1
1
1
1
0
1
2
0
1
2
1
1
1
1
0
2
2
2
1
1
1
1
0
2
1
2
1
1
2
2
2
1
0
0
1
1
1
0
1
0
1
2
1
0
1
2
1
0
1
1
2
1
1
0
1
1
0
0
0
1
1
2
1
1
1
1
1
0
1
1
0
1
0
0
2
1
0
2
0
1
2
1
1
2
0
2
1
1
0
2
1
1
2
2
1
1
1
1
0
0
0
0
1
1
1
0
1
1
1
1
2
1
1
1
1
1
1
1
1
0
2
1
1
1
0
0
1
1
0
0
1
1
2
1
1
0
0
2
2
1
0
0
1
1
2
1
1
1
1
1
0
0
1
0
2
1
1
1
1
2
2
0
2
0
2
1
1
2
1
6
1
2
0
0
1
2
1
2
2
2
1
1
0
0
1
1
1
0
1
0
1
0
2
1
1
1
1
1
0
0
1
0
1
1
2
1
1
2
0
1
1
1
0
1
1
0
1
0
1
2
1
1
2
1
1
1
2
1
2
1
1
2
1
1
1
2
2
1
1
1
0
1
0
1
1
1
0
1
1
2
2
1
1
2
1
0
1
2
2
2
0
1
0
1
2
2
0
1
1
1
1
1
2
2
1
1
1
1
1
2
1
2
0
1
2
2
1
2
2
1
1
1
2
1
2
1
0
1
2
1
1
1
1
0
3
1
1
0
0
1
1
0
2
0
0
0
1
1
0
1
1
2
1
0
1
1
2
0
1
2
1
2
1
1
1
1
0
1
1
2
1
1
0
0
1
2
2
1
2
1
1
2
1
2
1
1
1
1
1
2
2
0
1
1
0
0
1
1
1
1
1
1
1
0
2
2
2
1
1
0
2
1
0
1
1
0
0
1
1
2
2
1
2
2
1
1
2
1
1
2
2
2
1
1
1
1
1
1
0
1
2
1
2
1
1
0
2
1
2
3
2
2
0
2
0
1
1
1
1
1
1
1
2
0
1
1
1
2
1
1
1
1
0
1
1
1
2
1
0
0
1
1
1
0
1
1
0
0
0
1
0
0
0
2
1
1
1
2
1
0
1
1
0
1
1
1
1
2
1
1
2
0
2
1
1
1
1
0
1
1
2
2
1
1
1
1
1
1
2
2
1
1
2
1
1
1
1
2
1
1
0
1
1
0
1
1
2
1
1
1
0
1
0
0
2
1
0
1
1
2
1
2
1
2
0
0
0
1
2
1
1
0
2
0
2
2
1
0
1
0
0
0
2
2
1
1
1
0
2
1
2
1
2
1
1
1
0
0
0
0
1
0
3
2
1
1
1
0
0
2
0
0
0
1
1
1
2
0
1
0
1
1
1
0
1
0
1
1
2
1
1
0
1
1
1
3
1
1
2
0
0
1
1
2
1
1
2
1
1
1
1
1
1
1
2
0
1
1
1
0
1
1
1
2
1
1
2
1
1
1
1
2
1
1
1
1
1
2
1
0
0
1
1
1
1
1
1
1
2
1
1
1
1
0
1
2
1
2
0
1
1
1
2
2
1
1
1
1
1
0
0
1
1
1
0
1
2
1
0
3
1
1
1
2
2
1
1
1
2
1
2
1
1
1
0
1
1
1
1
1
0
2
1
1
2
0
1
2
2
1
1
1
2
2
1
1
1
1
0
1
1
1
1
2
1
1
1
1
0
1
1
1
0
0
3
1
1
1
2
1
2
1
2
1
1
0
1
1
1
1
1
1
0
1
0
0
1
0
0
0
1
1
1
1
1
0
0
1
1
1
2
2
0
1
2
1
0
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
2
1
0
1
0
1
0
1
2
0
1
1
1
0
2
1
1
1
0
2
1
1
1
0
2
0
1
1
1
1
1
2
1
2
1
2
1
2
0
2
1
2
1
1
0
0
0
1
0
1
0
2
2
2
2
2
0
1
0
1
0
2
1
1
2
1
1
1
1
1
0
0
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
0
0
1
1
1
4
0
0
1
1
2
1
0
1
1
0
1
1
1
1
1
2
1
1
2
0
2
1
0
1
1
1
1
2
1
1
1
1
0
1
2
2
1
1
0
2
1
1
2
2
1
0
2
0
1
1
1
1
1
2
2
1
1
1
2
0
1
1
2
1
1
1
0
0
1
1
0
0
3
0
1
1
2
1
1
0
1
1
2
1
1
1
2
1
2
0
1
2
1
1
0
0
1
3
2
2
2
1
1
1
1
1
1
1
1
2
2
1
1
0
2
2
1
2
1
2
1
1
1
2
2
1
1
1
1
1
1
1
0
1
2
1
2
1
0
1
2
1
1
1
0
1
1
1
2
1
1
2
2
1
1
5
1
3
1
2
2
1
2
0
0
1
0
1
1
2
0
2
0
2
1
1
1
2
2
1
1
2
2
2
0
1
1
0
1
1
1
1
2
1
1
1
0
2
1
1
0
2
0
0
2
0
1
1
1
1
0
1
1
0
1
1
0
1
2
1
0
1
1
0
2
1
1
2
1
1
1
2
0
0
2
1
2
1
2
2
0
1
2
1
2
1
2
1
2
1
2
3
2
1
2
1
2
1
1
0
0
1
1
0
2
2
1
1
1
1
1
1
1
1
1
1
1
2
1
0
2
0
1
1
1
0
1
1
1
1
1
0
2
1
1
1
1
1
1
2
1
1
1
0
0
1
1
1
1
1
0
1
0
2
1
1
1
2
0
0
1
0
1
1
2
1
1
1
1
1
3
2
1
1
1
2
1
1
1
0
1
0
1
1
1
2
2
2
1
0
0
2
3
2
1
1
1
1
1
0
1
1
1
1
1
2
1
1
1
1
1
0
2
0
1
0
2
2
1
0
2
1
1
1
3
0
2
2
2
1
1
0
1
0
1
1
2
0
1
1
1
2
2
2
1
1
1
2
2
2
1
2
0
1
2
1
1
1
1
1
1
2
0
1
1
0
2
0
2
2
2
1
2
1
1
1
1
1
0
1
1
1
1
0
2
1
2
2
1
2
2
1
1
2
0
1
0
2
1
0
2
1
1
1
1
0
1
0
1
1
1
1
1
1
1
1
1
2
1
1
1
2
0
1
1
2
1
1
1
1
1
1
1
0
1
1
1
0
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
2
2
1
2
1
1
2
1
1
0
2
1
1
0
2
1
0
2
2
2
0
2
2
1
2
2
1
2
2
1
1
1
1
0
0
0
2
1
2
1
2
2
1
1
1
0
1
1
1
2
2
1
1
1
1
0
2
0
1
1
1
1
1
1
1
1
1
3
2
1
1
2
1
1
0
2
1
0
2
2
2
0
1
1
0
1
1
1
1
1
1
0
0
1
1
0
1
1
1
2
0
2
2
2
1
1
2
0
2
1
1
1
1
0
1
1
1
1
0
2
0
0
0
1
1
2
1
1
1
1
2
0
1
1
2
2
0
1
0
2
1
1
2
2
1
1
2
1
2
1
1
1
1
1
1
2
1
0
1
0
0
1
1
0
2
2
1
1
0
2
0
0
1
2
1
2
1
1
2
1
2
1
2
1
1
1
1
2
2
1
2
1
1
1
2
0
1
0
2
1
2
2
1
1
3
1
1
0
2
1
0
1
0
1
1
0
1
1
1
1
1
2
0
0
1
2
1
1
0
1
2
0
1
0
1
0
0
1
1
1
2
1
2
1
1
2
0
1
0
1
0
1
0
1
2
0
1
0
0
1
1
1
0
1
1
1
2
1
1
1
0
1
1
1
1
1
1
2
0
2
0
0
1
2
1
2
1
1
2
0
2
1
1
1
1
2
1
2
1
1
0
1
1
1
2
1
1
3
1
0
1
2
0
2
1
1
0
2
1
2
1
2
1
1
2
1
2
0
1
0
0
0
2
1
1
1
0
0
1
1
0
1
1
1
2
1
1
0
1
2
0
2
2
2
0
0
1
2
1
1
2
1
1
1
1
0
1
1
1
1
1
1
0
0
1
0
1
1
1
1
1
1
1
1
2
1
0
1
2
1
0
1
2
1
0
2
2
2
2
1
1
1
1
2
1
1
1
1
1
1
0
0
1
1
1
1
0
1
0
2
1
2
0
1
2
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
1
2
2
0
1
1
1
1
1
1
0
1
0
1
1
1
2
1
2
2
1
1
2
1
0
1
1
0
0
2
2
1
1
1
0
1
2
1
2
1
2
0
2
0
1
1
1
1
1
1
0
2
0
0
1
1
2
1
0
1
2
3
1
0
0
1
1
1
2
1
2
2
0
2
1
1
1
1
0
2
1
1
1
0
0
1
1
1
1
3
1
2
1
0
0
2
1
1
1
1
1
1
2
2
2
0
1
0
1
1
1
1
0
2
1
2
2
0
0
0
1
1
1
2
1
0
2
0
1
1
1
2
2
2
0
1
0
2
1
0
2
1
1
2
1
1
0
1
1
2
1
0
1
1
1
1
1
3
0
2
1
1
1
2
0
1
0
1
1
1
2
1
0
2
1
1
1
0
2
2
1
1
0
1
1
1
1
1
2
0
1
1
1
1
1
1
1
0
0
1
2
0
1
1
1
1
0
1
0
0
0
1
1
1
0
1
1
1
2
1
2
1
2
2
1
1
1
0
1
3
2
1
1
1
1
1
2
1
2
1
1
1
2
1
0
2
1
1
1
1
0
0
1
1
1
2
1
1
1
0
1
1
1
1
0
1
0
0
0
1
0
0
1
2
2
2
2
1
1
0
1
2
1
0
1
1
2
1
0
1
1
1
1
2
0
2
1
0
1
1
1
1
1
1
2
3
1
0
0
1
1
1
1
1
1
1
1
1
2
2
0
1
0
1
2
0
0
0
1
0
1
1
1
1
2
2
1
1
1
1
1
1
1
0
0
2
1
1
1
1
2
1
1
0
0
1
2
0
1
2
0
1
2
0
1
2
2
1
0
0
0
2
2
1
1
0
1
1
0
0
2
1
2
1
4
2
0
1
1
1
1
1
1
0
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
3
2
2
2
1
1
1
0
0
1
1
2
2
2
1
1
1
1
2
2
2
1
2
0
0
0
1
1
1
1
1
1
1
2
1
1
1
2
1
3
1
1
1
1
2
1
1
1
3
1
2
1
1
2
0
1
1
2
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
0
1
0
0
1
2
1
1
1
1
4
1
1
0
1
0
2
1
1
0
0
1
1
1
1
0
1
2
2
1
1
1
1
0
1
1
2
1
1
2
2
2
2
0
1
1
2
0
2
1
0
2
1
0
1
1
2
0
1
1
1
1
0
1
1
1
1
1
0
0
1
1
2
1
2
0
1
0
1
2
2
0
2
1
1
1
0
1
1
2
0
2
1
1
1
1
2
1
0
1
1
2
1
1
0
1
1
1
1
0
2
0
0
1
0
1
1
0
1
1
0
1
1
0
2
0
0
2
1
1
0
2
0
1
1
1
0
1
1
1
1
3
1
1
0
2
1
0
1
0
2
1
0
1
1
1
1
1
2
1
2
0
1
0
1
2
1
1
2
1
1
1
2
2
1
0
1
2
1
1
1
1
1
1
1
1
1
1
2
0
1
2
1
1
1
1
1
2
1
1
2
1
1
2
0
1
2
1
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
1
1
0
1
0
1
1
1
2
1
1
1
1
0
1
1
1
1
0
2
2
1
1
0
2
1
1
2
0
0
1
1
0
1
0
2
1
1
2
0
2
2
1
0
1
2
0
1
1
1
1
1
2
0
2
0
1
1
1
1
1
0
1
1
1
1
2
1
1
0
0
1
2
1
0
1
1
1
2
0
1
0
1
2
2
1
1
2
1
1
1
0
1
2
2
1
0
0
1
8
1
1
1
1
0
2
0
1
1
1
1
0
0
1
1
1
0
1
2
2
0
0
1
2
1
1
1
1
2
1
1
2
0
1
1
2
2
2
2
1
1
1
2
2
2
0
0
0
1
0
1
2
0
2
1
1
0
0
2
1
1
1
2
1
0
2
1
1
1
1
1
1
1
1
2
0
0
1
1
2
3
1
0
1
1
2
1
0
1
1
1
2
1
1
0
1
2
2
2
1
2
1
0
0
1
1
1
2
1
1
1
2
1
0
1
1
2
2
0
3
2
2
1
2
1
0
1
1
1
1
1
1
1
1
0
1
1
2
0
2
0
0
1
0
1
2
1
1
1
2
2
1
1
1
1
0
0
0
1
0
1
1
1
0
1
1
1
0
0
1
2
1
0
2
1
1
0
1
0
1
1
2
1
0
1
0
2
1
1
1
1
1
1
1
2
1
2
0
1
0
1
2
2
1
1
2
1
1
0
1
1
0
1
0
1
1
2
1
2
1
1
1
0
0
1
1
1
1
2
1
2
1
1
1
1
1
1
0
1
1
0
1
0
0
2
1
1
1
1
1
2
1
1
2
1
1
1
1
2
2
1
1
2
0
0
1
1
1
2
1
1
1
1
2
0
0
0
1
1
1
0
1
0
1
2
1
3
1
2
2
1
1
1
2
2
1
1
2
1
1
0
1
1
1
1
1
1
1
1
1
0
1
1
1
0
1
1
1
2
1
1
2
1
1
1
1
1
2
1
2
1
2
0
0
0
1
2
0
1
1
1
1
2
2
0
1
1
0
0
2
1
2
1
0
1
1
1
1
1
1
1
1
0
1
1
0
0
0
1
1
2
2
2
1
1
1
1
0
1
1
1
1
2
1
2
1
0
1
1
1
1
0
1
2
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
0
2
2
1
2
1
1
1
1
1
1
2
1
2
1
1
1
0
1
0
1
1
1
1
1
0
0
2
1
1
0
1
1
2
1
2
0
1
1
1
3
0
2
1
1
2
2
1
1
2
1
1
1
1
0
2
0
1
1
0
0
1
1
2
0
1
2
2
1
1
1
0
0
1
2
0
0
1
1
1
0
1
0
1
1
0
1
1
0
2
1
1
1
1
0
1
2
1
1
1
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
0
2
0
2
1
1
1
1
1
1
0
2
1
0
1
1
0
1
1
1
0
1
1
0
2
2
1
1
2
1
1
0
0
2
1
1
2
2
0
3
1
0
1
1
1
2
1
1
1
1
2
2
1
2
2
2
2
1
1
0
1
2
1
1
1
2
1
1
1
1
1
2
1
1
1
2
0
1
1
1
1
1
1
0
0
2
0
1
1
1
2
1
0
0
2
2
1
2
2
1
1
0
1
1
0
1
0
0
2
1
1
1
1
1
2
1
1
1
1
2
1
0
0
2
1
1
1
1
0
1
2
1
1
1
2
1
0
1
2
2
1
2
1
2
1
1
1
1
1
0
0
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
0
2
0
2
1
2
1
0
2
1
1
1
1
1
0
1
1
1
0
2
1
0
1
5
0
1
1
2
2
1
1
1
1
1
0
1
2
1
0
2
1
1
1
2
1
0
1
2
1
0
1
2
1
1
1
1
1
0
1
1
1
0
1
1
1
0
1
1
1
1
2
1
1
1
1
2
1
1
1
2
2
1
1
1
0
1
1
1
1
1
1
0
1
0
1
1
1
1
1
1
0
0
0
2
1
1
1
1
1
1
2
1
2
0
1
1
1
1
0
1
2
1
0
2
2
1
0
1
1
1
2
1
0
2
1
1
1
1
2
1
2
0
0
1
2
1
2
2
0
1
1
0
1
1
2
2
2
1
2
2
1
1
2
2
0
1
2
1
1
0
2
1
0
0
1
2
1
1
2
2
1
0
1
1
0
1
2
2
1
2
2
1
1
1
2
1
1
1
2
0
2
2
1
1
0
1
1
1
1
1
1
1
0
2
2
1
2
0
1
1
1
1
0
0
2
0
1
1
2
1
0
1
2
0
1
1
2
1
0
0
1
1
0
1
1
1
1
2
1
2
1
2
1
5
1
1
1
0
1
0
1
1
0
1
1
1
2
1
0
0
1
2
1
0
0
2
0
0
0
0
2
1
1
1
1
1
1
1
1
1
1
1
1
0
2
2
1
2
1
2
1
1
1
1
1
2
1
1
0
0
0
1
1
2
2
1
2
2
1
1
1
1
2
0
2
1
3
0
1
0
2
2
1
1
1
1
1
1
1
0
0
2
0
1
0
1
1
1
1
1
2
2
3
1
1
1
1
0
1
2
0
2
2
1
1
0
1
1
0
2
1
2
2
1
2
1
1
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
2
1
2
2
0
0
1
1
1
1
0
1
2
2
2
1
1
1
0
0
2
1
0
0
1
0
1
0
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
0
1
1
2
2
1
2
2
1
1
2
1
2
1
1
1
0
0
1
0
2
1
1
1
1
1
3
0
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
0
2
2
2
2
0
1
1
1
0
1
2
1
1
1
1
1
0
0
2
1
1
2
0
1
0
2
1
2
1
1
0
2
1
2
1
1
2
1
1
1
1
1
1
1
1
1
0
1
0
2
1
1
2
1
1
2
1
2
1
1
1
0
1
1
1
1
1
2
1
1
1
1
0
2
0
1
2
2
1
1
1
1
1
2
0
2
1
1
1
1
2
0
0
0
0
1
1
1
1
1
0
0
0
1
0
1
1
1
2
0
1
0
1
2
1
1
1
2
2
1
2
1
2
2
1
1
0
0
1
2
1
2
0
1
1
1
1
1
0
2
1
1
2
1
2
1
1
2
0
2
0
1
2
0
1
1
1
2
1
0
1
1
1
1
1
2
0
0
1
1
1
1
1
1
0
1
0
1
1
1
1
1
2
1
1
1
1
0
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
0
1
0
1
1
1
2
1
1
1
0
0
2
0
2
1
0
2
1
1
0
1
1
0
1
1
1
1
2
0
0
2
2
1
1
2
0
2
2
2
2
0
1
1
2
2
1
1
1
2
1
1
1
0
1
1
1
1
3
1
2
2
1
1
1
2
2
0
1
1
1
2
2
2
2
0
0
1
1
1
1
0
1
1
1
0
1
0
2
0
0
2
1
1
2
1
1
1
1
0
1
2
1
2
0
1
1
2
1
1
0
1
1
1
1
1
1
2
1
0
0
2
2
1
1
0
1
1
2
1
1
0
1
1
2
1
1
0
1
0
0
1
1
2
1
2
1
2
1
2
1
1
0
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
2
1
0
1
2
2
1
2
0
0
1
2
2
0
2
1
0
1
1
2
0
1
1
1
1
0
1
0
2
1
2
1
1
1
1
0
1
1
1
2
1
1
2
1
1
1
2
1
2
1
1
1
2
2
1
1
1
1
3
1
0
1
0
1
2
1
1
1
3
1
1
1
1
2
0
1
1
1
1
0
1
1
1
1
1
2
2
2
1
1
0
1
0
1
1
2
1
2
0
1
2
1
2
1
1
2
2
1
2
1
1
1
2
0
2
2
1
2
1
1
2
1
2
0
0
1
2
1
1
0
1
1
1
1
2
0
1
1
1
1
0
1
2
2
1
1
2
1
1
1
1
1
1
1
2
1
1
0
1
1
1
4
1
2
1
1
2
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
0
0
1
1
1
1
0
1
2
1
0
2
1
1
0
1
1
2
2
1
2
1
2
1
0
1
2
1
1
0
2
1
2
1
2
1
2
1
2
2
1
1
0
1
1
0
1
1
1
2
0
2
2
1
1
2
2
1
1
1
1
1
1
1
1
0
1
1
2
2
2
1
1
3
1
1
0
1
1
2
0
1
1
0
1
1
0
1
2
1
1
1
2
2
0
1
2
2
0
1
0
1
1
1
1
1
0
1
0
2
0
2
1
1
1
0
1
2
1
1
1
1
1
1
1
2
2
1
1
1
0
0
1
3
1
1
1
1
0
1
2
1
0
1
0
1
1
2
2
2
2
2
0
1
1
2
2
1
0
2
1
1
1
0
0
1
1
1
0
2
2
2
2
0
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
0
1
0
1
0
2
2
0
1
0
1
1
0
1
0
1
1
2
0
2
1
2
1
1
2
1
1
0
2
1
1
1
1
1
1
1
1
1
1
0
0
0
2
1
1
0
2
1
1
0
1
2
2
1
1
1
1
1
0
1
2
1
1
1
1
1
1
0
1
1
1
1
0
1
1
1
1
2
2
0
1
1
1
1
1
1
2
0
1
1
1
1
1
2
1
1
1
2
1
2
1
0
2
1
0
1
1
1
1
2
1
0
1
1
0
1
1
1
1
1
0
2
1
2
1
2
1
1
1
0
0
1
0
1
2
1
1
1
1
2
1
1
1
1
0
1
1
1
1
1
1
0
1
0
1
2
2
2
1
2
2
1
1
2
2
1
2
0
0
2
1
1
1
1
1
1
1
0
1
1
2
2
1
1
1
2
1
1
1
1
0
0
1
2
1
1
1
1
2
0
2
1
1
2
1
1
1
1
1
1
0
1
1
2
2
1
0
1
2
1
1
0
2
1
1
1
1
1
3
0
2
2
2
3
1
0
1
1
0
0
1
0
0
1
1
1
0
0
1
1
1
2
2
1
1
0
1
2
2
0
0
1
0
0
0
1
2
2
1
1
0
1
1
1
1
0
0
2
0
0
1
1
1
0
1
1
1
0
1
1
1
0
2
0
2
1
1
1
2
0
1
2
2
1
1
1
1
2
1
2
2
1
1
1
1
1
0
0
1
0
2
0
0
1
2
2
0
1
1
1
0
1
1
2
2
1
1
1
1
1
2
0
0
1
1
1
0
0
0
0
1
2
1
2
2
2
1
2
1
1
1
1
1
2
2
2
2
0
1
1
1
1
2
1
2
0
1
1
1
2
1
1
1
2
1
1
2
2
1
1
2
2
1
1
1
1
1
1
1
2
0
0
2
2
2
1
1
2
1
2
2
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
1
0
1
1
1
1
3
1
0
1
0
1
1
1
1
1
2
1
2
1
0
1
1
1
0
1
1
1
0
1
2
1
0
2
1
2
0
1
1
0
1
1
0
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
0
1
1
1
0
2
1
2
1
1
2
1
0
0
1
1
1
1
0
1
0
2
1
1
1
1
1
1
1
1
0
1
0
3
0
0
2
0
1
1
0
1
0
1
1
1
2
1
1
2
1
2
1
1
1
2
1
1
0
1
1
1
2
1
0
1
1
0
0
1
1
1
1
1
1
1
1
2
1
3
1
2
2
2
1
1
2
1
1
1
1
1
1
1
0
1
2
1
0
1
2
1
0
1
2
0
1
1
2
0
1
2
0
1
1
1
1
1
1
1
2
0
0
1
1
1
1
1
1
1
1
1
1
2
1
0
0
1
1
1
1
1
1
1
2
0
2
1
2
1
2
2
2
0
0
1
2
1
0
2
1
1
0
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
2
1
1
1
1
3
2
0
1
1
1
2
1
0
1
1
2
1
2
1
3
1
1
1
1
0
1
0
0
1
1
1
0
2
1
1
0
0
2
1
0
1
1
1
1
2
1
0
1
2
1
2
0
1
1
1
2
3
1
1
1
1
3
1
1
1
0
0
1
0
1
1
1
1
1
2
1
0
2
0
1
2
1
1
1
1
1
1
1
2
2
1
0
1
1
1
2
2
1
2
2
0
0
2
2
1
1
1
1
1
1
1
0
2
0
0
2
2
1
1
2
1
0
1
2
0
2
2
0
1
1
1
1
1
2
1
0
1
1
1
0
2
1
1
2
1
1
1
1
2
1
0
0
1
1
1
1
0
0
2
0
1
0
1
1
0
0
2
1
1
2
1
0
2
1
0
1
1
1
1
2
1
1
1
1
1
2
1
2
1
1
1
0
2
1
1
1
0
1
2
2
0
1
1
1
2
2
1
2
1
2
0
1
2
0
2
0
1
1
2
1
0
0
1
2
2
2
1
2
1
1
1
1
1
0
1
1
0
1
1
1
1
0
1
1
1
0
1
1
1
0
1
1
0
1
1
1
1
1
1
1
2
1
1
1
3
0
0
1
1
1
2
1
0
2
0
1
1
2
0
1
1
1
0
1
1
1
1
1
1
0
1
1
2
1
0
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
0
1
1
0
1
1
1
1
2
0
1
1
2
1
1
2
1
1
1
0
1
1
1
1
2
1
1
2
2
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
0
1
2
2
0
1
1
0
1
2
1
1
0
2
0
2
1
1
1
1
1
2
1
1
1
0
1
1
1
3
1
1
1
0
0
0
1
1
0
1
1
1
1
1
2
0
1
2
2
3
0
1
0
2
2
1
1
1
1
1
1
0
2
1
1
2
0
1
2
2
0
1
1
1
2
1
1
0
1
0
1
2
1
1
2
1
1
1
1
1
1
1
2
0
1
0
1
1
1
0
0
1
1
1
1
1
0
0
0
1
1
1
0
1
0
2
1
1
0
1
2
2
0
1
1
1
1
2
1
2
1
1
0
1
2
1
1
1
1
2
1
1
0
1
1
0
1
1
1
1
0
2
1
1
1
2
2
1
0
2
1
0
1
2
1
2
2
1
2
1
2
1
0
2
2
1
2
1
1
1
2
1
1
2
1
1
1
2
1
2
1
2
2
1
0
2
3
2
3
0
1
1
0
2
2
0
1
1
1
0
1
0
1
2
1
2
2
1
1
2
1
0
1
1
1
1
1
1
1
1
0
0
2
1
1
2
0
2
2
0
2
2
2
2
1
1
2
0
1
2
2
0
2
0
1
1
1
2
0
1
1
2
0
0
1
1
1
0
2
1
0
1
1
0
1
2
1
1
0
2
2
2
1
1
2
1
2
1
1
1
1
0
1
2
1
1
1
0
1
0
0
2
2
1
2
2
1
2
1
1
2
1
1
2
1
2
2
2
1
2
1
2
1
3
1
1
1
1
1
2
2
1
1
1
1
1
2
1
2
0
2
0
0
0
1
1
0
1
0
1
1
2
1
1
2
1
0
1
2
1
1
1
2
2
1
1
1
0
2
1
1
0
0
1
1
1
1
1
1
3
0
2
1
1
1
1
1
2
1
2
0
0
1
1
0
1
1
1
1
1
0
0
1
0
1
0
2
1
2
1
2
1
2
0
1
1
1
0
2
1
1
1
1
0
0
2
1
1
1
1
1
0
1
2
0
2
1
1
1
0
2
3
1
1
1
2
1
1
0
2
1
1
1
4
2
2
1
0
1
1
0
2
1
1
2
1
0
2
1
1
1
1
0
1
1
1
1
0
1
1
1
2
1
2
1
1
2
1
1
1
1
1
0
1
1
1
0
2
1
0
1
1
1
2
1
1
2
1
1
1
1
2
1
2
1
1
1
1
2
2
1
0
1
0
0
0
1
1
1
0
1
2
1
1
1
1
2
1
1
1
0
0
1
1
1
1
1
2
1
0
1
1
1
2
1
1
1
0
2
0
1
1
3
0
1
1
1
2
1
0
1
2
1
1
1
0
2
1
2
2
1
2
2
0
1
1
1
1
1
1
2
1
1
2
1
0
1
0
1
0
1
1
2
1
1
0
2
0
2
2
1
0
1
0
2
1
1
1
1
2
1
2
2
2
1
2
1
0
1
1
1
1
1
0
2
2
0
1
1
1
1
1
2
1
0
2
1
1
2
2
0
1
0
2
1
1
1
2
1
1
0
2
0
1
1
1
0
0
1
1
1
1
1
1
1
1
1
2
2
1
2
0
1
0
2
2
1
2
1
1
1
2
1
1
1
2
1
1
1
0
2
1
1
1
0
0
2
3
1
2
1
0
0
1
2
1
2
2
1
2
1
1
1
0
1
1
1
1
1
1
0
2
0
2
1
2
0
1
1
1
1
1
1
1
1
0
1
2
0
1
0
1
0
0
1
0
0
1
1
1
0
1
1
0
1
1
1
1
0
1
1
2
1
2
2
1
1
0
2
0
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
2
2
1
2
2
1
1
1
0
1
1
1
1
1
1
1
1
0
2
1
1
1
1
2
0
1
1
1
0
1
1
1
2
2
1
2
1
1
0
2
0
1
2
0
1
1
1
2
1
0
0
0
0
1
2
2
1
1
1
0
1
1
1
1
2
0
2
1
0
2
0
1
2
2
1
2
1
1
0
1
0
1
1
2
1
2
0
1
2
1
1
1
1
1
1
1
0
1
0
1
0
1
1
1
0
1
2
2
1
0
2
1
2
0
1
0
1
1
2
1
1
0
1
1
1
0
0
2
1
2
1
1
2
0
0
1
1
2
1
1
2
1
1
1
1
2
2
0
0
2
2
1
1
1
1
1
2
1
0
2
1
1
1
1
3
1
1
1
1
2
1
1
1
1
1
3
1
0
1
0
2
1
0
1
2
1
1
1
0
2
2
0
2
1
1
2
0
1
0
2
1
1
2
2
1
2
1
1
1
1
0
1
2
2
1
2
1
1
0
1
2
2
1
0
1
2
1
0
1
2
2
2
0
2
1
1
1
1
0
1
1
1
1
4
1
1
0
1
1
1
0
0
0
1
2
1
0
0
1
1
1
1
1
0
1
1
1
1
1
1
1
1
0
1
1
1
1
0
1
2
2
2
1
1
1
1
1
1
1
2
1
1
0
0
1
1
2
1
1
1
1
1
2
0
1
2
1
2
1
1
1
1
1
1
2
1
1
1
2
0
2
1
2
1
1
1
1
1
0
2
1
1
0
1
0
1
1
2
1
2
2
1
2
1
2
1
0
1
1
0
0
1
2
1
1
1
2
1
1
1
0
1
0
1
2
1
0
2
1
1
1
0
1
1
1
1
2
1
2
2
1
0
2
2
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
0
1
1
1
1
1
0
0
1
1
1
1
2
1
2
1
0
1
0
1
2
3
2
1
0
1
0
1
0
1
0
0
2
2
1
2
1
1
1
2
2
0
1
2
0
1
2
1
1
1
2
1
2
1
1
1
0
1
1
1
0
0
1
1
1
1
1
1
2
1
0
0
0
1
0
0
1
1
0
1
1
1
1
1
1
2
1
1
0
3
2
2
1
2
3
1
1
0
0
0
1
0
1
0
1
1
1
2
2
2
1
2
1
2
1
2
2
1
2
2
1
1
3
1
1
1
0
1
1
1
1
1
1
1
1
1
2
3
2
1
0
1
1
1
1
1
2
0
2
2
0
0
1
1
1
1
1
0
1
2
1
0
1
1
2
1
1
0
0
1
0
1
1
1
0
1
1
1
1
1
0
1
3
1
1
1
2
1
1
1
0
1
1
1
1
1
2
1
0
1
1
2
3
1
1
2
1
2
2
0
1
0
1
1
1
1
1
0
0
1
1
2
1
1
2
1
0
0
1
1
1
1
1
0
0
1
1
1
1
0
2
0
1
3
2
3
0
1
1
1
2
2
2
1
0
1
1
2
3
2
1
1
0
1
2
1
1
1
1
1
1
2
1
1
1
1
1
0
1
1
1
1
2
0
1
1
1
0
0
1
2
1
1
1
1
1
2
2
1
1
2
2
2
2
2
1
1
0
1
1
0
2
0
0
1
0
1
1
1
1
1
1
0
1
1
1
0
1
1
2
1
2
0
1
2
1
1
1
1
2
0
0
0
1
2
0
1
1
2
2
1
2
1
1
0
1
1
2
1
1
1
2
1
2
1
0
1
1
0
1
1
1
1
1
1
1
2
0
1
1
1
2
2
1
1
1
1
2
1
2
1
1
0
2
2
0
1
0
1
1
1
0
2
2
2
2
1
2
1
2
0
1
0
1
2
1
1
0
2
0
1
1
2
1
1
1
1
1
1
0
1
1
1
2
1
0
1
2
2
1
1
0
0
1
0
2
0
1
0
1
1
2
2
1
1
2
1
0
1
1
1
2
1
1
0
1
0
0
2
1
1
1
1
2
2
1
2
1
0
1
1
0
2
1
0
0
1
2
2
1
1
1
1
1
1
0
1
2
0
1
1
1
1
1
1
1
1
0
2
2
1
2
2
1
1
2
1
2
1
0
1
1
2
1
1
1
2
0
1
0
1
1
1
1
2
1
2
0
0
2
1
0
2
1
1
2
1
0
1
1
1
0
1
1
4
1
1
1
1
2
1
1
1
1
2
0
0
1
1
0
1
1
1
0
1
0
1
1
1
1
1
2
2
1
1
1
2
1
1
2
1
1
2
1
2
0
1
0
0
1
1
0
1
1
1
0
2
1
1
1
2
2
1
2
1
0
1
1
2
1
1
3
0
1
1
2
1
1
1
1
0
1
0
1
0
2
1
1
1
2
2
1
1
1
2
1
1
1
0
2
1
1
1
1
0
0
0
1
1
0
2
1
0
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
2
2
1
2
1
1
1
1
0
1
0
2
1
0
0
2
2
1
1
0
1
2
1
2
0
1
2
1
0
2
0
2
0
1
0
2
1
0
1
1
2
0
1
0
1
2
1
2
1
2
1
0
0
1
1
1
1
0
1
2
0
1
1
2
2
0
1
1
3
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
0
1
2
2
1
1
1
1
1
1
1
1
2
2
0
0
1
1
2
0
1
1
1
2
1
0
1
1
0
2
1
1
1
2
2
1
1
0
1
1
1
1
1
1
0
0
2
2
1
0
0
1
1
1
2
0
2
0
1
1
2
1
2
1
0
1
1
1
0
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
0
0
2
1
1
1
0
1
1
0
1
1
1
1
1
1
1
0
1
1
1
0
0
0
1
1
1
1
1
0
1
1
1
2
0
0
1
1
1
1
3
0
1
1
0
2
4
1
0
2
1
1
0
1
2
2
1
1
1
1
1
2
0
2
2
1
1
0
0
1
1
1
1
0
2
0
2
1
2
2
0
2
1
0
1
2
1
1
2
1
1
0
1
1
1
2
1
0
0
1
1
1
2
1
1
1
0
1
1
1
1
1
1
1
0
1
2
2
1
1
1
0
1
0
1
2
0
2
2
1
2
0
1
2
1
0
1
1
0
0
0
0
1
1
1
1
0
1
0
2
1
1
3
1
0
1
1
1
1
2
1
1
1
0
0
2
1
1
0
1
1
1
0
2
1
0
2
0
1
1
1
1
0
2
1
1
1
0
1
1
1
2
1
2
2
2
2
1
1
0
2
0
1
1
1
1
2
2
0
1
1
1
0
1
1
1
2
1
0
0
1
1
1
2
1
1
1
0
1
1
1
1
1
1
0
1
1
1
0
2
2
1
1
2
0
1
1
1
2
1
0
1
1
2
1
4
2
0
1
0
1
0
3
0
1
2
0
1
2
1
2
1
1
2
1
2
1
1
1
2
1
1
0
0
1
2
2
0
1
1
1
1
2
1
0
1
2
1
1
1
2
1
1
1
0
2
2
1
2
1
0
0
1
1
2
1
1
1
0
2
2
1
1
1
1
0
1
1
1
1
1
1
1
1
1
2
0
0
1
1
1
1
2
0
1
2
0
1
0
1
2
1
2
0
0
1
0
2
1
1
2
1
0
1
1
1
1
1
1
1
2
0
1
2
2
2
1
1
1
2
1
1
1
1
2
1
1
2
1
1
2
1
2
1
1
2
1
1
1
1
2
0
2
2
2
2
1
2
2
1
1
1
1
2
0
2
0
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
3
1
1
2
1
1
1
1
2
3
2
1
2
1
1
1
2
1
1
0
0
1
2
2
1
0
1
2
2
1
1
1
1
0
1
1
1
1
1
2
2
2
1
2
1
1
0
1
0
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
2
1
1
0
1
1
2
2
1
2
1
1
1
0
2
2
2
2
2
1
0
1
1
2
1
1
0
1
0
1
1
1
1
0
1
1
1
1
1
0
1
2
1
0
1
2
1
1
0
2
1
1
1
2
2
1
1
1
1
0
1
1
0
1
1
2
1
1
2
2
0
2
1
1
2
1
2
0
1
0
1
1
0
1
1
1
2
1
1
2
2
1
0
1
1
1
0
0
1
0
1
0
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
0
2
2
1
2
0
1
1
1
1
1
1
1
0
1
2
2
0
1
0
0
1
1
1
2
1
0
1
1
0
2
1
1
1
0
2
1
1
1
1
1
2
3
0
1
2
1
1
1
2
2
0
2
1
0
1
2
1
0
0
1
1
1
2
2
1
2
2
1
1
2
0
2
2
1
1
0
2
1
1
0
2
1
1
2
1
1
2
2
1
1
2
0
1
1
2
2
2
1
1
1
1
1
2
1
1
1
1
2
1
0
1
2
0
1
1
0
1
1
1
0
2
1
1
1
0
2
1
2
0
1
2
2
1
2
1
1
0
1
1
1
1
1
0
1
1
1
1
1
1
1
1
2
0
1
0
1
1
1
1
1
0
2
1
1
1
1
1
2
0
1
2
2
1
0
1
1
1
1
2
1
1
2
1
2
0
1
1
1
1
0
2
2
2
1
1
1
0
1
1
1
1
2
2
1
0
2
0
2
0
1
1
0
2
1
1
1
0
1
1
1
0
0
1
1
1
1
2
1
1
1
0
2
0
1
1
1
2
2
1
1
1
2
1
2
1
1
1
2
1
1
1
0
1
1
2
2
0
1
1
0
1
2
1
0
1
1
0
1
2
2
0
1
1
2
0
1
1
2
1
1
2
0
1
0
0
1
1
1
1
1
1
1
1
1
0
0
1
1
1
2
2
1
2
0
1
0
1
2
1
2
1
1
1
2
1
2
1
2
1
1
1
1
1
0
1
1
1
2
1
1
2
2
1
1
4
1
1
1
1
1
2
2
1
1
1
1
1
1
0
1
0
1
2
1
2
2
1
2
1
1
0
0
5
2
1
1
0
1
1
1
2
1
1
2
1
1
1
2
0
0
1
1
1
2
1
2
1
2
1
1
1
1
0
1
1
1
2
1
1
2
2
1
2
2
0
1
1
1
1
2
0
2
0
1
2
2
0
5
2
1
1
1
2
0
1
2
1
1
1
2
1
1
0
1
1
1
2
1
1
1
1
1
2
2
0
1
2
0
1
1
2
1
2
2
1
1
1
1
1
1
1
2
1
2
1
1
1
2
0
1
2
2
2
1
2
2
1
1
1
0
0
1
0
2
1
0
1
2
1
1
1
1
1
1
2
0
1
2
2
1
0
5
2
1
1
1
1
1
0
0
2
1
1
1
1
2
0
1
1
1
1
1
1
1
2
1
1
3
2
0
1
1
1
1
0
1
2
0
0
1
1
2
0
1
1
2
2
1
1
1
1
1
1
0
1
0
2
0
0
2
1
0
0
1
2
1
0
1
1
1
2
1
1
1
1
2
0
0
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
2
0
1
2
1
0
1
1
1
1
0
1
3
0
0
1
2
1
2
1
2
0
1
2
2
0
1
1
0
1
2
2
0
2
2
1
2
1
1
1
1
2
2
0
2
1
1
2
0
2
0
2
1
2
0
2
1
1
1
0
0
0
1
0
0
0
1
0
0
0
1
2
2
1
1
1
1
1
1
1
7
1
1
1
1
1
2
1
2
0
2
1
1
0
1
2
0
0
2
1
2
1
1
2
2
2
1
1
0
1
1
1
1
1
2
1
1
0
2
1
1
0
2
2
2
1
1
2
1
1
1
1
1
0
2
0
2
1
2
1
1
2
0
2
1
2
2
1
0
1
1
2
1
2
1
1
1
2
1
0
1
1
1
3
1
2
1
1
0
2
1
1
1
1
1
1
0
2
1
1
1
0
1
2
2
0
1
0
1
1
3
1
1
1
2
2
1
1
1
0
2
1
1
1
2
0
1
2
0
2
2
1
1
1
2
1
1
1
2
1
2
1
2
0
1
1
1
1
1
2
0
1
1
2
1
1
2
1
1
1
1
1
1
1
0
1
1
1
2
0
1
1
2
1
2
1
1
2
1
1
1
1
1
2
0
1
3
2
0
1
1
0
1
2
1
1
0
1
1
1
0
2
1
1
1
1
0
0
1
0
0
0
1
1
1
1
1
1
1
0
0
2
1
2
1
1
0
0
0
1
0
1
1
1
2
1
2
1
0
1
2
1
1
0
2
2
1
2
1
1
1
1
2
1
1
0
0
1
1
1
1
1
1
1
0
2
0
1
0
4
1
1
1
0
0
0
1
1
1
2
2
0
0
1
1
2
1
1
2
1
1
2
1
2
1
1
1
0
1
1
1
1
1
1
2
1
1
1
1
1
2
0
2
1
1
1
2
1
1
1
0
1
2
0
1
1
2
1
1
2
1
2
1
1
1
2
0
0
0
1
2
1
0
0
0
1
0
1
1
2
1
2
1
1
0
1
1
1
1
1
2
1
0
2
1
2
1
1
0
0
0
1
1
1
1
1
2
0
1
1
1
2
2
0
1
2
0
1
1
1
2
1
1
1
1
2
1
0
1
2
2
1
1
1
0
1
0
1
1
1
0
2
0
1
2
1
2
0
1
0
0
1
2
1
0
1
2
1
1
0
1
1
0
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
2
2
2
2
0
1
2
1
1
1
2
2
2
2
2
2
0
2
0
1
1
1
2
1
2
1
1
2
1
1
1
2
2
1
1
2
1
2
2
1
0
1
2
1
2
2
2
2
1
1
2
1
1
1
0
1
1
1
0
1
2
0
1
1
1
1
1
1
1
1
1
2
1
1
0
2
1
2
0
0
1
1
1
1
1
1
0
1
1
0
2
2
1
1
1
1
0
1
0
2
2
1
1
1
1
1
1
1
1
2
2
2
0
1
1
1
1
1
2
1
1
2
0
0
2
2
1
1
1
1
1
1
0
1
2
0
1
0
2
1
1
1
0
0
1
0
1
1
1
5
1
1
1
2
1
0
1
2
1
1
0
0
2
1
2
1
1
1
2
2
2
1
0
1
1
1
0
1
1
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
0
2
2
1
1
0
1
1
0
1
1
2
1
2
1
2
1
1
0
1
0
1
1
2
1
0
1
1
1
0
1
1
1
2
0
1
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
0
0
2
0
1
1
2
1
1
1
0
2
1
2
1
1
1
1
0
1
2
1
1
2
1
1
2
1
1
0
0
1
2
3
2
2
1
1
1
1
1
1
2
0
2
1
2
0
1
2
2
0
1
1
1
2
1
1
1
1
1
0
1
1
1
1
2
1
1
0
1
2
2
1
1
0
2
1
0
1
1
1
1
2
2
2
0
1
0
1
1
1
1
1
1
1
1
0
1
1
1
1
1
0
1
2
1
2
2
1
2
0
2
2
1
1
1
1
1
1
1
1
1
0
1
2
1
1
1
0
1
1
1
1
2
1
1
1
0
0
1
1
1
1
2
0
2
1
2
0
1
1
1
1
1
2
2
2
1
3
0
0
1
0
1
1
1
2
1
0
1
1
1
1
2
0
1
1
2
2
0
1
2
1
1
0
1
0
2
1
1
2
1
1
2
1
2
1
1
0
0
1
1
0
2
1
0
0
2
0
0
1
0
1
1
1
2
1
2
1
0
1
1
1
0
0
1
2
2
1
1
2
0
1
1
0
0
0
1
2
2
1
1
0
1
0
2
1
1
1
1
1
0
2
1
1
2
0
0
0
0
1
2
0
1
1
0
0
2
1
1
1
1
1
1
1
2
1
2
1
1
1
3
0
1
1
1
1
2
0
1
1
2
1
1
1
2
1
1
0
0
1
1
0
1
1
1
1
1
0
1
0
2
1
1
1
1
1
0
1
0
0
1
0
1
1
1
1
1
2
1
1
1
2
1
1
1
2
0
1
2
1
1
1
0
0
1
1
0
1
2
0
2
0
1
0
1
1
1
2
0
2
1
1
1
1
0
1
0
0
1
1
1
1
1
1
0
2
1
2
1
0
1
0
1
1
2
1
1
1
1
0
1
1
1
1
2
1
2
1
2
0
1
2
1
2
1
2
0
2
1
1
1
1
2
2
0
1
1
2
1
0
0
1
1
1
1
1
1
1
0
0
1
1
0
1
1
0
1
1
1
1
0
1
2
1
1
1
1
2
2
0
0
0
2
1
1
1
1
1
0
1
0
1
1
2
1
1
0
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
2
0
2
2
0
1
2
1
0
1
1
1
1
1
0
1
1
1
1
1
2
1
1
1
2
0
2
0
1
2
2
1
1
0
0
1
0
1
0
1
0
1
1
1
6
0
1
2
1
0
1
2
1
1
1
1
0
1
2
1
1
1
2
1
2
1
0
0
1
1
1
1
1
1
0
1
1
1
1
2
2
1
1
1
1
1
0
2
1
0
0
2
2
1
1
1
2
1
1
0
0
1
1
1
1
0
2
1
0
0
1
2
1
2
1
2
1
0
2
1
1
1
0
1
2
1
2
2
1
2
2
0
2
1
1
0
0
2
0
1
1
1
0
1
2
1
1
1
1
1
1
1
1
1
2
2
1
1
1
2
0
1
1
2
1
2
1
1
1
2
1
1
1
1
2
2
1
1
1
1
1
0
1
0
0
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
0
0
2
1
0
2
1
1
1
1
1
2
1
1
1
1
1
1
2
0
1
0
2
0
1
1
1
1
1
0
1
1
2
1
1
1
1
1
2
0
1
0
1
0
1
2
1
2
0
2
0
1
2
1
0
0
1
1
1
0
2
1
1
1
2
1
0
1
1
0
1
1
1
1
1
1
1
0
1
1
0
2
0
1
2
2
1
2
1
0
1
1
1
1
1
0
1
0
1
1
0
1
1
1
1
1
2
1
1
1
1
0
0
1
2
2
0
0
1
1
2
1
1
1
1
1
1
1
0
1
1
1
1
2
1
1
1
1
3
1
1
1
1
1
1
1
1
1
1
2
1
0
2
1
1
2
1
1
1
1
2
0
0
1
1
2
1
1
1
2
0
2
1
2
1
1
1
2
1
2
1
0
1
0
0
0
1
2
1
0
0
2
1
2
1
1
2
0
0
1
1
1
1
1
2
0
1
1
0
0
0
1
1
0
0
0
1
1
1
1
1
2
0
2
2
1
3
6
2
0
1
1
1
1
1
0
1
0
1
2
1
1
2
1
1
1
0
1
2
1
1
2
1
2
0
1
1
1
2
1
0
1
1
1
2
2
0
1
2
1
1
1
2
1
1
2
0
1
1
2
1
1
0
1
0
0
1
1
1
1
0
0
2
0
0
4
1
1
2
1
1
2
1
1
1
1
1
1
2
1
0
2
1
1
0
0
0
2
1
1
1
2
1
1
2
1
1
1
2
0
1
0
2
0
2
0
1
0
1
1
1
0
1
2
1
1
1
1
1
1
1
1
0
2
2
1
1
2
0
5
1
1
1
1
1
1
0
0
1
1
1
1
1
0
1
1
0
1
0
2
0
2
2
2
1
1
0
2
2
1
0
1
2
2
2
1
1
2
1
0
2
1
1
0
1
2
2
1
2
2
1
1
1
1
1
1
1
1
2
0
1
1
1
0
1
0
1
1
2
1
1
2
1
1
1
1
2
2
2
1
1
1
1
1
1
0
0
1
1
2
1
1
0
1
2
2
1
2
1
1
1
0
0
1
1
0
1
1
1
3
1
0
0
1
1
1
0
1
1
1
1
1
1
1
0
1
0
1
1
0
1
2
0
0
2
0
2
2
2
1
1
0
1
1
2
1
0
2
1
3
1
1
1
1
1
1
1
0
2
1
1
2
1
1
2
1
2
1
2
1
2
1
1
1
1
1
1
0
2
1
0
1
1
1
2
1
0
0
0
1
0
1
0
2
1
1
2
0
1
2
0
1
0
0
1
1
0
2
1
2
0
2
1
2
2
0
2
1
0
1
1
1
1
1
1
2
0
1
2
1
0
1
2
1
1
2
1
1
0
1
0
1
0
1
1
0
2
1
0
1
1
1
2
1
0
2
1
1
1
0
1
1
1
1
1
0
1
2
2
1
1
1
1
0
1
2
1
0
1
2
0
1
0
1
1
1
0
0
2
1
1
1
1
0
1
1
0
1
1
1
1
2
2
1
1
2
1
2
0
2
2
2
3
1
2
2
1
2
1
1
2
2
0
2
1
0
2
1
1
2
1
1
0
2
0
0
1
1
1
1
0
2
2
0
1
1
2
1
2
1
0
0
0
1
2
0
0
0
0
2
0
1
1
1
1
1
0
1
2
1
1
2
2
0
1
1
0
1
2
0
2
1
2
2
0
3
2
1
1
1
1
2
0
0
1
2
1
1
1
1
2
2
0
2
0
0
1
1
0
1
2
2
0
2
2
1
1
0
0
1
0
1
1
1
1
1
1
1
0
0
1
1
1
1
1
1
2
1
1
1
2
0
1
1
1
0
2
1
0
1
1
1
1
1
1
2
1
1
0
1
1
1
2
1
1
2
0
1
1
1
0
1
0
1
0
1
1
1
0
1
1
0
1
0
2
0
1
1
2
1
1
2
0
2
0
1
2
1
0
4
2
2
2
1
1
0
1
3
1
1
1
1
1
2
1
0
1
1
0
2
2
1
1
1
2
4
1
1
0
1
1
2
0
2
1
1
2
2
1
1
0
0
0
1
2
1
1
1
2
1
0
1
0
0
1
1
0
1
2
2
1
1
1
2
1
1
1
1
1
0
1
2
1
1
1
2
1
2
2
1
1
2
2
0
2
1
1
1
1
1
1
1
0
1
1
1
1
1
1
0
2
2
1
1
2
0
1
1
0
2
1
1
1
2
1
2
1
2
2
0
1
1
1
0
1
1
2
1
1
0
1
0
1
1
1
1
1
2
1
1
0
1
1
2
2
0
1
1
1
1
2
1
1
1
1
1
0
1
1
2
2
1
2
0
2
1
1
1
2
1
1
1
2
0
1
0
1
0
1
1
1
1
2
0
1
2
1
1
1
2
1
1
0
1
0
2
1
1
0
1
1
1
1
1
1
0
2
2
1
0
2
1
1
2
2
1
1
2
1
2
1
1
1
0
2
0
1
2
1
1
1
2
2
1
1
2
2
1
0
2
1
2
1
1
2
1
1
0
2
0
1
2
1
1
1
2
0
1
1
1
1
1
1
2
0
1
0
0
1
2
1
1
1
1
1
2
2
2
1
1
1
2
1
1
2
0
0
2
1
1
1
0
1
1
1
1
1
0
2
1
2
2
1
1
1
1
0
1
1
1
2
1
1
1
1
1
1
1
1
1
0
2
1
1
1
1
0
0
2
1
1
1
1
1
1
1
1
1
1
1
2
1
0
1
1
1
2
1
2
1
0
1
1
1
1
1
1
1
1
0
1
0
0
1
2
0
1
1
1
1
1
1
1
1
2
1
1
1
2
2
2
2
1
1
1
2
1
1
1
2
1
1
0
0
2
1
0
1
2
2
1
1
1
0
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
0
1
0
1
1
1
2
1
1
1
1
1
2
1
0
1
1
2
1
0
1
0
2
2
2
1
0
1
1
0
2
1
1
1
2
1
0
2
1
2
0
1
1
1
1
0
1
1
1
1
1
1
1
2
1
1
1
0
1
2
1
0
1
1
2
0
1
1
1
0
2
1
1
1
1
2
1
1
1
1
0
1
1
2
1
1
2
2
2
1
2
2
0
2
1
1
1
1
2
2
1
1
2
1
2
0
1
1
1
2
1
2
1
1
1
2
1
0
2
1
1
1
2
1
2
0
0
1
2
0
2
1
1
2
1
2
1
1
1
1
0
0
1
1
2
1
1
2
1
1
2
1
1
1
0
2
1
1
3
1
0
1
1
1
1
1
2
1
0
1
1
1
2
0
1
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
0
0
2
0
1
1
1
2
1
1
0
1
0
1
1
0
2
0
2
1
1
2
0
1
1
1
0
2
1
2
1
1
0
2
1
2
1
1
2
1
0
0
2
2
5
1
1
0
1
1
1
1
1
2
1
1
1
2
0
1
1
1
0
2
0
1
2
2
1
2
1
1
1
0
0
1
1
2
2
1
1
1
1
0
0
2
0
1
2
1
1
1
2
2
1
2
1
2
2
1
1
1
0
1
1
2
1
1
1
1
1
1
1
2
1
0
1
1
1
2
0
3
2
1
0
2
0
1
1
1
1
2
0
1
2
0
1
1
1
1
2
1
2
0
1
1
1
1
1
1
0
2
1
0
0
2
2
1
1
2
1
1
1
0
1
1
2
2
0
1
2
0
1
1
1
1
1
1
2
1
0
1
1
1
1
1
1
1
2
1
1
2
1
1
0
1
2
2
1
1
1
1
1
1
1
0
1
1
0
1
1
1
0
2
2
0
0
0
1
1
1
2
2
1
1
1
1
2
2
1
1
2
0
2
1
1
0
2
1
1
1
0
2
2
1
1
0
1
0
1
2
2
1
0
1
2
1
0
0
1
2
1
0
2
2
2
1
1
1
1
1
1
1
0
0
2
1
2
1
1
1
1
0
2
1
3
1
1
2
2
2
1
1
1
2
0
2
2
0
1
2
1
0
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
0
1
1
1
2
1
1
1
0
0
0
0
0
1
1
2
0
1
1
1
1
2
1
2
1
0
0
0
1
0
1
1
0
1
2
1
1
2
0
1
2
0
1
0
1
1
1
0
2
1
1
1
2
2
1
1
2
1
0
2
1
1
1
1
1
1
1
1
1
2
1
1
0
0
2
1
1
2
0
0
0
2
1
2
2
2
0
1
1
1
2
1
1
0
1
2
0
2
1
1
1
2
1
2
2
0
2
0
1
1
1
1
1
0
0
1
2
0
0
1
2
1
0
1
2
0
1
1
1
1
1
1
2
1
1
2
0
0
1
1
1
1
1
0
1
2
0
2
1
1
1
0
2
2
0
1
2
1
2
1
1
1
0
2
2
0
0
1
1
1
1
1
0
0
2
1
1
1
1
1
2
2
1
1
0
2
1
2
0
2
2
4
1
1
1
1
1
1
2
1
1
1
1
1
2
1
2
1
1
2
0
1
1
1
2
1
1
2
1
2
1
2
3
1
1
1
1
1
1
2
1
1
2
1
2
1
1
1
1
1
1
2
0
1
2
1
1
1
2
1
2
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
0
0
2
2
2
0
1
1
2
1
1
1
2
0
1
2
1
1
0
1
1
1
1
1
1
1
0
1
1
0
2
1
1
1
1
1
1
1
1
0
0
0
0
0
1
1
0
1
0
1
0
0
1
1
0
1
1
1
2
1
1
2
1
1
1
2
2
1
1
1
1
1
2
1
0
1
2
1
1
1
1
1
1
1
1
0
1
1
2
1
1
1
2
1
2
0
1
1
1
1
1
1
0
1
1
1
2
0
0
1
2
1
2
1
2
1
1
2
2
1
1
1
0
1
1
2
1
1
1
1
2
1
0
0
1
1
0
1
1
1
1
1
1
1
0
1
0
1
1
0
1
1
0
3
1
1
1
1
1
1
1
0
1
1
2
1
1
1
1
2
1
1
2
1
1
0
0
1
1
2
1
1
2
2
2
2
2
0
1
1
2
1
1
1
0
1
1
1
1
1
1
0
0
0
1
0
0
2
0
0
1
1
1
1
1
2
0
1
0
2
1
1
2
0
1
2
0
1
2
1
1
1
1
2
1
1
1
1
1
2
2
0
0
1
1
1
2
2
1
1
1
2
0
0
1
1
1
0
2
1
1
0
1
1
0
1
1
1
2
1
1
1
1
2
2
0
0
1
1
1
1
1
2
0
1
1
2
0
1
1
1
2
0
0
1
2
2
1
2
1
2
1
1
1
2
0
2
0
0
2
1
0
1
1
1
1
1
2
0
0
1
1
1
1
0
1
1
1
1
1
2
0
2
1
1
2
2
2
2
1
1
0
2
1
0
1
2
0
2
2
0
2
0
1
1
1
2
1
0
0
1
1
2
0
1
1
1
0
1
1
0
2
2
0
1
1
1
0
2
1
1
1
0
2
1
2
1
0
1
1
0
2
1
2
0
0
1
2
2
2
2
1
2
1
1
2
1
2
1
2
1
2
1
2
1
2
2
1
1
0
1
0
2
0
1
2
0
1
0
2
1
2
0
1
0
1
1
0
1
0
0
1
1
2
1
2
1
1
0
1
1
0
1
1
1
1
1
1
1
1
1
2
1
1
2
1
3
1
1
1
0
1
1
1
0
1
2
2
1
1
1
1
0
1
1
2
2
0
1
2
1
0
1
2
1
0
1
2
1
0
1
1
0
0
1
0
2
1
1
2
1
1
1
1
1
0
2
1
0
0
1
1
0
1
2
1
1
0
1
1
2
1
2
1
1
1
2
2
1
0
2
1
1
1
1
2
1
1
2
1
1
1
0
1
0
1
1
1
1
2
1
2
1
2
1
1
2
1
2
1
2
1
1
1
2
1
2
1
0
1
2
2
1
1
1
1
0
2
1
0
1
0
1
1
1
3
1
1
1
0
1
1
1
1
1
3
1
1
1
1
1
1
1
0
0
0
0
1
1
1
1
2
0
1
1
1
1
0
2
0
1
0
2
1
0
1
1
1
2
1
0
2
1
1
2
2
3
0
1
1
1
1
0
2
0
0
1
1
1
0
1
1
1
2
1
0
0
0
0
2
1
0
1
1
0
2
1
1
1
2
0
1
1
1
0
1
1
0
1
1
1
2
1
1
2
0
1
0
2
1
2
2
1
0
1
0
1
2
1
1
2
1
1
0
1
0
2
1
1
1
1
1
0
1
2
1
2
1
0
0
0
2
1
1
1
2
1
1
2
0
2
1
2
0
1
0
0
1
2
1
1
1
1
1
1
0
2
1
1
1
2
1
0
1
1
1
2
1
0
1
1
1
1
1
1
1
1
2
0
1
2
1
1
1
1
5
2
1
1
1
1
1
1
0
0
0
1
2
1
1
2
1
1
0
1
2
1
2
0
1
1
0
0
1
1
2
1
1
1
2
1
2
0
1
2
1
2
1
0
1
2
1
2
0
1
1
1
2
1
0
2
1
1
1
0
2
1
1
1
0
2
0
0
0
0
1
0
1
1
1
1
1
1
2
0
2
1
2
0
0
2
2
1
2
1
1
0
0
1
1
1
1
0
1
2
0
1
1
1
1
1
2
2
1
1
2
1
1
1
0
2
1
1
2
2
1
2
1
2
2
1
1
1
2
1
1
2
1
1
2
1
0
0
0
0
2
1
1
1
0
1
0
1
2
2
1
1
0
2
1
2
1
1
1
2
3
1
1
2
2
0
1
1
2
1
0
1
2
1
1
1
1
1
2
2
1
1
1
1
1
1
1
0
0
2
1
1
2
1
2
1
0
1
2
1
1
0
2
1
1
1
2
2
2
2
0
1
1
1
1
1
0
1
0
2
0
1
0
2
2
1
1
1
1
1
1
1
1
2
1
1
2
2
1
0
1
1
3
1
1
1
0
1
1
0
1
2
1
1
0
1
1
1
1
2
2
1
1
1
1
1
1
1
0
1
1
1
2
1
1
2
1
1
1
0
1
1
2
1
0
2
1
1
1
2
1
0
1
0
1
1
1
2
1
1
1
2
1
2
2
1
2
1
1
1
2
1
0
1
0
1
1
0
1
0
1
0
2
2
1
0
1
1
1
1
1
1
1
1
0
1
1
1
1
0
2
1
0
0
2
1
2
1
2
2
1
0
1
1
0
1
0
2
1
1
2
1
0
0
2
2
2
1
0
1
2
1
0
2
1
1
1
2
1
1
1
1
1
1
1
0
2
1
1
1
1
1
2
2
1
0
1
1
1
1
2
2
1
0
1
1
1
0
1
1
1
2
2
1
1
1
1
2
2
1
1
1
2
0
2
1
2
1
1
2
0
2
1
1
2
1
2
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
2
1
2
1
0
1
0
0
1
2
1
1
1
2
1
1
1
1
1
2
2
1
1
1
1
2
0
2
1
1
2
1
1
1
0
0
2
2
2
1
1
0
2
2
2
1
2
1
0
1
1
1
2
1
1
1
1
2
1
0
2
1
2
1
1
1
2
2
1
1
2
1
1
0
1
1
1
1
1
1
2
1
1
1
0
1
1
1
2
2
0
2
0
2
0
1
1
1
2
0
0
2
1
2
1
2
1
1
0
2
1
1
1
2
1
2
1
1
1
2
1
1
1
2
1
1
1
4
1
1
1
2
2
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
0
1
1
0
2
1
2
2
2
1
0
1
1
1
1
1
1
1
2
2
1
2
1
0
1
1
2
1
1
0
3
1
1
0
1
2
1
1
1
2
2
0
1
2
1
1
0
2
2
1
1
1
1
1
1
1
1
2
1
1
0
0
1
2
0
1
1
0
1
0
1
1
1
0
1
1
1
1
1
1
2
1
2
1
0
0
1
1
0
1
1
2
2
0
1
0
1
0
1
2
2
2
1
0
2
1
1
1
2
1
1
1
1
1
0
1
1
1
1
2
0
1
3
0
1
1
1
0
2
1
1
1
2
1
1
0
0
2
1
1
1
2
1
2
1
1
1
1
2
0
1
1
1
0
0
0
1
2
1
1
1
2
1
2
0
2
0
1
1
0
1
3
1
1
1
1
1
1
1
2
1
0
1
0
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
0
2
2
2
0
3
1
1
0
2
1
2
1
1
1
1
1
1
1
0
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
0
2
1
1
1
1
2
1
2
2
3
1
1
1
1
2
1
2
2
1
2
2
1
0
1
1
0
0
0
2
2
1
1
0
1
1
3
2
1
0
0
1
2
1
1
1
0
2
1
1
1
1
1
1
1
1
1
2
1
0
2
2
2
1
0
2
0
1
2
1
1
1
2
1
0
0
1
2
1
0
1
1
0
1
0
2
2
2
1
1
0
1
1
1
2
0
0
3
0
2
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
0
2
1
1
0
1
1
0
1
2
1
1
1
2
1
1
2
0
1
1
1
1
0
1
1
2
2
1
0
1
1
1
0
1
0
1
2
1
1
1
1
1
1
1
2
1
2
2
1
1
1
2
1
1
1
1
1
3
2
0
1
0
1
1
1
1
1
0
0
3
0
1
1
1
0
2
1
2
1
1
1
1
1
0
1
1
1
2
1
1
1
1
1
2
1
1
1
1
0
0
1
1
1
1
2
0
1
2
1
1
1
1
0
1
1
0
0
2
1
1
1
0
1
1
2
1
2
1
1
2
1
0
1
1
2
1
0
0
2
1
2
1
0
0
1
2
2
1
1
1
2
1
0
2
1
1
1
1
1
2
2
1
1
1
1
1
0
0
1
2
1
2
2
1
0
2
1
1
2
0
1
2
2
1
2
1
1
1
1
2
2
2
1
0
1
1
2
0
1
2
1
1
2
1
1
1
0
1
2
2
1
2
2
1
2
0
0
1
1
1
1
0
2
1
1
1
1
1
0
1
0
1
2
3
2
2
1
1
1
2
2
1
1
2
1
1
1
1
1
1
0
1
2
0
1
1
1
0
1
1
1
2
1
0
2
0
0
2
2
2
1
1
1
2
2
2
2
1
1
1
1
2
1
3
2
2
1
1
1
1
1
0
1
1
1
0
1
2
1
2
0
2
1
1
1
0
1
1
2
0
2
1
1
2
1
2
1
2
1
1
1
2
2
1
1
0
1
0
1
1
1
1
1
2
2
2
0
2
0
2
1
0
1
2
0
0
2
1
1
1
0
1
0
0
0
1
2
2
1
1
0
1
1
1
1
0
1
1
2
1
1
0
3
1
2
1
1
1
2
1
1
1
1
1
0
1
1
1
1
1
1
1
2
1
0
1
1
1
1
1
1
1
0
1
0
0
1
1
1
2
1
0
0
1
2
2
1
1
2
1
2
0
2
2
1
1
1
2
0
1
0
1
1
1
2
1
1
1
1
1
1
1
1
1
1
0
1
1
0
1
1
1
1
2
1
0
2
1
2
1
0
1
2
1
1
2
0
1
1
1
2
2
0
1
1
1
2
1
1
0
1
1
0
1
0
2
0
0
0
1
2
1
1
2
2
1
1
0
0
1
1
1
1
1
2
2
1
0
1
1
1
1
1
1
1
2
2
1
1
1
1
0
2
0
1
1
4
1
1
1
1
1
1
1
1
1
2
1
2
0
0
1
1
1
0
2
1
1
1
0
1
1
2
0
1
2
1
2
1
1
1
1
1
1
2
1
2
1
2
1
2
0
2
2
0
1
1
1
1
0
2
2
2
1
2
1
2
1
1
0
1
1
3
0
1
2
0
0
1
2
3
0
1
1
1
1
2
0
2
2
2
2
2
0
1
1
1
0
1
0
1
1
0
2
2
1
2
0
1
1
2
0
2
1
1
2
1
1
1
2
1
2
0
1
1
1
1
2
1
1
0
1
1
1
0
1
0
2
1
1
0
0
0
1
2
1
1
2
1
2
1
2
0
1
0
3
1
1
1
2
1
1
1
1
1
0
1
1
2
1
2
1
2
1
3
2
1
1
1
2
1
1
1
0
1
1
1
1
1
0
2
0
1
1
2
1
1
2
2
1
1
1
1
2
1
2
1
1
1
1
2
1
1
1
2
2
2
1
1
1
0
1
1
1
0
1
0
1
2
1
2
1
2
2
1
1
1
1
1
1
0
1
1
1
2
1
2
1
2
2
1
1
1
1
1
1
2
1
0
2
1
1
1
2
2
1
2
1
1
0
1
5
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
2
0
1
1
1
2
1
0
1
0
1
2
1
1
1
2
0
1
1
1
1
1
1
1
2
1
1
0
0
0
0
0
2
1
1
1
1
2
0
1
1
0
0
2
1
1
1
1
1
0
2
1
1
1
0
1
1
1
1
2
0
1
1
1
1
1
2
2
1
1
0
1
4
1
1
1
1
2
1
1
1
2
1
1
1
0
1
1
1
1
1
2
0
2
0
0
0
0
0
1
1
0
1
1
1
1
1
1
1
2
1
1
2
1
1
0
1
1
3
1
1
1
2
2
1
0
1
1
0
1
1
1
2
1
1
1
1
1
1
1
0
1
1
0
1
2
2
2
1
2
2
0
1
2
1
2
1
2
1
2
1
0
1
0
0
1
1
1
0
1
0
0
1
1
2
2
1
0
1
2
1
1
2
1
1
1
0
2
2
1
2
2
2
2
2
2
1
1
1
1
1
2
1
1
1
1
1
0
2
1
0
0
0
2
0
1
1
0
1
2
2
1
1
2
3
1
1
1
1
0
2
2
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
2
1
0
1
0
1
1
1
1
2
1
0
1
1
1
1
2
0
1
2
1
1
0
1
0
1
1
1
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
1
2
2
2
2
1
1
1
0
3
1
1
1
1
1
1
1
1
1
1
1
0
1
2
1
0
0
1
0
1
2
1
0
1
2
1
1
1
1
1
1
0
2
2
0
0
1
1
1
1
2
2
1
1
2
1
1
0
2
1
2
1
1
1
1
1
0
1
1
1
1
1
1
0
1
0
0
1
2
1
2
1
1
1
1
1
0
1
1
3
2
1
1
1
1
1
2
1
1
0
2
0
0
1
0
1
1
1
1
2
1
1
2
1
1
1
0
1
1
1
0
1
1
2
2
2
1
0
0
2
1
2
0
2
1
1
2
0
1
0
1
1
0
2
1
1
0
2
2
2
1
0
1
2
1
1
2
0
2
0
1
2
2
2
1
2
0
1
2
1
2
2
1
1
1
1
0
2
0
1
1
1
1
0
1
2
1
1
2
1
1
1
1
2
1
1
1
1
0
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
0
0
1
1
2
2
0
3
1
0
0
0
1
1
0
1
1
1
1
0
1
2
1
1
1
1
1
2
1
1
0
1
2
1
0
1
1
1
1
0
2
2
1
1
0
1
0
2
0
1
0
2
2
2
2
0
1
1
1
1
4
1
1
3
0
2
0
5
1
0
1
1
1
2
0
1
1
0
1
1
0
0
1
2
1
1
1
1
2
2
1
1
1
2
2
1
1
1
1
2
1
1
0
1
2
0
1
1
1
0
3
2
0
1
1
1
1
2
1
1
1
0
1
0
1
2
1
1
1
2
1
1
1
0
1
2
1
2
0
1
0
1
1
1
1
2
1
0
1
1
1
2
1
1
0
1
2
1
1
1
1
0
1
0
1
2
0
1
1
1
0
1
1
1
0
1
1
1
2
1
1
1
2
1
1
0
2
1
0
1
1
1
0
1
0
1
1
2
1
1
2
2
0
1
1
1
1
1
1
1
2
1
2
2
1
1
1
0
1
2
1
1
1
2
2
1
1
1
2
0
2
1
2
1
2
1
1
1
0
2
0
1
1
1
1
1
0
2
2
0
1
2
1
1
1
1
1
2
1
0
1
1
0
1
1
1
2
2
2
1
1
1
0
1
2
1
1
0
0
1
1
2
1
1
1
2
0
1
1
0
1
1
1
0
2
1
1
0
1
0
0
1
2
1
1
2
1
2
0
1
1
2
2
0
1
2
1
2
0
1
2
1
1
1
0
0
1
0
1
1
1
2
1
1
0
1
0
2
1
1
1
1
0
1
1
1
1
0
2
0
1
1
1
0
1
1
1
1
1
1
1
2
1
2
1
1
0
1
1
1
2
2
1
1
1
1
1
1
1
1
1
2
0
1
2
0
1
1
1
3
1
1
0
1
2
1
1
2
0
1
2
1
2
0
1
1
1
1
1
2
1
1
1
3
1
2
0
1
1
1
2
1
1
1
1
1
0
1
1
0
0
1
1
2
1
2
2
1
1
1
1
1
1
1
1
0
1
1
0
1
1
2
1
1
1
1
2
1
2
1
0
4
1
1
1
0
1
0
0
2
2
1
0
1
1
2
1
1
1
1
2
1
1
1
1
0
0
1
1
1
0
1
2
0
1
1
0
1
1
0
1
0
1
1
2
1
2
1
2
2
1
1
0
2
1
1
2
1
1
1
0
1
0
0
1
1
2
1
1
1
1
3
0
1
1
1
2
1
1
0
1
2
2
1
1
0
1
0
2
1
2
2
1
1
1
1
1
0
2
1
1
2
0
1
1
1
1
1
2
2
1
1
1
1
1
2
0
0
1
2
1
1
2
1
1
1
1
0
1
0
1
2
1
0
0
2
0
1
1
0
1
1
2
1
1
0
2
0
2
1
1
1
0
2
1
0
1
1
2
2
2
0
2
2
1
1
2
0
2
2
1
0
0
0
1
1
1
1
0
1
1
2
1
1
1
1
0
1
1
1
1
0
1
2
0
1
1
1
2
1
2
2
0
2
1
1
1
1
2
1
1
1
1
0
1
2
1
2
1
0
1
1
1
0
1
1
1
1
2
1
0
2
1
2
1
0
1
2
2
1
0
2
2
2
1
1
2
2
2
1
1
3
2
2
1
1
0
0
1
1
1
1
1
2
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
0
1
1
1
0
0
1
1
1
1
1
1
0
1
2
2
2
1
2
0
1
1
2
1
1
2
2
1
0
1
2
0
0
2
1
2
1
2
2
1
2
1
1
0
1
3
0
0
2
1
1
1
0
2
1
2
1
1
1
3
1
0
2
0
1
0
1
1
1
0
0
2
1
1
1
1
0
1
1
2
2
2
3
1
0
2
1
1
1
1
1
1
1
2
0
0
1
1
2
1
1
2
1
1
1
1
1
1
1
2
0
1
2
1
1
2
1
2
1
1
2
2
1
1
1
1
2
2
0
1
0
1
1
1
1
0
1
1
0
1
2
1
0
2
1
0
1
2
1
1
2
3
0
1
2
1
1
2
0
1
0
0
1
0
0
0
1
1
1
1
0
0
1
2
1
1
1
2
1
1
0
1
1
2
1
1
1
0
1
1
0
1
1
1
1
1
1
1
1
1
1
0
1
2
1
1
2
0
1
1
0
1
2
2
1
1
1
0
1
1
0
0
1
1
0
1
1
1
1
2
1
1
1
1
3
0
1
2
2
1
1
1
2
2
0
1
1
1
1
1
2
1
2
2
1
0
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
2
0
1
1
1
0
1
1
1
3
2
1
0
0
0
0
0
2
1
1
1
0
1
1
0
0
1
1
0
0
1
0
1
1
1
0
1
1
3
1
2
2
2
3
1
1
1
1
1
0
1
1
2
2
2
1
2
0
1
0
2
1
1
1
1
1
1
2
1
0
1
1
1
1
1
2
1
1
1
1
1
0
1
2
2
1
1
0
1
0
1
1
1
1
1
1
1
2
1
0
2
0
1
1
1
0
1
1
1
1
1
2
2
0
2
2
2
1
1
1
1
2
1
2
1
0
0
0
1
1
2
0
1
2
1
1
1
2
1
1
1
1
1
2
1
2
0
2
1
0
1
1
0
1
0
2
2
1
2
1
1
1
0
0
1
1
1
1
1
1
1
2
2
1
0
1
1
1
1
1
2
2
1
1
2
1
1
1
2
0
1
1
2
2
1
0
2
1
0
0
1
2
1
1
1
1
1
1
0
1
0
1
2
1
0
2
1
1
0
2
1
0
2
2
1
1
1
2
2
0
0
2
2
0
2
1
0
1
0
1
1
1
0
1
1
1
0
1
1
1
0
1
1
0
0
1
0
1
0
1
1
0
2
1
0
0
0
1
1
2
0
2
2
1
0
0
1
2
1
0
1
1
1
1
1
1
0
2
1
2
1
0
2
1
1
1
0
2
1
0
0
1
0
2
2
2
1
2
1
2
2
2
0
2
1
1
0
2
1
0
1
2
1
2
1
2
1
1
1
1
0
2
1
0
1
1
1
1
1
0
1
1
1
0
1
1
1
1
2
1
2
1
1
1
2
2
2
2
2
1
0
2
1
1
0
2
1
2
2
1
1
0
1
2
2
2
1
1
1
1
0
1
1
2
0
1
1
0
2
1
2
0
2
1
2
1
2
0
2
2
2
1
1
1
1
0
1
2
2
0
2
1
1
1
1
0
2
1
1
1
2
1
1
2
0
1
0
1
0
1
2
1
3
1
1
0
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
2
1
1
1
1
1
0
1
2
1
1
1
2
1
1
1
0
1
0
1
1
1
1
1
1
2
1
2
1
0
0
1
1
2
2
1
1
0
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
0
1
1
1
1
0
1
1
1
1
1
0
1
2
1
1
1
2
1
2
0
2
1
1
1
2
1
1
1
1
1
1
1
1
0
2
1
0
1
1
1
0
1
2
2
1
1
1
2
1
0
1
1
1
1
0
1
1
0
1
2
0
1
1
1
0
1
0
1
1
1
1
1
1
2
2
1
1
1
1
1
0
1
0
1
1
1
0
1
1
1
1
1
1
1
2
2
1
0
2
2
2
2
0
1
0
0
0
1
1
1
1
1
2
1
1
1
1
0
1
3
2
1
1
2
1
1
1
0
1
0
1
2
1
0
2
1
1
1
2
0
0
1
1
1
2
1
0
1
0
1
1
1
1
1
1
1
0
1
2
1
2
1
1
1
1
1
2
1
0
1
2
1
1
0
2
0
1
2
0
2
1
0
1
1
2
2
1
1
1
0
0
1
1
2
1
1
1
2
1
1
2
3
1
2
1
1
2
1
0
1
1
1
1
0
1
0
0
1
0
2
1
1
1
2
1
1
0
0
1
1
2
2
1
1
1
1
1
1
0
0
1
1
1
1
0
0
2
1
0
2
2
0
0
1
0
1
2
2
0
0
2
1
1
1
0
2
1
1
2
1
2
1
2
0
0
0
0
1
0
0
1
2
2
2
1
1
1
1
1
1
1
1
1
0
0
1
0
2
1
1
2
2
1
1
1
1
2
1
2
1
2
1
0
1
2
2
0
1
0
0
1
2
1
1
1
2
2
2
1
1
1
2
2
1
0
1
3
1
0
1
1
2
1
1
2
0
1
0
1
2
0
0
0
1
0
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
0
1
0
1
2
1
1
1
1
1
1
2
1
1
2
1
2
1
1
0
0
2
1
1
1
0
0
1
24
1
1
2
1
1
1
1
1
1
1
0
0
2
1
1
4
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
2
1
1
0
0
1
0
1
1
1
1
0
1
2
1
0
2
1
2
0
1
1
0
0
0
0
2
1
1
2
1
1
1
0
2
2
1
1
2
1
1
1
0
1
1
0
1
0
1
1
1
2
0
1
2
1
2
1
1
2
1
3
1
1
1
1
1
2
2
1
0
1
1
2
1
1
2
1
0
2
1
0
1
3
1
1
1
1
1
0
1
1
2
1
0
1
1
2
1
1
1
1
1
0
1
1
2
2
0
2
2
2
1
1
1
1
1
0
0
1
1
1
0
1
0
2
2
2
1
1
2
0
1
0
1
1
2
2
0
1
2
1
2
1
1
0
0
1
3
0
2
0
1
2
1
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
2
1
1
2
1
2
2
2
2
2
1
1
2
1
1
1
2
2
2
2
1
1
2
2
1
1
1
1
0
0
1
1
1
1
1
1
1
1
0
1
1
2
0
0
2
1
1
2
1
1
1
1
1
2
0
2
1
1
1
1
1
1
1
1
1
0
1
1
1
1
0
0
1
1
1
0
0
1
1
0
2
1
0
0
1
1
1
1
2
1
1
1
2
2
0
2
0
1
2
1
0
2
1
2
0
0
2
1
2
2
2
1
1
2
2
0
0
1
2
0
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
0
1
2
1
1
1
2
1
1
1
1
1
1
1
1
0
1
1
1
2
0
0
2
1
1
1
1
1
0
1
2
1
2
1
0
1
0
1
1
1
1
0
1
2
0
2
1
2
1
1
0
1
1
1
2
1
2
2
1
0
1
1
0
1
0
2
0
3
1
0
0
1
1
2
2
1
2
1
1
0
2
2
1
1
1
1
2
1
0
2
1
0
0
2
0
1
1
0
2
1
1
1
1
0
0
1
0
1
1
2
2
2
2
1
1
1
0
0
3
2
1
2
1
1
1
1
2
1
2
2
1
2
1
1
1
1
0
1
1
1
0
0
2
1
1
2
1
1
1
1
0
0
0
1
0
1
2
1
1
1
0
1
2
0
1
1
1
0
1
2
1
1
1
2
1
1
2
1
1
0
0
0
0
1
0
2
1
0
0
0
2
1
2
1
1
2
2
2
1
1
0
0
2
1
1
1
2
1
1
1
0
2
2
0
1
1
2
1
1
0
1
1
0
1
1
0
2
1
1
1
1
0
1
0
1
1
1
0
1
1
1
1
0
1
1
1
1
1
2
0
2
1
1
1
2
0
2
1
0
1
1
1
1
0
1
1
1
1
0
1
1
1
1
1
1
2
2
1
1
1
2
1
1
1
1
0
1
1
0
1
1
1
1
1
2
0
1
1
0
2
0
1
1
1
2
1
0
1
1
1
1
0
2
1
1
1
1
1
1
1
1
2
2
1
1
2
1
0
2
2
0
1
1
2
2
1
2
1
1
2
0
2
1
2
2
0
1
2
1
2
0
2
1
0
2
2
2
2
1
2
1
1
1
2
1
0
1
1
1
1
1
1
1
2
1
2
2
1
1
4
0
2
1
2
1
1
2
1
0
1
1
1
1
1
0
2
0
1
2
0
2
2
1
2
1
1
1
0
1
2
1
1
1
1
0
1
2
0
1
2
1
2
2
0
0
2
1
2
1
3
1
2
1
0
0
1
0
1
1
1
2
1
1
2
1
2
1
1
1
1
2
0
1
2
1
0
0
1
1
1
1
2
1
1
2
1
1
2
1
2
1
1
0
0
1
2
1
2
1
2
1
3
0
1
2
2
0
1
1
1
1
0
0
2
0
0
2
1
1
1
1
1
1
0
1
1
0
1
1
1
1
1
2
1
1
1
1
1
3
2
1
1
1
3
1
2
1
1
2
0
1
2
1
1
1
1
0
0
1
1
1
1
2
1
1
1
2
2
2
0
2
2
1
1
1
2
2
1
0
1
1
1
1
0
2
0
2
2
1
1
2
1
1
1
1
1
1
1
2
0
1
1
1
1
2
0
1
1
1
1
1
1
0
0
1
2
1
0
1
1
2
0
1
1
1
1
0
2
1
2
2
1
1
0
2
1
1
2
1
1
1
1
2
1
0
1
1
1
2
1
0
1
1
1
1
1
1
0
1
1
2
1
1
1
2
1
0
2
1
1
0
0
1
1
1
0
1
1
2
1
0
1
1
0
1
0
1
1
1
0
1
1
1
2
0
1
1
2
1
2
1
2
1
1
1
2
2
1
1
2
1
1
1
0
0
2
0
0
2
2
1
2
1
1
2
1
0
1
1
1
2
1
0
0
2
1
0
2
1
1
1
0
0
1
1
0
1
1
0
2
0
1
1
2
0
1
1
2
1
2
1
2
1
1
2
1
1
1
1
1
2
1
0
2
1
2
1
1
1
0
5
1
1
2
1
1
1
1
1
2
1
0
1
1
1
1
1
1
1
0
1
2
3
1
1
2
2
1
0
2
1
2
0
1
1
2
0
2
1
2
1
1
1
2
1
1
2
2
1
1
2
0
1
0
1
1
0
1
1
1
2
1
1
1
1
1
1
0
1
1
1
0
1
1
2
0
0
2
1
1
1
1
1
1
1
0
1
1
0
1
0
1
0
2
0
0
1
1
1
1
1
1
1
0
1
2
1
1
1
0
1
1
0
2
1
2
0
0
1
1
1
1
0
1
0
2
0
0
2
1
0
0
1
1
0
1
0
1
1
0
1
1
1
1
1
1
1
1
0
1
1
2
1
1
1
1
1
0
1
1
1
0
1
1
1
2
2
0
1
2
0
0
0
2
1
1
2
1
3
2
1
0
1
1
2
1
0
1
0
2
1
2
1
0
0
1
1
1
2
1
0
1
1
2
2
0
1
2
1
1
2
1
2
2
0
1
0
1
0
1
1
1
1
2
4
1
1
2
0
2
2
0
0
1
1
1
0
2
0
0
1
2
0
0
1
1
1
1
0
1
1
0
2
0
1
1
1
1
2
0
0
2
1
1
1
1
2
1
1
1
2
1
1
1
1
0
1
0
1
1
4
0
1
0
1
1
2
1
1
4
2
1
1
2
1
1
2
2
1
1
1
3
2
1
2
1
0
2
0
1
1
2
1
1
2
1
0
1
2
0
1
2
1
2
1
2
1
0
2
0
1
1
2
0
2
0
1
0
1
2
1
0
1
1
0
1
2
0
1
1
1
1
1
2
0
2
2
1
1
0
1
1
0
1
1
1
4
1
1
1
1
1
1
1
2
1
1
2
1
1
2
1
0
1
0
1
0
1
1
1
0
1
1
1
2
2
1
0
0
0
0
2
1
2
2
1
1
2
0
1
1
1
2
1
1
1
1
2
0
1
2
1
1
1
2
1
2
2
1
1
1
2
1
1
2
0
0
1
2
1
0
2
1
2
1
0
1
1
2
1
1
0
2
2
0
1
1
0
2
0
1
1
1
2
1
1
1
0
2
1
1
1
2
1
1
1
2
1
0
1
0
2
1
0
2
1
2
1
1
1
1
1
1
2
0
0
2
0
0
1
1
0
2
2
0
1
1
1
0
0
1
1
2
1
1
2
0
2
1
1
1
1
1
1
1
1
1
2
1
2
1
1
0
1
1
2
0
0
2
1
0
1
2
1
1
1
1
1
2
1
1
1
0
1
1
2
1
2
2
0
2
2
1
1
2
2
1
2
1
1
2
1
1
2
1
0
1
1
1
1
0
2
1
1
1
1
0
1
0
1
0
0
2
0
1
1
1
1
1
2
1
2
1
0
1
0
2
0
1
1
1
1
1
0
0
1
0
2
1
1
1
2
1
2
1
1
0
0
0
1
2
0
2
1
1
1
0
0
1
1
1
1
1
1
1
1
1
1
1
0
1
1
2
1
1
1
1
0
1
2
2
2
1
0
0
2
2
1
1
2
1
0
0
2
1
1
2
1
1
1
1
1
1
1
0
2
2
2
1
0
1
1
1
0
3
1
1
1
0
1
1
2
1
2
0
0
1
2
2
1
0
0
1
1
2
2
0
1
0
2
0
0
1
1
1
2
1
1
2
1
2
0
1
1
2
2
1
1
0
1
0
2
1
1
1
2
2
1
1
2
2
1
1
1
1
1
1
1
1
0
1
2
1
0
1
1
2
1
1
1
1
1
2
1
0
0
1
2
2
2
2
1
1
1
3
2
1
0
1
2
0
1
1
1
1
0
1
2
1
1
1
1
1
1
1
3
1
1
0
1
1
2
1
2
1
1
0
1
0
1
2
1
0
1
1
1
1
1
1
0
0
1
6
1
1
2
1
2
2
2
1
1
1
2
0
2
1
1
1
1
0
0
0
1
1
1
2
2
0
0
1
1
1
1
1
1
0
1
1
1
1
0
1
0
2
1
1
1
1
1
1
1
1
1
0
1
2
1
1
2
1
1
0
2
0
0
2
0
1
1
1
0
1
1
0
1
0
2
1
0
1
0
2
1
1
1
1
1
1
1
0
2
2
1
2
1
2
1
0
1
2
1
2
0
0
1
1
1
1
1
1
2
1
1
1
2
2
1
2
0
1
0
1
0
1
0
0
1
1
0
2
2
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
0
1
0
1
1
1
1
1
0
2
2
2
2
2
2
1
1
0
1
2
0
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
1
1
0
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
2
0
0
1
2
1
1
2
0
1
2
2
0
1
1
1
1
0
1
2
1
1
0
1
2
2
2
0
1
0
1
2
2
1
1
1
0
1
1
1
1
1
1
2
0
2
1
0
0
1
2
1
1
1
2
0
1
2
0
1
1
1
0
1
1
2
2
1
2
1
1
1
1
2
2
2
1
1
2
0
1
3
1
1
0
0
1
1
0
2
1
1
1
1
0
1
1
1
1
1
0
2
1
0
1
1
1
1
0
1
1
2
0
1
1
1
1
1
1
1
0
0
0
1
3
1
1
2
0
2
2
1
0
0
1
1
1
1
0
1
1
2
0
0
1
0
2
1
1
1
1
0
1
0
1
2
1
1
2
1
1
0
0
1
1
1
1
1
0
1
2
1
1
2
2
2
1
4
0
0
1
1
1
1
1
1
1
1
2
1
0
0
2
1
1
0
1
1
1
1
1
1
1
2
1
1
1
3
0
1
3
2
1
0
1
2
0
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
3
1
1
2
0
1
1
1
1
2
1
1
1
1
1
0
3
0
0
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
0
1
1
1
4
2
0
1
1
0
2
1
0
1
1
1
1
0
1
0
1
1
1
2
1
2
1
1
1
1
0
1
1
1
2
1
0
0
0
1
2
1
2
1
1
2
1
2
0
2
0
1
2
0
1
1
2
1
1
2
1
2
1
1
0
1
0
1
1
1
1
0
2
1
1
0
0
1
1
1
1
2
2
1
2
1
0
0
2
1
1
1
2
2
1
1
2
1
2
1
2
1
2
1
1
1
1
0
1
1
2
1
1
2
1
0
0
0
2
1
2
3
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
0
1
2
1
2
2
1
0
1
1
0
1
1
1
1
2
1
1
2
1
1
1
1
2
0
2
1
2
1
2
1
1
1
1
0
2
1
2
1
1
1
1
1
2
0
0
1
1
2
1
1
0
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
2
2
2
2
1
0
0
0
2
0
2
1
1
1
1
1
1
1
2
2
1
1
1
1
0
3
1
1
1
2
0
2
0
1
1
1
1
0
0
1
2
2
0
4
1
0
0
1
2
0
1
1
1
2
1
1
1
1
1
2
1
0
1
1
0
1
0
2
1
0
1
1
1
0
0
2
2
1
2
1
1
2
2
3
2
0
2
1
2
2
1
0
1
1
1
1
2
1
1
1
1
2
2
1
1
1
1
0
0
1
0
2
2
1
2
2
1
1
1
1
1
1
0
1
1
0
1
1
2
1
0
2
1
1
2
0
1
2
0
2
0
1
1
1
0
2
1
1
1
2
0
1
2
1
1
1
1
2
1
1
0
0
1
2
1
1
0
2
1
1
2
0
1
0
1
1
1
1
2
1
1
0
2
0
1
1
2
1
2
1
1
2
1
1
1
1
0
1
1
1
2
1
0
1
1
0
1
2
1
2
1
2
2
1
2
1
1
1
1
1
1
0
0
1
1
1
1
1
1
1
1
0
2
2
1
0
1
2
1
1
2
2
1
0
2
1
1
2
1
2
1
2
0
1
1
0
2
1
0
1
0
1
1
3
2
2
1
1
1
1
1
0
1
1
1
1
1
1
0
2
0
0
2
1
1
2
1
1
1
1
2
0
2
1
1
1
1
0
0
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
0
2
1
1
2
1
1
1
0
2
0
2
0
1
0
2
1
2
1
1
1
0
1
0
1
1
0
1
1
1
0
1
1
2
2
1
0
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
2
1
2
0
1
1
2
1
1
1
1
1
1
0
1
1
1
1
2
2
1
1
1
1
2
1
1
0
1
0
1
1
1
0
0
1
0
1
1
1
0
1
1
2
1
1
0
1
0
1
0
1
1
1
1
2
1
1
1
1
1
1
1
1
0
1
1
0
0
1
1
2
1
1
1
1
0
2
1
1
0
0
0
2
1
1
1
1
0
0
1
1
0
1
2
1
1
2
1
0
1
1
1
2
1
2
1
1
1
2
1
1
0
0
2
1
1
2
1
1
0
1
1
1
1
2
2
0
1
1
2
1
2
1
1
2
0
2
1
1
1
1
1
1
1
0
2
2
0
1
0
1
1
1
0
1
1
1
1
1
0
1
1
1
2
1
0
1
2
1
1
2
1
2
1
0
1
1
1
1
1
1
1
1
1
1
1
0
0
1
0
1
1
0
1
2
2
2
2
1
1
2
0
0
1
2
0
0
1
1
1
2
0
1
2
2
2
0
1
1
1
0
1
1
0
1
1
1
2
1
1
1
1
1
1
2
0
1
2
1
0
3
0
1
1
1
2
2
1
2
1
1
1
2
1
0
1
1
1
2
1
1
0
0
1
0
2
1
0
1
1
0
0
3
1
2
1
0
2
4
0
2
0
1
1
0
0
1
2
1
2
2
1
2
1
1
2
0
1
2
1
1
0
1
1
1
0
1
1
2
1
0
0
1
1
2
2
1
1
1
2
0
1
1
1
2
1
2
2
1
1
1
1
2
1
2
2
1
1
0
1
0
2
1
2
0
2
2
2
1
1
1
1
1
1
1
1
1
1
1
0
2
0
0
2
1
0
0
1
1
2
1
0
0
1
2
1
1
2
2
2
1
1
0
2
1
1
1
1
1
1
1
0
3
1
1
1
2
1
1
1
2
0
1
2
1
1
2
2
0
2
1
2
1
1
2
2
2
2
1
2
1
1
2
2
1
2
0
1
0
2
1
1
2
1
2
2
1
1
1
0
0
1
0
0
1
1
0
0
0
2
0
0
1
1
1
2
1
1
0
0
1
2
0
0
1
1
2
1
1
1
0
2
1
0
0
2
1
0
2
1
1
1
1
1
1
1
1
5
1
2
1
2
0
1
2
1
2
1
1
1
0
1
0
1
0
2
0
2
1
1
1
1
1
1
1
2
1
3
2
1
1
1
2
1
1
2
1
1
1
1
0
1
0
2
1
0
2
1
1
1
2
2
1
0
1
2
1
0
1
1
2
1
1
1
1
0
1
1
1
1
1
1
2
0
1
2
1
1
1
1
1
1
0
1
2
1
2
1
2
2
1
0
1
1
1
2
1
2
0
2
2
2
2
0
1
1
0
1
1
1
1
1
1
1
1
2
2
1
1
0
1
2
2
1
2
3
2
1
0
1
1
0
1
1
1
1
1
2
0
0
1
1
0
2
1
1
1
2
0
1
1
0
0
1
2
0
1
0
2
1
0
0
1
1
3
0
2
1
1
0
0
2
2
0
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
2
1
2
2
2
2
2
2
2
1
1
1
1
1
1
1
2
0
2
2
1
1
2
1
2
0
1
1
0
1
2
1
1
1
0
2
1
0
1
1
1
1
2
1
1
0
0
0
1
2
0
1
0
2
0
2
0
1
0
0
1
1
1
2
0
1
0
1
1
1
1
1
1
1
1
2
1
2
2
0
1
2
0
1
1
1
2
1
1
1
2
2
1
1
2
0
1
0
1
2
1
1
1
2
1
0
2
2
0
1
2
1
1
1
1
1
2
1
1
1
1
1
1
0
1
2
1
2
2
1
1
2
1
1
1
1
0
1
1
1
1
2
1
0
1
2
1
1
0
3
3
0
1
2
2
1
1
1
1
0
0
1
1
0
2
1
1
1
1
2
0
0
1
2
1
1
1
1
1
1
1
2
1
2
0
2
0
1
1
2
2
2
1
2
2
1
3
1
1
1
0
1
1
1
1
1
1
1
1
0
1
1
2
2
1
1
0
1
1
1
1
2
1
0
2
1
1
0
1
2
1
1
1
1
2
1
1
1
2
1
1
1
0
1
1
1
0
1
0
2
2
1
0
1
1
1
1
0
1
2
2
1
0
1
1
0
1
1
1
0
1
1
2
2
1
1
1
1
1
1
0
0
1
1
1
1
1
2
1
2
1
0
1
1
2
2
0
0
1
1
1
1
1
1
2
1
1
2
2
2
2
2
1
1
0
0
1
1
1
1
1
1
1
1
1
1
1
1
0
1
2
0
2
1
2
0
1
2
0
2
2
2
1
0
2
2
2
2
1
1
0
0
1
0
1
1
1
1
1
0
1
1
0
1
1
0
0
2
1
2
0
1
1
1
1
1
2
0
0
1
0
2
1
1
0
0
2
1
1
0
1
1
2
1
1
1
1
1
1
1
2
0
1
1
0
1
2
1
1
0
1
1
0
1
2
2
2
1
0
2
2
1
1
0
0
2
1
1
1
2
2
1
0
2
1
1
1
1
1
1
1
1
0
2
0
2
0
1
0
2
2
1
0
1
2
0
1
3
0
2
1
2
0
2
2
1
0
1
0
1
1
1
1
1
1
1
0
1
1
2
1
2
2
1
2
1
1
1
1
0
2
1
1
1
2
1
1
0
1
1
1
2
0
1
1
1
0
1
1
1
1
2
1
1
0
1
2
2
2
1
1
1
1
2
1
1
1
1
1
1
0
1
0
2
0
1
1
1
2
1
0
1
2
0
3
1
2
0
1
0
2
1
2
1
1
1
2
2
1
2
1
2
1
1
1
2
1
1
1
1
2
1
1
1
0
0
0
1
1
1
1
1
2
2
1
2
2
1
2
1
0
1
1
1
0
1
1
1
0
2
1
2
1
1
1
0
0
1
0
0
1
1
2
1
0
1
2
2
1
1
2
2
1
1
1
1
1
0
1
1
1
2
1
0
1
1
0
2
1
2
1
1
2
1
1
1
1
1
2
1
0
1
1
1
1
1
1
1
2
1
1
2
2
2
2
1
1
0
1
1
1
0
1
2
1
1
1
3
1
2
0
1
2
1
1
2
0
1
2
1
1
1
1
0
2
1
1
1
1
3
2
1
1
2
0
1
2
2
0
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
0
0
0
1
1
1
1
2
1
0
1
2
1
1
1
2
1
0
0
1
2
1
0
1
1
0
2
2
2
1
2
0
0
3
1
1
2
2
1
0
1
1
2
1
0
0
1
1
1
1
1
1
2
1
2
1
0
1
1
1
2
1
1
1
1
1
1
1
2
0
1
1
2
1
1
1
1
1
3
0
1
0
0
1
0
0
0
2
0
1
1
1
0
1
1
1
2
1
2
1
0
1
2
0
2
1
0
2
1
1
1
1
2
2
1
2
3
2
1
2
2
1
2
2
1
1
2
1
1
1
2
2
1
2
0
1
2
2
0
1
1
0
0
2
1
1
2
0
1
1
1
0
1
1
0
2
2
1
0
1
0
2
1
0
2
1
1
1
1
1
0
0
1
1
1
2
1
0
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
0
2
1
1
1
1
1
1
1
0
1
0
1
2
1
2
1
1
1
3
2
2
2
1
1
2
2
1
3
1
1
2
1
2
2
2
8
2
1
1
2
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
1
0
1
1
1
2
1
2
1
1
2
2
1
0
1
1
1
1
1
0
0
1
1
2
0
1
1
1
0
1
1
1
1
1
0
2
0
1
1
1
1
0
2
0
1
1
0
1
1
1
1
1
1
1
0
0
0
2
1
1
1
1
0
0
0
2
0
1
2
1
2
2
1
2
1
1
0
2
1
1
1
1
1
0
2
1
2
1
1
1
1
1
1
1
1
0
0
1
1
2
0
1
2
1
1
2
1
1
1
0
2
1
1
2
2
1
1
1
0
1
0
1
1
1
1
2
1
1
1
0
0
0
1
1
0
0
1
1
0
1
2
0
1
1
1
1
2
1
0
2
1
1
0
1
2
1
2
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
2
1
1
1
0
1
0
4
1
2
1
1
1
0
2
0
1
1
0
0
1
0
1
1
1
1
1
1
0
1
1
2
1
1
1
1
2
1
0
2
1
1
1
0
1
2
1
0
3
1
1
0
0
1
1
1
1
0
0
1
0
1
0
2
1
1
2
2
0
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
2
0
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
2
1
1
1
1
0
1
2
1
0
1
1
1
2
0
1
1
1
1
1
1
2
2
2
1
1
2
1
1
1
2
1
2
1
0
2
1
1
0
1
1
1
0
2
1
1
2
1
1
1
0
2
1
1
1
2
0
1
2
0
3
0
1
0
1
2
1
2
2
2
1
1
0
2
0
1
1
1
2
1
1
2
2
1
1
1
1
1
1
1
2
1
0
1
1
2
1
1
2
0
1
0
0
1
0
2
2
1
1
1
1
1
1
1
0
1
1
0
1
1
1
1
1
1
2
1
1
1
2
1
2
2
1
1
3
2
1
1
0
1
2
1
1
0
1
2
2
1
0
2
0
0
0
2
1
1
1
1
2
1
1
1
1
1
1
1
2
0
0
2
2
2
1
1
1
0
0
0
1
1
1
2
2
2
1
1
2
0
1
2
1
1
0
1
1
0
1
2
1
1
1
0
1
1
0
1
1
1
2
2
1
1
1
2
1
2
1
1
1
1
2
0
1
2
2
1
1
1
1
1
0
1
2
2
0
1
2
0
1
1
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
2
0
1
2
0
1
0
2
1
1
1
1
0
1
1
1
0
2
0
1
0
0
1
0
1
1
2
1
1
1
2
1
2
1
0
1
1
1
1
2
1
2
1
1
1
2
2
1
2
1
1
1
0
1
1
0
1
0
0
1
2
1
0
1
0
2
1
2
0
1
1
1
1
0
1
1
2
1
2
1
1
2
0
2
1
1
1
2
1
0
1
1
2
1
1
1
1
1
0
2
0
1
1
0
1
1
1
1
1
2
2
2
2
1
1
1
2
0
1
1
0
0
1
1
2
1
2
1
0
1
1
1
1
1
2
1
1
2
0
2
0
1
0
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
2
1
1
2
1
1
2
2
1
1
2
0
2
1
1
1
2
1
1
2
0
1
1
2
1
2
2
0
2
1
1
1
1
2
2
1
1
1
1
0
1
2
2
2
2
1
1
2
1
0
1
1
1
1
0
1
1
2
1
2
2
1
1
1
0
1
2
1
1
0
1
1
1
1
0
1
0
1
1
2
2
1
1
1
1
2
0
1
0
1
1
1
0
1
1
0
1
1
2
2
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
2
1
0
1
1
1
2
2
1
1
0
1
2
0
0
1
0
0
1
1
1
2
1
1
2
1
0
0
1
2
1
2
1
0
1
2
0
0
2
1
1
1
0
1
1
1
1
0
2
1
0
1
1
1
1
2
2
1
1
1
0
0
1
1
0
0
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
2
0
2
0
1
1
2
1
1
0
1
1
1
0
0
2
0
0
0
0
1
1
2
1
1
1
1
1
2
1
2
2
2
1
1
1
1
1
1
0
1
1
1
1
1
1
2
0
0
1
1
1
1
1
0
0
1
0
1
2
1
1
2
1
1
1
2
1
2
1
2
2
1
1
1
1
1
1
2
1
2
0
1
0
1
1
1
1
2
1
1
1
1
1
1
1
2
0
0
2
1
1
2
1
2
0
0
1
1
1
1
0
1
1
1
0
1
1
1
0
1
1
0
2
0
1
1
1
2
1
1
0
2
2
0
1
1
2
1
0
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
0
1
2
1
0
1
0
1
1
2
1
1
1
1
1
1
1
0
1
2
1
2
1
1
1
2
1
1
0
1
1
1
1
1
1
0
3
0
1
2
2
1
2
2
1
1
1
1
1
2
0
1
1
2
1
1
1
0
1
1
1
1
1
0
1
1
1
1
1
2
0
0
2
1
2
1
2
1
2
2
1
1
2
1
0
1
1
1
1
0
1
1
2
1
1
1
0
1
1
1
0
1
1
1
2
1
0
0
1
2
1
0
0
1
1
0
1
0
2
1
0
1
0
0
1
1
1
2
1
0
1
1
2
1
1
1
0
1
1
1
2
1
1
2
1
2
3
1
2
0
2
1
1
0
2
1
1
1
2
2
0
0
1
0
1
1
2
1
2
1
1
1
1
1
0
2
0
2
1
2
1
0
0
1
2
1
1
1
0
0
0
1
2
1
2
2
2
1
1
1
0
1
0
3
1
0
1
1
2
2
3
1
0
1
1
1
1
2
1
0
1
1
0
1
0
2
2
1
0
2
1
2
1
1
2
1
1
0
0
1
2
3
1
1
1
2
1
0
2
2
2
1
1
2
1
2
2
1
3
1
1
1
1
1
2
2
0
1
1
2
1
1
1
1
1
0
1
0
0
0
2
0
1
2
1
3
1
1
1
2
2
1
0
1
1
1
0
2
2
1
1
2
2
1
2
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
0
0
1
0
1
1
1
1
1
1
1
1
2
1
1
3
1
0
0
2
1
1
2
1
1
1
2
1
0
1
1
1
2
0
1
1
1
1
2
2
1
0
1
1
2
2
1
2
1
1
2
0
2
2
1
1
1
1
2
1
1
1
1
1
1
1
1
2
0
2
1
1
1
2
1
1
2
1
1
1
2
1
2
1
1
1
1
0
2
1
1
2
0
1
0
2
1
1
1
1
1
1
2
1
2
1
1
2
2
1
1
1
0
0
1
1
1
2
2
0
1
1
1
1
1
1
1
0
1
2
2
0
2
1
2
1
1
1
1
2
1
1
1
1
2
1
2
2
1
2
0
1
1
1
1
1
0
1
0
1
1
1
0
1
0
1
1
2
2
1
1
1
0
1
2
1
1
0
1
2
1
2
1
0
0
0
1
1
1
2
1
1
2
1
1
1
1
1
1
0
0
2
0
1
1
0
2
1
0
1
1
2
1
0
1
2
1
2
1
1
1
1
1
2
0
1
1
0
1
1
0
2
0
2
1
0
1
2
1
0
1
0
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
2
1
2
1
1
0
1
2
1
1
1
1
0
0
1
2
0
2
0
1
1
2
1
0
1
0
2
2
1
2
1
1
1
0
1
1
1
2
2
1
0
1
2
2
2
1
2
1
0
0
2
1
1
0
1
2
1
1
1
1
1
1
0
0
2
1
1
1
3
1
0
0
1
0
1
2
1
1
1
1
1
1
0
2
1
2
1
1
1
1
3
1
2
2
1
1
1
1
1
0
1
1
2
1
1
2
1
2
1
1
0
1
1
1
1
1
0
1
2
1
1
2
1
1
2
2
2
1
0
2
0
1
2
1
1
1
0
1
1
1
1
0
2
1
1
0
2
2
1
1
1
1
1
1
2
1
2
1
1
1
0
1
1
1
1
1
0
0
1
2
1
2
2
2
1
0
1
1
1
2
0
1
2
2
1
0
1
1
1
1
1
1
0
1
2
0
1
1
1
2
1
1
0
1
0
1
1
3
1
1
1
2
1
1
1
3
1
1
1
2
1
1
1
1
1
1
1
2
0
1
0
1
1
1
1
1
1
1
1
0
1
2
0
1
2
1
1
1
2
1
0
1
1
1
2
1
2
0
2
0
1
0
1
0
2
1
0
2
1
1
1
0
1
1
1
0
2
2
2
1
2
1
2
1
1
1
2
2
2
1
2
1
1
2
2
1
0
0
3
2
0
1
1
1
1
0
2
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
2
1
1
0
0
1
1
1
1
1
0
1
1
1
1
0
1
2
1
2
1
0
1
0
1
1
2
2
0
1
1
1
2
1
1
1
2
1
2
1
1
1
1
0
1
1
1
0
2
1
1
1
0
0
1
0
2
0
2
1
1
2
1
1
1
2
1
1
1
2
1
0
2
2
1
2
2
0
0
1
1
1
1
1
2
1
1
2
1
2
1
1
1
1
1
0
0
1
1
0
1
2
1
0
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
0
1
1
1
1
1
1
0
2
1
1
1
1
1
1
1
1
1
1
0
0
1
0
0
1
1
1
1
2
1
0
0
2
1
1
1
1
2
0
0
0
0
0
1
1
1
2
0
1
1
1
1
1
2
1
1
1
1
2
2
1
1
1
1
2
2
1
0
1
1
2
0
1
1
2
1
0
1
0
2
2
0
1
1
0
1
0
1
1
2
1
1
0
1
1
1
0
1
2
1
1
1
1
2
0
1
1
1
1
2
1
1
2
2
1
2
1
1
0
1
2
1
1
1
2
1
0
1
1
1
1
1
1
2
1
1
1
0
0
2
1
1
1
0
1
1
1
3
2
1
2
2
2
1
1
1
1
1
0
2
2
2
2
1
1
1
1
1
2
0
1
1
0
2
0
1
1
1
2
1
1
2
1
2
1
2
2
1
1
2
1
1
1
1
0
1
2
1
3
2
1
1
0
1
1
2
0
2
0
1
0
0
1
2
1
1
3
1
2
1
0
1
1
0
2
1
1
1
1
0
2
1
2
2
1
0
2
1
2
0
2
0
1
0
2
0
1
1
2
1
1
1
1
1
2
2
1
1
1
1
1
2
0
0
1
1
1
1
1
1
1
2
1
2
1
1
1
2
1
1
1
1
0
1
1
1
1
2
2
1
1
2
0
1
1
1
1
1
0
2
1
1
0
2
2
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
0
0
1
0
1
0
1
1
2
2
1
1
2
1
1
0
2
1
1
1
1
0
0
0
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
0
2
2
0
2
1
1
2
1
2
1
2
0
1
1
0
2
0
1
0
2
0
1
1
0
2
1
1
1
0
0
1
2
0
1
0
2
2
1
1
1
1
2
1
2
2
0
0
2
1
1
1
0
2
1
0
2
1
1
0
2
1
0
1
1
1
2
0
2
1
2
0
1
2
2
1
1
1
0
2
2
0
2
1
1
1
0
1
1
0
4
1
2
1
2
2
1
1
2
1
1
2
2
2
1
0
1
1
1
1
2
1
1
1
0
1
0
1
1
1
2
1
2
1
0
2
2
1
1
2
1
2
0
1
0
1
2
2
1
1
3
0
0
0
1
2
1
1
2
0
1
1
2
1
0
2
1
0
1
2
2
0
1
0
0
2
2
2
2
1
2
1
1
1
1
2
2
1
1
1
0
1
2
1
1
1
1
2
2
2
0
2
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
2
1
1
0
0
1
1
1
1
1
1
2
0
1
1
1
0
1
2
0
1
0
0
1
0
1
2
1
2
2
1
0
1
0
0
1
1
1
1
2
1
1
1
0
1
1
1
0
1
2
1
1
2
1
2
2
2
0
2
2
1
1
2
1
2
1
0
2
1
0
0
1
2
0
0
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
0
1
1
2
1
1
1
0
1
1
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
0
2
2
0
1
1
1
1
1
1
2
1
1
2
0
1
1
1
2
1
0
0
1
1
1
1
0
1
1
1
1
1
0
2
2
2
1
1
2
0
1
1
1
2
1
0
1
2
0
2
2
2
0
1
1
1
1
1
1
0
1
1
2
1
0
2
2
1
1
0
1
0
1
2
1
1
1
1
1
1
0
0
0
2
4
1
0
1
0
0
1
1
2
1
2
1
1
1
1
1
0
1
1
1
1
0
1
1
1
2
1
1
1
1
2
2
1
0
1
1
1
0
1
1
1
2
1
1
1
1
0
1
0
1
1
1
2
1
2
1
1
0
1
2
0
2
2
1
0
0
2
1
1
1
0
1
1
1
0
2
2
1
0
1
1
3
1
1
1
1
1
1
1
0
2
1
1
1
1
0
0
1
2
0
1
1
1
1
2
1
1
1
2
2
1
2
0
1
2
1
1
2
1
1
0
1
2
0
0
1
1
1
1
1
3
1
0
1
1
0
1
0
1
1
1
1
1
1
0
2
1
1
1
1
1
2
2
1
1
2
1
1
1
3
1
2
0
2
0
1
1
2
2
2
2
0
1
0
2
1
1
3
1
0
1
4
1
2
0
2
4
1
1
0
1
1
1
0
1
2
1
1
1
1
0
0
1
1
0
2
2
0
1
2
1
0
1
1
0
0
2
1
1
0
1
2
1
0
0
1
0
2
1
1
1
2
1
0
0
1
3
2
1
1
2
2
1
2
3
1
2
2
1
2
2
1
1
2
0
1
2
1
1
2
0
1
1
2
1
1
2
1
1
1
0
1
1
2
1
1
1
1
2
2
0
1
0
1
1
1
0
2
2
0
1
2
1
2
1
0
1
1
2
1
2
1
2
0
1
2
1
0
2
1
2
1
2
1
1
1
1
2
1
0
0
0
2
1
1
0
1
1
1
1
2
1
0
2
1
2
0
1
1
2
1
1
2
1
2
2
1
1
1
2
1
0
1
0
1
0
0
1
0
1
1
1
1
1
2
1
1
2
0
2
2
0
2
1
1
1
1
1
0
1
0
1
0
1
2
1
1
1
2
0
1
0
2
2
1
1
1
1
0
1
1
1
1
0
2
1
1
1
0
1
1
0
1
0
1
1
1
1
2
0
1
1
1
2
1
0
2
0
1
2
1
1
1
1
2
1
0
1
1
1
0
1
1
1
0
2
0
0
1
2
2
1
0
1
1
1
0
1
2
1
0
1
0
1
2
1
1
1
1
2
1
2
1
2
2
1
1
1
1
0
1
1
1
0
1
0
2
1
0
2
2
2
2
0
0
1
2
1
1
1
2
2
1
1
4
1
0
1
1
1
1
2
1
2
2
1
1
2
2
1
0
0
1
2
2
2
0
1
2
1
0
1
0
1
1
1
1
1
1
1
1
1
2
1
0
0
1
1
1
1
1
1
1
1
0
2
2
0
1
1
2
2
2
1
2
1
1
0
0
2
0
0
1
0
1
2
1
1
1
1
1
1
2
1
0
0
1
1
1
1
1
2
0
1
1
1
0
0
1
1
2
1
2
2
2
1
2
0
2
2
1
2
2
1
1
2
0
2
1
1
1
2
2
2
1
1
1
1
0
1
1
2
1
2
2
0
2
2
1
1
1
2
0
1
1
1
1
1
1
2
1
2
0
1
2
1
0
1
1
1
0
1
1
1
2
2
1
1
2
3
1
1
1
1
1
1
2
1
2
1
1
2
2
1
1
1
2
1
1
1
0
0
0
0
0
1
1
1
1
1
1
2
1
1
1
1
1
2
0
0
0
1
1
1
1
1
3
2
1
1
1
0
1
1
1
1
1
1
1
1
0
1
2
2
2
0
0
0
1
1
1
2
0
2
1
1
1
0
0
0
1
0
2
1
2
1
1
1
1
1
1
2
0
2
1
1
1
1
1
2
1
1
2
0
1
3
1
0
2
2
1
0
1
0
1
2
2
1
1
2
1
2
2
1
1
1
0
1
1
1
1
1
1
2
1
1
0
1
0
1
2
1
1
1
1
1
1
2
1
1
2
1
3
2
1
2
2
2
0
1
1
1
1
1
1
1
0
0
0
1
1
1
0
2
0
1
0
2
1
1
0
1
1
1
1
1
1
1
1
0
0
1
0
1
2
2
1
1
2
1
1
1
0
1
2
1
1
1
1
1
1
2
1
2
2
1
1
0
0
1
0
1
1
1
1
2
0
0
1
1
1
2
0
2
1
1
0
1
1
1
2
1
0
1
0
1
1
2
2
1
0
2
2
0
0
1
2
0
1
1
1
2
1
1
2
1
0
0
0
2
1
1
0
2
2
1
1
1
0
2
2
2
1
1
1
0
1
2
2
0
1
1
2
1
1
1
1
1
1
1
1
1
0
1
1
0
0
0
1
2
1
1
1
2
2
0
2
1
1
2
1
1
0
1
6
2
1
0
2
1
2
1
1
2
1
1
1
1
0
2
1
1
0
2
1
1
1
0
1
1
1
1
3
0
2
1
1
1
2
2
1
1
0
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
0
0
2
1
1
4
1
0
1
0
2
1
1
2
0
1
0
1
1
2
0
1
1
2
2
0
1
1
2
2
1
1
2
1
1
3
1
2
0
1
2
2
1
1
1
2
2
1
1
1
0
1
1
1
0
1
1
1
1
2
0
4
0
1
1
1
1
1
0
1
0
1
2
1
1
1
2
1
1
1
2
2
1
1
1
1
4
0
1
1
0
2
2
1
0
1
1
1
1
2
2
0
1
0
2
1
0
2
1
1
2
1
1
1
0
0
2
1
1
1
2
2
1
1
1
1
1
2
1
2
0
1
1
2
0
1
1
1
1
1
0
1
2
2
1
1
2
1
1
0
1
1
1
1
1
1
1
1
2
2
0
1
1
1
1
1
1
2
2
0
2
1
1
1
1
1
1
1
1
1
1
1
0
0
3
2
1
1
1
1
2
2
1
2
1
1
1
1
1
1
1
2
0
1
2
1
1
2
1
1
1
0
2
0
2
2
1
1
1
1
2
0
2
0
0
0
1
1
2
1
0
1
0
3
2
0
1
1
2
0
2
1
2
1
0
1
1
1
0
1
1
1
2
1
2
2
1
2
0
1
1
2
1
1
1
1
2
1
1
1
0
0
2
1
2
2
1
2
1
0
1
0
0
1
1
2
0
2
2
1
1
0
1
1
1
2
1
0
2
1
0
0
1
1
0
1
0
1
3
1
0
1
2
1
2
1
1
1
1
1
2
1
0
2
1
2
0
2
0
1
1
2
0
0
0
1
1
1
1
2
1
1
1
2
2
2
0
1
2
1
2
2
1
1
1
2
1
2
1
2
1
1
2
1
2
1
1
1
1
1
1
1
2
1
2
2
0
1
0
0
1
0
0
1
1
1
1
1
1
1
0
1
1
2
1
1
1
2
2
1
2
0
0
3
0
1
1
0
1
2
1
1
1
1
0
2
1
1
1
1
0
1
1
1
1
1
1
1
1
1
0
1
2
1
2
1
1
2
1
1
2
2
1
1
1
1
1
2
2
1
1
2
1
1
1
1
2
0
1
2
2
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
0
1
1
1
0
1
2
1
2
1
2
0
2
2
1
2
1
1
1
2
0
0
2
1
1
1
1
1
0
1
0
1
2
1
0
1
1
0
1
2
2
1
2
1
0
1
1
0
1
2
1
1
0
2
1
1
1
1
2
2
2
1
2
1
0
1
0
2
1
0
1
0
0
2
0
1
1
1
0
2
2
0
0
1
1
2
2
2
1
1
0
1
1
1
2
1
2
2
0
2
0
0
1
1
1
1
1
1
2
2
1
0
0
1
2
1
2
0
2
1
1
3
2
1
1
0
1
1
1
1
1
2
1
1
1
2
1
1
2
1
2
2
2
1
1
0
1
1
1
0
2
0
2
1
1
1
1
2
1
1
1
1
1
1
1
1
2
0
2
1
0
0
1
0
1
1
3
1
1
1
1
0
1
2
1
2
1
1
2
1
1
2
0
1
1
1
0
1
0
2
2
1
2
2
1
1
1
1
1
3
1
2
1
1
1
2
1
1
1
0
0
0
0
2
0
2
2
1
1
2
1
1
2
1
0
1
0
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
0
1
1
1
1
1
1
0
1
0
0
1
1
0
0
1
2
1
1
1
1
1
1
2
2
1
2
1
2
2
1
4
1
1
1
1
1
0
1
1
1
1
1
2
0
2
0
1
2
1
1
2
1
1
1
1
2
1
1
2
1
1
0
1
1
1
1
1
0
3
1
0
1
2
1
1
0
1
0
2
1
0
1
1
1
2
0
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
0
1
1
2
0
1
0
1
1
0
2
2
1
1
0
3
0
1
1
1
0
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
2
1
1
0
1
1
1
1
1
1
2
0
1
0
2
1
2
1
1
2
1
1
1
1
0
0
1
1
1
1
1
1
0
2
1
2
1
1
1
0
1
1
1
1
2
1
2
1
0
2
1
0
2
0
0
1
0
2
2
1
1
1
1
0
0
2
2
2
1
2
2
1
0
1
2
2
1
1
0
1
1
1
0
0
3
2
1
1
0
2
1
1
0
2
2
2
1
1
2
1
1
0
1
1
2
1
2
2
2
2
2
0
1
1
1
0
3
1
0
1
0
1
1
0
0
0
0
1
1
1
2
2
1
1
1
0
1
2
2
0
1
1
2
1
2
0
0
1
1
0
1
1
1
1
0
2
0
1
0
1
1
1
1
2
1
1
1
1
0
2
2
1
0
0
0
1
1
1
1
1
1
1
1
2
1
0
1
3
1
0
1
1
1
2
1
0
1
1
0
1
2
0
1
2
2
0
0
2
2
1
0
1
2
1
1
1
1
1
2
1
1
0
1
1
1
1
2
1
2
1
2
1
1
1
1
1
2
1
1
1
2
2
1
2
1
0
1
1
2
1
1
0
1
2
2
1
0
1
0
1
2
2
2
0
2
0
1
1
1
2
1
2
1
1
1
2
0
1
2
1
1
2
2
1
2
1
1
1
1
1
1
1
1
0
1
2
2
1
2
2
2
1
1
2
1
2
1
1
2
2
0
1
2
0
1
2
0
0
1
0
1
1
0
1
1
0
2
1
1
1
0
1
1
2
0
1
1
1
1
1
1
1
1
1
1
1
1
2
0
1
1
2
1
2
1
0
0
1
2
1
1
0
2
1
1
2
1
1
1
1
0
1
1
1
1
1
2
0
0
0
1
1
1
2
1
1
1
2
2
2
0
1
2
1
1
0
1
2
0
1
1
1
0
1
1
1
1
1
1
1
1
1
0
1
0
1
2
2
1
0
2
0
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
2
0
0
2
1
1
1
1
1
1
1
2
2
0
1
1
2
1
1
1
1
1
1
0
1
2
1
0
2
1
1
0
2
1
1
2
1
2
2
2
1
0
2
1
1
1
2
1
1
2
2
0
1
1
0
0
2
0
1
0
1
2
2
1
2
2
1
2
1
0
2
1
1
1
1
1
1
1
1
1
2
0
1
0
1
1
1
2
1
1
2
1
1
1
1
2
4
0
1
1
0
1
1
0
0
2
1
0
0
1
1
1
0
1
1
1
1
1
0
1
1
1
2
1
0
2
1
1
2
1
0
0
1
0
1
1
0
1
1
1
2
1
1
1
2
1
2
1
1
2
1
2
1
0
1
1
0
2
0
1
0
0
1
2
1
1
0
0
1
2
0
2
0
0
2
1
2
2
2
0
1
1
2
1
2
2
1
0
1
1
1
1
0
1
2
0
2
1
0
2
0
1
1
1
2
0
2
1
1
0
1
0
1
2
2
1
0
1
2
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
0
2
1
1
1
1
2
2
1
0
0
1
1
1
1
1
1
0
1
0
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
0
1
2
1
0
1
1
2
2
1
2
2
1
1
1
0
1
1
2
0
1
1
1
1
1
1
0
1
1
0
1
2
1
1
1
2
1
1
1
2
1
1
1
0
1
1
1
0
0
1
1
1
1
1
1
2
1
1
1
0
0
1
1
1
1
1
0
1
2
0
1
2
0
5
1
1
1
0
2
0
1
1
1
1
2
1
0
0
1
2
1
1
1
0
1
1
1
2
2
1
0
1
1
1
1
0
1
2
1
1
0
2
0
1
1
1
0
1
2
1
2
2
1
2
2
2
2
2
0
0
1
1
0
2
0
2
1
1
1
2
2
1
1
2
0
2
0
1
2
1
2
1
2
0
1
1
1
2
2
2
1
1
2
1
2
0
1
0
1
0
2
1
1
1
1
1
1
1
1
0
0
1
1
2
2
1
2
1
1
1
0
2
1
1
1
0
1
1
2
1
1
2
1
1
1
0
1
1
1
1
1
2
1
2
0
2
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
2
2
2
0
1
2
1
1
2
1
1
0
1
2
1
2
1
1
2
1
2
0
1
1
1
2
1
0
0
1
1
1
1
1
1
0
0
1
0
2
1
1
0
1
1
1
1
0
3
1
2
0
2
1
1
1
0
0
0
1
1
1
2
1
2
3
1
1
2
2
2
2
1
0
1
2
0
1
1
1
1
1
1
0
1
1
0
2
2
2
2
1
0
1
0
1
1
1
1
2
0
1
1
1
1
0
1
1
1
2
1
0
0
1
0
1
1
2
1
1
0
1
1
0
1
0
1
0
1
0
2
0
0
0
2
0
1
1
1
0
2
1
2
1
1
2
1
0
1
0
1
1
0
0
1
2
2
2
1
1
0
2
0
1
1
2
1
1
1
1
1
2
1
2
1
0
1
1
1
1
1
2
2
2
1
0
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
0
1
2
1
1
2
2
0
1
1
1
1
0
1
1
2
1
0
1
1
0
1
2
1
1
1
1
1
0
2
0
2
2
2
0
2
1
0
1
1
2
1
1
0
2
1
1
1
1
1
2
1
0
1
2
1
1
1
2
1
2
2
1
0
1
2
1
1
0
1
1
0
1
2
0
1
1
1
1
2
2
0
1
1
2
1
1
1
0
2
0
2
0
1
2
1
2
0
1
1
1
0
1
1
1
1
0
2
1
1
2
1
2
1
1
1
1
0
1
0
1
2
0
0
1
1
1
1
2
1
2
0
1
2
0
0
0
0
2
1
2
2
1
1
2
0
1
1
1
2
1
2
1
0
1
0
2
0
2
1
1
1
1
1
2
2
0
1
2
2
1
1
1
1
1
1
2
1
2
1
1
1
1
0
2
1
1
1
1
1
1
0
0
1
1
0
1
1
0
2
2
2
1
1
2
2
1
1
0
2
1
1
1
0
1
1
1
0
2
2
2
1
1
1
0
1
3
1
1
1
1
1
1
1
0
2
1
2
2
1
0
1
0
1
0
0
2
1
2
2
1
1
3
2
3
2
2
2
1
1
2
2
1
0
1
1
2
1
1
1
1
2
1
1
2
1
0
1
0
2
2
2
1
2
1
1
2
2
1
1
1
1
2
1
1
1
1
2
1
0
0
0
1
2
1
1
1
0
1
2
1
1
2
1
1
0
1
1
1
2
2
1
0
0
1
1
1
2
1
0
1
2
1
1
1
0
1
1
1
0
1
0
1
0
2
2
1
2
2
1
1
1
1
1
2
0
2
1
0
0
2
0
2
1
1
2
1
0
0
1
1
1
2
0
0
1
1
2
1
1
1
0
0
2
1
2
1
1
0
1
1
1
0
1
1
1
1
1
1
1
0
1
1
0
1
2
1
0
1
2
0
1
2
1
0
1
1
0
1
1
1
1
0
2
1
1
1
2
1
2
1
2
0
1
2
2
1
2
2
1
1
1
0
2
1
0
2
2
1
2
2
2
0
1
0
1
1
0
3
0
1
1
2
0
1
2
0
2
0
1
1
2
1
1
1
1
2
0
1
1
2
2
0
1
2
1
1
2
1
2
1
0
1
2
3
2
2
1
0
1
1
2
0
1
2
1
1
1
0
1
2
1
1
1
0
1
2
1
1
2
1
1
2
1
4
0
0
0
1
1
1
1
2
0
2
1
1
2
1
1
2
1
2
1
1
1
1
1
1
3
0
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
0
0
1
1
2
1
1
1
1
1
1
2
1
1
0
1
0
1
2
2
0
1
1
1
1
1
1
2
1
2
1
1
1
2
2
1
1
2
0
1
1
2
1
2
1
2
0
1
1
1
2
0
2
1
1
0
1
1
1
2
2
1
1
1
1
1
2
2
0
1
0
1
0
0
0
1
2
1
1
1
0
1
3
2
1
1
1
1
1
2
1
1
1
0
2
1
0
2
1
1
1
1
0
3
1
0
2
1
1
1
0
1
2
1
1
1
1
1
2
2
1
1
0
1
1
1
2
2
2
1
1
0
0
2
2
2
1
2
0
2
1
1
1
2
0
1
2
1
1
0
1
1
1
1
2
1
1
0
1
2
1
0
1
1
2
0
1
1
1
1
1
1
2
1
1
0
1
0
2
2
1
1
2
1
0
1
1
1
1
1
1
1
1
2
1
1
1
3
1
1
1
1
1
2
2
1
1
1
1
2
0
1
0
2
1
1
2
2
2
0
0
1
1
0
0
2
2
0
2
2
2
1
1
0
2
1
2
0
1
1
0
0
1
1
4
2
1
1
1
2
0
2
1
1
1
1
1
0
1
0
2
1
1
1
1
1
0
0
0
1
0
2
1
1
0
1
0
0
1
1
0
1
1
2
0
2
2
1
1
1
2
0
1
1
1
1
1
2
0
2
1
1
1
1
0
1
1
1
1
2
1
1
0
1
1
1
2
2
1
2
2
0
0
1
1
2
2
1
1
1
0
1
1
1
1
3
1
2
1
1
0
1
1
1
2
1
1
1
1
3
0
1
2
0
2
0
1
1
2
1
1
0
1
1
1
1
1
2
2
1
2
1
1
2
0
2
1
2
2
0
2
2
1
1
0
2
2
2
2
1
1
1
1
1
1
1
0
1
0
1
1
1
1
1
1
1
1
1
0
1
1
0
2
0
1
1
0
2
1
1
1
2
2
0
0
1
1
0
0
0
1
1
1
1
0
1
1
0
1
1
1
1
1
1
1
1
2
1
1
1
1
1
0
1
1
0
0
0
1
1
1
1
1
0
1
1
2
2
1
1
1
2
1
1
2
1
1
0
1
1
2
1
1
1
1
0
2
2
2
1
2
2
1
0
0
2
0
1
1
1
1
1
2
2
1
0
0
1
0
1
2
1
1
0
0
0
1
0
0
1
2
1
1
1
1
2
1
2
1
0
2
0
1
2
1
1
1
0
1
1
0
1
1
1
1
0
1
1
1
1
1
1
1
1
1
2
1
1
1
1
0
0
2
0
1
2
1
0
1
1
1
1
0
1
1
2
0
1
2
2
2
2
1
1
0
1
2
2
1
1
2
0
1
1
1
1
1
1
1
1
1
0
2
0
1
1
1
1
1
2
1
0
1
0
1
1
1
0
2
1
1
1
1
1
2
0
1
1
1
1
1
1
1
1
0
1
2
1
0
1
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
0
0
0
1
0
1
1
2
2
1
1
1
1
1
1
1
2
1
1
0
1
1
2
1
1
1
2
1
0
1
1
2
1
1
0
2
0
1
1
2
0
1
0
2
1
1
0
1
2
1
1
1
2
2
1
1
1
0
1
2
1
2
1
1
1
2
1
0
1
1
0
1
0
1
2
1
1
0
1
1
2
1
1
1
2
1
1
1
0
2
1
0
2
1
0
2
2
1
1
1
1
0
0
1
1
1
1
1
1
1
0
1
0
1
1
1
2
1
1
1
2
1
1
2
1
1
2
2
1
0
1
2
1
1
2
1
1
2
2
1
1
1
1
3
0
1
1
2
2
1
1
2
0
1
1
1
1
1
2
2
2
1
1
1
1
1
2
0
1
2
1
0
1
1
1
0
2
1
0
1
1
2
1
1
1
1
1
0
1
1
2
1
1
2
2
2
1
0
1
0
1
1
2
1
0
0
1
0
1
1
1
1
2
2
0
0
2
1
1
1
2
2
0
0
1
1
1
1
0
1
1
1
0
0
0
1
1
1
1
2
2
1
2
0
1
1
0
2
1
0
0
2
1
4
0
1
1
1
0
2
1
1
1
2
2
2
1
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
1
1
3
1
1
1
2
1
1
2
0
0
0
1
2
2
1
1
2
1
1
1
1
1
1
1
0
2
2
1
1
1
2
1
2
2
2
1
1
1
1
1
1
0
1
2
2
1
1
1
1
1
1
0
1
1
1
1
2
1
3
1
1
0
0
1
1
1
1
1
1
0
2
2
0
1
2
1
1
0
1
1
0
1
2
1
2
1
1
1
1
0
1
1
1
0
2
1
2
1
0
1
0
1
2
2
1
1
1
1
1
1
0
1
1
0
1
1
1
0
2
1
1
0
0
1
2
1
2
1
0
0
1
2
2
1
1
0
1
2
1
1
0
1
1
1
1
2
1
1
0
1
0
1
1
0
1
1
0
0
2
0
1
1
2
1
2
1
1
0
1
2
0
1
1
1
1
0
1
1
0
1
1
1
2
0
0
2
0
1
2
2
1
1
2
1
1
2
1
1
1
2
0
3
3
1
2
1
1
2
1
2
2
2
1
1
1
1
1
0
1
1
1
2
1
1
1
1
0
1
2
0
2
1
1
1
1
1
1
1
2
2
1
2
0
1
2
1
1
0
0
0
1
1
1
1
2
1
1
1
2
2
1
0
1
2
0
1
1
0
0
2
2
0
2
1
0
1
1
2
1
1
2
0
1
1
2
1
1
1
2
0
1
1
1
0
1
1
0
0
1
0
2
2
2
9
2
1
1
1
1
2
0
1
0
0
1
1
1
2
2
1
1
1
2
1
1
0
1
1
1
0
2
2
1
1
1
0
1
1
0
1
1
1
2
0
2
1
2
0
0
1
1
0
2
1
1
1
0
1
1
1
1
1
0
1
1
1
2
2
0
1
1
1
0
2
0
1
1
2
2
0
1
1
1
0
1
2
2
0
1
0
1
1
2
1
1
1
1
1
1
0
1
1
1
1
0
1
1
1
1
2
2
1
2
2
0
2
2
1
1
1
1
1
2
1
1
2
1
1
0
2
0
1
1
1
1
1
2
2
1
1
1
1
0
2
2
2
1
1
2
1
2
1
1
2
0
1
2
3
0
2
2
2
1
0
0
0
0
2
1
2
1
0
0
0
1
2
2
1
1
1
1
2
0
0
2
0
1
1
1
0
2
0
1
1
1
1
1
2
1
1
1
2
1
1
1
1
0
0
2
1
1
1
0
2
2
1
0
1
1
1
1
1
1
1
2
0
2
0
1
1
1
0
1
1
1
1
1
1
1
1
2
0
1
1
1
1
1
1
1
1
2
1
1
1
1
2
2
1
0
1
1
1
1
1
0
0
1
1
2
1
1
2
2
1
0
3
1
1
2
3
1
2
0
1
0
2
2
0
1
1
1
0
2
1
0
1
2
1
0
0
2
1
3
1
1
1
1
1
0
1
1
1
0
1
0
1
2
0
3
1
2
1
1
2
2
1
1
1
1
2
1
2
1
2
1
2
1
0
0
2
2
1
2
2
1
1
0
1
2
1
1
0
0
1
2
1
1
2
2
1
1
2
0
1
1
0
1
0
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
2
1
2
1
0
1
0
1
2
1
1
1
1
1
0
1
1
1
0
0
1
4
1
1
1
1
1
2
2
2
2
1
0
1
0
1
1
2
2
1
1
1
2
0
2
1
2
1
0
2
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
0
0
2
2
2
2
0
2
1
2
1
1
0
1
0
2
2
1
0
1
1
1
1
1
1
0
2
0
0
0
1
1
0
1
2
1
0
2
2
1
0
1
1
1
0
0
1
1
1
1
2
0
1
2
0
1
1
2
1
1
1
1
1
2
1
2
2
1
3
2
1
2
2
2
0
1
1
2
2
1
0
0
1
1
1
1
2
1
0
1
1
2
1
2
2
1
1
2
1
0
1
1
0
1
1
1
2
1
0
1
1
2
1
1
2
1
1
2
0
1
0
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
2
1
2
1
0
1
1
1
2
0
1
1
0
1
0
1
1
0
1
0
1
1
1
1
1
2
1
0
1
0
1
1
1
0
0
1
0
1
2
0
3
1
1
1
1
1
1
1
0
1
1
2
1
0
1
2
2
1
2
1
0
1
1
0
0
1
2
2
1
1
1
1
0
0
1
0
0
0
0
1
2
2
1
1
1
2
2
1
1
1
0
0
1
1
2
1
1
1
2
1
1
1
0
1
0
1
2
1
0
1
1
1
1
1
0
1
1
2
2
1
1
1
1
2
0
2
1
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
2
2
1
2
0
1
2
2
1
2
1
1
0
1
0
1
1
1
1
0
2
2
1
1
1
1
2
2
1
1
2
1
0
1
1
0
0
2
1
2
1
1
1
1
1
1
2
2
1
1
0
1
1
1
1
2
0
1
0
1
1
2
1
0
0
1
1
0
0
1
4
0
2
1
2
2
1
1
1
1
0
1
2
2
2
2
0
1
0
0
1
2
2
0
1
2
1
0
2
1
0
2
1
1
1
2
0
1
1
1
0
0
0
1
2
2
1
0
0
1
1
1
1
2
1
1
1
1
2
2
1
2
1
2
2
0
0
2
1
2
1
1
1
2
2
1
1
1
0
1
0
1
1
1
1
0
1
1
1
2
2
0
2
1
1
0
1
2
1
1
1
1
0
0
1
2
1
1
0
1
1
1
0
1
2
2
1
1
2
2
2
0
1
2
2
2
0
1
1
2
2
0
1
1
2
1
1
0
1
1
2
0
1
1
1
1
1
0
1
1
9
2
2
1
1
1
1
0
1
0
1
0
0
2
1
1
2
1
0
1
1
2
2
2
0
0
0
1
2
1
1
1
2
0
2
1
1
0
0
1
3
1
1
2
0
0
2
2
0
2
2
1
2
1
0
2
2
1
2
2
0
0
1
2
0
2
1
1
2
1
1
1
1
1
0
2
1
1
2
0
2
0
1
2
1
1
0
1
1
0
1
0
1
1
1
1
1
1
0
0
2
2
0
1
1
1
0
4
1
1
1
1
2
1
0
1
1
2
1
1
1
0
1
1
1
1
1
1
1
2
1
2
1
1
0
1
1
1
0
2
1
0
2
0
1
1
1
1
1
1
0
1
3
1
2
2
1
2
2
1
0
1
1
0
1
1
1
1
2
1
0
1
0
1
1
1
2
2
2
1
1
1
1
1
0
2
2
2
1
2
2
1
1
1
1
1
1
2
1
1
0
2
2
2
1
1
1
1
0
0
1
1
1
1
1
3
1
1
1
1
1
1
0
2
2
1
1
0
1
1
1
2
1
1
1
1
2
2
1
2
2
1
0
0
2
1
1
1
1
2
1
1
2
0
0
2
2
3
2
1
2
2
1
1
1
0
1
1
2
1
1
1
0
1
1
1
1
0
1
1
1
1
1
2
0
2
0
1
1
1
1
0
1
2
1
2
1
3
1
1
1
1
1
0
1
1
0
1
2
2
0
2
1
2
2
3
2
2
2
1
0
0
0
2
1
1
1
1
1
2
1
2
2
0
0
2
1
1
0
0
2
1
1
1
1
1
3
2
0
1
1
1
1
1
1
1
1
0
0
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
2
0
2
1
2
0
1
1
1
1
2
0
1
2
1
0
1
1
1
1
2
1
1
1
0
1
0
1
1
1
1
0
1
1
2
0
1
1
2
0
2
1
1
1
2
0
1
1
0
1
1
2
0
1
1
2
1
0
1
1
2
1
1
0
0
2
1
1
0
1
1
2
1
0
2
1
2
1
1
1
1
2
0
1
1
2
1
1
0
1
2
2
1
1
1
0
2
1
2
2
1
1
0
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
0
1
2
0
2
1
1
1
0
1
1
1
1
2
0
1
0
1
2
1
1
1
2
1
2
0
2
1
1
0
1
1
2
1
0
1
1
2
1
1
1
1
1
0
0
1
1
2
1
2
1
0
2
1
1
0
2
2
2
2
1
1
1
1
0
0
0
1
1
2
1
1
1
1
0
1
1
1
0
1
0
1
1
0
1
1
2
2
1
2
1
0
0
1
1
2
2
2
1
1
1
1
3
1
1
1
1
0
1
2
2
1
1
1
1
2
1
1
1
1
0
2
1
1
2
1
1
2
1
2
1
2
1
0
1
2
2
1
0
1
1
0
2
0
1
1
2
1
1
0
1
1
0
2
1
1
1
1
1
1
1
1
1
0
1
2
2
2
0
1
1
1
1
1
1
1
0
2
0
2
2
1
1
2
2
2
0
1
1
2
0
1
1
1
1
1
1
2
1
0
2
2
2
2
2
1
2
2
1
0
1
1
1
0
1
0
0
1
0
2
0
2
2
0
1
1
2
1
2
1
0
1
1
1
2
0
1
0
2
1
1
1
0
1
0
1
1
2
1
1
1
1
1
2
2
1
1
1
1
1
2
1
0
2
1
1
0
1
1
1
2
2
1
0
1
1
1
2
0
2
1
1
1
2
0
1
2
1
1
1
0
2
1
1
1
0
2
1
1
1
1
1
1
0
0
1
1
1
2
0
2
0
0
1
1
0
1
2
1
1
1
0
1
2
1
0
1
0
0
2
1
0
1
1
1
2
2
1
1
2
1
1
1
1
1
0
1
2
1
1
1
1
1
1
0
1
1
1
0
1
1
2
2
4
2
1
0
1
1
1
1
1
1
0
1
1
1
0
1
2
1
1
2
1
2
0
1
1
1
1
2
0
1
0
2
1
2
1
2
2
2
2
0
2
1
1
0
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
0
0
1
1
2
2
1
2
1
1
1
1
2
1
1
1
1
0
1
1
1
2
2
0
1
1
0
2
1
0
1
2
1
1
2
1
1
1
1
0
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
0
2
1
1
2
1
0
2
1
1
0
1
1
2
1
1
1
2
1
2
1
1
2
1
2
1
1
1
1
2
1
1
2
1
1
0
1
1
1
0
1
1
2
0
0
1
1
1
1
1
2
1
1
1
1
1
0
1
0
2
1
1
0
1
2
1
1
0
1
0
1
1
1
0
1
2
0
1
2
1
2
0
1
1
1
1
1
1
2
2
2
1
1
1
1
0
2
0
2
0
2
1
2
0
2
1
2
1
1
1
0
2
0
1
2
1
2
1
2
1
1
0
1
0
1
1
1
1
1
2
1
1
1
2
0
1
1
1
1
1
2
1
2
1
1
1
1
0
0
3
0
0
1
0
0
1
2
0
2
0
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
2
2
1
1
1
2
1
1
0
1
1
0
2
0
1
0
1
1
1
2
2
1
1
1
1
0
2
1
1
1
1
1
1
1
1
1
0
0
1
1
1
1
1
1
0
1
1
0
1
2
1
1
2
1
1
2
1
0
1
2
1
1
2
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
0
1
1
2
1
1
2
0
1
2
2
1
0
0
1
1
1
0
1
1
1
0
2
2
1
2
2
1
1
1
1
1
1
0
1
2
2
1
1
2
1
2
0
1
1
0
2
1
1
1
1
1
1
1
1
1
2
2
2
2
2
0
1
1
1
2
1
1
1
2
0
2
1
0
1
1
1
1
1
1
1
2
2
1
0
1
2
1
0
2
0
2
1
1
1
0
1
1
1
1
0
1
1
0
2
1
1
0
1
1
1
3
1
2
0
2
2
2
1
1
1
2
1
1
2
2
1
2
1
2
2
2
1
1
1
1
2
0
1
2
1
2
1
2
1
1
0
1
1
1
2
1
1
2
2
1
1
2
1
1
0
2
0
2
2
2
2
1
0
2
1
1
1
1
1
0
1
2
1
2
1
2
1
1
2
0
1
2
0
1
0
0
1
1
2
1
1
2
1
1
2
1
0
2
2
2
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
2
2
1
1
1
2
1
0
1
1
1
0
0
1
1
1
0
1
2
1
1
2
0
1
1
1
1
2
1
1
1
0
1
1
1
1
1
0
1
0
1
0
1
2
1
2
1
2
1
0
1
1
1
1
0
2
1
1
2
1
1
1
1
1
2
1
1
2
1
1
2
1
1
2
0
0
2
1
1
1
1
1
2
1
2
0
1
2
0
1
2
10
1
2
0
0
2
2
2
2
0
1
0
0
1
3
1
1
1
2
2
1
1
2
1
1
1
1
1
2
1
1
2
1
1
1
1
2
1
0
2
1
0
1
1
1
0
2
1
0
2
0
2
1
1
0
2
2
1
2
1
1
1
2
1
2
1
2
1
1
2
1
2
2
2
1
1
2
1
2
1
2
1
2
1
0
2
2
1
1
1
2
2
1
2
1
1
2
1
2
0
1
2
1
1
1
1
0
2
2
1
3
1
0
2
1
1
1
0
0
1
1
1
1
1
1
2
2
1
1
2
0
0
0
2
2
0
1
2
2
1
1
1
1
1
2
2
1
0
2
2
2
1
0
1
1
0
0
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
0
0
2
1
2
2
0
1
0
0
1
0
1
1
1
1
1
0
0
0
1
1
1
2
0
1
1
2
2
0
1
1
1
2
0
0
1
1
1
2
1
1
1
0
2
2
1
1
0
1
2
1
1
1
2
0
2
1
1
1
2
1
2
2
1
0
1
1
0
1
1
1
1
1
0
1
0
2
2
1
1
2
1
0
1
1
2
1
1
1
1
2
1
1
1
2
1
2
1
0
1
1
1
1
1
1
0
3
2
1
1
1
0
0
2
2
1
1
1
0
1
1
1
0
2
1
2
1
1
2
1
2
1
4
1
0
2
1
2
0
1
2
0
1
1
3
3
0
1
2
2
1
0
1
1
1
1
1
1
1
1
1
2
1
0
0
1
1
1
0
1
1
1
0
1
0
3
1
0
2
1
1
1
1
3
0
1
2
1
1
1
1
0
1
2
1
2
0
1
1
1
1
2
1
2
3
0
0
1
1
2
1
1
0
0
2
0
1
2
2
1
0
0
1
2
0
1
1
0
1
1
0
1
0
0
1
1
0
0
1
1
1
2
2
1
2
1
1
2
2
1
1
0
2
2
1
2
1
2
1
1
1
0
2
1
2
3
2
2
1
1
2
1
1
0
1
2
0
0
1
0
1
1
1
0
3
0
1
1
1
0
0
1
3
1
1
1
1
1
1
2
1
1
2
2
1
1
1
0
0
1
2
1
1
1
1
1
1
1
1
1
0
1
1
2
1
1
0
0
2
1
0
0
1
1
1
1
1
0
2
1
0
2
1
1
1
0
1
2
2
0
1
1
2
1
2
2
3
1
1
1
1
0
0
1
1
0
2
1
1
0
2
1
1
1
2
0
0
1
1
1
1
1
2
0
1
1
2
1
1
2
1
1
0
1
1
2
2
2
2
2
2
1
0
2
0
0
1
2
1
1
1
1
1
1
1
0
1
2
2
1
1
2
0
4
0
1
1
0
1
1
0
2
4
1
1
2
2
2
2
0
1
1
0
1
0
1
1
1
2
1
0
1
1
1
2
1
2
1
1
1
0
1
0
1
1
0
1
1
1
0
1
0
2
1
1
1
3
1
5
1
1
2
2
0
1
2
1
1
2
1
1
1
1
2
2
1
1
1
0
2
1
2
1
2
2
0
2
1
0
1
1
1
0
0
0
2
1
1
0
1
1
1
1
1
1
1
1
1
1
2
0
1
1
0
1
1
1
2
1
1
1
0
2
2
0
0
1
2
3
2
0
1
0
1
2
1
2
0
2
2
1
1
1
1
0
0
0
1
2
1
1
0
1
1
1
0
1
1
0
2
1
1
0
0
1
1
0
1
1
2
2
0
0
2
0
0
1
2
0
1
2
1
2
0
0
0
2
1
1
1
1
2
0
1
1
1
1
1
2
1
1
2
2
0
1
2
1
1
1
2
1
1
1
1
2
2
0
1
2
1
2
1
2
1
3
1
1
2
2
1
2
1
3
1
2
1
1
2
1
0
1
1
2
1
2
2
0
1
1
2
1
1
1
1
1
1
0
1
2
1
1
1
1
1
1
2
1
1
2
1
1
1
0
1
0
1
1
1
2
1
1
1
2
0
2
0
1
1
1
1
1
1
2
2
4
1
1
1
1
1
0
1
1
1
2
2
1
1
1
0
1
0
1
0
1
2
2
1
1
1
1
2
1
2
2
2
1
2
0
1
1
1
1
0
1
2
1
1
1
0
1
1
2
1
1
0
2
2
0
1
1
1
0
2
1
2
1
2
0
1
1
1
0
2
1
1
1
1
0
1
1
0
1
0
2
2
0
1
1
2
0
2
1
1
2
1
1
1
1
2
1
0
2
1
0
1
3
2
1
1
1
0
1
0
2
1
0
2
1
2
1
2
2
1
0
1
2
1
0
1
1
2
2
2
1
1
2
1
0
1
0
1
1
1
0
1
2
0
0
0
2
1
1
2
1
3
2
1
1
1
3
1
1
1
0
2
1
1
0
2
1
1
1
2
2
2
0
2
1
1
1
1
0
1
2
1
0
2
1
1
1
1
1
0
1
1
2
1
1
1
0
1
1
1
1
1
0
2
1
1
2
1
2
1
2
1
1
2
1
0
1
2
0
1
2
2
1
1
1
2
1
2
1
0
1
2
1
2
0
0
2
0
1
2
0
2
1
1
1
1
1
1
2
2
1
1
1
1
1
2
0
1
0
1
0
1
1
2
1
2
2
1
1
1
1
2
1
2
2
0
2
0
1
2
2
1
1
1
0
1
1
0
1
1
1
1
2
0
2
0
1
0
1
1
1
1
1
3
2
0
0
0
1
1
0
1
2
1
1
2
1
1
1
2
1
1
2
1
2
1
0
2
1
1
1
1
1
1
2
1
1
1
1
0
1
1
1
1
1
0
0
1
0
1
1
0
1
2
0
0
1
2
2
1
0
1
2
2
1
2
1
1
1
0
1
2
1
1
0
1
0
2
1
1
1
1
1
1
1
0
2
2
1
2
1
0
0
2
0
2
1
2
2
1
1
1
2
1
2
1
1
2
2
2
2
2
1
0
0
1
1
1
1
1
1
1
0
1
3
1
0
2
1
2
0
1
0
2
1
1
1
0
1
1
1
0
1
2
1
0
1
0
1
2
1
2
0
0
1
1
1
1
1
0
0
1
1
1
1
1
0
1
2
2
1
2
0
1
2
2
1
0
0
2
1
1
1
0
1
1
3
1
0
1
2
1
1
2
2
1
1
1
2
2
1
1
0
1
0
0
1
3
0
1
1
1
1
1
0
1
1
0
1
0
2
1
1
2
0
1
0
2
0
1
1
0
0
1
0
2
1
1
2
2
0
1
2
1
2
1
1
2
0
1
0
1
1
0
1
1
2
1
1
1
2
0
2
2
1
1
1
2
0
1
2
2
1
2
1
2
1
1
2
1
1
1
1
2
1
1
1
1
1
2
1
1
0
2
1
2
1
0
0
1
1
3
2
2
2
1
2
1
0
1
2
1
1
0
1
1
1
1
2
1
1
1
2
2
1
2
1
0
0
1
1
1
0
1
0
1
1
1
1
1
1
1
1
1
2
2
1
1
1
0
0
0
1
1
2
2
2
0
1
2
1
1
0
2
1
0
1
1
1
2
1
2
2
1
0
1
0
1
1
1
2
1
2
1
1
2
1
0
1
1
0
1
0
0
0
1
2
1
1
1
1
1
0
1
1
0
1
1
1
0
0
0
0
0
0
2
1
1
2
1
0
0
1
1
2
1
0
1
0
1
0
2
0
2
0
1
1
0
2
2
1
1
0
3
2
0
1
0
1
0
1
6
0
1
1
2
1
1
1
1
2
1
2
0
1
1
2
1
1
1
1
2
0
2
1
1
2
1
1
1
1
1
1
1
2
0
1
1
0
0
2
0
2
1
1
1
1
0
1
1
2
2
2
1
2
0
8
0
0
1
2
1
0
1
2
1
2
2
2
1
3
1
1
2
1
1
0
1
1
1
1
2
1
0
1
1
2
0
1
0
0
1
2
1
2
1
0
1
1
2
1
1
2
0
2
1
1
1
1
2
2
1
2
1
1
0
0
1
1
1
0
1
1
1
2
2
0
0
0
0
0
1
1
1
2
2
2
2
2
0
1
2
1
2
1
2
0
1
2
2
2
2
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
2
2
1
1
2
1
2
0
0
1
1
2
1
1
2
1
1
1
2
2
1
0
2
2
1
2
1
1
1
1
0
1
1
1
1
1
0
1
1
1
1
2
0
0
2
1
0
1
1
1
1
2
0
1
0
1
2
1
1
1
1
0
1
1
1
0
1
1
2
1
1
1
1
1
1
2
0
1
0
1
2
1
1
1
1
1
0
2
1
2
1
1
1
1
2
0
1
2
2
1
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
2
2
0
0
1
0
0
1
1
1
1
1
2
1
1
2
1
2
1
1
2
2
2
1
1
1
1
2
1
1
1
1
1
1
1
1
0
0
1
2
0
1
2
1
1
2
1
2
2
1
1
1
1
1
1
2
1
4
1
0
1
1
1
1
2
0
1
1
0
0
1
0
1
1
0
1
1
1
0
1
2
2
1
2
1
0
1
1
0
1
1
2
1
2
1
2
1
1
0
0
1
1
1
1
1
0
1
2
1
1
2
0
2
0
1
1
1
1
1
1
0
0
1
2
3
1
0
1
0
0
1
2
0
2
2
2
1
2
2
1
1
1
1
0
1
1
1
0
1
1
2
1
1
2
1
1
0
1
1
0
0
0
1
1
0
0
1
1
1
0
1
1
1
1
1
2
1
1
0
1
2
0
1
1
0
1
2
1
1
0
1
2
1
1
0
1
1
1
1
2
0
2
2
2
0
2
1
1
2
2
0
1
1
0
1
1
1
1
1
0
1
0
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
0
1
1
2
2
2
0
1
1
1
2
1
0
1
2
2
1
1
1
1
1
2
2
1
1
2
2
0
2
1
0
1
1
0
2
2
0
0
1
2
2
0
1
0
1
1
1
0
0
2
1
1
1
1
1
1
0
1
2
1
2
1
0
1
0
1
0
2
0
2
1
1
0
0
1
1
1
1
2
1
1
1
0
1
2
1
0
0
1
2
0
1
2
1
2
2
2
1
2
1
1
1
1
0
2
1
1
2
1
1
0
1
2
2
1
2
1
2
1
1
1
0
2
1
1
2
0
1
1
0
2
0
2
1
0
1
1
2
1
2
1
0
2
1
2
2
1
0
0
1
1
1
1
1
1
1
1
1
2
1
1
1
0
1
1
1
1
0
1
1
1
1
1
1
0
1
1
1
2
2
1
2
1
2
1
1
2
2
1
0
2
1
1
2
1
1
1
1
2
0
1
2
1
1
1
2
2
1
2
1
1
0
0
2
2
0
1
1
2
0
2
2
1
0
1
1
2
0
1
1
2
2
2
1
2
1
2
2
1
1
0
0
1
1
2
1
1
1
1
1
1
2
1
1
2
0
1
1
0
1
1
2
2
1
1
1
1
0
2
1
1
1
1
0
1
1
1
2
1
0
0
1
1
1
0
0
1
1
2
1
0
0
3
1
0
0
1
0
1
2
1
1
1
1
0
1
1
1
0
1
0
0
1
4
2
1
0
1
2
1
1
1
0
1
2
2
1
0
0
1
0
0
1
1
1
1
1
1
0
1
2
0
1
1
1
1
0
1
2
1
1
1
1
1
1
1
0
1
1
0
0
1
0
1
2
0
2
1
0
1
1
1
1
1
4
2
1
1
2
1
1
0
1
1
1
1
2
1
2
1
0
1
1
2
1
0
1
1
2
1
0
2
1
1
1
1
1
2
1
1
1
1
1
2
0
1
1
0
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
1
1
2
0
1
1
1
1
2
2
2
1
1
1
2
0
1
1
0
2
0
0
1
1
1
1
2
1
1
1
2
2
2
1
1
2
0
2
1
1
0
1
1
0
1
1
0
1
1
1
0
0
0
2
1
1
1
1
2
1
1
0
2
2
1
1
1
1
1
1
0
1
2
0
1
1
0
0
2
1
2
1
2
1
0
2
2
2
0
1
2
1
1
2
2
2
0
1
1
1
1
2
1
1
1
1
0
1
2
1
0
0
1
1
0
1
1
1
1
0
1
0
1
0
1
2
0
2
2
1
1
1
1
0
1
2
1
0
1
1
2
1
1
2
2
1
1
0
2
1
1
1
1
0
1
2
1
0
2
1
0
3
1
1
2
1
1
0
1
0
0
3
1
1
0
1
2
1
1
2
1
1
2
1
1
1
2
1
0
1
0
1
1
1
2
2
1
0
1
1
1
1
1
1
1
0
1
1
2
1
1
1
1
1
1
0
1
2
0
2
1
1
2
2
2
1
1
0
1
0
2
1
1
3
1
2
1
1
0
2
2
1
2
1
2
2
2
0
1
2
2
2
0
1
2
2
2
1
0
0
2
1
1
1
0
0
1
0
0
2
1
1
1
0
1
1
1
1
1
2
2
1
2
1
1
2
0
1
1
2
1
0
1
2
2
2
1
2
1
1
1
2
1
2
1
1
1
0
2
2
1
1
1
1
0
1
2
0
0
2
1
0
1
1
1
2
1
0
1
1
0
1
1
1
1
1
1
2
1
0
1
1
0
3
2
0
1
1
1
1
1
0
0
1
0
2
0
1
1
1
0
1
0
2
1
1
1
1
2
2
3
1
1
2
1
1
1
1
1
2
1
1
1
1
0
1
2
1
1
1
0
1
1
2
1
2
1
1
1
1
0
1
0
2
1
1
1
1
1
1
1
1
0
1
2
1
0
0
1
0
2
1
2
0
2
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
2
0
1
1
1
1
1
1
0
1
1
1
1
4
0
1
1
1
2
1
2
0
1
1
2
1
1
1
1
1
1
2
2
2
1
1
1
1
2
0
0
2
1
0
0
0
1
1
0
1
1
1
0
2
2
1
1
2
0
1
0
3
1
1
1
1
0
0
1
1
1
0
0
2
0
1
1
0
1
1
1
1
2
1
1
0
2
1
2
1
2
0
1
1
1
1
0
1
2
2
0
1
1
1
2
3
1
0
1
1
1
1
1
1
2
1
2
1
1
0
0
1
1
1
0
0
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
0
2
1
2
0
1
1
1
1
1
1
2
0
0
0
2
2
0
1
2
1
1
0
0
0
0
2
0
1
1
1
1
2
2
1
1
1
1
1
1
2
2
2
1
1
1
1
0
1
1
1
1
1
1
1
2
1
2
0
1
1
1
2
1
0
1
1
1
0
0
0
0
1
1
0
1
1
1
2
1
2
0
1
1
1
0
1
1
1
1
1
0
1
1
1
1
2
0
0
1
0
1
1
1
1
1
1
1
1
0
0
1
1
1
0
1
1
0
0
1
1
1
1
1
0
1
1
1
1
1
0
1
1
2
1
1
2
0
2
1
2
1
2
1
1
0
2
1
0
0
2
0
1
1
1
1
1
1
1
2
1
1
0
2
1
2
1
1
1
0
0
1
2
1
1
1
0
1
1
1
0
1
0
2
1
1
1
1
2
1
1
1
1
2
1
0
1
2
1
1
1
1
0
0
1
1
3
1
2
1
1
1
1
1
1
2
2
2
1
2
1
1
1
2
1
0
1
2
1
2
0
1
2
1
1
1
1
0
1
3
1
1
1
2
2
2
2
1
5
1
1
1
2
1
0
2
2
2
1
1
0
1
1
2
1
2
0
2
2
0
1
1
1
1
0
1
1
0
1
1
1
1
1
1
1
2
1
2
2
1
1
2
2
1
2
1
3
0
0
1
0
1
1
1
0
2
0
1
1
2
2
1
1
1
0
0
1
1
1
0
0
1
0
1
1
1
1
1
0
1
1
0
2
2
1
2
1
0
1
2
1
2
1
1
1
1
0
1
1
1
0
1
1
1
1
2
2
0
1
1
2
1
1
1
1
0
1
0
1
2
1
1
3
1
2
1
1
0
1
1
1
3
2
0
1
1
1
1
1
0
1
2
1
0
1
1
0
2
1
1
2
1
0
0
2
0
0
1
1
1
1
1
2
1
1
2
0
1
1
1
0
0
1
2
1
3
1
0
1
1
1
1
1
1
0
1
0
1
1
2
1
1
0
2
3
1
1
1
1
1
1
2
2
1
1
1
1
2
1
2
2
1
0
1
0
1
1
1
2
1
1
1
0
1
1
0
1
1
0
1
1
1
1
2
2
1
1
1
0
2
1
1
1
1
0
2
1
2
1
2
0
1
1
2
1
1
2
0
1
2
1
1
2
0
1
2
2
2
1
2
1
2
2
1
1
2
1
1
1
1
1
2
0
1
1
0
0
2
1
1
1
2
1
0
1
2
1
2
1
0
1
1
2
1
2
2
2
1
2
1
0
1
1
1
0
2
0
2
2
2
2
1
0
1
1
1
2
1
2
2
1
1
1
0
0
1
2
2
1
1
2
1
1
1
0
2
1
1
1
0
2
2
1
1
1
1
2
0
1
0
1
2
1
1
0
1
1
1
1
1
0
1
1
1
1
2
0
1
0
0
0
1
0
2
1
0
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
0
1
1
1
1
2
1
1
1
1
2
2
1
2
1
1
1
1
2
1
1
1
0
1
1
1
0
1
1
1
0
1
2
1
1
2
1
0
1
2
2
1
2
1
1
2
1
1
1
2
0
2
1
2
1
0
2
1
2
0
1
1
0
2
1
1
2
1
1
1
0
2
2
0
1
1
1
0
1
1
2
2
1
1
0
2
2
1
1
3
1
2
1
1
0
2
1
2
1
1
0
1
2
1
1
1
1
1
0
1
1
2
2
0
1
1
2
1
1
1
1
1
2
1
2
1
1
0
1
1
1
2
1
1
0
1
1
0
1
1
1
2
1
2
1
1
1
2
1
2
1
1
1
1
1
1
0
1
2
1
1
1
1
1
1
1
2
1
0
0
1
1
2
1
2
2
1
1
1
0
1
1
2
1
1
1
1
0
0
1
1
1
0
1
2
1
1
0
2
0
1
1
2
2
0
0
1
2
1
1
0
1
1
2
1
2
1
2
0
1
1
1
1
1
1
1
1
2
1
1
1
0
1
1
1
0
0
1
0
0
1
1
0
1
1
1
2
1
1
1
0
1
0
1
2
1
1
0
1
1
1
1
1
0
1
1
1
2
1
0
1
0
2
1
1
1
0
0
2
2
1
2
1
0
2
2
1
2
2
1
1
2
1
1
1
1
1
0
2
0
0
1
0
1
1
0
2
1
1
1
2
1
0
2
3
0
0
1
0
1
2
0
2
1
1
1
1
2
1
1
2
2
0
1
2
2
1
0
1
2
1
1
1
1
1
1
1
0
1
1
0
1
1
0
2
1
1
1
2
2
1
1
0
1
1
1
2
1
1
1
1
1
2
1
2
0
1
2
1
1
2
2
1
0
1
2
2
1
1
2
1
1
1
1
1
1
0
2
1
1
2
2
1
1
1
2
1
2
1
1
1
2
1
1
2
1
1
1
1
1
2
1
1
0
1
0
1
1
0
0
0
0
0
2
1
1
1
1
2
0
1
0
3
1
0
1
0
0
1
0
1
1
0
2
2
1
1
1
1
2
1
0
0
2
1
1
1
2
1
2
1
1
1
1
0
1
2
0
1
1
1
2
2
1
1
2
2
1
1
2
2
2
2
1
1
1
0
0
0
1
0
1
2
0
1
1
3
2
1
1
1
1
2
1
1
2
0
1
1
1
1
1
1
1
1
2
0
1
1
0
1
2
2
1
1
1
2
1
1
2
0
0
2
2
1
1
1
0
0
1
1
1
1
1
1
1
1
2
1
0
0
0
0
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
2
2
2
1
1
2
2
1
1
1
2
1
1
1
1
0
1
2
2
2
1
0
0
1
2
1
1
1
0
2
1
1
1
1
0
1
2
1
1
2
1
1
1
2
1
1
1
1
2
2
1
3
0
3
1
1
1
2
1
0
0
1
1
1
2
1
1
4
1
1
0
0
2
2
1
2
1
2
1
0
1
1
0
0
1
1
1
0
1
2
1
1
1
2
2
1
0
2
2
1
1
2
1
0
1
2
1
0
2
2
0
1
1
0
1
1
2
1
1
1
2
0
2
1
2
1
0
1
1
1
0
0
0
1
0
1
2
2
1
2
1
2
1
1
0
1
1
0
1
1
1
2
1
1
1
1
2
0
0
2
0
1
1
1
1
2
0
1
0
0
2
1
1
1
1
0
4
1
1
2
1
3
1
1
1
1
1
1
0
1
2
1
1
2
1
1
2
1
1
1
0
0
1
0
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
2
0
1
3
1
0
2
0
1
1
1
2
1
1
1
1
2
1
0
1
0
1
1
1
1
1
1
1
1
1
2
0
0
1
1
1
0
1
1
1
1
0
1
2
1
1
1
1
0
1
1
1
2
0
0
1
0
1
1
1
0
0
1
1
2
1
2
2
1
1
1
1
1
1
1
2
1
1
1
2
1
0
1
0
0
1
1
1
2
1
0
0
1
2
2
1
1
0
1
2
1
1
1
1
1
1
1
1
1
1
3
0
0
1
1
5
0
1
1
1
1
1
3
1
1
0
1
1
1
0
2
1
0
1
2
1
1
0
1
2
1
1
1
1
1
0
1
1
0
1
1
1
1
1
1
0
2
1
1
1
1
1
0
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
2
1
1
1
0
0
1
1
1
1
0
2
0
1
1
1
2
2
0
0
0
1
0
1
1
2
1
4
2
1
1
0
1
1
2
1
1
1
1
0
1
2
1
1
1
0
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
2
2
1
2
0
0
1
1
2
1
1
0
1
0
2
0
2
1
1
2
1
1
1
0
1
2
1
1
1
1
2
1
2
1
1
2
2
1
0
0
1
2
2
2
1
1
1
0
2
2
0
0
2
1
1
1
2
1
2
2
1
0
1
0
0
2
0
2
1
2
1
2
2
1
1
0
1
1
0
0
1
2
1
1
2
1
2
0
2
1
2
1
3
0
1
1
2
1
2
1
2
1
0
1
0
1
3
1
2
2
1
1
2
2
2
1
2
1
1
1
1
1
1
1
1
1
1
0
1
0
1
1
0
0
0
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
0
2
1
2
1
1
3
1
1
1
0
1
1
2
1
0
0
2
1
2
2
2
1
1
2
2
1
0
1
1
0
1
1
1
0
0
1
1
1
1
1
1
2
1
0
0
1
2
1
2
1
1
0
1
2
2
2
2
1
1
2
1
1
1
1
0
2
1
2
0
0
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
0
1
0
1
2
1
0
2
1
1
1
1
1
0
2
1
2
1
1
1
0
2
2
1
1
0
0
0
0
1
0
1
1
2
1
1
0
2
0
2
0
1
2
2
0
2
1
1
1
0
2
1
0
1
1
2
2
1
1
1
0
1
1
2
1
1
1
1
2
3
1
1
1
1
1
1
0
2
1
2
2
1
2
0
2
1
1
1
2
2
0
1
1
0
2
1
2
1
1
2
3
1
1
0
0
2
2
1
1
0
1
2
1
1
1
1
1
1
1
1
1
1
1
0
2
1
1
1
2
1
2
1
2
2
1
2
1
1
0
2
1
2
1
1
2
1
1
1
1
2
0
0
1
2
2
1
0
1
2
0
1
1
2
1
1
1
0
2
1
0
1
1
0
1
0
2
2
1
1
2
0
0
1
2
0
2
1
1
2
1
2
1
1
1
1
1
1
2
2
1
1
1
2
3
1
1
1
0
1
2
1
1
1
0
2
1
2
1
1
1
1
1
1
1
0
0
2
0
2
0
1
1
1
2
1
1
2
1
2
2
1
1
2
2
1
0
1
2
1
1
0
0
2
2
0
0
2
0
2
1
1
1
1
1
2
1
1
0
0
0
1
1
1
2
2
2
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
0
1
1
1
2
1
1
0
1
2
1
2
1
1
1
2
1
1
1
2
1
1
2
1
1
0
8
2
0
1
1
1
2
1
2
0
2
1
1
1
0
0
1
2
1
1
1
0
1
2
1
1
1
1
1
1
1
1
0
1
0
0
1
1
1
1
1
1
1
0
1
1
3
1
1
1
2
1
2
0
1
1
1
2
2
0
1
2
1
0
0
2
1
2
1
0
1
0
1
1
2
1
1
0
1
1
2
2
1
1
2
2
1
0
2
1
1
0
1
1
1
2
1
1
2
1
0
0
2
0
1
1
1
1
2
1
0
1
1
1
0
1
1
0
0
1
0
1
0
2
0
2
2
1
2
1
2
1
0
1
1
1
1
1
1
2
1
2
1
0
1
1
0
0
1
0
1
1
1
1
0
1
3
1
1
1
2
1
1
1
2
0
1
0
2
0
2
1
1
0
2
1
2
2
1
2
1
1
0
1
1
1
1
1
1
1
2
1
0
2
0
1
0
0
1
2
1
1
2
1
1
2
1
1
0
2
0
1
1
1
2
0
0
1
1
0
1
1
1
2
0
0
1
1
1
2
1
2
0
1
1
2
2
1
1
1
0
2
2
2
0
1
2
1
1
2
1
2
1
0
2
1
1
1
1
2
1
0
1
1
0
1
0
2
1
1
2
0
2
0
1
0
1
1
0
1
0
1
1
1
2
0
2
1
1
1
3
1
1
1
0
1
0
0
1
1
1
0
1
1
1
0
2
1
1
1
0
0
0
2
1
0
1
2
2
1
0
1
1
2
2
0
0
0
1
1
2
2
2
1
2
1
2
0
2
3
1
1
0
2
2
1
0
1
2
1
1
1
1
1
2
0
0
0
1
1
1
1
1
1
0
1
2
1
1
1
0
0
1
0
2
2
0
0
1
1
1
1
1
1
1
2
1
0
0
1
2
1
2
1
1
0
2
0
0
1
2
0
1
1
1
1
1
1
2
2
2
1
1
1
1
2
2
1
2
1
1
1
1
1
2
1
1
1
1
1
1
2
0
1
2
2
1
1
0
0
1
1
1
0
1
1
2
1
2
1
1
1
1
2
2
0
1
1
1
1
1
1
0
2
1
1
2
2
0
1
1
1
1
1
1
2
0
1
1
1
2
0
1
1
2
2
0
1
2
2
0
1
2
2
1
1
1
1
2
1
1
0
2
1
2
2
1
1
1
2
1
2
1
1
2
0
1
1
2
1
1
0
1
1
0
1
1
1
0
0
0
2
2
2
1
1
1
1
1
1
1
0
1
0
1
0
0
0
10
1
1
0
1
0
1
0
2
2
1
2
1
1
2
2
0
1
1
1
2
1
1
3
0
0
2
0
1
1
1
1
0
1
1
1
1
1
1
2
1
1
1
1
1
1
1
0
1
0
1
2
2
1
1
0
1
1
2
1
1
2
2
1
1
2
1
0
1
1
0
1
1
0
1
1
1
1
2
1
1
0
1
1
1
1
2
1
2
2
1
1
1
0
1
1
2
2
1
1
2
1
0
1
1
0
1
1
1
2
0
2
1
1
2
0
1
0
2
1
0
2
1
1
0
1
2
2
2
1
1
1
1
2
1
1
1
1
1
1
2
1
2
2
0
1
2
1
1
1
2
1
0
1
2
1
1
2
2
1
2
1
1
2
1
0
1
1
1
2
2
1
1
0
2
1
1
2
0
0
2
1
2
1
1
2
2
1
2
1
1
0
0
1
1
2
1
2
2
1
1
2
2
1
2
1
2
1
0
2
1
0
1
0
1
2
0
1
1
1
2
1
0
1
1
1
1
1
1
1
1
3
1
1
1
1
0
1
1
1
1
1
1
1
0
1
1
1
1
2
0
0
1
2
1
2
0
3
0
1
1
0
1
1
0
2
2
2
1
1
0
0
2
2
1
0
0
0
1
1
0
1
1
1
1
0
1
0
1
1
1
1
1
1
1
1
2
1
2
2
2
1
1
0
1
1
0
2
1
1
1
2
1
1
2
1
1
1
0
0
1
2
1
1
2
1
2
2
2
0
1
1
1
1
1
1
1
0
1
1
1
1
1
1
2
0
2
1
0
1
2
1
1
2
1
2
1
0
1
1
2
3
1
0
1
3
2
1
1
2
1
1
1
0
0
2
2
0
1
1
1
1
1
1
1
2
1
1
1
1
0
1
2
2
1
1
2
1
1
2
1
1
1
1
1
2
1
0
2
1
1
1
1
2
1
1
1
1
0
1
2
0
1
0
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
0
1
3
1
1
1
0
0
0
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
0
1
0
1
0
1
0
1
1
1
1
1
1
1
0
1
1
1
2
1
1
1
0
1
0
2
1
1
0
2
1
1
2
1
2
2
1
1
1
1
0
0
2
1
0
1
1
1
1
2
1
0
2
1
0
2
1
1
2
1
2
1
2
1
1
1
0
1
1
1
1
1
1
2
1
1
1
0
1
2
0
1
0
1
1
0
2
0
0
1
1
0
2
1
1
2
2
1
0
1
0
1
0
2
1
1
2
1
1
1
1
1
1
1
0
1
0
1
1
1
1
1
2
1
1
1
1
1
1
0
0
1
3
1
1
2
1
1
1
1
0
1
1
0
1
1
1
1
0
2
1
0
1
2
1
1
1
1
0
1
2
2
1
1
1
1
1
2
2
1
1
1
0
1
1
1
2
1
2
0
1
1
2
1
1
1
1
1
0
1
1
1
1
1
1
2
1
1
2
1
0
3
0
2
1
1
2
1
1
1
0
6
2
1
1
1
2
1
1
0
1
1
2
1
0
1
0
1
1
2
1
1
1
1
3
1
2
1
3
2
0
2
0
1
1
0
1
1
2
1
0
2
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
3
0
0
0
1
1
3
2
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
0
3
2
1
1
1
0
1
0
1
1
0
1
1
1
1
0
1
1
1
2
1
2
1
1
1
0
1
0
0
2
1
0
0
0
1
0
2
1
1
1
1
1
1
2
0
2
1
1
0
0
1
0
1
0
1
0
1
2
0
0
1
2
3
1
1
1
0
1
1
2
1
0
0
2
0
0
1
1
3
0
1
3
1
2
1
1
1
1
2
0
2
3
1
1
1
1
2
1
3
2
2
1
0
1
1
1
1
2
1
0
1
1
1
2
2
0
0
1
2
2
2
1
0
1
1
1
2
1
2
1
2
2
1
0
1
1
0
2
1
0
1
0
1
2
1
1
1
2
2
2
1
1
1
1
1
1
1
1
1
1
2
2
0
2
0
0
1
1
1
0
2
2
1
1
1
1
1
2
1
0
0
0
2
0
1
1
1
2
0
1
1
1
0
1
1
3
2
1
1
0
0
2
1
2
1
0
0
1
0
1
0
2
1
0
0
1
1
1
1
1
0
1
1
0
1
1
1
1
2
2
2
0
2
0
1
2
3
1
1
2
3
1
1
0
1
2
1
1
0
1
1
2
2
1
0
1
1
0
2
0
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
0
1
1
1
0
2
1
0
0
2
1
1
2
2
1
0
2
1
1
2
0
0
0
0
2
1
1
2
2
1
1
0
1
1
2
1
1
0
1
1
1
1
2
2
1
1
2
1
1
1
1
1
0
2
1
1
2
1
1
0
2
1
1
1
2
1
0
1
2
2
1
1
1
1
2
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
2
1
1
2
0
2
1
1
0
2
1
1
1
0
2
1
0
2
0
2
1
1
1
2
1
2
2
2
2
0
2
1
1
2
1
2
0
1
2
1
2
1
2
1
2
1
1
1
1
1
1
2
1
2
1
3
2
1
1
2
1
2
0
2
1
0
2
0
2
0
1
1
2
0
1
1
1
1
1
1
1
1
1
2
1
0
2
0
2
1
2
0
2
1
2
2
0
0
0
0
3
1
2
1
1
1
1
0
1
1
2
1
2
2
2
2
2
0
2
0
1
0
1
1
1
1
2
3
1
0
1
1
1
1
2
2
0
1
1
1
1
1
0
0
1
0
1
2
0
0
0
1
1
2
1
1
1
1
0
1
2
1
2
1
1
2
1
1
0
2
1
2
0
0
1
1
1
1
1
0
1
2
1
1
0
1
0
1
1
0
1
1
1
1
1
1
1
1
1
1
0
2
1
1
1
1
1
1
2
1
1
1
2
1
1
0
1
0
1
1
0
3
0
1
1
2
1
2
1
1
0
0
0
1
2
1
1
1
1
2
2
1
1
1
1
3
0
1
2
0
1
0
0
1
1
2
1
1
1
0
1
1
1
1
2
1
2
2
2
1
2
1
1
2
1
0
2
1
1
0
1
1
1
1
1
1
1
2
0
2
2
1
2
1
1
1
1
1
1
1
3
2
2
1
0
1
0
1
1
2
1
1
2
1
0
1
2
1
0
1
1
1
0
1
1
1
1
2
2
0
1
2
1
0
1
2
0
1
0
1
1
1
1
1
0
1
0
1
1
1
0
0
1
1
1
1
2
2
0
1
1
1
3
1
1
2
1
2
1
1
0
1
1
0
1
1
2
1
1
2
1
0
0
1
2
2
0
1
1
2
2
2
1
1
2
1
0
2
0
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
1
0
1
1
1
1
0
0
1
2
1
1
0
1
1
1
1
1
1
0
0
1
1
1
1
0
1
1
1
0
0
1
1
1
1
2
1
2
1
0
1
0
1
1
3
2
1
1
0
1
2
1
2
2
1
2
1
2
1
1
1
2
1
2
0
1
1
1
1
0
1
2
2
2
1
1
2
2
0
0
1
0
1
1
2
1
2
1
1
1
0
1
2
0
2
1
0
2
1
1
2
1
2
1
1
1
2
2
1
0
1
0
0
1
1
0
2
2
1
1
2
0
1
2
2
1
0
1
1
1
2
0
1
1
1
1
1
2
1
1
0
1
1
0
1
2
2
2
2
2
1
1
0
1
1
0
2
1
1
1
1
1
1
1
1
0
1
1
2
2
1
1
1
0
1
1
1
1
2
1
1
2
1
1
1
0
1
1
1
2
1
1
0
2
1
1
0
1
0
2
3
1
1
1
2
2
0
1
0
1
1
1
2
1
0
0
0
2
0
2
1
1
1
1
1
2
1
2
1
1
1
2
0
1
1
1
2
1
1
2
1
1
0
2
1
0
2
0
1
0
0
2
1
2
1
0
0
1
1
1
1
1
1
2
0
1
2
2
2
0
1
1
1
1
1
0
1
1
1
1
1
1
0
1
1
1
1
2
1
1
0
2
2
0
1
1
2
2
0
2
2
1
1
2
2
1
1
1
0
2
2
0
2
0
0
1
1
0
2
1
1
1
1
2
1
2
1
2
1
0
0
1
2
1
1
2
1
1
0
1
2
2
0
0
1
0
1
0
1
1
1
1
2
1
0
2
1
1
1
0
0
2
2
1
2
1
1
1
1
1
2
1
1
1
4
1
1
1
1
1
0
2
0
0
2
2
1
2
2
1
0
0
2
1
0
1
2
2
1
0
1
2
1
1
0
2
1
0
2
2
0
2
0
0
1
1
1
1
2
0
1
2
0
1
0
2
0
1
2
1
2
2
1
1
1
1
2
0
1
1
0
1
0
1
1
0
2
1
1
0
1
1
1
1
1
1
2
1
1
2
0
1
0
1
2
2
2
2
1
2
2
1
1
3
1
1
1
1
1
2
0
1
1
1
0
1
1
2
2
1
2
0
5
1
0
1
0
1
1
1
1
1
1
1
1
0
2
1
0
1
1
1
1
2
0
0
1
1
2
1
1
1
2
1
2
0
1
1
1
1
1
1
0
1
1
0
2
2
1
2
3
1
0
1
1
1
2
1
1
1
1
1
1
1
2
2
0
0
1
1
1
2
0
2
2
0
1
1
1
0
1
1
1
1
2
1
2
2
1
1
3
0
7
2
2
2
0
1
2
1
1
0
2
0
2
0
2
1
1
0
2
1
1
2
1
1
1
2
1
2
3
2
1
2
0
2
2
1
1
1
1
1
1
2
0
1
2
2
2
0
1
2
1
0
0
0
0
1
1
2
1
0
0
1
0
1
1
0
1
1
1
0
1
1
1
1
0
0
2
2
1
2
1
0
1
2
1
0
1
1
2
1
1
1
1
2
1
1
0
1
0
2
1
2
1
2
1
1
1
3
2
0
1
1
4
1
0
2
1
1
1
1
1
2
1
1
0
1
1
3
2
0
0
1
3
0
0
2
1
1
1
1
2
2
2
1
2
1
1
1
1
1
2
1
2
1
1
1
2
1
2
3
1
1
0
1
1
1
1
1
0
1
1
1
2
2
1
1
2
2
1
1
3
1
1
1
2
1
0
2
1
1
2
1
1
0
1
1
1
1
0
1
2
1
2
1
1
1
1
1
0
1
1
1
1
1
1
1
0
2
1
1
1
1
1
2
1
1
0
2
1
1
0
2
1
1
2
1
1
2
1
0
1
1
1
1
1
1
1
2
2
0
1
1
1
2
1
2
0
1
2
1
0
1
2
1
0
1
2
2
3
0
0
1
0
0
0
1
1
1
1
1
1
1
1
1
1
1
0
1
1
2
0
1
0
1
1
1
1
1
2
1
1
1
2
1
1
1
0
1
2
1
0
1
1
2
1
1
2
0
2
2
2
0
2
1
1
2
1
1
1
2
0
1
1
1
1
2
1
0
2
0
1
2
1
0
0
1
1
1
1
1
0
1
0
2
2
0
1
1
1
0
0
0
1
0
1
2
0
1
2
1
1
2
1
2
1
1
1
0
2
3
0
2
2
1
1
1
1
2
1
0
1
0
1
1
2
1
1
0
1
1
1
1
0
0
2
1
1
2
1
1
0
2
1
1
1
1
1
1
0
2
1
0
1
1
1
2
1
1
1
1
0
1
2
2
0
3
1
1
1
2
1
1
1
0
2
1
1
1
1
1
1
0
1
1
1
2
2
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
2
0
0
1
1
1
1
0
1
1
2
2
1
0
1
1
2
1
1
1
0
1
2
2
0
1
1
1
0
2
1
1
1
1
1
1
1
2
1
0
2
1
1
1
0
0
1
1
2
2
1
1
1
0
0
2
1
2
1
1
1
1
1
0
1
1
0
1
2
1
0
1
1
0
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
0
1
0
2
0
1
1
1
1
0
2
3
0
1
1
1
1
1
1
2
1
2
1
1
0
2
1
1
0
1
1
1
1
0
1
2
1
1
0
1
1
1
1
1
1
0
3
3
1
2
1
2
2
1
1
1
0
2
1
1
1
1
0
1
0
1
0
1
1
1
0
1
1
0
1
2
1
1
1
1
0
2
1
0
2
1
2
2
2
0
1
1
0
0
1
1
1
1
2
1
1
1
2
2
1
2
2
2
2
2
2
1
1
1
1
0
2
0
1
0
2
1
1
1
2
2
1
0
2
0
1
1
0
2
1
1
2
1
1
0
1
1
1
1
2
1
2
0
1
1
0
1
1
1
2
0
1
2
1
1
1
1
2
1
1
2
0
0
2
1
0
1
2
1
1
1
1
0
1
2
2
2
2
1
2
1
0
1
1
1
2
1
1
1
0
0
1
1
0
2
2
1
1
1
0
2
1
0
2
0
1
1
0
2
0
1
2
1
1
2
0
1
0
0
0
1
1
2
1
1
1
0
1
2
1
1
0
1
0
0
1
1
1
0
1
1
1
2
2
1
1
1
1
1
0
2
2
1
1
2
1
1
1
0
2
0
1
1
1
0
1
1
1
2
1
1
1
2
1
1
1
0
1
1
1
1
1
0
0
1
0
0
0
1
2
1
0
1
2
0
1
1
0
1
1
1
1
1
1
2
2
0
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
2
2
0
1
1
1
1
1
1
2
2
2
0
1
1
2
1
0
1
1
1
1
1
2
1
1
0
1
0
0
2
0
2
0
1
1
0
0
0
1
1
0
1
0
1
0
0
0
2
1
1
1
1
1
2
2
2
1
1
1
1
2
1
1
1
2
0
1
1
0
1
1
2
0
1
1
1
0
2
1
2
1
0
2
2
2
1
2
2
1
1
2
1
1
2
1
2
1
1
2
1
2
1
2
0
2
1
1
2
0
2
2
1
1
0
2
2
1
1
0
1
1
1
2
0
1
1
0
2
1
1
2
1
1
0
1
1
1
1
0
1
1
1
0
1
2
1
1
0
1
0
0
1
1
1
1
1
0
2
1
1
0
2
1
0
2
1
1
1
1
0
1
1
2
1
0
2
0
1
0
2
0
2
1
0
1
2
1
2
1
1
2
2
1
1
2
1
2
2
1
1
1
2
2
1
0
1
0
1
1
1
1
1
2
1
0
0
2
0
0
2
0
1
1
2
2
1
2
1
0
0
1
1
2
2
1
0
2
2
1
2
2
2
2
2
1
1
2
1
1
1
1
1
0
1
1
1
1
1
1
1
1
2
0
1
1
1
1
2
0
1
1
1
1
2
0
1
1
1
1
2
1
1
0
3
0
1
1
1
1
2
0
1
1
1
1
1
1
1
1
2
0
0
1
1
2
1
1
1
2
0
1
2
2
1
0
1
1
1
0
1
1
1
1
0
1
1
1
0
1
1
1
0
1
0
0
1
3
2
0
1
0
1
2
2
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
0
1
1
1
2
1
2
1
1
1
2
0
0
2
0
0
1
1
1
0
0
1
1
0
2
1
1
0
1
2
1
0
1
2
1
0
1
1
1
1
2
0
2
0
2
1
1
1
0
2
1
2
1
0
1
1
1
0
1
1
2
2
2
1
4
1
2
1
2
1
1
2
0
0
2
1
2
1
1
2
1
1
0
2
1
0
1
0
1
1
1
1
0
1
1
1
1
1
1
1
0
2
1
1
1
0
2
1
0
1
2
2
1
1
0
1
0
1
2
2
1
0
1
2
0
1
1
1
1
0
2
1
1
1
1
0
2
0
1
1
2
1
1
1
2
1
1
0
2
2
1
1
1
2
1
1
1
1
1
2
2
0
0
2
1
1
1
1
1
0
1
2
1
0
2
0
1
2
0
1
2
1
1
1
1
1
1
1
2
0
1
2
1
1
0
1
1
1
1
2
2
0
1
1
2
1
2
1
2
2
1
0
2
2
1
2
1
1
1
3
1
1
1
0
2
1
1
1
0
0
1
1
1
1
2
2
0
1
1
2
1
1
2
1
2
0
1
0
1
2
1
0
2
0
1
2
2
0
0
1
1
0
0
1
2
2
1
0
1
1
1
1
1
1
2
1
2
1
1
1
1
1
2
1
2
2
2
1
0
1
1
1
1
0
0
1
1
0
1
1
0
1
1
1
1
1
0
2
1
0
2
1
2
2
1
2
2
0
1
1
1
2
0
1
0
2
6
0
1
0
1
1
2
1
1
0
2
1
2
1
1
1
2
1
1
1
1
1
0
2
2
1
1
1
2
1
2
1
1
1
1
0
1
1
1
1
1
1
1
2
1
1
0
1
1
0
1
1
2
1
0
0
0
1
0
1
0
1
1
1
0
1
0
1
1
1
1
1
1
0
1
1
1
0
1
1
1
2
2
2
1
1
1
1
1
1
1
1
1
1
1
0
0
1
0
0
1
2
1
1
1
1
2
1
2
1
1
0
1
1
2
2
1
1
1
1
2
2
1
1
1
0
1
1
1
1
0
0
2
1
2
2
1
2
2
0
2
1
1
2
1
0
0
2
1
1
2
1
1
1
1
1
2
1
2
2
2
1
1
1
0
1
0
2
0
2
1
0
0
0
1
1
2
1
0
2
1
2
0
2
1
0
2
0
2
1
1
1
0
0
2
1
0
1
1
1
1
2
1
1
1
2
2
2
1
1
1
2
1
0
1
1
2
1
0
1
0
1
1
1
1
1
0
1
1
3
2
2
3
1
0
0
1
2
1
1
2
1
1
1
1
1
1
0
1
1
0
1
0
1
2
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
0
1
0
1
0
1
1
2
1
0
1
2
2
0
1
0
1
0
1
1
1
2
1
0
1
1
2
2
2
2
1
1
2
2
1
1
1
1
2
1
1
2
0
1
0
0
0
1
2
1
1
1
1
0
0
1
2
2
1
2
1
1
1
1
0
2
1
1
1
1
2
2
1
1
1
1
2
0
0
2
0
1
2
2
2
1
1
2
1
2
2
1
2
1
1
1
1
2
0
1
1
3
2
1
1
1
2
1
1
2
2
2
1
2
0
1
1
1
1
1
0
1
1
1
0
1
1
0
0
1
1
0
0
0
2
1
2
1
1
0
1
0
1
2
1
1
2
1
0
1
2
1
2
0
0
1
0
1
1
1
1
2
1
0
3
1
1
0
1
1
2
1
1
1
0
1
2
1
0
2
1
1
1
0
0
1
1
1
0
0
1
3
2
0
1
1
1
2
1
0
2
0
1
1
0
1
1
1
0
2
1
1
1
1
1
0
2
2
1
2
1
1
1
1
1
1
1
1
1
1
1
2
0
2
1
2
0
2
1
2
1
1
1
1
2
2
1
1
1
0
0
1
1
1
1
1
0
2
2
4
0
0
0
1
0
1
1
1
1
1
0
1
1
1
0
1
2
1
0
2
1
0
0
2
1
2
0
2
1
1
1
1
1
1
0
1
0
1
0
1
1
1
1
1
2
0
0
1
1
0
0
0
1
1
0
2
0
1
1
0
0
2
2
1
1
2
1
0
1
1
1
1
0
1
2
2
0
1
1
2
2
1
1
1
1
0
1
1
2
0
1
1
1
0
2
1
1
0
1
1
0
1
1
1
1
1
0
1
1
1
0
1
0
2
1
0
2
1
2
2
1
1
1
0
1
1
1
1
1
0
1
1
0
1
1
2
2
2
1
2
2
0
1
0
2
0
2
1
1
0
2
1
2
2
0
2
1
1
1
1
1
0
1
1
0
3
2
2
2
1
1
1
1
1
1
1
0
1
2
2
2
1
2
2
1
0
0
1
1
0
0
0
1
2
0
1
1
3
1
1
1
1
1
2
1
2
2
0
0
3
1
1
1
1
2
0
1
1
0
1
1
1
1
1
0
2
1
1
2
2
0
1
1
2
1
1
2
1
1
1
1
0
0
0
0
1
1
1
2
3
1
1
1
1
1
1
1
0
1
1
1
1
1
0
1
1
1
1
1
2
0
1
0
0
1
0
1
2
0
1
1
1
2
1
1
1
1
1
1
0
1
1
1
1
1
2
1
1
1
2
1
1
2
1
0
0
1
1
1
1
1
1
2
1
1
0
1
0
1
1
0
0
0
1
0
0
0
2
1
2
2
1
2
1
2
2
1
0
1
2
1
2
1
0
0
1
1
1
2
2
2
0
2
0
1
1
2
3
1
1
1
1
1
0
0
0
1
1
1
2
2
1
0
0
1
1
1
0
2
2
1
2
2
1
1
1
2
1
1
1
0
1
2
1
1
1
1
1
1
2
1
2
2
1
1
1
1
4
1
0
1
1
1
1
1
2
1
1
0
0
2
1
0
1
2
2
1
1
1
0
1
2
1
1
0
1
0
1
1
0
0
2
1
1
0
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
0
2
0
1
1
1
1
2
1
1
2
1
0
1
1
1
0
2
2
1
1
1
3
0
0
2
1
1
0
1
1
1
0
1
0
1
2
0
1
2
2
1
1
1
1
2
0
0
1
1
1
2
1
1
0
1
2
1
1
1
1
2
2
1
1
1
2
1
1
2
1
1
1
1
3
0
1
2
1
1
1
2
1
0
1
2
1
1
1
1
1
2
1
0
1
2
1
2
2
2
0
1
2
0
0
1
1
0
1
2
2
1
0
1
1
2
1
1
0
1
1
1
2
2
2
1
1
1
1
1
1
2
1
1
2
0
1
1
1
0
0
1
2
1
1
2
2
1
2
2
1
1
0
1
1
1
0
1
1
0
1
1
1
1
2
2
2
1
0
0
2
2
1
2
1
1
1
1
2
0
1
2
1
1
0
2
2
1
0
1
1
1
2
0
2
1
1
1
1
2
1
1
1
1
1
1
2
0
1
0
1
1
1
1
1
1
1
1
0
1
2
2
1
3
1
0
1
2
1
3
1
1
0
1
1
3
1
0
1
2
1
1
1
1
1
1
1
1
1
1
0
1
1
0
0
2
1
0
0
0
0
2
2
2
2
1
2
0
1
1
2
1
2
1
1
1
0
1
2
1
1
1
0
1
1
0
2
1
1
1
2
1
0
1
2
0
1
1
1
2
1
0
0
2
1
1
0
1
1
0
2
2
1
1
1
1
0
0
1
2
1
0
2
1
0
1
0
0
2
1
2
1
2
1
0
2
0
0
1
1
0
0
0
1
0
2
0
2
1
0
2
0
1
0
2
1
1
0
2
1
0
0
2
1
0
1
0
2
1
2
1
1
0
1
0
1
1
1
1
0
0
1
1
1
2
1
1
2
1
1
1
0
1
1
1
1
2
0
2
2
1
1
1
1
1
2
1
0
1
1
1
1
1
0
2
2
1
1
1
1
1
1
1
2
1
0
0
3
1
2
1
1
1
1
1
1
1
1
1
1
1
1
3
1
1
0
1
1
1
1
1
2
2
1
1
1
1
1
2
0
1
1
0
1
1
2
1
1
1
2
1
0
1
1
1
1
1
2
1
1
2
2
0
2
1
1
1
0
1
1
1
1
0
0
2
1
2
1
3
2
1
1
1
1
1
2
0
2
2
2
1
1
1
1
1
2
1
2
0
0
1
2
2
0
0
1
1
2
0
1
1
2
1
0
1
1
0
1
1
2
0
1
0
1
1
2
2
1
2
0
2
2
0
1
2
1
1
1
1
1
1
2
1
1
1
0
1
2
1
1
1
2
0
1
0
1
2
2
1
1
0
1
1
1
2
1
0
2
1
1
2
0
2
1
1
1
2
2
1
0
1
1
0
2
0
0
1
1
1
1
1
1
1
0
0
1
1
1
2
1
1
1
1
1
2
2
0
1
1
1
2
2
0
2
2
0
0
2
1
1
1
1
1
1
0
2
1
1
1
1
1
0
0
2
1
1
1
2
1
1
1
1
1
2
1
2
1
1
0
0
2
1
2
1
1
1
1
1
3
1
2
1
1
1
0
0
1
1
2
1
0
1
2
1
2
1
1
1
1
1
2
1
0
1
1
1
1
1
0
1
0
0
2
2
2
5
1
1
2
1
2
2
1
2
2
1
1
0
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
2
1
0
0
1
1
1
0
1
2
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
2
1
2
1
0
1
1
1
1
1
2
2
1
1
0
0
1
2
0
2
2
2
0
1
3
1
2
1
0
1
0
1
0
1
1
0
0
0
1
1
2
0
1
2
1
1
1
1
1
2
2
0
1
1
1
2
0
1
1
1
1
1
1
1
1
1
1
1
1
0
1
2
1
0
1
2
1
1
0
2
2
1
1
0
1
2
1
1
1
1
1
0
2
2
0
1
2
2
1
2
2
3
0
1
2
1
2
2
0
1
1
1
1
1
2
2
1
1
1
0
1
0
0
1
1
1
2
2
1
2
1
1
2
2
1
1
1
1
2
1
2
1
1
2
1
0
1
1
0
2
0
0
1
1
1
2
1
0
1
1
1
2
3
1
1
1
0
1
1
1
0
1
0
1
1
0
2
0
1
2
1
0
1
0
0
0
1
1
3
1
1
0
1
1
1
2
1
1
1
0
2
1
2
1
1
1
1
1
1
0
1
2
2
2
2
2
1
1
2
1
0
1
0
0
1
2
1
1
2
1
0
2
1
1
1
2
0
1
1
1
1
1
1
0
0
2
2
1
1
0
1
1
1
1
0
1
2
1
2
1
1
1
2
0
0
1
1
1
1
0
2
1
1
2
0
1
1
1
1
1
0
2
7
0
1
2
0
0
0
0
1
2
1
0
0
0
1
1
2
2
2
1
2
1
1
2
2
0
1
1
1
7
2
1
0
2
1
1
2
1
1
0
2
2
2
1
1
1
1
2
1
1
0
2
1
2
0
1
2
1
1
1
0
1
1
1
1
1
1
2
1
1
1
0
1
1
1
1
1
1
1
2
1
1
1
2
2
1
2
1
1
1
1
1
1
0
1
1
1
1
1
2
1
2
1
2
1
2
2
0
2
2
1
1
1
1
1
1
1
1
0
1
2
2
3
1
1
1
2
1
1
2
1
0
1
1
1
2
0
2
2
1
1
2
1
1
3
0
1
1
0
1
2
1
2
0
1
2
0
1
0
1
1
1
1
1
0
1
1
1
1
0
2
0
2
1
1
1
1
1
1
1
1
0
1
1
1
1
1
2
1
1
1
0
1
1
0
2
1
1
2
1
1
1
1
2
0
1
1
2
0
1
1
1
2
1
0
1
2
1
1
1
2
1
0
1
1
1
2
1
2
2
1
2
2
1
1
2
1
0
2
1
1
1
1
1
2
2
1
1
0
1
1
2
2
1
2
1
2
1
1
0
1
0
1
1
0
2
0
1
1
1
1
0
1
2
0
1
1
2
1
1
1
0
1
1
2
0
0
2
1
1
0
2
0
1
1
1
0
1
1
1
0
2
2
0
1
1
1
1
1
1
1
1
2
2
1
2
2
1
1
0
1
0
0
1
0
1
1
1
2
1
2
1
2
2
0
1
1
0
1
1
2
1
1
1
1
0
1
1
1
1
2
1
2
0
1
0
3
2
1
0
1
0
1
1
1
0
1
1
1
1
2
1
1
1
1
1
1
1
0
1
0
0
1
2
1
2
1
1
1
1
1
2
0
1
1
1
1
1
2
1
1
1
1
1
1
0
1
0
2
0
2
1
1
1
1
2
1
1
1
2
1
1
0
1
1
1
0
1
1
1
1
1
0
1
2
1
1
1
0
1
0
2
2
1
1
1
0
1
1
1
1
1
1
1
2
0
1
1
2
1
1
1
1
1
0
1
2
1
1
2
0
1
1
0
0
1
2
1
0
0
1
2
1
1
0
2
2
1
2
1
1
3
1
1
0
0
0
2
1
2
1
1
1
1
2
1
2
2
1
1
1
1
1
2
2
0
1
1
2
2
1
2
1
2
1
1
2
2
1
0
1
1
2
1
1
1
0
1
1
1
1
1
1
1
0
1
0
0
1
0
2
0
1
1
1
1
1
4
1
1
1
1
2
1
2
2
2
1
1
2
2
1
1
2
0
1
2
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
0
1
2
1
1
2
1
1
1
1
1
0
1
0
1
1
1
2
1
1
2
2
1
1
2
1
1
1
2
0
1
1
1
2
1
1
1
2
1
1
2
1
1
2
0
1
2
2
1
0
2
1
1
1
1
0
1
1
2
0
1
1
1
2
2
2
1
0
1
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
2
0
2
0
1
1
1
2
2
1
2
1
1
0
2
1
1
1
0
0
1
2
2
1
1
1
2
1
0
1
1
1
0
2
0
2
1
1
2
2
1
1
1
1
2
0
1
1
1
1
1
1
1
1
1
3
1
0
1
1
1
2
1
1
2
1
0
2
1
1
1
2
4
2
0
0
0
0
0
2
0
1
2
0
0
2
1
1
1
2
2
2
2
1
1
2
1
1
0
2
0
2
0
1
1
0
2
1
2
1
1
2
2
1
1
2
1
1
2
0
1
1
1
1
0
1
1
1
1
0
1
0
2
1
1
2
2
0
0
2
1
1
0
0
2
0
1
1
1
1
2
1
1
2
1
0
1
2
2
1
0
2
1
1
0
2
1
0
0
1
1
1
2
1
0
1
2
2
1
0
1
2
1
2
1
0
2
0
2
1
1
1
1
1
2
1
2
1
0
1
1
0
0
1
1
2
5
1
2
0
1
1
1
0
1
4
0
1
2
1
1
0
0
1
1
1
1
0
2
1
1
2
1
2
2
1
1
0
1
1
1
1
1
1
1
1
1
2
0
1
1
1
1
1
1
0
2
0
1
1
3
2
1
1
1
0
2
2
1
2
2
1
0
1
2
1
2
1
0
0
2
0
1
0
1
0
1
1
1
1
2
0
1
0
1
2
1
2
2
0
0
1
0
1
1
1
2
1
1
1
0
1
1
1
1
1
1
2
0
1
1
1
1
0
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
3
1
1
0
0
1
2
1
1
1
1
2
0
2
0
1
3
1
2
1
1
2
0
1
1
1
3
1
1
1
2
1
2
1
1
1
0
2
1
1
2
1
2
1
0
1
2
2
1
1
1
1
1
1
1
2
0
2
2
0
1
0
0
1
2
2
0
1
2
0
1
1
0
2
1
2
1
0
1
1
1
1
1
1
2
2
2
1
0
0
1
1
1
1
1
1
0
1
1
1
2
1
1
1
1
1
2
2
1
0
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
2
0
2
2
0
0
1
1
1
1
1
2
2
2
1
2
1
3
0
2
1
1
0
2
1
1
0
1
0
1
1
2
0
0
1
1
2
1
1
1
0
2
2
0
2
1
2
1
2
1
1
1
2
1
1
1
0
2
1
1
1
1
1
2
0
1
1
2
2
2
1
1
1
1
0
1
1
1
2
1
1
1
2
1
1
1
0
1
1
2
1
1
1
1
0
2
1
1
1
1
2
0
1
1
1
1
1
2
0
1
0
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
0
1
2
1
0
0
1
0
1
1
2
0
0
1
0
1
1
1
1
1
1
1
2
1
2
1
1
1
0
1
2
0
1
1
2
2
0
1
1
1
2
0
1
1
1
0
0
0
1
1
2
2
1
1
1
2
1
0
1
1
1
0
0
1
2
1
2
2
0
2
2
2
0
1
2
1
1
1
1
2
1
1
1
5
1
2
1
1
1
0
0
1
0
1
1
1
2
2
2
1
1
1
1
1
1
1
2
0
0
1
1
3
2
1
1
2
1
1
1
0
0
2
1
2
0
0
0
2
1
0
1
1
1
0
1
2
0
1
1
2
2
1
1
2
1
0
1
0
2
0
2
1
1
1
1
1
2
2
1
1
1
0
2
2
1
2
1
1
2
1
1
0
2
1
2
0
0
2
1
1
1
0
1
1
2
0
2
1
1
0
1
2
1
1
1
1
2
1
2
1
1
1
0
0
1
2
1
3
1
2
1
0
1
1
2
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
1
2
2
1
0
2
1
0
0
0
1
1
1
1
1
2
1
0
0
1
2
0
0
1
1
2
0
1
1
0
2
2
2
1
1
2
0
1
1
1
1
2
1
1
2
1
0
1
1
1
1
2
1
1
1
1
0
1
1
1
1
1
1
2
1
1
1
2
1
1
0
0
1
1
1
0
0
1
0
1
0
2
1
2
0
1
1
2
1
0
1
2
1
2
0
1
1
1
0
2
1
2
1
2
1
1
0
1
1
2
1
1
1
2
1
1
1
0
1
1
2
1
2
1
1
1
1
0
2
1
1
1
1
1
1
0
1
2
2
2
1
2
1
2
1
1
1
2
2
1
2
1
0
1
2
1
1
1
0
0
1
1
2
0
1
1
2
1
1
1
0
1
1
2
2
0
1
2
1
2
0
1
1
1
1
0
1
0
1
2
1
2
0
1
2
0
1
0
1
2
2
1
1
1
2
1
1
1
6
1
1
0
1
0
0
0
1
1
1
1
1
1
1
1
1
2
1
1
0
2
0
1
2
1
1
2
1
1
1
1
1
2
1
0
1
1
1
1
1
1
0
0
1
1
2
0
1
1
0
1
1
0
1
1
1
1
2
0
1
2
1
2
1
1
1
1
0
1
1
1
1
1
2
0
1
1
1
1
1
2
0
1
0
0
0
1
1
2
0
1
1
1
0
1
1
1
1
2
0
1
1
1
1
2
1
1
2
1
1
1
1
2
1
2
1
1
1
0
0
2
2
1
0
2
0
0
1
1
2
1
1
1
1
1
1
1
1
0
1
1
1
1
2
1
1
2
0
1
1
1
1
2
1
0
0
0
2
1
0
1
0
1
1
1
1
2
2
3
1
1
5
1
1
0
1
1
1
1
0
1
2
1
1
1
1
1
1
0
1
2
1
2
1
1
1
0
2
0
1
2
0
1
2
1
1
1
0
1
0
2
0
1
1
1
1
1
2
0
1
1
1
1
1
1
2
1
1
0
1
1
1
0
1
2
1
1
1
0
0
1
1
1
0
1
1
2
2
1
2
2
0
0
0
0
2
2
1
1
1
0
1
2
1
2
2
1
1
1
0
0
1
0
1
1
1
1
0
1
1
2
1
0
2
1
1
1
0
0
1
1
1
1
1
1
1
2
1
0
1
1
1
1
1
0
1
0
1
0
0
1
2
1
1
1
1
0
0
1
1
0
2
1
1
1
1
1
3
0
1
1
0
1
0
1
0
1
1
2
0
0
0
0
0
1
2
1
2
2
1
1
2
2
1
1
1
2
0
0
1
0
2
1
1
1
1
2
2
1
1
0
2
1
0
2
1
1
1
1
1
0
1
0
1
2
2
3
1
2
2
1
0
1
2
1
0
0
1
1
1
0
1
2
1
2
1
0
1
1
2
1
1
0
0
2
0
1
0
0
1
2
1
1
0
1
1
1
2
1
1
1
1
1
2
2
1
1
1
0
1
1
1
2
1
2
1
1
1
1
2
2
0
0
1
2
2
2
1
2
1
1
2
0
1
2
2
1
2
1
1
1
0
1
2
2
1
3
0
0
2
0
1
1
1
0
0
2
1
1
0
1
1
0
1
1
0
1
1
1
1
1
0
1
2
1
1
1
1
1
1
0
2
1
2
2
0
1
0
1
1
1
1
1
1
0
1
3
1
2
1
1
1
1
1
1
0
0
1
2
1
1
1
1
1
0
0
0
1
0
0
2
1
0
0
3
1
1
1
1
1
2
2
1
1
0
1
1
1
1
1
1
1
1
1
1
1
0
1
0
2
2
0
1
1
1
1
1
2
1
0
2
1
0
1
1
0
2
0
1
2
1
1
1
2
1
2
1
0
1
1
2
0
1
1
1
1
1
2
1
2
1
0
1
1
2
1
0
1
0
1
0
2
2
2
0
0
1
2
1
1
0
2
2
1
1
1
1
0
0
1
0
0
1
1
1
1
0
1
1
1
0
1
1
1
1
1
1
2
2
0
1
1
0
1
1
2
1
2
1
1
1
1
1
1
4
1
1
2
2
1
0
2
2
1
2
1
0
1
2
2
1
1
1
1
0
0
1
2
2
2
1
1
1
2
0
1
1
1
1
1
1
2
1
2
2
0
2
1
1
4
0
0
2
0
2
0
0
0
0
2
1
1
2
2
1
1
1
0
1
1
1
1
2
0
1
0
2
1
2
2
1
1
1
0
1
1
0
2
2
2
2
2
1
2
2
1
1
0
1
0
2
0
2
2
1
0
1
0
0
0
1
1
1
2
1
0
2
0
1
0
0
1
1
1
1
1
1
5
1
2
2
0
0
0
1
1
2
1
1
2
1
1
2
1
2
1
0
0
1
1
0
1
0
0
0
0
1
1
1
1
2
2
1
1
0
2
2
1
1
1
0
2
1
0
0
1
1
1
0
1
2
1
2
0
1
2
1
0
1
1
1
1
2
2
0
1
1
1
0
1
0
0
1
2
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
0
1
1
0
1
1
0
0
1
0
1
1
1
0
0
1
1
1
0
1
0
2
2
1
1
1
1
0
1
1
2
1
1
1
2
2
2
0
2
1
0
2
0
2
1
1
1
1
1
0
1
0
1
1
1
1
1
1
1
1
2
0
1
1
2
1
2
0
0
1
1
1
1
2
1
1
0
0
0
1
2
1
1
0
1
1
2
1
1
1
2
1
1
1
1
0
1
1
1
0
1
0
1
2
1
2
0
1
1
2
1
1
1
2
0
1
2
1
0
1
1
1
2
0
0
1
1
0
2
2
0
1
0
2
0
0
2
1
1
1
1
1
1
1
3
1
1
1
0
1
1
1
1
1
2
1
1
1
3
1
0
2
1
0
1
0
0
2
1
2
1
2
2
1
1
1
1
1
0
1
1
2
2
0
1
1
1
1
1
2
2
2
1
1
1
1
1
2
0
1
1
0
1
1
1
0
2
2
1
1
1
1
2
2
1
1
1
2
1
1
1
2
2
1
1
2
1
1
1
2
1
2
1
2
2
1
1
1
1
1
2
1
0
1
2
1
1
0
2
1
2
1
1
2
1
2
2
1
1
2
1
1
2
0
1
1
0
0
2
2
1
1
1
1
1
2
1
1
1
2
2
1
1
1
2
1
2
1
1
0
0
2
2
1
2
2
1
0
1
1
1
1
1
1
1
2
1
1
2
2
2
2
2
1
1
1
1
1
1
2
1
1
2
1
2
0
1
1
0
1
2
1
0
0
0
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
0
1
1
1
0
1
2
0
1
1
2
1
2
0
1
1
2
1
1
1
2
2
0
0
2
1
1
1
0
1
1
1
2
1
1
2
1
0
2
2
2
1
0
2
1
1
1
1
1
2
1
1
2
1
1
0
1
1
1
2
1
2
2
0
2
0
2
2
2
0
1
1
1
0
2
0
2
1
1
2
1
0
1
0
0
0
1
2
1
1
2
4
1
0
1
1
0
0
1
1
0
0
1
1
1
2
2
1
2
1
1
2
1
1
1
1
1
1
0
2
1
1
1
1
2
0
1
0
1
0
1
1
1
1
1
1
0
2
0
2
1
1
0
2
2
1
1
1
1
1
2
1
2
1
0
2
1
0
0
1
1
1
1
1
1
1
1
1
0
0
0
0
1
1
1
1
0
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
2
1
0
1
1
1
1
1
1
0
2
1
1
1
1
2
1
2
1
0
0
1
2
1
3
0
2
2
0
1
0
1
1
1
1
2
1
1
1
2
1
2
1
1
1
2
1
1
1
1
1
0
1
2
1
0
2
0
0
0
1
1
1
3
0
2
1
1
0
1
1
1
0
1
1
3
1
2
1
0
2
2
0
1
1
1
1
2
1
1
1
1
1
1
1
1
2
2
2
1
1
2
0
2
1
1
1
2
1
0
0
0
2
2
0
0
1
1
1
1
1
5
2
1
0
1
1
1
2
1
1
0
2
1
1
1
1
1
1
1
0
2
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
2
2
1
0
0
1
1
2
0
2
2
0
2
0
1
1
2
2
1
1
1
0
0
1
1
0
1
1
0
0
1
1
1
1
1
1
0
2
1
0
1
1
0
0
1
1
0
1
2
1
1
1
1
1
2
1
1
1
0
1
1
1
1
0
2
1
1
1
2
0
0
1
0
1
2
0
0
2
2
2
1
2
2
1
1
1
2
1
0
1
1
0
0
2
1
1
1
1
1
2
0
2
1
1
2
1
1
2
1
0
0
1
2
1
0
2
1
1
0
1
1
0
1
1
2
1
0
2
2
0
1
1
1
0
0
0
1
1
0
1
1
0
0
1
1
0
1
2
1
3
2
2
0
2
1
1
1
1
1
2
1
0
1
2
1
2
0
0
2
2
2
1
2
2
1
2
1
1
1
2
1
1
1
1
1
1
0
1
1
1
2
1
0
0
1
1
1
2
1
1
0
2
2
1
2
1
1
0
1
1
1
0
0
2
1
1
1
1
1
2
0
0
0
0
1
0
1
1
2
0
0
2
1
1
1
4
1
1
0
1
1
1
2
2
1
1
1
1
0
1
1
2
1
1
2
0
1
1
0
2
1
1
1
2
1
1
1
0
0
1
1
1
2
1
0
1
1
1
1
1
0
1
1
0
2
1
0
2
1
1
1
1
0
2
0
1
1
1
1
0
0
2
1
2
1
1
1
2
0
1
2
2
2
1
1
1
0
2
1
1
1
1
1
0
2
2
0
1
1
1
1
1
1
1
1
1
1
1
2
0
1
2
0
2
1
1
1
1
2
2
1
1
2
0
1
0
1
0
2
1
1
1
0
1
1
1
2
0
2
2
1
2
0
2
2
2
0
1
1
1
1
0
1
2
2
1
1
1
0
1
1
2
1
1
2
1
0
1
1
1
2
2
0
1
0
2
1
0
1
1
0
0
2
2
1
0
1
2
1
0
0
1
1
1
1
1
0
1
0
1
1
2
1
1
1
1
1
1
2
0
1
1
1
1
1
0
2
1
2
1
2
2
1
2
1
1
1
1
2
2
1
1
1
2
2
2
2
1
2
2
1
1
2
1
1
1
1
1
1
1
2
1
0
0
1
1
1
1
2
1
2
1
2
1
0
0
0
0
0
1
2
1
2
2
2
1
1
2
1
2
1
1
2
1
1
1
1
1
1
0
2
2
1
1
1
1
0
1
1
1
1
1
1
3
2
1
1
1
2
1
1
1
2
2
1
0
2
2
0
1
1
1
1
0
1
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
2
1
1
1
2
0
1
2
1
0
1
1
1
0
1
0
1
1
2
0
1
0
0
1
1
0
1
1
1
1
0
2
1
1
1
1
1
1
1
0
1
1
2
1
1
1
1
1
3
2
2
0
1
1
2
1
2
0
1
0
1
1
0
0
2
0
1
1
0
1
2
1
1
2
1
1
2
2
2
2
0
1
1
2
1
1
0
1
1
1
1
1
1
1
1
2
1
0
1
0
1
0
1
1
1
2
0
0
1
2
1
1
1
1
1
2
2
1
1
1
2
1
1
1
1
2
1
1
1
1
2
0
0
1
0
2
1
1
1
1
1
0
0
1
1
2
1
1
1
2
0
1
0
1
1
2
1
1
1
5
1
2
1
1
1
1
1
1
2
1
0
1
0
1
1
1
1
2
1
1
1
1
2
1
2
0
1
1
2
0
2
1
2
1
0
0
1
1
0
2
1
1
1
0
1
2
1
1
1
0
1
2
1
1
0
1
0
1
1
1
1
1
1
2
0
1
1
0
1
1
0
1
1
1
0
0
1
0
1
1
2
1
1
2
1
1
1
0
0
1
0
1
1
2
0
0
0
1
2
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
0
0
2
1
0
1
1
1
1
1
2
2
1
2
2
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
0
1
1
1
0
0
1
1
2
1
1
1
1
1
2
1
1
0
1
1
1
1
1
1
1
1
2
1
1
0
0
0
1
0
2
1
0
1
1
1
1
0
2
1
0
1
4
2
1
2
0
0
2
1
1
2
1
1
1
0
1
1
0
1
0
2
1
0
0
2
1
1
2
0
1
2
2
0
1
0
0
1
0
2
1
2
1
2
2
1
1
1
2
1
1
2
1
0
1
0
1
2
1
2
1
1
1
1
2
2
2
1
0
1
0
2
0
1
1
0
1
2
1
1
1
0
1
2
1
1
2
1
2
0
1
0
1
1
1
1
1
0
1
2
1
1
2
2
0
2
1
2
1
2
1
0
0
0
1
2
1
1
2
0
0
0
2
1
0
1
1
0
1
2
1
2
1
2
1
0
1
1
1
1
1
1
1
0
1
1
0
1
0
1
1
1
1
1
1
1
1
2
0
1
1
2
1
1
1
1
1
1
2
0
0
0
1
1
0
0
0
1
0
2
1
2
2
3
1
2
0
0
0
0
1
1
2
1
2
1
1
1
2
1
1
1
2
2
2
2
2
1
2
1
1
1
0
0
1
1
0
1
1
1
1
2
2
1
1
2
1
2
2
2
0
1
1
1
1
2
1
1
2
1
1
1
0
1
2
1
0
2
1
1
1
2
0
1
1
2
1
1
0
1
1
2
1
2
1
2
1
0
1
1
2
1
1
0
1
2
2
1
2
1
2
1
1
1
1
0
1
1
1
1
1
0
1
1
0
0
1
1
2
0
2
0
0
1
0
1
1
0
1
1
1
2
0
1
2
1
1
2
2
1
2
1
0
1
2
2
2
2
1
2
1
1
2
1
1
2
1
1
2
1
1
2
0
1
1
2
1
2
2
1
1
1
1
0
1
2
1
1
2
2
0
2
1
1
2
1
1
1
0
2
2
2
1
1
2
0
1
1
1
1
1
2
1
2
0
1
0
1
2
1
1
2
2
2
1
1
1
0
1
1
0
1
1
1
1
2
1
2
0
1
0
1
2
1
0
2
1
2
1
2
1
2
0
1
1
1
3
0
2
1
1
2
1
1
2
1
1
0
0
1
0
2
1
1
1
0
1
1
2
2
2
2
1
3
1
1
2
1
1
1
2
2
1
1
0
1
2
2
1
1
1
1
2
1
0
1
1
1
1
2
1
0
2
1
2
1
1
1
0
1
1
2
1
1
1
2
2
1
1
1
2
1
1
1
1
2
2
1
3
1
1
0
1
1
1
2
1
1
1
1
1
1
2
1
0
2
1
2
2
1
2
1
0
0
1
1
1
1
2
2
0
1
1
0
0
0
0
1
1
2
1
1
1
4
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
2
2
1
2
2
2
1
2
1
1
1
2
1
2
1
1
1
1
0
0
1
0
1
2
1
1
1
0
0
1
0
1
0
1
0
0
1
2
1
1
0
1
0
1
0
1
2
2
2
2
2
2
1
0
2
1
1
1
2
1
0
0
1
0
1
1
1
1
1
1
1
1
1
0
1
1
1
0
1
2
2
1
1
1
1
0
0
2
2
2
2
0
0
0
1
0
2
2
1
1
1
2
2
1
1
2
1
0
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
0
2
2
1
1
2
1
1
0
1
1
1
1
2
1
1
1
2
1
1
1
2
0
2
1
1
2
0
1
2
2
1
0
1
0
1
1
2
0
0
1
1
3
1
1
0
1
1
0
1
1
1
0
0
1
2
1
2
1
2
1
0
1
1
2
1
0
2
2
1
3
1
1
1
0
1
1
0
2
2
2
1
1
1
2
2
1
1
1
2
0
0
2
2
1
2
1
1
1
1
0
2
0
0
1
1
1
0
1
1
4
1
1
2
2
2
1
1
2
2
0
0
1
2
1
0
1
1
2
0
1
1
1
1
0
1
0
0
2
1
1
1
1
1
0
0
0
1
1
1
1
1
2
0
1
0
0
1
0
1
2
1
0
0
0
1
0
1
1
1
1
2
0
1
2
1
1
1
0
1
1
1
1
1
1
1
0
0
1
1
0
1
1
1
2
2
1
0
1
1
2
1
2
2
1
0
0
1
0
1
2
2
1
1
1
1
1
2
1
1
2
1
0
0
2
1
1
1
1
0
0
0
0
1
1
2
2
0
1
0
1
1
2
1
0
2
1
1
0
0
1
0
1
1
2
1
1
0
0
0
1
2
1
1
1
1
1
0
0
2
2
0
1
1
1
1
1
1
2
0
0
2
0
1
1
3
1
1
0
7
1
1
1
1
2
2
2
0
1
2
1
0
1
1
1
1
1
2
2
0
0
0
0
2
2
1
2
0
1
2
0
1
1
2
1
1
1
1
2
1
0
2
2
1
1
2
1
2
1
1
2
1
0
1
1
1
1
1
1
0
1
1
2
1
3
1
2
1
1
1
1
2
2
2
1
1
1
2
1
1
2
2
1
1
2
1
1
2
1
1
2
1
1
2
2
1
1
1
0
1
1
1
2
0
2
2
2
0
1
1
0
2
0
1
1
1
1
1
1
1
1
1
0
2
1
1
1
1
2
0
1
1
2
2
0
2
2
2
1
7
2
1
1
1
1
2
2
1
0
0
2
1
2
1
1
0
1
1
1
1
1
0
0
1
0
1
1
0
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
2
1
0
1
2
0
1
1
1
1
0
2
1
1
2
1
1
1
1
1
1
1
2
2
1
0
2
1
1
1
1
2
0
0
0
1
3
1
0
1
1
2
1
1
2
2
2
0
0
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
0
1
1
2
1
1
2
1
2
1
0
1
1
2
0
0
1
2
1
2
1
2
1
1
1
2
1
1
1
1
0
0
1
2
0
2
1
0
0
1
1
1
1
2
1
2
2
1
1
1
1
0
1
0
2
0
1
0
2
1
1
2
1
1
1
1
1
0
1
1
1
1
0
0
1
1
1
2
1
1
1
1
0
0
1
1
1
1
1
1
1
1
1
1
2
2
1
0
1
1
0
1
1
1
0
2
1
2
1
1
1
1
0
1
0
1
1
1
1
1
1
1
2
1
0
1
2
1
1
0
1
1
1
1
0
1
1
0
1
0
1
1
1
3
1
1
1
1
1
0
1
2
1
2
2
2
1
2
1
1
0
0
3
1
1
1
1
1
2
0
0
1
1
1
1
1
0
2
1
0
1
0
1
0
1
0
2
2
2
0
0
2
0
1
2
0
2
1
1
1
2
1
1
1
2
2
1
0
0
1
0
2
2
1
0
0
2
1
0
3
1
2
1
1
1
1
1
0
0
1
1
2
3
1
1
2
1
1
1
0
0
2
2
2
1
1
1
1
1
2
1
1
1
1
2
0
2
1
1
2
0
1
2
2
1
2
2
1
1
0
1
1
0
1
0
2
2
1
0
1
1
0
1
1
1
1
2
1
0
1
2
1
1
1
1
0
1
0
1
1
0
2
6
1
2
1
1
1
2
1
2
1
1
0
1
2
0
2
2
0
2
3
2
1
1
0
1
1
2
0
0
1
1
0
2
0
2
1
1
2
3
2
1
1
1
1
0
0
1
2
1
1
0
1
1
1
2
0
1
1
0
1
0
2
1
1
1
2
1
0
1
1
2
2
1
0
2
1
1
2
2
1
2
0
2
3
1
1
1
1
1
2
1
1
1
0
1
1
1
1
1
1
1
1
1
2
2
2
2
1
1
1
2
1
0
0
0
1
1
1
1
0
0
0
2
1
1
1
1
1
1
1
2
2
2
1
0
2
2
1
5
1
2
1
2
0
0
1
1
1
2
0
2
1
1
0
2
1
1
1
1
2
2
0
2
0
1
1
1
1
1
1
1
1
2
0
0
0
1
1
1
1
1
2
0
2
1
1
2
1
1
1
1
1
3
1
1
2
0
2
3
1
1
0
1
0
2
1
1
0
1
2
1
1
1
1
2
1
2
0
1
2
1
0
1
1
1
1
0
1
1
1
0
1
1
2
1
1
2
2
2
2
0
1
1
1
2
1
0
0
2
2
1
2
2
2
1
1
2
1
1
1
1
2
2
1
0
0
0
1
0
1
2
2
2
3
1
0
2
1
1
1
2
1
1
2
1
2
0
2
1
0
2
1
2
0
1
1
1
1
3
2
2
1
1
1
0
1
1
2
2
5
1
1
0
1
1
3
1
1
1
1
1
1
1
1
2
1
1
0
1
1
1
1
1
1
1
1
0
2
2
1
1
1
0
2
0
1
0
1
0
1
1
1
2
3
0
1
1
0
1
1
1
2
0
0
1
2
0
1
2
2
1
1
1
0
1
1
0
1
1
1
1
1
1
0
1
1
1
0
2
1
1
0
1
1
1
1
1
2
2
0
1
1
0
1
2
1
1
2
0
1
2
1
1
1
1
1
1
3
1
0
2
2
2
2
1
1
2
1
1
1
0
2
1
1
1
1
1
1
1
1
1
1
1
1
2
3
1
1
1
2
0
1
1
2
1
0
1
1
0
2
1
0
2
1
1
1
2
0
0
1
1
1
1
1
2
1
1
2
0
1
0
1
2
1
0
0
2
1
1
1
2
0
0
1
1
0
0
1
1
1
1
1
2
2
2
1
1
0
0
1
1
0
0
1
2
0
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
0
1
1
2
1
1
0
1
1
2
1
2
1
1
0
1
1
1
0
1
2
3
1
2
1
0
1
1
2
0
1
2
2
1
2
1
1
1
1
1
0
2
1
0
4
1
1
2
1
0
0
1
1
3
0
0
1
2
1
0
1
1
1
1
1
1
0
0
1
1
1
1
2
1
2
1
2
1
0
1
1
1
0
1
1
0
0
1
1
1
1
0
1
2
1
1
1
1
1
2
1
1
3
1
1
2
1
1
0
1
0
1
1
0
4
1
1
1
2
1
2
0
1
3
1
2
0
1
2
0
1
0
2
0
1
1
1
1
1
1
1
0
1
1
2
1
2
1
1
2
0
1
1
0
2
2
0
1
1
1
2
2
1
1
1
2
2
1
1
1
2
1
1
1
1
1
1
1
1
0
1
2
2
1
0
1
1
1
2
1
1
0
1
1
1
1
1
2
1
1
1
1
2
1
0
1
1
2
1
1
2
1
1
0
2
1
1
0
2
2
0
0
2
0
0
1
1
1
1
1
1
2
1
2
1
1
1
0
1
1
0
1
1
0
0
2
0
0
1
1
1
1
1
1
1
1
1
0
1
0
2
0
1
1
1
1
1
1
1
1
1
1
2
1
1
2
0
2
2
0
0
1
1
1
1
1
0
1
1
1
0
1
0
1
1
1
1
1
1
1
1
2
0
1
1
1
2
1
1
1
0
2
2
2
2
1
1
1
1
2
0
1
1
1
0
1
1
2
1
0
0
0
1
0
1
1
1
1
2
2
0
1
0
2
1
2
0
3
1
0
0
1
1
0
0
0
1
1
0
1
1
1
0
2
2
0
2
1
1
2
1
4
1
2
2
2
2
1
1
2
0
1
2
1
2
2
1
1
0
1
1
0
0
1
1
2
1
1
1
0
1
1
0
2
2
1
1
1
1
2
0
2
1
0
1
2
1
0
0
0
1
1
2
2
1
1
0
2
1
1
0
1
1
2
2
1
1
1
0
2
1
1
0
1
0
1
1
1
0
2
1
0
1
2
1
4
1
0
0
1
1
1
1
1
2
1
2
1
1
2
0
0
0
2
1
1
1
0
1
2
0
0
2
1
2
1
2
0
2
2
1
3
2
1
1
1
2
1
1
0
1
2
2
2
1
1
1
1
1
2
2
0
2
0
2
2
1
1
1
0
0
1
2
1
1
1
1
1
2
1
0
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
0
1
1
1
1
0
2
0
1
2
2
1
1
1
2
1
1
1
1
2
2
1
0
0
2
1
2
2
2
0
1
1
1
2
1
1
1
1
1
0
1
1
1
0
1
0
2
1
2
0
1
1
1
1
0
1
1
1
1
1
2
0
0
1
1
1
2
2
1
1
1
1
1
1
1
2
4
0
2
2
2
1
1
1
1
2
1
1
1
0
1
4
2
1
0
0
1
1
1
1
0
1
0
1
1
0
1
2
0
1
0
1
0
1
1
1
0
2
2
2
1
0
2
0
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
0
2
1
2
0
0
1
0
1
2
1
2
1
1
0
1
0
2
2
2
1
2
2
1
1
0
2
0
1
2
0
2
2
0
0
0
1
1
2
2
1
0
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
2
1
1
0
1
2
1
2
1
1
1
0
1
0
2
1
0
1
2
1
0
2
2
1
1
1
1
1
0
1
1
2
2
1
1
1
1
1
1
1
0
1
2
0
0
0
1
0
1
1
1
2
2
2
1
1
1
1
1
2
1
1
1
1
1
0
0
1
1
1
0
2
2
1
2
1
1
1
1
0
2
1
0
2
2
1
1
1
1
1
1
2
0
1
2
0
1
1
2
1
2
1
1
2
0
1
1
2
1
2
1
1
1
2
1
2
1
1
0
1
1
0
1
0
0
1
1
1
2
2
0
1
0
1
3
1
1
1
2
0
2
1
0
1
1
2
1
0
1
2
1
1
1
0
2
1
1
0
2
1
2
0
1
1
2
1
0
1
2
1
0
1
2
0
2
1
1
1
1
1
2
0
2
1
1
2
1
2
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
4
1
0
1
1
2
0
1
1
1
1
1
1
2
1
1
1
2
1
1
0
1
1
2
1
1
2
2
4
0
1
0
1
1
0
1
1
0
1
2
1
1
1
1
2
1
1
0
1
1
2
0
1
0
0
1
2
1
1
1
1
0
1
2
2
1
2
1
2
1
0
1
1
2
1
1
1
1
1
1
0
2
2
2
2
1
2
2
1
1
1
1
2
1
0
2
2
2
2
1
1
1
1
0
0
1
1
1
1
1
0
1
0
1
0
0
0
0
1
2
1
0
1
2
1
1
2
2
0
2
0
2
1
2
2
0
2
2
1
2
1
0
0
1
1
1
2
1
1
1
1
0
1
1
2
2
1
1
1
1
1
1
2
1
1
0
0
1
0
2
2
1
1
1
1
1
0
1
1
1
1
2
0
1
0
1
1
0
1
1
1
1
1
1
0
2
1
1
1
1
0
1
1
2
1
1
1
1
1
0
1
2
1
0
2
2
1
2
1
1
1
1
0
1
4
1
1
1
1
1
1
0
0
1
1
1
1
1
1
2
1
1
1
2
0
1
1
1
1
1
1
0
2
1
1
0
1
1
1
0
1
2
1
1
1
0
1
1
1
2
1
1
1
1
0
2
0
1
1
0
1
1
1
1
2
1
2
2
1
1
0
1
1
1
1
1
1
1
2
1
2
1
0
1
0
1
1
0
1
1
1
1
1
1
1
0
1
0
1
0
1
0
2
1
1
1
0
1
2
0
2
0
2
2
0
2
1
0
1
1
0
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
2
2
1
1
2
1
0
0
1
1
2
1
1
2
0
1
2
1
1
1
2
2
2
1
1
1
2
1
1
0
1
1
2
2
1
1
2
1
1
1
1
1
0
1
1
2
1
0
1
2
1
1
2
0
1
1
1
1
1
1
1
1
2
2
1
1
0
1
1
0
0
2
1
2
1
0
2
1
2
1
1
1
1
1
0
0
0
1
1
2
1
1
1
2
2
0
1
2
1
2
0
1
1
0
0
1
2
2
1
1
2
1
2
0
2
1
2
1
1
1
1
1
0
1
2
4
2
1
0
0
1
1
1
2
2
0
1
1
1
2
1
1
2
2
1
1
2
0
1
1
0
0
1
1
0
0
1
1
2
2
2
0
0
1
0
1
1
1
1
0
1
0
1
1
1
1
0
2
0
1
0
2
1
0
2
1
1
1
2
1
1
0
2
1
2
1
1
0
1
2
1
2
2
1
0
1
1
1
1
0
0
1
0
0
2
2
1
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
1
1
2
1
2
2
2
2
1
1
2
2
1
1
2
1
1
1
1
1
0
2
1
0
2
2
1
1
0
2
1
2
1
0
1
1
1
1
2
0
1
2
2
0
1
2
1
2
1
0
1
1
2
0
3
2
1
2
0
1
0
1
2
0
1
0
0
2
2
0
1
0
1
1
1
1
1
1
2
1
1
0
1
0
0
1
1
1
1
1
1
1
0
2
1
1
2
1
1
1
0
0
1
1
1
0
1
1
2
0
1
1
2
3
0
1
1
0
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
2
1
1
1
2
0
1
2
1
1
1
2
1
1
0
1
0
1
1
2
0
1
1
1
1
2
1
1
1
1
2
2
2
1
1
1
0
2
1
1
2
0
2
1
2
2
2
2
1
1
1
1
1
2
0
1
0
0
1
1
1
0
1
2
0
1
1
2
1
1
1
1
1
1
0
2
2
1
1
0
2
1
0
1
1
0
2
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
1
2
1
1
1
2
1
0
1
2
1
1
1
1
1
0
1
2
2
1
0
2
1
1
1
2
1
0
1
1
1
1
1
0
1
1
1
1
0
1
0
1
0
2
0
2
2
1
1
1
1
1
1
1
1
3
1
1
1
0
1
1
1
0
1
1
2
0
1
1
1
1
0
0
0
1
1
2
1
1
1
1
2
1
0
2
1
2
0
2
1
1
1
1
1
1
1
1
1
2
1
0
1
0
1
0
2
1
2
1
1
1
1
1
1
2
1
0
1
1
2
1
1
1
2
1
1
1
0
1
1
1
1
1
1
1
3
2
0
2
0
1
1
2
0
1
1
1
0
1
1
1
1
2
1
1
1
0
1
2
1
0
1
1
2
0
2
0
2
1
1
1
1
1
2
1
1
1
2
2
0
1
2
1
1
1
0
2
1
1
1
0
0
1
0
1
1
1
2
0
1
1
1
0
0
1
1
0
1
1
3
2
1
0
2
0
2
1
1
1
1
1
2
1
1
0
1
1
1
1
1
0
1
1
0
1
2
1
2
2
1
1
1
1
1
2
0
0
1
1
0
1
1
0
0
1
1
1
1
1
0
0
1
1
1
1
1
1
1
2
1
1
0
2
1
1
1
1
1
2
1
2
0
2
0
1
1
2
1
1
2
1
1
1
0
1
0
1
0
0
0
1
2
1
1
1
0
1
0
1
0
1
1
1
2
0
1
2
1
0
2
1
2
1
0
2
3
1
2
0
1
1
1
1
2
1
1
2
1
0
2
2
1
1
2
1
1
2
1
0
1
1
0
2
1
0
0
1
1
2
1
2
1
1
1
2
0
1
1
0
0
1
2
1
1
0
1
1
1
1
2
0
0
2
2
0
1
0
2
1
2
2
2
1
1
1
1
1
2
2
1
2
0
2
2
0
1
2
0
0
1
0
2
1
2
1
1
1
2
1
2
1
0
1
1
2
1
1
1
2
1
1
1
0
1
1
1
2
1
2
1
1
0
0
2
2
1
1
2
1
2
0
2
1
0
2
3
2
0
1
1
2
1
1
0
1
2
2
1
1
1
0
1
1
0
1
0
1
1
0
1
1
2
0
1
2
2
1
1
1
2
2
1
1
2
1
1
0
1
1
1
2
1
1
1
1
0
1
1
1
0
1
1
1
1
1
0
1
0
1
1
1
1
2
0
2
0
0
0
2
1
0
0
0
0
1
0
2
2
1
1
1
1
0
1
1
0
0
2
0
1
1
1
1
0
1
1
1
1
1
2
1
1
1
1
0
2
1
1
2
1
1
0
1
2
1
1
1
1
1
0
1
2
2
1
1
0
2
0
2
1
1
2
1
1
0
1
2
0
1
1
2
1
0
1
2
0
0
0
1
1
1
2
1
2
1
1
1
2
2
1
1
2
2
2
1
1
2
1
1
0
1
1
0
1
2
2
2
2
1
0
1
0
1
1
2
2
0
1
1
0
0
2
0
1
2
2
2
1
2
0
2
1
1
2
0
1
2
2
1
1
2
1
0
1
2
0
2
1
2
0
1
2
2
1
1
0
0
0
1
1
0
1
0
1
1
1
1
2
0
0
1
1
2
0
2
1
1
1
2
0
1
0
1
0
1
1
0
1
1
0
1
1
2
1
0
0
0
1
1
0
1
2
2
1
2
1
1
0
1
1
2
1
1
1
1
0
2
1
2
2
1
2
1
2
0
0
1
2
1
1
1
1
2
1
2
2
1
2
0
2
1
1
1
2
0
0
1
1
2
1
0
2
1
1
1
2
1
2
2
1
1
0
1
1
0
1
1
0
1
1
1
1
1
1
1
1
0
0
0
2
2
0
2
1
1
1
0
1
1
1
1
0
1
1
0
2
1
1
0
2
1
1
1
0
2
1
1
0
1
2
1
0
1
2
0
1
1
1
2
0
1
1
1
1
1
1
0
1
1
2
1
0
2
1
0
1
1
1
0
2
1
1
2
2
1
1
0
1
1
0
1
2
1
1
1
1
0
0
1
2
1
1
0
0
1
2
0
2
1
1
0
1
2
1
1
2
1
2
1
2
2
1
2
0
1
1
0
2
1
1
0
2
0
2
2
0
1
1
2
2
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
0
2
0
0
2
0
0
0
1
1
1
1
1
1
2
0
1
2
0
1
1
1
2
2
1
1
1
2
1
2
1
2
1
0
3
0
2
1
1
1
1
1
0
1
1
1
2
2
2
1
2
1
1
0
2
0
2
1
1
2
1
1
1
2
0
1
0
1
1
1
0
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
1
2
1
1
0
1
2
2
1
0
1
2
2
2
2
2
0
1
1
1
1
1
1
1
1
2
2
0
0
0
0
0
0
1
1
0
1
0
1
2
1
1
1
1
1
2
0
1
1
2
1
0
2
1
1
2
2
1
3
1
0
2
1
1
2
2
1
1
0
1
1
1
1
2
1
1
1
2
0
0
2
1
1
1
1
1
1
1
2
0
1
0
1
1
0
2
2
1
1
0
1
2
1
0
2
0
2
1
1
1
0
1
1
1
0
1
1
1
2
1
1
1
0
1
1
0
1
1
1
1
2
2
0
3
2
1
1
1
1
0
2
1
1
2
1
1
1
2
1
1
1
1
1
0
1
2
1
3
0
1
2
2
0
1
1
1
1
1
2
1
2
0
1
1
2
2
1
2
1
1
2
0
1
1
0
1
1
1
1
0
2
2
1
2
2
0
1
0
2
2
1
1
1
2
2
2
2
1
1
0
0
2
0
2
1
1
2
1
2
0
1
1
1
2
1
2
0
1
1
2
1
1
2
1
1
1
1
1
0
1
2
1
1
1
2
2
1
1
2
2
1
2
1
1
1
1
2
1
3
2
1
1
2
1
0
0
1
1
1
0
1
2
3
1
2
0
1
1
1
0
1
2
1
0
1
2
0
1
1
1
1
0
1
0
2
0
1
0
1
2
1
0
2
0
2
1
1
1
1
1
2
1
1
1
2
2
1
1
1
2
1
1
1
4
1
1
1
0
2
1
1
0
1
0
1
1
1
1
0
1
2
1
1
1
2
1
1
0
1
1
1
0
1
1
2
1
1
2
1
2
1
1
0
1
1
1
1
1
2
1
1
1
2
2
0
1
1
1
1
1
2
0
1
1
1
1
0
1
1
0
1
1
1
1
2
0
1
2
1
1
1
3
0
1
1
1
1
0
0
1
1
2
1
0
0
0
3
1
2
0
0
1
1
1
1
0
2
2
0
2
2
1
2
1
1
0
2
2
0
0
1
0
2
2
2
1
1
2
2
1
0
1
1
1
1
0
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
0
1
1
1
2
1
0
1
0
2
0
2
1
0
2
0
1
1
1
2
1
1
2
1
2
0
1
0
1
0
2
1
2
0
2
1
0
1
0
2
1
1
2
2
1
1
1
1
2
0
1
0
0
0
2
1
1
2
2
0
0
2
1
0
0
1
1
0
0
0
0
1
2
1
2
2
2
1
0
1
1
1
1
1
2
2
2
2
2
1
1
0
2
0
2
0
1
2
1
1
2
1
1
2
1
0
2
1
1
0
0
2
1
1
2
0
1
2
0
1
2
0
1
1
0
1
1
1
0
0
1
2
0
1
1
1
1
1
1
0
1
1
1
2
1
0
1
0
1
0
1
2
2
2
1
1
0
1
0
0
2
0
2
0
1
2
1
1
2
1
1
2
0
2
1
0
1
2
2
2
1
1
1
1
1
0
0
0
0
1
1
1
2
1
1
0
1
0
1
1
1
1
0
1
1
1
1
2
2
2
0
0
1
2
0
1
0
2
2
1
2
2
0
0
1
2
1
1
1
1
2
1
2
1
0
2
1
0
2
0
1
0
1
2
1
2
0
1
1
1
2
1
0
1
2
1
2
1
1
1
0
2
0
0
1
0
2
2
2
0
1
0
1
1
1
1
2
1
1
1
0
1
0
2
1
2
2
1
1
1
1
2
1
1
0
2
0
1
2
2
1
1
2
1
1
2
1
0
0
0
2
1
1
1
2
2
1
1
1
2
1
1
1
2
1
1
0
3
1
1
0
3
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
0
1
2
1
1
1
0
1
1
1
0
0
2
1
1
0
2
1
1
0
0
2
1
1
1
1
2
2
0
2
1
1
1
1
1
1
1
3
2
1
0
1
1
1
1
2
1
1
1
2
1
1
2
1
1
1
1
0
1
0
1
2
1
0
2
1
2
2
2
0
0
0
1
1
2
1
2
0
2
1
1
1
2
2
2
0
1
0
1
1
1
2
1
0
2
2
1
2
2
1
1
1
2
1
1
1
1
2
1
2
0
1
1
1
0
2
1
1
0
2
1
1
2
1
0
2
0
0
1
1
0
1
1
1
0
1
2
1
0
2
2
2
0
1
1
1
0
2
1
1
0
1
1
1
0
1
1
1
3
0
0
4
2
1
0
1
2
0
1
2
1
1
1
1
1
0
0
1
0
1
1
1
1
2
1
1
2
1
2
1
1
2
2
1
1
0
1
1
1
2
2
1
2
0
2
2
1
2
1
1
1
1
2
1
1
1
1
0
0
1
1
0
0
0
2
1
1
1
2
1
1
1
0
2
1
1
1
2
1
1
2
1
0
1
0
1
2
0
1
1
0
0
2
1
1
1
1
1
1
1
2
1
2
1
1
3
4
2
1
1
1
1
1
2
1
1
1
0
1
2
0
2
0
1
1
0
1
0
1
2
1
1
1
0
1
1
1
1
0
1
1
0
2
1
0
1
1
2
1
0
1
1
2
1
2
1
1
1
1
2
2
1
0
1
1
1
1
2
1
1
1
2
0
0
2
1
0
1
1
1
0
1
1
1
2
0
2
1
2
0
2
2
1
3
2
1
0
1
1
1
1
2
1
1
0
2
1
1
1
1
1
1
1
1
1
0
1
1
1
1
2
1
0
2
0
0
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
2
2
1
2
0
1
1
1
2
2
2
1
1
1
1
1
1
2
1
2
1
1
1
1
2
2
1
2
1
2
1
2
0
0
1
1
1
1
1
2
2
1
1
0
2
1
1
1
1
1
1
1
1
1
0
1
1
2
0
1
1
1
1
1
1
1
1
2
1
1
1
1
0
1
0
2
0
1
1
1
2
2
2
1
2
3
1
1
1
1
1
1
1
1
0
2
1
1
2
2
1
1
0
1
1
0
1
2
0
1
0
2
1
1
1
2
1
1
0
1
1
1
0
1
2
2
0
0
2
2
0
1
2
2
1
2
1
1
0
1
1
1
1
1
0
2
0
0
1
1
1
2
1
2
1
1
2
2
2
1
1
1
3
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
0
1
0
1
1
1
1
2
0
2
0
2
1
1
1
2
1
1
2
1
0
2
0
1
1
1
1
1
2
1
1
2
1
1
1
2
2
2
0
1
1
1
2
1
1
2
1
2
1
1
1
2
1
2
2
1
1
1
1
1
1
1
2
1
0
1
1
2
1
0
1
1
0
2
0
1
2
1
2
1
1
2
1
1
1
1
1
1
2
1
2
1
0
1
1
2
2
1
2
0
0
1
1
1
0
0
1
1
2
1
0
1
0
0
0
1
1
2
1
0
2
1
1
1
1
1
2
0
1
1
0
1
0
2
2
1
1
1
1
1
2
1
1
2
2
1
2
2
1
0
0
0
1
2
1
1
1
0
1
0
1
1
1
0
2
0
1
2
1
0
2
1
1
0
1
0
2
2
0
0
2
1
0
2
0
1
1
0
1
1
0
0
1
1
2
2
1
2
0
0
1
0
1
2
1
1
0
2
2
2
2
1
1
1
2
0
1
1
2
1
2
2
0
2
0
1
1
1
1
1
1
2
1
1
1
1
1
0
2
1
1
0
2
2
2
2
2
1
1
2
1
1
2
1
1
1
1
0
1
1
1
0
1
1
1
1
0
2
1
1
2
0
2
1
2
0
1
2
2
1
0
1
2
1
2
1
2
2
1
1
1
2
1
0
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
0
1
1
2
1
2
2
1
2
2
1
0
1
1
0
1
0
1
0
0
0
1
1
1
1
1
1
1
0
1
1
1
1
1
2
1
0
1
1
1
0
1
0
1
1
1
0
1
0
2
1
2
1
1
2
1
1
1
2
2
1
1
2
2
0
1
1
0
1
2
2
2
1
1
1
1
1
2
0
1
1
2
0
2
2
1
1
2
1
1
2
0
1
1
0
2
0
1
1
1
1
1
1
1
1
1
0
2
1
1
0
0
1
1
2
1
1
1
0
1
2
0
1
0
0
1
1
1
1
1
1
1
1
2
1
1
0
1
1
1
2
1
1
1
2
1
1
1
2
0
1
0
1
1
1
2
1
2
1
1
1
2
0
0
2
1
1
1
1
1
0
1
2
2
1
2
1
1
0
1
1
0
2
0
1
1
1
2
2
0
1
1
1
0
1
1
1
2
1
1
1
1
1
2
1
0
1
1
1
1
2
1
1
2
1
0
1
1
1
0
1
1
1
1
1
1
1
1
1
1
2
1
2
1
0
2
1
0
1
1
1
1
1
2
0
1
0
1
1
1
0
2
0
1
1
0
0
1
1
1
1
1
1
0
1
2
3
0
1
2
2
1
1
0
1
0
1
0
2
1
1
1
1
1
1
0
2
1
1
1
1
1
1
1
1
1
1
1
1
0
1
0
0
1
1
0
1
2
1
1
1
0
1
1
1
2
2
2
2
1
1
1
1
1
2
2
1
1
1
1
0
0
1
0
2
1
1
0
1
1
1
0
2
1
0
1
2
0
1
1
0
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
0
1
1
2
1
0
2
1
1
1
0
2
1
1
1
1
0
2
2
1
1
1
2
1
1
1
1
2
1
1
1
0
0
1
2
1
2
1
1
1
1
1
1
2
0
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
0
1
1
1
1
0
1
1
1
0
0
2
2
2
1
0
2
1
2
1
2
1
0
1
0
2
2
1
2
0
1
2
1
1
1
1
2
1
1
1
1
1
2
1
2
0
1
1
2
1
0
1
0
2
1
1
1
1
1
0
2
0
1
2
0
1
1
0
1
1
1
0
2
1
2
0
1
1
2
1
1
2
2
0
0
0
1
1
1
1
0
1
3
0
1
1
1
0
0
1
1
1
2
2
2
1
1
1
2
2
1
1
0
2
2
1
2
1
0
1
2
2
1
1
2
1
2
0
1
1
1
2
1
0
1
3
2
1
1
1
1
1
2
2
1
2
1
1
0
0
1
1
1
0
0
2
1
0
1
1
1
2
1
1
1
2
1
2
1
1
0
2
1
2
0
0
2
2
0
1
1
1
0
1
1
0
1
1
0
0
1
0
0
0
1
1
2
2
0
1
1
1
1
1
2
1
1
1
1
2
1
1
0
1
1
1
2
1
2
2
1
1
1
1
0
1
1
1
1
1
0
1
1
1
2
2
1
0
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
0
1
0
1
2
1
1
2
1
1
0
1
1
1
1
1
0
1
1
0
1
0
5
1
1
1
1
0
2
1
2
1
2
1
1
1
2
1
0
2
1
1
2
2
0
2
2
1
2
2
2
0
2
0
1
2
1
0
1
2
1
0
2
1
1
1
1
2
1
0
1
0
2
0
2
0
2
1
1
0
0
1
1
1
1
2
1
2
1
0
1
1
1
1
1
0
1
1
1
1
1
1
2
1
1
2
1
0
0
1
1
1
1
1
2
1
1
1
1
2
2
1
1
0
0
0
0
1
1
2
1
1
1
2
1
1
2
1
0
0
0
2
1
2
0
2
1
1
1
1
0
1
1
2
2
1
1
1
1
1
2
1
1
0
1
2
0
0
1
2
1
2
0
1
1
1
1
1
2
1
2
1
0
1
1
1
1
2
1
2
1
1
1
1
2
2
2
1
1
2
2
2
1
0
1
2
1
1
0
1
2
0
0
2
2
1
0
1
1
1
1
1
1
2
0
1
1
1
1
2
2
1
0
0
1
1
5
1
1
2
0
1
1
0
2
1
2
1
0
1
1
1
2
1
0
1
1
1
1
0
0
1
1
1
2
1
1
0
1
1
1
2
0
2
1
0
2
1
1
1
2
0
1
1
2
1
1
2
0
1
2
1
1
1
0
0
1
0
1
1
2
3
1
1
1
0
1
1
1
2
1
1
1
2
1
0
0
1
1
1
1
1
1
2
1
2
1
1
1
0
2
1
1
1
2
1
2
1
0
2
1
1
1
1
1
0
1
1
1
0
2
1
2
1
2
0
1
2
2
0
2
1
2
1
1
1
2
2
1
1
1
0
1
0
1
2
1
1
2
1
0
0
1
1
1
0
2
2
2
0
2
1
1
1
0
0
1
1
1
0
1
1
2
1
1
1
2
0
0
1
0
1
1
2
1
1
0
2
1
2
0
1
1
2
1
1
1
0
2
1
2
1
1
1
1
2
1
1
0
1
1
2
2
1
0
1
1
0
2
1
1
1
1
0
2
2
1
1
1
0
2
1
1
2
2
2
2
1
1
2
2
1
2
2
1
1
1
1
1
1
1
2
0
0
0
2
0
0
0
1
2
1
0
1
1
1
1
1
2
2
2
1
2
1
2
2
0
1
1
1
0
2
2
1
1
1
1
1
1
1
1
1
2
1
2
0
0
2
1
1
2
1
0
2
1
1
0
1
2
1
1
1
1
2
0
1
1
2
0
1
1
1
2
1
1
0
1
1
0
2
1
1
2
1
1
1
2
1
0
1
1
0
0
2
0
2
1
1
2
2
1
0
1
2
2
2
1
1
1
1
1
2
1
1
1
1
1
2
2
0
2
2
2
0
2
1
2
2
2
1
2
1
1
1
0
1
1
2
1
1
1
1
1
2
1
0
1
1
2
0
1
1
1
2
1
0
1
1
1
2
1
2
1
1
1
1
2
0
1
1
0
1
1
1
0
1
2
2
2
0
0
0
1
1
1
1
1
2
2
0
1
1
1
2
2
1
1
1
2
0
1
1
2
1
1
1
0
0
0
2
1
2
1
1
1
1
0
1
2
0
0
4
1
1
1
1
0
1
2
1
1
0
2
1
1
2
0
1
1
2
1
1
1
2
0
1
0
1
1
1
2
0
0
2
1
0
1
0
0
1
1
1
1
0
1
2
1
1
2
2
0
0
1
2
1
2
2
0
2
1
1
1
1
1
2
2
2
1
0
0
1
1
1
1
1
2
2
1
1
0
0
1
1
1
1
1
2
1
2
1
1
2
1
2
2
2
1
2
1
0
1
0
1
0
1
1
1
2
1
1
1
2
1
1
1
0
1
2
1
2
1
0
1
1
1
1
2
0
2
1
2
1
1
1
3
2
1
1
1
2
0
2
1
0
2
1
1
1
1
2
1
0
2
2
2
2
0
1
1
1
1
1
2
1
1
1
2
2
1
0
2
1
1
1
0
1
1
1
1
1
2
1
1
1
1
1
1
1
1
0
1
1
1
2
0
0
0
1
1
0
1
1
1
1
0
1
2
1
2
0
1
1
2
2
3
1
1
1
2
2
1
2
0
1
1
0
0
0
1
1
1
2
1
1
2
1
2
0
1
1
0
1
0
1
1
2
1
1
2
0
0
1
0
0
1
2
1
1
1
0
1
1
1
1
1
1
2
0
1
1
1
0
1
1
0
1
0
2
2
1
2
1
2
0
0
1
1
1
1
1
1
1
0
0
0
0
1
0
1
2
1
1
2
2
1
1
1
1
3
1
2
1
1
2
1
0
1
0
1
0
0
1
1
1
2
2
2
1
1
2
1
1
1
1
1
1
1
2
1
1
0
0
1
1
1
0
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
0
1
1
1
0
1
0
0
1
2
1
0
1
1
0
0
1
1
1
1
1
1
1
1
1
0
1
1
2
2
1
2
1
0
2
1
2
0
1
1
1
0
1
0
0
0
2
1
0
1
1
2
2
1
2
1
1
2
1
1
0
1
1
2
1
2
1
1
2
1
2
1
0
0
0
1
2
1
2
1
2
1
1
1
1
1
2
1
1
1
2
1
1
2
1
1
0
0
1
1
1
1
1
1
0
0
1
1
2
2
0
1
1
1
2
0
0
1
0
1
1
0
2
2
1
1
1
1
1
2
1
2
0
1
1
1
2
0
0
2
0
0
1
2
1
0
2
0
2
0
1
0
1
2
1
1
2
1
1
2
2
0
1
1
1
0
0
1
1
2
1
2
0
0
0
0
1
1
1
1
2
0
1
1
0
0
2
1
0
1
2
1
1
1
1
1
2
2
1
1
1
1
1
0
1
1
1
0
1
1
1
1
0
1
1
2
1
2
2
1
1
0
2
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
0
0
1
0
2
2
1
2
2
0
2
0
1
0
2
1
1
1
1
1
1
1
0
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
2
2
0
1
0
1
2
1
1
0
1
1
2
2
1
1
1
0
1
1
2
1
1
1
1
1
1
2
1
1
0
1
0
2
1
1
1
1
1
1
1
0
1
0
1
2
1
1
1
1
1
0
2
2
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
1
2
0
1
1
0
1
1
0
0
1
1
1
1
1
1
2
1
2
1
2
2
1
1
1
1
1
2
2
1
1
0
0
1
1
2
0
1
1
1
0
1
2
1
1
3
1
1
1
2
1
2
0
1
2
0
0
1
1
0
1
1
2
1
2
2
2
1
1
2
2
1
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
0
2
1
1
1
1
2
1
1
1
1
0
2
1
2
1
1
1
1
1
0
1
1
1
0
2
0
1
1
1
1
1
1
1
1
0
1
0
2
1
1
1
2
0
0
1
2
0
1
2
1
1
1
0
2
1
1
1
1
1
1
2
2
0
2
2
1
2
1
1
2
2
5
2
2
3
1
0
1
2
1
0
1
1
1
1
1
2
1
2
1
1
2
2
2
1
0
1
1
0
0
2
2
0
0
3
0
1
1
2
2
0
1
1
2
2
1
2
1
0
0
0
1
1
1
1
3
2
0
1
1
1
1
1
2
1
2
2
1
1
0
0
1
1
1
1
1
1
0
0
1
1
3
1
1
1
0
1
1
0
1
1
0
1
1
1
1
2
1
1
2
1
1
0
1
1
1
0
1
1
1
1
1
0
2
2
0
2
1
1
1
1
2
1
0
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
0
0
1
1
0
1
0
1
0
1
1
1
1
0
0
0
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
0
4
1
2
1
2
1
1
0
2
1
1
1
1
1
1
2
1
1
1
2
1
0
2
0
1
1
1
2
0
1
1
2
0
0
0
1
2
1
2
2
1
1
1
2
2
2
1
1
1
0
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
0
2
1
1
2
2
2
1
2
1
1
1
0
1
1
2
2
1
2
0
0
1
1
1
0
2
1
2
1
2
1
2
1
1
1
0
2
0
1
1
1
0
0
1
2
1
1
1
0
1
2
2
0
0
2
0
1
1
0
1
1
2
1
1
3
1
2
1
0
1
1
2
0
2
1
1
1
1
2
2
1
1
1
1
0
1
0
1
2
2
0
1
1
0
1
2
1
1
1
2
1
1
0
2
1
1
1
1
2
2
1
0
0
1
1
1
1
0
1
2
1
0
1
1
2
1
2
1
0
1
2
6
0
1
1
2
1
2
2
2
1
1
1
0
1
2
1
2
1
1
2
1
0
1
1
4
1
1
1
0
1
1
0
1
0
2
2
1
1
1
0
2
1
0
0
0
1
2
1
1
1
2
2
2
1
2
1
0
1
1
1
2
1
1
0
1
2
0
1
2
1
1
2
2
1
0
1
2
0
2
0
1
0
2
1
0
1
1
1
1
0
1
2
1
1
1
2
1
2
0
1
3
1
2
1
0
1
1
2
0
0
1
1
0
2
1
1
0
2
1
1
2
1
1
0
0
0
1
0
1
1
0
2
0
1
2
1
2
1
2
0
0
1
2
2
2
1
1
0
1
1
2
2
0
1
1
1
4
1
2
1
1
1
2
1
2
1
1
0
0
1
2
1
1
2
2
1
1
0
1
2
1
1
2
1
1
1
1
1
2
1
2
1
2
0
1
0
2
1
1
0
1
0
2
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
2
0
2
2
2
1
1
2
0
1
1
1
2
1
1
0
1
1
1
1
1
2
1
1
1
0
0
1
2
1
0
0
0
1
2
1
2
1
1
0
1
1
1
0
1
0
4
1
1
1
1
0
1
1
2
1
1
1
1
2
1
1
0
0
3
1
1
1
1
0
1
0
0
2
2
1
0
1
1
1
1
1
1
1
1
0
1
1
1
1
0
2
1
1
0
2
1
2
1
0
1
2
1
1
1
3
2
0
0
2
1
1
0
1
1
1
1
1
1
2
0
1
1
1
1
1
1
0
1
0
1
2
1
1
1
1
2
1
1
1
1
1
2
2
2
0
2
1
1
1
1
2
1
1
1
0
2
1
1
2
1
1
1
1
2
1
2
2
1
1
1
1
1
2
1
2
1
2
1
2
2
1
0
2
0
1
0
1
3
1
1
1
1
1
1
0
1
2
1
0
1
1
1
2
0
1
1
1
1
1
0
2
0
2
0
1
1
1
2
2
1
1
1
1
2
2
0
1
0
1
0
1
2
0
1
2
1
0
1
1
1
1
2
1
1
1
1
1
1
1
1
0
2
1
2
1
1
1
1
1
2
2
0
1
1
2
1
0
2
1
1
2
2
1
0
1
2
1
1
0
2
1
1
1
1
2
2
1
1
2
2
0
2
1
1
1
0
1
0
2
1
1
1
1
0
0
1
1
0
1
1
1
2
2
2
1
1
0
1
1
1
1
1
1
1
3
1
1
2
1
2
0
1
1
1
0
1
2
1
2
0
0
0
1
1
0
1
1
2
1
1
1
2
2
2
1
2
1
0
1
0
0
1
3
2
1
2
1
2
0
1
1
2
1
2
2
0
1
1
2
0
1
0
1
1
0
1
2
0
2
1
1
0
1
0
2
1
0
0
2
1
2
1
2
2
2
1
1
0
1
0
2
1
1
1
2
0
1
1
1
1
0
2
1
1
1
1
1
2
1
1
0
0
2
0
1
1
2
0
1
0
0
0
1
1
1
1
2
1
2
0
1
2
3
0
1
0
1
0
1
2
1
1
2
0
2
1
1
1
0
1
1
3
1
2
2
1
1
1
1
2
2
1
1
1
2
0
1
1
1
2
2
2
1
2
1
2
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
0
1
0
1
2
1
1
0
2
0
2
1
1
0
2
1
2
1
2
2
1
1
1
1
0
0
1
0
2
1
0
0
1
0
2
0
1
0
0
1
2
1
0
2
2
1
1
1
1
1
1
1
0
1
2
0
1
1
1
1
1
1
1
1
0
0
2
1
1
2
1
0
1
2
1
1
1
1
1
1
0
0
2
1
0
1
1
1
1
0
2
1
1
0
2
0
0
1
2
0
1
1
1
2
0
0
0
0
1
2
0
1
1
1
1
1
1
1
1
1
0
1
2
2
1
1
1
1
0
1
1
0
0
1
2
2
0
1
1
0
1
1
1
1
1
1
2
0
1
1
0
2
1
0
1
1
1
1
1
0
2
1
0
1
1
1
1
2
0
1
1
1
1
1
1
1
1
0
0
1
1
1
1
0
1
2
1
1
1
2
2
1
2
1
4
0
1
2
0
1
1
2
1
1
1
1
2
1
2
2
1
0
2
0
1
1
2
1
1
0
4
1
1
1
1
1
0
1
0
2
2
0
2
2
0
1
1
1
2
1
1
1
1
1
2
1
1
0
1
1
1
1
0
2
2
1
1
1
2
1
1
1
0
2
1
1
2
1
0
1
1
2
1
1
0
0
2
1
2
1
2
1
3
0
1
1
1
2
1
1
1
2
0
0
1
1
1
1
1
1
0
4
2
1
2
0
2
0
2
1
0
2
1
1
2
2
2
1
1
1
1
1
0
1
1
1
1
0
0
1
2
2
2
1
1
1
1
2
1
1
1
2
1
2
1
0
3
1
1
1
1
0
1
2
1
1
0
2
2
1
1
2
2
1
0
3
0
2
1
1
0
2
2
1
1
1
1
0
0
2
1
1
2
1
2
1
1
1
1
2
1
1
1
0
1
1
1
1
3
1
0
1
0
1
1
1
1
0
1
1
1
2
0
1
2
1
1
0
2
1
1
1
1
2
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
0
1
2
1
1
1
0
0
1
2
2
1
1
1
1
1
1
1
1
1
2
1
2
1
2
1
2
1
1
1
1
0
0
1
0
1
1
2
1
1
1
0
0
2
3
1
1
1
0
2
1
1
0
1
1
1
1
2
1
1
1
1
2
1
2
1
1
2
1
1
1
2
2
0
2
1
1
2
1
2
1
1
2
2
1
2
1
2
0
1
1
4
1
1
1
0
1
2
1
1
0
0
2
0
1
0
1
0
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
7
1
1
1
0
1
0
1
1
1
1
2
0
1
1
1
2
1
1
2
0
1
2
0
2
1
0
1
0
0
2
2
1
1
0
1
1
2
0
0
1
2
1
1
1
1
1
0
0
1
1
1
1
2
1
1
1
1
0
1
1
1
1
1
1
1
0
1
1
1
1
1
2
1
1
1
2
1
1
1
2
0
2
1
2
0
1
2
0
1
2
2
1
1
1
1
1
1
1
1
1
1
2
2
1
1
0
1
1
1
1
1
2
1
0
0
2
1
1
0
2
1
0
1
1
1
0
0
1
1
1
1
0
3
1
1
1
1
2
1
1
0
0
2
1
2
3
0
0
1
2
1
1
1
1
2
1
1
1
1
0
1
2
1
0
2
1
2
1
1
1
1
1
1
2
1
1
2
0
1
2
2
2
1
1
1
1
1
0
1
0
0
1
1
2
0
1
1
1
1
1
1
2
2
1
1
2
2
1
0
1
1
1
2
1
1
0
2
2
1
1
2
1
1
0
0
1
1
2
2
2
0
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
0
1
2
0
1
1
1
1
0
0
1
2
1
1
2
0
2
1
1
0
1
1
0
1
0
2
1
1
1
1
2
1
0
1
2
0
0
4
1
0
0
0
1
1
0
2
4
1
2
3
0
0
1
1
1
1
1
1
1
0
1
2
1
0
0
1
2
0
0
2
2
1
1
1
0
1
0
1
0
1
1
1
1
1
1
2
0
2
0
2
1
0
1
0
1
0
2
2
2
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
0
1
0
0
2
1
1
1
1
2
2
1
1
1
1
3
0
2
1
1
1
1
0
0
0
2
1
2
2
0
1
1
0
1
1
2
1
3
0
0
0
0
1
0
2
1
2
1
1
2
1
1
2
2
2
0
1
1
1
0
1
1
0
1
1
0
1
1
0
1
1
2
1
0
2
2
0
1
1
1
0
1
2
1
1
2
1
1
0
3
0
2
1
1
1
3
4
1
1
0
1
1
1
2
1
1
2
0
1
1
1
1
2
1
1
1
2
1
1
2
0
1
1
1
2
1
1
2
1
1
2
2
1
1
1
0
1
1
0
0
1
1
2
0
1
1
1
1
1
0
1
1
0
1
0
1
1
1
1
2
1
0
1
1
2
1
0
0
1
3
1
1
2
1
1
1
1
1
0
2
1
1
2
1
2
0
2
0
2
1
1
1
1
0
1
0
1
2
1
1
0
0
1
1
1
1
2
0
2
1
0
1
1
1
2
1
2
0
1
1
0
2
0
2
1
0
1
1
0
1
1
1
1
2
2
1
0
1
1
0
2
1
1
1
1
2
0
1
3
1
1
2
1
1
0
1
2
1
0
0
1
1
2
2
1
0
2
1
1
0
1
1
2
3
1
1
1
2
1
0
2
1
0
2
2
1
1
1
0
2
2
0
1
1
2
1
1
2
1
0
1
2
1
1
1
1
1
0
0
0
1
3
1
1
2
1
1
1
1
0
2
0
0
0
1
1
2
2
2
2
1
0
1
1
1
2
2
1
0
2
1
1
0
0
1
1
1
1
3
0
2
2
0
1
1
1
2
1
2
2
1
1
2
3
1
0
2
2
2
0
2
2
0
1
1
0
1
1
1
1
1
0
1
0
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
2
2
1
1
0
1
1
1
0
0
1
0
1
2
1
1
1
1
1
2
0
1
2
0
0
1
1
1
1
1
1
1
1
0
1
1
2
0
0
2
1
0
1
2
2
2
2
1
2
0
1
0
1
2
1
1
1
1
2
1
0
2
1
1
1
2
1
2
2
1
2
1
2
1
1
1
3
2
1
2
1
2
2
1
0
1
3
0
2
2
1
1
2
1
2
1
1
2
1
0
1
1
1
1
0
2
1
1
1
1
1
1
1
0
2
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
2
1
0
2
1
1
0
1
1
1
2
1
1
1
1
1
0
1
1
2
2
1
2
1
1
2
0
1
0
1
2
2
1
1
1
2
2
3
0
0
1
2
1
1
2
1
0
0
1
1
2
1
2
0
0
0
1
1
1
1
0
2
0
2
1
1
2
1
1
0
1
1
1
2
0
1
1
2
1
2
2
2
1
2
1
1
1
1
2
2
1
1
2
2
1
2
1
0
1
2
0
0
0
0
1
2
1
1
1
1
1
1
0
2
1
0
1
2
1
2
1
1
1
3
1
1
2
1
1
0
2
1
1
1
1
1
2
0
1
0
2
1
0
2
0
0
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
2
0
1
1
1
1
1
0
1
1
1
1
0
1
1
1
2
1
2
2
1
1
2
2
2
1
1
0
1
1
0
1
1
0
0
1
2
1
1
0
1
1
1
1
1
1
1
0
2
0
1
1
2
1
2
0
1
1
1
0
1
1
0
0
1
2
1
1
1
0
1
2
2
1
0
1
1
1
1
0
1
1
2
1
1
2
1
1
2
1
1
1
2
1
1
1
1
1
2
1
0
1
1
2
1
0
1
1
1
1
1
2
1
1
1
2
2
1
2
1
2
2
1
1
1
1
1
2
0
0
1
1
2
2
1
2
1
0
1
2
1
2
1
1
1
0
1
1
1
1
0
1
1
2
2
1
1
1
0
0
1
2
2
1
1
1
1
1
0
2
1
1
0
0
1
1
1
2
1
2
1
0
2
0
1
0
0
2
1
1
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
1
0
1
2
0
1
2
1
1
0
1
1
2
1
1
0
1
2
1
1
1
1
2
1
2
1
1
2
1
1
1
1
1
1
0
1
1
0
2
3
0
2
2
0
0
1
1
0
1
1
1
1
0
2
2
2
1
1
1
1
1
2
1
1
2
2
0
2
1
2
2
2
2
2
1
1
1
1
1
0
1
3
0
2
0
1
1
1
2
0
1
1
2
1
1
1
1
2
2
1
1
1
1
1
0
2
1
1
2
1
1
2
1
2
1
1
2
1
2
1
1
1
1
1
2
1
0
1
1
1
1
1
1
1
0
1
2
0
1
0
2
1
1
1
1
1
1
1
1
2
0
1
1
1
2
1
0
0
1
1
1
0
2
1
2
1
2
1
1
1
2
1
1
0
2
1
1
1
0
1
0
1
1
1
1
1
2
0
2
1
0
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
0
1
1
2
1
1
0
1
1
1
0
1
0
1
2
1
1
1
1
2
2
1
2
1
1
1
2
0
2
1
1
2
1
1
2
1
1
1
1
1
2
0
1
1
1
2
1
2
1
1
1
2
1
1
0
0
1
2
2
2
2
1
1
2
1
0
1
2
1
0
0
1
1
2
1
1
0
1
1
1
2
2
1
0
1
1
1
1
0
1
2
1
1
1
1
1
0
1
0
0
0
1
2
0
1
0
1
0
2
2
1
0
0
1
0
1
0
1
1
2
2
1
0
2
0
2
0
0
2
1
2
1
1
1
0
1
1
1
2
1
0
1
1
2
2
1
1
1
0
0
1
2
0
1
1
1
1
1
0
2
1
1
2
1
0
1
1
1
1
1
2
1
1
1
1
1
0
1
0
20
2
3
2
1
1
1
0
1
0
1
0
1
0
1
1
2
1
1
2
2
0
1
1
1
1
1
2
0
2
0
1
2
1
1
1
2
1
1
1
2
0
1
1
1
1
0
0
1
0
0
2
2
1
0
0
1
0
1
0
1
1
1
2
2
1
2
1
2
1
1
1
1
1
0
0
1
1
1
2
1
1
0
2
1
2
1
1
1
1
0
1
1
1
1
2
1
0
1
2
2
1
3
1
0
1
1
1
0
1
1
1
1
1
1
3
2
0
1
2
1
1
0
1
1
2
1
1
2
2
0
0
2
2
1
1
1
1
2
1
0
2
1
1
1
0
2
2
2
1
1
1
0
1
1
2
0
1
0
1
1
0
0
2
2
0
1
1
0
0
1
1
2
2
1
1
1
2
1
0
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
2
0
1
2
2
2
2
1
1
1
2
0
1
1
0
1
1
0
1
0
1
2
0
0
1
0
1
0
1
2
2
2
2
0
1
1
2
1
1
0
1
2
1
2
1
1
1
1
2
2
2
1
0
1
2
1
2
1
1
1
1
0
1
2
1
1
1
2
2
1
1
2
0
1
1
1
2
2
1
6
1
1
1
1
1
2
0
3
0
1
2
0
0
0
1
0
2
1
3
2
1
1
1
2
1
0
2
0
2
2
1
0
0
0
2
2
0
1
1
2
1
2
2
1
2
1
1
0
1
1
1
1
2
1
1
2
2
1
1
0
0
1
0
2
1
0
0
1
1
1
1
0
0
1
1
0
1
1
1
1
2
1
1
1
2
1
1
1
1
2
0
1
1
1
1
2
1
2
2
1
2
0
1
2
1
0
1
1
1
1
1
1
3
1
1
2
0
1
1
1
0
1
1
2
0
3
1
1
2
1
0
0
1
0
1
1
1
2
1
0
0
1
2
1
1
1
1
0
1
1
1
1
0
1
1
2
1
2
1
1
2
0
2
2
1
1
0
0
2
1
1
0
2
2
2
1
1
0
0
0
0
1
1
1
2
2
1
2
0
1
0
1
1
1
0
2
1
2
1
1
1
1
2
1
0
1
1
1
0
1
2
1
1
1
0
1
1
2
1
1
0
1
1
1
1
1
1
0
0
1
0
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
0
2
1
1
0
1
1
1
1
0
1
0
1
1
1
0
2
2
1
0
1
1
0
1
2
2
1
2
1
1
3
1
2
1
1
1
1
2
1
0
1
1
3
1
1
1
0
1
2
2
1
1
1
1
0
1
2
1
1
2
2
1
2
1
2
2
1
1
2
1
1
1
1
1
2
2
2
1
1
1
1
1
1
0
1
2
2
1
1
1
2
2
2
1
1
0
1
0
2
2
1
1
2
1
1
2
0
0
1
1
0
0
1
1
1
1
1
0
1
1
0
2
2
2
1
2
2
1
1
1
1
2
1
1
0
1
1
1
2
1
1
1
1
1
2
1
1
2
1
0
1
1
1
2
0
1
2
0
2
1
1
0
0
1
1
1
1
2
1
1
4
1
1
0
0
1
0
1
2
1
1
0
1
2
2
1
0
1
0
1
2
1
1
2
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
0
0
0
1
1
0
2
2
2
2
1
0
1
2
1
2
2
1
2
1
2
1
2
1
1
1
0
1
1
1
1
1
2
0
1
1
2
1
2
2
2
1
2
0
2
1
2
1
2
1
1
1
1
2
1
1
1
2
1
2
1
1
1
2
2
0
1
2
2
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
2
2
1
0
0
1
0
2
1
1
0
2
0
1
1
2
2
1
1
1
1
0
0
1
1
1
0
1
1
1
1
1
2
0
1
1
2
1
2
1
0
2
0
1
0
2
1
1
1
1
1
1
1
2
1
1
1
1
2
1
0
0
0
1
1
1
1
0
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
3
1
1
1
0
1
1
2
1
2
2
0
1
0
0
0
2
1
1
1
0
1
1
2
1
1
2
2
1
1
1
1
2
1
1
0
0
2
1
1
0
1
2
2
1
0
0
2
0
1
0
0
1
1
2
1
0
2
1
1
2
1
1
1
2
0
2
1
0
2
1
1
1
1
1
1
1
0
1
0
2
2
1
2
2
1
1
1
1
2
1
2
2
2
2
1
2
2
1
1
1
1
2
0
1
2
0
1
1
0
0
0
1
0
2
1
1
1
1
1
1
2
1
1
0
1
1
0
2
2
1
0
2
1
1
1
2
2
1
2
0
3
2
0
0
0
2
1
2
0
1
0
2
1
0
1
1
0
1
2
0
1
2
1
2
0
1
1
0
1
1
2
2
2
2
1
4
1
2
2
1
1
1
1
2
1
1
1
1
1
1
0
0
1
2
1
0
0
2
2
1
0
1
1
1
1
2
1
1
1
1
1
1
2
0
1
1
1
2
2
2
1
0
0
2
2
0
1
0
2
1
1
0
1
1
2
0
2
0
0
1
2
1
1
1
1
1
2
0
1
0
2
1
1
0
1
1
1
1
1
1
1
1
1
1
2
1
1
1
0
1
1
0
2
1
0
1
0
1
2
2
2
0
1
2
1
2
1
2
2
1
1
1
0
2
2
1
1
2
0
2
1
1
1
2
1
1
1
1
1
0
1
1
1
1
2
1
2
1
0
1
1
1
2
1
0
2
1
2
1
1
1
0
1
2
0
2
1
1
1
1
1
0
0
1
1
2
1
1
1
0
1
1
1
1
1
1
2
1
2
1
2
2
1
2
1
2
0
1
2
2
1
1
1
2
1
0
2
1
1
1
1
1
1
2
1
1
2
1
1
0
1
0
0
1
2
1
2
0
1
1
1
1
1
0
0
1
1
2
2
2
1
1
0
2
1
1
1
1
1
1
1
0
2
1
2
1
1
2
1
1
2
2
1
1
2
2
0
1
0
1
1
2
1
1
1
1
0
1
2
1
1
2
1
0
1
3
0
2
1
1
2
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
0
1
0
1
0
1
0
2
0
2
1
2
0
1
2
2
1
2
1
1
2
1
1
0
2
1
0
1
2
2
1
1
0
1
0
1
1
1
2
2
1
1
2
1
1
0
1
1
0
2
1
1
1
2
2
1
1
1
2
2
0
2
1
1
0
0
1
0
0
2
0
1
2
0
0
2
2
1
2
2
1
1
1
1
2
1
0
1
1
2
0
0
1
0
0
1
0
2
2
1
1
2
1
1
1
1
2
2
1
1
1
1
0
2
1
1
1
0
0
2
1
1
1
1
1
0
0
1
1
1
2
1
2
1
1
1
1
0
2
2
2
0
1
1
1
1
1
1
1
0
0
1
1
2
0
1
2
1
2
1
1
0
1
2
0
1
1
1
1
2
2
1
1
2
1
1
1
2
0
0
1
0
1
2
2
0
2
1
1
0
2
2
0
1
2
1
1
0
0
1
1
1
1
0
1
1
1
1
1
2
1
1
1
1
0
1
1
1
0
0
0
1
1
2
0
1
1
1
2
1
1
1
1
0
2
1
0
1
1
1
2
2
0
1
1
0
1
1
1
0
0
1
0
1
1
1
2
1
1
2
1
1
2
1
1
1
0
1
1
1
1
1
0
1
1
2
1
1
1
1
1
1
1
1
0
2
1
1
4
0
1
1
2
1
2
2
1
1
1
1
1
0
1
0
0
1
1
2
1
1
2
0
2
2
1
1
1
2
2
2
1
2
2
0
0
2
1
1
1
1
0
0
0
2
1
1
2
1
1
2
2
1
2
0
0
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
1
0
0
1
2
1
1
1
2
1
2
2
1
1
1
2
2
2
2
0
0
1
1
0
2
1
1
0
1
2
2
1
2
2
1
1
2
2
0
2
2
2
2
1
0
1
1
1
2
0
2
1
0
1
2
0
1
2
2
1
1
0
2
1
1
1
0
1
2
0
1
1
0
0
2
1
2
0
1
0
2
1
1
1
1
1
0
2
1
0
1
1
1
1
1
2
2
1
2
2
2
1
0
2
0
1
1
0
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
0
1
1
1
1
0
2
1
2
1
0
2
1
0
0
0
1
1
2
1
2
1
1
1
1
1
0
1
1
1
1
0
1
2
2
2
0
0
2
1
1
0
1
1
2
0
0
0
1
1
1
1
2
1
1
1
2
1
1
1
2
2
1
1
1
2
0
2
2
2
1
2
1
1
0
2
0
0
1
2
0
0
2
1
0
1
0
1
1
2
0
1
0
1
0
2
1
0
2
1
1
1
1
1
1
1
0
1
1
2
0
1
2
1
2
1
1
1
1
0
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
2
0
1
0
0
1
0
1
1
2
1
0
1
0
0
0
1
2
1
0
0
2
1
2
2
1
1
0
2
1
1
1
1
0
1
2
2
1
0
2
2
0
1
1
0
1
2
0
1
3
3
1
2
1
0
0
1
0
2
1
1
1
2
2
2
2
1
0
0
1
2
1
1
1
2
1
1
3
1
1
1
2
1
1
1
1
2
1
2
1
1
1
1
0
2
1
1
1
0
1
1
0
1
1
1
1
1
2
1
0
0
2
0
1
1
2
1
1
1
1
2
1
1
0
2
0
1
1
1
1
2
1
0
1
2
0
1
1
1
1
2
1
2
2
0
2
2
1
1
1
2
0
2
1
1
2
2
1
2
0
1
0
1
2
3
1
0
1
1
2
0
1
1
1
1
0
2
1
1
2
0
1
2
0
2
2
1
1
1
1
1
0
0
1
0
1
2
1
1
1
1
0
1
1
0
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
2
1
2
2
0
2
1
1
2
1
1
1
2
0
1
0
1
1
1
2
0
0
2
2
1
2
1
1
0
2
1
1
2
2
0
1
1
1
1
2
2
2
1
1
0
1
1
1
1
1
1
1
2
2
2
0
0
1
1
0
1
1
1
2
1
1
1
1
0
0
1
2
2
2
2
1
2
1
1
2
1
1
1
1
2
1
2
1
2
1
1
2
2
1
0
1
1
1
1
1
1
2
1
4
1
2
2
2
1
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
2
1
1
2
1
2
1
1
1
1
0
0
0
1
2
2
1
1
2
2
1
0
1
1
1
1
1
2
2
1
1
1
0
1
1
1
2
1
2
2
1
0
1
1
1
1
1
0
1
1
1
1
1
1
0
1
1
1
1
1
1
2
1
0
1
1
1
1
1
1
1
0
1
2
1
1
2
2
1
2
1
1
0
1
0
2
2
0
1
0
1
2
2
0
1
1
0
0
0
1
0
0
2
1
0
1
0
1
1
1
1
1
1
1
0
0
1
1
1
1
1
0
2
1
2
1
0
1
0
2
2
0
1
1
1
1
0
1
0
2
0
1
1
1
1
1
1
1
0
1
2
1
2
1
1
2
1
2
1
1
1
1
1
2
0
0
1
1
1
1
1
1
1
2
1
2
1
0
2
1
0
1
1
2
0
0
2
0
1
2
2
1
0
1
1
1
2
1
1
0
0
1
0
0
1
1
1
2
1
1
1
1
2
1
1
1
1
1
2
2
1
1
2
2
2
1
1
1
0
1
1
2
1
2
1
1
0
2
0
2
1
1
0
2
2
1
0
2
2
1
1
1
0
1
0
2
1
2
1
1
1
1
1
2
1
1
0
0
1
2
2
0
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
2
0
0
1
1
2
1
2
0
1
1
1
1
1
1
1
3
2
2
1
0
1
2
0
1
0
0
2
1
0
2
1
1
1
0
1
1
0
1
1
1
2
1
1
0
2
1
1
0
2
1
1
1
1
2
1
1
1
1
0
1
1
2
1
2
0
0
1
1
0
1
1
2
2
0
1
2
1
1
1
0
2
1
0
1
1
1
2
1
1
1
0
1
0
0
1
2
2
1
0
1
1
1
1
2
1
1
2
1
1
0
3
1
1
1
1
2
2
1
1
1
0
0
1
1
1
0
1
0
1
2
1
2
1
0
1
1
1
1
2
1
1
0
1
1
1
0
0
2
0
1
2
2
1
1
2
0
1
0
2
0
2
1
2
2
2
2
0
1
1
1
1
1
2
1
2
2
1
0
1
1
1
1
2
1
1
1
0
2
1
2
2
1
1
3
1
0
2
1
0
1
1
1
1
1
0
1
0
1
0
1
1
1
1
1
1
2
0
2
1
0
0
1
2
1
1
1
1
0
1
2
1
2
1
1
2
2
0
2
2
0
0
1
10
0
0
1
2
1
0
1
3
0
1
0
0
2
0
1
1
2
0
0
1
0
1
1
0
2
1
1
1
1
0
1
1
1
0
2
1
1
0
1
1
0
1
0
1
1
0
2
0
1
0
1
2
2
1
2
1
1
0
2
1
1
1
1
1
0
0
0
1
1
1
1
1
0
2
0
1
1
1
1
1
1
2
2
2
1
1
2
1
1
0
1
2
2
1
1
1
1
1
1
1
2
3
0
1
1
4
1
2
1
1
1
1
1
1
1
1
0
2
1
1
2
2
1
1
1
1
2
2
1
2
1
2
1
2
2
1
2
2
1
0
2
2
1
1
1
2
1
1
3
1
1
1
2
1
0
0
0
0
1
1
1
0
1
1
0
1
2
2
1
2
1
1
1
1
2
1
2
1
0
1
2
1
2
0
1
2
1
1
1
1
1
1
2
2
1
2
1
0
1
2
1
1
2
1
1
1
2
2
1
3
1
0
1
1
1
1
2
1
2
3
1
1
1
1
1
0
0
1
2
1
0
1
1
1
1
1
2
2
1
0
1
2
1
1
1
2
1
2
1
1
2
2
1
1
0
1
1
0
1
2
0
1
2
1
1
1
1
0
1
1
1
0
1
1
1
2
1
2
0
1
1
1
1
1
1
2
1
1
3
1
0
2
2
0
2
1
1
0
0
1
0
2
1
2
1
0
1
1
0
0
2
1
0
2
1
1
1
1
1
0
1
1
1
1
1
1
0
1
1
3
2
1
1
1
1
2
2
1
1
1
1
1
1
2
2
1
1
1
0
0
1
1
2
2
1
1
1
1
1
1
1
0
1
2
0
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
2
2
0
2
2
2
2
1
1
1
2
2
1
1
1
1
1
1
3
2
1
1
2
1
2
1
1
2
1
1
2
1
1
2
1
1
1
2
1
0
1
1
1
1
1
3
1
0
1
1
1
1
1
2
1
0
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
2
0
0
1
0
1
1
1
0
1
0
2
1
1
1
1
2
1
1
1
2
1
0
1
1
2
2
2
0
0
1
2
2
1
1
3
1
2
1
0
1
1
1
1
2
1
1
1
1
0
0
2
0
1
0
2
1
2
2
0
0
2
1
1
1
2
2
1
1
2
1
1
2
0
1
1
1
1
1
1
0
1
1
1
2
1
1
2
2
1
1
1
1
1
0
0
1
0
2
1
1
0
0
2
1
1
1
1
1
1
1
1
0
0
1
2
4
3
0
1
2
0
2
1
1
1
1
1
1
1
1
1
2
2
2
2
1
1
1
0
1
1
1
0
1
1
1
1
0
3
1
2
1
0
1
2
0
1
1
1
0
1
3
0
2
1
0
1
2
1
1
0
1
1
1
2
2
1
0
0
0
2
1
1
1
1
2
1
1
0
1
1
1
0
2
0
1
0
1
1
2
1
3
1
1
0
1
0
1
1
1
1
1
1
2
1
1
1
2
1
1
2
0
0
2
2
2
1
1
1
2
1
1
1
2
1
1
1
0
0
1
2
1
0
0
1
1
2
1
1
0
0
0
0
1
1
0
1
1
1
2
1
1
2
2
1
1
1
0
0
1
1
2
1
1
1
0
1
1
2
1
1
1
2
0
1
0
2
2
2
0
2
1
1
1
0
0
0
1
1
1
1
1
0
2
0
1
2
0
1
0
2
2
0
1
1
2
2
1
1
1
0
1
0
1
1
2
1
1
1
0
0
1
2
2
1
1
1
2
1
0
1
2
2
1
1
1
1
2
0
2
1
1
1
1
1
1
1
0
0
1
1
1
0
1
1
2
0
1
0
2
1
1
0
0
0
2
1
0
2
1
2
2
2
1
3
1
1
2
2
0
1
1
2
2
0
1
2
2
2
1
2
0
1
2
2
1
1
1
0
1
1
1
1
2
1
1
1
1
0
1
1
1
1
0
1
2
1
0
0
2
0
0
0
1
1
1
1
1
2
0
1
1
1
1
2
1
1
1
1
1
2
0
0
1
1
1
1
1
1
0
0
1
1
1
1
2
1
1
0
0
2
1
1
1
1
1
2
0
1
2
1
1
0
1
1
2
0
1
0
1
0
0
2
1
2
0
0
2
0
1
0
0
2
1
2
1
1
0
1
1
0
0
1
1
0
1
1
0
2
0
2
2
1
0
2
1
0
1
2
1
0
2
1
1
0
1
2
1
1
1
0
2
1
2
1
1
2
0
1
1
0
1
2
1
1
1
1
1
1
1
0
0
0
1
1
2
2
2
0
1
0
1
2
1
1
1
0
1
2
1
1
1
0
0
1
1
0
1
2
0
1
1
1
1
1
1
1
1
0
1
2
1
2
1
1
2
0
2
0
2
1
1
0
0
1
1
2
0
2
1
1
0
1
1
0
0
2
1
0
1
1
0
1
0
1
1
1
2
1
1
1
1
1
1
0
0
1
1
2
1
2
1
2
1
0
2
1
2
2
3
2
1
1
1
2
2
2
1
1
1
1
1
2
1
0
2
2
0
1
2
0
1
1
0
1
1
1
1
1
2
1
1
2
0
1
2
1
2
1
2
0
2
1
0
0
1
1
1
1
2
1
1
2
0
0
1
1
2
0
0
2
1
1
0
1
1
1
1
1
1
1
0
2
2
1
1
1
0
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
2
1
1
1
0
1
1
2
1
1
1
1
1
1
2
1
0
1
2
1
1
2
1
1
1
1
1
1
0
1
1
1
2
2
2
1
1
1
2
2
0
1
0
1
0
1
2
2
1
2
2
1
2
1
1
1
0
1
0
2
1
0
1
1
0
2
1
1
0
1
2
1
2
1
0
1
2
1
0
2
2
0
2
1
2
0
1
1
1
2
1
1
1
0
1
1
0
1
1
0
2
1
1
0
1
1
1
0
2
0
1
1
1
1
1
2
1
1
1
1
1
2
2
0
1
2
3
0
1
0
0
0
1
1
1
1
0
2
1
1
0
2
2
1
2
1
0
0
0
0
0
1
1
2
1
2
2
1
1
0
2
1
2
0
0
1
0
1
1
0
1
1
1
2
1
1
0
1
1
2
2
1
1
1
1
2
1
0
0
0
2
1
2
1
1
1
1
0
1
0
0
1
1
1
1
2
0
1
1
0
0
0
0
0
2
1
0
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
0
1
1
1
1
0
2
1
1
0
1
2
1
1
0
0
1
1
1
1
1
1
0
1
1
1
2
1
1
1
2
1
0
1
2
2
2
2
0
0
1
1
0
2
0
2
1
1
0
1
2
1
2
1
1
2
1
0
1
0
1
2
1
2
1
0
0
1
0
2
2
1
0
2
2
1
2
1
1
1
1
0
1
1
0
1
0
1
1
1
2
0
2
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
0
1
1
1
1
1
1
1
0
1
1
2
1
2
2
2
1
1
1
1
1
1
0
1
1
1
1
1
2
1
1
2
2
2
1
1
1
0
1
1
2
0
1
0
1
1
1
1
1
1
1
1
2
0
1
1
0
1
1
1
0
2
0
1
0
0
1
0
1
1
2
1
2
1
1
0
0
1
2
0
0
1
1
0
1
1
0
1
0
0
0
0
1
1
1
2
1
0
1
1
1
2
1
1
0
2
2
0
2
2
1
1
0
2
0
1
1
0
1
2
1
2
1
0
1
1
1
0
1
1
1
2
0
1
1
0
1
2
2
0
1
1
1
0
1
1
2
0
1
0
1
1
1
1
1
1
1
1
0
0
0
2
1
1
1
0
1
1
0
1
2
1
0
1
1
1
1
1
0
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
2
0
2
0
1
0
0
1
1
0
2
1
1
1
1
2
1
1
2
1
1
1
2
0
0
2
2
0
1
0
1
0
2
1
1
0
1
0
1
1
2
1
1
1
2
1
0
1
2
1
2
1
1
2
1
1
1
2
0
1
1
1
1
1
2
2
1
1
1
1
1
0
1
1
0
1
1
1
1
2
2
0
3
1
2
1
1
2
1
1
1
1
1
2
1
1
1
0
1
2
0
0
0
1
1
1
1
1
1
1
2
0
1
1
1
1
1
1
1
1
0
2
1
0
1
0
1
0
2
2
2
1
1
1
1
0
2
1
1
2
0
2
0
1
1
2
0
1
1
1
1
2
1
0
2
0
1
1
2
0
1
0
1
1
2
0
1
1
1
2
1
2
1
2
3
1
1
1
0
2
0
2
2
1
1
1
0
0
2
1
0
2
0
1
1
1
1
2
1
0
1
1
1
1
2
0
1
2
1
1
2
1
1
1
2
2
1
1
1
0
0
1
1
1
0
1
0
1
1
1
1
1
1
2
1
1
1
1
2
0
1
1
1
1
1
1
0
1
1
2
1
0
1
1
1
1
0
2
1
2
0
0
2
1
2
1
1
1
1
2
1
1
1
1
1
0
1
1
1
1
1
1
2
1
1
0
1
1
1
2
0
2
2
3
1
1
1
1
0
2
1
2
2
0
1
0
0
1
0
1
1
2
1
1
2
1
2
1
1
1
0
2
1
1
1
0
1
0
1
1
1
1
1
1
1
0
0
2
1
1
1
2
1
1
1
0
2
2
2
1
1
1
1
1
1
1
2
2
2
2
2
1
0
2
0
1
1
1
1
2
2
1
1
2
2
2
1
0
1
1
1
1
1
2
2
0
2
2
1
1
1
0
1
0
1
1
2
2
0
1
2
1
2
1
1
1
1
1
0
1
1
2
1
1
1
1
1
1
2
2
2
1
0
2
1
0
0
1
1
1
1
1
1
1
0
1
0
1
1
2
1
0
1
1
1
1
0
1
0
0
2
1
1
0
0
0
1
0
2
0
2
0
0
1
1
1
2
1
1
1
1
1
1
2
0
2
2
2
4
1
1
2
1
2
1
1
2
2
1
0
0
2
1
1
1
2
0
0
1
0
0
2
1
1
2
0
3
1
1
1
3
0
1
2
1
0
1
1
1
1
1
0
1
2
1
1
1
1
1
1
2
0
0
3
2
1
1
1
2
1
0
0
2
2
1
1
1
1
1
2
2
1
1
0
1
2
1
1
2
1
0
1
1
0
1
0
2
1
1
1
1
1
1
1
1
0
2
0
1
1
1
1
1
1
2
1
1
1
2
2
1
0
1
2
1
1
1
1
1
1
0
2
0
1
1
1
1
1
2
2
1
0
2
1
1
1
1
2
2
2
1
1
1
1
1
0
2
1
1
2
0
1
2
1
1
0
1
1
1
2
2
0
0
0
2
1
2
1
0
0
1
2
1
1
0
1
0
1
1
1
1
1
2
2
1
1
0
0
0
1
2
1
0
1
1
1
0
2
1
0
0
1
1
1
1
0
1
2
1
1
0
2
1
1
0
1
1
2
2
2
1
1
1
0
1
1
1
1
1
0
1
1
1
1
2
1
0
1
2
2
2
1
1
0
1
0
1
2
0
1
0
1
2
1
1
0
1
0
2
1
1
1
1
1
1
2
1
2
0
1
1
0
1
1
0
1
1
2
0
1
2
1
1
1
2
0
0
1
3
1
2
2
1
1
0
2
2
0
0
1
2
1
2
2
1
1
2
0
1
1
1
2
1
1
1
0
1
1
1
0
2
1
1
2
1
1
0
1
1
2
1
0
1
2
1
0
1
1
2
0
1
1
1
1
0
0
1
1
0
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
2
0
1
1
1
2
0
0
2
1
0
1
1
1
2
1
2
1
2
2
1
1
1
2
1
2
2
1
1
2
0
1
2
0
0
0
1
1
2
1
2
1
1
2
2
1
1
1
0
1
1
0
2
2
1
0
1
2
1
1
2
0
0
1
1
1
1
2
1
5
2
2
1
0
1
1
1
1
1
0
1
2
2
0
1
2
1
2
1
2
1
1
0
1
2
1
1
1
1
1
2
0
2
2
1
0
2
1
1
2
0
2
1
1
0
1
1
0
1
1
2
2
1
1
1
1
2
1
1
1
1
1
0
0
1
1
1
0
1
1
1
1
1
2
1
0
0
1
1
1
0
0
1
1
2
1
0
0
1
2
1
0
2
2
1
1
2
2
1
1
1
1
1
2
1
1
1
0
1
2
2
1
1
1
1
2
2
1
1
1
1
0
0
1
0
1
2
1
2
0
1
2
2
1
1
1
2
0
1
2
2
0
2
2
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
4
1
0
0
2
1
1
1
1
1
2
2
2
1
2
1
2
1
2
1
1
1
0
1
1
1
0
1
1
2
0
1
2
1
2
1
1
1
1
1
1
1
1
1
1
2
0
1
1
1
1
0
0
1
0
1
1
1
1
1
0
4
1
1
2
0
1
1
2
1
1
2
1
1
1
0
1
2
1
2
0
1
1
2
0
1
2
2
0
0
1
2
0
2
1
1
0
2
1
1
1
1
1
2
2
1
0
1
1
1
1
2
1
0
2
1
2
0
1
1
0
1
1
0
1
1
2
0
0
0
1
0
2
1
0
2
0
2
2
1
2
2
1
2
1
1
1
1
2
0
0
2
0
0
1
2
0
1
0
0
1
0
0
1
1
1
2
1
0
1
1
0
2
2
2
2
1
1
1
0
1
0
1
1
0
0
2
1
1
1
1
0
2
0
1
1
0
1
1
2
2
1
1
2
0
1
0
1
0
1
1
2
1
1
2
1
1
2
1
1
1
0
0
1
1
1
2
1
1
1
0
2
1
1
1
1
0
1
1
2
1
1
1
1
0
1
1
0
1
2
1
1
2
0
2
1
1
1
0
1
2
1
1
0
0
1
0
3
1
1
1
1
1
1
2
0
1
1
2
2
2
1
0
1
1
0
2
2
2
2
1
0
1
2
1
0
1
1
1
1
1
2
1
2
1
1
1
1
1
2
1
2
1
1
2
2
0
1
1
1
2
1
1
1
1
2
2
1
1
1
1
2
0
0
1
2
0
1
1
1
1
1
2
1
0
1
0
2
1
2
2
1
2
0
1
1
1
2
4
2
2
0
0
1
2
2
0
0
1
1
0
1
2
0
0
0
0
1
1
1
1
1
1
0
1
2
1
0
0
1
0
2
1
1
2
1
1
1
1
1
0
2
1
1
0
2
2
0
1
1
0
3
1
0
1
1
1
1
1
1
0
1
1
0
2
1
1
2
1
1
1
0
1
1
1
0
0
0
1
0
2
1
1
1
1
1
1
1
0
0
1
0
2
1
1
1
1
1
0
0
1
2
2
0
0
2
1
1
1
1
1
0
1
2
2
2
2
1
1
1
0
1
1
1
1
2
1
1
1
1
1
1
0
1
1
2
1
0
1
0
1
0
4
0
1
1
1
1
1
2
2
2
1
2
0
1
0
1
1
0
1
0
2
1
1
1
2
1
1
2
1
1
1
0
1
1
1
0
2
1
2
0
2
1
2
2
1
2
1
1
0
1
1
1
1
1
1
1
2
1
0
1
0
1
1
1
2
1
1
1
2
1
1
0
1
1
1
2
1
1
1
1
3
0
1
1
0
2
0
1
2
1
1
1
1
0
0
1
2
1
2
1
0
2
0
1
3
0
2
1
0
1
1
1
2
1
1
2
1
1
1
2
2
1
1
0
1
2
2
1
2
1
2
1
2
0
1
2
1
2
2
1
1
3
1
1
0
0
1
2
1
0
0
2
1
1
1
0
1
1
1
1
0
0
1
3
1
2
1
0
1
1
0
1
3
1
1
1
1
2
2
0
2
1
0
1
1
2
2
1
1
0
2
1
2
0
0
0
1
1
2
1
0
1
1
2
2
1
0
1
1
2
1
0
1
2
2
0
2
2
1
1
1
2
1
1
2
1
1
1
0
1
1
1
1
1
2
1
1
0
2
0
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
0
2
1
1
2
1
1
1
2
2
2
2
2
2
2
1
1
0
1
2
0
3
1
2
2
0
1
2
1
0
1
2
1
1
1
2
0
1
1
1
0
1
1
0
2
1
1
1
1
1
0
0
1
0
1
2
1
1
2
2
0
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
7
0
0
1
0
1
2
1
1
2
1
1
1
1
1
1
1
2
1
2
1
0
2
2
1
1
1
0
1
0
1
1
1
2
2
1
0
0
1
1
1
1
1
1
1
0
2
1
1
2
2
0
1
1
1
1
2
1
1
1
1
1
1
1
1
1
0
1
1
1
0
2
1
0
1
1
1
0
1
2
2
0
1
2
2
2
0
1
0
2
0
0
1
0
2
1
1
1
1
1
1
0
2
0
0
2
0
1
1
2
0
2
1
0
2
2
1
1
2
1
2
0
1
0
1
2
2
1
1
1
1
2
1
0
1
2
1
1
1
0
1
0
2
1
1
1
1
1
0
1
1
2
1
1
2
1
1
2
3
0
1
1
1
1
2
1
0
1
0
1
1
2
1
2
1
0
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
1
1
0
0
1
1
2
0
1
2
1
1
2
1
1
2
2
0
1
1
1
1
1
1
1
1
1
0
0
2
1
1
1
0
0
1
0
1
1
1
1
1
1
3
2
1
1
1
2
0
1
0
0
2
1
1
2
0
2
1
1
1
1
2
1
1
2
1
1
2
2
1
2
0
1
1
1
1
1
0
2
1
2
1
2
0
0
1
0
1
1
0
1
1
1
1
0
2
2
1
1
1
1
1
1
1
0
1
0
3
1
1
0
1
1
1
1
1
0
0
1
1
1
2
0
2
0
1
1
1
1
2
0
1
1
0
1
1
2
1
1
1
2
2
0
1
1
2
0
1
1
0
1
1
1
1
1
0
1
0
1
1
2
1
2
0
1
1
1
1
1
1
1
1
0
1
1
1
1
1
0
1
1
2
0
1
1
0
0
1
2
1
1
2
1
1
1
0
1
2
0
1
2
11
1
3
2
2
1
2
1
2
1
2
2
1
1
1
1
2
1
1
1
1
1
1
0
1
1
1
1
1
0
2
2
0
2
1
1
1
1
0
1
0
1
1
1
0
2
0
1
1
0
2
2
0
2
1
1
1
1
1
1
2
1
1
0
2
2
2
1
1
2
0
1
2
1
1
1
0
1
1
0
4
0
3
1
0
2
1
0
1
1
1
0
1
2
1
0
2
0
1
1
2
1
1
1
1
1
2
1
2
2
1
1
2
1
2
1
2
1
1
2
0
1
0
1
1
1
1
1
4
2
2
1
1
1
1
1
1
1
2
0
1
2
1
0
1
0
2
1
1
0
2
0
2
1
1
1
1
1
1
0
1
2
1
0
1
2
1
2
0
1
2
1
1
1
1
2
1
1
1
2
2
2
1
1
1
1
2
1
0
1
2
2
2
2
1
1
1
0
1
2
1
1
1
2
1
0
2
1
1
1
2
1
2
2
2
0
1
0
1
1
2
1
1
2
1
1
1
1
1
1
1
2
0
2
2
0
1
1
1
1
2
2
2
1
1
1
0
1
1
2
2
1
0
0
1
1
2
1
1
0
1
1
1
1
1
2
1
1
2
0
1
0
1
0
2
1
1
2
2
1
1
2
0
1
2
2
2
1
0
1
1
1
1
1
2
1
1
1
1
1
1
1
0
2
0
1
0
0
0
0
1
2
1
1
1
0
1
2
0
1
1
1
0
0
1
2
0
0
1
0
0
1
2
2
0
1
1
2
2
2
2
0
1
0
1
1
1
1
1
1
1
1
1
2
1
1
1
0
1
2
2
0
1
2
1
0
1
0
1
0
1
1
1
0
1
1
0
0
1
2
0
0
2
2
2
0
0
1
2
1
2
2
1
0
1
0
2
1
1
2
1
1
2
2
1
1
2
1
0
1
0
1
1
1
1
1
2
1
2
1
2
1
0
1
1
0
1
1
1
1
1
0
1
1
1
2
2
0
1
2
1
1
2
1
2
0
1
0
1
0
2
0
1
0
2
1
0
1
2
1
1
3
0
2
1
1
1
3
1
2
2
0
0
1
1
0
1
1
1
2
1
0
0
1
2
2
2
3
1
2
1
3
1
1
1
1
1
0
3
0
0
2
0
2
2
1
1
2
1
1
1
0
1
1
2
0
1
2
2
1
1
2
2
2
1
1
1
1
1
1
1
1
0
1
0
1
0
3
1
1
0
2
1
1
1
0
2
2
1
0
0
1
2
2
1
0
1
1
2
2
0
1
2
1
1
1
1
0
0
1
1
1
0
0
2
1
2
2
0
1
1
1
2
2
1
1
0
1
1
0
0
0
1
1
1
0
2
1
1
1
1
1
1
0
1
2
1
1
1
1
1
1
1
2
0
2
1
2
0
1
2
0
1
1
1
1
1
2
0
2
2
1
0
1
1
2
2
2
1
1
2
1
2
1
1
0
3
1
2
0
1
2
1
0
1
1
0
0
1
1
1
2
1
2
1
1
1
1
2
0
1
0
0
1
1
1
0
1
1
1
2
2
0
2
0
1
0
0
0
1
1
1
0
1
1
2
1
0
1
2
1
1
1
2
0
1
2
0
1
1
2
0
1
1
0
2
2
1
0
1
1
1
0
2
1
1
2
1
0
2
1
2
2
1
1
2
0
1
1
1
1
2
2
2
0
1
0
1
2
1
1
1
2
1
3
1
2
1
1
1
0
0
1
1
2
1
1
1
0
1
1
1
0
1
1
1
2
0
2
1
0
2
1
1
1
1
1
1
1
2
2
1
0
1
1
1
1
1
1
2
1
2
1
1
0
2
1
0
1
0
1
1
0
1
0
1
2
2
1
1
1
0
1
0
1
1
1
2
2
2
1
2
2
2
1
1
1
1
1
1
1
2
0
1
1
1
1
0
2
1
1
1
2
1
1
2
1
2
1
2
1
0
1
1
1
1
1
1
0
0
0
2
0
0
1
2
2
1
0
1
1
2
1
0
1
1
1
1
2
1
1
1
2
1
2
0
1
1
1
1
1
1
2
1
2
0
0
1
1
1
1
1
1
2
1
1
1
1
1
2
1
2
1
0
1
1
1
1
1
2
0
2
2
1
1
1
2
0
2
1
1
1
2
0
2
1
1
1
1
2
1
0
3
1
2
1
2
1
2
1
0
2
0
1
2
1
0
2
1
0
1
1
2
1
2
1
0
1
0
2
2
1
1
1
2
0
1
1
1
1
1
1
0
1
1
1
2
0
2
1
2
1
1
1
1
1
1
2
1
2
1
3
2
0
0
1
1
0
0
1
2
0
1
1
2
0
1
1
0
0
1
0
1
1
0
1
1
1
0
2
1
1
0
1
1
1
0
1
1
1
1
0
0
1
1
1
0
1
1
1
1
2
2
0
1
1
2
2
0
1
1
1
1
1
0
1
1
1
2
1
4
1
2
0
2
1
2
1
0
1
2
1
2
0
0
1
1
1
0
1
1
1
0
2
0
1
1
2
2
1
1
1
2
0
0
1
1
1
1
0
1
0
1
0
0
1
1
0
0
1
1
0
1
0
0
1
2
2
0
1
2
1
1
1
0
1
2
0
0
1
1
2
1
1
2
2
2
0
1
1
1
2
1
2
1
0
1
1
0
1
1
0
1
1
0
1
1
2
1
2
1
1
1
1
1
2
1
2
2
1
1
1
0
2
0
1
1
2
2
1
0
2
1
0
0
2
1
3
0
1
2
1
1
0
1
2
1
1
1
1
1
1
1
2
1
1
0
0
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
0
2
1
1
2
1
0
1
1
1
1
0
1
2
1
0
1
2
1
1
1
1
1
0
1
1
1
1
1
1
1
0
1
2
1
2
1
1
0
1
0
2
2
1
1
2
1
0
1
0
0
1
0
2
1
0
1
2
1
2
2
2
1
1
1
2
1
1
1
1
1
1
1
0
1
0
1
1
1
1
2
1
2
2
0
1
1
1
1
1
1
1
2
1
1
2
2
0
1
3
1
0
1
1
1
1
1
1
1
1
0
1
0
2
1
0
2
2
0
0
1
1
0
0
0
0
1
1
2
1
1
1
0
1
2
2
1
0
0
1
2
0
0
0
2
2
1
1
2
0
2
0
2
1
2
2
1
0
1
1
2
1
2
1
1
1
1
1
2
2
1
1
1
2
0
1
1
0
1
2
1
1
1
0
1
1
1
0
2
1
0
2
1
2
1
0
1
1
2
0
0
2
1
1
1
1
1
1
2
0
0
1
1
2
0
1
2
1
1
1
0
2
1
1
1
1
1
1
2
0
2
2
2
0
1
1
0
1
1
2
0
1
1
1
1
2
2
1
1
1
2
1
1
1
1
0
1
0
1
1
1
2
2
1
0
1
2
0
1
2
1
1
1
1
1
0
0
0
1
1
1
1
1
2
1
1
1
0
1
2
1
1
1
2
1
2
1
1
2
2
0
1
1
2
1
1
1
1
1
1
1
1
1
0
1
1
1
1
0
0
1
1
0
0
0
1
2
1
2
1
1
1
0
1
2
1
2
1
1
1
2
1
1
1
1
0
0
2
0
1
2
1
2
2
0
1
2
1
1
1
2
1
1
1
3
1
2
1
1
1
0
1
0
0
1
2
1
2
1
1
1
1
2
1
2
1
1
2
1
1
1
1
0
3
1
1
2
0
1
1
1
1
1
1
1
1
1
1
0
1
0
2
1
0
0
1
1
1
1
2
1
1
2
1
0
1
2
0
1
1
1
2
2
0
1
1
1
2
1
1
1
1
0
1
0
0
0
0
1
2
1
0
1
1
1
1
2
1
1
1
1
1
1
0
1
1
0
0
0
1
2
1
1
2
2
2
2
2
0
2
2
1
1
2
1
1
1
1
0
1
2
1
1
1
1
1
1
1
0
1
1
2
1
1
1
0
2
2
0
2
1
1
2
2
1
1
1
1
1
0
0
2
1
0
0
2
1
1
1
0
2
1
1
1
0
2
0
1
1
1
3
0
2
1
0
2
2
1
1
0
1
1
0
1
1
1
1
1
1
1
1
1
2
1
1
0
1
1
0
1
0
1
0
2
1
0
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
0
1
1
1
2
1
1
2
0
0
1
2
2
1
1
0
1
1
0
2
0
1
2
2
1
2
1
2
0
2
1
0
2
2
1
1
1
1
2
2
1
1
1
2
1
1
0
1
1
1
2
1
0
0
0
3
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
0
1
0
1
1
2
2
0
1
1
1
1
1
2
0
1
1
0
1
0
1
1
1
1
1
1
1
2
1
0
1
1
2
0
1
0
1
2
1
1
1
2
1
0
1
0
1
1
1
1
1
1
0
0
0
1
1
1
2
0
2
3
2
1
1
0
0
1
1
0
1
5
0
1
1
1
1
1
1
0
0
1
2
1
2
2
1
1
1
1
0
0
2
1
0
2
0
0
2
1
2
1
1
1
1
0
1
1
1
0
1
2
1
1
1
0
2
0
1
0
0
2
2
1
1
1
0
1
2
1
1
1
1
0
1
2
0
2
1
1
0
1
1
1
2
1
1
1
1
1
2
1
0
1
1
2
1
1
1
0
1
1
2
0
2
1
2
1
2
1
0
1
1
0
1
2
1
0
1
1
1
0
1
1
1
0
1
1
2
1
1
2
1
1
1
1
1
1
2
2
1
1
2
1
1
2
1
1
2
2
0
1
1
0
1
1
1
0
1
1
1
0
0
2
1
2
2
1
2
1
0
2
0
0
1
0
2
1
1
2
1
1
0
0
1
1
1
2
2
0
0
1
0
1
0
1
1
0
1
2
1
0
2
1
1
1
1
2
2
1
1
1
1
1
1
2
0
0
0
0
1
1
2
2
2
1
1
0
1
1
1
2
2
1
2
1
1
1
1
1
1
2
0
1
2
1
1
1
1
1
0
2
1
0
0
2
1
1
1
1
1
1
2
1
0
2
1
1
1
0
1
1
0
1
0
1
1
1
1
1
2
1
2
0
1
1
0
1
1
1
1
0
1
2
1
1
1
1
1
2
1
1
1
1
1
1
0
2
1
0
1
2
2
1
0
0
2
0
1
0
0
0
2
2
2
2
1
2
3
1
1
0
0
0
2
2
0
1
2
2
2
1
1
1
1
0
1
2
1
1
2
2
1
1
1
1
1
1
1
1
2
1
0
2
0
1
1
2
1
1
1
0
1
0
1
0
2
1
2
1
0
1
1
1
1
2
2
0
0
1
1
1
2
1
2
1
1
1
1
0
1
1
0
1
0
0
2
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
0
0
1
1
2
0
1
0
2
1
1
2
2
1
1
2
2
1
2
1
1
0
1
1
1
2
0
1
1
0
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
0
1
2
1
0
1
1
2
2
1
1
2
1
0
0
2
1
2
0
1
3
0
2
2
1
2
1
1
0
2
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
1
0
2
2
0
1
1
1
1
1
1
1
1
2
1
2
1
0
1
1
1
1
0
1
0
1
2
2
1
1
1
1
2
1
3
1
2
0
0
1
0
1
1
1
1
0
2
1
2
1
0
2
1
0
1
1
1
2
1
1
1
2
2
1
2
1
1
1
0
2
2
1
2
0
1
1
1
2
2
1
2
1
0
1
1
0
0
2
1
1
1
0
1
1
2
1
1
1
1
1
0
1
2
1
1
1
1
1
2
1
0
1
1
1
1
0
2
1
1
0
1
1
1
1
1
0
1
1
1
2
0
1
1
0
1
1
1
1
1
1
1
1
0
1
1
0
1
1
0
2
2
1
1
0
2
1
1
2
1
0
1
1
1
1
1
1
0
1
1
0
1
0
1
1
1
0
1
1
0
0
1
0
2
1
1
1
0
1
1
1
1
1
0
1
2
1
0
1
0
2
2
2
1
1
1
2
1
1
1
1
1
2
1
1
1
2
2
1
1
1
2
1
1
2
0
1
1
2
1
1
0
1
1
0
0
0
2
0
0
1
2
1
1
1
3
1
3
1
1
1
1
2
1
1
2
1
1
0
1
2
0
1
1
1
1
2
1
1
1
1
1
1
0
1
1
2
0
1
1
1
1
0
1
1
1
1
2
1
1
1
1
0
1
0
1
3
1
1
2
1
2
1
1
2
1
1
1
2
1
0
1
1
1
2
0
1
2
1
1
1
1
0
1
0
0
1
1
1
1
0
1
2
2
2
1
1
1
1
1
1
2
1
0
1
0
1
1
0
1
2
1
1
2
2
2
1
0
0
2
1
1
2
2
1
1
1
1
1
1
1
1
2
1
1
1
0
2
1
1
0
1
1
1
1
1
2
1
1
1
2
2
1
2
2
1
2
2
1
1
1
1
1
0
2
0
1
1
1
1
2
0
1
1
0
2
1
1
0
1
0
1
0
2
0
1
1
1
0
1
1
1
1
1
2
1
1
0
0
0
1
2
2
1
2
1
0
2
1
1
1
1
1
2
0
0
1
1
2
0
1
1
2
1
0
2
2
0
0
2
0
1
2
2
1
1
2
0
1
1
1
2
1
1
0
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
2
0
1
1
1
1
2
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
0
1
0
1
2
1
1
2
1
2
1
1
2
2
1
1
0
1
1
2
2
2
1
1
0
1
1
2
0
2
4
1
2
1
2
1
2
1
1
0
1
1
1
2
0
1
1
0
0
2
0
1
2
0
2
1
2
1
0
3
0
1
1
0
1
1
1
2
1
1
1
1
1
1
0
2
1
1
1
0
1
1
0
0
2
2
0
1
1
0
2
0
0
1
1
1
2
1
1
2
1
1
1
1
2
1
1
1
1
1
1
2
2
1
0
1
1
1
1
0
2
1
1
2
1
2
1
0
1
0
2
2
1
1
1
1
1
1
1
2
1
1
2
2
0
2
1
0
2
1
1
2
1
1
0
1
1
2
1
1
1
2
0
0
1
1
0
1
0
2
1
1
0
1
1
2
1
1
1
2
0
1
2
1
1
1
0
1
2
1
2
1
2
0
2
1
1
2
1
1
1
1
0
1
2
0
1
1
1
1
2
2
1
1
1
0
1
1
0
2
1
0
1
1
2
2
0
2
1
1
1
1
1
2
0
0
2
0
1
0
1
1
1
1
1
1
1
2
1
2
1
1
1
1
0
2
1
1
0
1
1
2
0
1
2
1
1
1
1
0
1
1
2
0
0
1
1
0
1
1
1
1
0
1
2
1
1
1
1
1
1
0
6
1
1
1
0
1
1
2
1
1
0
2
1
1
2
1
0
1
2
0
2
0
1
1
0
1
1
2
1
2
1
2
1
1
0
1
1
0
1
2
1
1
0
0
1
0
0
0
1
1
0
1
2
1
1
1
1
2
0
0
1
2
1
1
2
2
2
0
1
2
2
2
2
1
1
0
2
2
1
1
0
1
1
0
2
1
2
1
1
1
1
1
2
0
0
0
1
1
1
1
1
1
0
1
0
1
0
2
0
1
1
1
1
0
2
1
1
1
1
0
2
0
1
1
0
1
1
0
1
2
1
2
1
1
1
2
1
1
0
1
2
2
1
1
1
2
2
0
1
2
2
1
0
2
1
1
0
2
1
1
0
1
0
1
1
2
1
1
0
0
2
1
1
1
1
2
2
1
1
1
0
1
0
1
0
2
2
1
1
2
0
1
1
2
1
2
1
1
0
0
0
1
2
0
1
0
1
1
1
1
2
1
1
1
1
0
2
2
0
1
1
1
0
2
2
1
0
1
2
1
1
1
1
1
2
0
1
0
1
0
2
1
1
1
0
0
1
0
1
2
1
2
1
2
1
2
1
1
1
0
1
2
0
1
1
1
1
1
1
1
0
1
2
1
0
1
0
1
1
2
1
1
0
1
0
1
5
1
1
0
1
1
1
2
0
1
2
1
1
1
0
1
1
2
0
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
2
1
2
1
2
2
2
1
2
2
1
1
1
1
1
1
2
1
2
1
2
1
1
2
2
1
0
0
1
1
2
0
1
1
1
1
1
0
1
2
1
1
1
1
1
2
1
1
3
1
1
0
2
2
1
1
1
1
1
2
0
3
1
1
1
1
0
1
0
3
0
1
1
0
1
0
0
2
2
1
0
0
0
1
1
1
0
1
1
0
1
0
1
1
2
1
2
1
1
1
0
2
2
1
2
1
1
1
1
1
1
1
1
1
1
0
1
2
0
1
0
1
1
2
1
1
1
1
0
2
1
2
2
1
1
2
2
2
1
1
1
1
0
1
2
1
1
1
1
2
2
0
0
1
1
1
1
1
0
1
1
1
1
2
1
1
1
1
1
2
1
0
2
0
1
1
1
1
2
1
0
0
1
1
0
2
1
1
1
0
1
1
2
1
1
2
1
2
1
1
1
1
0
1
0
1
1
1
0
1
2
1
1
1
1
1
2
1
1
1
1
1
1
2
2
1
0
0
2
0
2
1
1
1
1
1
0
2
1
1
0
1
0
0
1
1
1
1
1
1
1
0
2
0
1
0
1
1
2
0
1
1
0
1
1
1
1
1
2
1
0
1
1
1
1
1
2
1
1
1
1
1
0
0
1
1
1
0
1
1
1
0
1
0
1
2
1
1
0
0
1
1
1
2
1
1
1
2
1
0
1
2
1
0
1
2
1
2
0
2
1
0
1
1
1
1
1
1
1
0
1
1
1
1
2
1
1
1
2
2
2
0
0
2
1
0
1
1
2
1
0
2
1
0
0
2
1
1
1
2
0
2
2
2
1
1
2
1
2
1
1
2
1
2
1
1
0
1
2
1
1
1
1
2
1
2
1
1
1
1
2
2
1
1
2
2
1
1
2
2
1
0
1
2
0
1
1
2
1
1
1
0
2
1
1
1
1
1
2
1
1
1
1
1
1
1
0
2
1
0
0
1
2
1
1
1
1
2
1
4
2
1
2
1
1
1
2
2
0
0
1
1
2
1
1
1
2
1
2
1
1
1
2
1
1
1
1
1
0
1
1
1
0
2
1
0
2
1
1
2
2
0
2
1
0
0
1
0
1
1
1
1
0
2
1
1
3
1
0
1
1
1
2
1
1
1
1
0
1
1
1
1
1
2
2
1
1
0
2
1
1
2
1
0
1
1
1
1
1
1
0
1
1
1
1
2
2
1
1
1
0
1
2
0
1
0
1
1
0
1
1
2
2
1
1
1
0
0
1
1
2
1
0
1
2
2
0
1
1
2
0
2
1
1
0
1
1
1
0
0
0
1
0
1
0
1
1
1
0
0
1
1
1
1
1
1
0
2
1
1
0
1
0
1
2
1
1
1
0
1
1
1
1
1
1
2
0
1
1
0
2
1
1
0
1
2
1
1
1
2
1
1
2
2
2
1
1
2
1
1
1
1
2
1
2
1
0
1
1
1
0
1
2
1
0
0
1
1
1
2
0
0
1
1
0
1
1
0
0
2
1
2
1
1
2
1
1
1
1
1
1
2
0
1
0
0
0
1
2
1
1
1
1
0
2
1
1
1
2
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
2
2
2
2
1
1
1
1
1
1
1
1
0
2
0
1
1
1
2
1
1
1
1
0
1
1
2
0
1
2
2
1
2
1
1
1
2
1
1
2
1
1
1
1
1
1
2
2
0
1
1
1
1
2
0
0
1
0
0
1
1
0
1
1
1
1
1
1
1
1
2
2
0
1
1
1
1
1
1
0
2
1
2
0
1
1
1
0
0
1
1
0
0
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
0
2
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
0
1
1
1
0
1
2
1
1
1
1
1
0
1
1
1
1
1
0
0
2
1
0
1
1
0
1
2
2
0
1
1
3
1
2
1
1
2
0
2
1
1
1
2
2
1
2
1
1
0
2
1
1
1
1
1
1
2
2
1
0
1
0
1
1
2
0
1
6
0
1
1
2
2
1
1
1
0
2
2
1
1
1
1
2
1
1
1
0
1
0
2
1
0
2
1
1
0
1
1
0
1
2
1
1
1
1
2
1
1
0
1
2
1
2
1
0
1
2
0
1
0
1
1
2
2
1
1
0
2
1
1
2
1
1
1
1
0
1
1
1
1
2
1
1
1
0
0
2
1
0
0
1
1
1
1
0
1
1
0
1
1
1
0
1
1
1
1
1
2
1
2
1
1
1
1
2
1
0
1
1
2
0
1
1
0
1
0
1
0
0
0
3
0
2
1
1
2
1
0
1
1
0
1
1
1
2
0
1
0
1
0
1
2
1
2
1
2
0
1
1
2
1
0
1
2
0
0
1
3
2
1
3
2
1
1
2
1
2
0
1
0
1
0
1
2
1
0
2
1
1
1
2
2
2
1
1
0
1
1
1
1
1
1
2
0
0
0
1
1
1
2
0
2
1
1
0
1
2
0
2
2
1
0
0
1
2
1
1
2
2
1
1
1
1
0
0
2
1
1
1
1
1
2
1
1
1
1
1
2
2
2
1
1
1
0
1
1
2
2
1
1
2
1
1
1
2
0
0
0
1
0
0
2
1
1
0
0
1
1
1
1
2
0
0
1
0
1
1
2
1
2
1
2
1
2
1
0
1
1
0
2
1
0
3
1
1
0
1
1
2
1
0
1
1
1
1
1
1
1
0
1
1
0
2
1
1
2
1
0
1
2
2
0
2
0
0
1
1
1
1
0
1
2
1
1
1
2
1
1
1
1
0
1
2
2
1
1
0
2
1
1
0
1
0
0
1
2
0
1
1
1
1
1
1
1
1
1
1
1
0
1
1
0
0
1
2
1
1
1
2
1
1
2
1
1
1
1
2
1
2
1
0
1
1
1
0
0
0
0
1
1
1
0
1
1
1
2
0
1
3
1
0
2
1
0
0
1
0
2
1
1
0
1
2
0
1
2
1
1
1
1
2
1
1
2
0
1
1
1
1
1
0
1
1
0
1
1
1
1
0
0
1
1
2
2
0
2
2
2
0
2
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
2
0
2
1
2
2
0
1
1
1
1
1
0
2
1
1
1
0
1
0
2
2
0
0
2
1
0
1
2
1
1
1
2
1
2
1
1
2
2
1
2
1
2
0
1
1
0
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
0
1
1
1
1
2
1
1
1
0
2
1
2
1
2
2
1
1
1
1
1
2
2
1
1
2
1
0
0
1
1
1
2
0
0
0
1
1
2
1
1
0
0
2
2
2
1
1
2
1
1
2
1
1
1
1
2
1
1
2
1
1
0
1
1
1
1
0
1
1
1
1
2
1
2
2
0
1
1
1
1
2
0
1
1
2
1
1
0
1
2
1
1
1
1
0
0
1
1
1
1
1
0
0
1
2
1
3
0
1
1
1
1
1
0
2
1
0
1
1
1
0
1
0
1
1
1
1
1
1
0
1
1
1
1
1
0
1
2
1
1
2
1
0
2
1
1
1
1
2
0
0
1
0
2
1
1
1
1
1
2
1
1
0
1
2
2
2
1
1
1
2
1
0
1
1
1
2
1
1
1
1
1
0
0
0
1
1
0
1
2
1
1
1
1
0
1
1
1
1
2
1
1
1
1
0
1
1
4
1
0
1
2
1
0
0
2
1
2
1
0
1
1
0
1
1
1
1
2
1
1
1
1
1
1
1
0
2
2
1
2
1
0
1
4
1
1
1
1
2
1
1
2
0
1
2
0
2
1
1
1
1
1
1
1
2
1
1
1
0
1
1
0
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
2
1
1
1
1
2
1
2
1
1
2
1
1
0
1
1
1
1
5
1
1
1
1
1
0
1
1
0
0
1
1
2
0
1
1
0
2
1
1
1
1
1
0
1
1
1
1
0
0
1
1
1
0
1
1
1
1
1
1
1
1
1
0
1
0
0
0
1
2
1
1
1
0
0
1
2
0
0
2
0
0
1
0
1
1
1
1
1
0
0
1
1
1
1
2
0
0
1
1
0
2
0
0
1
1
2
2
2
2
1
1
0
2
1
1
2
1
0
1
1
1
0
1
1
1
1
1
2
2
1
1
2
0
5
0
1
1
1
1
1
1
2
2
0
1
1
1
1
0
1
2
0
0
1
1
1
2
2
1
0
0
2
1
1
1
1
1
0
0
1
1
1
0
1
2
1
2
2
1
1
1
2
1
1
1
1
1
1
2
1
1
2
1
0
1
1
2
1
1
1
0
2
0
2
2
1
1
0
1
0
1
1
1
0
0
1
0
0
0
0
1
1
2
1
1
0
0
1
1
1
1
0
0
2
1
2
1
2
1
2
0
0
1
2
1
0
0
2
1
1
1
2
1
0
2
1
1
0
0
1
2
0
0
1
0
0
1
1
1
2
2
1
1
1
1
1
2
2
1
1
1
1
0
2
1
2
1
1
1
0
1
1
3
2
1
1
1
1
1
0
0
1
1
0
0
1
0
1
2
1
1
0
1
1
2
2
2
0
0
1
1
0
1
1
1
0
1
0
0
1
2
1
1
1
2
0
1
1
1
2
2
1
1
0
1
1
2
1
1
2
1
0
0
0
1
2
0
1
2
2
2
1
2
2
1
1
1
2
1
1
0
1
0
2
0
2
1
1
2
1
1
1
1
1
1
1
0
0
2
0
1
1
1
3
1
1
1
1
1
1
1
0
1
2
0
1
1
0
2
1
0
1
1
1
2
2
2
1
1
2
2
1
0
1
1
2
1
1
1
1
0
2
2
1
1
1
2
0
1
1
2
1
1
1
1
0
0
1
1
2
1
0
1
1
1
1
2
2
1
0
2
1
1
1
1
1
0
1
1
0
2
1
1
0
1
1
1
2
1
1
1
2
2
2
0
1
1
0
1
1
1
0
1
1
2
2
2
0
2
1
1
2
1
1
1
1
1
1
2
2
1
2
1
1
0
0
2
1
1
1
0
0
1
4
2
2
1
1
1
1
0
1
1
1
1
1
1
1
0
1
2
1
0
1
2
1
0
2
1
1
1
1
1
1
2
1
0
1
1
1
0
1
0
1
2
3
1
2
2
1
1
1
1
1
1
1
0
0
2
1
2
1
2
2
0
2
1
1
1
5
1
1
2
1
1
0
2
1
1
2
0
1
1
2
0
1
2
1
1
1
2
1
1
1
2
2
0
0
2
1
1
1
1
1
1
2
1
2
1
1
5
0
2
2
1
0
2
1
1
1
2
1
1
1
1
2
1
2
1
2
1
0
1
1
1
0
1
1
1
1
1
0
1
1
1
0
1
1
0
1
2
1
2
1
1
2
2
1
1
2
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
0
2
2
1
1
1
0
1
0
1
2
1
0
2
2
1
1
2
1
1
2
2
1
1
1
1
2
2
2
0
1
0
0
1
1
1
0
1
0
1
0
3
1
2
1
2
0
1
1
1
0
2
1
2
1
1
2
0
1
0
1
2
1
1
1
2
1
1
2
2
1
0
0
0
0
1
1
1
2
2
1
1
0
2
1
1
2
2
2
2
1
1
1
0
1
0
1
1
0
2
0
0
1
0
2
1
1
1
1
1
1
1
2
1
2
1
2
1
2
2
1
1
1
1
1
2
1
1
0
1
1
2
0
2
0
1
2
1
0
0
0
1
1
0
0
0
1
0
0
1
1
1
1
1
1
1
2
2
1
2
0
0
2
1
1
1
1
2
1
2
1
1
1
1
1
2
1
2
1
1
1
1
1
2
1
0
0
1
1
1
2
1
1
1
0
2
2
1
1
1
2
2
1
1
2
1
0
0
1
0
2
2
0
2
0
1
1
1
1
1
2
1
1
1
2
1
1
3
0
1
0
2
0
2
1
2
2
1
1
1
1
1
1
2
1
0
1
0
2
2
1
1
2
1
2
1
0
1
0
2
1
1
0
1
2
1
2
1
2
0
1
1
1
1
2
1
2
1
0
1
1
0
1
2
1
1
1
1
2
2
1
1
1
0
1
0
1
0
1
1
0
2
0
2
1
2
1
1
1
2
0
2
2
1
1
2
0
2
1
2
0
2
1
1
0
1
1
0
1
2
2
2
2
2
1
1
1
1
1
1
0
1
1
2
1
1
1
1
1
0
1
1
2
2
1
0
0
0
1
2
2
1
2
1
0
0
0
1
1
1
1
2
1
2
1
1
0
0
0
1
2
1
1
0
2
0
0
1
1
1
0
2
1
1
2
1
1
0
1
1
0
2
1
2
1
1
1
1
2
1
1
1
2
0
1
0
1
2
0
1
3
2
1
0
0
1
1
2
0
1
1
1
2
1
2
1
1
1
1
1
1
2
2
2
1
1
0
1
1
1
2
2
1
1
0
2
1
0
0
1
1
0
1
1
2
1
0
1
0
0
1
1
1
1
1
2
1
0
2
1
0
1
1
2
1
1
2
1
1
1
1
1
1
1
1
2
2
1
1
1
2
0
1
2
3
0
2
1
1
1
2
1
1
1
0
1
0
0
2
1
1
1
1
2
0
1
1
1
1
1
0
1
1
1
1
1
1
2
1
2
1
1
2
2
2
1
1
1
1
2
1
1
1
1
1
2
0
2
1
1
0
1
1
1
1
4
2
1
1
2
0
2
1
1
2
1
1
1
0
0
2
1
0
2
1
1
0
0
1
1
1
1
3
1
1
2
1
1
1
1
1
1
2
1
1
0
1
1
1
1
1
1
1
1
0
0
0
1
1
0
2
1
0
1
1
1
0
1
0
0
0
0
2
1
2
1
2
2
1
1
2
1
1
2
2
1
0
2
1
1
2
1
1
1
1
1
1
1
1
2
2
1
1
1
2
2
2
1
1
0
1
2
1
0
0
0
0
1
1
0
0
1
0
1
1
1
2
2
0
1
0
1
2
0
1
2
1
2
1
1
2
0
1
2
0
1
1
2
1
1
0
1
1
2
1
0
1
1
1
1
0
1
2
0
2
1
1
1
1
1
2
1
1
0
0
0
0
1
2
1
2
2
1
2
1
2
1
2
2
2
0
1
2
2
2
1
2
1
1
1
1
2
1
1
1
2
1
2
0
2
2
1
2
0
1
2
1
1
2
1
1
1
1
2
1
2
1
1
1
1
2
1
1
0
0
1
1
1
1
2
1
1
0
1
1
0
2
1
1
0
1
1
1
2
1
1
2
1
2
1
2
1
1
1
1
1
2
0
1
0
0
3
1
1
2
1
0
2
1
2
0
2
1
2
0
1
0
1
1
0
1
1
1
1
2
1
2
0
2
1
2
1
1
2
1
0
1
1
0
1
1
1
1
2
0
2
2
1
0
1
1
1
1
1
1
1
1
1
0
1
0
2
0
0
1
1
1
1
0
1
2
0
2
0
2
1
1
1
1
1
1
0
1
1
1
1
0
3
2
1
1
1
2
0
2
1
1
1
2
0
0
1
0
2
2
2
1
2
1
1
2
1
2
0
1
1
1
1
2
1
1
0
0
2
1
0
1
2
0
1
2
1
1
1
2
1
1
1
2
2
1
1
1
2
1
1
0
1
1
2
1
1
0
1
1
1
1
0
1
2
2
0
1
1
0
1
2
1
2
1
1
1
1
1
0
1
1
1
2
1
1
1
2
1
1
2
1
0
1
2
1
2
1
1
1
1
0
3
1
1
2
2
1
0
0
1
2
1
0
1
2
2
1
1
1
1
0
1
1
1
0
1
1
1
1
1
1
0
2
2
1
2
2
1
1
1
2
0
1
0
1
2
1
1
1
2
1
1
1
0
0
2
1
0
2
1
2
1
1
1
1
2
1
1
0
0
2
2
2
1
1
1
0
2
0
0
0
1
0
2
1
1
1
1
1
2
1
1
1
1
1
1
0
1
2
1
2
1
1
2
1
2
1
1
1
2
1
1
1
2
2
2
1
0
1
2
1
1
1
1
2
2
1
1
2
1
1
2
1
2
1
1
2
1
2
1
3
0
1
1
1
1
1
0
2
0
0
0
1
0
0
2
0
1
1
2
1
1
2
1
1
1
2
1
1
0
1
2
0
1
0
0
0
1
1
1
2
1
1
1
1
1
0
0
0
1
1
1
1
1
0
0
2
1
2
0
1
0
0
0
2
2
0
1
2
0
0
0
1
1
2
0
1
2
1
2
0
1
1
1
1
1
2
1
0
1
1
1
1
1
1
0
1
1
1
3
2
1
1
2
0
0
1
0
1
2
0
1
1
0
0
0
1
0
1
0
1
1
1
1
1
2
1
1
2
1
1
1
2
1
1
1
1
0
0
1
0
1
0
0
1
0
2
1
1
1
1
1
2
1
1
1
0
1
1
1
1
1
1
1
1
2
0
1
2
1
1
2
2
1
1
0
0
0
1
2
0
0
1
2
1
2
0
1
1
0
1
1
2
1
0
1
0
1
1
1
2
1
1
2
2
1
1
2
1
1
1
2
1
1
1
1
2
0
1
3
0
0
1
1
1
1
1
1
1
1
1
2
1
2
2
2
3
2
2
0
2
1
1
1
1
0
1
0
1
1
2
1
1
1
1
2
0
1
1
1
1
1
1
1
0
1
1
0
1
1
1
1
0
1
1
2
1
1
3
1
1
0
2
0
1
0
1
2
2
0
1
0
0
1
1
1
1
1
0
1
1
1
0
1
1
1
1
2
2
1
1
0
2
1
1
1
1
0
1
1
1
1
2
1
1
1
1
1
1
2
1
2
0
2
1
1
3
1
1
1
1
1
1
1
0
2
1
1
1
1
1
1
1
2
2
1
1
0
1
2
1
2
1
1
2
0
1
1
1
2
2
1
1
1
1
0
2
1
1
0
1
1
2
1
2
0
1
2
2
2
1
1
1
2
1
1
0
0
1
0
1
1
2
2
2
0
1
1
1
1
2
1
2
1
0
2
1
1
2
1
1
0
2
1
0
2
1
1
1
2
1
1
2
0
0
5
1
1
1
1
1
2
2
1
2
1
2
1
0
2
1
0
1
0
1
1
1
0
0
1
0
1
2
1
1
2
1
1
2
1
1
2
1
2
1
1
1
1
1
1
0
1
2
1
1
2
2
1
1
1
1
1
1
1
0
2
2
1
2
1
2
0
1
1
1
1
1
1
2
0
1
0
1
0
1
1
2
4
2
2
1
1
1
1
1
1
2
2
1
2
0
2
1
2
1
1
2
1
1
0
0
1
2
1
1
1
1
2
1
1
1
1
1
2
2
1
1
1
0
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
2
2
1
0
1
2
0
1
1
1
1
0
1
1
1
2
2
2
1
0
0
0
0
2
2
2
1
1
1
2
2
1
2
2
1
1
1
1
1
2
2
1
1
1
1
0
2
0
1
0
2
1
2
2
2
1
1
2
1
2
2
1
0
1
1
2
1
0
1
2
0
1
2
1
1
0
2
1
1
1
0
1
2
1
1
1
1
1
1
1
1
1
1
1
1
0
2
1
0
1
2
2
1
1
1
1
1
1
1
2
1
2
3
2
1
1
1
0
0
0
1
0
0
2
0
1
0
1
0
1
1
2
1
1
1
1
0
0
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
2
0
1
2
1
2
2
0
1
2
1
0
1
1
2
0
0
1
2
2
0
0
1
1
1
1
1
1
1
1
2
3
1
2
2
1
1
1
1
2
2
1
1
1
0
1
1
1
1
1
2
1
2
2
1
1
1
1
2
0
1
1
2
0
0
1
1
0
1
1
0
1
1
2
1
1
1
1
2
1
2
1
1
0
1
1
1
1
1
2
2
0
0
1
1
1
1
0
0
1
0
1
0
1
2
1
0
1
1
1
1
1
1
1
1
2
0
0
1
1
2
2
1
2
1
1
0
2
1
1
1
2
1
1
1
1
1
1
1
0
1
2
2
1
1
1
0
1
1
2
0
0
1
1
0
1
1
2
1
1
1
0
1
1
0
2
1
2
1
0
1
2
1
1
2
0
1
2
1
0
2
1
1
1
2
3
1
1
1
1
2
0
1
2
1
1
1
2
1
1
1
3
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
0
2
1
0
2
1
1
1
1
1
2
4
1
2
1
0
1
1
1
1
1
1
1
0
1
1
0
2
1
1
1
0
0
1
1
2
2
1
1
1
0
2
1
2
1
1
1
1
1
0
1
2
2
2
2
1
2
2
1
1
1
1
2
2
0
1
1
1
1
1
1
2
2
1
1
2
0
1
2
1
1
0
1
0
1
1
1
0
1
0
2
1
1
1
2
1
1
0
2
1
1
0
1
1
1
1
1
1
1
0
2
1
2
3
1
1
1
1
2
1
1
0
1
0
1
2
1
2
1
1
1
1
2
0
1
2
1
1
2
1
1
1
1
1
1
1
3
1
1
2
1
1
1
4
1
2
2
0
1
1
2
2
1
1
0
1
0
1
0
2
1
1
1
2
1
0
1
2
0
1
1
1
2
1
2
1
1
2
1
0
0
1
1
1
2
1
2
1
1
0
1
1
1
3
2
2
1
1
1
2
0
1
1
1
2
2
2
1
1
0
1
3
1
1
1
0
0
1
0
2
1
1
0
0
1
0
1
1
1
2
2
1
1
3
1
1
1
0
3
1
2
1
1
0
2
1
2
1
1
2
0
2
1
2
2
2
1
1
1
1
1
2
0
2
1
0
1
1
1
1
1
1
1
1
0
2
1
1
1
1
1
1
1
1
2
2
1
2
0
1
1
0
1
2
1
1
1
1
1
2
1
1
1
0
2
1
1
0
1
2
1
0
1
2
0
2
0
1
1
0
1
1
1
0
1
1
3
2
1
0
1
1
1
2
1
1
1
1
1
1
2
1
2
2
2
1
1
1
1
0
1
1
0
2
0
1
1
2
0
1
1
0
1
1
1
0
1
1
2
1
1
3
1
1
1
0
1
1
1
1
2
2
1
1
2
0
1
2
1
0
2
1
1
1
1
1
2
0
2
2
1
1
0
1
1
1
1
2
1
2
2
0
1
0
2
1
1
2
1
2
0
2
2
2
1
2
1
1
0
0
1
1
1
1
1
1
1
0
1
1
1
1
0
1
1
1
1
2
1
2
1
1
1
0
0
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
1
2
1
2
0
0
1
1
0
2
1
0
1
1
1
2
0
2
1
1
2
0
1
1
1
2
1
1
1
1
1
0
2
2
1
2
1
0
1
2
0
1
1
1
1
1
1
0
1
1
1
0
1
1
2
1
1
0
2
1
1
1
1
1
0
1
1
1
1
1
0
1
2
1
1
1
1
0
1
1
1
1
1
0
0
1
1
2
0
0
1
0
1
1
1
1
2
2
1
1
1
0
2
2
0
0
2
0
1
2
0
1
0
0
1
1
0
1
1
0
1
1
2
0
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
2
2
0
2
1
2
2
0
2
1
1
0
1
1
1
1
1
1
0
2
1
1
1
1
1
0
1
1
2
0
2
1
0
2
2
1
2
1
1
2
2
2
2
1
0
2
1
0
1
0
1
1
0
1
2
0
2
0
1
1
1
2
0
2
0
1
0
1
1
0
1
2
0
1
0
2
0
1
0
1
1
1
2
1
1
1
2
1
0
0
1
1
1
2
1
0
1
1
1
2
0
1
1
1
2
1
1
1
1
0
1
0
1
2
1
0
1
1
1
0
1
1
1
1
0
0
2
1
1
0
0
1
1
1
0
1
2
1
2
1
1
1
1
1
1
2
1
1
1
0
1
1
1
2
1
2
1
0
1
0
1
1
1
1
1
1
1
1
0
1
2
0
0
2
1
1
1
0
1
2
1
2
0
1
2
1
0
1
1
0
1
2
1
0
1
1
0
2
0
1
0
1
1
2
1
0
1
0
1
1
1
0
1
2
0
2
1
2
0
2
1
1
1
0
1
2
1
2
1
1
1
1
0
1
1
1
1
1
3
1
2
1
1
1
1
2
1
1
0
1
1
1
0
1
1
1
1
1
2
2
1
2
1
2
0
0
1
1
1
1
1
0
1
1
1
1
1
2
1
0
1
2
2
1
1
2
1
2
2
2
1
1
1
1
1
0
1
0
1
1
2
1
1
0
1
2
2
2
1
1
1
1
1
1
1
1
0
2
1
1
1
1
1
1
2
1
1
0
1
2
0
1
0
1
2
1
1
1
1
0
2
1
2
0
2
1
1
2
1
2
1
1
1
1
0
1
0
2
2
2
0
1
1
1
3
2
1
2
1
0
1
2
0
2
1
1
0
1
2
1
1
2
1
1
2
1
2
2
0
0
1
1
1
1
1
1
1
0
1
1
1
1
2
0
1
0
1
1
2
1
2
1
1
1
1
2
2
0
2
2
1
1
0
1
1
1
0
2
2
2
1
0
2
1
2
2
0
0
2
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
0
1
1
1
1
1
2
1
1
0
1
0
0
2
0
1
1
1
1
0
1
1
1
0
2
1
1
1
2
1
1
1
1
1
0
1
0
2
1
1
1
1
1
2
1
2
1
0
3
1
1
4
0
1
1
1
4
0
1
2
2
2
1
1
1
2
1
1
3
1
1
0
0
1
1
1
0
1
1
2
1
1
1
0
0
2
1
0
0
1
1
2
1
2
2
1
1
1
1
2
2
2
1
1
1
1
0
2
1
2
2
1
2
1
1
0
1
2
1
1
1
1
1
0
1
2
1
0
0
1
1
2
1
1
2
0
1
0
1
0
2
1
1
1
2
2
2
2
1
1
1
0
1
2
2
3
2
1
0
1
0
0
1
1
0
1
2
0
1
0
1
1
2
1
2
1
0
0
0
1
1
0
1
2
1
1
2
1
1
1
1
0
2
1
0
0
1
1
1
1
0
1
1
1
0
0
1
1
1
1
1
1
0
1
1
2
1
2
1
2
2
2
0
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
0
2
1
1
1
1
0
1
2
2
1
1
2
1
2
1
1
0
1
1
2
1
1
1
2
2
1
3
0
2
0
1
0
1
1
0
2
2
1
0
1
0
1
1
1
2
1
1
1
1
2
2
2
1
1
1
2
1
1
1
1
0
1
2
1
1
1
1
1
0
1
0
1
0
1
1
2
1
2
1
1
1
1
2
3
2
0
2
1
1
0
1
1
1
0
0
0
0
1
0
1
0
1
1
2
2
2
1
2
1
1
0
1
1
1
2
1
2
0
2
1
1
1
2
1
1
1
2
0
1
1
1
1
2
1
2
1
0
1
0
1
1
1
1
1
3
0
0
1
1
1
2
1
1
0
1
1
0
1
0
1
1
1
1
1
1
0
1
1
2
1
1
2
1
1
2
1
1
1
1
0
1
2
1
1
0
1
1
1
2
2
1
1
1
1
0
2
1
2
1
1
1
1
1
1
2
1
2
2
2
2
1
1
2
1
1
2
0
1
2
1
1
0
1
1
1
1
1
2
1
2
0
1
1
2
1
2
2
1
1
2
0
1
2
1
2
2
1
0
2
1
1
2
2
0
1
0
2
1
2
1
1
1
0
0
1
1
1
0
1
2
1
1
2
2
2
1
1
1
2
2
1
1
0
2
1
1
1
1
1
1
2
2
2
2
2
1
2
2
1
1
2
0
0
1
0
0
1
0
1
1
1
1
2
1
1
1
0
1
1
0
2
1
1
0
1
1
2
1
2
1
1
2
1
2
1
2
2
1
1
1
1
0
2
1
1
0
1
1
0
1
1
1
1
0
1
2
1
1
1
0
1
1
1
0
0
1
2
0
1
2
2
1
2
0
1
2
1
1
2
1
2
1
1
1
1
0
1
2
0
2
1
1
2
1
0
1
1
1
0
1
1
1
1
0
0
0
1
1
1
1
1
1
2
1
0
1
0
1
1
1
1
0
1
2
1
1
0
1
1
1
1
2
2
1
2
1
2
1
9
2
1
1
1
0
0
1
2
2
1
1
1
1
1
1
1
1
1
1
0
1
1
2
0
1
1
0
1
2
2
1
2
1
1
1
1
1
1
2
2
1
1
0
1
2
1
2
1
2
2
1
1
2
1
1
0
1
0
1
2
2
1
1
1
0
0
1
1
0
0
1
1
1
1
0
1
1
2
1
0
1
1
1
1
1
1
1
1
1
1
1
2
1
2
0
1
0
1
0
2
1
1
0
1
0
0
1
1
1
2
1
1
2
0
1
1
1
0
2
0
0
1
1
1
1
1
1
2
1
2
2
1
1
2
2
1
1
2
1
1
1
0
1
1
2
1
1
0
1
2
0
1
1
1
1
0
1
1
1
0
1
1
1
1
1
2
2
1
2
0
1
2
1
1
0
1
1
2
2
2
1
0
0
1
2
1
1
2
2
1
1
0
2
2
1
1
0
0
1
2
1
0
2
2
1
1
1
1
0
2
1
0
1
0
2
1
1
0
2
0
1
1
1
1
1
1
1
0
0
1
0
1
2
0
2
1
1
1
1
1
0
2
1
1
1
0
1
1
2
1
1
1
1
0
1
1
2
2
1
1
2
2
0
2
2
2
1
0
2
1
3
0
0
0
2
1
0
0
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
4
0
1
0
0
1
1
1
1
2
1
1
0
1
2
1
1
1
2
1
2
1
2
0
2
1
1
1
1
1
1
1
1
0
0
0
2
2
1
1
3
1
2
1
1
2
1
1
1
1
2
0
2
1
1
2
0
2
1
1
0
1
1
2
1
2
0
1
1
2
0
1
0
0
1
1
2
1
0
2
1
1
0
2
1
0
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
0
1
2
1
1
1
2
2
2
1
2
2
2
1
0
2
0
0
1
1
1
0
2
1
0
1
1
1
1
1
1
0
2
0
1
2
1
2
0
0
1
0
1
0
1
0
1
1
2
1
2
1
0
1
0
0
2
0
0
1
1
0
0
0
0
1
1
1
1
1
0
2
1
2
1
7
1
1
1
1
1
0
0
1
2
0
1
1
1
1
1
3
2
1
1
2
1
2
0
0
1
2
2
1
1
1
1
1
0
1
0
0
2
0
1
2
1
1
2
1
1
1
1
3
1
0
1
0
0
1
2
0
1
1
1
2
1
1
1
1
0
1
2
1
1
1
0
2
2
1
2
2
1
2
2
2
0
1
2
1
0
2
0
0
3
1
1
1
2
2
0
0
1
1
1
1
2
1
1
1
2
2
2
1
0
1
1
1
1
2
2
2
1
1
2
0
1
1
1
1
0
0
1
1
1
0
0
0
1
0
1
2
1
1
2
2
0
1
2
1
1
1
1
0
1
1
0
1
2
1
1
2
2
1
1
1
2
2
1
2
2
1
1
0
0
1
2
2
2
1
1
2
1
1
2
0
0
2
2
1
2
2
0
1
1
1
1
1
1
1
2
1
0
1
1
1
1
1
1
2
1
0
2
0
2
0
2
1
1
2
1
1
1
2
1
2
1
1
1
1
1
0
1
1
0
0
1
1
1
1
1
1
0
1
1
1
2
0
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
1
0
1
1
1
0
2
0
2
1
1
1
0
1
1
1
2
1
1
1
0
1
1
1
2
1
1
1
1
1
1
1
1
1
3
2
2
1
0
0
1
0
0
0
1
0
2
2
1
0
1
1
1
0
0
1
1
1
0
1
1
1
1
1
1
1
2
1
1
2
2
1
1
1
1
2
1
1
2
2
1
1
2
2
1
1
1
1
2
2
1
1
0
1
1
1
1
1
2
0
0
2
0
1
2
1
1
1
1
2
0
2
1
1
1
1
0
1
1
2
1
0
1
1
2
0
1
1
2
1
1
1
3
0
0
1
1
1
1
1
2
1
3
1
2
1
1
1
1
0
0
1
2
1
1
1
1
0
1
2
1
1
2
1
1
2
2
1
1
0
1
2
1
1
1
2
1
0
1
2
1
1
0
4
2
1
2
1
1
0
1
1
1
1
1
1
0
0
1
1
0
2
1
0
0
1
1
2
0
1
1
1
1
2
1
0
1
1
3
2
1
1
1
2
2
1
1
0
1
1
1
1
1
1
1
1
1
0
1
2
0
1
1
1
0
0
1
1
1
1
2
1
0
1
1
0
0
1
0
1
0
0
2
2
1
0
0
1
0
0
1
1
1
2
0
2
0
0
1
1
1
1
1
1
0
1
1
1
1
1
1
2
2
1
2
1
0
2
1
0
2
1
2
1
1
1
0
4
1
1
1
1
1
1
0
1
2
1
1
1
2
0
1
1
1
1
1
1
2
1
0
1
2
2
1
1
1
1
0
0
1
1
1
0
1
2
1
1
1
1
1
0
0
2
1
1
2
1
1
1
2
1
1
2
0
2
1
0
1
0
1
1
0
1
1
1
1
1
0
1
2
2
1
1
1
0
1
1
2
1
1
1
2
1
0
2
0
1
1
1
0
1
1
1
1
2
2
1
2
0
2
1
1
1
1
2
0
1
1
2
1
2
0
1
2
0
1
2
0
2
3
2
1
0
2
1
2
0
2
1
1
0
1
2
1
1
1
1
0
0
1
1
1
0
1
1
2
1
1
0
1
0
1
1
2
1
2
0
1
0
0
1
2
1
2
0
1
1
3
1
1
1
1
1
1
2
0
1
1
1
0
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
0
1
1
1
2
1
2
1
0
2
1
2
1
1
0
1
1
1
1
1
2
1
1
1
0
1
1
1
1
1
1
0
7
2
1
1
2
1
2
1
1
2
2
0
1
2
1
1
3
1
0
1
1
1
2
2
0
1
0
0
1
2
2
1
1
2
1
1
1
0
0
2
1
1
1
0
2
2
1
1
1
1
1
1
2
0
2
1
1
1
1
1
1
0
1
0
1
0
1
2
2
1
1
1
1
2
2
0
2
0
1
1
0
1
1
2
2
1
1
2
2
2
1
1
1
0
0
0
2
1
1
0
1
0
1
0
2
1
3
1
2
2
2
1
1
2
1
2
0
2
1
2
0
1
1
1
1
0
1
1
1
1
2
0
1
1
0
2
1
2
1
1
2
0
2
2
2
1
1
0
1
2
1
1
0
2
1
1
1
2
1
1
2
2
0
2
0
2
2
0
2
0
2
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
2
0
1
0
1
2
0
1
1
1
1
1
2
2
0
1
1
1
2
1
1
0
2
1
2
2
1
0
0
1
1
2
2
2
0
2
1
0
0
0
1
1
1
2
2
0
1
0
1
1
2
0
2
2
1
1
2
1
2
1
1
1
2
1
0
1
1
1
1
1
1
1
1
1
2
1
1
3
2
1
1
2
1
1
1
0
0
1
2
1
1
1
1
1
2
1
2
2
2
2
2
1
2
1
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
0
0
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
0
0
0
0
2
1
2
1
0
1
1
1
2
0
0
1
1
1
1
2
1
2
0
1
1
1
1
2
2
1
1
1
1
0
0
1
2
1
1
1
2
2
1
0
1
1
1
0
0
0
1
1
0
1
3
1
3
0
0
2
0
0
1
2
1
2
1
1
2
1
1
1
0
0
2
1
3
2
0
1
0
2
1
0
2
1
2
1
1
2
1
0
2
1
1
1
2
1
1
1
0
1
1
1
1
0
1
1
1
1
1
1
2
2
1
1
0
1
1
2
1
1
1
2
0
2
2
1
0
1
1
0
1
1
1
0
0
1
1
1
1
1
2
0
0
1
1
2
0
1
1
0
1
0
1
1
2
0
1
1
1
0
0
2
0
1
1
1
1
2
2
1
0
1
1
1
0
1
2
0
0
1
1
2
2
2
1
1
2
1
1
0
2
0
0
2
1
1
1
0
1
1
0
1
2
1
0
1
2
1
2
1
0
1
1
1
1
1
1
0
1
0
1
1
1
0
1
1
0
2
2
2
2
1
1
1
1
0
0
3
1
1
0
1
0
0
1
2
1
1
1
2
2
0
1
0
1
1
1
1
2
1
1
0
2
1
1
2
1
0
2
2
1
1
1
1
1
1
1
2
1
1
1
0
0
0
1
1
1
1
0
0
1
0
0
1
1
1
1
1
2
0
1
1
2
1
1
2
1
2
1
1
0
1
0
1
0
1
1
1
0
1
1
2
1
2
1
1
0
2
2
1
1
1
1
2
1
1
1
1
0
1
2
1
1
1
1
1
1
0
1
2
1
0
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
2
1
1
0
1
2
0
1
0
1
1
0
1
0
1
1
1
1
1
0
2
1
1
1
0
2
1
2
0
1
1
1
1
1
1
1
1
1
2
2
2
1
1
2
1
0
1
1
1
1
2
1
2
1
1
1
1
2
1
1
0
0
1
1
2
1
1
1
1
1
1
2
2
1
1
1
0
1
1
1
1
1
1
0
1
2
2
2
1
1
1
1
1
0
1
1
1
1
1
2
1
2
1
2
0
1
0
1
1
0
2
1
0
1
1
2
2
0
2
1
1
0
2
2
0
0
2
1
1
1
0
1
0
0
1
1
1
1
0
2
1
2
1
1
2
1
1
1
1
1
0
1
0
2
2
1
1
2
1
0
0
0
0
4
1
1
1
2
1
1
0
1
1
2
2
1
1
1
2
1
1
1
2
0
1
1
2
2
1
2
2
2
1
1
2
2
0
0
1
1
1
1
2
1
0
2
0
0
1
2
2
0
1
1
1
2
1
1
2
0
0
1
2
1
0
2
1
0
1
2
1
2
0
0
1
1
2
1
2
2
2
2
2
0
0
1
1
1
1
2
2
1
2
1
2
0
1
0
1
0
2
1
1
1
0
2
1
2
0
2
1
1
2
1
1
1
1
0
1
2
1
0
1
1
2
2
1
1
2
1
1
1
1
1
1
0
1
1
2
0
1
1
2
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
0
1
2
1
2
1
1
0
1
1
1
0
0
2
0
0
0
0
2
1
0
1
0
2
1
1
0
0
0
1
0
1
0
1
1
0
1
2
1
1
1
1
2
1
1
0
0
1
1
2
1
0
2
1
2
1
1
0
1
1
1
1
0
2
1
1
1
1
1
0
1
2
2
1
2
2
1
1
2
2
0
2
0
1
1
1
1
1
2
1
2
0
1
2
1
1
5
1
1
2
0
1
1
1
0
2
1
1
2
2
0
1
1
1
1
2
1
0
1
1
1
1
0
1
1
1
1
0
1
1
1
0
1
1
0
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
0
1
0
1
2
0
1
1
1
2
2
0
1
1
2
2
2
1
0
2
1
1
2
1
2
1
1
1
1
1
1
2
0
1
1
2
1
1
1
0
1
0
1
0
0
2
2
1
2
0
0
1
0
2
0
1
1
0
1
1
1
1
1
1
1
1
0
0
1
0
1
1
2
2
1
1
0
2
2
1
2
0
1
2
2
2
3
2
1
1
1
2
1
1
1
2
2
0
1
2
1
1
0
1
1
1
1
2
2
1
0
1
2
1
0
1
1
2
0
1
2
0
2
1
1
1
0
1
0
1
1
1
0
1
0
1
1
1
0
1
1
2
0
1
1
0
1
1
1
1
0
2
0
1
1
1
1
2
1
2
1
1
1
1
2
1
1
1
3
0
0
2
1
1
2
2
1
1
1
1
1
2
0
0
0
0
1
1
2
2
1
0
2
2
1
2
1
2
1
0
0
1
1
1
1
1
1
1
1
2
2
1
0
1
0
1
2
1
1
0
0
1
0
0
1
1
0
0
1
1
2
1
2
1
1
1
0
2
1
1
1
2
2
1
2
1
2
0
1
2
0
1
1
2
2
0
1
1
1
1
1
1
2
1
0
1
1
1
0
1
1
1
1
1
1
1
0
1
2
1
1
1
2
1
2
0
1
2
2
2
2
0
1
2
1
1
1
2
1
0
1
1
1
1
1
0
0
1
1
0
1
0
0
1
1
0
1
1
1
0
2
1
1
0
1
1
1
1
2
2
2
1
1
1
2
1
1
1
0
1
1
1
0
1
1
1
1
1
0
0
1
1
0
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
0
1
2
2
1
1
0
0
1
2
1
0
4
1
0
1
2
1
0
0
1
1
1
0
1
1
1
1
3
0
1
2
1
0
1
1
1
0
1
2
2
1
1
1
0
0
1
1
2
2
1
1
1
1
1
0
1
2
2
1
2
1
1
0
1
1
2
1
1
1
1
1
1
1
1
1
0
1
1
1
2
1
1
0
2
1
1
1
1
1
1
0
1
1
3
1
2
1
1
0
1
1
0
2
1
2
1
0
1
1
0
1
2
2
0
0
2
1
1
2
1
1
1
1
1
1
1
1
1
2
2
0
0
3
1
2
1
1
2
2
1
1
0
2
0
0
1
1
0
1
1
0
1
1
2
1
2
1
1
2
1
1
0
0
1
1
0
1
1
1
1
1
2
0
1
1
1
1
1
1
1
2
2
0
2
2
0
1
1
2
1
0
2
1
1
2
0
2
1
1
1
1
0
1
1
1
2
1
2
0
1
0
2
2
1
1
1
1
1
1
1
1
1
1
1
3
1
1
0
1
2
2
0
0
1
0
1
1
1
1
1
1
1
1
0
0
0
1
2
1
2
1
2
1
1
1
0
1
1
0
0
1
0
1
1
0
0
2
1
1
1
1
1
1
3
1
1
1
1
2
1
1
1
1
1
0
1
1
2
1
1
1
2
1
3
1
1
1
0
0
0
1
2
2
2
1
2
1
1
0
1
1
1
2
1
0
1
2
1
1
2
2
1
2
0
1
1
1
2
1
0
1
2
1
1
0
1
1
0
1
1
1
1
1
1
1
0
2
2
0
2
0
0
2
0
1
1
1
1
1
2
0
1
2
1
0
2
1
0
1
3
1
1
1
1
0
1
2
1
1
1
1
0
1
2
0
3
1
2
2
0
1
0
1
1
2
2
0
1
1
1
1
3
1
1
2
2
1
2
2
2
1
0
1
1
1
1
0
1
2
1
1
0
2
1
0
1
1
3
2
0
1
1
0
0
1
2
2
1
1
1
1
1
1
0
2
1
1
1
1
0
1
2
1
1
1
1
1
3
1
0
0
2
2
1
2
1
2
2
1
1
1
1
0
1
1
0
1
2
1
1
0
2
0
3
1
1
1
1
1
2
1
2
1
1
1
1
1
2
0
1
2
0
2
0
1
2
1
2
0
1
0
0
0
1
1
1
2
1
1
1
0
0
1
1
1
2
2
0
1
2
1
2
2
0
2
1
0
0
1
1
1
2
1
2
1
1
2
1
2
1
1
2
1
2
0
0
1
0
2
1
1
1
2
0
1
2
0
0
0
0
1
0
2
0
1
0
0
1
1
1
2
1
2
1
1
1
2
1
1
0
1
1
1
1
1
0
1
1
1
1
1
1
1
0
2
1
0
1
1
2
1
1
1
1
1
1
1
2
1
0
1
0
1
2
2
2
1
1
1
1
1
0
2
0
1
0
1
1
1
1
1
1
3
1
1
1
2
2
1
2
1
2
1
0
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
0
1
2
1
1
1
1
1
1
1
1
1
0
2
1
1
2
0
1
1
1
2
1
0
1
1
1
2
1
2
1
1
1
1
1
0
2
0
1
2
2
2
1
1
0
0
2
1
2
1
1
1
2
1
1
2
1
1
1
0
1
2
1
0
0
1
2
1
1
0
2
0
1
0
1
1
1
2
1
0
1
0
0
1
0
0
2
0
2
1
1
1
1
0
2
0
1
1
0
1
0
1
1
1
2
1
1
1
1
1
2
1
2
1
1
1
0
0
2
1
1
2
0
2
0
0
0
2
1
2
1
2
0
1
1
0
1
0
1
2
1
1
1
1
1
1
1
1
1
1
1
0
0
1
1
2
1
1
2
1
1
0
0
2
1
2
0
1
0
1
2
1
0
0
1
0
1
1
1
1
1
0
1
1
1
1
1
1
1
2
1
0
1
0
1
0
2
2
1
1
2
1
2
0
1
1
1
1
1
1
1
1
1
1
1
2
1
0
1
0
0
2
1
2
1
2
1
1
1
2
2
1
1
1
1
1
2
1
1
1
1
0
1
1
1
1
1
0
0
1
1
2
2
1
1
1
1
1
0
1
1
1
1
2
2
0
0
0
1
1
1
2
1
1
1
1
1
1
0
0
2
2
0
2
1
1
1
1
0
1
1
1
0
1
1
1
1
1
2
1
0
0
0
1
1
0
1
0
1
1
1
2
1
1
1
1
2
2
2
2
0
1
1
1
2
1
2
1
0
2
1
0
0
1
2
1
0
1
1
1
0
1
1
1
2
2
2
0
0
2
1
1
0
1
1
0
1
1
1
1
0
2
1
2
0
2
1
1
2
1
0
1
1
1
0
1
1
2
1
1
0
1
1
0
0
1
1
0
1
1
2
1
1
1
1
1
2
1
2
1
1
2
1
1
1
2
2
1
2
0
1
0
1
1
0
2
1
1
1
0
1
0
2
1
1
1
1
2
1
1
2
1
2
0
2
1
1
2
1
1
1
0
1
2
0
1
2
2
1
1
2
1
2
2
2
2
1
1
0
2
1
1
1
1
1
1
0
0
0
1
0
3
1
1
1
2
1
1
0
2
0
1
0
0
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
2
1
2
0
0
1
1
0
1
0
2
1
0
0
0
1
0
1
2
1
0
1
1
1
1
2
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
0
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
0
0
1
1
2
1
0
0
1
1
1
1
0
1
1
2
0
0
0
1
1
1
1
2
1
1
1
0
2
1
1
1
1
3
2
0
0
1
1
2
1
1
2
2
1
2
1
1
1
1
1
2
2
2
1
2
0
2
1
1
0
1
1
1
1
2
1
0
1
1
1
1
2
0
1
2
0
1
0
0
1
1
1
0
1
0
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
0
1
1
1
0
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
0
2
0
2
2
1
2
1
1
1
2
1
1
0
0
1
1
1
1
0
2
1
1
2
1
1
1
2
1
1
1
0
0
1
0
1
1
1
1
1
1
1
4
2
1
1
0
2
1
0
0
0
1
1
1
1
1
2
2
1
1
0
1
2
2
2
1
1
1
2
0
1
1
1
1
2
1
1
2
1
1
2
3
1
1
2
1
0
1
1
0
1
2
0
1
1
1
1
0
2
1
0
2
1
1
1
2
1
2
0
2
1
1
2
2
1
1
0
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
0
0
2
1
1
1
2
1
1
2
2
1
2
2
1
0
1
0
1
1
2
1
3
1
0
1
2
2
2
0
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
2
0
1
1
1
1
1
1
2
1
1
1
1
1
2
0
1
0
1
1
1
1
1
2
1
0
1
4
1
1
0
1
0
2
2
1
2
2
1
2
1
1
2
1
0
0
0
2
1
0
0
1
1
0
0
1
2
1
2
1
1
2
1
0
2
0
1
2
2
1
1
2
2
1
0
1
0
1
2
0
2
2
1
0
0
0
1
2
2
1
2
2
0
1
1
1
0
0
2
1
1
1
1
1
1
0
1
1
2
1
1
2
1
1
1
1
1
2
0
1
2
1
0
1
1
1
2
1
2
2
1
0
1
1
1
2
2
1
1
1
1
1
2
0
0
2
2
1
0
0
1
1
1
1
1
0
0
1
1
2
0
1
1
0
1
1
1
0
2
1
1
2
0
1
1
0
0
1
0
1
1
2
1
1
0
0
1
1
2
1
1
2
1
2
1
2
2
1
2
2
1
1
0
2
1
1
1
2
1
1
0
1
1
1
0
2
0
1
0
1
1
1
1
2
2
1
0
1
2
1
1
1
1
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
2
1
1
2
1
2
0
2
1
2
2
1
1
1
1
1
1
2
2
2
1
1
1
2
0
2
0
2
1
1
1
1
0
1
1
1
1
0
1
1
1
2
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
0
2
2
0
2
2
2
1
2
1
1
1
1
1
1
1
2
1
2
2
1
1
1
0
2
1
2
2
2
1
1
2
2
1
1
1
1
1
0
2
1
2
2
1
1
1
1
2
0
2
1
2
2
1
0
0
2
1
1
2
1
1
2
0
2
1
1
2
2
1
0
2
1
0
1
1
1
3
0
1
1
2
1
2
0
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
0
1
0
2
1
2
1
1
0
2
1
1
2
1
0
1
0
1
1
1
1
1
2
1
1
1
1
0
0
2
0
1
1
1
1
2
0
1
1
2
1
0
1
1
1
2
1
1
1
0
1
1
0
1
1
1
2
1
1
1
1
2
1
2
1
2
0
1
2
0
1
1
2
2
1
2
2
0
1
2
2
2
2
0
1
0
1
0
2
0
1
1
1
2
1
1
1
0
1
1
2
0
1
0
0
1
0
0
0
1
1
1
1
1
1
1
1
1
1
1
1
2
1
0
0
1
2
2
1
1
1
1
1
0
1
0
0
1
1
1
0
1
2
0
1
1
1
0
1
1
0
0
0
3
1
1
1
1
1
1
1
1
1
2
0
2
1
2
1
2
1
1
1
2
1
1
1
1
1
2
1
1
1
0
0
4
1
0
2
0
1
1
1
1
2
0
1
1
1
1
1
1
1
2
2
0
1
1
0
0
1
2
1
1
1
1
2
1
1
1
2
2
2
1
0
2
2
1
0
1
1
0
1
1
1
1
1
1
0
1
0
1
2
2
1
0
2
1
1
1
2
2
2
1
1
1
2
1
1
2
1
1
2
0
2
0
1
0
3
2
1
0
1
1
1
1
1
1
1
1
1
0
0
1
2
2
2
4
1
0
1
1
1
1
1
0
1
0
1
1
1
2
1
2
1
1
1
2
1
0
1
0
0
1
0
1
2
1
1
1
1
1
1
2
1
2
1
0
0
1
0
2
1
1
1
1
1
1
0
2
1
0
1
2
0
0
1
0
1
1
0
1
1
1
1
2
0
2
1
1
0
2
1
1
2
1
2
1
1
1
0
1
2
2
0
1
1
1
1
1
3
1
0
1
1
0
2
0
0
1
2
1
2
2
1
0
2
2
1
1
2
1
0
1
2
1
1
1
1
1
1
1
1
0
0
2
1
1
1
1
1
1
2
1
1
1
1
1
1
0
1
1
0
2
2
1
1
1
1
1
0
1
0
0
1
0
2
0
1
0
1
0
2
0
1
1
1
1
0
1
1
1
0
0
2
1
1
1
1
1
0
2
2
0
1
1
0
1
1
1
0
1
2
2
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
0
1
1
1
0
2
1
1
1
1
0
1
1
1
0
0
1
0
2
2
2
1
2
0
2
0
1
1
2
2
1
1
0
2
1
1
1
1
0
0
0
1
2
5
2
1
1
2
2
1
1
2
1
2
0
1
2
1
2
0
4
1
0
1
1
0
1
1
1
0
1
1
1
1
1
1
2
1
1
2
1
2
0
1
0
2
0
3
1
1
1
0
0
2
2
1
0
2
2
1
1
1
2
2
1
1
1
2
1
2
2
2
0
1
2
1
0
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
2
1
1
1
2
1
1
1
1
2
0
0
2
2
2
1
1
2
2
0
1
2
2
0
0
1
1
1
0
2
1
1
1
1
1
1
2
0
2
1
1
1
1
1
2
1
2
1
1
2
1
0
1
1
0
1
2
1
2
1
0
1
2
0
2
1
0
0
1
1
1
0
0
1
0
2
1
1
1
1
2
1
0
1
2
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
1
1
0
1
0
1
2
1
1
2
2
0
1
0
1
2
1
1
0
1
0
0
1
1
1
1
1
1
1
0
1
2
1
2
1
1
2
1
0
1
1
1
1
1
2
1
1
0
1
2
1
0
1
1
1
2
1
0
2
1
1
2
1
2
1
2
0
1
0
2
1
2
1
1
1
1
1
0
0
1
0
1
2
1
0
1
1
1
1
1
1
1
0
2
1
2
1
0
0
0
2
1
2
1
2
0
2
1
1
1
1
1
1
1
2
1
1
1
1
2
2
2
1
2
2
1
1
1
0
0
2
2
1
0
1
0
2
1
1
1
1
1
2
1
0
0
0
1
1
1
1
2
0
1
0
1
0
1
0
1
2
0
1
1
0
1
1
2
1
1
2
2
2
2
1
0
1
2
2
1
1
1
1
2
2
1
1
1
1
2
2
0
1
0
2
1
1
1
2
1
1
1
2
2
2
1
2
1
0
1
1
1
1
1
0
1
2
1
0
2
0
1
2
1
2
1
1
0
1
1
2
0
2
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
0
1
1
1
0
1
2
2
1
1
2
1
1
1
1
1
0
1
2
2
1
1
1
0
2
3
2
1
1
2
2
0
1
1
1
2
1
1
1
1
0
2
0
0
1
1
2
1
2
1
1
0
1
0
1
2
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
2
1
2
2
1
0
2
1
2
0
1
1
1
0
1
1
2
2
2
2
2
1
1
1
1
0
1
1
1
1
2
2
1
0
2
0
1
1
1
2
1
2
2
2
1
0
1
1
1
2
2
1
1
1
1
1
2
1
0
1
1
1
1
1
1
1
2
1
0
5
0
1
1
1
1
1
0
2
0
2
1
1
1
0
1
1
2
2
2
3
2
0
1
1
1
2
1
1
1
1
2
1
0
1
1
1
0
0
0
2
2
1
0
0
1
1
1
2
1
1
1
1
1
2
0
2
1
0
1
1
1
1
2
1
0
2
1
0
1
2
1
1
1
0
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
0
2
2
1
1
1
1
1
1
2
2
1
1
2
1
1
1
0
1
1
2
2
0
2
1
0
1
0
1
1
1
2
0
1
1
2
1
1
3
0
1
1
2
0
0
1
1
2
1
1
0
1
2
0
1
1
1
2
1
1
2
0
1
1
2
1
1
0
0
2
2
1
0
1
1
1
1
2
1
2
2
1
1
1
3
1
0
2
1
1
1
1
0
3
3
1
1
1
1
1
2
1
0
2
0
1
2
0
1
1
1
1
1
1
1
0
1
0
0
2
1
1
0
0
1
2
1
2
0
2
1
1
1
1
0
1
0
2
2
1
1
1
1
0
2
1
1
2
1
0
0
1
1
2
1
2
1
1
1
2
1
1
1
0
1
1
1
2
2
2
1
1
0
1
0
1
1
0
1
0
0
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
0
2
1
1
1
0
0
0
1
2
2
0
1
0
1
0
2
0
1
0
1
1
1
2
1
0
0
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
2
0
1
1
1
1
0
0
1
1
1
0
1
1
1
0
1
0
1
0
1
2
1
2
2
1
1
1
2
2
1
2
1
0
2
1
2
1
2
1
1
1
1
2
1
1
0
1
0
2
1
1
1
1
1
2
2
2
0
0
1
0
0
1
2
1
1
2
1
1
0
2
1
1
1
1
1
1
2
1
2
0
1
1
0
1
3
1
2
2
1
0
1
1
1
1
1
2
2
1
1
1
3
2
1
0
2
1
2
1
1
1
0
1
1
0
2
2
2
0
1
2
1
1
2
2
1
0
1
1
2
1
1
1
1
2
1
1
1
0
1
1
0
0
1
1
1
1
0
1
2
0
1
2
1
0
1
0
1
1
2
1
1
1
2
0
1
1
0
0
1
2
2
1
2
1
1
1
1
1
0
0
2
2
0
1
2
2
2
1
1
2
1
1
0
2
1
0
3
2
1
1
0
1
1
1
2
1
2
1
1
2
1
2
1
1
1
1
2
0
0
1
0
2
2
2
1
2
1
2
0
1
2
1
0
0
1
0
0
0
2
1
1
1
1
1
0
1
1
1
2
1
2
1
1
0
2
0
0
1
2
0
1
2
1
0
1
1
1
2
1
1
1
1
1
1
1
1
0
0
0
0
1
1
1
1
1
1
0
2
0
2
1
2
1
2
1
1
0
2
1
1
1
1
0
1
1
1
1
0
2
1
0
1
1
2
1
0
0
1
1
1
2
1
1
0
1
0
1
1
2
0
1
0
2
2
0
2
2
1
1
1
1
2
1
2
1
0
1
1
1
1
2
1
1
1
2
1
1
1
0
2
2
2
1
2
1
1
1
0
2
1
1
1
1
3
0
1
1
1
2
1
0
1
1
1
1
2
2
2
1
1
0
1
0
1
0
1
1
1
2
2
1
1
2
1
0
0
2
1
1
1
2
1
2
2
1
1
1
0
1
0
1
1
1
1
0
0
1
1
2
1
2
1
0
2
1
1
1
1
1
1
1
1
2
1
1
1
2
2
0
1
0
1
0
0
1
0
1
1
6
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
0
0
1
2
1
1
0
1
1
1
1
1
2
0
1
0
1
1
1
2
0
2
1
2
1
1
2
1
1
1
2
1
1
1
0
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
2
0
1
0
1
0
0
1
2
1
1
1
1
1
1
1
0
1
1
0
1
1
0
1
1
1
1
1
1
1
2
2
0
0
1
1
1
1
0
1
1
2
1
0
1
2
2
1
1
1
1
1
0
2
0
0
1
1
1
1
0
2
2
2
2
1
1
2
0
1
1
1
0
2
1
1
1
0
0
1
0
1
1
0
1
1
0
1
1
0
2
0
2
2
1
1
2
2
1
1
0
2
1
0
2
0
2
1
1
1
2
1
1
2
1
1
2
0
0
1
1
0
0
0
0
1
0
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
0
1
1
1
0
0
1
1
2
1
1
1
2
0
1
1
1
1
1
11
0
1
1
1
1
1
1
1
1
0
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
0
2
0
1
2
0
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
2
2
1
1
2
0
0
1
2
1
1
1
1
1
0
1
0
1
0
1
2
1
0
0
1
1
1
1
0
1
0
0
2
1
1
2
2
1
2
2
1
2
1
0
1
1
2
0
1
3
1
2
1
1
0
2
0
1
0
1
0
1
1
1
1
2
1
0
1
2
2
0
1
0
2
1
2
1
1
1
2
1
1
1
1
0
0
2
1
2
3
1
0
1
2
1
1
1
2
0
6
1
2
2
1
2
1
0
2
0
1
1
1
1
2
2
0
1
2
1
1
0
1
1
0
2
1
0
0
2
1
1
0
1
1
0
2
1
2
1
1
2
1
1
1
1
1
2
1
2
1
1
2
0
2
0
1
0
1
1
1
2
1
0
1
1
1
2
2
1
1
1
1
1
0
1
1
1
2
0
1
1
1
2
1
1
1
1
1
1
1
1
0
1
1
0
0
0
1
1
1
1
0
1
2
1
1
1
0
1
2
2
0
2
0
1
1
1
0
2
1
1
2
2
2
1
2
1
1
1
0
2
1
2
1
0
0
1
1
0
0
1
1
1
1
2
2
1
2
1
1
0
1
0
1
1
0
1
1
1
0
1
1
1
0
0
0
3
1
2
2
0
1
2
2
1
2
1
2
1
0
1
0
1
1
1
1
2
0
1
2
0
1
0
1
1
0
1
2
1
1
2
2
1
1
0
1
1
2
1
1
1
2
1
0
1
0
0
2
0
0
2
2
1
1
0
1
1
0
1
1
1
1
1
0
1
2
2
0
1
1
2
1
2
1
2
2
1
1
0
2
1
0
1
1
2
1
0
2
1
2
1
1
1
1
1
2
3
1
0
1
1
1
1
1
1
1
1
2
1
1
2
2
2
1
1
1
1
1
2
1
1
2
1
2
1
0
2
2
1
1
1
1
1
1
0
2
1
2
0
1
1
0
0
1
1
1
0
1
1
0
0
1
1
0
2
1
1
1
1
1
1
0
1
2
2
1
2
1
1
0
2
1
0
0
1
1
2
0
1
0
2
1
2
1
1
1
0
1
1
1
1
1
1
1
1
1
1
0
1
2
1
1
1
1
1
2
1
1
2
0
1
2
2
0
1
2
1
1
0
0
2
1
1
1
1
0
2
1
0
2
1
0
0
2
0
2
1
0
2
1
2
1
1
2
1
2
1
1
1
1
1
1
2
1
2
2
1
2
1
0
1
0
2
1
1
1
2
1
2
1
1
0
0
3
1
0
0
0
0
2
2
2
1
1
1
0
1
1
1
0
1
1
2
0
1
1
1
2
0
2
2
0
2
1
1
0
2
1
0
0
2
1
1
0
1
1
1
1
0
0
1
1
0
1
0
2
2
0
1
1
1
1
1
1
1
1
1
0
1
1
1
1
0
2
1
0
2
1
1
1
1
1
2
1
2
1
1
1
2
2
2
0
1
2
1
0
1
0
0
1
1
2
1
2
1
1
1
1
1
1
2
1
1
0
1
0
2
0
0
1
1
0
1
1
1
0
2
0
1
2
1
1
2
1
1
1
1
1
1
2
1
2
1
1
2
2
1
2
1
1
1
0
1
2
1
1
2
2
2
1
1
1
2
0
2
1
1
1
2
1
2
2
1
2
0
1
2
0
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
0
0
2
0
0
1
2
1
1
1
0
1
1
0
4
1
1
0
2
2
1
2
1
1
0
1
1
1
0
1
1
1
2
1
1
1
0
0
2
1
1
2
1
1
1
2
1
2
2
0
2
1
0
1
2
1
2
2
1
1
1
1
1
2
1
1
1
2
2
2
1
1
2
1
1
1
2
1
0
1
1
0
2
1
0
0
1
1
1
1
1
1
1
2
1
0
0
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
2
1
1
0
2
0
1
1
1
1
0
2
1
1
1
1
2
1
1
1
1
1
1
1
0
2
0
1
0
1
2
1
2
2
1
1
0
1
1
2
1
0
2
2
1
1
2
2
0
0
2
1
2
2
2
0
0
1
0
1
1
1
0
1
1
1
1
2
0
0
1
2
1
1
1
0
2
2
0
2
2
1
1
2
0
1
1
1
0
1
1
0
2
2
2
1
1
1
1
1
1
2
2
0
1
1
1
1
0
1
1
2
1
1
0
2
2
0
1
3
2
1
1
1
2
2
1
1
2
0
2
1
0
2
1
0
1
2
1
1
1
1
1
0
0
1
1
1
1
1
0
1
0
1
1
0
1
1
2
1
0
1
1
0
0
2
1
1
0
1
1
0
1
0
2
1
1
1
1
1
0
2
1
0
1
1
1
1
1
2
1
2
2
0
0
1
0
2
0
0
1
1
0
0
1
1
1
2
1
0
0
1
2
1
2
1
0
2
1
1
1
1
2
1
2
1
1
1
2
1
1
2
0
0
1
1
2
1
0
2
1
1
1
1
1
1
1
1
2
2
1
0
2
1
2
1
1
0
1
2
0
0
0
0
1
1
0
0
1
1
0
1
1
2
1
2
2
1
1
0
2
2
1
1
1
0
1
1
1
1
2
1
1
0
1
2
1
1
1
0
2
1
1
1
1
1
1
1
0
0
1
1
2
2
2
1
1
0
1
1
1
2
2
1
1
1
1
1
0
2
1
0
0
1
1
2
2
0
0
1
2
2
0
1
1
2
1
2
1
2
1
1
1
2
3
2
1
1
2
0
2
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
2
1
1
2
1
1
0
0
1
1
1
1
1
2
1
2
0
2
2
0
2
1
1
1
1
0
0
1
0
0
2
2
0
1
0
2
1
1
4
0
1
0
0
1
2
2
1
1
1
1
1
1
1
0
1
2
0
2
2
1
2
0
1
1
1
1
1
1
1
2
2
2
1
0
0
1
1
2
0
1
0
1
0
1
1
1
1
1
1
2
1
0
1
2
0
2
0
1
1
1
1
1
1
1
0
0
1
1
1
2
1
2
0
1
1
2
1
2
1
1
0
2
1
1
0
1
0
2
2
1
2
1
1
1
1
0
1
2
1
2
1
2
0
1
0
1
1
1
2
1
2
1
1
2
2
1
1
2
2
2
0
1
2
1
2
0
1
1
1
1
1
2
0
1
1
1
0
2
2
1
2
1
0
1
1
0
1
1
1
1
0
1
1
0
1
2
2
1
1
4
1
1
1
0
2
2
1
1
1
1
0
0
0
3
1
1
1
1
1
1
1
1
1
2
1
0
1
2
0
0
1
1
0
1
1
1
1
1
1
2
1
1
1
1
1
1
0
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
2
1
2
1
1
2
0
1
1
1
2
1
1
0
1
2
1
1
1
2
1
0
2
1
0
0
1
1
0
1
1
1
1
1
1
0
2
1
1
0
1
2
1
1
1
1
0
1
2
1
1
1
0
0
2
1
0
1
2
2
1
1
1
2
2
1
2
1
0
1
1
1
1
2
2
2
1
2
1
1
0
2
1
1
1
1
1
1
1
2
2
0
1
1
1
1
1
1
1
1
1
1
1
1
0
1
0
1
1
1
1
1
2
2
1
0
1
0
1
1
1
1
0
1
0
1
1
2
1
2
2
1
2
0
1
0
2
1
0
1
1
2
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
0
1
2
1
0
3
1
1
2
3
1
1
2
2
1
0
0
0
0
2
2
1
1
1
0
1
1
2
1
2
0
1
2
1
1
1
1
1
0
2
2
1
1
2
1
1
1
1
1
0
2
1
1
2
1
0
2
2
1
1
1
2
1
1
2
0
1
1
1
1
2
1
1
2
1
1
1
1
1
0
1
1
0
1
1
1
1
2
1
1
2
1
1
0
1
1
1
1
2
0
2
1
1
2
1
0
1
1
1
1
0
1
1
1
2
1
1
2
2
0
0
1
2
1
1
1
0
0
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
0
1
2
0
1
0
3
0
1
2
1
2
2
1
0
1
2
1
3
1
2
1
1
1
1
1
1
0
2
1
1
3
1
2
3
1
1
1
1
1
3
1
1
2
1
0
0
1
1
0
1
0
0
1
2
1
2
1
2
2
1
1
1
1
2
1
1
1
1
1
2
1
0
1
1
2
1
1
1
0
0
0
1
1
0
2
1
1
2
1
1
1
1
1
1
3
2
1
2
2
1
1
1
0
0
0
2
1
2
1
1
0
0
2
1
0
1
1
1
1
1
0
1
1
1
1
2
0
1
1
1
1
1
1
2
0
1
1
2
2
1
1
2
0
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
3
2
1
1
2
0
1
1
1
1
1
1
1
1
1
1
1
1
2
2
0
2
1
0
1
1
1
1
1
2
2
1
1
1
1
0
1
0
0
1
1
2
1
2
1
1
2
1
2
2
1
0
1
0
1
0
2
1
2
1
1
2
1
1
2
1
2
1
2
0
1
2
1
2
0
2
1
1
0
0
1
1
0
1
1
1
1
1
1
0
1
1
1
1
0
0
1
0
1
2
1
1
2
0
2
1
1
0
2
0
1
1
1
0
0
1
0
2
1
1
1
1
1
2
1
0
1
1
2
1
2
2
0
1
1
1
1
0
2
1
1
2
1
2
1
1
1
1
0
1
0
1
0
1
0
2
2
1
2
1
2
2
2
0
2
2
1
1
1
0
0
0
1
1
1
2
0
1
1
1
1
1
1
0
1
2
0
0
1
2
2
2
2
1
1
1
1
1
1
1
2
2
1
0
0
1
1
1
1
0
1
1
2
1
1
2
2
0
2
2
1
1
1
1
1
0
2
0
1
0
1
2
1
1
1
2
2
1
2
1
2
1
0
0
2
2
1
1
2
0
1
1
1
1
1
1
0
1
1
1
1
1
1
0
1
2
1
1
1
2
1
1
0
1
1
1
2
1
1
1
1
2
2
2
1
2
0
1
1
0
0
0
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
0
1
2
1
1
1
0
2
2
2
1
2
1
1
0
1
2
2
1
0
2
0
1
0
1
0
1
0
1
1
2
1
0
1
1
0
1
2
0
1
1
1
0
0
0
1
1
0
0
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
0
1
2
1
1
2
1
0
2
1
1
0
2
2
0
1
1
1
1
1
1
0
1
1
1
1
1
2
1
1
0
0
2
2
0
2
1
0
1
0
2
0
1
1
1
1
1
1
1
1
1
0
1
1
1
0
1
2
0
1
1
0
1
1
1
1
1
1
2
2
1
1
0
1
2
2
1
1
1
2
1
1
2
1
0
1
1
2
1
2
1
0
1
0
1
1
1
1
2
2
2
1
0
2
1
1
1
1
1
1
3
1
2
1
2
0
1
0
1
0
1
2
1
1
3
2
2
0
1
1
0
1
2
0
2
0
2
1
1
0
0
1
1
1
1
2
1
1
1
1
2
1
1
1
1
0
0
1
1
1
2
0
2
1
1
1
3
1
1
0
1
1
1
2
1
1
2
0
1
1
0
2
1
1
1
1
2
0
1
2
1
1
0
0
1
1
1
1
2
0
1
1
2
1
2
1
1
1
0
0
1
0
1
1
1
1
1
1
2
0
1
1
1
1
1
1
0
1
0
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
0
1
1
2
1
0
1
1
2
1
1
1
1
1
1
1
1
1
1
1
0
1
1
2
0
0
0
1
1
1
0
0
1
2
0
2
3
1
1
1
2
1
2
2
2
1
2
1
2
1
0
2
1
1
1
1
1
1
1
1
1
1
2
1
1
0
1
1
2
2
1
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
0
1
2
1
0
1
1
0
2
1
2
1
1
1
1
2
2
1
1
1
1
2
0
1
0
2
2
1
1
1
0
1
1
1
1
1
1
1
1
0
0
1
1
2
1
1
1
1
2
2
1
1
3
1
1
1
1
0
2
1
1
0
0
0
1
1
0
1
1
2
1
1
2
0
2
1
1
1
2
0
1
1
2
1
0
1
1
1
1
1
3
1
2
2
2
2
0
1
1
0
2
2
0
1
1
1
0
1
2
1
0
1
1
1
1
1
0
0
1
1
1
2
2
2
1
2
2
2
1
0
1
1
1
0
1
1
0
1
1
1
1
1
1
1
1
1
1
2
0
2
1
2
0
0
1
1
0
0
1
1
2
2
0
1
1
1
0
0
2
1
2
2
2
1
2
1
1
1
1
0
1
1
1
1
0
0
0
1
1
1
0
0
1
1
1
1
2
0
1
2
0
2
0
1
2
0
0
1
1
1
1
1
1
1
1
0
1
1
1
1
3
0
0
1
3
0
0
2
1
1
2
1
1
2
1
0
1
1
0
0
0
1
1
0
1
2
2
1
1
1
1
1
1
1
1
1
2
0
1
0
2
2
1
2
1
1
2
1
0
1
2
0
1
1
0
1
1
2
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
2
1
1
1
0
1
2
2
2
1
3
1
0
2
1
1
1
1
0
1
1
1
1
0
1
1
1
1
0
2
2
1
1
0
1
2
1
1
1
2
1
1
1
1
0
1
1
0
1
2
1
1
1
2
2
1
1
0
1
1
1
0
2
1
1
4
1
3
1
1
1
2
1
1
1
2
1
1
1
1
1
1
0
2
2
0
2
1
0
1
0
1
0
1
1
2
2
1
1
1
1
0
2
1
2
1
1
1
1
1
1
1
2
1
0
1
2
1
1
1
1
1
2
1
0
1
2
2
1
2
1
1
1
1
1
1
1
1
1
1
0
2
2
0
1
2
0
2
1
0
0
1
0
1
0
0
1
2
1
0
2
1
0
1
1
1
0
1
1
1
1
2
1
2
1
1
1
1
1
1
0
1
1
1
0
1
1
0
1
0
1
1
0
1
1
0
1
1
1
0
1
2
0
0
1
1
0
0
1
2
0
1
1
1
2
2
1
2
1
0
1
0
1
0
1
0
0
1
2
1
1
1
1
1
2
1
0
1
1
2
0
1
1
1
0
2
1
2
1
2
1
2
1
2
2
2
0
1
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
0
2
1
1
1
2
1
2
2
1
1
2
1
1
3
0
1
2
0
1
1
0
0
1
4
1
1
2
1
2
1
0
1
1
1
3
2
1
0
1
2
1
1
2
1
1
1
0
2
2
1
2
1
1
1
1
1
1
1
2
1
1
2
2
1
0
0
1
2
1
1
1
2
0
1
0
1
1
0
1
2
1
1
0
1
2
1
2
1
1
2
1
0
1
1
2
1
1
1
2
1
1
2
2
1
2
1
2
2
1
1
2
0
1
0
2
0
0
0
0
1
1
1
2
0
0
3
0
1
1
0
2
2
1
1
2
1
1
0
2
1
0
1
1
2
1
1
2
0
2
1
0
1
1
2
2
0
2
1
1
2
2
1
1
2
1
1
0
1
2
1
1
1
2
0
1
1
0
1
0
2
1
2
2
2
1
2
1
1
1
0
0
0
1
1
1
1
1
0
1
2
0
1
1
1
1
1
1
1
1
0
1
2
1
0
2
2
1
1
1
0
2
1
0
2
1
1
2
1
1
1
0
2
1
2
1
0
1
1
0
0
3
0
1
1
1
1
2
1
1
1
2
2
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
0
1
0
1
0
1
1
1
1
1
1
0
1
1
1
0
1
1
1
1
2
1
2
2
1
2
1
2
1
0
1
2
2
1
2
2
4
1
1
1
0
2
0
2
1
0
0
1
1
1
2
0
2
1
1
1
1
1
1
0
1
1
1
1
2
1
2
1
0
0
1
2
3
1
2
1
0
0
1
1
1
0
0
1
1
1
1
2
1
1
1
1
1
1
1
1
2
2
1
1
2
1
0
0
1
2
1
1
0
1
0
1
1
1
1
1
1
0
0
0
0
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
2
2
0
1
1
2
1
1
0
1
0
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
0
1
2
1
2
3
1
1
1
1
2
0
1
1
1
1
0
2
1
2
1
0
0
0
2
1
1
1
1
1
1
2
0
1
1
1
1
1
1
2
2
0
0
1
1
1
3
0
2
1
2
1
1
1
1
1
1
1
2
1
1
1
0
0
1
2
2
1
2
1
1
1
1
3
0
1
0
0
2
2
2
0
0
0
1
1
1
2
1
1
2
2
0
0
0
1
1
1
1
2
2
1
1
0
1
1
0
0
2
1
1
1
2
2
1
2
2
1
0
0
1
0
2
0
1
1
2
2
1
0
1
1
2
0
2
0
1
1
2
2
2
1
1
1
1
1
1
0
0
0
1
1
2
1
0
1
1
1
2
2
2
1
1
1
1
2
1
1
1
1
0
1
1
1
1
2
1
2
1
0
2
0
2
1
1
1
1
1
0
1
1
0
2
1
1
1
1
0
1
0
2
0
1
0
0
1
1
1
1
1
1
1
0
1
2
1
1
1
1
1
1
2
1
1
1
1
0
2
2
1
1
1
1
1
2
2
0
1
1
1
1
1
1
1
2
1
1
0
2
0
1
1
1
1
1
3
0
1
1
0
1
1
2
1
1
1
0
0
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
0
2
1
2
0
1
1
0
1
1
1
2
0
1
2
1
1
1
1
0
0
1
1
1
1
0
1
2
1
1
2
2
1
0
1
0
1
1
0
2
1
1
2
1
1
1
1
1
0
1
2
0
0
0
1
0
0
0
0
1
1
1
1
1
1
1
1
2
1
1
1
1
1
0
2
1
1
2
1
1
1
2
1
1
2
2
1
1
0
1
1
1
1
1
1
1
0
1
1
1
2
1
2
1
1
0
1
1
1
0
1
1
2
1
2
1
1
1
1
1
2
0
1
2
1
0
2
2
1
1
1
0
0
1
2
1
1
2
1
1
2
2
0
1
0
1
1
1
2
1
1
1
0
2
0
1
2
1
1
1
1
0
2
1
1
0
0
3
1
1
1
1
1
1
1
0
1
2
1
0
1
1
1
1
0
1
1
1
2
1
0
1
1
1
2
1
1
1
1
0
1
2
1
0
1
0
1
1
1
1
0
0
1
2
1
1
1
1
1
2
1
1
1
0
1
2
1
1
0
2
1
1
1
1
0
0
2
2
1
1
1
1
2
1
1
1
1
1
1
0
1
0
1
1
1
1
1
1
1
0
1
1
2
0
2
0
2
2
1
0
0
1
1
1
2
1
1
1
1
0
2
1
1
2
1
1
1
1
2
1
1
1
0
1
2
4
2
1
1
1
0
1
1
0
0
1
2
1
2
2
1
1
0
2
2
1
0
2
1
2
1
1
1
0
1
1
1
2
1
1
2
1
1
0
0
0
1
2
1
0
1
0
0
0
1
2
1
0
2
2
2
1
1
1
1
1
1
0
1
1
1
1
1
1
2
0
1
2
1
2
1
0
1
1
1
1
1
1
1
1
2
1
1
1
2
1
2
0
2
0
0
1
0
1
0
2
2
1
2
0
1
2
1
1
2
1
1
1
2
1
0
1
2
1
2
3
2
2
1
2
0
1
0
0
0
1
2
0
2
1
1
1
1
1
2
1
3
1
1
1
1
1
1
0
1
1
1
0
1
1
1
1
0
0
1
1
1
1
1
2
2
1
2
1
0
1
0
2
2
2
0
2
0
1
1
3
2
1
1
1
2
1
1
2
1
1
1
1
1
0
1
2
0
1
1
2
1
1
2
1
1
1
0
2
1
1
2
1
1
1
2
0
0
1
1
0
0
1
1
0
1
1
1
0
1
1
0
0
1
1
1
1
1
1
0
2
1
1
0
1
1
1
2
1
2
0
1
2
1
2
0
2
0
0
2
2
1
1
0
1
0
2
1
2
1
1
2
2
2
0
2
3
1
1
1
1
1
1
0
1
0
0
1
1
1
0
0
3
0
1
1
2
1
0
1
2
2
1
1
1
1
1
2
1
0
0
0
0
1
0
1
1
1
2
1
2
1
1
1
0
2
2
2
0
1
1
1
2
0
2
0
1
0
2
1
1
0
0
1
1
0
1
2
1
0
1
1
2
0
1
1
1
1
1
0
1
2
2
0
1
2
1
0
1
1
1
2
1
1
1
2
1
0
1
1
0
1
2
1
1
1
0
0
1
2
1
1
1
1
1
2
2
1
2
1
1
1
2
1
2
1
0
1
2
1
0
2
1
0
1
0
1
0
1
1
1
1
1
2
1
3
0
1
2
2
1
1
2
1
1
1
1
0
1
2
1
1
0
2
1
1
1
0
1
2
2
1
2
0
1
2
1
1
0
1
2
2
1
1
1
0
1
1
1
1
1
1
0
1
1
1
1
1
1
2
1
1
1
2
1
0
0
0
1
3
0
2
0
0
2
1
1
2
1
2
1
1
1
2
1
1
2
1
2
0
1
1
2
1
2
1
2
2
2
0
1
0
0
0
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
2
0
2
1
1
1
1
1
1
2
0
0
1
2
1
2
2
0
1
0
0
0
0
0
1
1
1
3
1
3
1
1
1
1
1
1
1
1
1
6
2
0
2
2
2
2
1
1
2
0
1
1
2
1
0
2
1
2
0
1
1
2
0
1
1
0
1
0
0
1
2
1
1
0
2
2
0
1
2
1
1
2
1
2
1
1
2
1
2
1
2
1
0
1
1
2
1
2
1
2
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
0
1
1
1
0
1
1
1
1
1
1
1
1
1
0
1
1
1
2
2
0
2
2
1
0
2
2
1
2
0
1
1
1
2
2
1
2
0
1
1
1
1
1
1
0
0
1
1
1
1
1
0
2
1
2
1
0
1
1
1
2
1
0
2
1
1
1
1
1
2
1
1
2
2
1
2
1
0
1
2
1
0
0
0
2
1
1
2
0
1
1
0
1
0
2
1
1
1
0
1
1
1
1
1
2
1
2
0
0
0
2
1
3
1
0
1
1
1
3
1
0
1
0
2
2
1
0
1
0
0
1
1
1
1
2
1
1
1
1
2
2
1
1
2
0
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
0
1
1
0
2
2
1
1
1
0
1
2
1
1
0
1
0
0
2
0
0
0
1
1
1
1
1
2
1
1
0
0
5
1
0
1
1
1
2
1
1
0
1
2
2
0
2
0
2
1
0
2
1
1
1
1
1
0
1
2
2
1
2
1
2
0
1
1
1
0
1
1
1
2
1
0
2
1
1
1
2
1
1
0
1
1
2
2
2
1
1
0
1
2
0
1
1
1
1
0
1
0
2
0
2
0
2
1
1
1
1
2
1
2
1
1
2
1
0
2
0
1
1
1
1
2
1
1
2
1
1
0
1
2
1
1
1
2
2
2
2
1
1
1
1
0
0
2
1
0
1
2
1
1
1
1
2
1
0
1
1
0
1
1
3
1
1
1
1
0
1
0
1
1
0
1
1
1
0
2
1
0
0
2
2
2
0
1
2
0
0
0
2
0
2
1
1
1
0
0
1
1
1
0
2
2
1
1
2
1
1
1
2
2
4
1
2
1
0
1
1
0
0
2
0
1
0
2
2
1
0
2
2
1
0
1
2
1
3
1
2
0
1
1
0
2
1
1
2
2
0
1
1
2
1
0
1
1
2
2
1
0
1
0
0
2
2
0
1
0
1
1
2
2
1
1
0
1
0
1
0
1
1
1
1
1
2
1
1
0
1
1
1
2
2
1
1
2
1
1
2
1
2
1
1
1
1
1
2
0
2
2
1
1
1
1
1
13
1
1
1
1
1
1
1
0
0
0
1
2
1
0
2
1
2
1
2
1
1
0
2
2
2
1
0
2
2
1
2
2
0
2
2
1
1
0
2
1
1
0
1
1
0
2
0
1
1
0
0
2
1
1
1
2
1
1
1
2
1
1
1
0
2
1
0
0
1
1
2
1
0
1
1
0
1
1
1
1
1
1
1
2
0
0
1
1
0
1
2
1
0
2
1
1
2
2
1
1
2
1
0
1
0
0
1
1
1
1
1
1
0
1
2
1
1
1
0
1
0
1
1
2
1
1
1
2
1
1
2
2
1
1
1
1
0
0
1
2
1
1
2
1
1
0
1
2
1
0
0
2
1
1
1
2
2
0
2
2
2
1
0
0
2
1
3
1
0
0
1
0
0
1
2
1
0
1
0
0
1
1
2
1
1
1
1
1
0
0
2
1
1
1
2
0
1
1
0
2
1
1
2
1
2
1
1
1
0
1
1
2
1
1
1
1
1
2
1
1
2
1
1
1
0
1
2
1
2
0
0
1
1
1
1
2
1
1
2
2
2
0
2
0
1
1
1
2
0
1
1
1
1
1
1
1
1
2
0
1
2
1
1
1
0
1
0
2
2
2
2
1
1
1
0
2
2
1
1
1
0
1
1
2
2
1
1
0
1
1
1
1
0
1
1
1
2
1
1
0
1
2
1
1
1
1
1
2
1
2
1
1
1
1
2
0
1
1
1
1
2
2
1
1
0
1
0
2
1
0
1
1
2
1
1
0
0
0
1
1
1
1
1
2
1
1
2
1
0
0
1
0
0
2
1
1
0
1
1
1
2
1
1
1
1
1
1
1
2
1
0
0
2
2
1
1
1
1
0
1
2
1
2
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
0
1
1
1
1
2
2
1
2
1
2
1
1
0
1
2
1
1
1
1
2
1
1
1
1
1
1
1
0
1
2
1
1
1
1
2
1
0
0
2
2
1
1
2
1
2
1
1
1
1
2
1
2
1
1
1
2
2
0
2
1
1
2
1
2
1
1
0
1
1
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
2
0
0
1
2
1
1
1
1
1
2
1
1
0
2
1
1
1
1
1
0
0
1
1
0
1
0
0
1
1
0
1
1
1
1
2
1
0
0
1
1
0
1
6
0
2
1
0
1
1
1
1
1
2
1
1
1
0
1
1
0
1
1
0
2
3
1
1
1
1
2
0
0
1
1
1
1
1
2
2
0
0
1
0
1
1
1
0
2
1
1
2
2
2
1
1
1
1
1
2
1
0
2
1
1
1
0
1
1
2
0
1
1
2
1
1
0
2
1
2
1
0
0
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
2
2
1
1
1
1
0
1
1
1
1
1
1
0
2
1
1
1
1
1
1
1
2
1
1
1
0
1
2
2
1
1
2
2
1
1
1
1
1
1
1
1
0
0
0
1
1
1
1
1
0
0
1
1
2
1
2
1
0
1
1
1
0
1
1
1
1
1
1
1
1
0
1
1
1
1
2
0
7
1
1
1
1
2
0
3
0
2
1
1
1
1
2
1
1
1
1
2
2
1
1
2
1
2
0
1
1
1
1
2
0
1
1
0
2
1
2
2
0
1
2
1
1
2
2
1
1
1
2
0
1
1
1
1
1
1
2
1
1
0
0
1
0
1
0
1
1
2
1
1
1
2
1
1
1
1
0
1
1
1
2
1
1
0
1
1
1
1
1
1
0
1
3
0
1
1
1
2
1
2
0
2
2
0
1
1
1
2
2
0
0
1
1
1
1
1
2
2
1
1
1
1
1
1
3
1
1
1
0
0
2
0
2
1
1
1
2
1
1
1
1
2
1
1
1
1
1
2
1
0
2
1
1
2
1
1
1
0
1
2
1
1
2
1
1
1
2
0
1
1
2
1
1
0
0
1
1
1
0
0
1
2
0
2
2
1
1
2
1
1
1
1
1
1
1
0
1
1
0
2
1
1
1
1
1
0
1
2
3
1
1
2
0
2
0
2
1
1
2
2
1
2
2
1
1
0
1
0
1
1
2
0
0
2
1
1
2
2
1
1
0
0
1
1
2
0
1
2
1
2
0
1
1
1
2
1
2
0
1
2
2
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
0
1
0
0
1
2
1
0
0
2
2
1
1
1
1
2
2
1
2
1
2
1
2
2
1
1
2
1
1
1
2
1
1
1
1
1
1
0
1
2
1
1
1
1
2
0
1
1
1
1
2
0
2
2
1
1
0
1
2
0
1
0
1
1
0
0
1
1
1
1
1
0
1
0
1
1
1
2
1
1
1
1
2
1
0
2
1
2
1
0
1
2
2
2
1
1
2
2
1
0
2
0
1
2
1
0
2
2
1
2
0
1
0
2
1
2
2
1
2
2
1
0
0
1
1
1
2
1
1
1
2
2
1
1
0
1
1
2
1
0
1
1
1
1
0
1
2
0
1
2
1
1
2
0
1
1
0
1
1
1
1
1
1
1
2
0
2
1
1
1
2
0
2
1
2
1
1
1
2
1
1
1
1
1
1
0
0
1
0
2
1
1
0
1
1
1
1
1
1
1
1
1
1
0
1
1
0
2
1
1
1
0
1
2
0
2
0
1
5
2
2
2
2
3
2
1
2
2
0
1
0
2
1
1
1
1
1
1
1
2
1
0
1
1
2
0
1
5
1
1
1
2
0
2
1
0
3
2
2
1
0
0
2
0
2
1
1
1
1
1
1
2
2
1
1
2
0
2
1
0
1
2
2
1
0
1
0
1
0
1
0
1
1
2
0
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
0
1
0
2
2
1
1
1
0
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
1
0
1
1
2
2
2
1
1
1
1
1
1
1
1
2
1
0
1
1
1
2
1
1
1
1
1
1
0
1
0
0
1
0
1
0
0
0
1
1
1
1
0
1
1
2
1
1
0
1
1
1
1
1
1
1
2
2
1
1
1
2
2
2
1
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
2
1
1
3
2
1
2
2
1
1
1
2
1
4
1
1
1
0
1
1
1
1
0
1
2
0
0
1
2
1
1
1
0
0
1
2
0
1
1
0
1
3
1
1
1
0
2
2
2
1
0
2
1
1
0
2
2
0
1
2
0
0
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
2
0
2
1
0
1
1
2
1
1
2
2
2
1
0
1
0
0
1
0
0
1
0
1
2
1
2
1
2
0
1
1
1
1
1
2
1
1
1
1
2
0
0
1
0
0
1
2
2
1
1
1
0
1
1
1
1
1
1
2
0
1
1
1
1
2
1
2
1
1
2
2
1
1
1
1
2
0
1
1
0
1
1
2
3
1
1
2
1
1
1
1
1
0
1
1
1
1
1
0
1
1
0
0
1
0
1
1
0
1
1
1
1
2
0
1
1
2
1
2
1
0
2
2
2
1
1
1
2
2
2
2
1
1
2
2
2
0
2
0
2
0
1
2
0
0
2
1
1
1
2
2
1
2
1
1
1
1
1
1
0
2
1
1
0
2
1
0
1
0
1
1
1
2
1
0
2
1
1
1
1
1
2
2
1
0
0
4
1
1
1
1
1
1
0
1
0
1
1
1
1
1
1
0
1
0
1
0
1
0
1
1
1
2
1
1
1
2
1
0
0
2
1
1
2
1
1
1
1
0
1
2
0
0
1
2
1
0
2
1
0
1
1
0
1
1
1
2
2
1
1
1
1
0
2
1
2
1
1
2
1
1
0
2
0
1
1
2
1
1
2
0
0
2
1
1
0
1
1
2
1
1
2
1
2
2
1
0
4
1
1
2
0
1
1
2
0
1
1
2
1
1
1
2
1
0
1
1
0
1
2
1
1
1
2
2
1
1
1
0
1
1
1
0
1
2
1
2
1
1
1
1
1
2
2
1
0
0
1
0
2
1
1
1
1
2
1
1
1
1
0
0
1
1
1
0
0
0
0
1
0
2
1
1
1
0
0
1
1
1
1
2
2
0
2
2
1
0
1
1
2
0
2
0
2
2
2
1
1
1
1
2
0
1
0
2
2
1
0
3
1
2
1
1
2
1
1
1
0
1
1
2
1
1
1
1
1
2
2
0
0
1
1
1
0
1
2
1
1
1
2
2
1
2
1
1
1
2
1
2
0
1
2
0
1
1
1
0
1
1
1
1
2
1
2
0
0
2
2
2
0
2
2
1
1
1
1
1
2
1
1
1
1
0
1
0
1
2
1
1
2
1
2
0
0
1
1
1
0
1
0
1
2
0
2
1
0
2
0
0
2
1
1
1
1
0
1
2
1
1
2
2
1
1
1
1
1
0
1
1
2
1
1
1
0
0
1
0
0
2
1
1
1
0
1
2
2
1
0
0
0
2
2
1
1
1
1
0
1
0
1
2
1
1
2
0
1
1
0
1
0
0
1
1
2
2
1
0
1
0
0
2
0
0
1
1
2
1
0
2
0
1
1
2
2
2
2
2
2
1
1
2
0
1
2
1
1
1
0
1
0
1
1
0
0
2
2
1
2
2
0
1
1
1
1
1
2
1
1
1
1
1
2
2
0
1
1
0
0
1
0
3
1
0
1
1
1
1
0
1
0
2
0
0
2
0
1
1
1
1
1
2
1
1
1
2
0
1
2
0
1
2
2
2
0
2
2
1
2
2
2
1
1
0
1
1
1
1
0
0
0
0
2
2
1
2
1
2
0
1
1
1
1
1
1
0
1
2
0
1
2
1
1
1
2
2
0
2
1
2
1
1
1
2
2
1
1
0
1
1
1
1
1
1
1
2
1
0
1
2
1
2
1
2
1
1
1
1
1
0
0
0
0
1
0
1
0
1
1
1
1
1
2
1
2
2
1
2
2
1
1
0
1
0
2
1
4
0
1
3
1
0
1
2
1
2
0
1
1
1
2
1
1
1
0
1
2
1
1
2
0
1
0
2
2
1
1
1
2
0
1
2
0
1
2
0
2
0
1
1
1
1
1
1
2
0
1
2
1
1
2
0
2
2
1
1
1
3
2
1
0
1
1
1
1
0
1
1
2
1
1
2
2
2
1
1
1
0
1
1
2
1
4
1
1
2
1
1
0
1
0
2
0
2
0
0
1
2
2
1
2
0
2
1
2
1
2
0
1
2
2
0
1
2
1
1
0
2
1
2
1
0
1
2
2
1
0
1
1
1
1
2
1
2
2
0
0
1
2
1
2
1
0
1
1
0
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
2
1
1
2
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
0
0
2
1
1
2
0
2
1
1
0
2
0
1
1
1
1
1
0
1
1
1
1
1
1
1
0
2
1
1
0
0
1
1
2
1
1
2
1
1
2
1
1
0
1
1
0
1
2
1
0
1
0
0
1
1
1
1
1
1
2
1
2
2
2
2
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
0
2
0
2
2
1
1
2
1
0
0
1
1
1
2
1
0
1
2
1
2
1
1
1
0
1
1
1
1
1
0
1
0
2
1
2
1
1
1
1
0
2
1
2
2
0
0
1
1
0
1
0
1
1
1
0
2
1
0
1
0
0
1
0
1
2
1
2
1
1
1
1
1
1
1
1
1
0
1
1
1
1
2
2
1
0
0
2
0
1
2
1
2
2
2
1
2
1
1
2
1
1
2
0
2
2
2
1
2
1
1
2
1
1
1
2
2
2
1
1
1
1
1
0
1
1
1
1
0
1
0
1
1
0
2
1
1
2
1
2
0
0
2
2
2
1
1
2
1
2
2
0
0
2
0
0
1
1
1
1
2
1
2
1
2
1
1
0
1
2
1
1
1
0
0
1
1
1
1
1
1
0
1
1
1
1
1
2
1
1
0
0
1
2
1
1
1
1
1
2
2
1
2
2
1
1
0
1
0
0
1
1
1
1
1
1
1
2
1
1
1
2
1
1
0
2
1
1
1
1
1
1
1
0
1
1
1
1
1
2
1
2
1
0
1
1
0
1
1
1
1
0
2
0
1
2
2
2
0
2
2
1
1
0
0
1
3
1
0
0
2
0
2
1
0
1
1
1
1
1
0
0
2
2
2
0
1
1
2
1
0
0
2
1
1
1
2
1
0
1
1
1
2
1
0
2
2
3
2
1
1
2
0
1
1
2
1
1
1
2
1
0
1
2
1
1
1
2
2
0
0
1
0
1
1
1
2
1
1
0
3
1
1
1
2
1
0
2
1
1
1
1
1
1
1
1
1
2
1
2
0
1
0
2
1
0
1
2
2
1
0
0
1
1
2
2
2
1
1
1
0
2
1
1
0
1
1
1
1
2
1
0
1
1
1
1
1
0
0
1
2
1
2
2
1
1
1
2
1
0
1
2
2
2
1
1
0
2
2
1
1
1
0
0
1
0
1
1
0
1
1
2
2
0
0
1
1
1
0
1
1
1
1
1
1
1
1
2
1
1
0
1
2
2
1
2
1
1
1
1
2
1
1
1
1
1
2
1
2
2
0
1
2
1
2
2
0
0
2
1
2
1
0
1
1
2
0
2
1
1
2
1
1
0
1
1
2
2
1
0
2
0
1
2
0
0
0
1
1
1
1
1
0
1
1
1
1
2
1
2
2
1
2
1
1
1
1
0
2
0
1
1
0
2
1
1
1
0
1
0
1
1
1
1
0
2
1
1
0
2
0
1
1
2
0
1
0
1
1
1
1
1
2
2
1
1
1
0
2
1
2
1
1
0
1
1
1
1
0
0
0
1
2
2
1
0
1
1
1
1
1
1
1
2
1
1
1
1
0
1
2
1
0
0
0
1
1
2
2
1
0
0
1
1
1
2
1
0
0
2
1
2
1
1
2
1
1
1
1
2
0
0
2
2
1
0
1
1
1
1
0
1
0
1
1
1
1
1
0
1
1
1
1
0
2
1
1
0
2
0
1
2
1
1
2
1
2
0
2
2
1
1
1
2
1
2
2
1
2
1
2
0
0
0
1
0
0
1
0
2
1
2
0
1
2
0
0
1
2
1
0
1
1
2
2
1
1
1
1
1
2
2
1
0
1
1
2
2
0
2
2
1
1
1
1
0
0
0
2
2
1
1
0
0
0
1
0
2
0
1
2
1
1
1
0
1
0
0
2
0
0
0
1
0
2
1
1
1
1
1
2
1
0
3
3
1
1
1
1
1
1
1
0
1
1
0
1
1
0
1
2
1
1
1
1
1
1
1
2
1
2
0
1
2
1
1
1
2
1
1
1
0
1
2
1
1
2
1
4
1
1
1
2
1
2
1
1
1
1
1
0
1
1
0
2
1
1
2
0
0
2
1
1
1
1
0
1
0
1
1
1
1
1
2
1
2
2
1
1
1
1
0
1
2
1
1
2
0
0
1
1
1
1
2
1
1
1
3
1
1
0
1
0
1
1
1
2
1
2
0
2
0
1
1
1
1
1
2
0
1
1
1
1
0
0
2
0
1
1
2
2
0
1
2
1
2
1
1
1
0
0
1
1
2
1
2
1
0
2
1
3
1
2
0
1
1
1
2
2
1
0
2
2
1
0
2
0
1
1
0
2
2
1
1
0
2
0
1
1
1
4
1
2
1
1
2
1
1
1
2
1
1
2
1
1
3
1
1
1
0
2
1
1
0
1
1
1
2
1
0
1
1
1
3
2
2
1
0
1
1
1
1
2
2
1
0
0
1
1
1
1
1
3
2
1
2
0
0
1
1
2
1
1
1
0
2
0
0
1
0
1
1
0
0
0
2
1
1
1
2
1
1
0
1
1
2
0
3
2
1
1
2
2
1
1
0
0
1
1
1
1
0
1
2
1
2
1
1
2
1
1
2
1
1
1
1
1
0
1
1
0
1
2
1
1
1
1
1
2
0
2
1
1
1
2
1
2
1
2
1
2
1
1
1
0
1
1
1
1
1
2
1
1
1
1
2
2
0
1
0
2
0
2
1
1
1
1
0
1
1
1
0
1
1
2
1
1
1
2
2
1
1
1
2
1
0
2
2
1
1
1
1
1
3
1
1
0
1
2
1
1
0
2
0
1
2
2
0
2
1
1
0
2
1
1
3
1
1
1
1
1
2
1
1
0
1
1
1
0
2
1
1
1
1
0
0
2
1
2
0
2
1
0
1
2
2
3
1
1
1
1
1
1
0
1
3
1
1
2
1
1
2
0
0
1
1
2
1
1
0
1
1
0
0
1
1
1
2
2
0
2
2
1
1
1
0
0
0
1
1
0
1
1
1
0
1
2
1
0
2
2
1
1
2
2
1
1
0
0
1
2
0
1
1
2
0
1
1
1
1
2
1
0
1
2
1
1
1
1
1
2
1
0
2
1
1
1
2
1
1
1
1
1
2
1
1
1
1
0
2
1
1
0
1
2
1
1
0
1
2
1
1
2
2
1
0
1
2
2
1
1
0
1
0
1
1
2
1
2
1
1
1
1
1
1
1
1
3
1
1
1
2
2
0
0
2
2
0
1
1
1
1
2
2
2
0
2
1
1
1
1
1
0
2
1
1
1
1
1
1
1
1
1
2
1
1
2
2
2
0
1
0
1
2
0
1
2
0
2
1
2
1
1
1
1
0
0
1
2
1
1
2
2
1
1
0
1
0
0
1
1
3
0
0
1
2
0
0
0
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
0
1
0
2
0
2
1
2
1
1
1
2
1
0
2
1
0
1
1
2
1
2
0
1
1
1
1
2
3
1
0
1
1
0
1
2
0
0
0
1
2
2
2
1
1
2
2
1
1
1
1
1
2
2
1
1
1
1
1
1
2
0
2
1
1
1
1
1
2
0
2
1
1
1
0
1
1
2
1
2
1
2
1
1
1
2
1
1
1
1
1
0
2
1
1
1
2
1
2
1
1
0
1
1
1
1
2
1
1
2
2
2
1
1
1
1
1
1
0
1
1
2
0
1
2
1
2
0
3
1
2
2
1
1
1
2
0
1
1
2
1
1
3
2
2
1
1
1
1
0
2
1
0
1
0
1
1
1
1
1
0
0
1
2
1
1
1
0
1
1
1
1
1
2
0
2
1
2
1
2
1
1
0
1
2
1
2
1
1
2
2
1
1
1
1
1
1
1
1
1
2
0
0
0
1
1
1
0
1
2
1
1
1
1
2
0
1
0
3
1
2
1
2
1
0
1
1
1
1
1
1
1
1
1
2
1
1
1
0
2
2
1
1
1
0
2
2
2
1
1
1
1
1
2
1
1
1
1
1
0
0
1
0
2
1
1
0
0
1
1
1
2
2
1
1
1
1
0
1
1
0
0
1
1
0
1
2
1
2
2
0
1
0
1
0
1
1
2
3
0
2
1
1
1
1
1
1
1
1
1
1
0
1
2
1
2
0
1
1
1
1
1
1
2
2
1
1
1
1
2
1
1
0
0
0
0
0
2
1
1
2
0
0
1
1
2
0
2
1
1
1
2
1
1
0
1
1
0
2
1
2
1
0
1
0
1
1
2
1
1
1
2
2
1
1
1
1
0
0
1
0
0
1
1
1
2
2
1
3
2
0
0
1
1
1
1
2
1
1
0
1
2
1
1
1
2
1
1
1
1
1
2
2
1
1
0
2
2
1
1
1
2
2
1
1
1
1
2
1
2
0
1
2
0
2
0
1
0
1
0
1
1
2
1
1
1
1
0
0
1
1
1
2
0
1
0
1
3
1
0
1
0
1
1
1
2
1
1
1
0
1
2
0
1
1
1
1
0
1
1
0
1
1
1
1
0
1
0
1
4
1
1
1
1
1
1
0
1
1
1
1
0
1
2
0
1
2
0
0
2
1
2
0
1
1
0
1
1
1
1
2
2
2
1
1
0
1
2
1
0
1
1
1
1
2
2
0
0
1
2
2
0
0
2
0
2
0
0
0
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
0
1
1
2
1
1
0
1
1
1
1
0
1
1
1
2
2
1
0
3
0
2
0
0
2
0
1
2
1
3
1
1
2
1
2
2
0
1
1
1
0
0
1
1
1
0
0
1
0
1
1
1
1
1
1
1
1
1
1
2
2
2
1
0
2
1
2
1
2
1
1
0
1
1
0
1
1
1
1
1
1
1
0
1
1
1
1
0
0
0
2
1
1
1
1
0
1
0
2
1
0
1
1
1
1
0
1
1
2
1
0
1
1
2
0
1
1
1
1
2
1
1
1
1
1
2
2
2
2
1
1
1
1
1
0
1
1
2
1
1
0
1
2
1
0
1
1
1
2
2
2
1
2
1
1
1
0
2
1
2
1
1
1
0
1
0
1
2
0
0
2
1
1
1
1
1
1
0
1
2
1
2
1
2
0
2
1
2
0
1
0
2
1
1
2
2
3
1
3
1
1
2
2
0
1
1
1
1
2
1
1
2
1
1
2
2
1
1
1
0
2
2
1
0
1
1
1
2
0
0
1
2
0
1
1
1
1
1
1
1
1
0
2
1
1
0
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
0
1
0
1
0
1
2
1
0
1
1
2
1
2
2
2
2
1
1
1
0
0
3
2
1
0
0
2
2
1
1
2
1
0
1
1
1
2
1
1
0
0
1
1
0
0
3
1
2
1
0
0
2
1
1
0
1
1
1
0
0
1
0
2
2
0
0
1
0
1
2
1
1
2
0
1
0
1
1
1
2
0
1
1
1
1
0
0
1
1
1
0
1
0
1
2
2
2
1
1
1
1
2
1
2
1
0
1
1
1
1
1
1
0
1
2
1
1
2
1
1
1
1
1
2
0
1
2
1
2
1
0
1
2
1
0
2
1
1
2
1
1
2
1
2
3
0
1
1
1
1
2
1
1
0
1
1
2
1
1
1
1
2
0
2
1
1
0
1
1
2
1
2
0
1
1
1
1
1
1
2
2
1
0
2
1
2
1
1
0
2
1
1
0
1
2
2
1
1
1
1
1
1
0
2
2
0
1
1
2
0
1
1
1
0
2
2
2
0
0
1
1
0
1
0
2
2
0
1
0
1
1
2
2
1
0
1
2
1
1
1
1
1
3
1
1
1
2
0
2
1
1
1
1
1
1
2
0
1
0
2
1
1
1
2
2
0
1
0
0
2
1
1
1
2
1
1
1
1
1
1
1
2
4
1
0
1
1
0
1
1
2
1
1
1
1
0
1
0
1
0
1
0
1
0
0
1
1
1
1
2
1
2
1
1
1
4
1
1
2
1
2
1
0
2
1
1
0
3
1
1
1
2
0
1
1
2
0
1
1
0
1
1
1
2
0
0
1
2
2
1
1
1
0
1
1
1
1
1
1
0
1
2
0
1
2
2
1
1
1
1
1
2
0
0
1
1
1
1
1
1
1
0
1
1
1
1
1
0
1
2
1
2
1
2
2
0
2
1
0
1
1
1
0
2
1
2
2
1
1
1
1
1
2
1
1
1
2
1
2
0
2
1
2
2
0
1
1
0
0
0
2
0
2
1
0
1
1
1
1
1
2
1
1
1
1
2
0
2
1
2
1
0
1
1
1
1
0
1
2
1
1
1
1
1
2
1
2
2
1
1
2
0
1
0
1
2
1
2
0
0
2
1
1
2
1
1
1
1
1
2
1
1
2
1
0
1
1
0
1
0
1
1
0
0
0
1
0
2
1
0
2
1
1
1
2
1
1
0
2
0
1
2
1
1
1
1
1
2
1
1
0
2
1
0
0
1
1
1
1
2
1
1
1
1
1
0
1
0
1
1
1
0
2
1
1
3
2
1
1
1
2
2
0
1
1
2
0
2
2
2
1
0
1
1
1
2
1
1
2
2
2
0
1
1
0
1
2
1
2
1
0
1
1
2
1
1
2
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
0
2
1
1
2
0
1
1
1
1
1
1
1
1
0
4
1
1
2
0
1
1
1
1
0
2
1
2
1
1
0
2
1
0
1
2
2
1
2
0
1
1
1
1
1
1
1
2
2
1
1
1
2
1
0
1
1
1
1
0
1
2
1
1
1
1
1
1
1
1
1
1
1
0
0
0
1
0
1
1
2
2
1
1
0
2
1
1
1
1
1
0
1
2
1
1
1
1
2
0
1
0
1
1
0
0
1
2
1
2
1
1
1
1
0
1
1
2
2
0
2
1
1
1
1
1
0
1
1
0
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
0
0
0
1
0
1
1
1
0
1
1
0
1
1
1
0
1
1
3
1
1
2
1
0
0
1
1
1
1
0
1
1
2
1
2
1
2
1
0
1
1
0
1
0
1
2
1
1
1
1
1
2
2
2
1
0
1
0
1
1
1
2
1
1
0
0
0
1
1
2
2
2
1
0
2
2
1
0
0
2
2
1
1
1
1
2
2
1
0
2
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
0
0
1
1
2
1
1
0
1
1
1
1
2
1
2
1
1
0
2
1
0
2
2
2
2
2
1
0
1
1
1
1
2
1
1
0
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
0
0
0
1
1
2
0
1
2
1
2
2
1
2
2
0
0
0
1
2
2
0
1
0
1
2
1
1
1
0
1
2
2
2
2
0
1
1
0
0
1
1
2
1
2
0
2
1
2
2
0
1
1
0
1
1
1
2
2
0
1
1
2
1
1
1
0
1
1
1
1
0
1
1
1
3
0
1
1
1
2
0
2
2
1
1
2
1
1
0
1
1
0
0
1
1
2
1
1
1
1
2
0
0
0
1
1
2
2
2
0
2
1
2
1
1
1
1
1
2
0
0
0
2
1
1
1
0
1
1
1
2
1
0
1
1
0
1
2
1
0
2
1
1
1
1
1
1
1
1
2
2
2
1
2
0
1
0
1
2
2
2
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
4
1
1
1
1
1
2
0
0
2
2
2
1
1
0
2
1
1
0
2
2
0
1
1
1
0
1
1
0
1
2
1
0
1
1
1
2
1
2
0
0
1
2
1
1
1
2
2
1
1
1
2
0
2
1
1
1
1
1
1
1
2
2
2
1
1
1
0
1
1
1
2
1
2
2
1
1
1
0
2
1
1
0
3
1
0
1
0
1
1
1
1
1
3
1
0
1
2
1
0
1
1
0
2
2
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
0
1
3
2
2
1
2
2
1
1
1
2
0
2
2
1
2
1
1
1
1
1
0
1
2
0
1
2
1
1
0
1
1
2
2
1
1
2
1
2
1
1
1
2
2
2
1
0
1
1
1
1
2
1
1
1
2
1
1
1
0
1
1
1
1
2
0
1
1
1
3
1
1
1
1
1
1
0
0
2
2
1
1
3
2
1
3
2
2
1
1
1
2
1
1
1
1
1
1
2
2
1
1
2
0
1
0
1
1
1
1
1
0
2
1
0
2
1
1
2
1
1
1
1
1
1
1
2
0
2
2
2
1
2
1
1
0
1
2
0
1
1
1
1
1
3
0
0
1
2
1
2
2
1
1
2
2
2
2
1
0
1
0
1
1
2
1
2
1
1
2
1
0
1
0
1
2
1
0
1
0
0
0
0
1
2
1
2
2
1
2
1
1
2
1
1
2
0
2
1
1
1
1
2
1
1
1
2
2
1
0
1
1
1
0
2
1
1
1
0
2
1
1
2
1
0
1
1
1
0
1
1
1
1
1
0
1
0
1
2
1
1
1
1
1
0
0
1
0
0
1
2
1
1
1
1
2
1
1
1
0
2
1
1
1
2
1
1
0
1
2
1
1
1
2
1
1
1
1
1
1
1
1
0
1
1
1
1
1
2
2
1
2
1
3
1
1
1
2
1
1
1
2
1
1
1
1
0
2
1
1
1
1
0
1
1
1
1
2
1
1
2
1
1
2
1
1
1
0
1
1
1
1
0
1
0
0
1
2
1
1
0
1
1
1
2
0
1
1
1
1
1
1
1
1
0
1
1
1
1
0
1
0
0
2
0
0
1
2
1
1
1
1
1
1
1
1
0
1
1
0
0
1
1
2
0
1
1
1
2
2
2
2
1
2
1
1
1
1
2
2
1
1
1
0
2
1
0
0
0
2
0
2
1
1
1
1
1
1
1
2
1
2
1
2
1
0
2
2
2
0
0
2
2
0
1
0
1
0
1
2
1
1
1
2
1
1
2
1
1
2
1
1
1
0
1
1
1
1
1
1
1
0
1
2
2
1
2
1
4
1
2
1
1
1
2
2
1
0
0
1
1
1
2
2
0
0
1
1
1
1
0
2
2
0
1
0
0
2
0
1
1
1
0
1
1
1
1
0
0
1
2
2
0
0
1
1
0
1
1
2
2
1
0
1
1
0
1
0
1
2
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
0
0
0
1
1
1
1
2
2
2
1
1
1
1
2
2
2
2
1
0
1
1
1
1
1
1
3
1
1
1
1
2
2
1
1
1
2
1
1
0
2
2
1
1
0
2
1
1
1
1
0
1
2
0
1
1
1
1
2
2
0
1
0
1
0
3
0
1
2
1
0
3
2
2
1
2
1
1
1
2
2
1
1
2
1
1
0
1
1
2
2
1
1
1
1
1
2
0
1
2
2
2
1
1
1
1
1
0
0
2
1
1
1
2
3
1
1
0
2
1
2
1
1
0
1
1
2
1
1
1
0
2
2
2
2
1
1
2
1
1
2
2
2
1
2
0
3
1
1
2
1
0
1
1
1
2
0
2
1
0
0
1
1
3
0
1
1
1
1
0
2
0
1
1
1
0
1
1
0
1
1
0
1
0
1
0
1
0
1
1
0
1
0
2
1
1
1
1
1
1
2
1
0
0
1
0
1
1
2
1
1
1
0
1
0
0
0
2
1
2
1
1
1
2
0
2
1
2
1
1
1
1
1
1
0
1
2
1
1
2
1
2
1
2
1
1
2
1
2
1
1
0
2
2
2
1
2
1
3
1
2
1
0
2
1
2
1
0
2
0
2
1
2
0
1
1
1
2
1
2
0
1
1
1
0
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
0
1
1
1
1
2
1
2
1
2
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
0
1
1
0
0
0
2
1
1
0
1
1
2
1
1
1
1
1
2
1
1
2
1
1
1
1
0
2
2
0
2
2
1
0
1
1
1
1
1
1
2
1
1
2
1
1
2
1
1
0
1
2
1
2
0
1
2
2
1
0
2
1
1
1
1
2
1
2
1
2
1
1
0
1
2
2
0
1
1
1
1
1
1
1
1
1
1
2
1
0
1
2
1
2
1
0
1
0
1
1
2
0
0
1
1
0
1
1
2
1
2
1
1
0
1
1
0
2
0
1
1
1
1
0
1
1
4
2
1
1
0
1
1
1
1
1
0
2
0
2
1
1
1
1
1
0
1
1
2
1
1
1
2
1
2
1
1
2
3
1
1
1
1
1
0
1
1
1
1
0
2
1
1
1
2
0
2
2
2
0
0
1
1
0
1
2
1
1
0
1
1
1
1
1
2
1
2
1
1
0
1
1
1
1
0
0
2
1
2
2
2
2
1
1
0
1
0
1
2
1
0
2
1
1
1
2
1
1
1
2
1
2
2
2
1
0
0
2
1
0
1
1
1
1
1
1
1
2
0
1
1
1
1
1
0
1
2
1
0
0
0
1
1
1
1
2
2
1
0
1
1
0
1
1
2
1
1
1
1
1
1
0
0
2
1
1
0
2
1
1
1
0
2
0
2
1
2
1
1
1
1
1
0
1
0
1
0
1
2
2
2
0
2
1
0
1
1
1
1
1
0
1
0
2
0
1
0
2
1
0
0
1
1
1
2
1
1
0
2
2
1
1
1
1
1
0
2
2
1
0
2
1
1
1
1
0
0
0
0
1
1
2
2
2
1
1
1
1
2
0
0
2
1
0
1
0
1
1
0
1
1
0
1
2
1
1
1
1
3
1
2
1
1
1
1
0
1
1
1
0
2
1
0
0
1
1
0
1
2
1
1
1
1
1
1
1
2
0
2
2
2
2
2
1
1
1
0
0
0
1
1
1
1
0
2
1
0
2
1
1
2
1
2
1
1
1
0
1
1
1
1
1
1
0
1
1
1
1
1
1
1
2
1
1
1
1
1
0
2
2
3
0
1
2
0
2
0
1
1
1
2
1
2
1
2
1
1
1
1
1
1
1
1
0
1
1
1
2
0
1
1
0
1
0
0
2
2
1
1
0
1
2
1
1
1
0
1
0
2
0
1
1
1
1
1
2
0
1
2
1
1
0
1
1
1
1
2
1
0
2
1
1
1
0
1
0
1
2
1
1
1
1
1
2
1
1
0
0
1
0
2
2
1
1
1
1
1
2
1
0
1
1
1
0
0
2
1
2
1
1
0
1
1
1
1
2
1
1
2
1
2
1
1
1
2
1
1
1
0
1
1
0
1
2
1
0
1
2
0
1
2
1
0
2
1
1
0
1
1
2
0
0
1
1
1
2
1
2
1
1
1
1
0
0
1
2
2
1
1
0
1
0
1
0
1
0
0
2
2
1
1
0
1
1
1
1
1
0
1
1
1
1
1
1
1
0
2
1
3
0
2
0
1
0
1
1
1
1
0
1
1
2
0
1
1
2
1
2
0
2
2
2
0
2
2
1
0
0
2
1
0
2
0
0
2
1
1
2
1
1
1
1
2
1
1
1
1
0
1
1
1
0
1
1
1
0
1
0
0
1
2
1
2
2
1
1
1
1
1
2
0
1
2
1
1
0
1
1
2
1
1
1
0
1
1
2
1
1
2
0
1
1
2
1
1
1
1
0
0
1
1
1
0
0
1
1
1
3
2
0
1
1
1
1
0
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
6
1
1
1
1
1
1
2
1
2
1
2
1
0
1
1
2
1
1
2
2
1
1
1
0
2
1
2
1
1
0
1
1
2
1
2
2
2
0
1
2
1
1
0
0
2
1
1
2
1
2
1
1
0
1
2
1
1
2
0
2
1
1
2
2
1
0
1
2
1
0
1
1
0
0
1
1
2
1
1
1
0
2
1
0
2
1
1
0
1
0
1
1
1
1
2
1
0
2
2
2
2
1
1
1
2
2
0
0
1
2
0
1
1
1
1
1
1
2
1
0
0
0
0
1
0
0
0
1
0
1
5
1
1
1
0
2
1
1
1
2
2
1
0
0
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
0
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
0
1
1
1
2
2
2
2
1
1
1
3
1
0
1
1
1
1
1
1
2
2
0
1
2
2
2
1
0
2
0
2
2
2
1
1
1
1
1
0
1
1
1
1
2
1
2
2
1
0
1
1
2
1
2
2
1
2
2
2
1
1
1
0
1
2
1
1
3
2
1
2
1
0
1
1
0
1
1
1
1
1
0
1
2
1
2
3
1
1
1
1
2
1
1
1
1
2
1
1
0
0
0
2
1
1
0
2
1
1
2
1
2
0
1
1
0
1
2
1
1
1
0
1
1
1
1
1
2
2
2
2
1
0
1
1
1
1
0
1
1
0
0
1
0
1
2
2
1
2
1
1
1
1
2
0
1
2
1
1
2
0
1
0
1
1
1
0
1
0
2
0
1
1
0
0
2
1
1
1
0
2
1
0
0
1
0
2
0
1
1
1
1
1
2
1
2
1
1
0
2
0
2
1
1
2
1
1
1
2
2
2
2
1
1
2
1
2
1
1
1
1
1
0
1
1
1
0
0
1
1
0
1
2
0
1
1
1
0
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
0
1
2
1
1
1
1
1
1
2
1
1
1
0
0
0
1
1
0
1
1
0
2
0
1
1
1
1
1
1
1
2
1
0
1
1
0
2
0
1
0
1
1
0
1
1
2
0
1
1
2
1
4
2
2
0
1
1
1
2
1
2
1
1
1
1
0
1
1
1
0
1
1
1
2
2
1
1
1
1
1
1
2
1
2
0
2
1
0
2
2
2
1
0
1
2
1
2
1
1
2
1
1
0
1
1
1
2
1
1
2
1
1
1
1
1
0
0
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
2
0
1
0
2
2
2
2
1
0
0
1
2
1
0
0
0
2
1
2
0
3
1
1
1
2
0
2
1
0
1
1
0
1
2
1
1
0
0
1
2
0
0
1
2
1
1
1
1
1
1
1
2
0
1
1
1
1
2
2
1
0
2
0
2
1
1
0
1
1
0
1
1
1
2
1
1
1
0
0
1
1
1
0
1
0
0
2
1
1
2
0
0
2
2
2
3
0
1
2
1
1
2
2
1
1
1
1
1
0
1
1
1
2
1
1
1
2
2
0
1
1
2
0
1
0
2
1
1
0
0
2
1
2
1
1
2
1
1
1
1
1
1
2
1
1
2
0
1
2
1
2
2
1
1
1
1
0
1
1
2
0
1
1
1
1
1
0
0
2
1
1
0
0
1
2
2
0
0
0
0
0
2
1
1
1
2
2
2
1
1
0
1
0
1
1
1
0
1
2
1
1
2
1
2
2
1
2
0
3
1
2
1
1
0
1
1
1
2
1
1
1
0
2
2
0
2
2
1
2
1
0
2
2
1
1
1
1
1
1
1
1
0
1
1
1
2
1
2
1
1
1
0
1
1
1
1
1
2
2
4
1
1
1
1
1
2
1
0
0
1
1
2
2
0
1
0
1
1
2
0
1
1
1
1
1
2
1
1
0
1
0
1
1
1
2
1
1
2
2
3
1
0
2
1
1
0
1
1
0
2
1
2
2
0
1
0
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
0
2
1
2
2
0
2
0
3
1
2
2
1
1
0
2
2
0
1
0
1
0
0
1
1
1
2
2
2
0
1
1
2
1
1
1
1
1
1
2
0
1
1
1
0
1
1
1
1
2
1
0
2
0
1
1
1
1
1
1
0
1
0
1
1
2
1
0
1
2
2
2
0
0
1
2
1
1
1
0
1
2
2
2
1
2
3
1
2
1
2
1
1
1
1
1
1
0
1
0
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
2
1
1
2
2
1
1
2
2
0
2
0
2
0
4
2
1
1
2
1
1
0
0
0
1
2
1
1
0
0
1
1
0
2
1
1
1
2
2
0
1
1
0
1
1
1
1
0
0
4
1
1
0
2
0
2
1
1
1
1
0
1
0
1
1
0
0
1
1
1
2
2
0
2
1
2
2
1
1
2
1
1
2
0
1
1
1
1
1
0
0
1
2
3
0
0
1
0
1
1
1
1
1
0
1
2
1
0
1
1
1
0
1
2
2
0
1
1
1
0
1
2
0
1
1
1
1
2
0
1
2
1
1
2
1
1
1
1
1
1
0
1
0
2
1
1
1
1
1
1
1
1
1
0
0
1
0
0
2
2
2
0
1
1
1
1
0
1
1
2
2
1
2
1
1
1
1
1
0
0
5
1
0
1
1
1
2
0
1
2
0
1
2
2
1
2
0
1
1
1
1
1
0
1
1
1
2
1
0
2
1
1
1
1
2
2
1
1
1
0
1
1
0
0
1
1
1
1
1
2
1
1
1
2
2
1
2
2
1
1
1
0
1
1
0
0
1
1
1
2
1
0
1
1
0
1
1
1
1
1
1
1
0
2
1
1
1
1
1
2
1
1
2
1
1
2
1
0
1
1
1
1
2
2
0
0
1
2
0
1
0
1
2
1
2
2
0
0
1
0
2
0
2
1
0
2
1
0
2
1
1
2
2
1
2
0
1
1
1
0
1
1
1
0
2
1
1
1
1
1
1
2
2
2
0
2
2
3
1
2
0
2
1
2
1
1
1
1
1
2
2
2
1
1
1
1
0
1
0
1
0
1
1
1
1
1
1
1
1
1
0
2
2
1
2
1
1
2
2
1
0
1
1
1
0
1
1
0
1
0
2
1
1
1
1
3
2
2
1
2
2
1
1
0
0
1
1
0
1
1
0
2
1
1
3
1
1
3
2
1
1
1
0
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
0
0
1
1
1
1
0
0
0
1
2
1
1
1
2
1
1
1
1
1
1
1
0
3
1
0
1
1
1
2
0
1
2
1
1
1
2
2
1
1
1
0
1
2
1
2
0
1
1
1
0
1
1
2
1
2
1
1
1
0
1
1
0
2
0
0
0
1
2
0
4
0
1
1
2
1
1
0
1
1
0
2
2
1
2
1
0
1
1
1
4
2
1
1
2
0
2
1
2
1
1
2
1
1
1
2
1
1
2
1
0
2
2
3
1
1
1
0
1
1
1
0
1
1
2
1
2
0
1
1
1
1
2
1
1
1
0
1
2
1
0
2
2
2
0
1
1
1
3
2
2
1
1
1
1
1
2
1
1
2
1
0
1
1
1
0
0
1
2
1
1
1
1
2
2
0
1
2
2
0
0
1
0
0
1
2
2
1
1
0
2
0
2
1
1
1
1
1
1
2
1
2
1
2
1
0
0
1
1
0
1
1
0
1
1
1
1
0
1
0
0
2
2
1
2
2
1
1
0
1
2
2
0
1
2
0
2
1
1
0
1
2
1
1
1
1
1
1
1
1
0
1
1
1
2
0
1
3
1
1
2
1
1
1
1
1
1
0
1
2
0
1
1
1
1
1
1
0
1
1
2
1
0
1
0
0
1
0
2
0
1
2
0
0
1
2
1
0
0
1
2
2
1
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
0
2
1
2
0
1
0
2
1
0
1
2
1
1
1
1
1
0
2
1
1
1
1
0
1
2
0
2
0
1
2
1
1
1
2
2
2
1
1
1
1
0
0
0
1
1
1
0
1
1
1
3
1
1
2
1
1
1
1
1
2
2
0
2
1
1
1
0
1
0
1
1
1
0
0
1
2
1
1
1
1
0
0
2
2
1
1
2
1
2
2
1
1
2
1
1
1
0
1
1
2
1
1
2
0
0
1
1
2
0
1
0
1
0
1
1
2
2
1
2
2
1
1
2
0
0
1
2
1
1
0
2
2
0
1
2
0
1
1
2
1
0
0
0
1
1
0
1
1
1
2
2
1
1
1
2
1
1
1
1
1
1
0
2
1
0
1
1
1
0
2
0
2
1
0
1
1
1
1
2
1
2
1
1
1
1
0
1
1
1
1
2
2
1
1
0
1
1
0
2
1
2
0
0
1
1
2
2
1
2
2
1
0
1
1
1
1
0
1
1
2
2
0
0
1
1
2
2
2
2
1
1
1
2
0
2
1
1
1
1
2
2
1
0
2
1
1
1
1
2
1
2
1
1
1
1
1
2
2
1
1
1
1
0
1
0
1
1
1
2
0
0
1
2
2
3
2
0
1
0
2
1
2
2
1
0
1
0
2
1
0
1
0
1
1
1
2
1
1
1
1
1
0
0
1
2
0
0
1
1
0
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
0
1
1
0
2
0
1
2
1
1
1
2
2
1
1
1
1
1
1
1
0
1
2
1
2
1
2
2
1
1
1
0
2
2
1
1
1
1
1
0
2
1
1
1
1
2
2
1
1
0
1
1
1
1
1
1
1
0
1
1
1
1
2
0
0
1
0
2
2
2
1
2
1
1
1
1
1
1
2
0
2
1
1
1
1
1
0
1
1
1
2
0
2
1
1
1
1
0
1
1
2
1
2
1
1
1
2
0
1
2
0
2
1
1
1
1
1
1
1
2
0
1
2
1
1
1
0
1
0
2
1
2
0
2
1
0
2
1
1
1
1
2
1
0
0
2
1
1
1
2
1
0
2
2
2
1
1
1
2
1
1
1
1
0
0
0
0
1
1
1
2
2
0
1
1
1
1
0
2
1
2
1
1
1
2
0
1
0
1
1
1
1
1
1
1
2
1
0
1
0
0
1
0
2
1
2
0
0
2
1
3
1
2
1
0
1
1
0
1
1
1
1
2
1
1
2
0
1
1
0
1
1
1
0
1
1
1
1
3
1
1
1
2
1
2
1
2
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
0
1
1
2
2
2
3
2
1
1
0
2
1
1
1
0
1
0
1
0
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
0
1
1
2
1
0
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
2
1
1
0
1
2
2
1
0
1
1
1
0
0
0
1
0
2
1
2
0
0
0
1
1
2
1
4
0
0
1
1
1
0
1
1
2
0
0
1
2
2
2
1
2
0
1
1
0
1
2
2
1
1
1
2
1
1
1
1
2
1
0
1
1
1
2
0
2
1
1
0
0
1
1
1
2
2
1
1
0
1
0
1
0
1
1
1
1
1
2
1
1
2
1
1
0
2
0
1
2
2
1
2
2
2
1
1
1
1
1
0
2
0
0
1
0
1
1
1
1
1
1
0
0
1
1
1
2
0
2
0
1
1
1
2
0
1
1
1
2
0
3
2
2
1
0
2
1
1
1
2
0
2
1
1
1
1
1
1
1
2
1
1
2
2
0
1
1
1
1
0
1
1
1
1
4
1
0
1
1
1
1
1
1
1
2
1
1
1
2
1
2
2
1
1
1
2
0
1
1
2
1
3
2
2
1
1
2
3
2
0
1
1
2
1
1
2
1
2
1
2
1
2
1
1
1
1
1
1
1
0
2
1
0
1
0
1
0
1
0
0
1
1
1
1
1
1
0
1
1
2
1
0
1
0
0
2
0
1
1
2
2
2
2
1
1
1
1
0
1
1
1
0
0
0
1
2
1
1
2
1
1
1
1
1
1
1
0
1
1
1
0
1
1
0
1
1
2
0
1
2
2
1
1
1
1
1
0
2
0
2
2
1
2
1
2
1
2
2
1
2
1
1
1
1
2
0
1
0
1
2
1
1
1
1
1
1
1
1
1
0
1
1
1
0
1
1
1
1
1
2
1
0
2
0
2
1
1
1
1
1
1
1
1
1
1
0
1
1
2
1
1
1
1
2
1
1
1
0
2
1
0
1
2
1
1
1
2
1
0
1
1
0
0
1
1
2
1
2
1
2
1
1
0
1
2
1
1
1
1
1
1
1
2
0
2
1
0
1
1
0
1
1
2
1
2
1
0
1
1
2
1
3
1
0
2
1
1
1
1
1
3
2
1
1
0
1
2
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
2
1
0
1
1
2
1
1
2
1
0
1
1
1
2
0
1
0
0
1
1
2
0
2
2
0
1
0
1
1
1
1
1
1
2
1
1
2
2
0
2
1
1
0
1
1
1
1
1
0
1
1
1
1
1
1
0
0
0
1
0
2
2
0
1
1
1
1
1
1
1
1
1
1
1
1
2
1
3
1
2
1
1
1
2
1
2
1
2
0
1
0
0
1
2
0
1
1
1
1
1
1
1
1
0
1
0
1
1
2
1
1
1
0
1
2
1
1
1
1
1
1
2
2
2
2
0
1
1
2
2
1
1
1
1
1
2
1
2
2
1
0
1
1
0
2
2
1
1
0
1
0
1
2
1
1
0
1
1
1
1
2
2
1
2
1
0
1
2
1
1
1
1
1
2
2
2
2
1
1
0
1
0
1
2
0
1
1
0
1
1
1
1
1
1
1
1
1
1
1
0
1
1
0
2
2
1
1
0
0
0
1
1
2
1
1
0
1
1
1
2
0
0
1
1
1
1
1
2
1
2
1
1
3
0
1
2
1
1
2
2
1
2
2
2
2
1
1
2
2
1
1
1
2
0
0
0
0
2
0
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
2
2
1
0
1
2
2
1
2
1
0
2
2
2
0
1
0
0
2
0
2
0
1
2
1
1
1
2
1
2
1
1
1
2
2
2
1
1
1
1
0
1
0
1
2
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
2
1
1
2
1
1
2
1
0
2
1
2
1
0
0
1
1
1
1
0
2
1
1
1
1
2
1
2
0
1
0
2
1
1
2
1
1
1
0
2
0
1
1
1
1
0
1
1
2
2
1
2
0
1
2
0
1
0
1
1
2
1
0
1
0
1
3
1
2
1
2
2
1
2
1
0
0
1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
1
0
2
2
1
1
1
1
1
1
0
1
2
1
1
2
2
1
1
1
1
0
1
1
1
2
2
2
2
1
1
2
1
1
1
1
0
1
1
1
1
0
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
2
1
2
2
0
1
1
0
1
1
1
1
0
2
1
2
1
1
1
1
1
0
1
1
2
1
1
1
1
0
2
1
0
2
1
1
0
1
1
1
2
1
0
2
2
1
1
0
2
0
3
0
1
2
1
1
2
1
2
2
2
1
0
3
1
1
0
0
1
2
1
1
1
1
2
2
2
1
0
0
1
1
1
2
0
1
1
1
2
1
0
0
2
1
1
1
2
1
2
1
2
0
1
1
0
0
1
1
1
1
1
1
2
1
1
1
0
0
1
1
1
1
0
1
1
2
1
0
2
1
2
2
1
1
1
1
1
1
0
0
2
0
2
1
2
5
1
2
1
2
2
1
1
1
1
1
1
2
1
0
2
1
0
1
2
1
1
1
1
9
1
2
1
1
1
1
2
2
1
1
1
0
2
0
0
0
2
1
1
0
1
1
0
0
2
0
1
1
2
1
1
1
2
1
0
0
0
2
0
1
1
1
1
1
1
0
2
2
1
2
1
0
1
0
1
1
1
1
1
1
2
0
1
0
1
2
3
1
1
1
1
1
0
2
0
1
1
0
1
2
0
1
1
1
2
1
1
1
1
2
0
1
1
1
0
2
3
1
2
1
1
2
1
2
1
0
2
1
1
0
1
1
1
1
0
2
1
1
1
1
1
2
0
1
1
2
1
1
0
1
1
2
0
2
2
1
1
1
2
1
2
1
0
0
1
1
2
2
1
0
1
1
1
1
0
2
1
1
1
1
1
2
1
1
1
2
1
1
0
2
0
1
0
1
1
2
0
1
1
1
0
1
1
0
1
0
1
0
1
1
1
0
0
1
1
1
1
1
1
0
0
1
2
1
2
1
0
0
1
0
0
0
1
1
2
1
1
1
1
0
1
2
1
1
2
1
1
1
1
2
2
1
1
1
0
0
1
1
2
0
1
0
1
1
0
3
1
1
1
2
1
1
1
0
1
1
1
1
1
0
1
1
0
0
0
1
1
2
1
1
1
1
2
1
1
1
2
1
0
1
1
1
2
1
1
2
0
1
0
0
1
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
0
0
1
1
1
1
2
2
1
1
1
1
1
3
1
1
1
1
0
3
1
1
1
2
1
1
1
1
1
1
2
1
1
2
1
2
1
2
2
1
1
0
0
1
2
1
1
1
1
2
2
0
0
1
1
2
1
1
0
2
2
1
1
2
1
1
0
1
1
1
0
0
2
0
1
0
2
2
2
1
1
1
1
1
0
2
1
1
1
1
1
0
1
2
2
1
2
0
1
0
1
1
1
1
1
1
1
0
0
1
2
1
0
1
2
0
0
0
1
2
2
2
1
2
2
1
1
1
0
1
1
1
2
2
1
1
1
1
1
1
2
0
1
1
1
2
2
0
1
2
1
2
2
0
1
0
2
2
1
1
1
2
2
1
1
0
2
1
1
0
1
1
1
1
1
1
1
1
1
1
0
1
0
1
0
1
1
1
2
1
0
0
0
1
1
2
0
1
1
2
1
1
1
1
2
2
1
1
1
2
2
2
1
0
0
2
1
0
1
2
1
1
1
2
2
1
0
1
0
2
2
1
2
1
1
1
1
2
0
1
1
2
1
3
1
1
2
1
1
1
2
2
1
1
2
2
0
1
2
1
1
2
1
2
1
1
2
2
1
1
1
2
0
2
2
1
1
1
0
1
0
1
2
0
1
2
1
2
0
1
1
1
2
1
0
1
2
1
0
0
1
2
1
0
0
0
2
1
0
1
1
1
2
1
1
0
1
1
2
1
2
2
1
1
1
2
1
1
1
1
1
1
0
0
1
1
0
0
1
1
1
2
0
1
1
1
1
1
1
2
1
1
1
1
0
0
1
2
0
1
1
0
1
0
1
1
2
0
0
2
2
1
1
1
0
0
1
2
1
1
1
1
1
1
1
2
2
1
1
1
2
1
1
0
1
2
1
1
1
2
1
1
2
2
1
2
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
0
2
1
1
1
1
1
0
1
1
1
0
2
1
1
0
1
1
1
1
1
1
2
0
0
1
1
0
2
2
1
2
1
1
1
1
0
1
1
1
1
2
1
1
2
1
2
2
1
1
1
1
1
1
1
3
1
2
1
0
1
2
1
1
2
2
1
1
2
1
1
3
0
0
1
1
1
1
1
1
1
1
2
1
2
1
0
1
1
1
1
1
0
0
1
2
1
1
1
2
1
1
1
2
0
2
2
1
2
2
2
2
1
2
2
2
2
1
2
2
2
0
2
1
1
1
1
1
4
2
1
1
0
1
1
1
2
0
1
0
0
2
1
1
1
2
1
0
1
2
1
1
0
1
1
0
1
2
1
0
0
1
2
1
1
1
2
0
1
1
1
1
1
1
1
2
1
1
1
2
0
1
1
0
0
1
1
0
2
1
0
2
1
1
2
2
1
1
1
2
0
0
2
1
0
0
1
0
1
1
2
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
0
1
2
2
2
1
1
1
1
1
1
1
1
1
2
2
2
2
1
1
1
1
1
2
1
2
1
1
0
1
2
0
1
1
1
1
1
0
1
1
2
1
0
2
1
2
1
2
1
1
2
2
1
1
1
1
0
2
1
1
1
1
0
2
0
1
0
1
0
0
1
1
1
2
0
1
1
1
1
0
0
0
1
2
1
1
2
0
2
0
0
2
0
1
1
2
1
2
0
2
1
0
1
1
1
1
0
1
2
1
1
3
2
0
2
0
1
1
1
1
2
2
1
1
1
0
1
0
0
1
2
1
0
1
1
1
0
1
1
0
2
2
1
1
1
1
1
2
2
1
2
0
1
1
2
0
0
1
2
1
0
1
2
0
2
1
2
2
1
2
1
1
1
0
1
2
1
1
1
1
1
1
0
1
1
1
1
0
2
1
2
1
0
0
0
0
1
2
1
0
1
1
1
1
0
1
2
1
1
1
1
2
0
1
0
1
0
1
1
2
1
1
1
1
0
1
1
2
1
1
1
1
2
0
1
0
2
0
2
1
1
1
1
1
1
1
1
1
1
1
0
0
0
1
1
0
1
1
2
1
2
0
1
2
2
2
1
1
1
1
2
1
1
1
1
2
2
1
1
1
1
2
1
2
0
1
1
2
1
1
1
1
1
1
2
2
0
0
1
1
2
1
1
2
1
0
1
1
2
1
1
0
1
1
3
1
2
1
0
2
0
2
1
1
1
1
1
2
2
1
0
1
1
1
1
2
2
1
1
2
2
1
0
1
1
1
1
2
2
2
1
0
1
2
1
1
0
0
0
2
1
1
1
1
1
2
2
0
1
2
1
2
1
1
2
1
2
1
2
1
1
0
1
2
1
1
2
0
2
1
1
1
1
1
1
2
1
0
1
1
0
2
0
1
1
1
1
2
1
2
2
0
1
2
1
3
1
1
1
1
2
0
0
2
1
0
1
2
1
0
0
1
2
1
1
1
0
2
1
1
0
2
3
1
2
1
1
2
1
2
1
2
1
2
1
1
0
1
0
1
2
2
1
1
1
2
1
0
1
1
2
0
0
2
1
2
1
1
2
1
2
1
1
0
1
1
2
1
1
4
1
0
1
1
1
2
2
2
1
1
0
0
0
2
1
1
1
0
1
1
2
1
2
2
1
1
2
1
1
1
0
1
1
1
1
0
0
1
2
2
1
1
0
2
1
1
1
0
1
0
1
1
1
1
1
1
1
2
0
1
2
1
2
2
1
0
0
1
0
1
2
2
1
2
1
1
1
1
1
2
2
1
1
2
1
1
0
0
1
1
1
2
0
2
1
2
2
1
1
1
2
1
1
0
2
1
1
1
0
2
1
0
2
1
2
0
1
0
1
1
2
1
2
1
1
0
0
2
2
2
1
1
2
1
2
0
1
2
1
2
2
1
1
0
1
1
1
1
3
1
1
0
1
1
0
2
0
1
1
1
1
0
2
1
1
1
2
1
1
1
2
2
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
2
1
1
1
1
1
1
1
1
1
0
1
1
1
0
2
1
0
3
1
1
1
1
0
0
1
1
2
1
1
0
0
2
2
1
1
1
1
1
1
0
1
1
1
1
1
2
1
1
1
1
1
2
2
2
0
0
2
1
2
1
0
1
2
1
2
1
2
0
1
1
1
0
2
1
1
1
1
1
2
2
1
2
1
1
2
1
0
0
1
1
1
1
0
2
1
2
1
2
1
0
1
1
1
1
0
1
1
1
0
0
1
2
2
1
1
0
1
1
1
0
0
1
1
2
2
1
1
0
1
1
1
2
1
1
1
1
4
1
1
1
1
1
1
2
1
1
1
2
2
2
1
1
1
1
1
1
1
0
1
1
1
1
0
0
0
0
1
1
1
1
2
1
1
1
1
1
1
2
2
0
0
1
1
1
0
2
1
1
1
1
0
1
2
2
1
1
0
1
0
0
1
1
2
1
1
0
2
0
1
0
2
0
0
2
1
1
0
1
1
1
2
0
1
1
1
0
2
1
1
1
1
1
1
0
2
0
2
1
1
1
1
2
0
2
1
1
0
1
0
0
1
1
1
1
1
2
2
0
1
0
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
0
1
2
2
3
1
1
2
2
2
0
1
1
1
1
0
2
0
1
1
0
2
1
1
0
1
1
1
1
1
1
2
2
1
2
1
0
2
1
0
0
2
0
0
2
1
0
2
1
1
1
1
1
1
1
2
1
1
1
1
1
0
1
1
1
1
0
0
2
0
1
1
0
1
1
2
1
2
0
2
1
3
1
5
2
1
2
1
1
2
1
1
0
2
1
1
1
1
0
1
0
1
1
0
1
1
1
1
2
2
0
1
1
0
1
1
1
2
2
1
1
0
1
1
1
0
1
0
1
0
1
1
1
1
2
1
0
1
1
2
1
1
0
1
0
2
1
2
2
1
1
2
1
1
1
2
1
1
1
1
2
1
1
2
1
0
1
1
1
1
0
1
2
1
1
2
1
1
0
1
1
2
0
1
3
1
0
1
0
1
2
1
1
2
1
0
2
1
0
2
1
0
1
0
1
3
1
2
1
0
2
1
2
0
1
0
0
0
1
0
1
2
2
1
2
2
1
2
0
0
2
0
1
2
2
1
1
1
0
1
2
1
1
2
0
0
0
2
1
1
0
2
2
1
1
1
2
1
1
2
2
1
1
2
2
3
2
1
1
2
1
1
1
0
1
1
1
0
1
1
1
1
1
0
1
2
1
1
1
1
0
0
0
1
1
1
1
1
1
1
1
1
0
2
1
0
1
1
1
1
1
2
2
1
2
1
1
1
1
2
1
2
1
1
0
1
4
1
2
1
1
2
1
1
2
2
2
1
1
1
1
1
1
1
1
1
1
0
1
2
1
1
1
2
1
2
0
0
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
0
1
2
1
1
1
2
0
1
1
1
2
1
1
2
0
1
1
1
1
2
2
1
1
0
1
0
1
0
1
1
1
1
1
1
2
1
2
1
1
1
0
1
1
1
2
1
0
2
2
1
0
1
2
1
2
1
1
1
2
0
2
2
2
1
1
0
1
1
2
1
2
1
2
1
2
0
1
1
0
2
2
0
1
1
2
1
2
0
0
0
2
1
1
0
1
1
1
1
1
1
1
1
1
1
2
0
1
2
1
1
1
2
0
0
0
2
1
2
0
1
0
1
0
2
1
1
3
2
1
1
0
1
0
1
0
0
1
1
0
1
1
0
2
2
0
0
1
0
2
1
1
2
1
1
0
1
1
0
0
1
0
1
0
0
1
0
1
1
5
1
0
1
0
2
2
1
2
2
2
1
2
1
1
0
1
1
2
1
2
0
0
0
1
2
1
2
0
1
1
1
1
1
1
0
1
0
1
0
0
1
1
1
3
1
1
1
1
1
0
1
1
0
2
1
0
2
1
1
2
3
2
1
1
2
1
1
1
2
1
1
1
2
0
1
2
1
1
2
2
2
2
1
0
1
0
0
2
2
0
1
1
1
1
1
0
1
0
1
0
2
1
1
1
1
1
0
1
1
2
1
2
1
2
1
1
2
0
1
1
0
2
0
1
2
2
1
1
1
1
1
1
1
0
2
2
2
1
1
2
0
1
1
1
0
1
0
0
1
1
1
1
1
1
0
1
1
1
3
2
1
1
0
1
1
1
1
1
2
1
0
0
1
1
0
1
2
2
1
0
1
1
1
3
0
2
2
0
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
0
1
1
2
1
1
0
1
0
1
1
1
0
1
0
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
2
2
1
2
1
1
0
0
2
1
1
1
0
1
1
1
2
1
1
2
1
2
1
0
2
0
1
3
2
2
1
2
2
2
1
0
1
2
1
1
1
1
1
2
0
2
0
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
0
2
1
1
1
1
1
0
1
1
1
2
2
1
2
2
1
1
2
2
1
1
1
1
1
1
0
0
1
1
1
1
0
1
1
1
2
1
1
1
1
1
1
0
1
1
2
1
2
1
0
0
1
0
2
1
2
1
2
1
1
3
1
1
2
0
1
1
1
1
2
1
1
0
0
2
1
0
1
0
1
2
1
2
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
0
1
0
0
1
1
1
1
1
2
2
1
1
1
1
1
1
0
1
1
1
0
1
0
2
2
1
1
0
1
1
0
0
2
2
0
1
1
1
1
0
0
2
2
0
1
1
2
2
1
0
2
1
1
1
0
1
0
1
1
0
1
1
1
0
1
1
2
1
1
1
2
2
1
1
1
1
1
1
2
3
1
2
2
1
2
1
2
2
2
1
1
0
1
1
2
1
0
1
3
2
1
0
2
1
1
1
2
0
1
0
1
1
3
2
1
1
0
1
1
1
1
1
0
2
0
1
1
2
2
1
1
1
0
0
1
1
1
1
2
1
2
1
2
0
2
1
1
1
2
0
1
1
1
1
2
1
1
1
2
1
1
1
1
2
2
1
1
1
2
1
0
1
2
0
2
2
1
0
0
1
2
1
0
0
2
1
1
1
1
2
1
1
2
1
1
2
0
0
2
1
1
1
0
0
2
1
1
1
2
1
1
1
0
1
2
1
1
1
2
0
2
1
2
2
0
2
2
0
1
0
1
1
2
1
1
0
1
2
1
1
1
1
1
2
2
0
2
2
0
0
1
1
1
0
1
1
1
0
1
2
1
1
1
1
2
1
1
2
0
1
1
1
1
1
0
1
2
1
0
1
1
1
2
1
0
1
1
2
1
0
2
1
1
1
2
2
1
1
1
1
1
1
1
1
1
0
1
1
2
2
1
2
1
0
2
2
1
2
1
1
0
1
1
2
1
0
1
1
1
0
1
1
0
1
1
0
1
0
0
1
1
1
1
1
0
2
0
1
1
0
1
0
2
2
0
1
1
1
2
1
1
0
0
0
1
1
1
1
3
2
1
2
1
0
0
1
0
2
2
1
1
2
0
0
2
0
1
1
1
2
1
0
2
1
1
1
2
1
2
1
1
1
2
1
1
0
1
2
1
0
1
2
2
1
1
1
1
2
3
0
1
1
2
1
2
0
1
2
0
0
1
1
0
1
1
2
1
1
1
1
2
0
2
1
2
1
0
1
2
1
2
0
2
0
0
0
1
1
2
1
0
1
2
1
0
1
1
1
1
1
0
1
0
2
1
0
0
2
1
1
1
1
1
1
1
0
1
2
0
1
2
1
1
1
2
1
1
0
0
2
1
1
1
1
1
1
1
1
2
1
0
1
1
1
1
0
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
2
2
0
1
2
1
2
1
0
2
0
1
1
0
0
1
1
0
1
0
2
1
1
1
0
2
1
1
1
2
1
1
1
1
1
1
2
1
1
2
1
1
1
2
1
1
2
1
1
1
1
2
1
0
2
1
1
1
1
1
2
1
2
2
1
1
0
1
0
0
2
1
1
0
1
1
2
1
1
0
0
1
1
1
1
0
0
1
1
2
1
0
2
0
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
0
1
1
1
0
2
2
1
1
1
2
1
1
2
0
0
1
0
1
0
1
0
0
1
2
1
1
0
1
0
1
1
2
2
1
1
0
2
0
1
1
2
1
2
1
1
2
1
2
1
1
1
1
0
1
2
1
2
1
2
2
2
0
2
1
1
1
1
2
1
1
2
2
0
0
1
2
2
1
1
1
1
2
1
1
1
1
1
1
1
0
1
0
2
2
1
0
1
1
2
1
0
0
1
1
1
1
2
1
2
1
2
0
0
2
0
1
0
1
1
2
0
2
1
1
1
1
1
0
1
1
0
1
1
1
1
2
2
1
0
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
0
3
1
1
0
1
1
2
1
1
2
0
1
2
2
1
1
0
2
1
1
2
1
1
0
1
0
1
2
1
0
1
2
2
0
0
1
0
2
1
1
1
1
1
1
0
1
1
0
1
0
1
1
1
2
2
1
0
1
2
0
1
1
1
1
1
0
1
2
0
0
0
1
1
2
1
0
1
1
1
0
0
1
1
0
1
1
1
0
1
0
1
1
1
1
1
2
2
1
0
2
1
1
1
1
1
1
1
2
1
2
1
2
1
1
0
2
1
1
1
2
2
1
0
1
1
1
0
1
2
0
1
0
1
1
1
0
1
0
1
0
2
1
1
0
1
1
0
1
1
1
2
0
1
0
1
1
0
2
1
1
1
1
0
0
0
1
1
2
1
1
1
1
0
1
1
1
1
1
1
1
2
0
1
1
1
0
1
1
2
0
1
0
0
0
1
0
1
1
2
0
2
1
1
1
2
2
2
1
1
2
0
1
2
2
1
2
1
0
1
1
1
2
1
2
1
1
1
1
2
1
1
2
0
2
1
0
0
0
1
1
1
1
1
0
2
1
1
1
0
1
1
1
1
1
1
0
1
0
1
1
1
1
1
3
1
1
1
1
2
1
2
2
0
1
1
0
1
1
0
2
1
1
1
1
2
2
1
1
1
0
2
1
0
1
1
0
1
1
2
2
1
2
0
1
1
1
1
1
1
2
1
1
2
2
0
0
2
1
1
1
1
2
2
0
1
2
1
1
0
5
1
1
1
1
0
0
1
0
1
1
1
2
2
1
0
2
2
1
2
1
1
1
1
0
1
1
1
1
2
1
1
1
2
0
0
1
1
1
1
0
0
1
1
1
2
2
4
1
0
0
1
1
1
1
2
0
1
1
1
1
3
2
1
0
2
2
0
1
0
2
0
0
1
0
1
1
1
2
1
1
1
2
0
2
1
0
2
0
0
1
1
2
1
0
1
1
2
0
1
1
1
1
1
1
1
2
1
1
0
1
1
1
1
0
1
1
1
1
1
0
1
1
2
2
1
1
0
1
0
2
0
0
1
2
1
0
2
1
1
2
0
1
0
1
1
1
1
2
1
1
1
0
1
1
0
1
3
1
1
0
1
1
1
1
1
0
0
0
2
1
1
1
1
2
1
0
0
1
2
1
1
1
1
0
2
1
1
2
2
2
0
2
2
0
1
1
1
1
1
2
0
2
1
1
1
0
0
1
1
1
0
2
1
1
1
0
0
2
2
1
0
0
2
0
0
1
1
0
8
1
1
1
1
1
1
1
2
1
1
1
0
2
1
1
0
1
0
2
1
2
1
1
1
1
1
0
1
1
1
1
1
2
2
0
2
0
2
2
1
1
1
1
2
1
0
0
2
2
1
1
2
1
1
2
1
1
0
1
0
1
2
0
1
0
1
1
0
2
0
1
1
0
2
2
2
1
1
2
1
1
0
0
1
1
0
3
1
1
2
1
1
1
0
1
2
2
1
1
1
1
2
0
1
1
1
0
0
2
1
1
1
1
1
1
1
2
1
0
1
0
1
1
1
1
1
2
1
0
1
1
1
1
0
1
1
0
1
1
0
2
1
1
1
1
1
2
2
1
0
0
1
2
0
0
2
1
0
1
1
3
1
0
1
0
0
1
1
2
1
1
1
2
2
2
2
1
0
0
0
1
1
1
1
1
2
0
1
2
0
0
0
0
1
0
2
0
1
1
1
1
1
2
1
0
2
1
1
2
0
1
2
1
1
1
0
2
1
0
0
2
0
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
3
1
0
1
1
1
1
1
0
0
3
2
1
1
1
1
2
1
2
1
1
2
2
1
2
1
0
1
0
1
1
1
1
0
2
2
1
0
1
1
1
0
1
1
1
0
2
2
1
0
1
1
2
1
0
0
2
1
5
1
1
2
1
2
0
2
0
1
1
2
2
1
1
1
0
1
0
1
0
1
2
1
1
0
1
0
2
0
1
1
1
1
1
0
1
1
1
0
1
1
2
2
2
0
1
0
2
2
2
1
1
1
1
0
2
1
1
1
1
1
1
1
0
1
0
0
2
0
1
0
1
0
1
2
2
1
0
1
1
2
1
1
1
1
0
2
2
1
1
1
2
1
0
1
1
1
1
1
1
0
1
5
2
1
1
1
1
1
2
1
1
1
2
0
0
2
2
1
1
1
1
2
1
1
1
1
0
2
0
1
1
1
1
2
2
1
1
0
1
1
2
1
0
1
1
1
1
2
1
2
1
0
1
2
1
2
1
1
0
1
0
0
2
1
1
1
0
0
1
1
0
1
1
1
1
2
2
0
0
1
1
1
1
1
2
2
1
0
1
1
2
0
0
1
0
0
1
1
0
2
1
1
1
0
1
1
2
0
0
1
1
2
1
1
0
2
0
1
0
0
1
0
1
0
1
1
2
1
0
1
2
0
1
1
1
1
2
1
1
1
2
1
4
1
1
0
1
1
1
2
2
1
1
2
2
1
2
0
2
1
0
0
1
1
1
2
2
0
2
1
1
1
0
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
0
2
1
1
1
1
2
0
1
1
0
1
1
1
1
1
1
1
2
0
1
3
2
1
0
1
1
1
1
1
1
1
1
1
1
1
0
1
2
2
1
1
2
1
1
2
1
0
2
1
2
1
2
2
1
1
1
1
1
1
1
1
2
1
2
0
0
2
1
1
1
1
1
0
1
1
2
2
1
2
2
1
0
1
2
1
1
1
3
0
2
2
1
1
0
1
1
1
1
1
1
1
1
1
2
2
0
1
2
1
1
1
1
1
2
0
1
1
1
0
1
0
1
0
1
2
0
1
1
2
1
1
0
1
2
1
1
0
2
2
1
1
2
2
1
1
2
1
1
2
0
1
1
1
0
0
1
0
1
2
1
1
2
1
2
2
1
2
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
1
0
1
0
1
1
1
1
0
1
1
1
0
1
1
0
0
4
1
1
1
1
2
2
0
1
1
0
0
1
1
0
1
1
0
2
0
1
1
2
2
1
2
1
1
0
1
1
0
2
1
1
1
1
1
2
1
1
1
0
2
2
1
1
1
1
0
1
1
0
2
2
1
3
1
1
2
1
0
2
2
1
1
1
1
2
0
0
2
1
1
1
1
1
1
2
3
1
1
0
1
1
1
1
1
0
0
1
1
1
1
1
1
1
2
2
2
1
1
2
1
1
1
1
0
2
1
1
0
1
1
1
1
1
1
2
1
1
1
1
1
1
1
0
1
2
1
1
1
1
0
1
1
1
1
2
2
0
2
2
2
1
1
1
0
1
0
2
1
1
1
1
1
2
1
1
1
1
0
1
2
1
1
0
2
0
1
1
1
1
2
0
2
1
1
0
1
2
1
1
2
1
2
1
2
2
1
2
1
1
1
1
0
1
1
2
1
1
1
1
0
1
0
0
1
1
0
0
2
1
1
0
2
1
1
1
1
2
2
1
1
1
1
1
1
1
1
2
1
2
1
1
2
1
2
0
1
0
1
0
1
1
1
0
1
2
1
2
1
1
1
0
1
1
0
1
2
1
2
1
0
1
0
1
1
0
0
0
2
1
0
1
1
1
1
1
1
1
2
1
1
1
1
2
1
2
0
1
2
1
1
1
2
2
1
0
1
0
0
1
1
1
0
2
1
1
1
1
2
2
1
2
2
1
1
1
1
0
2
1
1
1
1
0
2
0
2
1
0
1
1
1
2
0
1
1
1
1
0
1
1
3
0
2
0
1
0
1
1
0
2
1
1
0
2
2
1
1
1
1
1
1
2
1
2
1
2
0
2
1
1
1
1
2
1
0
1
1
1
0
2
1
1
0
0
1
2
1
1
2
1
0
1
1
1
1
1
2
1
1
2
1
2
0
1
1
0
1
1
1
1
1
1
1
1
0
0
1
1
0
1
2
0
1
0
2
2
2
0
1
1
1
2
2
2
3
1
0
1
2
0
2
1
0
1
0
2
0
2
1
0
1
1
0
2
2
2
0
1
2
1
1
0
1
1
0
1
0
1
1
2
0
1
1
0
1
1
0
0
2
1
1
1
1
1
1
2
2
2
1
0
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
0
1
0
1
1
0
2
0
1
1
1
1
1
1
0
1
1
0
2
1
1
2
1
2
2
2
1
0
1
0
1
1
1
0
0
2
1
0
1
1
2
1
2
0
1
1
1
2
2
1
1
1
1
1
2
1
1
2
1
1
1
1
0
2
1
1
0
0
1
2
0
1
1
0
1
2
1
1
1
1
1
1
1
1
1
1
1
1
0
1
2
1
0
1
1
2
1
1
2
0
1
1
1
1
1
0
0
1
1
0
1
1
2
1
0
2
1
0
1
2
1
1
1
1
2
0
1
2
2
1
0
0
0
1
1
1
1
1
1
2
2
0
1
0
1
0
1
1
1
2
2
1
1
2
0
1
1
1
1
0
1
0
1
1
1
1
1
1
1
2
1
0
2
1
1
1
1
2
1
2
2
1
1
1
1
0
2
2
0
2
0
1
2
2
0
2
1
2
1
0
1
1
1
0
1
1
2
1
1
1
1
2
1
1
1
2
1
0
1
1
0
1
1
2
1
1
1
2
2
2
2
1
1
2
1
1
2
0
2
1
1
1
3
1
0
1
2
2
1
0
0
1
0
1
1
1
1
1
1
1
1
0
1
2
0
1
2
1
1
2
0
2
1
1
1
1
0
1
0
1
1
2
2
1
3
2
2
2
1
1
1
1
2
1
2
0
1
0
1
1
2
1
2
2
1
1
0
2
1
1
1
0
0
2
1
2
1
1
1
0
2
1
2
1
1
1
1
2
0
0
1
1
1
2
1
0
0
1
1
2
1
2
1
2
1
0
1
2
1
0
2
1
1
2
1
0
2
1
1
1
1
1
1
0
2
1
2
1
2
0
1
1
0
2
2
1
1
1
0
2
1
2
1
2
1
1
1
1
2
1
1
2
1
0
2
1
3
1
0
0
1
0
1
1
0
1
1
0
2
1
1
2
1
2
1
1
0
2
1
0
1
2
0
0
1
1
1
1
1
1
1
1
2
1
0
0
1
1
0
0
2
1
2
1
4
2
2
0
2
0
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
0
0
1
0
1
1
1
1
1
0
2
1
2
2
1
2
2
0
1
1
1
1
2
0
1
1
2
1
0
1
2
0
1
1
2
2
1
2
0
1
2
2
0
0
1
1
1
2
2
0
1
1
1
1
1
1
1
1
2
0
1
2
2
2
1
1
2
1
1
1
2
1
1
1
2
1
1
2
2
2
2
2
1
1
0
1
0
0
1
0
0
1
1
0
1
2
1
1
2
0
2
0
1
0
1
2
2
1
1
1
2
1
1
2
1
2
1
0
1
1
0
0
0
1
1
1
0
1
1
1
1
3
1
2
2
1
0
1
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
0
1
1
1
1
2
1
1
1
1
0
1
1
0
0
0
1
1
0
0
1
2
1
0
1
0
0
0
0
2
1
0
1
1
2
1
1
2
0
2
1
1
0
1
1
1
2
0
1
1
2
1
1
2
1
1
1
1
1
2
1
0
2
1
2
2
0
0
2
1
0
1
2
2
1
2
0
2
1
1
1
1
1
2
1
1
0
1
1
0
2
1
2
1
1
0
1
1
2
1
1
1
1
3
1
1
1
2
0
1
1
1
1
1
1
1
1
2
3
1
0
0
2
2
2
1
2
2
0
1
1
1
1
0
0
1
1
2
1
0
2
1
1
2
1
1
1
2
1
1
2
2
2
0
1
2
0
1
0
1
2
1
2
1
1
1
0
1
1
0
2
1
0
1
2
1
2
0
1
1
1
2
1
0
2
0
2
1
1
1
1
2
2
1
2
1
2
1
3
1
1
2
1
1
2
0
1
1
0
2
3
0
1
1
1
1
1
2
2
1
1
1
0
0
1
1
1
1
0
1
0
0
1
1
0
1
1
1
1
0
2
1
1
1
1
2
2
1
2
0
0
1
1
1
2
1
0
1
3
1
1
2
1
0
0
1
0
1
1
1
2
1
3
2
1
0
1
2
2
1
1
0
1
1
0
2
1
1
0
1
0
2
0
1
1
0
1
1
0
2
0
0
2
1
2
0
2
0
2
1
2
0
2
1
2
2
1
2
0
0
0
1
2
1
2
0
1
0
1
0
2
1
1
0
1
0
1
1
1
2
1
0
1
2
2
0
0
1
1
1
1
2
2
1
2
1
0
1
0
2
2
2
2
2
0
0
1
1
1
1
0
2
0
1
1
2
0
0
1
1
1
0
1
1
1
0
1
2
1
1
0
2
1
2
1
1
1
1
2
2
1
1
1
0
0
1
1
1
2
0
0
1
2
1
0
1
1
0
1
1
1
1
1
1
2
1
2
1
2
1
2
1
0
0
1
2
1
1
0
1
1
2
1
1
1
0
1
1
1
1
1
1
1
2
1
1
1
4
1
1
0
2
1
1
1
1
1
2
3
1
1
2
2
1
0
2
1
1
1
1
0
3
1
1
1
1
0
0
1
1
0
1
1
2
1
1
1
1
2
1
0
0
0
0
1
2
1
2
2
1
1
2
2
1
2
2
2
1
0
0
1
2
1
1
1
0
1
1
0
1
0
0
0
1
0
0
1
1
2
1
1
1
1
2
1
0
2
1
1
2
1
1
0
2
0
1
1
1
2
2
1
1
1
2
1
0
1
1
1
0
1
1
0
1
1
0
1
1
2
0
1
0
0
1
1
0
2
1
1
0
1
1
1
1
3
1
2
1
1
2
0
1
1
1
1
0
0
0
1
2
1
2
1
2
2
1
0
3
0
0
1
2
1
1
1
1
1
0
1
0
0
1
2
1
1
0
1
1
0
1
0
1
0
1
0
2
1
1
1
0
3
1
0
1
2
1
0
1
1
1
1
2
1
1
1
1
1
1
0
2
1
2
1
1
1
2
1
1
0
1
1
1
1
1
4
2
1
1
1
0
1
0
1
0
1
1
1
0
2
1
2
0
2
2
1
1
1
2
1
1
1
2
1
2
1
1
2
2
2
1
2
2
1
1
1
1
2
2
1
1
1
2
0
1
5
0
2
1
2
2
1
1
1
1
1
1
1
0
0
1
1
1
1
1
1
0
1
0
2
1
2
1
0
2
1
0
1
0
1
2
1
2
1
1
1
1
1
1
1
2
1
0
1
2
2
0
0
1
1
1
0
2
1
1
1
1
2
1
1
1
1
2
0
2
1
1
1
1
0
1
1
1
1
0
1
1
0
2
0
1
1
2
2
0
0
1
0
1
2
2
0
0
1
1
0
1
1
1
1
2
0
2
2
1
0
1
2
1
1
1
1
1
2
1
1
2
2
1
1
2
1
0
0
1
1
2
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
2
0
3
0
0
1
1
1
2
2
0
2
2
1
1
0
1
1
1
2
1
2
1
0
2
1
0
1
1
1
2
1
1
2
2
1
1
0
1
2
2
1
0
3
1
1
1
1
0
0
1
1
1
1
1
1
2
1
1
1
0
1
1
1
0
1
1
2
1
0
1
1
1
0
2
1
2
2
1
1
1
0
2
1
2
1
1
2
2
2
1
1
2
2
1
1
1
1
2
1
1
1
2
1
0
1
1
1
0
0
1
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
2
0
0
1
1
2
1
1
0
1
0
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
0
1
2
1
1
1
2
0
1
0
1
1
1
2
1
0
2
1
1
1
1
0
0
1
0
2
1
2
1
1
2
1
1
1
2
1
1
1
0
1
1
1
2
2
2
1
2
1
1
0
1
1
1
0
0
1
1
1
1
1
1
1
1
1
2
1
0
1
1
1
1
0
2
1
2
4
2
1
2
0
1
1
1
1
1
0
2
1
1
0
1
1
2
1
0
0
1
2
1
2
0
0
2
1
1
1
1
3
1
2
1
1
0
1
2
2
1
1
2
1
0
0
2
2
1
2
1
2
2
2
1
2
1
1
1
1
2
1
1
2
1
1
1
2
1
0
1
2
2
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
0
0
1
1
0
1
1
2
1
1
1
1
1
1
1
1
1
0
2
1
2
0
2
1
1
2
1
1
1
2
0
2
1
0
2
1
1
0
1
2
0
1
1
2
2
1
1
0
2
1
2
1
2
2
1
1
0
1
2
1
1
1
1
1
2
1
2
1
1
1
1
1
2
0
1
1
2
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
0
1
0
1
2
1
1
1
1
1
0
2
2
1
0
1
2
1
0
1
1
1
0
1
2
2
0
1
2
1
2
1
2
1
2
1
1
2
0
1
1
0
0
2
1
1
1
1
0
0
1
1
0
1
1
1
2
1
2
0
0
0
1
2
0
0
3
1
1
1
1
1
1
2
0
1
2
0
1
2
1
1
1
1
1
1
0
1
0
2
1
1
1
0
2
1
1
0
0
0
1
2
1
1
1
2
2
1
2
2
1
2
2
1
1
1
1
0
1
1
1
2
2
1
1
1
1
2
0
1
1
2
1
1
1
2
1
2
1
2
0
1
1
1
1
0
1
1
0
2
0
1
2
1
1
1
1
0
1
1
1
1
0
1
2
1
1
1
0
2
2
1
0
1
1
1
0
1
1
2
1
1
2
2
2
1
0
2
1
1
0
1
1
1
1
1
1
1
2
0
2
1
2
1
1
2
0
0
1
1
1
0
1
1
1
1
1
1
1
1
2
1
1
1
0
1
1
1
0
2
1
1
1
0
2
0
0
2
1
0
1
2
1
1
1
0
1
1
1
2
1
0
1
2
2
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
0
1
2
1
1
0
2
0
0
1
1
1
0
1
2
2
1
1
1
0
1
1
1
1
0
0
1
2
2
1
1
1
1
1
2
2
1
2
2
0
1
1
2
2
1
2
1
2
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
0
2
2
0
2
1
1
1
2
0
1
1
1
2
1
2
1
2
0
2
1
2
1
1
2
1
1
1
1
0
2
0
0
1
0
2
1
1
1
2
1
2
1
1
0
1
1
1
1
0
1
2
1
1
1
2
1
1
2
1
1
1
0
2
0
1
2
2
1
1
4
0
1
1
1
0
2
1
0
2
0
2
1
1
0
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
0
1
2
1
1
1
2
1
1
1
1
0
1
1
2
1
1
1
1
1
1
2
1
1
1
0
1
0
0
2
1
1
2
0
6
1
0
2
2
1
2
0
2
1
1
2
2
1
1
2
1
1
2
2
2
1
0
1
1
0
2
0
1
1
1
1
1
0
2
1
1
1
1
0
1
1
1
2
1
2
1
2
2
1
2
0
0
0
0
1
3
1
1
1
2
1
1
0
2
1
2
0
2
1
2
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
2
0
2
1
2
1
1
2
1
1
1
0
2
1
1
0
2
1
1
2
1
0
2
1
1
1
0
2
1
3
1
1
1
1
1
2
0
0
2
1
1
2
1
0
1
0
2
1
2
1
2
1
2
1
2
0
2
2
1
2
1
3
0
2
2
2
0
1
0
1
3
2
1
1
2
1
1
1
1
1
2
0
1
1
0
2
0
1
0
0
0
0
1
0
0
1
2
1
0
2
1
1
1
0
1
1
2
1
1
1
1
0
1
0
2
0
0
1
2
0
1
1
0
0
1
2
1
1
2
1
1
2
1
1
1
0
1
1
2
0
1
2
2
1
1
0
2
0
1
1
2
0
1
0
1
2
1
2
2
1
0
0
0
0
2
1
1
1
1
1
1
1
1
1
0
1
2
1
0
1
1
1
1
1
1
2
2
2
2
2
2
1
0
1
1
0
1
2
1
1
1
1
1
1
1
0
1
1
0
1
1
0
2
3
1
1
1
1
1
0
1
0
1
3
1
0
1
1
0
2
1
2
1
1
0
2
1
0
1
1
2
2
1
2
2
1
1
1
2
3
1
2
2
2
0
1
1
2
1
0
1
0
1
2
0
0
1
1
1
1
1
0
2
2
2
2
2
2
2
1
1
1
1
1
2
1
0
2
1
1
1
1
1
1
1
1
2
0
0
2
1
0
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
0
1
1
1
2
0
2
1
1
2
1
1
0
1
0
0
1
2
2
1
1
0
1
2
1
2
1
2
0
1
1
1
1
1
1
1
0
1
1
1
1
1
0
2
1
1
1
0
0
0
1
0
1
1
1
1
1
0
1
2
0
2
1
1
0
1
2
2
2
1
2
0
1
1
2
1
1
1
1
1
1
1
1
2
1
2
1
1
0
2
1
1
1
2
1
1
1
2
2
1
2
2
2
2
0
1
1
2
1
1
1
0
1
2
1
2
1
0
2
2
1
1
1
1
1
2
1
2
0
2
0
2
1
2
1
0
1
2
2
2
2
1
1
2
2
1
1
1
1
2
2
1
2
1
2
1
0
1
1
0
1
0
1
1
2
2
0
0
0
2
0
1
0
2
0
2
2
1
1
1
1
1
2
1
2
1
1
1
0
1
0
0
1
0
2
5
1
1
2
1
1
2
1
1
2
1
1
2
1
1
1
2
1
0
0
0
2
0
1
2
1
0
1
0
1
1
1
1
1
1
0
1
2
1
0
1
1
1
2
2
1
1
1
1
1
1
2
1
2
0
1
1
1
1
1
3
1
1
1
0
1
0
0
1
2
2
0
0
2
1
1
1
1
1
1
0
1
2
0
0
1
1
2
1
1
1
2
2
1
0
0
1
1
1
1
1
1
2
1
1
1
0
1
1
1
1
1
2
1
1
1
0
1
1
1
5
1
1
0
2
2
1
1
1
0
1
1
1
1
2
2
2
1
1
1
2
2
2
1
1
2
1
0
1
2
1
1
1
1
1
1
2
1
0
1
1
2
1
2
1
1
1
2
1
2
0
1
0
1
1
1
1
1
0
1
2
2
1
1
2
1
1
0
1
1
0
1
1
1
2
0
1
2
1
1
1
2
0
2
1
1
1
0
2
1
1
1
0
2
1
2
1
1
0
1
1
4
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
0
0
1
0
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
2
1
2
1
2
0
3
1
2
0
1
1
2
1
1
1
2
1
1
1
0
2
0
1
1
0
1
1
0
1
2
1
1
0
1
1
2
1
1
1
1
1
2
2
0
1
2
1
0
1
1
1
2
1
0
2
1
1
0
2
2
1
1
1
1
1
1
2
2
2
1
1
0
1
1
1
1
1
1
0
1
1
1
1
0
1
1
1
2
1
2
0
0
0
1
2
0
1
2
1
1
1
0
0
1
1
0
2
2
1
0
0
1
1
1
2
0
3
1
1
1
2
1
1
1
0
1
1
1
1
1
0
1
1
2
1
1
1
1
0
1
1
1
1
1
0
2
1
1
1
1
1
0
2
1
1
1
1
2
1
0
2
1
1
0
1
2
1
0
1
1
0
1
1
2
1
2
1
1
0
1
1
2
0
1
2
1
1
1
1
0
1
1
0
1
2
1
1
2
0
1
2
1
1
0
0
1
1
1
2
1
0
1
0
1
2
2
1
0
1
1
0
1
2
1
1
1
1
0
1
2
1
0
0
1
1
1
0
1
1
1
0
0
1
2
1
2
1
2
2
2
1
1
1
0
1
1
1
2
1
1
1
1
1
0
0
2
1
0
1
1
1
3
0
1
2
1
2
0
1
0
1
1
1
2
0
2
1
2
1
1
1
1
1
1
1
1
0
1
1
2
1
2
2
1
2
1
0
2
2
1
1
1
1
2
1
2
1
1
0
1
1
1
1
1
1
0
2
0
2
0
2
2
1
2
1
2
0
2
1
2
1
0
2
1
1
1
2
2
1
0
1
1
1
2
1
1
0
0
1
2
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
2
0
1
1
0
0
1
1
1
2
1
0
1
2
1
1
1
1
1
1
2
1
0
1
1
0
1
1
1
1
2
2
2
0
0
2
1
2
1
1
2
1
0
1
1
1
1
1
1
1
0
1
1
2
1
1
2
1
0
2
1
1
1
3
2
2
1
0
1
1
1
1
2
1
1
1
0
1
1
2
1
1
1
0
2
0
1
1
1
0
2
1
2
1
0
2
0
1
0
1
1
1
1
1
1
2
0
0
1
2
1
1
1
0
0
1
2
1
1
2
1
1
1
2
0
1
1
2
1
1
1
2
1
1
2
2
1
1
0
1
1
1
2
1
0
1
1
0
0
2
0
0
1
1
0
1
1
1
0
1
1
1
1
1
1
1
1
0
2
1
0
2
1
1
1
2
1
1
1
1
1
2
0
0
2
0
2
1
1
1
2
1
0
1
1
1
1
1
1
0
1
2
1
2
1
1
0
1
1
2
1
2
1
1
1
1
1
2
0
0
1
1
2
3
1
2
1
1
1
1
2
2
1
1
1
2
1
1
1
1
1
0
2
0
2
1
1
1
2
2
1
0
0
1
1
1
0
1
1
1
1
1
0
2
1
2
0
2
1
0
1
0
1
1
2
1
1
1
2
2
1
1
1
1
1
1
1
0
1
1
1
1
1
1
2
1
1
1
1
2
0
1
1
1
1
2
2
1
1
2
1
1
1
2
1
2
2
2
0
1
1
1
1
1
1
2
1
1
0
1
2
1
2
2
1
2
0
1
0
2
1
1
0
0
2
2
1
1
1
1
0
1
0
1
2
1
1
0
2
1
1
1
2
0
2
1
1
1
2
1
2
1
0
2
0
2
1
0
2
1
3
1
2
1
2
1
1
1
1
2
1
1
1
0
1
1
1
1
2
2
1
1
0
1
2
2
1
2
0
1
1
1
2
1
2
1
0
2
1
1
2
0
1
3
0
1
0
0
1
3
1
2
1
2
0
0
1
2
0
1
3
2
0
2
2
1
0
1
2
1
1
0
2
1
1
1
0
0
0
0
2
2
1
2
1
2
0
1
1
2
1
0
2
1
1
1
1
1
2
0
1
3
1
1
1
0
2
2
1
2
2
1
0
0
1
1
1
1
1
1
1
1
0
1
0
1
1
2
1
1
1
1
2
0
1
2
0
2
0
2
2
0
1
1
1
0
1
1
2
0
1
1
0
1
1
0
1
1
0
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
0
2
0
1
1
1
2
1
1
1
1
1
1
2
1
2
1
0
1
1
2
0
0
2
2
1
1
2
2
1
1
1
0
0
0
1
1
1
1
1
0
2
1
2
1
1
2
1
2
1
2
1
0
1
1
1
0
0
1
1
1
2
1
0
1
1
2
1
1
1
1
1
2
1
1
1
2
0
1
1
1
1
2
2
1
1
1
1
1
0
2
1
1
1
1
2
1
1
1
1
1
1
1
0
0
2
1
1
0
0
0
1
0
1
1
1
1
1
2
1
1
1
2
1
0
0
1
1
2
0
1
2
1
1
2
1
0
0
0
1
2
0
1
1
2
1
2
1
1
1
1
1
1
2
2
2
0
1
1
1
1
2
0
1
1
2
1
2
0
1
1
1
1
0
1
1
2
0
1
2
2
2
0
0
1
2
1
2
2
2
0
0
1
1
0
2
1
0
1
2
2
1
2
2
2
2
0
1
0
1
1
2
2
2
1
0
1
1
2
1
2
2
2
1
1
0
1
1
1
1
1
1
2
1
0
0
2
1
1
2
1
2
1
2
1
2
1
1
1
1
1
1
1
1
1
0
2
1
1
1
1
2
2
2
1
1
2
2
2
2
0
1
0
1
1
0
1
2
1
1
2
1
2
2
2
1
2
2
0
1
1
0
0
2
2
2
0
0
2
2
0
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
1
0
1
1
1
1
1
2
2
1
1
0
1
0
0
0
2
1
1
0
0
1
2
2
1
1
1
1
1
1
0
1
0
2
0
2
0
2
1
1
1
1
1
1
1
3
1
2
2
1
0
1
1
0
2
1
2
2
1
1
1
0
1
1
0
2
1
1
0
1
2
1
0
1
1
1
1
2
0
1
1
1
0
0
1
1
2
1
2
2
1
1
2
1
1
1
1
2
0
1
2
2
2
0
1
0
0
1
0
1
2
1
2
1
1
1
2
0
1
2
1
2
0
1
1
2
0
0
1
0
1
1
1
1
2
1
1
1
1
1
0
1
1
2
1
1
0
1
1
1
1
1
2
1
2
1
0
0
0
1
1
0
1
1
0
0
3
2
2
0
1
1
1
1
2
0
2
1
1
1
0
1
1
1
1
1
0
1
1
2
0
1
1
1
1
1
2
2
1
0
2
1
2
1
1
1
1
1
2
1
2
1
2
1
2
2
1
1
0
2
2
1
1
1
2
0
1
2
1
0
2
1
1
0
1
2
1
2
1
1
2
1
2
1
1
1
0
1
1
0
0
1
1
1
1
2
0
0
5
0
1
0
0
1
1
2
1
0
0
1
2
1
1
1
1
0
1
2
1
1
1
1
1
1
1
0
1
0
2
1
1
2
0
1
1
0
2
1
0
1
1
1
2
1
2
2
1
2
0
1
1
1
0
1
2
1
1
0
0
2
1
1
0
3
1
1
2
1
1
1
1
0
0
2
1
1
1
0
1
2
1
1
1
1
3
4
1
0
2
1
1
1
0
2
1
1
1
1
2
0
0
1
2
1
0
1
2
2
1
0
2
1
2
1
1
0
1
1
1
1
1
1
2
2
1
1
1
1
0
2
0
1
1
1
0
1
1
2
2
0
1
2
1
0
1
2
1
1
2
0
1
3
1
1
1
1
1
2
1
1
2
0
0
1
2
1
1
1
1
1
1
0
1
1
1
1
1
1
1
0
2
1
2
0
0
1
1
1
1
0
0
0
1
0
1
2
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
0
0
1
0
0
1
0
1
1
1
1
1
0
0
1
0
1
0
1
0
0
1
1
1
2
1
1
1
2
1
2
0
2
1
0
1
1
1
1
1
1
1
2
1
1
1
2
1
1
2
0
0
1
2
2
2
1
1
1
1
0
1
0
1
1
1
2
1
2
1
0
1
0
1
2
2
1
1
1
1
3
1
2
0
1
2
2
1
1
2
2
0
1
0
1
2
2
1
2
1
1
1
0
1
2
1
0
1
1
1
1
0
2
0
1
1
1
1
1
2
1
1
0
1
0
2
0
1
0
2
1
0
1
2
1
1
0
1
1
2
0
1
1
2
1
1
1
1
1
0
1
1
0
1
1
2
1
1
0
1
1
0
0
1
2
1
1
0
1
1
0
1
1
2
2
1
1
1
1
0
2
1
1
1
1
0
0
1
1
2
1
2
1
3
2
1
0
0
0
2
1
1
0
1
1
1
1
1
2
1
1
0
1
1
1
2
1
1
1
1
1
2
1
0
1
2
1
1
2
1
1
0
1
1
0
1
0
0
2
1
2
1
0
2
1
0
2
1
0
2
1
1
2
1
2
1
1
0
1
1
0
2
1
0
1
1
1
2
2
1
3
1
1
3
0
1
1
2
1
0
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
0
2
1
1
1
1
0
2
2
1
1
1
1
0
0
2
1
1
1
1
1
0
1
0
1
1
2
1
1
1
1
1
1
1
2
1
1
0
0
1
0
2
1
1
1
1
1
1
0
0
1
2
1
0
2
2
0
1
1
2
2
0
2
1
1
0
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
2
1
1
1
3
1
1
0
2
1
1
1
1
0
2
2
1
1
1
1
0
2
2
2
0
2
2
1
1
1
2
2
2
0
1
1
1
0
0
0
2
1
1
0
2
2
1
1
2
1
2
0
0
1
0
1
1
1
2
2
1
1
1
0
0
0
2
0
1
1
1
1
0
1
0
2
1
1
2
2
0
1
1
2
1
0
1
0
1
1
1
1
1
1
0
1
0
1
1
1
1
1
3
1
2
1
1
2
1
1
1
0
2
0
1
1
1
1
1
0
1
1
0
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
2
1
0
1
0
1
0
1
1
1
1
2
1
1
2
2
2
2
1
2
0
3
1
2
0
1
2
1
2
0
0
0
1
2
0
1
2
1
2
1
1
1
1
0
1
2
0
1
1
1
0
0
0
2
1
1
1
2
1
1
2
2
0
1
0
0
1
1
1
2
2
1
1
1
2
1
1
2
1
2
2
0
1
1
1
1
1
1
0
1
1
1
1
0
1
1
2
2
2
0
2
1
2
0
1
2
2
1
1
1
2
2
2
0
1
2
1
0
1
2
1
0
1
1
1
2
2
1
1
2
2
0
0
1
2
1
1
2
1
0
2
2
1
0
1
1
2
0
1
1
1
2
0
1
2
1
1
2
1
1
1
1
1
1
2
2
2
1
1
1
2
0
3
1
1
1
2
2
0
0
1
1
0
2
2
0
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
2
0
0
0
1
1
1
2
0
2
1
0
1
1
1
3
1
2
0
1
1
0
1
1
2
2
1
1
1
1
1
2
1
1
2
1
0
1
2
2
1
1
0
1
1
1
1
1
1
2
1
2
1
2
1
1
1
1
1
0
0
0
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
0
0
0
2
1
1
1
1
1
1
1
0
0
1
2
1
0
1
1
1
2
0
2
1
1
2
1
1
1
2
0
2
1
1
0
1
2
0
1
1
0
1
0
1
2
1
1
0
0
3
1
1
1
1
1
1
1
0
1
2
1
2
0
0
1
0
0
0
1
1
1
1
0
0
1
2
3
1
1
1
2
1
0
1
2
1
1
1
0
1
1
1
1
0
2
1
2
1
1
0
1
2
0
2
1
1
1
2
0
0
1
1
2
1
0
0
2
1
1
1
1
0
1
2
2
2
2
1
2
2
2
1
0
0
2
0
1
2
2
2
1
0
1
1
1
1
1
1
1
2
2
0
0
1
0
1
1
1
1
1
0
2
0
0
0
2
1
1
0
2
1
1
2
1
1
1
1
1
1
2
1
2
2
1
0
1
1
0
2
1
2
2
2
2
1
0
1
1
2
1
1
1
0
4
2
1
0
1
1
2
1
2
0
2
2
1
2
0
0
1
2
1
2
1
0
2
1
1
0
0
1
1
1
1
2
1
1
1
1
1
2
1
2
1
0
2
1
0
1
1
1
1
1
1
1
1
1
1
0
0
1
1
1
1
0
1
1
1
1
1
2
1
1
1
1
0
0
1
0
1
2
2
0
1
1
1
1
1
1
1
1
0
1
0
0
1
1
0
0
1
1
1
2
1
1
2
1
1
1
1
1
0
1
2
2
0
0
1
1
1
1
0
2
0
2
2
1
1
1
0
0
0
1
0
2
0
0
1
1
1
0
1
0
2
0
1
1
1
1
0
1
2
2
1
1
1
1
2
0
0
1
2
0
1
1
2
1
1
1
0
1
0
1
1
2
2
1
1
1
1
1
2
1
1
1
2
1
1
0
0
2
1
2
2
1
2
1
0
0
1
2
2
1
1
1
2
2
1
0
0
1
0
1
1
1
1
1
1
0
1
1
1
0
1
1
1
0
0
1
1
0
1
2
2
1
1
0
2
1
1
0
1
0
1
1
0
2
2
2
1
2
2
2
0
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
0
1
0
0
2
1
1
0
1
1
2
1
1
1
2
1
0
0
1
0
1
1
1
1
1
1
0
1
1
2
1
1
1
5
1
2
1
1
3
2
0
1
2
1
1
1
1
1
1
1
2
2
0
1
4
1
1
1
1
1
2
2
1
1
1
0
1
1
1
1
1
2
0
3
2
1
2
2
0
1
1
1
1
2
1
1
0
0
1
2
1
1
0
0
1
2
1
1
2
1
1
1
1
1
2
1
1
1
1
2
0
1
2
1
1
1
1
0
1
2
1
1
1
1
1
2
3
1
2
1
1
1
0
1
1
1
0
2
0
2
1
1
1
1
1
2
1
1
2
1
1
2
1
1
0
1
1
1
2
1
1
2
1
2
1
0
2
0
2
2
1
0
1
1
1
0
1
1
0
1
2
1
2
2
1
0
2
1
1
1
1
2
0
1
0
1
1
1
0
0
1
1
1
2
1
1
1
2
2
2
1
2
1
0
0
1
1
1
1
2
1
0
0
1
2
2
1
1
1
1
1
1
1
2
1
2
1
2
2
2
1
1
1
1
2
0
1
1
1
1
2
1
1
1
1
1
1
1
0
2
1
1
2
1
1
1
2
1
1
1
1
0
1
0
2
1
0
1
1
1
1
1
1
2
2
2
1
1
0
0
1
1
1
1
1
0
2
1
1
1
1
1
1
2
1
1
2
1
0
2
0
1
1
1
1
2
1
1
1
2
2
1
2
1
1
1
0
1
1
0
1
1
1
1
1
1
2
0
1
1
0
0
2
1
1
1
1
1
1
0
2
2
1
0
1
1
2
1
1
2
1
1
2
2
1
1
1
1
2
2
0
0
2
1
0
1
1
1
2
0
1
1
0
0
1
1
0
0
1
0
1
2
1
1
1
2
0
2
0
1
2
1
1
2
1
2
2
1
1
0
0
1
1
2
1
2
0
0
2
0
1
2
2
2
1
0
1
1
0
1
2
0
1
1
0
1
1
0
1
1
3
2
1
0
1
1
1
0
0
1
1
1
1
1
1
1
2
2
2
1
1
1
0
0
0
1
0
1
0
2
1
1
0
1
0
1
2
1
1
1
1
1
1
1
2
2
2
2
1
1
1
2
1
1
1
2
0
2
0
1
1
1
0
1
1
1
2
2
0
2
2
1
1
2
1
1
2
2
0
1
0
0
1
0
2
1
2
1
1
2
1
1
2
1
1
0
2
2
2
0
1
1
1
1
1
0
2
2
1
1
0
2
0
1
1
1
2
2
1
1
1
1
1
2
1
2
2
1
1
2
1
2
1
2
0
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
0
0
1
2
1
0
1
0
0
2
1
0
2
1
1
2
1
0
1
1
2
1
2
0
1
1
0
1
1
2
1
1
2
1
0
1
1
1
1
1
1
0
2
1
2
1
1
1
0
1
1
1
1
1
2
1
1
0
2
2
1
1
0
0
1
1
1
0
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
0
1
0
1
1
1
0
2
1
2
1
1
1
0
1
2
1
0
0
1
0
1
1
2
1
0
1
0
1
1
1
1
1
2
1
1
2
2
2
0
0
1
1
2
1
0
2
2
1
0
2
1
2
0
2
1
3
0
0
1
1
1
0
1
1
2
1
1
1
1
1
1
0
1
1
0
2
2
2
2
1
1
1
1
0
1
1
1
1
1
2
1
2
0
2
0
2
1
2
1
0
1
1
1
1
1
1
1
1
0
1
1
1
0
1
1
0
1
0
0
0
1
2
1
1
2
2
2
0
2
1
1
0
1
1
2
2
1
2
1
1
2
0
1
0
0
1
1
2
1
0
1
1
0
2
1
0
0
1
0
1
0
1
1
1
1
0
2
1
0
1
1
1
0
0
1
1
0
1
1
1
1
2
2
0
0
1
1
1
1
1
1
1
1
1
0
1
0
0
1
1
1
1
0
1
1
1
1
2
0
1
1
1
2
0
1
0
1
1
1
1
2
1
1
1
0
2
1
2
1
2
1
1
2
1
2
0
2
1
0
1
0
0
0
1
1
1
0
1
0
0
0
1
0
1
1
1
2
2
1
2
2
2
2
2
0
1
0
2
1
1
1
1
1
0
1
1
0
1
1
1
2
1
0
2
1
1
1
0
1
1
2
1
0
2
1
1
2
1
2
1
1
1
1
1
1
1
1
1
0
1
1
2
1
1
1
1
0
1
1
1
0
0
2
0
0
2
1
2
2
0
2
1
1
1
1
0
1
1
1
2
1
2
2
0
1
0
0
2
1
2
1
1
2
1
1
1
1
1
0
1
2
1
2
2
1
1
1
1
1
0
2
2
0
1
1
1
0
1
1
1
1
2
0
2
0
1
1
0
2
1
1
1
0
1
1
1
0
1
1
1
1
0
1
1
0
1
2
1
0
2
0
2
1
1
1
1
1
1
1
2
1
0
0
1
1
0
1
1
1
2
1
0
1
1
2
1
1
1
0
1
1
1
2
1
0
2
1
2
2
1
1
1
2
0
0
0
1
2
2
2
1
0
1
2
1
1
2
1
1
2
0
2
1
1
1
1
1
1
2
2
1
1
2
1
1
0
1
1
2
0
1
2
1
0
1
1
1
0
0
2
1
1
2
1
1
0
1
0
2
0
0
0
1
2
1
1
1
1
1
2
1
2
1
1
0
2
1
1
1
1
2
2
1
2
1
1
0
1
1
2
1
2
2
1
1
1
0
1
1
1
2
1
1
0
1
2
2
0
1
2
1
0
1
2
1
1
1
1
1
1
1
2
2
1
1
0
1
1
0
1
1
1
2
0
1
2
1
2
2
0
1
1
1
0
0
2
2
2
2
2
1
1
1
1
2
0
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
2
1
0
1
1
1
2
1
2
1
1
0
1
1
0
2
0
1
1
1
0
0
1
0
1
1
1
1
1
2
0
0
1
1
1
0
1
2
2
2
1
0
2
1
0
1
1
2
2
1
1
2
1
2
1
1
2
1
0
2
2
0
2
0
0
1
1
2
0
1
1
0
1
0
1
2
1
1
1
1
2
1
1
1
1
1
2
1
2
2
1
1
2
1
0
1
2
1
0
0
2
1
1
2
1
1
2
1
1
1
1
0
1
1
0
1
1
1
1
1
0
1
2
0
2
2
1
0
1
0
1
1
1
1
0
1
0
1
1
2
2
0
1
2
1
1
1
2
1
1
2
0
0
1
1
1
0
2
1
2
1
0
2
1
4
1
1
1
1
1
1
2
1
2
1
1
2
1
0
1
1
1
0
2
1
1
1
2
2
0
0
1
0
0
0
1
1
1
0
1
0
0
1
1
2
0
0
0
1
1
2
1
1
1
1
1
2
0
1
1
1
2
1
1
1
0
1
1
1
2
0
0
1
0
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
0
1
1
3
0
1
1
0
1
1
2
1
1
1
1
1
0
1
2
1
2
1
0
0
1
0
2
0
0
1
2
1
0
0
0
2
2
0
0
1
1
1
1
0
1
2
1
1
1
1
0
1
2
1
2
1
0
2
1
1
2
1
2
2
2
2
0
2
2
1
1
1
1
1
1
1
1
2
2
1
0
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
0
0
1
1
2
1
1
0
2
1
2
0
0
1
1
2
2
1
0
1
1
2
2
1
1
2
2
0
2
1
0
0
1
0
1
1
1
1
0
1
1
1
1
2
1
1
1
1
2
1
0
1
2
1
1
1
1
0
1
0
1
1
1
1
5
2
1
0
0
1
2
1
0
2
2
0
1
1
2
1
1
1
0
1
1
1
1
1
0
1
0
0
2
2
2
1
0
2
0
2
0
2
2
0
2
2
0
1
1
3
1
1
1
2
1
1
1
0
2
2
2
1
1
0
2
0
0
2
2
0
0
1
0
1
1
1
0
1
1
1
1
1
1
1
2
2
1
1
0
0
0
1
1
2
1
1
2
1
1
0
1
1
2
0
1
2
0
0
1
1
0
1
1
0
2
0
2
1
1
2
0
1
1
2
0
1
0
2
0
0
1
1
1
1
2
0
0
2
1
1
2
1
0
1
0
0
0
1
1
1
1
2
0
1
1
2
1
1
1
0
1
1
1
2
1
1
2
1
0
0
2
1
1
0
1
1
1
1
2
1
2
1
2
1
2
1
1
1
1
0
2
0
1
1
1
1
4
1
0
0
0
1
1
3
1
0
2
1
1
1
0
0
0
2
2
1
1
0
2
1
2
2
1
0
1
0
1
1
0
1
0
0
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
0
1
1
0
1
1
0
1
0
1
1
0
0
2
1
1
2
1
0
0
2
1
1
1
2
1
1
1
1
1
2
2
1
0
0
1
1
0
1
1
0
0
2
2
0
2
0
1
2
1
0
0
1
1
1
1
0
1
1
1
2
1
1
1
2
1
1
2
2
1
0
1
1
1
1
1
1
1
2
0
1
1
1
2
3
2
1
2
2
2
1
1
0
0
0
2
1
1
0
0
1
1
2
1
2
0
1
1
1
2
0
2
1
1
0
0
0
1
1
0
1
2
1
1
0
1
1
2
1
1
1
1
2
1
2
0
1
1
1
2
1
3
2
1
1
2
2
2
1
1
1
1
1
1
2
1
2
0
1
1
1
1
0
1
2
1
0
1
1
2
1
1
1
1
1
0
1
2
1
1
1
0
0
1
1
1
1
1
1
1
2
1
1
0
1
2
1
1
2
1
0
0
0
1
0
1
0
1
2
2
1
2
0
2
2
0
1
2
1
1
0
1
2
2
1
2
1
1
2
1
1
1
0
1
0
2
1
1
1
1
2
0
1
1
0
1
1
1
1
1
0
1
1
1
2
1
0
1
0
1
2
2
0
1
2
1
1
1
1
2
2
3
0
1
0
1
1
2
1
2
2
1
1
0
1
1
2
1
1
2
2
1
1
0
0
1
2
2
0
2
2
2
1
1
1
2
0
0
0
2
3
1
2
1
1
0
2
0
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
0
0
0
1
1
1
0
1
1
2
0
1
1
1
1
1
1
0
1
1
2
1
2
2
2
1
2
1
1
1
1
0
0
1
2
2
1
1
2
0
1
2
1
2
1
2
1
1
1
0
2
1
0
2
2
1
1
1
1
1
1
0
2
1
1
0
0
1
1
1
1
1
1
0
1
2
2
2
2
2
1
1
2
1
2
0
1
2
1
2
2
1
1
0
3
0
1
1
1
1
2
0
1
1
1
1
3
2
3
1
2
2
1
2
1
1
0
0
1
1
1
1
1
2
1
2
1
2
1
0
1
0
1
2
2
2
2
2
2
1
1
2
1
0
2
0
1
0
1
2
1
1
0
1
1
2
1
2
1
2
2
1
0
0
1
0
3
1
1
1
1
1
2
0
1
1
1
0
1
2
2
2
1
1
1
2
1
1
1
2
1
2
2
0
1
1
1
0
0
1
1
0
1
1
2
1
1
0
1
1
0
1
0
0
1
1
1
1
1
1
1
1
1
2
0
1
2
2
1
1
2
1
1
1
1
2
2
2
1
2
1
0
1
2
1
0
1
1
2
2
1
1
0
1
2
2
2
1
1
1
0
1
1
1
1
1
2
2
1
1
1
2
1
1
1
1
2
0
0
1
1
3
2
0
0
0
0
1
1
1
1
2
1
0
0
1
1
2
1
2
2
1
1
2
0
2
2
1
0
1
1
2
2
2
1
1
2
2
1
0
2
1
1
0
0
2
2
1
0
1
1
0
1
1
0
0
1
2
1
1
0
0
1
0
2
1
0
0
2
1
2
1
0
2
0
1
1
1
2
1
1
1
1
1
1
1
2
1
3
1
2
1
1
2
0
1
1
1
2
1
1
1
1
0
1
1
0
2
1
2
0
1
1
0
1
2
1
1
0
1
1
2
2
0
1
1
3
1
1
1
2
1
0
1
2
2
1
2
1
0
1
1
1
1
1
2
1
1
0
2
2
1
0
1
2
2
1
1
0
2
2
0
2
1
1
1
1
1
1
0
2
2
1
1
0
1
3
1
0
1
1
1
1
1
0
1
1
1
1
1
1
1
2
0
2
1
1
2
1
0
2
1
0
1
0
0
1
1
2
0
1
1
1
2
2
1
1
0
0
0
1
1
1
1
1
1
1
2
0
1
1
1
1
2
0
1
1
1
1
1
1
1
1
1
1
0
1
0
2
0
1
3
0
1
0
2
2
2
0
1
0
1
1
1
0
0
1
1
2
1
0
2
0
1
0
0
1
2
2
0
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
0
2
1
1
0
0
0
2
1
1
1
1
1
2
1
1
2
0
1
2
2
0
1
1
2
2
2
1
1
2
1
1
1
1
1
0
2
1
1
1
1
0
1
1
2
0
1
1
2
1
0
0
0
0
1
1
1
2
2
0
2
0
1
1
2
1
2
1
0
1
1
1
1
1
2
1
1
1
0
0
1
1
1
2
2
2
1
1
1
0
1
1
2
1
2
0
1
1
1
1
2
0
2
1
1
0
1
0
1
1
1
0
2
1
2
1
1
3
1
2
2
1
0
1
1
2
2
1
0
1
1
1
1
0
1
2
1
2
2
3
2
1
0
1
2
1
1
1
2
1
1
2
1
0
1
0
1
1
1
2
1
1
0
1
1
2
1
1
0
1
0
1
1
1
1
1
1
1
1
1
1
1
2
1
1
0
1
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
0
0
1
1
1
1
1
1
1
1
1
2
2
1
2
1
1
2
1
2
2
2
0
2
0
0
0
1
1
2
0
1
1
1
1
0
1
1
1
0
1
0
1
2
1
1
1
0
1
2
0
2
0
1
0
1
1
1
0
1
0
1
0
2
2
0
1
2
0
0
2
0
1
2
2
1
0
1
2
1
1
2
0
2
0
0
0
2
1
2
0
2
1
0
1
1
1
0
1
1
1
0
2
1
1
1
2
0
0
1
1
2
2
1
1
2
2
1
2
2
2
0
0
1
1
2
2
0
2
2
1
2
2
1
2
2
0
3
2
1
1
1
14
1
0
2
1
1
1
2
1
1
0
1
1
1
0
1
0
2
1
2
0
2
2
1
1
1
2
1
1
1
1
0
2
0
1
1
1
2
1
0
1
1
1
1
1
1
2
1
1
2
1
1
1
0
2
1
2
1
1
0
2
2
1
0
1
1
1
1
1
1
2
2
1
2
0
2
1
1
0
0
1
0
1
0
1
2
1
1
0
2
1
1
1
2
0
1
1
3
2
1
2
1
0
1
1
0
2
0
1
1
1
1
1
1
2
0
1
1
0
1
1
1
0
1
2
1
1
0
2
2
0
2
2
1
1
2
2
2
1
1
2
1
0
1
1
2
1
1
1
1
1
2
0
1
2
2
1
1
0
1
1
2
1
1
1
1
0
1
2
1
1
1
1
1
0
2
1
1
1
1
1
1
0
1
2
0
0
2
2
1
1
2
1
0
1
0
0
2
0
1
2
2
0
1
1
2
0
2
0
1
1
0
2
2
2
1
1
0
1
2
1
1
2
1
1
1
2
0
1
0
2
1
0
2
2
2
2
0
1
3
0
1
1
1
1
2
1
0
1
1
1
1
1
0
0
1
1
2
1
2
2
1
1
0
1
1
0
2
0
1
2
1
1
0
2
1
1
1
1
1
1
0
2
2
1
1
0
1
2
1
2
0
2
1
0
0
2
1
1
0
2
1
1
1
0
1
2
2
2
1
2
2
2
0
1
1
1
1
1
0
0
1
0
0
0
1
2
2
1
1
1
2
0
1
1
1
0
2
0
2
0
1
2
2
2
2
1
1
1
2
1
0
1
1
1
1
2
1
1
1
2
0
1
1
1
2
1
2
2
2
1
1
1
0
0
0
1
1
2
1
0
1
0
1
0
1
1
1
2
2
1
2
1
1
0
1
1
0
1
1
0
1
1
1
1
0
2
0
0
2
1
2
1
0
0
1
2
2
1
1
1
0
2
1
0
1
1
0
0
1
1
2
2
1
1
2
1
2
1
1
1
1
1
2
1
1
2
0
0
1
1
0
0
1
2
1
0
1
1
0
2
1
1
1
0
2
2
0
2
1
0
0
1
1
1
1
2
1
1
2
1
1
1
0
0
1
1
0
1
0
1
1
1
1
2
1
1
0
1
1
0
1
0
1
1
2
1
1
0
1
1
1
1
1
0
2
1
2
1
2
1
1
1
1
1
1
0
1
0
3
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
2
1
1
0
0
1
2
2
0
2
2
1
0
1
1
0
1
1
2
0
1
0
2
0
1
1
1
3
1
1
1
0
0
1
1
2
0
2
1
0
2
0
1
1
2
1
1
1
1
2
1
1
1
2
1
0
2
1
1
0
1
2
1
2
1
1
2
1
1
0
2
1
1
2
1
1
1
1
1
1
2
1
0
2
1
1
2
1
1
1
1
1
2
0
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
0
1
0
1
0
1
1
1
1
0
2
2
1
1
1
2
2
2
1
1
1
1
1
2
1
2
2
1
2
1
1
2
1
1
0
1
1
2
2
1
1
1
0
1
1
0
1
1
0
4
2
1
1
1
0
2
1
1
1
1
0
2
1
1
1
2
1
2
2
1
2
2
1
2
1
1
1
1
1
0
2
0
1
1
2
1
1
1
1
1
1
1
0
1
1
1
1
0
1
1
1
1
0
1
3
0
1
0
1
1
1
0
1
1
2
1
2
1
2
1
1
0
0
1
0
1
0
1
0
1
1
2
1
3
1
1
0
0
2
0
2
1
1
2
1
0
1
2
1
1
1
0
0
1
1
1
1
1
2
0
0
1
1
2
2
1
2
3
0
0
2
4
2
2
1
1
2
2
1
1
0
1
2
2
1
0
2
1
1
2
2
1
1
1
1
1
2
2
0
1
2
1
2
0
0
0
1
0
1
2
1
1
1
1
1
1
2
1
1
2
0
0
0
1
1
1
2
2
0
0
1
2
1
1
2
1
1
2
1
2
1
0
0
1
0
1
1
2
1
3
1
1
1
2
0
2
1
1
1
1
1
1
1
1
1
2
1
0
2
2
0
2
1
2
1
2
2
1
1
1
2
1
0
1
2
2
1
2
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
0
1
0
0
1
1
3
1
0
1
1
1
3
1
1
1
1
0
1
2
1
1
1
2
1
1
2
1
2
1
1
1
1
0
1
2
1
0
2
2
0
1
0
0
1
2
1
1
2
2
0
1
1
0
1
0
1
1
1
1
1
2
1
1
1
0
1
1
2
0
1
2
0
1
1
1
1
0
1
1
1
1
1
1
1
0
1
1
1
1
1
1
0
1
0
1
2
1
2
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
1
1
1
0
1
0
1
0
1
2
1
0
2
2
0
0
1
1
2
2
2
1
0
3
1
0
2
2
2
1
1
0
2
1
2
0
0
1
0
1
0
1
1
0
2
1
1
1
1
0
1
2
1
2
2
1
0
2
1
1
0
1
2
1
1
1
0
2
0
1
0
2
0
0
0
0
1
1
1
1
0
1
1
1
1
1
0
0
1
1
1
1
2
0
1
1
1
0
1
2
1
1
0
2
1
0
1
1
1
1
1
1
1
0
1
1
1
1
0
1
1
1
2
1
2
1
0
1
2
1
0
1
1
0
1
1
1
0
2
1
2
0
1
0
1
0
1
3
2
2
2
0
1
1
2
1
1
0
1
2
1
1
0
1
0
1
1
1
1
1
0
1
1
1
1
1
1
1
2
0
0
2
0
0
2
1
2
1
0
2
0
1
1
1
1
0
2
1
2
0
1
1
1
0
2
1
1
0
1
0
1
1
2
2
0
1
2
1
1
1
1
3
2
1
1
0
1
0
2
1
2
1
1
1
2
1
1
0
1
2
1
2
1
2
1
0
1
0
1
2
1
1
1
1
1
1
2
1
3
2
2
1
0
2
2
1
0
1
1
2
1
1
2
0
2
2
2
1
1
1
0
2
1
1
1
2
1
1
1
1
0
1
2
1
2
1
1
1
1
0
1
1
1
1
2
1
1
0
0
1
2
2
0
1
0
1
1
1
1
1
2
1
2
1
1
1
0
1
2
1
1
2
0
1
0
1
2
1
2
1
0
2
0
1
1
1
4
2
1
1
2
1
2
2
0
2
1
1
0
2
1
0
2
0
2
2
1
1
1
0
0
1
0
1
1
1
2
1
1
0
2
2
3
1
1
1
2
1
1
1
0
1
2
1
1
1
1
1
1
1
2
0
0
2
2
1
1
1
2
1
1
1
1
1
1
0
0
0
0
1
1
1
1
0
1
2
1
1
0
1
2
0
1
1
1
1
6
1
1
0
2
1
0
0
3
1
1
2
1
1
0
2
1
2
1
1
2
4
1
1
2
0
1
1
1
1
1
2
1
2
1
0
0
0
0
2
1
0
2
0
1
1
0
0
0
2
0
2
2
2
2
1
1
3
1
1
1
0
1
0
1
1
2
1
0
0
2
1
1
0
1
1
2
1
2
0
1
1
1
1
1
1
1
1
1
0
2
2
0
1
2
2
0
1
0
1
1
1
1
1
1
3
1
1
1
1
2
1
1
1
1
2
0
0
1
2
2
1
2
1
1
0
1
2
1
2
1
0
2
1
1
1
2
1
2
1
1
2
1
0
1
1
1
1
2
1
1
1
0
2
2
2
1
1
0
1
1
1
2
0
1
1
1
1
1
6
1
2
2
0
1
0
1
1
2
1
0
0
2
2
1
1
1
1
0
1
1
1
1
2
2
2
1
2
1
1
1
1
1
1
0
1
1
2
1
0
2
2
0
1
1
2
0
0
0
1
0
0
2
1
1
0
1
0
1
2
0
1
0
1
1
0
1
1
1
2
1
1
1
2
1
1
0
1
1
2
2
2
1
0
2
2
1
1
1
2
1
1
1
2
2
0
2
0
1
2
1
1
1
1
0
2
2
1
1
2
2
0
1
1
2
1
1
1
2
1
1
0
1
0
1
0
1
1
1
0
2
2
2
1
2
2
1
2
0
2
2
1
1
1
1
0
1
1
2
1
0
1
2
1
2
0
2
1
0
1
2
1
1
1
1
2
2
0
1
2
1
2
1
0
1
1
2
0
1
1
2
1
0
1
0
1
1
1
1
1
1
2
1
1
1
2
1
1
2
0
1
2
0
2
2
1
2
1
1
1
0
1
1
0
0
1
1
2
0
2
1
0
0
1
1
1
2
1
0
1
1
1
2
0
1
1
3
2
0
2
1
1
1
1
1
0
1
3
1
1
1
2
1
1
1
1
0
1
0
0
1
0
2
1
2
1
0
0
1
1
1
2
0
0
1
0
0
1
2
1
2
0
1
2
0
2
1
1
1
1
0
1
1
1
1
0
2
1
1
1
1
0
0
0
1
2
2
1
1
2
2
1
1
1
0
1
2
1
1
1
1
1
1
1
2
1
1
2
0
1
0
0
1
0
1
1
0
2
1
1
0
1
2
0
0
3
1
1
0
1
1
0
2
1
2
1
1
0
0
2
0
0
1
0
0
2
3
1
1
2
2
1
1
1
1
1
1
0
1
1
2
1
0
2
1
1
1
1
3
1
1
1
1
1
1
1
1
0
1
0
1
1
2
1
1
1
1
2
1
2
0
2
1
1
1
1
1
1
2
1
0
2
2
2
1
1
1
1
1
2
1
2
1
2
1
2
1
1
0
0
1
0
0
1
1
1
0
1
1
1
1
2
0
1
1
0
1
1
1
1
1
1
1
2
1
1
1
2
1
2
0
1
1
2
1
1
1
2
2
1
0
2
1
1
1
1
1
1
1
1
2
0
1
1
1
1
1
3
1
1
2
1
1
1
1
2
2
1
2
0
0
1
1
1
1
0
2
1
1
1
1
1
1
1
1
1
1
1
0
1
2
1
1
1
1
1
0
1
2
1
0
1
1
1
1
0
1
2
1
1
1
1
1
1
1
2
0
2
1
0
1
1
0
1
1
1
0
1
2
1
0
1
2
2
1
1
1
1
1
2
0
1
0
1
1
0
2
2
2
1
0
1
1
2
1
1
0
2
1
2
0
1
1
1
2
0
2
2
1
0
1
2
1
1
1
1
2
8
0
1
1
1
2
1
1
1
2
2
1
1
1
1
0
2
1
2
1
1
1
0
2
2
1
1
1
1
1
0
1
2
0
1
2
1
0
1
2
2
1
1
2
1
1
1
0
2
1
1
2
1
1
2
1
0
1
1
2
2
0
1
2
1
1
1
0
1
0
0
1
1
1
1
2
2
1
1
1
0
1
1
2
2
1
1
0
2
2
0
0
1
1
2
0
1
1
0
1
1
1
2
1
1
1
3
2
1
1
1
1
1
1
1
0
2
1
1
1
1
1
2
3
1
1
1
1
1
0
2
1
1
1
1
1
1
3
2
0
1
1
0
0
0
1
2
1
1
2
1
1
1
1
1
1
1
2
0
1
1
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
0
2
2
0
1
1
1
2
1
1
1
2
1
2
0
0
1
0
1
2
1
1
1
1
0
1
0
0
1
2
2
1
2
0
0
1
1
0
1
2
0
1
1
1
0
1
1
1
1
2
2
1
2
1
1
1
1
1
2
1
1
1
0
0
1
2
1
1
0
1
1
1
0
2
1
2
1
1
1
0
1
1
2
2
1
1
1
1
2
1
0
2
1
1
1
1
1
1
1
1
0
2
1
2
0
2
1
2
1
1
1
2
1
2
0
1
1
2
1
0
2
2
1
1
1
1
2
1
1
0
0
0
1
1
1
1
1
1
1
1
1
1
1
1
2
0
1
1
1
1
0
2
1
1
1
1
1
0
1
1
1
0
1
2
1
1
1
0
1
1
1
1
1
1
1
2
1
2
1
1
2
2
1
1
1
0
1
1
0
1
2
2
1
0
1
2
1
2
2
1
2
1
0
2
2
0
2
0
1
0
1
2
2
2
1
2
1
1
1
1
2
1
1
2
1
0
0
1
1
2
0
1
1
1
2
1
2
1
1
2
2
2
2
1
0
1
2
1
1
1
1
0
2
2
1
1
1
2
2
0
0
2
1
0
1
0
1
2
1
0
1
0
1
1
1
1
0
1
1
0
1
2
1
1
2
0
1
1
1
1
1
1
0
2
1
1
1
1
2
0
1
1
0
0
1
2
2
1
0
0
2
2
1
1
0
1
1
2
0
1
1
1
0
3
2
1
1
2
6
1
1
1
0
0
1
0
1
1
1
1
1
2
1
1
0
0
1
0
1
1
2
1
0
1
2
3
2
0
0
0
1
2
0
1
1
2
1
0
1
1
0
0
2
0
1
0
0
2
1
1
2
1
0
2
2
1
1
2
2
2
1
1
2
0
0
1
1
1
0
1
1
0
1
1
1
0
1
0
0
1
1
0
2
1
1
1
2
0
2
0
1
0
0
0
1
1
1
1
0
1
1
1
1
1
1
2
1
0
1
0
1
0
2
2
2
0
0
1
1
1
2
2
2
1
1
0
2
1
0
1
1
1
2
0
1
0
1
1
0
1
0
2
1
0
1
0
1
1
2
2
1
0
1
0
1
1
1
1
0
1
0
1
0
0
1
2
1
0
0
1
1
1
1
2
1
1
2
1
1
2
1
2
1
2
2
1
1
1
1
1
1
2
1
0
2
1
2
1
1
1
1
2
1
1
1
1
1
1
2
2
1
1
2
0
1
2
0
0
1
1
1
1
1
1
2
1
2
1
3
1
0
1
2
2
1
2
0
0
1
1
1
0
1
1
0
0
2
1
1
1
2
2
2
0
0
1
1
2
2
1
1
1
1
1
1
2
1
0
0
1
1
1
1
2
2
2
0
0
0
1
1
3
1
0
1
2
1
0
1
1
0
0
1
1
0
0
5
0
2
2
2
2
1
2
1
1
1
1
2
1
3
0
1
1
1
1
0
0
1
1
2
1
0
6
1
1
1
1
0
1
1
2
1
2
1
2
0
1
2
1
1
2
1
1
1
0
1
2
1
1
1
2
1
2
0
2
2
0
1
2
1
0
1
1
2
1
1
2
1
1
0
0
0
1
1
0
2
2
1
1
2
1
1
1
1
0
1
1
1
2
2
0
1
0
1
1
1
1
1
0
1
1
2
1
2
1
1
1
2
1
1
1
0
1
0
2
1
1
1
1
1
1
2
1
1
1
1
1
2
2
0
2
0
0
1
2
1
2
1
0
1
1
1
1
1
0
0
0
0
2
1
2
0
1
0
1
1
2
0
0
1
1
1
1
2
1
1
0
1
0
1
1
2
1
0
2
2
0
2
1
2
2
0
1
1
1
1
0
1
1
0
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
0
1
2
0
2
2
1
1
1
1
1
1
2
1
1
2
2
1
0
1
1
1
1
0
0
2
0
0
2
1
2
1
1
2
2
2
1
1
2
1
0
1
2
1
2
2
1
1
1
0
1
1
2
1
1
2
2
1
1
2
1
1
3
1
1
2
1
1
1
2
2
2
1
1
1
4
2
0
1
0
1
1
2
8
1
1
1
2
2
1
1
1
0
1
2
1
2
0
1
1
1
1
1
1
1
1
1
1
2
2
1
1
0
1
1
1
0
0
2
2
1
1
0
0
0
1
1
1
0
2
1
1
2
1
1
2
0
2
2
1
2
1
1
1
1
2
1
1
1
1
1
0
2
1
1
2
1
1
1
2
2
1
1
1
1
1
0
1
0
1
1
2
1
2
1
1
1
1
1
0
3
1
1
1
0
0
1
1
1
2
1
1
1
1
1
0
1
0
0
1
0
1
1
0
0
1
1
1
2
2
1
1
0
0
1
1
2
0
0
0
1
1
1
0
0
1
1
2
0
1
1
0
2
2
0
2
2
1
2
1
2
1
1
2
2
1
1
2
1
0
1
1
1
0
2
0
1
2
0
1
1
2
1
1
2
3
1
1
2
2
1
1
1
1
1
0
0
2
2
1
2
2
1
1
1
0
1
3
1
3
1
1
1
0
2
1
1
1
0
0
1
2
0
1
1
1
1
1
2
1
1
1
1
1
1
1
2
3
1
0
1
2
0
2
1
0
0
0
1
1
1
1
2
1
1
1
1
0
1
1
2
1
1
2
2
1
1
1
1
0
1
2
2
2
2
1
2
1
2
1
2
1
2
1
1
0
2
0
0
2
2
0
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
0
1
0
1
2
0
1
1
1
1
1
2
1
0
0
1
1
1
2
1
2
0
1
2
1
2
1
1
1
2
1
0
1
1
0
1
2
2
0
2
2
1
1
1
1
2
1
1
1
0
2
1
1
2
1
0
1
1
0
2
2
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
0
2
2
1
1
2
2
2
0
0
1
1
1
2
1
2
1
2
1
1
1
0
0
2
1
1
4
2
1
0
0
0
1
1
1
1
1
1
1
2
1
2
2
1
2
0
0
0
1
2
2
1
1
2
1
2
1
1
1
1
1
0
1
0
0
2
0
2
1
1
0
1
1
2
1
2
2
2
3
3
1
1
0
1
0
0
2
2
1
2
1
0
1
1
1
0
1
1
1
1
0
1
2
0
1
1
1
1
1
0
0
1
1
1
0
0
1
1
1
1
0
1
1
1
1
2
1
1
0
0
1
1
1
1
2
1
1
1
1
1
0
2
2
1
2
1
1
1
1
2
1
0
1
1
2
1
1
0
1
0
0
2
1
1
0
1
2
2
0
2
1
1
2
1
0
2
2
1
1
1
1
1
1
0
2
1
1
1
1
1
1
1
2
1
2
2
2
1
1
1
0
0
1
2
1
1
1
1
2
1
1
1
2
0
2
1
1
1
1
2
2
2
0
1
1
1
1
1
1
1
1
0
2
2
0
1
2
2
1
2
2
1
1
1
2
2
1
2
1
1
2
1
2
0
2
0
1
1
1
2
1
2
0
0
0
0
1
2
1
1
1
1
2
1
1
0
1
1
1
1
1
1
2
0
1
1
0
0
2
0
2
2
1
1
0
1
1
1
1
0
2
1
1
1
1
1
4
1
1
1
1
1
2
1
0
2
0
0
1
1
2
2
1
1
1
1
1
0
1
2
1
2
1
1
1
1
1
1
2
0
1
2
1
1
2
1
0
1
0
1
2
2
2
1
1
2
1
1
1
1
1
0
1
1
1
1
0
1
2
1
2
0
2
0
1
2
1
1
1
1
2
1
2
1
1
2
1
1
0
1
2
1
1
1
2
0
0
1
1
0
2
2
0
0
2
1
2
0
1
1
0
2
2
2
1
4
1
1
1
1
2
2
2
2
1
1
1
2
1
2
1
0
0
2
1
2
1
0
1
1
1
1
1
2
0
1
1
1
2
2
1
1
1
1
0
1
1
1
1
1
1
1
1
1
0
1
2
1
1
1
1
1
1
1
2
1
0
2
2
2
0
2
1
1
2
1
2
1
1
1
0
0
2
1
1
1
2
2
2
0
1
0
1
2
1
1
1
1
1
1
1
1
2
2
1
1
2
1
0
2
1
1
2
2
1
1
2
1
2
1
1
0
1
0
0
1
1
2
1
1
2
0
1
0
2
0
1
1
2
1
1
0
0
1
1
2
2
1
1
1
2
0
2
0
1
1
2
2
1
0
1
1
1
1
1
2
0
1
1
1
0
1
1
1
0
1
1
0
1
1
1
0
0
2
1
1
0
2
0
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
1
0
1
1
1
1
2
1
2
2
0
2
1
1
0
1
1
0
1
1
1
1
1
1
1
2
2
1
1
0
2
1
1
2
1
1
1
1
2
1
1
1
1
2
0
1
1
2
0
1
0
1
1
1
2
0
2
0
1
1
0
1
1
0
2
1
2
2
1
1
1
2
1
1
1
1
1
1
2
0
2
0
2
1
1
2
0
2
0
0
1
2
1
0
1
1
0
2
2
2
1
0
0
1
1
2
1
0
2
1
2
0
0
2
2
1
1
0
1
0
2
0
1
1
2
0
2
0
1
1
3
0
1
1
0
1
1
3
1
1
1
1
2
0
1
1
2
1
2
1
0
1
1
2
2
2
2
0
1
1
1
1
2
0
1
1
1
2
0
2
1
1
1
0
1
0
0
2
1
2
1
1
1
1
2
1
1
1
2
1
2
1
1
2
1
2
1
1
2
2
1
1
0
0
1
2
1
1
0
1
1
1
3
0
0
2
1
2
1
2
1
1
1
1
2
2
1
1
2
1
0
1
1
2
1
1
2
1
1
0
2
2
2
2
0
1
1
1
1
1
0
1
2
0
0
1
0
2
1
0
1
1
2
0
1
0
1
1
1
1
1
1
1
2
1
0
1
1
1
0
2
5
1
2
1
1
1
2
1
1
2
1
1
0
1
1
0
0
1
1
0
1
0
0
0
1
1
2
4
1
0
1
1
1
1
2
0
1
0
1
0
1
1
0
1
0
1
0
2
2
1
1
1
0
2
2
2
0
2
1
2
2
1
2
2
1
1
2
1
1
2
1
1
2
1
2
1
2
1
0
1
1
1
1
1
1
1
1
2
1
1
0
2
0
1
1
0
1
1
0
3
1
2
1
2
2
1
1
2
1
1
1
1
2
1
1
1
2
1
0
1
1
1
2
1
1
1
2
2
0
1
1
2
0
1
1
2
1
0
1
0
2
1
2
0
1
0
2
1
1
1
1
2
2
1
0
1
1
1
2
1
1
0
0
1
3
2
0
1
0
1
1
1
1
2
0
0
1
1
1
0
1
0
2
1
1
2
1
0
2
2
1
1
1
1
0
1
0
1
2
2
0
1
1
0
0
1
1
0
0
2
1
2
1
1
1
0
1
0
1
1
3
1
1
1
1
0
1
1
0
1
2
1
2
0
1
2
0
4
2
1
0
1
1
1
1
1
1
1
1
2
1
1
2
1
1
3
2
1
1
0
0
1
0
1
2
1
2
0
1
1
1
1
1
2
1
1
1
2
0
1
2
2
1
1
2
1
1
1
0
1
1
0
0
1
1
1
0
2
1
1
2
1
2
1
3
1
0
1
1
1
1
2
1
2
2
1
0
1
1
1
1
1
1
1
0
0
3
1
1
1
1
0
1
1
1
0
1
2
1
1
2
2
2
1
1
1
0
0
1
1
0
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
2
2
1
0
2
1
1
1
1
1
1
2
1
1
2
2
2
1
1
2
1
1
2
1
0
0
2
3
1
1
1
1
0
1
1
0
1
1
0
1
1
0
2
0
2
1
2
2
0
0
2
1
2
1
1
2
1
1
1
1
1
2
1
0
1
1
1
2
0
1
1
1
2
1
1
1
1
0
2
0
0
2
1
2
1
0
1
1
1
2
5
1
1
0
1
0
1
2
2
1
1
0
2
0
1
2
1
0
1
0
1
3
2
1
1
2
0
0
0
1
1
0
1
1
1
1
1
1
1
1
1
1
2
1
0
2
0
2
1
1
2
0
1
0
1
0
1
0
2
1
1
2
1
0
2
1
1
0
1
1
1
1
1
0
2
1
0
0
1
1
0
1
1
2
0
1
1
2
0
1
2
1
0
1
1
1
1
2
2
1
1
0
1
0
2
2
1
1
1
1
2
1
1
2
1
1
2
1
0
2
0
0
1
2
1
1
1
1
1
0
2
1
1
1
1
1
2
1
1
1
2
1
0
1
2
1
1
0
0
0
1
1
1
2
1
0
2
1
1
2
1
1
1
0
1
2
0
1
2
1
1
2
1
1
1
1
1
1
0
1
1
1
0
2
0
2
2
2
3
0
1
1
1
0
2
0
2
2
2
1
1
2
7
0
2
1
0
2
0
1
1
1
1
1
2
0
1
1
1
1
0
2
1
1
0
1
2
0
0
0
0
1
1
1
1
0
2
2
1
1
1
1
1
1
2
1
2
2
1
0
1
2
1
0
3
1
1
1
2
1
1
1
0
1
0
1
0
1
1
1
1
1
1
1
1
2
1
1
0
0
2
1
1
1
1
2
0
1
2
1
2
1
2
1
1
2
1
2
1
1
1
1
2
2
1
0
2
2
1
1
1
2
1
2
2
0
1
0
1
1
0
1
1
0
2
2
1
0
1
2
1
1
1
1
1
1
0
1
1
1
1
1
1
1
0
0
1
2
0
1
1
2
1
1
0
0
0
0
1
1
0
2
1
1
2
2
1
1
1
1
1
0
0
1
1
1
1
2
1
1
2
2
7
1
1
1
2
1
0
2
1
0
1
0
2
0
2
2
1
1
2
1
0
1
1
1
1
1
1
0
0
1
1
1
1
0
0
1
1
1
1
1
1
2
1
0
1
1
1
2
1
1
2
1
2
1
0
1
0
1
1
1
1
2
2
1
1
1
2
1
0
1
1
1
1
1
2
1
1
0
1
1
1
1
0
1
1
1
1
2
1
1
0
1
2
0
1
2
0
0
2
1
1
2
0
1
1
1
2
1
1
1
0
1
1
1
1
1
0
2
1
1
2
1
0
1
1
4
1
2
1
0
1
1
1
1
1
1
0
1
0
0
0
1
1
1
0
2
1
1
0
2
0
1
1
1
1
1
2
2
0
0
1
1
2
1
1
1
1
2
2
1
0
2
0
2
0
1
0
2
1
0
1
1
1
0
1
1
1
0
2
1
1
0
2
1
2
0
1
2
1
2
1
0
1
2
1
0
1
1
2
1
1
1
1
2
1
2
2
0
1
1
1
1
0
1
1
1
1
2
1
0
1
1
1
1
1
1
0
1
1
2
2
1
1
2
1
2
1
2
1
1
2
1
1
0
1
1
0
1
1
2
1
1
1
1
0
1
1
2
2
1
1
1
0
2
2
0
2
2
2
2
1
1
0
1
1
2
2
2
2
1
0
1
1
0
1
2
1
1
1
1
1
1
2
2
0
0
1
0
0
0
1
1
2
1
1
0
0
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
0
2
0
1
1
1
0
0
1
1
2
1
0
0
1
1
1
1
1
0
1
0
2
0
1
1
1
2
0
2
1
2
0
2
1
0
0
0
1
1
1
2
2
0
1
2
1
1
1
2
0
1
0
2
1
1
1
1
1
1
1
1
0
1
1
1
1
2
0
1
0
0
1
1
2
1
1
2
1
2
1
1
2
6
1
1
1
2
2
0
2
0
1
1
1
1
1
1
4
2
1
1
1
1
1
1
1
1
2
0
0
1
1
2
1
2
0
1
2
1
2
1
2
1
1
1
1
1
1
2
2
0
2
0
2
2
1
1
1
1
1
1
1
2
1
2
2
1
0
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
2
2
1
1
2
0
1
1
1
1
1
1
1
1
0
1
1
0
0
1
2
1
1
0
1
2
2
1
0
1
1
1
1
1
1
2
1
1
1
1
0
0
1
1
1
1
2
1
1
2
1
3
2
1
0
1
1
1
3
1
1
1
0
1
0
1
1
1
1
2
0
1
0
0
1
1
2
0
2
2
1
2
1
1
1
1
2
3
1
2
1
1
2
1
2
1
0
1
0
1
1
1
1
0
1
1
1
1
0
2
1
1
0
1
0
1
1
1
0
1
0
2
2
1
1
0
1
0
1
1
1
0
1
1
1
1
2
1
1
1
1
1
3
1
1
0
0
0
1
2
1
2
1
2
2
1
1
2
1
2
1
1
0
1
1
1
0
1
1
1
1
2
1
0
1
1
1
2
1
6
0
1
1
1
2
1
0
2
1
0
2
0
1
1
1
1
2
0
1
1
1
1
0
0
1
1
1
1
2
1
0
1
0
1
1
0
2
1
2
1
2
1
1
1
0
1
1
1
2
2
1
2
1
2
1
1
1
2
1
0
1
2
1
1
1
2
1
0
1
2
1
1
1
1
2
0
1
1
0
1
2
0
2
1
1
1
0
1
1
2
0
2
0
0
2
1
1
2
0
2
1
0
2
1
1
0
0
1
2
0
2
2
1
1
1
2
2
1
2
1
1
2
2
1
1
3
1
1
2
2
1
1
1
1
1
1
0
2
0
1
2
1
1
0
1
1
1
1
1
1
2
1
1
1
1
1
0
1
1
2
2
2
1
1
2
2
1
1
1
1
2
0
0
0
1
1
0
1
2
1
1
1
2
2
1
1
1
1
1
0
1
1
2
0
1
1
1
1
0
1
1
1
3
1
0
2
1
1
1
1
1
2
2
1
2
1
1
1
1
2
0
2
2
1
1
1
0
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
2
0
2
0
1
1
0
1
2
1
1
2
1
0
2
0
0
1
1
0
2
0
1
2
2
0
0
1
0
1
0
1
1
1
1
1
0
1
2
1
0
1
2
2
1
1
1
2
0
2
2
2
2
1
1
1
0
1
1
1
1
2
1
1
2
1
1
2
1
1
2
1
1
1
2
0
1
1
1
2
0
1
1
1
1
1
2
2
1
2
0
1
3
0
0
1
0
2
1
1
2
0
0
0
2
2
2
1
1
1
1
0
0
1
1
0
1
0
2
0
1
1
1
2
1
0
1
1
1
0
1
2
1
2
1
2
2
2
0
4
1
1
1
2
2
1
0
0
1
1
0
0
2
2
1
1
3
2
2
0
1
1
1
1
2
0
2
1
1
1
1
2
0
1
1
2
1
2
2
1
1
2
1
1
0
2
1
0
1
1
0
2
2
0
0
1
2
0
1
2
1
2
2
0
1
0
1
2
1
0
1
1
0
1
2
2
2
1
0
1
1
1
1
0
1
2
0
1
1
1
1
1
0
1
2
1
2
1
0
0
0
1
1
0
1
1
2
2
1
1
1
1
2
2
2
0
1
1
2
1
1
2
1
1
0
1
0
2
2
2
1
1
1
1
1
1
2
1
1
1
1
2
0
2
1
2
2
2
2
0
1
0
2
0
3
1
1
1
0
2
0
1
1
1
1
2
1
1
2
0
3
1
1
1
1
0
1
2
1
0
1
0
0
0
1
2
0
1
0
1
2
2
1
0
1
1
1
1
0
0
3
1
1
2
1
2
2
1
0
0
0
1
1
0
1
0
2
1
1
1
1
1
2
2
0
1
0
10
1
2
1
1
1
1
0
2
2
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
0
2
2
2
1
2
1
0
1
1
0
0
1
1
1
0
2
1
0
1
1
0
1
2
0
2
2
0
1
1
2
1
2
0
2
1
1
0
0
1
1
1
1
1
2
1
2
0
1
2
0
1
1
0
0
1
1
1
2
1
2
1
1
1
1
2
1
2
2
0
1
1
1
1
1
1
0
1
1
0
1
1
1
1
1
1
0
1
1
1
1
0
0
1
1
1
1
2
1
1
0
1
1
0
0
1
1
1
1
1
2
1
1
1
0
1
1
1
2
2
1
2
2
1
0
0
1
1
1
0
1
2
1
1
1
1
1
1
2
0
1
2
0
1
0
2
2
2
1
1
2
1
1
1
1
1
1
1
1
0
1
1
1
2
1
1
1
1
1
2
2
0
0
0
1
2
1
1
1
1
1
1
1
1
1
1
1
0
0
2
1
2
1
0
0
0
0
1
1
1
1
2
2
1
2
1
0
1
1
1
2
1
1
2
1
1
1
0
1
0
1
2
1
0
0
2
1
1
1
1
1
1
2
1
0
1
1
0
1
0
0
1
1
1
1
0
1
1
1
2
1
0
1
1
0
0
1
1
1
2
2
1
1
1
2
1
2
2
1
2
1
1
0
1
1
1
2
1
0
2
1
1
1
2
0
1
2
1
1
0
1
3
0
2
1
1
2
0
1
1
1
1
1
2
1
1
1
0
1
1
1
1
1
2
1
1
0
2
2
2
0
1
0
1
0
2
1
1
1
2
1
1
1
1
1
0
2
2
1
1
1
0
0
0
2
1
1
1
1
2
2
1
2
1
0
0
1
1
1
2
2
1
1
0
2
1
1
2
2
2
0
1
1
1
0
2
0
2
1
1
0
1
2
1
1
1
0
1
1
0
1
1
1
2
1
1
1
2
0
1
1
1
1
1
1
0
0
1
0
3
2
2
0
0
1
1
1
1
1
1
1
1
0
1
1
0
0
0
2
1
1
0
1
0
1
0
1
2
1
2
0
1
2
1
2
0
1
1
1
0
2
1
1
0
2
1
0
1
1
0
2
1
2
1
2
1
1
2
1
1
1
1
0
1
0
2
1
1
2
1
1
2
2
1
1
1
1
1
0
2
0
1
1
0
1
2
2
3
1
1
1
0
1
2
2
0
2
0
2
0
1
2
2
1
2
2
1
1
2
2
1
0
1
0
1
1
1
2
1
1
2
1
2
0
1
1
1
2
3
2
2
0
1
2
0
0
1
1
0
1
1
2
0
1
2
0
0
1
0
1
1
1
1
2
1
1
2
1
2
1
0
1
1
1
2
1
1
0
1
1
1
1
1
2
1
1
0
1
1
1
2
1
2
1
2
1
1
1
1
1
1
2
1
0
0
2
1
1
1
2
1
1
2
1
2
0
1
2
2
1
1
1
1
2
2
0
2
0
0
1
1
1
1
2
0
1
2
0
0
0
0
2
0
0
1
1
1
1
2
1
1
0
0
1
1
0
0
1
1
1
1
2
0
1
2
2
0
2
1
2
2
1
0
0
0
2
0
1
1
0
1
1
2
1
0
2
1
1
1
1
0
0
3
0
1
0
1
2
2
0
1
0
1
1
1
0
1
0
0
0
2
1
2
1
0
1
1
1
1
1
0
2
0
2
1
0
1
2
1
1
0
0
1
2
2
1
1
1
1
1
2
0
2
2
0
1
2
1
1
0
0
0
2
2
2
1
2
2
0
2
2
1
1
1
1
0
2
1
1
1
2
2
0
1
1
0
1
1
0
1
1
1
1
2
1
1
1
1
2
2
2
0
1
2
0
1
1
2
2
1
1
1
1
1
1
1
1
0
0
1
0
1
2
0
1
1
1
0
1
2
1
0
1
1
1
1
1
0
2
1
1
1
1
1
1
0
0
0
1
2
1
1
1
1
1
1
1
1
1
1
1
1
0
0
2
1
1
2
1
0
0
1
0
2
1
1
0
1
1
2
1
1
0
2
2
1
2
2
1
0
0
2
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
0
1
1
1
1
2
2
1
1
2
1
1
2
1
1
1
1
2
1
2
2
0
1
2
0
1
1
1
3
1
1
1
2
0
1
0
0
1
1
1
0
2
2
0
1
2
1
2
1
2
2
0
1
2
2
1
0
2
1
1
0
1
1
0
1
1
1
2
2
1
0
1
2
1
2
2
0
1
1
1
1
1
0
2
1
1
2
1
2
0
1
1
0
0
1
1
1
1
0
2
2
1
1
0
1
1
0
2
2
0
0
1
1
1
2
1
1
0
2
0
1
0
2
2
0
2
1
1
4
2
0
1
1
1
1
1
0
2
1
1
1
1
1
1
1
0
1
1
1
2
1
1
2
2
0
2
0
1
2
1
1
1
0
1
1
2
1
2
1
1
2
2
3
0
1
1
1
0
1
2
1
1
0
1
0
1
2
2
2
2
0
1
1
2
1
3
1
1
1
0
2
1
0
1
0
0
0
1
1
1
1
0
0
0
1
0
1
0
3
1
3
0
2
1
1
1
1
2
0
2
2
1
0
1
4
1
2
2
1
0
2
2
1
1
0
1
1
1
1
1
1
2
1
1
2
1
2
1
1
0
1
1
1
2
2
1
0
0
1
1
2
1
1
0
1
1
1
2
1
1
1
1
0
1
1
1
1
1
1
1
2
1
0
1
1
1
0
2
1
2
0
2
1
1
1
1
1
0
1
2
1
2
2
3
0
1
1
1
0
2
1
0
1
1
1
2
2
2
2
0
1
2
0
2
2
1
1
2
0
1
2
1
1
1
1
0
1
1
1
0
0
1
1
2
1
1
0
2
1
1
2
1
2
1
1
0
0
2
1
1
2
2
1
0
2
2
1
2
2
2
1
2
0
0
1
1
2
1
2
0
2
2
1
1
1
0
1
1
1
1
1
1
2
1
2
2
0
2
0
1
1
1
1
0
0
0
1
1
2
0
1
2
0
1
1
0
1
1
1
1
2
1
1
0
2
1
0
1
1
1
1
0
1
2
0
0
1
2
2
2
0
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
0
2
2
1
1
1
1
2
1
1
1
1
1
0
2
0
0
1
1
1
1
2
1
2
1
0
1
1
1
0
1
0
0
1
0
1
0
2
1
1
1
2
1
1
1
2
1
0
1
0
1
1
1
1
1
0
2
1
1
0
1
1
1
1
1
1
2
1
1
1
2
1
3
2
1
0
2
1
0
2
5
1
2
1
2
0
0
1
1
2
0
1
2
2
1
2
0
2
9
1
1
2
1
0
1
1
1
1
0
1
2
1
1
1
0
2
2
2
1
1
1
2
1
1
2
1
2
2
1
0
0
1
0
2
1
2
1
2
2
1
1
1
2
1
0
1
0
0
1
2
1
2
0
1
2
2
1
1
1
2
1
1
0
1
1
0
1
2
2
0
1
1
1
1
0
1
1
2
2
0
0
2
0
0
1
2
0
0
2
1
2
2
2
1
0
0
0
2
2
1
1
2
1
1
2
1
0
2
0
1
2
1
0
2
1
0
0
1
2
1
1
1
2
1
0
2
1
1
1
2
2
1
1
1
1
1
1
0
1
2
1
1
5
1
1
1
0
1
2
1
2
1
1
3
0
1
2
1
2
0
1
1
0
1
2
1
0
1
1
1
1
2
2
1
1
1
0
1
2
1
2
0
1
1
1
1
0
1
1
1
1
1
1
2
1
0
2
1
1
0
0
1
1
2
1
1
0
2
1
1
1
2
1
1
2
2
1
1
1
2
1
2
0
1
2
0
1
1
1
1
1
2
2
1
1
1
2
1
0
1
1
1
1
1
1
2
1
1
2
2
1
0
0
0
2
1
2
1
1
1
1
1
2
0
1
1
1
0
1
1
1
1
0
0
1
1
1
0
1
1
0
2
1
0
1
1
2
2
0
1
1
2
1
1
1
2
0
1
1
1
2
0
2
2
1
0
0
1
0
1
2
1
0
0
1
0
1
1
0
2
1
1
2
0
1
2
2
2
0
1
1
1
1
2
2
1
1
1
1
2
1
0
2
0
1
2
1
0
0
0
1
2
2
2
1
0
1
1
0
1
1
2
1
1
1
2
0
2
1
1
1
1
1
1
1
0
1
1
2
2
1
1
2
1
1
1
1
1
1
1
0
2
2
2
1
0
1
1
1
1
1
2
0
1
0
1
1
2
1
1
1
1
2
1
1
1
1
0
1
2
2
2
2
0
1
1
1
0
1
2
0
2
1
0
1
0
2
1
1
1
1
1
1
0
0
1
1
1
0
1
1
2
1
1
1
1
2
2
1
0
1
2
2
1
0
2
2
2
1
2
1
2
2
2
1
2
1
2
1
0
2
1
1
1
1
2
0
1
3
1
1
2
2
0
1
1
1
1
1
1
2
1
1
2
0
1
0
1
0
0
2
0
1
0
1
1
1
2
2
1
1
2
1
0
0
1
0
1
0
1
1
1
2
1
0
2
1
1
0
1
1
0
1
2
0
2
1
1
1
0
1
0
2
2
2
0
3
1
1
1
0
1
1
1
1
1
0
1
1
1
1
0
1
2
0
1
1
1
2
0
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
2
0
0
1
1
1
0
2
1
1
0
1
1
1
3
0
1
0
0
2
1
1
2
1
1
1
2
1
2
1
2
1
1
1
1
1
1
0
1
1
1
1
1
1
1
2
2
1
2
1
1
0
1
1
1
1
2
1
0
1
1
1
1
0
2
1
0
1
2
1
1
2
1
1
1
0
1
1
0
1
1
1
1
1
1
2
1
0
0
2
0
1
2
1
2
2
2
2
0
0
1
0
2
1
0
1
1
1
1
1
1
2
0
1
0
2
0
1
0
2
2
1
2
1
2
0
2
1
1
1
0
0
1
1
1
1
2
0
1
2
1
3
2
1
0
1
1
1
1
2
1
0
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
1
2
1
0
2
2
0
2
2
1
2
0
1
2
1
0
2
2
0
1
1
2
1
1
2
2
1
0
2
1
0
1
1
1
1
1
3
1
1
1
1
1
1
0
0
2
1
0
2
2
0
2
0
2
2
1
1
0
4
2
1
0
2
1
1
1
1
1
1
1
1
1
1
0
0
1
1
2
1
2
1
1
1
1
1
1
1
0
2
1
1
2
0
1
1
1
2
0
2
1
1
0
2
1
1
0
1
1
1
0
1
1
2
0
1
1
1
1
0
2
1
1
1
1
1
1
1
1
0
0
1
1
0
1
2
0
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
2
1
0
0
1
1
0
1
1
0
1
2
1
1
1
1
0
2
1
0
2
0
1
2
0
1
0
0
0
1
1
1
0
1
2
1
2
1
1
2
1
0
1
1
1
1
1
2
0
2
2
1
1
0
2
0
1
1
2
1
1
1
1
0
0
3
1
1
1
1
2
1
2
1
1
2
2
1
1
2
2
1
2
0
1
1
1
1
1
1
0
2
1
2
2
1
2
0
1
1
1
1
0
1
1
1
1
1
1
3
1
2
0
2
2
0
1
2
0
1
1
1
0
2
1
1
2
2
0
1
1
0
1
0
1
1
1
1
2
0
1
0
1
2
1
1
0
1
0
2
0
1
1
0
1
1
1
1
1
1
2
1
2
2
1
0
2
1
0
0
0
1
1
1
5
1
1
0
0
1
1
1
1
1
1
1
1
0
0
1
1
0
1
2
1
2
0
1
0
1
0
2
1
1
1
2
1
1
2
2
2
0
1
0
2
0
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
0
1
1
2
0
0
0
1
1
2
1
0
2
2
0
1
2
1
2
0
1
1
1
1
1
1
1
5
2
0
1
1
1
0
1
0
1
1
0
0
2
2
1
1
1
1
1
1
2
1
1
1
0
0
1
1
1
2
1
1
2
0
0
1
0
0
1
1
2
1
2
0
2
1
0
0
2
1
1
1
0
2
1
1
2
1
1
1
1
1
0
2
1
2
1
2
1
2
2
0
2
1
0
1
1
1
2
1
0
2
0
2
3
2
1
2
1
1
1
2
1
1
1
0
1
2
1
0
1
1
1
1
1
2
1
1
1
2
0
2
1
1
0
2
0
1
1
0
1
2
0
1
1
1
1
2
0
1
2
2
1
2
1
1
0
0
3
0
1
2
2
0
1
1
2
1
1
2
0
1
1
1
2
2
0
1
1
1
2
3
2
1
0
1
1
2
1
1
2
1
1
1
1
1
0
0
1
1
1
2
0
1
0
1
1
0
1
1
1
1
2
1
0
0
1
1
2
0
1
1
1
1
2
1
2
0
1
1
2
1
0
0
2
2
2
0
2
2
0
0
1
1
1
1
2
2
2
1
2
0
1
1
2
1
1
1
0
0
1
1
2
2
1
1
1
1
1
2
2
1
0
1
2
1
2
1
1
1
1
3
1
1
1
0
1
1
1
1
0
1
1
1
0
0
0
1
2
2
1
2
2
2
2
0
1
1
2
1
2
1
1
1
1
1
1
2
1
1
0
0
1
2
3
0
1
1
1
1
1
1
1
0
1
2
1
1
1
1
1
0
1
0
1
2
0
0
1
1
2
0
1
0
2
1
1
1
2
1
1
2
1
1
3
1
1
1
2
2
1
1
1
2
1
2
1
2
1
1
1
1
1
2
1
1
1
1
2
0
1
0
1
1
2
0
1
1
1
1
0
1
0
2
0
2
0
2
1
2
0
0
2
1
1
1
1
2
1
0
1
1
1
1
1
0
1
0
2
1
0
0
0
2
2
2
2
2
1
0
0
2
0
1
0
1
2
2
0
0
2
1
1
1
2
0
1
1
1
1
1
1
1
1
1
1
1
1
2
1
0
2
1
0
2
1
1
0
1
1
1
0
1
1
1
1
0
2
1
2
1
2
1
1
1
2
0
0
1
1
2
1
1
0
1
1
2
2
2
1
0
2
0
2
1
1
2
1
1
2
2
0
1
3
0
1
0
2
1
0
2
0
1
1
2
1
2
2
0
1
2
1
1
2
2
1
1
2
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
0
1
1
2
1
0
1
2
1
1
0
1
2
0
1
1
1
1
2
1
1
1
1
2
2
0
1
2
1
0
1
1
1
2
0
2
1
0
1
1
2
1
0
1
2
0
2
2
2
1
1
1
1
1
1
1
1
1
0
1
0
1
2
1
1
0
2
1
0
1
2
0
2
1
1
1
0
1
1
1
1
1
0
1
1
0
1
1
1
2
1
1
0
0
1
1
1
0
2
1
1
0
2
1
1
1
1
1
1
1
1
1
1
0
1
1
2
1
0
2
1
1
1
0
0
1
1
2
1
2
1
0
1
2
0
1
1
1
0
1
1
1
2
0
2
1
0
1
1
2
2
1
1
1
1
0
1
1
1
1
1
1
1
1
1
0
1
2
0
1
1
2
1
0
1
1
1
1
1
1
1
2
2
1
1
2
1
0
1
1
2
2
1
1
1
1
2
0
1
2
2
1
1
0
1
1
1
1
1
2
1
2
1
2
1
1
2
2
1
2
1
2
0
2
0
1
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
0
2
1
1
2
1
1
0
1
1
0
1
1
0
1
1
1
2
1
1
1
1
0
2
0
1
1
1
1
2
1
2
1
1
0
1
0
1
1
2
1
2
1
1
1
1
1
1
0
1
1
1
1
2
2
2
1
0
1
2
2
1
1
0
0
1
0
1
1
2
1
2
2
1
2
1
1
1
0
1
1
0
1
1
0
0
1
2
1
1
2
1
1
1
0
2
1
2
1
1
1
0
2
1
1
2
1
2
2
1
1
2
2
0
1
2
1
2
2
1
2
1
1
1
1
1
0
0
1
1
0
2
2
1
0
1
1
1
1
2
0
1
0
1
1
2
1
2
1
1
1
1
2
1
1
2
1
0
0
1
2
2
0
1
1
2
0
1
1
1
1
1
1
0
1
1
1
1
1
2
2
1
1
1
1
1
1
1
0
1
2
0
1
2
2
0
1
1
1
1
1
2
1
2
1
3
2
1
2
2
1
1
2
0
1
1
0
1
1
0
1
1
1
1
0
0
0
1
0
0
1
2
1
1
0
2
1
0
0
2
1
1
1
1
1
0
2
1
1
1
2
1
1
1
2
0
1
1
2
1
2
1
1
0
1
2
1
2
0
1
1
1
2
0
1
2
1
2
1
1
2
1
2
1
1
0
1
1
0
1
1
1
1
1
0
1
2
1
0
2
2
1
1
1
2
2
2
1
1
1
1
1
1
1
2
1
1
1
2
1
1
0
1
5
1
2
0
1
0
1
0
0
1
2
1
1
0
1
0
2
1
1
2
1
1
2
2
2
1
2
0
1
1
2
1
1
1
2
2
1
0
2
1
1
2
1
1
1
1
1
1
1
1
3
1
1
2
1
1
1
1
1
2
0
1
1
1
1
1
1
2
0
1
1
1
2
1
2
1
0
1
1
1
1
1
0
2
1
1
1
1
1
1
1
2
1
1
2
2
1
1
1
2
1
1
0
1
1
1
2
1
1
0
0
0
2
0
1
1
0
1
1
2
1
1
1
1
0
2
1
1
2
0
1
1
1
2
0
0
0
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
2
1
0
2
0
1
0
0
2
0
1
0
1
2
1
0
1
1
1
1
1
1
2
2
1
1
1
0
2
1
0
2
1
2
1
1
2
0
2
2
0
2
0
1
0
1
0
2
0
1
1
2
2
0
1
1
1
0
1
1
1
2
1
2
2
1
0
1
1
1
2
0
1
0
1
2
2
2
1
2
1
1
2
0
1
2
1
0
2
1
1
1
2
2
1
2
1
2
0
1
1
1
1
0
1
0
0
1
2
1
2
2
0
0
2
1
0
1
2
1
1
2
0
2
1
2
1
1
1
1
1
2
0
1
1
2
1
0
0
1
1
1
0
3
1
2
1
1
3
1
1
1
0
1
2
2
1
0
0
2
1
1
1
1
0
1
2
0
1
1
1
0
1
1
2
1
0
1
1
2
1
2
1
1
0
1
2
1
1
1
1
2
1
1
1
1
2
2
0
1
1
1
1
1
1
2
1
1
1
2
0
0
1
1
1
1
1
2
1
1
1
2
1
1
1
0
2
1
1
1
1
1
0
2
1
2
1
0
2
1
1
2
1
1
1
1
1
1
1
1
0
2
0
0
1
1
1
0
0
1
1
2
1
1
1
0
0
1
0
1
0
1
1
1
1
1
1
2
1
1
2
1
1
1
0
2
0
1
2
2
1
1
1
1
0
2
2
1
1
2
1
2
0
1
1
1
0
1
0
1
0
0
0
1
1
1
2
1
1
1
2
2
1
1
0
1
1
1
1
1
1
1
1
1
2
2
0
1
0
1
1
0
1
0
2
2
1
2
1
1
2
1
2
2
1
1
2
1
1
1
1
1
2
2
1
1
1
0
1
0
2
1
0
2
1
0
1
1
1
1
1
2
0
1
2
0
1
2
1
1
1
1
2
1
2
0
0
1
1
1
1
2
1
2
2
1
0
1
1
1
0
1
1
1
1
2
2
1
1
0
2
2
1
0
1
2
2
1
2
1
0
1
1
1
1
1
1
0
1
2
0
0
1
2
1
2
1
1
1
1
1
0
1
1
1
1
1
2
1
1
0
2
2
0
1
1
2
2
1
0
1
1
1
2
1
1
2
0
2
2
1
1
1
1
1
1
1
0
1
0
1
1
0
1
3
2
2
0
2
1
0
1
1
1
0
1
1
1
1
1
0
1
1
1
2
1
2
0
1
1
2
1
1
3
1
1
1
1
2
2
0
1
1
1
1
2
1
2
1
1
1
1
2
0
2
1
1
1
1
1
2
2
2
2
1
0
1
1
1
1
1
0
1
0
0
0
2
1
2
1
1
1
2
0
1
1
0
1
1
2
1
0
1
0
1
1
1
1
1
0
1
0
1
2
1
1
1
2
1
2
1
1
2
1
1
2
2
1
1
1
1
1
0
1
2
1
1
1
1
1
2
1
2
1
1
1
1
2
0
0
1
1
0
1
2
0
1
0
2
1
2
1
1
2
0
1
3
1
1
1
2
1
1
1
1
1
2
1
1
2
1
1
1
2
1
2
0
1
1
1
0
0
1
1
2
2
1
1
1
1
4
2
1
1
1
1
0
6
1
1
1
1
1
1
0
2
2
2
1
1
1
2
2
2
2
1
0
1
1
1
1
2
1
0
1
2
1
1
1
1
1
1
1
0
2
0
3
1
1
1
3
1
1
2
2
1
1
1
2
0
1
1
1
1
2
1
0
0
0
0
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
0
0
1
1
1
2
2
1
1
2
1
1
1
1
0
0
0
2
1
2
0
1
1
1
2
1
1
1
1
1
1
0
0
1
1
1
0
2
2
1
1
0
1
1
2
2
0
1
1
1
1
1
1
0
0
2
1
1
1
1
0
1
1
1
1
1
2
1
1
1
1
1
2
1
0
1
1
0
1
1
0
1
1
2
1
2
1
0
0
0
1
1
1
1
1
1
2
2
1
1
2
2
0
0
1
2
2
1
1
2
1
1
0
1
2
1
2
1
1
1
1
0
2
1
1
0
1
1
2
1
1
2
0
1
1
1
1
1
0
1
1
1
1
1
0
2
0
2
1
0
0
0
1
1
2
1
1
1
0
2
1
0
0
1
1
0
1
1
0
1
1
1
1
1
2
0
1
1
1
0
1
0
0
2
1
1
1
1
1
0
1
0
1
1
1
1
1
1
2
0
2
1
1
1
1
2
2
2
1
2
1
0
2
2
2
1
1
1
2
1
1
1
2
1
2
1
0
2
1
2
1
2
1
0
0
0
1
1
2
1
1
1
2
1
2
1
0
1
0
2
1
1
1
1
1
0
1
1
1
1
1
0
1
1
1
0
2
1
1
1
1
1
2
0
1
1
1
0
0
1
3
2
1
2
1
1
0
2
1
1
0
2
2
1
1
0
0
1
1
1
1
1
0
2
1
2
0
1
3
2
2
1
1
1
1
0
0
2
1
2
2
1
1
0
1
2
1
2
0
1
1
1
1
1
2
1
1
0
1
1
1
1
1
1
0
1
1
1
0
0
0
1
2
1
2
0
2
2
0
1
0
0
1
1
1
2
2
1
1
2
1
1
2
1
2
2
1
2
1
1
1
1
2
1
1
1
1
2
1
0
2
0
2
1
2
1
0
1
1
1
0
0
1
1
1
2
0
0
1
2
2
0
0
2
1
1
1
1
1
2
1
2
1
2
0
1
0
1
1
1
2
1
1
2
1
1
1
1
1
2
2
1
2
1
2
1
2
2
0
2
2
1
1
2
1
2
2
1
2
1
0
0
1
1
1
1
1
0
0
2
2
0
0
2
2
0
1
1
1
2
0
2
0
1
2
1
1
1
1
1
1
0
0
1
1
1
0
1
1
1
1
2
1
2
1
1
1
2
2
1
1
1
1
1
0
2
1
0
1
1
2
1
2
2
0
1
0
1
2
1
1
0
1
1
1
1
1
1
0
1
1
1
1
1
0
0
2
1
1
0
1
2
1
2
0
2
0
1
0
0
1
1
0
2
1
1
1
1
2
1
1
0
1
1
2
1
1
2
1
2
1
2
2
2
4
1
2
2
0
1
1
1
0
2
1
1
0
2
1
1
1
0
1
1
2
1
1
0
1
1
1
2
1
0
1
1
1
2
1
1
2
0
1
1
0
1
0
0
1
1
1
1
2
1
2
0
1
1
2
2
1
1
1
2
1
2
1
1
0
1
2
0
0
0
1
1
1
1
2
1
1
1
1
1
1
1
2
0
2
2
1
1
1
1
1
2
0
0
1
1
1
0
1
2
1
1
0
2
0
1
0
1
1
1
0
1
1
1
2
0
1
1
1
1
1
1
2
2
1
1
1
1
1
0
2
1
2
1
1
2
0
1
1
0
0
2
0
0
1
0
2
1
0
0
2
1
0
2
1
1
1
1
2
1
1
1
1
2
1
2
2
1
0
1
2
1
2
1
1
2
2
1
1
0
1
2
2
2
2
1
2
0
1
1
0
1
0
1
1
1
2
0
1
1
1
0
1
1
1
2
2
2
2
1
1
2
1
2
1
1
1
0
1
1
2
1
0
0
2
1
1
0
2
0
0
0
2
0
2
2
1
1
1
1
1
1
1
1
1
1
1
0
2
2
2
2
1
1
2
1
1
1
2
1
2
0
2
1
0
1
1
1
2
2
2
1
0
2
1
0
1
1
1
1
0
1
1
1
0
1
1
1
0
1
1
1
2
1
1
1
2
2
1
2
1
1
1
2
1
0
1
1
2
2
2
0
1
1
2
1
0
1
1
1
1
1
1
2
1
1
4
1
1
1
1
1
1
2
2
1
1
2
1
0
2
1
1
2
1
1
1
1
0
1
2
1
1
2
0
1
1
2
1
1
0
2
2
2
0
1
1
2
1
0
1
1
2
1
0
2
1
1
0
2
0
1
1
2
1
1
2
1
1
1
2
2
2
1
1
2
1
3
2
0
0
1
1
0
1
1
1
1
2
0
1
2
1
2
1
1
1
1
2
1
2
1
2
1
0
1
2
0
2
2
0
1
1
0
1
1
1
1
1
1
1
0
2
1
1
1
1
0
0
2
1
1
2
2
0
1
2
1
2
0
2
1
1
1
2
2
1
1
0
2
1
2
2
1
2
1
1
1
0
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
2
1
1
2
1
1
0
1
1
2
0
1
2
2
0
1
1
1
1
2
0
2
1
1
1
1
1
2
2
1
1
2
2
1
1
1
0
2
0
2
1
0
0
2
2
0
1
2
2
0
1
2
0
1
2
2
1
1
1
1
1
2
2
2
1
1
2
2
1
1
1
1
2
1
0
2
1
2
0
3
0
0
0
2
2
2
1
1
2
2
1
1
1
1
2
0
1
1
1
1
1
1
0
2
2
2
1
0
1
1
1
1
1
2
0
0
1
1
1
1
2
1
0
1
1
3
1
1
1
2
1
1
2
0
0
1
2
1
0
1
1
1
2
3
1
1
1
2
1
1
2
1
0
1
1
1
0
2
1
0
0
1
1
1
2
0
2
0
1
0
1
0
1
1
1
2
1
1
2
1
1
1
1
1
0
1
1
2
1
2
1
0
0
2
1
1
2
0
1
2
1
0
2
2
1
1
1
0
2
0
1
0
2
1
2
3
2
1
1
1
0
1
1
1
1
1
1
0
1
1
1
6
1
1
1
1
1
1
1
1
1
0
1
0
0
0
1
2
2
1
1
2
3
1
2
0
2
1
2
1
1
1
0
1
1
1
1
1
0
0
0
1
0
1
1
0
2
2
1
1
2
1
1
0
0
1
1
1
1
1
0
1
1
1
1
2
2
1
1
0
2
0
0
1
2
1
1
0
2
1
1
1
1
2
0
2
0
0
1
2
1
2
1
0
1
0
1
1
1
2
2
1
1
1
1
1
1
2
2
1
1
0
1
1
2
1
1
1
2
1
2
1
1
2
1
1
0
1
1
2
1
4
1
0
1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
0
1
1
0
2
2
1
0
1
3
0
0
1
0
1
0
1
2
0
1
2
1
0
1
2
1
1
1
2
1
1
0
2
0
1
1
0
2
1
1
1
2
1
2
1
1
2
1
0
1
1
1
1
2
0
0
2
2
0
1
2
1
1
2
1
0
2
1
0
0
1
0
1
1
0
0
1
1
1
2
0
1
0
2
1
0
0
1
0
2
1
0
1
1
0
1
1
1
2
1
1
2
0
1
0
2
1
2
2
0
1
1
1
1
1
1
1
1
1
0
1
0
1
0
0
2
1
0
1
1
1
1
1
0
1
0
2
2
2
2
1
0
2
1
1
2
2
1
2
4
1
0
0
2
1
2
2
1
2
1
1
0
0
0
1
2
1
0
2
2
1
0
0
0
2
1
1
1
0
1
0
2
2
1
0
1
1
1
1
2
1
1
1
0
2
2
1
1
2
1
1
0
1
1
1
1
1
0
2
1
0
1
0
1
1
1
1
0
0
0
0
0
1
1
1
0
1
1
0
1
2
1
1
1
1
0
1
2
3
1
1
1
2
1
1
1
1
0
2
2
1
1
0
1
1
1
1
0
1
2
1
1
1
1
1
0
1
1
1
1
2
2
1
1
0
1
1
1
1
1
2
1
1
1
1
2
0
1
1
2
0
1
0
2
1
1
1
0
1
1
1
2
1
1
1
0
2
1
1
1
1
2
1
2
1
0
1
1
1
1
0
1
1
2
3
2
1
1
2
0
2
1
1
2
1
1
1
1
0
0
1
0
1
1
2
1
1
0
1
1
1
1
1
2
2
1
0
0
1
1
1
1
1
1
2
1
1
1
1
1
0
1
1
1
1
2
1
0
1
1
1
2
0
1
0
1
1
1
1
1
2
0
0
0
2
0
2
1
1
1
1
0
1
1
1
1
1
1
1
1
0
1
1
2
1
2
0
1
1
2
1
1
2
1
1
2
1
1
1
2
1
0
0
2
0
1
2
2
2
3
0
1
1
1
1
1
1
2
2
1
2
1
0
2
1
0
0
0
2
1
2
0
2
1
2
2
0
1
1
1
1
0
2
3
0
2
1
1
2
2
1
1
0
1
0
0
2
1
2
1
0
1
2
1
1
0
1
0
1
1
0
0
0
0
2
2
1
1
1
1
1
2
0
1
2
1
2
0
1
2
1
1
1
1
0
1
1
1
1
1
1
0
1
1
1
0
1
1
2
0
1
1
1
1
1
1
1
1
1
2
1
1
0
2
1
0
1
1
1
0
1
1
1
0
0
1
1
2
0
2
1
1
1
1
1
1
1
3
1
1
0
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
2
2
1
1
1
2
2
1
1
1
2
1
1
0
2
1
1
1
1
2
1
0
0
1
1
0
1
0
1
1
1
1
1
0
1
2
1
1
2
1
1
1
1
1
1
2
3
1
3
0
2
2
0
1
1
0
1
2
1
0
0
2
1
1
1
1
1
2
1
0
1
2
1
1
1
0
2
1
0
1
1
1
1
1
0
1
1
1
1
1
1
0
1
1
2
1
1
1
1
1
1
1
1
1
1
0
2
2
2
1
1
1
1
1
1
1
2
0
1
2
1
1
2
2
2
2
1
2
1
0
1
1
0
2
4
0
2
1
1
1
2
2
2
1
1
0
2
1
2
2
2
0
1
1
1
1
2
2
1
2
1
3
1
1
1
1
2
1
1
0
1
1
0
1
1
1
1
1
1
0
1
1
1
0
2
1
2
1
0
2
2
0
1
1
2
1
1
1
2
1
2
2
0
1
1
1
1
2
2
1
0
1
1
1
0
1
0
1
1
0
1
1
0
0
1
2
1
0
2
1
2
1
2
1
1
2
1
1
2
1
0
1
0
0
1
1
0
0
1
0
1
1
1
0
1
1
0
1
0
1
1
2
1
1
1
1
0
1
1
0
0
0
2
1
2
1
1
0
1
1
1
2
1
0
1
2
1
2
1
1
1
1
1
1
2
0
2
1
0
1
2
2
1
1
0
1
1
0
1
1
1
1
1
2
1
1
2
1
1
1
0
2
1
6
2
1
2
1
0
1
1
1
0
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
2
1
1
1
1
0
1
1
1
1
0
1
0
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
1
3
1
0
1
2
1
1
2
2
0
1
1
1
1
1
2
2
3
2
1
1
0
2
0
1
0
2
1
1
2
2
1
1
2
2
1
1
2
1
2
2
1
1
1
1
1
2
2
1
1
1
2
2
1
0
1
1
1
0
2
2
1
1
2
2
1
2
1
1
2
3
1
1
0
1
2
1
1
2
1
1
1
1
1
1
2
2
2
0
2
1
1
0
2
1
1
1
1
1
1
0
1
0
1
2
1
0
1
1
1
0
1
1
1
1
2
0
1
1
1
2
2
1
2
2
1
2
0
1
0
1
1
1
0
0
1
2
1
2
1
1
1
1
1
0
3
1
1
1
1
1
0
2
1
0
2
1
1
2
0
2
1
0
2
1
1
0
0
1
1
1
2
2
1
1
1
2
0
0
1
1
1
1
0
1
1
1
0
1
2
1
1
1
2
3
1
0
0
1
0
2
1
1
1
3
1
1
0
2
1
1
0
1
1
1
1
2
1
1
2
1
2
0
0
0
1
0
1
1
1
0
1
1
1
0
1
0
1
1
0
1
1
0
1
1
0
0
1
1
2
1
0
2
2
1
2
1
1
0
1
2
2
2
0
2
1
1
1
1
1
0
1
1
1
1
1
1
1
0
1
1
1
2
1
2
2
1
0
1
1
1
1
0
1
1
1
1
1
0
1
1
1
1
2
1
0
1
0
0
1
1
0
1
1
1
2
5
1
2
1
2
1
0
1
1
1
1
0
0
0
1
2
2
2
1
2
1
1
0
0
0
1
1
0
2
1
1
2
1
1
1
2
1
1
2
1
1
0
6
0
2
2
1
1
1
1
0
2
1
1
1
0
2
2
2
1
2
1
2
1
1
0
2
2
2
0
0
2
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
1
2
1
0
0
1
1
1
1
1
1
2
1
1
0
1
1
1
1
1
2
1
1
1
0
1
0
2
1
1
1
1
1
2
1
2
2
1
1
1
2
0
1
2
1
3
1
1
1
1
1
1
1
1
1
1
2
0
0
1
1
1
1
2
1
0
1
2
1
2
1
1
1
1
0
2
1
1
1
1
1
1
1
0
0
1
2
1
0
1
1
0
1
2
0
1
0
1
0
2
1
1
1
1
0
0
1
0
1
2
1
1
2
1
1
0
1
2
1
1
0
0
1
0
0
0
2
0
3
1
1
2
1
1
1
1
2
1
1
1
1
2
0
2
1
2
0
2
1
1
1
1
1
2
0
1
1
1
1
0
1
0
1
1
0
1
1
1
2
1
2
1
1
1
1
1
1
1
2
0
1
2
1
2
1
2
1
1
2
2
1
1
2
0
1
0
1
1
0
0
1
1
1
0
1
1
1
1
2
1
1
0
0
1
1
1
1
2
1
1
1
1
1
0
2
2
1
0
0
1
2
1
0
1
1
1
0
1
2
1
0
1
2
0
1
1
1
0
1
0
1
2
1
0
1
3
1
1
0
0
0
1
2
2
1
1
1
1
1
2
1
1
2
2
2
1
1
1
1
2
0
0
1
2
0
1
1
1
1
1
2
2
1
1
1
1
1
1
2
0
1
2
2
0
0
0
1
1
1
1
1
1
2
2
1
1
1
1
2
0
1
1
2
2
2
1
1
1
1
1
1
1
0
1
0
2
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
2
1
1
0
1
1
0
1
2
0
0
2
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
2
1
1
1
1
0
0
1
0
1
1
1
1
1
2
2
1
1
0
1
1
1
0
2
1
0
1
0
2
1
2
0
2
1
1
0
0
2
2
1
1
1
1
1
1
1
2
1
0
1
2
1
0
1
1
2
1
0
1
2
2
1
2
2
1
1
1
1
2
1
1
1
2
2
2
1
2
1
1
1
1
1
0
0
2
1
2
2
1
1
1
1
2
1
1
2
1
0
1
1
1
1
1
2
1
0
1
1
0
1
2
0
2
1
1
1
1
1
0
1
1
1
2
2
1
0
2
1
1
2
1
1
1
2
2
0
1
1
1
0
1
1
2
0
2
1
1
1
1
1
0
1
2
0
1
2
2
1
0
1
0
1
1
2
0
1
1
1
1
1
1
2
0
2
2
1
0
1
1
2
1
2
2
1
2
1
1
2
0
1
1
1
2
1
0
3
1
1
1
1
1
1
0
1
1
2
1
1
1
1
2
0
1
1
1
1
1
1
0
1
1
2
1
1
0
1
2
0
1
1
0
2
2
0
0
1
1
1
1
0
2
0
1
1
1
1
2
0
1
2
0
1
1
0
0
1
1
1
1
2
1
1
1
2
1
1
1
0
1
1
1
1
1
1
0
1
2
1
0
2
2
1
1
1
1
1
1
0
1
1
4
1
2
1
1
1
0
1
2
0
1
1
1
1
1
2
1
0
2
1
2
1
1
1
3
1
2
0
1
0
1
2
2
1
2
2
0
1
2
2
1
1
1
2
1
2
1
1
1
0
1
0
0
1
2
2
0
1
0
0
0
1
3
2
0
2
1
1
2
2
1
0
1
1
1
1
0
1
1
1
1
2
0
0
1
1
1
2
1
2
2
0
1
2
0
0
1
0
2
2
2
1
0
3
0
1
2
1
1
1
2
1
2
2
0
0
0
1
1
1
0
1
0
1
0
0
2
1
0
2
2
1
1
1
1
2
0
1
1
1
2
2
1
0
2
1
1
1
1
1
0
1
0
1
1
2
1
1
1
1
2
2
0
1
2
1
1
1
1
1
1
2
1
2
2
1
0
1
0
1
1
2
1
0
1
1
1
1
2
2
1
2
1
1
2
1
2
1
2
1
1
1
1
1
1
1
2
1
0
2
1
0
1
1
1
1
1
1
3
0
1
0
1
0
1
1
2
1
1
0
0
1
1
0
1
2
1
2
1
1
1
1
2
1
0
0
2
1
2
1
2
1
1
1
1
1
1
1
1
0
1
1
0
1
1
1
1
1
1
1
2
2
1
1
2
0
2
1
1
0
1
1
1
1
1
0
1
1
2
1
1
1
1
1
1
1
2
1
1
0
0
0
1
0
1
1
0
0
1
1
0
1
2
1
2
1
1
1
1
1
1
0
0
1
1
1
0
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
3
1
1
1
1
0
1
0
1
1
0
0
1
1
0
0
1
1
2
1
1
1
2
1
2
1
1
1
2
1
2
1
1
1
0
2
1
1
1
1
1
1
2
1
1
2
1
0
1
2
0
0
1
2
2
0
1
1
1
1
1
1
0
1
2
1
1
0
2
1
2
0
2
1
1
1
0
0
2
2
0
2
0
1
1
1
1
0
1
1
0
1
1
2
2
1
1
2
1
0
1
1
2
2
0
0
1
1
1
1
1
1
0
1
2
1
1
1
0
1
1
2
1
2
1
1
2
0
1
1
1
0
0
2
2
1
3
0
1
1
0
1
1
0
1
1
1
2
1
1
1
2
1
1
2
1
1
2
0
1
1
1
6
1
1
1
1
1
1
1
1
1
1
2
2
2
2
2
2
1
2
1
1
1
1
2
1
0
1
1
1
2
1
1
0
2
1
1
2
0
2
2
1
1
1
1
1
2
1
1
0
2
2
1
1
1
1
1
0
1
1
1
1
0
1
2
2
1
1
1
1
0
1
0
2
1
1
1
0
2
1
2
0
1
0
2
1
0
1
1
1
2
1
2
1
1
2
2
1
2
2
1
1
2
1
2
1
0
1
1
1
1
2
1
0
0
2
1
1
0
1
2
1
0
0
1
1
1
0
1
0
1
1
1
0
1
0
0
2
2
2
1
1
1
1
1
1
0
1
1
1
0
1
1
1
1
1
1
1
1
1
1
0
0
2
1
0
1
1
1
0
0
3
2
1
1
2
1
2
0
2
0
1
2
1
1
2
1
2
1
1
1
2
0
1
2
1
0
1
1
2
0
1
1
0
1
1
1
2
1
0
2
0
1
1
1
0
0
2
1
0
1
0
0
0
0
0
1
2
1
1
1
1
3
2
1
2
3
1
1
1
1
0
2
1
1
0
1
1
1
1
2
1
2
1
1
0
2
1
2
1
0
1
0
1
1
2
0
1
1
1
1
1
0
1
1
1
1
1
1
2
1
0
1
0
1
0
0
1
1
1
2
1
1
0
1
1
2
1
0
1
4
1
2
2
0
0
0
1
1
2
2
1
1
1
0
0
1
1
1
1
0
2
1
0
2
0
1
0
1
2
2
1
1
1
0
1
1
0
0
1
1
2
1
1
1
1
1
2
0
1
0
1
0
1
0
2
2
1
1
0
1
1
0
1
1
1
2
1
0
1
1
2
2
0
0
1
0
2
1
2
1
1
0
1
1
1
1
2
1
0
0
1
0
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
2
0
1
1
1
2
2
2
0
1
0
1
1
0
1
0
0
2
0
1
1
1
2
2
1
1
2
1
1
1
2
2
1
0
1
1
2
1
0
1
1
1
1
2
1
2
1
1
1
3
1
0
2
1
1
1
2
1
1
1
1
2
2
1
1
0
1
0
1
3
2
1
1
2
2
1
1
2
1
1
0
0
2
1
1
1
1
1
0
1
0
1
0
0
0
1
1
1
1
2
2
1
0
1
0
2
0
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
2
2
1
2
2
0
1
1
2
1
1
2
1
1
0
1
2
2
1
1
1
0
2
1
0
1
0
1
2
1
2
1
1
3
2
1
1
1
1
0
0
0
0
1
0
2
1
3
1
1
1
2
1
1
2
1
1
0
0
2
2
2
2
1
0
1
1
0
1
1
2
0
1
0
1
1
2
1
2
0
2
2
1
1
1
2
1
2
1
2
0
1
1
1
1
2
2
1
0
0
2
0
1
0
0
2
2
1
1
1
1
1
1
1
0
2
2
1
0
1
0
1
0
1
0
1
0
1
1
1
1
1
0
1
2
0
1
0
1
2
1
1
0
1
1
1
0
1
1
2
2
1
3
1
0
0
0
1
1
2
1
0
2
2
1
1
1
0
2
1
0
1
1
1
0
1
0
0
1
1
2
1
1
1
1
1
2
0
1
1
2
1
1
1
2
2
1
1
2
0
1
2
2
2
0
1
0
1
1
1
0
1
1
1
1
1
2
1
2
0
2
2
2
1
1
1
1
1
0
2
2
1
1
1
1
2
1
0
1
1
3
1
1
2
2
1
1
1
1
1
1
2
1
1
2
0
1
1
1
1
0
1
0
2
1
2
1
2
1
1
0
1
1
0
1
1
1
1
1
2
1
1
0
1
1
1
1
1
2
3
0
1
2
0
1
1
2
1
2
1
1
1
1
1
0
1
1
0
2
0
0
2
1
1
2
1
1
1
0
1
2
0
1
1
1
1
0
2
2
1
1
1
1
1
0
1
2
1
2
0
1
1
1
1
0
1
2
1
1
2
1
2
1
1
1
2
2
1
1
0
2
2
2
1
1
1
2
0
1
1
0
1
1
0
0
0
0
0
1
2
0
1
2
0
1
1
1
1
1
2
4
0
1
1
1
1
2
1
1
2
1
1
0
0
1
3
0
2
0
1
1
1
1
0
1
0
1
2
1
2
1
0
1
0
1
1
2
1
0
0
2
0
0
1
2
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
0
1
1
2
1
1
1
1
1
0
1
1
1
1
1
2
0
1
1
1
1
1
1
1
1
2
1
1
1
0
1
1
1
0
1
1
2
2
2
1
2
1
1
1
1
0
3
0
1
0
1
1
1
0
1
1
1
2
0
1
1
0
1
2
1
2
2
2
1
1
0
0
1
2
0
1
2
2
2
1
1
1
1
1
0
1
1
2
1
0
1
2
1
2
1
1
0
1
1
1
2
0
1
1
0
1
1
2
1
2
1
1
1
1
1
2
0
1
0
2
1
0
1
1
1
2
2
1
2
0
1
1
1
2
1
1
1
1
1
1
2
2
1
2
1
1
0
3
0
1
1
2
1
0
1
1
1
2
0
0
1
1
1
1
0
1
0
2
1
1
0
1
1
1
1
1
1
0
1
1
1
0
1
1
0
2
1
1
1
1
1
1
0
1
1
1
1
0
2
1
2
0
1
1
1
1
1
1
1
1
2
2
2
1
0
1
0
1
0
1
0
1
1
0
0
1
2
0
2
0
1
1
0
2
1
1
1
2
1
1
1
0
0
0
2
2
1
1
1
2
0
1
1
1
2
0
1
1
1
1
0
1
1
1
1
1
1
0
0
1
1
1
1
0
0
2
2
1
2
1
1
1
1
1
1
1
1
1
2
2
1
0
3
1
2
1
1
1
2
1
2
2
1
0
2
1
0
1
1
2
2
1
1
1
0
1
2
1
0
0
2
1
2
0
1
0
1
1
1
1
0
1
1
1
1
1
2
1
1
0
0
1
2
1
1
0
1
0
0
0
2
1
0
0
1
1
0
1
1
1
1
1
1
1
2
1
1
2
1
1
0
2
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
0
1
0
1
1
0
1
1
1
1
2
1
2
2
1
0
1
1
1
0
1
1
1
1
2
2
1
2
0
1
1
0
2
1
1
1
0
1
0
0
1
1
1
1
1
2
2
1
3
2
2
2
1
2
1
2
1
1
0
0
1
1
1
1
0
2
1
1
2
2
1
1
1
0
0
1
2
0
1
1
0
1
1
1
1
1
1
1
1
0
1
0
2
1
0
2
1
0
1
0
1
1
1
0
1
1
1
2
3
1
1
0
1
1
0
1
1
1
1
0
2
0
1
0
1
0
2
1
1
1
0
0
1
0
2
1
2
1
1
1
2
0
1
2
0
1
1
1
1
1
1
1
0
0
1
1
1
2
1
1
1
1
1
1
1
2
0
0
1
1
1
0
1
0
1
1
0
1
1
1
1
1
1
2
1
1
1
1
1
2
2
0
1
0
1
1
0
1
0
2
1
2
2
0
2
2
1
1
1
1
1
0
1
0
1
1
0
0
1
1
1
2
1
1
1
1
1
2
2
0
1
0
2
1
1
1
0
1
1
1
1
2
2
1
0
1
1
1
2
1
0
1
2
1
2
1
1
1
1
1
0
1
1
1
1
1
1
0
1
1
1
1
0
2
2
2
2
2
1
0
1
1
0
1
0
2
2
0
1
1
2
2
1
1
2
0
1
0
1
1
1
0
1
1
2
1
0
0
1
1
2
1
1
1
1
1
1
3
1
1
1
1
1
2
0
0
1
1
1
1
0
2
1
1
2
1
1
0
1
1
1
0
2
1
0
1
0
1
1
1
1
1
1
0
1
1
0
2
0
0
0
0
1
2
0
1
1
1
0
1
2
2
0
0
1
0
1
2
2
2
1
1
2
2
1
1
1
0
1
1
2
1
1
2
1
2
2
2
1
2
1
2
1
1
1
1
1
2
0
1
2
1
1
1
1
2
1
0
1
1
1
0
2
0
0
1
1
1
0
1
1
1
1
2
1
2
1
1
2
1
2
1
1
0
0
2
1
1
2
0
1
1
2
1
0
1
0
1
1
0
1
1
1
1
1
1
1
1
1
1
1
2
1
0
1
1
1
2
1
0
2
2
1
1
1
1
2
1
0
2
1
0
0
0
1
0
1
1
1
2
2
1
1
2
0
2
1
2
1
2
0
0
1
1
1
0
2
1
1
0
1
1
1
1
1
2
1
1
1
2
1
1
2
1
1
1
2
1
2
1
2
0
1
1
2
1
1
1
1
2
1
0
1
1
2
1
1
1
2
1
1
2
0
1
2
1
1
2
1
2
1
2
1
0
1
1
1
1
0
2
1
1
2
1
1
1
0
1
0
1
0
1
1
1
0
1
0
0
1
1
1
2
1
1
1
1
1
1
1
2
0
0
2
1
1
0
1
2
2
1
1
2
1
1
1
0
1
2
2
0
1
1
1
1
2
1
1
1
2
0
1
1
1
1
1
2
1
1
1
2
1
2
1
0
2
2
0
2
1
2
2
2
1
1
1
1
0
1
2
2
1
1
2
1
2
1
1
1
2
0
2
1
0
0
0
1
1
0
0
1
0
1
2
2
1
1
2
0
1
1
0
1
1
2
2
2
1
1
2
1
2
0
1
1
1
0
1
0
2
0
1
1
1
0
1
1
0
1
0
0
1
1
1
0
1
1
0
1
0
2
1
1
2
1
2
0
1
1
0
1
0
1
1
2
1
0
0
1
1
1
0
1
0
2
2
1
0
1
1
1
1
1
1
1
1
1
2
0
1
1
2
1
1
0
1
0
1
1
0
1
0
1
2
1
1
1
1
2
2
2
2
1
2
1
0
0
2
1
1
1
2
1
2
0
1
1
0
2
1
1
2
1
2
1
1
1
2
1
1
1
2
1
0
1
1
2
2
1
0
2
1
2
1
0
1
1
2
1
1
1
2
0
1
2
1
2
1
1
2
1
1
1
1
1
3
1
1
1
2
2
0
1
0
0
2
2
0
2
1
1
1
1
1
1
1
0
0
1
1
3
2
1
0
1
0
2
1
0
1
1
0
2
1
2
2
1
2
1
1
1
2
2
1
2
2
2
1
1
2
1
1
1
2
2
1
1
1
1
2
0
1
0
1
1
0
2
1
1
1
1
1
0
1
1
2
1
1
2
2
1
1
2
1
0
1
1
1
0
2
1
1
1
4
1
2
2
1
1
1
1
1
1
2
0
2
2
1
1
0
1
1
1
0
1
1
1
1
1
0
1
1
1
0
0
1
1
0
1
2
1
2
0
0
0
1
0
0
2
1
1
2
1
1
1
1
0
2
1
1
1
2
1
2
0
1
1
0
1
1
1
0
0
1
2
0
1
2
1
1
2
1
1
1
1
2
2
1
1
1
1
0
1
1
2
1
2
1
0
1
1
2
1
0
2
2
1
0
1
1
1
1
1
1
2
2
1
1
1
2
2
2
2
1
2
2
1
1
2
1
0
1
1
1
2
1
0
1
1
1
1
1
2
2
0
1
0
2
0
1
1
1
0
1
1
1
2
1
1
0
2
2
0
2
0
0
0
1
1
1
0
0
2
0
0
1
1
2
0
1
1
2
1
1
1
1
2
0
0
1
1
1
1
2
1
1
1
1
0
2
1
1
0
2
1
1
1
1
1
1
1
1
1
2
1
1
0
0
1
2
1
1
2
1
1
0
1
1
2
0
1
0
2
2
1
1
2
1
1
1
2
1
0
1
0
1
2
1
1
0
1
2
1
2
1
2
0
0
2
1
1
1
1
1
2
1
1
1
0
2
0
2
2
2
0
2
0
1
0
1
2
2
1
2
0
1
1
2
2
0
2
1
2
0
1
1
0
2
1
1
2
1
1
1
0
0
2
2
1
0
2
1
1
0
2
1
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
0
1
1
0
0
2
0
1
1
2
1
3
1
1
1
1
1
0
1
2
1
2
1
1
1
1
0
2
1
1
1
1
2
1
0
1
0
1
1
1
1
0
1
1
0
0
1
1
1
1
1
0
1
2
1
2
1
2
0
1
1
1
1
1
1
1
1
0
2
3
1
1
1
1
2
2
2
1
1
1
1
1
0
1
1
1
0
2
2
2
0
0
2
1
1
1
0
2
1
2
0
1
0
2
1
1
0
1
1
1
2
1
1
1
1
2
0
1
1
1
1
1
2
0
0
1
1
2
1
1
1
1
1
2
2
1
1
0
1
1
1
2
2
1
2
2
1
2
2
1
1
2
1
1
2
0
1
2
0
1
1
1
2
1
0
2
1
1
2
2
0
1
1
2
1
1
1
1
0
0
1
1
1
2
1
2
2
1
1
0
1
1
2
2
1
2
0
1
1
1
1
1
0
1
1
1
2
1
0
0
2
1
1
1
1
2
0
1
0
1
2
1
1
2
1
2
1
2
0
1
1
1
1
1
3
1
2
1
0
2
1
1
1
2
1
1
2
2
1
1
1
0
1
2
1
1
2
0
0
2
1
1
1
2
2
2
1
0
1
2
0
0
0
1
1
1
0
1
1
2
1
1
1
1
1
1
1
1
1
2
1
2
1
0
1
1
1
1
1
1
2
1
1
2
1
1
1
0
1
1
1
1
1
0
1
1
0
0
1
1
0
1
0
1
2
0
1
2
1
0
1
2
1
0
1
0
1
0
1
1
2
2
1
2
2
1
1
2
1
1
2
2
0
1
1
1
1
2
2
2
1
1
1
1
2
1
1
1
0
0
1
1
2
2
0
1
0
0
0
1
1
1
0
2
0
2
1
1
0
1
1
1
1
1
0
1
1
2
0
1
1
0
1
1
2
2
0
1
1
1
1
1
1
2
0
1
2
1
2
1
1
4
1
1
1
2
0
2
0
0
0
2
1
1
1
0
1
1
2
1
1
0
1
0
1
1
2
1
1
1
1
1
0
1
1
1
2
1
1
0
1
1
0
0
1
0
1
2
1
1
0
1
2
1
0
2
1
1
1
1
0
1
2
0
2
1
2
1
0
0
1
1
0
0
2
0
0
1
2
1
2
1
1
1
1
1
0
1
0
1
1
1
0
0
1
0
1
0
0
1
1
2
1
1
1
0
2
0
2
1
1
1
1
1
2
1
2
2
1
1
1
1
1
0
1
1
0
2
2
1
0
1
2
1
1
2
1
3
0
2
1
2
1
1
0
0
2
1
0
2
1
1
1
0
1
1
1
2
1
0
1
1
1
1
1
1
0
2
2
1
2
1
1
0
1
2
1
1
0
2
1
1
1
1
2
1
1
1
1
2
1
1
2
0
1
0
1
2
1
0
2
0
2
1
1
0
2
0
0
1
0
2
1
0
1
1
0
1
0
1
1
1
1
1
1
1
1
1
0
1
1
2
0
1
2
1
2
0
2
2
1
1
0
1
1
1
2
1
0
2
2
2
1
1
2
1
1
2
2
0
1
1
1
0
0
1
2
1
1
2
1
1
1
1
1
2
3
2
1
1
2
1
1
1
1
1
1
1
1
1
0
1
0
1
1
1
2
1
2
1
1
0
1
1
2
1
1
1
1
0
0
1
1
1
2
1
2
0
1
2
1
1
1
2
2
0
1
1
2
1
0
2
2
1
1
2
1
1
1
0
6
0
1
1
1
0
1
1
1
2
2
1
2
1
0
2
2
0
1
3
1
0
2
1
1
1
1
1
1
1
2
1
2
0
0
2
1
0
1
1
0
2
1
1
1
1
2
0
1
1
0
1
1
2
2
2
0
1
1
2
1
0
1
2
1
1
1
1
1
2
2
2
1
1
1
1
1
2
2
1
2
1
1
1
1
2
0
2
1
1
1
2
1
1
2
2
1
2
1
2
1
1
1
2
1
0
0
1
1
1
1
0
0
1
1
1
1
2
2
0
2
1
1
1
2
0
1
1
0
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
0
2
1
1
1
1
1
2
1
1
1
1
0
0
1
1
2
1
2
1
1
0
1
0
1
1
1
2
0
2
0
1
2
2
0
1
1
1
1
1
2
0
1
1
2
2
2
1
1
0
1
1
0
0
0
1
0
2
0
0
0
1
1
0
1
1
0
1
1
1
1
1
0
0
2
1
1
0
1
1
0
2
2
1
2
1
2
1
1
2
2
0
2
2
1
1
1
1
1
1
1
0
1
0
1
3
0
0
1
1
1
1
0
1
1
1
2
1
1
1
2
1
1
1
1
1
2
0
0
1
2
1
1
2
2
0
2
1
1
1
1
1
2
1
1
2
2
1
1
2
1
1
1
2
0
1
1
1
2
1
2
1
1
0
1
1
2
0
1
2
1
1
0
1
1
1
1
1
2
0
1
1
2
2
0
1
1
0
2
1
1
0
1
0
2
1
1
2
1
1
1
1
1
0
1
2
1
0
1
0
1
1
1
1
2
1
1
2
1
2
0
1
2
1
1
2
1
0
1
1
2
2
1
2
1
0
2
1
4
2
1
1
0
1
1
0
1
0
1
1
0
2
1
1
2
1
1
2
1
2
2
1
1
1
1
2
1
2
1
1
2
1
2
1
2
0
1
1
1
1
0
0
0
1
2
1
2
2
2
2
2
1
1
2
1
1
1
1
0
1
1
2
0
1
2
1
0
1
4
1
1
1
1
1
1
1
0
1
1
1
1
1
0
0
0
2
2
1
0
1
0
1
0
0
1
1
1
0
2
0
1
1
2
2
0
0
1
1
0
1
1
2
1
2
0
0
0
1
2
1
1
2
1
1
0
1
1
0
2
0
2
2
1
2
1
0
1
0
1
1
2
1
2
1
2
0
0
2
0
1
2
1
1
1
0
0
1
2
0
0
0
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
0
1
1
0
1
2
0
1
1
1
0
1
1
1
2
1
0
2
0
1
0
1
1
0
1
1
1
1
2
2
0
2
1
1
1
1
2
0
1
1
1
1
2
2
1
1
1
1
2
1
2
1
0
2
1
1
1
1
1
1
2
1
1
0
1
1
1
1
1
0
1
1
1
1
1
0
2
1
1
2
0
1
1
1
1
1
2
0
2
0
1
1
1
1
1
2
2
1
1
1
2
1
1
0
1
0
1
0
3
2
1
1
0
1
2
1
1
1
0
1
1
1
1
1
0
2
2
2
1
0
0
1
1
1
2
1
0
1
1
0
0
1
1
2
1
2
1
1
2
0
2
0
1
1
2
2
2
1
2
1
2
1
1
2
1
1
0
1
1
0
1
1
0
1
2
1
2
0
2
1
1
0
1
1
1
1
2
2
1
1
0
2
2
0
2
0
1
0
2
2
1
1
2
1
0
1
2
1
2
0
2
2
0
1
1
1
1
1
0
0
2
2
1
1
1
1
1
2
0
1
1
1
0
1
1
1
0
0
2
1
2
1
1
1
1
1
1
2
0
2
2
0
1
3
1
1
1
0
1
1
1
1
0
2
2
0
1
1
1
0
1
1
1
1
0
0
1
1
1
0
1
1
1
1
2
1
2
0
0
1
1
2
1
1
1
1
2
4
1
2
1
1
1
2
1
1
1
1
2
1
2
1
1
2
2
1
1
1
1
0
1
1
1
0
1
0
2
0
2
0
2
1
1
1
1
1
0
1
1
1
1
2
0
1
1
1
1
2
1
2
2
0
1
1
1
1
1
1
1
0
1
1
1
1
1
1
0
0
0
1
0
2
1
0
1
1
0
1
1
0
0
1
1
1
0
2
1
2
1
1
0
2
1
1
1
1
0
2
2
1
2
2
1
1
2
0
1
0
1
1
2
1
1
1
1
1
2
1
1
2
2
1
0
1
2
1
1
0
0
1
0
2
2
2
2
0
0
0
1
1
1
0
2
0
0
2
2
0
1
1
1
1
1
1
1
0
1
1
1
0
2
1
0
1
1
2
0
2
1
2
1
1
0
0
2
1
0
0
1
1
0
0
1
2
1
1
0
1
1
1
1
1
2
1
1
1
0
2
0
2
1
1
1
1
2
1
0
2
1
1
1
2
1
2
1
2
1
1
1
0
1
1
2
1
1
2
1
1
2
0
0
1
1
1
1
1
2
0
0
1
2
1
2
1
1
1
1
1
1
1
2
1
0
1
2
2
2
1
2
1
1
0
2
2
0
1
1
1
1
2
2
0
0
1
0
0
0
1
1
1
0
1
1
0
0
2
1
2
1
1
1
1
1
1
1
1
1
1
1
0
1
0
1
1
0
0
1
2
1
1
2
1
2
1
1
1
1
2
1
0
1
1
0
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
0
0
2
1
2
0
2
2
2
1
1
0
0
0
1
1
2
2
1
1
1
1
1
1
1
2
0
1
1
0
1
2
1
1
0
1
1
0
0
1
1
0
1
1
1
2
2
1
1
0
2
0
1
2
2
1
2
2
1
0
0
1
1
0
0
1
1
1
1
2
0
0
2
1
1
2
2
0
0
2
3
1
0
2
2
0
1
1
2
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
0
2
2
0
2
1
0
1
1
1
1
0
1
1
2
1
2
2
1
0
0
1
1
1
0
2
1
1
1
1
1
1
2
4
2
1
1
2
1
2
2
1
0
0
2
0
1
1
2
1
0
2
2
1
0
1
1
2
2
1
1
0
1
0
0
0
1
2
2
1
1
1
0
2
2
1
1
1
1
1
2
2
2
1
2
1
1
1
2
1
0
0
17
0
1
1
0
1
1
2
1
0
1
0
1
1
0
1
1
1
1
0
1
2
0
3
0
2
1
2
1
0
0
1
0
1
2
0
2
1
1
2
1
1
2
1
1
1
1
0
1
2
0
1
0
1
2
0
1
0
1
1
0
2
2
2
1
0
1
1
1
0
0
1
1
1
2
1
1
1
1
2
2
2
2
1
1
1
0
1
1
1
1
1
0
1
2
1
2
3
1
1
0
1
1
1
0
0
2
1
1
1
0
0
1
1
0
1
1
2
1
0
2
0
1
1
0
2
1
0
1
1
1
1
1
1
2
1
3
0
1
0
0
2
1
1
1
1
2
0
1
1
1
0
1
1
1
1
1
0
2
1
1
1
1
2
1
2
2
2
1
2
0
1
1
1
2
1
1
1
1
0
1
2
0
1
1
0
2
2
0
1
2
2
1
1
1
2
1
1
1
0
2
2
0
2
0
1
1
2
0
1
2
2
1
1
1
1
1
2
0
1
0
1
1
1
1
1
0
1
2
1
1
1
1
2
1
1
2
1
1
1
2
1
1
1
1
0
1
2
0
0
1
0
1
1
1
2
1
1
1
1
1
1
1
0
1
0
1
0
1
1
1
2
2
2
2
2
0
0
1
1
2
1
0
0
2
2
1
1
2
1
1
1
2
1
1
2
2
2
1
0
1
1
1
2
0
1
1
1
2
0
2
2
2
1
1
1
0
1
1
2
1
1
0
1
2
0
1
1
0
2
1
0
2
1
1
1
2
2
1
1
2
0
1
1
1
1
1
1
2
1
1
1
3
2
1
2
1
2
2
1
2
2
1
0
1
2
1
1
1
1
0
1
0
1
0
0
1
1
2
1
1
1
1
1
0
0
1
1
1
1
1
2
1
2
1
1
2
1
1
0
0
0
1
0
1
0
1
2
1
1
2
2
2
2
1
1
1
1
2
1
2
1
2
2
1
1
2
1
0
1
1
1
1
1
0
2
1
1
0
2
1
2
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
2
0
1
2
1
2
2
2
0
1
1
1
1
1
1
1
1
0
1
1
1
0
0
1
1
2
1
1
1
0
2
2
1
2
2
1
0
1
2
1
3
2
1
1
0
1
1
2
1
1
1
0
1
2
2
0
2
1
0
1
1
1
1
0
1
1
0
0
1
1
1
0
2
1
0
1
0
1
2
1
1
1
1
2
2
0
1
1
0
1
0
1
1
1
1
1
2
1
2
1
1
1
2
1
1
0
1
1
1
1
1
2
2
1
1
2
1
1
2
0
1
1
0
0
1
0
2
1
1
0
2
2
1
1
1
0
1
0
1
1
1
2
1
2
1
1
1
2
0
1
1
3
1
1
0
1
1
2
2
2
0
0
1
0
1
2
1
0
2
1
1
1
1
1
0
1
2
1
1
1
0
1
1
2
0
1
2
1
0
1
1
0
2
0
0
1
1
1
1
0
1
1
0
2
2
1
1
1
0
2
2
1
0
2
1
0
1
0
1
1
0
1
0
0
2
2
0
1
1
1
1
0
1
0
1
2
2
1
2
1
1
1
1
2
1
2
1
2
1
1
1
2
1
1
1
2
1
2
2
1
0
2
2
1
1
1
2
1
1
0
1
1
2
0
1
1
1
0
1
0
2
1
2
1
1
1
1
1
0
0
0
0
0
1
0
0
2
1
0
0
1
1
1
1
1
1
2
0
0
2
0
1
1
0
1
0
1
2
2
1
1
0
2
1
0
0
1
1
2
1
1
0
0
0
2
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
2
4
1
1
2
0
2
1
1
1
0
0
1
0
2
1
2
1
1
2
1
1
1
0
1
2
2
1
1
1
1
0
2
1
1
2
1
3
1
2
1
1
2
2
2
2
2
0
1
1
1
1
0
2
1
1
1
1
0
0
1
1
2
1
1
0
0
1
1
0
0
0
1
1
1
1
1
1
1
1
1
0
1
1
1
1
2
2
1
1
1
1
2
1
1
2
0
0
2
1
0
1
1
1
1
0
1
1
1
0
1
1
2
1
0
1
1
1
0
1
1
1
1
1
1
1
1
0
2
0
0
1
1
2
0
1
1
1
2
1
0
1
2
2
1
0
1
0
1
1
2
2
1
0
0
0
2
1
1
0
1
2
2
1
1
0
0
1
2
0
0
1
1
2
1
1
2
1
1
1
0
1
1
1
1
1
1
0
0
2
1
1
0
0
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
2
1
0
0
2
2
2
1
1
1
1
1
2
1
2
0
1
2
1
1
1
1
1
1
1
2
1
2
2
1
0
0
1
1
1
1
1
1
1
2
1
1
1
2
2
1
0
1
1
0
1
1
1
1
1
1
1
2
1
1
1
0
2
0
2
1
0
1
0
2
1
1
1
1
2
1
0
0
0
2
2
1
1
1
0
1
1
0
1
1
1
1
0
1
1
1
1
1
2
0
1
2
1
2
1
1
1
2
1
0
1
0
0
1
2
0
1
0
2
1
1
2
1
2
1
1
2
1
1
2
1
1
1
1
1
2
1
2
0
1
1
1
0
2
2
1
1
0
1
2
0
1
1
0
1
1
2
1
0
2
1
1
0
1
1
1
0
2
0
1
0
1
1
1
1
2
1
1
1
0
1
0
1
1
2
2
1
1
1
1
1
1
1
0
1
2
2
1
1
1
1
1
0
2
1
1
1
2
1
1
1
1
1
1
2
0
2
1
1
0
1
2
0
1
2
0
1
1
0
1
1
1
1
1
0
1
1
1
2
1
2
2
0
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
0
2
3
1
2
2
1
1
1
2
1
2
0
1
2
1
2
2
3
1
1
1
2
1
1
0
1
1
2
2
1
2
1
1
1
1
2
1
1
1
2
0
1
1
0
2
1
2
1
1
2
2
0
2
2
2
1
0
1
1
1
1
1
1
1
2
0
0
2
2
0
1
1
1
1
2
2
1
2
1
2
1
1
1
1
1
1
1
2
0
1
1
1
1
1
1
1
1
1
2
2
1
0
1
2
1
1
1
2
1
1
1
0
1
2
1
1
2
2
1
0
2
1
1
2
1
1
0
2
1
1
1
1
1
0
1
1
0
1
1
1
0
1
0
1
1
1
1
1
1
1
2
1
2
2
0
0
1
1
1
1
2
1
2
2
1
1
1
0
2
0
0
1
1
1
2
1
0
0
1
2
1
2
1
0
1
2
0
1
1
2
1
1
1
0
2
2
0
0
1
1
1
1
2
1
1
0
1
2
1
1
0
0
0
1
2
2
1
0
1
1
1
1
1
2
1
1
1
1
0
1
1
1
0
1
1
2
1
2
2
1
1
1
2
1
1
2
1
1
0
1
2
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
0
1
1
1
1
0
0
1
1
2
2
1
2
1
2
1
1
0
1
2
1
1
0
1
2
2
1
2
1
1
1
1
0
1
0
1
1
1
1
1
1
2
2
1
1
1
0
1
2
2
0
0
1
1
3
1
1
1
1
1
1
2
1
1
2
2
1
1
1
2
2
1
0
1
1
1
1
1
0
1
2
1
0
1
1
1
2
1
1
1
1
1
1
1
1
0
0
2
2
2
0
1
1
1
0
1
0
1
0
0
1
2
0
2
1
1
1
1
1
1
1
1
0
0
1
2
1
1
0
1
2
2
2
2
1
1
2
0
0
1
1
0
2
0
0
0
1
1
1
2
1
0
1
0
0
2
1
1
1
1
1
0
1
1
2
2
1
1
1
1
1
1
2
0
0
1
1
1
2
0
1
1
1
2
1
1
0
0
1
1
1
1
0
1
0
2
1
0
2
1
1
2
1
1
1
1
2
1
0
1
1
1
1
1
2
0
2
1
1
2
2
2
1
1
0
1
0
1
2
2
0
1
1
1
0
1
1
0
2
1
1
1
1
1
0
0
2
1
0
0
1
1
1
2
2
1
1
0
0
1
1
2
0
1
0
1
1
0
1
2
0
2
2
1
1
2
1
1
2
1
1
2
2
1
0
1
1
1
1
1
1
2
1
1
0
1
0
1
1
1
1
1
2
1
2
2
2
2
1
1
1
1
1
1
0
1
1
1
1
2
0
0
1
2
1
2
1
0
0
0
1
0
1
0
1
1
0
0
1
0
0
1
1
1
1
1
1
1
1
1
1
0
1
1
1
0
1
1
2
2
0
0
1
1
1
1
1
0
2
1
1
1
1
1
1
1
1
1
0
2
5
0
1
2
2
1
1
0
2
0
0
1
0
0
1
2
1
1
1
1
1
1
0
1
0
1
1
1
0
1
1
1
1
3
0
2
1
1
1
1
1
1
1
2
1
1
1
0
3
2
1
0
1
2
1
1
2
2
1
1
0
2
1
2
0
2
2
1
2
1
2
3
1
1
2
2
2
1
1
0
0
1
1
1
2
1
0
1
1
0
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
0
1
1
0
1
2
1
3
0
0
1
1
1
1
1
2
1
2
1
1
0
1
0
1
1
1
1
1
1
1
1
2
1
1
1
1
4
1
1
1
2
1
1
1
0
1
0
2
1
1
1
1
1
0
2
1
1
0
1
1
1
1
1
1
1
2
1
1
1
2
1
1
0
1
2
2
1
0
1
1
1
2
0
1
1
1
1
1
2
2
1
3
2
1
0
1
0
2
2
0
0
1
1
1
1
1
1
0
1
1
1
1
0
1
1
1
2
1
2
1
2
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
2
1
0
1
1
2
1
0
1
1
1
2
1
2
1
0
1
1
1
0
1
2
0
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
0
0
2
1
1
1
2
2
0
1
2
2
1
1
2
1
1
2
1
1
1
1
1
1
1
1
2
2
1
1
0
2
1
1
1
0
1
1
0
1
2
1
2
0
1
1
2
1
0
1
1
2
0
1
1
1
1
2
2
1
0
1
1
1
1
1
1
1
2
1
1
2
1
0
2
1
1
1
1
1
0
1
1
2
1
1
2
1
0
1
2
1
1
0
1
2
0
3
0
2
1
2
1
1
1
1
0
1
2
1
0
1
1
1
0
0
1
0
2
2
2
1
2
1
0
2
1
1
1
0
1
2
1
1
1
0
1
1
0
1
1
2
0
1
1
1
0
1
1
2
2
1
3
1
2
1
2
1
1
1
0
1
2
2
1
2
1
1
3
0
1
1
0
2
1
0
1
0
1
2
1
1
0
1
1
0
0
1
1
1
0
2
1
0
1
1
1
0
1
2
0
1
0
1
2
1
1
1
1
1
2
1
1
1
1
1
2
2
1
2
0
1
2
1
1
1
2
2
2
1
2
0
1
0
3
2
2
1
1
0
1
1
0
1
0
1
1
1
0
0
1
0
1
1
2
0
2
1
1
1
1
1
1
2
1
0
1
0
1
1
1
1
1
2
2
1
2
1
1
1
0
2
1
1
2
2
1
2
1
2
0
3
1
2
1
2
1
2
0
1
1
2
1
2
1
2
1
2
1
1
1
0
2
1
1
2
1
1
2
2
2
1
1
1
1
1
1
0
1
0
1
1
0
1
1
2
1
1
0
2
1
2
1
2
2
1
1
0
2
1
1
1
0
2
1
1
2
2
1
2
1
0
2
1
1
1
1
1
2
1
1
1
0
2
2
2
0
2
1
1
2
1
1
2
1
2
1
0
2
1
2
1
0
1
1
1
1
0
1
1
1
1
1
0
0
1
1
1
1
0
1
0
1
1
1
2
1
2
1
1
2
1
1
1
1
1
1
2
1
2
1
2
0
0
2
2
1
1
1
0
1
2
2
1
1
2
0
1
1
0
1
1
2
2
1
2
0
1
2
2
1
1
1
1
2
2
1
2
0
1
2
0
2
1
2
1
1
1
1
0
1
1
1
1
1
2
1
2
2
1
1
1
0
1
1
1
1
1
1
0
1
1
1
2
1
2
1
1
1
2
0
1
1
1
0
2
1
2
1
1
1
1
0
0
1
2
1
2
0
1
2
1
0
1
2
2
2
2
1
2
2
1
1
2
1
1
1
0
1
1
2
1
1
1
2
1
1
0
1
2
2
0
1
1
1
1
1
1
1
1
0
0
0
1
1
1
2
0
1
0
1
2
2
2
2
0
1
2
1
1
1
1
0
1
2
1
1
1
1
1
1
1
1
1
1
2
2
1
1
0
1
1
1
1
2
2
1
1
1
1
0
0
1
0
1
1
2
1
1
0
1
1
0
1
2
0
1
1
2
2
1
1
0
1
3
0
4
1
1
1
1
2
1
1
1
0
2
2
0
1
1
0
2
2
0
1
2
1
1
2
1
2
1
0
1
2
2
1
1
1
0
1
1
2
0
0
2
1
2
0
1
1
1
3
0
2
1
2
2
1
1
0
1
2
1
2
2
1
2
2
1
1
1
1
1
1
1
2
1
2
1
2
1
2
0
1
1
1
0
2
2
1
1
1
1
1
1
1
1
1
1
1
2
2
0
2
1
0
1
1
1
1
1
1
1
1
1
1
0
1
1
2
1
1
0
1
1
3
1
2
1
1
3
1
0
1
0
1
2
1
1
2
1
0
1
1
1
1
1
1
1
1
1
0
0
1
2
1
1
1
1
1
1
1
1
1
1
1
0
0
1
2
1
0
1
2
0
1
2
1
0
0
1
2
1
1
2
1
2
2
1
1
1
1
2
0
1
1
2
0
1
1
2
1
2
0
0
1
1
1
2
2
1
2
1
1
0
1
2
1
1
1
0
2
0
1
1
1
0
2
2
2
1
3
1
1
0
1
2
1
2
1
2
1
1
1
1
1
1
0
1
0
5
1
1
1
1
1
1
2
1
1
1
1
0
1
1
1
1
1
2
1
2
1
2
1
2
1
1
1
1
2
0
2
2
1
2
1
2
0
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
0
1
1
1
2
0
2
0
2
1
1
1
1
1
1
1
1
1
2
1
0
2
1
1
1
1
2
1
1
1
0
1
2
2
2
1
2
0
1
2
1
0
1
1
2
2
1
1
1
1
1
2
0
0
1
0
1
1
0
2
2
1
1
0
1
1
1
1
1
2
0
0
1
1
1
1
2
0
1
1
2
1
1
2
0
1
2
1
1
2
1
1
1
2
2
2
0
1
1
1
3
1
1
2
1
2
1
0
0
1
1
2
2
0
2
2
0
2
1
0
1
1
2
1
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
2
0
0
1
1
2
2
0
1
1
0
2
0
1
0
0
2
1
1
0
1
2
1
0
1
1
2
2
1
1
1
2
0
0
0
1
1
0
1
1
0
1
1
1
1
1
1
2
1
1
1
0
2
2
2
2
2
1
1
1
0
1
1
1
2
1
1
0
1
2
1
1
0
0
1
1
1
1
1
1
1
1
1
0
2
1
0
1
1
1
0
2
1
1
1
1
2
0
2
0
1
2
2
2
1
2
0
0
2
2
1
0
1
1
0
1
1
1
0
1
0
1
2
0
2
1
1
2
1
1
1
1
2
3
0
0
1
2
1
1
2
0
1
1
2
1
1
1
1
1
2
2
1
0
1
2
0
2
0
1
1
1
1
1
1
1
0
0
2
1
2
1
0
1
1
2
2
2
2
0
1
1
1
2
1
1
1
0
1
2
2
0
1
1
1
0
2
1
1
1
1
2
2
1
1
2
2
1
0
0
3
1
1
1
2
0
2
1
1
1
1
0
0
1
1
1
1
1
1
2
1
2
1
2
2
2
1
1
1
2
1
1
0
1
1
1
2
1
1
3
1
1
1
1
1
1
1
0
0
2
1
1
1
2
2
2
0
1
1
1
1
2
0
1
1
1
1
1
2
0
1
1
1
0
1
0
1
0
2
0
1
2
1
1
1
2
1
0
0
1
1
0
1
0
1
1
2
0
1
2
2
0
1
0
1
1
1
1
1
0
2
1
1
2
1
1
1
0
1
1
1
1
0
2
1
1
1
2
1
0
1
1
1
1
1
0
0
2
1
2
1
0
1
2
1
1
1
0
1
1
0
0
1
1
0
1
3
1
1
1
1
1
1
2
2
1
1
0
1
1
1
1
2
1
1
1
1
1
0
1
2
2
2
1
1
2
1
2
1
1
0
1
0
1
1
2
1
1
1
1
1
1
1
4
1
2
0
0
0
1
1
0
1
0
2
1
1
0
2
1
1
2
2
0
1
2
1
2
1
1
2
1
0
1
0
1
1
0
0
0
2
3
0
2
0
1
1
1
1
1
1
0
1
0
0
1
0
2
0
1
0
2
2
1
2
1
0
0
3
1
1
1
2
1
1
1
0
0
1
0
1
1
1
2
2
2
1
2
0
1
1
0
1
1
1
1
1
2
1
1
1
1
2
0
0
1
1
0
1
1
1
1
1
0
1
1
1
2
0
0
2
1
2
2
1
2
1
2
1
1
1
1
2
2
1
1
1
2
2
2
1
1
3
1
2
1
1
1
1
0
1
1
0
1
2
1
2
1
2
1
1
2
1
0
1
2
1
2
1
1
1
2
1
1
1
2
1
1
1
0
1
1
2
1
2
2
1
0
1
1
0
2
1
1
1
1
0
2
1
1
1
1
0
2
0
1
1
1
1
1
1
0
1
0
2
0
0
1
2
1
1
2
1
1
2
1
1
2
1
1
1
2
0
1
2
0
1
1
1
2
1
1
1
1
2
2
1
1
0
2
2
1
1
0
1
2
1
1
1
1
1
1
2
0
2
2
1
1
1
1
1
1
0
1
1
0
1
1
1
2
1
1
2
1
2
0
2
2
0
0
1
0
2
1
1
1
1
1
0
2
9
1
0
2
1
0
0
2
0
1
2
3
0
1
1
1
1
2
0
1
0
2
2
2
1
1
0
1
3
1
0
1
1
1
1
1
1
1
2
1
1
1
1
1
0
1
1
1
0
1
2
1
1
0
1
2
0
1
1
1
2
2
1
1
1
1
1
2
1
1
0
1
1
1
0
1
1
2
1
0
0
1
0
1
1
0
1
1
0
1
0
0
1
1
2
1
2
2
1
2
2
1
1
1
1
1
2
2
1
1
1
1
0
2
1
2
2
0
1
1
1
1
2
2
1
1
2
1
1
1
2
1
2
1
0
1
0
2
0
2
2
1
2
1
1
2
1
1
1
1
1
0
1
1
1
1
1
0
0
1
1
2
1
1
2
1
1
1
0
1
0
1
1
2
1
2
2
2
1
0
1
1
2
1
1
1
1
1
2
2
2
1
1
2
0
1
2
0
1
1
0
2
1
1
0
1
1
1
1
2
3
0
1
1
1
0
1
0
0
2
1
2
2
0
1
1
1
1
1
0
1
1
1
1
2
2
2
1
0
1
1
0
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
0
1
2
2
1
3
1
2
1
0
0
1
1
1
0
1
2
1
1
1
0
1
0
1
2
1
1
0
0
1
4
1
1
1
1
2
0
1
1
1
0
2
1
2
1
2
1
1
1
2
0
1
1
1
1
0
1
1
1
1
0
0
2
2
1
1
1
1
1
1
2
0
2
1
2
1
2
0
2
2
1
2
1
1
0
0
2
1
0
1
1
1
1
1
1
1
2
1
1
2
1
0
1
1
2
2
2
1
1
0
1
1
1
2
1
1
1
0
1
1
1
1
1
1
0
1
1
0
1
1
2
1
2
1
1
1
0
1
1
2
1
1
0
1
2
0
2
0
2
0
1
0
1
1
2
1
1
1
1
0
1
0
2
0
2
1
1
1
2
1
1
2
1
2
1
0
1
2
1
3
0
2
0
1
1
2
1
0
1
1
1
2
2
2
1
1
1
0
1
2
0
0
1
1
2
1
0
1
2
1
1
0
1
2
2
1
2
1
1
0
1
2
0
2
0
2
1
1
1
1
2
1
2
1
1
0
1
0
0
2
1
2
0
2
1
1
0
1
1
1
0
0
1
1
1
2
2
1
1
1
1
1
1
0
1
1
2
0
1
1
1
1
2
1
2
1
1
2
1
2
1
1
1
0
1
1
1
1
2
0
1
1
2
0
2
2
0
1
0
1
1
2
1
1
1
1
0
1
1
0
3
1
1
1
1
1
2
1
2
1
1
1
1
1
0
1
1
1
2
2
1
1
1
2
1
1
2
2
1
1
1
2
2
1
2
2
1
1
0
2
0
1
1
0
1
1
2
1
1
0
2
2
1
0
1
1
1
1
1
1
2
0
2
1
1
1
1
0
1
2
2
2
2
0
1
1
1
1
1
1
1
2
1
0
0
1
1
0
1
1
2
2
0
1
1
0
1
1
1
2
1
1
0
1
1
2
1
1
0
2
1
1
0
0
1
0
1
1
1
0
0
0
1
0
1
1
1
1
1
1
1
1
2
1
2
2
1
1
1
2
1
0
1
2
1
1
1
1
1
1
0
1
1
1
1
2
1
0
1
0
1
1
1
1
1
0
2
0
0
0
1
1
1
1
1
2
2
1
1
1
1
2
1
2
1
0
1
1
2
1
1
2
1
1
2
2
2
1
1
1
2
0
1
1
1
0
0
1
2
1
1
0
1
2
2
2
6
1
2
1
1
1
0
1
0
0
1
2
1
1
1
1
1
1
1
0
1
1
1
2
1
2
1
1
1
2
1
0
1
0
1
0
1
0
1
2
2
0
1
0
1
1
0
1
2
1
0
1
0
2
2
1
2
1
1
2
1
2
3
2
1
1
1
1
1
1
2
0
2
2
1
2
1
1
1
1
0
2
0
4
1
1
0
1
1
1
1
2
0
1
2
1
1
1
1
1
1
1
1
1
1
1
0
1
1
0
1
1
1
1
0
0
1
1
2
1
2
0
1
0
1
2
2
2
1
1
2
1
4
2
1
0
0
2
1
1
1
1
2
1
0
1
0
1
1
1
1
2
2
1
1
0
0
0
1
1
0
2
0
0
1
1
1
0
2
2
0
1
1
2
1
2
0
1
0
2
0
2
2
0
2
1
0
1
0
1
1
2
0
1
0
2
2
1
1
1
1
1
1
1
1
0
1
1
1
1
0
0
1
0
1
1
2
1
0
0
1
1
1
0
1
1
1
1
1
1
1
1
0
2
2
0
0
0
0
1
0
0
1
0
1
2
1
1
2
1
1
1
0
1
1
1
2
1
2
1
0
0
2
1
2
1
1
0
2
1
0
1
1
1
1
2
2
2
0
1
2
0
2
0
1
1
1
0
1
1
2
1
1
1
1
2
1
1
1
1
1
0
0
0
0
2
0
0
2
1
1
1
2
0
2
0
1
1
1
1
0
1
0
2
1
1
1
0
1
1
0
2
1
0
1
1
1
0
2
1
0
0
2
0
0
2
1
1
3
1
1
1
0
2
0
2
2
2
0
2
0
2
0
0
1
2
2
2
1
1
1
1
1
1
0
1
1
2
2
0
1
2
0
2
2
0
2
1
2
2
0
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
0
1
1
2
1
1
2
0
1
1
1
1
0
2
2
1
1
2
2
2
0
0
1
1
1
1
1
1
2
1
1
0
1
2
1
1
0
1
3
1
1
2
2
2
2
1
1
1
0
1
2
1
2
1
1
1
2
0
1
1
0
2
1
0
2
1
1
2
1
2
1
1
1
1
2
1
1
0
0
2
0
2
0
1
1
1
1
0
0
2
1
0
2
1
1
1
1
0
1
1
1
0
0
0
1
1
1
1
0
0
0
2
1
1
1
1
0
1
1
1
2
1
0
1
2
1
1
0
1
0
1
1
0
1
2
3
2
2
1
2
1
0
2
0
2
0
1
2
1
1
0
1
1
2
1
1
0
0
1
1
1
2
1
3
1
1
2
1
2
2
1
3
1
1
2
2
1
0
1
1
0
1
1
1
2
2
1
0
1
0
2
3
2
2
1
1
1
1
1
1
2
1
0
2
2
2
0
2
0
1
2
2
1
1
1
0
2
1
1
1
1
1
1
1
1
0
2
1
1
1
2
2
6
1
1
0
1
1
1
0
0
3
1
1
1
1
1
2
2
1
1
0
1
0
1
1
1
2
1
0
1
1
0
1
2
1
1
0
1
0
1
0
1
1
1
1
1
1
2
2
2
1
2
0
1
0
1
1
2
1
1
1
1
2
2
1
1
1
0
2
1
1
1
1
0
2
1
2
1
2
0
0
0
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
0
0
1
1
2
1
1
1
1
1
2
0
2
2
1
1
1
1
1
2
1
1
1
1
1
0
2
1
0
2
1
1
0
2
1
0
1
1
1
2
2
1
1
1
1
1
1
1
1
0
2
1
1
2
1
2
1
0
1
2
0
1
2
2
1
2
0
1
2
1
1
1
0
2
0
1
1
2
1
1
2
1
1
2
1
0
1
1
1
1
0
0
2
0
1
1
1
1
2
0
0
0
2
2
0
1
2
1
0
2
1
1
0
1
1
2
1
2
1
1
2
1
1
1
2
2
1
0
1
2
1
1
0
1
2
1
0
0
1
1
1
1
1
1
0
0
1
2
2
1
0
1
1
1
2
1
1
1
1
2
2
2
2
1
0
1
1
1
1
1
1
2
1
1
0
1
0
1
0
1
2
1
1
0
0
2
2
2
1
1
2
2
1
1
1
1
0
1
1
1
2
1
1
1
1
1
1
1
2
1
0
1
1
3
0
1
1
1
2
2
1
1
1
1
2
2
1
1
0
2
1
1
1
1
1
0
1
1
1
1
2
1
1
1
2
1
1
1
1
5
0
3
1
0
1
0
1
0
1
1
1
1
1
2
1
1
2
1
1
3
2
1
1
2
1
1
1
1
1
0
1
1
1
1
1
2
1
1
1
1
2
0
1
2
0
1
0
2
1
1
1
1
1
2
0
1
1
1
1
0
2
1
1
1
1
1
2
1
0
1
1
1
1
0
2
2
1
1
1
1
0
0
1
0
1
0
1
1
1
2
1
1
1
1
1
2
1
1
0
1
0
2
1
0
0
0
1
1
3
1
0
2
1
1
1
1
1
1
0
2
2
1
1
0
1
1
0
2
1
1
1
0
0
2
1
1
0
1
1
1
1
1
2
2
1
2
1
2
1
1
2
1
2
1
2
1
1
1
0
1
2
0
0
1
2
2
1
1
1
1
1
1
1
2
0
2
1
1
2
0
1
0
1
1
1
1
2
1
2
1
1
1
1
2
1
0
2
1
1
2
2
1
1
1
1
0
0
0
0
1
1
1
2
1
0
1
2
1
1
1
0
0
1
1
1
1
1
1
1
2
1
2
1
1
2
1
1
0
2
1
1
1
1
1
2
1
0
2
1
1
1
1
2
1
0
1
1
2
1
1
0
1
1
0
1
1
1
1
2
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
0
1
0
1
1
1
1
1
1
2
1
2
1
2
1
2
2
1
1
1
2
1
1
0
2
1
1
2
1
1
1
1
4
2
1
0
0
0
0
2
1
2
1
1
2
1
1
1
3
2
1
2
1
2
0
1
2
1
0
1
0
1
1
1
1
0
2
1
4
2
2
0
1
0
1
1
1
1
1
0
0
1
2
2
0
1
1
0
1
1
2
1
1
0
0
1
1
1
0
0
2
0
0
0
1
1
1
1
1
0
1
0
2
2
2
1
1
0
1
1
2
2
0
3
0
1
2
0
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
2
0
0
2
2
2
1
1
0
1
0
1
0
1
1
1
2
2
2
2
1
1
2
2
2
1
1
2
2
1
0
0
1
2
2
0
1
1
2
1
2
1
0
1
1
1
1
1
1
1
1
0
2
2
1
1
0
0
1
1
0
1
1
2
1
1
2
0
1
2
2
0
1
1
0
1
1
1
2
2
1
1
1
2
1
1
1
1
1
1
0
2
1
0
1
1
2
2
2
0
1
1
1
2
1
2
1
1
1
0
1
2
1
0
2
1
2
1
1
2
1
1
1
0
2
1
1
1
1
1
1
1
1
2
1
2
0
1
1
0
1
2
1
2
2
1
2
1
1
2
0
0
2
2
1
1
1
1
2
2
1
1
0
0
1
1
2
0
1
0
1
1
1
1
2
1
1
1
1
2
1
1
1
0
1
1
2
1
1
1
1
1
1
2
0
1
0
1
1
2
1
1
0
0
1
0
1
2
2
2
1
1
2
1
0
1
0
0
0
1
2
0
1
2
2
0
1
1
1
1
1
1
2
0
1
1
2
2
0
1
0
2
1
1
0
1
2
1
1
1
1
0
1
0
2
2
1
0
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
0
1
2
2
0
0
2
0
1
0
1
2
1
0
1
1
0
1
2
0
1
0
1
1
2
2
1
1
0
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
0
1
2
1
1
1
1
2
2
1
1
1
1
1
1
0
1
1
0
2
2
1
1
1
0
2
1
2
0
1
1
1
1
2
1
1
1
1
1
0
1
3
0
0
1
1
1
2
1
1
1
1
0
1
2
0
2
2
2
3
1
1
2
1
1
0
2
0
1
1
1
1
2
1
1
0
1
1
1
1
1
0
1
0
0
1
1
1
2
2
0
1
2
0
1
1
1
1
2
1
1
1
0
1
1
0
1
1
3
1
2
1
1
0
0
1
0
1
2
0
1
1
0
1
1
1
1
1
1
0
1
2
2
2
2
0
2
1
1
1
1
2
1
1
1
1
1
0
0
1
2
1
1
1
1
2
1
2
1
2
1
1
1
1
2
1
1
1
1
0
1
1
0
1
1
1
1
1
1
1
2
1
2
2
0
1
1
1
3
2
1
2
1
1
1
1
1
0
0
1
1
1
1
0
2
2
2
2
2
2
1
1
1
2
2
2
1
0
1
2
1
1
1
1
2
1
0
2
1
1
1
2
0
2
0
2
2
1
1
0
2
0
3
2
1
2
1
2
1
2
1
1
2
0
0
1
1
2
1
1
2
1
1
1
1
0
1
1
1
1
1
2
1
2
2
2
2
1
1
1
0
1
2
1
0
1
2
1
0
1
0
8
1
2
2
2
0
1
1
1
1
2
1
1
1
1
1
1
1
1
2
2
1
2
0
1
2
1
0
1
1
1
1
1
0
1
1
2
0
1
1
1
2
1
0
1
1
0
0
1
0
2
2
0
1
2
1
1
1
0
0
1
2
1
1
2
2
2
1
1
1
1
0
0
1
1
0
1
2
2
2
1
1
1
0
1
2
1
1
1
1
1
1
2
0
1
0
2
1
0
0
1
1
1
1
0
1
2
1
2
2
1
1
2
2
2
1
2
2
1
0
0
0
1
0
1
1
1
1
2
0
3
1
2
0
2
2
1
1
2
1
0
1
2
1
1
1
1
1
2
2
0
2
0
1
1
1
0
0
0
2
1
0
0
0
0
1
2
2
2
2
1
1
1
1
2
0
1
1
1
2
1
1
4
2
1
1
1
1
1
1
0
2
1
1
2
1
1
1
1
2
0
0
2
0
1
0
1
2
1
2
1
1
1
0
2
1
1
1
0
1
2
1
1
2
2
1
1
2
2
2
1
1
1
2
2
2
1
2
1
0
1
0
1
1
2
1
2
1
1
0
1
2
1
0
0
1
1
2
1
0
1
1
1
1
0
1
0
0
1
0
1
1
1
1
1
0
1
0
1
1
1
1
1
1
2
2
3
1
1
0
1
2
0
1
1
1
1
0
1
1
1
2
1
2
1
2
2
1
0
0
0
1
1
1
0
1
1
1
2
1
1
1
0
0
2
1
1
1
1
1
1
0
1
1
2
0
1
1
1
1
1
1
1
1
0
1
1
1
0
1
1
1
1
1
0
1
2
2
2
1
2
1
1
1
1
0
1
2
0
1
1
0
1
2
1
1
1
1
1
1
2
1
1
0
1
1
0
1
0
1
2
0
1
1
2
1
2
1
1
1
0
2
1
1
2
1
1
1
1
1
2
1
1
0
0
1
2
1
1
1
1
2
1
1
0
2
0
1
2
0
1
1
1
0
2
1
2
1
1
0
1
1
1
2
1
1
0
1
1
2
1
0
0
1
1
2
1
0
1
2
1
0
2
1
2
1
2
1
2
1
0
1
0
0
1
2
1
1
1
1
2
2
0
1
1
1
1
1
0
0
1
1
0
1
1
2
0
0
1
2
1
1
0
1
1
1
1
1
1
1
1
0
0
1
0
1
2
0
1
1
1
1
1
2
0
1
1
2
1
3
0
1
1
2
2
0
1
1
0
1
0
2
1
3
1
1
1
0
1
1
0
2
2
0
1
0
0
1
1
1
2
1
1
1
2
1
1
2
2
0
1
1
2
1
1
0
0
0
2
2
2
1
1
3
2
1
1
0
1
1
1
1
2
1
1
1
1
0
0
1
1
2
0
2
1
1
0
1
1
1
1
2
0
1
1
1
0
2
1
1
1
0
1
1
2
2
2
1
1
1
0
2
0
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
0
1
2
3
0
1
0
0
2
1
1
1
1
1
3
1
1
1
2
1
0
0
2
2
0
2
1
1
2
1
1
0
1
2
1
2
0
2
1
1
2
1
1
1
1
0
1
0
2
0
2
1
1
1
0
2
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
1
1
2
0
1
1
1
0
1
1
1
1
1
1
1
0
1
1
2
0
1
2
2
1
1
0
1
1
1
0
2
2
1
1
0
1
1
1
1
2
0
2
1
1
1
0
1
2
1
1
2
1
1
0
1
1
1
2
0
0
2
1
1
1
3
1
0
1
2
1
1
0
2
1
2
0
2
1
1
1
2
1
1
1
1
0
0
2
2
1
1
1
1
0
2
0
1
1
1
1
2
2
1
0
1
4
2
1
0
1
1
2
0
1
2
1
2
1
1
2
0
1
1
2
2
1
1
1
0
1
1
1
0
1
1
0
1
1
1
1
1
1
2
1
1
2
0
0
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
0
1
0
1
2
2
1
0
1
0
0
0
0
1
2
1
1
0
0
2
1
0
1
2
2
1
2
2
1
1
1
1
1
0
2
1
1
2
1
1
1
2
1
0
1
2
3
1
1
0
1
1
1
0
1
0
1
2
2
0
2
1
1
1
1
1
2
1
0
1
0
1
0
2
1
2
1
0
1
1
2
1
2
1
1
1
2
1
2
1
1
0
1
1
1
0
2
2
1
2
1
1
1
1
2
1
1
1
1
0
1
1
1
1
2
1
1
2
2
1
1
2
1
2
0
2
0
4
0
1
1
0
1
1
2
2
1
1
1
2
2
1
1
1
1
0
1
1
0
1
1
2
2
1
1
2
1
1
2
1
2
1
1
2
0
2
2
0
0
2
0
2
1
1
0
2
2
0
0
4
2
1
1
1
1
1
1
0
1
1
1
0
1
1
2
1
1
1
2
1
2
0
1
1
1
0
1
1
1
0
0
2
0
0
1
2
2
2
0
1
2
1
1
2
1
2
1
0
2
1
1
2
1
1
2
1
2
1
1
1
1
1
1
0
1
1
1
1
2
2
2
2
2
1
0
1
0
1
1
0
1
1
0
1
0
2
1
1
1
1
2
1
2
2
1
2
1
1
1
1
1
1
1
0
2
0
1
1
0
2
1
2
1
1
2
0
2
0
1
1
0
2
0
0
2
2
2
1
0
1
0
1
0
1
1
2
1
3
1
1
0
1
0
1
1
0
1
1
1
1
2
1
1
2
0
0
2
1
2
1
1
1
1
0
2
4
0
1
2
1
0
1
0
1
1
1
0
0
1
1
2
1
1
1
0
1
1
2
0
0
0
1
2
1
1
1
2
2
1
1
2
0
1
2
2
2
1
2
1
0
1
2
2
0
2
1
1
0
1
0
1
1
0
0
1
1
1
0
1
0
1
1
2
1
0
1
2
1
2
2
1
1
1
0
1
0
0
1
0
1
1
1
1
0
1
1
1
2
1
1
1
0
1
1
1
1
0
1
2
1
0
1
1
1
0
1
0
1
1
1
1
1
2
1
1
3
0
1
1
1
1
1
1
1
1
1
0
0
1
2
2
2
2
1
1
0
1
2
1
1
0
0
1
2
0
1
1
1
2
1
2
1
2
2
1
1
0
2
1
1
2
1
1
2
1
1
1
0
1
0
3
2
1
0
0
1
0
1
0
1
0
2
1
1
1
0
1
2
0
1
0
1
1
2
1
1
1
2
1
2
1
1
2
0
1
0
1
0
0
1
1
1
1
1
1
2
0
1
0
1
1
1
1
2
1
2
0
1
0
1
1
1
1
2
2
1
2
2
2
1
2
1
0
2
1
2
1
2
1
2
0
1
2
1
1
2
1
1
1
1
0
0
1
1
2
1
1
1
2
1
2
2
1
0
0
2
1
0
0
1
2
1
1
0
2
1
0
1
1
1
0
1
1
1
2
0
1
0
1
4
1
0
1
1
1
1
2
0
1
1
3
1
1
2
1
2
1
0
1
1
1
1
1
2
1
1
1
1
1
2
0
1
1
0
0
1
1
1
1
1
1
1
1
1
0
2
1
1
1
0
1
1
1
0
2
1
1
4
1
1
1
0
3
0
1
0
2
1
0
1
1
1
0
1
1
1
1
2
1
1
1
0
2
0
0
1
1
0
1
1
1
0
1
1
2
1
0
1
1
1
1
2
1
1
1
0
1
0
1
1
2
1
2
1
2
2
1
1
1
1
0
2
1
1
1
1
1
1
1
2
2
1
2
1
1
1
1
1
0
1
0
1
2
1
2
2
1
1
2
0
1
1
1
0
1
1
1
1
1
2
2
1
2
1
1
2
1
1
1
0
2
1
1
2
2
1
2
2
1
1
1
1
0
0
1
1
2
1
1
1
1
1
1
0
1
0
1
0
2
1
0
1
1
1
2
1
0
1
2
2
3
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
1
1
0
2
1
1
0
1
1
3
1
1
2
1
1
2
1
0
1
2
2
0
2
0
0
1
2
1
2
1
1
1
4
1
1
1
2
0
0
1
0
1
1
1
2
1
2
0
0
1
2
1
1
0
1
1
1
0
2
2
1
1
1
1
1
2
1
1
0
0
2
1
1
2
1
1
1
0
0
1
1
1
2
1
1
1
2
1
1
0
2
1
2
0
1
0
1
1
1
1
2
1
1
2
1
3
2
1
0
1
1
2
1
1
1
0
1
1
0
0
1
1
1
1
1
2
2
0
0
1
1
1
1
1
1
1
1
2
2
2
1
1
2
1
2
1
1
2
1
1
1
1
1
1
1
0
2
0
2
0
1
1
0
0
0
2
1
1
1
0
1
2
2
1
2
1
2
1
1
1
1
1
2
1
2
0
1
2
2
1
1
1
0
1
0
2
1
0
1
1
0
1
0
1
1
0
2
1
1
1
1
2
0
1
2
1
0
2
2
1
2
1
2
1
1
1
0
1
1
1
1
2
0
1
2
2
0
1
0
0
1
1
2
1
1
0
0
2
1
1
1
0
1
1
1
0
2
0
2
1
1
1
1
1
1
0
1
1
2
2
1
2
1
1
2
0
1
0
0
1
1
1
1
0
1
0
2
0
1
1
0
1
1
1
1
0
0
1
1
0
1
0
1
2
0
1
1
1
2
1
1
0
1
2
0
1
1
0
1
0
1
1
1
1
0
2
2
1
1
1
2
4
0
1
1
0
1
1
2
0
1
2
1
1
1
1
1
1
1
0
1
1
1
1
1
1
2
1
1
1
0
1
1
1
0
2
0
0
3
0
1
1
0
0
0
2
2
1
2
3
1
1
1
1
2
0
1
0
1
2
2
2
0
2
2
1
0
1
0
1
1
2
1
1
1
1
0
2
2
1
0
1
2
1
1
1
1
2
1
1
1
2
2
1
0
1
1
1
0
2
3
2
1
2
0
0
1
1
1
1
0
1
0
0
1
1
1
1
0
1
0
1
1
2
0
0
1
1
0
1
0
1
1
0
1
1
2
0
2
0
0
1
1
2
2
1
1
1
0
0
1
1
0
2
1
0
1
1
1
2
1
1
1
1
1
2
1
1
0
1
0
1
3
2
1
2
1
2
1
1
1
1
1
1
1
0
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
2
1
1
0
1
1
1
1
0
1
1
2
0
1
2
1
1
1
1
0
1
2
0
2
2
2
0
1
1
1
1
1
2
1
1
1
0
1
2
1
1
1
1
0
1
1
1
0
2
1
0
2
1
0
1
1
1
1
1
1
1
0
2
1
1
1
1
0
1
1
0
1
1
1
2
1
0
0
1
2
1
0
2
1
2
1
1
0
0
1
1
1
1
0
1
2
2
0
2
1
0
2
1
1
2
1
1
2
0
1
2
0
1
1
1
1
1
1
1
1
1
2
1
1
0
2
2
1
2
1
1
2
1
1
1
0
1
0
2
0
2
0
1
0
2
1
0
1
1
2
1
0
1
2
0
2
2
1
1
0
0
2
0
2
1
1
1
1
1
0
0
1
2
0
1
1
0
0
0
1
1
1
1
0
1
1
1
2
1
1
3
2
0
2
1
1
1
1
1
2
0
1
1
1
2
1
1
2
2
1
1
2
1
0
0
1
1
0
1
1
0
1
1
0
1
1
1
0
2
1
0
1
2
0
0
0
1
1
1
1
2
1
1
1
2
1
2
2
1
2
1
1
0
0
1
1
1
1
0
0
2
1
1
1
1
1
0
0
1
2
1
2
1
2
0
1
2
0
2
2
1
2
0
1
1
1
0
2
1
2
1
1
1
1
1
1
1
1
0
2
0
1
1
0
2
2
2
2
3
2
1
0
2
1
2
1
0
1
0
1
0
1
1
1
1
1
1
3
0
1
2
1
0
2
0
1
0
0
1
1
1
1
0
1
1
1
3
1
0
1
0
1
1
1
0
2
1
1
2
1
2
1
0
2
2
1
2
1
1
1
1
1
1
0
2
2
1
2
2
2
1
1
1
1
1
2
2
1
1
1
1
1
2
2
1
1
1
1
1
1
2
2
1
2
0
0
0
1
1
0
1
1
2
1
1
0
2
4
1
1
1
0
2
1
2
2
1
2
3
0
1
2
1
1
1
1
1
1
1
2
0
2
0
0
1
1
1
0
1
0
1
1
1
0
1
1
1
1
1
1
1
2
0
1
1
1
2
2
1
0
1
2
2
1
1
0
2
0
1
1
0
1
1
1
1
1
1
1
1
2
0
1
1
1
1
1
1
0
2
0
0
1
0
1
1
1
0
1
1
2
1
2
1
1
1
1
1
2
2
2
1
2
2
1
2
2
2
1
2
1
1
0
1
1
2
1
2
1
1
1
1
1
0
0
2
1
1
2
1
2
1
0
1
1
2
1
1
1
1
2
2
2
1
2
2
1
0
2
2
2
0
1
1
1
1
1
2
2
2
2
1
2
2
1
1
2
1
1
1
1
1
1
1
0
2
1
2
1
1
2
1
0
0
0
2
1
2
1
1
1
1
2
1
1
2
1
1
1
0
2
2
2
2
2
2
2
2
1
1
2
1
1
2
1
1
1
1
2
1
5
0
0
1
1
1
1
2
1
1
1
2
2
1
1
1
2
2
1
1
0
1
2
0
2
1
0
2
0
1
2
1
1
1
2
2
1
2
1
0
1
1
1
0
1
0
0
2
1
0
2
0
1
1
1
1
1
1
0
1
1
1
2
2
1
1
2
1
2
0
1
1
1
2
0
1
1
1
3
1
1
2
1
1
1
2
1
1
1
1
2
1
0
0
2
2
0
1
1
1
0
2
1
1
1
1
1
1
1
1
1
2
2
1
3
1
1
4
1
2
1
1
0
2
0
0
0
2
1
1
1
2
1
2
2
0
2
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
0
2
1
1
1
2
1
0
1
0
1
0
1
1
0
1
2
1
1
1
2
1
2
1
2
2
1
1
1
0
0
0
0
0
1
0
1
1
1
1
0
1
0
1
1
1
1
1
0
0
2
0
1
0
0
2
3
0
1
2
1
1
0
1
0
1
1
2
1
0
1
1
1
1
2
0
1
1
1
0
2
1
1
1
0
1
2
1
2
1
1
1
0
2
1
1
1
1
0
2
1
1
1
0
1
0
1
1
1
0
2
1
1
2
2
1
0
1
1
1
1
0
2
1
2
0
1
1
0
1
1
1
1
1
0
1
0
1
1
1
0
2
1
1
2
2
0
1
1
2
1
1
1
0
0
0
1
2
2
0
2
4
1
0
1
1
1
1
1
1
1
1
2
0
1
1
1
1
1
1
1
1
1
2
1
2
1
1
0
1
1
2
2
1
1
1
1
1
0
0
0
0
0
1
1
1
0
1
2
2
0
2
1
1
0
1
2
0
2
1
0
1
2
1
1
0
2
1
1
0
1
1
0
1
1
2
1
0
0
1
1
2
2
1
1
2
2
0
2
2
1
2
1
1
1
2
1
3
2
2
2
1
2
1
1
1
1
1
1
0
1
1
1
2
1
1
1
1
1
1
1
1
0
2
1
2
1
0
5
2
2
2
1
2
1
1
1
0
0
2
2
0
1
2
1
1
1
2
0
2
1
2
1
1
0
1
2
1
1
1
2
2
0
2
1
1
1
0
2
1
0
0
2
1
2
2
1
1
2
1
1
1
2
2
1
0
2
1
1
0
1
2
3
1
1
0
1
1
2
2
1
2
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
2
0
2
1
1
0
2
1
2
1
0
0
2
1
1
1
1
1
1
1
2
0
0
1
2
2
1
2
1
1
1
1
0
1
2
0
0
1
1
2
1
1
1
1
1
2
1
0
1
1
1
0
1
0
0
1
1
1
1
2
1
1
0
2
1
2
0
1
1
1
1
0
1
1
1
2
1
1
2
1
0
1
2
1
4
2
0
0
1
2
1
1
2
1
1
1
1
1
0
1
0
0
2
0
2
2
1
0
1
1
2
2
2
1
1
1
1
0
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
0
2
1
2
1
0
0
1
1
1
2
1
1
0
1
1
1
2
2
3
1
1
1
0
1
1
1
1
1
1
2
2
1
2
2
2
1
1
1
1
1
0
0
1
0
1
0
1
1
2
0
2
1
2
1
1
2
2
1
1
2
1
2
0
2
1
0
0
1
1
1
2
1
1
1
2
1
1
1
1
1
1
0
1
1
1
1
1
2
1
1
1
1
0
2
1
0
1
1
1
1
1
3
0
0
1
0
1
2
0
0
0
1
1
1
2
1
2
1
1
1
1
1
1
1
2
2
1
1
1
3
0
2
1
1
1
1
1
2
1
1
1
1
1
1
2
0
1
1
1
2
2
1
0
2
1
1
2
1
1
1
1
0
2
2
1
2
2
1
1
1
2
1
1
0
1
1
2
1
1
1
1
1
0
1
0
1
1
0
0
1
1
0
1
1
1
1
2
1
1
0
2
0
1
1
2
1
1
1
1
2
1
1
1
1
1
0
1
2
1
3
1
1
2
1
1
1
1
2
1
1
1
1
2
0
1
1
0
1
1
1
2
1
2
1
1
2
0
0
0
0
2
1
2
2
0
2
1
1
1
2
1
1
1
1
1
1
1
1
0
0
1
0
1
1
0
1
0
1
1
2
2
0
1
1
1
0
1
1
1
1
1
2
1
1
2
2
2
0
0
1
1
1
2
1
0
2
2
2
1
1
1
1
1
1
0
1
1
1
1
0
2
1
1
2
2
1
1
0
1
1
0
1
1
1
1
1
1
1
0
2
2
1
1
0
1
0
2
2
1
1
1
2
1
1
1
1
1
1
4
2
2
1
1
1
1
2
2
2
1
1
0
2
1
1
1
0
1
0
1
1
2
0
2
2
2
1
2
1
1
2
1
1
0
1
1
2
1
1
1
2
0
1
1
1
1
0
1
1
1
1
1
2
1
0
0
1
1
0
2
0
1
2
1
1
1
1
2
0
1
0
2
1
0
1
1
1
2
1
1
3
1
1
0
1
2
1
2
1
2
1
1
1
1
1
1
1
0
1
0
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
0
1
1
2
2
1
1
0
1
0
2
2
1
1
1
1
0
1
2
2
1
2
2
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
2
1
0
1
1
1
2
1
2
2
1
1
0
1
1
2
1
0
0
1
1
0
1
1
1
2
0
0
1
0
2
1
1
1
1
0
1
2
2
2
1
1
1
1
1
1
1
2
0
0
1
1
2
0
0
2
1
0
1
1
2
0
1
0
0
0
3
2
2
2
1
1
1
1
2
2
1
1
1
1
1
2
2
1
0
1
1
2
1
2
1
2
1
0
2
0
1
0
1
1
1
0
1
2
1
2
1
2
0
2
1
1
1
0
1
1
2
2
1
1
2
1
2
1
2
1
2
1
1
0
2
1
1
1
2
1
0
0
1
2
1
0
2
1
2
2
1
1
1
1
0
1
1
1
1
0
1
2
1
1
1
2
1
2
0
2
1
2
2
1
2
1
1
2
0
2
1
1
1
1
1
1
1
1
1
1
2
2
1
1
0
1
1
1
1
1
1
1
0
1
0
1
0
0
1
2
1
1
2
0
1
1
0
1
1
0
1
1
0
2
0
0
1
3
2
0
2
1
1
0
2
1
1
1
1
1
1
1
1
1
1
2
1
1
0
2
1
0
0
1
1
1
2
0
1
1
1
0
1
1
2
0
1
1
1
0
1
0
1
2
0
1
1
1
2
2
1
1
2
1
0
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
2
1
0
1
1
2
1
1
1
1
1
2
0
1
2
0
1
1
1
0
2
2
1
1
0
1
1
2
2
2
0
2
0
1
0
1
2
0
1
1
1
1
2
1
1
2
0
2
1
1
1
0
0
2
2
1
1
1
1
0
1
0
1
1
1
1
2
0
0
1
1
1
1
1
1
1
0
1
1
1
1
1
2
2
1
2
1
2
0
1
0
1
1
0
1
0
1
1
1
0
1
1
1
1
1
2
2
1
1
1
1
1
1
1
0
0
1
2
1
1
2
0
0
0
2
2
2
2
1
1
1
1
1
1
0
1
1
0
1
2
1
1
2
1
1
2
2
1
1
2
1
0
1
2
1
2
1
0
1
1
1
1
1
1
1
1
1
1
1
1
0
1
0
1
1
1
2
2
1
1
1
1
1
1
1
0
1
1
1
1
1
0
1
1
1
1
1
1
1
1
0
0
1
1
0
2
0
1
1
1
0
1
2
1
1
1
0
1
0
2
1
1
2
1
0
1
1
0
1
2
0
1
2
2
0
2
2
0
0
1
1
1
0
2
1
0
0
1
1
1
1
1
1
2
1
1
1
0
1
1
2
1
1
1
1
0
1
0
1
0
1
2
1
0
2
0
1
1
0
1
1
2
2
1
1
1
2
1
1
2
3
1
2
0
1
2
0
1
2
1
1
1
0
1
2
2
2
0
1
1
1
1
1
0
2
1
2
1
0
1
1
2
0
1
0
1
1
1
1
0
2
2
1
1
2
0
1
2
0
0
0
1
0
2
1
1
2
1
2
2
0
2
0
1
0
2
2
0
2
0
2
1
0
1
1
1
1
1
1
0
2
2
2
1
2
0
1
1
2
2
1
1
1
1
0
0
2
1
1
1
2
2
2
1
0
1
2
1
1
1
0
0
1
1
0
1
2
2
1
0
1
1
1
1
0
2
0
2
0
1
0
2
1
0
1
1
1
2
1
0
2
1
2
1
2
1
3
1
1
1
0
1
0
1
1
1
2
1
1
2
1
2
2
1
2
1
2
0
1
1
1
1
1
1
0
0
1
1
1
1
2
1
2
1
1
1
2
1
0
1
2
2
1
1
0
0
2
1
1
1
0
1
2
0
2
1
0
1
1
1
2
1
1
1
0
1
2
2
0
1
1
1
1
0
2
2
2
2
1
2
1
1
0
1
1
1
1
1
0
2
0
3
1
1
0
1
1
1
2
1
2
0
2
1
1
1
1
0
1
1
2
0
2
1
1
1
0
1
1
0
1
2
1
1
0
0
1
1
1
1
0
1
1
1
2
1
0
1
1
2
2
2
2
1
3
0
1
1
1
1
2
1
1
1
2
1
1
1
1
2
1
0
1
1
1
0
2
2
2
1
2
1
1
1
2
0
0
1
2
1
1
0
0
1
1
1
1
1
0
0
0
0
1
1
1
1
0
2
1
2
0
2
2
1
1
1
1
1
2
1
1
0
1
1
1
1
0
2
1
0
0
1
1
0
1
1
0
1
1
1
1
1
1
0
2
2
2
1
1
1
2
1
0
1
1
1
1
2
2
0
2
0
1
2
1
0
0
1
1
2
1
1
1
0
1
1
1
1
0
1
2
2
1
1
2
1
2
1
2
0
1
2
0
0
0
2
1
2
2
1
1
0
2
0
1
0
1
1
0
2
0
1
0
0
1
1
2
2
0
1
0
1
2
2
1
1
1
1
1
1
2
0
2
3
2
1
1
0
1
1
0
0
2
1
0
1
1
1
0
1
1
1
1
2
0
2
2
1
1
0
2
1
1
1
1
2
1
0
0
0
2
1
3
2
2
0
1
1
1
0
1
0
0
1
1
0
1
0
0
1
1
1
2
1
2
2
0
2
1
0
0
1
2
1
1
2
1
1
2
1
2
0
1
0
1
2
2
3
2
0
2
1
1
1
0
1
1
2
1
1
0
1
1
2
1
0
2
1
1
1
1
0
1
1
2
1
0
1
1
1
1
1
1
1
2
3
1
1
1
2
1
1
1
0
2
1
1
2
1
0
1
0
1
0
1
1
0
1
1
1
1
2
0
1
2
1
2
1
1
1
1
1
2
0
0
0
1
1
1
0
1
1
0
2
1
0
0
1
1
1
0
1
1
1
0
1
1
3
2
2
2
1
2
1
1
1
2
1
2
0
1
1
2
2
0
1
1
1
1
0
1
0
1
2
1
0
3
1
1
1
1
2
1
1
1
1
2
1
0
0
1
0
1
0
1
1
1
1
1
1
0
1
2
2
1
1
0
0
2
1
2
2
1
2
0
1
2
1
2
2
2
1
1
2
1
1
1
1
1
2
1
2
2
3
1
1
1
2
1
1
1
0
1
1
2
1
2
2
2
1
1
1
1
0
1
1
1
0
0
1
1
2
0
2
0
2
1
0
1
2
2
2
1
2
1
0
0
1
1
1
1
0
2
2
0
1
1
0
1
1
1
2
1
1
1
1
1
4
0
1
3
1
1
1
1
0
1
0
1
1
1
1
1
1
1
1
2
1
0
1
1
2
1
1
2
1
1
1
1
0
1
2
1
1
0
2
2
1
2
3
1
1
1
1
1
1
2
0
1
0
2
1
1
1
2
1
1
1
1
1
0
1
3
1
1
0
1
2
1
1
1
1
2
1
0
1
1
0
0
1
2
1
1
0
1
1
0
1
1
1
0
0
1
1
1
1
1
2
1
1
1
1
2
0
1
1
1
0
1
1
0
0
1
1
1
1
1
0
1
1
1
0
0
0
2
0
1
1
1
2
2
1
1
1
2
2
1
0
2
2
1
2
1
1
1
0
1
1
0
1
1
0
1
1
0
0
1
1
1
1
1
1
2
1
1
1
0
0
1
2
0
1
2
1
2
1
2
1
1
1
1
1
1
1
1
0
2
1
1
1
1
1
0
1
2
1
1
1
2
0
1
1
2
1
2
0
2
1
1
0
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
2
0
1
0
1
2
1
1
1
0
0
1
0
1
2
1
1
0
1
1
0
0
1
0
0
1
1
0
1
1
0
1
0
2
1
1
1
2
1
1
1
1
2
2
1
2
2
1
2
1
2
2
1
2
1
1
0
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
0
1
0
1
1
2
0
2
2
2
1
1
2
1
1
1
0
1
0
1
1
0
2
2
1
0
2
1
1
0
2
1
2
1
1
2
0
1
1
0
1
2
2
1
2
1
1
1
1
0
1
1
1
1
0
2
1
0
1
1
0
1
0
1
0
1
2
1
1
0
1
1
0
1
1
2
1
1
2
1
1
2
1
1
1
2
1
1
1
0
1
1
0
1
0
1
0
1
0
2
1
0
0
1
1
1
0
1
0
1
2
2
2
1
1
1
1
1
2
1
1
1
1
1
0
1
1
0
1
1
2
1
1
1
2
1
1
1
1
1
2
2
2
1
1
1
2
2
1
1
1
0
1
2
1
1
1
1
2
1
1
2
0
1
0
1
0
2
2
1
1
0
0
2
1
1
1
1
2
1
0
1
1
1
1
2
2
2
0
2
1
0
0
2
1
2
0
1
1
2
1
0
1
1
0
0
1
0
1
0
0
1
0
1
2
1
0
1
1
1
1
1
1
2
1
1
1
1
0
1
1
1
1
2
1
1
2
1
1
2
2
1
2
0
1
0
3
0
2
1
2
1
1
1
2
1
0
1
2
1
1
1
0
1
1
1
1
1
2
1
0
1
1
2
2
2
2
1
0
1
2
1
1
1
0
0
1
0
1
0
1
1
1
1
0
2
0
2
2
1
0
1
2
1
1
1
1
0
1
1
1
1
1
1
3
1
2
0
1
1
2
1
0
0
1
1
1
1
1
1
1
2
1
1
1
1
2
2
1
1
1
1
0
2
2
1
1
0
2
1
2
1
1
3
1
1
0
0
1
0
1
1
0
1
0
1
0
2
1
0
2
2
1
3
2
1
1
0
2
1
0
1
1
2
1
0
0
1
1
1
1
0
2
2
1
1
0
1
1
0
1
1
1
1
2
1
0
0
1
1
2
0
1
0
1
0
0
1
0
1
1
2
2
0
0
1
1
0
0
2
1
1
1
1
2
1
2
1
2
1
1
2
1
1
1
0
1
1
1
0
2
1
2
1
1
1
0
0
0
1
0
2
1
1
1
1
1
1
1
2
0
0
2
1
2
1
1
0
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
2
1
2
1
2
0
1
1
1
1
1
0
0
0
1
1
0
1
1
1
2
1
2
2
1
2
1
2
1
1
2
2
1
0
1
1
2
1
0
1
1
0
1
1
2
1
1
1
1
1
2
1
2
1
2
1
2
1
0
1
1
1
0
1
1
0
1
1
0
0
1
1
1
2
2
2
1
1
1
2
2
1
1
0
1
1
1
0
1
2
1
1
3
1
0
0
3
0
1
1
1
1
1
0
2
1
1
1
2
0
1
1
2
2
1
2
1
3
2
1
1
2
2
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
0
1
0
1
4
1
0
0
1
0
0
0
1
1
1
1
2
2
0
0
2
1
1
1
1
1
2
1
1
1
2
1
2
0
1
1
1
1
1
1
1
1
0
1
1
2
1
2
0
1
2
1
2
1
2
1
0
1
1
1
0
1
2
0
1
2
1
0
0
2
1
1
1
0
1
1
1
2
3
1
1
1
2
2
0
2
1
2
2
1
1
1
0
1
1
2
1
1
1
2
1
0
1
2
2
0
2
1
1
0
1
1
1
1
1
1
2
0
0
1
1
1
1
0
2
1
0
1
0
2
1
1
1
1
1
1
2
1
1
2
2
1
2
1
1
1
1
2
2
1
1
1
1
1
2
1
1
1
1
1
2
0
1
2
2
1
0
1
1
1
0
2
1
2
5
1
0
1
1
1
1
1
0
0
1
2
1
1
2
1
1
2
1
1
0
0
2
1
0
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
0
2
1
2
1
1
1
1
0
2
1
1
0
1
1
1
0
2
1
1
1
0
0
1
2
1
2
1
1
1
2
1
0
1
0
1
0
1
1
1
0
2
0
2
1
1
1
1
1
1
0
2
1
1
0
1
2
1
1
1
2
0
2
2
1
2
1
1
2
1
1
1
0
1
0
1
1
1
1
1
0
2
1
2
1
1
1
2
1
1
0
1
2
1
0
1
2
1
2
1
2
2
1
2
2
3
0
1
1
0
2
1
0
1
2
1
0
1
1
0
1
1
2
1
1
2
0
1
0
0
1
2
0
1
2
1
1
1
0
1
1
1
1
1
1
1
1
2
1
2
0
2
2
0
2
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
0
1
1
1
1
2
0
1
2
1
0
1
0
1
2
0
2
0
1
2
1
2
1
2
1
0
2
0
2
0
2
1
2
1
2
1
2
1
2
1
0
0
2
1
2
2
1
1
1
1
1
2
1
0
0
1
0
1
0
1
2
1
0
0
0
1
1
1
2
2
2
1
2
0
2
1
2
0
0
2
1
1
1
1
1
1
1
0
0
3
1
1
1
1
1
1
2
1
2
1
0
2
2
1
2
1
2
0
0
1
2
1
1
1
1
1
1
1
1
1
1
0
2
1
1
1
2
1
1
1
1
1
1
1
1
0
1
0
1
1
1
2
1
1
1
1
1
0
2
1
0
1
1
1
1
1
1
2
1
0
1
1
1
1
1
0
1
0
1
0
1
1
1
0
2
1
1
1
1
1
1
2
1
2
0
2
0
1
1
1
2
1
1
2
2
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
2
1
1
1
2
1
0
2
1
1
1
1
1
2
1
1
0
2
2
1
0
1
0
1
1
1
0
0
2
1
1
0
0
2
0
0
0
2
1
1
1
1
2
2
1
1
1
1
3
2
1
1
1
2
0
0
2
1
1
1
1
1
1
1
1
1
1
2
0
1
2
0
1
2
2
0
1
1
1
0
1
0
0
1
1
2
1
1
1
1
2
1
2
2
2
2
1
1
0
0
1
2
1
0
1
1
2
2
1
0
0
0
1
2
1
2
1
1
1
0
1
1
0
2
1
0
1
0
0
0
2
1
1
1
1
2
1
1
0
2
0
2
1
1
1
2
0
0
2
2
0
0
1
1
2
1
1
2
2
0
2
1
0
2
2
2
0
1
1
0
1
2
1
2
2
1
2
2
1
1
2
1
2
0
1
0
2
0
0
1
1
1
1
1
1
0
0
0
0
2
1
1
0
1
1
1
1
0
2
1
1
1
3
2
1
2
2
2
2
1
2
1
1
2
0
2
0
1
2
0
1
2
0
0
2
2
2
1
0
2
2
1
0
1
2
1
1
0
1
1
1
1
1
0
1
1
0
1
1
1
2
1
1
0
1
2
2
0
1
1
1
1
1
1
1
1
1
1
1
2
3
1
0
1
1
1
1
1
1
1
0
0
0
2
1
0
1
1
1
1
1
0
1
1
1
2
0
2
1
1
2
2
0
0
2
2
1
0
2
1
1
0
1
1
1
1
1
2
1
2
2
2
2
1
1
1
1
1
2
0
1
0
0
1
0
1
1
0
1
1
2
2
2
1
1
1
1
1
1
1
0
1
2
0
1
0
1
2
0
0
1
1
1
1
0
0
1
1
1
1
1
0
0
1
0
1
0
0
1
0
1
1
1
2
1
1
2
1
2
1
1
0
1
1
0
2
1
0
0
1
0
1
1
1
1
1
1
0
1
1
1
1
1
2
2
1
0
1
1
1
1
1
1
1
1
2
1
1
2
1
1
0
2
1
1
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
0
1
1
1
2
1
1
2
1
1
0
1
1
1
1
1
0
1
0
2
2
1
2
2
1
1
1
1
2
2
1
1
1
1
2
1
0
0
1
0
1
0
1
1
2
1
0
1
1
1
1
1
1
0
1
1
1
1
0
1
1
2
2
1
2
0
2
0
1
2
0
2
1
2
1
1
2
1
1
2
1
1
2
1
1
0
1
2
1
2
1
1
0
1
1
1
2
1
2
2
1
1
2
2
1
0
1
2
1
1
1
3
1
1
1
2
2
1
0
2
1
1
3
0
1
1
1
1
0
1
1
2
1
1
1
0
1
2
1
2
2
1
2
1
2
1
1
2
1
1
1
2
1
2
1
2
1
1
1
1
1
1
0
1
1
0
1
1
1
1
2
2
0
0
1
1
1
1
2
1
1
1
2
2
1
0
1
1
1
1
3
2
2
1
1
2
2
1
1
1
1
2
0
0
1
1
2
1
1
0
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
0
1
2
0
2
2
1
1
0
0
1
1
2
1
2
0
2
1
2
1
0
0
2
1
1
2
2
2
0
1
2
1
1
0
1
2
1
2
0
1
0
1
1
1
1
2
1
1
0
0
2
2
1
1
1
1
0
1
1
0
1
1
0
1
2
1
1
2
0
2
1
0
2
1
0
1
1
1
0
1
1
1
2
1
2
1
1
1
1
1
1
1
0
1
2
0
1
1
1
1
0
1
2
1
0
1
2
1
1
1
1
1
1
1
0
1
0
1
0
1
2
1
1
0
1
1
2
1
0
1
2
1
0
0
2
1
2
0
0
0
0
1
1
1
1
1
1
0
1
0
1
1
1
0
1
3
1
2
2
1
2
0
1
1
1
1
0
1
1
0
2
1
0
1
2
1
0
0
0
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
0
2
2
0
1
0
1
2
0
2
0
2
1
1
1
1
2
2
0
2
0
1
2
1
2
0
2
1
0
0
1
1
2
0
1
1
2
0
1
1
1
1
0
2
0
1
1
1
1
0
1
2
1
1
1
1
1
1
0
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
0
0
0
0
2
1
0
1
2
1
1
1
1
1
2
3
1
1
1
2
1
0
1
2
1
1
0
2
2
0
1
2
1
1
2
1
1
0
0
2
0
1
2
1
1
1
1
2
1
2
0
1
0
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
2
0
0
1
1
1
0
2
1
1
1
2
0
1
1
1
1
1
1
0
1
1
2
0
1
0
1
2
1
0
1
1
0
1
2
1
1
2
2
1
0
1
1
2
0
2
1
0
1
1
1
2
0
2
3
1
2
2
1
1
1
2
1
1
0
2
1
1
1
1
0
1
1
1
0
1
1
1
1
1
1
1
1
1
0
1
2
0
0
1
2
1
1
1
1
1
0
2
0
2
1
1
0
3
0
0
1
1
1
2
1
1
2
1
1
1
1
1
0
1
2
2
1
1
1
1
2
1
2
2
1
1
1
0
1
2
1
1
1
1
0
0
1
0
1
0
0
1
1
1
0
1
0
1
1
1
2
1
1
1
2
2
1
1
0
1
1
0
0
2
1
0
1
1
1
1
1
1
1
1
7
2
3
0
0
2
2
2
1
0
0
0
1
2
1
1
1
1
0
1
2
2
1
2
1
0
1
2
0
0
1
1
2
2
1
1
1
1
1
2
0
1
1
1
1
1
0
1
1
2
2
1
1
1
0
1
1
2
1
2
2
1
1
1
1
0
2
1
1
0
1
2
0
0
1
0
1
1
1
1
1
0
1
2
1
1
3
2
1
1
1
1
2
1
0
1
1
1
1
1
1
2
5
2
1
2
1
0
1
1
0
1
1
1
0
0
1
1
0
1
0
0
2
1
1
1
2
1
0
2
1
1
1
3
0
1
2
2
1
1
1
1
1
0
1
0
1
2
1
2
0
1
1
0
2
1
0
2
1
1
1
0
2
2
1
1
1
0
1
0
1
1
2
1
0
1
2
0
2
1
1
2
0
1
1
1
0
0
0
1
1
2
1
0
1
1
1
1
2
0
1
1
1
2
2
0
1
1
2
1
1
2
2
1
1
1
2
0
0
1
0
2
1
1
1
1
0
1
2
0
1
1
1
1
1
1
1
2
0
2
1
0
1
1
1
1
1
1
1
2
1
2
1
2
1
0
0
1
2
2
1
0
0
1
1
1
1
1
2
1
1
1
1
1
1
0
0
1
1
0
1
1
2
1
1
1
2
2
0
1
2
1
0
0
1
1
1
2
1
1
1
0
1
2
1
1
2
1
1
2
0
2
0
1
1
1
0
0
2
2
1
0
0
0
2
2
2
0
1
2
2
2
1
1
2
2
1
1
1
2
1
2
2
1
1
0
1
2
2
0
1
2
1
1
2
2
1
1
1
2
2
0
1
0
2
0
1
1
1
1
1
0
1
2
1
1
2
1
0
1
0
1
2
0
1
1
1
2
1
1
1
0
1
1
2
1
0
1
2
2
1
1
2
2
2
2
2
1
1
0
2
1
1
2
1
1
2
1
1
1
1
1
0
1
2
0
1
1
1
0
1
2
1
1
1
1
1
2
1
1
2
1
2
1
0
1
0
2
2
2
1
1
1
0
0
1
0
1
1
1
1
1
1
2
1
0
2
1
1
1
2
0
1
0
2
1
1
2
0
2
0
0
0
3
1
1
2
2
2
0
1
1
1
1
1
2
0
1
1
0
1
0
1
2
0
1
0
1
1
0
1
1
1
0
1
1
1
2
1
1
1
1
0
1
1
1
0
0
0
1
1
1
2
2
1
1
2
0
0
1
0
2
0
2
1
1
1
1
1
0
2
2
1
1
1
2
0
2
1
1
1
0
2
1
1
1
1
1
2
1
2
1
2
1
1
2
1
2
0
0
1
1
1
2
1
1
1
2
1
0
1
1
1
1
2
2
0
0
1
2
1
1
0
1
0
2
1
1
2
0
2
2
1
0
1
1
2
1
1
1
2
2
1
1
2
1
0
1
1
1
0
1
1
1
0
1
1
1
1
1
2
2
2
0
2
1
1
1
2
0
1
2
1
1
1
1
1
0
2
0
1
2
0
1
2
2
1
1
1
1
1
1
1
0
2
1
0
2
1
0
2
0
2
0
1
1
1
1
1
1
1
1
1
1
1
1
0
2
1
2
0
1
1
2
1
0
1
2
1
1
1
1
0
0
2
1
1
1
1
1
1
0
1
2
1
1
0
1
1
1
1
2
2
1
1
1
1
1
0
1
0
1
1
0
1
2
1
1
1
3
1
2
2
0
1
1
1
1
1
2
1
2
0
2
1
0
1
1
0
1
1
2
2
1
1
1
1
1
1
1
2
2
2
1
1
2
2
2
2
1
1
1
1
3
0
1
1
2
1
1
1
1
1
1
1
2
1
1
1
0
2
1
2
1
2
1
0
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
0
0
0
1
1
1
1
1
0
1
2
1
1
1
1
1
1
1
0
0
1
0
1
1
2
1
2
1
0
2
2
1
1
1
1
2
1
0
0
0
1
2
0
1
1
0
0
1
1
1
2
1
2
2
1
1
1
1
1
2
2
0
1
2
0
1
0
1
2
2
1
1
1
2
1
1
0
2
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
0
2
1
2
2
2
1
2
1
1
1
1
2
1
0
2
2
1
1
0
2
2
1
1
0
1
1
1
1
2
0
1
1
0
2
1
1
1
1
2
1
2
0
0
2
2
0
2
1
0
1
1
2
1
0
0
2
1
1
2
1
0
1
1
0
1
1
1
1
0
0
1
1
1
1
0
2
0
2
1
1
2
2
2
2
2
2
0
1
1
2
1
1
2
1
1
1
2
0
1
0
1
2
2
1
1
0
2
1
1
1
2
1
1
1
1
1
0
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
0
1
1
1
1
1
1
0
1
2
2
2
1
1
2
1
1
2
1
1
1
1
1
1
2
1
1
0
2
2
0
1
2
2
1
1
1
2
1
2
0
1
1
1
2
1
1
1
2
1
4
1
0
1
0
0
1
1
1
0
1
1
1
1
1
0
1
0
1
2
0
1
2
0
1
1
1
1
2
1
0
1
1
1
1
1
1
2
1
2
1
1
2
1
1
2
1
1
1
1
2
2
1
1
1
0
0
1
1
2
1
2
0
2
1
1
2
1
1
2
0
1
1
1
1
1
3
1
1
2
1
2
1
1
0
3
1
0
2
2
0
1
1
1
1
1
1
1
0
2
1
1
2
2
0
1
1
0
1
1
0
1
1
1
1
1
1
0
1
1
2
2
0
0
2
2
1
1
0
2
0
1
1
0
1
2
1
1
0
1
1
1
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
0
0
1
1
1
2
0
1
1
1
0
0
1
0
0
0
1
1
2
1
3
0
1
2
1
1
2
2
1
0
0
1
0
1
1
1
2
2
0
1
2
1
1
2
1
0
1
0
1
2
1
0
1
0
2
0
0
1
1
0
1
1
0
2
2
1
1
2
0
1
1
0
1
2
1
1
1
1
1
0
0
2
1
1
1
2
2
1
0
1
1
0
1
2
1
1
1
1
2
2
0
1
1
0
0
1
1
0
0
2
1
1
1
1
0
1
0
2
0
2
0
0
1
1
1
1
0
1
1
0
1
1
2
2
3
2
1
1
2
0
1
0
1
1
2
0
1
0
1
1
2
1
2
1
2
2
1
1
1
1
0
1
1
1
1
1
0
1
0
2
2
1
1
1
0
1
0
2
2
0
1
0
2
1
2
1
1
1
1
1
0
2
0
0
2
1
2
1
1
1
0
2
0
1
2
2
1
1
0
0
0
1
0
1
2
0
2
2
2
0
0
1
2
0
0
1
1
1
2
1
2
2
1
2
1
1
1
1
0
1
1
1
0
2
2
1
1
0
1
1
1
2
1
1
2
2
0
1
1
1
1
1
1
1
1
2
1
0
2
1
0
1
0
1
1
1
1
1
1
0
2
1
0
0
1
1
1
1
1
1
0
1
1
1
1
1
1
2
1
2
1
1
2
2
2
1
1
0
1
0
1
0
2
3
1
1
1
2
2
1
0
1
1
1
1
2
1
1
1
1
1
1
0
2
1
1
2
0
0
1
2
1
2
0
2
0
0
2
0
0
0
0
2
1
0
1
0
1
1
1
2
1
0
1
2
2
0
2
1
1
1
1
1
2
1
0
1
1
2
2
1
1
1
2
2
0
1
0
1
1
0
1
2
2
1
0
1
2
2
2
2
2
2
1
2
2
2
2
2
1
0
0
1
1
1
1
0
1
1
1
0
1
0
2
1
1
1
2
1
1
1
1
1
2
1
1
1
0
1
1
1
1
2
2
2
1
1
1
2
1
1
0
2
1
2
1
2
1
1
1
1
2
2
1
0
1
2
1
1
0
2
1
1
1
2
1
2
1
1
1
0
1
1
0
0
1
0
1
0
0
2
1
2
0
1
0
1
1
2
1
2
1
2
1
1
0
1
2
1
1
1
0
1
2
2
1
2
1
2
1
2
0
2
2
0
0
1
1
2
1
1
1
1
0
1
0
2
1
1
1
0
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
2
1
1
1
2
1
1
2
1
1
3
0
1
2
1
1
2
0
0
1
2
0
1
1
1
1
2
2
1
0
1
2
0
0
1
1
1
1
1
0
1
1
1
1
1
1
1
1
0
0
2
0
2
2
2
1
1
1
2
1
1
0
1
2
0
1
2
2
0
1
2
1
1
2
1
2
0
0
1
1
1
2
2
2
2
2
1
1
0
2
0
1
1
1
2
1
0
1
1
1
1
0
2
0
1
1
2
0
1
1
1
1
0
1
1
3
1
1
2
1
1
1
2
2
0
0
2
1
1
0
0
2
2
1
2
1
0
0
1
1
2
1
0
2
0
1
1
1
1
0
1
1
2
2
2
1
1
1
0
1
1
1
1
0
2
1
1
2
1
1
1
1
0
1
1
1
1
1
0
1
2
2
1
1
1
1
1
0
0
1
2
2
1
0
2
1
1
2
2
1
2
4
1
1
1
1
0
1
4
1
1
0
1
0
2
1
1
0
0
1
2
2
0
1
0
1
1
0
1
1
2
1
1
1
0
1
2
1
1
1
2
1
1
0
1
1
0
0
2
1
1
2
1
0
2
1
1
2
1
1
1
2
0
1
1
2
1
1
0
1
1
2
0
1
1
2
1
1
1
1
1
0
2
1
1
1
2
1
1
1
2
0
1
1
1
0
1
0
1
2
3
2
2
0
0
1
1
2
0
1
2
2
0
1
1
0
1
1
2
2
1
0
1
1
1
2
1
4
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
0
1
0
2
1
1
1
1
0
1
1
0
1
1
2
2
2
2
1
0
1
1
1
0
2
1
1
1
1
1
1
1
1
2
1
1
1
1
3
1
2
0
1
2
1
1
2
1
1
1
1
1
1
0
1
1
2
1
2
0
1
1
1
1
1
1
1
2
1
1
2
1
0
1
1
2
1
1
1
2
1
1
1
1
1
1
0
2
2
0
1
0
2
1
1
1
1
0
1
2
1
2
2
1
2
1
1
2
1
1
1
1
1
1
2
0
2
1
0
0
2
1
2
1
0
0
1
1
1
1
2
1
0
1
2
2
2
1
1
1
1
1
2
0
2
0
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
0
1
0
1
1
0
1
2
1
1
1
2
1
1
0
2
1
0
1
2
1
2
2
1
1
2
1
1
0
1
1
0
1
0
2
2
1
0
0
0
0
0
1
1
2
1
1
1
1
1
1
2
0
0
2
1
1
1
0
2
2
1
2
1
1
2
1
1
0
1
1
1
2
2
1
1
2
2
1
2
1
0
1
1
1
0
2
2
2
2
1
1
1
2
0
2
1
1
1
1
1
1
2
1
1
1
0
2
0
2
2
1
1
1
1
1
2
1
2
1
2
1
1
1
1
1
1
1
1
2
2
1
2
1
1
1
1
0
1
1
0
1
1
1
2
1
1
1
1
1
1
0
1
1
1
2
1
2
0
1
1
1
2
0
1
2
1
1
1
1
0
1
1
1
1
1
2
1
0
1
2
1
2
1
1
2
0
1
1
2
2
1
1
2
2
0
1
0
1
1
0
2
2
2
1
1
1
1
1
1
2
0
1
1
0
1
0
0
2
1
2
1
2
2
1
2
1
1
2
1
2
1
0
1
0
1
1
2
0
1
1
2
1
1
1
0
1
1
0
0
2
1
1
1
0
1
1
1
2
1
2
1
1
1
0
1
1
4
1
1
1
2
0
1
1
0
1
1
2
2
2
1
1
1
0
1
0
0
1
2
1
1
1
1
2
1
0
1
2
2
1
0
1
1
1
0
1
1
1
1
2
1
0
2
1
1
0
1
0
2
1
2
1
1
2
0
1
2
0
1
1
2
2
1
2
1
1
1
1
2
0
1
0
1
1
2
1
1
2
2
1
1
1
1
0
2
0
1
2
0
1
1
1
1
0
1
0
1
1
2
1
0
1
1
2
1
1
1
1
1
2
1
1
1
1
1
0
1
0
2
1
1
1
1
1
1
2
0
1
1
1
1
2
2
0
2
0
0
2
2
1
0
1
0
1
1
1
1
3
0
2
0
1
0
2
0
1
1
1
1
1
1
2
2
1
1
1
1
1
2
2
1
1
2
1
2
2
1
1
1
1
2
1
0
1
1
1
1
1
0
1
1
0
1
2
1
1
2
1
1
2
2
0
0
1
1
0
1
0
1
0
2
2
1
0
1
2
1
1
0
1
1
3
2
1
2
2
1
1
1
1
1
1
0
1
0
1
0
1
0
2
1
1
1
1
1
1
1
1
0
1
1
2
1
1
0
2
1
1
2
1
1
3
0
2
2
2
2
1
1
0
1
1
1
0
2
2
1
1
0
2
3
1
4
1
6
1
1
1
1
1
1
2
1
0
1
1
1
1
1
1
2
1
2
1
1
2
0
1
1
2
1
1
1
1
2
2
1
1
2
1
1
2
1
0
0
1
1
1
0
1
1
2
0
1
1
0
0
0
2
1
1
1
1
0
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
2
1
2
2
1
1
0
1
1
0
1
1
1
1
1
1
0
1
1
0
1
2
2
2
2
1
1
0
0
0
1
1
1
2
2
2
1
1
2
0
2
1
2
0
1
1
1
1
1
1
0
2
0
1
1
2
1
2
1
1
2
2
2
2
1
2
1
1
0
1
1
2
0
1
1
1
1
1
0
1
1
2
1
1
2
1
1
1
1
1
0
1
1
2
1
1
1
2
1
1
1
1
2
2
1
1
1
1
2
1
1
0
2
1
0
1
0
0
1
0
2
1
0
2
0
2
0
0
2
2
1
1
2
1
1
0
1
1
2
1
1
1
1
0
1
1
1
1
0
2
1
2
1
1
2
2
1
2
1
1
2
1
2
1
1
0
1
1
2
1
1
1
1
2
1
1
3
2
1
1
2
1
2
0
1
1
1
1
1
1
1
1
1
1
2
1
1
0
2
0
1
1
0
2
1
1
0
1
2
1
0
1
1
1
1
2
2
2
2
1
0
1
1
1
0
0
2
1
1
2
1
0
0
1
1
1
1
1
0
1
1
1
0
0
1
2
1
1
0
2
1
0
4
1
1
1
1
1
1
1
0
2
1
1
1
1
2
0
1
1
0
1
1
1
2
1
1
2
2
0
2
2
2
0
1
1
2
2
1
1
1
1
2
2
0
2
1
3
1
2
1
2
1
2
1
1
1
1
0
2
2
1
1
2
0
1
1
0
1
2
2
0
0
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
2
2
1
0
1
1
1
1
1
1
2
1
1
1
2
2
1
0
1
1
2
1
0
1
1
0
1
2
2
1
0
1
1
1
1
2
1
2
0
1
1
1
2
0
1
1
1
0
0
1
1
0
1
1
2
2
2
1
0
2
2
2
0
2
1
1
0
1
1
1
0
3
2
2
1
1
1
1
0
2
1
2
1
1
0
2
2
2
1
1
1
1
2
1
1
0
1
2
2
0
2
1
1
1
1
1
2
1
1
1
2
1
1
1
0
2
1
2
0
1
2
1
2
1
0
1
2
1
0
1
1
1
2
0
1
2
2
1
2
1
2
2
2
2
1
0
0
0
1
1
1
1
1
1
1
1
1
2
1
2
0
1
0
1
2
1
1
1
2
1
1
1
2
1
1
2
1
1
1
2
2
1
1
0
1
1
1
1
1
1
1
1
0
1
1
1
0
0
1
2
1
2
1
1
1
1
1
0
2
1
1
1
2
1
1
1
2
1
1
0
1
2
1
1
0
1
1
1
1
1
1
1
1
1
0
1
0
1
1
0
0
1
1
1
1
0
0
2
1
1
1
1
2
1
0
1
0
0
0
1
1
0
1
1
1
1
1
0
2
0
1
1
1
1
1
2
1
1
1
0
1
1
1
1
2
2
0
1
2
0
1
1
1
0
1
1
0
1
1
2
0
1
2
0
2
1
1
1
2
0
1
2
0
0
1
0
2
1
1
2
1
1
1
0
1
1
1
1
2
0
1
2
1
2
2
1
1
0
1
0
0
0
1
0
0
2
0
0
1
1
3
1
1
1
1
1
0
0
2
2
1
2
0
2
1
0
1
2
2
1
0
0
1
1
1
1
2
1
2
1
0
1
2
0
1
1
1
1
1
1
1
1
1
0
2
2
1
2
2
1
1
1
0
1
1
0
1
2
1
0
1
1
1
1
1
1
1
2
1
2
1
2
2
1
1
1
1
1
1
1
2
1
2
1
3
0
1
2
1
2
1
2
2
1
0
1
1
1
1
1
1
0
2
1
0
1
1
1
1
2
2
1
1
1
1
2
1
1
1
2
1
0
1
1
1
1
0
2
1
1
2
1
1
2
1
2
1
1
2
1
1
0
1
1
1
1
0
1
2
0
2
1
1
2
2
0
1
0
2
1
1
1
2
2
1
1
1
1
1
2
0
1
2
1
1
0
1
1
1
0
3
1
0
0
2
1
0
1
1
1
1
1
1
0
1
1
2
1
2
1
1
1
2
1
1
1
0
1
2
1
1
0
1
1
1
1
1
0
0
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
0
0
1
2
0
1
1
1
1
1
1
1
1
1
1
0
1
0
1
2
1
2
1
4
0
1
1
2
1
2
2
1
2
1
0
1
1
2
0
0
3
2
0
2
0
1
0
1
1
0
0
2
2
1
1
1
1
1
0
2
1
0
2
2
2
1
2
2
1
0
1
2
1
1
1
0
0
0
1
0
1
1
1
1
2
1
2
1
0
2
2
1
1
1
2
1
2
2
0
1
0
1
0
1
1
1
1
1
1
2
1
1
0
1
2
0
1
1
1
1
2
1
2
2
1
0
4
1
1
0
0
1
2
0
0
0
0
1
0
1
2
0
0
0
1
1
2
2
1
1
1
2
0
2
1
1
2
3
0
1
1
1
1
2
1
1
2
0
0
1
1
1
0
2
0
1
1
0
1
1
3
1
1
0
1
1
1
1
0
0
1
1
1
1
1
2
0
0
1
1
1
1
1
2
1
2
1
1
1
1
0
1
2
1
2
1
0
2
2
1
2
1
0
1
2
1
0
2
1
2
1
2
1
2
2
0
1
1
1
1
1
1
1
1
2
2
1
1
1
2
1
0
2
0
3
1
2
2
2
0
1
1
1
1
1
1
2
1
0
0
1
2
1
2
1
2
2
1
1
2
0
1
1
1
1
1
1
2
1
1
1
1
6
2
1
2
0
2
0
1
2
1
1
1
1
2
2
2
1
1
1
1
2
1
0
1
2
0
1
1
0
0
1
1
2
1
1
1
2
1
0
2
1
2
1
0
2
1
2
1
0
0
1
2
1
1
2
1
3
1
1
1
1
1
2
2
0
1
1
2
0
2
1
1
1
1
1
1
1
1
1
0
1
1
2
1
1
1
2
2
1
2
1
1
1
1
0
1
2
1
1
0
0
1
1
2
1
2
1
2
1
1
1
1
1
0
2
0
1
1
2
0
1
1
2
1
1
2
0
2
1
1
1
1
1
0
1
1
1
1
0
1
1
1
2
1
0
1
1
0
1
0
1
2
1
2
0
0
1
1
1
1
0
2
1
1
2
1
0
1
1
1
0
1
1
2
1
1
0
1
1
2
2
1
1
0
0
2
0
2
1
1
0
2
2
1
2
1
1
1
1
2
1
1
1
2
2
1
2
0
2
2
1
1
1
1
1
1
1
0
1
2
0
1
2
1
1
0
1
1
2
0
1
1
1
1
1
1
2
2
1
1
0
1
1
1
1
0
1
1
3
1
1
0
1
3
1
1
2
1
1
1
1
1
1
1
1
0
1
0
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
2
2
0
1
1
1
1
0
1
0
0
1
1
1
0
2
1
0
1
1
2
1
1
1
1
1
1
2
1
2
2
2
1
3
0
2
3
0
0
2
1
1
1
1
2
0
0
0
1
2
1
1
2
1
1
0
1
1
1
1
2
1
0
0
1
1
1
1
1
1
2
1
1
1
2
1
1
1
0
2
1
1
1
1
0
0
1
1
1
0
1
1
1
1
1
0
0
2
2
1
0
2
1
1
1
1
2
0
1
1
2
0
1
1
0
1
2
1
2
2
1
0
1
1
1
2
2
2
2
1
0
1
1
0
2
1
0
0
1
0
1
1
1
1
1
1
0
1
1
1
1
2
1
2
1
2
1
1
1
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
0
1
1
2
1
0
2
1
1
1
1
0
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
2
1
2
1
2
1
1
1
1
0
0
1
1
2
1
1
0
1
2
1
0
1
0
2
1
2
1
1
0
1
1
0
1
1
1
1
1
1
1
1
1
2
0
1
1
1
0
2
2
0
0
1
1
0
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
0
0
1
2
1
2
1
1
1
1
1
1
0
0
0
1
1
1
0
2
0
1
2
2
2
2
1
1
1
0
1
2
2
1
1
2
1
1
0
1
1
1
2
1
0
1
0
0
1
1
2
0
1
1
1
1
2
1
1
1
1
0
2
1
2
2
0
1
1
1
2
0
1
1
2
1
2
1
1
1
1
1
1
2
2
2
1
1
0
1
1
1
1
1
1
1
1
1
1
2
1
1
0
1
2
1
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
0
1
1
1
1
1
1
1
1
1
0
1
1
0
1
1
3
0
1
1
1
1
1
0
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
0
1
1
1
1
2
0
1
1
1
1
2
1
1
2
1
1
1
1
1
0
2
1
1
1
1
1
1
1
0
1
1
2
2
1
0
1
2
1
1
2
1
2
1
2
0
1
0
1
1
2
1
1
1
1
2
1
2
1
2
1
1
0
1
2
1
1
2
1
1
1
1
1
1
1
2
0
0
2
0
1
0
2
2
2
0
1
0
1
1
2
1
2
2
1
3
1
1
1
0
0
1
2
1
0
2
2
2
2
0
1
1
0
2
0
1
1
1
2
0
1
2
0
0
1
1
1
2
1
1
2
1
2
1
1
1
1
2
0
1
2
1
1
1
1
0
1
0
1
2
1
2
1
0
1
1
1
1
1
2
2
1
1
1
2
2
0
1
0
1
0
1
1
1
1
1
1
2
1
1
0
0
1
1
2
0
2
1
1
1
2
1
1
2
1
2
3
1
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
0
2
1
1
0
0
2
1
0
1
1
1
2
0
1
1
2
1
0
1
1
1
2
2
0
2
2
1
1
2
1
0
1
2
1
1
2
1
1
1
1
2
1
0
1
2
0
1
1
2
1
0
0
1
1
1
2
1
1
1
1
1
1
1
0
1
0
2
2
2
1
0
2
1
1
2
2
1
2
1
2
0
1
2
0
1
1
2
1
1
1
1
2
1
0
1
2
1
2
4
2
1
1
1
1
1
2
0
0
2
1
2
0
0
1
1
3
2
1
0
1
2
1
1
2
2
1
1
0
1
1
1
1
1
1
1
2
2
0
0
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
0
0
0
0
1
0
1
2
1
1
2
1
0
1
1
0
1
3
0
0
1
1
2
1
1
0
0
1
1
2
0
1
0
1
0
2
2
1
1
1
2
1
0
2
1
0
1
0
1
1
1
0
1
1
0
0
2
0
1
2
1
1
0
0
1
1
1
1
0
1
1
3
1
1
1
2
0
2
1
1
1
1
1
1
2
2
0
0
1
1
1
0
1
1
2
1
1
1
1
2
1
1
0
1
1
1
1
1
1
1
1
1
9
2
2
0
0
1
1
1
0
0
1
0
1
2
2
0
0
1
1
2
0
2
0
1
1
1
2
0
2
2
1
1
0
1
1
2
1
0
2
1
1
1
1
0
0
2
3
0
2
1
2
1
1
1
1
1
1
0
0
1
1
1
1
1
1
2
1
0
1
1
0
1
1
2
1
1
1
1
1
0
1
1
0
0
3
2
2
1
0
1
1
0
2
1
1
2
2
1
2
0
1
2
1
1
2
0
2
1
1
1
2
1
1
1
1
1
2
1
0
0
2
1
1
1
0
1
1
2
1
2
2
2
0
1
1
2
1
1
1
2
0
2
2
2
2
2
1
1
2
1
0
2
0
0
1
1
2
1
2
0
1
1
0
0
0
0
2
2
0
1
1
1
1
2
2
2
0
1
2
1
1
2
0
1
0
1
2
0
1
0
1
0
0
1
1
2
1
1
1
1
1
1
1
1
2
0
1
1
1
1
0
2
1
1
2
1
1
1
1
1
0
1
2
2
1
1
1
1
0
1
1
3
1
2
2
3
1
0
1
2
1
1
1
1
2
1
2
1
0
1
0
0
0
1
1
2
1
2
1
1
2
0
1
1
1
2
0
2
1
1
2
3
0
0
1
1
1
1
1
1
1
1
0
3
1
2
2
1
1
1
1
1
1
2
1
2
0
2
1
0
1
2
2
2
0
1
1
2
0
2
1
1
1
1
0
2
2
1
0
1
1
1
1
1
1
2
0
0
2
2
2
1
0
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
2
1
1
1
2
1
1
1
2
1
1
2
1
1
1
1
0
2
2
1
1
1
2
1
0
1
1
1
1
1
2
2
2
2
0
1
1
1
1
0
1
1
2
2
1
1
2
1
1
1
2
1
0
2
1
1
1
2
1
1
1
2
1
1
2
2
1
1
0
0
1
1
0
1
1
1
2
0
1
1
0
1
1
2
2
1
2
0
1
0
0
1
2
2
1
2
1
1
0
1
0
1
1
0
1
1
1
1
4
1
1
1
1
2
2
1
1
1
1
1
2
2
1
2
1
1
1
1
0
1
0
1
2
0
0
1
0
2
1
1
0
2
1
1
0
2
1
0
0
2
1
0
1
1
0
1
0
1
0
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
2
0
2
1
1
2
1
1
1
0
2
2
0
0
1
0
0
0
1
2
0
1
1
1
1
1
1
1
2
1
0
2
2
0
1
1
1
0
2
1
1
1
2
1
1
1
1
1
1
1
1
1
0
1
0
1
3
2
0
2
2
0
1
2
1
0
0
1
0
2
0
0
1
2
1
1
1
1
0
1
0
1
1
0
1
1
1
1
1
2
2
0
2
1
1
0
1
1
1
1
0
0
1
2
2
0
1
1
0
1
1
1
2
1
1
0
0
1
0
1
1
1
0
1
0
2
1
1
1
1
0
1
1
0
0
1
1
1
1
0
1
1
1
1
2
3
0
1
1
2
3
1
1
1
0
2
1
2
2
1
1
2
1
2
1
0
0
1
1
2
2
2
1
1
0
1
1
1
0
2
0
0
1
1
0
1
1
1
0
1
0
1
2
1
0
2
1
0
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
2
1
1
1
2
1
0
0
1
1
0
2
1
1
0
1
0
0
1
0
1
3
0
1
1
1
0
1
0
1
2
1
1
1
1
1
0
1
1
1
2
1
2
1
1
1
1
1
2
0
1
2
1
1
1
2
2
1
2
1
2
1
1
1
1
1
2
0
1
0
1
1
0
2
1
2
1
1
1
0
0
0
1
1
1
1
1
1
1
1
0
2
1
0
1
2
2
0
1
0
1
2
2
1
0
2
1
1
1
0
0
0
1
2
2
2
1
0
1
2
1
0
1
2
0
1
2
1
2
2
2
1
1
1
2
1
1
1
1
1
1
0
0
2
1
1
0
2
1
1
2
0
1
1
2
1
2
1
1
1
2
1
0
1
0
2
2
1
2
1
1
2
1
1
1
1
1
2
1
0
1
1
2
0
1
2
2
1
1
1
1
1
1
2
2
0
0
2
2
0
0
1
1
2
1
1
2
1
1
1
2
1
1
0
1
0
1
1
1
1
2
0
1
2
1
1
0
1
1
1
1
0
1
1
0
2
1
2
1
1
1
1
1
1
1
3
1
1
0
2
1
0
1
0
1
1
1
1
1
1
1
0
1
1
2
1
0
1
1
0
2
1
0
1
1
1
0
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
0
1
1
1
1
1
0
0
1
1
2
2
2
1
1
1
1
1
1
1
2
1
1
1
0
1
1
2
0
1
1
1
1
2
1
1
1
1
2
2
0
2
1
1
1
1
2
1
2
1
1
1
1
2
1
1
0
1
1
2
0
0
1
1
1
1
1
1
0
2
1
1
1
0
1
2
1
0
3
0
1
1
1
1
0
1
2
1
2
2
1
1
1
1
1
1
1
1
0
1
0
1
2
1
1
1
1
2
1
0
1
1
1
1
1
1
1
0
1
0
0
1
0
1
0
1
2
1
2
1
1
1
1
1
0
2
0
1
1
1
2
1
0
1
1
1
1
2
1
1
1
0
1
1
1
1
0
1
1
1
2
2
0
0
1
1
1
1
3
2
0
1
1
0
2
2
1
1
1
1
2
1
1
2
0
2
1
1
0
0
1
1
0
2
2
1
0
2
1
1
0
2
1
1
1
1
1
1
1
1
1
0
1
0
1
2
0
0
1
1
1
1
2
1
1
0
2
2
2
1
1
3
0
2
1
2
1
2
0
2
1
2
1
1
1
0
2
1
1
1
1
1
1
2
0
1
0
1
2
1
2
1
2
0
2
0
1
1
1
2
1
2
1
0
1
1
1
2
1
1
1
2
1
1
1
1
1
0
0
1
0
0
2
2
1
0
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
0
2
2
0
1
0
1
1
1
1
1
3
0
0
2
2
1
0
2
1
2
1
1
1
2
1
1
1
1
2
1
2
2
0
2
1
2
0
1
1
1
1
1
0
0
2
1
0
1
1
0
1
2
1
2
1
2
1
1
1
1
0
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
2
2
1
1
0
1
0
1
2
1
1
2
1
1
1
2
1
0
2
0
1
1
0
1
0
1
2
0
1
2
2
1
0
0
1
1
1
1
1
1
1
2
1
2
0
1
1
2
1
1
2
1
1
1
2
2
1
2
1
1
2
1
0
1
1
2
0
1
1
1
2
0
1
1
1
2
1
1
1
1
0
1
1
1
2
1
1
2
2
1
0
1
2
0
0
2
1
1
1
1
2
1
2
2
1
2
0
0
1
0
0
1
2
1
1
2
2
1
3
2
2
1
0
1
1
1
1
2
0
2
0
0
2
1
1
2
1
0
1
1
1
1
2
1
2
0
0
1
1
1
1
1
0
1
0
1
2
1
0
1
1
1
1
2
1
1
1
2
0
1
1
2
1
0
1
2
2
0
1
2
1
2
2
1
1
1
1
0
1
1
1
0
0
1
1
1
1
0
1
1
1
1
2
1
1
5
2
0
1
1
0
1
1
1
1
1
1
2
0
1
1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
0
1
1
1
2
0
1
1
1
2
2
0
0
0
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
0
2
1
2
1
2
2
1
2
0
2
1
2
1
1
1
1
0
2
1
1
1
1
1
0
1
2
1
0
1
1
1
1
1
0
1
0
1
1
1
3
0
1
0
1
1
2
2
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
0
2
1
1
0
1
1
1
2
1
0
0
2
1
1
2
1
1
1
2
1
0
1
1
2
1
1
2
0
1
2
0
0
1
1
2
1
2
2
0
4
1
1
2
1
1
1
1
1
2
0
1
1
2
0
3
1
1
1
0
2
1
2
1
0
0
0
1
1
1
1
2
1
1
1
2
1
2
1
1
1
0
1
0
2
1
1
3
3
0
1
1
1
1
0
1
1
1
1
2
1
1
2
1
1
2
2
2
1
1
1
1
0
1
1
0
1
1
0
2
1
1
9
0
2
1
1
2
2
2
0
1
1
1
0
0
2
1
1
1
1
0
1
1
1
1
2
1
1
1
1
2
1
1
0
1
1
1
1
1
0
1
1
0
1
1
0
1
1
1
2
1
1
1
2
1
1
3
1
1
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
1
0
1
2
1
1
2
2
1
1
1
1
1
1
0
2
2
1
1
2
1
0
2
1
0
1
1
2
1
2
1
0
1
1
1
1
1
1
1
1
1
0
1
2
2
1
0
1
2
1
1
2
1
2
0
0
2
1
0
2
2
0
1
1
0
1
2
1
1
0
2
1
2
1
1
2
1
2
0
2
2
2
0
0
2
1
2
1
0
1
2
1
1
1
1
1
2
2
1
1
0
0
2
1
1
1
1
1
2
1
0
1
1
2
0
0
2
0
2
0
1
2
0
2
0
1
1
2
1
0
1
2
1
2
1
1
1
1
0
1
1
1
1
0
1
1
1
1
1
1
1
0
1
0
1
1
2
1
1
1
1
2
0
1
1
0
1
0
1
3
0
0
1
0
1
1
2
1
1
0
0
0
1
1
1
2
1
1
1
1
0
2
1
1
0
1
0
1
1
1
0
2
2
1
1
1
1
1
1
1
2
2
2
1
1
0
1
1
1
1
1
1
0
1
1
1
1
2
1
0
0
1
0
0
1
2
0
0
1
2
1
0
2
2
2
1
2
1
1
2
2
1
2
1
4
1
0
2
2
0
1
1
1
2
2
1
0
1
1
1
0
1
1
1
0
2
2
1
2
1
2
2
2
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
2
0
1
1
1
1
1
0
2
1
1
1
2
0
1
0
0
1
1
0
1
0
1
0
2
2
2
1
1
2
1
2
0
1
0
2
2
1
0
1
2
1
2
0
0
1
2
1
1
1
1
1
1
2
2
1
1
1
1
0
0
1
2
1
2
1
0
0
1
1
2
0
1
1
1
1
2
2
0
1
2
1
1
1
0
0
0
2
1
0
1
0
1
1
0
0
1
1
0
1
1
2
1
0
1
1
2
1
1
0
1
1
2
1
2
2
1
0
2
1
2
2
0
0
1
0
0
1
1
1
1
1
0
1
2
1
1
1
1
1
1
0
2
0
0
0
1
2
2
1
1
1
1
1
2
2
2
2
1
0
2
2
1
2
1
1
1
1
1
1
0
2
1
1
1
0
2
2
2
1
0
0
2
1
1
0
1
1
2
2
2
1
1
1
1
1
1
1
1
0
1
2
0
1
1
1
4
0
0
1
2
1
2
0
0
0
2
0
1
2
2
1
1
0
1
1
0
1
1
1
1
1
2
0
1
0
1
1
2
1
1
0
2
1
1
0
1
0
1
1
1
2
0
0
2
1
2
1
2
1
2
0
1
0
0
2
1
0
3
0
1
4
2
0
1
2
2
1
1
1
1
2
1
2
1
1
0
1
0
1
2
1
1
1
2
1
2
1
1
0
2
1
2
1
1
1
1
1
1
1
1
1
0
1
1
2
2
0
1
2
1
1
0
0
1
1
0
1
0
0
1
0
1
0
1
1
2
1
0
0
1
1
1
1
0
1
2
1
2
1
0
1
1
0
1
0
1
0
2
1
1
1
1
2
1
1
2
1
2
2
1
1
1
1
1
2
1
0
2
2
1
2
0
1
1
0
0
1
1
0
2
0
2
2
1
0
2
1
1
0
1
1
1
1
1
0
1
1
1
2
1
2
2
0
0
0
1
1
1
2
1
2
0
1
2
0
1
1
1
2
2
1
1
0
1
1
2
0
1
2
2
0
2
1
1
1
1
1
1
2
1
0
0
1
1
1
1
1
0
1
1
1
1
2
2
1
1
1
2
1
1
1
2
0
1
1
1
1
1
2
1
0
0
1
1
0
1
1
1
0
0
1
1
1
1
1
1
1
2
1
0
0
1
2
2
0
0
1
1
1
1
2
1
1
3
2
0
1
1
1
1
2
1
0
2
0
2
2
1
1
2
0
0
1
1
1
0
1
2
2
0
1
0
1
1
2
2
1
1
2
2
2
1
1
1
1
1
2
1
1
1
1
2
0
2
1
1
2
0
2
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
0
1
1
0
0
2
2
2
1
0
0
1
2
2
0
1
2
2
1
1
1
0
1
1
1
1
0
2
1
1
1
0
2
0
0
1
1
1
1
1
2
2
1
1
0
1
0
0
1
2
2
2
1
2
1
1
1
1
0
0
1
0
1
0
1
2
1
0
2
1
0
1
2
0
1
0
1
2
0
0
1
0
1
2
0
1
2
1
2
2
2
1
1
2
2
1
0
0
1
0
1
1
2
1
1
1
2
2
1
2
1
1
2
1
1
0
1
2
1
1
0
0
0
1
1
1
1
1
1
2
2
2
1
2
2
1
1
2
1
1
2
1
2
1
1
2
1
2
0
1
1
0
1
1
2
1
1
1
0
3
2
2
2
1
1
1
2
1
1
0
2
1
0
2
2
0
1
0
1
1
1
2
0
1
2
1
0
0
1
2
0
0
0
3
0
1
1
1
2
0
1
1
0
1
1
1
0
1
2
1
1
1
2
2
1
1
0
1
2
2
1
1
0
2
1
1
1
1
2
2
1
1
1
2
1
1
0
2
2
0
2
1
2
2
2
1
1
1
1
2
1
1
0
1
1
1
1
0
2
2
1
0
0
1
0
1
0
0
1
2
0
2
3
1
0
1
1
1
0
2
0
1
1
1
1
1
2
2
1
2
2
1
1
2
1
0
1
1
2
1
1
0
2
1
0
0
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
0
2
0
2
1
1
1
1
1
2
2
0
2
1
1
1
1
1
2
2
3
1
2
1
1
1
2
0
1
2
1
2
2
1
2
1
1
0
0
0
1
2
2
0
1
1
2
1
2
1
1
2
1
1
1
1
0
2
2
2
1
1
1
0
1
2
2
1
1
2
1
0
0
2
1
1
2
4
1
2
1
2
0
2
1
1
1
1
1
2
1
1
2
1
2
1
0
0
0
1
1
2
2
0
1
1
1
1
1
1
0
0
2
2
1
1
1
0
1
1
1
0
1
0
1
2
0
1
1
0
1
1
1
1
1
2
1
0
3
1
2
1
0
1
0
0
2
2
1
1
2
1
1
1
1
0
2
1
3
0
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
0
0
0
0
1
2
2
1
1
0
2
0
1
2
1
1
2
2
1
0
1
1
1
1
2
1
1
2
2
1
1
1
1
0
1
2
2
1
1
1
1
2
0
1
1
1
0
1
1
0
2
1
1
1
0
2
1
2
1
1
1
1
1
1
1
1
1
3
1
1
1
0
2
1
1
1
0
1
1
1
1
1
2
2
1
1
1
1
0
0
1
0
1
1
1
2
2
1
1
1
1
2
0
1
1
0
1
1
2
0
0
1
1
1
1
1
1
1
0
2
1
1
2
1
1
1
1
2
1
0
1
2
1
1
1
2
1
1
2
1
1
0
1
1
2
0
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
2
1
1
2
1
2
0
2
2
1
2
1
1
2
1
0
0
1
1
2
1
2
1
1
2
2
1
0
1
0
1
2
2
1
2
1
1
1
1
1
0
1
1
1
1
1
0
0
1
1
1
2
1
1
1
2
1
1
0
1
2
1
1
1
1
1
1
1
0
1
0
1
2
0
0
1
1
1
1
1
1
0
1
0
0
1
1
0
0
0
2
1
1
2
1
1
1
0
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
0
2
1
0
1
2
1
2
1
0
1
0
0
1
1
1
1
2
1
1
1
0
1
1
0
1
1
1
1
1
1
1
1
1
0
1
1
1
2
1
0
1
1
1
0
0
0
1
1
0
1
1
1
1
1
0
0
1
1
0
1
2
1
1
2
0
1
1
1
1
1
0
1
0
0
1
2
0
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
2
0
1
0
2
2
1
1
1
2
1
1
1
1
1
0
1
0
2
1
0
1
1
1
1
2
0
0
2
1
1
0
1
0
1
1
1
0
1
0
1
1
0
1
1
1
2
1
0
0
1
2
1
1
1
1
1
2
0
0
2
2
1
0
1
1
0
1
1
2
0
1
1
0
1
1
2
2
1
1
1
1
1
1
0
2
1
1
0
1
0
0
2
0
2
1
1
1
1
0
2
2
0
0
2
1
2
0
0
1
1
1
1
2
1
1
1
2
2
1
1
2
1
1
1
1
1
0
1
1
1
1
2
1
2
2
2
1
1
0
1
0
1
1
1
2
1
0
0
0
2
1
0
0
2
0
2
0
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
2
0
1
2
2
0
1
0
0
1
0
0
1
1
1
2
1
1
1
2
0
1
0
1
0
1
1
1
1
1
1
2
1
1
0
1
1
1
1
0
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
0
1
1
1
2
2
2
2
0
2
1
1
2
1
1
1
1
1
1
0
1
1
2
1
2
0
0
0
0
1
1
1
1
2
1
1
0
1
1
1
2
1
1
1
0
1
2
1
1
1
0
1
0
2
1
1
1
2
2
0
2
0
1
0
2
1
1
3
1
2
1
1
1
1
2
0
1
0
1
0
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
0
4
0
1
1
0
3
1
0
1
2
1
1
0
1
3
1
2
2
1
0
1
0
1
1
0
1
2
1
4
1
1
2
1
1
2
1
2
1
1
2
1
1
0
0
2
1
2
2
1
1
1
1
0
1
1
2
0
1
1
1
0
1
1
2
1
1
1
1
0
2
2
0
2
1
1
0
1
0
1
2
0
1
1
1
1
0
2
3
1
1
2
1
1
1
0
1
1
1
1
0
1
0
1
2
1
1
0
0
1
1
1
1
2
0
1
1
2
1
1
0
1
2
2
2
0
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
2
2
0
2
0
1
1
1
1
2
0
1
1
3
1
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
2
1
1
0
1
1
1
1
1
2
1
2
2
1
0
1
1
1
0
1
0
1
3
2
2
1
0
2
0
1
0
0
1
1
0
1
2
1
2
1
2
2
1
2
2
1
1
1
1
1
1
2
1
1
0
0
1
0
1
0
2
2
0
2
1
1
1
1
1
0
1
0
1
1
0
0
2
0
0
1
2
1
1
1
1
1
2
2
1
2
1
0
1
1
1
1
0
0
0
2
2
0
1
0
2
1
1
2
2
1
0
2
0
2
1
1
2
1
0
2
1
1
0
2
2
1
1
1
1
1
3
2
1
1
2
2
1
1
1
0
1
1
1
0
2
0
0
1
2
1
2
3
1
1
1
1
1
1
1
0
1
1
2
1
1
1
1
1
0
0
1
2
1
1
0
1
1
1
1
1
1
1
0
0
1
0
0
1
0
2
1
1
1
0
1
1
0
0
1
0
2
3
1
1
2
2
2
0
0
1
1
1
1
0
0
1
0
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
0
1
1
2
1
0
1
2
1
0
0
1
1
1
1
2
1
0
1
1
1
1
1
1
0
2
0
0
2
2
1
1
2
1
1
1
0
2
2
1
1
3
1
0
0
1
1
1
1
1
0
1
2
0
2
1
0
1
1
1
2
1
1
1
0
1
0
1
0
2
0
2
2
1
1
1
1
2
2
1
1
1
1
1
1
1
0
1
3
1
2
1
1
0
1
0
1
2
0
1
1
1
1
1
2
1
2
0
2
1
2
2
1
1
1
0
1
2
1
1
0
1
0
3
1
1
0
1
1
2
1
1
1
1
2
1
2
2
0
1
1
0
1
1
2
1
0
2
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
2
1
3
2
1
0
0
2
1
1
0
1
1
0
1
2
1
1
2
1
1
2
2
1
1
1
1
1
1
2
1
0
2
1
1
1
1
1
0
0
2
1
1
1
1
2
0
1
1
2
1
1
1
0
1
2
2
2
0
1
0
1
2
2
2
2
2
2
1
1
0
0
1
1
2
1
2
1
1
1
0
1
1
1
2
0
1
1
1
1
0
1
1
1
0
2
1
2
2
0
2
2
0
1
1
1
0
2
2
0
1
1
2
1
0
2
1
1
2
2
1
2
1
1
0
0
0
0
0
1
0
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
0
1
1
2
1
2
3
1
1
1
1
0
2
0
2
1
1
2
1
2
1
2
1
2
0
1
1
0
1
1
1
2
0
2
1
1
1
1
0
0
2
1
2
2
0
1
2
2
1
0
0
1
0
0
1
0
2
0
1
1
2
1
0
1
1
1
1
1
1
2
1
1
2
0
2
2
0
0
1
1
2
0
2
2
1
1
1
0
1
1
1
0
0
0
0
1
1
1
2
1
2
1
1
2
1
0
1
0
1
0
0
1
0
1
1
0
0
1
2
2
1
1
1
2
1
0
1
2
1
0
1
1
2
1
0
1
1
2
1
1
1
0
0
0
1
1
2
1
1
1
0
1
1
0
1
1
1
0
2
1
1
0
2
0
1
2
2
1
1
1
1
1
1
2
0
1
1
0
1
1
1
1
1
2
1
1
2
1
2
2
1
2
1
0
2
1
2
1
0
1
1
1
1
0
1
1
0
2
1
2
1
1
1
0
1
1
2
2
1
1
1
0
1
1
1
2
2
0
1
1
1
1
0
1
1
1
0
0
1
1
0
1
0
1
1
1
2
1
1
1
1
0
1
1
2
2
2
0
1
2
1
1
1
1
0
0
1
1
1
0
2
1
1
0
2
1
1
1
1
0
1
1
1
2
0
1
1
1
0
0
2
1
2
0
1
1
2
2
1
1
2
2
2
1
1
1
0
2
2
1
2
1
2
1
1
2
2
1
1
1
0
0
1
1
1
1
1
1
2
2
0
1
1
1
1
1
1
0
0
1
0
0
1
1
1
2
0
0
1
2
0
0
1
1
0
1
0
0
2
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
0
0
1
1
1
2
2
1
1
1
1
0
1
0
1
1
1
2
2
2
1
1
2
2
2
2
0
1
2
1
1
2
0
1
1
2
1
1
0
1
2
0
1
0
1
1
2
1
2
0
2
1
0
1
2
0
1
1
1
1
1
0
2
1
2
1
1
1
1
1
0
1
1
1
1
0
2
1
1
1
0
2
2
2
1
2
1
0
0
2
1
1
0
2
2
1
1
0
1
1
0
0
1
0
1
1
0
1
0
0
1
1
0
2
2
1
1
1
1
1
0
1
2
1
1
1
1
2
1
2
2
2
1
1
1
1
1
1
0
2
1
1
2
1
1
0
1
0
3
0
1
0
1
1
2
2
2
1
0
1
2
0
0
1
1
1
0
2
1
1
0
1
1
0
2
1
1
1
1
1
1
1
0
1
0
1
1
0
0
2
1
1
1
1
1
1
0
1
1
2
1
1
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
0
1
1
3
1
1
2
1
0
0
2
1
2
1
2
2
1
2
1
0
2
1
1
1
1
2
1
2
1
2
0
1
2
1
1
1
0
2
1
1
3
2
1
1
2
1
1
1
2
0
2
1
1
1
2
1
1
0
2
1
2
2
1
0
1
1
1
1
1
0
1
0
1
0
0
1
1
2
1
1
1
2
2
2
2
1
1
1
1
1
1
1
0
1
2
2
1
1
1
1
1
2
1
0
1
2
0
1
2
1
2
1
2
1
2
1
0
0
1
2
2
1
1
1
2
1
0
0
1
1
1
1
2
2
0
2
1
1
0
1
1
2
1
2
1
0
2
2
2
3
0
0
1
1
1
1
4
2
1
1
1
2
1
1
2
2
1
1
2
2
0
1
0
1
0
0
0
1
1
1
1
2
2
2
1
1
0
1
1
1
1
1
2
1
1
0
1
1
1
2
1
1
1
4
2
1
1
1
1
1
2
2
1
1
0
1
2
2
1
1
1
1
1
0
1
1
1
2
1
1
0
2
1
1
0
1
2
1
1
1
0
1
1
1
2
2
2
2
1
1
1
1
1
1
0
1
1
1
1
0
2
1
1
1
0
1
2
1
1
1
1
0
0
2
1
0
1
1
2
0
2
0
2
0
1
2
1
2
2
0
1
3
1
1
0
1
2
2
1
1
0
1
2
1
2
1
1
2
2
1
1
1
1
2
0
1
2
1
0
1
1
1
2
2
2
1
0
1
1
0
1
2
1
2
2
1
2
1
0
1
0
2
1
1
0
0
1
0
2
1
1
0
1
0
0
1
1
0
2
2
0
1
1
1
2
1
1
1
1
1
1
0
0
2
1
1
1
0
0
2
1
0
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
2
2
1
2
1
1
2
0
1
0
1
2
1
0
1
2
1
1
2
1
1
0
2
1
1
0
1
2
2
2
1
0
2
1
1
1
2
0
1
1
1
1
0
0
0
0
2
1
0
1
1
1
1
1
1
1
0
1
1
1
1
0
1
2
1
0
0
1
1
0
0
1
1
1
1
0
1
2
1
1
1
1
1
0
2
1
1
1
1
1
1
2
2
0
1
2
0
2
2
1
1
2
1
0
2
0
1
2
2
1
2
1
1
1
1
0
1
0
2
1
1
1
1
1
0
1
1
1
3
0
1
1
0
2
0
1
1
1
1
2
2
1
1
1
2
0
0
1
2
1
2
1
0
2
1
2
1
1
1
2
0
1
1
2
1
2
2
1
1
1
2
1
0
1
1
2
1
1
1
2
0
1
0
1
0
2
2
1
1
1
2
2
1
1
0
1
1
1
1
0
0
1
0
1
0
1
1
1
1
1
2
2
2
2
1
0
0
2
1
0
0
0
1
1
2
1
0
1
2
1
1
2
1
0
1
1
1
2
1
2
1
2
1
1
1
1
0
1
1
0
2
1
1
1
1
1
1
0
0
1
2
2
2
1
2
1
1
1
1
1
2
2
2
1
1
1
1
0
1
0
1
2
0
1
1
1
0
2
0
1
1
0
2
1
1
2
1
1
1
2
0
0
1
1
2
1
0
1
2
1
1
1
1
0
1
0
2
2
0
1
1
1
1
1
1
0
1
2
1
0
2
1
1
0
2
1
1
1
1
1
0
2
0
0
2
2
1
1
0
2
0
1
1
0
2
1
1
1
2
2
1
2
0
1
1
0
1
1
2
1
1
1
1
1
2
0
1
0
1
1
2
1
3
1
0
1
2
0
1
0
1
2
1
0
1
1
1
1
1
0
1
1
2
4
1
2
0
1
1
0
0
1
1
0
2
1
2
2
1
0
2
2
0
0
1
2
2
0
2
1
1
1
1
1
1
1
1
1
2
1
0
1
0
1
2
0
1
1
1
2
1
0
0
1
1
1
2
0
1
1
1
1
1
1
0
0
1
1
1
0
1
2
1
1
1
1
1
2
2
0
1
2
2
1
1
0
1
2
2
1
1
1
2
1
1
0
0
1
1
1
0
3
1
2
1
2
1
2
1
0
1
1
1
1
0
1
1
1
2
0
2
2
1
1
1
2
0
1
1
2
1
1
1
1
0
1
1
2
2
1
1
2
2
1
1
2
2
1
2
0
1
1
1
1
1
1
1
1
1
2
2
2
1
0
1
1
1
2
2
1
1
1
1
2
0
1
1
1
1
0
1
1
2
1
2
2
0
2
1
2
0
1
2
1
2
1
0
1
1
0
2
2
0
2
1
1
1
0
1
1
1
1
1
2
2
1
1
0
1
0
1
0
1
1
2
1
2
1
2
0
1
2
1
1
1
0
1
1
1
1
1
1
2
0
1
1
1
1
1
1
2
1
1
1
1
1
2
1
0
2
1
1
0
0
1
0
0
1
2
0
0
0
1
3
1
0
1
0
1
1
1
1
2
2
1
1
0
0
1
0
1
1
0
2
1
1
0
1
1
0
1
1
1
2
1
1
0
1
2
2
0
1
3
1
0
2
1
2
2
1
0
2
1
1
1
1
2
1
0
1
2
1
1
0
0
0
1
1
1
1
1
1
1
2
1
0
1
0
2
0
1
2
0
1
1
1
1
1
0
1
1
1
0
1
1
1
1
1
1
2
0
1
0
1
1
1
0
1
0
1
1
0
1
1
0
1
2
1
2
1
1
1
1
1
1
2
0
1
1
1
0
0
0
0
0
0
0
1
1
1
1
0
0
1
1
0
1
1
1
0
1
1
0
1
1
1
1
2
1
2
0
0
2
1
2
1
0
1
0
1
2
0
2
3
1
1
0
1
1
3
0
1
1
1
0
0
1
0
1
1
2
1
1
1
1
2
0
1
0
0
1
1
1
0
1
0
1
2
0
0
2
1
1
1
2
0
1
1
1
1
1
1
1
2
3
3
0
1
2
0
1
2
1
0
2
0
1
1
2
1
0
0
2
1
0
1
1
1
1
0
1
3
1
2
1
1
1
2
1
1
2
1
1
2
2
1
1
1
0
1
1
1
1
2
2
2
2
1
0
1
1
0
1
1
2
0
0
1
1
1
1
0
1
2
1
1
2
2
1
2
3
1
1
1
0
0
2
0
2
2
1
1
2
1
3
2
0
1
1
1
0
1
0
1
2
1
2
1
0
1
0
1
1
0
1
2
1
1
1
3
2
1
2
1
2
2
1
1
1
2
1
1
2
2
2
1
1
1
2
2
0
1
0
1
2
1
1
2
1
0
1
2
1
1
0
1
2
1
1
2
1
1
1
1
1
0
2
1
1
1
1
1
2
1
2
1
2
1
1
1
1
2
0
2
1
1
1
2
1
1
2
2
1
1
0
0
1
0
0
1
2
1
1
1
0
0
1
0
2
1
1
1
1
1
1
1
1
0
1
1
0
1
0
1
0
1
1
1
3
1
2
1
3
2
1
1
1
0
1
2
1
2
2
2
0
0
0
1
1
0
0
1
1
2
0
2
2
0
2
2
1
1
1
1
1
1
1
2
2
1
2
0
1
2
0
1
2
2
0
1
3
0
0
1
0
2
2
1
1
2
2
1
1
1
1
2
1
1
0
1
1
1
1
4
1
1
2
1
2
1
0
1
0
0
1
1
1
1
2
2
2
1
1
1
0
0
2
2
2
0
2
1
1
1
0
1
1
1
2
0
2
0
1
2
1
1
2
1
0
2
2
1
2
2
0
1
1
1
2
1
1
2
1
2
2
1
1
1
2
2
2
1
2
1
0
2
1
0
0
2
1
2
1
2
1
1
0
1
1
2
1
2
1
1
0
1
2
1
1
1
1
1
1
2
0
2
1
1
1
1
1
1
1
1
2
0
1
0
2
1
2
2
2
0
1
1
1
2
1
1
1
2
2
0
1
3
0
0
0
2
2
1
0
0
1
2
0
2
1
0
1
1
1
2
1
2
2
1
1
1
2
2
0
1
0
2
0
2
2
2
1
0
1
1
2
2
1
1
1
1
1
1
0
1
0
1
0
0
1
1
1
1
0
0
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
0
2
0
2
1
0
2
1
2
2
1
2
2
2
0
1
1
1
1
2
1
2
2
1
1
0
1
1
1
1
2
1
0
1
2
1
2
2
1
1
1
1
0
2
1
1
0
0
1
2
1
1
1
0
1
1
1
0
1
1
1
2
0
1
1
1
1
1
0
1
3
0
2
2
1
2
2
5
0
2
1
1
1
3
1
0
0
1
2
1
2
2
2
1
1
2
2
2
1
4
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
2
1
2
1
1
1
0
1
1
2
1
1
1
2
0
1
1
2
1
1
0
2
0
2
1
2
1
1
1
1
2
2
2
0
1
2
1
1
1
1
1
1
0
0
1
1
1
1
1
1
0
1
2
1
0
1
1
1
2
1
2
2
0
1
2
0
0
2
1
2
1
1
0
1
2
2
1
1
0
1
1
2
1
1
0
1
0
2
0
0
1
0
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
0
0
2
0
2
1
2
0
0
1
0
2
2
1
1
1
0
1
1
1
2
2
2
1
1
1
1
1
1
2
1
0
1
2
0
1
1
1
1
1
0
1
1
2
2
1
1
2
0
2
1
1
2
2
1
0
1
1
0
2
4
2
1
2
2
2
0
1
0
3
0
1
1
2
2
1
1
2
1
1
1
2
0
0
1
1
1
2
0
0
0
1
1
0
1
1
0
0
1
2
2
1
1
0
0
0
1
1
4
1
1
2
1
2
1
1
1
1
1
1
1
2
2
2
1
2
1
0
2
2
0
1
2
1
1
1
0
1
1
1
1
2
2
2
2
1
1
1
1
1
1
0
0
1
2
1
2
1
0
1
1
1
0
2
1
1
1
1
2
0
1
2
1
1
0
2
2
2
0
1
1
1
1
1
0
2
2
0
1
1
1
1
1
1
0
0
1
0
0
2
1
1
1
1
1
1
0
1
2
1
1
1
2
1
0
1
1
1
1
1
1
1
2
0
1
2
2
1
2
1
1
1
2
0
1
1
1
2
1
0
1
0
0
1
2
1
1
0
1
1
2
1
1
2
2
0
1
1
1
1
2
0
1
0
2
2
0
0
1
1
2
2
0
1
1
2
1
1
0
2
1
2
0
2
2
1
0
0
0
0
1
1
0
2
1
0
0
0
0
2
1
1
2
0
1
1
0
1
1
2
1
2
2
1
1
2
1
1
0
1
1
2
0
1
1
0
1
2
2
1
0
2
1
1
1
1
1
1
0
0
2
2
1
1
1
1
0
2
2
1
1
1
0
1
1
2
1
0
1
1
1
2
1
0
0
1
1
0
2
2
2
1
0
1
1
0
1
1
1
0
0
1
0
1
1
1
1
2
1
1
2
1
0
1
0
2
1
1
2
2
1
3
1
1
1
1
2
2
1
1
1
0
1
1
1
1
1
0
0
1
2
1
1
2
3
2
2
0
0
2
0
1
1
0
1
1
2
1
0
0
0
0
2
2
1
2
0
1
1
1
1
0
1
1
2
1
0
1
1
1
1
2
2
1
1
1
1
0
0
1
2
0
2
1
2
1
0
2
1
0
2
0
1
2
1
1
1
1
1
1
0
2
1
2
1
0
1
1
0
0
1
1
2
1
1
1
1
1
2
2
1
1
0
1
0
0
0
0
2
1
2
1
0
2
1
2
1
1
2
0
1
1
1
1
1
2
1
2
2
2
1
1
4
1
1
1
1
0
1
1
2
1
0
1
1
1
2
1
0
1
1
1
1
1
2
1
0
2
2
2
2
2
1
1
1
1
1
1
1
1
2
1
1
0
0
2
2
1
1
1
1
2
2
1
1
1
1
1
0
0
2
0
2
1
2
3
1
1
1
1
1
0
0
2
1
1
0
0
2
0
1
2
1
1
1
0
1
3
1
0
2
1
2
1
2
1
1
2
2
1
0
1
2
0
0
0
1
1
2
2
1
2
2
1
1
1
1
0
2
0
2
1
1
0
1
1
1
2
1
0
1
2
0
2
1
1
0
1
2
1
2
1
0
1
1
1
1
1
0
1
2
1
2
0
2
1
1
2
1
1
1
1
1
1
1
0
2
1
2
2
2
1
0
1
1
1
0
1
1
1
2
1
0
1
0
1
1
1
1
2
1
1
1
1
1
10
1
1
2
0
2
1
1
0
1
1
0
2
1
1
1
1
1
0
1
1
1
2
1
0
1
2
1
4
1
1
2
1
0
1
0
1
1
1
1
1
1
1
1
1
2
2
1
1
2
2
0
1
1
1
1
1
1
1
2
1
1
0
1
1
0
1
1
0
2
1
1
0
2
1
1
1
1
2
0
1
1
1
0
1
2
0
1
1
1
1
1
1
1
0
0
1
1
1
2
1
1
1
0
1
1
1
0
1
2
2
1
2
1
0
2
1
1
1
0
1
2
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
0
0
1
1
1
0
1
1
1
1
1
0
2
1
1
1
1
0
0
2
1
1
1
1
0
0
1
2
1
0
1
2
1
1
1
1
1
1
1
1
2
1
0
1
1
2
1
1
3
1
2
0
0
2
1
0
2
1
1
0
1
1
1
0
2
0
3
2
2
1
1
0
1
1
1
1
1
0
2
0
2
1
0
2
1
1
0
1
0
1
0
2
1
0
1
2
1
1
1
1
0
0
1
0
2
0
0
1
1
1
1
1
0
1
2
0
2
2
1
1
0
0
1
1
1
1
0
1
2
1
0
1
0
1
2
2
2
1
0
2
2
1
1
2
2
1
0
2
2
1
1
2
2
1
1
1
2
1
1
1
0
2
1
1
1
0
0
0
1
1
1
1
2
0
2
0
2
0
1
1
1
2
1
1
1
0
0
1
2
2
2
2
1
1
0
0
1
1
1
2
1
3
1
0
1
1
2
1
1
0
1
1
1
1
1
1
1
2
1
0
1
1
0
0
1
1
1
0
1
1
2
0
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
0
1
0
2
1
1
3
0
2
2
1
2
1
0
1
1
1
1
1
1
1
1
0
0
1
1
2
2
1
0
1
1
2
1
1
0
0
1
1
1
1
2
1
1
1
0
0
1
2
0
0
2
1
1
0
1
1
1
0
0
1
2
2
0
2
1
1
0
0
1
2
3
1
1
0
1
1
0
2
2
1
1
0
2
2
2
1
1
0
1
0
2
1
1
1
2
1
0
1
0
1
1
0
1
1
2
1
1
1
1
0
1
2
2
1
2
1
1
0
1
1
2
1
0
1
1
2
1
1
2
1
1
0
1
1
1
2
2
1
1
0
2
1
2
2
0
1
1
0
1
2
1
1
1
2
1
1
1
0
2
0
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
0
1
1
1
1
1
0
1
1
0
0
1
1
1
1
1
2
2
1
1
1
3
2
0
0
2
1
1
1
2
1
1
2
1
2
1
1
2
0
0
1
0
2
1
1
1
1
1
0
2
1
1
0
2
0
1
2
1
0
1
1
1
0
1
1
1
2
0
1
1
1
0
2
1
0
2
1
3
2
2
1
1
1
1
1
0
0
2
1
0
1
0
2
1
2
0
0
1
2
2
1
1
1
1
1
1
0
2
2
1
0
2
0
0
1
1
1
2
0
1
4
0
1
3
0
2
0
2
1
0
2
1
0
0
1
2
0
1
1
1
2
1
0
1
2
2
0
2
1
2
0
0
0
0
2
2
0
1
1
2
1
1
1
1
0
0
1
1
1
4
1
1
2
1
1
1
0
2
2
1
0
1
0
0
1
1
2
1
2
0
3
2
0
2
2
0
1
1
0
0
0
0
1
2
1
0
1
2
2
1
1
1
1
2
1
2
1
1
1
2
1
1
1
2
0
1
1
1
0
2
1
2
1
1
2
1
1
1
2
0
1
1
1
1
1
2
2
1
1
1
1
1
0
1
1
1
1
2
1
2
1
2
2
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
2
1
1
2
0
1
1
1
0
2
1
0
2
1
2
1
1
1
1
0
1
1
0
2
2
0
1
1
1
1
1
1
1
1
1
0
0
2
1
0
1
2
2
1
1
1
1
0
1
1
1
2
1
1
0
1
1
1
1
0
0
0
1
0
1
0
3
1
2
0
2
0
1
1
0
1
0
2
1
0
1
1
0
1
0
0
1
1
2
1
0
1
1
2
1
2
1
2
0
1
2
2
2
1
0
1
2
0
1
1
2
2
1
1
1
1
1
1
1
2
2
0
1
2
2
2
1
2
1
2
2
1
1
1
1
2
1
1
1
0
1
0
2
2
1
1
1
2
3
1
0
1
0
0
1
1
0
0
1
1
1
1
1
1
2
1
2
1
1
1
0
1
1
1
2
1
3
0
0
1
1
1
1
2
2
1
0
0
1
2
1
0
1
1
1
0
1
2
1
1
2
2
1
1
2
2
1
1
1
0
0
2
0
1
1
1
1
1
0
2
1
0
2
1
1
0
0
1
2
1
0
1
2
2
1
1
1
1
0
0
1
1
1
3
1
1
2
1
1
1
1
1
2
2
2
1
0
1
0
1
1
1
1
2
0
1
1
1
1
1
1
2
0
2
1
1
1
1
1
1
1
0
2
0
2
1
1
1
0
1
2
2
2
2
1
1
1
1
1
2
0
0
0
1
0
1
1
1
1
0
1
2
1
2
1
2
1
2
1
2
2
2
1
1
1
2
1
1
2
0
1
2
1
0
0
0
1
2
1
1
1
3
0
1
1
1
2
1
0
0
2
1
1
1
0
1
1
1
1
2
1
1
2
1
1
0
0
1
1
0
1
2
1
2
2
1
1
0
1
2
1
0
0
0
1
2
2
0
2
1
1
0
2
2
0
1
2
2
1
1
1
1
0
1
1
1
0
1
1
1
1
0
0
4
1
1
1
1
1
2
1
0
1
0
2
2
2
2
0
1
0
1
1
0
1
1
0
0
1
2
1
2
1
1
1
2
0
2
1
0
0
1
2
0
2
1
1
0
1
1
0
1
2
1
1
2
0
1
0
1
1
1
0
1
1
1
0
1
2
1
0
1
1
1
0
1
1
1
2
1
1
2
0
1
1
0
0
2
0
1
1
2
2
1
0
1
1
1
1
1
1
1
0
1
2
0
2
1
1
1
1
2
1
1
0
1
1
1
0
1
0
1
1
1
1
1
0
0
1
0
1
2
0
2
2
2
2
2
1
1
1
2
1
0
1
0
2
1
0
1
3
1
2
1
1
1
1
1
0
1
1
0
1
1
1
1
0
0
1
0
1
1
0
1
2
2
1
2
0
1
1
1
1
1
1
1
0
1
1
1
1
1
1
2
1
0
1
2
0
2
2
1
2
2
0
1
1
0
1
2
1
4
0
0
1
1
0
1
1
2
1
2
0
0
1
1
1
0
1
0
1
2
0
1
1
2
1
1
2
2
2
1
1
0
0
0
1
1
1
1
0
0
0
2
1
2
2
1
2
0
1
1
1
1
1
2
1
1
1
1
2
1
1
0
1
1
2
2
0
2
1
0
2
1
2
1
0
1
2
2
1
1
1
1
1
1
1
0
0
1
1
1
3
1
2
1
1
0
1
2
1
0
1
1
1
1
1
1
1
1
0
2
1
2
2
1
0
1
0
0
0
1
2
1
0
2
2
1
1
2
1
0
1
1
2
1
1
1
2
1
0
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
1
2
1
1
2
1
1
1
1
4
2
1
1
1
2
0
1
1
1
2
1
1
1
1
2
1
2
1
1
1
2
1
0
2
1
0
1
1
1
0
0
1
1
1
1
1
1
1
2
2
1
2
1
1
1
2
1
1
1
1
2
1
1
2
2
1
2
1
0
0
1
1
2
1
3
1
1
2
1
1
2
1
1
2
1
2
0
1
2
1
1
0
1
2
1
1
1
1
0
1
0
0
2
1
2
2
1
0
0
2
0
1
0
2
1
0
1
0
1
2
2
0
0
0
1
1
2
2
2
0
0
1
1
0
2
1
1
1
1
2
2
1
1
1
1
1
2
2
1
2
1
2
2
1
1
0
1
2
2
1
2
1
1
0
1
1
2
1
0
1
0
0
1
1
2
2
2
1
2
1
1
1
0
0
0
1
1
3
2
1
1
0
1
0
0
2
2
1
0
1
0
1
2
0
1
2
1
1
1
1
1
1
1
0
1
3
1
1
0
2
1
1
1
1
1
1
2
0
1
2
2
1
2
1
1
1
1
1
2
2
1
1
1
0
0
1
1
2
2
2
2
0
0
0
2
1
1
1
1
1
0
2
2
0
1
0
2
2
2
1
1
2
1
0
1
0
1
0
1
1
1
0
2
2
1
2
2
1
1
1
1
0
1
0
0
1
2
0
1
2
1
1
1
2
0
1
1
1
1
1
2
2
2
1
2
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
2
1
1
0
1
0
1
1
2
0
2
2
1
1
1
0
2
1
0
0
1
2
1
1
1
1
1
1
2
1
1
1
2
2
2
1
0
0
1
2
1
2
2
1
2
2
1
0
2
2
2
0
0
2
0
1
1
1
0
2
0
2
1
0
1
1
1
0
0
1
1
1
0
1
1
1
0
2
2
2
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
2
1
0
0
2
0
2
1
1
1
2
1
1
1
1
1
0
3
1
1
1
2
1
1
1
1
0
0
2
1
1
1
1
2
1
0
1
1
0
1
2
1
1
1
1
1
2
1
0
1
0
2
2
1
2
2
1
1
1
1
1
1
1
1
1
2
1
0
1
2
1
2
1
1
1
1
2
1
1
1
2
1
2
0
2
1
1
1
0
1
0
1
0
2
1
1
2
1
1
0
1
1
2
0
1
1
1
2
2
0
2
1
1
1
1
3
1
2
1
0
0
1
1
0
1
2
1
0
0
1
2
1
1
2
2
0
1
2
1
1
2
1
1
1
1
2
1
0
1
1
0
1
1
0
1
2
1
2
1
2
1
1
1
1
1
1
1
2
1
1
2
2
1
1
0
0
0
2
1
1
2
2
2
2
1
1
1
2
1
0
1
2
2
0
1
0
2
0
1
2
3
2
1
1
1
1
0
2
0
2
1
2
1
2
1
1
2
2
1
1
1
1
0
0
2
1
1
2
1
1
1
1
0
2
2
1
2
0
1
1
1
1
0
1
0
3
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
0
1
1
1
1
2
1
1
1
2
2
1
1
1
2
1
2
1
1
1
2
1
2
1
1
1
1
0
1
1
1
0
1
1
0
1
1
0
0
1
1
1
2
3
1
1
1
1
1
1
1
0
1
1
1
1
2
1
2
1
0
1
1
1
1
0
2
1
1
2
1
2
2
2
1
1
1
1
1
2
2
2
2
1
1
0
2
1
1
1
0
1
2
0
0
2
2
1
0
0
1
0
1
1
2
2
1
1
2
2
1
1
1
0
0
2
0
1
1
1
1
2
1
1
2
0
1
0
0
1
1
1
2
0
1
0
1
2
1
1
2
2
2
2
1
1
1
1
1
1
0
0
0
1
0
1
1
2
1
5
1
1
1
1
0
1
1
1
1
1
1
1
2
1
2
1
1
0
2
0
2
2
1
1
1
1
1
1
1
0
2
1
1
0
1
1
1
2
1
1
1
1
1
1
1
1
0
1
1
1
2
0
1
0
2
2
2
1
1
2
1
1
2
1
2
1
1
2
1
1
1
0
0
0
2
2
0
1
1
1
1
1
1
3
1
2
1
2
1
0
0
0
2
2
1
0
0
2
1
1
1
0
2
1
2
1
0
0
2
1
2
1
1
1
0
2
1
0
1
1
1
1
0
1
0
1
1
1
2
2
1
0
0
1
0
1
1
0
2
1
2
1
2
2
2
1
1
0
1
1
2
1
1
2
1
0
1
1
1
1
0
1
0
0
1
1
2
1
2
2
2
2
1
0
1
1
2
1
1
0
0
1
1
2
1
2
1
1
2
0
1
1
1
1
0
2
1
1
2
2
2
1
2
1
1
1
2
2
0
1
2
1
1
0
1
0
1
1
1
1
1
0
1
1
1
1
1
1
1
0
0
1
1
1
1
1
0
0
1
1
1
0
1
1
1
2
0
2
2
2
1
1
2
0
2
0
1
1
1
0
4
1
1
1
1
1
1
2
2
1
0
1
0
2
1
1
1
0
1
1
2
1
1
0
1
2
2
1
1
1
0
2
0
2
1
1
1
2
1
1
1
1
2
1
2
0
0
1
3
2
1
1
0
2
1
1
1
1
1
1
0
2
1
1
1
1
1
1
2
0
0
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
2
0
2
1
1
1
3
1
1
1
1
1
1
2
2
1
0
0
0
0
1
2
1
1
1
2
0
2
1
1
1
1
1
1
1
2
1
1
1
1
2
0
2
1
1
1
0
2
0
1
1
1
1
2
2
1
1
1
1
0
1
2
1
1
0
1
3
1
1
2
1
0
0
2
2
1
1
1
2
1
1
1
1
1
1
2
2
0
2
3
1
1
1
1
2
0
1
1
1
0
0
1
1
4
2
1
0
2
1
1
2
1
1
2
0
1
1
1
1
1
1
1
2
3
2
1
0
1
1
2
2
1
1
1
0
0
0
1
0
0
0
1
2
1
2
1
1
1
2
1
1
0
1
1
1
2
0
1
1
2
2
1
0
1
2
0
1
0
0
1
1
1
2
2
2
1
2
0
1
1
1
0
1
2
1
1
1
2
2
2
0
1
1
2
2
1
2
1
1
1
2
0
1
1
0
1
2
0
2
2
2
1
1
2
1
1
0
1
2
1
1
1
2
1
1
0
0
0
1
1
0
1
0
1
1
1
1
1
1
1
0
1
2
2
0
1
1
0
0
2
1
0
1
1
1
2
1
1
2
1
0
1
1
2
2
1
1
5
2
0
2
0
2
2
1
2
1
2
1
1
2
0
1
0
1
0
2
2
0
0
1
1
2
2
2
1
2
2
1
1
2
1
0
2
1
2
2
0
0
1
1
2
2
0
1
2
2
1
1
2
2
2
2
0
1
0
1
3
0
2
1
0
1
1
2
1
0
1
1
1
1
1
0
2
1
2
2
0
1
2
0
1
2
2
1
1
1
1
2
1
1
2
2
0
1
0
0
2
1
1
0
2
1
0
1
1
1
2
1
2
2
1
1
1
1
1
0
2
2
0
1
1
1
3
0
2
1
1
1
0
1
2
0
1
0
1
1
1
0
1
1
1
1
1
1
0
1
1
1
1
1
1
0
1
0
0
1
1
1
0
1
1
1
0
0
1
0
0
1
1
1
1
1
0
1
1
2
2
1
1
1
2
2
1
3
2
1
1
1
0
1
1
1
1
1
2
1
1
1
1
1
2
1
0
1
1
0
1
2
1
1
0
1
2
0
2
1
0
2
1
2
2
2
2
0
1
2
0
1
0
1
1
1
1
1
1
2
1
2
1
0
1
1
1
1
2
1
0
1
0
1
2
1
1
0
2
1
1
1
1
1
0
2
1
1
1
2
0
1
1
0
1
1
1
1
0
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
2
1
1
10
0
1
2
0
1
1
1
1
2
2
2
0
0
1
0
0
2
0
1
1
1
1
1
1
2
0
2
2
1
1
1
2
0
0
1
1
2
0
1
0
1
1
2
1
1
1
0
0
1
1
1
1
0
2
1
1
1
1
1
1
0
1
1
1
0
2
1
1
1
1
1
0
2
1
1
1
0
2
2
1
1
1
2
2
1
0
0
2
2
1
1
2
1
1
1
2
2
1
1
0
0
0
1
1
1
0
2
1
0
1
0
1
1
0
1
1
2
1
2
2
0
1
0
0
1
2
1
2
1
2
1
2
0
0
1
1
0
0
2
0
2
2
1
1
1
1
2
2
2
1
1
1
1
1
2
2
0
1
1
2
1
1
2
1
2
0
2
2
4
1
0
2
2
2
1
0
1
1
1
1
2
1
2
0
0
1
1
1
0
2
1
0
2
0
0
1
1
1
1
2
1
0
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
0
1
1
1
0
2
1
2
1
0
4
1
1
1
1
2
0
1
1
1
1
0
1
1
0
1
1
1
0
0
1
0
0
1
1
0
0
1
1
1
2
1
0
1
0
1
2
0
1
1
3
1
1
0
0
1
1
1
1
2
1
1
0
1
1
0
0
2
0
1
1
0
1
1
1
1
0
1
1
1
2
2
1
1
1
2
1
1
0
2
1
1
1
1
1
2
2
1
2
7
1
1
0
2
1
1
1
2
1
1
2
2
2
1
1
2
1
1
2
1
0
1
1
0
0
1
2
1
1
1
1
1
1
1
1
0
1
1
0
2
1
2
2
1
1
1
0
1
0
2
1
1
2
1
1
0
1
1
2
1
1
1
2
1
1
1
1
2
1
1
0
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
0
1
2
1
1
0
2
2
2
0
1
2
0
1
0
2
1
1
1
1
1
0
1
1
2
0
2
1
1
0
1
1
1
2
1
1
2
2
0
3
1
1
1
1
1
1
2
1
0
1
1
2
2
1
2
0
1
2
1
1
1
1
2
1
0
1
1
1
2
1
1
2
1
0
1
1
1
1
1
1
0
1
2
1
2
0
2
0
3
0
1
0
1
1
1
0
1
2
1
1
2
0
0
2
2
1
1
0
1
2
2
1
1
1
0
1
1
1
0
1
1
1
0
2
0
2
1
1
1
1
1
1
2
2
2
1
2
2
2
0
1
1
1
1
2
1
2
2
0
1
1
1
0
2
2
1
1
2
1
1
2
1
1
0
1
1
1
1
0
1
1
0
0
1
1
1
3
1
2
1
1
1
1
1
1
2
1
0
1
1
1
2
1
1
1
1
0
2
1
2
0
1
2
1
1
2
2
0
1
2
1
0
0
0
1
3
1
1
0
1
1
1
0
1
2
2
1
1
1
1
2
1
2
2
1
1
1
1
1
1
2
2
2
1
2
2
1
0
1
0
1
2
0
0
2
1
1
3
1
0
1
0
1
1
0
1
1
1
2
0
0
1
1
0
1
2
1
1
2
2
0
2
0
1
1
1
0
2
2
1
1
2
1
1
0
2
2
2
1
1
0
2
2
1
2
0
1
1
1
2
0
1
2
2
1
1
1
1
1
0
1
1
1
1
1
0
1
1
1
1
2
0
1
1
1
1
1
1
1
2
1
0
1
2
0
1
1
1
1
1
2
1
0
2
1
1
1
1
1
1
1
0
1
1
1
0
1
4
1
1
2
0
0
1
2
0
1
0
1
1
1
1
2
0
0
1
2
1
0
0
1
1
0
0
1
1
1
2
2
1
2
1
1
2
4
0
1
2
1
0
2
0
1
0
2
1
0
1
2
2
1
1
1
0
0
1
0
1
1
1
2
1
2
0
1
1
1
1
1
1
1
1
1
0
1
0
2
2
1
1
0
2
1
1
1
1
1
1
1
1
2
1
0
1
1
2
1
2
1
1
3
1
1
0
1
1
2
1
1
2
1
0
1
0
2
2
0
1
1
1
1
0
0
2
1
1
2
1
1
1
0
0
0
1
1
1
2
2
0
1
1
1
1
2
0
1
1
2
2
1
1
0
1
2
1
2
1
1
2
0
1
2
1
0
1
0
1
1
2
2
2
1
0
0
1
1
1
1
2
2
2
1
1
0
1
1
0
1
1
1
1
1
2
2
1
0
3
1
2
2
1
1
2
0
1
1
2
2
0
0
1
2
0
1
2
1
0
1
1
2
1
0
2
0
0
1
1
0
0
1
2
2
2
1
1
0
1
2
1
1
4
1
1
1
2
1
1
1
0
1
0
1
1
1
1
1
1
2
2
0
2
0
1
1
1
1
1
1
0
2
1
0
1
1
0
1
1
2
0
1
2
1
1
2
1
1
2
1
1
0
1
2
1
1
2
1
0
0
0
2
1
0
2
1
0
0
2
1
1
1
1
1
2
1
3
1
2
2
1
2
0
1
0
1
1
1
0
1
1
0
1
0
0
0
1
1
0
2
1
1
1
2
1
0
1
1
2
1
1
2
1
1
1
0
2
0
1
1
1
2
0
2
1
1
0
1
1
0
0
2
2
1
0
0
1
1
1
2
2
1
0
1
1
1
1
1
1
2
2
2
2
1
2
1
1
0
1
0
2
0
2
1
1
1
2
1
2
1
2
1
1
1
1
2
1
0
2
1
2
0
1
0
1
1
2
0
2
2
0
2
2
0
1
1
1
3
2
2
1
2
2
1
2
1
1
2
0
1
1
1
1
1
2
0
1
1
1
2
0
1
0
2
1
1
0
1
1
1
1
1
3
1
0
1
2
1
1
1
1
2
2
2
1
2
1
1
1
1
2
1
1
2
2
1
0
1
1
2
2
1
0
1
2
2
1
1
2
1
0
1
1
1
1
1
1
1
0
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
2
1
1
2
1
1
1
1
2
1
0
1
1
2
1
2
1
2
1
2
2
1
1
2
1
1
1
2
1
0
0
2
2
2
1
2
1
2
1
2
2
2
2
2
0
1
0
1
1
0
1
0
0
1
1
1
2
0
1
1
0
1
0
1
2
1
1
1
0
1
0
1
1
1
0
1
2
1
1
1
2
1
0
1
0
0
1
1
2
1
2
2
1
1
1
1
2
1
1
1
1
1
1
1
1
0
1
2
1
1
2
2
1
1
1
2
1
1
2
0
1
2
1
0
1
1
1
1
1
2
0
1
2
1
1
0
2
1
1
1
0
2
1
1
1
1
0
1
1
1
1
1
1
1
0
0
0
1
1
0
2
1
1
1
0
1
1
1
1
0
1
0
0
0
0
2
1
2
1
1
0
1
0
0
1
1
1
1
1
1
0
0
1
0
1
1
1
0
0
0
2
1
2
1
2
2
2
2
0
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
0
1
0
1
1
1
1
1
1
2
1
0
2
1
2
2
1
0
1
1
0
1
1
1
2
2
0
1
1
0
1
2
1
3
2
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
2
1
0
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
0
2
1
0
0
2
1
2
1
1
0
2
1
1
0
0
2
1
1
1
1
1
2
1
1
1
3
0
2
1
1
3
2
2
1
1
2
0
0
0
0
1
2
1
0
0
1
1
1
2
0
1
2
1
2
1
1
1
2
1
1
1
1
2
1
1
0
1
1
2
1
1
2
2
1
1
1
1
1
0
2
1
1
2
2
0
1
2
0
1
1
1
1
1
2
0
1
1
2
1
2
1
1
1
1
1
1
0
1
1
1
2
1
1
2
1
1
1
1
2
0
0
0
2
1
1
2
0
2
1
2
1
0
0
0
0
2
0
1
2
0
1
2
1
1
1
0
1
2
1
1
1
1
1
2
2
1
1
0
2
1
1
1
1
2
1
1
0
1
1
1
1
2
2
2
1
1
1
1
2
2
0
1
1
1
2
1
1
1
2
2
3
1
0
0
1
2
1
2
0
0
1
0
1
1
1
2
1
0
2
1
0
2
1
1
2
1
1
1
0
1
2
1
2
2
0
2
1
1
1
2
2
1
1
0
1
0
1
1
1
1
1
1
0
1
2
1
1
0
1
2
2
0
2
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
0
1
1
1
2
0
0
1
2
2
1
2
2
1
1
1
1
0
1
1
1
1
1
1
1
1
1
0
1
1
0
0
0
1
0
2
1
1
1
1
1
0
1
1
1
0
1
1
0
1
1
0
2
2
0
1
2
1
3
2
2
1
2
0
1
0
1
1
1
1
0
1
1
1
1
0
1
0
0
0
1
1
1
0
2
1
0
1
1
1
1
1
1
0
0
2
0
2
2
1
1
1
2
0
1
2
1
1
2
0
1
0
1
2
1
1
1
1
1
1
2
0
0
1
1
1
1
0
2
1
0
3
1
1
1
1
2
1
1
2
1
0
2
1
1
0
2
2
1
0
2
1
1
1
0
1
0
0
2
0
1
1
0
1
0
2
1
1
2
1
0
1
2
1
1
1
1
0
1
0
1
2
2
1
1
0
1
1
1
1
1
2
1
0
1
0
1
2
1
1
2
2
1
1
1
0
1
1
1
1
1
1
0
1
2
1
0
1
1
1
1
1
1
1
1
1
1
1
2
1
1
0
1
1
1
2
0
2
1
1
1
1
3
1
1
1
1
0
2
1
0
0
1
0
1
1
1
2
0
0
1
2
2
0
1
0
1
1
1
1
0
1
1
2
2
2
1
1
3
1
1
1
2
1
4
0
0
2
2
0
2
1
2
2
1
1
1
2
2
1
2
0
1
1
1
2
1
2
1
1
1
1
0
0
0
1
1
2
1
1
2
0
2
2
1
0
2
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
2
1
2
1
1
1
1
0
3
1
1
2
2
0
0
0
0
1
1
1
1
1
1
0
1
1
0
1
1
1
2
1
1
1
0
1
1
1
2
1
2
1
1
2
1
3
1
1
0
2
1
2
1
2
0
1
2
1
1
1
0
3
1
2
2
1
1
1
1
1
0
1
1
2
0
1
2
1
1
0
2
0
1
1
0
1
0
2
2
1
1
1
1
1
1
1
1
2
1
1
1
2
0
1
2
2
0
2
2
2
2
1
2
1
1
0
1
0
0
1
2
2
1
0
2
1
2
1
1
2
0
1
1
1
0
1
1
1
1
1
1
2
1
1
1
0
1
3
1
1
1
1
0
1
1
1
1
1
1
2
1
2
1
2
0
1
1
1
1
1
0
0
1
1
2
1
0
2
1
2
0
1
1
2
2
2
1
2
1
1
1
1
0
1
2
1
1
1
1
1
1
0
1
0
0
2
0
2
1
2
1
1
1
0
1
1
1
2
1
2
1
1
1
2
1
1
1
2
0
2
1
1
0
1
1
1
1
1
2
1
1
0
2
1
1
0
1
2
0
2
2
1
2
2
1
1
1
1
1
1
1
1
2
1
2
1
2
2
2
1
1
1
1
2
2
1
1
1
2
1
1
1
1
1
0
1
1
0
1
1
1
0
1
2
0
1
2
0
0
1
0
1
0
1
2
1
1
1
1
1
1
2
0
0
2
1
1
2
1
1
1
2
1
0
1
2
1
5
0
2
0
2
1
1
1
1
0
1
1
1
0
1
1
1
1
1
1
1
1
1
0
1
1
2
1
2
1
2
1
0
0
2
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
2
2
1
2
0
1
1
1
0
1
1
0
1
2
1
1
1
2
1
1
1
1
2
2
1
1
1
1
1
2
0
1
1
1
1
0
2
1
1
2
0
1
0
1
1
2
1
1
2
2
2
1
1
0
1
1
0
1
0
2
2
1
1
1
0
1
1
1
2
1
1
1
0
2
2
1
1
1
0
0
0
1
1
1
1
1
1
1
1
1
1
1
0
0
1
1
1
1
1
1
2
0
1
1
0
0
2
2
1
1
1
1
1
1
1
1
0
2
0
1
1
1
1
1
1
1
1
1
1
0
1
0
2
1
1
1
2
1
0
1
1
1
0
2
0
0
1
1
1
1
2
0
2
1
1
1
1
0
1
1
0
0
2
1
2
0
1
2
0
1
1
1
2
2
1
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
2
2
1
1
1
0
0
1
1
0
0
1
0
1
0
1
2
0
2
1
1
2
1
3
1
1
2
1
1
1
1
1
0
0
2
1
1
1
1
1
1
1
1
1
0
1
2
1
2
1
1
1
0
2
2
1
1
0
1
1
1
1
2
1
0
1
2
1
0
2
2
1
1
2
0
3
1
1
1
1
2
0
1
0
2
1
1
1
1
2
0
2
3
1
2
1
2
1
1
0
1
1
0
1
2
1
0
1
1
1
1
2
0
1
2
1
2
2
1
1
1
0
0
2
2
1
1
1
1
1
1
1
0
0
1
2
1
1
0
1
0
2
1
1
1
1
1
2
0
1
1
0
1
1
1
1
2
2
2
1
1
2
0
1
1
2
1
1
1
1
0
1
0
0
1
0
0
1
0
2
1
1
2
1
1
0
1
1
1
1
1
0
1
1
2
2
0
0
1
1
1
1
1
2
2
2
0
1
1
2
0
0
1
2
2
2
1
1
1
1
0
1
2
0
0
2
1
1
1
2
1
0
1
1
2
1
1
1
2
0
2
1
1
1
1
1
1
1
1
1
0
1
1
4
1
1
2
0
1
0
0
0
1
1
1
2
1
1
1
2
1
2
1
1
0
1
1
0
0
1
2
1
1
1
1
1
1
1
2
0
1
0
2
1
1
1
0
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
0
0
1
1
2
0
1
0
1
1
1
1
1
0
1
1
0
2
0
2
1
0
1
1
1
0
1
2
2
2
1
2
2
1
2
1
1
1
0
1
1
1
2
2
1
0
2
1
1
1
1
2
0
1
1
0
2
1
1
1
2
0
2
2
2
2
0
0
1
1
1
1
0
0
1
1
1
0
1
1
1
1
2
2
2
0
1
0
1
2
1
0
1
1
0
2
1
1
1
1
0
1
1
1
2
5
1
1
1
0
2
0
1
3
2
1
1
2
0
1
1
2
2
1
1
1
0
2
2
1
0
0
1
0
2
2
0
2
0
1
1
2
1
2
1
0
0
1
1
1
1
1
1
1
1
1
1
1
1
0
1
2
1
2
1
1
1
0
1
1
1
1
1
2
2
1
1
1
1
1
1
1
0
1
1
1
2
2
1
1
1
0
2
1
0
2
2
1
1
2
0
2
0
1
1
1
1
1
0
1
1
2
1
1
1
1
1
0
1
1
0
1
1
2
0
0
1
1
2
0
0
1
1
0
1
1
2
1
2
2
0
1
1
2
1
1
2
1
1
2
0
2
2
2
2
1
1
1
1
1
2
1
1
1
0
2
2
0
1
1
1
1
1
0
1
0
1
1
1
0
1
1
2
1
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
1
2
0
0
1
1
1
1
0
1
1
0
1
1
1
0
2
1
1
1
1
0
1
2
0
1
1
1
2
1
2
1
1
1
1
0
2
0
0
2
1
1
0
1
1
1
2
1
0
1
0
1
0
2
2
1
0
0
1
2
1
1
0
1
1
1
2
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
0
2
2
1
1
0
2
1
1
2
1
2
1
0
0
1
1
1
0
2
2
1
1
1
0
1
2
1
0
1
1
2
1
1
1
2
2
1
2
0
1
0
1
1
1
1
2
1
1
1
1
1
0
1
1
1
1
1
2
0
2
1
2
1
1
1
1
2
1
1
0
2
1
2
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
2
2
1
2
1
1
1
1
1
1
2
1
1
0
1
2
2
1
0
1
1
1
2
1
2
2
2
1
1
0
1
1
2
2
1
2
1
1
2
1
1
1
1
0
2
1
2
1
1
0
1
2
1
1
2
2
0
1
6
3
2
1
2
1
0
1
3
2
1
1
2
2
1
1
1
1
1
1
1
1
0
1
2
1
0
1
1
1
2
1
1
2
1
0
1
2
1
2
2
2
0
0
1
1
1
2
1
1
1
1
1
1
1
0
1
2
1
2
1
1
2
0
1
1
2
1
1
1
2
0
1
1
2
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
0
0
1
0
1
1
1
2
2
1
2
1
0
0
0
1
0
0
1
1
1
2
2
1
1
1
1
1
1
0
1
2
2
1
1
1
0
1
1
0
2
1
0
2
2
1
1
2
1
1
1
2
0
0
1
2
0
2
1
1
1
2
0
1
1
1
0
2
1
2
1
1
1
1
1
1
2
1
1
2
0
2
1
1
1
0
0
1
1
0
1
2
2
1
1
1
1
0
2
1
0
1
1
1
2
2
0
0
2
0
0
1
1
0
1
2
2
1
1
1
1
1
2
1
2
1
2
2
4
1
1
0
0
1
1
1
0
1
1
1
1
0
1
2
1
1
2
2
1
2
0
2
1
2
1
1
2
2
1
1
0
1
0
1
0
0
1
1
1
2
0
1
1
1
1
1
1
1
3
1
1
1
0
2
1
1
1
1
2
1
2
1
0
1
1
2
1
1
1
1
1
2
1
1
2
1
0
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
0
1
2
1
0
0
1
1
1
0
2
2
1
1
1
1
2
1
1
1
1
2
2
2
1
1
1
1
2
2
0
1
1
0
2
3
0
1
1
0
2
1
2
2
3
0
1
1
1
1
2
1
0
1
0
2
2
2
2
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
0
1
2
1
2
2
1
1
1
0
1
1
0
2
1
0
1
0
3
0
1
1
1
0
1
0
0
2
2
1
1
1
2
1
2
2
1
0
1
1
1
3
1
1
1
1
2
1
0
0
1
0
2
2
1
0
2
1
1
1
0
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
0
2
1
0
1
1
2
1
1
0
0
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
2
2
1
1
0
2
2
1
0
1
0
1
1
1
1
0
1
1
2
1
2
1
1
4
0
1
2
2
1
2
2
1
1
2
1
1
1
0
1
1
2
1
1
2
2
0
1
2
1
0
1
1
3
1
0
1
0
1
1
1
0
2
1
0
1
1
0
2
2
0
0
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
2
1
1
2
1
2
1
1
1
1
1
1
2
0
1
1
1
1
1
0
2
1
1
1
1
0
0
0
1
2
1
1
1
2
1
1
0
1
1
1
1
1
1
0
2
2
0
1
2
1
2
1
1
0
1
1
1
1
0
1
1
1
1
2
0
1
1
1
1
1
2
1
2
1
1
1
1
2
1
0
0
1
0
1
1
1
1
1
1
2
1
1
1
0
1
0
1
2
2
1
0
1
1
0
1
0
1
1
1
5
1
0
1
1
1
1
1
1
0
0
0
1
0
1
1
2
1
2
2
2
1
2
0
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
0
0
2
1
2
0
2
1
1
1
0
0
3
1
1
2
1
0
1
1
2
1
2
2
1
1
1
2
0
2
0
1
1
3
1
1
0
2
1
1
1
0
1
2
0
2
0
1
2
0
0
1
1
2
0
1
0
0
1
2
1
2
1
2
2
1
1
1
2
1
0
2
1
1
2
0
1
1
1
2
1
0
1
1
0
1
0
0
1
1
0
0
1
1
1
1
2
0
0
1
1
0
1
2
0
1
0
0
1
0
1
0
1
1
2
1
1
1
1
0
2
1
1
1
2
1
1
1
1
1
2
0
2
0
2
0
1
0
0
1
1
0
2
0
0
1
1
1
1
0
2
0
2
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
0
2
1
0
1
1
1
0
1
1
0
0
1
1
1
1
2
1
0
1
0
1
2
2
1
0
1
1
1
2
0
1
2
1
2
1
1
1
2
1
2
1
1
0
1
0
2
0
0
1
0
1
0
0
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
0
0
0
2
1
1
1
1
1
2
1
1
1
1
2
1
1
0
1
1
1
1
0
2
2
0
1
0
0
1
1
1
1
2
2
1
1
1
0
1
0
1
2
0
0
1
0
0
1
1
0
1
1
0
2
0
2
1
0
0
2
1
0
0
1
2
1
2
1
1
1
2
1
1
0
2
1
1
1
2
1
1
0
1
0
1
1
1
2
0
0
0
0
1
2
0
0
1
1
2
1
1
1
0
1
1
2
0
1
0
2
1
1
1
2
1
2
1
2
1
1
1
2
2
0
1
1
1
0
1
1
0
0
2
1
1
1
1
1
2
2
1
1
1
0
1
0
2
1
1
1
1
1
2
1
0
2
1
1
1
1
2
1
1
2
1
2
1
0
2
0
1
0
1
0
1
1
1
1
2
1
1
0
1
1
2
1
2
1
1
0
1
3
1
1
2
2
0
1
2
3
1
1
0
1
0
0
1
1
2
1
1
1
1
2
1
0
1
0
1
0
1
1
0
1
1
2
0
2
1
1
0
1
1
1
2
0
1
2
1
2
2
1
1
1
0
1
0
1
1
2
1
2
3
0
1
2
1
2
1
1
1
0
1
1
0
1
0
2
0
1
1
2
1
1
2
1
1
1
2
1
2
1
2
1
2
1
2
1
1
2
1
1
0
2
0
1
0
1
1
1
2
2
1
1
1
2
1
0
0
1
1
1
1
1
1
2
1
2
1
2
1
2
0
1
2
2
1
2
0
2
0
1
0
2
2
2
1
1
0
2
2
0
0
1
1
0
1
0
1
1
1
2
2
2
0
1
1
1
1
1
1
1
0
0
1
0
0
1
1
2
0
2
1
0
1
1
1
1
0
1
1
2
1
0
2
1
1
1
1
2
1
1
0
1
0
1
1
1
0
1
1
1
1
1
1
1
2
0
1
1
0
0
2
1
1
0
2
0
1
1
0
2
2
2
1
1
1
1
2
1
1
1
1
1
1
2
1
2
1
1
0
0
0
0
0
2
1
0
0
2
0
0
1
0
2
1
1
1
0
1
1
1
1
2
1
1
0
1
1
0
0
1
0
1
1
2
0
1
0
0
1
1
0
1
2
0
1
2
1
1
2
0
0
0
1
0
0
1
2
1
0
2
1
1
1
1
2
2
1
1
1
0
1
1
1
2
1
0
0
0
1
1
1
1
1
0
1
1
1
1
1
0
1
2
2
2
2
0
0
2
0
0
1
0
2
1
1
1
0
1
1
2
1
1
0
2
1
2
0
2
0
0
2
2
2
1
1
2
1
0
2
1
1
1
1
1
1
1
2
1
2
1
0
1
1
1
1
1
1
0
1
1
1
0
1
0
2
2
0
2
1
1
2
1
1
1
2
0
1
1
2
2
1
0
2
1
1
2
1
0
2
1
0
1
1
1
2
4
1
1
0
3
2
1
1
1
1
1
2
2
2
1
2
1
1
0
0
2
1
1
0
1
2
1
1
1
1
0
1
1
0
2
0
1
1
2
0
1
1
1
1
1
2
2
1
1
1
1
2
1
0
2
1
1
0
1
1
1
2
1
1
1
0
1
1
2
1
1
1
0
2
1
2
1
2
0
0
1
1
1
2
0
1
1
1
1
0
1
0
0
1
2
1
2
1
2
2
1
1
2
0
1
1
2
2
1
0
1
2
1
1
0
1
2
2
4
1
1
1
1
0
1
2
0
0
1
1
2
0
1
1
1
1
1
1
1
0
0
1
1
0
1
0
2
1
1
0
1
0
2
0
0
1
1
0
1
0
2
0
2
1
1
2
0
1
1
1
1
1
1
1
0
1
2
1
1
2
1
1
1
1
1
1
1
2
1
0
1
1
2
2
1
1
0
0
1
2
2
0
0
2
0
1
1
1
0
1
2
2
1
1
1
2
1
1
1
1
2
1
1
2
0
2
1
0
1
1
1
0
1
1
0
1
1
1
1
1
1
1
0
1
0
0
1
2
1
1
2
1
1
2
2
2
2
0
0
0
1
1
1
1
1
1
1
1
2
2
1
2
1
1
1
0
0
1
1
0
2
1
1
1
1
2
0
1
2
1
2
0
1
1
1
1
0
0
2
0
1
1
1
1
2
1
0
1
0
1
1
1
1
2
1
1
0
1
2
0
0
1
0
2
0
1
1
1
0
1
2
1
2
1
1
1
1
1
2
1
1
2
0
1
1
1
1
2
1
1
1
0
0
1
0
1
1
2
1
2
1
2
1
1
1
2
0
1
0
1
0
1
1
0
4
1
1
0
1
1
1
0
0
1
2
1
2
1
2
2
1
2
0
1
1
1
2
1
1
0
0
2
2
1
1
1
1
2
2
2
1
0
0
1
2
1
1
1
1
1
1
2
1
2
1
0
2
1
0
1
2
1
1
1
1
1
1
2
2
0
1
1
0
1
1
1
1
1
1
2
0
1
1
2
2
1
2
1
2
1
1
2
1
1
2
1
0
1
1
2
1
2
1
0
0
1
2
1
2
2
2
1
1
1
2
1
1
1
2
1
1
2
2
1
1
1
1
1
0
3
0
0
2
1
1
1
0
2
2
1
1
2
0
1
1
1
1
4
0
1
1
1
0
0
1
1
1
1
0
1
2
1
1
1
2
1
2
0
1
0
2
1
1
1
1
2
0
1
0
1
0
2
2
1
2
2
0
0
1
0
1
0
2
1
1
1
1
2
1
1
0
1
2
0
1
1
1
1
1
1
1
1
1
0
1
2
0
2
2
2
2
1
2
2
1
2
2
0
1
1
1
1
1
0
1
1
1
3
1
1
1
1
2
1
1
0
2
0
2
2
1
2
2
1
1
1
1
1
2
1
0
1
1
2
0
1
1
2
3
1
1
1
1
0
1
2
1
1
3
1
1
1
1
1
1
1
1
1
2
0
0
0
0
1
1
1
1
1
2
1
1
2
1
1
0
1
1
1
2
2
2
2
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
0
0
2
1
1
1
1
1
2
1
1
0
1
2
1
1
2
1
1
1
2
0
0
0
0
1
1
1
1
1
0
1
0
1
1
1
1
2
1
1
0
0
1
1
1
0
0
0
1
1
1
1
1
2
1
0
1
1
0
1
1
2
1
2
0
0
0
1
1
0
1
2
1
1
2
1
1
0
0
1
1
1
2
0
1
1
1
1
1
1
1
1
2
2
2
1
1
0
1
0
2
2
0
1
0
1
2
2
2
1
1
1
0
1
2
0
3
1
1
2
2
2
1
1
0
0
1
0
2
2
1
0
1
0
1
2
2
1
0
1
1
1
0
0
0
1
2
2
0
1
0
1
3
2
1
0
1
1
0
2
2
1
1
1
0
1
1
1
0
1
2
2
0
1
1
1
1
2
2
1
1
2
2
1
1
2
1
1
2
2
1
1
2
1
0
0
2
1
1
1
2
1
1
1
2
2
0
1
1
0
2
2
1
2
1
1
1
1
1
1
1
1
2
2
1
2
2
1
2
1
1
2
1
1
1
1
1
1
2
1
2
1
1
2
1
2
1
0
2
1
1
1
2
4
2
1
1
2
1
0
0
2
1
1
0
0
1
0
1
1
1
1
0
1
1
0
2
2
1
1
2
0
1
1
1
2
1
0
1
1
2
1
1
1
0
0
1
1
1
1
1
1
1
2
1
1
1
1
0
0
1
0
2
1
2
2
1
1
2
1
1
1
0
1
1
1
1
1
1
1
2
1
2
0
0
0
1
2
1
1
1
1
0
1
1
2
2
1
2
0
2
2
0
0
1
1
1
1
0
1
1
1
1
0
1
1
1
1
1
2
0
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
0
0
1
1
1
0
1
2
0
1
1
1
2
2
1
1
2
1
0
1
1
1
1
1
2
1
0
2
1
0
1
1
0
0
1
1
2
1
1
1
1
2
2
1
2
1
1
1
0
0
0
2
1
0
1
2
1
1
1
1
1
1
1
2
2
0
1
1
1
0
1
1
1
1
1
1
1
0
1
1
1
1
1
2
1
1
2
1
2
1
1
0
0
1
1
0
1
2
1
2
1
1
2
2
0
1
2
1
1
1
1
0
1
1
2
1
1
1
1
2
0
1
2
0
1
1
1
1
1
1
2
1
1
1
1
1
1
1
0
1
2
2
3
1
2
2
0
1
1
1
0
0
1
0
0
1
1
1
2
1
2
0
0
1
2
1
1
1
1
1
4
1
1
1
1
0
2
1
2
0
1
1
1
1
2
1
0
2
1
1
0
1
1
0
1
2
1
2
2
0
2
2
1
1
2
1
0
0
1
1
1
1
1
1
2
0
1
0
2
1
1
1
2
1
0
0
1
1
2
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
2
1
1
1
2
0
2
1
1
2
2
1
1
1
1
0
0
0
1
2
1
0
1
1
1
1
1
0
2
2
1
1
1
1
1
0
1
0
1
0
1
1
1
0
1
1
0
1
0
0
0
2
1
2
1
1
0
0
1
1
2
1
0
1
2
1
2
1
2
1
0
0
0
1
1
1
0
2
1
2
0
0
1
1
1
2
1
1
0
2
1
1
2
1
1
1
1
0
2
0
0
0
1
1
1
1
1
1
1
2
0
1
1
2
0
1
1
2
1
2
1
1
1
1
2
1
1
1
0
1
1
1
2
1
1
2
2
0
0
0
2
0
3
1
1
0
0
1
2
1
5
1
2
2
1
2
2
1
1
1
1
1
1
1
3
0
1
1
1
1
1
2
1
1
1
2
1
1
0
2
2
0
1
2
2
0
2
1
1
1
2
1
1
2
1
1
1
1
1
1
0
1
1
2
2
1
2
0
0
2
0
1
1
2
1
0
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
0
1
1
0
2
1
1
1
1
2
1
1
1
1
0
0
1
1
2
2
1
1
1
1
2
1
2
1
1
1
3
2
1
1
1
0
1
1
1
2
1
2
0
1
3
1
1
1
0
2
1
1
1
2
0
1
0
0
2
2
2
0
2
0
1
1
1
1
1
0
1
0
3
0
1
0
1
2
1
0
1
1
2
2
0
1
0
1
3
1
1
2
2
1
2
0
1
1
2
1
0
1
1
0
1
1
1
1
1
1
0
1
0
0
1
0
2
2
0
2
1
3
0
1
0
1
1
2
1
1
2
0
1
1
1
1
1
1
2
1
1
1
0
1
0
2
1
0
1
2
0
2
2
2
2
0
1
1
2
0
1
2
1
0
0
2
1
1
1
1
1
1
2
2
1
2
1
2
2
1
1
2
1
0
0
1
1
1
2
1
1
2
1
2
1
2
1
0
1
1
1
2
2
1
3
0
1
1
0
1
1
1
1
1
1
1
1
1
0
1
1
1
0
1
1
1
1
1
1
1
1
1
2
1
1
2
2
3
1
1
0
0
1
1
0
1
1
2
2
1
1
1
1
1
14
1
1
1
0
1
2
1
1
1
1
2
1
1
0
0
1
2
1
0
1
0
1
1
1
2
1
0
2
1
2
0
1
1
1
2
0
1
1
1
1
1
1
1
1
1
1
0
2
1
0
1
1
0
1
1
1
0
1
2
2
1
2
1
1
0
1
0
1
1
2
1
1
2
1
1
1
2
2
0
1
1
2
1
2
1
1
0
0
1
1
0
0
1
1
2
1
0
1
2
0
0
1
0
0
2
1
1
1
1
1
1
2
2
1
2
1
2
2
1
1
1
2
1
2
2
1
1
1
1
1
1
0
2
1
2
2
0
1
1
0
2
1
0
0
1
2
1
1
1
2
1
0
2
1
1
2
0
0
1
1
1
2
2
2
1
0
2
2
1
1
1
2
1
1
1
1
2
0
1
1
0
2
0
2
1
0
1
1
2
1
0
0
2
1
2
1
1
1
1
1
1
1
1
2
0
0
1
1
0
2
1
1
0
1
1
1
0
1
1
2
0
0
1
0
0
2
1
1
1
1
1
1
1
1
0
1
1
2
2
0
2
1
0
2
0
1
1
1
1
1
1
1
1
2
0
1
0
2
1
1
1
1
0
1
1
2
1
1
1
1
1
0
1
1
1
1
0
1
2
1
1
1
2
0
0
2
1
1
0
0
1
2
2
2
1
1
1
1
1
1
3
1
1
1
0
1
0
1
0
1
1
0
1
2
1
2
1
1
0
1
1
1
1
1
1
2
1
0
2
2
1
1
1
1
2
1
1
1
1
0
2
2
1
2
1
0
1
1
1
2
1
1
1
2
1
1
1
1
0
2
2
1
1
1
1
2
0
2
1
1
1
1
2
0
2
2
1
1
2
1
0
1
0
2
1
1
0
2
1
0
2
1
0
0
0
1
1
1
2
1
2
2
1
1
1
1
1
2
0
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
0
1
1
2
2
1
2
1
1
1
1
0
1
1
0
0
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
2
2
0
1
1
1
1
2
0
1
1
1
1
1
1
1
1
1
1
0
0
1
0
0
2
0
0
2
1
0
0
2
1
0
0
0
1
0
1
1
0
1
0
2
2
1
0
1
0
1
1
2
1
1
0
1
1
0
1
2
1
0
1
2
1
1
0
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
0
0
1
4
1
1
1
2
1
1
1
0
1
1
0
0
0
1
1
1
1
1
0
2
1
1
1
1
1
1
0
1
2
1
1
0
0
1
1
1
0
2
2
0
1
0
1
2
0
1
0
0
1
1
0
1
1
1
1
2
1
1
1
1
0
1
1
1
0
1
2
1
1
1
1
2
1
1
1
1
0
1
1
1
1
1
1
1
1
0
0
1
2
2
1
0
1
1
1
1
1
1
0
1
1
2
1
0
0
0
1
1
0
1
1
2
1
1
2
3
1
2
2
0
0
0
0
1
1
1
2
0
1
1
1
1
0
1
1
0
2
3
1
1
2
1
1
1
0
0
1
1
0
1
1
2
1
2
1
4
1
1
1
0
2
1
1
0
1
1
0
0
2
1
1
1
1
0
2
0
2
1
0
2
1
0
0
1
1
1
1
1
1
1
1
1
2
1
1
0
1
1
1
1
1
1
0
1
1
1
2
1
0
2
1
1
2
1
1
1
1
0
0
1
2
1
1
0
2
2
1
1
2
1
1
2
2
2
1
1
2
0
1
1
2
2
2
1
0
1
1
1
1
1
2
1
1
0
1
2
1
1
1
1
2
0
1
1
1
0
2
1
1
2
1
1
1
1
1
2
2
1
1
1
1
2
1
1
0
2
1
0
1
1
2
1
0
1
0
1
0
1
0
1
2
1
1
1
1
2
1
2
2
2
2
2
0
0
1
1
2
0
1
2
1
2
1
2
0
2
0
1
0
1
1
1
2
1
2
2
1
0
2
2
1
0
1
0
1
1
2
1
0
1
0
1
1
2
1
2
2
1
2
1
1
2
1
1
0
1
1
2
2
2
1
1
1
1
0
1
0
1
2
1
1
1
1
0
2
1
1
0
1
0
2
2
1
1
0
1
1
2
2
1
1
1
0
2
1
1
1
1
1
1
0
1
1
2
1
0
1
2
1
0
1
1
0
1
1
2
0
1
1
1
0
0
1
1
1
1
1
1
1
2
1
1
2
1
1
2
1
2
1
0
1
0
1
0
0
1
1
1
2
1
2
1
1
1
2
0
0
1
1
0
1
1
2
2
1
2
1
1
0
2
0
1
1
2
1
2
1
2
1
1
1
0
1
1
2
1
1
1
2
2
1
0
1
1
1
1
1
1
2
1
0
1
2
1
0
1
2
1
1
1
0
1
1
1
1
1
0
1
1
1
1
1
2
1
1
2
1
1
1
2
0
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
2
1
1
0
0
1
3
1
1
1
0
1
0
1
1
1
1
1
2
0
1
1
2
1
1
2
1
1
2
1
1
0
1
1
1
0
2
2
1
2
0
0
1
2
2
1
1
1
2
2
1
1
1
0
1
2
2
1
1
1
0
2
2
1
1
0
2
1
0
0
0
2
0
1
1
2
1
2
1
0
0
0
1
1
0
0
2
1
1
1
1
0
2
2
2
1
2
1
1
1
1
1
0
1
2
2
1
1
0
1
0
1
2
0
1
1
0
1
0
2
1
1
1
2
2
0
1
1
2
2
0
1
1
2
1
1
1
0
2
2
1
1
1
1
1
1
1
2
1
2
1
2
0
1
1
1
0
2
1
0
1
1
1
1
1
0
1
1
2
1
1
1
1
1
2
1
1
1
1
0
1
1
0
2
2
1
1
0
2
1
1
1
1
1
1
1
1
1
1
1
1
2
0
0
1
0
1
2
1
1
1
1
2
1
2
1
1
2
1
2
2
2
1
1
2
1
1
2
1
1
1
1
0
1
1
2
1
1
1
1
1
1
2
2
2
2
1
2
1
1
1
2
2
0
1
2
2
1
1
2
1
1
1
1
0
1
1
2
1
2
1
1
1
0
1
2
1
0
1
0
1
1
1
1
1
1
1
2
0
0
1
2
1
1
0
0
1
0
1
2
1
1
1
1
1
0
2
0
1
1
1
1
1
1
1
1
1
0
2
1
0
1
2
1
1
1
2
0
1
0
1
1
1
0
1
1
0
1
1
2
0
1
1
2
1
1
1
1
1
0
1
3
2
1
1
2
2
1
2
2
2
1
1
1
1
2
0
1
2
0
1
0
0
1
1
1
1
1
2
1
2
0
1
1
2
4
1
0
1
2
1
0
1
2
1
1
2
0
1
0
1
1
3
1
1
2
1
2
1
1
2
0
0
1
1
1
1
2
0
1
2
2
0
1
2
1
0
0
1
1
0
1
2
1
2
1
2
1
0
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
2
1
1
1
1
0
1
0
1
1
0
0
2
2
0
1
2
1
1
1
2
0
2
1
0
0
1
1
2
1
2
2
2
1
1
1
2
2
0
1
2
0
0
1
1
2
1
1
1
2
1
1
2
2
0
0
1
2
2
2
2
1
0
1
1
1
1
0
1
1
2
1
2
0
1
1
1
1
3
1
1
0
1
1
2
1
2
2
1
1
1
1
0
0
1
1
1
1
1
1
0
1
1
1
1
1
1
2
0
0
2
1
1
1
2
1
1
2
1
0
1
1
2
1
1
2
2
1
0
2
2
2
2
2
0
2
1
1
1
1
0
1
2
0
2
1
1
1
1
2
0
0
2
0
0
0
2
1
2
2
0
2
1
1
0
1
2
2
1
0
1
2
1
1
0
2
1
0
1
1
1
1
1
1
1
1
0
1
1
2
1
1
2
2
1
1
1
2
0
1
0
0
1
1
2
0
2
0
1
1
1
2
0
1
1
1
2
0
1
2
1
2
0
2
2
0
2
2
1
0
0
2
0
0
1
2
0
1
1
1
0
4
1
1
0
2
1
2
0
1
2
2
1
1
1
0
1
0
1
2
2
0
1
1
1
1
1
1
0
1
1
2
2
1
0
0
2
1
0
1
1
1
3
2
1
1
1
0
2
0
1
1
1
1
2
2
2
1
1
0
1
0
1
2
1
1
1
1
0
2
1
1
1
0
0
2
0
0
2
0
2
2
1
1
1
1
1
2
0
1
1
0
1
2
2
1
5
1
2
1
1
5
2
1
0
0
1
1
0
1
0
2
2
1
1
1
1
1
1
0
1
1
2
1
2
1
2
2
2
2
1
1
1
1
2
1
0
1
1
1
1
1
1
1
1
1
1
1
0
0
2
0
2
1
1
2
2
1
1
1
0
0
1
1
0
1
1
1
2
2
1
0
1
1
2
2
0
1
0
1
0
1
1
1
1
0
1
1
1
2
0
1
1
1
2
0
1
0
1
1
2
0
1
1
0
1
2
0
1
1
0
1
1
1
0
1
0
2
1
1
2
2
1
2
1
1
0
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
2
0
0
1
0
0
0
1
1
2
2
3
1
1
1
1
1
1
0
1
1
1
2
0
0
1
1
1
0
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
0
0
0
1
2
1
2
0
1
1
1
1
0
1
2
1
1
0
1
1
2
1
1
1
2
1
1
1
1
3
1
1
1
1
2
1
1
1
2
1
1
0
0
1
2
1
1
2
1
0
0
1
1
2
1
1
1
2
1
1
1
1
1
1
0
2
2
1
1
1
1
2
1
1
1
1
0
2
0
0
0
2
0
0
1
1
0
1
1
1
1
2
1
1
1
1
2
1
1
0
1
2
1
0
2
1
1
1
2
1
4
1
1
2
1
1
2
0
1
2
0
2
1
1
2
1
1
1
1
1
0
1
0
0
1
1
1
1
0
1
1
1
2
0
1
1
1
0
1
1
2
1
2
0
1
2
0
1
1
1
1
1
1
2
1
2
2
0
2
1
1
1
0
1
0
2
1
1
1
1
1
0
1
2
1
2
2
1
0
2
1
1
2
2
1
2
1
1
2
1
2
3
2
1
1
2
1
1
1
1
1
1
0
2
1
1
1
2
1
1
0
1
1
0
1
1
0
1
2
2
0
2
0
0
1
2
1
1
4
1
1
1
1
2
1
1
1
0
1
2
1
1
1
1
1
1
1
2
2
1
0
1
1
2
1
1
0
0
3
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
2
1
2
1
1
1
1
1
0
3
1
1
1
2
1
0
0
1
1
2
1
0
0
2
1
2
1
1
2
2
1
2
2
1
0
1
0
1
1
1
0
0
1
1
0
1
1
0
1
0
2
0
2
1
0
1
0
1
1
1
2
2
1
1
1
2
2
0
1
2
2
1
1
1
1
0
2
0
1
2
1
2
2
1
1
1
2
2
1
3
1
0
1
0
1
2
1
1
2
2
0
1
1
1
1
1
0
2
1
1
1
1
2
1
2
0
1
2
0
2
1
2
1
1
2
1
2
0
0
2
1
1
1
1
1
1
1
2
0
1
1
0
0
2
1
1
1
0
2
1
0
2
0
1
2
1
1
2
1
1
1
1
0
2
1
1
1
1
1
0
0
0
1
2
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
2
2
2
1
2
1
1
2
1
1
2
2
2
0
3
0
1
1
1
1
0
0
0
2
0
1
1
2
0
2
1
1
1
0
1
1
1
2
1
1
1
1
0
2
1
1
1
2
0
0
2
0
1
1
1
2
2
1
1
0
1
2
2
1
1
2
1
2
1
1
0
0
0
0
1
2
0
1
2
1
2
2
2
1
1
0
0
1
1
0
1
0
1
0
2
1
1
2
1
2
0
1
1
1
1
1
0
0
2
1
1
1
1
0
1
2
2
2
1
2
1
0
1
2
1
0
2
1
1
1
2
0
1
1
1
0
1
1
1
1
0
1
1
1
2
1
1
2
2
0
1
2
2
1
0
1
1
1
1
0
0
0
0
0
0
2
2
1
1
1
1
2
0
1
1
2
1
1
0
1
2
0
0
0
2
1
2
1
1
1
1
1
1
1
0
1
1
1
1
2
2
2
2
1
1
1
0
1
1
1
1
1
2
1
1
2
1
0
0
1
2
1
2
0
1
1
0
0
4
2
0
0
1
2
1
1
2
1
1
0
2
2
0
1
0
1
1
1
1
1
1
1
2
2
1
0
2
1
0
1
0
2
1
1
0
0
2
1
1
1
1
1
0
1
2
1
1
2
2
0
0
1
2
1
2
1
1
1
0
3
2
0
1
1
1
1
0
1
2
0
2
1
0
1
1
1
0
2
2
1
0
2
2
0
2
1
3
0
1
0
2
1
2
1
0
2
0
0
1
1
1
0
1
1
0
2
2
0
0
0
0
0
2
0
2
2
2
0
1
1
1
1
0
1
2
2
2
2
0
0
2
1
1
1
1
2
1
1
0
2
1
1
2
1
0
2
1
1
0
1
1
0
0
4
1
1
2
0
1
1
2
0
2
1
1
0
1
2
1
1
1
2
0
1
1
1
0
1
2
1
1
1
1
0
2
1
2
1
1
1
2
0
1
1
1
0
1
0
1
2
1
1
1
1
2
0
1
2
0
2
2
1
2
0
0
2
1
1
1
1
0
1
2
0
1
1
0
1
0
0
2
1
2
2
1
2
1
1
2
2
1
0
2
2
2
0
1
1
0
2
2
0
2
0
2
1
1
1
0
1
2
1
1
1
1
2
1
2
0
2
1
0
2
1
1
1
1
1
1
1
1
1
2
1
0
2
1
0
2
1
2
2
2
1
2
0
0
0
2
2
2
2
0
1
2
0
1
1
1
2
1
1
1
1
0
1
0
1
1
2
1
2
1
1
0
1
0
2
0
1
1
1
1
1
2
1
1
1
1
1
1
0
0
1
2
2
1
1
1
0
1
2
2
2
2
1
0
2
2
0
1
1
0
3
2
1
2
0
1
1
1
0
1
1
0
1
0
0
0
1
2
0
1
0
1
1
1
0
1
2
0
0
0
2
0
2
2
1
1
0
1
2
1
2
1
2
1
1
1
1
0
0
1
2
0
0
1
0
1
1
1
1
1
2
1
1
1
2
2
1
0
1
1
0
1
1
1
1
1
1
1
1
1
1
0
1
0
1
0
1
0
0
2
1
2
1
2
1
1
1
2
0
1
1
1
1
1
0
2
0
0
1
1
2
0
2
1
1
1
1
1
0
2
3
1
3
1
0
1
2
0
0
1
0
1
1
0
2
1
1
0
1
0
1
1
1
2
1
2
2
1
1
1
1
0
1
1
2
2
2
1
0
1
1
0
1
0
1
2
1
0
1
2
1
1
1
0
2
2
1
1
1
1
1
1
2
0
2
1
0
3
0
1
1
2
0
2
1
1
1
2
2
1
0
1
2
1
0
1
0
0
1
0
0
1
1
2
1
2
1
2
1
2
1
1
0
1
1
1
1
1
1
0
0
1
1
2
6
2
1
0
0
1
1
2
1
1
0
2
1
1
1
0
0
2
0
1
1
0
2
1
1
2
0
2
0
1
3
0
0
1
1
2
0
1
0
2
1
0
1
1
1
1
2
1
2
2
1
1
1
1
2
2
2
1
2
2
1
1
0
1
0
0
1
2
1
0
1
2
2
1
1
1
1
2
1
1
2
2
1
1
1
1
1
0
1
1
1
1
1
1
1
1
0
1
1
2
1
0
1
1
0
2
1
1
1
1
0
1
0
1
1
1
0
1
1
2
2
1
0
1
2
1
0
3
1
1
0
1
2
1
2
1
1
1
0
0
0
0
0
0
1
1
1
1
0
2
0
0
1
1
1
1
0
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
2
2
1
2
2
1
1
1
0
1
0
1
1
1
1
1
1
1
1
1
0
0
0
5
1
0
2
2
2
2
0
1
1
0
0
1
1
1
2
1
1
1
0
1
1
2
1
1
2
1
1
2
1
1
2
2
0
0
1
2
2
1
1
1
0
2
2
1
2
1
1
1
1
2
1
3
1
2
0
1
1
0
1
2
1
2
1
0
1
1
1
2
0
0
0
0
2
1
2
1
1
1
1
0
1
2
1
0
2
2
1
1
0
1
1
1
1
2
0
1
1
1
1
2
2
0
1
1
2
1
0
1
2
0
1
0
1
1
1
1
1
0
0
0
1
2
0
0
2
1
1
2
0
1
0
0
1
0
1
1
2
1
0
1
0
1
2
2
1
1
1
2
2
1
2
1
1
2
1
1
1
2
1
0
1
1
2
1
2
1
2
2
1
1
2
2
2
2
1
1
2
0
0
0
1
2
1
0
1
1
0
2
1
1
1
0
2
2
2
2
1
0
2
2
0
1
1
1
1
1
1
2
2
1
1
0
1
1
2
1
1
1
1
0
1
1
1
2
0
2
0
0
0
1
2
1
1
1
1
0
1
1
0
0
1
0
1
1
1
2
2
1
1
2
1
0
1
1
1
1
2
1
0
0
0
2
1
2
1
2
1
1
1
2
1
1
2
1
1
2
1
0
0
0
1
1
0
2
3
1
2
1
2
1
1
0
0
2
1
0
1
1
0
1
1
1
0
1
0
1
1
1
1
1
1
1
1
1
1
1
1
0
1
0
1
1
1
2
1
0
2
1
1
2
0
1
1
2
2
1
1
1
0
1
0
1
2
0
2
1
1
1
1
2
1
1
0
1
0
1
2
2
0
0
1
0
1
1
1
1
2
2
1
1
1
1
1
2
1
1
0
1
2
0
0
2
1
1
1
0
2
1
0
0
0
2
2
1
2
0
1
0
1
1
0
1
1
1
0
2
2
1
1
1
1
1
1
2
2
2
1
0
0
1
1
2
1
1
2
1
1
1
0
2
0
2
1
1
1
0
1
1
2
2
1
2
0
1
0
0
2
2
1
0
1
1
1
1
1
1
0
0
1
1
2
1
2
1
0
2
1
1
2
2
1
0
2
1
1
1
1
1
1
2
2
2
2
2
0
1
1
1
0
0
1
2
1
2
1
1
1
0
2
1
0
1
1
2
1
1
1
2
0
2
0
1
2
1
2
1
1
1
0
1
1
2
2
1
1
1
0
0
1
1
1
1
2
1
1
2
2
1
2
2
2
1
1
1
2
1
1
1
1
1
1
2
0
0
0
2
1
2
1
1
1
2
1
0
1
0
1
1
1
3
2
1
2
1
0
1
1
2
2
1
2
0
0
0
1
1
0
2
1
1
1
2
1
2
1
0
2
1
1
2
1
0
1
1
1
1
1
1
1
0
1
1
0
1
0
0
1
0
1
1
1
1
2
0
3
1
0
2
0
0
1
1
2
2
1
1
2
2
2
0
2
1
2
2
0
1
0
1
0
1
2
0
1
2
1
1
0
2
2
1
2
1
1
1
2
1
1
0
1
1
0
2
1
0
1
2
1
0
2
1
1
2
1
1
0
1
1
3
2
1
0
1
1
0
1
2
0
2
1
0
0
0
1
1
0
1
1
2
1
0
1
0
1
1
2
1
1
1
1
2
1
0
0
3
0
0
2
1
2
0
2
1
0
2
0
0
2
0
1
2
1
2
1
1
2
0
2
0
1
1
1
0
1
1
1
1
2
1
1
1
0
0
2
2
1
0
1
2
0
0
0
1
0
1
2
1
0
2
1
0
2
1
1
1
0
1
2
1
1
1
1
2
1
0
1
1
2
2
1
1
1
1
1
1
5
1
0
1
0
0
0
1
1
1
1
1
0
1
1
1
1
0
1
1
2
1
1
2
1
1
1
1
1
1
0
0
1
2
1
1
1
2
1
1
0
2
1
0
1
2
1
1
1
0
2
1
1
0
4
1
0
1
2
2
1
0
1
1
1
0
2
0
2
1
1
1
1
2
2
2
2
1
2
2
2
0
2
1
2
0
1
1
1
1
1
1
1
1
0
2
2
2
1
1
0
0
1
1
1
0
1
1
1
2
2
1
1
1
0
1
1
2
1
0
1
1
1
1
1
1
2
2
2
1
1
0
1
1
1
1
1
1
1
1
2
2
1
0
1
2
1
2
1
0
2
1
2
2
1
1
1
1
2
1
1
1
1
2
1
1
1
0
0
1
1
1
1
0
1
1
2
1
1
2
2
1
1
1
1
1
1
0
3
1
1
1
2
1
1
1
1
1
1
1
1
1
0
1
2
2
1
1
1
0
0
1
1
2
0
1
1
1
1
2
0
1
1
0
0
2
1
0
1
1
0
1
0
1
1
1
1
2
1
0
1
1
1
1
1
0
1
2
2
0
1
1
2
1
1
2
1
1
1
2
1
1
1
1
1
2
1
1
1
2
2
1
2
1
1
1
1
2
0
2
1
2
1
1
2
0
0
1
2
1
0
1
0
2
2
2
1
1
0
2
2
0
1
1
1
2
2
1
1
1
1
1
1
1
1
1
0
1
1
1
0
0
1
1
1
2
2
2
1
0
1
0
0
1
1
2
1
2
2
1
1
1
1
1
0
1
2
1
2
1
1
0
1
1
0
2
1
1
1
1
4
1
4
1
1
0
1
2
1
2
2
1
1
1
0
2
1
1
0
1
2
2
2
2
2
1
1
1
1
1
0
1
2
1
1
1
1
0
1
0
1
1
2
1
1
1
1
1
1
0
2
2
1
0
1
0
2
1
1
2
1
1
1
1
2
1
1
1
0
1
0
1
1
1
1
1
1
1
2
2
1
1
1
2
2
1
0
1
1
1
1
2
1
1
0
1
0
2
2
1
1
1
0
1
1
1
0
1
1
2
2
0
1
1
1
1
0
1
1
1
1
2
1
1
2
1
0
0
1
1
0
1
0
1
2
2
1
1
1
2
0
1
1
2
2
1
1
2
1
0
1
0
0
1
2
1
1
2
2
2
1
2
0
0
0
1
1
1
1
1
1
1
1
1
1
2
1
0
1
1
1
1
2
1
1
1
1
0
1
1
1
2
1
1
0
1
1
1
2
2
2
0
0
1
2
2
0
1
2
1
2
5
2
1
1
1
1
0
2
1
1
2
1
1
2
0
1
0
1
1
1
1
2
2
2
1
2
0
2
1
1
1
1
1
0
1
2
1
1
1
1
1
1
2
1
2
2
2
1
1
0
0
1
0
2
2
2
2
1
2
0
0
1
0
2
1
1
2
2
1
1
1
0
1
1
2
1
1
1
1
0
0
2
0
1
0
2
2
1
0
1
1
1
0
2
1
1
0
2
2
1
0
1
1
2
1
0
0
0
0
1
1
1
0
2
2
1
1
1
2
1
2
1
2
0
1
1
1
2
2
1
1
1
2
2
1
1
1
1
1
1
2
1
0
1
0
2
2
0
1
0
1
2
1
1
0
1
0
1
0
2
0
1
1
1
2
1
1
1
1
2
0
1
1
1
0
1
1
2
1
1
1
0
2
1
1
0
0
1
2
1
1
1
1
1
2
1
2
2
1
1
0
2
2
0
1
1
1
0
1
1
2
1
1
1
1
1
2
1
1
1
1
1
0
1
0
0
0
1
1
1
1
0
0
2
1
2
0
1
0
1
2
2
0
1
1
0
1
1
1
1
1
3
2
1
1
1
0
0
1
1
1
2
2
1
2
1
1
1
1
1
1
2
1
2
1
0
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
0
0
1
1
1
1
1
2
2
2
1
1
3
1
1
2
1
0
1
1
0
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
4
0
2
1
1
1
1
1
1
2
1
2
1
1
2
1
3
1
1
1
1
2
1
2
1
0
0
0
1
2
3
1
1
2
1
0
0
1
2
1
1
1
2
1
1
1
1
2
1
2
1
1
0
0
1
1
0
1
2
1
1
1
2
1
0
1
1
2
1
1
2
1
1
2
2
1
1
2
1
2
1
2
0
2
2
1
0
1
2
1
1
1
2
1
0
1
2
2
1
1
1
1
1
1
2
1
1
1
0
1
0
1
0
2
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
0
1
2
0
2
0
1
2
0
1
1
1
1
1
1
2
0
1
2
0
0
0
1
0
1
1
2
1
1
1
2
1
0
0
2
2
1
2
1
1
1
1
1
2
1
0
1
3
2
1
1
1
1
1
1
0
1
1
2
1
2
0
1
1
0
1
0
2
0
0
1
1
1
1
1
2
0
2
0
0
1
0
1
2
1
1
1
0
2
0
1
2
0
1
0
1
2
1
1
2
1
1
2
1
1
1
2
0
1
1
1
1
1
2
2
1
1
2
2
3
2
0
2
1
0
2
0
0
1
0
0
2
1
0
2
0
1
0
2
1
0
0
1
2
1
1
0
2
2
0
1
1
2
1
1
2
1
0
0
1
0
2
0
2
4
2
1
1
1
1
3
1
1
0
2
0
0
2
1
1
0
1
2
1
1
2
2
1
1
1
1
1
1
1
0
3
0
1
1
0
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
0
0
1
1
0
1
2
1
2
1
0
0
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
3
1
1
1
0
1
1
2
1
2
2
1
2
1
2
2
0
1
2
0
2
2
1
2
0
1
1
0
2
1
0
0
2
1
1
1
1
2
1
0
2
1
1
0
0
1
2
2
2
0
1
0
1
1
0
0
1
0
1
0
1
0
1
1
1
0
1
1
1
1
2
1
1
2
1
1
2
1
2
2
1
0
2
1
1
0
1
0
0
1
1
0
0
1
1
2
1
1
2
2
0
1
1
2
1
2
1
2
1
1
1
2
1
0
0
1
1
1
1
1
1
1
1
4
1
0
2
2
0
0
2
2
2
2
2
0
1
1
1
1
2
2
1
1
1
2
1
1
1
2
1
2
0
2
1
1
1
2
2
1
2
0
1
1
1
1
0
2
2
1
0
2
1
2
1
1
1
1
2
1
0
1
1
2
1
2
1
1
1
1
2
1
2
1
0
1
2
0
1
0
1
1
0
0
1
2
2
2
1
1
1
1
1
2
1
2
1
1
1
1
2
2
1
1
0
2
1
2
2
1
1
1
0
1
0
1
0
1
1
2
1
1
1
2
1
0
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
0
1
1
1
1
0
1
1
1
2
1
1
1
1
1
1
2
2
2
2
1
1
1
1
1
1
2
2
1
0
1
2
0
1
0
1
0
1
2
2
2
1
2
1
1
1
1
2
1
0
2
0
1
0
1
1
2
1
1
1
2
1
1
1
2
1
1
1
2
0
2
1
1
2
2
1
0
1
1
1
0
1
1
0
0
0
0
2
1
2
1
1
1
1
0
2
1
2
1
3
1
2
2
1
1
2
1
1
1
0
1
0
1
1
1
0
1
1
1
1
1
1
2
1
2
1
0
1
0
2
2
2
1
1
0
1
2
2
1
1
1
1
1
2
1
2
2
1
1
0
1
1
2
1
1
2
1
0
2
1
1
0
2
1
0
2
1
1
2
1
2
1
0
1
1
0
1
2
0
2
0
2
1
0
2
1
1
2
1
1
1
0
1
1
1
2
1
0
2
0
3
1
1
0
1
1
1
0
2
1
1
0
1
1
1
2
1
1
1
1
2
1
1
2
1
1
0
1
3
1
2
0
1
2
1
1
1
1
1
2
0
1
2
1
1
1
2
0
0
2
2
2
0
0
1
2
0
1
0
1
1
3
2
1
1
2
3
1
0
1
1
1
1
1
1
2
1
2
2
1
2
2
3
2
1
0
1
2
1
1
1
0
2
1
1
2
1
1
0
1
2
1
1
0
0
1
1
1
1
2
1
2
0
1
1
1
1
2
2
1
0
1
2
1
1
1
0
1
1
2
1
0
2
1
1
1
1
1
2
1
2
1
1
1
1
1
2
0
0
2
2
3
0
1
1
2
1
0
1
0
1
2
0
1
1
2
0
1
1
1
0
2
0
2
0
2
1
1
1
1
1
2
1
1
1
2
0
0
1
0
1
1
1
0
1
2
1
2
0
0
0
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
3
1
2
1
2
0
1
1
1
1
0
1
1
0
1
0
1
0
2
0
1
0
2
2
0
1
1
1
0
1
1
0
1
1
0
1
1
1
1
1
1
1
1
1
1
2
0
1
1
1
0
1
1
1
1
1
1
2
0
1
2
3
1
0
1
1
0
1
1
0
1
0
1
2
2
1
1
1
2
1
1
2
1
0
1
0
1
1
2
1
1
0
1
1
1
2
1
1
1
2
1
1
1
1
1
1
0
2
2
1
1
0
1
2
1
2
2
1
1
2
2
2
1
2
2
1
1
0
1
1
0
2
0
2
2
2
1
2
0
0
1
1
1
1
2
1
2
1
0
1
1
1
1
2
1
0
1
2
1
3
1
1
1
2
1
2
1
2
0
2
1
1
1
0
2
0
1
1
0
1
1
1
2
2
2
1
2
0
1
1
2
0
0
2
1
2
1
0
2
0
2
1
1
1
1
2
1
1
1
1
0
1
1
1
0
4
1
2
1
2
0
1
0
1
1
1
1
1
1
2
2
0
1
1
1
1
1
2
4
1
1
1
2
1
0
0
1
0
0
2
0
1
1
2
1
0
0
1
1
1
0
1
1
0
1
1
2
1
2
0
1
3
1
2
2
1
1
1
0
1
0
1
1
1
1
1
0
2
1
1
2
0
1
1
0
1
1
1
0
4
1
1
2
1
0
0
0
2
1
1
1
0
1
2
1
2
1
1
2
1
1
1
1
1
2
1
1
1
2
0
1
1
1
1
1
2
1
2
0
0
2
0
1
0
1
1
2
1
1
0
0
2
1
1
1
0
0
0
1
1
2
2
1
1
2
2
1
2
0
0
0
1
0
1
1
0
1
1
0
1
1
1
2
1
1
1
0
0
1
2
1
0
0
1
0
1
2
2
1
2
1
2
0
2
2
1
0
0
2
2
2
1
1
0
1
1
0
1
1
0
1
1
1
1
2
2
2
1
1
0
2
2
2
1
1
1
1
1
1
1
0
2
1
1
1
0
2
2
2
0
1
1
1
0
1
0
1
0
1
2
0
2
2
1
0
3
2
2
1
1
5
2
1
1
0
1
1
1
1
2
1
1
1
1
1
2
2
1
2
3
0
1
1
1
1
0
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
2
1
0
0
2
1
0
1
1
1
1
1
1
1
1
0
1
2
1
2
1
0
1
1
2
2
0
1
1
1
2
1
0
1
3
1
1
1
0
0
3
1
1
1
2
2
2
1
2
0
2
0
1
1
1
1
1
2
2
2
2
2
1
1
2
1
1
2
2
1
0
1
1
3
1
1
1
1
0
1
0
1
1
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
1
2
2
1
1
2
1
1
1
1
2
1
0
2
1
2
0
0
1
1
2
0
1
1
2
2
1
1
1
1
0
2
1
1
1
1
1
1
1
1
1
0
1
2
2
1
1
2
2
2
2
1
2
0
2
1
1
1
2
2
2
2
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
0
1
0
1
0
0
2
1
1
2
1
0
1
1
1
1
1
1
0
2
1
1
0
1
1
0
1
2
0
0
1
1
1
1
1
2
1
0
0
1
1
1
1
1
0
3
2
1
1
1
1
0
1
0
0
1
2
1
1
1
1
1
2
1
1
0
1
1
1
0
1
1
1
0
1
2
1
1
1
1
1
1
1
2
1
0
2
0
0
1
1
1
1
1
2
1
1
1
1
2
1
1
2
0
0
1
2
2
1
0
0
2
0
2
2
2
1
2
0
0
0
1
1
1
0
1
1
1
1
1
1
1
1
1
1
0
0
1
2
1
1
2
2
1
1
1
0
0
1
2
1
0
1
2
0
2
1
2
2
2
1
1
1
0
1
1
0
1
0
1
1
2
1
2
1
1
1
1
1
1
0
0
1
0
2
1
2
0
2
1
2
2
2
0
2
0
0
2
1
1
2
2
0
1
2
0
0
1
2
1
1
0
0
1
1
2
0
1
1
1
1
2
2
1
2
2
1
1
2
1
1
2
0
1
1
2
1
1
1
2
1
1
0
0
2
1
2
1
1
0
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
4
1
1
2
1
1
1
1
1
1
2
2
0
1
1
2
0
3
1
1
0
2
1
1
1
1
0
1
1
0
2
2
2
2
1
2
0
0
1
2
1
2
1
1
1
1
0
0
0
1
1
1
0
1
2
1
0
2
0
0
2
0
2
2
1
0
1
2
1
1
2
1
0
1
1
1
0
1
1
3
1
1
1
1
0
1
0
0
2
1
2
1
1
2
2
1
1
1
1
1
1
2
0
1
1
1
1
1
1
1
2
1
2
2
2
2
1
0
1
1
0
1
0
1
1
1
1
2
1
1
1
1
1
0
1
1
1
1
1
2
0
1
2
2
1
1
2
1
2
1
1
1
1
1
1
1
0
1
1
0
1
2
2
1
1
1
2
2
1
2
1
1
2
1
2
1
1
1
1
3
1
2
0
0
1
1
1
1
0
2
0
2
0
0
1
1
1
1
1
2
1
1
1
2
0
1
0
0
1
1
1
1
0
2
1
2
1
1
1
1
1
2
0
2
1
0
2
1
0
0
1
1
1
1
1
2
1
0
1
1
2
1
1
0
1
2
1
1
0
1
1
1
1
1
0
1
1
1
1
2
2
1
1
1
0
1
2
1
0
1
1
1
2
1
1
0
0
1
1
0
2
1
1
1
1
1
1
1
1
1
1
2
1
2
0
0
2
1
1
0
2
0
0
1
1
1
1
1
0
2
1
1
2
1
1
1
1
0
1
1
1
1
2
0
0
1
2
1
1
2
1
0
1
0
1
1
2
1
1
0
1
1
1
2
1
1
1
0
1
1
1
0
1
2
1
0
1
1
1
1
2
1
1
1
1
2
0
2
2
1
1
1
2
2
0
1
0
1
0
1
2
1
1
1
1
1
1
1
1
1
2
1
0
1
1
2
1
1
0
1
1
2
0
0
1
1
0
1
1
1
0
0
2
1
2
0
1
3
1
1
0
1
3
0
0
1
1
1
1
0
1
1
1
1
1
1
1
0
1
1
0
1
1
2
0
1
1
1
1
0
2
1
2
1
1
1
0
1
1
2
0
0
1
1
1
1
2
1
1
2
1
2
0
1
1
1
2
1
0
1
1
1
1
1
2
1
1
0
2
1
1
1
2
1
3
1
0
0
1
1
1
1
1
2
2
1
0
1
1
1
1
0
0
1
0
1
0
1
1
1
2
1
2
0
1
0
1
1
1
1
1
1
0
1
0
1
0
1
2
2
0
1
2
0
2
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
0
1
1
1
1
1
2
1
2
1
0
1
1
0
1
2
0
1
1
1
2
2
1
1
0
1
1
0
1
1
2
0
2
0
0
1
1
0
1
2
1
2
1
2
2
2
1
2
1
1
1
1
0
2
1
1
1
0
1
1
0
1
1
1
0
1
1
1
1
0
1
0
1
0
1
0
2
1
1
0
1
1
0
0
2
0
1
0
1
1
2
2
1
1
1
1
1
1
1
2
1
0
1
2
0
1
1
2
2
1
2
1
1
0
0
1
1
1
0
1
1
1
2
0
1
1
1
3
2
0
1
0
0
2
0
2
0
1
2
0
1
1
2
1
1
0
2
2
2
0
1
1
0
1
1
2
2
0
1
1
2
1
1
1
1
1
2
1
1
0
1
2
1
1
1
1
1
1
0
2
0
2
1
1
2
1
1
1
2
1
2
1
0
1
2
0
0
1
1
2
1
0
0
0
2
1
2
0
1
2
1
1
1
0
2
1
1
1
1
2
0
0
0
1
1
1
1
1
0
1
1
1
0
1
1
1
2
0
1
0
2
2
2
1
1
0
1
0
2
1
1
2
2
1
1
2
1
1
0
2
1
1
2
2
1
1
1
1
2
2
2
1
0
1
2
2
0
2
2
1
1
0
1
2
1
0
2
2
1
1
1
1
1
0
1
0
1
1
1
1
1
1
2
1
0
1
1
1
1
1
2
2
1
0
2
1
0
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
1
0
2
1
2
1
2
1
1
0
1
1
0
1
0
0
1
1
0
1
1
0
1
0
0
1
1
1
2
1
1
0
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
2
1
2
0
2
1
2
0
1
2
2
2
1
2
1
1
1
1
2
1
1
2
2
2
1
1
1
1
1
1
1
2
1
1
1
2
2
2
2
1
1
1
0
1
0
0
1
2
1
1
1
1
2
2
1
2
2
0
1
1
2
1
2
1
1
0
1
2
0
1
0
1
0
2
1
0
0
1
1
1
1
1
1
0
1
2
0
0
1
1
1
0
1
1
1
3
1
1
1
0
1
0
2
2
1
1
1
1
0
1
2
0
1
1
1
2
0
0
0
1
0
2
1
2
2
1
1
2
1
1
1
0
1
1
1
2
1
1
2
1
1
0
1
2
2
1
1
2
0
0
1
1
2
2
1
1
0
2
1
2
1
1
2
1
1
1
0
0
1
1
0
1
1
1
2
1
0
1
1
0
1
1
1
1
1
1
2
2
0
2
0
0
1
1
1
1
1
1
2
0
1
1
1
2
1
0
0
1
1
2
1
2
1
1
1
1
0
2
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
0
1
2
0
0
1
1
2
1
1
1
2
2
2
0
1
1
1
0
1
1
1
2
1
1
2
1
1
1
1
1
1
1
0
1
0
1
2
1
1
2
1
3
0
1
0
0
1
1
2
1
1
1
0
2
0
1
2
2
2
2
1
1
2
1
0
0
2
1
0
1
1
2
1
1
1
1
0
0
1
1
1
3
0
1
0
1
1
2
1
1
1
1
0
2
4
1
0
1
1
1
1
1
1
1
1
0
0
3
0
1
1
1
1
0
1
1
1
1
0
2
1
1
1
1
0
1
0
1
1
0
2
1
0
1
1
2
2
2
3
1
1
1
1
1
2
1
1
2
0
0
1
2
1
1
2
2
0
1
1
0
1
2
1
0
0
2
1
0
1
1
1
0
1
1
1
2
1
1
2
0
1
1
1
1
1
2
1
2
1
2
0
1
2
1
1
1
1
1
1
1
1
1
1
1
3
1
1
1
0
1
2
1
2
1
1
1
0
1
2
1
2
1
1
2
2
1
1
1
1
2
1
0
0
2
0
1
1
1
2
2
2
1
1
1
0
1
1
1
2
1
0
2
2
1
0
1
1
1
1
0
1
1
1
1
1
1
1
1
0
1
1
0
1
0
1
2
2
2
0
2
0
2
0
0
2
0
1
0
1
1
0
1
2
1
1
1
1
1
1
2
1
1
1
0
2
2
2
0
1
1
1
1
1
1
2
2
1
0
1
1
2
1
1
0
0
2
1
1
1
1
1
0
1
2
1
1
1
2
1
1
1
0
1
1
1
0
0
1
0
1
0
1
1
1
0
1
1
1
2
0
2
1
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
2
1
1
0
1
1
1
0
1
0
0
3
0
0
1
1
1
0
2
0
2
2
1
1
2
2
1
1
1
2
0
2
1
1
1
2
1
2
1
0
1
1
1
0
0
0
1
1
2
2
1
0
2
1
1
2
2
1
0
0
2
0
1
1
2
1
1
0
1
2
0
1
0
1
2
1
2
1
2
1
2
1
1
2
1
0
1
1
1
0
2
1
1
1
3
0
1
1
1
0
2
1
0
0
1
2
1
1
1
2
1
1
2
1
1
1
1
1
1
0
0
0
1
1
1
0
0
1
2
1
2
2
0
1
1
1
1
2
2
0
0
1
1
2
1
1
1
0
2
2
0
1
1
1
0
1
1
1
1
1
1
1
2
1
2
2
0
2
1
0
2
0
1
0
2
2
2
0
1
0
0
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
0
2
2
2
1
1
0
1
0
1
1
2
1
0
1
1
2
3
1
1
0
2
2
1
0
1
2
1
1
2
1
0
2
1
1
2
0
0
1
2
2
1
0
1
1
1
2
0
0
1
1
1
1
1
0
3
1
2
0
1
0
0
1
1
1
1
2
2
1
2
0
1
1
1
2
1
2
2
2
1
1
1
2
0
2
1
2
1
0
6
2
0
0
0
1
1
2
0
1
1
2
2
1
1
2
1
1
0
1
1
1
1
0
2
0
1
2
1
0
1
0
1
0
0
0
1
2
1
0
2
1
1
6
0
1
1
0
1
2
1
0
0
1
0
1
1
2
1
1
0
1
1
0
0
3
1
1
0
2
1
1
1
3
1
2
0
2
1
1
1
1
0
0
1
1
1
1
1
1
1
1
1
0
0
0
1
1
1
2
2
1
1
1
2
1
2
1
1
0
1
0
2
1
0
1
2
1
1
1
1
0
0
1
2
1
2
1
2
1
2
2
1
1
1
2
1
1
1
0
1
1
2
1
1
1
2
4
2
2
2
0
1
0
2
1
1
1
1
0
1
1
1
2
1
1
1
1
1
1
1
1
1
1
0
1
1
1
2
1
1
1
0
1
0
1
2
1
0
1
2
7
1
1
1
2
0
1
1
2
2
2
0
2
1
1
1
0
1
1
0
2
2
0
1
1
1
1
1
1
2
2
1
2
1
1
1
2
1
1
1
1
1
0
1
1
1
1
1
1
0
1
0
0
1
2
1
1
0
1
2
0
2
1
0
2
2
0
1
0
1
1
1
0
1
1
1
0
1
2
1
1
1
2
1
2
1
0
1
1
1
0
2
0
1
1
1
0
1
2
0
1
1
2
0
1
2
1
1
0
1
2
1
0
2
2
1
2
0
2
1
2
1
0
0
2
2
1
2
0
1
1
0
1
1
1
0
1
1
2
1
2
1
0
1
0
1
1
0
2
1
0
1
1
2
1
1
0
0
1
1
2
1
1
0
0
0
1
1
2
1
0
1
2
2
0
1
1
1
2
2
1
1
1
1
1
1
1
1
1
0
1
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
2
1
1
0
1
2
0
0
1
1
1
0
1
1
2
1
0
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
0
1
2
2
0
1
2
1
2
0
1
0
1
1
1
1
1
0
1
0
1
1
1
1
0
2
1
2
1
0
1
1
1
1
2
1
1
1
1
1
2
0
2
1
1
1
2
1
0
2
2
0
2
1
0
0
1
1
0
3
2
3
1
0
1
1
0
0
1
2
1
1
0
1
1
1
0
1
1
0
2
1
1
0
1
1
2
1
2
1
2
1
0
0
1
0
2
1
1
1
2
2
1
0
1
1
2
1
1
0
1
1
0
0
0
1
2
0
1
1
1
1
0
1
1
1
1
1
0
1
1
1
2
2
0
1
2
0
1
1
1
1
2
2
1
1
1
1
2
1
1
1
0
2
1
1
1
1
1
2
1
0
1
1
1
2
1
1
1
1
0
1
1
2
1
1
2
2
1
1
1
1
1
1
0
1
2
0
1
1
1
1
1
0
0
1
1
1
1
1
1
2
2
1
1
2
1
1
2
2
2
2
1
1
0
2
1
1
3
0
1
1
1
1
0
1
1
1
0
0
2
1
2
1
1
2
2
2
1
1
1
2
1
1
1
1
0
2
1
2
1
2
0
2
1
2
1
0
1
1
0
1
1
1
2
1
1
2
1
2
1
0
2
2
0
1
1
0
2
2
1
2
2
2
1
3
1
1
0
1
2
1
0
1
0
2
1
0
1
1
0
1
0
1
1
1
1
1
1
1
1
1
0
2
1
0
1
1
2
1
0
1
1
1
1
0
0
2
1
1
2
1
1
1
0
1
1
1
1
1
1
2
0
1
0
2
0
0
1
2
1
1
2
0
1
1
1
1
2
2
1
3
2
1
0
1
0
1
2
0
1
0
0
0
1
2
1
2
1
1
2
2
1
2
0
0
1
1
0
1
0
0
1
2
2
1
1
0
1
1
1
1
1
1
1
0
1
1
1
1
2
1
1
1
2
1
0
2
1
1
0
1
0
2
1
1
0
0
1
0
0
1
1
0
0
1
1
1
0
1
1
1
1
0
1
2
1
1
2
2
1
1
1
1
0
2
1
1
1
2
1
1
1
0
1
0
0
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
2
0
2
2
2
2
1
0
1
1
1
1
3
1
0
2
1
0
1
0
1
1
2
1
1
1
2
2
4
2
1
2
0
0
4
2
1
0
1
1
1
1
1
1
0
1
2
2
1
1
1
1
1
2
2
1
2
0
1
0
2
2
1
2
2
1
1
1
2
1
2
2
2
1
1
1
0
1
1
1
0
1
2
2
2
1
1
1
0
0
1
1
1
4
0
0
1
1
1
1
1
1
2
2
2
2
2
1
1
1
2
1
1
1
2
1
1
1
0
1
1
0
1
0
1
0
1
1
1
0
2
1
1
1
1
1
1
1
1
2
1
2
1
1
1
2
1
0
2
1
1
1
1
0
1
2
2
1
1
0
1
1
0
0
2
2
2
1
1
2
2
2
0
1
1
1
0
2
1
0
0
1
1
0
0
1
2
1
2
2
2
0
0
2
1
1
2
1
2
1
1
1
1
1
1
0
0
1
1
1
1
1
2
1
2
2
1
0
0
1
1
1
2
2
2
0
1
2
1
1
0
2
1
1
2
1
1
1
0
1
1
0
0
1
2
2
0
1
2
1
0
1
1
2
0
1
1
2
2
1
1
2
0
1
1
1
0
1
2
1
1
0
0
1
1
1
1
1
2
1
0
0
2
1
1
1
1
1
2
1
0
1
1
2
2
2
1
1
1
1
1
0
1
2
0
0
0
1
0
1
1
0
1
0
1
0
1
2
0
1
2
0
0
1
2
0
2
1
2
2
1
0
0
1
1
1
1
1
0
1
1
0
1
1
0
2
1
1
1
1
2
0
1
0
2
0
2
1
0
1
0
2
2
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
1
2
1
2
1
1
1
2
2
1
1
1
0
0
0
1
0
0
1
0
1
1
2
1
1
2
0
2
2
1
1
0
2
0
1
1
1
1
1
2
0
1
1
2
2
0
1
2
0
1
1
1
1
1
1
0
1
1
1
1
2
0
2
2
1
1
1
1
0
1
0
2
2
1
2
2
0
1
1
0
1
1
0
0
2
1
1
0
1
0
1
1
2
1
1
1
1
1
2
1
1
1
0
0
0
1
1
0
1
1
2
1
1
1
0
2
1
1
1
0
1
1
2
1
0
1
2
2
1
2
2
0
1
2
1
1
2
0
0
1
1
0
0
1
1
0
1
1
0
2
1
1
1
1
0
1
2
1
1
0
0
1
1
1
1
2
2
1
1
1
2
0
1
0
1
2
1
1
2
1
0
3
2
1
1
2
0
1
2
1
1
1
1
0
0
1
0
1
0
1
1
2
2
2
1
1
2
1
1
0
2
2
1
0
1
1
1
1
3
1
1
0
0
2
1
0
2
1
0
1
2
1
1
0
0
1
2
0
1
1
2
1
1
0
0
1
2
1
0
1
1
1
0
1
1
1
1
1
0
0
1
0
1
1
1
1
2
0
1
0
2
1
0
1
1
1
1
2
0
2
2
0
2
0
0
1
1
2
0
2
1
0
0
2
0
1
1
1
1
1
2
1
2
1
2
1
2
1
1
1
1
0
2
1
1
0
1
0
2
1
0
1
1
0
2
1
2
2
0
0
1
1
1
1
1
1
0
1
2
1
1
1
0
1
1
1
1
2
1
1
1
1
2
2
1
1
0
0
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
2
1
1
1
1
0
2
1
0
1
0
1
1
1
2
1
1
0
1
1
0
1
2
1
1
2
0
1
2
2
1
1
1
0
1
1
0
1
1
1
2
2
2
1
1
2
1
2
1
1
1
1
1
0
1
1
1
2
1
1
1
2
1
1
1
0
1
2
1
0
1
0
1
1
1
1
1
1
2
2
1
1
2
2
1
1
0
1
1
0
2
1
2
1
2
0
1
1
2
0
0
2
2
2
1
0
2
1
1
0
1
1
0
0
1
1
2
1
1
1
2
2
2
1
1
0
0
1
0
2
0
1
0
1
1
2
1
0
1
0
1
1
0
2
2
0
1
2
0
0
1
1
1
1
1
1
2
1
1
1
1
1
0
2
2
1
2
0
1
2
1
2
1
0
1
2
2
1
2
1
2
0
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
2
1
2
2
2
2
0
1
2
1
2
1
0
1
2
1
1
2
2
1
1
1
1
0
1
3
1
1
1
1
0
1
0
0
1
1
1
1
2
1
1
2
1
1
2
1
0
1
0
1
2
1
1
1
0
1
1
2
2
1
1
1
2
0
1
1
1
0
1
1
1
2
1
0
2
2
2
1
2
1
2
1
0
2
1
1
0
1
0
1
1
2
2
2
2
0
2
2
1
1
1
1
1
0
0
2
2
2
0
0
1
0
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
0
1
1
2
2
0
0
1
0
0
1
2
1
1
1
1
2
1
1
2
3
1
1
1
0
1
0
1
1
1
1
1
1
2
1
0
2
1
1
1
2
1
0
1
2
1
2
1
2
0
1
1
2
0
1
2
2
2
0
1
1
0
1
1
0
1
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
0
1
0
2
3
2
1
1
1
0
2
1
1
2
1
1
1
2
1
1
1
1
1
0
1
1
0
1
1
1
0
1
1
0
0
0
1
1
2
1
1
1
1
1
0
1
1
1
1
1
0
1
1
2
0
1
1
1
1
1
1
0
3
1
1
1
2
1
1
1
1
1
1
0
1
0
1
3
0
1
1
1
1
1
1
1
0
1
1
1
0
1
1
1
1
0
1
0
2
1
1
1
1
2
0
0
1
2
1
1
1
1
2
2
1
2
1
1
2
2
0
0
2
0
2
2
1
0
0
1
2
1
2
1
0
1
1
2
2
2
1
2
1
0
1
3
1
2
2
1
1
1
1
0
1
2
0
1
1
1
1
1
2
1
0
2
1
0
1
1
1
2
2
1
1
1
0
2
1
2
1
1
1
1
0
0
0
1
1
1
2
2
2
0
1
1
1
0
0
1
1
1
1
1
1
2
1
1
1
0
1
1
1
1
2
1
2
2
1
1
1
0
1
1
0
2
1
1
2
1
0
2
0
1
2
1
0
1
2
1
0
0
2
1
1
0
1
2
1
1
1
2
0
0
1
1
1
2
1
1
1
1
2
1
0
2
0
1
1
1
0
1
1
0
1
1
1
1
1
1
2
1
1
0
1
2
2
1
1
0
2
0
1
0
1
1
2
0
1
0
1
1
1
1
0
1
1
1
0
2
0
1
1
1
1
1
1
0
2
1
2
0
2
1
1
1
1
0
1
1
3
2
1
2
1
1
0
1
0
1
1
1
2
1
2
1
2
1
2
1
0
1
0
1
1
1
1
1
0
2
2
1
1
1
2
0
1
0
1
1
1
1
1
0
0
1
1
4
2
2
0
2
2
1
1
1
2
2
1
1
1
1
0
2
1
0
1
1
0
0
1
1
1
0
2
1
1
2
0
2
2
1
1
2
0
0
0
1
0
1
1
1
0
0
1
1
2
1
1
3
2
0
1
1
0
3
0
0
1
4
1
0
2
2
2
2
1
1
1
2
2
2
2
0
1
2
2
1
2
1
2
2
2
1
0
2
2
1
1
1
1
0
0
0
0
2
1
2
1
0
1
2
3
1
0
1
0
2
1
1
0
0
2
2
2
1
2
1
1
1
1
1
1
0
0
0
2
1
1
1
2
0
0
1
2
1
1
1
1
1
0
1
2
1
1
1
1
0
1
1
1
1
0
0
1
1
1
0
1
1
0
1
2
2
1
1
2
1
2
0
3
1
1
1
1
1
1
1
0
1
2
0
0
1
2
2
0
1
2
0
1
1
2
1
0
0
0
2
1
0
2
2
1
1
1
0
1
0
0
1
0
1
1
1
3
0
0
1
1
1
1
0
1
2
1
1
1
2
1
1
2
1
1
2
1
0
1
1
2
0
1
2
1
1
2
1
1
0
1
1
2
1
3
2
1
1
2
0
0
1
3
0
2
0
1
0
0
0
0
1
0
1
0
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
0
1
1
2
1
0
1
0
2
1
1
2
1
1
1
1
2
0
1
0
1
1
0
1
2
0
0
1
1
0
1
1
1
0
1
2
0
2
1
1
1
1
1
1
1
2
2
2
1
2
1
1
3
2
1
0
0
2
1
2
0
2
2
1
1
1
2
1
1
1
0
1
1
1
1
0
1
1
0
0
0
2
1
1
4
1
1
1
0
0
0
0
2
2
1
1
1
1
1
1
2
2
1
1
0
1
1
1
0
1
1
1
1
1
1
1
1
1
0
1
1
2
0
1
1
1
2
2
1
1
0
2
1
1
1
1
1
2
2
0
1
2
1
1
1
1
2
0
0
0
1
1
1
2
2
1
2
2
1
0
1
1
1
2
2
1
1
0
1
0
1
2
2
1
0
2
1
1
0
1
1
0
0
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
0
1
1
0
1
2
2
1
2
1
0
1
2
0
1
2
0
0
1
1
1
1
0
2
2
2
3
1
0
1
2
1
2
1
0
2
0
1
1
0
1
2
1
1
2
1
0
1
2
1
0
1
1
2
2
2
1
1
2
1
1
1
1
1
1
2
1
1
0
1
3
1
1
1
1
1
1
0
0
0
0
1
2
3
1
1
1
1
1
2
1
0
2
0
0
1
2
1
1
1
1
1
2
1
0
1
1
1
2
1
1
1
1
0
1
2
1
1
1
1
1
0
1
0
2
2
1
2
2
0
0
1
0
2
0
1
2
0
1
1
1
1
1
1
1
1
1
1
2
3
1
1
2
1
1
3
1
1
1
0
1
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
0
2
2
3
2
1
1
1
1
3
1
1
2
2
0
1
1
1
1
0
1
1
1
0
2
1
2
1
2
2
2
0
1
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
2
2
1
2
1
1
1
2
2
1
1
1
0
2
1
0
2
1
0
2
0
2
0
1
2
1
1
1
1
2
1
1
1
1
1
1
0
0
1
0
1
1
0
2
1
0
1
1
0
1
1
1
0
1
2
1
1
1
1
0
2
0
2
1
1
0
0
1
0
2
2
2
1
2
2
0
1
1
0
1
2
0
2
1
1
1
1
1
1
2
0
1
1
2
1
1
0
0
2
1
0
2
1
1
0
1
2
0
0
2
2
1
2
1
2
2
2
1
1
2
1
2
1
2
0
1
0
1
1
1
2
1
1
1
1
2
0
1
0
1
1
1
1
1
2
1
1
1
0
0
1
1
0
3
1
1
1
0
2
1
1
0
1
1
0
1
1
1
2
1
1
2
1
2
1
1
2
1
2
1
1
1
0
0
1
0
0
1
2
0
2
1
1
2
2
1
1
1
1
1
1
1
2
1
0
0
1
2
0
2
0
2
1
1
0
1
2
2
0
1
0
0
2
1
0
1
1
0
1
1
1
0
1
0
0
1
1
1
1
1
2
0
1
1
4
1
0
1
1
2
1
1
1
0
0
1
1
2
0
1
0
0
2
1
2
1
0
0
1
1
1
1
0
1
1
0
1
2
0
1
2
1
0
1
1
1
2
0
1
1
1
2
2
1
1
0
0
1
2
1
1
1
1
1
0
2
2
1
1
2
1
0
1
1
1
2
1
1
2
1
1
1
1
2
0
1
2
1
1
1
1
0
2
2
2
1
1
1
0
1
2
1
1
0
1
1
2
1
1
1
2
1
1
0
1
1
1
1
1
2
1
0
2
1
1
0
1
2
0
0
1
1
0
1
1
1
0
0
1
1
2
1
1
1
1
1
1
1
3
0
2
2
0
1
1
2
2
1
1
1
1
1
2
1
1
2
1
0
2
1
2
1
1
1
1
0
0
1
2
1
1
1
2
2
1
2
1
1
1
1
0
1
1
2
1
1
1
1
1
1
1
1
2
1
2
2
2
0
1
1
1
1
0
1
1
0
2
2
2
0
1
2
1
1
2
1
0
0
1
1
3
1
1
0
1
1
1
2
0
0
2
2
0
1
1
2
0
1
1
1
1
2
1
1
2
0
1
1
2
1
1
2
1
0
1
1
3
0
0
0
0
1
1
1
1
1
0
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
2
1
1
1
1
2
0
1
1
1
1
1
1
1
1
1
1
2
0
1
1
2
1
2
1
1
0
1
1
1
0
2
2
2
1
1
1
1
2
0
2
1
0
1
2
2
1
0
2
1
1
1
1
1
1
1
1
2
0
1
2
1
1
1
1
1
1
0
1
1
1
2
1
0
0
1
2
2
1
0
1
2
1
1
1
1
2
2
1
0
0
0
1
2
1
2
1
1
1
2
1
2
2
1
1
1
2
1
2
1
0
2
1
1
1
1
0
1
2
1
0
2
1
0
2
1
1
1
2
1
1
1
0
2
1
0
1
0
1
2
2
1
1
1
1
1
1
1
1
1
0
2
2
1
0
2
1
1
0
2
0
1
2
2
1
1
2
1
0
1
2
0
1
1
1
1
0
1
2
0
1
1
1
1
2
2
2
1
1
1
1
2
2
0
1
1
0
2
1
2
1
1
1
0
0
1
0
1
1
3
1
1
0
1
2
1
0
1
0
1
1
1
2
0
1
1
1
1
2
1
0
1
0
1
1
1
2
1
2
2
2
1
2
2
1
3
2
1
1
1
1
1
1
2
0
1
2
1
1
1
1
1
0
2
0
1
2
1
2
4
1
1
1
0
2
1
1
0
1
1
3
1
2
1
0
0
1
0
0
1
2
1
1
1
1
1
1
1
1
2
1
1
0
1
0
1
2
1
1
0
2
1
1
0
1
0
0
0
1
0
2
0
1
2
1
1
2
2
0
2
0
1
0
1
1
0
0
1
1
1
1
1
1
2
1
2
1
1
1
2
0
1
0
1
1
0
1
2
1
1
0
1
1
0
0
1
2
1
1
2
1
1
0
1
1
1
1
2
1
1
1
0
0
0
0
0
1
1
2
1
2
1
1
1
1
2
2
1
2
2
2
1
1
2
2
1
1
1
6
2
1
2
1
1
0
0
0
1
1
0
2
3
0
1
0
1
0
0
1
1
0
2
1
2
1
1
1
2
2
1
1
0
0
0
0
1
2
2
1
1
1
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
2
0
2
0
1
1
0
1
1
1
1
1
2
0
1
1
1
0
1
1
2
0
1
2
1
0
1
1
1
1
1
1
1
0
1
1
2
1
2
1
0
1
2
2
1
1
0
1
2
0
0
4
1
0
1
1
1
1
1
2
1
2
1
1
1
2
1
2
0
2
2
2
0
1
1
2
1
1
1
0
0
1
1
1
1
1
2
1
2
1
1
1
0
2
1
1
2
1
1
2
1
1
1
0
2
1
0
0
0
1
2
1
1
1
0
1
0
1
1
1
1
1
1
1
1
0
2
1
0
0
1
0
0
0
0
0
1
2
1
0
1
0
1
0
1
0
2
1
0
0
0
0
1
0
1
1
2
2
1
1
1
1
1
2
1
0
1
1
2
1
1
1
2
1
2
0
1
1
1
2
1
2
1
1
0
0
1
2
0
1
2
2
2
2
0
1
1
1
2
1
1
1
1
1
1
1
1
2
2
1
1
1
2
1
1
1
1
0
1
2
0
1
1
2
2
0
0
1
1
2
0
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
2
2
2
2
1
0
2
1
1
1
0
2
1
1
0
1
1
1
2
1
1
1
1
2
1
2
1
1
1
0
1
1
1
1
0
0
2
1
0
1
0
0
0
1
1
0
0
0
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
0
2
1
2
2
2
1
1
1
1
0
1
2
1
0
1
2
1
2
1
1
2
1
1
1
2
2
1
0
2
0
2
1
0
0
1
2
0
1
2
1
0
2
1
1
1
1
1
1
0
2
1
2
0
2
1
1
0
1
1
2
1
0
1
2
1
2
0
1
2
1
1
0
1
1
2
1
0
2
1
1
1
1
1
2
1
1
2
1
1
1
1
1
0
2
2
0
2
1
1
0
2
2
0
1
1
1
1
1
2
2
1
1
0
2
1
1
0
1
2
1
1
1
2
1
1
1
1
2
1
1
0
1
1
0
0
0
1
1
1
1
1
1
0
2
1
2
2
1
1
1
2
1
1
1
2
1
2
1
1
1
1
2
0
1
0
1
1
1
1
1
1
2
2
2
0
2
0
1
1
0
1
1
0
2
1
2
2
1
0
0
1
1
1
1
0
1
2
1
1
0
1
3
2
1
1
1
1
1
0
0
1
1
2
1
1
1
1
1
1
0
1
0
1
1
0
1
2
1
1
2
1
2
2
1
0
1
1
1
1
2
0
0
2
2
1
1
1
0
1
1
0
1
0
1
1
2
2
1
1
1
2
0
1
2
1
0
1
2
1
1
2
1
1
1
2
0
1
1
0
1
1
1
2
1
1
0
0
1
1
0
1
0
1
1
0
2
1
0
2
1
1
1
1
1
1
1
0
0
2
1
0
2
1
0
1
2
1
2
2
1
1
1
1
1
1
1
0
1
0
1
1
1
1
3
2
1
1
0
2
0
0
1
0
1
2
1
0
1
1
0
1
1
1
0
0
2
1
2
1
2
1
1
1
2
2
0
0
0
2
1
1
1
2
1
1
1
1
0
2
2
2
1
1
0
0
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
1
1
1
2
1
0
3
2
1
2
0
2
1
1
1
1
2
1
1
0
2
1
1
2
1
0
1
1
1
1
0
0
2
0
3
2
1
0
1
0
2
0
1
1
1
1
1
1
1
2
2
2
1
1
1
0
1
1
1
2
1
1
0
0
1
2
1
2
1
1
2
2
2
0
2
1
1
2
2
2
1
1
3
0
2
1
2
1
0
1
1
1
1
2
0
2
2
0
0
4
1
0
0
1
1
1
1
2
1
2
1
1
1
1
2
2
0
2
1
2
1
0
1
1
2
1
1
0
1
1
1
2
0
0
0
0
0
2
1
2
1
1
2
0
1
0
1
1
2
1
2
2
1
1
1
2
1
1
2
1
3
2
2
1
2
1
1
1
2
0
0
2
2
1
1
2
1
0
1
0
1
1
1
2
1
0
1
1
2
3
1
1
1
1
1
2
0
0
2
0
1
1
1
1
1
1
2
2
1
0
2
1
0
2
1
1
1
1
2
0
0
1
1
0
1
0
2
1
0
2
0
1
1
2
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
2
1
2
1
1
0
1
1
1
1
1
2
0
1
2
1
1
2
1
1
0
1
2
1
1
2
1
1
1
0
1
1
2
1
2
2
1
0
1
2
1
1
1
1
1
0
1
1
1
2
1
0
0
1
1
1
2
2
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
0
0
2
1
1
1
2
1
1
1
2
1
2
1
1
3
1
1
1
1
2
1
0
0
1
2
0
1
1
1
1
1
1
0
2
1
1
1
0
0
0
0
1
1
0
1
1
1
1
1
2
1
1
0
2
1
2
1
1
0
0
1
2
1
1
1
1
1
0
1
2
2
0
0
1
1
2
2
1
0
1
0
2
1
0
1
1
1
1
1
1
2
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
0
2
1
2
1
1
0
2
2
1
0
2
1
1
1
1
3
1
1
2
0
1
1
1
1
1
1
0
1
2
2
0
1
1
1
1
0
0
2
1
2
2
1
0
2
1
2
1
1
1
1
2
2
1
1
2
1
1
2
1
1
2
1
0
1
1
0
1
0
1
0
1
2
1
1
1
2
1
1
0
1
1
1
1
0
0
2
1
1
3
2
0
1
1
0
1
1
1
1
1
2
1
2
1
0
0
1
1
2
0
0
0
0
1
1
1
1
1
1
1
0
1
1
1
1
1
1
0
1
1
1
0
1
1
1
2
2
1
1
0
2
2
2
1
1
0
2
0
1
0
0
1
1
2
1
1
1
0
1
2
1
1
2
1
2
1
1
2
1
1
1
1
1
1
0
1
0
2
1
1
0
1
1
1
1
1
2
0
1
1
2
0
2
0
0
1
2
2
1
1
2
1
1
0
1
0
1
1
1
1
2
0
0
1
1
0
1
0
1
1
0
1
1
1
1
1
1
0
0
0
1
2
0
1
1
1
1
1
1
0
0
1
1
1
0
1
0
1
0
0
1
2
2
1
0
2
1
1
3
0
1
1
1
0
2
1
0
1
1
1
1
1
0
0
1
2
4
0
1
1
1
2
0
1
1
1
0
1
1
2
1
1
1
1
2
0
2
0
1
1
0
1
1
1
0
1
1
0
2
1
1
0
2
2
1
1
2
2
1
2
1
1
1
1
2
1
2
1
2
1
0
2
1
2
1
1
1
1
0
2
1
0
2
2
1
1
2
1
1
0
1
1
2
0
1
1
1
2
1
1
1
0
1
0
1
2
1
1
1
0
1
2
1
1
2
2
1
1
1
1
0
2
1
0
0
2
1
1
2
0
1
1
1
1
1
1
1
1
1
2
1
1
0
2
2
1
2
1
1
2
1
1
1
2
2
1
2
1
2
1
1
3
1
1
0
0
1
1
1
1
2
0
1
0
2
2
1
1
1
2
1
0
1
2
2
0
1
2
1
1
2
1
1
1
0
2
1
1
1
1
1
2
1
0
2
1
0
1
1
1
1
1
1
1
0
1
1
1
1
0
1
1
0
0
0
2
2
1
1
0
1
1
2
1
2
0
2
2
1
1
1
0
2
1
1
1
1
1
1
2
0
1
0
1
1
1
1
1
1
0
1
1
0
1
0
1
2
1
2
1
0
1
1
0
0
2
1
1
2
0
2
2
1
0
1
2
1
1
0
2
2
2
1
1
1
1
1
1
0
2
2
1
2
2
0
1
1
1
1
1
1
1
1
2
1
1
0
2
1
0
2
1
0
1
2
1
1
2
2
0
1
1
0
0
0
1
2
1
0
2
1
0
1
1
1
1
2
1
2
2
2
1
1
1
2
1
2
0
0
2
2
0
0
1
1
1
0
0
1
2
1
0
2
1
1
2
2
1
1
0
2
1
1
1
1
0
1
1
1
1
2
1
1
0
1
1
2
1
0
1
2
1
2
1
0
2
1
1
1
1
1
1
2
1
2
1
2
1
1
1
1
2
1
2
1
1
0
0
1
2
1
2
3
1
1
1
1
0
1
1
2
1
1
1
0
1
1
1
1
1
1
2
4
0
0
2
1
1
1
2
1
2
1
1
1
2
1
0
0
1
1
1
1
0
1
1
1
2
1
2
1
0
1
0
1
2
1
1
1
2
1
1
1
1
1
1
1
0
0
2
1
2
2
1
1
2
1
2
2
0
2
1
0
1
1
1
1
1
1
2
1
1
0
1
2
0
1
1
0
2
1
1
0
1
0
2
1
1
1
1
1
2
1
0
2
1
1
2
1
0
1
2
0
1
0
0
2
2
1
1
2
1
2
1
0
1
1
1
1
2
1
2
2
2
2
2
0
0
1
1
2
1
2
1
2
0
1
0
1
1
1
1
0
1
1
0
2
2
1
1
0
1
1
2
1
2
1
1
1
2
0
1
1
1
1
2
1
1
2
1
1
1
1
0
0
2
1
0
2
2
0
1
1
1
1
2
1
1
1
0
2
2
2
1
1
2
1
1
2
1
2
2
2
1
1
0
0
1
1
1
0
1
1
0
2
1
1
1
1
2
1
1
2
2
0
1
2
1
2
1
1
1
1
1
1
2
0
1
0
1
0
1
1
1
0
1
1
1
4
1
5
1
2
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
0
1
1
2
2
1
1
0
0
1
1
0
1
1
2
1
1
1
1
1
2
1
2
0
1
0
0
0
1
2
1
1
1
1
1
1
2
0
1
0
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
2
1
1
1
0
2
2
1
1
1
1
1
2
1
2
1
1
2
2
1
1
2
2
0
1
1
2
0
1
0
1
1
1
0
0
0
0
1
1
1
0
1
2
1
1
1
1
2
0
2
0
1
1
0
2
0
0
1
1
1
0
2
1
1
2
1
0
0
0
0
2
2
1
0
2
1
1
2
1
0
1
1
1
0
1
0
0
0
1
1
1
1
1
2
1
2
1
0
1
2
2
1
1
2
2
1
1
1
1
1
0
1
2
1
1
1
1
2
1
1
1
0
1
2
2
2
1
1
2
0
1
2
0
2
1
0
1
1
1
1
0
2
1
1
2
2
1
1
2
2
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
0
2
1
1
1
2
2
1
1
0
1
1
1
1
1
2
0
1
1
1
2
1
1
2
1
1
1
0
1
1
1
1
1
1
1
1
0
1
1
1
0
1
1
2
1
1
1
1
0
2
2
1
1
2
0
1
1
1
1
1
2
1
2
0
0
1
1
1
2
1
1
0
2
0
1
0
1
0
2
1
1
1
0
2
0
0
1
2
1
1
1
1
1
1
1
0
1
1
1
1
1
1
0
1
0
1
1
2
1
1
1
1
1
1
1
1
0
1
2
2
1
0
0
1
0
1
1
1
1
1
1
0
1
2
0
1
2
1
0
1
1
1
1
1
0
0
2
1
1
0
2
0
2
2
2
1
1
1
1
1
0
1
0
1
1
2
1
1
1
1
1
2
2
2
2
1
1
1
1
0
1
0
1
1
1
1
2
1
0
0
1
1
2
0
1
1
1
2
1
2
1
1
0
1
0
1
0
0
1
4
1
1
2
1
1
0
0
1
0
2
1
2
1
1
1
2
1
2
1
1
2
2
0
1
2
1
2
1
2
2
1
1
2
1
1
1
0
2
1
1
1
1
2
2
2
1
1
1
1
0
1
2
0
1
1
1
0
2
1
1
1
2
2
1
1
1
0
0
2
2
3
1
0
2
2
1
1
1
2
2
1
1
1
1
1
1
0
2
1
2
1
2
1
1
1
1
1
1
1
0
1
1
0
0
1
2
0
1
0
1
1
1
1
0
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
0
2
1
1
1
1
1
2
3
0
2
1
2
0
0
1
0
2
1
2
1
0
1
1
2
1
2
1
1
1
1
2
0
2
1
1
1
1
1
2
1
1
1
1
2
0
2
1
1
1
2
1
2
1
0
1
0
2
1
1
1
0
1
0
1
1
2
1
1
1
1
1
2
1
1
0
1
2
1
2
1
0
1
1
1
2
2
0
2
0
1
1
1
2
1
1
2
1
1
2
1
1
1
0
1
2
0
2
1
2
2
1
2
1
1
1
2
1
1
1
0
1
1
0
1
1
0
1
2
0
2
1
1
1
1
2
2
1
0
1
2
1
1
1
2
2
1
3
1
1
0
1
1
1
1
1
2
1
2
1
2
1
1
1
0
0
1
0
1
2
0
2
0
0
1
1
0
0
1
1
1
0
2
1
2
2
0
2
1
0
1
1
1
0
1
2
1
1
1
1
1
2
1
2
2
2
1
2
1
0
2
2
2
1
1
2
1
1
1
1
0
1
1
0
1
2
1
0
2
1
0
1
1
0
2
2
0
1
2
1
1
2
1
1
1
0
1
2
1
2
1
0
1
2
0
1
0
2
0
2
1
1
0
1
1
1
2
2
1
4
1
1
1
1
0
1
1
0
1
0
1
1
1
0
0
0
1
2
1
0
2
1
1
0
1
1
2
1
1
0
2
2
1
1
1
1
0
1
1
0
2
1
1
1
1
1
2
1
1
1
1
2
1
0
1
1
1
1
1
0
2
0
1
1
1
0
1
1
2
2
1
1
1
1
1
1
2
2
1
0
1
2
1
2
1
1
0
3
1
1
1
4
1
1
1
1
0
2
1
1
1
1
1
1
1
1
2
0
1
2
1
0
1
1
1
0
1
1
0
2
1
1
1
1
1
2
2
1
1
0
1
1
2
1
1
2
2
1
0
0
1
0
1
1
0
0
1
2
2
1
2
1
2
1
1
1
2
2
1
1
1
1
1
1
1
1
2
1
1
0
2
1
1
0
1
2
1
1
2
1
1
1
1
0
1
1
1
1
1
1
2
0
1
1
1
1
0
2
1
1
2
1
1
1
0
1
1
0
1
0
1
1
1
1
1
1
0
1
1
1
0
1
1
1
1
1
0
0
1
2
0
0
1
2
1
0
2
1
1
2
0
2
2
2
2
1
1
1
1
2
1
2
0
1
1
1
1
1
2
0
2
0
1
1
1
1
1
0
1
1
1
0
1
1
2
1
1
1
1
1
1
4
1
1
2
0
2
0
0
0
2
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
2
0
2
1
2
0
1
3
2
0
1
1
2
1
2
1
2
1
2
1
2
2
1
0
2
1
0
2
1
1
2
1
0
1
1
1
1
0
1
2
0
2
1
0
2
1
3
1
2
1
1
1
1
1
0
1
2
0
2
1
2
1
2
1
1
0
2
1
1
2
0
1
0
2
1
1
1
1
0
0
0
1
2
1
2
1
0
1
1
1
0
1
1
0
1
1
2
1
1
0
1
0
1
2
2
1
0
1
0
2
1
1
1
0
2
1
0
0
2
0
2
1
1
1
1
2
2
1
1
1
1
1
2
1
1
0
0
1
2
1
1
1
0
1
1
2
1
1
0
2
2
1
1
2
2
2
0
2
2
0
1
1
2
1
2
1
0
0
1
0
1
1
0
1
1
1
1
1
1
2
1
2
2
1
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
0
1
2
1
0
1
0
2
1
0
0
0
1
1
1
1
1
1
0
2
2
1
2
0
1
1
1
2
1
0
1
1
1
0
1
0
2
2
2
1
1
1
3
1
1
1
1
2
1
0
0
1
1
1
2
1
0
1
2
0
1
0
1
0
1
1
1
1
1
2
0
3
2
2
1
2
1
1
0
1
1
1
1
0
0
2
1
1
0
1
2
1
2
0
1
2
1
1
1
2
1
0
1
1
2
0
1
2
0
2
2
0
2
0
0
1
1
1
1
1
1
1
1
1
1
1
1
0
0
0
0
1
0
0
0
1
1
1
1
1
1
2
2
2
1
0
2
0
1
1
1
2
1
2
1
1
1
2
1
1
1
1
0
1
0
1
1
1
1
0
1
2
2
1
1
2
1
1
1
1
0
1
1
1
1
1
1
2
0
1
1
0
2
2
0
1
1
2
0
2
1
2
0
1
2
1
2
1
0
1
1
2
1
1
2
1
1
0
0
1
1
1
2
2
1
1
1
1
0
2
2
1
2
1
0
2
1
1
1
1
0
1
1
2
2
1
0
1
2
1
1
1
0
1
1
1
1
1
4
1
1
1
1
0
1
1
0
0
0
1
2
1
0
1
0
1
3
1
1
0
2
2
3
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
0
1
2
1
1
1
1
0
1
2
0
2
0
1
0
1
1
2
1
1
0
2
1
1
2
1
0
0
0
2
0
1
1
1
2
1
0
1
1
1
2
1
2
1
1
1
2
1
0
0
1
1
0
1
1
0
2
1
0
1
1
0
0
1
1
1
1
1
1
1
1
1
2
1
1
0
2
2
1
1
1
1
2
0
1
0
1
1
2
1
1
2
2
1
1
1
1
1
0
0
1
0
2
2
2
1
1
1
1
1
1
0
0
1
1
1
1
0
1
0
1
2
1
1
2
1
1
1
1
1
2
0
0
0
1
0
1
0
1
1
1
2
1
1
1
2
1
2
2
1
1
1
2
0
0
1
1
1
2
0
2
1
1
0
1
1
1
0
1
1
1
1
2
2
1
2
1
1
2
1
0
0
1
1
1
1
1
2
1
1
1
1
0
1
1
1
1
2
1
0
0
0
0
2
3
1
2
1
1
1
0
2
2
2
0
1
1
2
1
1
1
1
1
1
1
1
3
1
1
1
0
0
1
1
0
1
5
1
1
1
1
1
1
1
1
0
1
1
1
1
2
1
0
2
1
1
1
1
2
1
1
2
1
1
0
0
0
0
1
2
1
1
1
1
0
1
2
1
1
1
1
2
1
2
1
1
2
1
1
1
1
0
1
0
1
2
1
0
0
0
1
2
1
1
1
2
0
1
1
1
2
1
0
1
2
1
2
1
0
2
1
2
1
1
1
1
1
1
1
1
0
1
2
1
1
0
1
2
0
1
1
0
1
1
1
0
1
0
0
0
2
3
1
1
1
2
0
1
2
1
2
1
3
0
1
0
0
0
1
0
1
1
1
2
0
0
5
1
0
1
1
0
1
1
0
1
2
1
0
2
0
1
3
1
2
1
1
0
2
1
1
2
1
2
2
0
0
1
2
1
1
0
6
2
1
0
0
0
1
1
2
1
1
2
1
1
1
2
0
1
0
1
1
2
1
1
1
2
1
1
1
0
2
0
0
1
2
1
0
1
1
1
2
0
0
2
1
2
2
2
1
1
0
1
1
1
1
1
0
1
1
1
1
0
1
2
1
0
1
1
0
1
1
2
1
1
1
0
1
2
2
1
0
0
1
2
2
1
0
1
1
2
2
0
2
2
1
0
1
1
1
0
0
2
2
1
1
1
1
1
2
1
2
1
1
1
1
0
1
1
1
1
2
2
1
2
1
2
2
2
1
2
1
1
2
0
1
2
1
1
0
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
0
2
1
2
1
1
1
1
0
0
1
0
2
1
1
1
0
1
1
2
1
1
1
0
1
2
2
0
1
0
1
1
0
1
0
1
1
1
2
0
2
1
2
1
1
1
1
1
0
1
2
1
1
1
1
1
1
1
0
1
0
2
2
1
2
1
1
1
1
2
1
1
4
0
2
1
1
3
2
1
0
0
1
2
1
1
1
2
1
2
2
1
1
1
1
0
1
1
1
0
2
2
2
1
1
0
1
1
1
0
1
1
1
1
1
1
1
1
1
1
2
1
0
2
1
1
2
0
0
0
1
0
2
2
1
2
1
2
1
1
1
0
1
0
1
2
1
1
3
1
1
1
2
1
1
1
0
0
1
2
1
1
1
1
2
1
3
1
1
1
0
1
1
1
1
1
0
1
1
0
1
0
1
0
1
2
1
2
0
2
1
1
1
2
1
1
1
1
1
2
2
0
1
2
0
2
2
2
0
1
1
1
1
2
1
1
1
2
2
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
0
0
1
1
2
1
2
0
1
1
1
0
1
2
1
1
1
1
1
1
1
0
0
2
1
1
1
0
0
1
2
1
1
0
2
2
0
1
1
1
1
1
2
2
1
0
0
1
1
2
1
2
1
0
1
1
2
0
0
1
1
1
0
1
1
2
2
2
0
0
1
1
1
1
2
2
1
1
1
1
1
2
1
1
2
2
2
0
1
2
1
0
1
0
1
0
0
2
2
0
0
1
1
2
2
1
0
0
2
0
1
0
2
2
1
0
1
1
1
1
2
2
1
1
1
2
1
1
1
1
2
1
2
1
2
1
2
1
1
1
2
1
1
1
1
1
2
2
2
2
2
1
1
1
1
1
1
1
1
1
2
1
0
1
1
0
1
1
0
2
1
0
1
2
1
1
1
2
1
0
0
0
2
1
1
1
2
1
1
1
2
1
1
1
1
0
3
0
1
2
1
0
1
0
1
1
2
0
2
1
1
2
0
1
0
1
0
2
1
0
0
0
1
0
1
1
2
1
1
1
0
0
0
1
1
2
1
1
1
1
1
1
1
1
1
0
1
2
1
2
0
1
2
1
2
1
1
1
4
1
1
2
1
1
0
2
1
1
2
1
1
2
1
2
1
1
0
1
1
2
1
1
1
0
2
2
1
1
2
3
2
1
1
1
2
0
1
1
1
1
0
2
1
1
1
2
1
1
2
1
1
1
2
1
2
2
0
0
1
1
0
2
2
2
2
2
2
1
2
1
1
2
1
2
1
1
0
2
1
1
2
0
2
1
1
1
2
1
0
1
1
1
2
1
1
1
0
2
1
2
0
1
3
1
1
1
0
1
0
1
1
1
1
2
1
0
1
1
1
1
1
0
1
2
1
2
1
0
1
1
2
1
2
0
1
1
1
2
2
1
2
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
2
0
1
1
1
0
1
1
2
0
2
1
2
0
2
1
0
2
2
1
0
1
2
0
1
2
0
1
2
1
1
1
2
1
0
1
1
1
1
0
2
2
1
1
0
1
1
1
2
0
1
0
1
1
1
1
1
2
1
1
1
2
1
2
1
1
2
2
1
1
1
2
1
1
2
1
1
2
1
0
1
0
2
0
1
0
1
1
2
1
1
1
1
1
0
0
2
1
1
1
2
1
1
2
1
1
0
1
2
1
1
1
2
1
1
1
2
2
2
1
1
2
2
1
0
0
2
2
1
1
0
1
1
1
1
1
0
1
1
1
2
2
1
1
1
2
2
0
1
0
1
0
2
1
1
1
1
1
1
1
0
2
1
1
1
1
0
2
1
1
0
2
0
0
1
2
2
1
1
1
0
1
1
2
1
1
1
2
2
1
1
2
1
1
2
1
1
0
2
1
0
0
1
1
1
1
1
2
0
1
1
0
2
1
1
0
2
2
1
0
1
2
3
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
0
2
1
2
2
1
2
1
1
1
1
1
1
2
1
1
0
1
2
1
2
1
1
1
0
2
1
2
0
1
2
0
2
1
1
1
2
0
1
2
1
3
1
1
1
1
0
0
0
1
1
1
1
1
0
1
2
0
1
0
1
2
1
1
2
1
0
0
1
2
0
0
0
1
1
1
1
2
2
2
1
0
0
2
1
1
1
1
1
0
2
1
0
1
2
2
1
1
1
2
0
1
2
0
1
2
1
1
1
1
1
0
1
2
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
3
0
1
0
1
1
1
1
0
0
1
2
2
1
1
1
1
2
1
1
2
2
1
1
1
0
0
0
0
1
1
0
1
1
0
2
0
1
1
1
2
1
1
1
1
0
0
1
1
1
1
0
1
1
1
0
1
2
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
2
2
2
1
2
1
0
1
1
1
1
2
1
1
0
2
1
1
1
1
1
2
0
1
0
1
2
3
1
1
2
1
1
2
1
0
1
0
1
1
1
1
0
1
1
1
1
1
0
1
2
1
1
1
0
1
1
1
1
2
1
1
0
2
0
2
0
1
0
2
1
0
1
0
1
0
1
2
1
1
1
2
1
1
0
2
1
0
1
1
1
0
1
1
2
1
1
1
0
0
1
1
1
1
1
2
0
1
2
2
1
1
1
0
1
2
0
2
1
1
2
0
2
0
0
1
1
2
0
1
1
0
1
1
1
2
1
1
0
0
1
1
1
1
5
2
2
1
1
1
1
0
0
2
2
2
1
0
0
1
1
1
1
1
1
2
1
2
1
1
2
0
0
1
1
1
1
0
2
1
1
1
1
1
2
1
1
1
0
1
1
1
1
0
2
0
1
1
1
1
2
0
1
1
1
1
1
2
1
0
0
2
0
1
2
0
1
0
2
1
1
1
1
1
0
1
1
0
1
1
1
1
1
1
2
1
1
1
1
1
1
0
2
1
2
1
1
1
1
2
2
1
2
1
1
1
2
0
1
1
2
1
1
2
2
2
1
1
1
2
2
2
1
2
0
2
1
1
1
1
2
3
1
1
1
1
1
1
1
0
0
0
2
0
2
1
1
0
1
1
1
3
1
1
2
0
1
0
1
2
1
1
2
1
0
2
2
1
1
1
1
1
1
2
1
1
2
0
1
0
1
0
1
1
1
1
2
1
0
1
0
2
1
2
2
2
2
0
2
2
1
1
0
1
1
2
1
1
2
0
0
0
1
1
1
1
2
1
1
1
1
2
2
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
0
1
0
0
1
0
1
0
3
1
0
0
2
1
1
2
0
3
1
1
1
1
1
1
1
1
1
1
2
0
2
1
1
0
1
2
1
1
2
1
1
2
2
1
1
2
3
1
1
1
2
1
1
1
3
2
1
1
1
1
1
0
1
2
1
1
2
1
0
2
1
1
2
1
1
1
1
1
0
1
1
0
1
2
1
1
1
1
1
2
1
0
2
1
2
1
1
2
1
1
1
2
1
1
1
2
1
1
1
0
1
1
1
1
0
1
0
1
1
1
0
1
0
1
1
2
2
0
2
1
1
1
2
0
0
1
1
0
0
1
1
1
0
1
1
0
2
0
2
3
0
1
1
1
0
1
2
0
1
1
3
1
1
2
1
0
0
1
1
2
1
2
1
1
1
0
1
0
1
1
3
2
1
1
1
0
1
1
2
0
1
2
0
2
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
2
1
0
1
1
0
3
1
1
2
2
1
3
1
1
0
2
1
0
2
1
2
1
1
1
1
0
0
0
1
1
0
0
1
1
2
2
1
2
1
0
0
1
2
1
1
2
2
1
1
1
1
1
0
1
2
0
1
0
1
0
1
0
1
0
1
1
1
2
2
1
1
0
2
1
2
1
1
1
1
1
1
1
2
1
1
2
1
0
2
1
0
2
1
0
1
1
0
1
1
0
1
1
1
0
1
0
1
0
1
2
1
2
2
2
1
2
1
1
1
1
2
2
1
1
1
0
0
1
1
1
2
1
1
0
2
1
0
1
1
1
2
2
1
0
2
1
1
1
1
1
1
1
2
1
1
1
0
1
1
2
0
1
0
2
2
0
1
1
1
2
1
2
2
1
0
1
1
0
2
1
2
1
0
0
1
1
1
2
1
1
2
1
1
2
1
1
1
1
0
1
2
2
1
1
1
1
1
0
2
2
1
1
1
0
1
2
0
2
1
1
2
0
1
0
0
2
1
1
1
1
0
1
1
0
2
0
0
0
1
2
1
2
1
0
1
0
1
1
2
1
0
1
1
1
2
1
2
2
1
0
1
1
2
2
1
1
2
0
2
2
1
0
2
1
2
0
2
2
1
1
1
1
2
0
1
1
1
1
0
1
1
1
1
2
2
1
2
2
2
1
1
0
0
1
1
1
2
1
0
1
1
0
1
2
2
0
2
1
1
0
0
1
1
0
1
2
1
1
2
2
0
1
0
2
0
1
1
1
2
1
0
1
1
1
0
2
2
0
2
1
1
1
0
0
2
2
0
2
1
0
1
0
2
1
1
1
3
1
1
0
1
1
4
1
1
1
1
2
1
0
2
2
1
2
1
1
2
1
3
2
1
1
1
1
1
1
0
0
1
1
2
0
1
2
0
1
1
0
1
0
2
1
1
1
2
2
2
0
1
2
1
1
1
2
1
1
2
2
2
0
1
1
0
1
0
1
0
2
2
1
2
2
1
0
2
1
1
1
1
2
1
1
1
1
2
1
1
0
1
1
1
0
0
1
1
0
2
1
2
3
1
0
0
1
1
1
0
1
2
1
2
1
0
0
0
0
1
1
1
1
1
2
2
1
2
1
1
2
0
1
0
1
1
1
2
0
1
1
1
1
1
2
1
2
1
3
0
1
1
1
0
1
2
1
1
1
2
1
1
1
1
1
0
0
2
1
0
1
1
0
3
0
1
1
1
1
1
1
2
1
1
2
1
2
0
0
1
1
1
1
2
1
1
1
0
1
1
0
0
1
1
1
2
2
2
1
2
2
1
0
1
1
1
2
1
2
2
1
1
0
0
1
1
0
0
1
0
0
2
0
0
1
0
0
1
1
0
1
2
2
1
1
1
1
1
2
2
1
1
1
1
1
0
2
1
2
0
0
2
1
1
1
1
1
1
0
2
2
2
1
1
1
0
2
1
1
2
1
1
2
2
1
1
2
1
1
1
2
1
2
2
1
0
1
1
3
1
2
1
2
0
1
1
1
1
1
2
1
1
1
1
3
3
1
1
1
1
1
1
0
1
1
2
1
1
1
1
1
1
1
1
1
2
2
0
2
1
1
1
1
1
0
1
1
0
1
1
1
1
0
0
0
1
0
1
1
1
2
0
1
0
0
1
1
1
2
1
2
1
2
1
1
1
1
0
1
2
2
1
1
1
2
2
2
1
1
1
1
1
1
1
0
1
1
1
2
1
2
0
1
0
1
1
1
0
1
1
1
2
1
1
1
0
1
0
1
2
1
1
0
1
0
1
1
1
1
1
2
0
1
0
1
1
2
0
1
1
1
1
2
1
1
0
2
1
2
1
2
2
2
1
1
1
1
1
2
0
0
1
2
1
1
1
1
1
1
0
2
2
1
1
1
0
1
1
1
1
1
1
2
0
1
1
2
1
2
1
1
1
1
1
1
1
0
1
1
1
1
0
0
1
1
1
3
1
1
1
1
2
2
1
1
1
2
1
2
1
2
1
1
2
0
1
1
1
0
1
1
1
1
1
1
0
0
1
1
1
1
1
1
1
1
0
2
1
1
1
2
2
2
2
0
1
1
2
1
0
1
1
2
1
1
0
0
0
2
1
0
1
1
1
0
0
1
1
1
1
1
2
1
1
1
0
0
1
1
2
1
1
0
1
1
0
2
2
2
0
1
2
1
3
1
1
2
2
1
1
2
1
1
1
2
2
1
0
0
0
1
1
1
1
1
1
0
0
1
0
1
1
2
2
1
2
2
2
1
2
2
0
1
1
2
1
1
0
2
2
1
2
1
2
2
1
1
1
0
1
1
1
3
1
2
2
1
0
2
1
1
1
1
2
1
2
0
1
1
1
1
1
0
1
1
0
2
1
1
1
0
2
1
2
0
1
2
2
2
2
1
1
2
1
1
1
1
2
1
1
0
0
1
1
0
2
1
0
2
1
1
1
1
0
1
1
1
1
0
1
1
1
1
1
1
1
1
0
2
1
0
1
0
1
1
3
1
0
0
2
1
2
0
0
1
0
1
2
1
2
1
1
1
2
1
1
2
3
1
1
1
1
2
2
1
1
0
1
2
1
1
1
1
2
1
0
0
1
2
0
1
0
1
1
0
1
0
1
1
1
1
1
0
1
1
1
1
0
2
1
2
0
1
1
1
1
2
0
0
0
0
1
2
1
1
2
2
1
1
1
0
0
1
5
1
1
0
1
2
1
0
1
2
1
2
1
2
2
1
1
0
2
1
1
1
2
1
1
1
2
1
0
1
1
1
1
1
1
2
2
0
1
1
0
2
1
1
1
1
0
1
1
1
1
1
1
1
2
1
1
2
2
1
1
1
1
2
1
0
0
2
1
1
1
2
2
0
0
1
1
1
2
0
1
0
0
2
1
0
1
2
0
1
1
1
1
0
1
1
0
0
1
1
1
1
1
1
1
1
0
1
1
2
1
2
0
1
2
1
0
1
1
1
1
0
1
1
2
0
1
1
1
2
1
1
1
2
2
1
2
2
1
2
1
0
1
2
1
1
1
1
2
1
1
0
1
0
1
0
2
1
1
2
2
1
1
1
1
1
1
1
0
1
2
2
2
0
1
1
1
2
1
0
1
1
1
2
2
1
2
0
1
0
1
1
0
1
1
2
2
2
2
1
1
1
1
1
2
0
2
2
2
1
1
0
0
1
0
1
2
1
1
1
1
0
1
2
2
2
0
0
1
0
1
2
2
1
1
1
1
1
1
1
2
1
1
1
0
2
0
1
2
2
0
1
0
1
1
1
2
1
1
1
2
1
1
1
1
0
1
0
1
2
2
1
2
1
1
0
1
0
1
2
0
1
1
2
2
0
1
2
2
1
1
1
1
2
0
1
1
1
1
0
1
1
0
1
0
2
1
1
1
1
0
1
1
1
1
2
1
1
0
0
1
2
2
1
0
2
0
1
0
1
1
0
0
2
2
1
2
0
1
0
1
1
2
1
1
1
2
1
2
1
1
2
1
2
0
1
1
1
1
1
2
1
1
1
0
2
1
1
1
0
0
2
2
1
1
0
1
1
0
1
2
1
1
1
1
2
1
1
0
2
1
1
2
2
1
1
2
1
1
1
1
1
2
2
1
1
0
2
1
2
0
2
1
0
0
1
2
1
1
1
2
2
1
1
1
2
2
0
2
2
0
0
1
1
0
0
1
0
1
0
1
1
2
1
1
2
1
1
0
2
1
1
1
0
1
1
1
1
1
0
0
1
2
1
0
1
1
2
1
1
1
2
0
1
2
0
0
1
0
1
0
1
1
2
1
1
1
0
1
1
2
2
1
2
2
1
0
0
1
1
1
2
2
1
1
2
2
1
1
0
1
2
0
2
1
2
1
1
0
1
1
1
2
0
2
2
1
2
0
1
1
0
1
1
1
0
1
1
2
1
1
1
2
0
0
1
2
0
1
1
1
0
0
1
1
2
2
1
1
2
0
1
0
1
2
2
0
2
0
2
2
1
1
1
1
0
1
2
0
1
1
2
1
1
0
2
1
1
1
2
2
2
2
1
1
1
2
1
1
0
1
0
0
0
1
2
1
1
1
1
1
1
2
3
0
1
2
1
1
1
2
1
0
1
1
1
1
1
2
1
0
2
1
0
2
1
1
2
1
1
1
0
1
1
1
1
0
1
0
2
1
1
0
1
1
1
2
0
1
1
1
0
1
0
1
2
1
2
0
1
1
0
2
1
2
1
0
1
2
1
1
1
0
0
1
0
2
1
0
1
2
2
1
0
2
1
1
2
0
1
1
0
1
0
2
1
1
2
1
2
1
1
1
1
1
1
1
0
0
1
0
2
1
2
1
1
2
1
1
1
0
1
1
0
2
1
1
1
1
1
2
1
1
1
1
0
0
1
0
0
1
1
2
1
1
0
0
2
2
1
1
0
1
1
0
1
1
2
1
2
1
1
1
1
1
2
1
0
1
1
0
1
2
0
1
1
0
2
1
2
1
1
1
1
0
1
1
2
1
0
1
2
2
1
1
1
2
2
1
1
1
0
1
1
1
1
1
0
1
1
0
1
2
0
1
2
1
2
1
1
2
1
1
2
1
2
1
1
1
2
0
2
0
1
2
1
1
1
2
0
2
2
0
2
2
1
1
1
2
1
1
1
1
1
2
0
0
2
2
1
1
0
2
1
1
1
2
0
1
1
2
1
0
2
1
1
1
1
1
1
1
1
0
0
1
2
1
1
2
1
0
1
2
1
1
1
1
1
0
1
2
1
1
1
1
0
2
1
1
2
1
2
1
1
1
1
1
1
2
1
2
2
2
1
2
2
2
1
2
1
1
1
1
1
2
0
1
1
0
1
1
1
1
0
1
0
2
1
0
1
0
1
0
0
2
1
2
1
1
2
2
1
1
1
1
2
0
2
2
0
0
1
1
2
2
1
0
1
1
2
1
2
1
1
1
2
1
1
1
1
1
3
1
0
0
1
1
1
1
1
1
2
2
2
1
1
2
0
2
1
2
0
1
0
2
1
2
1
1
1
2
1
1
1
1
1
2
2
2
1
1
1
2
1
0
1
1
2
1
1
1
2
1
1
2
1
1
1
0
0
0
1
1
2
2
1
1
2
1
2
2
1
1
0
2
0
1
1
1
1
1
0
2
1
1
0
1
2
2
1
1
1
1
1
1
0
0
1
0
2
2
0
1
1
0
2
0
1
1
1
0
0
1
1
2
1
2
2
1
0
0
1
2
1
1
1
1
0
1
4
1
1
1
2
1
1
0
1
2
1
2
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
2
1
1
0
2
2
0
1
2
1
2
1
0
1
1
2
1
1
1
1
0
1
0
1
1
1
2
2
0
0
2
2
2
0
1
1
1
1
2
0
2
3
1
2
1
2
1
1
0
1
0
0
1
1
1
2
1
1
0
2
3
0
1
1
1
2
2
1
0
0
1
1
0
0
1
1
2
1
0
1
0
0
1
1
1
1
0
0
2
1
2
1
2
2
0
1
1
0
1
0
1
1
2
1
2
1
1
1
1
1
0
1
1
2
0
1
1
2
1
0
2
1
2
0
1
1
2
2
1
0
0
2
1
1
1
2
1
1
1
2
1
2
0
1
1
1
2
1
1
1
0
2
2
0
2
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
0
1
1
1
0
1
2
2
1
1
0
1
2
1
1
0
2
2
1
0
1
1
1
1
2
1
1
2
1
2
1
0
1
2
1
2
2
1
0
1
2
1
1
1
2
1
1
1
1
2
2
1
2
1
1
1
2
0
2
1
1
0
2
1
1
2
1
1
0
1
2
1
0
1
2
1
2
2
2
2
1
2
1
2
0
1
0
1
1
0
1
1
2
1
0
1
1
1
1
1
0
0
0
1
1
0
1
0
0
2
1
1
1
1
1
2
1
2
2
1
0
1
2
1
0
2
2
2
1
2
2
1
2
2
1
1
1
1
2
1
0
1
1
0
1
0
1
0
1
0
2
2
2
1
1
2
1
1
1
2
1
0
4
1
1
1
0
1
1
1
1
2
1
1
1
0
2
1
0
0
2
1
1
0
1
1
1
1
1
0
1
1
1
0
0
2
1
1
2
1
1
0
2
0
1
1
1
1
1
2
0
1
1
1
2
1
0
1
1
0
1
1
1
1
2
1
1
2
1
2
0
2
1
2
1
0
2
0
1
0
1
2
3
1
1
2
0
1
2
2
1
0
1
1
0
1
1
0
1
2
4
1
0
1
1
0
2
1
0
0
1
1
1
1
0
1
0
2
0
1
2
1
1
2
1
2
2
1
1
1
1
1
0
2
1
1
1
2
0
0
1
2
1
0
1
2
1
1
2
0
1
0
1
1
2
1
0
1
1
0
0
1
3
0
1
1
2
0
2
1
1
1
1
2
1
0
1
2
1
1
1
0
0
2
2
2
1
1
0
1
1
0
1
2
0
1
1
0
2
2
0
2
0
2
1
1
1
2
2
2
1
0
0
1
2
1
1
1
2
2
2
1
0
2
0
2
0
0
2
1
2
2
1
1
2
1
2
1
2
2
1
1
1
0
1
1
1
0
0
0
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
0
1
1
1
0
2
0
1
2
1
1
1
1
0
1
1
0
0
1
1
2
1
1
1
1
1
1
1
1
1
1
1
0
0
0
1
0
1
2
1
1
1
1
0
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
1
1
2
0
0
0
1
1
1
0
2
0
1
1
2
2
0
1
1
1
1
1
1
1
1
1
1
1
2
1
0
1
0
1
2
2
1
2
1
1
2
1
1
1
2
1
1
1
1
1
0
1
1
0
2
0
1
0
1
1
1
1
2
1
1
2
1
0
2
0
1
2
2
0
0
1
0
1
2
0
2
1
1
2
0
1
0
2
1
1
2
0
1
2
1
1
1
2
1
1
2
1
1
1
1
1
2
3
2
1
2
1
0
2
1
1
1
1
2
1
1
1
1
1
1
2
2
1
1
2
0
0
1
2
1
1
1
1
1
1
2
1
1
0
1
1
1
2
2
0
1
1
1
0
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
3
1
1
2
0
0
0
1
1
1
1
1
1
2
1
1
1
1
2
0
1
0
1
1
1
1
1
1
1
0
0
1
1
1
1
1
2
1
1
1
1
0
0
1
2
1
2
1
0
2
2
2
0
1
0
1
1
1
2
1
2
0
1
1
2
1
0
1
1
2
1
0
0
1
1
1
1
3
1
1
1
1
2
1
1
2
0
1
0
0
0
0
2
2
2
1
0
1
1
0
2
0
2
1
2
1
2
2
1
1
1
0
1
2
0
2
2
1
0
2
0
1
1
0
1
0
1
1
3
2
1
1
1
1
2
0
0
2
2
1
2
1
0
0
1
3
1
2
1
1
0
1
1
1
1
1
2
1
0
1
2
1
0
1
1
1
1
2
2
0
2
2
0
2
1
1
1
1
1
1
1
2
1
0
1
2
1
1
2
0
1
1
1
3
1
2
1
2
1
2
1
1
1
0
2
1
1
1
1
1
2
0
2
1
1
0
1
1
1
1
1
2
0
1
1
2
1
1
1
1
2
0
1
1
1
1
1
2
2
1
0
1
2
1
0
2
1
2
1
1
2
0
2
1
0
1
0
0
1
0
1
1
2
1
1
1
1
1
0
1
1
0
2
1
1
1
2
1
0
0
1
1
1
0
1
1
0
1
0
1
2
2
1
1
1
1
0
1
1
1
1
2
1
1
2
1
2
0
2
1
0
1
1
1
1
2
2
2
1
1
2
1
1
1
0
0
1
0
1
1
1
0
1
1
1
1
0
1
1
3
0
2
1
1
2
1
1
0
1
0
1
1
1
1
2
1
0
2
1
1
1
1
0
0
2
1
2
1
1
1
2
1
2
2
0
0
1
1
1
1
1
2
0
1
0
1
1
1
2
0
2
2
2
0
1
0
1
0
1
1
1
1
1
1
1
1
1
1
2
1
1
0
1
0
2
2
1
0
1
1
2
1
1
2
2
2
1
0
1
1
1
1
1
2
2
1
1
0
2
2
1
0
1
2
3
1
2
0
1
2
1
0
1
0
2
2
1
2
1
2
1
1
0
0
1
0
0
0
2
2
1
1
3
1
1
1
1
1
2
2
2
2
0
1
2
2
0
1
0
2
2
1
2
0
2
0
0
1
2
1
1
1
1
0
1
0
2
1
1
2
1
1
1
2
1
1
1
1
2
1
0
1
1
0
1
0
0
1
1
0
1
1
1
0
1
1
1
0
2
0
1
0
1
0
1
2
1
0
2
1
1
1
2
1
1
1
1
1
0
2
2
1
0
2
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
2
1
1
2
1
2
2
2
1
0
3
1
1
1
0
2
1
1
2
1
1
0
2
2
0
1
0
0
2
2
1
1
2
1
1
2
2
1
0
1
1
1
1
1
1
2
0
0
1
1
1
1
1
0
0
1
1
0
1
1
1
1
1
1
1
1
1
2
0
1
1
0
1
1
2
1
1
0
1
1
2
2
2
0
1
2
1
1
1
1
0
1
2
2
1
0
1
1
0
1
1
0
1
1
0
1
1
1
1
1
0
1
1
1
1
1
0
1
1
0
1
0
1
1
2
1
2
2
0
1
0
0
1
1
1
1
1
0
1
1
1
0
1
2
8
0
1
1
1
1
2
1
1
0
1
1
0
1
1
1
1
1
0
0
1
1
1
0
1
1
0
0
1
2
1
1
1
1
1
1
0
0
1
2
2
1
1
1
2
1
1
1
2
0
2
2
1
1
2
0
1
1
2
1
1
1
1
1
1
1
1
0
1
2
1
1
1
0
1
1
1
0
1
1
1
1
1
0
1
2
0
0
2
1
2
1
0
1
1
1
1
2
0
1
2
0
1
1
2
1
0
1
1
2
1
1
2
2
1
0
1
2
1
2
0
1
1
2
1
2
0
1
1
1
2
0
1
1
1
1
1
1
1
1
1
1
1
2
11
1
1
3
1
0
0
1
1
1
1
1
1
1
1
2
1
1
1
0
2
2
1
1
1
1
1
2
1
1
1
1
1
1
1
0
0
1
1
1
0
1
0
1
2
0
1
0
1
2
1
2
0
0
1
1
1
2
2
2
3
0
1
1
0
1
0
2
1
0
1
1
1
0
2
2
0
0
1
1
0
2
1
1
1
1
2
0
1
2
2
0
1
1
1
2
1
0
1
0
1
2
2
0
2
0
1
2
2
1
2
1
1
2
0
1
1
1
4
0
1
1
0
0
1
1
1
1
2
0
1
0
2
1
0
2
0
1
0
1
0
0
1
1
0
0
1
0
0
1
1
1
1
1
0
1
2
2
0
2
2
0
1
1
1
1
1
0
0
0
2
2
1
1
1
1
1
1
1
3
2
1
2
1
0
1
1
2
1
1
1
2
2
1
2
1
2
1
1
1
1
1
2
2
1
2
0
1
0
2
1
1
0
1
1
1
1
2
1
1
2
0
0
1
1
1
1
0
2
2
1
2
0
1
1
2
0
1
1
2
0
1
1
0
0
1
2
2
0
1
1
0
1
1
2
0
2
1
1
1
0
0
0
2
1
2
2
1
1
2
1
1
1
2
1
1
1
1
2
2
2
1
1
0
1
2
1
2
2
1
1
1
1
1
2
0
2
2
1
0
1
0
2
1
1
2
1
0
2
0
1
1
0
2
1
1
1
1
1
1
1
2
1
0
1
2
2
1
1
1
2
1
1
2
1
1
1
0
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
0
1
1
0
2
0
2
1
2
1
1
1
1
1
1
0
0
0
1
1
0
2
1
2
2
2
2
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
0
1
1
2
1
1
1
2
0
1
0
1
1
1
1
1
2
0
1
2
1
2
0
0
1
0
2
0
1
1
1
2
2
1
1
1
0
1
0
0
2
0
2
1
1
2
0
1
1
0
0
1
1
1
0
1
1
1
1
2
2
0
1
1
0
0
0
2
1
2
2
1
1
1
2
2
1
2
0
1
1
0
1
0
1
0
1
1
1
1
2
1
1
0
0
2
2
1
1
0
2
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
0
2
1
2
2
1
1
1
1
1
1
1
7
1
1
2
0
0
0
1
1
0
0
2
1
1
1
0
3
1
1
1
1
1
1
2
0
1
1
0
1
0
1
0
0
1
0
0
1
2
1
0
3
0
1
0
1
2
1
1
0
0
1
0
1
0
1
0
2
2
1
1
0
1
1
2
1
1
2
0
1
2
1
1
2
1
1
1
2
2
2
1
2
1
2
1
2
1
1
1
2
2
1
1
1
1
0
1
1
2
1
1
1
1
2
1
1
0
0
0
1
1
1
1
0
2
0
0
1
1
2
1
1
1
0
1
1
1
2
1
1
1
1
1
1
0
1
0
1
1
1
1
1
2
1
1
2
0
2
0
1
1
1
1
1
0
0
1
2
2
0
2
0
0
1
1
2
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
1
0
0
1
3
1
1
0
2
1
1
2
1
2
1
0
0
2
1
0
0
1
2
1
1
1
1
1
2
0
3
1
1
0
1
1
1
1
1
0
1
1
1
1
1
0
2
0
2
1
1
1
1
0
1
1
1
1
1
0
1
1
1
1
2
2
1
1
3
0
1
1
2
1
1
2
1
1
1
1
0
1
0
2
0
1
1
2
1
0
1
2
2
0
1
1
2
2
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
0
0
1
2
0
3
1
1
1
1
2
0
0
1
1
1
1
2
0
1
1
0
1
2
0
1
1
1
1
1
1
0
1
0
2
2
1
2
2
1
1
1
1
0
2
1
1
2
1
1
2
2
0
1
1
0
1
1
2
2
1
1
1
0
1
1
2
1
1
1
0
1
1
1
1
2
2
2
1
1
1
2
1
1
0
1
1
1
1
0
0
2
1
0
0
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
0
1
1
1
0
1
2
1
1
1
2
1
2
3
1
1
1
1
1
0
1
1
1
1
1
1
1
0
1
2
1
1
1
1
1
1
1
0
1
1
1
1
2
2
1
1
1
1
1
1
1
0
0
1
1
2
2
2
1
1
1
1
1
1
1
1
1
2
1
1
0
0
1
1
0
1
1
1
1
0
1
1
1
2
1
1
2
2
0
0
1
2
2
1
0
1
1
2
0
0
2
0
0
1
1
1
2
1
1
2
2
1
0
1
0
1
1
0
0
1
1
1
0
1
1
0
0
1
1
1
1
1
1
1
1
1
0
2
1
2
1
1
2
1
2
2
2
2
2
2
1
1
0
1
1
1
1
2
1
1
3
1
1
1
0
1
1
1
1
1
0
0
1
0
2
1
1
1
1
1
0
2
1
1
2
0
1
1
1
1
0
1
0
1
1
2
1
1
1
0
2
2
2
2
1
1
2
1
1
1
1
2
1
1
0
1
0
1
1
2
2
2
0
1
1
2
1
3
2
1
0
1
1
1
1
1
1
1
2
2
1
1
0
1
2
1
1
2
1
2
0
0
0
1
1
1
2
1
1
0
0
2
2
0
0
1
1
1
1
1
2
1
1
1
0
1
1
1
1
0
1
0
2
0
1
1
0
2
0
0
0
2
1
1
0
1
1
1
0
0
0
2
1
0
0
1
0
1
1
1
1
1
1
2
1
2
1
2
1
0
2
1
2
2
0
2
2
2
1
1
1
1
1
0
1
2
1
0
0
0
2
1
1
0
1
1
1
1
0
1
2
1
3
1
1
2
0
0
1
2
1
0
1
1
2
1
1
1
2
2
2
1
1
2
2
1
2
1
1
1
2
1
2
1
1
1
1
1
1
1
0
0
2
0
1
0
0
1
1
0
1
1
0
1
1
0
1
1
2
1
0
2
1
3
1
2
1
1
2
0
1
1
1
2
2
0
2
2
0
1
1
2
1
1
1
0
1
1
1
1
0
2
2
1
0
1
1
0
1
0
0
0
0
1
0
2
2
1
2
1
0
1
1
1
1
1
1
2
0
1
1
1
1
1
3
3
0
2
1
1
1
1
2
1
1
0
1
0
1
0
0
1
1
0
1
1
1
1
1
0
1
1
1
1
0
1
2
2
0
1
1
1
2
3
3
0
2
1
2
1
0
1
2
1
1
1
0
0
1
2
1
1
2
1
2
0
1
2
1
1
1
0
1
0
1
1
1
0
1
1
2
2
1
1
0
0
1
1
2
1
1
1
2
0
1
1
1
1
1
1
2
1
0
2
2
1
2
2
1
2
0
1
1
0
1
1
2
1
0
1
1
2
2
2
1
2
2
3
2
1
2
2
1
2
1
1
1
1
0
0
1
1
2
2
1
0
2
1
0
2
0
1
0
1
0
1
0
1
0
1
2
1
1
1
0
0
2
1
1
1
1
0
1
1
0
2
1
2
1
1
1
0
0
1
0
1
0
1
1
1
1
1
1
2
1
1
2
2
1
1
0
1
1
1
2
1
1
2
1
1
2
0
1
1
0
1
1
1
2
1
0
2
2
1
2
0
1
1
0
1
1
1
2
2
2
1
2
1
1
2
2
2
1
1
2
0
1
0
1
1
1
0
0
1
0
1
1
1
1
1
1
0
1
0
2
1
1
1
1
1
2
2
2
1
2
2
1
1
1
1
1
0
1
1
1
2
2
1
1
1
1
1
2
1
2
1
0
1
2
1
2
1
1
0
0
0
1
2
1
1
0
1
1
0
2
1
1
0
0
1
1
0
1
2
1
1
1
1
2
1
2
0
2
0
2
1
1
1
1
1
1
0
1
2
2
0
1
1
0
1
0
1
1
1
1
1
1
1
0
0
1
0
1
2
2
1
1
2
0
0
1
2
2
2
1
1
0
2
1
2
2
1
0
1
2
1
2
1
0
2
2
2
2
1
1
1
1
1
1
1
1
2
2
1
1
0
1
1
1
2
1
2
1
2
0
1
1
2
1
1
1
2
2
1
1
0
1
1
0
0
0
2
0
0
4
2
1
2
2
1
0
0
1
1
0
2
0
1
1
1
1
2
0
1
1
1
0
1
1
1
1
1
0
1
0
0
1
1
1
1
1
2
1
2
1
1
2
1
0
2
0
1
1
2
1
0
1
1
0
2
2
0
1
1
0
0
0
1
0
1
1
1
1
1
2
2
1
2
1
2
1
0
1
1
1
1
1
1
1
2
0
1
1
0
1
1
1
1
1
0
2
1
1
1
1
1
0
0
1
1
1
1
8
2
1
1
1
0
1
0
2
0
1
1
0
1
0
1
1
1
0
0
1
1
2
0
1
1
1
0
1
0
1
0
1
3
1
2
2
1
2
1
1
1
1
0
1
1
1
1
0
1
2
2
2
2
2
1
1
2
1
1
1
1
1
2
3
2
1
0
1
2
0
0
1
0
1
2
1
1
2
1
0
0
1
1
2
1
1
1
1
0
0
1
1
1
0
2
0
0
1
1
1
1
1
2
0
2
1
2
1
1
2
1
1
2
1
0
1
0
2
1
1
1
0
1
1
1
0
1
1
2
1
1
1
0
1
1
1
2
1
1
1
1
1
1
0
2
1
1
1
1
0
1
2
2
2
1
1
1
1
1
0
1
1
1
1
1
2
0
1
1
2
1
0
1
1
2
0
1
0
1
0
1
1
1
2
1
1
1
2
1
1
1
0
1
1
1
1
1
1
2
1
0
2
2
1
2
1
1
0
1
0
1
1
2
1
1
0
1
1
2
1
2
1
1
1
1
1
1
2
2
1
1
1
0
1
2
1
1
0
1
2
2
1
0
1
0
1
1
2
1
1
1
1
1
2
2
1
0
1
1
2
1
0
0
2
0
1
1
2
1
2
2
2
0
1
2
1
0
2
1
1
0
2
1
1
1
1
2
1
1
1
1
2
1
1
1
0
2
1
0
1
2
1
1
0
1
0
2
2
2
2
1
1
1
2
0
1
1
1
1
0
1
0
1
0
1
2
1
2
1
1
1
2
1
0
2
0
1
1
2
1
0
1
0
1
1
1
2
1
1
1
2
1
2
1
1
1
1
2
1
2
1
1
1
1
0
2
1
0
0
0
1
1
1
2
1
1
1
1
2
1
1
2
0
0
1
1
2
0
1
0
0
0
0
1
1
2
1
2
1
1
0
2
1
1
0
1
1
1
2
2
1
0
1
2
2
1
1
1
0
1
0
2
0
1
2
2
0
1
1
0
1
0
1
0
1
1
2
1
1
1
0
2
2
2
1
1
2
1
2
1
2
2
1
2
1
1
0
2
0
2
1
2
1
1
2
1
2
1
1
1
0
1
0
1
1
1
1
2
1
1
1
0
1
2
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
3
1
1
1
1
1
1
2
2
1
1
1
1
2
0
1
1
1
1
1
1
2
0
1
1
1
1
1
0
1
0
0
1
1
1
1
1
0
1
2
0
1
2
1
1
2
0
1
1
1
2
1
2
0
1
1
1
0
1
1
1
0
1
1
1
1
1
0
1
2
1
1
2
2
0
0
0
3
2
2
1
0
1
2
1
0
1
1
1
1
2
1
1
2
0
1
1
1
0
1
1
1
1
2
2
1
0
1
1
1
1
0
2
2
1
2
1
1
1
1
1
0
2
1
2
0
1
2
0
0
2
0
1
1
1
2
1
1
1
2
2
2
1
1
1
1
1
1
1
0
1
0
2
1
1
1
2
1
2
1
1
2
1
2
1
1
1
0
0
1
1
1
1
2
1
1
2
1
2
1
1
1
1
2
0
1
2
1
1
1
1
2
1
1
1
1
2
1
1
0
2
0
1
1
3
1
1
0
1
2
1
0
0
1
2
1
1
1
1
1
0
1
2
2
1
2
2
1
0
1
1
1
2
1
0
1
1
1
1
1
0
2
1
0
1
2
1
1
1
1
1
0
1
2
1
1
0
1
1
2
0
1
1
1
1
1
1
0
2
2
3
1
1
1
2
2
1
2
2
1
1
1
1
1
1
0
1
1
1
2
1
1
1
2
2
2
1
2
1
1
1
1
1
1
1
1
1
1
0
2
0
1
1
2
1
1
1
0
1
0
1
1
1
1
2
1
1
0
0
1
0
2
2
0
2
2
1
0
1
1
0
2
1
2
1
1
1
1
1
1
0
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
0
2
1
1
1
1
0
2
2
2
1
1
2
2
0
1
1
1
1
2
2
2
1
1
1
1
0
0
2
2
2
0
0
1
1
2
1
1
1
1
2
1
1
1
1
1
1
0
1
2
1
1
1
1
2
0
1
1
2
1
2
2
0
2
1
2
2
1
1
1
1
1
1
2
2
1
2
2
2
0
3
1
1
1
1
1
0
1
1
2
0
2
1
2
2
0
0
0
1
0
1
2
2
2
1
2
0
1
1
1
1
1
1
1
0
1
1
1
1
0
0
2
1
1
2
0
0
1
2
1
1
1
1
2
0
0
1
2
1
1
1
0
1
1
2
2
1
2
1
1
1
1
0
1
1
0
0
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
0
1
2
0
1
1
1
1
2
0
1
1
1
1
1
1
1
0
2
1
1
0
1
0
1
0
2
1
1
1
1
0
1
1
1
1
0
1
1
1
1
1
0
2
1
1
1
2
1
0
1
1
0
1
1
2
2
0
0
1
2
0
2
1
1
1
0
2
1
1
2
0
1
0
1
1
1
1
1
2
0
2
1
2
2
1
1
1
1
2
0
2
2
0
1
0
2
0
2
2
2
1
1
1
1
1
1
1
1
0
1
1
0
0
1
1
2
1
2
2
2
1
1
0
1
1
1
2
1
1
1
1
2
0
1
1
2
3
1
2
1
1
0
1
1
1
0
1
1
1
1
1
1
1
1
0
2
2
2
2
2
1
1
1
1
2
0
0
0
1
1
2
2
2
2
2
2
2
1
1
2
2
2
2
0
1
2
1
2
0
1
1
2
1
1
2
3
1
0
1
2
1
1
2
0
0
1
2
2
0
1
2
2
1
1
1
3
2
2
1
1
1
0
1
1
2
0
2
0
2
1
1
1
1
0
2
1
2
2
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
2
0
2
1
1
1
0
1
1
1
2
1
0
1
1
1
1
1
1
0
0
3
1
2
1
2
1
1
1
1
2
0
1
2
1
0
2
2
1
1
1
1
1
1
2
2
1
0
2
0
2
1
0
2
2
2
2
1
1
0
2
0
1
1
1
1
2
2
1
1
1
0
1
0
1
1
1
0
0
0
1
1
1
0
2
2
1
2
2
2
1
1
1
1
0
1
2
2
1
1
1
1
1
1
2
2
4
1
0
1
1
2
0
0
1
1
0
2
0
1
1
0
0
0
2
1
1
0
0
0
2
1
0
1
2
0
1
1
0
2
1
1
1
1
1
1
1
1
0
1
1
2
1
2
1
2
1
2
2
0
1
1
0
2
1
0
2
1
1
1
0
1
1
1
1
2
1
1
1
1
1
0
1
1
1
1
0
1
1
0
1
1
2
0
0
1
2
1
1
1
1
0
1
1
1
1
1
2
2
2
2
1
1
1
0
1
1
1
1
1
2
1
0
1
2
1
1
1
1
1
0
1
1
1
2
1
1
1
1
1
0
1
1
1
0
1
0
1
2
0
2
1
1
1
1
1
1
1
2
2
0
1
0
1
2
1
1
0
1
1
2
1
3
0
1
0
0
0
1
1
0
2
1
1
0
0
0
0
1
1
2
1
2
0
1
2
1
1
0
1
1
0
1
1
0
2
1
2
1
2
0
1
2
0
1
1
2
2
1
2
2
1
1
1
1
2
0
3
2
2
0
1
1
2
1
1
0
0
1
2
1
1
1
1
1
2
1
1
1
1
0
0
2
2
2
1
2
2
1
1
0
0
1
1
0
1
0
1
1
1
2
1
2
0
1
2
1
2
0
1
2
1
0
2
1
1
1
1
1
1
2
1
1
2
1
0
0
2
1
1
1
1
2
2
0
1
1
2
1
1
2
1
1
1
1
1
1
1
0
1
2
1
0
2
0
2
1
1
1
1
1
2
0
1
0
0
1
1
0
1
1
1
1
2
2
0
1
0
0
2
0
0
1
1
1
1
1
0
0
2
1
1
1
1
0
2
1
1
1
1
0
1
1
1
0
1
1
0
1
1
0
1
1
2
0
1
2
2
2
1
0
1
1
1
1
0
1
2
2
1
0
1
1
1
0
1
0
0
0
1
1
0
3
1
1
2
1
1
1
2
2
1
2
2
0
0
0
1
2
1
1
1
2
0
1
1
1
1
1
1
1
2
2
1
1
1
1
0
1
1
1
1
1
2
1
1
1
1
2
0
0
1
1
1
1
2
1
2
2
0
0
2
1
1
1
2
2
2
1
2
0
1
0
2
1
2
2
1
1
2
0
2
1
1
2
1
1
2
0
0
2
0
2
1
2
1
1
2
1
0
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
0
2
2
0
2
2
1
1
1
2
0
3
0
1
2
1
1
1
0
1
0
1
1
1
1
1
2
1
0
1
3
1
1
0
2
1
1
0
1
1
0
2
1
1
1
2
1
0
1
2
0
1
0
3
1
2
1
2
1
1
1
1
1
0
0
0
1
0
1
2
0
1
1
1
1
0
1
2
0
2
1
1
2
2
1
1
1
1
0
1
1
1
1
2
1
1
0
0
1
1
1
1
1
1
2
2
0
0
1
1
2
2
0
2
1
1
1
1
1
1
0
0
0
2
1
1
1
1
2
1
1
1
1
0
1
1
0
1
1
1
2
1
1
0
5
2
1
1
1
0
0
2
1
0
1
1
1
1
0
1
3
0
2
2
1
1
0
1
1
1
0
2
2
2
0
0
3
2
2
2
1
0
0
0
1
1
1
1
1
0
0
0
1
1
1
2
1
0
0
1
1
0
0
2
1
1
1
1
0
1
1
1
1
1
1
1
0
0
1
1
2
1
2
1
0
0
1
1
1
1
1
1
1
2
0
0
1
1
0
2
1
2
2
2
1
2
1
2
1
1
1
0
1
1
1
2
2
2
1
1
1
0
1
1
1
2
0
2
2
1
2
1
1
1
2
1
0
1
1
0
0
1
0
2
0
1
1
1
1
0
1
1
1
0
2
1
0
1
1
2
1
2
2
2
1
5
1
1
2
2
1
2
1
1
0
0
0
1
2
1
1
0
1
1
1
1
1
2
1
1
1
0
0
1
1
0
1
2
1
0
1
1
2
2
1
0
1
1
1
0
2
0
1
0
1
1
1
1
1
1
1
2
1
2
0
0
1
1
1
1
2
1
1
1
0
1
1
1
1
1
1
2
1
2
1
3
0
0
0
1
2
1
2
1
2
1
2
0
2
1
1
0
2
1
1
1
2
2
1
1
2
1
1
1
0
1
1
1
1
2
1
0
0
0
1
1
1
1
2
2
2
1
1
1
0
0
3
1
0
2
2
0
1
1
1
1
2
1
0
0
1
1
1
0
2
1
1
0
1
2
2
1
1
1
0
2
1
1
2
1
0
2
1
1
2
1
2
0
0
1
1
1
1
1
1
1
1
1
1
1
0
0
1
2
1
2
5
1
1
1
0
1
1
2
2
1
2
1
1
1
1
3
1
0
2
1
1
2
1
1
0
2
1
1
1
1
2
0
1
1
2
2
2
1
1
0
1
2
2
2
1
1
1
1
1
2
0
1
1
1
1
1
0
2
0
1
2
1
1
1
1
1
1
1
1
1
1
0
1
2
1
0
1
1
1
1
0
1
1
1
1
1
1
1
0
1
0
0
2
2
2
2
1
1
0
2
2
1
0
1
1
2
2
2
1
2
2
1
1
0
1
1
0
1
1
0
1
1
1
1
1
2
2
0
2
1
1
0
0
1
1
1
0
1
1
1
1
1
1
0
2
1
0
1
0
1
1
1
1
0
1
1
1
1
1
1
1
2
1
3
0
1
1
2
1
0
1
0
0
1
1
2
2
1
2
0
1
1
1
0
1
1
1
1
2
1
1
1
0
1
1
0
1
0
1
1
1
1
1
2
0
2
2
3
2
1
1
1
1
1
1
2
0
2
1
1
2
0
0
1
0
0
1
1
1
0
2
0
2
1
0
1
1
1
1
0
0
1
1
1
1
1
2
1
1
5
1
1
1
1
0
2
0
1
2
1
2
1
2
2
1
2
2
0
0
1
2
1
2
1
1
1
1
1
1
0
1
1
1
1
1
1
1
0
1
1
2
1
2
1
0
2
1
1
1
0
1
1
1
1
1
1
1
1
1
0
1
1
1
0
0
1
1
1
2
1
1
1
0
2
1
1
1
1
0
1
1
1
1
1
1
1
2
0
1
1
1
0
1
2
1
0
1
0
1
1
3
1
0
1
2
1
1
1
1
1
1
1
1
0
1
1
0
1
2
1
0
0
1
2
1
1
1
1
1
1
0
1
2
1
1
2
1
1
1
1
1
0
1
0
2
0
0
1
0
2
0
1
1
0
2
1
1
1
0
1
0
1
2
1
0
0
1
1
2
0
2
0
1
1
1
1
1
1
1
1
0
2
1
1
1
1
2
2
1
1
2
1
1
0
1
1
2
2
2
0
0
1
0
0
0
1
0
2
1
1
1
0
1
2
0
0
3
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
3
1
1
1
1
1
0
1
1
1
0
3
1
2
2
1
0
1
0
1
1
0
1
1
0
1
1
1
1
0
1
2
2
1
1
1
1
1
2
2
0
1
2
2
1
0
0
0
1
2
0
1
1
0
1
1
0
2
2
0
2
2
1
1
0
1
2
1
1
1
0
1
1
2
0
0
1
2
2
0
2
2
2
1
1
2
0
0
1
1
1
1
1
1
1
1
0
1
0
1
1
1
1
1
1
0
1
1
2
2
1
2
2
0
1
1
1
1
1
2
1
1
1
2
1
9
3
0
1
1
1
1
1
1
1
0
1
2
1
2
0
0
1
1
1
1
2
0
2
2
0
0
1
2
1
2
1
2
2
1
2
1
0
0
0
1
1
2
1
2
1
0
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
0
1
2
0
1
2
1
0
1
1
0
1
2
1
1
2
1
1
1
0
1
0
3
1
2
0
2
0
0
1
1
1
1
1
1
1
1
2
1
1
2
2
1
0
1
1
0
2
2
2
1
1
1
0
0
2
1
1
1
1
2
1
1
2
1
2
0
0
0
1
1
1
1
1
2
0
2
1
0
1
1
1
1
2
0
1
0
1
2
0
2
0
1
0
2
1
1
1
1
1
0
2
1
2
1
2
1
1
1
1
0
1
1
1
0
1
0
0
1
0
0
1
2
1
1
2
0
2
2
1
1
1
0
0
1
0
2
3
0
1
4
0
1
1
0
2
2
1
0
2
1
1
1
1
1
0
0
1
3
1
2
1
1
2
1
1
2
0
1
2
1
1
1
2
1
0
2
2
1
1
0
0
2
1
1
1
2
1
0
1
0
2
3
1
1
1
2
1
1
2
2
2
1
1
1
1
2
1
0
1
1
1
1
1
1
0
0
2
1
2
1
0
2
0
1
1
1
2
2
1
1
1
3
1
1
1
2
1
0
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
1
2
5
1
2
1
1
0
1
1
1
1
3
1
1
1
0
0
1
2
0
1
1
0
2
0
1
1
1
1
1
1
1
0
1
2
2
1
2
0
2
2
1
1
1
1
2
0
2
1
0
1
2
2
1
1
1
0
1
1
1
0
1
1
1
1
1
1
0
2
0
1
0
1
1
0
1
1
2
1
0
2
1
1
1
1
1
1
0
2
1
1
1
1
1
0
2
1
2
2
2
1
1
0
0
2
1
1
2
0
1
1
1
1
1
1
1
1
1
2
0
2
0
0
2
1
1
1
0
2
0
1
1
2
1
2
1
1
2
1
0
1
1
0
1
2
2
2
1
2
1
2
2
0
1
2
0
1
2
1
1
0
0
1
1
1
2
1
1
1
1
0
2
1
1
1
2
1
1
0
1
0
1
1
2
1
0
1
1
2
3
1
2
1
1
1
1
1
0
1
1
1
1
1
1
3
0
0
2
1
2
2
1
0
0
0
1
1
1
1
1
1
2
2
1
1
0
1
1
0
2
2
1
2
2
2
3
1
1
2
1
1
0
1
1
1
0
1
2
1
1
0
1
2
1
1
1
1
1
1
0
1
2
2
1
2
2
1
2
1
0
1
1
1
2
1
1
1
1
0
2
1
2
1
1
1
0
1
1
2
0
2
1
1
0
1
1
2
0
1
0
1
2
2
1
1
1
0
2
2
2
1
1
1
1
0
1
2
0
1
0
1
1
1
1
1
1
0
2
0
2
1
1
1
1
2
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
0
0
1
1
0
0
1
2
1
2
2
0
2
1
2
1
2
2
1
1
1
0
0
1
3
1
2
2
3
1
1
1
3
1
1
0
2
1
0
1
2
0
1
1
1
2
1
1
0
1
1
0
1
2
2
2
1
1
2
1
1
1
1
1
0
2
1
0
2
1
2
0
2
0
2
1
1
1
1
2
1
1
1
1
1
1
2
1
2
2
1
1
1
2
1
0
1
1
0
0
2
1
1
2
1
1
1
2
2
1
2
1
1
1
1
0
1
2
2
0
1
1
0
0
2
1
1
0
1
0
1
1
1
2
0
1
0
2
2
1
1
3
0
1
0
1
1
1
2
1
1
1
2
2
2
0
1
1
2
0
2
1
1
2
1
0
1
1
2
0
0
1
1
2
1
1
2
1
1
1
2
1
2
2
1
1
1
1
2
0
2
0
0
0
0
2
1
1
1
1
0
2
1
1
0
0
0
0
1
1
0
1
1
2
1
1
1
2
1
0
1
0
2
0
1
1
3
1
1
2
0
2
1
1
2
1
2
1
3
0
2
1
1
1
1
2
1
2
1
0
3
1
1
2
2
1
1
2
1
2
1
1
2
2
1
1
2
0
1
2
1
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
0
1
1
2
1
1
1
2
1
1
1
1
0
3
1
1
1
2
2
1
1
0
1
0
1
0
1
1
2
1
0
2
0
1
1
1
0
2
1
0
2
1
1
0
2
1
1
1
2
1
1
2
0
0
1
0
2
2
1
1
0
1
2
0
1
2
1
1
0
2
0
1
0
2
1
1
1
1
1
1
1
1
1
0
2
1
2
2
2
1
1
2
2
1
2
1
1
2
2
1
0
2
1
2
0
2
0
1
1
1
1
0
0
0
2
1
1
1
2
1
0
1
1
1
0
1
0
0
0
1
2
1
0
1
1
1
1
1
0
1
2
2
0
1
1
2
1
2
1
2
2
1
1
1
0
1
1
2
2
1
1
1
0
1
1
2
1
1
1
2
1
1
0
1
1
1
1
1
1
1
1
1
2
0
2
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
0
1
2
1
1
0
0
1
0
1
1
2
1
2
1
1
1
1
2
1
1
0
2
2
0
1
1
1
0
0
1
2
0
0
1
1
0
1
1
1
1
0
2
1
1
1
0
0
1
0
2
0
1
0
0
1
2
1
1
0
2
2
1
2
1
1
0
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
2
1
2
1
1
1
0
1
1
1
2
2
2
0
1
0
0
1
0
1
1
1
1
1
0
1
1
1
2
1
2
1
0
0
2
1
1
1
1
1
2
1
1
0
1
2
1
2
1
1
1
1
2
1
1
0
1
1
1
2
0
1
2
2
0
1
2
0
1
0
1
1
1
1
1
2
1
1
0
2
1
1
1
2
1
2
0
1
2
1
1
1
0
1
1
1
1
1
2
0
1
1
1
1
1
1
1
1
1
2
0
1
2
1
1
2
1
1
1
1
2
1
2
1
0
2
1
1
1
1
2
1
1
3
0
2
1
2
1
1
1
1
2
0
1
2
0
1
0
0
0
1
2
1
1
1
0
2
0
1
0
1
1
1
0
0
1
1
1
1
2
1
1
2
2
0
1
0
1
1
3
1
2
1
1
1
0
1
2
2
0
1
2
0
1
0
0
1
1
2
2
1
1
1
2
1
1
0
1
0
0
1
1
1
1
0
0
1
2
1
0
1
0
1
1
2
2
1
3
0
2
1
0
0
1
1
2
1
2
0
1
1
1
1
0
2
0
2
2
0
1
1
1
1
1
1
1
1
1
2
2
2
1
2
0
2
1
1
1
1
2
0
2
1
1
2
1
7
1
1
1
2
1
1
1
1
0
1
2
2
1
0
1
1
1
2
1
1
0
1
1
2
1
0
1
1
0
1
0
0
2
0
1
1
1
2
0
0
1
0
2
1
1
0
1
2
2
1
2
2
1
1
1
1
2
1
2
0
1
0
1
1
0
0
1
1
1
1
0
1
2
3
2
1
2
2
1
1
0
2
1
1
0
0
2
1
1
2
2
0
2
2
1
1
1
1
0
1
0
1
0
1
2
1
2
1
1
1
1
0
0
1
0
0
1
0
1
0
1
0
1
1
0
3
2
2
2
1
1
0
0
1
2
2
2
1
1
1
1
0
1
1
1
1
1
1
2
1
1
1
1
2
1
2
0
0
1
2
2
1
2
0
2
1
1
2
1
1
2
0
1
1
1
1
2
1
1
1
2
1
2
1
1
1
2
1
1
1
0
2
2
1
1
0
1
2
1
1
1
1
1
1
1
1
2
1
0
1
0
2
1
0
1
0
2
2
2
1
2
0
1
2
1
0
2
0
0
2
1
1
1
2
2
1
0
1
1
1
2
1
1
1
2
1
0
1
1
1
1
1
1
1
0
0
1
0
2
1
1
0
1
1
1
1
1
1
1
1
1
0
0
2
1
1
1
1
0
2
2
1
2
0
0
1
1
1
2
0
1
0
1
1
1
1
0
1
2
1
1
1
0
1
1
1
1
0
1
1
1
0
1
2
1
0
3
1
1
1
1
1
1
1
1
0
1
2
2
1
1
2
1
0
0
1
2
1
1
1
1
0
1
1
1
2
1
0
2
1
2
1
0
1
1
0
1
1
1
1
1
1
1
2
1
1
1
1
1
0
2
1
2
1
1
1
1
1
0
1
0
1
1
1
1
2
1
1
2
1
1
2
3
0
2
2
1
2
3
1
2
1
0
2
0
1
1
0
0
1
1
2
0
1
2
2
0
0
0
0
1
2
0
1
1
1
1
2
1
2
1
1
2
1
1
1
0
1
1
1
2
2
0
1
1
0
1
1
1
1
0
1
1
1
2
2
2
1
2
2
2
2
1
1
1
1
0
0
1
1
2
1
0
1
1
0
1
1
1
2
1
0
1
1
3
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
2
2
0
0
2
1
1
0
1
1
1
2
1
1
2
1
2
0
1
1
1
2
1
0
2
0
1
2
0
2
2
1
2
1
0
1
1
2
0
1
1
2
1
2
1
0
1
2
1
2
1
1
1
1
2
0
1
1
0
0
1
0
2
2
3
2
1
1
1
1
1
1
0
1
2
0
1
2
1
1
0
1
1
0
0
1
1
0
1
1
1
2
3
2
1
1
2
0
2
1
1
2
1
1
0
2
1
1
2
1
0
1
1
2
1
0
2
3
2
0
1
2
2
1
0
1
1
1
0
1
1
2
1
1
1
0
1
1
1
1
2
2
1
0
1
0
2
0
1
2
1
1
2
1
1
1
2
0
1
1
2
1
2
2
1
1
1
1
1
1
2
0
0
1
2
2
2
1
1
2
1
1
0
1
0
1
1
1
0
0
1
1
2
1
1
0
2
1
1
1
0
0
0
1
0
1
1
2
1
0
2
1
1
2
1
1
1
2
1
2
1
2
0
0
0
2
1
1
0
2
1
1
2
1
1
1
2
1
1
0
1
0
1
2
0
1
2
1
1
0
1
1
1
0
1
1
0
0
1
0
2
1
2
2
1
2
0
1
1
1
2
2
1
1
1
2
1
1
1
1
1
1
0
1
0
1
1
1
2
1
1
0
1
1
2
1
1
1
0
0
1
0
1
0
2
1
1
1
2
2
1
1
1
2
2
1
1
2
2
1
1
1
1
1
0
2
1
1
1
0
2
1
1
0
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
0
0
2
1
1
1
1
2
1
1
0
1
1
1
1
1
1
2
2
1
1
0
2
2
3
1
1
1
1
1
1
1
1
1
1
1
0
1
0
0
0
1
1
0
3
1
1
1
1
2
1
1
1
1
2
0
2
1
0
1
1
1
2
2
0
0
1
1
1
2
0
0
1
1
1
1
1
1
0
1
1
1
0
1
1
1
0
1
1
1
0
0
0
1
1
2
1
1
1
1
0
1
1
1
1
2
1
1
1
1
1
1
2
2
0
1
1
1
2
5
1
0
1
1
2
2
1
1
0
2
0
1
1
2
0
1
1
2
1
2
0
2
1
1
1
1
1
1
1
1
2
2
2
1
2
1
2
0
1
2
1
1
2
4
1
0
1
2
1
1
1
1
0
0
0
2
2
1
1
2
1
2
2
1
2
1
1
1
1
0
1
1
1
1
2
1
0
2
0
1
1
0
1
0
0
1
1
0
0
1
2
1
2
1
2
0
2
1
1
1
0
2
2
1
1
2
2
1
1
1
1
1
2
0
2
2
1
1
1
2
2
1
2
2
1
0
1
1
1
2
1
0
2
0
1
1
2
1
1
0
1
1
1
1
1
1
0
1
1
1
1
1
0
2
1
2
1
2
0
1
1
0
1
1
1
0
0
1
2
1
0
1
2
4
1
2
1
1
0
1
0
2
1
1
0
0
1
1
1
1
1
1
2
1
1
0
0
2
1
1
1
1
1
3
2
1
2
1
1
1
2
0
1
1
1
1
1
2
2
1
1
1
0
1
0
0
2
2
1
0
1
1
1
1
1
1
0
1
0
2
2
1
1
0
0
1
1
1
0
1
0
1
1
2
0
0
0
1
1
1
2
1
1
1
1
1
0
1
1
1
0
1
1
0
1
2
0
1
1
1
0
1
1
1
1
2
2
2
1
2
1
2
1
0
1
2
2
1
1
1
1
2
2
0
1
1
0
1
2
1
1
2
1
1
1
1
1
1
1
1
0
2
1
0
2
1
1
1
0
0
1
1
1
1
1
0
1
1
1
1
1
2
1
2
2
1
1
2
2
1
2
1
1
0
2
0
2
1
0
0
1
0
0
0
2
1
1
2
0
1
0
2
2
2
1
0
1
0
1
0
0
1
0
2
1
1
1
1
2
1
0
1
1
2
1
0
0
0
1
0
1
1
2
1
1
1
1
0
1
1
1
2
1
2
0
1
0
0
2
2
1
1
2
0
1
1
4
1
2
1
2
1
1
1
1
2
1
1
1
0
2
1
1
0
0
1
2
1
0
1
1
1
0
1
2
2
2
0
0
2
1
2
1
2
1
1
1
0
1
1
2
1
1
1
1
2
0
2
2
0
1
1
1
0
1
0
2
0
2
1
1
1
1
1
1
0
2
2
1
1
1
1
2
1
1
1
3
2
1
0
5
1
1
0
2
1
0
0
1
0
1
1
2
2
2
1
0
0
1
1
0
0
1
2
0
1
1
1
0
1
0
1
0
0
1
0
2
0
0
1
2
1
0
1
1
1
2
1
1
0
2
1
0
1
2
2
1
0
1
1
0
0
1
2
1
1
1
2
2
0
0
2
1
0
0
1
0
1
2
2
1
2
1
0
0
2
0
0
0
1
0
1
1
1
1
1
1
4
2
0
1
0
0
0
0
2
1
1
0
1
1
1
2
1
0
1
1
2
2
1
1
1
0
0
2
0
1
2
1
1
1
0
1
0
1
1
1
2
1
2
2
1
1
1
0
0
2
1
1
3
2
1
2
0
2
2
1
2
1
2
1
1
2
2
2
1
1
2
0
1
1
1
2
2
1
1
1
1
0
2
1
1
0
1
2
0
0
0
2
1
0
1
1
0
2
1
1
1
0
2
1
0
2
2
1
0
0
1
1
1
0
1
0
1
1
1
1
0
2
2
2
0
0
1
0
2
0
2
1
0
1
1
1
2
1
0
1
0
0
1
0
1
2
1
1
1
2
1
0
1
1
2
2
1
1
2
0
1
1
0
1
0
1
1
2
1
1
1
1
1
0
2
0
2
1
1
1
1
2
2
1
2
1
2
2
0
1
2
2
2
1
1
1
2
1
1
1
0
2
1
1
0
1
1
2
1
1
0
1
2
1
0
1
0
2
1
1
0
1
1
1
2
1
1
1
2
0
0
1
1
0
0
0
0
1
0
0
0
1
1
1
1
1
1
0
1
1
1
2
0
0
0
2
1
2
1
1
1
0
1
1
0
1
0
2
1
1
0
1
1
2
1
2
0
1
3
0
1
1
2
1
2
1
2
0
1
2
0
1
2
0
1
2
2
0
0
0
2
1
1
0
2
2
1
1
1
2
0
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
0
1
0
1
0
1
2
1
1
1
2
1
2
0
0
0
2
2
1
2
1
1
2
2
2
2
1
1
1
1
1
1
2
0
1
1
0
1
1
1
1
2
1
0
2
2
1
2
1
2
1
1
2
2
2
1
2
2
2
1
1
1
1
1
2
0
1
1
1
2
1
1
1
0
2
1
0
1
2
1
1
1
2
0
0
1
2
1
2
1
1
0
3
1
0
1
2
2
1
2
1
1
2
2
0
1
0
1
2
3
1
1
1
2
1
1
2
0
1
1
0
1
1
0
1
1
0
2
0
0
1
2
1
2
0
2
1
1
2
1
1
1
1
2
0
2
1
1
1
1
0
1
0
3
1
0
0
0
1
1
2
1
1
0
1
0
1
1
2
1
0
1
1
1
0
1
2
0
5
1
1
1
1
0
1
1
1
1
1
1
1
1
0
1
2
1
4
1
1
1
1
2
0
0
2
1
1
1
1
1
1
1
2
1
1
1
2
1
2
2
1
0
1
0
1
1
0
2
0
1
1
2
1
0
0
1
0
1
2
2
1
1
1
1
1
1
1
0
1
0
2
1
3
1
1
1
1
0
2
2
1
2
1
1
0
1
1
1
2
1
2
0
1
1
1
1
0
1
1
1
1
0
1
2
0
0
1
0
1
1
3
1
2
1
1
0
0
2
1
2
0
1
2
2
1
1
1
1
1
1
1
1
1
0
2
1
0
2
0
0
1
1
0
1
2
2
1
2
2
0
1
0
2
1
1
1
1
1
2
2
1
0
2
1
0
1
0
1
1
1
1
1
1
2
1
1
1
0
2
1
1
0
1
2
2
0
2
1
1
0
0
1
1
1
2
1
1
1
1
0
1
0
1
1
1
1
1
1
1
0
2
2
0
2
1
1
0
1
1
2
0
1
2
1
0
1
0
0
0
0
0
0
1
1
1
0
2
1
0
1
0
1
0
1
0
2
1
1
1
2
0
1
1
1
1
1
0
0
1
2
1
1
0
0
2
2
1
1
1
1
1
1
2
1
2
1
1
1
2
0
1
0
1
1
1
2
1
1
1
2
1
1
2
0
1
1
0
2
2
1
1
1
1
1
1
0
0
1
1
2
0
0
1
1
2
0
1
0
0
1
1
2
2
1
1
1
1
0
4
1
0
0
1
1
1
0
1
1
1
0
2
2
1
0
2
1
2
2
1
2
0
1
1
0
1
1
1
1
1
2
0
1
2
0
1
1
0
0
1
1
2
1
1
1
1
1
1
0
2
2
0
0
1
1
2
2
1
1
1
1
4
2
1
1
1
0
0
0
0
1
1
3
2
2
1
2
0
2
2
1
1
0
1
1
2
1
0
1
1
0
0
1
0
1
2
2
1
0
1
1
1
2
3
1
1
1
1
1
0
2
1
1
2
1
1
1
1
2
0
2
1
0
1
2
1
0
1
0
1
0
1
0
0
1
1
1
1
2
2
1
0
1
0
1
1
0
2
1
1
2
1
2
1
1
0
1
1
0
0
2
1
0
1
2
1
1
1
1
2
1
0
2
1
1
1
0
1
1
2
0
1
0
1
1
1
0
0
1
2
1
0
1
1
0
0
2
2
1
1
0
1
1
1
0
2
2
0
1
1
0
1
1
1
1
2
0
2
0
1
2
1
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
1
1
0
2
1
0
1
1
2
1
1
1
2
1
1
2
2
0
1
0
1
0
1
0
0
1
2
1
2
1
1
1
1
1
2
0
2
1
1
1
2
0
1
1
2
2
0
2
1
1
1
1
1
1
1
1
1
0
2
1
0
1
3
1
0
2
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
0
0
2
1
1
2
1
1
2
2
1
0
1
1
0
0
1
0
0
2
0
1
3
1
2
1
1
1
2
2
1
2
2
1
2
2
1
1
2
1
1
1
0
1
1
0
1
1
1
0
2
1
0
0
2
0
1
1
1
0
2
1
1
1
1
1
1
0
2
2
1
1
2
2
1
1
1
1
1
2
0
0
1
1
0
0
1
1
1
0
1
1
1
3
1
1
0
1
1
1
1
2
1
1
1
1
0
1
1
1
3
1
1
1
0
1
2
0
1
2
1
0
2
1
1
2
2
2
2
2
1
1
1
1
1
0
2
2
1
2
1
1
0
1
1
0
0
0
1
0
0
1
1
2
1
0
1
1
2
2
1
2
2
2
2
0
2
0
2
1
1
1
0
1
0
1
0
2
1
1
1
1
0
2
1
0
1
1
2
2
2
1
1
1
0
1
1
2
1
2
1
2
2
1
0
0
1
2
2
0
2
1
2
1
1
1
1
2
0
1
1
1
1
1
1
2
1
1
2
1
2
1
1
1
0
2
2
1
2
1
1
0
0
1
0
1
1
1
1
1
1
1
0
1
1
1
2
1
2
1
2
2
0
1
1
2
1
2
2
1
1
3
0
2
1
1
1
0
1
0
2
1
2
1
0
2
1
0
1
1
0
0
2
0
1
2
1
1
1
2
2
1
1
2
0
2
1
0
2
1
2
1
1
0
2
1
1
1
1
2
1
2
1
0
2
1
0
2
2
1
0
1
1
1
2
1
3
1
1
1
0
1
2
0
1
1
1
1
1
1
1
1
2
1
1
0
1
2
1
0
2
1
1
2
1
0
0
1
1
1
0
1
1
2
1
1
1
2
1
2
1
0
0
1
2
1
1
2
2
1
1
1
1
1
2
0
1
1
1
1
1
2
1
1
2
1
1
1
1
5
1
0
0
1
0
2
2
1
1
1
2
1
1
1
1
2
1
0
0
1
1
1
2
1
1
1
0
1
2
2
1
0
1
1
1
1
1
0
1
2
1
2
1
1
1
1
0
1
1
1
1
1
0
1
2
2
2
1
0
0
1
1
2
0
1
2
2
0
2
1
1
2
2
1
1
1
0
2
2
0
1
1
1
0
1
2
0
1
2
0
2
1
2
2
1
3
1
1
1
2
0
1
2
1
1
1
1
0
1
1
0
1
1
2
1
2
2
0
1
0
1
1
6
3
1
1
0
1
1
2
1
1
2
0
0
1
1
1
1
0
2
1
1
2
2
2
1
1
2
0
0
1
1
2
1
1
1
2
0
1
0
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
3
1
2
1
0
0
1
1
1
2
2
1
1
1
1
0
1
2
1
1
2
1
2
1
2
1
2
0
0
1
0
2
1
1
1
1
1
1
1
1
1
1
2
0
2
1
1
1
1
0
1
1
1
1
1
0
0
2
1
0
1
0
0
1
1
2
2
2
0
1
1
1
1
1
2
1
1
2
1
1
2
1
1
1
0
1
0
1
0
1
1
1
2
1
1
2
1
1
1
1
1
1
2
0
0
3
2
2
2
1
2
2
2
1
2
2
0
2
0
1
0
1
1
1
1
0
0
1
1
2
2
2
1
1
1
1
1
2
2
1
1
1
1
2
2
1
0
1
1
1
2
1
1
0
2
1
1
2
1
1
2
0
1
2
2
1
1
2
1
1
0
1
2
1
1
1
1
2
0
1
0
1
2
1
1
3
1
1
2
1
0
0
2
1
0
0
1
1
0
0
2
1
1
0
1
1
0
2
1
0
0
1
1
1
0
0
1
0
1
1
1
1
1
2
1
1
0
1
0
1
2
2
1
1
1
2
2
2
1
1
0
1
2
1
0
1
1
1
1
2
1
2
0
1
2
3
0
0
0
2
1
1
0
2
1
2
0
2
2
1
1
4
1
1
2
0
1
2
1
2
2
1
1
1
1
1
1
2
1
1
1
2
0
1
1
2
1
0
0
1
1
0
1
1
1
1
2
1
0
0
0
0
0
0
1
1
2
1
1
1
1
2
0
2
1
0
1
1
0
1
2
0
0
1
0
1
2
2
0
0
1
1
2
1
1
1
1
2
1
0
0
2
1
1
1
0
1
1
2
1
1
1
1
0
0
1
0
2
1
1
1
1
1
0
1
0
1
1
1
1
1
1
2
2
0
1
1
1
0
0
1
0
1
1
1
2
1
2
1
2
2
3
1
1
0
1
1
0
1
1
1
1
0
1
1
1
0
1
2
1
1
1
1
1
1
1
1
0
1
0
1
1
1
1
1
2
0
1
1
1
2
0
1
1
2
0
4
1
1
0
1
0
1
2
2
0
1
0
1
1
0
1
1
1
1
1
2
2
0
1
1
1
1
0
0
1
1
1
1
0
1
0
1
1
0
1
1
1
1
1
2
2
0
2
1
1
0
0
2
1
0
1
1
1
1
1
2
1
0
1
0
1
2
2
2
1
2
1
2
0
2
1
1
2
1
0
2
1
2
2
1
3
1
1
1
2
2
1
0
2
1
1
1
1
1
1
1
1
0
1
1
1
2
1
1
1
1
2
1
2
1
1
2
1
0
1
2
0
1
0
1
2
0
2
2
0
1
0
2
1
1
0
2
1
2
1
0
0
1
2
2
0
0
2
2
1
2
0
1
1
1
1
1
1
1
2
1
1
1
0
1
1
1
2
0
1
1
1
1
1
1
2
1
0
1
0
1
0
2
2
0
2
2
1
0
0
1
0
2
0
1
1
3
1
0
1
1
1
1
0
1
0
1
1
1
1
1
1
2
1
0
1
2
1
0
2
2
1
1
1
2
1
0
1
2
1
1
1
0
1
1
1
1
2
2
1
1
0
3
0
1
1
1
2
1
1
1
1
1
0
0
1
2
1
1
1
0
1
1
1
0
1
1
1
0
1
1
1
1
2
2
1
0
0
1
1
1
1
2
1
1
1
1
1
1
1
1
0
2
1
1
0
0
1
0
1
0
2
1
1
1
0
0
2
2
2
2
1
1
1
0
0
1
2
1
1
0
1
1
1
1
0
2
1
1
2
2
0
1
1
2
2
1
0
0
1
2
1
2
1
1
0
2
0
0
2
2
1
1
0
1
2
1
1
0
2
1
1
1
2
1
1
1
0
2
2
0
1
1
3
2
1
2
1
0
0
2
0
2
1
1
1
1
0
2
2
1
1
0
1
1
0
1
1
1
2
0
1
1
2
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
0
1
0
1
0
1
1
1
1
1
1
0
0
2
0
1
1
2
0
1
1
1
2
0
1
0
1
1
2
2
2
1
1
0
0
1
2
2
1
2
2
2
1
1
1
1
2
2
2
1
0
1
1
1
2
1
1
1
2
1
1
1
0
2
1
2
0
2
1
1
1
1
1
1
0
1
2
1
2
2
1
1
1
1
2
0
0
2
2
1
2
1
1
0
0
1
1
1
1
1
1
1
1
0
1
1
2
0
1
2
1
1
1
1
1
0
1
1
0
2
2
1
1
1
1
1
0
1
0
0
2
1
1
2
2
1
2
1
1
1
0
0
1
0
1
2
2
2
1
2
1
0
1
1
1
1
1
2
0
1
1
1
2
1
1
2
1
0
2
2
2
2
1
1
1
0
1
0
1
2
1
1
1
2
1
1
1
1
2
1
2
1
1
2
1
2
1
1
1
1
1
0
0
1
1
2
1
1
2
1
1
2
1
2
4
1
1
0
1
2
2
1
2
2
1
1
0
2
1
1
1
0
1
2
0
0
1
1
2
0
1
0
1
0
1
1
1
0
2
1
1
1
2
1
1
1
2
2
1
1
2
1
1
0
2
0
0
1
1
1
1
1
2
0
1
2
2
0
0
2
1
2
1
0
1
1
1
2
2
1
1
1
1
1
2
1
1
1
0
2
2
2
0
2
1
1
0
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
0
1
0
1
1
1
1
1
2
0
1
1
0
1
1
2
2
1
1
1
2
1
0
0
2
2
1
1
1
1
1
2
1
2
1
2
1
1
3
1
1
1
2
0
0
1
1
1
1
1
0
1
1
0
0
1
1
0
1
1
2
0
1
1
0
2
2
1
0
2
1
3
0
1
1
1
1
0
0
1
2
1
1
2
3
1
1
1
1
2
1
1
1
1
2
0
0
2
1
1
1
1
0
1
3
0
1
1
1
1
1
0
0
0
1
0
1
4
2
1
1
0
0
0
1
1
1
0
2
1
0
2
2
2
1
0
2
0
1
1
1
1
1
1
1
1
0
0
1
2
1
1
2
2
1
1
1
1
1
1
1
2
0
1
0
2
2
2
1
0
1
1
0
0
1
2
2
1
0
1
1
2
1
2
0
1
0
1
2
1
0
1
1
1
1
2
1
1
2
3
0
1
0
1
2
0
2
0
1
2
0
2
2
1
1
1
1
1
1
1
0
1
0
0
1
1
1
1
2
2
2
1
0
1
1
1
1
2
1
0
1
1
2
1
1
2
1
1
0
1
2
1
1
2
0
1
2
1
1
1
0
1
0
2
2
2
2
2
2
2
1
1
1
2
1
1
1
2
0
1
1
1
2
0
2
1
1
0
1
2
1
2
2
2
0
2
1
1
1
1
0
2
1
1
1
1
0
0
1
1
1
2
0
1
2
1
1
1
1
1
2
1
1
2
1
0
1
1
1
1
1
0
1
1
2
2
2
0
0
1
1
1
1
1
1
2
1
1
1
1
2
2
1
0
1
1
1
1
1
0
0
1
1
1
1
0
1
1
2
0
1
1
0
1
0
2
0
0
1
1
1
1
1
1
0
1
2
1
1
0
1
3
0
2
1
1
1
2
0
2
1
2
1
1
1
1
2
1
1
0
1
0
1
1
1
0
0
1
1
0
1
1
1
2
1
1
1
2
1
0
1
1
1
2
1
0
0
1
1
1
2
2
0
1
0
2
1
1
1
1
1
0
0
2
0
0
1
1
0
1
1
2
1
1
1
1
1
1
0
1
1
1
1
0
1
0
1
1
2
1
2
0
2
1
1
1
2
2
1
1
1
1
1
1
2
0
1
3
0
1
1
1
1
2
1
1
2
0
0
0
2
1
2
1
2
1
1
1
2
2
0
1
0
0
2
2
1
2
1
0
1
2
2
2
0
2
2
0
0
2
2
1
0
1
1
2
2
1
1
1
3
0
2
2
0
1
2
1
1
1
1
0
2
1
1
1
1
1
1
1
2
0
2
0
2
1
2
1
3
0
1
1
1
2
1
1
0
2
0
0
1
1
0
1
1
0
0
1
1
1
2
2
1
1
1
0
2
1
0
0
2
1
2
2
1
1
1
2
0
1
1
1
1
1
0
1
1
1
1
1
1
1
0
0
1
1
1
1
0
1
2
2
1
1
0
2
1
2
1
1
1
1
1
1
1
2
1
2
1
1
0
1
2
2
1
0
2
1
2
1
0
2
2
2
2
2
1
1
0
2
1
0
1
0
1
1
1
1
2
0
1
1
1
1
2
1
2
1
1
2
1
1
1
2
2
1
1
2
0
1
0
1
1
0
1
2
2
1
1
1
1
1
1
2
1
1
0
1
0
1
1
1
1
2
1
0
0
0
1
0
2
2
1
1
1
2
0
1
1
1
2
1
1
2
2
0
1
2
1
1
0
2
1
1
1
2
2
1
1
1
2
1
1
1
1
2
1
0
1
0
2
1
2
1
1
0
2
2
0
1
2
1
2
1
1
2
1
1
1
0
1
1
1
1
0
2
1
1
2
1
0
2
0
2
0
0
1
1
1
1
0
1
1
1
1
1
0
2
1
1
1
1
2
1
2
1
1
2
1
2
0
0
0
0
2
0
1
0
1
1
1
1
1
1
0
1
0
1
1
2
2
1
1
1
1
0
2
1
1
1
1
2
1
1
1
2
0
0
0
0
2
1
1
0
0
0
1
1
0
0
0
1
0
0
1
1
2
0
0
1
2
1
0
0
2
1
2
0
1
0
1
1
1
1
2
1
1
1
0
1
2
1
1
0
0
2
1
2
0
1
1
2
1
1
1
1
1
1
2
2
1
2
1
2
1
0
1
2
1
2
2
1
2
2
1
1
2
0
0
1
1
2
0
0
0
1
2
1
1
1
2
2
1
0
0
2
0
2
2
1
1
1
1
1
1
1
1
1
0
2
1
1
1
1
1
2
0
2
1
1
1
0
1
0
1
1
2
1
1
2
1
0
1
1
1
0
0
2
2
0
0
2
1
0
1
2
1
1
2
2
0
1
2
3
0
1
1
1
2
2
1
1
1
1
2
0
0
1
1
0
1
2
1
0
1
1
1
0
1
1
2
0
0
1
2
1
1
2
0
1
1
0
2
1
1
1
1
2
1
1
0
1
2
1
1
1
3
0
1
3
1
1
2
0
1
0
1
1
0
1
1
1
2
2
2
1
2
0
1
1
0
2
0
1
1
1
2
1
1
0
1
2
1
2
2
1
0
1
1
0
0
2
2
2
1
1
2
1
1
1
1
1
0
1
3
1
1
1
1
1
1
1
1
0
0
1
1
0
1
1
1
1
1
0
2
2
1
0
2
2
1
2
1
2
2
2
2
1
0
1
1
0
2
1
1
0
1
1
0
2
2
0
1
1
1
2
1
0
1
1
1
1
1
0
1
0
0
1
1
1
1
2
1
6
1
0
0
1
1
1
3
1
1
1
1
1
0
0
0
1
1
2
1
1
1
2
1
0
0
1
2
1
2
0
2
0
0
0
0
2
1
1
1
2
0
1
2
1
1
2
1
1
1
1
2
0
1
1
1
2
1
2
2
0
2
1
2
1
1
1
1
2
0
1
1
0
2
1
2
1
0
0
2
2
0
0
2
2
1
1
2
0
1
1
0
1
2
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
2
0
1
1
1
1
2
0
1
1
1
1
2
1
0
2
1
0
1
1
1
1
0
2
0
1
1
1
0
1
1
1
1
1
1
1
0
1
1
2
0
1
1
1
1
2
3
4
2
1
2
1
1
2
1
1
2
0
1
0
2
1
1
1
1
1
1
1
1
2
0
2
2
0
1
2
1
2
1
1
1
1
1
2
1
0
1
2
0
1
1
0
1
2
1
2
1
2
1
1
1
2
0
1
1
1
0
1
1
1
2
2
1
0
1
0
2
4
0
1
1
1
2
1
1
1
0
1
1
2
2
1
1
1
0
1
0
1
1
1
1
1
1
1
2
2
1
1
0
1
1
0
0
2
2
1
1
1
2
2
1
1
0
1
1
0
0
1
1
2
1
1
1
0
2
0
1
1
0
4
1
2
0
0
1
1
0
0
1
0
1
1
0
2
1
1
1
1
0
2
1
1
2
1
1
0
1
0
0
2
2
2
0
3
0
1
1
1
0
1
0
1
1
0
0
1
2
1
1
1
1
1
0
1
1
0
2
0
1
1
1
1
1
2
1
0
1
1
1
0
1
1
1
1
0
2
1
0
1
1
1
1
1
2
1
0
2
1
1
2
2
2
1
0
2
1
0
1
2
2
1
2
2
1
1
1
0
1
0
2
1
0
1
1
1
1
0
1
1
0
0
1
0
1
0
0
2
0
2
1
1
1
1
3
1
1
1
1
2
2
2
2
1
0
1
1
1
2
1
2
1
1
0
0
0
1
2
1
1
1
2
1
1
0
1
1
2
1
1
1
1
1
2
2
0
1
2
2
1
1
1
0
0
1
1
1
2
1
1
1
0
1
1
2
1
0
0
1
2
0
0
1
1
2
2
0
1
1
1
0
0
0
0
1
2
1
1
1
1
0
1
1
1
1
2
1
2
1
1
2
0
1
2
1
0
2
0
3
1
1
0
1
1
1
1
2
1
1
2
0
0
1
0
1
1
0
1
1
2
1
2
1
1
1
1
1
0
0
1
1
1
0
1
0
1
2
1
0
1
2
1
2
1
2
0
1
2
1
0
0
1
1
1
0
1
0
1
1
2
1
2
2
1
0
1
1
0
1
1
1
1
2
1
0
1
2
1
1
0
0
1
0
0
1
2
1
1
1
0
1
1
1
1
1
0
0
0
1
1
0
0
1
1
1
1
2
1
0
1
1
1
2
1
1
1
1
0
0
1
1
1
0
2
0
0
2
2
2
1
1
0
1
0
0
1
3
1
2
0
1
2
1
0
0
2
1
0
0
2
1
1
1
1
1
1
2
1
0
1
2
0
2
2
0
1
0
1
1
1
1
1
1
2
1
0
3
1
2
2
0
0
1
0
2
1
1
0
0
1
1
1
0
2
1
1
0
1
1
0
1
1
2
1
0
1
1
1
2
2
1
0
2
2
1
1
1
0
1
0
1
0
0
2
0
0
1
1
2
0
1
2
1
1
1
2
0
1
1
1
2
1
1
1
1
2
0
0
1
2
0
1
1
0
1
0
0
0
1
1
1
1
0
2
2
1
0
0
1
1
1
1
1
1
0
1
1
1
2
2
1
1
1
1
0
3
0
0
0
0
2
1
1
1
2
1
0
0
1
0
1
1
1
2
1
1
2
5
2
0
2
0
1
2
0
1
1
0
1
0
1
0
2
1
1
0
1
1
1
1
0
1
0
2
0
0
2
2
2
2
1
1
1
2
1
1
1
1
1
1
0
1
1
0
2
0
1
1
2
1
0
0
1
1
1
1
0
1
1
3
0
1
1
1
1
1
0
0
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
0
1
1
2
0
1
0
0
1
0
1
0
2
1
1
1
2
0
1
1
1
1
3
1
2
1
2
1
3
0
2
2
2
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
2
1
1
0
1
1
2
1
1
1
2
1
2
1
0
1
1
1
1
2
2
0
2
0
1
0
1
1
2
2
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
2
1
1
0
1
2
1
1
0
2
1
2
1
2
2
1
2
1
2
1
2
0
1
0
1
2
0
1
1
1
1
1
2
2
1
2
1
1
0
1
1
0
2
1
1
2
2
2
1
0
1
1
1
0
1
0
1
1
2
2
0
0
0
1
2
1
1
1
0
0
0
1
1
1
2
1
1
1
1
1
1
2
1
0
1
1
1
1
1
2
1
3
0
0
2
2
0
2
0
0
2
1
2
1
2
0
0
0
1
0
1
1
1
1
1
2
2
0
1
2
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
2
2
2
1
0
2
1
2
1
2
2
5
1
1
1
1
1
0
0
1
0
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
4
0
1
1
2
2
0
1
1
1
1
2
1
1
1
1
1
0
2
2
2
0
2
1
0
1
2
2
1
1
1
1
0
1
2
2
1
0
1
1
1
1
0
2
1
1
2
1
1
1
1
1
1
1
2
1
0
0
2
1
2
2
1
1
1
1
2
1
1
1
1
1
1
1
0
0
1
2
1
1
1
1
1
2
2
1
1
0
1
1
1
1
1
1
1
0
0
0
1
1
1
3
0
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
0
1
2
1
0
1
1
1
2
1
1
0
2
1
1
0
0
0
0
1
0
1
1
0
1
2
2
1
1
1
1
2
2
1
1
2
2
1
1
2
1
1
2
1
1
0
0
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
0
1
2
1
1
0
1
2
1
0
0
2
2
1
2
1
1
2
1
2
1
0
2
1
2
1
1
1
0
2
1
1
2
2
1
1
1
1
0
2
1
0
2
0
2
1
0
0
1
2
1
0
1
1
2
1
1
1
2
1
2
2
0
2
1
2
1
0
1
2
0
1
2
1
1
1
0
1
1
1
0
1
2
0
0
0
1
1
2
1
0
0
1
0
2
1
0
1
0
2
1
2
1
0
0
1
1
1
1
0
2
1
1
1
1
0
0
2
1
1
1
4
1
0
0
1
1
1
2
1
2
1
1
0
3
1
0
0
1
1
0
1
2
1
0
1
1
1
1
1
1
0
1
1
1
0
2
1
1
0
1
1
1
1
1
0
1
0
2
1
0
1
1
1
2
1
1
1
1
3
0
1
1
0
0
0
0
1
1
1
2
2
1
1
0
0
2
2
1
1
1
1
1
2
1
0
1
1
2
0
1
1
2
1
0
0
0
1
2
1
1
2
1
0
1
1
1
2
1
0
1
2
1
2
4
1
0
0
1
2
1
1
1
1
2
1
1
0
1
0
2
2
2
2
0
2
1
2
2
1
1
0
2
1
1
0
1
2
1
1
1
2
2
2
2
1
1
2
1
1
1
1
2
0
1
1
0
1
0
1
1
1
1
1
1
0
0
1
1
2
2
1
0
1
2
0
1
1
1
0
1
1
1
1
1
1
2
2
0
1
2
1
0
0
1
1
1
1
1
1
1
1
2
0
2
1
1
1
1
2
1
0
1
1
2
1
1
1
2
2
0
0
0
0
1
2
1
1
0
1
2
1
1
0
1
0
2
1
1
1
2
1
3
1
1
1
2
0
2
1
0
1
1
2
2
1
1
1
2
1
1
1
1
1
0
3
2
1
1
2
2
1
2
1
1
1
1
1
1
3
2
1
2
1
1
1
2
1
1
2
2
1
1
1
1
1
1
1
4
1
2
1
1
0
1
1
1
1
2
1
0
1
3
0
2
1
3
0
2
1
0
0
1
1
1
2
2
1
1
3
1
1
1
2
1
0
0
2
2
1
2
0
0
1
1
1
0
0
1
1
0
1
1
5
1
1
1
0
0
1
1
1
1
1
2
1
1
2
2
1
2
2
2
0
1
1
1
2
1
0
1
2
1
1
1
1
1
2
0
2
1
1
1
0
1
1
1
1
2
0
2
2
2
0
2
2
1
0
1
1
1
1
1
1
1
1
1
1
0
1
1
0
2
1
0
0
1
1
1
1
1
1
2
2
2
1
1
1
0
0
0
2
0
1
2
1
2
1
1
2
1
1
1
2
1
1
1
1
0
1
1
2
0
1
2
1
2
1
1
1
1
0
2
1
1
1
1
1
2
1
2
1
2
0
1
1
2
2
2
1
1
1
2
1
1
1
1
0
1
1
1
1
2
1
1
1
1
1
1
1
2
1
0
1
0
2
2
1
2
0
0
0
2
1
0
0
2
0
0
1
1
0
0
1
1
2
0
0
1
2
1
1
1
0
0
0
2
1
1
1
1
1
2
1
1
0
1
0
2
1
0
1
1
1
0
1
1
0
1
1
0
1
2
1
0
1
1
1
2
2
2
1
1
1
1
1
1
0
1
1
1
1
1
0
1
1
0
1
1
0
1
0
1
1
1
0
1
1
2
1
1
0
2
1
1
1
1
2
1
1
1
1
0
2
2
1
2
1
1
1
1
1
0
1
1
1
2
2
1
0
2
1
1
1
1
1
0
0
1
1
2
2
0
1
2
1
0
1
0
1
2
2
2
1
1
0
1
2
1
1
2
1
0
1
2
2
0
1
1
2
1
1
1
1
1
2
1
2
1
2
2
4
1
1
1
1
1
0
1
1
0
1
1
1
2
1
1
0
2
3
2
1
1
1
0
0
1
1
0
1
1
2
1
0
1
2
1
1
2
1
1
1
0
1
1
0
1
0
1
1
2
1
1
1
0
0
1
1
1
0
1
1
0
1
1
3
1
1
1
2
2
2
1
1
0
0
1
2
0
2
2
1
0
1
1
1
1
1
1
2
2
1
2
2
0
1
1
0
3
1
2
1
2
2
3
2
0
1
2
1
1
1
2
1
0
1
0
1
2
0
1
1
2
0
0
0
1
1
2
2
1
1
1
1
1
1
1
1
1
2
0
2
2
1
2
1
1
0
2
0
1
1
1
2
1
1
2
0
2
2
2
1
2
0
2
1
1
2
1
0
1
2
1
1
1
1
2
2
2
1
0
2
2
0
1
2
1
0
0
1
2
0
1
0
2
1
1
1
2
1
1
1
0
2
1
0
1
1
2
1
0
1
1
1
2
1
2
2
5
0
1
1
2
1
2
2
2
1
1
0
0
2
2
2
2
0
1
1
4
0
2
2
2
0
1
1
1
1
2
1
2
1
1
1
1
1
0
0
0
1
1
1
0
2
1
0
1
1
2
1
2
1
1
1
2
1
1
2
0
0
1
2
1
2
0
0
1
0
1
0
1
0
1
0
2
1
1
1
1
2
1
1
1
1
2
1
1
1
0
0
0
1
1
2
0
2
2
1
0
1
1
1
2
2
2
0
2
0
2
1
1
1
1
2
1
0
2
2
2
1
1
1
0
1
1
1
1
1
1
1
0
2
1
1
1
2
1
0
1
1
2
1
0
1
1
1
1
1
1
2
1
0
1
1
1
2
0
2
1
0
1
2
0
0
0
1
1
1
1
1
2
0
1
1
1
2
1
1
2
1
2
1
1
1
1
1
0
1
2
2
0
1
1
0
1
2
1
1
1
2
0
0
2
0
1
2
1
1
2
1
1
2
1
0
2
1
0
0
0
1
1
0
1
1
2
0
1
0
1
1
0
2
1
1
1
1
2
1
1
0
2
1
0
1
1
0
1
1
0
1
1
2
1
2
2
2
2
1
0
2
1
1
0
1
1
2
1
2
2
1
1
1
1
1
1
0
3
2
1
1
1
1
1
1
1
0
2
1
1
1
1
1
1
1
1
0
1
0
1
1
1
1
1
0
1
1
2
1
0
0
0
1
2
0
1
2
1
2
0
2
1
1
0
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
2
2
1
2
2
1
0
2
1
1
1
0
2
0
1
1
1
1
1
2
1
1
0
1
0
0
1
2
1
1
2
1
1
1
2
0
0
1
1
1
2
0
2
1
1
0
2
0
0
1
1
1
0
0
1
1
1
1
1
1
2
0
2
1
0
1
1
2
3
0
1
1
0
2
2
2
0
1
1
2
0
1
1
1
1
1
1
0
1
0
1
1
1
1
1
1
0
0
1
0
1
2
0
1
1
2
1
2
1
2
1
0
1
0
2
1
1
1
1
1
1
2
2
0
1
0
0
0
1
1
0
1
1
2
0
2
2
2
2
2
1
2
2
0
1
0
1
1
1
0
1
1
0
2
1
0
2
1
2
1
2
1
1
0
1
1
0
1
1
1
2
1
1
1
2
1
1
1
1
0
1
1
1
1
2
2
1
1
1
1
0
1
1
0
1
2
1
1
0
3
1
0
2
2
0
0
1
2
1
1
1
2
0
0
1
1
1
1
0
1
0
1
1
0
2
1
1
0
1
0
2
1
0
1
2
2
1
0
2
0
0
2
0
2
0
2
0
1
2
0
2
1
1
1
0
1
1
1
1
0
1
1
0
0
2
0
1
2
1
1
1
0
1
2
1
1
1
1
1
1
1
2
1
1
1
2
1
1
0
0
2
2
0
1
2
1
2
1
1
2
1
0
0
1
2
0
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
1
0
1
1
1
1
0
1
1
1
0
1
1
1
0
2
1
1
1
2
0
1
1
0
1
1
2
1
1
1
2
2
1
1
1
0
0
1
1
1
0
0
2
2
1
1
0
2
2
1
0
1
1
1
1
1
1
1
2
0
1
1
2
1
2
1
1
1
1
1
1
0
1
2
1
1
1
2
2
2
1
2
1
0
1
1
0
2
1
1
2
1
1
1
0
1
2
0
1
1
2
2
1
1
1
1
0
1
1
2
0
1
0
2
1
2
1
2
0
1
1
0
1
2
1
1
0
1
0
1
0
2
7
2
1
1
0
2
1
1
2
1
2
1
1
1
1
1
1
0
1
1
2
1
1
0
1
3
1
1
1
2
1
1
1
1
1
1
2
1
1
1
3
2
2
1
1
2
2
1
2
1
1
1
1
1
0
1
2
2
0
0
2
1
1
1
1
1
1
0
1
0
2
0
0
0
2
1
1
0
0
1
1
0
2
2
2
1
1
2
2
1
0
0
1
1
1
3
1
0
1
0
0
1
1
1
0
1
3
1
2
1
0
2
0
1
1
1
1
1
2
1
1
1
0
2
1
0
1
1
1
2
0
2
1
1
2
1
1
1
2
2
1
1
1
1
0
2
2
1
1
2
2
0
2
2
1
0
0
1
2
1
1
1
2
1
1
2
1
1
3
2
1
0
1
1
1
2
1
1
1
1
1
0
1
1
0
0
1
2
1
0
1
1
1
1
2
1
1
2
1
0
2
1
2
1
2
2
1
1
4
2
0
1
1
0
1
2
2
1
2
0
1
1
0
1
1
1
1
1
0
1
2
0
1
2
1
1
0
0
1
1
1
1
0
1
1
2
0
1
1
1
2
2
2
1
2
2
2
0
1
0
1
1
1
2
1
0
1
1
1
0
2
1
0
0
1
1
1
1
3
2
1
1
1
1
2
1
0
1
1
2
1
0
1
1
0
2
1
1
1
1
2
1
0
1
1
0
2
0
0
2
1
2
0
0
1
1
2
1
0
2
0
1
1
2
1
1
0
1
0
2
0
1
2
1
1
1
1
2
1
1
1
1
1
2
1
1
0
1
1
0
2
1
2
1
1
1
2
1
1
0
1
2
1
2
1
2
2
1
2
0
2
1
0
2
3
1
1
0
0
0
0
1
0
1
1
1
1
1
2
2
1
2
0
1
1
1
1
0
1
0
0
0
1
1
1
2
2
1
1
0
1
1
0
2
2
1
1
1
2
2
1
1
1
1
1
1
2
2
1
1
0
1
1
1
1
2
2
1
1
1
1
2
2
0
1
1
1
1
1
1
1
0
2
0
1
1
0
0
2
2
1
1
1
0
1
2
0
0
1
1
0
2
1
1
1
1
0
1
0
1
1
1
1
1
2
0
1
0
1
1
1
0
0
1
1
1
1
1
2
2
1
1
2
2
0
1
1
0
2
2
1
1
1
1
0
1
1
1
2
0
1
1
2
2
1
1
1
1
2
1
1
1
1
0
1
1
1
1
1
2
2
1
2
0
0
2
1
1
4
0
1
1
1
0
1
1
2
1
2
1
1
1
0
1
1
1
1
0
1
0
2
1
0
2
0
1
1
2
0
1
1
0
0
2
1
0
1
0
1
1
2
1
1
0
1
1
1
1
1
1
0
1
0
1
1
0
1
1
1
1
0
2
1
2
0
2
1
1
1
2
1
3
1
2
1
0
0
1
1
2
0
6
1
2
1
1
1
1
1
1
2
0
1
1
1
2
0
1
0
1
2
1
2
1
2
1
1
1
1
1
2
2
0
1
2
1
1
0
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
0
1
1
2
1
0
1
1
2
1
2
2
2
1
1
2
1
1
1
1
0
1
2
0
2
1
0
2
1
1
1
2
1
2
1
0
1
1
1
1
1
1
2
1
1
1
2
1
2
1
0
1
0
1
1
1
1
2
2
0
1
1
2
1
1
0
0
1
0
1
1
1
0
1
0
0
1
2
1
1
0
0
0
1
1
1
3
1
3
2
2
1
1
0
1
1
0
2
0
1
2
1
1
1
1
1
1
0
2
0
1
1
1
1
1
2
1
0
1
1
1
1
1
1
2
0
1
1
0
1
2
2
0
0
11
1
1
0
1
2
1
1
1
0
1
1
1
1
2
1
1
1
1
0
0
1
1
1
1
1
1
0
1
2
1
1
1
1
0
1
0
0
2
2
1
0
1
0
0
1
1
1
0
2
1
1
0
1
1
2
1
1
1
1
1
1
2
1
2
0
2
1
0
1
0
1
1
0
2
0
1
0
2
2
0
0
1
2
1
2
0
1
2
2
1
0
2
0
2
2
1
1
1
1
2
1
1
0
2
0
1
0
0
1
1
2
1
0
2
0
1
1
2
1
1
1
1
0
1
1
0
1
1
1
0
1
2
1
1
0
2
2
0
1
1
2
0
2
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
0
0
1
2
2
1
2
0
0
1
0
2
1
0
2
1
1
1
2
2
0
0
1
1
0
0
1
1
2
0
2
2
2
1
2
1
2
1
0
1
0
0
0
0
2
1
2
0
1
1
2
1
1
1
1
1
1
2
2
2
1
1
2
1
0
1
2
1
1
1
1
2
0
1
1
1
1
2
1
0
1
3
2
0
0
0
2
1
1
2
2
1
1
1
1
1
1
2
2
3
2
0
1
1
0
0
2
0
1
1
1
0
1
1
0
1
2
1
0
0
2
2
1
1
0
0
0
1
1
0
1
1
1
1
1
2
1
1
0
1
0
0
1
2
1
1
1
2
2
2
1
0
0
2
1
1
1
1
0
2
1
1
2
1
1
0
3
0
1
1
1
1
1
2
1
1
1
1
2
0
2
1
2
1
1
2
1
1
1
2
0
0
0
1
1
1
1
1
0
2
1
2
2
0
1
2
1
1
0
2
1
1
1
1
1
0
4
2
1
2
2
0
1
2
4
1
0
1
1
0
1
1
1
1
2
2
0
1
2
1
0
1
1
1
2
1
1
1
2
4
1
1
1
0
2
0
1
1
1
0
1
1
2
0
1
2
1
1
2
1
2
0
2
2
0
0
2
1
1
1
0
1
0
1
2
0
0
1
0
2
1
1
1
0
0
1
1
1
1
1
1
0
1
1
2
2
1
1
1
1
1
0
1
0
1
1
1
0
1
1
1
1
0
1
1
2
1
1
0
1
1
0
0
2
1
0
1
1
1
0
1
0
0
1
1
2
1
2
1
1
2
0
1
2
2
1
1
1
2
2
0
1
2
2
2
1
2
1
1
0
0
1
2
2
1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
1
2
0
2
1
1
2
2
0
2
1
1
2
0
1
1
1
0
1
2
1
1
1
2
1
1
1
2
1
2
1
1
1
2
1
1
1
2
1
2
0
1
1
1
1
1
1
1
1
3
0
0
1
1
1
1
0
1
2
1
1
1
1
1
1
1
0
2
0
1
1
1
1
2
2
2
2
1
2
1
2
1
1
2
0
0
0
1
1
2
0
0
0
1
1
1
2
1
1
1
2
1
1
0
2
0
1
1
1
2
1
1
1
1
1
1
2
1
1
2
1
1
1
0
1
1
2
0
2
1
1
1
1
1
0
2
1
1
2
1
1
2
1
0
1
1
1
0
2
0
0
2
1
1
1
2
1
1
2
0
2
0
1
0
1
1
0
2
1
0
1
1
2
1
2
1
1
1
1
1
1
1
0
2
0
1
1
1
1
1
1
1
2
1
2
0
1
1
1
1
1
0
2
0
2
0
2
1
0
1
1
1
1
2
1
1
0
1
1
2
1
0
1
1
1
1
0
1
1
1
1
1
1
1
2
1
2
0
1
1
1
0
0
1
1
2
2
0
1
1
2
2
1
1
2
2
1
0
2
1
1
0
1
0
1
1
2
0
0
2
2
1
1
1
1
1
0
1
1
1
2
0
1
1
1
1
2
1
2
1
1
0
1
1
2
2
0
2
1
0
0
0
1
2
1
2
2
0
1
0
1
1
0
0
2
0
1
1
1
0
2
1
1
1
2
2
1
1
2
1
1
2
1
0
0
2
0
1
1
0
1
1
1
0
1
0
0
1
2
2
1
0
1
2
1
1
1
2
1
2
1
0
1
2
0
2
1
2
1
1
2
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
0
2
0
0
2
2
1
0
1
1
1
0
0
1
2
1
0
1
1
1
1
1
0
1
0
0
0
0
1
1
2
1
1
2
0
1
2
2
1
2
1
1
1
2
0
3
2
0
1
1
0
1
1
1
2
0
0
0
1
1
1
1
1
2
1
1
1
1
2
1
2
1
1
2
1
2
1
0
1
0
1
0
0
0
1
0
1
0
0
1
1
1
1
1
1
2
3
1
0
2
2
2
1
1
2
1
1
1
1
0
1
2
1
1
1
1
2
1
1
2
1
2
1
1
0
2
0
0
1
1
1
1
1
1
1
2
3
0
2
2
1
1
0
0
1
1
0
0
1
1
0
2
0
1
0
2
2
0
2
0
3
0
2
2
1
1
1
1
2
1
2
2
0
1
1
1
2
1
1
1
2
0
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
2
2
1
0
1
1
0
1
1
1
0
2
2
2
1
1
1
1
1
2
1
2
2
0
1
1
1
1
1
2
1
1
1
1
1
1
0
2
1
1
1
2
1
1
1
2
1
1
1
1
1
0
1
1
1
1
0
3
1
0
1
1
1
2
1
1
1
2
1
1
1
0
2
0
1
2
1
1
1
1
2
1
0
1
1
1
0
1
1
1
1
1
1
1
0
2
1
2
0
0
1
1
1
1
2
1
1
1
0
1
0
0
1
0
1
3
0
2
1
2
1
2
0
1
1
2
1
1
0
2
0
2
1
0
1
1
2
1
1
1
2
1
2
0
1
1
0
1
1
2
0
1
1
1
1
1
2
2
0
1
2
1
1
1
1
2
1
1
1
1
2
1
2
0
0
1
1
1
1
0
1
1
1
2
1
2
2
0
1
1
0
0
1
1
1
1
1
1
2
1
1
1
0
2
1
1
1
1
1
0
1
1
7
1
1
0
0
2
1
1
2
1
0
0
2
1
2
0
1
1
1
0
2
0
1
0
1
2
1
2
3
2
1
0
1
0
1
0
2
0
0
2
2
1
1
0
1
1
0
1
1
2
1
0
1
0
1
1
0
1
2
0
0
1
1
1
1
2
1
1
2
1
1
1
1
0
1
2
2
2
2
2
2
1
1
1
1
1
2
1
1
0
1
0
0
1
0
1
2
1
1
1
0
0
1
1
1
1
1
0
1
1
1
0
1
2
1
1
2
1
1
2
2
1
2
1
2
1
1
1
2
0
0
1
1
2
0
2
0
0
1
1
1
2
1
1
1
7
0
1
1
1
1
1
1
1
2
1
1
0
2
2
1
2
1
1
0
0
1
1
0
2
0
0
1
1
0
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
0
1
1
1
0
1
1
2
2
1
1
2
1
1
1
0
2
2
0
1
0
0
2
1
1
2
1
1
2
2
3
2
1
1
1
1
1
1
0
1
1
1
1
1
0
2
1
0
1
1
1
1
0
1
1
0
1
1
1
1
2
0
1
2
1
1
1
1
2
2
0
1
1
0
2
1
1
2
1
1
1
1
0
2
0
1
2
1
2
1
1
2
1
1
0
2
1
2
1
2
0
1
1
1
1
1
2
1
2
1
1
2
2
2
2
0
1
1
1
2
0
1
1
1
1
1
2
1
0
1
2
0
0
1
0
0
1
2
0
1
2
1
2
1
1
1
0
2
1
0
0
0
1
1
1
0
1
1
2
1
1
2
1
1
2
0
2
0
1
1
1
0
0
1
1
2
0
1
2
1
1
1
1
2
0
0
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
2
2
1
0
1
1
1
1
3
2
0
0
0
2
1
1
0
1
0
0
1
2
1
1
0
2
2
1
1
0
1
0
2
1
1
1
0
2
0
2
1
1
2
1
2
1
1
1
2
1
2
1
1
1
1
1
2
0
0
1
1
2
2
1
1
0
1
1
1
1
1
0
1
2
1
2
2
1
1
1
2
1
1
0
2
1
2
1
1
1
1
1
1
1
1
2
0
2
1
1
2
1
1
0
1
1
2
0
2
1
2
2
0
1
1
0
0
1
1
1
1
2
0
1
0
1
1
1
1
3
0
1
1
1
2
1
1
1
1
1
0
1
1
2
2
1
2
2
0
1
1
0
2
1
0
1
2
0
1
1
1
2
2
1
0
1
1
1
1
1
1
1
2
0
0
2
2
2
1
1
0
0
1
1
2
1
1
1
1
0
2
1
2
1
1
1
2
1
2
1
1
1
1
1
0
1
1
0
0
1
0
0
2
0
1
0
1
2
1
1
1
2
2
1
2
0
1
2
1
2
1
1
2
1
2
2
0
2
2
2
0
2
1
3
1
0
1
1
2
0
1
0
5
2
1
1
1
0
0
1
1
2
1
1
0
2
2
1
1
1
1
0
1
1
1
1
1
0
1
1
2
0
1
2
2
1
1
1
1
2
1
1
2
1
2
1
2
1
1
1
1
1
1
1
0
1
1
1
1
0
2
1
1
1
2
0
1
2
2
1
1
1
1
0
1
1
1
1
2
1
2
1
0
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
0
2
1
0
1
1
1
2
2
1
2
0
0
1
1
0
1
2
0
2
1
0
1
2
1
1
2
1
1
1
1
1
0
1
1
1
2
1
1
2
1
1
0
2
0
1
1
2
2
2
2
1
2
1
2
2
0
2
1
1
0
0
1
0
1
1
1
1
1
2
1
1
1
1
2
1
0
1
1
1
0
1
0
0
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
0
1
2
2
1
1
1
1
2
1
0
2
2
1
1
1
1
3
2
0
1
1
2
2
2
1
0
2
1
1
1
1
1
1
1
1
2
1
1
0
2
2
0
1
0
0
1
1
1
2
1
1
2
0
0
0
0
1
2
1
0
1
0
2
0
0
1
1
1
1
1
1
2
1
1
2
1
2
1
1
0
1
0
2
0
0
1
0
1
0
2
1
1
1
2
2
0
1
1
1
2
2
0
1
1
1
1
1
1
1
1
0
1
0
2
1
2
1
2
2
1
2
1
1
2
1
1
1
1
1
1
0
4
1
2
2
1
0
1
1
2
2
1
1
1
0
2
1
2
2
0
1
1
0
1
1
1
3
1
1
1
0
1
1
0
0
0
0
1
1
2
0
1
1
1
1
1
1
1
2
0
1
1
1
2
0
1
2
1
0
0
1
0
1
0
1
1
0
1
0
1
1
2
1
0
1
1
0
2
0
1
1
1
0
1
1
2
1
1
1
2
1
2
1
1
1
0
1
1
2
2
1
1
1
2
1
1
0
1
1
3
1
1
1
1
1
0
1
1
1
0
1
1
0
1
1
2
2
1
2
1
1
1
1
1
1
1
0
1
0
1
0
0
2
1
1
2
1
0
2
1
1
1
2
1
1
0
2
1
2
1
1
1
1
1
1
1
2
1
1
2
2
1
2
2
1
1
1
0
1
1
1
1
1
1
1
0
1
1
1
1
1
1
2
0
0
2
1
1
1
2
0
2
1
2
1
2
2
0
1
2
0
1
1
1
1
0
1
1
1
2
2
2
2
1
2
1
0
1
2
1
1
1
1
1
0
2
1
1
3
0
1
1
0
2
1
1
0
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
1
1
1
1
1
2
1
1
0
1
2
2
1
0
0
1
1
0
0
1
1
2
1
1
2
1
1
1
1
1
2
1
1
1
0
1
2
1
2
2
1
0
0
1
1
1
2
2
1
1
0
1
1
0
1
1
1
1
0
1
1
2
1
0
1
1
1
1
1
0
1
1
0
3
0
1
1
2
0
1
2
0
1
1
2
1
0
0
1
1
2
1
0
1
1
1
0
2
2
1
1
1
2
1
1
1
1
1
0
1
1
1
1
0
1
1
1
2
1
2
1
2
1
2
0
1
0
1
1
2
1
1
2
0
1
1
1
1
2
2
1
1
0
1
0
2
1
1
1
1
2
0
1
1
0
2
1
1
1
1
0
1
1
2
1
2
1
2
2
0
1
1
2
2
1
1
2
2
0
2
1
1
0
1
2
1
1
1
1
0
0
2
0
1
1
1
1
2
1
1
2
1
2
0
2
1
2
1
2
2
1
1
0
2
2
1
1
1
1
1
1
1
0
1
1
1
2
1
0
2
1
1
0
0
0
1
2
1
1
0
1
1
2
0
1
2
2
2
1
0
1
2
1
2
1
2
1
1
1
2
1
1
0
1
2
0
1
2
1
1
1
1
0
2
0
1
1
1
2
1
1
1
0
0
1
0
1
0
1
1
1
1
2
2
2
2
1
0
1
1
2
2
1
0
0
1
1
0
2
2
1
2
1
0
0
1
1
1
2
1
1
1
0
1
0
0
1
2
1
1
2
2
1
1
1
1
1
1
2
0
1
1
1
2
0
1
0
1
0
2
0
1
2
0
1
1
1
1
1
2
1
0
1
2
1
2
2
1
2
1
0
2
0
1
1
3
2
0
2
1
2
2
2
1
1
1
1
1
1
1
1
1
0
2
1
1
1
2
1
1
2
1
2
2
1
2
2
1
1
1
1
1
1
2
2
2
0
1
1
1
1
2
1
1
1
2
1
2
1
1
1
2
1
1
2
1
1
0
0
2
0
1
1
2
2
1
1
1
1
0
1
1
0
1
1
1
1
1
1
2
1
2
1
0
5
2
1
0
2
0
1
1
2
1
0
2
1
1
0
0
1
1
1
1
1
0
0
2
2
1
1
2
1
0
3
2
1
0
2
2
1
1
1
1
2
1
1
0
0
1
2
0
1
0
2
0
2
2
2
1
2
2
1
1
1
1
2
2
1
1
1
0
1
0
1
1
1
0
1
1
1
2
1
2
1
0
1
2
1
2
1
1
0
3
1
2
1
1
1
1
1
1
1
1
1
1
0
2
0
1
1
2
0
0
1
0
1
1
2
1
1
2
1
2
1
1
1
1
2
1
1
1
1
2
0
2
1
0
1
1
1
2
1
2
1
1
0
1
0
2
1
1
2
3
2
1
0
2
2
1
1
1
2
0
2
2
2
1
1
1
1
0
2
1
1
1
2
1
0
1
2
1
2
1
1
0
1
1
0
1
2
0
0
1
1
1
1
2
2
1
1
2
0
1
1
1
0
2
0
0
1
1
2
1
0
0
2
1
1
2
0
0
0
1
1
0
1
2
2
1
0
1
2
1
2
2
2
1
1
1
0
1
0
1
0
1
1
1
2
1
2
1
1
0
1
1
1
1
1
0
0
1
2
1
1
1
1
1
1
0
1
1
1
1
0
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
0
1
1
0
1
0
2
1
1
1
2
1
0
1
0
2
1
2
1
1
0
1
2
1
0
1
1
2
1
1
2
2
1
1
1
1
0
1
2
0
2
1
1
1
2
1
4
2
2
1
0
1
1
2
0
2
0
2
1
1
1
1
1
2
1
1
2
1
1
2
1
2
2
1
1
2
1
2
1
1
1
1
2
1
1
2
0
1
1
2
1
1
1
1
1
1
0
2
1
1
0
1
0
1
1
2
1
1
2
2
1
1
1
1
1
0
0
2
0
2
0
1
2
2
1
1
2
1
2
1
0
2
1
2
1
2
0
1
1
0
1
0
2
0
0
1
0
1
1
1
0
1
1
2
1
1
1
1
1
1
0
3
0
1
2
1
1
0
1
1
1
0
0
1
1
2
0
2
1
1
0
2
1
1
0
1
1
1
1
0
0
1
2
0
2
1
1
1
1
2
1
2
1
2
1
0
2
1
1
0
1
1
1
2
1
2
1
1
0
0
1
1
2
2
1
1
0
1
0
1
1
0
0
1
1
0
2
1
1
0
1
1
1
2
1
1
2
1
0
1
1
2
0
0
1
2
1
1
1
0
1
0
1
1
1
1
1
1
2
1
2
2
1
0
1
0
1
1
1
2
2
1
1
2
0
1
1
1
2
2
2
0
1
1
2
2
2
2
0
0
0
1
1
0
1
1
1
1
0
1
1
1
1
1
1
0
1
1
0
1
1
2
2
1
1
3
0
0
1
1
2
2
1
1
1
0
2
1
1
2
1
1
2
0
0
2
0
1
1
0
2
3
0
0
7
0
1
1
1
0
0
0
1
1
1
0
1
2
3
2
2
1
1
1
0
1
1
0
1
1
1
0
0
1
2
0
1
2
0
1
2
1
0
0
1
1
1
1
1
0
0
1
0
1
0
1
2
1
2
1
1
1
1
1
2
2
1
1
0
0
1
1
1
1
0
2
1
2
1
1
2
2
1
1
0
2
3
1
0
1
2
1
0
1
0
2
0
1
1
1
1
1
2
1
1
0
2
1
1
1
1
0
1
0
2
1
1
1
0
2
0
1
0
2
1
2
1
2
1
1
1
1
1
2
1
1
0
1
1
0
1
2
2
2
2
1
1
0
2
2
1
2
1
1
1
1
1
2
1
0
1
1
1
1
1
1
2
0
1
1
2
1
1
0
1
1
1
1
2
1
1
0
2
2
2
1
1
2
0
1
1
1
1
1
1
0
1
0
1
1
1
1
1
1
1
1
1
1
2
0
1
1
1
1
1
0
1
2
1
1
1
2
0
1
0
0
1
1
1
1
1
0
0
1
1
2
1
2
1
1
1
0
1
2
2
1
0
2
2
0
1
1
0
2
1
1
0
1
1
0
2
1
0
0
1
2
0
1
1
1
2
1
1
1
1
1
1
1
1
0
1
2
1
1
2
1
0
1
1
1
0
0
1
1
0
1
1
1
0
2
1
1
0
0
1
2
0
0
1
0
1
1
1
0
1
1
1
1
1
1
1
2
1
0
1
0
1
1
2
1
1
1
1
0
2
1
1
1
1
0
1
2
1
1
0
2
1
1
2
1
1
0
1
2
1
0
1
0
0
1
2
1
1
1
2
2
1
1
1
1
0
1
2
0
2
2
2
1
1
1
2
1
2
2
1
2
2
1
1
1
1
0
3
0
1
1
1
1
1
2
1
0
2
0
2
2
1
0
1
1
2
1
1
1
1
1
1
1
2
2
2
1
1
2
1
2
1
1
0
2
1
1
1
2
2
1
1
0
1
0
1
2
1
2
2
1
0
1
3
1
1
1
1
1
1
2
2
1
1
2
1
2
1
1
1
1
1
2
1
1
2
1
0
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
0
1
1
2
0
0
1
0
1
0
2
2
1
2
1
1
1
0
1
1
1
1
1
1
0
1
0
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
2
2
1
1
1
1
0
1
0
1
0
0
2
1
1
1
2
1
1
0
1
2
2
1
4
1
2
2
1
1
1
2
1
1
1
1
0
0
0
1
1
2
2
1
1
1
0
1
1
1
1
1
1
1
0
1
1
1
1
0
2
0
1
1
1
0
1
2
1
1
1
0
2
2
1
0
1
1
1
1
0
1
2
1
2
2
2
1
0
1
2
1
0
0
1
0
0
2
0
1
2
1
0
2
1
1
1
2
1
1
2
1
1
1
1
2
2
1
1
2
1
1
0
0
2
1
1
2
1
0
0
1
1
1
2
1
1
1
1
1
1
0
0
0
1
1
1
0
1
2
0
2
0
1
1
2
1
3
0
1
1
1
1
1
0
1
0
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
2
0
2
1
0
1
0
1
0
2
1
1
1
2
1
2
0
1
0
2
1
1
1
1
1
2
0
2
1
0
2
2
1
1
0
0
1
1
1
1
1
0
1
0
1
1
1
0
1
1
1
0
1
1
1
0
1
1
1
1
1
0
1
1
0
2
1
0
2
2
0
0
2
1
1
1
1
1
1
1
1
0
1
1
1
1
1
2
1
0
1
1
1
2
2
0
1
1
0
1
1
1
0
0
1
2
0
1
1
1
1
1
2
1
2
0
2
2
2
1
2
1
1
2
1
2
1
0
1
0
1
2
0
1
1
1
1
2
1
1
2
1
1
2
1
0
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
0
2
2
2
1
1
1
1
3
4
1
2
1
1
1
3
1
1
1
1
1
0
1
2
0
0
0
1
1
1
1
1
1
1
1
2
1
1
1
0
1
1
2
1
1
0
1
2
0
1
1
1
1
1
0
2
1
1
0
1
1
1
1
1
1
0
1
1
1
1
1
2
1
1
1
1
1
1
1
0
0
0
0
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
0
2
2
1
1
2
1
0
1
1
0
1
1
1
1
1
2
0
1
1
2
2
2
1
1
2
1
1
2
2
1
1
1
2
2
0
2
1
2
1
1
1
1
2
2
1
1
1
2
2
1
2
1
1
1
0
0
1
2
1
1
0
1
1
1
0
0
1
1
1
1
2
2
2
1
1
2
1
0
1
0
1
2
1
2
0
2
1
1
0
1
0
1
1
0
1
0
1
2
2
0
1
1
1
2
1
1
1
1
1
1
1
1
3
1
1
1
1
1
1
1
1
1
2
1
2
1
1
0
1
1
1
2
0
1
1
2
1
2
2
0
2
2
1
1
1
1
2
1
2
1
3
1
2
2
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
0
1
2
1
0
2
0
2
1
1
0
1
1
2
1
2
0
1
1
1
1
1
0
0
2
1
2
2
1
0
0
2
1
2
1
1
0
1
1
1
1
2
2
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
2
0
1
1
0
1
2
1
1
1
1
2
1
0
1
1
1
2
0
2
1
1
1
0
1
2
1
1
1
1
1
0
1
1
1
1
0
1
1
1
1
0
1
2
1
1
0
2
1
0
2
2
0
2
1
1
1
2
1
2
1
4
0
2
1
1
0
0
0
1
1
2
1
1
2
1
1
1
1
0
0
1
2
1
1
1
1
2
0
1
2
1
0
1
1
1
2
1
1
1
1
0
1
2
2
2
2
2
0
1
2
2
2
2
0
1
1
2
0
1
1
1
1
1
2
1
1
1
2
1
1
1
2
2
1
0
1
2
1
1
2
0
1
0
0
2
1
2
2
0
1
1
0
0
1
1
1
1
0
0
0
1
1
2
0
1
1
2
1
1
2
1
1
2
2
2
1
1
1
1
1
2
2
1
1
1
2
0
1
1
2
2
1
1
1
1
1
2
2
2
0
1
0
0
1
2
1
1
2
2
1
1
3
2
2
1
1
2
2
3
2
0
1
1
1
1
1
1
0
1
1
1
1
1
0
1
2
1
2
2
1
1
1
0
1
1
0
1
1
1
0
0
1
0
1
1
1
1
2
2
0
1
1
1
2
1
2
1
1
1
1
1
2
1
0
2
1
1
1
0
1
1
1
0
2
1
2
2
0
0
1
1
2
1
1
1
1
1
0
1
1
2
1
1
0
0
1
2
1
2
2
1
1
1
2
2
1
0
0
0
2
1
1
1
1
2
2
2
1
2
1
2
0
1
1
1
2
1
1
1
1
0
2
1
1
0
1
1
1
1
0
1
0
1
1
1
0
2
1
1
1
2
1
1
1
1
1
0
0
0
1
2
0
1
1
2
2
1
0
1
1
1
1
1
1
1
0
2
1
1
1
0
2
0
1
1
2
1
2
0
1
1
0
1
2
1
2
2
1
0
2
1
1
1
1
0
1
1
1
2
2
0
1
1
2
1
1
1
1
2
1
1
0
1
1
1
2
1
1
0
3
0
0
2
0
1
1
2
1
2
1
1
0
0
2
1
0
2
1
1
1
1
1
1
1
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
0
2
1
1
1
0
1
0
1
0
1
1
1
1
1
1
2
2
0
1
1
2
2
0
2
1
1
0
1
2
2
2
1
1
1
1
1
1
0
0
1
1
1
2
1
1
1
0
1
1
0
1
1
0
1
0
2
1
1
2
1
0
1
2
0
1
1
1
2
1
0
1
1
1
1
1
1
2
2
0
0
1
0
1
1
1
2
2
1
2
0
1
2
2
1
2
1
0
1
1
1
1
2
1
2
1
2
1
1
0
1
0
1
1
1
1
2
1
0
0
2
2
0
0
1
2
1
1
1
0
0
1
2
1
1
1
1
1
1
0
0
0
1
2
1
1
1
2
1
0
1
1
2
1
2
0
1
2
2
0
2
2
0
2
2
2
1
1
2
1
2
1
0
1
1
1
3
2
1
2
1
0
2
1
0
1
1
1
1
2
1
1
1
0
1
0
0
2
2
1
0
2
1
0
1
1
0
1
0
2
1
1
1
1
1
2
1
0
0
1
1
1
0
2
1
3
1
2
1
1
1
0
1
1
1
1
1
1
2
1
2
1
0
1
1
1
2
0
1
1
1
2
0
1
1
1
1
1
2
1
2
1
1
0
0
1
0
1
1
1
0
1
1
1
1
1
1
1
1
1
2
1
1
0
0
0
1
1
1
0
1
1
0
1
1
0
2
2
0
1
1
1
1
1
1
0
1
0
1
1
0
1
2
0
1
2
1
1
2
0
1
2
1
1
2
1
1
0
0
1
1
2
1
0
1
2
2
1
1
1
1
1
2
0
0
2
1
1
2
1
1
1
1
1
1
1
2
1
1
2
2
2
0
1
1
2
2
0
0
1
1
1
2
2
1
2
2
2
1
0
1
0
0
1
1
2
1
2
2
0
1
3
2
0
1
0
1
0
1
1
1
2
1
2
1
2
1
1
1
1
1
1
1
2
0
1
1
2
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
1
2
1
1
1
2
1
0
1
0
1
1
0
1
0
1
1
3
1
1
1
1
1
1
1
1
1
2
1
2
2
0
1
1
1
1
2
2
2
1
1
2
1
1
0
0
2
1
1
2
1
1
0
1
1
1
1
0
1
2
1
2
1
1
1
1
2
0
1
1
0
2
1
1
1
1
1
1
2
0
1
1
1
1
1
1
2
2
0
1
1
2
1
1
1
1
1
2
1
2
0
0
1
1
1
1
1
1
0
2
0
1
1
1
1
1
1
2
2
1
0
1
0
2
0
2
1
1
1
2
1
2
1
3
1
1
1
1
1
2
0
0
1
1
1
0
1
0
0
0
1
0
2
0
2
1
1
1
0
1
1
1
0
2
0
1
1
0
1
2
2
1
1
1
1
1
1
2
1
2
2
1
0
1
1
1
1
0
1
1
2
2
1
2
2
0
2
1
1
1
1
0
1
1
2
1
1
1
1
2
1
1
2
1
0
1
0
0
1
1
1
0
1
2
2
1
1
1
2
1
1
1
0
0
0
2
1
0
1
0
0
1
1
1
1
2
1
1
2
0
1
1
1
0
0
0
2
1
1
0
1
0
2
2
1
1
1
2
1
1
1
1
1
1
2
1
2
1
1
1
0
0
1
1
2
1
1
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
3
1
3
1
0
0
2
0
2
0
0
2
0
1
2
1
1
1
1
1
1
1
1
1
1
1
0
1
2
0
0
0
2
1
0
1
1
2
0
1
1
1
2
1
1
1
1
1
0
2
1
0
1
0
1
0
1
1
1
0
1
1
2
0
1
0
1
2
0
2
1
1
0
2
2
0
1
1
1
1
1
2
0
1
1
0
0
1
2
1
1
1
2
1
1
1
2
2
0
0
2
1
1
2
1
1
1
1
1
0
0
1
1
1
2
1
1
1
1
1
2
0
1
1
1
1
1
1
1
2
1
0
1
2
2
1
2
0
2
1
2
2
2
1
1
1
0
2
1
2
2
0
2
0
0
1
2
0
0
0
2
1
1
2
1
2
2
0
0
2
0
1
0
1
1
1
1
1
2
1
2
0
2
1
1
1
0
1
1
2
0
2
1
1
0
0
0
2
1
0
1
1
1
2
1
2
1
1
1
0
1
2
1
0
2
1
1
1
1
1
1
1
1
1
2
1
1
1
0
0
1
1
1
1
1
1
1
1
1
2
0
2
1
2
0
1
1
1
1
1
0
2
1
1
1
1
2
1
2
0
0
1
1
0
1
1
1
2
1
1
2
0
2
1
0
1
1
1
0
2
0
0
1
1
1
2
1
1
0
1
1
1
2
1
0
0
2
1
1
1
1
1
0
1
1
1
0
0
1
2
1
2
2
1
2
1
1
2
1
1
0
2
1
1
1
2
1
1
2
3
3
1
1
0
1
2
2
0
2
1
2
2
2
1
2
2
2
2
0
1
0
0
2
0
0
2
2
3
0
2
1
1
0
1
2
2
1
1
1
0
2
1
0
1
1
2
2
2
0
1
3
1
2
2
1
1
1
2
0
1
1
2
0
0
1
1
0
1
2
1
1
1
1
1
0
2
2
1
1
1
1
0
1
1
1
2
1
2
0
2
2
1
1
1
0
1
1
2
1
0
1
1
1
1
0
2
2
1
0
1
1
2
0
1
1
1
1
2
1
0
1
1
2
0
2
1
1
2
1
1
0
1
0
0
1
0
1
2
1
1
1
0
1
1
2
2
0
2
2
1
1
2
1
1
2
1
3
2
0
1
1
0
0
0
1
1
1
1
2
2
1
0
1
1
1
0
1
2
1
1
1
0
1
5
0
0
2
2
2
0
1
2
1
1
1
1
1
2
2
1
1
1
1
2
1
1
1
2
0
1
1
1
1
1
1
0
1
1
0
1
1
0
2
0
1
2
1
1
0
2
1
1
1
2
0
1
0
2
2
1
1
2
1
1
1
1
1
2
0
1
1
0
2
1
2
1
0
1
2
0
1
0
1
2
0
1
2
1
1
1
0
1
0
1
2
1
1
1
1
0
0
1
1
1
2
1
1
0
0
0
0
1
1
1
1
0
1
0
1
1
1
0
4
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
0
1
1
1
1
1
1
1
0
2
1
1
0
1
2
1
0
1
2
3
1
2
2
0
1
2
0
1
0
1
2
2
1
2
0
1
0
2
1
1
1
2
1
1
1
1
0
1
1
1
0
1
1
1
2
1
2
1
1
1
1
1
2
2
2
2
2
0
0
1
1
1
1
1
1
1
1
1
0
1
1
1
1
0
1
1
1
2
2
1
2
2
1
1
1
1
1
1
2
1
2
1
1
1
2
2
1
1
0
1
0
1
1
1
2
2
2
1
1
1
1
1
1
1
0
0
1
2
1
1
1
1
1
1
2
1
0
0
0
0
1
0
0
1
1
2
0
1
1
1
0
1
1
0
1
1
1
0
1
1
0
1
0
0
1
2
1
0
0
0
2
1
2
1
1
2
1
0
1
2
1
2
2
1
1
2
1
2
1
2
1
2
1
1
1
1
1
0
0
1
2
0
1
1
1
1
2
1
1
0
1
2
1
2
2
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
0
1
2
0
1
1
1
2
1
1
1
1
1
2
2
2
1
1
0
2
2
1
1
0
1
2
0
2
1
3
1
1
2
1
2
1
2
1
0
1
1
1
1
1
2
0
1
2
1
1
1
1
2
2
2
2
1
2
1
0
2
2
1
1
1
1
1
1
2
0
2
0
1
1
1
2
2
1
1
1
1
1
1
2
1
0
1
1
2
1
1
1
1
1
1
1
1
1
1
1
0
1
1
2
1
1
2
1
1
1
1
1
1
1
0
1
0
1
1
1
1
1
0
1
1
1
2
0
2
0
0
0
2
1
1
2
0
1
1
1
1
2
2
2
0
2
0
1
2
2
1
1
1
1
2
1
0
1
2
1
1
1
1
1
0
1
1
1
2
1
0
1
2
2
1
1
1
1
2
1
1
2
1
2
0
2
0
1
1
2
1
1
1
2
1
2
2
0
1
2
1
2
1
2
0
2
1
0
1
1
1
0
1
1
1
2
1
1
1
1
0
1
0
1
1
1
1
2
1
2
1
1
1
1
2
1
1
2
1
0
1
0
1
0
2
1
1
0
1
0
2
1
1
1
1
1
1
1
0
1
1
1
2
1
1
1
1
1
0
2
0
2
1
1
1
1
1
1
1
1
2
1
2
1
2
1
0
1
0
1
1
2
1
1
0
1
0
0
1
1
0
1
1
1
0
2
1
1
0
1
1
1
1
1
1
0
1
1
1
1
1
1
0
1
0
1
0
1
1
1
2
1
2
1
1
2
1
2
2
1
0
0
1
1
2
0
0
2
1
1
1
2
0
1
2
1
0
1
0
2
1
2
1
0
2
0
1
1
1
1
1
1
1
0
1
1
1
2
2
1
2
1
1
2
1
2
0
0
1
1
2
2
2
3
1
1
1
1
1
1
2
1
0
0
2
2
1
2
1
2
0
1
1
1
2
1
1
1
1
2
2
2
1
0
1
1
2
1
2
0
1
1
2
1
1
2
2
1
1
2
0
0
1
0
1
2
2
0
2
1
1
0
1
1
1
1
2
1
0
1
0
1
1
1
1
1
0
0
1
1
1
2
1
2
0
1
1
1
2
1
0
1
0
1
0
1
1
1
1
2
1
0
0
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
2
2
2
1
2
2
1
2
1
1
0
1
1
2
1
0
0
2
1
2
2
1
1
2
0
1
1
0
1
1
1
1
0
1
1
1
2
0
1
1
2
1
1
1
0
2
1
1
1
1
0
1
1
1
2
0
2
2
0
1
1
1
1
2
1
2
2
1
1
1
0
0
1
1
2
0
0
1
0
1
1
1
0
0
1
1
1
1
2
1
1
1
1
2
1
2
1
1
2
1
1
1
1
0
1
0
0
1
0
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
0
2
0
0
0
0
2
0
2
1
1
2
1
0
2
1
2
1
1
0
2
3
1
2
1
1
1
1
0
1
2
1
1
1
2
1
2
0
1
1
1
1
0
1
1
0
2
2
2
0
2
2
1
0
0
0
1
2
1
1
2
2
2
1
1
2
0
0
1
2
2
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
9
1
1
1
1
1
2
2
0
1
2
2
0
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
0
1
1
0
2
1
1
2
1
0
0
1
2
0
1
2
1
0
1
1
2
1
0
2
2
1
1
2
1
1
1
0
1
1
1
2
1
2
2
0
0
1
2
2
1
3
1
0
0
1
0
0
1
1
1
2
0
1
2
2
1
1
2
5
1
2
1
2
1
1
0
1
1
2
1
2
2
1
1
2
2
1
2
2
1
1
2
2
1
1
1
2
1
1
1
1
2
1
1
1
1
1
2
1
2
0
0
2
2
1
1
1
2
1
1
1
0
1
2
1
1
1
1
1
2
1
2
1
1
1
0
0
2
2
2
0
1
0
3
2
2
2
2
2
1
1
1
1
1
1
2
1
1
0
2
1
1
0
1
2
1
1
0
2
1
0
0
0
2
1
2
1
1
1
1
1
1
1
3
1
0
1
1
1
2
1
0
2
0
1
2
1
2
2
1
2
0
1
0
1
1
1
1
1
4
2
1
1
0
1
1
2
1
2
1
1
2
1
1
1
1
0
1
2
0
1
0
2
0
0
2
2
0
1
2
2
0
1
1
1
1
2
4
2
2
1
2
1
1
0
1
2
1
1
1
1
2
1
1
1
1
1
1
0
1
1
0
1
0
2
2
1
1
1
1
1
1
1
1
1
2
2
1
1
0
1
2
1
1
1
1
1
1
1
1
0
0
1
1
2
1
1
2
2
1
0
2
1
1
0
1
1
1
2
1
2
1
1
1
1
1
2
1
1
2
1
1
2
0
1
1
0
2
2
2
0
0
0
1
0
2
1
0
1
2
1
2
1
1
1
0
0
1
2
1
1
1
1
0
1
1
1
0
1
2
0
1
1
1
2
1
2
1
0
1
2
0
1
0
2
1
1
1
1
2
0
1
0
1
0
1
1
0
1
1
1
1
0
1
1
1
1
1
2
2
2
2
1
0
1
1
0
1
1
2
1
1
1
2
2
1
1
1
0
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
0
2
1
0
0
1
0
2
2
0
0
2
1
1
1
2
1
1
1
2
1
1
1
2
0
1
1
0
2
2
0
1
1
1
1
1
1
0
1
1
2
0
2
0
1
2
1
1
1
0
1
1
2
1
1
1
3
1
1
1
2
1
1
2
2
2
2
1
1
1
2
2
2
2
0
1
2
2
1
1
0
1
0
1
1
1
1
1
0
1
0
1
1
2
1
2
2
0
0
1
1
2
1
2
1
1
1
1
2
2
0
0
0
2
0
1
2
1
0
2
0
0
1
2
0
2
1
1
1
0
1
1
1
2
1
1
0
2
1
1
1
1
1
0
0
0
1
0
2
1
1
1
1
2
1
1
1
2
1
1
2
1
0
0
2
1
1
0
1
1
0
2
0
2
1
0
1
2
1
1
1
0
1
1
1
2
0
2
2
1
1
0
1
1
2
0
0
1
2
1
2
1
1
0
1
0
1
0
1
1
2
2
1
1
2
2
1
1
1
1
1
1
0
0
1
1
0
1
2
0
2
2
1
2
0
0
2
1
1
1
1
1
1
2
0
0
0
2
0
0
0
1
0
1
0
1
1
2
1
2
1
2
1
1
2
1
0
1
1
1
1
1
2
1
2
1
2
1
1
0
0
1
1
2
0
1
2
1
1
1
1
1
1
1
1
0
1
2
1
1
1
1
1
2
0
1
1
0
1
0
1
2
0
1
0
1
1
0
2
2
1
1
1
1
1
0
0
1
2
0
1
1
1
1
2
1
1
1
1
2
0
2
1
2
0
1
3
0
0
1
1
1
2
2
1
1
0
1
1
0
1
0
1
1
1
1
2
1
1
2
0
1
2
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
0
1
1
2
1
1
2
1
1
2
1
0
1
0
1
0
2
0
1
1
1
0
0
0
1
1
2
2
2
1
2
1
1
2
0
1
2
0
1
1
2
1
2
1
0
2
0
1
0
1
0
1
1
1
2
2
0
1
1
2
0
1
2
0
2
2
1
1
1
1
2
1
2
1
1
2
2
1
0
2
2
0
1
1
0
1
1
1
1
2
1
2
1
0
1
1
2
2
1
0
1
1
1
1
1
2
1
1
1
1
0
1
0
1
0
0
0
1
1
0
1
2
1
1
0
1
1
2
0
1
1
1
1
1
1
2
2
0
0
1
0
1
1
2
1
2
2
3
1
1
0
0
1
0
1
1
1
1
3
1
1
1
0
2
1
1
2
0
1
1
1
1
1
2
2
1
1
1
1
1
0
2
2
1
1
2
1
3
0
1
0
2
1
1
2
2
1
1
2
1
0
1
1
2
1
1
1
0
0
1
1
1
1
1
0
1
1
1
1
2
1
1
2
2
1
1
1
0
0
2
1
1
1
0
0
2
1
1
0
2
2
0
1
1
1
0
1
1
1
1
2
1
2
1
2
1
1
0
1
0
1
1
1
1
1
2
1
1
1
0
1
1
1
1
1
1
0
1
1
1
1
1
0
2
1
1
1
1
0
2
1
1
1
1
1
1
1
0
0
1
0
1
2
2
2
0
1
1
2
1
1
2
1
1
2
1
2
0
1
1
1
0
0
1
2
0
0
1
0
2
0
1
1
2
0
0
2
1
1
1
0
0
0
2
1
1
1
0
2
1
1
1
2
0
1
1
1
2
1
1
1
3
1
1
1
1
1
1
2
0
1
1
1
1
1
1
1
1
0
1
2
1
1
2
0
0
2
1
2
1
2
0
1
1
1
1
1
0
1
0
1
1
2
0
1
2
2
1
2
2
2
1
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
0
1
1
2
1
1
3
1
0
1
1
0
1
0
0
2
1
0
0
0
1
0
0
1
2
2
2
2
2
0
1
1
2
2
0
1
1
1
3
2
0
0
1
1
1
1
1
1
1
1
1
1
1
0
0
1
2
0
1
1
1
1
1
1
0
1
1
1
1
0
0
0
1
2
1
2
1
1
1
0
2
3
1
0
1
0
2
2
1
2
1
2
1
1
0
0
0
1
1
0
1
0
2
1
0
2
0
0
0
1
1
1
1
1
2
1
0
1
1
1
0
1
2
1
1
1
2
2
0
1
1
1
1
1
1
1
2
1
2
1
1
1
0
2
1
1
1
0
1
0
1
1
1
1
2
1
1
2
2
0
2
1
1
1
1
0
1
0
0
2
1
1
1
1
1
0
2
1
2
0
2
0
1
2
1
2
2
1
1
0
1
0
0
1
1
1
2
0
1
1
1
1
2
1
1
1
0
1
1
1
0
1
1
1
1
1
2
1
2
1
1
1
0
2
1
1
0
0
1
1
1
1
0
2
2
0
2
1
1
1
0
1
1
1
1
1
1
2
1
1
2
0
1
0
0
2
1
2
0
1
1
1
1
1
1
1
1
0
1
2
1
1
1
1
2
1
0
2
1
1
2
1
2
1
0
1
1
2
2
0
1
0
0
1
0
1
1
2
2
2
1
1
1
1
1
1
1
3
1
1
2
1
1
2
2
1
1
2
0
2
0
1
1
1
1
2
1
0
1
2
0
1
1
2
2
1
1
2
1
0
1
1
1
2
1
0
1
1
1
2
1
1
2
1
1
1
1
2
0
1
1
1
1
1
1
1
1
0
2
2
1
1
0
1
2
1
0
2
1
1
1
1
0
1
0
2
0
2
1
1
1
2
1
0
1
0
2
2
2
1
0
1
1
2
1
1
0
1
1
1
1
2
1
2
1
2
5
2
0
2
2
0
1
1
1
2
1
2
2
1
1
1
2
1
1
1
1
1
1
1
1
1
0
1
1
1
1
2
1
1
1
0
1
1
0
3
2
2
1
0
2
2
2
0
0
1
2
1
2
1
0
2
2
2
0
1
2
2
1
1
2
1
1
0
0
2
1
1
1
2
1
1
2
1
2
2
0
0
1
0
1
1
1
2
1
1
1
1
1
1
1
1
0
0
1
0
1
1
2
1
0
1
1
1
0
1
1
1
1
1
1
2
1
1
1
0
1
1
0
1
2
1
2
2
1
2
0
1
1
0
1
1
1
1
2
1
2
0
2
2
2
1
1
1
1
0
0
2
1
1
3
0
0
1
0
1
1
1
1
0
1
0
0
1
2
1
1
0
2
1
1
2
1
1
0
1
1
4
1
1
1
0
1
1
1
2
1
0
3
1
1
2
0
1
1
2
1
1
2
1
2
3
1
1
0
1
2
1
1
1
2
1
1
1
1
0
0
1
2
0
1
1
1
1
2
1
0
1
1
1
0
1
1
0
1
1
1
2
2
0
0
1
1
1
0
1
1
1
1
1
1
1
1
1
2
0
0
1
0
1
2
1
1
2
1
2
1
2
2
2
0
2
1
0
0
2
1
1
0
2
1
0
1
2
2
2
1
2
1
1
1
1
0
1
1
1
1
1
1
2
1
0
2
2
1
1
2
1
1
2
1
2
0
1
2
1
2
1
0
2
1
0
1
1
1
0
2
2
0
1
1
0
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
0
2
0
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
1
0
2
2
1
2
2
1
0
1
1
1
1
1
1
0
0
1
2
1
2
0
1
0
1
0
3
2
1
1
1
0
1
1
0
0
0
1
2
1
1
2
1
2
2
1
0
1
1
1
1
0
1
1
1
2
1
1
2
1
2
1
2
0
1
0
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
0
0
1
1
2
1
1
1
1
1
2
1
1
1
0
1
1
0
1
2
2
1
1
2
0
1
1
1
1
1
0
1
1
2
2
1
1
2
2
2
1
1
1
1
1
0
0
2
1
0
2
1
1
1
1
1
1
0
1
3
2
1
2
1
1
1
1
0
2
1
0
1
1
0
1
1
0
1
0
1
1
0
2
1
1
2
2
0
0
1
2
1
1
2
1
1
1
1
0
2
1
2
1
1
2
1
0
1
1
2
0
0
2
0
0
0
0
1
1
1
0
1
2
1
2
2
3
2
1
1
1
0
3
1
1
2
1
0
1
1
1
1
1
1
1
0
1
1
2
0
1
2
1
1
1
1
1
1
1
0
1
1
2
2
0
1
1
1
1
1
2
0
1
0
2
2
1
1
1
1
1
1
1
1
0
2
0
0
2
1
1
1
1
1
2
1
2
1
2
1
0
1
1
1
1
0
2
1
0
2
2
1
1
1
1
0
2
1
1
0
2
1
1
0
0
0
1
1
1
0
1
1
1
1
0
1
0
1
1
1
0
0
1
1
1
1
1
1
1
2
1
1
1
5
0
2
1
1
1
1
0
0
1
1
1
1
0
0
1
0
1
0
0
2
2
0
1
1
1
1
1
1
1
2
2
1
2
1
2
2
1
1
2
1
1
1
1
2
0
1
0
2
2
2
2
2
2
1
0
0
1
1
1
1
1
1
2
1
0
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
0
1
1
2
1
1
2
1
0
2
1
0
1
1
1
1
0
1
0
1
1
1
2
2
2
0
1
2
2
2
1
1
1
2
0
1
1
1
1
1
0
0
0
0
1
1
2
1
1
2
1
1
0
2
2
1
1
1
2
1
1
1
1
2
2
1
2
0
2
2
2
3
0
0
0
0
2
1
0
0
2
1
1
2
1
1
1
0
1
1
1
1
1
2
0
1
7
1
1
0
1
1
2
0
2
0
1
1
2
0
1
2
1
1
0
1
1
2
2
2
0
1
1
1
2
1
1
1
1
0
1
1
1
1
2
1
1
2
0
1
0
1
1
1
0
1
2
1
1
1
1
0
2
1
1
2
1
1
2
0
0
3
1
2
1
0
0
1
1
1
1
1
1
1
2
1
1
2
1
2
2
1
1
1
2
0
1
0
1
2
2
1
2
1
0
2
0
0
3
0
0
1
1
2
2
2
1
1
1
1
2
1
1
1
0
2
1
2
1
2
1
1
1
1
2
0
1
1
1
2
1
0
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
0
2
1
1
1
1
2
2
0
1
0
0
2
2
2
0
0
1
1
0
2
0
3
1
0
2
1
0
1
0
2
0
1
0
2
2
1
2
1
1
0
2
2
1
1
1
1
1
2
1
0
2
1
0
1
0
0
2
1
1
1
0
1
1
2
1
1
1
2
2
1
1
1
2
0
0
2
2
2
2
1
0
0
4
1
1
2
0
2
1
1
2
1
0
1
1
2
1
1
0
1
0
2
1
2
1
1
2
0
2
1
2
1
0
1
1
1
1
0
2
1
1
2
1
1
1
1
0
2
1
1
1
1
2
0
1
1
1
0
0
1
0
1
1
1
1
1
1
0
3
0
2
0
1
1
1
0
2
1
2
0
1
0
2
1
0
1
1
1
1
1
1
2
0
1
1
1
0
1
1
1
1
0
1
2
0
1
1
0
1
1
1
0
1
2
1
2
1
1
1
1
1
2
1
1
0
1
0
0
0
1
2
2
1
2
1
1
1
1
2
2
1
1
2
2
1
1
1
2
2
1
2
0
1
1
1
1
1
2
1
1
1
0
1
1
0
0
1
0
0
1
4
1
0
0
1
2
1
2
2
0
0
2
2
1
1
2
1
1
1
1
1
2
1
1
1
0
2
2
0
1
1
0
1
2
1
1
2
2
1
1
1
1
1
1
2
1
2
1
1
1
2
2
1
2
0
0
1
0
2
1
2
0
2
1
1
0
1
2
2
1
1
2
0
1
2
0
1
1
1
1
1
1
3
2
1
2
1
1
1
2
1
0
0
0
1
1
2
1
1
1
1
4
1
1
0
0
2
1
1
1
1
1
1
1
1
2
1
1
2
1
0
2
0
1
1
0
1
1
1
2
1
1
2
1
0
2
0
1
1
2
1
0
1
0
0
1
0
1
0
0
0
1
2
0
2
0
1
1
0
1
1
1
0
1
1
1
1
0
2
0
2
1
2
1
2
0
2
2
1
1
1
1
2
1
2
2
1
1
2
0
0
1
2
1
1
0
0
0
0
0
1
1
1
0
1
2
2
2
0
0
2
0
1
1
0
0
1
1
2
1
2
1
0
1
1
1
1
2
2
0
1
1
1
1
2
3
2
0
1
2
0
2
2
0
1
2
2
1
1
1
2
1
1
1
1
1
2
1
1
0
2
2
0
0
2
1
2
2
1
2
2
1
1
2
1
0
1
0
1
1
1
0
1
1
1
1
1
1
1
1
1
1
2
2
1
0
1
2
1
1
1
1
0
0
1
1
2
1
0
1
2
0
1
1
0
1
1
1
2
1
1
0
1
2
1
1
1
2
0
0
1
2
0
1
1
1
0
1
1
1
0
1
1
2
3
1
1
2
0
0
2
1
1
1
1
0
2
0
1
1
1
0
2
0
1
1
1
0
2
0
1
1
1
2
0
0
1
2
1
0
2
0
1
1
2
0
1
1
0
1
1
1
1
1
1
1
1
1
3
1
1
2
1
1
1
1
1
1
2
4
0
2
1
1
0
1
1
1
0
1
1
1
2
0
2
0
1
0
1
0
0
2
2
2
0
1
1
2
2
2
1
1
2
1
2
1
2
2
1
0
2
1
1
1
1
2
3
1
1
2
2
0
1
1
1
2
2
1
1
1
2
1
2
1
1
1
1
1
0
2
1
2
1
1
2
2
1
1
1
0
1
1
1
1
1
1
2
2
1
0
1
0
1
0
1
1
1
1
0
2
1
1
0
1
0
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
2
1
1
1
2
0
1
0
1
1
1
1
1
0
1
0
1
1
1
2
2
1
1
2
0
0
1
2
1
1
1
1
1
0
0
2
1
1
1
0
1
0
1
1
1
1
2
2
1
0
1
2
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
0
1
1
0
0
0
2
1
2
2
2
0
1
2
1
2
1
1
1
1
2
1
1
2
1
1
1
1
2
2
1
2
0
1
2
1
1
2
1
0
1
0
1
1
2
1
1
1
0
1
1
1
3
1
2
0
1
1
1
1
0
0
1
1
2
1
1
3
2
0
1
1
1
1
0
1
1
1
1
4
2
2
1
2
0
0
2
1
2
1
2
0
1
1
0
2
1
2
1
1
1
1
1
2
2
1
0
1
1
1
1
2
1
1
2
1
1
2
1
1
0
0
1
1
0
0
1
1
1
0
1
1
0
1
2
2
1
1
2
2
1
1
1
1
0
1
2
1
0
1
3
2
1
1
1
2
2
2
2
1
1
1
1
0
2
0
1
0
2
0
0
1
1
1
2
0
2
2
1
2
1
0
2
1
2
1
1
1
1
0
1
1
3
1
2
1
0
0
1
1
2
1
1
4
0
2
2
2
1
1
2
1
0
1
2
1
2
2
1
2
1
1
1
1
1
1
1
2
1
1
2
2
1
1
2
1
1
0
1
2
0
1
1
1
2
1
2
1
0
2
0
1
1
1
1
2
1
1
0
2
2
1
1
2
2
0
0
1
1
2
0
2
1
2
2
1
1
2
0
2
1
1
1
2
1
1
2
2
1
2
1
1
2
2
1
2
1
1
2
2
0
1
5
1
0
1
1
0
1
1
0
2
1
1
1
1
1
1
4
1
1
1
1
2
1
2
1
1
3
1
1
2
1
1
1
1
1
2
1
1
1
2
1
2
1
1
0
1
2
1
1
0
1
1
2
1
0
0
0
2
2
0
4
2
1
1
0
1
1
0
0
1
2
1
2
1
1
2
1
0
1
2
0
0
1
1
0
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
0
0
0
0
1
2
2
1
0
1
1
1
1
1
0
1
1
0
0
1
1
0
1
1
2
1
1
1
1
1
0
0
1
0
1
1
2
1
1
1
2
2
1
1
1
0
1
1
1
1
1
1
1
1
2
2
1
0
1
1
1
1
1
1
2
1
0
0
2
1
1
0
1
2
1
1
0
0
1
2
0
1
1
1
2
1
1
1
1
1
1
3
1
1
1
0
1
2
1
1
1
0
2
2
1
2
0
1
2
2
1
1
2
0
2
0
0
2
1
1
2
0
2
1
1
0
1
0
2
1
0
1
0
1
1
0
1
1
1
2
2
3
1
1
1
1
1
2
2
2
1
0
2
2
1
0
2
0
1
0
1
1
1
1
1
1
0
1
1
1
1
2
1
1
1
1
2
0
1
1
1
2
2
1
2
1
1
1
1
2
1
1
1
1
2
0
1
1
1
1
1
1
1
1
0
1
1
1
2
0
0
1
1
2
1
1
1
2
1
2
1
1
1
1
0
2
1
1
2
2
0
2
1
0
2
1
0
0
1
1
0
1
0
1
1
1
1
1
0
1
2
2
1
2
1
1
1
1
1
0
2
0
0
3
1
2
1
1
0
2
2
1
1
1
2
1
1
1
1
0
1
2
1
2
1
0
1
1
1
1
1
1
1
1
1
2
0
1
1
2
1
1
0
1
1
1
2
0
1
2
2
0
1
1
1
2
0
0
1
2
1
1
1
2
1
1
2
1
2
1
1
1
1
1
0
1
1
0
0
1
1
0
1
0
1
2
1
1
0
2
0
1
1
1
1
1
0
2
1
1
1
2
1
0
1
2
1
1
1
1
0
2
1
0
1
2
2
1
2
0
1
2
2
2
0
1
0
2
2
0
1
0
1
1
2
0
2
2
1
1
1
1
1
1
2
0
2
1
1
0
2
2
1
0
0
1
2
1
1
2
2
0
0
1
1
1
1
2
1
1
1
2
2
1
1
2
1
1
1
0
1
1
1
1
1
1
0
1
1
1
1
1
1
1
2
2
1
0
1
1
2
1
1
1
2
1
1
1
1
1
2
2
2
1
2
2
1
1
1
1
2
1
1
1
1
1
0
1
1
2
1
1
0
1
0
2
1
1
2
0
1
2
1
2
1
2
1
1
1
0
2
0
1
1
0
7
2
1
1
1
1
0
1
1
1
1
0
1
1
1
2
0
3
1
1
2
2
2
1
3
0
0
1
2
0
0
0
1
0
2
0
2
2
2
1
2
2
2
1
1
1
0
1
2
1
0
0
2
1
1
2
1
2
1
3
1
1
1
1
1
2
1
2
1
1
0
2
2
1
1
1
1
1
1
0
2
2
2
1
2
1
1
1
2
1
2
2
1
1
1
2
1
1
1
1
2
1
1
2
1
1
0
1
1
0
2
2
1
2
1
0
1
2
1
2
2
1
2
1
1
1
1
3
2
0
1
1
1
1
0
2
2
1
1
1
2
0
2
1
0
1
0
1
1
1
2
2
1
1
1
1
0
1
2
1
1
0
0
1
2
0
2
0
2
2
1
1
1
2
1
1
1
1
2
1
1
0
1
2
1
0
1
1
1
1
0
0
1
0
1
2
0
1
1
1
1
1
1
2
0
0
1
1
2
0
1
2
1
2
1
1
2
1
1
1
1
0
1
1
0
1
2
1
0
1
1
2
1
0
1
0
0
1
1
1
1
1
0
1
1
1
1
2
1
2
1
0
0
1
1
0
0
2
2
1
2
2
0
1
2
1
1
1
1
1
0
1
1
1
0
1
2
1
1
0
2
1
0
2
1
0
0
0
1
1
1
2
1
1
0
1
0
1
1
1
0
1
2
1
2
1
1
0
1
2
1
0
1
1
1
1
1
0
2
2
1
1
2
1
1
2
1
2
1
2
2
1
0
2
2
0
0
1
1
0
1
0
1
2
0
1
1
0
1
11
1
2
1
1
1
2
1
0
2
1
0
1
1
0
1
2
0
1
2
1
1
1
1
2
2
1
0
1
1
1
2
0
1
2
2
1
1
1
0
1
1
1
1
0
1
1
1
1
1
0
1
1
1
1
1
0
1
1
1
1
1
1
1
1
2
1
1
0
2
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
3
2
2
1
2
1
1
0
2
2
1
1
2
1
2
2
1
2
1
0
0
2
1
1
1
1
2
2
1
5
2
2
1
0
1
1
1
0
2
0
1
0
2
1
0
1
1
0
0
1
1
2
1
1
1
1
1
1
2
2
1
0
1
0
1
1
1
1
1
2
1
1
1
1
0
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
2
1
0
0
1
0
1
1
0
1
1
2
2
0
1
0
0
1
2
2
2
1
2
2
1
0
1
2
2
1
0
0
0
2
2
1
1
1
0
1
1
1
2
1
0
1
0
1
2
3
0
0
1
1
1
1
2
1
1
1
2
1
1
1
2
2
1
1
1
0
2
0
2
1
0
1
1
0
1
2
2
0
1
1
1
1
0
0
0
1
2
0
1
0
1
1
0
2
1
2
2
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
2
1
1
0
1
1
2
2
2
2
1
1
1
1
1
1
1
2
0
1
1
2
0
1
0
0
1
1
1
1
2
1
1
1
0
1
1
0
1
0
0
2
0
2
1
1
1
0
2
3
2
2
1
1
2
2
1
1
1
1
0
0
1
1
1
1
1
1
2
1
2
1
1
2
1
0
1
1
2
0
1
1
2
0
2
0
2
1
1
1
2
1
1
1
0
0
1
1
1
0
0
0
1
1
1
2
1
1
1
1
0
2
0
0
1
0
1
0
2
0
1
1
1
1
1
2
1
3
1
1
2
1
2
0
0
1
1
2
1
0
1
1
2
3
2
11
2
0
1
1
0
1
1
2
2
0
1
2
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
0
1
1
2
1
2
1
1
2
1
2
2
1
2
1
1
1
1
1
1
1
0
1
1
2
1
2
1
2
0
2
1
1
1
1
1
1
2
2
2
2
1
1
1
1
0
1
1
1
1
1
1
0
1
0
2
1
0
2
0
0
1
0
1
1
1
0
1
1
1
2
2
1
1
1
1
2
2
1
1
0
2
0
1
0
1
1
1
1
1
2
2
0
0
2
1
0
1
2
1
2
1
1
1
0
1
1
1
1
2
1
1
0
1
2
1
0
0
1
2
0
2
1
1
2
1
0
1
1
1
2
2
1
1
1
1
2
1
2
1
0
1
1
0
1
0
2
0
0
1
2
0
1
1
1
0
1
1
1
0
1
0
1
0
2
1
0
1
1
1
2
2
2
3
1
1
1
1
1
1
2
1
1
1
0
1
1
1
2
0
0
2
1
0
2
1
1
0
1
1
0
2
2
2
1
1
1
1
1
0
1
1
1
0
1
1
1
2
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
2
0
1
1
1
0
1
1
1
1
1
0
1
1
0
1
2
1
0
2
1
0
0
0
1
2
1
2
0
0
1
1
1
1
1
2
0
1
0
0
0
2
1
1
1
0
2
1
1
1
0
2
2
1
1
0
3
1
1
2
1
0
1
0
1
1
1
1
1
1
1
1
0
2
2
1
2
1
1
2
2
2
1
1
1
2
3
2
0
1
0
0
0
2
1
2
1
2
2
1
1
1
2
2
0
0
0
2
0
1
1
1
1
1
1
0
2
1
1
0
1
1
0
2
2
2
2
1
0
0
0
1
1
1
1
3
2
0
1
1
1
2
1
1
1
1
2
1
1
1
1
2
2
1
1
1
0
2
0
1
2
1
1
1
2
1
2
1
2
1
0
1
2
2
0
1
1
1
1
1
2
2
1
2
2
2
1
0
1
2
1
1
0
1
1
1
1
2
1
1
3
2
10
2
0
1
0
1
2
3
1
1
1
2
0
1
0
1
1
0
2
2
0
0
0
2
2
1
0
1
1
1
2
1
0
0
1
1
0
2
1
1
1
2
2
1
1
2
1
0
1
0
1
1
0
1
1
2
1
2
1
2
1
0
2
1
2
0
2
2
0
1
1
1
1
2
1
1
1
1
1
2
0
1
1
0
1
0
1
1
1
2
1
1
2
2
1
1
2
1
1
2
1
0
1
1
1
1
0
0
1
1
2
0
1
1
0
3
1
1
1
1
1
1
1
1
0
1
1
2
1
1
1
1
2
0
1
0
2
1
1
0
2
1
0
1
1
0
1
2
1
2
2
1
2
1
0
0
1
2
1
1
2
2
0
2
1
0
2
1
1
1
1
2
0
1
1
2
1
2
0
2
1
1
0
2
1
2
1
1
1
2
2
0
1
2
1
1
0
0
1
1
0
2
2
2
2
1
0
2
0
3
1
0
1
1
1
0
1
1
1
1
2
1
2
2
2
0
1
2
1
1
0
1
1
1
0
1
1
1
1
0
1
1
1
1
2
0
2
0
0
1
0
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
0
2
1
1
2
1
0
1
0
0
0
1
1
1
1
1
1
1
1
2
0
1
1
1
2
1
1
1
2
2
2
1
1
1
0
1
1
0
2
1
1
1
2
0
2
1
1
1
1
2
0
1
2
0
1
1
1
1
1
1
1
1
0
0
1
0
2
1
1
1
1
0
2
0
2
1
1
1
0
1
1
0
1
0
1
2
1
2
1
1
1
0
1
2
1
2
1
1
1
2
1
0
1
1
0
2
1
1
1
1
1
1
2
0
1
1
2
1
0
1
0
1
1
1
0
2
1
2
0
0
1
0
1
2
1
1
1
1
1
1
0
1
0
1
1
0
1
2
3
0
1
2
2
1
0
2
0
2
2
1
2
1
1
0
1
0
1
1
1
1
1
2
0
1
0
1
1
1
2
1
1
1
2
2
1
0
1
1
1
0
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
0
2
0
2
1
2
0
1
0
0
0
2
1
1
2
1
2
0
1
1
0
2
2
2
1
0
1
1
2
0
1
2
2
0
1
1
0
1
0
1
1
2
1
1
3
2
1
1
0
1
1
1
1
1
1
1
2
1
2
2
1
1
1
2
1
0
0
2
1
1
1
1
2
2
1
1
0
1
1
2
1
1
0
0
2
0
0
1
1
2
2
1
1
0
2
2
2
0
1
1
0
1
1
0
1
1
1
1
1
1
0
1
2
0
1
1
2
1
1
1
2
1
1
1
2
0
0
1
1
0
1
1
1
0
2
0
0
2
1
0
1
1
2
0
0
1
2
0
1
0
1
1
1
2
1
1
1
0
0
0
2
2
2
2
2
1
1
2
2
0
0
2
2
0
1
1
2
1
2
1
2
2
1
2
1
1
1
1
2
1
0
1
3
1
1
1
1
1
1
1
0
0
1
2
1
0
1
1
1
2
1
0
1
0
1
0
2
0
1
0
1
0
1
1
1
1
2
1
1
1
1
0
1
0
1
1
1
0
1
1
1
1
1
0
1
2
3
0
1
2
1
1
1
1
1
2
0
0
1
2
2
1
1
1
1
2
1
1
1
2
2
0
1
1
1
2
1
1
1
1
1
0
1
1
1
2
2
1
2
1
1
1
1
1
0
1
3
2
1
1
0
1
2
1
0
1
1
2
1
0
1
2
1
1
2
1
0
0
2
1
1
1
1
1
1
1
2
2
1
2
0
1
1
1
2
2
2
1
1
2
2
1
1
1
1
0
2
1
1
1
2
1
1
0
0
1
1
2
0
2
0
1
1
1
0
1
2
0
0
1
1
1
2
2
1
2
1
2
0
1
0
1
0
0
1
1
2
2
1
1
1
1
1
1
2
0
0
2
0
1
0
1
1
2
1
2
1
2
0
3
4
1
0
1
1
1
1
1
1
2
2
1
1
1
0
2
0
0
1
2
1
1
0
0
2
0
2
1
0
0
1
1
1
2
2
2
1
1
1
0
1
1
0
2
1
1
1
1
1
2
1
1
1
1
0
1
0
1
1
1
2
2
0
2
0
1
1
1
2
1
1
1
2
1
1
2
1
1
1
1
2
1
0
2
1
2
0
0
2
0
0
1
1
2
2
1
2
1
1
0
0
1
1
1
0
0
0
0
1
1
1
2
1
1
0
1
1
0
1
1
1
1
1
1
2
1
1
1
1
1
1
0
1
1
1
1
2
2
1
1
2
2
1
1
1
0
1
2
1
1
1
0
1
2
1
1
1
2
0
1
2
2
0
1
0
1
1
0
1
1
1
1
1
2
1
1
0
2
1
2
1
1
2
1
0
0
0
1
1
1
2
2
1
0
2
1
2
1
0
1
1
1
1
1
2
1
0
1
0
1
0
1
1
0
2
2
1
2
2
1
1
1
0
1
0
2
1
1
1
2
1
1
1
2
1
1
1
0
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
0
0
1
1
1
0
2
1
1
1
1
0
1
1
1
1
0
1
0
1
2
0
2
1
0
1
1
1
2
0
1
0
2
1
1
0
0
2
1
2
0
2
0
1
0
0
0
1
2
1
1
2
1
0
1
1
1
1
0
2
1
1
0
1
1
0
1
1
1
2
1
1
2
1
1
0
0
0
1
0
1
2
2
1
2
2
1
1
1
1
2
2
2
0
1
2
1
0
2
0
1
2
1
1
2
0
1
1
1
0
1
1
1
1
2
0
0
1
1
1
2
2
1
1
1
3
0
0
1
1
1
1
1
1
0
1
1
1
1
1
2
1
1
1
2
1
2
1
1
2
1
0
1
1
2
2
2
1
1
1
1
0
2
0
1
1
2
1
1
0
1
2
1
2
1
0
2
0
1
1
1
2
0
2
2
1
1
1
2
1
0
2
0
1
2
2
2
0
2
1
1
2
1
1
2
2
1
1
1
1
0
1
2
1
1
1
1
1
1
0
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
2
1
0
2
2
0
1
0
1
1
0
1
2
1
2
1
0
2
1
1
1
1
1
0
2
1
1
3
1
0
2
1
1
2
1
1
2
1
5
0
0
1
1
1
1
1
1
1
1
2
0
1
1
1
1
0
0
0
1
1
1
2
1
1
1
2
0
2
0
5
1
1
1
1
0
2
1
1
1
2
1
0
2
1
2
2
0
2
0
1
1
3
0
2
1
2
1
1
0
1
1
1
0
2
1
2
2
1
2
1
1
1
1
0
1
1
0
1
1
1
1
0
3
1
0
1
1
1
0
3
1
1
0
2
0
1
0
1
0
1
2
2
1
0
1
1
1
1
1
0
1
1
2
1
2
0
1
2
1
1
3
1
2
2
1
1
2
1
1
2
1
1
1
0
1
0
1
0
1
1
1
0
0
1
1
3
0
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
0
2
1
1
2
1
1
1
2
0
1
1
1
0
1
0
1
1
2
1
0
1
1
1
0
1
1
1
1
0
2
2
1
2
1
1
1
1
2
0
1
1
2
1
1
1
2
2
1
2
1
0
0
2
1
1
2
1
2
0
1
2
1
1
1
1
1
1
0
2
0
1
2
1
1
0
2
1
3
2
1
1
1
1
1
2
1
1
2
2
1
0
0
2
0
0
1
1
2
1
1
1
1
1
1
2
0
1
1
1
1
2
0
2
0
1
1
0
1
2
1
0
1
1
1
0
1
1
2
1
0
1
1
1
1
1
1
2
1
0
1
2
1
1
1
1
0
0
2
1
2
1
1
1
1
2
0
1
1
2
1
2
1
1
1
2
1
1
1
0
1
1
0
1
1
0
1
2
1
1
0
0
1
1
1
1
1
0
1
0
1
1
1
1
1
1
1
1
1
1
1
1
0
1
2
0
1
1
2
2
1
1
1
2
1
2
1
1
1
1
0
1
1
1
2
2
1
1
2
0
0
1
1
0
0
1
2
0
1
2
1
1
1
1
1
1
1
2
1
1
1
2
1
1
0
0
1
1
1
0
2
0
0
1
1
1
0
2
1
1
1
2
1
0
1
2
1
1
0
2
2
2
5
1
1
1
1
0
2
1
0
1
2
1
0
2
1
2
2
1
1
1
0
0
2
1
1
1
1
1
2
2
1
0
1
1
1
1
2
2
2
1
1
0
1
0
1
1
2
1
2
1
2
2
1
1
2
0
0
2
1
1
1
1
1
2
0
1
1
1
0
1
0
0
1
1
1
2
1
1
2
1
0
2
2
1
1
0
1
0
1
1
1
2
2
2
2
1
1
0
0
1
1
0
1
1
1
1
2
1
1
1
2
0
0
1
1
1
1
1
1
2
1
3
1
0
1
0
1
2
1
2
1
0
1
2
0
0
1
0
1
2
2
0
2
2
1
1
0
2
1
2
1
1
0
1
1
1
1
0
1
2
1
0
1
1
0
2
1
1
1
1
1
1
1
1
0
1
0
2
3
2
1
1
0
0
1
2
1
2
1
0
0
1
1
2
1
0
0
1
1
2
2
1
1
1
1
0
1
1
1
0
1
0
1
1
1
2
1
1
2
1
2
2
0
1
1
0
2
2
1
1
1
1
0
2
3
2
0
1
1
1
1
1
1
1
0
1
1
1
1
2
1
2
1
1
1
1
2
1
2
2
2
0
1
0
2
0
1
0
1
1
0
1
0
0
1
1
0
2
1
3
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
0
0
0
1
1
0
2
2
2
5
2
1
1
0
1
1
1
0
1
1
1
0
1
1
2
1
1
1
1
0
0
2
0
3
2
0
1
0
1
0
0
2
0
0
1
2
0
1
1
1
0
1
1
1
2
1
1
0
1
1
2
0
1
1
1
1
1
1
1
0
2
1
1
0
2
1
1
1
2
1
2
1
2
1
1
0
3
2
1
2
1
1
1
1
1
1
0
2
0
0
2
1
0
1
1
1
1
0
1
1
2
0
1
1
1
1
1
2
1
1
1
2
4
0
0
2
1
2
2
1
1
1
1
0
0
1
1
0
1
1
1
1
0
2
1
1
0
0
1
1
0
1
1
1
2
1
1
1
2
1
1
1
3
2
1
1
1
1
1
1
1
1
1
1
0
2
2
0
0
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
2
1
1
1
2
1
1
0
0
1
0
2
1
2
1
1
1
2
1
0
1
1
2
2
2
1
1
0
0
1
1
2
2
1
1
2
0
1
2
1
1
1
2
1
0
0
1
1
2
1
1
1
0
1
2
3
1
0
1
0
0
2
2
0
2
1
0
2
1
1
0
1
0
1
0
1
2
1
0
2
2
1
2
0
1
1
0
1
0
2
2
2
2
1
1
0
1
0
1
1
0
2
2
2
1
1
1
2
1
1
0
3
1
0
2
1
2
2
2
0
1
1
1
1
1
1
1
1
2
1
1
0
1
1
2
1
0
1
0
1
2
0
1
0
2
1
0
1
1
1
1
2
2
3
1
1
1
1
0
1
2
2
1
1
2
1
0
1
0
2
1
1
1
1
0
1
1
1
2
1
2
1
1
2
2
1
2
1
1
2
1
1
0
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
0
2
2
1
2
0
2
1
1
1
1
1
1
1
1
0
1
0
1
1
2
1
0
2
1
1
1
2
1
1
1
0
1
2
0
0
2
1
1
1
1
1
1
1
0
1
1
2
0
1
0
1
0
1
1
1
2
0
2
1
0
2
1
2
0
1
0
2
1
1
1
0
0
1
0
0
0
1
1
1
2
1
1
1
2
0
0
1
1
1
2
1
1
1
1
2
1
2
0
0
1
1
2
1
1
1
2
2
1
1
1
2
1
1
2
1
2
0
0
2
1
1
1
0
1
2
0
0
1
1
2
1
2
1
2
1
1
2
0
1
1
1
1
1
1
2
2
2
2
2
2
1
1
1
1
1
1
2
0
2
0
1
0
2
0
1
1
1
1
1
1
1
1
1
0
2
2
1
1
1
1
1
0
1
1
1
1
2
0
1
0
2
2
3
0
1
1
1
2
1
1
1
2
2
2
0
1
2
0
0
1
1
0
0
1
0
2
2
1
1
2
1
2
1
0
0
1
0
0
2
1
0
2
1
2
2
2
0
1
1
1
0
0
0
1
1
1
1
1
0
2
0
1
1
1
2
1
0
1
0
2
2
0
1
0
2
0
2
2
1
0
1
1
1
1
1
1
0
1
1
2
2
1
1
0
1
2
1
1
2
2
1
1
0
1
1
1
1
0
1
1
1
1
1
2
1
2
0
0
1
1
2
2
1
0
0
1
2
1
1
1
1
1
2
1
1
2
1
2
1
1
0
2
1
0
2
1
0
0
0
1
2
2
2
2
0
2
1
1
3
2
1
2
1
0
1
1
2
1
2
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
1
1
0
3
1
1
1
1
0
2
1
2
0
1
1
1
0
1
1
0
0
0
2
1
1
1
0
1
0
1
1
1
1
1
0
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
0
1
2
1
1
2
1
1
0
1
2
0
1
2
2
0
1
1
0
2
2
1
2
1
0
2
0
2
1
2
1
2
1
1
1
1
1
1
2
0
2
1
1
1
1
1
1
0
1
2
1
1
1
1
2
1
1
0
2
1
2
1
0
1
2
1
1
1
1
1
0
0
1
1
1
1
1
1
0
0
1
0
0
0
0
1
2
2
1
1
1
1
1
1
1
1
1
2
0
0
0
2
2
1
1
0
1
0
0
1
1
1
1
1
0
1
0
1
1
1
1
1
1
1
1
1
0
1
1
0
1
1
1
1
1
2
3
1
1
1
1
1
1
0
1
2
3
0
1
1
1
1
0
1
1
0
2
2
0
1
0
1
1
1
2
1
2
2
0
1
0
0
1
1
1
1
1
1
0
1
1
1
0
1
1
1
0
2
1
0
1
1
0
0
2
0
0
1
1
0
1
1
1
1
2
2
0
1
1
1
1
1
1
1
0
1
2
1
1
1
1
5
0
1
0
1
2
1
0
1
2
1
2
1
0
0
1
1
2
1
1
2
1
1
1
2
3
2
1
1
1
1
1
2
0
1
1
2
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
0
1
0
1
0
0
1
0
1
1
1
0
1
2
1
1
1
1
2
1
1
1
0
1
1
0
1
1
1
1
1
2
2
1
1
1
1
1
0
0
1
2
1
0
0
1
1
1
0
1
1
1
1
0
2
1
0
1
1
1
1
2
0
1
1
0
1
1
2
1
1
1
2
1
1
1
0
1
0
1
1
2
1
1
1
2
1
1
1
1
1
0
1
1
0
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
0
2
1
1
1
0
1
0
2
1
2
2
1
1
0
1
1
1
1
2
0
1
0
2
1
1
0
1
1
1
2
1
1
1
0
1
2
0
1
1
1
0
1
2
1
1
2
0
1
1
2
1
1
2
1
1
1
0
0
1
2
0
1
2
1
0
1
1
2
2
1
2
1
2
2
1
0
0
1
1
2
1
2
1
1
2
0
2
0
2
0
1
2
1
2
1
2
1
0
2
0
0
1
1
0
1
1
2
1
1
1
2
1
1
1
1
1
1
0
1
1
2
0
1
0
1
1
1
0
1
1
1
2
1
1
2
0
0
1
1
0
1
1
0
2
2
1
1
0
1
2
2
1
0
2
0
0
1
1
1
1
1
2
1
1
1
0
0
2
1
0
1
3
1
2
1
1
2
0
2
1
1
0
1
1
1
1
2
1
0
2
1
1
1
1
1
2
2
1
2
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
0
0
1
1
1
1
1
1
1
1
2
2
0
1
2
1
1
1
0
0
0
0
1
3
1
1
2
1
1
0
2
2
2
1
0
1
0
1
0
1
0
1
0
2
1
0
2
2
1
1
1
1
1
1
1
2
1
1
1
0
1
2
1
1
1
1
1
0
1
0
1
1
0
2
0
1
1
1
1
1
1
2
1
0
1
1
0
1
1
1
1
2
2
0
1
2
1
1
2
1
1
0
1
2
1
2
1
2
2
1
0
1
1
1
1
1
2
2
2
1
0
1
0
1
0
2
2
2
1
1
2
3
0
0
2
1
1
1
1
1
1
1
0
1
0
2
1
0
1
2
1
1
1
2
2
2
1
1
1
1
0
0
2
2
2
3
1
1
1
1
0
1
1
1
1
2
2
0
0
0
2
0
1
0
2
2
1
3
1
1
1
2
0
2
0
1
1
1
1
1
1
1
0
0
1
1
2
1
0
1
1
1
1
0
1
0
1
2
0
1
1
1
1
0
2
2
2
2
2
1
1
1
1
1
0
1
1
2
1
0
1
0
0
0
1
1
1
1
1
1
0
0
1
2
1
0
2
1
1
1
1
1
2
4
0
2
1
1
0
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
0
2
1
0
1
1
2
2
2
1
2
1
2
1
1
0
2
0
1
1
1
0
1
1
1
1
2
1
1
1
2
1
1
2
1
2
1
0
1
2
0
2
1
2
1
1
0
1
1
0
1
1
2
0
1
2
1
0
1
1
1
1
0
1
1
1
0
2
1
2
0
1
1
0
1
1
1
2
1
1
1
1
0
1
1
1
1
0
2
2
1
2
1
1
1
1
0
1
0
1
1
1
0
1
0
1
1
1
1
2
2
1
1
1
0
1
2
0
1
1
2
2
1
0
0
0
1
1
3
1
1
1
1
1
1
1
1
1
0
1
0
1
2
1
1
1
1
1
0
1
1
1
2
1
2
1
2
1
2
1
2
0
1
2
1
0
1
1
1
1
2
2
0
2
1
1
2
1
1
0
0
1
1
1
1
1
2
2
1
1
1
1
1
1
0
1
1
2
1
2
8
1
1
0
1
1
0
1
1
2
1
0
1
1
0
1
1
1
1
2
1
1
1
1
0
1
2
2
1
2
1
2
1
1
1
1
0
1
0
2
1
1
1
1
1
2
0
1
1
2
1
0
0
1
1
2
2
2
2
2
1
0
2
2
1
1
0
1
1
1
1
1
1
1
1
1
0
1
1
2
2
0
1
2
2
1
2
1
1
0
0
1
1
2
1
1
0
1
2
1
0
1
1
1
1
2
2
1
2
0
2
1
1
1
1
2
1
1
1
1
0
2
1
1
1
1
1
1
2
1
1
1
2
1
1
0
0
1
2
1
1
1
1
1
0
1
1
0
1
0
1
1
1
1
1
1
1
1
0
1
0
1
0
1
3
2
0
2
1
2
0
1
1
2
2
1
0
1
0
2
1
1
1
1
1
1
2
1
2
1
0
2
1
1
1
1
1
1
1
1
1
1
1
0
2
2
0
1
1
1
1
0
2
1
2
0
0
1
1
1
0
2
1
1
0
1
2
1
1
2
2
2
0
1
1
0
1
2
1
2
2
1
1
1
1
1
1
3
2
1
3
0
0
1
0
1
0
1
2
0
1
0
0
1
1
2
0
5
2
1
1
1
1
1
2
2
2
1
2
1
1
2
2
1
1
1
1
1
2
1
1
1
1
2
1
1
1
0
1
1
2
0
1
1
2
1
0
1
1
0
1
1
1
1
2
1
1
2
1
1
2
1
1
1
2
2
2
1
2
2
1
2
0
0
1
1
1
2
0
1
1
2
1
0
1
1
1
1
1
2
0
1
1
1
1
2
1
1
2
0
1
2
0
1
0
1
1
1
2
1
0
1
1
2
2
0
1
1
1
1
0
0
2
1
1
0
1
1
0
1
1
0
1
2
1
0
1
1
8
2
1
0
1
1
1
2
2
1
2
2
0
0
1
1
1
1
0
1
1
0
1
2
1
0
0
1
1
2
1
0
2
1
1
1
1
0
0
1
1
1
1
0
1
1
1
2
2
1
1
1
2
0
0
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
2
1
3
2
1
2
2
1
1
1
1
0
0
1
0
1
1
1
0
1
0
1
0
0
1
1
1
2
1
2
1
1
0
1
0
1
0
2
1
1
1
1
1
1
1
1
1
2
0
1
1
1
1
1
1
1
1
2
1
0
0
1
1
1
1
2
1
1
0
2
2
1
1
1
1
0
2
1
1
0
1
1
1
1
0
1
1
2
1
0
0
1
2
0
0
0
1
1
0
1
1
1
0
1
1
1
1
1
1
2
1
1
2
2
1
1
0
0
0
1
1
1
2
1
2
1
0
1
2
1
1
1
2
1
2
1
1
1
1
0
0
1
1
0
1
1
1
1
0
1
0
1
1
0
1
1
1
1
2
1
1
2
1
1
1
1
1
0
0
2
0
1
1
2
1
2
1
1
1
1
1
2
2
2
1
1
2
1
1
0
0
2
1
0
1
1
2
0
1
2
1
2
1
1
2
2
1
1
2
1
2
1
1
1
0
1
2
2
1
1
1
1
0
2
1
1
1
0
1
1
1
0
2
0
1
2
0
2
2
0
0
1
2
0
2
1
1
0
2
2
2
1
1
2
0
2
1
1
2
0
1
1
1
1
2
2
0
0
1
1
1
1
2
2
1
2
1
1
1
1
1
1
1
0
2
0
1
2
1
1
1
1
2
0
1
0
1
1
1
1
1
2
1
1
1
0
2
1
1
2
1
0
2
1
1
1
0
1
1
2
2
1
1
0
1
1
1
2
2
2
1
1
2
2
1
2
1
1
2
0
2
1
1
1
0
0
0
0
2
2
2
1
1
1
2
1
0
1
0
0
1
1
2
2
3
1
1
1
0
1
1
2
0
1
0
1
0
1
1
1
1
1
0
1
1
2
1
1
1
1
2
1
1
2
2
0
2
1
0
0
1
2
0
0
1
2
2
2
1
2
1
1
0
1
1
2
2
2
1
0
1
1
1
2
1
0
1
2
1
1
2
0
2
1
0
1
0
1
0
1
0
1
1
1
2
0
1
1
1
3
1
1
2
1
1
1
1
2
1
2
0
2
1
0
1
1
1
1
1
0
1
1
1
0
1
0
1
1
2
2
2
1
2
2
2
1
2
1
2
1
0
1
1
2
1
0
1
1
0
2
2
1
0
2
1
1
1
1
1
1
1
0
0
0
0
1
1
2
1
0
1
0
2
1
0
0
1
2
1
1
2
1
1
1
1
2
2
0
2
0
2
0
1
0
1
2
0
1
0
1
2
1
1
0
1
2
3
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
0
1
1
1
1
1
0
1
1
1
2
1
0
1
2
1
1
1
2
1
1
0
2
1
1
0
0
1
1
1
2
1
1
0
0
1
1
1
0
1
1
1
1
1
0
2
1
2
0
1
1
1
1
1
1
2
2
2
2
1
0
2
2
1
1
0
1
1
2
1
1
2
1
1
1
2
2
0
1
1
1
2
0
2
1
0
0
0
0
0
1
1
1
1
1
0
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
0
0
1
1
2
1
0
1
2
1
1
1
1
2
0
2
1
1
2
2
1
2
1
1
0
0
1
1
1
1
2
1
1
1
1
2
0
1
1
1
1
0
3
1
2
1
0
1
1
1
2
1
0
2
1
2
1
2
2
2
3
1
1
0
2
1
1
2
1
1
1
0
1
4
1
0
2
1
1
1
1
2
5
1
1
1
0
1
1
1
2
0
1
1
2
1
1
0
2
1
1
2
1
1
1
1
1
1
2
2
0
2
1
0
0
2
0
0
0
1
0
1
0
1
1
0
1
1
1
0
1
2
2
2
2
0
2
2
2
1
1
1
2
0
2
1
1
1
0
1
0
2
0
0
2
2
0
2
1
1
1
1
1
1
2
1
0
1
2
0
1
1
2
1
1
1
1
1
1
1
2
0
2
0
1
0
1
1
2
1
1
1
0
1
1
1
0
1
1
2
1
1
2
1
2
2
2
1
2
1
0
1
1
0
1
1
1
2
2
2
1
1
2
1
2
2
2
0
0
1
1
1
1
0
1
0
1
1
2
2
1
1
2
1
0
1
1
0
2
2
1
2
2
2
2
0
2
1
1
1
1
1
2
0
1
0
0
1
1
1
2
1
0
1
0
1
1
2
1
1
1
2
2
0
1
1
0
1
1
2
1
1
2
1
1
1
1
2
1
1
1
1
1
1
0
1
1
1
0
1
0
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
0
1
1
1
1
2
2
1
1
1
2
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
0
1
1
2
2
2
2
2
1
2
0
1
0
0
1
0
1
2
1
2
1
1
1
1
1
3
0
0
1
1
1
1
1
1
1
1
2
1
1
1
2
1
0
1
2
1
1
1
1
2
0
1
0
2
0
1
1
1
1
1
2
1
1
1
1
1
1
0
1
3
1
1
0
1
0
2
0
2
3
2
1
1
1
2
3
0
1
1
1
1
1
1
1
1
1
1
0
1
1
0
2
0
1
1
2
1
2
2
1
2
1
0
1
1
1
1
1
2
0
0
0
1
1
1
1
2
1
1
1
1
0
2
1
1
1
0
1
2
1
1
1
1
0
0
2
0
1
1
1
1
1
1
1
2
0
1
1
1
0
1
2
2
2
1
1
1
2
1
1
2
1
2
2
1
2
1
0
1
1
1
1
2
2
1
0
2
0
2
1
1
1
0
2
0
1
1
1
1
1
2
1
0
0
1
1
1
0
0
2
1
2
1
1
2
1
1
1
2
1
2
1
2
1
0
1
0
1
0
0
1
2
0
1
1
1
2
0
1
1
1
2
1
2
1
1
1
1
1
1
0
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
0
2
2
1
0
1
1
1
1
1
2
1
0
0
2
1
1
2
2
2
0
1
1
1
2
0
0
2
1
3
2
1
1
0
2
2
1
1
2
1
0
1
2
0
1
2
1
1
2
2
2
1
1
2
2
1
0
2
0
1
1
1
2
1
1
0
0
1
1
1
3
2
1
3
1
1
1
1
1
1
1
2
1
1
0
1
2
1
1
1
2
1
1
2
2
1
0
1
1
1
0
1
2
1
1
1
1
2
1
1
1
0
0
1
1
1
1
1
0
1
1
1
1
0
1
2
1
2
2
1
1
1
2
1
1
1
1
2
0
1
1
1
1
1
0
0
1
1
1
2
2
1
1
2
0
1
1
1
0
1
1
1
1
2
1
0
1
2
2
1
1
0
1
2
0
1
1
1
1
2
1
1
1
1
0
2
1
1
2
1
1
1
1
0
2
2
1
2
2
2
1
1
0
1
1
0
1
2
1
1
1
1
1
2
2
0
1
1
0
1
0
0
2
0
1
0
1
1
1
1
1
1
1
1
2
2
1
0
0
1
1
0
2
2
1
1
1
1
1
2
1
0
0
2
1
2
2
1
2
4
1
1
2
1
0
2
2
1
0
2
0
1
0
1
1
1
1
1
1
1
0
1
1
1
2
1
1
2
1
1
0
2
1
1
0
0
2
1
1
1
0
1
1
2
1
1
1
0
0
1
1
0
0
1
1
1
2
1
0
1
1
1
2
1
0
1
1
1
1
1
2
1
1
1
1
1
1
1
0
1
2
1
1
1
1
1
4
1
2
2
1
1
1
1
2
0
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
2
0
1
1
1
1
2
1
1
2
1
1
1
2
0
2
0
1
2
1
0
0
2
1
1
1
1
1
1
0
1
2
0
1
1
1
0
2
1
1
2
2
0
0
2
1
1
1
1
2
0
1
1
0
0
2
2
1
2
2
0
1
1
1
1
0
1
1
1
2
0
1
1
1
1
2
1
1
2
1
3
0
1
1
1
0
2
0
2
0
1
1
1
1
1
1
0
2
1
1
2
2
1
2
2
1
2
2
1
1
1
2
1
1
0
3
1
1
1
1
0
2
0
0
1
1
1
1
2
0
1
1
1
2
2
1
1
0
1
2
1
1
0
2
2
1
1
2
3
2
1
1
0
0
1
1
0
1
2
2
2
1
3
1
1
0
0
2
2
1
1
2
1
2
2
1
0
1
2
0
0
0
3
1
1
2
1
0
0
1
1
2
2
0
0
2
1
1
1
1
1
1
1
0
1
0
2
1
2
1
0
0
1
1
2
1
1
1
0
1
0
2
2
1
0
1
1
1
1
1
2
2
1
1
0
2
2
1
1
1
1
2
1
0
2
1
2
0
0
1
0
1
1
2
3
2
1
1
1
1
2
1
1
0
1
1
2
0
1
1
1
1
1
2
0
1
2
0
2
1
1
1
1
2
1
2
2
1
1
1
1
0
1
1
1
2
1
0
1
2
0
1
0
1
1
1
2
1
2
0
1
0
0
2
1
1
0
1
1
2
2
1
1
2
2
1
1
1
2
1
0
0
2
1
0
1
0
1
1
0
1
1
1
0
1
1
2
1
2
0
1
2
1
1
1
1
2
0
2
2
2
1
1
1
0
1
0
0
1
1
1
0
2
1
1
1
0
1
1
1
1
1
2
2
2
1
1
1
1
2
0
1
0
1
1
1
1
1
0
1
1
2
1
2
2
1
2
1
1
1
0
1
1
1
2
1
0
0
1
2
1
1
1
1
0
1
1
1
1
1
1
2
1
2
1
2
0
1
0
0
2
1
1
0
1
2
2
0
1
1
1
1
1
0
1
1
0
1
1
1
0
1
1
1
1
0
1
1
1
1
2
1
0
2
1
0
1
1
1
1
0
2
2
2
1
0
1
0
2
1
1
1
1
1
1
2
2
0
2
0
1
0
1
1
1
2
0
1
1
2
1
1
1
1
0
1
2
0
2
0
1
1
2
1
1
3
2
1
1
1
0
1
2
0
1
1
0
1
1
1
1
1
1
1
2
1
2
1
2
1
0
1
1
0
0
0
1
1
0
1
1
2
0
1
1
1
0
0
1
1
1
2
0
2
0
0
1
0
2
2
2
1
1
0
2
1
1
2
1
1
1
2
1
0
1
0
1
0
1
0
0
0
0
2
0
0
1
1
0
1
1
1
1
1
2
1
1
2
1
1
0
1
1
0
1
1
1
0
1
1
2
1
1
1
1
1
2
2
1
2
2
0
2
1
1
2
2
0
1
0
0
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
0
1
1
0
1
2
2
1
1
2
1
1
0
0
2
0
1
1
1
1
0
2
2
1
1
1
1
1
1
1
1
0
0
1
0
1
0
1
1
1
2
0
1
1
0
1
1
1
1
2
1
2
1
0
0
1
2
0
0
1
1
0
0
1
1
1
1
0
2
1
1
2
2
2
1
2
1
2
2
2
2
1
2
1
1
0
1
2
2
2
1
1
2
1
2
0
0
1
2
0
1
1
1
2
1
1
2
1
1
1
1
0
2
1
0
1
2
2
0
1
1
2
0
0
1
2
1
2
1
1
2
2
1
1
1
1
0
0
1
1
1
2
3
1
1
1
1
1
0
2
0
0
1
0
1
1
1
2
1
1
1
2
2
2
2
2
0
1
1
1
0
2
0
1
1
1
1
0
2
1
0
1
0
1
0
0
0
2
2
1
0
2
1
2
1
1
1
1
3
1
1
2
2
2
0
2
1
0
1
1
1
0
0
0
1
1
2
1
1
2
0
2
0
1
1
0
1
0
0
2
2
0
2
2
0
1
2
1
0
1
0
2
0
2
0
1
1
1
2
1
0
0
2
0
1
1
1
2
1
1
2
0
1
2
1
1
1
0
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
0
1
1
2
1
1
0
0
1
1
1
1
0
0
2
1
0
0
1
1
1
0
0
1
1
2
1
2
5
1
1
2
1
1
1
2
1
1
1
2
0
1
2
2
1
0
1
0
0
1
1
1
2
1
2
1
1
1
1
0
2
2
1
0
0
1
1
4
2
0
1
2
1
1
1
1
2
1
1
1
1
0
1
2
0
1
1
1
1
1
1
0
1
1
1
1
2
0
0
1
4
1
1
1
1
1
2
1
0
1
1
1
1
2
1
1
2
1
0
2
0
0
1
0
0
1
1
2
1
1
1
1
0
1
1
2
1
0
0
2
2
1
2
1
0
2
2
1
1
0
2
1
1
1
1
1
1
1
2
1
1
1
1
0
1
5
2
0
0
1
0
1
1
1
1
0
1
1
0
1
0
2
1
1
1
2
1
1
1
0
1
1
0
2
1
0
0
2
1
1
2
2
2
0
1
1
2
0
1
1
0
2
1
2
0
2
1
2
1
0
1
0
2
2
2
1
0
1
2
1
1
2
1
2
2
2
1
1
2
2
0
0
0
1
1
1
0
1
1
1
1
1
1
2
1
1
2
1
1
0
2
1
0
2
1
1
1
2
1
1
1
1
2
2
0
1
2
0
1
1
0
0
1
2
1
1
2
2
1
1
0
1
1
1
0
1
1
2
2
1
2
1
1
1
2
0
3
0
0
1
1
2
1
1
1
1
1
0
1
2
1
1
1
1
2
1
0
0
2
1
2
2
0
1
1
1
0
1
1
1
1
1
1
0
0
0
2
1
1
1
0
1
2
0
1
1
1
1
0
1
0
1
2
2
1
1
1
1
2
1
0
1
0
2
1
1
2
1
2
1
1
1
1
1
1
1
0
4
1
2
0
1
2
0
2
1
1
1
0
1
0
1
1
2
0
1
0
0
1
2
1
1
1
1
1
1
1
1
0
1
1
2
1
2
1
1
1
1
0
2
2
0
2
1
1
1
1
2
1
0
1
1
1
2
1
2
2
1
0
1
1
0
1
0
0
2
0
3
0
0
0
2
0
2
0
1
1
2
1
1
2
1
0
1
1
2
1
1
2
1
1
1
2
2
1
1
1
2
1
2
2
1
0
1
0
1
1
2
1
1
1
1
1
1
1
1
2
0
1
1
1
1
1
2
1
2
0
1
0
1
2
0
1
2
1
1
1
1
0
1
1
0
2
1
2
1
1
1
1
0
1
1
1
1
2
2
1
2
1
1
2
0
1
1
2
1
1
0
1
2
2
0
1
2
1
1
2
1
1
1
1
2
1
1
1
1
2
1
2
2
1
1
2
2
0
1
1
3
1
2
1
0
1
1
1
1
2
1
0
1
0
1
0
2
1
1
1
2
1
1
1
0
0
1
2
1
1
2
1
1
1
2
0
1
0
1
1
1
1
2
1
2
2
1
2
1
1
1
0
2
1
2
1
2
3
1
2
1
0
1
1
2
1
1
0
1
1
1
1
0
2
0
1
2
2
1
0
1
2
1
0
1
0
2
1
0
1
0
1
2
1
2
1
1
1
1
1
2
0
1
2
1
2
1
1
1
1
1
2
0
2
2
0
2
1
1
1
1
2
0
0
1
1
2
0
0
2
1
0
1
1
0
0
3
1
0
1
1
0
1
1
0
1
1
1
0
2
3
0
1
0
0
2
1
2
2
1
1
1
1
0
1
0
1
1
1
2
2
0
0
0
1
0
0
0
2
1
1
0
1
1
1
1
0
0
1
1
1
1
0
1
0
1
1
1
0
0
2
1
0
1
0
1
1
1
2
1
1
1
1
0
1
2
1
2
1
2
2
0
1
1
0
1
1
0
1
0
2
1
1
1
1
1
2
1
1
0
0
2
1
0
1
2
1
1
1
0
3
1
1
1
1
1
1
1
2
2
0
1
1
0
2
2
1
2
0
2
0
1
1
1
2
1
1
1
1
0
1
1
1
2
1
2
1
1
2
1
1
2
2
1
2
1
1
1
1
1
1
2
2
0
1
2
1
0
2
1
2
1
1
0
1
1
1
1
1
0
2
1
2
2
1
1
0
1
1
2
1
0
0
1
1
1
1
0
1
1
1
3
2
2
1
0
1
1
1
1
3
1
1
1
1
1
1
1
1
1
2
1
1
0
2
2
0
1
1
0
1
1
1
1
2
0
0
0
0
1
1
2
0
1
3
1
2
1
2
1
1
1
1
1
1
1
3
1
0
0
1
0
1
0
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
2
1
2
1
1
1
4
2
2
0
1
3
1
1
1
2
0
0
2
1
1
1
1
0
1
2
1
2
1
1
1
1
0
1
1
0
2
1
1
1
2
2
0
1
1
1
1
1
0
1
0
1
1
0
1
1
0
1
0
0
1
0
2
2
1
1
1
2
1
2
2
1
0
1
2
1
1
1
2
1
1
1
2
1
1
0
2
1
2
0
1
1
2
0
4
1
2
1
1
2
0
1
1
2
1
1
1
1
1
2
1
0
1
1
2
0
1
1
0
0
2
1
1
0
0
1
2
0
2
2
1
1
1
1
0
1
1
1
1
1
1
0
2
0
2
1
1
2
2
2
1
0
2
0
0
1
1
1
1
0
0
1
1
0
1
2
0
0
1
0
0
2
1
1
1
2
1
1
2
5
1
1
1
0
1
3
1
1
1
1
2
1
1
2
1
1
2
0
2
0
1
0
0
1
0
2
1
1
1
1
0
1
1
1
2
1
2
1
2
1
1
3
1
1
2
0
0
0
1
0
2
1
1
1
0
1
1
0
2
1
0
1
1
1
1
1
2
2
1
1
1
0
2
2
0
1
1
0
2
1
1
1
2
1
1
2
1
0
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
1
1
1
1
2
0
1
1
1
1
1
1
1
1
0
2
1
0
0
1
2
2
1
1
1
1
1
2
2
1
1
0
0
0
1
1
0
2
1
1
1
1
1
1
2
2
1
1
1
3
1
1
2
1
0
1
1
1
1
1
1
1
1
1
1
1
1
0
0
1
2
1
1
0
0
0
1
2
0
1
1
1
1
1
1
1
1
1
2
1
1
1
0
0
0
1
1
1
1
1
1
2
0
0
0
2
2
1
2
1
2
2
1
0
2
1
1
1
1
1
2
0
0
2
1
2
1
1
1
0
0
1
1
1
0
2
0
1
1
0
0
1
1
2
2
1
1
2
1
1
1
2
2
0
0
1
1
2
2
1
1
1
2
2
1
3
1
1
2
0
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
0
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
0
0
1
2
1
1
1
1
1
1
0
1
1
1
0
2
1
2
1
1
2
0
1
1
1
1
1
1
1
0
1
1
2
1
1
1
1
1
1
1
1
2
1
1
0
2
1
1
1
1
2
2
1
2
2
2
0
1
0
0
1
1
2
1
2
1
0
2
2
2
1
1
2
1
1
1
1
1
0
2
0
1
1
1
1
1
2
3
0
0
0
1
1
1
1
2
0
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
0
0
1
1
2
1
1
1
1
1
1
2
1
2
1
1
1
0
2
0
1
1
4
1
1
1
2
1
1
1
1
1
2
0
1
1
2
2
1
2
1
2
1
2
1
1
1
2
0
2
1
1
1
1
1
0
1
2
1
0
0
1
2
1
1
1
0
1
2
1
1
1
1
1
2
2
2
2
1
1
1
1
2
0
1
2
0
1
1
2
1
1
1
2
0
0
1
1
2
1
1
1
0
1
2
1
1
1
1
0
1
0
2
1
1
0
1
0
1
1
0
1
2
1
2
1
2
0
1
1
0
0
0
0
0
0
1
0
1
1
0
1
1
1
1
1
1
0
1
2
0
0
0
1
0
1
1
0
1
1
1
1
1
0
2
1
0
1
1
3
1
1
1
1
2
1
1
0
2
2
1
1
2
1
0
1
1
0
2
1
1
1
1
2
1
2
2
1
1
1
1
1
1
2
0
2
1
1
1
1
1
0
1
2
0
1
1
2
2
2
0
0
0
0
0
1
1
0
0
2
2
1
1
2
1
1
0
1
1
0
0
1
2
1
1
1
1
0
0
2
2
1
2
1
1
1
2
1
1
1
1
1
1
0
1
1
1
1
2
0
1
0
1
0
1
2
1
1
1
1
2
1
2
2
1
1
1
2
1
0
1
2
2
0
2
1
1
1
1
1
2
2
2
1
2
2
0
2
1
2
2
1
1
1
2
0
0
0
0
2
1
2
0
0
2
1
2
1
1
2
1
0
0
0
1
0
1
1
0
1
2
0
1
1
2
1
1
1
1
1
1
1
1
2
1
1
0
1
1
1
3
1
1
2
1
2
2
1
1
2
1
1
2
0
0
1
1
1
1
1
1
0
1
1
2
1
1
0
3
1
2
0
2
1
1
0
1
1
2
1
1
0
0
0
0
2
1
1
0
2
2
0
2
1
0
1
1
0
1
1
1
0
1
1
1
2
0
2
1
0
1
2
1
0
2
0
1
2
1
1
2
0
0
0
1
2
1
0
1
1
2
0
1
1
1
1
1
1
0
0
0
1
2
0
2
1
1
0
2
1
2
2
1
1
1
0
2
1
1
1
1
1
1
2
0
1
2
1
0
1
1
1
1
1
1
1
1
0
0
1
1
1
1
1
1
0
0
1
1
1
1
0
0
1
1
2
1
1
1
2
1
1
0
1
0
1
1
1
1
1
1
1
2
1
1
1
0
1
1
1
1
1
1
1
1
1
1
2
0
1
1
1
2
1
1
0
0
1
1
0
1
1
1
1
0
2
2
1
1
0
2
1
0
1
1
1
1
1
1
1
1
1
0
2
1
1
1
1
1
1
1
1
0
1
0
1
1
1
2
2
1
0
0
1
0
0
1
2
1
1
0
1
1
2
2
2
2
1
1
1
2
1
1
1
1
2
2
1
2
0
1
1
1
1
1
1
1
0
0
1
1
2
1
1
1
0
1
3
1
1
1
2
1
2
1
1
1
2
1
2
2
1
1
2
1
1
1
1
1
1
0
4
2
1
1
1
2
1
0
1
1
0
0
1
1
1
1
1
2
1
1
2
1
1
0
1
1
1
1
2
1
1
2
1
1
1
2
0
1
1
0
0
0
1
2
1
1
0
0
1
2
1
2
0
1
1
0
1
1
1
1
2
0
2
0
2
0
2
1
1
1
1
0
0
2
2
1
2
0
1
1
1
0
1
1
1
1
1
0
1
2
1
1
1
3
0
0
0
1
1
1
0
1
1
1
2
1
1
2
2
1
0
1
2
1
1
1
2
1
1
1
1
1
1
2
1
0
0
4
1
1
2
1
0
0
1
0
0
0
1
1
2
1
1
1
1
2
1
2
1
1
1
2
1
1
1
1
0
0
1
1
2
0
1
2
2
1
1
2
2
2
1
1
1
1
1
2
1
0
2
1
1
2
2
1
2
0
1
2
2
0
0
0
0
1
1
1
1
1
1
2
2
0
1
1
1
1
1
1
0
2
2
1
1
1
2
1
1
2
1
1
3
2
0
1
1
1
2
1
1
1
2
2
1
0
1
1
1
1
5
1
1
1
1
1
1
0
1
1
0
1
1
0
1
1
1
2
1
0
1
2
0
2
1
2
1
1
2
1
0
1
1
1
2
1
1
0
1
1
1
1
1
1
1
1
1
1
1
2
0
1
1
2
1
2
2
2
2
1
1
1
1
0
1
1
1
0
1
2
1
1
2
2
0
1
1
0
1
1
1
1
1
0
1
1
2
2
0
0
1
1
1
1
0
1
1
1
0
1
1
0
1
2
1
1
2
2
2
1
1
1
1
1
0
1
1
0
2
2
0
0
0
1
0
1
0
0
2
1
2
0
1
1
1
2
0
0
2
1
2
1
1
0
1
2
0
1
1
1
1
0
1
0
1
1
2
1
1
1
1
2
1
1
2
1
0
2
1
0
2
0
0
2
1
1
0
1
1
0
2
1
1
1
1
2
3
1
1
1
1
0
1
1
0
1
0
1
1
1
2
2
1
0
2
1
0
1
1
2
1
0
0
2
0
1
1
1
1
1
1
0
1
1
1
1
1
1
0
2
1
1
2
1
1
1
1
1
1
1
0
1
2
2
2
0
1
1
1
1
1
1
1
0
0
1
2
1
1
0
1
0
1
2
1
1
0
1
1
1
0
5
1
0
1
1
1
1
0
2
2
1
0
1
1
1
0
2
0
0
1
1
1
2
2
2
1
3
1
2
1
1
0
1
1
2
1
0
0
0
1
1
0
0
1
1
0
2
1
0
2
0
1
1
1
1
2
1
1
1
1
4
1
1
1
1
0
0
1
1
1
1
1
1
1
1
1
0
1
1
2
1
1
1
1
1
0
1
1
0
1
0
2
1
1
1
1
0
1
1
2
1
0
1
1
1
0
0
1
1
1
2
2
1
2
1
2
1
1
0
1
0
0
1
1
2
1
2
0
1
1
1
1
1
1
2
1
1
1
6
1
1
1
2
1
1
1
0
1
0
1
1
1
1
2
2
1
1
2
0
1
1
2
2
1
0
1
1
2
1
1
1
2
1
0
1
2
1
0
1
2
2
1
0
2
0
0
1
2
1
2
0
1
0
2
0
1
1
2
1
0
2
2
1
2
0
0
2
1
2
1
0
1
1
1
1
1
1
1
2
0
0
1
1
2
0
2
1
0
1
0
2
0
0
1
2
0
0
0
2
1
2
1
1
1
2
1
1
2
0
1
1
2
1
2
0
1
1
1
2
1
1
1
1
0
0
1
2
2
1
1
0
2
1
1
0
1
1
1
0
1
2
1
1
0
2
1
1
1
0
2
1
1
1
0
1
1
2
1
0
0
1
0
0
1
1
0
0
0
0
0
2
2
1
1
1
2
1
1
1
1
2
1
2
1
0
0
1
1
0
2
1
2
1
0
1
1
1
1
0
1
2
1
2
2
1
1
1
2
0
2
1
1
0
2
0
3
2
1
1
1
1
1
2
1
1
2
2
1
1
1
1
2
1
2
2
0
1
2
2
1
0
2
0
1
0
1
2
1
1
1
0
1
1
0
1
0
1
0
1
1
1
2
1
2
1
2
1
2
2
1
2
1
1
1
1
1
0
1
1
2
1
1
1
0
1
0
2
1
1
1
1
1
2
0
1
1
2
1
1
1
1
1
1
1
0
1
0
1
1
2
1
1
0
2
0
1
1
1
0
0
2
1
1
1
1
1
0
1
2
1
0
2
1
1
0
1
1
2
1
2
2
1
1
1
2
2
1
1
0
1
1
1
2
1
1
0
1
1
1
0
1
1
1
0
1
1
1
1
2
1
2
2
1
2
0
2
2
1
1
1
1
1
1
0
1
1
1
1
1
1
1
0
1
1
1
0
2
1
1
2
1
1
2
1
1
2
2
1
1
2
2
2
1
1
0
2
0
2
1
1
0
2
3
1
1
0
0
1
1
2
1
1
1
1
1
1
1
1
1
0
1
2
1
2
2
2
0
0
0
1
1
2
1
2
1
1
0
2
1
2
1
1
1
1
4
0
1
1
2
2
1
1
2
2
1
1
1
0
1
0
2
2
1
1
1
0
2
1
1
0
1
2
0
2
1
2
1
1
1
1
2
0
2
0
1
2
0
0
1
0
1
1
2
0
1
0
1
1
2
1
1
1
1
1
2
2
1
0
1
1
1
1
2
2
1
1
0
1
1
1
1
1
1
1
0
1
1
2
1
1
1
2
0
2
2
2
1
1
0
2
4
2
2
1
2
1
1
1
1
1
0
0
0
2
2
1
0
1
0
1
2
1
1
0
0
2
2
1
2
1
1
2
1
1
1
2
2
1
1
1
1
2
2
1
0
1
2
2
1
1
0
1
2
0
2
0
2
2
2
1
1
1
2
0
1
0
3
0
0
2
0
1
1
1
2
0
1
2
1
1
1
2
0
1
0
2
1
1
1
2
1
1
1
0
0
0
1
2
1
0
1
2
2
1
1
0
2
1
4
2
1
1
1
2
2
2
1
1
1
1
3
1
1
0
2
1
1
1
0
1
2
1
1
2
1
1
1
1
0
1
0
2
1
1
0
0
1
1
2
0
2
1
0
1
1
1
1
2
1
1
0
3
0
1
1
3
2
0
1
1
2
2
1
0
1
0
1
1
1
0
1
1
1
1
1
1
1
1
0
1
2
1
1
0
1
1
1
2
1
1
1
1
0
1
0
2
1
2
1
1
1
2
1
1
4
0
2
2
2
2
2
1
0
1
1
1
2
1
1
1
2
1
1
2
0
2
0
1
1
2
0
2
2
1
2
1
1
0
1
1
1
0
1
1
1
0
1
1
1
0
1
1
2
1
2
2
2
1
1
0
0
0
2
1
1
0
3
1
0
2
1
0
2
0
3
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
2
1
0
0
1
1
1
1
1
2
1
2
1
1
2
2
2
1
0
0
2
0
0
1
1
2
0
1
2
1
1
0
2
2
0
1
1
1
2
0
1
2
1
0
1
1
1
2
1
1
2
1
1
3
2
0
1
0
2
0
0
1
1
1
2
1
0
1
1
1
1
1
1
1
1
1
0
0
2
2
1
1
1
1
1
2
1
1
1
2
1
1
0
1
0
1
2
1
1
1
1
1
1
0
0
0
0
0
0
1
1
1
2
2
1
1
0
1
2
2
2
1
1
1
0
2
1
1
1
0
0
1
0
1
1
1
0
1
0
1
0
1
1
1
0
1
1
1
2
1
1
2
1
1
1
1
0
2
1
1
1
1
2
1
1
1
2
1
2
1
1
1
0
1
1
1
2
0
2
2
2
1
2
1
1
1
1
0
2
1
2
2
0
1
2
1
1
1
1
2
1
1
1
1
1
0
0
2
1
1
1
2
1
1
1
0
1
0
1
1
0
0
1
0
2
1
1
0
1
0
0
2
0
1
0
2
0
1
0
1
1
1
1
3
1
1
0
2
1
1
1
2
1
2
2
1
1
2
0
2
1
2
2
1
1
1
2
0
1
0
1
0
1
0
2
1
1
1
1
1
1
0
1
2
2
1
1
1
1
1
0
1
1
2
1
1
2
1
1
1
2
1
1
2
1
0
1
1
1
2
1
0
1
2
1
0
2
1
1
2
0
1
1
2
0
0
2
0
1
1
2
1
0
1
2
1
2
0
1
1
2
1
0
1
1
1
2
1
4
2
1
1
0
1
1
1
1
1
1
1
0
0
1
1
0
1
1
1
1
3
0
0
1
2
0
0
3
1
1
1
2
1
1
1
2
2
2
1
1
1
0
1
0
1
0
1
1
1
1
0
2
1
1
1
1
1
1
0
1
1
1
0
1
2
0
0
3
1
1
1
1
2
0
2
2
1
0
0
1
2
1
2
1
0
0
1
1
0
1
0
1
1
2
0
2
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
0
2
0
1
2
1
0
1
2
0
2
2
2
1
1
2
1
2
2
1
0
1
2
1
2
0
1
2
1
0
1
1
1
0
2
1
1
2
1
1
2
2
1
1
1
1
2
2
0
0
1
2
1
1
1
2
2
2
1
1
1
1
1
2
2
1
1
1
2
1
1
1
1
1
0
2
1
1
0
2
2
1
2
1
1
1
2
1
1
1
1
1
2
1
2
0
1
1
1
1
1
1
1
1
2
1
1
1
2
2
2
0
2
1
2
1
2
1
2
1
1
2
1
2
1
1
2
0
0
1
0
1
1
2
1
2
0
0
0
1
1
0
0
1
2
2
1
0
2
1
2
1
2
2
1
0
2
0
1
1
1
0
1
0
0
1
2
2
0
1
1
2
1
2
0
1
1
1
1
1
2
1
1
2
0
1
1
1
1
2
1
1
1
1
0
1
0
0
1
2
0
1
0
1
2
1
2
2
0
0
2
1
1
2
2
1
1
0
2
1
0
2
2
1
0
2
0
1
2
0
1
1
1
2
1
0
1
1
1
2
2
0
1
1
1
0
1
0
1
2
1
1
1
1
0
0
0
0
1
2
1
1
1
1
1
2
0
0
1
1
0
1
2
2
1
0
1
1
0
1
1
2
1
2
0
0
1
1
1
1
2
1
1
1
1
1
1
1
0
1
1
1
1
0
1
1
1
1
2
2
1
2
1
1
1
1
1
1
1
2
0
0
1
0
1
2
1
1
0
1
1
1
2
1
0
3
2
1
2
1
0
1
1
1
1
2
1
1
1
2
1
1
2
1
1
2
2
2
0
1
2
2
1
2
0
2
1
1
2
1
2
1
0
0
1
2
1
2
1
2
1
3
1
2
1
1
1
1
0
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
0
0
1
1
0
1
1
1
1
1
1
1
0
1
1
1
0
2
2
1
1
2
2
0
1
2
1
1
1
2
1
1
1
2
0
1
4
1
2
1
0
2
1
1
1
1
3
0
0
1
2
1
2
1
1
2
2
1
1
2
1
1
1
2
2
0
1
2
2
0
1
2
1
0
1
1
1
2
0
1
1
1
1
1
1
2
1
1
1
1
1
0
2
1
0
1
0
2
2
1
1
1
2
2
0
2
1
1
2
2
1
1
1
2
1
0
2
0
1
1
0
0
2
1
1
0
2
2
1
0
1
1
0
2
1
1
0
1
1
1
1
1
0
1
2
0
1
2
2
1
1
2
1
1
0
1
2
2
2
2
2
1
1
2
1
1
3
1
0
1
0
0
1
1
2
1
1
0
1
1
1
1
1
1
0
1
2
0
1
2
1
1
0
1
2
0
1
1
1
2
1
1
2
1
1
0
1
2
0
2
1
1
2
2
2
1
1
1
0
1
1
0
1
1
1
2
1
1
1
1
1
2
1
0
2
1
1
1
1
2
1
1
2
1
1
2
1
2
2
0
1
0
1
2
1
0
1
1
2
2
2
0
1
0
1
1
1
2
2
1
1
2
1
1
0
1
1
0
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
0
1
1
2
1
1
2
1
2
1
0
2
1
1
0
1
2
1
1
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
2
0
0
1
1
1
2
1
1
2
1
1
1
2
2
1
1
1
2
2
1
1
1
1
0
1
1
1
1
1
1
2
1
2
1
4
0
0
0
1
1
1
0
1
2
3
2
0
0
0
1
1
0
2
1
1
2
1
2
0
1
2
0
1
1
3
1
0
2
1
1
0
1
1
1
0
2
0
2
2
1
2
0
1
0
0
2
0
1
1
1
1
1
1
1
2
1
1
1
1
0
2
1
2
0
1
2
1
2
0
1
1
1
1
0
2
2
0
2
0
1
1
2
1
1
2
1
1
1
1
2
1
0
1
1
1
1
2
1
1
2
2
0
2
1
2
0
1
1
1
0
0
2
1
1
2
1
1
1
2
1
1
1
0
1
1
1
1
1
2
1
1
0
1
2
1
1
1
0
0
1
0
2
1
1
0
0
1
1
0
1
2
2
2
1
1
2
2
1
1
2
2
3
1
2
2
0
1
2
2
0
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
0
1
1
0
1
3
2
1
0
1
1
0
0
1
0
2
1
1
1
1
1
1
2
1
3
1
1
1
2
2
0
0
1
0
2
0
1
2
0
1
1
2
2
1
1
2
1
1
2
2
1
1
0
2
2
0
1
1
0
2
1
2
3
1
1
1
1
0
1
3
1
1
1
1
1
1
0
2
1
1
0
1
2
1
1
1
1
1
1
1
1
2
1
2
1
2
1
1
1
1
0
2
1
1
2
1
1
0
1
1
1
2
2
1
1
2
1
2
1
1
2
2
0
2
1
2
1
1
2
0
2
0
1
1
0
1
1
1
1
0
1
1
2
2
2
1
1
1
2
1
1
1
0
1
1
2
1
1
1
1
2
1
2
0
1
1
0
1
1
0
1
2
1
1
0
2
1
2
1
2
0
1
2
1
2
1
0
2
1
0
2
0
1
1
1
1
1
1
2
0
2
2
1
2
2
1
1
1
1
1
2
0
2
2
1
1
1
0
1
2
2
0
2
1
1
1
1
1
0
1
1
0
1
2
0
0
2
2
2
2
4
1
2
2
2
2
1
1
2
0
1
0
0
1
2
1
0
1
1
1
1
1
1
0
1
1
2
1
1
1
0
1
2
0
1
0
1
0
1
1
2
3
2
0
0
0
1
0
2
0
0
1
1
1
2
0
1
1
1
2
1
0
1
1
2
1
1
1
1
1
0
1
1
2
2
1
2
1
0
1
2
1
2
0
1
1
2
1
1
2
2
1
2
0
2
2
0
1
1
1
1
1
2
2
1
2
1
1
1
2
2
2
1
2
1
1
1
1
1
1
1
1
1
0
1
1
0
1
1
2
1
0
1
0
2
1
1
0
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
0
1
1
1
1
2
1
2
1
1
1
2
2
2
1
1
1
0
0
2
1
0
2
2
1
1
1
2
0
2
1
1
1
2
2
1
2
1
2
0
0
0
1
2
1
2
1
1
2
1
2
0
1
0
1
1
2
1
1
1
1
0
0
1
0
0
2
1
0
1
1
0
1
1
1
1
1
1
1
2
1
1
1
2
1
2
2
1
0
2
0
1
1
1
0
0
1
2
1
1
1
1
1
1
1
1
2
1
1
1
0
2
0
2
1
2
1
2
1
1
1
1
3
1
1
0
2
0
2
1
2
1
2
1
1
1
1
1
0
1
1
2
1
1
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
3
1
1
1
1
1
2
0
1
1
0
2
1
0
0
1
0
1
0
2
0
0
2
1
1
0
1
0
1
1
1
1
3
1
1
1
1
1
1
1
1
0
1
1
2
2
1
1
2
1
0
0
2
2
1
1
1
1
1
1
0
0
1
1
1
2
1
2
1
0
1
1
0
0
0
1
2
2
2
1
2
1
1
1
1
2
0
0
1
1
0
0
2
1
1
0
0
1
2
0
1
1
0
1
2
2
2
0
1
1
1
2
2
0
2
1
2
1
1
2
2
1
1
1
1
1
2
1
2
1
1
0
0
2
1
2
1
2
3
1
1
1
1
2
2
0
2
1
1
1
0
0
2
2
0
2
2
1
1
2
0
1
2
1
1
1
1
1
1
1
2
2
0
1
1
2
2
1
1
1
3
1
0
1
1
2
0
1
0
0
1
1
1
1
0
2
1
0
1
1
2
0
1
1
0
2
0
2
0
2
1
1
1
0
0
1
1
1
1
1
1
0
1
1
2
2
0
1
1
1
0
2
1
2
0
2
0
1
0
1
2
0
1
0
1
1
2
2
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
2
0
0
2
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
2
0
0
1
2
2
1
3
1
1
0
1
0
2
2
2
0
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
0
0
3
1
1
1
1
1
0
1
2
1
3
2
2
0
1
1
0
1
1
1
0
1
1
1
1
1
1
2
1
1
2
0
1
1
2
1
1
1
1
2
1
1
2
1
2
1
0
1
1
0
1
1
1
1
0
1
1
1
1
0
1
1
1
2
1
2
2
1
2
2
1
2
1
2
2
0
3
1
2
1
1
1
0
1
1
1
1
1
1
0
1
2
1
1
2
1
1
1
0
4
0
2
0
1
1
0
2
0
1
0
1
1
2
1
1
2
3
2
2
2
1
2
1
1
2
1
1
4
2
2
2
1
1
1
1
1
0
1
1
1
1
1
1
1
1
2
2
1
0
0
1
1
1
2
2
1
0
1
1
0
2
2
0
2
1
2
2
1
2
1
1
1
2
1
0
0
2
1
0
2
1
2
1
1
1
1
2
0
1
0
2
0
1
1
1
1
0
1
1
0
1
1
1
2
2
1
1
1
1
0
1
1
0
0
1
2
0
0
2
2
0
1
1
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
0
1
2
0
1
0
1
1
1
0
1
1
1
1
1
0
1
2
2
2
0
1
1
1
1
1
1
2
2
0
0
1
1
2
0
2
1
2
2
2
1
1
1
0
0
1
2
1
0
2
1
0
1
1
1
0
1
1
1
1
1
0
0
1
1
1
1
1
2
0
2
1
1
1
2
0
1
1
1
0
1
1
1
1
2
0
1
1
1
2
0
1
1
1
1
1
0
1
1
1
1
1
1
2
1
0
1
0
1
1
1
0
1
1
1
1
1
2
1
2
2
2
1
1
1
2
1
1
1
1
0
1
1
1
1
2
1
0
1
2
1
0
1
1
1
1
1
1
2
1
1
2
1
1
0
1
1
1
1
2
1
0
1
0
1
2
1
1
0
1
1
1
1
2
0
1
1
1
2
2
1
0
1
0
0
1
1
1
1
1
2
0
1
1
0
0
0
1
1
0
2
2
1
1
0
1
1
2
2
1
0
1
2
1
1
0
1
1
2
1
0
1
0
2
2
1
1
0
1
2
1
1
2
1
1
2
2
1
1
1
1
1
0
1
3
1
2
0
1
1
0
2
1
1
1
1
1
1
0
1
1
2
1
0
1
2
1
0
1
1
2
2
2
2
1
2
1
1
2
0
0
1
1
0
1
1
1
0
0
1
1
1
0
1
2
2
1
1
1
2
1
2
0
1
0
0
2
2
2
0
1
1
1
1
1
2
1
2
2
1
0
2
0
1
1
2
1
2
2
2
1
1
1
0
2
1
2
1
2
0
1
0
1
1
0
2
2
2
1
0
1
0
1
1
1
0
0
2
1
2
2
1
1
1
2
2
1
1
0
1
0
1
1
1
2
0
1
2
1
1
2
2
1
0
2
2
1
1
1
1
2
0
1
1
1
1
0
1
2
1
1
2
1
0
0
1
1
0
2
1
0
1
2
1
2
1
1
0
1
1
1
1
0
0
1
2
1
1
1
1
1
0
1
0
1
2
1
1
1
1
2
1
1
0
2
1
2
1
1
1
1
2
1
1
0
1
1
2
1
1
2
0
1
0
2
1
2
1
1
1
1
2
1
2
1
2
1
1
2
3
1
1
3
1
1
2
0
2
1
1
0
1
1
1
1
0
1
0
1
1
1
2
1
1
2
1
2
0
1
2
0
2
1
2
1
1
1
1
2
1
2
1
0
2
1
1
1
0
2
1
2
1
1
2
1
2
2
2
1
1
1
0
1
1
1
0
0
1
0
2
1
1
1
1
0
2
1
1
1
1
1
1
0
2
2
2
1
2
1
2
0
1
2
0
1
1
1
1
0
1
1
1
1
2
0
0
2
2
2
0
0
2
1
0
1
2
1
0
0
1
1
0
1
0
2
0
0
3
1
0
2
2
1
1
2
0
1
1
1
1
2
1
1
2
1
0
1
1
1
2
1
1
1
1
2
0
2
1
1
0
0
1
1
1
2
0
1
2
0
0
1
2
1
0
1
1
1
1
1
0
1
2
1
2
1
1
2
1
0
1
2
1
0
1
1
1
1
0
1
0
1
1
1
1
0
1
1
1
1
2
2
2
1
0
1
1
1
1
0
1
1
2
2
0
0
2
0
1
1
1
1
0
1
1
1
1
1
0
1
2
1
1
0
1
1
1
2
0
1
1
0
1
0
1
1
1
0
0
2
0
0
2
2
0
1
0
2
1
0
2
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
1
1
1
2
2
2
1
1
1
2
1
1
2
1
2
1
2
1
1
1
1
1
1
0
0
1
2
1
0
2
2
1
1
1
2
0
0
1
1
0
1
0
2
1
1
1
1
2
1
1
0
0
2
1
2
0
1
1
1
2
1
1
1
1
2
1
2
0
0
1
1
1
2
1
0
1
2
2
1
1
1
1
2
1
2
0
2
1
0
0
2
2
1
1
0
1
1
1
2
1
0
1
1
1
0
1
1
0
2
1
2
2
0
1
1
1
2
1
1
1
1
0
1
2
2
1
1
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
0
2
2
1
2
1
1
0
2
2
1
1
1
1
2
1
1
1
3
1
1
1
1
1
1
1
0
3
1
1
0
1
2
0
2
1
0
0
1
0
2
0
1
5
1
2
1
2
0
1
1
1
1
2
0
2
2
2
1
1
1
2
1
1
1
2
1
1
1
1
2
2
1
1
1
1
1
2
2
1
1
1
2
0
1
1
1
1
1
0
1
1
1
2
1
1
1
2
1
1
2
1
2
2
2
1
1
1
0
1
1
1
0
1
1
0
1
2
1
1
1
1
2
1
1
1
2
2
2
2
0
1
1
0
2
0
1
1
2
2
1
1
1
1
0
1
1
1
1
0
0
0
1
1
1
0
1
1
0
1
0
1
1
1
2
1
1
2
1
2
0
2
0
2
1
1
1
1
1
0
1
1
1
1
1
1
0
1
0
2
1
1
1
2
0
2
1
2
2
1
1
0
1
1
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
1
2
1
0
2
1
1
1
1
1
2
0
2
2
0
2
1
1
2
0
1
1
1
2
1
2
2
0
1
1
0
1
1
1
1
1
1
1
2
1
0
1
1
1
1
1
1
2
1
1
0
1
1
1
2
1
1
0
1
0
1
1
0
0
1
2
1
0
1
1
1
1
1
1
2
0
2
0
1
1
1
0
1
1
0
2
1
2
1
1
1
0
1
1
2
1
2
1
1
0
1
0
1
0
1
1
1
2
1
2
1
1
1
1
2
1
2
1
0
2
1
1
1
1
1
1
1
8
1
0
1
0
1
1
2
2
0
2
1
1
1
1
2
1
1
1
1
2
2
0
1
2
1
2
2
1
1
2
1
2
2
2
1
2
0
1
2
1
1
1
1
1
1
1
1
1
1
0
1
2
1
2
1
0
1
1
1
1
1
0
1
0
1
1
1
1
0
1
1
0
1
2
2
1
1
1
1
2
0
1
1
1
2
1
1
2
1
0
0
1
1
0
1
1
1
1
1
2
2
1
2
0
1
0
1
1
2
1
1
2
1
1
1
2
2
1
1
0
2
2
2
1
2
1
1
2
1
1
1
2
0
1
0
0
1
1
1
1
1
1
0
0
2
0
1
1
1
2
2
0
2
1
2
2
1
0
2
1
1
1
0
1
1
0
1
1
2
1
2
2
1
2
1
1
1
2
0
1
0
0
1
1
2
1
1
1
1
1
0
0
1
1
2
1
1
0
1
2
1
1
1
0
2
1
1
2
0
1
1
3
2
1
2
2
2
0
1
0
1
1
2
1
1
0
2
1
1
0
1
0
1
1
2
1
1
2
0
2
0
1
1
0
1
1
1
1
2
1
2
2
2
0
1
2
1
1
1
0
1
1
1
0
0
1
1
2
2
1
0
0
1
2
3
2
1
1
0
1
2
0
1
1
1
2
2
1
0
1
1
2
1
0
1
1
1
1
1
0
1
1
2
1
3
0
2
1
0
1
1
1
0
1
0
0
1
1
0
2
1
1
1
2
2
1
1
2
2
1
1
1
1
2
2
1
1
2
0
2
1
1
2
2
1
1
0
1
2
2
1
1
0
1
1
1
1
2
0
2
0
0
1
2
0
1
1
0
1
1
0
1
2
0
1
1
1
0
2
1
1
0
2
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
0
0
1
1
1
1
0
0
1
2
1
1
1
1
1
0
2
2
2
0
1
2
1
1
0
1
2
1
2
1
2
1
1
1
0
0
1
0
0
1
1
2
1
1
1
2
0
1
2
1
1
2
2
1
1
1
0
1
2
1
1
2
2
1
2
2
1
0
0
1
1
0
1
1
1
1
2
1
2
1
0
1
0
1
0
2
1
1
1
0
1
1
1
1
0
1
1
1
1
4
1
1
1
1
2
1
1
1
1
0
3
1
1
0
2
1
0
1
1
0
0
1
1
0
1
1
2
1
1
0
2
1
0
1
0
0
2
1
1
2
1
2
1
2
0
1
0
0
2
3
1
1
1
0
0
1
1
0
1
0
0
2
1
0
0
0
1
0
2
2
1
0
2
1
2
1
1
0
0
2
1
2
1
1
1
0
1
0
1
1
1
1
0
1
2
0
1
1
2
1
1
2
1
0
1
1
1
1
2
1
1
1
1
0
1
0
0
0
0
1
2
1
1
1
0
1
1
1
0
1
1
1
2
0
1
1
2
0
2
1
2
1
1
2
2
2
1
2
0
2
2
1
1
1
0
2
1
1
1
1
0
1
2
1
1
1
2
2
1
1
2
2
1
1
2
0
1
1
1
1
1
1
0
0
2
2
2
1
1
1
1
2
2
0
2
2
2
2
0
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
0
0
1
1
2
2
1
1
1
2
1
1
1
2
1
0
1
1
1
1
1
0
1
1
0
0
1
1
0
2
1
1
1
1
2
0
2
1
0
1
2
1
1
0
1
1
1
1
1
1
1
2
0
1
1
1
0
1
1
2
1
1
1
2
1
0
0
1
1
1
1
1
1
1
0
0
2
0
1
1
2
1
1
1
1
0
1
1
0
1
1
1
1
2
1
1
1
1
1
2
1
2
0
1
0
0
1
2
1
1
0
0
0
1
1
1
1
1
1
2
1
1
0
1
1
1
1
2
1
1
2
1
0
0
2
0
1
1
1
1
0
2
1
0
1
2
1
1
1
1
1
2
1
0
1
1
2
0
0
1
0
1
1
1
2
1
1
1
1
3
1
1
1
0
2
1
0
2
1
1
2
2
1
1
2
2
1
1
1
1
0
1
2
1
1
1
1
1
1
2
1
1
2
1
2
2
1
1
1
0
0
1
1
1
2
0
1
2
1
1
1
2
1
2
1
1
0
1
0
2
1
1
1
1
1
1
1
1
0
1
1
1
1
0
1
2
2
1
2
1
1
1
1
0
1
0
2
1
2
2
0
1
1
2
2
1
0
1
1
1
1
0
1
0
1
2
1
1
1
1
2
1
0
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
0
1
0
2
1
1
0
1
1
1
2
2
2
1
1
1
1
0
1
2
1
2
1
1
1
1
2
0
2
1
2
1
1
1
3
1
1
1
2
0
2
0
2
1
1
0
0
1
1
0
1
1
1
2
0
2
0
1
2
0
1
0
1
1
1
1
2
1
2
1
0
2
0
1
2
1
0
2
1
1
2
2
1
1
2
1
1
2
0
2
1
1
1
2
2
1
2
1
1
1
1
1
0
1
0
2
2
1
0
1
1
1
1
2
2
0
0
1
0
1
0
1
1
2
0
1
1
2
0
1
1
0
1
0
0
1
1
2
1
2
1
1
1
2
2
1
1
0
1
2
1
1
1
1
0
1
1
1
2
1
1
1
2
2
1
1
2
2
1
1
1
2
2
2
1
1
2
1
2
2
0
1
1
0
2
1
1
2
1
1
2
0
2
2
0
2
0
1
0
1
1
1
1
2
0
2
1
1
1
1
0
1
1
0
1
1
1
0
2
2
1
1
1
1
0
1
1
1
0
2
2
1
2
1
1
1
1
1
2
1
1
2
0
2
1
1
1
1
2
1
1
1
2
1
2
2
0
2
2
2
2
1
1
1
1
0
2
1
0
0
1
0
1
1
2
1
1
1
0
2
1
0
1
0
1
2
1
0
1
1
1
2
1
1
1
1
2
1
1
1
0
0
0
1
1
1
2
1
1
2
1
1
1
1
1
2
1
2
1
1
0
0
0
1
0
2
2
1
1
2
0
2
2
0
1
0
1
2
1
1
1
1
0
0
2
1
0
1
2
1
0
0
1
1
1
1
1
0
1
2
1
1
0
0
5
2
1
1
2
0
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
0
1
1
0
2
1
1
2
1
1
1
1
0
2
1
0
1
1
1
1
1
0
2
0
1
2
0
1
1
1
1
2
1
1
1
1
1
0
1
2
2
2
1
0
0
1
2
2
0
1
1
1
0
1
1
1
1
1
0
1
1
2
0
1
1
1
0
1
2
2
1
1
1
1
1
2
1
2
2
0
1
1
1
1
2
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
0
0
0
1
0
1
1
1
0
2
1
2
1
1
2
1
2
1
2
2
1
0
0
2
2
1
1
2
1
1
2
0
2
0
1
1
2
2
1
1
1
2
1
1
2
0
1
1
2
1
1
1
2
1
1
1
2
0
1
3
0
2
2
1
1
1
0
1
1
1
0
1
0
1
0
2
1
0
2
1
0
1
1
0
3
1
2
1
2
1
1
1
1
1
2
2
1
1
1
1
1
2
0
2
0
1
0
2
1
0
0
1
1
1
2
2
2
1
1
0
2
0
1
2
1
2
3
2
0
2
1
1
2
0
2
2
1
1
2
0
2
0
0
1
1
0
1
2
1
0
1
1
1
2
2
0
1
0
1
1
1
1
1
1
1
0
0
1
1
2
2
1
1
1
2
2
0
1
1
1
0
1
1
1
0
1
0
1
1
1
1
0
1
1
1
2
2
0
1
1
2
2
0
2
0
1
3
2
2
1
2
1
1
0
1
2
2
1
5
1
0
1
1
1
1
0
0
2
1
1
1
1
1
1
1
1
1
2
1
1
1
0
0
1
1
2
1
1
2
0
2
1
0
0
2
1
1
1
1
2
1
1
0
1
2
0
1
2
1
0
2
1
2
1
2
0
1
1
0
1
1
1
1
1
1
2
1
2
1
0
1
0
1
1
2
0
1
1
1
1
0
1
2
1
1
0
1
1
2
1
2
1
1
1
1
2
1
1
0
1
1
1
0
0
1
1
1
0
1
0
2
1
1
1
1
2
2
1
1
1
1
2
0
2
1
1
1
1
1
1
1
1
1
2
1
0
1
1
2
1
1
1
1
1
1
0
0
1
1
1
2
1
1
2
1
1
2
1
2
3
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
0
1
1
2
0
1
1
1
2
0
1
2
1
1
1
2
1
1
1
1
0
1
1
3
1
1
1
1
1
2
1
0
1
1
1
2
1
1
3
3
0
1
2
2
0
1
1
2
1
1
1
1
1
1
2
1
0
1
2
0
1
2
1
1
3
0
1
2
1
0
2
1
0
1
0
2
1
1
2
1
1
1
1
1
3
0
2
2
0
1
1
1
1
1
1
1
1
1
0
1
1
0
0
1
0
1
1
2
1
2
2
1
1
1
1
2
2
1
2
2
0
2
0
2
0
1
1
1
1
0
1
1
2
1
1
0
1
2
1
2
2
1
1
0
1
3
1
1
2
2
2
1
0
1
1
2
0
0
1
1
2
0
1
0
2
1
1
0
2
1
2
1
1
1
2
0
0
1
1
0
1
2
1
1
0
0
1
1
2
2
1
3
1
1
1
1
1
1
1
1
1
1
1
0
2
1
1
1
1
2
1
1
3
1
1
0
1
1
1
1
1
1
1
2
1
0
0
2
0
2
1
1
1
2
0
1
1
2
1
0
0
0
1
1
0
1
2
1
0
2
2
1
0
1
1
0
1
2
1
1
1
0
2
0
0
1
1
1
1
1
1
1
2
1
2
1
1
0
2
1
1
1
1
1
0
1
1
0
2
0
1
1
1
0
1
2
0
1
1
1
1
1
1
4
1
0
1
0
1
0
1
1
2
0
2
2
1
1
1
1
1
1
2
1
1
0
1
1
0
0
0
1
0
1
1
1
0
1
1
0
1
1
2
1
0
1
1
1
0
0
1
2
2
1
2
1
1
2
2
1
1
1
1
4
0
2
2
0
1
2
2
1
1
1
0
1
1
0
1
2
0
1
2
2
0
1
1
1
0
2
2
1
1
1
2
1
1
0
2
1
0
0
1
0
2
2
1
0
2
1
1
0
1
1
0
1
1
3
0
1
1
1
3
1
2
0
1
1
1
0
0
1
2
1
1
2
1
1
1
2
1
2
2
1
0
2
1
1
0
0
1
0
1
1
0
0
1
2
1
1
0
0
1
2
0
1
1
2
1
1
1
1
2
1
1
0
1
1
2
2
2
1
0
1
2
1
2
1
1
2
1
2
1
1
1
0
0
1
1
0
1
1
2
1
1
2
1
0
2
2
1
1
2
0
1
2
0
1
1
1
2
1
2
1
2
1
1
1
0
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
2
2
1
1
1
1
0
2
1
2
0
1
1
0
1
1
1
2
0
1
1
1
1
1
1
0
2
0
1
0
1
0
0
1
1
0
1
1
0
0
2
0
1
0
1
3
1
0
3
2
2
2
2
1
1
1
1
1
0
1
1
1
2
1
1
0
1
0
2
1
1
1
0
1
2
1
2
1
2
1
1
2
2
1
2
0
1
0
1
0
2
1
1
0
1
0
1
2
4
0
1
1
1
2
1
2
1
2
1
1
2
1
2
2
0
1
1
4
2
2
0
1
1
1
2
2
2
1
1
2
2
1
2
2
1
2
1
1
1
1
2
2
2
2
1
1
0
1
2
0
2
1
3
1
1
1
1
1
2
0
2
1
2
1
1
2
1
0
1
1
1
1
1
1
1
0
1
1
1
0
2
1
1
1
1
2
0
1
1
1
1
1
1
1
0
0
2
2
1
0
2
0
0
1
0
0
1
1
1
0
1
1
1
1
1
0
0
1
0
1
0
1
1
1
1
2
2
1
3
1
2
2
1
0
1
2
1
2
0
3
1
1
0
2
2
1
1
1
1
1
2
0
1
2
0
2
1
0
1
0
1
1
0
1
1
2
2
1
0
0
1
1
2
1
0
2
1
1
1
1
0
0
0
1
1
2
1
2
1
1
1
1
1
2
0
0
1
0
1
0
3
1
0
1
0
1
2
1
0
1
0
0
1
1
1
1
1
0
1
1
1
2
0
1
1
1
1
1
1
1
1
1
5
1
1
1
1
5
1
2
1
8
1
1
2
0
1
1
0
2
1
0
1
1
0
1
2
1
3
1
0
1
1
2
1
1
2
1
1
1
1
2
0
0
1
1
1
1
1
2
1
1
1
0
1
2
1
2
1
2
2
0
2
1
2
1
1
2
1
1
2
2
0
1
2
2
1
0
1
1
0
2
1
2
1
1
1
2
0
1
1
0
0
0
2
0
2
2
1
0
2
1
1
2
1
1
1
1
1
0
0
1
1
1
1
1
1
1
0
0
1
2
2
1
2
1
0
1
1
1
1
2
1
1
1
1
0
1
1
1
1
1
1
3
2
1
2
1
0
0
1
1
1
2
1
1
2
0
0
1
1
2
0
0
0
1
1
0
1
1
0
1
0
2
0
1
1
1
1
0
1
1
1
1
2
1
2
2
0
0
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
0
1
1
2
2
4
1
1
1
1
0
1
0
2
1
1
2
1
1
1
1
1
2
1
1
0
2
1
1
2
1
1
0
0
3
1
0
1
1
1
1
1
1
1
1
2
1
1
1
1
0
1
2
1
1
1
1
2
1
2
1
1
1
1
1
0
0
1
2
1
1
1
1
1
2
1
1
2
0
1
1
1
1
1
1
2
1
1
2
1
0
0
1
0
2
1
1
0
1
0
2
0
1
1
0
1
1
0
2
1
1
2
1
0
1
1
1
0
1
3
0
2
1
2
1
1
2
0
1
1
1
0
0
1
0
2
2
2
1
1
1
1
1
2
2
1
1
1
2
1
0
1
1
1
0
2
1
1
0
2
1
1
1
2
0
1
2
0
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
0
1
2
1
0
2
1
0
2
1
1
1
1
1
0
2
2
2
0
1
1
2
2
1
1
2
2
1
1
2
1
0
0
2
1
1
1
1
0
1
2
0
0
1
0
1
2
1
1
1
2
0
1
2
1
1
1
1
1
1
1
1
1
0
1
1
1
2
0
1
2
1
2
2
1
0
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
0
1
2
0
1
2
1
1
0
1
2
0
0
1
0
0
1
2
1
1
2
0
1
2
1
1
1
1
2
1
1
1
1
1
2
0
1
1
0
1
1
1
1
1
1
1
1
2
2
0
1
1
1
1
2
0
1
2
0
2
0
0
0
2
2
1
1
1
1
0
1
1
1
1
1
1
2
0
2
1
2
1
1
1
1
1
1
1
1
0
1
1
1
1
1
2
1
1
0
1
1
2
2
1
1
2
1
1
1
1
1
1
0
1
1
0
2
1
1
2
2
2
1
0
0
1
1
0
2
1
1
0
1
1
1
1
0
0
0
1
1
1
1
2
0
2
2
1
0
0
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
2
1
0
1
0
3
1
1
1
1
0
1
0
2
2
1
2
1
0
2
0
1
0
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
0
1
1
2
0
1
2
1
2
2
1
2
2
1
1
2
0
2
1
2
0
0
0
1
1
2
1
4
2
1
2
2
2
0
1
1
1
1
1
0
2
2
1
0
2
1
1
1
0
2
1
1
1
2
2
1
1
1
1
1
0
1
0
2
2
1
1
2
1
1
0
0
2
1
1
1
2
1
1
2
0
1
1
1
0
1
1
1
1
0
0
2
2
2
2
1
0
1
0
2
1
1
1
1
1
4
1
1
2
2
1
0
2
2
1
1
1
1
2
1
1
0
1
1
2
2
2
2
0
2
0
2
0
0
2
1
1
0
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
0
2
2
1
0
1
0
1
2
1
1
1
1
1
0
1
1
1
0
1
1
2
1
2
1
1
2
1
2
2
1
1
3
2
1
1
0
0
0
0
1
2
2
1
2
2
0
1
0
1
1
1
1
1
0
0
2
0
2
1
1
1
0
0
1
2
1
2
2
2
1
1
1
1
2
1
2
2
3
1
0
2
3
2
1
0
1
1
1
0
2
1
0
1
1
0
1
1
1
1
2
0
1
0
1
1
1
1
1
1
2
0
1
0
2
0
1
1
0
1
0
1
1
1
0
2
2
0
1
1
0
0
1
1
0
1
1
0
1
1
1
1
2
0
0
0
1
2
2
1
2
2
1
2
0
0
0
1
1
2
1
2
2
0
1
1
0
1
1
2
0
1
1
1
2
2
1
1
0
2
1
1
1
1
0
2
0
1
1
0
1
0
1
1
2
1
1
1
0
0
1
0
0
1
1
1
1
1
0
1
0
0
1
0
2
1
2
2
1
1
2
2
1
1
0
1
2
0
1
1
0
1
1
1
1
1
0
2
0
2
1
1
2
1
1
1
1
0
1
1
2
1
3
1
0
0
2
1
1
0
0
1
0
1
1
0
1
2
1
1
1
0
2
0
2
0
1
1
1
2
1
1
0
1
2
2
0
0
2
1
1
1
2
0
1
2
2
1
2
1
1
1
1
1
1
2
1
1
0
1
1
0
0
1
1
2
1
1
1
1
2
2
1
1
0
1
1
1
1
0
0
2
1
0
2
2
1
1
1
4
2
0
1
1
1
1
1
1
1
1
0
0
1
2
2
2
1
1
1
1
2
0
1
2
1
2
0
0
1
0
1
2
2
1
1
2
1
0
1
2
1
1
1
2
2
0
2
2
1
2
1
0
0
2
2
1
1
0
2
1
2
2
1
2
1
0
2
0
0
0
0
0
1
1
0
1
1
0
2
1
1
0
1
0
1
0
1
2
1
1
0
1
1
0
1
2
1
1
0
0
1
1
1
2
1
1
1
1
2
1
1
0
1
2
2
1
0
0
0
0
1
1
1
2
2
2
1
2
1
2
1
1
2
1
1
1
2
1
0
1
1
0
0
1
1
0
1
1
2
1
1
2
1
1
1
0
1
2
1
0
1
1
2
2
1
2
1
0
1
1
1
1
1
2
1
0
0
1
1
1
2
1
1
1
0
0
1
2
1
0
2
1
2
2
0
1
1
1
0
2
2
2
0
1
0
0
2
1
2
1
1
1
0
0
0
1
1
0
0
2
1
0
1
2
1
1
2
1
0
1
2
1
3
1
2
1
0
1
1
2
2
1
1
1
0
1
0
0
2
1
2
2
1
0
1
1
1
1
0
1
2
0
2
1
2
1
1
1
1
0
1
1
2
2
2
0
2
1
1
1
1
1
1
2
1
0
0
1
1
4
2
2
1
1
0
0
2
0
0
1
2
1
1
2
2
1
1
1
2
0
2
2
2
1
1
1
2
1
1
1
1
1
2
1
1
2
2
2
2
0
1
1
1
2
0
2
0
1
0
1
1
1
2
0
0
0
0
1
1
2
1
1
1
1
0
2
1
1
1
0
3
1
2
4
2
1
1
1
1
0
0
0
1
0
1
2
2
1
2
1
1
2
1
0
0
1
0
0
1
1
0
1
1
1
1
1
1
1
1
1
1
0
2
1
1
2
2
1
1
2
1
1
1
1
1
1
1
2
1
1
2
2
2
0
1
0
1
1
1
2
1
1
1
1
0
2
1
1
0
2
1
1
0
1
2
1
1
1
2
1
1
1
1
1
1
1
1
0
2
1
1
1
1
1
1
2
0
1
2
1
1
1
1
1
1
1
1
1
1
0
2
1
0
1
2
1
2
0
0
1
1
0
1
0
2
1
1
0
1
1
2
2
0
1
1
1
2
1
1
0
0
1
1
2
1
2
2
1
1
1
1
1
0
2
2
1
0
2
1
1
2
1
1
1
1
1
1
0
0
1
0
1
1
0
1
1
0
1
2
1
1
1
1
2
2
2
0
1
2
1
0
0
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
0
2
2
1
0
1
2
2
1
1
0
1
1
2
2
1
1
1
2
0
1
2
0
0
1
1
1
4
1
2
2
2
1
1
1
0
1
0
1
1
2
1
1
1
1
2
1
1
1
1
1
0
2
1
1
0
2
0
1
1
1
1
1
0
1
1
0
1
0
0
1
1
0
0
1
1
1
1
1
1
1
1
1
1
1
2
1
0
0
1
1
1
0
2
1
1
2
1
1
1
0
0
1
1
2
1
2
0
2
2
1
1
1
0
0
2
1
1
1
1
2
1
1
1
0
0
1
1
1
1
2
1
1
2
1
1
2
1
2
1
2
2
2
1
2
1
1
1
2
0
1
1
1
0
2
1
1
1
0
0
1
0
1
2
1
2
1
2
2
1
2
1
1
1
0
2
1
1
0
1
2
2
2
2
1
1
0
1
1
1
2
1
1
1
1
1
1
1
0
1
2
2
1
1
2
0
0
2
1
0
1
1
0
2
2
1
1
1
1
1
2
0
0
1
0
1
1
2
2
2
1
1
1
2
1
1
0
2
0
0
1
2
1
0
1
1
0
1
1
1
1
2
1
1
1
0
1
0
1
0
0
2
1
1
1
1
0
2
2
1
1
1
2
1
1
1
1
1
0
0
1
0
1
2
1
2
1
0
1
0
3
1
1
2
1
1
1
1
0
1
3
1
1
1
1
0
1
0
1
1
1
2
2
1
1
1
1
2
1
1
0
1
2
1
1
1
1
1
1
2
1
2
1
1
2
1
0
0
1
1
1
1
1
2
2
1
2
1
1
1
1
2
2
1
2
0
1
0
1
1
2
1
1
0
1
0
1
1
2
2
2
2
0
1
2
1
0
1
0
2
1
1
2
2
0
1
1
0
1
1
1
1
1
1
1
1
2
0
1
0
1
2
1
1
0
0
2
3
1
2
1
1
2
0
1
1
0
1
1
1
2
1
1
0
1
0
2
1
1
1
1
1
1
2
2
0
2
1
2
2
1
1
1
1
1
1
2
1
1
2
1
1
2
1
1
0
1
1
1
2
0
0
2
1
1
1
1
1
2
1
4
2
1
0
1
1
1
1
1
0
2
1
2
0
0
0
0
1
1
0
1
1
0
1
2
0
0
1
0
1
0
2
1
1
1
0
1
1
1
1
0
1
1
2
2
1
0
1
1
0
1
1
2
2
0
1
1
1
1
1
1
0
0
1
1
2
1
2
1
0
2
1
1
2
1
1
0
0
2
1
0
2
0
2
1
2
1
1
1
1
2
1
1
2
2
1
1
2
1
1
1
1
1
1
0
2
1
1
1
1
1
1
2
1
1
1
0
1
1
1
1
1
0
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
0
0
1
2
0
1
1
2
0
1
1
2
2
1
0
1
0
0
0
1
1
1
0
0
0
1
1
1
0
1
1
1
0
0
2
1
0
1
2
7
1
1
1
2
1
1
1
1
1
1
2
1
2
1
1
0
1
2
2
1
1
1
1
1
1
1
1
0
1
1
1
2
1
2
1
1
2
1
1
2
0
1
1
2
1
1
1
1
1
2
1
2
2
0
2
0
2
1
1
1
1
0
1
0
1
2
2
1
0
0
0
1
1
1
2
1
1
1
2
1
1
1
2
0
1
0
1
1
1
1
0
0
1
2
1
1
1
1
2
2
2
1
1
2
1
1
1
1
1
0
1
2
0
0
1
0
0
2
1
1
1
1
1
2
0
0
2
1
1
2
0
1
2
0
0
1
2
0
0
1
2
2
2
0
1
0
0
1
2
1
1
1
0
1
2
3
1
1
1
2
0
2
1
2
1
0
2
1
1
1
1
2
1
1
2
1
1
0
1
2
1
1
0
0
2
2
1
2
2
1
0
1
1
2
2
0
1
1
1
0
1
1
1
2
2
0
0
2
1
0
0
0
1
1
1
1
2
0
0
1
1
2
0
1
2
1
1
1
1
1
0
0
0
1
3
2
0
0
2
2
1
2
1
0
1
1
1
1
1
0
1
1
1
1
1
0
1
2
1
0
1
0
1
1
1
1
2
2
2
0
0
2
0
1
0
1
1
1
1
2
1
3
1
1
2
2
1
1
1
0
1
1
1
1
1
0
0
1
1
1
0
2
1
1
1
1
2
0
1
0
2
1
0
1
2
1
0
1
1
1
1
2
1
2
0
0
1
1
3
1
1
1
1
2
1
2
0
1
1
2
0
0
1
1
1
1
2
2
1
1
2
2
1
2
1
1
2
1
0
1
1
1
1
1
3
1
1
2
2
2
0
1
1
1
2
1
1
1
1
1
1
1
1
2
1
0
2
2
1
1
1
1
2
0
2
1
2
2
0
1
1
1
1
0
1
2
2
2
1
1
2
1
3
0
1
1
1
2
2
0
1
0
2
1
2
1
2
0
1
2
1
1
2
1
0
1
2
0
1
2
1
1
1
1
1
2
1
1
2
2
1
1
1
0
1
0
1
0
1
1
2
1
1
0
1
0
0
2
2
1
1
2
0
1
1
0
1
1
1
1
2
1
1
2
1
2
2
1
2
1
2
2
2
2
1
2
1
2
1
1
1
1
1
0
2
1
1
2
2
2
1
0
1
1
2
0
0
0
1
1
1
1
1
1
1
3
1
1
2
1
2
1
1
2
0
2
1
0
1
0
0
1
2
0
1
1
1
1
1
1
1
1
1
1
2
2
1
1
0
1
1
1
1
1
1
1
2
0
1
1
1
1
1
1
2
1
1
0
1
0
1
0
0
1
1
0
1
1
2
1
2
1
0
2
2
1
0
1
1
0
1
3
1
0
2
2
1
1
1
1
1
1
2
0
1
1
1
1
1
1
1
1
2
1
2
2
1
1
0
0
0
1
2
1
0
1
2
1
1
1
2
1
1
2
0
1
2
0
0
2
1
0
1
0
2
1
2
1
1
1
1
3
2
2
0
2
1
0
2
1
1
2
1
0
1
2
2
2
1
2
1
1
2
0
2
1
2
1
2
2
1
3
1
0
0
1
1
2
1
1
2
0
1
0
1
2
2
0
1
0
1
1
1
2
1
2
1
2
1
1
1
1
0
1
2
2
2
1
1
1
1
1
1
1
0
1
1
1
1
1
0
0
1
1
1
1
2
1
1
1
1
1
1
1
2
0
2
2
2
0
0
2
1
0
2
1
2
1
1
0
1
2
2
0
1
1
2
0
1
0
1
1
1
1
0
2
0
0
2
0
2
1
0
0
1
1
0
0
0
1
2
1
1
1
1
2
1
2
1
1
0
1
1
0
0
1
1
1
2
1
3
0
1
0
1
1
1
2
2
1
1
1
2
1
1
0
0
1
0
2
1
3
1
1
2
1
0
1
1
1
2
0
0
0
2
1
1
1
1
2
1
1
2
1
1
2
2
1
1
0
1
0
0
0
2
1
0
0
0
1
1
0
0
0
2
1
1
2
1
1
1
2
2
2
2
0
1
1
1
1
1
2
1
1
0
1
1
2
1
2
1
0
2
0
0
2
2
1
1
1
2
2
1
1
1
2
1
1
1
4
1
2
2
1
1
1
1
1
1
0
0
1
0
2
1
1
1
1
2
2
1
0
1
1
1
1
1
1
2
0
1
1
1
1
1
0
0
1
1
0
0
1
1
1
1
1
1
1
0
2
1
1
2
1
0
0
2
2
1
1
1
0
1
1
0
1
1
1
1
2
2
1
1
1
1
1
2
2
0
2
1
1
1
1
1
1
2
2
2
2
2
1
1
4
1
0
1
1
2
1
1
0
1
1
1
2
1
1
0
2
1
1
0
1
1
1
1
1
1
0
1
0
1
1
1
2
2
1
0
3
1
2
1
1
2
1
0
1
1
1
4
1
1
2
1
1
0
0
2
1
2
2
1
0
1
1
2
1
1
1
1
1
2
1
1
2
2
1
1
1
2
1
0
1
0
0
1
2
3
1
0
1
1
0
1
1
2
1
1
1
0
2
1
1
2
2
2
1
0
1
1
0
0
1
1
1
1
0
2
1
1
1
1
2
1
1
1
1
1
1
2
1
0
1
2
1
2
1
3
1
0
0
1
1
2
2
1
1
2
1
1
1
2
1
1
1
1
1
1
0
1
2
1
2
2
2
1
1
1
1
0
1
2
1
1
1
1
1
1
2
1
1
1
0
2
2
0
2
1
1
1
1
0
1
1
1
1
1
0
1
1
2
2
1
1
1
1
0
1
0
1
1
0
1
1
2
1
0
1
0
1
1
1
0
1
1
0
1
0
1
1
1
0
1
0
1
0
1
1
1
2
2
1
1
1
1
1
1
2
1
1
2
0
1
1
0
1
1
1
1
2
2
1
1
1
1
1
1
1
0
2
1
1
2
1
2
2
0
0
0
1
1
1
2
1
1
1
2
0
2
2
1
2
1
2
2
0
1
1
1
2
1
1
1
1
1
2
1
1
1
0
1
0
2
1
0
2
0
1
1
2
2
0
1
1
0
2
2
1
1
1
1
0
0
1
0
1
1
0
2
2
2
0
1
1
1
0
0
1
2
0
1
0
0
0
1
1
1
1
1
1
1
0
1
0
2
1
2
1
1
1
2
2
2
1
1
0
1
0
1
0
1
2
1
1
4
1
0
1
0
2
1
1
2
2
2
1
1
1
1
2
1
1
0
1
2
1
0
2
1
1
0
1
2
1
1
1
0
0
1
1
2
0
1
2
1
0
0
1
0
1
2
1
2
1
1
2
2
2
0
2
1
1
0
0
1
2
1
1
2
1
2
1
1
2
0
2
1
2
0
0
2
0
1
1
1
1
1
2
1
1
0
2
0
1
1
1
1
2
2
1
0
1
1
0
1
0
2
0
2
1
1
1
2
0
0
1
2
1
2
0
1
1
0
0
0
1
2
1
0
2
1
1
2
2
0
2
2
1
0
1
1
2
1
2
1
1
0
1
0
1
1
1
0
0
1
1
1
1
2
1
0
0
1
1
1
1
1
2
1
1
2
1
0
2
1
0
1
1
2
1
1
1
1
0
1
1
1
1
1
1
2
2
1
1
3
1
0
1
1
1
2
0
1
0
2
2
2
0
1
2
1
0
1
2
1
1
0
1
1
0
2
0
1
2
0
2
0
0
1
1
1
1
0
1
2
1
1
0
2
1
1
2
1
0
1
3
2
1
1
1
0
1
1
1
2
1
0
1
1
0
2
2
2
2
1
0
2
1
1
1
1
1
0
1
0
1
3
1
0
1
2
1
1
1
1
0
1
1
3
1
2
2
2
2
1
1
1
0
1
1
3
3
1
0
0
0
1
1
2
1
1
2
2
0
1
1
1
1
1
1
1
0
1
0
1
1
0
0
1
0
2
0
1
1
0
1
1
1
0
1
1
1
2
1
1
1
1
1
1
2
0
1
2
1
1
1
1
1
2
2
2
1
0
1
1
1
1
2
1
0
1
0
1
1
1
2
1
1
1
0
1
1
1
1
1
1
1
0
1
1
0
0
2
1
1
0
1
2
1
2
1
1
2
1
0
1
1
2
1
2
0
1
2
1
2
1
1
0
2
1
0
1
1
1
0
1
1
1
1
1
1
1
1
2
0
2
1
0
0
2
1
1
2
2
1
0
1
1
1
1
0
2
0
0
2
1
2
1
1
1
0
1
1
1
0
2
1
1
2
1
1
0
1
1
0
1
1
0
1
1
1
2
2
1
0
2
1
0
0
2
1
0
0
2
1
0
1
1
1
1
1
1
2
1
1
1
1
0
2
1
0
1
1
0
1
0
0
1
0
1
1
1
1
1
1
1
1
1
0
2
2
2
1
1
0
1
0
1
1
1
1
1
1
1
2
1
2
2
1
2
1
2
1
1
2
1
3
1
2
2
1
1
1
0
2
1
0
2
0
1
2
1
1
1
2
1
1
2
1
1
1
1
2
1
2
1
1
2
1
2
1
2
1
2
1
1
0
1
0
1
1
1
2
1
0
1
2
1
1
1
2
1
1
1
2
1
1
0
1
1
0
0
1
1
1
1
1
2
2
1
2
2
1
1
2
0
1
2
1
0
1
1
2
2
1
0
2
1
1
1
3
1
1
0
1
1
0
2
0
2
1
2
1
1
1
1
2
1
1
1
4
1
0
1
2
1
1
2
2
0
1
1
0
1
1
0
2
1
2
0
1
0
2
1
0
1
0
1
1
0
1
1
1
1
1
0
1
0
0
1
1
2
0
2
2
1
2
1
1
1
1
2
1
1
1
1
0
0
0
2
2
1
1
1
2
0
1
2
1
0
2
1
1
0
1
0
1
0
1
1
2
1
1
2
1
1
1
1
1
1
1
1
2
0
2
0
1
2
0
2
2
1
0
2
1
1
1
0
1
2
1
1
2
2
0
2
0
2
1
1
1
0
1
1
1
1
1
0
1
1
1
1
1
1
1
1
0
0
2
1
1
2
1
2
0
0
2
1
1
0
1
2
1
2
1
1
2
2
1
0
3
1
1
1
1
2
1
1
0
2
0
0
1
1
0
2
2
1
1
0
1
2
1
2
0
2
2
2
1
1
1
1
0
1
1
1
2
0
2
1
1
0
1
2
1
2
2
0
2
2
1
1
2
1
0
1
1
1
1
1
1
1
1
2
0
1
1
1
2
1
1
2
1
2
1
2
1
1
3
1
2
1
1
1
0
1
1
1
1
1
1
0
1
1
0
0
2
1
2
1
1
0
0
0
1
1
0
0
1
2
1
1
2
0
2
0
1
0
0
1
1
2
0
1
1
2
0
1
0
1
1
2
1
0
1
1
2
1
1
1
0
1
2
1
2
1
0
1
0
1
1
1
1
0
1
2
2
2
1
1
1
1
1
1
1
1
1
0
1
1
2
1
2
1
0
1
1
1
2
1
1
0
1
1
1
1
0
0
1
0
2
1
1
1
2
1
1
1
2
1
0
1
1
1
2
2
2
1
1
2
0
1
1
1
0
1
1
1
0
0
0
1
1
2
1
2
0
1
1
1
1
5
1
1
2
1
2
0
1
1
1
2
2
1
2
1
1
2
0
1
0
1
1
1
1
2
0
0
1
1
1
2
2
2
0
1
1
1
1
0
0
1
2
0
1
1
2
1
0
0
1
2
1
1
1
2
1
1
2
2
1
1
0
1
2
1
1
2
1
1
0
2
0
1
2
1
2
1
0
1
1
1
3
1
1
1
0
0
2
2
1
2
1
0
1
1
1
1
2
1
1
2
0
1
0
0
1
1
1
1
1
1
2
2
2
1
0
2
1
1
1
0
2
2
1
1
1
1
1
1
1
1
0
2
0
0
1
1
1
1
1
0
1
1
1
1
2
1
2
1
2
2
0
0
1
1
1
1
2
2
1
1
1
0
0
1
1
0
1
1
1
1
1
2
1
0
1
2
1
1
1
1
1
1
1
1
0
2
2
1
2
1
2
0
1
0
0
0
1
2
1
1
1
1
2
1
1
2
1
1
1
1
0
0
1
4
2
0
2
2
1
1
1
0
2
2
1
2
0
1
1
2
1
0
1
1
1
1
0
0
1
2
1
0
1
1
1
0
1
2
1
0
1
1
2
1
1
2
1
1
0
1
1
1
0
1
1
1
2
0
1
0
2
2
0
2
1
0
2
1
1
3
0
1
1
1
1
0
1
1
1
1
0
1
1
1
2
1
1
1
0
2
0
1
1
1
1
1
2
1
1
0
1
1
1
2
0
1
1
0
1
2
1
1
1
1
1
1
0
0
0
1
2
2
1
1
1
2
2
1
0
0
1
2
1
1
1
1
1
0
1
1
1
1
1
2
0
1
1
1
0
1
1
0
1
1
1
1
2
1
1
1
1
2
0
1
1
1
1
1
2
1
2
0
1
2
1
0
1
0
1
0
0
1
1
2
1
1
1
1
2
2
0
1
1
2
1
0
1
0
1
1
1
1
1
1
1
0
2
2
2
2
1
1
1
1
0
1
0
1
1
1
1
1
2
2
1
0
0
1
2
0
2
1
1
0
2
1
2
1
2
2
0
1
1
0
1
0
2
1
2
1
1
1
1
0
0
1
1
1
2
1
1
1
1
2
2
1
1
1
1
2
0
1
1
1
1
1
1
1
1
0
1
1
1
0
2
2
1
1
0
0
1
1
1
1
1
2
1
2
0
1
0
1
1
2
1
1
1
1
1
1
0
0
2
1
2
1
1
1
1
2
2
2
1
1
1
2
2
2
1
1
2
2
1
0
2
2
0
1
1
1
0
1
1
0
1
1
1
1
1
0
1
1
0
1
1
1
1
0
0
2
1
1
1
1
0
1
1
1
1
1
1
1
2
1
0
1
1
1
0
1
1
2
2
1
1
1
1
0
1
1
1
1
0
1
2
1
1
3
1
1
0
1
1
1
1
1
1
2
1
1
2
1
1
0
1
1
1
1
2
0
2
2
1
1
1
1
1
0
1
1
0
1
1
1
1
1
1
2
1
1
2
1
0
1
1
2
2
2
1
0
1
2
2
1
2
2
1
1
1
0
0
1
2
2
0
2
0
1
1
0
1
1
1
1
1
1
2
3
1
0
1
0
2
0
1
1
1
1
1
0
1
2
1
2
1
1
1
1
0
1
0
0
2
2
1
0
1
1
1
2
1
1
1
1
2
1
2
0
1
2
2
2
2
2
1
0
1
1
2
2
0
3
1
1
1
0
0
1
1
1
1
1
0
0
1
1
1
2
1
1
2
1
1
0
0
1
2
0
1
1
0
1
1
1
1
2
0
1
2
2
1
1
2
1
1
1
2
2
1
0
1
0
1
1
1
1
1
1
1
1
1
1
0
1
0
0
1
1
1
1
1
0
0
0
1
1
2
2
1
0
1
0
1
0
1
2
2
1
1
2
2
1
1
1
1
2
0
1
2
0
1
1
1
2
2
2
1
0
1
1
1
1
0
2
1
1
1
1
2
1
0
0
1
0
2
0
2
1
0
0
1
1
2
1
1
1
1
2
1
1
1
1
2
0
2
0
1
1
0
1
2
1
1
0
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
0
2
1
2
1
0
0
0
1
0
0
1
1
0
2
1
2
1
0
2
1
1
1
1
1
2
1
1
2
0
0
1
1
3
2
2
0
2
1
1
1
2
1
1
1
2
2
1
0
1
0
0
1
1
1
0
1
1
1
2
2
1
2
2
1
0
1
1
1
1
1
2
0
1
2
0
1
1
1
1
1
2
1
1
2
1
0
1
1
0
1
1
2
1
1
1
1
1
2
1
1
1
0
1
1
1
1
1
1
2
2
0
1
1
1
3
1
1
1
1
1
2
0
0
0
0
1
2
2
0
2
1
0
1
0
2
1
1
1
1
2
2
2
1
1
1
3
2
2
1
1
1
2
0
0
1
2
1
1
2
1
1
1
1
1
0
1
1
1
1
0
1
1
2
0
1
0
4
0
1
1
0
1
0
1
1
1
2
1
2
1
2
1
1
2
1
2
2
2
2
1
1
2
1
1
0
1
1
2
2
1
1
1
0
0
1
1
1
1
1
1
1
1
1
1
2
1
1
1
0
1
1
2
1
1
1
1
0
0
1
1
1
0
1
2
0
1
2
1
1
3
1
1
0
1
1
0
1
2
1
1
1
0
1
1
1
1
0
2
0
1
0
1
0
2
0
2
2
1
2
0
1
0
1
0
0
1
3
1
1
1
0
1
1
2
1
1
1
0
2
2
1
1
1
0
2
0
0
1
1
0
1
2
1
1
0
0
1
0
1
0
2
1
1
1
0
0
1
1
1
1
1
1
1
1
1
1
0
2
2
1
0
1
1
2
2
2
2
1
0
2
1
0
1
2
3
1
1
1
2
1
1
0
2
0
2
1
1
2
2
2
0
2
1
2
1
1
0
1
1
0
1
0
1
1
1
1
1
0
0
2
1
0
1
1
0
0
2
0
2
1
0
2
1
1
1
1
1
1
1
1
1
0
2
1
1
1
1
0
1
1
1
2
2
1
2
1
1
2
2
1
1
1
1
0
0
1
1
1
2
1
1
1
0
1
0
1
1
0
0
1
1
0
2
1
1
1
1
0
1
1
2
2
1
1
2
1
1
2
1
1
1
0
1
1
1
1
2
0
1
1
2
1
1
2
1
1
1
2
1
1
0
1
1
2
1
2
2
2
0
0
0
1
1
2
0
1
1
2
1
1
1
0
2
0
1
1
2
1
1
2
1
1
1
0
1
2
1
1
2
2
1
1
1
2
0
1
0
1
1
2
1
4
1
2
1
0
1
1
0
1
1
1
2
1
0
1
1
0
2
1
1
1
2
1
2
1
0
0
2
0
0
1
1
1
0
0
1
1
1
1
1
0
2
0
1
3
0
1
0
1
1
1
0
0
0
3
2
2
1
2
1
1
2
1
2
2
0
1
0
1
2
0
1
1
1
1
0
1
1
1
0
2
1
1
0
1
1
1
1
1
0
1
2
2
2
1
1
1
2
1
1
1
2
0
1
2
2
2
2
0
1
2
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
2
2
1
2
1
1
0
1
2
0
0
1
1
0
1
0
1
0
1
1
1
2
0
2
1
1
1
1
2
0
2
1
1
1
1
2
1
1
2
0
1
1
1
1
1
3
2
1
1
2
2
2
0
0
2
1
2
0
0
1
2
1
0
2
1
1
1
1
2
0
2
1
2
0
1
2
1
0
1
0
1
1
0
1
1
2
0
1
1
2
1
2
2
1
0
2
1
0
1
0
2
1
2
0
1
1
1
2
2
1
2
1
0
2
1
1
1
3
2
1
0
1
0
1
0
1
0
2
1
0
1
1
2
2
1
1
1
1
1
0
1
1
1
3
1
1
5
1
2
0
0
2
1
1
1
2
1
2
1
2
1
1
1
1
1
1
1
1
0
1
1
2
1
1
0
1
0
1
1
1
1
1
1
0
0
1
2
1
2
1
0
1
1
2
0
1
1
2
1
1
1
2
1
0
1
0
2
2
0
0
0
1
1
1
1
1
1
1
1
1
2
1
1
0
0
1
0
1
2
1
1
1
1
2
0
1
0
1
0
1
1
1
2
1
1
0
1
0
1
1
0
1
1
1
2
2
1
1
1
0
1
2
0
1
1
1
1
2
1
2
1
1
1
1
0
1
1
0
0
1
2
1
1
1
0
1
1
1
1
1
1
1
0
3
1
1
0
1
1
1
1
1
0
2
1
2
0
1
1
2
1
2
2
2
1
1
1
1
1
1
1
1
0
0
1
1
1
1
1
1
1
0
0
1
1
1
2
1
2
0
2
1
2
2
1
2
2
1
2
3
1
1
2
2
1
0
2
1
0
1
1
0
2
2
1
1
1
1
1
1
1
0
1
1
0
0
2
1
2
2
1
1
1
1
0
0
0
1
1
2
1
1
2
2
2
2
1
0
1
1
2
1
1
0
1
2
0
1
2
1
1
1
9
2
1
0
2
1
1
1
2
0
2
1
1
1
1
0
1
1
1
1
2
2
1
0
1
1
0
2
0
2
1
1
1
1
0
1
2
1
1
2
2
2
0
3
1
2
1
1
1
1
0
1
1
0
2
2
1
2
1
0
1
0
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
0
2
2
1
1
1
1
0
0
1
0
2
1
1
0
1
1
1
0
0
1
1
2
1
0
0
3
1
0
1
0
2
0
0
0
2
1
2
2
1
1
0
2
1
3
2
1
1
1
0
0
0
1
1
1
1
0
2
0
2
1
1
0
2
1
0
1
1
1
1
1
0
2
1
0
1
0
1
1
1
2
1
0
1
1
2
1
2
2
2
1
1
1
0
1
0
1
2
2
1
2
1
2
0
0
1
1
0
1
2
0
0
1
1
0
2
1
2
1
1
2
1
1
0
1
1
1
0
2
1
0
1
1
1
2
2
1
1
1
2
2
1
1
2
2
0
1
1
1
1
0
1
2
1
1
1
1
0
1
2
1
0
1
0
1
0
1
2
2
0
1
1
2
2
1
2
0
1
2
1
1
0
1
2
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
2
1
2
1
1
2
1
1
2
1
2
1
2
1
2
0
3
0
1
0
1
1
1
2
0
1
1
1
1
1
1
0
1
1
1
2
2
1
2
1
1
0
1
0
1
1
1
1
2
1
1
0
1
0
1
1
1
0
2
0
1
0
1
1
2
1
1
1
1
1
1
0
1
1
0
1
2
1
0
1
1
2
1
2
2
1
0
1
2
3
1
2
2
2
1
1
1
2
1
1
1
1
2
2
1
1
1
2
2
1
1
0
1
1
1
1
2
1
1
1
2
0
0
0
1
1
1
2
3
1
0
1
1
1
0
1
1
2
1
1
2
1
1
1
1
1
2
1
2
2
1
2
1
1
1
2
2
1
0
0
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
0
1
2
1
2
1
2
3
2
1
1
1
1
1
2
0
1
2
1
2
1
1
1
0
2
0
1
2
1
2
2
1
1
1
0
2
1
1
1
1
2
1
2
1
0
2
1
0
1
1
1
2
1
2
0
1
2
1
1
2
0
1
2
3
0
0
1
1
0
1
1
2
1
1
1
2
2
1
4
0
2
0
0
2
1
2
0
1
1
2
1
0
1
0
2
0
2
0
2
2
0
1
1
1
1
1
0
1
2
2
2
0
1
2
1
2
1
1
1
2
1
1
1
1
2
0
1
1
1
2
1
1
2
1
1
1
1
1
1
2
5
1
2
0
1
1
1
1
1
1
0
2
1
1
0
1
1
2
1
1
1
1
1
0
2
1
1
1
1
1
3
2
1
1
0
1
1
2
1
0
1
1
2
1
1
0
1
1
2
0
1
1
1
1
0
2
1
1
1
1
0
1
0
0
1
0
2
1
1
0
1
1
2
1
1
1
0
4
1
0
1
2
1
1
2
0
1
0
1
1
1
0
1
1
0
2
2
0
0
1
1
1
2
0
1
1
1
2
1
1
1
2
1
1
1
1
1
0
1
1
0
2
1
2
2
1
0
2
2
0
1
2
1
0
2
1
1
0
2
1
0
1
0
0
1
1
1
0
0
1
0
0
0
0
1
1
2
0
0
2
2
1
2
1
1
1
1
1
1
0
0
0
1
1
1
2
1
1
0
0
1
0
1
1
2
0
1
2
1
1
1
1
1
0
2
1
1
1
0
0
1
0
1
1
1
1
1
0
2
1
0
3
2
1
1
0
0
1
2
1
2
2
0
1
0
0
1
1
1
0
1
1
1
1
1
1
1
1
2
1
2
1
1
2
1
2
0
1
0
1
2
0
1
1
1
2
0
2
1
1
2
2
1
1
1
1
0
2
0
0
2
1
0
1
2
1
1
1
0
2
1
2
1
2
2
1
0
1
1
0
0
1
1
2
1
2
1
1
1
2
1
1
3
1
1
1
1
0
1
1
0
2
1
2
1
1
0
1
2
2
1
2
1
1
2
0
1
0
2
0
1
0
1
1
0
1
2
1
0
1
1
0
1
0
2
2
1
0
2
1
2
1
2
1
0
1
1
1
1
2
0
1
1
1
1
2
2
4
2
0
1
2
1
1
1
1
1
1
1
0
2
1
1
1
1
1
1
1
1
2
0
1
1
1
1
2
1
0
1
1
1
0
1
2
3
1
1
1
1
1
1
1
2
1
0
2
2
0
1
1
1
1
1
2
1
1
1
0
2
2
1
2
1
1
1
0
1
2
1
1
1
1
0
1
1
1
1
1
2
1
1
2
1
1
2
1
2
0
2
1
1
1
1
1
0
1
1
1
1
0
1
2
2
2
2
1
1
1
1
1
1
1
0
0
1
0
1
3
0
1
1
1
1
1
1
3
1
2
2
1
2
1
1
0
2
0
1
1
0
0
2
1
2
2
2
2
1
1
1
3
0
2
1
1
0
2
2
1
1
0
1
2
1
1
0
0
3
0
3
0
0
1
1
1
1
1
1
2
1
2
1
0
2
1
2
0
1
1
1
1
1
1
2
0
0
1
1
1
0
5
2
1
3
1
0
1
1
2
2
1
2
2
1
2
2
1
2
0
0
2
0
0
1
1
2
1
2
1
1
2
1
0
2
2
1
1
1
2
1
2
1
2
1
1
0
1
1
0
1
2
2
1
2
1
1
0
1
1
1
0
1
1
1
2
0
0
0
1
2
1
2
2
1
1
1
2
1
1
1
1
1
1
0
0
1
1
2
0
1
2
1
2
2
1
0
1
1
0
0
0
2
2
1
2
2
1
1
1
0
1
1
1
1
1
1
1
2
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
0
2
1
0
0
1
1
1
1
1
2
1
0
2
1
1
1
0
1
2
1
0
1
0
2
2
1
1
2
2
2
2
1
2
1
1
1
1
2
0
2
1
0
1
1
1
1
1
1
0
1
2
2
1
2
0
2
1
1
1
2
2
1
2
2
1
1
1
1
0
1
2
0
1
2
0
2
0
1
2
2
0
2
2
2
0
1
2
0
1
1
1
1
1
2
0
1
1
1
1
1
0
1
2
2
1
2
1
1
1
1
2
1
1
1
1
1
2
1
1
1
0
1
0
1
1
1
1
1
0
1
0
1
1
1
2
2
1
1
1
0
1
0
1
1
1
1
1
0
1
0
0
1
2
2
1
0
1
1
2
2
1
1
1
1
1
2
2
2
1
1
1
1
1
1
0
2
1
1
1
2
0
1
1
1
0
1
1
2
1
0
1
2
0
2
2
1
1
2
0
1
1
1
1
2
2
1
2
1
2
2
1
1
0
2
2
2
2
1
0
0
1
2
1
2
1
0
1
0
1
2
1
4
1
0
1
1
1
1
1
1
2
1
1
0
2
0
2
1
0
0
2
1
2
0
0
2
1
1
1
0
2
1
1
0
1
1
0
2
1
1
1
1
1
0
0
1
1
1
0
2
2
1
1
2
2
2
1
1
1
2
2
2
1
1
2
2
1
1
1
1
1
1
2
0
0
1
0
1
2
1
0
1
1
1
0
1
1
0
2
1
0
0
2
2
1
0
1
2
0
1
2
1
2
1
1
2
0
2
0
1
1
2
0
2
1
1
1
1
1
2
0
2
1
1
2
1
1
0
1
1
1
0
1
1
0
0
1
1
2
2
1
2
1
1
1
1
2
1
1
1
2
2
1
2
1
1
1
1
1
2
1
2
1
1
0
2
1
1
1
0
1
1
0
0
1
1
0
0
1
1
2
1
1
1
1
1
2
1
1
2
0
1
1
0
1
0
1
0
0
0
1
0
2
1
1
0
2
1
1
1
1
1
1
0
1
0
1
1
0
2
1
1
2
1
1
1
0
1
0
1
1
2
2
1
1
2
1
1
2
2
2
1
2
1
2
1
0
2
1
1
1
1
0
1
0
1
1
1
2
2
1
2
1
2
1
2
1
1
1
0
0
1
2
2
3
1
1
0
1
1
1
1
2
2
1
1
1
2
1
2
2
1
1
3
2
1
1
0
1
1
2
1
2
2
1
1
0
1
2
1
0
1
1
0
1
1
1
1
1
0
2
1
1
2
1
1
2
1
1
1
1
1
1
2
1
0
1
0
0
0
1
2
1
1
0
1
2
1
2
0
1
1
2
2
2
1
1
1
2
1
2
2
2
1
1
0
2
1
1
1
1
1
1
2
1
2
1
2
1
1
2
2
2
1
1
1
1
1
1
2
1
1
0
1
2
1
2
1
0
1
2
1
1
1
0
1
2
1
2
0
2
1
1
1
1
0
2
1
2
1
0
2
1
1
1
2
1
1
0
0
0
2
1
0
0
1
2
0
1
1
1
1
1
1
0
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
3
2
1
2
1
0
2
1
1
1
1
1
1
1
3
1
0
0
1
2
0
1
1
2
1
1
1
1
1
0
0
2
1
1
2
1
0
1
1
1
0
1
1
1
0
1
1
2
0
1
0
1
1
1
2
0
1
2
2
1
1
1
2
1
1
1
1
1
2
1
0
1
1
1
1
1
1
1
1
1
1
0
1
2
1
1
2
2
1
0
0
2
0
1
2
1
2
1
1
1
1
2
2
2
1
1
0
1
2
2
1
1
2
1
1
2
1
2
1
2
1
1
0
1
1
2
1
1
1
1
0
1
1
2
1
1
1
1
0
0
1
2
1
1
1
1
1
1
0
1
1
1
2
1
1
0
1
1
0
1
1
2
3
0
1
2
0
1
1
1
1
2
0
0
2
1
1
0
1
1
2
2
1
2
1
1
1
1
1
0
1
1
1
1
2
1
1
1
1
2
1
2
2
1
0
1
1
1
1
3
1
2
2
0
1
1
0
1
2
1
0
2
2
2
1
1
2
1
1
1
1
1
1
2
1
0
2
1
1
0
0
2
1
1
2
1
1
1
2
1
1
1
1
1
2
1
0
1
1
0
1
1
1
2
0
1
1
1
1
2
2
2
1
1
1
2
2
2
1
1
0
2
1
2
1
0
0
1
1
2
2
2
1
2
0
1
1
2
1
1
1
1
1
2
1
2
1
2
1
1
1
1
2
1
0
1
1
2
1
0
1
0
2
1
2
2
1
1
2
2
1
1
2
2
1
1
2
1
1
3
1
2
1
1
0
1
2
1
2
1
0
1
2
1
2
0
0
2
1
1
0
2
1
0
2
2
1
1
1
1
1
0
1
0
1
1
1
1
1
1
0
1
1
2
1
1
2
2
2
0
1
2
1
1
1
1
2
0
1
2
1
1
1
2
0
2
0
1
1
1
1
1
0
1
2
1
3
2
1
1
0
2
2
0
0
2
2
2
0
4
3
1
1
2
1
1
1
2
1
1
1
1
2
1
2
1
0
2
1
1
1
0
1
1
2
2
1
2
1
1
0
1
0
0
1
1
1
2
2
0
2
1
1
1
1
1
1
0
1
0
1
1
1
1
2
0
1
1
2
1
1
1
1
1
1
0
2
1
2
1
1
2
2
0
1
0
0
2
1
2
1
0
1
2
1
1
2
0
2
1
1
1
1
1
0
1
2
0
0
1
0
1
0
1
2
1
0
1
2
1
1
1
1
0
1
1
1
0
1
1
1
1
1
1
1
2
1
1
1
1
2
1
0
1
0
1
1
2
2
1
1
1
1
1
0
1
1
1
1
1
6
0
2
1
1
0
1
1
1
1
1
1
3
2
1
1
1
2
2
2
1
1
1
1
0
1
0
2
1
2
2
1
1
1
0
1
0
1
0
0
1
0
1
1
1
2
1
1
1
3
1
2
1
0
2
2
1
1
1
1
1
0
2
1
1
0
2
0
1
0
0
0
1
1
1
0
1
1
1
1
1
1
0
1
2
0
7
0
1
1
1
1
1
0
2
0
0
1
1
1
1
1
1
2
2
2
1
1
1
0
2
2
1
2
1
0
0
1
1
1
1
1
1
1
1
0
1
0
2
1
1
0
2
0
0
2
1
1
0
1
1
2
1
0
1
1
1
1
1
1
0
1
2
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
0
1
0
2
2
1
1
0
1
1
2
2
3
2
0
1
1
1
1
1
1
0
2
2
1
2
1
1
2
2
1
1
0
1
1
0
1
1
0
2
1
0
1
0
2
2
1
1
1
1
3
2
2
2
2
1
2
1
1
2
1
1
1
1
1
2
1
2
1
1
2
1
0
2
0
3
1
2
1
1
4
2
1
1
1
2
2
2
1
1
2
0
0
1
2
0
1
1
1
1
2
8
1
1
0
1
1
1
1
0
0
1
2
1
1
1
1
1
1
2
1
0
1
2
1
1
1
1
0
1
0
1
1
1
2
1
1
1
2
0
1
0
1
0
1
0
1
1
2
1
1
2
0
1
1
1
1
2
1
0
2
1
1
1
1
1
2
0
1
0
1
1
1
1
0
14
1
0
1
1
0
3
2
1
1
0
0
1
1
0
2
1
1
1
1
1
0
1
1
2
1
1
1
0
1
1
1
1
1
0
2
2
1
1
0
1
1
1
1
2
2
2
1
1
2
1
0
1
0
2
1
1
1
2
2
3
1
2
1
1
1
1
2
1
1
1
2
0
0
1
1
0
2
0
1
1
1
2
1
1
1
2
1
0
0
0
1
2
2
1
0
1
1
2
1
1
1
2
0
1
2
2
1
2
1
1
2
3
1
1
2
1
2
1
1
0
2
1
1
1
2
0
0
1
2
2
1
1
1
2
2
1
1
1
2
1
1
1
2
1
2
2
1
0
1
1
2
2
1
2
2
0
1
2
1
1
2
1
1
1
1
1
1
0
1
2
1
2
2
1
0
2
1
1
1
2
1
1
1
1
1
2
1
0
0
1
0
0
2
1
1
0
2
2
1
1
1
1
1
1
2
1
1
1
3
0
0
1
1
1
1
3
2
1
1
2
1
1
1
0
1
6
1
1
0
1
2
2
0
2
2
0
0
1
1
1
1
1
0
0
1
1
1
1
0
1
0
1
2
2
2
2
2
2
1
1
2
1
1
2
0
1
1
0
1
0
1
1
0
1
2
2
2
2
1
1
0
0
1
1
1
0
2
0
0
2
2
1
2
1
2
2
2
1
1
2
1
2
1
2
0
2
1
2
2
1
0
1
2
1
1
2
2
1
2
2
0
1
2
1
1
1
2
1
1
1
1
1
1
0
2
1
2
2
0
1
1
1
2
2
0
1
1
2
1
1
1
2
0
1
2
2
1
2
0
0
0
1
2
1
2
1
2
1
1
0
1
1
1
2
1
2
1
1
0
1
1
1
2
1
1
2
1
1
2
0
1
1
1
0
1
0
1
1
1
1
1
2
1
1
1
1
1
2
1
0
1
2
0
1
1
1
1
0
1
1
0
1
1
0
0
0
2
1
1
1
1
1
1
1
2
2
0
2
1
2
1
0
0
1
1
2
0
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
2
0
1
2
2
2
1
2
1
1
2
1
1
1
1
1
0
2
1
1
0
1
2
2
1
1
2
2
1
2
1
2
0
2
1
1
0
1
1
1
0
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
0
1
2
2
2
1
1
0
1
1
2
1
1
1
1
1
1
2
2
1
2
1
1
0
1
2
1
1
0
0
1
0
2
1
1
2
1
1
1
1
2
1
0
1
1
0
2
0
2
0
2
0
2
1
1
2
1
0
0
0
1
1
1
1
1
2
2
1
1
1
1
2
1
2
1
1
0
2
1
1
2
1
2
1
1
1
1
1
1
1
1
0
1
1
0
2
3
1
2
1
0
1
0
1
2
1
0
1
1
0
1
1
0
1
1
1
3
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
0
1
1
2
1
0
1
2
1
1
0
2
1
1
1
2
1
1
2
0
2
1
1
1
1
1
0
1
1
2
3
1
2
0
0
1
2
1
1
1
1
1
2
0
1
0
1
2
1
1
0
2
1
1
2
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
2
1
1
0
1
0
1
1
1
1
1
2
0
2
2
1
2
3
2
1
2
2
0
0
1
0
1
0
2
1
1
1
2
2
1
1
2
1
1
4
1
0
2
0
1
0
1
2
1
0
1
1
1
1
1
1
3
1
1
1
1
1
1
2
0
3
1
3
3
0
2
1
1
2
1
0
1
0
2
0
1
1
1
1
1
1
2
1
2
0
1
0
2
1
2
0
1
0
2
1
1
1
1
2
1
1
1
2
1
1
1
1
3
1
0
2
1
2
1
2
1
2
1
1
2
1
1
1
2
1
1
0
2
1
1
2
1
1
1
1
0
1
2
1
1
2
1
0
1
1
1
2
1
0
1
0
0
1
1
0
2
0
1
1
2
1
1
1
1
0
1
2
1
1
1
0
1
1
2
1
0
1
2
0
0
0
1
1
0
0
1
1
2
0
1
1
1
1
1
0
2
1
1
0
1
1
1
1
1
1
3
1
2
1
1
2
0
1
1
1
2
1
2
1
1
1
2
0
1
1
0
2
1
1
2
0
2
2
1
2
1
0
1
1
2
2
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
0
0
1
1
1
1
1
1
2
1
2
1
2
0
1
0
1
1
1
1
1
2
1
2
1
1
0
0
0
1
1
2
2
2
0
0
1
2
2
0
1
1
1
1
0
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
2
0
1
1
1
0
2
1
0
1
0
1
1
0
1
1
1
1
1
0
1
1
2
2
1
0
1
1
1
1
1
0
1
0
2
2
0
1
1
2
2
1
1
1
1
2
0
0
2
1
1
2
0
0
1
2
1
1
1
1
2
1
0
0
1
2
1
2
1
1
1
1
1
1
2
1
1
2
1
1
2
2
1
1
2
1
1
1
1
2
2
0
1
1
1
1
1
0
0
1
1
1
1
1
1
2
0
0
1
1
1
1
1
2
0
1
1
1
2
1
0
1
1
0
1
1
2
1
0
1
1
1
0
1
1
1
2
2
2
2
1
1
1
1
1
1
1
2
0
2
1
1
1
2
2
2
3
1
1
1
1
1
0
2
1
1
1
0
2
1
2
2
2
0
0
2
2
0
1
1
1
2
1
0
0
1
0
0
2
0
2
1
1
0
1
1
1
1
1
2
0
1
1
1
0
2
2
2
1
2
1
0
0
2
2
1
0
1
1
1
1
1
1
2
1
0
1
1
1
1
1
1
0
1
1
1
1
1
1
0
1
1
2
2
0
1
1
1
1
0
1
0
1
1
1
1
2
1
1
1
1
0
2
1
1
1
1
1
1
1
0
1
2
1
1
1
1
1
1
2
1
2
1
0
1
1
1
0
1
2
2
1
2
1
1
1
1
1
1
2
2
1
1
1
0
2
2
1
2
2
0
1
1
1
0
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
0
2
1
1
1
2
1
2
1
1
2
2
0
2
1
2
2
1
0
0
1
1
0
2
0
1
1
2
2
1
1
0
1
2
0
2
2
2
0
2
1
1
1
2
1
1
1
1
0
2
1
1
1
1
0
2
0
1
1
1
1
0
1
1
1
1
1
2
1
0
1
1
1
2
1
1
1
1
1
1
2
1
1
2
0
2
1
2
1
2
1
2
1
2
0
2
1
1
2
1
0
1
1
1
2
1
1
1
2
1
1
2
0
1
1
0
1
1
1
1
0
2
1
1
1
0
2
1
2
1
1
1
2
0
1
0
1
1
0
1
2
1
2
0
2
1
2
1
1
1
1
0
1
1
2
1
0
2
1
1
1
2
1
1
1
2
1
2
2
0
1
0
2
1
2
1
1
2
0
1
2
1
1
0
2
1
1
1
1
2
1
1
1
1
1
1
2
0
2
1
0
2
1
0
1
0
1
1
3
1
2
1
2
0
0
0
1
2
2
1
1
0
1
2
1
1
1
1
1
1
1
1
0
1
0
2
1
1
1
2
0
1
1
2
1
1
1
2
1
1
2
1
3
1
1
1
2
1
2
1
0
1
1
2
1
0
1
1
2
0
1
0
1
1
1
1
0
0
1
1
2
0
1
1
1
1
0
2
2
1
1
0
2
2
1
1
1
2
1
1
0
1
1
1
1
1
1
1
1
1
1
2
0
1
2
1
1
1
1
0
1
0
1
1
2
1
0
2
1
1
3
1
2
1
2
1
2
1
3
2
1
1
0
2
2
1
2
2
0
1
1
1
1
1
2
2
1
1
0
1
0
0
1
1
1
2
2
0
0
1
1
1
0
1
1
1
0
1
3
0
1
1
2
1
1
1
0
1
2
0
1
1
1
0
0
2
1
2
1
2
0
2
3
1
0
2
0
1
1
0
1
1
1
1
1
1
2
1
1
1
1
0
1
2
1
1
0
1
2
1
0
2
1
1
1
1
1
1
1
1
1
1
1
1
2
0
2
1
0
1
1
1
1
1
1
2
2
0
2
0
2
2
0
1
2
1
0
1
1
0
1
2
1
1
1
1
1
2
1
1
0
1
1
1
1
2
0
0
0
0
2
1
0
1
0
1
2
2
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
2
0
1
0
1
0
1
0
1
2
1
1
1
2
1
1
1
0
1
1
0
1
2
1
1
2
0
0
1
1
1
1
1
1
0
1
2
2
1
1
0
0
1
0
2
0
1
1
0
1
1
1
1
0
1
1
1
0
1
2
1
1
1
2
2
3
0
1
0
1
1
0
0
1
1
1
1
0
1
1
2
1
1
1
1
1
2
1
1
2
0
1
1
1
0
0
1
1
0
1
0
1
1
2
1
0
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
2
2
1
1
0
0
1
1
1
0
0
2
0
2
1
1
1
0
1
2
0
0
4
2
1
2
1
0
3
2
2
2
2
1
1
2
2
2
1
1
1
1
1
2
0
1
1
1
0
1
1
0
1
0
1
1
2
2
1
1
1
1
1
0
1
0
2
1
2
1
1
0
2
1
0
1
1
0
0
1
0
1
0
1
0
1
1
2
0
0
1
1
1
1
2
1
2
0
1
1
0
2
1
1
1
1
1
1
1
1
2
0
2
1
3
1
1
1
2
2
0
1
1
1
0
1
1
1
2
0
1
0
1
3
1
0
1
1
1
2
1
1
1
1
0
1
1
1
0
0
1
1
1
0
1
1
1
2
2
2
0
0
1
0
0
1
0
0
0
1
1
2
0
2
0
2
1
1
1
2
2
2
1
0
1
1
1
1
2
1
0
0
2
1
1
2
0
2
1
2
1
1
2
2
2
1
0
2
1
1
1
1
1
2
1
1
2
1
1
0
1
1
1
1
2
1
1
2
1
1
1
0
1
1
1
0
2
0
1
2
0
1
1
1
0
1
2
2
0
1
1
1
1
1
1
2
1
1
1
1
1
2
1
0
2
2
1
1
1
0
1
1
0
1
1
1
1
2
2
0
0
2
1
1
1
2
0
2
1
1
2
1
1
2
1
1
1
1
0
1
1
0
1
0
0
0
1
1
0
2
1
1
1
1
1
1
1
0
1
2
2
0
1
1
1
1
2
1
1
2
2
1
1
0
2
1
1
0
1
1
0
1
2
0
0
0
1
1
1
2
1
3
2
1
1
0
2
1
1
1
1
0
1
1
0
1
2
2
1
1
1
1
2
0
1
2
1
2
0
2
0
1
2
2
1
0
0
1
1
1
1
1
0
1
1
1
2
2
0
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
0
1
0
1
0
2
2
2
1
1
0
1
1
2
2
0
2
1
2
1
0
0
2
1
1
1
2
0
1
1
2
1
1
1
1
0
1
1
0
1
1
2
0
2
1
0
1
1
1
2
0
2
1
0
1
0
1
1
1
1
1
2
2
2
1
0
2
1
1
1
0
1
1
1
1
1
1
0
0
0
1
0
1
0
1
2
1
1
1
1
1
1
0
1
1
2
1
2
2
1
1
1
0
1
1
1
1
2
0
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
0
1
1
0
2
1
1
0
1
1
1
1
1
1
2
1
1
0
1
1
1
2
1
1
0
1
1
1
0
1
2
0
1
2
1
1
1
1
2
1
0
0
1
2
2
2
0
1
1
1
1
2
1
1
1
0
1
1
0
2
2
2
2
2
1
0
1
1
2
1
1
2
1
2
2
3
1
2
1
2
1
1
0
0
0
1
0
1
2
1
2
1
2
2
1
1
1
2
0
1
0
0
2
1
0
3
1
0
1
1
1
2
2
1
1
0
1
1
2
0
0
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
0
1
0
2
1
1
2
1
1
2
1
1
1
2
1
2
0
1
1
1
0
0
1
1
0
2
1
1
2
0
1
1
1
0
2
0
0
1
2
2
0
0
0
1
0
0
2
0
1
1
0
1
1
0
1
2
1
2
1
2
0
1
1
1
1
0
1
0
2
0
0
2
1
1
1
2
2
0
1
2
2
1
1
0
1
2
1
1
1
1
0
1
0
0
1
1
1
1
1
1
0
0
2
1
2
2
1
2
1
2
2
1
0
0
0
2
1
1
1
0
1
1
1
1
1
0
1
0
1
1
1
1
0
0
1
2
1
1
1
0
2
1
1
1
1
2
1
0
1
11
2
1
2
1
1
1
1
0
2
1
1
1
1
0
0
1
1
1
1
1
1
0
1
1
1
1
1
0
2
0
0
2
0
1
1
2
0
0
2
0
1
2
2
0
1
1
1
1
1
0
1
2
2
2
0
2
0
0
1
0
1
2
2
1
2
1
1
0
1
2
2
1
0
0
1
1
1
0
1
1
0
0
1
1
1
1
1
1
1
0
2
1
2
1
1
1
1
1
1
2
2
2
1
1
1
1
2
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
0
0
1
0
1
0
2
1
1
1
1
1
1
1
0
3
0
0
1
1
1
1
2
0
0
0
2
1
0
2
2
0
1
2
2
1
1
1
1
1
2
2
2
1
1
1
1
1
0
1
1
1
0
1
2
0
0
1
0
0
1
1
2
2
2
1
1
2
1
1
1
2
0
1
1
2
1
2
1
2
2
2
1
1
1
0
1
1
0
2
1
1
2
1
1
1
2
0
4
1
2
1
2
1
0
1
2
1
1
2
1
1
1
2
1
2
1
1
0
0
1
2
2
1
1
0
0
1
1
2
1
1
1
1
2
1
2
0
1
1
1
1
1
1
2
1
1
1
2
1
1
0
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
2
0
1
1
1
1
2
1
1
2
1
1
0
1
0
0
1
3
1
1
1
1
1
1
1
1
2
1
0
2
1
2
2
1
1
2
0
1
3
2
1
1
2
5
1
1
2
0
1
1
1
1
1
1
1
0
1
1
2
1
2
2
1
0
2
2
1
2
1
1
2
2
1
1
1
1
0
1
1
0
1
0
1
1
2
1
0
1
3
1
2
1
1
1
2
0
1
1
1
1
5
1
1
1
1
2
2
0
1
2
1
1
2
2
2
2
1
1
2
1
2
0
0
1
1
2
0
2
2
0
1
1
1
1
1
1
1
1
0
0
1
0
1
0
1
2
2
1
1
0
1
2
1
0
1
1
1
1
2
0
1
2
2
2
4
1
1
1
0
2
2
1
0
0
0
0
2
1
1
1
1
1
1
0
1
0
0
1
1
2
0
2
0
1
1
1
1
2
1
1
1
0
0
1
2
1
0
1
1
1
1
1
0
1
1
2
1
1
2
2
1
1
0
2
1
1
1
0
2
2
2
0
0
2
2
2
2
2
1
1
2
1
0
1
2
1
2
1
2
0
1
0
0
2
1
1
1
0
1
1
1
0
1
1
0
2
1
1
1
1
1
1
1
1
0
1
0
1
1
1
2
2
1
2
0
0
1
1
1
0
2
1
2
0
1
1
0
2
1
1
2
1
1
1
2
2
0
2
1
2
1
0
0
0
1
2
1
1
1
1
0
1
2
1
1
1
1
1
0
1
2
1
1
1
1
1
1
1
1
0
1
2
1
0
1
1
2
1
1
1
1
1
0
1
2
1
1
2
1
0
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
2
0
1
2
1
1
1
1
2
1
0
1
0
2
1
1
1
2
2
1
1
2
1
1
2
0
1
1
0
1
0
1
2
1
0
0
1
1
1
2
2
1
1
1
1
0
1
1
1
2
1
0
1
1
0
1
1
1
0
0
1
0
2
1
0
1
1
1
0
1
1
1
1
1
1
0
1
3
1
0
1
0
0
2
1
1
1
1
1
1
0
0
0
0
1
2
2
0
0
1
0
1
2
1
2
1
1
1
0
1
1
2
2
2
1
0
0
1
1
1
1
1
2
0
1
1
2
2
2
2
1
1
1
2
1
1
1
2
0
1
0
1
0
0
1
1
1
1
1
1
1
0
2
1
0
1
1
2
0
1
2
1
1
1
1
0
1
2
1
2
2
2
1
1
1
0
2
1
1
1
1
0
1
1
1
1
1
2
1
2
1
1
1
2
1
2
1
2
0
1
0
0
1
1
1
1
1
0
2
1
1
0
0
1
0
1
2
1
0
1
0
2
1
0
2
0
0
1
1
2
2
1
1
1
2
1
1
0
1
0
1
1
0
1
0
2
0
1
0
1
1
1
1
1
2
2
1
1
1
0
2
0
1
2
1
1
2
1
1
1
1
2
1
1
1
2
1
2
3
1
2
0
1
2
1
1
0
0
1
2
1
1
1
0
2
2
1
2
1
1
1
0
2
0
0
0
1
2
1
1
2
0
3
1
1
1
1
0
1
1
1
4
1
1
1
1
1
1
2
2
0
1
0
1
1
1
0
1
2
1
2
0
1
1
2
2
1
1
0
3
2
2
1
2
0
0
0
2
2
1
1
1
1
1
1
1
3
0
2
1
1
2
1
0
2
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
0
1
0
1
1
1
1
1
2
1
2
1
1
1
2
1
1
1
1
2
2
1
2
1
0
1
0
1
1
1
1
1
2
1
0
1
2
2
0
1
2
0
1
1
1
0
1
1
1
2
2
2
2
0
1
1
1
0
2
1
2
1
1
1
1
1
2
0
0
1
2
1
1
0
1
1
1
0
1
2
1
1
1
1
1
1
0
1
1
0
1
1
1
2
2
1
1
1
1
0
1
1
1
1
0
2
2
1
2
0
1
2
1
1
0
1
1
1
1
0
1
1
0
1
1
2
1
1
2
1
1
1
1
0
1
2
2
2
0
1
2
1
1
1
0
1
1
1
0
3
1
1
1
1
1
1
1
2
2
0
1
2
2
1
1
0
1
2
1
0
1
1
1
0
1
1
1
1
1
1
0
1
1
2
1
1
1
2
1
1
1
0
0
1
0
1
2
1
2
1
2
2
1
1
1
1
1
2
0
1
0
2
0
2
2
1
2
2
1
1
2
1
1
2
0
0
1
1
2
0
2
0
1
1
1
1
0
2
0
1
1
1
1
0
2
1
1
1
1
2
1
2
1
1
1
1
0
1
1
2
1
1
0
1
1
2
1
2
1
3
0
1
1
2
2
1
1
1
2
0
1
0
1
1
1
1
1
1
1
2
2
2
2
1
0
1
2
1
1
2
1
1
1
1
0
1
1
1
2
1
1
1
0
1
2
1
0
2
1
0
1
1
1
1
2
0
2
0
0
1
2
1
0
2
1
2
1
1
1
1
1
2
1
0
1
2
0
1
2
1
2
1
1
2
1
1
1
1
1
1
1
1
2
2
3
1
3
1
2
1
2
2
2
2
0
2
1
2
2
1
2
0
1
1
1
1
1
1
0
1
1
1
1
2
2
1
1
1
1
0
1
1
1
1
2
1
1
1
2
1
1
2
1
1
0
1
0
0
1
1
1
1
1
2
1
1
1
1
1
0
1
1
1
2
0
0
1
1
2
1
1
0
1
1
2
1
1
2
2
1
0
2
2
1
1
0
1
0
0
1
0
1
1
2
2
1
1
1
1
1
0
1
2
1
2
1
1
1
1
1
2
1
1
0
0
1
2
1
1
0
2
1
2
1
1
3
1
2
1
1
1
0
2
1
1
0
1
2
1
1
1
1
1
1
1
1
0
0
2
2
1
1
0
0
1
1
0
1
1
1
2
1
0
1
2
2
2
3
2
1
1
2
2
1
1
0
1
0
0
2
0
1
1
2
1
2
2
0
2
1
1
0
2
2
2
2
0
2
1
1
1
1
2
1
1
1
1
1
1
0
0
1
1
1
1
0
1
0
1
2
2
1
1
1
1
1
1
1
2
1
1
2
0
1
1
1
0
1
1
1
1
2
0
0
0
2
1
0
1
0
0
1
2
1
0
0
0
1
0
2
1
2
2
2
0
0
0
2
1
1
1
1
0
1
1
1
0
0
2
1
1
1
1
1
1
0
2
0
1
1
0
2
1
1
1
2
1
2
1
1
1
1
1
1
1
0
2
0
1
1
1
1
0
2
1
1
2
1
1
1
2
1
1
0
2
0
2
1
1
3
1
1
1
1
2
1
1
2
1
0
1
2
2
2
2
1
1
1
2
2
1
1
2
1
1
0
1
1
1
1
2
1
1
1
1
2
1
1
1
0
1
1
2
1
1
1
1
1
1
1
1
1
2
1
0
2
0
1
1
1
2
1
1
1
1
1
0
0
0
1
0
1
1
2
0
1
1
1
1
1
2
1
1
1
1
1
1
1
1
3
0
2
2
1
0
1
1
0
1
1
1
1
0
1
3
2
1
1
0
0
1
1
1
1
2
1
2
1
0
0
0
1
2
1
2
1
1
1
1
2
2
1
2
1
1
1
1
0
0
1
1
1
1
1
0
1
1
2
1
1
0
0
0
1
1
2
0
1
1
1
0
1
2
1
2
1
0
1
1
1
1
1
0
2
0
2
1
1
0
2
2
1
2
0
1
2
1
1
0
1
1
1
1
0
2
1
2
1
1
1
2
1
0
2
0
1
1
1
2
0
1
1
1
1
2
1
2
1
0
2
1
0
3
1
0
1
2
0
2
0
1
0
1
1
2
2
1
1
1
1
1
3
0
2
1
1
1
2
1
0
1
1
0
2
1
1
1
2
0
0
1
2
1
1
2
2
1
1
0
2
1
0
1
2
1
1
1
2
1
1
1
0
2
0
1
0
1
0
1
1
1
1
1
0
1
2
1
1
1
1
1
1
0
1
2
1
0
2
1
1
0
1
1
1
2
1
0
1
1
0
2
1
1
0
2
2
1
1
0
2
1
1
2
0
1
1
1
3
0
1
0
0
1
1
2
1
0
0
2
1
2
1
0
2
1
2
1
0
0
1
1
1
2
2
2
1
1
0
1
1
2
1
1
2
1
2
1
1
2
2
0
1
1
0
1
2
1
1
1
1
1
1
2
0
1
1
0
1
1
2
2
2
1
1
2
1
2
1
1
1
1
1
3
1
1
1
2
1
0
0
1
1
1
1
2
1
0
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
2
2
1
2
2
1
1
2
2
0
1
0
1
1
1
1
0
1
0
2
0
1
3
1
0
1
1
1
2
1
1
0
0
1
1
1
1
0
0
1
1
0
3
1
1
1
2
2
1
2
1
0
1
1
0
0
0
1
2
1
1
1
0
2
2
1
1
0
0
1
1
2
1
3
0
0
2
2
2
0
1
0
1
2
2
1
2
1
1
2
1
1
1
1
1
0
2
1
1
0
1
1
1
1
1
1
2
1
1
0
2
3
1
2
1
1
2
1
0
2
1
2
1
1
2
2
1
1
0
2
1
1
1
2
1
2
2
0
0
1
1
1
0
2
1
1
0
2
1
2
2
0
0
1
1
1
2
2
0
0
2
1
0
1
1
1
2
1
2
1
1
2
1
0
1
1
1
0
0
0
2
2
2
1
1
0
2
0
1
1
1
2
0
2
0
1
1
2
1
2
1
1
1
1
1
2
1
2
1
1
1
1
2
1
0
2
1
0
1
2
1
1
2
1
0
1
3
1
1
1
1
2
1
1
1
1
0
0
1
1
0
1
2
1
0
2
2
0
1
2
1
1
2
2
1
1
0
1
0
1
1
2
2
1
2
1
1
1
1
0
2
1
2
1
0
2
1
1
2
1
0
1
2
1
2
0
1
1
1
1
0
1
1
0
0
1
1
1
0
0
1
2
2
0
1
2
2
3
0
2
1
1
2
2
1
1
2
2
2
1
1
1
1
2
1
1
1
1
1
1
0
1
0
1
2
1
1
1
1
1
1
2
1
0
1
1
1
1
2
1
1
1
3
2
1
1
2
1
1
1
1
2
1
2
1
2
0
1
1
1
1
1
0
1
0
0
2
1
1
0
0
1
1
1
1
0
1
1
0
1
1
1
1
0
2
1
1
1
1
2
1
2
1
1
1
1
2
0
2
1
2
1
2
1
1
1
0
1
0
1
1
1
1
2
1
2
1
1
2
2
1
1
1
1
0
1
1
2
0
1
1
1
1
1
1
1
0
2
1
0
2
1
2
2
0
2
1
1
1
1
0
0
1
1
1
1
1
0
1
1
0
1
2
0
2
0
1
1
2
2
1
1
2
0
1
1
0
1
2
1
1
0
1
1
0
2
2
1
1
2
1
1
1
1
1
0
0
2
1
2
1
1
1
1
2
0
0
0
0
1
1
0
1
0
1
1
1
1
1
1
2
1
1
2
2
2
1
1
1
2
1
1
1
0
1
2
1
1
2
1
1
1
1
1
1
0
1
0
1
2
0
0
1
1
1
1
2
2
0
0
2
1
1
1
2
1
1
1
1
1
0
1
0
1
0
0
2
1
2
1
1
0
1
1
0
0
1
1
0
0
1
1
2
1
1
0
1
2
1
1
1
2
1
0
1
1
1
0
2
0
1
1
1
2
0
1
1
1
0
1
1
1
1
0
2
1
2
1
3
2
1
1
2
1
1
0
1
1
0
1
0
2
0
0
2
0
1
1
1
1
1
1
2
2
2
1
1
2
0
1
1
1
1
2
1
0
2
1
1
1
1
1
1
0
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
0
2
2
1
2
0
1
1
1
2
1
1
0
1
1
0
2
2
1
1
1
1
1
0
2
0
1
1
1
1
0
1
0
1
1
1
1
1
1
2
1
1
1
1
1
0
2
0
1
1
1
1
1
1
1
1
1
1
2
1
2
5
0
1
1
0
2
1
0
1
0
0
2
2
1
0
0
1
1
1
1
0
1
1
2
2
1
1
1
2
1
1
0
2
1
2
0
1
0
2
0
1
0
1
1
1
2
2
1
1
1
2
1
0
1
2
2
1
1
1
1
2
0
1
1
1
1
0
1
0
1
1
0
1
1
2
1
1
2
1
2
2
1
2
1
1
0
2
0
1
2
1
1
2
1
1
0
1
0
2
0
1
1
1
3
1
1
1
1
2
2
1
0
2
1
2
2
1
0
1
2
1
1
2
1
1
2
1
1
1
1
1
0
0
1
1
2
2
2
1
1
1
0
2
1
1
2
2
1
2
1
1
1
1
1
0
0
0
1
0
2
1
1
1
1
1
1
1
1
1
1
2
1
0
1
1
2
1
1
1
1
1
1
2
2
1
2
1
1
1
1
2
2
1
2
1
1
1
2
1
0
0
2
1
2
1
1
2
0
2
1
1
1
1
0
2
1
1
1
2
2
1
0
2
0
0
0
0
1
1
1
1
0
1
1
2
1
1
2
2
0
2
1
2
3
0
0
2
1
1
1
2
1
1
1
1
1
0
2
2
2
2
2
2
2
1
2
2
1
1
0
1
2
2
1
1
1
2
1
1
1
1
0
1
1
0
1
1
1
1
2
1
2
2
0
2
1
1
1
1
1
2
3
0
1
2
2
1
2
1
2
1
1
1
1
2
0
0
1
1
0
1
1
2
2
2
0
1
2
1
1
1
1
2
1
1
2
1
0
0
3
2
1
1
2
1
0
2
2
0
1
0
2
1
1
2
2
1
1
1
0
0
0
0
1
1
0
1
2
2
2
2
1
1
0
1
1
2
1
0
2
2
0
2
1
1
1
1
2
1
1
1
1
0
2
1
1
0
1
0
0
1
1
1
1
1
0
1
2
2
2
0
2
1
1
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
3
1
4
1
0
1
0
2
1
1
1
1
0
2
2
2
2
0
2
0
1
0
1
1
1
2
1
1
1
1
2
0
1
0
2
0
1
1
2
1
0
2
0
0
1
1
1
1
2
1
1
0
1
2
1
2
3
0
2
1
1
1
1
1
1
2
1
2
1
2
1
1
1
1
1
0
1
1
1
2
0
2
1
0
1
1
2
1
2
0
2
3
1
0
1
2
0
1
1
1
2
1
1
1
1
0
2
1
1
2
1
1
1
3
1
1
1
1
2
1
0
1
1
1
2
2
1
1
2
2
2
1
1
1
1
0
0
2
0
2
0
2
0
2
1
2
2
1
1
1
1
1
0
2
2
2
0
1
1
1
1
1
0
2
1
1
1
0
1
1
1
1
1
1
1
2
1
1
1
1
0
2
1
2
1
1
2
0
1
1
1
0
1
1
1
0
1
0
1
1
1
2
2
1
1
1
2
2
2
0
0
1
0
4
1
2
1
1
1
2
1
1
1
0
0
1
1
2
1
0
1
0
1
1
1
1
2
1
1
0
2
1
1
0
1
1
0
0
1
1
0
1
1
0
2
1
1
1
1
1
1
0
1
2
0
1
1
1
2
1
1
1
2
2
0
0
2
2
1
1
1
1
1
1
2
0
2
1
1
0
1
2
1
2
1
0
1
1
2
0
1
1
1
1
2
0
1
2
1
1
2
1
1
0
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
2
0
2
1
0
1
0
1
1
1
2
1
1
3
1
1
0
2
1
0
1
1
2
0
2
1
2
1
0
2
2
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
0
0
1
2
2
0
1
0
2
1
0
1
0
1
2
2
1
0
0
0
3
2
2
0
1
1
0
1
1
0
0
1
1
1
0
2
1
2
1
0
1
0
1
1
0
2
2
1
0
1
1
2
1
1
1
1
0
0
1
2
0
0
2
1
1
2
2
2
2
2
0
2
1
1
1
0
1
2
0
1
1
1
2
1
1
1
0
1
1
1
1
0
1
1
1
1
1
2
1
1
1
0
1
1
1
1
0
0
1
2
1
0
2
2
1
1
1
2
0
2
1
2
1
2
1
1
0
0
1
1
1
0
1
2
1
1
1
1
0
2
2
1
1
2
1
1
1
0
1
2
1
2
1
2
1
1
1
2
1
1
1
1
1
0
1
1
0
0
1
1
0
2
0
1
1
0
0
2
2
1
2
1
0
1
2
0
0
2
1
1
0
1
2
1
2
1
1
1
0
2
1
2
1
1
1
1
1
2
1
2
2
2
0
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
0
1
1
1
2
1
0
2
1
1
1
1
1
1
0
2
1
2
2
1
1
0
1
1
2
2
1
1
2
0
1
1
2
1
1
1
1
1
1
0
3
1
1
2
2
1
0
1
1
1
1
1
1
1
1
0
2
0
1
2
0
1
1
1
1
2
0
2
1
0
0
2
1
1
0
1
2
1
1
2
0
1
1
0
1
2
0
1
2
1
1
1
1
0
2
1
1
2
2
1
0
1
1
0
1
1
1
2
0
1
0
2
2
1
1
2
1
1
2
1
1
0
2
2
1
0
0
0
0
1
2
1
1
1
1
1
1
1
1
2
0
1
1
1
2
0
0
1
1
1
1
1
2
1
0
1
1
1
1
1
0
1
1
0
1
1
2
1
2
1
1
1
1
1
1
0
0
1
2
1
1
1
2
1
1
1
0
1
2
2
2
2
0
2
1
2
2
2
0
1
1
0
1
2
1
2
2
1
1
2
1
0
2
2
1
2
1
0
2
0
1
1
0
1
2
1
1
0
1
1
0
2
1
1
0
0
1
1
0
0
1
2
0
1
2
0
1
2
1
0
2
0
1
1
1
2
1
1
1
1
1
1
2
1
1
2
2
0
1
4
1
0
1
0
0
1
0
1
2
1
0
1
1
2
0
1
0
2
0
1
1
1
1
1
1
2
1
1
1
1
0
3
2
2
1
1
0
2
0
0
1
2
2
2
1
1
1
1
1
0
0
1
1
2
1
0
2
0
1
1
0
0
1
1
1
1
1
3
0
2
1
0
0
2
0
1
2
1
0
1
1
0
1
2
1
1
2
1
0
2
1
2
1
0
0
2
0
1
1
1
1
2
1
0
1
1
1
1
1
2
2
1
2
2
0
1
1
1
2
1
1
1
2
1
0
1
1
1
2
2
1
0
1
2
1
1
1
2
1
1
1
1
1
0
2
2
1
1
0
2
0
1
1
1
1
1
2
2
0
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
0
1
1
0
2
0
2
0
1
2
0
1
2
2
1
1
1
0
1
1
1
2
1
1
1
2
1
0
2
1
0
1
0
1
2
2
1
1
1
0
2
1
1
1
2
1
1
2
1
2
1
2
1
2
2
1
1
2
1
1
2
1
2
1
0
1
0
1
2
2
1
1
3
1
1
1
1
2
1
1
1
0
1
4
0
1
1
1
2
1
1
1
0
2
2
1
0
2
1
1
1
0
1
1
1
0
1
0
1
1
2
1
0
1
1
1
0
2
0
1
2
1
0
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
0
1
1
2
1
2
0
0
1
1
1
2
0
0
1
2
1
1
1
1
2
2
1
2
1
1
1
2
3
0
2
1
2
2
1
1
1
1
1
1
0
2
0
1
2
1
1
0
0
1
0
1
2
2
1
2
0
1
1
1
2
0
1
2
1
1
2
2
3
1
2
1
1
1
2
1
0
0
1
1
1
1
1
2
1
0
1
1
2
0
1
1
2
1
1
1
1
2
1
2
1
0
1
2
1
0
1
1
1
1
1
0
0
2
2
1
1
0
1
1
1
1
1
2
1
1
2
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
1
2
2
2
1
1
2
2
1
0
5
0
0
2
2
0
1
1
1
1
1
2
2
3
0
0
1
1
1
0
1
1
1
1
2
1
3
2
1
1
2
0
2
1
1
2
1
1
1
2
0
1
1
1
1
1
1
1
1
1
2
1
0
1
1
1
2
1
1
2
1
0
0
1
2
1
1
2
0
1
1
0
1
1
1
1
2
0
1
1
1
2
1
1
0
2
0
2
2
1
0
1
2
2
0
1
1
1
1
1
0
1
1
2
1
1
0
2
0
1
0
1
1
0
2
0
1
1
1
1
2
1
1
1
2
0
1
0
0
1
0
1
2
1
1
0
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
2
0
2
1
1
1
2
1
1
1
2
0
2
2
1
1
0
1
1
1
0
1
2
2
2
0
1
1
2
1
2
1
1
1
1
0
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
0
2
2
1
1
0
1
1
4
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
2
1
2
1
2
0
1
1
1
2
2
1
1
1
0
0
1
0
1
0
2
0
1
0
1
1
1
1
2
0
0
1
1
1
1
2
2
2
1
1
0
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
2
0
1
2
0
2
1
1
3
0
0
0
0
3
0
2
1
0
1
1
1
1
1
1
1
2
3
1
2
2
1
2
1
1
0
1
1
2
1
1
1
1
0
0
0
1
1
2
0
0
2
2
1
1
1
0
1
2
1
1
1
1
1
0
1
1
2
1
2
1
2
1
1
1
0
0
1
0
1
1
1
0
0
1
2
1
1
1
1
0
0
2
1
0
1
1
1
1
1
1
1
2
1
1
0
0
0
1
1
1
2
2
2
1
1
1
0
1
2
1
1
1
0
1
0
1
1
1
2
0
1
2
1
1
2
1
1
1
1
0
1
1
2
0
3
0
2
1
1
0
0
1
2
1
2
3
1
1
2
1
1
1
0
0
1
1
2
0
2
0
1
2
2
1
1
2
1
1
2
2
0
1
0
1
0
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
2
1
0
1
1
1
2
0
1
1
2
1
1
1
1
2
1
0
2
1
2
2
0
2
1
1
1
1
3
1
2
2
2
2
0
2
0
1
2
2
1
2
1
1
1
1
0
2
1
1
1
2
1
2
2
1
1
2
1
0
1
2
2
0
1
2
1
0
1
0
0
1
1
2
2
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
0
2
1
3
1
2
1
1
0
1
1
0
1
1
2
1
1
2
2
2
2
2
1
1
0
2
0
2
0
1
1
1
1
0
0
0
1
1
1
0
1
1
0
1
1
0
1
2
1
1
1
1
0
2
1
1
1
1
1
1
2
2
1
1
0
0
1
0
2
3
0
0
1
0
1
2
2
1
1
2
1
2
1
0
4
1
1
1
1
1
1
1
2
0
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
1
2
2
1
1
1
1
2
3
1
1
2
1
1
2
2
1
0
0
2
1
1
1
0
1
1
3
0
1
0
1
2
1
0
1
1
1
0
2
1
1
2
1
1
1
1
0
1
2
1
1
1
0
2
0
2
1
1
1
1
1
1
1
1
0
1
1
1
1
1
0
1
0
1
1
2
0
1
2
2
1
1
1
0
1
1
1
1
1
1
2
1
0
1
1
2
1
1
2
3
1
0
1
0
1
0
0
1
1
1
0
1
1
1
1
0
2
1
1
1
1
1
1
2
0
1
1
1
1
1
1
2
1
1
2
2
0
1
2
1
2
1
1
1
1
1
2
1
1
0
2
1
2
1
1
1
1
2
1
1
1
1
1
2
0
1
1
0
2
1
1
1
2
2
0
1
2
0
0
1
0
0
0
1
2
1
0
1
0
2
0
0
2
1
1
1
1
0
1
1
2
1
2
1
1
1
4
1
2
1
1
2
1
1
2
1
3
1
1
2
2
2
2
2
0
1
1
0
1
1
2
1
1
0
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
3
1
1
2
1
0
1
3
0
2
2
0
1
1
1
1
1
1
1
1
2
2
2
2
1
1
1
1
1
1
1
1
1
2
0
1
1
2
2
1
1
2
1
2
2
0
1
1
0
2
1
2
1
0
0
2
1
0
2
0
2
2
0
1
2
1
2
0
0
1
1
1
1
1
0
1
1
2
2
1
0
2
1
1
2
1
2
3
2
0
1
1
2
1
1
2
1
1
2
2
1
1
1
0
1
1
1
1
1
1
1
1
2
2
1
1
2
1
0
1
1
2
1
1
0
1
1
1
1
1
1
1
0
0
0
1
2
0
0
1
3
1
2
0
1
2
1
1
1
1
0
0
0
1
1
3
0
0
1
2
1
1
1
1
2
1
2
0
1
1
0
1
0
0
1
1
2
1
1
1
1
1
1
2
1
1
0
2
1
2
1
1
4
1
1
1
1
3
0
2
0
0
1
1
1
2
1
1
1
1
1
2
2
0
1
0
1
2
1
1
1
1
1
1
1
2
1
1
1
2
0
1
1
1
1
2
1
2
1
1
2
2
1
1
1
1
1
1
1
2
0
1
1
1
2
1
1
2
2
0
1
1
1
3
2
1
2
2
2
1
1
1
0
1
2
0
0
2
2
0
1
1
3
1
2
1
0
0
2
1
2
2
2
2
1
1
2
1
1
2
2
1
2
1
1
1
0
0
1
2
1
1
1
0
2
1
2
0
1
1
1
1
1
0
1
1
4
1
0
2
1
1
0
1
0
1
1
2
1
2
1
2
1
1
0
0
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
0
1
0
1
1
1
1
0
1
2
1
2
1
1
1
1
0
1
2
2
1
1
1
1
0
0
1
0
2
0
2
0
1
0
1
1
1
2
0
2
0
1
1
1
0
0
0
0
1
1
1
1
2
1
1
0
1
1
1
1
0
0
1
2
2
1
2
1
2
1
1
1
0
1
2
1
1
1
1
1
0
3
1
1
1
1
1
2
0
0
2
1
1
0
2
1
2
1
1
2
2
0
0
2
1
0
2
1
2
2
1
1
0
1
2
2
1
1
1
1
1
0
1
1
1
1
0
1
1
2
1
2
1
1
1
1
2
0
1
1
1
0
1
1
1
1
0
1
1
1
1
1
0
0
1
1
2
2
0
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
0
1
1
0
1
1
1
0
0
0
0
1
1
1
1
1
0
0
0
0
0
1
0
1
1
1
0
1
2
1
1
0
1
0
0
1
2
2
1
1
2
1
1
1
1
1
2
2
2
2
1
1
1
2
2
1
1
0
0
2
1
0
1
0
1
1
1
0
1
0
0
1
0
1
1
2
0
2
1
2
2
1
1
0
1
2
1
2
1
0
1
1
1
1
0
0
2
1
2
1
1
1
1
1
1
2
1
1
1
1
0
1
2
2
1
2
2
1
1
2
0
2
1
1
1
0
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
0
1
1
2
1
1
1
1
1
0
1
2
0
0
2
1
1
1
1
1
2
1
2
3
0
1
1
2
1
1
2
0
2
1
1
2
1
0
1
0
1
2
0
1
2
3
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
2
0
1
1
0
0
2
1
1
1
2
0
2
1
1
2
1
2
1
1
1
1
0
1
2
1
1
0
1
1
1
1
1
1
2
4
1
1
1
1
0
1
1
2
3
1
1
1
0
0
2
2
1
0
2
1
1
1
1
1
1
0
2
2
1
0
1
2
0
1
1
1
3
1
0
0
1
0
2
1
1
1
0
1
0
1
0
0
2
2
2
1
1
1
1
2
1
0
1
1
0
0
1
0
1
1
2
2
1
1
2
1
1
1
1
1
1
1
2
2
1
2
1
1
2
1
2
0
0
2
1
1
1
1
1
1
2
1
2
0
1
1
0
2
0
2
2
2
1
1
1
2
1
1
2
1
0
2
1
1
0
1
1
0
1
0
2
2
1
2
0
1
2
1
0
2
2
1
1
3
1
1
1
1
0
1
1
1
0
1
1
1
0
1
1
2
1
0
2
1
2
1
1
1
1
1
1
1
2
1
2
2
2
1
1
1
0
1
1
1
0
0
0
0
1
2
0
1
1
1
1
1
2
0
0
2
0
0
0
1
1
0
0
1
1
1
1
1
1
1
0
1
2
1
2
1
2
2
1
0
0
1
1
1
1
2
1
1
0
1
2
1
2
0
1
2
1
1
4
1
1
2
0
0
1
1
2
1
1
1
0
2
1
1
4
0
2
1
1
0
0
2
0
1
1
2
1
0
1
1
0
1
1
2
1
1
0
1
1
1
1
0
1
1
4
1
1
2
1
1
1
0
1
1
2
2
0
0
2
2
2
1
2
1
2
2
1
1
3
2
1
2
1
1
0
2
2
1
1
2
1
0
2
0
1
1
0
2
1
1
2
2
1
2
1
1
1
1
0
0
0
2
3
1
1
1
1
1
2
2
1
1
1
2
1
1
1
1
0
1
2
1
0
1
1
1
1
2
1
1
2
2
1
1
0
1
1
1
1
2
2
1
1
0
1
2
0
2
1
0
1
0
2
1
1
0
1
1
1
1
1
2
2
0
1
2
1
2
2
0
2
0
2
2
1
0
2
1
2
2
1
2
0
2
0
0
1
2
0
3
1
1
2
1
0
0
1
2
1
1
1
1
1
1
1
0
2
1
1
2
1
1
1
1
0
0
0
1
2
1
1
0
1
1
1
1
1
0
1
1
1
0
0
2
1
2
1
2
2
1
1
1
0
0
1
1
1
1
1
0
0
0
1
1
0
2
1
0
1
1
1
1
0
1
1
0
1
0
1
0
1
2
2
0
2
1
0
1
2
1
1
1
1
2
2
1
2
1
2
2
1
2
1
0
2
1
1
1
1
1
0
2
1
1
1
1
1
1
1
1
0
1
2
1
2
2
1
0
2
1
1
1
1
2
3
1
0
1
1
1
2
1
2
0
0
1
0
1
0
1
1
1
1
0
0
1
2
2
2
1
1
2
1
2
1
1
2
1
1
1
1
1
2
1
1
1
2
1
2
0
1
1
1
1
2
1
0
2
2
2
0
1
1
1
1
0
0
1
0
2
0
1
1
0
1
0
1
1
1
1
2
1
1
1
0
1
1
1
1
0
0
1
2
2
1
1
2
2
1
0
0
1
2
0
1
1
2
2
1
1
1
2
1
2
1
2
1
1
1
0
1
1
1
2
2
0
1
1
2
1
1
2
0
2
1
1
0
1
1
1
0
1
2
0
1
2
0
1
0
1
2
1
1
0
0
2
2
1
1
1
0
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
0
2
1
0
1
2
1
1
1
2
1
2
1
0
0
0
1
1
2
1
3
1
2
0
1
2
1
0
1
2
1
1
1
1
1
2
0
1
1
0
2
0
1
0
0
2
0
1
1
1
1
2
2
1
0
1
1
1
1
2
2
1
2
1
1
0
1
1
1
1
0
0
1
1
2
1
0
2
1
1
1
2
1
0
2
0
1
2
0
2
1
1
0
1
1
1
0
1
1
0
1
1
1
2
0
1
1
2
1
0
1
1
0
2
1
1
1
2
2
1
1
2
2
1
1
1
1
3
0
0
1
1
1
0
1
1
0
1
2
2
1
2
2
1
1
0
0
0
1
1
1
1
1
3
2
0
1
2
2
2
1
0
1
1
2
0
1
2
0
2
0
0
2
0
1
0
1
0
0
0
1
1
1
2
0
1
1
1
1
2
0
1
2
1
0
0
1
0
0
1
1
1
2
1
0
0
2
0
1
1
1
2
1
1
1
1
1
0
1
2
2
1
1
0
1
1
0
2
1
2
1
1
0
0
1
1
1
1
2
1
0
1
1
0
1
0
0
0
2
1
1
2
1
2
2
0
1
0
0
0
1
0
0
1
0
1
2
0
2
2
1
1
0
0
1
2
1
1
1
1
1
0
1
1
1
1
1
0
1
1
0
1
1
1
1
0
1
0
2
1
1
0
1
0
2
0
1
1
1
2
2
1
1
1
0
0
0
1
2
1
1
2
2
1
1
2
2
1
1
1
1
1
0
1
0
1
2
2
1
1
1
2
0
0
0
0
1
1
1
1
2
0
0
1
1
1
1
1
1
1
1
0
0
2
1
1
1
0
1
1
2
2
0
0
1
2
0
1
1
1
1
1
3
2
1
1
1
2
0
0
1
1
1
1
1
2
2
2
1
2
1
1
1
0
1
1
1
0
1
1
2
1
0
0
1
1
1
2
2
1
0
2
1
1
1
1
1
1
1
1
1
2
1
2
2
0
1
2
1
0
1
1
1
1
2
1
2
1
1
2
1
2
1
1
1
0
1
0
1
2
1
0
0
1
1
1
1
0
0
0
1
1
1
0
0
1
0
1
0
1
1
2
2
1
1
1
0
1
1
1
1
1
1
0
1
1
2
0
1
1
2
2
1
0
0
1
2
0
1
2
1
2
2
1
1
1
1
1
1
1
2
1
1
1
0
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
1
1
0
1
0
2
1
0
1
1
1
1
0
2
1
1
1
0
1
2
2
1
0
1
1
0
1
2
2
2
1
1
0
1
1
0
1
1
1
0
1
1
0
1
1
2
1
1
1
0
2
1
2
1
1
1
2
1
0
1
0
1
1
1
1
0
0
1
1
1
0
1
2
0
0
1
1
1
1
1
1
0
2
1
1
1
1
1
1
0
1
0
0
1
0
2
1
1
1
1
2
0
1
1
0
1
0
1
0
1
1
1
1
2
0
1
1
0
0
2
0
1
1
0
1
1
2
0
0
1
1
1
1
1
1
1
1
1
1
2
1
2
1
0
2
1
1
2
1
0
1
1
0
1
1
1
1
2
0
2
1
2
1
1
1
2
1
2
2
1
2
2
2
0
1
0
3
1
1
1
1
1
2
1
1
2
1
0
1
0
1
2
1
0
1
1
0
2
0
1
1
0
0
1
1
1
1
2
0
3
0
2
1
2
1
0
2
1
0
0
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
0
0
2
1
1
0
1
2
2
2
0
2
1
1
1
2
1
0
0
1
1
0
0
1
2
0
0
0
1
2
1
1
1
2
0
1
2
1
0
0
0
4
1
1
0
1
2
2
0
2
1
1
1
0
1
0
2
1
2
1
1
1
1
1
2
1
1
2
1
0
0
0
1
1
1
1
1
1
1
1
2
2
2
2
0
1
1
0
0
2
0
1
1
0
1
1
1
2
2
1
0
1
2
0
1
1
1
1
0
2
1
1
1
0
1
2
1
0
1
1
1
2
1
1
1
1
0
2
1
1
1
1
2
2
1
1
2
2
0
0
1
1
1
1
1
0
2
2
2
2
1
0
1
1
0
1
2
2
1
0
0
1
1
1
1
1
1
1
1
2
1
1
2
1
1
0
2
1
0
2
1
1
1
1
1
2
1
0
2
1
1
0
1
1
2
1
1
0
2
1
1
2
1
1
0
0
1
1
1
2
2
2
1
1
1
1
2
1
1
0
0
0
2
2
0
1
1
1
0
1
1
0
1
1
2
2
2
2
1
1
0
2
1
0
1
1
0
0
1
2
2
0
1
1
2
1
1
1
2
1
1
0
0
2
1
0
0
1
1
1
1
2
1
1
1
0
0
1
1
1
0
1
1
1
2
1
0
0
1
0
1
1
1
2
1
1
2
1
2
0
1
2
0
1
1
1
2
2
0
1
1
1
0
4
1
0
1
0
0
2
1
0
2
1
0
1
2
2
1
1
0
1
1
0
1
0
1
1
1
1
1
1
1
2
1
2
1
1
1
1
2
2
1
0
0
1
1
0
0
0
0
1
1
0
1
1
2
1
0
2
2
1
1
2
1
1
1
0
2
0
1
1
2
0
1
0
2
0
1
1
2
1
0
0
1
1
1
2
3
1
1
1
2
2
0
1
2
1
1
1
1
1
2
1
2
1
1
2
1
0
0
1
2
2
1
0
1
1
2
1
1
1
1
1
2
0
1
2
1
0
0
1
1
2
1
1
2
1
2
1
1
1
3
1
1
1
1
2
1
0
1
1
0
0
0
1
0
1
1
0
0
1
1
0
0
2
1
1
2
1
1
1
1
1
0
1
1
1
0
1
2
0
0
1
0
1
1
1
2
1
1
1
0
2
1
1
1
0
1
1
2
1
1
1
2
1
1
0
1
0
0
1
1
2
1
1
1
1
2
2
0
1
2
1
2
1
2
1
1
1
1
2
0
2
1
1
1
0
1
1
1
2
1
1
1
1
1
1
1
0
0
0
0
0
0
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
0
1
1
2
1
2
1
1
1
1
2
2
1
1
1
1
1
0
1
0
1
2
1
1
1
2
0
2
1
0
0
1
2
2
1
1
0
0
2
1
1
1
1
1
1
1
0
1
1
0
1
3
2
1
2
1
0
1
1
1
2
1
1
1
2
2
0
1
1
2
1
1
1
1
1
0
1
1
2
1
1
1
1
2
1
1
1
1
2
1
2
2
1
1
1
1
2
1
1
1
2
1
1
1
1
0
1
1
0
1
1
2
0
0
2
1
1
0
1
1
0
2
1
0
1
0
1
2
0
2
0
1
1
2
2
1
2
1
1
1
1
2
1
1
1
1
2
1
1
0
2
2
0
2
0
1
1
1
1
1
1
1
1
1
0
2
1
2
2
0
1
1
2
1
1
1
2
1
2
1
1
2
1
1
2
1
1
1
1
0
1
2
2
1
1
2
1
0
2
0
1
1
2
0
0
1
1
1
1
1
1
1
1
2
0
1
1
0
2
1
0
0
0
2
1
1
2
1
0
0
0
1
0
1
1
1
1
0
1
1
0
1
2
0
2
2
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
2
0
2
1
1
1
0
2
1
1
1
0
1
1
1
2
1
0
0
0
3
1
0
1
1
1
0
1
1
0
1
2
1
2
1
2
1
2
2
1
0
1
1
1
1
2
1
1
1
0
1
0
1
1
2
1
2
2
0
1
2
0
1
1
1
1
2
2
2
1
0
1
0
1
1
1
1
1
1
1
2
1
1
2
1
3
0
2
1
1
2
1
2
1
2
1
0
1
1
1
1
1
1
1
1
1
1
0
0
1
1
1
1
1
1
1
2
1
2
1
1
1
2
1
1
4
1
1
1
1
1
1
0
1
1
0
1
1
1
1
1
0
1
1
1
1
2
1
0
1
1
2
1
0
1
2
0
1
2
2
2
1
2
0
2
2
1
2
0
0
1
0
2
1
3
2
0
2
1
2
2
1
1
1
0
1
1
1
2
1
1
1
0
1
1
2
1
0
0
2
1
1
3
1
1
1
1
0
1
2
1
0
1
1
1
0
2
1
0
1
1
0
1
1
2
1
2
1
1
2
1
0
1
1
1
1
3
2
2
1
1
2
0
2
1
1
0
0
0
1
2
0
1
1
1
2
2
0
1
1
1
0
1
2
1
0
0
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
0
0
1
2
1
1
1
0
1
2
2
1
1
1
2
1
2
0
2
2
0
2
1
2
1
1
2
1
2
1
1
1
2
1
0
1
0
0
1
1
1
0
2
1
1
1
1
2
1
1
1
2
1
0
1
1
0
1
1
0
2
1
1
0
1
1
1
1
1
1
1
1
1
1
1
0
2
0
1
1
1
1
1
0
2
1
1
1
0
1
1
1
0
2
1
0
2
1
1
1
0
2
1
1
0
0
1
1
1
1
1
1
2
1
2
1
0
0
1
1
0
2
2
1
0
0
0
1
2
2
1
2
1
1
1
1
1
1
0
1
0
0
2
1
1
2
1
1
1
1
0
0
1
0
2
1
1
3
2
1
0
2
1
2
1
1
1
1
1
2
1
1
2
2
1
1
1
0
1
0
2
1
1
2
1
1
1
0
0
2
2
2
0
2
2
1
2
1
1
1
2
1
1
0
2
2
2
1
1
1
0
1
1
0
1
1
1
0
0
1
2
2
1
1
1
1
2
1
0
2
2
2
2
1
1
1
1
1
2
1
1
2
0
1
1
1
1
0
1
2
1
1
1
2
0
1
1
0
0
0
0
0
1
1
1
0
1
1
1
1
2
2
1
0
1
1
3
1
1
2
0
1
1
2
2
1
1
0
2
2
0
1
1
1
1
1
0
2
1
2
0
0
0
0
1
1
2
1
1
1
1
1
1
1
2
0
0
2
2
1
1
1
1
2
0
1
1
1
2
2
1
1
1
1
1
2
1
0
1
2
2
1
0
1
2
1
1
1
1
1
2
1
2
1
1
1
1
1
0
2
1
1
0
1
1
2
1
0
2
1
2
1
3
1
1
2
1
0
1
1
2
1
0
2
1
0
1
1
1
1
1
1
1
0
4
1
1
1
0
2
1
1
1
1
1
1
2
4
1
2
1
2
1
1
1
0
1
1
1
1
0
1
1
0
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
0
0
1
0
4
1
1
2
1
1
0
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
0
1
1
1
0
0
1
1
2
1
1
1
1
2
0
0
0
1
1
1
1
1
1
1
0
1
1
2
1
2
1
2
2
1
0
0
1
1
2
1
1
2
1
1
2
0
0
2
1
0
1
1
1
2
2
1
0
2
2
1
0
1
1
2
2
0
0
1
0
1
1
2
1
1
0
1
0
1
0
1
2
0
1
0
1
0
2
0
2
1
1
1
2
2
1
1
1
1
0
2
2
2
1
1
1
1
1
1
1
1
0
1
2
2
1
2
2
1
0
1
0
1
1
0
1
2
1
2
0
1
1
1
0
1
2
1
1
1
0
1
2
1
0
1
1
2
2
1
2
2
1
1
0
1
1
2
1
0
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
0
1
0
1
1
2
2
2
1
2
0
1
1
3
0
0
1
0
1
2
2
1
1
2
1
0
1
1
2
1
1
0
2
2
1
1
1
0
1
2
2
2
0
1
1
2
1
2
3
0
1
2
1
1
0
2
1
1
2
1
1
2
2
1
2
0
2
1
0
2
1
2
1
1
1
1
1
2
1
0
1
0
1
0
2
0
2
1
0
0
0
0
1
0
1
1
0
1
1
1
2
2
1
1
1
0
0
2
1
0
0
1
0
1
1
1
1
1
1
1
1
1
0
4
1
2
1
1
0
1
1
1
1
2
1
1
1
2
1
1
0
1
1
0
1
1
1
2
0
1
1
1
1
1
0
1
0
1
2
1
1
2
0
1
2
2
1
1
1
2
1
1
1
1
1
1
1
0
2
1
2
1
0
1
0
1
0
0
1
1
1
1
1
1
2
1
2
0
0
1
1
0
1
1
2
2
1
0
2
1
1
0
2
1
1
2
2
1
0
2
2
1
1
1
1
1
1
2
0
2
0
1
1
0
1
0
0
2
1
1
2
1
1
0
0
1
1
1
2
2
1
0
1
1
0
1
1
1
0
0
1
1
0
1
0
0
2
1
1
1
2
1
1
1
1
2
2
0
2
1
1
1
1
2
2
2
2
1
2
1
0
2
0
1
0
1
2
1
1
2
2
2
0
1
1
1
1
0
1
2
2
1
2
2
1
0
1
2
2
1
2
0
1
1
1
2
0
2
1
2
2
0
0
1
0
1
2
1
0
1
1
1
2
1
1
0
1
0
1
2
1
1
0
2
0
2
1
1
1
1
1
0
1
2
2
0
1
2
2
1
4
2
1
1
1
1
1
1
2
1
1
1
1
0
2
1
0
1
1
1
3
1
3
1
1
0
1
2
1
2
1
2
2
1
2
1
1
2
2
1
2
2
0
2
1
0
0
2
0
2
2
0
1
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
2
1
1
2
1
1
2
1
1
2
2
1
1
0
2
1
1
2
0
1
0
2
0
1
2
0
1
1
0
1
1
1
0
1
2
1
2
1
1
2
3
1
1
2
0
1
1
1
0
2
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
0
1
1
3
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
0
1
1
1
2
1
1
1
0
1
1
0
0
1
1
1
1
2
0
3
1
2
0
1
1
1
0
0
2
2
1
1
2
2
0
1
0
2
1
2
1
2
2
0
1
1
0
1
1
1
1
1
1
2
1
1
1
1
1
0
1
1
0
1
1
1
1
1
1
1
1
1
1
1
0
1
2
1
1
1
0
0
1
1
0
2
2
1
0
1
2
1
1
4
1
1
1
1
1
0
2
2
1
1
1
0
1
2
0
2
2
1
0
2
2
2
1
2
3
0
2
2
1
0
1
1
1
3
0
1
0
1
0
1
2
1
1
0
2
2
1
1
1
1
0
2
1
1
1
1
0
0
1
1
0
1
6
1
1
0
1
1
2
1
0
2
1
0
0
1
0
1
2
0
0
1
1
0
2
1
1
2
1
1
0
0
1
0
1
0
1
2
1
2
2
0
1
2
1
1
1
0
2
1
1
2
1
1
2
1
1
1
1
1
0
2
0
2
1
1
1
2
1
2
1
1
2
1
0
1
2
2
1
1
1
1
1
0
0
2
1
0
1
2
1
1
1
2
1
1
1
2
0
2
1
2
1
0
2
1
1
1
1
1
1
2
1
1
1
0
1
1
3
1
2
2
0
2
1
1
0
1
1
1
1
1
0
1
2
0
1
1
2
1
1
1
2
1
2
1
1
2
2
1
1
0
1
1
2
1
1
0
0
0
1
1
1
1
0
1
1
2
2
1
2
1
1
2
1
1
1
1
2
2
2
0
0
1
2
2
0
2
1
1
1
2
1
0
2
1
1
2
1
1
2
0
1
1
1
1
1
2
1
2
0
2
2
0
0
1
1
1
2
0
0
1
0
1
0
2
1
1
1
0
1
1
1
2
0
1
1
0
1
1
1
2
0
1
1
1
2
1
0
1
2
1
2
1
2
0
0
2
1
1
2
1
1
1
1
2
2
0
1
1
1
2
1
2
2
1
1
2
0
0
1
1
1
0
1
2
1
2
1
0
0
2
0
2
0
1
2
1
2
0
2
1
1
2
1
0
0
5
2
1
2
1
2
1
0
1
1
1
0
0
1
1
2
2
1
1
1
1
1
1
0
2
0
2
0
2
2
1
0
2
1
1
1
2
0
1
2
0
0
2
1
2
2
2
1
1
0
2
0
1
0
2
1
2
1
1
1
1
1
1
1
1
2
2
0
0
0
0
1
1
1
0
1
0
2
2
1
2
1
0
0
2
0
3
2
2
1
1
1
0
1
1
1
1
1
1
1
1
2
1
1
1
1
1
0
2
1
2
1
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
0
1
0
1
0
1
1
1
1
1
0
1
1
1
2
2
4
2
1
0
1
1
1
1
1
0
2
0
1
1
0
3
0
1
1
1
1
1
1
0
0
1
0
1
1
1
1
2
1
2
1
1
1
0
2
1
2
1
1
2
1
1
2
1
1
1
0
0
0
1
2
1
2
1
5
2
2
2
2
0
0
1
1
1
0
2
1
2
3
1
1
1
0
1
1
0
1
1
2
1
1
1
2
1
1
1
1
2
1
0
2
1
1
0
1
2
1
1
0
0
2
1
1
1
0
1
2
2
2
2
1
1
1
2
2
1
1
0
0
1
1
1
1
1
0
0
2
0
0
1
1
0
0
1
1
0
2
0
1
0
0
1
1
2
2
1
2
1
2
1
1
2
2
0
1
1
0
1
2
0
2
0
1
0
1
0
0
0
2
1
1
2
1
1
1
2
0
1
2
1
1
1
2
1
2
2
1
0
1
1
2
1
1
0
1
2
2
2
1
2
2
3
0
0
1
0
1
1
1
1
2
1
1
1
2
1
0
2
1
1
1
1
0
2
1
1
1
1
1
0
1
2
2
1
1
2
2
0
0
0
1
2
0
1
0
1
1
1
1
2
2
1
0
0
1
2
1
0
1
1
0
0
0
2
1
1
1
1
0
1
1
2
1
1
8
1
2
1
0
1
1
1
0
2
0
1
1
1
2
2
0
1
2
2
1
1
0
1
1
2
1
0
1
2
2
2
1
0
2
0
3
2
1
1
2
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
0
0
0
1
0
1
1
2
1
2
1
1
1
1
1
0
2
1
1
1
1
1
0
2
1
1
0
1
1
0
2
1
1
1
1
2
0
1
1
2
0
2
1
2
1
2
1
2
0
1
1
0
2
1
1
0
1
1
1
1
0
1
2
2
2
1
0
2
0
1
1
2
1
2
0
1
1
2
1
1
2
0
1
1
1
1
2
0
1
2
1
1
2
1
1
1
2
1
0
1
1
1
1
1
1
1
1
1
1
2
3
2
2
0
2
1
2
1
0
1
2
2
0
1
1
2
1
1
0
1
1
0
1
0
1
1
0
1
1
2
2
1
1
1
0
2
0
2
1
1
2
1
1
1
0
4
1
1
0
0
1
1
0
2
1
0
0
1
1
1
0
2
1
2
1
1
1
1
0
1
1
0
2
1
2
1
1
1
1
0
2
0
0
1
1
1
0
1
1
2
1
2
3
0
1
1
1
1
1
1
1
2
1
2
0
0
0
2
1
1
2
1
0
2
1
1
1
0
2
2
2
0
1
0
0
1
1
2
0
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
0
1
1
0
2
1
1
0
1
1
1
1
2
1
2
1
0
2
1
1
1
2
2
1
2
1
1
1
3
1
2
1
0
1
2
0
1
1
2
1
2
0
1
1
0
0
0
0
2
1
2
1
2
1
1
0
2
0
0
1
2
1
2
2
1
2
1
1
0
1
2
1
1
1
1
1
2
1
1
1
1
2
1
1
2
2
0
1
1
2
1
1
0
2
0
0
2
2
2
1
1
1
2
1
0
0
1
2
1
1
2
1
2
2
2
2
1
1
0
0
1
1
1
1
1
2
3
0
1
1
2
0
2
1
0
1
2
1
2
2
2
1
1
2
1
1
1
2
2
1
2
0
0
1
1
1
0
1
1
1
1
1
0
0
1
1
2
2
2
1
2
2
1
0
2
0
2
0
1
1
1
1
1
0
2
1
0
1
1
1
2
2
1
1
2
0
1
3
2
1
2
2
2
1
1
0
1
1
2
1
2
2
1
2
0
1
2
1
1
1
1
2
0
2
1
1
2
0
1
1
0
1
1
1
0
1
1
2
2
1
0
1
1
4
1
1
2
0
1
0
1
0
1
0
1
1
2
0
1
2
1
2
0
2
2
2
0
1
2
0
1
0
1
2
1
2
0
2
2
0
1
0
2
1
1
1
1
0
1
0
1
1
0
2
2
1
1
1
2
1
2
2
1
2
1
1
1
1
2
1
0
1
1
1
2
0
2
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
0
1
2
1
2
2
1
1
2
1
0
1
0
1
1
2
2
1
1
1
1
1
1
1
2
1
1
0
1
1
2
0
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
2
2
1
0
4
0
2
1
1
1
1
2
1
1
1
1
2
1
2
2
2
0
1
1
2
1
1
1
1
1
0
1
2
1
1
1
2
2
0
1
1
0
1
1
1
1
1
1
1
2
1
2
1
1
2
1
2
0
1
1
2
1
1
2
1
1
1
2
0
1
2
1
1
1
0
1
1
4
1
1
1
0
1
1
1
1
0
1
2
0
1
1
1
1
1
2
1
0
2
1
1
1
2
1
1
1
2
1
0
2
0
1
1
2
0
0
1
1
1
2
1
1
1
1
0
2
2
1
1
1
1
2
1
1
1
1
1
1
2
0
1
1
2
2
2
0
2
0
2
1
1
2
2
2
2
2
1
2
1
1
1
1
2
0
1
2
2
1
1
0
2
0
0
2
1
1
0
1
1
1
1
1
1
1
2
1
0
2
0
2
2
0
1
2
1
1
0
1
1
2
2
1
1
2
1
1
1
1
1
0
1
2
1
0
1
1
1
0
1
1
1
2
1
2
1
0
2
2
1
2
0
2
0
1
1
1
1
2
1
0
1
2
1
0
2
1
1
1
1
1
2
1
2
2
1
1
1
1
2
1
1
1
0
1
1
1
3
1
1
2
1
1
0
2
1
1
2
0
1
1
0
1
1
2
1
0
0
2
1
0
0
1
0
1
0
1
1
1
0
1
0
0
2
1
2
1
1
2
1
1
1
2
2
2
1
1
2
1
1
1
2
2
0
1
1
2
0
1
2
1
1
0
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
2
2
1
2
2
1
1
0
1
2
0
1
0
1
0
0
1
1
2
0
2
1
1
0
1
1
0
1
0
1
2
1
1
0
2
1
0
0
1
0
0
1
1
2
0
2
1
1
1
1
0
0
0
0
0
1
1
1
1
0
1
1
2
1
2
1
1
0
1
1
1
1
1
1
0
1
0
2
1
1
1
1
1
2
2
1
1
0
1
1
1
2
1
1
1
1
0
1
1
1
1
0
0
2
1
0
1
1
1
1
1
1
2
1
0
1
1
2
2
0
1
0
1
1
1
0
2
0
1
1
2
1
0
0
1
0
1
0
1
1
1
1
1
1
0
1
0
1
1
0
0
0
1
0
3
0
2
1
0
0
1
1
1
1
0
1
2
0
2
1
1
1
1
0
2
1
0
1
1
1
2
1
1
1
2
2
0
0
1
1
2
2
1
2
0
1
1
0
1
0
0
2
2
0
0
2
2
0
2
2
1
2
1
0
1
0
1
0
0
2
0
1
1
1
2
1
1
0
1
2
2
1
1
1
0
0
1
1
1
0
2
1
1
1
2
1
1
1
0
0
1
1
3
0
1
1
1
0
1
2
1
0
2
2
1
1
2
1
2
0
2
1
0
1
1
1
0
2
1
1
1
1
1
2
2
0
1
1
1
1
1
1
1
1
0
1
1
1
0
1
1
2
2
1
0
1
1
1
0
0
2
1
1
2
1
0
1
1
1
2
0
1
0
1
1
1
0
0
1
2
0
1
2
1
1
1
2
1
2
1
1
0
1
0
0
1
1
2
1
1
1
1
1
1
1
1
1
2
1
0
0
1
2
0
1
2
1
0
0
0
1
0
1
0
2
1
1
1
0
0
1
1
2
1
1
0
2
1
2
1
1
2
1
1
0
1
1
1
0
1
0
1
0
1
2
1
1
0
1
1
2
0
1
1
2
0
2
1
2
1
1
1
1
0
1
0
1
1
0
1
0
1
2
1
1
1
1
0
0
1
0
1
3
2
1
2
2
1
2
1
0
2
0
1
1
2
1
0
0
1
1
3
1
1
1
1
2
2
2
0
0
1
1
0
1
1
2
0
2
0
1
1
1
1
2
1
1
0
1
0
1
0
0
1
1
2
1
1
2
1
2
0
0
0
2
2
1
1
1
2
0
0
0
1
1
2
1
1
0
1
2
2
2
1
0
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
0
2
1
2
1
1
2
0
3
1
1
1
1
1
0
0
0
1
1
1
2
1
0
1
1
1
2
1
2
2
1
0
1
1
0
2
0
1
0
1
1
0
1
1
1
1
0
1
0
1
2
1
1
1
1
1
3
0
2
1
1
1
2
1
1
1
1
1
0
1
1
0
0
1
2
0
1
2
1
1
1
0
1
1
0
1
2
1
0
2
1
1
1
1
0
1
0
1
0
1
2
1
1
2
1
2
2
0
0
2
1
1
1
2
1
1
1
1
1
1
1
1
1
0
1
2
0
2
0
1
1
1
1
2
0
1
2
2
1
0
2
1
1
2
1
2
1
1
1
1
1
0
1
2
1
2
1
0
2
1
0
1
0
2
1
0
1
2
0
1
2
1
2
0
1
1
2
0
0
2
1
2
1
1
0
0
1
1
0
0
1
1
0
1
1
0
1
1
0
1
0
0
2
1
1
2
1
1
0
1
0
1
2
1
1
1
1
1
0
1
1
1
1
2
1
1
1
1
1
0
1
1
1
1
1
4
1
1
2
1
1
1
1
1
0
1
2
1
1
1
0
1
1
1
2
0
0
0
1
1
1
1
1
0
1
1
1
2
1
0
1
2
1
1
1
1
0
1
1
2
0
2
2
1
1
1
1
1
1
1
0
0
0
1
0
1
1
1
0
1
1
1
2
1
1
1
2
0
1
2
0
1
1
1
0
1
2
2
1
1
1
1
1
1
1
1
0
2
1
1
1
1
2
1
1
1
1
2
1
2
0
1
0
0
2
1
1
1
1
1
2
0
0
0
0
2
1
1
1
1
1
1
1
1
0
1
1
2
2
2
1
1
1
0
1
1
2
1
1
0
2
0
2
2
1
1
1
1
2
1
2
0
2
1
1
1
1
2
0
1
2
1
2
2
1
2
1
0
2
0
1
1
1
1
1
1
0
1
1
2
0
0
2
2
2
1
1
1
1
2
1
1
1
1
1
1
1
1
0
0
1
1
1
3
1
1
1
2
1
2
1
2
1
2
1
0
2
1
2
2
2
1
0
2
3
1
0
1
1
1
1
1
0
2
1
2
0
1
2
2
1
1
1
5
1
1
1
1
0
1
0
1
1
1
2
1
1
0
2
1
1
2
1
1
1
0
1
2
1
1
1
2
0
0
1
1
1
2
0
1
1
1
0
2
2
1
2
1
1
1
1
0
1
0
1
1
1
0
1
1
2
1
1
2
1
0
1
1
1
1
2
0
2
2
1
2
1
1
1
2
1
0
2
1
1
1
0
1
1
0
1
1
1
1
0
0
1
1
1
1
1
2
1
1
1
0
1
1
0
1
1
1
1
0
1
1
1
1
1
2
2
2
1
1
2
1
2
1
1
1
1
1
0
0
1
1
1
1
0
1
1
2
1
1
0
1
0
0
1
1
1
0
1
2
0
0
1
1
2
1
2
1
2
0
0
1
1
1
1
1
2
0
2
1
1
1
0
1
0
1
1
1
1
2
1
1
1
1
0
1
1
2
1
1
1
1
1
0
0
2
0
2
2
2
1
0
1
1
1
1
1
2
1
0
2
0
2
1
2
2
0
0
1
1
1
1
1
2
1
0
1
0
0
1
0
2
2
0
1
0
2
0
2
1
1
1
0
1
0
2
1
0
0
1
2
0
1
1
1
0
0
0
1
1
1
1
0
1
2
1
0
1
1
0
2
1
1
1
1
1
0
1
1
1
1
2
0
2
2
2
1
1
2
1
1
1
1
1
1
0
1
1
2
0
1
1
2
1
2
1
1
2
0
1
2
1
0
1
1
1
1
1
0
1
1
0
2
0
2
1
0
1
1
2
2
0
1
1
1
0
1
2
0
0
1
0
1
1
1
2
2
0
0
2
2
1
1
0
2
0
2
0
1
2
1
1
1
0
0
1
2
1
2
2
1
1
2
1
1
1
2
1
1
0
1
1
2
3
2
2
1
1
1
1
1
2
0
1
2
1
1
1
2
1
1
1
1
0
1
2
1
2
2
1
2
2
1
1
2
1
0
1
0
2
1
1
2
1
5
2
2
2
1
1
0
0
1
1
0
1
0
1
2
1
2
0
1
2
1
1
1
1
1
1
2
1
1
0
2
0
0
1
1
1
2
1
1
1
1
0
2
1
1
0
2
1
2
1
2
0
1
1
0
2
1
1
1
2
2
1
0
1
2
1
2
2
2
1
2
1
1
2
1
1
1
2
0
1
2
0
1
1
2
1
1
1
0
1
0
1
0
2
1
1
1
1
1
1
2
1
1
1
1
0
2
1
1
0
1
1
1
0
0
1
0
0
2
0
2
2
0
0
2
0
1
2
1
1
0
1
0
2
1
1
0
2
1
0
1
0
1
1
1
0
1
2
1
1
1
1
1
1
2
0
0
2
2
2
1
1
0
1
2
1
2
1
0
2
1
0
1
1
1
1
1
0
1
2
0
0
2
0
0
1
2
2
1
1
2
2
2
0
1
1
2
2
0
1
1
1
1
0
2
2
1
2
0
0
0
0
1
2
0
1
1
1
1
2
1
1
0
1
2
1
0
1
0
1
1
1
1
1
1
1
1
0
0
0
2
1
2
1
1
1
1
1
1
2
1
2
1
2
2
0
2
2
0
2
0
2
2
1
1
1
0
1
1
1
1
1
2
1
2
2
2
2
1
1
1
0
2
2
1
1
2
1
0
1
2
1
1
1
1
0
1
0
0
1
1
2
1
1
1
1
1
1
1
2
0
1
1
1
0
0
1
1
1
1
1
2
0
2
1
2
2
1
0
0
0
1
2
3
1
2
2
1
0
2
2
1
1
1
1
1
2
6
0
2
1
0
0
2
0
1
1
1
2
0
2
1
1
0
1
2
0
2
1
1
2
1
2
1
1
1
0
1
2
2
1
2
0
1
1
0
1
0
2
2
2
0
2
2
1
1
1
1
1
2
1
1
2
1
1
0
1
2
1
2
2
2
1
1
1
1
2
1
0
1
1
1
1
1
1
1
1
0
2
1
2
0
1
2
2
0
1
1
2
2
1
0
1
0
0
1
0
1
2
1
2
2
3
2
1
2
1
1
2
1
2
1
2
1
1
1
0
1
1
1
2
2
1
1
2
1
2
1
1
0
1
0
2
1
2
1
1
1
1
2
2
1
0
2
1
2
2
2
1
1
1
1
0
1
1
1
1
2
1
1
1
1
3
1
1
1
1
0
1
0
1
1
1
2
2
1
1
0
3
1
2
1
2
1
1
1
0
1
1
2
1
2
0
1
2
1
0
2
1
1
2
0
1
1
1
0
2
2
0
1
1
0
1
1
1
1
0
1
1
2
1
0
0
1
1
1
0
0
1
1
0
1
2
1
1
1
2
1
2
2
1
0
1
2
0
1
1
2
2
1
1
1
2
1
0
0
2
2
1
2
1
3
1
1
1
0
1
1
1
1
1
0
0
1
1
1
0
1
1
1
0
1
1
1
0
0
0
1
1
1
1
0
1
1
1
1
1
1
4
2
1
1
1
1
1
2
1
1
1
0
2
1
1
2
1
1
1
1
1
0
1
1
1
1
1
1
1
2
1
1
1
1
2
0
1
1
2
2
1
1
1
1
2
0
2
1
2
1
0
1
0
2
0
0
1
0
0
0
1
2
2
0
0
1
1
1
0
2
2
1
2
1
1
1
0
1
1
2
2
2
1
2
0
1
1
0
3
1
2
0
0
1
1
2
0
2
1
0
1
1
2
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
2
1
0
1
0
1
1
1
3
1
1
1
1
0
1
1
1
1
2
1
2
2
2
1
0
1
2
0
1
1
1
1
1
0
2
2
2
1
1
1
1
1
0
2
0
2
2
2
1
0
1
2
1
2
1
2
1
2
2
1
0
1
0
0
1
1
0
1
1
0
1
2
2
1
1
1
1
2
1
2
0
0
1
1
1
2
1
2
1
0
1
1
1
1
1
1
0
1
1
0
2
1
1
0
2
1
1
1
1
0
1
0
1
1
1
2
1
1
0
1
0
0
0
2
1
1
1
0
2
0
2
1
1
1
1
2
1
0
2
0
0
2
1
2
2
1
1
1
1
2
1
2
1
0
1
0
1
1
2
1
0
0
0
2
0
1
1
2
0
1
1
1
1
2
1
0
1
2
0
1
1
1
2
1
1
0
2
1
0
1
0
0
0
0
1
0
0
0
1
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
0
2
2
1
1
1
1
1
2
1
0
1
0
1
1
1
1
0
1
2
0
0
1
2
1
1
2
1
0
1
1
1
2
4
1
1
0
1
1
1
1
2
3
0
0
1
1
1
1
1
1
0
0
1
0
0
1
1
1
1
1
1
0
2
1
0
1
1
0
2
1
1
0
1
0
1
1
1
0
1
1
2
1
1
2
1
2
1
1
1
0
1
0
2
1
2
2
1
1
1
2
2
1
2
1
1
1
1
1
1
3
1
1
1
1
0
2
2
1
0
1
0
1
3
2
2
2
1
1
1
0
1
0
1
2
1
1
1
1
2
2
0
1
1
1
1
1
2
0
0
1
2
1
1
1
1
1
1
2
1
2
1
1
2
0
2
1
0
1
1
2
1
0
0
2
1
1
2
1
1
1
1
1
1
1
1
1
1
0
1
1
2
1
2
2
2
1
1
0
1
0
1
1
1
1
0
1
1
1
0
1
1
1
1
2
1
2
1
2
2
1
0
1
1
1
1
0
1
1
1
1
0
0
1
2
1
1
1
0
1
0
1
1
1
2
1
2
1
0
2
1
1
1
2
0
0
1
2
1
0
2
2
2
1
1
1
4
2
2
1
1
1
1
1
2
1
1
1
1
2
1
1
2
0
0
1
1
0
1
1
1
0
0
0
1
1
0
0
0
2
1
1
1
1
1
1
2
1
1
0
1
0
1
1
1
1
2
2
0
2
2
1
1
1
0
1
0
1
0
2
2
0
1
1
2
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
0
2
1
1
2
1
2
1
1
1
1
2
1
2
1
2
2
1
1
2
1
1
1
1
1
1
1
0
0
2
2
1
1
2
0
2
1
1
0
1
1
1
1
0
1
1
0
1
1
2
1
1
1
1
1
2
0
1
1
1
1
1
2
1
0
1
1
2
0
2
1
1
0
2
1
2
1
1
2
1
0
1
0
1
1
2
1
2
1
1
1
2
0
2
0
1
1
0
2
0
1
0
1
1
1
1
1
0
2
0
2
2
1
1
1
1
1
1
1
1
1
2
0
2
0
0
2
1
1
1
0
1
1
1
0
1
1
1
1
1
0
1
1
2
0
1
1
3
0
1
1
2
2
0
1
0
1
0
1
1
1
1
2
0
1
0
1
0
0
1
1
1
1
1
2
1
2
0
2
0
1
1
1
0
1
1
0
1
1
5
0
1
1
0
1
2
1
1
0
2
0
1
1
0
2
2
3
0
1
1
2
2
0
0
1
1
1
0
0
2
0
2
1
2
2
1
0
0
1
1
2
1
2
1
1
0
1
1
1
2
2
1
2
1
1
0
1
2
0
1
2
0
1
1
1
1
1
2
1
0
1
0
1
0
1
1
0
0
1
2
1
1
1
1
1
2
1
0
0
2
2
2
2
1
0
0
1
0
0
1
1
1
1
1
2
0
0
2
1
0
1
1
2
0
1
0
2
1
0
2
1
0
2
1
2
1
0
1
1
1
1
1
2
1
2
1
1
1
1
1
0
0
1
0
0
1
1
2
2
2
2
1
1
2
0
1
1
1
1
0
2
2
1
1
2
0
2
2
0
1
1
2
0
1
0
1
1
0
0
0
0
1
1
1
1
0
0
1
1
2
2
2
2
0
0
1
1
1
2
1
2
1
1
1
0
2
0
2
1
1
0
1
0
2
1
2
1
1
1
1
0
1
1
1
0
0
0
1
2
1
0
2
2
5
0
1
1
1
1
0
1
0
1
1
0
1
1
1
1
1
1
0
2
1
1
0
0
1
2
1
2
0
1
1
2
2
2
2
1
1
1
2
1
1
0
2
2
0
1
1
1
1
2
2
2
1
1
2
0
1
0
1
1
0
1
0
1
3
1
1
0
1
1
1
0
2
1
1
1
1
0
1
0
2
0
1
2
1
1
0
1
1
1
1
1
1
1
1
1
1
0
2
1
1
1
2
0
1
1
1
1
1
0
2
0
0
2
1
1
1
1
2
2
1
1
1
1
1
1
0
1
0
1
2
1
0
2
2
1
2
1
2
0
2
1
1
0
1
1
0
2
1
2
1
0
1
1
2
2
0
0
1
1
1
1
2
2
2
1
2
1
0
1
0
2
2
1
1
2
3
0
1
1
1
0
1
1
1
2
1
1
2
1
1
3
1
1
2
1
1
1
1
1
1
2
0
0
1
0
1
0
1
1
1
2
0
1
1
1
1
1
2
0
0
1
2
1
1
1
1
2
1
2
2
1
0
0
2
0
1
1
2
1
2
0
2
0
2
2
1
2
1
1
2
0
0
1
2
2
0
1
0
1
1
1
1
1
1
1
0
2
1
1
1
1
1
1
1
2
2
1
2
1
1
0
1
2
0
2
1
2
0
1
1
2
0
1
2
1
0
0
2
0
2
1
1
0
1
0
0
1
1
1
2
1
0
0
1
1
2
1
1
1
2
1
1
2
0
1
0
2
1
1
1
1
1
1
2
1
2
1
1
1
1
2
0
1
1
0
1
2
2
1
1
1
1
1
1
2
0
1
1
1
4
0
1
1
1
0
1
1
0
1
1
0
2
1
1
0
1
1
1
1
0
2
1
1
0
1
0
1
2
1
2
2
0
0
1
1
0
2
1
0
1
1
1
1
1
1
0
0
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
0
1
1
1
2
1
1
2
1
0
1
0
1
1
2
1
2
2
2
1
0
2
2
1
1
0
1
2
2
1
1
0
2
1
2
2
0
1
0
1
2
1
1
0
1
1
1
1
3
0
1
1
2
1
1
1
1
1
2
0
1
2
1
0
2
1
2
0
1
1
1
1
1
2
2
1
1
1
1
0
1
2
1
2
1
2
1
1
0
1
2
1
0
0
2
0
0
1
1
1
2
1
1
0
2
1
2
2
0
1
1
1
1
1
2
1
0
1
0
0
4
1
0
2
0
1
1
0
0
2
1
1
0
2
2
1
1
1
0
1
1
0
1
1
2
1
1
0
1
1
1
0
2
1
1
1
1
2
1
0
0
0
2
1
1
0
2
1
1
1
1
0
1
0
0
2
1
0
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
0
2
0
1
1
1
0
0
1
1
1
0
0
1
2
1
0
1
1
0
0
1
1
0
1
1
2
1
0
1
0
2
0
2
1
1
3
2
1
1
2
1
1
2
1
1
1
1
2
0
1
2
1
1
1
2
0
1
1
1
1
2
2
2
1
1
2
0
1
1
1
1
1
0
4
1
1
2
1
1
1
1
1
0
0
2
2
1
2
1
1
2
1
1
3
2
0
1
1
2
2
1
1
1
1
1
1
1
2
1
1
0
1
1
1
1
1
1
1
0
1
1
2
1
1
1
1
1
1
0
1
0
0
2
0
2
1
0
1
1
1
1
1
1
0
1
1
1
2
0
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
0
1
0
1
2
1
1
2
1
1
1
1
1
1
0
1
0
1
0
1
1
1
0
1
0
2
1
1
0
0
1
0
2
1
0
1
1
2
0
2
0
1
1
1
2
1
2
0
1
2
1
0
2
0
2
0
1
1
2
2
1
1
1
1
1
1
0
1
2
1
2
1
1
2
1
1
1
1
0
1
2
1
1
1
2
0
1
0
2
2
0
2
1
2
2
1
0
1
2
2
2
1
1
1
1
0
1
0
1
1
2
1
0
2
1
2
1
1
1
1
1
1
0
1
1
1
1
2
1
0
1
0
0
2
1
1
1
2
0
1
2
1
2
0
1
2
1
2
0
1
1
1
1
1
0
1
1
1
0
1
2
0
1
1
1
0
1
2
2
1
1
1
1
1
1
2
2
1
0
2
1
2
1
0
1
1
1
1
0
2
2
1
1
1
1
1
2
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
0
1
1
2
2
1
1
1
1
1
1
1
1
1
0
1
1
1
1
0
1
2
1
1
1
2
2
0
3
1
1
1
1
0
1
1
2
1
2
1
1
1
1
0
2
2
1
0
1
2
1
1
2
1
2
0
1
2
3
1
1
0
1
0
0
2
1
1
0
0
0
1
1
1
1
1
1
1
2
1
2
1
1
1
2
1
1
2
2
2
1
0
1
2
0
2
0
2
0
2
2
1
1
1
1
0
1
1
1
2
2
0
1
1
2
1
1
2
1
1
2
0
2
1
1
2
1
1
1
1
2
2
0
1
0
1
3
1
2
2
0
0
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
0
2
1
2
2
0
0
2
2
0
1
1
2
2
2
1
1
2
1
1
0
2
1
1
2
1
1
2
1
1
1
1
1
2
1
2
1
2
0
1
3
2
0
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
0
1
0
0
1
1
0
1
1
1
0
1
2
1
2
1
1
1
1
1
0
1
1
1
0
2
0
0
1
2
1
1
1
0
0
1
2
0
1
1
0
1
0
1
1
1
1
2
1
0
2
0
2
1
1
0
1
1
2
1
2
1
1
1
0
1
0
1
1
2
0
1
2
1
1
0
1
2
0
1
1
1
1
1
0
2
1
0
1
0
0
1
1
1
1
0
0
0
2
1
1
1
2
1
0
2
1
1
1
1
0
1
1
0
0
0
2
1
1
1
0
2
2
1
1
0
1
0
1
2
3
2
2
1
1
1
1
1
1
0
2
1
0
0
0
2
1
0
0
1
1
2
1
1
1
0
2
1
1
1
1
2
1
2
1
1
1
1
2
1
3
1
1
2
1
0
1
2
2
1
1
1
3
0
1
0
1
1
4
2
1
2
1
1
1
2
2
1
1
2
1
1
0
1
1
1
1
1
2
1
1
2
1
1
2
0
1
1
2
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
2
2
0
0
1
2
1
1
1
1
1
0
0
1
2
0
1
2
2
1
1
4
1
1
1
2
2
2
1
1
2
0
0
0
1
1
1
2
0
1
1
1
1
1
1
0
0
0
3
1
1
1
0
1
1
0
1
1
1
1
2
1
1
1
1
2
1
1
2
0
1
1
2
2
1
0
0
0
1
1
1
2
2
0
0
0
2
0
0
0
1
0
1
1
0
1
1
1
2
0
2
1
2
1
1
1
1
2
1
0
1
0
1
2
1
1
0
1
1
2
1
0
1
2
1
2
1
1
1
2
1
2
1
0
1
1
2
1
2
1
1
1
0
1
1
2
0
2
0
2
1
2
0
1
2
1
1
0
2
1
1
1
2
2
0
1
0
1
2
0
1
2
2
2
1
1
1
2
1
2
1
2
1
1
0
1
1
2
1
1
1
1
3
2
2
2
1
1
1
1
1
2
2
1
1
0
1
1
2
1
1
1
0
1
0
1
0
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
0
2
0
0
0
1
1
2
1
1
1
1
1
2
1
1
2
1
2
2
1
0
1
0
2
1
2
0
1
1
1
1
2
1
0
1
1
2
1
0
1
2
0
1
1
1
1
1
2
3
1
2
2
1
1
0
0
2
2
2
0
2
1
1
1
1
0
1
1
1
2
1
2
0
2
1
1
1
1
0
1
1
1
2
1
0
1
1
0
1
0
1
1
0
1
2
0
0
1
2
1
1
1
1
0
1
1
1
2
1
2
0
1
1
1
2
0
2
1
1
0
1
1
0
2
0
2
1
1
1
1
1
0
1
1
1
2
2
1
0
1
0
1
1
1
0
0
1
0
1
1
1
2
1
1
1
2
2
1
1
1
2
1
1
1
1
1
1
1
1
1
0
1
1
1
1
2
1
1
2
1
0
1
2
0
2
2
1
2
0
1
2
2
0
1
1
2
1
0
1
0
2
1
2
1
1
2
1
1
2
1
1
1
1
0
1
0
1
2
1
1
1
2
1
1
2
1
1
1
1
1
1
0
1
2
1
1
1
2
0
1
2
1
1
1
1
1
1
2
2
0
0
1
1
2
1
1
2
1
0
2
2
1
1
0
1
1
0
0
2
1
1
1
2
2
1
1
1
1
0
3
2
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
2
1
2
1
1
1
0
0
1
2
2
1
1
1
1
1
1
2
1
0
0
1
0
0
2
1
0
1
2
2
1
1
1
2
1
1
0
2
1
1
2
0
1
2
1
0
1
0
1
0
1
1
1
1
0
0
0
2
1
1
0
1
1
0
0
1
2
1
1
1
1
1
1
2
1
2
0
1
2
1
1
1
1
1
1
1
1
1
0
0
1
1
2
0
0
4
2
1
1
1
2
0
1
2
0
1
0
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
0
2
2
0
1
2
1
1
1
1
1
1
0
0
1
0
1
1
1
1
1
2
2
2
0
1
1
1
0
1
1
2
1
1
1
1
1
1
1
2
1
1
1
0
2
1
1
2
1
1
1
2
2
2
2
0
1
1
2
1
1
1
1
1
1
0
2
1
2
1
0
1
0
1
1
2
1
2
0
2
1
0
1
1
1
1
1
1
3
1
2
1
1
2
1
1
1
1
2
0
1
1
2
1
1
0
2
0
0
2
1
0
0
1
0
1
2
1
1
1
1
2
1
0
1
1
1
1
1
2
1
1
1
0
2
1
1
2
1
1
0
1
1
2
1
1
2
2
0
0
2
2
2
1
0
1
1
0
1
1
1
1
2
1
2
1
1
0
1
1
1
1
1
1
2
0
1
1
0
1
1
1
1
1
0
1
0
2
1
1
1
0
2
1
1
0
2
1
1
1
0
2
2
1
2
2
2
1
1
1
1
0
1
1
2
1
1
2
0
1
0
1
1
0
0
1
1
2
2
0
1
1
0
1
1
1
2
1
1
1
0
1
1
1
1
2
0
2
1
1
1
0
1
2
0
2
2
1
1
0
2
1
1
2
1
0
1
1
1
0
0
0
1
1
1
1
0
1
1
1
0
1
1
1
2
0
1
1
1
1
1
0
2
1
1
0
1
1
2
1
1
2
1
1
1
0
1
1
0
2
0
1
0
1
1
2
2
1
1
2
1
1
1
3
1
2
1
2
2
2
0
1
0
0
2
2
1
0
2
1
2
0
0
1
2
2
1
1
0
1
0
1
0
0
0
2
1
0
1
1
2
2
2
1
1
2
2
1
0
1
1
1
1
1
1
1
0
1
1
0
2
1
1
0
1
1
0
1
1
1
0
2
2
2
1
1
1
1
1
2
1
2
1
2
1
2
1
0
0
2
2
2
0
1
1
2
1
1
1
1
1
0
0
4
2
1
1
1
0
2
2
1
1
1
1
0
1
1
2
1
1
1
0
1
3
1
1
2
0
0
0
1
2
2
0
1
1
0
2
1
1
0
1
0
1
1
1
0
2
2
1
1
1
2
0
1
1
1
0
1
2
2
2
1
0
0
2
1
1
0
0
1
0
2
1
2
1
1
0
1
1
0
1
1
2
2
1
2
1
0
2
1
2
1
0
1
1
1
0
0
1
1
1
1
2
1
0
1
0
0
2
2
2
1
0
1
1
1
1
1
1
1
1
1
1
0
1
1
0
1
1
1
2
0
2
1
1
1
1
0
1
2
1
1
1
1
1
1
0
1
0
2
2
2
1
2
1
1
1
1
0
2
2
1
0
0
1
0
2
1
1
2
2
1
0
1
1
1
1
1
1
1
0
2
1
1
1
1
1
1
0
1
1
2
1
1
1
2
0
1
2
1
2
2
1
1
1
1
0
0
1
1
1
1
1
3
1
1
1
1
1
2
1
0
2
1
0
2
1
1
2
2
1
0
1
1
2
3
2
2
1
3
1
0
2
3
2
1
0
2
1
2
0
1
0
2
2
1
1
1
1
1
1
1
1
1
2
1
0
1
2
1
1
1
1
1
2
2
0
1
1
1
0
1
0
1
0
2
2
2
0
1
1
1
1
2
0
1
1
1
2
1
2
1
0
1
3
2
1
1
1
1
0
2
1
0
1
1
1
2
2
2
1
1
1
1
3
2
0
1
0
1
1
1
2
1
1
0
1
1
1
2
1
0
2
1
1
1
2
1
2
2
1
1
1
1
0
1
1
1
1
0
1
1
2
2
0
0
2
1
1
1
2
1
1
0
1
1
1
1
2
0
1
2
1
1
1
1
2
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
2
2
2
2
2
1
2
3
4
2
1
1
1
1
2
1
1
2
0
0
0
2
0
1
1
0
2
1
1
2
1
1
0
2
1
2
2
1
1
1
1
1
1
0
1
2
1
2
1
0
1
1
1
1
1
0
1
1
0
1
1
0
2
1
1
0
1
1
1
0
2
1
1
1
2
0
1
1
1
1
1
1
0
2
1
1
2
1
0
1
1
1
2
2
2
0
1
2
2
2
1
2
1
1
1
2
0
1
2
0
1
1
1
2
0
1
1
1
2
1
1
1
1
1
2
2
1
1
2
1
1
1
2
2
1
0
1
2
0
2
1
2
1
2
1
0
2
2
1
1
2
1
1
1
2
0
1
1
1
1
1
1
0
2
0
3
0
0
1
1
2
1
1
0
1
1
1
1
1
2
4
2
1
0
0
0
1
1
1
1
1
1
2
2
1
1
1
1
1
1
2
2
1
1
1
2
1
0
1
2
1
2
1
2
1
0
2
1
1
1
0
2
1
1
1
1
2
2
1
1
2
0
1
1
1
1
1
2
1
1
1
0
1
0
2
1
1
0
1
1
1
0
1
1
1
2
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
0
1
1
1
0
2
1
1
1
2
1
2
1
1
2
1
0
1
1
1
1
2
0
1
1
0
1
1
1
0
2
2
1
0
1
2
0
1
0
0
1
1
1
1
1
2
0
0
0
2
0
1
2
0
3
1
2
2
1
1
1
0
1
2
2
2
2
1
1
0
1
0
0
1
2
1
1
2
1
0
1
1
1
1
2
2
1
3
0
2
1
1
0
0
1
2
1
2
1
1
0
1
2
2
0
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
1
0
2
1
2
1
1
3
1
1
1
1
1
1
0
1
1
1
1
1
1
0
1
2
1
2
1
1
1
1
0
0
1
1
2
1
0
2
2
2
1
2
1
1
1
2
1
2
2
1
2
1
2
1
2
1
1
1
2
1
0
2
2
1
1
1
2
1
2
0
2
1
1
1
2
1
1
1
1
0
0
2
1
1
1
2
2
1
0
1
0
0
1
1
2
1
1
2
2
1
1
2
1
0
1
1
1
3
2
0
2
1
1
0
1
0
0
2
1
1
1
1
0
1
2
1
1
0
2
1
1
2
0
2
0
1
0
0
2
0
1
0
1
2
1
2
1
1
1
0
1
1
1
1
1
1
2
0
1
1
1
1
1
0
1
2
2
1
0
1
1
1
1
0
2
1
0
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
0
1
2
1
1
1
2
0
2
1
1
1
1
0
1
2
1
1
1
1
1
1
1
0
2
1
0
1
3
2
2
1
1
1
2
1
1
1
1
0
2
1
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
2
1
2
1
0
1
1
2
1
1
0
0
1
1
1
1
2
1
1
1
2
0
0
1
1
1
1
1
1
1
1
1
1
0
1
1
0
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
2
0
2
0
1
1
1
1
2
2
2
1
1
1
1
1
3
1
2
1
1
2
0
0
0
2
1
0
0
1
2
1
1
1
0
1
0
1
1
1
2
1
0
0
1
1
1
1
1
0
2
0
2
1
1
2
1
1
2
1
1
1
2
1
1
1
0
0
1
1
0
1
1
1
0
1
0
2
2
2
2
2
1
1
1
2
1
0
1
1
2
1
1
0
0
1
1
0
1
1
1
2
1
1
1
0
2
1
1
1
1
1
1
2
2
1
0
0
1
1
1
0
0
1
0
2
0
1
2
2
0
0
1
0
1
2
1
1
0
2
1
1
1
1
1
1
0
0
2
0
1
2
1
0
1
0
1
2
1
0
1
0
1
1
2
1
1
1
1
2
0
1
2
1
1
1
1
1
0
2
1
2
1
2
3
0
1
1
1
2
0
1
0
2
0
2
0
1
1
1
1
1
0
0
0
1
1
0
1
1
0
1
0
0
2
0
1
1
2
1
2
2
0
1
1
1
1
1
2
1
1
1
1
3
0
2
0
1
0
1
1
2
2
1
1
0
0
1
1
1
2
1
0
2
1
1
1
0
1
2
1
1
1
2
1
1
0
1
2
2
1
2
2
2
0
1
0
1
1
1
1
1
0
0
0
0
3
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
3
1
2
1
2
1
1
1
1
2
0
2
1
0
0
0
1
1
2
1
0
1
1
0
0
1
1
2
1
2
1
1
1
1
1
1
0
1
2
1
1
1
2
1
1
0
1
0
2
1
1
1
1
1
2
2
2
1
1
1
0
2
1
1
0
0
1
1
0
1
1
2
1
1
1
2
1
9
1
1
1
1
2
1
1
2
1
0
1
0
1
2
0
1
1
1
1
1
1
1
2
1
2
1
1
1
0
2
1
2
1
1
0
1
1
0
2
1
1
1
1
2
1
0
1
1
0
1
2
2
0
1
1
1
1
2
2
1
2
1
2
1
2
0
1
1
1
1
1
1
1
2
2
1
0
1
1
1
1
1
1
1
2
0
1
2
1
1
0
1
0
0
2
2
1
3
1
2
2
1
2
1
3
0
1
2
0
2
2
1
1
1
1
0
1
0
1
2
1
0
1
0
1
1
1
0
0
1
2
1
2
1
0
2
2
1
0
1
1
1
2
1
0
1
1
0
0
1
2
1
1
0
2
1
1
2
2
1
1
1
1
1
0
1
2
2
1
1
1
1
1
1
1
2
1
0
1
1
1
1
0
1
2
0
1
1
1
1
1
2
1
0
1
1
2
2
1
0
0
1
1
1
2
1
1
2
1
1
0
1
0
2
1
1
2
2
1
1
1
1
1
1
1
2
1
2
1
2
2
2
1
1
1
1
1
4
1
2
1
1
1
0
1
2
1
1
0
2
1
2
1
1
1
2
1
0
1
1
1
3
1
1
2
1
2
1
1
2
2
1
1
2
2
2
2
1
1
1
2
1
1
0
2
1
1
1
1
1
1
1
0
1
1
2
1
2
1
1
1
1
1
2
1
1
1
1
0
1
1
2
2
1
0
0
1
0
1
2
2
2
2
1
1
1
2
1
1
2
1
1
2
1
0
1
0
0
1
2
0
1
2
1
0
0
0
0
1
1
2
1
2
1
1
1
2
0
1
1
1
1
0
0
1
1
2
1
0
1
2
2
1
1
1
1
3
1
1
0
0
2
1
1
1
1
0
1
2
1
2
1
2
1
1
1
1
0
0
0
0
1
1
3
1
1
1
2
1
2
2
2
1
0
2
1
0
1
1
1
2
0
1
3
1
1
1
1
0
1
1
1
1
1
1
1
1
2
2
1
2
0
2
1
1
1
0
4
0
1
1
2
1
0
2
1
1
2
0
1
2
0
1
1
1
1
1
1
0
1
1
1
1
2
1
1
1
2
0
2
1
1
1
0
0
2
1
1
2
1
0
1
2
1
1
1
1
2
2
2
0
1
1
2
2
2
2
2
1
1
0
1
0
1
1
1
1
0
1
1
1
2
0
0
1
2
0
1
2
2
1
2
2
1
1
0
1
1
0
0
2
0
1
1
1
0
1
1
0
1
1
2
2
0
1
1
1
1
2
2
2
1
1
1
3
3
0
2
1
1
0
1
0
1
0
0
1
0
2
0
1
1
2
2
2
2
1
0
1
1
1
2
2
2
1
2
2
1
1
1
1
2
1
0
2
2
0
1
3
1
2
1
0
2
1
2
2
1
2
2
1
2
1
1
1
1
2
1
1
1
1
2
0
1
1
2
1
1
0
1
1
2
1
1
1
0
2
0
1
0
0
1
2
2
1
1
1
1
1
1
1
2
1
0
0
1
1
1
1
2
1
1
1
0
2
2
1
2
1
1
1
1
0
1
2
1
2
0
1
1
0
0
0
1
1
1
0
1
1
1
1
0
2
1
1
1
2
2
1
2
0
1
1
0
0
2
2
1
2
0
2
1
1
1
2
2
1
1
0
2
2
1
1
1
1
1
0
0
0
1
1
1
1
2
1
2
2
1
1
1
0
1
1
0
2
2
1
2
1
1
2
0
2
2
2
2
0
1
2
1
1
1
1
1
1
2
1
1
2
2
2
1
1
2
2
1
1
0
0
2
0
0
1
0
1
2
1
1
2
2
2
1
1
1
1
1
0
1
0
2
1
1
1
0
1
1
2
2
2
1
1
1
2
1
1
0
1
1
0
0
1
1
1
1
1
1
1
1
1
1
2
1
1
1
0
2
2
1
0
1
0
1
1
1
1
0
0
1
2
1
1
2
1
2
1
2
2
1
2
1
0
2
1
1
1
1
1
0
1
1
1
1
1
1
3
0
1
1
1
1
1
1
1
2
1
2
1
1
1
2
1
1
2
1
1
1
0
2
1
1
2
1
1
1
1
1
1
0
1
1
1
0
0
1
0
1
2
1
1
1
2
2
1
1
1
2
1
2
0
1
1
1
2
1
2
0
1
1
1
2
2
1
2
1
0
2
1
0
2
0
1
1
1
1
1
0
0
1
2
1
1
2
1
1
1
0
1
1
2
1
1
1
1
1
1
3
2
2
2
0
1
2
2
1
1
0
1
1
1
0
1
1
0
1
0
1
1
0
1
1
2
1
1
1
1
2
2
1
2
0
0
1
2
1
2
1
1
1
1
3
1
0
1
1
1
2
1
0
2
0
1
2
0
1
0
1
0
1
2
1
2
1
2
0
1
1
0
2
1
2
1
1
1
1
0
1
0
1
2
2
1
1
2
1
1
1
0
1
2
1
0
0
1
1
2
1
1
1
2
2
2
0
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
2
2
0
2
1
0
1
5
0
2
1
1
2
2
1
1
2
2
0
1
1
2
1
2
1
2
0
1
1
1
1
1
0
2
1
1
1
0
2
1
1
1
0
1
0
1
1
1
0
0
1
0
1
4
1
2
1
1
0
1
1
2
2
0
1
1
0
0
1
2
1
1
1
2
0
1
2
0
2
1
0
1
2
2
2
1
1
1
1
1
2
2
0
1
1
2
2
0
0
0
0
1
0
1
1
1
0
1
2
0
2
1
1
2
0
2
1
1
1
1
1
2
0
2
1
1
1
1
2
1
0
1
1
1
1
0
1
3
0
1
1
1
1
0
1
0
1
1
0
0
0
0
0
2
1
2
0
2
1
2
1
2
1
0
1
1
0
1
1
1
1
0
0
1
1
0
1
1
1
1
1
2
2
2
1
1
1
2
2
1
1
1
1
2
0
2
0
0
1
2
1
1
1
2
0
1
1
1
1
2
2
0
1
1
2
1
1
1
1
2
0
1
1
1
0
1
1
2
2
1
0
1
1
1
1
1
2
2
2
0
3
0
2
1
2
2
1
1
0
1
1
1
2
1
1
2
1
1
1
2
2
1
1
1
2
1
1
2
2
2
0
0
0
2
1
1
2
0
1
1
1
1
1
2
1
0
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
0
1
1
0
1
1
0
1
0
1
1
0
1
0
2
1
0
1
0
2
2
1
1
0
2
2
2
1
1
0
1
0
1
0
1
1
1
1
0
1
2
2
1
1
1
1
1
1
1
1
0
1
2
1
1
2
1
2
0
2
1
1
1
1
1
1
0
1
0
2
1
0
1
1
2
1
2
1
1
1
0
1
1
1
2
1
0
1
1
1
1
1
1
1
2
1
0
0
0
0
0
1
1
2
0
1
1
1
0
1
1
1
1
1
1
0
2
1
1
0
0
1
1
1
0
1
1
1
1
1
1
2
1
0
1
1
1
1
1
1
2
2
2
2
1
2
0
1
2
1
1
2
2
1
1
2
1
0
2
1
2
1
1
2
1
0
0
1
2
2
1
2
1
1
1
1
1
2
1
0
1
0
0
2
1
2
1
1
1
1
0
1
2
0
1
1
1
0
1
1
0
1
0
2
1
1
1
1
1
2
1
3
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
0
0
1
0
0
0
1
1
4
1
0
1
1
2
2
1
2
2
1
1
1
1
1
2
1
1
0
2
1
2
2
0
0
0
0
2
2
1
2
0
1
1
0
2
1
0
1
1
1
1
1
1
1
2
0
1
1
1
1
1
1
0
1
2
1
2
1
1
1
0
2
1
1
1
0
1
1
1
1
0
0
1
2
2
1
1
0
1
1
1
0
0
1
1
1
1
2
0
2
1
1
0
1
0
0
2
1
0
1
0
1
2
1
0
2
1
1
0
1
1
1
1
1
1
1
2
2
1
0
1
1
0
1
1
1
0
1
1
1
1
2
0
1
0
1
1
1
2
1
1
1
1
0
1
1
1
0
0
0
1
0
0
1
1
2
1
2
0
0
1
2
1
4
0
1
1
1
1
1
0
1
2
1
0
1
0
0
0
1
0
1
1
1
1
1
1
1
0
1
1
2
2
1
1
1
1
1
1
1
0
0
1
1
2
2
1
1
1
2
2
0
2
1
1
1
1
1
2
2
1
2
1
0
1
1
1
1
0
1
1
1
1
1
2
0
2
1
1
1
0
2
1
2
1
2
1
0
2
1
1
0
2
1
1
2
2
1
1
2
2
0
0
1
2
1
2
1
2
0
0
1
1
1
0
1
1
1
1
0
1
1
0
0
1
1
1
2
1
1
1
1
0
1
1
1
1
1
2
2
1
0
2
0
1
1
1
2
1
1
1
1
0
1
0
1
1
0
2
1
1
0
1
1
2
1
1
1
1
1
1
1
0
0
1
0
1
2
2
2
2
2
1
1
0
1
1
3
1
1
1
0
2
0
1
1
2
2
2
1
2
1
1
2
0
1
1
1
2
1
0
0
1
1
0
1
0
1
0
2
1
1
1
0
2
1
2
0
1
2
2
1
1
2
1
1
0
1
2
1
1
1
0
1
1
1
1
1
1
0
1
1
1
2
1
2
2
1
1
1
1
1
2
0
1
2
2
1
1
1
1
1
1
2
0
0
1
0
1
1
1
1
1
1
2
1
1
1
1
1
2
0
0
1
1
2
1
1
0
1
1
1
2
0
0
2
1
1
0
1
1
0
0
0
2
1
1
1
1
1
1
1
1
1
2
1
0
1
0
2
1
0
1
1
0
1
2
1
1
0
1
1
1
1
1
2
1
2
1
2
1
1
0
1
2
1
1
0
2
1
1
1
1
2
0
3
1
1
2
2
2
2
0
1
2
0
1
1
1
1
1
1
2
1
2
1
2
0
0
1
1
1
1
1
2
0
1
2
1
0
1
2
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
1
0
2
1
0
1
2
0
1
0
2
1
1
1
1
1
1
1
1
1
0
1
1
2
1
1
1
2
1
1
1
1
1
0
2
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
0
2
2
2
2
1
1
1
2
0
1
1
2
1
1
1
2
1
1
2
1
2
1
2
1
1
1
0
1
1
1
0
1
2
2
1
1
1
1
1
0
0
2
1
2
1
0
0
2
1
1
1
0
1
1
0
1
1
1
2
0
2
2
0
0
2
1
1
2
1
1
2
0
2
2
2
2
1
1
1
0
1
1
1
1
1
1
1
4
2
0
1
1
1
1
1
2
1
1
2
1
1
2
2
1
2
1
0
1
3
1
0
1
2
2
1
1
0
1
1
1
2
0
2
2
1
1
1
0
1
1
1
1
1
2
1
1
1
1
0
1
1
1
1
2
2
2
1
1
1
1
0
0
1
0
2
1
1
0
3
4
2
1
1
1
1
2
0
1
1
1
1
1
1
0
2
1
1
1
0
0
2
1
2
2
0
0
2
1
1
0
0
1
0
2
1
1
1
1
3
1
0
1
1
1
2
1
1
0
1
0
1
1
1
1
1
0
1
2
0
0
1
0
1
1
0
1
0
1
1
1
1
2
0
2
1
1
1
0
0
0
1
1
1
1
0
1
2
0
2
1
2
0
0
2
1
2
2
1
1
1
1
1
0
2
1
0
2
1
1
1
1
0
2
1
2
0
2
1
1
1
1
0
2
1
0
2
0
1
1
2
0
1
1
0
1
1
1
1
0
1
1
1
1
1
1
0
2
2
1
1
1
2
1
1
2
2
2
1
1
1
2
2
0
1
1
1
2
3
1
1
1
0
1
3
1
1
1
1
1
0
2
2
1
0
1
1
0
1
0
2
1
2
1
2
1
1
1
0
1
0
1
0
0
0
1
2
0
0
2
1
1
2
2
1
2
0
1
0
1
1
1
1
1
0
1
1
1
1
1
1
2
1
2
1
0
2
2
1
1
1
1
1
2
0
1
1
1
1
1
0
2
2
1
1
1
2
1
1
1
0
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
1
1
0
0
1
1
2
1
0
1
1
0
2
0
1
1
1
0
1
0
1
1
1
1
0
1
1
2
1
1
1
1
1
1
1
1
1
1
0
1
2
1
1
1
0
1
2
1
0
1
2
1
1
0
0
1
1
1
0
2
1
1
0
1
2
0
1
1
1
2
1
1
0
1
0
1
1
1
1
1
0
1
2
1
1
1
0
0
1
2
2
1
1
2
1
1
1
0
2
1
1
2
1
2
2
1
1
0
0
1
2
1
1
1
0
0
1
2
2
2
2
2
0
2
1
1
1
1
1
1
1
0
2
1
1
2
1
1
1
1
0
1
2
0
2
0
4
2
0
2
0
1
1
2
1
1
1
1
0
1
1
0
2
2
0
1
0
1
1
0
1
1
0
1
1
2
1
1
1
1
1
1
1
1
2
1
5
0
2
1
1
1
0
1
2
1
2
1
2
1
1
1
2
1
2
0
0
1
1
0
1
1
1
0
1
2
1
1
2
1
1
1
1
1
1
1
2
2
1
2
1
1
2
1
1
0
0
2
0
0
0
1
1
0
1
1
1
1
1
2
2
0
2
2
3
2
0
2
1
0
2
1
1
2
1
1
2
1
1
1
1
1
2
0
0
2
0
1
1
2
2
1
1
0
1
1
1
1
1
0
1
2
1
1
0
0
0
1
1
1
2
1
0
2
0
1
1
2
1
1
3
1
2
1
2
1
0
2
3
2
1
0
1
0
1
1
1
1
1
1
2
0
2
1
1
1
2
1
0
1
0
2
1
0
0
1
1
0
1
1
2
2
1
1
1
1
1
0
1
2
0
2
1
1
1
0
0
1
1
0
1
2
1
2
1
1
1
1
1
1
1
1
2
1
0
1
2
1
1
2
2
1
0
1
0
2
1
1
4
2
1
0
1
1
1
2
1
1
1
1
1
1
2
0
1
1
1
1
1
0
1
1
1
2
1
1
1
1
4
1
2
2
0
1
0
2
1
2
1
0
2
1
0
0
1
2
0
1
2
1
2
2
1
2
1
2
1
0
2
2
2
0
1
1
2
1
1
2
0
2
1
3
0
2
0
1
1
2
0
1
1
1
1
1
2
0
1
1
1
0
1
1
2
1
1
1
0
2
1
1
0
1
1
1
2
1
1
1
1
0
2
1
1
2
1
1
1
0
1
2
1
1
1
0
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
2
0
1
1
1
2
2
1
2
0
0
0
1
1
1
0
1
0
2
2
1
2
1
1
0
0
1
1
1
1
1
2
2
1
1
2
2
2
0
0
1
1
0
1
1
0
0
1
1
2
1
1
1
2
0
2
2
1
1
1
1
2
1
1
2
2
1
1
1
0
1
1
2
0
0
2
1
1
2
1
1
1
1
1
0
1
1
2
2
0
1
1
1
1
1
1
2
0
1
0
1
1
1
0
2
1
2
1
1
2
1
1
1
1
1
1
2
1
1
2
1
1
2
0
2
1
0
1
1
1
0
1
0
1
0
1
2
1
0
0
1
1
1
0
1
1
1
1
1
0
1
0
2
1
0
1
1
0
1
1
1
1
1
2
1
0
0
1
2
2
1
0
1
1
1
1
2
0
1
0
1
2
1
0
1
1
1
2
1
4
0
2
2
1
1
0
1
1
1
1
1
2
1
1
1
1
1
2
0
0
1
1
2
1
1
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
0
0
1
2
1
1
1
1
1
1
1
0
1
0
1
1
1
1
1
1
1
1
1
0
1
1
1
2
0
0
1
1
1
1
0
1
2
0
1
2
1
1
1
2
1
1
1
3
1
1
1
0
1
2
2
0
2
2
0
0
1
1
1
1
1
0
2
1
1
1
1
1
0
2
2
0
2
2
0
1
1
2
1
1
1
1
0
2
1
1
1
2
0
2
0
0
1
1
0
2
1
1
1
1
0
2
1
1
1
1
1
1
0
0
0
2
2
2
2
1
0
1
2
1
1
0
0
1
1
2
2
2
1
2
1
1
1
1
1
1
0
1
1
1
1
1
1
0
1
0
0
2
1
1
1
2
1
1
0
1
1
1
1
2
2
1
1
0
1
1
2
0
1
1
2
0
2
0
1
1
2
1
1
1
1
1
0
1
1
2
2
1
2
1
1
1
1
1
0
1
0
1
1
2
0
2
1
1
2
1
0
1
1
2
1
1
2
0
1
1
1
1
0
1
0
1
1
2
1
1
1
0
1
1
1
1
1
0
1
1
2
1
1
1
1
1
1
0
0
1
1
1
1
0
2
1
0
0
1
2
2
1
2
2
0
2
1
1
0
1
0
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
0
1
1
0
0
2
1
1
0
1
1
1
2
1
0
0
2
0
1
1
1
1
2
2
1
1
1
0
3
1
1
0
0
0
1
1
2
1
1
1
1
1
3
2
1
1
1
1
1
1
1
1
2
1
0
1
0
1
2
1
1
1
0
2
2
2
0
2
0
0
1
2
0
1
1
1
1
1
1
2
1
1
1
1
1
1
0
0
1
1
1
2
1
0
1
0
0
1
2
0
1
1
1
1
2
1
1
0
1
1
1
1
2
1
1
2
2
2
1
1
1
1
1
0
2
1
1
1
1
2
2
1
1
2
2
0
1
0
1
0
1
1
1
1
1
0
1
0
1
1
2
2
2
2
1
1
1
1
0
1
1
0
1
1
1
2
1
1
2
1
1
0
1
0
1
1
1
1
2
1
1
0
1
2
1
1
0
2
2
1
1
1
0
1
0
2
0
1
2
1
1
2
1
1
1
1
1
1
0
1
2
2
2
1
1
0
1
1
2
2
2
1
1
2
0
2
0
2
1
1
1
2
1
1
2
1
2
0
1
2
0
2
1
1
0
0
0
2
1
2
1
0
2
1
1
1
1
0
2
1
1
1
2
2
1
1
0
1
1
1
2
1
1
2
0
1
1
2
1
0
2
2
1
0
2
1
1
1
1
1
1
1
1
1
0
1
1
1
1
2
1
2
1
1
0
1
2
0
1
2
0
1
1
1
1
1
1
1
0
1
1
0
0
1
1
2
1
1
2
1
0
1
3
2
1
1
0
2
1
4
1
1
2
0
2
2
1
1
2
1
1
1
2
1
1
1
1
0
3
2
2
1
1
1
0
1
1
2
2
1
1
2
2
0
1
2
1
1
0
1
0
1
2
1
0
1
1
1
2
1
1
1
2
0
1
2
0
0
1
1
0
1
1
1
0
2
1
1
1
1
1
1
1
1
2
2
1
1
1
0
1
2
1
1
2
1
2
0
2
1
1
0
1
1
1
2
2
1
1
2
2
0
1
0
1
2
2
1
2
1
1
0
0
0
1
1
1
0
0
1
1
2
1
1
1
1
2
1
2
0
1
1
1
1
0
0
2
1
0
1
1
1
1
2
1
1
1
1
0
2
0
0
1
2
0
1
1
1
1
1
1
2
2
2
1
1
1
1
1
2
1
2
1
2
1
2
2
2
1
2
0
1
0
0
1
0
1
1
3
1
1
1
1
1
2
0
1
1
0
0
0
0
1
0
0
1
1
1
2
1
2
1
0
1
0
3
1
0
1
1
1
0
1
1
0
1
0
0
1
1
2
1
1
2
1
1
2
0
1
1
2
1
0
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
0
1
1
2
1
1
2
1
1
2
2
0
2
1
1
1
1
1
2
1
0
1
2
1
1
1
0
1
1
2
0
1
0
1
0
1
3
1
1
1
1
1
0
0
2
1
2
1
1
1
1
2
0
2
3
2
1
2
0
1
1
2
1
2
0
1
0
1
1
2
0
1
1
0
1
1
1
2
0
2
2
1
1
2
0
2
2
0
2
1
1
0
2
2
0
2
1
1
1
1
1
1
2
0
1
1
1
1
1
3
0
2
1
2
1
1
1
1
2
0
0
0
1
1
0
1
2
2
1
2
1
2
0
2
1
1
1
1
1
0
1
1
0
4
2
0
1
1
1
1
1
1
0
2
0
0
1
1
1
1
1
1
1
0
2
1
0
1
1
1
2
0
2
1
1
2
1
1
1
1
1
0
2
1
1
0
1
0
0
2
1
2
1
1
1
1
1
2
0
0
2
1
2
1
1
1
1
1
1
2
1
1
2
0
2
0
1
0
1
0
1
1
1
2
0
0
1
0
1
2
2
2
1
0
2
2
1
1
2
1
1
1
2
1
1
2
2
1
1
2
1
0
1
2
0
0
1
1
1
0
2
2
2
0
1
1
1
0
2
1
1
1
2
1
2
0
1
1
1
0
2
1
1
1
1
1
1
1
1
0
1
0
1
1
2
1
2
1
2
0
2
1
1
1
2
0
2
0
1
1
1
2
1
2
0
1
2
2
1
1
2
0
1
2
1
2
0
1
1
1
2
2
1
1
1
2
1
1
1
1
0
0
1
1
0
0
1
1
1
2
1
1
1
1
1
0
1
2
0
1
0
1
1
1
2
0
2
1
2
1
2
1
1
1
1
1
1
0
0
1
2
1
0
2
2
1
0
2
1
2
2
2
1
1
1
1
1
1
1
0
1
1
1
2
4
2
2
1
1
1
1
1
1
1
2
1
3
1
1
1
1
1
2
1
1
1
1
2
3
1
2
1
1
1
2
0
2
1
0
1
1
2
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
4
1
1
1
1
0
0
0
1
0
1
0
1
1
1
1
1
1
3
1
0
0
2
2
0
1
1
1
0
0
1
0
1
1
1
1
1
2
2
2
1
1
0
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
2
1
1
0
2
0
1
2
1
1
0
2
1
1
1
2
2
2
1
2
1
1
1
1
0
1
1
2
2
2
1
2
2
1
1
1
2
1
1
2
1
0
1
1
1
1
1
1
0
0
1
0
2
1
0
0
1
1
2
1
1
1
1
2
1
0
2
2
1
1
1
0
2
0
0
1
1
0
2
2
2
2
1
1
1
0
1
2
0
2
1
0
1
2
1
2
1
1
1
1
1
2
2
2
0
1
1
0
1
2
1
2
2
2
1
1
2
1
1
1
3
1
1
1
0
1
1
1
0
1
2
2
1
0
2
1
2
1
1
1
1
1
1
1
3
1
1
1
0
1
1
1
1
2
0
2
1
1
2
1
0
1
1
1
1
1
2
2
1
2
2
1
1
1
0
0
2
0
2
1
2
1
0
2
0
0
1
1
0
1
0
1
1
1
0
1
1
0
2
0
1
1
1
1
0
0
2
1
0
1
1
1
0
1
1
2
0
1
1
2
1
0
1
1
1
0
1
1
1
1
2
1
1
0
1
1
1
0
1
0
2
1
1
1
1
2
0
1
0
1
1
1
0
1
1
1
2
0
1
1
0
1
1
1
1
1
1
1
1
0
0
1
1
2
1
1
2
2
0
1
1
1
1
1
2
1
1
0
2
2
0
1
0
1
2
1
2
1
2
1
1
0
0
1
2
0
0
1
1
1
1
2
2
1
1
0
2
0
2
0
2
1
1
1
1
1
1
2
2
1
1
2
2
1
1
2
1
0
1
0
1
1
2
0
1
0
1
1
1
2
1
2
0
2
2
1
1
1
1
2
1
1
0
1
0
1
0
1
1
1
0
1
1
1
2
0
1
1
0
1
1
1
1
1
0
2
1
1
2
2
1
1
1
2
2
2
1
1
1
0
2
1
0
2
0
1
1
1
1
1
1
0
1
1
1
1
1
1
1
2
2
1
2
2
0
1
2
4
1
2
1
0
2
2
2
0
1
1
2
2
1
0
1
1
0
2
0
1
1
2
1
1
2
0
1
0
1
1
1
0
1
2
2
1
1
1
0
2
2
2
1
2
1
1
1
1
2
1
1
1
2
0
1
1
1
1
2
1
1
0
1
2
1
1
1
1
1
1
1
1
0
2
5
1
1
1
1
1
0
1
1
1
2
2
1
1
2
1
0
1
2
0
1
2
1
2
2
0
1
1
1
2
1
2
1
1
1
1
1
0
2
1
1
1
1
1
2
1
0
2
1
1
1
2
1
2
1
1
0
1
1
1
1
1
1
2
2
1
0
1
0
1
1
2
0
0
3
0
2
0
0
1
0
0
0
1
0
1
1
1
2
1
0
2
0
0
1
3
0
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
2
2
2
1
2
1
1
1
2
1
2
1
1
1
1
1
1
1
1
0
1
1
0
1
1
1
0
0
1
2
1
1
2
1
1
1
0
1
1
1
1
1
2
1
1
1
2
1
2
0
1
2
1
1
0
1
0
1
1
1
3
1
1
1
2
2
1
1
1
1
0
1
2
1
2
0
1
1
1
1
3
3
1
0
2
2
1
1
1
2
1
1
1
2
1
2
1
1
1
0
0
1
1
0
0
1
0
1
0
0
1
1
2
1
0
1
1
0
1
1
1
0
1
1
1
1
1
2
2
0
1
0
2
1
1
1
1
1
1
1
2
1
1
1
2
1
0
1
1
1
0
0
1
2
1
1
0
1
0
1
2
0
1
1
2
2
0
0
1
1
1
1
2
0
1
1
0
0
0
1
3
1
1
1
1
1
1
1
0
1
1
0
1
0
2
1
1
1
1
2
1
0
2
0
2
1
2
2
1
1
0
1
1
1
1
1
2
1
0
1
0
1
1
2
1
1
2
1
1
2
1
2
1
1
1
0
1
1
1
0
1
1
1
1
0
2
1
2
1
2
2
1
2
1
1
1
2
1
1
0
2
1
1
2
1
0
1
2
0
1
2
1
2
0
1
1
0
1
1
1
1
2
0
1
1
1
2
1
2
2
1
1
2
1
2
1
1
1
1
2
2
2
1
2
1
1
0
2
0
1
2
1
2
2
1
1
2
1
1
1
1
1
0
1
0
1
1
1
1
0
1
1
0
1
0
1
2
1
0
2
1
1
2
1
0
1
1
2
2
1
2
2
1
2
2
1
1
0
0
1
1
1
2
1
2
1
1
1
2
0
2
1
2
2
1
1
1
1
1
0
2
0
1
0
2
1
1
3
1
1
2
1
2
2
2
1
0
0
1
2
0
1
1
1
1
0
2
0
0
2
1
1
1
0
1
1
0
0
1
1
2
1
2
0
1
1
0
2
1
1
1
1
1
1
2
1
0
0
1
1
1
1
2
1
1
1
1
2
2
1
1
1
2
2
1
1
1
0
1
1
1
2
1
1
2
1
2
1
1
1
1
1
1
0
2
1
2
1
1
0
1
1
1
1
1
0
1
1
2
1
0
2
1
1
1
0
0
2
1
1
1
1
2
2
1
2
2
2
1
2
2
2
0
0
1
2
2
1
1
1
0
0
1
0
1
1
0
1
1
2
1
2
2
1
1
1
1
0
1
1
0
1
0
0
1
1
0
0
2
1
1
1
1
1
0
2
1
1
1
1
1
1
2
1
2
1
0
0
1
2
1
2
0
0
2
0
1
0
2
0
2
1
2
1
1
0
2
2
1
1
1
1
0
1
0
1
1
1
1
1
0
1
1
1
2
1
0
1
1
2
1
1
0
0
1
1
1
1
0
1
1
1
2
2
1
0
2
2
1
0
0
1
1
1
1
0
2
1
0
1
1
1
2
1
1
1
0
2
1
0
1
2
1
1
1
1
2
1
0
2
0
1
0
1
0
1
1
2
2
1
2
2
0
1
0
0
1
3
1
1
2
0
1
2
1
1
2
1
3
2
0
1
1
1
1
2
1
1
2
2
1
1
1
1
1
0
1
1
1
1
0
1
0
1
2
0
1
2
2
1
1
1
1
1
1
1
1
0
0
2
2
0
1
2
1
1
1
1
0
1
2
1
1
2
1
1
1
1
1
1
1
1
0
0
2
1
1
0
1
2
1
3
1
2
0
1
2
0
1
0
1
2
2
0
0
2
1
1
1
0
0
0
1
2
0
1
1
2
0
1
1
0
1
2
1
2
1
1
1
1
1
1
3
1
0
2
1
0
1
1
1
1
1
1
2
0
1
1
0
1
2
1
1
1
1
1
0
1
0
1
0
2
0
1
1
0
1
1
2
2
2
1
1
1
0
1
1
1
0
1
2
1
1
1
0
1
0
2
0
2
1
0
1
1
1
1
2
1
2
1
1
0
1
1
1
1
0
1
1
1
2
1
1
0
1
0
1
0
5
0
1
1
0
1
1
2
2
0
2
2
1
1
1
1
2
0
2
1
1
0
2
1
2
1
3
2
0
1
2
1
2
1
1
1
1
1
0
1
1
1
1
0
1
1
2
2
2
1
1
1
5
1
1
1
2
1
1
2
0
1
1
1
2
2
0
1
2
2
2
2
1
1
1
0
2
0
1
1
1
2
1
2
1
1
1
1
2
1
2
2
2
1
1
1
1
1
1
2
1
0
1
2
1
1
1
0
0
1
0
2
1
1
1
0
2
2
1
2
2
2
1
1
2
1
2
0
1
0
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
0
1
0
1
1
2
1
1
1
2
1
2
0
1
2
1
1
0
1
1
0
1
1
1
1
0
1
2
0
1
1
1
1
1
1
0
1
1
1
1
1
1
0
1
1
2
0
1
0
1
1
0
1
1
0
1
1
0
1
1
1
0
1
2
2
1
1
2
1
1
1
0
1
0
1
0
2
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
0
1
1
1
1
2
2
2
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
2
1
0
1
2
1
2
1
1
2
2
2
0
0
0
1
2
1
0
1
0
0
2
1
1
0
0
2
1
2
2
2
2
0
1
1
1
1
0
1
0
1
2
1
1
0
0
2
1
2
1
1
2
1
0
2
0
2
1
4
1
1
1
1
1
1
1
2
1
0
1
1
0
1
1
0
1
1
1
2
1
1
0
1
2
1
2
1
1
1
2
2
1
1
1
1
1
1
1
1
1
0
0
2
1
1
1
0
2
1
1
0
1
2
2
0
1
0
2
2
1
2
1
1
1
0
0
1
0
1
2
2
1
1
0
1
1
1
1
1
2
2
2
1
0
1
1
2
2
0
2
2
2
0
1
1
1
2
1
1
1
1
1
0
0
1
2
2
2
1
1
1
0
1
1
1
1
0
1
0
2
2
1
1
2
0
2
1
1
1
2
2
1
1
1
2
2
1
2
1
2
1
2
2
1
1
0
1
1
2
0
1
1
0
1
2
1
2
1
2
1
1
2
0
2
1
1
1
1
1
2
1
2
1
0
1
0
2
1
2
1
2
1
1
2
1
0
0
2
0
3
1
1
0
0
1
2
1
1
1
2
1
1
1
0
1
1
1
2
1
0
1
2
0
1
1
2
2
1
0
1
2
2
2
2
1
2
1
0
1
1
1
1
2
1
2
0
2
2
1
1
1
1
1
0
3
1
1
1
0
1
1
1
1
1
0
2
1
0
1
1
2
2
2
1
2
2
1
1
1
2
1
2
0
1
0
1
1
1
1
0
2
2
1
0
1
1
2
1
1
0
1
0
2
1
1
2
1
1
1
0
1
2
1
1
0
0
1
1
1
0
1
1
1
1
1
1
1
1
1
0
0
2
2
1
2
0
2
1
2
1
2
1
2
2
0
1
1
2
0
2
1
1
1
1
1
1
0
0
1
1
2
2
1
2
1
1
1
1
0
1
1
1
0
2
0
1
1
2
1
2
0
0
1
1
1
2
2
1
1
2
1
1
0
1
2
1
1
1
1
2
1
1
1
1
1
1
0
2
1
1
1
1
2
2
0
0
2
1
2
1
1
1
0
2
0
1
2
2
0
2
2
1
0
1
1
1
1
1
1
1
0
1
1
1
2
0
0
0
2
1
2
1
1
0
1
0
1
1
0
1
1
1
1
1
2
1
2
1
1
1
1
1
0
2
1
1
2
2
1
2
1
0
1
0
2
1
0
1
2
2
2
1
0
0
1
1
0
0
1
1
1
1
1
1
2
1
2
1
0
2
1
0
2
1
1
1
1
2
1
0
2
1
1
2
1
1
1
0
2
2
0
2
2
1
1
2
1
2
1
0
0
0
1
1
1
0
0
1
0
1
2
1
1
0
1
0
2
1
1
1
1
1
2
2
2
0
2
1
1
1
1
1
1
1
2
1
1
1
1
2
1
2
1
1
1
2
2
1
0
1
1
1
2
1
1
0
2
1
1
1
2
1
1
1
2
0
0
1
1
1
2
2
1
1
1
2
1
1
1
0
1
0
1
1
1
1
1
1
1
1
0
1
2
1
1
0
0
2
1
1
2
0
2
1
1
1
0
2
2
3
1
1
1
1
2
2
1
2
1
1
1
1
2
2
0
2
1
2
1
1
1
1
1
1
1
2
0
0
1
1
0
2
1
1
1
1
2
2
2
2
1
0
1
1
1
0
1
1
1
1
1
0
2
1
1
1
1
1
0
0
0
1
0
0
2
1
2
2
1
1
1
1
2
1
0
0
1
0
1
2
2
1
3
2
1
1
2
1
1
0
1
0
0
2
0
0
1
2
2
2
2
1
1
0
2
1
1
1
0
2
1
0
1
1
1
2
1
2
1
1
1
1
2
0
0
0
1
1
0
0
2
1
0
1
2
2
1
2
2
1
2
1
2
0
1
1
2
1
0
2
0
2
1
0
1
1
1
1
1
2
2
2
2
1
2
1
2
1
2
0
1
1
0
0
1
0
1
0
1
1
3
1
1
1
1
1
1
0
1
0
1
0
1
1
1
2
2
1
1
2
1
0
0
1
1
1
1
1
2
0
1
0
1
1
1
1
2
1
1
1
1
0
1
1
2
1
0
2
1
1
1
1
0
1
2
0
2
0
1
1
2
1
1
1
0
2
2
1
1
0
2
1
1
3
1
1
0
1
1
0
1
1
1
1
2
2
0
1
1
0
0
1
1
1
0
1
1
1
1
0
2
1
1
2
2
1
2
2
1
2
1
1
1
0
1
0
1
2
1
2
2
1
1
2
1
1
1
1
1
1
0
1
0
1
1
0
2
0
0
2
1
1
1
0
1
2
0
0
0
2
0
2
2
2
0
0
2
1
2
2
0
1
1
1
1
1
1
1
1
0
0
0
1
0
2
1
1
1
2
1
1
2
1
1
1
1
1
1
1
2
2
0
0
0
0
1
0
2
1
2
1
1
2
1
1
1
1
2
0
0
0
0
1
2
1
1
1
1
1
1
1
1
2
1
2
2
1
1
1
2
1
1
0
1
0
1
2
2
1
1
0
0
1
1
2
2
2
1
1
1
0
1
0
2
1
4
1
2
0
2
1
1
0
1
1
2
0
1
1
1
1
0
1
1
1
2
1
0
1
1
1
1
1
0
1
1
2
1
1
2
1
1
2
0
1
1
1
1
0
0
1
3
2
1
0
1
2
0
1
1
0
0
1
0
1
1
2
0
2
0
0
1
2
2
2
2
1
1
1
2
1
2
0
2
0
1
2
1
1
1
1
0
1
0
1
0
0
1
1
2
1
1
0
1
1
1
0
1
0
1
0
2
1
0
2
2
1
0
1
0
1
0
0
0
1
1
1
1
1
1
1
2
2
1
2
1
0
0
2
1
2
1
1
1
1
1
1
1
3
1
1
1
2
0
0
1
1
0
1
0
0
1
1
1
1
0
1
1
0
2
2
1
1
2
1
1
0
0
1
1
2
2
1
2
1
2
1
2
1
1
1
1
2
0
1
0
2
1
1
1
1
1
2
1
1
0
0
1
0
1
1
2
1
0
1
3
1
0
1
1
1
1
1
1
1
1
1
1
1
0
0
1
0
1
3
2
1
1
2
1
1
1
1
0
0
1
4
2
1
2
1
1
0
0
2
0
1
0
2
1
1
0
2
0
1
2
0
1
0
3
1
1
0
2
1
0
1
1
1
1
1
0
2
1
0
1
1
1
1
1
2
1
1
1
1
1
1
2
3
1
1
1
1
1
1
0
1
1
1
1
2
1
2
2
1
1
1
0
0
1
1
1
1
1
0
0
1
0
0
1
1
1
2
0
2
2
1
2
2
1
2
2
0
1
2
1
0
1
0
1
2
1
1
1
2
1
0
2
2
1
2
1
1
2
2
1
0
1
1
0
2
2
1
1
0
1
1
1
1
1
0
1
1
1
1
1
1
1
3
1
0
2
0
1
1
2
1
0
2
2
1
2
0
1
1
1
1
1
1
1
2
1
1
1
0
2
2
2
1
2
3
1
0
0
2
2
1
1
1
2
2
0
1
1
2
1
1
1
1
1
0
0
1
2
0
0
1
0
1
2
2
1
2
1
0
1
1
1
1
2
1
1
1
1
0
2
1
2
2
1
0
1
2
1
2
2
1
0
1
1
1
1
2
2
0
2
1
1
1
1
2
1
1
0
1
1
1
2
1
1
3
0
0
2
0
1
2
1
0
1
1
0
0
1
2
2
1
3
2
1
1
1
1
1
1
2
1
0
2
2
1
0
2
1
1
0
2
1
1
1
1
0
0
1
1
0
0
1
1
3
0
0
1
1
1
1
2
0
1
1
1
1
1
0
2
2
1
1
2
1
1
1
0
2
2
1
2
1
1
1
0
1
1
2
1
1
1
1
1
1
0
2
1
2
1
1
1
2
2
1
0
1
0
2
2
1
1
1
2
0
2
0
2
2
1
2
2
1
2
0
1
2
0
1
0
0
1
1
2
2
1
0
1
1
2
0
1
2
2
1
1
0
1
2
1
0
2
0
1
1
1
1
1
1
1
1
1
0
1
1
0
1
2
2
1
0
1
2
0
0
2
0
1
1
1
1
1
1
1
2
0
1
0
2
1
1
1
0
1
1
2
1
1
1
2
2
0
0
0
0
1
1
1
1
0
1
1
2
1
1
2
0
1
1
1
1
0
0
1
1
2
2
1
1
1
2
4
2
1
2
1
1
0
2
1
3
1
0
1
1
1
1
1
1
2
2
0
2
0
1
1
1
1
2
1
2
1
1
1
2
2
2
1
0
0
1
2
0
2
0
1
1
1
2
1
1
0
0
2
1
0
1
1
1
1
1
0
2
2
1
2
2
0
2
1
2
2
1
0
2
1
2
0
2
1
2
2
2
1
0
1
1
2
0
1
2
1
1
2
1
2
1
1
1
3
0
1
1
0
2
0
1
1
0
1
2
1
2
1
1
2
1
0
1
1
0
0
1
1
2
1
0
0
0
1
2
2
0
1
0
2
0
0
1
0
2
1
0
1
1
1
1
1
1
1
1
1
0
1
0
0
1
1
2
1
1
0
1
1
1
1
1
1
1
1
1
1
1
3
1
1
1
2
0
1
2
0
1
1
1
0
2
1
2
2
1
1
1
1
1
1
2
1
3
2
1
1
1
1
1
1
1
1
1
1
0
1
0
1
1
1
2
1
2
0
2
2
2
3
0
0
1
1
2
1
1
0
4
2
1
2
1
2
0
1
2
1
1
1
0
1
1
1
2
1
1
2
2
0
2
1
2
1
1
1
1
5
2
1
2
2
1
1
0
2
1
1
0
1
5
1
1
1
1
2
0
2
1
2
2
1
0
0
2
2
1
2
1
1
0
0
0
0
1
1
1
2
1
0
2
1
1
1
0
1
1
1
1
1
1
2
0
1
1
0
1
0
0
1
0
2
1
1
2
1
2
1
1
2
1
0
0
1
2
1
0
1
1
1
0
1
0
1
1
2
1
1
1
2
1
1
1
1
2
1
0
2
3
0
1
1
1
1
0
1
1
1
0
1
2
1
2
2
1
1
2
0
3
1
1
0
1
0
1
0
2
2
1
0
1
1
0
1
1
1
1
1
0
1
1
2
0
1
0
1
1
1
0
1
0
0
1
1
1
1
0
0
1
1
1
2
0
1
2
2
1
1
2
1
1
2
1
1
1
2
2
1
1
2
2
1
1
2
1
1
0
0
1
0
1
2
1
0
2
1
1
1
1
1
2
1
0
1
2
0
2
1
1
2
1
0
1
1
1
1
1
2
2
1
1
1
1
2
2
1
1
1
1
1
1
1
0
1
1
1
0
2
2
0
1
1
1
0
2
0
1
1
1
0
2
1
1
0
1
0
0
1
0
1
1
1
0
1
1
1
0
2
2
0
1
2
1
1
1
0
1
1
1
2
1
1
0
2
2
1
1
0
2
1
1
1
1
1
1
1
0
1
1
2
2
2
1
1
2
1
0
1
1
1
2
3
2
0
0
1
0
1
2
1
1
0
2
1
1
0
0
0
1
1
1
1
1
1
4
0
1
1
1
1
0
1
1
1
1
1
0
2
1
1
2
1
1
2
1
1
1
1
1
1
1
2
2
1
1
1
0
0
1
1
1
1
0
1
1
1
1
1
1
0
1
0
1
1
1
2
1
1
1
0
1
2
1
1
2
1
2
1
1
2
2
1
1
0
1
1
1
1
1
0
1
0
2
2
1
0
1
1
0
1
0
1
1
1
0
1
0
2
1
2
2
2
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
0
2
1
2
1
2
1
0
0
1
0
4
1
1
1
0
1
0
1
0
1
1
2
2
1
1
2
1
1
2
1
1
1
1
1
1
0
1
1
1
0
2
1
1
1
0
1
1
0
2
0
2
2
3
1
1
1
1
2
1
1
2
1
1
2
1
1
1
0
1
2
0
1
1
2
2
1
1
0
2
0
1
1
1
1
2
1
1
0
1
1
2
1
0
1
1
1
2
0
2
1
0
2
2
1
0
2
1
1
2
1
2
1
1
1
0
1
1
2
2
2
2
0
0
2
1
1
2
1
1
0
2
1
1
1
1
1
1
0
1
2
1
1
0
1
0
1
2
1
1
2
1
2
1
0
0
2
0
2
1
2
0
2
1
2
1
1
1
2
1
1
1
1
1
1
0
2
2
0
1
1
0
1
2
1
1
0
1
1
1
2
1
0
0
0
1
1
1
1
0
1
1
2
1
1
1
1
3
2
1
2
1
0
0
0
1
1
2
0
1
1
1
1
0
0
1
2
1
1
2
1
2
1
1
0
1
5
0
1
2
0
1
2
1
1
1
1
1
1
2
1
0
1
2
2
1
1
0
2
1
0
2
2
2
1
1
1
2
2
1
0
2
1
1
0
1
0
1
0
1
1
2
2
1
0
2
1
1
1
1
1
0
1
2
0
1
0
2
1
2
0
1
0
2
0
1
1
1
2
0
1
1
1
0
1
1
1
1
2
1
0
0
6
1
1
0
1
1
1
1
0
1
1
1
0
1
2
2
1
2
2
1
1
0
0
0
2
1
1
0
1
3
0
0
1
3
1
2
1
1
0
2
1
0
2
0
1
2
2
1
1
1
1
5
2
0
0
2
1
1
0
1
2
0
1
1
1
1
1
0
1
1
1
1
1
1
1
1
0
0
1
1
1
0
1
2
1
1
1
1
1
0
0
0
1
1
1
1
0
2
1
1
1
1
1
1
0
1
1
1
1
1
2
2
1
2
0
1
0
1
0
1
0
2
1
1
1
1
1
1
1
2
1
2
2
0
1
1
2
2
2
1
1
0
1
2
0
1
1
1
1
0
1
1
1
1
0
2
0
1
1
1
1
0
2
2
1
2
2
2
1
0
1
1
2
1
1
1
2
0
1
1
1
1
1
1
1
1
1
1
1
2
0
0
0
1
1
1
0
0
2
1
1
1
1
2
1
1
1
0
0
1
2
2
1
1
1
0
1
2
1
1
2
1
0
2
0
1
2
1
1
1
2
0
1
1
2
1
1
1
1
2
1
1
1
1
0
1
1
0
2
0
0
0
2
1
0
2
1
0
2
1
0
1
2
2
1
2
1
1
2
0
2
0
1
1
0
1
0
2
1
1
1
3
2
0
2
2
1
1
0
2
1
2
1
1
2
2
2
2
1
1
0
2
1
1
2
1
1
0
1
1
0
0
0
1
1
1
0
2
0
0
1
1
1
2
1
2
1
1
1
2
1
2
0
0
1
1
1
1
1
1
0
0
1
0
1
1
0
0
1
0
1
1
2
1
1
1
1
2
0
0
1
1
1
1
1
0
1
2
2
1
3
1
0
1
1
0
0
1
1
0
1
1
1
1
2
2
0
1
1
1
1
1
2
1
4
0
0
2
2
0
1
1
2
2
0
1
0
1
1
0
2
1
1
1
1
0
2
1
0
1
0
1
1
0
1
1
1
2
0
2
0
1
1
1
1
1
2
0
1
1
2
2
0
2
2
0
3
1
0
1
2
1
1
0
1
0
1
2
0
1
1
2
1
1
2
1
1
1
0
1
0
0
1
1
1
2
1
1
3
1
2
1
0
1
0
1
1
1
2
0
2
1
1
1
1
1
0
1
1
0
1
2
1
1
1
1
2
1
1
0
1
2
0
1
1
0
0
2
0
1
1
1
2
2
1
1
1
1
0
1
1
1
2
1
0
1
1
1
0
2
0
1
1
1
1
1
2
0
1
1
2
1
0
1
2
1
0
1
1
1
1
1
0
0
1
2
1
1
2
2
1
2
2
0
1
0
1
0
2
1
0
1
1
2
1
2
2
2
1
1
1
0
0
2
1
2
2
0
0
1
1
1
2
0
1
2
1
1
4
1
2
2
0
1
2
1
1
1
2
2
1
0
1
1
1
2
1
1
2
1
0
2
0
1
1
2
0
1
0
0
1
0
1
1
3
2
2
0
1
2
2
0
1
1
0
1
2
1
2
0
1
0
3
1
1
1
0
1
1
0
1
1
0
2
0
0
1
1
2
2
0
1
1
0
1
1
1
1
2
1
2
1
2
1
0
2
1
2
1
2
1
1
2
2
2
0
1
2
1
2
1
1
0
1
2
2
1
1
1
0
0
1
2
2
0
1
0
1
2
1
1
0
1
1
1
1
1
1
1
1
0
0
2
1
1
2
1
1
2
1
1
1
2
1
1
1
2
1
1
0
1
1
1
2
0
2
1
2
2
1
1
0
1
2
0
0
2
0
1
0
1
1
0
1
1
2
2
1
1
1
1
1
1
1
1
2
0
1
1
2
1
0
1
0
1
0
1
2
1
1
1
2
1
2
2
0
1
1
1
1
1
1
1
1
0
1
2
1
1
1
1
1
2
0
1
0
1
1
0
0
2
1
2
1
1
0
2
0
1
2
1
2
1
1
2
1
2
1
2
1
1
0
1
1
2
1
0
0
1
2
1
2
1
1
1
1
1
1
0
1
2
2
1
0
1
2
1
1
2
1
1
1
1
1
2
1
1
2
2
1
1
1
0
2
0
1
0
1
1
1
0
1
1
2
2
1
0
2
1
2
1
0
1
1
0
1
1
1
0
2
0
1
1
2
1
1
1
2
2
0
1
1
2
0
0
1
1
2
2
1
1
2
2
1
1
1
1
1
2
1
1
2
1
0
1
1
1
2
1
0
2
2
0
2
1
0
0
1
2
1
2
2
1
1
0
2
1
2
1
1
2
1
1
2
1
1
1
1
1
2
1
0
2
3
1
1
1
2
1
2
1
0
1
1
1
1
2
1
1
1
1
1
0
1
2
0
2
0
2
2
2
1
0
0
1
2
2
1
1
1
1
2
0
1
1
2
1
1
0
1
2
0
1
0
1
1
1
1
1
2
2
0
1
0
2
1
1
2
1
2
0
1
1
1
1
1
2
1
1
2
0
1
1
1
2
1
2
2
1
0
1
0
0
1
0
0
1
1
0
1
0
1
1
1
1
1
3
0
1
2
0
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
0
2
1
1
2
1
1
1
1
1
0
1
0
0
1
1
2
1
2
0
2
1
0
1
0
1
1
2
0
1
0
1
1
1
1
0
1
2
1
1
0
1
1
1
1
1
0
0
1
0
2
1
1
1
1
2
0
2
1
2
1
1
1
1
2
1
1
1
1
1
2
0
1
1
1
2
0
2
1
2
1
1
1
4
1
0
1
2
1
1
2
0
1
0
1
2
1
2
1
2
1
0
1
1
1
2
1
1
1
1
2
1
0
0
2
1
1
1
1
1
2
0
1
1
1
3
1
0
0
1
1
1
1
1
0
0
1
2
0
2
0
1
1
1
1
1
1
0
1
10
2
1
0
1
1
1
0
0
1
2
1
1
1
0
0
2
1
0
1
0
1
1
0
2
1
0
1
0
1
1
1
1
0
1
1
1
0
2
1
2
0
2
1
0
2
1
2
1
0
0
2
0
0
1
2
1
1
1
1
0
2
0
1
1
1
2
1
1
2
2
1
1
1
1
1
0
1
1
1
0
1
1
2
1
1
1
1
1
2
2
1
4
2
0
2
1
1
2
1
0
1
2
2
1
1
0
3
1
0
0
3
1
1
1
1
2
3
2
1
0
2
1
1
2
1
0
2
2
1
1
1
2
1
1
1
0
1
0
1
1
1
1
1
1
0
1
2
1
2
1
1
1
0
1
1
2
1
1
1
1
1
1
1
0
2
0
2
0
1
0
0
2
2
1
1
1
1
2
1
1
1
2
1
1
1
1
1
2
0
0
0
1
0
1
0
2
1
1
1
1
0
1
0
1
2
1
1
0
1
1
1
2
1
1
1
1
2
1
1
1
1
2
0
0
1
1
1
0
0
0
0
0
1
2
1
1
1
1
0
1
1
1
2
2
1
0
1
1
1
0
1
1
1
1
2
1
0
1
2
0
2
1
1
0
2
1
0
0
1
1
1
2
1
1
1
2
1
1
1
1
2
0
0
1
0
1
2
2
1
2
1
2
1
0
2
2
2
1
1
1
1
0
1
1
2
2
1
0
2
0
0
0
0
1
1
2
1
2
1
1
1
1
1
1
1
1
2
1
2
1
1
3
1
1
2
1
1
1
1
2
1
1
1
2
2
1
2
3
2
1
2
1
1
1
1
1
1
1
1
2
2
2
2
1
0
0
1
1
1
1
1
1
0
1
1
2
2
2
2
1
1
0
1
1
2
0
1
0
0
3
1
1
1
1
2
0
2
1
1
1
1
0
1
2
0
2
0
1
2
1
1
2
1
1
0
1
1
2
0
0
1
1
2
0
1
1
2
2
2
0
0
0
1
1
1
1
1
2
3
1
1
1
3
2
0
1
1
2
1
1
0
1
1
1
0
1
1
2
1
1
0
2
0
0
1
1
2
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
0
0
2
1
1
0
2
1
1
1
1
0
0
1
1
1
1
2
0
0
1
1
1
1
0
2
1
0
0
1
1
0
0
1
0
1
2
2
0
0
2
0
1
2
0
1
1
1
2
0
2
0
0
0
1
2
1
1
1
1
1
2
2
1
2
1
3
1
2
2
1
1
1
1
1
1
1
0
1
2
1
0
0
1
0
0
2
1
1
1
1
1
1
1
1
1
0
1
1
0
1
0
1
1
2
1
0
0
0
1
0
1
1
2
1
1
2
2
1
1
2
0
1
0
2
2
1
1
2
1
1
0
0
0
1
2
0
1
1
2
1
2
0
1
2
1
1
1
1
1
1
1
1
1
1
2
2
0
1
1
1
1
1
2
0
2
1
1
2
1
1
0
0
1
1
2
1
2
0
1
0
1
1
1
2
0
1
1
1
2
1
1
0
2
0
1
0
1
0
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
0
1
0
1
1
1
1
1
1
1
1
1
1
1
0
0
1
0
0
1
1
0
0
1
1
2
1
0
1
1
2
0
1
0
1
2
1
1
3
0
2
0
1
0
2
1
0
2
0
2
0
1
0
1
1
0
1
1
2
1
0
0
2
2
1
1
2
1
2
0
2
0
1
1
1
1
1
2
0
1
0
1
0
1
1
1
1
1
0
2
1
1
1
1
0
1
1
2
2
1
1
1
1
1
1
1
1
1
0
1
0
0
0
1
1
1
0
0
1
2
0
1
1
1
1
1
0
2
1
1
2
0
0
0
0
1
1
1
1
1
1
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
2
1
1
1
1
1
1
1
1
1
0
2
1
1
1
1
2
1
0
2
0
0
2
2
0
1
3
1
0
2
2
1
2
2
2
1
2
1
1
1
0
0
0
0
1
1
1
2
2
1
1
2
0
2
1
1
1
1
0
1
1
0
0
1
1
1
1
1
2
1
1
4
1
1
0
1
2
1
0
1
1
1
1
1
1
1
1
0
2
1
0
0
1
1
1
2
0
2
0
1
0
1
1
0
2
2
1
1
2
2
2
1
0
1
0
1
2
1
0
1
2
1
1
2
1
1
1
2
1
0
0
0
1
1
7
1
0
1
1
1
1
1
1
1
1
1
2
1
0
1
1
1
1
1
1
1
1
1
0
1
1
0
1
1
1
0
1
1
3
1
2
2
2
1
2
1
1
1
1
1
2
2
2
1
1
1
2
1
1
1
2
2
0
1
2
0
1
1
1
0
2
0
2
2
0
2
0
0
1
1
2
1
2
1
1
1
2
1
1
2
1
2
1
0
1
2
1
0
2
3
0
1
1
1
1
2
1
1
2
1
1
1
1
2
0
1
1
0
2
1
1
0
1
1
2
0
1
1
5
1
1
2
1
1
1
1
0
1
2
1
1
0
2
0
1
1
1
1
0
1
1
2
1
1
2
1
0
2
1
2
1
1
1
1
1
1
0
1
0
0
2
2
0
1
1
1
1
2
1
1
1
16
0
1
1
2
1
1
2
2
1
1
1
1
2
1
1
1
2
1
1
1
1
1
0
1
0
2
1
2
1
1
1
0
1
0
1
1
1
0
1
1
1
1
1
1
2
1
1
0
0
0
0
1
0
1
1
1
1
1
3
1
1
1
1
2
1
1
2
1
1
0
2
1
2
2
1
2
1
1
2
1
1
2
1
1
2
2
1
1
0
0
2
1
1
1
2
2
1
3
2
1
1
0
1
1
1
2
0
2
1
1
2
1
0
2
1
2
1
1
1
1
1
2
0
2
2
1
1
0
0
2
1
2
1
2
1
2
1
1
2
1
1
2
2
1
3
1
2
2
0
1
1
0
2
1
2
0
2
1
1
1
2
1
1
1
2
0
2
1
1
1
1
1
1
1
1
2
1
1
0
0
2
0
1
1
0
1
1
0
2
1
1
2
2
1
0
1
1
1
1
2
2
1
2
1
1
1
0
1
1
2
0
1
1
1
0
2
1
0
1
0
2
1
1
2
0
1
1
1
2
1
1
1
0
1
1
1
1
0
1
2
2
1
1
1
0
1
1
0
1
0
1
1
2
1
2
0
1
1
3
0
1
0
0
2
2
1
2
2
2
2
1
2
2
1
1
0
1
2
0
1
0
0
1
0
0
2
1
1
2
0
1
1
0
2
1
0
2
2
1
0
0
2
0
2
1
1
2
0
1
0
1
0
1
1
1
1
2
2
1
1
2
1
2
1
1
0
1
1
0
2
1
1
1
0
1
1
2
1
2
1
2
2
2
1
1
0
1
2
1
1
1
0
1
1
2
2
1
1
1
2
2
1
2
0
2
1
2
1
0
2
1
1
1
1
1
0
1
1
2
1
1
2
1
2
1
0
1
2
1
1
2
1
1
1
1
2
1
1
1
1
2
2
1
1
0
1
1
1
1
1
2
2
1
0
1
1
2
1
1
1
2
1
1
2
1
2
1
1
0
1
1
1
1
4
1
2
0
1
0
1
0
2
2
1
0
0
2
0
1
1
2
2
1
1
2
1
0
1
1
2
1
1
0
1
1
2
0
2
0
1
1
2
4
2
1
2
1
1
1
1
1
1
1
0
1
2
1
0
0
2
0
2
1
1
1
1
0
1
1
1
1
1
0
1
0
0
0
2
0
1
0
2
1
1
0
1
2
1
1
1
1
1
2
1
5
1
2
1
2
1
0
2
2
2
1
1
0
1
1
1
1
2
1
0
0
1
1
2
0
1
0
1
1
0
0
1
2
1
1
0
2
1
1
1
1
1
1
1
0
2
0
1
1
0
1
1
1
2
2
1
1
1
2
0
1
1
1
1
1
1
0
1
0
2
1
1
1
1
2
2
1
1
1
1
1
1
1
0
1
2
1
1
1
2
0
0
1
2
2
2
2
1
0
3
1
1
1
0
1
1
0
1
0
2
2
2
2
0
1
2
1
0
1
1
1
0
0
1
1
0
1
0
1
2
2
1
0
1
1
1
1
1
1
2
0
1
1
1
0
1
0
1
0
1
1
1
0
0
0
0
2
0
1
1
2
0
1
2
2
1
1
1
1
0
1
1
1
1
1
2
0
1
0
0
1
2
0
2
1
1
0
1
1
1
1
1
1
2
0
2
1
3
1
0
0
1
1
1
2
0
1
2
2
1
1
1
1
1
1
1
2
1
1
0
0
1
1
2
1
1
0
2
2
2
2
1
1
0
0
0
1
1
1
1
1
1
1
2
1
1
1
2
1
1
0
1
1
1
0
2
0
1
2
3
0
1
2
2
0
1
1
1
1
0
1
0
1
1
1
1
2
1
1
1
0
1
0
2
1
0
1
1
1
2
3
2
1
0
1
1
1
1
0
2
0
1
1
2
1
1
1
2
0
1
0
2
1
0
1
1
1
0
1
2
2
1
1
1
1
2
1
0
1
1
1
1
0
1
1
1
1
1
0
1
1
2
0
0
1
1
1
2
1
0
1
2
1
2
1
1
0
1
1
1
2
1
0
0
1
2
0
2
3
1
1
1
1
0
0
1
1
0
1
1
0
2
1
2
0
1
0
2
1
1
1
1
1
1
1
0
1
0
1
2
2
1
2
1
1
1
2
0
2
2
1
1
1
1
1
1
1
1
1
1
2
1
2
0
0
0
1
0
2
1
0
2
1
1
1
2
1
1
1
2
0
1
1
0
0
0
2
2
1
0
2
2
0
1
2
2
1
1
1
1
1
2
1
1
1
1
2
0
0
1
0
1
1
1
2
2
1
0
0
2
2
2
0
1
1
1
0
1
1
2
1
1
1
2
1
0
0
2
2
0
2
1
1
1
1
2
1
1
1
1
2
0
1
2
2
2
2
0
2
1
2
0
1
2
2
2
0
1
0
1
2
0
1
1
1
0
1
1
2
0
0
2
2
1
0
2
1
1
2
2
1
1
1
0
0
1
1
0
1
1
2
1
1
1
0
0
1
1
1
2
0
1
0
0
1
1
0
1
0
1
1
1
2
1
0
2
1
1
1
1
1
1
1
1
0
1
1
0
1
2
1
2
1
0
1
1
1
1
2
2
1
2
0
2
1
0
1
1
1
1
1
2
1
1
2
0
2
1
1
1
1
1
1
1
1
1
0
1
0
0
1
2
1
2
0
1
2
1
0
1
1
2
1
0
1
1
0
0
1
1
1
1
1
2
1
1
2
2
0
0
0
0
0
0
1
1
0
0
2
1
2
1
1
1
1
1
2
1
1
0
0
1
2
1
2
3
2
1
2
0
1
1
2
1
1
1
0
2
1
1
0
1
2
1
1
0
0
1
1
1
2
0
1
1
1
1
1
0
1
2
1
1
1
1
2
2
2
1
1
3
1
1
1
1
0
5
1
1
1
1
1
1
1
0
2
2
1
0
2
1
2
1
0
2
2
1
2
2
1
2
1
1
1
2
1
2
1
1
1
0
1
1
0
2
2
1
2
1
0
1
2
1
1
1
1
1
2
1
1
1
1
1
0
2
1
0
1
2
2
0
2
1
2
0
1
0
1
2
1
1
1
3
1
1
2
0
1
1
1
2
0
0
3
1
1
1
1
0
1
1
1
1
2
1
1
1
1
2
1
2
1
2
1
2
1
1
2
0
3
0
1
1
1
1
1
1
1
1
1
1
0
1
2
1
2
0
2
2
1
0
2
1
1
2
1
2
1
1
1
0
1
2
3
2
0
2
1
1
1
1
0
1
1
2
0
0
1
0
1
2
1
1
2
1
0
2
1
1
1
1
1
0
1
1
2
0
2
1
1
1
2
1
0
0
1
2
2
1
1
1
2
0
1
0
1
1
0
1
2
1
2
1
1
1
2
2
1
1
1
1
1
1
2
1
1
0
1
1
2
1
0
0
1
1
1
0
2
1
2
1
0
0
1
0
1
1
1
1
1
1
2
1
0
1
2
1
1
1
1
2
2
1
1
2
2
2
2
2
2
2
1
0
3
1
1
1
1
1
0
2
2
1
1
2
1
0
2
0
1
1
1
1
1
1
0
1
0
1
1
1
1
0
2
1
1
2
2
0
2
0
1
1
2
1
1
1
1
1
1
1
2
2
2
0
2
1
0
1
2
1
1
1
0
1
1
0
0
1
1
1
1
1
1
0
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
0
0
1
2
2
1
1
2
1
1
2
1
1
2
0
1
1
2
0
2
2
1
1
1
0
2
2
1
1
3
1
1
2
2
2
1
1
1
1
2
2
2
1
0
0
3
1
2
1
1
1
1
2
2
1
2
1
1
1
1
0
0
2
2
0
0
1
1
2
0
0
1
2
1
2
2
1
0
1
0
1
4
1
1
2
0
1
1
1
1
2
1
2
0
2
3
2
1
1
0
1
1
1
1
1
1
2
1
1
1
2
2
1
2
2
1
1
1
1
1
1
1
2
2
1
1
1
1
2
0
1
0
2
1
1
2
0
0
2
1
1
1
1
2
1
2
1
1
1
1
2
2
2
1
1
0
1
2
1
1
1
1
1
1
1
0
2
2
1
1
1
1
1
3
1
1
2
0
2
0
2
1
1
2
0
1
0
2
1
2
2
2
2
2
1
1
2
1
2
1
0
0
1
1
1
1
1
1
1
1
1
0
3
1
1
1
2
0
1
1
0
1
1
1
1
2
1
1
2
2
1
1
2
1
2
1
1
1
2
1
0
0
1
1
2
1
1
0
2
0
0
0
0
2
1
2
1
1
1
2
2
2
0
2
1
1
1
0
2
2
1
1
1
2
1
1
2
0
1
1
1
0
0
1
1
2
2
2
1
1
1
1
1
0
1
2
0
1
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
2
1
0
1
1
1
1
1
2
0
1
1
0
1
2
1
2
2
2
0
2
1
0
1
0
0
0
2
0
1
1
1
1
1
1
1
1
1
1
2
0
1
1
0
1
1
1
1
1
0
0
1
2
0
1
0
3
2
1
0
2
1
1
1
1
1
1
1
2
1
1
0
1
2
1
2
0
1
1
2
1
1
2
1
2
2
2
0
1
1
2
1
1
1
0
2
1
1
0
1
2
1
1
1
0
1
2
2
1
0
2
1
2
1
2
0
2
0
1
0
0
1
0
1
1
1
2
1
1
0
1
2
0
0
2
0
1
1
2
1
2
2
1
0
1
2
1
0
0
1
0
2
1
0
1
1
0
1
1
1
2
1
1
1
1
1
1
2
1
2
0
1
0
1
0
2
1
2
1
1
1
1
1
2
2
2
0
1
1
2
0
2
1
1
2
2
1
2
1
2
0
1
0
1
1
1
0
0
1
2
2
1
1
0
2
0
2
1
1
1
1
1
1
1
2
1
0
2
0
1
1
1
1
0
1
0
1
0
1
2
1
1
0
1
1
1
2
1
1
0
1
1
1
2
1
1
0
0
1
0
2
2
0
1
0
2
1
1
0
1
2
1
0
2
1
1
0
1
2
1
0
2
1
1
1
2
0
0
1
1
1
2
1
4
1
2
2
0
1
1
1
1
2
0
1
2
0
1
1
2
3
1
1
1
1
1
1
1
1
1
0
1
0
1
1
1
1
2
0
1
1
1
0
1
1
0
0
1
1
1
1
2
1
0
2
2
1
2
1
1
1
1
1
0
1
0
1
1
2
1
0
1
1
1
0
0
1
1
1
1
3
1
2
1
2
1
1
0
1
1
2
0
1
1
2
1
2
1
2
1
2
2
0
0
1
1
2
2
0
2
1
1
3
2
1
1
1
1
1
2
0
2
2
1
0
1
1
1
1
3
2
1
1
1
0
1
0
0
0
1
2
0
1
0
1
1
1
1
2
0
1
0
1
2
1
2
0
1
0
1
0
2
2
1
1
0
2
1
1
1
2
1
1
2
1
1
1
2
1
0
1
1
1
0
2
1
0
1
2
1
0
0
1
1
2
1
1
1
1
0
1
1
1
1
2
2
0
2
0
2
2
1
2
2
0
2
0
1
0
1
2
1
0
1
1
1
2
1
1
2
1
1
1
0
1
2
0
0
1
1
2
2
1
2
1
1
0
1
2
2
1
2
1
2
1
2
1
2
1
1
0
1
2
0
1
2
1
1
1
0
1
2
2
1
0
0
0
0
1
0
1
1
3
1
1
1
1
2
1
1
1
1
2
1
1
2
1
2
1
2
2
1
1
1
2
0
1
1
2
0
1
2
2
1
1
2
1
0
2
0
1
2
2
1
1
1
2
1
1
1
1
1
1
1
0
0
1
1
1
0
2
1
0
1
1
2
2
1
1
1
1
1
1
1
1
1
0
1
1
1
2
1
1
1
2
2
2
0
1
0
1
1
1
1
1
0
2
0
0
2
2
0
2
1
1
1
2
1
2
1
1
1
1
1
2
1
2
0
0
1
2
0
1
1
1
1
1
0
1
0
0
1
0
0
2
2
1
2
1
1
1
1
1
2
2
0
2
2
0
2
1
1
0
1
1
1
1
2
0
1
0
2
1
2
2
1
1
0
1
1
1
2
2
1
1
1
0
1
4
0
0
1
2
2
1
0
2
1
1
1
0
0
2
2
1
2
1
2
1
2
1
1
0
2
1
1
1
1
2
2
0
1
0
1
0
1
1
1
2
0
1
1
1
2
1
1
1
2
2
0
1
1
0
1
1
1
0
1
1
1
1
1
2
1
1
0
0
1
1
0
1
0
1
1
1
2
0
1
1
1
0
1
0
1
2
0
1
0
1
1
1
0
2
1
1
1
2
1
0
2
2
2
0
0
1
2
1
1
2
1
2
2
1
2
1
2
1
1
2
1
0
1
2
1
1
1
2
0
0
0
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
0
2
1
1
0
0
0
1
0
2
1
0
1
0
2
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
0
2
0
2
1
0
1
1
1
1
1
2
1
2
0
0
3
0
1
0
0
2
1
0
0
0
1
0
2
0
1
0
1
1
2
1
2
1
0
1
0
1
1
2
2
1
1
2
1
0
2
2
2
1
1
1
1
0
1
2
1
1
2
0
1
1
2
2
2
1
1
2
1
0
2
1
1
2
2
0
2
1
0
1
1
1
2
1
1
2
1
1
1
0
1
1
1
1
0
1
1
1
1
1
1
0
2
0
1
1
1
2
1
0
1
2
1
1
0
1
2
0
0
1
1
0
1
2
0
2
0
0
1
1
0
1
1
0
1
1
0
1
1
1
0
1
0
1
1
0
1
0
1
1
2
1
1
1
1
2
5
1
1
1
1
2
2
1
2
2
2
2
1
1
0
1
0
1
1
1
1
2
0
1
1
1
0
0
1
0
2
1
1
1
1
1
2
1
1
2
2
1
1
1
1
1
2
0
2
1
1
0
2
2
1
1
1
1
1
1
0
2
2
0
0
1
0
1
1
2
1
1
1
1
1
2
3
0
1
1
0
0
0
2
2
1
2
1
1
1
1
0
1
0
1
1
2
1
1
1
1
1
5
1
1
1
1
1
1
0
1
0
1
2
1
1
2
2
0
1
2
0
1
1
1
2
2
2
2
1
1
1
0
0
2
1
4
1
1
1
1
1
2
1
1
1
0
2
1
1
1
1
0
1
2
2
1
0
1
1
1
1
2
0
1
1
0
1
2
1
1
1
1
1
1
1
1
2
2
1
1
1
1
0
1
1
0
1
0
2
1
1
2
1
1
2
2
1
1
2
1
1
1
1
2
0
2
2
1
2
1
2
0
1
1
1
1
1
0
1
1
1
2
0
1
2
1
0
1
2
1
2
0
1
2
0
0
2
1
2
1
1
0
1
1
1
2
0
2
1
2
1
1
2
0
1
2
1
1
2
1
1
1
0
1
1
0
1
1
1
0
1
0
1
0
1
2
1
2
0
2
1
1
1
1
1
0
0
2
1
0
0
1
1
1
1
1
1
0
1
0
1
1
0
0
0
2
0
1
2
1
1
1
0
2
1
0
2
1
2
1
0
1
1
2
1
2
1
1
0
1
2
1
1
0
0
2
0
1
3
1
1
1
1
0
2
1
2
1
1
0
0
0
1
1
1
1
2
1
0
2
0
1
2
2
1
1
1
1
1
1
1
0
1
1
0
1
2
0
1
0
0
1
1
1
1
1
0
1
1
1
2
1
1
1
0
1
2
0
0
1
2
1
1
2
1
1
1
1
1
2
2
1
1
0
2
1
1
1
0
0
1
1
1
1
1
1
0
1
1
2
1
2
1
0
1
1
1
1
1
1
1
2
1
1
1
1
1
2
2
0
1
2
1
1
1
1
1
1
0
0
2
0
1
2
5
1
1
1
1
1
2
2
2
1
2
1
1
1
1
1
1
2
0
1
1
1
1
1
1
0
2
1
1
1
1
1
1
1
2
0
0
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
0
2
0
0
1
0
1
0
0
1
1
0
1
1
1
1
1
1
1
2
1
0
1
1
1
1
2
2
2
1
1
2
2
0
1
1
1
1
2
1
1
0
2
1
1
1
2
2
1
2
1
1
1
1
2
1
1
1
0
1
1
0
0
2
1
1
0
2
1
1
0
1
0
0
3
1
2
1
2
1
0
1
1
2
0
1
1
1
0
1
0
2
2
1
2
3
0
1
2
1
2
1
2
1
0
2
2
1
0
1
0
1
2
1
0
2
0
2
0
2
1
2
2
1
2
0
1
1
2
1
2
0
1
0
1
2
1
1
1
1
2
1
1
0
2
1
1
1
0
0
1
1
1
1
1
0
2
2
1
0
1
1
2
2
2
1
1
2
1
2
1
1
2
1
1
0
0
1
2
1
1
1
0
1
1
1
1
0
2
1
1
1
1
0
1
2
1
2
0
1
0
1
2
1
1
1
2
1
1
2
2
2
1
1
1
0
1
2
0
1
0
1
0
2
0
1
1
0
1
1
1
2
2
2
2
2
1
1
0
2
1
1
2
1
1
1
0
2
1
1
1
1
2
1
1
1
1
1
0
1
3
1
2
2
3
1
1
1
1
1
2
1
1
4
1
0
1
0
1
1
0
2
2
2
2
1
2
1
1
1
1
2
1
2
1
2
1
1
1
0
0
1
2
2
1
0
3
0
0
1
1
0
1
1
1
3
1
1
1
1
1
1
2
2
1
0
2
0
1
3
2
2
1
1
2
0
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
0
1
1
1
1
1
0
0
2
1
1
2
1
0
0
0
1
1
0
1
1
1
0
1
2
1
1
2
1
0
2
1
1
1
1
1
0
0
2
1
0
0
1
0
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
0
1
1
2
1
1
1
1
1
0
1
1
0
1
0
0
1
1
2
1
1
2
1
5
1
2
2
2
0
2
0
1
0
1
1
1
2
1
2
0
0
0
1
1
0
1
2
1
2
1
2
1
0
1
1
0
1
0
1
1
1
0
0
1
1
1
1
0
2
0
1
0
1
0
1
1
2
1
1
1
1
1
1
1
1
1
1
2
2
0
1
0
1
2
2
2
2
1
1
1
1
0
1
1
1
1
2
2
1
1
2
2
2
0
1
1
1
0
2
0
1
1
2
2
1
0
2
1
1
1
1
1
1
2
2
2
2
2
2
1
1
1
0
2
2
1
1
0
2
1
1
1
1
1
1
0
2
0
0
1
1
1
2
2
0
2
1
0
0
1
1
1
0
0
1
1
0
1
1
1
1
1
1
4
1
1
1
0
1
2
1
1
1
1
1
1
0
1
2
1
1
0
1
2
2
0
1
1
2
0
2
0
1
1
2
1
1
2
1
1
0
2
1
1
2
1
2
1
1
1
0
2
1
1
2
1
0
0
0
0
1
0
1
2
1
2
0
1
2
1
2
1
1
2
2
2
1
2
1
1
1
1
1
0
1
1
1
2
0
2
1
1
2
2
1
0
0
2
0
0
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
1
0
0
1
1
0
1
0
0
2
1
2
1
1
2
1
1
0
1
0
1
1
1
1
1
0
1
1
0
1
0
1
2
1
1
1
0
1
1
1
1
0
2
1
1
1
1
1
2
1
2
3
2
2
1
0
1
2
2
1
1
1
1
1
1
3
1
2
0
1
0
1
2
1
0
1
1
2
1
2
1
1
1
1
0
1
1
0
2
1
1
1
2
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
2
2
1
1
1
2
2
1
1
1
0
1
1
1
1
0
1
2
1
1
2
2
2
2
1
1
2
1
0
2
2
2
0
1
1
1
2
1
0
2
0
2
0
1
4
0
2
1
4
1
3
1
1
0
2
1
1
1
0
1
2
1
2
1
4
1
0
0
1
1
1
1
2
1
0
2
1
0
1
1
1
2
0
0
2
2
0
1
1
1
2
1
2
1
0
0
0
0
0
1
1
1
0
2
1
0
1
2
0
2
0
2
1
0
0
1
1
1
0
1
0
2
0
2
2
1
1
0
2
1
1
0
2
1
3
2
1
1
1
2
0
1
1
1
0
2
0
1
1
2
1
1
2
1
1
2
2
0
1
1
1
1
1
1
0
1
0
1
1
1
0
1
2
0
1
1
1
2
1
1
2
1
2
1
0
1
2
2
0
2
0
1
0
1
2
1
1
1
2
2
0
1
1
2
0
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
0
0
0
0
1
1
2
0
2
2
1
1
1
2
2
1
1
2
0
0
0
1
2
2
1
0
2
1
1
1
2
1
0
1
1
0
1
1
1
1
2
1
0
1
1
0
1
0
1
2
0
1
1
1
1
1
2
1
2
2
1
0
1
2
1
1
1
2
1
0
1
0
1
1
1
1
1
0
2
0
1
1
1
1
1
1
1
1
0
2
2
1
0
1
1
1
1
0
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
2
1
1
2
1
1
0
1
1
1
1
1
1
0
1
1
1
2
2
2
1
1
1
1
2
0
1
2
2
2
0
2
1
0
2
2
1
1
1
0
2
0
1
1
1
1
2
0
1
1
1
1
0
2
1
0
1
1
1
1
2
2
1
1
0
1
1
1
2
0
1
1
2
0
1
1
1
2
1
1
2
1
0
1
1
1
1
1
1
2
0
0
1
0
1
1
1
1
0
0
1
1
1
1
1
0
1
1
2
0
1
2
1
2
1
2
1
1
1
1
2
1
2
1
1
1
1
2
2
1
1
0
0
1
0
1
0
1
0
1
1
1
4
1
0
2
1
1
0
1
1
1
2
1
1
2
1
1
0
1
0
1
1
1
1
2
2
1
1
1
2
1
1
1
0
0
1
1
1
1
1
1
2
1
1
0
1
1
1
2
1
1
1
1
2
0
0
1
2
1
0
0
0
1
0
1
2
2
1
1
2
1
0
0
1
1
1
2
1
1
1
0
1
1
1
1
1
1
1
2
1
1
1
0
3
1
0
1
1
0
0
0
2
1
1
2
0
0
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
0
1
1
1
0
1
0
3
2
1
1
1
2
0
1
1
1
1
0
3
1
1
2
1
2
1
2
2
1
2
0
1
2
1
1
1
1
0
1
2
0
1
1
2
1
0
0
0
0
0
0
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
0
1
1
1
1
2
1
1
0
1
1
1
1
1
0
1
1
2
0
1
0
1
2
1
1
1
1
0
1
2
1
1
3
1
2
2
0
1
2
1
1
1
1
2
1
1
2
2
1
1
0
2
0
0
1
1
2
1
2
1
3
1
1
1
2
1
1
0
1
1
1
2
1
2
1
2
1
1
1
0
2
1
2
1
1
1
0
0
2
1
0
1
0
1
2
1
1
2
1
1
1
1
1
1
2
1
2
2
0
1
1
2
0
1
1
1
2
0
2
1
1
1
1
2
0
1
1
1
2
1
0
2
1
0
0
2
2
1
1
0
3
1
2
1
0
1
1
2
1
2
2
1
2
1
2
1
1
2
0
1
1
1
1
1
1
2
2
1
1
1
1
0
1
2
2
1
1
1
1
2
1
2
2
0
1
0
2
2
1
1
2
2
1
1
0
1
2
0
0
1
1
1
0
1
1
3
0
1
2
1
1
0
1
1
1
2
0
1
0
2
1
2
1
0
1
0
1
1
2
2
1
1
2
1
2
0
2
1
1
0
0
1
1
1
1
1
1
2
0
1
2
1
1
1
1
1
0
0
1
1
1
1
0
1
1
1
0
1
1
0
2
2
2
1
1
2
1
0
0
1
1
1
2
1
2
2
2
1
2
1
2
0
2
2
0
2
1
2
1
1
1
0
1
1
1
1
2
2
2
1
2
0
0
0
1
0
0
1
2
1
2
1
1
0
1
0
1
2
1
1
1
0
1
2
2
0
1
1
1
1
0
2
2
0
1
1
1
0
1
0
2
2
1
1
1
1
2
0
1
1
2
2
0
1
1
1
1
2
1
1
1
1
0
1
0
0
1
1
1
0
1
2
1
0
1
1
0
0
1
0
2
2
2
2
0
2
2
1
2
1
1
2
2
1
0
1
1
0
2
1
1
1
2
2
1
0
1
2
2
0
1
0
2
1
0
1
1
0
0
1
1
1
1
1
1
1
1
1
1
0
2
0
0
1
0
1
0
1
2
0
2
1
1
1
0
2
1
0
2
1
0
2
1
1
1
2
1
0
1
1
1
2
1
1
1
1
1
0
1
2
2
0
1
1
1
0
2
1
2
1
2
1
1
1
1
0
1
1
0
1
2
1
1
1
1
0
1
1
1
1
0
1
1
0
2
4
1
0
0
1
2
1
0
1
2
2
1
1
1
1
0
1
1
0
0
0
1
0
1
0
2
1
1
1
2
2
2
1
1
0
1
1
1
1
2
1
1
1
1
1
1
0
2
1
1
0
1
2
0
0
1
2
0
1
0
2
1
1
2
0
1
0
1
0
1
1
1
1
1
1
1
0
1
0
1
1
2
0
1
1
0
2
2
1
1
1
1
1
2
1
0
1
0
1
1
1
1
1
1
1
2
2
1
2
1
1
2
1
3
2
0
1
2
0
1
0
1
0
1
1
1
1
1
1
2
1
1
1
1
2
1
0
2
1
1
0
1
0
2
1
1
1
2
0
1
1
1
1
0
1
1
1
1
0
2
1
1
1
1
1
1
1
0
1
1
2
1
1
2
0
1
1
2
1
1
1
1
1
1
2
1
2
0
2
1
0
2
1
1
1
2
1
2
2
1
1
1
0
2
2
0
1
1
0
1
0
1
2
2
2
2
1
0
1
14
2
1
0
1
0
1
2
1
0
2
0
1
1
1
2
2
1
1
2
1
0
1
2
2
1
2
0
1
1
1
1
2
2
1
1
0
1
1
2
2
1
1
1
1
1
2
1
1
3
2
1
2
1
1
1
0
2
0
0
1
2
1
2
1
1
0
2
1
1
1
2
2
1
1
1
2
2
1
1
1
1
2
2
2
0
1
1
2
0
0
1
3
0
1
1
2
2
2
1
1
1
1
0
1
1
1
2
2
1
1
1
1
2
2
0
0
0
1
2
1
1
2
1
2
1
0
0
2
1
1
2
1
1
1
1
2
1
1
0
1
1
1
1
1
2
1
1
1
2
1
1
2
1
2
1
1
2
0
2
1
0
1
2
1
1
1
0
1
0
1
1
1
2
1
1
1
2
1
1
1
0
2
2
1
2
2
2
1
0
1
1
1
1
1
1
2
0
1
2
0
0
0
1
1
1
1
1
1
1
2
2
1
1
2
1
2
3
2
0
1
2
1
1
1
2
1
1
0
1
1
1
1
2
2
1
2
1
3
1
1
1
1
3
1
3
2
0
2
1
1
0
1
2
1
1
1
2
0
1
1
2
1
0
1
2
2
2
2
1
2
1
1
0
2
1
0
1
2
1
1
1
1
1
0
2
1
2
2
1
1
0
1
1
1
0
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
2
1
1
2
2
1
1
1
2
1
1
0
2
1
1
0
1
1
0
1
1
1
2
0
2
1
0
0
2
3
1
1
2
1
2
1
1
2
1
1
1
1
1
0
0
0
0
0
0
2
1
1
2
2
2
1
0
2
1
1
2
4
1
1
1
0
1
1
0
1
1
1
0
1
0
2
1
1
0
1
2
1
2
1
0
2
1
0
1
2
0
1
1
2
2
2
2
1
1
1
1
0
1
1
1
1
1
2
2
1
1
2
1
2
1
1
0
2
1
1
0
1
1
1
0
2
1
2
1
2
1
1
1
2
1
0
1
1
0
0
1
1
1
1
1
1
1
0
2
1
1
0
1
0
1
1
0
1
2
1
1
1
0
0
0
0
1
1
0
1
1
1
1
2
1
0
2
3
2
1
0
2
2
1
0
0
1
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
0
1
1
1
1
2
1
1
0
1
1
1
0
2
1
2
1
1
1
1
1
0
0
2
1
0
1
1
1
2
1
0
1
0
1
2
1
1
1
1
0
1
2
0
1
0
1
1
1
1
1
1
1
1
0
1
0
2
2
2
0
1
1
1
1
1
1
1
1
0
0
1
1
1
1
1
1
1
0
1
1
1
1
1
1
0
1
1
1
2
1
1
2
0
0
0
2
1
1
1
1
2
2
1
1
0
2
2
0
0
1
1
1
1
1
1
1
0
1
2
0
1
0
0
1
0
1
1
1
0
1
0
4
0
1
0
0
0
1
2
1
2
1
0
1
1
1
2
2
1
1
1
1
2
1
2
0
1
1
1
1
0
2
2
2
1
0
2
2
1
1
0
1
1
1
1
1
1
0
0
2
0
0
1
1
0
1
1
1
1
1
1
1
0
1
0
2
1
1
2
1
1
1
1
0
0
1
2
2
1
0
2
2
2
1
0
1
1
1
2
2
1
1
1
0
1
1
1
2
0
1
1
1
1
0
0
1
0
0
1
1
1
0
1
0
0
1
1
0
1
1
1
0
0
1
1
1
1
1
1
0
2
1
2
1
1
1
1
1
1
2
0
1
0
0
1
1
0
1
1
0
1
1
1
2
1
1
2
1
0
0
1
3
1
0
1
1
0
0
1
1
1
0
1
1
1
2
2
2
2
1
1
1
1
2
0
1
0
0
0
0
2
2
0
1
1
0
1
0
1
1
0
0
1
0
1
2
2
1
1
2
1
1
1
1
1
1
2
0
1
1
1
1
1
2
2
1
1
1
1
1
0
1
1
1
2
1
2
1
2
1
0
1
2
1
1
1
1
1
0
1
1
1
2
1
1
0
1
1
1
1
1
1
1
1
1
1
0
1
1
1
0
2
2
0
2
0
0
2
1
1
0
0
2
1
2
1
1
2
1
2
1
0
1
1
1
2
0
1
0
0
2
0
1
0
0
1
1
1
1
1
1
1
0
0
1
0
1
1
2
2
1
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
0
1
1
1
0
0
0
1
2
1
1
3
0
1
1
1
1
1
0
0
0
2
1
2
1
1
1
2
1
1
2
1
1
1
1
1
0
0
0
0
2
0
1
1
2
1
2
0
2
1
1
0
1
1
1
1
2
1
1
1
0
1
2
1
1
0
0
1
1
2
1
1
0
2
2
2
2
2
2
1
2
1
1
0
1
1
0
0
1
1
2
1
2
2
1
0
1
1
1
1
2
1
0
1
1
1
1
2
2
2
1
2
2
0
0
2
2
1
1
1
1
0
1
1
1
1
2
2
0
1
5
1
2
2
0
2
0
2
1
0
2
1
1
1
2
1
2
0
0
1
1
1
1
0
0
2
1
0
1
0
1
1
1
1
1
1
1
0
2
2
1
1
0
2
1
1
2
1
1
0
1
1
1
2
1
2
1
0
1
1
1
0
1
0
1
1
1
2
2
1
0
0
0
2
1
0
1
1
1
0
0
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
0
1
1
2
0
1
0
1
1
1
1
2
1
1
0
2
1
1
1
1
1
0
1
0
1
2
0
1
2
1
0
2
1
1
1
0
1
0
3
1
1
0
1
0
1
1
2
0
1
1
1
2
1
2
0
0
1
1
0
1
2
1
0
1
1
2
2
2
0
0
1
0
2
1
1
1
1
2
1
1
1
1
1
0
1
1
1
1
1
0
1
2
2
1
0
1
1
2
1
0
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
2
1
1
1
0
2
1
0
1
1
1
2
0
2
1
1
2
2
2
1
1
1
0
2
2
2
2
0
1
1
2
1
1
0
1
1
0
1
2
2
1
1
1
1
2
0
0
1
1
2
1
2
1
1
2
2
1
0
1
1
2
1
1
2
2
1
2
1
1
0
2
1
1
1
0
0
1
1
0
1
0
3
0
1
2
1
2
1
1
2
2
0
1
1
0
0
1
1
1
0
1
1
0
1
1
0
1
1
1
1
1
1
0
2
0
1
0
1
1
1
0
1
1
1
3
1
0
0
1
2
1
2
1
0
1
0
2
1
2
0
1
1
1
1
0
1
1
1
2
1
1
2
1
2
1
0
1
1
1
1
2
2
1
2
1
2
1
1
1
1
1
1
1
1
1
0
1
0
2
2
1
0
2
2
0
1
1
1
2
2
1
2
1
1
1
3
1
1
2
1
1
0
1
1
0
1
1
1
1
1
1
1
0
0
1
1
0
1
0
0
1
1
1
2
1
2
1
1
0
0
1
1
1
2
0
1
1
2
1
1
1
0
1
1
1
1
0
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
2
2
0
1
2
0
1
1
2
1
2
1
2
1
2
0
1
0
1
2
0
0
2
2
1
1
1
1
0
2
1
1
1
0
1
2
2
1
1
2
1
2
1
1
1
2
1
1
1
2
1
2
1
1
1
2
1
1
1
1
1
2
1
1
2
1
1
1
2
2
1
1
0
0
1
1
1
0
1
1
2
1
1
3
1
2
2
1
1
0
2
0
1
2
0
1
1
1
1
1
1
1
3
0
1
1
1
1
1
0
0
0
0
1
1
2
1
2
1
1
1
2
1
1
1
0
1
0
1
1
1
1
1
1
2
2
1
1
1
0
2
1
1
1
1
1
1
0
1
1
1
2
1
2
1
0
0
1
2
2
1
2
0
1
2
1
0
2
0
1
0
2
0
1
4
1
0
1
0
1
1
0
1
1
0
1
1
2
1
1
1
1
2
1
0
1
1
1
1
2
0
2
1
1
1
0
0
2
0
1
0
0
0
0
1
0
1
2
1
2
1
1
1
1
1
1
2
6
2
0
1
1
2
2
1
1
1
1
0
1
1
1
1
1
2
0
0
1
1
1
1
2
0
1
2
1
1
1
2
0
1
1
1
1
1
1
0
2
1
0
2
1
1
0
1
2
2
2
0
1
1
1
3
0
2
1
2
1
0
1
1
3
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
0
1
1
1
1
0
1
1
1
1
2
1
0
2
2
2
0
0
0
1
1
1
0
1
1
2
2
0
1
0
1
1
1
2
0
0
2
1
1
1
0
1
1
2
1
3
2
2
3
0
1
0
1
0
0
2
0
2
0
3
1
3
2
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
0
1
1
0
2
1
2
2
1
0
0
0
1
1
2
0
1
1
0
2
2
2
1
1
0
1
0
1
2
2
2
2
1
0
2
0
1
0
1
1
1
1
1
1
1
2
1
0
1
2
0
1
1
1
1
1
0
1
0
2
1
1
1
1
1
1
0
1
0
0
2
1
2
1
1
0
0
1
2
0
2
0
1
2
1
1
0
1
2
2
1
0
1
1
0
1
3
1
1
1
1
1
3
1
1
1
1
1
1
0
1
0
2
2
1
1
1
2
1
2
1
1
2
1
1
1
2
1
1
1
5
1
1
1
0
1
1
1
0
0
1
1
0
1
1
1
0
2
1
2
2
2
1
1
1
1
0
1
2
0
1
2
0
1
0
1
1
1
1
2
1
2
2
1
0
1
0
1
1
2
1
2
1
2
1
1
1
1
2
2
1
1
2
1
1
2
1
2
0
1
1
2
2
2
2
0
0
0
0
1
0
0
0
2
1
1
2
1
1
1
1
1
0
1
0
1
1
0
1
1
1
0
4
0
1
2
1
1
2
1
1
1
2
1
0
0
1
2
0
0
1
2
1
1
1
1
1
2
1
1
2
0
2
1
1
1
2
1
1
1
2
0
1
1
2
2
2
0
1
1
0
1
2
2
0
1
0
1
0
1
0
1
3
1
0
2
0
1
2
0
2
3
2
0
0
1
1
0
1
2
2
0
0
2
1
2
2
1
1
1
1
2
1
1
0
1
1
1
1
0
1
1
1
1
0
1
1
2
2
1
1
1
0
1
2
2
1
0
1
2
1
2
1
1
0
2
0
1
1
0
1
1
0
0
1
1
2
1
1
1
1
1
0
2
1
2
1
1
4
4
1
1
2
1
0
1
2
0
1
2
1
1
1
2
1
1
1
1
2
1
1
0
2
1
1
2
1
1
2
0
1
1
2
2
2
0
1
0
1
2
1
2
1
1
1
2
2
2
1
1
2
2
1
0
2
1
1
1
1
1
1
4
1
1
1
1
0
2
1
1
0
1
2
1
1
1
0
1
2
1
1
0
1
2
2
1
0
0
1
1
1
0
1
0
1
1
1
2
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
0
1
1
1
1
2
1
1
2
1
2
2
1
1
0
1
1
1
4
0
2
1
0
1
1
1
1
1
0
2
2
1
2
1
1
1
0
1
1
1
2
1
1
2
1
2
0
1
1
1
1
1
0
1
1
1
1
1
1
0
1
1
1
1
1
1
0
2
2
0
3
0
2
0
1
1
1
0
2
2
0
2
0
1
2
1
2
1
1
1
0
1
2
0
2
0
1
2
1
2
0
1
1
0
2
1
1
1
0
0
1
2
1
1
1
1
2
2
1
1
1
1
2
1
1
0
1
2
1
2
1
1
1
2
1
2
1
1
1
2
2
1
0
1
2
0
1
1
1
1
1
1
0
1
1
2
1
2
0
1
1
1
1
2
3
0
1
2
1
0
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
0
2
0
1
1
1
1
2
1
1
1
1
2
1
0
0
1
0
1
1
0
1
1
1
0
1
0
0
2
1
1
1
1
1
1
1
2
1
2
2
0
2
2
1
1
0
2
1
1
2
1
0
0
1
1
1
1
2
2
1
2
4
1
2
1
0
1
2
0
2
1
0
0
2
1
1
1
1
1
1
1
2
0
0
1
1
1
2
3
1
2
1
2
0
1
2
2
1
0
1
2
1
2
1
1
2
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
0
1
1
1
0
1
0
2
2
0
0
1
1
1
2
0
1
1
0
0
1
1
2
0
1
2
1
1
1
2
0
1
0
1
1
2
1
1
1
1
3
1
1
1
2
1
1
2
0
1
1
0
0
1
1
0
1
1
2
2
1
2
0
1
1
1
0
1
0
2
1
0
1
2
1
1
0
1
1
1
2
1
2
1
2
1
0
1
2
2
2
1
0
0
1
1
1
2
1
1
1
1
1
2
0
2
2
1
1
1
1
1
1
1
1
0
2
1
1
1
0
1
0
1
1
1
1
0
2
2
1
1
1
0
0
2
1
0
0
0
1
2
1
1
1
1
0
2
3
1
1
1
1
2
0
2
1
1
1
0
0
0
1
1
2
2
1
0
1
1
2
1
1
1
1
0
1
0
1
1
0
1
1
1
1
1
1
1
2
1
0
1
0
1
2
0
1
2
1
1
0
1
0
2
1
1
1
1
1
0
2
1
1
1
0
2
1
1
2
1
2
1
2
1
1
1
0
1
1
0
2
1
1
1
1
1
1
1
1
2
1
0
0
2
1
1
1
2
0
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
0
1
3
2
2
2
2
0
0
0
1
1
1
1
1
1
0
1
2
0
2
2
0
2
2
0
1
1
2
2
1
1
1
2
1
1
1
0
1
1
1
1
1
1
1
1
1
1
4
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
2
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
0
0
0
0
1
1
0
0
1
0
1
1
0
1
0
2
0
1
2
1
1
1
2
2
0
0
2
1
1
0
0
1
2
1
0
1
1
1
1
2
1
2
0
0
2
1
1
1
1
2
1
1
1
2
1
1
1
1
2
0
1
2
1
1
1
1
2
0
2
1
1
2
1
0
1
2
1
0
0
1
0
2
1
1
3
1
2
0
2
1
1
0
2
1
1
0
2
2
1
1
1
2
2
1
1
1
1
0
1
2
1
1
0
1
0
1
2
1
2
1
1
1
0
2
1
2
1
1
0
2
1
0
1
2
1
1
1
2
3
2
0
0
1
1
1
1
2
1
1
1
0
2
0
1
0
1
1
1
1
2
0
1
2
1
1
1
1
0
1
1
1
2
2
1
1
0
1
1
1
1
2
1
2
1
1
0
1
1
1
0
0
1
0
1
1
1
0
0
2
0
1
2
1
1
1
0
2
1
1
1
1
1
0
1
1
1
0
2
1
3
0
2
0
2
2
2
2
2
1
1
1
1
1
3
2
0
2
0
1
2
0
2
1
2
2
0
0
1
1
2
0
2
1
0
1
0
2
1
0
0
0
1
1
0
2
0
2
0
2
1
2
0
1
1
1
0
2
1
1
1
2
0
1
2
0
1
2
1
1
0
0
2
0
0
1
2
1
0
1
2
0
2
0
1
2
0
0
1
1
1
0
2
1
2
1
1
2
1
1
1
1
0
0
1
1
1
2
2
1
1
1
2
1
0
0
1
2
1
4
1
1
2
1
2
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
0
1
2
1
0
1
0
1
1
1
1
1
2
0
1
2
1
2
1
2
6
0
1
1
2
0
0
0
1
0
2
0
1
2
1
2
0
1
2
1
0
0
1
1
1
1
1
0
1
0
0
1
1
2
1
1
1
1
1
1
1
2
0
0
1
1
1
1
0
0
1
1
1
0
1
0
0
1
1
2
1
0
1
2
1
2
1
1
2
1
2
1
1
1
1
0
1
1
2
1
0
2
1
0
1
2
2
1
1
1
2
1
1
1
1
1
1
1
1
1
0
1
1
2
0
2
1
0
2
2
2
2
0
1
1
0
0
1
1
1
1
0
0
1
0
0
1
2
1
2
2
1
0
0
1
1
1
1
1
1
1
1
0
1
2
0
0
0
2
1
1
1
1
1
1
1
0
1
2
1
0
2
1
1
1
2
2
1
1
1
1
2
1
2
1
0
1
1
1
2
1
1
0
1
2
1
0
2
1
0
0
2
0
0
1
1
0
1
2
1
0
1
1
2
1
1
1
1
1
1
0
1
1
1
0
0
0
1
1
1
2
0
1
1
1
2
1
1
1
2
2
2
1
1
2
1
0
1
1
2
2
2
0
1
0
1
1
1
1
1
2
1
2
2
1
1
2
1
1
1
1
2
1
1
1
1
0
2
1
1
0
0
1
0
1
1
1
2
2
1
0
3
1
2
1
1
1
1
2
1
1
1
0
2
1
1
2
1
0
0
0
1
1
1
1
2
1
2
2
1
2
2
1
1
3
1
1
1
1
0
1
1
0
2
1
0
0
1
2
1
1
1
1
1
2
1
2
0
0
2
0
2
1
1
2
1
0
1
1
0
1
1
1
1
1
1
1
2
2
1
1
1
1
0
1
2
1
1
1
2
1
2
1
2
3
2
1
1
1
1
1
2
1
2
1
1
1
2
1
2
1
1
1
0
1
1
0
2
1
0
1
0
1
1
1
1
1
2
0
2
1
2
2
1
1
1
1
1
2
2
0
1
1
1
0
1
0
1
1
1
1
2
2
2
1
0
2
1
1
2
2
1
1
0
1
1
0
1
0
1
2
1
1
1
1
0
0
1
2
1
1
1
2
1
0
0
1
1
1
2
2
1
1
1
2
0
1
1
1
1
1
1
1
2
0
1
1
0
0
2
1
1
1
2
1
0
2
1
1
2
1
2
2
0
1
1
1
1
0
2
0
1
1
1
1
0
2
0
2
0
2
1
1
1
0
1
1
1
1
1
1
1
2
1
1
1
1
2
2
2
1
1
2
1
1
1
1
0
0
1
1
1
0
2
2
0
1
1
1
0
1
0
2
1
1
0
1
1
0
0
1
0
2
0
1
0
1
3
2
1
1
2
1
1
2
1
0
1
0
0
1
2
0
1
2
1
3
0
1
1
2
1
1
2
4
2
1
1
1
1
1
1
1
2
1
2
1
0
0
2
1
1
1
1
0
1
2
1
1
1
2
2
0
0
0
1
2
1
1
1
1
2
1
0
1
1
1
1
1
0
1
1
1
2
1
1
1
1
2
1
2
2
1
0
2
0
1
1
1
1
0
0
1
1
0
2
1
2
1
1
1
0
2
2
1
0
0
1
1
0
1
1
0
0
2
1
1
2
1
1
1
1
0
1
1
2
1
1
0
2
1
1
1
1
1
1
1
1
0
1
2
2
2
1
1
2
1
2
1
1
1
1
1
1
1
0
1
1
1
2
1
1
1
1
1
1
2
1
1
0
1
2
1
1
1
1
2
1
1
0
2
2
1
1
1
2
0
1
1
1
1
2
1
1
1
1
3
1
1
2
1
0
1
1
1
0
2
0
1
2
1
1
1
1
2
1
1
1
0
2
1
0
2
1
0
2
1
1
1
1
1
0
1
2
1
1
1
2
0
0
2
1
1
1
1
2
2
0
1
2
2
2
1
2
1
2
1
2
1
2
0
1
2
1
1
1
1
2
1
2
1
1
1
1
2
1
1
1
2
2
2
1
2
1
1
2
2
0
0
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
0
2
0
2
1
2
2
0
1
2
1
2
0
2
1
1
2
2
1
1
1
1
1
1
1
1
1
0
1
1
1
0
1
1
1
2
1
2
0
0
1
2
1
1
2
0
0
1
1
0
2
1
1
1
0
1
1
1
1
0
0
1
1
0
1
1
1
1
1
1
0
0
2
1
1
0
0
2
0
1
1
1
2
0
0
2
1
0
1
1
2
1
2
2
1
1
2
1
0
1
0
1
1
2
1
1
2
2
1
1
1
0
1
0
2
2
2
0
1
1
2
1
1
2
1
1
0
0
1
1
0
0
0
2
1
2
1
0
0
1
1
2
1
1
1
0
2
2
2
1
1
2
1
0
2
2
2
0
2
1
2
1
1
1
1
1
0
1
0
2
2
2
1
2
1
0
1
2
1
1
0
2
0
1
0
1
1
2
0
1
1
2
1
0
2
0
2
0
1
1
1
1
2
2
0
1
1
0
1
2
1
1
0
1
2
1
0
1
1
1
2
1
2
0
1
1
2
1
1
1
2
1
1
0
0
1
2
1
2
1
2
1
1
2
1
1
1
1
0
1
1
0
2
2
1
1
0
1
1
2
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
0
2
1
0
1
1
0
2
1
1
0
1
1
1
2
1
2
1
1
2
0
2
1
1
0
0
1
2
2
2
1
1
2
1
1
1
2
0
0
0
1
1
1
1
1
0
3
1
1
1
1
2
1
0
1
1
0
2
1
2
2
0
2
1
1
0
1
1
1
1
0
1
0
1
0
1
1
2
1
1
1
1
2
1
1
1
2
0
0
0
1
1
2
2
1
0
0
0
1
1
1
0
2
1
2
1
0
1
1
2
1
1
2
0
0
2
2
1
1
1
1
0
1
2
1
0
2
1
1
1
2
0
1
0
1
2
2
0
1
1
2
2
1
1
1
1
1
1
0
0
1
1
0
1
1
2
1
2
1
1
0
1
1
0
1
1
1
1
2
1
1
1
4
1
1
1
0
1
1
1
1
1
1
0
0
0
2
1
1
1
0
1
1
0
2
2
1
1
0
2
1
0
1
1
1
0
1
1
2
1
1
2
1
2
1
2
1
0
1
1
1
1
0
1
2
1
2
0
0
1
1
1
1
2
1
1
1
0
1
2
0
2
1
1
1
1
3
1
1
1
1
0
0
1
0
2
0
0
2
2
2
1
1
1
1
1
1
2
2
2
2
1
1
2
1
0
2
1
1
1
1
0
1
2
2
1
1
0
1
1
1
0
1
1
0
2
1
1
2
0
2
0
2
1
1
1
2
1
1
0
0
4
1
1
2
1
0
0
1
2
1
1
1
1
0
2
2
1
0
0
2
1
1
0
1
2
1
0
1
1
1
1
0
0
2
2
1
1
2
1
0
1
0
2
0
0
2
2
1
0
0
0
1
1
1
1
1
0
0
1
1
2
1
2
2
1
1
2
1
1
2
1
1
2
1
1
0
1
1
1
0
1
0
1
2
1
1
2
1
2
0
2
1
2
1
0
2
0
0
1
1
0
1
1
1
2
1
1
1
1
1
0
2
1
2
2
1
2
2
2
0
1
2
1
1
1
0
1
1
1
1
1
2
0
1
2
1
0
1
1
2
1
0
1
0
2
1
0
0
1
1
1
1
0
1
2
1
1
1
1
1
0
2
1
1
1
1
1
0
0
0
2
1
1
2
1
2
2
2
1
1
0
0
1
2
0
1
1
0
1
2
1
1
1
0
2
1
1
1
1
1
0
1
1
1
1
1
1
2
2
0
1
1
0
2
1
0
1
1
1
1
2
1
0
1
2
1
2
1
1
2
1
1
1
1
1
1
1
0
0
1
1
1
1
1
0
0
2
1
3
1
0
1
1
1
2
2
2
1
1
1
1
1
0
1
1
1
1
1
1
2
1
1
1
1
1
2
1
2
1
1
1
0
0
2
1
0
1
1
2
1
1
0
0
1
0
1
1
2
0
1
1
0
0
1
1
1
2
0
1
1
2
2
1
2
2
0
2
2
1
3
0
2
0
0
1
2
2
0
2
1
2
1
0
1
1
1
2
1
0
1
0
1
0
2
2
1
0
1
1
1
1
1
1
2
1
1
0
1
1
2
1
2
2
2
2
0
0
1
2
2
1
0
2
1
1
1
1
2
2
0
1
2
2
1
1
2
2
1
1
1
1
0
2
1
0
1
1
1
1
2
1
1
1
1
1
1
0
1
1
0
1
1
1
0
1
1
1
1
1
1
1
3
3
1
2
2
0
1
0
2
2
2
1
1
1
1
0
1
0
2
1
2
1
0
1
1
1
1
2
2
1
2
1
1
0
2
1
1
2
1
1
2
1
0
1
1
0
0
2
0
1
2
1
0
1
3
1
2
1
1
1
2
1
0
1
1
1
1
1
2
2
1
0
0
1
1
1
0
1
3
1
1
1
1
2
1
0
1
0
0
1
0
1
1
2
1
1
1
0
0
0
0
1
1
1
1
2
0
2
1
0
1
1
2
2
1
2
1
1
0
2
2
2
2
2
2
2
2
1
1
2
2
1
0
0
0
1
2
2
1
1
1
1
1
1
2
2
2
2
2
2
1
2
1
2
1
0
0
1
1
0
1
0
1
1
1
0
1
1
1
1
0
1
1
1
0
1
1
1
1
1
1
2
1
2
0
1
1
1
1
1
1
1
1
3
1
1
0
1
1
1
0
2
1
2
1
0
2
1
0
2
2
1
0
2
1
1
1
3
1
2
1
1
1
1
1
1
1
1
0
1
1
1
0
1
1
0
1
1
1
1
1
1
1
0
1
1
1
1
1
0
1
1
1
1
0
1
0
2
1
1
2
2
1
1
1
1
2
0
1
1
0
2
0
0
1
1
6
0
1
2
0
1
2
1
2
1
1
1
2
1
1
0
2
0
1
1
1
1
1
1
1
0
2
0
2
1
1
1
1
2
2
1
2
1
2
2
2
2
1
1
1
2
1
0
1
1
0
1
1
1
1
2
2
1
0
1
0
1
1
1
2
1
0
1
0
1
1
0
1
2
0
1
0
0
1
1
2
2
0
1
0
1
1
1
2
0
1
2
2
0
1
1
2
1
1
1
1
1
2
1
1
1
0
0
2
1
1
1
1
2
2
1
1
0
2
0
0
1
1
1
2
0
0
0
1
1
1
0
1
2
1
1
0
1
1
1
1
2
1
2
0
0
1
0
1
1
2
2
3
1
2
1
1
1
1
0
0
1
2
2
2
1
1
0
1
1
1
0
0
0
2
1
0
0
2
1
1
0
0
1
2
1
0
1
1
0
2
0
0
2
0
1
2
1
1
1
2
2
1
1
1
1
1
1
2
2
2
1
1
0
1
1
1
2
0
0
2
0
0
1
0
1
0
0
2
1
2
1
0
1
1
1
1
1
2
1
0
2
1
2
1
1
1
2
1
0
0
1
1
1
1
2
1
1
2
1
1
0
1
1
1
0
1
1
3
1
3
1
2
1
0
2
1
0
0
2
2
2
1
1
1
1
1
1
1
1
1
0
1
1
1
2
1
1
1
0
0
1
1
1
0
0
1
1
1
3
2
2
1
1
2
1
1
0
1
1
1
1
1
0
2
0
1
1
1
1
1
1
1
0
2
0
1
0
1
2
1
1
0
1
0
1
0
2
1
1
1
2
0
1
2
2
2
1
1
1
1
0
1
0
1
1
2
1
2
1
2
2
2
1
1
1
1
1
1
0
1
1
2
1
2
0
1
1
2
0
0
1
0
3
2
1
1
0
0
1
2
0
0
1
1
0
2
1
0
2
0
1
0
2
1
1
1
1
0
0
0
0
1
1
3
0
1
1
1
1
0
1
1
0
2
1
2
0
1
1
1
1
0
2
1
2
1
0
1
1
2
1
0
1
1
1
1
2
0
1
0
1
1
0
1
0
0
1
0
0
1
2
1
1
1
0
1
1
2
2
1
1
1
1
2
2
0
1
1
0
0
1
0
1
1
2
1
2
0
1
1
1
0
1
1
2
1
1
1
1
1
0
1
2
1
1
1
1
2
2
1
1
2
1
0
1
1
1
1
1
1
2
2
1
1
0
2
0
1
0
2
2
3
1
1
1
1
1
1
2
1
0
1
2
1
1
1
4
1
1
1
1
1
2
1
1
2
1
0
1
1
0
2
1
1
2
2
1
2
1
1
1
2
2
1
1
1
1
0
1
0
2
2
2
1
1
2
0
2
0
1
1
0
1
2
1
2
1
1
1
1
2
1
1
1
0
1
1
1
2
0
1
1
1
1
0
1
2
0
2
1
0
1
2
2
2
2
1
1
0
2
0
2
1
1
1
0
0
2
0
0
1
1
1
2
1
1
1
1
1
0
1
0
1
2
1
1
1
0
2
1
1
1
2
1
1
1
1
1
2
1
1
0
1
1
1
2
1
1
2
1
1
2
2
1
1
1
1
1
2
2
1
1
2
0
1
0
1
0
0
1
0
1
1
1
0
1
0
1
0
0
1
0
1
1
1
1
0
0
2
2
1
0
0
0
1
1
0
2
2
0
0
1
1
1
0
0
0
1
2
2
2
1
1
2
0
2
0
1
1
0
1
0
2
1
1
1
0
1
1
1
2
1
1
1
1
1
2
1
2
1
3
1
1
0
1
2
0
1
4
1
1
1
0
0
2
1
1
0
1
1
1
2
1
1
1
2
2
1
1
2
1
1
1
2
2
0
1
1
1
1
1
0
1
1
2
1
1
1
1
1
2
0
1
1
1
1
2
1
1
1
0
2
1
1
0
0
1
1
1
1
1
1
0
2
1
1
0
0
1
1
0
1
1
1
1
1
1
1
0
1
2
1
1
1
2
1
1
2
1
2
1
2
1
0
1
1
1
2
3
0
0
2
0
0
1
2
1
1
0
2
0
1
1
1
0
2
1
2
1
2
2
1
2
2
0
1
2
1
0
0
1
1
0
2
0
2
1
1
1
1
1
1
2
1
1
1
2
2
1
2
2
1
1
1
1
1
0
2
3
0
2
1
1
1
1
0
1
0
2
1
1
2
1
1
1
1
1
1
1
1
1
0
2
1
0
1
0
0
2
1
1
0
1
1
1
1
0
2
1
1
1
0
1
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
2
0
1
1
1
1
1
1
2
0
1
0
0
0
2
1
2
1
1
1
1
1
1
1
1
1
1
2
2
0
0
0
2
1
1
1
2
0
1
1
0
2
2
0
1
1
2
1
2
1
2
2
2
1
2
0
2
0
2
0
0
0
1
1
2
2
0
2
1
2
1
1
2
1
1
2
1
1
1
1
1
1
1
1
2
0
1
1
0
1
2
0
1
1
2
2
0
1
2
1
2
1
1
1
1
1
1
1
1
0
2
1
1
1
0
0
1
0
2
1
2
1
1
1
0
1
0
2
1
2
0
2
1
1
1
2
2
1
1
1
1
0
2
1
0
2
1
1
1
0
1
1
0
1
2
0
1
1
1
0
1
1
1
1
1
2
0
1
1
1
1
1
0
2
2
1
1
1
1
0
2
2
2
2
1
1
0
2
2
1
1
1
0
2
2
2
1
2
2
1
1
1
1
1
0
1
1
1
1
0
2
1
1
2
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
0
2
1
1
2
1
1
1
1
0
1
1
1
1
2
1
0
2
0
1
1
2
1
1
0
1
0
1
1
1
0
1
1
1
1
1
2
1
1
0
0
0
1
0
0
0
0
2
1
2
0
1
1
1
0
2
1
1
2
2
1
1
2
0
1
0
1
1
1
1
0
2
1
1
0
1
2
1
1
1
2
1
1
1
1
1
1
2
1
2
1
2
1
1
0
1
0
1
1
0
1
0
0
1
0
0
0
1
1
1
1
0
1
0
1
0
0
1
1
1
2
1
2
1
2
1
1
1
0
2
2
1
1
1
2
1
1
0
1
1
0
0
2
1
1
2
2
1
1
0
2
2
1
0
1
1
1
1
1
0
1
0
1
1
2
1
1
1
1
0
1
0
2
0
1
2
2
0
0
1
1
1
1
2
2
0
1
0
1
2
1
1
1
2
1
1
0
2
2
0
1
1
1
2
1
1
0
0
1
1
1
1
1
1
2
0
1
0
0
1
2
0
0
0
0
2
2
1
1
0
1
2
1
1
1
0
1
0
1
1
1
2
0
2
1
2
2
1
1
1
2
2
1
1
2
1
1
0
1
0
2
1
1
2
1
2
1
2
0
1
0
1
1
1
0
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
2
1
2
1
1
1
1
3
2
1
1
1
0
2
0
1
0
2
1
0
2
2
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
1
1
0
2
2
1
1
1
2
2
1
1
1
0
0
1
1
2
1
1
0
2
1
1
1
2
0
2
1
0
0
2
1
0
1
1
1
1
1
1
1
1
1
1
0
2
1
1
0
1
2
1
1
1
2
1
1
0
1
2
1
0
0
1
1
1
1
1
0
0
1
0
1
1
1
0
1
1
0
1
2
1
2
1
2
1
0
2
0
1
1
1
2
4
2
1
2
2
2
1
1
1
2
1
0
1
1
2
0
2
0
1
0
1
0
1
1
1
1
2
1
0
2
1
1
2
1
1
0
1
0
1
0
1
2
1
1
0
1
1
0
2
0
1
1
1
2
1
1
0
2
0
0
3
1
1
1
2
0
0
1
1
2
1
0
0
1
1
1
0
0
2
1
1
2
1
2
1
1
0
1
1
1
2
1
1
2
0
1
1
0
2
1
1
2
0
1
1
2
0
0
1
0
1
2
1
1
1
1
2
0
2
1
1
1
1
1
1
0
1
1
1
0
0
1
1
2
1
2
2
1
0
1
1
2
1
1
1
0
1
1
1
0
1
1
1
1
1
1
1
0
2
1
1
0
0
2
1
0
1
1
1
1
1
0
1
1
0
2
1
1
2
2
1
2
1
1
1
1
2
1
2
1
0
1
0
1
1
2
1
1
1
1
0
2
2
0
1
1
2
0
2
2
0
1
2
0
1
2
2
3
1
2
1
1
2
1
1
1
2
0
0
0
1
1
1
1
1
1
1
1
0
1
1
1
0
0
2
2
0
1
1
1
1
1
1
2
1
1
2
1
2
2
1
1
2
1
1
1
2
1
0
2
0
1
1
1
1
2
2
1
2
2
1
1
2
1
1
1
1
5
1
1
1
0
1
2
1
1
1
1
1
0
0
1
1
0
1
1
1
2
1
1
1
2
1
2
1
1
1
2
0
2
1
0
1
1
1
0
1
0
1
2
0
2
1
1
2
1
1
1
1
1
0
1
1
2
2
0
0
2
0
1
0
1
1
1
0
2
0
0
5
1
1
2
1
2
3
2
1
0
0
1
1
1
1
1
1
0
1
1
2
0
1
1
1
1
1
1
3
0
1
1
1
0
0
2
2
2
2
1
0
0
1
1
1
1
2
1
2
2
0
1
2
1
1
1
2
2
1
1
2
0
2
2
3
0
1
2
1
1
2
0
1
0
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
0
0
1
1
1
0
1
1
1
1
0
0
1
0
0
1
1
1
1
2
1
0
2
1
2
1
1
1
1
2
1
1
0
0
1
1
2
1
1
1
0
0
2
2
1
1
1
1
1
1
0
1
1
1
1
1
2
2
1
1
2
1
0
1
0
1
2
2
1
1
1
2
0
1
1
1
2
1
1
1
0
1
2
2
2
1
1
1
1
1
2
2
1
1
1
2
1
0
0
0
1
1
1
0
1
1
0
2
1
1
1
2
1
1
0
1
0
0
1
1
1
1
1
1
1
1
1
1
2
0
2
0
0
1
2
0
1
1
1
0
0
1
1
0
1
1
0
1
1
0
0
1
3
1
1
1
1
1
1
1
1
1
1
1
0
2
0
0
1
2
1
1
1
2
0
1
2
2
1
2
1
1
1
3
3
1
1
1
0
1
1
1
1
0
1
0
2
1
2
1
1
0
1
0
0
1
2
1
1
1
1
1
1
0
0
2
1
2
1
2
2
2
1
2
2
2
1
1
0
1
1
2
2
0
1
1
1
1
1
2
0
1
1
1
0
1
0
0
1
1
1
1
2
1
1
1
1
0
1
1
1
1
1
1
1
0
1
1
1
1
0
3
1
1
1
1
0
1
1
1
1
0
1
0
1
2
1
1
1
1
0
1
0
1
1
1
0
1
1
2
0
1
1
1
1
1
0
2
0
1
1
1
1
1
1
0
0
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
7
0
2
2
2
2
1
1
1
1
1
0
0
3
2
1
1
0
0
1
2
1
1
1
1
1
0
1
2
2
2
1
1
1
1
2
1
1
1
1
1
1
1
2
0
2
1
2
1
1
1
1
0
1
2
0
1
0
1
1
1
1
1
2
2
2
1
1
0
2
1
0
2
1
1
6
2
1
1
1
1
1
1
1
2
1
2
1
1
1
0
1
2
2
0
0
0
0
1
1
2
2
0
2
1
1
1
1
1
1
1
0
1
2
1
1
1
2
1
2
0
1
1
1
2
1
1
1
1
0
12
0
1
0
1
1
1
1
1
1
2
1
2
0
1
2
1
1
1
0
1
0
1
2
1
1
2
2
1
1
1
1
1
1
1
2
1
0
1
1
0
2
0
2
1
2
1
1
2
2
1
2
2
0
2
2
2
0
0
2
1
2
1
0
2
0
1
1
1
1
1
2
1
2
1
1
0
1
2
1
1
1
1
2
1
1
2
1
0
1
0
1
1
2
0
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
2
0
1
1
0
2
1
2
1
0
2
1
1
2
1
0
2
1
0
1
1
1
1
1
1
2
0
2
2
1
1
2
2
1
1
1
1
2
1
1
2
1
1
2
2
1
1
1
1
1
1
1
1
1
2
2
0
0
1
1
2
0
2
1
0
2
0
0
1
1
1
1
1
1
0
1
1
1
1
0
1
0
2
1
1
2
1
2
2
1
1
1
1
1
2
1
0
2
1
2
2
0
2
1
2
1
1
1
1
2
1
3
0
0
2
3
1
3
0
1
1
0
1
1
1
0
1
2
1
1
0
1
1
0
2
2
2
1
0
1
1
1
1
1
1
1
2
1
1
1
2
2
1
2
4
1
0
1
1
1
2
1
1
1
1
1
1
1
1
1
1
3
2
0
1
1
1
0
2
2
1
1
1
3
0
1
2
1
1
1
2
1
0
2
1
1
1
2
1
1
0
2
2
1
1
2
1
1
1
0
1
1
1
0
1
1
0
2
1
0
0
1
0
1
1
1
1
0
2
1
2
0
2
1
0
2
1
0
1
2
1
1
1
1
1
1
2
1
2
1
0
1
1
2
1
1
0
1
0
0
1
1
1
1
2
1
2
1
2
1
0
0
1
1
2
1
0
2
1
2
1
1
0
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
1
1
2
1
1
1
2
2
2
1
1
1
0
1
1
1
1
3
3
1
1
1
1
0
0
0
1
1
2
1
1
1
1
1
2
1
1
1
0
2
1
1
1
2
3
1
2
2
0
1
3
0
0
0
1
1
1
0
0
1
1
2
0
1
1
1
0
1
0
0
0
1
2
2
1
1
0
0
1
2
0
1
1
0
1
1
0
1
1
0
2
1
1
1
1
1
1
0
1
1
2
1
1
1
1
0
0
1
1
2
2
1
1
1
1
1
0
0
1
1
1
1
2
1
1
0
1
1
1
1
1
1
1
1
0
1
2
1
1
1
2
1
3
1
1
1
1
2
1
1
1
1
1
1
2
2
1
1
2
0
0
2
2
1
2
1
1
0
1
0
1
0
1
0
1
1
2
1
0
1
0
2
1
2
1
1
1
1
1
1
2
0
1
1
1
1
0
1
1
0
0
1
0
2
2
1
0
0
1
0
1
1
1
2
2
1
1
1
0
1
1
0
0
1
1
0
1
0
0
1
2
1
1
0
2
0
1
1
2
1
1
0
2
1
1
2
2
2
1
0
1
1
1
1
0
2
2
1
0
2
0
1
1
2
1
2
2
0
2
1
2
2
0
1
1
1
1
1
1
0
0
1
1
0
0
2
1
1
1
0
0
1
1
2
1
1
1
1
1
2
1
0
2
1
1
2
1
1
2
2
1
1
1
1
1
1
0
0
1
2
2
1
0
1
2
1
2
1
1
1
2
1
2
1
1
2
1
1
2
1
1
0
0
1
1
1
1
0
1
1
1
1
2
0
2
1
1
1
1
2
0
2
0
1
2
1
1
2
1
1
2
0
1
1
2
1
1
1
1
0
1
1
2
1
1
1
2
0
1
2
0
1
1
1
1
1
0
2
1
1
2
1
1
1
1
2
0
1
1
1
0
1
2
1
1
2
2
1
0
1
2
1
0
0
1
1
1
0
1
1
1
1
1
1
0
1
2
1
1
1
1
1
1
2
1
1
0
1
0
1
1
2
2
0
1
2
1
1
2
2
2
1
1
1
0
2
1
2
1
2
1
1
1
0
2
0
1
1
2
1
2
1
1
2
0
2
0
1
1
3
1
1
1
1
1
2
0
1
1
1
2
2
2
0
0
1
1
1
1
1
2
2
1
1
1
0
1
2
1
1
2
0
0
2
1
1
2
1
1
0
0
0
1
1
2
1
0
1
1
0
0
1
0
1
1
0
1
1
1
2
1
1
1
1
1
1
1
0
2
1
2
1
1
1
1
0
0
0
1
2
1
0
2
2
1
1
2
1
2
2
1
2
1
2
1
1
1
0
1
1
2
1
1
0
1
1
2
1
0
2
1
0
1
2
1
2
2
0
1
0
2
1
1
1
1
0
2
0
0
1
1
1
1
1
2
1
2
1
1
2
1
2
1
1
1
1
0
1
1
1
1
2
1
1
1
1
1
1
1
1
0
2
2
1
1
2
2
0
2
1
1
2
1
3
1
1
1
0
2
1
1
0
0
0
1
2
1
2
1
1
0
1
1
1
1
1
0
1
1
0
1
1
2
1
1
0
0
1
1
0
0
1
1
1
1
2
0
1
0
1
1
1
1
1
1
1
1
1
2
1
0
0
2
1
1
0
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
2
0
2
2
2
1
1
1
1
1
1
1
2
1
1
0
1
2
0
1
2
1
1
2
1
1
2
1
1
1
1
1
2
1
2
2
2
2
2
2
1
0
2
1
2
2
2
2
2
1
2
0
2
2
0
1
3
1
1
1
0
1
0
1
1
1
0
1
1
2
1
0
1
1
1
1
1
2
0
2
1
1
1
1
0
1
1
1
0
1
1
1
0
0
0
1
1
1
1
1
0
2
1
2
2
1
1
0
1
1
1
1
2
2
1
1
0
2
3
2
2
0
1
2
0
2
1
1
1
0
1
1
1
1
1
0
1
2
1
1
2
0
0
0
1
2
0
0
0
1
2
2
1
0
1
1
1
1
1
1
0
2
0
1
2
2
1
1
2
1
1
0
0
1
1
1
1
1
1
0
1
2
0
0
1
1
2
0
1
2
1
0
1
1
1
2
1
1
2
1
1
0
0
1
2
0
1
0
1
1
1
1
3
1
1
2
2
2
1
1
1
1
1
1
1
0
0
2
1
1
0
1
1
1
1
1
1
1
1
3
1
1
1
1
1
5
2
1
1
1
2
1
0
1
1
1
1
1
1
1
0
0
1
0
1
0
0
1
1
1
2
0
2
1
2
0
1
3
2
2
2
0
1
1
1
0
1
1
2
1
1
1
2
1
1
1
1
2
0
2
0
2
2
2
2
2
1
1
1
2
1
1
2
1
1
1
1
1
0
1
2
1
1
0
1
1
2
2
0
2
0
1
1
1
1
0
0
1
1
2
0
2
1
1
1
1
1
2
1
1
2
1
0
1
2
1
0
1
0
1
1
0
1
1
1
1
0
1
1
0
2
1
1
1
1
0
0
0
1
2
1
1
1
3
2
1
2
2
1
1
0
2
2
2
1
1
2
1
1
2
1
1
1
2
1
2
1
0
1
1
1
1
4
1
0
1
1
1
1
2
2
3
2
2
0
1
2
2
2
2
2
2
1
2
1
1
1
0
2
1
1
1
1
0
2
1
2
0
1
1
3
1
1
1
1
1
1
1
1
1
1
1
0
1
0
0
0
2
2
2
2
0
0
0
1
4
3
1
1
0
2
1
1
2
2
1
2
0
0
1
2
0
1
2
1
1
2
0
1
0
1
1
1
1
2
1
1
1
1
2
1
2
1
0
2
1
1
1
1
1
2
1
1
1
1
0
0
1
1
1
1
0
1
1
1
1
2
0
0
2
2
2
1
2
1
0
2
1
1
2
0
2
0
1
0
2
1
0
2
0
2
2
1
2
1
1
1
0
1
1
1
1
2
1
1
2
1
3
0
0
1
2
2
0
1
0
1
2
2
1
1
1
1
2
1
1
1
0
1
2
1
0
2
1
1
1
1
1
1
2
0
1
1
1
2
0
3
1
2
2
1
1
1
1
1
2
2
2
2
1
1
2
2
2
2
1
0
2
1
1
0
1
2
0
0
0
1
1
1
0
0
2
1
2
1
1
1
1
1
0
0
1
0
1
0
1
0
1
0
2
1
4
0
0
1
2
2
1
2
1
0
1
1
0
0
2
1
1
1
1
1
1
2
1
0
1
0
0
0
2
1
1
0
1
2
2
2
1
2
0
0
2
2
2
0
1
2
2
1
2
1
2
0
0
0
1
1
2
1
1
0
0
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
0
2
1
1
1
1
2
0
1
1
1
1
1
2
1
1
1
0
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
2
2
0
0
1
1
1
1
1
0
2
1
1
2
0
0
2
1
1
2
1
1
1
2
0
2
1
2
2
2
2
0
1
1
2
1
1
1
0
1
1
1
0
0
1
1
1
0
1
1
1
2
1
1
1
2
1
1
1
1
2
1
0
2
1
1
2
1
0
1
2
1
0
2
1
2
0
2
2
0
1
2
0
1
1
0
1
0
0
1
1
2
0
1
1
1
1
4
1
1
2
1
2
2
2
1
0
0
1
1
1
1
2
1
0
0
0
2
0
2
0
1
1
2
0
0
1
1
0
1
0
1
1
2
1
0
1
1
0
1
1
2
1
0
2
1
0
1
0
0
1
0
1
2
0
1
1
1
2
1
1
1
2
0
1
2
0
1
1
1
1
0
2
1
1
1
1
3
1
0
2
1
2
1
1
1
0
1
1
1
1
0
1
1
2
1
0
1
1
1
1
1
1
1
0
0
2
2
2
1
0
0
1
3
1
1
1
2
1
1
0
2
0
1
1
1
1
1
1
1
0
2
2
1
1
2
1
0
1
1
1
1
1
1
2
2
1
1
1
1
1
2
0
1
0
0
2
1
1
1
1
1
2
1
1
2
1
2
1
0
3
1
2
1
1
1
0
1
1
1
2
1
1
2
1
1
1
0
0
0
1
1
1
2
1
1
1
1
1
1
1
1
2
0
1
1
1
1
2
2
1
1
0
1
1
1
2
1
1
1
2
0
1
1
0
0
0
2
1
1
1
1
2
1
1
0
1
1
2
0
1
0
2
0
2
2
1
0
1
0
1
1
2
1
0
2
2
0
1
1
2
2
0
0
1
1
2
2
1
1
0
2
1
1
1
1
0
1
2
1
2
2
1
1
1
0
2
1
2
2
1
1
2
1
1
0
1
1
0
0
1
0
1
1
2
1
1
1
1
1
1
0
1
1
1
2
1
0
1
0
0
1
1
1
1
1
1
1
1
0
1
2
0
1
1
1
2
1
1
2
0
1
2
0
0
2
1
1
1
1
1
1
0
0
0
0
1
2
0
2
3
1
0
0
1
2
1
1
2
0
1
2
1
1
1
2
1
1
1
0
1
2
0
0
1
0
1
0
2
1
1
0
1
3
1
0
1
3
1
0
1
2
1
1
1
1
1
1
0
1
1
1
1
0
2
1
1
2
1
2
1
2
0
0
1
2
2
1
1
1
1
1
1
1
0
1
1
1
1
1
0
0
1
0
0
3
0
1
0
1
1
2
1
2
1
1
1
2
2
2
1
1
2
0
1
1
2
1
0
1
1
1
1
1
1
1
2
2
1
2
1
1
0
0
2
2
1
2
1
1
1
2
1
2
1
1
0
1
1
2
1
1
1
0
1
1
1
1
2
2
2
1
0
1
1
1
1
1
2
1
1
1
1
0
1
1
1
0
1
1
1
1
1
2
2
3
2
1
1
1
1
1
1
1
2
2
1
1
1
1
0
1
2
2
0
2
0
1
1
0
2
2
1
1
1
2
1
2
2
2
1
1
2
1
1
0
1
0
0
1
1
1
1
1
1
1
0
2
0
1
1
1
0
2
1
0
1
0
1
0
2
2
1
1
0
2
1
1
1
0
1
1
1
1
0
2
1
1
2
2
1
2
2
1
2
0
0
0
2
1
1
1
2
0
0
1
1
2
1
2
1
3
1
0
0
2
1
2
2
1
1
1
1
1
2
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
2
1
1
0
1
1
2
1
1
2
1
1
1
2
1
2
2
1
1
1
1
2
1
0
1
2
1
1
1
1
2
1
0
1
2
0
0
1
1
0
0
2
2
0
0
2
0
0
0
1
1
1
2
1
1
0
1
0
1
1
2
1
1
0
1
1
1
2
0
2
1
1
0
1
0
1
0
1
1
0
2
2
1
1
1
1
2
1
1
0
1
1
1
1
1
1
0
1
1
0
2
1
1
2
1
0
0
1
1
2
1
0
1
2
1
1
1
1
2
1
1
2
1
2
3
1
2
3
2
2
1
1
1
1
1
1
2
0
0
1
1
1
1
1
1
1
1
1
2
2
0
0
1
1
1
1
1
0
2
1
1
1
1
1
1
0
1
1
1
2
0
0
1
1
2
0
0
1
1
1
1
2
1
1
1
2
1
1
1
0
0
1
0
0
1
1
1
1
1
0
1
0
1
1
1
2
1
1
2
2
2
1
0
1
2
2
1
0
1
0
1
1
1
2
1
1
1
2
2
1
1
0
0
1
1
1
0
2
0
0
1
1
1
0
1
3
2
1
1
1
1
1
0
0
1
1
4
1
2
1
1
1
1
0
1
1
1
1
5
0
3
1
1
1
0
2
2
2
2
1
2
1
2
0
2
2
1
1
1
2
1
1
2
1
1
0
0
1
2
1
1
1
2
2
1
0
0
1
2
0
1
2
0
1
0
1
2
1
1
0
1
2
1
2
1
0
0
2
1
1
1
1
1
1
0
1
1
1
1
1
1
1
2
0
1
1
1
1
1
1
2
0
1
1
2
1
0
1
0
2
2
1
1
1
0
1
1
1
6
1
1
0
1
0
1
1
0
1
1
2
2
2
2
1
1
1
2
1
1
1
0
1
1
0
1
1
1
1
0
1
1
0
2
2
0
1
0
1
1
0
0
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
0
0
1
2
1
1
1
1
0
1
1
1
1
2
0
1
2
1
2
0
2
1
1
1
2
0
1
1
1
1
0
1
1
1
0
2
1
0
1
0
1
1
1
1
1
1
2
1
1
2
1
0
0
0
1
1
2
0
2
3
1
1
1
0
1
2
0
1
1
2
1
2
0
1
1
1
2
0
1
1
1
0
0
1
0
1
0
1
0
1
0
1
1
1
2
1
1
1
2
0
1
1
1
1
1
0
1
2
1
2
2
1
0
1
1
2
0
1
1
2
1
1
2
0
0
2
1
1
1
2
1
1
1
1
0
1
1
1
2
1
2
2
1
0
1
0
0
1
0
2
1
0
1
1
1
1
1
2
1
2
1
1
1
1
0
1
1
2
1
1
2
1
1
2
2
2
2
1
1
0
2
0
2
0
1
1
1
1
1
1
6
0
2
1
1
1
1
0
0
2
0
1
1
1
0
0
2
1
1
0
1
1
2
1
1
1
1
0
2
2
1
1
0
1
2
2
0
1
1
1
1
2
1
0
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
0
0
2
2
2
2
0
2
0
1
1
1
1
0
1
2
1
1
1
2
1
1
2
1
2
1
1
1
2
0
2
1
0
2
1
0
0
0
1
0
1
1
1
0
1
1
1
1
3
0
2
1
1
1
2
1
0
1
1
1
1
1
1
0
1
1
0
1
1
1
1
1
1
1
0
1
1
0
1
2
2
2
0
1
2
1
1
0
1
2
0
1
0
1
2
1
1
1
2
2
1
1
1
0
2
1
0
1
1
1
1
1
2
2
0
2
2
0
2
0
1
0
1
1
1
2
1
2
2
1
1
1
0
1
2
2
1
3
1
1
1
0
1
0
2
1
1
1
1
0
1
1
1
1
2
1
2
1
1
1
1
1
1
2
1
2
0
0
0
1
1
1
0
2
1
1
1
0
0
1
1
1
1
1
2
1
1
0
1
1
1
0
1
1
2
1
0
2
1
1
1
1
1
1
1
0
0
0
1
1
1
2
1
0
0
2
2
1
1
2
1
2
1
1
2
1
2
2
1
1
0
1
1
2
1
1
2
1
1
1
1
2
2
2
1
1
2
1
2
0
2
1
0
2
0
1
0
1
1
2
1
0
1
0
0
2
1
0
2
1
0
1
1
1
1
0
0
2
1
1
1
2
2
1
0
1
1
0
1
2
0
2
2
1
2
1
1
1
2
2
0
0
1
1
2
0
1
2
1
0
1
1
1
1
1
1
1
2
1
2
1
2
1
0
1
0
1
0
2
1
1
0
0
1
0
1
1
0
1
1
1
0
1
2
2
1
1
0
1
1
1
1
1
1
1
0
1
1
2
2
1
1
1
1
1
2
1
1
0
1
0
1
1
4
2
1
1
0
0
0
1
2
1
2
1
3
1
2
2
1
1
0
1
0
2
1
2
1
1
1
2
0
1
1
1
0
5
0
0
1
2
1
1
0
1
0
1
1
1
1
0
1
1
1
2
1
1
2
2
1
0
1
1
1
1
1
1
0
0
0
0
2
1
2
0
2
1
0
1
1
1
1
0
1
2
1
0
0
1
1
2
1
1
1
0
1
1
1
1
1
0
2
1
0
1
1
1
0
2
3
1
2
2
2
1
1
1
1
1
2
2
1
0
2
0
1
0
1
1
1
2
1
1
1
0
1
1
2
0
2
0
1
0
1
1
0
1
1
0
0
1
1
1
1
1
1
2
0
1
0
1
1
1
1
0
1
0
1
2
1
1
1
0
1
1
2
1
2
1
0
0
0
2
1
1
1
0
2
2
1
2
4
2
1
2
1
1
1
0
1
0
0
1
1
2
1
1
0
1
1
1
1
0
1
1
0
0
1
1
1
1
1
2
2
1
0
2
0
1
1
2
0
1
2
1
1
1
1
1
1
1
1
1
0
1
1
2
0
0
1
1
2
1
1
1
0
1
0
2
2
0
2
0
1
1
1
1
1
2
2
1
2
1
1
2
0
0
1
2
1
2
1
0
1
1
1
1
1
0
1
1
1
0
1
2
1
1
0
0
1
1
1
0
1
1
2
1
0
0
2
1
1
2
1
2
1
2
1
2
1
3
1
1
1
1
1
1
0
2
1
1
1
0
6
1
1
1
0
1
1
0
1
2
1
1
1
1
0
1
0
0
0
2
2
0
1
1
1
2
0
0
1
1
2
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
0
1
1
2
1
1
0
1
0
1
0
1
1
1
0
1
1
0
1
1
1
1
1
0
1
1
1
2
0
2
1
0
1
0
1
0
2
1
0
1
0
2
1
1
1
2
1
1
1
2
1
1
0
0
0
2
0
2
2
1
2
1
2
1
1
1
2
0
2
1
1
2
1
1
0
2
1
1
2
1
1
1
1
2
1
1
1
1
1
2
1
0
1
2
2
1
1
1
1
2
1
1
1
0
1
2
0
1
0
1
1
0
3
1
1
1
1
1
2
1
0
2
1
2
0
2
1
0
2
1
1
1
1
2
1
0
1
2
1
0
1
1
1
1
1
1
2
2
0
1
1
0
0
1
2
1
1
1
2
2
1
1
1
1
1
2
2
1
1
0
0
2
1
2
2
1
1
1
1
1
1
1
0
1
2
1
0
1
1
0
1
2
0
1
0
1
1
1
1
2
1
1
1
1
1
1
0
2
1
2
1
1
1
1
1
0
1
1
1
1
0
1
1
0
2
2
1
2
1
0
1
2
1
2
0
1
1
2
2
1
1
2
1
1
1
2
1
1
0
1
0
1
1
0
1
0
1
1
1
1
1
1
2
1
1
2
1
2
1
2
1
0
1
1
1
2
1
1
0
2
1
1
2
1
1
0
0
1
1
1
1
1
0
0
2
2
1
1
1
1
1
1
4
1
2
0
1
2
2
1
1
1
1
1
0
1
2
1
1
1
2
0
1
1
2
0
0
1
0
0
1
1
1
1
1
2
1
1
1
2
2
0
1
2
2
1
1
1
0
2
2
1
1
2
1
0
0
1
1
0
1
1
2
1
1
2
2
1
1
0
1
1
2
1
1
1
1
2
1
1
1
2
0
1
0
2
0
1
1
2
1
2
1
1
1
1
1
0
1
2
0
1
0
1
1
2
2
1
0
1
0
2
2
0
1
0
2
0
1
2
0
0
1
1
1
2
2
1
1
1
2
1
0
1
1
0
2
0
2
1
2
1
1
1
1
1
2
1
1
2
1
0
0
2
0
1
1
0
2
1
1
0
1
1
0
1
2
0
1
0
2
1
0
0
1
1
2
0
1
0
1
0
1
2
2
0
0
2
4
1
1
0
2
1
2
1
1
1
2
1
1
1
2
1
0
1
0
0
1
0
1
2
1
1
1
0
1
0
1
1
1
2
0
1
0
1
0
1
2
2
1
2
2
1
1
1
1
1
0
1
1
0
1
1
0
2
1
1
1
0
1
0
1
1
1
0
0
1
1
1
1
0
2
1
1
1
1
0
0
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
0
2
1
1
2
1
2
2
1
1
2
1
1
1
1
1
0
1
0
0
1
1
1
1
1
1
3
0
1
0
1
1
0
1
1
2
1
1
0
1
1
0
0
1
1
2
1
1
1
0
0
0
1
0
1
1
1
1
1
1
1
2
0
1
2
2
1
2
2
1
1
0
1
1
2
1
1
1
0
0
0
6
1
2
1
1
1
0
2
2
1
1
0
1
2
1
1
1
0
1
1
1
1
1
1
1
0
1
1
1
1
1
1
2
1
0
2
1
1
1
1
1
2
1
1
3
1
1
0
1
1
4
2
0
2
1
2
1
1
2
1
1
0
1
2
2
1
1
0
1
1
1
1
1
2
1
1
2
1
1
1
1
2
1
1
1
1
0
1
1
0
2
0
1
1
0
0
1
1
1
1
1
2
2
2
1
1
1
1
0
1
0
1
1
1
1
0
1
1
1
1
0
1
1
0
1
1
0
1
1
2
1
2
0
2
2
1
1
2
0
0
2
1
1
1
2
1
2
0
2
2
1
0
1
1
0
2
2
0
0
0
1
1
2
1
0
2
1
0
2
0
1
1
1
2
0
0
1
1
1
1
1
1
0
1
2
2
1
2
2
1
1
1
1
2
1
1
1
1
1
1
1
2
0
1
0
1
1
2
1
1
1
2
1
2
2
1
1
0
2
1
2
0
0
0
1
1
1
0
1
2
2
2
2
1
1
0
1
1
1
1
1
0
2
1
2
1
1
1
1
0
0
2
1
1
1
1
2
2
2
1
1
0
2
2
1
2
0
1
0
2
1
1
0
0
2
1
1
1
1
1
1
1
1
1
2
1
0
2
1
1
1
1
1
0
2
1
2
1
2
1
1
1
2
2
0
7
1
1
2
1
1
0
0
1
1
0
1
1
1
2
1
2
1
2
0
1
1
1
0
1
1
0
1
0
1
1
2
1
1
0
2
0
1
2
1
1
2
1
2
1
0
2
0
1
1
1
0
1
1
1
0
1
0
1
1
1
2
2
1
1
2
2
1
0
1
1
1
1
1
0
1
1
0
0
1
1
1
1
1
0
1
2
0
1
2
1
1
1
2
0
0
0
1
1
1
1
1
1
0
1
1
1
1
2
2
0
1
2
1
1
2
2
2
1
1
0
2
2
1
0
1
0
0
2
0
1
2
1
1
1
1
1
2
1
0
1
1
0
1
2
2
1
2
1
1
0
2
1
1
2
1
2
0
2
2
2
1
1
0
2
1
1
1
0
0
2
2
0
2
2
1
1
1
1
1
1
1
2
1
0
1
1
0
1
1
0
1
1
2
1
0
1
1
1
2
0
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
0
2
1
2
1
0
0
2
2
2
0
2
1
2
1
1
1
1
1
1
1
1
0
0
2
1
1
1
1
1
0
2
0
1
1
1
0
1
2
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
0
1
2
2
0
2
0
1
2
1
1
2
0
0
2
2
0
1
1
0
1
0
2
0
1
2
1
0
2
2
2
0
1
2
0
0
1
1
0
2
1
0
2
1
2
2
1
1
1
1
0
1
0
2
1
2
2
1
1
4
1
1
1
0
1
1
0
1
1
2
0
1
1
1
2
1
0
0
1
1
2
1
0
1
1
1
0
5
1
1
2
1
2
1
1
0
1
2
2
2
1
1
1
0
0
1
1
0
2
1
2
1
0
2
1
1
0
1
1
1
2
1
0
1
1
1
1
0
1
2
1
0
1
2
0
2
1
0
0
2
0
1
2
1
1
2
0
1
0
2
1
1
0
1
1
2
1
1
1
2
1
1
1
1
1
2
0
1
1
1
1
1
2
1
2
1
0
0
1
2
1
2
1
2
1
1
0
1
2
1
0
1
1
1
1
2
2
1
1
2
0
2
1
0
1
2
0
2
2
2
0
1
1
0
1
1
2
1
2
1
1
2
1
1
2
1
0
1
2
0
0
2
1
2
0
1
1
1
1
1
2
1
0
2
0
2
1
1
2
1
0
2
2
1
1
0
2
0
2
1
3
1
0
2
1
1
1
2
2
0
0
2
1
2
0
2
1
2
1
0
1
2
1
1
1
2
1
1
1
1
1
2
1
1
0
0
2
0
2
0
2
1
1
2
2
1
1
1
1
1
2
2
0
0
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
1
1
0
1
1
1
1
1
1
1
1
0
2
1
1
0
1
2
1
1
2
1
0
1
0
0
1
0
1
1
2
2
1
1
1
1
1
0
0
1
0
2
1
1
1
1
1
0
0
1
1
2
2
1
2
1
1
1
1
2
1
0
0
1
1
0
1
1
1
0
2
1
2
3
1
0
2
2
2
1
2
1
1
2
0
1
1
1
0
1
1
1
1
2
1
1
1
2
1
0
1
2
1
2
1
2
0
1
1
1
1
1
1
2
1
2
2
1
1
2
0
1
1
1
2
1
1
0
1
0
1
1
1
1
0
2
1
0
0
1
0
2
0
2
2
0
1
1
4
0
1
1
1
1
1
0
1
0
2
1
1
0
2
0
0
1
0
1
1
2
1
0
0
1
2
2
1
1
1
1
0
1
0
2
1
1
1
3
1
1
1
2
1
0
1
1
1
1
1
2
1
2
1
0
1
1
1
1
2
2
1
0
2
1
0
1
0
2
1
0
1
1
2
1
1
0
0
2
2
2
1
0
1
2
2
2
1
0
2
1
1
1
1
0
2
1
0
2
1
1
2
1
0
1
1
2
0
0
0
1
0
1
1
1
1
0
2
1
1
2
1
0
2
2
0
0
0
1
0
1
1
2
1
1
2
1
3
1
0
0
1
2
2
1
2
1
1
1
1
0
1
1
1
1
0
1
1
1
1
0
1
1
0
1
1
1
0
1
1
1
0
1
0
2
0
0
1
2
1
1
1
2
2
2
1
0
4
1
2
0
0
1
0
1
2
1
1
1
2
2
0
3
1
1
1
0
1
2
0
0
1
1
2
2
2
1
2
1
2
1
1
0
1
0
1
1
1
1
1
1
1
1
0
1
1
0
1
1
1
1
0
2
0
1
2
1
2
1
1
2
0
0
0
1
1
0
3
1
3
1
4
2
1
2
1
0
1
0
1
2
0
2
1
1
2
0
1
0
0
1
0
2
1
0
1
1
1
1
1
1
1
1
0
0
2
2
1
1
1
3
1
0
2
1
1
1
2
2
1
0
1
1
2
1
2
1
1
1
2
2
2
1
0
0
1
1
2
1
1
0
2
2
2
0
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
0
3
1
1
1
2
0
2
1
0
2
1
1
1
2
1
0
0
0
1
1
0
1
1
1
1
1
2
1
2
1
0
0
2
1
1
1
1
0
1
1
0
2
1
0
0
2
1
2
1
1
2
0
2
0
1
2
2
2
1
1
0
2
1
1
2
1
1
0
2
2
1
1
1
1
1
1
0
1
0
2
2
2
3
1
1
1
0
2
1
1
1
1
1
1
1
0
2
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
2
2
0
1
0
1
1
1
2
1
1
0
1
1
2
0
0
2
1
1
1
1
1
2
1
1
1
2
0
1
2
2
1
0
2
1
1
1
2
0
1
0
1
1
1
1
2
1
0
1
1
0
1
2
1
1
0
1
1
2
2
1
1
2
0
2
1
1
2
0
1
2
1
1
1
1
1
1
0
1
1
0
0
1
1
1
1
1
1
1
2
1
1
1
1
0
2
2
2
2
2
1
2
1
1
1
0
1
1
1
1
1
0
1
2
1
2
1
1
2
2
1
0
1
2
1
1
2
1
1
1
2
2
2
1
1
2
1
1
1
1
1
1
0
1
1
1
0
0
2
0
2
1
2
0
1
1
2
1
2
1
1
0
2
2
0
1
1
1
0
1
1
1
1
1
1
0
0
1
1
1
2
1
1
1
0
1
1
0
1
2
2
1
1
2
1
1
0
1
0
1
0
1
1
0
1
2
2
2
0
1
1
0
2
2
1
1
1
0
1
2
1
2
1
2
1
1
1
1
2
0
1
0
1
1
2
1
1
0
1
0
1
1
1
2
2
4
2
0
1
1
1
1
2
1
2
0
2
1
1
1
1
1
2
1
1
0
1
0
2
0
1
1
2
2
0
0
4
2
4
1
2
1
2
2
0
1
0
1
1
1
1
1
1
2
1
1
0
2
2
0
1
0
1
2
2
2
2
1
1
1
1
0
2
1
0
1
1
2
1
2
1
2
1
1
1
0
1
2
1
1
0
1
2
0
0
0
2
1
1
1
1
1
0
3
1
0
1
1
1
1
2
2
1
2
1
1
1
0
1
1
0
0
1
1
0
1
2
1
1
1
0
1
1
1
1
0
0
2
1
1
1
2
2
0
1
1
1
0
1
0
2
2
2
1
0
0
1
1
1
0
1
1
1
1
1
3
1
1
1
1
1
1
2
2
1
0
0
1
1
1
2
1
2
2
1
1
1
1
2
1
2
1
0
1
1
1
1
2
1
1
0
0
0
1
1
1
0
1
0
0
1
0
1
1
1
1
1
2
2
1
2
1
2
1
1
1
0
1
1
2
2
2
2
1
1
1
2
1
0
2
1
2
1
0
1
1
0
0
1
0
2
1
0
2
2
1
1
1
1
2
1
2
0
1
1
1
2
1
1
1
2
0
0
1
1
1
0
0
1
0
2
1
1
1
1
0
0
1
1
1
0
1
1
1
2
0
2
1
1
2
1
1
1
1
0
0
0
1
1
3
1
2
0
0
1
1
1
1
0
0
1
1
0
1
1
2
1
2
2
2
0
2
2
1
1
2
0
1
2
2
1
1
1
1
1
1
2
1
0
1
1
2
1
1
2
1
1
1
1
1
2
2
1
1
2
2
1
0
2
1
1
2
1
1
1
1
1
2
2
1
1
1
1
0
1
1
2
2
1
1
0
1
1
1
1
1
3
2
1
1
2
1
0
1
1
0
2
1
1
1
1
0
1
1
0
0
1
2
0
1
2
1
0
1
2
1
1
0
2
2
1
1
2
1
1
2
1
1
1
0
1
1
0
0
2
1
0
1
1
1
1
2
0
0
0
1
1
1
1
1
2
1
0
0
1
1
2
1
1
0
0
1
1
1
1
1
2
1
1
2
1
2
2
2
1
1
1
1
2
0
0
1
1
2
2
2
0
1
0
0
1
1
1
1
2
1
1
2
1
1
1
2
1
1
1
1
1
0
0
1
1
0
0
2
2
2
0
2
2
1
1
2
0
2
1
1
1
1
0
1
1
1
0
0
1
2
1
2
1
1
1
1
2
0
1
1
2
1
1
0
1
1
1
1
1
1
1
1
1
1
2
1
0
0
1
1
1
1
2
1
2
1
1
2
2
0
2
1
2
1
2
2
0
2
0
0
0
1
2
1
1
0
1
1
1
1
0
1
2
1
1
0
1
1
1
0
0
1
1
0
1
0
0
1
1
2
1
1
0
0
1
2
1
0
2
1
0
0
2
0
2
2
0
1
1
1
0
1
0
1
1
2
0
1
0
0
1
2
1
2
0
0
1
1
1
1
2
1
1
0
1
2
1
2
2
0
1
3
0
1
2
1
2
1
1
0
1
2
0
1
3
0
2
1
0
0
1
0
1
2
1
1
0
2
1
2
2
1
1
1
1
1
1
2
1
1
0
0
0
0
2
1
0
1
2
1
1
2
1
1
1
2
0
1
0
1
1
1
0
1
1
1
0
1
1
1
1
0
2
1
1
0
1
0
1
2
0
2
0
1
1
1
2
1
1
1
1
1
2
0
0
2
0
1
2
0
1
1
0
1
2
0
1
1
2
1
0
1
0
2
1
2
1
1
1
1
0
2
1
1
2
1
1
1
2
1
2
1
2
2
0
1
2
2
0
1
0
1
2
1
1
0
2
2
1
0
1
1
1
1
2
1
1
1
1
0
0
2
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
0
1
0
1
1
1
1
1
1
1
2
0
2
2
1
1
0
1
0
0
0
3
1
1
1
0
1
1
2
1
0
1
1
1
1
2
1
1
0
1
0
1
1
1
0
1
3
0
1
1
1
2
1
1
0
1
2
1
0
0
2
1
1
1
0
0
2
1
1
0
2
1
1
2
0
2
1
2
1
1
0
1
1
1
0
1
0
0
1
1
1
2
2
1
0
0
1
1
1
1
0
0
3
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
0
0
1
1
2
0
1
2
2
0
1
1
1
0
1
2
2
1
1
1
1
1
1
1
0
1
1
1
2
1
0
2
1
1
1
1
2
2
1
1
1
2
1
1
1
1
1
0
1
1
1
1
1
1
1
0
1
1
1
1
2
2
1
2
1
1
1
1
0
1
0
1
1
1
1
2
1
2
2
1
1
4
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
0
0
2
0
1
1
0
3
1
0
2
4
1
1
1
2
2
0
2
1
1
0
1
1
1
1
2
1
1
0
1
1
1
2
2
1
1
2
0
0
1
1
1
1
1
1
2
0
3
1
2
2
1
1
1
0
1
1
1
1
2
1
2
1
2
0
1
1
1
2
1
1
2
1
0
0
1
0
1
2
1
1
1
1
0
1
1
1
2
2
1
0
1
2
1
2
2
0
1
1
1
2
0
2
2
0
1
0
1
1
1
1
1
1
1
2
1
1
2
0
0
1
1
1
0
0
0
2
0
0
1
2
1
1
1
1
0
0
1
1
1
1
1
2
1
2
2
2
2
3
0
0
1
1
2
1
0
1
1
2
2
1
1
1
0
1
2
1
1
2
1
2
1
1
2
1
1
1
1
0
0
1
1
1
1
2
1
2
0
2
2
1
1
2
2
0
2
2
2
2
1
1
1
1
1
2
1
1
0
0
2
2
1
1
1
1
0
1
1
1
0
1
2
1
2
2
2
1
1
2
1
2
1
0
1
3
1
2
1
1
0
2
3
2
1
2
1
2
1
1
1
1
1
1
0
1
2
1
1
1
1
1
1
1
1
2
2
0
1
1
1
1
1
1
1
2
1
0
1
2
0
1
1
1
1
1
1
1
1
1
2
1
0
2
1
1
0
1
1
2
0
1
2
0
1
1
3
2
1
1
0
1
0
2
1
0
1
1
1
2
2
1
1
2
1
1
3
0
1
0
1
1
2
1
1
2
1
1
2
0
0
1
0
0
0
2
1
2
0
2
0
1
2
2
1
1
0
1
1
0
1
1
1
0
1
1
0
0
1
0
1
1
2
1
0
1
1
1
1
2
0
1
1
0
1
1
2
2
0
1
1
1
1
1
0
0
2
1
1
1
1
1
2
2
1
1
1
2
1
0
1
1
1
1
0
2
2
1
0
2
1
2
1
0
1
1
0
2
0
1
1
1
1
1
1
1
1
0
2
1
1
1
1
1
1
1
2
1
0
1
1
1
1
1
3
0
0
1
1
1
1
0
1
1
1
1
1
1
1
1
2
0
0
2
1
0
0
1
2
1
1
1
1
1
0
2
0
0
0
1
2
2
0
0
1
1
1
1
1
1
2
1
1
2
1
0
3
2
1
1
1
1
1
0
1
1
1
0
2
0
1
2
1
1
1
1
1
0
2
2
2
2
1
2
2
1
0
2
2
1
1
1
0
1
2
1
1
2
1
1
1
1
2
1
0
1
1
1
0
1
0
1
2
2
0
0
1
2
0
1
1
0
0
0
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
0
1
0
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
0
1
1
0
1
2
1
1
1
2
1
0
1
2
2
2
0
2
2
2
1
1
1
1
1
1
2
1
1
1
0
0
0
1
1
2
1
0
0
0
1
1
2
1
1
1
1
0
2
2
1
2
2
2
1
1
2
1
0
0
0
1
0
2
1
0
2
2
2
1
1
1
1
0
2
2
1
1
1
1
0
0
1
2
2
1
2
0
1
1
1
2
1
2
2
1
0
2
0
2
2
0
1
1
2
2
2
0
1
0
1
1
2
1
1
1
2
1
0
2
1
2
1
2
2
1
2
1
1
2
1
2
1
2
1
1
2
1
1
1
2
0
1
1
2
0
2
1
0
0
2
1
2
1
2
1
1
0
1
1
2
2
2
2
1
2
1
0
1
0
1
1
1
0
1
1
1
1
1
1
1
1
2
1
0
1
1
2
1
1
0
1
1
1
0
0
2
1
0
2
0
1
0
1
1
1
0
1
1
0
1
1
2
1
1
1
2
1
1
2
2
1
2
1
1
0
1
4
1
2
2
2
0
2
1
2
0
0
0
1
0
2
2
2
1
2
1
0
1
2
0
1
2
1
1
1
0
1
2
2
2
1
2
1
0
1
1
1
2
0
2
1
1
1
1
2
0
1
2
0
2
1
2
1
1
1
1
1
6
2
0
0
1
1
2
1
0
0
0
0
1
0
2
1
2
1
0
1
1
1
1
1
1
1
1
0
1
0
1
2
0
0
1
2
0
0
1
0
1
1
2
0
1
2
1
1
1
1
0
1
2
2
0
1
1
1
1
1
1
0
0
1
2
0
0
2
1
1
0
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
2
1
0
2
1
1
2
1
1
0
2
1
1
2
2
0
1
1
2
0
2
0
1
1
1
1
1
2
1
0
0
1
1
1
2
0
1
1
1
1
3
0
1
0
1
0
1
1
1
1
1
1
1
2
1
2
1
2
1
1
0
1
0
0
0
0
1
0
2
1
2
1
2
0
1
1
1
0
1
0
1
2
3
0
2
0
0
1
1
1
0
1
0
0
1
1
1
0
0
1
0
0
0
1
0
1
1
0
0
1
1
0
2
2
1
2
2
2
1
1
1
2
0
1
1
2
0
2
1
1
1
2
1
0
1
1
2
0
0
2
1
1
1
1
0
1
1
1
1
3
1
2
1
1
1
0
0
0
1
0
2
2
1
2
0
0
0
1
2
0
1
1
1
1
0
2
1
2
1
2
1
1
1
1
0
1
2
1
1
1
1
2
2
1
0
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
3
2
2
0
0
2
2
1
1
0
2
0
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
0
2
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
2
1
1
0
1
3
2
1
0
2
2
1
1
1
0
0
1
2
1
0
2
1
1
1
4
0
0
1
1
1
1
1
1
2
1
1
1
1
0
1
2
1
1
0
0
1
1
2
0
2
1
1
2
1
1
1
1
2
1
1
2
1
2
1
2
2
2
1
1
0
1
2
0
1
1
1
1
1
1
2
1
1
1
1
1
0
4
0
0
1
0
1
0
1
2
2
1
1
1
1
2
1
1
1
0
0
1
1
2
2
2
0
1
1
0
1
1
1
1
0
1
2
1
1
0
1
0
1
3
0
2
2
1
1
0
2
0
0
2
2
1
1
0
1
1
1
1
0
0
0
2
0
1
2
1
1
1
1
1
2
1
1
1
1
0
1
1
1
2
1
1
1
1
0
1
2
1
1
0
1
1
0
1
0
1
2
2
0
1
1
2
1
1
0
2
1
0
0
0
1
2
2
1
2
1
2
0
1
1
0
0
1
1
2
1
1
0
1
2
2
1
1
2
1
1
1
1
1
2
0
1
1
2
2
1
1
1
1
1
2
0
1
2
1
0
2
1
1
1
1
2
1
1
1
1
2
1
2
1
2
1
1
0
1
0
1
1
0
1
0
2
1
2
1
1
2
1
1
1
2
1
2
1
1
1
1
2
1
2
1
1
1
0
1
1
2
1
2
1
1
0
1
1
2
1
2
1
1
1
2
1
1
1
1
2
2
1
2
0
0
1
1
1
2
2
1
1
1
0
1
0
1
1
2
2
1
1
2
1
1
0
1
1
2
1
2
1
1
1
1
2
1
2
1
0
0
0
0
1
1
1
2
1
0
1
1
2
1
1
1
1
2
2
1
0
0
0
1
0
1
1
1
1
1
0
1
1
2
1
1
1
0
1
2
1
0
1
0
1
0
0
2
2
1
2
0
1
1
1
1
0
2
1
0
1
1
1
1
1
2
2
1
2
2
1
1
0
1
2
0
0
1
1
0
2
0
1
2
1
1
1
1
0
1
1
2
2
1
2
1
1
0
0
1
2
1
1
1
1
1
1
1
1
0
1
1
1
0
0
0
1
0
1
1
1
1
0
1
2
1
1
2
1
0
3
1
2
1
2
1
0
2
2
1
0
0
0
0
0
0
0
1
1
1
2
0
1
0
1
2
1
0
2
0
1
1
1
3
1
1
1
1
1
1
1
1
1
1
0
1
0
1
2
2
2
2
0
2
1
1
1
0
1
1
0
0
2
0
2
0
1
1
1
2
1
1
0
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
2
0
1
1
0
1
2
1
0
2
0
1
2
1
0
1
1
1
1
1
0
2
1
1
1
0
2
1
1
2
2
0
1
2
1
1
1
1
2
2
1
2
0
1
1
2
2
2
1
1
2
2
1
1
2
1
1
2
1
1
0
1
1
1
2
2
0
0
2
2
0
2
1
1
1
1
1
1
2
1
1
1
1
1
2
2
1
2
2
1
1
0
1
1
2
1
1
1
1
0
1
1
1
0
0
1
1
1
1
0
1
0
1
1
1
1
1
1
2
0
1
0
2
1
1
2
1
1
1
1
1
2
2
1
1
1
1
0
1
1
1
1
2
1
1
2
0
0
1
0
1
3
1
0
1
1
1
0
1
0
0
1
2
2
1
0
0
0
2
1
1
1
1
1
1
0
0
1
2
1
1
1
1
1
0
2
0
0
1
1
0
0
1
2
0
2
1
1
0
1
0
2
1
1
1
2
1
2
1
1
1
1
2
2
1
0
1
0
1
1
1
1
0
2
0
2
2
1
2
1
1
2
1
0
2
1
0
1
1
0
2
1
0
1
1
1
1
1
2
1
0
1
1
1
2
2
0
2
1
1
1
1
0
2
1
2
2
1
1
2
0
1
1
1
1
1
1
1
1
2
1
0
2
0
2
0
1
1
3
1
1
0
1
1
1
1
1
1
0
1
0
2
2
2
2
2
1
1
0
0
1
2
1
1
1
0
2
0
1
2
1
1
1
1
1
1
1
1
1
1
1
1
0
0
1
1
1
1
1
1
1
2
0
1
1
1
1
0
1
1
1
1
1
1
1
0
2
1
1
2
1
1
1
2
1
1
1
2
1
1
0
1
0
0
2
1
1
1
2
1
0
2
0
1
0
2
1
1
0
1
2
0
1
1
1
1
1
0
1
1
1
2
1
0
2
1
1
1
1
1
1
0
1
0
0
1
1
1
1
2
2
1
1
0
1
1
2
1
1
1
1
0
1
1
1
0
0
1
2
1
2
1
2
2
1
1
1
0
1
1
0
2
1
1
1
2
1
1
1
1
1
1
1
2
1
2
0
0
1
1
1
0
1
1
1
1
0
1
2
0
1
1
1
2
1
0
0
1
0
2
0
1
1
1
1
1
1
1
0
1
1
0
1
2
1
1
1
1
1
1
1
2
0
2
2
2
1
1
0
1
1
1
1
1
2
1
1
1
1
1
0
1
2
1
2
0
2
0
1
1
1
0
1
0
1
2
0
1
0
1
1
1
0
1
1
1
0
1
1
1
1
1
2
1
0
1
1
2
2
1
1
0
1
1
1
2
1
2
2
1
1
0
1
0
2
1
1
1
1
2
2
2
0
1
2
0
1
2
1
1
0
1
1
1
1
1
0
1
1
1
1
2
2
2
1
1
0
1
1
2
1
1
2
1
1
0
1
1
1
2
0
2
2
1
0
1
1
1
1
1
1
2
1
0
2
2
1
1
1
1
2
1
2
1
0
1
0
2
1
1
1
1
1
1
2
2
1
2
1
1
0
2
1
1
1
1
1
0
1
1
1
1
1
2
1
1
0
1
1
2
2
1
0
1
0
1
2
1
1
1
1
2
2
2
1
1
1
1
1
1
0
1
0
1
0
1
1
1
0
1
1
1
2
0
1
0
2
1
1
1
1
1
1
2
1
1
1
1
1
0
1
1
1
1
0
2
1
0
2
1
1
0
1
2
1
1
1
0
2
2
1
1
1
2
1
1
1
0
2
1
1
0
0
0
2
3
2
0
0
1
1
0
2
2
1
1
1
1
2
1
2
1
0
2
0
3
1
2
2
1
1
0
1
0
1
1
2
1
1
1
1
1
1
2
1
2
1
1
2
1
1
0
0
1
1
2
1
0
1
1
1
1
1
1
0
1
2
1
3
0
1
2
0
0
1
1
1
0
1
1
1
2
1
1
2
2
1
1
1
1
1
0
0
0
1
1
1
2
1
1
2
1
1
0
0
2
2
2
2
1
1
1
0
2
0
1
2
2
2
1
1
2
1
2
1
2
1
0
1
1
2
1
1
1
1
1
0
1
1
0
0
2
2
1
2
1
0
1
3
1
2
2
1
1
1
1
2
0
2
1
1
1
1
0
2
0
1
2
2
1
1
1
2
0
1
0
1
1
0
1
1
0
0
2
1
0
1
0
1
1
1
1
1
2
1
2
1
1
0
1
1
1
2
1
0
1
1
1
0
0
1
1
2
0
2
1
1
1
1
2
1
1
1
2
1
1
0
5
0
2
1
1
0
1
0
2
0
0
1
1
1
1
1
2
1
0
2
1
2
2
1
2
1
1
1
1
1
2
1
2
1
1
1
2
1
2
0
1
0
1
1
1
1
2
2
0
1
0
2
1
2
1
1
1
1
1
1
1
1
1
0
2
1
1
2
1
1
1
0
2
0
1
1
0
1
2
1
1
1
2
2
1
1
0
2
1
1
0
1
1
1
2
2
0
1
1
1
1
2
1
0
1
1
1
1
0
1
0
1
2
1
0
1
2
1
1
2
1
1
1
2
2
1
0
1
1
1
3
0
0
1
1
2
1
2
4
1
2
0
2
1
1
1
1
1
2
2
2
1
1
0
2
1
1
1
2
0
0
1
2
1
1
1
2
1
1
1
2
0
0
1
1
1
1
1
1
0
1
1
2
2
0
2
1
2
0
0
0
2
0
0
1
2
0
1
1
1
0
1
1
1
2
2
1
1
1
1
0
1
2
1
1
1
1
1
0
2
1
1
0
0
0
2
0
1
1
2
1
2
2
2
2
1
2
1
1
0
1
1
1
2
1
1
1
1
1
2
2
1
1
1
1
1
0
1
1
0
1
1
2
1
0
1
0
2
1
0
1
1
1
2
1
1
1
2
1
2
0
1
0
0
1
1
2
2
0
0
2
1
2
1
2
0
1
1
1
1
2
1
1
1
1
1
1
2
2
2
2
2
1
1
1
0
1
1
1
1
0
1
2
1
1
2
1
1
1
0
0
2
0
0
1
1
1
2
1
1
1
1
1
0
2
1
1
2
1
0
2
0
2
2
0
0
0
0
1
1
1
1
2
1
1
1
1
2
0
2
2
0
2
2
0
1
2
1
1
1
2
1
0
1
1
1
1
0
0
1
2
1
1
2
1
1
0
1
1
1
1
1
0
1
0
1
1
2
1
1
1
1
1
0
2
1
0
1
2
1
1
1
1
1
2
1
1
2
0
1
1
1
1
0
2
1
0
0
1
1
1
1
1
1
1
2
2
1
1
0
0
2
1
1
2
2
1
2
2
1
1
1
2
1
1
0
1
1
2
2
1
1
1
1
1
1
1
0
1
1
0
4
0
2
1
2
1
1
1
2
1
1
1
2
1
1
1
2
1
1
2
1
0
1
2
1
0
0
1
1
1
0
0
1
0
0
1
1
1
1
2
1
1
1
0
1
1
1
0
3
1
1
0
1
1
1
1
1
2
1
1
1
2
4
1
1
0
1
1
0
1
0
0
3
1
1
1
2
1
2
2
2
1
1
1
1
1
1
2
1
2
2
1
2
0
2
1
1
0
1
3
0
2
2
1
1
2
1
0
1
1
1
1
1
1
2
1
1
0
1
0
2
0
0
1
1
1
1
1
0
0
1
2
0
1
1
0
1
0
1
1
2
0
3
1
1
2
0
1
0
1
2
2
1
0
0
0
2
2
1
2
1
0
1
2
1
1
2
0
1
2
3
0
1
2
1
1
1
2
1
2
1
0
0
1
1
1
1
0
1
2
0
1
1
1
1
0
1
0
1
1
1
1
1
0
1
1
1
0
2
1
1
1
1
1
0
1
2
2
1
0
1
1
1
2
2
0
1
2
1
2
0
1
2
1
1
1
1
2
1
1
0
0
1
1
1
0
1
0
1
0
0
0
1
1
2
1
0
1
1
1
2
1
1
1
1
0
0
0
1
2
1
0
2
1
1
1
1
2
1
1
1
2
1
1
1
1
0
2
1
2
1
1
0
0
1
1
1
0
1
1
2
2
1
1
2
1
1
1
0
1
1
1
0
1
2
1
0
2
2
0
1
1
2
2
0
2
1
1
0
0
1
1
1
1
1
2
1
1
1
1
1
1
1
2
0
1
1
2
1
1
1
1
1
2
0
1
1
1
2
1
2
4
1
0
0
1
1
1
1
1
1
0
0
1
0
1
0
1
0
0
1
1
1
0
1
1
0
1
2
0
0
2
0
0
1
2
2
1
1
1
1
1
1
2
2
2
2
1
2
0
0
1
1
0
1
1
1
0
2
1
0
0
1
1
1
2
1
1
1
0
1
1
2
0
1
1
2
1
1
1
1
1
1
1
0
1
1
0
0
1
1
1
1
2
1
0
2
1
2
1
1
2
0
0
2
1
1
1
1
1
1
1
2
1
0
1
1
1
1
2
1
1
1
2
0
1
1
2
1
2
1
2
1
1
0
0
1
1
0
1
1
1
1
2
1
0
4
1
1
1
1
1
1
1
1
1
2
1
2
0
1
1
1
0
1
1
1
1
1
0
1
1
1
2
2
1
1
1
2
1
1
0
1
3
1
0
2
1
2
1
1
1
1
0
0
1
2
1
1
2
1
0
1
1
2
1
2
1
1
1
1
0
0
1
1
2
1
1
1
2
1
1
2
1
0
0
2
2
1
0
1
2
1
0
0
1
0
2
1
1
0
1
2
0
1
2
2
1
0
1
0
1
1
2
1
0
2
2
1
0
1
2
2
2
2
1
2
1
1
1
1
1
1
1
2
1
1
0
1
1
2
2
1
2
1
1
0
1
0
1
1
1
1
1
1
1
1
1
2
1
0
1
2
2
2
1
1
1
1
1
0
1
1
1
2
1
1
1
1
0
0
1
1
2
2
1
1
1
1
3
1
0
0
0
1
2
1
2
2
0
1
0
1
1
2
0
1
1
1
1
0
2
1
1
1
1
1
2
1
1
0
1
2
1
1
1
0
1
0
1
1
0
2
0
2
1
1
2
1
1
2
1
0
2
1
2
0
2
1
0
1
1
1
1
1
1
1
2
2
2
1
2
1
1
0
1
0
1
1
1
3
2
0
1
1
1
2
1
1
0
2
1
0
1
0
2
1
1
0
2
1
2
2
1
2
2
1
1
1
2
0
1
0
0
2
0
1
1
2
1
1
0
1
0
1
2
1
0
2
1
0
2
1
2
2
0
1
0
1
1
1
1
1
1
1
2
0
1
1
2
0
1
1
0
2
1
0
1
1
1
1
2
1
1
2
0
0
1
1
1
1
1
1
1
2
2
1
2
2
2
2
0
1
1
1
1
1
1
1
1
0
2
1
1
2
1
1
0
0
1
1
1
1
1
1
1
3
3
1
1
1
1
0
1
1
1
0
1
2
2
2
2
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
0
1
1
0
0
1
1
1
1
1
2
1
1
1
1
1
2
0
0
2
1
2
1
2
2
0
1
2
2
1
0
1
1
2
2
2
1
0
1
0
0
1
1
2
0
0
1
2
1
2
1
0
1
1
1
2
2
1
0
0
1
0
1
1
1
1
1
1
1
1
2
1
2
0
1
1
1
1
1
0
0
0
2
2
1
1
1
0
1
1
1
2
0
0
1
0
1
1
1
1
1
1
0
0
1
2
3
0
1
0
1
1
1
1
1
1
1
1
2
2
1
2
1
1
0
1
2
2
0
2
1
0
2
0
1
1
1
1
2
1
1
1
0
1
1
1
2
1
1
1
1
0
1
1
1
1
1
0
2
2
0
0
1
0
2
0
0
0
1
2
3
0
2
2
1
1
1
1
2
2
1
0
1
0
0
0
2
2
1
2
1
1
0
1
2
0
1
0
1
2
0
0
2
2
1
1
1
2
1
1
1
0
0
1
1
1
2
1
1
2
0
1
1
2
2
0
2
1
2
0
1
0
0
0
1
1
1
1
1
1
1
0
3
1
1
1
0
2
2
1
2
0
1
0
1
1
1
0
1
1
1
0
2
1
0
0
0
1
1
1
1
2
1
1
2
0
2
1
1
1
2
2
0
2
2
1
2
1
2
0
2
0
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
0
1
1
1
0
2
1
0
1
1
1
1
1
1
0
0
1
1
1
2
0
0
0
2
2
2
1
0
2
1
2
1
1
1
1
0
2
0
1
1
2
1
2
1
1
1
1
2
2
1
2
0
2
1
0
0
2
1
2
2
2
2
1
1
1
0
1
3
1
0
0
2
1
1
0
0
0
2
1
1
1
1
1
2
2
0
2
0
0
0
2
2
1
2
2
2
2
2
0
2
1
2
1
1
1
1
0
0
0
2
1
2
1
2
1
1
1
1
1
1
1
1
1
0
1
1
0
1
1
1
1
1
0
1
4
1
2
1
0
1
1
1
0
1
1
2
0
2
2
1
2
1
1
2
1
1
0
1
1
2
0
0
0
1
1
1
1
0
0
3
1
2
1
0
1
1
0
1
1
1
1
1
1
1
1
2
2
1
1
1
0
1
0
1
2
0
1
1
1
1
1
2
1
1
1
1
1
0
1
0
0
1
1
1
1
2
2
2
2
2
0
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
2
2
2
3
1
2
0
1
5
1
2
1
1
0
1
2
0
1
1
2
2
0
1
0
2
2
1
0
1
1
1
1
2
1
2
1
2
1
2
1
1
0
1
1
1
0
1
1
1
1
1
1
2
2
1
0
1
0
0
0
1
2
1
0
2
1
1
0
1
2
1
1
0
1
1
0
1
2
1
0
0
1
1
1
0
0
0
2
1
0
1
2
1
2
1
2
1
1
0
2
1
2
2
1
1
2
1
1
1
2
1
1
2
1
1
2
2
2
2
2
1
2
1
3
1
1
1
1
0
2
2
0
1
1
1
1
2
1
2
0
2
1
1
1
1
2
1
1
1
1
1
0
2
3
1
1
2
1
1
1
2
0
2
2
1
1
2
1
1
2
0
2
1
0
1
1
1
0
1
0
1
2
1
1
2
1
1
1
1
1
1
1
3
1
2
2
1
1
2
1
0
2
1
1
0
0
1
1
0
1
1
1
1
2
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
0
1
1
1
1
1
0
0
2
1
1
1
2
2
1
3
2
0
2
1
1
1
0
1
2
0
1
1
0
1
1
1
0
1
1
1
1
1
0
1
2
1
1
1
2
1
1
1
2
1
1
1
0
0
1
0
0
2
1
2
2
2
1
1
2
0
0
0
2
2
1
2
2
1
1
1
0
2
1
2
1
1
1
1
2
2
1
1
0
1
1
1
2
2
1
3
2
2
0
0
1
1
0
2
0
0
2
1
0
1
0
1
1
0
1
2
0
1
1
1
1
2
0
1
1
0
1
0
2
0
1
0
0
2
2
1
1
2
1
1
1
1
1
0
1
0
0
2
1
0
1
1
0
1
1
1
2
1
2
0
1
1
0
2
1
1
1
1
2
2
1
2
1
2
0
1
1
0
1
1
1
1
1
0
2
1
0
1
0
1
1
0
0
0
1
0
1
1
0
1
1
1
1
1
1
1
2
0
1
1
1
0
0
1
2
1
1
1
1
2
2
1
0
0
1
2
1
0
1
0
2
1
2
1
1
1
1
3
1
1
2
2
2
1
1
0
1
1
1
2
2
2
2
0
2
0
1
1
1
1
0
1
1
1
1
1
2
1
1
2
1
2
0
2
1
1
1
0
2
2
1
1
0
1
1
1
0
1
2
0
2
1
2
0
0
0
1
0
1
1
1
1
1
1
1
0
0
1
0
1
1
2
1
1
2
2
0
0
0
1
1
2
1
2
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
2
0
2
2
1
0
1
0
1
1
0
1
2
1
1
1
1
1
1
1
0
1
0
1
1
0
2
1
2
1
1
0
2
0
1
1
1
0
1
1
1
1
0
2
1
2
2
0
1
2
0
2
0
2
1
1
2
2
1
1
0
1
1
2
2
2
0
0
1
1
1
1
0
1
1
2
0
0
1
2
0
1
1
0
1
2
0
1
1
1
1
0
1
1
1
1
1
1
1
2
1
1
1
1
1
2
0
1
1
1
1
1
1
1
0
1
1
1
1
2
2
2
0
1
0
2
2
2
1
1
1
2
0
1
1
2
3
1
1
1
1
0
0
0
1
1
1
1
2
0
0
1
1
2
4
1
1
1
0
1
0
2
2
0
2
1
0
1
1
1
1
1
1
0
2
1
2
2
2
0
1
1
1
2
0
1
1
0
1
1
1
1
0
1
1
1
1
1
1
0
2
2
1
1
1
1
0
1
1
0
1
1
1
2
1
2
1
1
0
1
1
0
1
0
1
1
1
0
2
0
1
2
1
1
2
1
1
0
0
0
0
2
2
1
1
1
2
0
1
2
1
1
0
1
2
1
0
2
1
2
0
1
1
1
0
1
1
0
1
1
2
1
0
2
0
2
2
1
1
1
1
1
2
0
1
1
0
1
1
1
0
2
0
1
1
1
0
1
0
2
1
0
2
0
1
2
1
2
1
1
1
0
0
1
2
1
2
1
2
1
0
0
1
0
1
2
1
1
2
2
1
1
0
0
1
1
1
1
1
1
1
1
2
1
1
1
0
1
1
0
1
1
1
2
1
1
2
2
0
1
1
0
0
2
1
1
1
0
1
1
1
2
0
0
1
1
1
1
0
1
0
1
2
0
2
1
2
1
0
0
1
1
1
2
0
1
0
0
1
1
2
0
0
1
1
1
1
2
2
0
2
1
1
0
1
1
0
2
2
1
1
2
1
1
0
1
0
2
1
1
0
2
1
1
1
1
2
2
1
0
2
2
1
0
1
0
1
2
1
1
1
2
0
1
1
0
2
0
0
0
1
1
0
1
0
1
1
2
0
1
1
1
2
0
2
1
1
2
2
1
1
1
1
1
0
0
1
0
1
1
1
1
0
0
1
1
1
1
1
1
1
0
1
1
1
1
0
1
1
0
1
0
1
1
0
1
1
1
2
1
2
1
1
1
2
2
1
1
1
2
0
1
1
1
2
1
1
1
1
0
0
1
0
2
2
1
1
2
1
1
1
1
0
1
1
1
1
2
0
1
0
1
1
1
1
2
2
1
1
0
1
2
1
1
0
1
2
1
1
2
1
1
1
1
2
2
2
1
1
1
1
0
1
0
2
1
0
1
1
1
1
0
2
2
1
1
2
1
1
2
1
1
1
1
1
0
1
0
2
1
1
1
1
1
1
1
1
0
1
0
0
1
1
2
0
1
1
1
0
1
2
1
1
2
2
0
1
1
1
1
0
2
1
1
0
1
2
1
1
2
1
2
1
1
1
2
1
1
1
1
2
1
2
1
1
1
2
1
0
1
1
1
2
1
0
1
1
0
1
1
1
1
1
2
1
1
1
1
2
2
0
0
0
1
2
1
1
1
1
1
2
1
1
1
1
0
1
1
1
1
2
1
1
0
1
2
1
1
1
0
1
0
1
0
1
2
0
2
2
1
0
0
1
1
0
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
0
2
0
1
2
1
1
1
2
1
1
2
1
2
1
1
1
0
2
1
2
1
1
2
1
1
0
1
1
2
0
1
0
1
1
2
1
1
1
2
1
0
1
1
2
1
2
1
3
1
1
1
2
0
1
1
1
1
1
2
1
0
2
2
0
1
1
1
2
3
0
1
1
1
1
2
1
1
2
0
0
2
1
0
0
0
0
1
0
0
2
1
1
1
2
2
1
1
1
1
1
1
0
1
2
1
1
1
1
1
1
1
0
0
1
0
1
0
1
1
1
1
1
0
1
4
2
2
1
2
1
1
2
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
2
1
1
0
0
2
2
1
1
0
1
0
1
1
1
0
0
1
0
0
1
0
1
1
1
2
1
0
1
1
2
1
2
2
1
1
1
0
0
2
1
2
1
0
1
0
2
1
0
1
1
2
3
1
1
1
2
1
1
1
2
1
0
1
0
0
0
0
1
1
0
2
1
2
2
0
1
2
2
1
1
1
1
0
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
0
1
2
1
2
1
1
1
1
1
2
1
1
2
2
0
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
0
1
1
1
1
1
1
1
2
1
2
1
0
0
1
1
1
0
2
1
1
2
2
1
1
0
2
1
2
1
1
2
2
1
1
1
1
2
1
2
2
1
1
1
0
1
1
1
1
0
2
0
1
2
0
1
1
2
1
1
1
2
0
1
1
2
0
3
2
1
1
1
1
0
2
1
2
0
1
0
1
2
0
0
1
1
0
1
0
2
1
2
1
1
1
0
2
2
0
1
1
1
2
2
0
1
1
1
1
1
1
1
2
1
2
1
2
1
1
2
0
0
1
1
0
1
1
1
1
1
0
2
1
1
1
1
0
1
2
1
1
1
2
2
1
2
2
2
1
0
0
1
0
1
0
0
1
1
1
1
2
2
1
1
2
2
0
1
1
0
1
1
1
1
1
1
1
1
1
0
1
4
2
0
1
2
1
1
1
1
1
1
1
2
1
0
2
0
1
0
2
0
1
1
1
1
2
1
1
1
1
1
0
3
2
2
0
1
1
0
1
1
0
1
1
1
0
1
2
1
1
1
1
1
2
1
2
1
1
0
1
1
1
1
1
1
0
2
1
0
1
1
1
0
2
1
1
0
2
1
2
1
0
1
1
0
2
1
1
2
1
1
2
2
0
1
1
0
1
2
0
0
1
1
0
1
1
1
1
1
0
1
1
1
2
1
1
1
1
1
1
2
1
0
1
2
1
1
1
0
1
1
1
1
1
0
2
1
0
1
1
1
1
1
0
1
1
1
1
2
1
1
2
1
0
0
0
0
1
1
0
1
1
0
0
1
1
1
0
2
0
2
1
0
1
2
1
1
1
1
1
1
1
1
0
0
0
1
1
1
0
2
2
1
1
1
1
2
1
1
1
0
0
1
1
0
1
1
1
1
1
0
1
1
1
2
1
1
2
0
1
1
1
2
3
1
1
0
0
1
0
2
2
1
2
1
1
1
2
1
0
1
3
1
1
2
1
2
1
0
1
0
1
1
1
1
1
2
1
0
2
1
1
2
2
1
1
2
1
1
0
1
1
1
1
2
0
1
1
2
1
2
1
4
1
1
0
2
0
2
0
1
2
0
1
1
1
1
1
1
1
3
1
1
2
1
1
1
1
2
0
1
0
1
0
1
1
1
1
2
1
0
1
1
1
0
1
0
1
0
1
1
1
0
1
1
2
1
0
1
1
1
2
1
0
1
1
0
0
1
1
2
1
1
1
1
2
2
2
1
1
0
1
2
1
1
1
2
1
1
1
2
4
1
2
0
0
1
3
0
1
1
1
1
1
2
1
0
0
0
1
0
1
2
0
2
0
0
2
1
1
1
1
1
0
0
2
1
2
0
1
0
2
1
1
1
2
1
0
1
1
2
2
1
1
1
0
1
1
1
1
2
2
2
1
1
2
1
2
1
0
2
0
0
2
1
1
0
1
0
1
1
0
1
2
1
0
1
0
2
0
1
0
1
1
1
0
1
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
0
0
1
0
1
0
1
0
1
0
1
1
2
1
1
1
0
0
1
0
2
0
0
1
0
0
0
2
0
0
1
1
1
2
1
1
0
0
1
1
2
1
1
1
2
1
2
1
1
1
1
0
1
1
1
2
1
1
2
1
1
1
1
0
1
1
1
2
1
2
1
1
1
0
1
1
1
0
1
0
0
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
1
3
1
1
2
1
1
1
0
1
1
1
1
0
0
1
2
2
0
1
0
1
0
1
1
2
2
1
1
2
1
0
1
1
0
1
0
1
2
1
2
1
1
1
1
0
1
1
2
1
2
2
2
1
1
1
0
3
2
1
3
1
1
1
1
1
0
1
2
1
1
2
1
2
1
0
1
1
2
2
1
2
1
1
0
2
1
1
3
0
0
0
0
1
1
1
1
0
2
1
2
0
1
0
1
0
0
1
2
2
1
2
1
2
1
2
0
1
2
1
0
2
1
1
1
1
1
1
0
1
1
2
1
1
1
1
2
1
1
1
1
1
0
0
1
2
1
1
0
1
0
1
0
1
1
1
1
0
1
1
1
1
2
1
1
1
0
1
1
2
1
1
1
2
2
0
3
1
0
0
0
1
0
0
2
1
2
1
2
1
0
1
0
0
0
1
2
1
1
2
0
0
1
1
0
1
1
1
1
0
2
1
1
2
1
2
0
2
1
2
2
1
1
0
1
0
1
0
1
1
2
2
1
1
1
0
2
1
1
1
1
2
1
2
1
0
0
2
0
1
2
1
1
2
1
2
1
2
2
1
2
1
2
1
1
1
0
3
1
1
1
1
1
1
2
0
1
1
0
1
1
1
2
1
1
1
2
1
1
2
0
0
2
2
1
1
2
2
0
1
0
2
0
1
1
2
0
1
1
1
1
0
1
1
1
1
1
1
1
0
2
2
1
0
2
2
2
1
1
1
0
2
0
1
0
1
0
0
0
1
3
2
1
0
2
1
1
2
0
0
1
1
0
0
1
2
2
0
1
2
2
1
1
1
1
2
1
1
0
1
1
1
1
1
1
1
2
1
1
1
0
1
1
1
1
1
0
0
0
0
1
1
0
1
1
1
1
1
2
1
1
1
1
0
0
1
1
1
1
1
2
1
1
2
2
1
1
1
1
0
0
1
1
1
0
2
2
1
0
1
1
1
2
1
1
1
1
2
2
1
1
1
0
0
4
1
1
1
2
0
1
2
1
1
2
1
0
2
2
2
1
1
1
2
1
1
0
2
0
2
0
2
2
0
2
2
1
0
1
1
0
0
0
1
2
1
1
2
1
0
2
1
0
1
1
1
1
1
1
1
1
1
2
1
1
2
0
1
0
1
2
1
1
1
2
0
0
0
1
1
1
2
1
1
1
1
2
1
1
1
0
1
2
1
1
0
0
0
1
1
1
1
1
1
1
2
0
1
1
1
2
0
1
1
0
1
1
1
0
1
1
2
1
2
0
1
0
0
2
0
1
3
1
2
1
1
1
1
1
0
1
1
0
1
2
1
1
1
1
2
0
2
3
1
1
1
1
0
1
1
1
2
1
1
2
0
1
2
1
1
3
1
2
1
0
2
1
1
0
1
1
1
1
1
2
1
1
2
2
1
1
2
1
1
1
0
1
1
2
1
1
1
2
0
1
0
1
1
2
1
1
3
2
1
0
1
2
1
1
1
1
1
1
2
1
1
1
0
1
1
1
1
2
1
1
1
2
3
1
2
0
1
1
1
0
1
1
2
0
1
2
1
0
1
1
1
0
1
1
1
3
2
1
2
1
0
0
1
1
2
1
2
1
0
1
0
0
1
0
0
1
0
1
2
1
1
1
1
2
1
1
0
1
0
1
0
1
0
0
1
1
1
1
1
2
1
1
2
0
0
1
1
0
1
1
3
1
2
0
1
1
2
0
0
3
0
2
0
2
1
2
2
0
1
2
2
1
0
1
0
1
1
1
2
2
1
1
0
2
0
2
1
1
1
2
0
1
1
0
1
2
1
1
2
1
1
1
2
2
1
0
1
1
1
1
2
2
1
1
1
0
0
1
1
2
0
1
1
1
1
2
1
2
2
1
1
2
2
1
1
1
1
0
1
0
1
1
0
0
1
1
1
0
2
1
1
1
2
0
1
1
1
2
1
2
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
3
2
1
1
1
1
2
1
1
1
1
0
2
2
1
2
2
1
1
1
2
1
0
1
1
1
0
0
1
0
1
1
0
1
2
2
2
1
2
1
1
0
0
2
1
1
1
1
2
1
1
2
2
2
1
1
1
1
1
2
0
1
0
1
1
1
1
2
1
1
1
0
1
2
0
0
1
5
2
1
1
1
0
2
2
1
1
0
1
1
1
1
3
0
2
1
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
1
2
2
0
2
1
1
1
1
1
1
1
0
0
0
0
1
2
1
0
1
1
0
1
1
1
0
0
1
1
1
1
1
2
1
1
1
2
0
0
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
0
2
1
1
1
0
0
1
1
1
0
1
2
1
2
0
0
0
2
1
1
2
2
0
1
1
1
1
1
1
0
1
0
1
1
1
1
0
1
1
1
1
1
2
0
2
0
2
1
1
1
1
1
1
1
0
1
1
1
2
2
1
0
2
0
0
1
0
1
1
0
1
1
1
1
1
0
0
0
1
2
2
3
1
1
0
1
0
1
1
2
1
1
2
2
0
1
0
2
1
1
3
1
1
2
2
1
1
0
0
1
0
2
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
0
1
1
1
1
2
2
1
3
1
0
1
1
1
1
2
2
0
1
1
0
2
1
0
2
1
1
0
1
0
2
1
1
1
1
0
1
1
2
2
2
1
1
1
1
1
2
1
1
2
1
1
1
0
1
1
0
3
0
1
0
1
2
2
1
1
0
0
1
1
1
1
1
1
2
2
1
2
1
1
1
1
2
2
0
1
1
1
1
2
1
1
1
0
1
1
0
1
0
2
1
1
0
1
1
0
1
2
1
2
2
1
1
1
1
1
2
1
1
2
1
1
1
2
1
2
1
0
1
0
1
0
1
1
0
1
1
1
1
0
2
0
3
1
1
0
1
1
0
1
1
1
2
2
1
2
0
2
1
2
1
1
0
2
1
1
0
0
1
0
2
1
1
2
2
1
0
1
2
1
2
2
1
2
1
1
0
1
1
2
1
1
1
1
1
0
0
1
1
0
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
2
2
1
0
0
2
1
2
1
2
1
1
1
1
1
1
0
2
1
1
1
0
2
1
2
1
1
1
0
0
2
1
2
0
1
1
1
0
1
2
1
1
1
1
1
1
1
2
2
0
1
0
1
2
2
1
1
1
0
1
2
1
1
1
2
1
0
1
0
2
0
4
1
1
1
1
2
0
1
1
2
1
1
1
1
2
1
1
1
2
1
2
1
2
0
2
1
2
0
2
2
1
2
1
1
1
2
0
0
1
1
0
0
2
1
2
1
0
1
1
1
1
2
1
1
0
1
2
1
1
0
1
2
1
1
1
1
1
2
1
1
0
1
10
0
1
2
1
1
1
1
1
1
1
0
1
1
0
1
1
1
1
1
1
1
0
2
1
1
1
1
1
1
1
0
0
0
2
1
2
1
0
1
2
1
1
1
0
0
0
1
0
1
1
1
0
1
1
1
1
0
2
1
2
0
1
1
1
1
0
2
1
2
2
1
0
0
2
0
2
2
2
1
1
1
1
2
2
1
1
1
0
2
0
0
1
1
1
2
2
2
0
1
1
1
0
1
0
1
1
1
1
0
1
0
2
2
1
1
1
1
0
2
2
2
1
1
1
2
1
1
1
1
1
1
1
1
0
1
0
1
1
2
1
2
1
2
2
1
1
1
1
1
1
1
1
1
2
2
1
0
1
1
1
1
1
0
2
1
1
1
0
1
1
1
1
1
2
0
1
1
1
2
1
0
1
2
0
1
1
1
1
1
2
1
0
1
1
0
2
1
1
1
1
0
1
2
2
2
1
0
0
1
1
1
2
2
1
1
1
2
1
2
1
1
1
2
0
2
2
2
0
1
2
1
1
1
1
1
0
1
0
1
1
2
2
1
1
0
1
1
1
0
1
1
3
2
1
1
1
2
1
0
0
1
1
1
2
0
1
0
0
0
2
1
2
1
0
2
0
1
1
0
1
1
0
2
0
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
0
1
1
1
1
1
2
0
0
1
0
0
1
1
2
2
1
1
1
1
2
2
1
1
2
1
1
2
2
0
1
1
1
2
2
0
2
2
2
1
1
1
2
1
2
2
2
1
0
1
1
1
1
1
1
0
1
1
2
2
1
2
1
0
1
0
1
0
1
1
1
0
2
2
0
1
1
1
1
0
1
1
1
2
2
0
0
0
0
1
1
0
1
0
1
1
1
1
0
0
1
1
0
2
0
2
1
2
0
1
2
1
1
1
2
1
0
1
1
1
2
0
2
1
1
2
1
0
0
2
1
2
1
1
0
0
2
0
2
1
0
0
1
2
1
2
0
1
2
2
0
5
0
1
0
1
1
0
1
2
1
1
1
1
0
1
1
1
1
1
1
0
1
1
2
1
0
0
2
1
2
1
2
1
0
1
1
1
1
1
5
4
0
0
2
1
1
2
1
1
1
2
1
2
2
1
2
1
0
1
0
2
1
1
2
2
1
1
0
1
1
1
1
1
0
1
1
1
1
1
2
0
1
1
2
1
2
1
1
2
2
2
1
1
1
0
1
2
0
2
1
1
1
2
2
0
1
2
1
1
1
0
1
1
2
1
0
2
2
2
1
1
1
2
1
1
0
1
1
2
2
1
0
2
1
0
1
1
1
1
1
2
0
0
0
1
1
1
1
1
0
1
0
1
1
1
1
1
1
1
2
1
2
0
1
3
2
0
1
1
1
2
1
1
2
1
0
1
2
2
1
0
0
0
1
2
0
2
2
2
0
1
2
1
0
2
1
0
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
0
0
1
0
0
2
1
1
1
0
1
0
2
1
1
1
1
1
2
0
0
2
1
1
1
2
0
2
1
0
1
0
1
2
1
1
0
1
2
1
1
1
1
1
1
1
2
1
1
1
1
2
0
2
1
1
1
1
0
1
0
1
2
1
0
2
1
2
1
1
1
0
1
1
2
1
1
0
1
1
0
0
0
0
1
2
1
1
2
1
1
1
1
1
2
2
1
1
1
3
0
1
2
1
1
1
2
1
1
1
1
0
0
1
1
1
1
1
2
0
1
1
0
1
1
1
0
1
1
1
1
1
1
2
1
2
2
2
1
2
0
2
0
1
0
0
1
1
0
2
2
0
1
0
1
1
1
2
1
1
2
1
1
2
1
1
1
1
1
0
1
0
0
1
1
2
1
0
1
1
1
1
1
0
1
1
1
1
2
2
1
0
1
2
1
1
1
1
1
1
2
1
0
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
0
1
0
1
1
1
2
1
1
2
1
1
2
1
1
1
2
0
1
1
1
1
1
0
0
1
1
1
1
2
2
2
1
1
2
2
2
2
2
2
1
2
1
2
2
1
2
2
1
2
1
2
0
2
1
1
2
2
1
1
0
0
1
1
1
1
1
1
1
1
1
0
0
2
1
1
2
2
2
1
0
1
0
1
2
0
1
2
0
0
2
1
1
0
2
1
2
0
1
1
1
1
2
1
1
1
1
2
2
1
2
1
1
2
2
1
1
1
1
1
1
2
1
2
1
0
0
2
2
1
1
1
1
1
1
2
1
1
2
2
1
0
1
2
2
1
2
1
2
0
1
1
2
1
1
0
1
1
1
2
1
1
2
1
0
1
0
0
2
1
1
1
2
1
1
1
0
1
1
1
1
2
1
2
1
1
0
2
2
0
1
0
2
1
1
0
1
0
0
0
1
0
0
1
0
1
1
1
1
2
1
0
0
0
1
1
1
1
1
1
0
1
1
0
1
1
1
1
0
3
0
1
1
0
1
0
1
1
2
1
0
1
0
1
2
1
1
1
0
2
0
0
1
0
1
1
2
2
0
0
0
1
1
1
1
1
1
0
1
0
1
2
2
1
0
1
2
2
1
2
0
1
1
1
0
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
0
1
1
0
1
1
1
1
0
2
2
1
1
2
0
2
1
1
1
1
1
2
1
0
1
2
1
2
1
1
1
2
0
1
2
1
0
2
0
1
1
0
0
1
1
1
1
2
1
1
1
1
1
1
1
1
1
0
2
0
1
1
1
1
2
0
1
1
1
2
0
1
3
1
1
1
0
2
1
1
0
1
1
1
1
0
0
1
0
2
2
1
1
2
1
0
1
0
0
0
1
0
1
1
1
1
0
0
1
0
1
1
2
1
1
0
0
2
1
1
0
1
1
0
0
0
1
1
1
1
2
1
1
2
0
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
2
1
2
1
1
1
1
1
2
2
2
1
1
1
1
2
1
2
2
0
3
2
1
2
1
2
1
1
2
1
1
2
1
2
1
2
1
2
2
0
1
0
2
1
1
0
1
0
2
1
0
1
0
0
2
0
1
1
0
2
1
0
0
1
1
2
1
2
1
1
1
2
1
0
0
1
0
1
1
1
2
0
1
2
2
1
1
1
1
2
2
0
1
1
2
1
0
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
0
2
1
2
1
2
1
1
1
2
1
2
2
1
1
1
1
1
1
0
1
1
2
2
2
1
2
1
0
1
2
2
1
0
1
1
1
2
0
1
0
1
0
1
1
1
1
1
1
1
2
2
1
1
1
0
2
1
2
1
1
0
1
0
0
1
1
2
1
1
1
2
1
0
1
0
0
1
2
1
1
0
1
1
1
1
2
2
0
1
0
1
0
1
0
1
0
0
1
1
1
1
0
1
1
1
2
1
2
1
1
1
1
2
0
2
0
1
1
0
2
1
1
1
2
1
1
1
1
1
1
1
0
1
1
1
0
1
1
1
1
1
1
1
0
2
1
1
0
0
2
1
1
1
1
1
1
0
7
0
0
1
2
2
1
1
1
1
0
2
3
1
2
1
1
1
2
0
0
1
2
1
0
2
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
0
1
1
2
0
0
1
1
1
2
2
2
1
1
0
2
1
2
0
0
1
1
1
0
1
1
1
0
1
1
1
1
0
1
1
1
1
0
0
2
2
1
1
0
0
1
1
1
1
1
1
0
2
1
1
4
0
0
0
2
2
1
0
1
0
2
1
1
0
0
2
3
2
1
1
2
0
0
0
1
2
0
0
1
1
0
1
1
1
1
1
0
2
0
1
2
2
0
3
1
1
0
1
2
0
0
1
0
1
0
1
2
0
1
1
2
1
1
0
1
0
1
2
0
1
0
1
2
1
0
1
3
1
1
1
1
1
2
1
0
0
1
1
2
0
2
1
1
0
1
1
1
1
1
1
1
1
1
1
2
0
1
1
2
1
1
0
1
1
1
0
1
0
2
2
2
0
2
1
1
2
1
2
1
1
1
2
1
2
1
2
1
0
1
1
1
2
1
2
1
1
1
1
0
1
1
1
1
1
1
1
0
0
2
1
3
1
0
3
1
2
1
1
1
0
1
1
1
2
1
2
2
0
1
1
1
2
1
2
1
2
2
1
2
2
1
0
2
1
0
1
0
0
7
0
1
1
1
1
1
2
2
1
1
1
1
1
1
2
2
1
0
1
2
0
4
1
0
1
1
1
1
2
1
0
2
1
1
1
1
0
2
1
2
1
2
0
1
0
1
1
1
4
0
0
1
1
1
2
0
2
1
0
0
0
1
1
0
0
1
1
1
0
0
1
1
1
1
1
1
1
1
3
1
2
1
1
1
2
2
1
0
1
0
2
2
2
1
1
1
1
2
1
1
2
0
2
1
1
1
1
1
0
1
1
2
1
0
2
4
1
0
1
1
1
1
1
1
2
1
1
1
1
1
0
2
2
2
2
2
2
3
2
0
2
1
2
1
1
1
0
1
0
1
1
0
1
3
1
1
1
2
1
1
0
1
1
2
1
2
1
1
2
0
1
0
1
2
2
1
1
1
1
2
1
1
1
1
2
1
0
1
1
1
2
2
0
2
0
1
1
1
0
0
1
1
3
1
1
1
0
0
1
1
1
2
2
1
2
1
1
3
1
1
2
1
1
0
0
1
2
0
0
1
1
1
1
2
1
1
1
0
2
1
1
1
1
2
0
1
1
1
2
1
1
1
0
1
0
3
0
1
1
1
1
2
2
1
1
2
2
1
1
1
1
0
0
0
2
0
2
2
0
1
2
2
2
2
2
1
0
2
1
1
1
2
0
2
1
5
1
1
1
1
2
0
2
0
1
0
1
0
1
0
1
0
1
1
2
0
1
0
1
2
1
3
1
1
1
0
0
1
1
2
2
2
0
1
2
2
2
2
0
1
1
1
2
1
1
1
0
1
1
2
1
1
1
2
0
1
1
1
1
0
2
1
0
2
3
2
1
0
2
1
2
1
1
1
2
1
0
1
1
1
1
1
1
1
2
2
0
1
0
0
2
1
0
0
1
0
1
1
0
1
1
0
2
1
1
1
1
1
0
1
1
2
1
1
2
1
1
2
0
1
2
0
0
0
1
2
0
2
1
1
0
1
1
2
2
1
0
1
1
2
0
2
1
2
1
1
0
2
1
1
0
2
1
2
1
2
1
0
1
1
1
2
1
2
1
1
0
1
2
2
2
1
0
1
1
3
1
0
1
0
1
1
1
2
2
1
1
1
1
0
2
2
1
1
0
1
1
1
0
2
2
1
0
2
2
2
0
1
1
0
1
1
1
1
1
1
2
2
1
2
2
1
0
1
1
1
0
0
0
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
0
0
1
2
1
2
1
2
1
1
2
1
1
1
2
0
2
1
1
1
1
0
1
2
1
0
1
0
2
1
1
1
0
2
1
1
2
1
1
1
1
0
1
0
0
1
2
2
1
0
1
1
0
1
1
0
0
0
1
2
1
1
1
1
2
1
1
1
1
0
2
2
2
2
1
2
1
1
1
1
0
1
1
1
1
1
1
1
1
0
0
1
1
0
1
1
1
2
2
0
1
0
1
0
1
1
1
0
3
1
1
1
1
1
1
1
1
1
2
0
1
1
1
2
2
1
1
1
1
1
1
2
1
0
1
1
1
1
1
2
1
0
1
3
1
1
1
2
2
2
1
1
2
1
1
0
0
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
1
2
2
1
0
1
1
0
1
1
1
1
1
2
2
1
1
1
0
0
1
0
1
2
1
2
1
1
0
1
0
1
0
2
2
0
2
1
1
1
2
1
1
2
2
1
1
1
2
1
2
0
2
1
2
1
3
0
0
0
0
1
1
1
2
1
2
2
2
1
1
0
2
0
0
1
0
0
1
0
0
1
1
2
1
2
1
1
1
1
2
0
1
1
0
1
2
0
1
1
1
1
1
1
1
2
1
1
0
0
2
2
1
1
2
1
1
1
0
1
0
1
1
1
2
0
1
2
0
1
1
2
0
2
2
1
1
2
1
1
2
0
0
2
1
1
1
2
1
0
1
2
2
1
2
1
0
2
1
1
1
1
2
2
1
1
1
1
1
2
1
2
1
1
1
2
2
1
1
1
1
1
2
1
1
0
1
1
1
2
2
2
0
0
2
2
2
1
3
1
2
1
2
2
1
1
1
0
1
1
1
1
1
0
2
2
0
1
2
2
0
1
2
0
0
1
2
0
0
2
0
2
2
1
2
1
0
2
1
0
2
1
0
1
1
1
1
0
1
2
2
1
1
1
0
0
1
1
1
1
2
1
2
2
1
1
1
1
1
2
1
1
0
2
2
1
1
1
2
2
0
1
1
0
2
1
1
0
2
2
0
1
1
2
0
1
2
0
1
0
2
1
1
2
1
3
0
2
0
1
1
3
1
1
1
2
1
1
0
2
2
0
2
2
1
1
2
1
2
0
2
2
2
1
2
1
1
1
0
0
1
1
2
1
1
2
1
0
1
0
0
0
1
1
1
0
2
2
1
1
1
1
0
1
2
1
2
1
1
2
2
2
0
1
2
0
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
0
0
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
2
1
1
2
1
0
1
2
1
0
2
0
1
0
1
1
1
2
2
1
1
1
2
1
1
1
2
1
2
2
1
0
0
2
1
2
1
1
0
1
2
2
1
1
2
1
1
2
1
1
1
1
1
1
1
2
0
1
1
0
1
2
1
1
0
0
1
2
1
0
2
1
1
2
1
1
1
1
0
1
0
1
1
2
2
2
1
0
2
0
1
1
1
0
1
1
1
2
0
1
1
2
1
1
1
1
1
2
1
2
2
0
1
2
1
2
1
1
1
1
0
1
0
1
1
2
1
1
0
2
1
2
1
2
0
1
1
1
1
0
1
1
0
0
1
1
1
0
1
0
0
1
1
0
2
1
2
1
1
2
0
1
0
0
2
0
0
0
0
0
1
0
0
2
1
0
1
1
1
1
2
2
1
0
2
1
1
1
1
0
1
1
1
1
0
1
1
0
1
2
0
2
2
1
2
2
1
1
2
1
1
1
1
2
2
1
1
1
1
1
2
1
1
1
1
2
2
1
1
1
1
1
2
1
1
0
1
2
0
2
1
1
1
1
1
1
0
1
2
2
2
0
0
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
0
1
0
0
2
2
0
1
1
1
2
1
2
2
1
4
1
1
0
2
2
1
1
0
1
2
2
1
1
2
2
2
2
0
0
2
1
2
1
1
1
1
1
1
1
1
1
1
2
1
0
1
1
1
1
0
1
1
1
1
2
1
0
1
1
0
2
1
2
0
1
0
0
1
1
1
1
0
1
1
0
0
2
1
0
1
1
1
2
2
1
1
1
1
1
2
0
1
2
1
1
1
0
2
2
1
2
1
2
1
1
0
1
2
1
1
0
1
0
2
1
2
1
1
1
2
1
0
1
1
2
2
2
1
1
2
1
1
0
2
1
1
1
1
0
1
1
1
1
1
2
1
1
0
1
1
0
0
1
0
0
1
2
1
1
0
0
0
1
1
2
1
1
1
1
1
1
0
9
0
2
1
1
1
1
1
1
2
0
1
1
1
0
1
1
2
0
2
0
1
2
1
1
0
2
1
2
0
2
1
1
1
1
2
2
1
1
0
0
1
2
1
1
1
2
1
2
2
1
2
0
1
1
0
1
1
1
1
2
2
0
1
1
0
1
2
1
1
0
1
0
1
1
1
0
0
1
1
0
1
1
0
1
0
1
1
2
1
1
1
1
1
1
0
0
1
2
3
0
2
1
1
1
0
1
1
1
1
0
1
1
1
2
2
1
0
0
1
0
1
1
1
0
1
0
2
1
1
2
2
1
2
0
0
1
1
0
0
0
2
1
1
1
2
1
1
1
2
0
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
0
1
1
2
1
2
2
1
1
1
0
1
1
0
1
2
1
2
1
1
2
1
2
1
0
0
1
1
0
2
2
0
1
2
1
1
1
2
0
1
1
1
1
1
0
1
1
2
0
1
0
2
1
1
2
1
2
0
2
1
0
1
0
2
2
0
1
1
4
1
2
2
2
2
1
2
1
1
0
1
0
1
2
1
1
1
2
0
2
2
2
1
0
2
2
2
1
1
1
2
0
1
0
0
1
1
1
1
1
1
1
1
1
2
1
2
2
1
1
2
2
1
2
1
2
2
2
1
1
2
1
1
1
2
1
1
0
2
1
1
1
1
2
2
2
1
1
0
1
1
1
2
1
0
1
1
1
2
1
2
1
1
0
2
2
0
0
3
1
1
2
2
0
2
1
0
1
1
2
0
0
2
1
0
1
0
1
0
0
1
1
1
1
1
0
1
1
1
1
1
0
1
2
0
1
1
0
1
0
1
1
1
2
1
2
2
2
2
1
0
2
1
1
2
2
1
0
1
1
1
2
2
1
1
1
2
1
1
1
1
1
1
1
1
0
0
1
1
1
0
1
1
2
1
2
0
0
1
1
2
1
2
1
1
1
0
2
1
0
0
2
1
1
1
1
0
1
0
1
1
0
1
1
2
1
1
2
1
2
1
2
1
1
1
1
0
1
2
1
0
1
1
0
1
1
2
0
1
1
0
1
2
0
1
1
1
1
1
1
0
1
0
1
1
0
2
2
1
1
1
1
0
1
2
0
2
1
0
1
1
1
1
1
1
2
1
1
1
3
2
0
1
2
2
1
0
2
0
1
1
2
1
1
1
0
1
1
3
0
1
1
1
0
2
1
1
1
1
1
2
2
1
2
1
1
0
2
1
1
1
1
1
1
0
1
2
2
2
1
1
1
2
1
0
1
0
1
2
2
1
2
2
1
1
1
1
2
1
1
1
1
1
1
1
0
0
1
1
1
1
0
1
1
1
0
0
1
2
0
1
1
1
1
2
2
1
1
0
2
1
2
1
1
2
1
1
3
4
1
2
3
0
1
2
1
0
1
0
0
2
2
1
0
2
1
2
0
1
1
2
2
1
1
1
2
0
1
1
0
0
1
1
0
2
0
2
0
0
2
1
1
1
1
1
2
0
1
1
1
2
1
0
1
0
1
1
1
2
1
1
0
1
2
0
1
1
1
0
1
2
0
1
0
1
0
1
1
1
1
0
2
2
2
2
1
1
2
2
1
0
0
2
0
2
1
0
1
1
2
1
2
0
0
1
1
2
1
0
2
1
1
1
1
1
0
1
1
1
2
1
0
1
1
2
1
1
0
1
1
1
1
0
1
2
1
1
1
1
0
1
1
1
1
2
1
1
1
1
2
1
1
1
2
0
1
0
1
2
1
2
0
1
2
1
0
1
1
1
1
1
1
0
1
0
1
2
0
1
0
1
0
2
1
1
4
1
2
1
3
0
0
2
1
1
2
1
2
2
1
2
1
1
2
1
1
2
1
2
2
0
1
1
1
2
1
1
0
1
1
1
1
2
0
1
1
0
1
1
1
1
2
0
1
1
0
0
2
2
1
0
0
2
0
1
1
1
0
2
1
0
1
2
2
0
1
1
0
1
1
1
2
2
1
0
0
1
0
1
1
1
1
0
1
0
1
1
0
1
1
1
1
3
1
2
0
1
2
1
1
2
1
1
1
2
2
2
1
2
1
1
0
1
1
1
1
2
2
0
1
1
1
1
1
0
2
0
1
1
1
2
1
1
0
1
1
1
1
1
1
2
1
0
1
1
1
1
1
1
2
1
2
0
0
2
0
1
1
1
0
0
2
1
1
2
1
2
1
2
1
2
1
1
1
1
0
3
1
0
0
2
1
1
0
1
2
1
1
1
2
2
1
1
1
1
0
2
2
1
0
1
0
1
1
1
0
1
2
1
1
1
1
0
2
1
2
1
0
0
1
1
1
0
0
2
2
1
2
1
1
1
1
0
1
2
1
2
0
1
1
2
1
1
2
0
0
1
3
1
1
1
0
1
1
1
2
1
1
1
0
0
1
1
1
1
0
1
2
0
0
1
1
1
0
1
0
2
1
0
1
0
1
2
1
1
1
1
1
1
2
1
0
1
1
1
2
1
0
0
0
2
1
2
2
1
1
0
1
1
1
1
1
0
2
0
1
0
2
2
2
0
1
1
1
1
1
2
0
2
1
1
1
2
1
1
1
1
2
0
1
1
1
1
2
0
1
1
2
1
1
1
1
1
2
1
1
1
2
1
2
1
1
2
1
1
2
0
2
2
0
2
1
1
0
2
1
1
1
1
1
1
1
1
2
0
2
1
1
1
0
1
1
0
1
2
2
0
1
0
1
1
1
0
2
1
1
1
2
1
2
1
4
2
1
0
1
2
1
0
1
1
2
0
2
2
1
1
1
1
2
1
1
1
0
1
0
1
0
1
1
1
1
2
1
0
0
1
1
1
1
1
1
0
0
2
0
1
1
1
1
0
1
1
1
0
1
2
0
1
0
2
1
1
1
2
1
1
1
1
1
0
0
1
1
1
2
1
1
1
1
0
1
1
1
1
0
1
1
1
1
0
0
2
1
2
1
0
1
1
1
1
0
1
2
1
1
2
1
3
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
0
0
2
1
0
1
1
0
1
2
1
1
1
2
2
1
1
0
2
0
1
0
1
1
1
0
1
1
0
1
1
0
0
1
1
1
0
1
2
1
0
2
1
1
2
0
2
1
1
1
1
1
2
1
1
0
1
1
0
2
1
1
2
2
0
0
2
1
0
2
2
1
0
1
2
0
0
1
2
1
1
1
2
1
2
1
0
1
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
0
1
2
1
2
0
1
1
1
2
1
1
1
0
2
1
0
2
1
1
2
1
1
2
1
1
0
0
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
2
1
2
1
1
0
1
1
1
1
1
1
1
1
2
2
2
2
1
1
0
1
0
2
1
1
1
2
1
0
1
0
0
1
0
2
1
2
2
2
1
2
1
1
0
1
1
0
1
0
1
1
1
1
0
1
1
1
1
2
1
2
1
0
2
1
1
1
1
2
0
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
0
1
1
2
1
1
1
1
1
0
1
1
0
1
2
2
0
1
1
1
2
1
1
1
0
2
2
1
0
1
0
0
2
2
1
1
0
1
0
1
2
1
1
1
1
1
2
0
0
2
2
1
1
1
1
0
0
2
1
1
1
1
1
1
1
2
1
1
1
1
2
1
2
1
0
1
1
1
1
1
2
1
0
1
2
1
1
1
2
0
1
1
1
1
1
1
1
0
0
1
1
0
1
0
2
2
1
1
1
2
2
2
0
1
2
1
1
2
1
2
2
1
0
0
2
2
0
1
0
1
0
1
1
1
1
2
1
1
1
1
1
0
1
0
0
0
2
0
2
1
1
1
0
2
1
1
1
0
1
1
1
0
0
2
0
0
0
1
1
1
1
1
1
0
1
0
1
1
1
1
2
1
2
0
1
1
1
2
1
1
2
1
1
1
1
1
1
2
0
1
0
1
2
2
1
0
1
1
2
1
0
1
2
2
1
2
2
1
0
0
0
0
1
1
1
1
1
2
1
2
1
1
1
2
1
1
0
1
3
2
1
2
1
1
1
1
1
0
1
1
1
1
1
0
1
0
1
1
1
2
2
2
1
2
1
0
2
0
0
0
1
0
1
1
0
0
1
1
1
1
1
1
0
2
1
0
1
0
2
2
1
1
1
2
0
0
2
0
1
1
1
1
1
1
0
1
2
1
1
0
1
1
1
0
1
1
2
1
1
1
1
1
1
1
1
1
2
0
1
2
1
2
2
0
1
1
1
2
1
0
1
0
2
1
0
0
1
1
1
1
0
0
2
1
0
2
0
2
1
1
1
1
1
2
0
0
1
0
1
1
2
2
0
1
0
2
0
1
2
1
1
0
2
2
2
0
0
1
2
1
1
1
0
1
1
1
1
1
0
2
2
1
2
7
1
1
0
0
1
2
1
1
1
1
0
4
2
0
1
2
2
1
1
2
1
1
1
2
2
1
0
2
1
1
0
2
2
2
1
1
2
1
1
1
0
2
1
1
1
1
1
1
1
1
0
1
0
0
0
1
1
0
1
2
2
2
1
2
1
0
2
1
1
0
0
2
1
0
2
0
1
1
1
2
1
1
1
1
3
2
0
0
2
1
0
1
1
2
2
0
1
0
2
1
2
0
2
0
0
1
1
2
2
2
1
1
0
1
0
2
2
1
1
1
0
1
1
1
1
1
2
0
0
2
0
0
3
1
1
0
1
3
2
1
1
2
1
2
1
2
0
1
1
1
1
2
1
1
1
1
1
1
1
0
0
0
1
2
0
2
0
1
1
1
2
0
2
0
1
1
2
1
0
1
1
0
1
1
0
1
2
2
1
1
2
0
1
1
1
0
1
2
1
0
0
0
1
0
0
0
1
2
1
2
0
0
0
1
2
0
1
2
1
1
2
1
0
1
2
0
0
1
0
0
2
0
1
2
1
1
1
0
2
1
2
0
1
1
1
2
2
2
1
1
1
1
1
1
2
1
2
2
1
0
1
0
3
0
1
0
0
1
2
0
1
1
0
1
1
2
0
2
1
2
1
2
1
0
2
2
1
1
1
2
2
2
0
2
1
1
1
1
2
0
0
1
0
1
1
1
1
1
1
1
1
0
1
1
1
1
0
1
1
1
1
1
1
1
0
1
0
1
2
1
1
0
1
0
0
2
1
1
1
1
1
1
2
1
1
2
1
1
1
1
0
0
2
2
0
1
1
2
0
1
2
2
1
1
1
1
1
0
1
1
1
1
1
1
2
1
0
2
1
0
1
1
2
0
1
1
1
2
2
2
1
1
2
0
1
1
0
0
1
1
1
2
0
0
1
1
2
1
0
2
1
2
1
1
0
1
1
1
0
1
1
1
0
2
2
1
0
2
1
2
2
1
1
0
2
2
0
0
1
2
1
2
1
1
2
2
2
1
2
2
2
1
1
1
1
0
1
2
0
1
0
1
1
1
0
1
1
2
0
2
1
1
0
1
1
1
1
0
1
0
1
1
0
1
1
1
2
1
0
0
2
2
1
1
1
1
1
1
2
1
1
1
2
2
1
2
2
0
2
1
1
1
1
1
2
1
1
1
0
1
1
2
2
1
1
1
1
2
1
2
1
2
1
2
2
1
0
2
1
1
2
2
1
0
2
2
1
1
1
1
1
1
1
1
2
0
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
2
0
1
1
0
1
1
1
1
0
1
2
1
1
1
1
0
1
0
0
1
1
2
2
0
1
1
2
1
3
1
1
1
0
0
0
1
1
0
0
1
1
1
1
1
1
1
1
1
0
3
1
0
0
0
2
1
2
1
1
1
1
1
1
0
1
1
2
0
1
2
1
1
1
0
2
1
0
1
1
2
0
0
2
1
1
0
0
1
1
2
2
2
0
1
1
1
1
0
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
0
1
2
2
1
2
1
1
1
3
0
1
1
1
0
2
1
1
0
1
1
1
1
2
1
2
1
1
1
0
0
1
1
1
1
0
1
2
0
1
1
2
1
0
1
2
0
1
1
2
0
1
0
2
1
1
1
2
1
1
1
1
1
1
2
1
1
2
0
1
2
1
2
1
1
1
1
2
0
1
2
0
1
0
1
1
2
2
0
1
2
1
1
1
2
2
2
1
1
1
1
0
1
2
1
2
1
2
1
0
1
0
1
1
1
2
2
1
2
2
1
1
0
1
0
1
1
1
2
2
1
1
2
1
1
1
1
2
0
1
1
2
2
1
1
1
1
0
1
1
1
1
0
3
1
0
0
1
1
1
1
0
1
1
1
1
1
1
0
1
1
1
1
0
1
0
2
1
1
1
1
1
2
3
1
2
1
2
1
1
1
1
0
1
1
2
1
2
0
0
1
1
1
2
1
1
1
1
0
1
2
1
1
0
2
0
1
1
1
1
1
1
0
1
1
1
2
2
2
1
1
0
2
0
2
1
2
0
1
2
1
0
2
0
1
1
2
0
0
1
0
3
4
1
1
1
0
0
2
2
0
0
1
1
1
2
1
0
2
0
1
1
0
1
0
1
1
2
1
1
1
2
1
1
1
1
0
2
1
1
2
1
0
1
2
1
2
2
2
1
1
2
1
2
1
2
1
0
0
0
1
2
1
1
1
2
1
1
0
1
2
0
1
1
1
0
1
1
1
1
1
2
1
1
1
2
1
1
1
0
0
1
0
2
1
1
2
0
1
3
1
1
0
1
2
1
2
2
1
1
2
1
0
1
1
1
0
2
2
2
0
0
1
0
1
1
2
1
1
0
2
2
1
0
1
2
0
1
2
0
2
2
1
0
2
0
1
1
1
0
0
0
0
1
1
1
0
1
1
1
2
1
0
2
1
1
1
2
1
1
1
1
2
0
2
1
1
1
1
1
2
1
1
0
2
1
1
1
1
1
1
2
2
1
0
2
2
0
2
0
2
1
1
0
0
1
1
2
1
2
2
1
1
2
2
1
2
2
1
0
2
0
1
2
3
1
1
1
1
1
2
1
1
0
0
0
1
1
0
1
2
1
0
0
1
1
1
1
0
1
1
1
2
0
1
1
2
0
1
0
2
2
1
2
2
1
1
1
1
2
1
1
2
1
1
1
1
2
0
2
0
2
0
1
1
0
0
2
0
1
0
1
1
1
1
1
1
0
0
0
0
1
0
0
1
1
1
2
1
1
1
1
2
0
2
1
1
1
1
1
0
1
0
2
1
1
1
2
1
2
1
0
1
0
2
0
0
1
1
1
0
0
1
1
1
1
2
1
1
2
0
1
1
0
1
1
0
1
0
1
2
2
1
1
2
0
1
1
1
1
1
2
2
1
2
1
1
1
1
0
0
2
1
1
1
0
2
2
2
1
1
0
1
1
1
1
0
2
1
1
2
1
1
1
2
1
2
1
2
0
1
1
1
3
2
1
0
1
1
1
0
1
1
0
2
1
1
2
2
1
2
0
1
1
1
1
1
1
1
1
1
0
0
1
1
0
0
1
1
2
1
1
3
2
0
1
1
1
1
0
2
0
0
1
1
1
0
1
2
1
1
1
1
1
1
1
0
2
2
1
0
1
1
0
1
1
1
2
0
0
1
1
1
1
1
1
0
1
1
1
0
1
1
2
0
1
1
2
2
1
2
1
0
0
0
1
1
2
1
0
2
1
1
1
1
1
3
1
0
1
1
1
1
2
1
1
1
1
0
1
0
1
1
1
0
2
0
0
1
1
1
2
1
1
2
0
1
1
1
1
0
2
1
1
2
1
1
1
0
1
0
1
1
1
1
0
1
1
1
2
2
1
0
1
1
0
1
2
1
0
2
1
1
1
0
0
2
1
2
0
2
2
2
1
1
1
1
2
2
0
1
0
1
1
0
1
1
2
1
1
2
1
0
1
1
1
2
1
0
2
0
2
1
1
1
1
1
2
2
1
2
2
1
1
1
1
1
2
1
1
2
0
1
1
1
2
1
1
1
0
1
2
2
1
2
1
0
0
2
1
2
0
1
1
1
0
1
1
2
1
0
2
1
1
2
1
0
1
2
0
2
2
0
1
1
2
1
1
0
2
0
1
2
0
2
1
0
1
1
2
1
1
0
1
0
1
2
1
1
1
2
1
2
0
1
1
2
1
3
1
1
0
1
2
1
1
1
2
1
0
1
1
1
1
1
2
1
2
2
1
0
1
1
1
1
1
0
0
0
2
1
1
1
0
1
1
0
0
1
1
1
1
1
1
1
2
0
2
1
1
0
0
1
0
1
1
1
1
1
1
1
1
2
2
0
1
1
0
1
1
1
1
2
1
1
2
1
0
0
1
1
0
1
1
1
2
1
1
1
3
2
1
2
1
2
2
0
1
1
2
1
1
1
1
1
1
2
2
1
1
1
0
0
2
1
2
0
1
1
1
0
1
1
1
1
2
1
1
1
2
2
1
3
1
0
1
1
1
1
2
0
1
1
1
0
0
0
4
1
1
1
0
0
0
2
1
1
1
1
2
1
2
1
1
1
1
1
1
1
2
0
1
0
1
1
0
1
1
1
2
1
0
2
1
1
1
1
0
1
1
1
1
2
1
1
2
0
1
0
0
0
1
1
1
0
1
1
2
0
1
1
3
1
1
1
1
1
2
1
2
1
1
0
1
1
1
2
2
1
1
2
3
1
2
1
1
0
2
2
1
1
1
1
0
1
0
0
1
1
2
1
0
0
2
1
2
1
1
2
0
2
1
0
0
2
1
1
1
0
1
1
1
1
2
1
1
1
1
0
1
2
1
1
1
1
0
1
1
0
1
2
1
1
0
1
1
2
1
1
2
0
1
0
1
2
1
2
1
1
2
1
0
2
0
2
1
1
2
2
1
1
1
2
3
1
1
2
0
0
1
1
2
1
2
1
1
1
1
1
1
2
1
1
2
1
0
1
1
1
1
2
2
1
1
0
1
2
0
0
2
0
0
1
1
2
1
1
2
1
1
1
0
2
1
1
2
0
1
1
1
2
0
0
1
0
0
1
1
2
1
0
0
0
1
2
2
0
1
0
1
0
1
0
1
1
2
0
1
1
1
1
0
2
1
0
2
0
1
1
1
0
2
2
1
1
1
1
0
2
1
1
0
1
1
1
1
1
1
1
1
1
0
1
2
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
0
2
0
1
2
1
1
3
1
2
2
0
1
1
1
1
1
1
1
0
1
1
1
1
1
1
2
1
1
1
1
5
2
0
1
1
1
2
2
2
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
0
0
0
1
1
1
1
2
4
1
1
1
1
0
1
2
1
2
1
0
1
2
2
1
1
1
2
2
2
1
0
1
2
0
1
2
1
1
1
1
3
2
1
1
1
1
1
1
0
1
1
1
1
0
1
1
0
1
1
2
2
1
1
1
1
1
0
0
1
1
0
1
2
1
2
1
0
1
2
2
0
0
1
1
0
1
1
1
1
3
1
1
1
1
1
1
1
1
0
1
1
1
1
1
0
1
2
2
1
0
1
1
0
0
1
0
0
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
0
1
3
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
2
1
1
0
1
1
1
1
1
1
0
0
1
1
0
1
2
0
2
0
0
1
1
2
0
2
1
2
1
1
1
0
1
2
1
1
2
0
1
2
0
0
1
1
0
2
2
2
2
0
1
1
2
2
1
0
0
1
2
2
2
1
1
1
0
2
0
2
1
1
0
1
1
2
2
0
1
1
4
1
1
0
1
1
2
1
1
0
2
2
0
1
2
1
1
2
1
2
0
1
0
2
1
1
1
2
0
2
1
1
1
1
1
1
0
2
1
1
1
1
2
1
1
2
1
1
1
2
1
0
1
2
0
0
1
2
1
2
2
0
1
1
4
1
1
2
0
0
2
1
1
1
2
1
1
2
2
1
1
0
2
1
1
2
1
1
1
0
1
1
1
2
1
1
2
1
2
1
1
1
2
0
1
1
0
1
2
0
1
2
1
1
2
1
4
0
1
1
2
0
1
0
0
1
0
1
1
1
0
1
1
1
1
1
2
1
1
1
1
1
0
1
1
1
0
1
1
1
1
0
2
1
2
2
0
1
1
1
2
2
1
2
2
1
0
1
1
0
1
0
2
1
0
0
1
1
1
1
0
0
1
2
0
2
1
1
3
1
1
1
1
1
1
0
2
1
2
1
2
2
3
0
1
0
2
2
0
0
1
2
2
1
1
1
1
1
1
2
1
0
1
1
2
2
1
0
0
0
0
1
1
0
0
1
1
1
2
2
2
2
1
1
1
1
0
1
1
2
1
1
0
1
1
1
0
2
2
0
1
1
0
1
1
1
1
1
1
2
2
1
2
2
2
2
1
0
0
1
2
1
2
2
1
0
1
1
1
1
2
1
1
0
2
1
1
2
0
1
0
0
2
1
2
1
1
1
1
2
1
1
1
1
1
0
1
1
0
1
0
2
0
1
2
1
1
1
0
0
1
2
1
0
2
0
1
2
1
1
1
0
1
1
1
1
2
0
1
1
1
0
0
1
1
1
2
0
2
1
1
1
1
2
0
1
1
1
0
1
2
2
1
2
0
0
1
2
0
1
1
2
0
1
1
1
2
1
1
1
1
1
0
1
1
2
1
1
2
1
0
1
0
0
1
2
2
1
2
1
0
1
2
1
2
0
2
1
1
1
0
1
2
1
0
1
1
1
1
1
2
0
2
1
1
1
1
1
1
0
1
1
2
2
1
1
1
1
0
0
1
2
1
0
1
1
1
1
0
2
0
1
1
2
1
0
1
1
1
1
0
1
3
1
1
1
1
1
1
2
1
1
0
1
2
1
2
1
2
1
1
0
2
1
2
0
0
0
1
1
2
1
1
0
0
0
1
1
2
0
1
1
0
2
1
1
2
1
0
1
0
0
1
1
0
1
1
1
1
1
2
1
2
1
0
2
0
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
0
1
1
1
1
1
0
1
1
1
2
2
1
0
1
0
0
2
1
1
0
2
2
0
1
2
0
2
2
1
1
1
1
2
1
2
2
1
2
1
2
2
1
1
1
1
1
3
1
1
1
0
2
2
1
1
1
2
1
1
0
2
0
1
2
0
1
1
1
1
1
2
2
1
2
2
1
0
1
1
1
2
0
0
1
1
2
1
1
0
0
1
0
1
1
1
1
1
2
2
1
1
1
0
1
1
0
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
3
0
1
1
0
2
1
0
1
1
1
1
0
1
1
2
2
0
2
2
0
0
1
0
1
2
1
2
1
1
1
1
1
1
1
1
2
2
1
2
2
1
1
1
1
0
1
2
1
1
1
1
1
0
1
1
1
0
1
0
1
2
1
2
1
1
1
0
1
1
1
1
2
2
1
1
1
0
0
1
0
1
2
1
1
0
2
1
1
2
2
1
1
2
1
0
1
0
1
2
1
1
2
2
1
1
2
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
0
1
2
3
2
2
2
0
1
1
1
0
1
1
2
0
1
2
0
1
2
0
1
1
1
1
0
0
1
2
0
1
1
1
1
0
0
1
1
2
1
1
0
1
1
1
0
0
3
1
1
1
1
0
1
1
0
2
1
1
0
0
0
1
1
2
1
2
1
0
1
0
1
1
1
1
1
1
2
1
0
2
2
1
1
1
1
1
1
2
2
1
2
0
2
0
1
2
1
1
1
1
1
1
1
2
1
1
1
1
2
1
0
1
1
0
1
2
1
1
1
1
0
0
1
1
1
3
1
1
1
1
0
1
1
1
2
1
2
1
1
0
0
1
2
0
1
1
2
2
1
1
2
2
1
1
2
0
2
0
1
0
1
1
0
2
0
2
2
1
1
1
0
1
2
1
1
1
0
1
0
1
0
0
1
1
1
1
2
2
0
1
1
1
1
1
1
1
1
1
0
0
1
1
1
2
1
0
2
0
1
0
1
2
1
1
0
0
1
1
2
1
1
0
1
2
1
2
1
1
1
0
0
1
1
2
2
0
0
2
1
1
1
0
1
0
1
1
2
1
0
0
1
1
2
0
1
2
1
1
3
1
2
2
2
2
1
1
0
1
1
1
1
0
2
1
3
2
2
1
1
2
0
1
1
0
0
0
1
1
0
0
2
1
0
2
0
1
1
1
2
1
1
2
1
2
1
1
1
1
1
1
2
1
2
0
1
1
1
2
1
0
2
1
1
0
1
1
1
2
0
1
1
1
1
1
1
1
0
1
0
0
3
1
1
2
2
2
1
0
1
2
1
1
1
1
1
1
1
1
2
2
0
2
2
1
0
2
1
1
1
2
1
2
0
1
1
1
2
0
2
1
1
1
0
1
1
1
1
1
1
1
0
3
0
0
1
2
1
2
2
1
2
2
0
1
2
1
1
1
1
1
1
1
1
2
3
1
2
1
1
2
2
1
1
2
1
2
0
2
1
0
1
3
0
1
0
0
1
1
1
1
1
1
2
1
1
2
1
2
2
1
1
1
0
1
1
1
2
1
2
1
2
1
1
2
2
1
1
1
2
1
2
1
0
1
1
0
1
1
0
0
0
1
1
2
1
1
1
1
1
2
2
1
1
1
1
1
2
2
1
2
1
0
1
2
0
0
1
0
2
1
1
1
2
1
1
1
2
2
1
1
1
0
0
1
1
1
1
0
1
1
1
1
1
1
1
2
0
1
0
1
0
2
1
2
1
1
1
1
0
0
0
0
2
1
0
1
2
2
1
1
1
0
2
1
2
1
1
2
0
1
1
1
1
1
1
1
2
0
1
0
2
0
1
1
1
1
1
2
2
2
1
1
0
2
1
0
1
1
1
2
1
1
1
0
2
0
1
1
2
2
2
1
1
2
1
1
1
1
2
1
2
2
1
1
1
0
1
0
1
1
1
1
1
1
1
1
1
1
2
0
1
1
5
1
2
2
1
1
1
1
0
0
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
7
1
0
0
1
2
1
2
1
1
1
1
1
0
1
1
1
2
1
1
2
2
1
2
1
0
1
2
2
1
0
2
1
2
0
1
1
1
1
2
2
2
1
2
0
1
1
1
0
1
1
2
1
0
0
0
1
1
2
2
1
2
1
1
0
1
1
1
2
1
2
1
1
1
1
1
1
2
1
2
1
2
1
1
1
0
1
1
1
2
1
1
1
1
2
2
0
1
1
2
0
1
0
1
2
2
1
2
1
1
1
1
2
2
1
1
1
2
0
1
1
2
0
0
0
1
1
0
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
0
0
1
0
1
1
1
1
1
1
1
1
0
1
1
1
0
2
1
1
1
1
1
1
2
1
1
1
1
0
2
3
1
1
0
1
2
1
1
1
2
2
2
1
2
1
1
0
0
2
2
1
1
1
1
1
2
0
2
1
1
0
2
1
0
2
0
1
2
1
0
1
1
2
1
2
0
1
2
2
1
1
1
1
1
1
1
2
1
1
1
2
2
1
0
1
2
1
1
2
1
1
0
1
1
1
0
1
0
1
1
2
0
1
1
1
1
1
0
0
2
1
2
1
1
1
1
2
2
2
0
1
5
1
0
1
0
1
0
2
1
1
1
1
1
1
2
1
2
1
0
1
1
0
1
0
1
1
1
2
1
1
2
2
1
2
2
1
1
0
1
1
0
1
0
0
2
1
2
1
1
1
1
2
0
0
0
0
2
1
1
1
1
1
1
2
1
0
2
0
1
1
1
1
2
1
0
2
1
1
1
1
2
2
1
1
1
1
2
1
1
0
1
1
0
0
0
0
2
2
2
3
1
1
1
2
2
0
1
1
1
2
1
2
1
1
2
1
2
1
0
0
1
0
2
1
2
2
1
1
1
1
0
0
1
1
1
1
0
1
1
2
1
0
1
2
0
2
2
1
0
2
1
0
1
1
1
1
0
0
2
1
1
1
1
1
0
2
1
1
1
2
1
2
0
1
1
0
1
0
2
1
1
1
1
1
2
0
2
2
0
1
1
1
0
0
1
1
1
2
1
1
2
2
1
1
1
1
2
0
1
0
1
2
1
1
1
2
1
1
1
1
0
2
0
2
2
0
2
2
1
0
1
1
2
1
1
2
1
1
1
2
1
1
1
2
0
0
0
1
1
2
1
1
1
1
1
0
1
1
1
1
1
2
0
1
1
2
1
1
1
1
1
1
1
2
1
0
1
1
1
2
0
2
0
1
2
1
1
2
0
1
1
1
2
1
1
1
1
1
1
0
1
2
0
1
1
0
1
0
2
2
3
1
1
2
1
1
1
1
1
0
1
1
2
0
2
0
1
0
1
2
2
1
2
1
1
1
1
1
0
0
1
1
1
1
0
2
0
1
1
2
1
2
1
1
2
1
1
0
1
1
2
2
1
1
1
1
0
1
1
1
2
0
0
1
2
1
1
2
2
1
0
1
2
0
1
1
1
2
1
1
1
0
2
0
0
2
1
2
0
0
1
1
1
2
2
0
1
1
1
2
1
2
1
2
1
2
1
1
1
1
2
2
1
0
1
2
1
1
3
2
0
2
0
2
1
0
1
1
1
1
1
2
2
1
1
1
2
0
0
2
1
1
2
1
1
2
1
1
0
1
1
2
2
1
1
1
0
2
1
0
0
1
1
1
2
1
1
1
0
2
2
1
1
0
1
1
1
1
2
2
1
1
1
0
0
2
2
1
1
1
0
2
1
2
2
2
1
1
0
1
0
1
1
1
1
1
1
1
2
1
0
1
0
1
0
0
1
0
1
1
0
1
1
2
1
0
1
1
1
1
2
1
2
1
1
1
1
0
1
1
1
2
1
2
3
2
1
1
1
1
1
2
1
1
2
2
1
1
1
2
1
1
1
0
1
1
1
1
2
2
1
1
1
1
0
0
1
0
2
0
1
1
1
2
1
1
0
1
2
0
0
1
1
1
1
0
1
1
0
1
1
2
1
1
1
0
0
2
1
3
1
2
1
1
0
0
1
1
2
1
1
0
1
1
2
0
1
1
1
2
3
1
1
2
0
1
1
1
1
1
1
1
1
1
1
1
0
1
2
2
1
0
1
2
1
1
1
1
0
1
2
1
0
1
1
0
3
1
1
1
0
2
1
0
1
2
1
1
2
2
1
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
0
1
1
2
1
2
2
2
1
1
2
1
2
1
0
2
2
1
0
2
3
1
0
5
0
1
2
1
2
1
2
1
1
0
2
1
1
0
1
1
2
2
1
1
2
1
0
1
1
3
1
1
1
1
0
2
2
0
0
2
1
1
2
1
0
0
0
1
1
1
2
0
1
1
1
0
1
1
1
1
1
2
1
1
2
0
1
0
0
2
1
1
1
0
0
0
1
1
2
0
1
2
2
1
2
1
0
1
2
1
1
1
1
1
2
1
1
0
1
1
1
0
1
2
0
1
1
0
2
1
0
1
0
1
2
1
0
2
1
1
2
1
1
1
1
1
1
0
1
2
1
0
1
1
1
2
1
1
0
1
0
0
1
1
1
1
2
1
1
1
0
1
1
1
1
1
2
2
1
1
1
2
1
0
1
1
1
1
1
1
1
0
1
1
1
1
2
1
1
1
1
0
1
1
0
1
2
1
1
0
0
1
2
0
1
2
1
1
0
2
1
0
2
1
1
1
1
2
2
2
1
0
0
0
2
0
1
0
1
1
1
1
2
2
1
2
0
1
2
1
2
0
0
1
0
1
1
1
2
4
0
1
1
1
0
1
0
1
2
1
2
1
1
2
1
0
0
1
1
2
1
0
1
2
0
0
0
1
1
1
1
2
1
1
1
1
1
1
1
0
2
1
2
1
1
1
1
2
1
1
1
1
1
1
0
2
0
2
1
1
2
1
0
1
1
1
1
1
0
1
2
1
1
2
2
0
0
0
1
1
1
0
1
1
0
2
0
1
1
2
2
2
2
2
1
2
1
2
1
1
0
0
1
1
2
2
0
0
0
0
0
1
1
1
1
2
0
1
1
0
5
1
0
1
1
2
1
2
1
2
0
1
1
1
2
1
2
1
1
0
1
0
1
0
1
1
1
1
0
0
1
1
1
1
1
0
1
1
1
3
1
2
1
1
1
1
1
2
1
2
2
1
0
1
2
2
2
1
1
1
2
2
0
0
1
0
1
1
2
2
2
1
2
2
1
1
0
1
1
2
0
1
1
1
1
0
1
1
1
1
0
0
1
2
1
0
1
1
1
1
1
0
1
2
3
2
1
1
1
0
1
1
1
2
2
1
2
1
1
1
2
1
0
1
0
1
0
2
0
1
1
2
1
1
0
1
1
2
1
1
1
1
1
1
1
0
1
0
0
2
1
1
1
1
1
0
2
0
2
1
0
1
2
0
0
1
0
1
1
2
1
1
2
0
0
2
1
1
1
0
0
1
2
1
2
1
1
0
1
1
1
0
0
1
1
1
2
0
1
1
1
2
1
2
5
0
1
1
1
2
1
1
1
0
2
1
1
1
2
1
1
2
0
1
1
2
0
1
2
2
1
0
0
1
0
1
1
2
0
0
1
2
2
1
2
2
1
1
0
1
2
1
0
1
0
1
1
1
1
1
1
0
2
2
1
0
1
0
1
1
1
1
0
0
1
0
2
1
1
1
1
1
1
1
1
1
1
1
0
1
0
4
0
1
2
1
1
2
1
1
2
0
0
1
1
2
1
1
3
0
1
2
1
1
1
2
1
0
2
1
1
1
1
1
2
2
1
1
1
1
2
0
0
0
1
1
1
0
0
1
1
1
0
1
2
2
1
2
1
1
1
2
1
1
1
2
1
2
1
2
1
1
2
1
1
1
0
1
1
1
0
1
1
2
1
1
1
1
1
0
1
1
1
2
1
1
1
0
2
2
2
1
1
2
0
1
1
0
1
2
1
1
1
1
1
1
1
1
1
2
1
2
1
2
1
1
1
1
2
1
1
1
1
0
2
1
1
1
1
2
1
0
2
1
1
1
1
1
0
1
1
2
1
1
2
2
1
1
2
1
1
0
1
1
1
1
1
1
2
2
1
1
0
1
1
1
1
2
1
1
0
1
0
1
1
1
1
0
0
2
1
2
0
1
1
1
1
1
1
2
1
0
1
1
1
2
1
1
1
2
1
1
0
1
1
0
1
1
1
1
1
2
2
0
2
0
2
1
2
2
1
1
0
0
1
1
1
0
0
1
1
1
2
1
2
2
1
2
1
2
1
1
1
2
1
0
1
1
1
1
1
1
1
1
1
0
2
2
2
1
1
2
0
2
2
1
1
1
1
0
1
1
2
1
1
1
2
1
1
2
1
2
1
2
1
0
1
1
1
2
0
2
2
1
0
0
2
1
1
2
2
1
1
1
1
0
0
0
2
1
0
1
0
1
1
1
0
0
1
2
1
1
1
0
1
0
2
0
1
1
1
1
1
0
1
2
0
1
1
1
1
0
1
2
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
0
1
0
1
1
0
1
1
2
1
0
1
1
1
1
3
1
0
0
1
1
2
1
2
1
1
1
1
1
0
1
1
0
0
1
0
1
0
0
1
2
1
2
1
2
2
1
2
1
2
1
2
2
0
1
1
1
1
1
2
1
0
1
2
1
1
1
1
2
1
2
1
1
0
0
0
2
2
1
1
1
1
1
0
1
2
2
2
2
1
2
1
2
1
1
2
0
1
0
0
1
0
2
0
1
1
0
1
1
1
1
1
2
2
1
0
1
1
1
1
1
1
2
1
1
1
2
1
2
0
1
1
0
1
1
1
1
0
1
1
0
2
1
2
0
1
2
1
1
2
0
1
1
0
1
2
0
1
1
1
1
1
1
1
2
1
1
0
1
1
2
1
1
0
0
1
1
2
1
2
1
1
1
1
2
1
1
2
2
2
2
1
1
1
1
1
2
2
0
0
1
1
0
1
1
1
1
1
2
2
0
2
1
1
0
0
0
1
2
1
1
0
2
1
1
1
0
1
1
1
2
1
1
1
0
2
0
2
1
1
0
1
0
1
1
0
1
0
0
1
0
2
1
1
1
1
1
1
1
1
2
1
2
1
1
0
0
1
1
1
1
2
2
2
2
1
1
1
0
1
1
2
0
1
0
0
0
0
1
1
0
0
0
2
0
1
2
1
1
1
1
1
3
1
0
1
2
0
0
0
1
1
2
2
1
2
1
0
0
1
2
1
1
1
1
1
0
1
1
1
4
1
1
1
0
0
0
1
1
1
1
1
1
0
1
1
0
2
1
0
2
2
0
2
1
1
1
1
2
1
2
1
1
1
2
3
1
2
0
1
1
1
1
0
1
2
0
1
1
1
1
1
2
1
2
1
1
1
1
1
1
2
0
3
0
1
1
0
1
1
1
1
0
1
1
0
1
1
1
2
0
1
1
1
0
0
1
2
3
0
2
2
1
1
1
1
1
1
1
2
2
1
1
2
2
0
1
0
1
1
1
0
1
2
0
1
0
1
2
0
2
1
1
2
1
1
0
1
2
1
1
1
2
1
2
0
2
2
0
0
2
1
0
2
1
2
2
1
2
2
1
1
0
1
1
1
2
2
1
1
0
1
1
1
0
0
2
1
1
0
1
1
0
0
0
2
1
1
2
1
2
1
1
2
1
1
0
2
2
0
1
1
0
2
1
1
1
1
0
0
1
0
1
1
1
0
2
0
1
2
2
0
1
2
1
0
1
1
1
1
1
0
2
1
1
0
1
1
0
1
1
0
1
2
1
2
0
1
1
2
0
1
0
0
1
1
1
1
1
0
1
1
0
0
1
2
1
2
1
1
0
1
1
2
2
2
2
1
0
2
1
1
1
1
1
1
1
1
1
0
2
1
2
0
1
0
1
0
1
0
1
1
0
2
1
1
2
1
1
0
0
1
1
1
2
0
0
2
1
1
1
1
2
0
1
1
1
0
0
1
1
2
1
1
2
1
0
1
1
1
2
2
2
1
1
1
1
1
1
1
1
1
0
1
2
0
1
1
2
2
1
1
0
1
1
1
0
1
0
1
0
1
1
1
1
1
1
1
1
1
0
1
2
2
1
1
1
1
2
0
1
1
1
1
1
1
0
1
1
1
1
0
1
2
0
1
1
1
1
1
1
0
0
1
1
1
2
2
1
1
2
1
1
1
1
2
0
1
0
1
0
3
0
2
1
1
0
1
0
2
1
2
1
2
1
1
1
1
0
0
0
2
1
2
0
1
0
0
0
0
0
1
2
1
0
2
1
1
2
0
0
0
2
1
0
2
1
2
2
2
1
1
1
1
1
2
1
0
1
1
1
1
1
0
1
1
1
1
0
1
0
1
2
2
2
2
1
0
1
1
1
1
2
1
1
2
0
2
1
1
1
2
0
1
0
1
1
0
1
1
1
1
1
2
1
1
1
0
0
1
1
1
2
1
0
0
0
1
2
1
1
0
1
1
1
1
0
1
0
1
1
0
1
1
1
1
1
2
1
0
1
2
2
1
2
1
1
1
2
1
1
0
1
1
0
1
1
1
1
0
1
2
1
0
0
1
2
0
1
1
2
2
0
0
0
1
1
2
2
2
1
1
1
1
1
2
1
1
1
1
1
2
1
0
1
1
1
1
1
1
2
1
0
1
0
1
0
1
1
0
1
0
0
0
1
1
2
0
1
1
2
1
0
1
0
2
2
1
2
1
2
3
1
1
0
1
1
1
1
0
0
2
2
2
1
1
0
0
1
1
2
1
1
1
1
1
1
1
2
2
1
1
2
1
2
1
1
1
1
1
2
1
1
1
0
1
2
1
0
1
2
0
2
1
1
1
0
1
1
1
2
1
1
1
1
1
2
2
1
2
1
1
1
2
1
1
1
2
0
1
2
1
1
2
1
0
2
0
1
1
2
1
0
0
1
1
1
1
0
2
2
1
2
2
1
1
2
0
1
1
1
3
0
1
1
1
1
1
1
2
0
2
1
1
2
2
1
2
1
3
1
1
1
2
1
1
1
1
2
1
1
0
2
2
1
2
2
1
1
0
1
1
1
4
1
2
1
2
2
2
2
1
3
1
0
1
0
0
1
1
1
2
1
1
2
1
0
1
2
2
2
0
1
1
1
1
1
1
1
0
1
1
1
2
0
1
1
1
0
1
0
2
1
1
1
1
1
2
1
2
1
1
1
2
1
2
1
0
0
2
1
2
1
2
2
0
1
1
1
1
1
1
1
1
1
0
2
2
0
2
1
1
1
1
0
1
2
0
1
2
2
1
1
0
0
2
1
1
1
2
2
1
0
1
1
1
2
0
0
2
0
2
1
0
0
1
1
2
1
1
2
2
2
1
0
1
0
1
1
1
1
1
2
1
0
1
1
0
1
2
1
2
0
1
1
1
1
1
1
1
1
1
2
2
1
0
2
0
1
1
1
1
1
2
0
2
0
0
1
0
2
1
1
2
1
1
1
1
2
0
2
2
1
1
2
0
1
1
0
2
2
1
0
1
1
1
0
1
0
1
1
0
1
2
2
2
1
1
1
0
2
0
2
1
1
1
0
2
0
1
2
1
1
1
2
0
1
1
1
0
1
2
2
0
1
0
1
0
1
2
1
1
1
0
1
1
0
0
0
2
2
1
0
1
1
1
0
1
1
1
1
0
1
0
2
1
0
1
1
1
1
1
0
2
1
1
2
1
0
1
1
1
1
2
1
2
1
0
1
2
2
1
1
1
1
1
2
2
1
0
1
1
1
2
0
1
1
2
2
2
1
2
3
2
0
2
0
0
1
1
2
1
1
1
0
1
1
2
1
1
2
1
0
0
1
0
1
2
0
0
1
1
2
0
1
2
0
2
1
1
2
1
1
1
1
1
1
0
0
0
1
2
3
1
1
2
1
1
2
2
2
1
1
1
1
2
1
1
2
1
1
1
2
1
1
2
1
1
2
2
1
0
1
2
0
0
1
2
1
2
1
2
1
1
1
1
1
1
2
1
0
2
0
1
1
1
1
2
1
1
2
0
2
2
1
0
1
1
1
0
1
1
2
1
1
2
1
1
0
1
1
2
1
2
2
0
2
2
2
1
1
1
0
1
0
2
2
0
1
2
2
2
1
1
1
1
2
1
1
0
1
2
1
1
1
1
0
1
1
0
0
1
1
1
0
2
2
1
0
2
1
2
1
1
1
2
2
1
1
2
1
0
1
0
1
1
0
0
1
0
2
1
2
2
1
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
2
1
0
0
2
1
1
1
1
1
1
2
2
1
0
1
1
0
2
1
0
0
1
1
1
1
0
1
2
1
1
1
2
2
1
1
1
1
1
1
2
1
0
0
1
2
2
1
2
1
3
2
0
0
0
2
1
1
1
0
1
0
1
1
0
1
1
1
1
1
1
2
1
0
2
0
2
1
0
1
2
2
2
1
1
1
1
1
0
1
1
1
1
1
2
2
1
2
1
4
2
1
0
2
1
1
2
1
1
2
0
0
0
1
1
1
1
1
1
0
0
1
1
1
1
1
1
0
2
2
1
1
0
2
0
1
1
1
1
1
1
0
1
1
1
2
1
0
1
1
1
1
1
0
0
1
1
1
2
1
1
1
0
1
2
1
2
2
0
1
2
2
1
1
0
1
1
1
1
1
1
2
1
0
1
1
1
1
1
1
0
0
2
1
1
0
2
1
1
1
1
1
2
1
1
3
1
0
1
1
1
1
1
0
2
2
1
0
2
0
0
2
1
0
1
2
2
1
1
1
0
1
1
1
0
2
0
0
1
0
0
1
0
1
1
0
1
1
0
2
0
2
2
1
2
2
2
1
0
2
1
1
1
1
1
1
2
1
1
1
0
1
1
0
2
5
1
1
2
0
1
0
0
2
0
1
0
0
1
1
0
1
1
2
0
0
0
1
1
1
0
2
1
1
0
0
1
1
1
1
1
1
0
1
1
0
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
2
2
4
1
1
1
2
1
1
1
0
2
1
0
3
1
0
1
2
1
1
1
1
0
1
0
1
1
1
0
2
1
0
1
0
1
1
1
0
2
2
1
2
1
1
0
2
2
1
1
1
1
1
1
0
1
2
1
2
1
1
1
2
1
1
0
1
1
1
1
2
1
0
1
1
2
1
2
1
1
1
0
2
0
1
1
1
1
2
1
2
0
1
1
0
0
0
1
0
1
1
0
0
1
2
1
2
2
1
2
0
1
0
1
1
1
1
1
0
2
1
1
2
0
0
1
1
1
1
1
0
0
2
2
2
2
1
0
0
1
2
1
1
0
2
1
1
2
0
1
0
3
1
1
2
2
1
1
1
1
1
2
1
1
1
2
0
0
1
0
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
0
1
2
2
0
1
2
1
1
1
3
1
1
2
2
1
1
1
2
2
2
1
0
1
1
1
1
1
1
1
2
1
2
2
1
2
0
1
1
0
0
0
0
1
0
1
2
0
1
2
1
0
0
1
2
0
0
1
1
0
1
4
1
2
1
1
2
2
0
1
1
2
1
2
1
1
2
0
2
1
1
1
1
2
1
1
0
0
0
2
2
1
1
1
1
2
1
1
1
1
1
1
1
1
0
0
1
0
1
1
1
2
2
1
1
0
0
1
1
1
1
2
2
1
0
1
2
1
0
1
2
1
0
1
1
2
2
1
1
1
1
1
2
0
1
1
1
1
1
0
2
0
1
1
1
2
2
1
2
1
1
2
1
1
2
1
1
0
1
1
1
1
0
1
1
1
0
1
2
1
0
1
1
1
1
1
1
1
0
1
1
1
1
2
1
0
0
1
1
1
2
1
1
1
2
1
0
1
1
1
1
1
1
1
1
0
1
1
2
1
1
0
2
2
2
1
1
1
2
0
1
2
0
0
1
1
0
1
1
1
2
2
1
1
2
1
0
1
1
1
1
1
1
1
1
2
1
1
2
2
2
2
2
1
1
1
2
1
1
1
2
2
0
1
0
1
0
1
2
1
1
2
1
0
2
1
2
0
3
1
1
2
1
2
1
1
2
2
0
1
1
1
0
2
2
2
1
1
0
1
0
1
1
1
0
1
2
0
0
1
1
1
1
1
2
1
0
1
1
1
0
1
2
2
0
1
0
0
1
1
1
1
1
0
2
2
2
1
0
1
1
2
2
0
1
0
0
3
1
1
1
1
1
1
0
1
1
0
1
0
0
2
1
1
0
1
2
1
1
0
1
1
1
0
1
1
1
1
1
1
2
1
1
0
2
1
2
1
1
1
1
0
2
0
1
1
1
1
2
1
1
1
1
0
0
2
2
1
1
1
1
2
1
2
2
1
1
1
1
1
2
1
1
1
1
2
1
1
1
0
2
1
0
1
0
1
1
0
1
1
1
1
1
1
2
0
0
1
1
1
2
1
1
2
1
1
1
1
1
1
1
0
1
1
1
2
1
1
0
2
0
1
1
1
0
1
0
2
1
1
1
1
0
0
0
2
2
2
2
1
1
0
0
0
1
1
1
1
0
2
1
0
1
2
1
0
1
1
0
0
1
1
1
1
2
1
1
0
1
1
2
2
0
0
0
1
1
1
0
2
1
2
2
0
2
1
2
0
1
0
0
0
2
1
0
1
0
0
1
1
2
2
1
1
0
1
1
0
1
2
1
1
1
0
2
1
1
1
2
2
1
0
1
1
0
1
0
1
2
1
2
1
0
0
2
1
1
0
1
1
1
1
0
2
1
1
1
1
2
2
2
1
1
2
2
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
2
1
1
0
1
1
0
1
0
0
0
1
2
1
2
1
1
1
1
1
1
1
1
2
1
1
0
1
1
1
0
2
1
1
0
1
1
2
2
0
0
3
1
1
1
1
1
2
2
1
2
1
2
2
1
0
1
0
2
0
2
2
1
1
1
1
1
1
0
1
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
1
0
2
1
2
1
1
0
1
0
0
2
2
0
0
2
2
0
1
1
0
1
1
1
0
2
1
0
1
1
1
1
1
1
2
2
1
1
1
0
2
1
1
1
1
1
1
1
1
2
1
2
1
0
0
1
1
2
0
2
1
1
1
2
1
0
1
1
1
2
1
1
1
1
0
1
1
2
0
0
1
0
1
1
0
2
1
1
1
0
0
1
1
2
1
2
1
1
0
1
2
1
1
2
2
1
1
1
1
2
1
1
0
1
1
2
1
0
0
2
2
0
0
0
2
0
1
0
1
1
1
1
1
1
1
1
0
0
2
2
1
1
0
1
1
1
2
1
1
2
1
1
1
2
1
2
1
1
2
2
2
2
1
1
1
2
1
0
1
2
1
2
1
2
0
2
1
2
1
2
0
0
1
2
0
1
2
2
1
2
0
1
1
2
1
2
1
2
1
2
0
1
1
2
2
1
1
1
1
1
0
2
1
0
1
3
0
2
1
1
2
1
1
1
0
0
1
2
2
1
1
0
1
1
2
1
1
1
1
2
0
0
2
1
2
0
4
0
0
1
0
0
1
1
1
2
1
0
3
1
0
1
2
1
1
1
1
1
1
1
2
2
0
1
1
2
2
1
0
1
1
1
1
0
2
2
1
1
2
1
1
1
2
1
1
1
1
0
0
2
2
1
2
2
1
1
2
2
0
1
1
1
1
1
1
0
2
0
2
0
1
1
0
1
2
1
2
0
1
1
2
5
1
1
2
1
1
2
1
0
0
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
0
1
2
2
1
1
1
1
1
1
1
0
2
0
0
1
2
1
1
1
2
0
2
1
0
2
1
2
1
2
0
0
0
1
1
3
1
2
0
0
2
1
0
1
1
0
1
1
1
2
2
2
2
2
1
2
2
1
1
1
1
1
2
2
1
0
1
1
1
1
1
1
1
1
1
0
0
2
1
1
2
1
1
0
1
2
3
1
1
1
0
0
1
0
0
2
1
2
2
2
2
1
2
0
2
1
1
1
1
1
0
2
1
0
2
1
1
1
1
1
0
0
2
2
1
2
2
1
1
0
1
1
2
0
1
0
0
1
1
1
2
1
0
2
0
2
1
0
2
0
1
1
1
0
1
0
1
0
1
1
0
2
1
1
1
1
1
2
2
0
1
1
1
1
1
1
2
0
1
2
1
1
1
1
1
0
1
1
1
2
1
1
1
2
1
1
2
0
2
0
1
2
1
1
1
1
2
1
2
1
1
2
1
1
0
1
2
1
2
1
1
0
1
0
1
1
1
1
1
1
1
0
2
2
1
1
1
1
2
1
1
2
2
2
1
1
1
0
0
1
0
2
0
0
2
1
1
1
2
1
2
1
0
1
2
0
1
1
0
2
1
1
1
1
1
0
2
0
1
1
0
0
1
1
1
2
1
1
1
0
1
1
2
1
1
2
1
1
1
1
0
0
1
2
2
1
0
0
2
0
2
2
1
1
0
1
1
1
0
2
2
1
1
1
0
2
0
0
1
1
2
0
1
1
0
0
1
1
1
1
2
0
1
2
1
0
0
1
1
1
1
2
1
1
0
1
2
0
0
2
0
2
2
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
2
1
1
1
2
0
1
1
2
0
1
1
2
2
2
1
0
0
1
1
1
2
2
1
2
2
1
1
1
0
1
1
1
1
1
1
2
2
1
1
1
0
1
2
1
2
1
1
1
0
2
0
1
1
2
1
1
1
1
1
1
1
2
2
1
2
2
1
0
1
0
2
1
1
2
1
1
1
1
2
2
1
1
1
1
1
2
2
1
0
1
1
2
1
2
0
0
1
1
1
2
1
2
2
1
1
0
1
1
1
2
1
2
1
3
1
1
1
0
1
2
1
1
1
1
1
1
2
2
1
0
1
1
2
2
1
0
0
2
0
0
0
1
1
1
2
0
0
1
0
1
0
1
2
1
0
1
1
1
2
1
2
0
1
2
2
1
1
1
2
1
1
1
1
1
2
0
1
2
1
0
0
1
1
1
2
1
0
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
0
1
1
1
1
2
1
0
1
2
1
2
1
0
0
1
1
2
0
1
1
0
1
1
1
1
0
2
2
1
2
2
2
2
1
2
2
1
2
2
1
2
2
0
2
2
1
2
2
1
2
1
1
0
2
1
1
1
1
2
1
1
2
0
2
0
2
2
2
0
2
1
1
2
2
1
1
2
2
1
1
1
0
1
1
1
1
2
1
1
1
1
0
1
1
1
0
1
1
1
2
1
1
1
0
1
1
1
1
1
2
0
1
1
1
1
2
1
2
2
1
2
2
1
1
2
0
1
3
1
1
1
1
2
1
0
1
2
2
1
2
1
1
0
1
1
1
3
1
1
1
1
1
1
0
2
1
1
2
1
2
1
1
0
0
0
2
1
2
1
1
1
1
0
1
1
1
2
1
1
1
1
2
2
1
2
2
1
1
1
2
1
0
2
1
2
1
1
1
1
1
2
2
2
1
1
1
2
2
1
1
2
2
1
1
0
1
0
1
2
1
0
0
1
1
1
1
1
0
1
1
2
2
2
1
1
0
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
2
3
0
1
0
2
1
0
1
0
1
2
1
1
0
1
2
1
1
2
1
3
1
1
1
1
0
0
1
1
2
0
0
1
0
1
2
1
1
0
2
1
1
1
2
2
1
0
1
1
1
2
1
0
1
1
1
1
1
1
1
2
0
2
0
2
2
2
0
1
1
0
0
1
1
1
2
1
2
1
1
1
1
0
2
1
1
1
2
1
1
1
1
1
1
0
2
1
1
0
2
0
1
2
4
1
1
1
1
4
1
1
1
1
1
1
1
1
1
1
1
2
1
0
1
0
1
1
0
1
1
0
1
1
2
1
2
1
1
1
1
2
1
2
2
2
2
0
1
1
1
1
1
0
1
1
1
1
1
1
0
0
1
0
1
1
2
2
1
2
0
0
0
2
2
1
0
2
1
2
0
2
0
2
0
1
1
1
2
1
1
1
1
1
1
0
2
0
1
1
2
0
1
0
2
1
2
1
1
1
1
1
2
1
1
0
1
2
1
1
2
0
1
1
1
1
0
1
0
1
0
2
0
2
0
2
2
4
1
1
2
0
0
2
2
2
0
1
1
1
1
1
1
0
0
2
1
0
1
2
1
1
1
2
2
2
1
2
0
1
0
0
1
1
1
1
1
0
1
0
2
0
0
1
2
2
1
1
1
1
2
1
0
0
1
1
1
1
0
1
2
2
1
1
2
2
1
1
2
1
1
0
1
0
2
0
1
0
0
2
2
2
1
0
2
1
1
3
1
1
2
1
1
2
1
1
0
1
2
1
1
2
1
2
2
1
0
2
2
1
0
1
3
2
2
1
1
2
0
1
0
0
0
1
0
1
1
1
1
0
1
2
0
0
2
0
1
2
1
1
1
2
1
0
1
1
2
1
1
0
0
2
0
1
2
0
0
2
2
0
2
1
2
1
1
2
0
0
1
1
2
1
1
1
0
1
1
0
1
2
1
1
1
1
0
1
1
1
1
0
1
0
2
2
2
1
0
1
1
0
2
1
2
1
1
1
0
2
0
2
1
1
0
2
0
0
0
2
1
0
1
1
1
1
1
1
1
1
1
0
2
1
0
2
0
0
1
2
1
0
2
0
1
0
1
1
2
2
1
1
0
1
1
2
1
0
1
0
0
1
0
2
1
0
1
1
2
1
1
0
0
2
1
0
2
2
1
1
3
1
2
1
1
0
1
2
1
1
0
1
1
1
1
1
1
2
2
1
1
1
2
1
2
0
2
1
1
1
0
1
1
1
1
2
1
0
0
0
2
1
1
1
1
1
2
2
1
1
0
0
2
1
1
1
2
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
0
1
0
2
1
2
1
1
1
2
1
1
1
0
0
2
1
1
2
0
2
1
1
0
1
1
2
1
1
1
1
0
1
1
2
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
0
2
0
1
2
1
2
1
0
1
1
1
1
0
1
0
1
2
1
1
1
1
2
1
0
1
1
2
2
1
1
1
1
1
0
1
1
2
1
2
1
1
0
1
1
2
1
1
2
1
2
1
2
1
1
2
1
2
1
1
1
2
0
1
0
0
1
2
1
0
1
1
0
2
1
0
1
2
2
0
0
0
1
1
2
1
1
0
1
1
1
1
0
2
1
2
2
0
1
2
1
0
1
2
2
1
1
1
0
1
0
1
2
2
2
1
0
0
1
0
2
1
1
1
1
1
1
1
1
1
2
2
1
0
1
2
1
1
0
1
1
0
0
1
1
1
2
0
1
1
1
2
1
1
2
2
1
2
2
1
1
0
1
0
0
1
1
1
1
1
0
1
1
1
0
1
1
1
1
2
1
1
1
1
0
1
1
1
1
2
2
0
2
1
2
1
1
2
1
0
2
1
1
1
1
2
1
1
1
0
1
0
0
1
2
1
1
1
1
1
2
1
1
0
1
1
0
1
0
2
1
1
1
0
2
1
1
1
1
1
1
1
1
1
1
2
1
0
0
1
1
2
2
1
1
1
1
1
1
2
1
0
1
1
2
1
0
0
1
2
0
1
1
1
1
1
0
1
2
1
1
1
2
1
1
2
2
1
0
1
2
2
2
1
1
0
1
0
1
2
1
1
0
0
1
0
2
1
1
1
1
2
1
2
0
1
1
0
1
1
1
1
0
1
1
1
2
2
1
1
1
1
0
1
1
2
1
2
1
1
2
0
2
1
2
2
2
2
1
1
1
1
2
0
1
2
2
1
0
1
1
1
0
2
0
1
1
1
2
1
1
0
1
2
3
1
1
2
0
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
2
0
0
1
1
2
2
1
1
0
2
1
0
0
0
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
2
1
1
2
1
1
0
1
1
1
0
0
1
0
1
0
1
1
1
1
1
2
0
1
0
1
2
1
2
0
0
1
2
1
0
0
0
1
0
2
2
0
0
1
2
0
1
2
1
0
1
1
1
1
1
1
1
1
0
2
2
1
1
2
1
1
1
1
0
1
1
1
1
0
1
2
1
1
0
1
1
2
1
1
1
2
0
1
1
2
1
0
2
1
1
1
0
1
1
1
2
1
2
0
0
1
2
0
1
2
1
2
1
2
1
1
2
2
1
0
1
1
1
1
0
1
1
2
2
2
1
1
1
2
1
0
0
1
4
2
1
2
1
2
2
1
2
1
1
1
1
1
1
1
0
2
1
1
1
1
1
1
0
1
0
2
1
2
0
1
0
1
0
2
2
1
1
1
2
0
2
1
1
0
0
1
1
0
1
1
2
1
1
1
0
1
1
1
0
1
2
3
1
1
2
1
1
1
1
1
2
1
1
0
1
0
1
1
1
2
2
1
1
2
1
1
2
2
2
0
0
1
1
1
1
0
1
1
1
0
1
1
0
2
1
1
1
1
1
1
1
1
0
1
0
1
1
1
1
1
0
1
1
1
1
1
0
1
1
0
1
0
1
2
0
2
1
2
1
1
2
0
1
0
1
2
1
1
2
1
0
1
1
1
2
1
1
2
1
1
0
1
0
2
1
1
2
1
9
1
2
1
1
1
1
1
0
1
1
2
1
0
1
0
1
1
1
2
0
1
1
0
2
1
2
0
1
0
1
1
2
0
1
1
0
0
1
1
0
1
2
0
1
2
2
1
0
2
1
1
1
0
1
1
1
1
0
0
1
0
1
1
1
2
2
0
1
2
0
1
0
1
1
1
1
1
1
1
0
2
0
2
0
1
2
1
1
1
2
1
2
1
1
1
0
1
1
2
1
0
0
2
1
0
1
2
1
1
2
0
1
2
2
2
1
0
1
0
0
1
1
1
1
1
1
2
0
1
1
0
2
0
1
2
1
2
0
2
1
1
0
2
0
1
1
0
1
2
2
1
1
1
1
2
2
1
1
1
1
1
1
0
2
1
1
1
1
1
1
1
2
2
1
2
1
1
1
0
0
1
1
2
0
1
2
0
2
1
0
1
0
0
1
1
1
0
2
1
0
1
1
0
1
1
0
0
1
0
0
1
2
2
1
1
1
1
2
2
1
1
2
1
0
0
0
1
2
0
0
1
0
1
0
0
3
1
2
1
1
2
0
2
1
2
1
1
1
0
2
2
1
1
1
1
1
0
1
1
2
2
1
1
0
2
1
1
1
1
1
0
1
1
2
1
2
0
2
2
1
0
1
1
1
0
1
1
1
1
0
0
2
1
1
1
1
0
1
1
2
2
1
2
1
0
1
2
0
2
1
2
2
1
2
2
1
0
2
1
1
2
2
0
1
2
2
1
0
2
0
1
1
1
1
0
1
1
1
2
1
0
1
1
0
1
1
2
1
0
1
2
1
2
1
2
1
1
2
2
0
1
2
1
1
2
1
2
2
3
1
0
1
2
0
1
1
1
1
1
2
0
0
1
1
1
1
1
1
3
1
2
0
2
1
3
1
0
0
2
1
1
1
1
2
2
0
0
1
2
1
1
1
1
0
1
1
2
1
2
1
1
1
0
1
1
1
1
2
1
1
1
1
0
2
3
2
1
1
1
1
0
1
1
1
1
2
1
0
1
1
2
2
0
2
1
1
0
2
1
1
1
2
1
0
2
1
1
1
1
0
2
0
1
1
1
0
1
1
0
1
1
1
2
0
0
1
0
2
1
1
0
1
1
1
2
2
1
1
2
2
1
1
1
1
0
1
2
0
2
1
1
2
0
1
1
1
1
1
1
2
0
1
1
0
1
0
2
1
1
0
1
1
0
1
1
1
1
0
0
1
1
1
2
1
1
0
1
0
1
1
1
0
2
0
1
0
1
1
2
1
0
2
1
0
2
1
2
2
1
1
2
2
2
0
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
2
1
1
0
1
1
2
2
0
1
0
1
1
1
1
1
0
1
1
1
0
0
1
1
0
0
1
1
1
1
1
2
1
2
1
1
2
1
2
2
1
1
1
0
0
1
1
1
0
1
1
0
1
1
2
1
1
1
1
1
0
0
1
2
1
1
1
0
2
2
0
1
0
1
0
1
1
1
2
1
1
1
1
0
1
1
1
1
2
2
2
1
1
2
1
1
1
2
1
2
1
1
2
0
1
1
0
1
1
1
1
0
0
0
1
2
1
2
1
2
1
2
2
2
1
0
1
2
1
1
1
0
1
1
1
1
1
1
0
2
2
1
1
1
1
1
0
1
0
1
2
2
1
2
0
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
2
0
1
3
1
2
1
2
0
2
1
1
2
1
2
1
2
0
1
0
0
2
1
1
1
1
0
1
1
1
1
0
1
0
2
1
2
1
1
1
1
1
1
2
1
1
2
0
0
1
1
0
2
1
0
1
1
0
1
2
1
0
1
0
1
1
1
2
2
1
1
1
0
0
2
0
0
1
1
1
1
1
1
1
1
1
1
0
2
2
1
0
1
0
1
2
2
1
1
1
1
2
1
2
1
2
1
2
0
1
1
1
0
2
1
1
1
1
0
1
1
1
2
1
4
1
0
1
1
2
0
0
0
2
1
1
1
1
2
0
1
1
2
1
1
1
1
1
1
0
1
1
1
0
2
2
2
2
1
2
1
2
2
1
1
1
1
1
1
0
1
2
1
2
1
2
1
0
0
0
1
1
1
0
1
2
1
1
0
1
1
2
1
1
1
0
1
1
1
2
1
1
2
1
0
1
1
1
2
1
0
0
1
1
1
2
1
1
1
1
1
1
1
4
0
2
1
2
0
1
1
1
1
0
1
3
0
0
0
1
1
1
1
2
0
0
1
0
0
2
2
2
1
2
1
0
2
1
2
2
0
0
0
1
2
2
2
1
2
0
1
1
1
1
1
2
0
2
0
2
2
1
1
1
1
1
1
1
1
2
1
1
1
0
1
3
2
1
1
1
2
0
1
1
1
2
2
0
1
1
1
2
1
1
2
2
1
2
1
0
1
2
0
1
2
2
0
2
1
1
2
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
2
2
0
1
2
1
1
1
2
1
1
2
2
2
1
1
2
1
2
0
0
1
2
0
1
0
1
1
1
1
1
2
1
1
2
1
1
0
2
3
0
1
1
0
0
1
1
2
0
1
0
2
0
1
1
1
1
1
1
1
4
2
0
1
2
1
1
2
0
2
2
1
2
0
2
2
2
1
1
2
1
0
0
2
1
0
1
1
1
1
2
1
1
1
2
1
0
1
1
0
1
1
1
1
1
1
1
0
1
1
0
1
1
0
1
0
1
0
1
2
1
1
1
1
0
1
2
1
2
2
1
1
4
0
1
1
1
0
1
1
1
1
0
1
0
1
1
1
2
1
1
2
1
0
1
1
2
1
0
1
1
0
1
1
2
1
1
2
1
3
0
0
1
0
2
2
0
1
2
1
0
2
1
1
2
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
0
2
1
1
1
0
1
1
0
1
0
1
0
0
0
1
2
2
0
2
2
1
1
1
1
1
1
1
2
1
3
2
1
1
2
0
0
0
1
1
0
5
2
1
0
1
1
2
1
0
1
2
1
1
2
1
2
0
0
1
0
1
1
0
1
1
1
2
0
2
2
1
1
2
2
2
1
0
2
1
1
1
2
1
1
2
1
0
0
0
1
0
2
1
1
3
0
1
0
1
1
1
0
1
1
2
1
1
1
1
0
1
1
0
1
2
1
3
1
2
1
0
2
0
2
0
2
2
0
1
1
1
0
2
0
2
0
1
1
1
1
2
2
1
1
1
1
1
1
0
3
1
2
0
1
1
0
2
1
2
1
1
1
2
1
1
0
2
1
1
1
1
1
2
1
2
0
1
0
1
2
1
1
2
1
1
1
1
1
2
1
1
0
2
0
1
1
1
0
1
2
2
2
1
1
1
3
1
3
2
1
0
0
1
2
1
3
1
1
2
1
1
0
1
2
0
1
1
2
1
1
0
1
2
2
0
1
1
0
2
0
1
1
1
2
2
1
1
1
1
1
0
1
2
1
1
1
2
2
0
2
2
1
0
3
0
2
1
1
2
1
1
1
0
1
4
1
0
0
1
1
0
2
0
1
1
1
1
0
1
0
1
2
2
2
1
0
1
2
1
1
1
1
1
2
0
0
1
2
1
2
1
1
0
1
1
1
1
1
2
1
0
0
1
1
1
1
1
1
0
1
1
2
2
1
2
2
2
1
1
2
0
1
0
1
0
0
1
1
2
2
2
1
1
1
1
0
0
0
0
2
2
2
0
1
1
1
1
1
1
0
1
0
2
1
1
0
0
1
1
2
0
1
1
0
1
1
1
1
1
0
1
2
1
1
0
1
1
1
1
1
1
2
2
1
1
0
0
1
1
1
1
1
1
0
0
1
1
1
1
1
0
0
1
1
2
1
1
0
2
1
1
1
1
2
1
1
0
1
0
1
1
1
1
2
1
1
1
2
2
1
0
2
2
1
1
1
1
1
2
3
2
1
1
1
1
0
0
2
2
2
1
1
0
1
1
2
0
1
1
1
1
2
2
2
1
0
1
0
0
2
2
1
0
2
0
1
2
0
1
2
0
1
1
1
1
2
2
1
0
1
2
0
0
2
1
3
1
2
2
0
0
0
1
0
2
1
2
1
0
1
2
0
2
1
1
0
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
3
1
1
2
0
0
2
0
1
0
1
2
1
0
0
0
1
2
2
1
1
1
2
1
1
1
1
1
2
0
1
1
1
1
1
1
1
2
1
0
2
1
0
2
1
1
1
1
2
1
2
1
0
2
1
0
1
0
1
2
0
1
1
1
0
1
1
1
1
1
1
2
0
0
1
1
1
2
2
1
0
2
1
1
1
1
1
1
1
1
0
0
1
1
1
1
0
1
1
0
2
1
1
2
0
1
1
1
2
1
1
1
0
2
2
2
2
0
1
1
1
0
0
1
1
2
1
1
1
2
1
2
1
2
1
2
1
1
0
2
1
2
1
1
1
0
0
1
1
0
1
0
0
1
2
1
1
1
1
1
2
1
1
1
2
0
1
1
1
1
1
1
2
3
0
1
2
1
1
1
0
0
1
1
0
1
1
0
1
0
2
1
1
2
1
0
0
2
2
1
1
1
0
0
2
1
1
1
1
2
2
1
1
1
1
0
1
2
1
1
2
1
1
2
2
1
1
1
1
0
0
1
1
1
1
1
0
1
4
1
1
2
1
2
1
1
0
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
2
0
2
1
2
2
1
1
1
1
1
0
0
2
2
1
2
1
0
0
2
2
1
1
1
2
2
1
0
1
0
1
1
1
1
0
1
1
0
1
1
2
2
0
0
1
1
0
1
1
1
1
2
1
0
1
2
0
1
3
0
2
1
2
1
1
1
2
2
1
1
1
0
2
0
0
1
0
1
2
1
1
2
1
2
2
1
1
1
0
1
2
1
0
0
1
2
2
1
0
1
1
1
0
2
2
1
1
1
2
2
2
1
1
1
0
1
1
1
1
2
1
2
1
1
0
1
0
1
2
1
1
0
0
0
1
0
3
0
2
1
1
1
0
2
1
2
0
1
1
1
2
0
2
2
1
0
2
1
2
1
1
1
1
1
3
1
0
0
1
1
0
1
1
1
2
2
1
0
1
1
1
2
1
1
2
0
1
1
2
2
1
2
2
1
2
1
1
1
1
1
0
1
1
0
1
2
1
0
0
1
0
1
0
1
0
1
1
2
1
0
1
2
1
2
1
1
1
0
0
0
1
2
1
1
1
0
1
1
2
0
1
0
1
2
1
0
1
0
0
1
1
1
1
2
1
2
1
0
1
1
1
1
1
2
1
0
0
1
2
2
1
0
1
1
1
1
1
1
1
1
2
1
0
2
0
1
1
1
1
1
1
1
1
0
0
0
2
1
1
0
2
1
1
1
1
1
2
1
1
2
1
1
1
2
0
0
1
2
1
2
0
1
1
1
2
1
1
1
1
1
2
2
1
2
0
1
0
2
1
2
1
2
0
1
0
2
1
2
1
0
1
1
1
1
1
1
1
1
2
1
1
1
2
1
0
1
1
2
2
2
2
0
1
0
2
1
1
1
1
0
2
1
1
0
2
1
1
0
0
2
1
2
0
2
0
1
1
1
1
0
1
1
1
1
2
2
0
0
2
1
1
0
1
1
1
1
0
2
0
0
1
2
1
1
2
0
2
1
2
0
2
1
1
1
1
1
0
1
0
1
1
1
1
1
1
0
1
1
0
2
1
1
1
1
1
1
0
2
1
1
0
1
1
1
0
0
1
1
1
1
0
1
1
2
1
1
0
0
1
1
1
2
1
1
0
0
1
1
2
2
1
1
1
0
2
1
0
1
0
2
1
1
1
1
1
1
0
1
0
1
1
0
1
2
2
1
2
1
1
1
1
1
1
1
1
2
2
2
0
1
1
1
1
1
0
1
2
1
1
1
1
1
1
2
1
1
1
1
1
0
1
1
1
1
1
0
1
2
1
1
0
0
1
0
0
1
0
1
1
0
1
1
1
1
1
2
1
1
0
2
2
2
3
1
3
0
0
2
2
1
2
3
0
1
1
1
0
2
0
0
1
1
2
1
1
1
2
0
1
1
1
2
0
2
1
0
2
1
1
2
2
1
1
1
1
2
1
0
1
2
1
1
1
1
1
1
2
1
0
2
1
1
2
1
1
1
0
1
2
1
2
2
1
1
1
0
1
1
1
1
0
2
1
1
1
1
1
2
0
1
2
2
0
2
1
0
1
0
0
3
1
2
2
1
1
1
1
1
1
4
1
1
0
0
1
1
3
2
0
0
1
0
1
0
1
0
1
1
1
0
1
1
1
2
0
0
0
1
1
1
2
1
1
1
0
2
0
1
2
1
1
1
0
1
2
1
2
2
1
1
1
1
0
1
0
1
1
2
2
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
0
1
1
1
1
1
1
1
2
1
1
2
1
1
2
2
1
2
1
0
1
0
0
2
0
1
1
2
1
1
1
0
1
1
0
1
0
1
1
2
1
0
1
1
2
1
1
1
0
1
1
1
2
1
0
1
0
2
1
0
2
1
1
0
0
1
0
0
1
2
2
1
1
1
1
1
2
2
1
1
0
1
2
1
1
0
0
0
1
0
2
1
0
1
1
2
0
0
1
1
1
0
0
0
0
1
1
1
2
1
1
2
0
1
1
1
2
0
0
2
2
0
1
2
1
2
1
1
1
0
1
0
3
1
1
2
1
1
1
0
2
1
1
1
1
1
0
2
1
1
2
2
2
2
1
0
1
0
2
1
2
2
1
1
1
1
1
0
1
2
2
1
1
1
1
1
1
2
2
0
2
1
2
0
1
2
1
1
0
0
2
1
1
2
2
0
2
1
1
2
0
1
1
0
2
1
1
1
2
0
1
1
2
0
1
0
1
1
2
1
2
1
1
2
1
0
1
1
1
2
2
1
1
1
1
1
2
2
0
1
2
1
1
0
2
1
3
1
1
1
1
1
1
1
0
1
1
2
1
1
0
1
1
1
2
0
0
2
1
1
2
1
1
0
1
1
1
1
2
1
1
0
0
1
1
1
1
1
1
2
1
2
0
0
1
1
1
0
1
1
0
1
2
1
2
1
1
0
1
1
0
1
0
0
1
1
0
2
1
2
1
2
1
0
1
2
2
1
2
0
1
1
2
1
2
2
1
0
0
1
1
1
1
1
1
1
1
1
1
1
2
1
0
1
1
1
1
1
0
2
1
2
1
1
1
2
1
1
1
1
1
1
1
0
0
1
2
1
1
1
0
0
1
1
2
2
1
2
0
1
1
2
1
1
0
1
0
1
2
0
1
0
0
1
2
1
0
1
1
1
0
1
0
1
1
2
0
1
1
1
2
2
1
2
2
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
0
2
1
1
1
1
2
1
1
1
2
1
2
1
0
1
0
1
1
0
2
0
0
1
1
0
1
1
0
1
1
1
1
1
0
0
1
1
2
1
2
2
1
1
0
1
2
2
0
2
2
1
3
0
1
2
0
0
1
0
0
1
2
0
2
2
1
0
1
2
2
1
1
2
2
0
2
2
0
1
0
1
1
1
2
1
2
1
2
1
0
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
0
1
0
0
1
1
1
3
1
1
2
1
2
0
2
2
0
1
1
2
0
1
1
0
2
0
1
0
0
0
1
1
1
1
2
1
0
2
1
2
1
1
2
2
1
2
1
1
1
1
0
1
1
0
1
1
0
2
1
1
1
1
2
1
2
2
1
1
1
1
0
1
1
0
1
1
1
1
1
1
1
0
1
1
1
0
1
1
2
0
0
2
1
1
1
2
1
1
0
2
1
0
1
0
1
1
2
0
2
1
1
1
1
0
1
1
1
2
1
0
2
0
1
2
1
0
1
2
1
0
1
6
1
2
1
2
1
1
1
1
1
1
0
1
1
2
1
2
1
0
1
0
1
2
1
1
2
1
1
2
1
1
1
2
2
1
1
2
2
1
1
1
0
1
2
1
1
1
0
1
0
0
2
1
1
2
1
1
2
1
1
1
1
2
0
2
1
1
2
0
2
0
0
1
0
2
1
1
1
0
0
1
1
2
1
0
0
1
2
2
1
2
1
2
0
1
0
0
1
1
1
1
1
1
1
1
1
1
1
0
2
2
1
1
1
1
1
2
1
0
1
1
1
1
1
1
1
2
1
1
1
0
5
0
0
1
1
1
1
1
0
2
2
1
1
2
1
1
1
2
2
1
1
1
1
2
1
1
1
2
1
1
2
0
0
2
1
1
1
2
1
0
1
1
0
2
1
1
1
1
1
2
1
2
1
1
1
0
2
0
1
2
1
1
1
1
1
2
2
2
1
0
1
1
2
0
1
0
1
1
1
0
2
1
0
2
1
1
0
1
1
0
1
2
2
2
1
0
2
0
2
1
2
1
1
1
2
1
1
1
2
2
1
2
1
0
2
1
1
1
0
1
1
1
1
1
1
1
2
0
2
1
2
0
1
2
3
2
0
0
1
1
2
1
0
1
2
1
2
1
0
0
2
2
1
1
2
0
1
1
1
1
0
1
1
2
1
2
0
0
1
1
1
0
1
1
0
2
1
1
1
1
1
0
1
1
1
0
0
1
2
1
1
1
1
2
1
1
1
2
1
2
1
1
2
0
1
2
1
0
3
2
1
1
3
1
2
0
0
2
2
1
0
1
1
1
1
0
2
2
1
2
2
1
2
1
1
2
0
2
2
1
0
1
1
2
1
1
2
1
1
1
2
1
2
2
1
1
1
2
1
1
1
1
0
0
1
2
2
0
1
1
1
0
0
2
1
1
1
1
1
1
3
1
0
3
1
1
0
0
1
2
1
1
1
0
0
0
0
0
2
1
2
1
1
1
2
0
0
2
1
0
1
2
1
1
2
2
1
1
1
1
0
1
0
1
1
2
0
1
2
1
1
2
0
1
2
1
1
1
1
2
1
0
1
2
1
0
0
1
2
1
2
2
1
0
1
1
1
1
1
1
0
1
2
0
1
1
1
1
1
1
1
0
2
1
2
2
2
2
1
1
0
1
1
1
0
0
1
1
0
1
0
0
0
1
2
2
2
1
3
0
2
1
1
1
2
1
0
1
0
1
1
1
2
2
1
1
2
1
1
3
2
1
1
2
1
1
0
1
2
2
1
1
1
1
1
1
0
1
0
2
0
1
0
0
1
1
0
2
1
1
2
1
1
2
2
0
1
0
1
1
1
1
1
0
0
1
2
1
1
2
1
1
1
1
4
0
2
1
1
1
2
2
1
0
0
2
0
1
1
1
1
2
1
2
1
1
1
2
2
1
2
2
1
1
0
1
2
1
1
1
1
2
2
1
1
1
1
1
1
0
1
2
0
2
0
1
0
0
0
0
0
2
0
1
0
1
1
1
2
1
2
1
1
2
1
2
2
1
1
0
1
2
2
0
1
0
0
0
2
1
2
0
2
2
1
1
1
2
0
0
1
2
1
1
1
2
2
1
2
1
1
1
2
0
2
1
1
1
1
0
1
2
3
1
2
2
0
1
2
0
0
0
1
1
1
1
0
1
0
2
1
2
0
2
0
1
1
1
1
1
1
2
0
0
0
0
1
1
1
1
0
2
3
0
0
1
2
1
1
1
1
1
2
0
2
1
0
1
2
2
1
1
1
2
1
1
1
1
1
1
2
0
1
1
1
2
1
1
0
1
1
0
0
1
1
1
0
1
2
1
1
1
0
0
1
1
1
2
1
1
1
1
2
1
2
1
2
1
2
1
1
1
1
0
1
0
1
1
2
1
1
2
0
0
0
1
1
2
2
1
1
1
2
1
0
2
1
1
1
1
1
1
1
0
1
2
1
2
1
1
1
1
1
1
1
1
2
1
2
1
1
2
3
1
1
1
1
1
1
1
1
1
1
1
0
1
2
2
1
2
1
0
2
2
0
1
1
2
1
1
2
1
0
1
1
0
0
1
0
1
2
0
1
1
1
2
1
2
1
0
0
1
2
2
2
2
1
1
0
2
2
2
0
0
0
1
1
1
1
1
1
1
0
1
1
1
1
1
1
0
2
1
0
1
1
0
0
2
1
1
1
1
1
2
2
2
1
2
2
1
1
2
1
1
1
2
2
0
2
1
1
1
1
1
0
1
1
1
3
0
2
0
0
1
1
1
1
0
0
0
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
0
1
2
2
1
2
0
2
1
1
1
0
2
1
2
2
1
1
2
0
1
3
2
1
1
1
1
0
2
1
1
1
1
2
1
1
1
1
1
1
0
1
0
1
1
0
0
0
1
1
2
2
2
1
2
1
2
2
1
1
1
0
1
1
0
1
1
0
2
0
1
1
1
1
2
1
1
2
1
1
1
1
2
0
1
1
2
2
2
1
1
1
0
2
2
2
2
2
2
1
0
1
0
2
1
1
1
0
1
2
1
1
0
1
1
1
0
1
1
1
1
1
1
2
1
2
1
1
1
1
0
1
2
2
2
1
0
1
1
1
1
0
1
1
1
1
2
1
1
0
2
2
1
1
2
0
2
2
0
1
0
0
2
1
1
1
2
1
2
1
1
0
1
0
1
0
1
1
2
1
1
1
1
2
1
0
1
0
0
0
1
1
0
0
1
0
1
2
1
1
2
2
1
1
1
1
0
1
1
2
1
1
0
2
2
2
2
3
1
1
2
0
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
1
2
0
2
2
1
1
1
1
1
0
1
2
2
1
1
1
1
1
0
1
1
1
2
2
1
2
1
2
1
2
1
2
2
2
1
1
1
3
0
0
2
2
1
2
1
0
1
0
1
2
0
0
1
1
2
2
1
1
2
1
1
1
1
2
0
1
1
1
2
2
1
2
1
1
2
2
1
2
1
1
1
2
0
1
1
1
2
1
1
2
0
2
0
1
1
0
1
0
2
2
2
1
2
1
1
1
2
1
0
2
2
2
3
1
1
1
2
1
1
1
0
1
1
1
1
2
2
0
1
0
1
2
1
0
1
1
1
2
1
1
1
1
2
0
0
1
1
0
2
0
1
1
1
0
0
1
1
1
0
1
1
1
0
1
0
2
1
1
0
2
1
2
1
1
0
0
1
1
2
2
1
1
2
1
1
1
0
1
1
0
1
1
0
0
2
1
1
1
2
0
0
2
1
0
1
2
1
1
2
0
1
1
1
1
1
2
1
2
1
2
1
1
2
1
1
1
1
2
0
1
1
1
2
1
0
0
1
1
1
1
1
2
1
1
2
1
1
2
0
1
1
2
2
2
3
2
1
0
1
1
0
2
1
1
0
2
1
0
1
2
1
2
1
1
1
1
1
2
1
1
1
1
2
1
1
2
2
2
1
1
0
0
1
1
1
1
1
1
1
2
0
2
1
1
3
1
3
1
1
1
0
1
2
1
1
1
1
2
0
0
0
0
1
0
1
1
1
1
0
1
1
1
1
1
2
1
1
0
2
2
1
2
1
0
1
1
0
3
1
1
1
2
2
1
2
1
1
1
0
2
0
0
2
2
0
0
0
1
0
1
2
1
2
1
1
1
0
2
1
1
2
1
1
1
0
0
1
1
1
1
1
1
0
1
1
1
1
1
0
2
2
0
1
1
1
0
1
1
1
1
1
2
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
0
2
2
0
1
1
2
0
1
1
1
0
1
1
0
2
2
1
1
1
1
1
3
1
2
1
2
2
1
1
2
1
1
3
2
0
1
1
1
1
1
1
0
1
1
1
1
2
1
0
2
1
2
2
1
1
1
2
1
1
1
2
2
0
0
2
1
1
1
2
2
1
1
1
1
1
1
1
1
1
0
1
0
1
0
2
0
1
1
1
1
1
1
1
2
3
1
1
1
2
1
2
1
1
2
2
2
1
2
2
1
0
0
1
1
0
1
2
1
1
0
1
0
0
1
2
0
1
2
2
1
2
1
0
1
0
1
2
2
1
2
1
1
1
2
1
1
1
0
1
1
0
2
1
1
2
0
2
1
2
0
1
2
0
1
1
0
0
2
1
1
2
1
0
1
1
1
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
0
1
1
1
0
2
1
1
1
2
1
0
0
1
1
0
1
0
0
2
1
0
0
0
1
1
1
2
0
1
2
1
1
1
2
2
2
0
0
1
1
1
2
1
1
0
1
0
1
1
1
1
0
0
2
1
1
2
1
0
1
1
0
0
1
2
1
2
2
1
1
1
0
1
1
1
1
0
0
1
1
0
0
2
0
1
0
1
1
1
1
2
2
1
1
1
0
1
1
2
1
2
1
0
1
2
2
1
1
1
0
1
0
2
0
1
0
1
1
0
1
0
1
2
2
1
1
1
1
1
1
1
1
0
1
1
2
2
1
1
1
1
1
3
1
2
2
1
1
1
1
1
1
1
2
1
2
1
1
0
1
1
1
0
0
2
2
0
0
1
1
2
1
2
1
1
0
1
1
1
1
1
0
2
2
1
2
2
2
0
1
2
2
1
1
2
0
1
1
1
2
2
1
1
2
2
1
2
1
2
0
1
1
1
2
0
2
1
1
2
1
1
2
1
0
2
1
0
1
0
0
2
1
1
0
1
2
1
1
0
1
1
4
0
0
1
2
1
1
2
0
1
2
0
2
1
1
1
1
0
0
2
1
1
1
1
2
1
2
2
1
2
0
1
0
1
0
1
1
0
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
2
0
0
2
2
1
0
1
2
2
2
1
1
1
1
2
1
1
0
2
1
0
1
2
0
1
1
2
0
1
1
3
1
2
0
2
3
1
1
1
2
0
1
0
1
1
1
1
1
1
1
1
0
1
1
1
0
2
2
1
0
1
0
0
1
1
2
0
1
1
1
0
1
0
2
1
0
1
2
0
0
0
1
1
1
0
2
0
2
0
1
1
2
0
1
0
1
1
1
1
1
2
1
1
0
1
2
1
1
2
0
2
1
2
2
1
2
1
1
2
1
3
0
3
1
0
1
1
1
2
1
1
1
1
1
2
1
1
2
1
1
1
1
2
0
1
1
0
1
1
0
2
1
1
1
2
1
1
0
2
1
1
1
1
1
1
1
2
1
1
1
1
1
0
0
2
2
1
1
0
1
1
1
0
1
1
1
1
1
1
0
1
1
1
2
2
2
1
1
2
1
1
1
0
1
0
1
2
2
2
1
1
1
1
1
1
1
2
0
1
1
1
0
1
1
0
0
1
1
1
1
0
1
1
0
0
2
0
2
0
1
1
1
2
0
2
1
0
1
1
1
2
1
1
0
0
2
1
0
0
0
0
1
1
1
2
0
1
1
2
1
1
2
2
1
0
1
2
2
1
1
1
1
2
1
1
1
1
1
1
7
1
1
1
1
0
2
1
0
1
0
1
1
1
1
1
1
1
0
0
1
1
0
1
1
1
1
0
0
0
1
2
1
0
0
1
2
1
2
2
1
1
1
1
1
2
2
0
2
1
1
2
0
0
1
1
1
1
1
1
2
1
2
1
1
1
0
2
2
2
1
1
1
1
1
2
1
2
1
1
1
0
2
1
1
0
2
0
1
2
1
1
1
2
2
1
2
1
1
1
1
0
2
0
2
1
1
1
1
1
2
1
1
0
2
2
1
0
2
1
0
1
2
1
0
1
1
1
1
0
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
0
0
2
1
2
1
2
1
2
0
1
2
1
2
1
1
0
1
1
1
1
0
0
1
0
2
0
1
1
1
2
2
0
1
1
0
2
1
1
1
2
2
1
2
0
1
0
0
2
1
1
1
1
2
2
1
2
0
1
2
1
1
1
2
1
2
2
1
2
2
0
1
3
2
1
1
1
1
2
2
2
1
1
2
1
2
2
0
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
0
1
0
1
1
2
1
1
1
0
2
1
2
1
1
2
2
1
1
2
1
1
1
1
2
2
2
2
0
1
1
0
2
1
3
2
1
1
2
2
1
1
2
2
2
2
1
1
1
1
0
1
2
0
1
1
1
0
1
2
1
1
1
1
0
0
1
0
1
1
2
1
1
1
1
2
2
2
2
1
2
0
2
2
1
1
1
0
0
2
1
1
3
1
1
1
2
1
1
2
1
0
1
1
0
1
1
1
0
0
2
1
2
0
2
1
1
2
3
0
1
2
2
1
1
1
1
3
1
0
2
2
1
1
0
2
1
0
2
1
1
0
2
0
0
0
1
1
1
0
2
1
1
1
0
0
1
0
2
1
1
2
1
1
2
2
1
2
1
1
2
1
1
1
0
2
0
1
0
1
1
1
0
1
0
1
1
2
1
1
1
1
2
1
2
2
1
1
0
2
1
1
0
2
1
3
0
0
1
1
0
1
1
1
2
1
2
0
1
1
0
2
0
5
1
1
1
0
2
1
0
1
1
0
0
1
1
2
1
2
1
1
1
1
1
1
1
1
0
1
0
2
1
1
1
1
2
1
2
1
2
1
1
2
2
2
0
2
1
0
0
1
1
0
1
0
0
0
0
2
1
1
2
1
1
1
2
2
1
1
1
1
2
0
1
0
2
1
2
1
1
0
2
1
2
1
1
1
0
1
2
2
1
1
1
1
1
1
0
1
1
0
2
2
0
1
1
1
1
1
0
1
1
1
2
0
1
1
1
2
1
1
1
0
1
2
1
2
2
2
1
0
1
1
1
2
1
2
2
0
1
0
2
1
2
1
0
1
2
4
1
0
1
2
2
0
1
2
1
2
2
1
2
1
1
0
1
2
1
0
1
1
0
1
1
1
1
2
1
1
0
1
0
1
1
1
2
1
1
0
1
1
1
2
1
1
0
0
1
1
1
2
2
1
1
2
1
2
2
1
1
1
2
1
2
0
0
0
0
2
0
1
0
1
1
0
0
0
1
1
1
1
0
1
2
1
1
2
2
1
1
1
0
2
1
1
1
2
1
2
0
1
1
1
2
2
1
1
1
1
1
1
2
1
1
0
1
2
0
0
3
2
2
1
2
1
1
1
1
1
1
1
0
0
1
0
0
1
0
0
1
1
1
2
2
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
1
1
1
2
2
1
1
1
0
1
1
1
1
2
1
1
2
1
1
1
2
1
0
1
1
2
0
2
1
1
1
2
2
0
0
0
1
1
1
2
1
0
2
0
1
2
1
2
1
2
0
1
1
2
1
0
1
1
1
1
2
0
0
2
1
2
1
2
0
1
1
1
0
1
0
1
2
1
0
1
0
1
1
1
0
0
0
1
2
1
1
2
3
0
2
0
2
1
0
1
1
1
0
1
2
0
1
1
1
0
1
1
1
0
2
1
1
1
0
2
2
2
0
0
2
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
0
1
1
0
0
1
0
1
1
1
1
1
2
0
0
1
1
1
1
1
1
1
2
0
1
1
2
1
2
1
1
0
1
0
1
1
1
0
1
0
1
2
2
1
1
2
1
0
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
2
2
0
1
1
1
1
0
1
1
1
2
0
1
0
0
1
13
0
1
1
1
1
1
1
0
2
1
2
1
0
1
3
0
1
2
2
1
2
1
2
1
0
1
1
1
2
0
1
1
0
1
1
1
2
0
0
1
1
0
0
1
1
2
1
1
4
1
0
0
2
1
1
1
1
1
0
1
2
1
2
1
2
1
1
2
2
1
1
1
2
1
1
2
1
1
1
1
1
0
1
1
2
2
0
1
2
2
1
1
0
1
2
0
1
1
1
1
2
1
2
2
2
1
1
1
1
0
2
1
0
3
0
0
1
1
1
2
2
1
2
1
1
1
1
2
2
1
2
2
2
0
1
1
1
0
2
0
0
0
2
0
1
0
2
1
2
2
2
1
1
1
1
1
0
1
1
2
1
3
1
1
1
0
1
0
1
1
0
2
3
1
1
1
1
1
2
1
1
2
2
1
1
1
2
0
1
2
0
0
1
1
2
1
2
1
0
1
2
1
1
1
2
1
1
0
1
1
2
0
0
1
1
1
3
1
2
1
0
0
0
2
1
1
0
2
2
0
1
2
1
1
1
0
1
1
1
0
0
2
0
1
1
2
1
1
1
0
1
1
1
1
0
1
2
0
1
2
1
0
2
1
2
0
1
1
0
1
2
0
2
1
1
1
0
1
1
1
2
2
1
2
1
1
1
0
1
1
0
0
2
0
0
0
1
1
1
2
1
1
1
2
2
1
1
1
1
2
0
2
1
2
2
1
1
1
2
1
1
1
2
1
0
1
1
1
0
1
1
1
2
1
1
0
1
1
1
1
2
2
1
1
2
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
0
2
0
0
0
1
1
1
0
2
2
1
1
0
1
2
1
1
1
0
1
2
2
1
1
1
1
2
2
0
0
2
0
3
1
1
1
2
2
1
0
2
0
0
2
0
1
1
1
1
2
0
1
0
1
1
1
2
1
1
1
2
2
2
1
1
1
3
2
1
1
1
1
1
2
1
1
2
2
2
2
0
1
2
2
1
1
0
2
3
1
0
0
1
2
3
1
1
1
1
0
1
1
2
0
1
0
2
0
2
0
1
2
2
0
0
1
2
1
1
1
1
0
1
1
0
1
1
2
1
2
2
1
1
1
1
0
1
2
2
2
2
1
1
1
2
1
1
1
1
0
1
1
1
0
1
0
0
1
2
1
1
1
0
0
2
0
1
2
1
2
2
2
1
1
2
1
2
1
1
0
1
3
1
2
2
1
1
0
1
1
2
0
3
1
1
2
1
2
0
0
0
1
0
2
1
1
2
0
1
1
0
1
1
1
2
1
1
0
1
1
1
2
1
1
1
1
0
0
2
0
0
1
2
2
1
1
1
2
0
2
2
0
1
0
1
0
2
1
0
1
1
3
1
1
2
1
1
1
1
1
0
2
0
1
2
1
2
2
0
0
2
1
2
1
1
0
1
1
2
1
1
0
1
1
1
0
1
0
0
1
3
1
1
1
2
1
1
1
1
0
1
1
2
0
1
2
1
2
1
1
0
1
1
1
1
2
1
2
1
1
1
2
1
2
1
1
1
2
1
2
1
0
1
1
1
1
1
0
1
1
3
2
1
3
0
0
1
1
1
1
2
1
1
1
1
1
0
2
0
1
0
1
1
1
3
1
1
1
0
1
2
1
1
1
2
1
1
0
1
1
1
0
1
0
1
0
2
2
1
1
0
1
1
1
1
2
1
1
1
1
1
1
1
0
2
1
1
1
1
1
0
1
1
1
1
1
2
2
1
1
1
3
1
1
1
1
1
1
0
1
2
1
1
1
1
1
3
0
1
1
0
1
2
1
1
2
2
1
1
1
1
0
3
0
1
1
1
1
0
1
0
0
0
1
1
1
0
0
1
1
2
0
1
1
0
1
1
1
1
1
1
0
2
1
1
1
1
2
1
1
1
1
2
2
1
1
3
2
1
1
1
1
1
1
1
1
2
2
2
1
2
1
1
0
1
1
0
1
1
2
2
1
1
2
1
0
1
0
0
1
1
2
1
1
1
1
1
1
1
0
1
1
2
1
1
1
0
2
1
2
1
1
0
1
2
0
1
1
0
0
1
2
1
1
0
2
2
1
1
1
1
1
0
1
2
0
2
1
0
0
1
1
1
1
1
1
1
1
1
2
1
1
0
1
0
1
1
0
1
1
1
0
1
2
2
1
0
2
2
1
1
1
0
1
1
0
0
2
1
2
0
1
1
1
1
1
1
2
2
1
1
1
1
0
1
1
2
1
2
1
2
1
1
0
0
0
1
1
1
1
2
2
1
0
2
1
2
0
1
0
1
2
0
1
1
1
2
2
1
1
0
0
1
1
3
1
2
1
2
1
2
1
1
1
1
3
2
0
2
0
2
1
0
2
1
2
0
1
1
0
2
1
0
0
2
2
2
2
2
1
0
0
1
0
2
2
1
2
1
1
2
0
1
2
2
0
1
1
0
1
1
1
0
1
1
0
1
2
2
1
2
1
0
1
1
0
1
2
1
1
2
1
2
1
2
1
1
1
0
0
1
1
2
1
1
0
1
1
0
1
1
2
2
1
2
0
0
0
1
1
0
0
2
1
2
1
1
1
2
2
1
2
0
2
2
0
1
1
0
2
0
0
1
0
1
1
2
0
2
1
1
0
1
2
1
2
1
1
1
1
1
1
0
1
1
0
1
2
1
1
0
2
2
0
1
1
1
0
1
2
2
1
0
1
1
2
0
1
1
1
2
1
2
1
1
0
1
1
1
1
1
1
0
1
0
1
1
2
0
0
0
1
2
1
1
1
1
0
1
1
0
1
0
2
1
1
1
1
2
0
0
0
1
1
1
2
1
2
2
1
0
1
1
0
0
1
1
0
0
2
1
0
0
2
1
1
2
1
1
1
1
2
1
1
1
0
1
1
1
1
1
1
1
1
1
2
1
0
0
2
0
1
1
0
0
1
1
1
2
2
2
1
2
2
1
1
1
1
0
2
1
1
1
2
1
1
2
2
1
2
1
1
0
2
2
1
1
1
1
2
0
1
2
0
0
0
0
1
0
2
1
1
2
1
1
2
1
0
2
2
0
1
1
1
1
0
2
1
0
1
1
1
1
0
3
1
0
1
0
2
0
1
1
1
1
1
2
0
1
0
1
0
1
0
2
2
1
2
0
1
2
1
0
1
1
1
1
2
1
1
2
1
2
1
0
1
1
2
1
1
2
1
1
0
1
2
0
1
0
1
1
0
1
1
1
2
1
1
1
1
2
1
0
2
0
1
0
0
2
2
1
0
2
1
1
0
1
0
0
2
0
1
1
2
0
2
2
0
1
1
1
0
1
1
1
1
3
1
1
1
1
1
1
1
1
1
1
0
1
0
1
2
2
1
1
0
1
0
1
1
1
2
1
0
1
2
1
1
2
0
0
1
0
1
1
1
1
1
2
1
2
0
1
1
2
0
0
1
0
1
1
1
1
0
1
1
1
1
1
1
2
2
1
2
1
0
2
1
1
1
1
1
2
0
0
1
1
1
1
0
1
0
1
1
1
0
1
1
1
0
1
1
0
2
2
2
0
2
0
0
2
1
0
1
0
1
0
1
1
1
1
1
0
1
1
2
0
1
0
0
1
1
1
1
1
1
1
1
1
2
0
2
2
0
0
1
1
2
1
1
0
1
1
1
0
1
1
2
1
2
1
1
1
1
2
2
2
1
1
1
1
1
1
2
1
0
2
2
2
1
0
1
1
2
2
2
1
1
1
0
2
1
1
0
2
1
1
1
3
1
1
1
1
1
2
1
1
1
0
1
3
1
2
1
1
2
1
1
1
2
1
1
1
1
1
2
1
1
1
1
0
1
2
2
1
0
1
1
0
0
1
1
2
1
1
2
0
0
0
1
1
2
2
0
2
0
1
1
2
1
1
1
1
1
2
2
1
1
2
2
1
2
0
2
2
1
1
0
1
3
1
1
1
1
0
2
2
1
1
1
1
1
2
1
1
2
1
1
2
1
1
1
2
1
2
2
0
1
1
2
2
1
2
1
0
0
0
1
0
2
1
0
1
1
1
0
2
1
2
1
1
2
1
2
1
2
1
1
2
1
0
0
2
1
1
0
1
1
2
2
0
0
6
1
0
0
1
1
1
0
2
1
2
1
1
1
2
1
1
1
2
1
1
1
2
2
2
2
0
0
2
1
1
1
0
0
1
1
1
1
2
2
2
2
1
1
1
1
1
1
1
2
1
1
2
0
2
1
1
1
1
2
1
1
2
1
0
2
1
1
1
2
2
2
1
1
1
1
0
1
2
0
1
1
1
1
1
2
0
1
1
1
1
1
1
1
1
1
0
1
0
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
0
2
1
2
1
1
0
1
1
0
0
0
1
1
3
1
0
2
1
1
0
2
1
2
0
1
2
1
1
1
0
1
1
0
2
0
1
1
1
0
1
0
1
1
0
2
2
2
2
1
2
2
1
1
1
2
2
1
1
0
1
1
1
0
1
3
1
2
2
1
0
1
2
0
0
0
1
1
1
0
2
0
4
2
1
1
1
0
2
1
2
1
1
2
0
2
6
2
1
2
2
1
1
1
1
1
0
2
1
1
1
0
1
1
1
1
1
1
1
1
2
1
0
0
1
2
1
0
1
1
1
1
2
0
2
1
2
0
1
1
1
2
2
2
1
1
1
1
1
2
2
1
2
2
0
2
1
1
0
1
1
1
0
0
2
1
1
1
1
0
1
1
2
0
0
1
2
1
2
1
2
1
1
2
2
1
1
1
1
2
0
2
2
2
2
1
1
1
1
1
0
1
1
1
0
0
1
0
0
0
0
2
1
1
2
1
1
2
2
2
2
1
1
1
0
2
0
1
0
2
0
1
2
1
1
1
1
1
1
1
1
2
2
1
1
2
0
2
0
2
0
1
1
1
0
1
0
1
0
1
0
2
1
1
1
1
2
2
1
1
1
1
2
1
0
3
1
1
1
1
1
1
2
1
0
2
1
1
1
0
0
1
1
1
2
1
1
2
1
1
3
1
1
2
2
1
2
0
2
1
1
1
0
0
0
0
2
0
0
1
1
2
1
1
1
1
0
1
2
1
2
0
3
1
1
2
0
1
0
1
1
0
1
1
2
2
0
0
1
0
2
1
1
1
1
1
1
0
1
0
1
0
0
1
1
2
1
1
1
2
1
1
0
2
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
0
1
1
0
0
1
1
1
3
2
1
0
1
1
1
1
1
0
2
1
1
1
1
2
0
2
1
1
1
1
1
2
1
1
1
2
0
1
1
1
1
1
3
1
2
1
1
1
2
0
2
1
1
0
1
1
1
0
1
2
1
2
1
0
1
0
2
1
1
1
1
1
1
2
1
0
2
1
1
0
2
1
1
2
1
0
1
1
1
0
2
0
1
1
1
1
2
1
1
0
1
1
2
2
2
2
1
1
1
2
1
2
0
1
0
1
1
0
1
1
1
1
1
0
1
1
0
1
1
2
0
0
0
0
2
1
0
1
1
2
2
1
1
1
1
1
1
1
2
1
2
1
2
1
1
1
1
0
1
2
1
0
1
1
1
1
1
1
1
1
0
1
2
2
1
1
2
1
2
0
2
2
1
1
2
0
1
1
0
1
1
2
1
1
2
1
1
1
1
1
1
2
2
2
0
1
1
2
1
0
2
1
1
0
1
1
1
1
1
2
1
1
2
1
2
2
1
0
1
0
1
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
0
2
1
0
0
2
0
1
1
1
2
0
1
0
1
1
1
1
2
2
1
1
2
2
2
1
0
1
1
1
0
1
2
1
0
1
2
1
2
0
2
1
0
1
1
1
1
2
1
1
2
0
2
1
1
1
2
1
1
2
1
0
2
2
0
0
1
1
2
0
0
1
2
0
1
1
0
1
1
2
1
0
1
2
1
2
0
1
1
1
1
2
2
0
1
1
1
1
1
1
1
1
1
0
1
2
0
1
2
0
1
1
0
2
2
1
0
1
2
2
2
1
1
1
1
0
0
2
1
1
2
2
1
1
1
0
1
2
1
1
1
1
2
1
0
1
1
1
2
2
0
1
1
2
0
1
1
1
0
2
1
1
2
1
1
1
0
1
3
2
1
2
1
2
1
0
1
1
2
1
1
1
5
2
1
1
1
1
0
0
1
1
1
1
0
0
2
0
0
2
1
0
1
1
2
1
1
2
2
2
2
1
2
0
1
1
2
3
1
1
1
2
1
2
2
0
1
1
3
0
0
1
0
1
1
3
1
1
1
1
1
1
1
0
0
1
1
0
2
2
1
0
2
1
1
1
1
1
1
2
2
1
1
1
2
2
1
2
1
2
1
1
1
1
1
1
2
2
1
1
0
1
1
2
2
0
1
0
2
0
0
1
2
1
0
0
2
2
0
2
1
2
0
1
1
0
2
2
1
0
2
0
1
1
2
0
1
0
0
2
1
1
1
0
1
2
1
0
2
1
1
0
2
1
3
1
2
1
2
1
1
2
1
0
1
1
1
0
1
2
0
2
1
1
2
1
0
1
1
0
2
1
1
0
1
2
2
2
2
2
1
1
1
1
1
2
0
0
1
2
0
2
1
0
2
2
1
2
1
1
1
1
1
1
1
2
1
2
0
1
1
2
2
0
1
2
1
1
1
2
1
1
2
2
1
0
0
0
1
1
2
2
0
1
1
1
2
1
0
0
0
1
2
0
1
1
1
2
0
1
0
1
2
1
1
1
0
2
1
1
1
1
2
0
1
1
0
2
1
2
2
1
1
0
0
0
1
1
0
1
1
2
0
1
1
1
1
1
1
2
2
1
1
2
2
2
1
0
0
2
2
1
1
0
1
1
1
1
1
0
2
1
0
2
1
1
0
1
1
1
1
1
1
0
1
0
2
2
1
1
1
1
1
0
2
1
2
1
2
1
1
1
1
2
1
0
1
0
2
1
0
0
0
1
2
1
0
1
1
0
3
2
0
2
0
0
1
1
1
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
0
0
1
0
1
2
2
2
2
2
1
1
0
1
1
1
2
2
1
2
1
1
0
0
1
1
1
1
1
1
2
2
3
0
1
1
0
1
1
0
1
1
0
1
0
2
2
0
1
1
0
1
1
2
1
2
1
1
3
2
1
1
0
1
1
0
1
2
2
3
1
2
0
2
2
2
1
1
0
1
1
1
1
1
2
0
1
0
1
1
1
2
0
0
1
0
2
2
0
1
1
0
0
2
2
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
2
1
0
1
2
1
1
2
2
1
1
1
1
0
2
1
1
0
1
1
1
1
2
1
1
1
1
2
2
1
1
1
1
0
2
1
1
2
1
1
1
0
1
1
1
0
1
1
1
1
1
2
2
1
1
1
2
2
1
1
1
2
1
1
0
1
1
2
0
2
4
1
1
1
0
1
1
1
0
0
1
1
2
1
0
1
1
1
2
0
0
1
1
2
1
1
2
2
1
2
2
1
1
1
2
1
1
0
1
2
1
0
2
1
1
0
1
0
2
1
1
0
2
2
0
0
2
1
1
1
1
1
1
0
1
2
0
2
1
1
0
2
0
1
0
1
0
1
1
2
1
1
1
1
2
0
0
2
1
0
0
0
2
2
1
1
2
1
1
1
2
2
1
0
1
0
2
2
1
2
2
2
1
1
2
2
0
0
1
0
1
2
0
0
0
1
1
1
5
1
2
1
1
2
1
2
1
1
1
2
2
0
1
1
2
0
1
2
0
1
1
0
1
1
1
1
2
0
1
1
1
0
2
2
1
1
1
1
1
1
1
0
2
1
1
1
1
0
1
0
1
1
1
1
1
2
1
1
1
2
2
2
1
1
0
2
1
1
2
1
1
1
1
0
1
0
1
0
1
1
1
1
0
1
1
1
1
1
2
1
0
2
1
0
1
0
0
1
1
2
2
1
0
1
2
1
2
1
1
2
1
1
2
1
0
2
2
1
2
1
2
1
0
1
1
0
1
1
2
1
0
1
0
1
0
1
0
1
1
1
1
1
0
1
0
1
1
1
2
1
2
2
0
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
3
0
1
2
1
2
2
1
1
2
0
1
1
1
0
1
1
2
1
2
0
1
0
0
1
0
0
2
1
0
1
1
1
1
0
2
0
2
1
1
1
1
2
1
1
1
1
1
1
2
1
2
2
0
2
1
1
1
1
2
1
2
1
1
0
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
0
1
2
0
2
0
1
1
1
1
2
0
1
1
1
1
1
1
2
2
1
2
0
2
0
0
1
1
1
1
0
0
1
1
1
1
1
0
2
1
2
1
1
3
1
0
1
2
1
2
1
1
0
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
1
2
1
1
2
1
2
2
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
0
1
2
0
1
0
2
1
2
1
1
1
0
2
2
0
1
0
1
0
1
0
1
1
0
1
1
1
1
1
1
2
2
0
1
1
1
1
1
2
1
0
0
2
1
1
2
2
1
2
0
1
0
0
1
1
3
1
1
0
1
1
0
1
2
1
1
1
2
2
0
1
2
2
1
1
2
1
1
1
1
0
1
0
1
1
1
0
1
1
1
0
2
1
1
0
1
2
1
1
0
2
2
1
1
8
2
2
2
1
1
1
1
1
2
2
1
1
1
1
2
1
0
2
1
2
2
2
1
1
1
1
1
0
0
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
0
2
1
0
1
2
1
1
1
2
0
1
0
2
1
2
1
2
1
1
0
2
0
0
2
0
2
1
2
0
1
0
1
1
1
1
1
0
1
1
0
1
1
1
1
0
0
2
1
1
0
0
2
0
2
1
1
1
1
1
0
1
1
2
2
0
1
1
1
1
1
0
1
0
2
2
0
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
1
2
2
1
1
0
2
2
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
1
2
1
2
1
1
1
0
1
1
2
1
1
1
1
1
1
0
1
0
1
1
0
1
2
1
1
1
2
0
1
1
1
1
1
0
0
2
1
1
2
1
1
1
1
1
2
1
1
0
0
0
1
2
1
0
1
1
2
1
0
1
1
1
0
2
1
2
1
2
0
1
0
0
0
1
1
2
1
0
1
1
1
1
4
1
1
1
0
2
1
0
2
1
1
1
2
1
1
2
1
1
2
2
1
1
1
1
1
1
1
1
2
1
2
2
2
1
2
1
1
1
2
1
1
1
1
1
1
1
1
0
1
1
1
1
0
1
2
2
2
1
1
1
2
1
1
1
2
2
0
1
1
1
1
1
2
2
1
1
1
1
2
1
2
1
1
2
0
2
1
1
1
0
2
0
0
2
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
2
2
2
1
2
2
0
1
2
0
1
0
0
0
1
1
1
2
0
1
1
1
1
1
1
1
1
1
1
2
2
0
1
1
1
1
1
0
0
1
1
1
2
1
1
0
1
1
1
1
1
0
0
1
1
1
1
0
0
1
0
0
0
1
2
0
1
1
0
1
0
1
1
0
0
2
2
1
1
1
1
1
2
0
1
0
2
2
1
1
2
1
2
2
1
1
2
1
0
1
2
1
2
1
1
0
2
0
0
2
1
1
1
1
1
1
2
1
1
1
0
1
1
2
2
2
2
1
1
1
0
1
2
1
2
1
1
1
1
1
3
1
1
2
1
1
1
2
0
1
0
1
1
0
1
2
0
1
1
2
2
1
0
1
2
1
2
1
1
1
1
1
1
0
2
0
2
1
1
1
2
1
1
2
1
2
1
2
1
1
0
1
2
1
0
1
1
2
0
1
1
0
2
0
1
1
1
2
1
0
0
1
0
0
1
0
1
0
2
1
2
2
1
0
1
0
0
2
0
1
2
1
1
0
3
0
0
2
1
0
0
1
2
3
1
2
1
1
2
1
1
2
0
1
0
2
2
1
1
0
2
2
0
1
2
2
1
1
1
1
1
1
2
2
1
1
1
2
2
1
2
1
1
1
0
1
2
1
2
0
1
2
1
2
1
1
0
2
1
2
1
2
1
1
1
1
1
1
1
0
1
1
1
2
2
1
0
0
1
1
1
1
0
1
3
1
1
1
0
2
1
2
0
0
1
1
2
1
1
2
1
2
0
2
2
0
2
0
1
0
1
1
1
1
1
1
1
2
2
1
0
1
0
2
1
1
0
1
1
1
2
1
1
2
1
1
1
1
0
1
1
0
1
2
0
0
2
1
1
1
1
1
0
1
0
1
1
1
2
1
1
0
1
2
1
1
1
0
1
1
1
1
2
1
2
1
2
1
1
2
1
2
2
1
2
1
1
1
0
1
1
1
1
2
2
0
1
1
1
0
1
2
1
1
1
2
1
1
1
2
1
1
0
2
2
1
0
1
2
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
0
1
0
1
1
0
2
1
1
0
1
1
2
1
1
1
1
2
1
1
1
2
1
0
1
1
1
0
1
2
1
0
0
0
0
0
1
2
1
1
1
2
2
2
1
1
2
0
1
2
1
2
1
0
0
0
1
2
1
2
0
2
0
1
1
1
1
0
2
0
1
1
0
1
1
1
1
1
0
1
1
1
1
1
2
2
2
0
1
2
2
2
1
1
1
1
1
0
2
1
1
0
1
2
2
1
1
1
1
0
1
2
2
0
1
2
0
2
2
1
1
2
0
1
1
1
1
1
1
0
2
1
2
1
2
1
2
2
1
2
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
2
0
2
2
1
1
1
2
1
2
2
0
1
1
2
2
0
0
1
1
1
2
0
0
1
1
1
2
0
1
1
2
1
0
0
1
1
1
2
1
1
2
0
1
2
2
2
1
1
1
1
0
0
1
0
1
1
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
0
1
2
2
1
0
1
1
0
1
1
1
1
0
1
1
1
2
1
1
2
2
2
2
1
0
2
1
2
1
2
1
0
1
1
1
1
0
1
1
2
1
1
1
2
0
1
1
1
1
2
0
1
1
1
0
0
1
0
1
0
1
2
3
1
2
1
1
2
2
2
1
2
1
1
1
1
1
1
1
1
2
1
1
2
2
1
2
1
1
1
4
1
1
2
2
8
1
2
1
2
1
0
2
1
2
1
2
1
1
1
1
1
1
0
1
0
1
0
0
1
1
1
1
0
2
2
0
2
0
1
2
1
1
1
1
2
1
1
1
2
0
1
1
1
1
1
1
0
2
0
1
2
1
1
0
0
2
1
1
1
2
1
1
0
1
0
2
0
0
2
1
1
3
1
1
1
0
2
1
1
1
1
2
2
1
1
0
1
1
1
2
2
1
1
1
0
0
1
1
0
2
1
1
2
1
2
0
1
2
0
1
1
1
1
1
2
0
2
1
1
0
1
1
2
0
1
1
1
1
1
2
0
2
0
0
1
1
1
0
2
1
1
2
1
0
1
1
2
2
1
1
2
2
1
0
0
1
0
0
2
1
1
1
2
1
1
1
0
2
1
1
1
1
1
1
2
1
1
1
1
2
0
2
1
0
1
1
1
0
1
2
2
2
2
1
2
1
0
1
1
1
2
1
1
1
1
1
2
2
1
1
1
2
1
2
2
1
2
1
0
0
2
1
0
2
0
2
2
0
2
1
1
2
2
1
2
2
0
0
1
1
1
3
1
2
2
0
1
0
0
1
1
2
1
1
1
0
2
1
0
1
0
0
1
1
0
2
2
1
1
1
1
1
2
2
1
1
1
1
1
1
0
1
0
2
2
0
1
4
2
2
1
0
1
1
1
1
1
2
1
1
0
1
0
1
0
1
1
1
1
0
1
1
1
0
1
1
0
0
1
1
1
2
2
2
1
1
1
1
1
2
0
2
2
2
1
0
2
2
2
1
1
1
1
1
1
0
0
0
1
1
1
0
0
1
2
1
2
2
1
1
2
1
2
0
1
0
1
0
1
1
0
1
2
1
1
0
1
2
1
1
2
2
1
1
2
2
1
0
2
1
1
2
0
1
1
1
4
1
1
2
1
1
1
1
1
2
1
1
1
0
0
1
1
0
2
2
1
0
0
1
1
0
1
1
1
2
1
1
0
0
1
1
1
1
0
1
0
2
1
1
1
1
2
1
2
1
0
2
0
1
1
1
1
0
1
1
1
1
2
1
1
3
1
1
2
0
2
1
1
0
1
1
1
2
1
2
2
1
0
1
2
2
1
0
0
0
1
1
2
1
1
1
0
0
1
1
1
3
1
2
0
1
1
0
1
1
0
1
1
1
1
1
1
1
2
1
1
2
1
1
2
2
1
1
2
1
2
0
1
0
1
0
1
1
1
1
1
1
2
1
1
1
2
2
0
0
0
2
0
1
2
1
1
0
1
2
2
2
1
2
1
1
2
1
1
0
1
1
2
1
1
1
0
2
1
0
0
2
1
0
0
1
2
1
1
1
1
1
2
1
0
1
2
1
0
0
1
1
1
1
0
1
1
2
1
1
2
2
1
1
0
0
2
1
1
2
1
1
0
2
2
1
1
1
1
2
2
1
2
1
1
0
0
2
0
1
0
1
1
2
1
1
1
1
1
2
0
2
2
0
0
1
1
2
0
1
1
1
1
1
1
1
2
2
1
0
1
1
1
2
0
1
2
1
1
2
2
2
1
2
0
2
0
1
0
1
1
1
0
0
1
2
2
2
1
2
1
2
2
0
0
1
1
1
1
1
0
0
1
1
1
0
1
2
1
1
1
1
0
1
0
1
1
1
0
2
2
2
2
1
1
1
1
1
1
1
1
0
1
1
1
2
0
1
1
1
1
0
1
1
2
1
1
1
1
2
1
3
1
1
0
1
2
0
1
2
0
1
1
0
2
1
1
1
1
1
1
2
1
0
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
0
0
2
0
1
1
1
1
2
2
1
2
0
1
1
0
0
0
1
1
1
1
2
1
1
2
1
0
0
1
2
1
1
1
1
1
1
1
2
2
1
1
0
1
2
0
2
1
1
1
1
1
1
3
2
1
1
2
1
0
1
2
0
0
0
0
1
2
1
0
2
1
1
0
1
1
1
2
1
1
2
0
1
0
1
2
2
1
1
2
1
1
2
2
0
2
2
2
1
0
1
1
1
1
1
1
1
1
0
1
1
1
1
2
1
1
1
1
1
0
2
1
1
1
1
1
1
0
0
2
1
1
0
1
2
0
2
0
2
2
1
1
2
0
0
1
1
0
0
2
1
1
2
1
2
0
1
2
2
0
1
2
2
1
0
1
0
1
1
1
1
1
1
0
2
1
1
2
1
1
0
1
2
2
2
1
1
1
2
1
1
2
2
2
1
1
0
0
0
2
1
1
1
2
1
0
1
1
0
2
2
1
1
1
1
1
1
0
1
1
1
1
2
1
1
0
1
1
2
8
1
2
0
1
0
1
1
1
1
1
2
0
2
1
1
1
0
0
2
1
1
1
2
1
1
2
2
2
2
1
1
0
1
2
0
2
1
1
1
1
1
2
2
2
0
2
1
2
1
2
1
2
0
1
1
1
0
2
0
1
1
1
2
1
1
1
1
1
1
2
1
0
0
0
2
0
0
1
0
1
1
1
1
2
1
1
2
1
1
1
1
1
2
2
1
1
1
1
2
1
1
0
1
1
1
1
0
1
1
1
0
0
1
1
2
1
1
1
2
1
0
1
2
0
1
0
1
2
1
1
1
2
1
1
1
1
1
0
0
0
0
2
0
1
0
0
1
2
1
1
2
1
0
1
1
1
1
1
1
1
1
0
1
2
2
0
1
1
1
0
2
1
1
0
1
1
1
1
1
2
1
1
1
1
2
1
0
1
1
1
1
0
1
2
2
1
1
2
2
0
1
2
2
1
2
1
2
2
1
1
1
1
1
1
2
0
0
0
1
1
1
1
0
0
1
0
0
1
0
1
0
2
1
1
1
0
2
0
1
1
3
1
0
2
0
1
1
1
2
1
1
1
0
1
1
1
1
1
2
2
1
1
2
1
2
1
2
3
1
1
0
0
2
2
1
1
1
2
1
2
0
0
1
2
1
1
1
1
1
1
1
1
1
2
1
1
0
1
1
0
1
1
2
1
0
1
0
0
1
2
0
2
2
1
2
1
1
1
2
2
1
0
0
0
1
0
2
1
1
1
1
1
0
0
0
0
2
1
0
0
1
1
1
1
1
0
0
1
1
1
1
1
1
1
1
1
1
1
0
1
0
1
1
1
2
0
2
2
2
1
1
1
1
1
1
1
1
0
1
0
1
0
0
0
2
2
2
0
1
1
1
0
2
1
1
2
1
1
1
1
1
2
1
1
1
0
1
1
1
1
1
1
1
1
1
0
1
2
2
1
1
1
1
1
1
1
2
0
1
0
1
0
0
1
0
1
1
2
2
1
0
1
0
2
1
0
0
1
1
1
1
1
0
2
2
1
1
1
1
1
1
1
1
1
0
2
1
1
2
0
1
2
0
1
1
2
1
1
0
1
0
2
1
2
1
2
1
0
1
2
1
1
0
1
0
2
2
1
1
2
2
1
2
1
1
1
1
1
1
0
1
1
1
1
1
1
2
2
2
0
2
1
1
1
2
2
0
1
2
1
1
0
1
1
2
1
1
2
2
1
0
1
1
0
1
0
1
1
1
2
1
2
1
1
1
0
2
1
1
0
1
0
1
1
2
2
2
3
2
1
2
1
1
1
2
0
1
2
0
1
2
1
2
0
2
1
1
2
1
1
1
2
2
0
2
1
1
2
1
0
0
1
1
1
2
2
1
2
1
1
0
3
2
0
1
1
0
1
1
1
2
1
1
1
1
1
2
2
1
0
1
1
1
3
1
2
2
2
2
1
0
0
0
0
1
1
2
1
1
1
1
1
1
1
0
1
0
2
1
1
1
2
1
1
1
1
0
1
0
1
1
1
1
1
1
1
0
2
1
1
1
2
0
1
1
1
2
0
1
1
1
2
1
0
1
2
1
1
1
1
1
2
1
0
1
2
1
1
1
0
1
1
2
0
1
1
0
1
1
0
1
0
0
0
1
1
1
0
1
1
1
2
1
1
1
1
1
1
1
1
0
1
0
1
1
1
0
1
1
0
2
1
0
1
1
2
1
1
1
0
1
2
0
1
1
0
0
1
1
1
1
2
2
1
0
1
2
0
1
1
2
1
0
1
0
1
1
1
1
1
2
1
1
1
1
1
2
1
2
0
2
2
2
1
1
2
1
0
2
1
1
2
2
2
1
1
1
1
1
1
1
1
1
0
0
1
0
1
1
1
0
0
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
0
2
1
2
1
1
1
1
0
2
1
1
1
1
2
2
0
2
1
1
1
2
2
1
1
1
2
1
1
1
2
1
1
1
2
2
2
1
2
0
1
1
2
1
1
0
0
1
1
0
0
0
1
1
1
2
1
2
1
1
1
1
1
2
1
1
0
1
1
2
1
1
1
1
1
2
0
1
1
1
2
2
1
1
1
0
0
1
2
0
1
1
0
1
2
2
2
0
2
1
2
1
2
2
1
0
1
1
2
1
1
1
1
1
2
1
0
1
1
2
1
1
1
2
0
1
2
1
0
2
1
1
0
0
2
2
1
1
1
1
1
2
1
1
0
1
1
0
2
1
2
2
1
2
1
1
1
1
2
1
1
3
1
2
0
1
5
1
1
0
2
0
1
1
0
2
0
1
1
2
1
1
2
1
1
1
1
0
1
1
1
2
1
1
1
1
1
1
0
1
1
2
1
1
1
1
0
1
2
0
1
2
1
1
2
1
1
2
2
3
0
1
0
2
1
1
1
1
2
1
2
0
2
0
1
1
1
1
2
0
1
2
1
0
2
1
1
1
2
1
2
2
2
1
1
2
1
1
1
1
2
1
1
0
2
2
0
1
0
1
2
1
0
1
1
1
2
0
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
0
1
2
2
1
1
2
1
1
1
1
1
0
0
2
0
1
1
1
1
0
1
1
0
1
1
1
1
2
1
1
0
0
2
1
0
2
3
1
1
2
1
1
1
1
0
2
1
2
2
1
2
1
0
1
1
1
0
2
1
1
1
2
2
1
0
1
2
2
1
1
1
0
0
1
2
1
0
1
2
1
1
1
1
2
1
0
1
1
1
1
1
1
0
0
2
1
2
2
2
1
1
1
1
0
1
2
1
2
1
1
1
1
1
1
2
2
0
1
2
1
0
1
1
2
2
1
1
0
2
2
1
2
1
0
1
2
1
1
2
1
1
1
0
0
0
2
0
1
1
1
0
0
2
3
2
2
0
1
1
1
1
1
2
1
0
1
1
2
0
1
0
1
1
0
1
0
0
2
1
1
1
1
1
2
1
1
1
1
2
1
2
1
0
1
0
1
2
1
1
2
2
0
1
1
2
1
1
2
1
1
1
1
1
2
0
2
1
1
2
1
1
0
1
0
0
1
0
1
1
1
2
0
1
0
1
1
2
0
1
1
1
1
1
1
0
1
1
1
1
0
1
1
1
1
1
1
1
1
0
1
1
1
1
2
0
0
1
1
2
1
0
0
2
1
0
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
0
0
0
1
1
1
0
1
1
0
2
1
1
1
1
2
0
1
0
0
0
0
1
1
1
1
1
1
1
1
1
0
1
2
0
0
1
2
1
0
2
1
1
1
1
1
2
1
2
0
1
0
0
1
1
2
2
1
1
0
2
1
0
0
1
1
1
2
2
1
1
1
1
1
1
0
1
0
1
1
1
1
1
1
1
1
2
1
0
3
1
1
1
1
1
1
1
0
0
2
1
1
2
1
1
1
1
1
2
1
2
1
0
2
1
1
1
2
1
1
1
1
2
1
1
1
2
2
2
0
1
1
2
1
1
2
1
2
1
2
2
2
2
1
1
1
0
1
1
1
1
1
0
1
0
1
1
1
1
1
2
0
0
2
1
2
1
1
1
2
1
2
0
0
0
1
2
1
1
1
2
0
1
1
1
1
0
0
0
0
0
2
1
1
2
2
0
1
1
1
1
1
1
2
1
1
2
1
1
1
0
1
1
2
1
1
0
2
0
0
1
2
1
1
2
2
2
1
1
1
1
0
0
3
0
1
2
1
1
0
2
1
1
1
1
1
0
0
0
0
2
1
1
1
2
1
1
2
1
1
1
1
1
1
1
0
0
2
1
1
1
0
1
1
1
0
1
0
1
0
1
1
2
1
1
2
1
0
2
1
0
0
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
0
1
0
1
1
1
2
1
1
2
2
0
1
1
0
0
1
1
1
1
0
1
1
0
0
1
1
2
1
1
1
1
1
2
1
1
2
2
0
2
0
2
1
2
1
2
0
1
1
1
1
2
0
1
0
1
1
0
2
1
0
1
2
1
1
0
1
1
2
1
0
1
2
2
1
0
2
0
1
2
1
1
2
1
2
1
2
1
2
2
1
1
0
1
1
1
2
2
0
1
1
2
1
1
2
0
1
2
1
1
1
1
1
0
1
1
1
0
1
0
1
1
1
1
1
2
1
1
0
1
1
1
0
2
0
1
2
1
2
1
0
0
0
1
1
0
1
1
1
0
1
1
1
1
1
1
1
1
2
1
0
1
0
2
0
0
0
2
1
1
1
2
1
1
0
1
1
1
1
1
1
1
1
0
0
1
2
2
2
0
1
1
1
1
2
0
2
1
0
1
1
2
0
2
1
1
1
1
1
1
1
1
2
2
1
1
1
2
1
0
2
0
1
2
0
1
1
2
1
1
0
2
2
1
0
1
2
2
1
1
0
2
0
2
1
1
2
1
1
0
2
1
1
1
2
2
0
0
2
0
1
2
1
1
0
1
1
2
0
1
1
1
2
2
1
1
1
1
1
2
0
1
1
1
1
0
1
1
0
2
0
1
1
0
2
3
0
0
1
0
1
1
1
1
2
1
1
1
2
1
1
1
1
0
0
1
1
1
3
1
2
0
1
1
2
1
0
1
1
0
1
1
2
0
2
1
0
2
0
0
2
1
1
1
0
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
0
1
0
0
1
0
0
1
1
2
0
1
1
1
1
0
0
1
0
0
0
1
1
1
2
0
1
1
2
0
1
0
1
1
1
1
0
1
0
1
2
0
2
1
1
2
2
0
1
0
2
7
1
1
2
0
2
0
1
1
1
1
1
0
1
1
1
1
1
1
2
1
1
2
2
1
1
1
0
0
2
0
2
1
2
1
2
1
1
2
0
2
1
2
1
0
2
2
1
1
2
0
1
2
0
1
1
1
1
0
0
2
2
1
1
1
2
1
1
1
1
2
0
1
1
1
1
0
0
1
0
1
0
1
1
1
2
3
1
1
1
0
1
2
1
1
1
1
1
1
2
2
2
0
0
1
1
2
1
1
1
1
1
1
1
2
0
2
1
1
1
1
0
2
0
1
0
1
1
1
1
0
2
1
0
1
0
1
2
1
2
0
1
0
0
1
2
1
1
2
1
1
2
1
3
1
1
0
1
1
2
1
1
1
1
1
1
0
1
2
2
2
1
2
2
1
1
1
2
2
1
2
1
2
2
1
1
1
3
1
1
1
1
1
1
1
1
1
3
1
1
2
2
2
1
1
2
1
0
2
2
1
0
0
2
1
2
2
1
1
1
1
2
2
2
0
1
0
1
0
1
2
0
1
1
2
1
0
4
1
2
1
2
1
1
1
2
1
1
2
0
1
1
1
1
0
1
0
1
0
0
1
0
2
1
1
2
1
0
0
1
1
1
1
1
1
1
1
1
0
1
0
1
1
1
1
0
1
2
1
2
1
2
1
1
2
1
1
0
1
1
2
1
2
0
2
1
1
1
2
1
1
1
1
1
1
1
1
0
1
2
1
4
1
0
1
1
0
1
1
0
2
2
1
0
0
2
1
1
1
2
1
5
2
1
1
1
2
1
0
0
2
2
0
1
0
3
0
2
2
1
2
1
1
1
1
1
2
1
1
0
2
1
1
1
2
1
2
1
1
3
0
1
0
1
1
2
1
1
1
2
1
2
1
0
2
0
1
0
1
1
1
1
0
1
1
2
1
0
1
3
1
1
2
0
0
1
0
1
0
2
1
1
1
2
1
2
1
1
0
0
0
1
1
0
1
0
1
0
1
2
1
2
2
0
1
1
2
0
1
1
1
1
1
1
1
2
1
2
2
2
0
1
2
0
1
1
2
1
1
0
0
0
1
2
2
2
1
1
0
1
0
2
1
0
1
1
1
1
1
1
1
1
2
1
2
1
1
0
1
0
1
1
1
1
1
2
1
1
1
2
2
1
1
1
0
1
0
0
1
1
0
1
2
1
2
1
1
0
1
2
1
0
1
1
1
0
0
1
0
2
2
1
1
1
1
1
1
0
1
0
1
2
1
1
2
2
1
1
2
1
1
1
1
2
0
2
1
1
1
1
1
0
1
1
2
0
1
1
0
2
1
1
2
2
1
1
2
0
0
1
1
1
2
1
1
1
1
0
1
1
0
1
1
1
1
1
1
1
1
1
2
1
0
1
0
1
1
2
0
1
1
0
1
0
1
1
0
0
0
2
2
1
0
1
1
1
1
1
2
0
1
0
1
0
1
1
1
2
1
2
2
2
1
1
0
0
2
1
1
2
1
1
2
1
2
2
1
2
1
1
1
1
1
1
1
0
1
2
1
0
1
0
0
1
0
1
1
1
1
1
1
1
2
1
1
1
0
0
1
1
1
0
1
0
1
0
1
0
1
2
1
1
1
0
0
1
2
1
1
0
2
1
1
1
1
1
0
1
0
1
0
1
2
1
1
0
0
0
1
1
2
2
2
1
0
0
2
1
1
2
1
1
1
1
1
1
0
0
2
1
1
1
0
2
2
1
0
1
0
0
1
0
0
1
2
1
1
1
1
1
1
0
2
1
1
2
2
0
1
1
0
0
1
1
2
0
1
0
2
2
2
3
1
1
0
2
2
2
2
1
1
1
1
0
1
2
0
3
2
1
0
1
2
1
0
1
1
1
1
0
1
1
0
1
0
1
2
1
1
2
2
2
1
1
2
1
1
2
0
2
1
3
1
2
1
1
1
1
1
1
0
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
0
1
0
1
1
1
2
0
0
2
2
1
1
1
1
0
1
1
2
1
0
1
1
1
1
2
1
1
1
2
2
1
1
0
1
0
1
1
2
0
1
1
1
3
1
2
1
0
1
1
4
1
1
1
2
1
0
0
1
1
0
0
1
1
1
1
2
1
0
0
2
1
1
1
1
1
1
2
0
1
1
1
1
2
2
1
1
1
2
1
1
1
2
0
0
1
1
1
0
1
1
0
1
1
2
2
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
2
1
0
1
1
0
2
1
1
1
2
1
1
2
2
2
1
1
1
1
1
1
1
1
1
0
0
2
0
0
1
1
0
2
1
1
1
0
1
0
1
0
2
1
2
1
1
1
0
1
2
1
0
1
0
1
1
2
2
2
1
1
1
0
1
1
0
2
1
0
1
2
0
2
1
1
2
0
2
2
0
0
2
2
1
3
0
1
1
0
1
2
2
1
0
2
1
1
1
2
0
1
0
0
1
0
1
0
1
1
0
0
1
1
2
1
1
1
0
1
0
2
2
1
0
2
2
0
1
0
1
0
2
2
1
0
2
2
0
1
1
1
0
1
1
1
0
1
2
1
0
2
0
1
1
1
1
1
2
2
1
0
2
1
5
1
2
1
2
1
3
1
0
0
0
0
1
2
1
0
1
2
1
1
1
2
2
0
1
1
2
1
2
2
1
0
1
0
1
1
2
2
0
1
1
2
0
1
1
1
1
2
1
1
2
2
2
1
0
1
2
0
1
1
0
1
1
1
2
1
1
1
2
1
2
1
1
2
0
2
1
1
1
1
0
0
1
2
1
0
1
1
1
1
1
1
1
2
0
2
1
1
2
0
1
2
1
1
0
1
1
1
0
1
1
0
1
0
1
0
0
1
1
1
0
1
1
2
0
0
1
1
1
2
0
1
1
1
2
1
1
2
2
1
1
0
2
1
1
1
0
1
2
1
1
1
2
0
1
1
1
1
1
2
2
1
2
1
0
1
1
1
1
1
2
1
2
1
1
1
2
2
1
1
0
1
2
1
1
1
0
1
0
0
2
1
0
1
1
1
1
2
2
1
2
1
1
1
2
1
0
1
0
0
2
1
2
2
1
0
0
0
1
1
0
2
1
0
0
2
2
0
1
2
1
1
1
1
2
1
1
1
0
1
1
0
1
1
1
0
1
1
1
1
0
1
1
1
2
0
0
1
1
0
1
0
1
0
1
1
1
0
1
1
0
2
2
2
1
0
1
0
0
0
0
1
1
1
1
2
0
2
1
2
2
0
1
1
1
0
1
1
1
1
1
2
1
1
1
1
3
0
2
1
1
0
1
2
0
0
1
1
1
1
0
1
1
1
1
1
0
3
1
1
0
2
1
0
2
1
0
2
0
1
2
2
1
2
1
1
2
1
1
2
0
0
1
1
2
1
2
0
1
2
1
2
0
1
1
1
1
1
0
0
1
0
1
0
1
2
2
2
1
1
2
1
2
1
1
0
1
1
1
1
2
2
1
1
2
1
1
0
0
0
1
2
1
0
2
1
1
2
1
1
0
1
0
2
2
0
0
1
1
2
1
2
1
0
1
0
2
2
1
1
1
2
0
0
1
1
0
1
1
3
2
1
1
2
1
1
1
1
1
1
2
1
0
1
1
1
2
0
1
1
1
1
0
1
1
1
1
1
2
1
1
2
1
1
1
1
2
1
1
1
1
0
2
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
0
2
1
1
2
0
1
0
1
2
2
0
2
1
0
2
1
0
1
1
0
2
1
1
1
1
1
0
1
1
1
1
0
2
1
2
2
1
2
1
2
1
2
2
1
1
1
0
0
1
0
1
0
1
1
1
2
1
1
1
2
1
0
2
1
1
1
2
1
1
2
1
0
1
1
1
1
1
2
1
1
2
0
1
2
1
2
1
1
2
2
2
1
1
1
1
1
1
1
1
2
0
1
1
1
2
1
1
1
0
1
1
1
1
1
2
3
0
1
2
0
0
0
0
1
1
1
1
1
1
1
2
2
1
2
0
1
0
0
1
1
1
1
2
2
1
2
2
0
2
2
2
0
1
1
0
0
1
2
0
0
1
2
1
1
0
1
1
2
1
1
0
0
1
1
0
0
1
1
1
2
1
0
1
1
1
0
2
0
1
1
1
2
2
1
1
0
1
1
1
0
0
1
2
1
1
1
2
3
1
1
1
1
2
0
1
1
0
2
1
1
1
1
1
0
1
1
2
1
1
1
1
1
0
0
1
1
1
1
1
2
1
1
1
0
1
1
0
1
2
0
0
0
2
1
1
2
1
2
0
1
0
2
2
1
1
2
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
2
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
0
1
1
1
2
0
0
1
2
1
1
1
2
1
1
2
2
1
1
1
1
2
1
0
2
1
1
1
1
0
0
1
1
2
1
1
1
0
2
1
1
0
2
2
0
0
0
1
1
1
0
1
3
1
2
2
1
1
0
1
2
1
2
1
2
1
1
2
1
0
1
2
1
1
1
2
2
0
1
1
1
0
1
0
2
1
1
1
1
0
1
1
2
1
1
2
0
2
1
2
0
1
1
1
0
0
1
1
1
1
2
1
1
2
1
1
1
1
1
0
3
0
1
0
0
1
2
1
1
1
3
0
1
1
1
1
1
1
0
0
1
1
1
1
3
1
1
2
1
1
1
1
1
1
1
1
0
1
1
2
0
1
1
2
2
1
1
1
0
1
2
2
2
0
1
0
1
0
3
1
0
2
0
1
1
1
1
1
1
1
0
1
1
2
1
1
2
1
1
2
2
1
1
1
0
1
1
0
1
2
0
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
2
0
1
0
1
1
2
1
0
0
0
1
2
1
0
1
2
2
2
1
1
1
2
2
0
1
1
1
0
0
1
1
2
0
2
1
1
2
1
1
1
1
1
1
1
2
0
1
1
1
1
0
2
1
1
2
1
1
1
1
2
4
1
0
0
2
1
2
1
2
0
1
2
0
1
1
0
0
0
1
1
1
0
2
0
2
1
1
0
1
1
1
0
1
1
1
1
2
0
1
1
1
2
1
2
1
1
2
1
1
2
1
1
1
0
0
1
2
1
1
1
0
0
0
1
2
1
1
1
1
1
0
1
0
2
1
0
1
1
1
1
1
1
2
2
1
1
2
1
2
0
1
1
1
1
1
2
1
0
1
2
2
1
1
2
1
2
1
2
1
2
1
1
1
2
1
1
1
2
1
1
1
1
1
1
0
2
2
1
1
1
0
1
0
0
1
1
2
1
0
1
2
1
1
1
1
1
1
1
1
1
0
1
0
1
2
1
1
1
2
1
1
1
1
1
0
0
4
0
0
0
0
0
2
1
2
1
1
2
1
2
2
2
2
0
0
0
1
5
1
1
1
0
1
1
1
1
1
1
0
2
3
1
1
0
1
1
1
1
2
1
2
1
2
1
1
0
1
0
1
1
0
2
1
2
2
1
1
0
2
2
1
1
0
1
1
1
1
0
0
0
1
1
1
1
3
0
0
1
1
0
2
1
1
0
1
1
1
0
1
1
0
1
1
1
1
1
0
1
1
1
1
2
1
1
0
0
1
1
0
1
1
0
1
0
1
0
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
0
1
2
2
0
2
1
1
1
1
2
1
2
0
1
1
0
1
1
1
2
1
1
1
2
1
2
1
0
1
1
2
1
1
1
0
0
2
1
1
1
0
1
5
1
1
1
1
1
1
1
1
1
2
2
1
1
3
1
2
0
1
0
1
2
1
2
1
1
1
1
1
2
2
1
2
2
1
1
2
2
1
1
0
1
0
1
2
0
2
1
0
1
1
2
1
1
1
2
1
1
1
0
1
1
1
2
1
1
1
2
2
0
2
1
2
1
1
0
1
1
1
0
0
1
1
0
1
1
1
1
0
0
2
1
2
2
1
2
1
1
0
0
1
1
1
1
2
0
1
0
1
1
1
0
1
2
1
1
1
1
1
1
0
0
1
1
1
0
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
0
0
1
1
1
3
1
2
1
1
1
2
1
0
1
1
2
1
0
0
1
2
1
1
0
1
1
1
1
1
2
1
0
1
1
1
1
2
1
1
1
0
1
2
2
1
2
1
1
1
1
1
2
1
1
1
1
1
0
0
1
1
1
1
0
1
1
0
0
1
1
1
2
0
1
1
0
1
0
0
1
1
1
2
2
2
1
0
2
1
1
1
2
1
2
0
0
1
1
1
2
1
1
1
2
2
1
1
3
2
1
2
1
0
1
1
1
2
2
0
1
2
0
2
1
0
1
1
1
1
1
0
1
1
1
2
1
2
1
1
1
1
1
0
1
1
0
1
1
0
2
1
0
2
1
0
2
1
1
1
1
1
0
0
1
1
1
1
0
2
0
0
1
2
2
1
1
1
1
2
0
0
0
2
0
1
1
2
1
1
1
0
0
1
1
1
1
1
1
2
1
2
2
1
1
1
1
2
2
1
1
1
0
1
1
1
2
1
2
2
1
2
5
1
1
1
2
1
1
0
1
2
1
2
2
1
1
0
0
0
0
1
0
1
0
1
2
0
1
1
1
1
1
1
2
0
1
1
0
1
2
0
1
1
0
2
1
0
1
1
1
1
0
1
2
0
2
1
1
2
2
2
1
1
2
1
2
0
1
1
1
1
0
1
1
2
2
0
2
2
1
2
1
2
0
1
0
1
1
1
1
2
1
2
1
1
1
1
1
0
2
1
5
2
0
2
1
2
2
1
1
1
1
2
0
2
1
1
1
1
1
2
0
1
1
1
2
1
1
1
1
1
1
0
0
2
0
2
2
1
1
1
1
0
2
1
1
1
2
1
1
1
1
1
2
1
4
2
1
1
2
1
1
1
0
1
1
2
1
2
1
1
0
1
0
1
0
0
1
1
1
1
1
3
0
1
0
2
0
1
0
1
1
1
0
2
0
1
2
1
1
1
1
2
1
1
1
2
2
2
1
1
2
0
1
0
2
1
1
1
0
1
2
1
2
0
0
1
0
0
1
2
1
1
0
1
2
1
0
1
1
1
2
0
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
2
1
1
1
1
1
1
0
0
0
1
2
1
2
2
1
1
2
2
2
0
1
1
1
1
1
1
1
1
1
1
1
0
1
1
0
1
0
1
2
1
1
1
2
1
0
1
1
1
1
1
0
1
1
0
1
1
1
1
1
1
1
1
2
1
1
0
0
2
2
0
1
0
2
2
1
1
1
1
2
2
1
0
0
1
1
1
1
1
2
1
2
1
1
1
2
2
1
2
1
1
3
1
0
1
1
1
2
1
2
2
1
1
1
2
1
0
1
0
1
1
1
1
2
2
1
1
1
1
0
0
0
1
1
1
2
1
3
1
2
1
2
1
1
2
1
1
1
1
1
2
1
0
0
1
1
2
0
2
1
1
1
1
1
2
1
1
0
0
1
0
0
0
2
1
1
2
0
1
1
1
2
0
1
1
2
2
2
1
2
0
2
3
0
2
0
1
1
2
1
1
1
1
1
1
1
2
1
2
2
1
0
0
2
0
0
2
0
0
1
0
1
0
1
1
1
2
2
1
2
2
1
1
1
1
0
2
1
0
1
1
0
2
2
1
1
1
1
1
0
1
0
1
2
1
1
1
1
1
0
1
1
0
1
1
2
1
1
1
2
2
1
1
1
2
1
2
1
1
2
1
2
2
1
1
2
1
1
1
2
3
2
1
1
1
1
1
1
1
0
2
1
0
1
1
2
0
0
1
0
2
0
1
1
1
1
0
1
1
1
1
2
1
0
1
0
1
1
1
1
0
2
1
1
1
0
2
2
1
0
1
1
1
1
9
2
1
1
1
1
2
1
1
0
1
0
2
0
1
1
0
0
1
0
2
1
3
1
2
2
2
1
3
2
2
1
1
0
1
2
2
2
1
0
3
1
1
2
0
1
0
1
0
1
0
1
3
1
0
1
1
1
1
1
1
2
2
0
1
1
1
1
1
2
2
0
1
2
2
2
1
1
1
1
1
2
1
2
2
1
1
2
0
1
1
1
1
1
2
1
1
1
0
1
0
0
1
1
1
2
2
2
0
1
0
0
0
1
1
2
1
1
1
1
1
1
2
1
1
1
0
1
2
1
1
1
0
1
0
1
1
1
1
0
1
1
0
1
1
4
1
1
2
1
0
2
1
1
0
1
0
1
0
1
0
1
1
1
1
1
1
1
1
0
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
2
1
2
1
0
2
1
1
1
0
1
1
1
2
2
2
4
2
1
0
0
1
1
1
1
1
0
1
2
2
1
2
2
1
1
1
0
1
0
1
2
1
0
1
1
1
1
1
1
0
1
1
2
0
2
0
1
0
1
2
0
1
2
1
2
0
1
1
1
1
0
1
0
2
1
1
1
0
1
1
0
0
2
0
1
1
1
2
2
2
1
1
1
2
0
1
1
1
1
2
1
1
1
1
0
1
1
1
0
0
1
1
1
2
2
0
1
2
0
1
0
0
0
1
1
1
1
2
1
0
1
1
1
1
2
0
0
1
0
1
2
2
2
1
1
1
1
1
1
1
1
0
2
1
1
0
2
0
2
1
1
1
1
1
1
1
1
0
1
1
2
1
2
1
1
1
1
1
1
2
1
1
2
0
1
1
1
1
1
3
2
1
1
2
1
1
1
1
1
3
2
1
1
2
1
2
0
1
0
1
1
1
0
0
1
1
0
2
2
2
1
1
1
1
0
1
1
1
1
1
1
1
2
2
2
2
2
2
1
1
2
2
0
0
1
1
1
1
2
1
1
0
1
0
2
0
1
1
1
1
0
1
1
2
1
1
0
1
1
1
0
1
2
0
1
0
2
1
1
0
1
2
1
1
0
1
0
0
1
0
0
1
1
1
2
1
0
1
3
0
0
1
2
1
1
1
2
0
0
0
0
1
1
2
1
1
1
0
2
1
1
1
2
1
1
1
1
0
1
1
1
0
0
1
1
1
2
1
1
1
3
1
0
0
1
1
1
1
0
1
1
1
2
2
2
1
0
1
1
1
0
1
1
0
1
2
1
1
1
1
1
1
0
1
0
1
0
1
1
1
1
1
1
0
1
1
1
2
0
2
1
0
1
1
2
0
1
1
2
2
1
0
0
1
2
1
0
0
1
0
2
2
0
1
0
1
1
1
0
2
2
0
1
2
1
1
2
1
1
1
1
1
0
1
1
1
1
1
1
0
1
2
2
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
0
1
0
2
2
1
1
1
0
1
1
1
0
1
2
1
2
1
0
1
0
1
1
1
1
0
1
1
1
1
1
2
2
0
4
2
1
1
2
0
1
1
1
0
1
1
1
0
0
2
1
0
1
2
1
1
1
2
1
2
1
2
2
1
1
1
1
2
3
2
1
1
1
1
1
2
1
2
2
1
1
2
2
0
1
2
1
2
3
1
2
0
1
1
2
2
0
1
1
0
3
2
2
1
0
1
1
1
1
2
2
0
1
1
2
1
2
1
1
1
2
0
2
1
2
1
1
0
2
0
1
2
0
1
1
1
0
1
1
2
0
1
2
1
2
0
1
2
2
1
2
1
0
0
1
1
1
1
1
2
0
0
2
0
0
1
1
0
1
1
1
1
4
2
1
2
1
1
1
1
1
0
1
1
1
2
0
0
2
2
1
1
1
2
1
1
1
2
1
1
2
1
1
2
1
4
0
2
1
2
0
2
1
2
1
2
2
1
1
2
0
0
1
1
1
1
0
2
1
1
2
2
1
1
1
1
2
0
2
2
1
1
1
1
1
1
2
0
3
1
1
1
0
2
1
1
1
0
1
1
1
0
1
1
1
2
2
1
1
1
1
0
1
1
1
1
1
2
1
0
2
1
1
0
1
0
3
1
1
1
1
2
2
1
0
1
2
2
0
0
1
1
1
2
2
2
1
0
2
1
1
1
1
1
1
1
1
1
0
2
2
2
1
1
2
1
2
1
1
1
1
2
1
1
2
2
1
1
1
0
1
1
2
1
1
0
0
1
1
0
1
1
1
2
1
1
1
1
2
0
1
1
1
0
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
0
2
2
1
1
1
1
0
0
0
1
1
1
1
1
1
2
2
0
2
1
2
2
1
1
1
2
1
0
1
2
2
1
1
1
2
2
1
1
1
2
2
1
1
1
2
0
1
1
0
1
1
2
2
1
1
1
1
0
2
1
1
1
1
1
0
1
1
2
2
1
1
1
1
0
2
1
1
1
0
1
0
2
1
2
1
2
0
1
1
0
1
2
0
2
1
1
2
3
1
1
1
1
0
1
2
1
0
1
2
2
1
1
1
1
1
1
1
1
1
1
2
0
2
1
1
1
1
0
0
1
2
2
1
2
2
2
1
0
0
0
0
2
1
1
2
1
1
2
0
1
2
1
1
2
1
1
0
1
1
0
1
2
1
1
1
1
2
1
1
1
2
2
2
1
1
1
0
2
1
1
1
1
2
1
2
1
2
1
2
1
2
2
2
2
1
2
1
1
1
1
1
1
1
0
1
2
2
1
1
2
2
0
0
1
1
1
2
0
2
0
1
1
2
0
1
1
0
1
2
0
1
1
1
2
1
1
1
1
1
0
1
1
2
1
1
1
1
2
1
1
1
2
1
1
0
2
1
2
3
1
1
1
1
1
0
1
2
1
1
1
1
1
0
1
1
0
1
2
1
1
1
1
2
1
0
1
2
1
1
1
2
1
2
0
1
1
1
0
1
2
0
1
0
1
0
1
0
0
0
1
0
1
0
2
1
1
1
1
1
1
2
1
2
1
0
1
2
1
1
1
1
2
1
1
2
2
2
1
0
0
0
1
1
0
0
1
0
0
1
1
0
0
1
1
2
1
2
0
1
0
1
2
2
1
2
2
1
1
0
1
2
0
2
0
1
1
1
2
2
0
1
0
0
1
1
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
2
0
1
0
1
1
1
1
1
1
0
1
1
1
0
1
1
1
1
1
2
0
2
1
1
2
0
0
1
1
1
1
1
1
2
0
1
1
0
0
2
2
1
1
1
0
1
1
0
1
0
2
0
2
2
1
0
2
0
1
1
1
1
0
0
0
1
2
1
1
0
0
1
1
1
1
2
0
1
1
1
1
1
1
1
2
1
1
0
0
2
1
1
1
1
0
1
1
1
2
1
1
1
0
1
2
1
2
1
1
1
1
0
2
1
1
2
1
1
1
0
0
0
1
2
2
1
1
1
1
2
0
0
1
2
2
1
1
2
2
1
1
0
0
5
0
1
1
1
1
1
2
1
2
3
1
1
0
0
2
1
2
2
1
0
0
2
1
0
1
1
1
2
2
1
1
1
2
1
1
1
1
1
1
0
0
0
1
2
1
1
1
1
1
1
2
0
1
1
1
2
1
1
2
0
1
1
1
0
1
0
1
2
2
1
2
2
1
1
1
1
0
1
1
1
1
1
1
2
1
1
1
1
1
0
1
1
2
1
0
1
0
1
1
2
1
1
2
1
1
1
2
1
1
2
1
1
0
1
1
1
0
1
1
2
2
0
0
1
1
3
0
1
1
1
1
0
0
1
1
2
1
1
0
1
1
1
0
1
1
1
1
2
1
1
0
0
2
2
1
0
1
1
0
1
0
1
1
1
1
1
0
1
1
1
1
1
1
1
1
2
1
1
1
0
2
1
1
2
1
0
0
2
1
1
1
0
0
1
1
1
0
1
0
1
1
2
2
1
0
4
1
1
2
1
1
1
1
2
1
0
1
2
0
1
2
2
1
1
0
1
1
1
1
1
1
0
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
0
0
1
0
0
1
0
0
2
1
0
1
0
1
1
1
1
1
1
1
1
0
1
1
1
3
1
2
0
1
0
1
1
2
1
1
0
1
1
2
2
0
1
0
1
2
0
1
1
1
1
0
2
1
1
2
2
0
0
1
2
0
2
1
1
1
2
2
1
1
1
1
2
1
1
2
1
1
1
2
1
2
2
1
0
1
1
1
2
2
2
1
1
1
0
1
1
1
0
0
1
1
1
1
2
1
0
2
2
1
2
1
0
1
1
1
1
1
2
2
2
1
1
3
0
1
1
2
2
1
0
0
1
1
0
0
0
1
1
0
2
0
2
0
0
1
1
1
2
1
1
1
1
1
1
0
0
0
1
1
2
1
2
1
2
1
1
1
1
0
1
1
0
2
2
1
1
2
1
1
1
1
0
1
2
1
1
2
1
0
2
0
0
1
2
2
2
2
1
1
2
1
1
2
1
0
1
1
1
1
1
1
0
1
0
0
2
2
1
1
1
0
1
0
1
2
0
1
1
0
1
0
1
2
1
2
0
1
0
1
1
0
0
0
1
0
1
1
2
2
0
1
0
1
0
1
2
0
1
2
1
0
1
1
2
1
1
0
3
2
1
0
1
2
1
1
0
0
1
1
1
0
1
1
0
1
2
1
2
0
0
1
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
0
2
1
1
0
0
2
0
1
1
0
1
0
1
1
1
0
0
0
1
1
1
1
0
2
1
1
1
1
0
1
0
1
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
0
0
0
1
0
1
1
1
1
2
0
1
1
2
0
0
1
1
2
1
0
2
2
1
2
1
0
2
0
1
0
0
1
0
2
1
2
1
0
2
1
2
1
2
1
1
0
0
1
1
1
2
2
1
1
1
1
2
2
1
1
2
2
1
1
0
1
1
1
1
2
1
1
1
2
3
1
1
2
1
1
0
2
1
1
1
0
1
1
0
1
0
2
1
1
1
1
0
1
1
1
1
2
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
1
0
1
1
2
2
1
1
1
1
0
0
1
1
1
1
2
0
1
2
0
3
2
2
1
1
1
0
1
1
1
2
2
1
1
0
1
1
0
2
0
1
1
1
1
2
0
1
0
1
1
1
1
1
1
1
1
1
0
0
0
0
1
2
1
2
2
1
2
1
1
1
0
2
1
0
1
2
1
1
2
0
2
1
2
2
1
1
2
2
1
1
1
1
2
1
1
2
0
1
0
1
1
0
1
2
1
1
2
1
0
2
1
0
1
1
0
2
3
2
0
0
2
1
2
2
1
2
2
2
1
2
1
2
2
1
0
2
2
1
2
1
0
0
0
0
0
1
1
1
2
1
1
1
0
1
1
1
0
2
2
1
0
0
1
2
1
2
1
2
1
0
1
0
1
1
1
1
1
0
1
1
0
1
1
0
0
0
1
1
1
1
0
0
2
1
1
1
3
1
2
2
0
2
1
1
2
1
1
0
2
2
1
1
1
1
0
1
1
1
1
0
1
1
2
1
1
1
1
1
1
1
1
0
1
0
1
1
1
1
2
0
2
1
1
2
2
0
1
1
1
0
2
2
2
2
0
1
1
0
1
1
0
0
2
0
1
0
0
2
1
1
1
1
1
1
1
1
2
1
0
0
1
0
1
1
0
0
1
1
2
2
1
1
1
1
1
0
2
0
0
0
0
1
2
1
1
1
2
1
1
0
0
2
1
1
0
1
0
0
1
1
2
1
1
1
2
0
1
1
2
0
1
0
2
1
2
0
2
1
1
1
1
0
1
1
1
1
1
1
2
2
0
2
1
2
2
1
1
2
1
1
0
0
1
1
0
1
0
2
1
0
1
2
0
1
1
1
2
1
1
0
1
1
1
2
1
1
1
1
1
1
3
0
2
1
1
1
2
1
1
1
1
0
1
1
0
2
2
2
2
1
0
2
1
1
2
1
2
1
3
2
2
2
1
2
0
2
5
1
1
1
0
1
1
2
2
0
1
0
1
1
1
1
1
1
0
1
1
1
1
1
1
1
2
1
2
0
0
1
1
2
2
0
0
1
1
1
1
0
2
2
2
1
2
2
1
1
2
2
1
1
1
0
1
0
1
1
1
1
2
0
1
0
0
1
1
1
2
2
1
1
1
1
0
1
1
0
1
1
1
0
1
2
1
1
1
1
2
1
0
2
1
1
2
1
2
1
1
0
2
1
2
2
1
1
3
1
1
1
2
1
0
0
2
1
2
1
0
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
0
1
0
1
1
2
1
1
1
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
0
1
1
0
2
2
2
0
0
1
2
1
1
0
1
1
0
2
1
2
2
1
0
1
2
1
1
1
1
0
1
1
1
1
1
0
1
0
0
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
0
2
1
0
1
1
1
0
1
1
2
1
1
1
1
2
1
1
2
1
1
1
2
2
2
1
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
0
6
1
1
1
1
0
1
0
1
0
1
2
1
1
0
2
1
1
0
1
0
0
1
0
2
1
0
1
1
0
1
1
2
0
1
2
0
1
0
1
1
2
1
1
1
1
1
2
0
0
2
1
1
0
1
1
1
1
0
2
1
0
1
1
1
1
1
1
1
0
2
2
2
1
0
1
2
2
1
0
1
2
1
1
1
2
2
1
2
1
1
0
1
1
0
1
2
1
0
1
1
3
1
1
0
1
1
0
1
1
2
2
1
0
1
2
1
0
1
2
2
1
0
1
2
1
2
1
2
1
1
2
0
1
1
1
2
2
1
2
1
1
0
1
0
1
0
1
2
1
2
1
0
2
1
1
2
1
2
1
1
1
1
1
1
1
1
0
2
0
2
1
1
1
0
0
2
0
1
1
1
1
0
1
1
1
2
0
1
0
1
2
1
0
1
1
1
2
0
2
1
1
0
1
0
1
0
1
0
1
1
1
1
1
2
0
1
3
1
1
1
1
1
1
0
1
2
1
1
1
2
0
2
2
0
1
2
2
1
1
1
2
7
1
1
1
1
2
1
1
0
1
1
1
0
2
1
1
0
2
1
2
1
1
2
1
1
0
0
1
0
2
1
1
1
2
2
1
2
1
1
0
1
0
0
0
1
0
1
1
1
0
1
0
0
0
2
2
2
0
2
1
1
1
2
1
2
1
2
0
0
0
1
1
0
2
1
2
1
2
0
2
1
0
2
1
1
0
2
2
2
0
1
2
0
2
1
2
2
1
2
2
1
1
0
0
1
1
0
1
2
2
0
2
0
1
1
2
1
2
0
3
2
1
2
2
1
2
0
2
1
1
0
1
1
1
1
1
1
2
1
0
0
2
0
1
2
0
2
2
1
0
1
1
1
2
1
1
1
0
1
1
1
1
1
2
2
1
1
1
2
1
2
1
1
0
2
3
0
2
1
3
0
1
0
0
1
1
1
1
0
1
0
0
2
1
1
1
2
1
0
1
0
2
2
2
0
2
0
1
1
1
0
0
0
0
1
2
1
2
0
1
0
2
2
0
2
2
1
0
2
0
0
1
1
1
0
2
1
1
1
2
2
1
1
2
0
1
0
2
2
1
0
2
1
1
0
2
2
1
1
2
1
2
2
2
1
1
1
1
1
2
1
2
0
0
1
1
0
2
0
1
0
1
1
3
2
1
0
1
1
2
1
1
0
2
2
2
1
1
0
1
1
0
0
2
1
1
2
1
0
1
2
0
1
0
1
2
0
0
2
1
1
0
1
1
1
1
1
2
1
1
1
1
1
0
1
1
1
2
1
0
1
1
1
1
0
1
0
0
1
2
1
0
1
1
1
1
1
1
1
1
1
0
2
1
1
1
2
1
1
1
1
2
2
1
1
1
1
1
2
1
2
0
2
1
1
1
2
5
1
1
0
2
1
1
1
2
1
1
0
0
0
1
1
1
0
1
3
1
1
1
1
2
1
1
0
0
1
2
2
2
1
1
0
2
1
1
2
2
1
1
1
1
1
1
0
1
1
1
2
0
2
1
1
2
1
1
1
1
1
1
4
2
0
2
2
1
1
1
1
2
1
1
1
2
1
0
0
1
1
1
2
1
1
1
1
2
1
2
2
0
1
1
1
0
2
0
0
1
1
0
1
2
2
1
2
0
2
0
1
1
1
0
0
0
0
0
1
0
2
2
1
1
1
0
1
0
1
1
0
0
1
1
1
2
0
2
2
1
1
2
1
1
2
1
1
2
2
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
2
0
0
0
1
1
2
1
1
1
2
2
0
1
1
2
0
1
1
1
1
1
1
2
2
2
1
1
0
2
1
1
1
1
1
0
2
1
1
0
2
1
0
1
2
2
1
0
1
2
1
1
1
1
1
0
1
0
2
2
1
0
0
2
1
2
1
1
0
0
0
4
1
1
1
1
2
1
1
2
1
2
2
1
0
1
2
1
2
1
1
1
2
2
0
2
0
0
1
1
0
1
1
2
1
1
1
0
1
1
0
2
2
0
1
0
1
0
1
1
2
1
1
2
1
1
0
1
1
2
2
1
2
1
1
1
1
0
2
2
2
1
1
1
0
2
1
1
2
1
2
0
2
1
1
1
1
1
2
1
0
1
1
1
1
1
1
1
1
0
0
1
1
2
1
2
2
1
1
2
1
1
1
2
1
1
0
1
1
1
2
1
1
1
1
2
2
1
0
1
1
1
1
1
2
2
0
0
1
1
0
1
0
1
2
0
1
1
0
2
3
1
1
1
2
1
1
1
1
1
2
2
2
0
1
1
1
1
1
1
0
0
2
1
1
0
1
1
1
1
1
1
1
0
1
1
1
1
1
2
1
0
1
2
1
1
1
1
1
1
1
2
1
1
0
0
1
1
1
0
1
1
2
1
1
1
0
1
0
1
1
1
0
1
2
2
2
1
1
1
1
1
0
1
0
1
1
0
2
0
1
1
2
1
1
2
1
2
1
1
1
0
1
1
1
1
0
1
1
1
2
1
1
2
2
2
2
0
0
0
2
0
0
0
1
1
1
1
1
0
0
1
1
0
1
1
1
0
1
2
2
1
3
2
2
3
0
1
1
1
1
0
1
1
1
0
2
1
1
2
1
1
1
2
0
1
0
0
0
1
2
1
1
1
0
1
0
1
1
2
1
2
1
0
2
2
1
2
2
1
1
1
0
1
1
1
1
1
0
0
1
1
1
2
2
1
1
0
1
1
2
0
1
2
0
1
1
0
1
1
1
1
2
1
2
1
0
1
0
2
1
0
1
1
1
1
1
2
1
4
1
1
1
0
0
1
1
0
2
1
1
0
0
1
2
1
1
0
1
0
1
1
1
0
0
1
1
2
2
1
0
1
0
1
1
3
1
0
1
1
1
1
0
2
1
0
2
1
1
2
1
0
1
2
1
1
1
1
1
1
0
0
2
1
2
1
0
1
2
1
1
2
1
2
2
1
0
2
2
0
2
1
1
1
1
0
2
1
1
0
1
0
0
1
1
1
0
1
2
1
1
1
1
0
1
0
2
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
0
0
0
1
2
1
1
1
1
2
1
1
1
1
2
2
1
0
0
1
1
2
1
1
1
2
2
1
2
0
0
2
1
0
2
1
1
1
0
0
1
1
2
1
1
1
1
2
1
1
1
1
0
1
1
0
1
0
1
0
1
0
0
1
1
0
1
2
1
2
1
1
2
2
2
1
1
0
1
0
1
0
2
1
1
0
1
1
1
2
1
1
1
1
2
1
1
0
0
1
1
0
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
0
0
1
1
1
1
2
1
1
0
1
1
1
0
2
1
1
1
2
1
1
2
2
1
1
1
0
1
2
1
1
1
1
2
0
1
1
2
1
0
0
1
0
0
0
0
1
3
1
1
1
1
2
2
1
0
0
1
1
1
1
2
1
1
1
2
1
1
1
0
1
0
2
1
2
0
1
1
1
0
1
1
0
2
1
1
2
0
0
0
1
1
1
1
1
0
1
1
2
1
1
2
1
0
2
0
1
2
1
1
2
1
1
2
1
1
1
2
0
0
1
1
1
2
2
1
1
0
2
0
2
0
0
2
1
1
2
1
1
2
2
1
0
0
1
1
1
1
0
0
1
0
1
0
1
2
2
1
0
1
2
1
0
2
0
1
1
0
1
2
1
1
3
2
1
0
1
2
1
0
2
0
0
1
1
1
1
0
1
0
1
1
0
2
2
1
1
2
1
1
0
0
1
1
1
2
1
1
2
1
2
0
2
1
0
2
0
1
1
1
1
1
2
1
1
0
1
1
1
1
1
1
2
1
1
1
0
1
0
0
1
0
2
1
0
1
2
0
1
1
0
2
2
2
1
1
0
1
1
2
2
1
0
1
2
0
1
1
1
2
0
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
0
1
0
2
1
1
1
2
1
1
1
1
2
2
2
1
2
1
1
2
1
1
0
1
1
1
1
1
0
1
1
1
1
0
2
1
0
0
0
1
2
3
1
0
1
2
0
0
1
1
1
2
1
1
1
2
2
1
2
1
1
0
1
1
1
1
0
2
1
1
1
0
1
0
1
1
2
1
2
0
1
0
1
0
1
2
1
1
2
1
1
1
2
1
1
2
1
2
2
0
1
1
1
2
0
2
1
0
0
0
1
1
1
1
0
4
0
1
1
0
1
0
0
1
2
1
1
1
1
0
0
2
2
1
1
0
1
0
1
0
2
2
1
1
0
1
1
2
2
1
1
2
1
2
1
0
1
1
1
1
1
2
0
0
1
1
1
0
2
2
1
1
1
0
1
1
1
2
0
1
1
0
0
2
1
1
0
1
0
1
2
1
1
1
0
2
2
1
2
1
2
0
1
0
1
4
2
2
0
1
1
0
1
1
2
1
2
1
1
2
0
0
2
1
0
1
2
1
1
0
1
1
1
0
0
2
1
1
1
1
1
0
1
2
0
1
0
1
2
0
1
1
1
2
0
1
1
1
0
2
2
2
1
1
1
1
2
1
0
1
0
2
1
0
1
0
0
2
1
0
1
2
1
1
2
1
1
2
1
0
2
1
2
2
0
1
1
1
2
1
1
1
1
1
1
2
1
2
1
1
2
2
2
1
1
0
1
1
1
1
0
2
0
2
2
2
2
0
2
1
2
1
0
1
2
1
0
1
2
1
2
1
2
1
3
0
2
1
0
1
2
2
1
0
1
1
2
0
1
1
1
0
1
1
1
2
0
2
1
1
1
1
3
2
1
2
1
0
1
1
1
2
1
1
1
0
1
2
1
2
2
1
2
1
1
1
1
1
0
1
1
1
2
0
0
5
0
1
2
1
2
1
1
2
1
1
1
1
0
1
0
0
1
1
1
0
1
0
1
1
1
2
1
1
0
1
1
1
1
3
2
2
1
1
2
1
1
2
1
1
0
1
0
1
1
2
0
0
1
1
2
1
3
2
1
1
1
1
0
1
2
1
0
2
2
1
1
2
1
1
2
0
1
1
3
1
0
3
1
2
0
1
2
0
0
1
0
1
1
1
0
0
2
2
0
1
1
0
2
1
1
1
1
1
1
1
2
1
1
1
0
2
1
0
0
1
1
2
1
2
1
1
1
1
1
0
0
2
0
2
1
2
2
2
1
0
1
1
2
2
1
0
2
2
1
2
0
1
2
1
1
1
2
1
1
1
1
1
0
1
1
0
1
1
1
2
1
1
1
1
3
1
1
1
1
1
0
1
2
0
2
1
1
1
0
0
0
2
3
1
0
1
1
1
1
1
1
1
2
1
1
1
0
0
2
1
0
1
1
1
2
1
1
0
2
2
1
0
1
1
1
2
1
2
1
1
1
2
0
2
1
2
2
2
1
2
1
1
1
1
2
0
1
1
0
2
2
0
1
1
1
2
2
0
0
1
1
0
3
0
0
1
1
2
1
2
1
0
1
1
2
1
1
2
1
2
0
1
1
1
1
2
1
0
2
1
0
0
0
1
1
0
0
0
1
0
1
1
1
1
1
2
2
0
1
0
1
1
1
1
1
1
1
2
1
0
1
2
2
0
1
0
1
1
0
2
1
2
1
1
1
2
0
0
2
1
1
0
2
1
1
1
1
0
1
2
1
1
1
0
0
0
0
1
1
2
1
2
0
1
0
1
1
0
1
1
1
0
2
1
1
1
2
2
1
0
1
1
2
1
2
1
0
1
1
1
1
3
0
1
1
2
1
1
0
1
1
1
1
2
2
2
1
1
0
2
2
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
0
1
1
2
0
2
2
1
1
1
1
0
1
2
1
1
1
1
2
1
3
1
1
0
2
1
2
1
2
0
1
1
2
2
1
1
0
0
2
1
2
1
2
2
1
1
2
2
0
2
1
0
1
1
3
2
1
1
1
1
2
0
1
2
1
2
0
0
0
2
1
1
1
3
1
0
2
1
0
2
1
1
1
0
1
1
1
1
1
1
1
1
2
2
1
0
1
1
2
1
0
1
1
2
2
2
1
1
0
3
2
1
1
1
1
1
0
0
0
1
2
2
0
1
0
1
1
0
1
1
2
1
1
2
0
1
2
1
1
1
1
1
2
1
1
0
1
2
1
1
1
2
1
1
1
1
1
1
0
0
1
1
2
0
0
1
2
1
1
1
1
1
0
0
1
1
1
0
1
1
1
2
1
1
1
1
1
1
0
2
1
1
1
2
2
2
1
2
0
2
0
0
1
0
1
2
2
0
1
1
0
0
1
2
2
0
1
0
1
1
2
1
1
1
1
0
1
2
1
2
1
1
1
1
2
1
1
0
1
0
2
0
0
1
2
2
2
1
1
1
0
0
1
0
0
1
0
1
1
2
1
1
2
1
0
1
1
2
1
1
2
1
2
0
1
1
1
1
1
1
1
2
1
0
1
1
0
3
1
1
2
1
0
0
1
2
1
1
0
0
2
0
2
1
2
1
1
2
2
1
1
1
1
2
0
2
1
0
1
1
1
0
0
1
2
2
1
1
2
0
1
2
1
1
1
1
1
1
1
2
1
1
2
0
2
1
2
1
0
1
1
1
1
2
2
1
1
1
1
2
1
1
1
0
2
1
0
1
0
1
1
2
1
1
1
1
1
1
1
2
0
1
2
0
1
1
2
0
1
1
1
0
1
2
1
2
0
0
1
1
0
1
1
1
0
1
2
0
1
0
2
2
0
1
1
0
0
1
2
1
1
1
0
1
1
0
0
1
1
1
0
0
0
1
1
1
1
1
1
1
0
0
2
1
2
2
0
0
0
1
1
1
2
1
0
1
0
1
1
1
2
1
2
0
1
1
0
2
0
1
1
0
1
1
1
1
2
0
1
1
1
0
0
1
1
0
2
0
1
2
2
1
2
2
2
1
2
1
0
1
1
1
1
1
1
1
1
1
3
1
1
0
1
2
3
1
1
1
1
1
3
0
2
1
2
1
0
1
1
0
1
1
1
1
1
2
2
1
1
1
1
2
1
1
1
0
2
1
2
0
1
1
1
0
1
2
1
2
4
1
1
1
1
2
0
2
2
1
2
1
1
1
2
2
1
1
1
2
1
0
2
1
2
2
2
2
1
1
2
0
1
2
1
0
1
0
2
0
2
1
2
1
0
1
1
1
1
1
1
0
1
1
2
0
0
1
0
1
1
1
1
1
1
1
1
0
0
2
0
3
2
1
1
1
1
1
1
1
0
2
0
1
1
1
1
2
1
2
1
2
1
1
2
2
3
1
2
1
2
1
1
3
1
1
1
0
1
1
0
1
0
1
2
1
1
1
1
1
1
1
1
2
1
2
1
2
0
2
1
0
1
1
1
1
0
2
0
2
2
2
2
0
2
2
2
1
1
2
1
2
1
1
2
1
0
1
0
1
2
1
0
1
1
2
1
2
0
1
2
1
1
1
0
2
2
1
1
2
3
1
1
1
2
1
2
0
0
0
2
1
2
1
1
1
2
1
0
1
3
1
2
2
1
0
1
2
2
0
1
0
1
1
2
2
1
1
1
2
2
0
1
1
0
0
1
1
0
1
2
1
0
1
1
1
0
1
1
1
1
2
1
1
3
1
2
0
1
0
1
1
1
1
0
1
1
2
1
2
0
1
1
0
1
1
2
2
1
2
1
1
1
2
2
0
1
0
2
1
2
1
1
1
2
1
2
1
0
2
0
1
0
1
2
1
2
0
0
1
1
2
0
1
3
2
0
1
2
0
1
1
2
2
0
0
1
1
1
2
1
1
0
1
2
2
0
2
1
0
2
1
1
0
1
1
2
1
1
1
2
2
0
1
1
1
1
0
0
2
1
1
1
2
0
1
3
1
1
1
2
0
0
2
2
2
2
1
0
1
2
0
1
1
1
0
1
2
2
0
1
0
1
1
2
0
0
1
1
1
2
2
1
1
1
1
1
1
0
1
1
0
2
1
1
1
1
0
0
1
1
2
0
1
1
0
2
2
1
0
0
2
1
1
1
1
1
2
2
1
2
1
1
0
1
1
1
1
2
0
0
2
1
1
1
1
1
1
2
1
1
0
1
2
1
1
3
1
1
2
1
1
1
0
1
1
2
1
1
1
2
1
2
1
2
1
2
1
2
1
1
0
1
1
1
1
1
1
0
2
1
1
2
1
1
2
0
0
1
2
1
1
1
1
1
1
0
1
1
1
1
2
2
1
1
1
3
2
1
0
2
2
0
1
2
1
1
2
1
0
0
0
2
1
1
1
1
1
2
1
1
1
0
1
2
1
1
1
1
2
2
0
1
1
1
0
7
1
0
1
1
0
1
1
0
1
1
2
1
0
1
1
0
1
1
1
1
2
0
1
1
2
2
1
1
0
1
1
1
0
1
1
2
1
0
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
0
1
2
2
0
1
0
0
2
1
2
1
1
0
0
1
1
1
1
1
0
1
1
2
0
2
0
1
1
0
1
0
0
1
2
1
0
1
0
1
1
1
2
2
1
0
1
2
2
1
2
1
0
1
2
1
0
2
0
1
1
1
1
0
1
0
2
1
0
2
2
1
2
1
2
2
0
1
0
1
1
0
0
1
0
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
0
1
0
1
1
2
1
1
1
1
1
2
1
1
2
1
2
2
1
1
0
1
1
0
2
2
1
1
1
2
2
1
1
1
0
0
1
1
1
1
0
1
2
1
0
1
0
1
1
2
1
1
1
0
2
1
1
1
1
1
0
0
2
1
0
1
1
2
0
1
1
1
2
1
1
1
2
1
2
2
0
1
1
2
1
1
1
1
1
2
0
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
2
0
1
2
1
2
1
1
3
2
1
0
1
2
2
1
1
1
2
2
1
1
0
1
2
1
1
1
0
2
2
0
2
1
0
1
1
0
0
1
1
1
1
1
1
0
2
1
1
0
1
0
1
1
1
0
0
1
2
0
1
1
2
1
0
2
1
0
1
1
1
1
0
0
0
0
1
1
1
1
0
1
0
2
1
1
2
0
2
0
2
1
0
1
1
1
1
1
1
2
1
2
0
1
0
1
1
1
0
1
2
0
1
2
0
1
2
1
0
0
1
1
2
0
1
0
2
1
1
2
1
1
0
1
1
1
1
1
1
1
2
1
1
2
1
1
0
1
1
1
1
1
0
1
0
1
0
1
1
2
1
1
0
1
1
1
2
2
1
1
2
1
2
1
0
2
1
2
1
1
1
0
1
1
1
0
2
2
1
1
1
1
0
1
1
2
1
6
2
0
3
1
1
1
0
3
1
1
1
1
1
1
2
1
2
1
1
1
2
1
1
2
0
1
1
1
0
2
2
0
1
1
1
2
1
1
1
1
1
1
0
1
2
1
0
1
0
1
2
0
1
0
1
1
1
2
2
0
1
1
1
2
1
2
1
1
2
1
1
2
0
1
1
1
1
1
2
2
1
2
5
1
0
3
0
1
1
1
1
0
1
2
1
1
1
1
1
1
1
2
3
1
1
2
0
2
1
1
0
1
1
1
1
2
1
1
1
1
0
2
1
2
2
1
2
0
1
0
1
2
1
2
1
1
1
0
1
0
0
0
2
2
1
1
2
1
0
2
2
1
2
2
1
2
1
1
1
1
1
1
1
1
2
0
1
1
1
1
1
1
2
2
1
0
1
2
1
2
2
1
2
1
1
2
3
0
1
1
2
1
1
1
1
1
1
2
1
1
2
2
1
1
2
1
1
2
0
2
1
1
0
1
0
1
1
0
1
1
2
2
1
2
0
1
2
1
1
1
1
1
1
2
1
0
1
0
1
0
1
1
1
2
1
1
1
0
1
0
1
0
0
1
1
1
1
0
1
1
1
1
2
1
1
1
0
1
2
1
1
2
1
1
1
0
2
2
1
1
2
0
1
2
1
1
1
1
1
2
1
2
1
4
0
2
1
1
1
1
1
2
1
1
1
3
0
0
0
1
1
0
1
2
1
0
2
2
0
0
1
2
2
0
1
2
1
1
1
1
1
1
2
2
7
1
2
1
1
1
1
2
1
1
0
2
1
0
1
2
1
0
2
1
2
1
1
0
2
0
1
0
1
1
2
2
2
1
2
2
2
2
1
2
1
0
0
1
1
1
2
0
1
1
1
2
0
0
1
0
2
1
1
0
1
1
1
1
1
1
2
1
0
1
1
2
2
1
1
2
0
1
1
1
1
1
1
1
1
1
1
1
1
1
2
0
1
2
2
1
0
1
1
1
1
1
1
1
0
0
3
1
1
1
1
1
0
1
1
1
0
1
1
2
1
2
2
2
3
1
1
2
1
2
1
1
1
1
1
2
1
2
1
1
2
2
2
1
2
1
1
1
0
2
0
2
1
1
1
1
1
2
1
1
0
1
2
2
0
1
0
0
1
1
1
0
1
1
0
1
2
2
1
1
1
1
1
2
0
1
1
0
1
1
1
1
1
2
1
0
0
0
2
1
2
1
2
1
2
1
1
1
1
1
0
1
1
1
1
0
1
1
1
0
0
1
1
1
0
1
1
1
1
1
1
0
2
1
1
0
1
2
2
1
0
1
0
1
2
1
1
1
1
1
1
1
1
2
0
2
2
0
1
1
1
2
1
2
1
0
1
0
1
1
2
1
1
2
1
1
2
0
2
0
1
2
1
1
1
0
1
1
1
0
1
2
0
0
0
1
2
1
0
1
0
1
1
1
2
1
2
1
1
1
0
2
1
1
0
1
1
1
0
0
1
1
1
2
2
1
0
1
0
0
2
1
2
1
0
2
1
1
1
2
1
0
1
1
1
1
1
1
0
1
1
0
1
2
1
0
1
1
1
1
0
0
1
2
2
2
0
0
1
1
1
0
1
3
1
2
1
1
2
1
0
1
2
1
1
1
2
2
2
2
1
0
1
0
1
1
1
1
1
2
1
1
0
0
2
1
1
0
1
1
1
0
1
1
2
1
0
0
2
1
2
1
1
2
1
0
1
2
1
2
1
0
1
1
3
0
1
2
1
1
1
0
2
1
1
1
1
1
2
0
2
1
1
1
0
1
1
0
2
1
1
1
2
1
1
1
0
0
1
1
0
0
2
0
1
2
2
1
2
1
2
2
0
1
2
1
0
1
1
1
1
2
0
0
1
1
1
1
1
1
1
1
1
1
2
2
1
2
0
0
1
2
1
1
1
2
0
1
1
1
2
0
2
1
0
1
1
1
0
1
1
1
0
1
1
0
2
0
0
1
3
1
0
1
0
1
1
1
2
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
0
2
1
0
2
1
2
1
0
1
1
2
1
1
2
1
1
0
2
1
1
1
1
2
1
1
2
1
1
2
1
2
2
1
0
1
1
2
2
1
0
1
1
1
2
1
1
0
1
1
1
1
2
1
1
1
1
0
1
2
0
1
1
2
2
1
1
2
2
1
1
1
1
0
1
1
0
2
1
0
1
3
2
3
1
0
1
1
1
1
1
1
1
0
1
2
1
2
1
1
0
1
0
1
1
1
2
0
0
1
1
0
1
2
1
1
1
1
1
2
0
0
2
1
1
1
1
1
1
0
0
1
1
2
2
1
2
1
1
1
1
3
2
0
1
0
2
2
2
2
2
1
1
1
1
2
1
2
2
0
1
1
1
1
2
1
1
2
1
0
11
1
0
1
1
1
1
1
1
0
0
1
0
2
1
0
2
2
0
2
1
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
1
1
1
0
0
1
0
3
1
1
1
2
0
2
1
1
1
2
1
1
0
1
1
0
2
1
1
1
1
2
1
2
1
1
2
1
0
1
2
0
0
1
1
2
1
1
0
2
1
2
2
0
1
1
1
0
2
1
1
0
1
1
1
1
2
2
1
1
1
1
1
0
1
1
0
1
0
1
2
2
0
2
1
0
2
1
1
2
1
0
1
2
0
1
0
0
0
0
1
1
1
0
1
1
1
0
1
1
1
1
1
1
3
1
2
1
1
1
2
2
1
1
2
1
2
0
1
1
1
1
1
0
2
0
1
0
1
1
1
1
2
1
1
2
1
1
2
2
1
2
0
0
0
2
1
1
1
0
1
1
0
1
1
1
1
1
0
1
2
1
1
1
1
2
1
1
1
2
1
1
1
0
2
0
1
2
1
0
1
2
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
1
1
1
1
2
0
0
1
1
0
2
2
0
2
2
0
1
1
1
3
0
0
2
1
1
1
1
0
2
1
1
1
1
0
1
2
1
1
1
2
0
2
1
1
2
1
2
1
0
2
0
1
1
1
1
2
2
1
2
1
0
1
2
1
0
0
2
2
2
2
1
0
1
1
1
1
2
1
1
1
1
2
1
2
1
0
1
1
1
2
1
2
1
2
1
2
1
1
1
0
1
1
0
1
1
0
0
1
2
2
2
1
2
0
2
1
1
2
2
2
1
1
1
1
1
1
1
1
0
1
1
0
0
2
1
0
0
0
2
1
1
1
1
0
1
1
0
1
0
2
2
0
2
2
1
2
0
0
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
2
0
2
0
2
0
1
1
0
2
2
1
1
3
2
2
1
2
2
0
1
1
1
1
1
2
2
3
1
1
1
1
1
2
1
1
1
0
2
1
0
1
2
1
0
2
2
1
2
1
1
1
2
1
2
1
0
1
0
0
1
1
1
0
0
1
1
0
1
1
2
2
2
1
0
2
0
2
1
1
0
2
1
0
0
0
1
1
1
1
1
2
1
1
1
1
0
0
0
1
1
2
1
2
1
1
1
1
1
2
2
0
0
1
1
1
1
1
1
0
1
1
1
1
2
2
1
1
0
1
2
0
0
2
0
1
1
1
0
1
1
2
0
1
0
1
0
1
0
1
1
2
1
1
0
0
0
1
1
1
1
1
3
1
1
0
1
1
0
1
1
2
1
2
0
1
1
0
1
1
1
2
1
1
3
1
1
0
2
0
1
1
2
2
1
2
1
1
0
1
1
1
1
2
1
1
1
1
2
1
1
2
0
1
1
1
1
0
0
2
1
1
0
0
1
1
1
1
2
1
1
2
0
2
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
1
2
0
2
1
2
2
2
0
1
1
0
1
1
0
1
1
1
1
0
1
1
1
1
1
0
1
1
2
2
1
1
1
1
1
1
2
1
0
2
0
1
0
1
0
1
2
2
0
1
0
1
1
1
2
1
2
1
1
2
1
0
0
1
0
1
1
1
1
1
1
2
2
0
1
1
1
1
1
2
1
1
1
1
1
0
2
0
0
1
2
0
0
1
1
1
1
0
1
1
1
2
1
2
2
1
4
1
1
1
1
2
1
1
2
1
1
1
1
2
2
1
2
1
1
1
1
1
2
2
2
2
2
2
1
1
1
0
1
1
2
2
1
1
1
1
2
1
0
1
1
0
2
1
1
1
2
1
2
1
1
1
1
1
1
2
1
2
1
1
2
1
2
2
1
1
0
1
1
1
0
1
0
2
1
0
0
1
1
1
1
2
1
2
1
1
1
1
2
1
0
2
1
1
1
0
2
1
0
1
1
0
1
0
1
1
1
0
1
2
1
0
1
0
1
2
1
1
1
1
3
1
0
1
1
1
0
1
2
2
1
2
1
0
2
1
2
0
3
1
1
1
1
1
0
0
1
1
1
2
2
2
1
0
2
2
0
1
1
1
0
0
1
1
1
1
1
1
1
1
0
1
1
1
0
1
1
1
1
2
1
1
1
0
1
0
1
2
0
2
1
0
1
1
1
0
1
1
2
0
1
1
2
1
1
1
2
0
1
1
2
2
1
2
1
1
1
1
2
0
1
2
2
1
0
1
0
1
1
0
1
1
0
2
0
1
1
1
0
2
0
1
2
2
1
1
1
2
0
1
1
1
1
1
1
1
1
1
0
1
0
0
1
2
0
1
1
1
1
2
2
0
1
1
0
0
0
1
1
1
2
1
0
2
2
0
0
0
1
1
2
1
1
2
1
0
1
0
0
1
1
0
1
0
1
1
1
1
1
1
1
2
1
2
2
1
1
1
2
1
2
1
1
0
1
1
1
0
1
2
1
2
1
2
1
1
2
0
0
2
1
1
2
1
0
0
2
1
0
1
0
1
2
1
2
0
1
1
1
0
0
1
1
1
2
2
1
0
1
1
1
2
0
1
2
1
1
1
0
2
1
1
1
1
0
1
1
2
1
1
0
2
0
0
1
1
2
1
1
2
1
2
0
1
2
0
0
1
0
1
0
0
1
1
0
2
0
2
1
0
1
0
1
1
1
1
0
2
2
0
1
2
1
1
1
1
0
0
2
2
0
0
1
1
0
1
1
1
1
0
1
1
1
1
2
1
0
1
1
1
1
1
2
1
1
1
1
1
1
0
1
1
1
1
0
1
1
1
1
1
1
1
2
0
1
1
1
1
2
0
2
1
2
2
2
1
1
1
2
2
1
1
0
2
1
1
1
1
0
1
1
1
1
1
0
1
2
0
1
1
1
1
1
1
1
1
2
2
1
0
0
1
1
1
1
1
1
0
1
1
1
1
1
1
1
0
1
1
1
2
1
1
1
0
1
1
1
0
2
0
1
1
2
2
1
1
1
0
1
0
2
1
1
2
1
1
0
1
1
0
0
1
1
1
1
2
2
3
1
0
2
2
2
1
1
2
1
2
1
1
2
1
1
1
2
1
0
1
1
1
0
1
1
1
1
1
2
1
0
2
2
1
0
1
1
1
1
0
2
1
1
1
0
1
1
0
0
1
0
1
0
1
0
1
1
1
0
2
1
1
0
0
0
0
1
1
1
1
2
2
2
1
1
0
1
0
1
0
2
1
2
1
1
1
1
1
0
2
1
1
2
0
2
2
2
1
1
0
1
2
1
1
0
1
2
1
2
0
1
0
2
0
2
2
0
0
1
1
1
0
1
1
2
2
2
1
1
0
3
2
2
0
1
0
2
0
1
0
1
2
1
0
0
1
1
0
0
0
1
2
1
1
2
2
1
0
1
0
2
2
1
1
2
1
1
0
1
0
1
1
1
0
1
2
2
1
1
1
0
0
2
2
1
0
1
0
0
1
1
1
1
1
1
1
1
1
2
1
1
0
1
1
2
1
0
1
0
1
1
0
1
1
2
0
1
1
2
1
2
2
0
1
1
2
0
1
0
1
1
1
1
1
1
1
2
1
1
1
2
1
0
0
1
1
1
1
1
1
0
1
1
0
0
1
0
1
2
0
0
2
2
2
2
1
0
1
1
0
1
0
1
1
2
1
1
1
1
1
1
2
2
0
1
0
0
0
0
2
2
1
1
0
1
1
0
0
1
1
1
1
1
2
1
1
0
1
1
1
1
1
2
1
1
0
0
0
2
1
2
0
1
1
2
1
0
0
1
0
1
1
1
2
1
1
2
1
1
1
2
1
1
1
0
1
1
0
1
3
1
2
2
2
0
0
0
1
0
1
1
2
2
0
1
2
0
1
0
0
0
0
1
1
1
2
0
0
1
2
1
1
1
1
1
1
0
2
1
1
0
1
2
1
2
1
1
1
1
1
1
0
1
0
2
0
0
0
1
1
0
1
1
1
1
1
1
2
1
3
0
1
1
1
1
2
1
0
2
1
0
1
2
1
1
1
0
0
1
1
0
1
2
0
2
2
2
1
1
1
0
1
1
1
1
0
1
1
1
2
1
1
1
1
2
2
2
1
1
1
0
1
1
2
3
0
0
1
1
1
0
2
2
1
1
0
2
1
1
1
1
1
1
1
0
1
1
0
1
1
2
1
1
0
1
0
2
1
0
1
1
1
1
1
0
2
0
1
2
1
1
1
1
0
2
0
1
2
2
2
1
1
2
1
1
2
0
2
2
1
2
2
2
1
0
0
1
1
2
1
1
2
2
2
2
1
1
0
0
1
0
1
2
1
1
1
1
0
1
1
1
1
2
0
1
1
1
2
0
0
1
1
1
0
0
1
1
0
1
1
1
1
1
4
1
1
1
0
0
0
1
2
1
1
1
2
0
2
1
1
1
2
1
1
2
1
2
1
1
1
2
0
1
0
2
1
2
2
1
2
1
1
0
0
1
0
2
1
1
2
2
1
1
1
1
0
0
0
1
1
0
0
1
2
1
1
1
1
2
1
1
1
1
1
1
0
0
2
1
1
2
1
1
0
0
1
4
1
1
1
1
1
1
2
2
1
2
0
1
1
0
1
1
1
1
1
0
1
1
1
1
1
1
1
2
2
0
0
1
0
1
1
2
1
1
2
0
1
2
1
0
2
2
1
0
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
0
4
0
1
1
1
1
1
2
1
0
1
0
0
1
2
0
1
1
1
2
2
2
0
0
1
2
0
0
2
1
1
1
1
1
1
0
1
1
1
1
1
0
0
1
1
1
1
1
2
1
2
1
0
0
2
0
1
2
0
1
1
2
1
2
1
2
2
2
1
1
1
1
0
1
1
2
1
2
2
2
1
1
0
0
1
1
1
3
1
1
1
2
0
1
0
2
1
1
2
1
1
2
0
1
0
2
1
1
1
1
1
1
0
2
2
1
1
1
2
1
1
1
0
1
1
1
0
1
2
2
0
1
1
0
1
1
1
2
1
1
1
2
0
1
2
1
1
2
2
1
0
1
1
1
1
1
1
1
2
2
1
1
1
2
2
0
1
1
1
1
0
1
0
0
2
2
0
2
0
2
1
0
1
1
1
1
1
1
2
1
1
0
2
1
2
2
0
2
1
1
1
2
1
0
0
1
0
2
1
1
0
1
2
0
2
1
2
1
2
2
1
0
0
1
1
1
1
1
0
1
1
0
1
0
1
2
1
0
2
2
1
1
1
0
1
1
3
1
1
1
1
0
3
1
1
1
1
2
1
1
1
2
1
1
1
0
1
1
1
1
1
2
1
1
1
2
2
2
1
0
2
1
1
1
2
2
1
1
1
1
1
1
2
2
1
1
2
1
0
1
0
0
2
1
1
0
1
2
0
2
0
2
2
1
2
1
1
1
2
0
1
1
0
1
1
0
0
1
2
1
2
1
0
2
2
1
2
0
1
1
1
1
0
1
0
1
1
1
1
2
1
1
1
0
1
2
1
1
1
0
1
1
1
1
1
0
2
1
2
0
1
1
2
2
2
1
0
1
1
0
1
1
1
1
0
0
1
1
1
2
1
1
1
1
1
2
0
2
0
1
1
2
1
0
2
0
1
0
1
1
1
1
0
0
0
1
1
2
1
1
2
1
0
1
1
0
1
1
1
2
2
0
1
2
0
1
1
1
1
3
2
1
1
0
2
1
1
0
0
2
2
1
1
0
1
2
1
1
1
0
2
0
1
0
2
2
1
1
2
1
1
1
1
0
1
1
1
2
0
1
1
1
1
0
1
1
1
1
0
1
2
0
1
1
1
2
1
1
0
1
1
1
1
2
0
1
0
1
1
0
1
0
2
1
1
1
2
2
2
1
1
1
1
0
1
1
3
1
0
1
2
2
0
0
1
1
1
1
1
1
2
2
1
2
1
1
1
1
0
1
1
2
0
1
2
2
1
0
0
1
1
1
1
0
0
2
0
1
1
0
1
1
1
2
1
1
1
1
0
1
2
0
1
1
0
2
2
2
0
0
1
2
1
0
2
2
1
1
1
1
1
1
0
0
0
1
1
0
1
2
1
1
1
2
0
1
1
1
2
2
1
1
1
0
1
0
2
1
1
1
0
1
1
2
1
1
2
2
0
1
1
1
2
2
1
2
2
0
2
1
1
2
1
4
0
1
1
1
3
2
1
0
2
1
1
0
0
2
1
2
0
1
2
2
1
1
0
0
0
2
1
1
1
2
0
1
1
1
0
0
1
2
0
1
1
1
1
1
1
1
2
1
2
1
1
1
0
1
1
1
2
1
0
1
1
1
2
1
1
1
1
0
1
0
1
2
2
1
1
0
1
1
1
1
1
1
3
1
1
1
1
0
1
0
1
1
0
1
1
0
2
0
1
1
0
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
2
1
1
2
1
2
1
2
1
1
1
1
1
1
1
0
1
0
2
1
0
1
2
1
1
2
1
0
1
1
1
1
1
1
2
1
0
2
1
1
1
0
0
1
0
2
2
1
2
1
1
2
1
0
1
0
1
1
0
1
0
1
1
1
2
2
1
1
2
0
2
2
2
2
1
0
2
1
1
1
1
1
1
1
1
0
1
1
1
0
1
2
0
2
2
0
2
0
1
2
2
0
2
1
2
0
1
1
1
1
0
2
0
1
1
2
2
0
2
1
1
1
1
1
0
0
1
4
0
4
0
1
1
1
2
1
1
2
1
1
1
0
2
2
0
1
1
1
1
1
1
0
2
1
2
1
1
1
0
2
2
1
1
1
2
1
0
2
1
1
1
1
1
0
1
1
0
2
2
1
1
2
0
2
2
1
2
1
2
1
0
1
2
1
1
2
0
0
2
1
1
1
2
1
0
2
1
1
2
1
1
0
0
1
0
1
0
2
2
1
1
2
1
1
1
0
1
1
1
1
0
1
1
2
1
1
0
0
1
1
2
1
1
0
1
2
1
1
1
2
1
2
1
0
0
1
0
2
2
0
0
2
1
1
2
1
1
2
2
1
2
1
1
1
2
1
1
0
1
1
0
0
0
0
1
1
1
1
1
1
2
1
0
2
0
2
0
1
1
2
0
1
0
1
1
0
1
1
1
0
2
0
2
2
1
2
0
1
1
0
1
1
2
1
0
1
1
2
1
1
1
1
2
0
2
1
1
1
1
2
0
1
2
2
0
1
1
1
1
0
1
1
1
0
1
1
0
2
2
1
2
0
2
1
1
2
1
1
1
1
1
1
0
1
0
1
0
1
0
1
1
2
1
0
1
2
1
2
2
1
1
1
1
2
1
1
2
2
2
1
1
2
1
2
1
1
1
1
0
2
1
1
1
1
1
1
1
1
1
1
0
0
2
1
1
2
2
2
1
0
1
1
2
1
1
1
1
1
1
1
0
1
1
2
2
0
1
1
1
2
2
1
0
2
0
0
1
0
1
2
1
1
1
1
2
2
0
2
3
1
2
1
1
1
2
1
1
1
1
2
1
1
2
1
0
1
2
1
0
0
1
1
0
1
2
2
1
2
2
1
0
0
0
1
2
0
0
2
2
0
1
2
1
0
2
2
1
2
1
1
2
1
1
1
0
1
2
0
2
1
1
0
0
1
2
1
2
1
1
0
0
2
2
1
0
3
1
1
2
1
2
1
0
2
0
1
0
2
1
1
1
1
1
0
1
0
1
1
1
0
0
0
1
1
1
1
1
1
1
0
2
2
1
2
1
0
2
1
1
1
1
0
1
1
2
1
0
1
1
2
0
0
1
2
1
2
0
3
1
0
0
1
1
1
3
1
1
2
1
2
1
1
1
3
1
0
2
2
1
1
2
1
1
1
1
2
2
2
2
1
0
2
0
2
1
1
1
1
1
2
2
1
2
1
1
0
1
1
1
1
1
1
1
0
0
0
0
0
2
0
1
0
1
1
0
1
2
1
1
1
1
1
1
0
1
1
2
1
0
1
1
0
1
1
1
2
2
2
0
0
0
1
1
1
0
2
1
1
2
1
1
3
2
0
1
0
0
1
1
1
1
1
1
1
1
1
1
1
1
3
1
1
1
1
1
0
1
1
1
1
1
2
2
1
2
2
1
3
2
2
1
1
1
1
1
1
0
0
2
1
2
1
1
1
1
0
1
1
1
1
0
2
1
1
2
0
2
1
1
1
2
3
0
1
2
1
0
0
1
2
0
1
2
2
1
1
1
1
0
1
2
1
1
1
1
2
2
1
1
1
1
2
1
2
1
0
1
0
2
0
1
1
0
0
0
1
1
1
1
1
1
1
1
0
1
1
2
1
1
1
1
1
1
0
2
2
2
1
2
1
1
1
1
2
0
1
0
2
1
2
0
1
0
3
1
1
1
0
0
1
2
1
1
1
1
0
1
1
1
2
0
2
1
1
0
1
1
2
0
1
1
2
1
1
1
0
1
2
1
1
1
2
2
0
1
0
1
1
1
1
1
2
2
1
1
1
1
0
1
1
1
2
1
2
2
3
0
1
1
1
1
0
2
1
2
1
0
2
0
1
0
1
2
1
2
0
2
1
1
1
2
1
1
1
2
2
1
0
1
0
2
0
0
1
1
1
1
7
0
2
1
1
2
0
1
1
1
2
1
0
2
1
2
1
2
2
2
2
0
1
1
0
2
1
2
0
1
1
0
2
1
1
0
2
1
2
0
2
2
1
2
2
0
1
2
1
1
1
1
1
1
2
0
0
1
1
1
1
1
2
1
2
1
2
1
1
1
1
2
1
1
1
1
1
0
2
1
1
2
1
1
2
1
0
0
2
1
1
1
1
1
2
0
1
0
2
1
0
1
2
1
0
1
2
0
0
2
1
1
2
0
1
1
1
1
0
1
2
2
1
0
0
1
1
1
2
1
2
0
1
1
2
1
0
1
2
1
1
1
0
1
1
2
1
0
3
2
1
1
1
0
1
0
1
1
2
0
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
2
1
1
2
1
2
1
1
1
1
2
0
1
1
0
0
1
2
1
1
2
1
1
2
0
1
1
0
1
1
1
1
2
1
1
0
1
1
1
1
1
0
1
1
1
1
2
0
2
1
0
1
1
2
2
0
0
1
0
1
1
2
0
2
0
1
2
1
2
1
2
2
0
1
1
0
2
2
2
2
2
1
2
2
1
1
2
0
1
1
1
0
1
0
1
2
2
2
1
1
2
2
1
2
1
2
1
1
1
2
1
0
1
2
1
0
1
1
1
1
1
1
0
2
1
0
2
2
0
2
2
0
2
1
1
1
1
2
1
1
1
1
1
1
0
2
1
1
1
0
1
1
1
0
2
0
1
0
2
1
1
1
1
1
2
1
1
1
1
1
0
0
1
1
1
1
1
2
2
1
2
3
1
1
0
1
1
0
1
0
1
1
1
1
0
1
1
0
2
2
2
1
1
0
1
1
0
1
1
1
1
1
1
0
1
0
0
1
2
1
1
2
1
1
0
1
1
2
1
1
1
0
1
2
1
1
1
2
1
0
1
2
2
0
1
2
0
2
2
1
2
1
1
2
1
1
1
1
2
1
0
1
1
0
2
1
0
2
1
1
1
0
2
2
0
1
2
0
1
1
1
1
1
1
2
1
2
1
1
0
1
1
2
0
0
1
0
2
2
1
2
1
1
2
0
2
0
1
1
1
1
1
0
1
2
2
1
2
1
1
1
2
2
2
0
1
1
1
0
0
1
1
1
1
2
2
1
2
1
0
0
1
1
1
1
0
1
1
1
1
2
0
0
1
1
1
2
2
2
1
0
1
2
1
2
1
1
2
1
2
1
0
0
1
2
1
1
1
2
1
0
2
1
1
0
1
2
2
1
1
1
1
1
1
1
2
1
2
1
1
0
2
1
1
2
1
1
0
2
2
0
1
1
0
1
3
0
0
0
1
0
1
0
1
2
2
1
1
2
1
1
0
1
2
1
2
0
0
1
1
1
1
2
1
2
0
1
1
1
0
1
1
1
0
1
2
2
1
1
2
1
1
2
1
0
2
0
3
1
1
1
0
2
0
2
2
1
2
0
1
1
2
0
0
1
1
1
2
1
1
2
1
0
1
1
2
1
1
0
1
1
1
2
1
1
1
1
2
1
2
1
1
1
0
0
1
0
1
0
3
2
2
2
1
1
0
2
1
1
2
0
0
2
1
1
1
2
1
0
2
1
2
1
1
2
2
1
1
0
1
2
1
0
0
2
0
1
0
1
0
0
2
1
0
1
1
1
1
2
1
1
0
1
2
0
1
0
1
1
2
1
1
1
0
1
2
1
1
1
1
0
1
1
1
1
0
1
1
1
1
0
2
1
1
1
1
1
2
0
1
1
1
1
0
0
2
0
1
1
1
1
0
2
1
1
0
1
1
1
2
0
0
0
2
0
1
1
2
1
1
1
1
1
1
0
0
1
1
0
2
1
1
1
2
1
1
2
2
0
2
1
2
1
1
0
2
1
1
1
1
1
1
1
1
1
0
1
2
1
1
1
1
1
1
1
1
0
0
2
0
1
1
1
2
0
1
1
1
1
1
1
1
1
1
1
0
1
1
2
1
1
2
1
2
0
1
1
1
1
0
0
1
2
2
0
1
0
0
1
1
0
2
1
1
0
1
1
1
0
2
1
1
0
1
1
2
1
1
1
1
2
2
0
1
1
2
2
1
1
1
1
1
1
1
1
1
0
1
0
1
1
1
2
0
2
2
1
1
0
0
1
1
2
2
1
1
1
1
1
1
1
0
1
2
1
0
1
2
0
1
2
1
1
0
2
1
2
1
1
0
0
1
2
0
1
2
2
2
1
2
2
1
2
0
0
2
3
1
1
1
0
1
1
2
0
1
2
1
1
1
1
1
1
2
1
0
1
0
2
1
1
2
0
0
0
1
2
0
1
1
1
1
3
1
1
1
1
1
1
1
1
0
1
1
0
0
0
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
0
1
1
1
1
1
1
2
1
0
2
2
2
1
1
1
1
1
2
2
1
1
1
1
1
1
1
0
2
1
2
1
1
2
1
2
1
1
2
0
2
2
1
2
1
1
1
2
1
1
1
2
0
1
1
1
0
1
1
1
0
1
0
1
5
0
2
1
0
2
1
1
0
1
2
1
2
1
2
1
1
1
1
2
1
2
1
1
1
2
0
2
0
2
1
1
1
1
0
0
0
2
1
0
1
2
1
1
1
1
2
1
2
1
0
2
1
1
2
1
2
1
1
1
0
1
1
1
2
2
1
1
3
1
1
2
0
1
1
1
1
2
1
1
1
0
1
0
0
2
0
1
0
2
1
1
1
0
1
2
1
1
2
1
1
1
2
0
1
0
0
1
3
0
1
1
0
0
0
1
1
2
1
2
2
2
1
1
0
0
0
2
1
2
1
2
0
1
1
2
0
0
0
1
1
1
2
1
1
0
1
0
0
1
0
0
1
1
1
1
1
2
1
0
1
1
2
2
1
1
1
1
1
2
1
1
2
1
1
0
2
2
1
1
1
0
0
2
1
2
1
1
1
1
1
1
0
1
1
0
1
1
1
0
0
1
2
1
1
2
1
0
1
2
0
2
1
0
0
1
1
2
1
2
2
2
1
0
1
2
1
1
2
2
1
1
2
1
1
0
1
1
1
1
1
1
1
1
1
0
1
1
2
1
2
1
1
1
1
1
0
0
2
1
2
1
1
1
2
0
2
2
2
1
1
1
1
1
2
1
0
1
0
2
0
0
0
2
0
1
0
0
2
0
1
1
2
1
0
2
1
0
2
1
0
0
1
1
1
0
1
1
0
1
0
1
2
1
1
0
1
1
0
1
1
1
1
2
2
0
1
0
0
6
1
2
1
0
1
1
1
0
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
0
0
0
1
1
1
0
1
2
2
1
0
1
2
1
1
1
2
2
1
1
1
0
0
1
1
1
1
1
2
2
0
1
2
2
2
0
2
1
1
2
2
3
1
2
1
1
2
0
2
0
1
1
2
0
1
1
1
1
1
1
1
0
0
2
2
0
2
0
2
2
0
2
0
1
2
1
1
0
0
1
1
1
1
1
0
1
0
0
0
0
0
2
0
1
1
1
0
1
1
0
2
0
1
2
0
1
2
1
0
1
2
1
2
2
1
1
1
1
1
0
1
0
2
1
1
1
2
0
2
1
1
1
2
1
1
2
1
1
1
1
1
1
0
0
1
1
1
1
1
0
1
0
1
2
0
0
0
1
2
1
0
2
1
1
0
2
2
1
0
1
1
1
2
1
1
1
0
1
0
0
1
1
1
1
2
1
0
1
2
0
1
0
0
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
2
2
2
0
1
2
0
1
1
0
0
1
0
2
1
1
2
1
1
2
0
2
0
1
0
1
1
1
2
1
2
1
1
2
0
1
1
1
1
1
0
2
1
0
0
0
1
2
2
2
2
1
1
2
1
1
2
1
0
0
1
2
1
2
1
1
1
1
1
1
0
1
1
1
1
0
2
2
0
1
2
0
1
1
0
1
1
1
1
0
1
0
2
0
1
2
2
1
1
0
2
1
1
1
1
1
1
0
1
0
1
1
1
0
2
0
1
1
1
2
0
1
1
1
2
0
1
0
1
1
1
1
2
0
0
2
1
1
2
1
1
1
2
1
1
2
1
2
1
0
0
1
1
2
1
1
1
1
0
1
1
1
0
1
2
2
1
0
1
1
1
1
2
2
1
0
2
2
1
2
2
1
2
0
1
1
1
1
2
1
0
2
1
1
2
0
1
1
1
0
1
2
2
2
3
1
2
0
1
2
1
0
1
1
0
1
2
0
0
1
1
1
1
0
0
1
2
2
1
1
1
0
1
1
3
1
0
2
1
2
1
0
0
1
0
0
1
2
1
1
1
1
0
0
1
1
0
0
1
2
1
1
2
1
0
0
0
1
1
1
2
1
1
0
0
2
2
1
1
1
0
1
1
1
1
1
1
0
1
3
0
0
1
1
2
1
1
1
0
2
0
1
1
1
1
1
1
1
1
2
1
1
0
1
1
1
1
1
2
0
2
1
1
0
1
0
1
1
2
1
1
1
0
2
1
2
2
1
1
2
1
0
0
1
1
1
1
1
1
0
0
0
1
1
0
2
0
1
1
1
1
1
1
1
0
1
0
1
1
1
0
1
1
1
0
1
1
1
1
2
0
1
1
0
2
1
0
1
1
1
1
1
2
1
2
2
0
0
1
2
0
1
1
1
1
0
1
1
2
1
0
1
1
1
1
1
1
1
2
2
1
0
0
2
0
0
1
1
2
1
0
2
1
0
1
1
1
2
0
2
1
0
1
1
1
1
1
1
1
0
1
1
2
0
1
0
0
2
0
2
0
1
2
0
2
2
2
1
1
0
1
1
1
2
1
2
0
1
1
1
1
0
0
1
1
1
1
0
1
2
2
1
1
2
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
2
1
1
2
0
1
1
1
0
1
1
2
1
0
1
2
1
1
1
0
2
1
2
0
2
1
1
1
1
1
1
2
0
1
1
1
1
1
0
1
1
0
1
1
2
2
2
1
1
1
2
1
2
1
1
1
0
1
1
1
1
1
0
1
0
2
2
2
1
2
1
1
0
2
1
1
0
2
1
2
0
1
0
1
1
1
1
1
1
1
0
1
2
1
0
1
1
1
1
0
1
0
0
3
1
1
2
1
1
1
2
1
1
3
0
0
0
0
0
1
1
1
0
1
1
1
1
2
1
2
1
1
1
1
2
2
2
1
2
1
0
2
2
0
1
2
2
1
2
2
0
1
1
0
1
0
2
1
0
0
1
1
0
0
2
1
0
1
2
1
0
0
0
1
2
0
1
2
0
0
0
1
1
1
2
0
1
2
1
1
1
1
0
0
2
0
2
0
1
0
0
0
0
2
0
2
1
1
1
1
1
0
1
2
1
1
2
2
1
1
0
1
1
2
1
0
0
0
2
0
0
1
0
1
1
1
2
2
0
1
0
1
2
2
2
0
0
1
1
1
3
1
2
1
2
1
1
0
0
0
1
1
1
1
0
1
1
1
1
1
2
1
1
0
0
0
2
1
1
0
2
1
0
3
2
1
0
1
1
1
1
2
1
1
0
2
1
0
2
2
1
2
2
0
2
1
1
2
1
1
2
2
1
2
1
1
1
1
1
0
0
1
1
0
1
2
1
1
2
1
2
1
0
1
0
1
1
1
1
1
2
0
1
2
1
1
0
0
1
1
1
1
1
1
2
1
1
1
1
0
1
2
0
2
2
0
0
0
1
0
0
0
1
1
1
1
1
0
2
1
1
0
0
2
1
1
1
2
1
0
1
1
0
1
1
1
2
1
2
1
2
0
0
2
0
1
1
0
1
0
0
1
0
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
2
0
2
2
1
0
1
1
1
0
0
2
1
2
1
1
1
2
1
0
0
1
1
1
1
0
1
1
1
0
2
1
0
0
1
1
0
2
1
1
1
1
1
1
1
1
1
2
1
2
0
2
2
1
0
1
2
1
0
1
1
1
1
1
1
1
0
1
1
1
1
1
2
0
1
0
1
1
1
1
1
1
1
1
0
1
0
2
1
2
1
2
0
1
1
2
2
0
2
1
0
1
3
1
2
2
1
2
1
2
1
0
0
1
1
1
0
1
1
1
1
0
1
1
0
2
1
2
1
1
2
1
1
1
2
2
1
1
1
1
0
0
1
1
1
1
2
1
1
2
1
1
1
0
1
0
2
1
1
0
1
0
0
1
1
1
0
0
1
1
0
1
1
1
1
1
2
1
2
0
2
0
1
2
1
0
1
1
1
2
1
1
0
1
2
2
1
2
1
1
1
1
1
1
2
1
0
2
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
2
1
1
1
1
0
2
0
0
1
1
0
1
0
1
1
1
2
1
0
2
1
2
1
1
2
0
2
1
1
1
1
6
1
1
2
1
0
1
2
0
2
0
3
1
1
2
1
0
1
2
1
2
2
0
1
0
2
1
1
1
1
2
1
0
1
2
1
0
1
1
1
0
1
0
1
1
1
1
2
2
0
2
1
1
1
2
0
1
0
0
0
0
1
2
0
2
2
1
2
1
1
2
0
1
1
1
2
3
1
1
1
2
0
2
1
1
0
0
0
1
1
1
0
3
1
0
0
0
1
2
1
0
1
1
1
1
2
1
2
1
1
1
2
1
1
0
1
1
2
1
2
1
0
1
1
1
1
0
0
1
1
2
2
0
1
1
1
1
1
0
1
1
0
1
2
2
0
1
1
2
2
1
1
1
2
1
1
0
1
1
2
2
2
1
2
1
1
1
2
2
2
1
0
1
0
0
2
2
1
0
0
2
0
1
1
1
2
1
1
1
1
1
2
1
0
1
1
1
0
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
2
2
2
1
1
1
1
1
1
1
2
1
1
1
2
1
1
0
1
0
2
3
0
1
2
1
1
2
1
2
1
1
0
0
1
1
0
0
1
1
2
1
1
2
1
1
1
1
1
0
1
1
0
2
0
1
0
1
2
1
0
0
0
1
1
1
1
0
0
2
0
2
1
1
0
2
1
0
2
1
1
0
0
2
2
0
0
1
1
0
2
0
2
2
1
0
1
2
1
0
1
0
2
2
2
2
1
1
1
0
0
2
1
0
1
1
1
2
2
1
1
2
2
1
2
0
0
1
2
1
0
2
1
1
2
0
1
1
1
2
1
1
2
1
1
1
1
2
1
1
0
2
1
1
1
1
0
0
0
0
0
2
1
1
1
1
0
1
2
1
0
1
2
0
1
1
1
1
1
1
2
1
0
1
0
1
1
0
2
1
2
1
0
1
0
2
1
0
1
0
1
1
1
1
1
1
1
0
1
1
1
0
1
1
1
1
2
1
1
2
1
2
0
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
2
2
0
2
1
2
0
3
1
4
0
1
0
2
0
0
1
1
2
2
1
0
1
2
2
1
1
0
0
1
1
2
2
0
1
1
0
0
1
1
1
0
1
2
1
1
0
1
1
1
1
1
2
1
1
1
2
2
0
1
1
2
1
0
1
1
1
0
0
2
1
0
1
1
2
2
2
1
1
1
0
0
1
1
2
1
1
1
0
1
1
1
1
1
2
0
1
0
1
1
1
1
1
1
2
0
2
1
1
1
1
1
0
1
1
1
1
0
1
1
1
2
2
1
1
1
1
1
1
0
2
1
1
1
2
1
1
2
1
1
0
1
1
1
2
1
0
2
0
0
0
0
2
1
0
1
2
1
1
2
0
1
1
1
1
1
1
1
0
0
2
1
1
2
1
2
0
1
2
0
1
1
0
0
2
1
1
1
1
0
2
1
0
1
1
0
1
2
1
0
2
2
1
1
1
0
2
1
1
1
0
1
1
2
1
1
1
1
1
1
0
0
1
1
1
1
0
1
0
2
1
0
2
1
0
2
1
0
1
1
1
0
1
1
1
1
1
1
1
1
1
2
1
1
0
2
1
1
1
1
2
2
1
1
2
1
1
1
0
2
1
0
1
1
2
1
1
1
4
0
1
2
1
1
2
1
1
1
1
2
1
1
1
1
1
0
3
1
1
1
1
1
2
1
2
1
1
1
1
0
0
1
2
1
1
2
0
1
1
2
0
1
1
1
1
0
1
1
1
1
1
0
1
2
1
0
1
1
0
1
2
1
1
2
1
0
2
0
1
0
2
2
1
1
2
1
1
1
1
0
1
1
1
0
2
1
2
2
2
2
2
1
2
1
0
1
1
0
2
1
0
1
2
2
1
1
2
1
1
2
1
1
1
2
2
1
2
2
3
0
1
2
0
1
0
1
0
1
0
1
0
0
1
2
0
0
2
1
1
1
1
1
1
1
2
2
2
2
1
0
1
2
0
1
1
1
1
1
1
1
0
1
1
2
1
0
0
1
1
0
2
1
2
0
4
1
2
2
1
0
2
1
1
2
2
2
1
1
0
1
0
1
1
1
1
2
3
0
1
1
3
1
1
2
1
1
1
1
1
0
1
1
1
1
0
1
1
2
2
0
1
1
2
0
2
1
2
1
1
1
2
2
0
1
0
0
1
1
1
0
1
1
1
1
0
1
0
0
1
1
1
2
1
2
0
0
0
1
1
0
2
0
0
2
0
1
1
1
1
1
2
2
1
0
2
0
1
1
1
0
1
1
1
0
2
1
1
1
2
2
1
1
1
1
0
1
1
1
1
1
2
1
2
0
1
1
2
1
1
2
0
1
1
1
2
2
1
1
0
2
0
1
0
1
1
2
1
2
1
2
0
1
2
2
1
1
2
1
1
1
0
0
1
1
1
0
2
2
0
0
1
0
1
1
2
1
0
0
1
1
2
1
1
1
0
1
1
1
2
2
1
1
2
0
1
1
0
1
1
1
2
1
1
1
1
2
0
1
1
2
1
1
0
2
1
1
0
1
1
0
0
0
1
1
1
1
1
0
2
0
1
0
0
2
0
1
2
1
2
1
0
1
0
0
1
1
1
1
0
1
1
1
1
1
0
1
2
1
1
1
2
1
0
1
1
1
2
0
2
0
0
1
1
1
1
0
1
1
1
1
1
1
1
2
1
1
1
2
2
3
2
1
1
1
1
1
1
2
1
1
1
0
1
1
2
0
0
1
2
1
1
1
0
1
0
1
1
2
0
1
0
2
1
1
2
1
2
2
1
1
0
2
0
1
2
1
1
1
1
0
1
1
1
1
1
1
1
2
0
0
1
0
0
1
0
1
0
1
1
2
2
2
1
1
1
2
0
1
1
1
0
2
1
1
2
0
3
2
0
1
0
1
1
1
1
1
1
2
2
1
2
2
1
1
0
2
0
2
2
0
2
0
0
1
1
0
1
0
0
1
1
1
1
1
1
1
1
1
1
2
1
1
2
2
1
2
0
0
2
1
2
1
2
1
1
1
1
1
1
2
2
1
1
2
1
1
2
0
1
0
0
1
1
0
1
1
1
0
2
1
0
1
1
1
2
1
2
0
1
1
1
1
1
1
0
0
0
1
2
2
1
1
1
2
1
1
2
1
1
2
1
2
1
1
1
3
1
0
0
1
1
1
2
0
1
2
2
0
1
0
2
0
0
1
1
1
0
2
1
2
1
1
1
1
1
2
1
1
1
0
1
1
1
2
1
1
0
1
1
0
1
2
1
0
2
1
1
2
0
2
1
2
0
1
1
1
1
0
1
2
1
0
1
2
2
1
1
1
2
1
1
1
2
1
1
1
1
0
1
1
1
1
1
0
0
0
4
1
0
1
1
0
1
1
2
1
1
0
1
0
1
0
2
1
0
1
2
1
1
2
2
1
2
1
1
2
1
1
0
1
0
0
1
1
1
1
2
3
0
1
2
0
1
1
1
2
1
1
2
1
2
1
1
2
1
1
1
1
2
2
1
1
0
0
0
1
1
1
1
0
1
1
2
1
1
1
0
2
2
2
1
1
1
1
0
0
1
0
1
0
0
0
2
1
1
2
1
1
0
0
2
1
1
0
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
0
0
2
2
2
1
2
1
1
1
0
1
2
1
2
0
4
2
1
1
1
2
1
0
1
2
2
1
1
1
0
1
2
1
1
2
1
1
1
0
1
2
1
1
0
2
1
3
2
1
0
2
0
2
1
1
1
1
2
0
1
0
1
0
1
1
1
1
1
1
2
0
2
2
2
1
2
1
2
1
2
1
0
1
2
1
2
1
1
1
2
2
1
1
1
1
1
1
1
2
0
1
1
4
2
0
1
1
1
1
1
0
2
1
0
1
2
0
1
0
1
0
1
1
2
2
0
1
1
0
1
0
1
1
1
1
0
1
1
0
2
2
1
2
1
1
1
1
1
2
1
0
2
2
1
0
0
1
1
1
1
1
1
0
1
1
1
1
1
0
0
2
2
2
1
2
1
0
2
1
1
0
2
1
1
2
0
1
2
0
3
2
1
1
1
2
1
1
1
1
1
0
1
1
1
0
1
1
1
1
1
1
3
2
2
0
1
1
1
0
1
2
1
2
1
1
1
2
1
2
1
1
2
0
1
1
1
1
0
0
0
0
1
2
1
2
1
1
2
2
2
1
1
1
2
0
1
0
1
2
1
11
1
1
0
0
0
2
1
1
1
1
1
1
2
1
2
1
1
1
0
0
1
1
1
1
0
1
1
1
1
0
1
1
2
2
1
2
1
1
0
1
1
1
1
1
1
1
1
2
0
3
1
4
1
1
1
1
2
2
1
1
1
2
1
0
1
1
2
0
1
1
2
1
1
1
0
0
2
0
2
0
0
0
2
2
1
1
1
0
1
1
2
1
1
1
2
1
1
2
3
3
1
2
0
2
0
1
2
1
2
0
2
2
2
0
1
1
2
1
2
2
1
1
1
0
1
1
2
1
0
1
2
1
0
0
1
2
1
0
1
2
0
1
0
0
1
1
0
0
0
2
1
1
0
1
2
1
1
0
1
2
2
2
1
2
1
2
2
1
1
0
1
1
1
0
2
0
1
0
1
2
0
1
1
0
1
1
1
1
1
3
2
2
1
1
0
0
1
2
1
1
1
1
2
4
0
1
1
1
2
1
1
0
1
2
0
1
0
1
1
1
1
1
2
0
1
0
0
1
2
1
2
1
1
1
2
0
1
2
2
1
1
1
0
0
1
2
0
2
1
0
0
1
1
1
0
2
1
0
2
1
0
1
1
0
1
1
1
1
1
1
1
1
0
0
1
1
1
0
0
2
2
1
0
1
1
2
1
0
1
2
0
1
1
1
2
1
1
0
1
1
3
1
2
1
0
1
2
1
1
1
2
2
1
2
1
3
2
1
1
2
1
2
2
2
2
0
1
1
0
1
2
1
1
0
2
1
1
1
1
1
1
2
1
0
0
1
1
1
0
1
1
3
2
1
2
1
0
1
1
2
1
2
1
2
1
0
1
0
1
1
0
1
2
2
1
0
2
1
2
3
1
0
2
1
1
1
0
1
1
3
1
1
0
1
2
1
1
1
1
0
1
0
0
1
2
0
1
1
2
0
2
1
1
1
1
1
1
1
0
1
1
1
2
1
1
0
1
0
1
1
0
2
2
1
1
0
0
1
1
1
2
2
1
1
0
2
0
1
0
1
3
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
0
0
2
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
0
1
2
1
1
1
0
1
0
0
1
2
2
1
2
2
1
2
1
2
1
0
1
1
1
1
1
1
1
2
0
1
1
1
1
1
1
2
1
0
1
1
0
1
2
1
0
2
1
1
1
2
1
2
1
1
2
0
1
2
2
1
1
1
1
2
1
1
1
2
1
1
2
0
2
0
1
1
1
1
1
0
0
0
1
2
1
2
1
0
1
1
1
2
2
3
2
1
2
0
1
2
2
0
2
1
0
1
2
2
1
1
1
1
2
1
1
2
0
1
2
0
2
1
0
1
0
1
1
2
1
1
0
2
1
0
1
1
1
0
1
2
0
1
2
2
1
2
1
1
1
1
1
1
2
1
1
1
0
1
1
2
2
0
1
1
1
1
1
0
2
2
0
2
2
1
1
0
2
1
2
1
2
1
0
1
1
2
0
0
2
2
1
1
1
0
1
0
2
1
0
0
2
0
1
1
1
1
2
1
0
0
1
0
1
1
1
2
1
2
1
2
1
0
1
1
2
0
1
2
2
1
1
1
1
2
2
1
1
1
1
1
1
2
2
1
0
0
1
1
0
1
0
1
1
0
2
1
1
1
1
2
0
1
1
2
2
1
0
2
2
1
1
2
2
1
1
0
2
0
0
2
0
1
1
1
1
1
2
0
1
1
0
1
1
0
1
1
1
1
2
2
2
2
0
1
1
2
1
0
0
1
1
2
1
1
3
1
0
1
1
2
1
1
2
1
1
0
1
0
1
0
0
0
0
1
1
2
1
0
2
0
1
1
1
1
1
1
2
1
2
1
0
1
0
0
1
0
2
1
1
1
2
0
0
1
2
2
0
2
0
0
1
0
1
0
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
3
2
1
2
1
0
1
2
1
0
1
2
1
0
0
1
1
2
2
1
2
1
1
0
0
1
1
1
2
1
0
1
2
0
1
3
0
2
1
1
1
0
1
2
1
0
2
1
0
2
1
1
1
1
2
1
2
2
1
2
1
2
1
1
0
2
1
1
0
2
0
0
2
1
0
1
1
2
2
2
1
2
0
0
0
1
1
1
1
2
1
1
1
1
2
0
0
0
1
1
0
1
1
1
0
1
0
1
2
0
0
1
0
1
0
1
2
2
1
2
2
1
1
2
1
1
1
2
2
1
2
1
0
1
0
2
1
1
2
1
0
1
1
0
1
2
1
1
1
1
1
1
1
0
1
1
0
2
0
1
1
1
1
1
1
0
1
0
1
2
1
1
1
1
1
2
1
2
1
1
1
2
2
2
0
2
1
0
0
1
2
0
1
1
1
1
1
2
1
2
4
2
0
1
1
0
1
1
1
1
0
2
1
2
1
1
1
0
0
0
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
1
0
1
0
0
0
1
1
2
1
1
0
0
2
1
1
1
1
1
1
1
1
2
1
1
1
0
2
1
1
1
1
1
2
2
1
0
1
1
1
1
2
1
2
1
0
1
1
1
1
2
1
0
1
1
2
2
1
1
1
1
1
1
2
2
1
2
0
1
1
1
2
1
2
2
2
6
0
5
2
1
2
0
1
1
1
0
1
1
1
1
1
2
1
0
0
1
1
1
0
1
1
2
1
1
2
0
1
1
0
0
2
1
2
1
1
1
0
2
2
1
2
1
1
2
1
2
1
2
2
2
1
1
1
1
1
0
1
1
1
2
1
1
0
1
1
2
0
0
2
2
0
1
2
0
0
1
1
2
1
1
1
1
0
0
1
2
1
1
0
1
1
0
2
1
0
1
0
1
0
1
1
2
1
1
1
1
1
0
2
1
1
2
0
2
1
0
1
1
2
1
2
1
1
1
1
1
0
2
0
3
1
3
2
1
1
1
1
0
2
2
0
2
1
2
1
2
0
0
1
1
1
1
2
1
1
1
0
1
1
2
1
1
1
1
1
1
0
2
1
1
1
1
0
1
1
1
2
1
0
1
1
1
2
1
1
2
1
1
2
1
2
2
0
2
1
1
1
1
0
2
1
2
1
2
1
1
0
2
2
2
2
1
1
1
1
1
0
1
2
1
1
1
1
1
1
1
2
1
1
0
3
0
1
1
2
0
1
0
0
0
0
1
0
1
1
1
1
2
2
2
1
1
1
0
1
1
1
0
2
1
1
1
1
1
1
2
2
2
1
2
1
1
2
0
0
1
1
1
1
1
1
1
1
0
2
0
1
1
1
1
0
1
2
1
1
1
0
0
2
2
1
1
1
1
1
1
1
1
2
1
0
0
1
2
2
1
0
1
1
1
1
1
1
1
2
0
0
2
2
1
1
0
1
0
1
2
0
2
1
2
0
2
1
1
1
1
1
1
1
1
2
1
2
0
2
1
1
1
2
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
2
2
0
1
1
2
0
1
0
2
0
1
2
1
1
1
1
0
1
0
1
1
1
1
2
1
1
1
1
1
0
0
1
0
1
1
1
2
0
2
0
1
1
1
1
0
0
1
1
1
2
2
2
2
1
1
0
1
1
1
0
0
0
2
3
0
2
2
0
1
1
1
1
1
1
1
1
1
0
0
0
2
1
2
2
2
2
1
1
1
2
0
1
1
2
2
1
1
2
1
0
1
1
0
0
2
1
1
0
1
0
0
0
1
1
1
2
1
0
0
1
0
1
1
1
1
1
1
1
1
2
1
1
1
2
1
2
0
1
2
1
1
1
1
0
0
1
1
1
1
0
2
0
1
1
1
2
1
0
0
2
1
0
1
1
1
1
2
1
1
2
0
1
2
2
1
1
1
1
1
2
1
1
1
2
0
1
1
1
1
0
0
1
1
0
1
2
1
1
0
1
0
1
0
0
2
2
2
2
1
1
1
1
1
0
0
1
1
1
1
1
0
1
0
0
1
2
1
0
1
3
2
2
2
1
1
0
1
1
0
1
1
2
1
0
2
1
2
1
1
1
2
1
2
2
0
2
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
2
2
5
0
1
0
2
1
1
1
1
1
1
1
1
0
2
2
1
1
0
2
0
1
1
1
1
1
1
2
1
1
1
2
1
0
1
0
1
1
1
2
0
1
1
1
1
1
1
0
2
1
1
1
1
2
1
0
0
1
1
1
1
1
0
2
2
0
2
2
0
2
1
2
1
2
1
0
0
2
1
1
2
1
1
2
1
0
0
0
2
1
0
0
0
0
0
1
1
1
1
1
1
0
1
2
1
1
1
1
0
2
1
0
0
0
1
1
2
1
1
1
0
1
2
2
0
0
1
1
1
2
1
2
0
0
1
2
0
1
2
1
1
2
1
1
1
1
2
1
1
1
2
0
3
1
1
1
1
1
1
1
1
1
0
0
1
2
2
1
1
1
1
1
1
0
1
0
1
1
1
1
1
1
0
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
1
1
0
1
1
0
1
2
0
1
2
0
0
1
0
0
1
1
1
2
1
1
2
2
1
1
1
1
1
1
1
2
0
1
1
1
1
1
3
1
0
1
1
1
2
1
0
2
2
2
1
1
1
1
2
2
0
2
0
1
1
1
2
1
1
1
0
2
1
1
2
1
2
1
1
2
1
1
1
2
0
1
1
2
0
1
1
1
1
1
1
1
2
2
1
0
1
3
1
1
2
1
1
1
4
0
1
1
1
1
1
2
1
2
2
1
1
2
2
1
2
1
1
1
2
0
2
1
1
1
1
1
1
2
0
0
1
2
1
2
2
3
1
1
1
2
1
1
2
0
1
1
2
2
1
2
1
2
1
1
2
1
1
2
2
2
1
2
0
1
2
0
1
0
2
1
0
1
1
2
1
0
1
2
0
2
2
2
4
1
2
1
1
2
2
0
3
1
1
2
6
1
1
2
0
0
2
0
4
2
1
0
1
0
1
1
1
2
1
2
1
1
1
2
0
1
0
2
1
1
2
0
1
0
1
1
1
1
1
1
2
1
0
2
2
0
2
1
1
1
1
2
0
2
1
1
0
1
0
2
1
1
1
1
1
0
0
1
2
1
2
2
0
1
1
0
0
1
1
2
1
2
2
1
0
1
1
0
1
1
2
1
0
1
1
0
0
1
0
1
1
2
0
0
1
1
0
2
1
2
1
1
0
1
0
0
1
1
1
1
1
2
1
0
1
2
1
0
1
1
1
0
1
0
1
2
1
1
2
1
2
2
1
0
1
1
1
1
1
1
1
1
0
2
1
2
1
1
2
1
0
0
2
1
1
1
1
2
1
1
1
1
1
2
0
2
1
1
1
2
1
1
1
1
1
1
1
0
1
1
1
1
1
2
1
1
1
1
1
1
0
1
2
0
1
0
1
2
0
2
1
1
1
0
1
2
1
2
0
0
1
2
1
1
1
1
1
1
2
1
1
2
0
0
0
1
2
1
1
2
0
1
1
1
1
3
1
2
0
0
1
0
2
1
1
1
2
1
1
1
1
1
2
2
0
2
0
1
1
2
0
0
1
2
0
2
3
2
2
2
1
1
2
1
2
1
1
1
1
2
1
2
2
0
1
1
1
0
1
0
2
0
2
1
1
1
1
0
0
0
2
1
1
1
1
1
2
0
1
1
2
0
1
1
0
0
0
2
0
2
0
1
2
1
2
1
1
0
1
1
0
1
1
1
2
2
2
2
2
2
1
0
2
0
1
1
0
0
1
0
2
0
2
1
1
1
1
0
1
1
0
1
1
0
1
1
1
2
0
0
1
1
2
2
1
0
1
1
1
0
1
2
2
2
0
1
1
0
1
0
1
1
1
2
2
2
1
0
1
1
1
1
2
1
2
1
2
2
0
1
1
2
1
1
1
1
1
1
1
1
2
0
1
0
2
2
1
1
1
0
1
1
1
2
1
1
1
1
1
0
1
2
1
1
0
1
2
1
2
2
2
1
1
2
0
1
0
1
1
3
1
0
1
3
2
0
2
2
1
1
2
2
1
1
1
2
1
0
2
1
2
1
1
2
1
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
0
2
0
1
1
2
1
1
2
0
2
3
5
1
1
0
0
1
2
0
1
1
2
1
2
1
2
2
2
1
0
2
0
0
0
1
1
0
1
1
1
1
1
0
2
1
1
1
0
1
1
1
2
2
1
1
1
2
0
1
0
1
1
0
0
1
1
0
2
2
2
1
1
1
1
1
1
1
2
1
0
2
1
1
1
0
1
2
1
1
2
1
0
1
0
1
1
0
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
0
1
1
1
1
0
1
2
0
0
1
0
0
2
0
1
0
1
1
2
0
1
2
1
1
0
1
1
1
1
1
1
1
0
1
0
1
1
2
0
1
0
0
2
1
1
1
1
1
2
2
0
1
1
1
1
0
2
1
1
1
2
1
0
1
1
2
1
1
0
1
1
1
2
2
1
2
2
0
1
1
1
0
1
2
2
1
1
0
1
1
2
1
1
1
1
1
1
1
1
1
0
0
1
2
1
1
0
1
0
2
0
2
1
1
1
2
1
4
1
2
0
0
0
2
1
2
0
1
2
1
1
1
1
1
2
2
1
1
1
3
2
1
3
1
1
0
1
1
1
1
1
0
0
1
0
0
0
0
1
1
4
1
0
1
1
2
1
1
1
1
1
1
1
0
1
2
0
1
1
1
1
1
1
0
1
1
0
1
2
1
1
2
0
2
0
1
1
0
2
2
1
2
1
1
1
1
1
2
0
2
2
1
1
1
1
1
2
0
0
1
1
1
1
0
1
2
1
1
2
0
2
1
0
1
2
1
1
1
1
2
1
2
0
1
1
2
1
1
1
1
0
1
2
1
1
1
1
2
1
1
0
2
0
0
1
2
0
1
1
1
2
1
2
1
1
1
0
1
1
1
1
0
2
1
1
1
1
0
1
2
2
1
1
1
1
1
0
1
0
2
1
1
1
1
0
0
0
2
0
2
0
0
1
0
0
0
0
1
1
2
1
2
0
2
0
0
0
2
1
1
0
1
2
1
0
2
2
2
0
1
1
2
1
1
1
1
2
0
1
0
0
1
1
1
1
1
0
1
2
0
2
2
1
1
1
0
1
1
2
1
1
2
1
0
1
2
1
1
0
1
1
1
1
1
1
1
1
2
1
1
0
1
0
1
1
1
1
0
1
1
1
1
1
2
1
1
1
0
1
1
1
4
0
2
1
1
1
1
0
2
1
1
1
1
2
0
1
2
1
2
2
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
1
0
1
0
1
2
1
2
1
0
2
1
1
1
1
0
0
1
0
2
2
1
1
1
0
1
1
1
2
1
1
1
0
1
1
0
0
1
0
1
1
0
0
1
1
1
0
1
1
0
0
0
0
1
1
2
2
1
1
0
2
1
0
2
2
2
2
1
2
1
1
0
1
1
0
1
0
2
0
1
0
2
1
1
1
0
1
1
1
1
1
0
2
1
0
2
2
1
1
1
1
0
2
1
2
2
1
1
1
0
1
2
0
1
3
0
1
1
1
2
0
1
0
1
1
1
2
0
1
1
1
1
2
0
1
1
1
1
1
1
1
0
1
0
1
1
1
1
2
1
1
2
1
1
2
1
0
1
1
0
1
0
1
1
1
1
1
1
1
1
1
0
1
1
0
1
1
1
2
0
1
0
1
0
1
1
1
1
1
1
1
0
1
1
1
1
1
0
2
1
3
2
1
1
0
0
1
0
1
0
1
1
0
0
0
2
1
2
2
1
0
2
1
1
0
1
0
2
1
1
1
2
1
2
0
0
1
1
1
0
1
1
0
1
0
1
1
1
2
0
2
1
0
2
0
1
0
2
1
1
1
1
1
0
1
1
1
1
1
1
2
0
1
2
1
0
1
1
1
2
1
1
1
1
1
0
1
0
1
1
1
1
2
1
1
2
2
2
0
1
1
1
2
1
0
1
1
1
2
0
1
1
2
1
1
0
2
1
1
1
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
0
1
1
2
1
1
1
1
1
1
1
0
1
2
1
1
2
1
1
0
2
1
1
1
0
1
0
1
2
1
2
1
0
1
1
1
2
0
0
1
2
1
2
1
1
1
0
1
0
2
1
2
1
1
1
0
1
0
1
1
1
1
0
1
1
2
0
0
1
1
2
1
1
0
1
1
1
0
1
1
1
2
0
1
0
1
2
3
1
1
1
2
1
2
0
1
1
2
2
2
1
0
1
2
0
1
1
2
2
1
1
0
0
1
1
2
1
2
0
1
0
1
2
1
1
1
1
0
1
0
1
1
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
2
2
1
1
0
2
0
2
2
2
1
1
0
0
2
1
1
1
1
0
2
3
1
1
1
1
1
1
1
1
1
1
1
1
0
2
1
1
0
1
1
1
1
1
2
1
0
1
1
1
1
2
0
3
1
0
1
2
1
1
2
0
2
2
0
1
1
1
0
0
1
1
0
1
1
2
1
3
2
1
2
1
1
1
1
1
0
0
1
1
1
2
1
2
2
2
1
2
1
1
0
1
1
2
1
0
1
1
1
0
1
1
2
1
1
1
0
1
1
2
2
0
0
2
1
1
1
1
2
1
2
1
1
2
0
2
1
1
1
2
1
6
1
1
1
0
0
0
1
1
3
2
1
1
1
1
1
1
1
0
1
0
2
0
1
1
1
1
1
0
0
2
0
0
2
1
2
1
2
1
0
1
1
2
1
0
0
1
2
1
1
1
0
1
1
0
1
1
1
1
0
1
0
1
2
1
1
1
1
0
1
0
2
1
1
2
2
1
1
1
1
0
1
0
1
0
2
1
0
1
2
0
1
2
0
0
2
1
1
1
1
1
0
1
1
1
1
1
3
1
2
1
1
1
2
0
2
1
0
1
1
2
2
1
1
0
1
1
2
1
1
1
0
1
1
1
0
0
1
1
0
1
2
2
1
1
0
1
1
0
2
1
2
1
1
1
2
2
1
0
1
1
1
2
2
0
1
0
0
0
2
1
2
1
1
2
0
1
2
2
0
2
0
0
0
2
1
2
0
2
1
1
0
1
1
1
1
2
1
1
0
0
0
1
1
1
1
1
1
2
2
1
2
0
1
1
2
1
2
1
1
1
1
2
0
1
1
1
1
1
1
1
0
1
0
2
2
0
1
2
1
0
2
4
1
1
1
2
1
2
0
0
1
2
1
1
1
1
1
1
1
2
1
1
2
2
1
2
1
1
0
1
1
0
2
1
2
0
0
1
1
1
1
1
1
2
1
2
0
2
1
0
1
1
1
1
2
1
1
0
1
0
2
1
2
1
1
0
1
1
1
1
2
1
1
1
0
2
2
1
1
1
0
0
2
2
1
1
0
0
1
2
0
0
1
0
1
3
0
2
2
1
2
2
0
1
1
1
1
1
1
1
1
2
1
1
0
2
1
0
2
1
0
0
0
0
1
1
1
1
1
2
0
1
2
0
1
1
2
1
0
1
1
1
0
1
1
0
2
0
1
0
2
1
2
0
2
2
1
1
0
0
1
0
1
1
1
1
2
1
1
1
1
0
1
0
1
2
2
0
1
1
0
1
0
2
1
1
2
2
2
2
1
1
2
1
0
1
2
1
1
2
1
1
3
2
2
3
0
0
1
2
1
1
1
2
2
0
1
1
0
0
0
1
2
0
1
1
1
1
2
1
0
2
1
1
1
2
0
1
1
0
0
1
1
1
1
0
0
1
1
1
0
2
1
1
2
0
2
0
1
1
1
1
2
1
1
2
1
1
1
2
0
1
1
2
0
1
0
1
0
1
2
1
1
1
1
1
1
2
2
1
2
1
0
1
1
1
1
1
2
2
0
1
2
1
1
0
2
1
1
1
1
0
2
1
2
2
2
1
2
1
1
1
2
2
1
1
2
1
0
0
1
1
1
1
0
1
1
1
1
1
0
1
1
1
1
1
0
1
1
1
1
1
0
0
1
1
0
0
1
1
2
1
1
0
1
0
1
1
1
1
2
1
0
2
2
1
1
0
0
1
1
1
1
1
0
1
1
1
1
1
1
0
1
0
1
1
1
1
2
0
1
0
2
1
0
1
1
1
1
2
1
0
1
2
0
0
2
2
1
1
1
2
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
2
2
1
1
0
2
2
1
1
1
1
1
0
1
1
2
1
1
0
0
2
2
1
1
2
2
2
1
2
1
2
0
1
1
1
1
1
1
1
1
1
1
1
1
2
0
1
1
1
1
2
1
1
1
0
1
2
1
1
1
2
1
1
1
1
0
2
1
1
1
0
1
1
2
1
1
0
1
1
1
1
1
0
1
1
1
2
2
2
2
1
1
2
1
2
0
0
1
2
1
1
1
1
2
2
2
3
1
2
2
1
1
1
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
0
1
0
1
1
0
0
1
1
1
1
1
1
0
1
0
1
0
2
2
1
2
1
2
2
1
2
1
1
0
2
2
1
0
1
1
2
1
1
2
1
1
1
1
0
2
1
2
1
0
1
1
5
0
2
0
0
0
1
2
2
2
2
1
1
1
2
1
2
0
2
1
1
0
1
2
1
1
2
1
1
0
1
0
1
1
1
2
2
1
1
1
1
1
2
0
1
1
1
0
2
2
1
1
1
1
1
1
1
1
0
1
0
2
2
1
1
2
1
1
0
1
1
0
2
0
2
0
0
2
1
0
0
0
1
1
2
3
1
2
1
1
1
1
2
1
0
0
1
1
1
1
2
0
0
2
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
0
1
2
1
0
0
1
2
1
1
0
2
2
2
1
0
2
1
1
1
0
1
2
1
1
2
1
1
2
1
0
0
2
0
1
1
1
2
2
0
1
0
0
1
2
1
1
1
1
1
1
1
1
0
2
2
1
1
0
0
1
1
1
1
2
1
1
0
1
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
0
1
1
0
3
0
2
0
0
1
1
1
1
0
2
2
2
2
2
2
1
1
2
1
1
0
2
1
2
0
0
2
1
2
0
1
1
1
0
2
1
1
2
1
1
0
1
2
0
1
1
0
0
1
1
1
2
0
1
1
0
1
2
1
1
2
1
0
0
2
1
1
0
2
2
1
1
0
2
0
1
2
0
1
0
1
1
2
2
1
0
0
0
1
2
2
0
0
1
1
2
1
1
0
0
0
1
1
2
1
1
1
1
1
1
1
0
1
1
0
1
0
1
0
0
1
1
1
1
1
2
1
2
4
1
1
1
2
1
1
2
0
1
0
1
2
1
1
2
1
2
2
0
1
1
1
0
2
1
2
1
1
1
2
1
2
1
0
0
1
1
2
1
1
0
0
1
0
1
2
0
1
1
1
1
1
0
0
1
1
2
1
3
1
0
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
0
1
1
0
2
0
1
0
1
1
1
0
0
1
2
1
0
1
1
1
1
0
1
0
2
0
0
0
0
2
1
1
1
2
0
1
1
1
2
0
1
0
1
0
1
2
2
1
1
1
1
2
2
1
1
1
1
0
2
1
0
2
1
0
2
1
1
1
1
2
1
2
1
1
0
1
1
1
2
1
1
0
2
1
1
2
1
2
1
4
0
1
0
0
3
0
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
2
1
1
1
0
1
1
0
2
1
1
1
1
0
1
1
1
2
1
1
1
1
2
1
1
1
1
1
2
1
2
2
1
0
1
1
1
1
0
2
1
1
1
1
1
2
1
1
0
1
1
1
2
1
1
1
2
2
1
2
1
0
1
2
0
1
1
2
2
2
1
1
1
0
1
1
0
1
1
1
1
1
1
1
1
2
1
1
0
0
0
1
0
2
2
2
1
1
2
2
0
1
2
2
0
1
1
1
1
2
1
2
2
1
2
1
1
1
0
2
2
1
1
3
1
2
1
0
1
0
1
1
0
1
2
2
1
2
0
1
1
1
1
0
1
2
1
2
0
1
2
2
1
2
0
1
1
1
1
0
2
1
0
2
1
1
0
1
0
3
2
1
1
1
0
0
1
1
2
1
1
1
1
1
0
1
1
1
0
1
0
2
2
1
0
1
2
0
2
1
2
0
2
1
0
1
2
1
0
1
1
1
1
1
2
1
1
2
2
1
1
2
2
1
2
1
1
1
1
1
1
2
1
1
1
2
1
2
2
2
2
1
1
2
0
2
1
2
3
1
0
1
1
0
2
1
0
2
0
0
2
1
1
1
1
1
1
1
1
1
2
2
0
0
1
1
2
2
1
2
2
0
2
1
1
2
2
2
2
0
1
1
0
1
2
1
2
1
2
2
2
1
1
2
1
2
1
2
3
2
2
2
1
1
1
0
1
0
0
1
0
2
1
0
1
2
1
1
1
1
2
2
0
1
0
1
1
0
0
1
1
1
2
2
1
1
0
0
1
1
1
1
1
0
1
0
1
1
1
3
0
2
1
2
2
1
1
0
1
1
1
1
2
2
1
1
1
1
1
1
1
1
0
1
1
1
1
1
0
1
2
1
0
1
0
1
1
1
1
0
2
2
1
1
2
1
1
1
0
0
1
1
1
1
1
1
1
1
2
1
3
2
1
2
1
0
1
1
0
1
2
0
1
2
1
0
1
1
1
0
0
2
1
1
2
1
2
2
2
2
0
2
0
1
1
0
1
1
2
1
1
1
0
0
1
1
0
1
1
1
1
1
0
1
2
1
1
2
1
1
1
0
1
1
1
1
0
0
2
1
0
2
2
2
1
2
2
1
1
0
1
0
1
0
1
1
2
1
0
2
0
1
1
1
0
0
1
2
1
1
1
1
0
1
1
2
2
2
1
2
2
1
1
1
1
2
1
1
1
1
2
1
1
1
0
2
0
1
0
0
0
1
1
0
0
2
2
1
1
0
1
1
1
1
1
2
1
0
0
1
1
1
1
1
0
3
0
0
1
1
1
1
2
1
1
1
2
1
0
1
2
2
0
0
1
2
2
1
2
1
0
2
2
1
1
1
1
1
1
0
2
1
1
0
2
0
0
2
2
1
1
1
1
2
1
2
1
2
1
2
1
1
3
1
2
1
1
0
0
1
0
1
1
1
1
2
1
2
1
1
2
2
0
1
1
1
0
1
2
2
2
2
0
1
1
1
0
1
2
1
1
1
1
0
1
0
1
1
0
1
0
1
0
2
2
1
1
1
1
1
2
2
1
0
1
1
0
1
3
1
1
1
1
0
1
1
2
1
1
1
0
2
1
2
1
2
1
1
1
1
0
0
1
2
1
0
0
1
1
1
1
1
1
0
1
1
1
2
1
1
1
1
1
1
2
1
1
0
1
1
2
0
2
1
2
1
2
0
1
1
1
0
1
1
1
1
1
0
1
1
1
1
0
1
1
2
0
1
2
0
1
1
1
1
1
1
0
1
1
1
2
1
1
1
1
1
0
1
1
1
1
2
0
1
1
0
1
2
1
1
2
1
2
1
1
1
2
1
0
1
1
1
2
1
2
2
0
0
2
0
0
0
1
1
0
2
1
1
1
1
1
1
1
2
2
0
2
1
2
1
0
1
1
1
1
1
2
2
0
1
2
1
2
0
0
1
1
0
1
1
1
2
2
2
1
0
1
1
2
0
1
1
3
1
1
0
1
0
1
1
0
0
1
0
1
0
2
1
1
1
1
1
1
1
0
0
1
1
1
2
2
0
2
1
0
0
1
1
2
1
3
0
2
1
1
0
1
0
1
0
1
1
2
0
2
2
2
1
2
2
1
2
2
0
1
0
1
0
0
1
0
1
1
1
0
2
1
1
1
1
1
1
0
2
0
1
1
1
2
1
2
1
1
1
0
1
1
2
1
1
0
1
1
0
2
1
1
1
1
2
2
0
0
1
1
1
1
1
1
0
1
3
2
0
0
1
2
1
0
1
1
1
1
1
2
2
2
0
2
1
1
1
1
2
0
1
2
1
0
1
0
1
1
1
1
0
0
2
1
2
1
1
1
1
2
1
2
0
0
1
2
2
1
1
0
1
2
1
1
3
1
1
0
2
1
1
1
1
1
1
1
1
2
2
1
2
1
3
1
2
1
2
1
2
2
0
1
1
2
1
2
1
1
0
1
0
0
1
1
1
2
0
1
0
0
2
2
1
0
0
0
1
2
1
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
1
0
0
2
1
2
2
2
2
2
1
1
1
2
2
1
1
1
1
1
0
1
1
2
1
1
0
2
1
1
1
1
1
2
0
0
1
1
1
2
1
0
1
1
0
1
0
2
0
1
1
0
1
1
1
0
0
2
1
1
1
1
1
1
0
4
1
1
2
0
1
1
1
1
2
0
0
0
2
1
0
0
1
1
1
1
0
0
1
2
2
1
1
0
2
0
2
1
1
1
1
0
1
1
1
1
3
1
0
2
2
2
1
2
1
1
0
2
2
0
1
0
1
1
0
1
1
3
1
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
1
1
1
0
0
1
1
0
2
1
1
1
1
1
1
1
1
1
1
0
0
1
1
1
2
2
1
2
1
0
0
1
1
2
1
2
1
2
1
2
1
1
2
1
1
1
1
0
2
1
1
2
1
0
1
1
1
1
1
1
1
0
2
2
1
1
1
2
2
2
1
1
1
2
2
1
1
1
2
2
1
0
1
2
0
2
1
1
0
2
2
1
2
1
1
1
1
0
1
0
2
0
1
1
1
1
1
0
1
1
1
2
2
0
0
0
1
1
3
0
2
1
0
1
2
0
2
2
2
1
0
1
2
1
0
2
2
1
2
1
0
1
2
2
2
1
0
1
2
1
0
1
1
2
1
2
1
2
2
1
2
0
2
1
0
1
1
1
0
0
1
2
1
0
1
2
2
2
2
1
1
1
1
0
1
2
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
2
0
1
1
3
2
1
2
1
5
1
1
1
1
2
2
2
2
0
0
2
1
1
1
1
2
1
1
0
1
2
2
1
1
2
0
0
0
0
1
1
0
1
1
1
2
0
2
1
1
2
1
3
1
0
1
1
2
1
0
1
1
1
2
1
1
1
1
1
1
1
1
2
1
2
1
2
1
1
1
1
1
2
2
0
1
1
2
0
1
0
1
1
0
1
2
2
1
0
2
1
0
0
0
2
2
1
2
1
1
1
2
1
1
1
0
2
1
1
2
1
2
0
1
2
1
1
1
1
1
1
1
1
0
3
1
1
2
1
2
2
1
2
2
2
1
2
1
2
1
1
1
1
1
2
0
2
1
1
0
1
1
1
2
1
1
0
2
1
2
1
1
1
1
2
2
1
0
1
1
2
2
1
1
1
1
2
2
2
1
2
3
1
2
1
0
0
1
1
1
0
0
2
1
1
0
2
1
0
1
2
2
1
2
1
1
0
2
1
1
1
1
1
1
1
4
0
0
1
0
2
1
1
2
1
1
2
0
1
0
0
1
1
2
1
1
1
1
1
3
1
1
1
0
0
2
1
1
0
1
2
1
2
1
0
2
1
1
2
1
1
2
1
1
0
1
1
2
2
1
1
1
0
0
2
1
2
1
1
1
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
0
1
2
0
1
1
2
1
2
0
1
1
1
1
1
2
1
1
1
2
0
2
1
2
2
2
1
1
1
2
1
0
1
0
0
2
1
2
1
1
1
0
1
1
2
2
2
2
1
1
0
1
0
0
1
0
1
1
1
1
1
1
0
1
0
1
1
1
0
2
0
3
2
1
1
1
1
1
0
1
0
1
1
0
1
1
2
1
1
1
1
0
1
2
1
1
1
0
1
1
2
2
1
1
1
1
2
1
2
2
2
1
2
0
0
2
1
1
3
0
1
1
0
0
2
1
0
1
1
2
1
2
2
0
1
1
1
0
1
1
1
1
2
1
1
1
2
1
2
1
1
2
1
0
1
2
2
1
3
1
1
1
2
2
1
2
1
1
1
1
1
1
1
0
2
1
0
1
1
1
2
2
1
0
1
2
2
1
1
0
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
0
2
1
1
1
1
1
2
1
1
1
2
1
0
2
1
0
1
0
0
0
0
1
1
0
2
0
2
2
0
1
0
0
1
1
1
1
1
1
2
2
1
1
1
2
2
1
0
1
0
1
1
0
0
1
0
0
1
0
1
2
3
0
1
1
1
1
0
0
1
1
1
0
2
1
1
0
1
0
1
1
2
0
1
2
1
1
2
2
0
1
2
0
1
1
1
1
1
0
0
1
1
2
0
0
1
2
2
2
1
2
2
1
1
1
1
0
0
2
1
1
2
2
1
1
0
1
2
1
1
2
1
0
1
1
1
1
2
1
1
3
0
0
1
1
1
1
1
1
1
2
1
1
1
1
2
0
1
2
1
1
2
0
1
2
2
2
1
2
0
0
1
1
2
1
1
1
1
0
2
0
1
1
0
2
2
1
1
1
1
1
0
1
1
1
1
0
0
2
2
3
0
0
2
1
0
2
2
1
2
0
2
0
2
1
1
1
2
1
2
0
1
1
2
1
0
1
1
1
2
2
1
1
0
1
0
0
1
2
0
0
2
1
0
2
1
1
2
1
1
0
1
1
0
1
1
2
1
1
2
0
1
2
1
0
1
1
1
1
1
2
0
1
1
0
2
2
1
0
0
1
1
1
1
0
1
1
1
1
1
0
2
2
1
1
2
0
1
1
1
1
1
0
0
1
2
1
1
1
1
1
0
1
1
0
2
1
2
0
1
0
1
1
2
1
0
2
1
0
1
1
1
0
2
2
2
1
1
2
1
1
1
1
2
0
2
1
0
1
2
2
2
2
2
2
0
1
2
1
0
0
1
2
1
2
4
1
2
1
1
0
1
1
0
1
2
2
1
1
2
2
1
1
1
0
0
0
0
1
1
2
2
1
0
1
1
2
1
1
1
1
0
1
1
1
0
1
1
2
1
1
2
2
1
2
1
1
1
1
1
1
1
0
1
1
0
1
0
0
0
0
1
0
1
1
0
2
0
1
2
1
1
2
0
1
0
1
1
0
1
2
0
1
1
1
0
0
1
1
0
1
0
1
0
1
1
1
1
1
0
2
1
1
0
1
2
0
0
2
0
1
2
2
1
3
0
1
1
0
2
1
0
0
1
1
2
1
1
0
1
2
2
1
1
1
1
1
1
1
1
1
0
1
0
0
1
1
2
1
0
0
2
1
1
1
1
0
0
1
2
1
2
2
1
1
1
0
1
1
2
2
0
0
2
1
2
1
1
1
2
1
0
2
0
1
2
1
1
1
2
1
2
2
2
1
1
2
1
2
0
1
0
2
0
1
1
1
1
2
2
1
0
2
1
1
2
1
1
1
1
1
1
0
1
1
1
2
1
1
2
1
1
1
0
2
1
1
2
1
1
0
1
2
1
2
1
1
1
1
1
1
2
0
1
2
1
1
2
2
1
1
1
1
2
0
2
2
0
1
1
1
2
2
2
0
1
1
0
1
2
0
1
1
0
1
1
0
0
0
1
2
0
2
0
1
2
1
2
1
1
1
1
1
0
1
1
2
1
1
1
1
2
2
2
1
2
1
1
1
2
2
1
2
2
2
1
0
1
1
1
0
2
1
1
2
1
1
1
1
1
1
0
1
1
1
0
0
1
2
1
1
2
1
1
1
1
2
1
0
1
1
0
2
1
1
2
1
1
1
1
1
1
1
0
1
1
1
2
2
2
0
1
0
1
2
1
1
0
1
1
1
2
1
1
1
1
1
2
1
3
1
1
0
1
1
2
1
0
1
2
1
1
1
0
1
2
1
1
1
2
1
0
1
0
1
2
1
0
0
1
1
1
1
2
1
0
1
1
1
2
1
1
0
2
1
1
1
2
1
1
2
1
1
1
2
1
2
1
1
2
1
1
1
2
1
2
2
2
1
0
1
2
1
0
1
1
0
1
2
2
1
2
2
1
1
1
0
1
1
0
1
0
2
0
1
0
1
1
1
1
1
1
0
0
1
2
2
2
2
2
0
0
0
0
1
2
0
0
1
1
1
2
0
0
1
0
1
2
0
2
0
2
1
1
0
2
1
0
1
2
1
0
1
0
0
1
1
0
1
2
0
1
1
1
1
1
2
1
1
1
1
2
2
1
1
1
0
1
1
2
1
1
2
1
1
1
0
1
2
1
1
1
2
1
2
1
1
1
2
1
1
1
0
0
1
1
4
0
1
1
1
1
2
2
1
1
1
4
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
0
1
1
1
1
1
1
1
2
1
0
0
2
0
0
2
2
1
1
1
1
1
2
1
1
1
0
1
1
1
2
0
1
1
1
1
1
1
2
1
1
0
1
1
0
1
1
0
1
1
1
0
1
2
1
1
0
1
1
1
1
0
2
1
0
0
1
2
2
1
1
2
2
1
1
2
1
1
1
2
1
2
1
1
2
1
0
1
1
1
1
1
2
1
1
1
1
1
0
1
0
1
2
0
1
1
2
1
1
1
1
1
2
0
2
1
1
1
3
1
1
2
1
0
2
2
0
1
1
2
2
1
1
0
2
3
2
1
1
1
1
0
0
0
1
2
1
1
1
1
1
1
0
0
1
1
1
1
1
0
2
1
1
1
2
1
2
2
0
1
2
1
0
2
1
2
2
1
2
2
1
1
1
0
0
0
2
2
0
0
1
1
0
1
1
2
1
1
2
1
1
1
2
1
1
0
1
2
1
1
1
0
1
1
0
1
2
1
1
2
1
2
1
0
0
0
0
1
0
1
1
1
1
0
0
3
1
0
2
0
2
1
0
1
1
1
3
2
1
0
1
0
1
0
0
1
1
1
1
1
1
1
0
2
2
1
2
2
2
2
1
2
1
1
0
2
0
1
0
1
1
1
1
2
1
1
1
1
1
1
2
1
3
1
2
1
1
2
1
1
1
0
1
1
1
2
2
1
1
1
2
1
1
0
1
0
1
0
1
1
1
1
1
1
1
1
0
2
2
0
2
1
0
1
1
3
0
1
1
2
2
0
2
1
2
0
1
2
0
1
2
1
3
0
1
0
0
2
0
1
1
1
0
0
2
0
1
0
0
0
1
0
0
2
0
0
1
1
1
2
0
1
1
2
1
1
1
1
2
1
1
2
1
1
2
1
1
0
1
0
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
2
1
0
1
0
0
1
0
1
1
2
1
1
1
1
1
2
0
2
3
2
1
1
2
1
1
2
1
1
1
0
2
0
0
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
2
1
2
3
1
0
0
0
1
0
1
2
1
1
1
1
1
2
1
0
1
2
1
1
0
1
1
0
1
0
1
0
1
1
1
2
1
1
0
2
2
2
2
1
0
0
2
1
0
1
2
2
1
1
1
0
0
1
1
0
2
1
0
0
1
0
2
2
1
2
0
1
0
1
2
1
1
1
1
2
2
2
1
2
2
2
1
0
1
1
1
1
1
0
2
0
2
2
2
1
2
0
0
1
1
1
1
1
1
0
1
2
1
1
1
1
1
1
3
1
1
1
1
1
1
2
2
2
0
1
2
1
1
1
1
2
1
1
2
1
0
1
0
1
1
1
0
1
1
1
0
2
1
0
0
1
1
1
1
1
2
1
1
1
2
2
1
1
0
1
1
0
2
1
0
1
1
2
1
1
1
0
0
0
0
1
1
0
1
1
2
0
2
2
1
1
2
2
1
1
1
1
0
1
1
1
1
0
1
1
0
1
0
1
1
0
0
0
0
3
0
1
1
0
1
2
1
1
0
1
2
1
2
1
0
2
1
0
2
1
1
1
1
0
0
1
2
1
1
1
2
1
1
1
1
1
2
1
1
1
2
0
1
2
1
1
2
0
0
1
2
1
1
0
1
0
1
1
1
1
2
1
2
1
0
1
1
1
1
1
0
1
1
0
1
2
1
1
1
1
0
0
1
2
1
2
1
2
0
1
0
2
0
2
0
1
1
0
1
2
1
1
2
0
1
1
1
0
2
1
1
1
1
0
1
0
1
1
2
0
1
1
0
1
1
2
0
0
1
1
0
1
0
2
2
2
2
0
1
0
1
1
1
0
1
1
2
2
1
1
1
0
1
1
1
0
2
2
1
2
2
1
0
2
1
2
1
0
2
2
2
1
1
0
0
0
0
2
1
0
2
1
0
1
1
1
1
1
1
0
1
1
2
1
1
0
1
2
1
1
3
0
1
1
1
1
0
2
0
1
1
1
1
1
2
1
1
1
1
2
1
1
1
0
0
1
2
1
0
0
0
1
2
1
0
1
1
1
2
1
2
2
1
1
0
2
0
1
1
1
0
1
1
2
1
1
1
1
2
1
1
1
0
1
1
1
1
1
2
2
2
0
1
2
1
2
1
1
0
1
1
0
1
1
2
1
1
2
2
0
0
1
0
1
1
2
0
2
1
1
1
2
1
2
2
1
1
1
1
1
1
1
2
2
2
1
1
0
1
1
2
1
1
1
1
0
3
1
2
1
1
1
1
1
2
1
2
1
0
1
2
2
1
1
1
1
1
2
2
0
2
1
1
0
1
0
2
0
1
1
1
0
1
1
0
2
1
0
1
2
1
2
2
0
2
1
2
1
1
1
1
1
2
1
2
1
1
1
2
1
1
0
2
1
1
0
1
1
1
1
0
0
1
0
1
1
1
1
1
1
0
0
1
2
0
1
3
2
2
2
2
1
1
1
1
1
0
2
0
0
0
1
1
2
1
1
0
1
1
0
2
0
2
1
0
0
1
0
1
0
2
2
2
1
0
2
2
2
0
0
0
1
0
2
1
2
0
2
2
1
0
1
1
1
1
1
1
1
1
0
1
1
1
0
1
1
1
2
1
1
1
3
1
1
1
1
2
1
1
1
0
1
2
1
2
2
1
1
1
1
2
1
2
2
1
1
1
1
1
1
2
1
1
2
2
1
1
2
2
2
0
1
0
1
1
1
1
1
1
1
1
0
1
0
1
2
0
1
2
1
0
1
1
2
1
1
1
0
2
1
0
0
0
0
0
0
1
2
1
1
1
1
0
0
1
0
1
0
2
2
1
1
0
1
2
1
2
2
0
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
2
1
1
1
1
0
1
1
1
1
1
2
1
2
1
1
1
3
1
2
2
2
2
0
1
2
1
1
2
1
1
1
1
2
1
0
3
1
1
1
1
1
2
0
0
2
1
1
0
0
2
1
0
1
0
0
2
1
0
2
1
1
2
1
1
1
0
0
1
0
2
1
3
1
2
1
1
2
2
1
1
2
1
1
0
2
2
0
1
1
1
2
1
1
2
0
0
1
1
1
1
0
2
0
2
1
0
2
1
2
2
1
2
1
1
2
1
1
1
1
1
2
1
0
1
1
1
1
2
1
1
1
0
0
1
1
1
1
3
0
2
0
1
2
4
1
1
1
1
1
1
2
2
2
1
0
2
0
1
1
1
1
2
1
2
1
0
1
1
0
1
1
1
0
2
1
1
0
2
2
1
2
1
1
1
0
1
1
1
0
2
2
1
3
1
2
0
1
1
0
1
1
1
1
0
0
2
1
2
4
0
0
0
1
2
2
0
1
1
2
1
0
1
2
2
2
0
0
1
3
1
0
1
0
1
2
2
1
1
2
0
1
2
2
1
1
2
0
0
3
0
0
0
1
1
1
0
1
1
2
1
0
2
0
1
1
0
1
0
1
1
1
1
1
1
0
0
1
1
1
1
0
7
1
1
2
2
1
0
1
1
0
2
2
1
1
0
1
1
2
0
1
1
1
1
1
2
0
0
2
1
2
0
1
3
2
1
2
1
1
0
0
0
2
1
0
1
0
2
2
1
2
1
1
2
0
2
1
2
1
0
0
1
2
2
0
1
1
2
1
0
1
2
2
1
3
0
1
2
1
1
0
2
2
2
2
2
2
1
0
1
0
1
1
1
1
1
1
0
1
0
1
0
0
1
1
1
1
1
1
1
2
0
2
1
0
1
0
2
1
1
1
2
0
1
1
1
1
1
2
0
0
1
0
2
2
2
1
1
1
0
1
2
1
2
0
1
2
2
1
2
0
2
0
1
0
1
1
0
2
1
2
0
1
1
5
1
0
2
2
0
1
1
1
2
1
2
1
0
1
1
2
0
0
1
1
1
1
0
1
0
0
0
1
2
0
1
1
1
1
0
2
1
2
1
1
0
2
1
1
0
1
1
1
1
1
2
1
1
1
1
1
2
0
1
1
0
4
1
0
1
1
1
1
1
1
1
1
2
0
1
1
1
4
1
1
1
0
1
0
1
2
0
2
2
0
1
1
1
1
1
0
0
2
2
2
2
1
1
1
2
0
1
0
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
0
2
2
2
0
1
1
1
1
2
1
1
1
1
1
2
0
1
1
0
0
1
1
0
1
3
2
1
1
2
0
2
1
1
1
1
0
1
1
2
1
2
1
2
1
0
1
2
1
1
2
1
3
2
0
0
0
1
1
2
2
1
2
1
1
1
1
1
0
1
2
1
0
0
1
1
1
1
1
1
2
1
2
1
2
0
0
1
1
2
0
1
1
1
0
1
1
1
0
0
1
1
1
1
1
2
1
1
1
1
0
1
1
1
0
1
1
1
1
0
2
2
1
1
2
1
0
1
0
0
0
2
0
0
1
0
1
0
0
1
1
1
1
0
0
1
0
2
1
1
1
1
2
0
1
1
0
1
1
1
1
2
0
2
0
1
1
2
2
1
1
1
1
2
0
1
2
0
1
0
0
1
1
2
1
1
0
1
0
1
1
1
1
2
1
1
2
2
3
2
1
1
0
0
1
1
1
2
1
1
1
0
1
0
2
1
2
1
2
2
1
1
2
1
2
1
1
2
1
1
1
1
3
0
0
1
1
1
0
1
1
1
1
1
1
0
2
0
1
0
1
2
2
1
1
0
0
2
2
1
1
1
1
1
1
2
1
1
0
1
2
1
1
0
1
1
1
2
1
2
0
1
1
1
1
2
2
1
2
0
2
1
1
1
0
1
1
1
1
2
0
1
1
0
0
1
0
1
1
1
0
2
2
0
2
0
1
0
1
1
1
2
1
1
1
1
1
1
1
1
0
0
1
1
2
1
1
0
1
1
4
1
1
1
2
1
0
1
0
1
0
1
0
1
1
1
2
1
0
2
1
0
1
1
2
1
2
0
1
0
1
1
1
2
1
1
1
1
2
1
2
0
1
0
1
0
0
3
1
2
0
1
2
2
1
2
1
0
1
2
1
2
1
2
2
1
0
1
1
2
1
1
1
0
1
2
1
2
0
1
1
1
1
0
1
1
2
1
1
1
2
1
0
1
0
2
0
0
1
4
0
2
1
1
1
1
1
1
1
0
1
2
2
2
2
1
0
0
1
1
2
1
2
1
2
0
2
1
2
1
1
2
1
0
0
0
2
1
0
0
1
0
1
1
1
0
1
1
1
2
1
1
1
0
0
1
1
2
0
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
2
0
2
1
2
1
2
0
1
1
1
0
1
1
0
1
0
0
1
0
1
2
2
1
1
1
0
0
1
1
0
1
0
2
2
0
1
1
1
0
1
2
1
2
1
1
1
1
0
1
1
1
0
1
1
1
1
2
0
1
1
1
1
1
0
1
1
1
1
1
1
1
1
0
1
0
1
1
1
1
0
0
0
0
3
1
0
1
2
0
2
0
2
1
1
1
1
0
1
1
1
1
1
1
0
1
1
1
1
1
2
1
2
1
2
2
1
1
2
3
1
0
1
1
1
2
1
1
1
1
1
2
2
1
2
1
0
1
1
1
1
0
1
2
1
2
2
0
1
1
1
1
1
2
1
1
1
1
2
2
2
1
0
1
2
1
0
1
1
0
1
1
1
2
1
0
0
2
1
2
1
1
0
2
1
1
0
1
0
1
0
1
1
2
1
1
2
1
0
1
2
1
0
1
2
0
0
1
1
1
2
0
1
1
1
0
0
2
2
1
1
1
2
0
1
1
0
1
0
2
0
1
2
1
1
1
2
2
0
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
2
0
1
1
1
1
1
0
1
1
1
1
1
0
1
2
1
0
1
1
1
1
1
1
1
2
1
1
0
1
1
0
1
2
0
1
2
1
1
1
0
1
1
2
0
2
2
2
2
0
1
1
2
0
2
2
1
1
2
1
2
1
2
1
0
2
1
1
1
2
1
1
1
1
0
1
1
2
1
2
1
2
0
2
1
1
1
2
2
1
2
1
1
1
1
1
1
2
2
1
2
1
0
2
1
1
1
2
1
1
1
1
2
0
0
2
2
1
2
1
1
1
2
1
2
0
2
0
2
1
1
3
0
1
0
1
0
2
1
1
1
1
2
2
1
2
0
1
2
1
1
0
1
2
0
1
1
1
0
0
1
2
0
1
2
1
2
2
1
1
0
2
1
1
0
1
2
1
0
1
1
0
1
1
1
1
1
0
0
0
0
1
1
2
1
2
1
1
1
1
1
4
0
1
1
1
0
1
2
1
2
0
1
1
1
1
1
2
0
0
1
1
1
1
1
1
1
0
0
1
1
1
1
0
2
1
1
1
1
1
1
1
1
1
2
1
1
0
1
2
0
1
1
1
1
1
1
1
1
0
0
1
1
1
1
1
1
1
1
0
1
2
1
1
1
0
1
0
1
2
0
1
1
1
0
2
2
2
1
1
2
0
2
2
2
1
1
1
0
0
1
1
0
1
1
1
1
1
1
1
2
1
1
2
1
1
2
1
2
0
1
2
1
1
1
1
1
1
1
0
1
0
2
1
1
2
1
1
1
1
0
1
1
1
2
2
2
2
1
1
2
2
1
1
1
2
2
1
1
1
1
2
1
1
1
2
2
1
1
1
1
2
1
2
1
1
0
0
2
2
1
1
1
2
0
1
1
1
2
1
2
1
0
1
1
1
0
1
1
2
1
1
1
2
1
2
2
0
1
2
2
1
1
1
1
1
2
0
2
0
0
1
1
2
1
2
0
1
0
2
1
1
1
3
1
1
1
1
0
2
1
1
1
1
1
0
2
1
1
1
3
1
1
2
0
0
2
0
1
0
1
0
1
1
2
0
1
0
0
1
1
1
0
1
1
1
1
0
1
1
2
1
1
1
1
2
1
0
1
0
0
2
2
1
1
2
0
1
2
0
1
2
2
2
1
2
1
1
0
1
0
0
2
1
1
0
1
1
1
1
1
0
0
0
1
1
1
1
1
0
0
1
1
1
1
2
0
0
1
2
1
1
1
1
2
1
1
1
1
1
1
1
0
0
1
2
1
0
1
1
1
1
1
1
2
2
1
2
2
0
1
1
2
1
1
1
1
0
2
0
0
1
1
1
0
2
1
2
0
0
0
0
1
1
1
1
1
1
1
1
1
1
1
0
0
0
1
1
1
1
1
0
2
1
1
1
1
1
0
1
1
1
3
1
1
0
2
1
1
1
1
0
1
1
1
1
1
0
1
2
1
2
0
1
1
2
2
1
0
0
1
1
2
1
1
1
0
0
2
0
2
2
1
1
0
1
0
2
2
0
2
1
1
1
1
0
2
0
1
1
1
3
1
3
1
1
1
1
2
2
0
0
1
1
0
1
1
1
1
2
1
2
2
0
1
2
0
2
2
1
1
3
2
2
0
1
0
1
1
1
1
1
1
0
0
1
1
2
2
0
1
0
1
1
2
1
3
1
2
2
0
0
1
1
1
0
0
3
1
1
1
0
0
1
1
1
2
2
1
2
1
2
1
0
2
0
2
1
0
0
0
2
1
1
2
1
0
2
1
1
1
1
1
0
1
1
1
1
2
1
2
2
1
0
1
1
1
0
2
0
1
1
1
1
1
0
1
1
1
1
2
0
2
1
1
2
1
1
1
1
0
1
2
1
4
2
2
1
2
1
1
0
2
1
1
1
1
2
1
2
1
1
1
1
1
0
2
1
1
1
1
2
1
1
0
1
0
0
1
1
1
1
0
1
0
1
1
1
1
0
0
1
1
1
1
2
2
1
1
0
0
1
2
2
0
1
2
0
2
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
0
1
2
2
1
1
0
1
1
2
1
2
2
1
1
1
1
1
2
1
1
2
1
1
2
2
2
2
1
2
2
1
2
1
1
2
1
1
1
1
1
1
3
0
0
0
1
0
1
1
2
1
0
2
1
1
0
1
1
0
1
1
2
2
0
1
1
1
1
1
2
1
1
0
1
1
0
1
1
2
1
1
1
0
1
1
0
2
1
1
1
1
1
1
1
2
2
2
0
1
0
1
1
1
1
2
2
1
2
1
1
1
2
1
1
1
1
0
2
1
1
1
1
0
1
1
2
1
1
1
3
1
1
2
2
2
2
1
1
1
0
0
1
0
1
2
0
1
1
2
1
1
0
0
1
1
1
1
2
1
1
1
0
1
2
0
2
0
2
1
1
1
1
2
1
2
0
2
0
2
2
0
1
1
2
2
1
1
1
0
1
1
1
1
2
2
2
2
2
1
1
2
2
1
1
0
0
1
2
2
2
1
1
1
1
2
1
1
1
0
1
1
0
1
1
0
0
2
1
0
1
1
1
1
1
2
1
1
0
1
1
1
1
0
2
1
2
1
1
2
1
1
1
0
0
1
2
1
2
1
1
0
1
1
1
1
2
2
0
2
0
2
0
2
1
1
1
2
1
1
2
0
1
1
1
1
0
0
1
1
1
0
2
1
1
1
1
1
1
1
2
1
0
1
1
0
1
1
1
1
2
1
1
1
1
1
2
1
1
2
1
2
1
1
0
0
1
1
1
0
1
2
1
1
1
2
1
2
2
1
2
1
1
0
1
0
1
1
1
2
1
1
2
1
0
2
1
1
2
0
2
0
1
0
2
1
1
2
1
1
0
1
2
2
1
1
1
1
0
2
0
2
2
1
0
2
0
1
2
1
1
2
1
2
0
1
1
2
1
2
1
0
1
1
1
2
1
0
1
1
1
0
1
0
0
0
2
0
1
0
0
1
1
2
1
1
1
1
1
0
1
1
2
1
1
2
2
1
2
2
1
1
1
1
1
1
1
2
1
2
2
2
1
1
0
2
0
1
2
1
1
1
2
0
0
0
2
1
2
1
0
1
1
1
0
1
0
1
2
1
2
1
2
1
0
1
1
1
1
0
1
0
2
1
1
2
1
1
0
1
0
0
0
1
0
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
2
1
0
2
2
1
1
2
0
1
2
1
0
1
1
1
2
0
2
1
2
1
1
1
2
2
3
1
1
0
0
2
1
0
1
2
1
1
0
0
2
1
2
1
1
1
1
1
2
1
1
1
1
2
1
1
2
0
2
1
0
4
0
0
2
1
1
1
1
0
0
1
1
0
1
1
2
1
1
1
1
0
1
2
1
1
2
1
1
1
0
1
1
1
1
1
1
1
1
0
0
1
0
1
1
1
2
1
0
4
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
0
0
0
0
1
0
1
2
1
0
1
2
1
0
1
1
0
0
1
2
1
2
1
1
2
0
2
2
2
1
2
0
1
1
1
1
0
2
1
1
1
1
0
1
1
2
1
0
1
1
1
1
1
2
2
2
2
0
1
1
1
1
2
1
1
1
0
2
1
0
1
0
1
2
2
1
3
1
1
2
1
2
2
1
1
1
1
3
0
2
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
0
1
1
1
2
2
1
1
1
1
1
1
1
2
1
2
0
1
0
1
1
2
1
1
1
1
1
2
2
0
1
1
0
2
1
1
0
1
1
1
0
1
1
0
1
2
0
2
1
1
1
2
0
1
2
2
1
1
1
0
1
2
1
1
1
1
1
1
0
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
0
0
0
2
2
1
1
1
1
1
1
1
3
1
1
1
2
1
1
0
1
1
1
2
2
1
0
1
1
1
1
1
1
0
1
1
1
2
2
1
2
1
1
0
2
0
1
0
1
2
1
0
2
1
1
2
1
2
2
2
2
1
0
2
1
1
2
2
2
1
2
1
0
1
1
1
1
1
1
1
1
1
0
0
1
0
0
1
2
1
2
1
1
1
1
2
1
0
2
1
0
2
2
1
2
0
1
0
1
1
1
0
2
1
1
2
1
1
2
1
1
2
1
0
2
2
0
0
1
2
2
0
1
1
0
1
2
0
2
1
2
1
1
2
1
2
1
0
1
2
0
1
1
1
1
2
1
2
1
1
2
1
2
1
2
2
1
1
2
2
0
1
1
1
1
2
1
1
1
0
1
2
2
1
2
2
1
1
0
1
1
1
1
1
0
0
1
1
1
1
1
2
1
1
1
0
0
1
1
2
1
1
1
2
1
1
1
1
1
1
0
2
2
1
1
0
1
0
1
1
1
1
1
1
0
1
1
1
2
0
0
0
0
1
2
1
1
0
1
1
1
1
2
2
1
0
1
1
1
1
2
2
2
1
1
1
1
2
1
0
2
0
0
2
0
2
1
1
1
1
1
2
1
1
2
1
1
1
2
2
1
1
0
1
1
1
3
1
1
1
2
2
1
1
3
1
1
2
1
2
2
1
0
1
1
0
0
1
1
2
1
1
1
0
0
0
1
1
2
1
1
2
0
1
2
2
2
2
3
1
2
0
2
1
0
1
1
1
1
0
1
2
0
2
1
1
0
1
1
1
1
0
1
0
1
0
1
1
2
1
2
1
2
0
2
1
0
1
0
1
1
2
1
2
1
1
2
1
1
1
1
1
2
0
1
0
1
2
1
0
1
0
1
1
1
2
0
2
1
1
2
2
1
3
2
1
1
1
1
1
1
0
1
1
2
1
1
0
0
1
1
1
1
1
1
2
2
0
1
1
1
2
1
0
1
0
1
2
1
1
1
2
2
2
1
1
1
1
1
2
0
2
2
1
2
1
0
1
1
1
1
1
2
1
2
0
1
2
2
1
1
1
1
1
2
1
0
2
1
1
0
1
0
2
1
2
1
2
2
2
1
0
1
2
1
0
1
2
1
0
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
0
1
1
2
2
1
1
0
1
1
1
1
1
0
1
0
0
0
1
0
1
0
1
1
0
0
0
1
0
1
1
1
0
1
0
1
1
1
1
1
2
0
1
2
2
1
2
0
1
0
1
0
1
0
2
1
3
2
2
1
1
1
1
1
0
0
2
1
1
1
2
2
1
1
1
1
0
1
0
1
2
1
0
0
1
2
2
1
1
0
1
1
3
1
1
2
2
1
1
2
1
1
2
2
0
1
1
1
1
0
1
2
0
0
0
0
1
1
2
4
1
1
0
1
2
1
2
1
1
1
2
1
1
1
1
2
0
2
1
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
0
0
2
1
2
1
2
2
1
0
1
1
1
1
2
2
2
1
1
1
1
1
1
2
1
1
0
1
1
1
1
2
1
1
2
0
1
0
1
2
0
1
1
0
1
0
1
1
3
1
2
2
1
1
0
1
1
2
1
1
2
2
1
1
1
0
1
1
0
0
0
0
0
0
2
0
2
0
2
1
1
0
1
2
1
2
1
0
1
0
1
1
1
5
2
2
1
1
0
0
2
1
1
1
2
1
0
2
2
1
1
0
0
1
1
2
1
1
0
1
1
2
1
0
1
1
1
1
2
1
2
1
0
2
2
1
2
0
1
1
3
1
1
1
2
1
1
0
2
2
0
0
1
1
1
2
0
1
3
2
1
0
1
2
1
1
2
1
1
1
1
0
0
0
1
1
2
1
1
0
1
1
2
2
1
1
1
1
1
2
2
0
1
1
1
2
1
1
1
2
1
2
0
1
0
1
1
1
1
1
1
2
1
2
2
1
1
2
2
1
2
2
2
1
1
1
2
1
1
1
1
1
2
1
1
2
1
3
2
1
1
2
1
1
0
1
1
1
1
0
3
1
1
1
0
3
2
1
1
4
2
0
0
1
1
1
1
1
1
2
0
1
0
0
1
1
2
1
1
2
2
1
0
1
1
1
1
1
0
2
2
0
3
2
2
1
2
1
1
2
1
1
1
1
1
1
0
1
1
1
2
1
1
1
1
1
0
1
1
0
2
2
1
2
1
1
0
2
0
1
1
0
2
1
2
1
1
0
1
1
1
0
1
1
1
1
1
0
1
2
1
1
2
0
1
1
1
2
1
1
1
1
1
1
1
1
1
0
1
1
0
0
1
1
1
1
1
1
1
2
1
0
1
0
1
1
1
1
1
1
1
0
1
0
1
1
1
1
0
0
1
1
1
1
2
1
1
1
1
1
2
0
1
1
2
0
1
2
1
1
0
0
2
2
1
0
2
1
1
0
1
2
2
2
0
1
1
1
1
1
2
1
1
2
2
1
2
1
0
1
0
2
0
1
1
1
2
2
1
1
1
0
2
1
1
1
1
1
1
1
0
2
0
0
1
3
1
1
1
1
0
0
0
1
1
1
1
2
0
1
1
1
1
1
1
1
1
0
2
0
1
0
1
1
2
2
2
0
1
1
2
0
1
0
1
0
2
1
1
1
1
1
1
0
1
1
1
1
2
2
1
1
1
2
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
0
1
0
1
0
1
2
2
1
2
0
1
2
3
2
0
2
1
0
1
0
1
1
1
2
3
1
1
2
2
1
1
0
1
1
1
1
2
2
2
2
2
1
1
1
2
0
1
1
2
1
1
0
0
1
1
1
2
0
0
2
2
2
1
1
1
1
2
2
2
1
1
2
2
2
2
0
1
1
1
1
1
1
2
1
1
1
1
3
1
1
0
0
0
1
2
0
1
2
1
1
1
2
1
0
1
1
1
0
2
1
1
3
2
1
1
1
0
2
1
2
0
1
1
2
1
1
1
0
0
1
0
1
0
1
1
2
0
1
0
1
1
1
0
2
1
1
1
1
1
1
1
1
1
0
0
2
1
2
1
2
1
1
0
2
1
0
1
1
2
1
1
1
1
2
2
1
1
1
1
1
2
1
2
2
2
1
1
1
1
1
2
1
1
1
1
1
1
0
2
2
2
0
1
1
1
3
0
2
1
1
0
2
1
1
1
0
0
2
1
1
1
2
1
3
2
2
1
1
0
1
2
1
0
1
0
0
2
1
0
2
0
0
1
1
2
1
1
3
0
1
1
0
1
2
0
1
1
1
0
1
1
2
1
1
0
1
2
2
1
1
2
1
1
1
1
1
2
2
2
1
2
1
2
2
1
4
1
1
2
1
0
3
1
0
2
2
1
1
2
2
2
1
2
2
1
1
1
1
1
1
0
0
2
2
0
1
1
1
2
1
2
1
0
0
1
0
1
1
0
1
1
2
1
1
2
1
1
2
0
1
0
0
1
2
1
1
2
0
2
1
1
1
2
1
0
1
0
1
0
1
1
1
0
0
1
2
2
1
1
1
1
1
0
2
2
2
0
1
1
1
2
1
1
1
1
0
0
1
1
1
1
2
1
0
2
1
1
2
0
2
1
1
0
0
1
0
1
0
2
1
1
2
1
1
1
1
2
0
1
0
1
1
0
2
2
0
1
1
0
0
0
2
1
0
0
0
1
1
2
1
0
1
0
0
1
1
1
1
2
0
1
1
1
1
0
2
1
0
1
1
2
1
0
1
1
1
8
2
2
1
1
1
2
1
1
2
0
0
1
0
1
1
2
1
0
0
0
2
1
0
0
1
1
1
0
2
1
2
1
1
1
1
0
1
0
0
1
2
0
1
0
0
2
0
1
1
4
2
2
1
0
1
1
2
2
0
1
1
2
1
1
1
1
1
0
2
2
2
1
1
1
1
1
2
1
2
2
2
2
0
2
2
1
1
1
0
1
1
1
1
1
1
1
0
1
2
1
1
1
1
1
0
1
1
2
1
1
1
1
1
0
1
1
2
0
0
2
1
1
2
1
0
2
2
0
1
0
1
1
1
1
1
2
2
1
1
2
1
1
2
1
0
1
1
1
1
2
2
2
1
2
1
2
1
1
1
1
2
2
1
1
0
1
1
1
2
1
2
1
2
0
1
2
1
2
1
1
1
1
2
0
1
0
1
1
2
1
2
1
1
1
1
1
1
1
1
3
1
1
0
2
2
1
1
2
0
0
2
1
1
1
0
1
1
1
0
0
0
2
1
1
1
1
3
1
1
1
2
0
1
0
1
1
3
1
1
1
0
0
2
1
1
1
1
1
0
0
1
1
0
1
0
1
2
1
3
1
2
1
2
1
1
1
1
0
0
1
0
2
1
2
1
1
0
0
0
1
0
1
1
0
1
1
0
0
1
2
1
0
2
0
1
2
1
1
0
1
2
2
1
1
1
0
0
0
0
1
1
1
1
0
0
2
0
1
2
1
1
0
1
0
2
1
1
0
3
1
2
1
1
2
1
1
3
2
2
1
1
1
2
2
1
1
1
1
1
2
0
1
1
0
1
1
1
2
0
0
2
2
1
2
0
0
2
1
1
2
0
1
2
1
0
1
1
1
1
0
0
1
1
1
1
1
1
0
2
0
1
2
2
0
2
2
1
1
1
2
1
2
0
1
1
1
2
1
1
1
1
1
1
1
2
0
1
0
1
0
1
2
0
1
1
1
1
2
0
1
1
1
1
1
1
0
1
0
1
0
3
1
1
1
0
2
2
1
1
1
2
1
0
0
1
1
1
1
1
0
2
1
1
2
1
1
1
1
1
2
2
2
2
0
0
1
0
1
1
0
1
1
1
1
1
1
2
1
2
1
2
1
0
2
1
1
1
0
1
1
0
2
0
0
1
1
1
0
2
1
0
0
2
1
1
1
2
1
1
1
0
2
0
1
1
1
1
2
2
1
0
1
1
1
1
1
1
1
1
1
1
1
2
1
0
1
2
1
1
1
1
1
1
1
1
3
2
1
0
1
0
0
0
0
1
2
1
2
1
1
1
1
0
1
1
1
1
1
0
1
1
2
1
1
1
1
2
1
2
2
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
2
0
1
0
2
1
1
1
2
1
0
0
0
1
1
1
0
2
1
1
1
1
2
1
1
1
0
1
0
1
1
1
1
2
0
2
0
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
0
2
2
2
2
2
1
1
2
2
1
1
1
1
1
0
1
2
1
3
1
1
1
1
2
0
1
1
1
1
4
1
1
2
2
2
1
2
2
0
1
0
0
1
2
2
1
0
1
2
1
1
0
0
1
1
1
2
1
1
1
1
2
1
2
0
1
2
1
1
2
2
1
2
1
1
2
1
1
1
1
1
2
2
1
0
2
1
0
1
0
1
1
1
0
2
1
2
1
2
0
1
0
1
2
1
2
0
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
2
0
1
2
0
1
1
1
2
1
1
1
1
0
2
1
1
0
1
1
0
2
1
1
1
0
1
1
1
0
1
1
0
1
1
1
1
1
1
2
1
0
2
1
0
2
1
1
1
2
0
2
0
2
1
2
0
2
0
1
1
1
2
1
1
1
1
0
2
1
1
2
2
1
5
0
1
1
0
1
2
2
0
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
2
0
1
1
2
1
0
1
1
1
1
1
0
1
1
0
1
0
1
1
2
2
1
2
1
2
1
1
1
1
2
1
1
2
2
0
2
2
0
1
1
1
0
1
1
2
1
1
0
1
1
1
1
1
1
2
0
2
2
0
0
1
1
1
1
1
2
0
1
1
0
0
0
2
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
3
1
0
0
1
2
2
0
1
1
2
1
2
0
1
1
2
1
1
0
0
0
2
1
1
1
2
1
1
1
1
0
0
1
1
2
1
0
0
1
2
1
1
2
1
0
1
2
2
1
2
1
1
0
0
1
1
2
0
1
0
2
1
0
1
2
1
1
0
1
0
2
1
1
0
3
1
2
1
0
0
1
1
1
2
1
2
0
2
1
0
2
1
0
1
1
0
0
1
0
1
1
2
0
2
1
1
1
0
0
3
1
1
1
1
2
0
1
1
1
0
1
1
2
1
2
2
1
0
2
2
2
1
1
0
1
1
0
0
1
1
1
1
1
1
0
1
1
1
1
0
0
1
1
2
0
1
1
1
0
1
2
0
1
1
1
2
2
1
1
0
2
0
2
0
0
1
2
1
0
1
0
1
1
1
1
1
0
2
2
2
0
2
1
1
0
0
1
1
2
1
0
1
1
1
1
1
1
1
0
1
0
3
2
0
1
1
2
1
2
1
1
3
2
2
1
1
0
1
1
2
1
1
2
0
1
1
0
2
0
0
1
2
1
0
1
1
1
1
1
0
1
2
1
0
1
1
1
1
1
2
1
1
1
1
1
1
1
2
0
1
1
1
1
0
1
1
2
0
1
1
0
1
2
1
2
2
0
2
1
2
1
1
1
1
0
2
1
0
1
2
1
1
2
2
1
1
1
2
1
1
0
1
2
2
0
1
1
2
1
2
0
1
1
1
2
1
1
1
1
1
2
2
1
1
1
1
1
0
3
1
1
0
1
1
2
0
0
1
2
0
2
1
1
1
1
2
3
1
2
3
1
1
2
0
2
1
2
1
1
1
0
1
0
0
0
2
1
1
1
0
1
1
1
1
1
1
1
1
1
1
0
0
2
1
2
1
1
1
1
0
1
1
1
1
2
0
2
1
1
2
1
1
0
2
1
1
1
2
1
1
1
1
3
2
1
2
0
0
1
2
1
2
1
2
1
1
2
1
1
0
1
0
1
1
1
1
1
1
2
0
2
0
1
1
2
1
1
0
0
1
1
0
2
3
1
2
1
0
1
1
1
1
1
2
1
2
1
1
0
1
1
1
1
2
1
1
2
1
1
1
1
2
1
1
1
1
2
1
0
1
0
0
0
1
1
1
2
0
1
1
1
2
1
2
1
0
0
1
0
0
0
1
1
0
1
1
1
1
1
1
1
1
0
1
2
1
1
0
1
0
1
1
0
1
2
1
1
1
0
0
2
2
0
0
2
1
1
1
1
1
1
1
1
1
1
1
0
1
1
2
1
0
2
2
1
1
1
2
2
2
0
1
2
1
1
0
1
0
1
2
2
1
1
1
1
2
2
1
2
1
1
1
0
2
1
0
2
1
1
0
1
0
1
0
1
1
2
1
1
0
0
1
1
1
0
1
1
1
0
0
1
1
1
1
0
2
0
0
1
0
2
1
2
1
1
0
1
2
0
2
1
1
2
0
0
0
0
0
1
1
2
0
1
1
2
0
1
1
1
0
1
1
1
2
1
0
0
1
2
1
1
2
1
1
1
1
1
1
1
0
1
0
0
2
1
0
2
2
1
0
1
0
1
0
1
1
0
1
1
0
0
1
1
2
1
2
1
1
1
2
2
1
2
1
1
1
0
1
2
0
1
2
0
1
0
1
1
2
2
0
1
1
2
1
0
1
1
0
2
0
2
1
1
3
1
1
4
0
1
0
1
1
0
0
1
1
1
0
1
1
2
1
2
1
1
0
1
1
2
0
2
1
1
1
1
0
1
2
1
2
1
0
0
1
0
0
1
1
0
2
0
1
1
0
2
1
1
1
2
1
1
0
2
2
0
0
1
1
1
1
1
2
1
1
1
1
2
0
2
0
2
1
2
1
1
0
0
1
1
1
0
2
2
1
0
0
1
1
2
0
1
1
1
0
2
1
1
1
1
2
2
1
0
1
1
1
1
2
1
2
1
0
2
1
2
1
1
1
0
1
2
4
0
1
1
1
1
1
2
1
1
1
0
1
1
1
1
2
2
1
1
1
0
1
2
1
1
0
2
1
1
0
1
1
0
2
0
0
2
1
1
0
1
1
1
2
1
5
2
2
1
1
1
1
1
2
0
2
1
1
0
0
2
1
2
1
1
1
1
1
0
1
1
1
2
2
2
2
1
0
1
0
1
0
0
1
0
2
0
1
2
0
1
1
1
0
1
1
1
2
1
1
0
1
0
1
1
2
1
1
5
0
1
2
1
2
1
2
1
2
0
0
0
1
1
0
1
1
2
1
0
1
1
1
2
1
1
1
1
1
0
2
0
1
1
1
1
1
1
2
2
1
2
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
0
1
1
0
2
2
1
0
1
1
0
1
1
1
1
1
1
1
0
0
1
1
2
1
2
1
0
1
0
2
1
1
1
1
1
2
2
1
1
3
0
1
2
0
1
1
1
2
1
0
1
2
1
0
2
1
2
2
1
1
2
1
1
2
2
1
3
0
1
0
0
2
1
1
1
2
1
0
1
1
2
1
1
0
1
1
1
2
2
1
0
1
2
1
1
1
2
1
1
0
2
1
2
1
1
1
1
1
0
2
1
1
1
0
2
2
2
1
1
2
1
1
1
0
1
2
0
0
1
1
1
1
1
0
1
1
2
1
1
1
2
1
1
1
1
1
2
1
1
0
1
1
1
1
1
1
1
0
1
1
1
1
1
0
0
0
0
1
1
1
1
1
1
2
1
0
1
0
0
1
0
1
2
1
0
1
2
0
1
0
2
1
2
1
1
1
1
0
0
0
1
0
2
1
2
1
1
0
0
0
0
1
1
0
1
1
2
1
1
1
1
1
2
1
1
1
0
1
1
0
2
1
2
2
1
1
2
1
1
0
1
2
2
1
1
2
1
1
1
1
0
0
0
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
1
0
1
0
0
1
0
2
1
1
2
0
0
0
1
0
1
2
2
2
1
2
1
1
0
2
2
2
1
0
1
1
1
2
1
2
1
0
2
1
2
1
2
1
2
2
2
1
1
1
1
2
1
1
2
1
2
1
0
0
0
1
0
1
1
1
1
1
0
1
1
1
1
1
1
0
1
1
0
1
0
1
2
1
2
1
6
1
2
0
2
2
2
1
1
1
1
1
2
2
0
1
1
1
2
1
1
2
2
1
1
1
1
0
1
1
2
1
2
1
0
2
0
1
1
1
0
2
1
1
1
1
0
2
1
2
2
1
1
2
0
0
1
1
1
0
1
2
0
1
1
0
1
0
1
1
1
0
1
1
1
1
1
0
1
1
2
0
1
1
1
2
1
3
1
1
0
0
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
0
1
0
1
3
1
0
2
1
1
1
1
0
1
1
0
1
0
2
2
1
1
2
1
2
1
0
1
2
2
1
0
1
1
1
2
1
2
2
1
1
2
1
1
2
1
2
1
1
1
1
1
2
1
0
2
0
2
1
1
2
1
1
0
2
2
1
1
1
1
1
0
1
1
1
1
1
0
1
1
1
1
1
0
0
1
1
1
1
1
1
2
2
1
1
1
2
0
0
2
2
1
1
1
2
2
0
1
1
0
2
1
0
1
1
0
1
2
2
1
0
1
1
0
2
1
1
1
1
0
1
1
2
0
1
2
0
1
0
0
1
2
2
1
1
1
2
1
1
1
2
2
0
1
2
0
1
2
1
0
0
2
1
1
0
0
1
0
2
1
1
1
2
1
1
2
2
1
0
1
1
2
2
2
1
2
1
1
1
1
1
1
0
1
1
0
1
2
2
1
1
0
1
1
1
1
0
1
1
1
1
1
1
1
0
0
0
2
1
2
2
1
2
1
2
1
1
2
2
1
1
1
0
0
2
1
3
1
1
1
0
1
1
1
2
1
1
1
1
1
1
0
2
1
2
2
2
1
0
0
1
1
0
0
0
1
1
1
2
1
1
1
1
0
2
0
1
1
1
1
2
1
2
1
0
1
2
1
0
1
1
1
1
2
1
0
1
1
1
1
2
2
2
1
1
1
2
0
2
1
1
2
1
2
1
0
1
1
1
0
1
0
1
0
2
1
1
1
1
2
0
2
2
0
1
2
1
2
1
1
1
2
2
0
2
1
0
0
1
1
1
1
3
0
0
1
1
2
1
1
1
1
0
0
2
1
1
0
1
1
1
0
1
0
2
0
1
0
1
0
1
1
0
1
1
1
1
1
1
1
1
2
1
1
1
0
0
2
1
1
0
1
1
1
2
0
1
0
1
0
0
1
2
1
1
2
2
1
2
0
2
1
1
2
2
1
1
1
1
0
0
0
0
1
2
0
0
2
1
1
1
0
2
2
2
0
2
1
1
0
1
1
0
0
2
1
1
1
1
2
0
2
1
1
1
0
1
2
2
2
1
0
0
2
1
2
0
2
1
1
1
1
2
1
1
0
0
0
2
1
1
1
2
1
2
0
1
0
0
0
0
1
2
2
1
2
1
2
0
1
1
1
1
1
1
0
0
1
1
2
0
0
1
1
0
2
1
1
0
1
2
0
1
0
1
1
1
2
1
1
1
2
2
1
1
0
1
1
1
1
2
1
1
1
1
1
0
1
0
0
1
1
0
1
1
2
1
1
1
2
1
2
1
2
1
1
1
0
1
1
2
1
0
0
1
1
1
2
1
1
1
2
2
1
1
2
1
2
0
0
1
1
1
1
1
1
2
0
1
1
1
0
1
0
1
0
0
1
1
1
2
1
1
1
0
1
0
2
1
1
1
2
2
2
1
1
0
0
2
1
1
1
1
0
2
1
2
0
0
1
1
1
2
2
2
1
0
1
2
1
0
0
0
0
1
2
2
1
1
1
2
2
1
2
1
1
1
1
1
0
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
0
1
2
2
2
2
0
1
2
1
1
1
1
0
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
0
1
1
0
1
1
1
1
2
3
1
1
1
2
1
1
2
0
2
1
1
1
2
2
2
1
1
1
2
1
0
1
2
0
1
2
2
1
1
1
2
1
1
1
1
2
1
2
1
0
1
1
1
3
1
0
2
1
1
2
2
2
1
1
2
0
1
0
1
1
0
1
0
1
1
1
2
1
0
1
0
1
1
1
1
2
1
0
0
1
2
1
1
1
1
1
1
0
4
1
0
1
1
1
0
1
1
2
0
1
1
1
0
2
2
2
1
1
2
0
1
1
2
1
1
0
2
1
2
1
1
1
1
0
0
0
1
2
1
1
0
1
0
2
2
1
2
2
2
1
1
1
0
1
0
1
1
1
2
1
0
1
0
2
1
2
2
1
1
1
2
1
0
0
4
0
1
3
2
1
2
1
2
1
2
1
1
1
2
1
1
1
1
0
0
2
2
1
1
1
1
2
2
1
2
1
1
2
1
0
1
1
1
2
1
0
0
2
1
1
1
2
1
1
1
1
0
1
2
1
1
0
1
1
1
0
2
2
1
2
1
3
0
1
1
2
1
2
2
1
1
1
2
1
1
1
0
1
1
2
1
1
2
0
0
0
1
2
0
1
1
1
1
0
0
2
1
0
1
2
0
2
1
0
0
1
1
0
2
1
1
0
1
0
1
1
1
2
2
0
2
2
1
1
0
2
1
1
0
1
0
2
1
1
1
1
2
1
0
1
1
1
0
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
2
1
0
1
0
1
1
1
0
0
1
1
1
1
0
1
1
1
1
2
1
0
1
1
0
2
1
2
2
1
0
3
0
1
1
1
1
2
2
2
0
1
2
1
1
2
0
2
1
0
1
1
0
1
1
1
1
1
1
0
1
1
2
1
2
1
1
0
2
1
2
2
1
1
1
1
1
1
1
0
1
0
1
0
1
2
2
2
0
2
2
1
1
1
0
0
1
1
0
1
1
1
1
1
1
1
2
2
1
1
1
0
1
2
2
0
1
0
1
0
1
2
0
0
2
1
1
1
1
1
1
0
2
0
1
0
1
1
0
1
1
1
2
2
1
1
2
0
1
1
1
1
1
1
1
1
0
0
1
2
1
1
1
0
2
0
0
1
0
1
2
1
1
1
1
1
1
2
1
1
1
2
2
1
2
1
0
1
0
2
0
1
2
1
0
1
1
2
2
0
0
2
1
2
2
2
2
2
0
1
1
1
1
1
2
1
1
1
0
1
1
2
0
1
2
1
1
1
1
0
1
0
1
1
2
0
2
0
0
1
1
0
1
1
1
0
1
1
1
1
1
2
1
2
0
0
1
1
0
1
1
2
1
1
0
1
1
1
1
1
1
1
1
2
0
0
2
0
2
1
1
0
0
1
1
1
1
0
1
1
1
0
1
1
0
0
1
2
2
2
0
1
0
2
1
1
1
1
0
1
2
1
1
1
2
1
2
1
1
1
1
1
0
1
1
1
2
0
1
2
2
1
1
1
1
0
2
2
2
1
1
1
1
1
0
1
2
1
1
1
1
2
2
1
1
1
2
0
2
1
1
1
1
0
1
1
2
1
1
1
1
1
1
2
0
2
2
1
1
1
2
1
1
2
1
1
1
1
0
0
1
1
1
1
1
1
1
0
2
0
0
1
1
2
1
2
1
2
1
1
2
1
2
1
2
2
1
1
0
2
2
2
1
1
2
1
2
2
2
0
2
1
0
1
2
1
1
1
1
1
1
1
0
1
2
1
2
2
1
2
2
1
2
2
2
1
2
1
1
1
1
2
0
1
1
2
1
1
1
1
1
1
1
0
0
1
1
0
2
1
1
0
2
1
1
2
2
2
2
2
1
2
0
1
0
2
0
1
0
1
1
2
0
2
1
1
1
1
1
1
0
2
2
0
0
1
1
0
0
0
0
1
1
1
1
1
1
2
2
1
2
2
1
1
1
1
1
1
0
1
0
1
1
2
0
2
1
2
1
0
0
1
1
0
2
2
1
2
0
2
1
1
2
0
1
1
0
1
1
1
1
1
1
1
1
0
2
2
0
1
1
2
1
0
3
2
1
1
1
2
0
0
2
2
2
1
2
2
1
1
2
0
0
1
1
1
2
2
1
0
2
1
1
1
0
0
1
2
0
0
1
0
1
2
1
2
0
0
1
1
2
0
1
1
0
0
1
1
0
0
1
1
1
1
0
0
1
0
3
2
2
1
3
2
0
2
1
1
0
2
0
1
2
2
2
0
1
1
1
1
3
2
1
1
0
0
0
1
1
1
1
1
1
1
1
1
0
1
2
1
2
0
1
1
1
1
1
2
2
2
1
1
1
2
1
1
2
1
0
1
2
0
1
1
1
1
1
1
1
1
0
0
1
1
2
2
0
1
1
1
0
2
1
1
0
1
2
0
2
1
1
1
1
1
1
2
1
1
1
1
0
0
2
0
0
1
0
1
1
1
2
0
1
1
2
2
2
2
1
0
2
0
2
1
1
1
1
2
0
0
1
2
2
0
0
1
2
1
2
2
2
1
1
1
1
1
1
2
0
1
1
1
2
0
1
0
1
2
2
1
1
2
0
2
0
2
1
1
2
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
1
1
0
1
1
1
2
2
1
0
3
1
1
1
1
1
2
2
1
2
1
1
1
2
1
2
0
1
1
2
2
0
0
0
1
1
1
1
1
2
1
1
1
1
1
1
3
2
1
0
1
1
1
2
0
1
1
1
2
0
1
1
1
1
0
1
1
2
2
1
1
0
1
0
2
1
1
1
2
0
1
1
1
1
1
0
1
2
1
1
1
1
1
0
0
2
0
1
1
2
1
1
0
2
1
1
1
1
2
1
1
1
0
1
0
1
2
2
1
2
1
1
1
1
1
1
0
1
1
2
0
2
1
1
1
0
0
0
1
2
0
2
1
1
1
1
0
1
1
2
0
0
1
1
0
0
1
2
2
1
0
1
1
1
1
1
0
0
1
1
1
0
1
2
1
0
1
0
1
1
0
1
1
0
1
1
2
2
1
1
1
1
1
1
3
1
1
0
0
1
2
1
2
1
2
1
2
2
0
1
1
0
1
2
1
2
1
1
0
1
1
0
1
0
0
2
0
2
2
0
1
1
1
0
0
1
1
1
2
1
1
1
0
0
1
2
0
1
2
1
2
0
1
1
1
0
0
2
2
1
0
0
1
1
1
1
0
1
1
1
3
0
1
1
1
2
0
0
1
2
0
1
1
1
0
2
2
0
1
2
1
0
1
1
1
1
0
1
1
1
1
1
1
2
1
1
0
2
1
0
1
1
1
2
1
0
1
1
0
0
1
1
1
1
1
2
1
2
1
1
0
1
1
1
0
1
0
1
1
0
0
1
2
2
1
0
0
0
1
1
1
1
0
1
0
1
1
1
1
1
2
2
1
0
1
1
1
1
0
1
1
1
1
1
2
0
0
1
0
1
1
1
1
1
1
2
2
2
1
1
2
1
1
0
1
2
2
1
2
2
1
3
1
1
2
1
3
0
1
0
0
1
1
2
1
1
1
2
0
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
2
0
1
1
0
0
1
1
2
1
0
1
1
0
2
0
1
2
0
1
2
1
2
1
0
1
1
1
2
1
1
1
0
0
2
1
1
1
1
1
1
0
0
1
1
1
2
1
1
0
1
2
2
1
1
0
0
1
2
2
2
1
2
1
2
2
1
1
2
1
1
1
0
0
1
1
0
0
2
1
0
2
0
1
1
0
1
1
2
1
0
1
1
0
2
2
1
1
2
0
1
1
1
3
1
1
0
0
1
1
2
1
1
1
0
1
1
2
0
0
1
2
2
0
1
1
1
1
0
1
1
1
0
1
0
1
1
2
2
2
1
2
1
1
1
0
1
1
1
1
1
1
0
1
1
1
1
1
1
0
1
2
1
2
2
2
1
2
1
2
1
2
1
2
1
1
2
2
2
1
1
1
1
0
1
1
1
1
1
0
2
1
2
1
0
1
1
1
1
1
1
1
2
2
1
1
2
1
1
0
2
1
0
1
1
1
1
0
0
0
1
1
1
0
1
1
1
1
2
3
1
2
2
1
2
0
1
1
2
1
1
1
1
2
2
0
1
1
1
2
2
1
1
0
1
0
1
1
2
1
0
1
2
2
1
1
1
2
0
1
2
2
2
1
2
0
1
1
0
1
2
2
1
0
0
1
2
0
0
1
1
0
1
2
0
2
1
1
2
1
1
1
1
1
2
0
1
1
2
2
1
1
1
1
2
1
2
0
1
1
1
1
1
1
1
1
2
0
1
1
1
1
2
0
1
2
1
1
1
0
1
2
1
1
1
1
2
0
1
1
2
1
2
0
1
1
1
1
1
0
1
1
2
2
1
3
0
2
1
1
2
1
0
1
2
1
2
1
1
1
1
0
1
1
1
1
1
0
1
1
1
1
1
2
1
1
1
2
1
2
1
2
2
1
2
4
2
0
1
2
1
1
1
2
2
0
2
1
0
2
2
1
1
2
1
4
1
0
0
1
2
2
0
1
0
1
0
2
2
2
1
1
1
1
0
2
2
2
1
0
1
1
1
1
1
1
1
1
2
2
2
0
2
1
1
1
1
1
1
0
1
1
1
1
2
0
2
1
1
0
1
1
1
1
2
1
1
1
1
0
2
0
1
1
1
0
1
2
2
2
2
1
1
0
1
1
0
1
1
1
2
2
2
2
0
1
1
0
1
1
2
3
2
2
1
0
0
1
1
1
1
0
1
2
1
2
2
1
1
1
0
1
0
1
2
2
1
0
2
1
0
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
3
1
2
1
1
0
2
1
0
1
0
1
1
2
0
1
0
0
1
2
1
4
1
1
2
0
1
1
0
1
1
1
2
1
1
1
1
1
2
1
2
1
2
1
2
1
0
0
0
0
2
1
2
1
1
1
1
0
1
1
1
2
1
1
1
0
2
1
2
1
2
1
0
2
1
1
2
0
1
1
1
1
2
2
0
1
1
2
0
0
0
2
2
1
1
1
1
0
1
1
0
1
1
1
0
2
0
2
1
1
1
0
2
1
1
0
0
0
1
2
1
1
0
1
0
2
1
2
1
1
1
2
1
1
1
2
2
2
1
0
0
0
1
2
2
0
1
2
1
1
1
1
1
1
1
2
2
2
1
2
0
1
0
1
2
1
1
1
0
0
4
0
0
2
2
2
2
1
1
1
1
2
0
0
0
1
1
1
2
1
2
0
1
1
2
1
0
1
2
0
1
1
2
0
0
1
2
0
0
1
1
0
1
1
1
0
1
1
1
1
1
1
0
1
2
0
1
1
1
1
2
1
4
2
1
1
1
0
2
1
1
1
0
0
1
2
2
1
0
0
1
1
1
2
2
1
1
2
1
2
1
0
1
0
1
1
1
0
1
1
2
1
0
2
1
1
1
2
0
0
1
0
0
1
1
1
1
1
0
1
1
2
1
1
1
1
1
1
2
4
0
2
0
0
1
1
1
2
1
2
0
1
2
1
2
2
2
0
2
2
1
1
1
1
1
1
1
1
1
1
1
1
0
2
1
1
1
1
1
1
2
2
1
0
0
0
1
1
0
0
1
0
1
1
2
1
1
3
1
2
2
0
1
1
2
3
2
1
1
2
1
1
1
1
2
0
1
0
2
1
0
0
2
2
1
0
0
1
0
2
2
0
1
1
1
1
0
2
2
1
1
2
1
1
1
2
1
2
1
0
1
2
0
1
1
1
1
1
2
1
7
2
2
1
0
2
1
1
0
1
1
2
1
1
1
0
2
1
2
1
0
1
1
0
1
1
0
2
2
2
1
1
2
0
1
1
2
0
0
0
1
3
0
0
1
1
1
1
1
1
1
2
1
1
1
1
0
1
1
2
1
0
1
0
2
0
1
1
2
1
0
1
0
1
2
0
1
2
1
1
0
1
1
1
2
1
1
1
0
0
1
1
2
1
1
1
2
1
1
0
4
0
1
2
1
1
2
1
1
2
0
1
1
1
1
1
2
1
0
1
1
1
1
2
1
0
0
1
1
1
1
1
2
2
1
1
1
1
1
0
1
2
1
1
1
1
1
1
1
0
1
1
0
0
1
1
1
2
1
1
0
0
2
1
1
1
1
0
0
2
1
1
1
1
1
1
1
1
0
1
2
2
1
1
2
0
2
2
1
1
1
1
2
1
0
0
0
1
0
1
2
1
1
1
2
1
2
1
1
0
2
0
1
1
1
1
0
1
2
0
0
2
0
1
1
1
0
1
1
1
1
0
1
1
2
1
1
1
1
2
0
0
0
1
1
0
2
0
2
1
2
1
0
1
2
1
2
2
1
0
2
1
1
1
2
0
1
0
2
0
2
1
2
2
1
1
2
1
1
2
0
0
2
0
0
0
1
1
2
1
1
1
0
2
1
1
2
2
0
2
1
0
2
2
1
0
1
0
2
1
1
2
2
1
0
1
1
0
3
1
0
0
2
2
0
1
1
1
0
0
1
1
0
2
3
2
2
1
2
0
0
1
1
0
1
1
1
1
1
0
1
1
1
1
1
1
1
1
0
2
2
0
0
2
1
2
0
2
2
1
2
2
1
2
1
1
0
0
1
1
1
0
1
1
2
0
2
1
2
1
2
1
1
2
1
0
0
1
0
1
1
2
1
2
1
2
1
2
0
2
1
2
0
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
2
1
1
1
2
0
1
1
0
0
1
0
2
0
1
0
2
1
1
2
1
0
1
2
1
0
1
2
0
2
1
1
1
1
0
2
2
0
0
1
1
1
2
0
1
1
0
1
0
0
0
1
1
0
1
0
1
1
2
1
1
0
1
2
0
0
2
0
0
1
1
2
3
0
0
2
2
1
2
0
2
0
1
0
2
0
1
1
1
0
1
1
1
1
1
1
1
0
1
0
2
1
2
0
1
1
2
1
1
1
2
2
1
2
1
2
1
0
1
1
0
1
2
0
2
2
2
0
0
2
1
1
1
1
1
1
1
1
0
1
1
0
1
0
1
0
7
1
0
1
1
2
1
1
1
2
1
0
1
1
1
1
1
0
1
2
1
2
2
0
0
1
1
1
1
0
1
2
0
1
1
1
2
1
1
1
1
1
1
0
2
1
1
1
2
1
1
0
2
1
2
1
1
1
1
1
1
1
1
1
1
1
0
2
1
1
2
1
0
0
1
0
2
1
1
1
1
2
1
1
2
2
1
1
1
1
2
1
1
1
0
2
2
2
2
1
1
1
0
1
1
1
1
2
1
1
2
1
1
1
1
2
1
1
0
1
1
2
0
2
1
1
1
1
2
2
1
1
1
1
1
1
0
1
0
2
1
1
0
2
2
1
2
0
0
0
1
1
1
2
0
0
2
2
1
0
2
2
1
1
1
2
1
1
1
1
1
0
1
1
1
0
1
1
1
1
1
2
0
2
1
1
1
1
1
2
2
2
1
1
1
1
0
1
1
0
1
2
0
1
2
0
1
1
1
1
1
0
1
0
1
1
1
1
2
1
0
2
1
1
1
1
0
1
2
2
2
1
0
2
2
1
1
1
1
1
1
2
1
0
1
2
1
0
2
1
1
0
1
1
1
1
1
1
1
1
1
0
1
0
1
1
0
1
1
2
0
2
3
2
2
0
1
0
2
0
1
1
1
2
2
1
0
2
2
2
2
1
1
1
1
0
1
0
1
1
1
2
0
1
2
2
1
1
0
2
1
1
0
1
1
2
1
2
0
0
1
0
0
3
1
0
0
0
1
2
1
1
1
1
1
2
2
1
1
0
1
1
1
2
1
0
2
1
2
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
2
1
0
0
2
1
0
1
1
1
1
1
0
0
2
0
1
2
1
1
1
1
0
0
2
1
1
1
1
1
1
1
1
1
0
1
1
0
2
1
2
2
1
1
1
2
0
2
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
2
2
1
1
1
2
1
2
1
1
2
0
2
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
0
1
0
0
1
1
1
0
1
1
1
1
2
2
1
2
1
1
2
1
3
1
1
1
1
1
1
1
1
1
1
1
1
0
2
1
1
1
2
0
0
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
0
1
1
0
1
1
1
0
1
2
0
1
1
0
2
1
1
1
1
1
0
1
1
2
0
2
0
2
1
1
1
2
1
2
0
1
1
1
0
1
1
1
1
0
1
1
1
1
1
2
0
1
0
0
2
1
1
2
1
0
1
1
1
2
0
1
1
1
2
1
1
2
1
1
0
1
2
0
2
0
1
1
1
1
1
1
1
2
2
1
0
0
1
2
1
1
0
1
1
1
2
1
1
1
0
1
0
1
1
4
1
2
2
1
1
0
1
1
2
1
1
1
0
0
1
2
0
1
1
1
1
1
1
2
1
1
0
0
2
1
1
0
1
2
1
1
1
3
2
1
1
0
1
1
0
1
13
2
1
2
2
0
1
2
0
1
1
1
1
2
1
2
1
1
0
2
1
2
0
1
1
0
1
1
1
2
1
2
0
0
1
1
0
1
2
0
0
1
2
1
2
1
0
1
1
2
1
1
1
3
0
1
1
1
0
0
1
1
1
2
0
1
0
0
1
1
1
2
0
1
1
0
0
0
0
2
0
1
2
1
1
1
1
0
1
1
0
2
2
0
1
0
0
2
2
1
1
0
2
0
1
1
1
1
1
2
2
1
2
0
0
0
1
1
2
2
1
1
0
3
2
2
0
1
1
1
0
2
1
2
1
1
1
2
1
2
1
1
2
1
0
2
0
1
0
2
1
2
0
0
1
2
0
1
2
0
1
1
1
0
1
0
1
0
1
0
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
0
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
0
0
1
0
0
2
1
2
2
1
2
1
1
1
1
0
1
0
1
1
1
1
1
2
2
1
1
1
1
1
1
0
0
1
1
1
1
1
1
1
1
0
1
0
1
0
1
0
1
1
2
0
1
1
1
0
1
2
1
1
0
2
1
1
0
0
1
2
1
0
1
1
1
1
1
1
1
1
1
0
1
2
2
3
1
1
1
0
1
0
0
2
2
2
1
1
0
0
1
1
1
1
0
2
2
2
2
1
0
1
0
2
2
1
1
1
0
1
0
1
1
2
0
1
1
4
1
1
1
1
0
2
1
1
1
1
1
2
0
2
2
0
3
1
1
2
2
2
1
2
2
1
3
1
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
2
0
2
2
1
1
2
1
1
1
1
1
1
2
1
1
2
2
2
1
2
2
2
1
1
1
1
0
1
2
1
1
2
2
2
1
1
1
2
1
1
0
1
1
2
1
0
3
1
0
1
1
1
1
1
1
2
1
1
0
0
1
2
1
0
1
1
0
1
1
3
1
2
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
2
2
1
0
1
0
2
0
1
1
1
0
1
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
2
1
1
0
0
1
1
2
1
0
1
1
1
2
1
1
1
2
1
1
1
0
1
2
0
1
3
1
1
1
0
0
1
1
2
1
2
1
1
1
0
1
1
2
0
1
2
0
1
0
0
1
2
1
1
0
1
0
1
1
0
2
0
0
1
1
1
1
2
1
0
1
1
0
0
1
1
0
1
2
1
1
1
2
1
2
0
1
1
0
2
2
1
1
1
0
1
1
1
1
1
1
1
2
2
0
2
2
1
2
2
1
1
1
1
1
1
1
1
1
1
2
2
1
2
0
2
0
1
0
2
1
1
0
1
0
1
1
1
0
1
1
4
1
2
1
1
2
1
1
1
1
0
1
0
1
2
2
1
2
2
1
1
2
2
1
1
1
1
1
1
1
1
1
2
1
1
0
0
1
1
1
1
2
1
1
1
1
0
2
1
1
2
2
1
2
1
2
1
1
0
1
2
2
2
0
0
0
2
1
2
1
1
1
1
1
1
1
0
1
1
1
1
0
1
1
1
2
1
0
1
2
0
2
0
1
2
0
1
1
0
1
2
1
1
1
2
1
1
0
1
0
1
2
1
1
1
2
1
0
2
1
1
0
1
1
2
1
1
1
1
1
1
1
0
2
1
1
1
2
2
1
1
1
1
0
2
1
2
1
1
2
1
1
1
1
1
1
1
0
1
0
1
1
1
2
2
1
0
1
1
0
2
1
1
2
2
1
0
2
1
1
1
0
2
1
1
1
2
2
2
1
1
1
1
1
2
0
1
1
1
2
1
1
0
1
0
1
1
1
1
1
1
2
1
2
1
1
1
0
2
1
1
1
2
1
1
1
1
2
2
0
2
2
1
1
1
1
1
2
0
0
1
2
1
1
0
0
1
1
1
1
0
1
2
2
2
2
1
2
1
2
0
2
1
1
0
2
1
0
1
1
1
2
2
1
1
2
1
2
1
1
1
0
1
0
0
1
1
2
0
2
1
1
1
2
1
1
0
1
1
1
1
1
1
0
2
1
1
2
1
0
2
1
1
2
2
0
1
2
2
1
1
1
1
1
2
0
1
1
2
1
0
2
1
1
1
1
1
1
2
1
2
0
1
0
0
1
0
1
1
1
1
1
2
1
1
1
0
0
1
1
1
1
1
2
1
2
0
2
1
1
1
1
1
1
0
2
1
1
1
1
0
1
0
1
2
2
2
1
1
0
2
1
4
1
2
1
1
1
2
0
2
1
0
1
1
0
1
2
0
1
0
1
0
1
1
1
0
2
2
1
1
1
0
2
0
0
0
0
1
1
1
0
1
1
1
0
0
0
2
1
1
1
1
1
2
2
2
2
1
0
2
1
1
1
2
0
1
1
0
1
2
1
2
0
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
0
1
1
1
1
2
1
2
2
1
1
0
0
1
1
0
1
1
2
3
1
1
1
2
1
2
1
1
1
1
0
1
1
1
1
1
2
1
1
0
2
1
2
1
1
1
2
2
1
1
2
1
1
2
0
2
2
2
1
1
0
2
1
1
1
1
1
1
1
2
2
1
0
1
0
0
2
1
1
1
2
1
1
0
0
0
1
1
2
2
1
0
1
0
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
0
2
0
1
1
1
1
1
0
0
1
0
1
2
1
1
1
0
2
0
0
0
1
1
1
0
1
1
2
2
2
1
1
1
1
1
1
0
0
1
2
1
0
2
2
1
2
1
0
2
1
1
1
1
1
1
2
1
3
1
2
0
1
1
0
2
1
1
1
0
0
0
2
1
1
1
1
1
1
1
1
1
1
0
2
2
1
2
0
1
0
1
1
1
1
2
1
2
1
1
2
1
0
1
0
2
0
2
1
0
1
1
0
2
0
2
1
1
1
2
1
0
2
1
1
1
1
1
2
1
2
1
1
0
2
1
1
0
1
1
0
2
1
0
2
1
1
1
2
0
1
1
2
1
1
2
1
2
2
0
1
1
0
1
2
1
2
1
0
2
4
1
0
1
1
6
1
1
2
1
1
1
1
2
1
1
1
1
0
0
1
1
1
1
2
1
1
1
1
2
0
1
1
2
0
2
0
0
1
0
2
1
2
1
2
0
1
0
2
0
0
1
1
1
1
1
1
1
1
0
2
1
2
1
0
1
1
1
0
0
2
1
0
1
2
0
1
2
0
2
1
1
0
1
1
1
1
1
1
0
1
1
0
0
0
2
1
2
0
2
1
2
1
1
1
1
1
2
1
0
1
0
0
1
1
2
1
4
2
2
1
1
1
1
1
0
2
0
0
1
2
1
1
1
0
0
0
1
1
1
1
0
1
1
1
1
0
1
0
1
1
2
1
1
1
1
2
1
1
0
1
2
2
2
2
1
1
1
1
1
2
1
1
0
0
1
1
1
0
1
0
1
2
2
1
0
1
0
1
1
1
0
2
1
2
1
1
1
1
2
1
1
0
2
0
1
1
1
1
3
1
1
1
1
1
1
2
1
1
1
1
1
0
0
2
2
1
0
1
0
2
1
2
2
0
2
1
2
0
1
2
3
1
1
0
2
1
1
1
0
0
1
1
1
0
2
1
0
0
1
1
1
0
1
1
3
1
2
4
1
0
0
1
2
2
1
1
2
1
2
2
2
1
1
1
0
1
1
2
1
0
1
1
0
1
0
2
1
0
2
1
0
0
0
1
1
1
0
0
0
0
0
2
1
0
1
2
1
1
1
0
1
1
1
1
1
1
0
1
1
0
1
2
0
1
0
0
1
1
0
1
2
0
1
0
1
1
0
1
1
1
1
1
1
1
0
1
2
1
1
2
2
1
0
2
1
1
1
1
1
1
0
2
1
1
1
2
1
1
2
1
0
0
2
1
1
2
0
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
0
0
1
1
1
1
1
2
1
1
1
1
1
0
2
0
1
1
1
1
1
1
1
3
0
0
1
1
1
2
1
0
1
0
0
0
2
1
2
0
1
1
0
0
1
1
0
1
2
0
0
1
1
1
1
2
2
0
0
2
1
2
1
1
1
1
0
1
1
2
1
1
0
0
1
1
1
0
1
0
1
1
3
1
0
2
2
1
1
1
1
1
1
1
1
1
2
1
0
1
1
1
2
2
2
1
1
1
1
0
1
2
2
2
1
1
1
1
1
1
1
0
1
2
2
0
0
2
0
1
2
2
1
1
2
2
1
1
1
0
0
1
1
1
1
2
0
1
2
0
1
1
1
0
1
1
1
1
1
2
0
1
2
0
1
2
0
0
1
0
1
1
0
1
1
2
2
1
0
1
1
2
1
1
1
1
1
1
0
1
1
1
1
0
1
1
1
2
0
1
2
0
2
1
1
0
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
0
1
1
2
1
2
0
1
1
1
2
3
1
0
0
1
1
1
1
2
1
1
0
1
1
2
1
1
1
1
1
2
2
2
0
1
2
1
1
2
2
2
0
2
1
1
1
1
1
2
1
1
1
0
1
1
1
1
2
0
1
1
0
1
1
2
2
0
1
0
2
1
0
0
2
1
1
3
2
0
0
1
2
0
1
0
0
1
1
1
1
1
1
1
2
2
0
1
1
1
1
1
1
2
1
0
1
1
0
2
2
1
1
1
1
2
2
0
1
1
1
0
0
1
2
1
1
1
1
1
1
0
1
1
0
0
0
1
2
0
1
1
2
1
1
0
0
1
1
2
1
1
0
1
1
0
1
1
0
1
0
1
0
1
1
1
0
1
1
1
1
1
1
0
2
2
1
1
2
2
2
1
1
1
1
2
0
1
2
1
1
2
1
1
1
2
1
1
2
1
2
0
1
1
1
2
1
1
1
2
2
2
0
0
1
1
1
1
2
1
0
1
1
1
1
0
0
1
2
1
1
0
1
0
2
2
1
1
2
1
2
2
1
1
1
1
0
2
1
1
1
2
0
1
2
1
0
2
1
2
1
2
2
1
1
0
1
1
1
1
0
1
1
1
1
0
1
1
1
2
0
0
2
1
1
0
2
2
1
0
1
1
1
1
3
2
2
1
2
0
1
1
1
1
1
1
0
1
2
1
1
2
1
1
2
1
1
2
1
0
1
0
1
1
1
1
0
0
1
2
1
1
1
0
1
1
1
2
0
1
2
1
1
2
1
0
1
1
2
5
0
1
1
1
1
1
1
1
1
3
0
0
0
0
0
1
1
1
1
2
2
2
2
0
1
1
1
1
1
2
0
1
2
2
1
1
1
1
0
1
1
2
2
0
2
0
2
2
1
1
2
1
1
2
1
0
1
1
1
1
0
1
1
1
1
0
0
1
2
1
0
1
2
1
2
1
1
1
2
1
1
2
0
0
1
1
1
1
2
1
1
0
0
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
0
2
0
2
1
2
0
1
1
0
1
1
1
1
1
1
1
2
1
1
1
4
2
0
2
0
1
1
2
1
0
0
1
1
1
1
2
0
1
3
1
2
1
1
1
1
2
1
1
2
2
1
1
1
0
0
1
0
2
1
1
2
0
1
1
1
1
0
0
1
0
0
1
0
2
3
2
1
2
1
2
1
1
0
1
2
1
2
2
0
0
1
1
0
2
0
1
0
0
1
1
0
1
1
1
2
1
0
1
1
0
2
1
1
0
1
2
2
1
2
1
1
1
0
2
1
1
0
1
2
0
2
2
1
1
1
1
2
1
1
2
1
1
2
0
1
1
1
3
2
1
0
1
1
1
1
0
2
1
1
2
1
0
2
1
2
1
2
1
1
0
1
1
1
0
0
1
1
1
1
1
1
2
2
2
1
2
1
1
0
1
0
1
2
2
1
1
1
1
1
1
0
2
2
1
2
1
1
1
1
0
1
0
1
1
1
1
1
2
0
2
1
0
1
1
0
1
1
2
0
1
2
1
0
2
1
2
1
1
1
1
0
0
0
2
0
0
1
1
2
1
1
2
1
2
2
2
1
1
2
1
1
2
0
0
2
0
2
1
0
0
2
1
1
1
2
0
1
1
1
1
1
1
1
1
2
1
2
1
2
0
2
1
2
1
0
1
1
1
1
1
1
1
0
0
2
1
1
1
0
2
1
1
1
1
1
1
2
1
2
2
1
0
0
0
1
1
1
1
1
1
0
1
1
2
2
0
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
0
0
1
2
1
1
1
0
1
1
1
2
1
1
2
1
1
1
0
1
1
1
1
1
0
1
1
1
0
1
1
1
1
2
1
2
1
1
0
1
1
2
0
1
1
1
0
0
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
2
1
0
1
1
1
0
0
2
0
2
1
1
1
2
0
1
1
1
0
2
2
0
3
1
2
1
1
1
1
1
1
2
2
1
1
1
1
2
1
0
0
2
1
1
1
1
1
2
1
2
2
1
0
1
1
1
1
1
2
1
0
1
2
0
2
1
1
2
0
1
1
0
1
1
1
0
0
1
1
1
0
2
0
1
2
1
1
1
1
3
0
1
2
1
0
1
2
1
0
2
0
1
1
2
1
3
1
1
1
0
1
1
1
1
2
2
1
1
0
0
2
1
1
1
1
1
2
1
1
0
1
1
0
0
3
0
1
1
0
0
1
1
0
1
1
1
2
1
1
1
1
1
1
1
0
1
1
1
1
1
1
0
1
0
1
1
2
2
0
0
1
2
1
1
2
1
1
2
1
1
1
1
1
1
1
2
1
2
2
1
1
2
1
1
1
1
1
0
2
0
1
2
0
0
1
1
0
1
1
1
1
1
2
0
1
6
0
1
1
1
1
2
0
0
0
2
1
1
0
1
2
2
0
0
1
0
2
2
0
4
1
1
2
1
1
1
0
1
1
1
1
1
1
1
1
1
1
2
0
1
1
1
1
1
1
1
2
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
0
1
1
0
2
0
1
0
1
0
2
0
1
0
1
1
1
1
0
2
1
3
2
0
1
1
2
0
2
1
1
2
1
0
1
1
2
0
1
1
0
1
0
1
0
1
2
1
1
2
2
1
1
0
2
0
1
1
1
2
1
2
1
1
1
0
1
2
1
0
1
1
0
1
1
1
0
1
2
0
1
0
1
2
0
0
1
1
1
1
1
0
1
0
1
2
0
1
0
1
0
1
1
2
1
0
2
1
1
0
2
0
0
1
1
1
1
1
1
2
1
1
0
0
1
1
1
1
0
2
1
1
1
0
1
2
1
1
2
2
2
1
2
0
0
1
1
1
0
2
0
1
1
0
0
1
0
0
1
0
1
1
4
2
1
1
2
2
0
2
1
1
2
1
2
2
1
1
1
1
2
0
0
1
1
0
1
0
1
1
2
1
1
0
2
2
4
0
2
2
1
0
1
1
1
0
1
0
2
1
1
1
1
0
1
1
1
2
1
1
1
0
1
2
2
0
1
1
2
1
2
1
2
1
1
1
2
1
0
1
2
1
1
1
1
1
1
1
1
0
1
1
1
1
1
3
2
1
1
1
1
1
2
1
0
0
1
1
2
1
2
1
0
1
0
1
1
1
1
1
1
1
1
2
1
1
2
1
1
0
0
2
2
0
1
2
1
1
0
0
1
2
0
1
1
1
1
2
1
1
1
0
1
1
1
1
0
1
1
0
1
1
1
1
1
2
2
1
1
2
2
1
1
1
2
2
1
2
1
2
1
2
1
1
1
0
2
1
0
1
1
0
1
1
1
2
0
0
2
0
2
0
1
1
2
2
1
0
0
1
1
2
1
1
1
2
1
1
1
0
2
2
1
3
1
1
0
1
1
0
1
2
1
1
1
0
2
1
1
2
2
1
0
2
2
1
2
1
1
1
2
1
0
3
2
2
1
1
1
0
1
1
1
2
1
2
1
0
1
1
0
2
2
2
2
3
1
2
0
2
1
1
1
1
1
2
2
1
2
1
0
2
0
1
2
1
2
1
0
0
0
1
1
2
2
1
1
1
1
1
1
0
1
1
1
0
1
1
1
1
2
0
1
1
1
1
0
1
1
1
2
1
1
2
1
1
1
0
0
1
2
0
1
1
2
2
1
0
2
0
0
0
0
0
1
2
0
0
2
2
1
1
1
1
1
3
0
0
1
1
1
2
1
2
1
1
0
1
2
1
2
2
1
1
1
1
1
2
2
0
1
0
1
2
1
2
1
1
1
0
2
0
1
1
1
1
1
1
2
1
2
2
1
0
2
1
0
2
0
2
2
0
1
1
1
2
4
0
0
2
2
2
1
1
0
1
2
2
1
0
1
1
2
4
1
1
0
2
2
1
2
0
1
0
1
2
1
1
1
1
1
1
0
1
1
1
0
2
1
1
1
0
1
1
1
0
2
1
0
2
1
2
1
1
0
0
1
2
1
1
1
1
2
1
1
2
0
1
1
0
1
1
0
1
1
1
1
1
0
2
1
1
0
1
1
0
2
2
1
0
0
1
0
0
1
2
1
1
1
1
1
1
2
1
1
0
2
1
1
1
1
1
1
0
1
1
1
0
3
0
1
0
1
0
1
1
0
2
0
0
1
1
2
1
1
2
1
2
0
0
1
1
1
0
2
1
0
0
1
1
0
0
0
2
3
2
0
2
1
1
1
2
1
1
1
1
2
0
1
1
2
1
0
1
1
1
1
2
1
0
1
1
0
1
0
1
0
0
1
1
1
1
1
1
0
2
2
1
1
2
1
2
1
1
1
2
0
1
0
1
1
1
1
2
0
2
1
1
2
0
1
1
2
2
0
3
1
0
0
2
2
1
1
0
1
0
1
2
2
0
1
1
0
0
0
2
1
1
1
1
1
0
0
2
1
1
1
0
1
1
1
1
1
2
2
1
1
1
2
1
1
2
1
2
0
1
2
1
2
1
1
2
1
1
2
1
2
1
2
0
1
1
2
1
1
0
0
0
1
2
2
1
0
1
2
0
2
1
2
1
1
1
1
1
0
1
1
1
1
1
1
0
2
1
1
2
0
1
1
1
0
1
1
0
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
0
1
1
1
1
2
0
1
2
1
1
1
1
0
1
2
1
0
1
1
2
1
1
2
2
1
0
1
0
2
1
1
0
1
3
1
1
1
0
0
1
1
2
1
0
2
2
1
1
1
1
1
0
2
0
1
2
1
0
1
1
0
1
1
2
2
0
1
0
2
1
1
1
1
0
1
0
1
1
2
2
1
1
2
1
1
1
2
2
1
1
1
0
0
1
0
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
0
1
1
1
0
2
1
1
1
1
1
2
0
0
0
1
2
2
0
1
2
1
1
1
1
1
2
2
1
0
2
2
1
1
1
0
1
0
0
0
2
1
1
0
1
2
1
1
1
1
1
1
1
0
1
1
1
1
1
2
1
1
1
1
1
0
1
0
1
1
2
2
1
0
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
2
1
1
1
1
2
1
2
1
1
2
1
1
1
1
0
1
0
1
2
1
1
1
1
0
1
1
0
1
3
0
1
2
1
1
1
1
0
2
1
0
1
0
1
2
0
2
1
1
0
0
0
1
1
0
1
0
2
1
1
0
2
1
1
1
1
1
1
1
0
0
1
1
1
1
0
1
1
1
1
2
1
2
1
1
1
1
1
0
1
1
0
1
1
1
1
2
0
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
0
2
1
1
1
1
1
0
2
1
1
1
0
2
1
1
2
2
1
1
1
1
2
0
1
1
0
2
2
1
2
1
1
0
1
1
1
1
1
1
0
2
2
1
0
1
1
1
2
0
1
1
2
1
2
1
2
1
2
0
1
2
1
2
1
1
0
1
0
2
2
1
1
1
0
1
1
1
3
1
2
1
1
1
0
1
2
0
1
1
1
1
1
0
0
1
0
0
0
3
1
0
1
2
1
1
3
1
1
1
2
1
1
1
1
1
1
1
0
0
0
2
2
2
0
1
3
1
1
1
2
1
1
2
1
2
2
1
1
1
1
1
0
1
2
2
1
2
2
2
1
1
0
1
0
1
2
1
2
3
0
1
1
1
2
0
1
1
0
0
1
0
1
1
1
1
1
1
1
2
0
1
2
1
0
1
1
0
1
1
0
0
1
1
0
1
1
1
1
1
2
1
0
1
2
1
2
2
1
1
0
1
0
1
1
1
1
1
1
1
1
2
1
1
2
1
1
0
2
1
1
1
2
0
2
1
1
0
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
2
0
1
1
1
1
2
1
1
1
1
1
2
1
2
0
0
1
1
2
2
2
0
1
0
0
1
0
1
1
1
0
1
2
1
3
1
0
0
1
0
1
0
2
2
0
1
1
2
1
1
0
1
3
1
1
1
1
1
1
1
1
1
1
1
0
1
0
3
0
1
0
1
2
2
1
2
2
1
1
1
0
1
1
1
2
0
1
1
1
1
1
1
1
1
1
2
2
2
2
0
1
1
0
2
1
1
1
1
2
2
0
1
2
1
1
1
1
2
1
1
0
1
1
1
3
1
2
1
1
1
1
1
1
0
2
2
0
1
3
0
1
1
1
2
1
1
1
0
0
1
2
1
1
0
1
2
1
2
0
1
0
1
2
1
0
1
1
0
1
1
1
1
0
0
1
1
1
2
2
1
0
2
1
1
1
1
2
2
0
2
0
1
0
3
1
2
1
1
1
1
0
1
1
1
2
0
1
2
1
0
1
0
1
2
0
2
1
1
1
2
1
0
0
1
2
1
1
0
1
0
1
1
2
2
2
1
1
2
1
2
0
2
2
2
1
1
1
0
2
1
1
0
1
1
0
1
1
2
0
2
1
1
2
1
1
1
0
0
2
1
1
1
2
2
1
1
1
1
1
2
1
1
0
2
1
1
1
1
1
1
2
1
1
0
1
1
2
1
1
2
1
1
0
2
1
2
1
1
1
1
2
1
2
1
0
2
1
0
2
1
1
1
1
0
1
0
1
1
1
1
2
1
2
1
1
1
1
0
1
1
0
1
2
1
1
1
1
2
1
1
1
1
1
0
1
0
1
1
2
1
0
2
0
2
0
2
2
1
1
2
1
2
1
1
0
1
1
1
1
1
0
0
0
1
1
1
1
0
0
2
2
2
2
1
1
1
1
0
0
0
1
0
2
1
2
1
1
1
2
0
0
1
0
2
2
1
0
1
1
1
1
2
1
1
1
1
0
1
1
1
2
1
2
0
1
1
1
1
1
1
0
1
1
1
0
1
0
1
0
0
1
0
1
2
2
1
1
2
0
0
0
1
1
1
1
2
2
2
2
0
1
1
1
1
1
2
1
2
1
1
2
1
0
0
0
2
0
2
2
1
2
1
2
2
1
1
1
0
1
1
1
2
1
0
1
1
0
1
1
1
2
1
1
1
2
1
1
2
1
1
0
2
1
0
1
0
1
2
0
2
2
1
1
2
1
1
0
2
0
0
1
2
2
1
1
1
1
0
1
1
1
0
3
1
1
1
2
1
2
1
0
2
3
1
1
0
1
0
1
2
2
1
1
0
2
2
1
2
2
1
0
1
1
0
1
1
1
1
2
1
0
1
2
0
2
2
1
2
2
1
1
1
1
2
1
0
1
1
0
1
1
1
1
1
1
1
1
1
1
0
1
1
2
1
1
0
2
1
1
0
1
0
0
1
1
1
1
2
3
2
2
2
1
1
1
0
3
0
1
0
0
1
2
1
1
1
1
1
1
1
1
0
2
1
0
1
2
1
1
1
1
0
0
1
1
0
1
1
2
1
1
2
1
1
0
0
2
4
1
0
1
0
2
1
0
1
1
1
0
1
1
1
1
0
1
1
1
1
0
2
0
0
1
1
0
1
1
1
1
1
2
1
1
0
1
1
1
1
1
1
1
1
0
1
2
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
0
2
0
0
0
2
1
1
1
1
1
0
0
1
1
1
2
1
1
2
1
0
2
0
1
1
2
1
0
1
2
2
1
0
2
1
1
1
1
1
2
1
1
0
0
0
1
2
1
1
1
0
0
1
1
1
1
1
1
2
2
1
0
1
1
1
1
1
1
0
1
1
0
2
1
0
1
1
1
2
2
2
0
0
2
0
1
1
0
2
2
1
1
1
1
1
0
2
1
2
1
1
2
1
2
1
1
1
1
2
1
1
1
1
2
2
0
1
1
1
1
1
1
0
0
1
2
1
1
1
1
1
0
2
2
0
1
0
1
1
1
1
0
0
1
2
2
1
1
1
2
0
1
0
1
0
1
1
1
1
2
1
2
1
2
1
1
2
1
2
1
1
0
0
2
2
0
1
1
1
1
1
1
2
1
3
2
1
0
1
1
2
1
2
1
1
1
1
2
2
1
1
1
2
0
2
2
2
0
0
2
1
2
2
1
0
1
2
0
2
1
1
0
2
0
2
1
1
0
0
0
1
1
1
1
2
1
1
1
1
0
2
1
1
2
0
0
1
0
1
0
1
0
2
2
0
1
1
1
1
1
0
0
1
1
1
0
1
0
1
1
1
1
1
0
0
2
1
1
0
0
1
1
0
1
1
1
1
1
3
1
1
1
1
2
1
1
1
2
1
2
1
0
1
1
1
1
1
1
0
2
1
1
1
1
2
1
1
0
1
0
1
0
0
0
1
1
0
1
1
0
1
1
2
0
1
0
0
0
1
2
0
1
1
1
0
2
2
2
1
1
0
1
0
2
1
0
2
1
1
0
1
1
0
2
2
0
1
2
1
1
0
1
1
1
1
1
2
0
1
0
2
1
1
2
2
0
1
1
1
2
2
0
0
1
2
0
1
1
1
1
2
0
1
1
2
0
1
1
0
0
0
1
2
1
1
1
1
1
2
0
2
2
2
0
1
1
1
4
1
1
0
0
2
0
2
2
1
1
0
2
0
1
2
1
1
1
1
1
1
1
1
2
0
2
1
0
2
1
1
1
1
1
2
1
0
0
2
2
1
1
2
1
2
2
1
2
0
1
1
1
0
0
1
0
1
1
1
1
1
1
2
0
2
1
1
1
0
2
0
1
0
1
1
0
1
2
1
1
1
1
1
1
3
0
1
2
1
1
1
1
1
1
1
2
2
0
1
2
0
1
0
0
2
2
2
0
1
1
0
1
2
2
1
0
1
2
2
1
1
1
1
0
0
1
0
1
1
2
2
2
2
1
0
2
1
2
0
1
2
1
2
1
0
1
0
1
0
1
1
2
2
1
1
3
1
2
1
1
1
2
2
2
0
1
1
1
0
2
1
1
1
1
2
1
1
1
1
0
0
0
1
0
1
3
0
2
2
1
1
2
0
1
1
1
0
0
1
1
2
1
1
4
2
0
1
2
1
2
3
0
1
1
1
1
0
2
0
1
1
1
1
0
1
1
1
1
1
0
1
1
0
1
0
1
1
1
1
1
0
1
1
0
1
2
1
2
1
0
1
2
0
1
2
2
0
0
1
2
1
2
3
2
1
2
1
1
1
1
2
1
2
1
2
0
3
3
0
2
2
1
1
2
1
0
2
1
1
0
1
1
1
1
2
1
0
1
1
0
1
1
2
1
0
0
0
1
2
2
2
0
1
2
2
1
1
1
2
2
1
1
2
2
2
0
1
0
1
1
1
2
0
1
1
2
1
1
1
1
0
1
1
2
1
0
1
2
1
2
2
2
2
2
1
1
1
0
2
2
2
0
1
1
0
0
1
1
1
2
2
1
0
2
0
1
1
1
2
0
0
1
2
0
1
1
2
1
2
1
0
1
2
1
1
1
2
1
2
1
1
2
2
0
2
0
2
2
1
1
1
1
2
0
1
2
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
0
1
0
0
1
1
2
1
1
1
1
2
2
2
2
1
1
1
2
2
1
0
1
0
1
2
1
1
3
2
0
0
1
0
1
0
1
1
0
1
1
2
2
1
1
1
2
2
2
1
1
0
1
2
1
1
2
1
1
0
1
1
0
1
2
1
2
1
1
1
0
1
2
2
1
1
0
2
1
1
1
3
0
1
1
2
1
5
1
1
1
2
1
0
2
1
0
0
2
1
1
1
1
1
1
1
1
1
2
1
0
1
1
1
0
1
2
1
0
1
1
0
0
1
1
2
1
1
1
2
0
1
1
1
1
1
2
0
2
2
1
1
1
2
2
2
1
1
1
1
2
3
2
1
1
0
1
2
0
0
2
0
0
1
2
1
1
2
1
2
1
1
1
2
1
2
1
0
2
1
2
0
1
0
1
1
1
1
1
0
2
0
0
0
1
1
0
1
1
0
0
1
1
1
3
1
2
1
0
1
0
0
1
1
1
2
0
0
1
1
0
1
1
1
1
0
1
1
1
0
1
1
2
2
0
0
2
2
0
0
1
1
2
1
1
0
0
1
1
1
0
1
1
1
0
1
1
2
0
1
0
0
0
2
0
0
1
1
1
1
1
1
1
1
1
1
1
1
0
1
2
1
2
2
1
0
0
1
1
3
1
2
2
1
1
1
2
0
1
1
1
0
0
0
1
2
2
0
1
1
1
1
0
1
0
1
1
1
1
1
1
0
1
1
0
3
2
1
1
0
1
1
0
2
0
2
0
2
1
0
1
1
1
1
1
1
2
2
1
1
1
1
0
2
2
0
1
1
0
0
1
2
2
1
0
0
2
1
2
1
1
1
1
0
0
1
1
1
1
2
0
0
0
1
1
1
2
0
2
1
1
2
1
1
0
1
0
0
1
0
1
0
2
1
0
2
1
2
2
1
1
1
1
0
1
1
2
1
1
1
0
1
0
2
1
1
2
1
1
1
1
2
1
0
0
2
2
1
0
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
2
1
1
3
1
1
1
1
0
2
0
1
0
1
1
1
0
1
2
1
0
2
1
0
1
1
1
4
2
2
1
2
2
2
1
1
1
0
1
1
2
1
0
0
1
1
2
2
1
2
2
2
2
1
1
1
0
1
0
2
0
1
0
1
1
1
1
2
1
1
1
1
1
5
1
1
2
1
1
1
2
2
1
1
1
2
0
1
0
1
2
1
1
2
1
2
1
1
0
0
1
2
1
1
2
2
1
0
0
1
1
1
1
1
1
2
0
0
2
1
2
2
2
1
0
1
1
0
2
2
2
1
0
0
1
0
1
2
2
1
1
2
2
2
1
0
2
0
1
1
1
0
0
1
1
1
1
1
1
0
1
2
0
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
0
3
2
0
1
1
1
0
0
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
0
1
0
2
1
1
1
1
1
2
1
2
1
2
1
0
1
1
0
2
1
2
1
1
0
3
2
1
1
1
0
2
1
1
2
1
2
1
1
0
1
1
1
2
0
1
1
2
1
1
1
1
1
1
1
0
1
2
2
1
0
1
1
2
1
1
0
1
1
1
2
0
2
2
2
2
1
1
1
0
2
1
2
0
1
0
2
0
0
1
1
1
1
1
1
1
1
2
1
0
2
2
1
0
1
1
1
0
1
1
1
1
0
0
1
2
1
1
1
2
1
0
1
1
2
1
1
2
1
1
1
0
1
1
1
1
1
0
1
1
1
1
2
0
1
0
2
0
2
1
3
1
0
1
2
1
1
1
1
1
1
2
0
1
1
1
1
1
1
1
2
0
2
1
1
0
0
1
1
1
2
1
1
1
1
1
1
2
1
1
0
2
1
0
2
1
0
1
1
2
1
2
2
1
2
1
0
2
0
0
0
1
1
1
1
2
2
1
2
1
1
1
0
1
1
0
1
1
1
0
1
0
3
1
1
1
3
1
1
1
1
2
2
2
0
0
1
0
1
2
1
3
1
1
2
1
0
1
1
1
1
1
1
1
2
1
2
2
1
1
1
0
1
0
0
2
1
1
2
2
1
0
1
1
1
1
2
0
1
0
1
2
1
2
0
1
0
1
2
0
1
1
0
1
1
1
2
2
1
1
1
0
0
1
1
1
1
1
2
1
1
0
1
2
1
1
2
1
0
0
1
0
2
0
1
1
2
1
1
1
0
1
1
0
1
1
1
1
1
1
1
0
1
1
0
1
0
1
1
2
2
0
2
1
2
0
2
1
1
1
2
1
1
1
2
1
2
0
2
1
1
1
0
1
0
1
1
0
1
1
1
0
2
1
1
1
1
1
1
1
0
0
1
1
1
1
2
1
0
0
2
0
2
1
0
1
1
2
1
0
1
1
1
1
0
1
0
1
2
0
1
1
2
1
1
1
1
1
1
1
0
1
1
1
2
1
1
1
1
1
1
0
1
2
0
0
1
1
0
0
0
1
0
0
1
0
2
1
1
1
2
2
2
1
2
1
1
1
0
1
1
1
1
2
2
1
1
0
1
2
1
1
0
2
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
2
1
2
1
1
0
1
0
1
1
2
0
0
1
1
2
1
2
1
0
0
3
1
0
1
2
0
3
0
0
2
1
1
2
1
1
2
0
1
1
1
1
1
0
0
0
1
1
2
1
0
1
0
1
0
1
1
1
0
0
1
1
1
2
1
1
1
1
1
2
1
0
1
1
2
2
1
1
1
1
2
0
0
2
2
2
2
1
0
1
1
1
0
1
1
1
2
2
0
1
2
1
1
1
1
2
1
2
2
1
2
0
1
0
0
1
1
1
1
0
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
0
1
2
0
1
1
0
2
0
1
1
1
2
1
1
1
2
1
1
2
1
1
2
1
1
2
1
0
1
1
1
1
0
2
1
1
1
2
0
1
1
0
1
1
0
4
1
1
1
2
1
0
2
1
2
1
0
1
1
2
2
2
1
2
2
1
1
1
1
2
1
1
1
1
1
1
0
0
1
1
2
2
1
2
0
1
1
1
0
1
1
2
0
1
2
2
1
1
1
1
0
1
2
0
1
2
0
2
1
0
1
2
1
1
1
2
2
1
1
2
1
2
1
1
1
1
3
2
1
1
0
2
0
2
1
1
1
1
1
1
0
1
1
1
2
1
1
0
2
1
1
2
1
2
2
2
0
1
1
2
2
2
2
0
1
1
1
1
1
1
1
1
2
1
0
1
1
1
0
2
1
2
1
1
2
2
1
0
2
2
1
1
1
0
2
1
1
1
1
1
1
2
2
1
1
2
1
1
1
1
0
1
1
0
0
0
0
2
1
1
0
2
1
1
1
1
2
2
1
1
1
1
1
1
0
2
1
0
1
1
1
1
0
0
1
1
0
1
1
1
1
0
1
1
2
1
2
1
0
1
1
1
1
1
0
1
1
2
1
0
0
1
1
1
2
2
0
1
1
2
0
0
0
0
1
1
1
0
0
1
1
0
1
0
2
0
1
1
1
1
1
1
0
0
0
1
1
1
1
1
0
1
1
0
3
1
1
1
1
1
1
0
1
2
0
2
1
0
1
1
1
0
1
1
1
1
2
1
1
1
1
0
1
0
1
1
1
1
0
1
2
1
1
0
2
1
2
2
0
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
2
1
0
1
0
2
2
0
1
0
1
2
0
0
1
1
0
1
1
0
1
1
2
1
1
1
0
1
1
0
2
1
1
3
2
2
1
1
0
1
1
1
1
1
0
1
1
2
1
2
1
1
1
0
2
1
1
1
1
1
2
1
0
0
0
1
0
2
1
1
2
2
1
1
0
2
2
1
1
2
1
1
1
2
1
2
1
1
0
0
1
1
1
1
1
2
1
1
2
2
1
3
0
1
2
2
0
1
2
0
2
1
0
1
1
2
2
0
1
1
2
1
1
1
1
0
0
2
1
1
2
1
1
1
3
1
1
1
2
2
1
1
1
1
1
2
0
0
1
1
1
2
1
0
2
1
2
2
2
0
1
1
1
1
0
1
1
2
1
1
1
1
2
2
2
1
2
0
1
2
1
1
0
0
1
0
0
0
1
0
1
0
1
1
1
1
2
1
1
1
2
2
2
1
1
2
0
0
1
2
0
2
1
0
2
0
1
0
1
1
2
2
2
1
1
1
1
1
0
1
2
0
2
0
1
3
2
1
0
1
2
2
1
2
0
2
2
1
1
1
2
2
1
1
1
1
2
2
2
2
1
1
1
2
1
0
1
0
1
2
1
1
1
1
0
0
2
0
2
1
1
1
2
0
2
2
1
1
1
2
2
1
1
1
1
0
1
0
1
2
0
1
2
0
1
2
1
1
0
2
1
0
0
1
0
0
2
2
2
2
0
2
1
0
1
0
1
1
1
1
0
1
0
1
2
0
1
1
2
3
1
1
1
2
1
1
2
1
0
0
1
2
1
1
0
1
0
1
1
2
1
2
2
1
2
1
1
1
2
0
2
1
1
0
1
1
1
0
1
1
1
1
0
1
1
2
0
1
1
1
1
2
1
2
0
1
2
1
0
1
1
0
1
2
1
0
2
0
1
0
1
1
3
1
1
2
1
1
2
1
1
0
1
1
1
1
1
0
3
1
2
1
1
1
1
1
2
1
0
2
1
1
1
1
2
1
0
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
1
1
2
0
1
1
0
1
5
1
1
1
0
1
0
2
1
2
1
1
1
2
1
0
1
2
2
1
1
1
0
1
0
1
1
1
1
1
1
2
1
2
1
1
3
0
3
1
1
1
2
1
1
1
1
1
2
1
1
2
1
2
2
0
1
1
1
2
1
1
1
1
2
0
1
0
1
1
1
1
0
1
1
0
1
1
1
2
1
2
0
1
1
2
1
0
1
2
2
1
2
1
2
1
3
0
0
1
1
1
1
2
0
1
1
1
1
1
1
1
1
2
0
2
1
1
0
1
1
1
0
1
2
0
1
2
0
1
1
1
0
1
2
1
2
0
1
2
1
0
1
1
1
1
1
2
2
2
1
1
2
1
1
1
2
1
2
1
1
1
1
2
2
2
1
0
1
0
2
0
2
0
1
2
2
1
1
1
2
1
1
2
1
2
1
0
2
1
1
1
1
0
2
0
2
1
0
2
2
1
1
1
1
1
1
1
1
0
1
1
0
2
1
2
0
1
1
1
2
1
0
1
0
2
2
0
1
1
1
1
2
1
0
1
2
1
0
1
0
1
2
1
1
0
1
1
1
0
1
1
3
1
1
1
2
0
1
1
1
0
1
2
2
2
0
2
1
2
2
2
1
0
1
0
1
1
1
0
0
2
2
2
1
1
1
0
1
1
1
2
1
1
1
1
2
0
1
1
1
1
3
0
0
1
2
1
2
2
2
1
1
1
2
1
1
2
1
1
0
2
0
1
1
2
0
0
2
1
0
1
2
0
1
1
2
1
1
1
1
1
0
0
1
1
1
1
0
2
1
1
0
0
0
2
2
1
2
1
1
2
1
2
1
1
2
0
1
1
1
1
0
1
2
1
0
2
2
1
0
2
0
1
1
1
1
1
2
2
1
0
0
1
1
1
2
1
1
1
0
1
1
2
1
1
1
1
0
1
0
2
1
0
2
1
1
1
1
1
2
1
1
1
1
0
1
0
1
1
2
1
1
1
0
0
2
0
1
0
1
2
1
1
2
1
1
1
2
0
1
2
1
1
2
1
0
0
1
1
0
0
1
1
0
0
0
1
0
2
1
1
1
0
2
0
1
1
1
2
1
1
1
1
0
1
0
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
0
0
0
1
1
1
2
2
2
1
0
0
1
2
2
3
1
2
1
1
1
1
3
2
2
0
1
1
1
2
1
1
2
1
1
1
1
1
1
1
2
1
0
2
2
1
1
1
1
0
2
1
0
2
1
0
1
2
2
2
2
2
2
2
1
1
0
2
1
1
1
2
2
1
0
0
1
2
3
2
1
1
2
0
0
0
2
1
2
1
2
2
1
1
1
0
0
0
0
1
0
1
1
1
1
1
1
2
0
1
2
1
2
2
0
2
1
1
2
1
3
2
1
1
1
1
0
2
0
1
1
1
2
1
1
1
1
0
0
1
2
3
1
2
0
1
2
2
1
3
1
1
1
2
1
1
0
1
1
1
1
2
2
1
1
1
2
0
1
1
1
2
1
1
2
2
1
0
0
1
1
1
1
0
1
1
1
0
1
2
1
1
1
1
1
2
1
1
0
0
1
0
1
1
1
1
1
2
0
1
1
0
0
2
1
0
1
2
1
1
1
1
1
1
0
1
1
1
2
1
1
1
1
1
1
1
1
1
1
0
2
1
1
1
1
1
2
1
1
2
1
1
1
2
2
1
0
1
1
1
1
2
0
0
1
0
1
1
2
1
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
2
0
1
1
1
1
2
1
2
2
2
0
1
1
1
1
2
1
0
1
1
1
1
0
1
2
2
2
2
1
1
1
1
1
1
0
2
1
1
1
0
0
1
1
0
1
1
1
1
2
1
2
0
1
1
0
0
1
1
1
1
1
1
1
0
0
1
0
0
2
0
1
1
2
1
4
1
0
2
1
1
1
1
1
1
2
1
2
0
2
1
2
3
2
2
2
2
0
1
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
1
0
1
1
1
1
2
1
2
1
1
1
0
1
3
0
1
0
3
1
0
1
0
1
2
1
1
1
0
1
1
1
0
1
2
2
1
1
0
1
1
1
1
0
1
0
1
1
1
1
0
2
1
1
1
1
1
1
1
2
1
1
0
0
1
1
2
1
1
1
1
1
1
0
0
0
1
2
1
2
1
2
2
0
2
1
1
1
1
1
1
1
0
0
0
0
1
1
1
1
1
1
1
0
2
0
1
0
1
2
1
2
1
1
1
0
0
1
2
1
1
2
0
0
2
0
1
0
0
2
1
1
0
1
1
0
1
1
1
1
1
1
1
2
0
2
2
1
1
1
1
2
2
0
1
0
1
3
1
1
2
0
1
0
1
1
1
0
1
1
0
1
1
2
0
2
1
1
0
2
0
0
2
1
0
1
1
1
0
0
1
1
1
1
1
2
0
1
1
1
1
1
1
1
0
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
2
0
2
1
1
2
2
0
1
1
2
2
1
0
0
1
2
0
2
2
2
2
2
1
1
1
0
2
1
1
1
0
3
1
2
1
1
2
2
1
2
3
1
1
1
1
1
1
0
2
1
1
1
1
0
1
1
1
1
2
0
2
2
0
1
2
2
1
2
1
1
1
2
1
2
1
1
1
0
1
1
2
2
1
1
0
1
1
2
2
1
0
0
2
0
1
2
2
1
1
0
2
2
2
2
0
2
0
1
1
1
1
1
2
2
2
0
2
1
1
2
1
1
0
0
0
1
2
1
1
0
1
1
1
2
1
1
2
0
0
2
2
0
2
1
1
0
1
1
0
2
0
1
1
1
1
2
0
1
1
2
1
1
1
1
2
1
1
1
0
0
3
0
2
1
1
3
1
1
2
1
1
1
1
1
1
1
1
1
1
0
0
1
1
0
1
0
1
1
1
0
1
1
2
1
0
1
1
1
2
2
0
2
1
1
1
1
1
0
2
1
1
2
0
1
1
1
1
1
1
1
1
1
2
1
0
3
1
1
1
1
1
1
1
2
2
1
2
0
0
1
1
1
0
1
2
1
1
1
0
0
2
2
1
2
1
1
0
1
2
0
2
1
1
1
1
1
1
2
2
1
1
0
1
0
1
2
0
0
1
1
0
1
3
0
1
2
1
1
2
1
1
1
1
1
1
1
2
0
2
2
0
2
1
0
2
1
0
1
2
1
1
0
1
1
1
1
1
1
1
1
1
1
1
2
1
1
0
0
1
1
1
0
1
1
2
2
1
1
1
2
2
0
1
0
1
0
2
1
0
1
2
0
2
1
0
1
0
1
2
2
0
0
1
1
1
2
0
2
0
1
1
0
1
1
2
1
1
3
2
1
1
0
0
0
0
1
2
1
1
1
1
0
0
0
1
1
1
2
1
1
0
1
1
1
1
1
1
1
1
2
1
1
1
0
2
1
1
2
0
2
1
1
1
1
0
1
1
1
1
1
0
1
1
2
1
1
1
1
1
1
0
0
1
2
1
0
2
1
1
1
0
2
1
1
0
1
1
1
1
1
1
2
1
1
1
1
0
1
1
1
1
1
3
1
1
1
1
2
1
0
1
1
0
1
2
0
2
2
0
1
1
2
1
1
1
2
2
1
2
2
0
1
0
0
1
1
1
2
2
1
2
0
1
1
1
1
1
2
2
2
0
1
0
0
0
2
1
0
1
0
1
2
1
0
2
1
2
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
2
1
1
1
0
1
2
2
2
1
1
1
0
2
1
1
0
1
1
1
0
1
1
1
2
0
2
1
2
0
1
1
2
1
2
1
0
2
1
0
1
2
1
2
0
2
1
1
1
0
1
2
1
1
1
1
1
1
1
0
2
2
0
0
2
1
2
2
1
2
1
1
1
0
1
1
1
1
1
1
1
1
2
2
2
1
1
0
2
2
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
0
1
1
0
0
1
2
1
1
1
2
1
1
2
0
1
2
1
1
0
2
0
1
1
1
2
2
1
0
0
1
0
1
1
1
1
1
1
1
1
1
0
1
1
0
1
3
2
2
1
2
1
1
2
1
2
1
2
1
1
0
2
0
0
0
1
1
1
1
0
0
0
1
2
2
1
2
1
1
1
1
1
1
1
1
0
2
0
1
2
1
0
0
0
2
2
0
1
1
1
1
2
1
0
1
1
0
1
2
1
1
0
1
1
1
0
1
2
0
2
1
1
2
1
1
0
1
2
1
1
1
1
1
2
0
2
1
1
1
0
1
0
1
1
1
1
1
2
1
1
0
1
1
0
1
1
2
1
2
1
0
1
1
1
1
1
1
0
1
1
1
1
0
2
2
1
3
1
1
1
0
1
1
1
1
1
1
1
0
2
2
1
2
1
2
1
2
1
1
2
1
1
1
1
1
1
1
1
1
0
1
0
0
1
1
2
1
1
1
0
1
0
1
2
1
2
1
1
1
2
1
1
1
1
2
1
0
1
0
1
0
2
1
1
2
1
3
2
1
1
2
2
1
1
1
0
2
0
1
0
1
2
1
1
1
1
1
1
2
1
1
2
1
1
1
2
1
1
1
2
1
1
0
1
2
0
2
1
1
1
1
0
0
0
0
1
1
0
0
0
0
1
1
1
2
1
1
0
1
1
0
2
1
0
2
2
2
2
1
1
0
0
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
0
0
0
1
1
1
2
1
0
1
1
1
1
0
1
1
2
2
0
1
1
0
1
0
0
0
0
0
0
2
1
0
1
1
1
1
2
1
2
2
1
2
2
1
1
0
0
0
2
1
0
1
1
0
1
1
0
0
1
0
0
1
1
1
1
2
1
0
1
1
2
0
0
1
2
2
2
1
1
1
1
1
2
1
0
0
1
1
0
1
1
1
2
2
0
2
1
1
0
1
1
0
0
1
1
0
2
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
0
1
2
1
1
0
0
1
1
0
1
1
1
2
2
2
1
0
1
1
0
1
2
1
1
1
2
0
2
2
1
1
1
1
2
1
2
0
1
1
0
1
0
0
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
0
2
2
1
1
2
1
1
1
1
0
1
1
1
1
2
0
0
1
2
2
1
1
0
1
0
2
2
1
0
1
2
1
2
0
1
0
1
0
1
1
1
1
0
1
0
2
1
1
1
2
0
2
1
0
1
0
2
0
0
1
1
1
0
1
1
1
1
1
2
1
2
2
0
1
2
3
1
2
1
1
0
2
0
2
0
0
3
0
0
0
0
0
0
1
1
1
2
1
1
0
1
1
1
1
1
1
1
1
1
2
2
1
2
2
2
4
1
1
2
2
0
3
2
1
1
1
0
1
1
0
1
1
1
1
1
1
0
1
2
2
0
1
2
1
2
2
2
1
2
0
1
2
1
0
1
1
1
1
1
2
1
0
1
1
1
0
2
1
0
1
0
0
1
3
1
0
1
0
2
2
1
1
0
1
0
1
0
1
2
1
2
1
1
2
0
0
1
2
1
0
1
0
1
1
1
1
1
0
1
1
0
1
2
2
2
1
1
2
2
2
2
2
1
1
0
2
1
0
2
0
2
2
1
1
1
6
0
1
1
1
0
2
1
1
1
0
0
2
2
1
0
2
1
3
2
1
0
0
1
1
2
2
2
1
2
0
1
1
1
2
2
2
1
0
1
1
2
1
1
0
1
2
1
2
2
1
1
2
0
1
1
2
1
1
2
1
3
0
2
2
1
1
1
1
1
0
2
0
2
0
1
1
0
2
1
1
1
1
1
1
1
1
0
1
2
1
0
2
0
1
1
1
1
1
2
1
0
1
1
1
2
1
0
1
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
0
2
1
1
1
1
2
1
2
1
1
2
1
2
2
2
0
2
1
1
2
2
1
1
1
1
0
0
1
1
1
1
0
1
1
1
2
1
1
2
1
0
2
2
2
1
1
1
1
1
2
2
0
1
1
1
1
1
1
1
1
2
1
1
1
1
1
0
1
2
1
1
2
2
1
2
1
1
2
1
1
1
1
1
2
0
2
2
0
2
1
2
1
1
1
1
2
2
1
1
0
1
1
2
2
2
1
1
1
2
2
0
1
1
0
1
2
1
1
1
1
1
0
1
0
1
1
0
1
0
1
1
0
1
1
1
2
2
1
2
2
1
0
1
1
0
0
1
2
2
1
1
1
1
2
1
1
0
0
0
1
1
2
1
1
1
0
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
2
2
2
0
0
1
1
1
1
0
1
1
1
1
0
1
1
1
1
1
0
1
1
1
3
2
2
1
2
2
1
0
1
1
1
0
1
0
1
1
1
2
1
1
1
1
1
0
1
1
2
0
2
2
2
2
1
2
1
1
1
0
1
2
0
1
1
2
2
0
0
2
0
2
1
1
0
1
2
1
0
1
1
1
0
1
1
1
1
1
2
1
1
1
0
0
2
1
1
2
2
1
0
0
3
1
0
2
1
0
0
1
0
2
2
1
0
1
0
1
2
0
1
1
2
1
2
1
1
0
1
1
0
1
1
0
1
1
1
1
2
0
0
2
0
1
1
0
0
1
1
2
0
1
1
0
1
1
1
3
2
1
2
0
0
2
2
1
1
1
0
1
0
1
2
1
1
2
0
1
1
0
1
1
1
2
2
1
0
2
1
1
0
2
0
1
1
2
2
0
1
1
2
1
0
1
0
1
1
1
2
0
1
0
2
1
1
1
1
1
0
1
1
2
1
2
1
0
0
1
0
1
1
1
1
1
1
2
1
1
1
1
1
2
1
0
2
2
1
1
1
1
0
0
0
0
1
1
0
2
2
0
1
2
1
0
1
0
2
1
1
1
2
2
0
1
2
0
1
1
2
1
2
1
1
1
1
0
0
2
0
1
0
1
2
0
1
1
1
2
0
1
1
2
1
2
1
2
1
1
0
2
0
1
2
1
2
1
1
2
1
2
2
0
2
2
1
1
2
1
0
0
2
1
2
1
1
1
0
1
1
2
2
1
1
2
0
0
1
1
2
0
2
1
2
0
0
1
2
0
0
1
1
1
0
1
2
1
0
0
1
1
1
1
0
0
1
2
1
2
1
1
0
1
1
1
1
2
1
1
1
1
1
1
3
1
1
1
0
1
1
0
1
1
2
1
1
1
2
2
1
1
0
0
1
1
1
2
1
2
1
1
0
0
1
0
1
2
2
0
2
1
2
1
1
2
2
2
2
0
2
2
2
1
0
1
1
1
1
2
1
2
2
1
1
1
2
1
2
0
1
1
1
1
1
2
2
1
1
1
2
1
2
1
1
0
1
1
1
2
2
1
2
1
1
1
1
0
1
1
0
1
1
1
1
0
1
1
1
1
2
2
0
1
0
1
0
2
1
2
1
1
2
2
1
2
0
2
2
1
0
1
2
1
1
1
2
0
2
1
2
1
1
2
1
1
1
1
2
2
1
1
1
1
2
2
1
3
1
1
1
0
2
0
2
1
1
2
3
1
2
2
0
1
0
1
0
1
2
1
1
1
0
0
2
0
2
2
1
1
1
2
2
2
1
2
1
1
2
1
1
2
1
0
1
1
1
0
1
1
1
0
1
1
1
0
2
1
1
0
1
1
2
1
2
1
1
1
1
1
1
2
0
1
2
0
1
1
1
0
1
1
1
0
2
0
0
0
2
1
0
0
1
0
1
0
2
1
1
1
1
1
1
2
0
1
1
1
0
1
1
0
3
1
2
1
1
1
2
1
0
2
1
0
0
2
2
2
1
1
1
1
1
0
2
1
2
1
1
2
2
1
0
0
1
2
1
2
2
0
0
1
0
0
1
1
2
2
2
2
1
2
1
1
1
2
1
1
1
1
1
1
2
0
0
1
1
1
2
1
2
2
2
0
1
0
1
0
1
1
2
1
0
1
1
1
1
1
0
1
1
0
0
2
2
1
2
0
0
1
1
1
1
1
1
1
0
0
1
1
1
1
1
1
0
1
0
0
1
1
1
1
0
1
1
1
1
2
1
1
2
0
0
2
1
1
0
1
0
1
0
2
2
0
1
1
2
1
1
0
2
1
0
1
1
1
1
1
1
1
2
2
1
1
1
1
0
1
3
1
2
2
2
1
2
1
2
1
2
1
1
2
1
1
0
1
1
2
2
1
1
1
0
0
1
1
1
2
0
1
1
2
0
1
1
1
1
1
1
1
0
1
1
1
2
1
1
1
1
1
1
0
2
1
1
1
2
1
2
0
1
2
2
1
1
1
1
2
1
1
0
2
1
2
1
1
2
1
1
2
1
1
1
1
0
2
0
1
1
1
0
1
0
2
1
2
1
0
1
1
1
1
1
1
2
1
1
1
0
1
0
1
0
2
0
1
1
0
1
1
0
2
1
1
1
1
0
1
2
1
1
1
0
1
2
0
0
4
1
1
1
3
1
2
1
1
1
2
2
1
0
1
0
1
0
1
2
1
2
2
0
2
1
1
0
1
1
0
1
2
2
1
2
1
0
1
0
0
1
0
1
1
1
1
1
1
2
1
1
1
1
2
2
2
1
1
1
0
2
1
1
1
1
0
1
1
2
1
1
1
1
1
2
0
1
1
1
2
1
2
0
1
1
0
0
0
0
0
2
0
1
2
0
1
0
2
0
1
1
1
1
2
0
2
1
0
1
4
0
1
1
0
0
1
1
1
1
0
2
2
1
1
1
1
1
2
1
2
0
1
2
1
2
0
1
1
1
1
0
1
0
1
1
1
1
1
1
2
1
2
2
1
2
1
0
2
2
1
1
0
1
0
1
1
2
2
1
1
1
1
1
1
2
1
0
1
0
3
1
1
1
0
2
2
2
1
0
2
2
0
1
1
1
2
0
1
2
0
2
1
1
1
1
1
2
1
1
2
0
2
2
1
1
1
1
1
3
1
2
0
1
1
1
0
1
0
1
1
0
1
2
1
1
1
0
1
1
2
3
1
0
1
1
1
1
1
0
1
1
1
1
0
2
2
1
0
1
0
1
1
1
2
2
2
1
1
1
2
1
0
2
1
1
1
2
0
1
0
2
1
2
1
1
1
0
0
0
0
0
0
1
1
1
1
0
1
2
1
2
1
2
1
0
0
1
0
1
1
2
1
2
1
1
0
0
2
2
1
0
1
1
0
0
1
2
1
1
1
0
0
1
1
1
1
2
1
0
1
2
1
1
2
1
1
1
1
0
2
2
1
0
1
4
0
1
1
1
2
1
1
1
1
1
1
2
1
1
0
2
2
1
1
1
1
1
0
1
1
2
1
1
1
1
0
1
1
1
0
2
0
0
0
1
0
1
2
1
1
1
2
1
0
1
0
2
1
1
1
0
1
2
0
1
1
1
2
1
1
0
0
1
2
1
2
1
1
1
1
1
2
0
0
0
2
2
1
3
0
1
2
0
2
1
2
0
1
1
0
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
0
1
0
1
3
1
0
1
1
1
0
0
1
1
1
1
2
0
2
2
0
2
1
1
2
2
1
1
1
1
1
2
1
1
1
0
1
0
1
2
0
2
2
1
1
1
0
0
2
1
0
1
1
1
1
2
1
2
0
0
1
3
1
1
2
1
1
1
1
0
1
1
1
1
1
2
2
1
1
1
2
0
1
1
1
0
0
1
2
1
1
1
0
0
0
1
0
2
1
1
0
2
0
1
1
1
2
1
1
0
1
1
1
1
1
1
2
0
1
2
0
1
0
1
1
1
1
1
2
2
0
1
0
2
1
2
0
1
1
0
2
2
1
2
1
1
1
1
0
2
2
2
1
2
1
1
1
2
0
2
0
0
0
2
3
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
2
2
2
1
0
0
1
1
1
1
2
2
0
1
1
2
0
1
1
1
1
2
2
2
0
1
1
1
1
2
1
1
1
1
2
1
1
1
0
0
2
1
1
2
1
0
0
2
2
1
2
2
0
0
0
1
1
1
0
1
0
1
1
1
0
1
2
0
1
1
1
1
1
2
1
1
1
0
1
1
1
2
1
0
1
1
1
0
1
1
0
1
1
1
0
0
2
1
0
1
1
0
2
1
2
2
1
2
1
1
0
1
0
1
1
0
1
2
1
1
2
1
2
2
2
1
1
1
2
1
1
2
2
1
1
1
1
1
0
2
0
1
1
2
2
0
1
0
1
2
1
2
2
1
0
1
0
2
2
1
1
1
1
1
0
2
1
1
2
1
1
1
1
2
1
1
1
2
2
1
1
2
2
1
2
1
1
1
1
0
2
1
1
2
2
0
0
2
0
1
0
2
0
2
0
1
2
2
0
1
2
2
1
1
1
1
1
1
1
1
2
0
1
1
2
1
1
1
1
1
0
1
2
2
2
1
0
2
1
1
1
1
2
1
1
1
2
1
0
2
2
1
1
2
1
2
1
2
1
2
1
1
1
1
1
1
1
2
2
2
2
2
0
0
2
2
1
1
0
1
0
0
2
2
4
1
1
1
0
1
2
0
1
1
1
0
2
2
1
4
1
2
2
1
2
1
0
2
1
1
1
1
1
0
0
0
2
1
1
2
1
0
0
1
1
2
1
1
0
2
0
0
2
1
1
0
1
0
1
0
2
0
1
1
1
1
1
1
0
0
2
1
2
1
2
1
0
2
1
1
1
1
1
3
1
1
1
1
0
1
2
1
1
0
1
1
2
0
1
1
0
0
0
0
1
1
1
2
0
1
0
2
0
1
0
2
1
3
1
1
2
1
0
2
1
1
1
1
2
0
2
1
0
1
2
2
2
1
1
1
0
0
1
0
1
1
1
2
1
1
1
2
2
1
1
1
2
2
1
2
0
2
1
2
2
1
1
2
1
0
0
0
1
2
2
1
0
0
0
3
2
1
0
1
1
1
0
1
0
2
1
0
2
1
2
2
0
1
0
1
2
1
0
1
0
2
1
1
1
2
0
0
0
1
2
0
1
0
1
2
1
1
1
0
1
1
1
1
1
0
1
2
1
1
1
2
2
0
0
2
0
2
1
1
2
2
1
0
1
1
1
1
1
1
0
1
0
1
0
1
1
0
0
1
2
2
2
1
2
0
2
2
1
2
1
1
1
2
1
1
1
1
2
1
2
1
0
1
1
2
1
1
1
1
1
1
2
0
0
1
0
0
1
1
2
2
0
1
1
2
2
1
1
0
1
0
2
2
1
1
2
0
1
1
2
1
2
1
2
1
2
1
1
3
2
3
1
1
1
0
1
1
1
0
0
1
1
2
1
1
1
1
0
1
1
0
1
1
1
1
1
1
1
0
1
1
1
0
1
0
1
2
1
1
0
2
2
1
0
1
1
2
0
0
0
1
1
0
1
1
3
0
2
1
1
1
0
1
1
2
0
0
0
0
1
0
0
0
1
0
2
1
1
1
1
3
0
1
1
2
1
2
1
1
1
1
1
0
2
0
1
0
1
1
2
1
1
1
2
0
1
0
1
1
1
1
0
1
1
1
2
0
1
2
1
2
0
1
1
2
2
1
2
2
2
0
1
1
2
1
1
0
1
0
1
2
0
1
0
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
0
1
1
1
0
1
1
1
1
1
1
0
1
1
2
0
2
1
1
1
0
0
0
1
2
1
1
2
1
2
0
0
2
1
1
0
1
1
1
1
1
1
0
0
1
1
0
1
0
1
1
1
1
0
0
0
1
1
1
0
0
1
1
1
0
0
1
1
2
1
1
1
2
2
1
0
2
0
0
2
1
0
1
1
1
2
1
0
2
1
1
0
2
0
0
1
2
1
1
0
1
3
1
1
2
0
1
1
1
0
1
1
0
1
1
1
2
1
2
2
1
1
1
0
1
0
3
1
1
0
1
1
1
1
2
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
0
0
2
1
1
1
1
0
1
0
1
0
2
0
1
1
1
1
0
0
0
0
1
1
1
1
2
1
0
2
2
1
1
0
1
0
1
2
1
1
1
2
1
1
1
0
1
0
1
0
0
0
0
1
2
2
1
1
1
1
2
1
2
1
1
1
0
1
0
1
1
0
0
0
2
2
1
1
2
0
0
1
2
1
1
0
2
2
1
2
0
1
1
0
2
2
0
2
1
1
2
1
1
1
1
1
1
1
3
1
1
2
1
1
1
1
1
2
1
0
1
2
1
1
0
0
0
0
0
1
1
1
1
1
1
2
0
2
0
1
1
1
1
1
0
2
1
1
1
1
0
0
1
1
1
2
2
1
2
1
1
2
0
1
2
1
1
2
1
2
1
1
1
2
2
1
0
1
1
1
0
0
1
0
1
1
0
0
1
0
2
1
1
2
1
0
2
1
0
1
1
1
1
1
2
2
2
1
0
1
0
1
1
1
1
1
2
0
1
1
1
1
0
1
2
1
1
0
2
1
1
2
0
2
1
1
2
2
1
0
1
1
2
3
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
2
2
1
1
1
0
1
1
1
1
1
1
1
0
1
2
0
1
0
1
1
2
1
1
1
2
2
1
2
0
1
1
1
1
2
0
1
1
1
0
1
1
2
1
2
1
1
2
1
0
0
0
0
2
1
1
0
0
1
1
2
1
1
1
1
1
0
1
1
1
0
0
0
1
1
2
1
1
1
1
0
2
1
0
1
1
0
0
1
1
1
0
1
1
0
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
3
1
1
1
1
1
1
1
0
0
0
0
2
1
1
1
1
1
1
0
1
1
1
0
1
2
2
2
2
1
1
2
0
1
0
0
1
1
2
1
0
1
0
1
1
1
2
1
1
2
1
1
2
2
1
1
1
2
2
1
1
1
0
0
2
2
2
2
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
2
0
1
1
1
1
1
1
1
1
1
2
0
0
1
0
2
1
2
1
1
2
1
1
0
2
2
1
2
1
2
1
0
1
1
1
0
2
1
1
0
1
1
1
1
0
1
1
2
1
0
0
1
1
2
1
1
1
1
0
2
2
1
1
0
1
1
0
1
1
0
2
1
2
2
1
1
1
1
1
1
0
1
1
1
0
1
0
2
2
2
1
0
2
1
0
2
1
1
1
0
1
0
1
1
1
1
0
2
1
1
1
2
0
0
1
1
1
0
0
1
1
2
2
1
1
1
2
1
2
1
1
1
2
1
2
1
1
0
1
0
2
1
3
1
1
2
2
1
1
1
1
0
1
2
1
1
1
1
2
0
1
0
1
1
1
1
1
2
2
1
2
1
0
1
1
1
1
2
2
2
1
1
0
1
1
2
2
2
1
3
0
2
1
1
2
1
1
0
1
1
0
0
2
1
2
1
2
0
0
1
1
1
1
2
1
1
1
3
1
0
1
2
2
1
1
2
1
1
1
2
1
2
1
1
1
2
1
0
1
2
0
1
3
0
1
1
1
1
1
2
1
1
0
2
1
1
1
2
1
2
0
2
0
2
0
1
1
1
2
3
0
1
0
1
1
0
1
1
1
1
2
1
1
0
1
1
0
0
0
2
1
1
1
1
1
1
1
2
0
1
1
1
1
2
0
1
2
1
0
1
0
1
0
0
1
1
1
2
0
0
2
0
1
0
0
2
2
1
0
1
1
1
1
1
0
1
2
2
2
0
2
1
1
0
1
0
1
2
2
0
1
1
0
1
1
1
1
2
1
1
2
1
0
1
0
2
1
2
1
1
1
1
2
2
1
1
1
1
2
2
2
1
1
1
1
1
2
1
1
2
0
1
1
1
1
2
1
1
2
1
1
1
1
2
0
1
1
0
0
1
1
1
0
1
1
1
1
1
2
0
2
1
1
1
1
1
0
0
1
1
1
1
0
2
1
1
1
0
1
0
2
2
1
1
2
2
0
1
0
1
1
1
2
1
1
1
2
1
2
2
1
1
1
1
0
1
2
0
1
0
1
1
1
1
1
2
0
2
2
1
1
0
1
1
0
1
1
1
1
1
2
0
0
1
2
0
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
2
1
0
2
1
2
1
1
1
1
1
1
2
1
1
0
1
2
2
0
1
0
0
1
1
2
1
1
1
2
2
1
1
0
2
1
1
2
0
2
0
1
1
1
0
1
1
1
1
0
0
2
0
0
1
1
2
0
1
1
1
2
1
1
0
0
1
1
1
1
2
1
2
1
1
1
0
1
2
1
1
1
1
2
1
0
2
2
1
2
1
0
2
1
2
1
2
1
0
0
2
1
2
0
1
0
2
0
2
1
1
0
2
2
1
1
1
1
1
1
1
0
1
2
1
0
1
1
1
2
0
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
0
1
2
1
0
1
1
0
1
1
0
0
0
0
0
1
2
2
1
1
0
0
1
2
2
1
2
0
0
1
1
1
1
1
0
2
2
1
2
1
0
0
2
0
1
0
1
1
2
2
1
1
1
2
0
1
2
2
1
2
0
1
1
2
0
2
1
1
1
1
1
1
0
1
0
0
0
1
0
2
1
1
0
1
1
3
1
4
1
1
1
1
1
2
2
2
0
0
2
2
2
1
1
0
1
1
0
0
0
1
1
1
2
2
0
2
1
0
1
1
1
1
1
0
1
2
1
1
1
0
2
0
0
1
0
1
2
1
1
2
1
0
1
1
1
2
1
1
1
1
1
1
2
1
1
2
2
1
1
1
1
2
2
2
1
1
0
2
1
2
0
1
1
0
1
0
1
2
0
1
1
2
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
0
1
0
1
2
1
1
1
0
2
0
1
0
1
2
2
0
2
1
1
1
0
2
0
0
1
2
2
1
2
0
1
1
1
1
1
0
0
0
1
0
1
1
1
2
0
1
2
0
2
0
2
1
2
2
0
1
1
2
1
2
1
1
1
1
1
1
2
1
2
1
1
1
2
1
1
1
0
1
2
1
1
0
1
1
2
2
2
0
1
2
1
2
2
2
1
2
0
2
1
0
1
2
1
1
1
1
2
1
1
2
1
0
2
2
2
1
1
3
1
1
1
1
0
2
1
1
0
1
1
1
1
0
2
1
1
1
1
1
1
1
2
0
1
1
0
0
1
0
2
1
0
1
2
2
1
2
1
1
2
2
0
2
0
1
1
0
1
1
1
0
2
1
2
1
1
1
1
0
2
2
1
2
1
1
1
0
0
0
1
1
2
1
1
0
0
1
0
0
1
1
1
1
2
0
0
1
1
1
1
0
1
1
1
1
0
1
2
0
2
1
1
2
2
1
0
1
0
1
0
1
0
2
2
1
0
1
1
1
1
1
0
2
1
1
0
1
1
1
1
1
1
2
1
2
1
1
1
1
1
2
0
2
0
2
0
3
1
1
1
1
1
1
1
0
0
1
2
1
2
0
1
0
1
2
0
1
1
1
1
1
1
1
1
2
2
0
1
0
1
1
1
2
1
0
1
0
2
1
1
2
1
0
2
0
1
1
2
2
0
1
1
0
1
1
0
0
1
0
1
1
1
0
1
0
1
1
1
1
1
1
0
2
0
1
1
0
0
1
1
0
2
2
2
1
0
1
1
1
0
0
1
2
0
1
1
0
1
1
1
0
0
0
2
1
1
1
0
1
1
2
0
1
1
1
1
2
2
2
0
1
0
1
1
0
1
1
1
1
0
1
2
1
0
2
3
1
1
1
1
1
0
0
1
1
3
1
1
2
1
1
1
0
0
0
0
0
2
1
1
1
0
1
0
2
3
0
0
1
1
1
0
1
0
1
2
0
1
2
1
1
1
0
0
2
0
1
1
1
1
1
1
0
0
0
1
1
1
0
0
1
1
2
3
1
0
1
1
1
2
0
0
2
2
1
4
1
2
1
1
0
2
0
1
1
2
2
2
1
1
1
2
1
1
2
1
2
1
1
0
0
1
1
2
1
0
1
1
0
2
1
1
1
1
1
1
1
0
1
1
1
1
1
0
0
1
1
1
2
1
1
2
1
0
2
1
1
1
1
1
0
2
1
0
0
2
1
1
2
2
1
0
1
2
0
1
0
0
1
2
1
1
1
1
0
1
1
2
1
2
1
1
0
0
0
2
0
1
1
0
2
2
1
2
2
2
1
2
1
0
1
1
2
1
2
2
1
3
0
1
1
1
1
1
1
1
1
0
2
1
0
1
1
1
1
1
2
1
1
0
1
1
1
0
0
1
0
1
0
1
0
1
2
2
0
2
1
1
1
1
1
1
0
2
2
0
1
1
1
1
1
1
1
0
1
1
1
0
1
2
0
1
0
2
1
0
1
0
0
0
1
1
0
0
1
1
1
3
1
0
1
1
1
2
1
1
2
1
1
1
1
1
2
1
0
2
1
1
0
1
1
1
1
1
1
1
1
0
1
1
1
2
1
1
0
0
1
2
1
2
1
2
1
1
2
1
2
1
1
1
1
2
1
1
0
1
1
1
1
2
0
2
1
1
2
1
1
1
1
2
1
0
1
2
1
2
1
2
1
1
1
1
1
2
1
1
1
1
1
0
1
0
0
1
0
1
1
0
1
2
1
1
0
1
1
2
0
1
0
1
0
3
0
2
1
1
2
2
3
1
1
1
1
1
1
1
0
1
1
1
2
2
0
3
0
2
1
1
1
1
1
1
1
2
1
0
2
2
1
2
0
0
1
0
1
1
1
1
1
2
1
1
0
2
0
1
1
2
2
1
1
2
1
2
1
1
1
1
1
1
0
1
0
1
0
1
1
2
0
3
0
3
0
0
1
0
1
2
0
2
0
2
2
1
0
2
1
1
0
1
1
1
1
2
1
0
1
1
1
2
2
1
1
1
1
0
2
1
2
1
2
2
0
2
2
1
1
0
2
1
1
2
1
1
2
1
1
2
1
1
2
1
0
1
2
2
1
2
2
0
0
1
1
1
0
2
0
1
1
2
1
0
2
1
1
1
1
1
2
1
1
1
1
2
1
2
0
1
1
2
1
1
1
1
1
1
1
3
0
1
2
1
0
2
2
0
1
2
2
2
1
1
1
1
1
1
1
2
1
2
1
1
0
1
1
1
1
0
3
1
1
1
2
1
0
1
1
1
3
2
1
1
2
0
1
2
1
0
1
1
2
1
1
2
1
1
0
2
2
2
1
2
0
2
1
3
1
1
1
1
2
1
2
1
1
1
3
1
0
2
0
1
2
2
1
1
1
1
0
0
1
1
2
0
2
1
2
1
1
2
0
1
1
2
2
1
0
1
1
2
1
1
1
1
1
2
0
2
1
1
1
2
2
1
2
1
1
1
1
1
0
1
1
0
0
2
2
1
1
2
2
2
0
0
1
1
2
1
2
1
1
1
0
1
1
1
2
1
1
0
1
0
2
1
2
1
0
1
1
1
2
0
1
0
1
1
1
1
0
0
0
1
1
2
2
1
1
2
1
2
0
0
0
2
1
0
1
0
2
1
1
1
1
1
0
1
1
0
1
2
2
1
1
2
1
0
1
1
1
0
1
1
1
1
1
1
1
2
2
1
1
2
1
2
2
1
1
2
0
2
1
1
1
1
0
0
1
1
0
2
1
2
2
1
1
1
1
1
1
2
1
1
1
0
1
1
0
2
1
2
1
1
0
1
0
0
1
0
1
2
0
0
1
2
2
1
1
1
0
1
2
1
0
1
2
1
1
2
1
1
1
1
1
2
1
1
1
0
0
0
2
2
1
1
1
2
2
1
2
0
1
0
1
1
1
1
0
3
0
1
1
0
1
1
2
1
1
1
0
2
1
2
1
1
2
1
3
1
1
2
1
1
0
1
1
3
1
2
1
0
1
0
2
1
0
1
1
0
0
1
1
1
2
1
2
2
1
2
2
1
1
0
1
1
1
0
1
2
1
1
1
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
2
1
1
2
1
1
0
2
1
1
1
2
1
1
2
0
2
1
0
0
1
2
1
1
0
1
0
2
1
2
1
1
1
1
2
0
1
0
1
0
1
2
1
2
2
0
2
1
2
0
2
1
1
0
0
2
1
1
1
2
0
2
1
0
2
1
1
1
1
1
1
2
2
2
1
2
1
0
1
1
1
2
1
1
1
1
2
1
0
1
0
0
2
1
1
2
2
2
0
1
2
1
1
0
0
0
1
1
0
0
1
2
1
1
1
1
1
1
1
1
1
0
1
2
1
2
1
1
1
1
2
1
1
0
0
2
1
1
2
0
1
1
1
1
1
1
1
1
0
1
0
1
1
0
0
1
0
0
1
1
1
2
1
2
1
1
2
1
2
1
0
2
1
1
1
2
1
1
0
1
1
1
1
1
1
1
1
0
1
1
1
1
2
1
1
0
0
2
1
1
1
0
1
0
1
1
1
1
1
2
1
2
1
2
1
1
1
0
1
1
1
1
1
0
1
1
1
1
0
1
0
1
2
1
2
1
0
1
0
1
1
1
2
0
1
0
2
1
1
0
2
1
0
1
2
2
1
2
1
0
0
1
1
1
1
0
2
1
1
2
1
2
2
1
1
0
0
2
1
1
1
0
1
1
1
1
1
1
2
1
1
0
2
1
1
0
2
1
1
2
2
1
0
2
2
2
2
3
1
2
1
3
1
0
0
2
1
1
0
2
1
0
1
0
4
1
0
2
1
2
1
1
1
1
1
0
1
0
1
2
0
2
1
1
1
1
1
1
2
2
1
2
0
1
1
0
0
2
1
0
0
0
0
1
2
0
0
1
1
2
1
1
2
2
1
1
1
0
1
1
1
0
0
1
2
1
1
1
2
0
0
1
0
1
1
1
1
1
1
1
1
2
2
0
1
2
1
0
0
1
1
0
1
2
0
1
1
1
1
2
1
2
2
1
1
1
1
2
0
1
0
1
1
2
1
1
2
1
1
2
1
1
1
1
0
2
1
1
2
0
1
1
1
1
1
1
2
1
0
3
2
2
0
0
0
0
2
1
0
1
1
1
1
1
2
1
0
1
2
0
1
0
1
1
1
2
2
0
1
1
1
1
1
1
1
1
2
1
1
0
1
0
1
2
2
0
2
0
1
1
1
2
2
1
1
1
1
2
1
1
1
1
0
1
1
1
2
0
2
0
1
1
1
1
1
0
1
2
0
0
1
1
1
0
1
2
0
1
1
1
1
1
0
1
1
1
1
0
2
1
0
1
1
2
1
1
1
2
2
1
1
2
0
2
2
2
1
1
1
1
14
0
0
1
1
1
0
1
0
1
2
1
1
1
1
0
0
1
1
1
1
2
2
0
1
1
0
1
1
2
1
1
0
2
2
2
1
1
1
2
1
1
0
0
0
1
1
1
1
1
1
1
1
1
1
0
2
1
2
1
2
1
1
1
1
2
0
0
1
1
2
1
1
1
1
1
1
0
2
1
0
1
1
2
0
1
1
0
2
2
1
1
1
0
2
2
1
1
0
1
1
2
1
2
2
1
2
0
0
1
1
2
0
1
1
1
1
2
2
2
0
1
2
1
0
0
1
1
2
3
1
1
1
1
0
1
1
1
1
2
1
1
1
1
1
1
0
1
2
1
1
2
1
2
1
1
1
1
0
1
1
1
1
1
3
2
1
1
1
2
2
2
0
1
1
1
1
0
2
0
1
2
1
1
1
0
1
2
1
1
0
0
1
0
1
2
1
2
1
1
1
1
1
0
2
1
1
1
1
1
1
1
1
1
0
2
1
0
2
1
1
0
1
2
1
1
1
2
1
1
2
1
1
1
2
0
1
1
1
0
1
1
1
1
2
1
0
1
0
2
1
2
1
1
2
1
1
0
1
2
2
2
1
0
1
1
1
0
2
1
2
1
1
1
2
2
1
1
1
2
2
1
0
1
1
2
0
0
1
1
2
1
2
2
2
2
1
1
0
1
1
1
0
1
2
1
1
2
2
1
1
3
0
1
1
0
1
1
2
2
1
2
2
1
1
1
1
0
0
1
2
1
1
2
1
1
1
1
2
1
1
2
2
1
1
2
2
1
0
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
2
1
1
1
1
2
0
1
0
1
1
1
2
1
1
1
1
2
2
0
2
1
1
2
0
1
0
1
0
1
2
1
0
1
0
2
0
0
1
2
1
1
0
2
2
1
2
1
1
1
0
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
0
1
2
2
2
0
2
2
1
1
1
1
2
2
0
1
1
2
2
2
1
2
0
2
1
2
2
2
2
2
1
1
1
0
1
1
1
1
2
0
2
0
1
2
1
2
2
2
1
2
1
4
2
2
1
1
2
0
1
2
2
1
1
1
1
2
1
1
0
2
1
0
1
1
1
1
0
2
1
1
2
1
2
1
2
1
1
0
0
1
1
1
2
0
2
1
1
1
2
0
1
1
1
1
1
1
0
1
1
0
0
0
1
1
0
1
0
2
1
2
1
0
0
0
1
0
1
1
2
1
2
1
1
1
0
1
1
1
1
1
1
0
1
1
1
1
2
1
1
1
2
2
1
1
1
2
1
0
0
1
0
1
2
1
1
1
2
1
0
1
1
1
0
2
0
1
2
2
1
1
0
2
1
1
2
1
2
1
0
2
1
0
2
1
2
1
1
1
1
0
0
0
2
2
2
1
1
1
0
1
1
0
2
2
1
1
1
2
1
2
0
2
1
1
2
1
0
1
2
1
1
1
2
2
2
1
2
1
2
1
2
1
1
0
2
0
1
1
0
2
1
2
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
0
1
1
1
0
1
3
1
2
0
2
2
1
2
2
2
1
2
2
2
0
0
0
1
0
1
0
1
1
2
2
1
0
1
2
0
1
1
1
2
1
0
2
1
2
2
1
1
1
0
1
2
2
1
2
1
1
1
1
1
0
2
1
0
1
0
1
2
0
0
1
1
0
2
0
0
1
2
0
0
0
1
0
1
2
1
1
0
1
2
1
1
0
2
1
2
1
1
1
1
1
1
1
2
0
0
1
1
1
1
1
1
0
2
1
0
1
1
1
2
1
3
1
2
1
1
1
1
0
0
4
2
0
1
2
0
1
1
1
1
0
1
3
1
1
1
1
1
0
0
0
2
1
1
1
0
1
1
1
1
0
2
1
1
2
1
1
1
1
1
1
0
1
0
3
0
1
0
0
1
1
0
2
1
2
1
0
1
1
1
1
0
0
2
0
1
1
1
0
1
1
1
1
1
2
0
1
2
1
1
2
2
2
1
1
1
1
0
0
1
1
1
1
0
0
1
1
1
2
1
2
2
1
1
1
1
0
1
0
0
0
2
1
1
0
2
2
2
1
2
1
1
0
0
2
1
1
0
2
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
0
1
2
1
1
1
1
1
0
0
2
1
2
2
0
1
9
0
1
1
1
0
1
2
1
1
1
2
1
1
0
1
2
1
1
1
1
1
0
1
2
1
1
1
2
0
1
1
1
0
1
2
0
1
1
1
1
0
0
0
1
1
0
0
2
2
2
2
1
1
2
1
1
1
1
2
1
2
2
2
1
1
1
1
2
1
1
1
2
2
1
2
1
2
0
2
1
1
2
1
0
0
2
1
2
0
3
1
2
2
2
1
1
2
1
1
0
2
1
1
1
1
2
0
1
1
2
1
0
1
0
2
1
1
1
1
1
1
2
2
0
1
1
0
1
1
1
0
2
1
3
0
1
1
0
0
1
0
1
1
0
1
0
1
1
2
1
1
1
0
0
0
0
2
1
2
1
2
1
1
0
0
1
1
2
1
1
1
0
1
0
1
2
1
0
0
1
1
0
1
1
2
2
1
2
0
1
1
1
1
0
2
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
2
2
1
2
1
1
2
1
1
2
1
1
0
1
1
1
2
2
1
0
1
0
4
1
1
1
1
1
2
0
1
2
1
2
1
1
0
2
1
0
1
1
2
0
3
1
1
1
1
2
2
2
2
0
1
1
0
1
0
1
1
1
0
1
2
0
1
1
2
1
1
1
1
0
1
2
2
2
1
2
1
1
1
1
2
2
2
0
1
1
0
1
1
0
2
2
2
1
1
0
2
1
2
0
1
1
1
0
0
1
2
0
2
1
1
0
2
2
1
1
0
1
1
1
0
1
1
1
1
1
1
1
0
1
2
1
1
0
1
1
1
0
2
1
1
2
1
1
0
0
0
0
2
2
1
0
1
1
3
1
2
0
1
1
0
2
1
1
1
1
1
0
1
1
1
3
1
1
1
0
1
0
1
2
1
1
0
1
1
1
0
1
2
1
0
1
1
1
1
1
2
2
0
1
0
0
2
0
1
1
1
2
1
2
1
0
1
0
2
2
1
2
1
2
1
1
3
2
1
1
1
2
2
2
1
1
1
1
1
0
2
2
1
1
1
2
1
1
0
2
1
1
1
0
1
1
0
0
2
1
0
1
1
1
1
1
2
1
0
0
1
2
1
2
2
1
0
2
2
1
0
1
1
1
1
1
2
0
1
0
1
1
1
2
2
2
1
1
1
2
2
0
1
0
2
1
2
1
2
1
1
3
1
2
1
1
2
1
2
2
2
1
0
0
1
1
1
0
2
1
1
1
1
2
1
1
1
0
1
1
1
0
1
1
0
2
2
1
0
1
1
1
1
1
1
0
1
1
1
0
1
0
0
1
2
1
1
1
1
0
0
1
2
1
1
3
0
0
1
1
1
1
0
2
1
1
1
1
1
2
1
0
1
2
1
0
0
1
1
0
2
1
0
2
1
1
0
1
2
2
0
1
0
0
2
1
1
0
2
1
2
1
1
1
1
1
1
0
0
0
1
0
0
1
1
1
2
1
1
2
0
1
1
1
1
1
1
1
2
0
1
2
2
0
0
2
2
1
1
0
1
1
0
2
1
1
1
2
1
0
1
2
2
1
0
1
2
1
1
1
0
1
1
1
3
0
2
2
0
1
1
0
2
1
1
1
2
1
2
1
1
3
1
1
0
2
1
1
2
1
1
0
1
0
1
2
2
0
2
1
0
1
2
2
1
1
0
2
0
1
1
1
1
0
1
1
0
2
1
2
1
0
2
2
2
2
2
2
1
1
0
1
0
1
1
1
0
2
1
0
2
2
1
1
2
2
1
1
0
2
3
0
1
0
1
0
1
1
0
1
0
0
1
1
1
2
0
2
0
1
1
2
0
1
1
1
1
1
0
0
1
1
2
1
1
2
1
0
2
1
2
1
2
2
1
1
1
2
2
2
1
1
0
1
1
2
1
1
3
2
1
0
2
1
1
0
1
1
2
1
0
1
1
1
1
1
0
2
0
0
2
2
1
2
1
1
1
1
1
1
1
1
1
2
2
2
1
0
2
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
1
5
1
1
0
0
1
2
2
0
0
0
1
2
0
1
1
2
0
1
0
1
0
2
1
2
2
0
1
1
1
2
0
1
1
1
1
1
0
1
0
2
0
1
1
0
2
1
1
0
1
1
1
3
1
0
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
2
0
0
1
1
1
1
0
2
1
1
1
1
0
1
2
0
1
1
1
2
1
0
2
0
1
0
1
1
1
1
1
0
1
1
1
1
1
1
1
1
0
1
1
1
1
1
0
1
1
1
0
1
1
1
2
3
1
1
1
1
1
1
1
2
1
1
0
0
2
2
0
1
1
2
1
0
1
2
1
1
1
1
0
0
2
1
2
1
0
1
1
1
0
2
1
2
1
1
1
1
1
1
1
2
2
1
1
0
1
1
1
1
1
2
1
2
0
1
1
2
1
2
1
1
1
2
1
1
1
0
0
1
1
3
1
1
3
2
0
0
1
0
0
1
1
1
1
1
2
2
1
1
0
0
1
2
1
1
1
1
0
0
0
1
2
1
0
2
1
0
2
2
1
1
2
1
1
1
1
0
1
0
1
0
2
1
1
1
2
1
0
0
2
1
1
0
2
1
2
1
1
0
2
1
0
1
1
1
1
2
1
1
1
2
1
3
1
1
1
2
1
2
1
0
1
1
2
0
1
2
1
1
1
1
2
1
2
1
1
1
1
3
0
2
0
1
1
0
1
1
1
2
0
1
1
1
2
2
1
2
1
2
1
0
0
1
2
1
0
2
0
2
2
1
1
1
2
1
1
1
0
2
1
1
1
2
1
1
1
1
2
1
0
0
1
1
1
1
1
1
1
2
2
1
1
2
1
2
0
1
0
1
1
1
1
2
2
1
1
0
1
1
0
0
1
1
1
1
1
0
1
1
1
1
1
2
2
1
1
1
2
1
1
1
1
1
0
1
1
1
0
1
1
1
1
0
1
1
1
2
1
1
2
2
1
1
1
1
2
2
1
2
2
2
1
2
2
1
1
1
2
0
0
1
0
1
0
0
1
1
1
2
1
1
1
1
2
1
0
2
1
1
2
1
1
1
2
1
0
1
3
0
1
1
1
0
1
1
2
1
2
1
2
1
1
1
1
0
1
2
2
1
1
2
1
1
1
1
0
1
1
1
0
2
0
1
2
0
2
1
2
0
2
1
0
2
1
0
1
1
1
1
0
2
2
1
1
2
0
1
1
1
1
1
2
2
1
1
1
2
0
0
1
2
0
1
1
1
2
1
2
0
1
0
6
2
1
1
0
2
2
1
2
1
1
2
1
1
1
2
1
1
1
2
2
1
1
2
1
0
0
1
1
2
1
1
1
2
2
0
1
1
2
0
0
1
1
2
1
1
1
0
0
1
2
2
0
1
2
2
0
1
0
0
2
1
0
1
1
1
2
1
2
1
0
1
0
2
2
2
0
1
1
0
1
2
1
1
2
1
1
1
2
1
0
1
1
0
1
1
1
1
1
1
0
1
2
0
1
0
1
1
1
1
1
1
2
1
1
1
0
0
2
2
0
1
2
2
1
1
2
2
1
1
1
1
1
2
1
2
2
0
0
0
1
1
1
1
0
0
2
1
2
4
0
2
1
2
1
2
1
1
1
0
2
1
1
1
2
1
2
3
1
1
1
1
1
1
1
1
1
2
2
1
2
0
1
2
0
2
1
1
1
1
1
1
1
1
1
1
3
0
0
0
1
1
0
2
2
0
1
1
2
0
1
0
1
1
2
0
0
1
1
1
1
2
2
1
0
0
2
1
1
0
1
1
0
1
1
2
1
1
0
1
1
1
2
2
2
1
1
1
2
2
1
0
0
1
0
1
2
1
0
0
1
0
1
0
1
1
0
1
0
1
1
1
2
0
0
1
1
0
0
2
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
2
2
0
2
0
0
2
3
0
2
0
0
1
0
1
1
1
1
1
1
2
1
0
0
0
3
0
0
1
1
1
1
1
0
2
2
1
4
2
0
1
2
1
0
2
1
0
1
0
1
2
1
1
1
0
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
0
2
1
1
0
2
2
0
1
1
2
1
1
1
1
1
1
1
1
1
0
1
0
2
0
2
2
2
1
2
1
1
2
2
2
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
0
0
2
1
2
1
1
1
2
2
0
0
1
1
0
0
2
0
1
1
1
0
1
1
0
2
1
1
1
0
2
1
1
1
1
1
0
1
1
2
1
1
2
1
1
1
1
2
2
1
0
2
2
2
1
1
1
0
0
0
2
2
0
0
1
2
1
1
1
0
1
1
1
1
2
2
1
1
1
3
0
1
1
0
1
2
0
1
2
2
1
1
1
1
1
0
1
2
0
1
1
0
1
0
1
1
1
1
2
2
2
0
2
2
2
0
1
1
1
1
2
1
2
0
1
0
1
2
1
1
0
1
1
1
1
0
1
0
2
0
1
1
0
1
1
1
1
1
0
2
2
1
1
2
1
2
1
1
2
1
1
1
2
0
1
0
1
0
2
1
1
0
1
0
1
1
0
2
1
0
0
0
1
2
1
2
1
2
1
1
1
2
0
1
1
1
1
1
1
1
2
1
2
2
1
2
1
1
2
1
0
2
1
1
4
1
1
1
1
2
1
1
1
1
0
2
1
2
0
1
2
0
2
1
2
1
0
1
1
0
1
1
2
1
2
2
0
1
2
0
1
1
1
1
2
1
1
1
1
1
1
1
2
3
0
1
0
1
1
1
0
1
0
1
1
2
1
1
3
2
2
1
1
2
1
2
0
2
0
1
1
2
1
2
2
1
0
1
0
0
2
1
2
1
2
1
1
1
1
1
2
0
0
0
1
0
1
1
1
2
1
1
2
1
0
1
1
1
1
2
5
1
1
1
1
1
2
2
1
1
0
1
1
1
1
1
1
0
1
2
3
3
2
1
1
1
1
1
0
1
1
1
1
1
1
2
0
2
1
2
2
1
1
1
1
2
1
0
2
1
1
2
1
1
0
4
2
1
1
2
2
2
0
0
0
1
1
2
1
2
1
1
1
1
1
1
1
0
1
0
1
0
1
0
2
1
2
2
1
1
0
2
0
1
2
2
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
1
2
1
2
2
2
2
2
1
1
1
2
2
1
2
2
2
2
1
1
1
2
1
0
2
1
0
1
1
0
1
1
1
1
1
1
1
0
1
0
2
0
2
2
1
1
0
0
1
1
1
1
1
2
0
0
1
1
2
1
1
1
0
2
1
1
2
1
2
1
1
1
0
1
1
1
0
1
0
1
1
1
1
1
2
2
1
2
1
1
1
1
1
0
2
2
1
1
1
0
1
1
1
2
1
0
1
0
0
1
2
1
0
1
1
1
2
2
1
3
0
2
0
0
1
1
0
0
2
1
0
0
1
1
0
1
2
1
1
1
1
1
2
0
1
1
1
0
1
0
0
1
2
0
1
2
1
0
1
1
2
1
1
1
2
1
1
1
0
1
2
0
1
1
1
1
0
1
0
1
1
2
1
1
2
1
1
1
0
0
1
1
0
2
2
1
0
1
1
1
1
2
1
1
1
0
1
1
1
0
1
2
0
0
1
2
1
2
0
3
0
1
1
1
2
1
0
2
1
1
1
1
1
1
1
0
1
0
0
1
0
1
1
0
1
1
1
1
1
1
1
1
2
1
1
1
1
3
3
0
1
1
0
1
1
2
2
0
0
0
1
1
0
2
1
1
1
1
2
1
1
1
0
0
1
1
1
1
0
3
2
1
1
1
1
2
1
2
2
2
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
0
0
0
0
1
1
1
2
2
2
2
1
2
1
2
2
1
1
0
1
1
2
0
1
1
0
1
0
0
1
1
1
1
1
2
2
0
2
2
0
1
1
1
0
0
2
1
0
0
0
0
0
2
1
1
2
1
1
0
1
0
1
2
0
1
2
0
2
0
1
1
2
1
1
0
2
1
2
1
0
1
1
1
2
1
1
1
2
1
2
2
1
1
2
2
2
1
0
1
2
0
1
1
1
2
1
1
2
2
0
1
2
2
1
0
2
1
1
2
1
1
1
1
1
2
1
1
1
0
2
1
0
0
1
1
1
1
1
1
1
1
1
0
1
1
2
1
2
1
1
1
1
1
0
1
0
1
2
2
1
1
1
1
2
0
1
1
1
1
1
0
1
1
2
0
1
1
2
1
1
1
2
1
1
1
0
0
2
2
2
1
2
0
2
0
1
1
1
1
0
1
1
1
0
1
1
2
1
1
1
1
2
0
1
0
2
1
1
1
1
1
1
2
1
1
2
1
1
0
1
1
0
1
2
1
2
0
2
0
1
1
1
1
1
1
0
1
1
1
2
0
0
1
1
0
1
2
0
1
1
0
1
2
1
1
1
1
2
0
1
0
2
2
1
2
2
1
1
1
1
1
2
2
2
1
2
2
1
1
1
1
1
1
1
2
2
1
2
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
2
1
0
2
1
1
2
0
2
1
2
1
1
1
2
1
1
2
1
2
1
2
2
0
2
0
1
2
1
2
1
1
2
1
1
2
1
1
1
2
1
2
1
1
1
0
1
1
1
1
1
1
1
1
2
1
2
1
0
2
0
2
6
1
1
1
1
1
0
1
1
1
1
1
2
0
1
1
1
1
1
2
0
1
2
2
1
0
2
2
1
1
0
1
0
1
2
1
1
1
2
1
1
0
0
1
0
0
0
2
0
2
1
1
1
0
1
2
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
0
3
0
2
1
1
1
1
2
2
0
1
1
0
1
1
1
0
1
0
1
0
1
1
0
1
1
0
0
1
1
1
1
1
1
1
1
1
1
1
1
2
0
0
1
1
2
2
0
0
1
1
1
1
2
1
0
2
1
0
0
1
1
2
2
0
1
1
2
1
0
2
0
1
0
0
1
0
1
0
0
1
1
2
2
1
1
1
1
1
0
1
1
1
1
0
1
2
1
2
1
1
2
1
1
1
1
0
2
1
0
1
1
1
1
1
1
0
0
0
1
1
1
0
0
2
2
0
2
2
0
1
1
1
1
2
1
0
1
2
1
2
2
1
1
1
1
1
0
1
2
1
2
0
1
1
1
0
1
1
0
2
1
2
1
1
1
0
0
1
2
0
0
1
1
1
1
2
2
2
1
0
1
1
0
0
1
1
0
1
2
1
0
1
1
2
2
1
0
1
1
1
0
1
1
0
0
0
1
1
2
0
1
0
1
1
1
1
1
1
2
1
1
2
1
1
1
1
2
1
2
1
0
1
2
1
1
0
1
2
2
1
1
2
2
2
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
0
1
1
2
1
1
2
2
2
0
1
2
1
1
1
2
1
1
0
1
0
1
1
1
1
0
0
1
1
2
1
2
2
1
2
1
1
1
0
1
1
1
1
0
1
1
2
0
2
2
1
1
2
2
1
1
0
2
2
1
0
1
1
0
0
1
1
2
1
1
1
1
1
1
2
0
0
1
1
0
0
1
2
0
2
1
2
2
0
0
2
0
1
1
1
2
1
2
1
1
0
1
1
1
2
2
1
0
1
2
1
1
1
2
1
0
2
0
0
2
0
1
1
0
1
1
1
1
0
1
1
2
1
0
1
1
1
1
1
1
1
2
1
0
0
1
1
1
2
2
1
1
1
2
1
2
1
1
0
1
0
1
1
0
0
0
1
1
1
2
1
1
1
1
0
1
0
2
0
1
0
2
2
1
0
0
1
1
1
0
1
1
0
2
1
0
1
1
1
1
2
0
1
1
2
2
1
0
1
1
0
1
0
1
1
0
1
2
1
1
1
1
1
1
1
1
0
1
1
1
0
1
0
0
1
1
0
0
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
0
2
1
2
2
2
0
2
0
0
0
0
0
1
2
1
1
1
1
0
2
1
1
1
1
1
1
1
1
1
0
1
2
2
1
0
1
2
1
1
1
0
2
0
1
1
0
0
2
1
0
1
2
1
2
0
1
1
2
2
2
1
1
2
1
1
2
0
1
2
1
7
0
0
1
0
1
2
2
1
0
1
0
1
2
1
2
2
2
0
0
1
0
2
0
0
0
1
2
1
1
1
1
1
1
2
1
1
1
0
1
1
2
1
0
1
0
2
0
1
1
2
1
1
2
1
2
1
1
1
1
2
1
1
0
1
2
1
0
2
1
0
2
1
1
2
2
0
0
1
0
2
0
1
1
0
1
1
1
0
1
1
1
1
2
0
1
1
1
2
1
2
1
1
1
0
1
1
1
1
0
2
2
0
0
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
0
1
1
2
0
1
0
1
1
1
2
0
0
1
1
1
2
2
1
0
1
1
1
0
1
0
2
2
0
0
1
2
0
1
1
2
0
2
1
0
1
1
1
2
1
1
1
1
1
2
1
1
0
2
1
1
1
1
2
2
0
2
1
2
2
1
1
1
1
0
1
1
0
1
0
1
2
1
1
2
1
1
1
0
1
1
1
1
1
1
0
0
1
2
1
1
1
2
2
2
1
1
0
1
2
1
1
1
1
2
0
1
0
3
2
2
1
1
1
0
1
2
1
2
1
1
0
2
1
1
1
1
1
1
1
1
0
1
0
1
0
2
0
2
1
1
1
2
1
2
1
2
1
1
0
1
2
2
1
1
1
1
1
1
1
0
1
1
0
1
2
1
1
0
1
0
1
0
1
0
0
1
0
1
0
2
1
0
1
1
2
1
1
1
2
0
0
0
1
2
0
1
1
0
1
2
0
1
1
0
1
1
2
0
1
1
2
1
1
1
3
1
0
1
1
1
1
1
0
1
1
1
1
0
1
2
1
0
1
1
1
1
1
2
0
1
1
1
1
0
1
0
1
1
0
1
3
1
1
1
1
1
2
1
0
1
1
2
2
1
1
1
2
2
1
1
1
2
1
1
0
1
1
1
1
0
2
1
1
1
1
1
1
0
1
1
1
1
1
0
1
1
1
2
1
2
1
2
1
0
1
0
2
0
1
2
2
1
1
1
2
1
0
1
2
2
1
1
1
1
1
0
2
1
1
1
0
1
1
2
1
1
0
1
1
1
1
1
2
1
1
1
2
2
1
0
1
2
1
0
1
2
1
0
1
1
2
1
0
2
1
1
0
2
1
1
1
1
0
1
1
1
1
1
1
1
0
1
0
1
1
0
1
2
0
1
0
1
0
2
1
0
1
2
2
1
0
1
2
0
1
1
1
0
0
0
2
1
2
1
0
0
0
1
1
0
1
2
1
3
0
3
1
2
1
2
2
1
3
1
1
1
1
2
0
1
1
2
0
1
2
1
2
2
0
1
1
1
2
2
1
2
1
1
1
1
1
1
2
1
1
1
0
2
2
0
2
2
2
1
2
1
1
2
1
1
0
1
1
2
1
2
1
2
1
1
2
0
1
2
1
0
0
2
1
1
0
2
1
1
0
0
1
1
2
1
2
1
1
1
1
1
1
1
2
2
1
1
2
0
2
1
2
1
1
1
1
1
1
1
0
0
0
0
1
3
0
1
3
0
1
2
2
1
1
1
1
1
2
0
1
1
1
1
2
1
1
1
0
1
2
1
2
0
1
1
1
0
1
2
0
0
1
1
2
0
2
1
2
1
2
0
0
1
0
1
2
1
1
2
1
1
2
2
1
0
1
2
1
1
1
1
1
2
2
1
1
0
1
2
0
0
2
1
2
1
0
0
1
0
1
1
1
2
1
1
1
2
1
2
1
1
1
0
1
1
0
2
1
0
0
2
1
0
1
0
0
0
1
1
0
1
2
1
2
2
2
2
1
1
0
2
0
1
1
1
0
1
1
2
2
1
2
1
1
1
1
0
1
1
0
2
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
2
0
1
2
0
2
1
0
1
0
2
0
0
1
2
1
2
2
2
2
1
1
0
1
1
2
1
0
1
1
1
1
1
1
1
1
1
0
2
1
1
0
0
1
1
2
0
1
1
1
1
0
1
0
2
1
1
1
1
2
2
1
1
1
2
2
2
1
1
1
2
2
1
1
1
2
2
1
2
0
4
1
1
1
2
1
1
1
1
1
1
0
1
0
0
0
2
1
2
1
1
2
2
2
0
0
1
1
1
1
1
1
0
2
1
1
0
0
1
1
1
0
1
2
0
0
1
0
2
1
1
1
1
0
1
1
2
1
1
1
1
0
1
2
1
3
1
1
0
1
1
1
1
2
1
1
1
1
1
2
1
1
0
1
1
2
1
0
1
1
1
1
1
1
2
1
1
2
1
1
1
0
1
1
0
0
1
1
2
0
1
1
0
2
0
1
1
0
2
0
2
0
1
2
1
0
0
1
2
2
1
0
1
1
1
2
0
1
1
1
0
1
1
1
1
2
0
2
1
1
1
3
1
0
0
2
1
1
2
0
1
1
2
2
1
1
1
1
1
0
1
2
0
1
2
1
1
2
1
1
0
1
0
1
1
1
1
2
2
2
0
2
2
1
1
0
1
1
1
1
1
1
0
0
2
2
1
1
1
2
0
2
3
1
0
2
1
2
1
0
2
2
1
1
2
1
1
2
1
1
1
1
2
2
0
2
1
1
1
0
1
1
1
1
1
0
2
1
2
1
1
0
1
1
1
2
0
1
0
0
1
2
2
1
1
1
1
1
1
1
1
2
1
0
1
2
2
1
1
1
0
1
1
1
0
1
0
1
2
1
2
2
2
1
0
1
1
2
1
1
2
1
1
1
0
1
1
2
0
2
1
0
1
0
1
3
1
1
1
2
1
1
1
1
2
1
1
2
1
1
2
1
0
1
1
1
1
1
2
1
1
1
1
1
1
0
2
2
0
2
1
2
2
2
1
1
0
1
1
1
2
1
0
1
2
2
0
2
1
0
0
0
0
1
2
2
1
1
2
2
0
1
2
2
1
2
1
1
0
1
1
2
0
1
1
2
1
1
0
2
0
0
1
0
2
1
0
1
2
2
1
1
2
1
1
1
1
1
0
1
1
2
0
0
1
1
1
1
0
0
1
1
2
3
2
1
1
1
1
0
0
1
0
0
1
1
1
2
0
2
1
1
1
1
0
0
1
1
2
1
1
2
1
0
1
1
2
1
0
2
2
1
1
2
1
1
2
1
2
1
1
0
1
0
1
0
0
1
0
1
0
1
1
1
1
1
1
1
2
1
2
1
0
1
1
0
0
0
1
0
1
1
1
1
1
1
1
1
2
0
0
1
1
0
2
1
2
1
0
1
1
0
2
2
1
1
1
0
0
1
1
1
0
2
1
1
2
1
2
1
1
1
1
2
0
2
0
0
1
2
1
1
1
1
1
1
1
0
2
1
1
1
1
2
0
1
1
1
1
0
2
1
1
2
2
2
0
1
1
1
1
1
0
2
2
2
1
2
1
2
1
2
2
1
1
1
2
0
1
1
1
1
1
0
1
3
1
0
1
1
1
1
1
1
1
1
2
0
1
2
2
1
1
1
1
1
2
2
0
1
0
2
0
2
0
1
0
1
1
0
1
2
1
1
2
1
1
1
1
1
2
1
2
1
0
1
2
2
1
1
1
1
1
1
1
0
1
1
0
1
2
1
1
1
2
1
0
1
1
0
1
1
0
1
1
1
1
2
1
1
1
1
1
2
2
1
1
1
1
1
1
1
0
2
0
1
0
1
0
1
1
0
1
1
1
1
1
2
2
1
1
1
2
2
0
1
2
3
2
2
0
1
2
0
1
1
0
2
1
0
1
2
1
1
2
3
2
1
0
1
1
0
1
1
1
1
0
0
0
1
2
0
1
0
1
1
0
0
1
1
0
0
2
1
1
0
2
1
2
1
2
1
1
2
1
1
0
1
1
1
1
1
0
1
1
2
0
0
1
2
1
1
2
1
1
2
1
1
2
1
0
0
1
1
1
1
0
2
0
2
1
2
1
0
1
0
1
1
2
1
1
2
2
1
1
0
0
1
1
1
2
1
0
1
2
2
0
0
1
1
1
1
2
0
0
0
1
0
2
2
1
1
3
1
1
1
2
0
2
2
1
1
1
0
0
0
1
1
0
0
1
1
2
1
0
0
0
1
2
0
0
1
1
0
2
1
0
1
1
0
0
2
1
1
1
1
0
1
1
1
2
1
3
1
2
2
1
1
2
1
0
0
1
1
1
2
1
1
1
1
1
1
2
0
1
3
1
0
2
0
0
1
1
1
1
0
1
2
1
2
0
1
1
2
1
1
1
2
0
1
2
1
2
2
2
2
1
0
1
3
1
1
1
1
1
2
1
1
1
1
1
1
0
1
1
1
0
1
0
2
1
1
1
1
0
1
1
1
1
1
0
0
1
1
0
2
1
1
4
0
1
2
1
2
0
1
1
1
0
0
1
1
1
1
1
2
1
1
1
2
1
1
0
2
1
1
1
1
1
1
2
2
1
2
0
0
1
1
1
1
1
1
2
1
1
1
1
2
1
2
1
0
1
0
0
2
1
1
1
2
2
2
2
0
1
1
1
2
0
1
1
1
2
1
1
2
1
2
2
1
1
0
1
1
0
1
0
2
1
1
1
1
1
1
1
1
1
2
2
0
1
1
0
0
1
0
2
1
0
1
1
1
0
2
2
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
2
0
1
1
1
1
1
0
2
1
1
0
3
2
1
0
1
1
1
1
2
1
2
1
1
0
1
1
2
1
1
0
1
0
1
1
0
1
1
2
1
2
0
2
0
1
1
1
1
1
0
1
1
1
1
1
0
2
0
2
0
1
4
1
1
0
0
0
1
1
1
1
1
1
1
1
2
0
2
1
1
2
1
2
1
1
1
0
2
1
1
2
1
1
0
1
2
2
1
2
0
1
1
0
3
2
0
0
1
1
1
1
1
1
0
0
1
1
1
2
2
1
1
2
2
1
2
0
0
0
0
1
1
0
1
1
2
0
1
1
1
1
1
2
2
1
0
0
1
2
2
1
0
1
1
2
2
1
1
1
2
0
1
1
1
1
1
2
0
1
0
1
0
2
0
2
2
0
4
1
1
1
0
1
1
1
0
1
1
2
2
2
0
0
1
2
1
1
2
1
0
0
1
1
1
1
2
1
1
0
2
1
1
2
1
1
1
0
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
0
1
1
1
1
2
1
2
2
1
2
1
1
1
0
2
0
0
1
1
1
0
1
3
1
1
2
1
1
1
1
0
1
1
0
1
1
1
1
0
1
0
1
1
1
1
1
0
2
1
2
1
1
2
1
0
1
1
1
1
0
1
1
0
0
2
2
2
1
2
1
1
1
1
0
1
2
2
2
0
0
1
0
1
3
2
1
1
1
0
1
1
0
0
1
0
1
0
1
2
1
1
1
1
0
0
0
1
1
0
1
1
0
0
0
2
0
2
0
1
1
1
2
1
1
1
0
1
1
0
0
1
1
1
2
1
1
1
0
1
1
2
1
1
0
0
1
0
1
1
2
0
1
0
1
2
1
1
0
1
1
2
1
2
0
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
2
1
1
2
2
1
2
0
1
1
1
1
1
1
0
1
0
1
2
0
0
1
2
1
0
1
1
1
1
0
1
1
0
1
1
2
2
0
1
2
2
1
0
1
2
1
1
1
1
1
2
1
1
1
1
1
1
0
1
1
2
2
1
1
1
0
3
2
2
1
2
2
2
2
2
1
2
1
1
1
1
1
0
2
2
2
1
1
1
2
2
0
2
2
1
1
0
1
2
2
0
1
0
1
1
2
1
0
2
1
2
0
1
1
1
1
0
2
2
1
1
1
0
1
2
1
1
0
1
1
1
0
0
3
1
0
0
1
0
2
0
1
2
0
0
1
1
0
0
2
2
1
1
1
1
0
3
0
2
1
5
0
1
1
1
2
1
1
2
1
0
1
0
1
2
2
1
1
1
2
0
2
1
0
1
1
0
0
2
0
0
0
0
2
1
1
1
1
0
1
0
0
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
2
0
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
0
1
0
2
2
0
0
2
1
1
2
2
1
0
2
2
1
1
0
2
2
2
0
2
1
2
2
1
2
0
1
1
1
1
1
1
1
1
2
1
1
1
0
0
2
1
2
1
2
1
1
1
2
1
1
2
2
1
2
1
1
1
2
0
1
2
1
1
1
0
1
2
0
1
2
2
1
1
1
1
1
2
1
3
1
1
1
2
1
1
1
2
2
0
1
0
1
1
1
1
1
1
1
1
1
1
0
1
2
1
1
1
1
0
0
0
0
1
1
2
1
0
1
1
1
1
0
2
0
2
1
0
1
1
1
2
0
2
0
1
0
0
2
1
1
2
1
1
2
1
0
1
1
1
1
1
2
0
1
1
1
1
1
1
1
0
2
1
2
1
1
1
1
2
0
0
1
1
1
1
0
1
0
1
0
1
1
1
1
2
1
1
2
1
2
1
0
1
2
2
2
1
1
0
1
1
1
0
1
0
1
2
0
1
1
1
0
1
2
0
0
1
1
2
1
1
1
0
1
1
0
1
2
1
1
1
2
1
1
0
1
0
0
0
1
1
2
1
1
1
1
0
2
2
0
1
1
1
2
1
2
1
2
1
1
1
2
1
0
0
1
0
1
2
1
2
1
2
0
1
1
0
1
1
1
1
2
1
1
1
1
0
1
1
0
1
2
1
2
1
2
0
1
1
1
1
2
0
0
1
1
1
1
2
1
0
2
2
1
1
1
2
0
1
2
2
1
0
0
2
1
1
2
1
2
1
1
1
0
1
1
0
2
0
1
2
1
1
1
2
2
1
2
0
1
1
0
0
2
2
0
2
1
0
2
1
1
1
1
1
1
0
1
1
1
1
1
2
1
2
1
1
2
1
2
1
1
0
1
0
1
1
0
0
2
1
0
1
1
0
2
2
0
1
1
2
1
1
1
1
2
2
1
1
2
2
1
2
2
1
2
1
2
2
1
1
1
1
0
1
0
1
1
1
1
2
2
1
0
2
1
2
2
1
0
1
0
1
1
2
1
0
0
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
2
1
1
1
3
1
2
0
1
0
1
1
1
1
1
1
2
1
1
3
1
1
0
1
2
0
1
1
1
2
2
1
1
1
3
1
2
1
2
1
1
2
1
1
3
1
1
0
1
1
0
0
2
1
2
0
0
1
1
0
0
1
1
1
1
1
1
2
1
2
0
0
1
0
1
0
1
1
2
0
1
1
0
1
1
1
1
1
1
2
1
2
2
0
1
1
1
1
2
1
1
1
0
1
2
1
1
2
2
1
1
2
1
1
1
1
2
0
2
2
0
0
2
1
0
2
2
1
1
2
0
2
1
0
2
1
1
1
0
1
0
1
2
1
2
1
2
1
1
2
1
2
1
1
1
1
1
1
1
2
1
4
0
1
1
0
2
1
1
2
0
0
1
1
0
1
1
1
1
0
2
0
1
1
1
3
2
1
2
2
1
1
2
0
2
2
1
1
3
1
2
1
1
1
2
1
1
1
0
1
1
0
0
2
1
0
1
1
0
0
0
1
2
1
1
1
1
1
0
2
1
0
2
2
1
1
2
0
1
1
0
0
2
1
1
2
2
2
1
0
1
1
1
1
0
1
2
1
1
0
1
0
1
1
1
1
0
2
0
2
2
2
1
1
1
1
2
0
1
1
0
2
2
2
0
2
1
2
1
1
2
0
1
1
1
2
3
2
0
1
2
0
1
0
1
1
1
1
1
0
0
1
1
1
1
2
0
2
2
1
1
0
1
1
1
0
1
1
2
0
1
1
1
1
0
1
0
1
0
1
2
2
1
0
1
1
1
1
2
1
2
2
1
1
1
0
2
1
1
2
2
1
1
0
2
1
1
1
1
2
0
1
1
3
2
1
1
1
1
2
1
1
1
0
2
1
0
1
1
2
1
1
0
1
1
1
0
3
1
2
1
1
1
2
0
1
1
2
2
0
1
2
1
1
1
0
1
1
0
2
2
1
0
1
1
1
2
1
1
0
1
1
1
1
0
2
1
1
2
2
0
0
0
0
1
1
0
1
1
2
2
2
1
1
2
1
1
1
1
1
1
1
0
2
1
0
1
2
1
0
2
0
2
1
0
2
2
0
1
2
1
2
1
0
0
1
0
1
1
2
0
1
0
1
2
0
0
1
1
1
1
2
2
1
1
1
2
1
0
1
1
2
2
0
1
1
0
2
0
1
1
1
1
1
1
2
1
2
2
1
1
2
1
2
1
1
2
1
1
0
1
0
1
0
1
1
1
0
1
2
1
1
1
1
2
1
1
1
1
2
1
0
0
1
1
0
0
1
2
2
1
1
1
0
1
1
2
2
1
0
1
2
1
1
0
0
2
2
2
2
1
1
2
2
2
1
1
2
0
1
1
1
2
1
2
2
2
0
2
0
1
0
2
2
2
0
1
2
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
2
2
2
1
1
2
2
2
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
0
1
1
1
1
1
1
1
1
1
2
0
2
1
1
1
1
1
1
1
2
1
2
1
1
1
2
1
1
2
1
2
1
0
0
1
0
1
1
1
2
1
1
1
1
2
1
0
1
1
0
2
1
2
1
2
1
1
0
1
2
1
2
1
1
0
0
1
1
3
0
1
1
1
0
1
2
1
1
2
1
1
1
1
2
2
0
1
0
2
0
2
2
2
2
1
1
1
0
1
1
0
1
0
1
0
1
0
0
3
1
1
1
1
2
0
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
0
2
0
2
1
1
0
1
1
1
2
1
2
1
1
2
1
1
1
1
2
2
2
0
1
0
2
1
1
1
2
1
0
1
1
2
2
1
0
0
1
1
1
2
0
1
1
1
0
1
1
0
1
0
2
1
1
0
1
2
2
1
1
1
1
0
1
1
1
0
1
1
1
1
1
2
0
0
2
2
1
2
0
1
1
1
1
0
0
1
0
1
1
2
1
2
1
1
0
1
1
1
1
2
1
0
0
0
1
1
1
0
2
2
1
0
1
1
1
0
2
2
2
1
2
0
1
1
1
1
1
1
1
1
1
1
2
1
0
1
0
1
1
0
1
1
1
0
1
1
1
1
0
1
0
1
0
0
2
1
0
2
2
0
0
1
1
2
1
2
1
1
2
0
0
1
1
2
1
1
1
1
1
2
1
2
0
2
1
2
0
2
1
1
0
2
0
0
2
0
1
1
1
1
0
1
2
1
1
3
0
1
1
1
1
1
0
2
1
1
1
1
1
2
1
2
1
2
2
1
0
1
2
2
1
1
0
1
3
2
1
1
1
0
1
1
1
1
1
0
1
2
1
1
1
1
2
0
1
1
1
0
0
0
1
2
0
1
1
2
1
2
0
1
1
2
1
0
1
1
2
0
2
2
0
0
1
1
1
2
0
0
2
0
1
1
1
0
1
1
0
0
2
2
1
0
1
1
1
1
1
0
2
1
1
1
1
2
0
1
2
0
1
2
1
1
1
1
0
1
2
0
1
1
1
2
1
2
2
0
1
2
0
2
1
2
1
1
0
1
0
1
1
1
1
4
1
1
1
0
0
0
1
0
1
1
0
1
1
1
1
0
1
2
1
0
2
2
1
1
1
1
0
1
2
0
2
1
0
0
1
1
1
1
1
1
2
0
1
1
2
2
1
1
0
2
1
1
0
4
1
0
1
1
2
1
0
0
1
4
2
2
1
1
0
0
1
2
1
0
2
1
2
1
1
2
1
0
2
2
1
1
0
2
1
2
0
0
0
1
2
1
2
2
0
1
0
1
1
2
2
1
1
2
2
2
2
1
2
1
2
2
1
1
1
0
1
2
1
1
0
2
1
2
1
1
2
1
1
2
1
1
1
2
1
1
2
1
1
2
1
1
1
2
1
0
1
1
1
1
1
1
1
1
1
2
2
1
0
1
1
1
1
0
1
1
1
2
0
0
2
1
1
2
1
1
1
2
1
1
0
2
2
0
1
0
2
1
1
3
1
1
0
2
1
1
2
1
2
1
2
1
2
1
1
0
0
0
1
1
0
0
2
1
1
1
1
1
1
2
2
1
1
2
0
1
1
2
1
2
2
2
0
1
1
0
1
0
0
1
2
0
2
1
1
0
1
1
1
1
2
1
1
1
1
1
2
1
1
0
0
0
0
0
0
1
1
0
1
2
1
1
1
1
1
0
1
1
0
2
2
1
1
2
1
1
1
0
1
0
1
2
1
0
1
2
0
1
1
0
1
2
1
1
1
1
2
1
1
2
2
1
1
1
1
1
2
1
1
2
0
1
2
1
1
0
1
2
0
0
2
1
1
5
1
1
2
0
1
1
1
1
2
0
2
1
1
0
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
2
2
2
1
1
1
0
2
2
1
0
1
1
0
0
0
1
1
1
0
1
1
1
1
0
1
0
1
2
1
1
1
2
0
1
2
1
1
1
2
1
1
1
1
1
1
1
0
1
1
2
0
2
0
2
1
1
3
1
1
1
1
1
1
1
1
1
1
1
0
2
1
1
1
2
2
1
1
1
2
0
1
1
0
3
0
1
1
1
1
2
0
1
0
1
1
0
1
0
1
0
1
1
2
2
2
1
0
2
0
2
1
1
2
1
1
1
1
2
2
2
1
1
2
1
1
1
2
1
2
2
0
1
3
2
1
2
1
1
1
0
2
2
2
1
1
0
1
1
2
1
0
1
1
2
1
0
0
1
1
2
2
0
1
1
2
2
2
2
0
1
1
1
1
2
4
1
2
0
0
0
1
1
1
1
1
1
0
1
0
0
0
1
1
1
0
1
1
2
1
1
0
1
1
1
0
2
2
1
1
0
0
0
1
1
2
0
0
1
0
1
1
2
0
1
4
0
0
2
1
1
1
1
1
1
1
0
1
1
2
1
2
0
1
1
1
1
2
1
0
2
2
2
1
2
1
1
0
2
2
1
0
1
1
2
1
1
2
2
0
2
0
0
0
1
0
0
1
1
1
3
0
1
1
1
1
1
1
1
0
0
1
1
1
0
1
1
0
1
2
0
1
1
2
1
1
1
0
1
1
2
2
2
1
1
1
1
2
1
2
1
1
1
1
2
0
0
2
2
2
1
2
1
0
1
1
1
1
1
1
2
2
0
1
1
1
0
1
1
1
2
1
1
1
1
2
1
1
1
2
1
1
1
0
1
1
2
1
1
2
1
1
1
0
1
1
0
2
1
2
3
1
1
1
0
0
0
1
0
1
0
0
1
2
1
1
0
1
2
1
1
0
1
1
0
2
1
1
1
1
0
1
1
1
1
1
0
0
2
2
1
0
1
2
2
1
1
1
0
1
1
2
1
2
1
2
1
0
2
1
1
1
2
2
2
1
1
1
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
2
2
1
0
1
1
2
0
1
2
0
0
1
1
0
1
1
2
1
2
0
1
2
1
2
1
2
0
1
2
1
1
1
2
1
1
2
1
1
2
2
1
1
1
0
1
0
1
1
1
1
2
2
2
1
0
3
1
1
1
1
1
1
1
1
0
1
1
0
0
1
0
1
1
2
1
0
1
1
1
1
0
2
1
1
1
1
1
1
0
0
1
2
0
0
1
1
1
2
0
1
1
1
1
1
0
0
2
1
1
1
1
1
1
1
1
1
0
0
1
2
1
0
2
0
1
1
1
2
1
1
1
0
1
2
1
0
1
1
1
0
1
1
1
1
1
0
1
1
1
1
1
0
1
0
0
1
1
2
1
0
1
1
1
2
1
0
2
0
1
1
1
2
2
0
2
1
1
0
1
0
3
1
0
1
0
1
0
1
2
1
1
1
1
1
0
0
2
0
1
1
1
1
1
0
1
1
1
2
1
2
1
1
1
1
2
0
1
2
1
1
1
0
0
1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
1
1
1
3
0
1
0
1
1
1
1
1
1
2
0
0
2
0
1
2
1
1
1
1
0
0
0
1
1
2
1
1
1
2
1
0
1
1
2
0
0
0
1
1
2
2
1
0
1
1
1
1
0
0
1
1
1
1
0
1
1
1
1
1
1
1
1
2
0
2
0
2
1
0
1
1
1
1
1
1
1
2
1
0
1
1
2
1
1
3
1
1
1
0
1
2
0
1
2
2
0
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
0
1
2
2
1
1
1
1
1
1
1
1
1
0
2
0
1
2
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
0
1
1
1
2
0
1
2
1
1
1
2
1
2
1
1
1
2
0
2
1
1
2
1
1
0
1
1
1
1
2
1
0
2
2
1
1
1
1
1
1
0
2
1
2
1
2
0
0
1
2
1
2
1
2
2
2
0
1
3
1
1
1
0
1
1
0
1
1
1
0
0
2
1
2
0
2
2
2
1
1
0
1
1
1
1
1
1
1
0
0
1
1
1
1
1
1
2
1
0
0
0
2
1
1
1
1
2
1
1
1
1
2
1
0
2
1
1
2
2
0
1
1
0
2
0
1
2
2
1
2
2
1
3
1
1
1
0
0
2
1
2
1
1
0
1
1
2
1
0
1
2
1
1
0
0
1
1
1
1
1
2
1
1
1
2
2
2
0
2
2
1
1
0
1
1
1
2
1
0
2
1
3
0
1
0
1
2
0
0
2
1
1
1
1
1
1
1
0
0
1
0
2
1
1
0
2
1
0
0
1
0
1
1
0
2
0
0
1
1
0
1
1
0
1
2
1
1
1
1
2
1
2
2
1
2
1
2
3
1
1
1
1
0
2
2
1
1
1
1
2
1
0
1
0
1
1
1
1
1
2
0
0
1
1
2
1
0
2
2
2
1
1
0
1
0
2
1
0
1
1
0
2
1
1
1
1
1
1
0
1
1
1
0
2
1
2
1
2
1
2
2
1
1
1
2
1
1
2
0
0
2
2
0
2
0
1
2
1
0
1
3
1
2
1
1
1
1
2
0
2
1
1
1
2
1
1
1
1
1
1
1
1
1
0
1
1
1
0
1
1
1
1
1
0
2
1
0
1
1
1
0
1
0
1
1
1
1
2
1
0
1
2
1
1
1
1
1
2
1
1
2
1
1
0
1
0
0
1
0
2
0
1
1
1
2
2
0
2
0
2
0
2
2
1
1
1
1
2
1
0
0
1
2
1
2
1
1
1
0
1
1
0
1
0
1
2
1
0
2
1
1
1
2
2
1
1
1
1
0
2
2
0
0
1
1
1
1
1
0
2
2
2
1
2
2
2
1
1
1
1
2
2
1
1
2
2
1
1
1
0
1
1
1
2
1
1
2
0
2
2
1
2
0
0
2
1
1
1
1
0
1
1
3
2
1
2
1
0
1
0
1
2
0
1
1
0
1
4
1
1
1
1
1
1
1
2
1
1
1
0
1
2
0
1
0
0
0
1
1
1
1
0
2
0
2
1
1
1
1
0
1
1
0
1
2
1
1
0
1
2
2
1
2
1
0
1
4
1
0
1
2
1
0
1
1
1
1
0
0
2
0
2
1
1
1
0
1
0
1
1
0
1
2
0
2
0
0
1
0
1
1
0
2
0
1
0
0
0
2
1
0
0
1
1
1
2
2
1
1
1
0
1
2
1
2
1
1
1
1
1
1
2
1
1
1
2
1
0
1
1
1
1
1
1
1
1
2
0
1
1
1
2
2
2
2
1
1
1
1
1
0
1
1
1
2
1
0
1
0
2
1
0
1
2
1
3
2
1
0
1
1
3
1
1
0
1
1
1
1
1
2
1
1
1
1
1
1
1
2
0
1
1
1
2
1
1
0
0
1
1
0
0
1
1
0
2
2
1
1
2
1
1
0
0
0
0
0
0
0
0
1
1
1
5
1
1
1
0
1
1
1
2
1
2
2
0
1
0
0
1
0
1
1
0
1
2
1
0
1
1
1
1
2
3
1
2
1
2
2
2
2
1
2
2
2
1
2
0
2
1
2
1
2
0
1
1
2
1
0
1
1
1
0
1
1
1
1
1
2
1
2
1
1
1
0
2
1
1
0
1
2
1
1
1
0
2
0
2
1
0
0
0
1
2
1
2
1
1
1
1
1
0
0
1
1
0
1
1
2
2
1
2
0
1
1
2
0
0
1
1
1
1
1
1
2
1
1
0
2
1
1
2
1
1
1
1
1
1
1
4
0
1
1
0
0
0
2
0
1
1
0
1
1
1
1
2
2
2
1
2
1
0
0
1
2
1
1
1
1
2
2
1
1
1
1
2
1
1
2
2
1
1
0
2
2
0
0
1
1
0
0
1
1
1
1
1
1
1
2
1
2
0
1
1
1
1
0
1
1
1
0
1
0
0
0
1
1
2
1
1
1
1
0
0
0
1
1
0
2
2
1
2
1
1
1
1
2
1
1
1
1
1
1
2
1
1
0
1
1
1
2
1
0
1
0
1
1
1
0
1
0
1
1
0
0
2
1
1
1
1
1
3
1
1
2
1
1
1
0
1
2
1
2
0
1
2
1
0
2
2
1
0
0
2
0
0
2
0
2
1
2
0
1
0
0
2
5
0
1
1
2
1
1
1
2
0
0
1
2
1
1
1
1
2
2
2
1
1
1
2
1
1
1
0
2
0
2
1
0
1
2
1
1
1
1
3
1
0
1
0
0
1
2
2
2
2
0
0
2
2
1
2
2
1
0
1
0
2
2
2
0
2
1
2
0
1
1
2
0
1
1
1
0
1
1
0
1
2
0
1
2
1
1
1
2
2
0
0
1
1
2
1
2
2
1
2
1
1
1
2
1
1
1
2
0
2
1
2
1
1
2
1
0
1
1
1
2
0
1
3
0
1
0
3
0
2
1
1
1
1
0
1
2
1
0
2
0
1
1
0
0
1
1
1
0
1
0
1
2
1
2
1
2
1
2
1
0
2
0
1
0
1
1
1
1
1
2
1
1
1
0
2
1
1
1
1
1
0
1
2
1
1
1
1
2
0
1
1
0
1
2
1
2
1
0
1
1
1
1
2
1
0
1
1
1
1
0
2
1
1
2
1
1
1
1
1
0
1
1
1
1
0
1
1
0
0
2
1
1
2
2
0
1
0
2
1
1
1
0
1
1
0
1
1
1
0
2
1
1
1
1
1
0
1
1
0
2
2
2
0
1
1
1
1
0
1
0
1
1
1
0
0
2
1
1
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
0
1
1
1
0
2
1
2
1
1
2
0
1
1
1
1
1
1
3
1
1
1
1
0
1
1
1
2
1
2
2
1
1
1
1
0
1
2
1
2
0
1
1
1
2
1
1
1
1
1
1
0
2
2
1
1
1
1
1
0
0
2
1
0
0
2
1
1
1
1
0
1
0
2
1
3
1
2
1
0
1
0
2
2
0
1
1
2
1
1
0
1
2
0
1
2
1
1
0
1
0
1
0
2
0
1
1
1
0
1
0
1
1
1
2
0
1
2
3
2
2
1
0
0
1
1
1
1
1
0
0
1
2
2
2
1
2
1
1
1
1
1
2
0
1
2
2
0
1
2
1
0
0
2
1
2
1
1
1
0
2
1
1
1
1
1
1
2
1
0
1
2
2
2
0
1
0
1
1
1
2
1
2
1
1
1
2
2
0
1
0
2
1
1
2
2
0
2
0
1
1
2
1
0
1
2
1
0
1
1
2
1
1
2
2
0
2
1
0
0
2
1
0
1
1
1
2
2
0
1
1
0
1
1
1
2
1
0
1
1
0
1
1
0
0
0
1
1
1
1
1
0
1
2
1
1
1
1
1
2
1
1
2
1
2
1
0
1
2
0
2
2
1
1
2
0
2
2
2
1
2
1
0
0
1
1
1
1
1
1
1
1
2
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
2
1
1
1
1
1
2
0
0
1
0
2
0
2
1
1
1
1
1
1
1
1
0
1
1
2
1
1
2
1
1
1
1
0
1
2
2
2
1
1
0
0
1
2
1
1
0
2
1
1
1
1
1
1
1
1
1
2
1
0
3
2
1
1
1
2
0
2
1
1
3
1
2
0
0
1
1
1
2
1
2
1
2
2
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
0
1
3
1
2
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
4
1
1
1
1
2
1
1
1
1
1
1
0
1
2
2
2
1
0
2
4
1
2
1
1
1
1
1
2
1
1
1
1
0
1
2
0
1
1
1
2
1
2
2
1
1
0
2
2
2
1
1
1
1
0
0
0
1
2
0
1
2
1
0
1
1
1
2
1
1
1
1
0
2
1
1
0
0
1
0
0
1
1
1
1
1
1
1
2
0
2
0
1
1
1
1
0
2
0
1
2
1
1
1
2
1
2
2
2
0
1
1
0
1
0
2
0
0
0
1
1
1
1
1
1
2
0
1
1
0
2
1
0
1
2
2
1
2
1
2
1
1
0
1
2
0
1
1
1
0
1
1
1
1
2
0
1
1
1
1
1
2
1
0
1
1
1
2
2
1
0
1
1
1
1
0
1
1
1
2
2
2
1
1
0
1
0
2
0
0
2
0
0
1
1
1
2
2
2
2
1
1
1
1
0
1
2
1
1
1
1
0
1
1
1
0
1
0
0
1
2
1
0
0
2
1
1
1
1
2
2
3
1
0
2
1
1
1
0
1
1
0
1
2
1
1
1
2
0
1
1
2
1
0
1
1
0
4
3
0
2
2
1
0
1
1
1
1
1
1
2
1
1
0
1
1
2
0
1
1
1
1
2
1
2
0
1
1
1
1
1
1
1
1
1
1
0
1
2
1
0
0
2
2
2
1
2
1
1
2
0
1
2
1
1
3
1
2
1
0
1
1
1
1
1
1
0
1
1
1
1
1
1
2
1
1
1
1
1
1
2
3
0
1
1
1
2
1
1
0
1
1
1
2
1
1
1
1
0
2
0
1
1
1
2
1
1
1
1
0
0
1
1
3
1
1
1
1
2
1
1
1
0
0
1
0
1
0
1
0
1
2
1
0
2
1
2
1
1
0
1
1
1
2
1
2
2
1
2
1
1
1
2
2
0
0
1
0
1
2
1
1
1
1
2
0
1
1
2
1
0
2
1
1
0
1
1
1
0
1
1
2
2
1
0
1
1
1
1
0
1
2
1
2
0
1
2
2
1
1
2
1
1
0
1
2
0
1
2
2
1
0
1
2
0
2
1
2
1
1
2
1
2
1
2
1
0
2
2
0
0
1
2
2
1
1
0
1
2
2
0
1
1
1
1
0
2
1
1
1
0
2
1
1
1
1
1
0
0
0
1
0
1
2
0
1
1
1
1
0
1
1
0
1
2
1
0
1
1
1
0
0
1
1
2
0
0
1
1
1
1
0
1
2
3
0
0
2
0
1
0
1
1
1
1
1
1
1
0
1
1
1
0
0
1
1
1
2
1
2
1
0
0
1
1
1
1
1
2
0
1
1
0
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
0
1
2
1
1
1
0
1
1
2
0
1
1
2
2
1
2
1
1
1
0
2
0
0
2
1
1
1
0
0
1
2
1
1
0
0
1
1
1
1
1
0
1
1
1
1
1
2
2
1
1
2
2
0
1
2
1
1
0
1
0
1
2
1
0
1
2
1
1
1
2
1
1
2
1
0
2
1
0
1
1
0
1
1
1
1
1
1
2
1
2
1
0
1
0
1
1
0
0
1
1
2
1
1
1
2
1
1
2
1
0
0
1
2
1
1
2
2
1
1
1
0
1
0
2
2
1
1
2
2
0
1
1
1
1
2
2
1
0
1
0
1
1
1
0
0
1
0
1
1
1
0
1
1
1
1
0
1
0
0
1
2
2
1
1
1
0
1
2
1
1
0
2
1
0
4
1
1
2
1
2
0
1
1
1
1
1
1
2
1
1
1
1
2
1
0
0
0
1
1
1
2
1
2
0
2
0
2
0
0
1
0
1
2
1
0
1
1
2
1
1
0
2
2
0
0
0
1
1
1
0
0
2
0
0
1
1
2
2
1
1
2
2
2
2
1
1
1
1
0
1
1
0
1
0
2
1
1
1
1
4
1
1
1
1
0
3
1
1
0
1
2
1
1
1
2
1
0
2
2
1
0
0
2
2
1
1
1
1
0
1
1
0
1
1
1
1
1
1
0
1
1
1
1
0
1
1
2
1
0
0
0
2
1
1
3
1
0
2
2
1
1
1
2
2
1
1
1
1
1
1
0
2
0
1
1
2
1
0
1
0
1
0
1
1
2
0
0
1
2
2
1
0
1
2
1
1
1
1
2
1
1
1
2
0
1
1
0
0
2
2
2
1
1
1
1
1
0
1
2
2
1
1
0
1
2
1
1
1
0
1
1
1
0
1
1
3
1
0
2
1
1
1
1
2
1
2
0
2
1
1
2
4
1
1
0
1
1
0
1
1
0
1
2
0
1
2
1
0
2
0
1
1
2
1
0
2
1
1
1
0
2
0
1
2
1
1
1
1
0
2
2
1
2
1
2
2
0
0
2
1
2
0
2
0
1
0
0
1
1
1
1
1
1
1
1
1
2
2
1
1
0
1
2
0
2
0
0
1
1
0
0
1
1
2
1
1
0
1
1
1
2
1
2
1
4
1
0
1
0
1
1
0
2
1
2
1
1
0
1
1
1
0
1
0
1
1
2
2
1
2
1
1
1
1
2
1
1
1
0
3
1
1
1
2
2
2
0
1
2
1
1
1
2
1
1
0
1
2
1
1
0
1
0
2
1
2
1
1
1
1
1
1
0
2
1
0
1
1
1
2
1
1
1
0
1
1
1
1
0
1
1
0
2
0
2
1
1
2
0
3
1
1
1
2
0
0
1
1
1
2
2
0
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
0
1
2
1
2
2
0
1
0
2
0
2
1
0
0
1
0
1
2
2
1
1
1
1
0
0
1
1
1
2
0
1
2
3
2
1
2
2
1
0
1
1
2
0
2
1
1
1
1
1
1
2
1
1
1
1
0
3
1
2
1
2
2
0
1
2
2
2
0
1
0
0
0
1
2
1
0
1
1
1
1
1
1
2
1
1
0
1
1
1
2
2
1
2
1
0
0
2
1
2
1
1
0
1
1
1
0
2
1
1
1
0
1
1
1
2
1
1
0
1
0
1
0
1
2
1
1
1
1
1
1
2
2
0
1
1
1
2
1
0
2
2
1
1
0
1
0
1
2
1
0
2
1
2
1
1
0
0
1
1
2
0
3
0
0
2
1
2
1
1
2
2
1
3
1
1
2
1
0
0
1
1
1
1
1
1
1
1
1
1
1
2
2
1
0
0
0
2
1
0
1
2
2
0
2
1
1
1
1
0
0
2
1
2
2
0
1
1
1
0
2
2
1
1
2
1
1
0
1
2
1
1
3
1
0
1
1
1
0
0
0
1
1
1
2
1
1
1
0
1
3
1
1
0
2
2
1
2
1
2
0
1
1
1
2
1
1
1
1
1
1
0
0
1
1
0
0
0
2
1
2
1
1
1
0
1
1
1
1
2
2
1
4
1
0
1
0
1
0
1
0
2
1
2
0
1
0
2
0
1
2
1
2
1
1
1
6
0
2
1
2
1
1
1
1
1
1
0
1
0
1
0
1
1
1
2
1
1
1
1
2
1
1
0
2
1
2
0
1
2
2
1
0
1
1
2
0
1
1
0
1
1
1
1
2
2
1
1
2
1
1
0
0
1
1
0
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
0
1
1
1
1
1
1
1
1
1
1
0
1
0
1
1
0
1
1
1
1
2
1
0
0
0
2
1
1
1
1
1
1
1
0
2
2
2
1
1
1
1
1
1
1
2
0
1
0
2
0
1
0
1
1
2
2
1
0
1
2
1
1
1
1
1
1
1
0
1
1
1
0
2
2
2
1
2
1
1
1
1
1
1
1
2
0
1
1
1
1
0
1
1
1
1
1
1
1
1
2
1
4
0
1
1
0
1
2
1
2
1
1
1
2
2
2
1
1
2
0
1
2
0
1
0
1
1
1
1
1
1
1
1
1
0
1
1
1
1
2
1
0
1
1
2
1
2
1
1
1
3
1
1
1
1
0
1
2
1
0
1
0
1
0
2
2
1
0
1
1
2
0
0
0
0
1
2
1
1
1
1
1
1
2
1
0
1
1
1
1
2
1
2
0
2
0
0
0
2
1
0
1
0
0
1
1
1
0
2
1
0
0
2
1
1
1
1
1
1
0
0
2
0
1
0
1
1
1
1
2
1
0
2
1
1
0
1
2
0
2
1
0
1
0
1
2
2
0
1
1
1
0
2
1
1
0
2
2
0
0
1
1
1
1
1
0
0
1
2
2
1
1
0
1
2
0
1
0
0
1
1
0
0
4
2
2
0
1
1
1
1
1
1
3
2
2
1
1
1
1
1
2
1
1
1
0
1
1
1
1
1
1
2
0
1
2
2
1
0
1
1
1
2
1
2
2
2
1
1
1
2
1
2
0
1
0
2
1
1
2
0
2
2
1
1
1
1
1
3
1
1
1
1
0
2
1
1
2
1
1
2
1
0
0
1
1
1
1
1
2
2
1
1
0
1
1
0
1
0
1
2
2
2
1
2
2
0
1
1
2
1
1
0
2
0
2
1
1
1
2
0
2
1
1
0
1
1
1
1
0
0
1
0
0
1
0
1
0
2
1
1
0
1
2
1
0
2
1
2
1
1
0
2
1
1
0
1
1
0
1
2
1
1
0
2
1
1
1
0
1
1
1
0
0
1
2
1
0
2
1
1
1
0
0
1
1
1
2
2
1
1
1
1
1
0
1
2
1
0
0
1
1
1
1
1
1
2
1
2
0
1
1
1
0
1
2
1
2
0
2
2
0
1
1
0
2
1
2
0
2
2
2
1
1
2
2
2
0
0
1
4
0
2
0
0
0
1
2
1
1
1
0
1
2
1
1
1
1
1
1
1
2
2
0
0
1
1
1
0
1
2
2
1
1
1
2
0
0
0
1
1
0
2
2
2
1
1
0
2
1
1
0
1
0
1
2
1
1
1
0
2
0
1
0
2
1
2
1
0
1
2
2
1
2
0
1
0
0
1
1
0
1
2
1
2
0
1
2
0
1
2
2
1
1
2
1
1
2
1
1
2
1
0
2
1
0
1
1
0
1
1
1
2
2
1
1
1
0
3
1
1
0
2
0
2
1
1
1
1
1
2
1
2
2
1
0
1
0
2
2
0
2
1
1
0
1
1
1
1
1
0
2
1
1
2
0
2
1
1
0
2
2
1
1
1
0
2
1
1
1
1
2
0
1
0
1
2
1
1
2
2
0
2
1
1
1
0
0
1
1
2
1
0
1
1
1
0
2
1
0
1
1
2
1
2
2
1
2
0
1
1
0
2
2
0
0
1
1
1
0
1
1
1
0
1
1
0
1
2
1
1
1
2
1
2
0
1
1
1
1
2
2
2
0
1
3
1
1
1
1
0
1
2
1
1
1
1
1
0
0
2
1
1
2
1
1
1
1
1
1
1
1
1
0
1
1
0
0
1
1
1
0
0
2
1
2
1
1
2
0
1
2
2
0
3
1
0
1
1
0
4
1
1
1
1
1
0
1
0
2
1
0
0
2
0
1
2
1
0
1
2
1
1
2
2
1
1
2
1
0
0
0
1
2
0
0
0
2
1
1
2
1
1
0
1
1
0
2
2
1
1
0
2
1
3
1
1
1
1
2
1
1
0
2
1
0
2
1
0
0
1
1
2
1
2
0
1
1
1
1
1
2
0
2
1
0
1
1
2
2
1
2
2
1
1
2
1
2
0
2
2
1
1
1
0
2
1
2
1
2
1
1
0
2
1
1
1
1
2
1
1
2
0
1
1
0
1
1
1
1
1
0
0
1
1
1
2
1
1
0
0
0
1
3
2
1
1
1
1
2
1
1
1
1
1
0
1
1
0
1
1
1
0
1
1
1
1
2
1
1
2
1
1
1
1
0
0
2
0
1
0
1
2
3
2
1
0
1
0
2
1
1
1
2
1
2
1
0
1
2
2
2
1
1
1
1
0
2
1
1
1
2
0
2
1
0
1
2
1
2
1
1
2
0
1
1
2
2
1
1
1
2
0
1
1
1
0
2
1
2
2
1
1
1
1
2
0
1
2
2
0
1
0
0
1
0
0
2
0
1
1
2
1
1
2
2
1
2
1
1
1
1
1
2
0
1
0
1
2
2
1
1
1
1
1
1
1
0
1
0
2
1
1
0
1
1
1
1
0
1
1
1
1
2
3
2
1
0
1
1
0
2
2
1
2
1
0
0
1
1
2
0
2
2
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
0
2
2
2
1
2
0
0
1
3
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
2
2
0
0
1
1
0
1
0
1
1
1
1
1
1
1
2
1
2
0
2
1
1
0
1
1
1
2
0
0
2
1
1
1
1
1
1
2
0
1
0
1
2
1
2
1
1
0
0
2
1
0
1
1
1
1
1
1
1
0
1
1
1
1
2
0
1
1
0
1
0
0
0
1
0
1
0
1
0
1
2
2
1
1
2
1
2
2
1
1
1
1
2
1
1
2
2
1
0
2
1
1
1
1
2
0
0
1
1
2
1
0
1
1
1
1
0
2
1
1
1
1
0
2
1
0
2
2
1
2
1
1
1
0
0
2
1
0
1
2
0
0
1
0
1
1
1
1
0
2
1
0
1
1
1
1
0
2
2
2
1
2
2
1
2
1
2
1
0
2
1
1
2
1
0
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
0
2
1
2
2
1
1
0
2
0
1
4
0
1
2
1
1
0
1
1
0
1
0
2
1
2
1
1
1
0
2
2
2
1
1
2
1
1
1
0
1
1
2
1
1
1
0
1
2
1
1
2
1
1
1
1
0
1
1
0
1
1
0
2
0
1
0
1
1
0
0
1
1
1
2
2
2
1
0
1
2
1
0
1
1
0
0
0
1
1
0
1
0
1
1
1
2
1
1
1
0
1
1
0
2
0
1
2
2
1
1
1
4
2
1
2
1
1
0
1
0
1
1
1
2
1
2
0
1
1
0
1
2
1
1
0
1
1
0
2
2
1
2
1
2
1
2
1
1
1
0
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
0
1
0
2
0
1
1
2
1
1
1
1
1
1
2
1
2
2
1
2
2
2
0
2
0
0
2
1
0
0
1
0
2
2
1
2
0
2
2
1
1
0
1
0
1
1
2
0
1
1
1
1
2
0
2
1
1
1
0
1
1
1
2
2
1
0
1
2
1
1
1
1
2
1
0
0
0
0
1
2
1
1
0
1
1
1
1
1
0
1
1
1
1
2
1
0
1
2
2
2
1
2
2
1
2
2
1
0
1
0
1
0
0
2
0
1
1
2
0
0
1
1
1
0
0
1
2
1
1
1
1
0
2
2
1
1
1
2
2
0
1
1
1
1
2
0
1
1
2
1
0
0
1
3
1
1
1
1
0
0
2
0
1
1
1
2
0
1
1
1
1
1
1
1
1
2
1
1
0
1
1
2
1
0
0
1
1
3
2
1
2
0
0
2
1
2
0
1
1
1
1
2
2
1
2
1
1
1
2
1
1
0
2
1
1
2
1
2
1
2
2
1
2
0
2
1
1
2
0
1
2
1
2
2
1
2
1
1
1
2
0
1
2
1
1
1
2
1
1
1
0
2
1
1
2
1
2
1
1
1
1
1
0
2
0
1
1
0
0
1
2
1
1
1
0
1
2
1
0
2
0
0
2
1
1
1
1
2
0
2
1
2
1
2
1
1
2
1
2
1
0
1
1
2
1
0
1
2
1
1
0
2
1
2
1
2
1
1
1
0
1
1
2
0
1
2
0
0
1
0
1
1
0
2
2
2
4
0
1
1
0
2
2
0
1
1
2
2
2
1
1
1
1
1
1
1
0
1
1
2
1
1
1
0
1
1
1
0
1
0
1
1
0
1
2
1
1
1
1
1
1
2
0
1
2
1
2
1
0
1
1
1
0
2
1
2
1
0
2
1
1
2
0
1
1
1
1
2
2
1
0
1
1
1
1
2
1
0
1
1
1
1
1
2
1
1
2
1
0
1
1
1
1
1
1
1
0
1
1
1
2
2
1
1
1
2
1
0
0
1
1
1
1
0
2
1
0
1
2
2
1
1
1
2
1
1
2
1
1
1
1
1
1
2
0
1
1
3
1
1
1
1
1
1
1
2
1
1
1
1
1
0
0
1
2
0
1
1
0
0
0
0
1
0
0
1
1
1
1
2
1
2
0
2
2
2
0
2
1
1
1
1
1
2
0
1
2
2
0
1
2
0
1
1
1
1
2
2
1
0
2
0
1
1
1
1
2
0
2
1
0
1
2
1
0
0
1
1
1
1
2
1
2
1
1
1
2
2
0
1
1
1
2
0
0
2
1
1
0
0
1
1
2
1
1
1
1
1
3
2
3
1
1
2
1
1
0
1
2
1
0
0
1
0
1
2
1
1
1
1
3
0
1
1
0
2
1
0
1
1
2
2
2
0
2
0
0
0
2
1
1
0
0
1
1
0
2
1
1
1
1
1
1
1
1
1
2
1
0
1
0
2
2
1
2
0
2
1
1
1
0
1
1
2
1
1
1
1
2
1
1
1
2
1
0
1
1
0
1
1
2
1
1
1
0
0
1
1
2
1
1
1
2
2
1
1
2
0
0
2
0
0
1
1
1
1
1
2
0
1
0
1
2
1
2
1
1
1
2
1
1
1
2
0
1
1
1
2
2
1
0
2
1
1
2
2
0
1
2
1
1
2
1
1
0
0
1
1
1
2
2
0
2
1
1
1
2
0
2
2
1
1
1
2
1
2
1
1
1
2
0
2
1
1
1
1
2
1
5
2
1
1
1
2
2
2
2
2
0
0
2
2
1
1
1
1
0
1
2
1
0
2
0
0
1
1
2
2
1
2
1
2
0
2
2
1
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
2
1
0
1
1
1
0
2
2
1
0
1
1
2
1
1
1
1
2
1
1
1
0
1
0
0
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
0
2
0
1
1
0
1
1
1
0
1
2
1
2
2
2
1
0
2
0
1
1
0
2
1
2
1
0
1
2
0
0
0
1
1
0
2
2
1
1
1
1
2
1
2
1
1
0
1
1
2
1
2
1
1
0
2
0
1
1
1
0
1
1
0
2
2
1
1
1
1
2
2
1
1
1
1
1
1
2
1
0
1
1
2
0
1
2
1
2
1
0
0
1
1
1
2
2
1
1
1
1
1
3
1
1
1
1
0
1
1
1
2
2
0
1
1
2
2
2
1
1
0
2
1
2
2
1
0
1
2
1
2
0
1
0
0
0
1
0
0
1
2
2
1
2
0
0
1
2
1
1
1
1
1
1
0
1
1
2
1
1
1
2
1
1
2
2
0
2
1
0
2
1
1
1
2
1
1
1
1
2
0
1
1
0
1
2
1
0
1
1
1
2
2
1
1
2
0
0
0
0
2
1
1
2
1
0
1
1
2
1
0
1
1
1
0
2
2
1
1
1
2
1
1
1
2
0
0
1
1
1
1
1
0
2
1
0
0
2
2
1
0
1
1
1
1
1
1
0
0
1
2
0
1
1
0
1
2
1
1
0
2
2
2
1
2
1
0
1
1
0
2
2
2
1
2
1
1
2
1
0
1
2
2
1
2
0
1
2
0
2
1
1
0
1
0
0
1
1
0
1
1
0
1
0
0
2
0
2
1
1
0
0
2
2
1
0
1
2
2
0
1
0
1
2
0
0
3
1
2
0
2
1
1
1
0
1
2
2
1
0
2
1
1
1
0
2
2
0
0
0
1
1
1
0
0
1
1
0
1
1
1
0
2
1
1
1
0
2
0
2
2
1
1
2
1
1
0
2
1
1
1
3
1
0
2
1
0
1
1
1
1
0
1
0
2
0
1
1
0
1
2
1
0
1
1
1
0
1
1
1
1
1
1
2
1
0
2
2
1
2
2
1
1
1
1
1
0
1
1
2
0
0
0
1
0
2
0
1
2
2
1
1
1
0
2
0
1
2
1
1
2
0
1
0
1
2
1
2
1
1
2
0
1
1
0
2
1
1
1
0
1
0
1
1
0
1
1
1
2
0
1
0
1
1
0
0
2
2
1
1
0
2
1
0
1
2
2
1
2
1
1
2
0
2
1
1
1
1
1
1
1
0
1
2
1
2
1
1
1
2
0
2
1
2
0
1
1
2
0
1
2
0
1
1
1
1
1
0
2
1
2
1
0
1
1
1
1
0
1
1
1
0
1
1
2
1
2
1
1
1
1
1
0
2
1
0
1
1
2
0
1
1
2
1
2
2
2
2
2
0
1
0
1
1
2
2
1
1
2
0
1
0
1
1
1
1
1
1
0
0
0
0
1
2
1
1
2
0
1
0
2
1
1
2
1
2
1
1
1
1
0
1
2
1
1
2
2
2
2
1
1
0
1
2
0
1
2
1
1
1
0
2
2
2
3
2
1
1
1
0
1
1
0
1
0
1
1
1
1
2
1
1
2
2
2
2
0
0
0
1
1
1
1
1
0
1
1
1
0
1
1
1
1
1
1
2
2
1
1
1
1
1
1
3
1
0
1
1
2
1
1
0
1
1
1
2
1
0
3
1
1
1
2
1
1
1
1
1
0
1
0
1
2
2
1
0
1
1
0
2
2
1
1
1
1
0
2
0
1
2
1
0
2
1
2
1
0
0
1
0
1
2
0
2
0
1
1
1
1
1
0
1
2
1
1
0
2
1
2
2
1
2
2
1
2
2
1
1
1
1
2
0
1
1
0
2
0
0
0
1
0
1
1
2
1
1
1
1
1
0
0
0
2
1
1
1
0
1
0
2
0
0
1
2
0
1
1
1
1
1
1
1
1
1
1
1
0
0
2
1
1
1
2
1
1
2
1
0
1
2
1
1
1
1
1
2
1
0
1
1
1
0
2
1
2
2
0
1
1
0
2
0
1
2
2
1
1
2
0
0
2
1
1
1
0
2
1
1
0
1
0
0
2
3
1
0
0
2
1
2
0
0
1
1
0
2
1
1
0
1
3
0
1
0
0
1
1
1
1
1
1
0
0
1
1
2
1
1
1
1
0
2
2
1
0
1
1
1
0
1
1
2
1
0
0
0
1
1
0
0
2
1
0
1
0
2
2
0
2
2
2
2
0
0
1
1
1
1
0
1
1
1
0
1
2
0
1
1
0
0
0
2
2
1
2
1
1
1
1
1
1
2
2
0
1
1
1
0
1
1
1
1
1
1
1
1
2
1
0
2
0
1
1
1
0
0
2
1
1
0
0
2
1
2
1
1
1
3
1
1
1
0
1
1
2
1
1
2
1
1
1
2
2
1
0
0
1
2
1
1
2
1
1
1
1
1
2
0
0
1
0
1
2
1
2
0
2
1
1
0
1
1
2
3
1
2
0
2
1
1
0
1
2
0
0
1
2
2
1
1
1
0
1
0
2
2
0
2
1
1
0
1
1
1
1
2
1
2
1
1
1
1
0
2
2
1
1
0
1
1
1
1
1
2
1
2
1
2
2
1
2
2
1
0
1
1
3
1
0
1
2
1
0
1
1
2
2
1
1
0
1
1
2
1
0
1
0
2
2
0
1
0
1
1
2
2
1
1
1
1
1
0
1
1
1
0
1
1
0
1
2
1
2
1
0
0
3
1
2
2
1
1
1
0
2
1
1
1
1
1
1
1
1
1
1
0
2
0
1
1
1
1
0
0
1
1
1
0
2
1
1
1
2
0
1
1
2
2
1
1
2
1
1
1
1
1
1
1
0
0
2
0
1
2
1
1
0
2
1
0
1
0
1
1
0
1
0
2
0
1
2
1
1
1
1
1
1
1
0
2
2
1
1
0
1
0
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
0
2
1
0
1
0
0
1
0
0
0
1
2
2
0
1
0
2
1
0
2
1
0
0
0
1
1
1
1
0
1
1
0
1
1
0
1
2
2
1
1
0
1
2
1
3
0
1
1
1
0
1
1
2
1
2
1
2
0
1
1
1
1
1
2
1
1
1
1
1
0
1
1
2
1
1
0
1
2
1
1
0
0
1
1
1
1
0
1
1
0
0
1
2
2
2
2
1
2
1
1
2
2
0
1
1
1
2
0
2
2
1
0
1
1
0
2
1
2
0
1
1
1
2
0
1
1
1
2
1
1
1
0
1
1
2
2
0
2
1
2
1
0
1
1
0
0
1
1
2
2
2
2
1
1
0
1
1
1
1
0
1
1
1
1
0
0
1
0
0
1
0
1
0
0
1
2
0
1
0
1
1
0
0
2
2
2
0
1
1
1
0
1
1
2
2
0
0
0
1
1
1
1
1
1
1
1
1
2
1
1
0
1
1
2
1
2
1
1
2
1
2
0
1
1
2
0
0
1
1
2
2
1
1
0
1
0
1
1
2
2
1
2
0
1
1
1
1
2
1
1
2
1
1
1
1
1
0
0
2
1
0
0
2
2
1
1
0
1
1
1
0
1
0
0
2
1
2
1
1
1
1
1
1
0
0
2
1
0
1
1
0
1
1
0
1
1
1
2
1
0
1
1
1
1
0
0
1
1
2
0
1
1
1
2
1
0
0
1
0
0
1
2
1
0
2
2
1
2
1
1
2
2
0
1
1
1
1
1
1
1
1
0
2
0
2
1
1
2
1
0
1
1
0
0
0
1
2
1
1
0
1
1
1
1
0
2
1
0
1
1
2
2
1
2
2
1
0
0
1
1
1
1
1
1
2
2
0
1
1
1
1
2
2
1
1
2
1
0
1
2
0
2
2
2
1
0
1
0
1
0
1
1
2
1
2
0
1
2
1
1
3
2
1
1
1
2
0
1
2
1
1
1
0
1
0
2
1
1
0
2
4
1
2
1
1
0
2
1
0
1
0
1
1
1
1
2
2
1
1
0
2
1
1
2
1
0
1
0
0
1
0
2
1
1
0
1
1
1
2
1
1
1
1
1
1
1
1
0
0
1
0
1
0
1
1
1
2
2
1
1
1
2
1
2
0
0
0
1
1
1
1
2
1
1
1
1
0
1
1
1
0
1
1
2
1
2
1
2
1
1
1
1
1
0
0
1
1
2
2
2
0
1
0
1
1
2
1
1
1
1
0
1
0
1
1
1
1
1
0
1
0
1
1
2
1
2
1
2
1
1
0
1
2
1
2
2
1
2
1
1
2
1
2
1
2
0
1
1
0
1
1
1
0
0
2
1
2
2
1
2
0
0
1
2
0
1
1
2
2
1
1
1
1
1
1
1
0
1
1
2
0
2
1
1
1
2
1
1
2
2
1
1
2
0
1
2
1
0
2
1
1
1
1
1
1
1
0
1
0
1
2
1
1
1
2
1
1
1
1
1
2
2
1
1
1
0
0
0
0
1
1
1
2
1
2
2
1
1
1
0
0
0
1
0
1
2
1
2
0
1
2
1
1
1
1
1
0
0
1
1
2
2
2
1
0
1
2
1
1
1
1
1
1
0
1
0
0
0
1
0
0
1
2
2
5
0
0
1
1
1
1
2
1
1
1
2
1
0
1
2
2
0
0
1
2
1
1
1
1
2
2
2
0
2
1
0
3
2
1
1
1
1
1
1
1
1
2
1
1
1
0
1
2
1
1
2
1
1
1
1
2
1
2
2
0
2
1
1
1
1
0
0
1
2
0
1
1
2
0
2
0
1
1
1
1
1
1
1
2
0
2
1
1
1
1
0
1
1
1
0
2
0
1
1
1
1
2
1
1
3
1
0
0
1
1
1
2
1
1
1
1
1
0
2
1
1
2
1
1
0
2
0
1
1
0
2
0
1
2
1
1
2
1
1
1
1
0
2
1
1
0
1
0
2
1
1
1
2
0
0
1
1
1
1
2
1
1
1
2
1
1
0
1
2
1
0
2
1
1
1
0
2
1
1
1
1
1
1
1
0
1
1
1
2
2
1
1
2
1
1
0
0
1
0
1
1
0
1
1
1
0
1
0
2
2
0
1
0
0
1
0
1
0
1
0
1
1
1
0
4
2
1
1
1
1
1
0
2
0
2
1
1
0
2
2
1
2
0
1
1
1
1
0
1
2
2
2
1
1
2
0
2
1
2
1
2
1
0
1
1
1
0
2
1
0
2
1
1
1
1
1
1
1
2
1
0
1
1
2
1
1
2
1
0
1
3
2
2
0
2
1
1
1
0
1
2
1
1
1
1
1
2
1
2
2
1
1
1
1
1
2
1
1
1
2
2
2
2
1
0
1
0
2
1
2
2
1
1
0
1
0
1
2
1
1
0
2
1
1
1
0
0
2
2
1
1
1
2
1
0
1
1
2
2
1
1
2
2
0
1
1
1
0
1
1
1
1
0
1
0
1
1
3
1
1
2
2
0
0
0
1
1
0
1
1
1
1
2
1
2
1
1
1
1
2
2
0
1
1
0
1
2
1
1
1
2
1
1
1
2
1
1
1
2
1
1
1
0
0
1
0
0
0
1
1
1
1
0
2
1
1
1
1
1
1
1
1
2
1
1
1
0
2
2
1
2
2
2
2
1
2
1
1
1
0
0
1
1
2
1
1
2
0
0
2
0
0
0
1
2
1
1
1
2
0
0
0
1
1
1
1
1
2
1
2
1
2
1
1
1
0
1
1
2
1
1
2
0
1
1
2
1
2
2
1
2
0
1
1
2
2
2
2
1
1
0
0
2
2
0
1
1
0
1
1
0
1
1
1
1
0
1
1
2
2
1
0
1
1
0
1
1
1
1
0
0
1
1
2
1
2
1
0
0
1
2
0
1
2
1
2
2
1
1
2
1
1
1
1
1
2
1
1
1
0
1
1
1
1
2
0
0
1
1
1
1
2
1
2
1
0
1
1
0
1
1
1
1
0
1
2
0
2
2
0
1
1
2
2
0
1
0
1
1
1
2
2
1
2
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
1
2
0
1
2
1
0
2
0
1
0
1
2
1
1
1
3
1
2
1
0
1
1
0
1
2
0
1
1
1
1
1
1
2
1
1
2
1
1
0
1
1
1
1
1
1
1
0
2
2
0
0
2
2
1
0
1
2
1
1
1
1
1
0
1
0
0
1
0
0
2
2
1
1
2
0
1
1
1
2
2
1
1
2
0
2
2
2
0
1
1
1
2
2
1
1
1
1
0
1
1
1
1
1
1
1
1
0
1
1
2
2
1
1
1
2
1
1
2
1
0
0
1
2
1
1
0
1
2
1
0
1
0
1
2
1
0
0
0
1
0
2
1
1
1
0
1
2
2
2
1
1
2
2
1
0
2
1
1
1
1
2
1
1
2
1
1
0
1
2
0
1
2
2
1
1
0
0
1
1
1
1
0
2
1
0
2
1
1
2
0
2
0
1
1
2
1
1
0
1
1
2
2
1
1
1
1
1
1
2
2
2
0
0
1
2
2
2
1
1
1
0
1
1
1
8
1
2
1
0
0
2
1
1
2
0
1
2
1
1
0
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
0
0
0
0
1
2
2
2
1
1
2
1
1
1
0
1
1
1
1
1
0
1
2
2
2
1
1
1
1
1
1
0
1
1
0
1
2
1
1
2
1
2
1
0
2
0
3
1
1
1
3
1
1
1
1
1
1
2
1
1
1
2
2
2
1
2
1
1
1
1
0
1
2
1
1
1
0
0
1
1
1
1
1
2
2
1
1
1
2
2
0
0
0
1
1
1
1
1
0
2
1
2
0
0
4
1
1
1
0
1
0
2
1
1
1
0
1
1
0
1
1
1
1
2
1
2
2
2
1
1
1
1
2
1
2
1
1
2
1
2
0
0
2
0
0
1
1
0
2
2
2
1
2
1
0
1
1
1
1
0
1
2
1
1
1
2
2
0
0
1
2
1
0
1
1
1
1
2
1
0
0
1
1
3
3
1
2
2
2
0
1
1
0
1
0
0
2
0
2
1
1
2
1
1
1
2
1
1
2
1
2
2
1
1
0
1
1
3
0
1
2
0
2
0
1
1
0
2
0
0
2
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
1
2
2
0
2
0
1
1
1
1
1
1
0
1
1
1
1
3
2
0
2
2
1
1
1
0
1
1
2
1
1
2
1
1
0
2
1
2
3
1
0
1
1
1
1
1
0
0
2
1
1
1
0
2
1
1
0
0
1
1
1
2
3
0
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
0
1
0
1
0
1
1
1
1
1
1
2
1
0
1
1
2
1
0
0
2
0
1
0
1
1
1
1
0
0
1
1
1
2
1
1
1
1
1
0
1
1
2
1
1
2
1
1
1
0
1
1
0
1
1
1
1
0
2
0
2
1
0
1
2
2
1
1
1
1
1
0
1
2
2
2
1
3
1
0
1
1
1
2
2
1
2
1
2
0
1
2
2
1
0
2
1
0
1
2
0
1
1
1
2
1
0
1
2
0
2
2
1
1
2
0
1
1
0
1
1
0
0
1
0
1
1
2
2
0
2
2
1
1
0
1
1
0
0
2
2
1
0
1
1
1
1
1
0
1
0
1
1
2
1
1
1
1
1
1
1
1
1
1
1
0
1
2
2
1
1
1
1
2
1
0
1
0
0
0
1
1
2
1
1
1
0
2
1
2
2
0
2
0
2
1
2
1
1
0
3
2
1
0
2
1
1
0
0
1
1
1
1
1
0
0
2
2
1
1
1
1
1
1
1
1
1
2
0
2
2
1
1
0
2
1
2
0
0
1
2
1
1
3
1
0
2
1
1
2
1
1
1
2
1
1
2
1
2
1
0
1
0
1
1
1
0
0
1
1
0
0
1
1
1
1
0
0
0
2
1
2
2
1
1
1
0
1
0
2
1
2
1
1
1
2
1
1
0
0
1
1
1
1
1
0
1
1
1
0
1
1
1
2
2
1
0
0
0
1
0
1
1
1
2
2
1
1
2
1
2
1
0
0
1
0
2
1
1
0
1
0
1
2
0
2
1
0
1
1
1
1
2
1
1
1
1
1
1
1
2
0
2
8
2
2
1
1
1
0
1
0
1
1
2
2
1
0
1
1
0
2
0
1
3
1
2
1
1
0
1
1
1
1
0
1
0
1
1
2
0
1
1
1
1
1
2
0
0
1
1
1
1
2
0
1
0
3
1
2
1
0
0
0
1
1
1
2
1
0
2
1
2
2
1
2
1
0
0
0
2
1
1
2
1
2
1
1
2
3
1
2
1
2
1
0
0
2
1
1
1
1
2
0
1
1
0
0
0
2
2
1
1
1
1
2
1
2
2
0
1
1
0
0
1
1
1
0
2
0
0
1
1
2
1
2
1
2
2
1
0
1
0
1
2
1
1
1
1
1
2
0
1
0
1
1
2
1
1
1
2
1
0
1
0
1
1
1
1
0
1
0
0
0
0
0
1
0
0
1
1
0
1
1
1
2
1
1
1
0
1
1
0
0
1
1
1
1
2
2
2
0
1
1
1
0
1
0
1
1
0
1
1
2
2
0
1
1
1
2
1
1
2
1
1
2
0
0
2
1
2
0
1
1
0
0
0
0
1
1
0
0
2
2
1
1
2
0
2
1
1
1
1
2
1
1
1
1
2
2
0
1
1
1
1
1
0
2
2
0
1
2
0
1
1
0
0
2
1
1
1
1
1
2
1
0
0
2
1
1
1
0
0
1
0
2
0
1
1
2
1
1
0
1
1
2
1
1
1
1
0
1
1
0
1
1
0
1
1
1
1
0
0
2
1
1
1
2
1
1
1
1
0
0
1
0
2
1
1
1
1
1
2
1
1
1
1
1
0
2
1
1
1
1
1
3
0
2
1
1
2
0
1
1
1
1
1
1
0
1
0
1
0
1
1
2
1
1
1
2
1
0
1
0
0
1
1
0
2
1
1
1
1
2
1
0
0
1
0
1
2
0
1
1
1
1
2
2
2
1
1
0
0
1
1
0
1
1
1
2
2
0
1
0
0
2
2
2
0
1
1
0
2
1
1
2
1
2
1
2
0
1
0
1
2
1
0
1
1
1
1
0
2
0
1
1
0
0
5
1
2
1
1
0
1
1
2
1
1
1
2
1
2
2
2
1
2
0
1
1
1
0
1
2
1
1
0
2
1
1
1
2
3
0
2
1
1
2
1
0
2
1
2
0
1
2
2
1
1
1
1
2
1
1
0
2
1
1
2
0
2
1
1
1
2
2
2
1
1
1
2
1
1
0
1
1
1
2
2
0
1
1
1
1
1
0
0
2
1
1
1
1
1
1
0
2
1
1
2
2
1
1
1
1
1
1
2
2
1
1
1
0
2
1
0
2
1
2
1
1
4
1
1
2
1
0
1
1
0
0
2
1
1
0
1
1
1
1
0
2
1
1
2
1
1
1
1
0
1
2
1
4
1
0
1
1
1
1
1
1
0
1
1
1
2
1
0
1
1
1
1
0
1
1
1
0
0
2
0
0
2
1
1
1
0
2
3
2
2
0
1
1
1
1
2
2
1
1
2
1
2
0
2
1
1
1
1
1
2
0
0
2
2
2
0
1
0
2
1
1
1
1
1
1
1
2
1
1
1
1
0
0
1
0
2
2
2
0
1
1
1
1
0
1
1
1
0
1
1
0
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
2
2
0
1
1
1
1
1
2
2
2
1
1
0
1
2
2
0
0
1
1
1
1
0
1
0
2
1
1
0
0
1
2
0
1
1
1
1
0
1
1
1
0
1
1
0
1
0
0
2
1
2
1
1
0
2
2
0
0
1
0
1
1
1
0
1
2
2
1
1
2
0
1
1
2
2
2
1
1
2
0
1
0
0
1
0
1
1
0
1
1
1
2
1
1
2
2
1
2
1
1
2
1
0
3
1
1
1
2
0
1
2
2
2
2
1
1
0
1
0
1
1
1
2
2
1
1
1
0
0
1
1
1
0
1
1
1
2
1
1
2
1
1
1
2
1
2
0
0
0
2
0
1
1
1
1
1
2
2
3
1
1
1
0
2
4
1
0
1
1
1
1
2
1
1
0
2
1
0
1
0
1
1
1
2
1
1
1
1
2
1
2
1
1
0
1
0
0
0
0
0
0
2
1
2
1
2
1
2
0
2
1
1
2
1
1
0
0
2
2
2
1
0
2
0
0
0
1
0
0
0
2
4
1
1
1
2
1
1
1
1
1
1
1
0
1
1
1
1
1
0
0
2
0
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
0
1
0
2
2
2
1
1
2
0
0
1
0
1
2
1
0
1
0
2
1
1
1
0
1
1
1
0
2
0
1
1
1
2
1
2
3
2
1
1
2
0
0
1
1
2
1
3
1
0
1
1
0
2
1
2
1
1
1
2
3
1
0
2
0
2
1
1
0
1
1
0
1
1
1
0
1
2
0
2
1
2
0
1
1
0
1
1
0
0
1
1
0
1
1
2
2
0
1
2
0
1
1
2
1
2
1
1
0
2
2
1
1
2
1
2
1
3
2
1
1
1
1
1
1
1
2
1
2
1
0
1
1
2
2
1
1
1
1
1
0
1
0
1
1
1
0
2
0
1
1
1
2
2
1
1
0
1
1
1
2
1
0
1
0
1
0
1
1
0
0
0
1
1
1
0
1
2
1
0
1
1
1
2
2
2
1
2
2
0
1
0
1
0
0
2
2
1
1
0
1
0
2
0
1
1
1
1
1
1
2
1
1
0
2
1
1
1
1
1
1
1
0
2
0
2
1
1
1
0
1
1
2
2
1
1
1
2
1
0
1
1
1
2
1
0
1
0
2
0
1
2
0
2
1
1
2
1
1
1
1
2
1
2
1
2
0
0
0
1
2
2
1
0
2
0
1
2
2
1
1
1
1
0
0
1
1
0
1
1
1
1
2
1
1
1
0
1
0
0
2
1
0
2
1
1
1
4
1
0
1
1
1
1
2
2
1
1
1
2
1
1
0
1
0
1
2
0
0
1
1
1
1
0
1
1
0
1
1
0
1
1
1
1
1
1
2
2
1
1
2
2
1
2
1
0
0
1
1
2
0
2
1
2
0
2
1
2
2
1
2
2
1
1
1
1
2
1
1
1
1
1
0
0
1
0
1
2
1
2
2
2
0
1
0
2
1
0
1
1
1
1
1
1
1
1
2
2
2
1
1
1
2
1
1
1
1
1
0
1
2
1
1
2
1
2
1
2
1
1
1
1
1
1
0
2
0
1
1
1
1
1
1
1
1
0
1
2
2
1
1
1
2
0
1
0
2
2
2
1
1
0
1
0
0
1
0
1
0
0
2
2
1
2
1
1
2
1
1
1
1
1
2
0
0
2
1
1
1
1
0
2
2
1
1
1
1
1
1
1
0
1
0
0
2
1
1
1
1
0
1
1
0
2
1
1
1
1
2
1
2
0
2
2
1
1
1
1
1
2
1
1
2
1
1
2
1
2
2
2
0
1
1
1
0
1
1
1
1
1
1
1
2
2
0
2
1
1
1
1
1
1
1
1
0
2
2
2
2
1
0
1
1
1
1
1
1
1
0
1
1
1
1
2
2
1
1
1
1
4
2
0
1
1
1
1
2
3
1
0
1
0
1
1
1
1
0
1
1
0
0
0
1
1
0
1
0
0
1
1
0
2
1
1
1
0
1
2
0
1
1
1
2
1
2
1
0
1
1
2
0
1
1
0
1
1
0
1
0
2
1
1
1
1
0
2
2
1
1
1
1
1
1
1
1
2
2
0
0
2
1
1
1
1
1
0
1
2
2
1
0
1
1
2
1
1
1
2
1
2
2
1
2
0
1
1
1
1
1
1
0
1
1
1
0
1
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
0
1
1
3
1
0
2
1
0
2
2
0
1
1
0
1
1
1
1
1
1
0
0
1
1
1
2
1
0
1
1
1
0
0
0
1
0
1
2
1
2
1
0
0
2
1
0
2
2
0
2
0
0
1
1
2
1
1
2
1
0
1
2
1
1
2
1
1
1
0
0
1
1
1
1
1
1
0
0
0
1
1
0
2
1
1
0
2
1
1
1
0
1
2
1
1
1
0
1
1
1
1
1
1
1
1
0
0
0
1
2
1
2
1
1
1
2
1
1
1
0
2
0
1
0
0
2
1
2
1
1
0
1
0
1
2
1
0
0
1
1
2
1
0
1
1
1
2
0
0
2
0
2
2
1
1
1
0
0
1
1
1
2
1
1
1
1
1
1
1
1
2
0
1
1
1
0
1
1
0
1
3
1
1
0
1
2
0
1
0
2
0
2
1
2
1
2
1
1
0
1
1
0
2
2
0
2
1
2
2
0
0
1
1
0
1
2
1
1
1
2
0
1
1
1
0
1
1
2
1
0
0
0
1
1
1
1
1
1
0
1
2
1
1
0
1
2
2
1
1
2
2
1
1
1
0
0
1
1
0
2
2
2
2
2
0
1
1
1
1
0
1
0
2
1
1
1
1
2
2
1
2
2
1
1
1
1
1
2
0
1
1
2
1
1
2
1
1
1
0
2
1
1
1
2
1
2
1
1
0
0
0
0
1
2
0
0
1
1
1
1
1
1
2
1
1
2
2
0
1
2
2
1
2
0
2
1
1
1
1
0
0
1
2
2
2
1
0
1
2
1
0
0
1
1
0
0
2
0
1
1
1
1
2
2
2
1
0
0
2
1
0
1
2
1
2
1
2
2
2
0
1
1
0
0
1
1
1
1
1
1
1
0
2
1
2
1
0
1
1
1
2
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
4
1
2
0
0
2
1
0
1
1
1
0
1
1
1
1
1
1
2
0
1
1
1
0
2
2
2
1
0
2
1
2
2
2
1
2
0
0
1
0
1
3
0
1
2
1
1
0
0
1
1
1
1
2
2
2
3
1
0
0
0
0
1
1
1
1
2
0
1
0
2
1
0
1
0
1
1
1
1
1
2
1
1
0
1
0
2
1
1
1
2
1
0
2
2
1
1
1
2
2
1
2
1
2
1
2
1
0
1
1
0
3
1
0
0
1
1
1
1
2
0
2
1
2
0
2
1
1
1
0
2
0
1
1
2
2
0
2
1
1
2
2
1
1
0
1
0
1
1
1
2
0
0
1
0
1
1
1
1
2
1
1
1
1
1
2
0
2
2
2
2
2
1
1
0
2
1
2
2
2
1
0
2
1
1
1
1
2
1
0
1
2
1
1
1
1
0
2
2
1
1
2
1
0
1
2
1
2
1
0
1
0
1
2
2
1
1
0
1
0
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
0
2
2
1
1
1
1
2
1
1
0
1
0
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
0
1
0
0
1
1
0
1
1
1
1
0
2
0
1
1
1
3
2
1
1
1
1
0
1
2
0
0
2
1
2
1
1
2
2
0
2
1
1
1
0
1
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
1
1
0
0
1
1
1
0
0
1
1
1
0
1
0
1
2
1
1
1
2
1
1
1
1
0
1
2
2
0
0
1
0
1
1
0
1
1
1
0
1
2
2
1
2
1
1
1
0
1
1
0
1
1
3
1
1
2
1
1
1
2
1
1
1
0
2
3
0
2
1
2
1
3
0
1
1
1
1
1
0
2
1
0
1
0
2
1
1
1
2
1
1
1
1
1
1
0
0
1
0
1
1
1
1
1
1
1
1
1
1
0
1
2
1
2
0
1
1
1
0
1
1
1
1
0
1
1
1
1
1
1
2
1
1
1
0
1
0
2
0
2
1
1
1
2
1
1
2
1
1
0
1
1
1
2
0
1
1
1
1
1
1
1
1
1
0
1
1
2
0
0
1
1
1
0
1
1
1
1
1
2
1
2
1
1
0
0
2
2
1
1
0
0
1
1
1
1
1
1
1
1
1
0
0
2
1
1
1
1
2
1
2
0
1
1
2
1
1
1
2
2
1
1
2
2
1
0
0
2
1
1
1
1
0
2
1
1
2
2
0
1
1
1
1
1
0
0
1
1
1
2
1
2
1
2
1
0
0
2
0
1
1
1
1
2
1
2
1
2
1
1
1
1
2
0
1
0
1
1
1
0
1
2
0
2
1
2
2
1
1
0
0
1
0
2
0
1
0
2
1
1
1
2
1
1
2
1
1
1
1
1
0
2
2
1
0
1
0
3
1
1
1
1
1
0
2
1
2
0
1
1
2
1
2
2
2
0
0
0
1
1
1
1
1
0
0
1
1
0
1
1
1
1
1
1
1
2
1
1
1
0
1
2
1
1
1
1
2
0
0
0
3
1
2
0
1
1
0
1
2
1
1
2
1
1
0
2
1
1
1
1
1
1
1
1
3
2
1
0
1
1
0
0
0
4
2
0
1
0
1
1
1
1
1
1
1
1
0
1
1
1
1
1
3
0
1
0
1
2
1
1
2
2
1
1
0
0
1
1
1
1
1
1
1
1
1
1
0
1
0
1
0
2
2
1
2
0
0
1
2
1
2
1
1
0
1
1
1
1
1
1
2
2
0
1
1
0
1
2
2
1
1
0
0
0
1
2
2
1
0
1
1
0
2
1
1
2
1
1
2
1
2
2
0
1
2
1
1
0
1
1
1
1
1
1
0
1
0
0
2
1
1
0
1
1
0
1
1
2
0
2
2
1
1
1
2
2
1
1
1
1
0
2
2
1
2
1
1
1
2
0
0
0
0
0
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
2
2
0
1
1
1
2
1
0
1
0
2
2
1
1
0
2
1
1
3
2
2
2
1
2
2
1
1
1
1
2
2
2
1
2
0
1
1
1
1
0
1
2
1
1
1
1
1
0
1
2
0
0
2
0
1
2
2
1
1
0
1
1
2
1
1
1
1
0
1
0
1
0
1
1
1
3
1
1
1
1
1
1
0
1
2
1
0
1
1
0
1
1
1
0
1
2
1
2
1
1
0
2
1
1
2
2
0
0
0
0
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
0
1
1
2
0
3
1
2
1
1
1
2
1
1
2
1
0
2
1
1
2
1
0
1
1
1
0
1
2
1
2
1
1
1
0
1
1
1
2
2
2
1
1
1
1
1
1
1
0
1
2
0
2
1
1
3
1
2
1
0
1
1
2
1
2
1
1
1
1
2
2
1
1
1
1
0
1
2
2
1
1
2
0
1
1
1
0
1
1
2
1
1
2
2
1
1
2
2
1
1
1
1
1
1
1
2
0
1
1
2
1
1
1
0
1
1
0
1
1
0
1
0
0
1
0
2
1
2
1
0
2
1
0
0
0
0
2
1
1
2
2
1
2
1
1
0
2
0
1
1
1
1
1
1
1
0
1
0
0
1
0
0
3
0
0
1
2
1
0
1
1
1
1
2
1
0
1
1
1
2
1
2
2
1
1
1
1
2
2
0
1
2
1
0
1
1
2
0
1
0
1
2
1
1
0
1
1
1
1
0
1
1
1
1
1
2
0
2
1
0
2
1
0
2
1
2
1
0
1
0
1
1
2
0
1
1
1
1
1
0
1
1
0
1
0
1
2
1
1
1
1
1
2
1
0
1
1
1
0
0
1
0
1
2
2
1
2
1
2
0
0
1
1
1
1
1
0
1
1
2
2
0
1
0
1
1
1
1
1
1
2
0
1
0
1
2
2
1
1
1
1
1
1
1
0
1
1
0
1
0
1
1
1
1
0
2
1
2
1
2
0
0
1
1
1
2
1
1
2
2
0
1
2
1
1
1
0
1
1
1
0
2
1
1
1
1
0
2
3
0
1
1
1
1
2
2
1
1
0
0
1
2
1
1
1
1
2
1
1
0
1
2
0
1
2
2
1
1
1
2
1
1
1
2
1
2
1
2
1
1
1
1
0
1
1
2
1
2
1
0
0
2
0
1
1
1
0
0
1
1
1
1
0
2
1
1
2
2
1
1
0
2
2
1
0
1
2
1
1
1
1
0
1
1
0
1
1
1
1
1
1
2
1
2
0
0
1
1
1
1
1
2
0
2
0
1
1
1
1
2
2
1
1
1
1
1
1
2
1
2
1
0
2
1
1
1
1
2
2
1
1
0
1
2
1
1
1
1
0
1
1
1
1
2
2
1
1
1
0
2
0
2
0
1
1
0
1
1
0
2
1
1
2
1
1
1
0
1
0
0
1
1
2
1
1
0
1
1
1
2
0
1
0
1
1
2
1
2
0
0
0
1
1
1
1
2
0
1
2
1
0
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
2
2
1
1
1
0
1
1
1
1
1
1
2
0
1
2
1
0
1
1
2
1
1
1
1
0
1
1
1
2
1
2
1
0
0
1
2
1
0
0
0
1
2
2
0
1
1
1
1
0
2
1
0
1
0
1
1
1
1
2
0
2
0
1
1
0
2
0
0
2
1
0
2
1
1
1
2
1
1
2
3
2
1
2
1
1
1
1
2
0
1
1
1
1
1
0
0
1
1
0
0
1
0
1
0
1
1
1
2
1
0
1
1
2
2
1
2
1
1
1
2
2
1
1
1
0
1
0
1
0
0
1
1
2
0
0
1
2
2
1
1
1
1
1
1
1
1
2
1
2
1
0
0
1
2
0
1
2
1
0
1
2
1
1
0
1
1
1
1
1
1
1
1
1
2
2
1
2
1
1
0
1
1
2
0
2
1
2
2
1
0
1
2
1
2
0
1
1
1
0
1
0
1
0
0
0
1
2
2
1
1
1
2
1
0
2
1
1
0
1
2
1
0
1
2
1
0
1
0
2
1
1
2
2
1
0
1
1
1
2
0
1
3
0
1
0
1
1
0
1
2
1
1
1
1
1
1
2
1
0
1
1
2
0
1
1
1
1
1
3
1
0
2
1
2
1
1
2
1
0
1
1
1
2
1
1
1
1
2
2
1
0
1
1
1
1
1
1
1
0
0
1
1
1
1
0
2
2
1
1
2
1
2
1
0
0
1
2
1
1
1
1
1
0
1
0
1
1
2
1
0
1
2
1
1
1
1
2
1
1
1
0
2
1
1
1
1
1
2
0
2
1
1
1
1
1
1
1
1
1
2
1
2
1
0
0
2
1
1
0
2
1
1
1
2
1
1
2
1
1
1
1
1
0
1
0
1
2
1
1
0
2
1
1
1
0
1
1
1
1
2
2
1
2
0
2
1
1
1
0
1
1
1
1
1
1
0
0
2
1
1
1
0
2
1
0
2
1
1
2
2
1
0
1
0
0
0
1
1
1
1
0
1
2
1
0
1
0
1
1
2
1
1
2
0
2
1
1
1
1
0
1
1
2
0
1
1
1
1
1
1
2
1
1
0
1
0
2
1
2
1
1
2
0
1
2
2
1
2
1
1
1
0
0
1
1
3
1
1
1
2
1
2
1
0
2
1
1
1
1
1
1
1
2
1
0
1
1
2
0
0
1
0
0
1
0
0
1
0
2
1
2
2
1
1
1
1
2
1
1
2
1
0
0
1
1
1
1
0
2
2
2
0
0
1
1
1
0
0
0
2
1
1
2
1
0
1
1
1
1
1
1
0
2
1
0
1
1
2
0
1
2
2
1
0
0
0
0
1
2
1
1
1
2
2
2
1
1
1
1
0
0
1
2
1
0
0
1
1
1
2
1
1
1
1
2
1
1
1
2
1
1
1
0
1
1
0
0
0
2
1
2
1
0
1
1
0
1
1
2
2
1
1
2
2
1
1
2
1
1
1
0
1
1
0
1
1
0
0
1
2
1
0
1
1
0
0
2
1
0
1
1
1
0
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
0
1
2
0
1
1
1
1
0
1
1
1
1
1
2
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
4
1
0
2
2
1
0
1
2
1
1
1
3
0
1
1
1
0
0
1
1
1
0
2
1
2
1
0
2
1
2
1
2
2
1
1
1
1
1
2
1
1
2
1
0
1
0
2
1
1
1
0
2
1
1
0
1
1
0
0
1
2
2
1
1
2
0
2
1
2
0
0
0
0
1
0
1
1
1
2
0
2
1
1
0
2
0
1
1
0
2
1
2
1
1
2
1
1
1
0
0
1
0
1
1
1
1
2
2
1
2
1
1
1
1
0
2
2
1
1
0
2
1
2
1
1
2
0
1
1
1
0
1
0
1
1
0
1
2
0
1
1
1
1
0
1
1
0
1
1
1
1
2
1
1
0
1
1
1
1
1
2
1
0
1
2
1
0
0
1
1
1
1
2
1
1
1
1
0
1
1
1
1
2
2
1
1
1
2
0
1
1
2
1
2
2
1
2
2
1
2
1
1
2
1
1
0
2
0
1
1
1
1
2
1
1
1
1
0
1
1
0
1
0
1
1
0
1
0
1
1
1
1
1
1
1
1
1
1
1
1
0
1
2
1
1
0
1
1
1
0
1
0
1
0
2
1
1
2
1
1
1
1
0
1
2
1
1
2
1
4
0
0
0
1
1
1
2
1
2
1
1
2
0
0
1
1
1
1
1
1
1
1
1
0
0
2
0
2
1
1
0
0
1
1
0
2
1
1
1
1
0
1
1
1
1
2
1
2
2
1
0
1
0
1
1
2
1
0
1
0
2
1
2
1
1
2
1
0
2
1
1
0
0
1
1
2
1
1
1
2
1
1
1
1
1
1
0
0
1
3
2
1
1
1
1
1
2
1
2
1
1
0
1
1
2
1
1
1
2
1
1
1
2
1
0
2
0
2
0
0
2
1
0
1
0
3
1
2
2
1
1
2
0
1
2
1
2
1
1
0
1
2
1
0
2
1
2
0
2
1
1
0
2
1
2
0
2
2
1
1
1
2
1
3
1
1
2
0
1
1
2
1
1
1
0
0
1
2
1
0
1
0
1
1
1
2
2
1
1
1
1
2
0
2
0
1
1
1
2
1
1
1
1
0
1
2
1
1
1
1
1
2
1
3
1
0
2
2
0
0
0
1
1
0
2
0
2
1
1
0
1
1
1
1
2
1
2
1
1
1
4
2
1
1
0
0
2
1
1
2
1
2
0
0
1
0
1
1
0
1
1
2
1
0
1
1
1
2
1
0
1
0
1
1
1
1
1
2
1
1
0
0
2
1
2
1
1
1
1
1
1
1
2
2
1
1
1
0
0
1
1
1
1
0
1
1
2
1
1
1
1
2
1
2
2
1
1
0
1
0
0
1
0
1
1
2
2
1
1
0
0
0
0
2
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
0
1
1
0
2
1
1
1
0
1
2
1
0
0
2
1
1
2
1
2
0
0
1
0
1
2
1
2
2
1
0
0
2
1
1
1
1
0
2
1
1
1
1
2
1
1
2
1
0
1
1
2
0
0
0
1
2
1
0
0
0
1
1
1
2
0
1
2
1
0
1
2
0
1
1
0
1
0
1
0
1
1
2
1
0
1
0
2
1
0
0
1
1
2
1
1
1
1
1
0
1
2
2
0
0
1
1
2
0
1
2
1
0
0
0
1
1
1
1
0
2
3
1
0
1
1
1
2
1
1
2
1
3
1
1
2
1
0
2
1
2
0
2
0
2
2
0
0
1
1
1
1
1
0
0
1
1
1
1
1
1
2
1
2
1
1
1
0
3
1
0
1
2
0
1
1
1
1
2
1
2
1
2
2
1
1
1
1
0
1
1
2
1
0
2
1
2
8
1
1
2
1
1
1
1
1
4
2
1
2
1
1
1
1
1
2
2
1
1
2
1
0
2
1
1
1
1
1
1
2
1
1
2
2
1
1
1
1
1
2
1
0
1
1
0
1
0
1
1
1
0
0
2
2
1
1
1
0
2
1
1
1
2
1
1
1
3
1
2
1
0
1
0
0
1
1
1
1
2
1
0
1
1
1
1
2
1
2
1
1
1
1
0
1
1
0
1
1
1
1
1
0
1
1
1
1
1
1
1
1
2
2
1
2
1
2
1
1
2
1
1
1
1
1
2
1
2
0
1
1
0
1
0
1
2
1
1
2
1
2
0
0
1
2
1
1
0
2
0
1
0
1
1
2
2
1
1
1
2
0
1
1
1
1
1
1
1
1
1
1
0
1
2
1
1
1
1
1
0
2
1
1
0
2
0
0
1
1
1
0
0
1
1
1
0
2
1
0
1
0
1
1
1
2
0
0
1
1
0
1
1
1
1
1
2
1
1
1
1
1
3
2
2
1
1
1
1
1
1
1
0
0
0
2
1
0
1
1
2
2
1
1
2
1
1
1
1
0
0
1
1
1
1
2
1
2
2
2
1
1
1
2
2
2
1
1
2
2
2
1
2
3
0
1
1
0
3
2
2
1
2
0
3
1
1
2
2
0
2
1
2
0
0
1
2
1
1
2
2
1
1
2
2
2
1
1
1
1
0
0
1
1
0
0
2
2
0
1
2
1
2
1
0
1
0
0
2
0
0
0
1
0
1
1
1
0
0
0
2
2
2
1
2
0
1
1
2
1
2
2
0
1
2
2
1
0
0
1
0
1
1
1
2
1
0
1
1
1
1
0
2
1
1
1
1
0
0
0
1
2
2
2
1
1
0
1
1
1
1
0
1
2
2
0
0
0
1
0
0
0
1
1
1
2
0
1
1
2
1
1
0
2
1
2
2
1
1
2
1
1
2
1
2
1
1
1
1
0
0
1
0
0
0
1
1
1
1
1
2
1
1
1
1
1
1
1
1
3
1
0
2
1
1
1
1
1
1
1
2
2
2
1
1
1
1
2
0
1
1
1
0
2
2
1
1
1
2
1
0
0
0
0
2
1
1
1
0
1
0
2
1
2
1
2
2
2
1
1
2
1
2
1
2
1
1
3
0
2
2
2
1
2
1
1
2
1
2
1
0
1
1
1
2
0
2
0
0
1
1
1
2
1
1
1
0
2
2
2
2
0
2
1
1
1
0
1
1
0
2
2
1
1
1
1
0
3
1
1
0
2
1
1
1
0
0
1
1
1
1
1
1
2
1
0
1
0
3
1
1
0
0
0
2
0
0
1
1
0
1
0
1
2
2
1
0
2
2
2
1
1
1
1
0
1
1
1
1
0
1
2
0
1
1
1
0
0
1
0
1
0
1
1
1
0
1
1
0
0
0
1
1
1
2
1
1
1
1
0
0
0
1
1
1
0
1
1
0
1
2
1
2
1
1
1
1
0
1
1
1
1
1
2
2
1
2
0
0
0
0
2
3
0
1
1
1
1
1
2
2
1
0
2
0
2
1
1
1
1
1
0
1
2
1
1
1
2
1
2
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
2
0
2
2
2
1
1
1
0
3
1
1
2
0
1
0
0
1
3
1
1
1
1
2
1
0
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
0
1
1
2
2
1
1
2
1
0
1
2
2
1
2
2
1
2
3
1
0
1
2
1
1
1
2
2
0
0
2
2
2
1
1
0
0
2
1
2
0
1
0
0
2
1
1
1
2
1
0
0
0
2
1
1
1
0
0
2
1
1
0
0
0
1
2
0
1
0
1
2
1
1
2
2
1
1
1
2
2
0
1
0
2
1
0
0
3
0
2
1
3
0
1
1
0
1
1
0
1
2
1
1
0
1
1
1
1
1
1
1
0
2
1
1
0
1
2
0
1
1
0
1
1
0
2
2
0
2
3
1
0
1
1
1
2
2
1
1
1
1
1
0
2
1
1
1
1
2
1
1
2
1
1
1
2
0
1
1
1
2
2
2
0
1
2
0
1
1
1
1
1
1
0
1
1
1
1
1
2
0
2
2
0
1
0
1
1
1
2
1
1
2
1
0
2
1
2
2
1
2
1
3
1
1
0
1
1
0
1
1
1
1
0
0
1
1
1
1
1
2
1
1
2
2
1
1
0
1
1
1
0
1
1
1
1
2
1
1
1
0
2
1
1
3
1
1
2
0
0
1
1
1
1
0
1
2
0
2
1
2
1
0
0
1
2
2
1
0
1
2
1
2
0
0
2
1
1
2
1
1
1
1
1
0
1
2
1
0
1
2
1
2
0
1
3
2
1
0
1
1
1
1
1
1
1
0
0
0
1
0
2
0
1
1
2
0
0
2
2
0
2
0
0
1
0
1
1
0
1
2
1
1
2
1
1
1
1
2
1
0
1
2
1
1
0
2
1
2
1
1
1
1
0
0
1
1
1
2
0
1
1
2
1
2
1
1
1
1
1
1
0
1
2
1
1
1
1
2
1
1
1
1
2
1
0
0
1
2
2
0
1
1
1
1
2
0
1
1
2
1
0
1
2
1
1
1
1
0
1
1
1
2
2
1
2
2
1
1
0
1
1
0
1
1
2
0
1
2
1
1
1
2
1
1
0
1
1
1
1
0
1
0
2
2
1
3
2
1
1
0
1
1
1
2
0
1
1
0
1
2
1
0
1
2
1
1
0
1
1
1
1
1
0
0
2
0
2
2
1
0
2
1
2
1
1
0
1
0
2
0
2
1
1
2
1
2
1
1
1
0
2
1
1
1
1
1
1
0
1
1
1
2
1
2
1
1
1
1
1
2
1
0
1
1
0
1
3
1
1
1
1
1
0
1
1
0
0
1
1
0
3
2
0
2
2
1
1
1
1
1
1
1
2
0
2
2
0
2
1
0
0
2
0
2
2
0
1
1
1
1
2
1
0
1
1
1
1
0
1
0
1
1
1
2
1
1
0
3
1
1
1
1
1
2
1
0
1
1
2
1
2
2
1
0
3
2
1
1
1
2
1
1
1
1
2
1
0
2
1
1
0
1
1
2
1
1
2
1
2
2
2
1
2
0
1
0
1
2
2
2
1
2
1
0
2
2
1
1
0
2
1
0
1
1
0
0
0
1
1
1
0
3
0
2
0
1
1
2
1
1
2
1
1
0
1
1
1
1
1
0
1
1
2
2
0
2
1
1
2
2
2
0
1
0
1
0
1
1
2
1
0
1
2
2
0
1
1
1
1
0
2
1
2
0
1
2
1
1
1
1
0
2
2
1
1
1
1
1
1
2
2
2
2
0
2
1
0
1
1
1
1
1
1
2
1
1
1
1
1
0
1
1
1
1
2
1
1
0
2
1
1
0
1
1
1
0
0
1
0
1
1
0
1
1
1
1
0
0
1
1
1
1
1
1
1
2
1
2
2
2
1
2
1
1
0
0
1
1
1
2
2
2
1
2
1
1
1
1
0
1
1
0
2
1
1
1
1
2
1
0
1
0
1
2
1
2
0
2
1
1
2
1
0
2
1
1
1
0
2
1
0
2
2
1
1
0
1
1
2
0
0
1
1
1
1
1
1
2
1
1
1
0
1
1
0
0
1
0
1
1
1
1
1
1
1
0
1
2
0
1
2
1
2
2
1
0
2
1
1
1
1
0
1
1
1
0
0
1
1
1
1
1
2
1
2
1
2
2
0
1
0
2
1
2
2
2
0
1
1
1
0
1
0
1
1
1
1
0
0
1
2
2
1
1
0
1
1
1
1
1
0
0
0
2
1
1
2
0
0
0
0
2
1
1
1
1
1
1
0
1
2
1
1
1
1
1
0
0
2
2
0
3
1
1
0
0
1
1
1
1
0
1
1
2
1
1
1
1
1
1
1
1
1
2
1
0
2
2
2
0
1
1
0
7
0
1
1
1
3
1
1
1
1
1
1
1
2
0
0
1
0
1
0
1
0
1
2
1
1
0
1
3
1
0
1
1
2
1
2
1
1
1
0
1
2
0
0
0
1
2
1
0
1
1
0
1
1
1
1
2
1
1
1
1
1
2
0
1
1
2
2
1
1
1
1
1
1
0
3
2
0
1
2
1
1
0
1
2
2
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
0
1
2
1
2
1
2
0
1
1
1
2
1
2
1
0
0
1
1
1
1
0
1
2
1
2
0
2
2
1
1
0
1
1
1
1
1
2
1
1
1
0
1
2
1
1
1
0
1
1
1
1
1
1
2
1
0
0
2
2
1
1
1
1
2
2
1
2
1
1
0
1
1
1
1
2
1
2
0
1
2
1
2
1
2
1
2
1
2
1
0
0
1
1
1
1
1
1
5
2
0
1
1
1
0
2
2
1
1
2
2
1
1
2
1
2
0
1
1
1
1
1
1
0
1
2
0
0
2
0
2
0
1
1
2
1
1
0
1
1
1
1
1
0
1
2
1
1
2
1
1
0
1
2
0
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
0
1
1
1
2
1
1
1
1
1
1
1
1
1
2
0
0
1
1
1
1
1
0
2
1
1
1
0
1
0
1
1
1
1
1
0
2
1
0
0
1
1
3
2
1
1
0
1
1
1
2
2
2
2
1
2
1
1
0
1
1
2
1
0
2
1
2
1
1
2
3
1
2
1
1
1
2
1
0
1
1
1
8
1
1
1
1
1
0
1
1
1
1
2
2
1
1
0
1
1
1
1
2
2
1
1
1
2
1
1
1
1
1
2
1
1
0
2
1
1
0
0
1
1
2
1
1
1
1
1
0
1
1
1
1
1
1
1
1
0
1
1
2
1
0
1
1
0
1
1
0
1
1
2
1
1
1
1
2
2
2
1
2
1
0
1
2
2
1
1
1
1
2
0
1
1
1
1
2
1
1
1
2
0
1
1
1
1
1
1
1
2
1
2
1
1
1
0
1
0
1
1
1
0
1
1
2
1
0
2
1
1
2
1
0
2
1
1
0
2
1
0
0
1
0
1
2
2
0
1
2
1
1
1
2
1
0
2
2
1
1
1
0
1
1
2
1
1
0
0
1
1
1
0
0
1
1
2
0
0
1
2
1
0
1
0
2
1
0
1
1
0
0
0
0
1
2
2
1
2
1
0
1
1
2
2
2
0
1
2
1
2
1
2
1
1
0
1
1
0
1
1
1
2
0
2
1
2
1
2
1
1
1
1
1
1
2
4
2
1
0
2
2
0
1
0
1
2
1
2
1
2
0
2
1
2
2
0
0
2
2
2
1
2
2
1
0
1
1
1
1
1
0
1
0
0
1
2
0
2
1
2
1
1
2
1
2
1
1
3
0
0
0
1
2
1
1
1
1
1
0
1
0
2
1
1
3
1
1
1
0
1
2
2
0
2
1
1
1
1
0
2
0
1
0
1
0
1
2
1
1
1
0
1
0
1
1
1
1
1
1
1
2
2
3
1
2
2
1
1
0
0
0
1
1
2
2
1
2
1
2
2
1
1
1
2
1
2
2
1
2
1
1
2
3
1
1
0
1
2
1
1
2
1
2
0
1
1
2
1
0
0
0
0
1
1
2
2
1
1
2
1
1
1
1
2
0
2
2
2
2
1
0
3
1
1
1
0
0
1
2
5
1
2
1
1
0
1
2
1
2
2
0
1
2
1
1
0
1
0
0
1
1
0
1
1
0
1
2
0
1
0
2
1
0
1
1
1
2
2
1
1
2
2
2
0
1
1
1
1
1
1
1
0
1
1
2
1
2
1
0
1
1
1
1
1
0
1
1
1
0
1
1
2
1
1
1
1
1
1
1
2
0
2
1
1
0
1
1
2
2
1
1
0
2
1
1
3
1
0
1
1
0
1
1
0
1
2
2
1
0
1
1
1
2
3
1
1
0
1
0
1
1
0
0
2
1
1
2
0
2
0
0
2
1
0
2
1
0
3
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
0
2
2
2
1
1
2
1
1
2
0
2
1
0
1
1
1
2
1
1
0
1
0
1
1
2
0
3
0
1
1
2
2
1
1
1
1
1
1
1
1
1
1
0
1
2
2
1
1
1
2
2
1
1
2
0
1
1
1
1
2
0
0
0
1
1
1
2
0
1
1
1
1
2
0
1
1
1
1
1
5
2
1
1
1
1
2
1
2
1
1
0
2
2
1
1
1
1
1
2
1
1
1
1
0
1
2
1
1
0
1
0
0
1
2
1
1
1
0
1
2
0
1
2
1
1
0
1
1
1
1
1
0
2
0
1
2
1
2
2
1
2
1
1
0
2
0
1
1
1
2
1
1
2
2
1
1
1
1
1
1
1
4
1
3
0
2
1
1
2
2
1
2
1
2
2
0
2
0
0
1
1
2
1
2
1
0
0
1
1
0
1
1
2
1
2
1
0
0
1
0
1
0
2
1
0
0
1
1
0
0
1
0
1
1
1
1
1
1
1
0
2
1
1
0
1
1
1
1
0
0
2
1
1
1
1
2
1
1
1
2
1
1
0
1
0
2
2
1
1
1
1
2
0
1
0
1
2
1
0
1
1
1
2
1
1
1
1
0
1
1
1
1
2
2
2
2
2
1
0
1
1
1
1
1
2
2
0
2
2
1
2
1
2
2
2
0
1
0
1
1
1
1
1
2
1
1
2
1
1
1
1
0
1
4
1
1
1
0
1
2
1
1
2
0
2
2
1
2
2
1
0
1
1
1
1
1
2
1
2
1
2
1
1
1
1
0
1
2
1
1
0
1
1
0
0
2
0
0
2
2
1
1
1
1
0
0
0
2
1
1
1
1
1
1
2
2
1
0
1
2
1
1
1
1
1
2
2
1
2
0
0
0
2
0
1
1
1
0
2
0
1
1
2
0
2
0
1
0
1
1
0
0
2
1
2
1
1
1
1
1
1
1
1
0
1
1
1
0
1
1
1
1
2
0
3
0
1
1
1
1
2
1
0
0
1
1
1
1
1
2
1
2
0
0
1
1
0
2
2
1
0
1
1
2
0
0
1
1
0
1
1
1
2
0
1
0
1
0
1
1
2
1
1
2
1
0
2
1
0
0
1
1
1
0
2
1
2
1
1
2
1
1
0
1
2
1
1
1
1
1
2
1
1
2
1
2
1
3
1
1
1
2
1
1
1
2
1
0
1
0
0
2
1
1
0
0
1
2
2
1
1
1
0
1
1
1
0
1
2
1
0
1
1
1
1
2
0
2
2
2
1
2
0
0
1
1
1
2
1
2
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
0
1
0
2
2
1
0
0
1
2
1
1
1
2
2
2
1
2
1
1
1
1
1
1
1
1
1
0
0
1
1
2
2
1
2
0
1
1
1
0
1
1
0
1
1
2
2
2
0
0
1
1
2
0
0
0
0
2
2
0
1
1
1
1
2
1
0
1
0
1
0
1
1
2
1
2
0
0
2
1
1
0
2
1
1
1
0
2
1
0
1
1
2
2
1
1
1
0
1
1
0
0
1
2
1
1
0
1
2
0
1
1
2
1
2
0
1
1
1
1
2
1
2
0
0
0
1
2
1
2
0
0
1
1
0
1
0
0
2
1
2
1
1
1
1
2
1
0
1
1
1
1
0
0
2
1
0
2
1
1
1
5
1
0
0
1
1
1
1
2
1
2
1
1
1
1
1
1
0
0
1
2
1
1
1
0
1
1
1
2
1
0
0
1
1
0
0
1
2
2
1
2
1
0
1
1
1
1
2
2
1
2
1
1
2
1
0
1
2
2
1
0
2
2
1
1
1
2
1
0
0
1
2
1
2
0
1
1
1
1
1
1
2
1
1
2
1
1
0
1
1
2
1
1
1
2
0
1
0
2
1
2
1
1
1
1
1
1
1
1
1
3
0
1
1
0
1
1
1
1
1
0
1
1
0
0
0
1
2
0
1
1
1
2
0
0
1
1
0
0
1
0
0
0
2
1
1
1
2
2
9
0
0
1
1
1
1
2
1
1
2
0
2
0
1
2
1
1
1
1
1
1
1
2
0
2
2
1
1
1
2
2
2
1
1
0
2
1
2
1
1
2
0
1
1
0
1
2
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
0
0
1
1
1
0
2
0
1
1
1
1
1
1
1
1
0
0
2
1
0
1
2
1
1
1
1
1
2
1
0
1
1
1
0
0
1
1
1
1
1
1
2
0
2
1
1
0
2
1
1
0
1
1
2
2
1
2
1
1
1
2
2
1
2
0
1
2
0
1
0
1
2
1
1
1
1
2
2
0
2
0
1
1
1
1
2
2
0
2
1
0
0
1
6
2
1
0
0
2
1
2
2
0
0
1
1
1
2
1
2
2
1
1
1
0
1
2
1
1
2
1
1
1
1
1
1
2
1
1
2
1
1
1
0
1
0
0
1
1
1
0
2
1
1
2
1
0
1
2
1
1
2
1
1
2
1
1
0
2
1
2
1
2
0
1
1
2
1
1
0
2
2
3
1
2
0
1
1
0
2
2
1
0
1
1
0
1
2
1
1
1
1
1
2
2
1
1
1
1
0
1
0
1
2
0
2
1
1
0
1
0
1
1
1
0
2
1
1
0
1
1
1
1
2
1
2
0
1
0
2
1
2
1
1
2
3
1
1
0
1
2
2
1
0
1
2
0
2
2
1
1
1
2
1
1
1
2
2
2
0
1
1
0
1
0
1
1
0
1
1
1
2
0
0
1
1
2
0
1
2
1
2
1
1
1
1
1
1
1
3
0
1
1
1
1
0
2
2
2
1
1
1
1
1
2
0
2
1
2
1
2
1
1
1
1
2
2
1
1
0
0
0
1
1
1
1
1
2
1
2
1
1
1
1
2
2
0
1
1
1
1
2
1
1
1
1
1
2
2
2
1
1
1
1
2
1
0
1
1
2
1
1
2
1
1
2
1
1
1
1
1
0
2
1
1
1
1
0
1
1
0
0
1
1
0
2
0
1
2
1
1
3
1
2
0
1
1
2
1
1
1
2
0
1
0
1
2
1
0
2
1
1
1
0
0
0
1
0
1
1
1
2
1
2
1
0
0
2
2
1
0
0
1
2
1
2
2
1
1
1
1
0
1
2
2
1
1
1
1
2
2
2
1
1
1
1
1
1
1
0
0
0
1
0
1
1
0
0
1
0
0
0
1
1
2
2
3
1
0
0
0
1
2
2
1
1
1
0
1
2
1
2
1
2
0
2
1
1
2
0
1
1
0
0
0
1
1
2
1
2
1
1
1
2
2
1
1
2
1
0
1
1
2
1
1
0
1
1
0
1
1
1
1
0
2
1
1
2
1
1
2
0
2
1
1
2
1
1
2
1
2
0
1
1
0
2
2
1
2
1
1
1
1
2
1
1
4
1
0
0
1
1
1
0
2
1
2
1
0
0
0
2
1
1
4
1
2
1
1
2
1
0
1
1
1
1
1
1
1
1
0
1
2
1
2
0
3
2
0
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
2
1
1
1
1
2
1
3
1
0
1
1
2
1
1
1
1
1
1
1
2
2
2
1
0
1
1
1
2
1
1
1
1
2
0
1
1
2
2
1
2
2
0
1
2
1
0
1
0
2
1
0
1
1
2
2
1
1
0
1
1
0
1
1
1
1
2
2
0
0
1
1
1
1
0
1
1
0
1
2
1
3
1
1
1
1
0
1
1
0
1
1
1
0
0
1
1
2
1
1
1
3
0
1
1
2
1
0
0
0
1
0
1
2
0
1
2
1
1
1
1
1
1
2
0
2
2
1
2
3
1
0
1
2
1
1
2
1
0
0
1
2
1
1
1
1
0
3
1
1
1
1
1
1
0
1
0
1
1
1
0
2
4
1
1
1
1
0
1
0
1
1
1
1
0
1
1
0
1
0
1
0
0
0
1
0
1
1
2
2
1
0
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
2
2
0
2
2
2
0
1
1
0
1
1
1
2
1
0
1
2
1
1
1
1
1
1
1
0
0
1
0
2
2
1
1
0
1
1
0
2
1
1
1
1
1
1
1
2
1
1
2
0
0
1
2
1
1
1
2
1
1
1
2
1
2
1
2
2
1
0
2
1
2
0
2
1
1
1
1
2
0
1
0
2
2
1
1
0
2
1
0
1
0
1
0
0
1
2
1
1
1
2
1
2
1
0
0
1
1
1
1
0
1
2
1
0
0
2
1
1
2
1
2
1
1
1
2
2
2
1
2
1
1
1
1
0
1
1
1
2
2
1
1
1
1
0
1
2
1
2
0
1
1
1
1
0
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
1
1
2
0
1
1
1
1
1
2
1
0
2
1
1
1
1
1
1
2
2
1
2
1
1
1
2
1
1
0
1
2
2
0
1
1
0
0
0
1
1
1
1
1
2
1
1
1
0
2
0
3
1
2
1
1
2
1
1
0
1
1
1
2
0
1
1
1
1
2
1
2
0
0
1
1
0
0
1
1
1
1
2
1
0
0
1
2
0
1
1
1
2
1
3
1
1
2
1
1
1
1
0
0
0
1
0
1
0
2
1
1
2
1
0
2
1
0
0
2
1
1
2
2
0
1
1
1
1
1
1
1
1
1
1
1
1
0
0
2
1
1
1
1
1
1
0
2
1
3
0
3
1
1
1
1
1
0
2
1
1
0
0
1
2
1
1
1
2
2
1
4
1
1
1
0
0
2
1
0
2
1
1
2
0
1
1
2
0
0
1
1
0
1
1
1
1
0
2
0
0
1
2
0
1
1
2
1
1
2
1
1
1
0
0
1
2
0
1
1
1
2
1
2
2
1
0
1
1
1
1
1
0
1
2
1
1
1
2
0
2
1
1
0
1
2
1
1
2
2
1
2
0
1
0
1
1
0
1
2
0
1
1
2
1
1
2
1
2
1
2
2
2
1
0
1
1
1
1
0
1
1
2
2
1
1
2
1
2
1
0
1
1
1
1
1
1
1
1
1
1
0
1
2
0
1
0
1
0
1
1
0
1
2
1
1
1
1
0
2
1
1
2
1
1
2
1
1
1
2
2
1
0
0
1
1
1
1
0
2
1
1
2
1
1
2
0
2
0
1
2
1
0
1
1
1
2
1
1
0
1
1
0
2
1
1
1
1
1
0
0
1
1
0
2
0
0
2
0
1
0
2
2
1
2
1
1
1
1
1
1
2
2
1
0
2
2
1
1
1
1
0
0
2
1
2
2
1
1
0
1
2
0
1
2
1
2
0
1
1
1
1
2
0
0
1
1
1
0
1
1
2
1
1
1
2
2
1
1
1
2
1
1
2
1
2
1
0
1
1
2
0
2
0
2
0
1
0
1
1
1
1
0
0
2
2
2
1
0
0
1
1
1
1
2
0
2
2
1
1
1
1
1
0
1
2
1
1
2
1
1
2
1
1
0
1
2
2
0
1
1
0
0
1
1
1
2
2
1
1
1
2
1
2
2
0
2
1
1
0
1
1
2
1
0
2
2
0
1
0
2
1
1
1
0
0
0
2
0
1
0
0
1
1
3
1
1
1
2
2
1
0
1
1
0
1
2
2
0
1
0
0
1
0
2
0
2
2
1
1
1
1
1
2
0
1
2
1
1
1
1
1
1
2
1
0
1
2
1
1
1
1
0
1
1
0
1
0
1
1
1
1
1
1
2
1
0
1
2
2
0
0
1
2
1
1
2
1
1
1
0
1
1
2
1
1
1
1
0
1
0
1
2
1
0
1
2
1
1
1
2
2
2
1
1
1
0
1
1
1
0
1
0
1
0
1
1
1
2
1
1
1
0
0
1
1
1
1
1
1
1
2
1
1
0
1
1
1
1
1
1
0
1
1
1
0
1
2
2
1
0
1
0
1
2
0
1
1
1
2
1
0
0
0
1
2
1
0
2
0
1
0
2
0
0
0
2
1
0
0
1
1
2
2
2
1
0
1
1
1
1
0
0
1
3
1
2
1
1
0
1
1
1
1
0
1
1
0
1
0
3
0
1
1
1
1
0
0
1
1
2
1
2
1
2
0
2
0
1
1
1
1
1
0
1
1
1
2
0
0
0
1
1
1
1
1
2
1
1
1
2
1
1
0
0
0
2
1
1
0
1
1
1
2
0
2
1
1
2
0
1
2
1
2
0
1
1
1
2
1
1
2
1
0
2
0
0
1
2
1
1
0
2
1
0
1
1
1
1
1
2
1
1
2
1
3
0
0
2
1
1
0
2
2
2
2
1
2
1
1
1
1
2
0
0
1
2
1
2
1
2
2
1
2
0
1
2
1
1
1
1
1
2
1
0
1
1
0
2
1
1
1
0
1
1
2
2
0
1
0
1
1
1
2
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
2
0
0
1
1
1
1
0
0
3
1
1
1
2
1
1
1
1
2
1
2
1
2
1
1
1
1
1
0
1
1
1
1
1
2
0
2
1
1
2
1
0
2
1
1
1
1
0
1
1
1
1
1
1
1
1
2
2
1
1
1
1
0
1
0
1
1
2
1
1
1
1
1
0
1
1
2
1
0
2
1
0
2
0
1
0
0
2
2
1
1
1
0
1
0
0
1
1
0
1
0
0
1
1
0
2
2
2
1
0
2
1
1
1
1
1
0
1
0
1
2
0
2
1
1
1
1
0
2
1
1
1
2
1
0
1
2
0
0
1
1
1
2
1
1
2
1
1
0
1
2
1
1
1
1
1
2
2
1
0
1
2
1
1
0
0
1
3
0
2
1
2
2
1
2
2
1
1
1
2
1
0
1
3
1
1
0
1
0
1
1
1
0
1
2
2
1
0
1
2
1
1
1
1
2
1
1
3
1
1
1
1
2
0
1
1
1
1
0
1
0
0
1
0
2
2
1
2
0
0
0
2
1
1
0
1
1
1
1
1
1
1
1
0
1
2
1
1
0
2
1
1
0
2
0
0
0
0
2
2
1
2
2
1
0
1
0
2
1
1
0
2
1
1
1
1
0
3
1
1
1
2
1
1
2
2
0
2
1
2
1
1
1
0
1
1
1
2
1
1
1
1
2
1
0
2
2
0
0
1
1
1
1
1
2
2
0
0
0
1
2
1
1
1
2
1
1
2
2
1
1
1
1
2
2
0
1
1
1
0
0
1
1
1
0
0
0
0
0
1
1
1
1
1
1
1
1
1
0
2
1
1
2
1
1
1
1
1
2
0
2
2
1
1
2
1
1
0
0
1
2
0
1
1
1
1
1
1
1
1
0
1
2
1
1
1
1
0
2
1
2
1
0
1
1
2
5
1
0
1
0
1
1
0
2
2
0
2
1
1
2
0
1
1
1
1
1
1
2
1
0
1
1
0
3
1
1
1
1
2
2
1
1
1
2
1
3
1
0
0
1
1
0
0
1
1
2
0
0
0
1
1
1
1
1
1
1
0
1
2
1
2
1
2
0
1
1
1
1
1
0
0
1
2
1
1
1
1
2
1
0
2
2
1
2
0
1
1
2
1
0
2
1
0
2
0
1
1
1
1
1
1
0
0
0
1
0
1
0
0
2
0
0
1
2
1
1
1
1
1
1
1
1
2
2
0
0
1
1
2
2
1
2
1
1
1
0
0
1
1
1
0
1
1
1
1
1
1
0
2
2
0
1
0
1
1
1
1
0
1
1
1
0
2
1
2
1
0
1
2
0
1
2
2
1
1
1
1
1
1
1
1
1
2
1
0
0
1
2
0
0
1
1
1
0
1
1
1
0
2
2
2
1
2
0
2
1
2
2
0
1
2
1
0
1
2
1
0
0
1
2
2
1
1
2
1
0
1
1
0
0
1
1
1
1
1
1
1
1
2
1
2
2
1
1
0
1
2
1
1
0
2
1
1
0
1
2
1
1
1
2
1
0
2
1
0
1
1
1
2
0
1
1
1
1
1
0
1
1
1
1
1
1
0
1
1
0
2
1
0
1
0
2
1
0
2
1
2
1
2
1
1
2
2
0
1
1
1
0
1
2
1
1
1
1
2
0
1
0
1
1
0
2
1
1
1
1
1
2
1
1
2
1
0
1
0
1
1
1
1
0
1
2
1
2
0
0
0
1
1
1
1
1
2
1
1
0
0
1
0
1
0
0
1
1
2
3
1
1
2
2
2
1
0
0
2
0
1
1
1
1
1
1
1
2
1
1
1
1
0
1
2
1
2
1
1
0
1
2
1
1
2
1
1
1
1
1
1
1
0
0
1
1
0
0
1
0
1
1
2
2
1
1
0
1
2
1
1
1
1
1
1
2
0
2
3
2
2
1
2
1
1
2
2
2
0
2
2
0
1
1
1
1
2
2
1
2
1
0
2
1
1
2
0
0
1
1
2
1
1
2
0
0
2
1
1
1
1
1
0
1
0
1
1
1
1
3
1
2
0
1
1
3
1
1
1
2
0
0
0
0
0
2
1
1
0
2
1
1
2
2
1
1
1
1
1
0
1
1
1
0
1
1
2
2
1
1
1
1
0
1
2
1
2
0
0
0
1
2
1
1
0
2
0
1
1
2
2
1
1
2
1
2
1
1
1
0
1
1
1
0
1
0
0
0
2
2
0
1
1
0
1
2
1
2
2
2
0
1
1
0
1
1
1
1
1
1
0
1
1
0
0
2
0
1
1
1
0
1
2
1
1
1
2
1
0
0
1
1
0
1
0
2
2
1
1
0
0
0
0
0
0
0
2
0
2
1
1
1
1
1
1
1
0
1
1
1
1
1
0
1
0
2
2
0
1
1
0
1
2
0
1
1
1
0
1
1
0
0
1
1
0
0
1
1
1
0
2
1
0
1
1
2
2
1
2
1
2
2
1
2
1
1
1
0
1
1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
2
1
0
1
1
2
1
1
1
0
0
0
0
0
1
1
1
1
1
1
1
0
1
0
1
1
1
1
0
1
0
0
1
1
1
0
1
1
0
1
0
1
0
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
0
0
1
1
1
1
1
1
1
2
1
1
1
0
1
1
0
2
0
2
0
1
2
2
2
1
0
1
2
1
2
1
0
2
0
0
0
0
1
1
2
0
1
0
2
1
1
1
2
3
0
1
2
2
0
1
0
2
1
2
0
0
1
2
1
1
2
2
1
1
2
0
1
0
1
1
1
2
1
1
1
1
0
0
1
1
1
2
1
1
1
0
0
2
1
1
1
1
1
0
0
1
0
1
0
1
2
1
1
5
0
1
1
1
1
3
1
0
2
1
2
1
2
1
2
1
1
0
2
0
1
0
1
1
0
2
0
1
2
1
0
0
1
1
1
1
1
1
1
2
1
0
1
1
1
1
1
1
2
1
1
1
1
2
1
0
1
1
1
1
1
1
1
1
0
1
0
1
1
1
1
1
2
1
2
1
1
1
1
2
2
1
1
2
1
1
1
2
0
0
1
1
1
1
1
1
1
0
2
1
2
0
2
1
2
1
1
1
0
1
1
1
0
0
1
1
0
1
1
1
0
1
2
2
1
1
1
1
2
1
0
1
1
1
1
2
0
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
1
2
2
2
1
2
1
0
2
2
3
2
0
1
0
1
2
1
1
1
1
1
0
1
1
2
1
1
1
2
1
1
1
0
0
1
0
1
1
1
1
1
0
2
0
0
1
2
1
1
0
2
0
1
2
0
1
1
1
1
0
1
1
1
1
1
0
0
2
1
1
2
1
2
2
1
2
0
1
0
1
2
1
0
1
2
1
2
1
2
1
1
1
1
0
1
1
1
2
2
0
1
1
1
0
2
0
1
2
0
2
1
2
1
0
2
1
2
1
1
0
2
1
2
0
0
1
2
2
2
1
0
2
2
1
1
2
1
1
0
1
2
2
2
1
0
2
2
1
1
1
1
0
2
1
2
2
1
1
1
0
0
0
1
2
1
2
1
2
0
0
1
2
1
1
2
1
3
0
2
1
0
1
0
1
0
0
1
2
1
0
0
0
0
1
1
0
1
1
0
1
1
1
1
1
2
1
2
1
1
0
2
1
1
1
0
1
1
1
1
1
0
0
1
2
1
2
1
1
1
1
1
2
1
0
1
0
1
0
1
2
1
2
2
1
0
0
0
1
2
1
1
1
1
2
1
2
1
2
1
2
0
1
1
1
1
1
2
1
0
2
1
2
1
1
2
1
1
2
0
1
0
1
0
1
1
1
1
1
2
1
2
0
1
2
1
2
1
1
0
0
1
0
1
1
0
2
1
1
0
1
2
2
1
2
1
0
1
1
2
1
2
1
2
0
1
2
1
1
1
1
0
1
1
2
1
1
2
0
0
1
0
2
1
1
2
1
2
2
1
2
1
1
3
2
1
1
1
0
1
2
1
0
1
1
1
1
0
2
0
1
2
3
0
0
3
1
1
1
2
1
1
2
0
0
2
1
2
2
1
3
1
1
1
0
0
2
0
1
2
0
0
1
1
2
1
1
1
2
3
0
0
2
2
1
0
0
1
1
1
0
1
1
0
2
0
2
1
1
1
1
1
1
0
1
0
2
2
0
1
1
1
1
0
1
1
1
1
1
1
2
0
1
1
1
0
1
1
1
1
2
1
1
1
1
1
1
0
1
1
1
0
1
1
1
2
1
1
2
2
1
2
2
1
0
1
1
1
1
1
1
1
1
0
1
1
1
2
1
2
2
2
2
2
1
2
1
0
1
0
2
2
1
1
2
0
1
1
1
3
0
2
1
1
1
1
2
2
1
2
1
2
1
1
2
2
1
2
1
2
2
1
2
1
0
2
0
1
0
0
2
1
1
1
2
2
0
1
2
2
2
1
0
0
2
0
1
1
2
0
1
2
2
1
1
0
1
0
1
2
1
2
0
1
1
1
1
0
0
1
2
1
1
0
2
1
1
1
0
2
1
2
1
1
2
1
0
1
1
1
1
0
1
1
2
0
1
2
1
2
1
1
0
1
1
0
2
1
1
0
1
1
1
2
1
1
0
1
1
0
1
2
1
0
0
0
1
1
1
0
1
2
1
2
0
2
1
1
1
1
1
1
0
0
1
0
1
0
2
0
1
1
1
0
2
1
2
1
0
1
0
1
1
1
1
0
1
1
1
3
0
2
0
1
0
1
0
2
1
1
2
1
1
2
1
0
1
1
1
2
0
1
2
1
2
1
0
1
2
0
0
0
0
1
1
1
1
1
0
2
1
0
1
2
1
1
4
1
0
3
1
1
0
1
0
2
1
1
1
1
2
1
0
1
2
2
0
1
2
1
0
1
1
1
1
1
1
1
2
1
1
1
2
2
0
1
1
2
1
2
0
1
1
1
1
1
0
1
0
0
1
1
2
0
0
2
0
1
0
0
0
2
0
1
1
2
1
1
1
2
2
1
1
1
1
1
1
1
1
2
1
0
2
0
1
2
1
1
1
1
0
0
2
1
1
3
2
1
1
1
1
1
1
1
1
0
1
1
1
1
1
2
0
1
2
0
1
1
2
1
1
1
2
1
0
0
1
1
1
1
2
0
0
1
1
2
0
1
2
2
2
0
1
0
1
1
1
0
2
1
1
1
1
1
1
1
2
1
2
0
1
1
0
0
1
1
1
0
1
1
2
1
1
0
2
0
2
2
1
0
0
1
2
2
1
0
1
1
0
0
1
1
0
0
0
0
2
0
1
1
1
2
1
2
2
1
0
1
1
0
2
3
1
1
0
0
1
1
2
1
1
1
1
1
0
0
1
2
0
2
1
1
1
0
1
1
0
1
1
0
1
0
2
1
2
1
0
2
0
0
1
1
0
1
2
2
1
1
0
1
1
1
3
1
1
1
1
2
2
1
1
4
1
1
1
1
1
0
2
1
2
0
0
1
1
1
1
1
1
1
2
1
1
0
0
2
2
0
1
0
0
1
1
2
0
0
0
1
2
1
0
0
1
1
1
1
2
1
1
1
0
2
2
1
2
1
0
1
1
1
0
1
2
1
0
2
2
2
1
2
1
1
1
2
2
1
2
1
0
1
3
1
1
1
0
0
1
1
1
1
2
0
1
1
2
1
1
1
1
1
2
1
0
1
2
2
2
1
1
1
1
2
0
1
1
1
1
2
1
2
2
2
1
1
1
1
1
1
0
0
1
0
1
2
2
1
0
2
2
1
1
0
1
1
1
1
0
0
1
1
1
2
2
1
1
1
1
1
0
1
2
1
1
1
2
2
1
2
2
0
2
1
1
1
1
1
2
0
1
1
2
1
1
1
1
0
2
2
1
2
2
1
1
1
1
1
2
2
1
1
1
0
2
1
1
0
1
1
0
2
0
1
0
1
1
1
1
2
1
0
1
1
2
1
1
2
1
1
1
0
1
2
1
1
1
0
1
1
1
0
0
1
1
1
1
1
1
2
1
1
0
1
2
1
1
1
0
1
1
1
1
2
1
1
1
1
1
1
2
0
1
1
2
3
0
1
1
1
1
1
1
1
0
1
1
1
1
1
0
1
0
0
1
2
0
1
1
1
2
1
0
0
2
3
2
0
0
1
1
1
1
1
1
0
1
0
1
1
2
2
1
1
0
0
1
0
1
2
1
1
1
1
0
1
0
1
1
0
1
1
1
4
1
1
1
1
1
0
1
1
0
0
0
2
1
0
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
0
2
0
1
1
1
1
1
1
1
1
1
1
1
1
2
0
2
1
2
4
1
1
0
1
2
1
2
1
1
1
0
1
1
0
1
1
0
2
2
2
3
1
2
1
0
1
2
1
1
1
2
1
2
0
1
0
0
0
1
1
0
1
1
1
1
0
0
1
1
2
3
1
0
1
1
1
0
1
2
2
2
0
2
1
1
0
1
1
1
1
0
0
2
1
1
2
1
2
0
2
0
3
1
1
0
2
1
2
1
1
1
2
1
2
0
2
1
1
1
2
1
1
1
0
1
1
2
1
1
0
1
0
0
1
1
0
2
2
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
2
1
0
2
1
1
1
0
1
1
1
1
1
1
0
3
0
2
1
1
1
1
0
2
1
2
1
1
1
1
0
0
1
1
1
1
1
1
0
2
0
2
2
1
2
1
0
0
0
2
1
2
2
2
1
2
2
1
1
0
2
2
2
1
2
1
0
1
1
2
2
1
0
2
1
0
1
1
1
4
1
0
1
2
1
2
0
1
1
1
0
2
1
0
2
1
0
1
1
1
1
1
0
2
2
1
1
0
1
0
0
2
2
0
2
0
1
1
2
2
2
2
0
1
0
0
1
1
1
1
1
0
0
1
1
2
1
2
2
2
1
1
1
1
2
1
0
1
1
1
2
1
1
1
0
2
1
0
1
1
0
1
1
1
2
1
1
1
2
1
0
1
1
0
1
1
1
1
1
1
2
2
0
2
1
0
1
1
2
0
2
1
1
2
0
1
0
1
2
2
1
1
1
2
1
1
0
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
1
0
0
1
1
1
1
2
1
2
1
1
2
1
0
1
0
2
2
0
3
1
1
2
0
0
1
0
1
1
1
1
0
0
1
0
0
1
0
2
2
1
2
1
2
1
1
1
2
1
1
1
1
1
2
0
2
2
2
1
1
1
1
0
1
0
2
2
0
1
1
1
1
1
1
0
0
0
1
2
0
2
2
2
0
2
2
2
0
1
0
1
2
3
1
0
1
0
1
2
1
1
0
1
1
2
1
3
0
2
1
1
0
1
1
1
1
0
1
2
2
1
1
2
1
1
1
1
0
0
0
1
2
1
1
1
1
1
0
1
2
1
1
1
1
1
0
1
2
1
1
0
1
1
2
1
0
0
1
1
1
2
2
0
0
1
1
1
0
0
1
1
1
1
1
1
0
1
2
1
0
1
1
0
0
1
0
1
1
2
3
0
1
2
2
1
0
1
1
1
1
1
2
2
0
2
0
1
1
0
0
2
1
1
2
1
1
2
0
1
0
0
2
0
1
1
1
1
1
2
1
2
1
1
0
1
0
1
2
1
0
0
2
2
1
1
2
0
1
1
1
1
1
0
1
2
2
1
1
1
1
2
0
2
1
1
0
1
2
0
0
0
2
1
1
1
1
1
1
2
1
1
0
1
1
1
1
2
1
1
3
2
1
1
2
2
2
1
0
2
1
0
2
2
1
0
0
2
2
2
1
1
1
0
1
0
1
0
1
1
0
0
0
1
2
0
1
2
1
1
2
1
1
2
3
0
1
2
1
2
0
1
1
2
1
0
0
1
1
1
1
0
1
0
1
1
1
2
0
2
1
1
1
2
0
1
2
1
2
1
0
1
2
1
0
1
1
2
2
1
1
0
1
1
1
2
1
2
1
1
1
1
0
2
2
1
1
0
0
1
1
1
2
1
1
1
1
1
1
1
2
0
1
2
0
1
1
1
0
0
1
1
1
1
0
2
1
0
2
1
2
1
1
2
2
0
1
1
1
2
0
1
1
1
1
0
2
1
0
1
1
2
0
3
2
2
1
1
1
2
1
1
0
2
1
1
0
1
0
0
0
1
1
0
0
0
1
1
2
1
1
1
2
1
0
2
1
1
0
1
1
1
1
2
1
0
0
1
1
1
1
1
1
1
2
2
1
1
1
1
1
0
1
1
2
1
2
0
0
1
1
2
0
2
1
1
1
1
1
1
1
0
0
0
0
1
1
2
1
1
1
1
1
2
2
1
1
2
0
1
1
1
0
1
1
1
1
1
0
1
1
1
0
2
1
1
2
2
0
2
1
1
1
0
2
0
1
1
2
0
1
0
1
1
3
2
1
1
1
1
0
0
1
2
1
1
2
1
2
1
2
1
1
0
0
2
0
0
2
1
1
0
2
2
0
1
1
2
1
0
2
1
1
2
0
0
1
1
1
1
2
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
1
0
2
1
2
2
2
0
1
1
2
2
1
2
1
1
1
1
2
0
1
1
0
1
0
2
1
1
1
2
1
0
1
2
0
1
1
0
2
0
0
1
2
0
1
0
1
0
1
1
1
2
0
0
2
0
0
0
2
1
1
0
2
1
2
1
1
1
1
1
1
1
1
2
1
2
2
0
1
1
1
1
2
2
0
3
1
1
1
0
2
2
0
1
0
1
1
1
0
2
0
1
1
0
0
2
2
1
0
2
0
2
0
2
1
1
2
1
1
1
0
2
2
2
1
1
1
2
1
0
1
1
2
1
2
2
2
1
1
0
1
1
1
0
1
1
1
1
1
0
1
0
0
1
1
0
1
2
1
1
2
1
1
1
2
0
1
1
0
1
1
1
2
1
2
0
1
0
0
1
2
1
2
1
2
1
1
0
2
1
1
1
2
0
3
1
1
0
1
0
1
1
1
0
2
2
1
1
2
1
0
1
2
1
1
0
2
0
1
2
2
2
1
2
2
2
1
0
0
0
2
3
1
1
0
2
1
2
0
1
2
1
1
1
1
1
1
1
2
1
1
1
2
0
2
0
1
0
2
1
1
1
1
0
1
1
1
2
1
1
2
1
1
1
1
1
1
1
0
2
1
1
0
1
1
1
0
1
1
0
1
1
2
0
0
2
1
1
1
1
1
0
2
1
0
1
1
0
1
2
2
1
1
0
1
0
2
0
1
1
0
2
0
1
2
0
0
0
1
2
1
1
2
1
1
1
2
0
2
3
1
1
1
1
1
2
2
0
1
1
1
1
1
1
2
1
1
3
1
1
1
2
1
0
1
1
1
1
1
0
0
0
2
0
1
1
1
1
0
1
1
1
0
1
1
2
2
1
1
1
3
1
1
1
1
0
1
0
0
0
1
1
2
1
1
1
0
2
1
1
0
1
1
0
1
1
1
1
1
1
0
1
1
0
2
1
2
2
2
2
1
0
0
1
2
1
1
1
1
0
1
1
1
1
2
1
1
1
1
0
1
1
0
1
2
0
1
2
1
1
1
1
0
1
2
1
1
1
1
1
2
1
0
1
1
1
1
2
1
1
1
1
0
2
1
1
1
1
1
1
0
0
1
1
1
1
2
0
1
1
3
1
1
1
1
1
0
1
1
0
0
1
1
1
1
1
1
1
2
1
2
1
0
2
1
1
1
2
1
1
2
3
1
1
1
0
1
1
1
2
2
1
0
1
0
2
0
0
2
1
1
1
0
4
1
1
2
0
1
1
4
2
1
1
2
1
2
1
0
0
1
1
1
1
1
1
2
0
1
1
1
1
1
2
1
1
1
1
0
1
1
0
1
1
1
1
1
1
1
2
1
2
1
1
2
2
1
2
0
0
2
0
1
1
1
1
0
1
2
1
1
0
1
0
0
1
1
1
2
2
1
1
2
2
1
1
0
1
1
1
1
0
1
1
2
1
1
1
1
1
0
1
2
0
1
2
1
1
1
0
0
1
1
1
1
1
2
1
1
1
0
2
1
1
1
1
0
1
0
1
2
0
0
1
2
0
0
2
1
0
1
1
2
1
1
0
1
1
1
1
1
1
0
2
2
2
1
1
0
0
3
1
0
2
1
1
1
1
1
2
1
1
2
1
0
1
2
1
1
1
2
0
1
1
1
1
1
1
2
1
1
2
0
2
1
0
2
2
1
1
0
1
0
0
1
1
1
2
1
1
2
1
2
1
1
1
1
1
0
1
0
0
2
0
1
0
0
0
0
1
0
2
1
0
2
1
1
1
2
1
1
2
2
1
1
3
1
1
1
2
2
1
1
0
2
1
1
1
2
1
2
1
0
1
1
1
1
0
1
0
1
2
2
1
0
1
1
1
2
1
0
1
2
1
1
1
1
1
1
2
0
1
1
1
2
1
1
1
1
2
2
2
1
0
1
0
1
0
1
1
1
1
1
1
1
3
1
2
2
1
1
2
1
1
0
1
1
1
0
1
2
1
2
1
0
1
2
1
1
0
1
1
2
2
1
1
1
0
1
1
0
2
1
0
1
1
2
2
2
0
2
1
1
1
1
1
1
1
2
1
2
0
2
1
2
1
0
1
2
2
1
2
0
1
0
1
1
0
2
1
1
1
1
1
1
1
1
1
0
1
1
0
1
2
1
1
1
2
1
1
2
0
1
0
1
1
2
1
1
1
1
1
2
1
1
0
1
0
1
2
1
1
1
0
1
1
0
3
1
1
1
1
2
1
0
1
0
0
1
2
1
1
1
1
1
1
1
1
1
2
1
1
0
1
1
0
1
2
2
1
1
1
0
1
0
1
2
0
0
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
0
1
1
1
1
2
1
1
1
2
1
1
1
0
2
0
1
1
1
1
0
1
1
1
1
0
2
1
0
2
1
1
1
1
1
2
2
1
1
2
0
1
0
0
1
0
1
2
0
2
1
1
2
1
2
2
0
1
2
1
1
1
0
2
1
0
1
1
1
1
2
1
1
0
1
2
2
1
0
1
1
1
1
1
2
2
1
0
0
1
1
1
1
1
1
0
0
0
1
0
2
1
2
1
1
0
1
0
1
1
1
2
2
2
1
1
0
2
2
1
1
1
1
1
2
2
1
1
1
2
1
1
1
1
0
1
1
2
1
1
1
2
1
1
1
1
3
1
0
1
1
0
1
0
1
2
2
1
1
0
3
1
1
1
1
0
2
1
1
2
0
0
0
1
1
0
1
2
1
1
1
1
2
1
0
0
1
1
1
0
1
1
2
2
0
1
1
0
0
2
1
0
2
1
1
0
0
1
2
2
1
0
1
1
1
2
1
2
0
1
0
1
2
1
1
0
1
0
2
2
0
2
2
0
2
0
2
1
1
1
1
1
0
1
1
1
1
1
0
1
1
0
1
1
1
1
0
2
1
2
1
1
2
0
1
0
0
1
2
2
0
2
1
1
0
0
0
2
1
1
3
2
2
0
0
2
1
1
0
2
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
2
0
1
2
1
1
1
1
1
1
0
2
0
2
2
1
1
1
1
1
1
1
1
0
0
1
2
1
2
1
1
1
1
1
1
1
1
1
1
0
1
0
2
1
0
2
1
1
1
1
1
1
1
1
1
2
1
2
1
1
0
2
2
1
2
1
1
0
1
1
1
1
1
1
2
1
0
1
1
2
1
1
1
1
1
1
2
1
0
1
2
0
2
1
1
1
2
1
1
0
1
1
1
1
1
1
1
0
1
1
2
1
1
3
2
0
0
1
1
1
2
1
2
1
1
1
1
1
0
1
1
1
1
1
1
0
1
2
1
1
2
2
1
0
1
1
1
2
1
1
1
2
1
1
1
0
1
1
0
2
2
2
1
0
0
1
2
1
0
1
1
2
2
2
1
1
1
1
0
0
1
2
1
1
1
1
0
1
1
1
1
1
0
2
1
1
1
2
1
1
1
1
1
1
0
2
1
0
1
1
1
2
0
1
0
0
0
2
1
1
1
2
1
0
0
1
1
0
1
0
1
1
1
2
1
1
1
1
0
1
1
2
0
2
2
1
2
0
0
1
1
0
1
2
2
1
1
2
1
1
2
1
2
1
1
1
0
0
1
2
1
1
1
1
1
0
0
2
0
2
1
1
0
1
0
2
1
1
1
1
1
2
1
1
0
0
1
1
2
1
1
1
2
1
0
1
0
1
0
1
1
1
2
1
0
1
1
1
1
2
0
1
1
1
1
1
1
1
2
0
0
0
0
1
2
2
1
1
2
2
1
1
1
2
1
0
2
2
1
1
1
1
2
1
0
2
1
1
0
2
2
0
1
1
1
2
1
1
1
1
1
2
2
2
0
0
0
2
1
1
0
1
1
2
1
1
2
1
2
1
1
0
1
1
1
0
1
0
1
1
1
2
1
0
1
1
1
2
0
2
1
0
0
2
2
1
1
0
1
1
0
2
0
1
1
2
1
1
1
2
2
1
0
3
1
1
1
1
1
2
1
1
2
1
2
1
2
0
2
0
2
2
2
1
0
2
1
1
2
1
1
1
1
0
1
1
0
1
0
1
1
1
0
0
1
1
1
2
0
1
1
1
0
1
0
1
2
1
2
0
1
2
0
1
0
1
1
1
1
0
0
2
1
2
1
1
1
1
0
1
2
0
0
2
1
0
1
1
0
2
1
1
2
2
0
1
0
1
1
2
2
1
1
2
1
0
1
1
2
2
1
0
1
1
1
0
1
2
1
1
2
0
1
1
2
1
1
1
1
1
1
0
2
2
1
1
2
1
0
2
1
1
1
4
1
1
1
0
1
1
1
1
2
2
2
2
2
1
0
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
0
2
1
0
2
1
2
1
1
2
1
1
2
1
0
2
1
2
1
1
1
2
1
2
1
1
1
2
2
1
2
0
2
1
2
0
2
0
1
2
2
1
1
1
2
0
1
2
1
1
1
1
1
1
0
1
2
1
0
2
1
2
1
0
2
2
1
2
1
1
1
1
1
0
0
0
1
0
1
1
2
2
2
1
1
0
0
0
2
0
1
0
2
1
1
0
2
1
1
2
1
1
1
1
1
1
2
1
2
1
0
1
1
0
2
1
0
0
0
2
2
1
1
1
0
1
1
2
1
2
1
0
2
1
1
3
1
0
1
0
1
0
1
1
1
1
1
1
2
1
1
1
0
1
1
1
1
1
0
0
1
1
1
2
1
1
0
1
1
1
0
1
1
0
0
0
2
1
1
1
0
1
1
1
1
0
0
1
1
1
0
2
2
1
2
2
0
2
2
1
0
1
1
2
1
0
2
2
0
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
1
0
1
3
2
1
0
2
0
1
0
0
1
0
1
2
2
1
0
1
1
1
1
1
1
0
2
1
1
1
0
2
1
0
1
2
1
1
1
1
2
2
1
2
1
1
1
1
1
2
2
2
1
1
1
2
1
1
2
1
0
2
1
2
2
0
0
0
1
2
1
1
1
1
0
0
2
1
1
1
1
1
1
1
1
2
1
0
1
1
1
1
2
1
0
1
1
0
2
1
1
1
1
1
1
1
0
1
1
1
1
2
0
0
0
1
0
2
0
2
2
1
1
1
1
0
2
1
1
0
1
2
3
1
0
0
1
1
0
2
1
1
1
1
2
1
1
0
2
1
1
2
1
1
0
1
2
1
2
1
1
0
2
1
3
1
2
0
1
2
1
3
2
0
2
1
0
2
1
1
0
1
0
2
1
1
1
1
1
1
1
2
1
1
0
0
1
1
0
1
0
1
0
1
0
1
2
1
1
0
1
2
0
1
1
2
1
2
0
0
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
2
3
2
0
0
1
1
2
0
2
1
0
1
3
1
1
1
0
1
1
1
0
2
0
1
1
0
0
1
1
0
0
1
1
1
0
0
0
1
1
1
1
1
1
0
1
0
1
1
1
1
1
1
1
2
2
0
1
2
2
1
1
1
1
1
1
2
3
1
1
0
2
1
0
2
1
1
0
1
2
2
1
2
1
1
1
2
0
1
1
1
0
0
1
1
2
2
2
1
2
0
1
1
1
2
1
0
1
1
1
1
1
1
1
1
1
1
1
2
1
0
0
0
1
1
1
1
0
1
2
0
1
1
1
2
1
1
1
1
0
0
1
1
0
2
2
1
2
1
0
2
1
1
0
1
1
1
1
0
1
2
1
1
1
3
1
1
1
0
0
1
1
0
1
0
0
1
1
0
0
0
0
2
2
1
1
2
1
1
1
1
1
1
1
1
2
0
1
1
1
2
2
0
0
1
2
1
0
1
2
2
1
1
0
0
1
1
1
1
1
0
2
0
2
2
1
1
2
0
1
1
1
2
2
1
1
1
2
1
1
2
1
1
0
1
1
1
1
1
1
1
1
2
2
1
0
0
0
1
1
2
1
0
0
1
0
1
0
0
0
1
0
1
2
0
2
1
1
1
0
1
3
2
0
1
0
1
1
0
1
2
1
1
1
1
0
1
2
1
2
1
1
0
1
2
1
1
0
2
1
2
1
0
1
1
1
1
2
2
1
1
1
1
3
2
0
2
1
2
0
1
1
2
1
1
2
1
1
1
1
1
1
1
0
3
2
0
1
1
1
1
2
0
1
4
1
1
2
0
2
1
1
1
0
2
1
1
0
1
2
2
2
1
1
0
2
1
2
0
1
0
1
1
0
1
1
1
1
1
2
1
1
1
1
0
1
1
2
1
0
1
2
0
1
0
1
1
2
1
1
2
1
1
1
2
1
2
0
1
1
0
3
0
1
1
1
2
1
1
0
0
1
1
1
1
0
0
1
1
1
1
2
0
2
1
1
0
2
2
1
1
1
1
1
1
2
2
1
2
3
0
2
1
1
2
2
2
2
1
1
0
2
2
0
0
1
1
1
1
0
0
1
2
1
1
1
1
1
3
1
1
1
1
1
1
0
1
0
1
2
1
1
2
1
1
1
2
1
1
0
1
1
2
1
1
0
1
2
1
0
2
1
1
1
1
1
1
0
2
0
1
2
1
1
0
0
1
2
1
1
1
1
1
2
0
0
3
1
2
0
1
0
1
1
2
1
1
1
1
1
2
1
0
1
0
2
1
2
2
2
1
1
2
1
1
2
1
1
2
2
1
1
2
1
1
1
2
2
2
1
1
0
1
1
1
0
2
1
2
1
0
1
3
2
1
1
1
2
2
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
4
2
2
1
1
1
0
2
1
1
0
1
1
1
1
1
1
1
2
2
2
2
1
1
1
2
1
2
1
0
1
1
1
2
2
2
2
1
1
1
2
1
1
1
2
1
0
2
1
1
1
2
1
1
1
1
1
0
1
0
1
1
0
0
1
2
0
1
1
0
1
2
0
1
1
1
1
1
2
1
0
1
2
2
2
0
0
1
1
1
0
0
1
0
1
0
2
1
0
1
2
1
0
1
1
1
0
1
1
2
2
2
2
2
1
1
0
1
1
1
0
1
2
1
1
2
1
2
0
2
4
1
2
1
1
1
2
2
1
1
0
0
1
1
1
2
2
0
1
1
0
1
2
1
0
1
0
1
1
1
1
2
1
0
0
0
2
1
1
2
0
1
1
2
1
1
1
2
1
2
2
1
1
1
2
2
1
1
2
2
1
1
1
1
1
2
1
2
0
1
1
1
1
1
1
2
1
0
2
1
2
1
2
2
0
1
0
1
2
1
2
1
0
2
2
2
2
1
1
0
0
1
2
2
1
1
2
1
0
4
1
1
2
1
2
0
1
1
1
1
1
1
0
2
1
1
0
1
1
1
1
2
0
1
2
1
1
2
1
0
1
2
2
1
0
1
1
1
1
1
1
1
1
1
2
0
0
0
1
0
1
1
0
1
0
1
1
1
1
1
0
1
0
2
2
1
2
2
1
1
0
1
1
1
1
1
2
1
1
1
1
1
1
0
2
1
1
1
1
2
0
2
0
0
0
0
1
2
1
2
1
0
0
0
1
1
1
1
1
2
0
2
3
2
1
0
1
1
2
0
2
0
2
2
1
1
0
1
1
1
2
1
2
1
2
1
1
2
1
2
1
0
1
2
1
2
1
1
1
2
0
1
1
2
1
2
1
1
1
0
1
2
2
1
1
2
2
2
1
1
2
1
2
2
2
2
2
0
0
1
0
2
1
0
1
2
2
0
0
1
1
2
0
2
0
0
1
0
1
0
0
1
1
2
0
1
0
1
0
2
0
3
2
2
1
2
0
1
1
1
0
1
1
0
1
1
1
1
1
0
1
2
2
1
1
0
1
1
1
1
1
0
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
0
1
2
0
2
1
1
0
0
1
1
1
1
1
3
1
1
1
1
1
2
0
2
2
2
1
1
2
0
1
1
1
1
1
2
1
2
1
0
1
1
1
2
0
0
2
1
1
2
2
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
1
0
1
1
1
2
1
0
0
1
1
1
0
1
1
2
1
0
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
0
0
0
1
1
2
1
1
1
1
1
1
0
1
1
1
2
1
2
0
1
0
1
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
1
2
0
1
1
2
0
0
1
1
1
0
1
0
1
4
1
2
0
2
1
1
1
3
1
1
1
1
1
2
1
1
1
1
0
1
1
2
2
1
1
1
1
2
1
1
1
1
2
0
1
1
1
0
2
1
1
0
0
1
1
0
1
0
1
1
3
0
1
2
1
1
1
0
0
1
1
1
1
0
1
1
1
2
2
1
1
0
1
1
1
1
1
1
1
0
1
2
0
1
2
0
2
0
1
0
2
2
2
1
1
1
1
1
1
1
1
0
1
0
0
2
1
1
1
1
0
1
1
1
1
1
2
1
1
1
1
2
1
2
2
2
0
1
1
1
2
1
0
1
1
1
2
0
1
1
1
1
2
2
1
1
1
1
1
2
1
1
0
1
1
1
1
2
1
1
2
0
1
1
1
0
1
2
1
0
0
0
1
1
1
1
1
1
2
0
1
0
1
1
2
1
2
1
2
1
1
2
1
1
2
1
1
1
2
2
1
1
1
0
1
1
1
1
1
0
1
0
1
0
1
1
1
2
1
1
0
1
0
1
1
2
1
1
1
2
2
1
1
1
2
1
1
2
1
1
0
0
0
0
2
0
1
0
2
4
2
1
1
1
1
2
0
0
0
2
1
2
2
0
1
2
1
2
1
1
2
2
2
0
1
1
1
1
1
2
2
1
1
2
2
7
1
1
1
0
0
0
1
0
1
2
1
1
1
1
1
1
1
2
2
0
1
2
2
0
3
1
1
0
1
2
0
0
0
1
1
1
1
2
1
1
1
1
1
1
1
1
0
1
0
2
2
2
1
0
1
0
1
0
1
1
2
1
0
2
1
2
1
0
1
1
0
0
1
2
3
0
0
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
2
0
0
1
1
1
1
1
2
2
2
1
1
2
2
1
2
1
1
1
2
1
0
1
1
1
0
1
0
0
2
1
1
2
1
4
1
0
1
1
1
2
1
2
1
1
2
0
0
2
2
2
1
1
1
2
2
2
1
0
1
1
0
1
1
1
1
0
0
2
1
0
1
2
0
2
1
0
2
2
1
0
0
1
1
1
1
1
0
1
1
1
1
0
1
2
1
0
1
0
2
1
0
1
0
2
1
1
0
1
0
0
1
2
0
2
2
1
1
1
1
1
2
1
1
0
0
2
0
1
1
1
1
0
1
2
1
0
1
1
2
1
2
1
1
2
1
2
0
0
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
0
2
0
0
2
1
2
1
1
0
1
1
0
0
2
1
1
0
0
1
1
0
2
0
1
0
0
2
0
1
0
0
1
0
1
2
2
1
1
1
1
1
2
2
0
1
0
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
1
2
0
1
1
0
1
1
0
1
2
0
1
0
1
2
1
2
2
2
0
1
1
1
2
1
2
0
1
1
1
1
2
0
1
2
1
0
1
0
1
0
1
1
0
2
1
1
0
1
1
0
2
1
2
1
0
1
1
0
2
0
1
1
1
2
1
0
1
1
1
2
2
2
0
2
2
2
1
1
1
1
1
1
0
2
2
1
0
1
2
2
1
1
1
1
1
1
0
1
2
2
2
1
2
1
1
1
1
2
2
0
2
2
1
1
0
1
1
1
0
1
1
2
2
3
1
2
2
0
1
1
1
0
1
2
0
2
1
0
0
1
1
1
1
1
2
1
2
1
0
0
1
0
1
0
1
1
1
2
2
1
0
2
1
0
2
1
0
2
2
0
1
0
1
1
1
2
2
1
0
1
2
1
0
2
1
1
2
1
0
1
0
2
1
1
1
2
2
1
1
2
1
2
2
1
1
1
2
1
1
1
0
1
1
2
1
0
1
0
1
0
0
1
2
1
2
0
1
2
2
1
1
1
1
1
0
0
1
1
1
1
2
1
1
1
1
1
1
0
1
2
1
0
1
1
1
1
1
2
2
1
1
0
1
1
2
2
2
2
0
0
2
2
0
1
0
0
1
1
2
2
0
2
1
0
1
1
2
1
1
0
1
1
0
1
1
0
1
3
1
1
1
1
2
1
0
2
1
2
2
1
2
0
1
1
1
1
0
2
1
0
0
2
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
0
1
1
2
2
0
1
1
1
1
1
1
0
2
1
1
1
0
1
2
1
0
0
1
1
0
1
0
1
2
1
1
2
1
1
2
1
1
1
1
1
1
0
1
1
0
1
1
2
1
1
0
1
1
2
1
2
2
2
1
2
2
1
1
1
1
0
0
1
1
1
1
1
0
1
2
1
0
0
2
1
2
1
2
1
1
2
2
1
1
2
0
1
1
2
1
0
1
1
1
1
1
2
0
0
1
1
1
1
1
0
0
1
1
1
2
1
0
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
0
1
1
1
1
0
3
1
1
0
2
0
0
1
1
1
1
1
2
0
1
1
3
1
2
1
1
1
1
0
0
1
1
1
1
0
1
4
0
2
0
2
1
1
1
1
1
1
1
1
1
1
0
0
0
1
1
1
1
1
1
1
1
1
2
1
0
1
2
0
1
2
2
1
1
4
1
1
2
2
1
1
0
1
1
1
1
1
1
2
0
6
1
2
2
1
1
0
1
2
0
1
2
2
1
1
1
2
1
1
1
1
2
2
1
0
2
2
1
0
1
0
1
1
1
1
2
1
1
1
0
1
2
2
1
2
1
1
0
2
2
1
1
4
1
2
1
1
1
1
1
1
1
2
0
0
2
1
2
0
1
2
1
2
1
2
0
0
1
1
1
0
2
2
1
0
1
1
2
1
0
2
2
1
0
1
1
1
0
0
1
1
2
1
2
2
2
1
0
2
1
1
1
1
1
1
1
1
0
1
1
0
1
1
0
0
1
1
1
0
1
1
0
1
1
1
1
2
1
1
1
0
2
1
1
1
2
2
2
1
2
0
3
1
1
1
2
0
1
0
1
1
2
1
1
1
1
1
1
1
1
2
0
2
1
1
0
1
1
1
1
2
0
2
1
1
1
0
2
1
0
1
1
1
1
2
2
1
0
1
0
0
0
1
1
1
0
1
1
1
1
1
1
2
2
1
1
2
1
1
1
1
1
1
2
1
0
1
0
1
2
1
0
1
1
1
0
0
2
1
1
2
0
1
1
2
0
1
0
0
2
0
1
0
2
0
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
2
0
0
1
0
4
2
1
0
1
1
1
2
1
1
1
2
1
2
0
1
2
1
1
0
1
0
1
2
2
2
1
2
0
1
2
2
1
0
2
1
1
2
1
0
1
1
2
0
1
2
2
2
0
0
1
0
2
1
1
1
1
2
2
1
2
1
0
2
1
1
0
2
2
3
2
2
1
1
1
2
0
0
1
0
0
2
1
0
2
2
0
1
1
0
2
1
1
2
1
1
1
1
1
0
1
2
2
1
0
1
1
0
0
0
2
1
1
1
0
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
0
1
2
1
1
1
1
2
1
0
1
1
2
0
1
2
2
2
0
1
1
1
1
2
1
1
0
1
1
1
1
1
1
2
0
1
1
2
0
2
2
2
1
2
2
1
2
2
2
1
1
1
0
2
1
0
2
0
1
1
2
1
2
2
2
2
2
2
1
1
1
0
1
1
2
1
1
1
2
1
0
1
0
1
0
0
0
1
2
1
1
2
1
2
0
1
0
2
1
1
0
2
0
1
1
1
1
1
1
1
1
1
0
1
2
2
1
1
1
1
2
0
1
0
0
1
2
0
0
1
2
0
0
2
1
1
1
1
0
0
1
1
1
1
1
1
9
0
0
1
1
1
1
1
2
0
0
1
1
0
1
2
1
1
1
1
0
1
1
0
0
2
1
1
2
1
1
0
1
1
0
0
1
1
1
0
1
1
1
1
2
1
1
1
1
1
2
0
1
0
0
2
1
0
2
1
0
1
1
2
2
0
2
1
1
1
1
1
2
1
1
1
1
2
0
1
2
1
2
1
2
1
0
1
1
1
2
1
2
1
0
1
2
1
0
1
1
1
1
1
1
1
1
2
2
1
1
0
2
1
1
1
0
1
0
2
0
2
1
0
0
1
0
2
1
0
1
2
0
2
1
0
2
2
1
2
1
0
1
2
2
1
0
1
4
1
2
2
1
1
0
2
1
1
2
2
1
0
1
2
1
1
1
2
1
1
2
1
1
1
0
0
0
2
2
1
1
1
0
1
1
1
1
1
0
1
1
0
0
1
0
1
2
1
1
2
2
1
2
1
1
2
1
1
1
1
0
1
1
0
1
0
1
1
1
1
2
2
1
1
0
1
1
1
3
1
1
1
2
1
1
0
0
1
1
0
2
0
1
0
1
1
1
0
2
0
2
1
2
0
1
1
0
1
1
0
1
2
1
0
0
1
2
1
2
1
0
3
3
1
1
1
0
1
1
1
1
1
1
1
1
0
0
2
0
1
1
2
2
0
1
2
0
1
1
1
0
0
1
1
1
0
2
1
2
1
1
1
0
1
2
1
2
0
0
1
1
1
1
1
1
0
2
1
1
2
1
1
0
1
0
1
1
1
1
1
0
2
0
1
1
0
1
1
3
1
1
1
0
1
1
0
1
1
2
2
1
2
1
0
1
0
1
0
1
1
1
1
2
1
1
2
1
1
1
0
0
0
1
0
0
1
1
2
0
1
0
2
2
1
1
1
1
2
2
0
1
1
1
0
2
1
2
2
1
1
1
1
2
1
2
1
1
1
1
1
1
1
3
2
2
0
2
1
1
1
2
1
2
1
1
1
1
1
1
1
2
0
1
1
1
1
1
1
2
1
0
2
0
1
1
1
2
0
0
1
0
2
1
1
0
1
2
2
1
1
1
0
1
1
1
3
1
1
0
0
1
2
0
1
1
0
2
0
1
2
2
1
2
2
1
2
1
0
2
1
1
0
1
0
1
1
1
1
0
1
0
1
0
1
1
2
1
1
0
0
1
1
3
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
0
2
1
1
2
1
1
2
2
1
2
1
2
2
2
2
1
2
1
0
2
0
1
1
1
1
1
0
1
1
0
1
1
1
1
1
2
2
1
1
1
0
1
1
1
1
1
0
0
2
0
2
2
1
0
0
1
1
0
0
0
1
2
1
1
0
2
2
2
1
0
0
1
2
1
2
1
3
1
2
1
1
1
1
1
1
1
1
0
0
1
2
2
2
0
2
1
0
2
1
1
1
0
2
1
1
0
1
1
1
1
1
0
3
2
2
1
1
1
1
1
1
1
1
1
1
1
2
0
1
1
1
1
2
1
3
2
0
1
2
1
2
1
1
1
1
2
1
4
0
0
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
0
1
1
0
0
0
1
1
0
2
1
1
1
1
2
2
2
0
1
1
1
0
1
1
2
1
1
1
0
0
0
1
1
2
1
1
1
1
1
1
0
2
1
1
1
2
1
2
1
1
1
1
1
2
0
2
2
1
1
2
1
1
0
0
0
2
0
0
1
1
1
1
1
1
1
2
0
1
1
0
1
2
1
1
0
0
1
1
1
2
1
1
1
0
1
0
1
1
2
1
1
1
2
0
2
1
2
1
0
1
2
0
0
2
1
2
1
2
0
1
2
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
0
2
2
2
1
1
1
0
0
1
2
2
3
1
1
2
1
2
0
1
0
2
2
1
1
1
1
1
1
1
1
2
0
0
2
0
0
1
2
2
2
1
2
1
1
1
1
0
2
1
0
0
0
2
3
0
1
1
2
1
0
1
1
2
0
0
2
1
1
1
0
1
1
0
1
1
1
1
0
3
2
1
0
1
1
0
0
2
1
2
2
1
1
1
1
0
1
2
0
2
1
1
1
0
1
1
1
1
2
1
1
2
1
0
1
2
1
2
1
1
1
1
1
0
1
0
1
0
1
1
1
0
1
0
0
2
1
1
2
0
2
2
1
1
2
1
1
1
1
0
2
2
2
0
0
2
1
0
1
1
2
2
1
1
0
1
2
1
2
1
1
1
2
1
1
1
0
1
2
2
2
0
1
2
2
1
2
0
0
1
0
1
2
1
1
2
1
1
1
1
0
1
0
0
1
2
1
1
1
0
1
1
2
0
0
2
1
1
0
2
1
1
1
2
1
1
1
2
1
2
1
1
0
0
1
1
2
0
1
1
1
2
1
1
2
1
1
2
2
1
1
1
1
1
1
2
1
1
0
0
1
2
1
2
1
1
1
1
2
1
0
1
1
1
2
0
2
1
0
1
1
1
1
2
0
1
0
1
1
1
1
2
1
1
0
1
1
0
1
1
1
1
2
2
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
1
2
2
0
1
1
1
1
2
1
2
2
1
1
0
1
1
0
1
1
0
0
2
1
1
1
2
1
2
1
2
2
2
1
1
1
1
2
1
1
1
1
0
1
0
1
1
0
2
1
1
1
0
1
1
1
1
1
0
1
1
0
1
1
1
1
2
1
1
1
1
2
2
1
3
1
1
2
0
0
1
1
0
1
1
1
0
3
0
2
0
0
0
0
2
1
0
1
0
0
3
1
1
1
1
1
2
1
0
1
1
1
2
1
2
1
1
2
0
1
1
1
1
1
1
1
1
1
0
0
1
2
2
1
1
1
1
1
1
0
1
1
2
1
1
1
1
1
3
2
1
1
2
0
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
0
2
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
0
1
1
2
2
0
0
0
1
1
0
1
1
2
1
0
1
1
1
1
1
1
1
2
0
1
2
3
0
1
1
1
0
1
0
2
1
1
1
1
1
0
0
1
1
1
2
2
1
1
1
1
2
1
0
0
1
1
2
1
1
0
1
1
1
1
1
1
1
0
1
2
2
1
0
1
1
1
1
1
1
0
0
0
2
2
2
1
1
0
0
2
1
2
1
1
1
2
1
0
1
1
2
0
1
2
1
1
2
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
0
1
2
1
1
2
1
2
1
1
1
1
2
2
1
1
2
2
1
1
2
0
1
1
1
0
2
2
2
0
2
2
1
1
2
0
1
2
2
1
0
1
0
1
1
0
2
1
1
0
1
1
1
1
1
2
2
1
1
1
0
0
1
2
0
1
2
2
2
1
1
0
2
1
1
0
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
0
1
0
1
1
1
1
2
1
1
1
1
1
0
1
1
1
2
1
1
2
3
0
2
2
2
1
1
2
1
2
1
1
0
1
0
1
1
0
0
1
1
2
2
2
0
1
1
1
1
1
2
2
0
1
1
2
0
0
1
2
2
2
2
0
1
1
1
1
1
1
1
0
0
2
0
0
0
1
0
0
1
2
2
1
1
1
2
2
1
0
1
1
1
1
1
1
1
0
0
1
2
2
1
1
0
2
1
1
2
2
1
2
1
2
1
1
2
0
2
2
0
1
2
2
1
1
1
1
2
1
2
1
1
1
2
1
1
0
1
1
1
0
1
1
2
1
1
2
2
1
2
1
1
1
1
1
0
1
2
0
1
1
2
1
1
2
1
0
2
1
1
0
2
1
0
1
2
1
1
2
1
2
2
2
2
2
1
1
1
1
1
1
2
0
1
2
2
1
1
1
2
0
1
1
1
1
0
2
1
1
1
1
0
1
1
0
1
1
1
0
1
1
1
1
1
4
1
1
1
1
1
1
2
2
2
1
2
2
1
2
1
2
1
2
1
2
1
1
1
1
1
1
1
0
1
1
0
1
1
2
1
1
1
2
0
2
1
1
1
1
1
1
0
1
1
1
1
1
1
1
0
1
1
2
1
1
0
2
0
1
1
0
1
2
1
1
0
2
1
2
1
2
0
1
1
1
1
0
0
1
2
2
1
1
1
1
1
1
0
0
1
0
1
0
1
1
1
1
1
2
0
2
1
1
2
1
1
2
1
2
1
0
0
2
2
0
0
2
1
1
1
1
1
1
1
2
1
2
0
1
0
2
1
1
2
2
1
0
2
1
0
1
0
0
1
1
1
2
0
1
1
1
0
1
1
2
1
1
1
1
2
1
1
2
1
2
1
2
2
0
1
2
0
1
1
1
2
1
1
1
1
1
2
1
0
0
1
0
1
1
1
1
1
1
0
1
1
1
4
2
0
1
1
2
2
1
0
1
1
0
1
2
1
2
2
1
0
1
1
2
1
1
1
0
0
0
1
1
1
0
1
0
0
1
0
1
1
1
1
1
2
2
1
1
1
1
2
0
0
1
1
1
1
1
1
0
2
1
2
0
0
1
0
2
0
1
1
1
2
1
0
0
1
1
2
1
1
2
1
2
2
1
2
1
1
1
0
1
1
1
2
2
0
2
2
1
1
2
0
2
0
1
1
1
0
2
4
1
2
2
0
2
1
1
1
1
1
1
1
2
0
1
1
0
1
2
0
1
1
1
2
1
1
1
2
1
2
1
1
3
1
2
1
1
1
2
1
1
2
0
2
2
1
2
1
1
1
1
1
1
1
1
0
1
1
1
0
0
0
1
2
2
1
1
1
0
1
2
1
2
1
0
0
1
1
0
0
2
1
2
1
2
2
1
0
1
1
2
1
2
0
1
1
1
0
1
1
1
1
1
1
2
3
1
1
2
1
1
1
2
0
2
0
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
0
2
1
1
1
1
1
0
0
2
1
0
1
2
1
2
1
0
1
0
1
2
1
1
1
1
1
0
2
1
0
0
1
0
0
2
2
0
1
1
1
1
1
2
0
0
2
0
1
0
1
1
1
1
1
1
2
0
0
1
2
1
2
2
1
0
0
1
0
1
1
1
1
2
2
1
2
1
1
2
1
1
2
1
0
2
1
1
1
0
2
1
1
1
1
1
1
1
1
1
2
1
0
1
1
1
0
2
1
1
1
1
2
2
2
1
1
2
1
1
1
1
0
1
2
1
2
2
1
2
2
1
1
1
0
1
3
2
1
1
1
2
0
2
0
1
2
1
2
0
1
1
0
5
2
2
0
1
1
1
2
0
1
2
2
1
1
1
2
1
2
1
1
2
1
1
1
1
0
1
1
1
0
1
1
1
1
1
2
0
1
1
1
1
2
0
0
1
1
0
1
1
2
0
0
2
1
0
1
0
1
1
0
1
1
1
2
0
0
0
0
1
1
0
1
1
1
1
1
1
1
1
0
1
0
0
1
1
0
1
2
1
1
1
1
1
0
1
1
1
1
1
1
1
2
1
2
0
1
1
2
2
1
2
1
2
1
2
3
1
1
1
0
2
1
2
1
1
1
1
1
1
1
0
1
1
1
1
2
2
1
1
1
1
1
1
1
0
1
2
1
1
1
1
1
0
1
1
1
1
2
1
1
1
1
1
2
2
2
1
1
1
1
1
1
0
1
1
2
1
2
0
2
0
1
1
1
1
1
1
1
4
2
1
0
2
1
2
2
1
1
1
0
1
0
1
0
1
1
1
0
0
0
1
1
1
0
2
1
1
0
1
1
1
0
0
1
0
1
0
1
1
2
2
1
0
1
2
2
1
1
1
0
1
1
1
1
2
1
1
1
0
0
0
2
1
1
0
1
0
1
2
2
1
2
1
1
0
1
2
1
0
0
1
1
1
0
1
1
2
2
0
1
1
1
1
0
1
0
2
1
0
1
2
1
1
1
1
2
1
1
2
1
1
1
1
0
1
1
1
2
2
1
0
2
1
1
0
1
1
0
2
1
0
2
0
1
0
2
1
0
1
0
0
1
1
1
1
1
1
2
1
0
0
0
1
1
1
0
2
2
1
0
2
1
1
1
1
1
0
2
2
1
0
2
0
2
0
1
1
1
1
1
0
2
1
1
2
2
1
2
0
1
1
1
2
2
1
0
1
2
1
0
1
1
2
2
1
2
1
1
2
1
2
0
2
1
1
2
2
1
0
0
2
2
0
2
0
1
1
0
1
0
0
1
1
2
1
0
1
2
0
1
1
2
3
1
1
1
1
1
1
1
0
0
1
1
0
1
1
2
1
1
1
1
1
1
1
0
2
1
1
2
1
1
0
1
2
0
1
2
0
1
1
1
1
2
1
0
0
2
1
0
1
1
2
1
0
0
1
0
1
1
2
2
3
1
2
1
1
1
2
1
0
0
1
2
2
1
1
1
2
2
1
1
0
1
2
0
1
2
1
1
0
1
1
2
1
1
1
1
1
1
1
2
2
0
0
1
1
1
2
0
1
1
1
2
2
1
1
0
2
2
0
1
1
0
2
2
2
1
0
1
1
1
1
1
1
2
0
1
2
1
1
0
1
0
1
2
1
1
1
1
1
1
1
1
1
1
0
1
0
2
2
2
1
1
1
1
1
1
1
0
0
1
1
2
0
2
2
1
1
1
1
2
1
0
2
1
2
0
2
1
2
2
1
0
2
1
0
1
2
1
1
1
2
1
2
0
0
1
2
1
1
2
0
1
2
0
0
2
2
2
1
1
0
1
2
1
1
1
2
0
0
1
1
1
0
1
1
1
0
1
1
0
2
2
1
1
1
1
1
1
1
1
4
0
1
1
1
1
0
0
1
1
1
0
2
1
1
1
1
2
2
1
1
1
0
1
1
1
1
1
2
1
1
1
1
0
2
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
0
2
1
1
1
2
1
2
1
1
1
1
1
1
2
1
2
2
0
2
1
2
2
1
1
1
1
1
0
2
1
2
1
1
0
1
2
1
2
2
0
2
1
0
0
1
1
1
1
0
2
1
1
1
1
2
1
1
1
2
1
1
0
1
0
0
1
1
1
1
1
0
1
2
1
1
1
1
1
1
1
2
0
1
2
1
1
1
2
0
0
1
0
1
1
2
0
0
1
0
2
1
2
2
2
1
2
1
2
1
2
1
1
2
2
1
0
1
2
1
1
1
1
1
1
1
1
0
2
1
1
1
0
2
1
0
1
1
2
2
1
1
0
1
2
1
1
0
1
1
1
2
2
0
0
1
2
1
2
2
1
1
2
2
1
1
1
1
1
0
0
3
1
1
1
1
1
2
2
2
1
1
1
1
2
0
0
0
1
1
1
0
1
1
1
1
1
2
1
1
0
0
0
1
2
2
1
2
0
2
2
1
2
1
1
1
1
0
1
1
1
1
1
1
2
2
2
1
1
2
2
1
1
1
1
2
1
2
2
1
1
2
2
0
0
2
1
1
1
1
1
3
1
1
1
1
1
1
0
1
0
0
0
1
1
2
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
0
2
1
0
2
1
1
0
2
1
2
1
0
2
1
1
1
1
0
2
2
1
2
2
0
1
0
0
3
1
0
1
0
2
0
2
1
0
1
1
1
1
1
2
0
1
1
1
2
1
1
2
2
1
1
2
2
1
1
0
2
0
1
2
1
1
1
2
1
2
2
0
1
3
1
1
1
1
2
1
1
1
2
2
2
0
2
1
0
0
0
1
0
2
0
1
1
1
0
1
1
1
0
2
2
2
0
1
1
1
1
2
0
0
2
1
1
1
1
1
2
1
2
1
1
2
1
2
0
0
0
1
1
1
1
1
2
0
1
2
1
0
2
1
0
0
1
1
1
0
0
4
1
2
1
0
1
1
1
2
1
1
1
1
0
2
2
1
1
1
0
2
0
2
1
1
1
1
3
2
2
1
1
2
1
1
0
1
2
1
0
2
0
1
1
0
1
1
1
2
1
2
0
1
0
0
0
1
1
2
1
2
1
0
0
2
1
1
1
0
1
1
1
0
1
1
0
1
1
0
1
1
1
1
1
1
2
0
1
2
0
1
2
0
2
2
1
1
2
1
1
0
2
1
2
1
1
1
2
0
0
2
1
1
1
0
0
2
2
0
0
1
1
0
1
1
1
1
0
2
1
0
2
2
1
1
1
1
0
0
0
2
0
1
2
0
2
1
2
1
0
1
1
1
1
1
1
0
0
2
1
2
0
1
2
2
2
1
2
1
1
2
1
1
0
1
1
0
0
1
1
1
1
1
1
1
1
0
1
2
1
1
1
0
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
0
1
2
1
1
1
2
1
1
1
0
2
1
1
1
0
1
0
0
2
2
0
1
1
2
1
1
1
1
1
1
1
1
1
0
1
1
2
1
1
1
1
0
0
2
0
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
0
1
1
2
1
2
2
2
0
0
2
2
0
1
1
2
1
1
0
2
1
1
1
1
2
1
1
1
2
1
0
1
1
1
1
1
1
1
1
1
2
0
2
0
1
3
2
0
1
0
0
2
0
0
0
2
1
0
0
2
1
1
0
0
4
1
0
2
2
2
0
1
1
0
1
1
2
0
1
2
2
2
1
2
1
1
1
2
0
1
0
2
1
2
0
1
1
1
0
1
2
1
0
0
1
1
2
2
2
2
1
1
2
2
0
1
1
2
0
2
1
1
1
0
1
2
0
2
1
0
1
1
0
0
1
1
2
2
1
1
1
0
0
1
1
0
1
1
1
1
1
2
2
1
0
0
1
0
1
0
1
1
0
1
1
2
2
1
1
0
1
1
2
2
1
1
2
0
0
1
0
1
1
1
2
2
1
0
1
0
1
0
1
0
1
1
1
0
1
1
1
2
2
1
2
1
2
1
1
1
1
1
2
1
0
2
1
0
2
2
1
1
0
0
2
2
2
2
1
1
1
1
0
1
2
2
1
0
3
0
1
0
1
0
2
2
1
1
2
2
1
2
1
0
0
1
1
0
2
0
1
1
1
2
1
1
2
0
1
1
0
1
1
1
2
2
1
1
0
2
1
1
2
1
1
1
0
1
1
1
1
1
1
2
1
1
2
1
0
1
1
0
2
1
2
1
0
1
1
3
1
1
1
1
0
1
1
1
1
1
2
0
1
1
1
1
2
0
2
1
1
2
0
1
0
1
2
2
1
1
2
1
1
1
2
1
1
2
1
1
1
0
2
2
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
3
1
1
0
1
1
1
2
2
2
2
1
2
1
0
0
2
1
1
1
2
0
0
0
1
1
2
1
1
1
1
1
1
0
2
0
1
1
1
1
1
2
2
1
1
2
2
1
1
1
1
1
2
1
1
2
2
1
3
1
1
1
1
1
1
1
0
1
1
2
1
1
2
1
1
1
1
0
1
1
0
2
1
2
1
1
2
1
1
0
1
1
2
1
2
1
0
0
2
2
2
1
0
0
2
0
1
1
1
1
2
1
1
1
1
1
0
1
2
0
0
0
0
2
0
1
1
1
2
2
2
1
1
1
1
1
1
2
1
1
2
2
2
1
1
1
0
1
1
1
1
1
1
0
0
0
1
1
2
1
0
1
0
2
1
1
0
2
1
1
1
1
1
0
0
1
0
2
0
0
1
1
2
2
1
1
2
2
1
1
1
1
1
1
1
1
1
1
0
1
1
0
1
1
2
0
1
1
2
0
1
2
1
2
1
1
2
2
0
2
2
2
0
1
0
1
1
1
1
1
0
1
1
0
1
1
2
2
1
1
1
1
0
2
2
1
1
2
0
1
0
2
1
2
2
2
2
0
2
1
1
1
1
1
1
0
0
2
2
1
0
0
0
1
1
2
0
1
0
1
1
1
1
1
0
1
2
1
0
2
0
1
2
1
1
1
0
1
2
1
2
1
1
1
0
2
1
1
1
1
0
1
1
1
1
1
1
2
1
1
1
1
1
1
2
0
0
2
1
1
2
2
1
0
1
2
0
0
2
1
1
1
0
1
1
0
2
2
1
0
1
1
1
1
1
1
0
1
1
1
2
2
0
1
0
1
1
2
1
1
1
1
2
0
1
1
2
1
1
0
1
1
1
1
1
0
1
0
1
1
0
1
0
1
1
0
3
0
1
0
1
0
0
0
0
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
2
2
2
2
1
2
1
0
0
2
1
1
1
1
1
1
0
1
1
1
2
2
1
2
1
2
1
1
0
2
1
1
2
0
2
1
2
0
2
1
1
1
0
1
0
1
1
1
1
1
1
0
1
1
2
1
1
1
1
1
2
1
2
1
2
0
2
1
1
2
1
1
2
2
2
1
1
0
1
1
1
0
1
1
0
1
1
1
1
2
2
1
1
0
2
1
1
1
1
0
1
1
1
1
1
1
1
0
1
1
1
2
0
1
2
1
2
1
2
0
0
1
0
1
0
1
1
1
2
1
1
1
0
2
1
1
1
0
0
0
1
0
1
1
2
1
2
2
2
1
1
0
1
1
1
1
2
2
1
0
1
1
1
1
1
1
1
1
0
1
0
1
1
1
1
0
2
1
1
0
1
2
1
1
1
1
1
1
1
1
1
1
0
0
2
1
0
0
2
1
0
1
1
0
1
2
2
1
1
2
1
0
0
0
0
1
1
1
1
2
1
1
2
1
1
1
1
0
1
2
1
1
1
1
0
0
0
1
1
1
1
0
0
2
2
0
1
0
2
2
0
1
0
2
1
1
1
0
1
0
1
1
0
0
0
1
0
1
1
1
2
1
1
1
1
1
1
2
1
0
1
2
0
2
1
1
0
2
2
0
1
1
2
3
4
1
1
1
0
2
2
1
2
1
0
1
1
2
2
1
1
2
1
0
2
2
1
1
0
1
1
0
1
2
2
2
1
1
2
2
1
0
1
1
2
1
1
2
2
1
2
1
0
1
0
0
0
1
1
0
1
2
1
1
0
1
1
0
1
2
1
1
0
1
1
1
0
2
1
1
0
5
3
1
1
1
2
3
1
2
1
1
1
1
1
1
2
2
0
1
0
0
1
2
1
1
1
1
0
0
2
1
1
1
1
2
2
0
1
0
0
1
0
1
1
2
1
1
0
1
2
1
0
1
1
1
1
2
2
2
2
0
1
1
2
2
1
1
1
1
1
1
1
1
2
1
0
2
1
1
1
1
0
1
0
0
1
0
1
1
1
0
1
2
1
1
0
0
0
0
0
1
0
0
0
1
1
0
1
0
1
2
1
1
2
0
1
0
2
2
3
2
1
2
1
1
1
0
1
1
1
1
2
1
0
2
1
1
1
0
1
1
2
1
0
1
1
1
0
1
1
1
1
1
0
1
0
1
1
1
1
1
1
1
1
1
1
1
0
1
2
1
1
1
1
0
1
0
0
1
1
2
2
2
1
1
2
2
2
2
2
1
0
0
0
1
1
1
1
1
2
0
1
0
1
1
1
2
1
1
0
2
1
2
1
0
1
1
1
0
1
2
2
1
1
2
1
0
1
0
0
2
2
2
0
1
1
2
0
2
1
1
2
1
2
2
1
1
2
3
2
2
1
1
1
2
1
1
1
1
0
1
1
2
1
1
0
1
1
1
3
2
0
1
1
3
0
2
1
0
1
0
1
0
1
2
1
0
1
1
2
3
1
1
0
2
2
2
2
1
0
1
1
0
2
2
2
0
1
0
2
0
1
0
1
1
2
2
2
1
2
1
1
1
2
1
1
1
1
1
2
1
0
1
1
1
1
0
1
1
1
1
2
1
1
1
1
1
0
2
0
1
1
0
1
1
2
2
1
2
2
1
2
2
2
1
1
1
2
0
1
1
0
2
1
1
1
0
1
1
1
1
1
0
1
0
0
2
0
1
0
2
2
2
2
1
1
1
0
1
1
1
0
1
1
1
0
1
1
1
2
1
2
1
1
0
1
2
1
2
0
2
2
1
0
3
2
1
1
1
1
1
2
0
0
1
1
0
1
2
2
0
1
1
1
1
1
2
1
1
1
1
1
1
0
1
1
0
1
0
0
2
2
0
2
1
1
2
0
1
1
2
2
1
0
1
1
2
1
1
1
1
0
1
0
1
2
0
1
1
1
2
1
1
2
1
0
2
1
1
1
2
1
1
0
2
2
1
0
1
0
2
1
1
1
2
1
1
1
1
0
0
1
2
1
1
1
1
2
1
1
2
0
1
1
1
0
1
1
2
1
0
0
1
1
1
0
1
1
1
2
1
2
1
1
1
1
0
1
2
0
1
1
1
0
0
1
1
0
1
1
0
1
1
1
0
0
0
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
2
0
1
2
2
2
1
1
1
0
2
1
1
0
1
1
0
2
1
1
0
0
1
2
2
0
1
2
2
1
1
2
1
1
1
0
1
1
2
0
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
2
1
1
1
2
1
0
1
1
1
1
2
2
2
1
1
0
1
1
2
0
2
1
1
1
2
1
1
2
1
2
2
4
2
1
0
1
2
1
1
1
1
0
1
1
1
1
1
1
1
1
0
1
0
2
2
0
2
0
2
2
1
0
1
1
0
1
2
1
2
1
1
1
2
1
1
2
0
1
1
1
1
2
2
1
2
3
2
2
1
1
0
0
1
1
1
1
1
0
0
1
2
1
0
1
1
1
0
2
0
0
1
1
0
2
2
1
0
2
1
1
0
0
0
1
1
1
1
1
1
0
1
1
1
1
0
1
1
1
1
0
1
1
2
2
3
1
1
1
2
1
0
1
0
1
1
2
0
1
0
1
0
1
1
1
0
2
0
1
1
1
1
0
1
2
1
2
2
2
1
1
1
1
1
1
1
1
2
1
0
2
2
1
1
1
1
1
0
2
1
1
1
1
1
2
1
1
2
1
0
1
1
0
0
1
1
1
2
2
1
0
2
1
2
1
0
2
0
2
0
0
1
1
1
2
3
0
1
0
2
1
1
1
0
2
2
0
1
1
1
1
1
1
2
1
1
2
2
1
1
1
1
0
1
2
2
0
1
1
0
2
1
0
1
0
2
2
1
1
2
1
2
0
1
0
2
2
1
0
1
2
1
7
1
1
1
0
1
1
1
2
1
1
1
0
1
1
1
1
1
0
1
1
2
1
1
2
0
1
1
1
1
1
1
1
0
2
0
0
2
0
1
2
1
0
1
0
1
1
1
1
1
1
0
1
1
1
1
1
3
2
2
0
1
1
0
1
0
2
1
0
1
1
1
1
0
1
0
1
1
1
2
2
0
2
1
1
0
1
0
1
1
1
2
1
0
1
0
1
2
1
1
1
1
1
3
1
1
0
2
1
1
1
2
1
1
1
0
1
2
1
1
2
2
2
2
1
1
1
2
1
2
2
1
1
1
1
1
0
1
2
2
1
1
1
1
1
1
1
1
1
0
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
2
2
0
2
0
2
0
0
1
1
1
2
1
2
1
1
1
1
1
1
2
0
2
3
1
1
2
1
0
2
1
1
0
2
0
1
0
2
0
1
1
1
1
1
2
1
0
1
0
2
1
2
1
1
1
1
1
1
0
1
1
1
2
1
0
0
2
0
1
1
1
1
0
0
0
1
1
1
2
1
1
2
1
1
1
2
1
2
0
1
0
1
1
2
1
2
1
0
1
0
0
0
1
1
1
2
1
1
1
1
1
1
0
0
1
2
1
0
1
1
1
1
1
1
2
1
1
0
2
1
1
0
1
1
0
2
1
2
2
1
2
0
2
2
1
1
2
0
0
1
1
1
1
1
3
2
1
1
0
0
0
1
0
2
1
0
0
1
1
1
2
1
1
0
0
2
1
1
1
2
1
1
2
1
2
1
0
0
1
0
0
1
1
1
2
2
1
1
1
0
0
0
1
1
1
1
1
1
1
0
0
1
0
1
1
0
2
2
2
1
0
2
1
1
2
1
2
6
1
1
1
1
0
1
2
1
2
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
2
1
0
1
1
1
0
0
1
1
1
1
1
1
0
2
1
0
2
1
1
1
1
1
1
1
1
1
1
1
2
1
2
0
1
1
1
1
1
1
0
1
1
1
0
1
3
1
1
1
2
1
0
1
0
3
0
1
2
1
1
0
1
2
1
1
1
2
1
1
1
0
1
1
2
0
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
0
0
1
2
1
1
1
1
2
1
1
0
1
1
2
1
1
0
1
1
0
1
1
2
1
1
0
1
2
1
1
1
2
1
0
1
1
0
1
1
3
1
1
2
2
1
2
2
1
0
1
1
1
3
2
0
2
0
2
1
2
1
1
0
1
1
2
1
1
1
1
1
2
0
1
1
1
2
0
1
1
0
1
1
1
1
1
1
0
0
1
1
1
0
0
1
0
2
1
1
0
2
1
1
1
0
1
0
2
1
1
1
2
2
1
1
0
1
1
1
2
2
1
2
1
1
1
0
1
0
0
1
2
1
1
0
1
1
0
2
1
1
1
0
1
2
0
1
1
0
1
0
1
1
1
1
1
1
2
1
2
2
2
1
0
1
3
2
0
2
2
1
2
1
1
0
2
2
0
1
2
0
1
1
2
2
2
1
1
1
1
1
1
0
1
2
1
1
1
1
0
0
1
1
1
1
1
0
0
1
1
1
0
0
0
1
2
2
1
0
1
1
0
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
1
0
1
0
0
1
1
1
1
0
1
1
2
1
1
0
1
2
1
1
0
1
0
2
0
1
1
0
1
0
2
1
1
1
1
1
1
0
1
2
1
2
1
1
1
1
0
0
1
1
2
1
1
1
2
1
1
1
0
1
0
1
2
2
2
1
1
1
0
1
2
0
1
2
1
0
3
1
1
1
1
1
1
1
1
1
2
0
1
2
1
1
1
2
0
1
1
1
2
2
1
1
2
1
1
0
1
1
1
1
0
1
1
2
2
2
1
1
1
2
0
1
1
1
2
1
1
0
1
1
1
1
0
0
0
1
1
1
0
1
2
1
1
0
1
2
0
0
0
2
1
1
0
1
1
1
1
1
2
1
1
1
1
1
1
1
0
1
2
1
1
1
1
1
1
0
0
1
0
0
2
1
1
1
0
1
1
0
0
2
1
1
0
1
0
1
3
1
1
1
1
0
1
0
1
1
1
0
2
1
0
1
1
1
1
1
0
1
1
1
2
2
2
1
2
0
1
1
2
1
1
1
1
1
0
1
1
2
2
1
1
0
2
2
0
0
1
1
1
1
0
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
1
0
2
1
1
2
1
1
2
2
0
2
2
0
1
1
1
0
1
1
0
1
1
1
1
0
1
2
1
1
0
1
1
1
2
2
1
1
0
1
1
1
0
1
0
0
2
0
0
1
1
2
1
2
0
1
2
2
2
0
1
1
1
1
1
1
0
1
2
1
1
1
1
1
1
1
2
2
2
1
1
1
1
2
0
0
0
1
2
1
0
1
0
2
0
1
1
1
0
0
1
1
0
1
1
1
1
1
0
1
0
1
1
1
1
1
3
2
1
0
1
0
1
1
0
0
1
1
2
0
1
1
1
2
2
0
1
3
1
2
2
2
2
3
2
1
0
0
1
1
1
1
2
1
2
1
2
2
1
1
1
0
1
1
1
1
2
2
0
0
2
1
2
0
0
1
0
1
0
1
0
2
2
0
1
2
2
0
2
0
1
2
1
0
0
0
1
2
0
1
0
1
0
1
1
0
1
1
1
3
1
2
0
0
1
2
2
1
2
0
1
0
2
1
1
2
1
0
0
1
2
2
1
1
1
0
0
1
1
2
1
0
1
1
0
1
1
2
1
2
1
2
1
1
1
2
1
2
2
0
2
2
2
1
1
0
0
1
1
2
0
1
1
1
1
1
0
0
1
1
0
1
0
1
1
0
1
0
1
0
1
0
2
1
1
1
2
1
1
1
1
2
2
1
1
1
0
2
2
2
2
0
0
2
2
1
0
1
2
1
1
1
1
1
2
2
0
2
2
1
1
0
1
0
2
1
0
2
0
1
1
0
1
1
1
1
1
2
1
1
0
1
2
1
2
1
0
1
2
1
0
0
1
1
1
1
2
1
0
2
1
0
1
2
1
1
2
1
1
2
1
1
0
1
1
2
1
1
1
1
2
1
1
1
1
1
0
2
1
1
1
1
2
2
1
1
1
0
1
1
1
1
0
1
0
1
1
0
2
2
1
1
1
1
3
2
2
0
2
0
2
1
1
1
2
1
1
2
0
1
2
3
2
1
0
0
0
2
2
1
1
0
0
0
0
1
2
1
1
1
0
1
1
0
0
1
2
1
0
1
1
0
1
2
1
2
1
1
0
2
0
1
1
0
1
1
1
2
0
2
0
0
1
2
1
2
1
2
1
1
0
2
0
1
1
0
1
0
2
0
0
1
1
0
1
0
1
1
2
1
0
0
1
0
1
1
0
2
1
1
0
1
0
1
1
1
2
1
1
0
1
2
1
2
2
1
0
1
1
0
1
1
1
1
1
1
0
2
0
2
1
1
2
2
1
0
2
1
1
1
1
0
2
2
1
0
0
0
1
1
2
0
1
0
1
1
1
0
2
1
1
1
2
1
1
2
1
2
1
1
2
1
2
2
1
0
2
0
1
1
0
0
2
1
0
0
1
2
1
2
0
2
0
2
1
2
1
0
1
0
0
1
1
1
4
2
1
1
0
2
0
0
1
1
2
1
0
0
1
1
0
1
1
1
0
1
0
2
2
0
1
0
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
0
2
1
2
0
1
0
2
1
1
0
2
1
2
0
1
1
1
1
1
1
1
1
1
4
1
2
1
2
1
2
1
1
0
1
1
3
0
1
1
0
1
0
1
2
0
1
1
1
0
1
0
1
1
1
1
0
1
2
2
1
1
1
1
1
1
2
2
1
1
2
1
1
0
2
1
0
0
0
1
1
1
0
2
1
2
1
2
2
1
1
1
1
2
1
2
1
2
1
0
1
1
1
1
1
1
1
2
1
0
0
1
1
1
1
1
1
1
2
1
1
1
2
1
1
0
0
1
1
1
1
1
0
0
1
0
0
1
0
1
0
2
2
1
0
0
1
0
1
2
2
1
1
2
1
2
2
1
0
2
1
1
2
1
2
1
1
1
0
2
0
0
2
2
1
2
1
1
1
2
1
0
0
1
0
1
1
2
2
0
2
0
0
1
0
1
0
0
1
1
1
2
0
1
1
1
1
1
2
1
2
1
1
2
1
2
2
0
2
1
1
0
1
2
1
1
1
2
0
1
1
1
2
1
0
0
1
1
1
1
2
1
2
1
1
2
1
1
0
0
1
1
2
1
2
1
1
2
0
0
0
1
0
0
1
1
1
1
1
1
1
0
1
1
2
0
1
2
1
1
1
2
1
1
2
1
2
1
0
2
2
1
2
1
1
1
1
1
1
1
1
2
2
1
2
1
0
1
0
1
0
1
2
0
0
1
1
1
1
0
0
0
0
2
1
1
1
0
1
1
1
2
2
1
2
2
1
1
1
2
1
1
0
1
1
1
1
0
0
1
1
0
1
1
1
1
1
1
1
1
0
1
2
0
1
0
0
2
2
2
0
1
1
1
1
0
1
2
1
2
0
2
0
0
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
0
0
1
1
1
0
1
1
0
1
2
0
0
1
0
1
2
1
1
1
2
0
2
1
0
1
1
1
2
1
0
2
1
0
1
1
2
2
0
2
1
1
1
0
1
2
0
0
1
1
0
1
1
1
1
0
1
0
1
2
1
2
1
0
2
0
1
1
1
0
1
1
2
1
2
2
2
1
2
2
2
1
2
2
1
0
1
1
1
2
1
1
2
0
1
1
1
2
1
1
1
1
1
1
1
2
1
0
2
1
0
1
1
0
1
0
2
0
1
1
0
0
1
1
1
1
1
1
1
0
1
2
1
1
1
1
1
0
2
2
1
1
2
0
2
1
1
2
1
0
1
1
1
1
2
1
1
0
0
0
2
1
1
0
1
2
2
1
1
1
1
0
3
2
2
2
1
1
1
1
1
2
1
1
1
1
0
0
2
1
1
1
1
1
1
0
1
1
1
0
1
1
2
0
0
1
2
1
2
0
2
2
1
1
1
1
2
0
1
0
1
2
1
1
2
0
1
0
2
0
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
0
1
1
0
1
0
1
1
1
1
1
1
0
1
2
1
2
1
1
1
1
1
1
1
1
1
2
2
1
1
2
0
0
1
2
0
1
0
0
1
1
1
1
1
2
2
1
1
1
0
1
1
0
1
2
1
0
1
3
0
1
1
2
0
1
1
1
1
1
2
1
0
0
2
1
1
0
2
1
2
2
1
1
1
1
1
1
2
0
1
1
0
1
0
2
1
1
0
1
1
0
0
1
1
1
1
1
1
1
1
1
1
1
2
1
0
2
1
0
0
2
1
0
1
0
1
1
1
2
1
0
1
1
1
1
0
1
1
1
1
2
1
0
1
1
2
2
1
2
2
2
0
1
0
1
1
2
2
1
0
1
1
0
0
2
3
1
2
1
0
1
2
1
0
1
0
1
0
2
1
2
1
1
1
1
1
2
2
2
1
1
1
1
2
0
2
1
2
1
0
1
1
1
2
1
1
0
1
1
2
1
1
0
1
1
1
2
0
1
1
1
1
1
0
0
1
1
1
2
2
2
1
1
2
2
2
1
0
1
0
1
1
1
1
0
2
0
1
2
1
2
0
1
1
2
1
1
1
1
0
2
1
2
1
2
2
0
2
1
1
1
1
0
1
1
1
2
2
1
0
2
1
1
1
2
0
0
2
0
1
0
2
1
1
0
1
0
1
1
1
1
0
3
0
1
0
2
1
1
2
2
0
2
1
1
2
1
2
1
1
1
2
1
0
2
0
2
1
1
1
0
1
1
1
1
1
1
1
1
0
2
0
1
1
0
1
1
2
2
1
1
0
1
1
0
1
0
1
0
1
0
1
2
1
0
0
1
0
0
0
2
1
1
1
2
1
2
1
1
0
2
1
1
0
0
0
0
2
2
3
0
2
1
2
0
2
1
2
2
1
0
2
0
0
1
0
1
2
0
1
1
3
1
1
0
1
1
1
1
2
1
1
0
1
1
1
2
1
1
1
1
1
1
1
1
2
0
0
0
2
1
0
0
2
1
2
1
2
1
1
1
1
0
0
1
1
1
2
1
1
1
1
1
1
1
1
0
1
2
1
1
0
1
2
2
1
1
1
1
2
0
0
0
1
1
2
1
0
2
1
0
2
1
2
2
2
1
1
2
0
1
0
1
1
1
0
1
0
1
1
1
1
1
2
1
0
2
1
1
1
1
1
1
0
1
1
1
2
2
4
1
1
0
1
0
0
0
0
1
3
1
0
0
1
1
1
0
2
1
1
1
2
1
2
1
1
0
1
0
1
1
1
3
1
0
2
0
1
0
1
1
0
1
1
1
0
1
0
2
2
1
1
1
0
1
0
1
1
1
0
1
2
0
0
0
1
1
1
1
1
1
1
0
1
2
0
2
0
1
1
1
2
1
0
0
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
0
1
1
1
1
1
2
1
1
0
0
2
2
2
2
0
1
2
2
2
2
1
2
2
2
1
2
2
0
1
0
1
1
1
1
0
1
1
0
2
0
0
1
1
1
1
1
1
1
0
1
1
1
0
0
2
0
1
1
1
1
1
1
1
1
1
0
1
1
2
1
2
1
1
1
1
1
1
2
1
0
2
2
0
1
1
2
1
0
1
2
0
1
2
1
1
1
1
2
2
0
1
1
1
2
0
0
1
1
1
0
1
1
2
1
0
1
2
1
1
0
2
2
0
0
1
0
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
0
2
2
0
1
1
1
1
1
0
3
1
1
1
1
1
1
0
2
1
1
2
2
0
1
0
2
2
2
1
1
1
1
2
3
0
2
0
1
0
1
2
2
2
0
0
0
2
2
1
0
1
2
1
3
1
0
1
1
1
2
1
1
0
1
0
1
1
1
2
1
1
2
0
1
0
0
1
0
2
3
2
0
1
0
1
1
0
1
0
0
1
1
1
0
2
1
2
1
0
1
2
1
1
0
2
1
1
1
1
0
2
0
1
1
1
0
1
1
1
1
2
1
2
0
2
1
1
1
2
1
1
2
0
1
1
0
1
1
1
1
1
4
1
1
1
0
1
0
0
1
1
2
0
1
0
1
1
0
0
2
0
1
3
1
1
1
1
0
1
1
1
1
2
1
0
0
8
2
0
0
1
1
0
2
1
1
2
1
0
1
1
0
1
1
0
1
2
1
1
1
2
1
0
2
2
1
1
1
0
0
1
1
0
1
1
1
0
1
0
0
2
1
0
0
2
1
1
0
1
1
2
0
2
1
2
1
1
2
1
1
1
2
1
0
0
2
1
2
0
1
1
0
1
0
1
1
0
2
1
2
1
1
1
1
2
0
3
0
0
2
1
2
1
1
1
1
2
1
1
2
2
0
1
1
0
1
1
1
2
1
2
2
2
0
1
1
0
3
0
1
2
1
1
4
0
2
0
2
0
1
1
1
2
1
1
1
1
1
2
2
1
1
1
2
2
2
0
0
1
1
1
0
1
2
1
2
2
1
2
0
1
1
0
1
2
0
1
1
1
1
1
1
1
1
2
2
1
2
2
1
2
2
1
2
1
0
2
0
1
2
0
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
0
1
1
1
2
2
2
1
1
2
2
0
1
2
0
0
2
1
1
1
2
1
1
0
2
1
0
1
0
0
2
2
1
0
2
1
0
1
0
0
1
0
2
0
1
2
2
0
0
0
2
1
1
1
2
1
1
2
1
1
0
2
0
1
0
1
0
2
1
1
2
1
1
0
2
1
0
0
2
1
1
0
2
1
1
2
1
0
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
0
1
2
1
1
1
0
1
2
1
1
1
1
0
1
1
2
1
2
1
3
2
0
1
2
2
1
2
1
0
0
0
1
1
1
2
2
0
1
0
2
0
2
1
0
1
2
1
2
1
1
1
1
0
1
1
0
1
2
0
1
1
0
0
1
1
1
1
1
1
1
2
0
0
1
1
2
2
2
1
1
2
1
0
1
2
1
1
2
1
0
1
2
0
2
2
1
1
1
1
1
1
1
1
1
2
2
0
1
0
1
1
2
1
1
1
1
1
0
0
1
4
1
1
2
1
1
1
1
0
1
1
2
2
2
1
2
1
1
2
1
1
2
0
0
1
1
0
1
2
1
0
1
0
1
0
1
1
1
0
1
3
1
1
1
1
1
2
0
2
1
1
1
2
1
0
1
1
2
1
0
0
2
1
0
1
0
1
2
1
1
2
2
0
2
1
2
1
1
1
0
1
0
1
0
1
2
1
2
2
1
2
0
1
0
1
2
0
1
1
0
1
0
1
2
2
2
1
1
2
0
1
1
1
1
2
1
1
0
1
2
0
1
1
1
1
1
1
1
1
0
1
0
2
1
1
1
1
2
1
1
2
0
2
1
0
2
3
1
1
1
0
1
1
0
1
1
1
1
1
2
0
1
1
2
1
2
1
1
0
1
1
1
0
2
2
1
1
0
2
2
0
1
2
1
2
1
1
0
2
0
0
1
2
1
1
2
1
2
0
0
3
0
1
1
2
0
2
2
2
1
2
0
1
1
2
2
1
1
1
1
1
0
1
2
1
1
2
1
2
0
2
2
1
0
2
1
1
0
1
2
2
0
2
1
1
0
1
0
1
0
0
1
2
1
1
1
2
0
2
2
1
1
1
1
0
1
1
0
2
0
1
1
1
0
2
1
2
2
1
1
1
1
0
1
0
2
1
2
0
1
2
1
0
2
0
2
0
1
1
1
1
0
1
1
0
2
1
1
1
1
1
1
1
0
1
1
3
1
2
2
0
0
2
2
2
1
1
1
1
2
0
1
1
2
1
0
1
1
2
1
1
1
1
0
1
1
2
2
1
1
2
3
1
1
1
1
3
1
1
2
1
1
1
2
1
1
0
0
1
1
1
1
0
1
1
1
1
2
3
0
1
2
2
1
2
0
1
1
2
1
1
2
1
1
1
2
1
1
1
1
1
2
2
1
2
0
2
2
1
1
1
0
0
0
0
1
2
2
0
1
1
5
2
1
2
1
1
1
0
0
1
1
0
1
2
1
1
1
1
0
0
1
1
3
2
1
0
1
1
1
1
2
1
2
2
0
0
1
1
1
1
1
1
1
0
0
0
1
1
1
2
0
1
1
0
1
0
0
1
0
1
1
2
2
0
0
1
2
1
2
1
0
1
1
1
1
0
1
1
0
1
1
1
0
1
1
0
1
2
1
2
0
1
1
1
2
1
1
2
1
0
0
1
0
0
1
1
1
1
1
1
2
1
1
1
1
1
1
0
1
1
1
1
1
1
1
0
2
1
0
1
1
1
2
1
3
1
3
1
2
2
1
2
1
1
1
1
1
0
1
1
1
2
1
1
1
2
1
1
1
2
1
0
1
1
2
3
2
2
1
2
2
1
1
1
1
1
1
2
2
0
2
1
2
1
0
0
1
2
1
0
1
0
2
2
2
0
1
1
1
1
1
0
2
0
1
2
0
0
2
1
1
2
1
2
1
1
2
1
2
1
1
1
2
0
1
0
1
2
1
1
1
1
1
2
1
1
2
1
1
2
1
0
0
0
1
0
1
1
1
2
2
1
1
1
1
2
1
2
2
1
1
1
2
1
1
0
1
1
0
1
1
2
1
2
0
0
2
1
1
1
2
1
2
2
0
0
2
1
2
0
1
1
2
1
1
2
2
1
2
1
1
1
2
1
0
1
1
1
0
1
3
1
1
1
0
2
1
0
1
1
0
0
2
2
1
1
1
1
0
1
1
0
1
2
0
2
1
1
0
2
0
1
0
1
1
1
1
1
1
1
1
1
1
0
1
1
1
0
1
0
1
1
1
1
1
0
1
1
0
2
1
1
1
1
1
2
1
1
2
2
2
0
1
0
2
1
2
1
1
1
1
1
1
0
1
3
3
1
2
2
0
1
1
1
0
0
2
1
2
1
1
1
0
1
2
2
2
1
1
1
1
0
2
1
1
2
1
1
0
1
1
2
1
1
1
1
1
1
2
1
0
0
1
2
1
1
0
1
1
1
1
2
1
1
0
1
2
1
1
2
0
1
1
0
1
1
2
1
1
7
1
1
0
3
1
2
1
1
1
2
0
0
1
1
1
2
1
1
0
1
1
0
1
1
0
0
1
1
1
1
2
3
0
0
2
0
2
2
0
1
2
0
1
1
1
0
1
1
1
2
0
1
1
0
1
2
0
2
2
0
1
2
1
2
1
1
1
1
2
2
0
0
1
1
1
2
1
1
1
2
0
0
2
2
1
1
1
1
1
1
2
0
1
0
0
0
1
0
1
2
1
1
0
1
1
1
1
2
2
1
0
1
1
0
1
0
0
1
2
0
1
0
1
0
1
2
1
1
1
1
2
1
1
2
1
0
1
1
1
1
1
2
1
2
1
0
1
0
1
1
1
2
2
0
0
0
2
1
1
1
1
1
0
0
1
1
0
0
2
1
1
1
1
1
1
1
1
2
1
1
1
3
1
2
1
1
2
1
2
1
2
2
2
2
1
1
2
2
1
0
2
2
1
1
1
0
0
1
2
1
1
1
1
2
1
1
0
1
1
1
1
1
1
1
1
0
1
1
1
0
1
2
2
1
0
1
1
0
1
1
1
1
1
1
1
0
2
1
1
2
1
1
1
2
0
1
0
2
1
1
2
0
2
1
1
1
1
1
1
2
1
1
1
0
2
0
0
1
2
1
2
2
0
0
0
1
0
0
1
1
1
1
1
0
1
0
1
2
1
1
1
2
2
1
2
0
1
1
0
1
0
1
1
1
1
1
1
0
1
1
0
0
2
1
0
1
1
0
1
1
0
1
1
1
1
1
2
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
0
1
2
0
2
1
1
1
1
0
1
1
1
0
0
1
1
1
1
1
1
1
1
1
1
1
3
0
0
1
2
1
2
1
0
0
2
1
2
2
1
1
0
0
2
0
0
0
1
1
1
0
1
0
2
0
2
1
2
1
0
1
1
1
2
0
0
2
1
1
1
1
2
0
0
0
1
1
0
1
1
1
2
1
1
2
1
1
2
0
2
1
1
1
1
1
1
1
0
2
1
1
1
1
2
1
1
2
1
0
1
1
0
1
1
2
1
1
1
1
1
1
0
1
2
2
0
1
1
0
1
0
2
0
2
2
0
0
0
1
0
1
1
0
1
1
0
1
1
0
0
0
1
1
2
1
1
0
1
2
1
1
2
0
1
1
1
0
1
1
0
1
1
1
0
2
0
1
2
0
1
1
1
2
1
0
1
1
1
1
1
1
1
1
2
1
0
1
1
1
2
2
0
1
1
1
0
1
2
1
1
1
2
2
2
2
0
1
1
0
1
1
2
2
0
2
0
1
1
2
1
2
0
1
1
1
2
1
1
0
1
1
2
2
2
1
1
2
0
1
1
1
2
0
0
0
1
0
0
0
1
1
2
2
2
2
1
2
2
2
1
1
1
1
1
2
2
1
0
2
0
1
1
1
0
2
1
2
1
1
1
1
0
2
1
0
2
1
0
1
0
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
1
2
1
2
0
0
1
1
1
1
2
1
1
1
1
2
2
1
0
0
1
1
1
2
2
1
1
1
1
1
2
0
0
1
1
1
1
2
0
2
1
2
0
1
1
0
2
1
2
0
1
1
2
1
2
2
1
1
1
1
0
0
1
1
1
1
2
0
1
1
1
1
0
1
1
1
1
1
2
0
0
0
1
1
0
1
0
1
0
1
1
0
1
2
1
1
1
0
1
0
0
0
1
1
1
0
0
2
1
2
0
0
2
1
0
0
1
1
1
1
1
2
1
1
1
2
1
1
1
1
0
1
2
0
0
1
1
1
0
1
1
2
1
2
2
1
0
1
1
1
1
1
1
0
1
1
1
1
1
2
0
1
1
2
1
1
1
2
1
2
0
1
1
1
1
0
2
2
0
1
1
2
2
1
0
0
1
0
2
0
0
1
1
1
1
1
1
2
0
2
2
1
2
1
1
0
1
2
2
1
1
1
1
1
1
1
0
1
1
0
1
1
0
1
2
1
1
1
2
1
1
1
1
2
1
1
2
2
0
1
0
2
2
1
1
2
0
1
2
1
0
2
0
1
2
0
1
1
0
1
0
1
1
1
0
1
0
1
2
1
1
2
1
2
2
1
1
2
1
0
1
1
0
1
1
1
1
1
2
1
1
3
2
2
2
0
2
1
1
2
0
1
1
2
1
0
1
1
1
1
1
1
2
1
1
1
2
2
1
0
1
1
0
2
1
1
2
1
1
2
0
1
0
1
1
0
1
1
1
1
1
0
2
1
0
1
1
1
2
1
1
0
0
1
2
1
0
1
1
0
1
2
1
1
1
1
1
1
2
1
1
1
1
3
1
1
1
2
2
1
2
1
0
1
2
2
0
0
2
1
1
1
1
1
1
1
2
1
1
3
1
2
1
1
1
2
0
1
0
1
1
2
1
1
2
0
1
2
1
1
2
1
0
0
1
1
0
1
0
0
1
1
1
2
1
1
2
1
1
1
2
0
1
1
1
2
1
1
2
1
1
1
2
1
2
3
1
1
2
0
0
0
1
0
2
1
1
2
1
1
2
1
2
1
1
0
3
1
2
1
1
0
1
2
0
1
1
1
2
1
1
1
1
1
1
1
0
1
0
2
1
1
1
1
0
1
1
0
1
1
2
0
1
0
1
1
1
3
0
1
0
2
2
2
1
2
2
1
1
2
1
1
1
1
1
1
1
1
2
2
2
1
1
1
2
0
2
3
1
1
2
1
1
2
1
1
1
2
2
1
2
1
1
1
1
2
0
0
0
1
1
1
2
1
1
1
1
2
2
1
1
1
1
2
2
0
1
1
0
1
2
0
0
1
1
0
1
1
1
1
1
2
1
0
0
2
0
2
0
1
0
1
2
1
2
1
1
1
0
0
1
1
1
0
1
1
1
1
1
1
1
2
0
1
0
2
1
1
0
1
1
0
2
1
1
3
2
1
1
1
1
0
1
1
0
0
1
2
1
1
1
1
2
0
1
0
2
1
1
1
1
0
1
0
2
1
1
1
1
1
2
1
1
2
1
2
2
1
2
0
2
0
1
1
0
0
1
1
1
2
0
1
0
2
0
0
1
1
2
1
1
0
1
1
1
2
0
2
2
1
1
1
1
2
1
0
0
1
0
0
1
0
1
1
1
1
1
1
2
2
1
1
2
0
0
2
2
2
2
1
1
1
2
0
0
1
1
1
1
1
3
0
1
0
2
1
1
3
2
1
1
0
2
1
2
1
0
1
2
2
1
2
1
1
2
2
1
1
1
1
2
2
1
1
0
1
1
1
1
1
2
1
0
1
1
1
1
1
1
1
0
1
1
0
0
0
1
0
0
0
1
1
1
1
7
0
1
1
1
1
1
1
2
2
2
2
0
2
1
0
2
1
1
0
1
2
1
2
2
2
3
1
1
2
2
1
1
0
1
2
1
1
0
0
0
2
1
1
1
1
1
2
0
1
1
2
4
1
1
1
2
0
1
2
2
1
1
2
2
1
1
4
1
1
1
1
1
1
2
2
1
2
2
2
0
1
0
1
1
1
0
1
2
1
2
2
0
2
0
2
0
1
1
1
0
1
1
1
1
1
0
1
1
2
0
0
1
1
1
2
0
1
2
1
0
1
2
1
1
2
2
1
0
1
1
1
1
1
1
0
2
1
1
0
2
1
1
1
1
0
1
1
1
1
1
1
1
1
1
2
2
1
2
1
0
1
0
1
0
1
0
0
1
1
1
1
1
1
1
1
2
1
1
0
2
0
1
1
3
1
1
1
1
1
1
1
1
1
2
1
1
2
0
0
1
1
1
1
1
0
1
2
1
1
2
0
0
0
2
1
1
2
2
1
1
1
1
0
1
1
1
1
1
1
1
1
2
2
1
1
1
0
1
0
1
0
1
3
1
2
0
1
1
1
1
0
2
0
2
1
0
2
2
0
1
0
2
1
1
0
1
0
1
0
1
0
1
1
1
1
2
2
1
2
1
2
0
0
0
0
0
0
1
0
1
1
1
2
2
1
1
1
0
2
0
2
1
2
1
0
2
1
1
1
0
0
1
0
1
1
1
1
1
2
2
1
1
2
2
0
1
1
1
1
2
0
1
1
1
2
0
2
1
1
1
1
0
1
0
2
2
0
1
0
1
2
1
2
0
3
0
2
1
2
1
1
1
0
1
1
1
1
2
1
2
1
0
1
2
1
1
3
2
1
1
0
0
2
1
1
1
1
1
1
1
1
2
2
2
0
0
1
1
1
1
0
1
1
1
1
2
0
3
1
1
1
1
2
0
1
1
2
1
1
0
0
1
1
1
0
0
1
1
1
1
1
2
1
1
1
2
2
1
1
2
2
2
1
0
1
1
0
1
2
1
1
1
1
1
1
1
1
2
1
1
2
2
1
0
1
1
2
1
0
0
2
1
2
0
1
1
0
1
1
1
1
1
1
1
1
2
0
1
1
1
1
1
2
0
1
2
2
0
2
2
0
1
2
0
1
1
1
2
2
0
1
1
1
1
1
2
0
0
1
0
1
2
2
2
1
0
1
1
1
1
0
1
2
1
3
1
1
1
1
2
0
1
1
1
0
1
1
1
0
2
0
1
1
0
2
1
1
1
1
1
1
1
1
1
0
0
2
1
2
1
1
2
0
2
1
1
0
1
1
1
0
1
3
1
1
1
2
1
0
1
1
0
2
1
1
1
2
1
1
2
1
1
1
2
0
1
0
1
1
2
0
1
0
2
2
1
2
0
1
1
2
1
0
1
0
1
0
0
1
1
1
0
0
0
1
2
2
1
2
3
2
0
2
1
2
1
2
0
2
2
1
2
0
1
2
0
2
1
1
0
1
1
0
1
1
1
0
1
2
1
1
1
1
0
0
0
1
1
1
2
1
1
2
1
1
0
1
0
1
0
0
0
2
2
1
0
1
2
1
1
0
1
2
2
2
0
0
1
1
0
3
2
1
0
1
2
0
1
1
2
1
0
1
1
1
1
1
2
1
2
1
3
0
0
0
1
1
2
1
2
1
0
1
1
1
0
1
0
1
1
0
1
0
3
1
2
1
1
1
0
1
1
1
1
0
1
2
1
1
2
0
1
2
1
0
0
2
0
0
1
0
2
2
2
2
1
2
1
1
1
2
1
1
0
0
1
2
1
1
2
1
2
1
2
1
1
1
2
1
1
1
1
0
1
0
1
0
1
1
1
1
1
1
0
0
1
3
2
2
1
0
1
1
2
1
1
2
1
1
1
1
0
1
1
1
1
1
1
1
0
1
0
0
1
1
1
1
1
1
1
2
2
1
2
1
2
1
1
1
2
1
0
1
2
0
1
1
1
2
1
1
1
2
2
1
1
2
1
1
3
1
1
2
1
1
2
1
1
2
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
0
2
0
1
1
0
0
1
2
1
2
0
0
2
1
1
2
1
1
2
1
2
1
1
2
1
0
0
1
1
1
0
1
1
1
1
0
0
2
2
0
1
1
1
1
1
1
1
2
0
1
1
1
1
1
0
1
1
2
2
1
0
1
1
0
1
1
2
2
1
1
1
2
2
2
1
2
0
2
1
0
1
1
0
2
2
1
1
2
1
1
2
0
1
1
1
0
2
2
1
2
1
0
1
1
1
1
1
0
2
1
1
0
1
1
3
1
1
1
1
1
2
1
2
2
1
1
1
0
1
1
1
0
1
2
0
1
2
1
1
2
0
2
1
0
1
1
1
1
1
2
1
1
0
1
2
1
1
1
1
1
1
1
1
1
0
1
1
1
1
2
1
0
0
2
2
1
1
2
2
0
1
1
0
1
1
0
2
1
1
2
1
1
2
0
2
1
1
1
2
2
1
2
2
1
1
0
1
0
1
0
2
1
1
2
2
2
2
2
1
1
1
0
1
1
1
2
1
1
2
1
0
0
1
1
1
1
1
1
1
2
1
0
1
2
0
1
1
1
0
0
1
2
1
1
1
1
2
2
0
1
2
0
1
1
1
1
1
0
1
1
0
0
0
2
1
2
0
1
2
0
1
0
2
1
1
1
0
0
2
2
1
1
2
1
1
1
1
1
0
2
0
2
2
2
1
2
1
1
1
1
2
1
2
1
1
1
0
2
1
1
0
1
3
1
2
2
1
1
0
1
2
0
1
0
0
1
1
0
1
1
0
1
2
0
1
2
0
1
0
1
0
1
2
1
1
1
1
0
0
1
1
1
0
0
1
0
0
0
0
1
1
0
2
1
1
1
0
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
0
3
1
2
4
2
0
1
2
1
2
1
1
1
0
1
1
2
1
0
0
2
2
2
1
1
1
1
1
1
1
1
1
1
2
0
2
1
2
0
0
2
1
1
2
0
1
1
1
1
1
1
2
1
0
2
0
1
0
1
0
1
0
1
1
1
0
1
1
1
1
2
1
0
1
1
1
1
1
1
2
0
1
1
1
1
2
0
0
2
2
1
2
1
0
2
1
1
2
2
0
0
1
1
1
1
0
2
2
0
1
0
2
1
0
1
1
3
0
1
2
1
1
1
2
0
0
1
1
0
1
1
2
0
1
0
2
1
2
0
0
0
0
2
1
2
2
1
1
1
1
2
2
1
0
1
1
2
1
0
1
1
2
1
1
0
2
2
1
1
0
2
1
2
0
1
1
1
0
0
1
1
1
1
1
1
1
1
2
1
1
1
0
0
0
0
0
1
1
1
1
1
1
1
0
0
2
2
1
1
1
1
1
2
2
1
1
0
1
0
1
1
1
1
2
2
2
2
1
2
1
1
1
1
1
1
0
2
1
1
2
1
1
1
1
1
0
0
0
2
0
1
0
1
1
2
1
1
2
0
1
1
1
0
0
1
1
0
1
2
1
1
2
1
1
1
1
2
0
0
0
0
2
1
1
0
0
1
1
2
1
1
2
1
1
0
0
0
1
1
3
2
2
1
1
2
0
1
1
0
1
1
0
0
1
1
1
1
1
1
1
1
1
1
1
0
1
2
1
2
0
1
0
2
2
1
2
2
1
1
1
0
1
1
0
1
1
2
0
0
1
1
1
2
1
0
2
2
1
1
2
1
1
1
1
1
1
0
1
0
2
1
0
1
2
0
1
1
0
1
2
1
0
1
0
1
2
0
1
4
1
1
1
0
1
1
1
1
2
1
1
1
1
1
1
2
0
3
3
2
0
1
1
0
1
1
2
0
1
1
2
1
2
1
1
1
1
0
2
2
1
1
0
0
1
0
2
1
1
1
1
1
1
2
1
1
2
1
0
0
4
1
3
1
1
1
1
0
1
0
1
1
4
1
0
1
1
1
1
2
1
1
1
0
1
1
0
2
0
0
1
2
1
1
1
1
0
1
2
0
0
1
2
2
1
1
2
2
1
0
1
0
0
0
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
2
1
1
0
2
0
2
2
1
1
1
0
2
0
0
1
1
0
1
1
2
1
0
1
1
0
0
2
1
0
2
4
2
1
1
1
1
0
1
2
2
2
2
0
0
1
0
1
0
1
1
0
1
1
1
1
0
1
1
0
1
1
1
2
2
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
3
0
1
1
1
0
1
0
2
1
0
1
1
1
1
2
1
0
1
0
1
1
1
1
1
2
2
2
1
1
2
1
0
2
0
0
0
1
1
0
0
1
0
1
1
0
2
1
0
1
1
1
0
0
1
1
2
1
2
3
1
0
1
1
2
1
0
0
2
1
1
3
1
1
1
1
2
1
1
2
1
2
2
0
1
1
0
1
0
2
1
1
0
1
1
2
2
0
2
1
1
1
0
1
0
1
1
1
3
1
1
0
0
1
0
1
2
1
0
1
1
1
2
2
0
1
1
1
2
1
1
1
2
2
1
1
0
1
1
0
1
1
2
1
2
1
2
1
1
1
2
0
0
2
2
1
1
1
0
1
1
0
2
1
1
1
0
1
2
1
1
2
2
0
1
1
1
1
2
1
1
2
2
2
2
2
1
1
1
1
1
1
0
1
1
2
3
2
1
1
1
1
2
2
0
1
1
2
1
0
1
0
1
1
1
0
1
2
2
2
2
1
0
0
1
0
2
0
1
2
1
0
1
1
1
1
1
1
2
1
2
1
0
1
1
1
0
2
1
2
2
1
1
2
2
1
0
1
1
1
2
1
1
2
2
1
2
2
0
2
1
2
0
2
0
2
0
2
1
2
1
1
0
1
0
2
1
0
0
1
1
2
0
2
1
1
1
2
1
1
1
0
1
1
0
0
1
1
4
0
2
1
0
1
1
1
1
2
0
1
2
1
1
1
2
0
1
1
1
2
0
1
1
1
1
1
0
2
1
1
2
0
1
1
1
1
0
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
0
2
0
2
1
1
2
0
1
1
0
0
1
1
2
0
1
1
1
1
1
0
0
0
2
1
2
0
1
1
1
1
2
1
1
1
3
1
1
0
1
2
1
1
2
2
2
1
1
1
0
1
1
1
1
1
1
2
1
1
2
2
0
1
0
1
1
2
0
0
1
1
1
1
2
2
1
1
0
1
2
1
1
2
2
1
0
0
1
2
1
2
1
1
1
1
1
2
0
2
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
2
1
1
1
2
1
1
2
2
1
1
0
2
0
2
0
1
0
1
1
1
2
2
1
1
1
1
1
1
0
1
1
1
2
1
1
1
1
1
1
1
1
1
1
0
1
2
2
1
2
2
1
1
1
1
1
1
1
1
2
1
1
0
0
0
2
1
0
1
1
1
2
0
1
1
1
2
1
0
1
1
1
0
1
1
2
0
1
1
1
1
0
1
1
2
0
2
0
0
0
1
1
2
1
0
2
2
1
1
1
1
1
2
0
2
1
0
0
1
1
1
1
2
2
1
1
1
0
1
0
2
1
1
1
1
2
0
2
2
1
0
1
2
1
1
1
1
0
1
2
1
2
1
1
1
2
1
0
1
2
1
0
2
2
2
2
2
2
1
1
0
2
2
2
1
2
0
0
1
2
0
0
1
2
0
1
1
2
0
1
2
0
1
1
2
1
2
2
1
1
0
0
1
1
1
2
0
1
0
2
2
1
0
0
0
1
1
2
1
1
2
2
1
1
1
1
2
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
2
1
0
1
1
0
1
1
0
1
1
0
1
1
1
1
1
2
0
2
2
2
1
1
1
2
1
1
1
2
0
1
2
1
2
1
2
2
1
0
1
1
1
2
2
1
1
1
0
2
1
2
1
1
0
2
2
0
1
1
0
1
1
1
1
0
0
0
1
1
1
1
2
2
0
1
1
0
1
2
1
1
2
4
1
1
1
2
2
1
2
1
2
1
2
1
0
2
1
0
1
0
1
1
0
1
1
1
1
1
1
1
1
1
2
1
1
2
1
0
2
0
2
1
2
1
0
2
1
2
1
1
2
3
1
1
1
1
1
11
2
2
0
1
0
1
2
1
0
0
1
2
1
2
1
0
1
2
1
1
1
1
1
0
1
2
1
1
1
2
1
1
1
0
2
2
2
0
1
0
1
1
1
1
0
2
2
2
2
1
2
1
1
1
1
2
1
0
1
2
1
0
0
1
1
1
1
1
0
1
1
1
1
1
1
0
1
0
0
1
1
2
1
1
1
1
1
2
2
1
1
1
1
0
1
0
1
2
1
1
2
1
0
1
2
0
1
2
0
2
0
1
2
1
2
2
1
0
1
2
2
1
1
1
1
0
1
1
2
1
1
1
1
2
0
1
1
1
0
1
1
1
2
0
1
1
3
0
2
1
0
0
1
1
1
0
1
1
1
1
0
0
1
1
1
0
2
1
1
1
1
1
1
1
2
1
1
1
0
1
1
1
1
1
1
1
0
1
1
2
1
2
0
2
1
1
5
1
0
1
1
1
1
1
2
1
2
1
2
1
1
0
2
0
1
0
1
2
1
1
1
2
1
0
1
2
2
1
0
0
1
0
1
1
1
2
0
0
1
2
1
1
1
2
1
0
1
1
1
0
0
2
1
2
1
0
2
0
1
2
1
2
1
1
0
1
2
1
0
1
1
0
2
2
1
1
0
0
1
2
2
2
1
2
1
0
0
2
2
8
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
2
2
1
1
1
2
1
1
2
0
0
1
0
0
1
2
1
1
1
2
0
0
2
1
1
1
1
0
1
2
1
1
1
0
1
1
0
1
2
0
1
1
1
1
0
1
1
2
2
0
1
1
0
0
1
1
2
1
0
1
1
1
0
1
1
0
0
2
1
1
2
2
0
1
1
1
0
2
2
1
2
2
2
0
0
1
1
1
2
1
1
0
1
2
2
1
1
1
1
1
0
1
2
0
1
0
0
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
0
0
0
2
2
1
0
0
1
2
0
0
1
1
2
2
2
2
1
1
1
1
1
1
1
2
1
2
0
0
1
1
1
1
1
1
2
1
0
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
0
1
1
1
0
2
2
1
2
1
2
1
1
1
1
1
0
0
2
2
1
1
1
1
1
0
2
1
1
0
1
2
3
1
0
0
1
1
1
0
0
1
2
1
1
0
1
2
1
1
2
0
1
2
2
1
1
0
1
3
1
2
1
2
2
0
1
1
2
2
1
2
2
1
1
0
1
1
2
1
1
2
2
1
1
2
1
1
1
1
2
0
0
2
1
1
2
2
0
1
1
2
1
1
1
1
1
0
1
1
2
1
0
1
1
2
1
0
2
1
0
1
1
0
2
0
0
1
2
1
0
0
0
2
0
1
2
2
1
2
1
2
1
1
0
1
2
2
1
0
1
1
0
1
1
0
0
1
0
1
2
1
2
1
1
0
1
1
1
2
0
1
3
2
2
3
1
1
0
0
2
0
2
0
2
1
0
1
1
0
1
0
1
1
2
1
1
1
1
1
0
1
0
1
0
2
1
1
1
1
1
1
2
0
1
1
1
0
2
1
1
2
1
1
1
0
1
0
1
1
1
2
1
1
0
0
1
1
2
1
0
2
1
1
1
0
1
1
0
1
2
1
0
1
1
2
1
0
2
2
2
1
1
0
1
2
2
2
1
0
1
1
1
1
1
1
1
1
1
1
0
1
1
2
1
2
2
1
2
0
1
1
2
1
1
1
2
1
2
0
1
2
0
0
2
0
0
1
2
1
1
1
1
0
2
1
0
1
1
0
1
2
0
1
0
1
1
0
2
2
1
0
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
0
1
2
1
1
0
2
1
0
1
2
1
1
1
0
1
2
1
1
1
0
1
1
2
1
1
1
0
1
3
1
0
1
2
0
2
0
0
0
1
1
2
1
1
1
0
1
1
2
0
1
0
3
2
2
1
0
1
2
2
2
1
1
1
2
1
1
2
1
1
1
0
1
1
1
1
2
1
0
0
1
0
0
2
1
1
1
0
1
0
1
1
1
0
1
1
1
0
2
1
0
1
1
1
0
1
1
1
1
1
1
2
1
1
0
0
0
0
1
0
1
2
1
1
2
0
1
1
0
1
2
1
1
0
1
1
1
1
2
2
1
2
1
1
1
2
0
1
2
1
2
1
0
1
1
0
1
1
1
1
0
1
1
0
1
1
3
3
2
2
2
1
1
0
1
1
2
1
1
1
1
1
1
1
1
0
0
1
1
0
2
0
2
1
2
0
1
1
1
2
1
1
0
1
1
0
0
1
1
2
0
1
0
0
0
2
2
2
0
2
0
2
2
2
1
0
0
0
2
2
2
1
1
1
0
2
1
1
1
1
0
1
2
3
1
2
2
1
1
1
1
1
1
1
1
0
1
2
1
0
1
1
1
1
2
2
1
1
1
0
2
0
1
2
2
1
2
1
2
0
1
0
1
2
0
2
2
2
0
2
1
1
2
0
1
1
1
1
2
1
1
1
1
1
1
0
2
1
1
0
2
0
1
2
1
0
1
1
1
0
0
0
1
0
1
0
1
2
1
0
1
1
2
2
1
1
1
1
2
1
1
1
1
0
0
0
2
0
2
1
0
1
1
1
0
2
0
1
0
2
2
2
2
1
1
1
2
1
1
1
2
1
2
1
2
1
2
1
1
2
1
1
0
0
1
1
1
1
1
3
2
1
1
1
2
2
1
1
1
2
0
1
2
2
0
1
1
1
1
1
1
1
1
1
1
1
0
1
1
2
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
0
1
1
0
0
0
2
1
1
1
0
1
0
1
1
0
2
2
1
1
0
1
1
1
1
1
1
0
1
1
1
1
2
1
0
1
1
1
2
1
1
0
1
2
2
1
1
1
1
1
1
0
1
1
1
1
1
0
1
1
2
0
1
1
1
2
1
2
1
1
1
0
1
1
1
1
2
1
1
3
2
0
2
1
1
0
0
1
0
1
2
0
1
2
1
2
1
0
2
1
1
0
2
1
0
1
0
0
0
2
0
2
0
1
1
1
2
2
2
1
1
1
1
2
1
0
2
0
2
0
1
1
1
1
1
0
1
0
1
1
2
2
0
1
0
1
1
2
0
2
1
1
1
1
2
1
2
1
0
2
0
1
1
1
0
2
1
0
2
1
2
1
0
0
0
2
1
1
0
2
0
1
2
1
1
1
1
0
0
2
1
1
1
1
1
1
1
1
2
1
2
1
1
0
1
0
0
2
0
1
0
2
1
1
1
2
2
1
1
2
2
1
1
1
1
2
1
0
1
0
1
2
2
1
1
3
2
2
0
0
2
0
1
1
0
1
0
0
1
0
1
2
1
1
1
2
1
0
1
2
1
1
0
0
1
0
3
2
1
0
2
2
1
2
1
1
1
1
0
0
2
2
1
0
1
1
1
2
0
1
1
1
2
0
0
1
2
1
1
4
0
1
2
2
0
0
1
1
1
1
1
0
2
1
1
1
0
2
1
1
1
0
0
1
1
3
1
1
1
0
1
2
1
0
1
1
1
1
1
1
4
1
1
1
1
1
2
1
1
2
0
1
2
1
2
0
1
1
1
1
0
0
0
1
1
0
1
1
1
1
0
0
0
0
1
1
0
0
1
1
0
0
1
1
1
1
0
1
1
0
1
1
1
0
1
1
2
0
1
1
2
2
2
2
2
0
1
0
1
2
1
1
1
1
1
2
0
2
1
0
0
0
1
1
1
1
1
1
1
0
2
0
0
2
0
0
0
2
1
0
1
1
0
2
1
1
1
2
0
0
1
1
0
0
0
0
1
2
0
1
1
1
0
1
0
1
1
0
0
1
2
1
1
2
2
1
2
0
1
1
0
2
2
2
1
1
0
0
1
1
2
1
0
0
1
1
1
1
2
1
1
0
1
0
1
2
0
1
0
1
1
1
2
1
1
1
2
0
0
1
1
0
0
1
1
1
1
1
1
0
1
2
1
0
0
1
2
1
1
0
1
1
1
0
1
2
2
1
0
1
0
2
1
0
1
1
1
2
1
1
0
2
2
2
1
1
1
1
0
1
1
1
1
1
0
1
1
1
1
1
0
1
0
2
2
2
1
2
0
1
0
1
1
1
2
0
2
1
1
0
2
0
1
0
0
1
0
1
1
1
1
2
0
1
1
2
1
2
1
1
1
0
2
1
1
2
0
1
1
2
1
1
1
0
0
0
1
0
1
1
1
1
1
0
0
1
2
0
0
1
2
1
1
0
0
1
1
2
2
2
1
1
0
0
1
0
0
0
1
1
0
2
1
2
0
1
2
2
2
2
1
1
2
1
2
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
0
2
0
2
1
1
1
1
2
0
2
2
1
2
1
2
1
1
0
1
1
1
2
0
0
0
1
1
1
0
2
0
1
1
1
0
1
2
0
2
1
1
0
1
2
1
1
1
0
0
1
0
1
1
1
1
1
2
0
1
1
2
0
1
0
0
1
0
0
1
2
1
1
1
0
0
1
2
1
1
1
0
1
1
0
2
1
1
2
2
0
2
0
0
0
1
0
0
0
2
1
1
2
1
0
1
2
1
0
0
0
0
0
1
1
1
1
1
1
1
1
1
1
2
1
0
1
0
1
2
1
1
2
0
1
2
1
1
2
1
0
1
1
1
1
1
1
2
2
1
1
1
1
1
1
2
3
1
1
0
1
1
1
2
1
2
1
1
2
1
2
0
1
0
1
1
1
0
1
1
0
1
2
1
2
2
1
2
1
1
1
0
0
1
1
0
1
1
0
1
2
1
0
2
1
2
0
1
1
1
1
0
1
1
1
1
2
2
2
2
2
1
2
0
0
2
1
2
2
1
1
0
1
1
1
2
1
1
0
1
1
0
1
1
0
1
0
1
1
2
2
0
0
2
0
1
2
1
2
1
1
2
2
0
1
3
0
1
1
2
0
1
1
2
1
0
2
1
1
2
1
1
1
1
1
1
1
0
1
1
1
1
1
0
1
1
2
2
1
1
2
1
1
2
1
1
1
0
1
1
2
1
1
0
1
2
1
3
0
1
1
1
1
1
1
1
1
1
1
0
1
2
1
0
0
0
1
1
0
1
2
1
0
2
1
1
2
0
2
1
0
0
1
1
1
1
1
2
1
2
1
2
0
0
1
1
2
0
0
1
1
2
1
1
2
1
1
1
2
2
1
1
1
1
0
2
2
1
1
1
1
3
1
1
1
1
2
1
0
0
1
0
1
1
0
1
1
0
1
1
1
2
0
1
2
0
2
1
0
0
2
2
2
1
0
1
2
4
1
1
1
0
1
1
2
2
0
1
1
2
1
1
0
0
2
1
1
1
1
1
1
2
1
1
1
1
2
0
1
1
0
1
2
2
1
0
1
0
1
1
0
0
0
2
1
0
2
1
2
2
0
0
1
2
1
0
1
1
1
1
2
1
0
1
1
0
0
0
2
1
3
1
1
1
1
0
2
1
1
0
0
0
1
1
2
1
0
2
1
1
1
2
1
1
1
1
1
1
1
1
1
0
0
0
2
1
2
1
0
1
1
1
2
2
1
1
1
1
1
2
1
1
1
0
0
2
2
1
1
2
1
1
1
1
1
1
0
1
1
1
2
2
2
1
0
1
1
1
2
1
0
2
1
1
1
2
2
1
1
1
2
2
0
3
0
0
2
0
2
1
2
1
1
0
1
1
0
1
1
1
1
0
1
0
1
1
1
2
2
1
0
1
1
1
1
1
0
0
1
1
1
1
0
2
1
1
1
0
0
2
2
0
1
1
1
0
0
1
0
1
0
2
2
1
0
1
2
1
0
1
1
1
1
0
1
1
1
1
1
1
0
1
0
1
1
0
1
1
0
2
2
1
0
1
0
1
1
0
3
1
2
0
1
1
1
1
1
1
0
2
0
1
1
0
1
1
1
0
0
1
1
2
1
0
2
0
0
2
1
1
1
2
0
2
1
2
0
2
2
0
2
2
3
0
1
0
1
1
1
1
1
1
1
0
2
1
1
2
0
1
2
1
0
5
1
0
0
0
1
2
1
1
1
1
1
2
1
2
0
2
2
2
2
1
1
1
1
1
0
1
2
0
1
0
1
2
1
1
0
0
1
2
0
0
0
2
0
1
1
1
2
0
0
0
2
1
1
0
1
1
1
2
1
1
1
1
2
1
1
1
2
2
0
2
1
1
1
1
0
1
1
0
0
2
2
1
1
1
1
2
1
1
1
1
1
1
1
1
2
2
1
1
2
0
0
1
1
1
1
1
2
1
0
1
1
2
1
1
2
0
1
1
1
1
2
1
2
1
1
2
2
0
0
2
1
1
2
1
0
1
1
0
0
1
1
1
1
1
1
1
1
1
0
1
1
0
1
1
2
2
0
1
1
1
1
1
0
1
2
0
2
2
1
1
1
1
1
0
0
1
1
2
1
0
2
0
1
0
1
0
2
0
2
0
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
2
0
0
1
2
1
0
0
1
1
1
1
0
1
1
1
0
1
1
2
2
1
1
0
1
1
0
1
1
1
1
1
2
1
2
0
2
1
2
0
2
2
3
1
1
2
1
1
0
1
2
1
0
1
1
2
2
1
1
2
0
1
1
1
1
1
1
0
0
1
3
1
1
1
1
2
0
1
0
1
0
2
1
1
1
1
2
0
1
2
1
1
1
0
1
1
2
1
0
2
1
1
1
0
1
1
0
2
1
1
1
1
2
0
1
0
1
1
0
1
1
2
1
2
2
2
1
0
1
1
1
0
1
1
0
1
1
0
1
2
2
0
1
0
2
1
1
1
2
1
1
1
1
1
1
2
2
1
1
2
1
2
3
1
1
0
1
0
2
2
1
0
0
0
2
1
0
1
0
1
1
1
1
0
2
1
0
1
2
1
2
1
1
1
1
2
0
1
1
2
1
1
1
1
1
2
1
1
2
0
1
2
2
1
1
2
0
0
2
1
2
1
1
1
1
0
2
2
1
1
0
1
1
1
2
1
2
1
0
2
1
1
2
1
0
2
1
2
1
1
1
2
0
0
0
0
1
1
0
1
2
0
1
0
1
1
2
1
2
2
1
2
1
1
0
1
2
0
1
1
3
1
0
0
0
1
1
2
1
2
1
1
2
1
2
2
0
0
2
1
1
1
2
0
1
1
1
2
0
1
0
1
2
2
1
0
2
1
1
2
0
1
0
1
1
0
1
1
2
1
0
2
1
1
0
1
1
1
2
1
1
1
3
2
1
1
1
2
1
1
3
1
0
1
2
1
0
1
2
2
1
3
0
0
1
1
1
0
0
1
2
1
2
1
1
1
1
2
1
2
1
1
2
2
2
3
0
1
2
1
2
0
1
1
0
0
0
0
1
2
1
2
1
2
3
1
1
1
1
0
2
0
1
0
1
1
1
1
1
2
1
1
2
1
1
2
0
0
1
0
1
1
1
2
1
0
2
1
1
1
1
1
1
1
0
2
2
1
1
2
2
2
0
1
1
0
2
1
2
1
2
1
1
1
1
2
1
0
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
1
1
2
0
0
0
2
1
1
1
1
1
1
1
2
1
1
1
0
2
1
0
1
2
1
2
1
0
1
1
1
0
0
1
2
0
1
2
0
0
2
0
1
1
1
0
1
1
0
0
1
1
1
1
1
2
2
0
1
1
0
1
1
1
2
2
0
2
1
2
1
2
1
1
2
1
2
1
1
1
2
1
1
2
2
0
0
1
1
2
1
2
2
2
2
1
1
1
1
1
1
1
1
1
1
0
1
0
0
0
1
1
1
1
1
1
0
1
0
2
0
1
1
0
0
2
2
1
0
2
1
1
1
1
2
1
1
1
2
0
1
1
1
1
1
1
2
1
1
2
2
1
1
1
2
2
2
0
2
2
1
0
1
1
0
1
1
1
2
1
0
2
0
2
1
2
1
0
2
2
1
1
0
1
1
0
1
1
1
1
1
1
1
2
1
2
1
1
2
1
1
2
0
1
2
2
1
1
1
1
0
1
1
1
1
1
1
2
1
2
0
1
2
1
0
0
1
1
0
0
0
1
2
1
0
2
1
0
1
0
2
1
0
1
0
2
1
2
0
1
2
0
1
1
1
1
1
2
2
1
1
1
0
0
0
1
1
1
1
1
1
0
1
1
0
1
1
2
1
1
3
1
2
1
1
3
1
1
1
1
2
2
1
1
0
1
1
1
1
1
1
0
2
1
1
1
2
0
0
1
1
1
2
1
0
1
0
1
1
2
0
1
1
0
1
0
1
1
1
2
1
1
2
1
1
2
1
2
2
1
1
0
1
1
2
1
1
1
1
1
2
0
0
1
1
1
1
0
1
0
0
1
0
0
1
1
1
2
1
2
1
2
1
2
2
0
0
1
1
1
2
1
2
1
0
0
1
1
1
2
1
1
3
1
1
1
0
1
1
1
1
1
0
0
0
2
1
1
1
0
0
1
0
0
1
2
1
2
1
1
2
2
2
1
1
2
2
0
0
1
1
1
1
0
0
1
1
1
2
0
1
1
1
1
1
1
0
0
1
1
2
2
2
1
0
0
1
1
0
1
1
1
2
1
1
2
1
2
1
2
0
1
2
0
2
2
2
1
0
1
1
1
1
0
1
1
0
0
0
1
1
1
1
2
1
1
0
2
0
2
1
2
1
2
1
2
2
2
1
0
1
1
0
1
1
1
0
2
1
2
0
0
1
0
1
0
1
1
1
1
2
1
0
1
1
1
1
1
0
1
2
0
1
2
0
2
1
1
1
1
1
1
0
0
1
0
2
1
1
2
0
0
0
2
1
1
0
4
1
0
1
1
1
2
2
2
0
2
1
0
2
1
1
0
1
1
1
1
1
0
1
2
0
2
2
1
2
1
2
2
2
1
1
0
2
0
1
2
2
1
1
0
1
0
1
1
1
1
1
0
1
2
1
0
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
0
1
2
0
2
1
0
1
1
1
0
1
2
1
2
1
0
2
1
1
1
0
0
1
0
2
1
1
1
2
1
1
1
0
1
1
2
1
1
1
1
1
0
1
0
1
1
0
0
0
1
1
2
0
0
0
1
1
1
1
2
1
1
0
1
1
0
1
1
1
1
1
1
2
1
1
1
2
0
0
1
1
2
1
2
1
1
2
0
1
1
1
2
1
2
2
1
1
1
1
2
1
1
1
1
2
2
2
1
2
1
2
2
0
1
1
1
2
0
0
0
0
1
1
0
1
1
1
0
2
0
1
0
1
2
2
1
1
2
1
1
1
1
1
1
0
1
1
0
2
0
1
1
1
0
1
0
1
1
1
1
1
0
2
1
2
1
2
2
2
1
1
1
1
1
0
1
1
1
1
0
1
1
2
1
1
1
1
2
1
1
0
1
0
1
2
1
1
2
1
0
1
1
0
1
1
1
1
0
1
1
0
1
0
1
1
2
1
1
2
0
0
2
2
1
1
0
0
1
1
1
1
0
2
2
1
1
0
1
1
0
1
2
1
0
1
0
1
2
0
1
1
0
1
0
2
1
2
0
1
2
0
0
0
1
1
1
1
1
1
1
1
0
0
1
0
1
1
1
0
1
1
0
0
2
2
2
0
1
1
0
0
3
1
1
0
2
1
1
0
1
0
1
1
1
1
0
1
1
2
3
1
1
1
2
2
0
3
1
2
1
2
0
1
2
1
0
1
0
1
0
1
1
0
1
0
0
2
1
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
0
0
1
1
0
1
1
1
1
0
1
0
0
0
1
0
0
0
1
1
0
0
2
3
1
1
2
0
1
0
1
2
1
1
1
2
1
1
0
1
1
1
0
1
1
0
1
1
0
0
2
0
2
0
2
1
2
2
1
1
2
2
1
0
1
2
1
1
1
1
1
1
1
1
0
2
0
0
1
1
2
2
1
1
0
2
1
0
1
2
1
1
1
2
1
0
1
1
2
0
2
1
0
1
0
1
1
1
2
0
1
2
1
1
2
1
1
1
0
1
2
0
0
1
1
1
2
1
1
1
1
1
1
0
1
2
1
0
0
0
1
1
1
1
2
1
1
2
1
1
2
0
2
0
1
1
1
1
1
1
1
1
1
0
2
0
1
0
1
1
2
0
0
2
1
1
2
0
1
1
1
1
0
1
1
1
1
1
2
1
1
2
1
0
1
0
1
1
1
2
1
1
0
0
0
1
2
2
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
1
0
2
1
2
1
2
1
1
1
0
1
1
1
2
2
2
1
2
1
0
1
1
1
1
0
2
2
1
0
2
1
0
1
0
1
2
1
1
1
2
1
1
1
1
0
0
1
1
0
1
2
1
0
0
2
1
0
2
0
1
1
1
1
1
1
1
2
1
1
0
2
2
1
2
1
1
1
1
2
1
1
1
2
1
1
1
1
0
2
1
1
2
1
1
0
1
1
0
1
1
1
0
0
1
2
2
1
1
2
1
1
2
1
1
1
1
1
1
2
1
2
0
1
1
1
1
0
1
1
1
0
1
1
0
1
1
1
5
0
1
1
0
1
1
2
1
2
0
0
1
1
1
3
2
1
1
2
2
1
1
1
0
1
2
1
0
1
1
0
0
1
1
2
0
2
1
1
1
0
2
1
0
1
0
1
1
0
0
0
1
1
1
1
1
2
1
1
2
3
1
1
2
1
1
1
1
2
1
1
1
2
1
1
1
2
0
1
1
0
0
1
0
1
0
2
1
1
1
1
1
1
1
1
0
2
0
1
1
1
2
2
0
2
0
1
2
0
2
1
2
1
1
1
0
0
0
1
2
1
0
0
1
2
1
3
2
1
1
2
0
0
1
2
2
2
0
0
1
1
1
1
2
1
0
1
1
1
1
1
0
1
1
1
1
1
1
0
2
0
1
1
1
2
0
2
1
2
1
1
0
1
1
2
0
1
0
1
2
2
0
1
1
0
2
1
1
0
1
1
1
1
2
1
2
0
2
0
2
1
2
0
1
1
1
0
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
0
2
1
1
1
1
0
0
1
0
1
1
1
1
1
1
0
0
1
1
0
0
1
1
2
1
0
0
0
1
1
1
0
1
1
1
1
1
1
1
1
2
1
0
1
1
2
1
0
1
1
0
1
2
1
1
1
1
1
1
0
1
0
0
1
2
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
0
1
2
1
1
2
0
1
0
1
1
1
1
2
1
1
1
1
2
0
3
1
1
1
1
2
0
1
2
0
2
0
0
1
1
2
1
1
2
1
1
1
1
1
1
0
1
2
1
2
0
1
2
2
2
2
1
0
1
1
0
1
0
2
2
0
0
2
2
1
1
0
2
1
1
1
2
0
0
1
0
1
1
1
0
0
1
2
0
0
2
1
1
1
2
1
2
1
1
2
2
0
0
0
2
1
1
1
2
0
1
2
0
2
1
2
0
1
2
1
0
1
2
2
0
1
2
1
1
1
1
1
1
1
0
1
2
1
1
1
1
1
1
1
0
0
0
1
1
2
1
1
1
1
2
1
1
0
3
1
0
1
0
1
1
1
1
1
1
2
0
1
1
1
1
2
1
2
1
1
1
0
1
1
0
1
1
1
0
1
2
2
1
1
0
1
0
0
0
0
2
1
0
2
1
1
0
2
0
1
1
1
1
1
1
1
0
2
2
1
1
1
5
1
0
1
0
0
2
0
1
0
0
2
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
2
2
2
2
1
1
1
1
0
1
2
1
1
0
1
2
1
0
1
1
1
1
2
2
1
0
1
0
2
0
1
1
1
0
3
0
1
2
2
1
1
1
0
2
1
0
1
2
0
0
2
1
1
0
1
0
0
1
1
1
1
1
2
2
1
1
2
1
1
2
1
0
1
0
2
0
1
2
0
1
0
1
0
1
2
1
1
0
1
1
1
1
1
0
1
1
1
2
2
1
0
1
2
1
1
1
2
0
0
1
2
1
1
2
2
1
0
0
1
0
0
2
1
0
0
1
1
0
2
1
0
1
1
0
1
4
1
1
2
0
1
1
1
1
1
1
2
1
2
1
2
2
2
0
1
1
0
1
1
0
0
1
2
2
0
2
1
1
0
1
2
3
0
1
1
2
2
0
3
2
1
1
0
2
1
1
2
0
1
1
2
2
2
1
1
1
2
1
1
1
0
2
2
1
1
1
1
1
1
1
2
2
2
2
1
0
1
1
1
2
1
1
2
2
0
1
1
2
1
1
1
0
2
1
2
1
1
2
2
1
2
0
1
1
0
0
1
0
0
2
1
0
1
2
1
2
2
0
2
1
0
2
1
1
2
0
1
0
0
1
2
1
1
1
2
0
1
0
2
0
1
2
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
0
0
0
2
1
1
1
0
1
1
0
1
1
2
2
0
2
0
2
0
2
1
2
1
2
2
1
1
1
3
0
1
1
1
1
1
0
2
0
0
1
1
0
0
1
1
1
1
0
1
1
1
0
1
1
1
2
2
1
0
0
2
2
1
1
1
1
1
1
2
2
1
1
0
2
1
0
1
1
0
1
1
1
1
1
0
1
1
1
1
0
0
1
2
1
1
0
0
2
1
1
2
1
1
1
0
1
1
0
1
1
1
0
2
0
2
2
1
1
1
1
1
1
1
1
1
0
1
1
1
1
2
1
0
0
1
2
1
1
1
1
0
2
1
1
0
2
1
1
2
2
0
1
0
0
1
2
1
0
1
0
1
2
1
1
1
1
2
1
0
1
2
1
2
2
2
1
1
2
2
1
1
1
1
0
2
1
0
2
0
1
2
2
2
1
1
0
1
2
0
1
1
2
2
1
1
2
1
1
0
2
1
0
0
1
0
0
1
1
1
1
0
2
1
1
1
1
1
2
0
0
2
0
0
1
0
2
1
1
2
1
1
1
0
1
1
1
1
1
1
2
1
2
1
2
1
1
1
2
1
2
2
1
2
2
1
2
2
0
0
1
1
2
2
0
2
1
0
1
1
1
1
1
1
1
2
1
2
1
1
1
2
1
3
0
0
2
1
2
1
1
2
2
3
1
1
2
0
1
1
1
2
2
0
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
0
1
1
1
0
2
1
1
2
2
1
1
2
1
1
0
1
1
1
1
1
1
0
1
1
3
0
2
2
1
2
1
1
1
1
1
0
1
0
0
2
1
1
1
2
1
1
2
2
1
1
1
1
1
2
2
1
2
1
1
0
1
2
1
2
1
0
1
2
1
2
0
1
1
1
0
0
0
2
2
1
1
2
2
1
1
0
1
1
2
1
0
1
0
1
2
1
2
1
1
1
1
0
1
1
1
1
1
0
1
2
2
2
2
1
1
1
2
0
2
1
1
2
3
2
2
1
2
2
1
1
1
0
1
2
1
2
1
1
0
1
1
0
2
1
2
1
0
0
3
1
1
1
0
1
2
2
1
1
3
2
1
1
1
1
1
1
1
1
1
1
2
2
1
0
1
0
1
1
1
1
2
1
1
1
1
1
0
1
0
1
1
1
1
0
2
0
1
0
1
1
2
1
1
2
1
0
1
0
1
1
2
2
1
0
0
1
2
1
0
0
1
0
1
0
2
1
0
3
1
1
2
1
0
2
0
1
0
2
0
0
2
1
2
1
1
1
1
1
2
1
1
1
1
2
1
1
0
2
1
1
2
1
1
1
1
0
1
1
3
2
1
2
1
2
2
1
2
2
0
2
2
1
1
1
1
1
0
1
2
2
1
1
1
1
3
1
0
1
1
1
0
0
0
1
1
0
2
1
0
1
3
1
1
0
0
1
1
2
0
0
2
1
1
1
1
1
2
1
0
1
0
2
0
1
1
2
1
2
0
0
2
2
0
2
2
2
1
1
1
2
2
1
1
0
1
1
2
1
1
2
1
2
0
2
1
1
1
0
1
0
1
2
2
1
1
0
0
0
1
0
0
1
1
0
1
2
0
1
1
2
2
2
2
1
1
1
1
0
0
0
0
1
0
0
1
1
1
0
1
2
0
0
2
2
0
0
1
2
0
1
1
2
0
1
1
1
1
1
0
0
1
1
1
1
1
1
1
1
0
2
0
0
0
0
0
1
1
1
1
1
1
1
1
2
0
1
0
0
1
1
1
1
1
1
1
0
1
2
1
1
1
0
2
1
0
2
2
1
0
1
2
1
1
2
2
0
1
2
1
1
1
2
2
1
3
1
2
1
0
1
2
1
0
1
1
2
1
0
0
1
0
0
1
1
0
1
0
1
1
1
0
0
1
1
2
1
2
2
0
2
1
3
1
1
1
2
2
1
1
1
1
0
1
0
1
1
1
0
2
1
2
0
1
1
2
1
2
1
1
1
1
3
0
2
2
1
2
1
1
2
0
1
1
1
2
1
1
1
1
2
1
2
1
1
0
0
0
1
3
1
1
1
1
1
2
1
2
0
1
1
0
1
1
1
1
1
0
0
1
2
0
1
1
0
0
1
2
1
1
1
1
1
1
1
1
1
1
2
2
1
1
0
0
0
0
1
2
0
0
1
2
1
1
1
2
1
1
2
1
1
1
0
1
0
1
2
0
2
5
0
1
2
1
1
1
0
1
0
0
2
2
1
0
0
1
0
1
1
2
1
1
1
1
1
1
1
0
1
2
0
1
1
2
0
0
0
0
1
1
0
1
1
2
1
1
1
1
1
0
0
2
2
1
1
2
2
1
1
3
2
1
2
1
1
0
2
0
1
0
1
1
1
1
0
0
1
1
1
2
0
1
0
0
2
1
1
0
1
1
1
2
1
1
2
1
2
1
0
1
1
1
2
2
1
3
0
1
0
1
1
1
1
2
2
1
1
1
0
0
1
1
1
2
0
1
1
2
1
3
1
0
0
2
1
1
1
1
1
0
1
1
0
1
2
1
3
1
1
1
1
1
1
1
1
1
0
1
1
1
2
1
3
2
1
0
0
2
1
1
1
0
1
1
1
1
2
1
1
1
0
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
0
1
1
2
2
0
1
1
0
1
2
0
1
0
1
1
1
1
1
1
1
1
2
2
2
1
0
0
1
1
1
0
1
1
1
1
1
1
1
2
0
2
1
2
1
1
1
1
2
1
1
0
1
0
0
1
1
2
2
1
1
2
2
1
1
0
0
1
0
1
1
1
1
2
2
0
0
1
1
2
0
0
0
1
0
2
1
0
0
1
1
1
1
1
1
1
1
1
1
0
1
1
0
1
1
2
2
0
2
2
1
1
1
1
1
1
1
2
2
1
2
2
1
0
1
2
1
1
0
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
0
1
2
2
1
0
1
1
1
1
2
2
2
1
0
2
1
2
1
1
1
0
2
0
2
2
2
1
1
1
1
1
1
2
1
1
0
1
1
1
0
0
1
2
2
1
1
1
2
1
2
1
0
1
1
3
1
1
1
2
1
0
1
0
1
1
1
0
1
1
2
1
1
1
0
1
1
2
1
1
1
1
1
1
2
1
1
1
3
1
1
0
1
2
2
0
2
1
1
1
1
1
1
1
0
1
1
1
0
1
1
2
0
1
2
1
0
0
2
2
1
1
2
1
1
1
0
1
1
2
0
1
2
2
1
1
2
1
2
1
2
0
0
1
2
2
1
2
0
1
1
2
1
2
0
0
1
1
1
0
1
1
1
2
1
0
1
0
2
1
1
2
0
1
0
1
1
1
0
1
1
1
2
1
1
1
1
1
1
1
1
0
1
1
0
0
1
1
0
1
0
2
0
1
0
1
1
2
1
2
1
1
2
1
1
0
1
1
2
1
1
1
1
0
0
1
2
0
0
2
1
1
1
0
1
1
0
1
1
2
1
0
1
2
2
0
1
2
0
1
1
1
1
2
1
1
1
0
3
1
1
1
2
2
2
0
2
2
0
2
2
1
0
1
1
1
1
1
0
0
3
1
1
1
1
1
2
1
2
1
1
1
0
2
0
0
2
2
0
0
1
1
1
1
1
2
0
1
1
1
1
1
1
1
1
0
0
0
1
1
2
1
1
0
0
0
1
1
1
2
1
1
2
1
0
1
1
2
2
1
2
3
1
2
2
1
2
1
1
2
4
2
1
1
0
1
2
1
1
1
1
0
1
2
2
0
1
1
1
1
1
1
1
1
3
2
2
2
1
1
1
1
1
0
1
1
0
1
2
2
2
2
0
2
1
0
0
0
2
0
2
2
1
2
2
1
0
1
1
2
0
1
2
1
1
0
0
1
2
1
0
2
1
2
1
1
1
1
1
1
1
2
1
0
2
2
2
1
1
1
1
0
2
0
2
2
2
1
2
1
0
0
1
1
1
2
1
1
1
1
1
1
1
1
2
0
1
1
0
0
1
2
2
1
1
1
1
1
1
1
2
1
1
2
1
0
0
1
1
2
1
0
1
1
2
1
1
1
2
2
1
1
1
1
2
1
1
1
1
2
2
1
0
0
1
1
0
0
1
1
0
1
1
1
0
0
1
2
1
2
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
2
1
1
1
1
1
2
2
0
3
2
1
1
1
1
1
0
1
0
1
1
1
1
1
1
1
1
1
0
0
1
1
0
1
1
1
2
0
2
1
1
1
4
1
2
1
0
2
1
2
1
1
1
2
1
2
1
0
1
1
1
1
1
1
0
1
1
1
1
0
2
1
1
1
1
1
0
1
2
0
0
2
1
2
1
1
1
1
1
2
2
1
1
0
0
1
1
1
1
0
1
2
1
2
1
2
2
1
2
1
2
1
2
1
1
2
1
2
0
2
1
1
2
3
1
2
1
0
1
2
2
2
0
1
1
1
1
1
1
1
0
2
1
1
0
0
1
1
1
2
2
1
1
1
1
1
1
1
0
0
0
2
1
1
1
1
0
1
0
1
0
2
1
2
2
1
1
0
0
1
1
1
0
2
2
1
2
1
1
0
1
1
1
1
0
0
1
1
1
0
2
1
1
0
0
2
3
0
1
1
1
2
1
1
1
3
2
1
1
1
2
1
1
2
0
1
0
1
1
2
1
0
1
2
2
1
2
1
1
1
1
0
0
0
1
2
0
2
2
1
0
1
1
1
1
1
1
2
1
1
1
1
0
2
2
3
0
2
2
2
1
2
1
2
0
3
1
2
0
1
1
1
0
1
0
1
1
1
1
0
2
1
2
1
1
2
1
1
0
1
3
0
2
2
2
1
2
1
1
1
1
2
1
1
2
2
1
1
2
1
1
2
2
0
0
1
1
1
2
1
2
1
1
2
2
2
1
1
2
1
2
1
4
0
1
1
1
1
1
1
1
2
1
2
0
3
1
3
1
2
1
1
2
2
0
1
0
1
1
0
2
1
1
1
1
0
1
1
1
1
0
0
1
1
0
0
1
0
2
2
0
0
2
1
1
0
2
1
1
1
1
1
1
2
2
1
1
1
2
1
0
1
1
2
1
1
1
1
1
2
0
1
1
0
2
0
2
1
1
1
1
1
1
1
1
1
0
1
0
0
1
1
1
0
1
1
2
1
0
1
2
0
2
0
2
2
1
0
4
2
2
1
2
1
1
1
0
1
3
2
0
1
2
2
2
1
1
1
1
1
2
1
2
1
0
1
1
1
1
0
1
1
2
0
2
1
2
0
0
1
2
2
1
1
2
2
1
1
0
2
1
0
1
1
2
0
1
0
4
1
1
0
2
2
1
1
1
0
1
1
1
1
2
1
1
2
0
2
1
2
1
1
0
1
1
1
1
1
1
0
1
1
0
0
1
1
0
1
1
1
1
1
1
0
1
1
1
1
1
2
1
1
1
0
1
0
1
0
0
1
1
0
1
0
2
1
2
1
1
1
2
1
2
1
2
2
2
2
1
0
2
1
2
2
1
0
1
2
1
1
1
1
1
2
1
2
2
0
2
0
1
1
2
2
1
2
0
1
1
0
1
0
0
2
0
1
1
0
2
2
1
0
0
0
0
2
0
0
1
1
1
0
1
0
1
2
2
1
1
1
1
1
0
1
0
1
2
1
0
1
2
1
0
0
1
0
1
2
1
2
0
1
1
2
1
3
3
2
2
0
2
1
2
0
2
0
2
0
1
1
1
1
1
1
1
1
1
2
0
2
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
1
0
1
2
1
1
1
2
1
0
0
2
1
0
2
1
1
1
1
2
1
1
0
2
1
2
2
2
1
0
1
1
1
1
1
1
1
1
1
1
0
0
2
1
1
1
1
1
1
2
1
1
1
2
1
0
1
1
2
1
1
0
0
1
2
1
2
2
2
1
1
1
1
1
0
2
1
2
1
0
1
0
1
2
2
2
1
1
2
0
2
1
1
3
1
1
1
1
0
1
2
1
2
1
0
2
1
1
2
2
1
0
1
1
1
0
0
1
1
0
1
1
2
0
1
1
1
1
2
0
2
0
1
1
0
1
1
0
0
2
1
1
1
1
1
1
1
1
1
0
1
1
1
2
2
1
1
0
3
1
0
2
2
1
1
2
1
2
1
2
1
2
1
2
1
1
1
0
1
0
1
2
1
1
2
1
0
1
0
1
1
2
2
1
1
1
2
0
1
0
1
2
0
1
1
1
1
1
1
0
1
0
0
1
2
1
2
1
2
2
1
1
1
1
2
1
1
1
1
1
0
1
0
1
1
1
2
1
1
0
0
1
1
1
2
4
1
2
0
0
1
0
1
1
1
1
1
0
1
0
1
1
1
0
0
1
1
1
1
1
1
1
1
1
0
0
0
1
2
1
1
2
0
1
1
1
1
1
0
2
0
0
1
0
1
1
1
1
1
0
0
1
0
0
2
1
2
1
1
2
2
1
2
1
1
1
0
2
1
1
1
0
2
1
2
0
0
0
1
2
0
2
1
1
1
1
2
1
1
2
1
1
1
1
0
0
1
2
1
0
1
3
1
1
0
1
1
1
2
2
0
1
1
1
1
1
0
0
1
1
1
0
1
2
0
1
1
2
1
1
1
0
0
3
1
1
1
1
2
2
1
1
1
0
1
0
1
0
1
1
2
1
1
1
0
1
1
1
0
2
0
0
1
2
1
1
0
3
1
0
2
1
1
0
1
0
0
1
2
1
2
0
2
0
0
0
1
0
2
1
1
1
1
1
1
1
2
1
0
1
1
1
1
1
0
2
1
2
1
1
0
1
1
1
1
1
2
0
1
0
1
1
0
1
1
0
0
1
0
1
2
1
2
1
0
1
1
0
1
1
1
0
1
1
2
2
1
1
2
0
1
1
0
1
1
1
2
1
2
1
2
2
2
1
1
2
0
1
2
2
1
1
1
1
0
1
1
1
1
1
1
1
1
2
0
2
1
1
0
0
1
2
1
2
0
0
2
1
1
2
2
1
0
1
1
1
1
0
2
1
2
0
2
1
2
0
0
2
2
1
2
0
1
0
1
1
2
1
2
1
1
0
1
1
1
1
2
1
1
1
1
0
2
1
1
2
0
1
1
2
1
1
1
1
1
2
0
1
0
1
0
2
1
1
2
2
1
1
0
0
1
0
0
0
1
1
1
1
1
1
2
2
1
1
0
2
1
1
1
1
0
2
2
0
2
0
1
0
2
2
1
1
1
2
1
1
2
1
0
1
2
0
1
0
1
2
1
2
0
1
1
1
1
1
0
0
0
1
1
1
0
1
1
0
1
1
0
2
1
1
2
2
0
1
0
0
0
0
1
1
1
1
2
1
0
2
1
2
0
1
1
1
0
0
1
0
1
1
3
2
0
0
2
1
1
1
2
1
1
0
0
0
1
2
1
0
1
0
0
2
1
1
1
1
1
1
1
1
2
1
1
0
2
1
1
1
0
2
0
1
2
0
1
2
1
0
2
0
1
1
1
1
0
2
1
0
1
1
1
0
1
1
0
0
1
2
1
0
0
1
1
1
1
1
1
0
1
3
1
1
1
1
1
0
1
2
1
1
2
1
1
1
2
2
1
0
2
0
2
2
2
2
1
1
2
2
2
0
0
1
1
2
0
2
3
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
2
1
2
2
0
0
0
1
1
0
2
0
1
1
1
1
1
3
0
1
1
0
1
1
0
1
2
0
1
2
1
3
1
1
0
6
2
1
2
1
0
1
1
2
1
1
2
0
1
1
1
1
2
1
1
2
2
0
1
1
1
1
2
1
0
1
1
1
0
1
1
2
1
1
1
1
1
1
0
1
1
1
0
1
1
1
1
2
2
0
2
2
1
1
1
0
1
1
2
1
0
1
1
1
2
1
2
1
4
0
1
1
1
1
0
2
0
1
1
0
1
2
1
2
1
0
1
1
1
1
1
1
0
1
2
3
1
1
0
0
1
1
1
1
1
1
2
1
2
1
1
1
2
0
1
1
1
1
1
2
2
1
2
1
2
1
1
1
2
1
0
2
1
0
1
0
0
2
2
1
1
0
1
1
2
2
0
2
0
1
1
2
1
2
2
1
1
1
1
1
1
2
1
1
2
1
1
1
0
1
2
0
1
1
1
2
1
1
1
2
1
0
1
0
0
2
1
1
1
0
2
0
1
1
1
0
1
1
0
1
1
0
2
2
1
1
1
1
0
0
3
1
0
0
0
0
2
1
1
1
2
1
1
1
2
1
1
1
1
0
1
1
1
0
1
2
1
2
1
2
1
2
1
1
2
1
1
2
1
2
2
1
2
0
0
1
1
1
1
1
1
1
1
0
2
3
1
1
1
2
1
1
1
1
1
3
1
2
1
1
0
0
1
2
1
2
1
1
1
1
0
1
1
0
1
1
1
1
1
1
1
1
1
1
0
2
1
1
0
0
2
1
1
1
2
1
0
1
0
2
0
2
2
1
1
2
0
2
1
1
1
1
2
2
0
0
1
0
1
2
2
1
2
0
1
1
0
1
1
2
0
2
1
2
2
0
1
0
2
1
2
1
0
1
1
0
1
0
1
1
1
0
2
1
1
1
2
1
2
0
1
1
1
0
0
1
1
2
0
2
1
2
0
0
2
2
1
0
0
1
1
1
1
1
1
2
1
2
1
1
1
2
1
1
1
1
0
1
0
2
1
1
1
1
1
1
1
1
0
1
1
0
2
1
1
1
1
2
2
1
2
2
1
1
1
2
0
2
0
1
1
1
3
0
2
2
1
1
1
1
1
3
2
1
1
1
1
1
1
1
0
2
1
2
0
1
1
0
1
1
0
1
0
0
1
1
1
1
0
1
2
1
2
2
1
2
1
1
1
1
1
0
2
1
2
2
0
1
0
2
1
2
2
0
1
1
1
1
0
2
0
0
2
1
2
1
1
1
1
1
1
1
0
1
1
1
2
1
1
1
0
0
0
1
1
2
1
1
1
1
1
1
1
0
1
1
1
2
0
2
2
1
2
1
1
1
1
1
0
0
1
2
1
2
2
1
0
1
1
1
1
1
0
1
1
2
1
2
1
0
1
1
1
1
1
1
1
1
1
0
0
1
1
1
0
0
1
1
0
1
1
1
1
1
1
1
0
1
1
0
1
1
2
1
1
1
1
1
1
1
2
2
1
2
1
2
3
2
1
1
0
0
1
1
0
2
1
2
1
2
0
1
6
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
0
0
1
2
0
1
0
1
1
0
0
1
2
2
0
1
0
1
2
1
2
1
1
2
1
2
2
0
2
2
2
1
1
1
0
0
1
2
0
1
1
0
1
2
1
1
1
0
0
2
2
1
0
1
0
1
3
0
0
1
1
1
2
2
1
1
1
1
1
2
1
1
2
0
1
1
1
2
2
1
2
1
1
1
1
1
0
2
2
1
1
1
1
0
0
1
2
1
1
1
1
0
1
0
0
2
1
2
1
0
1
1
1
1
1
1
2
0
2
0
1
1
1
1
1
1
2
1
3
0
2
1
0
2
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
0
1
2
1
1
2
1
2
1
2
0
2
0
1
0
1
0
3
1
1
1
0
1
1
2
0
1
1
1
0
2
1
1
2
1
2
3
1
1
1
2
0
1
1
0
1
2
2
1
1
2
2
1
1
0
0
1
1
1
1
2
2
1
0
1
0
2
1
1
1
1
0
2
1
1
2
1
1
1
1
1
1
1
2
2
1
0
2
1
0
2
0
3
1
0
1
1
1
1
1
1
2
1
0
1
1
1
0
0
1
0
0
1
2
1
1
0
1
0
2
1
2
1
2
2
0
1
1
2
2
1
1
2
0
1
1
1
2
1
0
2
2
1
1
0
1
1
0
1
2
0
2
0
2
0
2
1
1
0
1
0
1
0
3
2
0
1
1
1
0
2
1
1
2
1
2
0
1
1
1
2
0
1
2
2
2
1
1
1
1
0
0
0
1
1
1
2
1
1
1
2
1
2
0
0
1
1
1
3
1
1
0
2
1
0
1
0
1
1
0
0
1
1
1
2
0
2
0
1
2
2
1
0
0
1
1
1
1
1
1
1
1
0
0
1
2
2
0
2
0
1
1
1
1
1
1
1
1
0
1
0
1
0
1
2
1
1
1
1
2
1
1
1
0
1
2
1
0
0
2
2
2
0
0
2
2
1
2
2
1
1
1
2
2
0
2
1
0
1
0
2
2
0
1
0
1
4
2
1
0
1
1
0
2
3
0
2
1
2
2
1
2
2
1
1
0
0
2
2
1
2
0
0
1
1
1
1
1
1
0
1
2
1
1
1
1
0
1
0
0
1
0
2
0
0
0
0
1
2
1
1
0
1
1
1
1
2
1
0
1
2
1
2
2
1
1
1
1
1
1
2
0
0
0
1
0
2
1
2
1
1
0
1
0
1
1
1
1
2
2
1
1
1
0
0
0
0
1
1
1
2
0
0
1
0
1
1
1
1
2
0
2
0
1
1
2
1
1
1
1
1
1
1
1
1
0
0
0
1
1
1
1
0
0
3
1
1
1
1
2
0
0
1
1
1
0
1
0
1
1
2
1
1
0
2
2
1
1
0
1
1
0
1
1
1
1
2
1
1
1
1
0
1
0
1
1
1
1
0
1
1
1
2
1
2
0
1
2
1
0
0
1
1
1
1
0
2
1
1
1
1
1
1
1
2
2
1
1
1
1
5
2
1
1
2
0
2
1
1
0
1
1
1
0
2
1
0
1
1
1
1
2
1
1
1
1
1
1
0
0
0
2
1
0
0
1
1
2
2
1
1
1
0
1
1
0
2
1
1
0
1
1
0
0
0
1
2
0
1
2
1
1
1
2
0
1
1
1
1
1
1
2
1
1
1
1
0
2
0
1
1
2
1
1
1
1
0
1
1
2
2
4
0
1
1
2
1
1
1
1
2
0
1
1
0
0
1
1
2
0
1
1
1
1
2
1
1
2
0
0
1
2
0
1
2
2
1
1
1
2
1
1
0
1
1
1
0
1
1
3
1
1
2
0
0
0
1
1
1
1
1
1
2
2
2
2
1
1
2
2
0
2
0
2
0
1
1
1
1
1
1
1
0
1
0
2
1
1
1
1
1
0
1
1
0
1
1
1
0
1
1
0
1
1
0
1
1
0
0
2
0
1
0
1
2
1
0
1
1
2
0
0
2
1
1
2
2
2
1
1
1
1
1
1
1
3
2
1
2
1
0
1
2
1
1
1
1
0
1
1
1
2
3
1
1
1
1
1
0
0
2
1
0
2
1
1
2
1
0
1
1
2
2
1
0
0
0
1
1
2
0
1
2
2
1
1
2
2
1
2
2
1
0
1
1
1
1
1
2
0
2
1
2
0
2
1
1
1
1
2
1
2
2
2
1
0
1
1
2
1
1
1
1
1
1
1
0
1
1
2
2
1
1
2
2
1
1
2
1
0
2
1
1
1
2
1
2
1
1
0
0
3
0
1
2
1
2
0
1
0
1
0
1
0
2
1
2
1
1
1
0
0
1
0
2
0
2
1
0
2
0
2
1
1
1
0
0
1
1
1
1
1
2
1
1
2
0
2
1
2
1
1
2
1
1
1
0
1
1
0
0
1
1
1
0
0
2
1
2
1
2
2
0
0
0
0
1
1
2
2
1
1
1
1
1
0
1
1
1
2
0
2
2
1
2
1
1
2
0
0
1
1
1
1
1
1
1
2
1
0
1
1
1
1
1
1
1
0
1
2
0
2
0
1
1
1
1
0
1
1
1
1
1
1
1
0
2
1
1
1
1
1
2
1
2
1
2
1
1
1
1
1
2
2
2
0
2
1
1
2
2
1
6
1
1
0
1
1
0
1
0
1
2
1
1
2
1
1
0
1
1
0
1
0
0
1
2
0
1
2
1
2
0
1
1
1
2
1
2
1
0
1
1
1
1
2
2
1
1
1
1
2
3
1
0
1
1
1
2
1
1
0
1
1
1
0
0
1
1
3
1
1
2
2
1
1
4
1
2
1
0
2
1
1
1
2
1
2
0
1
0
1
1
2
1
1
0
1
2
1
2
1
1
0
1
0
0
0
0
1
1
1
1
1
1
1
0
0
1
2
2
0
0
1
1
1
1
2
1
0
1
0
0
2
1
0
1
2
0
0
2
1
2
1
1
1
1
1
1
1
0
2
1
2
0
1
0
0
0
1
1
1
1
1
1
0
0
0
1
1
2
2
1
0
2
1
1
1
1
2
1
0
0
1
1
0
1
0
1
1
1
1
2
1
1
1
1
1
1
0
2
1
1
2
1
0
2
1
1
2
1
1
0
1
1
2
1
0
1
1
1
1
1
1
1
1
2
1
1
0
1
0
1
1
0
0
1
1
1
0
1
1
1
1
1
2
1
2
0
1
1
1
1
0
1
0
2
1
1
2
0
0
1
1
1
1
0
1
1
1
1
1
2
1
1
1
2
0
0
1
1
1
1
0
1
1
2
0
0
2
0
2
1
1
1
1
2
1
1
1
2
0
1
1
1
1
1
0
0
2
0
0
1
2
1
2
1
0
1
1
2
3
1
2
5
1
2
0
2
2
0
1
1
1
1
0
0
0
3
1
0
1
2
1
0
1
1
1
1
0
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
0
3
1
1
1
0
1
1
1
1
1
2
0
0
0
1
0
2
0
1
1
1
0
0
1
1
2
1
1
0
1
0
2
1
2
1
1
0
1
1
1
0
2
2
1
1
1
1
2
0
3
0
2
2
1
1
0
0
1
0
1
1
0
2
1
1
2
1
1
1
2
1
0
1
0
2
1
1
1
1
1
2
1
1
1
2
1
2
2
2
1
1
1
1
2
2
1
1
2
0
1
0
1
1
0
1
1
2
1
2
1
3
1
2
2
0
2
1
2
1
0
1
1
1
1
1
2
2
0
1
0
1
1
1
1
1
1
2
1
2
1
2
2
1
2
2
2
1
1
2
0
1
2
0
0
1
1
0
1
0
0
2
2
1
1
1
1
2
2
2
2
0
1
1
1
0
1
0
1
1
1
1
2
1
0
1
0
1
2
2
0
1
1
1
1
1
2
1
1
0
1
1
2
2
2
0
1
0
1
1
0
0
1
1
1
2
1
2
1
1
0
0
2
1
1
1
2
1
1
0
2
1
1
0
1
1
1
2
1
1
1
3
1
2
2
0
1
0
0
0
2
1
0
2
0
0
1
1
2
2
1
0
1
0
1
0
1
1
1
1
0
1
1
0
2
0
0
2
1
1
0
1
1
1
1
2
1
0
1
1
0
0
1
0
0
1
1
1
1
1
1
1
1
1
0
1
1
2
1
2
0
2
1
0
1
2
2
2
2
0
1
6
1
1
1
1
0
2
1
1
1
1
0
1
1
1
0
1
0
1
1
1
2
2
1
1
1
1
2
2
2
1
1
1
1
1
2
1
2
1
1
1
2
1
1
0
1
1
2
1
0
2
1
1
1
1
1
1
2
0
2
0
1
1
1
2
1
1
0
2
2
1
0
1
1
2
1
1
0
1
1
0
0
1
1
0
2
1
1
1
1
1
1
0
1
0
2
1
0
1
1
1
1
1
1
0
1
1
0
1
1
2
1
1
1
1
1
2
1
2
1
1
1
0
1
1
1
0
1
1
1
2
2
1
2
1
0
2
1
1
1
1
1
2
2
2
0
0
1
1
1
1
2
1
0
2
1
1
1
1
1
1
2
0
1
1
0
1
0
0
1
0
1
2
1
1
0
1
1
1
2
0
0
0
0
1
1
1
1
0
1
1
1
2
0
2
1
1
1
1
1
0
1
2
1
1
2
0
1
1
0
1
1
1
0
1
0
0
1
2
1
1
1
1
1
1
0
1
1
2
2
1
0
0
1
0
1
2
2
1
1
1
1
2
1
1
2
1
2
0
1
1
1
1
1
1
0
2
1
2
0
1
0
2
0
2
0
1
1
2
1
2
1
1
1
2
1
2
1
1
1
0
1
1
0
1
2
1
1
1
1
1
2
1
1
0
2
2
0
2
1
0
1
2
1
1
1
1
0
1
1
1
1
1
1
0
1
2
1
1
0
1
0
2
1
1
1
2
1
2
2
0
1
2
1
2
1
0
1
1
1
0
1
2
1
1
2
2
1
2
1
1
1
0
1
1
1
0
1
0
1
1
1
1
1
1
2
1
1
0
1
1
1
0
0
1
1
1
1
1
0
1
1
1
0
0
1
1
0
1
1
0
1
1
0
1
1
1
0
2
1
1
0
2
2
1
0
2
1
2
2
0
1
0
2
2
1
1
1
1
1
2
2
1
1
1
1
1
1
1
0
1
1
1
1
1
1
2
2
2
1
0
2
1
1
1
0
0
1
2
2
1
1
2
1
1
1
2
1
2
1
1
2
2
2
0
1
1
2
1
1
0
2
0
1
2
1
1
0
2
1
1
0
1
1
2
2
1
1
1
1
1
1
1
1
2
2
2
0
2
0
2
0
1
0
0
1
1
2
2
1
1
1
2
1
1
1
2
0
0
1
1
2
2
1
0
1
2
1
1
0
1
1
2
2
2
1
1
2
1
1
1
2
1
1
1
0
1
1
0
0
0
0
0
1
2
1
2
1
1
2
0
1
0
2
1
1
1
2
0
2
1
1
0
0
1
0
2
2
3
0
1
0
1
1
0
1
1
1
0
1
0
0
1
0
2
0
1
2
0
1
1
1
1
1
0
0
1
1
0
2
0
2
1
2
1
1
0
1
1
1
1
1
1
0
0
0
1
0
2
1
1
1
0
1
1
1
2
1
2
0
1
2
1
0
1
3
1
2
1
0
0
1
1
1
1
1
1
1
2
1
1
1
1
2
0
1
1
0
1
1
1
1
1
1
2
1
1
2
1
2
1
2
1
0
0
1
1
1
1
0
1
1
0
1
1
0
1
1
1
1
0
1
0
0
1
1
2
2
1
2
1
2
1
1
1
1
1
1
0
1
1
2
1
0
1
0
0
2
1
0
1
2
1
0
1
1
2
2
2
0
1
0
2
4
1
2
1
2
1
1
1
0
1
2
1
1
1
1
2
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
0
2
2
2
0
2
1
1
1
1
2
1
1
1
0
1
2
1
1
0
0
2
1
0
1
2
1
1
1
2
1
1
1
0
1
3
1
0
0
1
2
1
0
0
2
2
2
1
1
2
1
0
0
2
0
1
1
2
1
1
1
2
1
2
1
2
1
1
0
1
1
2
0
0
1
1
2
2
1
2
2
2
1
0
1
1
1
1
2
2
1
2
2
1
2
1
1
1
2
1
1
1
1
0
0
1
1
1
1
1
1
1
0
0
2
0
0
2
1
2
0
2
1
2
2
0
1
0
1
0
0
1
1
0
0
1
0
0
1
1
2
2
1
2
1
1
1
2
0
3
1
2
2
0
1
0
1
1
1
1
1
1
1
1
1
1
1
1
0
2
1
2
1
0
1
0
2
1
1
0
0
1
3
1
1
1
1
1
2
1
2
1
1
1
2
1
3
1
0
1
1
1
1
0
1
1
1
2
0
1
0
0
0
1
1
1
0
1
1
0
1
0
0
1
1
1
1
1
1
1
0
1
1
0
1
1
0
1
2
1
0
1
2
1
1
1
1
1
1
2
2
2
1
2
1
0
2
1
0
2
1
0
0
1
2
1
2
1
1
2
0
1
0
2
1
2
1
1
1
2
1
1
1
0
1
1
0
0
1
1
1
1
1
1
0
1
1
2
1
1
1
1
1
1
2
1
0
1
0
1
1
1
2
1
1
0
0
0
1
1
0
1
1
1
2
1
0
1
1
2
1
1
1
1
2
1
1
2
2
0
1
0
2
1
0
0
1
0
1
0
0
2
1
2
0
2
1
1
2
1
1
1
2
3
1
1
1
0
1
1
0
2
1
1
1
1
1
1
0
2
0
0
1
1
1
0
1
1
1
2
1
1
0
2
1
0
1
1
0
2
2
1
1
1
1
1
0
1
2
2
1
1
0
2
1
1
2
0
1
1
1
1
1
0
1
2
0
1
1
1
1
1
1
0
1
2
1
1
1
2
0
1
2
1
0
1
2
2
2
1
2
2
0
1
1
1
0
1
0
2
1
1
2
1
1
1
2
1
1
1
1
0
1
2
2
1
1
1
1
0
1
0
1
1
2
0
2
2
1
0
1
1
2
0
1
1
0
1
2
2
0
0
1
1
1
1
1
1
2
1
1
0
0
2
0
2
0
1
1
1
1
1
2
1
2
1
1
1
2
1
0
2
1
1
2
0
0
0
1
1
1
2
0
2
2
0
1
2
1
0
1
2
2
2
0
0
1
1
2
1
1
1
0
0
2
0
2
1
1
2
1
2
1
1
1
1
0
2
1
0
2
1
2
1
2
1
0
1
4
1
1
2
2
0
2
1
1
2
0
1
1
2
1
1
1
1
1
1
0
1
0
1
1
2
1
1
1
1
2
1
0
1
1
1
2
1
1
1
2
1
1
3
1
1
1
0
2
1
4
1
0
1
1
1
0
1
1
1
2
3
1
2
1
0
1
1
1
1
1
1
1
1
0
2
2
2
2
1
1
2
2
1
0
1
1
1
2
1
1
1
0
2
2
1
1
2
0
1
0
1
0
2
1
1
1
1
1
0
1
0
1
0
1
1
2
1
2
0
0
1
1
1
1
0
1
0
1
1
1
1
0
0
1
0
4
1
2
1
1
1
0
1
1
0
0
0
1
0
1
1
1
1
0
2
1
0
1
2
1
0
0
1
1
2
1
1
2
1
2
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
0
1
0
1
1
1
2
1
2
2
1
1
3
3
1
1
2
1
1
0
1
1
1
1
0
0
2
1
1
1
3
2
1
1
1
2
1
1
2
2
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
0
0
0
0
1
1
2
1
0
0
1
1
0
1
1
1
1
1
2
0
0
1
1
1
1
1
1
1
1
1
1
1
0
1
0
1
1
2
1
1
0
2
1
1
1
1
1
1
0
1
2
1
1
1
0
1
1
1
1
2
0
0
6
2
0
1
2
0
1
1
2
1
2
1
2
1
1
0
1
1
0
1
1
0
1
1
1
1
1
2
2
1
1
1
1
1
1
0
0
1
0
0
1
1
1
2
1
1
1
2
1
0
4
1
2
1
1
1
1
2
1
0
0
1
1
0
1
1
0
1
2
1
1
2
1
0
0
2
2
1
1
1
1
0
1
2
1
2
1
1
1
1
1
1
1
1
2
2
1
1
0
1
1
3
2
2
1
0
1
1
2
1
2
1
1
1
1
0
1
1
1
2
1
1
1
2
1
1
0
0
2
1
1
1
2
2
0
1
0
1
1
2
1
1
1
2
1
2
1
1
0
1
1
2
1
1
1
1
2
1
1
0
2
2
1
0
1
0
1
1
0
1
0
1
2
1
2
1
2
1
2
2
1
1
0
5
1
1
1
1
1
0
2
2
1
1
1
0
0
2
1
1
1
2
1
0
1
2
0
1
2
1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
2
1
1
3
1
2
1
1
1
1
2
1
1
2
1
0
1
1
1
1
1
0
2
1
0
1
2
2
2
1
0
1
1
1
1
2
1
2
2
1
1
2
0
1
0
0
0
1
1
2
1
2
0
2
0
2
2
1
1
2
1
1
1
1
1
1
1
2
1
1
2
1
2
1
2
2
1
1
1
1
2
1
1
0
0
0
2
2
1
1
1
0
1
1
1
0
2
2
1
0
2
0
1
1
3
2
0
1
1
1
0
2
1
0
1
0
1
1
1
1
1
1
2
1
1
1
1
0
1
0
1
1
1
0
1
1
0
0
1
1
0
1
1
1
1
2
1
1
1
0
1
1
2
1
1
2
1
1
1
3
1
1
2
1
1
1
0
0
0
2
1
1
2
2
0
1
1
2
1
1
0
2
2
1
2
2
2
1
1
0
1
1
1
1
0
1
1
2
1
2
1
0
1
2
2
1
2
1
0
1
1
1
1
1
1
1
2
1
0
1
1
2
0
1
1
2
0
2
2
1
0
0
1
0
2
2
1
1
1
0
0
0
1
1
1
2
1
1
2
1
1
1
2
1
1
1
1
0
2
0
1
1
1
1
1
1
0
0
0
2
0
1
2
2
1
1
1
1
1
1
2
2
1
1
2
0
1
1
1
1
2
1
0
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
0
1
0
1
0
0
1
2
2
1
1
1
1
1
0
0
1
2
1
0
1
1
0
0
2
1
1
1
2
2
0
2
1
1
1
2
2
2
0
3
0
1
1
2
0
0
2
1
2
1
2
2
0
0
2
1
1
1
0
1
0
2
2
1
3
1
1
1
1
1
0
2
1
0
0
1
1
1
1
0
1
2
1
1
2
0
1
2
1
1
1
2
0
1
1
0
1
0
1
2
1
1
2
1
1
1
2
1
2
2
1
0
1
0
2
2
0
1
1
1
1
1
2
2
1
2
2
2
0
0
2
0
1
0
1
1
2
0
2
1
0
1
1
1
0
0
1
2
0
0
0
2
1
0
1
0
1
1
0
0
1
0
1
1
2
1
2
1
1
1
0
1
2
1
1
1
1
0
0
0
2
1
0
1
1
1
1
2
1
2
2
1
0
1
1
0
1
0
1
1
2
0
1
1
2
2
1
0
1
1
1
1
1
1
1
2
1
1
2
0
0
0
0
1
0
2
1
0
1
1
2
1
1
1
1
1
1
1
1
2
0
1
1
1
1
1
0
1
1
1
0
0
0
0
1
2
0
1
2
1
1
0
1
2
0
0
0
2
2
0
3
2
1
1
1
0
1
1
3
0
1
1
2
2
2
1
1
1
1
1
1
1
0
1
1
0
2
0
2
1
1
2
1
2
0
2
1
0
2
2
1
1
1
0
1
2
0
2
1
0
1
1
2
0
1
1
1
0
1
2
1
2
0
2
1
1
1
1
1
1
1
1
1
1
2
0
1
1
1
1
1
0
0
1
2
1
0
1
0
1
2
1
0
1
1
2
0
1
1
1
1
1
1
1
0
2
0
2
2
1
0
1
2
0
2
2
1
1
1
1
2
1
1
0
0
2
0
1
0
2
1
1
0
0
2
1
2
2
1
1
1
1
0
3
2
0
1
0
1
1
1
0
1
2
0
0
1
1
2
0
1
0
0
1
0
2
2
1
1
2
2
0
2
0
1
1
1
1
1
1
0
2
2
2
2
1
2
0
1
1
1
1
2
1
0
1
0
1
1
2
1
1
1
0
1
1
2
2
1
0
1
2
2
1
2
1
1
0
1
1
0
0
1
1
2
2
1
1
2
1
1
1
2
1
1
1
0
0
1
1
0
1
1
1
1
2
3
1
0
1
0
1
2
2
0
1
2
1
2
1
1
2
1
2
1
2
1
0
1
0
1
0
0
2
0
1
1
1
1
1
1
1
0
1
2
1
1
0
1
0
2
1
2
0
2
1
1
1
1
1
0
0
1
0
2
1
0
0
1
1
2
1
1
2
0
1
2
2
1
1
2
1
1
1
1
1
0
1
1
2
2
2
1
1
0
1
2
0
1
1
0
0
1
1
0
1
1
0
0
2
1
1
1
1
2
1
2
0
1
3
1
1
2
0
2
1
1
0
1
1
1
1
2
1
0
2
1
1
1
0
1
1
1
1
1
1
2
1
1
1
0
1
1
1
2
1
0
1
1
1
0
0
1
1
0
2
1
1
1
1
1
2
1
2
1
0
1
1
1
1
1
2
1
1
0
0
1
0
1
2
0
1
1
1
1
1
0
1
0
1
1
0
1
1
2
1
1
0
0
1
1
2
0
1
1
0
1
2
1
1
1
1
2
1
1
1
1
1
2
1
0
1
0
2
1
1
0
1
0
1
2
1
2
2
2
2
1
1
2
1
1
1
2
1
1
0
1
1
1
1
0
1
0
2
0
2
0
2
1
1
1
2
1
0
2
1
1
2
1
1
2
0
2
1
0
1
2
1
1
1
2
1
1
1
2
1
1
1
2
1
0
1
1
1
2
1
0
2
1
0
2
1
1
1
2
2
5
1
1
1
2
1
1
1
1
1
0
0
1
2
1
2
1
1
0
1
1
0
1
1
1
2
1
1
2
0
1
0
0
0
1
2
1
1
1
0
1
2
2
1
2
2
0
2
1
2
2
1
1
0
1
1
1
1
0
1
1
1
1
1
1
0
0
1
0
1
2
1
1
0
1
1
2
1
1
1
1
1
1
1
2
0
1
2
1
2
2
1
2
2
0
1
1
0
0
2
1
1
1
1
2
1
1
2
0
0
1
2
2
1
1
1
2
0
1
1
0
1
0
1
1
1
0
1
1
1
1
0
1
1
1
1
1
1
2
0
1
1
1
2
2
0
1
1
1
1
2
1
1
2
1
1
0
1
1
2
1
1
1
1
1
0
0
0
1
2
1
0
2
1
1
1
1
2
1
2
1
1
1
1
2
1
1
1
1
0
1
2
2
1
0
0
2
0
1
1
1
0
0
1
1
2
0
0
2
2
0
1
1
0
2
1
1
0
2
2
1
2
1
0
2
2
1
1
0
2
2
0
1
0
1
0
1
1
2
0
2
1
1
2
1
1
2
1
2
1
2
2
1
2
2
2
1
2
1
0
1
1
2
1
2
1
3
1
1
1
2
1
1
1
1
1
2
4
1
1
0
1
1
1
2
1
1
2
1
1
1
1
1
0
0
2
0
3
0
1
2
2
1
1
0
1
1
1
1
3
2
1
1
0
1
1
1
1
1
0
2
0
1
0
2
2
0
2
1
2
0
2
0
2
2
1
1
1
1
1
1
1
1
2
0
1
1
1
1
2
0
1
1
1
0
1
1
2
1
1
2
1
0
1
2
1
1
2
3
1
1
2
1
1
1
1
1
1
2
1
0
1
0
1
1
2
1
1
1
2
1
2
1
0
1
0
1
2
2
1
0
1
2
1
1
1
0
2
1
2
2
2
1
1
2
1
1
2
2
0
1
0
1
1
2
1
2
1
1
2
0
1
1
0
0
1
0
2
2
0
1
1
1
1
2
1
2
2
1
1
2
1
0
2
0
0
1
2
1
1
0
1
0
1
1
2
1
2
0
2
2
1
2
0
1
1
0
1
1
1
0
3
2
1
1
2
2
1
0
1
2
1
1
1
1
1
1
2
2
1
1
0
1
1
1
0
2
2
1
0
1
0
1
1
2
0
2
1
1
0
2
1
0
1
0
0
1
1
1
0
0
2
1
1
0
0
0
2
3
1
0
0
1
1
0
1
1
2
1
1
1
0
1
2
1
2
1
0
0
1
2
0
1
1
3
1
0
1
1
2
2
2
1
0
0
1
1
1
1
1
1
1
2
1
2
1
0
1
2
0
0
2
2
0
0
1
1
1
1
1
1
1
1
1
1
1
0
1
1
0
1
0
1
1
1
1
0
3
1
0
1
1
0
1
0
1
0
2
1
2
1
1
1
1
0
2
1
1
2
1
1
1
1
0
0
2
0
2
1
0
2
0
0
1
1
2
2
1
1
1
2
1
1
1
1
1
1
1
0
1
1
1
0
1
1
0
1
1
2
0
0
1
2
1
1
1
1
0
2
2
1
2
1
0
1
1
0
1
2
1
0
1
1
1
1
1
1
0
1
1
1
1
1
1
2
2
1
1
1
1
0
2
1
2
1
1
1
0
0
1
1
0
0
1
2
1
1
1
1
1
0
1
1
1
2
1
1
1
1
1
0
1
0
1
1
0
1
1
1
1
1
1
0
1
1
2
0
1
2
2
1
1
1
1
1
0
1
0
1
2
2
1
1
0
1
0
0
1
2
1
2
0
1
2
1
3
1
1
1
1
2
2
1
1
2
2
1
1
0
2
0
1
1
1
1
1
1
0
2
1
1
1
1
1
1
0
0
0
2
2
0
1
1
2
2
1
1
0
0
0
2
1
0
0
1
0
1
1
0
1
2
1
1
1
0
1
1
2
2
1
1
1
1
1
1
0
0
1
1
1
1
1
1
1
0
0
1
1
1
1
0
2
1
1
1
2
1
1
1
1
1
1
2
1
1
2
1
1
2
1
0
1
0
0
1
1
0
1
1
1
2
2
2
2
0
1
2
4
0
2
1
1
1
1
2
0
2
1
1
2
1
0
1
2
2
1
1
2
10
1
1
2
1
0
0
0
1
1
1
1
1
2
1
1
1
1
1
1
0
1
2
2
1
0
1
1
1
2
2
1
1
1
2
2
2
1
1
1
2
2
1
1
0
2
0
2
2
1
2
1
1
1
0
0
2
1
0
1
2
1
1
1
0
0
2
1
1
2
0
2
0
0
1
1
1
1
1
2
0
1
1
1
2
2
2
1
2
2
0
1
0
0
1
2
1
1
2
1
3
1
1
1
2
1
2
0
1
1
1
1
1
2
0
1
1
2
1
2
1
2
1
2
2
1
1
1
0
0
1
1
0
0
1
0
1
2
1
1
1
1
2
1
1
0
0
1
1
1
1
1
2
1
1
0
0
1
2
1
2
1
2
8
1
1
1
1
0
0
1
1
2
1
1
1
1
1
2
1
1
1
0
0
1
1
1
1
1
0
1
1
1
1
2
1
2
1
1
1
1
0
1
1
2
1
1
2
0
1
1
2
0
1
0
1
1
1
0
2
1
1
2
1
0
2
1
1
1
2
0
1
2
1
1
2
1
0
2
2
0
1
1
1
1
0
1
0
1
1
1
2
2
1
2
0
1
1
1
2
1
1
0
2
1
1
1
2
0
1
1
2
1
1
0
0
1
1
2
1
1
1
0
0
1
1
2
1
1
1
1
1
0
1
1
2
1
2
0
1
1
2
1
1
1
2
0
1
2
0
1
1
1
2
2
0
2
1
1
0
1
1
0
2
1
0
2
0
1
1
1
0
1
1
2
1
1
2
2
1
1
0
1
0
0
2
1
1
0
0
2
1
1
2
1
1
1
1
1
1
1
1
1
0
1
1
1
1
2
1
0
1
0
2
0
1
1
2
1
1
1
1
1
1
1
0
0
0
1
2
1
0
1
0
0
1
0
2
0
0
0
2
1
1
0
0
1
1
1
1
1
2
0
1
1
2
2
2
1
1
2
1
2
1
0
0
1
0
1
0
1
1
1
1
1
0
1
1
1
2
2
1
0
3
1
0
2
1
1
0
1
2
1
0
0
2
1
1
1
2
1
1
1
2
2
1
0
1
1
0
1
2
2
1
1
1
1
1
0
2
1
1
1
1
1
1
1
1
1
1
1
1
1
0
3
1
1
1
2
1
0
2
1
2
0
1
0
1
0
2
0
1
1
1
1
0
1
1
1
0
2
1
1
0
2
1
2
1
1
1
0
1
2
1
0
2
1
0
1
2
1
2
1
2
1
0
0
1
1
0
0
2
0
1
2
1
2
2
1
1
2
2
1
1
0
1
0
0
2
0
2
1
0
4
2
2
1
1
1
0
1
2
1
0
2
1
2
1
4
0
1
1
0
1
0
1
1
0
1
1
1
2
1
0
1
1
1
2
2
2
1
0
1
2
2
1
2
1
0
2
2
0
2
0
0
0
1
1
1
2
2
1
1
1
1
0
2
1
0
0
1
1
1
0
1
1
1
2
0
1
1
0
1
1
1
1
1
1
2
2
2
1
1
2
1
1
1
0
1
1
1
1
1
1
1
2
1
2
1
1
1
3
2
1
2
1
1
1
2
1
1
2
1
0
1
1
0
1
1
1
1
1
0
1
1
1
0
1
1
1
2
1
1
1
1
1
0
1
0
1
2
1
1
1
1
2
1
2
2
1
0
1
2
2
1
0
1
0
0
0
1
1
1
1
2
1
2
2
1
4
1
1
0
1
1
2
0
1
1
2
1
2
2
0
1
1
0
2
2
1
1
0
1
0
1
0
2
1
1
2
2
1
1
1
1
2
0
2
1
2
0
1
1
0
1
1
1
1
1
2
2
0
1
1
2
2
1
0
0
1
1
2
2
1
2
2
2
1
0
1
1
0
2
1
1
1
1
2
0
0
1
1
1
2
1
2
1
1
0
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
3
1
1
1
0
1
1
1
2
2
1
1
2
2
1
0
0
1
0
2
1
0
2
1
1
2
1
2
1
1
0
2
1
0
0
2
1
1
0
0
0
0
1
1
1
1
1
1
0
2
0
1
1
1
2
0
1
0
1
1
0
2
1
1
2
2
3
0
1
1
2
2
2
2
1
2
1
1
1
2
1
1
1
3
0
2
2
2
1
1
2
1
3
2
0
1
1
1
0
1
1
1
1
1
0
1
0
1
1
0
0
2
1
1
1
1
2
1
2
2
1
2
1
1
0
3
1
2
1
0
1
2
1
2
1
1
1
0
1
2
1
0
2
0
2
2
2
1
0
1
1
0
3
1
0
0
2
1
2
2
0
1
1
1
0
2
2
1
2
1
0
2
1
0
1
0
2
1
1
1
2
1
1
1
1
2
1
0
2
1
1
2
1
1
1
1
0
2
1
0
2
2
2
2
1
1
1
1
2
1
0
1
1
1
1
1
2
0
2
1
2
1
1
0
2
2
0
0
1
0
2
2
2
0
2
1
0
1
1
2
1
1
1
1
1
2
1
0
1
1
1
2
1
1
1
2
1
1
1
0
2
1
3
0
2
1
1
0
1
1
2
1
0
1
1
1
2
2
1
2
1
1
1
1
1
2
1
1
0
0
2
2
1
1
1
0
2
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
0
1
0
1
1
1
1
1
2
3
1
1
0
1
2
0
1
2
2
2
0
0
0
2
0
2
2
1
0
1
2
2
1
0
1
0
2
1
0
0
1
1
1
0
0
0
1
2
1
0
0
1
2
0
2
1
1
1
1
0
2
2
1
1
2
1
2
1
1
2
2
2
2
1
1
1
1
1
0
0
2
1
2
2
1
0
0
1
1
1
1
0
1
2
2
1
0
2
1
2
1
0
1
0
0
1
2
2
2
2
0
2
2
1
1
1
1
1
1
1
2
0
0
0
1
2
2
2
1
1
1
2
1
2
1
2
1
2
2
1
2
2
1
0
1
1
0
0
2
1
0
1
1
0
2
2
2
1
1
2
2
0
2
1
1
0
1
1
1
1
1
1
1
1
1
1
0
1
1
1
2
1
2
1
1
0
2
0
0
0
1
0
0
2
0
2
2
1
1
1
1
1
1
0
0
2
0
1
1
2
0
2
2
0
1
1
1
0
1
1
0
0
0
0
1
2
1
1
0
2
0
0
0
1
2
1
1
1
0
0
1
1
1
0
1
1
0
1
2
1
1
0
1
1
1
2
1
1
1
0
0
2
1
0
2
1
2
1
0
2
1
2
1
0
2
2
0
2
0
2
0
0
1
1
0
1
0
1
0
1
1
0
1
0
2
1
1
1
1
1
2
2
1
1
2
2
1
0
2
2
1
2
1
1
1
2
1
1
1
0
2
1
1
0
1
1
1
1
1
1
1
1
0
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
0
1
1
2
1
1
2
1
2
1
1
2
1
0
1
1
1
0
1
2
1
1
1
1
2
1
1
1
1
2
0
2
1
1
2
1
0
0
0
1
1
1
2
1
1
0
0
2
1
2
1
1
0
1
2
1
1
1
0
1
2
0
0
2
2
1
1
1
1
0
0
1
1
1
1
2
2
2
2
1
1
1
0
1
2
1
1
1
1
1
1
2
1
1
2
1
0
1
1
1
0
1
2
1
1
1
0
0
1
0
1
2
0
1
2
1
1
1
1
0
1
1
2
1
1
1
1
0
1
0
0
2
1
2
0
0
2
1
0
2
2
2
0
0
1
1
1
0
0
1
0
0
1
1
1
1
2
1
2
0
1
1
1
1
0
1
1
1
1
0
2
1
0
2
1
1
1
1
1
2
1
1
1
1
1
0
0
1
2
2
1
1
0
0
2
1
1
0
0
1
1
1
1
2
1
1
1
2
1
1
0
0
1
2
1
2
1
1
1
1
0
1
1
1
1
1
2
1
1
2
0
1
1
1
2
1
1
1
1
1
2
1
2
2
1
1
0
1
1
0
1
1
1
1
1
1
1
0
1
2
0
0
0
0
1
1
1
0
1
0
2
0
1
0
1
1
2
1
1
1
1
0
1
1
1
1
2
2
1
0
1
2
1
3
1
2
2
1
1
1
1
1
1
1
0
2
0
1
0
1
1
1
0
1
1
1
2
1
1
2
1
2
1
0
1
1
1
1
3
0
1
0
2
1
1
1
1
2
1
1
2
1
1
1
0
2
1
1
1
1
1
0
2
1
1
1
3
2
1
0
0
1
3
1
0
1
0
0
3
0
2
2
1
1
1
1
0
2
1
0
0
2
1
0
1
1
0
1
1
2
1
0
1
0
0
1
1
1
2
1
0
0
1
0
0
1
1
1
2
1
3
1
1
2
2
1
1
1
1
1
2
2
1
1
0
1
1
1
1
0
2
1
1
1
1
2
2
2
0
2
1
2
0
1
2
2
1
0
1
0
0
2
1
1
0
2
0
2
0
1
7
1
1
2
1
0
2
0
1
1
1
0
2
1
1
2
1
1
1
2
0
1
2
2
1
1
1
1
1
1
1
1
1
1
2
0
2
1
0
1
2
1
2
1
1
2
1
2
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
0
2
1
3
1
2
2
2
1
2
1
1
2
1
0
1
2
0
2
0
2
2
0
2
0
1
1
0
1
2
1
1
1
1
1
1
0
0
3
1
2
2
1
1
1
2
1
1
1
2
1
2
0
0
2
1
1
1
1
1
1
1
0
1
2
2
1
1
1
1
1
0
1
1
1
1
1
1
0
1
1
1
0
0
1
1
1
1
1
1
3
1
2
1
2
1
0
1
1
2
2
2
1
1
1
1
1
2
1
0
2
0
1
1
1
2
0
1
2
0
1
2
1
2
0
1
2
1
1
1
2
1
1
2
1
1
1
1
0
2
1
0
2
1
2
1
1
1
1
0
2
3
1
1
1
1
1
1
2
1
0
1
2
1
0
0
0
1
1
1
1
1
1
1
3
1
1
0
1
0
0
1
2
1
1
1
0
1
1
1
0
2
1
1
1
1
2
1
0
2
2
1
0
1
2
2
0
1
1
1
1
2
1
1
1
2
1
1
0
1
0
1
1
1
2
1
1
0
0
2
1
1
1
1
1
0
1
1
1
1
1
1
2
2
1
0
1
2
1
1
0
2
0
1
2
0
1
1
1
0
1
0
1
0
1
1
1
0
2
1
1
1
0
1
2
0
2
0
0
1
1
0
1
1
0
1
2
2
2
2
0
1
1
1
1
1
1
2
0
2
1
0
1
1
1
1
0
1
1
1
1
0
0
1
0
1
2
0
0
0
1
1
1
1
1
2
0
1
1
1
2
0
2
1
2
1
1
1
1
1
1
0
1
1
0
0
2
1
1
2
1
1
1
2
2
2
2
0
1
1
0
0
0
1
2
1
5
1
2
1
1
2
3
1
0
2
1
1
1
1
1
2
1
2
1
1
2
1
0
1
2
0
2
2
2
1
2
2
1
1
2
1
0
0
2
0
0
1
2
1
1
1
1
0
1
2
1
1
1
1
2
0
1
1
1
1
1
2
2
2
1
0
1
1
0
1
2
1
1
1
1
1
2
2
1
1
1
1
1
1
1
0
2
0
1
2
1
1
1
2
1
0
2
0
0
1
0
1
2
1
2
2
1
2
2
0
2
2
1
1
2
1
1
1
1
1
2
0
0
2
1
0
1
1
2
1
1
2
1
1
1
1
0
2
0
2
1
1
1
1
2
1
0
2
0
2
2
2
2
1
2
1
1
1
1
1
0
1
1
2
1
1
0
2
0
0
1
0
1
0
1
2
0
0
0
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
1
0
4
1
1
1
1
1
1
2
1
2
0
1
0
1
0
0
1
1
1
1
1
1
2
2
2
2
0
1
1
2
0
1
1
1
2
1
2
2
0
2
1
0
1
1
2
1
1
1
1
2
0
1
1
0
1
0
0
0
1
1
1
1
0
1
1
1
2
2
1
1
2
0
1
1
1
3
1
1
1
1
1
0
1
0
1
1
2
2
0
1
0
2
0
2
0
0
1
1
2
2
2
0
1
0
2
1
1
0
2
1
2
1
2
2
2
1
2
0
1
0
1
1
1
0
1
0
0
2
2
1
0
0
1
1
2
1
1
1
2
1
1
1
2
1
2
0
1
2
0
2
1
0
1
0
1
0
1
1
1
1
2
1
2
0
2
2
1
1
0
1
0
1
1
1
1
1
2
0
0
1
2
2
1
0
2
2
0
0
1
1
1
1
1
1
3
1
0
1
1
1
1
2
1
1
1
1
1
1
2
0
1
0
0
0
1
1
1
0
2
1
2
2
2
0
2
1
1
0
2
1
1
1
1
1
0
0
6
1
0
1
1
1
2
1
1
2
1
1
0
0
2
1
1
1
2
0
2
1
0
1
0
0
1
1
1
1
1
0
1
1
0
1
2
2
0
1
1
1
0
1
0
2
1
1
2
1
1
1
2
1
1
2
1
0
0
1
2
0
1
1
1
0
0
1
1
1
0
1
2
1
1
1
0
0
1
1
1
2
1
1
1
1
2
1
0
1
1
1
2
1
1
0
2
1
1
0
1
2
0
0
1
1
1
1
1
1
2
2
1
1
1
2
1
1
1
0
2
1
2
1
0
1
0
1
1
1
1
1
1
1
1
0
1
1
1
1
2
0
2
1
2
2
1
0
2
1
1
1
0
1
0
2
1
1
1
1
0
2
0
1
1
2
2
1
1
0
0
1
1
0
1
1
1
1
1
2
1
2
1
1
2
1
0
2
2
2
1
1
1
1
2
0
2
1
0
1
1
1
1
0
0
2
1
1
0
1
0
2
1
1
1
1
1
1
0
1
0
0
0
1
0
1
1
1
1
2
1
2
1
1
3
2
1
0
1
1
1
1
0
2
2
1
2
0
2
1
1
1
2
1
1
1
1
1
1
2
1
2
1
1
0
1
1
1
1
2
1
2
1
1
2
2
1
1
0
1
1
1
2
1
1
2
2
2
1
1
0
1
2
0
0
0
2
0
1
2
2
0
1
0
1
1
1
1
1
1
1
0
0
1
1
2
1
2
0
1
1
1
1
1
2
1
1
1
1
1
1
0
2
1
1
0
1
3
1
1
1
2
1
2
0
1
1
1
1
1
0
1
0
1
1
2
1
1
1
1
2
1
2
1
1
0
1
1
1
0
2
1
1
2
2
1
2
1
0
0
1
0
1
1
2
1
2
1
0
2
1
1
1
1
1
0
1
1
2
2
0
1
1
1
0
1
1
1
0
1
1
1
3
1
1
0
1
0
1
2
0
1
2
1
1
0
1
1
0
1
1
2
1
0
2
1
2
1
1
1
1
2
2
4
1
0
1
1
2
1
1
1
1
0
0
1
1
1
0
1
2
1
2
1
1
1
1
1
2
1
1
1
0
1
1
0
2
1
1
1
1
1
1
1
1
0
2
0
2
0
0
0
0
1
2
1
0
1
1
2
0
1
2
1
1
1
1
1
2
0
1
1
0
1
0
0
0
1
1
1
2
0
1
1
1
0
1
1
0
0
1
2
0
0
0
0
0
2
0
1
2
1
1
0
1
0
1
2
1
1
1
2
0
0
3
0
0
1
1
1
1
1
1
1
0
0
2
1
1
1
2
1
0
0
1
2
1
2
2
1
0
1
0
0
1
1
2
0
1
1
1
1
1
4
0
0
2
2
1
1
1
2
2
1
1
0
0
1
0
2
1
0
0
0
2
1
1
1
1
0
1
1
2
1
2
1
1
0
2
1
1
1
0
1
1
0
0
0
1
0
2
2
1
0
2
1
0
1
2
0
2
2
2
2
1
2
1
2
1
0
1
2
2
2
0
1
1
2
2
0
0
1
1
1
1
1
2
1
0
0
1
0
2
1
2
1
0
2
1
0
0
2
1
1
2
0
2
1
0
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
0
1
1
1
1
0
2
1
1
0
1
0
1
0
1
0
2
0
1
0
1
2
1
2
1
1
2
2
2
0
2
1
1
2
0
0
1
1
0
1
1
0
1
1
0
0
2
2
1
2
1
0
1
1
1
2
1
1
2
1
1
1
1
2
1
1
1
2
1
1
1
1
1
2
1
1
2
1
1
1
2
1
0
0
1
2
1
1
2
1
2
0
2
3
2
0
0
2
0
1
1
1
2
1
2
0
2
1
1
0
1
1
1
2
1
0
2
1
0
0
0
1
1
0
1
2
2
1
2
1
2
1
0
2
1
0
1
1
1
1
1
1
1
1
1
1
1
3
1
0
0
1
2
0
0
2
2
1
1
0
1
1
0
1
1
2
1
0
4
0
2
1
1
1
0
2
1
1
0
1
1
2
1
0
1
0
1
0
1
1
2
1
1
1
0
0
1
1
1
1
1
1
1
0
1
2
2
0
1
1
1
2
1
1
1
1
2
2
0
0
1
1
1
1
1
2
1
1
0
2
2
1
0
1
2
2
1
0
1
1
0
1
1
2
1
1
0
0
1
1
1
1
1
1
0
2
0
2
1
0
0
0
1
2
1
0
1
1
0
1
0
0
1
2
1
1
2
2
1
0
1
2
1
0
2
0
1
0
2
2
1
1
1
1
1
2
1
2
1
1
1
0
1
2
2
1
1
1
1
1
0
1
1
1
1
0
0
1
0
1
2
0
0
1
1
0
1
0
1
2
0
1
2
2
1
0
2
1
1
1
3
2
1
2
2
0
2
2
2
1
2
1
1
2
2
1
2
0
2
1
1
1
2
1
0
1
1
1
0
2
0
0
2
1
2
1
2
1
1
1
1
1
1
1
1
1
0
2
2
2
1
0
1
1
2
1
1
1
0
1
1
1
1
0
1
1
2
2
1
0
1
1
0
2
1
1
0
2
0
1
2
1
1
1
1
2
1
1
1
1
2
1
0
1
1
2
0
1
0
1
0
2
2
2
1
2
2
2
6
2
1
0
0
1
1
1
2
1
2
1
0
1
1
1
2
1
1
1
0
0
2
1
0
2
0
1
3
1
1
2
2
1
1
1
1
1
1
0
0
1
0
2
1
1
1
0
0
0
1
0
0
2
1
1
1
0
1
1
1
0
3
2
0
1
0
1
1
2
1
1
2
1
1
1
0
2
1
1
0
1
2
1
1
0
2
3
2
1
2
0
0
1
0
0
1
2
1
1
1
1
1
1
1
0
1
1
0
1
2
1
0
1
0
1
1
1
1
1
1
1
0
2
1
1
1
1
1
2
2
2
0
1
1
1
1
1
1
1
0
3
0
1
1
2
3
0
1
1
1
2
1
1
1
0
0
1
0
1
2
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
0
1
1
0
2
1
1
0
1
1
0
1
0
2
1
2
0
1
1
2
1
1
2
1
0
1
1
2
1
1
2
1
1
1
2
2
2
1
0
2
1
1
0
1
2
1
1
1
0
1
1
2
1
1
2
2
2
1
1
1
2
1
1
1
0
1
2
1
1
1
0
0
2
1
1
2
0
2
1
1
1
1
2
1
1
1
1
1
1
1
1
0
1
1
1
0
1
2
2
1
1
1
0
0
1
2
1
2
2
1
0
0
1
3
0
1
1
1
2
1
1
2
1
1
1
1
0
1
1
1
2
1
1
2
1
0
0
1
3
0
1
2
0
1
1
1
1
1
2
1
0
1
2
0
1
1
2
1
2
1
1
1
1
2
2
1
1
0
2
1
0
1
1
0
1
2
1
1
0
1
1
3
1
1
1
1
2
0
0
1
1
0
1
1
1
2
0
3
0
1
1
1
1
1
1
1
0
2
1
2
1
0
2
1
2
1
2
0
1
1
1
1
1
1
1
1
1
1
0
2
2
1
1
0
1
1
0
0
1
1
0
1
1
1
1
1
1
1
1
1
2
1
2
1
2
2
1
2
1
1
0
0
2
1
2
1
1
1
2
1
1
0
0
0
1
0
3
0
0
1
1
2
1
0
1
1
2
1
1
4
2
0
1
0
2
1
2
0
0
0
2
1
1
1
1
2
1
1
1
1
2
1
1
0
0
0
1
2
2
2
1
1
1
2
0
0
1
0
1
0
1
1
1
0
1
1
1
1
1
0
1
0
0
1
1
1
1
0
1
1
1
1
1
2
1
2
1
1
1
0
2
1
1
2
2
1
0
2
1
2
1
1
0
0
1
2
1
1
1
2
1
1
0
1
1
0
0
2
1
1
1
2
1
1
0
2
1
0
2
1
0
1
0
1
1
1
1
2
3
1
1
1
3
4
2
0
2
2
1
1
1
1
1
1
0
2
1
2
2
1
0
1
0
1
1
3
1
1
2
0
1
1
1
1
1
0
2
2
1
2
1
0
0
1
1
1
2
0
1
2
0
0
2
1
1
1
1
0
1
0
2
1
1
2
1
0
0
1
2
0
1
2
0
1
1
2
1
2
1
0
1
1
0
0
1
1
1
1
0
1
1
1
1
2
0
1
2
2
1
0
2
2
2
1
2
2
1
0
1
2
1
1
2
0
1
1
1
1
1
0
2
1
1
0
1
0
2
1
0
1
2
2
1
1
0
1
2
1
1
0
1
1
2
1
0
2
2
1
0
2
0
2
2
1
1
0
1
1
2
1
1
1
1
0
0
1
0
1
1
1
0
2
0
1
1
2
1
2
0
2
1
1
1
2
0
0
0
1
0
1
3
0
2
0
1
1
0
0
2
2
0
2
1
2
2
1
0
1
1
1
1
1
1
0
1
1
0
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
1
1
0
1
0
2
0
0
1
0
1
1
1
1
1
0
0
2
2
2
2
1
2
1
0
2
1
2
1
1
0
1
0
1
2
1
0
0
1
2
2
2
2
1
2
2
1
1
1
1
0
1
2
0
2
1
3
2
1
1
1
1
1
0
0
1
2
1
2
1
1
1
2
1
2
1
1
2
2
1
1
0
0
2
1
1
1
1
1
1
1
1
1
1
1
1
1
0
2
1
2
1
2
1
3
2
2
1
1
2
0
2
1
0
2
1
1
0
1
1
1
1
1
1
0
0
2
0
1
1
1
2
0
1
1
0
2
1
0
1
1
1
1
2
2
1
0
1
1
1
0
2
1
1
0
1
1
2
1
1
1
1
1
1
0
0
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
0
0
0
0
1
2
2
0
2
1
1
1
1
1
2
2
2
1
1
1
0
1
1
1
0
1
1
0
1
2
1
2
1
1
1
0
0
1
2
1
0
2
2
1
0
1
1
1
1
0
2
1
0
1
1
1
1
2
0
1
2
1
1
0
1
1
1
1
2
1
1
1
1
1
0
1
1
1
1
1
2
1
1
0
2
1
2
0
1
2
1
1
1
1
1
0
1
0
1
1
0
2
2
1
1
0
1
1
1
2
1
0
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
0
2
1
1
0
0
1
1
2
1
1
2
2
2
1
1
1
1
2
0
0
2
1
1
1
1
1
0
2
0
0
1
1
1
5
2
1
2
1
2
1
1
2
1
1
1
1
1
1
1
1
2
0
1
1
1
1
1
2
1
1
1
1
2
0
2
1
2
0
1
1
1
0
2
1
2
2
1
1
1
0
0
1
2
0
1
2
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
1
0
1
1
1
1
1
2
0
0
1
3
0
1
2
0
1
1
1
0
0
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
0
0
1
0
1
0
1
1
0
0
1
1
1
1
1
1
1
1
1
1
0
2
0
1
0
1
0
1
1
1
1
0
2
2
1
1
1
2
1
2
0
0
1
1
2
2
1
1
2
2
1
0
0
2
1
0
2
1
1
1
0
2
2
2
0
1
1
0
1
1
1
1
2
2
2
1
2
1
1
0
1
2
1
1
1
2
2
1
2
1
1
1
1
1
1
0
1
1
2
0
1
0
2
2
0
1
1
1
1
0
0
1
1
1
1
2
1
2
0
2
1
2
0
0
1
1
1
1
1
1
2
1
0
2
2
2
1
0
1
2
1
0
0
2
1
1
3
2
1
0
1
1
1
2
1
1
1
1
0
0
0
3
0
0
0
1
0
2
2
1
1
2
1
1
2
1
0
1
1
1
0
1
1
0
1
0
1
0
0
1
1
1
0
1
1
1
1
0
0
1
1
1
1
2
1
1
1
2
0
0
1
1
1
0
0
1
1
1
2
1
2
0
2
0
0
1
0
0
2
1
1
2
1
0
1
1
0
2
2
1
1
1
1
1
1
2
0
2
1
1
0
1
0
0
1
1
1
2
2
2
1
1
1
0
0
1
2
1
1
1
1
2
1
2
2
2
2
0
0
2
1
1
1
1
1
1
2
1
1
2
2
1
1
1
0
0
1
2
2
1
0
0
1
1
1
1
1
1
1
1
2
1
0
0
0
1
1
2
0
1
1
1
0
2
2
1
1
1
1
0
1
2
3
0
1
1
0
1
1
1
1
1
1
2
2
1
0
2
0
2
0
0
1
0
1
1
2
1
1
0
1
1
1
0
1
2
1
1
1
1
0
1
1
0
0
1
1
0
2
1
0
0
0
2
1
1
1
0
0
1
1
0
1
1
1
1
1
2
1
1
0
1
1
1
0
1
1
2
2
3
0
0
1
0
2
1
1
2
0
1
0
1
1
0
0
1
0
2
1
1
2
1
0
2
0
2
1
1
2
0
2
1
0
0
1
2
1
0
2
1
1
1
1
2
1
1
1
0
1
1
1
0
1
1
0
1
1
2
0
2
1
1
1
1
1
1
0
1
0
1
2
1
1
1
0
1
1
1
1
2
1
0
0
1
1
1
1
0
0
2
0
1
0
1
1
1
2
1
1
2
1
2
1
1
2
1
1
0
1
1
1
1
0
0
1
1
3
2
2
0
0
2
0
0
1
1
1
1
0
1
0
2
1
0
1
2
2
2
1
0
2
1
2
2
1
0
1
2
1
0
1
1
1
1
0
2
1
0
0
1
2
1
2
1
1
1
1
0
1
2
1
0
0
2
1
1
1
2
1
1
1
2
0
1
0
1
2
1
0
1
2
2
0
1
8
2
1
1
1
1
1
1
0
0
0
1
1
1
1
0
1
2
1
1
2
2
2
1
1
0
1
1
1
1
1
1
1
0
1
2
1
1
2
1
2
1
1
2
1
0
2
1
2
1
1
0
1
1
0
1
0
0
2
1
2
2
2
0
1
1
2
1
1
1
2
1
1
2
1
1
1
2
0
1
0
1
0
2
0
1
1
1
1
0
1
1
2
0
1
0
1
1
2
1
1
1
0
1
1
1
2
0
1
1
1
1
0
0
1
1
0
0
1
0
2
0
1
2
0
0
1
1
0
2
1
1
1
2
1
2
1
2
1
1
0
1
1
1
2
1
1
1
1
0
1
1
0
0
1
0
1
1
1
2
1
1
2
0
1
2
1
1
1
1
1
2
0
0
1
1
1
1
1
1
2
1
2
1
1
1
1
2
0
2
1
1
0
1
1
1
1
1
0
1
3
1
1
2
0
0
2
1
2
1
1
1
2
1
3
2
1
2
0
1
1
0
0
2
2
1
0
1
0
1
0
1
1
1
1
1
2
1
0
0
1
1
2
2
2
1
1
2
1
2
2
0
1
1
1
1
1
0
3
1
1
1
0
1
2
2
1
2
1
1
1
1
0
1
1
1
2
0
2
1
2
1
2
3
1
1
2
1
0
0
0
0
1
1
1
2
0
0
1
1
2
1
1
1
2
1
1
2
0
0
2
2
1
2
0
1
2
1
0
1
1
0
1
1
2
0
1
2
2
1
0
1
2
0
1
0
1
1
0
0
1
1
1
0
1
1
2
1
1
1
1
2
1
1
2
0
0
2
1
2
0
1
1
1
0
1
0
0
1
0
3
2
1
0
1
2
2
1
1
1
2
1
0
1
1
2
0
1
2
1
1
1
1
2
1
1
2
0
2
1
1
0
1
2
2
1
1
1
2
1
2
0
1
3
1
1
4
1
2
1
2
2
0
2
1
1
1
2
1
3
1
1
2
2
1
1
1
2
1
1
1
1
1
2
2
1
1
2
2
0
2
0
2
0
2
1
2
1
0
1
1
1
1
2
0
0
1
1
1
0
1
0
1
1
1
2
1
1
0
0
1
1
0
1
1
1
2
1
1
2
1
1
2
1
0
2
2
1
2
1
2
1
1
2
1
1
1
1
1
1
1
2
2
0
0
0
1
1
0
2
0
0
1
1
0
1
1
2
0
0
1
0
1
1
1
1
1
0
0
1
2
0
2
1
2
1
1
1
1
2
1
2
1
2
0
1
1
1
0
2
1
2
1
1
1
1
2
2
0
1
2
2
1
1
2
1
1
1
1
2
1
2
1
2
1
2
1
1
1
2
1
1
2
0
0
0
1
1
0
1
1
0
1
2
0
2
1
2
0
0
0
1
2
0
1
2
2
1
2
2
2
1
0
1
0
2
0
2
1
0
2
0
2
2
0
1
1
1
1
1
1
1
1
1
2
0
1
1
1
1
0
0
0
2
2
1
0
1
2
1
2
2
2
0
1
1
2
1
1
1
1
2
0
0
1
2
1
1
1
2
0
0
2
0
2
1
1
1
1
0
1
2
1
1
1
1
1
0
1
2
2
1
1
1
0
1
2
2
1
2
1
0
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
2
2
1
1
1
2
1
1
1
2
0
1
1
1
1
2
0
1
1
1
1
1
2
1
1
0
1
1
1
1
1
1
1
2
0
1
1
2
1
1
1
0
2
1
1
0
2
1
0
1
2
1
1
1
1
0
2
1
2
1
1
1
1
0
1
1
0
2
1
1
1
1
1
1
1
1
0
0
1
0
0
0
1
0
1
0
2
2
1
0
1
1
0
0
1
1
1
1
1
1
1
1
1
1
1
0
2
1
1
1
1
2
1
1
1
2
1
1
2
1
1
1
2
1
1
0
0
3
1
1
1
1
1
1
0
0
1
1
1
1
0
0
1
2
2
1
1
1
1
1
1
1
1
0
1
1
0
0
0
1
2
2
1
1
2
1
0
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
2
1
1
0
1
2
2
1
1
1
2
1
2
2
1
2
2
1
1
1
1
1
0
0
1
2
1
1
5
0
1
2
1
0
1
2
1
1
1
2
1
1
1
1
0
0
1
2
2
2
2
2
1
1
1
1
2
2
1
1
0
2
0
0
1
0
1
1
0
1
2
1
0
1
1
1
0
2
0
0
1
1
1
2
1
0
2
1
0
1
1
1
2
1
1
1
0
2
2
0
0
2
2
2
2
1
2
5
4
1
1
0
1
1
2
1
1
1
1
1
1
1
2
0
0
1
0
2
1
1
0
1
1
0
2
1
2
1
4
2
1
0
1
1
2
2
0
1
0
2
2
1
1
2
1
1
1
1
2
0
1
1
1
0
2
0
2
1
2
1
0
0
2
2
2
7
1
1
2
2
1
3
1
1
1
2
1
1
1
1
0
0
1
2
1
3
1
0
1
1
0
3
0
2
1
0
1
0
2
2
1
1
1
1
1
1
1
1
1
0
1
1
1
0
1
2
1
2
1
1
2
1
1
1
1
1
1
1
2
1
0
1
1
1
0
0
1
0
1
1
1
1
1
1
1
2
1
2
2
1
1
1
0
0
2
1
3
1
1
0
1
1
1
1
2
2
2
0
0
0
1
0
1
2
2
1
1
1
1
1
1
1
2
1
1
0
2
1
0
0
1
2
1
2
1
1
1
1
2
0
1
1
1
1
0
0
0
2
1
1
1
2
1
1
1
0
0
1
1
1
2
1
1
0
0
1
1
0
1
0
1
2
1
2
0
0
1
1
1
2
1
2
1
4
2
1
1
2
1
1
2
0
1
1
1
1
2
1
1
1
3
1
0
2
2
2
0
1
2
1
1
0
2
1
2
1
2
0
1
1
1
1
1
1
2
1
1
1
1
2
1
1
0
2
0
1
1
1
1
2
1
1
2
1
1
0
2
2
0
0
1
0
2
2
1
1
1
2
1
0
2
2
1
2
1
0
1
1
0
1
1
2
2
1
1
1
1
1
0
0
2
1
1
1
1
0
1
1
1
2
1
1
1
1
1
1
1
1
3
1
1
0
1
1
1
1
1
1
1
2
0
1
1
2
2
0
2
1
0
1
0
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
2
1
2
0
1
3
1
1
1
1
0
1
0
1
1
2
2
1
1
1
1
1
1
1
1
1
2
1
1
0
1
0
1
1
1
2
0
0
2
1
1
2
2
2
1
2
1
2
1
1
0
0
0
1
1
1
2
2
1
1
0
1
2
1
1
1
2
2
2
0
1
0
1
1
1
2
2
1
1
0
1
1
2
3
2
0
1
0
1
2
1
2
0
1
1
1
0
1
0
1
1
2
0
0
0
2
2
1
1
1
2
0
1
1
0
1
0
2
1
1
2
1
1
1
1
0
2
1
1
2
2
0
2
0
2
1
1
2
0
1
1
0
1
1
2
0
1
1
1
0
0
1
0
1
1
1
1
1
0
1
1
1
2
1
1
2
1
0
0
0
0
1
2
1
1
1
1
1
0
1
2
0
1
2
1
1
0
1
1
1
1
1
0
1
1
1
1
0
1
1
1
2
0
1
0
2
2
1
0
1
1
1
0
1
2
1
1
1
0
1
1
1
1
1
0
1
1
1
1
0
1
0
1
0
3
2
2
1
1
1
2
2
2
1
1
0
1
2
1
1
0
1
0
1
0
1
0
2
0
2
0
1
1
1
1
0
1
0
2
1
1
1
2
2
1
2
1
1
0
1
1
2
0
1
1
0
1
1
1
1
1
2
2
0
1
1
1
1
1
0
1
0
1
0
2
1
1
1
0
1
1
2
1
0
0
2
1
0
0
1
1
1
1
2
0
1
1
1
1
1
0
0
0
1
1
1
1
0
1
1
1
0
1
1
2
0
1
1
2
2
0
1
1
1
1
1
0
1
0
1
1
1
1
2
2
1
1
1
2
1
0
2
1
2
1
1
1
1
0
2
1
1
1
1
2
1
0
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
0
0
1
1
1
2
1
1
1
0
2
2
1
1
1
1
2
0
2
0
1
2
0
1
0
1
1
0
1
0
1
0
1
0
1
2
1
0
0
0
0
2
0
0
0
1
0
1
1
1
1
2
2
1
2
1
2
2
1
1
1
1
1
1
1
2
2
0
1
1
1
1
0
1
1
0
2
0
1
1
1
2
1
1
2
1
1
1
1
1
1
1
0
1
1
2
0
2
1
0
1
1
1
1
0
1
1
2
0
2
1
1
1
1
1
1
2
0
1
1
1
2
1
1
2
1
2
2
1
2
0
1
1
1
0
2
0
1
1
0
1
1
1
0
2
2
2
1
1
1
1
1
2
2
1
1
3
0
1
1
0
0
1
1
2
0
1
1
2
0
2
1
0
2
1
1
1
1
1
0
1
1
2
1
1
1
0
1
1
1
1
1
0
1
3
1
2
0
2
1
2
1
2
0
1
1
1
2
1
1
1
1
1
2
0
2
2
1
1
2
1
1
1
0
1
0
1
1
1
1
0
0
1
1
0
0
0
1
1
1
0
1
2
1
1
2
1
1
1
2
1
2
2
2
2
0
2
0
1
2
1
1
2
1
1
0
1
0
1
1
0
0
0
2
1
1
1
2
1
1
1
0
1
1
1
1
0
1
1
1
1
1
0
2
2
0
2
1
1
0
1
2
2
1
2
2
1
2
2
2
2
1
1
1
2
1
2
2
2
1
1
1
1
2
1
2
1
1
0
2
2
1
1
0
1
1
0
2
0
1
1
1
1
0
0
0
1
1
1
3
0
0
0
1
1
2
1
1
2
1
1
1
2
0
0
1
2
0
1
2
0
1
1
2
1
0
1
0
2
1
0
2
1
1
0
1
1
1
1
1
1
1
1
1
1
0
2
1
1
0
1
1
1
0
1
1
2
1
1
0
1
0
1
0
2
2
2
2
2
3
1
1
0
0
0
1
2
1
2
2
0
1
3
1
2
0
1
2
1
1
1
0
2
3
1
2
1
2
1
0
1
2
0
2
1
2
2
1
2
1
0
1
1
1
2
2
2
1
0
1
1
0
1
1
0
0
1
1
1
1
1
2
1
2
2
3
2
0
0
2
1
1
1
3
2
1
1
1
1
0
1
0
2
0
3
0
2
1
1
0
0
1
1
1
1
1
2
1
1
0
2
1
1
1
2
1
1
1
1
1
2
2
1
1
1
1
2
1
1
1
0
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
0
2
0
1
1
1
1
0
2
0
1
1
0
0
1
0
1
0
0
1
2
0
1
1
1
1
1
2
0
1
2
1
0
1
0
0
0
1
1
1
1
1
0
1
1
1
0
2
1
1
2
1
0
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
0
1
1
1
0
2
1
1
0
1
0
1
1
1
2
2
1
1
1
2
2
1
0
2
2
0
1
3
1
1
1
0
1
1
1
2
0
0
2
2
1
1
1
1
0
2
1
0
0
1
1
1
1
1
1
1
1
1
1
1
1
2
1
0
1
1
1
1
1
1
0
2
1
1
1
1
2
1
1
2
0
1
2
1
2
2
1
1
2
2
0
0
1
1
1
1
1
0
1
0
2
1
0
1
1
2
2
0
1
1
1
1
1
1
0
0
1
2
1
2
2
0
1
1
0
2
1
1
1
1
0
0
0
2
2
0
1
1
1
0
2
1
1
1
2
2
1
1
0
1
1
0
1
1
0
0
2
1
0
0
0
1
1
1
2
1
2
1
0
2
1
1
1
1
2
1
2
2
2
1
1
2
0
1
0
0
1
0
1
1
1
1
1
2
1
1
1
2
1
2
0
1
0
1
1
1
2
1
1
1
0
2
1
1
2
1
0
1
0
2
2
0
0
1
1
1
0
1
1
0
1
1
1
0
1
2
1
0
1
0
2
1
2
1
1
2
1
4
1
0
1
1
0
1
1
2
1
0
1
2
1
0
1
1
1
1
2
1
2
1
1
2
2
2
0
1
1
0
1
1
0
2
2
0
2
1
1
1
1
1
0
0
0
1
2
0
2
1
0
1
1
1
0
0
2
1
1
0
1
0
0
1
2
1
1
1
1
1
0
1
1
1
2
1
2
0
1
2
2
2
1
0
0
1
1
2
1
1
1
1
0
1
1
1
0
2
1
1
1
1
0
0
0
1
1
1
1
1
1
1
0
1
2
2
1
1
1
1
0
2
1
1
1
1
1
0
1
2
0
1
1
2
0
1
0
0
1
1
1
1
2
1
1
1
0
1
1
1
2
1
1
2
1
2
1
1
0
0
1
2
1
2
1
0
1
1
1
0
2
1
1
1
1
0
1
0
1
0
1
1
1
1
2
1
1
1
0
2
1
1
1
1
1
2
2
1
0
1
1
2
1
1
2
1
1
1
1
0
1
2
0
2
1
1
2
1
1
1
2
1
1
0
2
1
1
1
1
1
2
0
1
2
1
1
1
1
0
1
1
0
1
1
1
0
1
0
1
1
1
1
1
0
1
1
0
1
1
2
1
0
1
1
1
0
1
1
5
4
0
1
1
1
2
2
1
2
1
1
2
2
2
1
2
1
0
1
0
2
1
1
2
0
2
0
2
1
1
2
2
1
1
1
2
0
1
1
1
2
2
0
1
1
2
1
1
1
1
0
1
0
1
1
1
0
0
2
1
1
1
2
2
2
1
1
0
0
2
1
0
0
0
2
1
1
0
1
2
1
1
1
1
1
1
1
1
1
2
1
2
1
1
0
2
1
1
1
1
1
0
0
1
0
1
1
0
2
1
2
1
1
1
1
1
2
0
2
1
1
1
1
2
1
0
1
0
1
1
1
1
1
1
0
2
1
0
1
0
1
0
1
2
0
0
1
1
0
1
2
1
0
2
0
1
2
1
1
2
1
2
1
0
2
0
2
0
0
1
0
1
1
1
0
1
2
1
1
2
1
1
0
1
1
2
1
2
0
1
1
1
2
1
1
1
0
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
2
1
1
1
0
0
2
2
1
0
0
1
1
1
0
1
1
1
0
1
2
2
1
2
0
1
1
0
0
2
1
1
0
1
2
0
1
2
1
1
1
1
2
0
1
1
0
0
0
0
2
1
2
0
3
1
2
1
2
1
1
2
1
1
0
1
2
1
0
1
1
0
1
2
1
0
2
1
1
1
1
2
2
0
2
1
2
0
0
2
1
1
0
1
1
2
1
2
1
2
0
1
0
2
1
1
0
1
0
0
0
1
1
1
1
1
0
2
1
1
1
1
1
2
0
1
2
1
1
2
1
1
1
2
1
2
2
1
2
1
2
1
1
1
2
2
1
1
1
1
2
1
0
1
1
1
2
0
1
1
1
1
2
2
1
1
2
1
0
1
1
1
1
1
0
0
1
1
1
2
1
1
0
2
2
1
1
1
2
1
1
3
1
1
1
2
1
1
0
1
1
1
2
1
1
0
1
0
1
1
0
1
1
1
2
1
0
1
0
1
1
0
2
1
1
1
1
0
1
2
0
1
2
0
1
2
0
1
1
1
2
1
0
1
2
1
2
1
1
1
2
1
0
0
1
1
1
1
1
1
2
0
1
1
1
1
1
2
0
1
1
1
2
1
1
0
1
1
1
1
1
0
2
0
2
0
1
2
1
2
2
0
1
1
2
0
2
0
1
2
1
0
1
1
1
1
2
0
2
1
2
1
2
1
1
2
2
0
0
0
1
1
2
1
1
0
1
1
1
1
1
1
2
1
0
1
0
1
2
0
1
1
1
2
1
2
0
2
3
1
1
1
1
1
2
0
1
2
1
1
2
1
2
2
1
1
2
1
1
1
1
1
1
2
1
0
1
1
2
1
0
0
1
1
1
2
2
1
2
1
2
1
2
1
2
2
1
2
0
1
0
1
0
2
2
2
1
1
1
2
1
1
0
0
1
0
2
1
1
1
1
1
1
2
0
1
2
1
1
1
1
2
1
1
1
1
1
2
2
1
1
1
2
2
1
0
1
2
0
0
1
1
1
1
1
2
2
1
1
1
1
1
0
1
1
1
2
1
2
1
1
2
1
1
0
0
0
2
1
1
2
2
1
1
0
1
1
2
0
2
1
0
0
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
2
1
0
1
1
1
1
1
2
1
0
1
1
0
1
2
0
1
1
2
1
2
1
2
2
1
0
0
1
0
1
1
0
1
1
1
1
0
0
0
1
1
2
0
1
1
1
1
2
1
1
1
1
2
0
1
2
2
0
2
2
0
1
2
1
1
0
0
1
2
1
2
0
0
1
2
1
1
0
0
1
1
0
1
2
2
2
2
1
1
0
2
1
0
0
1
0
0
1
0
1
1
0
2
2
0
1
1
0
1
1
2
1
1
0
1
2
0
2
1
1
1
2
1
0
0
1
1
1
1
1
1
0
1
1
1
0
1
1
2
1
0
1
2
1
1
1
1
1
2
0
0
2
1
0
1
1
1
0
1
1
0
1
2
0
1
2
1
1
1
1
1
1
1
2
2
1
0
1
0
1
1
2
1
1
1
2
2
2
2
1
0
0
1
1
2
1
3
1
0
2
2
2
0
2
0
1
0
2
1
0
3
1
2
1
1
1
0
1
1
1
2
2
1
2
1
1
1
0
1
2
1
2
1
1
1
1
1
2
0
1
2
0
1
2
1
1
2
1
1
0
1
1
1
2
1
0
1
0
2
0
1
5
0
2
0
0
1
0
0
1
1
3
0
1
1
1
1
0
0
0
2
0
1
0
1
1
2
1
0
1
0
2
0
1
1
0
1
1
1
1
1
1
0
1
2
2
2
2
1
2
1
1
0
1
1
1
1
1
1
1
1
1
1
2
0
1
1
0
1
1
2
1
2
1
1
2
1
4
0
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
1
3
0
1
2
0
2
2
0
1
1
1
1
1
0
1
1
0
1
0
0
2
0
2
1
1
1
0
0
0
1
2
2
2
1
1
1
0
1
1
0
1
2
0
1
1
0
1
1
1
1
1
1
1
1
1
0
0
2
3
1
2
1
1
1
1
0
1
1
1
1
1
2
1
1
0
1
1
2
1
1
0
1
1
1
1
2
1
2
1
2
0
1
0
0
1
0
1
1
1
0
2
2
1
1
1
2
0
2
1
0
1
1
0
1
2
1
1
2
0
1
1
2
1
1
3
0
1
2
0
1
1
1
0
1
1
1
1
1
0
1
0
1
0
1
1
1
1
2
1
0
0
1
3
0
1
0
2
1
1
1
2
2
1
1
1
1
1
2
1
1
2
2
0
1
1
2
0
2
1
2
1
0
1
0
1
2
2
0
1
2
1
1
1
0
1
1
1
1
0
1
0
1
1
0
1
2
2
2
0
1
1
1
1
2
1
1
1
1
1
1
1
0
1
1
1
0
1
2
1
1
1
2
1
1
1
2
1
1
0
3
1
0
1
1
1
0
2
1
1
1
1
1
1
1
0
0
1
0
0
2
2
1
1
1
1
1
1
1
1
1
0
1
2
1
1
2
2
1
2
2
1
2
1
0
0
2
2
2
2
0
1
1
1
0
0
2
0
1
1
1
0
1
0
1
1
0
0
1
2
1
0
2
1
1
2
1
1
1
0
1
1
1
0
0
2
1
1
1
1
1
0
2
1
0
2
1
1
1
1
1
0
0
0
1
0
0
1
2
2
1
2
1
0
0
1
2
1
1
1
0
0
1
1
1
2
2
1
2
1
2
1
0
2
1
1
1
2
1
1
1
1
1
1
1
4
2
1
0
2
0
1
1
1
0
2
1
1
1
0
1
0
0
1
0
1
1
1
0
0
1
2
1
1
1
1
2
1
1
1
1
2
0
1
1
0
0
1
1
0
0
1
1
1
1
0
1
1
2
1
0
1
1
1
1
1
1
0
1
1
1
1
1
1
0
0
1
1
1
2
1
1
2
1
2
1
1
1
0
0
1
1
1
1
0
0
1
2
1
0
0
1
2
1
1
1
1
1
0
1
2
1
1
1
1
0
2
1
0
1
2
1
1
0
1
1
1
1
0
2
2
1
2
2
1
1
0
2
0
1
0
1
0
1
1
2
2
1
2
1
1
0
2
1
1
1
2
1
0
1
1
1
2
1
2
1
2
1
2
2
0
0
1
1
1
1
0
1
1
0
1
2
1
2
1
1
2
1
1
2
2
0
1
1
0
1
1
1
1
1
2
1
2
1
2
2
1
0
0
1
2
1
0
1
1
1
0
1
1
1
2
2
1
1
1
1
2
1
1
1
1
0
0
1
0
2
2
1
1
0
0
1
2
2
2
0
1
1
0
0
1
1
1
0
1
1
1
0
1
1
0
2
0
1
2
1
1
1
2
0
2
1
1
2
1
0
1
1
1
1
1
2
2
1
0
1
0
2
0
2
0
1
1
2
1
2
1
1
2
1
1
2
1
1
1
2
1
2
1
0
0
2
1
1
1
2
1
1
1
2
0
1
1
1
0
1
2
2
1
2
2
0
1
2
1
2
1
1
1
0
0
1
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
0
0
0
1
0
2
2
1
1
0
1
1
2
1
1
1
1
2
2
0
1
2
1
0
2
0
2
1
1
1
0
1
2
2
1
1
1
1
1
2
0
1
2
1
2
2
1
2
1
1
1
0
1
0
2
2
2
0
1
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
0
1
1
1
1
1
1
2
1
1
0
1
1
1
1
2
2
1
0
1
0
1
1
1
2
2
0
1
1
1
2
0
2
1
2
1
1
1
1
0
2
2
1
1
1
1
0
0
1
1
1
0
2
1
0
0
1
0
2
1
1
1
2
1
1
1
1
1
0
0
1
1
1
1
1
1
2
0
1
0
1
0
1
1
1
1
2
1
1
1
1
2
1
1
1
0
1
0
1
1
2
1
0
3
1
1
1
1
2
1
1
2
1
1
0
1
0
0
0
1
0
1
1
0
1
1
1
1
2
1
0
1
1
1
1
1
2
2
0
0
1
1
2
0
2
0
1
1
2
1
0
2
1
1
2
1
2
1
1
0
1
1
2
1
1
1
1
1
1
2
0
1
1
0
1
1
1
2
1
1
1
1
0
2
1
1
1
2
1
1
0
0
2
1
0
2
2
2
2
2
0
1
1
0
1
1
0
1
1
2
1
0
1
0
1
1
1
1
0
2
1
1
2
2
2
2
1
2
0
2
1
1
1
2
1
1
1
0
1
1
0
1
2
2
2
1
0
1
1
0
2
1
0
0
2
1
0
2
2
1
1
1
1
2
1
1
2
1
0
2
1
2
1
2
1
0
0
1
1
0
2
1
1
1
1
1
1
2
2
2
0
2
2
1
2
1
2
1
1
1
2
0
2
3
1
0
0
1
2
1
1
3
1
1
1
1
1
1
1
0
1
0
2
2
1
2
0
1
1
2
1
1
0
0
1
1
1
1
1
1
0
2
1
2
2
1
0
1
2
0
1
1
1
0
2
0
0
0
2
1
7
1
2
2
1
2
0
2
0
1
2
1
2
0
1
1
1
0
1
1
0
1
1
1
1
2
1
2
1
2
1
1
1
1
1
1
3
1
2
1
1
2
0
2
1
2
1
2
2
2
0
1
1
1
1
0
1
0
2
2
1
1
2
1
1
2
1
1
1
2
2
0
1
1
1
1
1
1
2
1
1
2
1
1
1
1
0
2
0
2
2
1
1
0
1
1
1
1
1
2
1
1
2
0
2
1
1
0
2
1
2
1
2
1
1
2
2
1
0
2
1
1
2
1
0
1
2
0
1
1
1
1
0
1
2
1
1
2
2
0
2
2
1
2
2
1
2
1
1
2
1
1
1
1
1
1
0
1
0
1
2
1
2
2
2
1
1
0
0
1
1
0
1
0
1
0
1
1
1
1
1
1
1
1
2
1
0
1
0
2
1
1
1
2
1
0
2
1
2
1
2
1
0
1
0
1
1
0
2
1
2
0
1
1
0
2
3
1
3
0
2
1
2
1
1
2
1
0
1
0
1
1
1
2
1
1
1
2
0
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
2
1
0
0
1
0
0
2
2
1
0
2
1
2
0
1
1
2
1
0
2
1
1
1
1
1
2
1
2
1
2
1
1
1
1
1
1
2
1
2
1
0
0
2
2
2
1
0
0
1
1
1
1
0
0
0
2
0
1
1
2
2
1
2
1
0
1
1
1
0
1
1
0
1
1
1
1
2
0
1
1
1
1
1
1
0
0
2
1
2
2
1
0
2
0
0
1
0
2
1
0
1
0
0
0
2
0
0
1
1
2
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
1
0
1
1
2
1
1
2
1
1
1
1
0
1
1
2
1
1
1
1
1
0
1
0
1
1
1
2
1
1
1
1
2
2
0
2
0
1
1
2
2
1
0
2
1
0
1
1
1
1
2
1
1
1
0
1
0
1
1
1
1
0
0
0
0
1
1
0
1
2
1
1
1
2
1
0
1
2
1
1
1
0
2
2
1
1
3
1
2
1
3
1
1
1
1
2
0
0
2
2
2
1
1
2
1
2
1
2
1
1
1
0
2
1
1
1
1
1
1
1
2
2
2
2
1
1
1
1
1
1
2
1
0
1
0
2
1
1
1
1
1
2
1
2
1
1
1
1
1
3
1
0
0
1
1
2
0
1
1
1
1
0
1
1
0
1
1
3
0
2
1
3
1
1
3
1
1
2
0
1
1
2
0
1
1
1
0
1
0
2
1
2
1
1
1
1
1
1
2
0
1
1
1
2
1
1
2
1
1
2
1
0
1
0
2
2
0
0
2
1
0
2
0
1
2
1
0
1
0
1
2
1
2
2
1
2
1
1
0
2
1
1
1
2
0
0
0
1
2
2
2
1
1
1
0
1
1
1
1
1
0
2
0
2
1
1
1
1
1
0
2
1
1
2
1
1
1
1
1
1
0
0
0
1
3
1
1
0
1
1
1
1
1
1
0
0
1
1
1
1
1
0
0
1
1
2
1
1
2
1
1
1
1
1
1
1
2
1
0
2
1
2
2
1
1
2
1
1
0
2
1
0
0
1
1
0
1
1
0
0
1
1
1
0
0
1
0
1
2
2
0
2
1
3
1
2
1
1
1
0
1
1
1
1
0
1
1
1
1
1
3
1
2
2
2
1
1
1
0
1
1
0
1
1
0
1
2
1
1
1
1
0
1
1
0
1
2
4
0
1
1
0
2
1
1
0
2
0
1
0
1
1
3
2
0
2
2
1
0
1
0
0
1
1
1
2
2
0
1
1
1
2
1
1
1
1
1
1
0
1
1
2
1
0
0
1
1
1
1
2
2
1
1
1
0
1
1
1
1
2
2
2
1
1
1
1
2
1
2
1
1
0
0
1
1
1
0
0
2
1
1
2
2
0
1
1
1
1
1
2
2
1
1
1
0
1
1
1
1
1
1
2
1
0
1
2
1
1
1
1
1
2
0
1
2
1
0
1
2
1
1
1
1
1
1
0
2
2
1
1
1
0
2
0
1
1
0
0
1
1
1
1
1
1
2
1
1
2
1
0
1
3
2
1
1
1
1
0
1
0
2
1
0
2
0
1
1
1
2
1
2
2
1
0
1
1
2
1
1
1
2
0
0
2
1
1
1
0
1
1
1
1
2
1
0
0
0
1
0
0
2
1
0
2
1
1
0
1
2
1
1
0
1
1
2
1
1
1
1
1
1
1
1
0
1
1
1
2
2
2
2
2
1
1
1
2
1
2
2
1
1
2
2
2
0
2
0
1
1
2
1
1
0
0
1
1
1
1
1
1
2
1
2
2
2
1
1
2
1
0
1
1
1
2
1
1
0
2
1
0
1
1
2
2
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
2
0
1
1
0
0
2
0
2
1
2
0
1
2
2
2
2
1
2
0
1
1
2
1
1
1
1
1
1
1
1
1
0
1
0
2
0
2
1
0
1
1
1
0
1
1
0
1
2
1
1
2
1
1
2
1
1
2
1
2
1
2
0
0
0
1
1
1
1
0
1
2
1
2
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
0
1
1
1
2
0
1
1
1
1
1
2
1
2
1
2
1
1
1
1
1
0
1
1
0
1
1
1
1
0
1
2
1
1
1
1
1
0
1
1
1
1
1
0
0
3
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
2
0
2
0
0
0
2
2
1
0
0
0
1
1
0
0
0
2
0
1
0
1
1
1
1
2
1
1
2
1
1
2
4
1
2
0
2
1
1
1
1
0
1
1
2
1
1
1
2
0
1
1
1
1
1
1
2
2
1
1
1
0
1
1
1
2
1
1
0
0
1
1
2
1
1
1
1
0
1
1
1
2
1
1
0
1
2
0
1
2
1
1
0
1
1
1
0
1
1
1
1
1
2
1
1
1
2
1
1
1
0
2
0
1
1
0
2
1
2
2
1
1
2
2
2
0
2
1
1
1
1
1
0
1
1
1
1
2
1
1
2
1
1
0
1
1
1
1
0
1
0
1
2
0
1
2
1
1
1
0
2
1
2
0
1
2
1
1
0
2
1
0
2
1
1
1
1
1
1
2
0
1
0
1
1
1
0
1
1
1
1
1
2
2
1
1
1
1
0
0
1
1
2
2
1
1
1
1
1
0
1
1
1
2
1
2
1
1
0
0
1
2
1
2
0
1
1
0
1
1
1
0
1
1
1
1
1
0
1
0
1
1
1
1
1
0
0
1
1
1
1
2
1
0
1
1
1
2
0
0
0
1
0
2
1
0
1
1
1
1
0
1
0
0
0
2
0
1
1
2
2
1
0
0
1
2
0
1
2
2
2
1
2
0
0
1
0
1
2
2
0
2
1
0
1
1
0
1
0
0
2
2
0
1
2
2
1
1
1
2
1
0
0
0
0
1
2
1
1
0
1
1
1
1
2
0
1
2
1
0
2
2
1
1
1
1
1
2
0
2
1
2
2
1
1
1
1
1
1
1
2
0
1
1
1
1
0
1
1
2
0
0
2
1
0
2
1
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
0
1
2
2
0
0
1
2
0
1
2
1
2
2
2
1
0
1
1
2
2
0
2
1
1
1
1
1
2
1
1
2
0
1
0
1
0
2
0
2
0
1
2
2
0
0
2
2
2
1
0
2
1
3
1
2
1
1
1
1
1
1
2
0
2
0
1
0
1
2
2
1
2
1
0
0
2
2
2
2
2
1
0
1
1
2
1
2
2
2
0
0
2
1
1
1
1
0
0
1
1
2
0
1
1
2
1
1
2
0
1
2
2
2
1
1
1
1
2
2
0
2
1
0
1
1
1
2
2
2
1
2
2
1
1
0
2
1
1
1
1
1
1
0
0
1
1
0
1
1
0
0
2
3
1
1
1
1
0
1
1
2
2
1
1
1
1
2
2
1
1
1
1
2
2
1
2
0
1
1
0
1
1
1
2
1
1
3
1
1
1
1
0
0
1
2
1
3
1
2
1
0
1
1
2
1
1
2
1
1
0
0
1
2
0
0
1
1
0
1
0
2
1
1
0
0
2
1
2
1
2
0
1
1
1
0
2
0
2
1
1
2
0
0
2
0
0
2
1
1
1
1
1
0
2
3
1
1
1
1
1
1
2
0
0
1
1
2
0
0
2
1
0
1
1
2
1
1
1
2
0
2
1
1
1
1
1
1
1
2
0
2
1
1
1
1
1
0
1
2
0
2
1
2
1
2
1
0
1
1
0
2
1
2
1
2
0
1
1
2
2
1
0
1
1
0
2
1
1
0
0
2
0
1
0
2
1
0
1
1
0
0
1
2
1
2
1
2
1
0
0
0
2
1
1
0
1
1
1
0
1
1
1
1
1
0
1
0
1
0
1
0
1
2
1
1
2
2
1
2
2
0
1
0
1
1
1
1
1
1
2
2
1
2
1
2
2
1
1
0
1
0
1
2
1
1
0
1
2
1
2
1
1
1
3
1
1
1
1
1
1
0
2
1
0
1
1
2
1
1
1
1
2
1
2
2
2
1
1
0
0
1
2
1
1
1
2
1
1
2
1
1
1
1
0
1
1
2
0
2
1
1
0
1
2
2
2
1
1
1
2
1
1
1
1
1
2
0
2
1
1
2
1
1
1
1
1
0
1
1
2
1
1
1
0
1
1
1
0
1
1
1
2
1
0
1
0
1
1
2
1
0
2
2
1
2
1
2
1
2
1
1
1
1
2
2
2
1
1
1
0
0
1
1
1
1
1
0
1
1
1
0
1
1
1
1
1
1
0
1
0
1
2
2
1
1
1
1
1
2
1
0
2
0
1
1
1
1
0
1
1
2
2
1
2
2
1
1
1
1
1
1
1
0
1
2
1
1
1
1
1
1
2
2
0
1
1
1
2
0
1
1
1
0
1
1
2
2
1
1
1
0
0
1
1
1
0
1
1
1
0
2
2
1
2
2
1
2
1
1
2
2
0
1
1
2
2
2
2
1
1
1
0
1
1
0
1
2
1
1
0
0
1
1
1
1
0
0
1
1
1
1
0
2
1
2
0
1
1
0
0
1
1
3
0
1
1
2
1
0
1
2
2
1
2
1
0
1
2
0
0
1
1
2
0
2
1
0
0
1
1
1
0
1
1
2
2
1
2
1
0
1
1
1
1
1
2
1
1
2
0
1
0
1
0
1
1
1
1
1
2
2
1
0
0
2
0
2
0
1
1
2
2
2
0
1
0
1
0
1
1
0
1
1
1
1
2
1
1
1
0
2
1
2
0
1
2
1
1
0
2
1
1
0
1
1
1
1
1
0
1
0
0
1
1
2
0
0
1
2
2
2
2
1
2
1
0
1
1
2
0
2
1
1
1
1
2
2
1
1
1
1
1
1
2
1
2
1
2
1
1
1
2
1
1
1
1
0
1
1
2
2
1
1
2
0
2
1
1
2
2
0
1
1
1
0
1
2
0
0
2
1
1
2
0
1
1
0
2
0
0
0
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
0
0
2
0
1
1
2
0
2
1
1
1
2
1
2
0
0
1
1
1
0
2
1
1
0
0
2
0
0
1
1
0
1
1
1
1
0
1
2
2
1
1
0
1
0
1
1
2
1
1
0
1
1
0
1
1
0
1
1
2
2
0
2
1
1
1
0
2
1
1
1
1
1
1
1
0
1
2
1
1
1
1
0
0
1
1
2
1
0
1
1
1
2
1
2
0
0
1
1
0
2
1
0
1
0
1
1
1
1
0
0
0
0
1
0
1
0
2
1
0
1
0
2
1
0
0
1
1
2
1
0
1
1
1
0
1
0
1
2
1
1
1
2
1
0
1
1
0
1
2
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
3
1
0
1
0
0
2
2
1
0
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
0
0
1
0
2
1
0
2
1
1
1
1
2
0
1
1
1
2
1
0
2
0
1
1
1
1
1
2
1
0
1
1
1
1
1
1
1
0
2
2
1
2
1
0
2
1
0
1
1
1
0
0
1
1
0
1
1
2
1
1
1
1
6
2
0
0
2
1
1
1
0
1
2
0
2
1
1
3
1
1
1
1
1
2
1
1
2
3
2
1
1
1
0
2
1
2
1
2
1
1
1
2
1
1
1
0
2
0
1
1
0
1
1
2
1
2
0
0
1
1
1
1
1
1
0
0
1
0
1
2
1
1
2
1
0
2
0
1
1
1
0
0
2
1
1
1
2
1
1
2
0
1
2
2
0
1
0
1
2
3
0
1
2
1
2
1
1
2
0
1
1
1
1
2
2
0
1
1
1
2
1
0
0
1
1
0
2
1
1
0
0
1
1
1
1
0
1
2
1
1
1
1
1
1
1
1
0
1
1
1
1
2
0
1
2
1
2
1
2
3
2
1
0
1
0
1
2
2
1
2
2
1
1
1
1
1
0
2
1
2
1
2
1
1
1
1
1
1
1
1
0
1
1
1
2
1
1
1
1
2
1
0
1
1
0
3
0
1
1
0
2
1
2
1
2
1
1
2
0
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
0
1
0
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
0
0
1
1
1
2
1
0
1
1
1
1
2
1
1
0
2
1
2
1
1
1
1
1
1
1
1
3
2
1
2
1
1
1
0
1
0
1
1
1
1
2
0
0
1
1
1
1
0
1
2
0
1
2
1
2
1
0
1
0
0
0
0
0
1
1
2
1
2
2
1
1
1
1
0
0
1
2
1
1
1
2
3
0
0
2
1
2
2
1
2
1
2
0
2
1
1
2
1
2
1
0
1
1
2
1
1
1
0
0
1
1
1
1
1
0
1
1
1
1
1
2
0
1
1
2
2
1
1
1
2
1
2
1
1
1
1
1
2
2
1
2
1
1
2
1
0
1
1
0
2
0
0
2
1
2
2
1
1
1
1
0
0
1
0
2
1
1
1
2
2
1
2
1
0
1
1
1
0
1
2
1
1
1
1
1
3
1
1
1
2
1
1
0
2
2
2
0
2
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
0
1
1
1
0
1
0
1
1
0
1
1
1
0
1
0
1
0
2
1
1
0
1
0
1
1
2
1
1
0
1
1
1
1
1
1
1
1
0
2
0
3
1
1
0
1
2
1
3
1
0
1
0
2
1
2
1
2
1
1
0
2
0
0
2
1
0
1
1
1
1
1
0
2
1
1
2
2
0
1
1
1
0
1
1
2
1
2
2
2
1
3
1
6
1
1
2
1
2
1
1
1
1
1
1
0
1
1
1
2
1
2
1
2
0
2
0
0
0
2
1
0
2
0
1
2
1
0
1
1
1
2
2
1
0
1
1
0
1
1
1
1
1
1
1
1
1
1
2
0
0
1
1
0
2
0
1
0
2
0
2
1
2
1
1
1
2
0
0
1
1
1
1
1
2
1
1
0
1
4
0
1
1
1
2
2
0
2
1
2
0
1
0
1
0
1
0
0
1
1
1
2
1
2
0
2
2
0
1
1
1
1
1
1
1
2
1
1
1
1
0
2
1
1
1
1
0
0
2
1
2
2
1
0
2
1
1
1
0
1
1
1
1
1
1
1
1
1
1
2
0
2
0
1
1
1
0
2
1
1
0
0
3
0
1
1
0
1
1
2
1
1
2
1
1
0
2
0
2
1
2
1
1
1
1
1
0
2
1
0
0
0
0
1
1
1
1
2
1
1
1
0
1
2
1
2
1
0
1
1
0
2
1
1
1
1
1
2
1
2
1
2
0
1
1
1
1
1
1
1
0
0
1
0
2
1
1
1
1
1
0
0
1
2
1
1
1
2
2
1
1
2
1
0
0
0
0
1
1
1
1
2
2
2
2
0
0
0
1
0
1
0
1
1
1
0
2
0
0
2
1
1
0
1
1
1
1
1
0
1
2
0
1
1
2
1
2
0
1
1
1
1
1
2
1
1
2
1
1
1
2
1
0
1
2
1
0
1
1
2
2
2
1
1
1
1
1
1
0
1
0
1
2
1
1
1
1
1
0
2
2
1
0
1
1
1
1
0
2
1
0
2
0
1
1
0
1
1
0
1
2
1
1
2
1
1
1
0
1
0
0
1
1
2
2
0
1
1
0
0
1
1
1
1
0
1
1
1
1
1
2
1
1
2
1
0
1
2
1
0
1
1
1
1
1
0
2
0
1
2
0
1
2
1
2
2
1
0
0
2
1
0
1
1
2
1
1
1
2
2
2
2
1
2
1
1
2
1
0
1
1
1
1
1
0
0
2
1
1
1
2
1
2
2
2
1
1
1
1
1
0
1
1
0
0
1
1
2
0
2
3
1
1
1
0
2
1
1
2
1
2
0
0
1
1
1
1
1
2
1
0
2
1
1
0
1
1
2
1
1
2
1
1
0
2
0
1
2
2
2
1
1
1
2
1
0
0
1
1
1
2
0
0
1
1
2
0
1
0
0
1
1
0
0
0
1
1
0
0
1
1
2
1
1
1
2
1
2
0
0
1
0
1
0
0
1
1
1
1
2
0
1
0
0
1
0
1
1
0
1
2
2
0
2
1
1
2
0
1
1
2
1
1
1
2
1
1
1
1
1
1
1
0
1
1
1
2
1
1
2
0
0
1
2
1
2
0
2
1
1
0
1
1
1
0
1
1
0
1
1
1
1
1
2
1
1
1
1
0
1
0
2
1
1
1
1
2
2
1
1
2
1
2
0
1
2
1
0
1
2
1
0
1
1
2
2
1
1
2
2
3
0
1
1
1
2
1
1
1
1
1
1
2
2
0
1
0
1
1
2
1
1
0
1
2
1
2
0
1
0
1
1
1
1
1
2
2
1
0
1
1
1
0
2
2
1
1
1
1
0
0
0
1
1
1
2
1
2
0
1
1
1
0
2
0
2
2
2
1
1
0
1
1
2
1
0
1
1
0
1
1
1
2
1
1
1
1
2
1
1
1
1
0
1
2
1
0
0
2
1
1
0
1
2
1
1
1
0
1
1
1
1
1
3
2
1
1
1
2
1
0
0
0
1
1
0
1
0
1
1
0
2
2
1
2
0
0
2
1
1
1
2
1
1
1
0
1
1
1
1
1
2
1
2
1
1
1
1
2
2
0
1
2
2
0
1
1
1
1
0
1
1
2
0
0
1
2
2
2
1
2
1
0
2
2
1
1
2
2
1
2
1
0
0
0
2
1
1
2
1
1
1
1
0
1
2
1
1
0
1
1
1
1
1
1
1
2
0
2
1
3
1
1
1
0
1
2
0
2
2
2
2
1
2
1
1
0
1
2
1
1
1
2
1
1
0
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
2
0
1
0
1
0
1
1
1
1
1
1
0
2
0
1
1
2
1
0
1
2
1
1
1
1
1
0
1
1
2
1
0
1
1
1
2
1
0
0
0
1
0
2
2
1
2
1
1
0
1
1
1
1
0
1
1
1
1
0
0
0
1
1
1
1
0
1
2
1
1
1
1
1
2
2
2
2
2
1
2
1
1
1
4
1
1
1
0
1
2
1
1
2
0
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
0
0
2
1
1
1
2
1
1
1
2
1
1
0
1
1
1
1
1
2
1
1
2
1
1
2
0
1
1
1
0
1
1
1
0
0
1
0
2
1
1
1
1
1
1
1
2
1
0
1
1
0
1
2
1
2
1
1
0
1
0
1
0
0
1
2
2
1
1
1
1
1
0
2
1
1
1
0
1
0
1
1
1
1
1
1
2
1
1
1
2
2
1
2
1
1
0
2
1
2
0
0
2
0
1
1
1
1
1
1
1
0
1
1
1
0
1
0
1
1
1
2
0
2
0
0
1
0
0
1
0
1
1
1
1
2
2
2
0
2
1
1
0
0
2
0
2
2
0
1
2
1
1
0
0
2
2
0
1
0
1
0
2
2
1
0
1
1
2
1
1
2
2
1
1
1
1
0
1
1
1
1
1
2
1
1
1
2
0
0
1
1
0
1
1
1
1
1
2
1
1
1
0
0
1
1
1
2
1
1
0
0
0
2
0
1
0
1
2
2
1
2
1
0
1
2
0
1
0
1
0
2
1
2
3
3
1
2
1
1
1
1
1
0
1
0
1
0
0
0
1
1
0
1
2
2
1
0
2
1
1
1
1
0
1
1
0
0
1
2
0
1
0
0
0
1
1
1
1
0
1
1
1
1
2
1
1
2
2
1
2
1
1
1
1
1
1
1
2
2
1
2
2
0
2
1
1
1
0
0
0
2
1
1
1
1
1
2
2
2
0
1
0
0
1
1
1
1
2
2
0
1
1
1
1
0
2
2
1
2
1
1
1
2
1
1
3
0
1
2
1
1
0
4
3
1
2
2
1
1
2
2
2
1
2
0
1
0
1
1
1
1
1
1
1
1
0
0
1
1
0
0
1
3
1
2
0
1
2
1
1
1
0
0
1
2
1
1
1
1
2
0
1
0
2
1
1
1
1
2
1
1
1
0
0
1
1
1
1
1
1
1
2
1
2
1
1
1
1
0
0
1
4
0
0
1
2
1
2
1
1
0
0
1
1
1
1
1
1
2
1
0
1
1
2
1
1
1
0
0
1
0
2
1
1
1
4
0
1
1
1
2
2
0
0
1
1
1
1
0
0
2
1
1
2
2
1
1
0
2
0
1
2
2
0
1
1
1
0
2
1
1
3
1
2
1
2
1
1
1
2
0
1
2
1
1
1
0
1
1
1
1
0
0
2
1
1
1
0
1
1
1
1
0
0
2
1
1
1
2
1
0
1
1
1
1
1
2
0
1
1
2
1
2
1
0
1
1
1
1
2
0
0
11
2
2
2
2
0
1
1
1
0
1
0
0
2
1
2
1
0
2
1
2
0
2
0
0
0
1
1
1
2
0
1
0
1
1
0
0
2
1
2
1
1
1
0
1
1
2
1
1
1
0
1
0
1
0
2
1
2
0
1
2
1
1
2
1
1
0
1
1
1
2
2
1
2
1
0
1
1
1
0
0
1
1
1
0
1
1
2
2
0
1
1
1
1
2
1
0
0
1
1
1
2
1
1
1
0
2
1
1
0
2
1
1
0
1
0
2
1
1
2
2
2
0
1
1
1
1
1
1
1
1
1
1
0
2
1
0
1
1
1
0
1
1
1
1
0
2
1
0
1
1
1
0
1
1
1
0
1
0
1
1
2
1
1
1
1
0
1
1
1
0
0
1
0
0
1
1
0
1
1
0
1
0
1
1
0
2
0
1
2
0
1
1
2
1
0
0
1
0
1
1
0
0
1
1
2
1
0
1
1
0
2
1
1
1
1
1
1
2
1
1
2
2
1
2
2
1
1
0
0
0
2
1
1
1
1
2
1
1
0
0
2
1
1
1
1
2
1
0
1
0
0
1
1
1
1
1
2
1
1
1
0
2
0
1
1
2
1
1
0
1
2
1
0
0
3
1
2
1
1
1
2
1
2
1
2
0
1
2
2
0
1
2
1
4
1
1
1
2
1
2
0
2
1
1
1
1
0
1
1
1
1
0
2
0
1
1
1
1
0
2
0
1
0
2
2
1
0
1
0
0
0
2
1
0
2
1
1
1
1
1
0
2
1
2
0
1
1
1
0
0
0
1
1
0
1
2
2
2
1
0
1
2
2
1
2
1
1
1
3
1
1
1
1
1
1
1
1
0
1
1
1
0
1
1
2
1
1
1
1
2
2
1
2
0
2
1
1
1
0
2
1
1
2
0
1
2
1
1
1
1
2
0
1
0
1
1
1
1
1
1
1
1
1
0
2
1
1
2
0
1
1
1
1
0
0
1
1
1
1
1
1
1
1
1
2
1
0
2
1
1
1
0
1
1
1
2
2
2
0
2
1
1
2
2
0
1
0
1
0
1
2
1
2
1
1
1
2
1
2
1
1
1
1
1
2
0
1
1
0
1
1
0
1
1
1
2
1
0
0
1
1
2
1
1
2
1
1
0
1
2
2
1
2
1
1
1
1
1
2
2
2
2
1
0
2
1
2
1
1
2
1
1
1
1
1
2
1
1
1
1
0
1
1
1
0
0
1
2
1
1
0
0
1
2
1
2
1
2
2
1
2
2
2
2
0
0
1
2
1
1
1
2
2
1
0
0
0
1
1
1
1
2
1
2
0
2
1
2
1
0
0
0
2
0
1
0
1
1
2
2
1
1
1
0
1
1
1
1
2
0
0
2
1
1
0
1
1
2
1
2
1
1
1
1
0
1
2
1
1
1
0
1
1
1
2
1
0
0
1
2
1
0
1
1
1
2
0
1
1
2
2
1
1
1
2
1
2
0
0
1
1
1
0
2
2
0
0
1
2
1
0
1
1
1
1
0
2
1
1
0
1
0
2
1
1
2
1
1
0
1
2
1
1
1
2
1
1
2
1
1
1
1
1
0
1
0
0
2
2
1
2
1
1
1
1
1
2
0
1
1
1
1
1
0
2
1
1
2
1
2
2
3
1
0
0
1
1
1
0
1
1
1
2
1
1
1
2
1
0
2
1
1
2
1
1
0
0
1
1
2
2
0
1
2
1
1
1
1
1
1
1
2
0
1
2
2
1
0
2
2
1
1
1
1
2
2
1
1
1
1
2
1
0
0
1
1
1
1
0
2
0
1
1
0
0
1
2
1
1
1
0
0
2
1
1
1
1
1
2
1
2
2
4
2
2
1
1
1
1
2
2
1
1
0
0
0
1
1
1
1
2
2
2
1
2
2
1
2
0
1
1
2
1
1
1
0
1
0
1
1
0
0
1
1
2
1
0
2
1
2
1
0
0
1
0
1
1
0
1
1
0
1
1
1
1
1
3
1
1
2
2
1
2
1
1
0
1
1
0
1
1
0
0
1
2
0
1
0
1
2
1
1
2
2
1
1
1
1
1
0
2
0
2
0
1
1
2
1
0
1
1
1
2
1
1
1
0
1
2
1
1
1
0
1
1
3
1
1
1
1
0
2
2
1
0
1
0
1
1
1
1
0
0
1
1
2
0
2
1
0
1
0
0
0
2
1
1
2
1
1
1
1
1
0
0
1
1
2
2
0
2
1
1
1
3
2
2
1
1
1
2
2
2
1
1
1
2
0
1
1
1
1
1
0
1
2
0
1
1
1
0
2
0
1
0
0
2
2
0
2
1
1
2
2
0
1
2
2
1
2
1
2
1
2
0
2
1
1
0
1
1
3
1
1
1
1
0
0
1
2
2
1
2
1
2
1
1
0
0
1
1
1
1
1
1
0
0
2
1
1
2
1
1
1
1
1
1
1
0
2
1
0
1
1
2
1
0
1
1
1
1
1
1
1
0
2
1
2
1
2
0
1
0
1
1
2
0
1
1
1
1
1
1
1
1
0
1
0
1
1
0
1
2
1
1
1
2
1
1
1
0
1
0
2
0
1
1
1
1
0
1
3
1
0
0
1
1
1
0
0
1
0
2
0
1
1
1
1
1
2
2
1
2
1
2
1
1
2
0
1
1
1
2
2
1
1
1
1
1
0
1
2
2
2
2
2
1
0
0
1
2
1
1
2
2
2
2
1
0
1
2
2
2
1
0
0
2
1
1
2
1
1
0
0
1
0
1
1
2
1
1
1
0
1
1
1
2
1
1
2
2
0
1
0
1
0
1
1
1
1
2
1
1
0
1
0
0
1
2
2
2
0
1
1
1
1
0
1
1
1
1
0
1
0
1
2
2
1
1
2
2
0
1
2
1
1
1
0
1
1
0
1
0
0
2
1
1
2
1
1
1
1
2
0
1
0
1
0
1
1
1
1
1
1
0
1
0
2
1
1
2
1
2
1
1
2
1
1
1
1
2
2
1
1
1
1
0
1
1
1
1
1
0
1
0
1
1
0
1
2
1
1
1
1
0
1
2
1
0
1
1
1
1
2
0
0
1
0
2
1
2
2
2
2
1
1
1
1
1
2
2
0
2
2
2
1
0
1
1
1
1
1
2
1
1
0
2
2
1
0
0
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
0
1
2
0
2
4
1
2
1
1
2
1
0
1
1
1
1
0
2
2
1
2
0
1
0
1
1
0
1
0
1
0
0
1
2
1
2
1
4
1
1
2
0
1
0
1
1
2
1
0
1
1
1
0
0
1
2
1
1
1
2
1
1
1
1
1
1
0
1
0
1
1
0
1
0
1
0
1
1
2
2
1
2
2
2
0
0
0
2
1
0
2
1
4
2
1
2
1
0
1
2
1
2
1
0
1
1
2
0
1
0
1
1
0
0
1
1
1
0
2
1
2
1
0
1
1
1
1
2
0
1
1
1
2
2
1
1
1
1
1
1
1
0
2
0
1
2
0
0
1
1
2
0
1
0
1
1
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
0
1
2
1
1
1
0
1
2
1
1
0
1
2
1
1
1
1
1
1
1
2
1
1
0
1
1
1
0
1
0
0
1
1
1
2
0
1
1
0
2
1
0
2
2
1
1
0
1
2
1
1
1
1
2
2
1
0
1
1
1
0
1
1
2
1
1
1
0
1
0
2
1
1
1
1
2
1
3
1
0
1
1
3
0
1
2
1
1
1
2
1
1
1
0
1
2
0
2
1
0
0
1
1
0
1
1
1
1
1
0
1
1
1
1
0
2
1
1
1
1
1
0
0
1
1
1
1
1
1
1
0
1
1
1
0
0
2
1
1
1
0
1
0
1
0
1
1
1
1
0
1
1
1
2
2
1
1
2
0
1
1
1
2
1
1
1
3
1
5
0
1
1
1
1
2
2
2
1
1
1
1
1
1
0
1
0
1
2
1
1
2
0
1
1
1
1
2
0
1
1
1
1
2
1
1
1
2
0
2
1
1
1
0
2
0
2
1
1
1
1
1
2
1
2
1
1
0
0
1
1
1
2
1
0
2
1
1
1
0
0
2
1
1
1
2
0
0
1
1
2
1
1
2
1
2
1
1
1
1
2
1
2
1
2
1
0
2
2
1
1
0
0
1
0
1
2
1
1
1
2
1
1
0
1
1
1
0
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
2
0
1
1
2
0
1
1
1
1
2
1
2
2
1
0
1
1
0
1
1
0
1
1
3
1
3
2
4
1
0
2
2
1
0
1
1
1
1
1
2
0
1
2
0
1
1
1
2
2
0
1
1
1
1
1
0
0
1
1
0
1
1
2
2
3
0
2
2
0
0
0
1
2
1
2
1
1
0
0
1
1
0
1
2
1
2
1
0
1
1
1
2
1
0
1
2
0
1
1
1
1
1
1
0
1
2
1
1
1
1
2
2
1
1
0
0
1
1
1
1
2
0
1
0
1
1
0
3
1
1
1
2
2
0
1
2
1
2
0
2
1
1
2
1
1
1
2
1
1
0
1
1
1
1
1
1
1
1
2
0
1
0
1
2
1
1
1
1
0
2
0
0
0
1
2
1
1
1
3
0
1
1
1
2
0
1
1
2
1
1
1
1
2
1
2
2
1
0
1
1
0
0
0
1
1
1
2
2
2
1
1
1
1
1
0
2
2
1
0
1
1
1
1
0
2
1
2
1
0
1
2
1
1
2
0
1
1
2
1
1
1
1
1
1
0
1
2
1
1
1
2
1
0
0
0
1
0
2
1
1
1
1
1
1
1
1
2
1
1
2
0
2
1
1
1
2
1
1
1
2
2
0
2
0
0
2
0
1
1
1
1
1
1
1
2
1
0
1
0
2
1
1
2
0
0
1
1
1
1
1
2
1
2
0
2
0
2
1
0
1
1
1
0
2
0
0
1
2
1
1
1
1
0
1
1
0
2
1
1
1
0
1
0
1
1
0
1
2
2
2
2
1
2
1
1
2
1
1
1
0
2
1
1
0
2
2
3
1
1
2
1
0
1
0
0
0
1
1
2
0
1
2
0
2
2
1
1
1
1
0
1
1
1
0
1
1
2
1
1
1
1
2
1
2
2
0
2
1
0
2
1
1
0
1
2
1
1
2
1
1
0
1
2
0
1
1
1
1
0
1
1
0
2
1
0
1
0
0
1
0
1
1
0
0
0
1
1
1
0
1
2
1
2
1
2
1
2
1
1
2
1
1
1
0
1
1
1
1
0
1
1
1
1
1
1
0
1
2
2
2
2
1
2
1
0
1
2
1
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
1
0
0
1
1
1
0
1
1
0
2
1
0
0
1
1
1
2
1
1
1
1
1
0
1
1
2
1
1
1
1
2
1
1
1
1
1
1
2
1
1
0
1
1
1
0
2
0
2
1
0
1
0
0
1
1
1
0
1
1
1
1
1
1
1
1
2
0
1
2
2
1
0
1
1
0
1
1
1
2
0
0
2
2
2
1
2
1
2
1
2
1
3
2
1
1
1
0
2
1
1
1
2
1
2
1
0
1
2
1
1
1
1
2
1
0
1
1
1
2
0
0
1
1
2
1
1
1
1
2
1
1
1
1
1
1
2
0
1
0
2
1
1
1
1
1
1
0
2
2
0
1
1
1
1
1
1
1
1
1
0
2
1
2
1
1
1
2
2
2
2
1
0
1
2
2
0
2
1
2
1
2
1
0
1
1
2
0
1
2
2
1
0
1
1
1
1
2
1
0
1
1
0
0
1
2
1
3
1
1
2
2
0
1
2
0
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
0
1
1
1
1
0
1
1
2
2
0
1
1
1
2
1
1
1
1
0
1
0
1
1
0
1
1
1
0
0
0
0
1
1
1
2
1
1
0
1
1
1
1
1
1
1
1
2
1
0
2
1
1
1
2
2
0
1
0
1
2
1
0
2
0
0
0
1
0
1
1
3
0
1
2
1
2
0
1
1
0
0
1
1
2
0
1
2
0
1
0
1
1
2
2
1
2
2
2
1
1
1
0
2
1
0
2
2
1
2
0
1
1
1
1
4
0
1
1
1
1
0
1
1
0
1
1
1
1
2
1
1
1
1
1
2
1
2
1
2
1
1
2
0
1
1
2
2
0
0
0
1
1
1
2
1
1
1
1
1
1
1
0
1
1
1
0
2
1
1
2
1
0
1
0
1
1
1
2
0
1
0
1
2
1
1
1
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
0
1
1
0
1
0
0
1
1
2
1
1
1
1
1
1
0
2
1
1
1
2
1
2
1
1
1
1
1
3
2
1
1
0
1
1
0
1
1
1
2
1
2
1
1
2
1
2
1
1
2
1
1
0
1
0
0
1
2
1
0
2
1
1
0
1
0
0
1
1
1
1
3
2
0
1
1
2
1
1
1
1
2
1
0
0
0
0
2
2
0
2
1
2
1
1
2
1
2
2
1
2
2
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
2
2
0
1
2
1
2
1
1
1
1
0
1
1
1
1
2
1
0
0
1
1
1
1
0
0
2
1
2
1
1
1
2
1
1
1
1
0
0
0
0
1
2
1
2
2
1
1
1
1
1
1
0
2
1
0
1
1
1
0
2
2
1
1
1
2
1
2
0
0
1
1
1
2
1
2
2
1
1
1
2
0
2
0
2
2
2
2
1
1
1
2
1
0
1
1
1
0
1
2
1
1
1
0
2
2
1
1
1
3
1
2
1
1
2
1
1
1
2
0
1
1
1
1
0
2
2
1
1
0
1
1
1
1
1
1
1
1
0
1
1
2
2
2
1
1
0
1
1
1
1
1
1
1
0
1
1
2
0
2
0
2
0
1
1
0
0
1
1
2
1
1
1
1
0
2
1
1
1
1
1
1
1
0
1
2
1
1
2
1
2
2
0
1
0
1
1
2
1
2
1
0
1
1
1
1
2
1
0
4
0
1
1
2
1
1
1
1
0
1
1
2
1
1
2
1
0
1
2
1
1
1
1
0
0
0
1
1
0
1
2
1
1
0
2
1
1
2
1
0
1
1
1
1
2
1
1
1
1
1
1
2
1
0
1
0
1
1
2
1
2
1
1
0
0
0
1
1
1
1
1
0
1
1
1
1
0
1
1
2
1
1
0
2
0
2
0
1
2
1
1
1
2
1
1
1
1
1
1
1
1
0
2
0
1
1
2
0
1
0
0
2
0
2
0
1
7
1
1
3
1
1
0
1
1
1
1
1
2
3
1
1
2
1
1
1
1
0
2
1
2
2
1
1
1
0
0
1
1
0
1
1
1
1
1
1
2
1
1
2
1
1
1
0
3
0
0
1
1
0
1
1
1
1
1
0
1
1
2
1
0
2
0
1
1
1
1
1
2
1
0
0
3
1
1
1
1
1
2
2
0
2
1
2
1
1
1
1
1
1
0
1
1
2
0
1
1
1
1
1
2
0
2
2
1
1
0
1
2
1
1
2
1
1
2
1
2
0
1
1
1
2
1
1
1
0
1
1
1
0
1
2
1
0
1
0
2
2
1
1
2
1
2
1
1
1
0
0
0
1
1
1
1
2
1
1
1
0
1
1
1
0
0
3
1
0
0
0
1
1
1
1
3
1
1
1
2
0
0
1
1
1
1
1
1
2
0
2
1
2
2
2
1
1
1
1
1
0
2
1
2
1
1
2
1
1
0
1
1
1
1
1
1
2
2
1
2
1
1
1
2
3
1
1
1
2
1
1
0
1
1
1
0
1
0
1
1
0
1
1
1
1
1
1
2
0
0
0
1
1
1
1
1
1
0
1
2
0
1
2
2
1
2
1
0
1
0
2
1
1
1
0
1
1
1
1
1
2
1
2
2
0
1
1
2
1
0
0
0
1
2
0
1
1
1
1
1
1
2
1
0
1
1
1
1
1
0
0
2
1
0
1
2
2
0
1
1
1
2
2
0
1
0
1
1
1
1
2
0
1
1
1
1
1
1
1
1
2
1
2
3
2
0
0
0
2
0
0
1
2
0
1
0
0
3
1
1
2
1
2
0
1
1
2
1
1
1
1
0
2
2
1
1
0
1
1
1
0
1
1
0
1
1
1
1
0
0
1
0
1
1
2
0
1
1
1
0
0
1
2
0
1
0
1
1
1
2
1
1
1
1
0
2
1
2
2
1
2
3
2
1
1
2
0
1
2
1
1
1
1
2
1
1
1
2
0
1
2
1
2
2
1
1
2
1
2
1
1
1
2
1
1
3
1
2
1
2
1
2
0
1
1
0
1
2
1
1
2
1
2
1
1
1
1
3
0
1
2
0
2
1
1
0
1
0
1
1
2
0
2
1
1
1
1
1
0
2
3
0
2
2
1
1
1
1
1
1
0
2
1
1
1
1
1
1
2
2
2
1
0
0
1
0
1
2
1
0
1
1
0
1
0
2
1
1
1
2
1
1
2
1
1
2
0
0
2
1
1
1
0
1
2
0
2
1
2
2
3
0
1
1
1
0
1
0
1
1
1
1
1
1
2
1
1
0
1
1
0
0
2
1
1
0
1
1
1
1
1
1
0
1
1
2
0
1
0
1
2
2
0
1
2
1
1
0
1
2
2
2
1
1
3
1
1
1
1
1
2
1
1
2
0
1
1
0
2
1
2
2
2
1
1
1
1
1
0
0
1
0
1
2
1
2
1
2
0
2
1
0
1
1
1
1
2
1
1
2
1
0
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
2
1
0
1
2
0
1
1
1
2
0
0
1
1
1
0
1
0
2
1
1
1
2
2
1
1
1
1
0
1
0
0
2
1
0
1
2
2
1
0
0
1
2
4
1
0
2
2
1
2
0
1
2
0
1
2
1
1
1
0
0
0
0
2
1
1
2
1
0
0
2
0
1
1
0
1
1
0
2
1
1
2
1
2
1
1
0
2
0
1
2
1
1
1
1
2
1
1
0
1
1
0
1
0
0
1
1
2
1
2
1
1
0
1
1
1
1
1
1
2
2
1
0
1
1
1
1
1
0
0
2
1
0
2
2
0
1
1
1
2
1
2
2
2
0
1
1
1
2
1
2
1
1
1
1
1
1
1
0
2
1
2
1
2
1
1
0
1
0
2
1
0
2
2
1
2
1
1
1
1
1
1
1
0
2
1
1
1
0
2
2
4
1
2
1
1
1
2
2
1
2
1
1
1
1
0
1
1
1
1
2
1
1
0
0
1
1
1
1
2
1
1
0
1
0
1
1
1
1
1
1
0
2
1
2
2
1
1
2
1
1
0
1
1
1
2
2
1
1
1
1
0
1
0
1
1
1
1
1
1
0
1
1
1
2
2
1
2
0
2
0
2
0
2
2
1
0
2
1
0
1
1
0
1
0
2
1
2
1
1
2
1
1
0
2
1
2
2
1
0
1
1
2
1
2
1
1
1
1
2
4
2
2
1
0
0
1
2
3
2
1
2
1
1
2
1
1
1
1
2
2
1
1
0
1
1
0
1
2
0
1
1
2
1
2
1
1
2
0
2
0
1
1
2
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
2
1
1
2
1
1
1
0
1
1
2
1
2
1
2
1
2
1
0
0
0
0
1
2
1
0
1
0
0
0
0
1
2
1
0
2
1
3
0
1
2
0
2
0
1
1
1
2
2
6
1
0
1
0
1
0
0
2
1
2
1
1
0
1
0
2
1
2
2
2
1
1
2
1
2
1
1
0
2
1
1
1
1
0
0
0
1
0
0
1
1
3
1
2
1
0
1
1
0
1
2
1
2
2
1
1
1
1
1
1
1
2
0
1
0
1
1
1
1
1
0
2
2
2
1
1
2
2
1
0
2
3
1
1
2
2
1
0
0
2
0
0
1
1
1
1
1
0
0
1
1
1
0
1
1
1
2
0
1
1
1
1
1
2
0
1
1
0
1
1
0
0
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
1
3
0
2
1
0
1
2
2
1
2
2
1
1
1
2
1
1
1
0
0
0
1
2
2
3
0
1
0
1
2
0
0
0
1
2
1
1
1
0
1
1
1
2
2
2
0
0
2
1
1
1
1
0
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
0
1
1
0
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
0
1
2
0
1
1
2
0
0
1
1
1
1
0
1
1
1
1
1
1
0
1
1
1
1
2
0
2
1
2
1
2
1
1
2
1
1
0
1
1
1
1
2
0
2
1
5
1
0
1
1
2
2
1
1
1
1
1
2
0
2
1
0
1
1
2
1
1
1
1
1
1
2
1
1
1
0
1
0
1
0
2
0
3
0
1
0
0
1
2
1
2
2
1
2
1
2
2
2
1
0
2
1
2
1
1
1
0
1
1
1
2
1
2
2
1
1
1
0
1
0
1
2
1
0
2
1
0
1
2
1
1
1
1
1
1
1
0
2
2
1
2
1
1
0
1
2
2
2
1
1
1
1
1
1
1
2
1
2
1
2
0
1
1
1
1
1
1
2
1
0
2
1
2
2
1
2
1
1
2
1
0
1
1
0
1
2
1
2
0
1
1
0
1
1
2
0
1
1
2
2
0
1
1
1
1
1
0
0
2
2
1
1
1
2
0
1
1
1
1
1
2
2
0
0
1
1
1
1
2
2
1
0
1
0
1
1
1
2
0
1
1
2
0
1
1
2
1
1
1
1
0
1
1
2
1
1
1
0
0
1
1
2
1
1
0
1
2
0
0
0
1
1
1
2
1
0
1
1
1
1
1
2
1
0
0
0
0
1
0
2
1
0
1
1
1
1
0
0
1
0
1
1
0
2
2
1
0
1
1
1
1
0
2
2
0
1
1
1
1
2
1
1
2
2
0
1
1
2
2
1
2
0
2
1
1
1
0
0
0
1
0
2
0
1
1
1
1
1
1
0
0
2
1
0
1
2
1
0
0
2
1
2
1
0
1
2
1
1
1
2
1
1
1
0
1
1
1
1
1
0
1
0
2
1
1
1
1
1
1
1
1
1
0
1
0
2
0
1
1
1
0
1
1
1
1
0
0
2
0
1
2
1
0
1
1
2
1
1
2
1
1
1
2
0
1
1
1
2
1
2
1
1
0
1
0
0
2
0
1
1
1
1
1
1
1
0
1
0
2
1
0
1
0
1
1
0
0
0
1
2
1
0
1
0
1
2
1
1
2
1
2
0
2
1
2
1
1
0
3
1
2
2
1
2
2
0
1
1
1
1
1
1
1
1
2
2
1
1
0
1
0
0
1
0
1
2
2
1
1
1
1
1
1
0
1
2
1
1
0
1
0
1
2
1
2
1
1
0
1
1
1
1
1
2
1
0
2
0
1
0
2
1
1
1
1
1
1
2
2
1
1
1
1
1
0
2
0
0
0
2
1
2
1
1
1
1
0
1
0
2
2
0
1
0
2
0
1
1
1
1
0
2
0
1
1
0
2
1
1
0
1
0
1
1
1
0
0
0
1
1
2
1
2
0
2
2
2
1
1
1
1
2
0
1
2
1
1
1
2
2
2
0
0
1
0
2
0
1
1
1
0
1
1
1
0
2
1
1
0
2
1
0
1
0
0
0
1
0
1
1
0
1
0
1
1
1
0
0
0
2
2
1
0
2
2
1
1
2
1
2
1
1
1
7
0
1
1
1
1
1
0
1
1
2
0
1
1
1
0
0
1
1
0
1
1
1
1
1
1
1
1
1
0
1
2
0
2
1
1
0
1
1
2
0
1
1
1
1
0
1
0
2
0
1
1
1
2
0
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
1
1
2
0
0
1
1
0
0
1
2
1
1
1
0
1
0
1
1
1
1
1
1
1
1
0
2
2
2
1
0
1
0
1
1
2
1
1
2
1
1
2
0
1
2
0
2
0
0
1
1
2
1
2
0
1
1
1
2
2
1
1
2
2
1
2
1
1
1
1
1
2
1
1
2
1
1
2
1
0
1
2
1
1
1
1
1
0
1
0
2
1
0
0
0
1
0
2
2
1
1
1
0
0
0
2
0
1
1
1
2
1
2
1
2
2
1
1
1
1
2
1
1
2
1
1
1
2
1
2
1
0
0
1
1
1
1
1
1
2
2
1
1
0
1
1
0
2
1
1
0
1
2
0
1
1
1
1
1
1
1
2
3
2
2
0
1
1
1
1
1
1
2
0
1
1
2
1
1
2
1
1
1
2
0
0
0
1
1
1
1
1
1
0
1
0
1
2
1
1
1
0
2
1
1
1
1
1
1
0
1
3
3
2
1
1
2
1
1
0
1
1
1
0
0
0
0
0
1
0
1
1
0
1
2
2
1
1
1
0
2
1
1
2
2
1
0
1
1
1
0
2
2
1
1
0
1
1
2
1
2
1
1
1
1
2
2
1
1
1
0
1
1
1
2
1
1
2
0
1
1
0
0
1
1
1
1
3
1
0
1
0
0
1
1
0
1
0
1
1
2
1
1
0
2
0
0
1
1
1
1
2
1
1
1
1
2
1
1
0
1
0
0
1
1
1
1
2
1
2
1
1
2
1
1
1
2
1
1
0
0
2
2
1
1
2
1
1
2
2
2
1
2
1
2
1
0
1
2
1
1
2
1
0
2
0
1
1
2
2
1
1
0
1
0
1
1
0
1
1
0
1
1
2
2
1
1
0
0
2
1
0
4
1
0
0
2
2
1
1
2
1
1
1
1
1
1
0
1
3
1
1
0
1
2
1
0
0
0
1
0
1
2
1
0
0
2
2
2
0
1
1
1
1
0
1
2
1
1
1
1
1
2
0
2
2
1
1
0
1
1
1
1
2
1
1
2
2
1
2
2
0
1
1
1
2
1
1
2
1
1
1
0
0
1
2
2
1
1
0
1
2
1
1
2
1
1
1
1
1
2
2
1
1
2
1
0
2
1
1
2
1
1
1
0
1
1
1
1
1
1
1
0
1
0
1
2
0
1
1
0
1
1
2
1
1
1
1
0
1
1
2
1
0
1
1
1
1
0
1
1
0
1
0
1
1
1
1
0
1
1
2
1
2
1
2
1
2
2
0
2
1
2
1
0
1
2
2
1
1
0
2
1
3
1
2
1
1
1
1
0
1
2
1
1
0
1
0
2
1
3
1
1
0
1
0
1
1
1
0
0
2
2
2
1
1
2
1
1
1
1
1
1
2
2
2
1
0
2
1
2
1
0
0
0
1
2
0
1
1
1
1
1
1
1
1
0
1
1
1
2
1
2
0
0
2
1
1
1
0
1
1
0
0
1
2
2
2
2
0
2
1
1
1
2
1
0
0
1
1
1
2
0
0
1
2
1
0
1
1
2
1
1
1
0
1
1
2
0
1
1
0
1
2
1
2
0
0
0
1
1
1
1
1
2
1
0
1
2
0
0
2
2
0
0
1
1
0
5
1
1
1
1
1
1
1
1
1
1
0
2
2
2
1
1
1
1
0
1
3
0
1
0
1
1
1
1
2
1
1
1
2
1
1
2
0
0
1
1
1
1
1
1
1
0
2
2
1
1
1
1
2
0
2
2
1
1
2
1
0
1
0
1
2
2
1
1
2
1
0
0
1
2
1
1
1
0
1
1
0
0
1
1
2
0
1
1
1
0
2
2
2
1
1
1
1
0
1
1
1
2
1
1
0
1
0
2
1
0
2
0
1
1
0
2
1
1
1
0
3
1
2
1
0
1
2
1
1
0
1
2
1
1
1
2
0
1
0
1
2
1
2
0
2
1
1
1
1
1
1
2
2
2
0
2
2
2
1
2
0
1
2
2
2
2
1
2
1
1
2
1
1
0
1
1
1
1
0
1
0
1
1
3
1
2
0
0
1
2
2
1
2
2
1
1
1
1
1
1
2
1
1
1
0
1
1
0
0
2
1
1
1
1
0
1
1
1
1
1
1
1
2
1
0
1
1
0
1
2
1
1
0
0
1
1
1
1
2
1
0
1
0
1
1
1
2
0
1
2
0
1
1
1
5
0
1
2
1
1
2
1
1
1
2
1
0
1
1
2
0
1
2
1
2
0
0
1
0
1
1
1
1
2
2
1
2
1
0
1
2
0
2
1
1
2
1
1
2
0
0
0
0
2
0
2
1
0
1
2
1
2
1
1
0
0
1
0
1
1
0
1
1
1
0
0
1
1
2
2
0
1
0
1
1
1
0
0
1
1
1
1
1
1
1
1
1
2
2
1
1
2
2
0
1
0
1
2
1
2
1
2
1
1
0
1
1
1
1
1
2
0
0
3
2
2
1
2
1
0
1
1
1
1
2
0
0
0
1
1
1
1
2
2
0
2
1
1
1
1
0
1
1
1
1
1
2
1
1
0
1
1
2
1
1
1
1
0
0
1
3
1
1
0
2
1
2
1
1
0
0
1
1
1
1
2
1
2
2
1
1
1
0
1
1
2
1
2
0
1
2
1
2
1
1
0
1
0
2
1
1
0
1
1
2
1
2
1
1
1
2
1
2
0
0
2
1
2
2
1
1
1
2
1
1
0
2
0
2
1
0
2
1
0
2
1
1
1
0
0
0
1
1
2
2
2
2
0
1
1
2
2
0
1
1
0
0
1
1
1
0
1
0
1
1
2
1
2
0
2
1
1
1
0
1
0
0
1
0
1
0
1
1
1
2
0
1
2
1
0
1
1
2
1
1
1
2
2
0
0
2
1
1
1
0
1
1
1
1
1
1
2
1
2
1
1
1
1
0
2
1
1
1
2
1
0
1
0
0
1
0
2
1
1
2
0
0
1
1
0
1
0
0
1
1
2
1
0
0
1
2
0
1
1
2
0
0
0
2
1
1
1
1
1
1
1
0
1
2
2
0
2
1
1
2
1
1
1
1
1
1
1
2
1
0
1
2
0
1
2
1
2
0
2
1
0
2
0
2
1
1
1
0
2
1
0
2
2
1
2
0
2
1
1
1
2
0
1
1
1
2
1
2
0
1
0
1
1
1
1
1
1
1
2
1
1
1
2
1
0
1
2
2
2
1
2
1
1
3
2
2
1
1
1
0
1
1
1
0
1
1
1
1
1
1
0
1
1
1
1
2
1
2
0
2
1
1
0
1
2
2
0
1
1
1
1
1
0
1
2
0
1
0
1
1
2
1
1
2
1
2
2
2
1
0
0
2
1
1
1
2
1
1
1
2
1
2
1
1
0
1
1
1
1
1
1
1
1
1
1
2
0
1
0
2
1
1
1
0
2
1
1
1
0
1
2
1
1
1
1
1
2
1
0
0
0
1
0
0
0
0
2
1
1
2
1
1
0
0
0
1
2
2
2
1
0
1
0
1
1
0
2
0
1
1
1
2
1
2
1
1
0
1
1
2
1
0
1
1
1
1
1
1
1
1
1
2
1
0
1
1
1
1
0
1
2
1
1
1
2
1
1
2
2
2
1
1
1
1
2
0
1
1
2
0
0
1
2
1
1
2
0
1
0
0
0
1
0
1
1
0
4
1
1
1
0
2
1
1
2
1
1
0
1
1
0
2
1
2
0
2
0
1
2
1
1
0
0
1
1
2
1
0
2
1
1
1
1
2
1
2
1
2
1
1
1
1
1
0
0
2
1
0
1
1
1
0
2
0
0
2
2
1
0
1
1
2
1
1
1
1
1
0
2
1
1
1
2
0
1
2
1
1
2
2
1
1
1
1
2
1
1
1
0
1
1
1
1
2
1
1
1
0
1
2
1
0
1
1
1
2
0
0
1
1
1
1
1
1
1
2
1
2
1
0
1
1
2
0
0
0
1
1
0
2
1
0
0
0
0
1
0
1
1
1
1
1
1
3
2
1
2
1
1
1
1
2
1
1
1
0
0
1
1
1
1
1
0
2
1
1
1
0
1
1
0
0
1
0
1
2
1
0
1
2
2
2
1
0
1
0
2
2
1
1
1
2
1
1
2
2
1
1
1
0
2
0
2
1
1
1
1
1
1
1
2
1
1
1
2
2
0
1
1
1
1
1
1
2
0
1
1
1
0
1
2
2
1
1
1
1
1
1
0
2
1
1
1
1
2
2
1
2
1
1
2
1
1
1
0
1
1
2
1
2
2
1
0
1
1
1
0
2
1
1
1
2
1
1
1
0
1
1
1
1
2
1
1
2
0
1
1
1
0
1
1
0
2
1
1
1
1
2
1
2
0
1
2
1
1
1
1
2
2
1
1
1
1
1
0
1
1
1
0
2
1
1
0
0
2
1
1
2
2
1
1
0
0
2
2
2
2
2
1
0
1
1
2
0
1
2
1
2
1
1
1
4
1
1
0
0
0
2
1
2
0
1
1
1
0
0
2
2
1
1
1
0
1
0
0
1
0
1
2
1
1
2
1
2
1
1
0
0
0
1
0
1
2
1
2
2
1
1
2
1
0
1
0
0
0
1
1
1
2
0
1
2
0
1
0
1
1
2
1
2
1
1
2
1
2
2
0
1
1
2
2
1
1
2
1
1
1
1
1
0
1
0
0
2
1
0
1
1
4
1
1
1
1
1
1
0
2
2
1
1
1
5
0
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
1
0
0
1
1
1
2
1
2
1
2
1
0
2
0
2
0
1
2
2
1
1
1
1
1
2
0
1
1
2
1
1
2
2
1
0
2
2
0
2
0
2
0
0
2
1
2
1
0
1
1
1
2
1
2
1
1
1
1
2
1
0
0
1
1
1
1
2
1
1
0
0
0
1
1
1
1
1
1
2
1
0
0
1
2
1
1
1
1
0
2
1
2
1
1
1
0
0
1
0
0
0
1
1
0
0
1
2
1
1
1
2
1
1
1
2
1
1
1
2
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
0
1
2
0
0
1
1
1
2
1
0
2
2
1
0
0
0
2
1
0
1
1
1
1
1
2
1
0
1
1
2
1
1
1
1
1
1
1
0
2
0
1
1
2
1
0
1
0
2
1
0
2
1
2
1
1
1
1
1
2
2
1
2
2
1
1
1
1
1
0
0
1
2
1
1
1
1
1
1
2
1
1
0
0
1
1
1
2
1
0
2
2
1
0
1
1
2
1
2
1
2
0
0
1
0
1
0
1
1
2
1
1
0
1
0
1
1
2
2
3
1
2
1
1
2
2
2
1
0
1
1
0
1
1
1
2
1
0
1
1
1
1
0
2
1
1
1
1
1
1
2
1
2
1
0
1
1
1
1
1
2
1
1
1
1
4
1
1
2
1
1
1
1
1
0
2
1
2
0
2
2
2
1
2
0
1
2
1
2
2
1
2
1
1
1
4
1
1
1
1
2
1
1
0
1
0
1
1
1
1
2
0
2
1
1
3
0
1
2
0
1
2
0
1
1
1
1
2
2
1
0
1
2
0
0
1
1
0
1
1
1
2
1
1
2
2
1
0
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
0
1
0
1
2
1
1
1
0
0
1
1
2
1
1
0
1
1
1
2
2
0
1
0
1
1
0
1
1
1
1
1
1
0
2
1
2
0
2
1
0
0
1
0
2
0
0
1
1
3
2
0
2
0
1
1
1
0
2
2
2
1
1
1
1
1
1
0
0
2
1
1
0
1
1
2
1
2
1
0
1
2
1
1
1
2
1
0
1
1
1
1
1
2
1
1
2
1
1
1
1
0
1
1
1
1
1
0
0
1
1
1
1
1
1
1
1
0
0
0
1
0
1
1
2
1
2
1
0
1
1
2
1
1
0
0
1
2
1
0
1
0
1
0
2
2
2
2
2
1
0
1
1
1
1
1
1
4
2
2
1
2
1
1
1
2
1
0
0
1
1
1
1
2
1
0
2
1
1
2
1
1
1
1
0
1
1
0
1
0
0
1
1
2
1
2
0
2
0
1
1
2
1
1
0
1
0
1
0
2
2
2
1
1
2
2
1
1
2
2
3
0
1
2
1
1
1
2
1
0
1
1
2
0
1
1
0
1
1
1
0
1
1
2
1
1
1
2
0
1
2
1
1
2
2
1
1
2
0
1
3
1
2
0
2
1
1
1
2
0
2
1
1
1
2
1
3
0
1
1
1
1
1
1
0
0
1
1
2
0
1
0
1
1
1
0
0
1
0
1
1
0
0
1
1
1
1
2
1
1
0
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
0
3
0
2
2
2
1
1
1
1
1
1
1
2
1
2
1
1
2
1
1
2
0
0
0
0
1
1
1
0
2
0
2
0
0
1
1
1
2
1
1
1
1
1
2
1
1
0
0
1
1
1
2
0
1
1
2
2
0
1
1
0
1
0
1
0
0
1
1
1
1
0
1
1
0
0
0
0
1
1
2
1
1
2
1
2
2
2
1
1
0
0
1
2
1
1
1
0
1
0
1
1
2
1
2
1
2
1
0
1
1
2
0
1
0
0
2
1
1
2
1
1
1
2
1
1
1
2
1
1
1
0
2
1
0
1
1
1
1
1
1
1
2
2
1
0
1
2
1
1
1
1
1
1
0
2
1
1
1
0
1
1
1
1
2
1
1
2
1
1
1
0
1
2
1
1
2
1
1
1
1
0
1
0
0
1
0
2
1
2
1
1
1
1
1
1
0
1
0
1
3
0
2
2
1
1
2
1
2
0
0
2
0
1
0
1
1
0
0
1
1
2
2
1
1
2
0
1
2
1
1
1
2
1
1
1
2
1
1
1
2
2
1
1
2
1
0
1
1
2
1
1
1
0
1
1
0
1
0
1
0
2
1
2
2
1
0
1
1
1
1
1
1
1
1
2
1
1
1
0
1
1
0
1
1
2
1
0
1
1
1
2
0
1
0
0
1
1
1
0
1
2
0
1
1
1
0
0
2
1
1
1
1
1
1
2
1
1
1
1
2
1
0
1
0
1
2
2
2
1
2
0
3
2
2
2
2
1
1
0
0
1
1
1
1
1
0
0
0
2
2
1
1
1
1
1
1
1
0
1
0
1
0
1
0
1
1
2
1
0
0
1
1
1
0
1
1
1
1
1
2
1
0
5
3
1
0
1
0
2
2
1
1
0
1
2
2
1
1
1
1
0
1
1
2
0
2
1
2
1
1
0
1
1
0
1
1
1
1
2
1
2
0
2
2
0
0
1
1
1
1
0
1
0
0
1
0
1
0
1
2
1
2
0
1
0
0
2
1
1
0
0
2
1
1
0
1
1
0
1
2
0
1
1
2
1
2
0
1
2
1
1
1
1
1
1
1
0
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
2
1
1
0
1
1
0
1
1
1
0
1
1
1
1
1
1
2
2
1
0
1
2
2
1
2
1
1
1
1
1
1
1
1
0
1
1
0
2
2
0
2
1
2
1
1
0
1
0
2
0
1
1
2
1
1
2
1
2
2
3
0
2
0
1
1
2
2
1
1
1
0
0
1
0
1
1
0
0
2
0
1
1
0
2
1
2
1
2
3
1
0
2
1
1
1
0
1
0
1
0
0
1
1
0
0
0
1
0
2
2
0
1
0
1
1
2
2
1
0
1
1
1
1
0
1
1
1
1
1
1
1
1
2
1
2
1
2
1
1
0
1
1
1
1
1
0
1
1
1
0
1
1
1
0
2
1
0
2
2
0
1
2
1
0
1
1
0
0
1
0
2
0
2
1
1
0
2
1
1
1
1
2
0
2
2
1
1
1
2
1
2
1
1
1
2
1
2
1
1
2
3
1
1
0
1
2
1
1
1
1
1
2
0
1
0
2
1
0
1
1
0
1
1
3
1
2
1
0
2
1
3
1
0
0
0
1
0
2
2
1
0
0
2
1
1
0
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
2
0
1
0
1
0
1
1
1
2
1
0
2
1
2
1
1
2
1
2
2
1
0
2
1
2
1
1
1
0
2
1
1
1
0
2
0
1
1
1
1
2
2
2
0
1
2
0
1
2
1
0
1
2
1
0
2
1
0
0
1
1
2
2
2
0
0
2
1
1
1
1
2
2
1
1
2
1
0
1
1
1
0
2
1
1
1
2
0
1
1
1
0
2
2
1
0
1
1
0
1
1
1
1
0
2
2
1
0
1
1
1
2
0
1
1
0
1
1
0
2
1
1
1
2
1
1
0
1
1
1
0
1
1
2
1
2
1
0
1
2
2
1
1
2
1
1
2
0
0
0
2
0
2
1
1
1
1
1
0
0
2
0
1
1
1
0
1
1
0
1
1
1
1
2
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
0
1
0
1
2
0
1
1
2
2
2
2
0
0
1
0
1
1
1
1
1
1
0
0
2
1
2
0
1
1
1
1
1
0
8
2
3
1
2
0
1
0
0
1
0
0
1
1
1
2
1
2
0
1
1
0
0
1
0
0
1
1
1
2
1
1
0
1
1
2
2
1
0
1
2
1
0
2
1
0
1
0
0
2
1
2
2
2
1
2
0
2
1
2
1
1
1
1
0
1
2
1
1
0
1
1
1
0
1
1
2
1
1
1
1
2
1
1
0
1
1
1
1
1
2
1
1
0
1
1
1
1
1
1
1
1
0
1
2
2
1
1
1
0
1
0
2
2
1
1
2
1
0
2
1
1
2
1
1
1
1
0
1
0
2
1
0
1
1
1
0
0
1
1
0
3
0
0
1
2
0
1
1
1
1
1
1
1
2
0
1
3
2
0
2
1
1
0
1
0
2
2
1
0
2
1
1
1
1
2
0
0
1
3
1
1
1
1
0
1
0
1
1
2
1
1
2
0
1
1
1
0
0
1
0
1
1
1
0
2
2
1
2
2
0
1
1
2
1
0
2
1
2
1
2
2
1
0
1
1
0
2
1
3
1
1
1
0
1
1
1
2
0
0
1
3
0
1
1
1
1
0
1
1
2
2
1
1
1
2
1
1
0
0
1
1
1
1
1
1
0
1
1
1
1
0
1
1
1
1
1
2
2
0
1
1
1
2
2
1
1
0
1
0
1
0
2
1
1
1
2
2
1
0
0
1
0
1
0
2
0
1
1
5
1
2
1
1
1
0
0
1
1
1
2
2
1
0
2
1
1
2
1
1
0
1
1
1
1
1
2
0
1
1
2
2
3
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
3
1
1
1
1
1
1
1
1
1
1
1
1
0
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
1
2
2
1
1
1
2
2
1
2
1
2
1
1
0
0
1
1
2
2
1
1
1
1
0
1
1
1
1
1
1
0
0
0
2
2
0
0
3
2
1
1
0
2
0
1
1
2
2
2
0
0
2
2
1
1
1
1
1
0
0
2
1
2
1
1
1
1
2
1
1
0
2
2
1
0
1
1
1
1
1
0
1
0
0
1
1
0
1
1
1
1
2
1
1
0
1
2
0
5
1
0
1
1
1
0
2
2
1
1
0
1
2
1
1
1
1
1
1
1
0
1
2
1
2
2
1
1
1
1
1
1
1
1
2
0
1
1
1
2
1
2
1
1
1
2
2
1
1
0
0
1
1
1
1
2
1
0
1
0
0
2
1
1
1
1
1
1
1
1
1
0
0
1
2
1
1
1
1
1
1
1
1
0
1
1
1
1
0
1
1
1
1
1
2
2
0
1
2
2
1
1
2
2
1
0
1
1
1
1
2
1
1
0
2
2
1
1
1
1
1
1
0
1
1
1
0
1
0
1
0
2
2
0
2
0
1
0
2
1
0
2
0
1
1
1
2
1
0
1
1
2
1
1
1
1
1
1
1
1
1
1
1
0
2
1
1
2
1
0
0
0
2
0
1
2
2
2
2
2
1
2
1
2
1
0
1
1
0
0
2
1
1
2
2
1
1
2
1
1
2
1
0
2
0
1
1
0
1
2
1
2
2
1
1
1
1
0
0
0
0
1
0
1
0
2
1
1
2
2
1
1
0
1
0
1
2
2
0
1
1
1
2
2
2
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
0
0
1
2
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
0
2
0
1
1
1
1
0
1
2
1
1
2
1
2
1
1
3
1
1
2
2
1
1
1
1
1
1
1
0
1
0
0
1
1
1
0
1
2
1
1
1
2
2
1
1
1
0
0
2
1
0
2
1
0
1
1
0
1
1
0
0
1
1
1
0
1
1
2
2
2
1
1
1
1
0
1
0
1
1
1
2
1
1
2
0
1
1
0
0
2
0
1
0
2
1
1
1
1
0
1
1
1
1
2
1
1
0
1
2
1
0
1
2
0
1
1
1
0
0
1
1
1
1
2
2
1
1
1
1
1
2
1
0
2
0
1
1
0
0
1
2
1
1
0
2
1
2
1
2
1
1
2
1
2
1
0
1
1
2
2
0
0
1
1
1
1
1
0
2
1
1
1
1
1
2
1
2
2
1
0
1
1
1
1
1
1
1
0
1
1
1
0
2
1
1
1
1
1
1
1
1
2
1
1
1
1
4
1
0
1
1
2
1
1
2
0
1
0
1
0
0
2
1
0
1
1
2
2
1
4
2
2
1
1
1
1
1
0
1
2
2
2
1
1
2
0
0
1
1
1
1
1
1
1
1
2
0
1
1
0
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
2
1
1
2
1
1
1
1
2
2
1
3
2
0
1
1
1
1
1
1
1
0
1
0
2
1
2
2
1
1
1
1
1
1
1
2
1
1
2
1
3
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
0
1
2
1
1
2
1
2
1
2
2
2
1
1
1
1
1
2
1
1
2
1
1
2
1
0
1
2
1
1
1
2
1
2
1
1
0
1
1
1
2
1
1
1
0
2
0
1
1
2
1
1
2
0
2
2
1
1
1
1
1
0
1
2
2
1
1
1
0
1
1
1
1
1
1
0
1
1
1
2
1
2
3
1
1
1
0
0
2
2
1
1
1
1
1
2
1
2
2
0
1
2
1
1
1
1
1
0
1
2
0
2
2
1
0
1
1
3
2
1
1
1
0
2
0
2
1
1
0
0
0
1
1
1
0
1
2
0
2
0
1
1
2
1
0
2
3
0
1
2
1
1
1
1
0
1
2
2
1
1
1
1
0
0
1
1
2
1
2
2
2
1
3
1
1
2
2
1
0
0
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
0
2
0
2
1
1
1
2
2
1
2
2
0
2
2
1
1
2
1
2
1
2
1
1
1
0
2
2
2
0
0
0
0
1
0
2
1
1
0
2
1
1
0
1
3
0
2
1
1
1
1
0
1
2
1
1
2
2
1
1
1
0
0
0
2
1
1
2
2
2
1
1
1
1
1
2
2
1
1
1
1
2
1
0
1
1
2
0
2
1
2
2
2
2
1
1
1
2
0
2
0
1
1
2
1
1
1
1
1
1
2
1
1
0
2
2
2
1
2
1
1
1
1
2
2
1
1
1
1
1
0
2
1
3
1
0
1
2
1
0
1
2
3
2
1
1
1
1
1
1
1
0
2
0
1
1
2
1
1
2
0
1
1
1
2
1
0
1
2
1
0
0
2
0
1
1
2
1
0
1
1
2
1
0
2
1
1
2
1
1
1
1
1
1
1
2
0
1
1
1
0
2
0
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
2
2
1
2
4
0
2
2
2
1
0
1
2
2
0
2
1
0
0
0
0
2
1
5
0
0
1
2
2
1
2
1
1
1
0
2
0
2
0
2
1
3
1
1
2
1
1
2
0
1
1
1
0
1
0
1
0
0
1
0
1
1
0
2
1
1
0
1
1
2
2
2
1
0
2
1
0
0
1
1
2
0
0
0
0
0
2
1
2
1
1
0
1
1
2
2
2
1
1
1
0
1
2
1
0
1
0
1
1
0
1
0
0
1
1
1
1
1
2
2
0
2
1
1
1
1
1
1
1
1
0
1
2
2
0
0
1
1
2
2
1
0
1
2
1
1
2
2
2
2
0
2
1
1
2
0
1
1
2
0
1
1
0
1
2
2
1
1
2
2
0
0
1
1
1
1
1
2
2
0
1
2
1
0
0
1
0
2
0
1
0
1
0
1
1
1
1
2
2
0
1
2
1
0
0
1
0
1
0
0
0
1
1
1
2
1
1
1
1
1
0
1
1
0
2
1
1
1
2
2
1
2
2
1
1
1
0
1
0
0
1
1
1
1
1
1
1
1
2
1
1
1
1
1
0
2
1
1
0
0
1
2
2
1
2
2
1
0
2
1
1
1
1
1
1
0
0
2
2
1
1
1
1
0
1
1
1
1
1
1
1
2
1
2
1
2
1
3
2
1
0
1
1
1
2
2
1
1
0
0
1
1
1
1
2
1
2
0
1
2
1
1
2
1
1
2
2
2
1
2
2
0
2
1
1
2
1
0
1
0
1
1
2
1
0
0
2
1
0
2
2
1
1
0
2
1
1
2
1
1
1
2
1
0
1
1
1
0
2
1
1
1
1
1
1
1
0
2
2
0
1
1
2
1
1
1
1
1
0
0
1
2
3
1
0
0
0
0
1
1
1
1
1
2
0
1
0
1
0
1
1
1
0
1
1
1
1
2
1
1
1
1
2
1
0
1
1
1
1
1
1
1
2
2
1
1
1
1
2
1
0
1
1
1
0
1
1
0
1
2
0
1
1
2
2
1
1
1
1
2
2
2
2
0
1
1
1
0
2
1
0
1
1
2
1
1
2
2
2
0
1
4
1
1
0
1
2
2
1
1
1
0
1
1
2
2
2
1
0
0
2
1
1
0
1
1
1
0
1
1
0
2
1
1
1
1
1
0
1
0
1
1
1
1
1
0
0
2
1
1
1
2
1
1
0
1
1
0
1
1
1
0
0
1
0
1
2
2
2
1
1
1
1
1
1
2
0
1
2
1
1
0
1
1
1
1
1
2
0
1
0
1
1
1
1
1
2
2
1
1
1
1
1
0
2
0
0
2
1
1
0
1
1
1
1
1
1
2
1
1
2
0
2
1
1
2
1
1
1
0
0
1
0
1
2
2
1
1
1
1
1
1
1
1
0
2
2
1
1
2
0
1
1
2
1
1
0
1
1
2
1
0
1
2
1
2
2
1
1
1
1
0
1
1
2
0
2
2
2
1
1
1
0
2
1
1
1
1
0
1
2
2
1
1
1
0
1
1
1
2
1
1
2
2
1
1
1
0
0
1
0
1
2
1
1
0
1
1
1
1
2
1
1
1
1
0
1
1
1
2
0
2
1
0
2
2
1
0
0
1
1
1
1
0
1
1
1
2
1
1
0
2
1
1
0
2
0
0
2
0
1
1
2
1
1
2
1
2
1
0
2
1
1
0
1
1
1
1
1
1
1
0
2
1
2
1
1
1
0
1
1
0
2
1
0
1
1
0
2
0
1
1
1
1
1
0
0
0
2
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
2
1
2
2
0
1
0
1
0
1
1
2
0
1
1
1
0
0
2
1
0
1
1
1
1
1
1
0
1
0
2
1
1
1
0
0
1
1
2
1
0
1
0
1
1
2
2
1
1
1
1
0
2
1
2
1
1
1
0
1
0
1
0
1
2
0
1
1
1
1
2
0
2
0
2
1
0
0
1
0
2
2
1
2
0
1
2
2
1
1
2
2
1
2
1
1
0
1
0
0
0
0
1
0
1
1
1
0
1
1
2
0
1
1
1
1
0
1
1
1
2
1
1
1
2
1
1
1
0
2
1
2
0
1
2
0
1
1
0
1
1
1
3
1
1
1
0
1
1
1
0
0
1
1
1
2
0
2
2
1
1
2
1
2
1
0
1
2
1
2
2
0
0
2
0
0
0
0
0
1
1
1
0
0
1
2
1
1
0
1
2
1
1
1
0
1
1
1
0
1
2
1
1
1
1
1
1
1
1
1
1
0
3
1
0
1
1
2
1
1
2
1
1
2
1
0
1
2
1
2
1
1
0
2
1
2
1
1
2
2
0
2
0
1
1
1
1
1
0
1
0
2
0
1
1
1
2
0
1
1
2
2
0
2
1
0
1
1
0
1
1
0
2
1
2
1
1
2
1
1
2
0
2
0
2
0
1
1
0
1
1
1
1
0
0
1
1
1
2
0
1
1
2
1
2
1
1
1
2
1
0
1
2
1
2
2
2
1
0
1
1
2
1
1
1
4
1
1
2
0
0
1
2
3
1
1
2
1
2
0
1
2
0
0
2
2
1
1
1
0
1
2
2
2
1
1
0
2
2
2
1
1
1
2
0
2
1
1
1
1
2
1
1
1
1
1
0
1
2
1
2
1
1
1
2
1
1
2
1
0
1
1
1
1
1
2
1
2
1
1
2
2
1
0
2
1
1
1
2
1
1
1
1
1
0
0
0
1
2
1
2
2
2
2
1
1
1
1
0
1
0
2
0
2
1
1
2
0
1
1
0
2
2
0
1
0
2
1
0
2
1
1
1
1
1
0
2
1
1
4
1
2
1
2
2
1
0
1
0
2
0
1
1
2
0
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
0
1
1
1
1
0
1
1
1
2
1
1
2
1
1
0
2
1
1
1
1
1
2
0
1
1
2
0
2
0
2
0
1
2
2
1
2
1
1
1
1
2
0
0
2
2
2
0
0
1
1
2
0
2
2
1
2
0
2
2
0
1
1
2
0
1
1
0
1
0
0
0
1
1
0
1
2
1
1
2
0
2
1
1
0
1
0
1
2
1
1
2
1
2
1
1
2
1
1
1
0
0
1
2
1
1
1
1
1
1
2
2
0
1
1
1
1
1
1
1
3
1
0
1
0
1
1
1
1
0
1
1
1
2
1
2
2
1
1
1
0
1
2
1
2
2
1
1
2
1
1
1
1
0
2
2
0
0
1
2
1
1
2
0
2
1
2
1
2
0
1
2
1
1
1
1
1
0
0
1
1
1
1
1
2
1
1
1
1
1
0
2
1
1
1
1
2
1
1
1
1
0
0
2
1
1
0
2
2
1
1
1
1
1
1
1
2
0
1
1
2
2
1
2
2
2
0
2
1
1
2
0
1
1
1
1
0
1
1
1
0
1
1
1
0
0
1
2
1
0
0
1
1
1
1
1
2
2
2
1
1
0
1
2
0
2
0
1
1
1
0
0
1
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
0
2
2
1
1
1
2
1
1
0
1
0
2
0
2
2
3
1
1
1
0
2
2
0
2
1
1
1
1
2
1
0
2
1
0
0
1
1
1
0
1
1
1
1
1
0
1
1
2
0
1
0
1
1
1
2
0
0
1
0
1
4
2
1
1
2
2
2
1
0
1
1
1
1
0
1
1
1
1
1
1
0
1
0
1
1
1
1
1
2
1
1
0
0
2
1
1
0
1
1
1
0
1
1
2
1
0
1
1
1
1
0
1
0
1
1
1
1
1
1
0
0
2
1
0
0
1
1
1
0
3
2
0
0
0
2
1
1
0
1
2
1
0
2
1
0
1
2
1
2
0
2
1
0
1
2
1
2
1
1
0
2
1
2
1
2
1
1
1
1
2
0
2
2
2
1
1
1
2
0
1
2
1
1
1
2
1
1
2
2
1
1
1
1
0
2
2
1
1
1
1
1
1
0
1
1
2
1
1
1
0
1
1
1
1
3
2
0
1
2
1
1
0
1
2
1
2
2
1
1
2
0
2
1
0
1
1
0
1
1
0
1
0
1
0
1
1
1
2
2
2
2
2
1
0
1
0
2
1
1
2
1
1
0
1
1
2
1
0
0
2
1
1
1
1
0
2
1
1
1
2
1
1
1
1
0
2
2
0
0
1
2
1
2
1
1
1
0
1
2
0
1
1
1
1
0
1
1
1
1
0
0
1
1
1
2
2
1
1
1
1
1
1
2
2
1
1
1
1
1
1
0
0
0
2
2
1
3
1
2
0
3
1
1
1
1
1
0
0
1
1
2
0
1
1
1
2
1
1
1
1
0
0
1
1
2
1
1
2
2
1
0
0
0
1
3
0
2
1
0
2
1
1
1
0
1
1
0
1
1
1
1
2
0
1
2
0
2
2
0
0
1
1
1
0
1
1
1
1
1
1
0
1
1
2
1
1
1
1
1
2
0
1
1
1
1
1
0
1
0
2
2
1
2
0
1
0
1
2
1
2
1
1
0
1
1
0
1
1
2
1
2
1
1
2
1
1
1
1
2
0
0
1
3
0
0
1
1
1
0
0
1
1
0
2
1
1
0
1
1
1
1
2
0
2
1
1
2
1
1
1
1
0
0
2
1
0
2
1
0
1
2
0
2
0
1
0
1
1
2
1
1
1
0
1
0
1
2
1
1
1
0
0
1
2
1
0
1
0
2
1
1
0
1
1
2
2
0
2
1
1
2
0
1
1
1
0
2
1
1
1
1
0
1
0
1
1
1
1
1
0
1
1
0
1
0
2
1
2
1
2
1
2
2
2
2
1
1
1
1
1
2
1
0
1
1
1
1
4
2
1
1
1
1
0
2
2
1
0
0
1
1
1
1
0
2
0
1
1
2
0
2
1
1
2
1
1
0
0
0
2
1
0
1
1
0
2
1
1
0
2
2
1
2
1
1
1
2
0
2
1
1
1
1
1
1
1
2
0
0
1
1
0
1
1
1
2
0
1
2
1
1
1
1
0
2
1
1
1
1
1
1
0
2
0
2
1
1
1
1
1
2
2
1
1
1
1
0
1
0
0
1
0
1
1
1
0
1
0
2
1
1
1
0
1
2
1
2
1
1
0
1
1
1
2
2
1
1
1
0
1
2
1
1
1
2
2
1
1
1
1
1
1
1
4
1
1
0
1
1
1
1
1
1
1
0
1
1
2
1
2
2
2
1
0
1
2
1
1
1
1
1
0
1
1
1
1
0
1
1
1
2
0
2
2
0
2
1
1
1
0
1
2
1
1
1
0
2
1
0
1
1
1
1
0
2
0
1
0
2
0
0
2
1
0
0
1
0
2
0
1
0
0
1
1
1
2
0
2
0
1
2
1
0
0
0
1
1
2
0
1
0
2
1
1
1
0
0
2
2
0
2
1
2
1
2
2
1
2
1
0
1
1
2
2
2
1
1
0
1
2
1
1
1
1
1
1
2
1
1
0
1
0
1
2
0
1
2
2
1
1
1
1
1
1
1
0
0
1
0
0
1
2
1
2
0
2
2
1
2
1
1
1
1
1
1
1
1
1
1
1
0
0
2
2
1
1
1
0
0
2
1
0
2
1
1
2
1
1
0
1
1
2
1
1
0
1
1
0
0
2
0
2
1
1
2
1
1
1
1
1
1
1
0
0
1
1
1
2
1
1
0
1
1
1
1
4
2
1
1
1
1
0
1
1
1
2
0
0
2
1
0
2
2
1
0
1
1
1
1
1
1
1
0
2
1
0
1
0
2
1
1
0
1
0
1
1
1
1
2
0
1
1
1
1
1
1
2
2
1
0
2
0
1
1
1
1
1
1
1
1
0
1
1
0
2
0
0
1
2
1
1
1
2
2
1
2
2
1
1
1
0
1
1
0
0
1
0
1
2
0
2
1
0
0
1
2
2
0
0
2
1
1
1
1
1
0
1
1
1
2
2
0
1
0
2
1
1
1
1
0
2
0
0
2
1
2
0
1
1
2
1
1
1
1
0
2
2
1
1
0
0
0
1
2
1
1
1
1
1
1
0
1
1
0
2
1
2
2
1
0
1
2
2
2
0
2
0
1
1
1
1
0
2
1
3
1
1
0
1
0
0
0
1
1
0
0
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
0
0
1
1
1
1
1
2
1
2
0
1
0
0
1
1
1
2
1
0
0
0
2
0
0
1
1
1
1
1
1
0
0
1
2
0
1
0
0
0
2
0
1
1
2
0
2
2
1
1
1
2
1
1
0
1
1
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
4
1
1
2
3
0
1
1
2
1
1
1
1
1
1
1
1
1
1
1
0
1
2
2
0
2
0
0
1
1
2
1
1
2
1
2
1
2
0
2
1
2
1
2
1
1
2
1
0
1
1
2
2
1
1
1
1
1
0
1
1
2
1
1
1
2
1
1
0
2
1
1
1
1
1
0
2
0
2
1
0
1
1
1
0
3
1
1
1
0
1
1
1
1
1
2
2
1
1
1
0
0
1
1
1
0
1
2
1
2
1
1
1
1
2
1
1
2
1
2
1
1
1
1
0
0
1
1
1
0
1
2
0
1
1
1
1
1
1
2
1
1
1
1
0
1
2
1
1
1
1
1
2
1
1
2
1
2
1
1
2
1
1
2
1
1
0
1
0
1
2
1
1
1
1
1
1
1
2
0
2
1
1
1
1
1
1
2
2
0
1
1
0
1
2
3
0
0
1
1
1
2
1
1
0
1
1
2
2
1
0
0
1
0
1
0
0
2
1
2
1
1
1
1
1
1
1
1
1
1
0
1
1
1
0
1
1
1
1
1
0
1
0
1
1
2
0
0
1
1
1
2
2
0
2
1
1
1
1
0
0
1
2
2
1
1
1
0
0
1
1
1
1
1
2
2
1
1
1
0
1
0
0
0
1
1
0
1
1
2
1
2
1
1
0
1
1
1
0
2
1
1
1
1
2
2
1
1
0
0
1
0
1
1
2
2
1
2
2
2
0
1
1
2
1
2
0
2
1
1
2
1
1
1
0
1
0
1
1
1
2
1
2
1
0
2
2
2
1
0
0
1
1
2
1
1
2
2
1
1
0
0
1
1
0
1
1
1
2
0
1
1
1
2
1
1
2
2
1
1
2
2
1
2
1
1
1
2
2
0
0
1
1
1
0
2
0
2
1
1
1
1
1
1
2
1
1
0
1
1
0
2
2
1
2
1
1
1
2
5
1
0
1
1
1
1
0
1
1
2
2
1
1
2
1
2
1
1
0
2
2
0
1
2
0
1
1
2
1
1
0
13
2
2
2
1
1
1
2
1
2
1
0
1
1
1
1
2
1
1
1
0
2
1
2
3
1
1
1
0
0
1
2
1
2
1
2
1
1
1
0
1
1
2
0
2
0
2
1
1
1
1
1
0
1
0
2
1
0
1
0
1
0
2
1
1
1
1
0
1
1
2
0
0
2
2
2
1
0
2
2
2
1
1
2
1
2
2
1
2
0
1
1
0
1
1
1
2
1
1
1
1
2
0
2
0
2
1
0
1
0
1
1
2
2
1
1
2
1
1
1
0
2
1
0
2
1
1
1
0
2
1
1
1
1
1
1
1
1
1
2
1
0
1
1
0
0
2
0
2
1
0
1
1
1
0
0
0
0
0
1
1
1
1
0
2
1
1
1
1
2
2
2
2
0
2
1
2
1
2
0
1
1
2
1
1
2
0
1
1
0
1
1
1
1
1
1
2
1
1
0
1
2
0
1
2
1
2
1
1
0
1
1
0
1
1
0
1
1
0
0
1
1
1
1
0
0
0
1
1
2
1
2
1
2
1
1
1
0
2
2
1
1
1
1
1
1
0
2
0
1
4
0
1
2
0
1
0
2
1
1
3
2
2
1
1
2
2
1
1
0
1
2
0
1
1
1
1
1
1
1
1
0
0
0
1
1
2
2
0
1
2
1
1
2
3
1
2
1
1
1
1
1
1
1
1
2
1
0
2
1
2
3
1
2
3
2
0
2
1
1
2
1
1
2
1
1
1
2
1
1
0
1
0
2
1
0
1
1
1
2
1
1
1
2
1
1
2
2
0
0
1
1
1
0
0
2
0
1
2
0
1
1
0
1
1
1
0
1
1
1
1
1
0
1
1
1
0
2
1
0
1
2
2
2
0
1
1
1
0
1
1
1
0
1
1
0
1
0
1
1
0
2
2
1
1
2
1
0
1
0
0
4
1
0
1
1
0
1
2
2
1
1
1
1
1
1
1
1
1
2
1
1
1
0
0
1
0
2
1
2
0
1
2
1
1
1
0
0
2
1
1
1
1
1
0
1
1
0
1
2
1
1
1
1
2
1
1
2
1
0
0
1
1
1
1
0
1
1
1
1
1
1
0
0
1
2
1
2
1
1
1
1
0
0
0
0
1
1
1
1
1
0
2
1
0
2
0
2
0
1
1
3
1
2
0
0
0
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
0
0
0
2
0
1
1
2
1
1
2
1
0
1
2
1
0
1
0
2
1
1
1
1
1
3
0
0
1
1
2
1
0
2
1
1
0
0
1
2
1
2
2
0
1
2
0
0
0
1
1
2
1
2
1
1
1
2
1
3
1
1
1
3
1
0
1
2
1
0
1
1
0
1
2
1
1
1
2
1
0
1
1
1
0
1
1
3
1
1
2
1
1
2
1
2
1
2
2
2
0
2
1
3
0
1
1
1
0
0
1
2
2
0
2
1
1
1
1
1
1
1
1
0
1
0
1
1
0
1
1
1
1
1
1
1
2
1
1
0
1
0
1
0
1
0
2
1
0
1
2
2
1
1
2
0
2
1
1
1
1
0
0
2
0
1
0
2
2
1
1
1
1
1
1
1
1
1
1
0
2
1
2
2
0
1
0
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
0
0
1
2
0
1
1
1
1
0
0
0
2
0
1
2
1
1
1
1
0
2
1
1
1
1
1
0
0
1
2
0
1
2
3
0
1
1
1
1
2
1
0
1
0
1
1
1
0
2
1
1
1
3
0
0
1
1
2
1
1
2
0
1
0
2
1
1
1
0
1
2
0
0
1
1
1
1
0
2
2
1
0
1
0
1
1
1
1
2
1
1
0
1
1
0
1
2
1
1
0
2
0
2
0
1
2
1
2
1
2
2
2
2
2
2
1
2
1
2
2
1
1
2
2
1
1
0
2
1
0
1
1
2
1
1
1
1
1
1
1
0
1
1
2
2
1
0
1
0
0
1
0
2
1
1
2
1
1
1
3
1
0
0
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
2
1
1
1
1
2
2
1
1
1
1
1
2
1
0
2
2
1
1
1
0
0
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
2
2
0
1
1
1
1
1
1
0
1
1
2
1
1
1
2
0
1
1
2
1
2
2
2
2
1
1
1
1
2
1
2
1
2
1
1
2
1
0
1
1
1
1
0
2
2
0
1
1
0
1
1
1
1
1
1
2
1
1
1
0
1
0
2
3
1
1
1
0
2
2
1
1
0
0
1
0
0
2
2
1
2
0
1
1
1
1
1
1
2
1
1
1
1
2
0
2
1
2
1
0
1
0
2
1
2
2
2
2
2
1
1
1
2
2
0
1
0
1
1
1
1
1
0
1
2
1
1
2
2
1
2
1
1
0
2
2
2
1
1
1
1
1
1
0
1
1
1
1
2
1
1
2
1
1
0
1
1
2
1
1
0
2
0
1
1
1
2
1
1
0
2
1
1
1
1
2
2
1
1
0
1
1
1
2
2
0
1
1
1
1
2
1
1
1
2
2
0
1
1
1
1
2
1
2
1
1
2
2
1
2
2
1
1
0
1
1
1
2
1
1
0
1
0
1
0
1
1
0
1
1
1
1
0
1
1
1
1
1
2
1
1
1
0
1
1
1
0
1
1
1
1
0
2
1
1
8
0
0
1
1
1
1
0
1
1
1
1
2
1
1
1
1
1
0
2
1
0
1
1
1
1
0
1
1
1
0
1
1
0
2
1
1
1
2
1
2
0
1
0
0
2
1
1
1
2
1
0
0
1
0
1
0
1
1
2
2
0
1
1
2
0
1
0
1
1
1
1
1
1
1
2
0
1
2
2
1
0
1
1
1
0
1
0
1
2
0
1
1
0
1
0
1
2
3
1
0
1
1
0
2
1
0
1
2
1
1
0
1
2
0
1
1
2
1
2
1
1
2
2
0
2
0
1
1
1
3
2
0
1
0
2
0
1
0
1
1
1
0
1
0
0
1
1
0
0
1
1
0
1
2
0
0
0
2
1
1
1
1
1
1
0
1
2
1
1
0
1
1
1
1
2
1
0
1
2
1
0
1
2
2
1
1
1
0
0
1
1
1
1
2
1
1
2
2
1
1
3
2
1
1
2
2
1
1
1
2
2
1
2
1
1
2
2
1
2
1
2
0
1
1
2
1
1
1
1
1
1
2
2
1
0
0
2
1
0
1
2
1
2
0
2
1
1
1
2
2
1
1
0
1
2
1
1
1
1
1
2
1
0
2
1
2
0
2
0
1
0
1
0
1
2
0
1
2
1
2
1
1
1
1
1
2
2
1
1
2
2
0
1
1
2
0
1
1
0
1
2
1
1
1
2
1
0
1
1
0
1
2
1
1
1
1
1
1
1
0
1
1
1
2
1
1
1
1
1
1
0
2
1
2
1
1
1
2
1
1
1
1
0
2
1
1
2
1
1
1
0
1
0
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
2
1
0
0
2
1
2
1
2
0
1
2
0
0
1
0
2
2
1
1
1
1
1
1
2
1
0
2
1
2
1
1
0
1
0
1
0
1
1
2
1
1
2
1
1
2
1
1
2
2
0
1
1
2
1
1
1
1
1
1
1
1
0
2
0
0
1
1
1
0
1
0
1
0
2
1
0
0
1
2
2
1
1
0
0
1
1
1
1
2
0
2
1
2
2
2
2
0
1
1
2
1
1
0
1
1
0
1
2
1
0
1
2
1
0
1
3
1
1
1
0
2
2
1
0
1
2
1
0
0
1
2
0
1
2
1
2
2
2
1
2
2
1
1
1
1
2
1
2
1
2
2
2
2
0
1
1
0
1
0
1
0
1
1
2
1
0
2
1
1
1
0
1
1
1
0
3
1
1
2
1
1
0
1
0
0
1
1
2
2
1
1
1
1
1
2
0
2
0
0
0
0
2
0
1
1
2
1
1
0
1
1
0
2
2
0
1
1
0
1
0
2
2
2
2
0
1
1
1
1
1
1
1
1
0
2
1
1
1
2
2
1
1
1
2
0
1
1
0
0
0
1
0
1
0
0
0
1
1
2
0
1
1
0
0
1
1
1
1
0
1
1
1
0
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
1
0
1
2
1
1
1
1
1
1
2
0
2
1
1
1
1
2
1
1
2
1
1
1
1
1
1
0
3
0
1
2
1
1
2
1
1
2
2
2
0
1
1
1
1
0
1
0
1
1
1
2
2
1
1
1
0
1
1
0
1
2
1
1
1
1
1
1
1
1
1
1
1
0
2
1
1
1
1
1
0
1
2
1
2
1
0
1
1
1
1
1
1
0
1
1
2
1
1
0
1
1
1
0
2
1
1
1
1
1
1
0
1
1
4
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
0
2
1
1
1
1
2
2
0
0
0
1
2
0
1
1
1
1
1
0
1
2
1
1
0
4
1
2
0
0
1
2
1
2
0
1
0
0
1
0
1
1
1
0
1
1
1
1
0
1
1
2
2
2
1
0
1
1
1
2
1
1
0
1
1
0
1
1
1
0
1
1
0
1
1
2
0
3
1
1
0
0
1
0
0
2
1
1
1
0
2
1
1
2
1
1
1
2
1
2
1
0
2
0
0
1
2
1
0
0
2
2
1
1
0
0
0
2
1
1
0
1
0
2
1
1
1
1
2
1
2
1
2
1
1
0
1
1
1
1
1
1
1
1
2
4
0
0
1
2
1
2
2
1
1
0
1
1
0
2
1
0
1
0
1
2
1
0
1
0
2
1
2
2
1
1
0
1
1
2
1
2
1
2
2
1
1
1
2
2
2
1
1
1
1
0
1
1
1
0
1
2
1
0
1
0
1
1
1
1
1
0
2
1
1
2
1
1
1
1
0
0
1
1
1
0
1
0
1
2
0
1
1
0
1
2
1
1
0
1
2
1
1
1
1
1
1
0
1
1
1
2
2
1
1
0
1
1
1
0
2
0
1
1
1
0
0
1
2
2
2
1
1
2
0
1
1
1
1
2
1
0
2
1
2
1
1
1
2
1
0
2
2
0
2
1
1
2
0
2
0
1
1
0
1
2
1
1
0
1
1
1
1
1
1
1
0
2
1
2
2
1
0
1
1
0
1
1
2
0
1
1
1
1
1
0
1
0
1
1
2
0
2
1
2
1
2
1
0
2
1
2
0
1
0
1
0
1
1
1
0
2
2
2
0
1
0
1
1
1
0
1
1
1
1
2
0
1
1
1
1
2
1
1
1
1
1
1
2
0
1
0
1
1
0
0
1
1
1
1
0
2
1
1
0
1
2
1
0
1
1
1
2
1
0
0
0
0
2
0
0
0
1
0
2
1
0
1
1
2
1
0
1
2
1
1
0
2
1
0
2
1
1
1
2
1
1
2
1
0
2
1
1
1
1
2
1
0
0
0
0
1
2
1
1
2
2
1
1
2
1
0
2
2
2
1
2
1
0
2
2
2
1
2
1
0
2
0
1
1
1
1
1
0
1
0
1
2
0
1
1
0
1
1
0
1
0
2
0
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
0
0
2
1
2
2
1
2
1
2
1
0
1
1
1
0
0
1
1
1
2
1
1
2
1
1
2
1
2
1
1
2
1
2
1
0
2
0
1
2
1
2
1
3
0
1
1
2
2
1
1
2
2
1
3
2
1
1
1
0
0
1
1
1
1
1
1
1
0
0
1
1
1
0
1
2
1
0
3
2
0
2
1
2
1
1
1
2
1
1
1
2
1
1
0
1
1
1
0
2
0
1
1
0
1
1
1
1
2
2
1
0
1
1
2
0
2
0
2
1
2
1
1
1
2
1
1
1
1
1
1
0
2
3
0
0
1
2
1
0
2
2
1
0
2
2
1
2
2
1
1
0
2
1
0
2
0
2
2
2
0
1
2
1
2
0
0
1
2
1
1
1
1
1
1
1
1
1
1
1
1
0
2
0
1
0
1
1
1
1
1
1
2
1
1
1
2
0
1
1
1
1
0
0
0
0
0
0
2
0
1
1
0
1
1
1
0
1
0
1
1
0
1
0
1
1
2
1
1
1
2
5
0
1
1
0
1
1
0
1
0
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
0
1
1
1
2
1
1
0
0
2
1
2
1
1
0
1
2
1
0
0
0
1
1
1
1
2
1
0
2
1
2
2
0
1
2
1
1
0
1
1
1
2
1
1
0
1
1
1
0
0
0
2
0
1
1
1
1
1
3
1
1
1
1
2
1
1
1
0
1
1
1
1
1
0
0
1
0
1
1
2
2
2
1
1
0
1
0
1
1
0
1
2
1
1
1
1
2
2
2
1
1
0
1
1
1
1
1
0
1
0
2
1
2
1
0
1
0
2
0
1
1
0
1
1
1
1
1
2
2
1
3
0
1
1
1
0
0
0
1
1
1
1
1
1
1
1
2
1
1
1
2
1
2
0
0
0
2
1
2
1
2
2
1
1
1
1
1
0
2
0
1
2
2
2
1
0
1
1
1
0
0
1
1
1
2
1
1
1
1
2
0
2
1
1
1
2
1
1
1
2
1
2
1
2
1
1
4
0
1
1
1
1
1
2
2
2
2
1
2
1
1
1
2
1
2
2
1
1
1
1
1
2
1
1
1
1
1
0
1
1
2
1
2
2
1
1
1
1
0
1
2
1
0
1
1
2
2
0
1
0
0
1
1
1
0
1
0
1
1
1
1
2
2
1
1
0
1
2
1
2
1
1
3
1
1
1
1
1
0
2
1
2
2
1
1
2
1
1
2
1
0
1
1
1
1
2
1
2
0
1
2
2
0
1
1
2
2
0
1
0
0
0
1
1
3
1
2
1
0
1
2
0
1
0
1
2
0
1
0
1
2
1
1
2
1
1
0
0
0
1
2
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
0
2
1
2
1
2
1
2
2
2
1
1
0
1
0
1
2
1
0
1
1
2
2
1
1
1
1
1
1
2
1
2
1
1
2
2
2
0
1
0
1
1
3
0
2
2
2
1
0
0
2
1
1
1
0
1
1
0
1
2
1
2
2
2
2
2
2
1
1
1
1
1
1
1
1
2
2
0
1
0
1
1
2
0
0
1
1
0
0
1
0
2
2
1
0
1
1
1
1
2
1
0
1
0
1
1
2
2
1
1
2
1
1
1
1
1
0
0
1
2
1
1
1
1
0
1
1
1
0
1
1
1
1
2
1
1
1
2
2
1
1
1
0
2
1
1
2
1
1
1
1
1
2
1
1
0
0
0
1
2
0
1
1
0
0
1
1
1
1
1
2
1
2
2
1
1
1
1
1
0
0
1
1
2
2
0
2
1
2
2
1
1
1
1
0
2
1
1
1
0
0
0
0
1
0
2
1
1
1
2
1
2
2
1
2
2
2
1
1
1
0
2
1
1
1
1
2
1
0
1
1
1
1
1
1
1
1
2
1
1
0
2
1
1
1
1
1
1
1
0
1
1
0
2
2
1
0
1
1
1
1
1
2
2
2
1
4
1
1
2
1
1
0
1
1
1
1
2
1
1
3
0
0
2
1
1
1
0
0
0
1
1
1
1
2
2
1
0
2
1
0
1
1
2
1
1
1
1
1
0
1
1
1
0
1
1
2
2
2
2
0
0
1
0
1
2
2
2
1
1
2
1
2
2
2
1
0
1
2
0
1
2
1
1
1
2
1
1
1
0
1
1
2
1
1
1
1
2
1
2
1
5
0
1
2
2
0
1
0
0
1
2
1
2
1
1
1
1
2
1
0
1
1
2
1
1
2
1
2
0
2
1
2
2
0
1
2
1
2
1
2
1
2
1
0
0
2
1
1
2
1
2
1
2
0
2
1
1
0
1
1
0
0
1
2
1
1
0
1
0
0
0
1
2
1
1
2
2
0
0
1
1
0
1
2
1
0
1
0
1
1
1
1
1
1
0
2
1
1
2
1
0
0
1
2
1
1
0
3
1
1
2
2
1
0
0
0
1
0
1
2
1
1
1
0
2
0
1
2
1
1
0
0
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
2
1
2
1
0
1
1
2
0
0
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
0
1
1
1
0
1
1
1
1
1
1
0
1
2
1
0
0
1
3
1
1
1
2
2
1
2
0
2
0
1
1
1
1
1
1
2
1
1
0
1
1
1
1
1
2
0
2
1
1
2
0
2
1
1
2
0
0
1
0
0
1
1
0
2
1
1
1
1
1
1
0
2
0
0
1
1
1
3
0
1
1
1
1
1
0
1
1
2
0
1
1
0
0
1
1
0
1
2
1
2
0
1
2
1
1
1
2
1
0
1
0
1
1
0
2
1
2
2
2
0
1
1
2
1
0
1
2
1
1
1
1
1
1
1
2
0
1
0
2
0
1
0
1
0
1
1
2
1
1
0
1
0
2
0
0
1
2
1
1
1
1
2
0
2
1
1
2
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
0
1
1
1
0
0
0
0
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
2
2
1
2
1
1
0
0
0
1
2
1
1
0
0
2
1
1
1
1
2
2
1
2
1
1
2
1
2
1
2
0
0
2
1
2
1
1
0
0
1
0
1
2
2
2
1
0
0
2
1
2
1
1
1
1
0
1
1
1
1
0
2
1
1
1
1
1
1
1
1
1
2
1
2
2
1
2
1
1
1
1
1
2
1
1
2
0
1
1
1
1
0
2
1
2
0
2
1
1
1
1
0
2
1
2
0
1
1
2
1
2
2
1
1
1
0
1
1
1
1
1
0
0
1
1
1
0
2
2
1
2
1
2
1
1
2
1
1
3
2
1
2
2
0
2
0
1
0
1
1
2
2
1
1
1
2
1
1
0
0
1
1
3
0
1
1
2
0
0
0
1
2
0
1
1
1
1
1
1
1
1
1
0
2
2
1
1
1
0
1
1
1
1
1
2
0
1
2
2
1
1
1
1
2
1
1
1
0
2
2
1
2
1
2
0
1
0
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
0
1
1
1
1
0
1
1
1
1
1
2
1
2
0
0
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
1
2
1
1
1
0
2
1
1
0
2
1
1
0
1
1
2
2
2
1
2
0
0
3
1
0
0
0
2
2
1
1
0
1
0
1
1
1
2
2
2
1
0
0
2
0
1
1
1
2
1
1
0
0
1
1
1
2
2
2
1
1
2
1
2
2
1
1
2
0
1
1
2
0
0
1
2
1
2
1
1
0
1
0
1
1
0
1
0
3
0
1
2
1
0
2
1
1
0
1
1
2
2
1
0
2
1
1
2
2
1
1
1
0
2
1
0
1
2
2
0
1
1
0
0
2
1
0
2
1
1
1
3
1
0
1
3
1
1
1
2
1
2
0
1
2
1
1
0
1
1
0
1
1
1
1
0
1
0
0
1
1
2
1
1
0
1
0
0
2
0
1
2
0
1
1
2
2
1
1
1
1
1
1
0
1
0
2
4
1
1
1
0
1
2
1
1
2
1
1
1
2
1
0
1
1
1
1
1
1
1
0
1
1
1
2
2
1
1
1
2
1
2
0
2
2
0
2
0
2
2
2
1
2
0
0
1
1
0
0
1
0
1
1
1
2
1
2
1
1
2
1
1
0
1
0
0
0
1
2
1
2
3
3
1
1
2
0
1
2
2
1
1
1
0
3
1
2
0
1
1
1
1
1
0
1
2
0
1
0
1
1
1
1
0
1
0
2
1
1
2
2
2
1
1
1
2
1
0
2
2
2
1
0
2
1
2
1
2
0
1
0
1
2
1
1
0
1
1
1
2
0
1
0
2
2
1
1
0
0
1
2
1
4
1
1
0
1
0
2
1
2
2
3
2
1
2
1
0
2
1
2
1
1
1
1
1
1
0
1
0
1
1
2
1
1
2
1
1
1
0
1
1
1
1
1
1
1
2
0
1
1
0
2
1
0
1
1
1
1
0
1
1
1
1
1
1
0
1
2
0
1
2
0
1
1
0
2
1
0
1
1
1
2
0
2
0
1
1
1
1
2
1
0
0
1
1
1
1
1
0
1
2
1
1
3
1
1
1
2
0
0
2
1
1
0
2
0
1
2
2
2
1
1
1
1
1
1
1
0
2
1
1
1
1
2
1
0
1
2
1
1
2
2
0
0
1
2
0
1
2
1
1
2
1
1
0
0
2
1
2
2
1
1
1
0
0
0
1
1
0
0
1
3
0
1
0
2
1
0
1
1
1
1
0
1
1
1
1
1
0
3
2
1
1
1
2
2
1
1
1
1
1
1
2
1
1
0
0
1
1
2
1
2
0
1
1
1
1
1
0
1
1
2
1
1
2
1
2
2
1
0
1
1
0
1
0
0
2
1
1
1
0
0
2
1
1
1
1
1
0
2
1
0
0
2
1
2
1
1
1
1
2
1
2
3
1
1
1
0
1
1
0
1
1
1
0
2
1
1
1
2
1
0
2
0
2
1
2
1
1
1
1
0
2
1
0
0
0
0
1
1
1
0
0
1
0
1
2
1
3
1
0
1
1
1
2
0
0
0
2
1
0
1
0
1
0
2
1
1
0
1
1
2
1
1
1
1
1
0
0
1
0
1
2
1
0
1
2
0
1
2
1
1
1
2
2
1
1
0
0
1
1
1
0
2
1
1
1
1
2
0
1
0
0
1
1
1
2
2
2
0
0
2
2
1
0
1
2
1
1
1
1
0
1
2
0
4
2
1
1
1
2
1
1
1
2
1
1
1
2
1
1
0
1
1
1
1
1
1
2
3
1
2
1
1
1
0
2
2
1
1
2
1
1
1
2
1
2
1
2
1
1
0
1
1
2
0
0
1
1
0
2
1
1
1
2
2
0
0
1
0
0
1
1
3
2
0
1
1
2
1
0
1
0
1
2
1
2
2
2
1
2
1
2
0
1
0
1
1
1
1
0
0
1
1
1
0
1
2
2
2
2
2
0
1
1
2
2
1
2
1
2
1
1
2
2
0
1
1
3
1
4
1
0
1
2
0
1
1
1
1
2
2
0
1
2
2
2
1
1
1
0
0
1
1
1
0
2
2
1
2
2
1
2
1
0
0
0
0
2
1
0
1
1
0
2
0
1
2
0
2
1
1
1
1
1
0
1
1
2
2
1
0
1
0
2
0
1
1
0
1
2
2
0
1
0
0
2
0
0
2
1
1
1
1
1
1
0
1
1
1
0
0
1
1
1
0
1
2
2
1
1
0
2
2
2
1
2
2
0
0
0
2
0
0
1
1
3
1
1
0
1
1
1
1
1
1
0
1
1
1
2
0
1
2
1
1
1
1
1
1
1
1
1
1
3
2
1
1
1
0
1
2
1
1
1
1
1
1
1
1
1
2
1
0
0
2
1
0
0
1
0
2
1
1
1
1
1
0
1
1
1
1
1
2
1
1
2
2
1
2
0
0
2
1
1
2
2
2
1
1
1
1
2
1
0
0
1
1
0
1
1
1
1
1
1
2
0
1
0
2
1
2
2
0
3
1
2
0
0
1
0
1
1
1
2
1
0
1
0
0
0
1
1
3
1
2
2
2
2
1
1
1
0
2
1
0
1
0
2
1
0
1
2
2
0
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
2
1
2
1
2
1
2
1
1
1
1
0
1
0
1
2
2
5
0
0
1
0
2
1
0
0
1
0
0
1
1
1
1
1
1
1
2
1
0
0
2
2
1
1
1
1
2
1
1
1
1
2
1
1
0
1
2
0
1
1
0
1
0
1
1
0
1
0
1
1
1
0
2
1
1
1
1
1
1
1
1
0
2
1
2
2
0
1
1
1
2
0
2
1
1
1
1
1
2
0
1
0
2
2
1
2
0
2
2
2
0
1
0
1
0
1
0
1
1
1
1
1
1
2
1
0
0
2
1
1
0
0
1
1
1
1
0
1
1
1
1
1
1
0
0
1
2
1
0
1
2
1
2
1
1
0
0
1
1
0
1
1
1
1
1
0
0
1
1
0
1
1
1
1
1
2
2
1
1
1
1
0
0
2
1
2
1
1
2
1
1
0
1
0
0
1
1
0
2
2
1
1
0
1
0
1
1
1
1
1
0
0
2
0
1
1
1
1
1
1
0
2
1
0
3
1
1
2
3
1
1
1
1
1
1
1
1
1
1
0
2
1
1
1
1
0
0
1
2
0
1
0
1
1
0
2
2
0
1
1
1
1
1
1
0
2
1
1
1
2
2
1
1
1
1
2
1
1
2
1
1
0
1
1
0
0
1
1
1
2
1
1
1
1
1
2
1
2
2
0
2
2
1
1
1
1
1
0
2
1
0
2
0
1
0
1
0
2
0
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
0
0
2
1
0
1
1
2
0
1
1
1
1
1
1
2
2
0
1
1
1
1
1
1
1
2
2
0
2
1
0
0
0
1
1
1
1
0
0
2
1
1
1
1
1
0
1
0
1
1
0
1
2
2
1
1
2
1
1
0
2
0
1
1
2
1
2
1
1
0
2
0
2
2
0
0
1
2
0
2
1
1
2
1
0
0
1
1
1
1
1
1
2
1
2
0
0
1
1
1
1
1
0
2
2
1
0
2
0
2
1
0
1
1
1
1
1
0
2
1
1
1
1
1
0
1
1
1
0
0
1
1
1
0
1
0
1
1
3
2
2
1
2
3
1
1
1
1
1
1
1
0
0
1
2
0
2
2
0
1
1
0
1
2
1
0
1
1
0
0
1
2
2
1
0
1
0
1
2
1
1
1
1
1
1
1
1
1
1
0
2
1
2
1
1
0
1
1
1
1
2
1
1
1
1
2
0
1
2
1
2
1
2
0
1
1
2
1
0
0
2
1
0
1
0
1
2
0
2
1
1
1
2
1
1
1
0
2
2
2
1
0
0
1
0
1
1
0
0
0
2
1
2
1
1
1
0
1
0
0
1
0
2
1
2
1
1
0
1
1
0
1
1
2
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
2
0
1
1
2
0
0
1
1
2
1
0
0
0
1
2
0
1
1
0
1
1
1
1
0
1
0
1
0
1
0
2
0
0
0
2
2
0
2
0
1
1
3
2
1
1
1
2
1
1
0
0
0
1
1
2
2
1
0
2
1
1
2
2
2
0
2
5
1
1
2
1
0
1
1
1
0
2
2
2
2
1
1
1
2
1
1
1
1
1
1
1
1
0
2
2
1
1
2
1
1
1
0
0
2
1
1
1
2
1
1
1
2
1
2
1
1
1
1
2
2
1
1
2
1
1
2
1
2
1
2
2
0
2
1
1
1
1
2
1
2
1
1
1
1
2
1
1
2
1
1
1
1
2
1
1
2
0
1
1
1
0
1
2
1
1
2
0
1
1
0
0
1
1
0
0
1
2
0
1
0
1
0
1
1
1
1
1
0
1
1
2
1
2
1
1
1
1
1
2
1
0
1
1
1
2
2
1
1
1
1
2
2
2
0
2
1
0
0
0
0
2
1
1
2
1
0
1
1
1
1
1
1
1
2
2
1
2
1
1
1
0
1
1
0
0
1
1
1
2
1
1
1
1
2
1
2
0
2
1
2
1
2
0
1
2
2
0
1
1
2
2
1
1
1
1
1
2
1
1
0
1
1
1
1
0
1
1
1
0
1
0
2
2
1
1
1
1
2
1
1
1
0
2
2
1
2
1
2
0
1
0
1
2
0
1
2
1
0
2
2
0
1
1
1
2
1
1
1
2
3
1
2
1
1
2
1
1
0
2
1
1
0
1
2
2
1
1
2
2
1
1
1
1
0
0
2
1
1
1
3
1
2
0
1
1
1
1
1
0
1
1
1
1
2
0
0
2
2
0
1
0
1
0
2
0
1
2
1
1
2
3
1
1
1
0
1
1
0
1
0
2
1
1
2
1
1
1
0
1
0
1
1
2
2
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
0
1
1
1
1
1
1
2
1
0
1
1
0
1
1
0
1
2
1
1
1
0
1
1
0
1
2
1
1
0
0
1
1
1
2
1
1
0
1
2
2
0
2
2
0
1
2
0
1
1
1
2
0
1
1
1
2
1
1
2
2
0
1
1
1
2
0
1
1
1
2
0
1
2
1
1
2
1
1
1
1
0
2
1
1
2
0
2
1
1
2
2
0
1
1
0
0
1
0
1
1
2
1
1
1
1
1
1
1
0
1
0
1
1
1
1
1
2
1
0
1
0
1
1
1
1
2
2
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
2
1
2
0
1
2
1
1
0
2
1
1
1
2
1
0
1
1
1
0
1
1
1
1
2
2
1
0
1
2
1
0
1
1
0
2
1
2
1
1
1
1
2
0
1
1
2
2
1
2
1
1
1
1
1
2
1
0
0
2
0
1
2
2
1
1
1
0
3
2
0
1
0
2
1
2
0
2
2
1
0
1
0
1
2
1
1
2
0
1
1
1
0
1
1
1
1
0
1
2
1
1
2
1
1
1
1
1
2
1
1
2
1
0
0
0
1
1
2
1
1
1
1
1
1
0
2
0
0
1
0
0
0
1
1
0
1
1
0
1
1
2
0
1
1
2
1
1
1
2
1
1
1
1
0
0
1
1
2
1
1
1
1
0
2
2
2
2
0
1
1
1
0
1
0
1
1
0
1
1
2
2
0
2
1
1
0
1
1
0
1
0
1
2
0
0
1
0
1
1
2
0
0
1
2
1
0
1
0
2
0
1
1
1
1
2
2
1
1
1
1
0
1
1
1
2
2
1
1
2
0
1
1
1
1
1
1
1
1
0
1
2
1
2
1
1
2
1
1
1
1
1
1
0
1
1
1
1
0
2
2
1
1
1
1
1
1
2
1
1
1
2
1
1
0
1
1
1
1
1
1
2
0
1
1
0
1
0
1
1
1
1
2
2
1
1
1
1
0
1
1
2
1
1
1
0
1
1
2
1
1
2
0
1
0
1
0
1
1
1
2
0
1
1
3
0
1
0
2
0
2
2
2
2
2
2
0
1
0
2
1
0
2
1
2
2
1
1
1
1
2
1
0
1
0
1
1
0
0
2
2
3
2
0
1
2
0
1
2
1
0
0
2
1
0
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
2
1
1
1
1
1
1
1
1
0
1
1
2
1
1
2
1
0
1
0
1
2
2
1
1
1
1
0
2
1
1
1
1
1
1
1
0
2
0
0
2
2
2
1
1
1
1
1
0
1
1
1
2
2
0
1
1
2
2
1
2
2
1
1
1
2
1
1
1
1
1
1
0
2
1
1
0
1
1
0
1
0
1
1
1
1
2
1
1
1
1
1
2
2
0
1
0
2
1
1
1
1
1
0
1
1
0
2
2
1
2
0
2
1
0
2
1
1
1
1
2
2
2
1
0
2
1
0
1
2
1
2
1
3
1
1
0
1
2
1
1
2
1
1
2
1
1
1
0
1
1
1
1
1
0
0
2
1
1
1
2
1
1
0
1
0
0
1
1
2
1
0
0
1
1
1
1
0
1
1
1
1
1
1
2
1
1
2
1
0
2
1
1
1
0
2
1
1
0
0
0
1
1
1
1
1
1
1
1
2
0
1
2
1
1
2
2
1
1
0
2
0
1
0
2
0
1
1
1
2
2
1
2
1
0
0
1
2
1
0
0
0
1
1
1
0
1
1
1
1
1
2
1
1
1
0
2
1
0
0
2
1
1
0
1
1
0
1
2
3
1
0
1
1
1
2
0
2
2
1
1
0
1
1
0
1
1
0
1
1
1
1
1
1
1
0
1
2
2
1
1
1
2
0
2
0
1
1
1
1
2
1
2
1
0
1
1
0
2
1
2
1
2
1
1
0
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
2
0
1
0
2
1
2
1
0
2
0
0
1
1
2
1
2
1
1
1
3
1
1
1
2
2
0
1
2
1
0
1
1
0
0
2
2
1
1
1
1
1
1
1
1
0
0
2
2
1
1
1
2
1
1
0
2
0
1
2
2
1
0
0
2
1
1
1
1
1
2
0
2
2
0
1
1
1
0
2
2
0
1
1
1
0
2
1
0
2
1
1
1
1
1
1
1
2
1
0
1
0
2
1
1
0
1
0
1
2
0
1
1
1
1
0
1
0
1
1
2
1
0
1
0
1
0
1
1
1
1
1
0
2
2
1
0
1
0
1
0
1
0
1
1
1
1
0
2
1
2
1
0
1
1
2
1
2
1
0
2
1
1
2
3
1
1
2
2
1
0
2
1
2
1
1
1
0
1
1
1
1
0
2
0
1
2
1
2
1
1
2
0
2
0
0
1
0
2
2
2
2
1
1
1
1
0
0
1
1
1
2
1
1
2
1
2
1
2
1
1
1
1
2
0
1
1
0
0
1
1
1
1
1
2
1
1
1
1
1
1
1
0
1
2
0
1
1
1
2
0
1
1
1
0
2
1
2
1
2
1
1
1
1
2
0
2
1
0
2
2
1
0
1
2
1
0
1
2
1
2
1
1
1
1
0
1
1
1
0
2
0
2
1
1
1
2
0
1
1
1
2
1
2
1
2
2
1
0
2
1
2
2
1
1
0
1
1
1
0
1
1
1
0
1
1
0
0
1
1
1
0
2
0
0
0
2
0
1
1
0
1
1
2
0
2
2
2
2
0
0
1
0
0
0
1
1
2
2
1
1
1
1
2
1
0
2
1
1
1
0
1
1
2
1
1
0
1
1
1
2
2
1
1
2
1
1
2
1
1
2
1
1
1
1
0
0
1
1
2
1
0
1
1
2
1
1
1
1
1
0
2
1
1
1
1
1
1
1
2
2
1
0
1
0
1
1
2
1
0
2
2
1
2
1
1
1
0
0
2
2
1
1
1
1
2
1
0
1
2
1
2
1
3
1
1
0
2
0
2
0
2
1
2
1
0
1
0
2
1
1
1
0
1
2
2
0
0
2
2
0
0
0
1
2
3
0
2
1
1
2
2
2
1
1
0
1
1
1
1
2
2
2
2
1
1
2
0
0
0
1
1
2
0
2
1
0
1
1
2
1
1
1
1
1
1
0
1
2
2
1
2
2
2
2
2
1
1
1
2
2
2
1
1
1
1
0
1
2
2
1
1
1
0
0
1
1
1
2
2
1
1
0
1
1
2
0
1
0
1
2
1
2
0
0
1
1
0
1
1
1
2
2
1
2
1
0
1
2
1
1
0
1
1
1
1
2
1
0
1
1
1
0
1
1
1
1
1
2
2
1
1
3
1
0
0
1
1
1
1
1
1
1
0
2
2
1
1
2
1
2
1
1
2
1
0
1
1
0
2
2
0
1
1
2
1
2
0
0
1
1
5
1
1
2
1
1
0
1
2
1
2
1
2
1
1
1
1
0
2
1
2
2
0
1
1
2
1
1
1
0
0
0
1
1
1
0
1
1
1
1
1
0
2
1
1
1
1
1
1
0
2
1
0
1
1
1
0
1
0
0
1
2
1
2
0
1
1
2
1
0
1
1
0
1
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
0
1
0
1
1
3
1
1
1
1
0
1
2
1
2
0
1
1
1
1
1
1
3
0
1
1
1
1
2
1
1
0
0
1
2
1
1
1
1
1
1
1
1
1
2
2
1
1
0
2
1
2
1
2
1
0
2
1
0
0
0
1
1
0
2
1
0
0
0
2
2
1
0
2
0
1
1
1
2
1
1
0
1
3
1
1
2
1
0
1
1
1
2
1
0
1
0
0
1
3
1
2
1
2
0
0
0
2
1
1
2
1
0
0
0
0
2
1
1
1
1
1
1
0
1
1
1
2
1
1
1
2
1
1
1
0
1
0
0
1
2
1
1
2
1
0
3
1
1
1
0
1
1
1
1
1
1
0
2
0
1
1
1
0
1
1
1
1
1
1
2
1
0
0
2
2
1
1
2
2
1
1
2
2
0
0
1
1
1
1
2
1
0
2
1
2
0
1
2
2
1
1
1
1
2
1
0
1
1
1
1
1
1
0
2
1
0
1
1
1
2
2
1
1
1
2
1
1
0
2
1
0
2
2
1
1
1
0
0
1
0
2
0
1
0
1
1
1
2
2
1
1
2
2
0
0
1
1
2
0
5
0
0
1
1
1
1
1
0
1
0
1
0
1
0
1
1
1
1
2
0
1
0
1
1
0
2
1
2
0
1
1
1
2
2
1
1
1
0
1
1
1
1
1
1
1
2
1
1
2
0
2
1
1
0
0
1
1
2
1
1
1
0
0
0
2
0
2
1
1
1
2
0
2
3
1
1
2
1
0
2
0
2
1
0
1
2
1
1
1
1
2
1
1
1
2
1
0
0
2
1
0
0
2
2
0
1
1
0
1
1
1
2
0
0
1
0
0
1
1
1
1
1
2
2
0
1
0
2
1
1
1
1
1
2
1
5
0
1
1
0
2
1
2
0
1
0
2
1
2
1
1
1
1
2
2
2
2
2
1
1
2
0
1
1
1
2
1
1
1
2
1
0
1
1
1
2
1
1
1
1
2
0
0
2
1
1
2
2
1
2
1
1
0
1
0
1
1
0
2
1
1
1
1
2
1
1
2
1
1
1
2
1
1
1
0
1
1
1
1
2
2
1
1
1
0
0
2
1
1
2
2
0
1
1
1
1
1
2
4
1
1
0
1
1
1
1
2
2
2
2
1
1
0
0
1
0
2
1
1
1
1
2
0
2
0
2
1
1
1
2
2
1
2
0
2
1
2
0
1
1
1
1
2
1
1
1
2
1
0
1
1
2
2
1
0
0
0
2
1
1
2
2
1
1
0
2
0
1
0
1
1
1
1
2
1
1
1
1
1
1
0
2
0
0
1
1
1
1
0
2
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
2
1
0
1
1
1
1
0
1
1
0
2
1
2
1
2
1
1
1
1
1
0
1
2
1
2
1
0
0
1
1
0
1
2
0
1
1
2
1
2
1
0
2
1
0
2
1
2
1
0
1
2
1
2
1
1
1
2
0
1
2
0
1
1
0
2
1
0
0
1
1
2
1
1
1
0
0
0
1
2
1
1
2
1
1
0
0
1
1
1
1
1
0
1
1
2
0
1
0
1
2
1
1
0
2
2
1
2
1
1
0
2
1
2
1
1
0
1
1
1
2
1
2
2
0
1
2
2
0
0
0
1
2
1
1
1
1
0
1
1
1
2
2
0
2
1
0
0
2
1
1
1
1
2
1
0
0
2
1
2
1
0
1
1
1
1
1
1
1
0
1
2
1
2
2
1
1
2
0
1
1
1
1
0
1
1
0
2
0
2
1
1
0
1
2
2
1
2
2
2
1
2
0
1
0
0
2
1
0
1
1
0
1
1
0
3
1
1
0
1
1
1
1
1
0
0
1
0
2
2
1
1
2
1
0
1
0
1
1
1
1
1
1
1
0
0
2
2
0
1
2
0
1
2
2
1
2
1
1
1
1
0
0
1
0
1
0
1
0
1
1
1
1
1
0
1
1
1
3
1
2
1
1
1
1
1
1
1
2
1
3
1
2
1
2
2
1
1
0
0
1
2
2
2
1
1
1
1
2
2
1
2
0
2
1
0
0
0
1
1
0
2
1
2
0
1
1
1
1
2
1
2
1
1
2
1
1
2
1
2
1
1
0
1
0
1
2
1
2
1
1
1
2
1
1
3
1
0
1
1
0
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
0
2
1
2
2
1
0
1
1
2
1
1
1
1
2
2
2
1
1
1
0
1
0
0
1
2
0
2
1
1
1
1
2
0
1
0
2
1
0
1
1
1
1
2
1
0
1
2
0
2
1
1
1
0
1
1
1
0
1
0
1
1
1
0
1
1
2
2
1
1
0
0
0
1
1
3
0
2
2
1
0
1
0
2
1
2
2
0
1
1
1
0
1
0
1
1
2
0
0
1
1
1
0
2
2
1
0
1
0
2
2
1
0
1
1
1
2
1
1
1
2
0
1
1
2
1
1
2
1
0
2
0
1
0
1
2
1
0
2
1
0
1
2
1
1
1
2
1
1
2
1
1
0
2
2
0
2
2
2
0
0
1
1
1
1
1
2
1
1
1
1
0
1
1
0
0
1
1
1
1
0
1
1
2
2
1
0
2
1
0
0
1
2
0
1
2
1
1
1
0
1
0
1
0
1
2
1
1
1
1
2
1
0
1
1
1
1
1
1
2
1
0
2
2
0
1
0
1
0
1
1
1
2
1
1
2
0
1
1
1
1
2
1
0
1
1
1
2
1
1
0
1
1
0
1
2
2
0
0
1
0
1
1
1
1
1
1
1
1
0
1
1
1
2
1
1
2
2
1
1
1
1
2
1
1
1
1
2
2
1
1
0
1
2
1
2
1
1
3
1
2
2
2
0
2
1
2
0
1
1
1
1
1
2
1
0
1
2
1
0
0
1
2
2
0
1
2
2
1
2
1
1
1
1
2
0
1
0
0
2
0
3
0
0
2
1
2
1
1
2
2
1
1
1
1
1
1
1
1
1
2
0
1
1
1
0
2
1
0
0
1
0
1
0
2
3
1
1
1
1
2
1
2
2
1
1
0
1
2
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
2
1
1
0
1
1
1
1
1
2
1
1
1
1
0
1
1
1
0
1
1
1
2
1
1
1
0
1
0
0
1
0
1
2
1
0
1
1
0
2
0
2
2
2
1
1
2
1
1
2
0
1
0
3
1
1
1
2
1
1
0
1
1
2
2
2
1
1
2
2
1
1
1
0
1
1
0
1
2
1
1
2
1
2
1
2
1
1
1
1
1
1
1
1
0
0
0
1
2
2
1
1
0
1
2
1
1
0
0
1
1
2
1
1
1
1
1
0
0
1
2
1
2
0
1
0
0
1
1
1
1
2
1
1
0
1
1
1
1
0
2
1
2
2
1
1
1
1
2
2
2
1
1
1
2
1
1
1
1
1
2
2
1
0
2
0
1
2
1
1
1
1
1
0
1
0
1
1
2
0
1
1
1
1
3
2
1
2
1
0
0
1
2
0
2
1
1
1
0
3
1
1
1
1
1
1
2
1
2
1
1
1
0
0
1
2
1
1
2
1
1
1
0
1
1
1
2
1
2
1
1
0
2
1
2
0
2
1
1
2
0
2
1
1
1
0
2
0
1
1
1
2
2
1
2
1
1
1
1
1
1
2
0
1
2
1
0
1
1
1
1
1
1
1
1
0
1
1
2
1
1
2
0
1
2
1
1
1
2
2
2
2
1
1
1
2
2
1
1
0
2
0
1
1
2
1
1
0
2
2
1
2
2
0
1
0
0
1
1
0
0
2
2
1
2
1
2
0
0
0
1
1
0
1
1
1
1
0
0
2
1
2
0
0
2
1
1
2
1
1
0
2
0
2
0
2
2
1
2
2
1
1
2
2
1
2
2
2
2
2
2
0
2
0
1
1
1
1
2
1
0
1
1
1
1
1
1
0
1
1
1
2
1
0
0
1
0
1
1
1
0
2
2
1
1
1
1
2
1
2
2
0
0
1
0
1
0
0
0
1
1
1
1
1
0
1
1
0
1
1
2
1
0
0
1
1
1
1
0
1
0
1
1
2
1
1
0
1
1
1
2
1
2
1
1
1
2
1
1
2
1
1
1
2
1
0
0
2
0
0
1
1
2
1
1
1
1
0
0
2
2
1
1
1
0
0
0
0
1
2
1
1
2
0
1
0
1
1
1
1
0
0
2
2
0
2
1
1
1
2
0
0
1
2
1
1
1
2
1
0
1
1
1
2
2
2
1
1
0
1
1
1
0
1
0
1
1
0
0
1
1
0
1
1
2
2
2
1
0
1
2
1
1
2
0
2
1
2
1
1
1
0
1
0
1
1
0
0
2
0
1
1
1
2
1
2
1
2
1
1
1
2
1
1
1
2
2
1
2
0
0
1
1
2
1
0
1
1
2
0
1
1
1
2
1
1
1
1
1
0
2
1
1
1
1
2
1
2
1
1
2
1
0
1
1
1
1
2
1
1
0
1
2
1
0
0
1
2
1
0
0
1
1
0
2
1
2
2
2
0
0
2
2
0
0
1
2
1
2
0
1
1
1
2
1
2
1
0
1
1
1
1
1
1
1
1
2
0
1
1
1
2
2
1
0
2
1
1
1
1
1
1
1
0
2
1
1
0
1
0
1
1
1
1
1
2
1
0
0
2
2
1
1
1
1
1
0
1
1
2
1
1
2
2
1
1
1
1
1
1
1
1
3
2
1
1
1
0
0
1
0
1
1
1
2
2
2
1
1
2
1
2
1
1
2
1
2
0
1
2
0
2
1
0
0
3
1
1
2
1
2
0
3
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
0
1
1
0
2
1
1
2
1
2
1
2
1
2
1
2
1
2
1
2
2
1
2
2
1
1
1
1
1
1
0
1
1
2
0
2
1
0
1
1
1
3
2
0
1
2
2
1
2
2
1
1
2
1
1
2
0
0
1
0
1
0
1
2
0
0
0
1
0
1
2
1
1
1
1
0
1
0
2
1
2
1
0
1
1
1
1
2
2
1
0
1
2
1
1
1
1
2
1
1
2
2
1
2
1
1
2
2
1
0
0
1
1
2
1
1
2
0
1
2
0
0
1
2
1
1
0
1
1
1
4
0
1
1
2
2
0
1
1
1
1
2
2
1
2
1
1
1
0
1
1
2
2
1
1
2
1
1
1
0
3
1
1
0
1
1
2
1
0
1
1
1
2
1
1
1
1
1
2
2
2
1
2
1
1
1
1
1
1
1
2
1
1
0
0
2
2
1
1
1
0
1
0
1
2
0
2
2
2
0
0
2
1
0
1
1
2
2
1
0
1
1
1
2
0
1
1
1
1
1
1
0
1
1
0
1
2
0
0
1
1
0
1
1
1
1
1
2
1
0
1
0
1
2
2
1
1
1
1
1
2
1
0
0
2
1
0
1
1
2
4
1
0
2
0
1
1
0
1
1
2
1
1
0
2
2
3
1
2
1
0
2
0
1
2
2
1
1
1
1
1
1
1
0
0
1
2
0
1
1
2
1
2
1
1
0
0
1
1
1
0
2
0
1
2
0
3
1
1
1
1
0
1
1
1
2
1
1
1
0
1
1
1
1
1
0
1
1
1
0
1
3
1
2
2
1
2
1
0
1
2
2
1
2
0
1
0
0
2
3
0
0
2
1
4
2
2
2
2
0
1
0
1
1
1
0
1
1
1
0
2
1
2
2
0
1
0
1
1
0
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
0
1
0
1
1
2
2
0
1
2
1
2
2
1
1
0
1
1
0
1
1
2
1
1
0
2
0
2
2
2
1
1
0
2
1
1
1
1
1
2
1
0
1
0
1
1
2
1
1
1
2
1
2
2
2
0
2
1
1
1
1
1
0
1
0
1
0
0
2
2
2
1
0
0
1
1
1
1
1
1
0
0
1
1
1
2
2
1
2
2
1
1
0
1
0
2
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
0
1
1
1
1
0
0
1
0
1
0
1
1
1
1
1
0
2
0
1
0
0
1
0
1
2
1
2
0
2
2
0
1
0
2
0
1
1
0
1
0
1
1
2
0
2
1
1
0
0
2
2
1
0
1
1
1
1
1
1
0
1
1
1
1
1
2
1
2
1
1
1
1
1
2
0
0
1
0
1
0
1
2
2
2
0
1
1
0
0
2
1
1
0
0
1
1
0
1
1
3
1
1
1
1
2
2
1
0
0
0
0
0
0
0
1
1
0
1
1
1
1
1
1
1
2
0
1
1
1
3
1
0
0
1
0
2
0
1
1
0
2
0
0
3
1
1
1
1
2
2
1
1
1
0
2
1
1
1
1
1
2
0
2
2
2
0
2
1
1
1
1
1
1
1
1
0
2
2
1
2
0
2
1
1
1
2
1
1
1
1
2
0
1
2
1
1
0
0
0
0
1
2
6
1
1
1
2
1
2
1
1
2
1
0
1
1
0
1
0
1
1
1
2
2
0
1
1
0
1
1
1
1
1
3
1
2
0
0
0
0
2
0
1
1
2
1
1
1
0
1
1
1
1
1
1
1
1
2
1
2
1
2
1
1
2
0
1
1
0
1
1
2
1
0
1
0
1
1
2
2
1
1
2
2
0
0
1
1
0
1
1
0
1
1
1
0
1
1
1
1
1
1
1
1
1
0
0
1
1
1
1
1
1
2
1
2
0
0
1
0
0
1
1
0
0
1
2
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
2
1
1
0
1
1
0
1
0
2
2
1
1
1
0
0
0
1
1
1
1
1
0
1
1
2
1
2
2
1
2
1
0
0
1
1
0
0
1
1
2
2
0
0
0
1
1
1
1
1
2
1
1
1
1
0
1
0
1
2
1
1
2
1
0
0
2
1
1
0
2
1
1
1
1
1
0
0
1
1
1
1
1
1
1
0
1
1
0
2
1
1
1
0
2
0
1
1
1
1
1
0
2
0
1
1
2
2
0
2
0
1
1
1
1
2
0
1
1
1
0
0
2
1
1
1
1
2
1
2
2
0
2
1
2
3
1
1
1
2
1
1
1
2
1
2
1
2
1
0
0
2
0
1
2
1
0
0
2
1
1
1
1
0
1
0
1
1
2
1
1
1
2
0
1
2
1
1
2
2
1
0
0
0
0
1
1
1
0
2
1
2
1
1
1
0
1
2
0
1
3
2
2
2
1
1
1
1
0
2
2
0
1
1
1
1
1
0
1
1
1
1
0
2
1
1
2
1
0
1
1
2
1
1
1
1
1
0
2
1
1
1
1
1
2
1
1
1
1
1
3
0
1
0
1
0
2
2
2
1
1
0
2
1
1
1
0
2
1
1
2
1
2
1
2
1
1
1
1
0
1
2
2
1
1
2
0
1
1
1
1
1
0
1
1
1
1
2
0
1
1
0
2
2
1
0
1
1
2
3
1
0
2
2
1
2
2
1
0
1
2
0
2
1
0
1
0
1
1
1
1
0
1
1
1
2
0
2
1
2
1
1
1
2
1
1
1
2
2
1
1
1
1
0
0
3
0
0
2
1
2
1
0
1
0
1
1
2
1
1
1
1
2
1
0
2
1
2
0
1
1
1
1
1
1
2
0
1
2
1
1
2
2
1
1
1
1
2
1
1
1
1
2
1
0
1
2
1
1
1
1
1
1
2
1
2
1
2
2
0
2
0
1
1
1
2
1
1
1
1
0
1
0
1
1
1
1
0
1
1
1
1
1
2
1
1
1
1
2
2
1
1
1
1
1
2
1
1
2
1
1
2
2
1
1
1
1
2
1
1
1
2
0
0
2
1
2
2
2
0
1
1
1
0
1
1
1
0
2
1
1
1
2
1
1
2
0
2
0
1
2
2
1
0
1
0
1
0
0
2
1
1
0
1
1
1
0
1
1
1
2
2
0
1
1
1
1
0
0
0
2
1
1
0
0
2
1
2
1
1
1
1
2
0
1
1
2
1
1
0
1
0
1
1
1
0
1
1
1
2
1
2
0
1
1
1
1
1
2
1
0
1
0
2
1
2
2
2
2
1
0
2
1
1
0
2
1
1
0
1
1
1
2
1
3
1
1
1
0
0
2
2
1
1
1
1
0
1
1
1
2
2
1
2
1
1
1
2
2
1
1
1
1
2
1
2
2
1
1
1
2
1
2
1
2
1
1
1
1
1
2
1
1
1
1
1
1
0
0
1
1
1
3
1
0
1
1
0
1
1
0
1
1
1
0
0
1
2
2
1
1
1
0
1
0
1
1
2
0
1
1
1
1
0
1
1
1
1
1
1
1
1
1
2
0
1
1
0
1
2
0
0
1
2
2
1
1
1
1
1
1
1
2
1
2
1
0
1
2
2
1
2
0
1
1
2
1
1
0
1
2
2
1
1
1
1
0
0
1
1
1
2
2
2
1
0
1
1
2
1
1
1
1
1
2
1
0
2
1
0
0
2
1
1
1
2
1
2
1
0
2
2
1
0
0
1
2
1
1
1
0
1
1
0
1
2
1
2
2
1
0
0
1
0
1
1
1
1
1
1
1
0
1
2
2
0
1
1
1
2
2
0
1
1
4
2
2
1
1
1
1
3
0
0
1
0
0
1
2
2
0
1
2
1
0
1
1
1
2
0
2
3
1
1
1
1
0
0
1
1
2
2
2
1
0
1
2
1
1
2
1
1
2
0
0
1
2
2
0
0
1
1
0
1
1
0
1
1
1
1
1
0
0
1
0
1
1
2
1
0
4
2
1
0
1
0
1
0
0
0
1
1
2
1
0
1
0
1
0
2
1
2
1
2
2
2
0
1
1
1
1
2
1
3
1
1
0
1
1
1
1
1
1
1
1
2
1
1
1
0
2
1
1
0
2
0
1
2
2
1
1
1
2
0
2
1
2
2
0
2
1
2
3
1
2
1
2
1
1
1
0
0
2
1
1
2
0
1
1
2
2
1
0
1
1
1
2
2
1
0
1
1
0
2
1
1
0
1
0
1
1
1
1
2
2
1
0
3
1
1
0
0
0
2
2
1
1
0
1
0
0
0
0
1
2
0
2
1
1
0
1
1
2
0
2
2
2
1
1
0
0
2
2
0
1
2
1
1
1
2
1
2
1
1
1
1
2
1
2
0
0
1
2
2
1
0
0
1
0
2
1
2
2
1
1
1
2
1
1
2
1
2
2
0
2
1
0
3
0
2
1
1
1
2
1
1
2
1
2
1
1
1
1
1
3
0
1
0
0
1
1
2
1
2
0
1
0
2
1
1
1
0
2
0
1
2
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
2
2
1
1
0
2
2
1
1
2
2
1
1
1
1
1
0
1
1
2
1
1
1
0
1
2
1
1
0
1
2
2
1
1
1
1
1
0
2
1
2
1
1
2
1
0
1
0
1
0
1
0
1
0
0
2
0
1
1
2
1
1
1
0
0
1
1
2
2
0
2
1
1
2
1
2
1
1
2
2
2
2
0
1
2
0
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
3
0
1
1
1
1
0
1
2
2
1
1
1
1
1
1
0
0
1
1
0
1
2
1
1
1
0
0
1
0
1
0
1
1
1
0
0
1
2
1
1
2
1
1
1
2
1
2
1
1
1
1
0
1
1
2
2
0
1
1
2
1
2
1
0
2
0
2
1
1
1
1
1
2
0
0
1
1
2
0
2
1
2
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
2
0
1
2
2
1
0
0
0
3
0
1
1
1
0
1
2
0
0
0
0
2
0
1
2
1
1
0
2
1
1
0
1
1
1
2
1
0
1
1
1
0
1
2
1
1
2
0
1
1
0
1
1
3
2
1
1
1
1
1
0
1
1
0
1
1
0
1
2
1
0
1
1
2
2
1
1
1
0
2
1
1
1
0
2
0
0
2
1
2
1
0
2
0
1
0
1
1
2
1
1
1
2
1
1
1
1
0
1
1
1
1
1
2
1
1
1
1
1
1
2
0
0
2
1
1
0
1
1
1
0
0
0
3
1
0
3
2
1
1
1
1
0
0
2
2
2
1
1
1
0
1
0
1
1
1
1
1
0
1
1
2
1
1
1
3
2
1
2
1
1
1
0
1
1
2
1
1
2
2
0
1
0
0
1
1
2
0
0
0
1
0
1
0
1
0
2
1
2
1
1
1
0
1
1
0
0
1
0
1
0
1
0
2
1
2
1
0
0
1
0
2
0
1
1
2
1
2
2
1
1
2
1
1
1
2
1
0
0
1
1
2
2
1
2
1
1
1
3
2
1
1
0
1
0
2
1
1
2
1
1
1
0
1
1
0
0
2
1
1
1
1
1
1
0
2
1
1
2
0
1
2
1
1
2
1
1
1
1
1
1
1
1
1
0
1
1
1
0
1
3
2
1
1
1
0
1
1
1
0
1
1
0
0
0
1
0
1
1
1
1
1
3
2
1
2
1
1
2
1
2
1
1
0
1
1
1
1
1
0
1
0
1
0
2
1
1
0
1
1
1
1
1
1
1
2
2
1
2
2
2
2
1
1
2
0
1
0
1
0
0
1
0
1
0
1
1
2
1
2
1
1
1
1
1
2
1
0
0
0
0
1
2
1
0
1
2
1
2
1
2
1
0
0
2
1
1
1
1
0
1
0
0
2
0
0
1
2
2
1
0
1
1
1
1
1
0
1
1
2
1
1
2
1
1
1
2
1
2
1
1
0
1
2
1
2
1
1
0
1
2
1
1
1
1
1
1
2
1
2
1
1
2
2
1
0
0
1
2
1
1
1
2
1
1
1
2
1
1
2
0
2
1
1
1
1
0
1
2
1
2
1
2
2
1
0
0
2
1
1
1
0
0
2
1
0
1
1
2
2
2
1
1
1
1
1
0
1
1
0
1
1
1
2
1
1
1
1
2
1
1
0
1
0
1
2
2
2
0
0
0
1
0
1
1
2
1
1
1
1
0
1
1
2
2
2
2
2
1
1
2
0
0
2
2
4
2
1
1
2
1
1
2
1
2
1
2
2
2
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
1
0
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
0
0
1
1
1
1
1
2
2
1
1
1
0
2
1
1
0
1
0
1
0
1
0
2
1
1
0
1
0
1
1
1
1
0
1
2
0
0
2
1
1
1
0
2
2
2
1
1
0
1
1
1
1
1
1
1
1
2
1
1
1
1
1
0
1
1
2
0
2
1
1
1
1
1
0
2
0
1
2
0
1
1
1
2
0
2
3
0
1
1
1
1
0
1
0
1
1
2
0
1
1
0
2
1
1
1
2
1
1
1
0
2
1
1
1
1
1
1
1
2
0
1
1
1
0
0
1
0
1
1
1
1
0
1
1
2
2
0
1
2
1
1
2
1
0
2
1
2
1
2
1
1
1
1
1
1
0
1
0
1
1
1
1
0
1
1
1
2
2
0
1
0
1
0
2
1
1
1
0
0
0
1
1
1
1
2
0
1
1
1
1
2
1
1
1
1
2
2
1
2
1
1
1
1
0
2
0
3
0
1
0
1
0
2
1
2
1
0
1
2
1
1
2
2
0
2
1
1
2
2
1
0
2
0
1
0
0
1
1
1
1
2
0
0
1
1
6
1
0
0
1
1
1
1
1
1
1
0
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
2
0
2
2
1
2
1
4
1
1
1
2
2
1
1
0
1
0
1
1
0
1
1
2
1
0
2
2
1
1
1
1
1
1
0
1
1
0
1
0
2
1
1
1
1
0
2
1
1
1
1
1
2
1
2
0
0
1
1
1
1
2
0
0
1
0
2
1
2
0
2
1
1
0
1
1
2
0
2
1
1
0
1
3
1
1
1
2
1
2
1
0
1
0
2
1
0
1
0
1
2
0
2
0
0
2
2
1
2
0
0
1
1
2
1
1
0
1
0
1
1
1
2
1
0
1
2
1
2
1
0
0
2
0
0
0
0
2
1
2
1
2
2
2
1
0
1
1
2
2
1
2
2
2
1
1
2
2
1
1
1
1
0
3
1
1
1
1
2
2
1
2
1
2
2
2
0
2
1
0
2
2
1
0
1
1
0
1
1
1
1
2
0
0
0
1
0
2
1
2
1
1
1
1
1
2
0
1
1
0
0
1
0
0
1
2
1
1
0
1
1
1
1
1
1
0
0
1
1
1
0
1
1
2
1
2
0
1
1
0
0
0
0
1
1
1
1
1
2
1
1
1
2
1
1
2
1
0
1
2
2
0
1
1
2
1
1
0
1
1
1
0
0
0
0
1
1
0
2
1
1
0
0
2
1
1
1
1
0
1
0
0
2
1
0
1
1
0
1
1
1
1
2
1
2
0
1
2
1
1
1
2
1
1
1
2
2
0
1
1
1
0
1
1
1
1
1
1
1
1
0
2
1
2
2
1
1
1
1
0
1
1
2
1
1
1
2
2
4
1
1
1
1
1
0
0
0
1
0
2
0
0
1
2
1
1
1
1
1
1
2
1
2
2
1
2
0
0
1
1
1
2
1
1
1
1
0
0
1
2
1
1
1
1
2
1
1
1
2
1
0
2
0
0
1
1
1
0
1
1
1
1
1
0
1
1
1
1
2
1
2
1
1
1
1
0
1
1
2
2
1
1
1
1
1
1
1
0
1
1
2
0
1
1
1
1
0
0
1
1
2
2
1
1
1
1
1
1
1
1
1
1
2
0
1
2
0
2
1
1
0
2
0
1
1
1
2
1
1
1
1
2
1
0
1
1
1
1
2
0
1
1
1
2
2
2
0
2
1
1
1
1
2
1
1
2
0
2
1
1
1
2
1
1
1
2
2
1
1
1
0
0
2
1
1
0
0
1
1
2
0
2
0
0
1
2
0
1
1
1
1
1
2
0
2
0
1
1
2
0
2
2
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
2
2
1
1
1
0
0
1
0
0
1
1
1
3
1
0
0
1
1
1
1
1
1
0
1
1
1
1
1
1
0
0
1
1
1
1
3
2
2
2
2
2
0
0
1
1
0
1
1
1
0
2
2
1
2
2
1
0
0
1
0
1
1
1
1
2
1
1
1
0
2
1
1
2
1
0
2
1
1
1
1
0
0
1
0
0
0
2
2
2
0
1
1
1
1
1
1
2
1
0
2
1
2
0
2
1
3
1
0
1
1
1
0
0
1
1
2
0
1
1
0
0
0
1
1
1
1
1
1
0
1
0
1
1
1
1
1
1
1
1
1
1
2
1
0
2
1
1
2
0
1
1
0
0
1
0
1
1
0
1
1
1
0
1
2
1
1
2
0
1
1
1
2
1
2
1
2
1
0
1
1
1
2
2
1
1
1
1
2
1
1
2
0
1
1
1
1
1
1
1
2
1
0
1
1
1
2
1
1
2
1
1
1
1
0
2
0
2
0
1
2
1
1
0
1
1
0
2
1
2
0
1
1
1
1
0
2
2
0
1
2
1
1
2
0
0
1
1
0
2
2
1
1
2
2
2
1
2
1
2
1
1
2
1
1
1
1
1
0
1
2
1
1
1
2
1
0
2
1
1
1
0
1
1
0
1
1
1
2
0
2
2
1
1
1
1
1
1
1
0
1
0
2
2
1
1
1
1
1
1
1
0
1
1
1
1
1
1
0
1
1
1
2
1
1
1
1
0
0
1
1
1
1
1
1
2
1
2
1
0
0
2
2
1
1
1
2
2
2
0
2
1
1
1
1
1
1
2
1
1
2
2
0
1
2
1
0
1
0
0
0
1
2
0
1
2
1
1
0
1
1
0
1
0
1
1
0
1
1
2
1
2
1
1
0
1
1
1
2
1
1
2
2
2
2
1
1
1
1
2
1
0
1
1
1
1
2
0
1
1
1
2
1
0
1
1
1
0
1
1
2
1
1
1
1
1
2
1
0
1
0
1
0
1
1
1
1
1
1
1
1
1
2
1
1
1
0
2
0
2
1
3
1
1
3
1
2
2
2
0
1
0
1
0
2
1
1
0
1
1
1
0
1
0
2
0
1
0
0
1
1
0
1
1
1
1
1
1
1
1
2
0
2
2
1
1
5
2
0
2
1
0
1
1
1
1
2
1
2
1
2
2
1
1
1
1
2
1
1
1
1
1
1
0
0
1
1
2
1
1
1
1
1
1
1
1
2
0
2
0
1
1
0
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
0
2
0
1
1
1
2
1
1
0
2
1
2
1
1
2
1
1
1
1
1
0
2
1
1
1
1
1
1
1
1
1
0
0
2
0
0
0
3
1
1
1
0
1
0
1
2
1
0
1
1
2
1
0
1
1
1
2
2
1
2
2
1
2
1
0
2
1
1
1
1
0
0
1
2
1
1
1
1
1
1
2
1
1
2
2
4
1
1
1
1
0
1
1
1
1
2
2
0
2
1
1
1
1
0
1
1
2
1
0
2
0
1
2
2
2
1
1
2
1
1
0
1
1
2
1
0
1
0
1
2
2
2
2
0
0
1
1
1
1
0
1
1
1
1
0
0
1
1
1
2
0
1
2
1
0
2
0
2
0
0
1
1
1
2
0
2
1
2
1
2
0
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
3
2
2
0
0
1
1
0
1
2
0
1
1
1
1
1
1
0
0
0
2
1
1
1
2
1
1
1
2
2
1
2
1
1
1
1
1
2
1
1
1
0
1
0
1
2
1
2
2
0
2
1
1
1
1
1
1
1
1
0
1
2
2
0
1
2
1
1
0
2
1
0
2
1
1
1
0
1
1
1
0
2
0
2
0
1
1
2
2
1
1
2
0
1
0
2
1
2
1
0
2
1
3
0
1
1
1
0
1
2
1
1
2
0
2
1
1
0
0
2
0
1
1
0
2
1
1
1
1
2
1
1
1
1
2
2
1
2
1
2
2
1
2
1
1
2
0
2
0
1
0
1
1
2
2
1
0
0
0
1
2
0
0
2
2
1
2
1
1
2
2
1
1
0
1
0
0
0
1
1
1
0
0
0
1
1
1
1
1
1
2
1
1
1
1
0
1
1
2
1
1
0
1
1
1
1
2
1
2
0
2
0
0
2
0
1
1
1
1
1
1
1
1
2
1
0
2
2
2
1
1
2
2
2
0
1
1
0
0
2
2
1
1
0
1
0
1
1
2
1
2
1
1
0
1
2
1
1
0
1
2
1
1
1
2
0
1
1
0
1
1
0
2
1
1
0
0
1
0
0
0
1
2
1
0
2
0
1
0
2
1
2
1
1
0
2
1
1
2
0
2
2
0
0
1
1
1
0
1
1
0
1
0
1
1
0
1
1
2
1
1
1
2
1
0
1
1
0
2
0
1
1
1
1
1
1
2
1
0
2
1
2
2
1
2
1
1
1
0
1
2
0
0
1
1
2
1
0
1
1
0
1
1
1
0
0
1
1
1
1
2
1
1
1
1
1
1
0
1
2
1
0
1
1
2
1
1
0
2
1
5
1
2
0
1
1
1
1
1
0
0
1
2
2
1
1
1
2
2
0
0
2
1
0
2
1
0
2
2
1
0
2
1
2
2
0
1
1
1
1
1
2
1
1
2
2
2
1
2
1
1
2
0
2
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
0
0
0
2
1
2
1
1
1
1
1
2
2
0
2
2
2
1
1
1
2
2
1
0
1
0
2
0
2
0
2
0
1
2
1
1
1
0
1
1
1
1
2
1
1
0
1
1
2
2
1
1
1
1
1
2
0
0
2
0
1
2
2
1
1
1
1
1
1
0
1
1
1
1
2
1
1
1
1
1
0
1
1
1
0
2
1
0
0
1
0
2
0
0
1
1
0
0
0
1
1
2
0
1
1
1
0
1
1
1
0
1
0
1
2
1
1
1
1
1
1
1
1
2
0
1
0
1
2
1
1
1
1
1
0
1
1
2
0
2
1
1
0
0
2
2
1
0
1
1
1
1
1
0
1
1
0
1
1
1
1
2
0
0
1
1
0
0
2
1
1
2
1
1
2
1
0
2
1
2
1
1
0
2
2
1
1
1
1
1
0
1
1
2
1
1
1
1
0
2
1
0
1
2
0
2
1
2
0
2
1
2
1
2
1
2
1
1
1
2
1
1
1
2
1
1
0
2
2
1
1
2
2
0
1
4
1
1
0
1
1
1
0
1
1
1
1
2
2
1
2
0
1
0
1
0
2
2
0
1
0
2
1
1
0
2
1
1
2
2
1
0
0
1
1
1
2
1
1
1
1
1
1
1
0
1
2
1
2
1
1
0
2
2
0
0
2
2
2
1
1
1
4
2
1
4
1
1
1
2
2
0
1
1
2
2
0
2
1
2
0
1
1
1
0
1
1
1
0
1
1
1
0
1
0
1
1
1
1
0
2
1
2
1
1
0
1
1
0
3
1
1
2
0
2
0
0
0
0
1
2
0
1
2
2
0
2
0
0
1
1
2
0
1
1
1
2
0
0
2
1
1
3
1
1
2
0
2
1
1
0
1
1
1
0
1
1
1
1
1
1
1
1
1
0
1
2
1
1
2
2
2
1
3
2
1
1
1
1
1
1
2
0
1
1
1
0
2
1
1
1
2
2
1
1
1
0
0
1
1
1
2
1
0
0
1
0
1
1
1
1
0
1
1
2
2
1
1
1
1
0
2
1
0
1
1
1
2
0
0
1
1
1
1
1
1
1
0
0
1
1
1
2
2
2
1
1
1
1
1
1
0
0
0
1
1
2
1
0
1
1
1
1
0
1
1
1
1
1
2
1
1
0
1
1
0
2
1
1
0
1
0
1
1
1
1
1
2
1
0
2
1
1
1
2
1
0
1
1
1
0
1
1
0
2
0
1
1
0
1
3
0
1
0
1
1
0
2
1
1
1
2
1
0
1
1
1
1
3
0
1
2
2
1
2
2
0
1
1
2
1
1
2
0
1
1
1
1
1
2
0
1
1
2
1
1
1
0
1
1
0
1
1
0
2
1
1
0
2
0
1
1
2
2
1
2
2
2
1
0
2
0
1
1
2
1
0
1
1
1
1
1
1
0
1
1
1
1
1
1
0
1
1
1
1
0
1
1
1
3
1
1
2
2
0
1
1
0
0
2
1
1
1
1
0
2
1
2
2
2
1
1
0
1
2
2
0
1
0
1
1
1
1
2
0
1
1
1
1
0
2
2
1
1
1
1
1
1
1
3
1
2
2
2
0
1
1
0
1
0
0
0
1
1
2
0
1
0
0
1
2
1
1
1
1
0
1
1
1
1
1
1
1
2
1
2
2
1
1
1
2
0
1
2
0
1
1
0
1
0
1
0
1
2
1
1
1
1
1
1
1
1
2
1
0
1
1
1
2
2
2
2
1
0
2
1
1
1
1
2
0
0
1
2
0
3
0
0
1
2
0
0
0
1
0
0
1
0
0
2
0
1
2
2
1
0
1
1
2
0
2
0
2
1
1
0
1
1
1
2
1
0
1
1
1
1
1
1
1
2
1
0
0
2
2
1
1
1
2
1
1
2
0
1
2
1
1
1
0
0
3
1
2
2
2
0
1
0
1
1
1
1
1
0
1
1
2
2
2
2
2
1
2
0
2
1
1
0
1
1
1
1
1
0
1
1
1
0
2
1
1
1
1
1
1
0
1
1
1
1
1
2
1
1
1
1
1
2
0
1
1
1
1
1
2
1
1
0
1
0
2
1
1
0
1
2
0
0
1
1
2
2
2
0
1
0
1
1
1
1
1
1
1
1
0
0
1
0
1
2
1
1
1
2
1
1
1
2
1
0
1
0
2
1
1
1
1
1
0
1
2
2
1
2
1
1
1
1
1
0
1
0
1
1
1
1
0
1
1
0
0
1
1
1
2
2
1
0
1
0
1
0
1
1
2
2
1
1
1
1
0
3
1
1
0
1
2
1
1
1
1
1
2
1
0
0
0
2
1
2
1
1
1
0
1
2
1
0
1
2
1
0
0
0
1
1
0
2
2
1
1
0
1
2
1
1
2
2
1
3
1
0
2
2
2
1
0
1
0
1
0
2
0
2
2
0
1
2
1
0
1
0
0
1
2
1
1
0
0
1
1
2
2
2
1
1
2
1
1
1
1
0
0
1
2
1
2
1
2
2
0
0
1
0
1
2
0
1
1
1
1
1
0
1
1
2
0
1
2
2
2
0
1
2
1
2
1
1
2
0
1
1
1
1
0
2
1
1
0
2
2
1
2
2
1
1
1
1
2
1
1
2
2
1
1
2
1
1
2
1
0
1
1
2
1
1
0
0
1
0
1
0
1
0
2
1
2
2
1
0
3
0
1
1
1
1
1
0
0
2
1
0
1
0
2
0
1
0
2
0
0
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
0
0
3
0
0
1
1
1
1
2
1
2
1
1
1
1
1
1
3
1
0
2
3
1
0
1
0
0
1
0
0
2
1
1
1
0
2
1
1
1
1
1
2
2
1
0
1
1
2
2
2
1
1
1
0
1
2
2
1
1
2
2
2
1
1
1
1
1
1
1
2
2
1
0
1
0
1
1
0
2
0
1
2
0
2
1
0
1
1
1
2
1
2
2
0
2
1
0
2
0
0
2
2
1
2
0
1
1
2
1
1
2
1
1
1
1
1
2
2
1
0
0
1
2
3
1
1
2
2
1
1
1
0
2
0
2
0
2
1
1
0
1
0
0
1
1
1
0
2
2
0
1
1
2
0
0
0
2
1
1
0
0
1
2
1
1
2
1
1
1
0
1
1
2
2
3
1
2
0
1
1
0
0
1
1
1
0
0
1
0
1
0
1
1
1
1
2
0
1
1
0
1
1
1
2
1
1
0
1
1
0
1
2
1
2
1
1
1
1
1
0
1
1
1
1
1
2
2
1
1
1
1
1
1
1
0
2
0
1
0
1
1
1
1
3
2
1
1
1
2
2
2
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
0
2
2
1
2
3
1
1
1
0
1
2
2
1
2
2
0
2
1
0
1
1
2
2
0
0
0
2
1
1
1
3
2
1
0
2
0
1
1
1
1
1
0
2
1
2
1
0
2
1
0
1
2
1
1
1
1
1
1
0
1
2
1
1
0
1
2
2
1
0
1
1
0
1
0
2
1
0
2
2
0
1
0
1
1
1
1
1
1
2
1
1
2
1
0
1
1
0
1
1
2
0
2
1
1
1
1
1
1
0
0
0
1
1
1
2
0
1
0
0
1
2
1
0
0
2
1
0
2
1
1
0
1
1
2
1
2
1
2
1
1
2
1
2
1
1
1
2
2
0
1
1
1
1
1
2
1
2
2
2
0
1
0
1
2
2
2
0
1
1
2
0
1
1
1
0
1
2
1
0
1
1
1
1
2
2
0
1
1
0
1
1
2
1
1
0
2
1
1
1
0
0
1
1
1
2
1
1
1
1
1
1
1
1
0
0
0
2
0
2
1
2
1
2
2
1
1
2
0
1
2
2
1
0
1
1
1
1
1
1
1
1
1
1
0
2
2
0
1
1
1
1
2
2
0
1
0
0
1
2
2
0
1
1
1
1
1
1
1
0
0
2
1
1
0
2
1
0
1
1
1
2
1
1
1
1
1
1
1
1
1
0
2
0
2
0
2
0
1
1
1
1
0
1
1
0
2
1
1
2
1
0
1
0
1
1
1
2
1
2
1
2
1
1
1
2
2
1
1
0
1
1
0
0
2
2
1
0
1
1
0
1
1
0
2
0
1
1
1
0
2
1
1
2
2
2
2
2
0
0
2
2
1
0
2
1
1
0
1
2
2
2
2
1
1
1
1
2
1
1
1
0
2
2
0
1
0
1
0
2
1
0
2
2
0
1
1
2
2
0
1
1
1
0
1
2
2
2
2
1
1
2
1
1
1
0
1
1
2
1
0
1
0
1
1
1
1
1
0
2
1
0
1
1
0
1
1
1
2
1
1
1
1
0
2
1
2
0
1
2
2
2
2
2
1
1
2
1
0
1
1
1
0
1
2
2
1
1
0
1
1
2
1
2
0
1
1
2
1
2
0
0
1
1
0
1
2
0
1
1
0
1
1
1
2
1
1
0
0
1
1
2
0
1
1
1
2
1
1
1
1
0
2
2
1
1
0
2
1
1
1
1
1
2
1
0
1
2
1
1
1
0
1
1
1
1
1
2
1
2
1
1
0
1
0
2
1
1
1
2
0
0
1
1
1
2
1
1
0
2
1
1
1
0
1
1
1
1
0
1
2
1
1
0
1
1
1
0
2
0
2
3
0
2
2
1
2
2
1
0
0
1
1
2
0
2
1
1
1
1
1
1
0
2
1
1
1
1
1
1
1
1
1
0
1
1
1
1
0
1
0
1
1
1
1
0
1
0
1
1
2
0
1
1
1
0
0
0
1
1
0
1
0
2
0
1
1
1
1
2
1
0
1
1
1
0
2
1
2
1
1
2
2
1
2
1
2
1
1
2
2
1
1
0
1
1
1
1
1
1
2
0
1
1
1
0
1
2
2
2
2
1
2
2
2
1
1
1
1
1
2
0
0
1
0
1
1
0
1
1
1
0
2
2
1
2
1
2
1
1
2
1
1
1
1
2
2
1
1
1
1
2
1
0
2
1
1
0
2
1
2
1
1
4
1
1
1
1
1
1
1
0
2
2
2
1
0
2
2
1
1
0
1
1
1
0
0
1
1
0
1
1
1
1
2
1
1
1
2
1
1
2
1
0
1
0
1
2
1
1
2
0
0
1
0
0
1
0
1
1
0
1
2
1
2
1
2
2
0
1
1
2
2
2
2
0
0
2
0
2
2
2
1
1
2
2
1
2
1
1
0
0
1
1
1
1
2
1
1
1
1
0
0
0
1
2
1
1
1
1
1
2
0
1
1
2
0
0
1
2
0
1
1
2
1
1
1
0
1
0
1
1
2
1
1
1
2
2
2
1
1
1
0
2
1
2
1
1
1
2
2
1
1
2
2
2
1
2
1
2
0
1
0
0
1
1
3
1
1
1
1
0
0
1
0
1
0
1
1
0
2
0
2
2
2
2
0
1
1
0
1
0
1
1
1
0
2
2
2
1
2
2
1
1
1
1
2
1
0
1
2
1
1
2
1
0
2
3
1
1
0
1
1
1
0
1
1
1
2
0
1
1
1
0
1
1
2
2
1
2
1
1
1
1
1
0
1
1
1
2
0
1
1
1
1
2
1
1
1
2
5
1
2
2
2
1
1
1
1
1
0
1
1
0
2
0
1
2
0
0
2
2
1
0
0
2
2
0
0
1
0
0
1
1
1
2
1
0
0
1
1
1
2
1
1
2
2
2
0
1
2
1
2
0
2
0
0
0
1
1
1
0
1
1
1
1
1
2
0
1
1
2
0
2
1
0
2
1
2
1
1
1
1
1
1
1
0
1
0
1
2
0
1
1
1
1
1
0
1
0
0
1
1
1
1
1
0
0
1
2
2
0
1
0
1
1
1
1
0
2
0
2
1
0
1
2
0
0
1
1
2
0
1
0
0
1
1
1
1
0
1
2
1
1
1
4
2
1
2
1
0
1
2
0
0
2
1
1
1
0
2
1
2
0
1
1
1
1
0
1
1
0
2
1
1
1
1
2
1
1
1
1
1
2
0
1
1
1
1
1
1
1
1
1
1
0
0
1
3
1
1
2
1
1
1
0
1
2
1
2
2
1
1
1
1
1
1
0
1
0
0
2
1
1
2
0
2
1
1
1
0
0
2
1
1
2
0
0
1
1
1
2
1
0
1
1
0
1
1
1
2
1
1
2
1
1
1
1
1
0
1
1
1
1
2
1
1
1
1
1
2
2
1
2
1
2
1
1
0
1
2
1
0
1
1
2
0
0
1
1
1
0
1
2
1
2
1
0
1
0
1
1
0
0
2
1
0
1
2
0
1
2
0
1
2
0
2
2
2
1
1
2
0
2
1
0
2
2
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
2
1
2
1
2
2
2
2
1
1
1
1
2
2
2
2
0
0
1
1
1
1
1
1
2
0
1
1
1
1
1
0
1
1
1
2
0
1
1
1
2
0
2
2
1
0
0
2
2
1
2
3
0
0
1
1
3
2
1
2
1
2
0
0
2
1
0
1
1
1
0
2
1
1
1
1
0
1
0
1
1
2
2
1
1
1
1
0
2
2
1
2
1
1
2
1
1
2
1
2
0
1
1
0
2
2
2
0
2
0
2
1
0
1
1
0
2
1
1
0
0
0
1
1
2
1
2
0
0
2
1
1
2
2
1
1
1
0
1
0
2
2
2
2
2
1
1
1
0
1
2
1
2
1
2
2
2
1
1
1
2
1
1
0
0
1
2
1
1
1
1
0
2
2
0
0
2
1
1
2
1
2
0
1
1
1
1
2
0
1
0
0
1
1
0
1
2
1
0
1
2
1
1
1
1
1
3
1
1
2
1
0
1
1
2
1
0
2
1
1
1
0
1
0
1
1
1
0
2
0
0
2
1
0
0
1
1
1
1
1
2
1
0
1
1
1
1
0
2
1
2
1
2
1
1
0
2
3
1
0
1
1
1
1
2
0
2
1
0
0
1
1
1
1
1
2
2
1
1
1
1
0
1
1
1
1
1
2
0
0
1
0
1
0
1
1
1
1
2
0
2
2
0
0
2
0
2
0
1
2
0
2
2
0
1
1
0
1
1
0
1
2
2
0
2
1
0
0
1
1
1
0
1
2
1
0
1
0
1
2
1
2
2
1
2
0
1
0
0
1
0
2
1
1
2
1
0
2
1
0
0
0
1
1
0
1
0
2
1
2
0
1
1
0
1
1
0
2
1
2
1
1
1
1
1
0
0
1
2
1
1
1
0
1
1
2
0
2
1
1
1
0
1
1
0
2
0
0
1
1
1
2
1
1
2
1
1
1
0
1
0
2
0
0
1
2
1
0
1
0
1
2
2
1
1
0
1
1
2
1
2
1
1
0
2
0
1
2
1
2
1
1
0
1
2
0
1
1
1
0
1
1
0
1
1
1
0
2
2
1
1
1
1
1
1
1
2
0
1
0
0
1
1
2
1
1
1
1
0
2
1
1
1
2
1
1
2
1
0
2
0
1
2
1
0
0
1
2
0
0
2
3
1
0
1
0
1
2
1
1
0
1
1
0
0
2
0
1
1
2
1
0
1
1
1
0
1
0
0
1
2
2
1
1
2
1
1
0
0
1
6
1
0
1
1
1
0
1
1
1
1
1
2
1
1
1
2
0
1
1
1
0
1
1
1
2
1
2
1
1
1
1
1
0
5
1
1
1
1
1
1
1
0
1
0
0
1
1
1
1
0
1
1
2
1
1
1
1
1
1
1
1
2
1
2
1
2
1
2
1
0
1
1
0
4
1
1
1
1
0
1
2
1
2
1
2
1
1
1
0
2
2
1
2
0
1
0
0
1
0
1
0
0
0
1
2
2
0
1
1
2
2
0
1
0
1
2
1
2
1
2
1
1
0
2
0
1
1
1
1
2
1
1
1
1
1
2
0
2
1
1
1
1
0
1
0
2
1
1
1
1
2
1
1
2
1
1
0
2
2
1
0
0
1
1
2
1
0
1
2
0
2
1
0
1
1
1
2
1
2
1
2
1
1
1
1
1
2
0
2
2
1
2
1
2
2
2
2
1
0
1
1
0
1
2
2
1
2
0
0
2
1
2
1
1
1
1
1
0
0
2
1
1
1
2
0
0
1
1
0
1
1
2
1
1
1
3
1
1
2
1
2
1
0
2
0
1
1
2
1
0
2
1
1
1
0
1
1
2
1
2
2
1
1
0
1
1
1
1
2
1
1
1
1
1
1
1
2
0
1
1
1
1
1
2
1
1
1
1
2
0
1
1
2
2
2
1
1
0
0
1
1
2
1
0
2
2
1
1
0
0
2
4
0
0
1
3
7
1
2
0
0
1
1
1
1
1
1
1
1
0
0
1
1
0
1
2
1
1
1
1
1
0
2
2
1
1
0
1
1
2
1
2
0
0
0
2
1
1
0
1
2
2
0
0
1
2
0
0
2
1
2
1
1
1
0
2
0
2
1
2
2
2
0
0
0
1
2
1
1
0
0
2
1
0
2
1
0
1
0
1
1
0
2
1
1
0
2
1
0
2
1
1
0
0
2
0
1
2
2
2
0
1
0
1
1
0
2
1
2
1
0
0
2
2
0
0
1
2
1
1
0
0
0
1
1
2
1
0
1
1
1
2
2
2
1
1
2
0
2
1
2
1
1
2
0
0
1
1
1
1
2
2
2
1
1
0
1
2
2
1
1
1
1
1
1
1
0
1
0
0
2
1
1
1
1
0
1
0
0
1
0
1
1
1
1
0
1
2
1
0
2
1
1
0
1
1
2
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
0
1
1
1
0
2
1
1
1
1
1
2
1
0
1
1
2
1
2
0
0
2
0
2
0
1
0
1
2
1
1
0
0
1
1
1
1
1
1
2
1
2
1
2
1
0
2
0
1
0
0
2
1
3
2
1
1
2
0
2
1
1
1
3
1
1
1
1
2
2
2
1
1
2
1
1
0
1
1
1
1
1
1
1
2
1
1
2
0
1
2
1
1
0
0
0
0
2
1
0
1
2
1
1
1
0
0
0
1
0
1
2
2
0
2
1
1
1
1
1
1
0
1
0
2
1
1
0
1
1
1
1
1
1
1
1
0
1
2
1
1
1
2
2
2
0
1
2
1
1
1
0
1
1
1
1
1
1
1
2
1
0
0
1
0
0
1
2
1
1
2
0
2
1
2
0
0
1
1
1
3
1
1
2
2
2
2
0
1
0
1
1
0
1
1
2
0
1
0
1
0
0
2
2
1
2
0
0
1
1
1
0
1
1
1
1
2
1
0
1
2
2
0
1
2
1
0
1
0
1
2
1
2
2
2
1
1
2
1
1
1
1
1
1
1
3
1
0
1
1
2
0
1
1
0
1
1
0
2
2
1
1
1
1
1
2
2
2
1
1
1
1
2
1
1
1
2
1
0
1
1
0
1
1
1
1
1
1
2
1
2
2
1
0
1
0
1
1
1
0
1
0
1
1
2
2
1
1
1
1
1
2
2
0
2
2
1
2
1
1
0
0
2
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
1
2
2
1
2
1
1
0
1
1
1
1
2
2
0
0
1
0
2
1
1
2
1
2
0
0
1
0
2
1
1
0
1
2
1
1
0
3
1
1
2
1
1
0
1
0
0
1
1
1
1
1
0
1
1
1
1
2
1
2
2
0
0
1
1
2
2
1
0
2
1
1
1
1
2
1
0
0
1
1
2
0
1
1
0
1
1
0
1
1
3
1
1
0
0
1
2
2
0
1
1
1
1
0
2
1
0
2
1
1
2
1
2
1
2
0
1
1
1
1
2
2
1
1
1
0
1
2
2
1
2
0
1
1
2
2
2
1
0
0
1
0
1
0
1
1
0
1
2
1
2
2
1
0
0
1
1
0
2
0
1
1
2
2
1
2
1
0
1
2
2
1
2
1
4
2
0
1
1
1
1
1
1
0
1
1
0
1
0
1
2
1
0
1
0
2
1
1
0
1
1
1
1
0
1
1
2
1
1
1
2
0
1
1
1
1
2
1
0
1
1
0
1
1
2
0
0
1
0
1
1
2
1
1
0
0
2
2
1
0
2
1
1
1
1
1
0
0
1
1
1
0
2
1
0
2
1
0
1
2
0
1
1
0
0
1
1
1
0
1
1
0
1
1
0
0
1
0
1
1
1
2
0
1
0
1
2
2
1
1
1
1
0
1
1
1
2
1
0
1
2
0
1
2
1
0
1
3
1
1
1
2
2
1
2
1
0
1
1
1
1
1
1
1
0
1
1
2
0
2
0
1
2
1
1
1
1
1
0
2
1
1
2
2
1
1
0
1
0
2
1
1
1
1
2
2
0
1
0
1
1
0
1
0
1
1
2
2
1
0
1
1
0
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
0
1
1
0
1
0
1
2
0
2
2
2
1
2
1
2
1
1
1
1
1
2
1
1
1
0
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
0
0
0
1
2
2
0
1
2
1
0
2
1
0
2
1
1
0
1
1
0
1
0
1
2
1
0
1
1
2
1
0
2
0
0
2
0
1
1
2
1
1
1
0
0
2
1
2
0
1
1
1
0
1
1
1
1
1
0
1
1
1
2
2
0
1
2
2
1
1
1
0
0
0
0
1
2
3
1
0
0
1
1
0
1
1
0
1
1
1
1
1
1
1
2
0
1
1
1
0
0
1
2
2
1
1
2
0
1
2
0
0
2
2
0
1
1
2
0
1
1
0
2
2
1
1
1
2
1
2
1
1
1
1
1
2
1
2
1
0
1
1
1
2
0
2
1
0
0
0
1
2
1
1
1
2
2
2
2
1
0
1
1
0
2
0
1
0
0
0
2
0
2
1
2
0
1
2
0
1
2
0
1
0
0
0
0
1
1
2
2
1
0
1
1
0
2
0
1
1
2
1
2
0
1
0
1
1
1
0
1
1
0
1
1
1
1
1
1
2
2
0
1
0
0
2
1
0
1
2
0
2
0
2
2
2
2
2
2
2
1
1
0
0
1
1
1
2
1
1
1
1
2
2
1
1
0
0
1
2
2
0
0
1
0
1
1
2
1
1
2
0
2
2
1
2
1
1
1
0
1
1
1
1
2
1
1
1
1
1
3
1
1
1
1
2
2
2
1
1
1
1
1
1
1
0
2
2
1
1
0
0
2
1
2
1
0
0
1
0
2
0
1
1
0
0
0
2
1
1
2
1
0
1
1
0
2
1
2
1
1
4
1
1
1
0
0
0
1
2
2
2
3
2
2
1
0
2
2
2
1
0
0
1
1
0
2
2
1
0
2
1
2
1
2
1
0
0
1
1
1
1
0
2
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
3
1
1
2
2
1
2
1
2
1
2
2
1
1
0
0
2
1
0
1
2
2
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
2
1
0
1
1
1
1
1
0
1
1
1
2
0
2
1
1
0
1
0
0
2
1
1
0
1
2
1
1
1
1
1
1
2
1
0
1
1
0
1
0
1
0
2
2
1
2
0
0
0
2
1
1
3
2
3
1
2
1
1
1
1
1
2
3
1
2
0
0
0
0
0
1
1
1
0
0
1
1
1
2
1
0
2
3
1
1
1
1
1
0
2
1
1
1
1
1
2
0
1
1
0
1
2
0
0
0
2
1
1
0
1
1
1
0
0
1
1
3
1
1
1
1
1
2
1
0
0
3
1
0
1
1
1
1
2
1
1
0
0
1
3
0
1
0
0
2
0
1
2
2
0
2
1
1
1
2
1
0
2
1
1
1
0
1
0
2
1
0
1
1
0
0
1
1
1
2
2
2
2
2
2
2
1
1
2
1
1
1
2
2
2
1
0
2
1
1
0
0
0
0
1
1
1
1
0
1
2
1
1
0
1
1
1
0
1
1
0
1
1
1
2
0
2
1
2
1
1
1
1
1
3
0
0
1
2
1
1
1
0
2
2
2
2
1
1
1
1
1
2
1
1
2
2
1
2
2
2
2
0
0
0
0
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
0
1
1
2
2
0
1
1
1
0
1
1
0
2
1
1
2
0
1
1
1
1
1
1
1
1
0
0
4
2
1
1
0
2
0
0
2
0
1
1
2
2
1
1
2
1
0
4
2
1
1
1
1
2
1
1
1
3
1
1
0
1
0
1
0
2
1
1
1
1
1
1
1
2
1
1
1
2
0
1
1
2
1
0
1
2
2
2
1
3
0
0
1
0
1
0
1
1
1
1
0
0
1
0
1
2
1
1
1
1
1
2
1
1
1
1
0
1
0
1
1
1
3
0
3
1
0
0
1
1
2
1
0
0
2
2
1
1
1
2
1
1
1
0
2
2
0
0
2
2
1
1
1
1
1
1
0
0
2
1
1
0
1
2
1
1
1
2
1
1
0
2
2
0
0
2
1
1
0
1
1
2
2
0
1
1
2
2
1
1
0
1
2
0
1
2
0
1
1
1
2
0
2
1
1
1
2
2
1
1
0
0
2
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
0
1
2
0
1
1
0
1
0
1
1
1
1
1
0
0
2
1
2
4
1
1
0
1
0
1
1
1
1
2
2
2
0
1
2
2
1
3
1
1
1
1
2
0
1
1
1
1
1
1
1
1
1
0
1
0
1
1
1
1
1
1
2
1
0
2
1
2
2
1
1
1
0
2
0
1
1
1
0
1
1
1
2
0
1
0
2
1
1
1
1
1
1
2
1
2
1
0
2
0
2
1
1
1
1
1
1
1
0
1
1
1
1
1
2
2
0
1
1
2
2
1
2
1
1
1
1
1
1
0
2
1
0
0
1
0
1
2
0
0
1
2
1
2
1
1
1
1
1
1
0
1
2
1
0
1
1
1
1
1
1
1
2
1
1
0
1
1
1
0
0
0
2
1
1
1
1
1
1
1
1
0
0
1
1
2
1
1
1
1
1
0
2
0
1
1
1
1
1
1
2
0
0
2
1
2
0
0
2
0
2
1
1
1
1
1
2
1
1
1
1
1
0
1
2
2
0
2
0
1
1
2
2
1
1
2
0
2
1
1
0
0
1
1
0
0
1
1
1
0
1
2
1
0
1
1
0
1
0
1
1
0
1
1
2
0
1
1
1
1
2
0
1
1
2
2
1
0
0
0
1
1
0
2
1
2
2
2
1
0
1
1
2
1
0
0
0
2
2
2
1
0
1
2
2
1
1
1
2
0
1
1
1
1
1
1
0
1
1
1
0
2
0
0
1
2
0
0
1
1
1
1
1
2
2
0
2
1
1
1
1
1
0
1
1
2
0
1
1
2
1
2
1
1
1
0
2
1
2
2
1
0
1
0
2
1
1
0
2
1
1
0
1
2
0
1
1
1
0
1
1
1
1
2
3
1
1
0
1
2
0
1
0
1
1
1
1
2
1
1
1
1
0
1
1
2
1
1
1
0
0
2
1
1
0
0
1
1
2
3
2
1
1
1
0
0
1
1
0
2
1
1
2
2
4
2
1
1
1
1
1
1
1
2
1
2
0
1
1
0
1
2
2
1
1
2
1
1
1
0
2
1
1
1
1
0
2
1
1
2
1
0
1
1
1
1
2
1
2
1
0
2
2
1
0
0
2
1
0
1
1
1
1
1
0
2
1
2
1
1
0
1
1
1
1
1
0
1
0
2
2
1
1
1
1
0
2
1
1
1
2
1
2
2
2
1
1
0
2
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
1
1
1
2
1
0
0
1
1
1
0
0
1
1
0
2
2
1
1
0
2
2
1
1
1
0
2
0
2
2
0
1
1
0
1
0
1
2
0
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
0
0
1
2
1
1
1
1
1
1
1
1
3
1
0
2
2
1
1
1
1
1
2
2
2
0
1
1
1
1
0
1
1
2
2
1
2
2
1
0
1
1
1
2
1
2
2
2
1
1
1
2
1
2
1
1
1
1
2
2
1
2
1
0
2
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
0
2
2
1
1
1
1
1
1
2
2
0
1
0
1
1
1
1
1
0
1
2
1
1
1
1
2
2
1
2
1
1
1
1
1
1
0
1
1
2
1
2
1
1
0
2
1
0
2
2
0
1
0
1
0
0
1
0
0
1
1
1
2
1
0
1
1
1
1
1
1
1
0
1
1
2
1
0
2
1
1
2
1
0
2
1
0
1
1
1
2
1
2
2
2
1
1
1
2
1
1
1
0
0
1
0
1
1
0
0
1
2
1
1
1
2
3
2
1
2
1
2
1
2
2
0
1
1
0
1
1
1
1
1
2
1
0
1
1
1
1
0
1
2
1
1
1
2
1
1
0
0
0
2
1
2
2
1
2
1
2
2
1
0
1
1
0
1
1
1
0
1
1
2
2
0
1
2
2
2
1
1
0
1
1
1
2
1
0
0
1
2
0
1
0
1
1
1
1
1
1
1
0
1
1
1
2
1
2
0
2
2
0
0
1
2
1
2
2
1
1
0
2
1
0
1
1
1
1
1
2
0
1
2
1
2
1
2
3
2
1
2
1
0
1
2
1
0
1
0
2
2
0
0
0
2
0
2
1
1
0
2
2
2
2
0
0
0
1
2
1
1
3
1
1
1
2
1
2
0
1
1
1
1
0
0
1
2
1
0
2
2
1
2
1
0
0
0
1
1
1
1
1
0
2
2
2
1
1
2
2
0
1
0
0
1
1
1
0
1
0
0
2
2
2
1
1
0
0
0
2
1
1
1
0
1
1
1
1
0
2
2
2
1
1
2
2
1
1
2
1
2
1
3
2
0
2
1
0
0
1
0
1
1
1
2
1
0
2
1
1
1
1
1
1
1
1
2
1
1
0
1
1
2
0
2
0
1
1
1
1
1
1
2
2
0
1
2
1
1
0
2
1
1
1
1
0
1
0
2
1
2
2
0
0
1
1
1
1
0
0
2
0
2
1
1
2
1
2
1
2
1
1
2
0
1
0
1
1
1
1
2
1
1
1
2
1
2
2
1
2
1
1
0
1
2
1
0
1
2
1
1
0
1
2
0
1
1
1
1
1
1
1
1
1
2
1
1
1
0
1
0
0
1
1
1
0
1
1
2
2
1
1
1
1
1
0
2
0
1
1
1
0
0
1
1
1
1
1
1
1
1
0
1
1
0
1
2
1
1
1
0
1
2
1
2
1
1
1
1
0
0
2
1
1
1
0
1
1
1
1
0
1
1
1
2
1
1
1
0
1
1
2
1
1
0
1
1
1
1
1
0
2
0
2
1
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
0
1
1
2
1
2
1
1
0
2
0
2
1
1
1
0
1
2
0
0
1
1
1
10
0
2
2
1
0
1
1
1
1
1
0
1
2
1
1
0
2
0
1
1
0
0
2
2
1
1
1
2
2
2
1
1
1
1
1
1
1
2
0
1
1
2
1
0
1
0
1
1
0
2
1
1
1
3
0
1
1
1
1
0
1
0
2
1
1
1
1
1
0
1
0
1
2
1
1
1
1
1
1
1
2
1
2
1
0
2
1
0
2
1
1
1
1
0
1
1
0
0
2
2
1
1
0
1
1
2
0
0
2
0
0
1
1
1
0
1
0
0
1
2
1
1
0
2
2
1
1
0
1
0
2
1
0
2
0
2
1
0
1
1
2
1
1
3
1
1
2
0
1
2
1
1
0
1
2
1
1
1
1
2
1
1
0
0
1
2
2
0
2
1
2
5
2
0
1
1
1
1
0
2
2
1
2
0
1
1
2
2
1
1
1
1
2
1
1
1
1
0
0
2
1
2
1
0
1
1
2
1
1
1
2
2
1
0
0
2
2
1
1
1
1
1
1
1
2
1
1
0
2
1
2
1
0
0
1
0
0
2
1
1
2
1
1
2
0
2
0
1
2
1
1
0
0
1
2
2
1
1
2
1
1
1
0
0
1
1
2
1
2
1
0
1
1
1
1
1
1
0
1
2
0
2
1
1
1
2
1
1
1
0
2
2
1
2
2
1
2
1
1
2
1
0
0
0
1
1
2
1
1
1
2
0
1
1
0
2
0
2
1
1
1
1
2
1
1
2
0
2
1
1
0
1
1
1
1
1
1
1
1
0
0
0
1
1
2
2
1
1
1
0
1
1
1
1
1
0
1
2
1
2
2
2
1
1
1
1
0
0
1
1
1
0
0
1
0
1
1
0
2
1
1
1
2
2
1
2
0
1
2
2
2
2
1
0
0
0
1
1
1
2
1
2
1
2
0
2
0
2
2
2
0
1
0
1
1
2
1
1
1
1
1
2
1
2
1
2
0
2
1
1
1
2
0
0
3
1
1
1
0
1
1
1
2
2
0
0
2
0
1
1
1
0
1
1
1
2
2
2
1
1
1
0
1
1
1
0
1
1
1
1
1
1
0
2
1
1
2
2
1
2
1
0
1
1
2
0
1
1
1
2
2
2
0
1
0
1
1
1
1
1
1
1
1
1
2
0
0
1
0
0
1
0
1
0
1
2
2
0
1
2
1
0
1
1
1
2
1
0
0
1
0
1
1
1
1
1
1
1
1
0
2
1
1
1
2
0
2
0
1
1
0
1
2
1
1
0
1
0
1
1
2
1
2
2
2
3
1
1
1
4
2
2
0
1
1
1
1
1
1
1
0
1
0
1
2
1
1
2
1
1
0
0
1
2
1
1
1
2
1
2
1
1
0
0
1
1
1
1
1
2
1
1
2
0
0
1
1
0
1
0
1
0
0
1
1
1
1
1
1
2
2
1
1
0
0
1
0
1
0
0
2
1
1
1
0
0
1
1
0
1
0
2
0
1
0
2
1
2
0
2
1
1
2
1
0
4
1
1
2
1
0
1
1
0
1
2
1
0
0
0
0
2
1
0
1
1
0
1
2
2
1
1
2
1
2
1
2
2
1
2
1
0
0
1
2
1
1
1
1
0
2
1
1
1
1
1
0
1
0
1
0
1
2
1
1
0
2
1
1
1
1
1
0
1
1
2
1
0
0
1
2
1
2
0
1
2
1
2
1
2
1
1
0
0
2
0
2
2
1
1
1
1
1
2
2
1
2
0
2
2
1
1
2
2
1
1
1
1
0
2
2
1
1
1
2
1
1
1
0
0
1
1
1
1
1
0
1
0
1
1
1
1
1
1
0
1
1
1
1
1
1
2
2
1
0
1
2
0
1
1
1
2
2
1
1
0
0
1
2
1
1
1
2
1
1
1
1
1
1
1
0
0
1
1
1
2
1
0
2
2
1
0
1
1
0
1
1
2
2
2
1
0
2
2
1
1
2
2
1
2
0
1
1
0
1
1
1
2
2
1
1
0
2
0
1
2
1
1
2
1
2
2
0
2
1
1
2
1
0
2
2
0
1
0
2
2
2
1
2
1
0
1
1
1
1
1
0
1
0
0
1
0
1
2
1
4
1
0
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
2
2
2
0
0
2
1
1
1
1
0
0
1
1
1
2
1
0
0
1
0
1
1
1
0
2
1
1
2
2
2
2
1
1
1
2
2
0
0
0
2
0
1
2
0
1
1
2
0
1
1
2
1
1
0
1
1
1
1
0
1
1
1
2
0
1
1
2
0
0
1
2
2
2
1
1
2
1
2
1
2
1
2
2
1
2
1
1
1
1
0
1
1
2
1
1
1
0
4
0
2
1
1
1
2
1
0
2
1
0
1
1
1
0
1
2
0
1
1
0
1
0
1
1
1
1
2
1
1
1
2
1
2
0
1
2
0
1
1
0
2
0
2
1
1
0
1
1
2
0
1
1
1
2
1
1
1
1
2
1
1
1
1
0
1
0
1
1
1
1
2
1
1
1
2
1
1
1
2
2
6
0
2
0
1
1
1
2
2
2
0
1
2
0
1
1
1
2
1
2
1
1
2
1
0
1
1
1
2
2
2
1
2
1
2
1
2
1
1
1
0
2
1
2
0
0
2
1
2
1
0
2
1
0
0
1
1
1
2
1
1
1
0
2
1
3
0
1
1
2
1
0
1
1
3
3
1
1
0
1
1
0
1
0
1
1
1
2
2
0
0
0
1
2
1
1
1
2
2
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
1
2
1
2
1
1
1
1
1
1
1
2
1
2
1
1
0
1
1
1
2
1
1
1
2
0
2
1
1
0
1
2
1
1
1
3
2
1
2
1
1
1
0
1
2
1
1
1
2
1
1
1
2
1
0
2
1
1
1
1
1
2
2
2
1
0
1
0
1
2
2
1
0
1
0
0
1
1
1
1
0
1
1
2
0
1
0
1
1
1
1
2
1
1
1
2
2
2
1
2
0
1
0
1
1
0
0
1
1
0
1
2
0
0
0
2
1
1
1
2
1
2
1
1
1
1
2
2
0
1
0
2
1
2
0
1
1
0
1
1
2
2
1
2
2
1
1
0
1
0
1
1
1
0
1
1
1
0
1
1
1
0
2
0
1
1
1
0
2
1
2
1
1
1
1
2
1
2
1
1
1
2
1
1
1
2
0
0
1
1
2
2
1
2
0
2
0
0
0
1
0
1
1
3
0
1
1
1
0
2
1
1
0
2
1
2
2
0
2
0
2
2
0
2
2
0
2
1
1
1
0
1
1
1
0
1
2
3
2
0
1
1
1
1
1
1
2
1
2
1
1
1
2
0
0
0
1
2
0
0
2
2
1
1
1
0
1
2
1
0
1
2
2
1
2
0
1
1
1
2
2
0
0
2
1
1
1
0
1
1
1
0
0
1
0
1
0
0
1
1
1
4
1
1
1
1
2
1
2
1
1
1
2
1
1
0
1
1
0
1
2
0
1
1
0
2
0
0
0
0
2
1
3
1
1
1
0
2
1
2
2
1
1
0
1
1
2
1
1
2
1
1
1
1
0
2
1
0
1
1
1
0
1
2
2
0
1
1
1
1
1
0
2
1
0
0
2
2
3
0
0
3
0
1
0
1
2
1
1
2
0
1
1
0
0
1
2
1
2
1
1
1
1
2
1
1
1
2
1
1
1
1
1
0
2
1
1
0
1
1
2
1
0
1
1
1
1
2
1
1
1
1
1
2
0
2
1
1
1
1
2
1
2
2
1
2
0
1
1
2
1
0
2
1
1
2
2
1
2
2
0
1
0
2
2
0
1
2
1
2
1
2
2
0
2
0
2
1
1
1
0
2
2
0
1
1
1
1
0
1
1
2
1
1
2
2
1
0
1
1
1
0
1
0
1
2
1
0
1
2
1
2
0
1
1
1
2
1
1
1
1
0
2
2
2
2
0
1
0
1
0
1
2
1
2
0
0
1
1
0
2
1
1
1
1
1
1
1
2
1
1
1
2
2
1
0
0
2
0
2
0
1
1
2
1
1
1
2
1
2
2
2
1
1
1
1
1
1
1
1
2
1
1
1
0
1
0
1
1
1
1
2
0
0
0
1
1
1
2
0
1
2
1
1
0
4
2
2
1
3
0
1
1
1
2
0
1
0
1
1
1
2
2
2
2
0
1
1
2
1
1
1
1
0
2
1
1
2
0
0
2
1
2
1
1
1
1
1
1
0
1
0
1
1
1
1
2
0
2
1
1
0
1
1
1
1
1
2
2
2
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
0
0
1
1
1
2
0
2
1
0
0
2
0
1
1
2
2
2
1
1
1
2
0
2
0
2
1
1
0
0
2
1
1
1
1
0
1
1
2
0
1
1
0
0
1
1
1
0
1
0
0
1
1
0
1
2
0
2
0
2
0
1
1
0
1
1
2
0
1
2
1
2
0
1
1
1
0
2
1
1
2
0
1
0
1
1
0
1
1
1
1
1
2
1
0
1
0
2
2
0
2
1
0
1
2
0
2
2
0
1
1
2
0
1
0
0
0
2
1
1
1
0
1
1
0
1
1
0
1
0
0
2
1
1
1
1
2
1
1
1
0
2
1
1
0
1
0
0
2
0
1
1
4
1
1
1
1
1
2
1
1
1
0
1
1
1
3
1
1
2
1
1
2
1
2
2
1
1
1
2
1
1
2
0
1
0
0
1
1
1
1
0
1
0
1
1
0
1
1
1
2
1
2
1
2
2
1
1
2
0
1
2
0
0
2
1
1
1
1
1
1
0
0
2
0
1
1
2
1
0
1
1
0
3
2
0
1
1
0
1
0
1
0
2
1
1
0
1
1
1
1
2
1
2
1
0
1
1
1
0
2
0
1
1
1
0
1
1
1
1
1
1
2
2
1
0
0
1
0
2
1
1
2
1
1
1
1
1
0
0
2
0
1
2
2
2
2
0
0
1
0
1
1
0
0
1
2
0
0
2
2
2
1
1
1
1
0
2
0
1
2
0
2
2
1
2
1
1
2
1
0
1
1
1
1
0
1
2
2
1
0
2
0
1
1
2
1
1
0
0
2
2
0
1
1
1
1
0
1
1
1
1
1
1
0
1
1
1
1
0
1
0
1
2
0
1
1
0
0
1
1
0
1
2
2
1
1
0
1
0
2
1
1
1
1
1
1
1
1
2
1
0
2
1
1
2
1
2
1
0
2
1
1
1
1
1
0
1
0
2
1
2
0
1
1
0
1
1
1
0
1
2
1
2
1
2
2
0
2
2
0
2
1
1
1
1
1
0
1
2
1
0
1
1
0
0
1
1
1
0
0
1
1
1
1
1
2
1
1
1
1
0
1
1
1
1
1
1
1
1
1
11
2
1
2
1
1
2
1
2
0
1
2
0
1
0
1
1
0
1
0
1
0
1
2
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
2
1
2
2
0
1
0
1
2
0
1
1
1
2
2
1
1
1
1
0
1
0
1
2
0
1
1
2
2
1
1
2
1
1
2
2
1
1
1
1
1
1
2
0
1
2
2
2
1
2
1
0
1
1
0
1
0
2
1
2
1
2
1
1
0
1
0
0
1
0
1
0
1
2
1
0
1
1
1
0
1
1
0
0
0
2
1
2
1
1
0
1
0
1
1
0
1
2
1
2
1
1
0
1
1
1
1
2
2
1
0
1
0
1
1
1
1
2
2
0
1
1
1
2
1
1
1
0
0
0
1
0
1
1
1
0
0
1
2
2
1
1
1
2
2
2
1
2
2
1
2
2
0
2
2
1
1
1
2
1
1
1
0
0
1
2
1
1
1
2
0
1
0
2
1
1
1
1
1
2
1
0
0
1
1
1
1
1
2
2
0
1
1
1
1
1
1
1
2
0
1
2
1
2
4
2
0
0
1
1
1
2
1
2
0
2
1
1
0
0
1
1
1
0
1
2
0
2
2
1
1
4
1
1
1
1
2
1
1
1
1
2
0
1
2
0
1
2
1
0
0
1
1
1
1
1
0
2
2
0
1
0
1
0
0
1
1
0
0
0
1
2
0
1
2
2
0
0
1
1
1
1
0
2
0
1
2
0
2
1
1
1
1
2
2
1
1
2
0
1
1
0
2
1
2
1
2
2
0
1
2
2
0
0
0
1
1
1
2
2
1
1
2
1
1
0
2
2
1
0
1
0
2
1
1
1
0
1
1
2
1
0
1
1
1
2
2
0
2
2
1
1
1
0
1
1
2
1
0
0
2
2
1
1
1
1
2
0
2
0
1
1
1
1
1
2
0
1
2
0
2
0
1
1
1
0
2
2
1
0
1
0
1
1
0
0
1
1
1
2
1
1
1
1
1
1
1
0
1
0
2
1
0
0
0
2
1
0
0
1
2
2
1
0
2
2
0
2
1
2
2
1
1
2
0
1
1
1
1
0
1
1
0
1
1
2
3
1
0
1
0
1
2
0
1
1
1
1
1
0
0
1
1
0
0
1
0
2
2
1
1
1
2
2
2
1
1
1
0
2
3
1
1
1
2
1
0
0
1
2
1
0
1
1
1
0
2
0
2
1
1
2
1
1
1
1
1
1
1
1
1
2
0
1
2
0
1
2
0
0
0
2
1
0
2
1
1
1
2
2
1
1
0
1
0
0
1
0
1
1
1
1
2
2
0
1
1
0
1
0
0
1
1
1
0
1
1
0
0
2
3
0
2
1
3
3
2
1
2
2
1
1
1
1
1
1
1
0
2
0
2
1
1
1
1
2
1
0
1
2
1
0
1
1
1
1
1
1
1
1
4
0
0
1
1
2
1
0
2
1
1
2
1
1
0
1
2
1
0
1
0
0
1
0
2
2
3
1
2
0
2
1
1
0
1
1
0
1
1
1
2
1
1
2
1
0
1
0
1
1
1
1
2
2
0
2
1
0
0
2
1
2
1
2
1
0
1
2
1
1
1
0
1
0
1
0
2
2
1
0
1
0
0
1
2
2
1
1
1
2
2
0
2
2
1
1
0
2
2
1
1
1
0
1
1
2
2
1
1
1
1
2
1
2
1
1
1
1
1
1
0
1
1
1
0
1
1
1
0
0
0
0
0
2
1
0
1
2
0
1
1
1
1
2
0
1
2
1
1
0
2
2
1
1
1
1
2
2
1
1
2
1
2
1
1
0
1
2
1
1
2
1
2
1
1
0
1
2
5
1
2
1
1
1
1
1
1
1
2
3
2
0
1
1
2
1
2
0
1
0
1
0
0
1
1
1
2
1
1
1
1
1
1
1
0
1
1
2
1
2
1
2
1
1
1
1
1
0
2
1
0
1
1
1
1
2
5
0
2
1
1
2
1
1
1
1
1
1
0
0
0
1
3
0
1
2
1
1
1
0
1
1
2
1
1
1
0
1
1
1
0
2
1
0
1
1
2
1
2
1
0
1
2
1
1
0
1
2
0
0
1
0
1
1
1
2
0
1
1
1
0
2
1
2
1
1
1
1
1
0
1
1
1
2
1
1
1
1
1
2
0
1
1
2
1
1
1
1
0
1
1
0
2
1
1
1
0
1
0
0
1
0
2
1
0
1
1
2
0
0
1
0
1
1
0
1
1
2
0
0
0
2
1
1
1
0
0
0
1
2
2
0
2
1
2
1
1
1
1
2
0
1
1
0
2
1
1
0
1
1
1
0
1
1
2
1
2
2
1
1
0
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
0
0
2
1
0
1
1
0
2
1
1
2
2
0
2
2
1
1
1
2
0
1
2
2
2
1
1
1
2
0
1
1
1
0
1
0
1
1
1
0
0
1
2
1
1
0
1
0
1
1
0
1
1
1
1
2
1
0
1
2
2
1
0
1
2
1
0
1
1
1
2
1
0
1
0
3
0
1
1
0
0
1
1
0
1
1
1
1
1
1
1
1
2
1
0
1
2
2
1
1
1
1
2
0
3
2
1
0
1
2
2
2
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
2
1
0
1
1
1
1
1
1
1
1
1
2
1
0
0
2
1
1
1
1
2
2
4
1
2
2
2
2
0
2
0
2
4
0
2
2
1
2
1
1
1
1
1
2
1
1
1
2
1
1
2
2
2
1
2
1
2
1
2
1
1
1
1
0
0
3
1
1
0
1
2
1
2
2
1
1
1
2
1
0
1
0
1
0
2
1
2
0
2
1
1
1
2
0
1
1
1
1
2
1
1
1
1
0
2
1
2
0
1
1
1
1
1
1
0
2
1
2
2
0
1
1
1
1
1
2
1
1
1
2
2
0
0
1
1
0
3
1
1
2
1
1
0
0
2
1
0
1
0
0
1
1
1
2
1
1
0
0
1
0
1
0
2
2
1
2
1
1
1
1
1
1
0
1
1
1
0
1
1
0
1
2
1
2
1
0
1
1
2
2
0
1
3
1
1
1
2
1
2
1
1
1
1
2
2
0
2
0
1
2
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
2
1
0
1
0
0
0
2
1
2
0
1
2
0
2
1
2
0
2
2
1
1
2
1
1
1
1
0
1
1
0
1
3
0
0
1
1
1
1
0
1
1
1
0
1
0
1
1
1
1
0
3
1
1
1
2
1
1
1
1
1
1
1
0
2
1
2
1
1
2
1
1
0
2
1
0
0
1
2
1
0
1
1
0
1
1
0
2
1
2
1
1
2
1
1
1
2
1
0
2
1
0
1
1
0
1
2
2
1
1
1
2
1
0
0
1
1
2
2
1
1
2
0
1
1
1
0
1
2
2
1
1
0
0
0
1
0
0
1
1
1
1
1
1
4
1
3
1
1
2
0
1
1
1
1
0
1
1
1
2
1
1
1
0
2
0
1
1
1
1
1
1
1
2
2
1
1
0
1
2
1
0
1
1
1
1
1
0
0
1
0
2
1
1
1
1
0
2
1
0
1
2
2
0
0
2
0
1
2
1
2
2
1
1
2
1
1
1
1
2
0
1
1
1
0
2
1
1
1
2
0
1
2
1
1
2
2
2
1
1
1
1
2
1
1
0
1
0
2
1
1
0
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
0
0
1
0
1
1
1
1
1
1
1
0
2
1
1
0
1
1
0
1
1
1
0
1
1
2
1
1
1
1
1
0
2
1
0
2
1
0
1
0
0
0
1
2
1
1
1
1
1
0
1
1
1
2
1
1
1
1
0
2
0
1
1
1
1
1
1
1
2
1
0
2
1
1
1
1
2
1
0
2
1
1
1
2
0
1
2
1
2
1
1
1
0
1
0
0
1
0
1
1
0
1
1
2
1
1
1
2
2
1
1
1
1
2
2
0
2
1
1
1
2
1
2
1
1
0
0
0
1
2
2
1
0
1
1
2
2
2
2
2
1
2
1
1
1
1
1
2
1
2
1
0
1
1
2
0
0
2
1
0
1
0
1
2
1
1
2
1
0
1
1
1
1
2
0
0
2
1
1
2
1
1
1
1
0
0
0
0
1
2
1
5
2
1
1
2
2
0
1
2
0
1
1
1
2
0
1
1
0
1
1
1
1
0
2
1
0
2
1
1
1
1
1
1
4
2
1
1
1
0
1
0
1
2
1
0
1
0
2
1
1
1
2
0
1
1
1
1
2
0
0
1
1
1
1
0
0
0
1
2
1
1
1
1
1
0
0
1
1
1
1
1
0
0
1
0
0
1
2
1
1
0
2
0
1
1
1
1
1
1
2
1
1
1
1
2
1
2
1
1
1
0
1
1
0
1
3
1
2
0
1
1
0
2
1
1
1
1
2
0
2
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
0
1
1
0
1
2
1
1
1
1
1
0
1
1
2
1
2
1
0
0
2
2
2
2
2
1
1
2
1
1
1
1
2
2
2
0
2
0
1
1
1
1
2
1
1
2
1
0
1
1
2
2
2
2
1
1
0
1
1
0
2
2
1
1
0
1
2
2
2
1
0
0
1
1
1
0
0
0
2
0
1
1
1
1
1
2
1
1
0
2
2
2
0
2
2
0
2
1
1
0
2
1
2
1
1
1
1
2
2
2
1
1
1
2
1
1
0
1
1
1
1
0
1
2
2
2
0
1
1
1
1
2
0
1
1
0
1
2
1
0
1
2
1
0
1
0
1
1
1
1
1
1
0
1
1
1
1
2
1
3
1
0
2
0
1
0
1
1
1
1
1
1
1
0
1
1
0
2
1
1
1
1
1
1
2
1
1
0
2
1
2
1
1
2
2
2
0
1
1
1
0
1
1
1
2
1
1
1
2
1
1
1
1
0
1
2
1
1
1
1
1
0
1
1
2
1
1
2
2
2
1
2
1
2
1
1
1
1
0
2
1
0
1
2
0
2
1
2
0
0
1
1
1
2
1
1
1
0
2
2
1
1
1
1
0
0
2
1
1
1
1
0
2
1
1
1
1
1
1
2
2
1
1
2
2
1
1
3
1
1
1
1
1
0
1
2
2
3
0
1
0
2
1
0
0
0
1
0
0
1
2
1
2
1
2
1
1
1
0
1
1
1
0
0
2
1
0
1
1
1
1
1
1
1
2
0
1
0
0
2
0
0
2
1
1
1
1
2
0
1
1
2
1
1
2
1
1
0
1
0
0
1
1
1
1
1
2
1
1
0
1
1
1
0
1
1
2
2
1
1
0
1
1
1
0
1
2
0
1
1
2
1
1
1
1
1
1
0
1
1
2
2
1
1
1
1
1
1
1
2
2
0
1
1
1
1
1
2
1
2
1
0
0
1
1
1
2
1
0
0
2
1
2
1
1
1
1
1
1
1
0
2
1
0
1
1
1
1
2
1
1
1
0
0
1
1
1
0
2
1
0
1
1
1
0
2
1
1
1
0
1
1
0
1
2
2
0
2
2
1
1
1
2
2
0
2
0
0
2
0
1
1
1
1
1
2
2
1
1
0
2
1
1
1
2
1
1
0
1
2
1
1
1
1
1
1
2
2
1
1
2
1
1
1
0
0
1
2
0
1
1
0
1
1
1
0
0
2
1
2
1
0
0
0
1
1
1
1
1
2
1
1
1
2
1
1
2
1
0
1
1
1
1
1
1
1
0
0
1
1
1
1
1
1
0
0
2
0
2
2
1
1
1
1
1
2
1
1
2
1
2
0
2
1
1
0
1
1
0
1
1
1
1
1
2
0
1
1
0
0
1
1
1
1
1
1
2
1
1
1
1
0
0
0
0
0
0
1
2
0
1
2
1
0
1
2
2
1
0
1
2
2
0
1
1
1
2
0
1
1
1
1
2
1
2
1
1
1
2
1
0
0
0
3
2
1
2
1
1
2
1
2
1
1
2
1
1
1
0
1
0
1
0
1
0
1
1
2
1
1
1
1
1
0
1
0
2
1
1
1
2
0
0
1
0
1
0
1
0
0
1
1
0
1
0
2
0
1
1
1
0
1
1
0
1
0
1
3
2
0
1
1
1
0
1
2
0
0
1
1
2
2
1
0
2
1
1
1
1
1
2
1
0
1
1
1
1
2
2
0
1
1
1
1
0
1
1
1
1
1
1
2
1
1
0
1
1
0
1
2
1
1
2
2
0
1
1
1
0
1
0
1
1
0
2
2
1
1
0
1
1
1
2
2
1
1
0
1
1
1
1
1
2
0
1
0
0
2
1
2
1
2
1
1
0
1
6
1
1
1
1
1
0
1
1
2
1
1
1
1
1
1
0
1
1
1
1
0
1
2
1
0
0
0
1
0
1
2
1
1
2
1
0
2
0
2
1
0
2
2
0
0
1
0
1
1
1
2
1
2
2
1
2
0
2
1
0
2
0
1
0
0
1
2
1
1
1
1
2
2
0
0
0
2
0
5
2
1
1
1
1
1
0
1
1
1
2
1
1
2
1
1
2
0
2
1
1
1
1
2
1
2
1
2
1
0
2
2
0
1
1
1
0
1
0
1
0
1
0
1
1
1
1
2
2
1
2
2
1
1
1
2
1
0
0
2
1
1
0
1
0
1
1
2
1
2
1
0
2
1
1
1
2
2
1
1
1
2
2
1
2
1
2
0
0
2
0
1
1
1
1
1
0
0
0
0
0
1
1
0
1
1
2
1
2
1
1
1
1
0
2
2
0
1
1
1
1
1
1
1
1
1
2
2
1
1
0
1
1
1
1
1
1
1
1
2
0
0
2
2
1
2
0
1
2
0
0
1
1
2
1
1
0
1
1
1
0
0
0
0
1
0
1
2
0
2
0
0
2
1
1
2
1
2
2
2
1
2
2
1
1
1
1
0
1
1
1
1
1
2
1
2
1
0
1
1
1
1
1
1
0
1
0
0
0
1
1
1
1
1
0
1
1
0
1
1
0
0
1
1
1
1
0
2
0
2
1
1
2
0
1
1
1
2
1
1
1
1
1
2
1
2
0
1
1
1
1
1
1
1
0
1
0
1
1
2
1
0
1
1
2
2
0
2
0
2
0
0
1
2
1
2
1
1
1
2
2
1
2
1
1
2
1
1
0
0
1
0
1
1
1
1
1
0
3
1
1
1
1
2
2
0
2
0
0
2
1
2
0
2
1
1
0
0
1
1
2
1
1
2
1
1
0
1
1
1
1
1
1
1
2
0
0
1
1
2
0
1
2
1
1
1
2
2
1
1
2
1
2
1
1
0
1
0
0
1
1
0
1
1
0
2
1
1
0
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
2
0
1
1
1
0
2
1
1
1
1
0
2
2
0
1
0
0
0
2
0
1
0
0
1
1
1
2
1
0
0
0
1
1
0
2
0
1
1
0
2
1
2
2
1
1
1
1
2
0
2
2
1
1
2
1
1
1
0
1
2
1
1
1
1
1
2
1
2
2
1
1
1
1
2
2
0
1
1
2
2
2
0
1
1
0
1
0
0
1
1
1
2
2
2
1
2
1
0
1
2
2
1
1
1
1
1
1
1
1
2
2
1
1
2
0
1
2
0
0
0
1
1
1
0
0
1
2
1
2
1
1
2
1
2
1
1
1
2
1
1
0
1
0
0
2
0
0
0
0
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
2
2
2
0
2
1
2
1
1
1
2
1
0
0
1
1
1
1
1
0
1
2
1
1
1
1
1
1
0
2
2
0
1
0
2
2
1
2
1
2
1
1
1
1
0
1
1
1
1
1
1
0
1
1
2
0
2
1
0
2
1
0
1
2
1
2
1
1
1
1
2
1
1
1
2
1
1
0
0
1
1
1
0
1
1
0
0
2
1
1
1
1
1
1
1
0
2
2
0
2
1
2
1
1
1
1
1
0
0
1
1
1
2
1
0
0
1
1
2
0
0
2
0
2
0
1
1
2
1
1
2
2
0
2
1
1
1
1
2
0
1
1
0
1
0
1
0
1
2
1
1
1
1
1
1
1
2
2
2
1
1
0
0
1
1
2
1
2
2
1
0
2
0
1
1
1
2
0
0
1
2
2
1
2
0
1
1
1
1
1
1
1
1
1
1
0
1
1
0
0
0
1
0
0
1
1
1
1
1
1
1
1
1
2
2
1
0
2
2
1
0
0
1
1
1
1
2
1
1
2
1
1
0
1
1
2
1
2
1
1
0
2
1
1
2
1
3
2
1
2
1
1
1
1
1
1
0
2
0
0
2
1
1
1
0
1
1
1
2
1
1
1
2
0
0
1
1
0
1
2
2
1
2
1
2
1
1
0
2
1
2
3
2
1
2
2
1
1
1
0
1
1
0
2
2
0
1
2
1
1
0
1
2
2
2
1
1
1
1
1
1
1
0
1
1
1
1
0
1
1
0
1
1
1
1
1
2
2
1
1
2
1
0
0
3
1
1
1
0
1
1
1
1
0
0
0
1
2
0
0
1
0
1
2
1
2
1
0
0
0
1
1
1
2
2
1
1
0
2
1
0
2
2
0
1
1
1
2
2
0
2
1
2
1
1
1
1
2
0
1
0
1
2
1
0
1
1
1
0
0
2
1
1
0
1
1
1
1
2
1
0
0
3
1
2
1
1
2
0
2
1
1
1
2
1
0
2
2
1
1
1
1
1
1
4
1
1
1
0
1
1
1
1
1
1
1
0
1
1
0
1
1
1
1
0
0
0
1
0
2
2
0
0
1
1
0
0
2
1
1
0
1
1
0
1
1
0
1
1
2
1
0
1
1
1
1
2
2
1
1
0
1
1
1
1
0
1
1
1
1
1
1
1
1
0
1
1
2
1
1
1
2
2
2
1
2
1
2
0
0
0
1
2
1
1
1
2
1
1
0
2
1
2
2
1
1
1
0
2
0
2
0
2
2
1
2
1
2
1
2
0
0
1
1
1
2
1
2
2
1
1
0
1
1
0
1
0
1
0
1
0
1
1
1
1
1
0
1
0
1
1
1
1
0
2
1
1
2
0
1
1
2
1
1
0
0
2
1
1
0
1
2
1
2
2
1
1
2
0
1
1
0
1
1
1
0
1
2
1
0
2
2
0
1
1
1
1
2
2
2
1
3
1
2
1
2
1
0
1
1
1
2
1
2
1
0
2
2
0
1
1
1
1
1
0
1
2
1
1
1
0
0
2
1
1
2
1
1
1
0
1
1
1
0
0
1
2
1
2
0
1
2
1
2
1
2
1
1
2
1
1
2
0
1
1
1
1
1
2
0
1
1
1
0
1
0
1
2
2
1
0
1
1
2
1
0
2
2
2
2
1
1
1
0
1
0
0
1
0
2
1
1
1
0
1
0
1
1
0
1
1
1
1
1
1
1
3
1
2
2
2
1
2
1
0
2
2
1
1
0
2
1
0
2
0
2
1
1
1
1
1
2
1
0
1
0
1
1
0
1
2
1
0
1
1
1
1
2
0
1
1
2
1
1
1
1
2
0
1
1
2
1
1
2
2
0
1
2
0
0
0
1
2
2
3
1
1
0
1
1
1
0
1
2
1
0
1
2
1
0
0
1
1
0
1
2
2
1
1
1
1
1
2
1
2
1
0
1
1
0
0
1
1
2
1
1
1
1
1
2
1
1
0
0
0
1
1
1
1
2
2
0
1
2
1
1
1
1
2
1
2
2
1
0
1
1
1
1
1
2
1
0
1
0
0
1
1
1
0
1
2
1
0
1
2
1
2
0
2
1
1
1
1
1
1
1
0
1
1
0
2
0
1
1
1
1
0
1
0
1
2
2
0
1
1
1
1
1
0
1
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
2
1
1
1
1
2
1
0
1
0
0
1
1
1
1
1
2
2
2
0
0
1
2
1
0
1
0
1
1
1
0
0
1
0
2
1
3
1
0
1
1
0
0
0
1
2
2
1
2
1
2
1
2
1
1
0
1
1
1
1
1
1
0
0
1
1
1
0
0
1
1
1
1
2
1
0
1
1
1
1
1
0
2
1
1
2
2
2
1
1
1
2
0
1
0
1
0
1
1
1
1
1
1
1
1
2
0
1
1
1
1
2
2
1
1
1
1
2
0
0
1
2
1
2
0
1
1
2
1
1
1
2
2
1
0
1
0
0
2
0
1
1
1
0
1
2
0
1
1
1
1
2
0
2
0
1
5
2
1
1
1
0
1
0
1
2
1
0
2
2
2
2
2
2
0
1
2
1
1
1
2
1
1
1
2
1
1
2
2
1
1
1
1
1
1
2
1
1
1
2
0
2
2
1
0
0
1
1
0
0
2
1
1
3
1
0
2
1
1
1
0
1
2
0
1
1
1
1
0
1
1
0
1
2
0
0
2
1
1
0
2
2
1
1
1
1
0
1
0
1
1
1
1
1
1
1
1
1
1
0
1
0
0
1
0
1
2
1
2
1
0
1
1
1
0
1
2
1
1
1
1
0
1
2
2
2
1
0
2
1
0
1
1
1
1
1
1
1
2
1
1
0
2
1
3
2
1
1
2
1
2
0
0
2
0
1
0
2
1
1
1
0
1
2
1
2
1
1
0
1
0
1
1
1
2
0
1
1
2
1
0
1
0
2
0
1
1
1
1
1
2
1
1
0
2
1
1
1
2
1
1
1
0
0
1
0
1
2
0
2
1
2
1
1
0
1
1
1
1
1
1
1
0
2
2
1
2
0
3
1
1
1
1
1
1
1
1
2
0
1
2
2
1
2
1
0
1
0
1
2
1
0
1
0
1
2
1
1
2
1
2
1
1
1
1
2
2
1
0
2
1
1
4
2
0
2
1
1
1
1
2
2
2
0
1
2
2
2
1
1
1
2
1
1
1
1
1
1
1
0
1
0
0
1
1
1
2
1
1
2
1
1
0
2
1
0
1
2
0
0
0
0
1
0
2
1
0
0
1
0
1
0
1
1
1
1
0
2
1
2
2
2
1
0
1
1
1
1
1
0
2
1
2
0
1
1
2
3
1
0
2
2
0
0
1
2
1
2
2
1
1
1
1
0
0
1
1
2
1
1
1
1
2
0
1
1
2
0
0
1
1
1
1
2
1
3
0
2
0
1
1
2
1
1
1
2
0
1
1
0
1
0
2
1
0
1
1
1
2
1
1
1
0
0
1
0
1
1
1
1
1
1
1
2
1
1
0
0
0
3
1
1
1
1
1
1
1
1
0
1
2
1
1
1
1
1
0
1
0
2
2
0
1
0
2
1
0
1
0
0
2
3
1
2
1
1
2
1
1
1
1
2
1
1
2
2
1
1
1
1
0
0
1
1
1
2
1
1
2
0
0
2
3
0
1
1
1
1
1
1
0
3
1
1
0
2
1
2
1
2
1
1
2
0
2
2
1
0
1
0
1
1
2
1
1
1
1
0
1
0
1
1
0
2
0
1
1
2
2
1
2
0
1
2
1
0
2
0
0
1
1
1
1
1
2
0
0
1
2
0
0
1
1
2
0
1
1
1
0
2
2
1
1
2
2
2
1
1
1
1
1
2
1
1
2
2
1
0
1
1
0
1
1
1
2
2
1
1
1
0
1
1
1
2
0
1
1
0
1
2
1
0
2
1
2
1
0
1
2
1
2
1
1
2
0
1
1
1
1
2
1
1
2
1
1
0
2
0
1
1
1
0
0
0
1
0
0
1
1
1
0
1
1
1
1
1
0
1
0
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
2
1
1
0
1
1
0
1
1
1
0
1
1
1
1
2
1
2
1
1
1
2
1
1
1
0
0
1
1
3
1
2
0
1
1
1
2
2
1
1
1
0
1
2
1
1
0
0
0
1
0
1
1
1
2
0
0
1
1
1
2
1
1
1
1
0
2
1
1
1
2
1
0
1
0
1
0
1
2
0
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
2
1
1
1
0
2
1
2
1
1
2
1
1
1
2
1
0
1
0
1
2
1
0
1
2
1
1
2
1
1
1
0
1
1
1
0
1
2
1
1
1
1
2
1
0
1
0
1
0
1
2
1
1
1
1
1
1
1
2
1
2
2
1
2
1
1
2
0
1
0
1
1
2
1
2
1
1
0
2
1
1
1
1
1
2
1
1
0
2
2
1
1
2
5
1
1
0
1
2
1
2
0
2
1
1
1
2
4
1
0
1
1
2
2
2
1
2
1
0
0
0
1
1
1
1
1
1
0
1
1
0
2
0
1
1
3
0
3
1
2
0
1
1
1
1
0
2
0
2
0
1
1
0
1
0
1
2
1
1
1
1
0
0
1
0
1
1
1
1
0
2
0
2
2
1
1
0
3
0
1
0
2
0
1
2
1
1
1
2
1
1
0
2
2
1
1
1
0
1
1
0
1
1
1
1
0
2
1
2
2
2
2
2
1
1
0
1
1
1
0
1
0
1
0
1
1
1
0
0
1
0
1
0
4
1
1
1
0
1
1
0
1
2
2
1
1
3
1
2
0
1
1
1
2
0
0
0
1
2
0
1
0
1
1
0
2
2
1
1
0
1
0
1
2
0
1
1
2
2
1
2
0
1
2
1
3
1
1
1
2
1
1
1
1
0
2
0
2
1
1
1
0
1
0
1
0
1
2
1
1
1
0
2
3
1
1
1
1
1
2
0
1
0
2
0
1
2
0
1
0
2
1
1
1
1
0
1
0
1
0
1
1
1
1
1
1
2
1
0
1
2
1
1
2
1
1
0
0
1
1
1
1
1
2
2
2
1
2
2
2
1
1
1
0
0
1
0
1
0
2
1
0
1
0
1
0
1
3
2
2
2
1
2
2
2
1
1
0
1
1
1
1
1
1
0
1
1
2
1
0
2
1
1
0
0
2
2
1
0
2
2
1
6
0
2
2
1
0
1
1
1
0
0
1
2
1
0
1
2
0
2
1
1
1
1
0
0
2
1
2
2
2
2
0
1
1
0
1
1
1
1
1
1
0
1
2
2
2
2
0
2
0
1
1
2
1
0
1
2
1
1
1
1
1
1
0
0
2
1
0
1
1
0
3
1
2
1
1
2
2
1
1
0
1
2
1
1
1
0
0
1
2
1
1
1
1
0
2
0
0
3
2
2
1
1
1
1
0
1
1
1
1
1
1
1
2
1
1
1
1
1
4
0
1
2
1
3
1
2
0
1
0
1
0
1
2
2
0
0
2
0
2
1
1
0
2
2
1
2
1
0
1
2
2
0
0
2
1
2
2
0
1
1
0
1
1
1
2
1
1
2
0
1
1
2
1
1
1
1
2
0
2
0
2
1
1
1
1
1
0
0
2
1
1
2
0
0
1
2
0
1
1
1
1
2
0
1
1
3
2
1
2
1
2
1
1
1
1
1
1
0
2
2
1
2
2
2
0
3
2
2
1
0
1
1
1
0
2
1
1
1
2
1
2
2
1
1
0
0
2
1
0
0
0
0
2
1
2
1
1
1
1
1
0
1
1
2
1
1
1
0
2
1
1
0
0
1
1
1
1
0
2
1
2
0
0
1
1
0
0
2
1
2
2
2
1
1
2
0
0
1
1
1
1
2
2
1
1
1
0
1
1
2
0
1
1
2
0
1
1
1
2
0
1
1
2
2
1
0
1
2
1
0
2
1
0
1
1
2
0
1
1
2
0
1
2
1
1
2
1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
2
0
1
1
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
2
2
0
1
0
1
2
1
0
0
1
1
1
2
1
2
0
2
2
2
0
1
1
1
3
1
1
1
1
1
2
2
1
1
1
1
1
0
1
2
0
0
0
1
0
1
1
1
1
2
2
1
1
2
1
1
2
0
2
1
1
2
1
1
2
1
1
1
1
2
1
0
1
1
1
1
0
1
1
0
0
0
1
1
1
1
2
1
1
1
2
0
2
0
1
2
1
0
0
0
1
1
1
1
1
1
0
2
1
1
1
0
0
1
1
2
1
1
2
1
1
1
0
1
1
1
1
0
2
0
1
1
0
2
0
1
0
1
2
2
1
2
1
2
1
1
1
2
2
0
1
2
1
1
2
1
1
0
2
1
1
2
2
1
2
0
2
2
2
1
0
1
1
1
3
1
1
1
2
1
1
2
0
1
1
1
1
2
1
1
2
1
5
0
1
1
2
0
1
2
0
0
1
2
1
0
0
0
0
1
1
2
0
0
1
1
2
1
2
0
1
2
1
1
0
1
2
2
2
1
1
0
2
1
1
1
1
1
0
0
1
1
2
0
1
1
1
2
1
0
1
0
1
0
0
1
1
1
1
2
2
3
1
2
0
2
1
1
1
0
2
2
0
1
1
0
2
1
2
1
0
1
0
2
1
0
1
3
1
1
0
1
1
1
1
2
1
0
1
1
0
2
2
1
1
2
1
1
6
2
0
2
0
0
1
1
2
0
1
1
0
3
1
1
0
1
0
1
1
1
0
1
0
1
1
0
1
2
0
0
1
2
1
1
0
1
0
1
0
1
2
0
0
0
1
0
0
1
1
0
1
1
0
0
1
1
2
1
0
1
1
1
1
1
0
1
0
0
1
1
2
1
1
2
0
0
1
0
0
1
1
1
1
1
1
1
1
1
2
0
0
2
2
2
2
1
2
1
0
2
1
1
1
1
1
1
2
1
1
1
2
1
2
1
0
2
1
2
0
2
3
2
2
0
0
0
0
2
1
0
0
2
2
1
0
1
2
1
0
1
0
1
1
1
2
2
3
2
1
0
1
0
0
1
2
1
2
1
2
1
2
0
0
2
1
1
1
1
1
1
1
1
1
1
2
1
0
1
2
1
1
2
2
1
1
1
0
1
1
0
1
1
2
1
0
1
1
0
2
1
1
1
1
1
1
1
1
1
1
0
0
1
2
1
1
0
1
1
1
2
1
0
1
1
1
2
2
1
1
1
1
1
2
1
2
1
0
1
2
0
2
1
1
0
1
0
0
0
1
2
1
1
2
1
2
1
1
0
1
1
1
1
0
0
0
2
1
3
1
0
1
1
1
0
0
1
1
1
1
2
2
0
1
1
2
1
1
1
2
1
1
1
0
1
0
1
1
2
2
0
0
0
0
2
1
1
2
1
2
1
2
0
1
2
0
1
1
1
1
1
1
0
1
1
1
1
1
1
0
1
1
1
1
2
2
2
0
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
0
1
1
1
2
1
1
0
0
2
0
1
2
0
2
1
1
0
1
1
1
2
2
2
1
1
2
0
2
0
0
1
1
1
0
0
1
2
1
2
2
1
1
2
0
1
2
1
1
1
1
1
3
0
1
0
1
2
1
0
0
1
1
1
2
1
1
1
1
1
1
0
1
1
1
1
2
1
1
0
0
1
2
1
1
1
1
1
1
0
2
1
1
0
0
2
0
1
1
2
0
1
1
1
1
1
1
0
2
1
2
1
1
1
1
2
0
1
1
0
2
2
1
1
1
2
1
1
1
1
1
2
0
2
0
1
1
0
2
1
2
1
0
1
1
2
0
1
0
1
2
0
1
2
1
1
1
0
1
0
1
1
1
1
1
2
2
0
1
1
2
0
1
0
1
2
1
1
0
2
2
2
1
2
1
0
1
1
1
0
1
0
1
2
0
0
1
0
1
1
1
2
2
2
1
1
0
1
2
2
1
0
2
1
0
1
0
1
0
1
1
1
1
0
1
1
1
1
2
1
1
1
0
1
2
0
1
2
0
1
1
1
2
1
1
1
1
2
0
1
1
2
2
1
1
1
0
1
1
1
1
2
2
1
0
1
2
1
1
2
1
1
1
1
0
1
0
2
2
2
2
1
1
1
2
1
1
1
0
1
0
0
1
1
2
1
2
1
0
1
1
0
1
2
0
1
2
0
1
1
1
2
2
1
0
2
1
1
2
1
0
1
0
2
1
1
1
1
2
1
1
2
0
2
1
1
0
1
2
1
0
2
1
2
1
1
1
0
1
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
2
0
1
2
2
2
2
0
1
2
1
1
2
0
2
1
0
1
1
1
0
1
0
1
1
2
1
0
2
2
2
1
2
1
1
1
1
2
1
1
1
1
1
2
2
2
2
1
1
1
2
2
0
1
1
0
1
1
2
2
0
2
1
1
1
2
1
0
1
0
1
1
3
1
1
1
1
1
2
1
1
0
0
0
1
1
1
1
1
1
1
2
1
2
2
1
1
2
1
1
0
1
2
1
1
2
1
1
2
1
0
1
2
0
1
1
1
2
1
1
2
1
1
1
0
1
1
1
2
0
2
0
1
1
0
2
1
1
1
1
1
1
1
1
0
0
0
2
2
2
0
0
1
2
1
1
1
0
1
1
1
0
0
2
0
2
1
1
0
1
1
2
0
2
0
0
0
1
1
1
3
2
1
1
1
2
2
0
2
0
1
0
1
2
0
1
0
1
2
1
1
0
1
1
2
1
1
0
0
2
0
1
1
1
2
1
1
1
1
1
0
1
1
0
1
2
1
2
0
1
1
0
0
1
1
1
1
0
1
1
1
1
1
2
1
0
0
1
0
1
1
1
1
1
1
0
1
0
1
0
2
0
2
2
1
0
1
1
1
1
1
2
2
1
2
6
0
0
3
1
0
1
1
2
2
1
1
1
0
0
2
1
0
0
1
1
1
1
1
1
0
1
2
1
0
1
0
1
1
0
4
2
0
1
2
1
1
0
0
1
1
2
1
1
1
1
1
1
2
1
2
1
2
0
1
1
1
1
2
2
2
0
1
2
2
0
1
1
1
1
1
2
2
1
1
1
2
1
2
1
1
2
1
0
1
0
2
1
0
1
0
1
2
1
1
2
1
1
1
1
2
1
0
1
1
1
1
2
1
1
1
1
1
1
2
1
1
0
2
2
1
0
1
1
2
1
0
2
0
0
1
1
1
1
1
1
1
1
1
2
0
0
0
1
0
0
0
2
1
2
2
1
2
2
1
2
2
2
1
1
1
1
0
0
1
1
1
2
1
1
2
1
1
1
1
2
0
2
0
2
1
2
1
1
1
1
2
1
1
2
1
0
0
3
1
1
1
1
1
2
2
2
3
2
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
0
1
1
1
0
1
0
0
2
1
0
1
0
0
2
0
1
0
1
1
2
1
1
1
1
1
0
1
2
2
0
0
0
5
1
1
2
2
1
1
2
1
0
1
2
1
1
2
1
1
1
1
0
1
1
1
1
2
1
1
2
0
2
1
0
2
1
2
1
1
1
1
2
2
1
2
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
0
2
2
2
0
2
1
2
2
1
1
1
2
0
2
0
1
1
1
0
1
0
0
1
1
1
1
1
0
1
1
0
2
1
1
1
0
0
2
3
1
1
1
0
1
0
1
2
2
2
1
1
0
1
1
1
1
0
0
1
2
1
1
2
2
2
1
2
2
2
2
1
1
1
1
1
1
2
2
0
2
2
1
2
0
0
0
1
0
2
0
1
2
0
1
2
1
1
2
2
1
1
1
1
2
0
0
1
0
1
2
2
1
1
1
1
2
2
1
5
2
0
1
0
1
1
1
2
2
0
1
2
1
2
1
1
1
0
2
1
1
2
2
1
2
1
1
0
2
1
1
1
1
1
0
1
2
1
2
1
1
1
1
1
0
2
1
1
1
0
2
2
1
1
0
1
2
1
0
1
1
1
1
0
1
0
0
0
2
1
0
1
1
2
1
1
1
0
2
1
3
1
2
1
2
1
2
1
1
0
1
1
2
1
0
0
1
1
0
1
1
1
0
1
0
0
2
2
0
1
1
0
1
2
1
0
1
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
2
2
1
1
2
0
1
1
2
1
1
1
1
1
1
0
1
1
0
1
1
0
2
1
2
0
1
1
2
1
2
1
0
3
1
0
1
1
2
1
2
2
1
2
1
1
1
0
1
1
1
2
1
1
0
2
1
1
1
0
1
0
2
0
1
1
1
3
1
1
1
1
1
0
2
0
2
1
1
2
2
2
1
2
0
1
0
0
0
2
1
2
1
2
2
1
0
1
2
1
1
2
1
1
1
1
2
1
1
1
0
2
0
0
1
0
1
1
2
1
3
0
1
1
1
0
3
2
0
0
0
1
0
1
1
2
1
0
0
0
2
1
1
0
0
1
0
0
2
2
2
0
2
0
0
1
1
1
1
0
0
1
1
1
0
1
0
1
1
1
2
0
2
0
1
1
2
2
1
0
1
1
1
2
1
1
1
0
2
1
0
0
1
1
0
1
1
1
2
2
0
0
2
1
2
2
0
2
1
1
1
2
1
2
0
1
1
1
0
1
1
1
2
1
1
2
0
0
0
2
3
2
1
0
0
0
2
1
2
0
2
1
2
0
1
2
1
1
1
2
2
1
0
5
1
1
1
0
1
2
2
0
1
2
2
0
1
1
2
1
1
0
1
1
1
1
2
1
1
1
2
0
2
0
0
1
2
1
0
2
1
1
1
0
1
1
1
1
1
1
0
2
2
1
1
2
1
0
1
1
1
2
0
0
0
1
1
1
0
2
1
1
1
1
1
2
0
2
1
2
0
1
1
1
0
1
1
1
1
0
2
2
1
2
0
1
1
0
1
1
1
0
1
1
1
0
1
0
1
1
1
1
0
0
1
2
2
2
0
2
1
2
0
1
0
1
1
1
1
1
0
0
2
1
1
0
1
2
2
0
2
1
1
0
1
1
1
2
2
2
1
2
1
2
1
1
0
1
2
0
0
1
2
1
0
1
1
1
1
2
2
1
1
2
1
1
2
1
0
1
2
1
1
2
1
2
1
0
2
1
0
1
0
1
2
1
1
1
1
1
0
1
0
1
1
1
1
0
1
2
1
1
1
0
0
1
2
1
1
0
1
1
1
0
1
1
0
2
1
1
1
1
1
1
2
2
1
0
1
0
1
1
2
1
1
1
0
1
1
2
0
1
2
0
0
1
0
1
1
0
1
1
2
0
1
1
1
2
0
1
0
0
2
0
1
0
2
1
1
1
1
1
0
1
1
0
0
1
0
1
1
1
1
0
0
1
2
0
1
1
2
1
2
1
1
2
2
0
1
1
1
1
0
2
1
0
0
2
2
1
2
1
2
0
0
0
1
1
0
1
2
1
1
1
1
1
0
0
2
1
1
1
2
1
0
2
1
1
0
1
1
0
1
1
1
2
1
1
2
2
2
1
1
1
0
2
1
0
1
2
1
1
1
0
1
0
1
1
2
2
2
0
0
1
0
1
0
2
1
1
1
0
2
2
1
1
1
1
2
1
1
1
1
0
0
1
1
1
1
1
1
2
2
0
1
1
0
1
1
0
2
2
2
2
2
1
0
2
2
1
1
0
2
1
1
1
1
1
2
0
1
1
2
1
1
1
1
2
2
2
1
2
2
2
2
1
1
2
2
0
1
0
1
1
1
0
0
1
1
1
2
1
1
2
1
2
0
2
1
2
0
1
2
1
1
4
1
0
2
1
0
0
2
2
1
1
1
1
1
2
1
1
1
1
0
0
1
2
3
0
1
1
0
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
2
2
1
1
1
2
1
1
1
1
2
1
1
0
1
1
1
1
1
2
0
1
1
0
0
0
0
2
0
0
1
0
1
2
1
1
0
0
1
1
0
0
2
0
2
1
1
1
1
1
1
1
1
1
1
1
4
1
1
2
1
0
0
2
1
1
1
1
1
2
2
0
0
1
2
0
1
1
1
0
2
2
0
1
1
2
0
2
1
1
1
1
2
1
2
1
1
1
1
1
0
1
1
1
2
1
2
2
2
0
1
1
1
1
0
1
1
1
0
0
0
0
1
2
2
0
1
0
1
1
0
1
0
0
2
2
1
0
0
0
2
2
1
2
2
1
1
0
2
0
2
2
0
1
1
2
2
1
1
1
0
0
0
4
0
0
1
0
1
1
1
1
2
1
0
1
1
2
1
0
0
1
2
2
2
2
1
1
1
1
0
1
1
2
1
0
2
1
1
1
1
1
1
1
1
2
0
1
0
1
2
0
1
0
0
1
1
2
1
2
0
0
1
1
1
1
1
1
1
1
1
1
1
2
2
2
0
3
1
0
2
1
1
3
1
0
2
2
0
0
1
2
1
1
2
0
1
1
0
0
0
1
1
1
2
1
0
1
2
0
0
1
1
1
0
1
1
0
2
1
1
2
1
1
1
1
0
1
0
0
2
1
1
0
2
0
0
1
1
0
2
1
0
0
2
0
1
1
2
0
2
2
1
1
1
2
3
1
0
1
2
2
1
1
0
1
1
1
1
0
0
1
1
1
1
0
1
0
1
1
1
1
1
1
0
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
1
0
1
0
0
1
0
1
1
1
0
2
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
0
1
0
0
1
1
1
1
1
1
2
0
1
1
1
0
2
0
1
0
1
1
1
2
2
1
2
1
0
0
1
0
0
1
1
1
2
2
1
0
0
0
1
1
1
2
1
0
0
0
0
2
0
2
0
0
1
0
1
1
1
2
2
0
1
0
2
2
1
1
2
2
3
1
1
1
1
2
1
1
1
1
1
1
0
1
0
1
0
1
1
1
0
2
2
1
1
1
1
1
2
0
2
1
1
0
1
0
1
2
0
0
2
1
1
1
1
0
1
1
0
1
2
1
1
2
1
2
1
1
2
0
1
2
0
2
1
1
0
1
0
2
1
1
1
2
1
1
0
0
2
1
3
1
1
1
0
1
0
1
1
2
2
1
2
1
1
0
1
1
0
1
2
2
1
1
1
1
1
2
0
0
1
2
0
1
2
1
1
1
2
1
0
1
0
1
1
1
2
1
0
1
0
2
3
1
0
1
1
2
1
2
2
2
1
0
2
1
1
1
0
1
2
1
1
1
2
1
2
1
0
1
0
2
2
0
2
0
1
1
2
1
1
0
0
1
1
1
0
1
0
2
1
1
1
2
1
1
2
0
0
1
0
1
2
1
2
0
1
1
1
1
0
1
0
0
2
0
1
1
0
1
1
1
0
1
0
0
1
1
0
1
1
1
2
1
1
1
2
1
1
2
2
0
0
1
1
0
0
1
2
0
2
1
2
0
1
1
1
1
1
1
1
1
1
2
1
0
1
1
2
1
1
2
0
1
1
0
1
1
1
1
2
1
1
0
0
1
1
0
1
1
1
0
1
1
1
1
2
2
2
1
2
2
1
1
1
1
2
2
0
0
1
1
1
1
2
0
1
1
1
2
1
1
0
1
1
2
1
1
1
2
1
0
2
1
1
2
0
1
2
0
1
1
0
1
1
1
1
1
1
1
2
2
1
1
1
0
1
0
0
1
1
1
1
0
2
1
0
1
1
1
1
1
1
1
0
0
3
2
0
0
2
1
1
0
2
1
0
2
1
2
0
1
1
2
1
1
2
2
2
2
0
1
3
1
1
1
1
0
1
1
1
1
1
1
2
0
2
1
1
1
1
1
1
1
1
1
2
0
0
1
1
2
3
2
0
0
1
2
2
1
2
1
1
1
1
1
0
2
1
1
0
1
2
1
1
2
0
1
0
1
0
1
1
0
1
0
1
1
1
0
1
1
1
0
1
0
1
0
2
0
1
1
0
2
2
1
1
1
1
1
1
2
1
1
2
1
1
0
1
2
0
1
2
0
1
2
0
1
1
0
1
2
2
1
0
1
1
1
0
0
1
1
1
1
2
1
1
1
1
1
2
1
1
2
2
1
0
0
1
0
0
0
1
1
1
0
1
2
0
1
2
1
0
0
2
0
0
1
0
0
0
0
1
1
0
1
2
2
1
1
1
1
1
1
1
2
2
2
1
1
1
0
1
0
1
1
2
1
1
1
2
1
0
2
0
1
0
1
1
2
2
2
0
1
1
1
1
2
0
0
1
4
2
1
0
0
1
2
0
0
1
1
1
0
1
0
3
1
0
0
2
2
0
1
1
0
1
1
1
0
1
1
0
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
0
0
1
1
2
1
0
1
2
0
2
2
1
0
1
1
0
0
2
1
1
1
2
1
0
1
1
1
1
2
0
2
2
1
1
2
1
1
1
1
1
2
0
0
1
2
1
2
2
0
0
1
1
0
1
2
0
2
1
0
2
2
2
1
0
0
1
2
2
0
2
0
1
1
1
1
2
2
0
1
1
1
2
0
2
1
1
0
1
3
2
1
1
1
1
1
2
1
1
1
1
2
2
1
0
1
0
0
0
1
2
2
1
1
0
0
2
2
1
1
2
1
2
1
2
1
1
1
0
0
1
1
0
2
1
1
2
1
1
2
1
3
0
1
1
1
1
0
1
2
2
0
2
2
1
0
0
1
3
0
2
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
2
1
1
2
1
1
2
1
2
2
2
2
0
1
1
0
0
1
2
1
2
0
1
1
2
2
0
0
1
1
1
1
1
1
0
0
2
1
1
1
1
2
1
1
2
1
2
1
1
2
1
1
1
1
2
2
2
2
1
1
1
2
1
2
1
2
1
0
2
2
1
2
0
2
0
1
2
1
1
1
0
1
1
1
2
1
1
0
2
2
0
2
0
2
2
1
0
1
2
1
2
1
1
1
0
1
5
0
1
1
0
1
0
1
1
2
1
2
2
1
2
1
1
0
2
0
1
1
1
1
2
2
1
1
0
0
1
2
3
0
0
2
1
1
1
1
2
0
1
0
1
0
1
0
2
1
0
0
1
1
0
1
1
1
1
3
1
1
1
1
1
1
2
0
1
2
2
2
1
1
2
2
2
1
3
2
1
1
1
1
1
0
1
1
1
0
2
1
1
1
2
1
0
0
2
1
1
1
0
2
1
1
2
2
0
2
0
1
1
1
1
1
1
1
1
0
1
1
2
1
1
2
2
1
1
1
2
1
0
1
2
2
2
1
0
0
1
1
1
1
0
2
1
1
0
1
1
2
1
0
1
1
0
1
0
2
2
1
1
1
1
1
1
2
3
2
2
0
1
1
1
1
0
0
1
1
1
2
2
1
0
3
2
0
1
2
0
1
2
1
2
2
1
2
1
2
1
1
1
0
1
1
1
0
1
1
1
1
1
3
1
2
1
0
1
2
1
0
3
1
2
2
1
2
1
1
1
1
2
2
1
2
0
1
0
2
0
2
2
1
1
2
1
1
2
2
1
0
0
0
2
2
1
1
1
0
1
2
0
2
1
0
2
1
2
1
2
2
1
1
1
1
1
1
0
1
0
1
1
1
1
1
1
1
1
2
1
2
0
1
1
1
1
0
1
0
0
0
1
1
0
2
1
1
0
1
1
2
0
0
2
0
2
0
1
1
2
1
0
1
1
2
1
0
1
0
1
2
1
1
1
1
0
0
1
1
1
1
2
0
1
0
1
1
1
0
0
2
1
0
1
1
1
1
2
2
1
1
1
2
0
0
1
0
2
1
1
0
1
1
0
0
0
1
2
1
0
1
1
1
1
1
0
1
1
0
1
1
1
1
0
1
3
1
1
0
1
1
1
2
1
2
0
1
1
2
1
2
0
1
1
2
1
0
1
1
2
2
0
1
2
3
1
1
1
1
1
1
1
0
2
2
0
0
1
2
1
1
1
0
1
1
2
1
1
2
1
0
0
1
1
0
1
0
0
2
2
1
1
0
0
1
0
0
2
1
0
0
1
2
0
0
0
2
1
0
2
1
1
0
0
0
2
1
2
1
1
1
1
1
1
0
1
2
1
0
1
1
1
1
1
1
0
2
1
1
2
0
0
0
2
1
2
1
0
1
1
1
1
1
1
1
1
1
1
1
1
0
2
2
1
0
1
1
1
2
1
2
1
1
1
1
2
0
1
0
1
1
1
1
0
1
1
0
2
0
0
2
2
1
1
1
0
1
1
1
1
2
1
0
2
1
2
1
0
1
1
2
0
1
1
1
1
1
2
2
1
2
1
2
1
1
1
1
1
1
2
1
1
2
1
1
2
0
2
1
2
2
1
1
2
4
1
2
1
2
0
2
0
0
2
1
1
2
1
1
0
0
1
1
1
1
1
1
2
0
0
1
1
1
1
1
2
0
1
1
2
2
1
0
1
1
3
1
1
2
2
2
2
1
2
0
2
0
1
0
1
1
0
0
0
1
1
1
1
2
0
1
2
2
1
2
2
1
1
1
2
0
1
1
1
0
1
1
0
1
1
1
1
0
2
1
1
0
1
1
1
1
1
2
2
2
1
2
1
1
2
0
0
1
1
1
0
1
1
1
0
2
1
2
1
1
1
1
0
1
2
1
2
0
0
2
1
1
0
1
1
1
2
1
2
0
2
2
1
1
2
2
0
0
1
1
2
1
2
1
1
1
1
1
1
1
1
0
2
1
2
1
0
0
2
2
1
2
0
2
1
2
1
1
1
1
1
2
1
2
1
1
1
1
2
0
1
2
0
1
1
1
1
1
2
0
1
1
2
1
2
1
1
1
0
0
1
1
2
2
2
1
1
1
0
0
1
1
2
2
0
0
2
1
1
1
0
1
2
1
0
2
1
2
1
2
2
2
2
1
2
2
0
0
1
1
1
1
1
1
3
1
1
2
2
1
1
1
2
1
1
0
2
1
1
0
2
1
1
2
1
2
2
0
0
1
1
1
1
0
1
1
1
0
1
1
1
1
2
0
0
1
1
2
1
1
0
0
2
2
2
1
1
1
2
1
1
0
1
0
0
1
0
1
1
1
1
1
0
0
1
1
2
1
1
1
1
1
1
1
0
1
1
1
0
2
1
1
1
1
1
1
1
1
0
1
1
2
1
1
2
1
1
1
1
2
1
1
0
0
1
1
1
1
1
1
1
1
1
1
1
0
0
1
0
2
1
1
0
2
0
1
1
1
2
0
1
2
1
2
1
2
2
1
0
2
1
1
1
2
1
1
1
0
2
2
2
2
1
1
1
0
1
1
1
0
2
0
2
2
1
0
1
1
1
1
2
2
2
1
1
1
2
0
1
0
1
1
2
0
1
1
1
0
0
2
0
0
0
1
2
2
1
2
2
1
1
1
1
1
1
2
0
1
1
2
1
0
1
1
0
1
2
1
1
1
0
0
0
1
2
3
0
0
2
1
1
1
1
1
0
1
1
1
1
2
1
0
2
2
1
0
0
0
1
0
0
0
1
1
2
1
1
1
2
2
2
1
1
1
1
1
1
1
1
1
1
1
2
2
2
2
1
0
0
2
0
0
1
2
0
1
1
1
1
1
0
1
1
1
1
0
3
2
1
0
1
0
2
1
3
1
1
0
1
1
1
0
1
1
1
1
2
1
2
2
1
2
2
1
0
1
1
1
2
1
1
1
0
0
2
2
1
0
0
1
0
1
1
0
1
0
1
0
1
2
1
2
2
1
0
0
1
1
1
2
1
2
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
0
1
1
1
1
1
1
1
2
1
0
2
1
2
1
1
0
1
0
1
0
1
1
0
1
1
0
1
1
4
0
1
1
1
1
0
0
0
1
0
1
1
0
1
1
2
2
1
1
2
2
1
2
2
1
1
1
1
2
2
2
1
0
1
1
1
1
2
0
1
1
0
1
1
0
2
2
1
1
0
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
0
2
2
0
1
1
1
0
1
0
1
1
1
2
2
0
1
2
1
1
1
1
0
2
1
1
2
0
1
0
1
2
0
0
0
1
2
1
0
1
1
0
1
1
1
2
0
1
1
1
0
0
1
2
1
1
0
1
1
1
1
1
0
2
1
2
2
0
0
1
1
2
1
2
2
1
1
2
0
1
1
1
0
1
0
2
0
1
2
1
0
2
1
0
1
2
1
1
1
2
0
2
2
1
2
2
0
2
1
1
2
1
0
1
0
1
2
1
2
1
2
2
1
2
0
2
0
1
2
0
1
1
2
1
2
2
1
1
1
1
0
1
1
0
1
1
2
0
1
1
1
1
1
2
2
1
1
0
2
1
0
1
2
1
1
1
2
1
1
1
0
2
1
2
1
1
2
0
2
2
0
1
1
0
1
1
1
0
2
1
1
0
1
0
1
1
1
0
2
1
3
0
1
2
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
1
0
0
1
1
2
1
1
0
2
0
1
1
2
1
2
1
1
1
1
1
1
0
1
0
0
1
1
2
2
0
2
2
1
1
2
1
1
1
1
1
1
0
1
1
1
2
1
2
0
2
0
0
0
1
0
1
1
2
1
1
1
1
1
0
1
1
0
1
1
1
1
1
1
1
0
1
1
0
1
1
1
2
2
1
2
0
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
2
0
0
0
1
1
2
1
1
1
1
0
0
1
0
1
1
2
0
1
0
1
0
1
1
1
0
0
1
1
2
0
0
1
0
1
1
1
1
0
1
0
1
1
1
0
2
1
0
2
1
1
1
1
1
1
1
1
2
0
2
2
1
1
0
1
2
1
1
1
1
1
2
1
0
1
1
1
1
2
1
1
1
2
1
2
0
2
2
1
1
2
2
1
2
0
0
1
1
3
1
2
1
1
2
1
0
2
1
3
1
2
1
2
1
1
0
0
1
1
2
2
2
2
0
1
1
2
1
2
1
1
2
1
2
1
0
0
1
0
1
1
1
1
1
0
0
1
1
2
0
0
1
2
1
1
1
1
1
1
1
1
1
1
0
3
2
1
1
1
1
1
2
1
0
1
0
1
1
1
1
1
1
0
1
0
1
1
2
2
2
2
0
0
2
1
0
1
0
1
2
1
0
2
0
1
2
1
2
2
0
1
1
2
1
2
2
1
1
2
2
1
0
1
1
1
1
2
1
0
2
0
1
0
1
1
2
2
1
0
2
2
0
0
1
1
1
1
2
0
1
1
1
0
2
0
2
1
1
0
2
1
1
0
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
2
1
1
1
1
2
0
0
1
1
0
2
3
1
1
1
1
2
1
1
1
0
2
1
0
1
0
2
2
2
1
1
1
1
2
1
1
1
2
1
1
1
1
2
2
2
2
2
0
2
1
1
0
0
1
1
2
1
1
1
1
1
2
1
1
0
1
1
1
1
1
2
2
1
2
0
1
2
1
0
1
2
2
1
0
0
1
0
0
1
2
1
3
0
2
1
1
1
4
1
0
2
3
1
2
1
2
1
1
0
1
1
0
1
1
0
0
1
0
0
0
2
1
1
1
1
1
2
1
2
2
0
0
1
1
1
1
1
0
0
1
1
1
1
1
1
3
1
0
0
2
1
1
1
1
2
1
0
0
1
2
1
1
1
0
0
0
1
1
1
1
3
1
1
1
0
1
0
1
1
1
2
1
2
1
2
1
2
1
1
0
1
1
2
0
2
1
1
0
1
2
1
1
1
1
2
1
0
2
1
1
0
1
1
2
1
1
1
1
1
1
0
1
1
1
1
1
3
2
1
1
1
1
2
2
1
1
0
0
1
2
0
1
1
0
1
1
1
1
2
1
2
1
1
1
1
1
1
0
1
1
1
1
3
1
2
1
0
0
0
1
0
1
2
0
1
2
1
1
2
0
1
2
1
1
2
0
1
1
2
1
2
1
0
2
0
0
1
1
1
1
0
0
1
2
1
0
0
1
0
1
0
0
2
2
0
2
1
1
2
1
2
1
1
2
2
1
1
1
2
0
1
1
1
1
1
2
2
1
1
1
2
1
0
0
0
0
1
0
0
1
0
2
2
2
1
0
1
2
1
2
0
1
1
1
2
1
1
1
1
1
1
1
1
1
1
0
0
1
1
0
1
1
1
1
0
2
1
0
2
1
2
2
1
1
1
1
1
1
1
1
2
1
1
1
2
0
1
1
1
2
1
2
1
1
0
3
1
1
1
1
1
0
1
1
1
0
1
0
1
1
2
2
1
1
0
2
1
1
0
1
2
0
2
1
0
0
2
1
2
1
2
1
2
1
1
1
2
2
3
1
1
1
2
1
0
1
1
1
2
1
0
0
0
1
0
1
0
1
1
0
1
1
0
1
2
1
1
1
2
0
0
2
1
2
0
3
2
1
2
2
3
1
0
1
1
0
1
0
2
2
2
2
1
1
2
1
1
1
1
1
2
1
1
0
1
2
1
2
1
2
1
0
2
1
2
1
2
0
0
0
0
2
1
1
2
1
2
2
1
1
1
1
1
0
2
1
0
1
1
2
2
1
1
0
0
1
0
1
1
1
1
1
0
0
1
1
1
1
2
0
1
2
0
2
1
2
1
1
1
1
1
1
0
1
1
2
1
3
1
1
1
1
2
1
1
1
1
1
1
1
1
2
3
1
2
2
0
1
1
1
1
2
2
2
0
1
1
1
0
0
2
2
2
1
1
1
0
0
2
2
1
2
1
2
2
1
1
1
1
1
1
0
2
2
1
1
1
1
3
2
2
0
1
1
0
0
1
1
1
1
1
1
1
0
0
1
1
1
2
1
1
2
0
0
1
1
1
0
0
1
0
2
2
1
0
1
1
0
1
0
1
0
2
1
1
0
1
0
1
1
1
1
1
2
1
1
2
2
1
1
2
1
1
1
1
1
2
1
1
1
1
0
1
1
0
2
1
1
0
1
2
2
2
1
1
1
1
0
1
2
1
1
1
1
0
1
1
1
1
1
1
2
0
0
1
1
2
1
1
2
1
1
1
2
1
1
1
1
2
2
1
1
1
1
1
2
0
1
2
2
1
0
0
1
1
0
2
2
2
1
1
1
1
3
1
1
1
0
2
1
0
1
0
0
2
2
2
0
1
2
1
2
1
2
1
2
2
1
0
1
1
2
2
1
1
2
2
1
0
1
1
0
1
1
2
2
0
1
2
0
0
1
0
1
2
1
1
0
1
1
1
1
1
0
1
0
0
1
2
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
2
1
1
2
1
2
0
0
0
1
1
2
1
1
1
2
1
1
1
2
1
0
0
2
1
0
1
1
0
1
2
1
1
2
2
1
0
0
2
1
2
0
0
1
0
0
2
0
0
1
1
1
2
1
0
1
1
1
1
1
0
1
1
1
1
2
0
1
0
0
1
1
2
0
1
2
4
1
1
1
2
1
0
0
1
0
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
0
2
1
2
0
0
2
1
1
1
2
1
1
1
0
2
1
1
0
1
2
1
1
2
0
2
2
1
1
0
1
0
1
1
1
0
1
1
1
1
1
1
0
1
0
2
2
0
2
0
2
1
1
1
1
0
2
1
1
1
2
1
1
0
1
1
1
0
1
2
1
2
4
2
0
1
2
1
1
0
0
0
2
1
1
1
1
1
0
1
1
0
3
0
1
1
2
2
1
1
1
2
1
1
1
2
2
1
1
2
1
1
2
0
0
1
1
0
0
2
1
0
0
2
1
2
0
2
2
2
1
1
0
1
0
1
1
2
1
1
1
1
0
0
2
1
2
1
0
1
1
1
0
1
1
1
1
1
1
2
1
2
2
2
2
2
0
0
1
2
0
0
1
0
0
1
1
1
0
0
0
1
2
1
0
1
1
0
2
1
2
1
1
1
0
2
1
1
2
1
0
1
1
1
0
0
2
0
0
0
1
2
2
2
1
3
0
1
1
1
1
2
2
2
0
1
1
1
0
0
2
1
1
1
0
1
0
0
1
0
0
0
0
1
2
2
1
1
1
2
0
5
1
0
1
1
1
0
1
0
2
1
0
2
1
2
1
1
0
1
2
2
0
1
0
1
0
1
1
1
1
1
1
1
2
1
1
1
1
0
1
0
1
0
2
1
2
2
1
1
0
1
1
1
1
2
1
2
2
0
2
2
0
2
0
2
0
0
1
2
2
2
1
0
1
2
1
0
1
0
2
0
2
4
2
1
1
1
2
2
1
2
2
2
0
1
3
0
1
0
1
1
1
1
1
1
0
1
2
1
1
1
2
0
1
1
1
1
2
0
1
1
0
1
2
2
0
1
0
1
1
1
0
0
1
2
1
0
1
3
1
0
0
1
1
0
1
1
1
1
1
2
1
1
1
1
1
1
1
2
0
2
0
1
2
2
1
1
2
0
1
1
1
2
1
1
0
0
0
1
1
1
1
2
2
2
2
0
0
0
1
2
2
1
1
1
2
1
1
2
1
2
0
1
1
2
1
0
1
1
1
0
1
2
0
2
2
1
0
1
2
1
1
0
1
1
1
0
2
1
0
1
2
1
0
2
0
0
1
1
1
1
1
0
2
1
1
1
1
4
0
2
1
1
1
2
2
1
1
0
1
0
0
1
1
2
0
1
2
2
2
1
2
1
1
2
1
2
0
1
2
1
1
1
2
1
2
2
0
2
1
2
0
1
0
2
1
1
0
1
1
0
3
1
1
1
1
1
1
1
0
1
1
1
2
3
2
2
1
1
1
2
1
2
0
1
1
1
1
1
0
1
1
0
1
1
0
0
1
0
1
1
1
0
1
1
2
0
1
1
0
1
2
2
0
1
1
1
0
1
1
1
0
0
1
2
2
2
1
2
1
0
0
1
1
1
1
0
1
0
1
2
2
0
2
0
1
0
1
2
1
1
2
1
0
1
1
0
2
1
0
1
1
2
1
1
0
1
1
0
1
0
1
0
1
1
1
1
1
1
2
2
2
1
1
1
1
1
0
1
1
0
0
2
1
1
1
2
0
2
1
2
1
1
1
2
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
2
1
0
2
1
1
0
1
0
1
1
2
0
0
1
1
0
1
1
1
1
1
1
0
1
1
2
1
1
2
1
1
2
2
0
0
0
1
2
1
0
1
2
0
1
2
0
1
1
1
1
1
1
1
0
1
1
1
2
0
0
0
2
0
1
2
1
2
1
1
1
0
2
1
0
0
1
1
0
0
1
1
0
2
2
1
1
1
1
1
0
2
1
1
0
1
1
2
1
2
0
1
1
1
1
1
1
2
1
4
2
1
2
1
2
0
1
1
2
1
0
1
0
1
0
2
2
0
3
1
1
1
2
2
1
1
1
2
1
1
2
0
1
1
0
1
1
0
2
0
1
1
2
1
1
1
1
0
1
1
1
1
1
2
1
0
1
1
0
1
2
0
1
2
1
2
1
1
2
1
1
1
2
2
1
1
1
1
0
1
1
2
1
2
1
2
1
1
1
0
1
1
1
1
1
1
1
2
0
1
1
1
1
1
1
2
1
0
1
1
1
1
1
1
1
2
1
2
1
1
0
1
2
1
1
2
2
2
0
1
2
1
1
1
2
0
1
0
0
2
1
2
1
2
1
1
0
1
1
1
2
2
0
2
1
1
2
1
0
1
2
1
1
2
0
0
1
1
2
1
2
1
2
2
2
0
1
1
1
1
2
0
0
1
1
0
2
0
2
1
1
0
0
1
2
0
0
1
1
1
1
0
0
1
0
2
3
1
2
0
1
0
1
1
1
1
0
1
2
1
1
0
1
2
3
1
0
1
1
2
1
1
1
0
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
1
1
0
0
1
1
1
1
2
1
1
2
1
2
2
1
0
1
2
0
0
2
0
0
0
1
1
1
2
1
1
1
1
2
2
1
2
1
2
1
2
0
2
1
1
1
0
1
2
0
1
2
1
0
0
1
2
1
1
2
1
1
0
1
2
1
1
2
1
1
2
1
0
1
1
1
1
1
1
0
2
1
2
2
1
0
1
1
1
2
1
2
0
1
1
1
1
1
0
2
1
2
0
1
1
0
1
1
1
1
2
1
1
0
0
0
1
1
1
1
2
1
2
2
2
1
0
2
2
0
1
1
1
2
1
2
0
1
0
2
0
1
2
1
2
0
1
3
3
2
1
0
1
0
2
1
1
1
0
1
0
0
0
2
1
0
1
1
1
2
0
2
1
1
0
1
2
1
1
1
1
1
1
1
2
1
0
2
2
0
1
1
2
0
2
1
1
1
2
1
2
1
2
1
2
1
3
0
0
1
1
1
1
1
1
1
1
1
2
1
1
0
1
1
2
0
1
0
1
1
2
1
1
0
1
1
1
1
1
1
2
2
1
1
1
0
2
7
1
1
1
2
0
0
1
1
1
1
0
0
2
0
1
2
0
1
1
2
1
1
1
1
1
2
2
2
0
2
2
2
0
1
1
0
1
1
1
1
1
2
1
1
1
0
1
1
2
1
0
1
2
1
1
2
1
1
1
1
1
1
0
1
1
2
2
1
1
1
1
0
1
1
1
2
0
1
2
0
1
1
1
1
1
1
0
0
2
2
1
2
0
0
2
1
0
1
2
1
1
0
1
1
2
1
2
2
1
1
1
1
1
0
1
1
1
1
0
0
2
1
2
0
2
1
2
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
0
3
1
2
2
2
1
0
1
0
2
1
1
1
1
0
2
1
1
2
1
1
1
0
2
1
1
2
1
2
2
1
0
1
1
1
2
0
1
1
0
1
0
1
0
1
0
1
2
1
1
0
0
1
1
1
1
2
1
1
2
1
1
0
1
1
1
0
1
0
0
2
1
1
2
0
1
1
0
2
0
1
1
1
1
1
2
1
2
1
1
2
1
1
2
1
0
2
1
0
1
2
0
0
2
2
0
1
2
0
1
0
0
0
2
1
0
2
1
1
1
2
0
1
1
0
0
0
1
1
2
2
2
1
2
2
1
1
0
0
1
1
2
1
1
2
2
1
0
0
1
1
2
2
2
0
1
1
2
2
2
1
1
1
1
1
1
1
2
0
2
2
0
1
1
2
1
2
1
0
1
1
1
2
2
1
1
1
1
1
1
1
2
2
2
1
0
1
1
2
1
1
2
1
1
1
2
1
0
1
1
1
0
1
0
1
0
2
2
0
1
1
1
1
3
1
1
2
2
1
1
2
1
1
0
1
1
0
1
2
1
4
1
2
1
1
1
1
1
1
0
1
0
2
1
0
1
2
1
1
0
1
2
1
2
1
0
0
0
1
3
1
0
2
2
2
1
0
2
1
1
1
1
0
0
0
0
1
1
0
1
1
2
1
1
1
1
1
0
1
2
1
1
0
1
1
2
1
1
2
1
3
1
2
2
0
2
1
1
2
0
1
1
2
1
0
1
1
1
2
2
1
2
1
0
2
0
1
0
2
1
2
1
2
0
0
1
0
1
0
1
2
1
1
1
0
0
0
0
1
0
0
2
1
1
0
2
0
1
0
2
2
1
1
1
0
2
1
1
1
1
1
1
0
1
3
2
2
1
2
1
1
1
1
1
1
1
0
1
0
1
0
1
1
1
1
2
1
1
1
0
2
0
1
1
0
1
2
1
1
0
0
2
1
2
1
1
1
2
0
1
1
1
2
1
0
2
2
1
1
2
2
1
2
1
1
2
1
1
0
0
1
1
1
2
1
2
1
1
0
1
0
1
2
1
0
2
0
2
1
1
0
1
1
2
0
0
1
1
0
1
1
0
1
1
1
1
1
1
1
1
2
1
1
1
1
1
0
0
2
2
1
2
2
2
1
1
1
2
1
1
2
1
1
0
1
0
2
1
1
0
3
3
0
0
1
0
1
1
0
2
1
1
0
2
1
2
1
0
1
2
0
1
1
2
1
0
1
0
2
0
1
1
1
1
1
1
1
1
0
0
1
1
0
0
0
1
2
1
2
1
1
1
1
1
1
1
2
3
1
1
1
0
0
1
1
1
1
2
1
1
1
2
1
2
1
0
1
1
2
0
2
1
1
0
0
1
1
1
1
0
1
0
1
1
1
1
1
1
2
0
1
2
1
2
2
1
1
0
1
1
1
1
2
1
0
1
0
2
0
1
0
2
0
1
2
1
0
2
0
1
2
2
1
0
2
2
0
1
1
1
1
1
2
2
1
1
0
1
1
1
1
1
2
1
1
1
1
1
0
1
0
0
2
1
1
1
1
2
2
1
1
0
1
1
1
1
0
1
1
2
0
0
2
1
0
1
1
1
1
1
0
2
2
1
1
1
0
1
1
1
1
1
0
0
1
0
0
0
2
1
1
1
2
1
2
0
1
0
0
0
1
0
1
1
2
0
0
2
1
0
2
2
0
1
1
0
2
1
1
2
2
0
2
1
0
2
0
1
2
1
1
0
2
1
0
2
0
1
1
2
1
1
2
0
1
1
1
1
1
1
1
1
1
1
2
2
0
1
0
1
2
0
1
1
1
2
2
1
1
2
0
2
1
2
1
1
2
1
0
1
1
1
0
0
0
1
2
2
1
1
1
0
0
1
0
0
1
0
2
1
2
1
1
1
1
2
0
1
2
0
0
2
1
1
2
1
1
0
0
1
1
2
0
0
0
2
1
1
1
0
2
1
0
1
0
2
1
2
1
0
0
1
1
2
2
1
1
1
2
0
1
0
1
1
2
1
1
1
0
2
1
0
1
2
1
0
1
1
1
1
2
1
1
1
1
0
1
1
0
0
1
0
2
1
1
1
0
1
2
1
0
1
1
1
1
2
1
1
2
0
0
1
1
1
1
1
1
2
2
1
1
0
1
1
0
1
4
1
1
1
1
1
1
2
2
1
2
2
1
0
1
0
0
1
2
1
1
0
0
1
1
0
1
1
1
1
0
1
1
1
1
0
1
1
2
1
0
2
2
1
1
2
1
1
1
2
1
1
1
2
2
0
2
1
1
1
2
1
0
1
1
1
1
2
2
2
1
1
2
0
2
2
1
0
1
0
1
1
1
0
1
2
1
1
1
0
1
1
2
1
1
1
0
2
0
1
1
0
2
0
1
1
1
2
0
2
1
2
1
1
1
1
0
1
1
1
2
1
1
2
1
2
2
1
1
2
0
2
1
0
0
0
1
0
1
1
1
1
1
0
0
2
2
2
1
1
1
0
0
0
2
0
1
1
3
1
2
2
0
0
0
0
0
1
1
1
1
1
1
1
0
1
1
2
1
2
1
2
1
1
1
0
0
2
1
2
2
0
1
0
0
1
1
1
1
2
0
1
1
1
2
2
1
2
1
1
0
2
1
1
1
0
1
2
1
0
2
0
1
1
1
1
0
1
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
5
1
1
1
1
2
1
1
1
1
1
1
2
1
2
1
0
1
2
1
1
1
1
0
1
2
0
1
2
1
1
1
2
0
2
1
0
2
1
1
0
2
1
2
1
1
1
0
1
0
1
1
1
1
1
9
2
1
1
2
1
1
1
0
1
1
1
1
1
2
0
1
0
1
2
1
1
1
1
1
2
2
1
1
0
0
1
0
2
0
1
2
0
0
1
2
0
3
1
1
0
1
0
1
1
1
0
1
1
0
0
1
2
1
0
2
2
0
0
1
1
1
1
1
2
1
1
0
1
0
1
0
1
2
1
1
1
2
0
2
0
2
1
2
1
1
1
1
2
1
1
2
1
1
0
1
0
1
0
2
1
1
1
2
1
0
1
1
1
1
1
1
1
1
1
0
1
1
1
2
1
1
1
2
1
1
1
2
1
0
0
0
1
1
2
1
1
2
1
2
0
1
2
0
0
1
1
0
1
0
2
2
2
1
0
1
0
1
0
0
2
2
1
0
1
1
2
1
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
0
1
1
2
2
1
1
2
0
2
1
1
0
2
0
2
1
0
1
1
0
1
2
0
1
2
1
1
2
0
1
1
1
2
1
1
2
1
1
2
2
1
1
1
0
0
1
2
0
1
2
1
1
0
1
2
1
2
1
1
0
2
1
1
2
1
1
1
1
1
1
1
1
1
1
0
1
2
1
2
0
1
1
0
1
0
2
0
1
1
1
0
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
2
1
2
2
1
1
1
1
1
2
2
2
0
1
1
1
2
0
0
1
1
0
1
1
1
2
2
1
0
3
1
1
1
2
0
1
0
1
1
0
2
1
1
1
2
1
2
1
3
2
1
1
2
0
0
0
1
1
2
2
1
2
1
2
1
0
1
0
1
1
1
1
1
1
0
1
2
2
2
1
1
1
2
2
1
0
1
1
2
1
0
1
0
2
0
1
1
1
0
1
1
1
1
1
1
0
1
1
2
1
2
1
2
1
7
1
2
1
0
1
2
2
2
0
1
2
1
2
0
2
0
0
1
0
1
1
1
0
1
0
1
2
0
1
2
1
0
0
1
1
1
1
2
1
1
0
1
1
1
1
0
2
1
2
0
1
2
1
1
1
1
1
1
1
1
2
1
0
0
1
1
0
2
1
1
0
1
2
2
1
1
1
2
1
2
1
1
0
0
1
0
1
1
0
2
2
1
2
1
2
1
1
1
1
1
2
1
1
1
0
1
2
1
1
1
0
1
1
0
0
1
0
0
2
0
1
1
1
1
0
1
1
1
2
1
1
1
1
2
1
1
2
1
1
0
0
1
1
1
0
1
2
1
1
2
1
0
0
2
1
0
2
2
1
1
2
2
1
1
2
1
0
0
1
1
1
1
2
0
1
1
0
1
1
2
1
0
2
1
2
1
2
1
1
2
0
0
1
0
0
0
0
1
0
0
1
1
0
1
1
1
1
1
2
0
1
0
2
2
0
1
1
0
2
0
1
0
0
2
1
1
3
2
2
0
1
1
1
1
2
1
1
1
0
1
2
2
1
1
1
0
1
1
3
1
1
1
2
2
1
1
2
0
0
1
2
1
0
1
1
0
0
1
0
1
1
0
1
3
2
1
2
1
0
1
1
2
1
0
1
2
0
2
2
1
1
1
2
0
1
1
0
1
1
0
1
0
1
1
1
1
1
1
1
1
2
1
1
1
0
1
1
2
2
1
1
1
2
1
1
2
1
2
2
0
1
1
1
1
1
2
1
0
1
1
2
0
2
1
0
1
1
1
1
1
2
2
1
1
0
0
1
0
1
2
1
0
1
1
2
2
1
1
1
2
1
0
1
1
2
1
0
1
1
0
1
1
0
2
1
2
1
1
1
0
0
0
1
0
1
0
1
0
2
0
1
1
1
1
1
2
1
1
1
1
2
1
1
0
1
1
0
0
2
0
1
2
2
1
1
2
1
0
2
1
1
1
1
2
0
1
1
2
0
1
0
1
2
0
1
1
1
2
0
1
1
1
2
2
0
1
1
1
2
2
1
0
2
2
1
1
2
0
0
2
1
1
2
1
1
1
1
1
1
0
2
0
0
0
1
1
1
1
1
0
1
2
2
0
1
1
1
2
0
0
0
1
1
2
1
1
2
1
1
1
1
0
2
1
0
1
1
0
2
1
0
2
1
2
1
2
1
1
1
1
2
1
3
1
1
0
2
1
2
1
1
3
1
0
2
1
1
1
2
1
2
1
1
1
1
1
1
0
1
2
0
1
1
1
1
1
0
1
1
2
1
1
5
0
2
0
0
0
2
1
1
1
0
0
0
2
1
0
1
1
1
1
2
2
1
1
0
0
1
0
0
0
1
1
1
1
1
1
2
1
2
1
2
2
1
1
2
2
1
2
1
1
1
2
1
1
2
1
1
1
1
0
1
1
1
2
2
1
1
0
1
1
23
1
1
2
1
1
2
1
0
0
1
2
1
2
0
2
1
1
1
1
0
1
0
1
0
2
1
1
2
2
1
1
1
1
0
2
2
1
1
2
1
1
1
2
1
0
2
1
0
2
1
1
1
1
0
2
1
2
1
1
0
2
2
1
0
1
0
0
1
0
1
1
2
1
1
3
1
1
0
1
1
2
0
0
0
0
1
2
2
2
0
0
2
1
1
1
1
0
1
2
1
2
2
1
1
1
2
2
1
1
0
1
2
1
1
1
2
2
2
2
1
0
2
1
1
1
1
1
0
1
2
2
1
1
0
1
2
2
1
3
1
2
1
0
1
1
2
1
2
1
1
1
2
2
2
0
2
1
0
1
1
1
1
2
0
1
2
0
3
0
1
1
1
1
0
2
0
2
2
0
1
1
1
4
1
2
2
1
1
1
1
1
1
1
2
0
1
0
1
1
1
1
2
1
1
2
1
2
1
2
1
1
1
1
0
1
1
1
1
1
0
0
2
2
1
2
0
1
1
1
1
1
1
2
2
1
2
0
1
0
2
1
2
1
1
1
0
0
1
0
2
2
1
0
0
1
1
1
2
0
1
2
0
1
1
1
1
1
1
2
1
0
1
1
1
1
0
2
2
2
1
1
1
0
0
1
2
1
1
1
1
0
2
1
1
1
0
2
1
1
1
0
1
2
1
2
2
1
1
1
1
1
1
1
2
6
1
1
1
2
1
1
2
0
1
1
0
0
3
1
1
2
2
1
1
0
0
1
1
1
1
1
0
1
2
1
2
1
1
1
2
2
1
1
1
1
1
1
1
2
2
1
1
0
1
0
1
0
0
1
1
1
2
1
1
1
0
2
1
0
2
0
1
1
1
2
1
1
1
2
1
2
1
1
1
0
1
1
2
2
1
1
0
2
2
0
1
2
1
1
2
1
1
0
1
2
2
2
2
1
1
1
1
2
2
1
1
2
4
1
0
0
2
1
1
0
0
1
1
1
1
1
1
1
1
1
0
1
1
0
0
1
1
1
1
2
2
1
0
0
0
1
2
1
1
1
0
1
2
0
1
0
1
0
2
1
2
0
2
1
2
1
1
1
1
1
1
3
1
1
1
0
1
0
1
1
2
0
1
2
1
2
1
1
0
0
1
2
2
1
0
1
1
2
1
1
2
1
1
2
0
1
1
1
1
2
1
1
1
0
2
1
2
0
0
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
0
1
0
1
1
1
2
1
1
2
1
2
2
0
1
2
1
1
1
1
1
2
0
0
0
1
2
2
2
1
1
1
1
0
1
2
2
0
0
1
1
0
1
1
1
0
0
1
2
1
1
0
0
2
1
1
2
0
1
0
1
0
2
1
2
1
2
2
1
2
2
2
0
2
0
1
1
1
2
1
0
1
0
1
1
1
1
2
1
2
1
1
2
1
2
1
1
2
1
1
1
1
1
1
1
2
1
2
1
2
0
2
0
0
0
1
2
0
1
0
0
1
1
1
1
0
1
1
0
1
1
1
0
0
2
0
0
1
1
1
0
2
1
1
1
1
1
2
1
2
1
0
0
1
2
1
1
0
1
1
0
0
2
1
1
0
1
1
1
1
1
1
1
1
1
0
2
2
2
1
1
4
1
1
0
0
1
1
1
2
1
1
1
2
2
1
1
2
1
0
2
1
1
1
1
0
0
1
2
2
1
1
2
2
1
1
0
1
2
0
1
1
2
0
1
1
1
1
1
1
1
2
0
1
0
1
2
2
2
0
2
2
1
0
1
1
0
1
3
1
2
0
1
2
2
1
1
1
2
1
2
1
1
0
2
1
1
0
2
1
0
1
1
1
1
2
0
0
1
2
0
1
2
2
1
1
1
1
1
0
1
1
1
1
1
0
2
0
0
1
1
2
1
1
1
1
0
1
0
0
1
2
2
1
0
1
2
1
1
1
1
2
0
1
0
1
2
2
2
1
1
0
1
1
1
1
1
1
2
1
2
0
0
1
0
1
0
0
0
1
2
1
1
2
2
0
2
0
2
2
1
0
2
1
1
1
2
1
0
1
1
1
1
1
0
0
2
2
3
1
1
1
0
1
0
0
1
1
0
1
1
2
2
0
0
2
1
1
2
1
4
1
1
2
1
1
0
1
0
1
1
1
1
1
0
1
1
1
1
2
1
1
0
1
1
1
1
1
0
0
0
0
1
2
1
1
0
1
2
1
0
2
1
1
2
2
1
0
1
0
1
1
1
2
2
2
1
0
2
1
1
1
1
1
1
0
1
0
2
1
3
1
1
0
2
3
1
1
2
1
1
2
1
0
1
2
1
1
2
1
0
1
1
1
0
0
1
2
1
0
1
1
0
2
1
1
0
1
0
1
1
1
4
1
1
1
2
1
2
2
0
2
0
1
0
1
0
1
0
2
1
2
1
0
1
0
1
1
0
1
0
1
1
2
1
1
2
1
2
1
0
2
1
2
2
1
1
1
1
0
1
1
2
1
1
1
1
1
0
2
0
0
1
0
1
1
2
1
2
0
1
1
2
1
1
1
1
1
1
1
1
0
1
1
1
0
0
1
1
0
1
2
1
1
1
1
2
1
1
1
1
1
1
0
0
2
2
0
1
0
1
1
1
2
1
0
1
1
0
1
1
2
1
1
1
1
0
1
2
1
0
1
1
1
1
1
0
2
2
0
1
2
1
1
2
0
0
1
1
1
0
1
1
1
1
1
2
2
1
1
2
1
1
2
2
2
1
1
0
2
1
1
2
0
2
2
0
2
1
1
0
2
2
1
2
0
0
1
2
1
1
1
0
0
1
2
2
1
2
1
1
0
2
0
0
2
1
2
1
1
2
0
0
2
1
2
1
1
1
1
0
2
1
2
1
1
2
1
2
1
1
1
1
2
1
2
1
1
2
1
1
0
1
1
2
1
2
0
1
1
2
2
2
2
1
1
1
2
1
1
2
1
2
1
1
1
2
0
1
1
2
2
2
0
0
1
1
1
1
1
2
1
0
1
2
1
1
2
0
0
2
0
1
2
1
1
0
1
0
1
0
1
2
1
1
2
2
0
0
2
0
1
1
1
0
2
1
1
1
1
0
1
1
3
2
2
0
2
1
0
1
1
2
2
1
2
0
1
2
2
1
1
0
1
1
0
2
0
0
1
1
1
1
0
1
2
1
1
0
2
1
1
0
2
1
2
1
1
1
3
1
1
1
1
2
1
1
0
2
1
0
2
0
1
1
2
1
2
0
0
1
1
1
0
1
1
4
2
0
2
2
0
2
1
0
1
0
0
1
2
0
14
0
1
1
1
1
1
2
0
1
1
1
0
1
1
2
1
1
1
1
2
1
1
2
2
1
0
1
1
0
2
2
1
1
1
0
2
2
2
0
1
1
0
1
0
2
1
1
1
2
1
0
2
1
1
1
2
1
1
1
1
2
2
1
1
1
1
0
0
2
1
0
1
2
0
2
1
0
0
0
0
2
1
1
1
2
0
0
0
1
1
0
2
2
1
2
2
1
1
2
2
1
2
1
1
2
1
2
1
2
2
2
1
1
1
0
1
2
1
1
0
1
0
1
1
1
0
1
2
2
0
1
2
1
0
1
0
2
1
1
1
1
1
2
1
2
1
0
1
0
3
1
2
2
2
1
1
2
2
1
1
1
1
1
1
0
2
1
1
1
0
1
2
1
1
1
1
3
1
0
1
1
1
1
0
0
1
2
2
1
0
2
1
1
1
1
1
1
0
0
1
1
2
2
1
2
1
1
1
1
1
0
2
0
1
2
2
0
0
1
1
1
2
1
2
2
0
1
0
1
2
2
1
0
1
1
1
0
2
1
0
1
2
2
1
1
2
1
1
1
1
1
1
1
1
0
2
0
1
0
1
1
1
1
1
1
2
0
0
1
1
0
1
1
1
1
0
1
1
1
1
1
1
0
0
2
1
1
1
1
1
0
0
0
1
1
0
1
1
2
1
1
0
1
1
1
0
1
1
1
1
2
1
0
2
1
1
0
1
0
0
2
2
0
1
1
2
2
0
1
2
1
2
1
2
0
2
2
1
1
0
1
0
0
2
2
1
1
2
0
1
1
1
1
0
1
1
1
1
0
0
2
1
1
1
3
2
0
2
0
2
1
0
1
1
1
2
2
0
0
0
1
2
1
2
1
1
1
0
1
1
0
0
0
0
1
0
2
2
1
0
2
1
2
1
1
1
1
0
2
1
2
1
1
0
0
0
0
2
2
1
1
1
0
2
2
2
1
1
2
1
2
1
1
0
1
1
0
0
1
2
1
0
1
1
1
1
2
1
2
2
1
1
2
2
1
1
1
0
1
0
1
0
1
2
1
1
0
1
2
1
1
2
1
1
2
1
1
1
1
1
2
1
2
1
2
1
0
1
1
1
2
1
1
1
2
2
1
1
1
1
2
1
1
0
1
0
0
1
1
2
2
0
1
1
1
1
1
0
1
2
1
1
2
1
0
2
1
1
1
1
1
1
1
1
2
1
2
1
2
1
0
1
2
2
1
1
1
1
1
2
1
2
1
2
1
1
1
1
1
4
0
1
0
2
1
1
2
1
0
1
2
0
1
1
1
1
2
2
1
1
2
0
1
0
1
2
1
3
0
3
1
2
0
1
1
1
0
0
2
1
1
1
2
1
1
1
1
2
0
0
1
2
1
1
2
2
0
0
1
0
0
0
2
1
2
1
0
2
1
1
2
0
1
1
0
1
1
2
0
0
1
0
1
1
2
0
1
0
0
1
1
1
2
2
2
1
1
1
0
1
1
0
1
1
1
2
1
1
1
1
1
1
0
1
1
0
1
0
1
0
0
1
0
2
1
0
1
2
0
2
0
1
2
1
0
1
1
2
2
2
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
0
2
1
2
2
1
1
1
0
1
1
1
0
2
2
1
2
0
0
0
1
1
2
2
1
2
1
2
0
2
2
1
1
6
2
2
2
2
1
0
1
0
1
1
1
1
0
1
0
1
1
0
1
2
2
1
2
1
0
1
0
3
1
0
2
2
1
0
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
0
2
2
0
1
1
3
1
1
0
2
1
1
1
2
0
1
1
1
2
2
1
1
2
1
2
1
1
1
1
1
1
1
0
2
0
1
0
0
1
1
1
2
2
2
1
1
1
1
1
1
0
1
0
1
1
2
1
1
1
2
2
0
2
1
1
0
1
2
2
2
2
1
1
0
1
1
1
1
0
1
2
0
2
2
1
0
0
2
2
2
1
1
1
1
2
2
1
1
0
1
1
2
2
1
1
1
1
1
1
1
1
2
2
0
1
1
0
1
2
1
1
2
2
1
1
1
2
1
1
1
2
0
2
1
1
1
0
1
0
1
1
0
1
1
1
1
0
0
2
1
1
1
2
1
2
1
1
2
0
0
1
1
0
2
3
2
0
1
2
1
1
2
0
1
1
0
1
1
1
1
1
1
0
1
1
2
1
1
2
1
1
1
2
1
0
1
1
0
1
1
1
0
0
0
0
1
0
1
2
0
1
1
0
2
2
1
1
2
1
1
1
1
0
1
0
0
2
1
1
1
1
2
0
0
2
2
1
2
1
1
2
0
1
1
1
1
1
1
2
1
1
2
0
1
1
1
2
1
1
2
1
1
1
1
0
1
2
1
2
1
1
2
3
0
0
1
1
0
2
1
0
1
0
1
2
1
2
1
1
1
2
0
1
1
0
2
0
1
0
1
2
1
1
1
2
1
1
1
2
1
1
1
0
0
1
1
1
0
1
0
1
0
0
2
1
1
1
1
2
2
2
0
1
1
1
1
1
1
1
1
0
2
1
1
1
0
1
0
0
1
0
1
0
0
2
2
0
1
1
2
3
1
0
1
1
1
1
1
2
2
0
1
1
0
1
1
1
1
1
1
0
0
2
0
1
2
2
1
0
1
0
1
2
2
1
1
2
1
0
1
2
1
1
2
1
1
1
2
2
1
2
1
1
1
1
0
2
0
0
1
1
1
0
1
1
1
1
1
1
1
1
1
2
1
0
1
2
2
0
1
0
2
2
2
2
1
1
2
1
0
2
0
1
0
1
1
0
0
1
2
1
2
2
4
1
1
1
1
1
2
1
1
1
1
1
0
0
0
0
2
1
1
1
0
2
1
2
1
0
1
1
1
1
1
1
2
1
1
1
0
1
1
1
1
1
1
1
1
1
2
0
1
0
0
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
2
2
0
1
1
2
2
1
1
0
1
1
2
0
0
1
0
2
1
0
1
1
0
2
1
1
0
1
1
0
2
1
2
1
1
1
1
1
1
1
1
2
0
2
1
1
2
1
1
1
1
0
1
1
0
0
1
1
1
1
0
1
0
1
1
1
0
1
0
0
0
1
2
0
0
1
0
2
0
3
1
0
1
1
1
1
1
0
1
1
0
2
0
2
1
1
1
1
0
0
1
2
0
2
1
1
0
1
0
1
1
0
2
1
0
2
1
0
2
1
1
1
0
1
1
2
1
2
1
1
1
1
0
1
1
2
1
0
0
1
2
1
2
0
1
1
0
1
1
1
0
1
2
1
0
1
1
1
2
2
1
5
1
1
1
1
0
1
2
1
0
1
1
0
1
1
1
1
1
0
2
1
0
0
1
0
1
2
1
1
0
2
1
0
0
2
0
1
0
2
0
2
2
2
2
1
2
1
0
2
0
1
1
1
0
1
1
0
1
1
1
2
1
1
2
1
1
0
1
1
0
1
2
2
1
0
2
2
1
3
1
1
2
1
2
1
2
0
2
1
1
1
1
1
0
1
0
0
0
2
1
0
1
1
1
1
0
1
0
2
1
1
1
1
1
1
2
1
1
2
0
1
1
1
1
1
1
2
1
0
2
2
1
2
1
1
1
2
1
1
1
0
1
2
0
1
1
0
1
1
1
1
2
2
2
1
1
2
2
1
1
1
1
1
0
2
1
2
1
1
1
0
1
1
1
0
1
1
2
1
1
1
1
2
1
1
2
2
1
1
1
0
1
1
1
1
1
1
0
2
1
1
3
1
0
1
1
1
1
2
0
1
1
1
1
2
1
1
1
1
0
1
0
0
0
2
0
0
0
2
2
0
1
0
1
1
0
1
1
0
0
1
1
0
0
0
1
1
2
1
1
1
1
1
0
2
0
1
1
1
2
1
1
1
2
1
1
1
2
0
2
1
0
1
2
1
0
1
0
0
0
1
2
1
1
1
0
1
1
0
1
1
0
1
1
1
1
1
1
1
2
1
1
2
1
0
1
1
1
0
0
1
1
2
1
1
0
0
2
0
1
2
1
0
2
2
2
1
1
1
2
2
1
2
1
2
1
1
0
1
1
1
1
1
2
1
1
0
1
1
2
0
0
0
1
2
1
1
1
2
1
1
1
0
1
1
0
0
1
2
2
1
1
1
1
0
1
2
1
2
2
1
2
0
1
1
1
1
1
2
0
1
2
1
1
1
0
1
1
1
1
1
2
0
1
1
1
1
0
1
1
1
0
2
1
0
0
0
1
0
1
1
1
1
1
1
0
2
1
0
1
2
0
1
2
3
1
1
1
1
1
0
1
2
1
1
2
1
1
1
1
2
1
0
2
0
1
0
1
1
1
0
0
2
2
0
2
2
1
0
1
1
1
1
1
1
0
1
1
0
1
1
2
1
2
1
0
0
1
1
0
0
0
1
1
2
2
1
0
0
2
0
1
1
1
0
0
1
1
1
0
1
0
2
1
1
1
2
1
1
0
1
1
0
2
0
2
1
1
0
1
2
2
1
1
1
0
0
2
1
1
2
1
1
0
1
1
1
2
1
1
1
1
0
2
1
1
1
1
2
2
1
1
1
2
0
2
1
1
1
1
2
1
1
1
1
1
1
0
1
0
1
1
1
1
1
1
1
2
1
1
1
0
0
1
1
0
1
1
1
1
1
2
2
1
2
1
1
1
1
0
1
1
1
0
4
1
1
1
1
1
0
0
2
1
2
1
0
2
2
0
1
1
1
0
1
2
1
1
2
1
1
2
3
1
0
1
0
2
0
0
0
0
1
1
1
1
2
1
0
1
1
1
0
2
0
1
2
0
1
1
1
0
1
1
2
1
1
1
0
2
0
1
0
3
1
0
2
2
1
1
0
1
1
1
2
1
0
1
2
0
1
2
2
1
0
0
1
0
1
1
0
2
1
1
0
1
2
2
2
2
1
0
1
1
1
1
0
2
0
0
1
0
1
0
1
1
2
2
1
1
2
2
2
1
1
2
0
1
2
1
1
1
1
1
1
1
1
1
2
2
2
0
1
0
2
1
0
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
0
2
1
2
0
1
1
0
1
1
1
1
1
1
0
2
0
0
1
1
1
1
1
0
2
1
3
1
1
1
0
1
1
2
1
1
1
2
1
2
2
0
1
1
1
1
1
0
1
1
1
1
2
1
2
1
1
2
2
1
0
1
0
1
0
1
1
0
1
0
1
2
1
0
0
1
0
1
1
1
1
2
0
1
0
1
0
1
0
1
0
1
1
1
0
1
1
0
2
1
2
1
2
1
2
1
0
2
1
0
2
2
2
1
1
2
3
0
0
1
1
1
2
2
1
2
2
1
2
1
2
1
1
1
0
1
2
1
1
2
1
2
1
0
2
2
0
1
0
0
1
1
0
1
1
2
1
1
1
1
1
1
1
0
1
1
1
2
1
2
2
1
1
0
1
1
1
2
0
1
1
1
1
1
1
1
2
1
1
2
2
1
1
2
2
1
1
0
2
2
2
0
1
1
3
2
2
0
2
1
1
3
2
2
1
1
2
0
2
2
1
1
1
1
1
1
1
2
1
0
2
0
1
1
1
2
2
2
1
0
1
2
1
2
2
2
0
0
2
1
1
2
1
1
1
0
2
2
0
1
0
1
1
2
0
0
1
1
0
1
1
1
1
1
1
1
2
2
1
1
0
1
1
1
1
0
1
0
0
1
2
1
1
2
0
1
1
1
2
2
1
0
0
1
1
1
2
2
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
2
1
0
1
3
1
1
1
1
1
1
1
1
1
1
0
0
0
1
1
2
1
1
1
2
2
1
2
1
1
1
0
0
1
1
2
1
1
1
1
0
1
1
1
1
1
1
1
1
1
2
2
2
1
1
2
2
2
1
1
2
0
1
2
0
2
1
2
1
1
1
1
1
1
1
1
0
1
1
1
1
0
1
1
1
0
1
0
1
2
1
1
2
1
1
2
1
2
0
0
1
1
1
1
1
1
1
0
2
0
1
0
1
1
1
1
1
0
0
1
2
1
1
1
1
2
0
2
1
1
1
2
2
1
1
1
0
0
1
1
0
1
0
1
0
2
1
0
1
1
1
1
2
0
1
2
1
2
2
1
1
1
0
1
1
1
2
2
0
1
1
0
2
1
2
1
0
1
2
1
1
1
1
2
1
1
2
2
1
1
1
1
2
2
1
3
1
0
0
1
1
1
1
1
1
2
1
1
1
2
1
2
0
1
0
0
0
1
0
1
1
1
2
1
1
1
0
1
1
1
0
1
1
1
1
0
1
1
0
1
2
1
0
1
0
2
1
0
1
1
1
1
1
1
2
1
1
1
2
1
2
1
2
2
1
2
1
1
1
1
1
2
2
1
1
0
1
1
1
2
1
1
2
0
0
1
0
1
0
2
0
1
1
1
1
1
0
0
0
1
0
2
0
1
0
1
1
1
1
1
1
1
1
1
2
0
1
2
1
1
1
1
1
0
1
1
0
1
1
2
1
1
2
2
1
0
0
1
1
1
1
0
2
2
2
0
1
2
1
1
1
2
1
2
1
2
2
1
1
0
0
0
3
0
1
1
1
0
1
0
1
2
0
2
1
2
0
1
0
1
0
2
1
2
2
2
1
2
1
2
1
2
1
0
0
0
1
1
1
1
1
1
0
2
1
1
1
1
2
1
1
1
1
1
2
1
1
2
0
0
1
1
2
0
0
1
3
1
0
1
1
1
1
1
2
2
2
1
2
2
1
2
2
2
1
1
1
1
0
1
2
0
1
1
1
1
0
1
1
1
1
2
1
1
1
1
1
1
2
0
2
2
2
1
2
2
2
2
1
1
2
1
2
1
2
1
1
1
1
1
1
0
1
1
1
0
2
1
1
1
2
0
1
1
1
1
2
1
1
1
1
1
0
1
1
1
2
1
0
1
0
1
0
1
1
1
1
1
2
1
0
1
2
2
0
1
1
0
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
0
1
2
1
2
2
1
1
0
0
1
2
1
0
1
0
0
1
2
2
1
0
1
1
1
1
1
2
0
2
0
1
1
1
0
0
2
2
1
0
1
1
1
1
0
1
1
0
2
1
0
2
2
1
1
0
0
1
0
1
1
1
1
1
2
2
1
1
1
1
0
1
1
1
2
2
2
2
1
1
0
0
1
1
0
1
2
2
1
0
1
1
1
0
2
1
0
1
2
2
1
0
4
1
0
1
0
1
1
1
1
0
1
1
2
1
1
0
1
0
1
2
1
1
2
1
0
1
0
2
1
1
1
1
2
0
0
1
1
0
0
1
0
2
1
1
1
2
0
1
1
1
0
1
1
1
1
1
2
1
2
1
0
1
0
0
1
2
1
1
2
1
2
0
1
2
0
0
1
0
1
2
2
1
0
0
2
1
1
1
0
2
0
1
0
1
1
2
1
1
1
2
2
1
1
1
0
1
2
1
1
1
1
2
2
1
1
2
1
1
2
1
1
0
0
2
0
2
2
1
0
1
2
1
1
2
1
1
1
0
1
0
1
1
2
1
1
2
1
0
1
1
1
1
0
1
1
2
2
1
2
2
1
2
1
1
1
1
1
1
2
2
0
3
1
1
0
1
1
1
0
0
1
2
0
1
1
2
4
0
1
0
1
1
1
2
0
1
1
0
0
1
1
1
2
2
1
1
0
1
0
0
2
0
1
1
1
2
1
1
1
0
1
2
0
0
2
1
0
0
1
1
1
0
1
1
1
1
2
1
1
2
2
0
2
0
1
1
1
0
2
1
1
1
1
0
0
0
1
1
1
2
2
0
1
2
1
0
1
0
1
1
2
1
2
2
2
1
0
1
2
1
0
1
0
1
1
1
2
2
1
0
1
2
2
2
1
0
1
0
0
2
2
1
0
1
1
2
0
0
2
1
1
3
1
1
0
2
2
2
1
1
1
1
1
0
1
1
1
2
1
1
2
2
1
1
1
1
1
1
1
1
0
1
1
2
1
2
1
2
1
2
2
1
1
2
0
2
2
2
2
2
1
1
0
0
1
1
1
0
1
1
0
1
1
2
2
1
2
0
2
0
2
1
1
1
2
0
1
1
2
2
0
1
1
2
1
1
2
1
0
2
1
0
2
1
1
1
0
2
1
1
0
1
0
2
1
2
1
1
2
0
1
0
2
0
2
1
1
0
1
1
2
1
2
1
2
1
1
2
1
1
1
1
2
2
0
2
2
1
1
2
1
2
1
0
2
1
1
2
2
0
1
2
2
0
1
0
1
0
1
1
1
1
1
0
0
0
2
1
0
2
1
1
1
1
1
1
2
1
1
1
1
1
0
1
1
2
2
2
1
2
0
1
2
1
0
1
1
1
1
1
2
2
0
2
1
2
2
2
1
1
2
2
0
1
2
0
1
1
0
1
0
2
1
0
2
1
0
0
1
1
1
0
2
2
1
0
2
0
1
1
0
1
0
1
1
1
1
1
2
0
1
2
2
2
1
1
1
1
0
2
0
1
1
1
1
1
2
0
0
1
0
1
1
2
2
1
1
1
2
2
0
1
4
1
0
1
1
1
1
1
2
0
2
1
0
2
1
1
2
1
1
1
0
2
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
2
1
0
2
1
1
1
1
1
2
0
1
2
0
2
2
1
0
0
1
0
1
2
2
1
2
2
1
2
0
0
2
1
1
0
1
1
2
2
1
1
1
1
0
2
2
2
2
1
0
0
0
0
1
2
2
0
1
1
1
1
2
1
2
0
0
2
1
0
2
2
2
0
1
2
1
0
0
1
1
1
1
1
0
2
0
1
0
1
2
1
2
2
2
2
1
2
1
0
2
1
1
2
1
2
1
0
0
2
1
1
2
1
0
1
2
1
1
0
2
1
1
0
2
1
2
2
2
1
0
3
1
0
0
0
1
1
2
0
1
1
2
1
2
2
2
2
0
1
1
0
1
1
1
1
1
1
0
1
1
1
1
0
1
1
2
2
1
2
1
1
2
1
1
2
1
1
1
2
1
2
2
1
1
1
2
0
1
1
1
1
0
0
1
1
0
1
1
1
0
2
1
2
1
0
1
0
1
1
1
1
1
1
1
0
1
1
1
0
1
0
1
1
1
2
1
0
2
2
2
0
1
1
2
1
1
0
1
1
2
1
0
0
1
1
0
1
1
1
1
2
1
0
1
1
1
1
1
2
0
2
1
2
0
1
2
1
1
1
1
1
0
1
1
1
2
1
0
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
1
1
0
1
0
2
1
0
1
1
0
0
1
0
0
1
2
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
0
1
2
1
1
0
2
1
1
1
1
0
0
1
0
2
1
1
0
1
2
0
1
1
0
2
1
2
1
1
1
2
1
0
2
1
1
2
0
1
1
0
1
1
1
2
1
1
2
1
0
0
0
1
1
1
2
2
1
1
1
1
0
1
1
1
0
2
1
1
1
2
2
1
0
2
1
1
0
1
2
2
0
2
1
2
2
0
1
1
1
2
0
0
1
1
2
1
2
2
1
2
1
1
1
2
2
1
0
1
0
0
1
1
1
0
1
0
1
1
1
0
1
1
0
1
2
2
1
1
1
0
2
1
2
0
0
0
1
1
1
1
2
1
0
1
1
1
1
1
3
0
1
0
1
1
1
1
1
1
0
0
1
0
2
1
2
1
0
0
2
2
0
1
1
2
0
1
0
1
2
1
2
2
2
1
1
1
0
1
1
1
0
1
1
2
2
1
0
2
0
1
1
2
2
1
1
2
1
0
1
1
0
0
1
1
1
2
1
2
3
0
1
2
2
2
0
1
1
1
0
1
1
2
1
2
1
1
0
0
1
2
2
2
0
2
1
2
1
2
2
0
2
1
0
2
2
2
1
0
0
1
2
1
1
1
0
1
1
2
2
1
1
1
0
0
2
1
1
1
2
2
1
1
0
1
2
1
2
0
2
0
1
1
2
1
1
1
1
1
2
1
0
1
1
2
3
2
2
1
2
0
1
2
4
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
2
1
2
1
1
1
1
0
2
0
1
1
1
1
0
1
1
2
1
1
2
2
1
1
1
2
1
1
2
1
1
0
1
2
0
2
0
2
2
1
1
1
0
2
0
1
0
1
1
1
1
2
0
1
1
1
1
2
1
0
1
2
1
1
1
1
1
0
1
1
2
2
0
1
1
1
1
1
0
1
1
1
1
1
0
1
0
2
1
2
0
1
1
1
2
0
1
1
0
1
2
1
1
1
0
1
1
2
0
1
0
2
1
2
0
0
1
2
1
2
1
1
2
1
0
1
0
1
1
2
1
1
1
3
1
1
1
1
3
1
1
1
1
0
1
2
1
0
1
2
1
1
0
1
1
1
1
1
1
0
1
1
1
1
1
0
1
1
2
0
1
2
1
1
1
1
1
1
1
0
1
1
0
1
1
1
1
1
1
0
1
2
1
0
2
1
1
1
0
1
1
1
1
1
1
1
2
1
2
1
1
2
2
0
1
2
1
1
1
3
2
1
1
1
2
2
0
1
1
1
1
1
0
0
0
1
1
1
1
1
2
2
1
0
0
1
1
1
1
1
1
0
2
1
1
0
1
2
1
1
1
1
1
0
1
1
2
1
1
0
1
1
0
2
1
0
1
0
1
1
1
1
2
1
0
3
2
0
0
2
1
0
1
1
1
1
1
1
1
1
0
1
0
3
1
1
0
0
2
1
2
0
2
1
1
1
1
1
1
0
1
1
0
2
2
1
1
1
1
1
2
1
1
2
1
2
0
0
1
1
1
1
1
1
2
0
0
3
0
1
2
1
0
0
0
1
1
0
1
1
2
1
0
1
1
1
2
2
0
2
1
1
0
1
1
0
0
2
1
0
0
1
1
1
2
2
0
1
1
2
0
2
2
2
1
1
0
1
2
1
1
0
1
0
1
0
0
1
2
0
0
0
2
1
2
1
1
2
1
1
1
1
1
1
0
1
1
1
1
2
2
1
1
1
0
0
1
2
1
1
2
0
0
1
0
2
1
1
1
1
1
1
0
1
2
1
1
1
1
2
1
1
1
1
2
1
2
1
1
1
1
0
1
0
1
1
2
0
2
2
1
2
2
1
1
1
1
0
0
1
2
1
2
1
1
1
2
1
1
1
2
1
0
1
0
1
1
1
1
2
1
1
2
8
1
1
0
1
1
0
2
2
2
4
0
1
1
1
1
1
1
0
3
1
0
1
1
1
1
1
1
2
1
2
1
2
2
1
1
0
0
2
1
0
0
1
2
0
0
0
2
1
2
1
2
1
1
1
1
1
0
0
1
1
1
2
0
1
1
1
1
1
1
1
1
1
0
1
1
0
1
1
1
2
1
1
0
2
1
0
0
1
1
1
2
1
0
2
0
0
2
1
0
1
2
1
1
1
1
2
1
1
2
2
0
1
1
3
1
0
1
1
1
2
1
2
0
1
1
1
1
0
1
0
1
1
1
0
0
1
1
0
1
0
1
1
1
1
1
2
1
0
1
2
1
1
0
0
2
4
0
1
3
1
1
2
1
1
1
1
0
0
1
0
1
1
0
1
1
2
1
2
2
2
0
1
1
0
2
1
1
2
1
1
0
0
1
1
1
0
0
0
0
0
1
1
1
0
1
2
1
2
1
2
1
2
2
2
1
3
0
1
1
0
1
1
2
1
1
0
2
1
1
1
2
1
1
0
1
1
1
0
1
1
0
2
2
2
2
1
1
1
1
2
1
1
2
2
0
0
2
1
1
1
1
0
1
0
1
1
0
1
0
0
1
1
1
0
1
1
1
3
1
1
1
2
1
1
1
0
2
1
2
1
1
1
0
2
2
1
0
0
1
1
1
0
0
1
1
0
0
1
1
2
2
1
1
1
2
1
0
1
2
2
1
1
1
1
1
1
1
1
0
0
2
0
1
1
0
1
1
1
2
0
2
1
1
1
2
1
1
1
0
1
0
0
1
1
1
1
1
2
1
1
1
2
0
0
2
2
2
2
1
2
0
2
0
0
0
2
2
1
0
1
2
2
1
0
2
1
2
1
0
2
2
0
1
1
1
1
0
1
1
1
3
0
1
0
1
1
0
2
0
1
0
2
2
1
1
1
0
1
2
0
1
1
1
2
2
3
0
1
1
2
1
1
1
0
1
1
2
0
1
1
1
0
1
1
0
2
1
0
1
0
1
1
0
1
2
1
1
0
1
1
1
2
2
0
1
0
2
0
2
2
2
1
1
1
1
0
2
2
0
1
1
1
1
1
2
0
1
2
1
0
2
2
1
2
1
0
2
0
2
1
1
2
0
1
2
1
2
0
1
0
1
2
1
1
1
2
1
2
2
1
1
0
1
0
0
2
2
2
1
2
2
0
0
1
1
0
1
1
1
0
1
1
2
0
1
1
1
1
1
0
1
1
1
0
1
2
0
2
1
2
1
1
2
1
0
1
2
0
0
0
1
1
1
0
1
1
3
1
1
1
0
2
2
0
1
1
0
2
2
1
1
0
1
1
0
0
0
1
1
1
2
1
2
1
0
1
1
1
2
1
2
1
1
1
1
1
2
1
0
2
2
2
0
1
0
1
1
1
1
1
1
0
0
2
2
1
1
1
0
0
1
1
0
0
1
1
0
2
1
1
1
1
2
1
0
1
2
1
0
1
0
1
1
2
1
0
0
1
1
1
0
1
0
1
1
2
1
1
2
1
1
2
2
1
1
1
1
1
1
1
1
2
1
1
1
0
0
1
1
2
1
1
0
1
2
1
1
2
1
1
3
2
2
2
2
1
2
1
0
2
1
1
2
1
1
1
2
1
1
1
2
1
2
1
0
1
2
2
1
1
2
1
2
1
1
0
1
1
1
1
0
1
1
0
0
1
2
1
1
1
2
1
0
1
1
1
1
1
0
1
1
1
1
0
0
1
2
3
2
1
0
1
2
1
0
1
2
3
0
1
2
1
0
2
2
0
1
1
1
2
1
1
1
3
0
1
1
0
1
1
1
1
0
0
0
1
0
2
1
1
1
2
1
1
2
1
1
1
1
2
1
1
0
1
1
0
1
1
1
2
2
0
0
1
2
1
2
1
0
2
1
0
1
3
1
2
1
2
2
1
2
1
1
2
0
1
1
2
1
1
1
1
0
1
0
2
1
2
1
2
2
2
1
1
0
2
2
0
2
1
0
1
1
1
1
2
1
1
1
1
1
2
2
1
1
2
2
1
0
1
2
1
2
1
0
2
1
2
2
1
0
1
0
2
0
2
1
1
1
0
1
2
1
0
1
1
1
2
1
1
1
1
2
0
0
1
2
1
0
1
1
1
0
0
1
1
0
1
2
1
2
0
0
0
0
1
0
1
2
0
0
1
1
0
1
1
1
0
1
2
2
1
0
1
1
2
1
1
2
1
2
0
1
0
2
1
0
2
1
1
1
1
0
2
2
2
1
1
1
1
2
1
1
1
1
2
2
1
2
2
1
1
1
2
1
2
1
1
1
1
2
2
1
1
1
0
2
4
0
1
0
2
1
0
1
1
1
1
2
1
0
2
2
1
2
1
1
0
0
1
1
1
1
0
1
1
2
1
0
2
1
2
2
1
1
0
1
1
1
2
1
2
1
0
2
1
0
0
1
4
1
1
1
0
2
2
2
2
2
0
1
2
1
1
1
1
1
2
2
2
0
1
1
1
2
2
1
2
1
0
1
1
2
1
2
0
1
1
1
2
0
2
1
1
0
2
1
2
1
1
1
1
1
2
2
1
1
1
1
1
0
2
1
0
0
1
0
1
1
1
1
0
2
1
2
1
2
1
1
4
1
2
1
0
1
0
1
2
1
2
1
1
0
1
1
1
0
1
1
1
1
0
1
0
1
0
1
1
0
1
1
0
2
1
0
1
0
1
0
0
2
1
2
1
1
1
1
0
2
1
1
1
1
2
2
1
0
1
0
1
1
1
0
1
1
1
1
1
2
0
1
2
1
2
2
1
0
1
1
0
1
0
1
1
2
0
1
0
1
2
2
1
1
0
1
1
1
1
1
2
1
2
2
1
2
1
1
2
0
2
1
1
1
1
1
0
1
0
1
1
0
1
0
1
0
1
0
2
2
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
0
0
1
1
1
2
2
1
0
2
1
1
1
1
1
1
1
1
2
2
1
1
1
0
0
1
0
1
0
2
2
1
3
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
0
0
1
1
1
1
0
1
0
1
1
0
1
0
1
1
1
1
1
2
2
1
1
1
2
1
1
1
0
1
1
0
2
1
1
0
1
0
1
0
0
1
1
1
0
1
1
1
0
2
1
1
1
2
0
2
2
2
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
1
0
2
1
1
0
1
1
2
1
1
0
1
2
0
1
4
1
1
1
1
0
1
1
2
1
0
3
2
0
2
0
1
2
2
2
0
1
1
2
1
0
0
2
1
2
1
1
0
1
1
0
1
2
1
1
2
2
1
1
2
1
2
1
2
1
2
0
0
0
1
1
1
2
2
2
1
1
0
1
0
1
1
1
1
0
1
1
2
1
0
2
1
1
1
0
0
1
1
2
1
2
6
1
0
0
1
1
2
1
0
1
2
1
0
1
1
1
3
1
1
0
1
1
0
1
1
0
0
1
1
1
1
1
1
0
0
1
2
1
0
1
0
1
2
1
1
2
1
1
0
1
1
2
2
1
0
1
1
2
1
1
1
1
1
1
0
2
1
1
0
1
1
2
1
1
0
1
1
2
1
1
1
1
1
1
1
2
1
1
2
0
2
2
2
1
1
1
2
0
3
1
1
1
0
0
0
1
1
1
1
0
1
1
0
1
1
1
2
1
1
1
2
2
1
2
2
2
0
1
0
0
1
1
1
2
0
0
1
1
1
2
0
1
2
1
2
1
1
1
1
2
2
2
2
0
2
2
0
1
1
1
2
1
0
1
2
0
1
1
0
2
0
1
1
1
0
1
0
2
2
1
1
1
0
1
0
1
1
1
0
1
2
2
2
1
0
2
1
0
0
1
0
1
2
1
1
1
1
2
1
2
1
1
1
1
2
1
0
2
1
0
1
1
1
1
1
2
0
1
2
1
0
1
1
3
1
1
0
1
1
2
0
2
1
1
0
1
1
1
1
2
0
2
1
1
1
1
2
1
1
1
1
2
0
2
2
2
2
1
1
1
1
0
1
1
1
1
2
1
1
1
0
1
0
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
2
1
2
1
1
1
2
1
0
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
2
0
0
1
0
1
5
1
1
0
1
1
1
1
2
2
1
0
0
3
1
2
1
1
1
0
1
0
1
1
2
1
1
2
0
1
1
1
1
2
1
1
1
1
1
0
1
1
0
1
0
0
1
0
0
3
1
2
1
1
2
1
2
1
2
2
1
2
0
1
1
1
2
1
1
2
1
1
1
2
0
0
1
1
1
1
0
1
1
2
2
2
2
1
1
0
1
1
1
0
1
1
1
1
0
1
1
1
1
0
2
2
0
1
2
1
1
1
1
2
1
1
2
0
0
2
1
1
2
1
2
2
1
0
1
0
1
1
2
3
1
0
1
1
2
1
2
0
2
1
1
1
0
2
2
1
1
1
2
2
0
1
1
0
0
0
1
1
2
2
1
2
1
1
2
0
2
1
1
1
0
1
1
2
0
1
0
1
1
2
1
2
1
1
1
1
1
1
2
1
0
1
1
0
1
1
2
0
1
1
1
1
1
1
2
2
1
0
1
1
2
1
0
3
0
1
0
0
1
1
1
1
2
2
1
0
0
1
1
1
2
0
1
1
1
1
2
2
1
1
2
1
1
1
2
1
0
2
2
0
0
1
2
1
1
0
1
0
1
1
0
2
1
2
2
1
2
1
1
1
1
0
0
1
0
0
2
2
1
1
2
1
1
1
1
1
0
1
1
1
1
1
2
1
0
1
1
1
1
1
2
0
1
2
0
0
1
1
1
2
1
2
0
2
1
1
2
2
2
1
2
0
1
0
2
2
1
1
1
1
1
2
1
1
2
1
1
1
0
0
0
2
1
1
2
2
1
1
2
2
1
1
1
1
1
0
2
1
1
1
0
0
1
0
1
1
1
0
0
1
1
2
1
1
0
0
2
0
0
1
0
0
2
2
2
3
1
1
1
2
1
1
1
1
1
1
1
2
0
0
2
1
1
0
1
1
1
2
0
1
0
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
0
1
1
0
0
0
1
2
1
2
1
2
1
0
2
1
2
2
1
1
0
0
1
1
1
1
0
1
1
2
1
0
1
0
0
0
0
1
2
1
1
2
0
1
2
2
0
2
0
2
2
1
1
1
1
2
1
1
1
0
1
1
1
1
1
1
2
0
0
1
0
1
2
1
0
0
1
2
0
2
1
2
1
1
1
0
1
1
2
0
0
2
1
1
1
1
2
2
1
1
2
0
0
1
1
2
1
0
1
0
2
2
2
1
0
0
2
0
1
1
1
1
1
0
1
1
1
0
2
2
1
1
1
2
0
0
2
2
0
0
1
1
1
2
0
1
1
1
2
0
1
1
0
2
1
1
2
0
1
1
1
1
1
1
1
2
1
1
0
1
0
1
0
0
0
1
2
0
2
1
1
1
2
1
2
2
0
1
1
0
1
2
1
1
0
1
1
1
1
1
1
2
1
4
0
2
1
0
2
2
1
1
1
2
2
1
2
1
1
1
1
2
1
0
0
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
0
1
1
1
2
1
2
2
1
0
2
1
1
2
0
1
0
2
1
1
2
2
1
1
0
2
1
1
0
1
1
1
0
2
1
1
1
2
1
1
1
1
2
2
1
1
1
1
1
1
0
0
0
0
1
2
0
1
0
0
1
1
1
2
3
0
2
1
0
2
2
0
2
0
1
0
2
1
1
2
0
3
1
1
2
0
1
2
1
1
1
2
1
1
1
1
1
0
2
1
0
1
1
1
1
1
1
2
1
1
1
0
1
0
2
1
1
1
1
2
0
1
1
1
1
1
1
2
0
1
1
1
0
1
1
0
1
0
1
0
1
0
2
1
2
0
0
0
1
1
1
1
2
1
1
1
1
1
2
2
0
0
1
1
1
1
0
2
0
1
2
1
1
0
0
0
0
1
0
1
2
0
2
1
1
1
1
1
0
2
2
0
2
2
0
1
1
1
0
1
1
1
2
0
0
0
0
1
1
0
2
2
1
1
0
1
1
0
1
2
1
2
1
1
2
1
1
1
1
1
1
0
1
1
1
0
1
1
1
1
0
1
2
1
0
1
0
0
0
1
1
1
0
0
1
1
1
1
0
2
2
1
1
1
1
2
2
0
2
3
1
0
1
2
1
1
1
1
2
2
2
1
0
1
2
2
0
1
1
1
1
1
1
1
1
2
1
0
1
2
1
0
1
1
1
0
2
1
2
0
1
2
1
1
1
1
1
1
0
0
1
0
1
1
1
1
3
0
1
1
1
1
1
1
2
2
2
1
0
1
2
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
2
1
2
0
1
1
0
0
1
1
1
1
1
2
1
1
1
1
1
2
0
2
2
1
1
2
1
1
0
1
1
0
1
1
1
1
2
1
0
0
2
2
2
0
0
1
1
3
1
1
2
1
0
1
0
1
0
2
2
0
1
0
2
1
2
1
2
1
1
1
1
1
0
2
1
0
2
1
1
1
2
1
2
1
1
1
1
0
1
0
0
2
1
1
1
1
1
2
1
0
2
0
1
1
1
1
4
1
1
1
0
1
2
1
1
2
2
1
1
1
2
2
1
1
2
1
1
1
0
0
0
0
1
1
2
1
1
1
1
2
1
0
1
0
2
2
2
2
1
2
0
0
0
1
2
1
1
2
0
1
1
2
2
2
2
0
1
2
0
1
1
2
2
1
1
1
2
2
1
1
0
2
1
1
1
2
1
1
1
1
0
0
0
1
1
3
1
1
1
0
1
1
1
1
2
2
1
1
1
1
1
1
1
1
2
0
1
1
2
0
0
1
0
2
6
2
2
1
1
0
1
0
1
1
0
1
1
1
1
1
1
2
3
2
1
2
1
1
2
1
1
2
1
1
2
1
2
1
2
1
1
1
2
1
1
0
0
0
2
3
1
2
2
1
2
1
2
1
1
1
0
2
1
1
1
1
1
2
2
0
1
1
0
1
1
1
2
2
1
0
2
1
0
3
0
1
1
1
2
1
1
0
2
1
0
2
2
0
0
0
1
1
0
2
1
1
1
2
1
0
1
1
1
1
1
3
1
0
2
1
2
1
1
1
1
0
1
1
1
1
1
0
1
1
1
1
1
2
1
2
1
1
0
0
1
1
1
1
1
1
1
1
2
2
1
1
1
0
2
2
1
1
2
2
1
2
1
1
0
0
3
1
2
1
1
1
1
1
2
2
1
2
1
0
1
1
0
2
0
0
1
0
1
0
0
0
3
1
1
1
1
1
2
2
2
1
1
1
1
0
1
1
2
1
1
0
1
0
1
1
2
0
1
1
2
0
1
1
1
1
0
1
3
1
1
1
1
1
0
0
1
1
2
1
2
1
1
1
0
1
1
2
0
1
0
2
2
0
1
2
0
2
1
2
0
0
0
1
2
1
1
1
0
1
1
0
3
2
2
0
1
1
0
0
1
2
0
1
2
0
1
0
2
1
0
0
0
1
1
0
1
0
2
0
2
1
1
1
1
2
1
1
1
0
1
1
0
1
1
1
1
0
1
1
1
0
1
2
0
1
2
1
1
1
0
2
1
0
1
0
0
0
0
2
1
1
1
1
1
1
1
1
1
1
0
0
0
1
2
1
2
1
0
1
0
1
0
1
1
1
1
1
1
1
2
1
0
1
1
0
1
2
2
1
0
1
1
1
2
1
1
1
1
2
1
1
1
1
0
1
2
2
2
0
2
1
2
1
0
0
1
1
2
1
0
1
1
2
2
2
1
0
1
1
1
2
0
1
1
1
2
1
0
0
1
0
1
0
1
0
0
1
0
1
0
1
1
2
2
2
1
1
1
1
2
2
1
1
0
1
1
1
0
2
1
2
2
0
1
1
1
0
2
0
1
0
2
0
0
2
1
1
1
0
0
2
0
1
1
0
1
1
0
0
0
1
0
1
1
0
1
0
1
0
1
2
1
0
1
2
0
1
1
2
1
1
2
1
1
2
1
2
1
2
1
1
1
1
1
1
2
1
0
1
2
2
2
1
1
1
2
1
1
1
0
1
1
1
1
2
1
1
1
1
1
1
1
1
2
2
1
1
0
0
1
1
1
0
1
1
1
0
2
1
0
2
0
1
1
1
0
1
0
1
1
0
2
1
1
1
1
1
0
0
1
0
1
2
0
1
2
0
2
1
1
2
2
1
0
1
1
2
1
1
1
1
1
0
1
2
1
1
2
1
1
2
2
0
1
0
1
1
1
2
2
0
0
1
1
1
1
2
0
1
0
1
1
1
0
1
2
1
1
2
2
1
2
0
1
1
0
1
0
0
2
2
1
0
0
1
0
2
2
0
2
0
1
1
1
1
1
2
0
1
1
1
2
1
1
0
2
2
2
2
1
2
2
1
1
2
2
2
1
1
1
1
2
1
1
0
0
1
2
0
1
1
1
1
1
1
1
1
1
3
1
1
1
1
1
1
0
1
0
1
0
0
0
2
2
1
0
1
1
1
2
0
1
0
1
2
1
1
1
2
1
2
1
1
1
1
2
1
2
2
2
1
0
1
1
1
1
1
1
2
1
0
1
2
1
2
2
0
1
1
1
1
2
1
1
0
2
1
1
2
2
1
1
0
0
1
2
2
1
2
1
2
1
0
1
1
0
1
2
0
2
0
1
1
1
0
1
1
1
0
2
1
1
0
1
1
1
1
1
1
2
3
2
0
1
2
0
1
1
1
1
1
2
2
2
1
2
1
1
1
2
1
2
0
1
1
0
0
1
1
0
2
2
1
1
1
0
1
0
0
1
0
1
0
1
0
0
1
1
1
1
1
1
1
0
1
1
1
1
0
0
1
1
0
0
2
0
0
1
0
2
1
1
0
1
1
1
2
2
2
1
2
0
1
1
2
1
0
1
2
1
1
2
2
1
0
0
1
1
1
0
1
1
2
2
1
1
1
2
2
1
2
1
2
1
1
2
1
1
1
2
2
2
2
0
1
0
2
2
1
0
2
1
1
1
1
1
2
1
2
1
1
1
0
3
0
2
0
2
3
1
1
2
1
1
1
2
1
1
1
2
2
1
1
1
2
2
1
1
1
0
1
0
1
1
2
1
2
3
1
1
1
2
2
1
1
0
1
1
1
2
1
1
1
1
2
1
1
2
1
0
2
1
0
1
2
2
2
1
1
1
0
1
1
1
2
1
2
1
0
1
1
1
1
1
2
1
2
2
2
1
1
0
1
1
1
1
2
0
1
2
1
1
1
1
0
0
1
1
1
0
1
2
1
2
1
1
1
2
0
1
2
1
1
1
2
1
1
0
0
0
2
0
0
2
1
1
1
2
0
1
1
1
1
1
1
0
1
2
2
1
1
1
1
1
2
2
2
0
1
2
0
0
1
2
1
1
0
1
1
1
1
0
1
1
1
1
1
2
0
1
0
1
1
2
1
1
1
2
1
1
2
2
0
1
0
1
1
2
0
1
0
1
2
0
0
1
1
1
0
1
2
1
1
2
1
1
2
0
0
0
1
1
0
1
1
2
2
1
1
1
0
0
2
1
1
1
3
2
1
2
1
0
1
1
2
2
2
1
1
0
2
2
1
1
1
1
2
1
1
1
2
2
2
0
0
2
1
0
1
0
1
1
2
1
1
1
1
0
1
1
1
1
0
2
0
2
1
1
1
1
0
2
1
0
1
1
2
1
1
1
0
1
2
2
1
1
0
1
0
1
1
1
1
0
0
1
1
1
1
3
1
1
1
2
1
1
2
1
1
1
2
0
0
2
1
0
1
1
0
1
1
1
2
2
1
1
1
0
2
1
0
1
0
1
1
0
1
2
1
1
2
0
1
2
1
2
1
0
1
1
1
2
1
1
0
1
1
1
2
0
1
1
1
1
3
1
1
1
1
1
1
1
2
1
0
2
1
1
2
1
1
0
0
1
1
1
1
1
1
0
2
1
1
2
1
2
1
2
1
1
1
0
1
0
2
2
2
1
0
1
1
2
0
1
0
1
0
0
0
1
1
3
0
1
0
2
1
1
1
1
1
1
0
1
0
2
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
2
1
2
1
0
1
2
2
1
1
0
2
1
1
1
2
1
0
1
1
1
1
2
1
2
1
1
0
2
1
1
2
1
1
2
2
1
2
2
1
2
1
0
1
0
1
1
1
1
0
1
1
0
1
1
2
1
2
3
1
1
1
1
1
0
1
1
1
1
0
1
2
1
2
1
1
2
1
0
2
2
1
1
0
1
1
0
1
1
0
2
1
2
1
1
0
0
1
1
1
0
2
2
0
1
2
0
1
0
1
0
1
1
1
1
1
2
0
1
0
1
0
0
0
1
1
0
0
0
1
1
1
1
2
0
1
1
2
1
1
1
1
0
0
0
1
0
1
1
1
1
1
1
2
0
2
1
1
2
2
1
2
0
3
1
2
1
2
1
2
1
0
2
1
2
0
0
0
0
1
0
1
1
2
0
1
0
1
0
1
0
1
1
2
1
2
1
3
1
1
1
2
1
1
1
0
0
2
1
2
1
0
2
4
2
2
1
2
0
2
1
1
0
2
2
2
0
2
1
1
1
1
2
1
3
0
1
0
1
1
2
1
1
1
0
1
1
2
1
1
1
0
1
1
1
1
2
1
0
0
1
2
1
1
0
1
1
1
1
1
0
0
1
2
1
1
1
0
0
2
1
1
0
1
1
0
0
1
1
1
1
1
0
1
0
2
0
1
1
0
0
1
1
1
1
1
0
2
1
1
1
1
1
1
1
0
2
1
0
1
0
1
2
1
1
1
1
0
1
2
0
0
1
1
1
1
2
1
1
1
1
2
1
0
0
1
1
1
0
0
1
2
2
1
1
1
1
1
2
0
1
1
1
1
1
1
1
1
0
2
2
0
1
0
1
0
1
2
2
2
1
2
1
0
2
1
1
2
1
0
1
0
1
1
1
1
1
1
2
1
2
2
2
1
2
2
1
2
2
2
2
1
2
0
1
1
1
0
2
0
1
1
1
1
0
1
1
1
0
1
1
2
1
0
1
1
1
1
1
0
2
1
1
1
1
2
1
2
1
2
2
1
2
1
1
2
1
1
0
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
0
0
0
0
0
2
0
1
2
0
1
2
1
1
1
1
1
2
1
2
1
1
1
2
1
0
2
2
1
2
0
1
1
1
1
0
0
1
2
1
2
0
0
0
2
2
1
1
0
0
3
2
2
2
2
0
1
0
1
1
2
1
1
0
1
0
2
0
0
2
2
1
1
1
0
1
2
1
0
0
1
1
0
2
2
0
1
0
1
2
1
2
1
1
1
0
1
1
0
1
2
1
1
0
3
3
2
2
0
1
2
1
1
1
1
1
0
1
1
0
1
1
0
1
1
1
2
1
1
1
0
2
1
2
1
0
1
1
0
1
0
4
2
1
1
1
1
2
1
2
0
1
0
2
1
2
1
1
2
1
1
2
2
1
1
2
2
2
2
1
0
2
1
1
1
2
1
2
2
1
1
1
0
0
2
2
1
0
1
1
1
1
1
2
1
1
1
1
1
1
2
1
2
2
1
2
0
1
0
1
2
1
1
0
2
1
1
0
2
2
1
2
2
0
0
1
1
1
0
1
2
0
0
0
2
0
2
1
1
1
1
0
0
0
0
1
1
0
1
1
1
1
1
1
0
0
0
1
1
0
0
2
1
1
0
0
1
1
1
1
1
0
1
1
2
1
1
1
0
2
2
1
0
0
1
1
2
3
2
1
0
0
1
0
1
0
1
2
2
1
1
0
1
1
1
1
1
0
0
0
1
1
0
1
2
0
2
0
1
1
2
1
0
1
1
1
2
1
1
0
1
1
1
0
1
1
2
1
1
1
0
1
0
1
0
1
0
0
0
1
2
1
1
0
0
0
1
1
1
1
1
1
0
1
1
2
1
1
1
1
1
0
1
2
1
1
1
1
1
2
2
1
2
1
0
0
1
1
2
1
2
0
1
2
0
0
0
1
2
1
0
0
0
0
1
2
0
1
1
1
1
1
1
0
2
1
0
0
1
1
1
0
1
2
0
0
0
1
1
1
2
6
1
0
0
1
0
0
1
2
0
1
0
1
1
1
2
1
2
1
1
1
2
0
3
0
0
0
1
1
1
1
1
1
0
1
2
0
0
2
2
1
2
2
1
0
1
1
1
2
2
1
0
1
2
1
2
1
0
1
2
1
1
1
1
1
1
1
1
2
1
1
2
2
1
1
0
0
1
1
2
1
1
2
2
2
2
1
1
1
0
1
1
1
2
3
1
0
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
2
1
1
1
2
2
2
1
0
2
1
0
1
0
1
0
1
0
0
1
1
1
0
2
2
1
0
2
1
1
1
1
1
2
3
1
4
2
0
1
1
0
2
1
2
0
2
1
2
2
1
2
1
1
2
1
1
1
2
2
1
0
2
0
1
1
1
2
1
2
1
2
1
0
1
2
2
1
0
1
2
1
2
1
1
0
1
2
1
3
1
0
2
3
0
1
1
1
1
2
1
2
1
2
1
1
1
1
2
1
1
0
2
1
1
1
1
0
2
0
1
1
0
0
4
2
1
1
2
1
0
1
3
1
0
1
2
2
1
1
1
1
1
1
1
2
1
1
0
0
1
2
0
0
1
0
1
1
1
2
1
1
1
0
2
0
1
1
2
0
2
1
1
1
1
0
1
1
1
2
1
0
1
1
2
1
1
1
0
1
1
1
1
1
1
0
1
1
1
1
2
0
2
2
1
0
0
2
1
1
1
1
1
0
3
2
2
1
1
3
1
1
1
2
1
1
0
0
1
1
1
1
0
1
1
2
1
1
2
0
1
0
2
2
0
2
1
0
0
1
0
0
1
1
1
2
2
0
2
1
0
1
1
1
1
1
1
1
1
2
1
1
0
1
1
0
1
1
1
1
2
1
0
0
0
3
2
0
1
0
1
1
1
1
1
2
2
1
0
1
1
1
1
1
0
1
1
2
2
2
1
1
1
2
0
0
1
0
1
2
1
1
1
1
2
1
1
0
1
1
2
2
1
2
1
1
0
1
0
1
2
1
1
1
2
1
1
0
2
2
1
1
0
1
1
2
2
2
0
2
1
2
1
0
1
1
0
1
1
1
1
1
0
2
1
1
1
1
0
1
2
1
1
1
2
1
2
2
1
0
1
1
0
1
1
0
0
2
1
1
2
1
1
2
0
1
2
0
0
1
1
2
1
0
1
1
0
2
0
2
2
2
2
1
1
1
2
0
7
3
1
0
1
1
1
1
0
2
1
1
2
1
1
1
1
2
1
0
0
1
1
2
1
1
0
1
0
1
0
1
1
1
1
2
1
0
1
1
1
1
2
2
1
1
1
0
2
1
1
1
1
1
1
1
0
1
2
2
2
1
1
1
0
2
1
0
1
0
0
0
1
1
0
2
2
2
1
1
0
2
1
2
1
1
0
2
1
1
2
1
1
1
1
1
1
2
1
1
0
1
1
0
0
2
1
1
0
1
2
1
2
1
0
1
1
0
1
1
2
0
1
1
1
0
1
0
1
0
0
1
1
0
1
1
2
1
1
0
2
2
0
1
0
0
1
1
1
0
2
1
1
2
1
0
1
0
1
1
2
1
2
0
1
1
0
1
1
0
2
1
1
1
1
0
0
1
1
1
1
1
0
0
1
0
1
1
2
1
1
0
0
1
0
1
2
1
2
1
0
0
1
2
1
2
2
0
1
2
2
1
0
1
1
2
1
1
0
2
1
2
3
1
2
0
2
2
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
2
1
2
2
0
1
1
2
1
1
1
1
1
1
1
0
1
0
1
1
0
3
0
1
1
1
1
1
0
1
1
1
1
0
1
2
1
2
1
1
2
1
1
2
1
0
1
2
0
1
1
0
0
1
0
2
1
1
1
2
1
0
1
1
0
0
2
2
1
1
0
1
0
0
0
1
2
2
0
0
2
1
0
0
1
0
1
1
1
2
0
2
1
2
1
2
1
1
1
0
1
1
1
1
2
1
1
2
1
2
1
2
1
1
1
1
1
1
0
1
1
0
1
1
1
1
1
1
1
2
1
1
1
1
0
1
0
1
2
1
2
0
1
1
2
1
1
1
2
2
1
1
2
2
1
1
1
1
0
1
1
1
2
0
2
2
2
1
0
1
0
2
2
1
2
1
1
1
0
2
1
1
1
0
1
1
1
0
1
1
1
0
2
1
1
0
1
1
0
2
2
0
1
1
1
2
1
1
1
1
0
1
0
1
1
1
1
1
2
1
2
1
1
1
2
2
1
1
0
1
1
1
2
1
2
1
0
2
0
1
1
1
1
1
1
1
1
1
2
1
2
0
1
1
0
0
0
2
0
1
0
2
1
2
1
2
2
1
2
1
1
1
2
1
0
0
1
0
1
1
2
0
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
2
4
1
1
0
1
1
1
1
2
1
1
1
1
0
1
1
1
0
1
1
1
0
0
0
1
2
0
1
0
1
1
0
1
0
1
0
0
2
1
0
2
2
0
1
1
1
0
0
0
0
2
1
0
1
1
1
2
0
1
1
0
0
0
2
1
1
1
1
1
1
1
2
2
0
1
1
2
0
0
2
0
1
0
1
0
2
1
1
1
1
0
0
1
1
0
1
0
2
1
1
0
1
1
2
2
2
1
0
1
2
1
1
1
1
1
2
1
1
1
1
0
2
1
1
0
2
0
1
2
2
0
1
1
1
1
0
0
0
2
1
1
0
1
1
2
0
1
1
1
4
0
1
0
1
0
0
1
1
0
0
0
1
1
0
1
1
1
1
2
1
1
2
1
1
1
0
1
2
1
1
1
1
1
1
2
1
1
1
2
2
1
0
1
1
1
0
1
1
1
2
2
2
2
1
0
0
1
0
2
2
2
1
1
0
1
1
2
1
0
0
1
1
2
2
1
2
1
1
1
1
0
1
1
3
1
1
1
1
1
2
1
1
0
1
0
0
0
1
0
1
2
0
1
1
1
2
2
2
1
1
2
0
1
1
2
0
1
0
2
1
1
1
1
2
0
2
1
0
0
1
2
1
1
1
1
1
1
1
1
0
1
0
2
1
1
0
1
0
4
1
1
1
2
1
1
1
2
0
1
0
1
1
0
0
1
2
1
2
1
1
1
2
1
1
0
0
1
1
2
0
1
2
1
1
0
2
2
1
1
2
0
1
0
1
2
1
2
0
2
1
1
1
1
1
0
0
1
2
1
1
2
2
0
1
1
2
1
1
1
1
1
1
2
0
1
1
1
1
2
0
1
0
0
0
2
1
2
1
1
2
1
1
1
1
2
1
2
1
0
1
2
2
1
1
1
0
1
2
1
1
2
2
1
1
0
2
1
1
1
0
1
1
1
1
1
2
1
2
2
0
1
2
2
2
4
0
1
1
1
1
1
2
2
2
1
1
0
0
1
1
2
1
1
1
2
0
1
2
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
0
2
0
2
1
0
2
1
1
0
1
1
1
1
2
1
1
0
0
1
1
1
0
0
1
0
2
0
0
0
0
1
0
1
1
1
2
0
0
0
0
1
1
0
1
1
1
2
1
1
1
2
1
2
2
2
2
1
1
1
1
1
1
2
1
1
1
1
0
1
0
1
1
1
1
2
1
2
2
2
0
1
2
1
2
1
2
1
1
0
0
1
2
1
2
0
1
1
1
2
1
1
1
1
1
1
0
2
1
2
1
2
1
2
0
1
2
1
3
1
1
0
1
1
1
2
1
2
2
1
1
0
2
1
0
1
1
1
1
0
0
2
1
1
1
0
1
2
0
1
1
1
1
1
0
1
0
0
1
1
0
0
1
0
2
1
1
0
2
0
1
0
1
2
1
0
0
2
1
2
2
1
2
1
0
1
1
2
0
1
1
1
1
0
0
2
2
0
1
0
1
1
1
0
2
1
1
1
0
1
2
1
1
2
2
1
1
1
2
2
2
2
0
0
2
0
0
0
1
2
2
1
1
1
1
0
1
0
1
2
2
0
1
1
2
0
1
0
2
1
1
2
1
0
1
1
1
1
1
2
2
1
1
2
2
1
3
1
1
1
1
1
0
0
1
1
1
1
1
2
0
1
1
1
1
0
1
1
1
2
0
1
1
1
2
0
1
1
1
1
1
2
1
1
1
1
1
0
1
0
0
2
1
1
1
1
0
1
1
1
1
1
2
1
1
1
0
2
1
1
0
2
0
1
1
1
2
0
2
1
0
1
1
1
2
0
0
2
1
3
1
0
0
1
1
1
1
1
1
1
0
1
1
2
1
1
0
2
2
0
2
1
1
1
1
0
0
2
1
2
2
0
0
2
2
1
0
2
1
2
1
0
3
0
1
1
1
2
1
1
1
1
1
1
1
1
2
0
1
1
1
1
2
1
1
1
0
2
2
1
0
1
2
2
1
1
1
1
1
0
1
1
0
1
3
2
0
1
0
1
1
0
2
1
2
1
2
1
2
2
1
1
1
2
1
0
0
1
1
1
1
2
1
1
1
1
1
0
1
1
3
0
2
1
2
2
1
1
1
1
2
1
1
2
1
1
0
0
1
1
0
1
1
1
0
1
2
1
0
1
1
2
1
1
2
2
1
1
1
1
1
1
1
1
2
0
2
1
1
1
2
1
0
2
1
1
1
1
1
1
1
3
1
1
3
0
2
1
1
0
2
0
0
1
2
2
2
2
1
1
2
1
1
1
1
0
2
1
2
1
1
1
0
1
2
1
2
1
1
1
1
0
2
1
2
1
0
1
1
1
0
1
0
1
1
0
2
1
1
0
1
1
1
0
1
1
0
2
1
0
1
0
1
1
2
1
0
1
2
1
0
0
1
1
0
3
2
1
2
0
1
2
0
1
1
0
1
1
1
0
1
1
1
0
0
2
1
2
2
1
1
1
0
1
1
1
0
1
1
1
1
2
1
1
2
0
1
1
1
1
0
2
0
1
1
0
2
1
2
2
1
1
1
0
1
1
1
1
0
1
1
1
1
0
3
1
1
1
1
1
2
1
0
1
2
2
1
0
1
1
0
1
0
1
0
2
1
1
2
1
1
2
1
1
0
1
0
0
3
0
1
0
1
0
0
0
0
1
1
2
1
1
2
2
0
0
0
1
1
1
1
0
1
2
2
0
1
1
2
1
2
2
1
2
1
4
1
1
1
0
1
1
0
1
2
1
0
2
2
2
1
2
2
1
1
0
1
0
0
2
1
1
0
1
2
2
1
2
1
1
2
0
1
1
2
0
0
0
1
1
1
0
2
1
1
1
1
1
1
0
0
0
1
2
1
1
1
1
0
2
1
1
1
2
0
1
1
1
0
0
1
1
0
2
1
1
0
1
2
1
1
2
1
1
1
0
1
1
2
1
1
1
1
2
0
1
1
1
1
1
0
2
0
2
1
0
1
1
1
0
2
1
2
0
0
1
1
0
1
0
1
0
1
2
0
2
3
1
0
2
1
2
1
1
1
2
2
1
1
1
1
1
2
1
1
1
1
0
2
1
2
0
1
4
1
1
1
3
1
1
1
2
0
0
2
1
1
1
0
1
1
1
1
1
1
1
1
2
0
2
2
0
0
1
1
2
0
0
1
2
0
1
1
1
1
1
1
1
1
0
1
0
1
1
1
2
3
3
1
1
1
1
1
1
1
0
1
1
0
1
1
1
1
2
1
2
1
0
1
1
1
1
1
5
1
1
1
2
0
1
1
1
1
1
1
1
1
1
1
0
0
2
0
2
1
1
2
1
0
2
1
1
0
1
2
1
2
1
0
1
2
1
1
2
2
1
1
1
1
0
0
1
2
1
1
1
1
1
0
0
2
1
1
1
1
1
1
0
0
1
0
1
1
1
1
0
2
1
1
1
2
1
1
2
1
1
2
1
0
1
0
1
1
1
2
1
1
1
1
1
1
2
1
2
2
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
0
1
0
2
0
2
2
1
1
1
3
0
0
0
0
2
2
1
1
0
1
1
2
1
0
2
1
1
1
0
1
1
2
1
1
0
1
0
2
0
1
2
1
0
1
1
1
1
0
1
0
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
0
1
2
2
3
0
0
1
1
1
0
2
2
2
1
1
1
2
3
1
1
2
1
0
1
1
0
1
1
0
1
1
2
1
1
0
1
2
0
1
1
1
0
0
1
1
0
1
1
2
1
2
1
2
0
2
1
1
1
2
1
0
0
1
1
1
2
1
1
1
1
1
1
0
0
3
1
1
1
1
1
1
1
0
2
2
2
0
0
2
1
1
1
1
1
1
2
1
1
0
2
1
0
1
0
2
1
1
1
0
1
1
1
1
0
1
0
1
1
2
1
1
0
0
0
1
0
1
1
1
0
2
1
1
1
1
2
0
1
2
2
0
1
1
0
1
0
1
1
1
1
2
1
4
1
1
1
1
2
2
1
2
1
1
0
1
1
2
0
1
2
0
2
2
2
0
1
0
1
2
1
1
1
2
0
1
1
1
2
1
1
1
2
1
0
0
1
0
2
1
1
1
1
0
0
0
1
1
2
1
2
1
2
2
2
0
1
1
1
0
2
1
1
1
2
0
1
0
0
1
0
0
2
1
1
2
0
0
0
3
0
0
2
2
2
2
2
1
2
2
1
2
0
0
1
1
0
3
1
2
1
1
1
1
0
2
2
0
2
2
1
1
2
1
1
2
0
1
2
1
2
0
1
0
0
1
1
1
1
1
2
1
1
0
1
1
2
1
1
0
1
1
2
1
2
0
1
1
2
1
1
0
0
1
2
1
1
1
2
0
2
0
2
1
1
1
1
1
1
0
1
1
0
1
0
1
0
1
1
0
0
1
1
1
1
0
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
0
0
0
0
2
3
1
2
1
0
1
1
1
2
2
1
1
1
1
0
1
1
0
1
1
0
1
1
0
1
1
1
1
0
1
1
0
1
1
1
2
1
1
1
1
0
1
2
1
0
2
1
1
0
1
0
0
1
0
2
1
1
0
1
1
2
1
2
0
2
0
1
1
2
0
2
1
1
1
0
1
1
2
2
2
1
1
2
0
1
1
2
0
1
0
1
1
1
1
1
1
1
2
0
0
1
2
1
1
0
1
1
1
2
1
0
1
2
1
1
1
1
1
0
2
2
1
1
0
2
1
1
1
0
0
1
1
1
2
0
0
2
1
1
1
2
0
2
1
1
2
1
1
1
1
1
1
1
1
0
0
1
1
1
1
0
2
1
2
0
1
2
1
1
1
0
0
1
1
2
1
1
1
2
1
2
0
0
0
1
2
1
1
1
1
0
2
1
2
1
1
1
1
0
1
0
1
1
1
0
1
1
2
1
1
1
2
0
0
1
2
0
1
2
1
0
1
0
2
1
0
2
2
2
0
1
0
1
1
1
1
2
1
0
1
1
2
0
1
2
1
4
1
1
1
1
1
1
2
0
0
1
1
2
1
1
1
1
1
1
0
1
1
1
2
2
1
1
2
2
1
1
1
0
0
1
2
2
0
1
1
1
0
1
1
1
1
2
2
1
0
2
0
0
0
0
0
1
2
2
1
0
1
1
0
1
1
1
1
2
2
0
1
1
0
0
1
0
1
1
1
1
0
1
0
2
1
2
1
2
2
1
1
0
1
0
0
1
0
0
1
0
1
1
1
1
1
2
1
2
2
1
1
2
1
1
1
1
1
0
0
0
0
0
2
2
2
1
0
2
2
2
1
2
2
1
1
2
2
1
2
0
2
1
0
1
1
1
1
1
2
1
1
2
1
1
2
1
1
0
2
1
1
1
1
1
1
1
1
0
0
0
1
1
1
1
1
1
1
0
1
2
1
1
1
0
1
2
1
3
0
0
0
0
2
1
1
2
1
2
1
7
1
1
1
2
1
1
2
0
1
0
1
1
2
2
1
1
1
1
2
0
1
1
1
2
2
2
2
1
2
0
1
1
2
2
0
2
1
1
1
0
0
1
0
2
1
1
1
2
2
2
1
1
1
2
1
0
0
1
2
1
1
1
0
2
1
1
1
2
1
2
1
2
1
1
0
2
1
1
2
1
1
0
1
4
3
2
0
1
1
1
2
1
1
1
1
1
0
0
2
2
1
0
0
1
0
1
2
1
1
0
0
0
1
0
1
1
1
1
1
1
1
2
2
2
1
2
1
0
0
1
1
1
1
0
1
1
2
1
2
0
1
1
1
2
1
1
0
1
2
1
2
0
1
1
0
1
1
3
0
1
2
1
1
1
1
0
2
1
1
1
0
0
1
1
1
1
0
2
1
1
1
1
2
0
1
1
1
2
3
1
1
1
2
2
1
1
1
2
0
1
2
2
1
1
0
2
2
2
1
0
2
2
1
0
1
1
1
0
0
2
1
2
2
2
1
1
1
1
1
0
1
2
2
1
2
0
2
2
1
0
2
1
1
1
1
2
1
2
0
1
1
2
1
1
0
1
1
0
2
2
1
1
1
1
1
0
1
1
1
2
1
1
1
0
2
2
0
0
1
2
0
1
0
2
1
1
1
1
0
0
2
0
1
0
2
1
2
2
0
1
1
5
1
2
1
1
2
0
1
2
3
2
1
1
0
1
1
0
0
2
0
1
1
2
1
3
2
1
2
2
1
0
1
1
1
0
2
1
1
3
0
0
2
2
1
2
1
1
1
1
0
1
1
1
2
1
0
1
0
1
0
1
0
1
2
1
1
1
1
1
1
0
0
1
1
1
0
2
1
1
1
1
0
2
2
1
2
1
3
0
1
2
2
1
0
1
1
1
0
1
0
1
2
1
0
2
1
0
1
1
1
0
1
1
0
1
0
0
0
2
2
1
1
0
1
2
2
1
0
1
0
1
0
1
1
1
1
2
1
1
1
1
1
0
1
1
1
1
1
3
0
2
2
1
0
1
1
1
1
0
1
1
1
1
2
0
0
0
1
0
1
1
1
1
1
3
1
1
1
0
2
1
1
1
1
0
0
1
1
1
2
0
2
1
1
2
0
1
1
0
1
1
1
1
1
1
0
2
0
0
1
1
1
1
0
2
0
1
1
1
0
1
1
1
1
0
1
1
2
0
0
1
1
0
0
1
1
2
2
0
0
1
0
1
1
2
2
1
0
0
1
1
0
1
1
1
1
1
1
1
1
0
1
1
1
1
2
1
1
1
2
2
1
1
2
1
1
1
2
1
1
2
1
1
1
1
0
1
1
0
2
2
1
0
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
2
1
1
1
2
2
1
1
3
1
1
2
1
0
1
1
1
1
1
1
1
2
1
2
0
1
1
1
0
1
1
2
0
1
2
2
1
0
0
1
1
1
1
0
2
2
2
0
1
2
0
1
2
2
2
1
2
1
1
0
0
1
1
2
1
2
1
1
1
0
3
0
1
1
2
1
2
1
1
2
2
1
2
1
1
3
1
1
1
1
1
0
2
2
1
1
1
1
1
2
1
2
1
1
1
1
0
1
1
1
1
1
1
1
1
2
1
1
0
1
1
1
1
0
2
2
2
1
1
1
1
2
1
0
0
2
0
1
2
2
0
0
2
1
1
1
1
1
1
1
2
1
3
2
1
1
2
1
1
1
2
0
2
1
1
0
2
1
2
1
1
0
1
2
0
0
1
1
1
1
1
1
0
1
0
1
2
1
0
1
1
2
1
2
2
2
1
1
2
1
0
1
2
1
2
2
1
2
2
1
1
0
2
1
1
0
2
2
1
0
1
1
1
0
1
2
1
0
3
1
1
1
0
2
2
1
0
0
1
0
1
1
1
1
0
0
0
5
1
1
1
0
0
1
1
1
1
0
1
2
2
0
2
2
1
1
0
1
1
2
0
2
1
1
1
1
0
1
2
1
1
1
1
0
0
0
2
1
1
0
1
1
1
0
0
1
1
1
1
2
1
1
1
1
1
1
0
4
1
1
1
2
1
1
2
1
1
1
1
2
1
1
1
2
1
1
0
2
0
2
1
0
2
1
2
2
0
2
0
2
0
1
1
1
1
1
0
0
2
1
2
0
3
1
1
1
1
1
2
0
1
1
2
2
1
1
0
1
2
1
1
2
1
1
2
1
0
1
0
0
0
1
2
1
0
1
2
2
1
2
2
2
0
1
1
1
2
0
1
1
0
1
1
0
1
0
1
2
2
1
1
0
2
3
0
1
1
1
1
0
1
0
2
2
1
1
0
0
1
1
0
2
1
1
2
2
1
0
1
1
1
1
0
1
0
1
2
2
0
1
1
0
1
1
2
1
1
2
1
2
1
2
0
2
1
1
1
0
1
1
1
2
0
1
0
2
0
0
0
1
2
2
1
1
1
2
1
1
1
0
2
1
1
2
1
1
1
2
1
0
1
1
2
0
1
1
3
2
1
2
1
2
1
1
1
0
1
1
1
1
1
1
2
0
0
1
1
0
2
0
1
1
3
1
1
1
1
2
1
1
0
1
2
2
2
1
0
0
1
0
1
1
1
2
2
1
0
2
3
1
1
1
0
1
1
0
1
1
1
1
1
2
2
1
1
1
1
1
3
1
1
1
0
0
0
1
2
2
0
2
2
0
0
4
0
2
1
1
0
0
0
0
2
1
0
1
1
1
1
1
1
0
0
2
1
1
0
2
1
2
1
2
1
0
1
0
1
0
0
2
1
2
2
1
0
1
1
2
1
2
0
1
0
2
1
3
1
0
1
1
2
2
1
2
2
1
1
0
1
2
1
1
1
0
1
1
2
1
1
1
1
0
1
1
1
1
1
0
2
0
1
2
2
1
1
0
0
1
0
2
1
0
1
0
0
0
3
1
2
0
1
2
2
1
0
2
1
1
0
1
0
2
1
1
2
1
2
1
0
0
1
1
1
0
2
2
2
1
0
2
1
1
3
1
0
0
1
2
2
2
2
3
1
1
2
1
2
0
1
2
1
1
1
1
1
1
2
0
1
0
1
1
0
0
1
1
0
1
2
1
2
0
1
1
2
2
1
0
1
2
1
1
1
1
0
1
2
0
1
1
2
2
1
0
1
0
1
1
2
1
1
2
1
1
1
1
2
0
1
2
1
1
1
1
0
2
0
1
1
1
2
1
2
2
1
1
2
2
1
0
0
1
1
0
1
1
0
2
0
2
1
3
1
1
0
0
1
1
1
0
0
1
1
0
2
1
1
1
1
0
2
0
1
1
0
1
1
1
0
2
1
0
0
2
1
0
1
1
2
1
1
1
0
1
0
2
1
2
2
1
0
1
1
1
2
0
0
1
1
2
1
2
0
1
2
0
1
1
1
1
0
1
1
0
0
2
1
0
1
1
1
0
1
1
1
1
1
0
1
0
1
0
1
1
0
2
0
2
2
0
1
1
1
0
1
1
1
1
1
2
0
2
1
2
1
1
1
1
0
0
2
1
2
1
2
1
2
1
1
1
2
0
1
1
1
1
1
1
1
1
2
1
2
0
2
1
2
2
0
0
1
1
1
1
0
2
1
1
0
0
1
0
1
2
1
0
1
0
2
2
2
1
1
1
2
1
1
1
0
2
3
1
1
1
1
1
0
1
1
1
1
0
1
1
1
0
1
0
1
0
1
1
1
0
1
0
2
0
0
1
1
2
1
2
14
1
1
1
1
1
1
1
2
1
0
1
1
2
1
1
0
2
0
1
0
2
1
0
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
0
0
1
1
1
1
2
2
0
0
0
0
2
0
1
1
1
1
2
2
1
2
1
1
0
2
0
2
1
2
2
2
2
1
2
1
1
2
1
0
1
2
2
1
1
1
1
1
0
1
1
1
0
1
0
1
0
2
1
0
2
2
1
1
2
1
1
2
0
1
1
0
2
1
1
1
0
1
2
0
1
1
1
1
0
1
2
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
2
2
2
1
1
2
1
1
1
1
1
0
1
1
0
1
1
1
0
1
1
1
1
2
1
1
1
1
0
1
2
1
0
0
1
2
1
1
1
1
1
1
2
1
0
0
1
0
1
1
1
0
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
2
1
3
1
2
1
1
1
0
1
2
2
1
2
1
2
1
2
1
0
1
0
2
1
2
1
0
1
1
1
1
0
1
0
2
1
1
1
2
1
2
1
0
1
0
1
1
1
1
2
1
1
1
1
1
1
2
1
2
0
0
1
1
1
1
1
1
0
1
1
1
2
0
2
0
1
2
1
0
1
2
0
1
2
1
0
1
1
1
1
1
1
1
1
1
2
0
0
1
1
1
2
1
1
1
1
2
1
2
0
2
1
1
0
1
1
0
1
0
1
1
1
2
2
1
0
1
1
1
1
1
2
2
1
0
1
2
2
1
0
1
0
2
0
2
1
2
0
1
1
0
1
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
2
1
1
0
1
0
0
2
1
1
1
2
1
0
0
1
2
1
1
1
1
0
1
1
1
1
0
1
2
2
1
2
0
1
1
1
1
0
1
1
1
0
2
1
2
1
0
0
1
1
0
1
1
0
1
2
1
1
1
1
2
1
1
1
1
0
2
2
1
1
1
1
2
0
1
1
2
1
1
1
1
0
1
2
2
2
2
2
1
0
1
2
2
2
1
1
2
1
1
0
1
2
2
1
1
1
1
2
1
1
2
1
0
1
2
1
1
1
1
0
1
2
1
1
2
0
2
0
0
1
1
1
1
1
1
0
1
1
1
0
1
1
1
1
2
2
1
1
0
1
1
1
1
2
1
0
1
0
1
1
5
2
0
1
1
3
2
1
1
1
2
1
1
1
1
1
1
0
0
2
1
2
2
2
1
0
1
1
1
2
1
2
2
1
1
1
0
1
0
1
0
2
1
1
1
1
0
2
1
1
2
1
1
2
0
1
1
0
1
0
0
0
1
2
1
1
1
0
1
0
2
2
1
1
1
0
2
2
1
0
1
2
1
1
1
0
1
2
1
1
1
1
1
2
2
0
0
0
2
1
1
1
1
1
2
1
1
1
1
0
1
2
1
0
1
0
2
1
1
1
1
2
2
2
1
0
2
2
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
2
2
1
1
1
0
2
1
0
1
1
1
1
0
2
1
1
1
1
0
2
1
1
1
1
1
0
1
0
1
1
1
0
0
1
1
0
2
0
0
2
1
1
2
0
5
2
1
0
1
2
1
0
2
0
1
1
1
1
1
1
2
1
1
0
1
1
1
0
1
0
1
1
3
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
2
0
1
2
1
1
1
1
1
2
0
1
1
0
1
1
1
2
1
2
0
1
1
2
1
1
1
1
1
1
0
1
1
1
2
0
2
0
0
1
1
2
0
1
2
1
1
1
1
0
1
2
2
2
1
1
2
1
1
0
2
1
2
2
1
1
1
1
1
1
0
2
0
1
0
1
1
1
1
1
2
1
1
1
1
2
1
0
1
2
1
1
0
1
0
1
1
0
1
1
1
2
1
1
2
0
2
2
1
2
1
1
0
1
1
1
1
1
1
1
2
1
1
1
1
0
1
1
1
0
2
1
1
1
1
1
1
2
1
2
0
2
2
0
2
1
1
2
1
1
1
0
1
2
1
0
1
1
1
2
0
1
1
1
1
0
2
1
1
2
1
0
1
2
1
1
1
1
1
0
2
1
1
1
1
2
1
0
1
0
1
0
1
2
0
1
1
2
1
1
1
0
2
0
1
2
1
0
1
1
1
1
1
1
1
1
1
1
1
0
2
1
0
1
1
2
1
0
0
2
2
2
2
2
1
2
2
1
0
2
1
0
0
1
1
1
1
0
2
1
2
1
1
2
0
1
1
1
1
1
0
1
1
1
1
1
1
0
2
2
1
1
1
2
1
0
1
0
1
1
1
1
2
1
1
2
1
1
1
1
0
1
3
0
1
1
1
2
0
0
1
4
1
2
0
0
1
1
1
1
2
1
1
0
2
2
0
1
0
1
1
1
1
2
1
1
1
1
2
3
2
0
1
1
0
1
1
1
2
1
1
2
2
1
1
1
1
1
1
1
1
0
0
1
1
0
0
1
0
1
1
0
1
1
1
1
1
1
0
1
2
0
1
1
1
0
1
2
1
1
0
0
1
1
2
2
2
1
0
1
1
1
1
2
0
0
2
1
1
1
2
1
1
0
2
0
1
1
1
1
1
1
0
1
1
1
1
1
3
0
1
1
2
2
2
2
1
0
1
1
1
1
2
1
1
1
1
1
1
0
1
2
2
1
1
2
1
1
0
2
0
1
1
1
0
1
1
1
1
1
1
1
0
0
0
2
1
2
1
2
1
1
0
2
1
0
1
1
2
0
1
1
2
1
1
1
1
0
1
1
2
2
0
1
1
1
2
1
0
1
0
0
1
1
1
1
1
1
1
1
1
1
1
2
2
2
2
0
2
1
0
1
1
0
1
2
0
2
2
0
0
2
2
2
1
1
1
0
0
2
2
1
2
0
1
1
1
1
2
1
1
1
1
1
1
1
2
1
0
1
1
1
1
1
1
1
0
1
1
2
0
2
1
1
2
1
2
0
1
0
1
2
1
1
1
1
1
1
0
0
1
2
1
2
1
1
2
2
1
2
1
2
0
1
1
0
0
1
1
0
2
0
1
1
0
1
1
1
0
1
1
1
1
1
0
1
1
1
2
0
1
1
1
0
1
2
1
1
1
1
1
2
2
1
1
2
1
2
0
1
1
0
1
1
1
1
0
0
1
2
1
1
2
2
0
1
1
1
1
1
2
0
0
1
1
1
1
1
0
1
3
1
2
2
1
2
2
1
1
2
2
1
1
0
1
0
1
1
0
1
1
2
1
0
0
1
2
0
0
1
1
0
1
0
1
1
2
0
3
0
0
1
2
1
1
2
1
1
1
1
2
0
1
1
1
1
2
1
1
1
2
1
0
2
1
2
0
1
1
2
1
0
1
1
0
1
1
1
1
0
1
2
2
0
2
1
1
1
1
0
0
0
1
0
1
1
1
0
0
1
1
2
1
1
0
1
1
1
1
2
1
1
1
2
1
1
1
1
1
2
2
0
0
0
1
2
1
2
1
2
1
1
0
1
0
2
2
2
0
0
2
2
0
0
1
0
2
1
2
0
2
2
2
1
1
1
0
1
1
1
0
2
2
1
2
1
1
1
2
0
1
0
0
1
1
0
2
1
1
2
1
1
1
2
1
2
2
1
1
2
0
1
1
1
1
1
1
2
2
1
1
3
1
1
1
0
1
2
1
1
1
1
1
1
0
1
2
1
1
1
1
2
0
1
0
1
2
1
0
2
1
2
0
1
1
2
2
1
2
2
0
1
1
2
1
2
1
3
0
2
2
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
4
1
1
1
0
1
3
0
1
2
2
1
0
1
2
3
0
1
1
1
2
0
1
1
0
2
1
1
2
1
2
1
0
2
0
1
1
1
3
0
2
2
1
1
1
1
2
1
1
1
1
1
2
1
0
0
1
0
1
2
1
0
2
1
1
0
2
0
0
1
0
2
1
1
1
2
1
2
1
1
1
1
2
1
1
1
2
0
2
2
1
2
1
0
1
2
0
2
1
0
1
2
0
1
1
1
2
2
0
0
1
1
1
1
1
1
1
0
2
1
2
1
0
1
1
2
1
1
2
1
1
2
1
1
1
2
1
2
0
2
0
1
0
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
0
2
0
1
1
0
1
0
1
2
0
3
1
3
1
0
1
0
1
1
2
1
0
1
1
2
1
0
1
1
1
0
1
1
1
1
0
0
2
1
1
1
1
2
1
0
1
1
1
1
1
0
1
1
2
1
1
2
0
1
1
1
0
0
0
0
1
1
1
0
1
1
0
1
1
1
1
2
0
2
3
1
1
0
1
1
2
1
0
1
1
1
0
1
0
0
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
2
0
0
1
2
1
1
1
1
1
2
0
1
2
0
1
0
1
1
1
1
2
1
2
1
1
1
1
0
1
1
1
2
1
0
0
1
1
1
1
2
2
2
0
0
1
2
1
2
2
0
1
0
1
1
0
2
0
2
1
1
0
1
2
1
2
1
1
1
0
1
1
1
1
2
2
2
0
1
1
0
0
1
1
1
2
0
1
0
2
0
0
1
0
1
0
1
2
0
1
2
1
1
1
1
7
0
1
1
1
1
0
0
2
1
0
1
1
0
1
1
1
0
1
0
1
0
2
2
1
1
3
1
2
0
1
1
1
1
1
1
4
1
1
1
0
2
1
1
1
0
1
1
1
1
2
2
1
1
1
0
0
2
2
1
2
1
0
2
1
1
2
2
1
1
1
1
1
0
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
0
1
1
0
2
0
1
1
0
2
2
1
0
1
1
1
2
1
1
1
1
1
1
1
1
0
1
1
2
0
1
2
1
1
1
2
1
0
1
2
1
0
0
1
2
1
2
0
2
0
1
1
2
1
0
1
1
1
2
1
1
1
0
1
1
2
2
1
1
1
1
1
2
1
0
0
0
0
1
2
1
2
1
0
2
1
1
2
1
1
1
0
2
0
1
1
1
1
1
1
1
1
2
2
1
1
2
1
2
0
1
1
0
0
0
1
0
1
2
1
1
1
1
2
2
2
2
1
1
0
1
1
1
1
1
0
2
2
2
2
1
0
2
2
1
0
2
1
1
1
0
1
2
1
1
0
1
0
0
2
2
1
0
1
1
1
1
0
1
1
1
2
1
1
1
3
0
1
2
1
1
1
1
0
1
1
1
0
2
1
1
1
1
2
1
1
0
1
0
1
1
2
0
0
1
1
1
1
0
1
1
1
1
1
0
0
1
1
2
2
1
1
2
2
0
2
2
2
2
1
1
2
0
1
2
1
0
2
2
1
1
1
0
1
1
1
2
1
1
0
1
1
1
0
2
0
2
1
1
2
1
0
0
1
1
1
0
0
2
1
1
0
1
1
1
1
1
0
1
1
1
0
0
1
0
0
1
0
3
1
1
2
0
1
1
2
1
1
2
0
0
1
0
0
1
1
1
1
1
2
0
0
0
1
1
1
1
1
1
2
0
1
2
1
1
0
2
2
1
2
0
2
1
1
1
2
0
0
2
0
2
1
1
2
2
1
0
1
1
2
1
2
1
0
1
2
0
0
2
2
0
2
2
1
1
1
2
0
2
1
0
2
0
1
1
1
1
1
2
2
0
1
1
1
0
1
1
0
0
1
0
1
1
0
1
1
2
2
1
1
1
1
1
1
2
1
2
1
1
2
1
2
1
1
1
2
0
2
1
1
1
1
1
2
1
1
1
1
0
0
1
2
1
0
1
2
1
1
1
1
0
0
1
1
2
1
1
1
0
1
1
2
0
1
1
2
2
1
2
1
1
2
1
2
1
1
1
1
0
1
1
1
1
1
1
0
1
1
2
1
1
0
0
1
1
2
1
1
1
1
1
0
0
1
1
1
1
0
2
1
1
1
1
2
1
1
1
1
1
1
1
2
0
2
0
2
1
1
1
0
0
1
1
1
2
1
2
1
1
2
1
1
0
0
1
2
1
1
1
1
2
1
1
1
1
1
0
2
1
1
1
1
1
1
1
1
2
1
2
2
1
1
0
1
1
1
2
1
2
0
1
1
1
1
1
1
1
1
2
1
1
1
0
0
1
1
2
0
1
1
1
1
1
0
0
1
2
1
0
2
1
1
1
1
1
1
0
1
0
3
1
1
1
0
0
1
1
1
2
1
1
0
1
1
1
2
0
2
1
0
1
1
0
1
1
0
1
1
1
1
1
1
1
1
0
2
1
1
0
1
1
1
0
1
1
1
0
0
1
1
2
2
0
1
1
1
1
2
2
1
2
0
1
0
1
2
0
1
1
2
0
1
1
0
2
1
1
1
0
1
1
1
2
1
1
1
0
1
1
1
2
0
1
3
1
0
2
1
1
0
2
2
1
1
0
1
2
1
1
0
1
0
1
2
0
2
2
1
1
0
1
1
2
1
1
1
1
0
1
1
2
2
1
1
0
1
2
0
1
1
0
1
1
2
2
1
1
1
1
1
2
0
2
1
1
0
0
0
1
0
1
0
1
1
2
2
1
1
1
2
1
4
1
1
1
1
2
1
1
1
0
1
1
1
1
1
2
1
1
1
1
1
1
0
1
1
1
1
2
0
0
1
2
1
1
1
1
1
1
1
0
1
1
1
4
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
0
1
1
2
0
0
0
1
1
2
0
3
1
1
1
2
2
1
3
0
1
1
2
1
0
2
1
1
0
1
2
1
2
2
0
1
0
1
1
1
0
1
0
0
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
0
1
1
0
1
0
1
1
1
1
1
0
1
0
1
0
1
1
0
1
0
2
0
2
0
1
0
1
2
1
1
1
1
0
0
1
1
2
2
1
2
2
2
1
1
1
1
0
2
1
1
0
0
1
1
1
1
1
1
1
1
1
1
1
1
2
0
1
2
1
1
0
0
1
1
0
2
2
2
2
2
1
1
1
1
1
1
1
1
0
0
1
0
1
0
0
1
1
1
2
1
2
2
0
1
1
1
0
1
1
1
2
1
2
2
1
2
0
2
1
1
0
2
0
2
0
1
1
1
1
2
1
1
1
2
1
1
2
1
1
1
2
0
2
0
0
1
1
2
0
1
1
2
0
1
2
1
1
2
1
2
2
0
2
1
0
1
0
1
1
1
1
2
1
1
1
1
1
1
1
1
0
1
1
1
2
1
0
2
1
0
1
2
1
0
1
1
2
1
2
0
1
1
1
2
1
0
1
0
0
1
2
1
2
1
2
0
1
1
1
2
2
1
1
1
3
1
0
2
1
1
0
1
0
1
2
0
1
0
0
0
1
2
0
2
2
2
1
1
1
1
2
1
1
1
0
1
1
1
1
0
1
3
2
2
1
1
1
1
2
0
1
0
1
1
1
1
0
2
2
0
0
2
1
1
1
1
1
2
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
0
1
2
2
1
1
1
1
0
2
2
1
1
1
1
1
1
2
1
1
2
1
2
2
0
1
1
1
0
1
1
2
1
1
2
2
1
2
0
0
2
1
1
0
1
1
1
1
0
0
2
1
1
0
0
2
1
1
1
0
0
1
1
2
1
1
2
2
2
1
1
1
1
2
1
1
1
0
1
1
1
1
0
1
2
0
1
1
0
1
1
1
0
1
2
2
1
0
2
2
1
1
1
0
1
1
0
2
2
1
1
1
2
1
0
2
2
2
1
1
2
1
1
1
1
0
0
0
0
0
1
0
0
2
1
0
1
1
0
2
1
1
2
1
1
1
0
1
3
1
2
2
2
1
2
1
1
1
2
2
2
1
1
2
0
0
2
1
1
0
1
1
2
2
2
0
1
1
1
1
2
1
2
1
1
2
1
0
1
1
2
1
1
1
0
2
1
1
2
1
1
1
1
1
0
1
1
1
2
0
1
0
2
1
0
2
0
0
1
2
2
1
1
1
0
1
0
1
2
1
1
0
1
2
1
1
1
2
1
0
1
2
2
1
1
2
1
1
0
1
1
1
1
1
1
1
0
0
1
1
1
2
2
2
0
1
0
2
1
1
2
1
1
1
0
1
1
1
1
1
1
1
1
1
0
0
0
1
1
2
1
0
0
1
0
1
1
1
1
0
2
2
1
1
1
1
2
0
1
2
3
0
2
2
2
1
2
2
1
1
1
2
1
1
2
1
0
1
0
0
1
2
2
1
1
1
2
1
1
2
2
0
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
2
1
0
1
1
0
0
1
1
1
1
0
1
1
2
1
1
0
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
2
0
2
0
1
1
2
0
1
1
2
2
1
1
1
1
1
2
1
0
2
1
2
1
1
0
1
1
1
2
1
1
2
1
1
1
1
1
2
2
1
2
2
2
1
1
1
2
0
2
0
0
2
0
1
1
1
2
0
1
1
1
1
1
1
1
2
1
1
1
1
0
1
1
1
0
1
0
0
2
0
1
0
1
1
0
0
1
1
1
1
1
1
1
1
1
2
1
0
1
1
3
0
1
2
1
1
1
0
2
1
1
0
1
2
1
0
0
0
1
2
2
1
1
1
2
1
2
1
0
1
1
1
0
2
1
1
1
1
0
2
1
1
2
1
1
2
1
1
1
1
0
1
0
1
2
1
2
1
2
3
2
0
1
1
0
2
0
1
1
0
0
1
0
1
2
1
1
1
1
1
1
1
1
0
1
2
1
2
1
3
0
1
1
4
1
1
1
1
2
1
2
1
1
1
1
0
2
0
1
0
1
2
1
2
1
0
2
0
1
1
1
1
0
0
1
1
2
0
2
1
2
0
1
1
0
1
1
2
0
1
1
1
0
1
1
1
1
2
1
1
1
2
2
1
0
2
2
0
0
1
1
1
2
1
0
0
1
1
1
1
2
1
1
0
2
0
3
1
2
1
1
1
0
2
2
1
1
1
1
1
1
1
1
2
4
0
2
1
1
1
1
1
1
2
1
1
1
2
1
1
2
2
0
2
1
2
0
1
1
0
1
1
1
2
2
1
1
1
1
2
1
1
1
2
0
1
1
1
1
2
1
0
2
1
1
0
1
1
1
1
1
1
1
2
1
1
2
1
2
1
2
1
1
1
0
1
2
1
1
2
2
1
1
1
2
1
0
0
2
0
1
1
1
1
1
1
0
2
1
1
1
0
1
0
0
1
1
1
2
1
1
1
2
1
0
2
2
1
1
1
1
1
1
0
0
1
1
1
1
1
0
1
1
2
1
1
1
0
1
2
0
1
0
1
2
1
2
1
1
1
0
2
1
0
1
1
2
2
1
1
1
2
1
1
1
1
3
1
1
1
0
2
2
1
1
1
1
1
2
1
0
1
0
1
2
1
2
0
1
1
2
1
1
1
0
1
0
2
2
1
1
1
0
1
2
1
1
1
2
1
2
0
1
1
2
2
1
2
0
2
1
1
1
0
2
1
2
0
2
1
1
1
1
1
1
1
1
0
1
3
1
1
1
1
2
1
1
0
0
1
1
2
2
1
1
1
2
1
2
2
0
0
2
1
2
1
0
2
1
1
1
2
1
1
0
1
1
1
0
0
1
1
2
2
1
0
0
1
0
1
0
1
1
0
0
2
0
2
1
1
2
1
1
1
1
1
1
1
1
2
2
1
1
0
0
1
1
2
1
2
1
1
1
1
1
1
2
0
0
1
1
1
1
1
0
2
1
1
1
0
1
1
1
0
2
1
0
2
0
2
3
1
1
0
1
1
2
1
2
2
1
2
1
2
0
1
1
0
0
2
0
1
2
1
2
2
1
1
1
1
1
2
0
1
1
2
1
1
1
1
2
0
1
1
2
1
1
1
0
0
2
2
1
1
0
2
2
1
1
1
2
1
1
1
0
1
0
1
1
1
1
1
1
0
2
1
0
0
1
3
1
1
1
0
2
0
2
0
1
3
2
1
0
1
1
2
1
2
1
0
3
1
0
1
1
2
1
1
1
1
0
1
1
1
1
2
1
1
2
2
0
1
1
0
2
2
1
1
1
0
2
1
1
0
3
1
0
1
2
0
2
0
1
1
1
1
2
0
5
1
0
0
1
1
0
2
1
0
1
1
1
0
1
1
1
2
1
0
2
3
2
0
0
2
1
2
0
2
2
2
1
0
1
0
0
0
1
2
0
1
0
1
1
2
1
1
1
1
2
2
2
2
1
1
1
1
1
2
1
1
0
0
1
1
1
1
0
1
2
2
0
2
1
1
3
0
0
1
2
0
0
2
0
1
1
1
1
1
1
1
0
1
2
2
2
2
1
0
1
1
2
1
0
2
2
2
1
1
1
1
1
1
1
2
1
1
1
0
1
3
1
1
0
1
2
1
1
0
1
1
1
1
1
1
2
2
1
2
1
1
2
0
1
1
0
0
2
1
1
1
1
2
1
0
2
1
2
0
1
1
2
1
1
2
1
1
1
1
1
1
1
1
0
1
1
2
1
1
1
2
1
1
2
1
0
1
1
0
1
1
0
0
1
1
2
1
2
1
2
2
1
1
1
1
1
1
2
2
2
1
1
1
1
0
1
1
2
0
0
1
2
1
1
2
1
1
0
0
1
3
2
1
1
1
5
2
2
1
1
2
2
2
1
1
2
3
1
1
0
1
1
0
0
2
2
1
1
1
1
2
2
1
2
1
2
1
1
0
2
2
2
1
0
1
3
1
1
1
1
1
1
2
1
1
0
0
2
2
0
2
1
1
0
1
2
1
0
1
1
1
2
2
1
1
1
1
1
1
1
1
0
1
2
1
0
2
2
2
2
1
1
1
2
2
0
1
1
1
1
0
1
1
1
1
1
2
1
0
0
1
0
1
2
1
0
2
0
1
0
1
0
2
2
1
0
1
1
0
2
2
1
0
0
1
1
0
1
1
0
0
0
2
1
0
2
1
1
2
1
3
0
0
1
1
0
3
1
0
2
1
2
1
0
0
1
2
0
1
0
2
0
2
2
1
2
1
1
1
2
1
1
2
1
1
2
2
1
1
1
1
0
1
0
1
0
1
2
2
2
1
0
2
1
1
0
2
1
1
0
1
1
2
1
2
2
2
2
1
1
0
0
3
0
2
0
1
1
2
2
2
0
0
1
1
2
2
0
1
2
1
1
1
0
1
0
2
2
2
0
1
1
0
1
0
2
8
2
0
2
2
0
0
1
1
1
2
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
2
2
0
1
1
1
1
1
0
2
1
1
1
2
0
1
0
2
2
1
0
1
1
0
1
1
0
0
2
1
2
1
1
1
2
1
1
0
2
2
2
1
1
2
2
1
1
1
1
1
1
2
1
1
1
0
0
2
1
1
1
0
2
1
1
1
1
0
2
1
1
0
1
0
1
3
0
1
2
2
2
0
1
1
1
0
0
2
0
1
1
2
1
1
2
1
2
2
1
1
1
0
1
1
1
0
1
2
2
1
1
1
1
1
1
2
0
1
2
2
1
2
2
2
1
1
1
0
1
0
0
1
1
2
0
0
2
1
1
1
1
2
5
2
1
2
1
1
1
0
1
1
1
0
1
0
1
1
1
0
2
2
1
0
2
1
2
1
1
2
1
1
1
1
0
1
1
1
1
2
0
1
2
0
0
1
1
1
1
1
1
1
1
0
2
0
1
2
1
0
2
1
0
0
1
0
1
0
2
1
1
1
1
1
0
2
2
1
0
1
1
0
0
0
1
1
0
2
1
1
0
1
0
2
1
1
2
1
1
1
1
0
0
1
1
1
0
1
1
0
1
2
1
0
0
1
1
1
1
1
1
1
0
1
1
0
0
0
1
0
1
2
1
2
1
1
1
2
0
1
2
1
1
1
2
1
0
2
1
2
1
1
2
1
2
0
0
0
1
0
2
1
0
1
1
2
0
0
1
2
1
2
2
1
0
0
1
0
2
1
1
1
1
1
1
2
2
2
0
1
1
2
1
1
2
2
2
0
1
0
1
1
1
1
1
1
1
0
0
1
1
0
2
1
1
1
1
1
1
2
0
1
1
2
0
1
1
2
2
1
1
0
1
2
2
1
1
0
0
1
2
2
1
1
0
0
2
1
2
2
0
1
2
1
2
2
1
1
1
1
1
2
1
1
0
1
1
1
2
0
1
1
1
0
1
0
1
2
2
0
2
1
1
2
1
1
1
1
2
2
0
1
0
2
0
1
1
1
0
1
1
0
0
0
1
2
2
0
1
0
1
0
1
2
2
0
1
0
1
0
3
0
1
0
1
0
2
1
1
1
2
2
0
2
2
1
2
1
1
1
1
1
2
1
1
0
1
1
0
1
2
1
0
1
2
2
1
1
1
0
2
2
1
1
1
0
1
0
0
1
1
2
0
1
0
1
1
2
1
1
1
1
2
2
0
0
1
1
0
1
1
5
0
1
1
1
2
1
1
0
1
0
1
1
1
2
2
1
1
1
1
1
0
1
2
1
1
0
1
2
0
1
1
2
0
1
2
0
1
1
1
2
2
2
2
1
1
1
1
1
0
2
0
2
2
0
0
1
1
2
0
0
0
1
1
1
1
1
1
0
0
1
0
2
0
2
1
1
1
1
1
1
2
2
1
1
1
0
2
0
1
2
1
1
1
1
0
0
2
1
1
1
1
1
1
1
0
1
1
1
0
1
2
0
1
1
0
2
0
1
1
1
1
1
1
0
1
0
0
1
0
2
1
1
2
0
1
1
1
1
1
2
2
2
1
1
1
1
1
1
2
1
2
1
1
1
0
1
1
1
2
1
1
1
0
1
1
1
1
1
2
0
1
0
2
0
0
1
2
1
0
1
2
2
1
1
2
1
1
1
1
1
1
2
1
0
1
0
1
1
1
2
1
2
1
1
0
0
1
1
1
0
0
1
2
2
1
1
1
1
1
0
1
2
0
0
2
1
2
1
1
1
1
0
1
0
1
1
1
1
2
1
1
2
1
0
1
2
2
1
4
1
1
1
0
1
1
0
1
1
1
0
1
2
0
1
0
1
1
1
1
1
1
1
2
1
2
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
0
2
1
2
2
0
1
1
1
2
1
1
0
0
0
2
2
2
1
2
2
2
2
2
1
0
0
0
2
1
1
1
1
1
2
1
1
1
0
1
1
1
1
0
0
1
1
1
1
1
1
0
1
1
1
0
2
2
1
1
1
0
1
1
0
2
0
1
1
0
0
1
1
2
1
1
0
2
1
0
1
1
1
0
0
1
0
1
3
0
2
1
2
1
0
1
0
1
1
2
0
1
1
1
1
1
2
1
1
0
2
2
1
0
1
1
2
1
0
1
1
1
1
0
1
1
1
1
1
1
1
0
1
1
1
1
1
1
2
0
1
0
2
1
1
1
2
1
1
2
0
0
1
1
0
0
1
2
1
1
0
1
2
0
1
1
0
1
1
2
1
2
1
0
1
0
2
1
1
3
1
2
1
2
1
2
0
1
1
1
1
2
1
2
0
0
1
1
0
2
1
2
1
1
1
2
0
1
2
2
1
1
2
2
0
2
1
1
1
1
0
1
1
1
1
1
2
1
0
0
1
1
1
0
1
0
1
1
1
0
1
1
1
1
2
1
1
2
2
1
1
2
0
1
1
2
1
0
0
1
1
2
1
1
2
1
0
0
0
1
1
0
1
1
1
0
1
0
1
1
2
1
1
1
0
1
0
2
2
2
2
3
1
2
0
3
0
0
2
2
1
0
1
2
0
1
1
1
2
1
0
2
2
1
1
0
0
1
1
1
1
1
2
0
1
2
1
0
1
0
1
1
1
1
1
1
0
1
1
1
1
1
1
2
2
1
2
0
0
1
1
1
1
1
1
2
1
1
1
1
0
1
1
0
1
2
1
1
1
1
1
0
1
0
0
1
1
2
1
2
1
2
0
1
1
0
1
1
1
1
1
1
1
0
0
2
2
0
2
1
1
0
2
2
1
1
0
0
1
0
1
2
2
0
0
2
1
2
2
1
1
1
1
1
1
0
1
0
2
1
0
0
1
1
1
2
1
1
1
0
1
1
0
1
2
1
1
1
1
1
1
2
2
2
0
1
1
1
3
1
2
0
1
1
1
1
1
1
2
0
1
1
2
1
2
1
1
0
2
2
1
0
1
2
1
1
1
2
1
1
1
1
2
2
1
1
1
1
2
1
2
1
0
1
1
1
0
1
1
2
1
1
0
1
1
2
1
1
2
1
1
2
0
1
2
3
0
0
2
1
1
1
1
1
1
2
0
1
2
1
1
1
1
1
0
2
2
1
2
1
2
2
2
2
2
1
1
0
1
0
1
1
1
1
0
1
1
1
2
1
2
3
0
1
1
0
2
0
1
0
0
0
2
2
2
0
1
1
0
2
2
1
0
2
1
1
1
1
1
1
1
2
2
1
1
0
0
2
1
2
1
0
1
1
2
2
2
2
1
2
2
2
1
2
0
1
0
2
1
0
1
1
1
1
0
0
1
0
6
2
1
0
0
2
2
1
0
0
2
2
1
1
2
1
0
1
0
1
0
1
1
1
2
1
1
1
1
1
0
1
1
0
2
1
2
0
3
1
2
0
0
1
1
1
0
1
2
2
2
1
1
0
1
0
1
2
1
0
2
1
2
1
1
2
1
1
1
1
1
0
1
1
2
0
2
1
2
1
2
1
1
1
1
1
1
1
0
1
2
2
1
2
1
2
1
0
0
1
0
1
0
1
1
0
1
2
2
1
2
0
0
1
0
1
1
0
2
0
2
0
1
0
2
1
1
2
0
1
1
1
0
1
4
2
2
0
1
1
1
0
1
2
1
1
0
1
0
1
1
2
1
1
1
1
1
2
1
1
2
0
1
0
2
1
0
1
0
0
1
2
0
0
1
1
1
0
1
1
1
1
1
0
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
0
2
2
1
2
1
1
1
0
1
1
1
2
0
1
1
1
1
0
1
2
1
1
2
1
0
2
2
2
1
1
2
1
1
1
1
1
2
1
0
2
2
1
2
0
2
1
2
2
1
0
0
1
1
1
0
1
1
1
2
1
0
1
1
1
1
2
1
1
1
1
1
1
1
0
1
2
2
1
1
1
1
1
0
1
1
0
1
1
1
1
2
3
1
1
1
1
0
0
1
1
1
1
2
1
1
1
0
2
1
1
1
0
0
1
0
0
1
1
1
1
1
2
0
2
1
2
0
1
1
2
1
0
2
1
1
1
2
2
1
0
0
2
1
1
0
2
0
1
1
1
0
0
1
1
1
0
1
1
1
0
1
0
1
1
0
2
0
1
1
0
1
1
1
1
1
2
2
1
2
2
1
2
2
1
1
1
0
2
1
1
1
1
1
0
0
1
0
1
0
1
2
2
1
1
1
0
1
1
1
1
0
1
1
3
1
1
1
1
1
2
0
1
2
0
1
1
0
1
1
1
0
1
2
0
1
2
2
2
1
0
0
1
0
1
2
1
1
1
1
0
0
0
1
2
0
1
2
2
0
1
3
1
1
1
1
2
1
0
1
1
1
2
2
0
1
0
1
2
1
0
1
0
0
2
0
2
2
2
1
1
1
1
1
0
1
1
1
1
1
1
0
1
1
2
0
2
1
2
1
1
2
1
0
1
1
1
0
1
1
2
0
1
0
2
1
1
0
2
1
1
0
0
1
1
1
1
0
1
1
1
2
0
1
1
1
2
1
0
1
0
1
2
1
2
1
0
2
2
0
1
1
0
1
2
1
1
1
2
2
1
1
1
1
2
1
1
1
2
2
2
1
2
1
1
2
0
0
1
2
0
2
1
2
1
0
1
1
2
1
1
1
1
1
1
2
1
2
1
1
0
1
0
1
1
0
1
1
1
1
2
2
1
0
1
1
2
2
1
1
2
2
1
1
2
1
0
1
1
0
0
0
2
0
1
3
1
1
0
2
2
1
1
0
1
0
2
1
1
0
1
1
0
1
2
1
2
2
2
1
2
1
1
0
0
0
2
0
0
0
1
1
0
1
1
0
1
1
0
1
0
1
0
1
1
1
1
0
1
0
1
2
1
1
1
1
1
2
1
2
1
1
1
2
0
2
1
0
1
0
1
0
1
2
2
1
1
1
2
2
0
1
1
1
0
0
0
1
2
2
2
1
2
0
1
2
1
1
1
1
0
1
2
2
0
0
1
1
1
2
2
1
2
1
1
1
1
2
2
2
1
0
2
1
1
2
0
0
1
0
0
2
1
1
1
1
2
1
1
1
2
0
1
1
1
1
1
1
1
0
3
2
1
2
1
2
1
2
1
0
1
1
2
1
1
0
0
1
0
2
1
1
1
2
3
1
1
1
0
1
2
1
0
1
1
0
1
1
1
1
1
0
1
1
1
0
1
1
1
1
0
0
1
1
1
2
0
1
1
1
0
1
2
1
1
1
0
1
1
0
2
2
0
1
2
0
0
0
1
2
2
1
0
1
1
2
0
2
2
0
0
1
0
1
0
1
0
1
0
1
1
1
1
1
1
0
0
1
2
0
0
2
1
1
1
1
0
1
1
1
1
1
1
0
1
1
1
1
2
2
0
1
1
2
1
1
0
2
1
1
1
1
1
0
2
1
0
1
1
0
1
1
0
2
1
0
2
1
0
1
1
1
1
1
1
1
1
1
1
1
2
0
1
3
2
1
1
1
1
1
2
0
1
1
2
1
1
1
1
1
0
4
2
1
1
2
1
2
1
1
2
1
1
1
2
1
0
2
1
1
1
1
0
1
1
2
2
1
0
1
2
1
1
1
1
0
1
2
0
1
2
2
1
1
0
2
1
1
1
0
0
0
1
0
0
1
0
2
2
2
2
1
1
1
1
0
1
2
1
0
1
1
1
2
1
2
1
2
0
1
2
2
2
3
1
0
1
1
0
1
2
0
1
0
1
0
2
1
1
2
0
0
2
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
2
1
0
2
1
1
1
0
1
1
2
1
1
1
1
1
1
1
2
2
1
1
0
0
1
1
1
1
1
0
1
2
3
0
1
0
1
0
0
1
0
0
1
0
2
2
0
0
1
2
2
1
1
2
1
1
2
1
1
1
1
0
2
0
1
0
2
1
1
0
1
2
1
0
2
0
1
1
0
2
1
2
1
1
0
2
0
1
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
3
2
0
0
1
0
1
1
1
1
2
1
2
1
2
1
1
2
1
1
1
1
1
1
1
0
2
2
0
2
1
2
0
0
1
2
1
1
3
1
1
0
2
0
0
1
1
1
1
1
1
1
1
1
2
2
1
1
1
3
1
0
1
1
2
1
1
2
0
2
1
1
1
0
1
1
1
1
0
1
2
3
1
1
2
0
1
1
0
2
2
0
0
0
2
1
0
1
1
1
0
2
1
0
2
1
2
1
3
1
1
2
1
1
2
0
1
0
2
0
0
1
2
2
1
1
0
0
1
2
1
2
1
1
1
1
2
1
1
0
1
2
1
1
1
1
0
1
2
2
0
1
2
1
1
2
2
2
1
1
1
1
1
0
1
2
1
1
1
1
2
1
2
3
2
1
0
1
1
1
1
0
1
1
1
1
1
2
1
0
1
1
3
1
2
0
0
0
0
0
1
0
2
1
1
0
0
1
1
0
2
2
1
1
0
1
1
1
2
1
1
1
1
0
1
0
0
1
1
0
1
1
0
1
2
0
0
0
1
1
0
0
1
1
3
1
2
1
1
2
1
1
0
0
1
2
1
2
1
1
1
1
1
1
0
2
2
0
1
2
0
1
2
1
0
1
2
1
0
2
1
2
2
1
2
1
1
1
1
0
2
2
2
1
1
2
1
0
0
1
0
1
0
0
1
1
1
1
0
0
1
0
2
1
2
0
1
3
0
0
0
1
1
1
2
1
2
0
1
1
2
2
1
2
1
1
0
2
1
2
1
1
1
1
1
1
2
0
2
1
0
0
1
0
2
0
0
1
0
1
1
2
1
2
1
0
1
1
1
1
2
2
1
1
3
2
0
1
2
1
2
1
2
1
1
4
1
1
1
1
2
0
1
0
1
1
1
3
1
1
0
2
3
2
1
2
0
2
2
1
1
1
1
0
1
1
1
2
1
1
1
2
1
1
0
1
1
2
1
2
1
2
1
1
1
2
1
1
2
1
1
1
1
1
2
0
0
1
0
1
0
0
1
1
2
2
3
1
1
0
1
1
1
0
1
1
1
1
1
1
1
1
0
1
1
2
1
2
1
2
0
1
1
0
0
2
2
0
1
1
0
2
1
1
1
0
1
2
0
0
0
2
1
2
1
2
1
0
1
0
1
0
1
1
0
1
1
1
2
2
2
1
0
1
1
1
1
1
1
1
1
0
1
1
1
1
1
0
1
1
1
2
1
0
2
1
1
2
1
0
1
1
1
1
1
2
0
1
1
1
2
1
0
1
1
0
0
1
1
1
2
1
2
0
1
0
1
1
1
2
1
1
2
0
2
1
1
0
2
0
0
2
1
1
1
1
1
0
0
1
1
2
0
1
0
0
1
1
1
1
1
0
1
2
0
0
2
2
1
1
2
1
1
2
0
2
1
1
2
2
1
1
1
1
3
1
1
2
2
2
0
1
0
2
0
1
2
0
1
0
1
1
2
1
1
2
0
1
1
1
0
0
1
0
2
2
2
2
1
2
1
2
0
1
1
1
1
0
1
1
2
0
2
2
0
1
1
0
1
2
2
1
1
1
0
1
1
1
1
1
3
1
0
0
1
0
1
2
1
2
1
2
2
0
1
0
2
1
1
1
1
2
2
1
1
1
1
1
2
1
1
1
2
1
1
1
0
1
1
1
1
3
0
2
1
1
2
1
1
1
1
1
1
0
1
2
2
1
1
1
2
2
1
2
1
2
1
1
1
2
3
1
1
1
1
1
1
1
2
2
0
1
1
2
2
1
1
0
1
1
1
0
2
1
2
1
1
1
1
1
1
0
1
1
1
2
2
1
1
1
1
2
1
2
1
0
2
1
2
0
0
1
1
2
0
1
1
0
2
2
1
2
1
0
1
0
1
1
0
0
2
2
1
0
2
1
1
1
2
1
1
2
1
2
2
1
0
2
1
2
1
1
1
0
1
2
2
1
4
2
1
1
0
2
1
1
2
0
0
0
2
2
1
2
0
0
1
2
2
0
1
1
2
2
2
1
1
1
2
1
2
3
1
1
1
0
1
1
1
1
1
2
1
1
1
0
1
1
2
1
1
0
1
1
1
2
1
1
0
1
1
2
0
0
1
2
2
1
1
1
1
1
1
1
1
2
2
1
1
1
2
2
1
1
2
2
0
1
1
0
1
1
1
2
1
1
1
0
1
1
1
1
1
1
0
1
1
2
2
0
2
1
0
0
1
1
1
1
1
1
1
0
0
0
1
1
1
1
1
1
2
0
1
1
1
1
2
2
1
0
0
0
0
2
2
0
1
2
1
1
1
1
2
1
2
1
1
2
2
1
0
2
2
0
1
0
1
0
1
1
0
0
1
1
1
0
0
1
1
0
1
1
1
1
0
1
1
1
2
1
1
1
2
1
1
1
1
2
1
2
1
2
1
2
0
1
2
1
1
2
1
1
1
0
2
1
1
0
0
1
1
1
1
0
0
1
1
2
1
0
0
0
0
0
0
2
1
1
1
1
1
2
2
1
0
1
1
0
1
1
2
0
1
0
0
1
1
1
1
1
0
1
2
1
1
0
2
0
2
0
1
3
1
0
1
2
0
0
0
1
1
1
2
1
1
1
1
1
1
0
2
1
1
0
1
2
1
1
2
0
2
1
1
0
2
1
1
1
2
1
2
1
2
1
2
0
2
0
1
1
1
2
2
0
1
1
1
1
2
1
1
1
1
1
0
1
2
0
0
2
1
1
1
1
1
1
1
0
1
1
1
0
2
2
1
2
1
1
2
0
1
2
1
0
0
1
0
2
2
1
1
0
1
0
1
2
2
1
2
1
0
1
1
1
1
0
1
2
1
2
1
0
1
1
0
2
1
1
1
1
1
2
0
2
1
1
1
1
2
0
1
0
1
1
0
1
1
1
1
1
1
1
1
0
1
1
1
1
1
0
1
1
2
1
1
0
1
2
0
1
1
0
1
2
1
1
1
1
1
2
2
0
1
1
0
0
2
1
0
1
1
1
1
1
1
0
1
2
0
0
1
2
2
1
1
1
1
1
2
1
1
0
0
0
0
2
1
0
0
1
1
1
1
1
2
1
0
2
0
2
1
2
0
1
1
2
0
2
0
1
0
1
0
2
1
1
1
0
1
1
2
1
2
0
2
1
2
1
1
1
2
1
1
0
1
1
1
1
1
0
1
0
2
2
1
1
1
1
0
1
1
1
1
0
1
0
1
2
1
0
1
1
1
1
2
1
1
1
0
0
2
0
2
2
1
1
1
1
1
1
0
2
2
1
0
1
1
2
2
0
1
1
1
1
1
0
1
1
1
1
0
0
1
1
1
1
1
1
1
1
1
0
0
0
0
1
0
0
1
2
2
1
1
1
1
1
2
1
1
1
0
1
0
1
2
1
1
1
2
1
0
1
2
1
2
1
2
0
0
1
2
1
1
1
1
2
1
2
1
1
1
1
1
0
1
0
2
0
0
1
2
0
1
0
1
1
2
1
1
1
0
0
2
1
1
0
2
2
0
1
0
1
2
0
2
2
2
2
1
1
2
2
1
2
1
2
1
2
1
2
1
1
0
1
0
0
1
1
1
1
1
0
1
1
1
0
0
0
2
1
1
0
2
1
1
1
1
1
0
1
0
0
1
1
0
1
0
2
1
1
0
2
2
0
1
2
1
2
1
2
1
2
1
0
2
1
2
1
1
1
1
1
0
1
2
1
1
1
1
1
0
1
1
1
0
2
1
1
1
1
1
1
2
0
1
1
1
2
0
1
1
2
2
1
1
0
1
3
1
1
2
1
1
2
1
1
0
2
1
2
0
0
1
2
1
3
1
1
1
1
2
2
2
1
0
1
2
0
1
1
0
0
0
1
1
1
0
0
1
1
0
2
1
2
1
0
1
1
1
1
2
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
0
0
1
0
1
0
1
2
1
1
1
0
2
0
2
2
1
1
1
1
1
1
2
0
1
2
0
1
2
1
0
1
1
1
2
1
2
1
2
0
2
1
1
1
1
1
1
1
0
2
2
2
1
1
1
1
0
0
1
0
1
0
0
0
1
2
0
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
0
2
2
0
1
2
0
0
1
1
1
1
1
0
2
1
1
1
0
1
0
1
2
1
2
1
1
1
2
1
1
1
3
0
1
1
2
2
0
1
1
1
1
1
0
1
1
0
1
1
0
0
1
2
1
1
1
2
1
1
2
1
2
2
1
1
2
1
1
0
0
1
1
1
0
0
2
2
0
1
1
1
2
2
1
1
2
1
1
2
0
2
1
1
1
1
1
2
1
1
1
1
2
1
0
1
0
0
0
0
2
1
1
1
1
0
1
1
0
1
1
0
1
1
1
2
2
2
1
1
1
1
0
0
0
1
0
1
2
0
1
2
1
1
0
2
1
2
1
1
1
1
1
1
2
0
1
2
1
0
0
1
0
0
1
2
1
4
1
0
1
0
1
1
2
0
1
1
1
1
2
1
0
0
1
1
1
1
0
2
0
1
1
1
1
1
0
1
0
1
0
2
1
1
1
0
0
1
2
2
1
2
1
1
1
0
1
1
0
1
2
1
0
1
1
1
2
1
1
0
0
2
1
1
1
2
2
2
1
2
0
2
1
1
1
1
1
1
2
2
1
1
0
2
1
1
2
3
0
2
1
0
1
1
1
2
1
1
1
1
1
1
1
2
0
1
1
0
1
1
3
0
0
1
1
1
0
1
1
1
0
1
0
2
1
1
1
1
0
0
6
0
1
0
1
2
2
1
2
0
1
0
0
1
0
1
2
0
0
1
2
1
0
1
2
2
1
2
2
0
1
1
1
2
1
1
2
1
0
2
1
1
1
0
1
0
0
1
2
1
1
1
0
0
1
1
1
2
2
2
1
0
1
1
1
1
1
1
1
1
0
2
2
2
1
2
0
0
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
0
1
5
0
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
0
0
1
1
0
2
1
2
2
1
1
0
0
1
1
2
2
2
1
2
1
2
2
1
1
1
1
0
2
0
1
1
1
2
1
1
0
1
1
2
0
1
1
1
0
2
0
2
1
0
1
1
0
1
1
1
1
2
2
0
2
2
1
2
1
1
1
0
1
1
1
1
1
0
2
1
2
2
1
1
1
1
2
0
2
0
0
1
0
1
1
1
1
1
1
1
1
2
2
0
1
0
1
3
0
2
1
1
1
0
0
1
0
1
2
1
0
1
1
1
0
1
1
0
1
0
2
1
2
2
2
2
1
3
2
2
0
1
1
2
1
1
2
0
1
0
0
1
0
0
1
1
1
1
1
1
1
2
1
1
0
1
2
2
1
2
1
2
3
1
0
1
1
1
1
1
2
2
1
2
1
1
0
2
2
0
1
1
1
3
1
0
1
2
1
2
1
2
1
1
0
1
1
1
0
1
0
1
2
1
2
0
1
1
1
1
0
2
1
1
1
2
1
2
2
0
1
1
2
1
0
1
1
2
1
1
2
1
0
0
1
2
1
1
0
0
1
0
1
1
2
1
1
0
2
1
2
1
1
0
3
2
0
1
0
0
1
0
1
2
1
4
1
2
1
0
1
1
0
1
0
2
0
0
0
0
1
2
2
1
2
1
0
1
1
1
1
2
1
0
0
0
2
2
1
2
1
1
0
1
2
1
2
1
0
0
0
1
2
0
1
2
1
1
0
0
1
1
1
1
1
2
2
1
1
1
0
2
2
0
0
1
1
0
2
2
1
1
0
1
1
1
1
1
0
1
1
2
1
1
1
2
2
0
1
1
1
1
2
2
1
1
1
2
0
1
1
1
1
1
1
2
0
1
3
2
0
1
0
0
0
0
1
1
0
1
2
1
1
2
1
2
2
1
0
1
0
1
1
1
1
2
1
2
1
2
1
2
2
1
1
1
1
0
1
2
1
0
1
1
0
2
1
1
1
1
1
1
2
1
0
1
1
0
1
1
1
1
2
0
0
0
1
0
1
1
2
1
1
1
1
1
1
1
1
0
1
1
0
1
2
1
0
0
1
1
1
0
2
1
0
2
1
1
1
1
1
2
0
1
2
1
1
1
1
0
0
1
1
1
1
1
0
2
2
0
0
1
1
1
0
2
1
1
0
1
1
1
1
1
1
1
1
0
2
0
0
1
1
3
0
2
0
2
0
0
2
1
2
1
3
1
2
0
1
0
2
2
2
0
2
1
0
0
1
1
0
1
2
1
1
0
0
1
1
2
1
1
0
1
0
1
2
1
1
1
0
0
1
1
2
2
1
1
1
1
1
0
1
2
1
1
1
3
0
1
1
1
2
0
1
2
1
1
0
2
2
0
0
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
0
2
1
1
0
1
1
1
1
2
1
0
1
1
0
1
1
1
1
1
1
2
1
2
1
1
1
0
1
0
1
1
2
0
1
2
0
1
1
1
1
1
1
0
1
2
2
0
1
2
2
0
1
2
1
2
2
1
0
1
2
0
1
1
0
0
3
1
1
1
0
1
0
1
3
2
1
0
1
0
2
2
0
1
0
2
1
0
2
3
2
1
1
1
1
1
1
0
0
1
1
1
2
2
2
0
2
0
1
1
2
0
1
1
2
2
1
0
1
1
2
0
1
1
0
1
1
1
1
1
1
1
1
2
1
1
0
1
1
0
1
1
1
0
1
1
1
2
1
0
1
1
2
1
1
1
0
1
2
1
1
0
2
0
1
1
1
1
2
1
1
2
1
2
1
1
1
2
1
1
0
1
1
1
1
1
1
1
1
1
0
0
1
2
0
0
2
1
2
1
2
1
0
2
1
3
1
1
2
0
1
0
1
1
1
1
1
2
1
1
1
1
1
2
0
0
0
0
1
1
1
1
1
1
2
0
2
0
2
1
0
1
1
1
0
1
1
1
1
1
1
1
0
1
2
1
2
2
0
1
2
2
2
1
1
0
2
0
0
2
1
2
1
1
2
0
1
1
1
2
2
1
0
1
0
0
1
0
1
1
1
1
1
2
3
0
1
1
1
1
2
0
0
1
1
1
1
1
1
1
0
0
1
1
0
1
2
2
2
0
1
0
1
2
0
1
2
1
1
2
1
1
1
2
1
2
1
1
1
1
2
1
1
2
1
1
2
1
2
0
1
0
1
0
1
0
1
1
2
0
0
1
2
1
1
1
0
1
1
2
1
1
2
1
1
1
1
2
0
1
0
2
1
1
2
2
1
1
1
2
1
1
1
0
0
1
2
1
1
1
2
0
1
1
0
0
1
2
1
2
0
0
1
2
0
1
1
1
1
1
1
0
0
2
1
2
0
2
0
2
1
2
2
0
0
1
1
1
1
1
1
2
1
0
3
2
1
1
1
0
2
1
1
2
2
2
2
1
1
2
1
1
1
2
2
1
1
1
1
1
1
2
2
0
0
1
2
1
1
2
0
0
2
2
1
0
0
1
0
0
0
1
1
1
1
0
0
1
0
1
1
2
1
1
2
1
1
0
1
0
2
2
2
1
0
0
1
2
1
1
2
2
1
0
1
1
2
0
2
2
2
2
1
1
2
1
1
1
2
1
0
1
2
1
1
1
2
1
0
2
2
1
1
1
1
0
1
2
0
0
1
0
1
0
1
0
2
1
2
2
1
1
2
2
1
1
1
0
1
0
1
1
3
2
2
1
1
1
1
0
2
2
1
1
1
1
1
2
0
1
2
1
1
2
2
1
1
2
1
2
2
1
0
1
2
0
1
1
1
2
0
1
0
1
1
1
0
1
2
1
0
0
2
2
2
1
1
2
0
1
1
1
2
1
1
1
2
1
1
1
1
0
2
1
1
1
0
2
2
2
1
0
1
0
1
1
1
1
0
1
2
1
2
1
1
1
1
1
1
1
0
1
1
2
0
1
1
0
1
2
1
1
1
1
1
0
0
0
0
1
2
1
2
0
1
1
0
1
1
0
1
1
0
2
1
2
0
1
1
1
2
1
0
1
1
2
2
2
2
1
1
0
2
0
1
1
1
2
1
3
1
1
1
2
1
1
1
1
2
2
1
1
2
2
2
1
0
1
1
1
0
1
1
1
1
0
2
1
1
1
0
1
0
1
1
1
1
2
2
0
0
2
1
1
1
1
1
1
1
0
2
1
2
1
1
1
1
0
1
1
2
2
1
2
1
0
2
2
0
0
0
0
0
1
1
1
1
1
1
1
0
1
1
0
1
0
2
1
1
2
2
2
1
1
0
1
0
2
0
1
1
1
1
0
0
1
0
1
2
1
1
1
2
0
1
0
1
0
2
1
1
0
1
2
1
0
1
1
2
1
0
1
1
1
1
0
1
0
1
2
1
0
1
2
1
1
2
0
1
0
1
0
1
1
1
1
1
2
1
0
1
2
1
0
0
0
1
2
2
1
1
1
1
1
1
0
1
2
1
1
1
0
2
1
2
1
1
1
2
1
2
1
0
2
2
1
1
1
2
1
1
1
0
2
2
1
0
1
1
1
2
1
0
1
1
2
1
0
0
2
1
1
0
1
2
1
1
1
1
1
2
1
1
2
1
1
1
2
1
0
0
2
2
1
0
0
1
1
1
1
0
2
1
1
1
1
1
1
2
1
1
1
1
1
0
1
0
0
0
2
1
0
3
1
1
0
1
0
4
1
1
1
1
1
0
2
1
0
1
0
0
1
2
1
1
2
0
1
0
1
1
2
1
1
0
2
1
2
1
1
1
2
1
0
1
0
0
0
1
0
2
2
0
0
2
1
2
0
1
1
0
1
1
0
1
1
2
1
1
0
1
0
2
1
0
1
1
0
2
2
0
2
1
1
1
1
2
1
0
2
0
1
1
1
1
2
2
1
1
1
0
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
0
0
0
0
1
2
1
1
0
2
0
1
2
1
1
1
2
0
2
1
1
1
1
1
1
2
2
1
1
1
2
1
1
1
2
0
1
1
1
2
1
1
1
0
1
2
1
1
1
1
0
2
0
1
0
1
1
0
2
0
1
0
1
2
2
1
1
1
2
1
1
1
0
2
1
1
1
0
1
1
0
0
1
2
0
2
1
1
1
1
1
1
1
1
1
1
0
0
1
0
1
1
1
1
1
2
1
1
1
2
0
1
1
1
1
1
1
1
2
2
1
0
1
2
0
0
1
0
2
1
1
0
1
0
1
1
1
1
2
2
1
1
2
1
2
1
1
1
2
1
0
1
1
2
1
0
0
2
1
1
1
1
1
1
1
2
0
0
0
1
1
1
1
1
1
0
0
1
1
2
1
0
1
1
0
1
3
0
1
0
0
1
1
0
1
1
0
1
1
1
1
1
0
1
1
1
0
1
1
1
1
2
2
1
1
2
0
2
1
1
1
1
2
2
1
2
2
1
0
1
2
1
1
1
2
1
1
0
1
1
1
2
1
1
1
1
1
1
1
1
0
0
1
1
0
2
1
1
1
1
1
1
1
1
2
0
1
1
2
1
2
2
2
1
1
2
0
1
2
1
1
2
1
1
0
0
1
0
2
2
0
1
2
2
1
0
1
1
0
2
1
1
0
0
4
0
1
1
1
1
2
2
1
1
1
0
2
1
0
1
0
1
1
2
0
1
2
1
0
2
3
1
0
1
2
1
1
1
1
0
1
1
1
2
0
1
0
2
1
2
0
1
0
1
1
1
0
1
1
1
1
1
1
0
1
0
0
0
1
1
1
1
1
1
1
1
2
1
0
0
1
2
2
1
1
1
1
2
1
0
2
0
1
1
1
2
0
2
1
1
0
1
2
0
2
1
1
2
0
1
1
1
1
2
2
2
2
2
1
1
1
0
2
1
1
2
2
2
2
1
1
0
1
1
0
1
0
1
1
2
0
1
1
1
1
1
1
0
1
2
2
0
1
1
0
1
1
2
2
1
0
0
0
1
1
1
1
2
2
0
0
0
3
1
1
1
1
1
2
1
2
0
1
0
1
2
1
3
1
1
0
1
1
1
0
0
1
1
1
0
0
0
1
2
1
2
1
2
1
2
1
0
1
0
1
0
1
1
1
0
1
0
0
1
2
2
9
0
0
1
1
1
2
0
2
2
1
1
0
2
1
1
0
1
0
1
1
1
0
1
1
1
2
1
2
2
1
2
2
1
1
1
1
1
0
1
1
0
1
1
2
1
1
1
1
1
2
2
1
0
2
1
2
2
0
1
2
1
1
0
1
2
0
1
2
2
0
0
0
2
1
1
0
1
2
1
1
1
1
2
2
0
1
2
2
2
1
1
1
2
1
1
3
2
1
1
1
1
0
0
1
1
1
2
2
1
1
1
2
2
1
2
1
1
2
1
0
1
0
1
2
1
1
1
2
1
1
1
1
1
2
1
2
1
1
2
1
1
1
2
2
1
0
1
1
0
1
0
2
1
1
0
2
2
0
0
3
1
0
1
0
0
2
2
2
1
0
2
2
2
1
1
1
1
1
0
0
0
1
0
1
0
1
1
1
1
1
2
2
2
0
1
0
1
0
1
0
1
1
0
2
0
1
2
1
1
2
1
0
1
0
2
0
0
1
1
2
0
3
0
2
2
1
1
1
1
2
0
2
2
2
0
1
1
4
0
1
2
1
2
2
1
0
0
1
1
0
1
1
1
2
2
1
2
1
2
1
1
2
2
1
2
1
1
2
1
0
1
1
1
1
1
0
1
0
1
0
2
1
2
0
1
1
0
1
2
2
1
1
1
1
1
2
1
1
3
1
0
1
2
0
1
1
1
1
1
1
1
0
1
0
2
1
0
0
1
1
2
1
2
1
0
1
2
0
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
0
1
1
2
1
1
1
2
0
0
1
2
1
2
2
1
2
2
1
1
1
2
2
0
2
1
2
2
0
1
1
2
2
2
2
0
1
1
0
1
1
1
0
2
1
2
0
2
1
0
2
1
1
1
1
1
2
1
2
0
1
2
1
1
1
0
1
1
1
1
1
1
1
2
1
1
1
1
1
0
2
5
1
1
1
0
2
2
0
0
1
0
0
0
2
1
1
2
1
1
1
0
1
2
2
2
0
1
2
2
0
1
1
1
1
1
0
2
2
2
1
0
1
1
1
1
0
1
0
0
1
1
1
1
0
0
1
1
1
0
1
2
1
1
1
0
1
1
1
1
1
0
1
0
2
2
1
2
0
0
1
1
0
0
1
1
2
1
2
1
0
1
1
1
2
1
2
1
2
1
0
2
2
1
2
1
1
1
1
0
0
1
2
1
0
1
0
2
2
1
2
1
1
1
2
1
2
1
2
1
2
1
2
1
1
1
1
2
0
1
0
1
2
1
2
1
0
0
1
0
2
0
1
1
1
2
0
0
2
0
0
1
0
2
2
0
2
1
1
2
1
0
1
1
1
1
0
0
2
0
2
1
2
1
2
1
1
1
1
1
2
0
2
2
2
1
1
1
1
1
2
1
0
0
3
2
1
0
0
2
1
1
0
0
1
1
2
2
2
2
0
0
1
0
0
0
1
1
0
1
0
1
0
0
2
2
1
0
1
1
0
0
0
2
2
2
1
0
0
1
1
0
1
1
1
2
2
1
1
0
1
0
1
1
2
2
1
1
0
2
1
1
2
0
1
0
1
0
0
2
1
0
1
1
1
2
1
0
1
2
2
1
1
1
1
1
2
1
1
0
1
0
1
3
0
1
1
1
0
4
1
1
1
1
1
0
2
1
2
1
2
1
1
1
2
2
0
1
1
1
1
1
0
0
2
2
0
1
2
1
0
0
2
1
1
1
1
1
1
1
2
1
1
0
1
0
1
0
1
1
0
1
0
1
1
2
1
2
1
0
1
1
2
2
1
1
2
1
2
0
0
1
1
2
1
1
2
2
1
0
1
1
2
2
2
1
1
0
0
1
2
1
2
1
1
1
2
0
1
1
0
1
0
1
1
1
1
2
2
1
1
1
1
1
0
0
1
2
3
1
0
1
2
2
1
1
2
2
1
0
2
1
1
1
2
1
1
1
1
0
0
1
2
2
1
1
2
2
2
1
0
0
1
1
1
1
1
0
1
1
2
0
1
0
2
1
1
0
4
1
1
0
2
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
0
0
1
0
0
1
2
1
0
1
1
1
0
0
2
1
1
1
1
1
1
1
4
0
1
1
2
1
2
1
0
1
2
1
1
1
2
1
1
2
1
1
1
1
0
2
1
1
0
1
0
1
1
1
1
2
1
1
1
1
2
1
1
0
2
0
2
2
1
1
1
2
2
2
1
1
1
1
2
0
0
1
1
1
0
1
1
1
0
1
1
2
1
1
1
1
1
1
0
1
1
0
0
0
0
1
0
2
1
2
1
0
0
0
2
1
1
1
1
1
1
1
2
3
2
1
0
1
1
2
1
1
2
0
1
2
1
1
2
1
0
2
1
1
1
2
2
1
1
2
2
2
2
0
1
0
1
2
1
2
1
1
1
1
2
1
1
2
1
1
1
2
2
1
1
0
1
0
2
2
1
1
0
0
1
1
1
1
1
2
1
1
1
0
1
1
1
0
1
1
1
1
2
2
4
1
1
1
1
2
0
2
0
1
2
2
1
1
1
0
1
1
1
0
1
1
0
1
2
3
1
1
1
1
1
1
0
2
1
1
2
2
0
1
1
1
1
1
2
1
1
2
0
0
1
0
1
2
0
1
0
1
1
1
1
2
2
2
1
1
0
1
0
3
0
2
0
1
2
0
1
0
0
1
1
0
2
1
1
0
0
1
0
1
2
1
2
0
1
1
2
1
2
0
0
1
1
1
1
0
2
3
1
1
1
0
1
2
1
1
1
1
2
2
1
0
1
1
3
1
2
0
1
1
1
1
2
1
2
1
0
0
0
1
1
1
2
1
1
1
1
0
0
2
2
2
1
1
1
0
1
1
2
1
1
1
1
1
1
2
1
1
1
2
0
1
2
0
1
2
1
1
1
1
0
2
1
1
2
0
1
0
1
0
1
0
0
1
1
1
1
1
1
2
0
2
2
2
1
1
1
2
1
0
2
1
1
1
1
1
2
1
1
1
1
0
0
1
1
1
1
1
1
0
1
2
1
1
0
1
0
1
2
1
1
2
0
1
1
2
0
1
1
1
1
0
1
0
0
1
2
0
0
0
1
1
0
1
1
1
1
1
3
3
2
1
0
0
0
0
1
1
1
1
2
1
1
0
1
2
0
1
1
1
1
1
1
1
1
0
1
0
1
2
0
0
2
1
1
1
0
1
1
0
1
2
1
1
1
0
0
0
1
1
0
2
1
2
1
2
0
0
0
1
0
0
1
1
0
1
2
1
1
1
2
2
0
1
1
2
2
2
2
0
2
0
2
1
1
1
2
1
1
2
1
2
1
1
2
1
1
1
1
2
1
2
0
0
1
0
2
2
2
0
1
1
2
1
0
0
2
1
1
1
1
0
2
2
1
1
1
2
1
0
1
2
0
0
2
1
1
1
1
0
0
1
0
1
1
1
1
1
0
1
1
1
0
1
1
1
1
1
2
1
1
0
0
0
1
2
0
1
1
1
1
2
2
1
2
1
1
2
1
1
2
1
1
1
2
0
1
1
1
0
1
2
0
0
1
1
1
2
1
0
1
1
2
1
0
1
1
1
2
2
1
0
1
0
1
1
2
1
1
0
2
1
1
0
0
1
0
0
1
0
1
1
2
1
1
1
1
2
1
0
1
1
1
1
1
2
1
0
0
1
1
0
0
0
3
0
1
1
1
0
2
1
2
1
1
1
0
0
1
1
1
1
2
1
2
1
1
1
3
0
0
1
0
1
1
0
1
1
1
1
1
0
1
1
2
0
0
2
2
1
0
2
1
0
1
1
1
1
1
1
1
1
2
2
1
1
1
2
0
2
0
1
1
0
1
1
1
1
0
2
0
0
0
0
1
2
1
0
1
2
1
2
1
0
1
0
1
0
0
2
3
2
1
1
0
1
1
1
2
1
1
2
1
2
2
1
2
0
1
1
1
1
2
0
1
1
2
1
2
0
2
2
1
2
1
2
1
1
1
1
0
1
0
0
2
1
1
1
1
1
1
2
1
1
0
2
2
1
0
1
0
0
0
2
0
2
1
0
2
2
2
0
1
0
1
1
1
1
0
1
2
1
1
1
0
1
1
0
3
2
1
0
2
1
0
1
2
1
2
2
1
1
0
2
1
1
0
1
2
0
2
1
1
0
1
1
1
1
1
3
1
1
2
2
1
1
2
1
1
0
1
1
0
2
1
2
2
1
2
0
1
1
2
2
1
2
1
1
1
0
2
1
1
0
2
1
1
2
0
1
1
1
1
0
2
0
1
0
3
2
1
1
2
0
1
1
2
1
1
0
0
2
0
0
2
1
1
1
1
1
2
2
0
2
1
1
0
2
2
1
1
0
1
2
1
2
0
1
0
1
1
1
1
1
1
2
2
1
1
0
1
0
0
1
1
2
2
1
1
0
2
2
2
1
1
0
1
1
0
2
2
0
2
1
1
2
0
2
1
1
1
2
2
1
1
0
1
2
2
0
0
0
1
3
1
1
1
0
1
0
1
1
1
0
2
1
1
2
1
1
0
2
1
0
1
2
2
1
0
1
1
0
1
1
0
1
1
2
2
2
1
2
2
2
1
0
2
2
1
1
0
1
1
0
0
1
1
1
1
2
1
1
1
1
1
1
0
1
2
1
0
2
1
1
1
1
1
0
1
2
1
1
0
2
1
1
1
0
1
0
0
1
2
1
1
1
1
1
1
2
1
2
1
2
0
1
3
1
2
1
1
2
1
1
0
3
0
1
1
1
0
0
1
1
0
1
1
1
1
1
1
0
1
1
0
2
1
1
1
1
0
0
1
0
1
0
1
1
0
2
1
0
2
1
1
1
1
0
1
1
2
1
0
1
2
0
2
1
0
0
1
1
1
1
0
1
0
1
1
1
2
2
1
1
2
1
1
1
2
1
1
0
1
0
1
2
2
2
1
1
1
1
0
1
1
1
1
0
1
0
2
2
1
1
2
1
1
2
2
0
0
1
2
1
1
1
1
0
2
2
0
1
2
2
0
1
1
0
0
0
1
1
1
1
1
2
1
1
1
0
1
1
2
1
1
1
1
1
0
1
1
0
3
1
1
1
2
1
1
1
0
1
2
1
1
1
0
1
3
2
1
1
0
1
0
5
0
2
0
0
0
1
0
1
1
1
1
2
1
0
1
1
1
0
1
2
2
1
1
1
1
1
1
2
2
0
1
2
1
1
2
1
1
1
1
2
3
1
0
1
1
1
1
0
0
1
1
1
1
1
2
1
0
2
2
0
2
1
1
1
1
1
2
0
1
2
2
1
0
1
1
1
1
1
1
1
0
1
1
1
1
2
2
0
1
0
2
2
0
2
2
1
2
1
2
0
1
0
0
2
0
1
2
1
3
2
1
1
1
2
2
0
1
1
1
1
1
2
1
1
1
2
2
2
1
1
1
1
1
1
1
1
2
0
0
1
2
1
2
1
1
1
2
1
1
2
2
1
1
0
0
0
2
2
1
1
1
1
1
1
2
2
0
1
1
1
2
2
1
2
1
1
1
2
1
2
0
1
1
1
0
1
0
2
0
2
2
1
2
2
2
1
0
1
2
1
1
2
0
1
0
1
0
1
2
0
0
1
2
1
2
2
1
1
0
0
0
0
1
0
1
2
1
1
1
0
0
1
2
1
2
1
1
1
2
1
1
1
1
2
1
0
1
1
1
1
2
0
0
2
1
0
1
0
0
1
1
1
1
1
0
2
2
1
0
0
0
1
1
0
2
1
1
2
1
2
1
1
1
1
1
1
1
0
1
2
1
1
1
1
2
1
1
1
0
1
0
0
1
3
2
0
1
1
1
1
1
2
1
1
2
1
0
2
1
2
1
1
1
1
0
0
2
1
0
1
1
1
0
1
1
1
2
1
1
0
1
0
1
1
0
3
1
2
0
2
1
2
1
1
1
1
1
0
0
0
1
0
1
3
1
2
0
0
2
1
1
0
0
0
2
1
0
0
1
1
1
0
1
0
0
2
0
1
1
0
1
1
1
2
0
1
0
0
0
2
1
0
2
1
1
2
2
0
1
0
1
2
2
1
0
0
0
0
1
1
1
2
1
1
0
1
2
2
2
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
0
2
0
2
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
0
0
0
1
2
1
1
2
1
0
1
3
1
2
1
1
2
0
1
1
0
2
0
1
0
1
1
0
0
2
1
1
1
1
1
1
1
1
2
1
2
0
1
1
1
2
0
1
1
0
1
0
1
1
0
0
1
0
2
0
0
1
1
1
1
2
1
2
2
1
2
3
1
1
1
0
0
0
2
1
0
1
2
0
2
2
1
0
2
0
0
0
0
1
0
1
1
1
1
2
1
2
0
2
1
0
3
1
1
1
1
1
1
1
2
2
2
1
0
0
1
1
1
0
2
1
2
1
2
0
2
2
1
1
0
2
1
2
1
1
1
2
0
1
0
0
1
1
1
1
2
1
2
1
2
1
1
0
2
1
1
1
1
2
1
1
2
1
1
2
1
1
0
0
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
0
1
0
2
1
1
2
1
0
1
2
1
1
0
0
2
1
0
1
2
2
2
1
1
1
1
1
1
1
0
1
1
1
1
2
0
1
1
0
1
1
1
1
1
0
1
0
2
1
0
2
2
1
1
1
2
1
1
2
1
0
1
1
1
1
1
1
1
1
1
1
1
1
2
1
0
1
1
0
2
1
1
2
1
2
0
0
0
0
1
1
2
2
1
2
0
1
1
1
1
2
0
1
1
1
1
1
2
1
2
0
0
2
0
0
0
1
1
1
1
0
1
0
1
2
0
0
1
2
2
2
2
1
1
1
6
1
1
0
1
1
1
1
0
0
3
2
2
1
1
0
2
1
1
2
1
2
2
1
3
1
2
0
2
1
1
1
1
1
1
1
1
1
1
2
1
0
0
0
1
2
2
0
1
2
1
1
1
2
1
0
2
1
1
1
0
1
1
1
1
0
1
0
1
0
1
1
1
2
1
1
0
0
0
2
1
2
1
0
1
0
1
0
1
3
0
1
1
0
2
0
1
1
2
1
0
2
2
1
1
1
0
0
1
1
1
1
1
0
0
1
2
1
2
2
2
1
1
1
1
1
1
0
1
0
2
2
2
2
2
1
1
1
0
1
1
2
1
0
2
1
1
0
1
1
1
1
2
2
0
0
2
1
1
1
1
2
1
0
1
1
1
1
1
1
1
0
2
2
1
0
2
2
2
1
2
2
2
1
1
1
0
1
2
0
1
1
2
1
0
1
0
0
2
1
1
1
2
1
0
1
1
1
0
1
1
1
0
2
1
1
1
2
0
2
1
1
1
1
2
1
2
1
1
1
1
1
2
2
0
0
1
1
2
0
1
1
0
1
1
1
1
2
2
1
1
1
1
1
0
1
1
0
1
1
1
0
2
2
1
2
0
2
1
1
2
1
0
2
0
2
1
1
1
0
2
2
2
1
2
1
1
0
1
1
1
2
1
1
1
2
1
2
1
1
2
1
1
1
2
1
0
0
2
1
1
1
1
1
1
1
0
2
2
2
1
2
0
0
2
0
2
1
1
2
2
1
1
1
1
1
2
0
2
1
1
1
2
2
0
2
1
0
0
2
1
2
1
1
0
1
1
1
2
0
1
4
1
2
1
2
1
2
2
2
2
2
0
1
0
1
1
1
2
2
0
1
4
1
2
1
2
1
1
0
2
1
1
2
0
0
0
1
1
1
2
1
2
2
0
0
2
0
2
0
1
2
1
0
1
1
1
0
1
2
1
2
1
1
1
2
1
1
1
0
2
1
0
1
2
1
0
1
1
0
1
1
2
2
1
1
0
1
1
0
1
2
2
1
0
2
1
1
1
0
0
2
2
1
1
1
3
1
1
1
2
1
1
2
1
1
1
1
1
1
0
1
0
1
2
1
1
2
2
0
2
1
1
1
1
1
1
1
2
0
1
1
0
1
1
1
0
2
1
1
0
0
1
2
1
0
0
1
2
2
1
1
2
1
1
2
1
0
2
1
1
1
0
1
2
2
1
1
0
1
1
2
2
1
2
2
2
1
1
0
2
1
2
2
2
1
3
1
2
1
0
0
2
2
1
1
2
1
1
2
2
1
1
3
1
2
1
1
1
1
0
2
1
1
2
1
1
1
1
1
0
1
2
0
1
1
1
1
1
1
1
1
1
2
1
1
0
1
1
1
0
1
1
1
1
0
2
2
1
1
1
0
2
1
1
0
2
1
2
2
1
1
2
0
0
2
1
1
1
4
0
1
2
1
1
1
1
2
1
1
0
1
1
1
1
0
0
1
1
1
0
2
2
0
2
1
0
2
1
1
2
0
1
0
1
2
0
1
0
2
0
3
2
1
0
1
2
1
1
2
1
0
0
2
1
1
1
2
0
1
1
2
0
3
1
1
2
1
1
0
1
2
0
1
2
1
2
0
1
2
0
1
2
1
1
0
1
0
1
1
1
1
1
1
1
1
0
0
1
1
1
4
0
1
0
1
1
0
0
2
1
1
1
0
1
1
0
1
1
0
0
2
0
2
0
2
1
2
2
0
1
2
0
2
1
0
1
1
1
2
1
1
0
1
2
1
1
1
1
2
2
1
0
0
1
1
1
2
0
1
1
0
1
1
2
1
1
1
0
1
0
1
1
1
2
1
1
1
1
1
1
2
2
2
1
2
2
2
1
1
0
1
2
1
0
2
0
2
0
0
0
0
2
1
1
1
1
0
1
2
1
6
2
0
1
1
0
2
1
1
1
1
1
1
1
0
2
0
2
0
1
1
1
1
0
1
1
2
2
1
1
1
1
2
1
1
0
1
1
1
1
1
1
1
2
1
1
2
0
1
1
2
0
0
2
1
2
0
0
0
2
0
1
1
2
1
2
1
2
1
1
2
1
2
1
1
0
0
1
0
0
1
2
1
1
1
1
0
1
1
0
1
2
1
1
1
1
2
2
1
1
0
2
2
1
2
2
1
0
2
1
0
0
1
1
0
1
1
2
1
1
1
1
1
1
3
0
1
1
2
0
1
0
2
1
1
2
1
2
4
1
1
1
2
0
1
0
1
0
2
1
0
1
1
2
1
0
1
0
1
2
1
1
1
1
1
1
1
0
0
0
2
1
0
1
0
1
0
1
1
2
1
2
0
0
1
2
0
1
1
0
0
2
1
1
1
1
2
2
0
1
1
1
1
1
1
1
2
1
2
1
0
1
2
1
1
1
1
1
1
2
1
2
1
0
2
1
2
1
0
2
1
0
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
2
2
0
1
1
1
1
1
0
1
0
2
0
1
1
2
1
0
1
0
0
1
1
1
2
0
2
1
1
1
0
1
2
1
1
0
2
1
1
0
1
2
1
1
1
2
1
2
1
1
0
0
1
0
2
1
1
1
1
2
2
1
1
1
1
1
1
2
1
1
2
2
0
0
0
2
1
1
0
1
1
1
1
2
0
1
2
1
1
1
1
1
0
1
1
2
1
0
1
0
1
0
2
0
1
2
1
1
0
1
0
0
0
0
1
2
1
1
1
2
1
1
1
0
0
1
1
1
0
1
2
1
1
1
2
0
1
1
2
2
2
1
0
2
2
1
1
0
1
0
2
1
1
1
1
1
0
0
1
1
0
1
0
0
2
1
1
2
1
2
2
0
1
1
1
1
1
1
2
0
1
0
2
3
1
1
1
1
1
1
0
1
1
1
1
1
0
1
0
2
1
1
2
1
0
0
1
1
1
0
2
1
1
2
1
3
1
0
1
3
1
1
3
1
2
1
0
1
0
2
1
2
0
2
1
1
1
2
1
0
2
0
2
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
0
1
0
0
1
1
1
2
0
1
2
1
0
2
1
0
1
0
0
2
1
1
1
2
0
2
1
0
1
1
1
1
1
0
0
1
2
1
2
2
1
1
1
0
1
2
1
2
1
0
0
1
1
2
1
1
1
1
3
1
2
0
2
1
2
2
1
1
1
1
1
2
0
0
1
1
2
0
2
0
0
1
0
1
1
1
3
2
0
1
0
0
2
2
1
0
2
2
1
0
2
1
1
1
1
1
1
0
1
1
0
1
1
1
1
1
1
2
1
0
2
1
2
1
0
1
1
1
1
1
2
0
2
1
1
1
0
0
1
2
1
1
1
1
2
1
2
1
2
0
1
1
1
1
3
1
1
1
1
1
1
1
0
1
2
2
0
4
0
0
1
1
1
2
2
2
0
2
1
0
1
0
2
1
1
1
1
1
1
2
1
1
2
1
0
1
1
1
1
1
1
1
0
1
1
0
0
1
0
2
2
1
1
1
1
1
0
1
1
1
1
2
0
1
2
0
2
1
0
1
1
1
1
2
0
2
1
0
1
1
2
1
2
1
1
1
1
0
3
0
1
2
1
1
1
2
0
2
1
0
1
1
1
1
0
2
1
2
1
1
1
1
1
0
1
1
2
0
1
2
1
1
1
2
1
1
1
0
1
2
2
1
1
1
0
1
1
1
2
1
0
2
1
2
1
2
2
0
2
2
0
1
1
1
1
2
1
0
1
1
1
1
1
1
0
1
1
1
1
1
1
0
0
2
2
1
1
2
1
1
0
1
1
0
0
1
2
1
2
1
1
1
0
0
0
0
6
1
0
2
0
2
1
1
0
1
1
1
1
1
1
2
2
1
0
0
1
0
1
1
1
0
2
1
1
1
1
0
1
1
0
1
0
2
2
1
2
1
1
0
2
2
2
1
1
2
2
1
1
2
1
2
1
0
1
0
1
1
0
1
1
0
1
1
1
1
2
1
1
2
2
2
2
1
0
1
1
0
2
0
2
1
0
2
1
1
3
2
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
0
0
1
1
1
1
1
2
1
1
1
0
0
0
1
1
0
0
1
1
1
0
3
1
1
1
0
1
1
1
0
2
1
1
1
2
1
0
0
1
1
1
1
1
2
2
0
1
2
1
1
0
0
0
2
2
1
1
1
1
1
0
0
1
1
1
0
0
0
1
1
2
0
1
1
1
1
2
1
1
1
2
0
1
1
2
1
1
0
1
1
2
0
2
0
0
1
1
0
1
1
1
1
1
2
0
2
1
2
1
1
0
0
1
1
1
1
1
1
2
1
1
1
1
2
1
2
2
1
2
0
2
0
1
1
0
2
0
1
2
0
0
1
1
1
1
2
1
2
2
0
1
2
2
0
1
2
1
2
2
1
1
1
0
2
1
1
1
0
1
1
1
1
2
1
2
0
2
1
2
1
1
1
1
2
2
2
1
2
0
2
2
1
0
1
2
1
1
1
1
2
2
1
1
2
1
1
2
2
0
0
1
0
1
1
1
1
1
2
0
1
1
1
1
1
2
1
2
1
2
1
1
2
1
1
0
1
0
1
0
1
1
2
1
1
3
0
1
2
2
1
1
1
1
2
2
2
1
1
1
0
2
1
0
1
0
1
0
0
2
0
2
0
1
1
0
1
3
0
1
1
0
1
0
3
1
1
1
1
1
2
1
2
1
0
0
1
1
2
0
0
4
1
2
0
2
2
1
1
1
1
1
0
1
1
0
0
1
1
1
1
1
2
1
2
0
0
1
1
2
3
1
1
1
2
0
1
2
0
0
1
1
1
1
1
1
1
1
1
2
2
2
1
0
2
1
0
2
1
0
2
1
1
1
1
2
0
1
1
1
1
0
2
1
0
1
1
2
1
3
1
0
1
1
0
1
1
1
1
1
0
2
2
1
2
0
1
1
1
2
2
0
0
1
2
0
1
0
1
1
1
2
1
1
1
2
1
1
2
0
2
1
1
2
0
0
2
2
0
1
1
1
2
1
1
1
1
1
1
1
1
2
2
2
1
1
3
2
0
2
2
2
1
2
2
1
1
0
1
1
1
1
1
2
1
2
1
0
1
1
2
0
2
1
2
1
0
1
0
2
0
1
2
2
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
1
1
1
0
2
2
1
1
1
2
1
1
1
1
1
0
1
2
1
1
1
1
0
0
1
1
1
1
1
1
2
2
1
2
1
1
0
1
0
0
2
1
1
2
1
1
0
1
1
1
1
1
1
1
0
1
0
2
1
1
0
1
0
1
1
0
2
1
1
2
2
1
1
0
2
1
2
1
2
1
2
0
2
2
1
2
2
2
0
2
1
1
1
2
1
1
1
2
1
1
1
1
1
0
2
1
2
0
1
2
1
0
1
0
1
2
1
2
0
0
2
1
0
2
2
1
2
1
1
2
0
1
2
1
1
1
0
2
1
0
2
1
1
0
1
2
1
0
0
1
0
1
1
2
1
2
2
0
1
2
2
0
1
2
2
1
1
2
1
2
1
1
0
0
1
0
1
1
1
0
1
1
1
1
1
2
1
0
2
4
1
2
0
1
1
1
1
1
1
1
1
1
1
0
1
2
1
0
2
1
1
1
0
2
0
1
1
1
1
2
1
0
1
0
0
2
1
2
4
1
1
1
2
1
1
2
0
2
0
1
0
2
0
1
0
1
1
1
1
0
2
1
1
2
1
1
0
1
1
1
1
1
2
0
1
1
0
1
1
1
1
1
0
2
0
1
1
1
1
1
1
0
1
1
0
0
1
0
1
1
1
0
0
1
1
1
2
1
2
1
2
0
2
1
0
1
1
1
2
1
1
0
1
1
1
1
1
0
2
1
2
1
1
0
1
1
1
2
2
0
0
2
1
0
1
1
2
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
2
1
2
2
1
2
1
0
0
2
1
2
2
1
2
1
1
2
1
1
1
2
2
1
1
1
0
1
1
0
1
1
2
1
1
0
1
2
3
0
1
1
1
2
1
0
1
1
1
0
2
1
0
2
1
1
1
1
0
1
1
1
0
1
1
1
1
0
0
0
1
1
0
1
0
0
1
1
1
1
2
2
1
2
1
0
1
1
0
1
1
2
1
1
0
1
1
1
1
1
1
2
0
1
2
1
0
0
2
1
0
2
1
2
0
0
2
1
1
0
1
2
1
1
2
1
2
0
1
1
2
1
0
1
2
1
0
1
1
2
1
1
1
1
1
1
0
2
1
2
1
1
1
1
2
2
1
1
1
1
2
1
2
1
2
1
0
1
2
1
1
2
0
3
1
0
1
1
1
1
1
0
1
1
2
2
1
1
1
1
2
1
0
2
0
3
1
1
1
2
1
2
1
1
0
2
1
1
0
0
2
2
1
1
2
1
2
0
1
2
1
2
2
0
1
2
1
0
1
1
0
1
1
1
2
1
1
1
1
1
1
1
0
0
1
2
1
1
2
1
1
1
0
1
1
2
2
2
3
1
1
1
2
1
1
0
1
1
1
0
0
2
1
1
1
1
1
1
1
2
1
1
1
0
2
1
1
1
1
0
1
2
1
0
1
1
2
2
1
1
1
2
1
0
1
1
2
0
1
1
1
1
1
1
2
1
2
2
1
0
1
1
1
1
1
1
1
2
2
0
2
3
0
1
0
0
1
1
2
1
1
1
1
0
1
2
0
1
0
1
1
1
1
1
1
1
1
0
1
0
1
1
1
1
0
1
1
1
2
1
1
0
2
2
1
0
1
2
1
1
1
2
1
1
1
1
0
1
0
2
2
2
1
1
1
1
2
1
1
0
0
0
1
2
1
1
1
2
2
2
1
1
1
0
0
1
0
1
2
2
1
2
1
0
1
1
1
2
1
2
2
0
2
1
2
0
2
2
0
1
2
0
1
1
2
1
1
0
0
0
2
0
1
2
2
1
0
2
1
0
1
0
2
2
2
1
0
2
1
1
2
1
2
0
1
1
1
0
0
4
1
0
2
2
0
1
1
0
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
0
5
1
1
1
1
1
1
2
1
0
1
0
0
0
1
1
2
1
1
0
1
1
1
2
0
1
2
1
2
0
2
1
1
0
1
0
1
2
0
1
1
1
1
1
1
1
1
2
0
1
2
1
1
1
1
2
1
1
1
2
2
1
1
1
0
0
1
2
1
1
0
2
2
0
0
2
2
2
1
2
1
2
1
1
0
0
1
1
1
1
1
1
0
2
0
1
1
2
1
1
0
2
1
1
2
1
0
2
0
0
0
1
1
0
2
2
1
1
2
1
1
0
0
2
2
0
2
0
1
3
1
1
1
1
2
1
1
1
2
0
1
2
0
2
3
1
2
2
1
1
1
2
0
1
0
0
1
1
1
1
1
2
2
0
2
1
2
2
1
2
2
0
2
1
1
1
1
2
1
0
1
1
1
0
1
1
2
1
1
1
0
0
1
1
2
1
1
0
5
2
0
0
2
2
1
1
1
1
1
0
2
1
1
0
1
1
1
1
2
2
1
1
1
2
2
1
1
1
2
1
1
1
0
2
0
1
0
1
0
2
0
1
1
1
0
0
0
1
1
1
1
0
1
0
1
1
0
1
0
1
0
1
2
1
2
2
1
1
2
1
0
1
2
2
2
1
1
2
1
2
1
2
2
1
2
1
0
1
1
1
2
2
1
1
1
0
0
0
1
2
0
1
2
2
0
1
0
2
1
2
1
1
2
1
1
0
2
1
1
0
1
0
1
2
1
1
1
1
1
0
1
0
1
0
2
1
1
2
1
1
1
1
1
1
1
1
0
0
0
2
0
2
1
1
1
1
1
1
2
2
1
1
1
1
0
2
1
1
1
1
1
2
2
2
1
1
0
2
2
0
1
2
1
0
2
1
1
1
1
0
1
1
1
1
1
0
1
0
2
0
2
1
1
2
1
0
1
0
0
0
0
1
1
1
2
1
1
1
0
2
2
1
1
1
0
1
3
1
2
0
1
1
0
1
2
1
1
1
2
1
1
3
2
1
1
2
2
1
1
0
4
1
1
1
1
0
2
1
0
2
2
0
1
0
1
1
1
1
2
1
1
1
1
1
1
0
0
1
1
0
2
1
2
1
1
0
1
0
1
0
1
1
2
1
1
1
2
2
0
0
1
1
1
0
2
1
0
1
1
2
1
1
1
2
1
2
0
0
0
1
1
1
2
1
0
1
1
1
1
0
1
1
2
1
2
1
0
2
1
1
2
1
2
1
1
1
1
0
0
1
2
1
1
2
1
2
0
1
2
2
1
2
1
0
1
1
1
1
1
0
1
1
0
1
1
1
0
1
1
2
0
1
2
1
1
2
1
0
2
2
1
1
1
2
1
1
0
1
1
1
0
1
2
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
2
0
1
1
1
1
2
1
0
1
1
0
2
1
2
0
0
0
0
2
1
1
1
2
1
2
1
2
2
1
1
1
1
2
1
1
1
1
0
0
1
2
1
1
1
1
1
0
1
1
6
1
1
0
0
0
2
2
1
1
1
2
1
1
2
0
2
1
0
1
1
1
2
1
0
1
0
1
2
1
0
2
1
1
0
1
1
0
1
0
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
0
1
1
1
0
0
0
2
2
2
1
2
2
1
1
2
0
2
1
0
0
0
0
1
1
0
1
0
2
1
2
2
1
0
0
1
1
1
0
2
1
0
0
0
0
2
0
1
1
1
2
0
1
0
1
1
1
2
1
1
1
1
1
0
1
1
2
1
1
1
1
0
1
2
2
1
1
1
1
0
0
0
2
0
1
1
1
2
1
0
0
0
2
1
2
0
0
1
1
2
1
0
0
2
2
0
0
1
1
0
2
0
1
1
1
0
0
2
1
0
1
0
1
2
1
1
0
2
1
1
0
1
2
2
1
1
0
1
2
0
0
1
1
1
1
0
1
2
1
2
0
3
1
0
0
0
0
0
1
1
1
1
1
1
2
1
1
0
0
0
2
1
0
0
0
1
0
0
2
1
2
2
1
0
0
1
2
1
2
0
2
1
2
1
1
1
1
1
0
1
1
2
1
1
0
1
2
1
1
2
1
1
2
0
0
1
1
0
1
1
0
1
0
0
0
1
2
1
1
1
1
1
0
1
0
1
1
1
1
2
1
2
2
0
0
2
2
1
1
0
1
1
1
2
1
1
2
0
2
1
1
1
2
0
0
1
0
1
1
1
1
2
2
1
1
1
1
2
2
1
1
1
0
3
1
1
0
1
0
1
0
1
1
1
1
1
1
0
1
1
1
0
0
1
2
0
2
1
1
2
0
2
0
1
1
0
1
1
0
2
1
2
1
0
1
1
1
1
2
2
1
0
1
2
0
1
1
1
1
2
0
2
1
1
1
2
2
0
2
0
1
2
2
2
2
1
1
0
1
2
1
2
1
1
0
1
1
1
2
2
0
2
0
1
1
1
1
1
1
1
1
1
1
2
0
2
1
0
1
1
1
1
1
1
1
0
1
1
1
0
0
1
2
1
1
2
0
2
0
2
2
1
1
1
0
0
1
1
1
0
1
0
1
0
1
0
2
0
1
0
0
2
2
0
1
1
3
2
0
1
1
1
0
2
1
1
2
0
1
1
0
2
2
2
1
1
2
1
1
1
1
2
1
1
1
1
0
1
0
1
1
2
1
0
1
0
2
0
2
2
1
1
1
2
1
1
1
1
1
1
0
1
0
1
0
1
1
1
1
2
1
1
0
0
0
2
1
1
1
0
2
1
2
1
2
1
2
1
1
1
2
0
2
2
1
1
1
1
2
2
1
0
1
0
1
1
1
1
0
2
1
2
1
1
1
2
1
1
1
1
1
2
1
1
1
1
0
1
1
1
0
1
1
2
1
1
0
1
1
2
1
0
1
0
0
1
2
2
2
0
2
1
1
1
2
0
2
1
1
1
2
0
0
2
1
1
2
1
2
2
1
1
1
1
1
1
0
1
1
2
1
0
1
1
0
2
2
0
2
0
2
1
2
1
0
1
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
2
0
1
0
1
1
1
1
0
0
1
1
1
1
1
2
10
1
1
1
2
1
1
2
0
1
2
1
1
2
1
2
1
0
2
1
1
3
1
1
1
0
2
1
1
1
1
1
1
0
1
2
1
0
1
0
1
2
1
2
1
1
0
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
1
1
0
0
2
1
2
0
1
2
1
1
1
1
1
1
2
1
0
1
1
1
1
1
1
1
1
0
1
1
1
2
1
2
1
0
0
1
2
2
1
2
1
1
0
2
1
1
2
1
1
2
0
1
2
2
1
1
1
1
0
1
1
0
1
0
2
1
0
1
1
1
1
0
1
1
0
0
2
0
1
1
1
1
1
2
1
2
1
1
1
2
2
1
1
1
1
1
1
1
0
1
0
0
2
1
1
2
1
2
2
2
0
1
1
1
1
0
1
1
2
1
1
1
0
1
2
2
1
1
2
1
0
1
2
1
2
1
0
0
1
1
1
1
2
1
1
0
1
1
0
1
1
2
2
1
0
1
2
1
1
1
2
3
1
1
2
2
0
1
2
1
2
3
1
1
2
1
1
2
1
2
0
1
2
1
1
1
1
2
2
1
1
1
1
0
2
0
2
1
1
1
0
1
2
2
2
2
3
1
1
1
0
1
1
1
1
0
1
1
1
0
2
1
1
2
1
1
0
1
1
1
0
1
2
0
1
1
0
2
2
0
1
2
2
4
1
1
1
0
1
1
1
0
2
2
2
1
1
1
1
2
1
1
0
1
2
1
1
1
1
1
1
0
1
1
1
0
2
2
0
1
1
1
1
2
1
2
1
1
2
0
2
0
1
1
1
2
2
2
1
2
1
1
1
2
1
0
1
0
2
1
2
1
2
0
1
2
0
1
0
1
1
2
1
2
1
2
1
0
1
1
1
2
6
1
1
1
2
1
1
0
2
1
1
1
0
0
1
1
1
0
3
1
1
0
1
0
1
1
2
0
1
0
1
1
2
1
0
0
1
2
2
1
0
0
1
2
1
0
0
1
0
1
1
1
2
1
0
0
0
0
1
1
1
2
1
1
4
0
1
3
0
1
1
1
1
2
1
1
1
1
0
0
5
1
0
1
1
1
1
1
0
1
2
0
1
0
1
1
1
2
1
1
2
0
1
2
1
1
0
1
2
0
2
0
1
0
1
1
2
2
0
1
2
1
0
0
0
0
0
0
1
1
1
0
1
0
2
0
1
0
2
2
1
1
0
0
1
2
3
1
2
1
1
1
0
3
1
0
1
2
0
2
0
1
1
0
0
1
2
0
1
0
1
1
1
1
0
1
1
1
1
1
1
0
1
1
1
0
1
0
0
1
1
2
2
1
1
2
1
1
2
1
2
0
2
1
1
0
2
0
1
0
0
0
1
0
0
1
2
0
1
2
1
0
1
0
2
2
1
2
1
2
2
1
1
0
2
1
1
1
1
1
0
1
1
0
1
0
0
2
1
1
1
1
0
0
2
1
1
1
1
1
1
0
1
1
0
0
1
0
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
0
1
1
2
1
0
0
2
2
1
2
1
1
2
2
1
2
0
1
1
1
1
1
1
1
1
0
1
1
2
1
1
0
0
1
2
0
1
1
1
1
2
2
2
0
0
1
1
1
1
1
0
0
1
1
0
1
1
0
0
1
0
2
1
0
2
1
1
1
1
2
0
1
1
2
0
1
0
1
2
0
2
0
1
0
0
0
2
0
1
1
2
0
2
1
1
2
1
1
2
2
1
1
1
2
1
0
1
0
2
1
1
1
0
2
0
1
1
1
0
0
2
1
1
0
1
1
1
0
1
0
1
1
2
1
2
0
2
1
1
1
2
1
1
1
1
1
0
1
1
1
1
2
2
1
1
0
0
1
1
1
1
1
2
1
1
2
1
2
2
2
1
1
1
0
0
2
2
1
1
0
1
0
1
1
1
1
1
4
1
1
2
1
1
0
1
1
0
1
1
2
1
2
0
3
0
2
0
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
0
2
1
0
2
1
1
1
1
0
1
0
2
1
1
1
2
1
1
2
2
2
1
1
2
1
1
1
0
0
1
2
0
1
0
0
0
1
0
2
1
1
0
2
1
1
1
1
2
1
1
1
1
0
1
1
1
1
1
2
0
1
3
1
1
2
0
0
0
1
1
1
0
1
1
2
7
0
2
1
1
1
0
0
2
0
2
1
5
1
0
0
1
2
2
2
2
4
0
0
1
0
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
2
1
2
0
1
1
1
0
1
2
1
1
2
0
1
1
2
1
0
2
2
0
2
0
0
0
0
1
2
1
1
0
1
0
1
0
2
2
3
1
1
1
2
0
1
1
1
1
1
2
0
1
1
1
0
1
2
1
1
1
1
1
1
1
1
1
1
1
0
1
2
1
0
2
0
1
1
3
1
1
1
1
1
1
1
0
1
2
2
2
2
0
2
0
0
1
1
0
1
1
1
1
2
2
1
1
1
2
1
1
1
0
1
0
1
2
1
1
1
2
1
2
1
2
0
2
1
1
1
0
2
1
0
1
1
1
1
2
3
1
1
1
1
1
2
0
2
1
1
0
1
1
0
1
1
0
2
1
0
2
1
2
1
1
2
1
1
1
1
0
1
1
1
2
2
1
1
1
1
1
0
0
1
1
1
2
2
0
1
2
1
1
2
1
1
1
2
1
0
2
1
1
0
2
2
0
1
0
1
0
1
1
0
0
1
1
1
1
2
0
2
2
2
1
2
0
2
1
2
1
2
1
2
1
1
1
0
1
2
0
1
0
1
1
1
1
1
1
1
2
1
1
1
0
2
1
1
1
1
1
1
1
1
0
1
0
1
1
1
1
1
0
2
0
0
2
0
1
1
1
1
1
2
2
1
0
1
0
1
1
0
2
1
2
1
1
2
2
1
1
2
2
2
0
1
1
1
1
1
1
2
1
2
2
1
2
0
2
2
2
2
1
2
1
1
1
2
0
0
1
0
2
1
1
0
1
1
0
1
1
2
1
1
2
1
0
1
1
0
1
1
0
1
3
1
0
0
1
0
2
1
4
2
1
1
0
1
2
0
0
1
1
1
1
2
0
1
2
0
0
1
1
1
1
1
1
0
1
2
1
2
2
1
1
0
0
1
2
0
1
1
2
2
2
1
1
1
1
1
1
1
1
1
1
0
1
1
1
0
0
0
1
1
1
1
0
2
2
0
1
1
2
1
1
2
1
1
2
2
1
1
2
1
1
1
2
0
1
1
2
2
1
1
2
2
0
1
0
1
0
1
0
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
0
1
1
1
2
1
0
1
1
0
1
2
2
1
1
0
2
2
2
1
2
1
0
1
2
0
0
1
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
0
2
1
1
1
1
1
2
1
1
1
1
1
0
1
1
1
1
0
1
1
0
1
2
1
1
2
0
2
1
1
1
1
0
2
1
2
0
4
0
2
1
1
1
1
1
1
2
0
0
1
1
0
0
1
2
0
0
2
0
0
0
2
1
1
2
1
1
2
2
2
2
1
1
1
1
0
1
1
1
1
1
2
2
2
1
1
0
0
0
1
0
1
1
1
1
1
1
1
0
2
0
1
1
2
2
1
0
2
1
1
0
1
1
1
1
1
1
1
1
1
1
1
2
2
2
2
1
0
1
2
1
1
1
1
1
1
1
0
1
0
0
1
1
2
1
2
0
2
1
3
1
2
2
2
0
0
1
0
1
1
1
1
2
2
1
1
1
0
1
2
1
2
1
1
1
1
1
2
1
0
1
2
1
1
2
0
2
1
1
2
1
2
1
0
0
0
0
2
2
0
1
2
1
1
2
1
0
1
1
2
2
1
0
1
2
1
1
1
1
2
1
1
4
0
2
1
1
1
2
8
2
1
1
3
1
1
1
2
1
1
1
1
1
2
1
0
2
0
2
0
1
2
0
1
0
2
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
0
1
1
0
2
1
1
2
1
0
1
1
2
1
1
0
1
1
1
1
0
1
1
1
0
1
0
2
1
1
1
2
0
1
1
1
1
1
1
1
3
1
1
1
1
1
6
1
2
1
1
2
2
0
1
1
0
1
1
2
1
0
0
0
0
1
1
1
2
2
1
2
1
1
1
2
2
1
1
0
1
0
1
0
1
1
1
0
0
0
1
1
2
0
1
2
1
1
1
1
1
1
1
1
0
2
1
1
1
2
1
2
1
2
1
1
0
1
1
0
2
2
1
1
1
2
1
1
1
2
1
0
1
1
0
1
0
1
1
0
1
1
1
1
0
2
1
0
1
1
0
1
1
2
0
1
1
1
0
1
0
1
1
1
0
1
1
1
1
0
1
0
0
0
1
2
0
0
1
1
0
1
1
1
1
2
0
2
1
0
0
1
2
1
1
1
2
1
1
2
2
0
1
1
2
1
0
0
1
0
0
0
2
1
2
0
1
1
1
0
1
0
0
0
1
1
2
0
2
2
1
1
2
0
1
1
2
2
2
1
1
1
0
1
1
1
1
1
0
1
1
0
1
1
0
1
1
1
1
1
1
1
0
0
1
0
1
1
1
4
1
1
0
0
1
1
1
0
1
2
1
1
1
1
1
2
1
2
1
0
1
1
1
1
1
1
2
1
0
0
2
2
3
1
1
1
1
1
1
2
0
0
1
1
1
2
1
2
2
1
0
1
0
1
0
2
2
3
1
1
1
1
1
2
1
1
1
2
1
0
1
5
1
0
1
1
1
2
1
2
1
1
2
1
0
1
1
2
1
0
2
2
1
1
1
0
1
1
0
1
2
0
2
0
1
1
0
1
0
1
2
0
1
2
1
1
1
0
1
1
1
1
1
1
2
1
1
0
2
0
2
1
1
1
1
0
0
1
2
1
1
2
1
2
1
0
2
1
0
1
2
1
2
1
2
2
1
1
1
2
1
2
1
1
2
0
0
2
1
1
1
0
2
1
1
2
1
1
0
0
2
1
1
0
1
1
2
1
1
1
1
1
1
1
1
2
1
2
1
1
1
0
1
1
1
0
3
0
2
1
1
0
2
1
1
0
2
1
1
2
2
2
1
0
1
2
1
2
1
1
2
1
2
1
0
2
1
0
0
1
1
1
1
0
1
1
1
1
1
1
0
1
1
2
1
1
1
0
1
1
2
1
1
1
1
0
1
1
0
1
1
0
1
2
1
1
1
2
1
2
1
1
1
1
0
1
1
1
2
2
2
1
1
2
1
1
1
2
1
1
2
2
1
2
0
1
1
2
0
1
0
1
1
0
2
1
1
1
1
0
0
0
0
1
1
1
2
1
1
1
1
2
1
1
1
1
3
1
2
1
0
0
2
2
2
2
1
1
1
1
0
1
1
0
2
0
1
1
1
0
1
0
1
0
1
1
0
2
1
0
2
0
0
0
1
3
2
1
1
2
2
2
0
1
1
1
1
5
1
1
1
0
0
1
1
1
0
1
1
1
1
3
2
1
0
1
0
1
1
2
1
1
0
1
1
2
1
1
0
1
1
2
2
2
2
1
0
1
1
1
1
1
1
1
1
0
1
1
0
2
1
1
1
1
1
1
1
0
1
2
2
0
1
1
1
0
0
1
0
0
1
1
2
1
2
2
1
1
2
1
0
1
1
0
1
1
2
0
2
1
1
1
1
1
1
0
0
1
1
1
1
2
1
2
1
2
1
0
1
2
1
1
1
0
2
1
1
1
2
1
2
1
2
1
1
1
1
2
1
2
0
2
2
1
2
2
1
1
2
1
2
2
1
1
2
2
1
2
1
0
1
0
2
1
2
1
1
0
1
1
0
1
1
1
1
1
1
1
1
1
1
1
0
1
1
0
1
2
0
1
1
2
1
1
0
1
2
1
1
1
2
2
2
1
1
2
1
0
1
0
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
0
0
0
2
1
2
1
2
2
1
2
1
0
1
2
0
2
2
1
1
1
2
1
1
2
1
1
1
0
1
1
0
2
1
2
2
1
1
0
0
1
1
0
1
1
1
0
1
2
1
1
1
1
1
1
2
0
2
1
2
1
0
0
0
2
1
2
2
1
1
2
1
0
2
2
0
1
0
1
1
2
1
0
0
2
2
0
0
1
1
2
1
2
1
1
1
2
2
0
0
1
2
1
0
1
0
0
1
1
1
1
2
2
1
2
1
1
1
2
1
1
1
1
2
1
1
1
2
2
1
2
2
0
0
1
1
2
1
1
1
2
2
2
2
1
1
1
0
0
0
1
1
2
0
1
1
1
1
0
1
1
2
1
2
2
1
1
2
0
1
1
2
1
1
2
1
2
1
0
1
0
0
2
2
2
1
0
1
1
2
1
0
0
0
1
0
2
1
2
1
1
1
1
0
1
1
1
1
1
2
1
1
2
2
0
1
2
2
1
1
0
0
0
1
1
2
1
1
1
1
2
2
1
1
1
1
1
1
1
0
1
1
1
0
2
1
1
1
2
1
1
0
0
1
1
1
2
2
1
2
1
1
2
0
1
0
0
1
0
2
1
1
1
0
1
1
1
2
2
1
1
1
3
2
1
0
2
2
1
2
1
1
1
1
1
1
1
1
2
2
0
0
1
1
1
0
2
1
0
0
1
1
2
0
0
0
1
2
2
2
2
1
2
0
1
1
0
1
1
1
0
0
1
1
1
1
1
0
1
0
1
2
2
1
0
0
1
1
1
1
2
2
1
1
0
2
0
1
0
1
0
2
1
2
1
0
1
1
1
2
2
0
1
0
1
2
2
2
2
1
2
1
1
1
1
0
0
1
2
1
1
2
1
1
1
1
2
2
1
0
2
2
1
1
1
2
2
2
1
1
1
2
1
1
2
1
1
1
1
0
1
1
2
1
1
0
2
0
1
1
1
1
1
1
1
0
1
0
0
1
1
1
1
1
2
1
1
0
0
0
0
1
0
0
2
0
1
1
0
0
0
0
0
2
1
0
1
1
2
1
2
2
1
0
1
2
1
0
2
0
1
1
2
2
0
2
1
1
2
2
0
1
0
1
1
1
1
1
0
1
1
2
2
1
2
1
1
1
0
1
1
1
2
1
4
0
2
0
2
2
1
0
2
1
2
0
1
1
0
1
2
1
2
1
1
0
0
2
0
0
2
2
2
1
0
1
1
2
0
1
1
1
2
2
1
2
0
1
1
2
0
1
0
2
1
0
0
0
1
1
1
0
0
1
1
1
2
1
1
2
2
1
2
0
0
2
1
0
1
0
1
0
1
0
1
2
2
1
2
0
0
2
0
1
2
1
0
1
2
1
1
1
0
1
1
2
1
2
1
1
0
3
0
1
2
1
2
0
2
2
2
2
1
0
0
2
2
0
1
2
1
2
1
1
1
1
1
1
1
2
0
3
1
1
1
1
1
1
1
1
1
1
1
1
2
0
2
1
1
0
1
1
1
1
1
0
1
1
1
2
2
1
0
0
1
1
1
2
1
1
2
1
2
2
1
1
1
1
2
1
1
1
2
1
1
1
1
1
0
2
1
0
1
2
1
2
0
1
2
1
2
2
1
1
1
1
0
2
1
2
1
0
1
0
2
1
1
1
3
1
2
1
0
1
2
0
2
1
2
1
1
1
1
1
1
1
0
1
1
0
1
1
0
2
1
2
1
1
1
0
0
1
1
2
0
2
1
1
2
2
1
2
1
1
1
1
2
1
2
1
1
1
1
2
1
1
1
2
0
0
1
2
1
2
1
0
2
2
1
1
1
1
1
1
1
1
1
2
1
0
1
1
0
1
1
0
1
0
1
1
1
2
0
1
1
1
1
0
1
2
1
0
2
0
1
1
0
2
0
1
1
0
1
2
2
1
1
1
1
1
1
0
1
2
1
1
1
1
1
0
0
1
1
1
1
0
1
0
2
2
2
1
2
2
1
1
1
1
0
1
1
1
1
1
0
1
1
1
0
1
1
1
0
0
2
1
2
1
2
1
2
2
1
1
2
0
1
0
2
1
1
1
1
2
2
1
1
1
2
2
1
1
2
2
1
1
2
1
1
1
1
0
1
1
0
2
1
2
1
0
1
1
2
2
1
1
2
1
2
0
2
1
1
2
2
0
1
1
0
2
2
1
0
2
1
1
0
0
1
1
1
2
1
0
1
0
2
2
1
1
1
2
1
1
1
1
2
0
1
2
1
1
1
1
1
1
1
0
1
1
0
1
0
0
1
0
1
1
2
1
1
3
2
0
2
2
1
1
3
2
1
1
1
1
1
1
1
2
2
2
1
2
1
0
2
1
1
0
0
1
1
1
1
1
1
2
1
1
1
0
1
1
2
0
1
2
1
0
1
1
1
1
0
1
2
1
2
1
2
0
2
0
0
0
1
0
0
0
1
1
0
1
1
1
1
0
3
1
2
1
1
1
1
1
1
1
1
2
1
1
0
1
2
1
0
2
2
1
1
1
0
2
2
0
1
2
1
1
1
1
1
1
1
1
1
0
2
2
0
1
1
1
0
0
1
2
2
1
1
1
2
1
0
0
0
2
2
1
1
1
1
1
2
1
0
2
1
1
1
1
1
2
0
1
1
2
1
0
0
0
1
0
1
0
0
1
1
0
1
1
1
0
1
1
1
1
1
2
1
1
1
2
0
1
1
2
1
1
2
0
2
1
1
0
2
0
1
0
1
1
2
0
1
0
1
2
0
1
2
1
0
1
0
1
1
1
1
1
1
2
1
1
1
1
1
2
3
2
1
1
2
2
0
2
1
0
0
1
0
0
1
1
1
1
2
1
1
1
1
2
1
0
0
2
2
1
0
2
1
2
1
0
2
1
0
1
0
2
1
1
1
0
2
1
1
1
1
0
0
1
2
0
3
0
2
1
2
0
2
2
1
1
1
1
2
1
1
1
2
0
0
2
1
2
1
1
2
1
0
2
1
0
2
0
1
2
1
2
1
1
1
1
1
1
2
3
1
1
2
1
2
1
1
2
1
2
1
0
1
1
0
2
2
1
2
1
0
1
0
0
0
1
1
0
0
2
0
1
0
2
2
2
1
4
2
2
2
1
1
1
1
1
1
2
3
1
1
0
1
1
1
0
1
0
0
1
0
0
1
2
1
2
1
1
1
2
1
1
0
1
2
2
2
1
1
1
1
1
1
0
1
2
1
1
1
1
1
1
0
1
0
1
2
2
0
1
0
1
1
2
1
1
2
0
1
1
1
1
0
1
2
1
0
1
1
2
0
2
0
0
1
1
1
1
1
2
2
1
1
0
1
1
0
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
0
1
1
0
0
1
0
1
1
0
1
0
1
1
1
2
1
1
1
1
1
1
1
0
3
1
1
1
2
1
1
1
1
1
0
1
2
2
1
0
0
0
0
0
2
2
2
1
1
1
2
1
2
1
2
0
1
1
0
0
1
0
1
2
1
1
0
1
0
1
0
1
1
0
1
2
1
1
1
2
1
2
2
1
1
1
1
1
0
2
1
1
1
1
1
0
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
0
2
0
2
1
1
0
1
1
1
0
1
0
0
1
0
1
0
1
0
0
1
1
2
1
1
1
2
1
1
2
0
0
1
1
0
1
1
1
1
1
1
1
1
1
0
1
1
2
1
1
1
1
2
0
0
0
1
2
1
1
0
1
1
1
1
1
1
0
2
0
0
1
2
1
1
0
0
0
2
1
0
1
2
0
0
1
1
1
2
1
2
2
1
1
1
0
0
1
2
0
1
2
1
2
1
1
1
2
1
0
0
1
1
1
1
2
2
1
1
1
1
1
0
1
1
1
1
1
0
2
0
0
1
0
1
1
2
1
2
2
3
1
2
2
1
1
1
2
1
1
1
0
1
1
1
2
0
1
1
0
0
1
2
1
1
1
1
3
0
1
2
0
1
1
0
2
2
1
1
2
1
1
1
0
1
1
2
2
1
0
2
1
0
2
2
1
1
1
1
1
0
1
0
1
1
1
1
1
2
0
2
1
1
0
1
0
1
1
1
2
0
1
0
0
1
0
1
1
1
0
2
1
1
0
0
2
0
0
1
0
0
1
1
1
1
0
1
0
0
0
0
0
1
1
1
2
2
1
2
1
0
1
1
0
0
1
1
1
1
1
2
1
1
2
2
0
2
1
1
0
1
1
0
3
1
1
1
1
1
1
1
0
1
0
1
0
2
1
1
1
1
2
1
2
0
0
1
1
1
1
1
1
1
1
1
1
2
0
0
2
1
1
1
1
0
1
2
2
1
1
1
4
0
0
2
1
0
1
0
2
1
1
2
1
1
1
1
1
0
1
2
2
0
1
0
0
1
2
0
0
1
0
2
1
1
0
0
1
1
1
1
1
2
1
1
0
2
0
0
1
2
1
2
2
0
1
1
1
2
2
1
1
2
1
0
2
1
1
1
2
1
1
2
2
0
2
1
0
2
1
1
1
2
2
0
1
1
1
1
0
1
3
0
1
1
1
1
1
0
0
1
0
1
0
1
1
1
0
1
0
1
2
1
2
1
2
1
2
1
2
1
1
1
1
0
2
1
1
1
0
2
1
0
1
1
2
2
1
0
1
2
0
1
1
2
2
2
2
0
2
1
2
0
1
1
0
1
2
1
1
3
1
1
2
1
2
1
2
1
0
1
1
2
1
2
1
1
1
0
1
2
1
1
1
1
1
1
2
2
0
1
1
1
2
1
1
0
2
2
1
1
1
0
0
2
2
0
2
0
2
1
2
1
0
1
1
1
2
1
0
1
1
2
1
1
1
1
1
0
1
1
0
1
2
0
0
1
1
1
1
1
2
1
1
3
1
2
1
0
1
1
1
0
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
0
1
1
2
1
1
2
1
1
1
0
0
0
2
0
0
0
2
2
0
0
0
2
1
0
1
1
1
1
0
1
1
1
1
1
1
2
2
1
1
0
1
1
2
1
1
1
2
2
0
1
0
2
0
1
1
0
1
1
1
1
1
1
1
1
3
2
1
1
1
0
1
0
0
2
1
1
1
1
2
0
1
1
2
2
1
0
1
0
2
1
0
1
1
2
2
0
1
2
1
0
1
1
1
2
1
2
1
0
1
0
2
0
2
1
1
2
1
1
1
2
2
1
1
2
1
1
2
1
0
0
1
1
2
2
2
2
1
1
1
2
1
0
1
3
1
1
1
1
1
2
1
1
1
1
2
2
1
1
2
2
2
1
1
2
2
1
2
1
1
1
0
2
2
2
0
1
0
1
2
1
2
1
1
1
1
1
1
2
2
1
2
1
0
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
0
1
0
1
1
2
1
2
2
2
1
2
0
0
0
0
2
2
1
1
2
0
0
2
0
2
4
1
1
2
1
1
1
1
1
1
1
1
1
1
0
0
0
1
1
1
0
1
1
0
1
3
2
1
1
0
0
0
1
1
1
2
1
1
1
2
1
1
1
0
1
0
1
2
1
0
2
2
1
2
2
1
1
1
2
2
1
1
2
2
2
2
1
1
1
1
0
2
0
2
1
0
2
2
2
1
1
1
1
1
0
1
0
1
1
2
0
1
1
1
1
2
2
1
0
2
1
2
2
2
2
1
0
1
2
0
1
1
2
0
2
1
2
1
1
1
1
2
2
2
1
0
1
1
1
1
2
0
1
1
1
1
1
2
2
1
3
1
0
1
5
1
1
1
0
0
1
1
1
0
0
2
1
1
2
2
1
1
1
1
1
1
2
1
1
2
2
2
1
1
0
0
1
1
1
1
1
1
1
2
1
1
0
0
1
2
1
2
2
1
0
2
1
1
1
2
0
1
2
2
0
1
2
1
1
1
2
1
0
0
0
2
0
0
1
1
1
0
0
2
1
1
1
4
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
3
1
0
0
2
1
1
0
2
1
1
1
0
1
0
0
1
2
2
1
2
1
1
2
1
1
0
1
2
4
0
2
2
1
0
1
1
0
2
1
1
2
2
1
0
2
2
1
2
1
1
0
2
0
1
1
0
2
1
0
1
1
2
1
1
0
2
1
1
2
1
2
1
2
1
1
1
1
1
1
1
2
1
0
0
1
0
1
2
0
0
0
2
1
0
2
0
1
2
1
1
1
2
0
1
0
0
1
0
1
1
1
1
1
0
1
1
2
1
0
1
1
1
3
1
1
1
1
2
0
2
1
2
1
1
2
1
1
1
1
2
2
2
0
1
1
0
0
1
0
1
1
1
1
1
0
1
1
1
1
0
3
1
1
1
1
1
2
1
1
1
1
3
0
0
1
2
1
2
0
1
1
2
0
1
2
2
1
1
0
2
1
1
1
0
1
0
0
1
1
1
1
1
0
2
0
2
2
2
1
1
1
1
1
2
1
1
1
2
1
1
1
0
1
1
1
1
2
0
1
2
1
1
1
1
0
1
0
3
1
1
1
1
1
2
2
1
1
2
1
0
0
1
2
2
1
2
2
1
1
1
2
1
0
1
1
1
0
1
2
1
2
2
1
0
2
1
0
1
1
1
1
2
2
1
2
1
1
1
1
1
3
1
1
0
0
1
2
2
2
1
0
2
1
0
1
2
1
2
0
2
1
2
1
0
0
2
2
1
1
1
1
0
1
0
0
2
1
1
2
0
2
1
1
2
1
0
2
2
1
2
1
0
2
1
2
2
1
0
2
1
1
1
1
0
2
1
2
2
2
1
2
2
1
1
1
1
0
1
1
1
1
2
1
1
0
1
0
1
0
1
1
0
1
1
2
1
0
0
1
2
1
1
1
2
1
2
1
1
0
0
5
0
1
1
3
1
0
1
2
1
2
1
1
2
0
0
1
1
1
1
0
2
1
0
1
1
1
1
1
2
1
1
2
2
2
2
2
0
0
1
2
0
0
1
1
2
2
1
1
2
2
1
1
2
2
1
1
1
2
1
1
1
1
2
0
1
0
0
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
0
0
0
1
1
0
2
1
2
1
1
2
2
1
0
0
0
0
0
2
2
1
0
1
1
0
0
1
0
1
1
1
0
2
1
1
1
1
2
1
1
1
1
1
1
0
1
0
1
0
1
1
1
1
2
2
1
2
1
1
1
3
0
1
1
2
1
2
1
1
1
1
1
2
2
0
1
1
1
1
2
1
1
1
1
1
2
1
2
2
1
0
1
1
2
0
2
1
1
1
1
2
1
1
1
1
2
1
1
0
2
1
0
0
1
2
0
2
1
2
1
1
2
2
0
1
1
1
0
1
1
2
1
1
1
1
2
0
1
2
1
1
2
0
0
0
3
2
0
2
0
2
2
0
1
2
1
1
2
1
0
1
1
1
2
1
1
0
2
0
2
0
1
1
2
1
1
0
1
0
0
0
1
1
2
0
1
0
0
2
1
2
1
0
0
1
1
1
3
0
1
1
1
2
0
2
1
2
0
2
0
0
1
1
0
2
1
2
0
1
1
1
1
1
0
0
1
2
0
0
2
1
1
1
1
2
0
1
2
2
1
2
1
0
1
2
1
2
1
0
0
0
2
1
2
0
1
2
0
1
2
0
1
1
4
1
1
2
2
1
0
0
1
2
1
1
1
0
1
2
0
1
1
0
1
1
1
0
1
1
0
1
2
1
1
1
1
1
0
1
1
1
1
0
2
0
1
1
3
1
1
1
2
2
1
0
1
1
1
1
0
1
1
1
2
2
1
1
1
1
1
0
2
1
1
1
2
1
1
1
0
1
1
2
0
0
1
0
0
1
2
0
1
0
1
0
2
1
2
2
1
1
2
1
1
1
2
0
1
3
1
0
1
1
0
1
1
1
1
0
1
1
1
2
1
1
1
2
2
2
1
1
2
0
1
2
1
1
0
0
1
1
1
2
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
2
1
1
1
1
1
0
2
2
1
2
1
0
1
2
0
1
1
0
1
1
0
2
1
2
1
1
3
1
1
2
2
1
1
0
0
1
0
0
0
2
0
1
2
1
1
2
1
2
1
1
0
1
1
1
1
1
2
2
1
2
0
1
1
1
2
0
1
1
1
2
1
1
2
1
1
1
2
1
1
1
2
1
0
0
1
0
1
1
1
0
2
1
1
1
2
1
1
2
2
2
1
0
2
0
2
2
0
3
2
1
1
0
0
1
0
1
1
2
2
1
1
1
1
1
2
2
1
1
2
1
1
0
1
2
2
1
2
0
2
0
4
1
2
1
2
2
1
1
0
1
2
1
0
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
2
2
1
1
0
2
0
2
0
1
1
2
1
1
1
1
1
1
1
0
0
2
1
1
1
1
0
2
2
1
2
1
1
2
1
0
0
0
1
1
2
1
2
2
1
1
1
0
1
1
0
2
1
1
2
2
1
2
0
0
0
0
0
1
0
1
0
1
2
0
0
1
2
0
1
0
0
1
2
0
0
1
0
1
1
0
1
1
1
2
0
1
1
0
2
1
2
1
2
2
1
1
2
0
1
0
0
0
1
2
0
1
1
1
1
1
1
1
1
0
1
0
1
1
1
1
1
1
1
1
2
0
2
1
0
0
1
1
1
0
2
2
0
1
0
1
1
1
2
1
1
1
2
2
1
2
1
0
1
1
1
2
2
1
1
0
1
1
2
1
1
1
1
2
1
1
0
1
2
2
1
0
1
2
2
1
2
2
1
1
2
2
2
0
2
2
1
1
2
1
1
0
1
1
1
1
1
1
2
1
0
1
0
1
2
0
1
2
2
1
1
1
1
1
1
0
1
1
1
1
0
1
1
2
1
0
1
1
0
1
0
2
1
0
1
1
1
1
1
0
2
1
2
1
1
1
1
2
0
1
1
2
1
2
0
0
1
0
0
2
2
1
1
1
0
1
2
1
1
2
0
0
0
0
0
2
2
0
0
2
0
2
1
0
1
1
1
1
1
0
1
1
1
1
1
0
1
1
1
1
1
1
2
0
1
2
1
1
1
1
0
1
0
1
1
1
0
0
1
1
1
2
1
2
1
1
2
0
1
1
1
2
2
1
1
1
0
1
0
1
2
1
2
2
2
1
2
2
1
1
0
0
2
1
1
2
2
1
2
1
1
1
2
1
2
1
0
1
1
1
1
1
1
1
1
1
1
0
2
0
0
1
1
0
1
2
0
1
1
1
1
2
1
1
0
1
2
1
0
2
1
2
2
1
1
0
1
0
0
0
1
1
1
2
1
2
1
1
0
1
1
0
0
1
0
3
1
1
2
1
1
0
0
1
0
1
0
2
0
0
1
1
1
2
3
2
1
1
1
1
0
1
0
1
1
2
1
1
0
1
1
1
1
0
2
2
0
1
1
1
1
1
2
1
2
0
2
1
1
1
1
0
1
1
1
1
0
0
2
2
1
0
1
1
1
2
1
1
1
1
1
1
0
1
0
1
2
1
1
1
1
0
1
0
2
0
1
0
1
1
1
1
2
1
1
1
1
2
1
1
1
0
2
2
1
0
1
1
1
1
1
1
1
2
2
1
2
2
1
1
1
1
0
1
2
0
2
1
0
0
1
1
1
1
1
0
2
0
2
0
0
2
1
1
0
1
0
0
1
1
1
1
2
2
1
1
1
0
2
1
0
1
2
1
1
2
1
1
0
1
1
1
1
1
1
0
1
2
0
2
1
1
1
1
2
1
0
1
1
1
1
0
2
0
1
1
1
0
1
0
1
0
1
2
1
0
1
2
1
1
0
2
1
0
0
0
1
1
1
1
1
1
1
0
1
2
1
2
1
1
1
1
1
1
1
2
1
2
2
2
2
1
2
2
1
0
1
0
1
1
1
1
1
0
1
0
1
0
1
2
2
2
2
0
1
1
0
0
2
1
0
0
2
1
0
1
2
1
0
1
2
1
1
1
2
1
0
1
0
0
1
1
0
1
2
2
1
1
0
0
2
1
1
1
0
1
1
2
2
1
1
1
0
1
2
1
0
1
1
2
1
0
2
1
0
2
2
2
1
1
1
1
0
1
1
2
1
1
1
1
1
0
1
1
1
2
1
1
1
2
1
1
0
1
2
0
0
0
2
1
2
1
2
2
1
2
1
1
2
1
1
1
0
0
1
1
1
0
1
0
1
2
2
0
1
0
1
0
0
2
0
2
3
1
1
2
0
1
0
0
0
1
2
1
2
2
2
1
1
0
0
1
1
1
1
0
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
0
1
0
1
1
1
1
2
1
1
1
1
0
1
1
0
1
1
1
2
1
2
2
2
2
1
1
1
1
2
1
2
2
1
2
1
1
1
2
0
2
0
0
2
2
2
1
0
1
1
1
2
1
3
0
2
1
1
1
2
0
2
2
1
1
1
2
2
0
1
1
0
2
1
0
1
2
1
1
1
2
0
2
2
1
1
1
1
1
1
0
0
1
1
2
1
1
1
0
2
0
1
1
1
1
1
0
0
1
1
1
0
0
2
1
1
1
1
1
1
1
3
1
0
2
1
1
2
0
1
1
2
0
1
1
1
0
0
1
2
0
1
1
1
0
1
2
1
3
2
2
1
1
1
1
1
2
1
0
1
0
2
1
1
0
0
1
1
0
1
0
1
1
1
1
2
1
1
2
1
1
0
1
1
1
2
1
1
1
2
2
1
0
2
0
2
1
1
1
2
0
2
1
2
1
1
1
1
2
1
1
2
1
0
1
0
0
2
1
0
1
1
1
0
1
1
0
1
2
2
1
1
0
0
1
1
2
2
1
1
1
2
1
2
1
1
1
1
1
1
0
2
1
1
1
1
1
0
0
1
0
1
2
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
2
0
1
0
1
2
2
1
1
1
2
1
1
0
2
0
1
1
1
2
2
2
2
0
1
2
0
1
1
2
0
1
1
3
0
1
0
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
1
0
2
1
0
0
2
1
1
1
0
0
2
2
2
1
1
1
2
0
1
2
1
1
1
1
1
1
1
1
1
0
2
1
0
0
2
2
1
2
0
2
1
2
2
1
2
1
2
1
0
1
1
2
1
0
1
0
1
1
1
0
0
1
0
2
1
1
1
0
1
2
0
1
0
2
1
2
0
0
2
1
2
1
1
1
2
1
1
1
2
1
1
2
2
1
1
2
1
1
1
1
1
1
0
1
2
1
1
2
1
1
1
0
1
1
1
1
1
1
1
1
1
0
2
1
1
1
2
1
1
0
1
2
2
1
0
1
1
1
1
1
2
1
0
0
1
2
0
1
1
1
0
2
0
1
1
1
0
1
2
1
2
2
1
2
0
1
1
2
0
0
0
1
1
2
0
1
1
1
1
2
0
1
1
2
2
2
1
0
1
2
0
1
0
1
0
1
0
1
1
2
1
2
2
2
2
1
1
0
2
0
2
1
1
2
1
1
1
1
0
1
2
0
1
0
1
0
1
0
0
2
1
0
2
1
2
2
1
1
1
1
1
1
1
0
2
0
1
1
1
1
2
1
1
1
1
1
1
0
1
2
0
0
2
1
1
1
1
1
0
1
1
0
0
1
1
0
2
1
1
1
0
2
0
2
0
1
0
2
1
1
2
1
1
1
2
0
1
1
1
1
0
2
1
2
1
5
1
1
2
1
1
1
1
0
0
2
1
0
2
2
1
0
0
1
1
1
0
0
1
2
1
2
1
1
1
0
2
0
1
1
1
1
1
0
1
0
0
0
1
1
3
0
1
2
2
1
2
1
1
2
1
0
1
1
0
2
2
1
2
1
0
1
0
1
1
2
0
1
1
1
0
0
1
1
0
1
0
2
1
1
1
1
1
1
2
2
2
1
1
1
2
1
1
1
1
0
1
2
1
2
1
0
2
1
1
1
2
1
1
0
1
1
1
1
1
1
1
1
1
2
1
1
2
0
2
1
0
0
0
1
2
1
0
0
1
1
1
2
1
2
0
1
2
1
1
0
1
1
1
2
2
1
2
0
2
1
1
2
1
1
1
0
1
1
1
2
1
1
1
0
1
1
1
1
0
1
1
1
1
2
0
1
1
1
0
2
2
1
1
1
1
1
1
1
0
1
1
1
0
0
2
1
2
1
1
1
1
2
1
1
1
0
1
0
0
2
0
1
1
2
1
1
1
2
1
1
1
0
2
0
1
1
1
1
0
2
0
2
1
0
1
1
1
1
0
1
1
2
0
1
1
1
2
1
1
1
1
1
4
1
2
1
1
1
2
2
0
0
1
1
1
1
0
2
2
1
0
2
0
0
2
1
0
1
1
2
2
2
0
1
2
1
0
1
1
3
1
1
1
0
2
2
1
0
1
0
1
0
1
1
2
1
1
1
2
1
1
2
1
1
1
1
0
1
0
1
0
1
2
2
2
1
2
0
2
0
1
2
0
1
1
1
2
1
1
1
0
2
0
1
1
2
0
0
2
2
2
1
1
1
1
2
1
0
1
2
0
2
1
1
2
1
1
1
0
1
1
2
1
1
2
5
1
1
1
0
1
1
1
4
1
2
1
1
3
1
1
0
2
2
2
1
1
1
2
2
2
0
1
2
2
1
2
2
1
1
0
0
1
1
1
1
2
1
1
1
1
0
0
0
1
2
0
1
2
1
1
1
1
0
1
1
2
1
2
1
1
1
1
0
1
1
1
0
1
2
2
1
1
2
1
1
2
0
1
2
3
2
0
1
0
2
0
2
0
1
1
0
0
1
2
1
1
1
1
1
1
0
0
2
2
1
1
0
0
1
2
3
2
2
1
0
2
1
1
2
1
0
1
1
1
1
1
1
2
1
0
1
1
1
1
2
0
0
0
1
1
2
1
1
1
2
2
0
1
1
1
0
0
1
2
1
1
1
0
2
1
1
0
1
0
1
1
0
0
1
0
1
2
2
2
1
1
1
1
2
0
0
2
1
0
0
2
1
1
2
1
1
1
1
1
1
0
2
1
1
1
2
0
0
1
0
1
1
1
2
1
2
0
1
2
1
2
1
1
1
2
2
0
1
1
0
2
2
1
1
1
2
0
1
2
1
1
2
1
1
1
1
1
0
1
1
1
1
0
3
2
2
0
2
1
1
0
1
1
1
1
1
3
1
1
0
1
2
0
1
1
0
1
0
0
2
1
2
2
1
2
0
0
1
1
1
1
1
1
2
0
1
2
0
1
0
1
1
1
1
1
2
1
1
2
1
1
1
0
1
1
2
1
2
1
0
1
2
0
0
1
2
1
2
1
1
1
1
2
1
2
2
2
1
2
1
0
4
2
2
1
1
2
1
0
1
1
1
2
1
1
0
1
1
2
1
2
0
2
1
1
0
0
0
2
0
1
1
1
1
1
2
0
2
1
1
1
1
2
1
1
1
1
2
1
0
2
1
2
1
1
2
1
2
1
1
2
2
0
0
2
2
2
1
1
1
1
2
1
1
2
1
1
2
2
1
1
0
1
1
1
2
1
2
1
0
1
1
2
1
2
2
1
1
1
1
1
0
0
1
1
1
2
1
1
2
1
1
0
1
1
0
1
1
1
0
1
2
1
2
1
2
0
2
2
1
1
2
1
1
1
1
1
2
2
2
0
0
1
2
1
1
2
0
1
2
1
1
1
0
0
1
2
0
0
1
1
0
1
1
1
1
1
1
1
1
2
1
2
1
1
0
2
0
1
1
2
1
1
0
0
0
1
0
1
1
0
1
4
1
1
1
1
1
1
0
3
1
0
0
2
2
2
0
2
1
2
0
1
1
1
1
1
1
0
1
2
1
0
2
0
2
1
1
1
2
1
2
0
1
1
5
1
1
1
0
0
0
1
1
1
1
2
1
3
0
1
2
2
1
2
1
2
0
1
1
2
1
2
0
1
2
0
1
1
2
1
2
1
1
0
2
1
2
0
0
1
0
2
1
2
1
1
0
0
0
0
1
1
0
1
1
0
2
1
2
1
0
0
1
1
1
1
1
1
1
1
0
2
3
2
1
1
0
1
1
1
2
1
1
0
2
1
1
1
0
1
0
2
1
1
2
1
0
1
0
0
1
1
1
1
2
1
2
2
2
1
1
1
1
1
1
0
2
1
1
1
1
2
2
0
0
2
1
0
0
0
2
1
0
0
0
1
1
1
0
0
2
0
0
1
2
2
2
1
0
1
1
1
0
1
2
2
2
2
1
0
2
1
0
0
1
1
2
1
2
2
2
1
0
1
0
0
0
0
1
2
1
0
2
1
0
2
2
0
1
2
0
2
1
1
0
0
0
1
1
1
1
2
1
1
0
1
1
1
0
0
0
1
2
1
1
0
1
1
1
0
2
0
0
1
1
2
1
2
1
1
2
0
0
1
2
1
2
0
1
0
0
1
1
1
1
1
0
2
2
3
0
0
1
2
1
0
1
1
1
2
1
1
0
1
0
1
0
2
2
1
1
1
1
1
1
1
1
2
1
2
1
1
0
2
1
2
1
1
1
2
1
0
0
1
0
1
1
1
2
0
0
2
1
2
2
1
2
0
1
2
1
0
2
1
2
2
1
0
1
1
1
1
0
0
0
2
1
1
1
1
0
0
0
1
1
1
2
4
2
1
1
1
0
1
0
0
1
1
2
1
1
2
2
1
2
1
0
0
0
1
2
1
1
1
1
1
1
1
2
2
1
1
1
1
0
0
1
0
1
2
2
1
0
1
1
0
1
0
1
1
2
1
1
2
2
0
0
1
1
0
2
1
2
1
1
0
0
2
0
1
0
1
2
1
1
2
2
2
3
2
0
0
1
2
1
0
1
1
1
1
0
1
2
2
1
2
2
2
1
0
1
1
1
1
1
1
0
1
1
1
1
1
1
2
2
2
1
1
0
2
1
1
1
1
0
2
1
0
0
1
1
1
1
1
1
0
2
1
0
1
0
1
2
1
1
1
0
1
1
1
1
0
1
1
0
0
1
1
1
1
2
0
0
0
1
1
1
1
2
3
2
1
3
2
1
2
1
0
1
1
1
1
1
1
2
0
1
2
3
0
0
1
0
1
1
1
1
2
0
1
0
1
0
0
0
2
1
1
1
1
0
2
0
1
2
0
1
2
1
1
1
2
0
2
2
1
2
1
2
1
1
1
0
1
1
0
2
1
1
2
2
2
1
1
1
2
3
2
0
1
2
1
1
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
2
2
1
2
1
2
1
1
1
1
1
1
1
0
1
2
1
1
2
0
0
2
0
1
1
1
2
1
0
2
1
0
1
2
1
1
1
0
1
0
1
1
2
1
0
0
1
2
2
1
1
2
1
0
2
0
1
0
1
3
1
0
1
0
1
1
0
0
2
1
0
1
1
1
0
1
1
2
1
1
0
1
1
1
1
5
0
1
2
1
2
1
2
2
1
2
2
0
1
2
2
2
0
1
1
1
0
1
1
2
1
1
2
0
0
4
2
1
0
1
1
1
1
2
1
2
1
1
1
1
2
1
2
1
2
2
2
0
1
0
1
1
1
0
1
1
1
0
3
1
2
2
0
2
0
1
0
0
0
1
2
1
0
2
1
1
2
1
2
2
1
1
0
2
1
1
1
0
1
1
2
1
1
1
2
1
0
0
0
2
1
1
1
1
1
2
1
1
1
3
0
1
3
1
2
1
1
1
1
0
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
0
2
2
1
1
0
1
0
1
1
2
1
2
0
0
0
1
1
0
2
1
1
1
1
0
1
1
1
1
2
0
2
1
2
1
1
2
1
0
0
2
1
2
0
1
0
1
0
2
1
1
2
1
1
2
1
1
1
2
0
1
0
1
1
2
1
1
2
1
0
1
1
1
2
1
2
2
0
1
1
1
2
1
0
1
0
1
2
1
1
1
2
2
2
1
0
1
1
1
1
2
1
1
1
1
0
2
1
1
0
0
1
1
1
0
0
1
1
1
2
1
1
1
2
1
0
1
1
2
1
0
1
1
1
0
1
0
0
0
1
1
1
0
1
1
1
1
2
1
1
1
2
0
0
0
1
1
2
1
2
0
2
0
0
2
1
1
1
1
0
1
1
2
1
2
1
1
2
0
1
2
0
0
1
1
0
2
1
1
1
1
1
2
2
2
1
1
1
1
1
1
13
2
1
0
1
0
1
0
1
0
1
2
1
0
1
2
1
0
2
1
2
1
1
0
2
1
2
1
0
1
2
0
3
2
0
1
2
0
0
1
0
0
2
1
1
1
1
1
0
1
1
1
0
1
1
2
1
1
1
1
1
1
1
1
1
2
1
2
1
3
1
0
1
1
0
1
2
1
1
2
1
1
2
0
1
2
1
1
0
1
1
1
1
1
1
0
1
1
1
0
1
1
1
2
1
1
0
1
1
1
1
1
1
1
0
1
1
0
1
1
1
2
1
2
1
1
1
1
0
1
1
1
1
1
0
1
1
1
0
1
0
0
1
2
1
1
2
2
2
0
2
1
1
1
1
0
2
1
2
1
1
1
0
1
1
2
0
0
1
1
1
0
1
1
1
1
1
1
1
2
1
0
2
1
1
2
1
0
2
1
2
1
1
0
1
1
1
0
1
1
1
0
0
0
1
1
1
1
2
0
1
1
1
1
2
1
1
1
1
2
1
1
0
1
1
0
1
1
2
1
2
0
2
1
0
1
1
0
1
1
1
1
1
1
1
1
2
0
1
1
2
0
2
0
0
0
1
0
1
0
0
2
2
1
2
2
0
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
2
1
1
2
1
2
2
0
1
2
2
1
0
1
1
2
1
2
1
0
1
0
1
0
1
1
1
0
0
1
1
1
2
1
1
1
1
2
2
1
1
1
0
1
2
0
1
3
1
1
1
0
1
2
1
2
2
0
1
0
1
2
1
0
2
0
1
0
1
1
0
1
1
1
1
0
1
1
1
0
2
0
2
1
1
1
2
0
1
2
1
2
1
2
2
1
0
2
2
0
2
2
0
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
2
1
0
1
1
1
0
2
2
1
1
2
1
2
2
2
1
0
1
1
2
2
0
2
0
0
1
1
1
2
1
1
1
2
2
2
2
1
1
0
1
1
1
2
1
1
1
1
1
2
2
2
0
2
0
0
2
1
2
0
1
0
1
1
1
2
1
0
1
1
0
2
1
0
1
1
1
1
1
1
1
2
1
2
1
1
1
1
0
2
1
1
1
2
1
2
0
1
1
1
1
1
2
2
1
1
1
1
1
0
1
0
1
2
1
1
1
1
2
1
1
1
1
2
2
2
0
0
0
1
1
0
2
1
1
2
1
2
0
1
0
0
2
2
1
1
1
1
1
1
0
0
2
1
1
1
0
0
0
1
1
0
1
2
1
2
0
1
0
1
2
2
2
1
2
1
1
2
0
2
1
2
1
1
2
1
1
1
1
3
2
1
1
2
0
1
0
1
2
0
2
1
1
1
2
1
1
1
1
1
1
2
2
1
1
2
1
1
1
1
1
0
1
2
1
2
1
1
1
1
1
1
1
2
1
0
0
1
0
1
1
2
2
0
1
2
2
1
1
2
1
1
1
1
1
2
2
0
0
1
0
1
0
1
1
1
2
1
1
1
2
1
1
0
0
1
1
0
2
1
1
1
1
0
4
1
1
0
1
2
1
0
0
1
1
5
0
2
1
0
1
1
2
1
1
1
2
1
1
1
1
1
1
0
2
0
2
1
1
1
0
1
1
1
1
2
1
1
2
2
1
1
2
0
0
1
1
1
3
1
1
2
0
4
1
1
0
2
2
1
1
2
1
2
2
0
2
1
1
1
2
1
0
1
2
2
2
1
0
1
1
2
0
2
2
1
1
0
2
1
1
1
1
2
2
1
0
2
1
0
2
1
1
0
0
1
2
2
1
1
1
0
0
1
1
1
0
1
1
1
1
1
1
2
2
0
0
1
1
2
1
1
1
0
1
1
0
0
0
1
2
1
1
2
1
0
1
0
2
1
0
2
1
1
1
0
1
0
1
1
1
1
1
0
1
1
1
1
1
1
2
2
2
2
0
1
0
1
0
1
1
2
1
0
1
1
2
1
1
3
1
2
1
1
0
1
0
1
2
1
1
1
1
2
1
1
1
1
1
1
1
0
0
0
1
0
1
1
0
1
0
3
1
0
1
2
1
1
1
0
2
1
1
1
1
2
1
0
2
1
2
1
1
0
1
1
0
2
1
2
1
0
0
1
1
1
0
2
1
2
1
0
1
2
1
0
1
1
1
1
0
1
1
0
1
1
0
0
2
0
1
1
1
0
1
1
1
1
1
1
1
2
1
1
1
1
0
1
1
2
1
2
1
0
2
0
1
1
1
0
1
0
1
0
0
1
2
2
2
1
2
1
1
1
2
0
1
2
2
2
0
2
0
0
1
1
1
1
2
2
0
1
0
1
1
1
2
2
2
1
1
0
1
2
0
2
1
2
1
1
1
1
1
0
0
1
2
2
1
1
1
1
1
1
1
2
1
2
1
1
2
1
2
0
2
0
2
0
2
1
0
3
2
2
1
0
1
1
0
1
1
1
0
2
1
1
1
1
0
1
2
1
1
2
1
0
0
2
1
0
1
0
2
2
1
2
0
1
0
0
2
1
2
1
1
2
1
1
1
0
1
0
1
2
1
1
1
2
1
1
1
1
2
1
0
2
1
2
2
1
1
1
1
1
1
1
1
2
1
2
0
1
0
0
0
1
2
0
1
0
0
1
2
2
2
2
0
0
1
2
0
1
2
1
1
1
2
2
1
1
1
0
1
2
0
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
0
1
0
0
1
1
2
2
1
1
1
0
1
1
1
2
0
1
1
1
1
1
2
1
1
1
1
2
1
2
2
2
1
1
0
1
2
2
1
1
2
1
1
0
1
2
1
1
1
2
0
1
2
1
1
0
0
1
2
2
0
4
2
2
0
0
1
1
1
1
1
2
1
1
1
1
2
1
1
0
1
1
2
1
1
4
1
0
1
0
1
1
0
0
1
0
0
1
2
2
1
1
1
2
1
1
0
1
0
1
1
1
1
1
1
0
2
0
1
0
0
1
1
1
1
1
0
1
0
2
0
1
1
0
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
0
1
1
0
0
2
1
1
1
1
0
1
2
0
1
2
2
1
2
1
2
0
2
1
1
0
1
2
1
1
1
1
1
1
1
1
1
1
1
1
0
0
0
3
1
1
2
1
2
1
1
2
0
2
1
0
1
0
1
1
1
0
1
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
0
2
2
1
1
1
1
2
1
1
0
1
0
0
1
0
1
1
2
2
1
2
0
2
0
1
0
0
1
1
2
1
0
1
1
2
0
1
2
0
1
2
1
1
2
2
0
1
0
1
1
0
1
1
1
2
1
0
1
1
1
2
2
1
1
0
2
1
1
1
0
1
2
3
0
1
1
0
2
1
0
1
0
0
1
1
1
2
1
2
1
1
3
0
0
0
3
1
2
2
2
1
0
2
1
0
1
2
1
2
1
0
2
1
1
1
0
1
0
2
1
2
0
2
2
1
2
1
1
1
1
2
1
2
0
0
3
2
2
1
1
2
1
1
1
1
2
1
1
2
1
1
1
3
2
1
1
0
1
1
2
1
1
1
0
2
1
2
0
1
0
1
1
1
2
1
2
0
1
1
1
1
1
2
1
1
2
1
2
1
1
2
1
0
2
1
0
1
0
1
2
0
0
1
1
1
1
0
1
1
1
1
0
1
1
1
8
2
1
1
1
1
2
1
1
1
0
1
0
1
0
0
7
2
2
1
2
1
0
1
2
1
2
0
1
1
0
1
1
1
1
2
0
1
1
1
0
1
1
1
1
1
2
1
2
1
1
0
0
1
0
1
0
2
2
2
1
1
2
1
0
1
1
2
2
2
1
1
0
1
1
1
0
0
1
1
1
2
1
0
1
1
1
1
1
0
1
1
0
1
1
0
1
1
2
0
1
1
2
1
2
1
2
2
1
0
2
1
1
2
1
1
0
1
1
0
2
1
2
1
1
1
0
2
1
1
1
2
1
2
3
1
0
1
1
1
1
1
0
1
1
0
0
2
0
1
1
1
0
2
2
1
2
2
1
1
1
1
2
1
1
0
1
1
0
1
1
1
1
0
1
0
0
1
1
1
1
1
1
1
0
0
1
1
2
0
1
1
2
1
1
0
0
1
1
1
1
2
0
1
1
1
1
0
0
1
1
1
1
0
0
1
1
1
0
1
0
2
1
2
0
1
2
1
1
1
0
1
1
2
1
1
1
1
1
0
1
1
2
1
1
1
1
1
1
2
2
0
1
1
0
2
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
2
1
0
1
2
0
2
0
1
1
1
2
1
2
1
0
2
0
1
0
2
1
2
1
0
1
1
0
1
1
0
0
0
0
1
2
1
1
2
2
1
1
1
2
0
2
1
1
1
2
1
0
1
1
1
1
0
2
2
0
0
2
1
0
2
1
2
1
2
2
1
2
1
2
1
1
1
2
1
1
2
1
1
2
1
1
2
1
2
2
0
0
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
0
0
0
2
2
1
2
1
1
1
1
1
1
1
2
0
2
0
2
1
2
1
1
1
1
0
1
1
1
1
1
0
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
0
0
2
2
1
1
0
1
1
1
0
1
1
1
1
1
3
1
1
1
0
1
0
1
1
1
1
0
1
2
1
1
0
1
2
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
0
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
0
0
0
0
1
2
1
1
1
0
0
1
0
2
2
0
1
0
2
1
0
2
0
0
1
1
2
2
1
0
1
0
2
1
0
0
2
1
2
1
0
1
0
2
1
1
0
2
2
0
1
2
2
2
0
1
1
0
2
1
2
2
1
1
1
0
4
1
1
1
1
1
2
2
2
1
1
2
1
1
1
1
1
2
1
2
1
1
1
2
1
0
1
1
1
1
0
1
1
0
1
1
1
1
1
2
0
1
1
0
1
1
2
1
1
2
1
1
0
2
1
1
1
1
1
1
0
1
2
1
1
1
3
1
2
1
1
1
0
1
1
2
3
2
0
1
0
1
1
1
2
2
0
1
2
2
1
2
2
1
1
0
1
1
0
1
1
2
1
1
1
1
1
0
1
1
2
1
1
1
1
0
2
2
0
1
1
2
0
2
1
0
2
2
0
1
2
0
2
0
2
2
1
0
0
1
0
1
2
1
2
1
0
0
1
2
0
1
1
0
1
1
1
1
2
1
1
2
0
2
1
1
0
1
0
1
2
1
1
1
1
1
1
2
1
1
0
1
1
2
1
2
0
0
1
1
1
1
1
1
1
1
2
0
0
2
1
1
1
1
1
1
1
0
0
2
1
1
1
1
2
1
1
1
2
1
0
1
1
0
1
1
1
1
2
2
1
1
1
0
1
1
0
1
2
0
1
1
1
0
0
1
1
2
1
0
0
0
0
1
0
2
1
1
1
2
0
1
1
1
0
1
0
2
1
2
1
1
4
1
1
1
0
2
0
1
2
1
0
0
0
3
1
0
1
1
2
0
1
1
2
2
0
2
1
1
1
1
1
0
1
1
2
1
1
1
1
0
1
1
1
2
1
0
1
2
1
1
2
1
0
0
1
0
0
1
1
1
1
2
1
1
2
0
1
1
0
1
0
0
1
0
2
2
1
1
1
1
0
0
1
1
1
2
2
2
1
2
1
1
0
0
0
0
0
1
0
1
1
1
1
2
0
1
1
1
0
2
1
2
2
0
0
1
1
1
0
2
1
1
1
1
2
1
1
1
1
2
0
0
0
1
0
1
2
0
3
1
2
1
1
2
1
2
2
1
1
1
0
1
3
1
1
2
1
2
1
0
1
1
1
2
0
0
1
2
0
0
0
0
1
1
1
1
2
1
2
1
1
2
2
1
1
1
1
1
1
1
0
2
1
1
1
1
1
1
0
0
2
6
1
1
2
1
1
2
0
1
1
1
1
0
1
0
1
1
0
1
2
1
1
0
1
2
0
1
1
2
1
2
2
1
0
1
1
1
2
1
1
1
0
0
2
2
1
1
2
1
2
2
1
2
0
0
2
2
1
1
1
1
1
0
1
1
0
1
1
1
1
0
1
1
1
0
1
0
1
1
1
1
1
1
1
1
2
1
1
0
1
1
1
1
1
1
0
2
1
1
2
2
1
2
0
1
1
0
0
2
1
1
1
2
1
1
0
1
1
2
1
2
2
1
1
1
1
1
0
2
1
1
2
1
1
1
1
1
1
2
1
0
1
1
2
1
0
0
0
1
1
1
1
1
1
1
2
3
1
2
1
1
1
1
2
1
2
1
0
2
1
1
2
0
1
2
1
1
1
1
1
1
1
2
0
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
0
1
0
1
0
1
2
1
2
1
0
2
1
0
2
1
0
1
1
1
1
2
0
0
2
1
2
2
2
0
1
1
0
2
1
1
2
1
1
2
1
2
2
1
1
1
0
0
2
0
2
1
1
1
2
1
2
0
1
1
1
0
2
0
0
2
2
0
1
1
2
1
1
0
0
1
0
2
2
1
2
0
2
1
0
2
1
1
0
1
0
2
1
2
1
2
1
1
0
1
0
1
1
2
1
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
0
1
1
0
1
1
1
1
1
1
0
0
2
0
0
1
2
1
2
1
1
1
2
0
1
1
2
1
2
1
2
1
1
2
1
0
2
1
1
0
1
2
1
1
1
0
1
1
1
2
2
1
1
1
1
0
2
0
1
0
1
0
0
1
1
1
0
1
2
1
1
1
1
1
1
2
1
1
0
2
0
2
1
2
1
1
1
1
1
2
1
0
1
1
2
2
1
2
1
2
1
1
1
0
1
2
2
2
0
1
1
1
2
0
1
2
1
0
1
0
1
2
0
2
0
1
1
0
0
2
0
1
1
1
1
0
2
1
0
1
2
1
2
2
2
1
1
1
1
0
0
1
2
1
0
1
2
2
1
2
2
2
2
1
1
1
1
1
1
1
0
0
1
1
2
0
1
1
1
1
2
1
1
7
1
1
2
0
0
0
1
2
1
2
0
1
0
0
1
1
2
1
0
0
1
1
1
1
1
2
1
1
3
1
0
0
1
2
1
1
2
1
0
2
0
1
2
1
1
2
1
1
1
1
1
0
1
1
1
1
2
1
1
1
2
1
0
2
0
2
1
2
1
1
1
0
1
1
1
1
2
1
0
1
1
1
1
1
1
1
1
2
2
0
0
0
1
1
2
0
1
2
1
0
1
1
1
1
0
0
2
1
1
1
1
0
0
1
0
1
1
1
2
0
1
1
1
1
2
2
0
0
0
1
1
1
1
2
1
2
1
1
1
1
1
1
2
1
3
1
2
0
2
1
2
3
1
0
0
5
0
2
1
1
1
1
2
3
2
1
1
0
1
2
0
3
1
2
1
2
1
2
2
1
2
2
1
1
1
1
1
2
1
0
2
0
0
0
1
0
1
0
1
0
2
2
1
1
0
0
1
1
0
0
0
0
1
1
1
1
1
2
1
1
1
1
2
0
1
1
1
1
1
1
2
1
1
0
0
1
0
1
0
2
1
1
1
2
0
2
1
0
1
2
1
1
1
1
1
0
2
0
1
2
2
1
2
2
1
0
2
1
0
1
1
1
0
2
2
0
1
1
2
1
1
1
1
1
1
0
2
2
1
1
2
0
2
0
1
1
1
1
1
2
2
1
1
1
1
1
0
1
0
0
1
1
0
1
1
1
0
0
1
1
1
1
0
1
1
1
2
0
2
1
1
1
2
1
1
1
1
1
2
1
2
1
0
2
0
2
1
2
2
1
1
1
1
1
0
1
1
0
2
0
0
1
2
2
0
1
1
2
1
2
0
1
4
1
1
2
2
2
1
2
0
1
2
1
2
1
1
1
2
2
2
2
2
1
1
2
0
1
0
0
1
1
0
2
1
1
2
1
1
0
1
0
2
1
0
1
0
1
1
2
1
1
1
2
1
1
0
1
1
0
2
1
0
1
2
1
1
2
1
1
1
1
0
2
1
0
0
0
1
1
1
0
0
1
1
2
3
0
2
2
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
2
2
1
0
1
1
1
2
1
1
1
1
0
2
2
1
2
2
2
1
1
1
0
2
1
1
0
1
1
1
1
1
1
1
2
0
1
0
2
0
1
1
1
1
1
1
1
2
1
0
1
0
1
1
1
1
2
0
0
1
1
1
0
1
1
1
1
1
2
2
1
3
1
2
0
0
2
1
2
1
0
1
1
1
1
1
2
1
2
1
1
1
0
1
2
1
1
1
1
0
1
1
0
1
1
1
1
1
1
3
2
1
1
0
2
1
0
2
1
2
1
1
1
2
2
1
1
2
2
1
2
1
0
2
2
1
1
1
2
0
1
2
1
1
1
2
1
1
2
1
2
2
1
1
1
2
2
2
1
2
1
1
0
0
1
1
1
1
1
0
1
1
1
1
1
0
1
2
0
1
2
0
1
1
1
1
1
0
1
2
1
2
1
1
0
1
1
2
1
1
1
1
1
1
0
1
0
2
1
1
0
1
2
1
1
0
1
1
2
1
2
1
0
1
1
1
0
2
1
1
1
0
1
0
1
1
0
2
1
1
2
0
1
1
0
1
1
2
1
1
0
2
1
2
2
1
0
1
0
2
1
1
1
1
1
0
2
1
1
1
1
1
1
0
0
1
1
1
1
2
2
1
2
1
2
2
1
2
1
1
2
1
0
1
0
1
2
2
1
3
1
0
2
1
2
0
1
1
1
2
1
1
1
0
1
1
1
0
1
1
2
1
2
1
0
2
1
1
0
1
1
1
1
1
1
0
1
1
1
1
2
1
2
2
0
1
1
2
2
1
0
2
1
1
0
1
1
1
0
1
1
1
1
1
0
2
0
1
2
1
1
0
1
1
2
2
1
1
1
0
2
1
1
0
0
1
1
0
1
1
1
0
1
1
0
0
1
1
1
2
1
1
0
1
1
0
1
1
0
1
1
1
1
1
1
0
2
1
0
2
2
1
1
1
2
0
2
1
0
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
0
0
1
1
0
1
0
1
0
2
0
1
1
2
1
1
1
0
1
1
2
1
3
0
0
2
2
1
2
0
1
1
0
0
1
1
0
1
0
2
2
0
1
2
1
0
1
1
1
1
0
2
1
0
1
2
1
2
0
1
1
2
2
0
2
2
1
1
1
1
2
1
1
2
2
2
0
1
3
1
1
1
2
1
2
0
1
2
2
0
2
1
2
1
1
0
0
1
1
1
1
1
2
0
4
3
2
1
0
1
2
1
1
0
2
1
1
2
1
2
1
1
1
1
0
1
1
2
0
0
1
0
1
1
1
1
1
1
1
1
2
1
1
1
1
1
0
1
1
1
0
0
2
1
2
1
1
2
2
0
1
1
0
1
2
1
1
2
2
0
0
1
1
1
1
1
3
1
2
1
2
2
1
1
1
1
1
1
0
1
2
2
1
2
1
2
1
2
0
0
1
1
2
1
1
2
1
1
1
0
1
1
2
1
0
1
2
2
1
1
1
1
1
2
2
1
0
2
0
1
1
1
2
1
2
1
1
1
2
1
1
1
0
2
2
1
1
1
0
1
2
1
0
1
2
2
0
1
0
0
1
1
1
1
1
1
2
1
2
0
2
1
1
1
0
0
0
1
0
2
1
2
2
0
2
1
1
1
1
0
0
1
1
3
0
0
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
0
1
2
0
0
1
1
1
0
1
1
2
1
1
1
1
1
1
0
0
1
1
1
1
0
1
0
1
1
1
2
1
2
1
0
1
1
1
3
0
1
0
0
1
2
1
2
0
1
1
0
1
1
2
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
0
2
1
1
2
1
1
0
1
2
1
1
1
1
1
1
1
0
1
1
1
0
1
0
2
0
2
2
1
1
1
2
0
1
0
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
0
1
1
1
2
0
1
1
0
1
0
2
1
0
0
0
2
2
0
1
0
2
2
1
1
0
1
1
0
1
0
0
2
1
0
2
1
1
2
0
1
2
1
2
2
2
1
0
1
2
2
2
1
1
1
2
0
2
0
0
2
1
1
2
2
1
0
1
1
0
1
0
0
0
1
0
1
0
1
1
0
0
1
0
1
0
2
0
2
0
2
0
1
2
0
1
2
1
1
1
0
1
1
1
1
1
2
1
1
2
1
1
1
0
1
1
2
0
0
0
0
1
0
0
0
1
1
2
1
1
1
0
1
1
1
1
0
1
1
1
1
1
2
2
1
1
1
1
2
1
1
2
0
1
1
1
2
2
1
2
0
0
1
1
3
1
2
1
0
0
2
1
1
2
1
1
1
2
1
2
1
1
0
1
2
2
2
0
1
2
2
0
1
0
1
1
1
1
1
1
0
1
1
1
2
1
1
0
1
1
0
2
0
1
1
0
0
2
1
2
1
1
1
2
0
2
1
1
1
3
0
1
1
1
2
1
0
1
1
1
0
2
0
0
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
0
1
2
2
1
1
0
0
1
1
1
0
1
2
0
2
1
1
1
1
2
1
1
2
2
1
2
0
0
0
1
1
0
2
1
1
2
1
1
0
2
1
1
1
1
2
2
1
0
2
0
0
1
1
2
2
1
2
1
2
1
1
1
1
0
1
2
2
1
1
0
2
1
2
2
0
2
0
2
2
1
1
2
0
1
2
2
1
1
2
1
1
1
1
1
0
1
1
1
2
2
2
1
1
1
0
1
1
2
1
1
1
2
2
0
1
1
0
2
1
1
0
0
1
2
0
2
1
2
1
1
0
1
0
1
1
2
1
2
2
0
0
1
1
0
2
1
1
1
2
1
0
1
0
1
0
1
0
0
1
1
1
1
1
1
0
2
2
0
2
1
1
1
1
1
1
0
0
1
0
1
2
0
1
0
1
1
0
1
1
1
1
1
2
1
1
1
0
2
0
1
0
0
0
2
1
0
1
2
0
1
1
2
2
2
1
2
1
2
1
0
1
1
0
2
2
1
2
0
1
1
1
2
0
1
1
1
1
1
0
1
2
1
1
2
0
2
0
2
1
1
0
1
2
1
1
0
2
1
2
2
2
0
1
1
1
1
4
2
1
2
1
1
1
2
1
1
1
0
1
1
0
1
0
2
2
0
1
2
2
1
0
2
2
2
1
0
1
2
2
1
1
0
1
0
0
2
1
1
2
0
1
1
2
1
1
0
2
2
2
2
1
2
2
2
2
1
1
1
1
1
2
1
1
1
1
0
1
1
2
1
2
0
1
1
1
1
1
0
0
1
1
1
0
0
2
2
1
0
1
1
1
1
1
0
0
0
0
0
1
0
0
1
2
1
2
1
1
1
1
1
0
2
1
2
1
1
2
0
1
0
1
1
2
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
2
0
0
1
1
0
0
2
1
1
1
1
0
1
0
2
0
1
2
0
2
1
2
0
1
2
2
1
2
2
1
0
1
1
2
1
0
1
1
1
2
2
1
0
0
1
1
1
1
2
0
1
0
1
0
1
2
0
2
1
1
2
1
1
0
2
1
2
0
1
1
2
1
0
1
1
1
1
0
1
1
1
3
1
1
2
1
2
1
1
2
1
1
1
2
1
2
1
1
1
1
0
0
1
0
0
0
1
1
1
1
0
0
1
2
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
1
0
1
2
1
2
1
0
1
1
0
1
1
0
1
0
1
2
2
2
1
1
0
1
0
2
1
1
1
1
0
0
1
0
2
1
1
2
1
1
1
2
2
2
0
2
1
1
1
1
0
1
2
2
1
1
1
2
1
1
1
1
1
1
0
0
0
1
0
1
1
1
2
1
1
1
2
1
0
1
1
1
1
1
2
2
1
1
1
0
1
0
1
1
1
1
1
1
1
1
1
2
1
1
0
1
0
0
2
0
2
2
1
1
2
1
1
1
2
2
2
1
2
1
0
2
0
2
1
0
0
2
0
0
0
2
1
1
0
2
2
1
2
1
1
0
1
1
1
1
1
2
1
2
1
1
1
2
1
2
1
1
1
2
2
1
2
1
1
0
1
1
1
1
1
1
2
1
1
1
1
2
0
1
1
1
2
1
1
2
0
1
1
0
2
1
1
1
0
0
1
2
0
2
1
1
1
1
1
1
0
0
1
0
1
1
0
1
1
1
1
1
1
0
2
1
1
1
1
1
0
2
1
1
1
2
1
2
1
1
7
1
0
0
1
1
1
2
1
1
0
2
1
2
0
0
2
1
0
2
2
1
1
2
1
2
1
0
0
1
1
2
1
1
2
1
0
1
1
1
1
0
1
2
1
1
1
1
1
2
1
0
1
1
1
2
1
2
1
1
1
1
1
2
0
1
2
2
0
2
0
0
1
1
1
1
1
0
0
2
2
1
2
1
1
1
0
1
1
1
1
0
2
1
0
0
2
1
3
1
0
1
2
1
0
0
1
3
2
1
1
0
2
2
0
1
2
1
1
1
1
1
2
1
1
1
1
0
2
0
1
1
1
2
1
2
0
1
2
1
1
1
1
1
2
1
0
1
1
1
1
0
2
1
1
1
1
2
1
0
1
1
2
0
0
0
1
1
0
1
0
0
1
2
1
1
1
1
1
1
1
2
0
1
2
2
1
1
0
1
1
1
1
0
1
0
2
2
1
1
1
1
1
0
1
2
2
0
2
2
2
3
1
0
1
0
2
0
1
0
0
0
1
0
1
1
1
0
1
1
1
1
2
1
1
0
1
0
2
1
0
0
1
1
1
1
1
1
0
1
0
1
1
2
0
0
1
1
0
2
1
1
2
2
2
2
2
2
2
0
1
2
2
1
0
0
1
0
1
1
1
2
1
4
0
1
0
0
1
1
0
1
1
1
1
2
1
0
1
2
1
2
3
1
2
1
0
2
1
2
1
0
2
1
1
1
1
2
1
0
0
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
0
2
1
1
0
0
1
2
1
2
1
2
1
1
1
3
1
1
2
0
0
1
1
1
2
0
0
1
1
2
1
1
1
0
1
1
1
1
1
1
1
1
0
1
1
1
2
0
2
1
1
1
1
2
1
2
1
1
0
1
2
2
1
1
2
2
1
1
2
1
1
1
0
2
1
2
0
1
1
2
1
0
1
1
1
1
1
2
1
2
0
0
2
0
1
2
1
1
1
0
0
1
2
2
0
0
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
0
1
0
1
1
1
1
1
0
1
0
1
0
1
2
0
2
1
1
2
2
1
1
2
1
0
1
0
1
1
1
1
1
1
1
1
3
2
2
1
1
0
0
1
2
1
2
1
1
1
1
0
0
1
1
1
2
2
3
1
1
3
1
2
2
1
1
1
1
0
2
1
0
0
2
1
1
2
2
2
1
1
1
2
2
1
1
2
1
0
1
1
0
1
2
1
1
1
2
2
2
0
1
2
1
1
1
1
0
1
1
1
1
2
0
1
1
0
1
1
1
1
1
1
1
1
1
2
2
2
0
3
1
1
1
1
2
0
2
1
1
2
2
0
1
1
0
1
1
1
1
0
1
2
1
2
0
2
2
0
1
1
1
1
1
1
2
2
0
1
2
2
1
1
0
1
0
1
1
1
1
0
0
2
1
2
1
1
0
1
1
1
2
1
0
1
0
2
1
0
1
1
2
0
1
1
1
2
1
1
0
1
1
4
0
2
1
0
2
1
1
1
1
2
1
2
2
0
1
2
1
1
2
2
2
1
1
1
2
2
1
1
2
1
0
1
1
2
1
2
0
0
1
3
1
0
2
1
1
1
1
2
1
1
1
0
2
2
1
0
0
2
2
2
1
0
2
2
1
1
1
0
2
1
1
1
0
1
0
1
2
0
1
0
2
1
1
2
0
0
1
1
1
1
2
2
2
1
1
1
2
1
1
2
0
1
1
0
1
1
2
1
1
2
1
1
1
3
2
1
2
1
1
1
1
0
0
2
1
2
2
1
1
1
2
1
1
1
1
2
3
1
1
2
1
1
2
1
0
2
1
1
1
1
1
1
2
4
1
0
1
0
1
1
2
1
1
1
1
2
0
1
1
1
2
1
0
0
0
2
2
1
1
2
1
1
1
2
2
2
0
1
1
1
0
1
1
1
1
1
1
1
1
1
0
1
1
0
1
1
0
1
0
0
1
2
1
1
2
1
1
1
2
1
0
1
1
1
1
3
1
1
2
2
1
2
1
1
2
2
0
1
0
0
2
1
1
0
1
0
1
1
0
0
0
1
2
2
1
1
2
0
1
1
0
0
1
0
0
1
0
2
0
0
1
1
1
3
1
1
0
1
1
0
2
1
1
2
1
2
1
1
0
0
1
1
1
1
1
1
1
1
2
1
0
1
1
1
1
0
1
1
1
1
1
1
3
1
1
0
2
1
0
1
2
1
1
1
1
1
1
1
2
1
1
1
2
1
0
1
2
0
0
0
1
1
0
1
1
2
1
2
0
1
1
2
1
1
3
1
2
2
1
1
1
2
2
2
0
1
1
1
1
1
1
1
0
0
0
1
1
2
1
2
2
0
0
2
0
1
1
2
1
0
1
1
1
2
2
2
0
2
1
1
1
1
1
1
0
2
1
0
1
1
2
1
1
1
2
1
1
1
1
1
0
1
1
1
2
1
2
0
1
1
1
2
2
1
2
1
2
1
1
2
1
2
0
1
1
1
1
1
1
0
2
1
1
2
1
1
0
1
1
1
1
0
1
1
0
1
2
0
1
1
1
0
2
2
1
0
1
1
1
1
1
1
1
0
1
1
1
1
1
0
1
1
2
1
1
1
0
2
1
1
1
2
1
1
1
0
1
2
1
1
1
1
0
2
1
1
1
1
1
1
0
1
2
0
2
1
0
0
1
1
2
1
2
1
1
1
1
1
1
0
1
2
1
1
2
1
2
3
0
0
1
0
0
0
2
1
0
1
1
2
0
1
1
2
0
1
2
1
1
1
1
1
1
2
1
1
1
2
1
2
1
2
1
1
1
3
2
2
1
1
0
1
0
1
2
1
1
0
1
1
1
2
0
1
2
2
1
1
1
0
2
0
1
1
1
1
2
0
0
2
1
2
1
2
0
1
0
2
1
1
0
1
0
1
1
1
2
1
1
0
1
1
0
1
1
1
1
0
1
1
1
5
1
2
1
1
1
1
0
1
0
3
2
2
8
1
2
1
0
1
2
1
0
1
1
1
0
2
1
2
0
0
1
1
1
1
1
0
1
2
2
0
1
0
0
0
1
1
1
0
1
1
2
0
0
1
1
1
1
0
1
2
1
1
1
1
0
1
2
1
2
0
1
2
1
0
0
1
1
1
2
1
1
1
1
1
0
1
2
1
2
1
1
0
3
1
1
1
2
2
1
1
1
0
1
1
1
1
1
1
1
1
0
2
0
1
1
2
1
1
0
1
0
1
1
1
0
0
1
1
2
0
2
1
0
1
2
2
2
1
1
1
0
0
1
1
2
0
0
1
0
0
1
2
2
1
1
1
1
1
1
1
0
1
0
1
0
1
1
1
1
1
1
1
1
2
1
2
0
0
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
0
2
2
1
4
2
2
1
0
1
0
2
0
1
1
2
1
2
2
2
1
1
1
0
2
2
1
2
1
1
0
0
1
1
1
1
2
2
1
1
1
1
1
1
1
2
2
0
1
2
1
2
2
1
2
2
1
1
0
0
1
1
2
1
2
2
0
0
1
1
1
1
1
1
2
2
1
1
1
0
0
1
2
2
1
2
0
1
0
1
1
0
1
0
1
2
2
0
1
1
5
0
1
1
1
0
0
2
1
1
1
1
1
1
1
2
2
1
1
1
1
3
1
2
1
1
1
1
1
2
1
2
1
1
0
1
1
1
1
0
1
0
0
2
1
0
2
6
2
1
2
0
1
1
1
1
1
1
1
1
1
0
0
1
1
1
2
0
1
1
1
1
1
2
1
0
1
1
1
0
2
2
0
0
0
1
2
0
1
1
1
1
2
1
2
1
0
1
1
1
1
1
1
0
2
1
0
0
2
2
1
3
0
0
1
1
1
1
2
2
2
1
0
2
0
0
1
1
1
2
1
2
0
1
1
1
1
1
0
1
0
1
2
1
1
0
2
1
1
1
1
1
0
1
1
2
2
2
1
0
1
1
0
1
2
1
1
1
2
0
2
1
1
0
1
2
1
1
1
1
1
2
0
2
2
1
1
1
1
1
1
1
2
0
1
1
2
1
1
1
0
1
1
1
1
2
1
0
1
1
1
1
2
1
1
1
0
2
1
2
1
1
1
1
1
1
1
2
0
0
1
1
1
2
1
1
0
2
1
1
1
1
1
2
1
0
1
0
1
0
1
1
1
0
1
2
1
1
0
2
1
1
1
1
1
1
1
2
0
1
0
1
2
0
1
1
1
1
0
1
0
0
1
1
1
2
1
1
1
0
1
2
1
1
2
0
1
0
0
1
1
1
0
2
0
2
2
1
1
1
1
0
1
1
1
1
1
0
1
0
2
2
0
1
1
1
2
0
0
2
1
1
2
0
0
2
1
2
2
1
1
1
1
1
2
1
1
2
2
0
1
1
0
2
1
0
1
0
0
1
2
1
1
3
2
0
1
1
1
0
1
0
2
1
1
1
1
1
1
1
1
1
2
1
0
1
1
1
1
2
1
1
1
1
1
3
1
1
2
1
0
1
0
2
2
1
1
2
1
0
1
1
3
1
2
0
2
2
1
1
0
3
1
1
3
1
1
1
0
1
2
1
2
1
1
0
1
3
1
0
1
0
1
1
1
1
1
0
2
1
1
1
1
1
1
1
2
1
1
0
2
0
1
0
2
1
2
0
1
2
0
1
1
1
1
2
1
2
10
1
1
1
2
0
3
2
1
1
0
1
1
0
1
1
2
1
1
5
1
1
1
1
4
1
2
1
1
1
2
1
1
3
1
2
2
2
1
1
1
1
2
1
0
2
1
2
0
0
2
1
0
1
1
1
1
2
1
2
2
2
1
1
1
1
1
1
0
1
1
1
0
1
0
1
2
0
1
1
1
1
1
0
0
0
1
1
1
2
0
1
1
1
0
1
1
1
2
1
2
2
2
1
1
2
0
1
1
1
1
14
1
0
0
2
0
1
0
1
1
1
1
1
1
2
1
1
2
1
0
2
2
0
2
0
2
1
1
2
1
1
0
1
2
2
2
0
1
1
0
1
0
3
0
1
1
1
1
2
1
2
1
1
0
0
1
1
2
1
0
2
2
1
2
1
2
0
1
1
2
0
0
1
1
0
1
1
0
1
2
0
1
0
1
2
0
0
2
1
0
1
2
1
1
1
2
1
1
1
1
1
1
1
0
2
2
0
2
1
1
0
2
1
0
0
1
0
1
1
2
1
2
1
1
2
0
2
1
2
0
2
2
1
1
1
0
0
0
1
1
1
2
1
2
1
0
1
1
0
1
1
2
2
1
1
1
0
2
1
1
0
1
0
0
2
2
1
0
2
1
1
0
1
2
1
0
0
1
1
2
0
1
2
1
1
1
2
0
2
2
2
1
1
1
1
2
0
1
1
2
1
0
1
1
0
2
1
3
0
0
0
1
1
2
0
0
1
1
1
1
1
1
1
1
0
0
1
1
2
0
1
1
1
2
1
1
0
0
1
0
3
1
1
1
1
1
2
0
1
2
1
2
2
1
1
0
0
1
3
0
1
1
1
1
2
1
1
1
2
0
0
1
2
1
2
0
2
2
1
0
0
2
1
0
0
2
1
1
1
1
1
0
1
1
2
1
1
1
2
1
1
1
2
1
1
1
2
2
1
0
1
1
2
1
0
2
1
1
0
1
3
2
1
1
1
1
1
1
1
0
0
0
2
1
0
0
1
1
0
1
0
1
1
1
1
1
1
2
2
0
1
2
1
0
2
0
1
1
0
1
2
0
0
2
0
0
1
1
2
1
1
1
0
0
1
1
0
1
0
1
1
0
0
1
1
1
1
2
2
2
2
1
0
2
2
1
1
2
1
0
0
1
1
1
2
1
0
0
2
1
1
1
1
2
2
2
1
1
0
1
0
1
1
2
1
1
1
1
1
1
0
2
2
0
2
2
1
1
0
2
1
1
2
1
2
2
1
2
2
1
1
0
1
0
1
0
1
0
2
2
1
2
1
0
1
0
1
2
1
1
1
1
1
0
1
1
2
1
0
2
1
2
1
1
1
1
1
2
3
1
0
1
1
1
2
1
2
2
2
1
2
2
2
1
2
0
0
2
1
1
0
0
0
1
1
1
1
1
0
1
1
1
1
3
2
2
2
1
1
1
1
0
2
0
2
1
1
2
1
1
2
1
0
1
2
2
2
0
0
1
0
1
2
1
1
1
1
1
1
1
1
0
0
1
2
2
1
1
1
2
0
1
1
2
0
1
1
0
0
1
1
1
1
1
2
2
1
1
1
2
1
2
0
1
1
1
1
1
1
1
0
1
0
1
1
0
1
2
1
2
1
2
1
0
1
0
1
2
2
2
0
1
1
2
3
2
2
2
0
1
0
2
1
2
1
1
1
1
1
0
0
1
1
2
2
1
2
2
1
1
1
1
1
2
0
1
0
2
1
2
1
2
2
2
1
2
1
1
1
2
1
2
1
0
1
0
1
1
1
2
0
1
1
1
1
2
1
1
1
1
2
1
2
1
2
0
1
0
1
0
2
1
1
0
1
1
2
1
2
1
2
0
0
2
0
1
1
2
1
1
0
2
2
2
0
0
1
1
0
1
2
2
1
0
1
1
1
1
1
1
1
0
0
0
1
2
1
1
2
1
1
1
2
2
1
2
2
1
1
2
1
1
3
3
1
2
2
0
2
1
0
0
0
0
2
2
1
1
1
1
0
2
0
1
1
0
2
1
0
0
2
2
1
1
0
0
1
2
2
2
1
1
2
0
1
1
1
2
2
2
1
1
1
0
0
0
0
2
1
1
0
1
1
1
2
1
2
1
2
2
1
0
2
1
2
1
2
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
0
0
1
0
1
1
2
0
1
1
1
1
1
2
1
1
1
0
0
0
0
2
1
1
1
1
0
0
2
2
1
0
1
3
0
1
1
1
1
1
2
1
0
1
2
0
1
0
2
1
0
1
2
1
0
1
2
1
0
0
1
1
1
1
1
2
0
1
0
2
0
1
2
0
1
0
1
1
0
1
0
1
1
2
1
0
2
2
2
2
1
1
0
2
0
0
2
1
1
2
1
1
1
1
1
2
2
1
2
1
1
0
0
1
1
1
1
0
2
1
1
1
1
1
1
1
0
1
1
1
0
2
2
1
0
1
2
1
1
1
1
1
1
1
0
1
0
0
1
1
1
1
0
1
2
1
2
2
1
0
0
0
0
1
1
0
1
1
1
2
2
2
1
0
1
0
1
2
2
0
2
1
0
1
0
1
1
2
2
2
1
0
2
1
1
2
0
1
0
2
1
1
0
1
0
2
1
0
1
1
2
0
2
1
0
1
1
0
1
1
1
1
1
2
2
2
1
2
1
0
2
1
2
2
1
1
1
1
2
0
0
2
0
2
1
0
1
0
1
2
1
1
1
1
2
1
0
1
0
1
2
2
1
0
1
2
1
2
1
0
1
1
1
1
1
1
2
1
2
1
0
1
1
1
0
1
2
1
1
2
0
2
2
1
2
1
1
2
1
2
1
1
0
1
1
1
0
0
1
1
1
1
1
1
1
1
1
2
0
1
0
1
1
1
0
1
1
1
2
2
2
1
1
2
1
1
1
1
1
2
0
1
1
1
1
2
2
1
0
1
4
1
1
1
1
1
1
1
2
1
2
1
1
0
2
1
0
1
1
2
0
2
1
1
1
1
1
2
1
0
1
0
1
1
0
0
2
1
2
1
0
0
0
1
2
2
0
1
2
1
1
1
1
1
1
0
0
1
1
1
2
1
1
2
1
1
1
0
2
1
1
1
1
0
1
2
2
0
1
3
1
1
1
2
1
0
1
1
1
1
1
1
1
2
3
1
1
1
1
1
1
0
1
1
1
0
1
1
1
1
2
1
0
1
1
2
1
0
1
0
3
2
1
0
1
1
2
1
1
0
1
0
0
0
2
1
2
2
2
0
1
2
1
1
2
0
1
2
1
1
0
1
2
1
1
1
1
1
1
0
1
1
1
0
2
1
0
1
1
0
1
2
1
2
1
1
2
1
0
0
2
1
1
1
0
0
1
2
1
2
0
1
2
2
2
1
1
0
1
0
1
1
2
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
3
1
1
1
0
1
2
1
0
1
1
0
1
1
1
2
2
2
0
2
1
0
1
2
1
1
1
2
1
0
1
1
2
1
2
2
2
1
1
1
1
2
2
1
1
0
0
1
1
1
2
1
1
1
1
1
1
0
2
1
1
1
0
2
1
3
2
2
1
0
1
1
1
1
0
2
1
6
1
1
2
1
1
1
2
1
1
0
2
2
1
0
1
1
2
1
0
0
0
1
2
2
2
2
2
1
1
1
1
1
1
1
1
1
1
0
0
2
0
2
0
2
1
1
1
2
1
1
2
0
1
1
1
1
1
0
1
1
2
1
2
1
2
2
2
2
1
1
2
1
1
1
2
1
2
2
1
1
0
1
2
2
2
0
1
2
1
0
1
1
0
0
0
1
1
2
0
1
1
0
2
0
0
1
1
0
1
2
0
1
1
0
1
0
3
1
1
2
1
1
1
1
0
2
1
0
1
1
0
1
2
0
0
1
0
1
0
0
2
0
0
1
1
2
2
2
0
0
1
2
0
1
1
1
1
1
2
1
0
2
2
1
1
1
3
1
0
1
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
0
2
1
1
2
1
2
1
1
2
2
1
1
2
0
2
1
1
0
2
1
2
1
0
1
2
0
0
1
1
1
1
1
2
1
1
1
1
1
1
0
1
0
2
1
1
1
2
2
1
1
1
2
1
1
2
2
1
0
1
1
1
2
1
0
2
1
1
0
0
1
0
0
1
0
1
1
0
1
2
1
2
1
0
2
0
1
2
0
0
1
2
3
1
2
1
2
1
0
1
1
1
2
0
1
2
0
1
1
2
0
1
0
0
2
1
2
1
0
1
1
2
2
1
2
2
0
1
2
1
1
2
0
1
2
0
2
1
0
2
1
1
2
2
2
2
2
2
1
1
0
2
1
1
2
2
1
2
1
1
1
1
1
0
1
0
2
0
0
2
2
2
1
2
1
1
1
2
1
0
1
1
1
1
2
2
2
1
2
2
1
0
1
1
0
1
1
2
1
1
2
0
1
0
1
0
1
2
1
2
0
1
1
2
3
1
2
1
1
2
2
0
1
1
0
1
1
1
1
1
1
1
0
0
0
4
0
1
0
0
0
1
1
1
2
2
1
1
0
2
1
1
1
1
2
0
0
1
0
1
1
0
1
1
1
0
1
2
1
2
1
1
1
2
0
1
1
1
2
1
2
1
0
1
2
1
2
1
2
2
1
1
1
1
0
0
1
0
0
2
1
2
1
0
0
2
1
1
0
1
1
1
1
1
2
2
0
2
0
1
1
2
0
1
0
1
0
1
2
1
0
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
0
1
1
1
0
2
0
2
1
2
1
0
2
0
1
0
0
0
2
1
0
1
1
0
2
1
0
1
2
1
1
1
0
0
1
0
0
1
0
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
0
2
0
1
2
0
0
2
1
1
0
0
1
1
2
1
0
0
1
0
1
1
2
2
1
1
1
2
0
2
1
1
1
1
2
2
1
2
1
1
0
1
2
2
1
1
2
0
1
0
2
1
1
0
1
1
0
1
2
2
4
1
2
1
1
1
1
2
2
1
1
3
2
1
1
0
1
1
1
2
2
1
1
0
2
1
1
1
1
0
0
0
2
0
1
0
0
1
1
0
1
1
1
1
1
2
1
1
1
1
1
0
0
0
1
1
2
1
2
1
1
1
2
1
1
1
2
1
1
1
2
2
2
1
1
1
1
1
1
2
0
1
1
1
1
1
1
1
0
0
1
1
1
1
2
0
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
0
1
1
1
0
0
1
1
1
1
1
1
1
2
1
0
1
2
2
2
2
1
1
1
4
2
1
1
1
2
1
1
1
1
2
0
0
1
1
1
1
0
2
0
1
1
1
1
2
2
1
2
0
1
1
1
0
2
1
2
1
1
0
1
2
0
2
1
1
0
0
0
1
1
1
1
2
1
2
1
1
0
2
1
1
1
1
2
1
2
2
0
0
1
0
0
2
1
2
1
1
0
0
0
2
0
1
2
0
0
1
1
0
0
1
1
2
0
1
1
1
1
1
1
1
1
0
1
2
1
2
1
1
0
1
1
0
4
1
1
1
1
1
1
1
1
1
2
2
1
0
2
0
1
1
0
1
1
1
1
0
1
0
1
1
3
1
0
2
2
1
2
0
1
0
1
0
1
1
0
1
2
4
1
1
1
2
1
0
1
0
1
1
0
1
1
0
1
1
1
1
0
1
1
1
1
1
1
2
0
1
0
0
2
1
1
1
1
1
1
0
2
0
1
1
0
1
1
0
1
2
1
1
1
0
1
0
1
1
1
1
1
2
2
0
0
1
2
1
0
0
1
1
2
1
1
0
0
1
1
2
2
2
1
2
2
2
0
2
1
2
0
1
2
2
1
1
1
1
1
0
1
2
1
1
1
1
1
0
2
2
1
1
1
2
1
1
1
0
0
2
2
1
1
1
1
1
1
0
2
2
1
2
1
1
1
2
0
0
1
1
1
1
1
2
1
2
0
1
1
1
1
1
1
2
2
0
1
1
2
1
1
2
1
1
0
2
3
1
1
1
1
0
1
2
1
1
1
2
1
1
1
0
0
1
1
1
0
1
2
2
1
2
0
0
0
2
0
2
2
1
1
0
1
2
1
1
1
1
1
2
1
1
1
0
0
0
1
1
1
1
1
1
0
1
0
2
0
1
1
2
0
0
0
2
1
0
3
1
0
1
1
1
1
2
1
2
2
2
1
0
0
1
2
0
2
1
1
1
1
1
2
1
2
1
0
1
0
2
1
1
2
0
1
2
1
1
2
1
1
1
2
2
1
2
1
2
1
0
1
2
1
2
2
1
1
1
2
1
1
2
0
0
1
1
1
2
1
1
1
1
1
2
2
2
0
2
1
1
1
3
2
1
1
0
1
0
2
0
1
2
1
1
0
1
1
0
1
1
1
1
0
2
2
2
1
2
1
1
1
0
1
1
1
0
1
0
0
1
1
2
2
0
0
2
0
0
1
1
1
1
1
2
2
1
0
0
2
2
1
1
1
0
2
1
0
1
1
0
1
1
2
0
1
2
1
1
1
1
1
1
1
1
2
1
0
1
1
0
0
1
0
1
1
2
2
1
1
2
0
2
2
2
0
1
0
1
1
0
1
1
1
1
0
1
1
1
0
0
0
1
2
1
1
1
1
1
2
1
1
0
0
1
0
1
1
2
2
1
1
2
1
2
1
1
0
1
1
1
1
1
2
2
2
1
1
2
1
1
1
2
2
0
1
1
1
1
1
0
0
1
2
1
1
0
1
1
1
0
2
1
1
1
1
1
0
1
1
0
2
1
2
1
1
1
3
1
1
1
0
0
1
1
2
2
1
2
0
1
1
1
2
1
0
1
2
1
1
1
1
1
0
1
0
2
1
2
1
0
1
1
1
2
0
1
1
0
0
2
2
1
0
2
1
2
1
0
1
0
2
1
0
1
1
1
1
2
0
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
2
2
2
1
0
1
2
2
1
1
1
0
0
1
1
1
0
1
1
0
1
0
1
1
1
2
2
1
1
0
1
0
2
1
1
2
3
1
0
2
2
0
2
2
2
1
1
0
1
0
1
1
0
1
0
1
2
2
1
2
1
1
0
2
1
1
0
1
0
1
1
2
0
1
1
1
1
1
2
1
2
2
1
1
1
0
1
1
1
0
1
2
2
1
1
1
1
1
1
1
1
1
1
1
0
1
1
2
1
0
2
0
1
1
1
1
0
1
1
3
0
1
0
2
1
1
2
2
0
0
4
0
1
1
2
1
1
1
0
2
2
1
1
0
1
3
0
1
2
2
1
3
1
1
0
1
1
1
2
1
1
1
0
2
3
0
1
1
2
2
1
1
2
1
1
1
2
1
1
1
2
2
1
2
1
2
0
1
1
2
0
0
1
3
0
1
1
1
1
2
1
1
1
0
0
1
1
1
0
2
2
0
1
1
2
1
1
2
1
1
1
1
0
2
2
2
0
2
0
0
1
0
2
1
1
1
1
1
0
0
1
0
1
1
1
1
2
1
1
0
1
1
1
0
1
2
2
1
2
1
1
1
0
0
1
0
1
2
1
1
1
1
0
7
0
0
1
1
0
0
1
2
2
2
1
1
0
2
2
1
2
1
2
1
2
1
2
1
1
1
2
1
1
2
1
2
0
1
1
1
2
2
0
0
1
0
1
1
1
0
1
0
1
0
2
0
1
1
2
1
1
2
0
1
0
2
1
0
1
1
0
0
1
0
0
1
1
0
1
1
0
1
2
3
1
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
3
1
0
0
0
0
0
0
3
1
2
1
2
2
1
2
2
1
1
1
0
1
0
0
1
2
1
2
1
0
1
2
1
1
1
1
1
1
1
0
1
1
1
0
1
2
1
2
0
0
1
1
1
1
1
0
0
1
2
1
1
0
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
0
0
1
1
0
0
2
1
1
2
2
0
2
0
2
1
0
1
2
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
0
0
1
1
0
0
2
1
1
2
0
1
1
1
1
0
1
0
1
1
0
2
2
0
1
1
0
2
1
1
1
1
0
0
1
0
1
2
2
1
1
1
0
2
2
0
1
2
2
1
2
1
1
1
1
0
1
1
1
1
1
1
2
0
1
0
2
1
2
0
3
2
0
1
2
2
0
0
1
1
1
1
0
1
1
1
0
1
2
0
1
1
2
1
2
1
1
2
0
1
1
0
2
0
1
0
1
1
2
2
1
2
2
2
1
1
1
0
0
1
1
0
1
1
1
1
1
1
2
1
1
0
2
2
1
0
2
1
1
1
1
1
1
1
0
1
0
0
0
1
2
1
0
1
1
1
1
1
0
1
1
1
0
1
1
2
1
0
1
1
0
1
1
1
1
1
1
1
1
0
1
1
0
3
1
2
1
0
1
0
0
1
2
2
1
1
0
1
3
0
1
1
1
1
0
1
1
0
1
1
1
1
2
1
1
1
3
0
2
1
1
1
1
1
1
1
1
2
0
1
1
0
1
3
0
0
0
1
1
0
1
1
0
0
2
0
2
0
0
1
1
1
1
1
0
2
0
1
2
1
2
0
1
1
1
1
1
2
1
0
1
1
1
1
3
2
2
1
2
1
1
0
1
0
0
1
2
0
2
0
1
1
2
1
2
1
0
2
0
1
0
1
0
4
0
1
0
1
0
2
0
2
1
1
1
1
0
1
1
1
2
1
0
1
2
1
2
2
1
1
1
1
1
1
1
1
1
2
1
2
1
1
0
5
1
2
0
1
1
1
2
1
1
1
1
2
0
0
1
1
0
1
1
2
1
1
2
1
1
1
1
2
2
1
0
1
0
1
1
0
2
1
1
1
1
1
1
1
0
1
1
1
1
1
2
0
2
2
1
2
1
1
0
0
0
0
3
2
1
1
1
0
0
1
1
1
2
2
1
1
1
2
0
1
1
1
0
0
1
2
1
2
1
2
2
2
0
2
1
2
0
1
0
0
1
1
1
2
1
1
0
2
1
1
1
1
1
0
1
1
2
1
1
1
0
1
2
1
1
1
1
0
1
1
2
1
1
1
1
2
1
1
1
1
1
2
2
1
0
1
1
1
1
2
2
2
0
1
1
2
2
2
2
2
1
0
0
1
0
0
1
1
1
1
1
1
1
1
0
0
1
1
2
0
2
1
1
0
1
2
1
2
1
0
1
1
1
0
1
1
1
1
1
0
1
1
2
0
2
0
0
1
0
0
1
1
2
1
0
1
2
1
0
0
1
1
2
2
0
0
1
2
2
0
1
1
2
0
1
0
1
1
0
1
1
0
1
0
1
1
1
0
0
2
0
1
2
0
1
1
1
1
0
1
1
0
0
1
1
1
0
1
0
2
1
1
0
2
1
1
1
3
1
2
1
1
2
1
2
2
1
0
0
1
1
2
1
1
2
1
2
1
0
1
1
0
0
1
1
2
2
1
1
2
1
1
0
0
0
1
1
1
1
0
1
1
1
1
0
1
0
1
2
2
1
0
2
1
2
1
1
1
2
2
1
1
1
0
1
1
2
1
1
2
0
2
1
1
1
2
0
1
1
1
1
1
0
4
1
2
1
1
2
2
2
2
2
0
1
1
1
1
1
1
1
1
1
1
1
2
0
1
2
1
0
1
2
1
1
1
0
1
2
1
1
1
0
2
1
1
0
0
1
1
0
1
2
1
1
2
1
2
1
0
1
1
1
0
1
2
1
1
0
1
1
1
1
2
1
1
1
1
2
1
1
1
0
0
1
1
1
0
1
1
1
1
1
1
1
0
1
1
2
2
2
1
1
1
2
1
1
0
1
2
2
2
2
1
2
0
1
1
0
0
1
1
1
1
2
2
0
1
1
1
1
0
1
2
0
1
0
2
1
2
0
1
1
1
2
1
2
1
1
2
1
1
1
1
2
1
0
1
1
1
1
1
2
1
1
2
1
2
2
1
1
0
0
1
1
1
2
1
1
1
1
1
2
1
1
1
0
2
2
2
1
0
2
1
1
2
2
1
1
1
2
1
2
1
2
1
2
1
2
2
1
0
0
0
0
1
2
0
2
1
0
1
1
0
1
1
1
1
0
2
1
1
1
2
1
1
1
0
1
1
2
1
2
2
1
1
2
1
1
0
1
1
2
1
2
1
2
0
1
0
1
1
0
1
0
0
0
1
2
1
1
1
2
1
2
2
0
1
0
0
2
1
2
0
2
2
4
2
1
0
2
1
1
1
2
0
1
2
1
1
1
2
1
1
1
2
1
1
1
1
2
1
2
1
2
2
1
1
1
1
1
1
1
1
2
0
1
1
2
2
1
0
1
1
0
1
1
1
1
1
0
0
0
0
4
3
1
0
1
0
0
2
1
1
2
0
1
1
2
0
0
2
2
1
1
2
1
1
1
1
0
1
1
0
1
1
1
1
3
1
2
1
1
1
0
1
2
2
1
1
0
1
1
1
1
1
2
1
2
0
1
0
1
1
1
1
2
0
1
2
1
0
0
1
1
0
2
2
1
1
1
2
0
1
1
2
1
0
0
1
1
0
0
2
1
1
0
2
1
0
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
2
2
0
0
1
1
1
1
2
0
2
1
0
0
2
1
1
0
1
2
1
1
1
2
0
1
0
1
1
1
2
2
1
2
2
1
1
0
1
1
1
0
1
1
1
2
1
1
2
0
1
1
0
0
1
1
0
2
1
0
1
2
2
0
0
1
1
0
1
3
6
2
1
1
1
0
1
2
0
10
1
0
2
2
0
1
1
1
0
1
1
2
1
1
1
0
1
2
2
1
2
1
1
2
2
1
2
1
1
2
1
1
1
1
1
1
1
0
1
0
1
2
1
1
1
2
2
2
2
2
1
1
1
1
0
1
1
1
0
2
0
1
1
1
1
1
0
2
1
1
2
1
0
2
1
0
1
1
2
0
0
0
0
1
1
0
1
0
2
1
1
1
1
1
1
2
0
2
0
1
1
1
2
2
0
2
1
1
1
1
0
2
0
0
2
1
2
1
2
0
1
2
1
1
0
1
0
0
2
2
2
2
0
1
1
2
0
2
1
1
1
1
1
2
1
2
1
1
1
1
1
2
0
0
2
1
0
1
2
1
1
2
1
0
2
1
1
1
0
0
2
1
1
2
1
2
0
2
0
1
1
2
1
0
1
2
1
1
2
2
2
1
1
1
2
0
0
0
0
1
1
0
1
1
1
1
1
0
1
0
1
0
0
0
1
1
1
1
2
2
0
0
2
1
1
1
2
0
1
1
1
1
1
2
2
0
1
2
1
1
1
2
2
1
0
3
1
2
2
2
0
1
2
1
1
1
1
1
1
2
2
1
1
1
1
0
1
1
1
2
1
0
1
2
1
0
1
1
1
1
1
0
0
1
1
1
2
0
1
2
2
1
1
1
0
1
1
2
0
1
0
1
1
2
0
0
1
1
0
2
0
1
0
0
2
0
1
2
1
2
2
0
1
0
0
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
0
3
1
1
0
1
1
1
2
1
1
1
1
2
2
1
1
1
1
1
0
1
1
1
3
1
2
1
2
0
0
1
1
1
0
0
2
1
1
2
2
1
1
1
0
1
1
2
2
2
0
1
2
1
1
1
1
2
1
1
0
1
0
2
0
0
2
1
2
1
2
1
1
2
1
1
1
1
1
2
1
2
1
1
0
1
1
1
1
1
1
1
2
1
0
1
1
0
0
2
0
1
0
2
1
1
1
2
2
1
0
1
2
1
0
0
1
1
2
2
1
2
2
1
0
1
1
0
2
0
1
1
0
1
0
1
1
2
2
1
1
1
0
2
1
1
0
2
1
0
1
2
1
2
1
1
1
1
1
3
2
0
1
0
1
1
2
0
2
1
1
1
0
1
2
1
1
0
0
0
1
2
1
2
2
0
1
1
0
1
1
0
0
1
1
1
2
0
1
2
1
2
2
2
1
1
0
1
1
1
2
2
2
1
0
2
2
2
1
0
1
2
0
1
1
2
1
1
1
1
1
0
2
1
0
1
2
1
2
2
1
1
2
0
1
0
0
1
1
1
0
0
1
1
0
2
0
2
1
2
0
0
1
1
1
1
1
1
2
1
0
0
2
1
1
1
2
0
1
1
1
2
2
2
2
1
0
1
2
1
1
1
1
1
1
2
1
1
0
2
1
1
1
2
0
2
1
1
1
1
0
2
2
0
1
1
1
0
0
2
0
2
1
1
1
1
0
1
1
1
0
2
1
1
1
2
0
1
2
2
1
1
2
2
1
0
0
1
0
3
0
1
1
1
2
0
1
0
1
2
1
2
0
2
1
0
2
1
2
1
1
1
2
0
1
0
3
1
2
1
3
1
1
0
2
0
1
1
2
1
1
1
1
1
1
2
1
1
2
1
1
1
0
2
2
0
1
1
1
0
1
0
2
0
1
2
5
1
0
2
2
0
1
1
0
2
0
1
1
0
1
2
1
2
1
1
2
2
0
1
2
2
0
1
2
1
1
1
0
1
2
1
1
1
2
2
0
1
0
1
2
1
2
0
2
1
1
2
2
1
1
0
0
1
0
2
0
1
1
1
2
0
1
1
0
1
1
2
1
2
1
1
1
0
0
0
1
2
1
1
2
0
1
1
0
1
1
5
1
1
0
1
0
0
2
0
0
2
1
0
1
1
1
1
1
2
2
1
0
0
1
2
1
2
1
1
0
1
0
1
1
1
1
0
1
0
1
1
1
1
1
2
0
1
1
1
2
1
1
1
2
1
1
0
0
1
1
0
0
2
0
0
1
5
1
2
0
0
1
1
1
2
1
1
1
0
2
0
1
1
1
0
2
1
2
2
1
1
2
0
1
1
1
2
2
2
0
0
1
1
1
1
1
1
1
1
1
1
0
2
1
2
1
1
0
1
1
1
1
2
1
1
1
1
0
2
1
0
0
1
1
1
1
0
1
1
0
1
2
0
2
2
1
1
1
1
1
2
0
1
1
1
1
2
0
2
2
1
2
0
1
1
1
2
2
0
0
1
0
1
4
1
1
1
0
0
1
2
1
1
1
1
1
2
1
1
1
0
2
1
1
0
2
1
1
1
0
1
1
0
1
1
1
1
1
1
1
1
2
2
1
1
1
0
2
2
1
1
2
0
1
1
0
1
2
0
2
2
1
1
1
1
1
0
1
1
1
0
2
2
1
0
2
0
0
0
2
1
1
1
0
2
0
2
2
1
1
0
0
1
2
0
1
2
0
2
2
1
0
1
2
0
2
1
0
1
2
2
0
1
1
2
0
1
1
1
2
1
2
1
2
1
2
1
1
1
0
1
1
1
2
2
1
1
0
1
1
1
2
2
0
1
0
1
2
1
2
1
2
1
1
0
0
0
2
0
2
0
2
2
0
1
0
0
1
1
1
2
1
1
2
1
0
1
0
1
2
2
0
2
1
2
1
1
1
1
1
1
0
0
0
0
1
1
2
3
1
1
1
0
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
0
0
1
2
2
0
0
2
1
1
1
1
2
1
2
1
1
2
1
1
0
0
0
1
1
1
0
2
1
2
0
1
1
2
1
1
1
1
0
1
1
1
2
1
0
1
2
0
2
1
0
1
0
1
2
1
0
1
1
1
0
1
0
1
2
2
1
0
2
1
1
1
1
1
0
1
2
1
1
1
1
1
0
1
1
1
2
1
0
2
0
0
1
1
1
1
2
0
2
1
1
0
0
1
0
0
1
0
1
1
1
1
1
1
2
1
0
1
0
1
1
1
0
1
2
1
2
1
0
0
1
1
2
0
1
2
1
1
1
2
1
1
1
1
0
1
1
0
1
1
1
1
2
2
2
1
1
1
0
1
0
2
0
0
1
2
1
1
1
2
1
1
2
1
1
0
1
1
2
1
1
2
1
0
1
1
1
2
1
1
1
1
1
2
1
1
2
1
0
2
2
0
1
1
0
1
0
1
2
1
2
1
1
2
0
1
1
2
1
1
1
1
1
2
2
2
1
1
1
1
2
1
1
2
1
1
2
2
0
2
2
0
1
1
0
2
0
1
1
2
0
1
1
3
0
2
1
1
0
0
1
1
1
1
1
1
2
2
1
1
2
1
2
2
1
2
1
1
1
1
2
2
2
1
1
0
0
2
1
1
2
1
2
0
2
1
1
2
1
1
2
0
0
0
3
0
1
2
2
2
1
4
0
0
2
1
0
1
1
2
0
1
1
2
1
0
1
1
1
1
1
0
0
3
0
2
1
0
2
3
1
1
1
2
0
1
1
1
1
2
1
0
0
1
1
1
0
1
1
1
0
2
1
1
1
0
0
1
0
2
1
1
3
2
2
1
0
1
3
2
1
1
1
2
1
2
2
2
1
1
1
1
1
1
1
0
1
1
2
1
1
2
1
1
0
1
2
1
1
2
1
0
0
0
2
0
1
1
2
1
2
2
0
1
1
1
0
0
1
0
2
1
1
1
1
1
0
1
1
1
1
1
0
1
1
1
1
2
2
2
0
1
2
2
1
1
1
2
0
1
2
0
1
1
1
1
1
1
0
4
2
1
2
0
1
2
2
0
2
0
1
1
1
1
0
0
1
1
1
0
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
1
2
0
1
1
1
1
2
1
1
0
2
0
1
1
1
0
0
2
1
0
0
2
1
1
0
1
1
1
0
0
1
0
2
1
1
2
2
1
1
1
1
0
2
2
2
2
1
2
2
1
1
1
0
2
1
1
1
2
1
1
1
0
2
0
1
1
1
1
1
1
1
1
2
1
0
1
1
1
1
1
0
0
0
0
1
1
1
1
1
0
0
0
2
0
2
2
1
0
1
1
1
1
1
0
1
1
1
1
1
0
1
2
1
2
0
1
1
1
2
1
1
3
1
1
0
1
1
1
1
1
1
2
0
1
0
0
2
1
0
2
1
1
2
1
4
0
1
2
0
2
0
0
2
1
0
1
1
1
0
2
0
2
1
0
1
1
0
1
1
1
2
0
1
0
0
2
1
1
1
2
2
1
2
2
0
1
1
0
1
1
1
1
0
1
0
1
1
0
2
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
0
0
0
0
2
1
2
1
2
1
2
2
0
1
1
1
0
1
0
1
0
2
1
0
0
1
1
2
2
1
0
1
0
1
1
2
2
1
0
0
1
2
1
1
1
0
1
1
0
1
1
1
1
1
1
1
1
1
1
0
0
1
0
0
2
1
0
0
1
0
0
1
0
1
2
2
0
2
1
2
1
1
0
2
1
0
1
1
2
1
1
2
0
0
1
1
1
2
1
0
0
2
1
2
2
0
1
0
2
1
1
1
0
1
1
1
1
2
2
1
1
2
1
2
2
1
1
1
1
1
2
1
0
1
1
1
2
1
1
1
0
1
1
1
1
0
0
0
1
2
2
0
2
2
0
1
1
1
2
2
1
0
2
1
1
1
2
1
2
0
1
1
2
0
1
1
1
1
2
0
1
1
0
1
0
0
0
1
0
0
0
2
1
1
1
1
1
1
0
1
1
0
1
1
1
1
1
0
0
0
1
2
2
2
1
1
0
0
1
0
1
0
1
1
1
1
1
1
2
2
2
2
1
1
0
2
1
2
1
1
1
3
0
0
2
1
0
1
2
1
1
1
1
1
2
0
1
0
2
0
1
1
2
2
2
0
2
2
1
1
2
2
0
1
0
1
2
1
1
1
2
0
1
1
1
1
1
2
1
1
0
1
2
1
2
1
1
2
1
1
1
1
1
2
1
2
1
1
1
0
0
1
0
1
0
1
2
0
0
2
0
0
1
1
0
1
1
1
1
2
1
2
2
0
1
0
0
1
1
0
2
1
0
1
1
2
1
1
2
1
1
1
1
2
0
0
1
0
1
2
0
1
2
1
0
1
0
0
2
1
1
1
1
0
2
2
2
2
1
0
0
2
1
2
1
1
1
1
1
1
1
0
0
1
1
2
1
1
2
1
1
1
1
1
0
1
1
2
0
0
1
1
0
0
0
1
1
1
0
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
3
1
1
1
1
1
0
0
1
1
1
1
0
0
2
1
1
1
2
0
1
1
1
2
1
0
1
0
0
0
1
1
1
1
0
1
2
2
1
0
2
1
0
0
2
1
2
1
2
1
1
1
0
0
0
1
1
0
1
1
1
0
2
1
1
2
1
2
1
1
0
1
1
1
2
0
3
1
2
3
1
0
1
1
0
2
1
0
2
1
1
2
0
1
1
1
1
2
2
0
1
1
1
1
0
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
1
0
2
1
2
0
2
2
1
1
0
1
1
1
1
1
1
1
1
0
2
2
2
1
2
2
0
1
1
1
1
2
0
1
2
1
1
1
1
1
1
1
1
1
1
0
2
1
0
2
1
1
2
0
3
1
1
1
2
2
0
1
3
1
1
1
1
0
2
1
1
1
1
2
1
0
1
1
1
0
1
3
1
1
0
1
2
2
1
0
1
1
1
0
0
2
1
1
1
0
1
0
1
1
1
1
1
2
1
2
1
2
1
2
1
1
1
1
2
0
1
2
1
1
0
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
0
2
1
1
1
1
1
1
0
1
0
2
2
0
1
1
2
1
1
1
1
2
1
1
0
1
0
1
1
1
1
0
2
0
2
1
0
1
2
1
1
1
1
0
2
2
1
1
0
1
0
1
0
1
2
0
1
1
2
1
1
0
0
2
0
1
2
2
0
1
1
2
1
1
0
2
1
1
2
0
1
2
1
2
2
1
1
0
2
1
1
2
1
1
1
1
2
1
0
0
0
0
1
1
1
2
1
2
0
0
0
1
1
1
1
0
1
1
1
2
2
0
0
1
1
1
1
2
1
0
0
0
1
2
2
0
2
1
1
2
1
1
1
1
2
1
1
2
1
0
2
1
1
1
0
1
1
1
2
1
2
1
1
2
2
0
1
1
2
2
1
0
0
0
1
1
1
1
1
0
1
1
2
1
0
2
2
2
1
0
1
1
2
1
1
3
1
0
0
1
0
1
2
1
3
2
0
1
2
0
1
2
1
1
2
0
0
1
1
0
1
1
2
1
1
1
1
1
2
1
1
2
0
1
1
1
1
1
1
2
0
0
2
0
1
1
1
1
0
0
1
1
1
2
1
0
1
0
0
2
1
2
0
1
0
1
2
1
1
1
1
0
0
1
1
1
1
1
2
2
2
2
0
1
2
1
2
0
1
1
1
1
1
2
1
1
0
1
1
2
2
1
1
1
2
2
2
1
1
2
2
1
1
0
2
0
0
0
1
2
1
2
1
0
1
1
0
1
1
1
1
1
0
1
1
1
0
0
1
0
0
1
0
0
1
1
1
1
1
1
1
1
1
1
0
1
0
1
2
2
2
2
1
1
1
2
2
1
1
0
1
1
1
1
1
0
2
2
1
1
1
2
1
0
1
1
1
1
1
1
1
1
1
1
1
1
2
0
1
1
2
0
1
1
1
2
1
1
0
1
0
0
0
1
2
0
1
2
2
0
2
0
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
0
1
1
1
1
2
1
0
0
1
0
2
1
1
1
1
2
1
0
0
2
0
1
1
0
1
2
0
1
1
0
1
2
1
2
1
1
1
1
0
1
1
1
2
1
1
1
0
0
2
1
2
0
1
0
1
0
0
0
1
1
2
0
2
1
2
1
1
2
1
2
2
0
2
1
1
2
1
1
1
1
1
0
1
1
0
1
1
0
2
1
0
0
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
0
1
1
1
1
1
2
1
1
0
0
1
1
1
2
2
2
1
1
1
1
1
0
1
1
2
1
1
1
1
1
1
0
0
0
0
2
2
1
0
1
1
1
1
1
0
1
1
0
1
2
2
1
1
2
2
2
1
1
1
1
2
1
1
1
1
1
0
2
1
0
2
1
1
0
1
1
2
2
1
0
2
1
1
1
2
2
2
1
1
1
0
2
0
2
1
1
0
1
0
0
0
1
1
1
1
1
2
1
1
1
0
2
1
0
0
2
2
1
1
2
1
4
0
1
0
1
1
2
1
2
1
2
0
0
1
1
0
1
2
1
2
1
2
1
2
1
0
0
3
1
2
1
1
1
1
1
1
0
1
1
1
1
1
0
0
2
2
1
2
2
3
0
0
0
0
0
0
2
1
2
2
2
1
1
1
1
2
2
1
1
2
1
2
1
1
1
2
2
1
1
1
0
0
0
1
2
2
1
2
1
0
2
1
2
2
2
1
1
1
1
0
1
1
1
1
2
1
2
1
2
1
1
2
1
1
1
1
2
1
1
1
1
1
0
2
1
0
1
1
1
2
1
1
0
1
1
2
2
0
0
1
1
2
2
2
1
1
1
2
1
0
2
1
2
1
1
1
2
1
0
2
0
1
0
0
0
1
1
2
1
0
1
1
2
0
0
0
1
0
1
0
2
1
0
1
1
2
2
0
3
1
1
1
0
2
1
1
2
1
2
2
2
0
1
0
1
1
2
1
2
0
1
1
2
1
1
1
1
0
1
3
1
2
1
1
2
0
1
1
1
0
1
0
1
0
1
1
2
1
0
0
0
0
1
1
1
1
1
0
1
1
1
2
1
2
1
2
1
1
2
1
1
0
0
1
1
0
0
1
1
1
0
2
1
2
1
2
1
1
0
2
0
1
1
2
1
2
1
1
1
2
1
0
2
1
1
0
1
2
1
2
1
2
1
2
1
1
0
1
2
2
2
1
1
1
0
2
1
2
1
2
1
1
1
1
1
1
2
2
1
1
2
1
2
0
1
2
2
0
1
2
1
1
2
1
0
2
2
1
1
2
1
2
2
1
1
2
0
1
2
2
1
1
0
1
1
2
2
1
0
0
1
2
1
1
2
1
1
0
1
1
0
0
1
1
3
2
0
1
1
1
1
1
4
0
1
1
0
0
1
1
2
1
1
1
1
0
0
1
1
1
0
1
1
0
1
2
1
1
1
1
0
1
2
0
0
2
1
0
1
1
1
1
1
2
0
1
1
2
1
1
0
2
2
1
2
1
1
2
1
0
1
2
1
1
1
0
2
2
2
1
1
1
1
2
1
1
2
2
0
1
0
1
1
2
1
1
0
2
2
0
0
1
0
1
1
1
1
1
2
1
1
1
1
1
0
1
0
1
1
2
1
2
1
0
1
0
1
0
0
1
0
1
0
0
1
1
3
2
1
1
1
1
1
2
1
1
0
2
1
0
0
2
0
2
1
1
1
2
1
1
1
4
1
0
1
1
1
1
1
2
1
0
0
0
0
2
1
0
2
2
0
1
1
1
1
0
0
1
1
1
2
2
0
0
1
1
1
1
2
0
0
0
2
0
2
0
1
1
2
2
1
1
1
2
1
0
2
0
1
2
1
1
0
1
1
0
2
1
1
1
1
2
0
0
2
1
0
1
0
2
2
1
1
1
1
3
1
2
1
0
1
0
2
1
2
1
2
1
0
1
2
1
0
1
1
2
1
1
1
1
1
1
1
0
2
1
0
1
1
2
2
0
0
2
0
1
0
1
1
1
1
2
0
1
1
1
1
1
2
0
0
1
1
2
1
1
1
1
2
2
2
1
1
1
1
1
2
1
1
0
2
2
1
1
2
1
1
1
1
2
1
1
1
2
0
0
1
0
0
2
2
1
0
1
0
0
1
1
1
1
2
1
1
1
1
2
2
0
1
0
1
1
3
0
1
1
2
2
1
2
1
1
2
1
1
0
0
2
1
0
0
1
2
1
0
1
2
1
1
1
2
1
0
1
0
1
0
1
1
2
1
2
0
1
2
1
2
1
2
1
0
2
2
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
0
1
1
2
0
1
1
2
1
1
1
1
1
2
2
0
2
1
0
1
1
0
0
1
0
0
1
1
1
2
2
0
1
2
1
1
0
1
0
1
1
1
0
0
1
2
2
1
1
1
0
1
2
1
1
1
0
1
1
0
1
2
2
0
1
1
2
0
1
1
0
1
2
1
1
1
0
1
1
2
1
0
1
1
1
0
2
1
0
1
1
1
1
0
1
0
0
5
1
1
0
0
1
0
1
2
1
1
1
1
1
2
1
0
2
2
1
0
1
0
0
1
0
0
2
1
0
1
1
1
1
0
1
1
1
1
0
0
1
1
2
1
1
1
0
1
1
1
1
1
0
1
1
2
2
2
0
1
2
0
0
1
1
2
0
0
0
1
1
1
0
0
0
2
1
1
1
0
2
0
0
5
2
1
0
1
2
1
1
2
1
1
0
1
1
0
2
0
0
2
1
1
1
1
1
0
1
2
0
1
2
1
2
0
2
3
1
1
0
1
1
1
1
2
1
1
1
2
3
1
1
0
1
1
1
1
2
0
1
0
1
1
1
1
1
0
1
1
1
2
1
1
1
1
1
0
1
2
1
1
1
1
2
0
1
1
0
1
1
1
1
1
1
2
1
1
1
1
1
1
1
0
1
2
1
2
0
1
1
0
2
2
0
2
3
1
2
0
2
1
0
1
1
2
2
0
2
1
2
0
1
1
1
1
1
2
0
1
0
4
1
2
2
1
1
2
0
1
1
1
1
0
1
1
2
1
0
0
1
1
1
2
1
1
1
1
0
1
1
2
1
2
1
2
2
0
1
0
1
1
2
2
1
2
1
1
1
1
2
0
1
1
1
0
1
1
0
1
1
2
0
2
2
1
2
1
2
1
2
1
1
1
1
2
0
0
1
2
1
0
2
1
1
1
1
2
1
1
0
1
0
1
2
1
1
1
1
1
1
2
0
1
0
2
1
1
1
1
2
1
1
0
2
1
1
0
1
1
2
1
1
2
1
1
1
2
1
1
1
1
0
1
0
1
2
1
1
1
2
0
1
2
1
1
0
1
2
0
0
1
0
0
2
1
1
2
1
1
1
1
1
1
2
1
0
0
1
0
1
0
2
1
1
0
1
1
2
2
0
2
1
0
0
1
2
3
1
0
1
1
1
1
1
2
0
0
0
1
1
2
3
1
2
0
2
0
1
1
1
2
1
1
1
2
0
0
0
1
2
1
0
1
0
1
1
1
2
1
1
1
2
1
1
0
0
1
0
1
1
2
1
2
1
1
2
1
2
1
1
1
1
1
1
1
2
0
1
1
3
2
1
1
1
0
1
1
2
0
1
0
1
1
0
1
2
2
1
2
0
1
1
1
1
1
1
1
1
2
0
1
1
1
1
1
1
1
0
2
2
1
1
0
1
1
1
1
3
2
1
1
1
1
0
2
2
0
1
1
0
1
2
0
1
0
1
1
2
0
1
1
0
1
0
1
1
0
1
2
2
2
1
1
2
0
0
1
0
1
0
0
1
0
1
1
1
1
2
2
0
1
1
1
1
2
2
1
2
2
1
1
0
1
0
2
1
1
0
2
1
0
0
2
1
1
1
1
2
0
1
1
1
2
2
1
2
1
1
1
2
0
1
0
1
0
1
1
1
2
1
1
1
1
1
2
1
1
0
0
1
1
1
0
0
1
1
1
1
3
2
1
2
2
1
1
1
1
1
2
1
0
0
1
2
1
1
0
2
1
0
1
1
1
2
1
1
1
3
0
1
1
1
1
1
1
0
1
0
1
1
2
1
1
1
1
1
1
2
1
1
2
0
1
1
1
1
0
0
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
4
1
1
1
2
2
2
1
0
2
2
2
0
1
2
0
0
0
1
1
0
1
1
1
2
2
0
2
1
1
1
0
2
0
1
1
0
2
1
1
1
0
1
1
1
0
1
2
2
1
1
1
1
1
1
0
2
2
1
0
2
0
1
2
1
1
2
2
1
5
2
2
0
1
1
1
2
1
0
1
1
1
1
0
1
1
1
1
1
1
2
2
2
1
3
1
1
2
0
1
0
0
0
0
1
1
5
2
1
2
2
1
2
1
2
0
1
1
1
0
1
1
1
2
2
2
2
0
2
1
0
0
1
1
0
2
1
1
0
2
1
0
1
1
2
1
1
1
2
2
0
0
1
0
1
0
1
0
0
1
2
0
1
1
0
2
1
1
1
0
2
0
1
0
2
1
0
2
1
2
1
0
1
1
0
1
1
1
2
1
1
1
1
0
1
2
2
1
0
2
1
1
2
1
1
0
0
1
1
2
2
1
1
1
1
1
1
1
1
0
3
1
2
2
1
2
0
2
1
1
0
1
1
0
0
0
1
2
0
2
1
2
1
1
0
1
1
0
0
1
0
0
1
0
1
0
2
1
1
1
1
2
1
2
2
1
1
2
1
2
1
1
2
1
1
2
1
1
1
2
1
1
2
2
0
1
2
1
1
1
1
2
0
1
2
1
1
1
1
0
1
2
1
2
1
2
1
0
1
1
1
1
1
1
0
1
3
1
1
1
1
1
0
2
1
0
1
1
2
0
2
0
2
0
1
0
1
0
1
0
2
0
1
0
1
1
1
1
2
1
0
1
1
1
0
1
1
1
1
1
1
1
1
2
0
2
2
0
1
1
1
1
0
2
1
1
1
0
2
1
1
0
0
1
2
0
0
1
1
1
1
0
1
1
1
1
1
1
1
0
1
1
0
0
3
0
2
2
0
1
0
1
0
1
3
1
1
1
0
1
0
1
1
2
1
0
0
2
2
1
1
0
1
2
1
1
1
1
1
1
1
1
1
1
0
0
1
1
1
0
1
2
2
1
3
2
4
0
1
0
2
1
1
0
1
2
1
1
2
1
1
2
0
0
1
1
1
0
1
2
2
2
0
1
0
1
1
0
0
2
2
0
0
0
1
0
1
1
2
1
1
1
1
1
1
1
2
0
1
1
1
1
2
1
0
1
3
1
1
1
0
0
1
2
1
1
0
1
2
1
1
2
0
0
1
2
2
1
1
2
2
1
1
2
2
0
2
0
0
1
1
1
0
0
1
1
1
1
1
1
1
1
1
2
1
1
1
0
0
0
1
0
2
1
1
1
2
0
1
2
3
0
1
2
1
3
2
1
1
1
2
1
0
1
1
2
1
1
1
2
0
1
0
1
1
2
0
1
1
1
1
1
2
1
1
1
1
0
1
2
1
1
2
1
1
1
0
1
2
1
1
0
2
0
0
0
1
0
1
1
1
1
2
1
0
1
1
1
2
1
2
1
0
1
1
3
1
2
1
1
2
0
1
2
0
2
2
0
0
2
1
0
2
0
0
2
1
2
0
1
1
2
2
0
1
2
1
1
1
2
2
2
2
0
1
2
1
0
2
1
1
1
1
2
0
1
1
0
2
1
1
0
1
1
1
2
0
3
0
1
1
0
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
2
2
1
1
1
1
0
2
2
2
1
1
0
2
1
1
0
1
2
2
1
1
1
3
1
1
1
1
0
2
1
1
0
1
1
0
1
1
2
1
2
2
0
0
1
1
0
1
0
0
2
1
1
1
0
1
2
0
1
1
1
0
2
1
1
2
1
1
2
0
1
2
0
0
2
1
2
0
2
1
2
1
1
1
1
1
1
2
1
2
2
1
0
1
1
1
0
0
1
0
1
2
1
0
1
1
1
1
1
0
1
2
1
1
1
1
1
0
1
1
1
0
1
0
1
1
0
2
2
1
0
1
2
0
1
2
1
2
0
0
0
0
2
1
1
1
1
0
2
1
1
2
1
2
1
1
1
0
1
2
0
2
1
2
0
1
1
1
1
1
1
1
2
0
0
1
0
2
0
1
1
1
2
1
1
2
0
0
0
1
2
1
2
1
0
1
1
0
1
1
1
1
2
2
1
1
0
0
1
0
2
0
0
2
1
0
2
0
1
1
1
1
0
0
1
1
2
1
1
1
0
1
0
1
0
1
1
0
1
1
0
1
1
1
1
0
2
2
1
2
2
0
1
1
1
1
1
1
2
1
0
1
2
1
0
1
1
1
1
1
1
2
1
1
1
1
2
1
0
1
2
2
1
1
0
0
1
1
2
1
1
1
0
1
0
1
0
1
2
1
2
1
2
0
1
3
1
1
2
2
1
0
2
1
0
2
1
0
2
1
1
1
2
1
0
0
1
1
2
1
1
2
2
1
1
1
1
1
2
1
2
0
1
2
1
0
0
1
0
1
2
1
0
1
1
0
2
1
1
0
0
1
1
0
0
1
1
1
0
1
2
1
1
2
2
1
1
0
0
0
2
1
1
0
1
1
0
0
1
2
2
2
1
1
2
1
0
1
1
1
0
2
0
1
1
0
2
2
0
2
2
1
2
1
1
1
1
1
2
2
1
1
1
1
0
2
4
2
1
1
1
1
1
0
1
1
0
0
0
2
1
0
0
1
2
0
1
2
1
1
2
0
1
0
1
1
1
1
1
2
1
1
2
0
2
2
2
1
2
1
1
1
1
2
1
0
2
2
2
1
2
2
1
0
2
1
1
1
1
2
1
1
1
1
2
0
1
2
0
1
2
1
2
2
2
1
2
4
0
0
2
0
2
1
2
1
1
1
0
1
0
2
0
1
1
0
0
1
1
1
1
0
1
2
1
1
1
1
2
1
0
1
2
1
1
0
0
1
2
0
1
1
2
1
1
1
0
1
2
0
1
1
1
1
2
1
1
1
0
2
1
1
1
2
1
1
2
1
2
2
2
1
0
1
1
0
1
1
1
1
1
1
2
0
0
1
0
6
1
0
0
1
1
1
1
1
1
3
1
0
0
1
1
1
2
1
2
2
1
1
1
2
1
1
0
1
0
1
1
2
2
1
1
3
0
1
2
1
1
2
0
0
2
1
1
1
0
2
1
2
0
0
1
1
1
2
1
1
0
1
0
1
0
1
0
1
0
1
1
0
1
1
0
1
1
0
0
0
1
1
0
1
0
2
2
2
2
0
2
0
0
0
2
0
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
2
2
2
1
2
2
1
1
1
0
0
1
1
1
2
1
1
0
1
0
1
1
1
2
1
1
2
0
0
1
1
1
0
1
2
1
1
1
1
0
1
1
2
1
0
1
1
1
0
1
1
1
1
2
1
1
0
1
1
3
2
2
2
2
0
2
0
2
1
0
2
2
2
1
1
2
0
0
1
0
1
2
1
2
0
1
1
1
1
1
1
2
1
1
0
1
1
1
1
0
1
1
0
1
0
1
2
1
1
1
0
1
0
1
1
1
0
2
1
1
1
2
0
1
1
1
1
2
1
1
1
1
0
1
0
2
1
2
1
2
1
2
0
1
2
1
1
4
2
1
0
1
0
1
2
1
1
2
2
1
2
0
2
2
1
0
2
0
1
1
1
1
1
1
1
0
1
1
2
0
1
1
1
2
1
2
2
2
1
0
2
1
1
3
0
2
1
1
1
1
1
1
1
1
2
2
2
2
1
1
2
1
0
2
1
0
2
1
1
1
1
2
2
2
1
0
0
0
0
1
0
1
1
1
1
1
1
0
1
1
0
2
1
1
1
2
2
2
0
0
2
1
2
0
1
1
1
1
0
0
0
1
1
1
1
1
1
0
1
1
0
1
1
2
2
0
0
0
1
1
0
1
1
1
2
1
1
0
1
0
2
1
1
1
1
1
1
1
1
0
1
2
1
2
0
1
1
2
1
1
0
1
1
0
1
2
0
1
0
1
1
0
1
0
2
1
1
0
1
0
2
2
1
1
1
2
0
0
1
1
1
1
0
1
1
1
1
0
0
0
1
1
0
2
1
1
2
1
0
2
1
1
0
1
1
1
1
1
2
0
2
1
1
1
0
2
1
1
2
0
2
1
2
1
0
0
1
1
2
2
0
1
1
2
1
1
0
0
1
1
2
1
1
2
1
1
1
0
1
1
1
0
2
2
1
2
1
0
1
1
1
0
0
2
1
1
2
0
1
1
1
1
0
1
1
2
1
2
2
0
1
1
2
1
0
0
1
1
0
0
1
1
1
2
0
0
1
1
1
1
0
2
2
1
1
1
1
1
0
1
1
1
1
1
1
0
0
0
1
1
1
0
2
0
1
1
0
1
2
0
2
1
0
0
0
1
1
1
1
2
2
2
1
0
1
1
1
0
1
0
0
2
1
2
1
2
0
2
1
1
1
1
1
0
1
2
0
0
1
1
1
0
0
0
1
2
1
0
0
1
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
1
0
1
2
0
0
0
1
1
1
1
2
1
1
1
3
1
0
2
1
1
2
1
1
1
1
1
0
1
1
2
0
2
1
2
0
0
1
1
1
1
0
2
1
0
0
1
1
1
1
1
0
1
1
0
0
0
1
1
1
1
0
1
0
1
1
1
1
1
1
1
1
3
1
1
2
1
1
0
1
2
1
0
2
1
1
2
2
1
0
1
1
0
0
2
1
1
2
0
0
2
1
1
1
2
2
1
1
0
2
1
1
2
0
1
1
1
1
2
0
1
2
1
1
2
2
0
1
0
1
0
2
0
1
0
1
1
2
1
1
2
1
0
0
0
2
1
1
1
1
0
1
1
2
1
1
1
1
2
1
2
2
1
1
2
1
0
1
2
2
1
2
2
2
1
1
2
1
1
1
1
1
1
1
1
0
1
0
2
0
1
1
2
1
2
1
1
1
1
1
1
1
1
2
1
2
1
0
0
1
2
2
1
0
1
2
1
2
0
2
0
0
2
0
2
1
1
1
0
1
1
1
0
0
0
0
1
2
1
1
1
1
1
2
0
0
2
0
2
1
1
0
1
1
1
2
1
1
0
0
0
1
1
3
1
2
0
1
0
0
1
1
1
0
2
0
0
1
2
3
2
1
1
2
1
1
0
1
1
2
1
4
1
1
0
0
0
2
1
1
1
1
1
1
1
2
2
1
2
1
1
1
1
0
1
1
2
0
1
0
1
2
0
1
1
0
2
1
1
2
1
0
1
1
1
2
1
0
1
2
1
3
1
1
2
2
2
1
0
1
0
0
1
1
0
1
1
2
1
1
1
0
2
1
1
0
1
2
2
0
0
1
1
1
1
1
1
0
2
1
1
2
0
1
1
1
2
0
1
1
2
1
1
1
0
2
1
1
0
1
1
1
1
1
0
0
2
1
1
1
1
0
2
1
1
1
1
2
1
1
0
1
2
1
1
2
0
1
1
1
1
0
1
1
1
0
1
1
1
0
1
2
1
0
1
0
0
1
0
1
1
1
0
2
1
1
2
1
0
2
1
1
1
1
0
2
0
1
1
2
1
1
1
1
1
1
0
0
1
0
1
1
1
2
1
1
1
1
1
1
2
1
2
2
1
1
2
1
1
1
1
1
3
1
2
1
1
1
2
1
0
1
1
2
0
1
2
1
1
3
2
0
1
2
0
1
0
1
1
0
0
2
2
1
0
1
2
1
2
1
1
1
2
1
2
1
1
2
1
0
1
1
1
0
0
1
0
2
1
0
1
1
2
1
2
1
0
2
1
0
0
1
0
1
1
1
1
1
0
1
1
0
1
1
2
1
1
1
2
1
0
2
0
1
2
2
0
0
1
1
0
0
2
2
1
0
2
1
1
1
0
1
0
1
0
1
1
1
1
1
1
1
1
1
0
2
2
1
1
0
0
0
1
1
1
1
1
2
0
0
1
1
2
2
1
2
1
1
0
1
0
1
1
2
0
0
1
0
2
2
1
1
1
2
2
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
2
2
1
1
2
1
0
0
2
1
0
2
1
1
1
1
1
0
1
1
0
2
1
2
1
1
1
1
1
1
1
1
0
1
1
1
1
0
2
1
1
1
1
1
1
1
1
1
1
0
1
0
0
1
1
2
0
1
1
1
1
1
2
2
1
2
1
1
0
1
2
0
1
0
1
1
2
1
2
2
1
1
1
2
2
0
2
1
1
2
1
0
1
2
3
1
1
0
1
1
3
2
2
1
1
1
1
1
2
1
0
1
0
1
1
1
2
1
1
1
1
1
1
0
0
1
1
1
1
1
2
2
1
1
1
1
1
0
1
0
1
2
1
2
0
1
2
2
1
0
0
0
1
1
2
0
0
2
1
1
2
1
0
1
1
2
1
0
0
1
1
1
2
1
0
0
0
2
1
1
1
0
1
2
1
1
1
0
0
1
2
2
1
0
2
2
0
1
0
0
2
2
1
1
2
1
0
1
1
1
0
1
0
2
1
0
1
1
0
1
1
1
1
1
0
0
1
0
1
0
0
2
1
2
2
1
2
1
1
0
2
1
1
1
2
0
1
1
0
1
1
0
1
2
1
1
1
0
1
0
2
1
0
0
1
2
0
0
0
0
2
0
1
1
2
1
1
1
1
2
1
0
2
2
1
1
2
2
1
0
2
1
1
2
1
0
2
2
2
2
1
0
2
2
1
1
0
0
1
1
0
0
0
0
0
1
2
2
2
2
1
1
1
1
0
1
0
2
0
1
0
2
1
0
0
1
1
1
1
1
1
1
1
1
1
0
1
2
0
2
1
1
2
1
1
1
1
2
1
1
1
0
0
1
1
1
1
0
1
2
0
1
2
1
1
1
1
2
2
1
1
0
1
1
1
0
1
2
1
2
2
1
1
2
0
1
1
1
0
1
1
0
1
1
2
1
1
0
2
1
0
0
1
0
0
0
1
0
1
2
1
0
2
1
1
2
0
2
1
2
1
4
2
1
1
1
1
2
0
1
1
0
0
1
1
2
2
1
0
1
0
1
1
1
2
0
1
1
2
1
2
0
1
1
1
1
1
2
1
2
0
1
0
0
1
1
1
2
0
1
1
1
1
0
0
0
2
2
0
0
1
1
2
1
0
0
0
1
1
0
1
2
1
1
0
0
0
0
1
1
1
1
2
1
0
0
2
1
1
1
2
1
0
1
1
2
1
1
2
1
1
1
1
2
1
1
1
1
1
0
1
1
1
2
1
1
2
1
1
1
1
1
0
1
1
0
2
1
1
0
1
1
2
1
1
1
2
0
1
1
2
1
2
1
1
0
1
1
1
2
0
1
1
0
0
2
0
0
0
2
0
0
2
2
2
1
0
2
1
1
1
1
0
2
0
2
2
2
1
0
2
2
0
2
1
0
0
1
1
2
1
1
1
1
0
1
0
1
0
1
1
1
1
1
0
1
1
1
2
1
2
1
0
1
1
0
2
0
1
1
1
0
1
1
1
0
0
1
1
1
1
0
1
1
0
1
1
3
0
1
2
0
0
2
1
1
1
1
1
1
1
0
1
1
2
1
0
1
1
0
0
1
1
1
1
1
1
3
1
1
1
0
1
1
0
1
1
1
1
1
1
0
0
1
1
2
1
1
1
1
1
1
1
0
1
1
1
0
0
1
2
0
0
0
2
1
1
2
1
1
1
0
1
1
1
0
1
1
2
1
0
1
1
1
1
0
2
2
2
1
0
1
1
0
2
2
0
1
2
1
1
1
2
1
2
2
2
2
1
0
2
0
1
1
1
0
1
2
1
0
0
0
1
1
1
1
3
1
2
1
1
0
2
0
2
0
1
2
0
1
1
1
1
1
1
2
0
1
1
1
0
1
1
0
1
1
0
2
0
1
0
1
2
2
1
0
0
1
2
1
0
0
1
1
0
2
1
2
1
0
1
2
1
0
2
0
1
1
1
0
1
1
1
1
1
1
0
0
0
1
0
2
0
0
1
0
0
2
1
1
2
1
1
1
1
1
3
1
1
1
2
1
1
2
1
0
1
2
0
1
1
0
2
0
1
1
1
1
1
2
1
2
1
2
1
0
1
1
2
0
1
1
0
1
1
2
1
2
1
2
0
1
1
1
1
1
1
1
1
2
1
0
1
1
2
0
1
2
1
2
1
1
4
3
2
0
0
0
1
2
0
0
1
2
1
1
1
2
1
1
1
1
0
2
1
0
2
2
1
1
1
1
2
0
1
1
2
2
1
1
1
1
2
1
0
1
1
1
2
1
1
1
2
1
1
1
2
1
0
0
1
0
1
1
3
1
0
1
0
0
1
2
0
0
1
1
2
2
1
1
2
2
2
1
0
1
1
2
2
1
1
2
0
1
1
2
1
1
0
2
0
2
0
1
1
0
2
2
1
1
0
1
1
1
1
1
1
2
1
1
1
2
1
1
2
2
2
1
0
0
0
0
3
1
2
1
0
1
2
1
1
2
1
1
1
1
0
1
1
1
1
2
2
2
1
1
1
1
0
0
1
1
2
0
1
1
1
2
2
0
1
1
2
1
1
1
1
0
2
0
1
1
0
1
1
1
2
1
2
1
1
2
1
0
2
2
1
0
1
2
2
1
1
1
1
2
1
1
0
0
0
1
1
0
1
1
2
2
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
0
2
2
0
1
1
0
1
2
1
1
1
2
1
1
2
0
1
1
1
1
3
2
1
1
1
1
2
0
0
0
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
2
2
1
1
2
2
1
2
0
0
1
1
1
4
1
0
1
2
1
2
1
0
2
1
1
1
1
1
1
1
1
2
0
2
1
2
0
2
0
1
0
0
1
1
1
2
1
1
1
0
1
0
0
0
1
1
1
1
1
2
1
0
1
1
0
2
1
2
0
1
1
1
1
1
3
1
2
0
1
0
2
1
1
1
1
1
2
0
1
1
1
0
1
1
1
1
0
2
2
1
1
0
2
1
0
1
1
2
1
1
1
2
1
1
0
1
2
2
1
0
0
1
2
0
1
2
0
1
0
0
1
1
1
1
0
1
1
0
2
2
1
2
1
2
1
1
1
1
1
1
1
2
2
2
1
0
1
2
0
1
2
0
1
1
1
1
1
2
0
1
1
2
2
1
2
1
2
1
2
1
1
1
1
1
1
1
0
1
2
1
1
2
1
1
2
1
2
1
0
0
0
2
2
0
1
1
0
0
1
1
1
2
0
0
1
1
1
1
1
1
1
1
2
0
1
1
1
1
1
1
1
1
1
1
0
0
2
2
1
2
1
1
1
1
1
1
2
1
1
1
1
2
0
1
1
0
0
2
2
0
1
0
1
1
0
2
1
1
1
1
0
2
1
1
2
2
1
2
1
2
0
1
2
0
2
0
1
2
2
0
0
1
1
1
1
0
0
0
2
2
1
1
1
2
2
1
1
1
1
1
1
1
1
3
1
2
2
2
1
2
1
0
1
2
2
0
1
0
2
0
2
1
2
1
0
1
0
1
1
0
0
1
1
1
1
2
1
1
1
0
2
1
0
1
1
0
0
2
1
0
1
1
1
1
1
1
1
1
1
2
1
0
1
1
2
1
0
0
2
0
1
2
1
1
1
1
0
2
1
1
0
1
1
1
2
2
1
0
1
2
1
0
1
2
1
1
1
2
1
0
2
1
1
2
0
1
3
2
2
2
1
1
0
1
1
1
1
2
2
1
2
2
1
1
1
1
2
2
1
1
1
1
1
0
2
2
2
1
1
1
1
1
1
0
1
1
0
1
0
1
1
1
1
1
2
0
1
1
2
1
0
1
1
1
1
1
1
1
2
2
0
2
1
1
1
1
0
0
0
1
2
1
1
1
1
1
1
1
0
1
1
1
0
1
1
0
2
1
1
1
0
2
0
1
0
1
1
1
0
1
1
2
1
1
2
0
1
1
1
2
2
0
2
1
0
0
0
1
2
0
1
1
0
0
1
1
1
1
2
1
2
0
1
3
1
1
2
2
1
1
1
1
1
0
1
2
2
0
0
2
0
1
1
0
2
1
1
0
2
1
1
1
1
3
1
2
1
1
1
2
0
1
1
2
1
1
1
0
2
0
2
1
1
1
1
2
1
2
1
1
1
0
1
1
1
1
1
2
1
1
2
1
1
0
1
0
1
1
1
2
0
1
1
0
0
2
2
2
2
1
1
1
2
1
2
0
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
0
1
2
0
2
1
1
0
0
2
2
1
2
1
1
2
1
2
1
1
1
0
1
1
1
1
2
1
2
1
2
1
1
1
1
1
2
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
2
0
1
1
2
0
1
1
1
1
2
1
2
1
1
1
1
1
0
2
1
0
2
1
1
2
1
1
1
1
1
2
0
0
2
0
1
0
1
0
2
1
0
1
0
1
2
1
0
2
2
1
1
0
1
1
1
1
2
2
1
1
1
0
1
1
0
2
2
2
2
1
1
0
0
1
1
1
1
1
2
2
2
1
1
1
1
2
0
1
1
1
0
1
0
1
0
1
1
0
2
1
1
1
1
1
1
0
1
2
2
2
0
1
0
1
1
0
1
1
1
2
0
2
1
0
1
1
2
1
1
2
0
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
2
0
2
1
1
1
1
1
1
1
0
0
1
1
1
0
0
2
2
1
1
1
0
0
1
1
1
1
0
1
1
1
1
1
0
1
1
2
0
0
1
0
0
1
0
2
1
1
1
1
2
2
0
0
2
0
1
0
1
1
2
0
2
0
1
1
1
2
1
1
2
2
1
0
1
1
1
1
1
2
1
1
2
2
1
0
0
2
1
0
1
1
1
2
1
2
1
0
2
1
2
1
2
1
2
1
0
1
1
0
2
1
1
0
1
0
1
1
2
2
2
1
1
5
1
1
2
1
1
1
0
2
1
1
1
2
0
1
2
1
1
0
2
1
2
2
1
2
1
1
1
1
1
2
1
1
2
1
0
1
2
1
1
2
2
0
0
1
1
1
2
1
1
2
1
1
1
1
1
2
1
0
0
1
1
2
1
1
1
1
1
1
1
1
1
0
1
1
1
2
2
0
2
1
1
0
0
0
1
1
1
1
1
1
1
1
1
0
1
1
2
1
0
1
1
1
1
0
1
1
1
0
0
1
1
1
1
1
0
1
0
2
2
0
1
1
1
0
1
1
1
0
2
0
1
1
0
1
1
1
1
2
2
1
2
1
1
1
1
1
0
1
0
0
1
0
0
1
0
1
2
2
1
1
1
0
0
1
1
2
2
1
1
2
1
2
0
1
1
2
1
0
1
1
0
2
0
1
1
2
1
0
1
1
1
0
1
2
0
1
2
0
1
1
1
0
1
0
1
1
1
1
1
0
2
0
1
2
1
2
1
1
1
1
1
1
1
0
0
0
2
0
1
2
2
0
2
1
2
2
1
0
1
4
2
1
1
2
0
1
0
1
2
0
1
2
2
1
1
1
1
0
2
0
2
0
2
2
1
1
0
0
2
2
2
5
1
2
0
1
1
1
0
0
1
1
0
1
1
1
1
1
1
2
2
1
0
1
2
2
1
2
2
1
1
2
2
1
2
1
1
1
1
2
1
1
2
0
1
0
1
1
2
1
2
1
2
1
1
1
1
0
1
2
1
1
2
2
1
1
1
0
0
2
0
0
1
2
1
2
2
1
1
5
0
0
2
2
0
1
0
2
2
1
0
1
2
0
1
1
0
1
1
1
1
1
1
0
1
1
1
0
0
1
0
1
1
0
2
1
0
1
2
2
1
1
1
3
1
0
1
1
1
2
1
1
1
1
1
1
2
0
1
1
1
2
1
0
1
1
0
1
1
1
0
2
0
1
0
0
2
1
1
2
1
2
2
2
2
1
0
2
1
2
1
2
2
0
0
0
1
0
0
1
1
0
2
1
1
1
1
1
1
2
1
1
1
2
2
0
0
0
2
1
0
1
1
1
2
1
2
1
0
1
1
2
1
1
0
1
1
0
1
1
1
1
1
0
0
2
1
1
2
1
2
2
2
1
1
0
1
1
1
1
3
1
1
1
2
2
1
2
0
2
3
1
0
1
0
4
0
1
0
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
1
0
2
2
1
1
2
2
1
1
2
0
0
2
1
1
1
1
1
1
2
0
0
1
1
2
1
2
2
1
1
0
1
1
1
0
0
1
2
2
0
1
0
2
1
2
1
0
2
1
0
2
2
2
0
0
1
1
1
0
1
1
1
2
0
2
1
2
1
1
0
1
0
2
1
1
1
1
0
1
1
2
2
1
1
1
2
0
3
2
1
2
0
1
1
1
1
1
1
0
1
2
1
1
1
0
1
1
1
1
3
1
1
2
0
0
2
1
1
2
1
1
1
1
2
1
0
1
1
3
1
1
1
2
1
1
0
1
1
1
1
1
1
1
1
1
0
2
0
1
1
2
1
1
1
2
1
1
0
1
2
2
1
0
2
3
1
1
3
1
1
1
1
2
1
2
1
0
5
0
0
0
0
1
1
1
1
3
1
1
1
1
0
1
1
2
1
2
1
1
1
1
2
2
1
0
1
0
0
1
1
0
1
1
2
1
0
1
1
1
3
2
0
0
1
0
2
1
1
1
2
0
1
0
1
0
1
2
1
2
1
0
1
1
0
0
1
1
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
1
1
0
1
2
1
2
1
1
1
2
1
3
0
1
1
2
1
1
2
1
1
1
2
1
4
1
1
1
0
2
1
0
2
1
0
3
1
1
1
2
1
1
0
0
0
2
1
1
2
2
1
1
2
0
1
1
0
1
4
1
2
1
2
1
1
1
1
1
1
2
0
1
2
1
1
1
1
2
2
1
2
1
1
1
2
1
0
1
0
0
1
0
2
1
1
1
1
0
0
1
2
0
1
1
1
1
1
2
1
1
1
0
2
1
2
0
2
2
1
3
1
1
1
1
1
2
1
2
1
1
0
1
1
0
2
2
1
2
0
2
1
0
1
1
2
1
1
1
1
0
0
0
1
1
0
0
0
2
1
0
2
0
1
1
1
1
0
0
2
1
2
0
1
0
0
1
1
1
0
1
2
1
1
2
1
0
0
0
0
2
2
2
0
1
0
1
1
1
0
1
1
2
2
2
1
2
1
1
1
2
1
1
1
0
1
2
2
1
1
1
2
1
2
0
0
0
1
0
1
0
1
1
2
1
0
2
2
3
1
1
1
1
2
0
1
0
2
1
2
0
1
1
1
1
2
0
0
2
0
1
1
1
1
0
0
2
1
2
2
0
1
2
1
1
1
0
1
2
1
0
1
1
1
1
2
2
2
2
2
1
1
2
0
0
2
1
1
1
1
1
1
0
1
1
1
1
1
1
1
0
1
2
0
0
1
0
2
0
1
1
1
0
2
1
2
0
1
1
1
1
0
1
1
2
1
0
1
0
1
0
2
2
0
1
1
1
0
0
0
1
1
1
1
3
2
1
1
1
0
1
1
2
1
1
2
1
0
1
1
0
0
1
0
1
1
0
1
1
0
1
0
1
1
1
2
1
0
2
0
1
1
1
1
1
0
2
0
0
1
1
1
1
1
2
2
0
1
1
1
0
1
2
1
1
1
1
1
2
0
1
0
0
0
1
1
1
0
1
0
0
2
0
1
2
0
0
0
0
2
1
0
1
1
1
1
0
1
2
1
1
1
2
1
0
1
2
1
0
1
1
2
3
1
0
1
1
1
1
1
1
1
1
0
2
2
1
1
2
1
2
1
2
2
1
1
1
5
1
1
1
1
2
2
1
1
1
1
1
0
1
0
0
0
0
2
2
0
1
2
1
1
1
2
1
1
1
1
2
1
1
3
0
1
1
1
2
2
1
1
1
2
1
1
1
2
0
1
2
1
1
1
1
1
1
1
0
2
0
2
1
1
0
1
2
0
1
1
0
0
0
2
2
2
1
1
1
0
1
1
1
1
0
0
1
2
1
1
1
2
1
1
1
1
1
2
1
1
1
2
0
2
1
1
1
1
1
2
1
1
1
0
1
1
1
1
2
0
1
1
1
1
1
1
1
1
1
2
2
2
1
0
0
1
1
1
1
1
0
1
1
1
2
2
2
2
1
1
2
1
1
1
1
2
1
2
0
1
0
2
2
1
1
1
1
1
2
1
0
0
1
1
1
1
0
1
1
1
1
1
1
0
0
1
0
0
1
2
1
1
1
0
0
0
0
1
1
0
1
1
2
4
0
0
1
0
0
1
1
1
2
0
2
1
0
2
1
2
1
2
1
0
1
1
1
1
2
2
1
2
1
2
1
2
1
2
1
1
0
2
1
1
0
1
2
0
1
0
1
1
2
1
2
2
2
0
1
1
1
1
1
1
2
1
1
2
0
1
2
2
1
1
2
1
1
0
0
1
2
1
1
2
2
2
1
1
4
0
1
0
1
1
0
0
1
0
0
1
2
1
1
2
1
2
2
1
1
1
1
2
1
0
2
1
1
1
1
1
1
2
0
2
1
1
1
2
1
1
0
1
1
0
0
2
2
0
2
1
1
0
1
0
1
1
1
0
1
2
1
1
0
1
2
0
1
2
1
0
1
1
1
0
1
2
2
1
1
1
1
1
1
1
1
1
2
1
1
0
1
2
0
1
2
1
0
2
3
2
2
1
1
0
1
1
1
1
1
0
1
1
2
1
2
1
1
1
1
0
0
1
1
1
2
1
0
1
0
2
1
0
1
1
1
1
1
1
1
0
1
1
1
1
2
1
1
1
1
1
0
2
1
1
2
0
1
0
1
1
1
0
0
1
2
1
0
0
0
1
1
1
0
1
1
1
1
1
2
0
1
1
2
1
1
1
1
1
1
0
1
0
1
0
1
1
0
1
2
2
1
1
1
1
2
1
1
0
1
1
2
0
1
0
0
1
1
1
1
0
1
1
1
1
0
1
2
0
1
1
1
1
1
1
2
1
2
0
1
1
1
1
1
2
2
2
1
0
1
1
0
1
1
1
1
1
1
1
0
1
2
1
2
1
1
2
0
2
1
1
3
0
1
2
1
1
2
1
3
0
2
1
1
1
1
1
1
1
1
1
2
1
2
2
2
1
2
1
2
0
2
1
1
1
1
1
2
2
1
0
1
0
2
1
1
1
1
0
1
1
1
2
2
1
0
1
1
1
1
2
1
0
2
1
1
0
1
0
0
1
2
1
1
1
1
0
1
0
1
1
0
1
2
1
1
1
1
1
1
2
0
1
1
1
1
2
2
1
1
1
1
1
1
0
3
1
1
2
1
0
2
0
1
1
1
2
2
1
1
1
2
1
2
1
1
1
1
1
1
1
2
1
2
0
0
1
1
0
1
1
1
2
0
1
1
1
2
1
1
0
1
2
0
1
1
2
2
1
2
1
0
1
1
0
0
1
2
1
1
1
2
1
1
1
1
2
0
2
1
2
2
0
1
2
0
1
0
1
0
1
1
1
0
2
0
3
1
2
0
2
1
0
0
0
2
1
0
0
0
2
0
1
1
1
0
0
1
1
0
1
1
2
1
1
0
1
2
0
1
0
1
2
1
1
1
1
1
1
2
0
1
0
1
1
1
2
0
0
0
0
1
1
1
1
1
2
0
2
0
0
0
1
2
0
1
0
1
1
2
0
2
1
3
1
1
0
1
1
1
1
1
1
1
1
1
1
2
2
1
2
2
2
1
2
1
2
2
1
1
1
3
2
1
2
1
1
2
2
2
1
1
1
1
1
1
1
0
2
1
1
1
0
1
1
1
2
0
1
2
1
1
1
0
1
2
1
1
0
1
2
1
2
1
2
1
0
2
1
2
0
1
2
2
1
1
1
1
1
1
0
2
1
1
3
1
1
0
2
2
2
0
1
2
1
1
1
2
1
1
2
1
0
1
1
1
1
1
0
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
0
1
0
2
0
1
1
2
1
2
0
1
2
0
1
1
1
1
1
1
1
1
2
1
1
0
1
1
1
1
1
1
0
1
1
1
1
0
1
1
1
1
1
2
1
2
1
1
2
0
0
1
1
1
0
1
2
2
1
2
1
1
2
0
1
1
1
1
2
1
1
1
1
2
0
2
2
2
0
0
1
1
1
2
2
0
0
1
1
2
1
1
1
0
1
1
2
1
1
1
0
2
1
1
0
2
2
1
1
2
0
0
2
1
1
1
1
2
1
1
1
0
1
1
1
1
1
0
2
1
1
1
2
3
1
0
2
0
1
2
1
1
1
2
2
2
1
1
2
0
1
2
1
0
1
2
1
1
1
0
1
0
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
3
0
1
2
0
1
2
1
2
0
1
2
1
2
1
0
0
1
1
0
1
1
0
1
0
1
1
2
1
1
1
0
1
2
0
1
1
1
0
2
2
1
1
2
2
2
1
1
1
1
1
2
1
0
1
1
1
2
1
1
1
1
0
1
0
3
1
0
2
1
1
0
1
1
1
2
1
1
1
1
1
1
1
0
1
1
1
0
1
1
1
1
2
1
1
1
1
1
2
0
1
1
1
6
1
2
1
0
2
0
1
1
0
1
4
1
1
1
0
1
0
1
2
0
2
2
1
1
2
1
1
0
1
1
1
1
1
2
1
1
1
0
1
0
1
1
0
2
0
1
1
0
1
1
1
2
1
1
2
1
1
1
2
1
1
0
1
0
1
1
1
1
1
2
2
0
2
2
3
1
1
1
2
2
0
1
2
1
1
1
0
1
0
2
1
1
1
1
0
0
2
0
1
2
0
1
1
0
1
0
0
1
1
1
1
0
0
2
1
0
1
2
1
1
0
1
2
2
0
1
1
0
1
1
2
1
0
0
1
1
0
0
1
2
1
0
1
0
1
1
1
3
1
1
2
1
1
1
2
1
1
0
1
0
1
1
1
0
1
1
1
0
0
0
1
1
1
2
2
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
0
2
1
0
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
0
1
2
1
1
1
1
2
1
0
0
1
1
1
1
2
0
0
1
1
0
0
1
2
2
1
2
1
1
1
1
1
0
1
1
1
2
0
1
2
1
2
0
2
1
3
2
2
1
1
0
1
0
1
1
1
1
2
0
0
0
1
0
0
0
2
1
1
1
0
2
2
2
2
0
1
1
0
2
2
1
1
2
1
1
1
2
2
1
2
1
2
2
1
1
0
2
0
1
1
2
0
1
2
1
1
1
2
1
1
1
2
1
2
0
1
2
1
1
1
0
1
1
1
1
0
1
1
0
1
2
1
3
2
0
1
1
1
1
2
1
1
0
1
1
1
1
1
0
1
1
1
0
1
1
1
1
2
2
0
1
0
1
1
2
2
1
1
1
1
1
1
1
1
0
2
1
0
2
1
2
1
0
1
1
1
1
2
1
0
1
2
1
2
1
1
1
1
2
2
0
1
0
1
0
0
0
1
1
1
1
2
1
2
2
0
1
1
1
2
1
0
1
2
1
1
2
1
0
1
1
1
3
1
2
0
1
1
2
1
1
1
0
1
0
2
1
0
1
2
2
0
1
2
0
2
0
2
0
1
2
3
1
2
1
2
2
1
1
1
1
1
2
1
1
1
1
1
1
0
1
1
0
1
1
1
2
1
1
2
2
1
2
0
0
0
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
1
0
2
1
1
1
1
1
1
1
1
1
1
1
1
2
0
2
1
1
2
1
2
1
1
1
1
1
0
1
0
0
1
1
0
3
2
2
0
1
0
0
0
0
1
2
2
1
1
1
0
1
0
0
1
1
1
2
0
1
0
1
1
1
1
1
0
1
1
1
1
2
0
0
1
0
1
1
1
1
1
2
2
1
0
0
1
2
1
2
1
2
2
0
0
1
1
2
0
1
0
1
1
2
0
1
0
1
1
0
1
0
2
1
1
0
2
1
1
0
1
0
0
1
1
0
1
0
1
1
2
0
2
1
2
2
2
2
1
2
1
2
2
2
1
1
2
0
4
1
1
1
0
1
1
2
1
0
1
1
1
0
1
1
2
2
0
1
2
2
2
1
1
0
1
2
3
0
1
2
2
1
1
2
2
1
1
1
1
2
1
1
1
0
0
1
1
3
0
2
1
1
1
1
1
1
2
1
2
1
0
1
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
2
1
0
2
2
0
1
1
0
1
2
1
0
0
0
1
0
0
1
2
0
0
1
1
1
1
0
1
1
0
1
1
1
1
0
1
1
0
2
0
1
0
1
1
1
0
1
1
0
2
2
1
1
1
0
2
1
1
1
1
1
1
1
1
0
1
3
2
0
2
1
1
1
1
1
1
1
2
0
2
1
0
2
1
0
2
1
1
1
2
1
1
1
0
0
0
1
2
1
2
3
2
1
0
1
2
0
1
1
1
2
1
1
0
21
0
1
1
1
2
1
1
1
1
1
1
1
4
1
0
1
0
2
2
4
2
1
1
1
1
0
1
1
0
1
1
1
0
0
1
1
1
0
1
1
1
0
1
2
1
1
0
0
2
2
1
0
1
1
2
0
2
1
1
1
1
1
0
0
1
0
1
1
2
1
2
0
0
0
1
1
1
1
1
2
2
2
1
1
0
1
0
2
1
2
1
1
2
1
1
2
1
2
1
0
1
1
0
1
1
2
0
1
1
1
1
1
2
1
1
0
0
1
1
1
1
1
2
0
1
0
0
1
1
0
1
1
1
1
1
1
3
0
3
2
2
2
1
1
1
1
1
1
0
1
2
0
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
6
1
1
1
2
2
1
2
1
1
1
1
1
1
0
1
1
1
1
0
1
2
1
1
1
1
1
1
2
2
0
2
1
1
2
1
1
2
1
3
1
1
0
1
1
1
0
0
1
1
1
1
0
2
3
0
1
1
1
1
1
2
1
1
1
0
2
0
1
1
0
1
1
1
1
1
2
1
0
2
1
1
1
1
2
1
1
1
2
2
1
0
1
1
1
1
1
0
1
1
1
1
0
1
0
1
1
0
1
1
1
1
1
0
1
1
1
2
2
1
0
1
0
1
0
1
2
1
1
1
2
1
1
2
1
1
2
0
1
1
0
1
1
1
1
1
2
1
0
0
1
0
0
0
2
1
2
0
0
1
2
2
1
0
2
1
2
1
2
0
0
0
1
1
2
1
1
1
1
1
0
1
1
2
1
2
3
2
0
0
2
2
0
1
1
1
0
0
1
1
2
2
1
1
2
1
0
1
0
1
1
0
1
2
1
2
1
2
1
0
0
1
2
2
1
0
1
2
2
2
1
1
1
1
1
1
1
0
0
1
2
1
1
1
1
1
1
1
1
1
1
0
1
2
0
2
2
1
2
2
1
0
1
1
0
0
0
0
2
1
0
2
1
1
1
1
1
1
2
1
2
1
1
2
0
1
1
2
1
1
1
1
0
2
0
0
1
1
1
3
1
2
0
1
1
1
1
1
1
1
2
1
2
2
1
0
0
2
0
1
2
2
0
1
2
0
1
0
2
2
1
2
0
1
0
1
1
2
1
0
2
1
2
1
1
0
1
0
2
2
1
1
1
1
1
2
0
1
1
2
1
1
2
1
2
2
1
1
0
1
1
0
2
1
1
2
1
2
3
1
2
2
2
3
0
2
1
0
1
1
0
1
2
0
2
2
0
1
2
1
0
2
1
3
0
1
0
1
2
0
1
0
0
0
2
1
1
1
0
0
1
1
1
1
1
1
0
1
1
0
1
1
1
2
1
2
1
2
2
1
0
2
2
0
1
0
1
2
1
1
1
1
0
1
1
0
1
1
1
2
0
1
2
2
2
1
2
1
2
0
1
2
1
1
1
1
1
0
0
1
0
1
1
0
0
1
2
1
1
0
0
2
0
1
1
1
1
0
2
1
2
1
0
1
2
2
2
0
0
2
2
1
0
1
1
1
2
0
0
1
1
1
1
0
1
0
1
1
1
2
2
1
2
0
1
0
1
3
1
1
1
0
0
0
0
1
1
1
1
0
1
2
0
1
1
2
1
1
0
1
1
1
1
1
1
1
1
1
1
1
0
2
1
1
1
1
2
1
2
2
1
1
0
2
1
2
2
1
1
1
1
1
1
1
0
2
2
1
1
1
1
1
1
0
1
0
1
2
2
2
1
1
1
1
0
1
1
1
0
1
1
1
1
1
0
1
1
2
1
1
1
1
1
0
1
0
0
1
1
2
2
1
2
2
1
1
1
1
1
1
0
1
2
1
2
2
2
1
1
2
0
1
1
2
1
0
1
1
2
1
1
1
2
2
1
0
0
1
2
1
0
2
1
2
2
1
2
2
1
0
1
1
2
2
0
1
0
0
1
2
1
2
0
1
1
0
1
0
1
1
1
1
1
0
1
0
1
0
1
1
2
0
2
0
0
1
2
0
0
1
2
2
0
0
1
2
2
2
0
2
2
1
1
1
0
1
1
1
2
1
2
1
1
2
1
1
2
2
2
1
1
2
1
1
0
0
0
0
2
1
1
1
1
0
1
1
2
1
1
1
1
1
1
0
1
2
2
1
1
1
2
0
2
1
0
0
0
0
2
2
2
2
0
1
0
0
0
1
1
1
0
1
2
1
0
1
2
1
1
1
1
1
1
2
0
1
2
1
1
0
2
2
1
1
0
1
1
1
0
1
1
0
1
1
2
1
2
1
2
2
1
1
0
2
1
0
2
1
1
2
1
1
2
2
1
1
1
1
0
1
1
0
1
2
1
2
1
2
1
1
1
1
1
1
2
1
1
1
2
0
1
1
0
1
1
1
2
1
2
1
0
0
1
1
0
1
1
2
2
2
0
1
2
0
0
1
1
1
1
1
1
2
2
1
2
1
0
1
1
1
2
0
0
2
1
2
1
1
0
1
3
2
1
2
1
2
3
1
2
2
1
2
1
1
1
1
2
1
1
1
2
2
1
1
0
1
1
1
1
0
2
0
1
1
0
1
2
1
1
1
0
1
0
2
2
2
2
0
1
1
1
2
2
0
2
0
1
2
0
1
2
1
1
1
1
1
1
0
1
1
1
1
2
2
0
0
0
2
0
1
0
0
1
1
0
1
1
1
1
2
1
1
0
1
2
1
0
2
0
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
0
1
2
1
1
0
0
0
2
1
2
1
1
0
0
0
1
2
1
1
2
0
2
2
0
1
1
2
1
0
0
2
1
0
1
1
1
1
1
0
1
1
1
2
2
1
0
1
1
1
0
2
1
1
1
2
0
0
2
2
1
0
2
1
1
2
2
0
2
1
0
0
1
0
0
0
1
1
0
0
1
0
1
1
2
1
1
1
2
0
2
0
1
0
2
1
2
0
2
1
0
2
1
0
1
0
1
2
2
2
1
0
1
2
3
1
2
1
0
0
1
1
2
1
0
1
0
1
1
1
0
1
0
1
0
0
1
1
1
0
2
1
0
1
2
1
0
1
2
1
2
1
1
1
1
2
1
1
1
1
1
3
2
1
2
1
1
1
1
2
1
2
1
0
1
2
0
1
2
1
1
1
1
1
1
0
0
1
0
2
1
1
2
0
1
1
1
0
2
0
1
2
0
2
1
1
1
0
1
1
2
1
1
1
0
1
2
0
1
2
1
0
2
0
1
1
1
0
2
0
0
1
1
0
1
2
1
1
1
1
2
2
1
1
1
2
2
1
1
1
1
0
1
1
0
1
1
1
1
1
1
0
1
2
1
1
2
2
1
0
1
1
1
1
1
0
1
1
0
2
0
0
1
1
1
1
1
2
1
1
1
1
1
1
0
1
1
1
2
0
2
1
0
2
2
2
2
1
2
1
2
0
1
1
2
1
1
1
2
1
1
1
0
2
2
0
1
2
0
2
0
1
1
0
2
1
1
2
1
1
2
2
1
0
1
1
2
1
1
2
2
1
0
1
1
1
1
1
2
1
1
0
2
2
1
1
1
0
1
2
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
2
0
2
0
0
1
1
2
2
1
0
1
2
1
2
1
3
1
0
0
1
0
1
1
1
2
2
1
0
1
0
1
1
0
1
0
0
2
1
1
2
1
2
2
2
0
1
1
1
2
2
0
0
1
2
1
1
2
1
0
0
1
1
1
2
2
1
2
2
0
1
1
1
1
1
1
1
1
1
1
2
1
0
1
0
1
1
2
0
2
1
1
0
0
1
0
1
0
1
2
1
2
0
2
1
1
1
1
1
2
1
1
1
0
1
0
1
1
0
1
1
2
0
1
1
0
1
0
1
1
1
1
1
1
0
2
1
0
2
1
0
1
1
1
2
1
2
2
1
1
0
1
1
1
1
0
1
1
2
1
2
0
0
1
2
0
1
1
0
0
0
0
1
0
1
0
1
0
0
2
1
1
1
0
1
0
1
1
0
1
1
2
1
1
2
0
0
2
1
1
0
1
0
1
1
1
0
1
1
1
2
0
1
2
0
1
1
2
2
1
2
1
1
1
1
0
1
2
1
2
1
2
1
2
2
1
1
0
1
2
0
2
1
2
1
1
2
1
2
1
1
1
1
0
2
0
1
1
0
1
2
0
0
1
0
1
1
1
1
1
1
2
1
1
2
0
2
0
2
2
1
1
2
2
2
0
1
0
2
2
2
1
0
0
2
1
1
2
0
1
2
1
1
1
1
1
1
3
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
0
1
1
0
2
2
0
0
0
0
2
2
1
2
1
2
1
0
1
1
0
1
1
1
1
1
2
0
0
1
2
1
2
0
1
0
1
2
2
0
2
1
0
2
2
1
1
1
1
2
1
2
1
1
1
0
0
2
2
2
0
2
1
0
1
2
0
1
1
1
1
1
0
1
0
0
1
0
2
1
2
0
1
0
2
1
2
1
0
1
1
2
1
0
1
0
1
0
0
1
1
1
2
0
1
1
2
0
2
2
1
1
2
1
1
1
1
1
1
0
2
2
2
1
1
2
0
0
1
1
0
1
0
1
0
1
2
0
2
1
0
1
1
1
1
1
2
0
1
1
1
1
2
2
1
0
1
2
1
1
1
1
1
1
1
2
2
2
1
2
0
2
0
0
1
2
3
0
2
2
0
1
1
1
1
1
2
2
1
0
1
1
1
1
1
1
1
1
0
0
1
1
2
2
1
2
1
1
0
1
1
1
1
0
1
1
1
2
0
2
1
1
1
0
0
0
2
2
1
0
0
0
2
1
0
0
1
1
1
1
2
2
1
0
0
1
2
1
1
1
2
0
1
0
0
1
1
1
2
1
1
1
1
1
1
2
1
2
0
0
1
0
2
2
0
0
1
0
0
0
1
3
1
1
1
1
0
2
2
1
2
1
0
1
1
3
2
2
1
2
1
1
1
1
1
0
0
0
1
2
1
0
1
2
0
1
1
1
1
0
0
1
0
1
2
1
1
1
1
0
1
0
0
1
1
2
2
1
3
1
0
2
1
0
1
0
1
0
2
2
1
1
2
2
1
2
1
1
0
3
0
1
2
2
0
0
1
2
1
1
2
0
2
1
0
0
2
1
1
0
1
1
0
1
1
3
2
1
1
0
2
0
1
1
1
1
1
1
1
1
2
1
0
0
1
0
1
2
1
0
0
0
1
1
1
1
2
1
1
1
2
0
1
0
2
0
2
2
1
1
3
0
1
1
0
4
1
1
2
2
1
1
1
0
1
1
1
1
2
1
1
2
2
1
0
1
0
1
1
1
2
0
0
2
0
2
0
1
2
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
0
1
1
2
1
1
1
1
0
0
1
1
1
1
1
2
0
0
2
1
1
1
1
1
1
0
2
1
0
1
2
1
1
0
2
1
0
0
1
1
0
2
1
2
1
3
2
0
1
1
1
0
1
0
1
1
1
1
1
1
2
2
1
1
1
0
1
0
1
2
2
2
2
0
0
6
1
1
1
0
2
0
1
1
2
1
2
1
2
2
0
1
1
1
2
1
1
1
1
0
1
1
2
2
0
1
1
0
1
0
1
1
2
0
1
2
2
1
2
0
1
1
0
2
2
0
1
1
1
0
2
1
1
0
1
1
2
1
1
1
1
0
1
1
0
1
0
1
1
0
2
0
1
2
2
2
1
2
2
1
1
1
0
0
0
1
0
1
0
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
0
1
1
1
1
1
0
0
0
1
1
1
2
2
1
2
0
1
1
0
1
2
2
1
1
1
2
1
1
1
2
1
0
1
1
1
1
2
2
1
0
1
2
1
1
1
2
2
1
0
1
2
0
1
1
2
2
1
2
0
2
1
2
1
1
2
1
1
2
1
1
1
1
2
0
2
1
0
1
0
0
1
1
1
0
1
1
3
2
1
0
1
2
0
1
1
0
1
1
0
2
2
0
1
1
1
1
0
0
2
1
2
2
0
1
1
1
0
0
0
1
1
0
1
1
1
0
1
1
2
0
0
2
1
0
2
1
2
1
0
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
0
2
1
2
0
1
1
1
1
1
0
1
0
0
3
0
1
1
2
1
1
0
1
1
0
1
2
1
1
0
1
1
0
1
2
0
1
1
0
1
2
1
1
2
2
2
1
2
1
1
2
1
1
2
1
0
1
2
2
0
0
2
0
1
0
0
2
1
1
1
0
1
0
3
1
1
1
0
1
2
1
1
1
2
0
0
2
2
1
1
2
2
1
1
0
1
1
1
0
0
1
1
2
1
1
1
1
1
2
1
0
2
0
1
0
1
0
0
2
1
0
0
1
1
1
2
0
0
1
1
0
2
1
2
1
1
1
1
1
1
1
0
1
1
1
1
1
0
2
1
1
2
2
2
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
0
2
1
1
1
1
1
1
2
0
1
2
1
1
0
0
0
0
1
0
1
2
1
1
0
1
0
1
1
1
2
2
1
0
1
1
2
1
1
0
1
1
2
2
2
0
2
2
1
0
1
1
1
1
1
2
1
2
1
1
0
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
1
0
1
2
0
1
2
2
2
1
2
1
0
1
1
1
2
1
1
1
1
1
0
1
1
1
1
1
2
3
2
1
1
0
1
1
1
1
1
2
0
1
2
1
0
1
2
2
1
1
1
0
1
0
1
0
2
1
1
2
3
1
1
1
1
1
1
1
1
1
2
2
1
1
1
0
1
0
1
0
1
1
2
2
1
1
2
0
2
0
1
1
1
1
1
1
1
0
2
2
0
1
0
0
2
0
1
0
0
2
0
1
2
1
1
0
0
0
1
2
0
2
1
1
0
1
1
2
0
0
0
1
0
1
2
2
1
1
1
2
2
1
2
1
1
0
1
1
1
1
0
1
0
1
0
1
1
0
2
1
0
2
1
0
0
1
3
0
1
0
0
1
1
1
1
1
1
1
1
2
2
1
2
1
1
1
1
2
1
1
0
1
2
1
0
2
2
3
2
1
0
1
2
2
1
1
1
1
2
2
2
1
2
1
1
1
0
1
1
1
1
2
0
1
0
1
1
2
1
1
0
2
1
0
1
1
1
1
1
1
0
1
0
2
2
1
1
1
1
1
1
0
1
1
1
0
2
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
0
1
0
1
1
0
0
1
1
1
2
1
2
1
1
1
1
0
1
0
2
1
1
0
1
1
1
1
2
2
1
0
0
1
2
0
1
1
1
1
1
1
0
1
1
1
0
1
2
1
1
2
1
4
2
0
2
1
2
0
2
2
1
1
1
2
1
1
1
0
1
3
1
1
1
0
1
0
2
2
1
1
1
1
2
2
0
1
0
0
1
0
0
0
1
0
1
0
1
2
1
1
0
1
1
1
1
1
1
1
2
1
2
1
2
2
2
0
2
1
1
1
1
1
1
1
2
2
0
0
0
1
0
0
1
0
1
1
1
1
2
0
1
0
0
1
1
1
1
1
1
0
0
1
2
1
1
2
1
2
1
1
0
1
2
1
1
1
1
2
1
0
1
1
2
1
2
2
1
2
1
0
1
0
0
1
1
2
0
1
0
0
1
1
1
1
0
0
1
0
1
2
1
1
0
1
1
2
1
1
0
1
1
1
1
1
1
1
2
0
0
0
1
1
1
2
1
1
1
1
0
1
1
1
2
0
2
1
0
0
1
0
1
1
1
2
0
1
1
1
1
0
2
0
1
3
2
1
1
1
1
1
1
1
1
1
0
1
0
1
1
2
1
2
1
1
2
1
1
1
2
1
1
0
0
1
1
0
1
1
2
0
1
1
1
1
1
2
0
1
1
1
2
2
0
1
0
1
1
0
1
1
1
2
0
1
0
2
1
1
2
2
1
1
1
1
0
1
2
0
0
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
2
1
1
0
1
1
0
1
2
0
1
1
1
0
2
2
1
0
1
1
1
0
1
1
2
1
1
1
1
2
1
0
1
0
1
1
0
0
0
1
1
0
0
1
1
1
1
1
2
0
1
2
1
0
0
0
2
1
3
0
1
0
1
1
1
1
1
0
1
1
1
2
0
1
1
1
0
0
2
1
0
1
1
1
1
1
0
2
1
0
1
1
0
2
0
2
1
1
2
1
0
1
1
2
2
1
1
0
2
1
1
2
1
1
1
1
0
2
1
1
1
1
1
1
1
0
1
1
2
1
2
1
0
1
2
2
0
0
1
1
1
1
2
1
2
0
2
2
2
1
1
1
1
1
0
2
0
0
0
1
1
1
1
2
1
2
4
5
2
1
0
2
1
0
0
1
2
0
1
1
0
1
0
1
1
0
2
2
1
1
1
0
1
0
1
1
1
1
1
1
1
1
0
1
2
1
1
1
1
1
0
1
0
1
2
1
2
1
0
1
1
0
0
0
1
1
0
1
1
1
0
1
1
2
1
1
1
0
1
0
0
1
1
2
1
0
1
1
1
2
0
1
0
2
1
1
1
1
0
1
2
0
0
1
2
0
1
0
1
1
1
0
0
1
2
1
0
1
1
1
2
2
1
0
1
2
1
1
1
1
0
1
2
0
0
1
1
1
2
1
0
1
1
2
0
2
1
0
2
1
1
0
0
0
1
2
1
1
0
1
0
1
2
1
2
1
1
2
2
2
0
1
1
1
2
1
2
0
1
1
0
1
0
2
1
1
1
1
2
0
2
0
1
2
3
2
1
0
1
1
1
1
1
0
1
2
1
0
1
1
0
0
1
1
1
2
2
1
1
1
1
1
1
1
1
1
0
1
0
1
0
1
2
0
1
1
1
0
1
0
2
1
1
1
1
0
0
2
0
1
0
2
2
1
1
2
2
2
0
1
1
2
2
3
1
0
1
0
2
0
1
2
1
1
0
1
1
0
1
0
0
1
1
0
1
1
0
1
2
1
1
1
1
0
1
3
1
1
2
2
2
1
0
1
2
2
1
0
1
0
1
0
1
1
1
2
1
0
0
2
2
1
1
2
2
1
1
0
1
2
2
2
2
1
0
1
2
2
1
0
0
0
1
2
1
1
1
2
1
1
1
1
0
0
2
1
1
1
0
1
1
1
0
1
1
2
1
1
1
2
1
1
1
1
4
0
1
2
1
1
1
0
1
0
1
2
2
1
1
1
0
1
1
2
2
1
1
0
1
2
1
1
1
1
0
1
1
2
1
0
1
0
1
2
1
1
1
1
1
1
1
2
2
0
2
1
1
1
1
0
2
1
1
1
0
0
1
2
2
1
0
2
0
1
0
2
0
1
1
0
2
0
1
1
0
1
1
1
0
0
2
1
1
1
1
1
1
2
0
1
1
1
2
2
1
2
1
1
0
2
1
1
1
2
1
2
1
1
1
4
1
2
0
1
1
0
3
0
1
1
1
1
2
1
1
2
0
2
1
3
1
1
1
1
0
0
1
2
1
1
2
2
1
1
1
1
1
0
1
0
1
1
2
2
0
1
1
0
0
2
1
1
1
1
1
1
1
1
1
1
2
1
1
0
2
2
1
1
2
1
1
1
1
1
1
2
0
2
2
0
1
1
0
1
0
0
0
0
2
1
0
1
1
2
1
1
1
1
1
0
0
1
1
2
0
2
2
1
1
1
1
0
1
0
2
0
1
2
1
1
1
1
1
1
3
1
0
2
0
1
0
1
1
0
0
1
1
1
2
1
1
2
2
1
2
2
0
1
2
1
1
2
1
1
1
2
1
1
2
1
1
1
0
1
0
1
2
1
0
2
2
1
1
1
2
1
0
0
0
1
1
1
1
0
0
2
0
2
1
0
1
0
1
1
1
0
1
1
1
1
1
1
2
1
0
2
1
0
1
1
1
2
0
0
1
1
0
2
1
1
1
1
2
2
0
0
0
1
1
0
1
2
1
2
1
1
1
1
1
2
0
0
0
1
1
2
1
2
2
1
1
1
2
1
1
2
2
0
1
0
0
0
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
0
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
0
0
1
2
2
1
2
1
2
2
0
1
2
2
0
1
1
1
0
1
1
2
0
1
0
2
1
1
1
2
1
0
1
1
2
0
2
0
1
2
1
1
1
2
0
1
1
1
2
0
2
1
2
2
1
1
1
1
0
1
1
1
0
1
1
1
1
1
2
1
2
2
2
0
1
1
0
1
2
0
1
2
0
1
1
0
1
0
1
2
0
2
1
2
1
2
1
1
1
1
1
2
1
1
1
1
1
2
2
1
2
1
1
2
0
1
2
1
2
1
0
2
1
2
2
0
0
1
0
1
1
1
1
1
2
2
2
1
0
0
1
1
3
0
1
1
1
2
1
1
2
2
0
1
3
2
0
1
2
1
2
1
2
2
1
1
0
1
1
1
1
1
1
2
1
2
1
2
0
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
0
4
1
1
0
0
1
0
0
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
0
0
1
2
2
2
2
1
1
1
1
0
1
1
0
1
0
1
1
2
1
1
1
0
2
1
1
2
1
2
0
1
2
0
1
1
1
1
2
2
2
1
1
1
1
0
1
2
1
1
1
1
0
0
1
2
1
0
2
1
2
0
1
1
0
1
0
1
1
2
2
0
0
1
2
0
1
1
2
1
2
0
1
0
1
2
1
1
0
1
1
1
2
0
1
0
2
0
2
0
1
2
1
2
1
0
1
2
2
1
1
2
2
1
2
1
2
0
2
0
1
1
0
3
1
2
1
2
0
0
1
1
1
2
1
1
1
1
1
1
2
0
0
1
2
0
1
1
1
1
1
1
0
1
0
1
0
1
1
2
1
1
2
1
2
0
0
0
2
1
2
0
1
0
1
1
0
1
1
0
2
2
1
2
1
1
0
1
1
0
1
0
2
1
1
0
0
1
0
0
2
1
1
1
1
1
1
2
1
1
1
1
1
1
0
2
1
2
1
1
1
2
0
1
1
0
1
1
1
1
1
0
1
2
1
0
1
0
1
1
2
1
0
0
0
2
1
2
0
2
2
1
1
2
1
0
1
1
1
1
1
0
1
1
1
1
1
1
0
1
1
0
1
0
0
1
2
2
2
1
0
2
1
1
2
0
2
1
1
2
1
0
1
0
1
0
1
1
1
1
1
3
1
1
1
0
1
0
1
2
1
6
2
0
0
2
0
1
0
2
1
0
2
1
2
1
2
1
1
1
0
0
0
2
1
2
1
1
1
0
1
0
2
0
1
1
1
3
0
1
0
1
1
1
1
1
1
3
1
1
0
1
2
2
1
0
1
0
0
1
2
0
1
1
2
1
2
1
0
1
1
1
2
1
0
1
2
2
1
1
1
1
1
0
0
0
1
1
1
1
0
0
1
2
0
2
0
1
2
0
1
2
1
2
0
2
1
1
2
0
1
2
1
0
1
1
2
0
2
1
0
1
1
1
2
1
1
2
1
1
1
2
0
2
1
1
1
1
2
1
2
1
0
0
1
1
1
1
1
1
1
1
0
2
0
1
1
1
1
1
1
1
2
2
1
0
0
0
1
1
1
1
2
2
2
2
0
1
0
1
0
1
0
0
1
2
2
1
2
0
0
1
0
1
1
1
1
1
0
1
1
2
1
1
0
1
1
1
0
1
1
2
1
0
0
21
1
1
1
1
1
1
1
2
2
0
2
1
0
1
1
0
1
2
2
1
0
0
2
1
1
1
1
2
1
1
1
0
1
3
1
1
1
2
2
0
1
0
0
0
1
0
0
1
1
0
0
1
2
1
1
1
1
2
1
0
2
2
1
1
1
2
1
1
1
2
1
1
2
2
0
2
1
1
1
1
2
2
2
1
1
2
1
0
1
1
1
1
2
2
1
2
0
1
2
1
1
0
1
1
1
0
1
1
1
1
2
1
1
1
0
1
1
1
2
1
1
2
1
1
1
1
1
2
0
2
0
1
0
1
1
2
1
1
1
2
1
2
0
3
2
1
1
1
1
0
1
1
2
2
1
1
1
1
0
2
0
2
1
0
1
0
1
0
1
4
1
1
2
1
1
1
0
2
1
1
1
2
2
1
1
0
0
1
1
0
2
4
2
1
1
1
1
1
1
2
1
1
0
1
1
1
1
1
0
2
2
0
0
0
2
0
1
1
2
1
1
2
1
0
0
1
1
2
1
2
1
2
1
1
0
0
0
0
1
2
0
0
1
1
0
2
0
1
2
1
0
2
0
1
1
1
1
1
1
1
1
0
2
1
1
0
2
1
1
1
1
1
1
1
1
0
1
2
0
1
2
0
0
1
1
2
3
0
1
2
1
2
1
1
1
1
2
1
1
1
1
0
1
1
1
1
2
2
1
2
2
1
0
1
0
1
1
1
1
0
0
1
2
0
1
2
2
1
1
2
0
1
1
1
1
0
1
2
0
2
3
1
2
1
1
1
1
1
0
0
1
1
5
2
1
1
2
2
0
2
2
2
2
1
2
1
0
2
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
0
0
1
1
0
1
1
1
0
2
1
1
0
3
2
0
1
0
2
1
1
1
2
1
1
2
2
0
1
1
1
2
2
1
2
1
1
2
2
2
1
1
0
0
0
2
2
1
0
1
1
1
0
0
0
0
2
1
0
1
1
1
1
2
2
0
1
1
1
1
0
2
1
2
0
2
0
2
1
1
1
1
2
1
1
3
1
1
1
1
2
0
1
2
1
1
1
1
1
2
1
0
0
1
1
0
2
1
1
1
0
1
1
2
1
1
1
2
1
2
1
1
0
2
1
2
0
1
0
1
1
1
0
0
1
0
0
1
0
1
2
1
1
0
0
2
0
1
1
2
1
2
2
4
1
0
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
0
1
0
2
1
0
2
2
3
1
1
1
1
2
1
0
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
0
1
2
1
1
2
1
2
1
2
0
1
1
0
2
1
2
2
1
2
2
1
1
1
2
0
1
1
2
1
2
1
1
2
0
1
1
1
0
2
1
2
1
0
2
0
0
1
1
0
0
1
0
0
1
2
1
1
2
1
1
1
0
0
1
1
0
1
1
2
1
2
1
1
1
2
1
1
1
1
2
2
1
1
1
0
2
1
1
0
0
1
3
0
2
2
2
2
0
0
2
1
2
2
0
1
1
2
2
1
1
1
1
1
0
1
1
2
1
1
2
2
1
1
0
1
0
2
1
0
1
2
4
2
2
3
1
1
2
1
2
0
3
1
0
2
1
1
0
0
0
1
1
1
1
1
1
2
1
1
0
0
1
1
1
1
1
2
0
2
0
1
1
2
2
0
1
1
1
1
1
2
0
1
1
1
2
1
0
0
1
1
0
1
0
0
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
0
0
1
1
2
1
1
0
2
2
2
2
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
2
1
0
0
1
0
1
2
0
1
1
1
0
2
1
1
1
1
1
2
1
2
1
1
3
1
1
1
0
1
0
1
1
1
1
1
2
1
1
2
2
0
1
0
2
1
1
0
2
2
1
1
1
1
2
1
0
1
2
0
1
1
2
0
1
1
1
0
1
1
1
1
0
1
0
0
1
0
2
1
0
1
0
1
2
1
1
1
0
0
2
2
1
1
2
1
2
2
0
1
1
1
2
1
2
1
1
1
0
1
1
2
0
1
2
0
1
1
1
1
1
1
1
0
1
1
0
1
2
0
0
1
1
0
1
2
1
1
0
1
1
2
2
1
0
0
1
1
2
1
2
2
2
2
1
1
2
2
1
1
1
1
1
2
2
0
0
0
0
2
1
1
1
1
0
2
1
1
1
1
0
1
0
0
2
1
1
2
1
1
2
0
0
1
4
2
1
0
2
2
0
1
2
1
0
1
1
1
1
2
0
2
1
1
2
1
1
1
2
2
1
0
0
1
1
0
2
1
1
1
0
1
2
0
0
0
1
1
2
0
0
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
0
1
1
1
0
1
2
1
2
1
1
0
1
2
0
2
2
2
2
2
0
1
2
2
1
1
0
0
0
1
2
1
1
1
1
2
2
0
1
2
1
0
1
0
1
0
2
1
0
2
1
0
1
1
0
1
1
1
1
1
2
0
1
2
0
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
2
1
0
2
1
2
1
2
0
2
1
1
1
1
0
3
1
2
0
1
1
1
1
1
1
2
1
1
0
1
1
0
1
1
1
0
1
1
3
1
1
1
2
1
1
1
1
1
1
0
0
1
2
0
1
2
1
0
1
1
2
2
2
1
2
0
2
1
1
1
1
1
2
2
1
1
0
1
0
1
1
1
1
2
1
1
0
1
2
1
1
1
2
0
2
1
1
2
1
1
2
2
1
2
1
1
1
2
1
0
1
1
1
1
2
2
1
2
1
1
1
0
2
0
0
1
1
1
1
2
1
1
0
1
1
0
1
1
2
1
1
1
1
2
1
0
1
1
0
0
1
1
1
1
0
1
2
0
1
0
0
0
1
1
1
0
1
1
2
2
1
1
1
2
0
2
1
0
1
1
1
2
2
1
0
2
1
1
2
2
0
1
1
1
1
2
0
1
1
1
1
1
3
0
2
2
1
2
1
0
2
2
2
1
2
0
0
2
0
0
1
0
1
1
2
1
0
1
1
1
0
3
1
0
0
1
2
0
1
1
1
2
1
0
2
2
1
0
2
1
0
1
1
0
2
1
1
1
1
0
1
0
2
1
0
1
1
2
1
0
1
1
1
1
1
0
0
1
2
0
0
2
1
1
0
1
0
1
1
2
1
1
1
0
0
1
0
0
1
2
1
2
1
1
1
2
0
1
2
2
0
1
0
1
0
0
1
1
1
1
0
1
1
1
1
0
1
1
0
1
2
1
2
2
1
2
1
0
1
1
0
1
1
0
1
1
1
2
1
2
1
1
2
0
2
0
1
1
2
1
1
1
2
2
1
1
2
2
1
0
1
0
1
1
1
1
0
1
1
1
1
1
2
0
2
2
1
1
1
2
2
1
1
1
0
1
2
1
1
1
2
1
1
0
1
1
1
2
1
1
1
2
1
1
0
1
0
1
2
1
1
2
2
0
0
1
0
0
1
0
2
2
1
1
1
2
1
0
1
1
1
1
1
1
0
3
2
2
2
1
1
1
0
1
1
1
0
1
0
0
1
2
0
1
2
1
1
0
1
0
0
1
0
0
2
2
1
1
0
1
2
2
1
0
1
0
0
1
1
1
1
2
1
1
2
1
1
1
1
1
0
2
0
0
1
2
1
0
1
2
1
1
1
0
1
2
2
2
0
0
1
1
1
0
0
1
1
0
1
2
1
1
1
1
1
1
1
1
1
0
2
1
1
0
1
1
1
1
0
0
1
2
2
1
0
0
1
1
2
1
1
1
2
1
1
1
1
0
2
1
2
0
1
0
2
2
1
1
0
2
1
1
0
1
1
1
1
0
2
1
0
1
1
0
0
2
2
2
1
1
1
1
2
1
0
1
1
0
1
1
0
1
0
0
1
1
0
1
2
2
1
2
1
1
1
1
0
2
0
2
1
0
2
2
0
2
1
0
2
0
1
1
1
2
2
0
1
1
1
2
1
0
1
1
1
0
2
1
1
2
2
0
0
1
1
2
2
1
1
1
0
2
1
1
1
1
0
1
2
1
1
1
2
2
1
1
1
1
1
1
0
2
1
1
1
1
1
1
1
1
1
0
1
1
2
2
1
2
1
0
1
0
1
2
0
1
1
1
1
1
2
1
2
1
2
1
1
1
0
1
1
2
2
1
1
1
0
0
1
2
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
0
1
1
1
1
0
0
1
1
0
1
0
1
0
1
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
2
0
1
2
0
0
0
1
0
1
1
2
1
1
2
1
2
1
2
1
1
2
0
2
2
2
1
1
0
1
1
1
1
1
0
2
0
1
1
3
1
1
1
0
0
1
1
3
1
1
1
1
1
1
2
1
1
1
1
2
2
1
1
1
1
1
0
2
1
1
1
1
2
3
0
1
1
0
2
0
2
1
2
0
0
0
1
1
1
2
1
0
2
0
1
0
0
1
1
1
1
2
1
1
1
1
2
0
0
1
1
0
1
2
0
1
0
0
1
0
0
2
1
0
2
1
2
1
1
1
2
1
2
1
3
1
1
1
1
1
1
0
0
2
0
1
1
0
2
0
0
2
3
1
1
1
0
2
1
1
0
1
2
2
1
1
0
1
1
0
1
0
1
1
1
1
1
0
1
1
2
1
2
1
2
0
2
1
0
1
1
2
1
1
0
2
1
1
1
1
1
1
2
1
1
1
2
0
2
1
2
2
1
1
0
1
1
0
1
0
1
2
1
2
1
2
0
2
1
1
0
0
1
1
1
2
1
0
1
0
1
1
0
1
0
1
1
1
1
3
1
1
1
1
2
0
1
2
1
1
1
0
0
0
2
2
0
1
2
1
0
1
0
1
1
1
2
0
2
1
1
1
1
2
1
0
1
2
0
1
1
0
0
1
0
0
1
0
0
3
1
1
0
1
1
3
1
0
1
2
1
2
1
1
1
2
1
2
2
0
2
1
0
1
0
2
1
2
1
2
2
0
1
1
0
1
1
1
1
1
0
0
1
1
1
0
1
1
1
1
1
1
2
2
2
2
1
1
2
2
2
0
2
1
0
1
0
2
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
2
1
2
0
0
1
0
2
0
0
1
1
3
2
1
1
1
2
1
1
0
0
1
1
2
1
2
2
0
1
1
0
1
2
1
0
2
1
1
2
0
3
0
1
2
0
1
0
0
2
0
2
1
2
0
0
1
1
1
1
1
1
1
0
1
1
2
2
2
1
0
1
1
1
1
0
1
1
1
1
1
0
1
0
1
0
0
1
1
1
1
3
2
4
2
0
1
1
1
2
1
2
2
1
1
2
1
2
0
2
1
0
1
2
1
2
0
0
2
1
2
1
1
2
0
1
1
1
0
2
1
0
0
0
1
1
0
1
1
2
0
0
0
0
1
1
0
1
1
1
1
1
3
1
0
1
1
2
1
1
1
0
1
1
1
1
2
1
0
1
1
0
1
1
1
1
1
2
0
2
1
1
0
1
0
1
2
4
0
2
1
2
1
1
2
1
2
2
1
0
2
1
2
1
1
1
2
1
1
3
1
1
1
1
0
1
1
3
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
0
2
2
1
0
2
2
1
2
1
1
1
1
1
1
1
0
1
0
2
1
0
1
1
1
1
0
0
2
2
1
1
2
1
1
2
1
1
1
1
1
0
1
1
1
1
0
1
1
2
1
0
1
0
1
2
0
1
0
1
1
1
1
1
1
1
0
1
1
1
2
1
1
1
1
0
0
0
0
1
2
1
0
1
0
2
1
2
1
1
1
1
2
0
1
2
0
1
1
1
1
1
0
1
1
2
1
1
0
1
2
0
0
2
2
1
1
1
1
2
0
0
1
1
0
1
1
2
1
0
1
1
0
1
1
1
2
1
1
1
0
1
1
2
0
1
2
1
1
0
0
1
1
2
1
0
2
1
1
1
1
1
1
1
1
0
2
0
1
0
0
2
1
1
0
1
1
1
1
0
1
1
1
1
1
1
2
1
1
1
0
1
1
0
2
0
0
1
1
1
2
1
1
1
0
0
1
1
0
0
1
1
0
2
2
0
1
1
1
1
2
1
2
2
1
0
1
1
0
1
1
2
1
1
0
1
2
1
1
1
1
1
1
2
1
1
1
1
1
0
1
0
1
1
0
1
1
1
1
1
1
1
0
1
1
2
0
1
3
2
1
1
0
1
0
1
1
1
1
1
2
1
1
1
1
0
1
1
1
0
1
1
2
1
0
2
2
0
0
1
1
0
1
2
1
0
1
1
1
1
3
0
0
1
2
1
0
2
2
0
0
0
1
1
2
1
0
1
1
1
1
1
1
2
2
2
2
1
0
1
1
0
0
0
0
1
2
1
1
0
0
1
2
0
0
1
1
0
1
2
3
0
0
1
2
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
0
2
0
1
1
1
1
1
0
2
2
1
2
1
1
2
1
1
0
1
2
1
1
0
1
2
1
3
2
0
1
2
2
0
1
1
0
0
1
2
1
1
0
0
2
2
2
1
0
1
1
1
2
1
1
0
2
1
1
0
0
1
1
1
1
1
0
2
1
0
1
1
1
1
1
1
2
1
2
1
2
1
0
1
1
2
1
1
1
0
1
0
1
1
0
2
0
0
1
0
0
1
1
1
1
1
0
2
2
1
1
1
1
1
1
2
1
1
2
1
0
1
1
1
1
2
1
2
0
1
1
1
1
1
1
0
1
1
1
1
1
1
1
0
1
2
1
0
1
0
0
0
2
1
0
1
1
2
1
0
1
0
1
1
1
0
2
1
1
1
1
2
1
1
1
1
1
0
1
1
0
1
1
1
1
1
1
1
2
1
1
0
1
2
1
1
1
1
1
2
1
1
2
0
0
0
1
1
2
0
1
1
2
0
1
0
2
1
3
1
2
1
1
2
1
2
2
1
1
1
2
1
0
1
1
1
2
1
1
0
0
1
1
1
1
1
1
1
0
0
1
1
0
1
2
1
2
1
2
1
1
0
1
0
2
2
3
1
0
1
0
1
1
3
1
2
1
1
1
2
1
2
0
1
1
1
1
1
1
1
1
2
0
2
0
1
1
1
1
1
0
0
0
0
1
0
2
2
1
0
2
3
1
1
1
1
1
1
0
1
1
1
1
1
0
1
1
1
2
2
0
1
1
1
2
1
1
1
0
1
2
2
1
1
1
1
2
1
2
0
0
1
1
1
3
0
1
0
2
1
1
1
1
2
1
1
1
0
1
1
2
2
1
1
0
1
1
0
0
1
0
1
2
1
1
1
1
0
1
1
2
1
1
1
1
1
1
0
1
1
2
2
1
0
0
1
0
1
1
1
1
1
2
1
1
2
1
2
2
0
2
1
0
2
0
2
0
2
1
1
1
1
1
1
2
0
0
0
2
1
1
2
0
1
1
1
0
0
0
0
1
1
1
1
0
1
1
5
0
1
2
1
2
0
1
1
1
1
1
2
1
0
1
0
0
1
2
0
0
1
0
2
2
0
2
1
1
2
1
1
1
1
0
1
2
2
1
1
1
0
1
1
2
1
2
0
0
1
1
0
1
2
0
0
1
2
0
1
1
1
0
0
1
1
1
0
1
1
2
2
1
2
2
1
0
0
1
1
3
0
1
1
1
0
2
0
2
1
0
1
2
1
0
1
0
2
2
1
1
2
1
1
0
1
0
1
2
0
0
1
1
0
1
0
1
1
2
2
1
2
0
2
1
1
0
1
1
0
1
1
1
2
0
2
5
2
1
2
0
5
0
2
1
1
1
0
1
2
1
1
0
1
0
1
3
2
1
2
1
1
1
1
1
1
1
1
3
2
0
0
2
2
1
0
2
1
2
2
2
1
1
2
1
2
0
0
1
1
2
1
0
0
3
1
2
1
1
1
1
0
2
1
1
0
1
0
1
0
1
2
1
1
0
1
1
0
2
0
1
1
2
0
2
1
2
2
2
1
1
1
1
1
2
1
3
1
0
1
0
1
2
1
2
2
0
1
0
1
0
1
2
1
0
1
1
0
2
1
2
2
1
1
1
2
2
1
1
1
1
2
1
1
1
1
2
0
2
1
2
1
0
0
1
2
0
0
0
1
1
1
1
0
1
1
1
1
1
0
1
1
0
1
2
1
2
0
1
1
1
1
1
0
1
1
1
1
1
1
1
0
0
1
1
1
3
1
1
1
0
2
0
0
2
2
2
1
1
1
0
1
1
0
1
2
1
1
1
1
2
1
1
0
2
1
1
1
1
2
1
0
1
3
1
1
0
1
2
0
2
0
2
1
0
1
1
0
1
1
0
0
1
1
1
1
0
0
1
1
0
0
1
2
2
1
1
0
1
0
2
2
1
0
2
2
1
1
1
0
2
0
0
0
1
1
1
1
1
1
0
1
1
1
1
1
1
3
1
1
1
2
1
1
1
2
0
2
2
2
1
0
0
1
1
1
1
1
1
0
1
1
0
1
0
0
2
1
1
0
1
1
0
1
1
0
2
1
0
2
1
0
0
2
1
1
1
2
1
1
2
2
1
2
1
0
1
1
0
1
1
1
0
1
0
1
2
1
1
1
1
0
1
1
1
1
1
2
3
1
1
1
1
0
2
0
0
0
2
2
1
2
1
0
1
1
1
1
1
1
1
0
0
2
3
2
2
1
0
1
1
0
0
1
2
1
0
1
1
2
1
1
2
2
2
2
1
0
0
1
1
1
1
0
1
1
2
1
2
1
2
0
2
0
2
2
1
2
1
1
0
1
1
0
1
2
1
1
1
1
0
2
2
1
0
3
0
1
1
1
2
1
1
3
0
0
1
1
1
2
1
0
1
1
1
0
2
0
1
1
2
1
1
1
2
1
1
0
0
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
1
1
2
2
2
1
1
1
1
0
0
1
1
1
0
0
0
0
0
1
2
1
1
0
2
1
1
1
1
2
1
1
1
1
1
0
2
2
1
1
1
1
1
1
1
0
1
0
2
0
1
2
0
2
2
1
2
0
1
1
1
2
1
1
1
1
1
0
1
1
1
1
1
1
2
1
1
2
1
1
1
1
0
1
2
1
0
3
0
1
2
1
1
1
2
1
2
1
1
1
2
1
2
1
1
1
2
0
1
0
2
0
2
1
1
1
1
2
1
1
1
0
1
0
1
0
0
1
1
1
2
1
1
0
1
1
0
1
1
1
0
1
1
1
2
0
2
1
1
1
1
2
1
1
1
1
0
1
3
1
0
1
1
1
1
1
1
1
1
0
1
0
0
1
1
2
1
0
1
1
2
2
1
1
1
1
1
2
1
0
1
2
0
1
1
0
1
1
0
2
2
1
1
1
1
1
1
0
1
1
1
1
1
1
1
2
2
2
1
2
2
2
1
2
1
1
2
1
0
1
1
2
1
1
1
1
1
0
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
2
1
1
1
1
0
3
0
2
2
0
2
2
1
1
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
0
1
1
2
0
2
1
0
2
0
1
2
0
2
2
1
2
1
2
2
2
1
1
2
1
1
1
1
1
1
1
1
2
2
2
0
1
0
1
4
1
1
2
2
1
1
0
1
1
1
0
1
4
2
1
1
1
2
1
1
1
1
2
1
1
1
0
1
2
1
1
2
1
1
1
2
2
1
1
2
1
1
1
1
2
3
0
1
2
1
1
1
1
2
0
0
0
1
1
0
1
0
0
1
2
1
1
2
0
1
2
2
1
1
1
1
1
2
1
2
1
1
0
0
1
2
2
1
1
0
1
0
0
1
1
1
1
1
0
2
1
0
1
2
2
1
1
0
2
0
2
2
1
1
1
2
1
2
1
2
2
0
2
1
0
1
1
2
2
1
2
0
0
2
1
1
0
1
1
1
1
0
2
2
1
1
1
1
1
0
1
2
0
1
1
0
0
0
2
0
1
1
1
1
1
1
1
2
1
2
0
0
1
1
1
1
1
1
0
0
2
2
2
0
1
0
1
2
1
1
1
0
1
1
2
2
0
1
0
0
0
2
0
0
1
1
0
0
1
1
1
2
1
2
1
2
1
1
1
0
2
1
2
1
1
1
0
1
1
2
2
0
2
2
0
0
1
1
2
1
1
1
2
1
1
2
2
1
1
1
0
2
1
1
1
3
2
1
2
1
2
1
1
1
2
1
2
1
2
2
1
1
1
0
0
1
1
0
1
1
0
2
1
1
0
0
1
1
1
1
1
1
1
2
1
0
0
1
1
1
1
1
1
0
1
1
1
2
1
1
1
1
2
1
2
0
2
2
0
1
1
2
1
2
1
2
1
1
2
1
1
0
0
2
0
1
0
1
1
1
0
1
1
2
0
1
1
2
2
1
0
2
1
1
0
1
1
1
0
0
2
1
1
1
1
1
1
2
0
1
0
0
2
2
1
0
1
2
1
1
0
1
1
1
0
1
0
1
1
1
0
0
1
1
1
0
2
1
2
1
2
2
0
1
1
2
2
0
2
0
1
0
1
1
1
2
1
0
2
1
1
1
1
2
0
2
1
0
1
1
1
0
1
1
1
1
1
0
1
1
1
1
1
1
0
1
1
1
0
0
2
1
1
1
0
0
1
1
0
0
0
0
0
1
1
0
1
1
2
1
0
1
1
1
1
0
0
2
1
0
0
1
1
1
1
2
1
1
0
0
1
1
1
1
1
2
0
0
3
1
0
1
0
1
1
2
1
2
6
2
2
1
1
2
0
0
1
1
1
0
2
0
1
1
1
2
1
0
1
1
0
1
1
1
1
0
1
1
1
1
1
2
1
2
1
1
1
2
1
2
2
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
2
1
1
0
1
2
3
2
0
2
1
2
1
1
1
1
1
2
1
0
1
1
0
1
1
1
2
2
1
0
1
1
1
2
2
1
1
2
1
1
2
0
0
1
2
1
1
1
1
1
2
0
0
1
1
1
0
2
2
0
2
0
2
1
2
0
1
1
1
0
1
2
1
0
1
2
1
2
1
0
1
2
1
2
1
1
1
0
1
1
0
1
0
1
1
0
1
1
0
0
1
1
1
2
0
2
2
1
0
1
1
1
1
1
2
1
1
0
1
1
2
1
1
0
1
1
0
0
0
0
2
0
1
0
1
2
1
1
1
2
1
1
1
1
0
1
1
1
1
0
2
0
2
1
0
1
0
1
1
0
1
2
1
3
1
0
1
1
2
0
2
1
2
0
0
2
1
1
1
0
1
2
0
0
1
1
2
1
2
0
2
1
1
1
0
1
0
1
1
1
2
0
1
3
2
2
1
1
1
0
1
1
1
1
1
2
1
0
0
1
1
2
2
0
1
1
1
2
2
1
0
1
1
0
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
2
2
1
1
1
0
1
1
2
1
2
1
1
0
1
2
1
1
1
0
0
0
1
0
1
1
1
1
1
0
1
2
0
2
1
2
1
1
1
1
0
2
1
0
0
2
2
2
1
1
1
1
1
1
1
1
1
0
1
1
2
0
2
2
1
1
1
2
2
1
0
0
1
0
1
1
1
1
2
2
1
2
1
0
1
1
0
0
0
0
1
0
0
0
1
1
1
2
2
0
0
1
1
1
1
1
1
2
1
0
1
1
1
1
0
1
0
1
0
1
1
2
0
2
1
2
1
0
1
1
1
0
2
1
2
0
1
0
1
0
1
0
1
1
0
0
2
1
0
1
1
1
1
2
1
1
1
0
1
0
2
1
0
0
2
0
1
1
1
2
2
0
1
1
0
2
0
1
1
1
2
1
1
0
1
1
1
1
1
1
1
1
1
2
0
1
1
0
2
1
3
1
0
1
2
2
1
0
1
1
2
1
1
0
0
2
1
2
0
1
1
1
0
1
3
2
1
0
2
1
1
0
2
1
1
3
1
2
1
2
1
0
2
2
1
1
1
1
2
0
1
1
1
2
1
2
0
1
2
0
1
2
1
1
1
2
1
1
0
1
1
2
1
1
1
1
2
0
1
1
2
0
1
2
2
1
1
2
1
1
0
1
1
1
1
1
1
1
2
0
1
2
2
2
0
1
1
1
1
0
0
2
2
1
0
1
1
2
1
1
2
1
1
2
1
0
1
1
0
1
1
1
1
1
1
0
1
0
1
1
1
1
0
1
1
1
1
2
1
0
1
1
2
0
1
2
1
1
2
1
1
1
1
1
1
1
1
0
2
1
1
2
1
0
2
1
1
0
1
2
2
0
0
0
2
2
2
1
1
2
5
2
1
1
2
1
0
1
1
2
2
0
1
0
2
2
2
0
1
2
2
1
0
0
0
1
1
0
1
1
0
1
1
2
0
1
1
0
1
1
1
1
1
1
0
0
0
0
2
1
1
1
1
3
2
1
2
1
1
1
1
2
1
1
0
0
2
0
0
1
1
2
1
2
2
1
0
1
1
1
1
1
1
1
2
1
2
0
0
0
2
1
2
1
1
0
1
1
2
1
2
0
1
1
0
1
2
2
1
2
1
0
2
2
2
1
1
1
1
1
1
1
2
1
2
1
1
2
1
2
2
1
2
0
1
1
1
2
1
1
2
1
1
0
1
1
1
1
1
1
2
3
1
1
1
1
1
2
1
1
0
1
2
2
1
1
1
2
0
2
0
2
1
1
1
1
1
2
2
2
2
1
1
1
1
0
1
1
2
1
0
1
2
2
1
1
2
1
0
0
1
1
2
1
1
0
1
1
1
2
2
1
0
0
0
1
1
1
2
0
1
1
1
0
2
1
1
1
1
1
1
1
0
2
1
1
1
1
1
1
3
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
0
1
0
1
1
1
1
2
1
2
1
1
0
1
1
1
1
2
1
1
1
1
0
1
1
1
0
0
1
0
1
0
0
0
1
1
1
0
2
2
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
2
1
1
1
2
0
1
0
0
1
0
1
2
1
1
1
1
1
2
1
2
1
1
1
0
2
2
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
0
0
2
1
1
0
1
2
1
2
0
0
1
0
3
1
1
1
2
1
1
2
1
2
1
2
1
2
2
1
1
2
0
1
3
2
1
0
2
1
1
1
2
1
0
1
1
0
2
1
0
1
1
1
2
1
0
1
1
2
0
1
1
1
1
2
2
1
0
2
1
1
1
0
1
1
2
1
1
2
0
1
1
0
1
1
1
2
1
0
0
0
0
1
2
1
1
1
2
1
2
2
2
1
1
0
2
1
2
2
1
1
1
2
1
1
1
0
1
2
1
1
1
1
1
1
1
1
0
1
1
0
1
1
1
2
2
1
1
1
2
1
2
0
1
1
1
2
2
1
1
1
1
0
2
1
1
0
1
1
1
1
1
2
2
1
0
2
1
0
1
1
1
1
2
0
2
1
2
1
1
1
2
0
1
1
1
2
0
1
1
2
2
1
2
0
1
2
1
0
1
1
0
1
1
2
2
1
0
2
1
1
1
2
0
1
1
2
1
1
1
0
1
2
1
1
1
0
2
1
1
2
1
1
1
2
2
2
1
1
0
1
1
2
1
1
0
0
1
1
0
1
0
3
0
2
1
2
0
0
0
1
1
0
1
1
0
1
1
2
1
1
1
0
1
1
1
1
1
2
1
1
1
2
0
2
1
0
1
1
1
0
1
1
1
1
0
0
3
0
1
1
1
2
1
1
0
1
0
1
0
2
0
1
1
2
1
1
1
0
1
0
1
0
2
1
1
2
0
0
2
1
2
0
1
2
1
1
0
2
0
2
2
2
2
0
1
2
2
1
1
2
2
0
1
0
1
0
1
2
0
1
0
1
2
1
1
2
0
1
1
2
1
1
2
3
0
1
1
1
2
1
1
1
1
2
2
2
1
1
2
0
0
3
3
1
1
0
0
1
2
1
0
0
0
1
2
2
1
1
1
0
1
2
1
0
1
2
1
0
2
0
0
2
1
1
1
0
1
2
0
0
1
0
1
2
0
1
1
1
1
0
0
1
0
0
2
2
1
1
1
1
1
1
0
3
1
2
1
1
0
0
2
2
1
2
1
2
1
0
1
0
3
2
1
1
1
2
1
0
2
2
3
1
1
0
1
0
0
1
2
0
2
1
1
1
1
1
2
2
1
2
1
1
0
0
0
2
1
3
1
2
0
1
1
2
1
0
1
1
1
1
1
1
1
2
0
1
2
1
2
0
0
1
0
2
1
1
1
0
0
0
0
1
1
1
1
2
0
2
1
2
1
1
3
1
1
1
1
0
1
1
2
1
0
1
0
1
0
2
1
2
1
1
0
2
0
1
1
1
1
0
2
1
1
1
2
1
0
1
1
1
1
0
1
1
1
2
3
2
1
2
1
1
2
2
1
0
0
0
1
0
0
1
1
1
1
0
1
2
1
1
1
1
1
2
2
1
0
1
1
1
0
0
2
1
0
1
2
0
0
1
2
2
2
0
2
1
1
0
2
1
2
0
1
1
1
2
1
1
1
0
1
1
1
2
1
1
1
1
1
2
1
1
0
2
1
1
0
2
1
2
0
2
1
2
0
1
0
1
0
1
1
1
1
0
1
0
0
1
0
2
1
0
1
0
0
0
1
1
1
2
2
1
1
0
1
0
1
1
1
1
2
1
2
0
1
0
1
1
1
0
1
0
1
2
2
0
1
1
1
1
0
1
1
1
1
1
1
0
1
2
1
0
0
1
0
2
2
1
1
1
1
2
1
1
1
2
1
1
0
2
2
1
1
0
1
0
1
0
2
2
1
0
0
1
1
1
1
2
0
1
2
1
1
1
0
0
1
1
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
0
2
2
1
1
1
1
1
1
1
1
0
0
2
0
0
1
2
1
2
0
2
2
1
1
1
1
1
2
0
2
1
2
0
0
1
2
1
0
1
1
0
1
1
0
1
2
1
1
2
1
0
2
2
2
1
0
2
1
2
0
0
0
2
0
1
1
1
1
2
2
2
1
1
1
1
2
0
3
2
1
3
1
2
0
1
2
1
1
2
2
2
1
1
2
0
1
1
2
1
1
1
2
2
2
1
1
1
0
0
0
0
1
2
1
1
0
1
1
1
0
1
2
0
2
2
0
2
2
1
0
1
1
2
1
1
1
2
1
1
1
1
1
1
1
0
1
2
0
0
2
1
2
1
1
1
1
2
1
1
0
0
2
0
1
0
2
1
0
1
1
1
1
0
1
0
1
1
2
4
0
2
2
1
0
1
0
1
2
2
1
0
2
1
1
2
1
1
1
0
1
0
1
1
1
0
0
0
0
2
1
2
0
1
2
1
1
1
2
0
1
1
1
1
2
2
1
1
2
1
1
2
1
2
2
1
1
1
1
0
1
1
0
1
2
0
0
1
1
2
0
0
1
2
2
2
0
2
1
1
1
1
1
1
1
1
0
0
1
2
1
2
1
2
2
0
0
0
0
1
1
0
0
1
2
1
1
1
1
0
0
2
1
1
1
0
1
1
2
1
2
1
1
1
1
1
1
2
1
0
1
0
1
2
3
0
1
0
2
1
2
0
1
2
1
0
1
1
0
1
0
1
1
1
1
4
2
0
1
0
1
1
1
1
1
2
1
2
1
1
0
2
1
1
1
1
1
1
1
0
1
1
1
1
1
0
0
1
0
2
3
2
1
2
1
1
0
1
0
2
1
1
1
0
1
2
1
1
1
1
1
1
0
2
1
0
0
1
0
1
2
1
0
2
2
1
0
2
0
0
1
2
0
2
1
1
1
2
0
1
1
1
1
1
0
1
2
1
0
0
1
1
0
1
1
2
1
1
1
1
2
1
1
0
1
2
2
1
1
1
2
1
1
1
1
1
0
0
2
2
1
2
1
0
1
1
0
1
1
1
2
1
2
0
1
0
2
2
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
0
2
2
2
1
2
1
0
1
1
1
1
1
1
1
1
1
1
0
1
1
2
0
1
3
1
0
1
2
2
0
1
2
1
0
2
1
1
1
1
1
1
1
2
1
1
0
2
1
1
2
1
2
1
1
0
1
1
0
2
2
1
1
0
1
1
0
1
1
0
1
0
1
0
1
1
2
1
1
2
1
2
1
0
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
0
2
0
0
0
2
1
1
1
1
2
2
0
2
1
1
2
1
1
0
1
2
2
1
0
1
2
1
1
1
1
2
1
1
1
1
2
2
0
1
1
0
0
2
1
1
2
1
1
2
1
1
1
2
2
1
0
0
1
1
1
1
1
2
0
1
1
2
1
2
1
2
1
2
0
1
0
2
0
2
2
2
1
1
0
1
1
0
1
0
2
1
0
2
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
0
1
1
1
1
1
2
2
1
1
1
1
0
1
0
0
1
0
1
1
2
1
1
2
2
1
2
0
1
1
1
1
1
1
1
1
0
3
0
1
0
0
0
1
2
0
1
2
1
1
1
1
0
0
1
1
0
1
0
1
1
0
2
0
1
2
1
1
1
1
2
2
1
1
1
1
1
1
0
0
2
0
0
2
2
1
1
2
0
0
1
1
0
1
1
1
1
2
2
1
2
0
1
0
1
0
2
0
0
0
1
0
1
2
1
0
1
2
1
0
1
0
1
1
0
1
2
1
0
0
2
1
1
1
0
1
1
0
1
1
1
0
1
1
0
1
1
2
0
0
1
1
1
0
2
1
1
0
2
2
0
1
1
1
0
2
1
0
1
1
1
0
2
2
2
1
1
2
1
1
1
0
0
1
2
5
1
1
1
0
1
1
2
1
0
1
2
1
0
1
0
0
2
1
2
1
2
1
1
1
0
2
1
1
1
2
1
2
0
1
1
0
1
0
1
1
4
2
1
1
0
2
1
1
1
2
1
2
1
1
1
2
0
0
1
0
2
2
0
0
1
1
1
0
1
1
5
0
1
2
0
0
1
0
2
1
1
2
0
0
0
2
0
0
0
1
1
2
1
1
0
1
0
0
0
1
2
2
0
2
1
1
1
1
2
1
2
0
1
1
3
0
1
2
2
2
0
1
1
1
1
0
1
1
1
1
1
1
0
2
1
0
1
1
0
2
0
2
1
1
1
1
0
2
0
1
1
2
2
1
1
1
0
2
1
1
2
1
1
3
1
1
0
1
2
0
0
1
3
2
1
0
1
0
1
2
0
2
0
2
1
2
1
1
1
1
2
2
1
2
1
0
1
0
1
1
1
1
0
1
1
1
1
2
1
2
1
1
1
1
2
1
1
0
1
0
1
1
1
0
0
1
1
2
2
1
1
1
2
2
0
1
2
1
1
2
0
1
1
2
1
1
0
2
1
1
1
2
1
2
2
1
2
1
2
2
0
1
2
0
1
2
1
2
2
1
1
1
1
1
0
0
0
2
0
0
2
1
1
1
2
0
2
1
0
1
1
2
1
0
2
0
0
2
2
0
1
1
2
1
2
1
1
0
0
1
0
1
1
1
0
1
1
1
2
1
1
1
1
0
0
2
1
1
1
1
2
0
1
0
0
1
0
1
1
1
2
1
0
1
0
0
1
1
1
1
1
1
2
1
0
1
1
0
1
1
1
1
1
1
1
1
2
1
2
1
1
1
2
1
1
3
1
1
0
2
1
1
0
1
3
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
2
1
1
0
1
1
1
0
0
1
1
1
2
0
0
2
0
2
1
2
1
1
1
1
0
1
1
0
2
1
1
1
2
1
1
2
0
1
1
2
1
1
1
1
1
1
1
1
1
0
1
0
1
1
1
0
2
2
0
2
1
1
0
1
1
0
2
2
1
1
2
2
0
0
1
1
2
1
1
0
2
1
1
0
2
2
2
1
0
0
1
1
2
0
2
1
0
2
1
1
1
1
2
0
1
1
1
0
1
0
0
1
0
0
1
1
2
1
1
0
1
1
1
0
0
1
1
1
1
0
1
1
0
1
2
1
1
1
2
2
0
1
1
1
1
0
1
2
2
2
1
1
0
0
1
1
1
0
1
5
1
0
2
1
1
2
1
1
0
1
2
2
1
1
1
0
1
1
1
1
1
2
1
1
0
0
1
0
1
1
1
2
0
1
2
2
1
1
1
1
2
2
1
1
1
2
1
2
2
2
1
1
1
0
1
2
1
2
1
1
2
1
2
2
1
1
2
1
1
2
1
1
1
2
1
2
1
2
0
1
1
0
1
1
1
2
1
1
1
0
1
1
1
2
1
1
1
2
1
1
0
2
2
1
0
0
1
1
1
1
1
0
1
2
1
1
2
1
1
2
1
0
2
0
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
0
1
1
1
2
2
1
1
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
0
1
2
1
1
0
0
2
1
2
2
1
1
2
1
2
1
2
1
2
1
1
1
2
2
0
1
1
1
1
1
1
1
0
1
2
2
2
0
1
2
0
0
1
1
0
0
0
0
2
0
1
1
1
0
0
1
0
1
2
1
0
1
2
0
1
2
1
1
1
0
1
1
1
1
0
2
2
0
1
1
1
1
0
1
0
1
2
1
1
0
2
1
0
2
1
1
2
1
1
1
0
2
1
1
2
1
0
2
1
1
0
2
1
2
1
0
1
2
0
1
1
1
2
1
1
2
1
2
0
2
2
1
0
1
1
2
0
2
2
2
1
0
1
2
2
1
1
1
0
2
1
2
1
1
0
2
1
0
1
1
0
1
1
1
1
1
1
3
1
1
1
1
2
1
1
4
1
1
0
1
2
2
1
1
1
3
1
0
1
1
0
1
1
0
1
0
1
1
1
2
2
1
1
1
1
1
3
1
0
1
2
1
1
0
1
0
1
0
2
2
1
1
1
1
1
1
2
2
2
1
2
1
1
1
2
2
1
2
1
1
2
1
1
0
1
1
1
0
1
0
1
1
1
1
0
1
1
2
0
2
2
0
1
0
1
1
1
2
2
2
2
2
1
0
1
1
2
2
0
1
1
2
2
0
0
1
1
1
1
1
1
2
0
2
2
0
1
3
4
0
1
1
0
1
1
1
1
0
1
2
1
0
1
1
1
1
2
3
0
0
0
1
0
1
2
2
2
2
0
1
2
1
0
1
1
1
0
1
1
1
2
1
1
2
2
2
1
0
1
0
2
0
1
0
0
1
1
1
1
1
0
1
1
2
0
1
1
0
0
0
1
2
2
1
2
1
1
1
0
0
1
1
1
1
1
0
1
1
1
1
1
2
1
1
0
1
2
1
1
0
1
0
2
2
1
1
1
1
1
1
1
2
1
1
2
2
1
2
1
1
1
1
1
0
0
1
2
1
1
1
2
1
1
1
1
1
2
0
1
2
0
1
1
2
1
1
1
1
1
1
0
1
2
2
1
1
2
2
1
2
1
1
0
2
0
1
1
1
1
2
1
1
0
1
0
1
2
1
1
2
1
1
2
1
1
0
1
2
1
0
2
1
0
1
1
1
2
1
1
1
0
0
1
1
1
1
1
1
1
1
0
1
1
2
1
1
0
1
0
1
1
2
0
0
1
1
1
0
1
0
1
2
1
1
0
1
1
1
1
1
1
2
3
1
1
1
1
1
1
1
0
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
0
2
2
2
2
2
0
2
1
1
2
1
1
2
2
1
0
2
2
1
0
1
2
0
1
0
2
1
1
0
0
1
1
1
1
2
2
1
1
1
0
1
1
1
1
3
2
1
0
0
0
1
0
1
1
1
1
0
1
0
1
1
1
1
2
2
2
2
1
1
1
1
1
2
1
1
1
0
1
1
1
4
0
1
0
1
0
1
1
1
2
1
2
1
1
2
1
0
2
2
0
0
1
1
1
0
2
1
0
1
1
1
0
1
1
1
0
2
0
1
0
1
1
0
1
1
1
1
2
2
1
1
1
1
1
2
1
1
2
1
1
1
0
2
2
1
1
1
1
1
2
1
1
0
1
1
1
0
0
1
1
1
0
1
1
1
2
1
1
0
2
1
1
0
1
1
2
1
2
2
1
1
1
0
1
0
2
2
0
1
1
1
0
2
1
1
1
0
1
1
1
1
1
1
2
1
2
1
0
0
1
2
1
1
1
1
1
2
1
2
1
4
0
0
0
0
1
2
1
2
1
1
2
1
0
0
1
1
1
1
1
1
1
1
2
1
2
1
1
1
0
1
2
1
1
0
1
0
1
1
1
1
2
1
1
0
1
1
1
0
1
1
1
0
1
2
1
1
1
1
1
0
2
0
2
1
0
1
1
0
1
2
1
1
1
1
1
1
2
2
1
1
1
2
2
1
1
1
1
1
0
0
2
2
1
2
2
1
1
1
1
2
2
1
1
1
2
2
3
1
1
0
2
0
2
1
2
0
1
1
1
1
0
0
0
1
2
1
1
2
1
1
0
1
1
1
1
0
1
0
1
1
1
1
2
1
2
0
1
2
0
2
1
1
1
2
2
1
2
1
1
1
1
0
1
0
0
1
2
0
1
1
1
1
1
2
1
1
2
1
0
0
2
2
1
1
1
1
1
1
0
1
0
1
2
1
3
1
1
0
0
1
0
1
1
1
1
2
1
1
2
1
3
1
2
0
0
0
1
1
1
1
0
0
0
1
1
0
1
1
0
0
1
0
1
1
1
2
1
1
2
0
1
1
1
1
2
1
1
2
1
0
1
1
1
0
0
1
0
1
1
0
1
1
1
2
2
1
1
1
1
2
2
2
0
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
0
2
2
2
1
0
0
1
0
2
1
1
0
1
1
1
2
1
1
0
1
0
1
0
1
0
1
1
2
1
3
1
0
0
1
1
3
2
2
2
0
2
2
0
0
1
1
0
1
2
0
1
1
1
1
1
2
1
1
0
2
2
0
1
2
2
1
0
0
2
1
0
1
1
4
1
2
0
0
0
0
1
1
1
1
0
0
2
0
1
2
1
1
1
0
1
1
1
2
1
1
2
0
2
1
0
2
1
2
0
1
1
1
1
1
2
1
0
1
1
2
1
2
1
0
1
2
1
0
1
0
0
1
0
0
2
0
1
1
0
2
2
1
1
1
0
0
2
2
0
1
2
1
0
0
1
1
1
1
0
1
2
1
0
1
1
1
0
2
3
2
1
2
2
2
0
0
2
1
0
1
1
1
1
1
1
0
1
2
2
0
1
1
1
1
1
1
1
0
1
1
1
0
0
1
1
1
1
1
2
1
1
1
1
2
1
0
1
1
2
1
1
1
0
1
2
1
1
0
1
0
0
2
1
0
1
0
0
1
2
0
1
1
1
1
1
1
0
0
0
1
2
1
1
0
0
2
0
2
1
1
0
1
1
2
2
1
0
1
1
1
0
1
2
2
2
0
0
1
0
3
1
1
1
1
1
2
2
1
0
2
0
2
1
0
0
1
2
2
1
0
1
1
1
0
0
1
1
0
1
1
2
1
1
1
0
1
2
1
1
0
1
1
0
2
0
1
1
0
1
1
1
1
1
2
1
0
0
1
2
2
1
0
1
1
1
1
1
0
1
2
1
2
0
1
2
0
1
2
1
1
2
1
1
1
1
2
2
1
2
2
2
1
1
2
2
1
2
1
1
2
1
0
1
0
0
1
1
2
1
0
0
0
0
1
0
2
1
1
1
1
2
0
1
1
2
2
0
1
0
1
2
1
2
1
1
0
1
1
1
2
1
1
0
2
1
1
1
0
1
2
1
2
0
1
1
0
1
2
2
1
1
1
2
0
0
1
1
1
2
1
2
1
1
0
1
1
1
1
2
1
1
1
0
0
1
2
1
2
1
1
0
1
0
1
1
1
0
0
1
2
2
0
2
1
0
0
1
1
1
2
1
1
2
1
1
1
1
0
1
2
2
1
2
1
1
1
1
0
1
0
1
2
1
0
2
1
2
2
1
1
0
1
1
0
3
0
1
1
2
1
1
0
2
2
0
1
1
0
0
0
1
1
1
1
2
1
1
1
0
1
1
1
1
2
2
1
0
1
2
2
1
2
1
1
1
1
2
0
0
1
2
1
0
1
2
1
0
1
1
1
1
1
1
0
0
1
0
2
1
1
1
1
0
0
1
0
1
1
2
1
1
1
1
0
0
2
2
2
0
2
0
1
1
1
0
1
1
0
2
1
1
0
0
2
0
1
0
2
2
1
1
2
1
1
2
0
1
2
1
2
1
2
1
1
1
1
1
2
2
0
1
1
1
2
1
2
0
1
2
1
1
1
1
0
2
1
1
1
1
1
1
1
1
1
1
0
1
2
1
1
1
2
1
1
1
2
0
1
0
1
0
2
1
1
1
1
0
1
0
0
1
2
1
0
1
2
0
1
0
2
1
1
0
0
0
0
0
1
1
1
1
1
1
2
2
1
2
1
1
2
2
1
1
1
0
2
1
1
1
3
0
1
2
1
2
2
1
0
2
0
1
1
0
2
0
1
1
0
1
1
2
2
2
1
1
0
2
1
2
2
1
0
1
1
1
2
1
0
1
1
1
1
1
0
1
1
1
2
1
1
1
2
1
0
2
1
2
1
1
0
1
1
0
2
1
1
1
0
1
1
2
2
1
1
2
1
1
1
2
1
1
2
0
0
2
2
1
0
1
2
0
0
2
1
1
2
0
0
0
1
0
0
1
1
0
1
1
1
1
0
0
1
1
2
2
0
2
1
1
1
1
1
1
2
1
1
0
2
0
2
1
1
0
1
1
1
2
1
1
2
1
0
1
1
1
1
1
2
2
0
0
1
0
1
1
1
1
1
1
0
2
1
1
0
0
2
2
6
1
1
2
1
1
0
1
0
1
1
1
1
1
0
1
1
1
3
1
0
2
1
1
2
1
1
1
2
1
1
0
1
1
0
0
1
0
1
1
1
0
1
1
1
1
1
0
2
1
1
1
1
1
2
0
2
2
2
1
1
2
1
1
1
1
2
2
0
1
2
2
1
1
2
0
1
0
1
1
0
0
2
1
0
1
1
1
2
1
0
1
2
1
1
2
2
0
0
1
0
0
1
1
2
0
2
2
1
1
1
1
1
2
1
2
0
1
1
1
0
0
1
2
2
1
2
0
0
2
1
1
2
0
4
1
1
1
2
0
2
1
1
1
1
1
1
1
0
1
1
0
1
1
2
2
0
1
1
2
1
1
2
0
1
1
1
1
2
0
0
1
1
1
1
2
1
1
1
1
1
2
0
2
1
2
1
1
0
1
1
2
1
1
2
1
1
1
1
0
2
0
1
1
1
1
1
1
1
1
2
1
0
2
1
0
2
1
1
1
1
0
1
1
1
0
2
2
2
1
1
2
2
2
1
2
1
2
2
4
1
2
0
1
0
1
0
3
1
1
2
2
1
1
1
0
0
1
1
0
1
1
0
1
0
1
1
0
2
0
1
0
2
1
1
1
2
2
0
2
1
2
1
0
1
1
2
1
1
1
1
1
1
1
1
2
1
0
1
1
2
2
1
0
2
0
1
1
2
2
1
3
1
0
1
2
1
0
0
1
2
2
1
2
2
2
1
1
1
1
1
2
1
1
1
2
1
1
1
2
1
1
6
0
1
1
1
0
1
1
0
1
0
2
0
1
1
1
1
1
0
1
1
0
0
2
0
1
2
2
1
0
1
1
1
0
1
2
0
1
2
2
1
0
1
1
0
0
2
1
1
2
0
2
2
2
1
0
2
1
1
2
1
1
0
1
1
1
2
2
2
1
2
1
1
1
1
2
0
2
0
0
0
0
2
2
1
0
1
1
1
0
2
1
0
1
0
1
2
1
0
1
3
1
1
1
1
1
0
1
2
1
1
0
1
1
2
2
1
0
2
2
2
0
1
1
0
1
1
1
0
0
1
1
1
1
0
0
1
1
2
2
2
2
1
1
0
1
1
1
1
1
2
1
0
1
2
0
1
1
1
2
1
1
0
1
1
2
1
1
1
2
1
2
2
1
1
1
1
1
2
0
1
1
3
1
0
1
1
1
1
0
1
1
0
2
0
0
0
1
1
1
0
0
0
1
1
1
1
1
1
0
1
1
2
3
1
1
1
1
2
1
0
1
0
2
1
1
1
1
2
2
3
1
0
0
1
2
1
0
0
2
3
1
1
1
1
1
1
1
1
1
2
2
0
0
1
1
2
2
0
2
1
1
1
2
3
0
1
2
0
0
1
1
0
1
2
3
2
2
1
1
1
1
1
1
2
1
2
0
0
0
0
0
1
1
1
2
1
1
1
1
1
1
2
0
1
2
0
2
1
2
1
1
1
1
0
2
1
1
0
1
0
1
2
1
0
2
0
1
2
0
0
0
2
1
2
1
1
1
2
1
1
1
1
1
0
1
2
1
1
1
2
1
0
1
1
0
1
1
1
1
1
1
1
2
2
1
1
1
0
1
0
1
1
1
2
2
1
2
0
1
1
0
1
1
2
1
1
1
2
2
1
0
0
1
1
1
2
1
2
1
1
1
0
0
1
1
0
2
1
1
1
2
0
1
0
0
2
2
1
1
1
0
1
1
1
2
1
1
1
0
7
1
1
1
2
1
2
1
1
2
1
1
0
1
1
1
1
0
1
1
0
2
1
0
1
0
1
1
1
0
1
2
1
2
0
0
1
1
1
1
2
0
1
2
1
1
0
1
2
1
1
1
0
1
1
1
0
0
1
1
2
1
1
0
0
1
2
1
2
1
2
2
1
0
0
1
1
0
0
1
0
1
2
1
1
1
2
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
0
0
1
1
1
0
0
1
1
2
1
1
1
2
2
1
1
2
2
2
1
0
0
1
2
1
1
2
1
0
2
1
1
1
0
1
1
1
1
1
0
1
1
0
3
1
2
2
1
3
1
2
1
0
1
1
1
2
1
1
1
0
0
0
2
1
0
1
1
0
0
1
1
1
1
1
0
1
2
1
0
0
1
1
2
2
1
0
0
0
1
1
1
1
1
0
1
1
1
0
2
1
1
1
1
2
2
1
1
1
1
1
0
1
1
1
1
3
2
2
2
1
0
1
2
2
0
1
1
0
1
1
1
1
1
1
0
1
2
0
0
2
0
2
1
1
0
0
1
1
0
1
1
3
1
0
1
1
1
1
2
2
2
1
1
1
1
2
2
1
1
0
1
1
1
2
2
1
1
1
2
1
0
1
0
1
1
1
0
1
1
2
2
2
1
2
1
1
1
1
2
0
1
0
1
2
2
1
1
1
1
1
2
2
1
1
1
0
2
1
0
1
2
1
2
1
1
1
1
0
2
1
2
1
1
0
1
0
1
1
1
1
1
2
1
2
1
1
1
0
1
1
1
1
2
2
1
2
1
0
1
1
2
2
1
1
1
1
1
0
1
2
1
0
2
1
2
2
2
1
1
2
0
0
1
1
1
0
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
0
0
1
0
1
0
1
2
1
1
0
1
2
1
0
0
2
1
1
2
1
2
2
0
1
13
1
1
2
0
2
0
0
1
1
1
1
2
1
1
0
1
1
2
1
1
1
2
1
1
2
1
0
2
1
1
2
1
1
1
1
0
1
1
1
1
1
1
0
1
0
1
2
1
1
1
1
0
0
1
1
0
1
0
1
2
2
1
0
1
1
1
0
0
1
0
1
2
1
0
1
0
1
1
1
1
0
2
1
1
1
1
0
1
1
1
3
0
1
1
0
1
2
0
2
1
0
0
0
1
1
1
0
1
1
2
0
2
1
1
1
2
1
1
0
2
1
0
1
2
2
1
0
1
0
1
2
1
1
1
2
1
1
0
2
1
0
2
1
3
1
2
1
1
2
0
0
1
2
2
0
1
1
0
1
0
0
0
2
2
1
1
1
0
2
0
2
2
1
1
1
2
0
0
0
1
1
0
1
1
0
1
1
0
0
0
2
1
0
2
2
2
0
1
1
2
2
1
2
1
1
3
3
1
1
1
0
1
0
2
2
0
0
2
2
2
1
1
2
1
1
1
1
2
1
1
0
1
2
0
2
2
1
1
1
0
0
1
1
2
2
0
1
1
1
1
0
1
0
1
2
1
1
1
1
1
1
2
2
1
2
0
1
1
2
1
2
2
0
2
1
2
2
1
2
1
1
2
1
2
1
2
1
2
1
0
1
1
1
2
1
1
0
1
1
0
1
1
2
2
0
0
1
1
1
1
1
0
1
1
1
2
1
1
0
2
1
1
1
1
1
1
2
1
1
2
0
2
0
0
0
0
1
1
2
1
1
0
2
2
2
1
1
1
1
2
1
1
1
2
1
0
0
1
2
1
1
0
2
2
1
0
0
1
0
0
2
1
1
1
1
0
1
1
1
0
2
1
2
1
0
1
1
1
1
1
1
1
1
0
1
1
0
1
1
0
2
2
1
1
1
1
1
0
1
1
1
1
2
1
1
0
2
1
2
1
0
0
1
1
1
1
2
2
1
1
1
1
1
2
1
1
1
0
2
1
1
0
0
1
2
2
0
2
0
1
2
2
1
2
2
1
0
0
1
0
2
0
0
1
1
1
1
1
1
2
2
0
2
0
1
1
1
1
2
1
2
1
1
2
1
2
2
1
1
1
1
1
2
2
0
1
1
1
1
1
0
2
0
1
0
1
2
2
2
1
0
1
1
1
1
2
1
2
1
1
1
1
1
1
2
1
0
2
1
1
0
1
0
0
1
2
2
2
1
0
0
0
1
2
1
0
1
1
2
2
1
1
1
2
1
2
1
1
1
2
1
1
1
1
1
0
1
1
2
1
0
1
1
1
0
1
2
0
1
2
2
0
2
1
1
0
2
1
3
1
0
0
2
2
1
0
1
1
2
0
1
1
1
1
1
0
0
1
1
2
1
0
0
2
1
2
1
0
1
0
1
1
0
1
0
0
0
1
1
0
2
1
0
1
1
4
0
2
1
1
1
2
1
0
0
3
1
1
1
1
2
2
0
1
1
1
1
1
0
0
1
2
1
0
2
1
1
1
0
0
0
2
2
0
1
0
1
1
1
0
0
0
1
1
1
2
2
1
2
1
1
1
1
2
2
2
1
0
2
2
1
1
0
2
1
1
0
2
1
0
1
0
2
0
0
1
1
1
0
0
2
2
1
1
2
3
0
0
1
1
0
2
2
1
1
0
2
2
1
1
1
0
4
1
2
2
1
1
2
2
0
2
0
2
2
1
1
1
1
2
0
2
0
2
1
1
1
0
2
1
1
1
1
2
1
2
2
0
1
2
2
1
2
1
1
2
1
2
0
1
0
2
1
0
2
1
2
1
2
1
2
1
1
0
2
1
0
1
0
1
1
2
1
0
1
1
0
1
1
1
2
1
1
0
1
1
1
1
1
0
1
1
1
1
1
1
0
1
1
2
1
2
1
1
0
1
0
1
0
1
2
1
1
0
0
2
2
0
1
0
1
1
1
1
0
0
1
1
0
1
2
0
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
12
1
1
4
1
2
1
1
2
3
0
0
2
1
1
1
1
1
2
1
1
2
0
1
0
1
1
0
1
2
1
1
2
2
1
0
1
1
1
1
1
1
0
4
1
0
2
1
3
2
1
1
0
1
1
1
1
0
1
1
2
1
2
2
1
1
1
1
0
1
1
1
1
2
0
2
1
1
4
1
0
1
1
1
1
0
1
1
1
1
2
1
1
1
1
0
1
1
1
2
5
1
1
1
2
1
1
1
1
1
1
1
1
1
1
0
0
1
1
1
2
0
0
2
1
1
1
2
1
1
0
2
1
2
1
1
0
2
1
0
1
1
1
1
0
1
0
1
1
0
1
1
1
0
1
0
3
1
2
2
1
0
0
1
1
0
1
1
2
2
1
1
1
0
1
2
0
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
0
0
0
2
0
1
0
2
1
0
1
1
1
1
2
1
1
1
1
1
1
0
2
1
1
1
1
0
1
0
1
2
0
2
1
2
1
2
1
1
1
0
2
0
1
1
2
1
2
2
2
1
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
0
0
2
2
1
1
2
1
1
1
0
0
1
1
0
1
1
1
1
1
1
1
2
1
2
2
2
2
1
1
2
1
2
1
1
1
1
1
1
0
0
0
1
2
0
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
0
0
1
1
1
1
2
1
1
1
2
1
0
1
0
2
2
3
0
2
1
1
1
1
1
2
2
0
1
1
0
1
2
0
1
1
1
1
0
2
0
2
2
0
1
0
0
0
0
1
1
1
1
1
0
0
1
1
2
1
1
2
1
0
1
2
1
0
2
2
1
2
1
1
2
1
1
2
2
0
1
2
1
1
0
3
1
2
1
1
1
1
1
2
1
1
1
1
2
2
1
0
2
1
0
1
1
1
1
0
0
0
1
0
1
1
1
1
1
1
0
1
1
2
2
1
0
1
2
1
2
1
1
0
0
0
1
0
2
1
2
0
2
1
1
1
2
2
2
1
0
0
2
0
2
2
0
1
1
1
2
1
2
1
1
1
1
0
2
1
1
1
2
1
1
1
1
1
0
1
0
0
1
1
2
2
2
2
2
0
1
2
1
1
1
2
2
0
1
0
1
1
2
1
2
1
2
0
2
1
2
0
2
2
1
1
0
2
2
1
1
1
1
0
1
1
0
1
1
2
2
1
0
1
0
0
1
1
1
1
1
1
1
1
1
1
2
0
1
2
1
0
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
4
1
1
1
1
1
1
2
0
1
1
2
1
1
2
1
0
2
1
2
1
2
0
1
1
1
2
0
1
1
1
1
1
0
1
0
0
2
2
1
0
2
0
0
1
0
2
1
1
0
1
1
2
0
2
1
2
1
2
1
2
2
1
1
1
1
1
0
1
1
1
1
1
0
0
1
1
0
2
2
1
1
1
0
1
1
0
1
1
2
1
1
0
1
1
1
1
4
1
2
0
1
2
1
0
1
1
1
1
0
1
2
1
1
0
2
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
0
2
1
0
2
1
1
2
1
0
1
1
1
1
1
0
1
1
2
1
2
1
2
1
1
2
1
1
2
2
2
1
1
1
1
2
1
0
1
0
1
2
1
1
1
1
1
1
1
0
0
1
0
0
2
1
1
1
2
1
1
1
1
1
1
1
2
2
1
0
2
0
1
0
1
1
1
1
3
1
2
2
1
1
1
1
0
1
0
1
1
2
1
1
1
1
2
0
1
2
1
1
1
1
1
0
2
0
2
0
2
2
1
2
1
2
0
2
0
0
1
1
1
2
1
1
1
0
1
1
0
3
0
1
1
1
0
2
2
1
1
1
1
1
1
1
2
1
0
1
1
0
2
1
2
1
1
1
2
1
1
0
4
0
1
1
0
1
1
2
1
0
0
1
2
1
2
1
1
2
2
1
1
1
0
1
0
0
1
1
1
3
2
0
1
0
2
1
1
1
1
0
2
2
1
1
1
1
1
0
1
0
1
1
1
1
1
1
2
0
1
1
2
1
3
1
1
1
1
1
1
1
0
1
1
2
1
0
1
1
1
1
1
1
0
1
2
2
1
1
2
1
1
2
2
2
1
1
4
1
2
0
1
1
2
1
1
1
1
0
1
1
2
1
1
1
1
1
0
1
1
0
1
1
1
1
0
2
1
0
0
1
2
1
2
1
1
0
0
1
1
1
1
2
1
1
1
0
1
1
0
0
2
1
1
0
0
1
0
0
0
2
1
1
1
1
2
1
0
1
1
1
2
0
1
2
1
1
1
1
0
1
1
0
2
3
1
1
0
0
0
0
0
1
1
1
2
1
2
1
2
1
0
0
1
1
2
1
0
2
1
0
3
0
1
1
1
2
1
1
1
1
2
0
1
1
1
0
1
1
0
1
1
2
1
1
2
1
1
1
1
3
1
1
1
0
1
1
0
1
0
1
1
3
1
2
2
0
0
1
1
1
1
1
1
0
1
1
1
1
1
1
2
1
0
1
1
2
0
1
1
1
2
0
2
1
0
1
2
1
1
0
2
2
1
0
2
1
0
0
2
1
1
1
0
1
0
2
1
2
2
1
0
1
1
1
1
1
1
1
1
2
2
0
1
0
1
1
0
0
2
1
2
1
1
1
1
3
1
1
0
2
2
0
0
2
1
1
0
1
1
2
2
1
1
1
2
1
2
1
1
1
1
0
2
1
1
1
1
1
0
0
1
2
1
0
1
0
1
0
1
1
2
2
1
1
1
2
1
1
1
0
0
1
1
2
2
0
1
0
1
0
0
0
1
1
1
1
2
1
1
0
0
1
1
1
1
0
0
1
1
0
0
0
1
1
2
2
1
1
1
2
2
1
1
2
1
1
1
2
3
2
1
1
2
2
0
1
1
1
1
1
1
2
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
0
1
1
1
1
2
3
0
2
0
2
1
1
1
1
0
1
2
0
1
0
3
0
0
2
1
1
1
0
0
1
1
1
0
1
1
0
1
0
1
1
1
2
2
1
2
0
3
2
0
0
2
1
1
1
2
2
3
1
2
1
1
1
0
1
1
0
1
1
1
1
1
1
1
2
2
2
2
0
1
1
0
0
1
1
1
1
2
1
0
1
1
1
0
0
2
1
2
0
2
1
1
1
1
1
1
0
1
1
0
2
1
1
0
0
1
0
1
1
2
1
1
1
2
1
1
0
0
1
0
1
1
1
1
2
2
0
2
1
0
1
1
1
1
0
1
1
1
0
1
2
0
0
0
2
1
1
1
1
1
1
2
1
3
1
2
1
0
1
2
2
1
0
1
3
1
1
2
2
1
1
1
2
1
2
1
0
1
3
2
0
1
1
1
1
1
0
1
2
0
1
1
1
0
1
1
1
2
1
1
1
2
1
1
0
1
1
1
2
1
0
2
2
1
1
1
2
1
1
1
0
2
1
2
1
2
1
2
0
0
0
0
1
2
0
2
0
0
1
2
1
1
1
0
2
1
0
2
1
0
1
1
1
1
2
1
0
2
0
1
2
1
2
0
0
1
0
0
0
1
2
1
1
1
1
1
1
0
1
2
1
0
2
0
1
1
2
2
1
2
1
1
2
1
1
0
1
1
0
2
0
1
1
0
0
1
2
2
1
1
1
1
1
0
2
1
2
1
2
2
1
1
1
0
1
1
2
0
1
1
1
2
2
0
2
1
1
1
1
2
2
1
2
2
2
2
1
1
1
1
2
0
1
1
1
0
1
1
1
1
0
1
1
1
1
1
1
2
1
1
1
2
1
1
0
0
1
1
1
1
2
1
1
1
0
2
0
0
0
1
0
0
1
2
2
1
1
0
0
2
1
1
1
1
2
2
2
1
1
2
1
2
1
1
1
2
1
1
0
2
0
1
1
1
1
0
1
2
1
1
0
2
1
1
1
1
1
0
1
1
1
1
2
1
2
1
1
0
1
1
1
1
1
1
1
2
1
1
1
1
2
0
0
1
1
1
0
1
1
1
0
1
0
0
2
0
1
1
0
1
1
2
1
1
2
2
1
1
1
0
2
1
0
0
1
1
2
1
1
1
1
1
0
2
2
2
1
1
1
1
0
0
1
1
2
1
1
1
1
1
0
1
0
2
1
1
2
1
0
0
2
2
1
0
1
1
1
1
1
1
1
2
1
1
0
0
1
1
1
2
1
1
1
1
2
1
1
1
2
0
0
1
1
1
1
1
0
2
1
1
3
1
0
1
1
1
2
1
0
1
1
1
1
0
1
0
0
1
1
2
1
1
0
1
2
2
1
1
0
1
1
1
1
0
0
2
1
0
0
0
1
1
2
1
1
2
1
1
0
1
0
1
1
3
1
1
2
0
1
0
1
2
1
0
1
1
1
1
1
1
2
1
0
1
1
0
0
0
1
0
1
0
2
1
1
1
1
2
1
1
1
2
1
0
0
1
2
0
2
1
1
1
1
0
1
1
1
0
0
2
2
2
2
1
1
0
1
2
3
1
0
0
1
2
1
2
0
1
1
1
1
2
1
2
1
2
1
1
1
1
1
0
1
0
0
2
0
1
0
1
1
0
1
1
1
0
2
1
1
2
2
1
1
1
0
1
1
2
1
0
0
1
1
1
1
1
2
1
2
0
1
0
2
1
1
1
1
0
1
1
0
1
1
1
1
0
1
1
0
0
1
2
1
1
1
0
1
1
1
0
1
2
0
2
0
0
0
2
1
1
1
1
1
2
0
0
1
0
1
1
2
1
1
1
1
2
1
2
0
0
0
1
1
2
1
1
0
0
0
0
2
0
2
1
2
1
1
0
1
1
1
2
0
1
2
2
0
1
1
0
2
1
2
1
2
1
2
1
1
0
2
0
0
2
1
1
0
1
1
1
0
1
1
1
1
1
1
1
1
0
0
1
1
1
1
1
1
1
1
0
1
0
1
2
1
1
1
3
0
0
1
1
2
0
2
1
1
1
1
1
1
2
1
2
1
1
1
0
1
1
1
2
2
0
0
1
1
1
2
2
2
1
0
1
1
1
1
1
0
1
1
1
0
2
0
1
1
1
1
0
2
1
1
1
1
2
0
1
1
2
2
1
0
2
0
1
1
1
1
0
1
0
2
2
2
1
0
1
3
1
1
0
0
1
1
1
1
1
3
1
0
1
1
0
2
2
1
0
1
1
2
1
1
2
2
0
1
1
1
2
1
1
1
1
2
1
0
2
1
1
2
2
1
1
1
1
1
2
1
2
2
1
1
2
2
1
2
1
0
2
0
1
1
0
2
2
2
0
2
1
2
1
1
1
0
1
1
1
1
1
0
1
1
0
1
1
2
1
1
2
2
2
0
1
0
2
1
1
1
1
0
0
0
2
0
0
2
1
1
1
1
2
1
2
1
1
1
0
1
0
1
0
0
1
0
0
1
1
0
2
0
1
1
0
1
2
1
1
1
1
1
1
1
1
0
0
0
1
1
1
1
2
2
1
0
1
1
2
2
0
1
1
0
1
1
1
1
2
0
2
1
0
1
2
1
1
1
1
2
1
0
0
2
1
1
2
2
1
1
1
1
1
2
0
1
1
2
0
1
2
2
0
0
1
2
2
1
1
0
1
1
1
2
0
2
1
1
1
1
2
0
1
1
0
1
2
1
1
1
2
0
1
2
1
0
0
2
2
1
1
0
0
1
1
0
0
0
0
1
0
1
0
0
2
2
2
1
0
1
0
2
2
1
2
1
2
1
1
2
0
0
2
1
2
0
0
1
2
1
2
2
2
1
2
1
2
1
1
1
0
1
1
1
2
0
0
1
1
1
2
1
0
0
2
1
2
1
1
2
1
1
1
2
2
2
1
1
1
0
1
0
1
2
0
1
2
1
0
0
1
0
1
1
0
1
0
0
1
1
1
1
0
0
0
1
1
0
2
1
0
1
2
1
0
0
2
0
0
0
1
1
0
1
2
1
0
1
1
1
0
0
1
1
1
1
2
1
1
1
1
1
2
1
0
1
1
2
1
1
1
1
1
1
1
1
0
2
0
4
2
1
2
0
1
2
1
1
1
1
1
2
1
1
1
2
0
1
2
1
1
1
2
1
2
1
0
1
1
2
1
2
1
1
0
1
1
1
0
0
0
1
3
1
0
0
2
1
1
0
1
1
0
2
1
1
2
2
1
2
0
0
3
1
1
1
0
1
1
1
2
1
1
2
0
1
1
1
1
1
2
3
1
1
1
2
1
1
0
2
0
2
2
0
1
1
1
2
1
1
2
1
1
1
2
0
2
2
0
0
0
1
1
2
2
2
1
0
1
1
0
1
1
1
0
0
0
1
1
2
2
2
1
1
2
1
2
3
1
1
1
1
1
1
1
0
1
1
1
1
2
1
2
0
1
1
1
1
0
1
2
0
0
1
1
1
2
1
0
2
0
0
1
0
2
1
1
1
2
2
0
2
1
1
1
1
1
0
0
2
0
1
2
1
1
0
1
1
1
1
1
1
1
1
2
1
2
2
2
0
0
1
1
2
0
1
1
1
1
2
0
1
1
1
1
1
1
1
1
2
0
0
1
1
0
1
0
1
0
0
1
1
1
1
1
2
1
1
1
2
1
1
0
1
1
1
0
1
0
0
1
2
1
1
1
2
3
1
0
2
1
2
1
1
2
1
1
1
1
1
1
2
1
1
2
2
0
1
1
1
3
1
0
2
0
2
2
1
1
1
1
1
1
1
2
2
1
1
0
1
0
1
1
0
1
2
1
1
2
1
2
2
0
1
1
1
2
1
1
1
4
2
1
0
2
2
1
2
1
1
0
0
1
2
1
1
1
1
1
1
1
2
2
2
0
1
1
0
1
2
1
1
0
2
1
1
2
0
0
1
0
2
1
2
1
1
0
2
1
1
0
1
1
1
2
2
2
0
1
0
1
2
0
1
1
1
1
1
2
1
2
0
1
0
2
2
0
0
2
3
1
0
1
4
2
1
1
1
2
1
0
1
1
1
1
0
2
1
0
1
2
1
1
1
1
2
1
1
2
0
2
1
1
2
1
1
2
1
0
1
2
2
2
0
1
1
1
2
0
0
2
1
1
1
2
1
2
1
0
1
2
2
1
0
0
1
1
1
2
2
2
1
1
1
1
1
1
1
1
1
0
1
1
1
0
1
1
1
0
0
2
2
0
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
1
3
1
0
1
2
2
0
2
2
2
0
1
1
2
1
0
0
1
1
1
2
1
2
1
1
1
1
2
2
1
1
0
1
0
2
1
2
2
1
2
1
1
2
2
1
2
0
2
0
0
1
2
1
1
0
2
0
2
2
1
2
0
3
0
0
1
0
1
1
0
0
1
2
1
0
1
1
2
0
1
0
1
1
1
1
2
1
1
1
2
1
1
2
2
1
0
1
1
0
2
1
1
1
2
1
1
2
1
2
2
0
1
1
0
2
2
0
0
2
2
2
1
1
0
2
0
1
0
1
1
0
2
2
1
0
0
0
0
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
0
1
0
2
0
1
1
1
2
5
1
1
1
1
1
1
0
1
2
2
1
0
1
1
1
1
0
1
1
0
2
2
2
1
2
1
1
1
1
1
2
2
1
0
1
1
1
0
2
1
0
0
1
1
0
0
1
1
2
1
0
2
1
1
0
1
2
1
0
1
1
1
2
0
0
2
1
1
2
1
1
2
1
1
2
2
1
2
1
1
1
1
0
1
2
2
2
1
1
2
2
2
0
2
1
0
1
2
1
1
1
1
0
1
2
1
1
1
1
2
1
1
1
2
0
0
1
1
2
1
2
0
2
2
1
2
2
2
1
1
1
2
1
1
2
2
0
0
0
1
1
1
1
1
1
1
1
0
2
0
2
1
0
1
2
1
1
1
0
1
0
1
0
0
1
1
1
1
0
0
1
1
0
1
1
1
1
1
1
2
3
0
2
1
1
0
1
0
1
1
1
1
1
2
0
1
1
2
1
1
1
1
2
1
3
1
1
2
2
1
2
1
3
1
1
1
1
1
2
0
1
0
0
2
0
1
1
1
1
1
0
1
1
1
0
0
1
1
2
2
0
1
0
0
1
1
2
0
1
2
0
1
1
0
2
0
1
2
1
1
0
1
0
0
1
1
1
2
1
1
1
2
0
1
1
1
1
0
1
0
1
1
1
0
1
2
1
0
1
0
1
1
1
0
2
2
1
1
1
0
2
1
2
2
3
2
0
0
1
0
1
2
0
1
1
1
2
1
2
1
1
2
1
1
1
1
1
1
1
1
4
1
2
1
1
1
2
1
1
2
3
1
2
1
2
2
1
2
1
0
1
0
2
2
1
1
0
1
1
1
2
2
2
1
0
2
1
1
2
1
1
1
1
0
1
2
1
0
1
1
1
2
0
0
1
2
2
2
1
1
1
2
1
2
0
0
1
2
1
1
0
1
2
1
1
1
2
1
1
0
1
1
2
1
0
1
1
0
1
2
1
2
1
0
2
1
1
0
1
0
2
1
1
0
2
1
2
1
2
1
2
1
2
1
1
1
2
1
2
0
1
2
1
0
1
2
1
1
1
2
1
1
2
1
0
1
2
1
1
1
0
1
1
0
0
2
0
2
1
1
2
1
0
0
0
1
1
1
0
0
2
1
2
1
2
1
1
2
1
1
3
1
0
1
2
2
1
1
2
0
1
0
2
1
2
1
1
1
1
1
2
1
1
2
2
2
2
2
0
2
1
2
1
1
1
0
2
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
0
2
1
1
1
1
0
1
2
1
2
1
1
0
1
0
0
1
1
0
0
1
1
0
2
1
1
1
1
1
1
2
0
1
1
1
1
1
0
1
1
1
0
1
1
1
2
0
0
2
1
1
0
1
0
1
2
0
1
1
1
0
1
1
1
0
0
1
1
1
1
1
1
1
0
2
1
1
0
2
1
0
2
1
2
1
0
3
1
2
2
1
0
1
1
1
0
1
1
1
2
1
1
2
1
1
1
1
1
1
0
0
1
1
2
1
0
1
0
1
3
0
1
0
0
1
2
2
1
2
1
2
0
1
1
1
2
1
2
2
4
1
0
1
0
1
1
1
1
2
1
1
1
1
1
1
1
1
2
2
1
1
1
0
0
1
0
1
0
0
1
1
1
1
2
2
2
2
2
1
0
2
1
0
2
1
0
1
2
1
2
2
1
2
1
2
1
0
1
1
2
0
2
1
2
2
0
1
1
0
2
2
0
2
0
2
1
1
1
0
1
1
0
9
1
2
0
0
1
0
2
1
0
1
1
2
0
2
2
1
1
1
0
1
0
0
1
1
1
1
1
1
0
1
1
1
1
2
1
1
0
0
0
2
1
2
4
1
0
2
1
1
2
2
1
1
2
2
1
1
1
2
1
1
1
1
1
1
1
0
2
1
2
1
0
1
2
1
1
0
1
1
1
2
1
0
1
2
1
1
1
1
0
1
1
1
0
1
2
1
2
0
2
1
2
1
1
1
2
1
0
1
1
0
1
1
1
2
1
1
2
2
1
2
2
1
1
1
3
0
0
0
0
1
1
1
1
0
1
1
2
2
1
0
1
1
1
0
1
2
0
0
1
1
2
1
0
2
2
1
2
2
1
1
1
1
1
1
0
2
1
2
2
0
1
1
0
1
1
1
1
1
1
0
1
2
1
0
2
1
0
1
1
1
1
1
1
1
1
0
1
1
0
1
1
1
1
2
1
0
2
2
1
1
0
1
1
1
1
1
1
0
2
0
1
1
2
1
1
1
1
0
1
1
0
1
1
1
1
1
2
1
1
0
0
1
1
1
2
0
2
0
1
1
1
1
1
2
3
2
1
2
1
2
1
1
1
0
1
0
1
0
1
1
1
1
1
0
0
1
1
0
1
0
2
1
1
1
0
2
1
1
0
1
1
2
2
0
1
2
1
0
2
2
1
0
1
1
1
1
1
1
3
1
0
0
1
1
1
2
2
1
2
2
1
2
1
2
1
1
2
1
1
1
1
0
1
1
1
1
1
1
2
1
2
1
2
1
1
0
1
2
1
1
2
1
1
1
1
1
1
2
0
0
1
1
2
0
1
2
1
0
1
1
0
0
1
2
0
1
1
0
0
1
0
2
0
0
2
2
2
2
2
1
0
1
1
0
0
0
1
1
2
2
1
0
2
1
1
1
0
1
2
2
2
1
0
0
0
2
1
1
1
2
1
0
0
1
1
2
1
2
0
1
2
2
1
0
1
1
1
0
1
0
2
0
0
0
0
1
2
1
1
1
1
1
1
2
1
0
1
1
2
0
1
2
1
1
1
2
1
1
2
1
2
1
1
0
0
2
1
1
2
1
0
1
1
1
0
2
1
1
1
1
2
0
1
1
2
1
0
0
2
1
0
2
1
1
2
0
1
2
0
1
1
1
0
1
1
1
0
2
2
1
2
0
2
1
0
1
1
1
1
2
2
2
1
1
1
1
2
1
1
1
1
2
2
2
1
1
1
1
2
1
2
1
1
1
0
1
1
1
1
1
0
0
1
0
1
1
1
1
2
1
1
1
1
1
2
1
0
0
0
0
1
1
0
1
2
0
1
1
1
1
1
1
0
1
3
2
0
1
1
1
1
2
2
1
2
2
0
1
0
0
1
0
1
0
1
1
0
1
0
1
0
2
1
1
2
1
1
1
0
0
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
0
2
1
1
0
2
1
1
0
0
1
1
1
2
2
0
1
2
0
1
1
2
2
1
1
1
1
1
0
1
2
0
2
1
0
2
1
2
1
1
0
1
0
1
0
1
2
0
1
0
1
1
2
1
1
1
1
2
1
1
1
1
1
2
2
1
2
1
1
2
1
2
2
1
0
1
2
1
1
0
2
2
1
2
0
1
1
2
1
1
1
2
0
1
1
0
1
1
0
0
2
0
1
1
0
1
1
1
1
2
0
1
1
1
2
1
1
0
1
2
1
2
2
1
0
1
1
0
1
1
0
1
1
1
1
0
2
2
2
2
0
1
1
1
1
2
1
1
1
1
0
2
0
1
1
0
1
0
1
2
0
1
2
1
2
1
1
0
1
0
0
0
0
1
2
0
1
1
1
0
1
1
0
3
1
1
1
1
2
0
1
2
0
0
1
2
1
2
2
2
1
1
1
1
1
0
0
1
1
1
1
1
2
1
1
0
1
1
1
1
2
1
3
1
1
2
1
1
0
3
1
2
0
2
1
0
2
1
0
0
1
1
0
0
1
1
1
0
0
0
1
2
1
2
1
1
2
2
1
1
0
0
2
2
0
2
0
1
0
2
1
0
1
1
0
0
0
2
2
1
1
1
1
0
1
0
2
0
1
0
1
1
2
1
1
2
1
0
1
0
1
2
0
2
1
1
2
2
1
1
2
1
2
1
1
2
2
0
2
0
0
1
1
1
1
1
2
0
0
1
1
2
1
1
0
1
0
4
1
1
1
0
0
1
1
2
0
1
2
1
1
1
0
1
0
0
1
1
2
1
0
0
2
2
1
0
2
2
2
2
1
1
1
0
0
1
1
0
1
2
1
2
1
2
1
0
1
1
1
0
0
0
1
0
2
2
1
1
1
1
1
1
1
2
2
2
0
0
2
2
2
1
1
2
3
1
0
0
1
1
1
3
1
2
1
1
0
1
1
2
1
1
2
1
1
0
1
1
1
0
1
2
0
0
1
1
1
0
2
2
1
3
1
1
2
1
2
1
2
1
1
2
3
2
1
1
1
1
2
0
0
0
1
3
2
2
1
1
1
0
1
1
2
1
1
0
0
0
2
0
0
1
1
0
1
2
1
1
1
1
1
1
2
2
1
3
1
0
0
0
1
1
1
1
1
1
2
2
1
1
1
1
0
2
1
1
2
1
1
0
1
2
0
2
1
1
1
1
2
1
1
1
2
2
1
0
1
1
0
2
1
1
1
0
0
2
1
2
1
1
2
1
1
2
1
2
1
1
1
1
0
1
1
1
1
1
2
1
1
0
1
1
2
2
1
1
1
1
2
1
2
2
1
1
1
1
2
1
1
2
1
2
1
0
1
0
1
0
2
1
2
2
1
1
1
1
2
1
1
0
0
1
1
0
1
2
1
2
1
0
1
2
0
1
1
1
1
1
1
0
1
2
1
0
1
0
1
1
2
1
0
0
0
0
1
2
1
2
0
0
1
1
1
1
1
0
2
1
0
2
1
1
2
1
1
1
1
1
2
2
0
0
1
0
0
1
0
1
1
2
1
1
0
1
0
1
1
1
1
1
1
1
0
1
1
1
2
2
1
2
1
1
1
1
2
1
1
0
0
1
1
1
1
0
2
2
0
2
1
1
1
0
2
0
0
0
2
1
0
2
1
2
1
0
1
1
1
0
1
0
0
1
1
2
1
1
1
1
1
1
1
0
1
0
1
2
2
1
1
1
0
1
2
2
0
1
2
0
1
0
1
1
1
0
0
2
1
0
0
1
1
1
1
2
2
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
0
2
0
1
0
1
1
2
0
2
0
1
1
1
2
0
1
1
0
2
2
1
0
1
5
1
0
1
1
2
2
1
1
0
2
0
3
0
1
1
1
1
0
1
1
1
1
1
1
0
1
0
1
0
0
1
0
0
1
1
1
1
0
1
1
1
1
0
0
2
1
0
2
1
0
2
0
0
1
1
0
0
1
2
0
1
1
2
1
1
1
1
2
1
1
1
1
1
1
0
1
1
1
0
0
1
0
1
2
1
1
1
1
0
1
0
0
1
0
1
1
1
1
1
0
1
0
1
0
2
1
1
1
1
0
1
1
0
1
6
2
1
0
1
1
1
0
0
0
2
1
1
0
1
2
0
1
0
1
0
2
1
1
1
1
1
2
2
2
1
0
1
1
1
1
2
1
0
2
1
2
0
2
1
1
2
1
1
1
1
0
0
1
1
1
2
3
0
2
0
1
1
1
1
1
1
1
2
1
1
1
2
0
2
1
1
1
0
0
1
0
1
1
1
3
1
2
1
1
1
1
1
1
1
1
0
2
1
0
0
1
0
1
1
2
1
1
1
1
2
1
0
0
0
2
0
1
1
2
2
1
0
2
1
1
2
2
1
2
1
2
1
1
2
1
2
1
1
1
0
2
0
0
1
1
0
0
1
0
1
1
0
1
0
2
2
2
2
3
2
1
1
1
1
0
1
2
0
1
1
0
2
1
1
0
1
0
2
0
1
0
1
2
0
2
1
1
1
1
0
1
1
1
1
1
2
2
1
0
0
0
1
0
1
0
1
1
1
0
0
0
1
2
1
0
1
0
1
0
1
2
1
0
2
2
1
1
1
0
0
1
0
1
1
0
1
1
0
2
0
1
1
0
0
1
0
1
0
2
1
1
3
2
1
2
1
2
2
0
1
2
2
1
2
1
2
1
1
1
1
0
2
1
1
0
0
2
0
1
0
1
1
1
1
0
1
2
1
1
0
0
2
1
2
2
1
1
0
1
0
1
1
1
0
1
0
1
0
1
1
2
3
0
0
2
0
1
1
0
1
2
0
1
1
1
1
1
1
1
1
1
0
2
1
1
1
1
2
4
1
1
1
1
0
1
1
1
1
1
1
2
1
1
1
1
2
1
2
2
1
0
1
1
0
1
1
1
1
1
1
2
0
2
1
1
0
1
1
1
2
1
0
1
2
1
2
1
2
2
1
2
0
0
1
2
1
2
2
2
0
2
0
2
1
1
2
1
2
0
1
1
1
1
1
1
1
1
0
1
0
1
0
1
1
2
1
1
2
1
1
2
1
1
1
2
0
1
1
1
1
1
1
0
2
1
1
1
0
0
2
1
1
0
2
1
2
0
0
2
1
1
1
1
2
0
0
2
1
0
0
4
1
1
1
2
1
1
1
1
3
0
0
0
0
2
1
0
0
0
2
0
1
0
0
0
2
2
1
2
1
0
1
1
0
0
1
1
1
0
0
2
2
1
2
2
1
0
2
1
2
1
1
1
2
2
2
2
0
0
2
1
1
1
1
1
1
1
0
1
1
2
1
1
2
1
0
1
1
1
1
1
2
1
2
1
0
2
0
0
1
1
1
2
1
2
0
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
0
0
2
1
1
1
0
1
1
1
1
2
0
1
1
1
1
2
1
2
0
2
0
0
0
1
1
2
1
1
1
2
1
0
1
2
1
1
0
0
1
1
2
2
1
1
2
0
0
2
1
1
1
2
1
0
0
2
0
1
1
0
1
1
1
0
1
1
0
2
1
1
1
1
0
0
1
1
1
2
1
1
1
2
1
1
2
1
0
2
0
0
1
2
2
0
2
1
0
2
1
1
1
2
1
2
2
1
1
2
1
1
2
0
0
1
0
0
2
1
2
2
0
1
0
1
1
1
2
1
1
0
1
1
0
0
0
2
0
1
1
1
1
1
0
1
1
2
1
1
2
0
0
1
2
1
0
0
1
1
0
1
1
2
1
0
0
2
1
1
0
2
1
1
2
0
2
0
0
2
1
2
1
4
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
0
2
0
0
1
1
0
3
1
1
1
1
2
2
1
0
1
1
1
0
1
0
2
1
1
0
0
1
2
2
0
0
0
1
0
2
1
1
0
0
2
0
0
1
1
0
1
2
0
1
2
1
1
1
0
1
1
1
1
1
0
2
0
1
2
2
0
1
0
2
1
2
2
1
0
2
1
2
1
2
2
2
1
2
0
1
0
1
1
1
1
0
1
1
1
1
1
1
1
0
1
0
1
1
1
2
1
1
2
1
1
2
0
2
2
1
1
0
1
1
1
1
1
1
1
0
1
0
2
1
1
1
1
0
1
1
1
1
2
1
2
1
2
1
0
2
0
1
1
2
1
1
1
1
0
1
0
1
0
1
1
2
0
0
0
1
1
1
1
2
2
1
1
1
0
1
1
1
1
1
1
2
0
1
1
1
2
2
3
1
2
0
1
2
1
0
1
1
0
2
1
0
3
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
2
1
1
0
1
2
0
0
1
2
1
2
1
1
2
1
2
1
0
1
0
1
1
1
1
1
1
1
0
1
1
1
1
1
1
0
2
0
0
1
2
1
0
1
1
0
1
1
1
2
2
1
2
1
2
1
1
1
0
1
0
1
1
2
2
1
1
2
0
2
0
0
1
1
1
0
0
1
0
1
1
1
1
0
1
2
1
2
1
0
1
2
2
1
0
0
0
1
1
0
1
1
1
1
1
1
0
1
2
1
2
1
0
1
1
1
1
2
1
0
0
1
0
1
1
1
1
1
1
1
2
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
0
1
0
1
2
1
0
0
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
0
2
0
2
1
1
2
2
1
2
2
1
1
0
1
0
2
0
1
1
0
1
0
2
0
0
1
2
1
0
2
1
0
1
1
1
1
2
0
2
1
1
1
1
1
1
1
1
1
0
1
1
1
0
2
1
1
1
0
1
3
1
1
0
1
0
0
2
2
1
2
2
2
2
1
2
1
1
1
2
1
1
1
2
2
1
1
2
1
2
1
2
1
0
0
2
1
1
2
0
1
1
1
2
1
1
1
1
1
2
1
0
0
1
3
1
0
1
1
1
1
1
1
2
1
1
1
2
1
1
1
2
2
1
1
1
1
2
2
2
0
1
2
2
1
1
0
1
1
1
0
1
3
0
2
2
1
0
2
1
1
1
1
1
1
2
1
2
2
1
1
1
2
1
1
2
0
1
2
0
0
1
0
2
0
2
1
2
2
2
1
1
0
2
0
1
2
1
1
0
2
1
2
1
2
1
1
1
1
2
1
1
1
2
1
2
0
1
1
1
1
1
1
1
1
2
2
1
1
0
1
1
2
2
1
2
0
1
0
1
2
2
1
0
1
2
1
1
1
1
2
1
1
0
1
2
2
0
1
1
0
1
0
0
2
0
1
0
1
2
1
1
2
1
1
2
1
0
1
2
2
2
0
0
1
1
2
1
1
1
2
1
1
1
2
1
1
0
1
1
1
0
1
4
1
1
1
1
0
1
0
0
0
2
2
0
0
1
0
0
2
2
2
2
1
1
1
1
0
1
0
2
2
2
1
1
2
1
1
1
1
1
1
1
2
1
1
2
1
0
0
1
1
0
0
0
0
2
1
0
1
1
2
1
1
1
2
2
0
2
2
1
1
1
2
2
1
1
1
2
1
1
1
1
1
1
2
0
3
1
1
1
0
2
0
0
1
0
1
2
2
0
2
1
1
2
1
1
0
1
2
2
2
0
1
1
1
1
0
0
1
1
1
2
1
0
1
1
1
1
0
1
1
1
2
2
2
2
1
1
1
1
1
1
1
0
1
1
1
1
1
2
1
0
1
0
1
1
1
1
1
1
1
1
0
1
1
1
0
2
1
0
1
1
1
2
2
3
1
2
2
1
1
1
1
0
2
2
2
2
2
1
1
4
1
1
1
0
2
1
1
1
1
1
1
2
1
1
0
1
0
0
0
2
1
1
1
0
0
1
1
2
1
1
1
13
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
0
2
1
1
0
0
0
1
1
1
1
1
0
1
0
1
1
1
2
1
2
1
1
1
1
2
1
1
0
1
2
1
0
1
1
2
0
2
0
2
1
2
1
1
1
2
1
1
1
2
0
2
0
1
0
1
0
1
2
0
1
1
2
1
3
0
1
1
1
1
0
1
1
1
3
1
2
1
0
2
1
2
1
2
0
2
2
1
2
1
1
0
2
1
1
0
1
1
2
1
1
1
1
1
0
1
1
0
1
0
1
0
3
1
2
1
0
1
1
2
1
1
2
0
1
2
1
1
1
1
2
1
1
1
0
0
1
1
0
1
1
1
1
1
2
1
1
2
1
1
0
1
1
1
1
1
2
1
1
0
1
0
0
2
0
4
1
1
0
1
1
0
0
1
1
2
1
1
0
0
2
1
1
0
0
2
2
0
3
1
1
0
0
2
3
0
1
1
1
1
2
2
1
1
1
1
1
1
1
1
0
1
1
1
1
1
2
1
1
2
1
2
0
0
1
2
2
1
1
1
1
1
0
1
1
1
1
1
1
1
0
1
0
1
1
0
1
1
1
0
1
1
0
2
1
0
1
1
1
1
1
0
1
1
2
0
2
0
1
1
2
2
1
2
0
1
0
1
1
1
1
1
2
1
1
1
2
1
1
2
0
1
0
0
1
0
2
1
1
1
0
0
1
1
1
2
1
0
2
1
1
0
2
2
0
1
1
1
1
0
0
1
0
0
2
0
2
0
0
1
0
2
1
2
0
2
1
2
1
1
1
1
1
2
1
1
1
1
0
2
1
1
1
1
0
1
4
2
1
0
2
1
2
0
2
1
1
1
2
1
1
2
2
2
1
1
2
1
2
1
2
0
0
1
1
1
2
0
1
1
1
2
1
0
1
1
1
1
1
1
0
1
1
2
1
0
0
2
2
2
0
1
2
0
1
1
1
0
0
1
3
1
1
0
1
0
2
1
2
1
1
2
2
0
1
0
1
0
1
2
2
0
0
0
1
1
2
1
0
2
2
0
2
1
1
0
1
1
1
1
1
1
1
2
1
3
1
1
2
1
1
1
1
0
1
0
2
1
1
1
1
1
1
1
2
0
1
1
0
1
1
1
1
0
1
1
1
0
1
1
2
0
2
2
2
1
0
0
1
1
0
1
1
1
1
0
2
2
1
2
2
1
0
0
1
1
1
0
1
1
0
1
1
2
1
1
0
1
0
1
1
1
1
0
2
1
0
0
0
1
0
1
2
2
0
1
1
0
1
1
0
1
1
0
1
1
1
1
0
1
2
2
1
2
2
1
2
1
1
1
1
0
1
0
1
2
1
1
2
2
1
1
1
0
0
0
0
4
0
1
0
0
2
2
2
1
1
1
0
1
1
1
1
1
0
0
4
2
1
0
1
1
2
1
0
0
2
0
2
2
1
1
1
0
1
0
1
0
0
1
1
0
0
1
0
0
2
2
1
2
0
2
1
0
1
2
0
0
2
0
1
1
1
2
1
1
1
0
2
1
1
1
1
1
0
0
0
1
1
1
2
1
1
2
1
1
0
0
2
1
1
1
1
2
0
1
1
2
1
2
0
1
1
1
0
0
1
2
1
0
0
0
1
1
1
3
1
1
1
0
1
1
1
1
1
1
1
0
1
2
2
2
2
2
1
1
1
3
0
0
2
0
1
1
0
1
2
1
1
2
0
1
1
1
1
1
2
2
2
1
2
2
0
1
1
1
0
2
0
2
1
0
0
1
2
2
1
2
1
1
2
1
1
0
0
1
1
0
2
2
1
1
3
2
1
2
2
1
2
1
1
2
1
1
2
1
0
1
2
1
1
1
1
1
2
0
1
1
1
0
1
1
1
1
0
1
0
1
0
2
1
1
2
0
0
1
0
1
0
1
1
0
1
1
2
2
1
2
2
2
1
0
1
4
1
1
1
2
1
0
1
1
0
1
1
2
1
0
1
1
2
1
2
3
1
1
1
2
1
1
2
1
1
0
1
1
1
2
1
1
2
2
0
0
2
2
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
0
2
1
1
1
2
1
2
2
1
0
0
1
2
1
0
2
0
2
0
1
1
1
1
1
1
0
1
1
1
2
1
1
1
2
1
2
1
0
1
1
1
1
1
1
1
1
1
1
0
0
1
2
2
1
0
2
1
0
1
0
1
0
1
2
1
1
2
1
1
1
1
1
2
1
1
0
1
1
2
1
2
1
1
0
2
1
0
1
1
1
1
0
2
1
2
0
1
1
1
0
1
1
1
0
2
2
1
1
0
1
0
2
1
0
2
1
0
1
2
2
2
1
1
1
0
1
0
0
1
2
1
1
1
1
0
2
2
0
1
1
0
1
0
2
1
1
0
1
1
0
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
2
1
2
1
1
2
1
1
2
1
0
1
1
2
2
1
0
0
0
0
1
0
1
0
0
1
0
1
2
1
1
2
3
1
0
1
3
1
1
1
2
2
1
2
1
2
2
2
0
1
0
0
0
0
0
1
1
1
1
1
1
1
1
1
2
2
1
1
1
0
2
0
1
1
1
1
2
0
1
0
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
0
0
1
1
0
1
2
1
2
1
1
2
0
1
2
1
1
2
2
0
1
1
1
1
0
1
1
1
1
0
2
1
1
2
1
1
1
1
1
0
0
0
1
2
0
0
0
1
2
0
0
1
1
0
2
0
1
0
1
0
2
1
2
1
0
1
1
1
1
1
2
1
1
0
1
1
1
0
0
1
2
1
1
0
1
1
1
2
1
1
2
0
2
2
2
2
0
2
1
2
2
1
0
2
2
0
1
1
1
1
0
2
0
1
1
2
2
0
1
1
2
0
1
1
2
1
2
1
1
1
1
1
0
0
0
1
1
0
1
1
0
0
1
0
3
2
1
2
1
1
0
1
1
1
1
1
0
0
1
0
2
0
1
1
1
0
1
1
1
1
0
0
0
2
1
1
1
1
0
0
0
1
0
2
1
1
1
1
2
1
1
2
1
1
1
2
3
1
2
1
0
1
1
1
1
1
0
1
1
1
1
1
1
1
1
0
1
2
1
2
0
0
0
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
0
0
1
1
1
2
0
0
1
2
1
1
1
1
1
0
1
1
1
1
1
0
0
1
0
1
1
2
1
0
0
1
1
1
0
1
0
1
1
1
0
0
1
1
1
2
1
1
1
1
1
1
1
0
0
1
1
1
0
1
0
1
0
1
1
1
1
1
1
1
1
1
2
1
1
1
4
2
1
1
2
1
0
0
1
2
1
1
1
1
0
1
1
1
1
3
1
1
0
1
2
1
0
1
2
3
1
1
0
2
1
2
3
0
1
1
2
1
1
1
1
0
2
1
1
0
1
1
1
1
1
1
1
1
1
1
1
0
1
0
1
2
0
0
1
2
2
1
0
3
1
1
1
1
1
1
2
2
2
1
1
0
1
0
2
0
1
1
0
1
1
1
1
1
1
2
1
1
0
2
0
1
0
2
1
0
1
1
2
1
2
1
1
2
1
1
0
0
0
2
1
1
1
1
1
2
1
1
0
1
0
2
1
2
1
2
1
1
1
1
1
1
1
2
1
0
1
0
2
0
1
1
0
0
0
0
2
2
1
1
0
1
1
1
1
0
1
1
1
2
2
1
0
0
0
1
2
1
1
1
1
1
2
1
2
0
3
2
0
1
2
1
1
1
1
1
2
1
1
0
1
0
1
0
1
1
1
2
1
0
2
1
2
0
0
2
0
2
2
0
1
1
2
2
0
2
0
1
1
2
1
0
1
2
1
1
1
2
1
1
1
2
0
2
1
0
2
1
0
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
1
0
0
1
0
2
1
0
1
1
3
2
2
1
1
2
2
2
2
2
0
1
0
1
1
2
0
1
1
3
1
2
1
1
0
2
1
0
1
0
0
2
1
2
0
1
1
1
1
1
0
0
1
0
1
0
1
1
2
0
1
1
1
2
2
1
2
1
0
1
1
1
2
2
0
1
0
1
3
0
2
1
0
1
1
0
2
1
2
2
1
3
0
1
2
1
1
1
0
0
1
1
2
2
1
0
0
1
1
1
1
1
0
1
1
1
1
0
1
1
1
2
1
0
1
0
1
1
2
1
2
1
1
1
2
1
0
2
1
1
1
1
2
2
1
1
1
0
0
1
1
2
1
1
0
1
1
1
1
1
0
1
2
1
1
1
1
1
2
0
2
1
2
1
3
1
2
2
1
1
2
1
1
1
1
1
1
0
1
1
1
0
1
1
0
0
2
0
0
2
0
2
2
1
1
1
1
0
1
1
1
1
2
1
2
0
0
2
1
0
1
2
1
0
1
0
1
2
2
1
1
2
1
2
1
2
1
2
2
1
1
1
0
2
1
1
0
2
1
1
2
0
1
1
2
1
1
1
1
1
1
1
1
1
2
0
1
1
0
1
1
2
1
1
2
1
1
3
1
2
2
0
1
1
1
1
0
1
0
1
1
3
3
2
1
0
0
0
0
0
1
2
1
0
1
1
0
1
1
1
2
1
2
1
2
1
1
1
1
0
1
1
0
1
1
2
1
2
0
2
1
1
1
2
2
0
1
1
2
1
1
0
1
0
1
1
1
1
0
2
1
0
1
1
2
1
2
2
1
1
1
2
2
2
1
1
3
0
1
1
2
1
1
0
1
0
2
0
0
1
2
1
2
2
0
0
1
0
2
1
1
2
2
0
1
2
1
2
1
1
2
1
1
1
1
1
1
1
1
0
1
2
2
2
1
1
0
2
1
1
1
2
0
3
1
2
1
2
2
1
2
1
0
1
1
2
1
1
0
1
1
2
1
1
1
1
2
1
1
0
1
0
2
2
0
0
1
0
1
0
1
1
1
1
2
1
0
1
1
1
1
2
2
1
0
1
2
1
1
0
2
0
1
1
1
3
0
1
1
2
0
1
0
1
1
2
2
1
0
1
1
0
1
1
2
1
1
1
1
0
1
1
1
1
2
2
0
1
0
1
1
1
2
0
2
1
1
1
1
2
1
1
1
2
0
0
1
2
1
2
1
0
1
2
1
1
2
1
1
1
1
0
2
1
1
1
1
1
0
2
2
1
4
0
0
1
1
1
1
1
1
1
0
0
0
1
2
1
1
0
1
0
0
1
1
1
2
1
1
1
1
1
1
1
1
1
0
1
1
1
2
1
2
2
0
1
0
1
0
0
0
1
1
1
0
0
2
1
2
1
0
2
1
2
1
0
0
1
2
0
2
3
1
2
0
0
2
1
0
1
1
1
0
2
1
1
2
1
1
0
0
1
1
0
2
0
1
1
2
0
1
1
1
0
1
1
1
1
1
1
1
1
0
1
2
0
1
2
2
1
0
2
1
1
0
0
1
2
1
0
0
1
1
1
0
1
2
0
1
2
1
2
2
2
1
1
0
1
0
1
1
1
2
1
0
0
0
1
2
0
0
1
1
1
1
0
2
0
1
0
2
1
1
0
2
2
0
0
0
1
1
1
2
1
1
2
2
2
2
0
1
2
1
2
1
1
2
1
1
1
0
1
0
1
0
2
1
1
0
1
0
2
2
1
1
2
1
1
0
1
1
0
1
1
1
1
1
2
1
0
0
1
0
1
1
0
2
0
2
2
0
1
2
1
1
0
1
1
1
1
1
1
2
1
0
2
2
1
2
2
1
2
0
1
1
1
2
2
1
0
1
0
0
0
1
1
1
1
2
1
0
1
0
2
1
1
1
1
2
2
1
2
1
1
1
1
1
2
2
1
1
1
0
1
0
2
1
2
2
0
1
0
1
1
1
2
0
1
0
1
1
1
2
1
2
1
2
1
2
0
1
2
1
2
1
1
1
1
2
1
1
1
0
0
1
1
1
1
2
0
1
1
2
1
1
1
1
0
0
0
1
0
1
1
1
1
1
1
2
3
1
0
1
0
0
0
1
1
1
1
0
2
2
2
1
1
1
0
2
5
0
1
1
0
1
1
2
2
2
0
1
2
1
1
0
2
2
1
2
1
1
1
1
2
1
1
0
2
2
2
0
1
1
1
1
1
1
0
1
0
0
2
1
1
0
1
0
0
2
0
1
1
2
1
2
1
0
1
1
2
1
1
3
1
2
1
1
2
0
1
0
1
0
1
1
1
0
0
2
1
1
1
3
1
2
1
2
2
1
0
0
1
1
1
1
2
1
2
1
1
1
1
1
1
1
0
1
1
1
1
1
1
2
1
1
2
2
0
0
1
0
1
1
1
1
0
1
1
1
1
1
1
1
1
1
2
1
0
0
1
1
1
2
1
1
0
1
1
1
2
0
1
0
1
1
0
1
0
1
1
1
1
1
0
1
1
2
2
1
1
2
1
1
0
1
1
1
2
0
1
1
0
1
2
1
1
1
1
1
2
2
0
1
1
0
2
1
2
2
1
2
1
1
0
1
1
1
0
2
2
2
1
2
1
1
1
1
1
1
1
1
1
2
0
0
2
1
2
1
2
0
0
1
0
1
2
1
1
1
1
1
1
0
2
1
1
3
0
2
0
2
0
2
1
1
1
1
0
1
1
0
0
0
0
1
0
2
1
1
1
1
0
1
1
1
0
2
1
2
2
2
2
1
1
1
2
1
1
0
2
0
1
1
0
1
1
1
0
2
1
0
1
1
2
1
2
2
0
2
2
2
1
1
0
1
1
1
1
1
1
0
1
0
0
0
1
1
1
2
1
0
0
1
2
1
0
0
1
0
1
1
2
0
2
1
1
0
2
1
1
1
0
1
0
0
0
1
1
2
1
2
0
0
0
0
1
0
2
1
2
0
2
2
0
1
1
2
2
0
1
0
0
2
1
2
1
0
1
1
0
1
1
1
1
2
1
1
1
1
1
1
1
2
1
0
0
0
1
1
0
1
1
0
2
0
2
1
1
1
1
0
0
1
2
0
1
1
1
1
2
1
0
0
2
1
2
1
1
1
1
0
1
0
2
0
3
1
0
1
1
2
1
0
1
1
1
0
1
1
1
1
2
1
2
2
0
2
1
1
1
1
2
1
0
1
2
1
0
2
0
0
1
1
2
1
0
1
2
2
2
0
0
1
1
1
1
1
1
0
1
1
1
0
1
1
1
1
2
0
2
1
1
1
0
1
0
1
0
2
1
1
2
1
1
0
2
2
1
0
1
1
1
1
1
0
0
1
1
1
2
1
2
1
0
2
1
0
1
1
1
1
1
1
1
2
1
1
1
0
0
2
1
2
1
1
1
1
0
1
1
2
0
0
2
1
1
2
2
1
1
1
1
0
2
0
1
1
1
1
1
0
1
2
2
2
2
0
2
1
2
3
2
2
0
1
1
0
2
0
1
3
1
1
1
2
0
1
2
1
0
2
1
0
0
1
2
1
2
1
2
0
1
1
1
1
2
1
1
1
1
0
2
2
1
0
1
1
1
1
1
1
0
1
0
1
1
1
1
1
1
1
1
2
1
1
0
0
1
1
1
1
1
2
1
1
0
0
1
0
1
1
2
2
1
3
2
1
1
0
1
1
2
1
1
2
2
1
0
3
0
1
1
1
1
2
2
1
0
1
1
0
0
2
0
1
0
2
1
1
1
1
1
0
1
1
1
1
1
0
0
1
1
1
1
2
2
1
0
1
1
1
1
0
2
1
0
1
2
1
0
1
1
0
2
1
2
0
1
2
1
0
1
2
0
2
1
1
2
0
1
1
1
1
1
1
2
1
1
2
0
0
2
1
0
2
1
0
2
2
0
1
1
1
1
1
1
1
0
2
2
1
1
0
0
2
1
2
1
1
1
1
2
1
0
1
2
1
1
1
2
0
1
1
0
0
2
2
1
1
0
1
1
2
1
1
1
1
0
0
1
1
0
2
0
1
1
0
2
1
2
1
1
2
1
1
1
1
2
1
1
2
1
2
1
0
2
1
0
0
1
1
1
0
0
1
1
1
2
0
0
0
1
1
1
0
1
1
1
1
1
0
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
1
0
0
1
1
0
2
1
2
2
1
1
0
1
0
1
2
1
2
2
0
1
2
1
2
1
1
3
2
1
1
1
3
2
1
1
1
2
1
1
1
1
0
2
1
2
1
1
0
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
2
0
1
2
0
2
1
2
1
1
1
0
1
2
1
1
2
1
1
1
1
0
0
1
1
1
2
1
2
0
1
2
1
0
1
2
1
0
1
0
0
1
1
1
0
1
2
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
0
2
0
1
0
1
1
2
0
1
1
0
0
1
0
1
1
1
1
1
1
2
0
1
1
0
2
1
1
2
2
1
1
2
1
1
1
0
2
2
2
2
2
1
1
1
0
2
1
2
2
2
1
0
2
1
1
2
1
2
0
1
1
1
0
1
1
1
1
1
1
0
2
1
1
1
2
1
1
1
0
0
0
1
1
2
2
2
1
1
0
1
1
2
1
1
0
1
0
2
1
1
1
1
1
1
1
1
0
1
1
1
0
2
1
2
3
2
2
1
0
0
0
2
0
1
1
1
0
0
1
1
1
1
1
3
2
1
0
0
1
0
1
0
1
0
1
1
2
0
0
2
2
1
1
1
1
0
0
1
2
1
1
2
0
1
1
1
1
1
1
0
1
2
1
1
2
1
1
2
1
1
1
1
1
1
0
0
2
1
1
1
2
1
1
0
1
0
0
2
1
1
1
0
1
1
1
0
0
1
0
1
1
1
3
1
0
1
1
1
1
1
1
1
1
1
2
1
0
1
2
1
1
1
1
1
1
1
1
1
1
0
1
1
1
0
0
1
1
0
2
1
1
1
0
1
1
1
1
2
1
0
1
1
1
1
2
0
1
0
2
1
1
1
1
1
1
2
1
0
1
0
1
1
0
1
1
1
0
0
1
1
1
0
1
1
1
0
0
1
1
0
0
1
1
1
1
2
1
1
1
1
0
0
1
1
2
0
1
1
1
1
1
2
2
1
1
1
1
1
1
4
1
0
2
1
0
0
1
1
2
1
0
1
1
1
1
1
1
1
2
0
1
1
1
1
0
1
1
0
2
2
1
0
1
0
0
2
1
0
3
0
1
1
1
1
1
1
0
1
1
1
0
1
2
1
1
1
0
1
1
0
0
0
0
1
1
1
0
1
1
1
1
0
3
2
1
2
4
2
1
1
1
2
1
1
1
1
1
1
0
1
0
1
1
1
1
2
1
1
0
1
2
1
1
1
1
1
0
1
2
1
1
1
0
1
1
1
1
1
0
1
2
1
4
2
1
1
2
1
0
0
1
1
0
1
2
1
1
1
0
1
2
1
1
2
2
0
1
1
1
1
1
1
1
2
0
1
1
1
1
1
2
1
1
0
0
2
1
0
1
2
1
0
1
2
1
0
1
3
1
0
1
1
1
1
0
1
0
2
1
1
1
2
1
1
1
1
1
1
0
0
1
2
2
2
1
1
2
1
2
0
1
1
1
1
1
0
1
2
1
1
0
1
1
1
0
0
1
0
1
1
1
0
2
1
2
1
0
1
0
1
1
0
2
0
2
1
1
1
0
0
2
1
1
1
1
1
2
1
1
2
2
0
0
1
1
1
3
1
2
1
2
1
2
2
1
1
3
2
0
1
1
0
1
2
1
1
0
1
2
1
0
1
1
2
0
1
1
1
1
2
1
0
0
2
1
0
2
1
2
0
2
0
0
3
1
0
1
1
1
2
0
2
1
0
1
1
2
1
1
2
1
2
2
1
1
2
1
1
0
2
0
0
1
2
0
1
1
0
0
1
1
1
1
1
2
1
1
0
2
0
2
1
2
0
2
1
1
1
0
2
1
1
1
0
1
0
2
1
1
1
1
1
1
1
1
1
1
1
1
3
1
0
1
0
2
2
2
1
1
2
0
2
2
1
0
1
1
2
2
1
1
0
0
2
0
0
2
1
0
2
2
0
0
1
1
2
2
1
0
0
1
1
1
2
1
2
2
1
2
0
2
1
1
1
1
2
0
1
1
1
1
2
0
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
1
2
1
1
1
0
1
1
1
1
0
0
2
1
1
0
2
0
1
0
1
2
2
1
2
1
2
1
2
0
0
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
0
2
2
0
2
1
2
1
1
0
1
1
1
1
0
1
0
0
0
0
1
1
1
2
2
0
0
1
2
1
1
2
0
0
1
1
1
2
2
2
1
0
1
0
1
1
2
2
2
2
0
1
1
0
1
1
1
1
1
2
0
1
2
1
2
1
0
1
1
2
1
1
2
1
1
1
1
1
2
1
1
2
1
0
0
1
2
0
1
2
0
3
0
2
0
1
0
0
1
1
1
2
0
0
1
2
1
1
1
3
1
1
1
0
1
1
2
1
1
1
1
2
1
1
1
0
1
1
1
1
0
0
1
1
0
2
2
0
1
2
2
1
0
0
0
1
2
1
2
0
1
0
1
2
2
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
2
0
1
0
1
1
1
1
1
1
1
1
1
3
2
1
1
0
2
0
1
1
1
1
1
0
2
1
1
1
1
1
1
0
2
1
2
1
0
0
1
1
1
2
1
0
1
2
0
1
1
0
1
0
0
1
1
2
2
1
1
0
1
0
1
1
0
1
0
1
1
0
2
2
2
0
1
1
0
1
1
2
1
1
1
0
0
1
1
0
1
1
1
2
1
1
1
1
1
5
1
0
1
0
4
2
1
3
2
2
1
1
0
0
2
0
1
2
2
1
0
0
1
0
1
2
1
1
1
2
1
0
0
2
1
0
0
1
0
0
2
1
1
1
2
1
2
1
1
1
0
1
0
1
2
1
2
1
2
1
1
0
0
0
2
2
2
2
0
1
1
1
2
1
2
1
0
2
1
1
1
1
1
1
0
2
2
0
1
1
1
2
0
1
2
2
1
1
1
1
1
2
1
2
1
1
2
1
1
2
0
1
0
0
1
1
2
0
1
0
1
1
2
0
2
1
1
1
1
1
1
1
1
1
1
1
2
1
0
1
2
1
0
1
0
2
1
2
1
2
1
0
0
1
2
2
1
1
0
0
2
1
1
1
0
2
1
1
1
1
4
1
1
0
1
1
2
1
1
2
1
1
2
1
1
2
1
2
2
1
1
0
1
1
0
1
0
1
1
1
0
1
1
0
2
2
4
1
1
1
1
1
1
1
0
1
2
2
1
1
1
1
1
1
1
1
2
2
2
0
1
1
0
1
1
1
1
1
1
0
1
0
1
1
0
1
1
0
1
0
0
1
2
0
0
1
2
1
0
1
2
1
0
0
1
0
2
0
0
4
1
0
0
0
0
1
2
1
0
2
1
2
1
1
2
1
2
1
1
0
0
2
1
1
2
0
1
1
1
2
2
1
2
0
0
2
0
1
1
1
0
1
0
1
1
1
1
2
0
1
2
0
3
1
1
1
0
0
0
1
1
0
1
0
2
2
2
0
1
1
1
2
0
1
2
0
0
1
0
0
1
0
0
2
1
2
1
1
0
0
1
1
1
1
2
2
0
0
0
1
1
1
2
1
2
2
1
1
1
1
2
1
0
0
1
2
1
1
1
1
2
1
1
2
1
1
1
1
2
1
1
2
1
1
1
0
1
1
0
0
1
2
1
0
1
1
0
2
2
0
0
1
0
1
1
1
1
0
1
1
0
1
1
0
1
2
2
2
2
1
0
1
1
0
0
1
1
0
1
0
1
2
2
0
0
0
1
1
2
1
2
1
2
1
0
1
1
0
0
2
0
2
0
2
1
1
2
2
2
1
0
2
1
1
2
1
1
1
1
1
1
1
1
1
3
2
0
2
2
1
1
1
0
2
1
1
1
2
0
0
1
1
1
1
1
0
2
1
0
1
2
0
1
2
1
2
1
1
1
0
0
1
1
1
2
1
1
1
0
2
1
1
1
0
1
0
0
1
0
1
1
1
1
1
0
1
0
2
0
1
2
1
2
1
1
2
1
2
1
2
0
2
0
0
0
0
1
1
1
0
1
1
2
1
1
1
2
1
1
0
2
1
0
1
0
1
2
2
1
0
1
1
1
0
1
2
0
2
2
0
1
1
1
1
1
1
1
2
0
1
2
1
2
1
0
2
0
1
2
1
1
2
1
2
0
2
1
2
1
1
2
2
0
1
1
2
1
1
0
3
0
1
1
1
0
0
1
0
1
1
0
2
1
1
0
2
2
3
1
0
2
1
2
0
1
1
1
1
0
1
0
1
0
1
0
1
1
0
1
0
0
2
1
0
1
0
1
0
1
1
1
0
1
1
0
1
0
2
0
1
0
1
1
1
2
2
2
1
1
1
2
1
2
1
2
1
2
2
2
0
1
2
1
1
1
1
1
2
1
1
1
2
0
2
0
2
1
1
1
2
2
1
1
0
2
1
1
2
1
1
2
2
1
2
0
1
1
1
0
0
3
0
0
0
1
2
1
0
1
1
1
0
2
2
0
0
0
1
1
1
0
1
0
1
0
2
1
1
0
2
2
1
1
1
1
0
2
1
1
0
1
0
1
1
0
2
1
1
1
0
0
0
2
1
1
2
1
1
0
2
0
1
1
2
2
2
0
1
1
1
2
1
5
1
1
3
0
1
1
2
1
2
0
1
1
2
1
1
0
2
0
1
1
1
2
1
2
1
2
1
1
0
2
1
1
0
1
1
1
0
1
2
1
1
1
2
2
0
1
1
1
0
2
1
1
1
1
2
1
2
0
1
2
0
1
1
1
1
2
2
1
1
2
1
0
2
1
1
1
1
1
1
0
1
1
0
1
2
1
0
1
1
1
1
2
1
2
1
2
1
2
3
1
1
1
1
2
2
1
2
2
1
2
2
1
0
0
1
1
1
0
1
1
0
1
1
1
1
1
2
2
1
0
2
1
2
1
1
0
1
1
1
1
0
1
2
1
2
1
1
0
1
0
2
1
2
1
2
0
1
1
1
0
1
2
0
2
2
2
1
0
1
2
0
1
0
2
0
2
3
0
1
1
0
0
1
2
1
2
1
0
2
0
0
0
2
1
1
1
1
2
1
2
2
0
2
1
1
2
0
2
1
2
2
0
0
1
2
1
0
2
1
0
2
0
1
1
0
0
0
1
1
0
1
0
1
2
1
1
1
1
1
1
1
3
1
1
2
1
1
0
1
2
1
0
1
1
1
2
2
1
2
1
2
2
2
2
1
1
2
1
1
1
0
2
2
2
2
1
2
0
1
0
1
1
0
0
2
2
0
1
1
1
1
2
2
1
2
1
1
0
0
2
0
1
0
0
1
0
1
2
1
1
1
1
2
1
1
1
3
2
1
1
1
0
1
1
1
0
1
2
2
1
2
1
2
2
1
2
2
1
0
2
1
1
0
1
1
1
1
1
2
1
1
1
0
1
1
1
1
2
1
2
0
1
0
2
1
2
0
0
0
1
1
0
1
1
1
1
1
1
0
1
0
0
1
2
0
2
2
1
1
0
2
1
0
2
2
1
1
0
1
0
1
0
1
1
2
1
1
1
1
2
1
0
1
1
1
1
1
1
2
1
1
1
1
1
1
0
2
0
3
0
1
1
2
1
1
3
0
0
1
0
1
2
0
1
1
1
1
1
2
2
1
2
1
0
1
1
2
1
2
1
0
1
2
2
2
0
1
2
1
2
2
0
2
1
1
1
1
1
1
2
2
1
1
0
1
1
1
1
0
1
0
0
2
1
1
1
0
1
1
1
1
1
1
2
1
1
1
1
2
1
0
1
0
1
2
1
1
0
1
2
1
0
0
3
0
2
1
2
2
0
2
2
0
0
0
2
1
0
1
1
0
0
1
1
1
0
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
0
1
1
1
0
1
1
1
2
1
1
0
2
1
1
0
0
1
1
0
1
2
0
1
1
1
2
1
1
1
1
0
0
0
2
1
1
1
1
2
1
1
0
2
0
2
0
1
1
1
1
1
2
2
1
1
2
0
1
2
1
1
1
2
2
1
1
0
1
0
1
0
1
1
0
1
0
1
0
2
1
1
2
0
1
1
1
0
1
1
1
0
1
0
1
0
1
2
1
1
1
0
1
0
2
1
3
0
0
1
0
2
2
1
2
1
1
0
1
2
1
2
2
0
0
1
0
1
2
2
1
0
1
3
1
1
1
1
1
1
1
1
0
1
0
1
0
1
2
0
1
1
1
2
1
0
1
1
1
0
1
2
0
2
1
1
1
2
1
0
0
1
2
2
0
0
2
2
2
2
0
2
1
1
0
1
1
1
1
1
2
0
0
1
0
1
1
1
0
1
0
1
1
1
1
1
1
1
0
2
2
1
0
2
2
0
0
1
0
1
2
1
0
1
1
1
1
1
1
0
0
2
1
1
2
1
1
2
1
0
2
2
1
1
1
1
2
1
2
0
1
2
0
1
0
1
1
1
1
0
1
2
2
0
1
0
0
2
2
2
1
2
2
0
1
1
1
3
1
2
5
2
2
0
1
1
2
2
1
1
1
1
1
2
1
2
1
2
1
1
1
0
2
2
1
1
1
1
0
1
1
2
1
2
2
1
2
2
1
0
1
1
2
2
2
1
2
1
1
1
2
1
2
2
0
0
1
1
1
2
2
0
0
0
1
2
2
2
1
2
1
2
2
0
1
1
1
1
1
2
2
1
1
1
2
1
1
2
0
1
1
1
2
0
1
2
1
0
1
1
1
2
0
2
2
2
1
0
1
2
2
0
2
1
0
1
1
0
2
2
1
0
1
0
1
1
2
1
2
1
1
2
2
1
1
3
1
1
2
1
1
1
1
2
0
1
2
2
1
1
2
1
1
1
2
2
1
1
0
2
1
1
1
1
0
1
0
1
1
2
1
1
2
1
1
1
2
2
1
0
0
2
1
1
1
0
1
2
1
0
0
1
1
2
2
0
1
1
0
0
0
2
2
0
1
1
1
1
1
1
1
0
1
2
2
1
1
2
2
1
1
1
2
1
2
1
1
2
1
0
2
1
0
2
1
1
1
1
1
0
0
0
2
1
1
1
0
5
1
1
2
2
1
2
1
1
0
2
2
1
0
2
2
1
1
2
0
2
1
1
2
2
0
1
1
1
1
2
2
1
1
2
2
1
1
2
1
2
1
1
1
1
0
1
0
1
1
0
2
1
1
0
1
1
0
0
2
1
1
1
0
0
1
1
1
1
3
1
1
0
1
0
1
2
1
2
0
2
1
1
1
1
0
1
1
1
1
1
1
2
2
0
0
1
2
2
0
2
2
0
1
1
2
1
1
1
1
1
0
1
1
1
0
1
0
1
0
1
1
1
1
1
4
1
1
1
1
0
2
1
0
1
0
1
1
1
1
1
0
0
2
1
0
2
1
2
2
2
0
0
2
2
1
2
2
1
0
1
0
1
0
2
2
0
1
1
1
1
1
2
1
1
0
0
1
1
1
1
1
1
1
2
1
1
1
1
1
1
0
1
0
2
1
2
1
0
1
0
1
1
1
2
0
1
1
2
3
0
0
0
2
1
1
1
0
1
1
2
2
0
1
1
1
1
1
1
1
1
0
1
2
2
1
2
1
0
1
2
0
0
1
0
1
3
2
2
1
1
0
1
0
2
1
2
1
1
1
0
1
1
1
1
1
1
2
1
1
1
2
1
0
1
1
1
1
1
2
0
1
0
0
1
1
1
1
2
0
2
1
1
1
1
1
1
1
1
2
0
2
2
1
2
1
1
2
1
2
1
1
1
2
1
0
0
0
1
0
1
2
0
2
2
2
1
1
1
0
1
2
0
0
2
2
1
1
1
1
1
1
1
0
0
1
2
0
0
1
1
2
1
0
1
1
1
2
1
0
2
1
1
1
2
0
1
0
0
1
2
1
0
0
2
2
0
2
0
1
2
2
2
1
1
1
2
2
1
1
1
0
0
0
0
2
1
2
1
1
1
1
1
1
0
2
1
1
0
2
2
2
1
2
1
1
0
0
1
0
2
1
1
1
0
2
0
1
1
1
2
1
1
1
2
1
1
1
2
1
2
2
0
1
1
1
1
0
2
2
1
1
1
0
0
1
1
2
0
0
2
1
2
2
1
1
0
0
1
1
1
1
1
1
2
1
1
2
1
0
0
2
2
0
1
2
2
1
2
2
1
2
1
1
1
0
2
1
1
1
0
0
1
1
1
1
0
2
2
1
1
1
1
1
1
0
0
1
0
1
0
1
2
1
1
1
1
1
2
2
1
1
1
1
0
0
2
1
1
1
0
1
2
0
2
2
1
1
0
2
1
1
1
2
0
1
0
1
1
1
1
0
0
1
1
0
2
0
1
0
2
1
1
2
1
0
2
2
0
1
0
0
1
1
0
2
0
1
1
0
2
1
1
1
1
2
1
1
1
1
1
2
0
2
1
0
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
0
1
1
1
3
1
2
1
2
1
2
2
0
0
1
1
0
1
1
1
1
0
1
1
1
1
1
0
1
1
1
1
1
2
2
0
0
1
2
2
0
0
0
2
2
2
2
2
1
1
1
1
1
2
2
0
1
1
2
0
0
2
1
1
1
2
1
1
1
3
2
1
0
0
2
2
2
3
0
1
0
1
1
1
1
1
1
0
3
1
2
1
1
1
1
2
2
0
1
0
1
1
1
0
1
1
1
1
0
1
0
1
1
2
1
2
1
2
1
0
1
1
1
1
0
1
0
1
1
1
1
1
1
0
2
0
1
1
1
1
0
1
3
1
2
1
1
1
1
1
2
1
1
1
1
2
1
1
0
1
0
2
1
2
1
1
1
1
2
2
1
2
1
1
2
0
0
1
1
2
1
1
1
1
1
1
2
3
1
1
1
0
1
2
2
1
2
2
1
1
0
1
1
0
1
1
1
1
1
2
2
2
2
0
1
2
2
0
1
2
2
1
1
1
1
0
0
1
0
1
0
1
2
1
2
2
2
0
0
0
1
1
1
2
0
1
2
1
1
0
1
1
1
1
0
1
1
1
0
1
1
1
2
0
0
0
1
1
0
0
1
0
2
1
0
1
1
1
1
1
1
1
0
1
0
1
2
0
1
0
0
0
0
1
1
1
1
1
1
1
1
2
0
2
1
1
1
2
1
1
0
0
1
2
1
1
0
2
2
1
2
0
1
0
0
2
1
1
1
1
0
0
0
1
1
2
1
1
0
1
1
1
1
0
1
0
1
1
1
1
2
1
1
1
2
1
1
1
0
3
2
1
1
2
2
0
2
1
3
1
2
1
1
0
1
1
1
1
0
2
1
1
0
1
0
1
0
1
2
0
1
0
0
1
2
1
1
1
1
1
2
0
1
1
1
1
2
1
1
1
1
1
0
0
0
0
1
0
1
0
1
1
0
0
1
0
1
0
1
0
1
2
1
1
1
1
1
1
1
3
1
1
0
1
0
1
0
1
1
2
0
1
2
1
2
2
1
2
2
1
1
1
0
2
1
1
1
0
1
1
1
1
1
1
0
1
1
1
2
2
2
2
1
0
1
2
1
1
1
1
1
1
2
1
1
1
1
0
1
2
1
2
1
2
1
1
1
1
2
2
1
1
1
0
1
0
2
1
0
2
2
1
1
1
1
0
1
1
1
2
0
1
0
1
1
1
1
0
2
1
0
1
1
1
1
1
1
1
0
1
1
1
2
1
1
2
1
1
2
2
1
1
2
2
1
1
1
2
1
2
0
1
0
1
1
0
2
1
1
0
1
1
2
1
1
1
1
2
1
0
1
1
1
1
0
0
0
2
1
0
0
2
1
1
1
1
1
2
0
1
1
2
1
0
2
1
2
1
0
0
1
1
0
2
1
2
1
2
2
0
0
1
2
1
1
1
0
0
2
1
2
1
1
1
1
1
2
0
0
1
1
1
1
1
1
1
1
1
0
1
2
1
1
1
1
3
1
2
1
1
1
1
2
1
1
1
1
1
1
0
1
1
1
1
2
1
1
0
1
1
1
1
1
0
2
1
1
1
1
1
2
0
1
2
2
0
1
1
0
1
1
0
2
1
0
1
0
1
1
1
0
2
1
2
2
1
1
2
2
1
2
1
1
0
2
1
2
1
1
0
0
1
0
1
2
2
1
0
1
0
1
0
1
1
0
1
1
1
2
3
1
1
1
1
1
0
1
1
1
0
1
1
2
0
1
1
1
2
1
2
0
0
1
1
2
0
1
1
2
1
0
1
0
1
0
0
1
1
1
1
2
1
2
1
1
1
1
2
1
1
1
2
1
1
2
0
2
0
2
1
2
0
1
2
0
1
1
1
1
0
1
1
2
2
0
1
1
2
1
1
0
0
1
2
0
1
1
1
1
1
0
2
2
0
1
1
0
1
1
1
1
0
1
0
0
1
1
2
1
2
1
0
2
1
2
1
2
0
0
1
2
0
1
1
1
1
0
1
1
1
1
2
1
1
0
2
1
0
2
1
1
1
2
0
0
0
2
0
2
2
1
0
1
1
1
0
0
1
0
2
1
2
0
0
1
0
0
1
1
0
1
1
2
0
1
1
1
1
1
0
2
1
1
1
1
2
1
1
1
0
1
0
1
1
0
1
0
0
3
2
1
1
1
2
1
0
0
1
2
2
2
1
1
1
2
1
2
1
1
2
2
1
2
1
1
1
1
1
1
0
1
1
1
1
1
0
1
1
2
1
1
1
1
0
1
1
1
1
1
3
1
1
0
1
1
1
0
0
0
2
1
1
2
2
1
1
0
1
2
1
1
2
2
1
1
1
1
0
1
2
2
1
1
1
0
0
1
1
2
1
0
2
2
2
1
1
1
0
0
1
0
2
0
1
0
2
1
1
1
0
1
1
1
2
2
2
0
2
2
1
0
2
2
0
0
1
1
0
2
0
1
1
1
1
0
1
1
2
0
0
1
1
0
1
1
1
2
2
1
0
2
2
3
0
2
2
0
1
0
2
1
1
1
0
2
1
2
1
1
1
1
1
2
2
0
1
0
1
0
1
1
0
1
0
1
1
1
2
1
1
0
0
0
1
1
1
1
0
2
1
1
1
1
0
2
2
1
2
0
1
1
2
1
1
1
0
1
2
1
1
0
1
1
1
2
1
1
2
1
0
2
1
0
1
1
0
2
0
1
2
1
1
2
2
2
2
0
2
1
1
1
0
1
1
0
2
0
2
2
2
0
2
0
1
1
0
2
0
1
1
0
0
2
1
2
0
1
1
2
0
0
0
2
1
1
1
2
2
1
0
1
0
0
2
4
1
2
2
2
2
0
1
1
1
1
2
4
1
1
2
2
1
1
1
1
1
1
2
1
2
2
1
1
2
1
1
2
2
2
1
0
0
0
2
2
1
1
1
0
2
1
2
1
1
1
1
0
0
1
0
2
1
0
1
1
2
1
1
1
0
1
2
2
1
1
1
1
1
1
1
0
2
0
1
1
1
1
1
1
2
1
1
1
1
2
0
0
1
1
0
1
2
0
1
1
0
0
1
1
1
1
0
2
2
1
1
1
1
2
0
0
1
1
1
1
2
1
1
2
1
1
1
1
1
1
0
1
1
0
1
2
1
2
2
1
1
0
1
0
1
1
1
1
1
1
0
2
1
0
2
2
2
0
1
1
0
0
1
1
1
0
0
1
0
2
1
0
2
2
1
1
3
0
2
1
0
1
1
1
0
0
1
1
1
1
1
1
1
0
2
2
1
1
1
0
2
2
1
1
1
5
1
1
3
2
0
1
1
0
1
2
1
1
2
1
2
1
1
2
1
0
2
0
1
1
1
0
2
0
0
2
1
1
0
2
2
0
1
0
1
0
2
1
1
1
2
1
1
0
0
1
0
1
1
1
1
1
0
1
1
1
1
1
1
2
1
1
1
0
0
0
2
1
0
0
1
2
1
1
1
1
1
1
1
0
1
1
1
1
2
2
0
1
2
1
2
1
1
1
1
1
1
2
1
1
1
0
1
1
2
1
1
1
0
1
1
0
1
1
1
1
1
0
2
1
2
0
1
1
1
1
2
1
1
0
1
0
0
2
0
1
1
1
1
1
1
1
1
1
0
0
0
1
2
0
1
1
0
2
1
2
3
0
1
0
0
2
1
1
3
2
1
2
1
1
1
0
2
1
1
2
0
0
1
1
1
1
0
2
0
1
2
1
0
1
1
2
2
1
1
0
1
0
0
1
1
1
2
2
1
2
1
1
2
1
1
1
1
1
1
0
2
2
4
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
0
1
0
0
2
2
1
0
1
0
2
0
1
1
0
1
1
1
2
2
2
1
2
1
2
2
1
1
1
1
1
1
2
1
0
1
0
2
1
2
0
0
0
1
1
1
2
1
1
3
1
1
2
1
2
0
1
0
1
1
1
1
1
0
0
2
1
1
1
1
1
0
0
2
1
2
1
2
1
1
0
1
2
0
1
1
2
1
0
1
1
0
0
2
1
1
2
1
2
2
0
0
1
1
2
0
3
3
0
0
1
0
1
2
1
1
1
1
1
1
0
2
2
2
2
0
1
2
1
1
1
1
1
1
1
2
0
0
0
1
0
0
1
2
2
1
1
1
3
2
1
2
1
1
1
1
2
0
0
1
1
2
1
1
1
1
2
2
1
1
0
1
1
2
0
0
1
0
1
1
2
0
2
1
1
1
1
2
0
1
1
2
2
1
2
1
1
2
1
0
1
0
2
1
1
2
0
1
1
0
2
2
0
1
0
1
1
0
0
1
1
1
1
0
1
0
0
1
1
0
1
1
2
1
0
0
2
2
0
2
0
0
1
1
0
1
1
2
0
1
1
0
1
1
0
1
1
0
1
2
0
0
0
2
2
1
2
1
1
1
1
1
2
1
1
1
2
1
0
1
2
1
1
2
1
2
1
0
1
1
1
1
3
2
0
1
0
3
2
2
1
1
1
0
0
0
1
2
1
1
0
0
2
1
0
1
1
2
2
1
2
1
1
1
0
0
2
1
1
2
0
2
1
1
1
2
0
1
1
2
1
1
4
1
2
1
0
0
1
1
1
2
1
2
0
0
1
1
1
0
1
0
0
1
1
2
1
1
2
1
0
1
0
2
1
0
2
1
1
2
1
1
2
1
1
2
1
1
1
1
1
0
2
0
1
1
1
2
1
1
1
1
0
1
1
1
1
1
0
1
2
2
1
0
0
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
0
0
2
1
1
1
1
2
1
1
1
2
1
1
2
1
1
1
0
2
2
1
1
1
2
1
1
1
1
1
1
1
1
0
2
1
0
1
2
0
1
2
0
1
1
2
1
1
2
1
1
1
1
7
1
1
3
1
0
2
1
1
1
1
0
2
1
1
0
2
0
1
1
2
2
2
1
2
2
1
1
1
1
1
2
0
2
1
2
1
1
2
2
0
2
1
0
2
0
2
2
1
2
2
0
1
1
2
1
1
1
1
0
0
2
1
2
1
0
1
0
1
0
1
1
1
0
2
2
1
1
1
2
1
2
1
1
1
0
1
1
2
1
2
1
0
0
1
0
1
1
2
1
3
1
1
0
2
2
0
0
2
1
1
0
0
1
2
1
1
2
0
1
1
1
0
1
1
1
1
2
0
1
1
0
1
2
2
2
2
2
1
2
1
1
1
1
2
2
0
0
0
1
1
1
0
1
2
1
2
1
2
0
2
1
0
1
2
1
0
1
1
2
1
1
1
2
2
1
1
1
1
1
2
0
2
1
2
1
0
2
1
2
1
2
0
2
0
1
1
0
2
1
2
2
1
1
0
2
1
1
1
2
1
1
1
0
2
1
1
0
1
1
1
0
2
1
1
1
2
1
2
1
1
0
1
1
1
1
0
0
1
1
0
1
0
2
3
1
1
1
1
1
0
2
1
2
0
1
2
1
1
1
2
2
3
2
0
1
1
1
1
1
0
0
1
1
1
0
2
1
1
0
1
1
0
1
1
0
0
1
1
1
2
1
1
2
1
2
1
1
1
1
1
0
2
2
1
1
1
1
1
1
1
0
2
0
0
1
0
1
0
1
2
1
2
1
1
1
1
1
0
2
1
1
1
1
1
2
0
1
2
1
1
1
0
2
1
0
1
1
1
1
2
0
1
1
0
2
1
1
1
0
1
0
1
1
1
1
2
2
1
1
1
0
1
1
1
1
1
0
0
1
1
0
2
1
1
1
1
2
2
1
1
1
1
1
1
0
1
1
1
1
1
1
1
0
2
2
1
1
0
1
0
0
1
2
1
1
1
2
2
2
0
1
2
1
1
1
1
0
1
1
0
0
0
0
1
1
0
2
2
0
1
1
1
1
2
1
1
1
1
0
1
2
1
2
0
1
1
2
1
1
1
1
1
2
1
1
2
1
0
0
1
1
0
0
1
1
1
0
1
0
1
1
2
2
1
2
0
1
1
2
1
1
0
1
1
0
1
1
1
0
1
1
1
0
1
2
0
0
2
0
1
1
0
1
0
1
0
1
0
1
1
1
1
1
2
0
2
1
1
0
1
1
2
1
1
0
2
2
1
2
1
2
1
0
2
1
1
2
1
1
1
0
2
0
2
1
0
2
1
1
1
0
1
0
1
1
2
4
1
1
1
1
1
0
1
1
1
2
1
0
1
1
2
1
0
1
1
0
1
0
3
2
1
1
1
0
0
1
1
0
1
0
1
0
0
1
1
0
1
2
1
1
0
1
2
2
2
1
1
1
0
1
1
2
1
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
0
1
1
2
1
1
1
2
2
1
1
1
0
2
1
1
1
1
2
1
2
1
1
1
2
2
1
2
1
2
1
2
0
1
1
1
1
1
1
2
1
0
1
1
1
1
1
2
1
0
1
1
0
1
1
1
1
1
2
1
1
1
1
0
2
0
0
0
2
1
0
1
2
2
1
0
1
1
1
1
0
2
1
1
2
2
1
1
0
1
1
1
0
0
2
2
1
2
1
0
1
1
1
0
0
1
1
2
1
1
1
2
2
1
1
1
1
0
0
2
1
1
1
1
2
1
1
1
1
2
2
2
1
0
0
1
1
1
0
0
0
1
0
0
0
1
1
2
1
2
1
2
1
1
1
1
1
2
1
1
2
2
1
1
1
2
2
1
0
1
2
0
1
1
0
2
0
1
1
0
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
0
1
1
1
2
1
1
2
0
1
1
1
1
0
0
1
1
0
0
0
0
1
1
1
0
2
1
1
1
1
0
1
1
0
2
0
0
1
1
0
1
2
2
1
1
1
1
2
1
0
2
1
2
1
1
2
1
2
1
2
1
1
1
1
2
1
0
1
1
0
1
2
0
1
1
1
0
1
1
0
1
1
1
1
2
1
0
2
1
0
1
2
1
0
2
2
2
2
2
1
1
0
2
2
2
2
3
2
1
0
2
2
2
1
1
1
0
0
0
1
0
0
2
1
0
1
1
1
0
2
1
1
2
1
1
1
1
0
1
0
2
2
1
1
2
0
1
1
1
1
2
1
2
2
1
1
1
0
0
2
0
1
1
2
1
0
1
1
1
1
0
1
1
0
2
1
2
1
2
3
0
2
0
0
2
1
1
1
0
1
1
0
2
1
1
0
1
0
1
2
2
1
2
1
1
0
1
0
0
1
1
0
1
2
1
0
2
2
1
0
0
0
2
1
0
2
2
2
2
2
1
0
1
1
1
0
2
1
1
1
1
1
2
0
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
2
1
1
0
2
2
2
1
2
1
1
1
0
0
0
1
0
2
0
1
0
1
0
1
1
1
2
0
1
1
1
3
1
1
0
1
1
2
1
1
1
0
1
1
1
0
1
1
1
1
1
1
0
1
2
2
1
2
1
1
1
2
0
0
0
1
1
1
1
0
2
1
1
0
2
1
1
0
1
0
1
1
2
1
2
2
1
1
1
0
2
1
1
0
1
0
1
1
0
1
1
2
1
2
1
1
1
1
1
2
0
1
1
2
2
1
1
1
0
2
1
0
0
0
0
0
2
0
1
2
1
2
1
2
0
2
0
1
0
2
0
2
1
0
1
2
1
0
1
2
1
1
0
0
1
1
0
2
2
2
1
0
0
1
0
2
0
1
1
0
1
0
1
1
0
2
1
1
1
1
2
1
2
1
1
2
1
1
2
1
1
0
0
1
0
1
1
1
0
2
1
2
2
2
1
2
0
2
1
1
2
1
0
2
1
0
1
1
1
1
0
0
1
0
2
1
0
1
0
1
2
1
1
1
2
1
1
0
1
5
1
1
1
2
2
1
1
1
1
0
1
2
0
2
1
1
1
0
2
1
0
1
0
1
0
2
1
1
1
1
1
1
0
0
1
2
1
0
1
1
2
2
1
1
2
1
2
1
2
0
0
1
1
1
1
1
1
1
1
2
2
2
1
1
0
1
1
1
1
1
0
2
1
0
1
1
1
1
2
2
4
1
0
1
1
1
1
0
1
0
1
0
1
0
2
1
1
2
2
0
1
1
1
0
0
1
1
1
1
1
0
1
1
1
1
1
2
2
1
1
2
1
1
0
1
1
2
0
1
2
0
1
1
0
1
0
0
1
0
1
2
2
2
0
1
2
1
1
2
0
1
1
2
1
3
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
0
1
0
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
2
1
0
0
1
2
1
1
1
0
2
1
1
1
1
1
0
2
0
1
2
0
2
0
0
0
0
1
2
2
0
1
1
1
1
2
2
1
0
1
1
1
2
1
1
2
1
1
0
2
2
1
0
0
1
1
0
1
2
0
0
0
1
1
2
1
1
1
2
0
2
1
2
1
1
1
1
0
0
1
0
0
0
0
1
1
1
1
1
2
1
1
1
1
0
1
0
1
1
1
2
1
1
1
2
2
1
1
0
1
2
1
2
0
2
1
1
1
1
3
2
2
1
0
1
1
1
1
2
2
0
0
2
0
1
2
2
1
1
2
1
1
1
2
1
0
0
0
0
1
1
1
1
1
2
1
1
1
1
1
2
2
1
1
1
0
1
0
1
1
2
2
0
2
1
1
1
0
1
2
1
1
2
2
1
1
1
1
1
2
0
1
1
1
2
2
2
3
2
1
1
0
1
2
0
1
1
1
3
1
0
1
1
1
1
1
1
2
0
1
1
0
0
2
2
1
3
1
1
1
1
0
1
1
1
3
2
1
1
2
0
2
1
2
1
1
1
1
2
2
0
1
0
2
2
1
1
1
0
1
0
1
2
0
1
2
0
1
1
1
1
0
1
1
1
0
0
1
0
2
1
1
1
0
1
1
0
0
1
0
2
2
1
2
1
1
1
1
1
1
0
1
2
1
0
2
1
0
2
1
0
1
1
0
1
1
1
1
0
0
2
1
1
1
1
1
1
2
1
1
1
2
2
1
1
0
2
1
1
1
2
0
2
1
1
1
1
1
0
1
0
1
0
4
0
1
0
1
1
1
1
0
2
1
1
1
1
1
2
1
1
1
2
0
1
2
0
0
0
1
2
1
3
1
1
2
0
2
1
2
2
1
1
1
1
0
1
0
1
1
1
1
1
2
1
2
1
1
1
1
0
1
2
1
1
1
1
1
0
1
0
0
1
1
0
1
1
0
1
1
2
2
0
1
2
1
1
2
2
1
2
2
2
2
2
1
0
1
0
1
1
2
1
0
1
2
1
1
0
1
1
1
2
1
0
1
1
2
2
1
1
0
1
3
2
2
0
1
1
0
2
2
2
1
2
1
1
1
2
1
0
1
2
0
1
0
0
0
4
0
2
1
2
0
0
1
1
3
2
0
0
0
1
1
1
2
1
0
0
1
2
1
1
1
2
3
1
1
2
1
2
2
1
0
1
1
1
1
1
1
0
0
2
2
2
0
3
1
1
2
1
1
1
1
1
2
2
0
0
0
1
2
2
0
2
1
1
1
2
2
1
0
2
1
2
1
1
0
1
1
0
1
0
0
2
0
1
1
1
1
0
2
1
2
1
1
1
1
0
1
1
0
1
0
1
2
1
0
2
2
0
1
0
1
1
3
1
0
1
0
1
2
1
2
2
0
1
1
1
2
1
0
1
0
1
0
1
1
0
0
2
2
0
1
1
1
2
1
1
0
1
1
1
1
2
1
0
2
1
0
1
1
1
1
1
1
1
1
2
2
1
2
1
2
1
1
2
2
1
1
2
0
1
1
2
1
1
0
1
0
1
1
1
1
0
1
1
1
1
1
1
1
1
2
1
1
1
1
0
1
2
3
1
0
1
0
1
1
2
1
1
0
1
0
2
1
2
2
1
0
1
2
1
2
0
1
1
1
1
1
1
1
1
0
1
1
1
1
2
0
1
1
1
0
1
1
3
0
1
1
0
2
0
1
1
1
0
1
2
2
0
2
1
0
0
1
2
1
1
1
1
0
1
0
2
1
1
2
2
0
2
2
0
1
3
1
0
2
0
1
1
2
1
1
1
2
1
2
1
2
2
0
1
2
1
3
1
1
2
0
1
0
1
1
1
2
0
2
2
2
1
1
0
1
0
1
0
1
1
2
1
1
1
2
1
1
0
1
0
1
1
0
1
1
1
1
1
1
1
2
1
0
1
2
1
2
0
0
0
0
1
1
1
1
0
0
1
3
2
0
1
2
1
1
1
0
1
2
2
1
2
2
0
0
0
2
0
2
0
0
1
0
2
1
1
0
1
2
1
0
2
2
2
1
1
1
2
2
1
2
1
1
1
0
1
1
1
1
1
2
1
2
1
1
1
1
0
1
1
2
1
1
1
2
0
1
2
1
0
0
2
1
2
1
1
1
1
2
1
1
1
1
4
1
0
2
2
1
2
1
1
1
0
1
1
1
2
2
1
0
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
3
1
0
0
2
1
1
1
1
1
0
1
0
2
2
0
0
2
1
0
0
1
0
2
1
1
2
1
1
1
1
0
1
1
0
1
1
2
1
2
2
0
0
0
1
1
0
0
0
1
1
1
0
2
2
1
1
0
1
0
1
1
1
1
2
0
1
1
0
1
0
0
1
2
0
0
1
1
2
2
1
0
2
0
2
2
0
2
2
1
1
0
1
1
1
1
0
1
1
1
1
1
0
1
1
2
0
2
1
0
1
1
1
2
1
1
1
2
1
2
2
2
0
1
1
0
1
1
1
0
1
1
0
2
1
0
1
1
2
1
2
0
1
1
0
1
1
1
0
2
2
2
1
1
1
2
1
2
1
1
1
2
1
1
1
1
6
1
2
0
2
1
2
2
2
0
0
1
0
3
0
2
2
0
2
2
0
0
1
1
2
1
1
1
0
2
0
1
2
1
1
0
1
1
2
1
1
0
1
2
0
2
2
1
2
1
1
1
0
1
2
2
2
2
2
2
2
2
1
0
1
2
2
1
1
0
1
2
1
1
2
1
0
0
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
0
3
1
2
1
1
1
1
0
1
2
1
1
1
2
1
2
2
1
0
2
1
0
2
0
2
2
1
2
0
1
1
0
2
1
1
1
1
2
1
1
2
1
1
1
2
1
1
1
2
1
0
1
1
1
2
1
2
0
0
1
2
1
1
3
0
0
1
2
1
1
1
2
2
0
1
2
1
0
2
2
1
1
1
0
0
1
0
1
1
1
1
0
1
2
2
1
0
1
1
2
1
1
0
2
1
2
1
1
2
0
1
1
2
1
2
1
1
1
1
0
1
1
1
2
0
0
1
2
1
0
1
1
0
1
1
0
1
1
3
2
0
1
2
1
1
1
2
0
1
0
1
1
1
0
2
2
1
1
2
1
1
0
1
1
1
0
2
0
1
0
1
1
0
0
2
1
1
1
0
2
1
2
0
0
1
0
1
1
0
1
1
3
1
0
0
2
1
1
1
1
0
0
2
0
1
1
1
1
1
1
0
1
0
1
1
0
2
1
2
1
1
0
1
1
1
1
1
1
1
1
0
2
1
1
2
1
1
1
1
1
1
0
1
1
1
0
3
0
1
1
1
1
1
1
0
0
0
1
2
1
1
0
0
1
1
0
0
0
1
1
1
2
1
0
2
1
1
1
1
1
1
0
1
1
0
1
1
0
1
1
1
2
2
0
1
2
0
1
1
1
1
1
1
1
2
1
1
0
1
2
2
2
1
0
1
2
0
1
1
0
1
0
2
1
1
1
1
1
1
0
2
1
1
1
1
1
0
1
1
1
1
2
0
0
1
1
1
1
1
1
1
0
0
1
1
0
1
2
1
1
2
1
0
1
0
1
1
1
1
1
1
0
1
0
1
1
1
0
1
0
1
0
2
0
3
4
1
2
2
0
2
1
1
2
1
0
1
2
2
2
1
1
1
1
1
0
0
2
1
1
0
1
1
0
2
2
0
1
1
1
1
1
0
2
1
0
1
0
1
1
1
0
2
1
1
1
1
2
1
1
0
0
1
0
1
1
2
0
1
1
1
2
1
0
1
1
1
1
2
0
2
2
0
2
2
0
1
0
1
0
1
1
1
1
2
1
0
1
1
0
1
1
2
1
2
0
1
1
1
2
1
2
1
0
1
2
2
1
2
1
0
2
1
2
2
1
1
1
1
2
1
0
1
0
1
1
2
1
2
1
1
1
0
1
1
1
2
1
0
2
1
1
1
1
0
1
2
2
0
1
1
1
1
1
1
0
0
0
1
1
3
0
2
1
3
1
0
0
2
1
0
1
3
1
0
1
1
1
2
0
2
1
0
1
0
1
2
2
1
1
2
1
1
2
1
2
2
2
1
2
0
2
0
2
1
1
1
1
1
1
1
0
2
2
1
1
1
1
2
1
1
1
2
1
2
1
0
1
0
0
1
2
1
1
1
1
2
1
1
0
0
2
2
2
0
0
1
1
1
0
1
1
1
2
1
0
2
0
2
2
1
0
2
0
1
3
1
1
2
1
1
2
1
2
1
1
1
0
1
2
1
1
1
1
0
2
0
0
1
0
0
1
2
1
2
1
1
2
1
0
2
1
2
1
1
1
0
2
3
0
2
1
2
0
1
1
1
1
1
1
2
2
2
2
1
1
2
1
1
1
2
2
1
1
3
0
1
2
1
2
1
2
0
1
3
0
2
2
1
1
1
1
0
1
2
1
1
0
1
1
1
2
1
0
1
2
1
0
0
0
0
1
2
0
1
1
2
1
0
1
1
1
0
1
2
1
0
1
1
0
2
0
2
2
1
0
0
1
2
1
2
1
2
0
3
2
1
1
1
2
1
1
0
1
2
1
1
2
1
1
2
0
2
2
2
1
1
0
1
0
0
0
1
2
1
0
1
1
0
1
1
0
1
0
2
1
1
1
0
2
1
2
1
0
0
0
1
1
1
2
1
0
2
0
2
0
2
0
2
0
1
2
1
1
2
2
1
0
0
1
1
1
1
0
1
2
0
1
0
0
1
1
1
1
1
1
0
1
2
2
1
2
2
1
2
1
0
1
1
1
2
1
1
1
2
1
1
1
1
0
1
1
1
1
1
2
1
1
1
1
1
1
2
1
2
2
0
1
1
2
2
2
1
1
1
1
1
1
2
1
2
1
0
1
1
1
1
2
2
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
2
2
0
1
1
2
1
1
0
0
1
1
1
0
1
0
0
1
0
1
2
1
1
2
2
1
2
1
1
1
1
2
0
1
0
1
1
2
1
1
1
2
2
1
0
1
0
1
0
0
0
2
1
2
1
1
2
1
1
2
0
1
1
0
1
2
0
2
0
2
2
0
0
2
1
2
1
1
0
0
1
2
0
2
1
1
1
2
2
0
1
2
0
0
0
1
1
1
1
2
1
1
0
0
2
1
2
2
2
3
0
1
0
1
1
1
2
1
2
1
0
1
1
2
1
1
1
2
2
2
1
1
2
2
1
1
2
0
2
2
1
1
1
1
1
1
1
0
1
2
0
2
2
1
0
0
1
1
2
1
1
0
1
1
1
1
0
0
1
1
1
0
2
0
1
1
1
0
1
1
0
1
1
0
1
0
1
0
1
0
1
1
1
0
2
0
1
1
1
2
1
0
1
0
2
1
0
2
3
2
1
1
2
1
0
1
1
1
1
2
0
2
1
0
2
0
0
2
1
2
1
1
1
0
1
1
0
1
1
0
0
1
2
0
1
1
2
0
1
0
1
1
1
2
0
1
1
2
0
1
0
2
1
1
0
2
0
1
0
0
1
1
1
2
1
2
1
1
2
1
1
1
1
0
1
2
1
0
1
2
1
3
1
2
0
2
1
1
0
2
1
2
2
0
0
0
1
1
0
1
2
0
3
1
1
1
0
1
1
1
1
2
1
0
2
1
0
2
1
1
2
2
1
1
1
1
1
0
1
1
2
0
0
1
1
1
0
1
2
2
0
0
1
1
2
1
1
1
1
2
1
2
0
1
2
0
0
0
1
2
1
1
1
1
1
4
0
0
1
2
0
1
0
1
2
1
1
1
2
2
2
0
1
1
1
2
1
1
0
1
1
1
0
0
1
0
0
1
0
1
1
0
2
1
1
1
1
1
0
0
1
0
0
1
0
0
1
0
1
1
1
0
1
0
0
1
0
1
3
1
2
0
0
1
1
0
1
0
1
1
1
1
1
0
0
3
1
2
1
0
1
1
0
0
3
2
1
1
2
2
1
0
1
0
1
1
0
0
1
1
0
0
2
1
1
1
1
0
2
1
0
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
2
0
0
1
1
0
1
2
1
2
1
1
0
1
2
1
1
0
1
1
0
2
1
1
2
2
0
1
2
1
0
1
2
1
0
2
1
1
1
1
1
1
2
0
0
2
1
2
1
1
1
0
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
0
0
0
2
2
2
0
1
1
1
2
0
2
0
0
2
2
1
2
2
1
1
1
0
0
2
2
0
1
0
0
2
2
1
2
1
0
2
0
0
0
1
1
1
2
1
2
0
1
1
1
1
2
1
0
2
1
1
0
0
1
2
2
2
1
1
0
0
1
2
1
2
1
1
0
0
4
1
1
2
2
0
1
1
2
1
2
1
0
1
2
2
0
2
0
0
1
2
0
1
2
1
1
1
1
2
1
1
1
1
1
1
1
0
1
1
2
1
0
0
0
1
1
0
1
2
2
1
1
1
0
1
1
2
1
1
0
2
1
0
1
0
1
0
0
2
0
1
2
1
2
1
1
1
1
0
2
1
2
2
0
1
0
2
1
1
1
2
2
1
1
0
1
3
0
1
1
0
1
1
1
1
1
0
0
2
2
1
2
0
1
1
0
1
0
0
1
0
0
2
1
1
2
1
1
1
1
1
1
1
1
1
1
0
2
1
1
0
1
0
2
2
0
1
1
0
1
1
1
1
1
1
1
4
1
2
1
1
2
2
0
2
0
1
0
0
1
1
1
2
1
0
1
0
1
0
1
1
2
1
0
0
1
0
1
1
2
1
1
0
1
1
1
0
3
0
2
1
1
1
1
2
2
1
1
1
1
2
2
1
2
1
1
1
0
1
1
1
0
1
2
1
1
0
0
1
2
2
1
2
2
1
2
2
1
1
1
0
2
2
1
1
0
0
1
1
1
1
1
1
1
1
1
0
1
0
1
2
1
0
1
1
1
2
0
2
1
0
0
1
0
1
1
1
0
1
1
1
1
2
1
0
1
1
1
1
2
1
0
2
2
1
1
2
0
0
1
2
0
2
0
2
2
1
2
1
2
0
1
1
1
0
1
2
0
0
2
1
1
1
2
1
1
0
1
2
3
0
1
1
2
1
1
1
2
1
1
2
2
3
3
1
1
1
2
1
2
1
1
1
1
0
2
1
2
0
0
1
1
1
1
1
2
1
2
0
1
1
0
2
1
1
3
1
0
1
1
2
1
1
1
1
2
1
1
1
2
1
1
1
1
2
0
2
2
1
3
0
1
1
1
3
2
1
2
1
1
0
2
1
1
1
1
1
1
2
1
2
1
1
0
1
0
0
1
1
1
1
2
1
2
2
2
2
0
2
2
1
2
1
2
1
2
0
2
2
0
1
0
1
2
1
2
1
1
2
2
0
1
1
1
1
2
1
0
1
3
1
1
0
1
0
2
1
0
1
1
1
1
1
1
1
1
0
2
0
1
2
2
0
2
1
2
1
2
0
2
2
1
1
1
1
1
0
1
1
1
2
1
1
1
1
2
1
1
2
2
2
1
1
3
0
1
1
1
2
0
1
1
1
2
1
2
1
2
0
1
2
0
2
1
1
1
2
1
1
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
0
1
0
1
2
2
1
1
2
1
1
2
1
1
1
2
0
2
1
1
1
1
0
1
1
1
1
1
1
1
2
1
2
0
0
0
0
1
0
2
1
1
1
2
1
2
2
1
1
1
1
1
0
1
2
0
1
0
1
1
1
1
2
1
1
1
1
1
2
1
1
2
2
1
2
1
1
0
1
2
0
1
2
0
1
1
1
1
1
1
3
1
1
1
2
2
1
1
2
1
1
1
1
2
2
1
1
1
2
0
1
2
2
2
1
2
2
0
1
1
1
2
1
1
2
1
0
1
1
1
1
1
2
2
1
1
2
1
1
1
2
1
1
0
0
0
0
1
1
1
1
1
1
2
2
2
0
1
0
2
1
1
0
1
1
1
2
1
2
1
1
1
1
0
1
2
0
2
1
1
3
0
2
1
1
2
1
1
1
0
1
0
0
1
0
1
0
1
1
0
1
0
2
1
1
0
0
1
2
1
1
1
2
1
0
1
2
1
2
0
1
0
1
1
1
2
2
2
2
1
1
1
2
2
0
1
1
1
1
1
1
1
2
1
0
0
1
1
1
2
2
1
1
0
0
1
0
0
1
2
1
2
0
1
2
1
0
1
1
1
1
1
2
1
1
0
2
1
1
2
1
1
1
1
0
1
1
1
2
3
0
1
1
0
2
0
0
0
2
0
1
1
2
1
2
0
2
0
2
1
2
1
1
2
0
0
1
1
0
1
0
1
0
2
2
1
1
1
1
2
1
2
1
2
2
1
2
0
1
1
1
0
1
2
1
1
1
2
2
1
1
2
2
1
1
0
1
1
0
1
0
0
2
3
0
1
0
2
1
2
1
0
1
1
2
1
1
0
0
1
0
3
2
1
0
1
1
0
1
2
1
1
2
0
1
2
2
1
1
0
1
0
0
0
1
1
2
1
1
0
1
1
1
1
2
1
1
1
1
0
2
1
1
1
1
1
1
1
1
1
2
0
1
1
1
1
1
1
1
0
1
1
1
0
1
1
2
0
0
1
0
2
0
2
1
2
1
1
1
0
2
1
2
2
1
1
1
1
0
1
0
0
1
1
1
1
1
1
2
1
1
1
1
0
3
1
1
1
1
1
0
1
2
0
0
2
4
0
1
2
0
1
2
1
1
1
0
0
1
1
2
1
1
1
1
0
0
2
1
2
1
2
2
1
1
1
0
1
1
0
0
1
2
2
2
1
1
2
0
1
0
1
2
1
0
0
1
0
1
1
1
2
1
2
2
1
1
1
2
2
1
2
1
0
1
1
1
1
1
1
1
0
0
1
1
1
0
1
2
1
1
1
2
2
0
1
1
1
0
0
2
1
1
1
0
2
0
1
1
0
1
2
1
1
1
0
0
2
1
1
0
2
0
1
0
0
1
1
1
2
0
1
3
1
1
1
1
1
0
1
1
1
1
0
1
1
0
2
0
1
1
1
1
0
2
0
1
1
1
1
2
1
2
1
2
1
1
1
2
1
1
1
1
1
2
0
2
0
0
2
2
1
1
1
1
0
1
1
0
1
2
1
2
0
1
1
1
1
0
1
2
1
1
1
2
1
0
1
2
1
2
1
1
4
2
2
2
1
2
1
2
1
1
0
1
0
1
1
1
2
0
0
1
2
1
1
2
1
0
0
0
1
1
1
1
2
1
1
0
1
1
1
0
1
1
1
1
1
0
0
1
0
1
1
1
1
2
2
1
0
1
1
0
2
1
2
2
1
0
1
1
0
0
2
0
0
1
1
1
0
4
0
1
1
1
1
1
1
1
2
2
0
1
1
0
1
1
1
1
1
1
2
1
1
1
1
0
1
1
1
1
0
1
2
1
1
1
1
1
1
0
1
1
0
1
1
2
2
1
1
1
1
1
1
1
0
0
1
1
1
1
2
1
2
0
1
1
1
0
1
1
0
2
0
1
2
1
1
0
1
1
2
1
0
2
1
1
2
1
1
1
1
2
1
2
0
1
1
1
1
1
1
0
1
2
1
0
2
2
0
0
1
1
2
2
2
1
0
0
1
0
1
1
1
2
1
0
2
2
0
2
1
0
1
1
1
0
0
2
1
1
1
0
0
1
2
0
2
1
2
1
1
1
2
0
1
2
0
1
2
1
2
1
1
0
2
1
2
2
2
1
1
1
1
1
0
1
1
2
2
1
2
0
1
1
0
1
1
1
2
1
0
1
1
2
1
2
0
1
1
0
0
1
1
1
1
0
1
0
1
1
2
1
1
1
1
1
1
1
1
1
2
1
0
0
2
2
1
1
0
2
2
2
1
1
0
1
1
1
2
1
1
0
0
1
1
1
2
1
2
1
0
1
2
4
1
0
1
2
3
1
0
1
1
1
0
1
2
2
1
2
0
1
2
0
1
1
1
1
2
1
2
1
1
2
1
2
1
2
2
1
1
2
1
1
1
1
0
1
1
0
2
1
1
2
2
1
0
2
1
1
2
1
0
1
2
0
1
2
1
2
2
1
1
2
2
1
1
2
1
1
0
2
1
0
1
1
1
1
1
1
1
1
2
0
1
1
0
1
0
2
0
1
0
2
1
1
2
0
1
2
2
1
2
2
1
2
1
2
1
1
1
2
0
1
2
1
2
1
2
0
2
1
2
1
1
2
1
1
0
0
0
1
2
4
0
1
1
0
1
0
1
1
1
1
2
0
0
1
2
2
1
0
2
2
1
1
1
0
2
2
1
1
2
1
0
1
1
0
2
0
1
0
1
2
1
2
0
3
0
1
1
1
1
1
1
4
0
1
1
1
0
0
1
1
2
0
1
4
2
1
1
1
1
1
1
0
0
2
1
1
1
1
1
2
0
0
1
0
2
2
2
2
1
0
2
1
1
2
0
1
1
1
0
0
1
1
0
1
1
2
0
1
0
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
2
0
1
1
2
1
1
1
0
1
1
1
1
2
1
1
2
0
0
1
1
0
0
0
1
1
1
0
2
0
1
0
2
1
0
0
2
1
1
1
2
0
2
0
1
2
1
1
1
2
0
1
1
0
2
2
0
0
1
1
2
2
2
2
1
1
2
1
2
1
1
0
1
0
2
1
0
0
0
1
2
1
2
1
0
0
0
0
2
0
1
1
1
2
1
1
1
0
1
1
0
0
1
1
1
1
2
1
2
1
0
1
2
1
0
1
1
1
2
2
2
2
1
0
1
1
1
2
1
0
0
0
2
1
0
2
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
0
2
1
1
0
1
0
0
2
1
1
0
0
1
1
1
1
1
0
1
1
1
2
2
0
2
0
1
2
2
1
0
1
2
1
2
1
1
1
2
0
0
1
2
2
2
0
0
2
0
0
1
1
1
1
1
1
1
1
1
0
1
1
1
1
0
2
2
0
1
0
1
1
1
0
1
0
0
2
1
2
1
1
1
4
1
1
1
2
5
0
1
1
1
0
2
1
0
2
1
2
0
2
2
0
2
0
2
2
2
2
2
1
1
0
1
2
2
2
2
1
1
0
0
0
1
1
0
1
1
1
1
1
0
1
0
2
0
2
1
0
2
1
2
2
1
0
2
1
3
0
1
1
2
0
2
1
1
2
0
1
0
0
1
1
0
2
1
1
1
1
0
1
2
1
1
1
1
1
1
1
1
0
1
0
2
2
0
1
0
2
1
1
1
2
1
1
1
0
0
0
0
1
2
1
0
1
0
1
0
1
0
1
1
2
0
1
1
1
1
1
1
2
1
1
0
1
0
1
1
2
0
1
2
2
1
1
2
1
0
1
2
0
1
2
1
1
0
1
0
1
1
2
1
2
1
1
1
2
0
1
1
1
1
1
1
0
1
0
2
1
2
1
0
0
2
0
1
0
1
1
1
1
1
1
0
2
1
0
1
0
2
1
1
0
3
1
1
1
2
0
1
0
1
1
1
1
1
0
1
1
1
1
1
1
1
1
0
2
1
1
2
2
1
0
2
1
0
2
0
2
0
0
1
1
1
2
0
0
0
0
2
0
1
2
0
1
0
0
1
1
1
2
1
2
0
1
2
1
1
0
2
1
1
1
0
1
0
0
1
0
2
0
2
1
1
0
1
1
0
1
1
1
2
1
2
1
0
2
3
2
2
0
1
1
0
0
0
0
1
2
2
2
1
0
1
1
1
1
1
2
1
0
0
1
1
2
1
2
1
0
1
1
0
2
1
1
1
0
1
1
2
1
2
0
2
2
0
0
1
1
0
0
1
1
0
0
2
2
1
1
0
1
2
1
1
1
1
0
1
1
1
0
2
1
1
0
0
0
0
1
0
1
1
1
0
2
1
1
1
0
1
0
1
0
1
1
0
1
2
1
0
1
1
0
1
1
1
1
2
1
1
1
2
2
0
1
2
0
1
1
0
2
1
1
1
1
0
1
2
1
1
1
1
1
2
0
1
1
2
1
2
1
0
2
0
0
0
2
2
1
1
1
1
1
1
1
1
1
1
1
2
0
2
1
3
2
1
2
1
2
1
1
0
1
1
0
2
2
1
1
1
1
3
1
1
1
1
2
1
0
1
1
0
2
0
1
2
1
2
1
1
2
2
2
1
2
0
1
1
0
1
2
1
2
1
2
1
2
2
1
0
1
0
1
0
1
1
1
2
2
1
1
2
1
1
0
1
2
0
2
1
1
1
1
0
2
0
1
1
1
0
0
1
0
2
2
2
2
0
2
1
2
1
2
0
1
1
0
1
0
2
0
1
3
2
1
0
1
1
1
2
1
1
0
1
1
0
2
2
1
1
1
1
2
2
2
2
1
1
1
1
1
2
1
0
1
1
2
0
2
0
0
1
1
1
0
1
1
1
2
1
1
0
1
2
2
2
2
1
1
1
2
1
1
0
1
1
0
1
1
0
0
0
1
0
1
1
1
1
1
0
1
1
0
1
2
1
0
2
1
2
0
0
2
0
1
0
1
1
1
2
2
0
2
1
0
0
2
1
0
1
2
1
1
1
0
1
0
0
1
1
1
1
1
1
2
2
0
0
1
2
1
2
2
1
0
0
1
1
1
2
1
1
1
1
1
0
1
1
2
1
1
2
0
1
1
1
0
2
1
2
2
2
2
1
2
4
1
0
0
2
2
1
1
2
2
2
2
1
2
0
1
1
1
0
1
2
2
1
1
1
2
2
2
0
2
1
2
1
1
1
2
3
0
1
1
1
0
1
0
1
0
2
2
2
1
2
1
0
2
1
1
0
0
1
0
1
1
1
1
1
1
1
1
1
1
1
2
0
2
1
2
2
1
1
2
0
1
0
1
1
0
1
0
1
0
1
1
1
1
1
7
1
1
1
0
1
1
1
2
1
0
2
1
1
0
1
2
2
1
1
2
0
1
1
2
1
2
2
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
2
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
0
0
0
2
1
1
2
0
0
1
1
0
0
1
2
0
1
1
0
0
2
0
1
2
0
0
2
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
0
2
2
1
1
1
1
1
1
0
1
0
1
1
1
1
1
2
1
2
1
1
1
1
2
0
1
1
1
2
1
0
1
1
2
1
2
1
0
1
1
1
0
1
1
1
1
1
0
1
0
2
1
1
2
0
1
2
1
1
2
2
1
0
1
1
1
1
1
2
1
1
1
2
0
2
2
0
1
0
2
2
1
1
1
1
1
0
2
1
1
1
0
1
1
2
1
0
1
0
1
1
1
1
1
0
1
0
1
1
1
0
1
1
2
1
1
1
1
1
1
1
3
2
1
0
2
1
1
1
1
2
2
2
1
0
1
1
1
1
0
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
2
1
2
2
1
1
1
1
0
1
1
0
1
0
0
2
1
2
2
1
0
0
0
1
1
0
1
2
0
1
2
0
1
2
1
1
2
1
1
0
1
1
0
1
0
1
1
1
2
1
1
1
0
0
1
1
1
0
1
2
1
0
0
0
1
1
1
0
2
1
2
0
2
0
1
0
1
1
1
2
0
1
1
1
0
0
0
0
1
1
2
1
2
1
1
1
1
1
0
0
2
1
0
0
1
1
2
1
1
1
1
1
2
1
0
0
2
1
1
1
0
1
1
2
2
1
1
1
2
1
1
2
0
0
2
1
0
1
1
2
1
0
1
1
1
0
1
1
1
2
2
1
0
0
0
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
0
1
1
1
2
1
0
1
1
1
0
1
1
2
2
1
1
0
2
2
1
2
0
1
1
0
1
0
1
1
1
2
1
0
2
1
0
1
2
0
1
1
0
0
1
1
1
1
1
1
2
1
1
0
1
2
1
2
1
0
1
2
0
0
0
0
2
2
2
2
1
0
2
2
1
2
2
1
1
1
1
1
1
1
1
1
0
0
0
1
2
1
0
1
0
1
1
1
1
2
1
0
1
1
0
1
1
1
1
2
1
1
2
2
1
0
2
2
1
4
1
0
0
1
0
1
0
1
1
1
1
1
1
0
1
1
1
1
2
1
1
1
1
2
1
2
0
1
1
1
2
0
2
1
0
1
0
0
1
1
0
1
1
1
0
1
1
2
0
0
1
1
0
0
0
0
2
1
0
0
1
2
2
0
1
1
3
0
1
2
2
1
1
1
1
1
1
0
2
1
1
2
2
2
2
1
1
1
1
0
1
1
0
2
0
1
2
2
1
1
1
1
1
2
2
1
1
2
1
0
2
1
1
2
1
1
0
1
1
1
1
1
2
1
1
1
1
0
0
1
0
0
1
1
2
2
1
0
1
2
1
1
0
2
1
1
1
1
1
2
0
1
1
1
2
2
2
0
2
1
2
1
0
1
1
1
0
0
1
0
2
2
1
0
0
1
2
3
2
2
0
1
1
1
1
0
1
1
0
1
0
1
0
1
2
1
1
0
1
1
1
1
2
1
1
0
1
1
2
1
1
1
2
2
0
1
1
0
1
1
1
2
0
0
0
1
1
2
1
0
1
0
1
2
0
1
2
1
2
1
1
0
1
0
1
0
1
2
0
2
1
1
1
1
1
1
0
1
2
1
2
1
1
0
1
2
2
1
2
2
2
0
0
1
1
1
1
1
0
1
0
1
2
1
2
0
2
1
0
0
1
0
0
1
1
0
1
0
1
1
1
0
1
2
0
1
2
1
1
2
1
2
2
2
1
1
2
1
1
2
1
2
1
1
1
0
2
1
0
1
1
1
1
1
1
1
2
1
1
0
2
1
2
0
1
1
1
3
1
2
0
1
1
1
2
0
2
2
1
1
1
2
1
1
2
1
1
2
1
0
1
1
0
1
2
1
0
1
0
1
1
2
1
0
1
2
2
1
1
0
2
2
1
1
1
1
1
1
1
1
1
0
1
0
2
1
1
1
2
0
1
0
0
2
0
2
1
1
2
1
1
2
0
1
0
2
1
1
1
2
0
2
0
1
2
1
0
1
2
1
2
1
0
2
2
0
2
2
1
2
1
3
1
0
0
0
1
2
3
1
0
2
1
1
1
1
1
2
1
1
1
1
2
1
0
0
0
1
1
2
0
1
1
2
1
0
2
0
1
0
2
1
2
1
1
1
0
3
1
1
2
1
1
1
1
1
0
1
1
1
2
1
2
0
0
1
1
0
2
1
0
1
2
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
0
0
1
1
0
1
0
1
1
1
0
1
1
3
1
2
2
1
1
2
1
1
1
0
1
2
1
1
0
2
0
1
0
2
3
1
1
1
1
1
1
1
1
4
2
1
1
2
2
1
1
0
1
1
1
1
2
1
2
2
1
0
0
1
1
1
1
0
1
1
1
1
1
0
3
3
1
1
1
1
1
2
4
1
2
2
1
1
2
1
2
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
2
1
1
1
2
0
1
1
2
2
0
3
1
1
2
0
2
1
2
0
0
0
1
1
1
2
1
1
1
1
2
1
1
1
0
1
1
2
2
1
0
1
0
1
0
1
2
1
1
1
0
1
1
1
1
0
1
1
0
1
0
0
0
2
2
1
1
0
2
1
1
1
2
2
1
1
0
0
1
1
0
0
0
1
1
1
0
2
1
2
1
1
2
1
1
0
0
1
1
2
1
1
1
1
1
1
0
2
0
4
1
2
1
1
1
1
1
1
1
2
2
0
1
0
2
1
1
0
2
1
1
0
1
1
1
1
2
1
1
1
2
2
1
1
2
0
1
2
0
2
0
2
1
0
1
0
0
0
2
2
2
0
2
2
0
1
1
1
1
0
1
2
1
0
1
2
1
1
2
2
0
1
2
1
0
1
2
1
2
0
1
2
1
1
1
1
2
0
0
2
1
1
3
1
0
0
1
2
1
0
0
2
2
1
1
1
0
2
2
1
2
1
1
0
0
0
1
2
0
1
0
0
0
2
1
1
1
1
2
2
1
1
1
2
1
0
0
3
1
0
0
0
1
1
1
2
1
1
2
1
1
1
1
0
1
1
1
1
2
1
0
2
2
1
1
1
1
0
2
1
2
1
1
1
1
1
2
1
1
0
1
2
1
2
2
1
2
1
1
1
2
0
1
0
2
1
0
2
1
2
0
1
2
0
0
2
1
0
2
2
1
0
1
2
2
0
1
1
2
1
1
1
1
1
1
1
2
2
1
2
0
1
1
0
1
1
0
0
0
1
1
0
1
2
0
0
0
1
1
1
0
2
1
2
1
1
0
1
1
1
1
0
2
2
1
0
2
1
1
0
1
2
1
1
1
1
1
1
1
2
1
2
1
2
1
2
2
1
1
1
1
1
0
1
1
1
0
1
1
2
1
1
2
1
1
2
1
0
1
0
1
0
2
1
0
1
2
2
1
1
0
1
1
2
2
1
1
0
1
1
1
0
0
1
1
2
2
1
2
1
1
1
1
1
0
1
0
1
2
0
1
1
1
0
0
0
1
1
1
0
0
2
1
1
1
0
2
1
2
1
1
2
1
1
0
0
2
0
1
1
0
1
2
1
0
1
1
1
1
1
0
2
1
1
0
1
1
2
1
0
2
1
2
0
1
1
1
3
3
1
1
1
2
1
2
2
0
2
1
1
1
2
1
1
0
1
0
1
1
0
1
1
1
1
2
1
2
1
2
1
1
1
1
0
0
1
2
1
2
2
1
0
1
1
1
1
1
1
2
0
0
2
0
1
1
1
1
1
2
1
1
2
1
0
1
1
1
1
1
2
1
1
1
2
2
0
0
2
1
1
0
0
1
1
1
1
1
2
1
1
1
1
1
0
1
1
1
0
1
1
1
1
0
1
1
0
1
2
1
1
1
1
1
1
1
0
0
1
2
2
1
2
0
1
1
2
2
1
2
2
2
1
1
2
1
2
1
1
0
1
1
1
1
2
0
1
1
2
1
1
2
0
1
2
1
0
2
1
2
0
0
0
0
0
1
0
1
1
1
1
1
0
1
0
2
1
2
1
1
1
1
2
1
0
2
2
2
1
0
0
2
2
1
0
1
1
1
0
1
1
1
2
1
2
2
0
0
2
2
1
1
2
1
5
1
1
2
0
1
1
1
1
0
2
0
2
1
0
0
1
1
1
0
1
2
1
0
1
1
2
1
1
1
1
0
1
1
0
1
1
1
2
2
2
2
1
1
1
1
1
1
0
2
2
1
2
0
0
1
0
0
2
1
2
1
0
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
1
0
1
2
2
2
1
1
2
1
0
1
2
1
2
2
2
2
2
1
1
1
1
1
1
1
0
1
1
0
0
2
1
0
1
2
1
2
1
1
1
0
2
2
0
1
1
1
1
1
1
1
1
0
0
1
1
1
2
1
1
1
1
0
1
2
0
1
1
1
0
0
1
1
1
1
2
0
0
2
2
0
2
0
2
2
1
1
2
1
2
1
1
1
1
0
2
1
0
1
2
2
0
1
0
0
1
2
0
1
1
1
1
1
1
2
1
2
0
0
1
1
2
2
2
0
1
2
2
1
0
0
0
0
1
0
0
3
1
1
1
1
2
1
0
0
2
1
1
2
1
1
0
2
1
3
0
1
2
1
2
1
1
1
1
2
1
1
1
1
2
2
1
1
1
1
1
2
0
2
1
1
2
2
1
2
0
0
1
1
0
1
0
1
1
0
1
1
2
1
1
1
2
1
0
1
1
1
0
1
1
0
2
1
2
2
2
2
0
1
2
2
2
1
1
1
1
2
1
2
1
2
0
2
1
1
1
1
1
0
1
2
1
1
1
2
1
2
2
0
1
1
1
1
0
0
1
0
2
0
2
1
1
0
1
0
1
2
1
1
1
2
1
0
1
0
1
1
1
1
1
1
2
1
0
1
2
0
0
1
1
1
1
0
1
1
1
2
2
0
1
1
1
1
2
1
0
1
1
1
1
1
1
2
1
0
0
1
1
2
1
1
1
1
0
1
0
1
0
0
0
0
1
1
1
2
2
0
3
1
1
3
0
1
2
2
1
2
1
2
2
2
1
2
1
1
1
1
0
2
1
1
1
1
0
1
2
1
1
1
1
0
2
1
0
0
1
1
0
1
1
1
2
0
0
1
0
1
1
0
1
1
2
0
0
2
1
1
2
1
1
0
1
1
1
1
1
1
2
2
1
1
1
0
1
1
2
1
0
2
0
1
2
1
0
1
1
1
0
1
2
1
1
1
2
1
1
1
2
0
2
0
1
1
1
0
1
1
1
1
1
1
1
0
1
1
1
0
1
1
1
1
2
1
2
1
1
1
3
0
0
2
2
2
0
1
1
0
1
2
2
1
1
1
0
1
1
1
1
1
0
2
3
1
1
1
1
1
0
0
1
2
1
1
0
1
1
0
0
0
1
1
0
2
1
1
1
1
2
2
1
1
1
0
1
1
1
1
1
0
1
1
1
1
1
2
1
2
1
2
1
1
1
1
2
0
1
0
1
1
0
2
0
1
2
1
1
0
1
0
0
1
2
2
2
2
2
1
1
1
1
1
1
2
1
1
1
1
1
0
0
1
1
1
1
1
1
0
1
2
2
1
0
0
2
1
0
0
1
1
1
1
0
1
0
2
2
0
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
0
1
1
1
0
2
0
1
2
1
1
0
1
1
2
0
2
1
1
0
2
1
2
2
2
1
1
2
2
1
1
2
1
0
1
1
1
2
0
2
1
1
2
0
1
1
1
2
1
2
0
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
2
1
0
1
2
1
1
1
1
1
1
1
2
1
0
1
1
1
0
1
0
2
2
1
1
1
0
1
0
2
1
0
2
2
1
0
1
2
1
2
1
2
1
2
2
1
0
1
2
2
1
1
1
1
1
1
2
1
0
1
1
0
1
0
1
1
1
0
1
0
1
1
1
1
1
0
1
1
1
2
0
0
1
2
2
2
1
1
0
1
1
1
1
2
0
1
1
2
2
1
1
1
1
1
0
2
2
1
0
2
0
1
0
1
2
0
0
1
1
0
2
1
1
2
2
1
1
2
2
1
1
1
2
2
1
2
1
1
2
0
1
0
1
1
0
1
1
1
1
1
2
2
2
1
1
1
1
2
1
0
1
1
0
1
0
0
2
2
1
2
2
1
0
1
1
2
2
0
1
0
0
1
1
1
1
0
1
2
2
0
1
1
0
2
1
1
1
1
0
0
1
2
1
1
1
1
2
1
0
1
1
0
0
2
1
1
2
1
1
2
1
2
0
0
1
1
1
0
1
1
1
1
2
2
1
1
1
2
1
1
2
2
0
2
1
0
1
1
2
0
1
1
2
2
2
1
2
0
2
2
0
1
1
1
1
1
1
1
1
1
2
0
2
1
2
1
1
0
1
1
2
1
2
0
0
1
1
1
1
1
2
2
1
1
2
2
2
1
0
0
2
1
1
1
1
0
0
1
2
1
2
2
1
2
0
1
1
1
1
1
0
1
0
1
1
1
1
2
0
1
0
1
0
1
2
0
2
1
1
1
2
0
0
1
0
0
1
1
2
1
1
1
2
2
1
2
0
0
0
0
1
1
1
1
0
1
0
0
1
0
1
1
1
1
2
1
0
2
1
0
1
2
1
1
2
2
1
5
2
1
1
0
0
0
1
1
0
0
1
1
1
2
2
2
1
2
2
1
1
1
1
0
1
1
2
1
0
0
1
0
2
2
1
1
1
1
0
2
0
1
0
4
1
1
2
1
1
2
1
1
1
0
1
2
1
1
1
1
0
1
2
0
1
2
1
0
2
0
2
1
1
1
1
1
0
1
1
2
2
2
1
1
0
1
1
1
2
0
1
0
1
0
1
1
1
2
1
1
0
1
1
1
1
1
1
1
0
1
1
2
1
1
1
0
0
0
1
1
0
1
0
2
1
2
2
0
1
1
1
2
0
2
1
0
1
1
2
1
0
0
2
2
1
0
2
1
1
1
1
1
1
0
0
0
1
1
0
1
0
1
1
1
1
0
2
0
2
2
2
2
1
0
1
0
1
1
2
0
0
2
1
1
0
1
2
1
1
1
1
1
1
1
1
1
1
0
0
1
1
2
2
2
1
1
1
2
1
1
2
1
1
0
1
1
0
1
0
2
2
1
1
1
2
1
1
0
1
0
2
2
1
1
2
1
1
0
3
2
2
1
0
2
1
1
1
1
0
0
2
0
2
1
2
2
1
1
2
1
1
1
1
0
0
0
2
1
1
1
2
2
2
1
1
1
1
1
0
0
2
1
1
3
0
1
1
2
2
1
1
2
2
1
1
2
2
2
1
1
1
1
1
1
0
0
2
2
2
1
0
3
1
0
1
2
2
2
1
0
0
1
1
1
1
2
1
2
2
2
2
1
0
1
1
1
1
1
1
2
1
0
2
1
1
2
2
1
1
0
1
1
0
1
0
1
2
1
0
1
0
1
1
2
1
1
1
1
1
1
2
3
2
1
1
1
3
2
0
1
0
1
1
1
2
1
1
0
2
2
1
0
1
1
1
0
2
1
1
1
1
1
0
0
1
1
1
2
1
1
1
1
0
1
0
0
1
1
1
1
1
0
1
1
2
1
0
1
1
0
2
0
1
2
2
0
0
2
0
2
1
2
0
2
1
0
3
0
0
2
1
1
0
1
1
2
2
0
1
1
1
3
1
1
0
1
0
1
1
1
1
0
1
0
1
1
1
0
1
1
0
1
1
2
2
2
0
1
1
0
2
1
1
1
1
1
2
1
1
0
1
1
1
1
1
1
1
1
2
1
2
1
1
0
0
1
1
1
2
1
2
1
1
0
1
1
1
2
1
2
1
0
1
0
0
1
1
2
1
2
0
1
1
2
1
1
1
2
0
1
1
1
0
0
1
1
1
1
1
1
1
0
0
3
1
1
1
1
2
1
2
2
1
1
2
1
0
0
2
1
1
1
0
2
1
1
2
2
2
0
0
2
1
1
0
1
1
2
1
0
0
0
0
0
0
3
1
1
0
1
0
1
1
1
2
1
1
1
2
0
1
1
2
1
2
1
1
0
2
2
1
0
0
1
0
0
1
1
0
1
1
1
2
1
0
2
1
2
1
1
1
1
0
1
1
1
1
0
1
0
1
1
1
1
1
0
0
2
1
1
1
0
1
1
2
1
1
0
1
2
1
1
0
1
1
0
2
0
1
2
1
1
0
0
1
2
1
1
1
1
1
2
1
0
1
1
2
3
2
1
1
1
1
2
1
1
1
2
0
2
2
1
0
1
0
0
1
1
3
1
1
2
0
0
1
1
1
1
0
2
0
1
1
2
1
2
2
1
1
2
1
2
1
1
2
1
1
1
2
1
1
0
1
1
0
1
2
2
0
0
2
2
1
1
1
1
1
2
1
1
1
1
1
1
2
0
1
2
1
0
2
0
0
1
2
1
1
1
1
0
0
1
2
2
1
2
1
0
2
2
2
1
0
1
1
2
1
1
1
1
1
1
2
1
0
1
1
1
1
1
2
0
2
2
1
0
2
1
1
1
1
0
2
1
1
1
1
0
2
0
1
1
0
1
1
0
1
1
1
1
0
2
0
1
2
1
1
1
1
1
1
1
0
1
2
1
1
1
2
1
0
2
1
1
2
2
1
1
1
1
0
1
2
0
1
1
1
1
0
1
2
0
0
0
1
1
0
1
1
1
0
2
1
1
2
1
1
0
0
0
2
2
2
0
0
1
0
1
0
1
1
1
1
1
1
1
1
2
1
2
1
1
0
1
0
1
0
0
1
1
1
0
0
2
2
2
0
2
1
2
1
2
2
3
1
1
0
0
1
1
1
2
1
2
1
2
2
1
2
1
2
0
1
0
0
1
1
1
1
0
1
1
1
1
1
1
0
1
1
1
2
2
1
1
2
2
1
1
1
2
0
1
1
2
1
1
0
1
1
1
2
1
1
1
1
2
2
1
0
1
2
0
1
1
1
1
2
1
1
2
1
1
0
1
1
1
2
0
0
1
0
2
1
0
2
0
2
2
1
2
1
1
2
1
1
1
2
1
1
1
1
1
0
1
0
1
1
1
1
1
1
2
0
0
1
1
0
1
1
1
1
0
1
1
2
2
1
2
1
1
0
0
1
0
1
3
2
1
2
1
2
0
1
2
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
0
1
0
1
1
1
1
2
0
0
0
3
1
1
2
2
1
2
2
0
0
1
1
1
1
1
2
1
1
0
0
1
1
1
1
2
1
1
0
1
2
2
1
0
2
1
0
2
1
1
2
1
1
1
2
0
1
1
2
2
1
0
1
1
1
2
1
2
1
1
1
1
2
0
2
1
0
2
1
1
1
2
0
1
1
0
1
1
1
1
2
0
1
1
1
1
1
2
2
2
0
2
1
1
1
1
1
1
0
0
1
0
1
1
1
2
3
1
0
1
1
0
1
1
2
1
1
1
0
0
0
1
2
1
1
1
1
0
1
1
1
1
1
1
2
2
1
1
0
1
2
2
0
2
1
1
0
2
1
1
1
1
1
0
4
1
1
0
1
0
2
0
1
1
1
1
1
1
2
5
1
1
0
1
1
1
1
1
0
1
1
1
1
1
2
1
1
2
2
2
0
0
1
0
2
1
0
1
1
2
2
0
2
1
1
0
1
1
2
1
1
0
1
1
1
0
1
0
1
1
2
2
1
1
0
1
1
1
1
1
2
2
2
1
2
2
1
0
1
1
1
1
2
2
2
2
1
1
0
2
1
1
0
0
1
2
2
2
1
1
2
1
0
1
1
1
1
1
1
1
1
0
2
2
1
1
1
1
1
2
1
2
1
1
0
1
1
2
1
1
2
1
1
2
1
0
3
2
1
1
1
1
1
1
0
1
1
1
0
2
1
0
1
0
2
1
0
0
0
0
0
1
0
1
0
1
1
2
1
1
2
1
1
2
1
1
1
0
2
1
0
2
2
1
0
1
0
1
1
2
0
1
1
1
1
1
2
1
1
1
1
1
2
1
2
0
1
0
0
1
0
1
0
1
1
2
0
1
1
0
0
2
1
0
1
0
1
2
0
1
1
2
2
0
1
2
0
1
1
0
0
1
1
1
0
1
1
0
1
2
0
1
2
0
1
1
2
2
1
1
1
2
2
0
2
1
1
0
2
0
1
0
1
0
1
1
0
0
1
1
1
0
2
1
1
1
0
0
1
2
0
1
1
2
3
1
1
0
1
4
1
2
0
2
1
1
1
0
1
1
1
2
1
1
2
1
0
2
0
1
1
1
1
0
1
2
1
1
2
1
1
2
1
1
0
1
1
2
0
1
1
1
1
0
0
1
1
1
1
1
1
0
2
0
2
1
0
0
0
1
2
1
0
2
2
1
2
1
2
1
0
1
0
1
1
2
2
0
0
1
1
0
1
1
2
2
1
1
2
2
2
0
1
0
1
1
0
1
2
1
1
1
1
1
1
1
2
1
2
1
2
2
1
2
0
2
1
1
0
0
1
1
2
2
0
0
1
1
2
1
1
1
0
1
0
0
1
1
1
2
1
1
2
2
1
2
1
1
1
1
1
2
0
0
0
1
2
0
0
0
0
1
3
0
0
1
1
1
1
2
1
0
1
0
1
1
0
1
1
1
1
1
1
0
2
0
2
1
0
1
0
2
1
1
1
1
0
1
2
1
1
1
1
1
0
1
1
2
1
2
0
1
1
1
1
4
2
1
0
1
2
1
1
1
0
1
0
2
1
0
1
1
1
2
2
0
1
0
1
1
0
0
1
0
1
1
1
1
1
0
1
1
1
1
1
1
1
1
2
1
1
1
0
0
1
0
1
0
2
1
1
0
1
0
0
1
1
0
1
1
1
2
1
1
0
1
1
2
0
2
2
1
1
1
1
1
2
1
2
1
1
1
1
2
2
0
2
1
1
2
0
1
1
1
1
0
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
2
2
0
0
1
1
2
1
1
2
1
1
2
2
0
1
0
1
2
0
2
0
1
1
0
0
2
1
0
1
1
0
0
2
0
1
1
2
1
1
0
1
0
2
0
2
1
1
2
1
1
1
1
1
2
1
2
1
2
2
2
0
12
1
2
1
2
0
1
0
2
1
1
1
1
1
1
1
2
0
1
1
1
2
1
2
2
1
0
0
2
0
1
2
0
1
1
0
2
1
1
1
2
0
1
1
2
0
0
2
1
0
1
1
1
1
3
1
1
2
1
1
1
1
2
2
1
1
1
2
1
1
1
0
1
1
1
0
1
0
1
1
0
1
1
0
3
1
1
1
1
1
2
1
2
1
0
0
1
1
1
1
2
1
1
2
1
1
1
1
0
0
2
0
1
1
0
1
1
0
0
1
1
1
1
0
1
1
1
1
2
1
2
1
1
0
2
1
1
0
0
1
1
1
1
2
2
1
1
2
0
0
1
1
0
1
0
1
0
1
1
2
1
2
0
1
1
2
0
1
0
1
0
1
0
1
1
0
1
1
1
1
1
1
0
1
2
0
1
2
1
2
2
1
2
1
1
1
1
2
2
1
1
2
1
1
1
2
2
0
1
1
2
1
1
1
0
2
1
2
1
1
1
2
2
2
0
1
1
0
2
1
1
1
1
1
2
2
1
1
1
1
1
0
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
3
1
1
1
0
0
1
0
1
1
0
2
1
1
1
2
0
0
0
1
0
0
0
0
1
1
1
1
1
2
1
2
2
0
1
2
0
0
2
2
1
1
1
1
2
1
1
1
0
1
1
1
1
2
2
1
0
0
0
2
2
1
1
1
0
0
2
3
1
0
1
0
0
2
0
0
1
2
2
2
2
1
1
1
1
1
0
2
1
1
1
1
1
1
2
2
1
2
2
2
1
0
1
1
2
1
0
2
1
0
1
2
0
0
2
2
1
1
1
1
1
1
1
1
0
2
1
2
0
0
1
2
1
0
1
1
1
1
0
0
1
1
0
0
2
0
1
1
0
2
1
1
1
2
1
2
1
1
1
1
2
1
0
1
0
1
2
2
2
0
0
1
0
1
0
1
1
0
0
1
1
0
1
1
2
1
1
1
2
0
1
1
2
2
2
1
1
1
1
1
1
0
1
1
1
1
1
1
0
0
1
2
1
0
1
0
1
1
0
2
1
1
1
0
1
1
1
1
0
1
1
0
1
0
1
2
1
0
2
1
1
0
1
0
1
1
1
1
3
1
1
1
1
1
0
1
0
1
2
2
1
1
2
1
1
1
0
2
2
1
2
1
1
1
1
1
0
1
3
1
2
1
0
2
0
1
2
1
1
1
1
0
1
1
1
2
1
2
1
0
1
0
2
1
0
1
2
1
1
2
1
2
0
1
1
1
1
1
2
2
2
2
0
3
1
1
0
1
1
0
1
1
0
1
1
1
1
1
2
0
1
1
2
0
2
1
1
1
1
2
0
1
1
2
1
0
1
1
2
2
0
2
1
1
2
2
0
1
1
2
2
1
1
1
1
0
0
1
1
0
0
1
2
1
2
1
0
1
1
1
0
4
1
1
2
2
0
0
1
0
1
0
1
1
2
1
1
1
2
1
1
1
2
1
2
2
1
1
1
0
1
1
1
0
1
0
1
0
0
0
2
1
2
1
1
2
2
1
1
0
1
1
1
2
1
1
1
1
0
1
0
0
1
0
1
0
1
2
1
2
1
1
1
1
0
2
1
2
1
1
1
1
1
1
0
2
2
1
0
0
2
0
1
1
1
0
0
2
2
2
2
1
1
2
1
1
2
0
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
0
1
1
2
1
2
1
1
1
0
1
1
2
1
2
1
0
1
1
0
1
1
1
1
1
1
2
1
1
0
1
1
1
2
0
2
1
1
1
2
1
1
2
2
1
1
1
0
0
0
0
0
1
0
1
0
1
1
2
0
1
0
0
0
1
1
1
2
0
0
1
1
1
2
0
1
1
1
1
1
0
2
2
0
0
2
1
1
1
2
1
2
1
1
1
1
1
2
1
0
1
2
1
1
2
1
1
1
2
2
1
2
1
0
1
0
1
0
2
2
1
1
1
1
2
0
1
1
0
1
1
1
1
1
1
2
1
0
1
1
1
1
1
1
1
0
2
1
1
1
2
1
1
1
2
0
1
1
2
0
1
0
1
2
2
0
1
1
1
2
0
1
0
1
1
2
0
2
1
2
1
1
1
0
1
0
1
1
0
2
1
1
1
0
1
1
2
1
1
2
1
1
1
1
2
1
0
1
1
2
2
1
1
2
0
1
1
1
0
1
0
1
2
0
0
1
1
1
1
1
2
2
0
1
1
0
1
0
1
2
2
2
2
0
2
1
0
0
1
1
1
1
2
2
1
0
1
0
0
1
1
1
0
3
1
1
1
1
1
0
1
1
1
0
2
0
2
0
1
0
0
1
0
1
1
0
2
3
1
2
1
1
2
1
2
1
1
0
0
0
0
1
1
1
1
2
2
1
1
2
1
0
1
1
0
2
1
2
1
1
1
0
1
2
1
1
1
1
1
0
1
2
1
1
0
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
0
1
1
2
1
5
1
1
0
1
2
1
1
1
1
3
1
1
1
1
1
1
1
1
0
1
1
1
1
2
2
0
1
1
2
1
1
3
0
1
2
1
2
1
1
1
1
1
1
0
0
1
2
1
0
1
2
1
1
1
0
1
1
1
2
1
1
1
1
0
1
1
2
0
1
2
1
1
1
1
1
2
1
1
2
1
1
0
1
1
1
1
1
1
2
1
1
1
1
0
1
1
0
1
1
1
1
1
1
0
1
0
1
2
1
0
1
1
0
2
1
1
1
1
0
2
2
0
1
2
1
1
0
0
1
0
0
1
1
2
0
1
1
0
1
2
0
1
1
2
0
0
1
1
1
1
2
1
1
1
1
0
2
1
0
1
1
1
1
1
1
2
1
2
2
1
1
2
2
2
1
0
2
1
2
1
0
1
2
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
2
3
1
1
0
1
1
0
1
3
1
0
3
1
2
1
1
0
1
2
1
2
1
2
2
1
0
0
1
1
1
0
1
0
2
0
1
0
1
3
0
0
0
2
0
0
2
1
1
0
1
2
2
0
1
0
0
2
2
0
1
2
1
1
1
1
0
0
1
1
0
1
1
0
1
1
1
2
2
1
2
1
1
0
1
2
1
1
2
0
1
2
1
2
2
1
1
1
0
1
0
1
0
1
2
0
2
1
1
1
1
1
0
1
1
1
0
1
0
1
3
0
1
1
1
1
2
1
0
0
2
1
1
2
0
2
1
2
1
0
1
2
2
1
1
1
1
1
0
2
0
2
0
1
0
1
1
2
1
1
1
1
1
0
1
1
0
2
2
1
1
1
1
1
0
2
2
1
1
1
1
2
1
1
2
1
1
0
1
1
1
1
1
2
1
1
0
1
1
1
1
1
0
1
2
0
1
0
2
2
2
2
1
1
1
0
1
1
0
1
0
1
2
0
2
2
1
0
0
1
0
1
1
2
1
0
1
0
2
2
1
1
1
0
0
1
1
0
1
2
1
1
0
1
1
1
1
1
1
1
1
0
1
2
1
2
1
1
1
0
2
1
0
0
1
1
0
1
1
1
1
1
1
1
1
1
0
2
1
0
2
1
1
2
0
1
1
1
1
2
2
1
1
1
1
0
2
1
1
0
3
0
1
1
0
2
2
1
2
2
2
1
2
1
1
2
2
2
0
2
1
2
1
0
2
1
1
1
1
0
1
1
2
1
1
1
2
1
0
1
1
2
0
1
1
2
1
1
2
1
1
1
1
3
2
1
2
0
1
1
1
2
1
1
2
1
2
0
0
0
1
2
1
2
0
1
0
1
1
1
0
1
0
1
1
0
1
0
2
2
1
0
1
0
2
1
1
1
2
1
1
2
1
1
1
2
3
2
2
1
2
1
1
1
1
1
0
1
2
1
2
1
1
1
1
1
1
0
0
2
1
1
1
0
1
1
0
1
1
0
1
1
0
2
1
0
1
1
1
1
1
1
2
0
0
1
2
1
1
0
2
1
1
2
2
0
0
1
1
2
2
0
1
1
0
1
1
0
1
1
2
1
2
2
1
2
2
1
3
3
2
1
1
2
2
1
1
1
0
1
2
1
2
1
1
1
0
0
1
2
0
0
0
0
0
1
1
1
1
1
0
1
1
0
2
0
0
1
1
2
0
1
1
1
1
1
0
1
1
1
0
2
0
2
2
1
2
1
1
1
1
0
0
1
0
2
3
0
0
1
0
1
1
0
0
2
0
0
1
2
2
0
1
1
1
1
1
2
1
2
0
2
1
0
2
1
1
1
1
0
2
2
0
0
1
1
0
2
1
1
1
1
1
1
1
2
1
0
2
1
2
0
0
2
1
1
1
1
1
1
0
0
1
1
1
0
0
1
1
1
1
1
0
0
0
1
2
2
1
1
0
1
1
2
1
1
2
0
1
1
1
2
1
3
1
1
1
1
1
0
1
1
1
2
1
1
1
1
0
2
1
0
1
1
1
2
1
0
1
2
1
1
1
2
1
2
0
1
0
1
1
1
3
1
1
2
1
1
0
1
1
1
2
1
1
1
0
2
2
2
2
1
1
1
0
1
1
0
0
2
2
1
1
0
2
0
1
0
2
2
1
1
2
1
1
3
1
1
1
1
2
0
0
1
1
1
1
1
1
1
2
2
1
1
2
2
1
2
2
0
0
1
1
1
0
2
1
1
2
1
1
2
1
1
2
1
1
1
1
0
2
1
0
0
1
0
1
2
0
2
2
0
2
2
1
2
2
1
0
2
0
0
0
2
0
2
1
1
1
0
2
1
2
1
0
1
1
2
1
2
0
2
0
1
2
2
0
1
2
1
1
0
0
0
1
1
1
2
1
1
2
1
2
0
1
1
2
1
1
1
2
2
1
1
1
1
1
0
1
0
0
1
0
1
1
0
1
2
1
2
1
2
0
0
1
0
1
2
1
2
1
0
1
0
1
1
1
0
1
1
2
1
1
0
1
0
1
2
0
1
0
2
1
1
0
1
2
0
1
1
1
0
0
1
1
0
2
1
1
1
1
0
1
0
2
1
2
1
1
0
1
1
1
1
2
1
1
1
0
2
0
3
1
2
2
0
2
1
2
2
0
1
1
0
1
0
2
2
1
1
1
0
1
1
1
2
1
1
1
1
0
1
0
1
1
1
1
1
1
1
0
1
1
0
1
0
1
0
2
0
0
1
0
1
1
2
1
2
1
1
2
2
1
2
1
0
0
1
0
1
1
1
2
1
3
0
1
1
0
2
2
3
1
1
2
0
1
1
1
0
2
2
1
0
2
1
1
1
1
1
1
2
1
1
0
1
1
1
0
1
2
0
2
1
2
1
0
2
0
1
1
1
1
1
0
1
0
1
1
2
1
0
1
1
1
0
1
0
2
1
1
2
1
0
2
2
2
1
1
1
1
0
1
0
2
0
2
2
1
2
0
1
0
1
2
1
1
1
0
1
0
1
0
1
1
1
1
2
1
0
1
0
1
2
1
1
1
1
1
1
2
2
1
2
0
1
1
0
0
1
1
0
1
1
1
2
1
2
1
2
4
1
1
1
2
0
1
1
1
1
1
1
0
0
1
0
2
1
1
3
0
0
1
1
1
0
1
1
1
2
1
2
1
1
1
2
1
2
1
2
2
1
1
1
0
1
1
1
1
0
0
1
1
2
1
2
0
2
1
1
2
0
1
1
2
1
1
2
0
1
1
0
0
1
1
1
1
2
0
1
2
1
1
0
1
2
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
0
1
1
0
1
2
2
1
1
2
1
2
1
0
1
2
2
1
1
1
2
4
1
1
1
2
0
1
1
0
0
1
1
2
1
1
1
0
0
0
2
1
1
0
0
1
0
2
1
0
2
0
1
0
1
0
1
1
1
1
1
1
1
2
1
2
0
1
2
0
1
2
1
2
2
1
0
0
1
1
2
1
1
1
0
1
1
1
2
0
2
0
0
2
1
1
0
1
0
1
0
2
1
1
2
2
3
1
0
0
1
1
1
1
1
2
1
1
2
1
1
3
1
2
2
2
2
1
1
2
1
1
1
1
0
1
1
1
0
1
1
1
1
2
3
0
1
0
2
1
1
1
0
2
2
2
1
0
1
1
1
1
2
2
1
2
0
2
1
2
1
3
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
2
1
1
0
1
1
2
0
2
2
1
1
1
1
3
1
0
0
0
2
0
1
1
2
2
0
2
1
1
1
0
1
1
1
0
0
1
0
1
2
1
0
1
1
0
0
1
1
2
1
2
1
0
1
1
0
1
2
1
1
2
1
0
2
3
1
1
1
1
0
0
2
1
1
1
1
1
1
0
1
1
2
2
1
2
1
1
1
0
2
1
1
1
0
1
3
4
0
1
0
1
1
2
1
1
2
0
2
1
1
0
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
2
0
2
2
1
1
1
1
0
2
1
2
0
2
1
2
1
0
0
0
0
1
1
1
1
1
1
2
0
0
1
1
1
2
1
1
1
1
1
1
1
0
2
1
1
2
1
2
2
1
2
1
1
1
1
2
1
1
0
1
1
2
1
2
1
1
0
1
2
1
1
1
2
0
1
0
2
1
1
1
2
1
0
2
1
2
1
2
1
1
1
2
1
1
1
1
2
1
1
1
1
1
0
1
0
0
1
1
1
1
1
1
0
1
2
1
1
0
0
1
0
0
1
1
2
2
1
2
2
2
1
1
1
1
1
3
1
0
1
1
2
1
2
1
1
1
2
2
1
1
2
1
1
1
1
1
1
0
1
0
1
2
1
2
2
1
1
2
2
1
1
1
0
0
3
2
1
1
0
1
1
1
1
0
2
1
1
1
2
1
2
1
1
1
1
0
1
2
1
2
1
2
1
2
0
2
1
0
2
1
1
1
1
0
2
1
1
2
2
1
1
2
2
2
1
1
0
1
0
2
2
2
1
1
1
2
1
1
1
1
0
0
1
2
2
1
2
1
0
1
2
1
3
0
0
3
2
1
2
1
1
1
1
3
2
1
1
1
1
1
1
1
1
1
0
2
1
2
1
0
2
1
1
2
1
1
1
1
2
0
0
0
0
0
2
2
1
0
0
1
0
2
1
2
0
0
2
2
1
2
1
1
1
2
1
1
1
1
1
1
1
1
0
1
0
2
1
2
1
1
1
1
0
0
1
2
1
1
2
2
0
2
0
1
1
2
1
1
1
1
2
2
2
1
2
1
1
0
1
0
1
2
0
1
0
1
2
0
2
1
2
1
1
1
2
1
1
0
2
1
2
0
0
2
1
0
1
1
1
2
1
1
2
1
1
1
0
0
0
1
1
1
0
1
2
1
0
1
1
3
1
0
0
1
1
2
1
1
1
2
2
0
2
2
0
0
1
2
1
0
1
1
2
2
2
1
1
1
0
1
1
2
2
2
2
2
1
0
2
1
2
2
2
3
0
0
1
0
1
1
2
2
2
0
1
1
0
0
1
1
1
1
1
4
1
0
1
0
1
1
1
2
0
1
1
2
2
2
2
0
1
1
1
1
1
1
2
1
2
1
0
2
2
2
1
1
1
2
2
0
1
0
1
0
2
1
0
0
1
1
1
1
1
1
1
0
0
1
0
1
2
1
1
2
1
0
2
2
1
1
1
1
2
1
0
0
1
0
1
1
0
2
1
1
1
1
2
1
0
1
0
0
0
1
1
0
0
2
1
0
0
1
1
1
1
1
2
1
1
2
1
0
2
1
2
1
1
1
0
2
1
1
1
1
1
0
2
0
0
1
1
1
1
1
0
1
1
2
0
1
1
2
1
1
2
1
1
1
1
1
0
3
1
1
1
1
1
1
1
1
1
0
1
1
2
0
1
1
1
0
1
1
0
1
0
1
3
1
2
0
2
0
2
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
0
1
2
1
0
1
1
2
1
2
1
2
0
2
1
1
2
0
0
0
0
2
1
1
2
1
1
1
1
1
2
2
3
1
0
1
1
2
1
2
2
2
0
1
2
1
2
2
1
1
1
0
1
0
1
1
0
2
1
0
1
1
0
0
2
0
0
2
1
1
2
0
2
1
1
1
0
1
1
1
2
0
1
2
0
1
2
2
2
0
1
0
1
1
0
2
0
1
1
2
1
0
1
1
1
1
0
1
1
2
1
0
1
1
1
1
1
1
0
1
1
1
1
0
1
1
2
2
2
1
0
2
1
0
1
2
1
1
1
0
0
1
1
3
1
0
1
0
0
1
1
2
1
3
1
1
0
1
2
1
1
0
0
1
2
1
2
0
2
1
1
2
1
1
2
2
0
2
2
1
1
1
0
1
1
1
1
1
1
1
1
2
1
1
0
1
0
1
1
1
2
1
1
0
1
1
1
1
1
1
2
1
0
2
0
1
0
0
2
1
0
1
1
1
0
1
0
2
1
1
0
0
1
1
1
1
1
0
1
2
2
2
2
1
1
1
1
1
1
0
1
1
0
1
1
1
1
2
1
0
1
1
1
0
2
0
2
1
1
1
1
2
1
1
2
2
2
1
1
0
1
1
2
0
0
1
1
2
0
1
0
1
1
2
2
2
2
2
1
2
2
2
2
1
1
2
0
1
1
1
1
0
1
1
0
1
1
1
2
0
1
1
1
2
3
1
2
2
1
1
1
1
0
1
2
1
0
0
1
0
1
2
1
1
0
0
0
0
1
2
1
1
0
1
0
1
2
0
1
2
0
0
2
1
1
0
0
1
1
1
1
1
0
1
2
2
2
0
1
1
1
1
0
1
1
2
2
2
2
2
1
1
2
0
2
1
1
0
1
1
1
1
1
1
2
1
2
0
0
1
0
1
1
1
1
1
2
0
1
2
1
2
1
2
0
1
0
1
1
1
0
2
1
2
1
2
1
1
1
1
0
2
0
2
2
2
2
1
0
1
1
0
0
1
2
0
1
2
1
1
1
1
2
1
0
3
0
2
1
1
1
0
1
1
1
2
0
0
0
1
1
0
0
2
1
1
2
1
1
0
0
2
1
1
1
2
1
1
1
0
0
2
1
1
1
1
1
2
1
1
2
1
1
1
2
1
1
1
2
2
1
1
1
1
1
2
0
2
1
2
1
1
1
2
1
1
0
2
1
2
1
0
2
1
1
0
1
1
1
2
2
1
0
1
1
1
0
2
1
2
2
2
1
1
1
2
2
1
1
1
3
2
1
1
1
2
2
1
1
1
1
0
1
2
1
2
2
1
1
1
2
1
1
1
1
1
0
1
1
2
1
1
0
2
0
1
0
1
0
1
1
1
0
1
1
1
1
0
1
2
1
1
1
1
0
2
0
1
2
0
0
1
0
2
1
1
1
1
0
0
1
1
2
0
1
0
2
2
0
0
1
1
2
1
1
2
1
1
1
2
0
1
1
2
1
2
1
2
2
0
0
1
1
1
1
1
1
0
1
1
1
1
2
1
0
1
0
1
3
1
2
1
0
0
0
1
0
1
1
1
1
0
0
1
1
2
1
1
2
0
1
1
2
1
0
0
1
1
1
2
0
1
1
2
1
0
2
3
1
1
1
1
1
1
0
0
0
1
1
1
0
0
1
2
1
1
2
2
2
1
1
1
1
2
1
1
1
2
1
2
0
1
1
2
1
1
1
1
0
1
1
1
1
2
1
0
0
2
0
2
2
2
1
1
0
2
1
2
2
0
1
1
2
2
1
0
2
1
0
1
1
1
0
0
0
1
0
1
0
1
1
2
1
1
1
1
1
2
0
1
1
1
1
0
2
0
1
1
1
2
1
1
0
1
0
2
1
0
0
1
0
2
1
0
1
0
1
1
1
1
1
1
2
0
2
1
1
1
0
1
1
2
2
1
2
2
1
0
0
1
1
2
2
1
1
1
1
1
1
1
1
1
1
2
0
1
3
0
2
1
2
1
0
1
3
1
2
2
1
0
2
2
1
1
1
1
2
2
0
1
1
1
2
1
1
0
2
1
2
1
1
0
1
1
1
0
1
1
1
3
2
1
2
1
1
1
1
1
0
1
1
1
2
1
1
2
1
1
1
1
1
0
2
1
1
2
1
0
2
1
1
2
2
1
0
1
1
1
1
1
0
0
1
2
0
1
1
2
2
1
2
2
1
1
1
2
0
0
0
0
2
1
1
1
0
1
1
1
1
0
1
1
1
1
0
1
1
1
1
2
1
1
1
0
2
1
1
1
1
0
1
1
0
0
2
2
1
1
1
1
2
1
3
2
2
1
1
0
2
3
1
1
1
1
1
2
1
2
1
0
1
2
0
0
0
0
2
0
0
2
0
0
1
0
0
0
2
0
1
1
1
1
0
1
0
1
2
1
0
1
1
1
2
0
2
1
1
0
1
1
1
1
2
0
1
1
0
1
2
2
1
1
0
1
1
1
2
0
1
0
1
2
1
1
1
2
1
1
0
1
1
2
1
1
1
1
1
1
2
0
2
1
1
1
1
0
0
1
2
1
0
2
1
2
1
2
2
1
1
1
2
2
0
1
1
1
1
2
0
1
2
0
1
0
1
2
2
2
1
0
1
1
1
1
2
0
0
1
1
1
0
2
2
2
1
1
2
2
1
1
1
2
2
2
1
1
1
0
1
1
2
2
1
2
1
1
2
2
0
1
0
2
1
0
0
1
0
0
2
1
0
1
2
1
1
2
1
0
1
2
1
2
1
2
1
1
2
1
1
1
1
0
1
0
0
1
2
1
2
2
0
1
0
1
1
1
1
2
1
1
2
0
0
1
2
0
2
0
0
1
1
0
2
2
0
0
2
1
1
1
0
2
1
0
2
2
1
2
2
1
2
2
1
1
2
2
1
2
1
1
0
0
2
1
2
1
2
0
1
2
2
2
0
0
1
0
0
0
1
1
2
0
3
1
1
3
2
2
1
1
2
1
1
1
1
1
1
0
1
1
0
1
0
1
2
1
1
1
2
1
0
2
2
0
2
1
0
2
0
1
1
1
1
0
1
0
1
1
1
1
1
1
0
1
1
3
2
0
1
0
1
0
1
2
1
1
0
1
2
0
1
1
2
1
2
1
2
0
1
1
1
1
1
0
0
1
1
1
1
2
0
1
1
1
2
2
1
0
2
2
1
1
1
1
2
0
0
2
1
1
0
1
2
0
1
0
2
1
2
2
1
1
2
0
1
1
1
1
1
2
0
1
1
0
0
1
1
0
2
1
0
1
1
0
1
0
0
1
1
2
1
2
0
1
1
0
1
1
0
1
0
1
1
2
1
1
0
0
0
2
1
0
2
1
0
1
2
1
1
1
1
1
2
1
0
1
0
1
1
0
2
0
2
1
1
1
2
0
2
2
1
1
1
1
1
1
1
2
2
0
1
1
1
2
2
0
2
1
1
1
1
1
0
2
1
1
2
1
0
1
1
1
1
1
2
0
0
1
0
1
0
1
2
1
1
0
0
1
1
1
0
0
1
1
8
1
0
1
0
1
2
1
2
2
1
0
1
1
0
0
2
1
1
1
0
1
1
2
1
1
1
2
1
1
1
0
1
1
1
1
1
1
0
0
0
1
1
1
0
1
1
1
2
2
1
1
1
1
1
1
0
1
1
1
2
1
1
1
2
1
2
1
1
1
1
0
1
2
1
1
1
2
1
1
0
1
1
2
0
0
1
0
1
1
0
2
1
1
0
0
2
2
2
0
0
1
2
1
1
1
1
1
2
2
1
2
1
0
1
1
0
0
1
0
1
1
0
2
1
2
0
1
1
1
1
1
1
1
2
1
1
1
0
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
0
1
1
2
0
1
1
1
2
1
2
1
1
0
2
1
1
2
2
0
1
1
3
1
2
1
1
0
1
2
1
1
1
1
2
1
1
1
2
0
2
1
1
2
1
2
0
2
0
1
1
2
1
1
2
1
0
1
2
0
0
1
0
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
2
2
0
1
2
0
1
1
2
2
1
1
1
2
2
0
1
2
2
1
2
1
1
1
1
1
1
2
1
0
1
1
1
1
2
1
2
3
1
2
1
1
0
1
0
3
0
1
0
2
0
2
2
1
2
1
3
1
1
2
0
1
1
1
0
1
0
0
0
1
0
1
1
1
1
2
0
1
1
0
2
0
1
1
1
1
2
1
1
0
0
0
1
0
1
1
0
1
0
1
1
0
2
1
1
0
2
1
0
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
2
1
1
1
1
0
1
0
2
1
1
1
0
0
1
1
1
1
2
2
1
1
0
1
1
1
0
1
1
1
1
1
1
1
1
1
0
1
3
0
2
1
1
1
1
2
2
1
1
1
0
1
0
1
2
1
1
0
0
1
1
0
1
2
1
1
1
1
1
1
2
2
0
1
0
1
1
1
1
1
1
2
0
1
2
1
0
2
0
2
0
1
2
1
2
1
1
1
1
1
1
1
1
2
0
1
0
1
1
2
1
2
2
0
1
2
0
2
1
2
1
2
0
1
6
0
2
1
1
1
2
1
1
2
1
1
1
1
0
0
1
1
1
1
1
0
0
0
1
1
1
1
1
1
1
1
2
1
0
0
1
1
1
1
1
1
0
1
1
0
2
2
1
2
0
1
1
1
2
0
3
2
1
2
1
1
1
1
0
1
1
0
1
2
1
1
1
1
2
0
1
0
1
1
0
1
0
1
2
2
3
1
1
1
1
1
0
1
0
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
0
1
0
1
1
0
1
1
1
1
0
2
2
2
1
1
1
1
1
1
2
2
2
1
0
0
1
0
2
1
1
1
1
1
1
2
2
0
1
2
1
2
1
0
2
1
1
2
1
1
2
0
2
1
0
3
1
1
1
1
0
1
1
2
2
2
1
0
1
0
1
1
1
2
1
0
0
1
2
1
2
2
1
2
1
0
1
2
1
2
1
2
1
1
3
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
0
2
2
0
2
1
0
1
1
1
1
1
1
2
1
1
2
1
1
1
3
1
2
1
1
0
0
1
2
1
2
2
0
1
2
2
1
1
0
0
1
1
1
0
1
0
2
2
1
1
1
0
0
1
2
2
0
1
1
0
1
2
2
0
2
0
1
2
1
1
0
2
2
0
1
0
2
2
1
1
0
1
1
0
1
1
2
1
2
1
2
0
2
1
1
1
1
2
2
0
1
1
1
1
1
1
1
0
1
1
0
1
1
1
1
0
2
1
1
2
2
1
0
0
0
2
1
1
0
2
1
2
1
1
0
1
1
1
0
1
1
2
2
2
1
2
0
0
0
1
0
1
1
1
1
1
2
2
0
1
1
0
2
0
1
0
0
1
2
0
2
2
0
0
1
1
0
0
1
0
1
1
1
1
3
1
1
1
2
1
1
1
1
1
0
0
2
1
1
0
0
1
2
1
0
1
1
1
1
0
0
2
2
1
1
1
2
1
1
0
1
2
1
1
0
0
1
1
1
2
0
0
1
1
1
2
0
2
1
1
1
1
2
1
0
2
2
1
1
1
1
1
1
1
1
3
0
0
1
1
1
1
1
0
2
1
1
1
0
1
2
1
1
1
1
2
2
2
1
2
2
2
1
1
0
1
1
1
0
0
1
1
1
1
1
1
1
1
1
2
1
1
1
3
1
1
1
1
1
1
1
1
1
2
1
1
1
3
1
0
1
1
1
1
2
3
0
1
0
1
0
0
1
2
0
0
2
2
1
1
1
1
0
2
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
0
1
1
0
1
1
2
1
1
2
1
0
0
2
1
1
2
2
1
1
1
0
1
3
0
1
2
1
1
1
0
2
1
2
1
2
2
2
1
2
1
2
1
1
0
2
1
1
0
1
1
0
1
1
0
1
1
1
0
2
1
2
0
1
1
2
0
1
1
0
1
2
0
2
0
0
1
1
2
0
2
2
1
1
1
1
0
1
1
1
0
0
2
1
0
1
0
1
2
1
0
2
2
2
2
1
2
0
2
2
0
2
2
1
0
1
0
1
1
1
2
1
1
1
1
0
0
1
1
0
2
0
2
2
1
0
1
4
0
2
2
0
2
0
1
1
1
2
1
1
0
3
1
2
1
2
1
0
1
1
1
1
2
2
1
1
1
0
1
2
1
0
1
1
1
0
1
1
1
1
4
1
0
1
2
0
1
1
1
1
2
2
1
2
2
1
1
0
0
1
1
1
0
1
1
0
1
1
2
0
1
2
1
1
1
1
2
0
1
1
2
0
0
1
0
1
1
1
1
1
2
2
1
0
1
1
2
2
1
2
1
2
2
1
2
2
2
2
0
1
0
1
1
3
1
1
1
1
0
0
1
1
1
1
1
1
1
1
1
2
1
0
2
2
2
1
2
1
0
1
1
1
1
0
2
1
1
2
0
1
0
2
1
1
1
1
0
0
2
1
1
1
1
0
0
0
0
0
3
1
1
1
1
1
0
2
1
2
0
1
0
0
1
1
1
0
1
1
1
2
2
1
0
0
0
0
1
2
1
1
2
2
0
1
0
0
1
0
0
0
1
2
1
1
1
1
1
2
2
1
2
0
1
2
1
1
0
1
2
1
0
3
0
1
1
3
0
1
1
1
1
0
0
2
0
2
1
2
1
1
2
2
1
1
1
2
2
1
1
2
1
2
2
2
1
1
0
2
1
1
0
2
0
0
0
2
1
0
2
3
1
1
1
0
2
2
2
1
1
2
0
1
1
0
2
0
1
2
1
1
2
2
1
2
0
1
2
1
2
1
2
1
0
1
2
2
1
1
2
0
1
1
8
1
1
1
1
1
1
0
1
1
2
1
1
1
0
1
0
0
1
3
1
2
1
3
0
1
1
0
0
1
1
1
2
0
0
1
0
0
1
2
2
0
2
1
1
2
1
1
2
1
0
0
1
2
0
1
1
1
0
1
2
2
0
1
1
0
1
1
0
1
1
1
1
1
0
1
1
0
1
1
1
0
0
1
1
1
1
1
1
2
2
1
1
1
1
2
1
0
0
1
0
1
2
1
1
1
0
0
1
1
1
0
0
2
1
1
2
1
1
1
1
0
0
0
2
1
1
2
0
2
2
2
1
1
2
2
1
2
0
1
0
1
0
2
1
0
1
1
2
1
1
0
1
2
1
2
1
1
1
2
0
2
1
2
2
2
1
1
1
1
1
3
1
1
2
1
1
1
2
2
2
0
1
0
0
1
1
2
2
2
1
1
1
0
0
2
0
1
2
1
0
2
1
1
2
1
0
2
2
1
1
1
0
1
1
2
1
0
2
1
1
0
2
1
0
1
1
2
2
0
1
1
0
1
1
1
0
0
1
0
1
1
1
2
2
1
1
1
0
1
2
1
0
1
1
1
2
2
1
1
2
0
1
0
2
2
0
1
1
0
0
2
1
1
1
1
1
1
1
0
1
1
2
1
1
0
1
1
1
2
0
1
2
0
1
1
2
0
1
0
2
2
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
0
0
2
0
2
0
1
1
1
1
0
1
1
1
2
1
0
0
1
2
0
1
2
2
1
1
1
0
2
0
1
1
1
1
0
1
1
1
1
2
1
2
1
1
0
0
0
1
2
1
1
1
1
1
1
1
1
2
2
1
1
2
0
0
2
2
2
1
2
2
1
0
1
1
2
1
1
2
1
1
1
1
0
1
1
2
1
1
0
0
0
1
1
1
1
0
0
2
1
1
1
1
1
2
1
2
2
1
1
0
1
1
2
2
0
0
1
1
1
2
1
1
0
1
2
2
1
1
1
1
1
1
0
1
0
0
1
1
1
1
1
1
2
0
0
0
2
0
2
1
1
0
1
0
1
1
3
2
2
1
0
2
2
1
1
0
0
1
0
1
2
0
1
1
0
1
1
0
1
1
1
0
0
1
1
1
2
0
2
1
1
1
2
2
2
2
1
1
1
0
1
2
2
3
0
1
0
1
1
1
2
1
2
1
2
0
0
4
0
1
0
1
2
0
2
1
1
0
1
0
1
2
1
0
1
0
0
2
1
1
1
1
1
1
2
1
0
1
0
1
1
0
0
0
0
1
1
1
0
1
1
0
0
0
1
2
1
1
1
2
1
1
1
1
2
1
2
1
2
0
1
1
0
1
2
0
1
0
1
0
2
0
2
0
0
1
2
2
1
1
1
1
2
0
2
0
2
1
1
2
1
1
1
1
0
0
1
1
1
1
0
0
1
1
0
2
10
0
1
2
1
1
1
1
1
2
1
2
1
2
0
1
0
2
1
1
0
1
1
1
1
2
2
0
1
1
0
0
2
1
0
1
1
1
2
1
0
1
0
1
2
2
2
0
2
0
2
1
1
1
1
3
2
0
0
0
0
2
2
1
0
1
2
3
1
2
1
2
1
1
0
0
1
2
1
1
0
2
0
0
1
1
1
1
0
0
2
2
1
0
1
2
2
0
1
1
0
1
2
1
1
1
1
1
0
1
0
2
1
1
0
0
1
0
2
1
1
0
0
0
0
1
2
0
1
0
1
0
1
1
0
0
2
2
0
2
1
0
2
1
1
0
2
1
1
1
1
0
0
0
0
1
1
1
1
1
2
2
1
0
1
1
2
1
0
0
1
2
1
0
1
1
1
1
1
1
2
1
2
1
0
2
2
1
0
2
1
1
2
2
2
1
1
1
2
2
1
1
2
1
1
0
2
0
0
1
0
1
1
0
2
1
0
2
1
1
4
0
0
2
2
1
1
2
2
2
2
1
1
1
2
0
2
0
1
1
2
1
2
1
1
1
1
1
2
2
1
2
1
1
2
1
0
0
1
2
2
1
0
0
1
1
1
1
1
1
2
1
0
1
1
1
0
0
0
1
1
1
1
0
1
2
1
1
2
1
2
2
0
1
1
1
1
1
1
2
0
1
1
1
1
1
0
1
0
2
2
1
0
1
1
0
0
1
0
2
0
1
1
1
0
1
1
2
2
2
1
2
1
1
1
1
1
0
1
0
0
1
1
2
1
1
1
2
1
0
1
2
1
2
2
1
1
1
1
0
1
2
1
1
1
1
2
1
1
0
1
1
1
2
2
1
2
1
1
1
1
2
1
0
1
2
1
1
2
2
1
0
1
1
1
1
2
2
1
1
2
2
0
1
2
2
2
0
1
1
1
1
0
1
1
1
1
1
1
0
0
2
2
1
0
0
1
1
2
1
0
1
1
0
2
0
1
2
1
1
1
1
1
1
0
1
0
1
0
1
1
1
2
1
1
2
0
1
2
1
1
1
0
1
0
2
0
1
1
2
1
2
0
1
1
2
1
0
1
2
1
0
2
1
0
1
1
0
1
1
1
1
1
2
0
1
0
2
1
0
2
2
1
0
1
1
0
1
0
1
0
2
2
0
1
1
1
2
0
1
1
1
1
0
1
1
0
1
1
1
1
1
2
2
1
1
1
2
1
0
0
1
0
1
1
1
0
1
2
1
1
1
0
1
1
1
1
1
1
1
1
0
0
2
1
0
2
0
1
2
1
2
0
0
0
2
1
0
1
1
1
1
1
1
2
1
1
1
0
1
0
2
2
1
1
1
1
2
1
2
1
1
0
1
1
1
1
0
2
0
1
1
1
1
1
2
2
1
1
0
2
0
1
0
1
1
1
0
1
0
1
1
1
0
2
2
1
2
1
1
1
0
1
1
1
0
0
2
0
1
1
1
0
1
0
2
0
2
1
0
0
1
1
1
1
1
1
1
0
1
1
2
0
2
2
1
1
1
1
1
1
0
2
0
1
2
0
2
1
1
0
0
2
1
0
1
1
1
1
1
1
0
0
1
0
1
1
0
2
1
0
1
1
1
1
0
1
1
1
0
1
2
2
2
2
2
1
1
1
3
0
2
1
1
1
2
0
0
1
1
0
0
2
2
2
1
1
1
0
1
2
0
2
2
1
0
1
0
2
0
2
0
1
0
1
2
0
0
0
2
1
2
1
0
0
1
1
1
1
1
2
2
3
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
2
1
0
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
0
1
1
2
1
1
2
1
1
1
0
0
1
0
1
1
1
2
0
1
1
0
1
0
1
1
1
2
1
0
1
2
2
2
2
1
2
1
2
1
0
1
1
1
1
2
1
1
1
0
0
1
1
1
0
2
0
1
1
0
1
1
0
1
0
1
2
1
2
1
0
2
0
1
1
1
0
1
0
1
1
1
2
1
1
1
0
2
1
1
1
1
0
1
1
1
2
1
0
2
0
1
1
1
2
0
1
0
0
1
1
1
1
0
2
1
1
2
1
0
0
0
1
1
1
2
0
1
0
1
1
2
1
2
1
1
1
1
2
1
2
1
2
2
1
0
1
2
1
1
1
1
1
2
1
1
2
2
1
2
2
0
1
0
1
1
0
0
0
1
0
1
1
1
0
2
0
0
1
1
1
1
0
1
2
2
1
1
1
2
0
1
0
2
1
2
1
1
2
2
1
2
2
2
1
1
0
2
2
1
1
1
0
1
2
0
2
0
2
1
1
0
1
2
0
1
2
2
1
1
1
2
1
1
2
1
1
2
1
2
1
2
1
1
2
2
2
1
0
1
1
1
0
1
1
2
1
1
1
1
1
0
1
1
1
2
2
0
1
1
0
1
0
1
0
1
1
1
2
1
1
2
2
1
1
1
1
0
1
1
0
1
1
1
1
1
1
0
2
1
2
1
1
1
1
2
2
1
0
4
0
1
1
2
0
0
1
1
2
2
1
2
1
2
1
0
0
2
1
1
2
2
1
2
1
0
0
1
0
2
1
1
1
2
1
2
1
0
0
0
1
1
1
1
2
0
2
0
0
2
1
2
1
1
2
1
1
0
0
1
0
1
2
0
2
1
2
1
0
0
1
1
1
0
1
1
0
1
1
1
1
0
2
1
1
2
1
1
0
1
2
1
1
1
1
1
2
0
2
0
1
1
1
1
2
2
1
4
1
1
1
1
0
1
0
1
0
2
2
2
1
1
1
1
0
0
2
2
2
2
1
1
1
1
1
3
1
2
0
2
1
2
2
1
1
2
2
0
0
1
1
1
1
1
2
1
1
2
1
1
1
0
1
1
0
1
1
1
0
2
1
2
1
1
2
1
1
1
1
1
2
1
1
1
1
0
0
0
2
3
1
2
0
1
1
1
2
2
2
0
2
1
1
2
0
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
0
1
2
1
0
1
1
2
1
1
0
2
2
1
1
1
4
1
1
1
1
2
1
1
2
2
1
0
1
1
1
0
1
0
1
1
2
0
1
2
1
1
1
1
0
1
1
1
0
0
1
2
0
1
1
1
2
1
1
1
1
1
0
0
1
2
1
1
1
2
0
1
1
0
1
2
1
1
1
0
0
2
2
1
1
1
1
2
2
1
2
0
0
1
1
1
1
1
1
1
2
0
1
1
1
1
0
1
0
1
1
0
1
1
1
1
1
1
2
1
1
1
0
1
1
2
0
1
2
1
1
0
2
1
1
1
0
1
0
3
0
1
2
2
1
2
0
0
0
1
1
0
2
1
1
0
1
2
1
0
2
1
1
2
0
1
1
1
1
1
1
1
1
1
1
0
1
0
1
2
2
0
0
1
3
1
2
1
1
1
0
1
1
1
0
0
2
0
2
2
2
1
1
1
0
1
0
1
1
1
1
0
2
1
2
0
0
1
2
0
0
0
1
2
0
1
2
1
1
1
1
0
1
1
1
0
0
2
0
0
1
1
2
1
0
0
1
1
0
2
1
0
1
0
1
1
1
2
1
1
0
1
1
1
1
1
1
1
2
1
2
0
3
1
0
2
2
2
1
1
0
1
1
0
1
1
1
1
1
1
1
1
1
1
2
0
6
1
1
1
1
0
1
1
1
0
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
0
1
1
0
1
1
1
1
0
0
0
1
1
0
0
1
1
0
2
1
0
1
1
0
0
1
1
0
1
0
2
1
2
2
2
2
0
0
1
1
1
2
1
1
1
2
1
1
2
0
1
1
1
1
2
1
0
1
1
0
1
2
2
1
2
2
0
1
1
1
0
2
2
1
0
1
1
2
2
1
1
0
1
0
1
1
1
1
2
0
1
1
1
1
2
1
1
1
1
0
1
1
1
2
1
2
0
0
1
0
2
1
1
0
1
1
0
2
2
2
1
1
0
0
0
1
0
0
1
1
1
1
1
1
1
2
1
1
1
0
1
0
1
0
2
1
2
0
1
1
0
1
1
0
2
1
1
0
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
2
1
0
2
1
0
1
0
1
1
1
2
0
1
2
0
2
1
1
0
0
2
0
0
0
1
1
0
2
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
1
1
2
1
1
1
2
2
0
1
2
2
0
2
2
2
2
1
1
0
1
1
1
1
1
0
1
0
2
0
0
0
1
1
0
1
2
2
4
1
0
1
1
3
1
0
1
1
0
2
0
0
1
1
2
1
2
0
1
0
1
1
2
2
2
2
0
2
1
1
1
2
2
1
1
2
0
1
1
1
2
1
1
2
1
1
1
2
0
0
1
2
1
1
1
1
2
0
1
0
2
1
1
1
2
1
1
1
1
2
2
2
0
0
0
1
1
1
1
0
2
0
2
1
0
0
1
1
0
2
2
0
0
1
0
0
1
2
1
2
1
1
2
1
2
1
2
1
2
2
0
1
0
1
0
0
1
1
2
0
1
1
1
1
0
2
1
1
0
0
0
1
1
2
2
0
2
0
1
1
0
0
2
1
0
1
0
2
1
1
1
1
2
1
0
1
1
1
1
2
1
1
0
1
0
1
1
1
0
1
1
1
2
1
0
2
0
1
1
1
1
2
0
2
1
2
0
0
1
1
1
1
1
0
1
0
0
0
0
1
1
1
1
1
1
2
0
1
2
0
2
1
0
1
1
0
1
0
2
0
0
0
1
1
1
1
1
0
2
1
1
0
0
0
2
2
1
2
1
1
1
2
0
1
1
1
1
1
2
0
1
1
1
2
1
1
1
1
0
2
1
2
0
2
2
0
1
2
1
0
1
0
0
1
2
1
0
2
2
1
1
1
4
1
1
1
0
1
1
0
2
0
2
0
0
1
1
0
1
1
2
1
0
1
1
0
1
2
1
1
1
1
1
1
1
1
2
2
1
1
2
2
1
1
1
1
1
0
1
1
1
2
0
2
1
1
1
2
1
0
1
0
2
1
1
1
1
0
2
1
2
1
0
2
0
1
0
1
1
3
0
1
0
1
1
0
2
1
1
0
0
1
1
0
2
0
1
1
0
2
2
2
1
1
2
1
2
1
1
1
0
0
1
1
1
0
0
1
1
0
0
1
2
1
1
1
1
1
1
2
1
0
0
1
1
0
1
2
2
2
2
1
1
2
0
2
1
1
2
1
1
0
2
4
0
1
1
1
0
2
1
1
1
0
1
1
2
2
1
1
2
1
0
1
2
2
1
1
1
2
1
2
1
0
1
1
1
1
1
0
1
1
1
0
1
1
1
0
0
2
1
0
1
1
0
0
2
2
1
2
1
0
1
1
1
1
1
1
1
0
2
1
1
1
1
2
1
1
2
0
1
1
1
2
1
2
1
2
0
2
1
3
1
2
1
2
2
1
1
1
0
0
0
1
0
2
2
1
1
2
0
0
1
1
1
0
2
2
2
1
1
0
1
2
1
0
1
2
1
0
1
0
1
2
2
1
1
0
0
1
1
2
1
1
0
1
1
2
1
1
0
2
1
2
1
1
0
1
1
1
0
0
1
1
1
2
2
1
1
0
1
1
1
1
0
2
1
1
1
0
1
1
1
1
1
2
2
1
0
1
1
2
1
0
1
1
1
1
1
1
1
1
1
0
1
2
0
2
1
1
0
2
0
1
3
1
1
1
1
2
0
2
1
1
1
0
2
1
2
1
2
1
2
1
2
0
0
1
1
2
0
1
1
2
1
2
1
0
2
2
1
1
2
1
0
1
1
1
1
2
1
3
2
1
0
2
2
2
1
2
1
1
2
1
2
1
2
1
0
2
1
1
2
1
1
2
2
0
1
2
0
2
0
1
1
0
0
0
0
1
1
1
1
1
1
1
2
1
1
0
2
1
0
0
2
1
1
1
0
0
1
0
2
1
1
2
1
0
0
2
2
1
0
1
0
1
1
1
1
1
1
0
2
1
0
1
0
1
1
1
1
2
2
0
1
1
1
1
3
1
1
1
1
1
1
1
1
0
0
1
2
2
1
2
2
3
2
1
0
2
2
1
1
1
2
1
1
1
0
0
1
1
1
1
2
1
0
2
0
2
1
0
2
1
1
1
1
1
0
1
1
1
0
1
2
1
1
2
1
1
2
2
2
0
1
0
1
1
0
1
1
1
1
2
1
0
2
2
0
3
2
2
2
1
2
1
2
0
1
1
1
1
0
2
1
1
1
1
1
1
2
0
2
1
2
2
0
1
0
0
1
2
0
2
1
0
0
1
2
1
1
0
2
1
1
1
1
1
1
2
0
2
1
2
1
1
1
2
1
1
1
1
0
0
2
1
2
1
1
2
2
0
1
0
1
1
1
3
2
1
0
0
2
1
0
1
2
1
1
1
1
2
0
0
1
1
0
0
1
0
2
1
1
1
2
1
1
1
1
1
0
1
1
1
1
0
1
2
0
2
1
1
0
1
1
2
0
2
1
0
1
1
1
1
1
1
2
0
0
2
1
2
1
1
1
1
1
0
2
1
2
0
2
2
1
1
0
0
1
1
1
1
1
0
0
1
1
1
1
1
1
7
2
1
1
1
1
1
3
0
1
1
2
1
2
1
2
0
2
2
2
1
0
1
1
1
1
1
2
1
1
2
1
1
1
0
1
1
1
1
1
1
1
0
0
2
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
2
1
0
1
1
1
2
2
1
1
1
1
0
1
1
1
1
2
2
1
2
1
1
1
1
0
2
0
1
1
2
1
2
1
1
2
1
1
1
2
1
1
2
1
1
1
0
1
1
1
0
1
1
1
0
1
2
2
2
1
0
2
0
0
1
2
2
2
2
1
0
1
1
1
0
1
1
1
1
2
0
1
1
0
1
0
1
1
0
2
0
1
1
1
1
1
1
1
0
0
0
1
0
2
2
1
2
1
1
1
1
1
1
0
1
2
1
0
2
0
1
0
2
1
0
1
1
1
1
1
1
0
1
0
0
0
2
2
1
0
1
1
1
2
2
1
1
1
1
2
0
0
0
1
0
0
1
1
1
1
2
1
1
2
1
2
2
1
1
0
0
0
2
1
2
1
2
1
1
1
0
1
0
1
1
2
2
1
2
1
1
1
1
0
1
1
1
1
1
0
1
0
1
0
0
2
1
1
1
2
1
2
1
1
1
0
0
0
1
0
1
1
2
1
2
1
1
0
1
2
1
0
1
1
1
0
1
0
0
1
2
1
1
1
1
2
0
1
1
1
1
1
0
0
1
1
2
0
1
0
1
1
2
2
2
2
0
1
1
1
0
1
1
1
1
1
1
1
1
0
0
1
2
1
1
1
1
2
2
2
1
1
2
1
1
1
1
0
0
1
1
1
1
1
0
1
1
1
1
2
1
1
2
1
2
1
0
1
0
0
0
1
1
2
1
1
1
1
1
0
0
1
1
1
2
2
1
0
1
1
1
1
1
0
1
0
1
1
2
1
0
2
1
1
1
1
1
1
1
1
0
0
2
2
0
1
1
2
3
1
0
1
1
1
1
2
0
1
0
1
0
2
1
2
0
1
0
0
1
1
1
1
2
2
2
1
1
0
2
1
1
1
1
2
1
1
1
1
2
1
1
2
2
2
0
1
1
2
2
1
2
2
1
1
1
1
2
1
2
1
2
1
1
1
2
2
1
1
1
1
1
0
1
1
1
1
2
1
0
1
1
1
2
1
1
1
1
1
1
1
1
1
0
1
1
1
1
2
2
1
2
2
1
1
0
2
1
2
2
1
1
1
1
0
1
1
2
0
1
1
0
2
2
1
1
1
1
1
2
1
2
2
1
2
1
1
2
0
2
1
1
1
0
1
0
0
1
1
2
1
1
2
1
1
3
1
1
0
1
1
1
0
2
1
2
1
0
1
1
0
1
1
1
1
1
1
1
1
0
1
1
0
1
0
2
2
1
2
2
1
1
2
1
1
2
1
2
1
0
1
2
0
1
0
1
0
1
1
2
2
2
1
1
2
1
1
0
0
1
2
1
0
2
1
1
1
1
1
1
1
1
0
0
1
1
1
1
1
1
1
0
0
1
0
1
1
1
1
0
0
2
1
1
1
1
0
1
1
1
1
2
1
1
1
1
1
0
1
1
0
2
1
2
1
2
1
1
0
0
1
1
1
1
1
0
1
1
1
2
1
1
1
1
1
2
1
2
1
1
0
1
1
1
2
0
1
0
0
2
0
1
2
1
2
1
1
1
1
0
0
2
1
1
1
0
1
2
2
0
1
1
1
2
2
0
0
1
1
0
0
3
1
2
1
2
0
1
1
2
1
1
1
0
1
1
1
0
1
1
0
2
1
1
0
2
1
1
2
1
1
1
2
1
0
1
1
1
1
1
0
0
2
1
1
0
1
1
1
1
1
0
0
1
1
1
2
2
1
2
0
1
1
0
1
0
1
1
2
0
1
1
2
1
1
1
2
0
1
2
0
0
1
2
1
0
1
1
1
2
1
0
0
1
3
2
0
2
1
0
0
1
1
2
1
1
1
0
1
1
2
0
0
1
0
0
0
1
1
1
1
2
2
0
0
1
0
2
0
0
1
1
1
0
2
0
2
1
1
1
1
1
1
1
1
1
2
1
0
0
1
2
0
0
1
2
0
1
1
1
1
1
1
0
1
1
1
2
1
1
1
2
4
0
1
2
1
1
2
2
1
1
0
1
1
1
1
0
1
2
1
1
1
1
2
1
1
2
0
1
1
1
0
2
1
1
1
0
2
1
0
1
2
2
2
1
0
1
1
0
2
1
2
1
0
1
2
0
0
0
1
1
1
0
2
1
1
1
0
2
1
1
1
1
2
2
1
0
1
2
2
1
1
0
1
2
1
0
2
2
1
0
1
1
2
2
1
1
2
0
2
0
1
1
1
0
0
1
0
1
1
1
1
2
1
1
1
3
1
1
1
0
1
1
2
0
2
1
1
1
1
1
1
0
1
2
2
1
1
1
2
1
0
1
1
2
0
1
1
1
1
1
1
1
1
1
2
2
2
2
1
1
0
1
0
1
0
0
0
1
1
2
1
3
1
2
0
1
1
1
2
2
1
1
1
1
2
1
1
0
2
0
2
0
1
2
1
1
1
3
1
1
1
3
0
1
1
0
1
2
1
1
1
1
1
2
1
1
0
1
1
2
1
1
1
1
0
0
1
1
1
0
2
1
0
2
1
1
0
2
1
2
2
1
0
1
1
1
2
1
1
1
1
0
1
1
0
1
0
2
0
1
1
0
0
1
0
1
2
2
1
1
0
1
2
1
1
0
0
1
2
2
1
0
2
0
0
2
0
1
1
1
2
1
1
1
1
2
0
1
2
1
1
0
0
1
1
1
1
0
1
2
1
0
2
2
1
1
0
1
0
1
2
1
0
0
0
0
1
0
1
0
1
1
1
2
1
0
1
1
0
1
0
2
1
1
1
0
1
1
1
2
1
0
1
1
2
0
2
1
2
2
0
2
2
1
0
1
2
0
0
1
2
1
1
1
1
0
2
0
1
1
1
1
0
1
1
2
2
2
0
1
1
1
2
1
2
2
1
1
1
1
0
1
1
1
1
2
1
0
1
2
1
0
1
1
2
1
2
1
1
0
1
1
1
0
1
1
2
1
1
1
0
1
2
2
1
0
0
1
1
1
1
3
0
2
0
1
1
0
1
1
1
1
2
2
1
1
1
2
1
1
1
1
1
1
0
0
2
2
1
1
1
1
2
1
2
1
0
0
2
2
2
1
0
2
2
1
1
2
2
1
0
1
0
0
0
1
1
0
2
1
2
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
0
2
2
1
0
2
1
1
1
2
1
0
1
1
2
1
1
2
1
1
1
0
1
2
0
2
2
1
1
1
1
1
1
0
2
1
1
2
0
1
1
1
1
1
0
1
2
1
2
1
2
1
1
2
1
1
0
2
2
1
0
0
1
1
2
1
0
1
1
0
2
1
2
1
2
2
2
0
1
0
1
2
1
1
1
0
1
1
4
1
1
1
0
0
0
1
1
1
2
1
1
1
1
1
1
0
2
0
0
1
1
0
1
1
1
0
0
1
1
2
2
1
1
1
1
1
1
1
0
1
1
1
1
0
1
0
1
1
1
0
1
2
0
1
0
2
2
2
0
0
1
1
1
1
1
1
1
3
1
0
2
1
1
2
1
2
1
5
2
1
2
0
0
2
1
1
1
4
0
1
1
2
1
2
1
1
2
2
1
1
1
1
1
1
2
1
1
2
1
0
1
1
1
2
1
0
2
1
1
1
1
1
1
0
0
2
2
1
1
2
1
2
0
1
1
1
1
2
1
2
0
2
1
1
1
2
1
1
2
2
1
1
0
0
0
2
2
2
0
1
2
1
1
0
1
1
1
1
2
0
2
2
1
1
0
1
0
0
2
1
2
1
2
1
1
2
1
1
0
1
0
2
2
1
0
1
0
1
1
0
1
1
2
2
2
0
2
2
0
2
2
2
1
1
1
0
1
0
2
1
2
0
0
0
1
2
2
0
3
1
1
1
2
2
1
1
1
0
0
0
0
1
1
1
1
1
2
1
1
2
0
0
1
1
1
1
1
1
1
1
1
0
2
1
2
1
1
1
2
0
1
1
2
1
2
0
0
1
0
1
2
2
1
1
2
1
2
0
1
1
1
1
2
1
0
0
0
1
2
1
1
1
0
1
1
1
1
1
1
1
2
0
2
1
1
2
2
2
1
0
1
2
1
1
1
1
1
1
2
0
0
2
1
0
1
1
2
0
1
1
1
1
0
1
0
1
0
2
1
2
1
1
0
2
0
0
0
2
2
1
0
2
0
0
3
1
0
1
0
1
1
0
0
1
1
2
0
0
1
1
2
2
2
1
0
2
1
1
2
2
1
1
0
0
0
2
2
0
1
1
1
1
0
3
1
1
1
1
0
1
1
1
1
1
0
0
2
1
0
1
1
1
1
1
1
1
0
1
1
1
1
1
1
2
2
2
2
1
1
1
2
1
1
1
1
1
1
1
1
1
2
0
2
1
1
2
0
1
1
0
2
1
0
2
0
0
2
2
1
0
2
0
1
1
0
1
2
1
0
2
1
1
1
1
1
0
0
0
1
0
1
0
1
1
1
1
1
0
1
1
1
1
2
1
2
0
2
1
2
1
0
2
0
1
1
1
1
1
1
1
2
1
2
1
0
1
1
1
1
1
2
0
0
0
1
0
1
1
2
2
1
0
2
2
2
1
1
0
2
1
0
2
1
0
0
1
1
1
0
1
1
2
3
1
0
1
3
1
0
2
0
1
1
2
0
1
1
2
2
1
0
0
1
0
0
1
2
1
2
0
1
1
2
1
1
1
0
1
1
2
1
1
1
2
1
1
0
1
1
1
1
1
3
1
2
0
0
0
1
1
1
2
0
0
0
2
1
1
1
2
1
1
1
1
2
0
1
1
1
1
2
1
0
1
0
1
0
2
1
2
0
1
1
1
0
1
1
1
1
2
0
1
0
1
1
1
0
1
2
1
1
0
1
2
1
0
0
0
1
0
2
1
2
1
1
2
1
1
2
1
2
1
2
1
1
1
1
2
1
1
2
1
2
2
1
0
3
1
1
1
1
0
1
1
0
0
1
1
0
1
1
1
1
1
2
1
3
2
1
1
1
1
1
1
1
1
2
2
1
0
1
2
1
1
1
1
1
1
1
1
0
2
1
2
1
0
1
1
1
0
0
2
1
1
1
0
1
1
1
2
1
2
1
2
0
0
2
1
2
1
0
1
2
1
5
1
2
1
0
1
1
1
0
1
1
2
2
2
1
1
1
2
1
2
0
2
1
1
0
1
2
1
1
2
0
1
2
1
1
1
1
1
1
1
1
1
1
0
2
1
0
1
1
2
1
1
1
1
0
0
1
1
0
1
2
1
1
2
1
3
1
1
1
1
1
2
1
1
1
0
1
1
1
1
0
2
1
2
1
1
2
1
0
1
1
2
0
2
1
1
0
1
1
1
1
1
1
3
0
0
1
0
0
2
2
0
1
0
1
2
2
0
1
0
1
1
2
1
2
1
1
0
1
1
0
1
0
2
0
2
2
2
2
1
1
1
1
1
0
1
0
0
1
1
2
0
1
0
1
1
1
1
1
1
2
0
0
0
1
1
2
1
1
0
0
3
1
2
2
0
1
1
1
1
1
1
2
2
2
1
2
2
1
1
1
2
0
2
2
2
1
1
1
2
2
2
1
1
0
0
1
1
1
0
2
0
1
1
2
1
0
2
0
1
1
1
0
1
2
1
1
2
2
0
2
2
2
1
1
0
1
2
0
1
1
0
1
2
7
1
1
1
1
1
0
1
1
1
2
1
1
1
0
1
2
1
2
1
2
1
0
2
2
0
2
1
1
2
0
2
1
2
0
0
0
0
2
1
3
2
2
1
1
1
1
2
0
1
2
2
1
0
1
1
1
1
2
2
1
2
2
1
2
1
0
1
0
0
0
1
2
1
0
1
0
1
1
1
1
1
1
1
0
1
2
1
1
1
2
1
2
2
1
1
1
2
1
3
1
1
0
1
2
2
0
2
0
1
1
1
1
1
0
1
1
1
1
1
2
2
1
2
1
1
1
0
1
2
2
1
2
2
2
0
1
1
0
1
2
2
1
1
1
2
2
1
0
2
0
1
0
1
1
1
1
1
0
1
2
0
0
1
0
2
2
1
1
0
1
1
1
1
0
2
2
1
2
1
1
1
2
1
1
2
2
2
1
2
1
2
0
2
1
1
1
1
1
1
2
2
0
2
1
1
2
1
1
0
0
1
0
1
1
1
1
1
2
2
0
1
1
2
2
1
2
2
1
0
1
1
1
1
1
2
2
0
2
1
1
1
1
1
3
1
0
2
0
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
0
1
0
1
2
1
2
0
0
2
1
1
1
0
0
1
2
1
1
2
1
2
1
1
2
0
2
2
1
0
1
0
1
0
0
1
1
1
2
0
1
1
1
0
1
0
1
1
1
1
3
1
1
2
2
0
1
1
1
2
1
0
1
0
1
1
1
2
1
2
1
1
1
1
1
0
1
0
1
0
3
1
0
0
1
1
2
0
0
2
1
2
1
1
1
1
2
0
1
0
2
2
0
0
1
1
2
0
1
1
1
1
1
1
1
1
0
1
1
2
1
0
1
1
1
1
0
1
2
2
1
1
0
1
1
1
2
1
0
1
0
1
1
2
1
1
1
0
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
2
0
2
0
1
1
2
2
2
2
1
0
0
1
0
2
0
1
1
1
0
1
1
1
0
0
1
1
1
2
0
0
1
0
1
1
1
1
1
1
2
0
1
2
0
2
3
1
1
0
1
1
1
2
1
1
0
1
1
0
2
1
2
0
2
2
1
0
1
0
0
1
1
0
2
2
2
1
1
1
2
1
0
1
1
1
1
2
0
0
2
1
1
0
0
0
0
1
2
1
1
0
0
1
0
1
1
0
0
0
2
2
0
2
1
0
1
1
1
0
1
2
1
0
0
1
1
0
0
1
0
2
2
1
1
1
0
0
2
0
2
2
1
1
2
0
1
1
1
0
1
0
1
1
1
1
0
3
0
2
1
2
0
1
1
1
2
1
2
1
1
0
2
0
1
1
1
1
1
0
2
1
2
1
0
0
0
1
0
2
1
2
1
1
1
1
1
2
1
1
0
1
1
1
1
3
1
1
2
2
2
2
1
1
2
0
1
1
1
1
2
2
1
1
0
1
1
1
0
1
2
1
0
2
0
1
1
0
1
0
0
1
2
0
1
1
1
0
0
0
1
0
0
1
1
2
2
1
1
0
1
1
1
2
1
2
1
1
0
1
0
0
1
2
1
1
1
1
1
2
2
2
1
0
1
1
0
0
2
0
0
2
2
0
1
2
0
2
2
1
1
0
1
1
1
1
1
2
1
0
2
1
1
2
1
1
2
0
0
1
0
2
2
1
1
1
0
0
2
1
1
1
1
1
1
1
0
2
2
1
1
1
1
2
1
2
2
1
0
1
2
2
1
1
2
0
2
3
1
1
1
1
1
1
1
0
1
2
1
1
1
2
0
2
1
1
0
1
0
1
2
1
0
2
2
0
0
0
1
2
2
1
1
1
1
1
0
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
3
1
1
0
0
1
1
1
1
1
0
1
1
0
1
1
0
0
1
1
2
0
0
1
1
0
1
1
1
1
2
0
1
1
1
1
0
2
3
1
2
1
2
1
0
0
2
1
1
1
1
0
1
2
0
1
0
2
2
1
1
0
0
0
1
1
2
1
0
1
0
1
0
2
2
0
2
1
1
1
1
1
2
1
1
1
0
1
1
3
1
1
2
1
0
1
0
2
0
2
1
2
1
1
0
2
1
2
1
2
1
1
1
1
1
1
1
1
0
1
1
0
1
3
2
0
1
0
5
2
2
1
0
1
0
0
2
1
0
1
1
0
1
1
1
1
2
1
0
0
1
0
2
0
2
2
1
1
1
2
1
2
0
2
2
0
2
0
2
1
1
2
0
2
1
1
1
1
1
1
1
1
1
1
0
1
2
0
1
2
1
2
1
0
2
1
1
1
1
1
0
1
1
0
2
0
0
0
0
1
1
1
2
1
0
0
2
0
3
1
1
2
1
0
2
0
0
1
1
0
0
1
1
1
2
1
1
1
0
2
1
1
1
3
2
1
2
2
1
1
1
1
0
1
1
1
1
1
1
2
2
1
0
1
1
0
1
1
1
2
0
1
2
0
0
1
0
0
0
1
0
0
2
1
4
0
1
1
1
1
1
2
1
0
0
0
1
1
1
1
0
1
2
1
1
1
0
1
0
1
1
1
3
2
0
0
2
0
1
1
0
2
2
0
0
0
2
0
1
2
2
0
2
0
2
1
1
0
2
1
2
2
0
0
0
1
1
0
2
1
2
2
2
1
1
1
1
0
1
1
1
2
2
1
1
1
0
1
2
1
1
2
1
1
2
0
2
1
2
1
1
0
1
2
0
2
1
2
1
0
1
1
1
2
1
2
1
2
1
1
0
0
0
2
0
1
1
0
1
1
1
1
2
1
2
1
1
0
2
1
2
0
0
0
1
1
1
2
1
2
0
1
1
2
0
0
1
2
1
1
1
1
1
2
1
1
0
0
1
1
1
1
0
2
0
2
6
1
2
2
1
2
1
0
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
2
2
0
2
0
1
1
1
1
2
1
1
1
1
1
1
1
1
0
1
1
1
1
1
2
1
2
2
1
2
1
1
2
1
1
1
2
2
1
1
1
1
0
0
0
2
1
1
1
2
1
1
2
1
1
1
1
1
2
2
2
1
0
0
1
1
1
1
2
2
2
1
0
1
1
1
0
0
1
0
1
0
2
1
1
2
0
0
0
1
0
2
1
3
0
0
1
1
0
1
2
2
2
0
2
1
0
1
2
0
2
1
1
1
0
2
1
2
1
1
1
0
1
1
1
1
1
1
0
2
2
1
2
1
0
2
2
1
1
1
1
2
0
1
0
1
1
2
0
1
1
1
1
2
0
2
0
2
1
1
1
2
1
0
2
2
1
0
2
2
0
0
0
1
0
2
2
1
1
2
0
0
1
1
1
0
1
2
2
1
0
2
2
2
2
0
2
1
2
1
1
0
1
2
1
1
0
1
0
1
0
1
1
2
2
1
1
1
1
1
1
0
1
2
1
2
0
0
1
1
3
1
1
1
2
2
1
2
1
1
0
1
1
1
2
1
2
0
1
0
0
1
1
1
1
2
2
1
2
1
2
1
0
1
0
1
1
1
0
2
0
0
0
2
1
1
1
0
0
1
1
0
1
2
0
1
1
0
1
0
2
1
1
2
2
2
0
2
2
1
1
2
1
5
1
1
0
0
1
1
1
2
1
2
2
2
2
0
1
1
1
0
1
1
1
2
0
1
1
1
2
2
1
1
1
1
0
1
1
0
1
2
1
1
1
1
1
0
1
2
1
2
2
0
1
1
2
2
1
2
1
1
1
2
1
1
0
1
0
0
1
2
1
1
1
1
1
1
2
1
1
2
1
1
1
2
1
1
2
1
0
2
1
1
1
1
2
2
1
1
1
2
2
1
2
0
1
1
2
2
2
0
1
2
2
0
2
2
1
2
0
1
1
1
2
1
2
0
2
1
1
3
1
1
1
1
3
2
2
1
2
0
1
2
0
0
1
0
0
1
2
1
2
2
0
1
1
1
2
1
2
0
1
2
2
1
1
1
2
0
1
2
1
1
0
1
1
1
1
0
0
1
1
2
1
0
1
1
1
1
1
2
0
1
1
0
1
1
1
1
0
1
2
1
0
0
1
1
1
1
0
1
0
1
0
2
2
2
1
2
0
2
0
1
0
0
0
1
1
0
1
1
1
0
2
2
1
1
1
1
1
1
1
1
2
1
1
0
2
1
2
1
0
1
2
0
0
1
1
2
1
0
1
1
2
0
1
1
1
3
1
1
1
1
1
0
1
2
1
0
1
2
1
0
1
2
1
0
1
0
1
1
1
1
1
1
1
1
0
1
1
2
1
0
2
2
1
1
0
2
1
1
1
0
1
2
2
2
0
1
1
1
1
2
2
1
1
1
0
1
2
2
1
1
2
1
1
0
2
1
1
1
1
0
1
1
1
1
1
1
1
2
1
1
1
2
1
0
1
2
1
0
0
1
1
0
1
1
1
1
0
1
1
1
0
0
1
1
0
1
1
1
1
1
1
1
1
1
1
1
0
0
1
1
0
1
2
0
1
1
1
1
0
1
2
1
0
1
0
1
1
1
1
2
1
1
1
2
1
1
1
0
1
1
1
2
0
2
2
0
1
1
1
0
1
0
1
1
0
1
0
1
1
2
0
0
0
1
0
2
0
0
1
1
1
1
2
1
1
1
2
1
1
1
0
1
1
1
1
2
1
2
0
0
0
1
1
0
1
0
1
2
1
1
1
1
2
0
1
0
1
1
2
1
1
0
2
1
0
0
1
2
3
2
1
1
1
0
0
2
1
1
1
1
1
1
1
2
1
1
1
2
0
1
0
0
2
1
2
1
1
0
2
0
0
1
1
1
1
1
1
1
1
0
1
1
2
1
1
1
1
1
1
1
1
1
1
0
1
2
1
1
1
2
2
1
1
1
0
1
1
2
1
1
0
1
1
1
1
0
0
0
1
1
2
0
0
0
1
2
1
1
1
2
1
2
2
0
1
0
2
1
1
1
1
1
1
1
0
1
0
1
1
1
0
2
2
1
0
1
2
1
1
1
1
1
1
1
2
1
1
2
2
2
2
0
0
1
1
0
1
2
1
2
0
0
1
1
2
1
1
1
2
0
2
1
1
0
2
2
1
1
1
2
1
1
0
1
3
0
2
2
1
1
1
1
2
1
1
0
1
1
1
0
2
1
2
1
2
1
1
0
0
1
1
0
1
1
2
0
1
2
0
2
1
1
1
1
1
1
1
0
1
0
2
1
1
1
1
0
0
2
3
2
1
1
1
1
0
1
1
1
1
0
1
1
2
1
1
1
1
1
1
1
2
1
1
1
3
1
1
1
1
1
1
1
2
1
1
2
1
1
1
2
1
0
1
2
0
0
1
1
1
1
0
0
1
0
0
3
1
2
2
0
1
3
1
1
1
1
2
2
1
0
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
0
1
2
2
1
1
1
1
1
1
2
1
1
0
0
1
1
1
1
1
1
1
0
1
1
1
1
1
0
0
1
1
0
1
2
2
2
3
1
1
1
0
0
1
1
0
1
0
1
2
1
1
0
0
1
1
1
1
2
1
0
2
1
1
0
1
1
1
2
1
2
1
0
0
1
1
1
1
1
1
1
0
0
0
1
2
2
1
0
1
1
2
0
0
1
0
1
1
1
1
0
2
1
1
0
0
1
1
1
1
1
1
1
1
0
1
0
1
2
1
1
1
2
0
1
1
2
1
2
1
1
2
1
1
2
1
1
2
1
1
1
2
1
2
1
0
1
2
1
1
2
1
1
2
1
0
2
0
1
0
1
2
1
2
1
1
1
0
1
1
0
1
0
0
1
0
1
0
1
2
0
1
2
1
0
1
0
1
1
2
2
0
1
2
0
1
1
1
1
1
2
0
0
2
2
2
0
1
1
1
1
2
0
2
0
3
1
1
1
1
1
1
1
0
0
1
1
2
1
1
2
2
0
1
0
2
1
0
1
0
1
1
0
1
1
2
1
1
1
2
1
1
2
2
1
0
2
1
1
1
1
1
0
1
2
1
0
1
2
1
1
1
0
0
0
0
3
2
2
1
1
0
1
1
0
2
1
0
2
2
1
1
0
1
0
1
1
2
1
1
2
1
2
1
2
2
1
1
1
0
2
1
2
1
2
1
1
1
0
2
0
1
1
1
0
0
1
1
1
1
1
1
0
1
1
1
1
1
1
2
2
1
2
1
1
1
0
0
0
2
1
0
0
1
0
2
2
1
1
2
1
1
0
1
2
1
0
0
0
0
2
1
0
2
1
0
1
0
0
1
1
1
1
0
1
0
2
1
1
2
1
2
2
0
1
1
2
1
0
2
1
0
0
1
1
1
1
2
1
0
1
1
2
1
0
0
1
2
1
1
1
2
0
0
2
0
0
1
2
0
1
2
0
1
0
1
1
0
1
1
1
2
1
2
1
2
1
1
1
1
2
2
1
0
2
2
2
1
1
1
1
1
1
1
2
0
1
3
1
1
1
0
2
0
1
0
2
0
2
1
0
0
1
1
1
1
0
1
1
2
0
1
1
1
1
0
1
1
1
1
2
2
1
1
2
1
2
2
0
1
1
0
0
1
2
1
1
1
1
0
1
0
1
1
1
1
2
3
1
1
1
2
1
2
3
2
1
1
1
1
1
1
2
0
1
1
0
1
1
1
1
1
0
0
2
0
2
0
1
1
1
4
1
2
0
1
2
0
0
2
1
1
2
0
0
0
1
0
1
1
2
1
1
1
2
1
1
2
1
1
1
0
1
1
1
2
1
2
0
0
1
3
1
2
1
1
2
1
1
1
2
1
0
0
1
1
2
0
1
2
1
0
0
0
0
2
2
1
2
0
1
0
0
1
1
2
1
2
1
1
0
1
1
0
2
3
0
1
0
1
1
1
1
1
1
1
1
2
0
1
1
2
0
1
0
2
2
0
2
1
1
0
1
1
1
1
0
1
0
2
0
1
2
2
1
1
1
0
0
4
0
1
1
1
1
0
1
1
1
2
0
1
1
0
0
2
2
2
1
0
2
0
1
1
1
1
1
1
1
1
1
0
1
2
0
1
1
1
2
3
0
0
0
1
1
1
1
0
0
2
1
1
1
1
2
1
1
2
2
2
2
1
1
2
0
1
0
1
2
1
1
1
1
1
1
0
2
0
1
2
0
1
1
2
0
2
2
1
0
1
0
1
0
1
0
2
1
1
2
1
1
0
1
1
1
1
1
0
1
0
1
1
2
1
1
0
1
1
2
1
2
3
2
1
1
1
0
2
1
2
1
1
1
2
2
1
1
1
1
0
1
2
2
1
0
1
1
0
1
1
1
1
2
2
2
1
1
2
2
1
1
1
1
1
1
1
1
0
0
1
2
1
0
1
1
1
2
1
1
0
1
2
2
1
2
0
1
0
1
0
0
2
2
1
0
1
1
0
1
2
2
0
0
1
1
2
1
1
1
1
1
1
2
2
2
2
0
0
1
1
2
1
1
1
1
1
1
1
0
1
1
0
0
1
1
1
0
2
1
1
0
0
2
0
2
0
1
1
1
2
1
2
2
2
1
0
2
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
0
1
0
0
1
1
1
1
2
1
1
0
0
1
2
2
1
1
2
1
0
2
1
0
0
1
2
2
2
2
0
2
0
1
0
1
1
1
1
2
1
0
1
2
1
1
1
1
2
0
0
1
2
1
2
0
1
2
0
1
2
2
0
1
1
1
1
2
1
1
0
1
1
1
1
1
0
1
0
2
0
1
0
1
1
2
1
0
1
1
2
1
2
1
1
1
0
0
1
2
1
0
0
0
2
1
0
0
1
2
1
1
1
1
1
1
1
1
1
1
1
2
0
0
1
1
2
1
2
1
1
0
1
2
2
0
2
0
1
1
2
1
2
2
1
0
2
1
1
0
0
2
0
1
1
1
1
0
0
1
1
3
1
1
1
2
2
1
1
1
1
2
1
1
2
0
0
1
0
1
2
0
2
1
1
0
2
0
1
1
1
0
1
0
1
3
0
1
1
0
2
0
2
1
1
1
0
1
1
0
1
0
1
1
1
1
1
1
1
2
1
1
1
0
1
1
2
1
1
2
1
2
2
1
2
1
1
1
1
1
1
0
2
2
2
1
0
1
1
1
0
1
0
1
0
1
1
1
2
2
1
2
1
1
2
1
1
0
0
2
0
2
1
1
2
0
0
2
1
1
0
1
1
2
2
2
2
2
1
1
1
1
1
0
1
1
1
1
1
1
1
2
1
1
1
1
0
1
1
1
1
2
1
2
2
1
2
2
1
1
1
3
0
2
2
0
2
1
1
3
0
1
1
1
2
2
0
2
0
1
1
1
1
0
1
1
1
10
0
1
1
1
1
1
1
0
1
1
1
2
1
1
1
1
2
1
2
1
0
0
0
0
1
1
0
1
2
0
0
1
2
1
0
2
1
1
1
0
2
1
1
1
1
1
1
1
1
1
2
2
1
1
1
2
2
0
1
2
1
2
0
1
1
1
2
2
1
2
1
2
1
1
1
1
1
1
1
1
1
2
0
1
1
0
2
2
1
1
0
1
2
1
1
2
1
1
1
0
1
1
0
2
2
1
1
1
4
2
1
1
0
1
1
0
1
1
0
1
0
3
1
1
1
1
1
1
2
1
1
1
1
2
1
2
1
1
0
1
2
1
0
1
1
2
1
0
1
1
0
1
1
1
0
0
2
2
1
1
0
1
2
1
2
1
0
1
1
0
1
1
2
0
1
2
2
0
2
1
1
2
2
1
1
2
1
2
0
1
1
2
1
2
1
1
1
2
1
1
1
1
0
1
2
1
1
1
2
0
1
2
2
0
1
0
1
2
1
2
1
1
0
1
0
2
1
1
1
0
1
1
1
2
1
1
1
1
2
1
0
0
0
0
1
0
0
2
1
2
2
1
2
1
2
1
1
1
1
1
2
4
1
1
1
1
1
2
2
1
2
1
1
0
0
1
2
1
1
0
1
1
2
0
0
1
2
1
1
1
2
0
1
1
1
0
1
2
0
0
1
1
2
1
1
1
1
1
1
1
0
2
0
2
2
1
1
2
1
0
0
1
2
0
1
0
1
1
1
0
1
0
1
0
0
2
2
1
1
1
0
1
0
0
1
2
1
0
2
2
2
2
1
2
0
1
2
2
1
0
1
1
1
1
0
1
1
0
2
0
1
0
1
0
0
0
2
0
1
1
1
0
2
1
1
1
2
0
1
1
1
2
1
1
0
2
1
1
1
1
1
1
1
1
2
2
0
0
1
1
0
0
2
0
0
1
2
1
1
1
0
0
2
1
2
2
2
1
2
1
1
2
2
1
0
1
1
2
0
1
2
0
1
1
0
1
0
1
1
2
1
1
1
1
1
0
1
0
0
1
2
1
1
1
1
1
1
1
1
2
0
1
1
1
2
1
2
1
1
0
1
0
2
1
0
1
1
2
2
1
2
2
1
2
2
0
1
1
1
0
1
1
1
1
2
1
1
1
2
2
1
1
2
0
1
2
1
1
2
1
1
1
1
0
2
2
1
1
1
1
0
0
1
1
2
0
0
1
2
1
2
0
1
1
1
1
0
0
2
1
1
2
1
0
2
0
1
2
2
1
0
0
2
1
0
0
0
2
0
1
0
1
0
1
1
1
1
0
2
0
0
1
1
1
1
0
1
0
0
1
1
1
0
1
1
1
2
1
0
2
1
0
1
1
1
2
1
0
1
1
2
2
1
2
0
1
1
1
0
0
1
1
1
1
0
2
1
1
1
1
0
1
0
1
1
1
0
2
1
1
1
1
2
2
1
1
1
1
2
1
0
1
0
0
1
1
1
1
1
0
1
1
0
3
1
1
2
1
1
1
1
1
2
1
1
2
1
1
2
0
0
2
2
1
0
1
0
2
1
0
1
1
0
1
2
1
0
2
1
0
1
0
2
1
0
0
1
0
1
2
1
1
1
1
1
1
1
1
0
1
0
1
0
1
0
1
1
1
1
2
0
0
1
0
0
0
2
1
1
2
0
1
1
2
2
1
2
2
1
0
2
1
1
1
1
2
1
0
0
1
1
0
2
0
1
1
3
0
2
1
1
2
2
1
0
1
0
2
1
2
1
1
0
1
2
1
1
1
1
1
1
2
2
1
2
0
2
1
2
2
2
1
2
0
2
2
1
1
2
0
1
1
1
0
0
1
1
1
0
1
1
1
0
0
0
1
2
0
2
1
1
1
1
0
1
1
1
1
0
1
0
1
1
0
1
0
1
2
0
1
1
1
2
1
0
2
1
1
1
1
0
1
1
1
2
2
1
1
1
0
1
2
1
2
1
1
1
2
0
0
1
0
1
0
0
1
2
1
1
0
1
2
3
2
1
1
1
1
2
1
0
1
1
1
1
1
2
1
0
1
0
1
0
1
1
2
0
1
1
1
2
2
1
1
2
1
1
1
1
2
2
1
1
2
1
1
1
2
1
1
1
1
0
0
1
1
1
0
1
1
1
1
0
1
0
2
2
1
1
1
2
0
0
2
2
1
1
0
1
2
1
2
0
1
1
2
1
1
0
1
0
0
0
1
1
1
2
1
0
0
1
0
0
1
2
1
0
1
1
1
1
1
1
1
0
1
2
0
1
1
1
1
0
2
1
0
2
1
1
0
1
1
1
2
2
1
0
1
0
1
1
1
0
2
0
2
1
1
1
1
1
1
0
1
0
1
1
0
1
0
0
1
2
1
1
1
1
0
1
1
0
1
1
0
2
1
1
1
1
2
1
0
2
1
1
0
1
0
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
0
2
1
2
2
2
1
1
1
1
2
2
3
1
3
1
2
1
1
2
1
2
1
0
0
0
0
0
1
2
0
2
2
1
0
0
1
1
0
2
2
1
1
0
0
1
1
1
2
0
1
1
1
1
1
0
1
1
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
0
2
2
1
1
3
1
0
1
0
2
1
2
0
1
1
2
0
0
1
1
1
2
1
1
0
1
0
4
1
2
0
2
1
2
0
0
1
0
2
1
2
2
1
2
1
2
1
1
1
1
1
1
1
1
2
0
2
1
1
1
1
0
2
1
1
2
1
2
1
2
0
0
0
1
1
1
1
1
1
2
1
2
1
2
1
0
2
1
2
2
0
2
0
0
1
2
1
1
1
2
1
2
1
1
1
2
1
0
1
0
1
3
1
1
2
0
1
1
1
0
2
1
1
0
2
0
0
1
2
1
2
0
1
0
1
1
1
1
2
1
1
1
0
1
2
1
1
1
1
1
1
0
2
1
2
1
0
1
1
1
1
1
1
2
1
1
0
0
1
1
1
2
1
0
2
1
2
0
2
0
2
2
1
1
1
1
1
2
1
2
1
1
2
1
3
2
1
0
1
1
1
1
1
1
0
0
2
1
1
1
1
1
1
1
1
1
1
2
2
0
0
1
0
1
1
1
2
1
1
0
1
1
2
1
1
1
1
0
1
0
0
1
0
2
1
2
0
2
2
0
1
0
1
1
0
1
1
1
1
0
2
1
0
1
1
2
2
2
1
2
2
0
1
1
1
1
1
1
3
2
1
2
0
0
1
1
1
0
2
1
2
0
1
1
1
2
0
1
1
1
1
1
1
1
2
1
2
1
2
1
1
0
1
0
0
2
1
1
1
1
1
1
2
0
0
2
1
1
1
1
1
1
1
0
1
1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
1
1
1
1
0
1
0
1
2
2
0
1
1
1
1
1
1
1
1
1
1
0
0
0
1
1
1
0
2
0
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
0
1
0
0
1
1
1
1
0
0
1
2
1
0
1
1
1
0
2
2
2
2
1
1
0
1
0
1
2
2
2
1
1
1
1
0
0
1
1
1
1
1
1
1
1
1
0
1
1
2
1
1
1
2
1
1
1
0
1
1
2
2
2
1
1
1
0
2
1
0
1
2
1
0
1
0
1
1
2
2
2
1
1
1
0
0
1
1
1
1
2
0
2
1
1
2
0
1
2
2
0
1
1
0
0
0
1
2
1
0
1
1
2
0
1
1
2
1
1
0
0
1
2
0
1
1
0
2
1
2
2
1
3
1
1
0
0
1
1
0
1
1
3
1
0
2
0
1
1
1
0
1
1
1
0
0
0
1
1
1
2
0
1
1
1
1
1
1
1
0
1
2
2
1
0
1
1
1
1
1
1
0
1
2
1
2
2
1
2
1
1
3
1
1
0
1
1
2
1
0
1
0
1
1
2
0
1
0
1
1
1
2
0
1
1
0
1
2
0
2
2
0
1
1
2
1
0
1
1
0
1
2
0
0
0
2
0
1
0
1
0
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
2
1
2
1
0
1
1
0
1
0
1
1
1
2
1
1
0
1
1
0
2
0
2
0
2
1
0
2
1
2
2
1
0
1
1
1
1
1
1
2
0
1
1
2
0
2
1
2
0
0
1
1
0
2
2
1
1
0
0
0
0
1
3
0
2
1
1
2
0
2
0
2
2
2
1
1
1
2
0
1
0
0
1
0
0
1
0
0
1
0
2
2
1
1
1
0
0
0
2
1
0
0
1
0
1
1
2
0
0
1
2
1
1
1
1
1
0
2
2
1
1
1
2
2
1
0
1
1
2
1
0
1
2
1
2
1
2
1
2
0
1
2
2
0
1
2
2
2
1
1
1
1
1
1
1
2
1
1
1
0
2
1
2
0
0
1
0
0
1
0
2
1
2
1
1
0
1
1
1
1
1
0
1
1
1
2
1
2
1
1
0
0
1
0
1
0
1
1
1
1
1
1
1
2
2
1
1
0
1
0
0
1
2
1
2
1
0
0
2
1
1
1
1
0
1
1
1
1
1
1
0
0
0
2
1
0
0
0
2
1
1
1
1
0
1
1
1
1
0
1
1
0
2
0
1
1
1
1
0
0
1
1
0
1
1
1
2
1
1
0
1
1
0
2
1
1
1
1
1
1
1
1
1
1
0
2
1
1
0
0
1
1
1
1
1
3
1
2
2
1
1
1
1
0
0
1
0
1
1
1
1
1
1
1
0
0
0
1
1
0
1
1
0
1
1
0
1
1
2
2
2
1
0
1
2
2
0
1
1
1
1
1
1
1
1
1
2
3
2
1
2
2
1
1
0
0
2
1
1
0
1
0
1
0
2
2
2
0
1
1
0
0
2
0
0
1
1
3
1
1
0
0
2
1
0
0
0
0
0
1
2
1
2
2
1
1
2
2
0
1
0
2
0
1
0
2
1
1
2
2
2
2
0
2
1
0
2
1
1
2
0
0
2
1
1
1
0
1
1
2
2
1
1
0
2
1
1
1
1
1
1
2
1
2
2
0
1
1
1
1
1
0
0
1
1
0
1
0
1
0
0
1
2
1
1
1
1
1
0
2
0
2
2
0
2
1
1
1
1
2
2
2
1
1
1
1
2
2
0
0
1
2
2
2
2
1
2
2
1
2
1
1
2
1
1
2
0
1
1
1
1
1
0
2
1
2
0
2
0
1
1
2
0
1
1
2
0
1
1
1
1
0
2
1
1
0
1
1
0
2
1
0
1
1
1
0
0
0
2
1
0
1
2
0
1
1
1
0
1
2
1
0
1
0
0
0
0
1
0
0
0
1
1
2
2
2
1
0
1
0
0
1
2
1
1
1
1
0
1
1
1
0
0
2
1
2
2
0
0
1
0
2
1
1
1
1
1
2
1
2
0
1
2
1
1
1
1
1
1
1
1
1
1
0
0
0
0
0
2
2
1
1
1
1
0
0
0
1
2
2
1
2
2
1
2
1
0
0
0
1
1
0
1
0
1
0
1
1
1
0
1
1
1
1
1
1
2
3
2
1
1
1
1
1
1
2
0
1
0
1
1
1
1
1
1
1
1
1
2
1
1
1
0
2
0
1
2
1
1
1
2
1
1
2
2
2
2
1
2
2
1
1
1
0
1
2
1
1
1
0
1
0
2
1
2
2
0
1
1
1
2
1
1
1
2
1
0
1
1
1
1
2
1
1
0
2
2
1
1
0
2
1
0
2
0
0
1
1
1
1
1
2
1
2
2
1
1
1
2
1
1
1
0
1
1
0
1
2
1
1
1
1
1
0
0
2
1
2
0
1
1
1
0
2
2
0
2
2
2
1
1
0
1
1
0
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
2
1
1
1
0
1
0
1
1
1
1
0
0
0
2
0
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
0
1
0
4
0
1
1
1
0
1
0
0
1
1
0
1
0
1
0
0
2
0
1
1
2
1
2
1
1
1
0
2
1
1
1
0
1
3
0
0
1
1
1
0
1
1
1
2
1
1
1
0
1
1
2
2
0
1
2
1
2
1
0
1
1
2
1
2
0
1
1
1
1
0
2
1
0
2
1
1
0
2
1
1
0
0
2
2
1
2
1
0
0
2
1
2
0
1
0
1
0
1
1
0
1
1
0
1
1
1
1
2
2
1
2
1
1
6
2
1
1
2
1
2
1
1
0
1
2
1
1
0
2
2
2
1
0
1
1
1
1
0
0
1
1
0
1
1
2
1
2
1
1
1
1
2
2
1
2
1
1
2
0
1
1
2
1
2
0
2
1
1
1
1
0
1
0
1
1
1
1
0
2
2
2
0
1
2
2
2
1
1
1
1
1
1
2
0
1
0
0
2
1
2
0
1
1
2
1
1
1
1
0
1
2
3
1
1
1
1
2
1
1
1
1
1
0
1
0
2
0
1
0
0
2
0
1
1
1
0
0
2
1
1
1
2
0
1
0
2
1
1
1
2
0
1
1
0
2
1
1
0
1
1
2
2
0
0
0
1
1
1
1
2
1
1
1
1
2
1
2
1
0
3
1
0
2
1
0
0
1
1
0
1
1
1
1
0
0
2
1
1
0
1
1
2
1
2
2
1
2
1
1
1
1
1
2
1
1
1
2
2
0
1
2
2
1
2
1
1
0
2
2
2
1
1
0
1
1
2
2
1
1
0
1
1
0
0
1
0
0
1
1
1
1
0
1
2
0
2
2
1
1
4
1
1
0
2
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
1
0
2
1
1
1
1
1
1
3
2
2
0
1
1
1
1
1
1
0
1
2
1
2
0
1
2
1
1
0
1
1
1
2
0
1
1
1
2
1
1
1
1
1
0
1
1
0
1
2
1
0
2
1
1
2
0
0
1
0
0
1
2
1
1
1
0
1
1
1
1
0
1
2
1
2
1
2
0
1
1
1
1
1
0
1
0
1
1
1
2
1
1
1
1
2
2
1
0
1
1
1
1
3
1
1
0
0
0
2
1
2
1
1
0
1
1
1
1
1
1
0
1
1
1
1
1
2
1
0
1
1
1
2
1
1
1
2
1
1
2
2
0
1
0
2
1
2
2
1
2
1
1
0
1
2
2
1
0
1
1
1
2
2
0
0
0
1
2
1
0
0
1
1
1
0
1
1
1
2
1
2
2
0
1
2
2
0
1
1
0
1
1
1
1
1
1
2
1
1
1
2
0
1
0
1
1
1
0
0
1
0
1
2
1
1
1
1
1
0
1
0
1
1
1
1
1
1
1
0
1
0
0
1
1
0
1
0
0
1
2
2
1
1
0
0
1
2
1
2
1
1
1
0
1
1
0
1
1
1
2
1
1
1
1
2
1
1
1
1
1
2
1
1
0
1
3
1
0
2
0
1
2
1
0
2
0
1
1
2
2
2
0
1
2
2
1
1
1
1
1
1
2
1
1
2
1
1
1
1
0
1
2
0
2
3
1
1
1
2
1
1
2
1
1
1
0
1
1
2
2
1
1
1
1
0
1
1
0
1
1
1
1
1
0
1
1
2
2
1
2
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
2
1
0
2
1
0
1
2
2
2
0
0
2
2
1
1
1
0
0
1
0
1
0
0
1
0
1
0
3
0
0
1
0
2
0
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
2
0
1
0
0
1
1
1
2
0
1
1
1
1
2
2
2
1
0
1
2
0
1
1
1
1
1
1
0
1
2
1
1
1
0
1
1
1
0
2
1
2
1
1
1
1
1
1
0
1
1
1
1
2
1
1
2
0
1
1
1
2
0
0
0
0
2
0
1
0
0
1
1
1
2
2
2
1
0
2
0
1
1
2
2
1
2
1
1
1
1
0
1
0
1
1
0
1
1
1
1
0
1
0
1
1
0
1
1
0
1
2
2
2
0
1
1
1
1
0
2
2
0
2
1
1
1
1
1
1
1
0
2
1
2
0
1
1
1
1
0
1
1
1
1
1
1
1
0
0
1
1
1
1
1
2
2
1
1
1
0
1
1
0
0
0
1
1
2
1
1
2
2
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
0
1
0
0
0
1
0
2
0
2
1
1
1
2
1
2
1
2
1
1
0
1
2
1
1
1
1
0
1
1
2
1
1
1
1
1
2
1
0
1
1
1
1
1
0
2
0
1
1
1
1
2
0
1
1
1
1
1
0
2
2
1
1
0
1
0
1
3
2
2
1
2
0
1
2
2
0
2
1
2
0
1
1
1
1
1
0
1
1
1
1
2
0
0
0
2
0
1
2
0
1
1
1
1
1
1
2
1
2
1
1
1
0
2
2
1
2
2
1
1
1
1
1
2
1
1
2
0
1
2
0
0
1
2
1
1
0
1
0
1
2
2
1
1
0
1
2
2
1
1
1
0
1
1
1
0
2
1
1
1
1
2
0
1
1
1
1
1
1
1
1
3
1
2
2
2
1
1
1
0
1
2
1
0
0
1
2
1
2
2
0
2
2
2
2
2
1
0
1
1
2
0
1
1
1
1
0
0
1
1
1
1
0
0
1
1
1
2
2
2
1
2
1
1
1
0
0
1
1
1
1
1
0
0
0
2
2
1
1
2
2
1
1
0
1
2
0
1
0
0
2
2
1
1
1
5
4
0
1
2
1
2
1
0
1
1
2
1
1
1
2
2
1
1
1
2
0
2
1
1
2
1
1
1
1
0
0
0
1
1
0
1
1
2
2
2
1
1
2
1
1
2
1
1
1
2
1
0
1
1
1
0
2
1
1
1
1
0
2
1
1
2
2
1
1
0
0
0
0
1
1
2
1
0
2
1
1
1
2
1
1
2
1
1
1
1
1
0
2
0
0
1
0
1
1
1
1
1
2
2
0
0
1
1
2
0
2
1
0
2
1
0
2
2
1
1
1
1
2
1
1
1
0
2
1
1
1
0
2
1
1
1
2
1
0
1
1
1
3
0
1
1
0
2
0
1
1
1
1
2
1
2
1
1
2
1
1
0
0
1
0
1
2
1
0
2
1
1
1
1
1
1
1
1
2
1
0
2
2
1
1
1
2
1
0
2
1
1
3
1
2
2
1
0
1
1
1
2
1
0
1
0
2
1
1
1
1
1
2
0
2
0
2
1
0
1
5
1
1
0
0
2
2
1
1
1
1
1
1
1
0
1
2
1
1
1
1
2
1
0
2
2
2
0
2
1
1
2
0
0
2
1
1
2
2
1
1
0
1
0
2
1
1
1
1
1
1
2
0
1
1
2
1
2
1
0
1
2
0
0
2
1
1
0
1
1
1
1
1
2
1
3
1
2
2
2
1
2
0
2
1
1
0
0
1
1
1
1
1
1
1
2
1
1
1
1
0
1
2
2
1
0
2
0
0
0
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
2
2
1
1
1
1
0
0
1
2
2
0
1
2
0
1
0
2
2
1
2
0
1
0
0
0
1
1
2
1
0
2
1
0
1
1
0
1
1
1
2
1
0
1
1
1
0
1
1
0
2
1
2
0
1
1
1
1
2
0
1
1
1
1
2
2
1
0
1
0
1
1
1
1
1
1
1
0
1
1
1
1
1
2
2
1
2
1
1
0
0
1
2
1
2
0
1
2
0
0
1
0
1
2
1
1
1
2
1
2
1
1
0
0
2
1
1
2
0
0
1
2
1
2
2
1
1
0
2
1
1
2
2
1
1
0
1
1
0
1
0
1
2
1
1
2
2
2
2
1
1
1
1
0
0
2
1
1
2
2
1
1
1
1
1
1
1
1
2
1
2
2
0
1
1
1
1
1
1
0
1
0
0
3
1
1
0
1
1
1
1
1
1
2
2
1
1
0
0
2
1
2
2
0
0
1
1
2
1
2
1
1
2
1
1
0
1
2
1
0
1
1
2
1
2
1
1
1
0
1
1
2
1
1
2
1
2
0
1
0
1
1
0
2
1
1
1
1
1
1
2
0
2
0
1
1
1
2
0
2
0
0
1
2
0
0
1
1
2
1
1
0
1
0
1
1
2
0
1
0
1
1
1
2
1
0
1
1
2
1
2
0
2
0
1
2
2
1
1
1
2
1
1
0
1
1
0
0
1
2
1
0
1
0
1
1
1
1
0
0
1
2
0
0
2
1
1
1
1
2
2
1
1
0
1
2
0
2
0
1
1
1
0
1
1
1
1
0
1
1
1
0
2
2
2
2
0
2
1
1
1
1
2
1
1
1
1
2
0
0
1
2
2
2
0
0
0
2
0
2
1
1
1
0
1
2
0
0
1
0
1
0
2
1
1
1
1
0
0
1
1
0
1
2
0
2
0
1
1
2
1
1
1
0
2
1
1
1
2
1
1
1
1
1
1
1
1
0
1
1
1
1
2
1
2
1
0
1
1
1
1
2
1
0
2
2
0
1
0
2
1
1
1
2
1
0
2
1
1
0
1
0
1
0
2
2
1
3
1
2
0
1
0
1
0
2
1
1
1
1
1
2
1
1
0
1
1
4
1
1
1
2
1
0
0
0
1
2
1
0
1
1
1
0
1
2
1
0
1
0
1
1
1
1
1
1
0
1
1
2
2
1
1
1
1
2
0
0
0
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
1
1
0
1
2
0
2
0
1
1
0
1
2
1
1
0
2
1
0
1
0
0
0
0
1
1
1
1
2
1
1
1
0
1
1
0
1
0
2
1
1
2
0
2
1
1
1
2
2
1
2
1
0
0
1
1
1
2
1
1
2
1
0
1
2
1
1
1
1
1
1
1
2
1
1
1
1
0
2
0
1
1
1
0
1
1
2
1
1
1
1
1
0
0
2
0
0
0
1
0
0
1
1
0
1
0
0
1
1
1
2
2
2
1
2
0
2
1
1
1
1
1
1
2
0
0
1
1
2
0
2
1
1
1
1
1
1
1
3
1
1
1
1
1
1
1
1
1
0
2
2
0
2
2
1
1
0
2
2
2
2
2
1
2
1
2
1
1
1
2
1
1
1
1
1
0
1
2
1
0
1
1
1
1
2
0
2
1
2
1
1
2
1
2
2
1
0
2
3
1
1
1
1
2
0
0
1
2
0
0
1
2
1
1
0
1
0
1
1
1
1
2
2
1
1
2
1
2
1
1
1
0
2
0
1
1
0
1
0
1
2
2
0
1
1
2
1
1
0
2
0
1
1
0
1
1
1
2
2
0
1
2
1
0
2
3
1
1
1
1
1
1
1
0
1
1
0
1
2
2
1
1
1
2
1
0
2
2
2
1
2
1
0
1
2
2
0
0
1
2
2
1
1
2
0
0
1
1
0
2
4
0
1
0
1
1
0
0
1
1
1
1
1
1
2
1
2
2
1
1
0
1
1
1
1
0
1
1
0
2
1
2
2
1
0
1
1
1
1
1
1
1
2
0
1
0
1
2
1
1
2
1
2
1
1
2
1
1
1
1
0
2
0
1
1
2
1
1
1
0
1
1
1
1
1
2
0
2
1
1
0
1
1
1
2
1
1
2
1
0
1
1
2
2
1
2
1
1
1
1
1
0
1
1
0
1
1
0
0
1
1
2
1
1
0
1
0
3
1
1
1
1
1
1
2
2
2
1
0
1
1
0
1
1
1
2
1
2
1
1
2
0
1
1
1
0
0
0
1
0
1
0
2
1
2
1
0
0
3
1
2
0
2
1
1
1
1
1
1
1
1
1
0
0
2
1
1
1
0
1
1
0
0
0
1
1
1
1
1
1
0
1
2
2
2
1
1
1
1
0
0
1
2
2
2
1
0
1
0
1
1
0
2
1
0
0
1
1
1
0
1
0
1
1
1
2
0
2
1
3
0
2
1
2
1
1
1
1
1
0
1
1
1
2
0
1
2
0
1
0
2
2
0
2
2
0
1
0
0
0
1
2
0
1
1
0
1
0
2
1
0
2
0
0
1
1
2
3
1
0
1
0
1
1
2
1
1
1
2
2
1
1
0
1
0
1
2
2
1
1
2
2
3
1
2
2
0
1
0
1
0
1
2
2
0
1
1
1
1
1
2
1
2
1
1
1
2
1
1
1
1
1
2
2
2
2
1
2
0
1
1
0
1
2
2
1
1
1
2
1
1
1
0
1
1
2
2
1
0
1
0
2
1
1
1
1
0
1
1
0
1
1
1
2
3
0
1
2
3
0
2
1
1
0
1
0
1
0
1
0
2
1
1
1
2
1
0
0
2
2
1
0
1
2
1
0
1
1
1
1
1
2
1
1
0
1
1
0
1
2
2
1
2
1
1
1
1
1
1
0
1
1
0
1
1
2
2
2
1
0
1
0
1
2
1
0
1
2
2
1
1
1
2
1
1
1
2
2
0
2
1
1
1
1
0
1
2
1
2
2
1
1
2
1
2
2
1
1
1
2
0
1
1
1
0
1
0
1
1
2
1
1
1
2
2
1
1
2
1
0
1
0
0
0
2
1
2
1
1
0
0
1
1
0
0
0
2
1
1
1
2
1
1
0
0
1
0
2
2
1
0
0
0
1
2
0
1
0
2
1
1
1
2
2
0
1
0
2
0
1
1
1
1
1
1
1
1
1
1
1
2
0
2
1
0
0
0
0
1
1
1
1
1
0
1
0
1
0
1
0
1
2
2
1
2
2
0
2
1
1
1
1
1
0
1
1
2
1
1
1
0
1
2
1
0
1
1
1
3
1
1
1
1
1
0
0
0
1
0
2
2
2
1
1
0
1
1
2
1
1
1
0
2
2
1
1
1
0
1
1
2
0
1
1
0
1
2
1
0
1
1
0
1
1
0
1
2
2
1
1
0
1
1
1
1
1
1
0
1
2
2
2
2
1
2
0
0
2
1
1
1
1
1
1
1
1
1
1
0
1
1
0
0
1
2
1
2
2
0
1
2
0
1
1
1
1
3
1
2
2
1
2
1
0
0
1
0
1
3
0
1
1
1
1
1
0
1
1
1
2
2
1
2
1
1
0
1
0
1
1
2
1
1
0
1
0
2
1
1
1
1
1
2
0
1
1
1
0
1
2
1
1
1
1
2
1
1
1
3
2
1
2
1
2
0
0
1
2
2
0
2
1
0
1
1
2
1
2
2
2
0
2
2
0
1
2
1
0
2
2
1
2
1
1
1
1
0
1
0
0
1
0
1
0
1
0
2
1
1
2
1
0
1
2
2
1
2
0
0
1
2
1
1
0
2
1
0
1
1
1
1
0
2
0
1
0
0
2
1
1
1
1
1
1
0
2
0
0
1
1
1
0
1
1
1
1
1
2
2
1
1
1
1
1
2
0
2
2
1
0
1
1
1
1
1
2
1
1
0
2
0
0
0
1
2
2
1
1
0
2
1
0
1
1
0
1
1
0
2
1
1
2
0
0
1
2
1
1
1
2
2
1
2
1
0
0
1
1
0
1
2
2
1
2
1
1
1
2
0
0
1
2
1
0
1
1
1
3
2
1
1
1
1
0
1
1
1
1
2
2
2
1
1
1
1
2
0
1
1
1
0
0
2
2
1
2
0
4
0
0
0
0
3
1
1
1
0
1
1
1
1
2
1
1
2
1
2
1
1
1
1
1
2
1
1
1
1
3
0
2
1
2
1
2
1
1
0
2
3
1
1
1
0
1
1
2
0
0
1
2
1
2
1
2
0
3
1
0
0
1
1
0
1
1
1
1
0
2
1
1
1
1
1
1
1
2
1
0
0
0
1
1
0
1
1
0
2
2
1
0
2
2
1
0
0
0
1
0
1
2
1
1
1
2
2
2
1
2
1
1
0
1
1
2
0
1
1
1
0
0
1
1
1
1
2
0
1
1
1
2
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
0
1
1
1
1
1
1
0
2
0
1
1
0
1
1
1
2
2
2
1
3
1
0
0
1
2
2
0
1
1
0
2
1
1
1
1
0
1
1
1
0
2
1
0
1
1
0
0
0
1
2
1
2
0
1
1
1
1
0
1
1
1
1
1
0
0
1
2
1
1
2
1
0
1
2
1
0
1
1
1
2
1
2
1
2
0
1
1
1
0
0
2
2
1
0
1
2
1
2
1
3
1
1
1
0
2
0
0
1
1
0
2
2
2
1
1
2
1
1
1
2
0
0
1
1
1
1
1
1
1
2
1
1
2
1
2
1
3
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
0
0
0
0
1
2
1
1
1
2
2
0
1
1
1
1
1
1
2
2
1
1
1
0
2
1
0
1
2
1
1
1
1
1
1
2
1
1
3
2
1
2
2
1
1
1
0
1
1
1
1
1
0
1
1
0
0
1
1
1
3
1
1
1
1
2
0
0
1
1
1
0
1
0
1
1
1
1
0
1
1
1
1
2
1
1
1
1
0
1
1
2
1
2
2
1
1
1
1
2
0
1
1
1
0
1
2
1
2
1
0
1
2
1
1
1
1
1
0
1
1
0
1
1
1
1
2
0
1
2
0
0
1
2
1
1
1
1
1
1
0
1
0
0
0
1
1
0
1
1
1
1
1
2
2
2
1
1
1
1
2
0
2
1
1
1
0
2
1
0
0
0
0
1
1
1
1
0
2
1
1
1
1
2
1
1
1
4
1
2
0
1
1
1
1
1
1
2
1
0
1
1
2
1
0
1
2
1
2
0
1
1
1
1
0
1
2
1
2
0
0
1
2
0
1
1
2
1
0
0
1
2
1
0
1
2
1
1
1
1
3
1
1
1
1
1
1
1
1
2
1
1
1
0
2
1
0
1
2
1
0
2
1
1
1
2
2
1
1
2
1
1
1
1
1
2
1
1
2
1
1
1
1
0
2
1
2
1
1
0
0
2
1
2
1
1
1
2
2
2
2
2
1
1
0
3
1
0
2
2
2
2
1
2
1
1
1
0
1
0
3
1
1
1
1
2
1
0
1
1
1
1
1
1
1
1
2
0
1
1
1
2
1
1
2
0
0
0
1
1
1
1
1
1
0
2
1
2
0
1
0
1
0
0
1
2
1
1
1
0
1
2
2
0
1
2
2
1
1
0
1
2
0
2
1
1
2
1
1
1
1
0
0
2
1
1
1
1
1
1
2
1
0
0
1
1
1
0
1
1
1
1
1
1
0
0
1
1
1
0
0
0
1
1
1
0
2
2
1
1
1
0
1
2
2
0
1
1
1
1
2
0
0
0
1
1
0
0
1
1
2
2
1
0
2
2
1
1
2
0
1
1
1
1
2
1
0
1
0
0
0
1
1
1
0
1
0
0
1
2
1
2
0
0
0
2
0
0
2
1
1
0
0
1
1
1
0
2
0
0
2
1
2
0
1
1
0
2
2
1
2
2
2
2
0
1
3
2
1
1
1
0
0
1
1
0
3
1
1
2
0
1
1
1
1
0
1
0
1
0
0
1
1
2
2
1
1
2
1
2
1
3
1
2
2
2
0
1
0
0
1
0
2
1
0
1
1
1
1
1
2
1
1
1
1
0
1
1
1
0
0
2
1
1
1
1
1
1
1
1
1
1
1
3
2
1
1
2
1
1
0
0
1
2
2
1
1
1
1
1
2
2
1
1
2
1
2
1
1
1
1
1
0
1
2
2
0
2
1
2
0
1
0
1
0
0
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
2
1
1
0
1
2
2
1
3
1
1
1
1
2
2
1
1
1
0
1
2
2
1
1
1
2
1
1
2
1
0
2
0
0
1
0
2
0
1
1
1
1
1
1
1
2
1
0
1
1
1
2
0
1
2
2
1
0
2
0
0
2
2
1
1
0
1
1
0
1
1
2
1
3
2
2
1
1
1
0
0
1
2
1
1
1
2
1
1
0
0
2
2
6
1
1
0
1
1
1
1
2
0
1
1
1
1
1
1
2
1
1
2
2
1
1
0
1
1
1
1
1
0
2
2
1
1
1
1
2
1
1
0
1
0
0
1
0
1
2
1
2
1
1
1
2
0
1
1
1
0
0
1
1
1
1
1
1
1
1
0
1
2
2
1
0
0
0
0
3
1
1
1
0
1
1
1
1
1
1
0
1
1
0
1
2
1
1
1
2
1
2
1
0
1
1
1
1
0
2
2
1
0
2
1
1
2
1
2
0
3
1
1
1
1
2
2
0
2
1
1
1
2
0
1
1
1
2
1
1
1
1
1
1
0
1
2
2
2
1
2
0
1
1
0
1
1
1
1
2
1
1
0
2
0
1
1
1
0
1
1
1
0
1
0
2
1
0
1
0
1
2
0
0
1
1
1
1
1
0
1
1
0
1
1
1
2
1
2
1
0
1
1
1
0
0
2
2
0
1
1
2
1
2
1
0
0
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
0
1
0
0
0
2
1
0
2
1
1
1
0
1
2
2
1
1
1
1
1
1
1
1
1
2
1
2
0
1
1
1
1
1
1
1
2
1
2
0
1
1
1
2
1
1
2
1
0
1
1
0
0
1
1
1
2
2
1
0
1
1
1
1
2
1
1
0
0
2
1
1
2
1
1
1
1
2
2
1
2
1
2
1
2
1
2
2
1
1
1
1
2
0
1
1
1
1
1
0
0
1
1
0
1
0
1
1
1
1
1
1
0
1
1
2
1
1
1
1
0
1
1
1
1
0
0
1
1
1
2
2
2
2
1
1
1
1
1
1
0
0
1
2
1
0
0
3
1
2
1
0
2
1
0
1
1
1
1
2
0
2
2
1
1
1
2
2
1
0
1
2
1
1
2
0
1
1
2
1
1
1
2
1
1
1
0
2
1
0
1
1
1
0
1
0
1
0
1
1
1
1
0
1
1
1
1
2
0
2
1
2
1
0
2
1
2
1
0
1
1
2
0
2
1
1
1
1
0
0
2
1
1
1
2
0
1
2
0
1
0
0
1
2
0
2
1
1
1
1
1
1
0
1
0
1
1
1
2
0
1
1
0
1
1
0
1
1
1
1
0
1
2
0
2
1
1
1
1
3
1
1
1
1
2
2
2
2
1
0
2
1
0
1
2
1
2
1
2
1
1
1
0
2
1
1
0
1
1
1
0
0
0
1
1
2
1
0
0
0
1
2
1
0
2
1
2
0
2
1
0
1
2
1
2
2
1
1
0
1
0
2
0
2
1
1
2
0
1
1
0
4
0
1
0
0
3
1
0
1
2
1
1
1
0
2
1
2
1
1
1
1
2
1
1
1
1
3
1
1
1
2
2
1
1
2
2
0
1
0
1
1
1
2
0
2
1
0
0
1
1
1
1
1
1
1
0
1
2
2
1
1
1
1
0
1
1
2
1
2
0
2
1
1
1
1
1
0
1
0
0
0
1
1
1
1
1
1
1
2
1
2
1
1
1
0
1
2
1
1
1
2
0
2
0
1
2
2
1
2
0
1
0
0
1
2
1
1
1
4
1
1
2
1
0
0
0
1
1
1
0
2
1
0
1
0
2
1
1
0
0
1
1
2
1
1
2
0
1
0
1
2
1
2
1
2
0
2
1
0
2
1
1
1
1
1
0
1
1
1
0
1
0
1
2
0
1
0
1
1
2
1
2
0
1
1
2
1
1
0
1
2
1
1
1
2
1
1
0
1
0
1
1
2
1
1
2
0
0
1
1
2
1
1
0
0
1
2
1
0
0
0
1
1
1
0
0
0
0
0
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
3
2
0
0
2
1
1
2
0
2
1
0
2
2
0
2
0
2
1
0
0
1
0
0
1
3
1
1
2
0
0
0
1
0
0
0
1
2
2
0
0
1
0
1
1
2
1
0
0
1
2
1
2
0
0
0
0
2
1
1
1
2
0
0
2
1
0
0
1
1
0
0
1
1
1
1
1
2
1
2
3
2
0
1
1
3
2
1
0
1
1
0
1
2
0
1
1
2
0
1
1
1
1
1
2
2
2
1
1
0
1
1
0
1
0
1
1
1
1
0
2
2
2
0
0
1
6
2
2
1
1
1
2
1
1
1
0
2
0
0
1
1
1
0
1
0
1
1
2
0
0
0
2
1
1
1
0
1
1
5
0
1
0
1
1
2
0
1
1
2
1
1
1
0
0
1
3
1
1
0
2
2
1
0
1
2
1
1
0
0
2
1
1
1
0
1
0
0
1
0
1
1
2
1
1
1
1
1
2
2
0
0
1
2
1
0
1
2
1
0
1
0
1
1
1
0
1
2
1
1
0
0
1
1
1
1
1
1
0
1
1
1
2
1
1
1
1
0
1
1
2
1
1
2
1
0
1
1
1
0
2
1
1
1
2
3
1
2
1
1
1
0
0
0
1
1
1
0
1
2
1
1
0
1
0
1
1
1
1
0
2
2
0
1
2
2
2
0
2
1
1
2
0
1
2
2
2
2
2
0
1
1
0
1
4
0
1
2
0
0
0
2
1
1
1
1
1
1
1
0
2
1
1
2
0
1
0
2
2
1
0
0
0
1
1
0
1
1
0
2
0
1
1
1
1
2
1
2
0
1
0
1
0
3
2
1
0
1
1
1
1
1
1
2
2
1
1
2
4
1
2
3
1
1
0
1
1
0
1
1
2
1
1
1
0
1
1
1
1
1
2
1
2
1
0
2
1
1
2
1
1
1
1
3
2
1
1
1
2
0
1
0
2
1
2
2
1
0
1
0
2
1
1
1
1
0
1
0
1
1
1
2
1
1
0
1
2
1
1
2
0
2
2
2
1
0
0
1
1
2
1
0
1
1
0
0
1
1
0
1
1
1
0
0
1
1
0
0
2
2
1
1
2
1
1
0
1
0
0
1
1
1
2
3
1
0
0
1
1
0
1
0
0
1
1
1
2
1
1
1
3
2
1
1
1
2
1
1
1
1
2
1
1
1
1
0
2
1
0
2
1
0
2
2
1
2
1
1
2
1
1
1
2
0
1
0
2
1
0
2
1
2
2
2
1
7
2
0
1
2
1
2
2
0
1
2
2
3
2
2
1
2
0
1
1
1
1
1
1
1
0
2
2
2
2
2
1
1
1
2
2
1
0
1
0
2
1
1
1
1
2
0
0
0
0
0
1
1
1
1
1
1
2
1
1
2
1
1
2
1
2
2
1
2
1
1
1
1
0
1
4
1
2
0
2
1
1
2
1
0
0
2
0
1
0
1
2
0
1
1
2
1
1
0
1
2
1
0
1
0
1
2
1
1
1
1
1
2
2
0
1
1
0
2
1
0
2
1
2
2
1
0
1
0
1
1
1
1
1
1
1
1
1
2
0
0
2
1
1
2
1
2
0
0
2
1
1
2
0
2
1
1
2
1
1
1
2
1
2
1
1
0
1
0
1
4
2
1
1
2
2
1
0
0
1
1
2
0
1
2
1
0
2
2
1
0
0
1
1
2
0
0
0
0
0
1
2
2
1
2
1
2
1
1
2
0
2
2
1
0
1
0
1
1
0
0
2
2
2
1
0
1
0
1
1
1
2
1
1
1
2
1
1
1
2
1
1
2
0
1
1
1
1
1
0
0
0
2
2
1
1
1
0
1
0
1
1
2
1
0
1
0
0
1
0
1
1
2
0
1
1
1
1
0
1
1
1
1
0
1
0
1
0
0
1
1
1
1
1
0
1
2
1
1
1
1
1
1
2
1
0
1
1
3
1
1
1
1
1
0
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
0
2
1
1
2
2
1
1
1
2
1
1
0
0
2
0
0
2
1
1
2
1
1
2
1
1
1
2
1
1
0
0
1
0
0
2
1
1
2
0
1
1
1
2
2
1
1
2
1
2
0
0
2
1
2
3
1
2
0
1
1
1
2
0
1
1
2
1
3
0
0
1
1
0
0
1
0
1
2
1
2
1
2
1
2
2
1
1
0
0
1
0
1
0
1
0
1
0
0
0
1
2
1
2
0
1
0
0
0
0
1
1
1
1
2
2
1
1
2
4
1
1
1
2
1
0
2
1
1
2
1
1
1
0
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
0
1
2
0
1
2
1
0
1
2
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
0
1
1
1
1
0
1
1
1
0
1
2
1
2
2
2
1
1
0
0
1
2
2
2
2
0
2
4
1
2
0
1
2
1
1
1
0
2
1
2
0
1
0
2
2
0
1
1
1
0
1
2
1
1
1
0
0
1
2
0
1
2
1
1
1
0
1
0
1
0
1
2
1
1
0
1
2
1
1
1
1
0
2
1
1
2
1
2
2
1
1
2
1
1
0
1
3
1
0
0
2
1
1
2
1
0
1
1
2
1
0
2
1
1
2
1
0
0
0
1
1
1
1
2
0
1
1
2
1
1
0
1
1
1
2
1
2
1
1
0
0
2
1
1
1
1
2
1
2
0
1
1
1
2
0
2
2
1
1
1
2
2
1
2
0
0
1
0
1
0
0
1
1
2
2
0
0
1
1
0
1
2
0
0
1
2
1
1
1
0
1
2
0
1
1
1
1
1
0
0
0
1
1
1
1
2
2
2
1
1
1
2
1
0
1
2
0
1
1
3
2
0
1
1
2
0
1
0
1
0
1
0
1
4
0
1
2
0
1
1
2
1
1
1
1
1
1
1
0
2
0
1
1
0
1
1
1
0
2
1
1
0
2
1
2
1
0
0
1
3
1
1
2
1
1
0
1
1
2
1
1
1
2
1
1
1
0
2
1
3
1
1
0
2
1
1
1
1
2
1
1
1
2
1
1
1
0
1
1
1
1
1
0
1
0
2
1
0
1
2
0
1
2
1
1
1
2
2
1
0
0
1
1
1
0
1
1
0
1
0
1
0
2
1
1
1
1
1
2
1
1
0
1
1
1
2
0
0
2
1
1
1
0
0
1
2
0
1
1
1
0
1
0
1
1
2
1
2
2
1
2
1
1
1
1
1
1
0
2
1
2
1
2
0
1
3
4
1
2
1
0
2
0
2
2
1
0
1
0
0
1
1
1
1
1
1
0
2
1
1
1
1
0
2
0
1
1
0
1
1
2
2
1
2
2
1
0
1
0
1
2
1
2
0
1
0
1
2
0
1
0
1
0
0
1
2
1
1
2
1
1
2
1
1
0
0
1
0
2
0
1
0
1
2
1
1
0
2
1
0
1
0
2
2
0
2
1
0
0
2
0
0
1
1
1
1
0
1
0
1
1
1
0
1
2
1
1
0
1
0
1
1
1
0
1
1
2
1
1
0
2
1
2
1
0
2
1
0
1
1
1
1
3
2
1
0
2
1
1
1
2
0
2
1
1
0
1
0
2
1
1
1
1
2
1
0
1
1
1
1
1
1
2
1
0
0
0
1
2
1
0
2
1
1
2
1
1
1
0
1
3
2
1
1
1
2
1
0
1
2
1
0
2
0
1
0
1
1
1
1
1
0
1
0
0
1
1
2
1
1
0
2
4
1
1
1
1
1
1
0
2
2
2
1
2
1
2
1
0
1
1
1
1
0
1
0
2
1
0
2
1
1
0
1
1
1
1
0
1
1
0
1
2
1
0
1
1
0
1
2
2
0
0
2
2
2
0
0
0
2
0
0
2
1
1
1
1
2
1
1
1
1
2
0
0
1
0
1
2
2
0
2
2
1
1
1
0
1
1
1
0
0
1
1
0
1
0
1
1
1
0
2
1
1
0
1
0
1
1
1
1
1
2
0
1
1
1
1
1
1
0
1
2
0
0
2
2
1
1
2
1
1
1
2
0
1
2
1
0
0
1
2
0
1
1
0
1
1
0
1
1
0
0
1
1
1
1
1
2
0
0
1
1
1
0
1
2
1
1
2
1
1
0
1
1
1
1
1
1
1
0
0
1
1
2
0
1
1
1
2
1
0
0
0
0
1
1
2
1
1
1
1
1
1
1
2
1
1
0
1
1
2
1
1
0
1
0
1
0
2
1
1
2
2
1
1
0
1
1
2
1
2
0
1
2
2
2
2
1
1
0
2
2
1
1
2
1
1
2
1
2
1
0
0
1
0
1
1
1
1
1
2
1
1
2
1
1
1
1
0
2
1
1
2
1
1
1
0
1
2
0
0
1
1
1
1
1
2
1
2
1
2
1
0
0
1
1
2
2
1
0
1
2
1
1
1
1
1
1
1
1
2
1
1
0
0
1
1
0
0
0
2
1
1
1
0
1
1
0
2
2
1
1
2
1
2
2
2
0
1
1
1
2
1
0
1
1
2
1
1
1
1
1
2
1
0
2
1
1
1
1
2
1
1
1
2
1
1
1
0
1
1
2
2
1
1
2
1
2
1
0
1
2
0
1
0
0
1
0
0
2
0
1
1
2
0
1
1
2
1
1
1
1
1
2
2
1
1
1
1
0
1
1
1
1
0
1
1
0
1
2
1
2
2
1
1
2
1
0
2
1
1
1
2
1
1
2
1
1
0
1
1
0
2
1
0
0
2
1
1
0
2
1
0
0
1
2
0
2
2
2
0
1
1
2
1
0
1
1
1
1
0
1
1
1
2
1
1
1
0
1
2
1
1
2
2
0
1
1
1
1
0
0
1
1
1
2
1
1
0
1
2
1
0
1
2
1
2
1
0
2
2
1
2
2
3
0
0
1
1
1
1
1
2
0
1
1
2
2
0
1
1
1
1
0
1
1
1
1
2
1
1
1
0
1
2
0
1
1
1
0
2
1
1
2
1
2
1
1
1
0
1
1
2
0
1
1
1
2
2
2
0
0
2
1
1
0
2
1
0
1
0
0
1
1
1
2
1
2
1
1
1
2
0
1
1
1
1
1
2
2
1
1
2
1
1
0
0
1
1
1
1
0
1
1
1
2
0
1
1
2
1
1
2
1
2
1
1
0
2
1
1
2
0
1
1
1
1
2
0
2
1
1
1
0
0
2
1
2
0
1
2
2
0
0
1
2
1
1
1
2
1
0
1
1
1
1
0
1
2
1
2
0
1
1
2
0
1
1
1
1
1
1
1
1
2
1
1
2
2
1
2
1
2
1
1
1
1
1
1
1
0
0
1
2
0
1
1
1
1
1
1
1
2
1
1
1
0
1
1
1
0
2
1
1
1
0
0
2
1
0
1
1
0
0
1
1
2
0
1
1
1
2
0
2
0
3
1
2
1
1
1
1
1
1
2
1
1
1
0
2
1
2
1
0
2
1
1
2
1
0
1
1
1
1
2
0
1
2
2
1
1
1
1
1
2
1
1
0
0
1
1
1
2
0
1
1
2
1
2
3
1
2
1
0
0
1
1
1
0
1
1
0
0
2
1
1
1
1
1
1
1
1
2
1
2
1
1
1
2
1
1
1
1
1
2
2
1
2
2
1
2
1
1
1
0
2
1
1
2
1
1
2
1
2
1
1
2
4
2
1
0
1
2
0
1
1
2
1
1
4
1
2
2
1
1
1
1
1
1
0
1
2
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
0
0
1
1
0
1
0
1
1
1
1
1
2
2
2
1
2
3
0
1
0
0
1
1
2
0
1
1
0
0
1
0
1
0
2
1
1
1
1
0
1
1
1
2
1
2
0
1
1
2
1
2
1
0
2
0
1
1
2
1
2
1
1
1
1
2
0
1
1
1
1
1
0
1
1
2
1
1
2
1
1
1
2
2
1
1
1
2
0
2
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
0
0
1
1
1
1
0
0
1
0
1
1
1
0
0
0
1
1
2
1
1
1
0
0
1
1
0
1
2
2
2
1
1
1
0
1
1
2
1
1
1
1
1
1
1
2
1
1
0
0
2
1
0
0
0
3
1
0
1
1
0
1
1
2
0
0
1
1
1
1
0
1
0
1
1
0
2
1
1
1
0
3
0
1
0
0
0
2
1
1
1
1
2
1
2
0
2
0
2
2
1
1
1
1
1
1
2
0
0
1
1
1
1
0
1
1
2
2
1
1
1
0
0
1
1
1
1
2
1
1
0
1
1
1
1
2
0
1
1
1
1
2
1
2
0
0
1
2
1
2
1
1
1
1
1
0
0
2
1
2
0
2
2
2
0
2
2
1
2
0
0
1
0
1
0
0
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
0
1
1
1
1
2
2
2
0
1
2
0
2
1
3
1
0
1
1
1
0
3
1
2
0
1
1
2
1
1
2
2
2
1
2
2
1
1
1
1
0
2
2
1
1
1
1
1
1
1
1
1
0
0
2
0
0
1
1
1
2
2
1
2
2
2
1
0
0
1
1
0
0
0
1
1
1
0
1
0
2
1
2
1
2
2
2
1
1
1
1
1
1
0
1
1
1
2
1
1
0
1
1
1
1
2
1
0
1
1
0
0
0
2
1
2
0
1
2
3
1
0
1
2
1
1
1
2
0
1
1
2
0
1
1
1
1
1
1
2
1
0
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
0
1
2
2
1
2
0
1
1
1
2
1
2
2
1
2
1
3
2
1
2
0
1
2
1
0
2
0
1
2
1
2
2
0
1
2
1
1
0
1
1
1
2
1
1
1
1
0
0
2
1
1
1
1
1
1
1
1
1
1
0
1
0
0
0
1
1
1
1
1
2
0
1
1
1
1
0
1
1
1
0
1
0
0
1
1
2
0
1
2
2
2
1
1
1
1
2
0
1
1
2
1
0
2
2
1
2
0
1
2
1
2
2
1
1
1
2
2
1
0
2
2
1
0
2
1
1
2
1
0
0
1
1
1
0
0
1
2
0
1
0
1
1
2
1
1
1
1
1
4
0
1
0
2
1
1
0
1
1
1
1
1
1
1
0
1
1
0
2
1
2
0
1
0
2
2
2
1
0
1
0
0
0
2
1
1
1
1
2
1
2
1
2
2
2
0
0
1
1
1
1
2
0
1
1
1
1
0
2
0
0
1
0
1
1
1
2
1
1
1
1
0
0
2
2
1
1
0
1
1
1
1
1
0
1
2
0
1
2
1
1
1
1
2
2
0
1
1
2
1
0
0
0
1
1
1
4
0
1
0
1
1
1
1
2
1
2
1
0
1
0
1
1
0
2
1
1
2
0
2
1
1
2
2
1
0
1
0
1
1
1
0
1
1
1
0
1
1
1
0
1
1
1
1
2
0
1
0
1
1
1
2
1
0
1
0
1
0
1
0
1
2
1
1
1
1
2
2
1
2
1
2
1
1
2
2
2
1
1
2
2
1
2
2
0
2
1
1
0
0
0
1
1
1
1
1
2
0
1
1
1
1
1
1
1
2
2
2
1
1
0
1
0
1
1
0
2
0
0
1
1
1
2
0
1
1
0
1
2
1
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
2
1
2
1
1
0
0
1
2
1
1
1
1
1
0
2
2
2
1
1
2
2
0
1
2
1
1
0
2
0
2
1
1
1
1
1
2
2
2
2
2
1
2
0
1
2
1
3
0
1
1
1
1
1
0
0
1
1
1
0
1
1
2
1
0
0
0
2
0
0
1
2
2
2
1
2
2
1
2
1
1
1
2
1
1
1
1
1
0
1
0
2
1
2
1
2
1
2
1
2
2
1
0
2
1
0
0
1
1
1
1
0
2
2
1
1
0
4
0
0
2
0
4
1
0
2
0
1
1
1
3
2
1
1
1
0
2
0
2
2
1
0
2
1
1
2
0
1
1
1
1
1
1
0
1
1
1
1
2
1
1
2
0
0
1
1
1
1
1
1
0
1
1
1
2
1
1
0
0
1
1
1
2
1
1
0
1
2
1
1
1
1
2
2
2
2
1
1
2
1
0
1
1
3
1
1
1
1
1
1
1
1
1
2
1
0
2
2
2
1
0
1
1
1
0
0
1
1
1
0
1
1
0
1
2
2
1
0
1
1
1
2
0
1
1
1
1
1
2
0
0
0
1
1
1
1
1
1
1
2
1
0
1
1
2
2
0
1
0
1
1
1
1
1
1
0
1
1
0
2
0
2
2
1
1
1
1
0
0
1
1
1
2
2
0
1
1
1
2
1
2
1
0
1
1
2
1
0
1
0
1
1
1
1
1
1
1
1
0
2
1
2
0
1
2
1
1
2
0
2
0
2
1
0
1
1
1
0
0
1
1
2
2
1
1
3
1
1
1
1
1
0
0
2
0
1
1
1
0
1
1
1
2
1
2
0
1
1
2
1
0
1
1
1
1
0
0
0
2
2
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
2
2
1
2
1
1
1
1
3
0
0
1
1
0
0
1
1
1
2
4
1
1
2
1
2
1
1
1
1
1
0
2
1
1
2
1
1
2
1
3
0
1
1
2
0
2
2
1
2
1
1
1
0
0
0
0
1
0
1
1
1
0
0
0
1
2
1
1
2
2
1
1
0
0
1
1
0
0
1
1
1
1
1
2
0
1
1
1
1
1
2
1
2
0
0
1
0
1
1
1
1
1
1
1
2
1
1
1
1
0
2
0
1
2
0
1
1
0
1
0
2
2
1
0
1
2
1
1
1
1
0
1
0
0
2
1
2
2
0
1
1
3
1
1
1
1
2
2
1
0
1
1
1
0
1
1
0
2
1
2
1
2
1
2
0
0
1
1
0
0
1
1
2
2
1
0
2
1
2
1
1
2
1
1
0
0
1
1
1
0
0
1
1
0
1
0
2
3
2
2
2
0
1
1
0
2
1
1
0
1
1
1
1
1
2
1
1
2
2
1
0
0
1
1
2
0
1
1
1
2
1
2
2
1
0
0
2
1
2
2
1
1
1
0
1
0
2
1
2
2
1
2
2
1
1
0
1
2
2
0
0
1
1
1
1
1
1
1
1
1
2
1
2
2
0
1
2
1
1
0
1
1
2
1
1
1
2
0
1
1
1
0
1
1
1
0
1
0
1
1
0
3
1
1
0
1
1
1
1
1
2
2
1
2
0
0
0
1
1
1
0
1
1
1
2
1
1
1
1
0
1
1
0
1
0
1
2
2
2
2
2
2
1
1
1
2
1
2
1
1
1
2
1
1
0
0
1
0
0
2
0
1
1
1
2
2
1
1
1
2
1
0
1
1
1
1
0
1
1
2
2
1
1
2
1
0
1
1
1
2
0
0
1
2
1
1
1
2
1
1
0
1
0
2
1
1
1
1
2
1
0
2
1
1
0
0
0
1
1
1
2
0
0
2
1
1
0
1
0
1
2
0
1
1
2
0
2
0
1
0
0
2
1
1
1
1
0
0
0
0
2
1
0
1
1
0
1
1
1
1
1
0
2
1
1
1
2
0
1
1
1
1
1
1
2
1
2
1
1
1
2
1
2
2
1
1
0
1
1
2
2
0
1
1
1
1
1
2
1
1
0
1
1
0
1
1
2
2
1
1
1
1
1
1
1
1
1
0
1
1
1
0
2
0
0
1
1
1
1
1
2
2
0
2
0
0
2
0
1
1
1
1
1
1
1
2
1
0
1
1
1
1
1
1
0
2
0
0
0
0
1
0
2
0
1
1
1
1
0
0
2
1
2
2
0
1
1
0
1
1
0
1
1
2
1
2
1
1
2
0
1
0
1
1
2
2
3
2
2
1
2
1
0
1
0
1
1
1
1
2
1
1
1
4
0
1
1
2
1
1
1
1
1
1
1
0
1
0
1
1
1
1
1
0
1
1
2
1
1
2
1
1
1
1
1
1
1
3
1
1
0
0
0
1
0
2
1
1
0
0
2
1
1
2
2
1
2
2
2
1
1
0
1
0
0
0
0
1
1
0
0
1
1
1
2
1
1
1
1
1
2
1
0
1
1
2
0
2
0
1
1
1
0
1
1
0
2
2
7
1
2
1
2
0
1
1
1
2
1
0
0
0
0
1
1
1
1
1
1
2
1
2
1
1
1
0
1
1
1
1
1
1
0
0
0
1
1
1
1
1
0
1
0
1
1
0
0
0
1
1
1
1
2
0
1
2
0
0
0
2
1
1
0
1
0
2
1
2
1
1
1
1
1
1
0
2
1
1
1
0
1
2
0
2
1
1
0
1
1
1
1
1
1
0
1
2
2
1
1
2
0
2
1
1
0
0
1
1
1
2
1
1
3
1
1
2
1
1
1
0
2
1
1
1
1
0
1
1
1
2
2
1
1
1
0
2
0
1
1
1
1
1
1
2
3
1
1
0
1
2
1
1
0
1
1
1
2
1
1
2
2
1
2
1
1
1
1
0
1
1
1
1
0
0
1
0
2
0
2
2
1
0
1
2
0
1
1
2
1
0
2
1
1
1
1
1
2
0
1
0
2
1
2
1
0
0
0
0
1
1
1
1
2
0
0
0
1
0
1
1
2
1
1
2
0
0
1
1
1
0
2
0
2
2
1
3
1
0
0
1
0
1
1
1
2
1
0
2
2
0
2
0
1
0
1
2
0
1
1
1
1
0
1
1
1
1
0
1
2
1
2
0
2
2
1
0
0
2
1
1
1
1
1
1
2
2
1
0
1
0
1
0
0
1
1
0
1
1
2
1
0
1
1
1
0
1
2
1
0
2
2
0
1
2
1
1
1
1
1
1
1
0
1
1
2
0
1
3
2
1
2
1
2
1
2
1
1
1
2
0
1
1
1
2
2
2
0
2
1
2
1
1
1
2
1
1
1
1
2
1
1
1
0
1
2
0
2
0
2
0
1
1
1
1
1
2
0
1
1
1
2
1
0
0
2
2
0
0
0
2
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
0
1
1
1
1
1
1
1
1
1
0
1
1
1
1
2
0
1
2
2
2
1
1
1
2
1
1
1
1
1
0
1
1
1
2
2
1
2
1
1
0
1
1
1
0
1
2
1
1
2
1
2
0
0
0
3
1
1
1
1
1
0
1
0
2
0
1
1
1
1
1
1
1
1
2
1
2
2
0
0
0
1
1
1
0
1
1
1
1
2
2
1
1
1
1
1
0
2
1
3
1
0
2
1
2
1
0
0
1
1
1
4
1
1
1
0
0
1
0
1
3
1
2
0
1
1
2
0
1
0
1
1
0
1
2
1
2
2
0
0
1
0
1
2
1
1
0
0
0
1
1
1
2
1
0
1
0
1
0
1
0
2
1
0
2
1
2
2
2
1
0
2
1
1
1
1
1
1
2
2
0
1
2
1
1
1
1
1
1
0
2
0
2
1
0
1
0
1
2
1
0
0
0
2
3
0
4
2
1
2
2
2
1
2
1
2
0
2
1
1
1
0
1
1
1
1
1
2
0
2
1
1
1
1
1
1
2
0
0
1
1
1
1
0
1
1
2
1
0
1
1
1
1
1
2
1
1
1
2
1
0
1
1
1
0
1
2
1
2
2
2
1
0
1
2
2
0
1
0
1
0
2
1
0
1
3
0
1
2
0
2
1
1
2
1
1
1
1
2
0
0
1
0
2
1
2
2
1
1
1
0
2
0
2
2
1
1
1
1
0
2
1
2
1
0
0
3
1
0
1
1
1
2
1
2
1
2
0
0
0
0
2
1
2
1
0
0
1
2
1
1
2
1
1
0
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
0
1
0
1
0
1
1
1
1
1
0
1
1
1
1
0
2
1
1
1
1
2
2
1
0
2
2
1
2
1
0
0
2
1
1
1
1
2
1
1
1
1
2
1
0
0
2
1
1
1
1
1
0
1
1
2
2
1
1
0
1
1
1
0
1
1
0
3
1
2
2
0
1
1
2
2
1
1
0
0
1
1
0
2
1
1
2
2
2
1
0
1
2
2
2
1
0
1
0
2
1
2
1
2
1
1
2
1
1
1
2
1
1
1
1
2
1
0
1
1
1
1
1
1
1
0
2
1
1
1
1
2
0
2
1
0
1
2
2
2
1
1
1
0
1
1
1
1
1
1
1
0
3
1
1
0
0
1
2
0
1
1
0
0
1
1
0
0
1
1
0
0
2
0
2
2
2
1
1
2
1
1
1
2
1
1
0
1
2
2
1
0
1
1
1
1
2
0
0
2
1
1
1
1
2
1
1
2
2
0
1
2
0
2
0
1
1
1
0
1
2
2
0
1
1
1
2
0
1
1
0
2
0
1
1
2
1
1
0
2
0
1
0
1
2
1
1
0
0
0
2
1
2
1
1
3
1
2
2
2
2
1
1
1
2
0
0
1
1
1
0
1
0
1
2
1
1
1
1
1
1
1
2
1
1
0
1
1
1
2
0
1
1
2
2
2
2
1
0
2
0
1
2
1
0
1
0
0
0
1
0
0
1
1
1
1
1
1
1
2
3
0
2
2
0
2
1
1
0
0
0
1
0
1
0
0
2
0
1
1
1
1
2
2
2
1
0
1
1
2
1
2
0
1
1
0
0
1
1
1
1
2
2
1
1
2
0
2
0
1
1
1
1
2
1
2
0
2
2
2
2
1
1
1
0
2
1
1
1
0
0
2
1
2
2
1
1
2
1
0
1
2
1
1
1
0
0
1
1
2
1
1
1
1
2
1
1
1
0
1
1
1
1
1
2
0
0
1
1
2
1
0
1
1
1
1
2
2
1
1
2
0
1
1
1
2
1
1
1
2
1
1
0
2
1
0
0
1
2
0
1
1
2
1
1
0
0
0
1
1
1
1
1
0
2
1
0
2
1
0
1
1
2
2
1
0
1
0
1
1
1
1
1
1
1
0
0
0
0
2
1
1
0
1
1
1
0
2
2
1
1
1
1
2
1
1
1
2
1
1
0
2
1
1
2
1
1
0
1
0
2
2
2
1
1
1
1
1
0
0
1
1
2
1
1
1
1
2
1
2
1
2
1
2
1
1
1
1
1
0
1
1
2
1
1
2
1
2
1
0
1
2
2
1
1
0
0
0
1
1
2
2
0
1
1
0
2
1
1
1
2
2
1
1
0
0
2
1
1
1
0
1
2
1
1
1
1
1
0
1
1
2
1
2
1
2
0
0
0
1
1
1
0
1
1
1
1
1
0
1
1
1
2
2
2
1
2
1
0
2
0
1
1
1
1
1
1
0
1
0
2
0
2
1
1
0
1
1
1
2
1
2
1
1
1
1
0
1
2
2
1
0
1
2
2
1
1
1
1
0
1
1
1
1
1
0
2
0
2
1
2
0
2
2
1
2
0
2
1
1
1
2
0
2
1
1
1
1
1
1
1
2
1
0
1
0
1
1
0
0
0
1
2
0
0
2
1
1
2
2
1
1
0
1
1
2
1
1
1
1
1
1
0
1
1
1
2
1
0
1
0
2
1
1
1
1
0
1
1
0
2
1
0
2
0
1
2
0
1
2
2
1
0
0
0
1
0
2
2
1
1
2
1
0
1
1
2
1
1
3
1
0
1
1
2
2
1
0
1
0
0
2
2
0
1
1
2
0
2
1
2
0
1
2
2
1
1
2
1
1
1
2
2
1
1
0
1
0
1
1
2
1
2
0
1
1
0
2
2
1
1
1
1
1
1
2
1
0
0
0
3
1
1
0
1
1
0
1
2
0
1
1
1
1
1
1
3
1
0
1
1
0
1
1
1
2
0
0
0
1
0
1
1
2
0
2
0
0
1
0
1
1
2
0
3
1
1
1
1
0
1
0
0
0
1
1
0
1
1
0
1
1
2
1
1
1
2
1
2
1
1
1
2
1
1
0
0
1
1
1
1
0
0
2
1
1
1
1
0
0
2
1
1
1
0
1
2
2
1
2
1
1
1
0
1
0
1
1
2
2
1
2
1
2
1
0
1
1
1
1
0
1
1
7
0
1
2
1
1
1
1
0
2
1
1
2
1
1
2
1
1
2
1
2
1
1
0
2
2
1
2
1
1
1
0
0
1
1
0
0
2
1
0
1
0
0
2
2
0
2
1
1
1
1
1
2
1
1
1
1
0
0
1
1
1
1
0
0
1
1
1
1
1
1
1
2
1
0
1
1
0
1
1
1
2
2
0
0
1
2
1
1
1
1
0
1
1
1
1
1
2
2
1
1
0
1
2
1
2
0
2
1
0
1
1
0
1
1
2
2
0
1
1
2
2
1
0
1
2
0
1
1
1
1
1
1
1
0
1
1
2
1
2
2
1
1
1
1
1
2
1
1
2
0
1
1
1
2
1
2
1
0
1
1
1
1
1
1
0
0
2
0
0
2
1
1
0
2
1
1
1
2
1
1
2
0
1
0
1
0
1
2
1
1
2
1
1
2
2
2
0
2
1
0
1
0
0
0
1
1
1
2
1
1
1
0
1
1
1
1
0
2
1
1
1
1
1
4
1
1
1
2
1
2
1
1
1
2
1
2
2
1
2
1
2
3
3
1
1
1
1
2
1
1
1
0
0
1
0
1
0
1
1
1
2
1
2
2
0
1
0
1
1
1
1
1
1
2
2
1
1
0
1
2
2
0
0
2
2
2
1
0
1
1
1
1
1
1
0
0
0
1
2
2
1
1
1
0
1
2
0
2
1
0
1
1
1
1
2
2
1
1
2
0
2
1
2
1
1
1
2
0
0
1
1
1
0
1
1
1
0
2
1
1
2
2
1
1
2
0
1
1
0
1
1
2
1
2
1
1
1
1
1
2
1
1
0
2
0
0
1
0
0
0
0
0
2
1
1
2
0
1
2
0
1
1
2
2
1
2
0
1
0
2
1
1
1
1
1
1
0
0
1
2
2
1
0
0
0
2
2
1
2
2
2
1
0
0
1
1
1
1
1
2
1
2
2
1
1
0
1
0
1
1
1
1
1
1
1
0
2
1
0
0
0
0
2
2
1
0
1
1
2
1
1
0
1
1
1
1
1
1
1
1
1
1
2
1
1
1
0
1
2
0
1
1
1
1
2
1
1
2
1
1
1
2
1
2
0
2
2
1
1
1
1
2
2
0
1
1
2
1
1
1
1
0
2
0
2
1
2
1
1
0
0
1
1
1
2
2
1
2
2
1
1
2
1
1
2
1
1
1
1
3
2
0
1
1
1
1
1
1
2
1
0
1
1
2
1
1
1
1
2
0
2
1
1
3
2
0
2
0
1
1
0
1
1
2
2
1
1
2
1
1
1
2
1
1
0
0
1
1
0
0
1
1
4
1
1
0
1
1
0
1
1
1
0
1
0
2
1
2
1
0
2
2
0
1
0
2
2
2
0
2
1
2
0
0
0
0
2
2
1
0
1
1
2
0
0
2
1
1
0
1
1
0
1
2
2
1
0
1
2
1
1
0
1
1
0
1
0
0
1
1
1
2
2
1
0
2
0
1
0
2
2
0
1
1
2
1
1
1
0
1
2
1
1
1
2
2
0
0
0
2
2
1
1
1
1
0
1
1
2
1
1
2
0
1
1
1
2
1
1
1
0
0
0
1
1
1
1
2
2
1
1
0
1
0
0
1
1
1
0
1
2
2
2
2
2
1
2
1
1
0
1
1
1
0
1
1
1
0
2
1
1
1
1
1
1
0
1
2
0
1
0
1
1
1
1
2
0
1
1
2
1
1
1
2
2
1
2
0
0
1
1
1
0
1
1
0
1
2
2
2
1
1
1
0
0
1
2
1
1
2
1
1
0
1
1
1
1
2
2
1
1
1
2
1
0
1
0
0
1
1
2
1
0
2
1
1
0
2
1
2
2
1
1
1
1
2
0
1
1
1
1
3
1
1
1
2
2
1
2
1
1
0
1
1
2
2
2
1
2
2
1
1
1
2
2
0
2
2
0
2
2
3
1
1
2
1
0
1
0
2
1
2
2
1
1
1
2
1
0
1
0
0
1
2
0
1
0
1
1
1
0
2
2
0
0
0
1
0
0
1
1
1
1
1
0
0
2
1
1
0
1
1
1
2
1
1
1
1
1
0
1
1
0
1
1
2
1
1
0
1
1
1
1
0
1
2
1
0
0
2
1
1
0
1
1
0
1
2
0
0
1
1
0
1
0
1
2
1
1
2
1
1
3
1
1
1
1
1
2
2
1
1
1
2
1
2
1
2
1
1
2
1
0
1
1
1
1
1
0
1
2
2
0
1
1
0
0
2
1
1
5
1
2
2
0
0
0
1
1
1
1
1
2
1
1
1
1
0
1
1
0
1
1
1
2
1
1
2
0
1
1
1
2
1
0
2
1
1
1
1
1
1
0
1
1
1
0
1
1
1
1
1
2
2
2
0
0
2
0
1
4
0
1
1
1
4
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
0
1
1
2
0
1
1
1
1
1
1
1
0
1
1
1
1
0
1
1
2
1
0
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
0
0
0
0
2
1
1
0
2
2
1
0
1
0
2
1
1
2
1
1
1
2
0
1
0
1
0
2
1
2
1
0
1
1
0
2
2
2
2
0
0
2
1
2
1
0
0
2
2
0
1
1
0
1
0
1
2
1
2
1
2
1
2
1
1
2
2
1
2
1
2
1
2
1
2
0
1
1
2
1
1
1
0
0
2
1
3
1
1
0
1
1
0
0
2
0
1
1
1
0
0
1
2
1
2
0
0
1
1
1
1
2
2
3
1
1
1
2
0
1
2
0
0
2
1
1
1
1
0
1
0
0
1
1
2
1
1
1
2
1
1
1
1
2
2
0
4
1
0
0
1
1
0
2
1
0
2
0
0
1
1
1
1
0
0
1
1
0
1
1
2
2
1
1
1
1
0
1
1
1
2
1
2
0
2
2
1
0
2
0
1
1
0
1
1
0
2
2
2
1
0
0
1
1
1
1
0
0
1
0
1
2
1
1
1
1
1
1
1
1
1
2
0
2
1
0
1
1
1
1
1
1
1
1
1
1
2
2
0
1
1
1
0
0
1
0
2
1
0
1
2
1
1
1
0
1
1
0
1
1
0
1
1
1
2
0
2
1
2
1
0
1
1
0
2
1
1
2
1
1
0
1
1
1
0
2
1
1
1
0
1
1
0
1
2
0
0
0
2
0
2
0
1
2
1
2
2
2
2
1
1
2
2
1
1
1
1
2
1
2
2
1
1
1
1
1
0
0
1
0
0
0
2
2
0
1
1
1
2
2
1
1
1
1
1
1
0
1
1
3
1
0
1
2
1
1
1
2
1
0
1
0
1
1
1
2
2
1
4
0
2
1
1
1
0
1
1
1
3
1
1
1
1
1
0
1
1
1
1
1
1
2
2
2
0
2
2
1
1
2
1
0
1
1
0
1
1
1
0
1
1
1
1
2
2
1
1
1
0
2
1
1
1
2
0
0
1
2
1
1
2
0
1
1
2
1
1
1
1
1
2
1
1
2
1
3
1
1
1
1
1
1
2
2
1
2
1
1
0
1
1
1
1
1
1
3
1
0
1
2
1
2
1
1
2
0
1
1
1
2
1
2
1
1
1
1
2
1
0
1
1
1
2
2
0
1
1
1
1
0
1
2
1
1
1
1
2
0
0
1
1
1
0
1
0
2
0
2
2
0
1
2
0
1
1
0
1
0
0
1
1
0
1
2
0
0
1
2
1
1
0
0
2
1
1
1
1
1
0
0
2
2
1
1
2
1
1
0
1
2
1
1
2
2
2
1
1
1
1
1
1
1
1
1
1
1
0
2
1
0
1
1
1
1
1
1
0
1
2
1
2
2
0
2
1
2
2
2
2
0
2
2
1
2
1
1
1
1
2
2
1
0
0
0
0
1
2
1
1
2
1
2
1
1
0
1
0
1
2
2
2
0
1
1
1
1
2
1
2
1
0
2
1
1
1
0
1
2
0
2
1
2
0
0
1
1
1
0
0
1
1
2
1
1
0
0
1
1
1
1
0
1
1
1
0
2
0
1
0
2
1
1
1
1
1
1
1
2
2
2
2
3
2
2
1
1
0
1
0
1
2
2
1
1
0
0
0
2
1
1
1
1
1
1
0
0
1
0
3
0
1
0
1
1
1
1
0
1
1
0
1
1
1
1
1
0
0
1
1
1
0
2
0
1
0
1
1
1
1
0
1
2
1
0
1
1
1
1
0
0
2
1
2
1
1
1
1
0
2
1
2
1
3
2
1
1
1
4
1
1
1
2
1
1
1
1
1
0
2
1
1
2
0
1
1
1
2
1
1
0
0
2
1
1
1
1
2
1
2
0
1
1
1
0
2
2
2
1
1
1
2
0
0
1
1
1
0
1
1
2
1
1
1
1
0
1
0
1
2
2
1
0
2
0
2
1
0
0
0
1
1
1
2
0
0
1
1
1
1
0
1
1
1
1
1
2
1
0
0
1
1
1
2
2
2
1
2
2
1
2
3
1
1
1
0
0
1
0
1
2
0
1
0
1
1
1
1
1
1
2
1
1
1
1
1
2
0
1
0
1
1
2
2
1
1
1
0
1
1
1
2
1
0
2
0
1
0
0
1
1
1
1
0
0
2
1
1
3
1
2
1
0
1
0
0
1
2
0
1
1
0
1
1
2
1
0
2
1
0
1
1
1
1
1
0
2
1
0
1
1
0
1
2
1
1
1
0
1
1
1
0
2
1
1
1
2
1
1
1
1
1
2
1
2
2
1
2
1
1
1
1
1
1
0
2
0
0
0
0
2
1
1
2
2
1
0
1
0
1
1
1
0
0
1
2
1
1
1
1
0
2
1
2
2
2
1
1
1
1
2
0
2
0
0
2
1
1
0
0
2
1
0
0
1
2
0
1
1
1
2
0
1
1
0
2
2
1
1
1
0
0
5
1
1
0
0
2
1
2
2
0
1
1
1
1
0
1
1
1
0
1
0
1
0
0
1
0
1
2
0
0
1
2
0
2
2
0
1
1
2
0
1
1
1
1
0
0
1
2
1
1
2
1
1
2
1
1
1
1
2
1
0
1
0
0
1
1
0
0
3
1
1
1
1
1
1
1
0
1
2
0
1
1
0
1
0
3
0
1
2
2
2
1
2
1
3
0
1
1
1
1
2
1
1
0
0
0
1
1
1
1
0
1
0
1
2
0
1
1
0
1
1
2
2
1
1
1
1
1
1
1
1
0
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
0
1
1
1
0
1
1
2
1
0
1
1
2
0
1
0
1
1
1
1
0
0
3
1
1
0
1
1
2
2
1
1
1
1
0
2
2
0
2
1
1
1
2
2
1
0
1
1
2
2
1
1
1
2
1
0
1
0
1
1
1
1
1
2
2
2
1
1
1
0
2
1
1
1
1
1
1
1
1
1
1
1
1
0
1
2
0
1
1
1
1
1
1
0
2
0
1
2
1
1
2
1
1
1
1
0
1
0
0
2
0
2
1
2
1
2
2
1
1
1
0
0
0
2
1
1
1
1
2
1
1
1
1
1
2
0
1
1
0
1
1
2
1
2
2
1
2
1
1
0
1
1
2
0
1
0
2
1
1
1
1
2
1
1
2
1
1
1
1
1
3
2
1
0
2
1
2
2
2
2
1
1
1
1
1
2
1
2
2
1
1
2
2
0
1
2
1
0
1
2
2
1
1
1
1
1
1
1
0
0
1
1
1
1
2
0
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
3
1
1
1
0
2
2
1
1
0
2
2
1
1
1
1
0
1
1
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
0
1
1
0
1
1
1
1
0
1
1
2
0
1
1
2
0
2
1
0
1
1
1
1
1
1
1
1
1
1
0
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
0
1
1
2
1
1
0
1
1
1
1
0
0
1
0
1
2
1
1
0
2
2
1
1
1
0
1
2
0
2
0
2
2
0
2
2
1
1
2
1
1
1
1
2
1
2
1
0
1
1
1
1
1
0
1
1
1
1
2
1
0
2
1
1
2
2
1
3
2
2
1
1
2
0
0
1
2
1
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
2
1
2
0
0
2
1
2
1
1
1
2
2
1
1
0
1
1
1
0
1
1
1
0
0
1
2
1
0
2
1
1
1
1
2
0
1
0
2
0
1
0
0
1
1
0
2
2
1
1
1
1
1
0
2
2
1
2
2
1
0
1
0
2
0
1
1
1
2
1
0
0
1
1
1
1
1
1
1
2
1
2
0
1
0
1
1
1
0
2
1
2
0
1
1
2
1
1
1
2
1
2
0
2
1
0
1
1
1
4
1
0
1
3
0
0
0
1
0
1
1
2
0
2
3
2
2
2
2
1
1
1
0
1
1
1
1
0
1
1
1
1
0
1
1
0
1
2
1
1
0
0
1
0
1
1
1
1
1
1
1
1
2
2
1
1
2
1
3
2
1
2
0
2
1
1
1
1
2
1
2
0
1
2
2
1
2
1
1
1
1
1
1
0
2
1
1
1
1
2
2
0
3
1
2
1
2
0
1
1
1
1
2
1
1
2
2
1
1
1
1
1
0
1
1
1
2
1
2
2
1
1
1
1
2
1
1
1
2
0
1
1
3
0
2
1
2
1
1
1
2
1
0
2
0
1
1
1
2
2
0
2
1
0
0
4
1
0
2
1
2
2
1
2
0
1
2
1
1
2
1
1
0
1
1
2
0
1
2
3
1
2
1
1
1
1
1
1
1
2
0
2
1
1
1
2
1
2
1
0
2
1
1
0
2
0
3
0
1
0
0
0
0
1
2
1
0
2
1
1
2
2
2
1
1
0
0
1
1
2
2
1
0
2
1
2
2
1
0
0
2
0
2
1
2
2
1
1
1
0
1
2
1
1
1
2
1
0
1
0
0
0
1
2
0
0
2
1
0
1
1
2
1
1
1
1
1
1
1
2
1
0
1
1
0
2
1
2
0
1
1
0
1
2
2
1
1
1
1
1
1
2
1
1
1
2
1
1
0
2
1
0
1
2
1
1
1
0
0
1
1
1
2
1
1
0
1
1
1
1
1
1
1
1
2
1
2
2
1
0
2
1
1
1
0
0
1
0
3
2
2
1
1
0
2
2
1
1
2
1
0
1
0
2
1
1
1
1
1
1
0
1
1
2
1
1
1
1
1
2
2
1
1
1
2
1
1
1
1
1
0
1
1
2
1
0
2
1
2
0
1
1
1
1
1
1
0
1
2
0
1
0
2
1
3
1
2
1
1
0
2
2
0
0
1
1
1
1
1
1
0
0
0
0
2
1
1
1
1
1
1
0
1
1
1
0
2
1
0
1
0
0
1
1
1
1
2
2
1
1
1
2
0
0
1
1
1
1
1
1
1
2
2
0
1
0
1
0
0
1
0
0
1
1
0
2
2
1
1
1
1
1
2
1
2
1
2
1
1
0
1
2
1
0
1
1
1
2
1
1
0
2
1
1
1
1
2
2
1
0
0
1
0
1
1
1
1
1
3
1
0
1
0
0
1
1
1
0
2
1
1
1
2
0
0
1
1
1
1
1
1
1
2
0
2
1
2
2
1
1
1
0
1
0
2
1
2
2
0
1
1
1
2
1
0
1
1
1
1
0
0
2
1
1
1
1
2
0
1
0
1
2
1
1
1
2
1
0
1
0
0
1
2
1
1
1
0
0
0
1
1
2
1
0
2
0
1
0
1
0
0
2
0
0
2
1
1
2
1
2
1
1
1
2
0
1
1
1
0
0
2
0
0
2
1
2
2
1
0
1
1
1
1
2
2
1
1
2
0
1
1
0
0
1
0
0
0
0
1
1
1
2
1
2
1
0
0
0
1
0
2
0
1
1
2
2
1
2
0
2
1
1
1
1
1
1
0
2
0
1
1
1
1
0
2
1
2
2
0
1
3
0
1
0
1
1
2
1
0
1
1
0
1
1
1
1
1
0
0
1
1
1
2
1
1
1
0
2
1
1
1
2
0
1
1
1
1
1
0
1
1
1
0
0
2
1
2
1
1
2
0
2
0
0
2
2
1
2
1
1
0
1
1
1
1
1
0
2
2
1
1
2
0
1
1
2
1
2
1
2
2
3
1
1
1
1
1
2
0
1
1
1
2
3
1
0
0
0
1
1
2
1
0
1
1
0
1
1
1
2
1
2
1
2
1
1
0
0
1
2
1
2
1
2
1
2
1
1
1
0
2
1
1
1
0
1
0
1
2
2
1
1
0
1
1
0
1
2
2
0
0
1
2
1
2
2
0
1
2
1
1
2
0
0
2
1
1
1
1
0
1
0
1
1
1
1
1
1
1
1
2
0
1
1
0
0
1
1
2
1
2
0
1
1
2
1
1
0
2
1
1
1
1
1
1
1
1
2
0
1
1
1
1
1
0
2
1
2
1
1
0
0
0
1
1
1
1
1
0
0
1
3
1
2
2
1
0
3
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
2
1
1
0
1
1
1
1
2
1
0
1
0
1
1
0
0
1
0
1
2
1
0
1
0
0
1
1
0
1
1
1
2
0
1
0
0
1
1
0
1
0
1
1
0
0
0
1
1
0
1
1
1
1
1
2
0
0
1
1
1
1
2
2
1
2
1
0
0
0
0
1
1
0
1
2
1
0
1
0
1
2
1
1
1
1
3
0
1
1
1
2
1
2
0
1
1
1
2
1
1
2
0
2
1
2
0
1
1
0
2
2
2
1
1
0
2
6
2
2
2
0
1
2
1
1
1
0
1
1
2
0
1
3
1
0
1
1
1
2
3
2
0
1
1
1
1
0
1
1
0
3
0
0
1
1
1
1
1
0
1
1
1
0
1
2
1
0
2
0
1
2
1
1
1
1
1
0
1
2
1
1
2
0
2
1
0
2
1
2
1
2
0
1
1
1
2
0
0
2
0
1
2
1
0
2
1
1
2
1
3
1
2
2
0
2
0
0
0
0
0
1
2
1
2
1
1
1
1
1
1
2
1
0
1
1
2
0
1
1
1
0
1
1
2
1
2
1
2
1
1
1
1
0
1
1
1
1
1
1
1
1
0
2
0
0
2
1
1
1
1
1
1
0
2
0
2
1
0
1
0
0
0
2
1
1
1
1
1
0
2
1
1
1
1
2
1
1
2
1
0
4
2
1
0
2
0
0
1
2
0
1
1
1
1
1
2
0
1
2
2
2
1
1
0
0
2
0
1
0
2
2
2
1
2
1
1
1
1
1
2
1
1
2
0
1
2
1
0
2
0
1
1
2
1
1
2
1
2
1
0
1
1
1
1
1
2
2
2
1
1
0
2
2
1
1
1
0
2
0
1
2
1
1
1
1
3
2
2
1
0
1
2
1
1
1
2
1
2
0
0
1
0
1
2
2
2
1
2
0
1
2
2
0
2
1
2
1
1
1
2
1
2
2
1
2
1
1
0
1
1
1
1
2
0
2
1
1
1
1
1
1
2
1
1
1
1
1
1
0
0
1
1
1
2
1
1
1
0
0
1
1
1
1
0
1
1
1
0
1
0
1
1
1
0
2
1
1
1
1
1
1
1
2
0
1
1
0
1
1
1
0
0
1
1
2
0
2
3
0
0
1
1
0
0
1
1
1
2
1
1
2
2
0
2
1
1
2
1
1
1
1
2
1
0
1
0
2
0
2
1
1
1
1
1
1
1
2
1
1
1
0
0
1
2
2
1
1
0
0
1
1
1
1
1
3
1
1
2
2
1
1
1
1
0
1
0
1
1
2
1
1
1
1
1
1
1
2
0
1
3
0
2
0
1
1
2
1
1
2
0
0
1
0
1
1
0
1
2
1
1
2
1
1
1
1
1
0
0
2
2
1
0
0
1
0
1
1
1
1
0
2
1
3
1
1
1
1
1
1
1
1
2
1
0
1
1
1
1
2
0
1
1
1
3
1
1
1
2
0
1
1
1
2
2
1
0
1
1
1
1
1
0
1
0
2
0
1
2
1
1
2
1
0
0
2
0
1
1
0
2
1
1
1
1
2
0
1
1
0
1
0
3
1
1
1
0
1
1
0
1
1
2
1
2
2
1
2
1
3
1
0
1
1
1
0
0
1
1
0
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
0
1
2
1
1
2
1
2
1
2
0
1
1
2
1
2
1
1
2
1
1
0
1
1
2
1
1
0
0
1
1
0
1
1
0
1
1
1
0
2
1
1
1
1
2
2
0
2
1
1
0
1
1
0
0
0
1
1
1
1
2
2
2
2
1
1
3
0
2
0
1
0
1
0
1
2
1
1
0
1
1
0
1
1
2
0
1
0
1
1
0
2
1
1
2
2
1
1
1
1
2
0
2
1
1
1
1
0
1
2
1
0
1
1
3
0
1
0
1
0
2
2
1
0
2
1
1
1
1
1
1
2
1
2
1
1
1
0
1
1
1
0
1
1
1
1
0
2
2
0
0
1
0
1
2
0
0
1
1
1
1
0
0
1
1
2
1
0
1
1
1
1
1
2
2
0
1
0
2
0
0
0
1
2
1
2
1
0
1
1
3
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
0
2
1
0
2
0
2
1
1
0
2
2
2
1
0
1
1
1
2
1
2
1
0
0
1
1
1
0
2
0
1
1
1
1
1
0
1
1
1
2
1
1
2
1
1
0
1
1
1
0
1
2
1
2
0
2
1
0
0
0
0
1
0
0
2
2
1
0
0
2
2
1
1
0
1
1
2
2
2
0
2
1
0
1
1
1
2
1
0
1
2
1
2
0
2
1
1
1
1
2
2
1
2
1
1
1
0
1
0
0
0
2
0
0
0
0
0
0
1
2
1
1
1
2
1
2
0
1
1
1
1
0
0
0
1
1
0
2
1
0
2
1
2
1
1
1
1
2
1
1
1
1
2
0
1
1
1
0
1
0
1
1
1
2
1
1
0
1
1
1
0
1
1
0
1
1
2
1
1
0
1
1
1
0
0
0
2
1
2
0
2
1
1
2
1
1
1
1
1
1
0
2
1
2
1
2
1
1
2
1
1
2
2
2
2
1
1
1
1
1
1
2
1
1
1
1
1
0
1
1
2
2
1
0
1
2
0
0
1
1
1
1
0
1
2
0
1
2
1
0
1
0
2
1
0
0
1
1
1
1
1
0
0
1
1
1
1
1
1
2
2
1
1
1
1
0
1
1
1
1
1
1
0
1
1
0
1
1
1
0
1
1
1
1
1
1
2
1
2
2
0
1
1
0
2
1
0
1
2
1
1
2
0
1
0
0
0
1
0
1
2
1
1
1
2
1
1
0
1
2
2
2
0
1
1
0
1
1
1
2
1
2
1
2
1
1
0
3
0
1
1
2
1
1
1
5
1
0
2
2
1
1
1
0
2
1
1
2
1
0
1
2
1
2
1
0
1
0
1
2
0
2
2
0
1
1
0
1
1
1
1
1
2
1
1
1
0
1
1
0
3
1
0
1
0
0
2
1
2
1
0
0
1
1
1
2
2
1
2
1
1
2
1
0
2
0
1
1
1
0
0
0
1
1
1
1
1
2
1
1
1
2
1
1
0
1
1
2
1
1
1
2
1
1
1
1
0
2
1
1
3
1
1
0
1
0
2
2
2
2
0
2
0
2
0
1
0
1
0
2
0
1
1
1
0
1
1
0
1
1
0
2
1
1
1
3
0
1
1
1
2
0
0
2
1
1
1
1
0
1
1
2
1
2
1
2
1
1
2
1
2
1
1
2
1
1
2
0
2
1
1
1
1
2
0
1
0
1
1
2
0
1
1
1
1
0
1
1
1
1
1
1
1
1
2
1
1
1
3
0
1
0
2
1
1
0
1
2
1
2
1
2
0
0
1
2
2
2
0
2
1
1
1
0
1
1
0
1
0
1
2
1
1
1
1
1
2
1
1
1
2
0
0
1
0
1
2
1
0
0
2
1
1
1
2
2
1
2
0
2
2
0
2
1
0
1
2
1
2
2
1
2
2
2
0
1
0
2
1
1
1
1
2
1
0
1
2
1
1
2
0
2
2
1
0
2
1
0
1
1
2
1
2
0
0
2
1
1
1
0
1
1
1
2
0
1
0
1
0
1
2
1
0
1
2
1
0
1
1
1
1
1
0
2
0
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
0
0
1
2
1
0
1
0
1
2
1
0
1
0
1
0
0
1
2
1
1
1
1
1
0
2
2
1
0
0
1
5
0
1
0
1
0
1
1
1
1
0
2
1
0
1
1
2
1
0
0
0
1
1
0
1
1
1
0
1
1
0
2
1
1
2
1
1
2
1
0
2
1
0
2
1
1
2
0
2
1
2
0
1
2
1
0
1
2
1
1
1
0
0
2
0
1
1
0
0
1
1
1
0
2
1
1
2
1
1
0
2
2
0
0
2
2
0
1
0
0
1
0
1
8
0
1
1
1
2
2
0
0
2
1
0
1
2
1
2
0
1
2
2
2
1
2
2
1
1
1
0
1
1
2
0
2
1
0
0
1
2
1
1
1
1
1
2
0
2
2
1
1
0
1
0
0
1
1
1
0
2
1
2
1
0
1
1
2
1
2
0
1
1
1
2
1
1
1
1
1
1
0
0
1
0
1
0
2
0
1
1
0
2
2
2
1
2
0
1
0
1
1
1
2
1
1
2
1
1
1
1
1
0
1
1
0
0
1
0
1
2
2
2
2
0
1
1
2
2
1
0
1
1
0
1
1
0
0
1
0
1
1
0
1
1
1
1
1
1
0
1
1
1
1
2
2
0
1
1
2
0
2
0
1
2
1
0
0
1
2
1
1
3
3
1
1
4
1
1
2
2
2
0
1
1
1
2
0
1
0
0
1
1
1
1
0
1
0
0
1
1
1
0
2
1
1
2
1
2
1
2
1
2
2
2
2
0
1
1
1
2
0
0
0
2
1
2
1
1
1
0
2
2
0
1
1
1
1
1
1
1
1
0
1
2
1
1
1
0
1
2
2
0
1
1
1
1
2
2
0
1
1
2
1
4
0
2
1
1
0
0
0
2
1
0
1
1
0
1
1
1
1
2
1
2
1
0
2
1
1
1
1
2
1
1
0
1
2
1
0
2
3
1
0
0
0
1
1
1
2
1
2
1
1
1
1
2
2
1
2
2
1
0
0
2
2
1
0
1
1
1
1
2
0
1
0
0
1
1
0
3
2
1
2
1
1
1
2
2
1
1
1
1
1
2
1
0
0
0
2
2
1
2
0
1
1
0
3
0
0
2
3
1
1
0
1
2
1
2
1
1
2
0
1
1
1
0
1
1
0
0
1
2
0
0
1
1
0
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
2
0
1
0
1
1
2
2
0
1
0
1
1
0
2
0
1
0
0
3
1
1
1
2
2
0
1
1
1
1
5
2
0
1
2
1
1
1
1
1
1
1
0
0
1
0
1
2
0
1
0
1
1
0
0
1
1
1
2
2
1
2
0
0
1
1
1
1
2
1
0
1
1
2
1
0
2
1
1
2
1
0
1
1
2
0
0
1
1
2
2
1
0
1
1
1
0
0
2
1
2
1
2
0
2
1
1
1
0
0
1
2
2
1
2
0
1
1
1
2
2
2
0
1
0
2
0
2
1
1
2
1
1
1
1
1
0
1
2
1
0
2
1
2
1
2
0
1
0
1
1
1
1
0
1
1
0
1
3
0
1
0
3
2
2
0
0
1
2
0
1
0
0
0
0
1
1
1
1
1
1
2
1
0
1
0
0
0
1
1
1
1
1
0
2
0
1
1
2
1
1
1
2
0
1
1
1
1
2
1
1
1
0
1
1
1
2
2
0
0
1
1
2
1
1
2
2
1
2
1
1
0
1
0
0
1
1
0
1
1
3
2
1
1
1
0
1
3
1
0
1
0
1
2
1
1
1
1
1
1
1
1
1
1
1
3
1
1
1
1
1
1
1
1
0
1
0
1
3
1
1
1
0
2
1
1
1
0
0
0
0
1
1
1
2
0
1
1
0
1
2
2
1
0
1
1
1
2
1
2
1
1
2
1
1
1
1
2
0
2
0
1
1
1
1
1
1
0
1
1
1
2
2
1
2
1
2
1
1
2
2
1
0
2
1
1
1
2
1
0
3
2
1
1
1
2
2
1
2
0
0
1
1
0
1
0
1
1
1
1
1
2
0
1
2
1
1
0
0
2
1
1
0
1
2
1
0
1
2
2
0
3
1
0
1
2
2
1
1
2
1
1
1
2
1
2
2
0
2
1
1
2
1
1
1
1
1
1
1
1
2
2
1
0
1
1
1
1
2
1
1
1
1
1
2
1
2
2
1
1
1
1
1
0
0
1
3
0
2
0
1
2
1
3
1
1
0
2
1
2
0
1
1
1
2
2
2
1
0
1
1
1
0
1
1
1
0
1
1
2
1
0
1
0
1
1
1
1
1
1
2
1
0
1
1
1
0
1
1
2
2
1
0
1
2
1
1
1
2
1
0
0
1
1
1
0
2
2
0
1
0
1
2
1
1
1
2
1
1
2
0
2
1
1
0
2
1
0
1
1
1
2
0
1
0
1
1
1
1
1
2
1
1
1
2
2
1
0
2
0
0
2
2
2
1
0
2
1
2
1
2
1
1
1
1
1
1
1
2
2
1
1
1
0
2
1
2
1
1
2
1
0
1
0
1
1
2
1
1
1
1
0
0
1
1
2
1
1
1
1
1
1
1
1
1
2
0
1
1
1
1
1
1
0
1
1
1
1
2
1
1
1
0
2
1
1
1
2
1
0
2
0
1
2
1
1
1
2
1
1
0
1
0
0
1
0
1
2
2
1
0
2
2
1
2
1
1
1
1
0
2
1
0
1
1
2
1
1
0
1
1
1
1
2
1
1
0
1
2
2
1
1
1
0
1
1
2
1
0
1
0
1
3
0
1
1
1
0
1
1
4
1
2
1
2
1
1
1
1
0
2
1
1
0
1
1
2
1
3
0
2
1
1
1
0
1
2
1
1
0
2
1
1
2
1
2
3
1
1
2
1
1
2
2
1
1
2
0
1
0
1
1
2
0
2
1
1
2
0
2
0
2
1
2
2
1
1
1
1
1
0
1
2
2
2
0
2
0
1
0
1
0
0
1
2
1
0
1
1
0
1
2
1
0
2
1
0
2
0
1
0
1
1
1
1
1
1
1
0
1
1
0
2
0
2
1
1
1
2
2
1
1
2
1
0
2
0
0
1
1
1
1
1
0
2
2
1
2
0
1
1
2
2
1
2
1
1
1
1
1
0
0
1
1
2
0
0
1
0
1
2
0
1
1
0
1
0
2
1
0
0
1
2
0
1
2
1
0
2
1
0
2
2
1
1
2
0
1
1
1
0
1
1
0
1
2
0
0
1
2
2
1
1
2
0
1
0
1
1
2
1
1
1
1
1
1
1
1
0
0
2
1
2
0
1
1
0
1
1
2
1
1
1
1
0
1
1
0
2
1
2
1
0
2
0
1
0
1
1
0
1
1
0
2
1
1
2
1
1
0
1
0
2
1
2
0
1
2
2
1
0
0
1
0
2
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
0
2
2
0
1
1
0
2
0
2
1
1
1
2
0
1
1
1
2
1
1
1
1
2
0
0
0
1
1
2
2
1
0
1
2
1
0
0
0
1
0
2
1
2
1
0
0
2
2
1
1
2
2
1
0
1
1
1
2
1
1
2
0
1
1
0
2
0
0
1
3
1
1
2
1
1
2
1
1
2
1
1
1
2
0
2
1
2
0
0
2
0
0
1
1
0
2
1
2
0
0
2
0
0
0
2
0
1
1
0
0
1
0
1
1
0
0
1
2
2
2
0
1
0
2
1
0
0
1
1
1
1
1
2
1
0
2
1
1
1
2
2
2
0
1
0
0
0
1
1
0
1
1
2
1
1
2
0
1
3
2
1
1
1
2
1
0
1
2
1
1
1
1
1
1
1
0
1
1
1
1
1
0
1
1
1
1
1
0
1
1
2
1
1
1
2
2
2
0
1
2
0
2
1
1
1
1
0
2
1
0
0
2
1
1
1
1
1
1
1
2
0
2
0
1
0
1
1
1
2
2
1
2
2
1
2
4
0
0
1
1
1
1
0
1
1
1
1
1
2
0
1
0
1
1
0
2
2
1
1
0
1
1
1
1
1
0
1
0
2
2
0
2
1
2
2
1
0
1
1
1
1
0
1
1
1
1
1
1
1
0
0
1
1
0
1
0
0
1
1
2
2
4
1
1
2
1
2
2
1
1
1
1
1
0
0
0
0
2
1
1
0
1
1
1
1
1
1
0
2
0
1
2
1
2
1
0
2
1
1
1
1
1
1
2
1
2
2
0
0
2
1
0
1
0
1
0
1
1
1
2
2
1
1
1
2
1
0
2
1
1
1
2
1
1
2
0
2
1
2
2
1
0
1
1
2
1
1
2
1
1
1
1
1
1
0
0
1
0
1
1
1
2
0
1
2
0
1
1
1
1
1
2
0
1
2
1
1
2
1
1
1
2
1
1
0
0
1
0
2
1
4
1
0
0
1
2
1
1
1
1
1
2
0
1
1
2
0
0
1
1
1
2
0
0
2
0
0
0
1
1
1
0
0
1
1
0
1
0
2
2
0
0
2
2
1
0
2
1
0
0
2
1
1
1
1
1
0
2
1
1
1
1
0
1
2
1
1
1
1
1
0
2
1
2
1
1
2
1
1
1
1
2
2
1
0
0
1
1
1
1
0
1
1
1
1
2
1
1
2
0
1
2
0
1
0
1
1
1
2
2
2
1
0
1
1
1
0
1
1
2
0
1
1
2
0
0
0
1
1
1
1
1
1
2
0
1
1
0
0
2
1
1
0
0
1
0
2
1
1
1
1
1
0
1
2
1
0
1
0
1
1
1
1
1
0
1
2
1
1
0
1
0
1
2
1
1
2
0
0
2
1
1
0
1
1
0
0
1
2
1
0
0
2
1
1
1
1
0
1
1
1
0
2
0
1
2
1
1
1
1
1
1
1
0
1
0
1
1
1
2
2
1
1
1
1
1
0
0
1
1
1
1
1
1
0
1
1
3
1
1
0
1
1
2
0
0
2
1
1
1
2
1
2
1
1
1
1
2
0
0
2
0
1
2
0
1
0
2
1
1
2
1
1
1
1
1
2
2
2
1
2
1
1
1
0
1
1
1
1
1
2
2
1
0
2
0
1
1
1
1
1
2
0
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
0
1
0
2
2
1
1
0
2
1
0
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
0
1
0
0
2
2
1
0
1
2
1
2
1
1
1
2
1
2
1
0
1
1
1
0
1
2
0
0
1
2
1
1
2
2
2
2
2
1
1
1
0
1
1
0
2
2
1
1
0
2
0
0
0
1
1
1
1
1
1
0
1
2
0
1
1
1
0
1
1
1
3
1
2
0
1
2
1
2
0
1
0
1
2
1
0
1
1
1
1
1
1
1
2
1
1
0
0
1
1
0
0
1
1
0
2
0
2
0
1
1
1
0
1
1
1
1
1
1
0
1
0
2
0
2
2
1
2
1
0
1
1
0
0
1
2
1
1
1
1
1
1
1
2
2
1
0
1
1
0
0
1
1
1
0
1
2
1
0
2
1
1
1
1
1
1
0
0
1
2
1
1
1
1
1
2
1
1
2
0
0
0
0
1
1
1
1
0
2
0
2
1
1
1
2
2
0
1
2
1
0
0
2
0
2
1
1
2
0
2
1
1
0
2
1
1
1
1
1
2
1
2
0
1
2
1
1
0
1
2
1
1
0
0
0
3
0
1
1
1
1
0
1
1
1
1
1
2
2
2
0
0
0
2
1
1
1
1
1
2
1
1
1
1
0
0
0
1
1
1
1
0
1
1
1
2
1
2
1
0
1
1
0
1
0
2
2
0
2
0
1
1
1
0
1
1
2
1
3
2
3
1
2
1
1
1
1
0
1
2
0
2
1
0
1
2
1
1
1
1
1
1
0
1
1
1
1
2
2
1
0
1
1
1
2
0
1
2
1
2
1
1
0
0
1
1
0
1
2
1
1
1
1
1
2
1
0
1
2
1
0
0
1
0
1
1
1
0
1
2
1
1
1
0
1
1
1
0
0
2
2
1
1
1
1
1
3
2
1
0
1
0
1
0
1
1
2
0
1
1
0
2
2
2
1
2
0
1
1
2
2
2
1
1
1
1
1
0
2
0
0
2
1
2
0
1
2
1
1
1
2
1
1
1
2
1
2
1
1
1
0
0
1
2
2
2
0
1
2
0
1
1
1
0
0
1
1
1
1
1
1
1
2
0
2
1
1
2
2
1
1
0
1
0
2
2
2
0
1
1
1
1
1
1
1
0
1
0
2
1
1
1
2
0
0
1
1
1
1
1
1
1
1
0
1
2
1
1
0
1
2
1
0
1
2
2
1
1
1
1
1
2
1
0
2
2
2
1
2
1
1
1
2
1
1
1
0
1
1
0
1
2
1
1
1
1
1
1
1
1
2
1
1
0
2
1
1
1
2
1
1
1
2
1
1
2
0
0
2
1
1
3
2
1
1
1
1
0
1
1
2
2
1
1
0
1
1
1
2
0
1
1
0
0
1
2
2
1
1
2
1
1
1
0
2
1
0
1
0
1
1
1
2
2
2
1
0
1
0
1
1
1
1
0
1
1
2
1
0
0
1
1
2
2
1
1
1
1
1
1
1
0
0
1
0
1
1
1
0
1
0
4
0
0
1
1
1
2
1
1
2
1
1
1
1
1
0
2
2
2
0
1
0
1
1
2
0
1
0
1
1
0
2
1
0
1
1
0
0
1
1
1
0
0
1
1
0
2
1
1
1
1
1
1
0
1
1
1
1
1
0
1
0
1
2
1
1
1
0
1
1
1
2
1
2
1
1
1
1
1
1
1
1
2
1
1
2
2
1
0
0
0
0
2
1
1
1
2
0
1
1
1
0
1
1
1
2
3
2
2
0
1
1
0
1
1
1
0
1
1
1
1
0
0
1
1
0
2
0
1
2
1
1
1
2
2
0
2
2
1
1
2
2
2
1
2
0
0
2
0
1
1
1
0
2
1
3
1
0
1
1
2
1
0
2
0
1
2
2
1
1
1
1
0
1
1
2
1
1
1
1
2
1
1
1
1
0
1
1
1
0
1
1
0
0
2
0
0
1
1
1
0
1
1
1
1
1
1
1
2
0
1
1
2
2
0
0
1
0
1
1
0
1
1
1
2
1
1
2
2
1
1
1
2
1
1
1
0
0
0
1
0
1
0
1
1
1
1
0
2
2
1
1
1
2
2
2
1
1
2
0
1
1
0
1
1
1
2
1
1
1
0
1
2
1
1
0
1
0
1
2
2
1
0
2
1
1
2
2
1
1
0
1
1
1
1
0
0
1
0
1
1
0
1
1
2
1
1
0
1
1
0
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
0
1
1
1
1
2
1
2
2
1
1
0
2
2
2
3
1
1
1
2
1
2
0
1
2
2
1
1
1
1
2
2
2
0
2
1
1
1
2
0
1
1
1
1
2
1
1
2
0
3
1
1
1
1
0
0
1
1
0
1
2
1
0
0
2
0
2
1
1
1
1
0
0
0
0
1
1
1
2
2
0
0
1
3
1
3
1
2
1
1
1
0
1
2
2
1
0
0
1
0
1
2
1
0
2
2
1
3
0
2
1
1
2
2
2
0
1
1
1
2
0
2
2
1
2
1
2
2
1
0
1
0
1
0
2
1
0
2
0
0
1
2
0
0
2
2
0
1
1
1
1
0
1
1
2
1
1
2
1
1
0
1
0
1
1
1
1
1
0
0
1
1
1
1
1
1
0
2
0
0
1
1
1
1
1
0
1
2
0
1
1
1
1
1
2
1
1
2
0
1
1
2
2
2
0
2
1
0
1
0
1
1
1
0
1
1
1
1
1
3
1
1
2
2
1
2
1
0
0
2
1
1
2
1
1
2
1
1
1
1
1
0
0
0
1
1
1
1
2
2
1
1
1
2
1
1
0
1
2
2
2
0
1
1
0
1
1
1
0
0
2
1
0
0
1
2
1
2
1
2
0
1
1
1
1
0
1
1
1
0
1
0
1
0
1
1
1
1
1
0
1
2
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
0
1
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
0
1
2
3
0
0
1
1
2
1
2
1
0
2
1
0
1
2
2
1
0
1
1
0
0
1
2
2
1
1
1
0
0
1
2
2
1
1
1
1
2
0
1
1
0
1
1
1
2
2
2
1
2
2
1
1
2
2
0
1
2
1
1
1
1
1
1
1
2
0
1
1
2
1
1
0
1
2
1
1
0
1
1
1
1
0
1
2
1
0
1
1
0
1
1
1
1
2
1
0
1
2
0
0
2
1
0
2
0
1
2
2
2
0
1
1
0
1
2
1
2
1
0
0
1
1
1
1
2
2
1
1
0
1
2
4
1
1
1
1
1
1
0
2
2
1
1
1
1
2
1
3
1
2
2
2
1
2
1
1
1
2
1
0
1
2
0
2
0
1
1
2
1
1
5
1
1
2
1
1
0
1
1
1
1
2
1
2
2
2
2
1
0
1
1
1
3
2
0
1
1
1
1
2
0
0
1
1
2
0
2
0
2
2
1
1
1
1
1
1
0
2
1
1
1
2
2
2
0
2
2
2
1
2
1
2
1
0
1
2
1
1
1
2
1
0
1
6
1
1
1
0
1
1
2
1
2
0
2
1
0
1
1
2
0
0
1
0
1
0
0
1
2
0
0
2
0
1
1
1
1
1
1
1
1
0
2
0
1
1
2
1
0
1
2
1
1
1
1
1
1
0
1
1
0
0
2
1
2
0
0
1
1
1
1
1
0
2
1
2
1
1
2
1
1
2
1
1
2
1
1
0
1
1
0
2
0
1
0
1
1
1
1
1
2
0
0
2
1
3
1
3
2
2
2
1
1
1
0
1
1
2
1
2
1
1
0
0
2
0
1
1
0
0
1
2
1
1
1
1
2
2
1
2
1
1
1
2
1
1
1
1
1
1
1
2
0
1
0
0
0
0
1
2
1
2
2
1
2
1
1
1
1
2
0
1
2
1
0
2
1
1
1
0
1
0
0
3
1
1
2
1
0
0
1
1
2
1
1
3
1
0
1
1
0
2
1
1
1
1
1
1
0
1
0
0
1
1
0
1
1
1
1
1
1
1
1
1
1
1
2
1
0
1
1
1
2
1
1
1
0
0
1
1
2
0
1
2
2
1
2
0
2
0
1
1
2
1
0
0
1
0
1
1
1
1
0
1
0
0
1
2
1
0
2
1
1
1
1
0
1
1
1
1
1
1
1
1
3
0
0
1
1
2
1
1
1
1
1
1
2
2
1
2
0
1
1
1
1
0
1
1
2
0
1
1
1
2
1
2
0
2
0
3
1
1
0
1
1
0
2
2
1
1
3
0
1
2
1
1
2
0
1
1
1
1
0
2
2
2
2
1
2
1
0
1
1
0
2
1
0
0
1
1
1
0
1
0
2
1
1
0
0
1
1
1
1
0
1
1
1
0
2
2
1
1
1
1
1
0
2
1
2
0
0
0
1
2
2
1
1
1
1
1
1
1
2
1
1
0
1
0
1
1
1
2
3
1
0
0
0
1
1
1
2
2
1
0
0
1
0
0
0
0
1
1
1
1
2
0
1
1
0
0
1
2
0
0
1
1
2
3
2
1
1
1
0
1
1
1
2
1
2
0
2
2
1
0
1
0
1
0
2
1
1
1
0
0
0
1
1
0
0
1
1
1
0
1
2
1
1
0
1
1
1
1
1
2
2
0
2
1
1
1
1
0
1
1
1
1
2
1
1
0
1
1
2
1
2
1
0
2
1
1
2
1
2
1
0
0
1
1
1
2
0
2
2
1
1
1
1
1
2
1
1
0
0
1
2
0
2
1
1
3
1
1
1
0
1
0
2
0
0
1
0
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
3
2
1
0
2
1
0
2
1
0
1
1
1
1
1
1
0
2
1
1
1
2
2
0
1
1
0
1
2
0
0
1
1
1
0
0
1
1
0
1
0
1
1
1
2
1
2
1
1
1
0
1
1
1
1
1
1
1
2
2
1
1
1
2
1
0
1
1
0
1
1
0
1
2
1
0
1
0
2
2
1
1
2
0
1
2
2
2
1
0
2
2
1
1
0
1
2
0
0
1
2
1
1
1
1
0
1
1
2
1
1
1
1
0
0
1
1
0
2
1
2
0
2
2
2
1
2
1
1
1
1
2
1
1
2
2
0
2
0
1
1
1
0
2
1
1
0
1
1
1
0
1
1
1
0
1
1
1
2
1
0
1
0
0
2
1
1
0
1
1
1
1
1
1
2
1
2
2
2
3
0
0
2
1
2
0
2
1
1
0
1
2
2
1
1
2
0
0
1
1
2
1
1
1
1
0
0
2
0
1
1
1
1
0
1
1
2
1
1
1
1
1
0
1
1
1
1
2
0
2
1
0
2
1
1
1
1
0
1
0
1
1
1
1
1
2
0
1
2
1
0
2
1
1
1
0
1
1
2
2
1
1
1
2
0
1
2
1
0
2
2
0
1
1
2
1
1
1
1
1
1
2
1
2
2
1
2
1
3
2
1
2
0
1
1
1
0
0
0
1
1
1
2
1
2
2
1
1
1
2
1
0
1
1
1
1
1
1
1
2
1
1
1
2
1
1
2
0
1
1
1
1
1
1
1
1
0
1
2
0
2
1
1
1
2
2
2
2
1
1
0
1
2
1
1
1
1
1
1
1
1
2
0
2
1
1
2
1
2
1
1
1
2
0
0
1
1
2
1
1
0
0
0
1
1
2
1
1
3
3
1
0
1
0
2
2
1
2
1
1
0
1
1
0
1
2
1
1
1
1
1
2
1
1
1
2
1
1
2
3
1
2
1
1
0
1
1
0
1
1
1
2
2
1
1
2
1
1
1
1
2
1
0
0
0
2
2
1
0
0
1
1
2
2
2
0
1
0
1
1
0
0
2
1
1
1
1
1
2
0
2
1
1
1
1
1
1
0
1
2
1
1
0
1
1
1
0
1
0
2
2
1
1
2
0
2
1
1
0
1
0
4
1
0
2
1
0
1
2
0
1
1
1
1
2
1
1
1
3
1
0
1
1
1
2
1
1
2
1
1
3
0
1
0
2
1
3
0
1
0
1
0
1
0
0
1
2
0
2
0
2
1
0
0
1
1
1
0
2
2
1
1
2
2
1
1
1
2
2
0
1
2
1
2
0
1
3
1
1
0
1
0
1
1
1
1
0
0
0
0
1
1
0
0
1
1
2
0
1
1
0
2
2
1
1
1
1
1
2
1
1
1
2
2
0
1
1
2
2
1
2
0
2
1
0
1
2
1
1
1
2
0
2
0
1
1
0
2
0
0
1
2
2
2
0
0
2
2
1
1
2
2
1
0
1
2
1
2
1
0
1
1
2
0
0
1
0
1
2
1
2
0
1
1
2
2
0
2
2
2
1
1
1
1
1
1
1
0
1
1
2
1
1
0
1
1
2
1
1
1
1
0
2
0
2
1
1
2
1
1
0
1
1
1
0
1
0
1
1
2
1
2
0
1
0
1
2
0
2
2
1
1
1
2
1
1
2
1
1
1
1
0
2
1
1
2
1
1
1
1
0
1
2
1
1
2
1
1
2
1
1
0
2
2
1
2
1
0
1
1
0
2
1
1
1
1
0
2
1
1
1
1
2
2
1
0
0
0
1
1
0
1
0
1
1
1
2
1
1
1
0
1
1
2
1
2
1
1
2
1
1
1
1
1
1
1
2
2
0
0
0
0
1
2
1
2
2
1
2
2
1
1
2
2
1
0
0
0
2
1
0
2
2
3
1
1
0
1
2
1
1
1
0
1
0
1
1
2
1
1
2
1
0
1
0
1
1
1
1
2
1
1
1
0
1
1
2
1
1
2
1
1
2
1
0
1
1
2
1
1
2
2
1
2
2
1
1
0
1
2
4
2
0
1
0
2
1
1
0
0
1
1
1
2
1
1
1
1
1
1
1
2
0
2
2
0
2
1
1
1
1
1
0
2
0
1
1
3
2
0
2
1
2
1
2
0
0
0
1
2
1
1
0
1
1
1
1
1
1
1
2
1
0
2
1
1
0
0
0
1
1
1
1
0
2
2
2
1
0
1
0
1
0
1
0
0
0
0
1
2
1
1
0
2
2
1
1
2
1
0
1
1
2
2
1
1
1
1
1
2
1
1
1
1
1
1
1
0
2
3
0
1
0
2
1
1
1
1
1
1
1
2
1
1
2
2
1
0
1
0
1
1
2
1
0
0
2
2
0
1
1
0
3
0
2
2
1
1
2
1
2
1
1
1
1
0
0
1
0
1
1
1
1
2
2
0
2
1
1
1
2
1
2
0
0
1
1
1
2
1
1
2
1
0
2
1
2
2
1
1
2
2
1
2
0
0
1
2
2
2
1
1
1
1
1
2
0
2
2
0
1
2
1
1
1
1
1
0
1
2
1
1
1
1
0
2
0
0
1
1
1
2
1
0
2
0
0
2
2
1
1
1
1
1
0
2
1
1
0
1
2
1
1
1
1
2
1
0
0
2
1
1
1
2
0
1
1
1
1
1
1
0
0
1
1
0
1
1
1
1
2
2
0
2
1
0
0
1
1
1
1
1
0
1
1
0
1
1
1
2
2
0
0
1
0
0
0
1
0
1
1
1
2
2
0
1
0
2
1
2
1
2
0
1
1
1
2
1
0
0
2
2
0
0
1
1
1
1
1
1
2
2
1
1
1
1
0
1
1
0
1
1
0
2
0
1
2
0
0
0
1
2
2
1
1
1
0
1
0
0
2
1
1
0
0
2
1
0
1
1
0
1
1
2
1
1
1
2
1
2
1
2
0
1
1
1
1
1
1
0
2
0
1
2
1
1
0
2
1
1
0
1
0
1
2
1
1
0
1
1
2
2
1
2
1
1
1
1
2
2
0
0
1
2
2
1
1
0
0
0
1
0
1
1
1
1
1
1
0
1
2
2
1
1
1
1
0
2
0
2
1
1
1
0
2
2
0
1
1
1
2
1
0
0
1
0
0
2
1
1
2
1
0
1
1
1
1
1
1
1
1
2
1
1
0
0
0
1
1
0
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
2
0
1
0
1
0
1
2
2
0
1
0
1
1
0
1
0
0
2
1
2
1
1
2
1
0
0
0
2
1
0
2
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
0
2
1
2
0
1
0
1
2
2
1
0
1
1
1
1
2
1
1
1
1
1
0
1
2
2
2
1
0
1
0
1
2
1
0
2
0
2
1
2
1
2
1
1
1
1
2
0
0
0
1
2
0
0
1
2
1
2
0
2
0
1
0
1
1
1
1
1
2
1
2
2
1
2
1
1
1
1
1
1
2
1
1
2
2
2
1
2
1
1
1
2
1
2
1
2
1
1
1
2
2
2
1
0
1
1
0
2
1
1
1
1
2
2
0
1
1
2
1
1
1
1
2
2
1
1
1
0
0
0
1
0
2
2
2
2
1
2
0
0
1
2
2
0
0
1
1
2
2
1
2
2
0
0
1
1
1
1
2
2
1
1
1
1
1
1
0
1
1
2
1
2
2
0
1
1
0
1
1
2
1
2
0
2
1
1
1
2
0
1
1
1
1
1
1
1
1
2
0
1
1
0
2
2
2
1
1
1
1
1
1
0
1
0
1
0
1
0
1
1
2
2
0
2
2
1
1
1
0
2
2
1
1
1
0
2
3
1
1
2
2
1
0
2
0
1
0
1
1
1
2
1
1
2
1
1
0
1
1
2
2
0
2
2
0
1
0
0
1
0
1
0
0
1
2
1
0
1
1
0
1
2
1
1
1
3
2
1
2
1
0
1
0
0
1
1
1
2
2
1
1
1
1
0
2
1
2
1
2
1
1
1
2
2
0
0
1
0
1
0
1
2
1
2
1
0
1
2
2
1
2
0
1
1
1
1
1
1
5
1
0
1
1
0
1
1
1
2
0
2
1
1
0
1
2
0
1
0
1
1
0
1
1
0
2
0
2
2
1
2
1
1
2
2
1
1
1
0
2
2
0
0
1
1
0
1
1
0
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
0
0
1
0
1
0
1
2
1
1
2
1
1
1
1
1
1
1
1
0
2
0
2
0
2
1
2
0
1
2
1
1
1
2
1
1
1
2
1
2
1
1
2
1
0
1
1
2
1
0
0
1
2
1
1
2
1
0
1
1
1
1
0
2
0
1
1
0
1
2
1
0
2
1
2
2
0
1
0
0
0
1
1
2
0
1
1
2
2
2
1
1
1
1
2
1
2
1
1
2
1
1
2
2
1
1
1
1
2
2
1
3
1
0
0
2
1
1
2
0
1
1
1
1
0
1
1
1
1
2
1
1
1
1
1
2
2
3
0
1
1
2
1
0
2
2
1
1
0
2
2
2
1
0
0
0
1
0
1
0
1
1
1
1
2
3
1
2
1
1
1
2
0
0
1
0
1
1
1
0
1
0
0
1
1
1
0
2
1
1
2
2
0
1
2
1
3
1
2
2
2
2
1
1
1
1
2
1
2
2
2
1
2
0
2
1
1
0
1
1
0
1
1
0
0
0
1
0
1
0
0
1
2
2
0
1
0
0
1
0
0
0
1
0
1
1
1
1
1
2
1
0
0
1
2
2
0
2
1
1
1
1
2
1
1
1
1
2
2
0
0
1
1
1
2
1
0
1
1
1
0
1
2
1
1
1
2
1
0
1
0
2
2
1
2
1
2
2
1
1
1
1
2
0
1
2
1
1
1
1
2
2
1
2
1
2
1
2
2
0
2
2
1
0
1
2
1
2
2
1
2
1
1
1
1
0
1
0
3
1
1
0
2
2
1
1
1
1
1
0
1
1
1
1
1
1
1
1
3
1
1
0
0
1
2
2
1
1
6
0
1
0
1
0
1
1
0
1
2
0
0
1
0
1
1
0
2
2
0
2
1
1
1
2
2
2
1
0
1
1
1
0
0
0
1
1
2
1
1
0
1
0
1
0
1
1
1
1
1
1
1
1
1
0
1
1
1
2
2
2
2
2
1
0
1
2
0
0
1
1
1
0
1
1
1
2
0
1
0
1
2
1
2
1
1
2
0
0
1
1
1
1
2
1
1
0
0
1
1
2
1
1
2
1
1
1
1
2
0
2
2
1
0
1
1
0
2
2
1
2
2
1
1
2
2
1
1
0
1
1
2
2
1
2
1
1
1
3
0
1
1
0
0
2
0
2
1
1
0
2
2
0
1
0
1
1
0
0
0
2
0
0
2
1
1
1
1
2
1
1
1
1
1
3
0
2
1
2
1
2
1
2
0
2
1
1
0
1
2
0
0
2
0
1
0
2
0
4
1
2
2
1
2
2
1
1
1
1
1
1
0
1
0
1
0
2
2
1
1
1
1
1
2
2
1
1
1
1
1
0
1
1
0
1
1
2
2
1
1
1
1
0
3
2
0
1
1
1
1
1
0
1
1
2
1
1
2
1
0
0
1
1
1
2
1
2
1
1
1
1
1
0
2
0
1
1
0
1
0
0
1
3
2
1
2
1
1
1
1
1
0
0
1
1
0
1
1
1
1
1
0
1
0
0
1
1
0
1
0
1
1
1
0
1
0
1
2
1
1
2
1
1
2
0
2
3
1
1
2
0
1
1
1
0
1
0
1
1
2
2
2
1
0
2
1
1
3
1
2
0
1
1
1
1
0
1
1
2
1
1
1
0
1
0
1
1
0
1
0
1
0
1
1
1
0
1
1
1
2
0
2
1
0
1
1
2
1
1
1
1
1
1
2
2
1
2
2
1
0
2
0
1
2
0
1
2
0
1
1
0
1
0
1
2
1
0
1
1
1
0
1
0
2
2
1
2
2
1
0
1
1
1
1
2
0
0
1
1
0
0
1
1
1
0
1
2
1
1
1
1
0
3
1
0
2
3
1
0
1
1
0
1
1
2
0
0
1
2
1
1
0
1
2
1
0
2
2
2
1
1
2
1
0
2
1
1
0
1
1
0
1
1
1
0
1
1
1
0
2
1
1
2
1
1
1
1
1
1
2
0
1
1
0
2
1
1
2
1
2
2
1
1
2
2
6
1
1
2
1
3
1
1
1
1
1
1
2
2
1
1
1
1
1
1
0
1
2
1
2
1
2
1
0
1
2
1
0
1
1
0
0
2
1
2
1
2
2
1
2
1
2
0
0
2
1
0
1
0
1
1
1
1
1
2
1
1
1
1
1
1
0
2
2
2
1
0
0
0
1
0
0
0
0
1
2
1
0
1
2
2
1
0
1
1
1
2
2
1
1
1
3
1
2
1
2
1
1
1
2
0
2
2
1
1
2
0
1
1
1
1
0
0
2
0
0
1
1
0
2
1
1
0
1
1
0
2
0
2
2
2
0
1
1
1
1
1
1
1
2
0
0
1
2
1
0
2
2
1
0
0
1
0
2
1
1
1
1
2
0
1
2
0
1
1
1
1
0
1
1
0
1
2
0
0
2
1
0
1
1
2
1
1
1
0
1
1
2
1
0
2
2
1
1
0
2
1
0
0
0
5
0
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
2
2
1
3
0
1
0
2
1
0
1
1
2
1
2
2
2
0
1
2
1
0
2
1
0
1
2
1
0
2
1
1
1
0
1
1
2
1
1
0
1
0
2
1
2
1
1
1
1
1
1
1
2
1
1
0
1
0
1
0
1
0
0
1
1
1
0
0
1
1
2
1
1
0
1
3
1
1
1
2
1
0
1
1
2
1
2
0
1
2
2
0
1
2
1
0
1
1
1
1
1
1
0
1
2
2
2
0
1
0
2
1
1
1
0
2
1
1
0
0
0
1
0
1
1
2
1
1
1
1
0
1
1
0
2
1
1
1
0
2
1
1
1
1
2
2
0
0
2
0
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
0
1
1
1
1
1
1
2
0
1
1
2
1
1
2
1
1
1
1
1
1
1
2
1
1
2
2
0
0
0
1
1
1
1
0
2
1
0
0
2
1
1
0
1
0
0
1
1
1
1
1
1
0
2
2
2
1
1
1
1
0
1
1
2
1
2
2
1
0
1
1
1
1
1
0
0
1
1
1
2
0
1
3
0
0
2
1
0
2
2
2
0
0
0
1
2
1
2
2
1
0
0
2
1
2
1
2
1
1
1
1
1
2
1
1
1
2
1
2
1
2
1
2
1
1
1
1
2
1
2
1
1
0
1
1
0
2
1
1
1
1
0
1
1
0
2
0
2
2
1
0
1
1
2
0
0
1
1
0
2
0
2
0
0
1
1
1
2
0
1
1
1
1
1
1
0
1
2
1
1
1
2
2
0
1
1
1
1
1
1
1
1
2
1
1
0
2
2
1
2
2
0
2
2
1
0
0
0
1
0
0
1
0
1
1
1
1
2
2
0
1
1
1
1
1
1
1
1
1
0
2
0
1
1
2
1
2
0
1
1
1
2
2
1
1
2
1
1
2
1
2
2
2
0
1
0
1
1
1
0
0
1
2
1
2
1
1
2
1
1
0
1
1
1
2
0
0
2
2
0
0
2
2
1
1
1
1
0
1
1
1
0
2
2
1
0
1
0
1
1
2
1
1
1
1
0
1
1
1
1
0
0
1
1
0
0
1
0
1
1
1
0
1
2
1
1
2
2
1
1
2
0
2
0
0
1
2
2
1
1
2
2
2
2
1
1
1
1
2
2
1
1
0
0
0
1
1
0
0
1
0
2
1
1
2
0
0
2
0
2
1
2
9
1
0
1
1
0
0
1
2
1
0
2
1
1
1
1
2
1
2
1
0
1
1
1
0
0
1
0
0
0
2
1
1
1
2
0
2
1
1
0
0
1
0
1
2
1
1
1
4
1
0
2
1
1
1
1
1
1
0
1
1
1
1
2
2
1
2
0
1
1
0
1
0
2
2
1
1
1
1
1
1
0
2
0
1
1
1
1
0
1
2
1
1
2
1
2
0
2
1
0
1
0
1
2
1
1
1
2
1
1
1
1
2
1
1
1
1
0
1
1
2
1
0
1
0
1
0
1
2
2
1
1
1
1
2
1
1
2
1
0
0
1
1
1
2
1
0
1
1
1
1
1
1
2
2
0
1
1
1
2
2
1
0
1
1
1
1
1
2
1
2
2
1
0
1
1
2
0
1
1
0
1
2
2
1
1
1
2
1
0
1
1
2
0
0
0
1
1
1
0
2
2
1
1
2
1
1
0
0
0
0
1
2
1
1
1
2
1
1
1
3
1
1
1
1
1
1
1
1
1
0
1
2
1
3
1
0
1
1
1
1
2
1
2
2
1
1
1
1
1
0
0
1
1
2
1
1
1
1
4
2
1
1
2
1
1
0
0
3
1
1
2
2
1
1
1
0
1
1
1
1
1
2
0
1
1
2
0
2
1
1
1
1
0
1
1
2
2
0
1
0
1
2
2
1
1
0
0
1
1
2
1
1
2
1
1
2
1
1
1
2
2
1
0
1
1
2
1
1
1
1
2
1
1
2
0
1
1
1
1
2
0
2
1
0
1
1
1
1
1
1
1
2
0
1
2
0
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
0
2
1
0
0
1
2
1
1
0
1
1
1
1
1
2
3
0
1
1
0
0
0
2
3
1
1
1
1
1
1
1
1
1
2
2
1
2
2
0
0
1
1
1
1
0
1
2
1
2
1
0
1
2
1
1
1
0
2
2
1
1
1
1
2
1
1
1
0
1
2
2
2
3
1
1
1
1
1
2
0
1
2
1
2
1
0
1
2
0
2
1
1
2
0
1
0
0
1
0
2
1
2
1
1
1
1
2
0
0
2
0
1
1
0
0
1
1
3
3
1
1
1
1
0
1
1
0
2
2
1
2
1
2
1
0
1
1
1
1
1
1
1
2
1
3
1
1
1
2
0
0
0
2
2
1
1
2
1
1
1
0
1
0
1
0
1
1
1
1
2
1
1
1
1
2
0
0
1
0
1
1
1
1
0
1
2
2
2
0
0
2
2
1
1
1
1
2
1
0
2
2
0
2
0
2
1
0
2
1
1
2
1
1
1
1
2
1
1
1
0
0
1
1
0
1
2
1
1
0
0
1
1
1
1
1
0
1
0
1
1
0
1
0
1
1
1
1
2
1
1
1
0
0
1
2
0
0
1
1
1
1
1
1
1
0
0
0
0
1
1
3
1
1
1
0
3
1
1
1
1
1
0
2
0
2
0
1
0
1
0
0
0
1
0
1
1
1
1
2
0
1
0
0
1
0
2
1
2
1
2
1
1
1
2
1
0
1
0
2
1
1
1
1
0
2
2
1
0
0
2
1
0
2
1
2
2
1
2
2
2
0
3
1
1
1
2
0
1
1
0
1
1
2
2
1
1
2
1
0
1
2
2
1
1
0
0
0
2
0
2
1
3
1
1
2
2
1
2
1
1
0
1
1
1
1
1
2
2
1
2
1
1
1
0
2
2
2
0
2
1
2
2
2
2
1
2
1
1
1
2
2
1
1
0
0
2
1
1
0
0
1
1
1
0
0
2
1
0
1
1
1
2
2
0
1
1
1
1
1
2
1
1
0
1
2
1
1
1
2
1
2
1
2
2
0
1
1
0
2
1
1
1
1
2
2
2
1
1
0
0
1
1
1
2
0
1
1
1
1
1
1
3
0
2
0
0
2
1
0
2
2
1
0
0
0
0
1
1
0
1
1
1
2
2
1
1
1
0
1
1
1
2
1
1
0
0
3
2
0
2
1
1
1
1
0
1
1
2
1
1
1
0
2
1
1
1
1
1
0
1
1
1
2
2
0
1
1
1
0
2
4
1
0
0
0
1
2
0
1
1
0
0
1
0
2
2
1
1
1
2
0
2
1
0
1
1
0
2
2
1
1
1
2
0
2
1
0
1
1
1
1
1
1
1
2
0
1
0
1
1
1
1
1
0
2
2
1
2
2
1
1
1
1
4
1
1
0
1
1
0
1
1
0
1
1
1
1
2
1
3
1
1
0
2
1
2
1
2
0
2
2
1
1
2
2
2
2
1
1
0
1
2
1
0
2
1
1
0
2
0
0
0
1
1
0
1
1
2
1
0
1
2
1
2
1
1
2
2
1
0
0
2
1
1
2
2
2
1
1
1
1
1
1
1
1
0
2
1
0
1
1
2
1
1
2
1
1
1
2
2
0
1
1
1
2
1
0
1
1
2
1
1
1
1
1
1
1
2
1
2
0
1
1
1
2
1
2
0
3
2
1
1
1
1
2
1
1
1
1
2
1
2
2
1
1
1
1
0
1
1
0
1
1
2
0
2
1
1
1
0
0
2
1
0
2
1
1
1
1
2
0
1
1
2
1
0
0
2
1
1
1
0
0
2
0
2
1
0
0
1
1
1
0
2
1
0
1
1
0
2
0
2
1
0
1
1
1
0
1
0
1
2
1
1
2
1
1
0
1
0
0
0
1
1
2
1
2
2
0
1
2
1
2
2
2
1
1
0
0
1
0
2
1
1
1
1
0
2
1
1
1
1
2
0
1
1
0
0
0
1
1
1
2
1
1
0
2
0
2
0
0
1
1
1
2
1
1
1
2
2
0
1
1
1
2
1
1
1
2
0
2
0
0
1
2
0
0
2
0
1
2
1
1
1
1
2
1
1
1
1
1
1
2
1
1
2
1
1
1
0
0
0
1
2
1
2
1
2
1
1
1
0
2
1
1
2
1
2
0
1
2
1
0
1
2
0
1
1
1
1
2
2
1
0
3
0
1
2
1
1
1
1
1
2
0
1
1
0
1
1
1
0
1
0
1
2
1
1
1
0
1
2
1
2
0
1
1
1
2
0
0
1
0
1
1
1
3
1
1
0
1
0
1
1
2
1
1
1
0
2
2
0
2
0
1
0
2
0
0
1
1
2
1
1
1
1
1
1
0
1
2
1
1
1
1
2
2
0
0
1
2
1
1
1
2
2
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
2
1
0
1
0
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
1
1
0
0
0
1
0
1
2
0
0
2
1
0
2
1
1
1
1
0
0
1
1
1
1
2
2
1
0
3
2
1
1
1
0
0
1
0
1
1
0
1
1
1
2
1
1
1
1
1
2
1
0
1
0
0
0
0
1
0
1
0
1
1
0
1
0
1
2
2
1
1
1
1
2
2
1
2
0
1
0
0
0
1
1
0
0
0
2
2
1
1
1
1
1
1
1
1
1
1
2
1
0
1
1
2
1
2
1
1
1
0
0
2
2
0
1
1
1
1
1
1
1
2
1
1
0
1
1
0
1
0
2
2
2
1
2
0
1
1
1
1
1
2
1
0
1
0
2
1
2
1
1
0
2
2
1
2
1
2
0
1
1
0
3
1
1
1
1
0
2
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
0
1
2
1
2
2
1
0
1
1
1
1
1
1
0
0
0
2
1
0
1
0
2
1
1
1
1
1
1
1
1
2
1
0
1
1
1
0
1
0
2
1
2
1
0
1
1
2
0
1
1
2
0
1
1
0
1
0
1
2
1
1
0
1
0
1
0
1
1
0
1
1
1
1
1
0
1
1
0
1
1
1
1
1
0
1
1
1
1
1
1
0
1
1
2
1
0
1
0
1
1
1
2
1
1
0
1
2
1
0
2
1
0
1
2
1
0
1
1
1
2
2
1
1
1
1
0
0
1
3
1
1
1
1
2
0
0
0
2
1
2
1
0
0
2
1
2
2
1
1
2
1
1
2
1
1
1
1
2
2
1
1
1
0
1
1
2
1
0
1
1
2
1
1
1
3
1
1
0
1
0
1
1
2
1
0
1
1
2
2
2
1
2
1
2
1
1
1
0
1
1
1
1
2
1
1
1
1
1
2
0
1
0
2
1
2
0
0
2
1
2
1
1
1
1
1
1
2
3
0
1
1
2
1
2
2
1
1
0
0
1
0
2
1
1
1
0
1
0
0
2
2
1
1
1
2
0
0
1
2
1
0
1
2
1
1
1
2
2
0
1
0
1
0
1
2
0
1
2
1
2
0
1
0
0
0
1
1
0
0
0
0
1
1
0
1
0
1
1
1
0
1
1
1
2
2
1
1
0
1
1
2
0
0
0
1
1
2
1
2
1
2
2
1
2
1
0
1
1
2
2
2
0
1
2
1
2
1
1
1
2
1
1
0
0
1
2
1
0
1
2
0
3
0
1
1
2
1
2
0
1
0
0
1
1
1
1
1
2
0
2
0
1
2
0
1
2
2
1
1
2
2
1
1
1
2
2
2
1
1
2
1
1
2
0
2
1
2
2
0
0
2
1
0
0
1
0
0
1
1
1
1
1
1
1
1
2
1
1
0
2
2
1
1
1
2
1
0
1
1
1
2
1
2
2
1
2
0
0
1
2
1
2
0
2
0
1
0
2
0
1
1
2
0
0
1
0
1
1
1
1
1
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
0
2
1
1
1
1
2
1
1
1
1
1
2
0
3
1
1
1
1
1
1
1
1
1
2
0
1
1
1
1
1
1
1
2
2
1
1
1
2
1
1
1
2
0
1
2
2
1
0
1
2
1
1
0
3
2
2
1
1
1
2
1
0
1
2
1
1
0
1
1
1
2
1
1
0
2
1
1
1
1
0
1
1
1
1
1
1
1
1
2
1
0
1
0
1
1
1
0
2
1
2
3
0
1
0
2
1
1
1
1
2
1
0
1
1
1
0
0
1
1
2
0
0
1
1
1
2
1
1
0
2
1
0
1
0
0
0
1
1
0
2
2
0
0
2
1
2
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
0
3
3
1
1
2
0
0
1
2
1
2
1
1
1
1
0
1
1
1
1
1
1
1
1
1
2
1
1
0
1
0
2
1
1
1
0
1
1
1
1
2
1
2
1
1
1
1
0
0
1
2
1
2
2
1
1
2
2
1
2
0
1
0
0
1
1
3
2
2
2
1
1
0
1
1
1
1
0
1
0
0
1
1
2
1
2
2
1
1
0
0
2
2
2
1
1
1
0
2
1
1
1
1
1
0
1
0
0
2
1
1
0
0
2
3
1
0
0
0
1
1
0
0
0
1
2
1
2
2
1
2
1
0
1
1
1
1
2
0
1
1
1
1
2
1
0
1
0
2
1
1
1
2
2
1
2
1
1
0
2
0
0
1
1
1
1
0
0
1
2
2
1
0
1
2
2
0
2
0
1
1
0
1
0
2
1
1
2
3
1
1
2
1
0
0
0
1
0
1
0
0
0
1
1
0
1
1
1
2
1
0
1
1
0
2
1
0
2
1
1
1
1
1
1
2
1
1
1
1
0
0
1
1
1
3
0
1
1
1
0
2
1
2
1
2
1
2
0
2
1
1
1
1
2
1
1
0
1
2
1
1
1
1
1
2
0
0
0
1
0
1
1
2
4
1
0
0
1
1
1
1
0
0
0
0
1
2
1
0
1
1
1
1
1
2
1
1
1
1
0
1
0
1
1
1
1
1
1
2
2
0
1
1
3
0
2
1
1
0
2
1
2
1
1
2
1
2
0
0
2
1
2
1
2
3
1
2
0
1
1
1
1
1
1
1
0
1
1
1
1
1
1
0
2
2
2
1
2
1
1
2
1
0
1
1
1
0
1
1
1
1
1
0
1
1
2
1
0
1
2
1
4
1
1
2
1
1
1
2
0
0
1
1
1
1
2
0
2
1
1
1
1
1
0
1
0
1
1
1
1
3
1
1
1
0
1
1
1
0
1
1
2
1
1
1
2
1
1
0
0
2
1
1
0
2
0
2
1
3
0
0
2
1
1
1
0
1
1
2
2
1
2
0
1
2
1
2
1
1
1
1
2
1
1
1
1
2
1
2
1
1
2
1
1
1
1
0
1
1
1
1
1
2
2
1
1
1
0
2
0
0
1
1
1
2
2
2
1
1
2
1
1
1
1
0
0
2
1
1
1
0
1
1
2
1
2
2
1
0
1
2
0
0
1
1
1
2
0
1
1
1
1
2
1
1
2
0
0
1
2
0
0
1
1
1
2
2
1
2
2
1
1
1
1
1
0
1
1
1
1
1
2
1
1
2
1
0
0
1
1
2
1
2
1
1
1
1
0
2
1
1
2
1
2
0
1
2
1
1
1
1
1
2
1
2
2
0
2
4
1
0
1
0
1
0
0
1
1
1
1
0
1
1
0
0
2
0
1
2
0
0
0
1
1
2
1
1
1
2
2
2
1
0
2
1
1
2
1
1
1
1
0
3
1
0
0
0
2
0
0
0
1
2
1
0
1
0
2
1
0
2
0
1
2
0
1
2
1
1
2
2
1
0
2
1
1
2
1
1
2
0
2
0
0
1
1
1
0
1
1
1
0
2
1
2
0
1
1
1
1
1
1
1
1
2
2
1
2
0
1
1
2
2
0
1
2
1
1
1
0
0
1
1
0
1
1
1
2
1
2
1
1
0
1
1
1
1
2
1
0
3
2
1
1
1
1
1
0
0
1
0
2
1
1
1
0
0
1
1
1
2
2
1
1
1
1
0
1
1
1
2
1
1
1
1
2
1
1
1
1
0
2
1
2
1
1
2
2
1
1
2
1
1
1
2
1
2
2
1
2
1
2
0
0
1
2
1
0
2
1
2
1
1
1
0
0
1
2
1
0
1
1
1
2
1
1
1
2
0
2
1
1
0
1
2
2
0
2
2
1
0
0
1
0
1
1
2
1
1
2
2
1
1
1
2
1
1
1
3
1
1
2
1
1
0
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
0
0
1
2
1
3
1
0
2
1
0
1
2
0
1
0
0
0
1
0
2
1
0
0
1
1
1
1
0
1
1
0
1
2
0
2
1
1
1
2
2
1
2
1
1
0
2
1
1
1
1
1
1
1
2
1
0
1
2
1
1
2
1
0
0
1
0
1
1
1
1
1
1
2
1
0
1
0
1
1
2
2
1
0
2
0
1
1
2
1
2
1
1
1
1
0
1
2
0
0
1
2
1
0
2
1
1
0
1
1
0
1
1
1
1
2
0
1
1
0
0
1
1
0
1
2
1
2
1
1
1
1
0
0
1
2
2
2
1
1
0
2
0
0
1
1
2
1
0
1
1
1
2
1
1
2
2
2
1
1
2
2
2
0
0
0
1
1
1
1
1
1
1
0
1
1
2
1
2
1
2
0
1
0
1
1
1
0
1
1
2
1
1
1
1
1
1
2
0
1
1
0
0
1
1
2
1
1
1
2
2
0
1
1
1
1
1
1
1
0
1
1
1
0
1
1
1
1
1
1
0
2
2
0
1
1
0
1
1
1
1
0
0
1
1
2
1
1
0
1
0
0
2
1
1
1
1
1
1
1
0
2
1
0
1
1
1
1
1
0
4
0
1
0
1
1
0
0
1
1
1
1
0
1
2
2
1
2
2
1
2
1
1
1
2
0
2
2
1
1
2
1
1
1
1
1
1
0
3
2
1
1
4
2
1
2
1
0
2
1
1
1
0
2
1
1
1
1
1
0
2
1
1
1
0
0
2
1
1
1
2
1
2
2
0
0
0
0
1
2
1
2
1
2
1
1
2
2
1
1
2
1
0
0
1
0
1
0
1
1
1
1
1
1
0
1
1
1
0
2
0
2
1
1
0
2
2
1
2
1
1
0
1
1
2
3
1
2
1
1
2
1
1
0
2
0
0
1
0
1
1
2
0
1
0
1
2
1
0
1
2
1
1
2
1
2
1
0
1
1
1
1
1
2
0
1
1
1
1
1
2
1
0
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
2
0
1
1
1
1
0
2
1
2
1
0
1
2
0
0
1
1
1
1
2
0
0
1
2
2
0
2
1
1
2
1
1
2
2
1
1
0
0
3
1
2
1
1
2
0
0
2
1
1
2
2
0
1
1
1
0
1
1
1
1
1
2
1
1
1
1
0
2
0
2
2
2
1
1
1
0
0
1
1
1
1
1
0
2
2
2
0
1
2
1
1
2
0
1
1
1
1
1
1
2
2
1
2
0
0
1
0
1
0
1
1
2
2
1
1
1
2
1
0
0
2
1
2
2
1
2
2
1
1
1
2
2
0
0
1
2
0
1
2
1
0
1
2
1
0
1
1
1
2
3
1
1
1
1
2
0
2
2
1
3
0
1
1
1
0
1
2
2
0
1
1
2
1
0
1
2
1
0
2
0
1
2
1
2
0
1
2
1
2
0
1
1
1
2
1
1
1
1
1
0
1
1
1
0
0
1
1
0
1
1
1
0
2
2
1
0
1
0
2
0
1
1
1
0
1
2
3
0
2
1
1
2
2
1
1
1
1
1
0
1
1
2
1
0
1
2
1
2
1
1
2
1
1
1
1
0
0
1
2
1
2
1
0
0
1
2
0
0
2
1
1
0
1
2
1
0
0
0
1
1
1
1
0
1
2
1
1
1
0
2
1
2
0
2
1
1
1
2
1
0
0
2
0
1
1
0
2
2
1
1
0
2
0
2
1
2
0
2
1
1
1
1
1
2
2
1
2
1
2
2
2
1
1
1
1
1
0
1
1
1
1
1
2
0
1
1
2
1
0
0
0
0
1
1
1
1
1
0
0
1
1
3
1
1
0
2
1
1
1
0
2
1
2
1
1
0
1
1
2
1
1
0
0
2
1
1
2
2
0
1
1
1
1
1
1
1
1
2
0
2
0
1
1
1
1
0
1
1
3
1
2
2
1
2
1
1
0
1
2
1
2
1
1
1
1
0
1
0
0
1
1
1
2
1
1
0
1
1
1
1
1
0
0
1
0
2
2
1
1
1
0
1
1
1
0
1
1
1
0
1
1
1
1
0
1
1
1
0
0
1
1
4
1
1
1
1
1
2
0
0
0
1
2
1
1
2
0
2
0
1
1
0
1
0
2
1
2
2
2
0
1
2
0
1
1
2
0
1
1
0
2
0
1
1
2
1
1
0
2
1
1
1
1
1
1
0
1
1
1
1
2
2
1
1
0
1
1
1
2
1
0
1
1
1
1
1
1
1
1
1
1
2
1
1
2
0
2
2
1
2
1
1
2
2
1
2
1
1
1
0
1
2
1
0
0
1
0
1
2
1
0
0
1
1
0
1
2
2
1
2
2
2
2
0
0
1
2
1
1
2
0
0
1
2
0
1
1
0
2
0
0
2
1
1
2
0
2
1
1
1
1
1
0
1
2
1
1
2
1
2
2
2
1
1
1
1
0
0
1
2
1
1
0
0
2
2
1
1
0
2
2
1
2
1
2
0
1
1
0
1
2
2
1
1
1
1
0
1
2
0
1
2
1
1
1
0
1
1
1
0
2
1
0
2
1
1
1
2
2
2
1
0
2
2
0
1
1
1
2
2
0
1
2
1
2
1
0
1
0
1
1
2
0
1
1
0
1
0
1
1
1
0
2
1
1
2
2
1
1
1
0
0
2
0
2
1
0
1
1
2
2
0
0
1
1
2
0
1
1
1
1
1
1
2
1
1
1
0
2
1
0
2
2
1
1
2
2
1
1
1
0
1
1
1
1
0
1
1
1
0
1
0
0
2
1
2
1
1
2
2
1
0
1
1
1
3
1
1
1
0
1
1
2
2
1
2
0
1
1
1
0
1
0
1
2
4
1
1
1
1
1
2
1
0
2
2
1
1
1
2
1
1
1
0
0
2
1
1
1
0
2
1
1
2
3
2
1
0
2
0
1
0
1
0
1
2
1
1
0
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
2
1
2
2
1
1
0
1
2
1
2
2
1
0
1
2
1
1
1
1
2
0
1
1
1
1
0
1
1
0
2
0
0
5
1
1
0
1
2
1
2
0
0
1
2
1
2
0
1
1
1
1
1
1
2
2
2
1
1
1
1
1
2
1
2
1
0
1
1
1
1
1
1
0
1
0
1
2
1
2
1
0
0
2
0
2
1
1
0
2
1
2
1
1
2
1
2
1
1
0
2
2
1
2
0
1
1
1
1
1
1
1
1
1
1
0
0
1
1
1
1
1
1
1
0
1
1
1
1
1
1
0
2
2
1
0
0
1
2
1
3
1
0
1
1
1
2
1
0
1
1
1
0
1
0
1
0
0
2
1
1
1
2
1
1
1
0
2
0
1
1
0
1
0
2
1
0
1
0
1
1
1
2
1
0
1
0
1
0
0
2
1
1
3
1
1
1
0
2
1
0
2
1
0
2
1
0
0
1
1
1
1
0
1
0
1
1
1
2
1
1
0
1
2
1
1
1
1
1
1
0
1
2
3
0
1
0
0
1
1
1
0
1
1
2
1
1
2
0
1
0
3
1
2
0
1
2
0
1
1
1
1
0
1
1
1
1
1
1
1
1
0
1
1
1
0
1
2
1
0
1
1
1
1
0
1
0
0
2
1
2
1
2
0
0
2
1
0
2
1
1
1
2
2
1
1
1
1
0
1
1
2
2
0
0
0
1
2
1
1
1
0
1
2
2
2
1
2
1
1
2
1
1
0
1
2
1
0
0
1
1
0
1
1
1
2
1
1
1
1
1
1
1
1
2
0
1
1
1
1
1
0
0
1
2
1
1
1
0
2
1
1
1
0
1
1
2
1
0
0
1
0
1
1
1
0
1
1
1
1
2
2
0
1
1
1
1
1
1
1
2
1
0
2
1
0
1
2
1
1
1
1
1
2
0
1
0
1
1
2
0
0
1
2
1
1
0
0
1
0
1
1
2
1
1
1
2
1
0
2
2
1
0
1
0
2
0
1
0
1
0
1
1
2
1
2
3
0
1
2
1
1
1
1
0
0
1
2
0
1
1
1
0
1
2
1
1
1
2
1
1
1
1
2
1
1
2
1
1
0
2
1
1
1
0
0
1
1
1
2
0
1
0
4
0
1
2
1
2
0
1
1
1
1
1
2
2
0
0
1
0
1
0
2
0
0
2
1
2
3
0
1
0
1
2
1
1
0
1
1
1
1
0
0
1
0
1
1
2
2
2
1
0
0
1
1
1
2
2
1
0
1
1
2
1
0
1
1
1
1
0
1
1
1
1
0
0
2
1
0
0
2
1
0
0
1
1
0
2
1
2
1
1
2
0
2
2
1
0
1
0
0
2
1
0
0
1
1
1
1
1
1
2
1
2
1
0
1
1
2
1
0
2
2
2
2
1
1
0
1
0
2
0
1
1
0
1
1
1
1
1
0
1
0
2
2
1
0
0
0
1
1
1
0
0
2
2
1
0
0
2
1
1
1
1
0
1
0
2
1
1
1
0
0
2
1
2
1
1
2
2
1
0
1
0
1
1
1
1
1
0
0
0
2
1
0
0
0
3
1
2
1
1
2
2
1
1
0
0
0
1
1
2
2
0
1
0
1
2
1
2
0
1
2
2
0
0
1
2
0
1
1
2
1
2
2
1
2
0
1
1
2
1
1
1
2
1
1
2
2
1
1
1
0
1
1
1
0
1
1
1
1
2
0
0
1
0
2
1
0
0
0
1
2
1
1
1
1
1
1
1
0
1
1
1
1
0
1
1
0
2
2
1
1
1
1
2
0
1
1
0
1
1
1
0
2
1
1
2
2
0
1
1
1
2
1
1
0
2
1
2
1
1
2
2
0
1
0
1
2
1
1
2
1
0
0
1
0
1
1
2
0
0
1
1
2
1
0
0
2
0
0
2
0
0
1
1
1
0
2
0
1
1
1
2
0
1
1
1
2
2
1
1
2
1
1
0
0
1
1
1
0
1
1
1
0
2
2
1
2
1
0
0
1
1
1
1
1
2
2
2
0
1
1
1
0
1
0
1
1
1
1
1
1
1
0
1
1
0
0
1
0
1
1
4
1
2
1
1
2
1
1
1
1
1
1
1
0
2
1
1
1
1
1
0
0
1
1
1
1
1
2
2
1
2
1
1
0
1
1
1
0
1
2
1
1
2
1
0
1
1
1
1
0
1
1
1
1
1
0
0
2
1
0
1
0
1
1
0
0
1
0
1
1
1
2
2
0
0
1
1
0
1
0
1
0
0
1
2
2
0
1
1
0
1
1
0
0
1
1
1
1
0
2
2
2
1
2
1
2
1
0
1
2
0
0
1
1
1
0
1
0
0
2
1
1
0
1
1
2
1
0
0
0
2
2
2
2
1
2
2
0
1
1
0
1
1
1
1
1
1
1
3
1
1
1
1
1
2
1
1
1
2
2
1
0
2
2
2
1
1
1
1
1
0
1
1
0
2
1
1
1
0
0
1
1
1
0
2
0
3
1
1
1
1
1
1
1
2
1
1
1
0
1
1
1
1
1
1
2
3
1
0
2
0
0
1
1
1
1
0
1
1
1
1
1
0
2
0
1
1
0
0
0
0
2
1
2
1
2
1
1
0
1
2
3
1
0
1
0
1
1
1
1
1
0
3
2
1
0
2
1
1
1
1
2
2
1
2
0
2
2
2
0
0
2
1
1
1
1
1
1
1
1
0
2
2
1
1
1
2
1
2
1
1
0
2
1
1
1
1
2
1
1
0
1
1
2
2
0
0
0
1
1
1
2
2
0
1
1
1
1
1
0
2
1
1
2
2
1
1
2
1
2
1
1
1
1
0
1
1
2
1
1
0
1
2
1
1
1
0
3
2
1
1
0
0
2
1
1
2
1
1
1
1
1
1
0
1
1
0
0
1
1
1
0
0
0
1
1
0
1
1
2
1
0
1
1
1
0
1
1
1
1
1
0
0
1
0
2
1
1
0
0
0
1
0
2
1
1
1
1
1
1
2
1
2
3
1
2
1
2
2
1
1
1
0
0
0
0
0
0
1
1
0
1
1
2
0
1
0
1
1
1
2
2
0
0
1
1
1
1
1
1
1
0
1
2
1
1
1
1
2
1
0
1
1
1
1
2
1
1
2
2
1
0
1
1
1
0
0
0
1
2
1
1
1
1
1
2
1
1
1
1
1
0
0
1
4
1
1
1
1
1
0
2
1
2
0
1
1
0
1
1
1
2
0
1
2
1
1
1
1
0
2
1
2
1
0
1
1
1
1
1
0
1
0
1
1
2
1
0
1
0
0
0
1
0
1
1
1
0
1
1
0
1
2
0
1
1
1
0
0
1
2
1
1
1
1
1
1
2
1
2
1
2
1
1
2
1
1
1
2
1
2
1
1
1
1
1
2
2
2
1
1
0
1
1
1
2
1
1
0
1
1
1
1
2
1
0
0
1
0
1
0
1
2
1
1
0
1
2
1
0
1
1
0
1
2
2
0
3
1
1
1
1
1
1
1
1
2
2
1
2
0
1
1
1
2
2
2
1
2
1
0
0
2
1
1
0
2
2
1
1
1
0
2
0
1
1
1
1
2
1
2
0
1
1
2
1
3
2
1
1
1
2
1
1
1
1
1
1
2
0
1
1
1
0
2
0
1
0
1
1
2
0
0
0
0
1
1
0
1
1
1
1
0
1
1
1
1
0
0
0
2
0
2
1
0
1
1
0
0
1
1
1
2
1
1
1
1
2
2
0
2
1
1
1
1
1
1
1
2
1
1
0
1
0
2
1
1
1
2
1
1
0
0
1
1
0
0
1
0
2
2
2
2
2
1
1
1
2
1
2
2
0
1
1
1
1
1
0
3
1
0
1
0
2
1
1
0
1
1
1
1
2
1
2
1
1
0
0
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
0
1
1
2
3
1
0
1
1
1
1
0
1
1
1
1
0
0
0
0
1
1
1
7
1
0
0
1
1
2
1
0
1
2
1
1
1
0
2
2
1
2
1
0
1
1
2
2
2
1
0
2
1
1
1
1
1
0
1
1
0
0
1
1
1
1
0
1
1
1
0
1
1
1
1
1
1
1
1
0
1
1
0
1
1
1
0
1
1
1
1
0
1
1
2
1
0
1
2
0
1
2
1
1
0
1
1
2
0
1
0
0
1
0
0
1
2
1
1
1
2
1
2
1
0
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
0
2
2
1
1
1
2
1
2
1
1
1
1
0
0
0
1
1
0
2
2
1
0
1
1
1
0
0
1
0
1
1
0
1
2
1
0
2
1
1
1
2
0
0
0
0
0
1
1
2
2
1
2
1
1
1
0
1
0
2
2
2
0
0
1
1
2
1
1
1
2
1
1
2
1
1
1
1
2
1
2
1
1
1
0
0
1
1
1
1
0
2
1
1
1
1
2
1
1
1
1
0
1
1
1
1
2
2
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
2
2
2
1
0
1
1
1
0
1
0
1
2
1
2
0
1
1
1
1
1
1
1
0
0
1
0
1
1
1
1
1
2
0
1
0
0
1
2
0
1
0
1
2
2
1
1
1
1
2
1
2
1
0
1
1
1
1
1
2
0
0
2
1
1
2
0
1
0
1
1
1
2
1
1
1
1
1
1
1
0
1
2
2
1
0
0
1
1
1
0
1
1
0
2
1
2
1
2
1
1
0
1
0
2
1
1
0
1
1
2
1
1
0
1
1
2
1
0
2
1
1
1
0
1
2
2
2
2
1
2
1
1
0
0
1
0
1
1
2
1
1
1
1
1
2
2
2
1
2
2
0
0
1
1
2
1
0
2
1
1
2
2
0
1
0
1
2
0
1
1
1
1
1
1
1
2
1
1
1
1
1
0
2
1
1
1
0
2
0
2
1
1
1
0
1
2
2
1
1
1
0
2
1
2
1
1
1
2
0
2
1
0
1
0
1
1
1
0
2
1
0
0
1
2
0
1
0
2
1
1
1
1
1
1
2
1
1
2
1
1
3
1
1
1
1
1
0
0
0
0
0
1
1
1
1
1
2
1
1
1
0
1
1
1
0
0
2
1
1
3
1
1
1
0
0
1
1
1
1
2
1
1
1
0
1
2
0
1
2
2
0
0
2
1
2
0
0
0
2
1
1
1
1
2
1
1
1
1
1
0
0
2
1
1
1
0
1
0
1
3
1
1
1
1
1
1
0
0
1
1
1
2
1
1
1
0
2
1
1
1
0
1
0
1
1
1
0
0
2
1
1
1
2
1
1
0
1
1
2
1
0
1
0
1
1
0
0
0
2
1
2
1
0
1
1
0
0
1
0
1
1
1
4
1
1
1
1
1
1
1
0
0
0
0
1
2
0
0
0
3
2
2
0
1
2
2
1
2
0
1
1
2
2
1
1
0
1
1
1
1
1
2
1
1
0
2
1
1
1
0
1
1
1
0
2
1
3
1
1
0
2
1
1
0
1
2
1
2
1
1
1
0
0
1
1
1
1
2
0
1
1
0
2
1
1
1
0
0
1
1
0
1
0
1
0
2
2
0
0
3
0
1
1
2
1
2
1
1
1
1
1
1
0
0
2
1
0
0
1
1
2
0
0
1
5
1
1
0
1
1
1
2
0
1
2
2
0
1
3
0
1
1
0
1
1
2
1
1
1
1
0
2
1
2
0
2
1
0
1
0
1
2
0
1
1
1
0
0
1
0
1
1
1
2
1
1
1
1
2
0
0
2
0
2
2
2
1
1
0
0
2
1
1
1
1
0
0
1
2
2
1
1
1
1
1
1
0
1
1
2
0
0
2
1
1
1
1
1
1
1
0
0
0
1
1
1
0
2
1
1
1
1
0
2
0
1
2
1
0
2
0
1
1
1
1
0
2
0
1
2
1
0
2
1
1
0
1
1
0
2
1
3
1
2
0
1
0
1
0
1
2
0
0
2
1
1
1
0
0
2
2
0
0
1
1
1
1
1
0
1
1
2
2
0
1
2
1
1
1
1
0
1
2
1
2
1
1
1
1
1
1
1
1
1
1
0
2
0
1
2
1
0
2
2
1
2
2
1
2
1
2
0
1
2
1
1
1
2
1
2
0
1
0
2
0
2
1
0
2
0
1
1
0
2
2
1
2
1
2
1
1
1
2
0
1
2
1
0
1
0
1
1
3
0
1
0
1
0
1
0
2
0
0
0
1
1
1
1
1
3
0
1
2
1
0
1
2
1
2
2
1
1
0
2
0
1
1
1
1
2
1
0
1
0
1
2
1
2
1
0
1
1
2
1
0
1
2
1
1
2
1
1
1
2
1
1
1
2
0
1
1
2
1
0
0
2
0
1
2
2
1
1
1
2
1
1
1
1
1
1
0
0
0
1
1
2
1
1
0
1
0
1
1
1
2
1
1
2
2
1
1
1
2
1
2
1
2
2
0
1
0
0
1
3
1
1
1
0
1
3
1
1
1
1
1
1
1
2
1
2
2
2
1
1
1
2
2
1
1
0
1
0
0
0
0
2
0
1
0
1
0
0
1
1
1
1
0
2
1
1
2
2
1
1
1
1
2
0
2
1
0
1
1
2
1
0
1
2
1
1
1
2
0
2
1
0
1
1
1
0
2
1
1
0
1
0
2
1
0
2
2
1
1
1
1
1
2
1
1
1
0
1
1
2
3
1
1
0
2
0
2
0
2
1
1
0
2
1
1
1
2
2
2
2
1
1
1
0
1
1
1
1
1
1
0
2
1
2
1
0
1
0
1
0
2
1
1
0
1
1
1
1
1
2
1
2
0
0
1
2
1
2
0
1
1
0
0
1
2
0
2
1
0
2
0
2
2
2
1
1
1
1
1
1
1
2
1
2
2
0
1
1
3
1
0
1
0
1
1
1
1
1
2
2
0
1
2
2
2
0
2
2
0
1
2
2
1
1
2
1
0
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
2
0
2
1
1
2
2
1
2
1
0
0
1
0
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
0
2
1
1
1
1
3
1
0
2
1
1
0
1
1
1
1
1
2
1
1
0
0
1
1
0
0
1
0
1
0
0
2
0
1
1
1
1
1
2
1
1
2
1
1
1
1
2
1
2
1
2
1
1
1
1
2
1
0
0
2
1
1
1
1
1
1
0
1
1
1
2
1
2
2
1
1
0
1
2
2
2
1
2
1
0
0
1
0
1
1
0
1
1
1
1
1
1
1
1
0
0
0
3
2
0
1
0
0
0
1
1
2
1
2
1
1
1
1
1
1
0
0
1
0
2
0
1
1
0
1
2
1
0
1
1
0
1
2
1
0
1
1
1
1
0
0
1
2
1
2
1
2
2
0
2
1
4
0
0
2
2
1
1
1
1
2
0
1
1
2
1
0
2
2
0
2
2
2
1
0
0
0
1
3
1
0
3
1
1
1
1
0
1
2
2
1
0
0
2
1
1
0
0
1
0
2
3
1
1
1
0
0
0
1
1
1
0
0
1
1
0
0
1
1
1
2
1
2
2
1
2
2
2
0
0
2
3
1
1
2
2
2
0
1
2
1
2
1
1
3
1
2
1
0
1
0
2
1
1
1
1
1
1
2
1
0
1
2
1
0
0
2
0
2
1
1
0
1
1
1
1
1
0
1
2
1
0
1
1
1
1
0
2
1
0
1
1
2
0
0
1
2
1
1
1
2
1
1
1
2
2
1
1
1
1
0
1
1
1
1
1
0
1
0
2
1
1
2
1
2
2
2
2
1
0
1
2
1
1
1
0
1
1
1
1
2
1
6
1
1
2
0
1
1
1
2
1
2
1
1
1
0
1
0
1
0
0
0
0
1
0
1
1
0
2
0
1
1
0
1
0
1
2
2
1
1
1
0
1
0
1
1
1
1
1
1
1
1
1
1
0
1
1
0
1
1
2
1
2
1
1
2
1
1
2
1
2
0
0
0
0
1
2
2
2
1
0
1
1
2
2
1
1
1
1
1
1
1
2
0
0
0
0
1
0
1
2
2
0
1
1
0
0
1
0
0
1
0
1
0
0
1
1
0
1
1
1
0
1
0
2
0
3
1
0
1
0
0
2
1
1
0
1
1
0
0
1
1
1
1
1
2
1
1
1
1
1
1
1
1
0
2
0
2
1
1
1
0
1
1
1
2
1
1
1
1
2
1
2
1
0
1
1
1
2
1
1
2
0
3
1
1
1
2
1
1
2
2
2
1
1
2
2
0
0
1
1
0
2
2
1
1
2
1
1
1
1
1
0
2
1
2
1
0
1
1
2
1
1
2
2
1
0
1
1
2
1
0
0
1
0
1
1
1
1
1
2
0
2
1
1
1
2
0
1
2
1
1
1
0
0
2
2
0
0
1
1
1
1
1
2
1
0
0
1
1
1
1
1
1
1
1
2
1
0
1
1
0
1
1
1
1
1
2
0
1
0
0
2
1
1
1
1
0
1
1
2
2
1
1
1
1
2
2
0
2
1
1
1
1
1
1
1
1
2
1
1
1
0
0
1
1
2
1
1
2
2
1
0
0
1
1
2
2
2
1
1
1
1
1
1
0
1
1
1
1
0
1
1
1
1
1
1
1
1
0
1
2
1
0
1
1
1
0
0
2
1
0
1
1
1
0
0
0
1
1
1
2
1
0
1
2
1
2
1
1
1
0
1
2
1
1
2
1
0
1
2
0
3
0
0
1
0
0
0
2
1
2
1
0
0
2
0
1
2
1
1
0
1
1
1
0
1
1
1
0
1
2
1
1
1
1
2
2
2
2
1
2
1
2
1
1
1
0
1
1
0
1
2
1
2
1
1
1
1
1
1
1
1
1
0
0
0
1
1
1
1
0
1
1
0
1
0
1
2
0
1
0
0
2
1
0
2
2
1
2
1
1
2
2
1
2
2
0
0
1
1
1
2
0
1
1
0
2
0
1
2
1
1
1
0
0
1
1
1
1
1
1
1
1
1
1
2
1
1
1
0
2
2
0
2
1
1
1
0
2
1
0
1
1
1
1
2
1
1
1
1
2
2
1
2
1
1
1
0
1
1
1
0
0
1
1
0
1
2
0
1
1
0
1
1
2
1
1
1
1
1
2
2
1
1
1
1
0
1
0
0
1
1
0
1
2
1
2
2
1
1
1
1
2
1
0
1
0
1
1
1
2
0
0
0
2
0
1
0
2
0
2
2
1
0
1
1
2
1
2
2
0
0
1
1
1
1
2
0
0
0
1
0
1
1
0
1
1
0
1
1
0
1
1
0
1
1
1
1
0
2
0
1
0
1
1
0
1
1
1
2
1
0
1
2
1
0
1
1
0
0
1
1
0
1
2
2
0
1
1
1
1
1
1
1
1
0
1
1
1
0
2
0
0
1
1
2
0
1
1
1
0
1
0
0
0
1
1
1
1
2
1
2
1
1
1
0
1
0
1
2
2
1
0
1
1
2
1
1
2
2
1
1
1
1
2
0
1
1
1
1
2
1
0
1
1
1
1
2
1
0
2
1
0
1
0
1
2
0
2
1
0
1
3
1
1
1
1
1
1
1
0
1
1
1
1
0
1
1
1
1
1
1
2
1
0
2
1
0
1
2
0
1
2
1
2
1
2
1
1
0
1
0
2
1
1
1
1
1
0
1
1
2
2
0
0
0
1
1
1
2
2
2
2
2
2
0
1
1
2
1
2
1
1
1
2
1
0
0
1
2
1
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
1
1
0
1
1
0
2
1
1
1
1
0
0
1
1
1
0
0
1
0
2
0
2
1
2
1
1
1
0
1
2
2
2
2
0
1
3
0
1
1
2
1
0
1
1
1
2
2
2
1
1
1
2
1
1
2
0
1
0
1
0
1
2
1
1
2
0
1
2
1
1
0
0
2
2
1
1
2
1
0
2
0
1
2
0
1
1
1
2
2
1
0
0
1
1
1
2
2
1
1
0
1
1
2
1
1
0
1
1
2
1
2
1
0
1
1
2
0
2
1
1
1
2
1
1
1
1
1
1
0
1
0
1
1
2
0
2
0
0
1
1
1
2
1
5
0
1
1
2
2
0
2
1
3
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
0
1
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
1
3
1
1
1
1
1
1
2
1
1
1
2
2
0
2
1
0
0
2
1
2
2
2
2
1
1
1
1
1
0
0
1
1
1
1
1
1
0
1
0
2
0
0
1
0
1
1
1
1
1
2
2
1
1
0
1
3
0
1
1
1
2
0
0
1
0
0
2
1
1
0
1
1
0
0
2
2
2
1
2
2
1
0
1
2
1
1
3
0
2
2
2
1
1
1
2
2
0
2
2
1
0
0
1
1
1
2
1
0
2
0
1
2
1
2
0
0
1
1
2
0
0
0
2
1
1
0
2
1
2
0
1
2
1
0
2
1
1
2
1
1
2
2
1
2
1
0
1
2
2
3
0
2
0
1
1
2
2
2
2
1
1
1
1
0
1
1
1
1
1
1
1
2
0
2
1
1
1
1
0
1
0
1
0
0
1
0
1
0
0
0
1
1
1
2
1
1
1
1
7
1
1
1
2
0
0
1
2
1
0
0
1
2
1
1
1
2
1
2
1
1
1
2
1
2
1
0
1
1
1
1
1
0
1
1
2
2
1
1
1
0
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
2
0
2
1
1
1
1
1
1
1
1
0
1
2
1
0
0
2
0
1
1
1
1
1
1
1
2
2
1
1
1
1
0
1
0
0
2
0
2
1
2
1
1
1
1
1
1
2
1
0
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
0
1
2
1
1
2
1
2
1
0
1
1
1
0
1
0
1
2
0
1
1
1
1
1
1
1
1
0
0
1
1
1
1
1
1
1
1
1
1
1
2
1
0
0
1
2
1
2
2
1
2
1
1
1
2
2
2
1
1
2
1
0
1
1
1
1
1
1
2
0
1
1
2
2
1
1
0
0
1
1
1
1
1
2
1
1
1
1
0
1
1
1
0
1
0
2
1
0
0
1
1
1
2
1
0
2
2
1
1
2
2
2
1
1
1
1
0
0
1
2
1
2
1
1
1
1
2
1
0
1
2
0
1
2
1
1
1
0
1
2
2
0
3
1
1
2
2
1
2
1
2
1
1
1
1
0
0
0
1
1
1
1
1
0
1
0
1
1
0
1
1
1
1
1
0
1
2
1
1
2
1
2
0
0
2
1
1
1
0
1
0
2
1
1
1
2
2
1
0
1
1
2
0
1
1
0
1
1
2
1
0
2
1
2
0
1
0
1
0
1
2
1
1
0
1
0
1
1
0
0
2
0
0
0
2
1
1
0
1
0
0
1
0
1
1
2
1
0
0
2
1
1
0
1
2
1
1
1
0
1
1
1
0
0
1
1
2
1
1
2
2
1
1
1
1
1
1
1
2
2
1
0
1
1
1
1
0
1
1
1
0
1
0
2
0
1
0
1
2
1
2
1
0
1
2
1
0
1
1
2
2
1
0
0
1
2
1
3
2
2
1
1
0
1
0
1
1
1
0
1
2
1
0
1
1
2
2
1
1
2
0
2
1
1
0
1
1
2
2
0
2
1
0
1
0
1
1
1
2
1
1
2
1
2
2
0
2
2
1
1
2
2
1
0
0
2
1
0
2
1
2
0
1
0
1
2
1
1
1
2
1
0
2
1
0
0
2
1
0
1
2
2
1
1
1
0
2
1
1
2
1
2
2
2
1
0
0
2
1
0
1
1
2
1
1
1
1
1
1
1
1
3
2
1
0
2
0
2
2
0
1
1
1
1
0
1
0
1
0
3
1
0
1
1
0
1
1
1
1
1
2
2
2
1
0
2
0
1
2
2
0
2
2
0
0
1
0
1
1
1
1
1
1
1
1
3
1
1
2
1
1
1
1
2
1
1
1
1
1
1
2
1
0
2
0
1
1
1
2
1
1
2
1
1
1
1
3
1
0
1
1
1
1
1
0
2
2
0
2
1
1
1
0
3
0
2
1
0
1
2
0
1
1
1
2
1
0
1
1
2
1
1
1
1
2
1
1
3
2
2
0
2
1
0
0
0
1
0
2
2
1
0
2
0
1
1
1
0
1
1
2
0
0
1
1
0
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
2
0
1
1
0
2
1
0
1
1
2
1
2
1
0
0
0
1
1
0
1
2
0
1
0
1
2
0
1
1
1
1
1
1
1
0
2
1
2
1
1
2
1
0
1
0
2
1
1
0
1
0
1
2
1
2
0
2
1
1
1
1
1
1
2
2
1
0
1
1
2
0
1
0
0
2
1
2
1
1
2
1
2
2
2
2
1
0
0
1
2
2
0
1
1
0
1
0
1
1
1
0
0
1
2
0
1
0
2
0
1
1
0
1
1
2
2
2
2
2
13
2
1
1
1
1
2
1
0
1
1
1
1
1
1
0
2
2
0
1
1
0
2
0
0
0
1
0
0
1
1
1
0
1
1
2
0
1
1
2
0
1
0
1
2
2
1
0
0
1
1
1
0
1
1
1
1
0
2
1
0
0
1
1
1
1
1
1
1
1
0
1
0
1
1
0
1
0
0
0
2
2
1
1
2
1
2
2
1
1
1
0
2
2
2
0
1
1
0
1
1
2
0
1
1
1
2
2
1
1
1
1
1
2
1
1
2
0
1
1
0
1
2
1
1
2
0
1
1
2
1
0
1
0
0
2
1
1
1
0
2
0
1
2
0
0
1
0
0
1
1
0
1
2
1
1
2
0
0
2
0
0
1
0
1
1
0
1
2
1
1
1
1
2
1
0
1
0
2
0
2
0
1
1
2
0
0
1
1
2
0
2
0
1
2
0
0
2
2
0
1
1
1
2
2
1
0
1
1
1
1
1
1
2
1
1
1
2
1
2
0
1
1
1
1
0
2
1
0
2
2
1
2
1
0
1
0
2
1
1
2
0
1
1
1
1
2
0
1
1
2
2
1
2
0
2
0
1
0
2
1
1
1
1
0
2
1
2
0
2
2
0
2
1
1
0
2
2
2
1
0
2
1
2
2
1
2
1
0
1
1
0
2
0
0
1
1
2
0
0
1
1
1
1
1
1
1
0
2
1
1
2
1
0
2
1
0
0
1
1
2
1
0
0
1
0
0
1
1
2
1
1
2
0
2
1
2
1
0
1
1
2
1
1
2
1
0
2
1
1
1
0
1
0
0
1
0
1
1
1
3
0
2
1
2
2
1
0
2
2
0
1
3
0
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
1
0
1
1
1
2
1
0
2
1
2
2
2
1
1
1
1
2
0
2
1
1
1
0
2
0
0
1
1
1
1
1
1
2
2
1
1
0
1
1
1
1
1
2
1
1
1
1
0
2
2
2
0
1
1
2
2
0
1
1
2
2
2
2
1
0
0
1
1
0
1
1
1
0
1
1
1
0
2
1
0
1
1
0
0
1
2
1
0
1
0
2
1
0
1
1
2
0
2
1
1
1
1
1
0
0
1
1
1
2
1
0
1
1
0
1
1
0
1
1
1
1
2
0
1
1
2
2
1
1
2
1
1
2
1
1
1
2
1
2
1
2
1
1
1
1
2
2
1
1
1
2
1
1
1
2
2
1
1
2
1
0
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
0
1
1
0
2
1
1
1
1
1
1
1
1
2
0
0
1
2
0
0
2
1
1
2
2
2
1
0
0
0
1
2
1
1
0
1
1
1
0
1
1
1
1
1
2
1
1
0
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
0
1
1
1
2
2
1
1
1
1
1
1
1
1
1
0
1
2
0
1
2
1
1
1
1
1
1
0
1
1
1
0
1
1
2
1
0
0
2
1
1
1
0
1
1
1
1
1
0
0
2
1
0
1
1
1
1
1
2
2
1
0
0
0
2
3
1
1
1
0
1
2
2
1
1
0
1
0
1
0
2
1
0
2
0
0
1
2
1
2
1
0
1
1
1
1
2
1
1
1
2
0
1
1
1
1
1
0
2
2
1
2
2
0
1
2
1
1
1
1
2
1
2
1
1
0
1
1
0
1
1
2
0
2
1
1
2
1
1
3
2
1
1
1
1
0
2
0
1
1
2
5
1
1
1
1
2
1
1
2
1
1
2
2
1
0
0
0
0
1
1
2
2
1
1
1
1
0
1
0
1
1
2
1
1
1
2
2
1
1
1
2
2
2
0
1
2
1
1
1
1
2
2
1
0
0
1
0
1
1
0
0
0
2
1
0
0
1
1
1
2
2
0
0
1
0
1
0
0
0
1
0
1
1
1
1
1
0
0
1
2
1
1
1
1
0
0
0
0
1
1
0
1
1
1
1
0
2
1
2
1
1
2
0
2
2
2
2
0
1
1
2
1
2
2
1
1
1
2
2
2
1
1
1
1
1
1
0
2
2
2
0
0
1
2
1
0
2
2
2
2
0
1
1
0
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
0
2
0
2
2
0
1
1
1
2
1
0
2
0
1
1
0
1
0
1
1
1
1
2
1
1
0
1
2
1
1
2
1
1
2
1
2
1
3
2
1
0
1
2
1
0
1
1
0
1
1
1
0
2
0
0
0
1
0
1
1
1
0
1
1
0
0
1
1
1
2
1
1
2
1
1
0
1
1
1
1
1
1
1
2
2
2
1
1
0
0
0
0
1
1
1
1
1
2
1
1
1
0
2
1
1
3
1
1
2
0
0
1
1
0
1
1
2
1
2
1
1
0
2
2
1
1
1
1
1
1
1
1
2
0
2
0
1
1
1
0
1
1
1
1
1
1
2
1
2
1
0
2
1
2
2
1
2
2
1
2
0
1
2
1
0
1
1
2
2
1
0
1
2
1
2
0
1
2
1
1
1
1
1
1
0
1
1
1
1
2
1
1
1
2
1
2
1
1
0
1
2
1
1
1
1
1
1
1
1
2
1
0
0
0
1
0
2
2
1
2
1
1
1
1
0
2
0
1
0
1
1
0
1
1
1
1
1
2
1
1
0
1
1
0
2
0
1
1
2
1
4
1
0
1
1
1
1
1
2
2
1
0
1
1
1
2
0
2
1
1
1
2
2
2
2
1
1
1
1
2
0
1
2
2
1
1
1
2
1
2
0
1
1
0
2
2
1
1
2
1
2
1
2
1
2
1
2
1
0
1
0
1
1
1
0
2
1
0
1
2
2
1
0
1
2
1
1
1
1
0
2
2
0
2
2
1
2
1
2
2
0
2
2
0
2
1
0
1
0
1
1
1
2
2
2
1
2
1
2
1
2
1
1
0
2
0
0
1
1
0
2
0
1
5
1
1
0
2
2
1
1
1
1
0
1
1
1
1
2
1
1
1
0
2
2
0
1
0
0
1
0
2
1
2
1
1
1
0
1
1
1
0
1
1
0
1
1
1
1
2
1
1
1
2
0
0
1
1
1
2
0
1
0
0
2
1
1
1
0
2
0
0
0
1
3
2
1
1
1
2
2
1
1
1
2
1
0
1
1
1
0
2
1
1
1
1
1
2
1
2
1
1
1
1
1
0
1
2
2
1
1
1
1
0
1
2
1
2
1
0
1
2
1
1
1
2
2
1
2
1
1
1
0
0
0
1
1
1
2
0
1
1
1
2
1
1
0
1
1
0
0
1
1
1
2
1
2
2
2
2
0
1
2
0
1
0
1
1
0
1
1
0
0
1
1
1
2
0
1
1
1
1
1
0
0
1
0
2
2
1
2
1
1
0
1
1
2
0
0
1
2
1
1
0
0
2
2
2
1
0
2
0
2
3
2
1
0
0
1
2
0
1
0
1
1
2
2
1
0
1
1
1
2
1
1
0
0
1
2
1
0
1
1
1
2
1
1
1
1
1
0
1
1
1
1
0
2
1
2
1
2
1
2
0
1
1
2
2
1
2
0
0
1
2
1
0
1
3
1
2
1
2
1
1
1
0
0
1
2
1
0
2
0
1
2
2
0
2
0
0
0
2
0
1
2
2
1
1
1
1
1
1
1
1
1
2
1
1
0
2
1
2
0
1
2
2
1
1
2
0
1
1
1
2
2
0
0
1
1
0
0
1
1
1
2
2
1
2
2
1
0
1
1
2
2
1
0
2
2
1
1
2
1
1
0
1
2
0
0
1
1
1
1
0
0
0
3
1
1
1
2
1
1
1
2
1
2
1
1
1
1
2
2
2
0
1
0
1
2
1
0
0
2
2
0
1
0
2
1
1
1
1
1
0
1
1
0
1
2
1
1
2
1
1
0
1
2
0
0
1
1
1
0
2
1
1
2
2
1
0
0
0
2
2
2
1
1
0
2
0
1
1
0
2
1
1
1
0
1
1
2
1
1
2
1
2
0
1
1
2
1
1
1
2
0
1
1
2
0
1
1
1
1
1
0
0
1
0
1
1
1
1
0
2
0
1
1
0
1
1
0
0
1
1
0
0
1
0
2
2
2
0
1
1
1
2
0
0
1
1
2
0
1
0
2
0
1
1
2
1
1
4
1
1
1
1
1
0
1
0
1
0
1
1
1
2
1
2
0
0
1
1
1
1
1
1
2
2
0
0
0
1
1
3
0
2
1
0
1
2
1
0
0
1
3
1
0
2
1
1
1
1
0
1
0
2
1
0
1
0
1
1
1
2
0
1
0
2
2
0
1
3
0
2
1
0
3
1
2
1
1
1
1
1
0
0
0
2
1
1
2
1
1
1
1
0
0
1
1
1
1
0
2
0
1
1
0
0
2
1
2
0
1
1
2
1
2
0
1
1
0
1
1
0
2
0
1
1
1
0
4
1
1
2
1
2
1
0
1
1
0
1
1
1
2
1
2
2
1
0
1
1
1
0
2
3
1
2
2
0
1
0
2
2
0
0
1
0
0
1
0
2
1
1
2
1
2
1
1
2
0
1
0
2
1
1
1
2
1
1
1
1
1
0
5
1
2
1
1
1
1
1
0
2
0
0
0
1
0
1
1
0
0
1
1
1
2
1
1
2
1
1
2
2
1
1
1
1
1
0
1
1
2
2
1
1
1
1
2
2
0
2
1
1
1
1
0
2
1
2
1
1
2
0
1
1
2
0
1
2
1
1
0
1
1
1
1
1
1
1
1
2
1
1
1
1
2
0
1
1
2
2
1
3
1
0
0
1
0
0
2
2
1
1
1
0
0
0
2
1
1
1
1
0
2
1
0
0
1
1
1
1
1
3
1
1
1
0
1
2
1
2
1
2
2
1
1
1
2
1
1
2
1
2
2
0
0
1
1
1
1
1
2
1
0
1
1
1
1
2
1
2
0
1
1
1
2
1
0
1
1
0
2
1
1
2
0
1
1
1
1
1
2
0
2
2
1
1
1
1
1
0
2
1
0
0
0
0
1
1
1
2
1
1
0
1
2
1
1
2
1
1
2
1
0
2
2
1
1
1
1
2
1
2
1
2
2
0
0
2
0
1
0
3
0
1
1
1
0
2
3
2
0
1
0
1
0
2
2
1
1
1
1
1
0
2
2
0
2
1
1
0
1
1
1
1
0
0
2
1
1
0
1
1
2
2
1
0
1
1
2
1
1
2
2
1
0
1
2
3
0
1
1
0
1
1
2
2
0
1
1
2
1
1
1
1
1
2
1
1
0
2
1
0
1
1
2
1
1
1
2
1
1
0
2
0
0
0
1
2
1
2
1
1
0
0
1
1
1
2
2
2
1
0
2
1
2
1
1
1
2
1
1
0
0
2
2
1
2
0
0
1
1
2
1
1
0
0
2
0
2
0
0
0
1
0
1
2
0
1
2
2
0
1
1
1
1
0
1
0
1
2
2
0
1
0
1
1
0
0
1
1
1
2
2
1
2
2
1
1
1
1
0
1
2
1
1
1
2
1
1
1
1
1
2
1
1
2
1
0
0
1
0
1
2
0
1
0
2
1
2
0
1
2
0
1
1
2
2
0
1
1
1
0
2
1
2
2
1
1
0
1
2
1
1
1
2
0
0
1
1
1
1
1
1
1
1
1
2
2
1
0
2
2
1
2
2
2
1
1
1
1
1
1
2
1
2
2
1
0
1
0
0
2
0
1
1
2
0
2
1
2
2
1
1
1
0
0
1
1
2
2
0
0
0
0
1
2
1
0
2
2
1
2
1
1
1
0
1
0
1
0
0
0
2
0
2
2
1
0
2
1
0
1
1
0
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
0
0
1
2
2
1
1
0
0
2
1
0
1
0
0
1
0
2
0
2
1
1
2
2
0
1
2
0
1
1
2
0
0
0
1
1
1
1
2
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
0
0
1
1
2
1
0
1
2
1
1
0
1
0
2
1
1
1
1
1
0
1
1
1
2
1
1
1
1
1
2
1
1
2
1
1
0
0
1
0
0
1
1
1
1
1
1
1
1
1
1
0
1
1
0
0
1
0
1
2
1
2
1
1
1
0
1
1
1
2
0
2
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
0
1
2
0
1
1
1
0
0
0
0
1
2
0
0
2
0
2
0
1
1
2
1
2
1
1
2
1
1
1
1
0
1
2
2
0
0
2
2
1
0
0
0
2
1
0
1
1
2
2
2
2
0
1
1
0
0
1
1
2
1
1
1
1
1
2
0
2
2
1
2
1
0
1
0
1
2
1
1
0
2
1
1
1
1
1
0
1
1
2
1
1
2
2
1
2
1
2
3
0
1
1
0
2
1
1
0
1
1
0
2
0
2
1
1
1
2
1
0
1
0
0
0
0
3
1
1
1
1
1
2
1
2
1
0
1
1
1
1
0
0
1
1
0
1
0
1
1
1
1
0
3
0
1
2
1
1
3
2
1
0
2
2
1
0
0
1
1
0
1
0
1
0
0
0
0
1
0
2
1
0
1
0
1
1
0
1
2
0
2
2
2
1
1
2
1
1
2
0
0
2
1
1
1
1
2
0
2
1
1
1
1
0
2
3
1
1
1
1
1
1
1
1
0
1
0
0
2
1
0
1
0
2
2
1
2
2
2
1
1
1
1
1
0
1
0
1
1
1
1
1
0
1
1
0
0
2
1
0
1
1
1
1
0
1
2
1
2
1
0
0
1
1
1
2
1
1
0
1
1
0
0
0
0
1
2
1
2
1
2
1
1
0
2
1
1
1
1
1
1
1
1
0
1
1
1
1
0
2
1
1
1
1
1
0
2
1
1
0
0
1
1
1
1
1
2
1
1
1
1
0
0
1
1
0
1
1
1
0
0
1
0
1
1
0
2
2
1
1
1
1
1
0
0
4
1
0
0
1
0
2
1
2
2
0
0
0
1
1
0
0
1
1
0
1
1
1
0
1
0
1
1
1
1
0
2
0
1
1
2
0
1
2
2
2
2
1
1
1
2
0
0
1
1
2
2
1
2
1
2
1
2
2
2
0
0
2
0
1
0
1
2
0
1
1
1
2
0
0
1
1
1
1
1
1
1
2
2
1
2
1
1
1
2
2
0
2
1
1
2
1
1
1
1
1
1
2
0
1
0
0
2
0
1
2
1
2
2
1
1
0
1
0
2
1
2
2
2
1
2
1
1
1
1
0
1
2
1
2
1
1
1
1
1
2
1
1
1
1
0
1
0
1
2
0
0
1
0
1
2
1
1
0
1
1
1
2
2
2
0
2
1
1
0
1
2
1
0
1
1
1
1
0
1
1
1
2
1
0
2
2
1
2
2
0
0
1
1
1
0
0
1
1
1
2
0
0
1
2
0
0
0
2
1
0
1
1
1
1
2
1
1
1
0
1
0
1
2
0
2
2
1
1
2
1
1
1
1
1
2
1
2
3
1
2
1
1
1
1
1
0
0
1
2
2
1
1
0
0
2
1
1
1
2
1
1
0
0
2
1
1
1
1
2
0
1
1
2
2
0
0
1
1
0
1
0
1
0
2
1
1
1
1
2
2
1
0
2
2
1
1
2
2
2
1
2
1
0
1
0
2
1
2
1
1
0
1
0
0
1
2
1
2
0
4
1
0
0
2
1
1
1
1
1
1
1
2
2
1
1
1
1
2
3
2
1
2
1
0
0
1
1
1
1
0
1
1
0
1
2
0
1
2
2
0
0
1
1
2
1
1
1
1
1
1
1
1
2
2
1
2
0
2
0
2
1
2
2
2
1
1
1
1
1
0
0
1
1
1
1
1
1
1
1
1
0
1
4
1
1
1
2
1
2
1
1
0
2
1
2
2
1
1
0
1
1
0
1
0
2
1
2
1
1
1
1
1
1
2
0
1
1
0
1
0
2
2
1
1
1
2
0
1
1
1
2
2
0
1
0
0
2
1
3
1
0
1
1
1
1
1
1
1
1
2
1
1
0
0
2
2
2
2
1
0
2
1
4
2
1
1
0
1
1
1
1
2
1
2
0
3
2
1
0
2
1
2
1
0
1
0
2
0
2
0
2
1
0
1
1
1
0
1
1
1
1
2
0
2
1
2
1
2
1
0
1
0
1
1
1
1
1
1
2
1
1
2
1
1
1
4
1
1
2
1
1
2
1
1
2
2
2
1
2
2
0
2
2
1
0
0
1
1
0
1
1
0
2
1
2
0
1
2
0
1
0
1
1
0
1
2
2
1
1
0
1
0
1
1
2
0
2
2
0
1
1
1
0
3
1
2
2
0
1
1
3
2
2
1
2
1
2
2
1
1
1
0
1
0
1
2
1
2
0
1
1
2
2
1
1
1
2
0
1
1
1
1
0
0
0
3
0
1
1
2
1
2
1
1
2
1
1
1
1
1
1
0
1
0
1
1
3
1
2
1
1
1
1
2
1
1
1
1
0
0
2
1
1
2
1
1
0
2
1
1
2
0
1
2
2
0
0
1
1
0
1
2
1
1
1
1
1
0
2
0
2
2
2
1
1
1
0
1
1
0
1
2
1
0
1
1
2
0
2
2
1
2
1
1
2
0
1
1
0
1
2
0
2
1
2
2
1
2
1
1
2
2
2
1
1
1
1
1
2
1
3
1
0
0
2
1
1
1
2
0
1
1
1
1
1
1
1
2
1
1
2
1
0
3
1
1
1
1
1
2
1
2
1
1
1
1
0
2
1
1
2
0
1
2
2
1
1
2
0
1
1
1
1
2
0
1
0
0
0
2
2
1
1
1
0
0
1
2
1
1
0
2
1
2
1
1
1
1
1
0
2
1
1
1
1
0
0
0
2
2
0
0
1
2
1
1
1
0
1
2
1
2
1
1
0
2
2
1
0
0
2
1
1
1
0
1
1
1
2
1
1
2
1
2
2
1
1
2
1
1
2
0
1
1
1
0
2
1
0
1
1
2
2
1
1
1
2
2
2
1
0
1
2
0
0
2
1
4
1
1
2
0
1
2
2
2
1
2
2
0
1
0
1
1
1
1
2
0
1
0
0
1
0
2
1
2
2
1
1
1
1
1
2
0
2
0
0
0
0
1
2
0
1
2
2
1
1
1
2
1
1
0
2
2
1
3
1
1
1
1
1
1
1
0
1
1
2
0
1
1
1
1
1
2
1
1
1
1
1
1
1
0
0
1
3
0
1
1
2
0
1
2
1
1
1
0
2
1
1
0
1
1
1
1
0
0
0
2
1
1
0
1
1
1
4
0
0
1
1
2
1
2
1
1
2
1
1
0
1
1
1
0
1
1
1
2
1
2
2
1
1
2
1
1
0
1
1
2
2
1
0
0
1
2
1
1
1
1
1
0
1
0
2
0
1
0
1
1
1
2
2
1
1
2
0
1
0
0
1
2
1
1
1
3
1
0
1
1
1
0
1
2
2
1
2
0
1
2
2
1
1
0
1
0
1
0
1
1
2
1
1
0
1
1
1
1
0
0
2
1
1
1
2
1
2
1
2
0
2
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
2
1
0
2
1
0
2
1
0
1
0
2
2
2
2
1
0
0
1
1
0
1
0
2
1
2
1
1
1
2
1
2
1
2
2
1
2
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
0
1
2
1
0
0
1
1
1
0
1
2
1
0
1
0
1
2
2
1
1
1
0
1
1
1
2
1
1
1
1
1
1
1
1
0
1
1
2
1
1
1
2
1
1
2
1
2
2
1
1
1
0
1
2
1
1
2
2
1
1
1
0
2
1
0
2
2
1
1
0
1
1
1
1
1
1
0
1
0
2
0
0
1
1
0
0
0
1
1
1
0
1
1
1
1
1
1
1
3
1
0
1
1
1
2
1
1
1
3
0
1
1
1
2
2
1
0
1
1
2
1
2
0
0
0
1
1
0
1
1
0
1
1
1
2
2
2
1
2
2
1
0
0
2
1
2
0
1
0
1
1
0
1
1
0
0
1
1
1
2
1
2
1
1
0
1
1
1
2
1
1
1
1
0
0
1
1
0
1
2
2
2
1
1
1
2
2
0
2
0
1
1
1
2
0
1
1
1
2
2
0
1
0
0
0
1
0
2
1
1
0
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
0
0
0
0
0
0
0
2
2
1
0
0
1
1
2
1
1
2
2
1
1
0
1
2
1
1
1
0
1
1
0
1
1
1
0
2
1
0
1
5
1
1
2
1
1
2
1
2
1
1
2
1
2
2
2
0
0
0
2
2
1
0
1
2
1
1
0
1
1
2
3
1
1
1
2
0
2
0
1
2
1
1
1
0
1
1
0
0
1
0
2
2
2
1
2
0
1
1
2
0
0
1
2
0
0
1
2
1
2
2
1
0
1
1
1
2
0
2
1
1
0
1
1
0
1
0
1
2
2
2
0
1
0
1
0
1
2
1
0
0
1
0
1
0
0
1
1
2
1
1
1
1
1
1
0
0
1
0
1
1
1
2
2
0
1
1
0
2
0
1
0
1
2
1
1
1
1
1
1
0
2
1
1
2
1
1
1
1
2
2
2
1
2
2
1
1
2
0
1
0
2
1
2
2
1
1
2
2
0
1
2
1
0
1
2
1
1
1
2
0
0
2
1
0
1
1
2
0
2
1
1
3
2
1
2
0
0
2
2
0
0
1
1
0
1
0
2
0
1
1
1
2
0
1
1
1
2
1
1
1
0
0
1
0
1
1
1
1
1
1
2
0
0
4
1
1
1
0
1
1
1
1
1
0
2
1
0
1
2
2
1
2
0
1
2
1
1
0
1
1
1
0
2
1
1
0
1
4
0
1
1
0
0
2
1
2
1
1
2
1
0
1
1
1
1
1
0
1
1
1
1
2
1
1
2
2
1
2
0
2
0
0
0
1
0
1
2
1
1
1
3
0
2
1
1
2
2
2
1
0
0
1
1
0
0
2
0
1
1
1
2
2
1
1
0
1
1
1
1
1
1
1
2
1
2
1
1
1
2
1
1
1
0
2
2
1
1
0
1
0
2
1
1
2
1
0
1
0
0
1
2
1
1
1
1
1
1
1
2
1
2
1
0
1
1
1
1
1
1
0
2
2
2
0
1
1
1
2
0
1
0
1
1
2
1
1
1
1
1
2
2
1
2
1
1
2
0
2
2
2
0
2
1
1
0
1
2
1
1
1
2
1
1
1
2
1
2
1
1
2
1
2
3
0
0
1
1
1
1
1
0
1
0
0
2
1
0
1
2
1
1
0
0
1
1
1
1
1
2
1
1
1
2
1
2
0
1
1
2
1
1
1
1
2
0
0
2
2
1
0
1
2
2
1
0
2
2
2
1
1
1
1
0
1
0
2
1
1
0
0
0
1
3
2
1
2
1
1
2
2
1
2
2
0
1
2
2
1
1
1
0
1
1
2
2
2
1
1
2
1
4
1
0
1
0
2
1
2
1
1
2
2
2
1
1
2
1
0
2
0
1
1
2
0
1
2
1
1
2
1
2
0
1
0
1
1
0
1
3
0
1
2
1
0
1
1
2
2
1
1
0
2
1
2
2
2
0
1
0
1
2
2
1
1
1
1
2
1
1
1
0
0
1
0
2
1
0
1
2
2
2
1
1
1
1
0
2
1
2
1
1
1
1
0
1
1
1
0
2
2
1
1
2
0
1
0
1
0
0
1
1
2
0
2
1
1
0
1
1
2
2
0
1
1
1
1
2
2
3
0
1
0
2
0
1
1
1
2
2
0
0
1
0
2
1
1
1
0
1
0
1
0
0
1
2
1
0
2
2
1
2
1
2
2
0
2
1
1
2
1
1
2
1
1
1
3
1
1
0
1
2
2
1
1
1
0
1
1
2
0
1
1
2
1
1
1
1
1
1
1
1
2
0
2
0
1
1
2
1
1
0
0
1
1
1
0
1
0
2
0
0
1
2
1
2
1
0
1
0
1
0
1
3
1
2
1
1
0
0
2
0
0
1
2
0
1
0
0
2
1
2
1
0
1
1
2
1
0
1
0
1
0
2
2
1
1
1
1
1
1
0
1
2
1
1
0
0
0
1
1
0
1
1
0
2
4
1
0
1
1
0
2
1
1
1
2
2
0
2
1
1
1
2
0
0
2
0
1
2
1
2
2
2
1
0
0
2
1
1
1
1
1
1
2
1
0
1
0
2
3
0
1
2
1
2
0
0
1
2
1
1
1
2
1
1
1
0
0
0
1
0
1
0
2
0
1
2
2
1
2
1
2
0
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
2
0
1
0
2
0
2
1
1
1
2
0
0
1
1
1
1
0
1
0
0
2
1
1
1
1
1
2
1
0
1
0
2
1
2
0
2
0
1
2
0
2
2
1
1
0
1
1
1
0
1
1
1
2
2
1
1
0
1
1
1
1
0
1
1
2
2
0
1
0
2
1
1
1
1
2
2
3
1
2
2
2
1
2
2
2
1
1
1
2
1
2
1
2
0
0
1
1
2
2
1
2
0
1
1
2
1
0
1
0
0
1
1
1
2
0
0
0
2
2
1
2
1
2
0
0
0
1
2
2
0
0
1
1
1
0
0
2
2
0
2
1
0
1
1
1
1
1
1
1
2
1
0
2
1
0
1
1
2
0
0
1
2
0
0
0
1
1
2
1
0
2
2
0
1
1
1
3
1
0
2
1
2
1
0
1
1
0
2
2
0
1
1
1
2
0
0
0
1
1
1
2
0
1
0
1
1
2
2
1
0
1
1
2
1
1
0
2
1
1
1
0
1
2
0
1
2
1
1
2
1
0
1
1
1
1
2
2
2
1
0
1
1
1
1
2
0
1
0
0
0
1
1
1
2
2
1
1
1
1
0
0
2
0
0
2
0
1
2
1
1
1
1
1
1
0
1
0
1
1
1
1
1
0
2
2
2
1
1
1
1
1
2
1
1
2
0
1
1
1
1
1
1
2
0
2
3
2
2
2
0
1
1
1
1
3
1
0
1
1
2
2
0
2
0
1
1
1
1
1
1
1
1
1
2
1
0
1
1
1
0
1
1
0
0
2
0
2
1
2
1
1
1
1
0
1
1
1
1
1
1
3
0
0
0
1
1
1
0
1
1
1
1
0
1
1
1
0
1
2
1
1
1
2
0
1
0
0
1
0
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
2
1
0
1
0
2
0
1
0
2
1
1
1
2
1
1
1
1
2
1
2
1
2
0
1
1
1
1
1
3
0
1
0
1
2
0
1
0
1
1
1
1
2
2
2
1
1
1
1
3
1
0
1
0
1
1
1
1
2
2
1
1
1
0
2
1
0
2
1
0
1
1
1
2
1
1
0
1
1
1
2
1
0
2
1
1
1
2
0
2
1
2
1
1
2
1
1
2
1
2
0
1
1
1
1
1
1
0
1
1
0
2
1
2
0
1
2
0
0
2
2
1
1
2
1
2
0
1
2
1
1
1
1
2
2
2
0
1
0
1
1
1
1
0
0
2
1
1
2
1
1
1
1
2
0
1
2
1
2
1
0
1
1
2
1
2
1
0
0
1
2
1
2
0
0
2
0
2
0
0
1
2
1
1
1
1
1
2
1
1
0
2
0
0
2
1
1
2
0
1
2
1
1
2
1
1
2
3
1
1
1
0
0
2
0
0
1
2
0
0
2
1
1
1
0
1
1
1
0
1
1
1
1
2
1
1
1
2
2
1
2
1
1
0
2
1
0
1
2
1
1
1
1
1
0
2
0
1
0
0
2
1
1
2
1
0
1
1
1
1
1
2
1
1
0
1
1
1
2
1
0
1
0
1
0
1
2
1
2
2
1
2
1
1
0
1
2
3
2
2
0
2
0
2
0
1
1
1
1
1
1
1
2
0
2
0
1
2
1
2
1
1
0
1
1
1
1
2
1
0
0
1
0
0
2
1
1
0
1
1
0
1
1
0
0
1
0
2
2
2
2
0
1
1
1
1
1
1
2
0
1
1
1
1
1
1
1
1
1
2
1
2
2
0
1
1
1
1
1
1
2
1
1
0
0
1
0
0
1
1
1
0
2
1
1
0
1
2
1
1
1
0
1
1
1
0
1
2
0
0
2
1
1
1
1
1
1
1
1
2
1
1
0
1
1
2
1
1
1
0
2
0
1
0
0
2
1
1
0
2
1
4
1
1
3
0
1
1
1
2
0
3
1
1
0
1
1
1
2
0
2
1
0
3
1
0
2
1
1
1
2
2
1
1
1
0
1
0
0
1
1
0
1
0
1
2
0
1
0
2
1
2
1
0
0
0
0
0
2
2
1
0
0
1
1
1
1
0
1
2
0
2
1
1
2
2
1
2
1
1
1
1
1
1
1
2
1
0
1
1
1
2
1
1
1
1
0
1
1
2
1
1
0
1
2
1
1
0
1
2
1
0
2
0
0
1
1
2
1
1
1
1
1
1
0
2
2
0
2
1
0
0
1
0
0
1
2
2
2
1
1
2
1
0
1
2
0
1
2
1
0
1
1
1
1
2
1
2
1
1
0
0
0
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
2
1
0
0
0
1
2
1
0
0
1
1
1
0
2
1
0
1
1
1
1
2
0
1
2
1
1
0
0
2
1
1
2
2
1
1
1
0
0
1
1
2
1
2
1
1
1
0
2
1
1
1
1
2
1
1
2
1
1
0
1
1
1
1
2
2
2
4
1
1
2
2
1
2
2
1
0
1
2
0
2
0
0
0
0
0
1
1
0
1
1
2
1
2
2
2
1
1
1
1
0
1
1
1
1
0
0
0
2
1
0
1
1
1
1
1
2
0
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
2
2
0
2
2
1
1
2
2
1
0
2
0
0
0
1
1
2
2
2
1
1
1
0
1
1
2
3
1
1
0
0
1
2
1
1
1
1
1
2
1
2
1
2
1
1
2
1
0
1
1
1
1
2
2
0
1
1
2
1
1
2
2
0
1
0
2
3
2
1
1
2
1
1
1
1
1
1
2
1
1
0
0
1
2
0
1
1
1
1
0
1
1
2
2
2
1
1
1
2
2
2
1
0
1
1
1
1
0
1
0
1
1
2
1
1
1
1
1
1
1
2
1
0
1
1
1
1
1
1
1
0
0
0
2
0
1
2
1
1
1
2
1
0
0
1
0
1
1
1
2
1
1
0
0
1
2
1
0
2
0
2
2
1
2
2
0
2
0
2
0
2
1
2
1
2
5
1
1
3
0
1
0
0
1
1
1
1
1
1
2
1
1
2
1
2
2
1
1
1
1
0
1
0
1
0
1
1
1
0
3
4
1
1
0
1
0
1
1
2
1
1
1
1
1
1
1
2
1
0
1
1
2
2
0
2
0
1
1
1
0
2
1
2
0
2
1
0
1
2
1
1
1
2
2
1
0
2
0
2
0
1
1
2
3
1
0
1
2
3
1
1
0
1
1
2
1
1
1
1
1
1
0
1
1
0
2
1
3
2
2
1
1
0
2
1
2
1
0
1
2
0
0
2
2
2
1
1
1
2
1
2
0
1
1
0
1
1
0
1
1
1
1
2
1
2
1
1
0
1
1
2
1
2
1
0
1
2
1
1
1
1
2
1
1
1
1
2
2
1
2
1
1
1
1
2
0
1
1
2
2
1
1
1
2
2
3
1
2
1
1
2
1
1
2
1
1
1
0
1
2
0
1
1
0
1
1
1
1
0
1
0
1
2
0
0
3
2
2
1
1
1
1
2
1
1
2
1
2
2
0
1
0
1
1
2
1
1
1
2
2
0
1
1
1
3
1
2
0
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
2
1
0
2
1
0
2
1
1
0
0
1
0
2
2
2
1
1
2
0
0
1
1
2
1
1
1
1
2
1
1
2
1
1
1
2
0
1
1
1
1
1
2
1
1
1
0
2
1
2
0
1
0
0
2
0
0
2
2
1
1
0
1
0
2
0
0
0
2
1
1
1
1
0
0
1
0
1
2
1
0
1
2
1
1
1
2
0
1
0
1
1
1
2
2
0
1
1
2
0
1
1
1
1
0
1
1
0
2
1
2
0
0
0
2
0
2
1
0
1
1
0
1
2
1
1
1
1
2
1
0
1
1
1
0
2
0
1
1
0
1
1
1
0
1
2
1
1
2
2
1
0
1
0
1
2
2
0
0
0
2
2
1
0
1
1
1
1
1
4
1
2
1
1
0
1
1
1
2
1
0
1
2
2
1
2
0
2
1
2
1
1
1
1
2
1
2
1
2
2
0
1
1
1
0
0
0
3
2
1
1
1
2
1
1
1
0
0
3
1
1
1
1
0
0
1
1
2
2
1
1
1
2
2
1
1
1
1
2
1
1
2
0
1
2
0
0
2
1
2
1
2
1
1
1
1
1
1
0
1
1
1
1
2
1
2
0
2
2
0
1
1
2
2
2
1
1
2
2
1
1
1
1
1
0
2
0
0
1
1
3
2
1
2
3
1
1
1
0
1
1
1
0
1
2
1
1
0
1
1
1
1
1
1
2
1
2
2
0
2
2
1
1
2
1
0
1
1
0
0
1
1
1
1
0
1
1
1
0
1
1
1
1
1
1
1
1
2
2
0
0
2
0
2
2
1
2
1
1
1
0
1
1
2
1
1
1
0
1
1
1
1
1
1
2
0
2
1
2
1
1
2
1
1
0
1
0
0
1
1
2
1
0
1
2
1
0
1
1
0
1
1
1
2
2
2
1
1
1
1
2
1
1
2
1
2
2
2
1
2
1
1
2
1
1
2
0
2
0
1
2
1
2
0
2
0
0
2
1
1
2
0
2
1
1
1
1
1
1
1
1
1
0
0
3
1
1
1
1
0
1
0
1
1
0
1
1
2
1
1
1
1
3
2
1
2
1
0
1
2
1
2
0
1
1
2
1
1
0
1
1
1
1
1
0
2
2
1
1
1
1
2
1
1
2
1
1
1
1
1
2
0
0
0
1
1
1
0
2
2
1
1
0
1
2
1
2
2
2
1
1
1
1
1
1
2
1
1
0
1
2
1
0
0
2
1
2
2
2
0
1
1
2
1
1
2
1
1
1
1
0
0
1
0
0
1
1
1
0
1
0
1
2
1
1
1
1
1
0
1
2
1
1
1
1
1
1
1
0
0
1
1
0
1
1
1
2
1
2
0
0
2
2
1
1
1
0
0
1
2
1
2
2
0
1
0
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
2
0
1
2
1
0
1
0
1
2
2
1
2
1
1
0
0
1
2
0
2
1
0
1
2
2
1
0
1
2
2
2
1
3
1
1
0
1
0
1
1
1
2
1
2
1
2
1
0
2
1
1
2
0
2
1
1
0
1
1
0
1
1
2
1
1
1
2
1
1
1
0
1
1
0
1
0
2
2
1
0
1
1
1
1
0
1
1
0
0
1
2
1
1
1
0
2
1
1
1
0
1
1
0
2
1
1
0
1
1
0
1
0
1
1
1
1
1
2
2
0
1
1
1
1
1
1
1
2
1
1
2
2
1
0
1
2
1
2
1
0
1
1
2
1
1
1
0
1
1
0
1
0
1
1
1
1
1
1
0
1
2
0
0
0
1
1
1
2
2
1
2
2
1
1
1
2
0
2
2
1
1
0
0
1
1
1
1
1
0
1
3
1
0
1
1
0
1
1
0
1
0
1
1
1
1
0
2
1
1
1
2
0
0
1
4
1
2
1
2
1
0
2
0
1
1
0
1
1
1
1
1
2
2
0
1
0
2
0
1
2
0
0
1
1
0
1
0
2
0
1
0
1
1
2
0
2
2
1
2
2
1
2
0
2
1
3
2
3
1
1
0
1
1
1
0
1
2
1
2
1
0
2
1
1
1
1
1
1
1
1
1
0
0
2
1
2
1
1
1
1
0
1
2
1
0
1
1
1
1
0
1
0
2
1
0
2
2
0
0
2
2
1
1
1
1
2
1
1
1
1
1
2
0
1
0
1
0
2
1
0
2
0
1
0
0
2
2
1
1
1
1
1
1
0
0
1
1
0
0
1
0
1
0
2
0
2
0
2
1
1
1
1
0
1
1
1
2
2
1
2
2
1
1
1
2
1
1
1
0
1
1
1
0
1
1
1
1
2
2
2
2
1
1
0
0
0
2
1
1
0
1
1
1
0
1
1
2
1
1
1
0
1
2
1
1
1
0
2
2
1
1
1
6
1
1
0
1
1
1
1
2
1
1
2
1
2
1
2
1
1
1
1
2
2
1
4
1
1
2
0
2
1
0
0
1
1
0
1
1
1
1
0
1
0
1
1
0
1
0
1
0
2
2
1
1
1
1
1
1
1
1
2
0
1
1
1
0
0
1
1
2
0
1
1
2
2
0
2
1
0
2
1
1
1
2
0
2
1
2
1
0
1
0
0
0
0
1
1
1
1
1
1
2
0
1
2
0
1
1
2
2
2
2
1
2
1
0
0
1
2
1
2
0
2
1
0
2
0
2
1
1
0
1
0
1
2
1
1
1
1
1
0
0
2
1
1
2
0
1
2
1
0
2
0
0
1
1
1
2
1
1
2
1
0
2
0
1
1
0
1
1
1
0
1
2
1
0
0
1
1
2
2
2
1
1
0
2
1
1
1
0
1
0
2
1
2
0
1
0
1
1
0
1
1
2
1
1
1
0
1
1
0
2
0
1
1
0
1
0
2
0
1
2
0
1
2
1
2
1
1
1
1
1
0
2
0
0
2
1
1
0
0
2
2
1
2
1
1
2
2
1
1
2
1
1
0
1
0
2
1
0
2
2
0
2
1
1
1
1
2
1
0
2
2
2
2
0
1
1
0
0
0
0
1
1
2
2
2
1
2
2
1
0
0
1
2
0
2
2
2
1
0
2
2
2
0
4
1
0
1
0
0
1
0
1
1
0
1
1
1
2
1
1
2
1
1
0
0
2
2
1
2
1
1
1
1
0
1
1
0
2
1
1
1
1
1
1
1
1
2
1
0
1
1
1
0
0
1
0
1
1
1
0
1
1
1
0
1
1
1
1
1
2
1
2
1
1
2
2
0
2
1
0
1
1
2
2
0
1
1
2
2
0
1
3
1
1
1
1
2
1
0
1
2
2
0
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
2
1
1
1
0
1
0
1
0
1
2
2
2
1
2
1
2
1
1
1
0
0
0
1
1
2
0
1
1
0
1
2
1
1
0
1
1
1
1
2
0
1
0
2
2
1
2
1
2
1
1
1
1
0
2
2
1
2
0
1
2
2
2
1
2
1
1
1
1
1
1
1
2
0
1
2
1
2
1
1
0
1
1
1
1
0
2
1
2
2
0
1
0
1
0
1
1
2
1
0
1
1
1
0
1
1
1
1
1
2
0
1
1
1
1
2
0
0
0
2
2
0
1
2
2
1
0
0
1
2
1
3
1
2
2
2
1
0
2
1
1
2
1
1
1
1
1
2
1
1
1
2
0
1
1
2
1
1
1
0
2
1
2
1
1
0
1
1
3
2
1
0
1
0
1
1
1
1
0
1
0
1
1
1
1
0
2
1
2
2
1
2
0
1
1
0
2
2
2
2
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
2
2
0
1
2
2
0
2
2
2
2
2
3
0
1
0
1
1
1
1
1
1
0
2
1
2
0
1
1
1
0
1
1
1
2
1
0
1
1
0
2
1
1
1
0
2
1
1
1
2
1
0
0
1
2
1
2
1
1
1
0
0
2
0
1
1
0
2
1
1
1
0
2
1
0
1
2
1
1
1
1
1
1
0
0
1
1
1
1
0
1
1
1
1
2
0
0
1
1
0
2
0
0
1
1
0
1
2
0
1
0
1
1
0
2
1
1
1
1
1
1
1
2
1
1
0
0
1
1
1
1
0
2
1
1
0
2
1
0
1
1
1
1
1
1
0
1
0
2
0
1
1
2
1
2
1
0
2
2
0
1
0
1
1
1
2
1
1
0
1
2
0
1
1
2
1
1
0
2
1
2
1
2
1
0
0
1
2
1
1
1
1
0
2
1
0
1
2
1
0
1
1
0
0
0
0
1
1
2
1
1
1
1
1
0
2
2
1
0
0
2
1
0
1
1
0
1
1
1
0
1
0
0
1
1
1
0
1
1
2
1
0
1
1
0
1
1
1
1
1
1
2
1
1
0
1
1
0
1
0
2
2
1
1
0
1
1
2
1
0
1
1
1
1
2
1
1
1
1
1
2
2
1
1
1
0
2
0
2
1
1
2
1
1
1
1
2
1
0
0
1
1
1
0
2
1
0
0
2
1
0
1
0
1
1
1
1
1
0
1
0
2
0
1
1
0
0
1
0
2
1
0
1
0
0
1
2
0
1
0
1
1
1
1
1
0
2
0
1
2
0
1
1
2
2
1
2
1
2
2
1
2
0
1
1
0
0
1
1
2
1
1
1
2
1
2
0
0
0
1
2
1
1
0
1
1
0
2
0
2
0
1
1
0
1
1
1
1
1
1
2
2
3
1
1
0
1
2
1
1
1
1
1
1
0
0
1
1
2
1
2
1
1
0
1
1
2
2
2
1
0
1
1
1
0
1
1
1
1
1
0
0
1
0
2
2
2
2
0
0
1
0
2
0
1
0
1
2
3
1
1
2
0
1
1
2
1
0
0
1
1
0
2
1
0
2
1
1
1
0
2
0
1
2
1
1
0
2
2
1
2
1
1
1
1
1
0
2
2
0
1
1
1
1
2
1
0
2
1
1
0
0
0
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
0
0
0
1
0
1
0
1
2
1
1
1
0
1
2
0
0
1
0
1
0
1
2
1
0
2
2
2
1
1
0
2
1
1
1
4
0
1
0
2
1
1
1
1
1
1
2
0
1
2
1
1
0
2
1
2
1
1
2
1
0
0
1
1
1
2
0
2
1
2
1
1
1
1
1
0
1
1
1
1
1
1
2
1
0
1
3
1
2
1
1
1
1
1
1
0
0
2
1
2
0
1
0
2
1
2
2
1
2
2
2
2
2
1
1
0
0
0
2
0
1
0
0
1
2
2
1
1
1
1
2
2
0
1
1
3
2
0
2
1
0
0
2
1
1
1
1
1
0
1
0
1
1
1
1
1
1
1
0
0
2
2
1
0
1
1
1
0
2
1
2
1
0
1
1
1
1
1
1
1
1
2
0
0
1
1
1
1
1
1
1
1
2
1
2
1
0
2
1
2
0
1
1
1
1
1
1
1
1
1
1
0
1
2
1
1
1
1
2
1
1
1
1
1
1
0
1
0
1
1
1
2
2
1
1
1
2
1
2
1
1
2
1
1
2
1
2
2
1
1
1
1
1
1
1
1
0
1
1
1
0
0
1
0
1
1
1
3
1
1
1
1
1
1
0
2
1
2
2
1
1
2
1
1
1
2
0
0
1
1
0
1
1
1
1
0
1
1
1
2
1
1
1
1
1
2
1
0
0
0
1
1
2
1
1
1
0
1
0
1
0
0
1
0
0
0
0
1
1
1
1
1
0
0
0
1
0
1
1
1
1
2
1
1
1
1
1
1
0
0
2
2
0
0
1
0
2
2
2
1
1
2
2
1
2
0
0
0
1
2
1
1
0
2
0
1
1
1
1
1
1
1
1
1
0
0
0
1
2
1
2
0
1
1
1
0
2
1
1
1
1
2
3
1
1
0
1
1
1
1
0
1
1
0
1
1
1
1
1
2
0
2
0
2
0
2
1
2
0
1
2
1
1
1
0
0
1
1
1
1
2
2
0
2
1
2
0
1
1
1
1
1
1
1
2
2
1
0
2
1
2
1
2
2
0
1
0
1
2
1
1
1
1
1
0
1
2
0
1
0
1
0
1
2
1
1
1
1
1
2
1
1
1
2
1
1
2
2
1
2
1
0
2
2
1
1
1
1
1
1
0
1
1
0
1
1
1
1
1
0
0
1
1
0
1
2
1
1
0
1
2
0
0
1
1
2
1
1
2
0
0
1
2
2
0
1
1
1
1
0
2
0
0
1
1
1
1
1
0
1
2
1
1
1
0
1
2
1
1
1
2
1
2
1
2
1
0
1
0
2
2
2
0
1
2
2
0
2
2
1
1
2
1
2
1
0
2
1
1
0
1
2
1
1
0
2
2
1
0
1
1
1
1
1
1
2
0
2
1
0
1
1
1
2
1
1
1
0
0
1
2
1
1
1
0
0
1
1
1
1
1
1
1
0
0
0
1
1
2
0
0
1
1
0
1
1
1
1
0
2
1
2
2
1
1
0
1
2
1
1
1
1
1
1
1
1
0
1
1
1
1
2
0
1
1
0
1
1
0
1
1
0
1
0
2
1
1
2
1
1
1
1
1
1
0
1
0
0
1
2
0
1
1
0
1
1
0
2
0
1
1
2
1
0
0
2
1
1
2
2
0
0
2
2
1
1
1
1
0
1
2
0
1
1
1
0
1
0
1
0
2
3
1
1
1
2
1
0
2
1
0
2
1
2
1
0
1
1
1
1
1
0
2
1
1
1
1
2
0
1
1
0
1
1
0
1
1
2
1
2
2
2
1
1
1
2
2
2
2
1
0
1
0
1
2
1
1
0
1
3
1
1
1
2
1
1
1
1
2
0
1
1
1
0
2
1
1
1
0
1
1
1
0
1
0
0
1
2
0
1
1
2
2
2
0
1
0
2
1
1
0
0
1
1
0
1
0
1
1
2
1
1
1
1
1
1
2
0
1
2
1
0
1
0
1
2
2
2
1
2
1
1
0
1
1
1
2
1
2
1
0
0
0
1
0
1
1
0
1
0
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
0
2
1
2
1
1
0
1
0
2
1
2
0
0
1
1
1
1
1
0
1
1
0
0
0
0
0
2
1
2
1
0
0
1
1
1
0
2
1
0
1
0
0
3
2
1
1
2
1
1
1
1
2
1
1
1
1
1
1
2
0
1
0
1
1
2
0
1
2
1
1
1
1
1
1
1
2
2
1
2
2
2
0
0
0
0
2
0
1
2
2
1
0
2
2
2
1
0
1
1
0
2
1
1
2
1
1
1
1
0
1
0
0
1
0
1
0
1
0
0
1
0
2
1
0
1
1
1
0
1
2
2
1
0
2
1
2
2
2
2
2
0
2
1
1
2
1
2
2
1
1
2
0
1
2
2
2
2
1
1
1
1
1
1
1
2
0
1
0
1
1
2
3
1
1
1
1
2
1
4
0
1
1
1
0
1
1
0
1
2
1
1
0
2
2
1
1
1
2
1
1
0
1
1
1
1
4
2
1
1
2
1
1
0
1
1
2
0
1
1
1
0
1
1
2
0
0
2
1
2
1
0
1
1
2
1
0
0
2
2
2
0
2
0
2
1
2
1
2
0
0
1
2
0
0
1
1
1
0
1
0
2
1
1
0
1
1
2
0
1
1
0
2
1
0
1
1
2
1
1
1
2
2
1
2
1
2
2
1
1
2
2
0
1
1
2
1
0
1
3
1
1
0
1
0
2
0
0
0
1
1
1
2
1
0
1
1
0
2
1
2
1
1
1
2
2
0
2
2
2
1
0
1
2
0
1
2
2
0
1
2
2
0
2
1
1
1
1
1
1
2
0
1
1
2
1
1
1
2
0
0
2
1
1
1
1
2
2
2
1
1
0
0
0
1
0
2
0
0
1
0
1
0
1
1
1
1
1
1
0
2
2
1
2
0
1
2
0
1
2
2
1
2
1
1
1
1
1
0
2
0
1
2
0
2
1
2
0
0
1
2
1
0
3
0
1
1
1
2
0
2
2
1
0
1
1
0
1
1
1
1
1
2
1
0
1
1
0
2
0
2
1
1
0
2
1
1
1
1
2
0
1
1
1
2
3
1
1
2
1
0
1
1
2
2
1
1
0
1
2
1
2
0
0
1
1
0
1
1
1
0
1
2
1
0
0
1
2
1
1
1
1
0
0
1
0
1
1
2
0
0
1
1
0
1
1
1
1
1
1
4
1
1
0
2
0
1
1
2
1
2
2
0
2
1
1
0
0
2
1
0
0
1
1
2
3
3
1
1
1
0
4
1
2
0
0
1
0
1
2
1
1
1
2
2
0
1
1
1
2
1
0
1
2
0
0
1
2
0
2
0
1
0
0
2
0
1
1
1
1
2
1
0
1
1
1
1
1
1
0
2
2
1
1
1
2
3
1
0
1
0
1
2
2
1
1
1
1
1
3
0
1
1
0
0
1
1
0
2
1
1
0
2
1
1
1
1
4
2
2
0
0
1
2
0
1
0
1
1
1
0
2
1
1
2
0
1
1
2
0
1
1
2
2
1
3
1
1
2
2
0
2
1
1
1
0
1
0
1
0
1
1
1
0
1
1
1
1
1
1
1
0
2
2
1
1
0
1
1
1
1
2
0
2
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
0
1
1
1
1
1
2
2
1
1
2
1
1
1
2
1
1
1
1
0
1
2
2
2
2
1
1
1
0
1
1
0
1
1
2
1
0
1
0
2
1
1
1
1
2
1
1
1
3
2
1
1
1
1
2
1
1
2
2
1
1
2
1
2
0
1
1
2
0
0
1
0
1
2
0
2
2
0
1
1
1
2
2
1
1
1
2
0
1
1
2
1
1
1
2
0
1
2
2
1
1
0
4
0
0
1
1
1
0
1
0
0
2
2
1
1
1
1
1
1
2
0
2
0
1
0
0
2
1
3
1
0
1
1
1
0
2
0
1
1
1
2
1
1
1
2
2
1
1
1
1
0
0
2
1
0
2
2
1
2
1
1
1
0
1
2
1
1
1
0
1
1
1
0
2
2
1
0
0
1
1
2
2
0
1
2
1
2
0
0
0
2
1
1
0
2
1
0
1
2
1
1
2
2
1
1
1
1
1
2
1
1
1
0
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
0
1
1
0
0
1
1
1
2
1
0
1
0
1
1
2
0
1
1
1
0
1
1
1
1
1
1
0
1
1
1
1
2
1
0
1
2
0
0
2
0
1
1
0
0
2
1
1
1
0
1
2
1
1
0
1
1
0
1
2
1
0
1
1
1
1
2
1
0
2
2
2
1
1
0
0
1
2
0
2
1
1
0
1
1
2
0
0
0
1
1
0
1
1
1
0
1
2
2
1
1
1
2
1
1
1
1
1
1
1
1
0
1
1
0
0
1
1
1
1
2
0
1
1
0
1
1
1
2
1
1
1
1
1
1
1
1
2
0
0
1
2
0
1
1
2
1
0
2
1
0
0
0
0
0
1
2
0
1
0
1
1
1
1
1
2
1
2
1
1
1
0
1
1
1
2
1
1
0
1
1
0
2
1
0
0
1
1
1
1
1
1
1
1
0
0
1
2
1
1
2
1
1
2
1
2
1
0
1
0
1
1
1
4
2
2
1
1
1
2
2
1
1
2
0
1
1
0
1
0
1
1
2
1
1
1
2
1
1
1
1
1
0
1
1
0
1
2
1
2
2
1
1
0
1
4
1
0
0
2
0
1
2
2
0
1
1
1
2
0
1
2
0
0
1
1
1
0
2
1
1
1
2
0
0
0
2
0
2
1
1
0
1
1
0
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
2
0
1
1
1
2
2
2
1
1
1
1
0
1
1
2
0
1
1
1
1
2
1
1
1
1
2
0
0
1
1
2
1
2
1
0
0
1
1
1
0
2
1
0
1
1
0
2
1
1
2
1
1
1
1
1
1
1
0
2
1
0
0
1
2
0
0
0
2
1
2
2
0
0
2
1
2
1
0
0
1
1
1
2
1
1
1
0
1
1
2
2
2
1
1
0
0
2
1
2
0
1
1
2
1
2
2
2
2
1
1
1
2
2
1
0
1
1
1
0
1
1
0
0
1
0
0
1
1
0
1
1
2
2
1
1
0
1
2
1
0
4
0
1
1
1
1
1
2
1
0
1
1
1
1
1
1
3
1
1
1
1
1
1
1
2
1
1
1
1
1
2
0
2
2
0
0
0
1
1
1
0
1
1
1
0
2
1
1
0
1
1
1
0
1
2
1
2
1
0
1
2
1
2
0
1
2
1
2
2
0
2
2
1
0
1
1
2
0
1
0
1
2
2
1
0
2
1
2
1
1
2
1
2
1
2
1
2
0
1
0
0
1
1
1
0
1
2
1
1
0
0
1
0
2
1
1
1
1
1
0
1
1
1
0
1
1
0
2
1
1
2
1
2
0
1
1
1
2
1
0
1
0
2
0
1
1
1
1
1
1
1
1
1
2
1
1
0
2
2
1
1
1
0
0
0
1
1
1
1
2
1
2
1
1
1
1
0
1
2
2
0
1
2
1
4
1
0
2
1
0
1
2
0
2
0
1
1
1
0
1
1
2
1
1
0
2
0
1
1
1
2
1
0
2
3
1
2
1
1
1
0
0
1
2
1
4
1
0
2
1
1
2
2
0
1
1
2
1
1
1
1
2
2
0
0
1
1
2
1
1
1
1
1
1
2
2
0
1
1
2
2
1
1
1
2
2
2
1
1
1
1
1
2
1
1
1
2
1
2
2
1
0
1
0
1
1
1
0
1
1
1
0
1
1
1
1
1
0
0
3
0
2
3
1
1
2
1
1
2
1
2
2
1
1
1
1
1
1
2
2
0
1
1
1
0
0
1
1
1
1
1
2
0
1
1
2
1
0
2
0
2
2
1
1
1
1
2
2
0
1
1
0
1
1
1
0
0
1
1
1
1
2
1
0
0
1
1
0
1
1
0
2
1
1
2
1
2
1
1
1
1
1
2
2
2
1
1
1
1
1
1
2
0
1
0
0
1
2
2
2
0
1
1
2
1
2
2
1
1
0
1
0
2
1
0
1
0
1
1
1
1
0
2
1
1
1
1
2
1
1
1
0
1
1
1
0
1
1
2
0
1
1
1
1
2
1
1
0
0
1
2
1
0
1
1
0
2
1
2
1
1
1
0
1
3
1
1
1
1
0
1
2
1
1
1
0
0
0
2
1
1
0
1
0
2
1
0
1
1
2
1
1
1
1
2
0
0
1
1
1
0
1
1
1
2
1
0
1
1
2
1
0
0
1
1
0
2
1
1
2
2
0
1
2
1
0
1
1
2
0
0
1
1
0
1
0
1
1
1
0
2
2
0
2
1
2
1
1
1
0
5
3
1
1
1
0
0
1
1
1
1
1
2
0
1
0
1
0
1
2
0
1
0
2
1
1
1
0
2
0
2
0
2
1
1
0
1
1
1
0
1
2
2
0
1
1
2
1
1
1
1
0
0
1
0
2
1
1
0
1
0
2
1
2
2
1
0
1
0
2
1
1
1
1
1
2
2
2
1
0
1
1
1
1
1
0
1
1
1
0
1
0
0
0
1
2
0
2
0
2
0
1
1
0
2
1
1
0
2
2
2
1
0
0
0
0
3
0
1
1
0
1
0
0
1
1
2
1
1
1
1
0
0
1
1
1
1
1
2
1
2
1
0
1
1
1
2
2
0
1
1
1
2
1
0
1
1
0
2
1
1
0
2
1
1
2
1
0
2
2
0
1
2
0
1
2
1
2
1
1
1
2
2
0
0
1
1
0
2
0
0
1
1
1
2
2
0
2
1
2
2
2
0
0
1
1
1
1
0
0
1
0
1
1
0
2
2
0
2
1
0
0
2
0
0
2
2
2
1
0
1
1
1
1
1
2
1
2
2
2
1
1
1
2
1
1
1
1
1
2
2
2
2
1
1
2
1
2
2
1
1
1
0
0
1
1
2
1
1
2
1
1
2
1
1
1
1
1
2
1
1
2
1
2
1
0
1
0
1
1
0
0
1
1
1
1
1
2
2
1
1
1
2
1
2
2
2
2
0
0
0
1
2
1
1
1
2
1
1
0
1
1
0
0
0
1
2
1
0
1
1
0
1
1
1
0
2
1
0
0
0
1
1
2
1
1
2
1
1
0
1
1
1
1
0
1
0
1
1
1
2
1
1
1
1
0
1
1
1
2
1
0
1
2
2
2
2
2
2
1
1
2
1
2
1
1
2
1
1
1
0
0
1
2
1
1
2
0
2
0
0
0
1
1
1
1
2
2
0
1
2
1
2
1
1
0
2
1
1
2
1
0
0
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
1
1
0
0
0
2
1
2
0
1
1
2
1
1
2
1
1
1
0
2
0
1
1
0
1
1
0
1
1
2
1
1
1
2
0
0
1
2
2
0
1
1
1
1
1
2
2
1
1
1
1
1
1
2
0
1
1
2
2
0
1
0
1
2
1
1
1
1
2
1
1
2
0
2
1
1
2
1
0
0
1
1
1
1
2
2
2
2
1
0
0
2
1
1
0
2
1
0
0
0
0
0
0
1
1
1
0
1
2
1
1
1
1
2
1
0
1
2
0
0
2
1
1
2
1
1
2
2
0
1
0
1
1
2
2
1
2
1
0
0
1
1
2
1
0
0
1
1
1
2
0
0
0
1
0
1
1
1
1
1
1
2
0
1
1
2
1
1
1
1
1
1
0
2
0
0
1
2
1
1
0
2
0
2
2
2
0
1
1
1
1
1
1
1
1
2
0
1
0
1
1
0
1
2
0
1
1
0
0
1
1
1
0
0
1
0
1
0
0
0
1
1
2
1
0
1
2
1
1
1
1
0
1
1
1
0
2
2
2
1
1
1
2
1
2
1
1
1
1
1
2
0
2
1
0
0
0
1
0
1
1
2
1
2
1
0
1
1
3
0
1
0
1
0
2
1
2
1
1
1
1
1
1
2
0
2
1
1
2
1
1
1
1
1
1
2
4
1
1
2
0
2
1
2
1
1
2
1
1
2
1
2
1
0
0
1
1
1
2
1
0
1
3
1
2
2
0
1
1
2
1
1
0
1
1
1
1
2
2
1
1
1
1
0
1
1
2
1
0
1
1
0
2
1
1
2
1
0
1
1
0
1
1
0
1
1
1
0
0
2
1
2
1
1
2
0
1
0
1
1
1
1
1
1
1
1
1
1
1
0
0
1
2
0
1
0
0
1
0
1
0
1
1
0
1
1
1
1
2
0
2
1
0
1
0
1
2
0
1
0
1
0
1
1
1
0
2
0
0
1
0
1
1
1
1
2
1
1
1
1
1
1
0
0
1
1
2
2
1
1
2
1
1
1
1
2
1
1
1
0
1
2
2
1
1
0
1
1
1
1
0
1
1
0
0
1
2
2
1
0
2
0
1
1
1
1
0
1
0
0
0
2
1
0
1
1
1
0
1
1
0
1
0
0
1
1
2
2
1
1
0
1
2
1
2
1
1
1
1
2
1
0
1
2
1
1
1
0
1
1
1
1
1
1
1
1
1
0
0
1
0
0
1
2
1
1
2
1
1
1
1
1
2
1
0
2
0
0
1
1
0
1
1
0
1
1
1
1
1
0
1
2
2
0
1
1
1
1
0
0
1
1
2
2
1
0
1
2
0
0
1
1
1
1
0
0
2
1
1
1
1
1
1
1
2
0
2
1
1
1
1
1
1
1
0
1
1
0
1
1
0
2
2
1
1
1
2
2
1
1
0
2
1
1
1
0
1
1
1
0
0
2
1
0
1
0
1
0
1
1
1
1
1
0
0
2
2
0
1
1
2
1
0
1
2
0
1
1
0
1
1
1
2
1
1
0
1
0
1
1
1
1
1
1
2
1
2
2
1
1
0
1
2
1
1
1
1
1
1
1
1
0
2
1
1
0
0
2
0
1
1
1
1
1
1
1
1
2
0
1
1
1
0
2
2
1
1
1
1
2
1
1
1
2
1
2
1
1
0
1
1
1
1
0
1
0
0
2
0
1
0
1
1
0
0
2
1
1
1
0
1
4
1
0
1
1
0
1
1
1
1
2
1
1
1
1
2
0
0
2
2
1
2
1
2
1
1
0
1
1
0
0
1
1
2
1
2
1
2
2
1
1
1
1
1
0
0
1
1
1
1
1
1
0
1
2
1
2
1
2
1
2
0
1
0
1
2
0
1
2
1
1
1
1
1
1
2
2
1
1
0
1
2
1
0
0
1
0
1
1
2
1
1
1
1
1
0
1
1
0
1
1
2
2
1
0
1
0
1
1
1
1
1
2
2
0
1
1
1
1
1
2
0
1
1
1
1
2
1
1
2
1
1
1
1
0
1
0
0
0
1
1
1
0
1
0
0
0
1
2
2
1
0
1
1
1
1
2
0
1
2
0
0
0
1
2
1
1
2
2
1
0
3
2
1
2
0
2
0
1
0
1
0
1
1
1
1
0
2
0
2
1
1
2
2
0
3
1
1
0
1
1
2
1
1
1
2
1
2
1
1
1
1
1
0
1
2
2
1
0
0
1
0
1
1
1
2
0
1
1
1
2
1
1
2
0
1
1
0
2
2
2
2
1
1
0
2
1
1
1
1
0
5
0
0
1
2
0
2
1
0
2
1
2
2
1
2
1
1
1
1
2
1
1
1
0
1
1
0
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
0
1
2
1
2
1
0
1
0
1
0
1
0
2
1
1
1
1
0
1
1
2
1
2
2
0
1
1
0
1
1
1
2
1
1
1
2
1
2
0
1
1
2
1
0
1
1
1
0
1
1
2
2
1
0
0
1
0
1
1
2
1
1
0
2
2
0
1
0
1
1
0
2
0
1
0
2
1
0
1
1
1
0
1
1
1
1
1
2
1
0
1
1
1
2
0
0
2
0
1
1
1
1
1
2
2
1
1
1
0
1
2
0
1
0
1
1
1
2
2
1
1
1
1
0
2
0
1
1
1
1
1
1
0
1
0
0
0
0
1
1
1
1
1
0
2
0
1
2
1
1
0
0
1
1
0
1
0
1
1
2
0
1
2
0
2
0
0
1
1
0
1
1
0
2
1
1
1
1
1
1
1
2
1
1
1
1
1
0
2
2
1
0
1
1
1
0
1
0
1
1
1
2
1
0
1
1
2
1
1
2
1
1
2
1
1
1
0
0
2
0
1
2
2
1
1
1
1
4
1
1
0
1
2
0
2
2
1
1
1
1
1
1
1
1
2
0
1
1
2
1
1
1
0
1
0
1
0
0
0
1
1
2
2
1
1
0
2
2
2
2
2
0
2
1
1
1
1
1
1
1
2
1
2
1
1
1
2
2
1
1
0
2
2
1
1
0
1
1
1
0
1
2
1
0
1
2
1
1
0
0
1
2
0
0
0
1
1
1
2
2
1
1
2
1
0
1
1
0
0
1
0
0
0
2
2
1
1
0
1
1
1
2
2
1
1
1
1
0
2
0
2
0
3
2
0
1
0
2
1
1
1
0
1
2
2
0
2
0
0
1
1
1
2
0
1
0
1
2
1
1
1
3
1
2
0
1
2
0
1
2
2
2
1
1
2
3
0
0
1
1
1
2
1
1
2
0
1
2
2
2
1
0
2
0
1
0
1
0
2
0
1
1
2
2
2
1
2
2
0
1
2
0
0
1
1
2
1
1
1
2
1
1
1
2
2
1
1
0
0
0
2
1
1
2
2
0
2
2
2
0
0
1
0
0
1
1
2
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
0
0
1
1
1
0
1
1
1
2
0
2
1
1
1
1
1
0
1
1
1
1
1
2
0
1
2
1
2
1
0
2
1
1
1
0
1
2
1
1
1
2
0
1
1
1
1
1
2
2
2
2
1
1
0
2
0
1
1
0
1
1
1
1
2
1
0
0
1
1
1
2
2
2
1
0
1
3
1
2
1
1
1
1
1
1
1
2
3
2
1
1
2
1
0
1
2
0
1
2
1
1
1
2
2
2
2
1
1
0
1
1
1
1
0
2
1
2
2
2
0
1
2
0
0
1
1
2
0
1
0
1
0
0
2
2
1
2
1
2
1
0
1
1
1
1
0
1
1
0
2
0
1
0
0
0
1
2
2
0
1
2
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
2
0
2
2
2
2
1
0
0
2
2
1
2
2
0
1
1
1
0
0
0
2
2
2
1
1
0
1
0
1
2
0
1
0
2
1
2
0
1
2
1
2
2
1
1
0
1
1
2
0
2
1
2
1
2
1
2
1
1
1
1
1
1
1
2
0
1
0
2
1
1
1
0
1
1
2
0
1
2
0
1
1
1
1
0
2
2
0
1
0
2
1
0
1
0
1
1
2
2
1
1
1
2
1
0
2
1
2
2
1
1
1
1
0
1
1
2
2
0
1
0
1
1
1
3
1
2
1
1
1
0
2
0
1
2
1
1
0
2
1
1
0
0
1
1
2
0
0
1
1
1
0
2
2
2
0
1
0
0
1
2
0
1
1
0
1
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
1
1
2
0
2
0
0
1
2
2
1
1
1
1
1
1
1
1
1
1
0
0
1
1
1
1
1
0
1
0
2
2
1
2
1
1
1
0
1
1
2
2
1
0
2
1
1
1
0
2
0
1
1
2
1
1
0
2
0
0
1
1
0
2
0
0
0
2
1
0
0
1
2
0
0
1
1
1
2
1
2
1
1
2
1
2
1
0
0
0
2
1
1
1
3
1
1
1
1
2
0
1
1
1
1
1
0
1
0
2
1
2
1
1
0
2
1
0
2
3
1
2
1
1
0
1
0
0
2
0
0
2
2
1
2
1
1
1
2
2
1
1
0
0
1
1
1
0
2
2
1
1
0
1
1
1
0
1
0
0
0
1
0
0
1
1
1
1
1
1
0
0
2
0
1
1
1
0
2
1
1
2
0
1
1
2
1
0
1
0
0
2
2
1
0
0
0
0
1
1
1
0
1
2
0
2
1
1
1
1
1
1
2
1
1
1
1
0
1
2
2
2
1
2
0
0
0
1
0
0
2
1
1
2
2
1
2
0
1
0
1
1
1
1
1
0
2
1
0
0
1
2
2
2
1
1
1
2
1
1
1
0
0
0
0
1
0
1
1
0
0
0
1
0
1
0
2
1
1
1
1
2
1
0
2
0
0
1
1
0
1
0
1
1
1
1
1
2
2
2
0
1
1
0
1
1
2
1
2
0
1
0
0
1
1
0
0
1
2
1
2
1
1
1
1
1
1
0
0
1
1
2
0
1
1
2
0
0
2
1
2
1
1
1
0
1
0
1
0
1
0
1
2
1
1
1
1
1
1
1
1
0
0
1
1
0
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
0
1
0
1
1
1
0
1
0
0
2
2
1
1
2
0
1
1
1
0
0
1
0
1
1
1
1
0
1
1
1
1
1
1
2
2
1
1
1
1
0
1
1
1
2
1
1
0
1
1
1
0
1
1
0
2
1
1
1
1
1
0
1
1
0
0
1
2
1
2
0
1
1
1
1
2
1
0
2
1
0
2
1
0
1
1
2
2
2
2
0
0
1
1
1
2
0
1
0
0
1
2
0
1
1
1
0
2
0
0
2
0
2
0
2
1
4
1
1
0
0
0
1
1
1
1
0
2
0
2
0
0
0
2
2
1
1
2
1
1
1
1
1
1
1
0
1
0
1
1
1
1
1
1
1
1
2
2
1
2
2
1
0
1
0
1
0
0
3
1
3
0
1
1
2
1
1
1
0
0
0
1
1
1
2
1
1
1
0
1
2
0
1
1
2
1
1
2
2
1
1
1
1
1
1
2
2
1
1
1
2
1
1
0
1
0
1
0
0
1
1
2
1
1
2
1
1
1
1
2
0
1
1
2
1
2
0
2
1
2
1
1
1
1
1
2
1
1
0
1
1
1
2
1
0
1
1
1
2
1
1
1
2
1
0
1
1
1
1
1
1
1
0
1
0
2
1
0
3
1
0
2
2
0
1
1
1
2
2
2
2
1
1
2
2
4
1
1
2
0
0
0
0
1
2
1
2
1
0
1
0
1
0
1
1
1
0
2
0
1
1
0
1
1
2
1
2
1
2
2
1
0
0
2
2
0
1
0
2
1
1
1
0
1
1
0
1
0
1
1
1
0
1
2
1
1
1
1
1
0
1
1
1
1
1
1
0
2
1
3
2
1
0
1
0
2
1
1
1
0
2
1
1
1
1
1
2
1
2
1
1
0
2
3
1
1
2
0
2
1
1
1
1
0
1
1
1
1
0
1
1
0
1
1
2
1
2
0
2
0
0
0
1
2
2
1
2
1
0
1
0
1
2
1
1
1
1
2
1
1
1
0
1
2
2
1
1
1
0
2
0
2
2
0
1
2
1
0
1
1
0
0
1
0
2
1
0
1
1
0
1
1
1
1
1
1
1
1
1
1
1
0
0
1
2
2
0
1
2
1
1
1
1
2
0
1
1
1
0
1
2
0
2
0
1
2
0
1
0
1
0
0
1
0
0
0
1
0
0
1
2
1
2
2
1
2
2
2
2
1
1
1
1
1
1
1
1
1
0
1
0
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
2
1
1
0
1
1
2
1
1
2
1
1
1
1
0
1
1
1
3
0
1
0
2
1
1
1
0
1
1
1
1
1
0
1
1
0
0
1
1
1
1
1
0
1
1
0
0
2
0
1
0
0
1
2
0
0
1
1
1
2
0
1
2
1
2
0
3
0
2
1
1
3
1
1
0
0
2
0
1
2
2
1
0
1
1
1
1
2
1
0
1
3
1
1
1
0
1
1
1
2
2
2
2
1
1
0
0
1
1
1
0
0
1
2
2
0
1
0
0
0
1
1
0
2
0
0
0
2
2
1
1
1
1
1
0
0
4
1
1
1
0
0
2
0
1
1
0
0
1
1
2
2
1
2
1
1
1
1
0
0
2
2
1
1
1
1
1
0
1
0
1
1
5
0
0
1
2
1
1
1
0
2
1
1
2
2
0
1
1
0
1
0
1
0
0
1
1
2
1
1
1
0
1
1
0
0
1
0
2
0
2
0
0
1
1
1
0
2
1
1
1
2
0
0
0
0
1
1
0
1
2
0
2
2
0
0
0
1
1
1
2
1
1
1
0
0
0
0
0
2
1
2
1
1
1
1
0
1
1
0
1
2
1
1
0
1
2
1
1
1
1
2
2
1
1
1
0
2
1
2
1
1
1
1
1
1
0
1
2
1
1
0
2
0
2
2
1
2
2
0
0
0
2
1
0
2
2
2
1
0
0
1
1
0
0
1
0
1
0
1
0
3
1
1
2
1
0
1
2
2
1
2
0
2
0
2
0
2
1
1
2
2
1
1
1
1
2
1
0
0
2
1
1
0
2
1
1
1
1
0
1
1
1
1
1
1
1
0
1
0
0
1
1
1
1
1
0
2
1
1
0
0
1
1
1
1
1
0
1
1
1
1
1
1
1
1
0
1
1
1
1
0
1
1
0
0
1
2
1
0
1
1
1
0
1
1
1
1
1
1
1
2
1
1
2
2
1
1
1
1
0
1
2
2
2
2
1
3
0
0
1
1
1
0
0
1
1
2
1
0
2
1
1
0
1
1
0
1
1
1
1
0
2
1
1
0
1
1
2
1
2
0
1
2
0
0
2
1
1
2
0
1
1
1
1
2
1
1
1
1
0
1
1
2
1
0
1
1
2
1
1
1
1
1
0
2
0
1
2
2
2
2
1
3
0
1
2
2
1
1
1
1
1
0
1
1
1
2
1
2
1
0
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
0
1
1
2
1
2
2
1
1
0
1
1
1
1
1
1
0
1
2
1
1
2
1
1
0
3
1
2
1
2
2
1
1
1
1
0
1
1
1
2
1
2
2
1
0
0
1
1
0
2
1
2
0
1
2
1
1
0
1
0
1
0
2
1
0
1
2
1
1
1
1
0
2
1
0
0
2
0
1
0
0
2
1
2
2
1
0
1
2
1
1
1
1
1
1
2
1
0
0
1
2
0
1
1
1
1
2
1
1
1
0
1
2
2
1
1
1
2
0
1
1
2
1
1
2
1
0
1
2
0
2
1
1
0
0
0
1
2
1
0
1
2
0
2
0
1
1
1
0
1
1
1
0
1
0
2
1
0
1
1
1
1
2
1
0
0
1
0
1
0
1
2
1
1
1
2
1
0
1
2
1
1
1
0
1
1
1
0
2
2
1
1
2
1
2
1
1
0
0
1
0
1
2
1
1
1
1
1
1
0
1
1
2
0
2
1
0
2
2
1
1
2
1
0
1
1
2
0
1
1
1
1
1
0
1
1
2
2
0
1
0
1
2
0
1
1
1
1
1
1
1
0
1
2
1
1
0
1
1
1
2
2
2
1
1
1
2
1
2
0
1
2
0
2
0
2
1
1
1
0
1
2
2
0
0
1
1
1
1
0
1
1
2
2
1
0
1
1
2
1
1
1
2
1
1
2
2
1
1
1
1
0
1
3
2
1
1
1
1
1
2
1
1
2
1
1
0
1
1
1
1
1
0
1
1
1
2
0
1
1
1
2
2
1
1
0
2
0
2
0
2
0
0
1
0
1
2
1
1
1
2
0
0
1
1
2
1
1
0
1
1
1
2
2
2
2
1
2
1
2
0
1
1
0
1
1
0
0
2
2
0
2
0
2
2
0
1
1
3
0
0
0
1
1
1
1
0
1
1
0
1
1
1
1
1
1
1
0
0
1
1
0
1
1
1
1
0
1
1
2
1
1
1
1
1
2
1
1
1
1
2
2
1
1
1
1
1
0
1
1
1
1
1
1
1
2
1
1
1
1
0
1
1
1
0
0
0
1
1
2
0
0
2
0
1
1
1
1
1
1
0
0
0
1
2
3
1
0
0
1
1
1
1
0
0
0
0
1
1
2
1
0
2
0
2
1
2
1
0
1
1
1
1
2
1
2
1
1
0
1
0
1
0
1
1
1
1
1
0
1
1
1
1
1
0
2
2
2
1
0
1
1
1
2
1
1
1
1
1
1
2
2
1
2
2
1
1
1
1
1
0
0
1
0
1
2
1
2
0
1
0
1
2
1
0
1
0
0
1
0
0
1
2
1
1
1
1
1
2
1
2
1
0
2
2
0
0
0
1
1
0
0
0
1
1
2
2
2
0
0
0
2
1
1
0
0
1
0
0
1
1
1
2
0
1
2
1
0
2
0
0
0
2
2
1
2
1
1
1
1
1
1
1
1
1
1
1
3
2
0
1
2
0
1
2
1
1
0
1
1
1
0
1
2
2
2
1
1
0
1
1
1
1
0
1
1
1
1
2
2
0
1
2
2
1
0
1
0
2
1
1
2
1
0
1
0
0
0
1
1
1
1
0
0
0
1
1
1
1
1
0
0
2
1
0
1
1
1
1
1
1
0
1
1
1
1
1
1
2
0
0
0
2
0
1
1
1
2
1
1
0
1
0
1
1
1
1
1
2
0
2
3
1
2
0
1
2
0
1
0
0
1
1
0
1
0
2
1
1
0
1
1
1
1
1
1
1
1
1
1
1
2
1
0
2
1
1
2
1
1
1
1
2
1
0
1
0
1
1
1
0
2
0
2
1
1
1
1
2
1
1
2
1
1
2
0
1
1
0
1
2
1
1
0
1
2
1
1
1
2
2
1
1
0
1
1
2
4
1
1
0
2
1
1
2
1
1
1
2
1
0
2
1
1
1
0
1
1
1
0
0
0
2
2
1
0
0
2
2
1
2
1
1
1
1
1
2
1
1
1
1
2
2
1
1
0
1
1
2
1
2
1
1
2
1
0
0
0
1
1
1
0
2
2
0
1
1
1
3
2
1
0
2
1
1
1
1
2
2
1
0
1
0
1
1
1
1
1
2
1
1
0
1
1
0
0
1
2
1
2
1
2
0
1
1
2
1
2
0
1
1
1
1
1
0
2
0
2
2
0
1
2
2
0
1
1
0
2
3
1
2
1
1
2
1
1
1
1
2
1
0
1
1
0
1
2
1
1
1
2
1
1
1
1
2
1
2
1
2
1
1
1
1
0
0
1
2
1
1
0
1
0
1
2
1
1
2
1
1
0
1
2
1
1
1
1
1
1
2
1
2
1
1
1
0
0
1
0
0
1
1
1
1
1
1
1
0
1
1
0
0
1
2
1
1
0
0
1
0
1
2
0
2
0
1
0
2
1
1
1
2
1
2
1
2
1
0
2
1
2
1
2
1
0
1
2
0
0
0
0
1
2
1
0
1
2
0
0
2
1
0
1
1
0
1
0
2
2
2
2
1
3
2
2
1
0
1
0
1
1
2
2
0
1
1
1
1
1
1
1
1
0
1
0
0
1
1
1
1
2
1
1
1
0
1
1
0
1
0
1
2
0
2
2
0
1
1
0
1
1
0
2
1
1
1
0
1
0
1
1
2
2
1
1
2
1
1
2
2
2
1
2
1
2
0
1
2
1
1
1
2
1
1
1
2
0
1
1
0
1
0
1
1
1
1
1
0
2
0
1
1
1
0
1
0
1
1
3
1
1
1
1
2
2
1
2
2
1
0
0
1
1
0
1
0
1
0
2
0
1
2
1
1
1
0
1
1
2
0
2
2
1
0
1
1
1
2
0
1
0
2
1
2
1
1
1
1
2
1
0
3
1
0
1
1
2
0
2
2
2
0
0
1
1
2
2
0
2
2
1
1
1
0
2
1
0
2
0
0
0
1
1
1
0
0
2
0
1
1
2
0
1
0
1
0
0
2
1
1
0
0
1
0
1
1
1
1
1
1
1
1
2
2
0
1
2
1
2
0
2
2
0
1
1
1
1
1
0
1
0
1
0
1
1
1
2
2
2
0
2
1
1
1
1
1
1
2
1
1
0
2
1
1
2
1
1
2
1
0
1
1
3
2
1
1
1
1
1
1
0
1
0
0
1
1
1
1
1
1
2
1
1
0
3
0
2
1
1
1
1
0
0
1
2
2
1
1
0
1
0
2
0
1
2
1
0
1
0
0
0
1
1
0
1
2
1
1
0
1
1
2
1
1
0
1
1
1
2
0
1
1
3
1
1
1
1
1
1
1
0
3
1
2
2
1
1
1
1
2
1
0
1
2
1
1
1
1
0
2
1
2
0
1
1
1
1
0
2
0
1
2
3
2
2
1
1
1
1
1
1
2
1
1
1
2
1
0
1
1
1
2
0
1
1
4
0
2
0
0
1
2
1
1
1
1
1
0
1
1
1
1
1
2
1
1
0
1
1
2
1
1
1
0
1
0
1
1
1
0
0
0
1
1
1
0
2
1
1
2
2
1
1
0
0
1
0
1
1
1
1
1
1
1
1
1
0
1
2
2
2
1
1
0
2
0
1
1
2
1
1
1
1
1
0
1
1
2
1
1
1
1
1
1
1
1
2
2
1
1
1
0
1
2
1
1
1
0
1
1
0
1
1
0
1
1
0
0
2
2
4
1
1
0
0
1
0
1
1
0
1
2
1
1
0
1
0
2
2
2
1
1
0
1
0
1
2
1
1
1
2
2
1
1
1
0
1
1
0
1
1
1
1
1
1
2
1
1
0
1
1
1
1
2
2
0
1
2
1
1
0
1
2
1
1
2
2
2
2
1
1
1
2
1
1
0
1
0
2
1
2
1
1
1
1
0
1
2
0
0
1
1
1
2
1
0
3
1
2
1
2
2
1
1
0
1
1
1
1
0
2
0
1
0
1
2
1
1
2
2
2
1
0
2
1
2
1
1
0
2
1
1
1
0
2
2
1
0
2
0
1
0
1
1
1
1
0
2
1
1
1
1
1
1
2
0
0
1
1
2
0
1
1
1
2
1
1
2
0
1
0
2
2
1
1
0
2
1
1
1
1
0
1
1
1
1
1
2
1
0
1
1
0
1
2
2
0
1
1
1
1
1
1
1
1
0
1
2
2
2
1
0
1
0
1
0
1
1
0
1
2
2
1
0
2
1
1
2
2
1
2
1
1
1
1
1
0
2
2
2
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
2
1
2
0
1
0
1
0
1
1
1
2
1
1
0
1
1
2
1
1
0
2
1
2
1
1
1
1
1
2
1
0
2
1
1
2
0
1
1
2
0
0
1
1
0
1
1
1
1
2
1
1
0
0
1
2
0
0
2
1
1
0
0
1
2
1
0
0
1
2
1
0
1
0
0
1
2
2
0
1
1
1
2
0
2
0
0
1
0
1
2
1
1
0
2
0
1
1
0
0
1
1
1
1
1
1
1
0
1
1
1
2
1
0
1
1
2
2
1
0
1
0
1
1
2
0
2
2
0
0
1
1
2
1
0
0
2
2
1
2
2
3
1
0
1
2
2
1
1
1
2
1
2
0
1
1
1
1
1
1
0
1
1
2
0
0
0
1
1
0
1
1
2
1
1
1
0
1
1
2
1
1
0
1
1
0
0
1
2
2
0
2
2
2
0
0
0
2
1
2
1
0
1
1
1
1
2
1
1
0
2
1
1
1
1
0
1
2
2
2
1
1
0
1
2
1
1
1
1
1
1
1
2
0
2
1
0
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
1
1
0
1
2
1
1
0
1
1
0
1
0
0
1
1
1
2
1
1
0
1
2
1
0
1
1
1
1
2
0
0
1
1
2
1
1
1
0
1
1
0
1
1
1
0
0
2
1
1
2
1
2
1
1
1
1
2
1
0
2
6
0
2
2
1
1
1
1
1
0
0
0
1
1
0
1
1
2
2
1
1
1
0
1
2
2
2
1
0
1
0
0
1
2
0
2
0
1
0
1
1
1
2
0
1
0
2
2
2
0
1
1
1
2
0
1
1
0
1
2
1
1
1
1
0
1
0
0
1
2
2
2
1
0
1
2
1
0
0
2
1
1
1
2
1
2
2
2
2
1
1
2
1
1
1
1
0
0
0
2
0
1
0
1
1
0
1
2
1
0
0
2
1
2
0
1
2
0
1
2
0
1
1
2
1
2
0
3
1
0
1
1
2
0
0
2
1
1
1
1
1
1
1
2
0
2
1
1
0
0
1
1
1
2
0
1
1
1
0
1
1
1
1
0
1
1
0
1
0
1
0
2
2
1
1
1
0
1
2
1
0
1
1
1
1
0
1
2
0
3
2
0
1
1
0
1
0
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
0
1
1
1
2
1
1
2
1
2
1
1
1
1
0
1
0
1
1
2
0
2
2
1
2
1
2
1
0
0
1
1
0
1
2
1
0
1
2
1
1
1
1
1
1
1
1
2
0
2
1
0
0
0
1
0
2
1
1
0
0
1
2
1
0
1
4
0
1
2
1
2
1
1
1
0
1
1
1
1
1
2
0
1
1
1
2
1
2
1
0
0
2
0
0
1
0
2
0
0
2
1
2
0
0
2
2
0
0
1
1
1
1
1
0
0
1
2
1
1
1
2
1
2
0
2
0
1
2
1
1
0
1
1
1
1
1
1
1
1
0
2
0
1
1
2
1
1
0
2
2
1
1
1
2
0
1
0
1
1
1
1
0
1
1
1
1
1
1
1
2
0
1
1
1
1
1
1
0
2
2
1
1
1
0
0
1
0
1
2
1
2
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
0
1
0
2
1
1
1
1
1
0
1
2
1
0
1
0
0
2
1
1
2
1
1
1
1
1
1
1
0
1
1
1
1
1
1
2
0
0
2
1
1
1
1
1
2
2
0
1
2
0
2
1
1
1
1
2
1
2
1
1
0
1
1
1
0
2
1
1
1
2
1
0
1
1
0
1
2
1
1
1
2
2
1
0
2
0
1
2
1
0
1
1
1
1
2
1
2
1
2
1
0
1
1
1
3
0
1
2
0
1
1
1
2
1
2
1
1
1
0
1
1
0
2
2
2
1
1
0
0
2
0
1
1
0
1
1
2
2
1
0
2
1
2
0
1
1
2
2
1
1
0
0
1
0
1
0
0
1
0
1
0
0
1
1
0
1
0
0
1
2
1
1
1
2
2
1
1
2
0
2
1
2
2
1
1
1
1
2
1
1
1
1
1
2
1
0
1
0
1
2
1
0
0
1
2
1
2
1
1
2
1
0
0
3
2
2
0
2
0
1
1
1
1
1
1
1
1
2
1
2
1
1
1
0
2
2
4
0
2
1
1
1
0
1
1
1
0
1
1
1
2
1
1
2
0
0
1
2
0
1
1
1
1
0
0
1
1
1
1
2
1
1
2
2
1
0
0
0
1
0
1
2
1
1
2
0
1
0
1
1
1
1
2
2
1
1
1
0
0
2
1
1
1
1
0
0
0
2
2
0
2
1
1
1
0
0
1
1
1
1
2
1
0
0
1
1
1
0
2
1
2
1
1
1
0
0
0
1
1
2
2
2
0
2
2
1
1
2
0
1
1
1
2
0
2
1
2
0
2
2
1
1
1
1
1
2
2
2
1
2
0
0
1
0
1
2
1
0
2
0
0
1
1
2
0
0
1
1
0
0
1
6
1
0
1
1
1
0
2
1
2
1
2
1
0
1
2
1
2
1
2
1
1
0
1
2
1
0
2
2
0
0
0
2
1
0
1
1
0
1
2
0
2
0
2
0
1
1
2
1
1
1
1
2
0
1
2
2
1
2
2
2
1
1
0
0
2
1
0
1
1
1
1
1
1
1
1
3
1
0
1
1
1
1
1
1
0
1
1
1
2
0
1
0
2
0
1
1
2
2
2
2
1
2
1
2
1
1
0
1
0
0
1
1
1
1
1
2
1
0
2
1
1
1
1
1
2
1
2
1
1
0
1
2
1
0
2
0
2
2
1
1
2
1
0
1
1
0
1
0
1
1
1
1
2
2
1
2
2
1
0
2
1
2
1
1
0
0
2
0
1
1
2
2
1
1
1
1
0
0
1
1
1
1
1
1
2
1
1
1
1
0
2
1
2
1
1
1
1
1
2
1
1
2
2
2
2
2
3
0
1
0
1
1
1
0
2
2
1
0
1
0
1
1
1
0
2
2
1
1
1
1
1
0
1
1
1
0
1
1
2
1
1
0
1
1
0
2
0
1
1
1
1
0
2
0
1
1
0
2
2
0
0
0
1
1
0
1
0
0
1
0
0
0
1
0
1
1
2
0
1
1
1
2
2
1
2
2
1
1
2
1
1
0
1
1
1
1
1
1
0
2
1
1
1
1
1
2
2
2
2
0
1
1
1
2
2
0
2
1
1
0
2
1
0
1
1
2
1
0
2
1
1
1
0
1
1
1
1
1
2
3
2
1
1
1
0
0
2
2
0
1
1
1
2
1
1
1
1
1
1
1
1
2
2
2
1
2
2
2
1
1
1
1
1
0
1
2
2
1
1
0
0
1
0
2
1
1
0
0
1
1
1
2
0
1
1
0
1
1
1
2
1
1
1
1
2
1
1
1
0
0
1
0
2
0
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
0
3
2
0
1
1
1
2
1
1
1
0
2
1
2
1
1
0
1
0
1
1
0
2
0
2
2
1
1
1
1
1
1
0
1
0
1
1
1
2
0
1
0
1
2
1
0
0
2
1
1
1
1
1
1
1
2
0
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
2
1
0
1
2
0
1
2
1
2
1
1
4
1
0
1
0
1
1
1
1
1
1
2
1
2
1
2
1
0
0
1
0
1
1
2
1
1
1
2
1
2
2
1
2
1
1
1
1
0
1
2
1
0
0
1
0
1
1
2
0
1
1
2
1
0
2
1
1
1
0
1
0
0
1
0
1
1
2
2
1
1
1
1
1
0
0
2
1
1
1
1
2
1
1
1
1
1
1
1
1
0
0
2
1
0
2
1
0
0
1
1
0
2
1
2
1
1
0
0
2
1
2
2
2
0
2
1
1
1
2
1
1
1
1
1
1
1
2
0
1
1
1
1
1
1
2
1
2
0
1
2
2
1
1
1
1
2
1
1
0
0
1
2
1
1
0
1
0
1
1
1
0
0
1
1
0
0
1
1
0
1
1
1
0
1
2
0
0
0
1
2
1
1
0
0
2
1
2
1
1
2
2
0
0
1
1
2
0
1
2
2
1
1
1
0
1
1
1
1
1
1
2
0
2
1
1
1
1
1
1
2
2
1
1
2
2
3
1
2
0
0
1
1
1
1
2
1
0
1
0
0
1
0
1
0
0
0
0
0
2
1
0
1
0
1
2
2
1
5
1
0
1
1
2
0
0
1
1
1
1
1
1
2
1
1
2
0
1
0
0
0
2
1
0
2
0
2
0
1
1
0
0
1
1
1
0
1
2
1
1
1
0
2
0
1
1
2
1
2
2
1
2
0
0
1
2
1
1
1
2
1
3
1
2
0
1
2
1
0
0
1
2
2
2
5
1
1
1
1
1
2
1
1
2
1
2
0
2
1
1
2
1
1
2
1
0
1
1
1
1
1
0
1
1
0
2
0
3
0
0
1
1
2
1
1
1
0
2
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
0
0
0
0
1
1
1
1
0
1
1
0
2
2
1
1
1
2
0
1
1
1
2
0
1
0
1
1
1
1
0
1
2
1
1
2
1
1
1
1
2
1
2
0
0
0
2
1
2
2
0
1
1
2
0
0
0
1
1
0
2
1
4
1
1
1
1
2
0
1
0
1
1
1
1
2
1
1
0
1
1
1
1
1
0
0
2
0
2
0
2
1
1
1
0
1
2
1
1
0
1
1
1
2
2
0
1
1
0
1
0
1
2
1
2
1
2
1
1
2
1
1
1
1
1
1
1
2
1
0
2
1
1
1
1
2
0
0
1
0
1
2
2
1
1
1
1
1
1
1
1
1
0
0
0
2
1
0
2
1
2
1
1
1
1
1
0
1
1
1
1
2
0
1
0
2
2
1
0
0
0
1
2
0
1
1
1
0
1
2
1
1
1
0
1
2
2
1
0
1
1
1
3
1
2
1
1
1
2
1
1
2
0
1
1
1
1
2
1
1
1
1
1
1
0
0
1
1
1
2
0
1
1
2
1
1
1
2
1
3
2
2
1
2
1
0
1
0
1
0
1
1
1
1
1
2
2
1
1
1
1
0
1
0
2
0
1
1
2
0
2
1
1
0
1
2
1
1
1
0
1
1
1
1
0
2
1
1
1
2
2
1
0
1
1
1
0
1
1
1
1
0
1
2
0
0
1
1
1
1
1
0
1
1
0
1
1
0
0
1
1
2
0
1
1
1
2
1
1
0
1
1
1
1
1
1
1
0
1
0
1
1
1
1
1
2
1
1
2
1
1
1
2
2
1
2
2
2
0
1
2
1
0
1
1
1
2
1
0
0
0
1
1
3
1
1
1
2
0
0
2
1
1
2
1
1
1
1
1
3
0
0
1
1
1
1
2
1
0
1
0
0
2
1
2
1
1
1
1
0
1
1
2
1
0
2
1
1
1
1
0
1
0
1
0
1
0
1
0
1
1
1
2
1
0
1
0
1
1
1
1
0
2
2
1
1
0
1
0
1
1
2
1
1
1
1
1
1
2
2
2
2
0
1
1
1
1
1
1
1
1
2
1
0
0
1
2
2
2
1
2
2
1
1
0
0
0
0
2
1
1
1
2
2
1
2
2
1
1
2
1
2
2
0
1
3
1
1
0
1
1
1
1
1
1
0
1
2
1
1
1
3
1
1
1
2
1
1
0
0
2
2
1
1
2
0
0
1
1
2
0
0
1
1
0
2
1
1
2
2
3
0
0
1
1
2
1
1
0
0
0
0
0
1
0
1
1
1
0
1
2
2
1
1
0
1
1
1
1
2
1
2
2
1
1
2
2
1
1
1
2
1
1
0
1
0
2
0
0
1
1
1
1
0
0
2
1
2
1
2
1
1
0
0
1
1
0
1
1
2
1
2
1
1
1
1
1
2
1
0
1
0
1
1
2
2
2
1
0
1
1
1
1
2
0
1
1
2
1
1
1
0
1
1
2
1
2
1
0
1
2
1
2
2
1
0
0
1
1
1
2
0
0
2
2
0
1
0
0
0
0
0
1
1
1
1
0
0
2
1
2
1
0
1
1
1
2
1
0
1
1
2
0
2
1
1
1
1
1
1
1
1
1
1
2
0
1
0
2
2
2
2
2
2
1
2
0
2
2
1
2
1
0
1
1
1
1
0
2
0
0
1
1
0
1
1
2
2
0
2
1
0
1
1
1
1
2
0
0
2
2
1
0
1
0
1
2
1
1
1
0
2
1
0
2
2
2
1
1
2
1
2
1
1
1
1
0
1
1
0
0
1
0
1
1
2
0
1
2
0
1
0
1
2
2
2
0
0
0
3
1
2
1
1
1
1
2
1
1
1
1
2
0
1
0
2
0
1
0
1
1
2
1
1
1
2
1
1
1
1
1
0
1
2
2
2
2
1
1
0
0
2
2
1
1
2
1
1
2
2
1
1
2
3
1
1
2
1
1
1
2
2
1
1
1
1
1
1
2
1
0
0
0
0
1
2
0
1
1
1
1
2
1
1
1
0
1
1
2
2
1
1
1
1
1
2
1
1
2
0
1
2
1
1
1
2
0
0
2
2
1
1
1
2
0
2
1
1
0
1
2
1
1
1
0
2
0
1
2
1
1
1
0
0
1
2
2
0
1
1
2
1
2
2
1
0
1
2
1
2
1
1
0
1
0
1
1
1
2
0
1
0
1
2
0
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
0
1
0
1
1
1
1
1
0
2
2
1
1
1
1
1
1
1
0
1
2
1
1
1
2
1
2
1
2
2
1
2
2
1
1
2
0
1
1
1
1
1
1
1
1
2
1
1
2
1
1
0
2
1
1
0
1
1
2
0
1
1
1
1
1
0
2
1
1
0
2
1
1
1
1
1
0
1
0
2
2
1
1
1
1
0
1
1
1
2
2
0
2
1
0
2
1
2
2
0
2
1
1
1
1
1
2
1
1
0
1
1
1
1
1
1
2
0
3
1
1
2
2
0
0
1
1
2
1
1
0
1
1
1
0
1
1
1
1
2
1
1
1
1
2
1
0
1
1
2
1
2
1
2
1
1
1
0
1
1
0
1
0
1
0
2
2
2
1
1
1
0
0
0
1
1
2
1
1
1
1
2
2
1
1
2
2
2
2
3
1
1
2
2
0
1
0
1
1
0
0
2
1
1
1
1
0
0
2
3
2
1
2
1
1
2
1
1
1
1
2
1
1
1
0
0
0
2
2
2
0
2
0
1
2
1
1
2
1
1
1
1
0
0
1
4
0
1
3
0
1
1
1
2
1
0
0
1
2
1
1
0
1
2
2
1
1
2
0
1
0
1
1
1
1
2
0
0
2
1
1
1
2
1
0
1
1
1
1
1
1
1
1
0
1
1
2
1
1
2
1
1
1
1
1
0
2
2
1
1
2
1
2
1
0
1
1
1
2
3
1
1
1
1
1
1
2
1
1
2
1
1
1
0
2
2
0
0
1
0
2
2
1
0
2
1
1
1
0
2
0
0
1
2
2
1
1
2
1
1
1
2
2
1
1
0
0
2
1
0
2
1
1
1
1
1
0
3
1
1
1
1
1
1
1
1
1
0
1
1
0
0
1
1
0
1
2
0
1
0
1
1
2
1
2
1
0
0
1
1
1
1
1
2
0
2
0
2
1
0
2
1
0
1
1
0
2
1
1
2
2
1
2
0
1
2
2
1
0
1
4
1
1
1
1
2
2
2
1
0
2
3
1
1
1
1
2
1
0
1
1
1
1
2
1
1
1
1
1
1
2
1
1
2
0
1
0
1
2
1
1
0
1
1
1
3
1
0
1
1
1
0
1
2
1
1
1
1
1
1
2
1
1
0
2
0
1
2
1
2
1
2
1
1
1
1
0
1
1
1
2
1
1
2
0
2
0
0
2
1
1
2
1
1
2
0
1
1
1
1
1
0
3
1
1
1
2
1
1
2
1
1
1
2
1
1
1
0
2
1
1
1
1
1
1
1
1
1
0
1
1
2
2
1
0
1
2
1
1
2
0
0
1
1
0
1
0
0
0
1
1
0
1
2
1
1
0
1
2
2
1
2
1
0
1
1
1
1
0
0
1
1
1
2
0
0
0
1
2
1
1
1
1
0
1
2
0
1
1
2
0
0
2
0
0
2
1
3
1
1
1
0
1
1
1
1
1
1
1
0
1
2
1
2
1
1
1
0
0
2
2
0
1
1
0
1
1
2
0
1
2
2
1
2
1
2
1
2
2
1
1
2
3
1
1
1
1
0
2
1
0
1
2
1
0
1
0
1
2
1
0
2
0
2
0
1
2
1
0
1
1
2
1
1
1
1
2
0
1
1
1
1
1
1
2
1
1
2
2
0
0
1
0
1
1
1
1
2
1
3
1
0
1
1
1
1
1
1
0
2
1
1
2
1
1
0
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
0
0
1
1
1
1
2
0
1
1
1
1
1
1
2
2
2
0
1
1
0
1
1
2
2
1
0
2
0
1
1
0
1
2
1
0
2
0
1
1
0
1
2
2
1
1
1
0
1
0
1
1
2
0
0
1
0
0
1
0
1
1
2
1
0
1
1
1
1
1
1
2
1
1
1
1
2
1
0
1
2
1
1
2
1
1
2
0
0
2
1
2
2
1
1
1
1
1
2
1
2
1
1
2
0
1
0
1
1
1
1
1
1
2
1
1
1
1
0
0
0
1
1
1
1
1
1
1
1
0
1
0
1
1
1
1
1
0
2
0
1
1
0
1
0
1
2
2
1
2
1
1
1
1
0
2
1
1
0
1
1
1
1
1
2
2
1
0
0
1
0
2
1
1
1
2
0
2
0
1
1
1
0
1
0
1
1
2
0
2
2
1
1
1
2
1
2
1
1
0
0
1
1
1
1
1
2
1
0
2
2
2
1
1
1
2
1
1
1
0
1
0
2
1
0
2
0
0
1
1
0
1
0
1
0
2
1
1
2
0
1
2
0
0
2
2
1
0
2
1
2
1
0
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
2
0
1
1
0
0
2
1
1
2
1
1
0
1
0
1
0
1
1
1
2
2
1
2
2
2
2
1
1
0
1
1
2
2
2
1
1
0
2
1
1
1
1
0
2
1
1
1
0
0
2
1
1
0
1
2
0
1
1
1
1
2
1
2
0
0
2
1
1
2
1
1
0
1
2
2
1
1
2
1
1
0
0
2
2
1
2
0
2
0
1
1
0
2
1
1
1
1
1
1
1
1
2
1
0
1
1
1
1
2
0
1
0
2
1
0
0
1
1
1
1
1
1
0
1
1
1
0
1
1
1
2
1
0
2
0
0
2
1
1
1
0
1
1
1
2
1
1
0
1
1
1
1
1
0
1
1
0
2
1
2
2
2
1
2
1
1
1
2
1
1
1
0
1
1
1
0
0
1
1
0
1
0
1
2
0
2
1
0
1
0
1
2
1
1
1
1
0
1
1
1
1
1
2
0
0
1
0
0
0
2
0
1
0
0
1
1
0
2
1
2
1
0
2
1
1
1
1
2
2
2
2
1
1
1
1
1
2
1
1
0
0
1
1
1
1
1
1
0
1
1
1
2
2
2
2
0
0
1
2
1
1
2
1
1
1
1
1
1
2
2
1
0
1
0
1
2
1
2
2
2
1
1
1
1
2
2
0
1
2
1
1
2
2
1
1
0
2
1
1
1
0
1
2
1
1
1
2
1
1
0
1
1
1
1
1
1
1
2
0
1
1
1
1
0
2
1
0
0
1
0
1
1
1
2
1
0
1
0
3
2
1
1
1
1
1
1
0
0
1
0
1
1
1
2
2
1
0
2
2
1
1
1
0
1
0
1
1
1
0
1
1
2
1
1
1
1
2
1
1
0
1
0
1
1
1
1
1
1
2
0
1
2
0
1
1
0
2
0
1
2
1
2
1
1
0
2
0
1
0
1
1
0
1
0
0
1
0
1
1
1
2
1
1
0
1
1
2
0
1
1
1
0
1
1
0
1
1
1
1
0
0
2
2
1
2
1
1
1
0
0
1
0
2
2
1
1
1
1
0
0
1
2
2
1
1
2
1
0
0
1
1
2
3
0
1
1
0
1
0
1
0
2
2
0
1
2
1
2
0
1
1
1
1
1
0
2
1
2
1
1
0
1
1
1
1
1
1
2
1
1
2
2
2
2
2
0
1
0
0
1
2
2
1
1
2
1
1
1
2
1
2
1
2
1
1
1
2
0
2
2
1
1
1
1
2
3
1
3
0
1
1
1
1
2
0
2
1
0
2
0
0
0
1
1
0
2
1
1
1
1
2
1
0
0
0
1
1
2
1
1
1
1
1
1
1
0
1
1
0
1
1
1
1
2
1
1
1
0
2
1
1
0
0
1
1
1
1
2
1
2
2
2
2
1
0
1
1
1
0
1
2
2
2
0
1
1
1
2
1
1
1
3
1
0
1
1
1
1
1
2
1
1
1
1
2
1
2
2
2
1
2
2
1
1
1
2
1
1
2
0
1
2
0
2
1
2
1
0
2
1
0
1
2
0
1
0
0
1
1
0
1
2
0
2
2
2
1
1
2
0
0
0
1
0
2
1
2
0
0
1
0
4
2
2
1
1
0
1
1
2
2
1
1
0
2
2
1
1
1
1
1
1
1
1
1
1
0
1
1
0
1
0
0
0
1
1
1
1
0
0
0
0
1
2
2
0
0
1
1
2
0
2
1
0
1
0
2
0
1
0
1
0
2
0
0
0
1
1
1
1
0
2
1
1
0
2
1
1
0
1
2
2
2
1
0
0
1
1
1
0
1
1
2
1
1
1
1
1
0
2
2
1
1
1
1
1
1
1
2
1
2
0
2
1
1
1
0
1
1
1
0
1
1
0
2
2
1
1
1
1
0
1
2
1
0
1
0
1
1
2
1
1
3
0
2
1
1
0
1
1
1
1
1
1
2
1
1
1
1
0
2
1
1
2
1
1
1
1
2
0
2
2
1
0
2
0
2
1
1
1
2
1
1
1
2
1
2
1
1
2
1
1
0
0
0
2
2
1
2
2
2
1
1
2
2
0
1
1
1
1
2
1
1
1
1
1
3
0
1
0
1
0
0
0
1
1
1
1
1
2
1
1
2
1
0
1
1
1
1
0
0
2
1
0
2
0
0
2
0
2
0
1
1
1
1
2
1
2
1
1
1
2
2
1
1
0
1
1
0
0
1
0
0
1
2
1
1
0
1
0
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
0
2
1
2
0
1
1
0
1
1
1
2
1
0
1
2
1
0
0
1
1
1
7
1
1
1
0
2
2
0
1
1
2
0
2
3
0
1
0
3
1
2
1
0
1
1
1
1
1
0
2
1
1
1
1
1
1
0
1
1
1
0
1
1
1
1
1
1
1
1
0
2
0
0
2
1
1
2
2
1
0
1
1
0
1
1
1
1
2
1
0
1
1
1
1
1
1
0
1
1
2
1
2
1
0
0
1
1
1
0
0
1
1
1
1
1
2
0
1
1
0
2
0
1
1
1
1
1
0
0
1
1
1
1
1
1
1
0
2
1
2
1
1
1
1
1
2
2
2
1
1
2
1
2
1
0
1
1
1
1
0
0
1
0
1
1
1
1
1
1
2
2
1
2
2
1
1
2
0
1
0
1
4
0
0
2
1
2
2
1
1
0
1
1
0
2
1
1
0
0
1
1
0
0
1
3
0
1
0
1
1
1
1
0
0
0
0
1
1
2
1
0
2
0
0
1
0
1
1
2
1
1
1
2
1
0
2
2
1
1
0
1
1
2
1
1
0
1
0
1
1
2
1
1
0
1
1
2
1
1
1
1
1
1
0
1
0
0
0
2
1
1
1
1
1
0
1
0
1
2
2
1
0
1
1
1
1
0
2
0
1
1
0
1
1
0
1
1
2
0
1
1
1
2
1
1
1
1
1
1
2
1
1
1
0
1
0
1
1
2
1
1
1
1
0
0
1
2
2
1
2
3
1
2
2
0
1
1
1
1
1
2
1
1
1
1
1
1
2
1
0
0
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
2
0
2
1
0
0
1
1
1
1
1
1
2
2
1
0
1
1
2
2
1
1
1
1
4
1
1
1
2
1
0
1
2
2
2
2
2
1
2
1
1
0
1
1
1
1
1
0
1
1
1
2
1
0
2
0
1
0
0
1
0
2
2
2
1
1
0
1
1
1
1
2
1
1
1
1
1
1
1
0
1
1
1
2
1
0
1
1
1
1
1
2
1
2
0
1
1
1
1
1
2
2
1
1
1
1
1
1
2
2
1
1
1
1
0
1
1
1
1
1
1
0
1
0
1
0
1
1
0
1
1
1
0
0
2
2
1
1
1
1
1
1
0
1
1
1
1
1
1
1
0
2
1
2
1
2
2
2
1
2
1
1
1
1
1
2
1
1
2
0
1
1
0
2
1
1
1
0
0
0
2
1
1
3
1
1
0
1
0
1
0
0
1
0
1
0
0
1
1
0
1
2
0
4
1
1
1
0
1
0
2
1
1
1
2
1
0
0
1
1
1
1
1
1
1
1
1
1
0
1
1
2
0
1
1
1
1
2
2
1
2
1
0
0
0
1
0
1
0
0
1
1
0
2
1
1
0
2
1
1
0
2
1
0
0
1
1
0
2
1
1
1
0
1
0
1
0
1
2
1
1
0
0
0
1
2
1
1
0
0
1
1
1
1
2
2
2
1
1
2
0
0
2
0
1
1
1
0
0
0
2
1
0
2
0
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
0
1
0
2
2
0
1
1
1
0
1
2
1
1
1
1
2
1
2
1
2
0
0
1
1
1
0
2
1
0
1
1
1
2
2
2
2
1
0
2
2
1
0
2
1
0
1
1
1
1
0
0
1
3
1
1
1
1
1
1
2
0
1
1
0
2
0
1
0
1
0
1
1
1
2
2
1
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
0
2
1
0
2
1
1
1
1
2
1
1
1
1
0
1
2
2
1
1
0
0
2
2
1
1
1
1
0
0
2
1
1
0
2
1
2
0
1
1
0
1
1
1
1
1
1
1
2
2
1
1
1
0
2
1
1
2
1
1
0
1
1
1
1
2
1
0
1
0
1
1
1
1
1
1
2
1
1
1
0
0
1
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
2
1
1
2
2
1
2
0
0
1
0
0
2
1
0
1
0
0
1
0
0
0
1
1
0
0
2
1
0
2
0
1
1
1
1
0
2
0
1
0
2
2
1
2
1
1
1
2
0
0
1
1
1
2
2
2
1
1
1
1
0
2
1
0
1
1
0
2
1
2
1
1
1
4
0
1
1
0
2
1
1
1
1
1
1
2
1
1
6
1
0
1
0
1
0
1
1
1
0
1
0
1
1
0
2
2
1
1
2
0
2
1
0
1
1
0
1
1
1
2
1
1
1
0
1
1
0
1
2
1
0
1
1
1
2
1
2
1
1
0
2
0
2
1
0
1
1
0
2
1
1
1
0
1
1
2
1
1
1
0
0
1
1
1
2
1
2
1
1
1
2
1
0
2
1
1
2
1
2
0
1
0
1
2
1
0
0
1
1
1
1
1
1
1
1
0
0
0
0
2
2
0
0
1
1
0
1
1
1
1
0
2
2
2
1
1
1
1
1
2
1
0
1
2
2
1
1
0
1
1
0
2
1
1
1
1
1
1
1
2
2
1
1
1
0
1
0
1
1
1
0
1
1
1
1
0
1
1
1
2
1
1
1
2
2
1
0
2
1
0
1
1
1
1
1
2
1
1
0
2
1
1
2
0
1
1
2
1
2
0
2
1
2
1
0
1
2
1
3
3
1
1
1
2
1
2
2
1
1
2
1
1
2
1
1
2
1
0
0
1
1
2
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
0
2
0
1
2
1
2
0
1
1
2
1
2
2
1
1
0
1
1
1
0
1
1
1
1
2
0
2
0
2
1
1
1
1
1
0
0
0
1
5
1
0
1
1
1
2
1
0
0
2
1
1
1
0
0
1
1
1
0
1
1
0
1
1
1
1
2
2
1
1
0
1
1
2
0
1
1
1
5
0
1
0
1
1
1
1
1
0
1
0
2
1
1
1
2
1
2
2
0
0
1
0
7
2
1
1
1
2
1
1
2
2
2
1
2
0
1
2
2
1
1
2
1
3
1
1
0
1
0
1
2
0
2
1
0
2
1
2
0
1
2
2
2
2
1
1
1
2
0
1
1
1
4
2
1
1
2
1
0
0
2
1
3
1
2
2
1
1
1
2
1
0
2
0
0
1
1
2
0
1
1
1
0
2
1
2
2
1
2
0
1
1
1
1
0
1
0
0
1
1
1
1
1
0
2
2
2
2
1
1
2
1
1
2
1
1
2
1
1
0
2
1
1
6
2
1
0
1
1
2
1
1
0
1
1
1
2
0
1
1
4
0
1
2
1
0
0
1
1
1
2
1
1
1
1
1
2
1
1
1
2
0
2
1
2
2
1
1
2
0
1
1
1
0
1
1
0
1
2
1
1
1
0
1
1
0
2
1
2
2
1
2
1
1
1
1
1
2
1
0
1
0
1
1
2
1
0
2
1
1
0
2
1
1
2
2
1
1
0
0
1
2
1
1
0
2
2
2
1
2
0
1
2
1
2
0
1
0
1
0
1
2
1
2
1
1
1
1
0
1
1
2
2
1
1
1
1
1
1
0
0
2
0
1
1
1
0
1
2
1
0
1
4
1
1
0
1
0
1
2
1
0
1
2
1
1
1
1
1
2
1
1
0
1
1
1
2
1
1
1
1
1
2
1
1
2
2
1
2
2
1
0
1
0
1
1
1
1
1
1
0
1
1
0
0
1
1
2
1
1
1
3
2
1
1
2
2
1
2
2
1
2
1
2
0
0
1
1
2
1
1
2
0
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
0
1
1
1
1
1
0
2
0
0
0
1
1
2
1
2
1
0
0
1
0
1
1
2
1
1
1
0
2
2
1
1
1
1
1
1
1
2
1
1
0
1
1
1
1
2
1
1
0
1
1
1
1
2
2
2
2
1
1
1
1
2
0
0
1
1
2
2
1
1
1
1
0
0
1
1
0
1
1
2
1
0
1
1
1
0
1
1
1
1
2
0
1
1
0
1
0
0
0
0
2
2
1
1
0
1
1
1
1
2
2
1
1
1
1
2
2
1
2
1
2
0
2
2
1
1
1
1
1
2
1
0
2
1
2
1
0
1
1
4
1
2
1
1
0
1
1
2
0
0
0
1
1
2
2
0
1
2
1
1
0
3
1
1
0
1
2
2
1
1
1
1
1
1
1
0
1
1
2
0
0
1
0
1
1
1
2
1
2
0
0
1
0
1
1
1
1
0
1
0
1
2
0
0
1
1
0
2
2
2
2
3
0
0
0
1
0
1
0
1
2
0
0
1
1
3
2
1
2
2
1
0
2
1
2
1
1
0
2
2
1
1
1
1
0
2
1
1
0
0
0
1
1
2
0
1
0
1
1
0
1
3
1
1
0
1
2
0
1
1
1
1
1
0
1
0
1
1
0
0
1
0
1
1
1
1
1
2
0
2
0
0
1
2
1
1
1
1
2
2
1
2
1
2
0
0
1
1
1
2
2
2
0
1
1
0
1
1
1
0
1
2
1
1
1
1
0
0
2
1
1
2
0
1
2
1
1
0
0
1
0
1
1
2
0
1
1
1
0
1
2
1
0
0
1
0
1
1
0
2
1
1
1
0
2
1
0
1
1
0
0
2
1
1
1
0
0
1
2
1
1
1
1
2
1
1
2
0
0
2
1
2
2
1
0
1
0
1
1
0
1
1
2
2
0
1
1
1
1
1
1
0
1
1
2
1
0
1
2
0
0
1
1
2
1
2
2
1
0
1
2
1
1
2
2
2
2
1
1
2
0
1
0
1
0
1
1
1
1
1
1
0
0
0
0
1
1
2
0
1
0
0
0
0
0
1
1
1
2
2
2
2
0
1
1
1
1
0
0
0
1
0
1
0
2
1
1
2
2
1
1
1
1
2
0
1
1
1
1
1
5
0
1
1
1
1
0
0
1
1
1
0
0
1
1
1
1
0
1
1
1
1
0
1
2
2
2
1
0
1
0
0
0
2
1
2
2
0
1
1
2
1
1
1
1
2
1
1
1
2
1
1
2
1
0
1
2
2
1
1
1
2
2
1
0
0
0
1
1
0
1
1
1
1
2
1
0
1
1
0
1
1
1
0
2
2
2
1
1
0
0
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
0
1
0
0
2
1
1
1
2
0
0
1
2
1
0
1
1
1
2
1
1
2
0
2
0
1
1
1
1
4
1
1
2
1
1
0
2
1
2
1
1
1
1
1
2
0
0
1
2
0
1
1
1
1
1
1
1
0
0
2
1
1
1
1
1
1
1
1
1
1
2
0
2
1
1
0
2
0
1
2
0
1
2
0
1
1
1
1
2
0
1
1
2
0
0
1
1
1
2
1
0
1
1
1
1
1
1
1
1
1
2
1
2
0
2
1
0
2
0
1
1
1
0
2
2
1
0
1
1
1
1
1
0
1
1
1
1
1
2
2
2
1
3
1
1
2
1
1
2
1
0
1
1
1
1
1
1
1
1
2
2
1
1
1
0
1
1
1
1
0
2
1
1
0
1
1
2
1
0
1
1
1
1
1
0
1
1
0
1
1
1
1
1
1
2
1
1
2
2
0
2
2
1
2
2
2
2
2
0
1
1
3
1
1
1
1
2
1
0
1
0
0
1
1
0
2
1
1
2
1
2
0
2
0
1
2
1
1
1
1
0
1
1
2
0
1
2
2
1
1
1
2
1
1
1
1
2
1
1
1
1
0
1
1
1
1
1
0
2
2
1
1
1
1
1
1
1
2
2
1
1
0
1
2
1
0
1
1
1
1
1
0
1
1
0
1
1
0
1
2
1
1
1
2
0
1
0
2
1
2
1
1
1
1
0
1
1
1
1
2
1
1
1
1
1
0
0
1
1
1
1
2
1
0
1
0
0
1
2
2
2
2
2
1
1
0
0
1
2
1
0
2
1
2
0
1
1
1
0
1
1
1
1
2
2
1
1
2
3
2
1
1
1
1
1
1
1
1
0
2
1
0
1
1
1
1
2
0
1
1
0
1
2
2
1
2
1
1
1
2
1
0
2
1
1
1
0
0
0
0
2
0
1
0
1
1
1
1
0
1
1
1
0
1
1
2
2
1
1
1
1
1
2
0
2
0
1
2
1
1
1
1
2
1
1
1
0
1
1
0
1
1
2
1
0
0
1
2
2
1
1
1
1
1
1
0
2
1
0
1
0
1
1
2
1
0
1
1
4
1
1
1
1
0
1
1
1
0
1
1
0
2
1
1
0
2
1
1
1
1
2
1
2
2
2
2
1
3
2
0
0
0
1
1
2
2
2
1
1
1
0
0
2
2
1
1
0
2
1
1
3
2
1
2
0
0
1
2
1
1
1
1
2
2
1
1
1
1
0
2
2
1
1
1
1
2
2
2
1
0
2
0
0
2
2
0
1
1
2
0
1
1
2
1
1
1
0
1
1
1
0
0
2
2
1
1
0
2
1
1
0
1
2
0
0
1
1
2
1
1
1
0
2
2
1
1
1
0
0
1
1
1
2
1
1
1
0
1
2
1
1
0
2
1
2
1
0
1
1
2
1
0
1
1
1
1
1
1
1
2
4
1
1
2
0
1
1
2
0
2
1
1
1
0
1
2
0
0
1
1
0
0
1
2
1
2
0
1
1
1
1
0
2
0
2
1
2
0
1
1
1
2
1
1
1
0
1
2
2
2
2
1
1
2
2
2
1
0
1
2
2
1
2
1
1
0
0
1
2
0
0
1
1
1
1
1
1
1
1
0
2
0
1
1
1
1
1
0
0
2
2
0
1
2
1
1
1
0
0
1
1
1
1
0
2
1
1
1
1
0
2
3
1
1
2
1
2
0
0
1
1
1
1
1
2
1
2
2
2
2
1
1
1
1
2
1
1
1
2
1
1
0
1
2
2
0
1
0
0
1
1
1
1
2
1
0
1
0
0
1
1
0
0
1
1
0
1
1
2
0
1
0
1
0
2
0
1
1
0
1
1
2
2
2
1
0
2
1
1
0
1
0
0
1
0
2
2
1
2
2
1
1
1
0
1
0
1
2
2
1
1
1
2
2
0
1
1
1
1
1
1
0
1
2
1
1
1
1
1
2
1
1
1
2
0
1
1
0
1
1
0
1
1
2
0
1
1
0
2
1
1
1
1
1
1
0
1
1
1
2
0
0
2
1
2
1
2
1
2
1
1
2
1
2
1
1
1
1
1
0
2
0
0
3
2
0
0
0
2
1
0
1
2
1
0
2
0
0
1
1
1
1
1
0
1
1
1
1
1
1
0
0
1
2
1
1
2
1
1
1
1
1
2
2
1
2
1
1
0
2
1
1
1
1
1
0
2
1
1
1
2
1
0
0
1
1
1
2
0
3
2
2
0
2
0
2
1
0
2
0
1
1
1
1
1
2
1
1
1
0
1
2
1
1
1
1
0
0
1
1
2
0
1
0
1
2
0
1
2
1
1
2
2
1
2
0
0
1
1
0
1
1
2
0
1
1
2
1
0
1
1
2
1
2
1
1
0
1
1
1
0
2
1
2
0
1
1
1
1
1
3
1
2
3
2
2
4
1
1
2
1
1
1
2
1
0
1
2
0
0
1
1
1
2
0
2
1
2
0
1
1
1
1
1
2
2
1
0
0
1
1
1
0
1
2
0
1
2
1
1
1
0
2
1
0
1
1
2
1
1
0
1
0
1
2
1
2
1
1
1
1
2
2
1
1
1
1
1
2
2
0
2
2
2
1
1
0
0
2
1
1
0
2
1
0
1
1
1
2
1
0
2
1
2
1
2
1
1
0
1
1
3
2
2
2
1
1
1
1
0
2
0
1
2
3
1
1
1
1
1
1
1
3
3
4
1
0
2
1
0
2
0
2
2
1
1
2
1
1
1
1
2
0
1
1
1
1
1
4
1
1
1
1
1
1
2
1
1
0
1
1
1
2
1
1
1
1
2
0
0
2
1
1
1
1
2
1
1
1
2
1
2
1
1
0
2
1
0
1
0
2
2
2
1
0
1
2
1
0
1
1
1
0
1
1
2
1
1
1
2
0
1
1
0
1
0
0
1
2
0
0
2
1
2
2
2
2
1
1
2
2
1
1
0
1
2
1
2
1
0
1
1
0
1
0
1
2
1
1
1
2
0
2
0
2
1
1
1
2
1
2
0
1
0
1
1
1
0
1
1
2
1
0
0
0
1
1
2
1
1
0
1
1
2
1
0
0
2
1
0
1
1
2
1
0
0
2
1
0
3
1
1
2
1
2
2
2
1
2
3
1
1
2
1
1
0
1
2
1
1
1
0
2
2
1
1
1
1
1
1
0
0
2
2
2
0
1
1
0
0
0
2
1
0
1
1
1
1
1
0
1
1
0
1
1
0
1
0
1
1
2
2
1
0
0
0
1
2
1
0
2
0
2
1
2
3
1
1
2
2
0
2
1
2
2
2
1
1
1
2
1
0
1
2
1
1
2
2
0
2
1
1
1
2
1
1
2
1
1
1
0
1
0
1
1
0
2
1
1
2
1
1
1
1
2
0
1
1
0
1
2
0
0
1
1
1
1
1
0
1
1
2
0
1
2
1
1
1
2
0
0
1
1
1
1
1
1
0
1
1
2
2
2
1
0
2
2
2
1
2
0
0
1
2
1
0
0
1
1
0
1
1
1
2
2
1
1
1
1
1
1
0
1
2
1
0
0
0
1
1
1
1
1
0
2
1
2
0
1
2
1
1
1
2
1
1
1
1
1
1
0
1
1
1
0
1
1
1
0
2
0
1
1
0
0
1
1
1
0
1
1
1
2
1
1
0
1
0
1
1
1
2
1
1
0
1
1
1
1
1
3
2
1
1
1
1
0
0
1
2
0
1
1
1
1
1
1
1
2
1
2
0
1
1
1
1
2
1
1
1
1
1
1
1
1
1
0
1
2
0
1
1
1
0
2
0
0
1
1
1
0
0
2
1
1
1
2
0
2
1
2
0
1
1
2
0
1
1
1
1
1
1
1
1
2
1
2
1
2
1
1
1
0
1
1
1
6
2
2
1
1
1
1
0
1
2
2
1
0
1
1
1
0
0
2
1
1
1
1
1
1
2
0
3
2
2
2
1
1
1
1
3
2
2
2
1
1
1
1
1
1
1
0
1
0
1
1
1
0
0
1
1
1
1
1
1
1
1
1
1
1
0
1
0
2
1
2
1
1
0
0
2
1
0
2
0
1
1
1
1
0
1
2
2
0
2
1
1
1
1
2
1
0
0
1
1
2
1
1
1
1
1
0
2
1
2
1
0
0
2
1
1
0
1
0
0
0
0
1
1
0
2
0
2
2
1
2
1
1
1
1
1
1
1
0
0
1
0
1
1
1
0
1
0
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
0
2
1
2
1
1
1
0
1
0
0
1
2
1
3
1
0
1
2
1
1
2
2
1
1
1
2
1
0
2
1
0
2
2
0
1
1
1
2
1
2
2
1
2
1
1
1
2
0
0
2
2
2
1
1
1
1
1
1
2
0
0
1
1
1
1
2
0
0
0
1
0
2
1
1
2
1
1
1
1
0
1
0
0
2
2
2
0
3
0
1
1
1
1
1
2
1
2
2
1
2
0
1
3
1
1
1
1
1
1
1
0
2
1
1
1
1
2
1
1
0
2
1
2
1
1
0
1
1
0
1
2
1
1
2
1
2
0
0
1
0
2
2
1
1
1
0
1
1
1
0
0
3
0
1
2
0
6
1
1
1
1
1
1
2
1
2
1
1
2
1
1
2
2
1
2
1
1
1
1
1
1
2
0
1
1
1
1
1
0
0
1
1
1
0
0
0
0
1
1
1
2
0
2
1
0
2
0
2
1
0
2
1
2
1
1
1
1
2
2
1
2
2
2
1
1
1
2
1
1
1
2
1
1
1
1
2
1
2
1
1
2
0
1
1
2
0
1
2
1
0
1
1
2
1
1
2
1
1
1
1
0
1
2
1
1
1
0
1
0
1
0
0
1
1
2
1
1
2
2
1
1
0
2
1
1
1
2
1
0
2
1
1
1
1
1
0
0
1
2
3
1
1
1
0
2
0
1
1
2
1
1
3
3
0
1
1
2
2
2
2
1
2
0
1
1
1
1
1
1
0
1
1
1
1
1
1
1
0
1
1
0
3
1
1
2
1
0
1
1
0
1
1
2
2
1
2
2
1
2
1
1
0
1
2
0
2
0
1
0
2
1
1
0
0
0
1
1
1
1
1
1
1
0
1
0
0
0
0
2
1
1
1
0
1
2
4
1
1
1
1
1
2
2
0
1
1
1
0
1
1
0
2
1
2
0
1
1
1
1
0
0
1
1
1
2
0
2
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
0
2
0
2
2
2
2
1
1
2
2
0
1
1
0
1
1
1
2
0
0
1
1
0
1
1
2
2
2
0
0
1
0
2
2
2
1
1
1
1
0
2
1
1
1
0
0
0
1
2
0
2
1
1
1
0
1
1
2
2
1
1
0
2
0
1
0
1
1
1
1
1
1
2
0
1
1
0
0
1
1
1
1
0
1
1
0
0
2
0
0
0
1
0
2
1
2
2
1
0
1
1
1
3
0
2
1
1
1
0
2
1
0
1
1
0
2
1
1
1
1
1
3
1
0
1
2
1
1
0
2
1
1
2
1
1
1
1
0
0
0
2
0
2
1
1
2
0
1
1
2
1
2
2
0
2
1
2
1
1
1
1
1
2
1
0
1
0
0
0
1
2
1
1
2
1
1
0
1
1
1
3
0
1
0
0
0
2
1
1
1
2
0
2
2
0
0
1
1
2
1
0
1
1
2
0
1
3
1
1
1
1
0
2
0
0
1
2
1
1
2
1
2
0
1
1
1
1
1
2
2
1
1
0
2
1
1
1
1
2
2
2
1
0
2
0
2
1
2
1
0
1
0
1
1
0
1
1
1
2
0
1
2
1
1
1
2
1
1
2
2
0
1
1
1
0
1
1
0
1
1
1
2
1
1
0
1
1
1
0
1
1
0
2
0
1
1
1
1
0
1
1
1
0
0
1
2
1
1
1
1
2
1
1
2
2
1
1
0
2
2
0
1
1
1
1
1
0
2
1
2
1
1
2
2
0
0
0
1
2
1
0
0
1
1
0
1
1
0
1
0
2
2
2
2
0
1
0
2
1
2
4
0
0
2
2
2
0
1
1
1
1
2
2
1
0
1
1
1
1
0
1
1
0
1
0
0
1
2
1
1
0
2
1
2
1
2
1
2
2
1
1
1
0
1
2
0
0
3
0
0
2
1
0
1
0
2
1
1
0
1
1
1
2
0
1
1
0
2
0
2
1
1
0
1
2
2
1
1
2
1
2
1
0
2
1
2
0
2
1
0
0
1
2
1
1
0
0
0
2
1
1
2
0
1
2
0
1
1
2
0
1
1
1
1
2
0
2
2
2
2
1
1
2
1
1
1
1
2
1
1
1
2
0
1
0
1
1
1
0
1
1
1
2
2
2
0
2
1
0
2
0
1
1
2
0
1
2
1
1
1
2
2
1
2
0
1
0
2
1
1
2
1
0
2
1
1
1
1
1
0
0
1
1
1
1
1
2
0
1
1
1
1
2
2
1
2
0
1
1
1
2
2
1
2
2
1
1
1
2
2
1
0
0
1
1
3
1
1
0
1
0
1
2
1
1
1
1
2
1
1
1
1
2
1
0
1
1
1
1
1
0
0
0
1
2
1
1
0
0
0
1
0
1
1
0
2
1
0
1
1
0
0
1
2
0
1
1
1
1
1
1
2
1
1
0
1
0
0
2
2
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
0
1
0
1
1
2
1
3
1
2
2
1
0
1
0
0
0
1
0
2
1
0
1
1
2
1
1
1
2
0
1
2
1
0
1
1
1
1
1
1
0
1
1
1
0
1
1
2
1
0
1
1
0
2
1
0
1
0
1
2
1
1
1
2
2
2
0
1
1
1
1
1
2
1
1
2
1
2
1
1
1
1
1
1
0
1
2
0
1
1
0
1
1
1
1
2
1
1
1
1
1
1
0
0
0
0
2
1
1
0
1
2
1
1
1
1
2
0
0
0
1
2
1
1
2
2
2
1
1
0
1
1
1
1
1
0
0
1
1
2
0
1
1
2
1
1
1
1
2
2
0
0
1
2
0
0
3
0
1
1
1
1
1
0
2
1
0
2
0
0
1
1
2
1
0
0
1
1
1
1
1
1
2
1
2
1
2
1
0
0
1
1
1
1
0
2
1
2
1
0
1
0
1
1
2
0
1
1
2
1
2
1
1
1
0
1
1
1
1
1
1
1
1
0
0
1
1
2
1
1
2
1
0
1
0
2
1
2
1
1
2
1
2
2
1
2
1
1
1
1
1
2
0
1
1
1
1
1
1
1
2
1
2
1
1
1
2
1
1
0
1
1
0
1
1
0
2
1
1
0
1
1
1
1
1
2
2
0
0
1
1
0
1
1
0
1
1
1
1
0
2
1
1
2
1
1
1
1
1
0
1
1
1
1
1
1
0
1
1
1
1
1
1
0
1
1
1
1
0
2
1
2
2
1
1
0
0
1
3
4
1
1
0
1
1
1
1
1
1
2
0
1
2
3
2
0
1
1
1
0
1
0
1
2
0
0
0
2
1
0
0
1
1
1
2
1
2
1
1
1
2
1
0
1
0
1
1
0
1
1
1
1
1
1
1
1
2
2
2
1
2
0
1
0
1
0
2
1
2
0
1
1
1
1
1
1
1
1
2
1
0
2
2
2
1
1
1
1
1
2
1
1
0
1
0
1
0
1
2
1
0
1
2
2
1
1
0
1
0
2
1
0
1
2
1
1
1
1
0
2
0
1
1
2
2
0
2
1
1
1
2
0
1
1
1
1
2
2
2
1
1
1
1
0
2
1
0
2
1
1
1
1
2
1
1
1
0
1
1
0
2
1
2
0
0
1
1
1
2
0
1
1
2
1
1
0
0
0
0
0
1
1
1
1
1
1
1
1
1
1
1
0
1
1
2
1
0
0
2
0
0
0
1
1
0
1
1
0
1
1
1
1
1
1
1
1
2
2
1
1
1
3
1
0
1
1
2
1
1
1
1
2
1
2
0
1
1
2
1
0
1
0
2
1
0
1
2
0
1
1
2
2
1
2
1
2
2
2
1
1
1
0
2
1
1
1
1
0
1
1
1
2
1
0
1
1
1
1
1
1
0
1
1
0
1
2
1
1
2
0
0
3
2
0
1
1
1
2
0
2
1
1
2
1
2
1
1
2
1
2
0
2
1
1
1
0
0
0
2
1
2
2
1
1
2
1
1
0
2
1
2
1
1
2
1
1
1
1
0
1
0
1
2
0
1
1
1
1
0
2
1
1
1
1
2
1
2
0
1
1
1
1
2
1
1
1
2
1
2
1
0
1
0
0
1
1
1
1
1
1
1
1
0
2
1
0
2
0
1
0
1
0
2
1
0
1
2
1
1
4
1
1
0
1
1
1
2
2
1
0
1
2
0
1
2
1
0
1
1
0
0
0
1
1
0
1
1
1
1
1
1
1
1
1
0
1
1
0
1
2
1
0
2
1
1
1
2
1
1
0
1
1
1
2
0
1
1
2
1
1
1
1
2
1
1
2
1
1
2
0
1
1
2
0
1
2
0
1
2
0
2
1
1
1
2
1
0
1
0
1
1
2
1
1
0
2
1
1
1
1
1
1
1
0
2
2
1
1
1
1
1
1
1
1
1
1
0
1
0
1
1
1
2
2
1
0
1
1
0
1
0
2
1
1
1
2
1
1
1
1
0
0
1
1
0
1
1
1
2
0
1
1
1
1
2
0
2
1
1
0
2
3
2
1
2
1
1
2
1
1
1
3
1
1
1
2
2
1
0
0
2
1
1
1
1
1
1
0
1
1
2
1
1
0
1
2
2
1
1
1
2
1
0
1
2
1
0
1
1
1
1
1
1
1
0
1
1
1
2
0
1
0
1
1
0
1
2
0
0
0
0
1
1
1
0
0
0
1
1
0
2
1
1
1
0
0
1
1
0
1
1
1
2
1
2
0
1
1
1
1
1
1
2
2
1
1
0
2
1
1
0
2
1
2
1
1
0
2
1
1
0
1
2
2
1
1
1
1
1
0
1
1
2
0
1
1
1
2
1
2
1
0
1
1
1
1
1
1
0
1
1
0
2
0
1
1
2
1
1
1
1
1
2
1
1
1
0
1
1
2
0
2
2
2
0
1
1
0
2
1
1
2
0
1
2
0
1
0
1
1
2
1
1
2
1
1
2
1
1
0
1
1
0
0
0
1
0
1
0
2
1
1
1
1
1
0
2
2
1
1
2
1
0
1
1
2
1
1
1
1
1
0
1
1
1
2
1
2
1
2
1
2
1
1
1
1
1
1
0
2
1
0
1
2
0
1
0
1
1
1
2
0
0
2
0
2
2
2
1
0
2
1
2
1
1
1
2
1
1
2
1
2
1
0
1
1
2
1
1
1
1
0
1
1
1
0
0
1
1
0
1
2
1
1
2
1
1
1
0
2
1
2
0
1
1
2
1
2
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
2
2
1
2
1
2
2
1
2
1
1
1
1
1
1
0
1
2
1
1
0
2
1
1
1
1
2
2
1
2
1
1
2
2
2
0
1
0
0
1
1
1
0
0
0
2
1
2
2
0
0
0
1
1
1
0
1
2
1
1
1
2
1
0
1
1
1
0
1
1
0
1
0
2
0
1
1
0
1
1
0
1
0
1
1
1
1
0
0
1
2
0
1
1
1
1
1
2
1
0
2
1
1
1
1
2
2
1
2
1
0
1
0
2
0
2
1
1
1
1
1
1
1
1
0
1
1
2
2
2
0
1
1
1
1
2
2
1
1
1
1
2
1
1
1
2
1
1
1
0
2
1
2
1
0
0
1
2
1
1
1
1
1
0
1
1
0
2
1
1
1
2
2
0
1
2
0
1
2
2
0
1
1
2
0
1
2
1
1
1
1
1
1
0
1
5
2
1
1
1
1
2
2
1
1
1
1
1
2
2
1
0
1
1
1
0
1
2
1
0
2
2
1
2
1
1
0
1
0
0
1
1
1
0
0
1
1
0
1
0
1
0
0
1
1
1
1
1
1
1
2
0
1
2
2
1
2
2
2
2
2
2
1
1
1
0
1
1
0
1
1
0
0
1
1
0
0
1
2
1
1
0
2
1
2
0
1
1
0
1
1
1
2
2
3
1
1
2
2
0
0
2
1
1
0
1
1
1
1
1
2
1
2
2
2
0
1
1
2
1
1
0
1
1
2
2
0
1
1
2
1
1
0
1
1
0
1
1
1
2
1
2
2
1
1
1
2
1
1
0
2
1
1
1
1
1
1
0
1
2
2
1
0
0
1
1
0
1
1
1
1
1
1
1
1
2
1
1
1
1
0
2
0
2
0
1
0
2
1
0
0
1
2
2
2
1
1
1
1
0
1
1
1
1
0
1
1
0
1
0
2
1
2
0
1
0
1
1
0
1
1
1
1
0
1
1
1
1
2
2
0
2
1
2
1
0
1
1
0
0
1
0
1
1
1
0
1
1
1
1
2
2
2
1
0
1
1
0
1
1
1
2
1
1
1
2
1
2
1
2
2
1
1
1
1
1
2
2
1
2
2
1
1
1
0
1
1
1
2
2
2
2
1
2
1
1
1
0
0
1
1
1
0
1
1
2
1
2
1
2
0
1
1
1
2
1
2
1
1
2
1
1
2
1
1
1
1
2
1
0
1
2
1
1
0
1
0
0
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
0
1
1
1
2
1
2
1
1
1
1
1
0
2
1
1
1
1
1
1
1
1
2
0
1
2
1
1
1
2
1
2
1
1
1
1
0
1
1
0
2
1
1
1
1
1
2
1
0
2
0
1
0
2
2
0
2
0
1
0
1
1
0
1
1
2
0
0
2
2
1
1
0
1
1
1
1
1
2
1
2
1
1
1
1
2
2
1
1
1
1
0
1
1
2
0
0
0
2
1
1
1
1
3
0
1
1
3
1
0
1
1
0
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
0
1
0
1
1
1
1
1
0
0
1
2
2
0
1
2
0
1
2
0
2
1
1
1
1
1
1
0
0
0
1
0
1
1
1
0
1
1
1
1
1
0
2
1
1
1
2
1
0
0
1
5
0
1
1
1
1
1
0
0
2
1
1
1
1
2
4
1
1
2
1
1
1
2
2
1
1
1
0
2
2
1
0
2
0
1
1
2
1
1
0
1
1
1
1
0
2
2
1
0
1
1
1
1
1
1
0
1
1
0
1
2
2
0
2
1
1
1
2
1
1
1
2
1
1
1
1
2
1
0
0
1
1
1
1
0
0
1
2
0
1
1
2
1
1
0
2
1
1
0
3
0
0
2
1
0
0
1
2
2
1
2
1
2
1
2
2
1
1
2
0
1
0
1
1
2
1
1
1
1
3
0
1
1
1
1
2
0
1
1
1
3
0
1
0
2
1
2
1
1
1
1
1
0
2
2
2
1
0
1
1
1
1
0
1
1
1
1
1
2
1
2
1
1
0
1
1
1
1
0
2
2
1
1
2
1
0
0
0
1
1
0
2
2
1
1
2
0
1
1
1
1
1
2
0
0
1
0
0
2
0
2
1
1
1
0
2
1
2
1
0
1
0
1
1
0
1
7
2
2
2
0
0
1
1
1
0
2
2
1
1
2
1
1
0
0
1
1
1
1
1
0
2
1
0
1
1
1
2
1
1
2
2
1
1
2
1
1
2
2
2
1
0
1
1
1
4
0
1
2
1
0
1
2
2
0
0
1
2
1
1
0
2
2
1
1
1
1
1
1
1
1
0
0
0
0
1
1
0
1
0
1
2
1
1
0
0
1
1
1
1
2
1
1
1
1
0
2
2
1
0
1
2
1
0
1
0
2
0
1
0
1
0
1
1
2
2
1
2
1
1
1
1
1
2
0
1
1
0
2
2
2
1
0
1
1
1
0
1
2
0
2
0
1
2
2
2
0
1
1
0
1
2
1
1
0
1
2
0
2
1
1
0
2
1
1
0
1
1
1
1
0
2
1
1
1
0
0
1
0
1
1
2
1
2
1
1
0
1
1
1
2
1
0
4
2
0
1
0
0
1
2
1
0
1
1
1
2
1
2
1
0
1
0
1
2
1
0
1
2
0
1
2
1
1
3
1
2
0
1
2
1
2
0
0
0
1
1
1
1
0
1
0
1
1
1
0
2
1
0
0
1
0
1
1
1
2
3
0
0
2
1
0
1
1
1
2
1
1
3
1
1
1
1
1
2
1
1
1
2
1
0
1
2
0
1
2
1
1
1
0
2
1
2
1
0
0
1
2
1
1
2
2
0
0
1
0
1
1
1
2
1
1
2
1
1
2
0
1
0
2
1
0
1
1
0
1
1
1
0
0
1
1
2
1
0
0
2
1
1
1
3
0
1
0
1
1
2
2
1
2
1
1
2
1
0
2
1
0
0
1
1
1
1
1
1
1
1
1
0
1
1
1
0
0
1
0
2
0
1
2
2
0
0
1
1
1
1
1
1
0
2
1
2
2
1
0
1
2
0
2
0
2
2
1
0
1
2
0
0
3
2
1
2
2
0
1
1
0
2
0
1
0
1
2
1
1
1
1
0
1
1
0
1
1
2
2
2
2
1
1
0
1
1
2
2
1
1
1
0
1
2
1
2
2
0
0
1
2
1
1
1
0
2
1
1
2
1
1
2
1
1
0
1
0
2
1
1
1
0
1
0
1
1
1
1
1
1
1
2
2
1
0
1
1
0
1
1
2
1
0
1
2
0
2
1
1
2
0
0
0
1
1
2
1
1
1
2
1
1
1
1
3
1
1
1
0
0
2
1
0
2
1
1
1
0
1
1
1
1
1
1
1
0
2
1
0
0
1
0
2
0
2
1
1
1
0
2
0
1
0
2
2
1
2
1
1
1
2
1
1
2
1
0
2
2
3
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
2
1
1
0
2
2
1
0
1
2
0
1
1
1
0
0
2
1
2
0
0
0
2
2
1
1
2
1
1
0
0
1
1
2
0
0
1
0
2
1
1
1
1
1
2
2
0
1
1
2
0
0
2
0
0
2
1
1
1
2
2
1
2
1
1
2
1
1
2
0
2
2
1
1
2
1
2
1
0
1
0
1
0
2
2
1
1
1
2
0
1
1
1
1
2
1
2
0
1
1
1
0
2
1
2
1
1
1
0
1
0
2
2
0
2
0
1
2
1
0
0
0
0
1
1
0
1
1
1
0
0
1
0
1
0
0
1
0
1
1
1
1
0
1
0
1
1
1
1
1
2
0
1
1
1
1
1
0
0
1
1
2
2
1
1
2
0
1
2
1
1
2
1
0
1
2
2
0
2
1
6
0
1
1
2
1
1
1
0
1
1
0
1
1
2
1
2
4
1
0
1
1
2
2
2
1
1
1
1
1
1
2
1
1
0
0
1
1
0
1
1
1
1
2
1
1
2
2
1
0
0
0
2
1
2
1
2
2
2
2
1
1
0
0
2
1
1
0
2
2
0
1
2
1
1
0
1
0
1
1
2
1
1
0
0
1
1
1
0
0
4
1
0
0
0
1
1
1
1
1
1
1
0
1
1
1
1
1
1
0
1
2
0
2
1
1
1
1
2
0
1
0
3
2
1
0
1
1
1
2
2
2
0
0
1
0
1
2
1
2
1
1
1
1
1
0
2
1
1
2
1
1
1
1
0
2
2
2
2
2
2
0
2
1
1
2
1
0
0
1
1
1
0
2
2
1
0
0
1
1
2
0
1
1
2
1
0
1
0
0
1
1
1
2
1
1
1
1
0
1
0
2
1
1
1
1
2
1
1
1
1
1
0
2
1
0
1
1
2
2
1
1
0
0
0
2
1
2
1
2
1
1
2
1
1
0
1
0
1
2
1
2
1
2
0
0
1
2
1
1
1
1
1
2
2
0
1
1
1
1
1
0
0
1
0
0
1
0
1
2
2
1
1
1
1
0
2
1
1
1
1
3
0
1
2
1
1
2
1
0
1
0
2
1
1
0
1
2
2
0
1
1
1
1
1
1
2
2
1
0
2
2
2
1
0
0
0
1
1
1
2
1
0
1
0
0
1
1
1
1
1
0
0
1
1
0
1
2
0
1
1
1
0
1
0
0
1
1
2
0
2
1
1
1
1
2
1
1
1
0
0
0
2
0
5
1
1
1
1
2
0
1
2
1
2
1
0
1
1
2
1
0
1
1
1
1
0
2
0
0
1
2
1
1
2
1
1
0
1
0
1
1
0
0
2
0
2
0
1
1
0
0
1
1
1
2
0
1
1
1
0
2
0
1
1
2
1
0
1
0
1
1
1
0
1
2
1
0
1
1
1
1
1
1
2
1
1
2
1
1
0
1
1
1
1
1
0
0
1
2
1
1
1
2
2
1
1
2
0
1
0
1
0
2
2
1
2
0
2
1
0
0
1
0
2
0
1
2
1
2
2
0
1
1
2
1
0
0
1
2
1
0
0
1
0
1
2
1
1
1
0
1
0
1
2
1
0
2
1
1
1
1
1
1
0
0
0
1
1
1
2
2
1
0
0
1
0
1
2
0
1
1
1
1
0
1
0
1
2
0
1
1
1
1
1
0
1
2
1
0
1
1
1
2
1
1
1
0
1
1
1
0
1
1
1
1
0
0
1
1
2
2
1
0
1
2
2
1
1
0
1
2
2
1
2
0
2
0
2
1
0
1
0
1
2
0
1
1
1
2
0
1
1
1
1
0
1
1
2
1
1
0
1
2
1
2
0
1
2
2
1
1
1
0
2
2
2
1
2
1
2
0
0
2
2
1
0
1
1
2
2
2
1
0
1
1
2
1
1
1
2
1
0
0
2
2
2
1
1
1
0
0
2
2
0
1
0
2
1
1
1
2
2
1
1
1
1
1
1
1
0
0
0
2
2
1
2
1
1
0
1
1
0
2
0
1
1
1
1
0
1
2
1
1
1
1
1
1
0
2
1
1
2
1
1
2
2
1
1
1
2
0
2
2
0
2
1
1
2
1
1
1
0
1
1
1
2
1
0
2
0
1
1
2
1
1
2
1
1
2
1
1
2
0
2
0
2
1
1
1
1
1
0
1
1
1
1
1
1
1
0
1
0
0
2
2
2
2
0
0
2
1
0
1
0
1
0
0
0
2
1
2
0
2
1
1
1
1
0
2
1
2
2
2
1
2
2
1
2
0
1
2
2
1
2
1
1
2
1
1
2
2
1
1
0
1
0
1
1
1
0
0
0
1
2
1
1
1
1
3
1
0
1
1
1
1
0
1
2
1
1
0
2
1
1
2
0
0
0
0
2
1
0
2
0
1
1
1
0
0
0
2
1
1
1
1
2
0
1
1
2
1
1
0
0
1
0
1
2
0
1
1
0
1
2
2
0
2
1
1
1
2
0
0
1
1
1
1
0
1
1
2
1
0
0
6
2
1
1
1
1
0
0
2
1
1
1
1
1
0
1
1
1
1
1
0
0
0
1
0
1
1
1
2
1
1
2
1
1
1
2
2
1
0
0
1
1
0
1
1
1
1
2
2
1
1
2
1
2
1
1
1
1
0
1
1
0
2
2
1
2
0
2
2
1
1
1
1
0
1
2
1
0
0
1
1
1
1
1
1
1
0
1
2
2
1
2
3
1
1
0
2
1
1
1
1
2
1
1
0
1
1
1
1
0
1
2
2
1
1
1
1
1
2
0
1
1
1
0
2
2
2
0
0
1
1
1
1
1
0
1
2
0
2
2
3
2
1
1
1
1
1
1
1
1
0
1
1
1
1
1
0
1
1
0
2
1
1
1
1
1
1
1
2
1
1
2
2
2
1
0
1
2
1
1
0
1
1
0
1
1
2
2
1
2
3
1
2
1
1
0
1
1
1
1
2
0
1
2
2
0
2
0
1
1
0
1
0
2
0
3
2
0
1
2
2
1
2
0
1
1
0
0
1
1
0
1
2
1
0
2
1
1
1
1
1
2
0
2
1
2
1
1
0
1
2
2
0
1
1
1
1
2
1
2
2
0
1
0
0
2
1
1
1
1
1
1
2
2
2
0
0
1
0
1
0
0
1
1
1
1
1
2
1
1
1
0
2
1
2
3
1
1
2
2
1
1
1
1
0
0
2
2
1
1
1
1
1
2
1
0
0
1
1
1
1
1
0
1
1
0
1
0
2
1
1
0
1
2
1
0
1
1
2
1
1
0
2
2
1
0
1
1
0
1
1
2
1
1
1
1
1
1
2
1
1
2
1
1
1
1
0
1
2
1
1
1
0
1
0
2
1
1
1
1
1
2
1
1
2
1
1
0
0
1
0
1
2
1
2
2
1
1
0
1
1
0
1
2
2
1
0
1
0
1
2
2
0
1
0
1
1
1
1
1
0
1
2
1
1
0
1
0
1
1
2
1
1
2
0
1
2
1
1
2
2
1
0
2
2
1
0
2
1
2
2
0
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
2
1
1
2
1
1
1
1
2
1
1
1
1
1
1
0
1
0
2
1
1
1
0
1
1
2
1
2
0
1
1
1
1
1
0
2
1
2
1
2
0
1
1
0
1
1
2
1
2
1
2
1
1
0
1
1
2
1
0
1
1
1
1
2
2
1
0
1
0
1
0
2
1
1
1
1
1
0
1
0
1
0
0
2
1
2
0
1
1
1
2
1
0
1
0
0
1
2
0
0
1
1
0
1
1
1
1
2
0
1
1
0
2
1
2
0
3
1
1
1
1
1
1
0
1
0
1
1
1
1
0
1
1
1
0
2
1
1
1
2
2
1
1
1
1
1
1
0
1
0
1
0
0
1
2
0
1
1
1
3
1
1
1
1
1
1
1
1
0
1
0
2
1
1
1
1
1
0
1
2
1
1
1
0
1
1
1
1
1
1
0
2
1
0
1
1
2
1
1
3
2
1
0
2
0
1
1
0
1
2
1
0
2
1
2
1
1
1
2
1
1
2
1
0
2
1
0
1
1
0
1
1
1
1
0
2
0
0
2
1
2
1
0
0
0
0
2
2
0
2
0
0
1
0
1
1
2
4
1
1
1
0
0
1
1
0
1
1
1
0
1
1
1
1
0
1
1
2
3
1
1
1
1
0
1
1
1
1
2
0
0
3
1
1
0
0
1
0
1
0
2
1
0
1
1
0
1
2
0
1
1
2
1
2
1
1
1
2
1
1
1
2
2
0
1
0
1
1
0
1
1
1
1
1
1
0
1
0
1
2
0
1
1
1
2
1
1
2
1
1
1
0
1
1
1
1
1
1
1
2
2
1
1
2
2
1
1
2
1
1
1
2
2
1
1
1
1
1
1
2
2
1
2
1
0
1
0
0
1
1
1
1
1
2
1
2
1
2
2
1
1
0
1
1
1
2
1
1
2
2
0
0
1
2
1
2
1
1
0
1
1
1
1
2
1
1
0
0
3
0
2
0
2
1
1
0
1
1
1
1
1
1
1
0
2
2
2
2
2
1
1
0
1
0
3
0
4
1
1
1
0
2
0
2
0
1
1
1
1
1
2
1
2
1
1
0
1
1
1
1
1
1
1
0
1
3
0
1
2
0
0
1
1
1
1
2
1
1
1
1
1
1
1
2
1
0
1
1
0
1
1
2
1
0
1
1
1
1
2
1
1
1
1
3
1
0
2
1
1
1
1
1
2
2
1
1
1
2
0
1
2
0
1
1
2
2
2
2
1
1
0
0
1
1
0
1
1
0
1
2
1
0
1
1
2
0
1
0
1
2
1
0
1
1
1
1
1
2
4
1
1
1
2
3
1
1
0
2
0
0
1
1
1
0
1
2
1
2
0
1
1
1
1
1
3
1
0
1
0
0
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
2
3
2
2
0
1
1
2
1
2
1
1
2
2
1
1
1
2
1
0
1
1
1
0
1
2
1
1
1
0
1
2
1
0
2
2
1
0
1
1
1
1
0
0
1
0
1
1
1
1
1
0
1
1
2
1
1
0
1
1
0
1
1
1
2
1
1
0
1
1
1
0
1
0
0
1
2
1
0
0
1
0
0
1
2
2
2
1
1
1
1
0
1
1
1
1
1
2
2
0
1
0
1
0
4
1
2
1
1
2
1
1
1
2
2
0
1
1
1
1
1
1
2
0
1
2
0
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
2
1
0
1
2
1
1
1
2
1
0
2
2
1
1
1
1
1
2
2
1
3
0
1
0
0
1
0
1
0
1
1
1
0
1
2
1
1
0
1
2
1
0
1
1
0
1
1
2
1
2
1
1
0
0
2
1
1
3
2
2
2
0
2
2
2
1
1
1
1
1
2
0
1
0
0
2
0
1
2
1
0
2
0
2
1
1
1
1
1
1
1
1
1
1
0
2
1
0
1
2
1
2
1
1
2
1
0
1
1
0
1
2
2
1
1
2
1
1
2
2
2
1
2
1
1
1
2
0
1
1
2
2
1
1
0
2
2
1
0
1
2
2
1
2
2
0
0
1
2
0
0
1
1
1
1
3
1
1
1
1
1
2
1
1
1
1
1
0
1
1
1
2
1
2
1
2
1
1
1
0
2
2
0
1
1
1
1
2
2
1
1
1
0
1
1
0
1
2
1
2
1
1
1
2
0
1
1
1
0
1
1
1
2
1
0
1
1
0
1
1
1
1
1
1
2
0
0
0
0
1
1
0
1
1
0
2
1
2
2
1
1
0
0
1
2
2
1
1
1
1
1
0
1
1
0
1
1
0
1
1
1
0
1
1
1
1
1
0
2
1
1
1
2
1
2
0
1
1
2
0
1
2
1
1
1
2
0
2
0
2
2
1
2
0
2
1
1
1
0
1
1
1
1
1
0
2
2
2
1
1
1
1
1
1
2
1
0
1
1
1
0
0
2
1
1
0
1
0
1
0
0
0
1
1
0
0
0
1
1
1
0
2
1
2
1
0
0
2
1
1
2
2
2
1
1
1
1
1
1
0
1
2
1
2
1
1
1
1
2
1
1
1
0
0
1
1
2
1
1
1
2
2
1
2
1
0
1
0
3
0
1
1
1
2
1
1
1
2
1
0
1
3
0
0
0
1
1
1
2
0
1
1
1
2
1
1
1
2
1
2
1
1
1
2
2
1
0
1
1
2
3
1
1
1
0
1
4
1
1
1
1
2
2
2
2
1
2
1
2
2
1
1
0
0
1
2
1
1
2
0
1
1
1
2
0
0
1
0
0
1
0
1
1
2
1
2
1
2
0
0
1
1
1
1
1
1
1
1
0
2
0
1
1
0
1
1
2
1
1
1
1
1
1
1
0
0
0
0
0
1
2
1
1
1
0
0
2
1
1
0
1
2
1
0
0
0
1
1
0
0
0
1
1
2
2
1
1
1
1
1
0
1
1
1
1
1
2
1
1
1
2
2
0
0
0
1
0
1
0
0
1
2
1
0
0
1
1
2
1
1
2
0
1
1
0
1
1
1
2
3
1
1
1
2
1
1
0
1
1
2
2
0
0
1
1
1
1
2
1
1
0
1
1
1
4
1
1
2
1
1
1
1
1
2
1
0
0
1
2
0
1
1
1
1
1
1
1
0
2
1
1
1
0
2
1
1
0
0
1
2
1
2
1
1
1
0
0
0
0
1
0
1
0
1
1
1
1
0
2
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
0
2
1
2
0
0
0
2
1
1
1
1
0
1
1
1
0
0
1
2
2
1
1
2
1
2
2
2
2
2
1
1
1
1
0
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
0
1
1
1
0
1
1
1
1
1
1
1
1
1
1
0
2
1
0
1
1
0
2
0
1
1
1
0
1
0
1
1
1
0
2
1
1
2
2
1
1
2
1
1
2
1
2
0
0
1
1
1
2
1
2
2
1
0
0
2
1
0
1
1
0
1
2
0
1
0
1
0
1
1
2
0
2
0
2
2
1
2
1
0
1
1
1
2
1
0
1
1
1
0
2
1
0
1
1
1
0
2
1
0
1
2
0
0
1
1
1
1
1
0
1
1
1
2
1
1
0
2
0
2
2
1
0
1
2
1
1
1
1
1
0
2
1
0
2
1
0
0
1
1
0
1
1
2
0
0
1
2
2
0
1
2
0
1
0
1
1
2
1
0
1
1
2
1
1
1
0
1
1
1
0
1
2
0
1
1
1
1
0
0
2
2
1
1
1
0
1
0
1
2
1
0
2
1
1
1
1
1
1
0
1
3
1
2
1
1
1
0
2
2
1
1
0
1
2
0
0
1
0
2
1
1
1
1
1
1
1
3
1
2
1
1
0
2
1
0
0
0
0
2
1
1
0
2
2
1
0
0
1
1
1
1
1
1
1
1
2
1
1
0
3
1
0
1
1
2
1
1
1
1
1
1
2
0
1
0
1
2
1
1
1
1
1
1
1
0
1
2
1
2
1
1
1
3
2
1
1
1
1
1
1
2
1
0
0
1
1
2
1
1
1
1
1
2
0
1
0
1
2
1
2
1
1
1
1
1
1
2
0
1
1
1
1
2
1
2
1
1
0
1
1
0
0
1
2
0
1
2
1
1
1
0
0
1
0
1
1
2
1
1
2
1
1
2
1
1
0
1
2
0
1
0
0
0
2
0
1
0
1
1
1
3
3
1
2
0
1
0
1
1
2
1
2
2
1
1
1
2
1
0
0
1
1
0
1
1
0
1
0
0
1
0
0
1
1
1
1
1
1
0
0
2
2
0
1
1
1
1
2
0
1
1
1
1
1
2
2
1
1
2
1
1
2
1
1
1
1
1
1
2
1
2
2
1
1
1
0
2
1
1
1
1
1
1
1
1
3
1
3
2
2
0
1
0
1
1
1
0
1
2
1
0
1
1
1
1
1
2
1
2
1
1
0
1
2
0
1
1
1
1
1
1
0
2
1
2
1
0
1
0
1
1
1
1
0
1
1
1
1
1
2
1
1
1
0
2
1
0
2
0
1
1
1
1
1
1
1
3
1
0
2
1
1
1
0
0
1
1
1
1
1
3
1
0
1
1
1
0
1
1
0
1
1
0
0
1
2
0
1
1
1
2
1
0
0
1
1
1
1
1
2
2
1
0
2
1
1
2
0
1
1
1
1
0
1
1
0
1
2
3
1
2
1
2
1
2
1
2
1
0
2
3
1
1
1
1
1
0
1
2
0
2
1
1
1
1
0
2
1
1
1
2
0
1
2
1
2
1
0
1
1
2
1
1
0
2
0
0
0
2
1
2
1
0
0
1
1
1
0
0
1
0
1
3
0
3
1
1
1
0
1
1
1
1
0
1
0
0
1
0
2
1
1
0
0
0
2
1
2
0
1
2
1
1
2
1
2
1
0
1
0
0
0
1
0
2
1
2
0
1
1
2
1
1
1
1
1
2
2
1
1
2
0
1
1
1
2
1
0
1
1
1
0
1
1
1
1
2
0
1
1
1
0
1
1
0
2
1
0
0
1
0
2
0
0
1
1
1
1
0
2
0
1
0
2
1
2
1
1
1
2
0
1
2
1
1
0
1
0
2
1
1
2
1
1
0
0
1
1
0
1
1
1
1
2
0
1
1
2
0
2
1
1
2
0
0
1
0
1
1
1
0
0
1
2
0
2
1
2
2
1
2
1
1
2
1
2
1
1
1
0
1
1
1
1
2
1
1
1
1
1
1
1
0
0
2
0
2
1
2
1
1
1
1
1
1
0
2
2
2
1
1
1
1
1
2
1
2
1
0
0
0
2
1
1
1
1
1
2
1
1
0
2
0
1
2
1
1
2
0
2
1
2
1
2
2
1
1
0
0
1
0
1
0
0
2
1
2
1
1
1
1
2
2
0
2
0
1
0
1
1
1
1
2
0
1
1
1
0
1
1
1
1
2
1
1
0
1
1
1
1
1
2
1
1
0
2
2
2
2
2
1
1
1
1
0
1
1
1
1
1
1
0
1
1
1
1
1
2
1
1
0
1
0
0
0
2
1
1
2
2
1
1
3
0
0
1
2
2
2
1
1
2
2
1
1
1
1
1
1
0
1
2
2
1
2
1
1
1
1
2
0
1
2
0
2
2
1
1
2
2
1
1
1
0
0
2
1
1
1
0
1
0
0
1
2
1
2
1
2
2
2
1
0
1
2
0
0
0
1
2
0
1
1
1
2
0
0
1
0
1
2
0
1
1
1
0
1
1
1
0
0
2
2
1
1
1
1
0
0
0
1
1
1
1
0
0
2
2
1
1
1
1
2
1
2
1
2
0
1
0
1
0
1
1
1
1
0
2
1
1
1
1
1
1
2
1
1
1
0
1
1
0
2
2
0
1
0
1
1
2
1
1
1
1
1
1
1
2
1
1
1
4
2
1
2
1
1
1
1
2
0
2
2
1
0
1
0
1
2
1
1
1
0
0
2
1
2
2
2
2
1
1
1
1
1
1
1
1
2
1
1
2
2
0
0
1
1
1
1
0
1
2
1
1
2
1
0
2
1
0
1
2
0
1
1
1
1
1
0
2
0
0
0
1
2
1
1
0
1
0
1
1
1
2
2
1
1
2
2
0
1
2
2
0
0
2
1
2
1
0
0
0
1
1
0
2
0
1
1
0
1
1
1
1
1
2
3
2
1
1
1
1
1
1
0
0
2
1
2
1
2
1
0
1
1
2
1
1
1
1
1
0
1
1
2
1
1
2
1
0
1
2
2
2
1
1
1
0
2
1
1
1
1
1
2
1
1
2
1
1
0
2
2
1
1
1
1
1
0
2
1
1
1
1
2
1
0
2
1
2
0
1
1
1
0
1
2
0
0
0
1
2
1
2
1
1
2
1
1
1
0
1
2
1
1
0
2
0
2
1
1
1
2
1
1
1
1
0
1
0
1
1
1
1
0
1
1
1
1
1
1
0
1
1
2
1
1
1
2
1
1
1
2
2
1
2
0
1
1
1
2
0
1
0
0
2
2
1
0
2
1
1
1
1
2
1
1
2
1
1
0
1
2
0
1
1
1
1
2
1
2
1
1
2
1
1
0
1
1
2
1
2
0
1
1
1
1
1
2
1
0
0
1
1
1
0
1
1
1
0
1
1
1
0
2
0
1
1
2
1
1
0
0
0
1
0
1
0
0
1
1
1
1
2
2
1
2
1
1
1
2
0
1
0
1
1
1
2
1
1
1
0
1
1
1
1
0
0
2
2
1
1
1
2
2
1
1
1
1
1
2
2
2
1
1
1
1
2
1
1
1
2
1
1
1
1
2
2
1
1
0
2
0
1
2
2
0
1
1
2
1
0
1
1
1
1
1
1
1
1
0
1
1
2
2
1
1
0
1
0
1
2
1
0
0
2
0
1
0
2
1
1
0
2
2
1
0
2
2
0
1
0
0
1
1
2
2
1
2
1
0
0
2
0
0
2
1
0
1
0
1
2
1
2
1
1
1
1
2
1
1
1
0
0
2
1
1
1
2
1
1
2
1
1
1
1
2
2
1
1
1
1
2
1
1
1
2
2
2
2
1
1
1
1
2
2
1
0
1
2
1
2
2
1
2
0
0
1
1
0
2
0
0
1
1
1
1
2
2
3
0
0
1
0
0
0
1
1
1
2
2
1
2
2
1
2
2
1
1
1
1
0
2
0
1
1
3
1
2
1
1
2
1
1
1
1
1
1
2
0
2
1
1
0
1
1
1
0
0
1
1
1
1
1
1
0
1
1
0
0
0
2
1
1
0
0
1
1
0
0
2
1
2
1
2
1
0
1
0
1
0
1
2
1
1
1
0
0
2
1
1
1
1
1
0
1
0
2
1
1
1
1
1
0
1
1
2
2
1
4
1
1
0
1
2
2
0
1
1
8
0
2
3
2
1
1
1
1
1
2
1
1
1
1
2
1
1
1
0
3
1
2
1
1
0
2
1
1
1
2
0
2
0
0
1
2
0
1
1
0
0
2
1
1
0
1
1
2
1
1
1
1
0
1
0
1
1
1
0
1
0
1
0
1
1
1
2
1
1
1
2
1
2
0
1
1
0
1
1
0
2
1
0
0
1
0
1
2
1
1
1
1
2
0
1
1
2
1
1
1
1
1
1
1
0
1
0
0
0
2
2
1
1
1
1
2
0
0
5
2
1
2
1
0
1
0
0
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
0
0
2
0
0
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
0
1
1
1
1
1
2
1
1
0
3
0
0
2
0
1
1
1
0
1
2
1
1
1
1
1
1
1
0
4
1
2
0
2
1
0
2
1
0
1
1
0
1
1
2
1
1
2
1
1
0
1
1
1
0
2
1
1
1
0
2
1
1
1
1
0
1
2
0
0
1
1
1
0
0
1
1
2
1
2
0
0
1
2
2
1
1
1
2
2
1
1
2
0
1
2
0
0
2
1
1
1
1
1
0
1
1
1
2
0
3
2
1
2
0
1
1
0
1
1
2
1
1
1
0
1
3
0
0
1
0
1
1
0
1
1
0
0
1
1
1
2
1
0
1
1
1
1
2
0
1
1
1
1
1
1
0
1
1
1
1
1
0
1
1
0
2
1
1
0
1
1
1
1
2
2
1
1
1
1
1
0
2
2
2
1
1
0
2
1
0
1
2
1
1
1
0
0
1
1
1
2
1
1
1
1
2
1
1
1
1
2
2
1
1
1
1
1
1
1
0
0
0
2
2
1
1
2
1
0
2
2
2
1
1
0
2
1
1
0
1
1
2
0
2
1
2
0
0
1
1
1
1
2
1
2
1
1
2
1
2
1
0
0
2
1
1
1
0
1
1
0
1
1
2
0
2
1
2
2
0
1
1
1
0
0
0
1
0
1
2
2
0
0
1
1
1
2
2
2
1
0
2
2
0
2
1
2
1
2
1
1
2
2
1
1
1
1
1
0
1
2
2
2
1
2
3
1
1
1
1
1
2
1
1
0
2
1
2
0
0
2
2
1
0
1
1
2
1
1
1
1
0
0
1
0
0
0
1
1
1
1
2
1
2
1
0
2
1
1
1
0
1
1
0
1
1
2
1
2
1
1
2
1
1
1
1
2
2
1
1
2
1
2
1
1
2
0
1
2
1
0
0
2
1
0
0
1
2
1
2
1
1
1
2
1
1
0
0
1
2
2
0
1
0
2
2
0
0
2
0
2
1
2
0
0
1
1
1
0
1
1
2
1
0
0
1
1
2
0
1
0
1
2
2
2
0
1
1
2
1
0
1
0
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
2
1
1
0
1
1
1
1
2
0
1
2
2
0
1
1
0
0
1
0
2
1
2
0
0
0
0
1
0
0
1
1
0
1
1
1
2
1
1
1
1
2
2
1
1
0
1
1
1
2
0
1
2
0
2
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
0
0
1
1
1
1
1
0
1
1
1
0
1
1
2
0
2
1
0
1
0
1
1
1
2
2
0
1
0
1
1
1
0
0
2
1
2
0
1
1
1
0
0
1
1
0
1
1
1
0
1
0
0
1
0
1
4
1
2
2
0
2
0
1
0
1
0
2
2
1
1
1
2
1
2
1
0
2
1
2
1
2
1
1
1
1
1
2
2
1
0
2
1
2
2
1
2
1
1
1
2
2
2
1
0
1
1
2
1
1
1
1
0
2
0
2
2
1
1
2
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
2
1
2
1
1
0
2
0
0
0
1
1
1
1
2
1
1
1
1
0
1
1
1
0
1
2
0
1
1
1
2
0
1
2
1
1
2
1
4
0
1
0
1
1
0
0
2
1
2
0
1
1
1
1
1
1
1
1
2
1
2
0
1
1
1
1
2
1
0
1
0
2
1
2
2
0
1
0
1
0
2
1
3
1
2
2
2
0
2
1
1
2
1
1
0
1
1
1
1
2
1
1
2
0
1
0
2
1
1
2
1
2
1
1
1
1
0
0
0
1
1
0
1
1
1
2
0
1
1
1
0
1
0
1
1
1
1
1
1
0
1
0
1
1
1
1
2
1
2
0
2
1
0
0
2
2
1
2
1
1
0
0
2
1
0
1
1
1
0
2
1
1
1
1
0
1
1
2
2
1
1
2
0
2
2
1
2
1
1
2
1
0
1
2
2
1
0
1
1
1
2
1
1
1
1
2
1
0
1
0
1
0
1
1
1
2
0
2
1
1
1
0
1
0
1
2
2
2
1
1
1
1
2
1
1
1
0
1
0
1
2
1
1
1
1
1
0
1
1
1
1
1
0
0
1
0
2
1
0
2
0
0
2
1
1
0
1
0
1
1
0
1
2
1
0
1
1
0
0
0
1
2
1
1
1
2
1
1
1
2
1
1
1
1
2
2
2
0
2
0
2
2
1
1
1
1
0
1
2
1
1
1
0
1
2
0
1
1
2
1
1
2
2
1
1
0
0
1
1
1
2
0
1
1
2
1
2
1
1
2
2
1
1
1
1
1
0
1
1
0
1
0
0
1
1
0
0
1
0
2
1
2
1
1
0
2
1
1
1
1
2
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
2
1
0
0
1
1
1
0
0
1
1
3
2
1
1
0
1
2
0
0
1
0
0
1
1
2
1
1
1
1
0
2
0
4
1
2
1
0
2
1
1
1
0
1
1
1
2
2
1
1
2
2
1
1
0
1
1
2
2
1
0
1
1
1
1
2
1
0
1
0
1
2
1
1
1
2
2
0
2
1
1
1
1
1
1
1
1
1
1
0
0
1
1
1
2
2
2
0
1
1
1
2
1
0
1
1
2
0
0
1
2
1
2
1
1
0
1
1
1
1
1
0
1
0
1
1
1
2
1
2
1
0
1
1
2
1
0
1
1
1
1
1
0
1
0
1
4
1
1
1
0
0
0
1
1
0
1
1
2
2
2
2
1
1
1
0
0
1
1
1
1
0
0
1
1
1
0
2
1
0
1
1
2
1
2
2
0
1
1
0
1
0
0
1
2
1
0
1
1
1
0
1
1
1
1
0
2
1
1
0
1
2
3
0
1
1
1
0
2
1
0
1
1
1
1
2
1
1
1
1
2
1
0
1
1
2
0
1
0
2
1
2
2
2
1
1
2
2
2
1
1
1
0
2
2
0
0
1
0
0
1
1
1
1
2
2
1
0
1
2
2
0
1
1
2
1
1
1
0
1
1
1
1
2
0
1
1
0
1
2
2
2
1
1
1
1
1
1
0
3
1
1
1
1
1
2
1
1
1
1
0
1
2
1
0
2
0
0
2
2
0
0
1
0
1
0
1
2
0
1
2
1
1
2
1
1
0
1
1
0
1
2
0
0
1
1
0
1
0
1
1
0
1
1
0
1
1
1
1
1
2
1
1
1
1
1
1
0
0
0
1
1
1
2
2
1
1
1
1
1
2
0
1
1
1
1
0
1
0
1
0
1
1
1
1
1
2
1
1
0
2
1
1
1
0
1
2
3
1
1
0
0
1
0
0
1
1
1
1
0
1
0
1
1
0
1
1
1
1
0
1
1
2
0
1
2
1
0
2
0
1
1
1
0
1
1
1
1
1
1
0
2
1
0
2
1
1
2
2
2
2
1
0
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
0
0
0
2
0
1
1
2
1
2
0
1
1
1
0
1
0
2
1
1
1
1
0
1
1
1
1
1
1
1
1
1
2
2
0
2
1
0
2
1
1
2
1
1
2
1
0
0
2
1
0
0
1
1
1
1
1
0
0
2
0
0
1
1
1
1
1
1
1
0
1
2
0
2
1
2
1
1
2
1
0
2
1
2
2
0
1
1
1
1
1
1
1
1
2
2
1
2
0
2
1
1
1
3
0
1
2
1
2
0
1
0
2
1
0
2
1
1
2
1
1
2
2
0
1
1
1
1
2
0
2
1
1
1
0
1
1
1
0
1
1
1
1
1
1
0
1
2
1
1
1
1
1
1
1
1
1
2
0
0
1
0
0
2
2
1
1
1
1
1
0
0
2
1
0
0
0
1
1
0
1
1
1
1
1
2
1
2
1
2
2
1
1
0
0
1
1
0
1
1
1
1
1
2
2
1
1
0
0
1
0
1
2
0
2
1
1
1
0
1
1
2
0
0
1
2
1
2
1
0
1
0
1
1
0
1
1
0
2
1
1
1
1
0
2
1
2
1
0
1
1
0
1
1
1
0
1
0
2
2
1
0
0
2
1
1
1
1
0
2
2
2
2
1
0
1
1
1
1
2
1
1
1
1
1
2
0
0
1
0
1
1
2
1
2
2
0
1
2
1
0
1
2
2
1
1
1
0
0
1
1
0
2
1
1
1
2
1
2
2
1
0
1
1
1
2
1
1
2
1
1
1
1
2
2
1
1
1
1
0
1
1
1
1
0
2
1
0
1
1
1
1
1
1
1
1
0
1
1
2
0
0
0
1
0
0
2
0
0
1
1
1
1
0
0
2
2
1
0
2
1
1
1
0
1
2
2
0
1
2
1
2
1
1
2
1
2
1
1
1
1
2
2
1
1
1
1
2
0
0
0
1
1
1
0
1
1
1
2
1
0
1
2
1
1
2
1
2
1
1
1
3
0
1
2
1
0
1
1
1
2
1
1
0
2
1
1
1
2
1
0
1
1
1
2
1
1
2
1
1
2
2
1
1
1
1
0
2
4
2
1
1
1
1
1
1
0
1
0
2
2
1
1
0
2
1
0
2
1
2
1
1
2
1
1
0
0
0
1
1
1
1
2
1
1
1
0
1
1
1
2
1
0
1
1
1
0
1
1
1
0
0
1
1
1
1
1
1
1
0
1
1
2
1
1
1
2
0
1
1
1
2
2
0
2
1
1
1
1
1
2
1
0
1
0
1
1
2
1
1
2
1
2
0
2
0
1
1
1
1
2
1
2
2
3
2
1
1
1
2
0
2
0
1
1
1
0
1
1
1
1
1
1
1
2
2
1
0
1
1
2
1
0
1
0
0
1
1
0
1
1
1
0
2
1
1
0
1
1
1
1
2
0
2
1
2
2
0
2
0
1
0
1
1
2
1
1
0
1
1
1
1
1
0
0
1
1
1
1
0
0
2
0
0
1
1
0
0
0
4
1
0
2
2
1
1
0
1
1
0
1
1
0
2
0
1
0
1
1
1
1
1
1
0
1
1
1
2
1
2
1
2
2
1
1
1
1
1
2
2
1
1
2
1
2
1
1
1
1
1
0
1
0
2
1
1
2
2
1
1
1
1
1
1
1
1
2
1
2
1
0
1
1
1
0
0
1
0
1
1
1
1
0
1
1
2
0
1
1
1
1
2
1
0
1
1
0
1
1
3
0
1
1
2
0
0
1
2
1
1
1
0
0
2
1
0
2
2
1
0
0
1
0
0
1
0
1
0
1
1
2
0
0
0
2
0
1
1
0
2
1
1
1
2
1
1
1
0
2
1
1
2
1
2
1
1
3
2
2
1
1
0
1
1
1
1
0
1
2
1
0
2
0
1
1
1
2
0
1
1
1
0
1
1
1
1
1
2
2
2
0
0
0
2
2
0
1
2
1
1
0
0
1
2
2
0
1
1
2
1
1
1
1
1
1
1
1
1
1
0
4
2
1
0
1
1
1
1
1
0
1
0
2
1
0
1
2
1
2
1
0
0
0
1
0
1
1
2
0
1
2
1
1
1
1
2
1
0
1
1
1
1
0
2
2
2
1
1
0
1
2
1
1
0
1
0
2
1
2
4
0
1
1
2
2
2
0
0
2
2
2
1
1
1
2
1
1
1
0
2
2
1
0
1
2
2
1
2
1
2
1
2
1
1
2
1
1
1
2
1
2
0
2
2
0
1
1
1
1
2
2
1
0
2
1
0
2
1
2
1
1
0
1
1
0
1
1
0
1
1
2
0
0
2
1
2
2
0
1
0
0
1
1
2
1
0
1
1
0
1
0
2
1
1
1
0
1
0
1
1
0
1
1
1
1
1
0
1
1
1
1
1
0
1
1
0
0
1
2
1
0
0
2
2
1
0
1
0
2
1
1
1
1
2
2
1
1
1
1
0
1
0
1
0
0
1
1
2
1
0
1
1
1
2
0
0
1
2
1
0
1
2
1
1
1
1
1
0
2
2
1
0
0
1
2
0
1
0
0
1
2
2
1
1
0
1
1
2
1
0
2
0
0
1
1
0
1
1
1
1
1
1
0
1
1
1
2
2
2
0
1
0
1
0
1
0
1
1
2
2
0
0
2
1
1
2
1
1
1
1
1
1
0
1
1
1
2
2
1
0
0
2
1
1
1
1
1
1
0
1
1
1
0
0
1
2
1
1
0
0
0
0
1
1
1
2
2
0
2
0
1
1
1
1
1
2
2
0
0
1
2
1
1
1
2
0
1
1
0
0
2
0
1
1
1
1
0
1
1
1
2
1
2
1
0
0
1
1
1
1
1
0
1
1
1
1
1
1
0
0
1
1
1
2
1
1
0
1
1
1
1
2
2
2
1
0
2
0
1
1
1
2
2
1
0
0
1
1
1
1
2
2
1
1
1
1
3
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
2
0
1
1
0
0
1
2
1
1
1
0
1
1
0
0
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
1
1
2
1
1
0
1
1
1
1
0
0
0
0
0
0
1
1
1
1
0
2
2
1
2
1
2
1
0
0
1
1
1
1
1
1
1
1
1
1
1
2
0
0
1
2
0
1
2
0
2
0
0
2
2
1
0
1
1
1
2
1
1
1
0
0
1
0
1
1
1
1
0
1
1
2
1
0
1
2
0
2
2
2
0
1
0
0
0
2
0
1
1
1
1
2
2
2
1
1
1
1
1
1
0
2
1
1
2
2
2
1
2
1
1
0
0
0
2
2
1
2
0
1
2
1
0
0
2
1
1
1
0
1
0
0
2
3
0
2
2
1
0
1
2
1
0
0
1
0
1
1
1
1
1
1
1
2
1
1
1
2
0
1
0
1
0
0
1
1
1
2
1
2
1
0
3
2
1
2
1
0
1
1
1
1
0
3
1
1
0
1
0
0
2
2
5
0
1
1
1
1
1
2
1
1
1
0
1
0
1
1
2
1
0
0
1
0
1
1
2
1
1
1
1
1
1
0
1
1
1
0
1
0
0
1
1
0
2
0
1
1
0
1
0
0
1
1
1
1
0
0
1
1
0
1
2
0
2
1
1
1
1
2
1
2
1
1
4
2
0
1
1
0
1
2
0
1
1
1
1
1
1
1
2
1
2
1
2
0
0
1
0
1
1
0
2
1
2
1
1
1
1
3
0
0
2
1
1
1
0
1
1
2
1
1
0
1
1
0
1
0
0
2
1
1
1
1
2
1
2
2
1
1
1
2
1
1
1
1
2
0
1
1
0
1
2
0
1
1
1
1
0
2
1
0
0
1
1
1
0
1
2
1
0
1
1
1
1
1
1
1
2
1
1
2
1
1
1
2
0
0
2
1
1
1
1
0
2
1
1
1
1
2
1
1
1
0
1
2
0
1
1
1
2
1
1
0
1
1
1
1
0
1
0
2
1
2
0
1
1
0
1
0
1
0
1
2
0
1
1
1
2
2
0
1
1
0
1
3
0
0
1
1
1
1
1
2
1
0
2
1
0
0
1
1
1
1
2
0
0
1
1
1
2
1
1
1
0
2
1
1
0
1
1
2
2
1
0
0
0
3
1
2
1
0
1
1
1
2
2
1
0
1
1
1
2
1
1
0
1
1
1
0
1
2
1
2
0
1
1
1
2
2
1
1
1
1
2
1
1
1
1
2
2
1
1
1
0
0
2
1
1
1
0
1
1
1
2
1
2
1
0
0
1
0
1
2
0
2
1
1
1
2
2
1
0
2
1
1
2
1
2
1
1
1
1
1
1
1
1
2
2
0
0
0
1
2
1
1
1
1
2
1
2
2
1
0
2
2
1
1
1
1
1
2
3
0
2
1
1
0
2
1
2
0
1
0
2
1
1
1
1
2
0
2
0
0
1
1
0
0
1
2
1
1
0
2
0
1
0
1
1
1
2
1
1
1
2
1
2
0
1
1
0
2
1
1
2
2
2
1
1
0
2
1
1
0
2
0
0
1
0
0
0
0
2
1
1
1
0
2
1
2
1
1
0
1
1
2
2
2
1
2
1
1
1
2
1
1
1
1
2
2
1
1
1
0
1
1
1
1
1
0
1
2
0
0
1
2
1
1
2
1
1
1
1
1
1
1
1
0
0
1
1
1
0
0
3
1
1
1
2
0
0
1
0
1
2
1
1
1
2
2
0
1
0
1
0
2
2
1
1
1
3
0
0
2
2
0
0
2
1
1
1
1
1
0
0
1
2
1
1
1
1
1
2
1
1
1
2
2
1
0
1
0
1
2
1
0
1
1
2
1
0
0
2
0
1
2
2
1
1
0
1
0
1
2
1
1
2
1
0
2
1
0
0
2
1
2
1
0
2
2
1
0
1
0
1
2
2
1
1
1
0
2
0
1
2
1
0
1
1
1
1
2
1
0
1
1
1
1
2
2
1
2
1
1
2
1
1
6
2
1
0
1
0
1
2
1
2
1
1
1
1
1
1
1
2
0
1
1
1
3
1
2
1
2
0
0
1
1
2
1
0
1
1
1
0
1
0
0
2
3
1
1
2
0
1
1
1
0
0
1
1
1
1
2
1
0
1
2
1
1
0
1
2
1
2
1
2
0
2
2
1
0
1
1
0
0
1
2
0
1
1
1
1
1
1
1
2
1
2
1
2
1
0
2
0
1
1
2
2
0
1
1
1
1
0
2
1
2
1
1
0
1
2
0
2
1
1
0
2
1
0
1
1
1
0
0
1
2
1
2
1
2
2
2
1
2
1
1
0
1
1
0
1
1
1
1
1
3
1
1
0
2
1
1
2
2
0
1
0
1
1
0
1
1
0
1
1
2
0
0
1
1
1
1
1
1
0
2
2
1
2
0
0
2
1
0
2
0
3
0
2
2
2
1
1
0
1
1
1
1
0
1
1
2
0
2
1
2
2
1
1
2
2
1
0
1
1
2
2
1
2
1
0
1
1
0
1
0
2
2
1
1
2
0
0
0
0
1
1
0
1
1
0
0
2
1
1
1
2
2
0
0
0
1
2
0
1
1
1
0
1
1
1
1
2
1
1
1
0
2
0
1
1
1
0
1
1
1
1
1
1
0
1
1
1
1
1
1
0
1
2
1
1
0
1
1
0
0
1
2
2
1
1
1
1
0
2
2
2
1
1
1
2
1
1
2
1
2
2
2
1
1
2
0
1
0
1
2
0
2
1
1
2
0
2
2
1
2
1
0
1
2
1
0
0
1
2
2
1
1
0
1
0
1
0
1
0
1
2
1
1
1
1
1
2
2
0
1
1
1
2
2
1
1
1
0
0
1
0
1
0
1
1
2
1
1
1
1
1
1
1
1
1
0
2
2
1
1
2
0
2
1
1
1
1
0
1
1
0
1
2
1
1
1
0
2
1
1
1
0
1
1
1
0
1
1
2
1
1
1
1
1
0
0
2
1
0
0
2
1
2
2
2
1
0
1
2
1
1
1
1
2
1
2
0
1
2
1
2
1
1
2
0
0
2
1
1
2
1
2
1
1
0
0
2
2
1
2
1
1
2
1
0
1
2
4
1
1
2
0
1
3
1
1
0
0
0
2
2
0
1
1
1
0
1
1
1
2
1
1
1
1
1
1
2
0
1
0
2
0
1
1
1
2
2
1
2
1
1
1
0
1
1
1
2
0
1
1
0
0
0
2
0
1
1
1
1
1
1
4
2
1
1
2
1
1
2
0
0
3
1
1
0
0
2
2
2
1
1
1
1
1
1
1
1
1
1
1
0
1
2
1
1
2
1
1
1
2
2
2
2
2
1
0
3
1
2
2
1
1
1
1
1
1
3
2
0
5
2
1
1
1
0
1
1
2
2
3
0
1
1
1
0
1
1
3
1
2
1
1
2
2
2
0
2
1
0
1
1
0
1
1
0
1
1
0
2
1
1
1
2
1
1
2
1
2
1
2
1
2
0
1
1
1
1
0
0
3
1
2
2
1
2
1
0
1
1
1
0
4
1
0
1
1
1
2
2
1
1
2
1
1
2
1
1
1
2
1
1
0
2
1
1
1
1
1
0
0
2
2
1
1
1
1
2
0
1
1
1
1
1
0
2
1
0
2
1
2
2
1
1
1
2
2
1
1
2
1
1
1
2
0
0
1
0
0
2
0
1
1
1
1
0
1
1
1
1
2
1
0
0
3
2
1
0
1
1
1
1
1
1
1
2
2
2
2
1
2
1
1
1
1
2
1
1
1
1
2
0
1
1
1
1
0
1
0
2
3
1
1
0
2
1
2
1
2
4
0
1
1
1
0
2
2
3
1
1
1
2
1
0
1
1
1
0
1
1
1
0
1
2
0
0
1
1
1
1
1
1
0
2
2
1
1
1
2
2
0
2
1
0
1
1
1
1
2
1
0
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
0
1
0
1
0
1
2
1
0
1
2
0
1
0
1
1
0
1
2
3
0
1
0
2
0
1
0
2
0
0
1
2
1
1
0
1
2
1
0
0
2
1
1
0
2
1
1
1
1
2
0
2
0
0
1
1
3
1
1
0
0
1
2
0
1
2
1
2
1
1
0
1
1
2
0
1
2
1
0
2
0
0
2
1
1
1
1
2
2
1
1
1
1
1
2
1
1
1
1
2
1
1
1
0
0
2
0
1
0
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
2
0
0
1
0
1
2
1
1
1
1
2
1
2
1
1
2
0
2
1
2
1
1
0
1
2
1
1
0
0
1
2
1
0
1
0
2
0
2
2
1
1
1
1
0
0
2
4
0
0
1
0
1
1
0
1
1
1
1
1
2
1
0
1
2
1
1
1
1
0
1
1
1
2
0
1
1
1
1
3
0
1
1
1
1
0
2
1
1
1
2
2
1
0
0
0
1
1
1
1
1
0
1
2
1
2
2
0
1
1
1
2
1
1
1
3
1
1
1
1
2
1
1
1
2
3
0
2
1
1
1
1
2
1
1
1
1
2
2
1
1
2
1
2
1
1
1
0
1
1
2
1
1
1
1
1
2
1
1
2
0
1
0
0
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
2
1
1
2
1
1
1
0
2
3
1
0
2
1
2
1
0
2
2
1
3
0
2
2
2
1
2
0
1
1
2
1
1
2
2
1
2
1
2
1
1
0
1
1
2
2
1
1
2
1
1
1
0
2
2
1
1
1
1
1
1
1
1
0
1
1
1
1
2
0
1
2
0
1
1
2
0
1
1
1
2
2
1
1
0
1
2
1
2
2
1
0
1
1
1
1
1
2
2
0
1
1
1
1
1
2
1
1
0
0
0
0
0
1
0
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
2
0
1
1
1
0
1
0
1
1
2
1
1
1
2
1
1
1
1
1
1
0
1
3
1
1
2
1
1
0
2
1
2
0
1
1
0
1
1
1
1
1
0
1
2
1
1
2
0
1
1
1
1
2
1
0
2
1
2
1
2
1
2
0
3
1
1
0
0
1
1
1
2
2
2
2
1
1
1
1
0
1
1
0
2
1
1
0
1
1
0
1
0
1
2
1
0
1
1
1
0
1
1
1
2
1
1
2
1
1
1
2
1
1
1
2
1
1
0
2
2
1
1
2
1
1
1
1
1
1
0
1
1
1
2
0
0
1
2
1
0
0
0
1
1
1
0
1
1
2
2
0
2
1
1
0
2
0
2
1
0
1
2
0
1
2
2
0
2
2
1
0
1
2
2
1
1
1
1
1
0
0
2
1
1
1
1
0
2
1
1
2
0
1
0
1
1
1
2
2
1
0
2
1
2
1
1
1
2
1
2
0
1
0
0
0
1
2
2
1
0
1
1
0
1
1
1
1
2
2
0
1
1
1
2
0
1
2
2
0
1
3
0
0
1
2
1
1
1
1
2
2
1
0
2
1
2
1
1
1
1
1
1
0
1
1
2
1
2
2
1
0
2
0
1
1
1
1
1
0
1
2
0
0
2
1
1
0
1
1
0
1
1
1
1
1
1
0
1
1
1
1
1
1
1
2
1
0
1
0
1
0
0
1
1
1
1
1
2
1
1
1
0
1
2
1
0
1
0
1
0
2
2
1
2
0
0
1
2
1
0
0
4
0
1
0
2
1
0
1
1
0
1
0
1
0
1
1
0
1
2
2
0
2
0
3
1
0
3
0
0
2
1
1
0
2
1
1
2
0
1
0
2
2
1
1
2
0
0
1
1
1
0
2
1
1
2
1
0
1
3
0
1
1
0
1
1
1
2
1
1
1
1
2
0
1
2
2
2
2
1
1
2
2
1
2
1
1
2
1
1
0
0
0
1
1
2
1
0
0
2
1
1
3
1
0
1
3
2
2
1
1
0
1
0
1
1
0
2
1
0
1
0
0
1
0
0
2
2
2
2
0
1
1
2
1
0
2
0
0
1
0
1
1
0
1
1
1
1
0
1
2
0
2
2
1
0
1
2
2
0
1
1
1
2
2
2
2
1
1
1
1
0
0
1
1
1
1
2
2
2
1
1
0
0
1
1
1
0
2
2
0
1
1
1
2
2
2
2
1
2
0
2
0
1
1
2
1
1
0
1
1
1
1
0
1
2
1
1
0
1
2
1
2
1
2
0
1
1
1
0
1
1
2
1
0
1
1
1
1
2
0
2
0
2
2
1
1
1
0
2
0
0
1
1
1
0
1
2
0
2
1
1
2
2
0
0
0
1
2
1
1
1
1
2
2
1
1
1
1
1
1
1
1
0
1
2
2
0
1
2
1
1
2
1
2
0
1
0
1
1
0
1
0
1
1
1
2
1
2
2
1
2
0
1
1
0
2
0
1
2
0
1
0
1
1
1
0
1
2
1
2
2
1
2
2
1
1
1
2
1
1
1
1
0
1
2
1
1
2
2
1
2
0
2
1
1
1
2
2
1
1
2
1
2
1
2
2
1
1
1
0
1
2
1
1
2
2
2
0
2
1
1
0
1
1
0
1
1
2
1
1
2
2
1
1
1
1
1
0
2
0
1
1
1
0
0
2
2
2
0
0
2
1
1
0
1
0
2
1
1
0
1
1
1
0
1
0
2
1
0
2
2
1
1
0
1
0
0
1
1
1
0
1
2
2
0
2
1
1
2
0
1
1
1
2
0
1
1
0
1
1
1
1
1
0
1
1
1
2
0
2
0
1
2
2
1
1
1
1
1
2
1
2
0
1
1
0
2
1
1
0
1
1
2
1
1
0
1
1
1
0
2
1
1
1
0
1
1
1
1
0
2
2
1
1
0
1
2
1
1
3
1
1
1
1
0
1
0
0
1
1
1
2
1
1
0
2
2
1
1
1
2
1
1
1
0
0
0
2
0
0
0
2
2
1
2
1
2
1
2
1
1
1
2
2
1
2
1
0
1
1
1
2
2
2
1
0
0
1
1
0
1
1
1
0
0
1
1
1
1
1
2
1
2
0
1
1
1
1
2
1
2
1
2
2
1
2
1
1
2
2
1
1
2
1
1
1
0
1
0
0
1
0
0
2
2
1
2
2
0
2
1
1
1
1
1
1
2
2
0
0
2
1
1
1
1
1
0
1
0
0
2
1
1
1
0
1
1
1
0
0
2
1
1
1
1
1
0
1
1
1
1
2
2
1
1
1
1
2
1
0
2
2
2
2
1
2
1
4
0
0
1
0
2
0
1
3
0
1
0
1
1
1
1
1
2
1
1
2
2
1
0
1
1
1
1
1
3
1
1
1
2
1
1
2
1
1
2
1
0
2
1
0
0
1
1
2
1
1
1
0
0
1
0
1
2
1
0
1
2
1
2
1
1
0
1
1
1
1
1
1
1
2
0
1
1
1
1
0
1
1
1
2
2
2
1
2
0
2
0
2
0
1
1
1
1
1
1
1
1
0
1
1
1
2
3
2
1
1
0
0
1
0
0
1
1
1
2
2
1
1
2
1
2
2
0
1
1
0
1
1
1
1
2
1
1
2
2
2
2
1
1
1
1
0
0
0
1
2
1
0
1
2
1
1
1
0
0
3
1
1
2
1
2
2
1
1
0
3
0
1
2
0
2
0
1
1
2
2
1
1
1
2
1
1
0
1
0
2
1
1
2
1
0
1
2
0
1
1
1
0
2
2
1
0
1
2
1
1
2
1
1
1
1
2
1
1
1
1
2
0
1
1
1
1
1
0
3
2
1
0
1
1
2
1
1
1
1
0
1
1
1
1
0
1
1
1
0
2
1
0
2
0
1
2
1
0
1
2
1
1
1
1
2
1
0
1
1
1
2
1
1
1
2
1
0
2
1
0
0
1
1
2
1
2
0
0
0
1
2
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
2
3
1
0
2
0
1
0
1
1
2
1
0
1
1
1
1
2
2
1
1
1
1
2
1
1
2
0
0
1
2
2
1
1
2
1
0
0
0
3
0
1
1
1
1
3
0
1
1
1
0
1
1
1
0
1
0
1
1
1
1
1
1
1
0
1
1
1
1
0
2
1
1
2
0
1
0
4
1
1
2
1
1
2
1
1
0
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
0
1
2
1
1
1
0
1
2
0
1
1
1
1
2
1
0
0
0
1
2
2
1
0
1
0
2
0
2
0
0
1
1
2
0
0
1
0
1
2
2
1
0
3
0
0
1
1
2
1
0
1
1
1
1
1
2
1
1
0
1
1
1
1
0
1
1
0
2
2
1
0
0
1
2
1
0
1
1
0
1
2
0
1
1
1
0
0
2
2
1
2
1
1
1
1
1
2
1
1
1
0
1
1
1
1
2
2
2
1
1
2
1
1
1
1
0
1
1
2
1
1
2
0
2
1
1
1
1
1
1
1
0
1
1
2
1
2
0
2
0
3
1
2
0
1
1
2
2
0
2
0
2
1
1
1
1
0
1
1
0
0
2
0
4
2
2
0
0
1
1
1
1
2
1
1
1
1
2
1
1
2
2
1
2
0
1
1
0
0
0
0
0
0
0
1
1
1
2
1
1
2
1
2
1
2
0
1
1
1
2
1
0
1
2
1
0
1
1
1
0
1
0
2
1
0
1
1
1
0
2
1
1
2
0
2
2
1
2
2
1
1
0
1
0
1
1
1
0
2
1
0
1
1
1
0
0
1
1
1
2
1
1
1
0
1
0
0
1
2
1
1
1
1
0
0
1
1
1
0
1
1
0
1
2
1
0
0
1
1
0
1
2
1
1
1
2
1
1
1
1
1
2
1
2
0
2
1
2
0
0
1
2
0
1
1
2
2
0
2
2
1
2
0
0
1
1
2
1
2
0
0
1
1
2
0
1
3
1
1
2
2
0
0
1
0
2
0
2
2
1
1
2
1
0
0
1
1
1
1
2
2
1
0
1
0
0
1
1
2
1
0
2
2
0
0
0
1
2
0
2
1
0
0
1
2
2
2
1
2
1
2
2
1
1
0
0
1
1
2
2
1
3
2
2
1
0
2
1
0
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
2
0
1
1
1
1
2
2
1
0
2
1
1
0
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
2
2
1
2
1
1
1
2
0
2
1
1
1
0
1
0
1
0
1
0
1
2
1
1
1
1
1
0
1
1
1
2
0
1
2
1
1
1
1
1
1
0
2
2
1
1
1
0
1
0
0
0
0
1
0
3
1
1
1
1
2
2
2
2
0
1
0
1
0
0
1
2
0
0
1
1
1
1
1
1
2
1
1
2
0
1
1
1
2
1
1
1
1
1
0
0
1
1
2
1
1
1
2
2
1
0
1
0
0
1
0
2
1
0
0
0
1
1
2
0
3
0
2
1
1
1
0
2
2
1
1
2
0
2
0
0
1
2
1
0
0
1
0
1
0
1
0
0
1
2
2
0
1
0
1
2
2
1
0
1
1
1
1
0
2
1
1
2
1
1
1
1
2
1
1
1
1
1
2
1
0
1
0
1
1
2
1
1
0
0
1
2
0
1
1
1
1
1
2
1
2
1
2
2
0
2
1
1
2
1
2
2
1
1
0
1
1
1
1
1
0
1
0
1
2
0
1
2
1
1
1
2
0
2
1
0
2
2
0
1
1
1
2
1
1
2
2
1
2
2
2
1
1
1
0
2
2
0
1
1
1
1
1
1
0
1
1
1
1
0
1
1
0
1
1
1
0
0
1
2
1
1
1
0
1
1
0
1
0
1
1
0
1
1
1
0
1
1
0
1
0
1
1
2
1
1
2
1
1
1
0
1
1
1
2
1
2
1
1
2
0
2
1
2
1
0
0
1
1
0
0
1
1
1
1
1
1
1
2
1
0
1
2
0
1
1
1
1
1
1
2
2
1
0
2
1
1
1
0
1
1
2
1
2
1
0
2
1
1
1
1
1
0
1
0
2
0
1
1
1
2
1
2
1
2
0
1
1
1
1
1
2
0
2
1
2
0
2
1
1
1
2
1
0
0
2
0
1
2
1
2
2
2
1
2
1
1
1
1
1
1
0
1
1
0
1
2
0
0
1
2
2
2
1
0
1
0
1
1
1
1
0
0
0
1
2
0
2
0
1
1
1
1
1
1
2
0
0
1
1
1
1
1
1
1
1
0
1
0
2
1
1
0
1
1
1
1
1
1
1
1
1
0
1
1
1
1
2
2
1
2
1
2
2
0
1
0
0
2
2
1
1
1
0
1
1
1
0
1
1
1
1
1
3
2
1
0
0
2
1
2
1
1
0
1
1
1
1
2
1
2
2
1
1
2
1
2
2
2
1
2
2
1
1
0
1
1
1
1
1
1
0
1
1
1
1
1
0
1
2
2
0
2
1
0
0
1
0
2
2
1
2
1
0
1
0
1
1
2
0
1
1
0
1
1
1
1
1
1
2
0
1
1
1
2
1
1
0
1
1
1
1
2
0
1
2
1
0
0
1
1
2
0
1
1
2
4
2
2
2
1
1
1
2
1
1
2
1
0
1
0
1
2
0
0
1
1
1
1
1
0
0
2
0
2
1
2
1
0
2
0
0
0
4
1
1
1
2
1
0
2
1
1
1
0
1
0
0
0
2
1
0
1
1
1
2
1
1
1
1
2
1
2
1
0
1
1
1
1
1
1
1
2
2
2
0
2
3
1
2
1
2
1
2
2
2
0
1
0
2
2
2
1
1
5
1
0
0
1
0
4
1
0
1
0
1
2
2
1
2
0
1
2
1
1
1
2
1
2
2
2
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
0
0
1
2
2
0
1
1
2
0
1
1
0
0
1
2
2
1
1
0
2
1
2
1
3
1
2
2
2
0
0
1
1
2
1
1
0
1
1
2
0
1
1
1
1
0
2
0
0
2
2
1
2
2
1
1
1
1
1
1
1
1
0
1
2
2
1
1
2
1
1
1
1
3
1
1
0
2
1
1
0
2
1
1
1
0
2
1
2
1
1
1
3
0
1
2
0
1
1
1
1
1
0
1
1
1
2
0
1
0
1
1
1
1
1
1
2
2
2
1
0
1
1
1
1
0
1
0
1
1
1
1
1
2
1
1
0
1
1
0
1
2
1
1
1
1
2
1
2
0
2
0
0
1
1
1
1
2
2
0
1
1
2
1
1
1
1
0
1
0
1
0
2
1
2
1
0
1
1
1
0
2
2
2
2
1
1
1
2
1
0
1
2
2
2
1
2
0
1
0
1
0
1
2
2
1
2
1
2
2
0
1
2
1
1
1
1
2
1
1
0
0
2
0
0
1
0
0
0
1
2
1
0
2
0
1
1
1
1
1
1
1
0
1
1
0
2
1
0
1
1
0
1
1
0
1
1
0
0
2
1
0
0
1
0
0
1
1
1
1
1
1
0
2
1
1
1
0
1
2
0
3
3
1
1
0
1
1
0
0
1
1
1
1
1
2
2
1
2
1
0
1
1
1
1
1
2
3
0
1
1
1
2
1
2
0
1
1
1
2
0
1
1
2
0
2
1
2
1
1
0
1
1
0
0
1
0
1
0
2
1
2
0
1
0
1
0
1
2
1
0
0
0
1
1
1
0
2
1
1
2
1
1
1
0
0
1
2
0
1
0
1
1
0
1
2
1
1
1
1
0
0
1
1
0
2
0
1
0
1
1
1
2
2
0
1
1
1
0
2
1
2
2
1
2
2
0
1
0
1
1
2
1
0
2
1
1
1
1
2
1
1
1
1
0
1
1
2
0
2
2
1
2
1
0
2
0
2
1
1
1
1
1
1
1
2
1
1
2
3
1
1
1
1
1
1
0
1
1
1
2
2
1
0
1
1
2
1
1
1
1
1
0
0
2
1
1
1
1
2
2
2
1
1
1
1
2
2
1
1
1
0
2
1
0
2
1
1
1
1
0
1
1
2
0
2
1
0
0
1
0
2
2
2
1
1
1
1
1
0
0
1
2
2
2
1
1
1
0
0
1
0
2
2
1
0
0
0
1
1
1
1
1
1
1
0
1
2
0
1
1
0
0
0
1
1
2
0
2
1
1
2
0
0
1
1
0
0
2
1
1
0
1
1
0
1
1
1
2
1
0
1
1
2
1
0
0
2
0
1
0
1
1
2
1
1
0
1
1
1
2
1
1
1
2
2
0
1
2
0
1
2
2
1
1
1
0
1
1
2
1
2
2
1
1
2
2
2
0
0
1
0
1
1
1
1
3
1
1
1
2
1
2
1
2
2
0
2
1
1
2
2
2
1
1
2
0
2
1
1
1
1
1
0
2
1
1
1
1
0
0
1
1
1
1
1
0
2
1
1
1
2
0
2
1
0
0
1
2
1
1
1
1
0
1
2
1
1
0
2
1
1
0
1
1
1
1
1
1
1
1
1
2
0
1
1
1
2
2
1
1
2
2
1
2
0
1
2
0
0
2
4
0
2
1
0
2
2
1
1
1
1
1
1
2
2
2
1
2
1
0
2
1
2
1
1
2
1
2
2
1
2
1
0
0
1
1
1
1
0
0
1
1
1
0
0
0
0
1
1
1
1
2
0
1
1
1
2
1
1
0
0
2
1
1
2
2
0
0
1
1
2
0
0
1
1
1
0
1
2
2
0
1
1
1
1
1
2
1
1
2
1
0
1
1
2
0
0
2
2
1
0
1
1
2
0
1
2
2
1
2
1
2
1
1
1
0
1
0
1
1
1
1
1
1
1
1
1
1
1
1
0
0
1
0
0
1
1
0
1
1
2
1
1
0
0
1
1
2
1
2
1
0
1
2
2
2
1
1
1
2
0
1
2
1
1
1
0
1
2
0
1
1
1
1
1
1
0
2
1
2
1
2
1
0
1
0
0
2
1
1
0
0
1
1
1
1
0
2
1
1
0
0
3
1
1
0
1
1
1
1
1
2
1
1
2
0
1
0
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
0
1
1
2
1
1
1
1
1
0
0
1
1
0
1
1
1
1
1
1
1
1
0
0
1
1
1
1
2
2
1
1
1
1
1
1
0
2
0
1
1
1
1
2
1
1
1
1
1
1
0
1
0
0
1
1
0
0
2
2
1
2
1
1
0
1
0
1
0
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
2
0
2
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
2
1
1
1
2
0
1
1
1
1
1
1
0
0
1
2
1
1
2
0
1
0
2
2
0
9
1
0
1
2
0
2
1
0
1
2
1
1
2
1
1
1
1
1
1
0
1
2
2
2
1
1
1
1
1
1
2
0
2
2
1
0
1
0
1
1
1
2
1
1
0
2
0
1
2
0
0
2
1
0
1
0
2
0
1
0
1
0
2
1
1
1
1
0
0
0
1
1
1
2
3
2
2
0
0
1
2
2
2
0
0
1
2
2
0
1
2
1
1
3
2
0
1
1
2
1
1
2
0
1
1
2
2
2
2
1
2
2
2
1
2
1
0
0
2
1
2
2
1
0
3
1
0
1
1
2
0
1
1
1
1
2
4
0
1
1
0
2
0
0
1
1
2
1
0
0
0
1
1
1
1
1
2
1
1
1
1
2
1
2
2
1
1
1
0
1
2
2
0
3
2
2
1
0
0
1
1
0
1
2
1
1
0
2
1
1
1
2
1
1
0
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
2
1
2
2
0
0
0
1
2
1
2
1
1
1
0
0
1
1
0
0
0
1
0
2
2
2
1
1
2
0
1
1
2
0
1
1
0
1
1
1
1
0
1
0
1
1
1
0
1
1
2
2
0
2
0
0
0
2
1
1
0
1
2
2
1
1
1
2
2
1
5
1
1
1
1
2
1
1
1
2
1
2
1
2
1
1
0
0
0
1
2
2
2
1
1
0
1
1
1
1
1
1
1
1
1
2
2
2
0
0
1
1
1
1
1
2
1
2
1
1
1
0
1
1
1
1
0
1
2
1
1
1
1
2
2
0
1
1
2
3
2
1
2
0
0
2
1
1
2
1
1
2
0
1
1
1
0
1
0
0
1
0
2
0
1
2
1
1
1
2
1
1
0
2
2
1
1
1
1
1
1
2
0
0
1
1
1
2
0
0
1
1
1
0
1
2
1
0
1
1
1
2
1
1
1
1
0
2
1
1
2
2
0
1
1
0
1
1
0
0
0
1
1
1
1
0
1
2
1
1
2
0
1
1
1
1
2
1
1
1
2
0
1
1
1
1
1
0
2
0
1
1
1
1
2
1
1
0
1
3
2
1
1
1
1
2
1
1
1
0
1
1
1
1
1
2
0
0
1
1
2
1
1
0
1
1
0
0
1
1
2
2
1
0
1
1
0
1
1
1
2
1
2
1
0
0
1
1
4
2
1
1
2
0
2
0
0
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
0
1
1
0
2
0
2
1
4
1
1
0
1
2
1
2
2
1
0
1
2
1
2
3
1
1
0
1
1
0
1
2
1
2
1
1
1
1
1
0
1
1
2
1
1
2
1
1
0
1
1
2
1
1
1
0
0
0
1
0
1
2
0
1
1
1
1
1
1
1
1
1
2
2
0
0
0
1
1
2
1
1
1
1
1
1
0
2
0
0
1
1
2
3
3
0
1
2
1
1
0
2
1
1
3
0
1
1
1
1
0
1
1
1
1
0
0
1
1
0
0
1
1
1
1
1
1
1
0
1
1
1
1
1
0
2
0
2
1
0
2
1
1
0
1
2
1
0
1
1
0
1
1
1
0
2
1
0
2
1
1
1
1
4
1
1
0
0
1
1
1
1
1
0
1
1
1
1
0
2
1
1
1
2
0
1
0
1
1
1
1
0
1
1
1
0
0
2
1
1
1
1
1
2
0
1
1
2
1
2
0
1
1
0
0
0
2
1
2
2
1
0
2
1
0
0
1
1
1
0
0
2
1
1
2
1
1
1
0
0
1
0
1
1
1
1
1
1
3
0
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
0
0
1
1
1
1
2
1
2
2
1
0
0
0
1
1
0
1
1
0
1
0
1
3
1
2
1
1
1
1
2
2
0
0
0
1
1
1
2
0
1
0
2
1
1
1
1
1
1
1
1
2
0
0
1
1
1
1
2
1
1
1
0
1
1
1
0
1
2
1
0
0
1
1
1
0
1
1
1
2
0
1
2
1
1
1
0
1
2
1
1
0
1
2
1
1
0
1
1
1
0
0
0
1
1
1
2
2
1
0
0
1
1
2
1
0
0
1
1
0
0
1
1
1
2
2
0
1
1
1
2
2
2
1
2
1
0
2
2
1
1
2
1
0
1
1
2
1
5
1
1
1
1
2
2
1
1
0
2
1
1
0
1
1
1
1
2
1
0
1
1
0
0
0
0
1
3
1
2
1
2
5
0
1
1
2
0
1
1
2
1
1
2
1
1
2
0
1
2
1
2
1
1
3
2
1
1
1
1
0
2
1
1
1
2
0
1
1
1
1
1
1
0
1
1
2
1
0
2
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
0
0
2
1
2
1
1
2
0
2
1
0
2
0
2
1
1
1
1
1
1
1
1
1
0
2
1
1
1
1
0
1
2
2
1
1
1
0
2
1
1
1
1
1
0
1
0
3
1
1
1
1
0
1
0
0
2
0
2
1
1
3
1
1
1
1
2
1
1
2
0
2
1
2
1
1
1
2
1
1
2
0
0
0
1
3
2
1
2
1
1
1
0
1
0
1
1
2
1
1
1
2
1
1
0
1
1
1
1
1
1
2
1
2
1
0
1
1
1
0
1
1
1
1
0
2
1
1
2
1
0
1
1
2
2
1
0
1
1
2
0
1
2
0
4
2
2
1
1
1
2
2
1
1
2
2
0
1
1
1
0
0
0
0
2
1
2
1
0
1
1
2
2
1
1
0
1
0
2
1
1
1
2
1
1
2
1
0
1
0
0
0
3
2
0
1
1
1
1
1
1
1
1
1
1
2
1
1
0
6
1
1
1
2
1
1
1
0
1
0
2
2
2
0
2
0
0
1
2
1
1
2
2
1
1
0
1
1
1
0
1
1
1
1
1
2
0
2
2
0
2
1
2
1
1
1
1
1
1
1
2
2
1
2
1
1
1
0
1
0
0
0
1
2
2
0
0
1
1
0
0
1
2
1
2
1
3
0
1
2
1
0
1
2
1
1
2
1
1
0
2
0
1
1
2
2
1
1
0
2
1
0
2
1
1
1
2
0
1
2
0
1
1
0
0
1
1
1
2
0
0
1
1
0
0
2
2
1
1
0
0
1
3
1
2
1
2
2
1
1
2
2
0
1
1
1
1
1
0
1
1
1
0
1
0
1
1
0
2
1
4
0
1
1
0
1
1
1
1
2
2
0
1
0
1
1
1
1
2
1
0
0
1
1
2
0
1
1
1
1
1
2
2
0
2
1
2
1
0
2
1
2
1
0
0
0
2
1
1
1
0
0
1
2
1
1
1
2
0
1
1
1
1
0
0
1
1
2
2
1
0
1
1
1
2
1
2
1
0
1
2
0
0
1
0
1
2
1
2
1
1
1
1
1
2
0
2
2
1
2
2
1
0
0
2
1
1
1
2
1
1
1
2
1
0
2
0
2
0
1
0
2
2
1
1
0
1
0
1
2
2
0
1
1
0
0
0
0
2
2
1
1
0
2
2
2
2
0
1
1
0
1
0
1
1
0
0
1
0
2
1
1
1
1
1
1
1
2
0
2
1
1
1
0
1
1
1
1
0
1
1
1
2
1
1
1
2
2
2
1
1
1
1
2
1
2
1
1
2
1
1
2
2
2
1
1
1
2
1
0
1
2
2
2
0
1
2
1
0
1
1
1
0
1
1
1
0
1
0
0
1
3
1
1
2
0
1
1
1
1
1
0
1
1
0
2
1
0
2
0
0
0
2
2
1
2
1
0
0
1
1
1
1
2
3
2
1
0
1
1
2
1
2
0
0
1
2
1
1
1
2
4
2
2
0
0
0
2
2
1
2
0
1
1
1
0
2
1
1
0
1
1
1
1
0
1
0
1
1
0
2
1
1
2
1
0
0
0
1
1
1
1
0
1
1
1
1
2
0
0
1
1
1
2
2
0
1
2
1
1
1
1
0
1
1
0
1
1
2
1
2
1
1
1
2
1
2
2
0
1
1
1
0
1
0
0
0
1
1
2
1
1
1
1
1
1
0
1
1
1
1
1
2
1
2
2
2
2
0
1
1
1
1
2
2
1
1
2
1
1
2
0
1
1
1
0
2
1
1
2
1
1
2
1
1
2
1
2
1
0
2
2
2
0
1
1
1
1
0
0
1
1
1
0
1
1
1
2
1
1
1
0
1
2
0
2
0
1
1
2
1
1
1
0
2
1
1
0
0
1
2
1
2
1
1
2
1
0
0
0
1
2
2
0
0
1
1
1
1
1
2
1
0
2
1
1
2
0
2
1
0
0
0
0
0
0
1
0
1
0
1
1
2
1
0
1
1
1
1
1
0
1
0
2
1
2
1
1
2
2
1
1
2
0
0
2
0
1
1
1
0
1
1
0
0
0
1
1
1
0
1
2
1
1
2
2
2
2
1
1
0
0
2
0
0
1
1
1
2
0
2
0
1
1
2
1
2
0
2
0
2
1
1
3
2
2
1
0
1
1
0
1
1
1
2
1
2
2
2
1
1
1
2
0
1
2
0
0
2
2
1
1
1
2
1
0
1
0
1
1
0
1
2
1
0
1
2
0
1
1
1
1
1
1
1
2
0
1
0
0
1
1
1
1
0
2
0
2
1
0
1
1
1
2
1
2
1
1
2
0
0
0
2
1
0
1
1
0
1
2
1
1
0
0
1
2
4
1
1
0
1
1
1
1
2
2
1
1
1
3
1
1
1
0
1
0
0
1
1
0
1
1
3
0
1
0
1
0
2
1
1
2
1
0
2
1
0
1
1
1
2
2
0
1
1
1
1
1
2
0
2
1
1
2
2
0
1
1
2
1
1
0
0
1
1
0
1
2
0
1
2
1
2
1
1
1
2
0
1
0
0
2
1
1
0
1
0
0
2
0
2
1
1
2
2
1
1
1
0
2
1
0
1
1
1
0
0
1
1
3
2
0
1
0
1
1
1
1
1
1
1
1
1
0
1
1
1
2
1
0
1
0
0
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
3
2
0
0
1
1
0
1
1
1
1
2
4
2
2
1
1
1
1
2
0
1
2
2
2
1
0
1
0
2
0
0
1
2
1
0
2
2
1
2
1
0
1
1
2
1
0
1
2
0
2
0
1
2
1
1
3
2
0
2
1
1
1
1
1
1
1
3
1
1
1
1
0
0
1
0
0
1
2
1
1
1
1
1
1
1
1
2
0
2
1
2
1
1
0
0
1
0
1
0
1
1
0
0
1
1
2
2
0
0
1
1
1
0
1
0
1
1
1
0
0
1
1
2
0
1
0
1
1
2
0
1
0
2
2
0
0
0
1
0
1
1
1
1
1
2
1
2
2
0
2
0
1
0
2
0
1
1
1
0
2
1
1
0
0
0
0
1
2
1
1
1
0
0
2
2
1
2
1
1
2
0
1
1
1
1
0
0
1
0
1
2
2
1
1
1
0
0
1
2
1
0
1
1
1
1
2
1
1
1
1
1
0
1
1
1
3
2
1
0
1
0
0
1
1
2
2
1
1
0
1
1
1
1
2
1
1
2
0
1
1
2
1
1
0
0
2
1
0
2
1
0
1
1
1
0
1
1
4
2
1
0
2
2
1
2
3
1
1
1
1
2
2
1
1
1
1
3
1
1
1
2
2
0
1
1
1
2
1
1
1
1
1
1
1
1
1
0
0
2
2
2
1
0
0
1
1
1
2
1
2
2
1
2
1
1
1
0
1
1
1
1
2
0
2
1
1
1
1
2
1
1
1
2
1
2
1
1
2
1
2
1
2
1
2
1
0
1
2
1
1
1
1
0
2
1
1
1
1
0
2
1
2
0
1
1
1
2
1
1
1
1
1
2
1
0
0
2
0
1
1
1
2
1
1
1
3
0
1
2
2
0
2
1
1
0
2
2
0
1
2
1
1
1
1
0
1
0
1
1
1
0
2
0
1
1
2
2
2
6
0
1
2
1
1
1
1
2
1
2
2
1
0
1
1
2
1
2
1
0
0
1
1
2
1
1
2
1
1
0
1
1
1
0
0
1
2
2
1
1
0
0
1
1
1
0
1
0
1
0
1
2
2
1
2
1
0
2
1
0
0
1
2
1
2
2
1
0
1
0
2
1
2
0
2
2
1
2
1
0
0
0
1
0
0
1
1
2
1
2
1
2
0
1
0
0
1
1
1
2
1
0
2
0
0
0
2
1
0
1
0
2
0
2
1
4
1
1
2
1
1
2
1
1
0
0
1
2
1
2
1
1
1
2
1
1
1
2
1
1
2
1
1
1
1
0
2
0
0
3
1
1
1
2
2
1
2
2
0
1
0
0
2
1
2
1
1
1
1
1
2
0
0
1
1
2
2
0
2
1
1
3
1
1
1
2
0
1
1
2
0
0
2
1
1
0
1
1
1
1
1
1
1
1
1
1
0
1
0
1
0
1
2
1
2
2
2
2
1
1
0
0
1
0
1
0
1
1
0
1
2
0
1
0
1
1
2
1
0
1
1
1
2
1
1
0
0
1
1
1
2
2
0
0
1
0
1
1
0
0
0
1
1
2
1
0
2
1
1
1
0
1
1
1
0
1
2
1
1
2
2
0
1
1
1
2
1
0
1
1
1
1
1
2
0
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
2
0
0
1
1
2
2
1
1
1
1
0
1
1
2
2
1
0
0
1
1
1
1
2
1
1
1
2
1
1
0
0
1
1
2
1
2
2
1
0
1
1
1
1
1
1
1
1
0
1
2
1
1
2
0
1
2
1
0
1
0
1
1
0
0
0
2
1
1
0
1
0
1
1
1
1
0
1
1
1
1
2
1
1
1
1
1
0
0
1
1
1
1
0
1
2
1
2
0
1
1
2
1
1
1
1
2
2
2
1
0
1
1
2
1
1
1
1
1
0
0
2
2
1
2
2
0
0
2
1
1
1
0
1
2
1
0
2
1
2
0
1
1
2
0
2
1
2
0
2
1
0
1
1
1
1
1
2
2
1
1
2
0
1
1
1
1
1
1
1
1
2
1
2
2
1
0
1
3
0
3
1
2
0
1
1
0
2
1
1
1
1
2
2
1
2
2
1
1
1
0
1
1
1
1
1
1
0
0
1
2
1
1
0
2
1
1
1
0
1
1
2
1
0
1
1
1
0
2
2
1
0
1
1
1
3
0
1
2
1
1
1
0
2
0
1
0
1
1
0
2
1
0
1
2
1
1
0
2
0
0
0
1
0
1
1
0
1
2
1
3
0
1
2
2
3
0
2
0
1
1
1
2
1
1
0
1
1
1
1
1
2
1
1
1
1
1
0
2
2
2
2
0
1
2
0
1
0
1
1
2
1
0
1
1
2
1
1
0
1
0
1
1
1
0
1
1
1
1
0
1
1
1
0
0
1
1
1
1
1
1
1
1
0
1
0
1
0
1
1
1
1
2
1
1
1
0
2
1
2
1
0
1
1
2
0
2
0
1
0
1
1
2
1
1
2
0
1
0
1
1
2
1
2
1
0
1
2
1
1
2
2
1
2
2
0
3
1
0
1
2
0
1
1
4
1
1
0
2
1
1
0
2
1
1
0
1
2
0
2
1
1
1
2
1
1
1
1
0
1
1
2
1
1
1
1
1
1
2
1
1
1
0
1
1
2
1
1
1
1
2
1
2
1
1
1
3
2
1
1
1
1
2
1
0
0
2
1
1
2
0
1
0
1
1
2
1
0
1
1
1
1
0
2
2
1
1
1
1
1
1
1
2
2
0
1
2
2
2
0
0
1
1
1
1
1
1
1
2
0
2
0
1
1
1
1
0
1
1
1
1
1
0
2
1
2
1
1
0
1
1
1
1
1
2
2
1
0
1
1
0
1
1
1
2
1
1
1
0
1
1
0
1
2
2
1
1
1
1
0
1
1
2
2
2
2
0
1
1
0
1
1
1
1
1
0
0
1
1
4
1
1
2
1
1
0
0
0
0
0
0
1
0
1
0
0
1
1
0
2
0
3
0
0
1
1
1
1
0
0
1
2
2
2
2
0
2
2
1
0
1
1
1
1
0
1
0
1
1
0
0
0
1
1
1
1
1
2
1
1
1
0
0
1
2
0
0
1
1
0
0
1
0
0
1
1
1
2
1
1
2
0
1
1
0
1
2
1
1
1
1
1
2
2
0
1
1
0
1
1
0
1
1
0
2
1
0
0
1
0
2
1
1
1
1
0
1
1
1
1
1
1
1
3
1
2
0
0
2
0
2
0
1
1
1
0
1
1
1
0
2
3
1
0
0
1
0
1
1
1
0
0
2
1
0
2
1
1
1
1
2
1
2
1
0
1
1
0
0
0
2
2
1
0
2
0
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
0
1
2
1
1
1
1
0
1
1
1
0
1
0
1
1
0
1
1
1
1
1
1
0
2
1
1
1
2
0
0
1
1
1
2
1
0
1
1
1
1
2
2
1
1
1
1
2
1
2
1
1
1
0
1
1
1
1
0
1
1
1
0
1
2
1
2
2
1
1
0
1
0
2
1
3
1
1
0
3
2
0
2
2
1
0
0
1
1
2
2
1
1
1
1
1
1
2
2
0
1
0
2
1
1
1
0
1
1
0
1
2
1
1
1
1
1
1
1
0
1
0
1
2
2
1
1
2
1
1
2
0
0
1
2
2
1
1
0
0
1
1
2
0
2
1
2
2
1
2
1
1
0
2
2
0
1
1
1
1
2
0
1
1
0
1
2
1
1
1
1
1
0
6
2
1
0
0
1
1
1
1
0
1
1
2
1
1
0
1
2
2
1
2
1
0
0
2
0
1
2
2
2
1
2
0
0
2
1
1
1
1
1
0
1
1
2
2
1
2
1
1
1
1
1
0
2
0
1
1
1
1
1
1
2
1
2
1
1
1
2
1
1
1
0
0
0
0
1
1
0
0
1
0
1
0
1
1
0
0
2
0
1
2
1
1
0
2
2
2
1
3
2
1
1
1
1
2
1
1
1
1
1
1
1
2
0
1
1
1
2
3
1
1
1
1
2
1
1
1
0
1
1
1
1
1
0
1
1
1
1
0
1
2
2
0
1
1
1
1
1
0
2
1
1
1
2
0
0
2
2
1
1
1
2
1
1
1
1
0
0
1
1
1
1
0
1
1
1
2
2
1
1
2
1
1
1
1
0
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
0
0
3
1
0
2
2
1
1
2
1
1
0
1
1
2
1
0
2
1
0
2
0
1
1
1
2
1
2
2
1
1
2
1
1
1
0
2
0
0
2
2
1
1
1
1
1
1
1
0
1
2
1
1
1
1
1
0
1
1
1
1
0
2
2
2
1
1
1
2
0
1
1
1
2
0
0
0
1
2
1
1
2
1
0
1
1
2
3
1
2
1
0
0
2
2
2
2
0
1
2
0
1
2
2
1
1
1
1
1
0
1
2
1
1
1
1
1
1
2
1
2
1
1
0
0
1
2
1
0
1
1
0
1
0
2
1
2
0
0
1
2
1
2
1
1
1
1
1
0
3
1
1
2
2
1
0
1
1
2
1
1
0
0
1
0
1
2
1
0
2
1
1
1
1
2
1
1
1
1
0
1
0
1
1
1
1
1
2
1
2
0
1
1
0
1
1
2
1
0
0
0
1
0
1
1
1
1
2
1
0
1
0
1
1
1
0
2
1
1
1
1
1
2
1
1
1
1
1
2
1
2
2
0
1
0
2
0
0
1
1
1
0
1
1
0
1
2
2
1
2
1
1
1
1
1
1
1
0
1
3
1
1
2
1
1
1
0
1
2
1
2
1
1
1
1
0
1
1
0
0
1
1
2
0
0
2
1
0
1
2
2
1
2
1
2
0
0
1
1
1
2
2
1
1
0
1
2
1
0
1
0
1
1
2
1
1
1
1
1
1
1
1
1
0
1
1
1
2
1
0
2
2
2
1
0
3
1
1
0
1
1
1
0
2
1
1
2
0
1
2
1
0
1
1
1
1
0
1
1
1
0
2
0
1
1
0
1
2
0
1
1
1
1
1
1
1
1
1
2
1
1
2
1
0
0
1
1
1
1
2
1
0
1
0
0
1
1
1
1
1
2
1
1
0
0
1
1
0
0
2
3
1
1
1
2
1
1
1
1
2
1
0
1
1
1
0
1
1
1
1
2
1
0
1
1
1
1
1
0
2
0
1
1
0
1
2
1
2
1
1
1
1
3
1
1
3
0
1
0
0
3
1
2
2
2
1
1
0
1
0
1
1
2
0
2
1
1
1
1
0
1
1
1
1
2
1
3
1
2
1
1
2
1
0
1
1
2
1
1
0
2
1
1
1
2
1
0
2
1
2
1
1
1
2
1
1
1
2
0
1
1
1
1
0
1
2
1
1
1
1
1
0
2
1
1
1
1
2
0
0
1
1
2
2
1
2
1
1
1
2
0
0
2
0
1
0
0
2
2
1
1
2
2
1
2
2
1
1
2
1
1
1
0
2
4
1
1
2
0
0
2
0
1
2
1
1
1
1
2
1
1
1
0
1
0
1
2
1
2
1
1
1
1
1
1
2
1
1
1
0
0
1
0
1
2
1
2
1
1
1
1
1
0
1
1
1
1
1
1
1
1
0
2
1
0
1
2
1
1
1
1
2
1
1
0
2
1
1
1
1
2
2
1
1
1
0
0
1
0
0
1
1
1
1
0
1
0
1
2
1
1
1
1
1
2
1
0
1
1
2
1
0
0
1
1
2
1
0
1
0
1
0
1
1
0
1
1
1
0
1
2
1
1
1
2
1
1
3
0
2
1
3
0
1
1
1
0
1
2
0
0
0
0
1
1
4
0
1
0
1
0
1
1
3
1
0
1
1
1
1
1
1
1
1
1
1
2
1
0
2
1
2
1
1
0
0
1
1
0
0
0
1
1
1
0
2
1
2
1
1
1
1
2
0
1
1
1
2
1
1
0
1
0
1
2
1
1
2
2
2
0
2
2
2
1
1
2
0
2
0
0
1
1
2
1
6
1
2
0
1
0
1
1
2
1
1
2
1
0
1
1
1
1
1
0
1
2
1
1
0
0
2
1
2
1
1
0
0
0
2
1
1
1
1
1
1
1
2
2
4
1
0
1
2
1
1
1
1
1
2
1
1
0
1
1
1
1
0
1
1
0
0
3
0
1
2
1
0
0
1
2
1
1
1
1
1
2
0
2
1
0
1
0
1
1
1
1
1
0
1
1
2
1
1
1
1
2
1
1
1
1
1
1
0
2
1
1
1
1
1
2
2
1
2
1
2
1
1
1
1
0
0
1
1
3
1
1
2
1
2
2
1
0
2
0
2
1
1
0
1
1
1
1
0
1
1
2
2
1
1
0
1
0
1
2
0
1
2
1
0
1
1
1
0
1
0
1
2
1
1
1
1
1
1
2
1
1
2
1
2
0
1
2
2
1
1
1
0
1
1
0
1
1
1
1
1
1
1
1
3
1
0
1
1
2
1
2
2
1
0
0
1
1
1
1
1
0
0
0
1
2
0
0
1
2
1
0
2
1
1
3
1
1
1
1
0
0
1
1
1
1
2
1
0
1
2
1
1
1
0
0
1
2
1
0
0
1
2
1
1
1
1
1
0
1
2
1
1
1
1
1
0
1
0
0
1
2
1
1
1
1
0
1
2
0
1
1
0
0
2
1
2
1
1
1
0
3
1
1
1
0
2
1
1
2
2
2
1
0
0
2
2
1
1
2
2
2
0
2
2
0
5
1
1
0
2
1
1
0
2
1
3
1
1
1
1
0
2
1
1
1
1
2
1
1
1
1
0
2
2
1
0
2
0
2
1
0
0
2
1
1
1
0
1
1
2
1
2
0
0
2
1
1
0
1
0
1
1
1
2
1
3
1
1
1
1
0
1
1
1
1
1
1
0
0
1
2
1
2
1
0
2
0
2
1
0
2
1
1
1
0
1
1
0
1
0
1
0
0
2
1
0
1
1
1
1
1
2
2
1
1
2
1
1
1
1
0
1
1
1
3
0
1
1
1
2
2
1
1
1
2
0
1
1
0
0
1
1
0
2
2
2
1
2
1
1
1
2
1
1
1
1
2
2
1
2
1
1
1
2
0
2
2
0
2
1
0
1
2
1
1
1
2
2
1
1
1
0
3
1
2
1
2
2
1
1
2
2
1
1
2
0
2
2
1
1
1
1
2
1
1
0
2
2
2
1
2
1
0
1
1
2
2
0
0
1
0
0
0
1
1
1
1
0
2
1
0
0
0
1
1
1
0
1
1
1
1
0
1
0
2
1
0
0
0
1
0
1
0
2
2
1
0
1
1
0
2
1
1
1
1
1
1
1
1
1
1
0
0
0
1
0
1
2
0
2
2
1
0
2
1
1
1
1
0
1
1
1
1
1
2
0
2
2
1
1
1
2
2
1
1
1
1
2
1
0
2
1
1
2
0
2
2
0
1
1
0
0
1
0
1
2
1
1
1
1
1
1
1
2
2
1
0
1
1
0
1
1
0
1
2
1
0
1
1
1
0
2
0
1
1
0
2
1
0
0
2
1
2
1
1
0
1
2
1
1
1
1
2
1
0
1
2
2
0
1
1
0
1
1
3
1
0
1
1
3
1
1
0
2
0
2
0
0
1
1
2
0
0
2
0
1
1
0
1
1
0
1
1
2
1
2
2
2
1
1
1
0
1
1
2
2
2
1
0
0
0
2
1
0
0
1
0
4
0
3
1
0
1
2
1
0
1
1
0
0
1
0
1
1
0
0
0
2
0
1
2
0
1
0
0
1
0
2
1
0
1
2
1
1
1
1
1
1
1
1
1
3
0
1
1
2
1
1
2
2
2
1
2
0
1
1
1
2
1
1
1
0
1
0
0
1
1
1
0
1
1
0
1
0
2
2
1
1
1
2
2
1
2
2
0
1
2
1
0
0
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
0
0
2
1
1
1
1
1
0
1
1
1
1
1
1
1
2
1
1
0
1
1
2
0
0
0
1
1
1
1
0
2
0
1
1
0
1
1
2
0
0
1
2
1
2
0
0
0
2
1
2
1
1
1
0
1
1
2
2
0
1
0
1
0
2
2
1
2
1
1
1
2
1
1
1
0
0
0
2
0
2
0
1
2
0
1
1
0
1
0
0
0
0
1
1
1
1
1
0
2
1
0
2
1
2
1
1
2
0
0
2
1
2
1
0
0
1
2
2
1
1
2
2
1
2
1
0
2
1
1
0
1
1
1
0
0
1
1
1
2
1
1
2
1
2
1
1
0
1
1
2
2
1
1
1
0
0
1
0
0
0
0
0
1
1
2
1
1
1
1
1
1
1
0
0
1
1
0
0
1
2
2
0
1
2
2
1
1
1
2
1
2
1
2
1
0
1
1
1
0
1
2
0
1
1
1
0
0
0
1
1
1
2
1
1
2
2
1
1
2
2
1
0
0
1
1
1
1
0
0
3
2
1
2
0
1
1
0
1
1
2
0
1
1
1
2
1
1
2
1
0
1
1
0
1
2
1
1
2
2
0
1
1
2
0
2
0
1
2
2
0
0
1
1
0
0
1
0
2
1
1
1
1
1
1
2
0
2
0
1
2
1
0
2
0
2
1
1
0
1
1
1
0
1
1
1
1
0
1
1
1
0
1
1
1
2
2
3
0
1
0
1
2
1
1
1
2
1
1
0
2
0
1
1
1
1
0
1
0
1
0
0
1
0
1
1
1
1
0
1
1
2
1
1
2
0
1
1
1
1
2
2
1
1
2
1
0
2
1
0
1
1
2
1
1
1
1
0
2
1
0
1
1
1
0
1
2
1
0
1
1
1
2
2
2
1
2
1
0
1
2
0
1
2
3
1
1
0
1
1
0
2
1
2
1
1
1
1
1
1
0
0
1
1
1
1
1
1
1
2
1
0
2
1
1
0
0
1
1
2
1
2
1
0
1
0
0
1
2
1
1
0
1
1
3
1
1
1
0
1
2
1
1
1
0
1
1
0
1
1
1
0
1
2
1
0
1
0
2
0
2
0
0
1
1
1
2
2
0
0
2
0
1
2
1
1
1
0
1
1
1
0
1
1
2
0
1
1
0
1
0
0
1
1
1
1
2
0
0
1
2
1
1
1
1
2
1
1
1
0
0
0
1
1
1
1
1
0
2
1
1
1
1
0
2
0
1
0
1
1
1
3
2
1
1
1
2
1
1
1
1
0
1
1
2
0
0
2
0
2
0
3
1
1
1
1
1
0
1
1
2
2
2
1
1
2
1
0
1
1
2
1
1
1
0
0
0
1
1
1
2
1
1
0
0
1
2
1
1
1
1
0
2
1
1
0
1
1
1
2
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
2
2
0
1
1
1
0
2
1
1
1
2
1
0
1
1
2
0
0
1
1
2
1
1
2
2
1
1
1
2
2
1
1
1
0
1
2
1
1
1
0
1
0
1
1
1
1
1
2
2
1
0
1
0
0
2
1
1
1
2
2
0
5
1
1
1
1
0
0
1
0
0
3
2
1
0
1
0
1
0
1
1
1
1
0
1
1
2
0
2
2
1
2
1
1
1
0
1
2
2
1
1
0
0
3
1
1
0
2
0
0
1
0
2
2
1
1
1
3
1
1
2
2
0
2
0
1
1
1
1
2
1
3
2
0
0
1
0
2
0
0
2
0
2
1
1
1
2
1
1
1
1
2
1
1
0
1
2
1
1
1
2
1
1
1
1
1
0
2
2
1
0
2
0
2
2
1
0
0
1
0
1
0
1
0
2
0
1
1
0
0
0
1
0
1
0
1
0
2
1
0
2
1
1
1
1
1
1
1
0
0
1
3
1
0
2
2
1
1
0
1
1
2
2
0
2
1
2
1
1
1
0
1
0
1
1
0
1
1
1
0
0
1
1
1
1
1
1
1
0
2
2
1
0
1
0
1
1
1
1
1
2
1
0
1
1
1
0
1
1
1
1
1
1
1
1
1
2
1
1
1
0
1
2
1
1
0
1
1
1
1
2
2
1
2
2
1
1
1
1
1
0
2
2
1
1
1
0
1
1
1
1
2
1
2
0
0
0
0
2
2
1
1
1
0
0
1
3
2
1
1
0
1
2
3
0
2
1
1
1
2
2
1
3
1
0
1
1
2
0
1
1
1
1
1
1
2
0
0
0
2
1
1
0
2
1
1
1
1
1
0
1
1
0
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
2
2
2
1
1
1
1
2
2
1
2
1
1
1
0
1
1
1
1
0
1
1
1
1
1
1
2
1
2
1
0
1
1
2
0
1
2
1
2
2
1
1
1
1
1
1
1
0
0
1
1
2
0
1
1
1
2
1
1
1
2
2
1
1
1
2
0
0
1
1
2
1
1
2
0
1
0
1
1
1
1
2
1
1
1
1
0
2
1
0
1
2
2
1
1
1
1
1
0
0
1
2
1
0
1
2
1
1
1
1
2
1
1
1
2
1
0
1
1
2
0
0
1
1
1
1
2
1
0
0
1
1
1
2
2
2
1
1
1
1
1
0
2
1
0
1
0
1
2
1
1
2
2
1
2
2
1
0
1
1
1
1
1
2
0
0
0
1
0
2
0
1
1
1
1
1
1
1
3
1
1
1
2
2
2
0
2
2
0
1
2
1
1
1
0
0
1
1
1
1
2
2
1
1
0
2
3
1
3
0
1
1
1
2
2
1
1
0
2
0
1
1
1
2
1
1
1
1
2
0
1
1
1
1
1
0
0
1
1
0
0
1
1
2
1
2
1
1
1
2
1
1
0
1
1
1
2
1
1
0
3
1
1
0
1
1
3
1
0
0
0
1
1
1
1
1
1
2
2
1
2
0
2
1
1
1
2
2
1
0
1
2
1
2
1
0
0
0
1
2
1
0
2
1
0
1
1
1
1
1
1
1
2
1
0
0
0
1
0
0
0
1
1
1
1
1
1
2
1
0
2
1
1
1
1
1
2
1
0
1
1
1
0
1
0
0
1
1
0
1
1
0
1
1
1
2
2
2
1
0
1
1
1
0
1
2
0
2
1
2
1
1
4
0
1
1
1
1
0
2
1
1
1
1
1
1
0
1
2
1
1
1
1
0
2
0
0
1
2
0
1
0
0
1
2
0
1
0
1
1
0
1
1
1
1
1
2
1
2
1
0
0
0
1
1
0
1
0
1
2
1
1
0
1
1
1
1
1
1
1
1
1
2
1
0
1
3
0
2
1
1
0
2
1
1
1
1
2
2
2
1
1
1
0
2
1
0
0
2
1
1
0
1
1
1
2
1
1
1
1
2
0
1
2
3
1
2
1
1
2
0
0
1
0
1
1
2
2
2
0
1
1
1
1
1
0
1
1
1
1
1
0
1
0
2
0
1
0
2
1
1
0
1
1
1
1
0
0
2
1
0
1
0
1
0
1
2
1
0
2
1
1
1
1
1
0
2
0
2
1
1
1
1
0
1
3
1
0
0
1
0
1
0
1
1
2
2
2
0
1
2
1
2
1
0
1
2
1
1
1
1
0
1
2
0
1
1
1
2
6
1
1
2
1
2
0
0
1
0
0
1
1
2
2
1
1
1
2
0
1
2
1
0
2
2
1
1
2
2
1
1
2
0
1
1
1
2
1
1
2
1
2
1
1
1
1
1
0
0
0
1
0
2
1
0
2
1
2
1
2
2
0
2
2
0
1
2
1
1
1
1
0
1
1
1
0
1
1
1
0
1
1
0
0
2
1
1
0
0
0
2
1
2
1
0
1
1
0
1
2
1
1
0
2
1
0
1
2
2
0
1
1
2
1
1
2
1
1
2
1
1
0
0
1
1
1
1
1
2
2
1
0
1
1
0
1
1
1
1
1
2
0
2
1
1
1
1
0
2
1
1
1
1
1
2
1
1
2
1
1
1
2
1
1
0
0
2
2
1
2
2
1
1
0
2
0
0
1
0
1
1
1
1
0
1
1
2
1
0
1
1
1
0
1
2
1
1
1
2
0
1
1
0
1
1
1
0
1
1
1
1
1
1
2
1
2
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
2
0
0
0
3
1
1
0
2
1
1
2
2
1
0
1
2
0
1
1
0
1
2
2
1
0
1
0
0
1
1
1
2
1
2
0
1
2
1
2
0
0
0
2
1
2
2
1
0
1
2
0
1
1
1
1
1
1
0
0
0
1
1
1
2
1
1
2
0
1
1
2
1
1
1
1
1
0
1
1
2
1
1
2
1
1
1
1
0
1
2
0
1
1
0
2
0
2
2
1
0
1
2
0
0
2
2
1
1
0
1
2
1
0
1
2
2
1
0
1
1
0
1
1
2
0
1
0
1
2
1
1
2
0
0
1
0
0
0
2
1
1
1
1
0
2
2
2
1
0
1
1
1
1
1
0
0
1
1
1
0
0
1
2
1
2
2
1
0
0
0
2
2
1
0
2
1
0
1
1
0
1
0
1
1
1
2
1
1
0
2
1
1
1
1
1
1
1
1
1
0
1
2
0
1
1
1
1
1
2
1
1
0
0
2
0
0
1
2
0
2
1
1
2
1
0
1
0
1
1
2
0
1
1
1
2
2
0
1
2
1
1
0
2
0
0
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
0
1
2
0
3
1
1
2
1
1
1
1
0
2
1
0
2
0
2
2
0
0
1
1
2
3
1
1
1
0
1
1
2
0
1
1
2
0
1
1
1
1
1
2
2
1
0
0
1
0
1
2
1
1
1
0
1
1
1
2
2
2
1
1
1
2
1
1
1
1
1
1
1
2
1
0
2
1
2
2
1
2
1
2
1
2
0
2
2
0
1
1
0
1
2
0
2
2
1
1
1
0
1
1
1
1
1
2
0
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
0
0
1
2
1
1
1
1
1
1
1
1
1
2
1
0
0
2
2
2
0
0
2
1
2
1
1
1
0
0
1
1
1
0
0
0
1
1
2
0
2
1
1
1
1
0
1
0
2
0
2
2
2
1
2
1
1
1
2
2
0
0
0
2
2
2
2
1
1
1
1
1
1
2
1
2
0
2
1
2
0
0
2
1
1
1
1
1
2
1
0
1
2
1
1
1
1
0
2
1
1
1
1
1
3
2
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
1
1
2
1
0
1
0
0
2
2
1
2
2
0
2
2
1
1
1
1
1
1
2
1
2
2
1
1
2
1
1
1
2
1
2
1
1
1
0
1
1
2
1
1
2
1
1
1
1
2
0
1
0
1
1
2
0
1
2
0
2
1
1
1
0
0
1
1
2
1
0
1
1
0
0
1
0
2
2
0
0
2
1
2
1
0
2
1
1
0
0
0
1
1
0
1
1
1
0
1
2
1
1
1
1
1
0
1
2
1
2
1
2
1
1
0
1
1
2
1
1
1
2
0
1
2
1
1
1
1
1
1
1
1
1
0
1
1
2
1
1
0
2
2
1
1
1
0
1
2
1
1
1
1
2
1
1
2
2
1
1
1
1
1
0
2
1
1
2
0
1
1
1
0
2
0
1
1
1
1
1
0
1
1
0
1
3
0
0
1
2
0
2
1
2
0
2
2
1
1
1
1
0
2
0
1
0
1
0
1
1
0
1
1
0
2
1
0
1
2
2
1
1
1
1
1
0
1
1
2
0
1
2
2
0
1
1
1
1
1
0
2
1
1
1
1
0
1
1
1
0
3
1
1
1
2
1
2
1
0
0
0
2
2
0
2
1
1
1
0
0
1
0
2
1
0
1
1
1
1
1
2
0
0
0
1
1
1
1
1
1
1
0
2
0
1
1
1
1
0
1
1
1
0
2
1
1
0
1
2
2
3
1
1
0
2
1
1
0
2
1
1
0
0
2
1
0
0
0
1
2
1
1
2
1
0
1
4
1
1
1
0
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
2
1
1
0
1
1
2
1
1
1
1
1
1
0
1
0
1
1
2
1
1
2
1
2
1
2
1
1
0
1
0
0
0
1
1
1
2
1
0
0
1
2
1
1
0
0
2
1
0
1
0
1
2
1
2
1
0
0
1
1
1
0
2
2
1
1
0
0
3
1
1
0
1
2
1
1
0
1
1
2
1
0
1
1
1
2
1
1
2
1
0
1
2
2
0
1
2
2
1
1
1
0
1
2
2
1
0
1
2
2
2
0
1
2
2
1
0
1
2
1
2
1
2
1
0
1
1
2
0
1
1
2
0
1
0
2
1
1
1
1
2
1
1
0
1
1
3
1
1
1
1
1
1
2
3
1
1
1
2
2
2
1
0
2
1
2
1
1
2
1
1
1
1
1
0
0
1
1
2
1
0
1
1
0
0
2
0
1
1
2
1
6
1
1
0
0
1
2
0
0
0
1
2
2
1
1
0
1
1
2
1
2
1
1
2
1
1
0
1
1
1
1
2
0
1
3
1
1
1
2
1
1
1
0
2
1
1
1
0
2
1
0
1
0
0
0
1
2
0
1
1
0
1
1
1
1
1
2
1
2
1
1
2
0
1
2
0
1
0
2
1
1
0
1
2
0
1
2
1
0
1
1
1
0
1
1
1
1
0
1
2
0
1
0
0
2
2
0
1
0
1
2
1
1
3
0
1
0
1
1
3
2
1
0
0
0
1
1
1
0
2
2
0
1
1
1
0
1
1
0
0
1
1
2
0
0
1
1
2
0
0
1
3
1
1
2
1
2
1
2
2
1
0
1
2
1
1
2
1
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
0
1
0
2
1
2
0
1
1
1
1
1
2
1
1
1
1
1
0
1
2
1
2
0
0
1
0
1
3
2
0
1
1
1
0
2
1
0
0
0
0
1
0
1
0
0
2
0
0
1
1
2
0
2
2
2
2
1
2
2
1
1
1
1
1
1
0
1
0
1
1
2
0
1
0
2
1
1
0
1
1
2
0
0
1
1
0
1
0
2
1
1
2
1
2
1
0
1
1
2
1
0
0
2
1
1
2
2
2
1
0
0
1
1
0
1
0
1
1
1
1
1
1
2
2
1
2
1
1
2
1
1
1
1
2
2
1
2
1
1
3
1
0
1
0
2
1
0
1
1
2
1
1
0
1
2
1
1
1
0
1
1
1
0
1
1
1
0
0
1
1
0
0
2
2
0
1
1
2
1
0
0
1
0
1
2
2
1
0
1
1
0
1
2
0
0
1
1
1
1
2
1
2
1
0
0
1
0
0
1
2
1
2
1
1
1
1
0
0
1
1
1
1
0
0
1
1
1
1
1
0
1
1
1
1
1
1
1
2
2
1
1
0
0
0
2
2
1
1
1
1
1
0
1
2
1
2
1
2
1
0
1
1
1
1
1
1
1
2
1
1
1
1
2
2
1
0
2
1
2
1
1
1
2
2
0
1
1
1
1
2
0
2
0
1
1
1
1
2
1
1
0
0
2
1
1
1
1
1
1
1
1
0
1
0
2
1
1
1
0
1
2
0
1
1
1
1
1
2
0
1
1
2
1
1
2
1
1
1
1
1
1
0
1
0
1
1
2
1
1
0
1
1
1
1
1
1
1
1
1
1
1
0
2
1
0
1
1
2
1
1
0
1
2
2
1
1
1
0
1
1
1
0
2
1
1
0
1
0
1
0
0
1
1
1
2
1
1
1
2
1
1
1
0
1
1
2
2
1
2
1
1
2
2
1
1
1
0
0
2
2
1
2
2
1
1
1
1
2
1
0
0
1
2
1
0
2
1
2
1
1
1
2
1
1
1
2
1
1
0
0
1
1
1
1
3
0
1
1
1
1
0
1
2
2
0
1
1
1
0
1
3
1
0
1
2
0
1
2
1
2
2
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
2
1
0
1
1
0
1
1
2
1
1
0
3
1
0
0
1
1
1
1
1
0
1
0
1
1
1
1
2
2
1
1
1
2
2
1
1
0
1
2
2
1
1
1
0
1
1
0
0
0
0
1
1
2
0
2
1
1
1
1
0
1
0
0
2
1
1
1
1
3
1
1
0
1
1
0
2
1
1
1
1
1
1
0
1
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
1
2
1
1
2
0
0
1
1
1
1
1
1
2
2
2
1
1
2
2
1
1
1
2
2
1
1
1
1
2
1
1
1
2
1
1
1
1
1
0
2
2
0
0
1
2
0
1
0
1
1
1
1
1
1
2
1
1
0
1
2
2
0
2
0
1
1
1
1
0
1
1
0
0
1
1
2
2
2
1
1
1
2
3
0
1
1
1
1
0
0
0
1
1
0
1
1
1
0
0
1
1
1
1
0
1
1
0
0
1
1
1
1
2
1
0
0
1
2
2
1
2
1
2
0
0
1
1
1
1
1
2
1
1
1
1
1
1
0
0
1
0
0
1
1
1
1
2
1
2
0
1
0
1
2
2
1
1
2
0
1
2
2
1
2
2
0
1
1
0
2
0
1
1
2
2
1
1
1
1
1
0
2
1
1
0
2
1
1
1
1
1
2
2
1
2
2
1
0
0
1
1
1
2
1
1
1
1
2
1
0
0
0
2
0
1
1
0
2
1
1
0
1
1
0
1
0
0
1
0
2
0
1
1
1
1
1
2
0
1
1
1
1
0
0
1
0
0
1
0
1
1
2
1
1
1
0
1
0
0
2
0
1
2
0
1
1
1
0
1
2
1
0
1
0
2
1
0
2
1
1
1
1
2
1
1
0
2
1
1
2
0
1
1
1
1
1
0
1
5
1
2
0
1
0
1
1
1
0
1
1
1
1
1
0
2
0
1
0
1
0
2
1
2
0
2
1
1
1
1
0
0
1
1
1
1
1
2
1
1
2
1
2
0
1
2
2
1
1
0
1
1
1
1
1
0
1
2
0
2
1
1
1
1
1
1
2
1
1
2
2
2
2
1
2
2
2
0
1
2
1
1
1
1
2
0
1
1
1
1
1
1
1
0
2
1
1
0
1
1
0
1
1
1
1
1
2
2
2
1
2
1
1
0
1
1
0
2
0
0
1
0
1
1
1
1
2
2
2
0
1
0
1
2
1
1
1
0
2
1
1
2
1
1
1
1
1
1
1
1
0
1
1
2
0
2
1
1
2
0
1
1
1
1
1
2
2
1
1
2
1
0
1
2
3
1
0
1
1
1
0
1
1
1
1
2
0
1
1
0
1
0
0
1
1
1
0
1
1
0
1
0
1
0
1
1
2
1
0
1
1
1
1
1
1
4
0
2
1
1
2
2
0
1
2
2
1
0
1
1
2
1
0
0
1
0
0
1
2
1
1
2
1
2
2
2
2
1
1
1
1
0
1
0
2
2
1
1
1
0
2
1
1
0
0
1
2
2
1
1
1
1
1
2
1
2
2
0
1
1
1
1
1
1
1
1
2
0
1
2
2
1
1
2
1
1
1
2
2
2
2
1
1
2
1
1
1
1
1
0
0
0
1
0
1
0
0
0
1
0
1
1
1
2
1
0
0
0
3
2
1
1
3
2
2
1
1
0
2
1
1
2
0
1
2
0
1
0
0
1
1
1
1
2
0
1
2
0
1
1
1
1
1
0
1
1
1
1
1
0
2
1
1
2
1
1
1
1
2
1
0
2
0
1
0
1
2
1
1
1
0
1
2
0
1
1
1
1
0
2
1
2
0
1
1
1
0
1
1
1
0
1
1
1
1
0
1
1
0
1
2
1
2
2
1
1
1
1
2
0
2
0
1
4
1
1
0
2
0
0
0
0
0
1
2
0
2
0
1
1
0
0
0
0
2
1
1
1
2
1
2
1
2
1
1
0
0
2
1
1
0
0
2
2
1
0
1
2
2
1
1
0
1
1
1
1
1
1
1
1
0
0
1
1
1
1
0
2
1
2
2
1
1
1
1
1
3
0
1
2
1
1
2
1
1
1
1
0
1
0
2
1
1
1
1
1
1
1
1
0
1
1
0
0
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
0
1
1
2
0
2
1
0
1
1
1
2
1
1
1
1
1
2
1
1
2
0
2
1
1
1
1
2
1
1
0
0
1
1
0
1
1
1
1
1
1
1
1
1
2
1
0
1
1
1
0
0
2
1
1
2
1
2
2
1
1
1
2
2
2
0
1
1
1
1
1
1
1
1
1
0
2
1
1
0
2
1
0
2
1
4
1
2
1
1
1
2
2
2
1
1
1
2
1
1
1
1
2
1
0
1
0
1
1
1
1
1
1
1
0
1
0
1
2
1
0
1
1
0
1
1
1
1
0
1
2
0
1
1
1
2
1
1
1
1
1
2
2
1
0
1
1
1
1
1
1
0
1
1
1
2
1
0
1
1
2
1
1
1
1
0
1
0
1
1
1
1
1
2
1
0
2
2
2
1
1
1
1
2
1
2
1
2
1
2
1
1
0
2
1
1
0
2
1
2
2
1
2
2
1
2
2
1
2
1
2
0
1
1
0
0
0
0
1
2
2
1
0
1
0
1
1
0
1
2
0
1
1
1
1
1
1
1
0
1
1
1
1
1
2
1
0
2
1
1
2
0
1
0
1
0
0
0
1
1
1
0
1
1
1
2
1
1
2
0
1
1
0
1
2
1
0
1
1
1
0
1
2
2
2
1
1
2
0
1
1
2
1
1
1
2
1
1
0
1
1
2
1
0
1
0
1
1
0
1
1
2
2
0
1
1
1
1
0
0
2
1
1
0
1
1
2
2
1
1
1
0
1
1
2
1
0
2
2
0
2
1
2
1
1
2
1
1
2
1
1
0
1
1
1
1
2
1
1
0
1
1
1
0
1
2
1
1
0
1
2
2
2
0
0
1
0
1
1
2
0
2
2
1
2
1
3
1
2
1
1
1
1
1
1
1
2
1
1
1
2
1
2
0
1
2
1
1
1
1
0
1
2
0
1
2
1
2
1
1
2
2
1
1
2
1
2
1
0
1
0
1
0
1
0
0
1
2
1
1
1
0
1
2
1
0
0
0
1
1
2
1
0
0
0
0
2
1
1
1
1
1
2
1
1
1
2
1
0
1
1
1
1
0
1
1
2
1
0
1
1
1
1
0
1
1
1
1
1
2
2
2
0
1
1
1
2
0
1
2
2
1
0
2
1
1
2
1
1
1
1
0
1
1
0
0
1
1
1
1
0
0
1
0
2
2
0
1
1
1
1
1
2
1
2
2
1
1
0
0
2
1
1
2
1
1
1
0
1
2
1
2
1
1
1
1
0
0
1
2
1
1
1
0
2
2
2
0
1
2
1
1
2
1
1
1
1
0
1
1
2
0
1
0
2
0
1
2
1
2
0
2
1
0
1
1
1
1
1
2
1
2
1
0
1
1
1
1
1
1
1
1
1
1
0
0
1
1
1
2
1
0
1
1
1
0
1
1
1
1
1
0
2
2
1
1
1
1
0
1
0
0
0
1
0
1
0
0
1
1
2
0
1
1
0
1
1
0
2
0
2
1
1
1
1
1
1
1
0
1
1
1
1
1
0
1
1
0
2
0
0
0
1
1
0
2
1
1
1
2
1
2
1
1
2
1
0
2
1
1
0
1
1
1
1
1
1
0
0
0
1
1
1
1
0
0
1
1
0
1
1
0
2
1
1
2
0
2
0
1
1
1
1
2
0
1
1
0
2
1
1
1
1
1
2
0
1
1
1
1
2
1
1
0
1
1
2
1
1
2
0
1
1
1
1
1
1
0
1
0
1
1
1
1
1
1
1
1
1
1
1
0
1
1
0
2
1
1
2
0
1
0
1
0
0
2
1
2
1
2
0
1
1
0
1
1
1
0
1
0
1
1
1
1
1
2
2
2
1
1
1
1
1
2
2
1
0
2
2
1
1
1
0
1
0
1
0
2
1
1
1
2
0
1
2
0
2
2
0
1
1
2
0
2
0
1
1
2
2
2
0
2
0
2
1
1
2
1
0
0
1
0
1
0
0
1
2
2
2
1
2
1
1
2
1
1
2
1
2
1
1
2
1
1
2
2
1
1
1
2
0
0
1
1
0
1
1
1
0
2
0
1
1
1
0
0
1
0
1
2
1
2
0
2
1
1
1
1
1
2
0
2
2
1
0
2
1
1
0
1
0
0
1
2
2
1
1
2
0
1
1
0
1
1
1
0
2
1
1
1
1
2
1
1
0
2
1
2
0
1
2
1
1
2
2
1
1
2
1
2
1
2
2
2
1
1
1
2
1
0
1
1
2
1
1
2
1
2
1
2
1
2
2
1
2
2
1
0
1
1
0
1
1
1
1
2
2
1
2
1
2
2
1
1
1
1
0
1
2
0
0
2
1
0
0
2
1
0
2
0
0
0
0
0
0
1
1
1
1
0
2
1
1
2
2
1
0
1
0
1
1
1
2
0
1
0
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
0
1
1
1
1
1
0
1
1
2
2
1
1
0
1
1
1
2
1
1
0
1
1
2
1
1
2
2
1
1
0
1
2
1
2
2
1
1
0
2
0
2
2
0
2
2
2
1
1
2
2
2
2
1
2
5
0
2
0
1
1
1
0
2
0
1
2
0
1
1
1
2
2
1
2
2
2
1
2
2
1
0
2
0
2
1
1
0
2
2
0
0
1
1
1
1
1
1
2
2
1
1
1
0
1
2
2
2
0
1
1
1
1
1
1
0
0
2
2
1
1
0
0
1
1
1
3
0
2
1
2
1
1
1
1
0
2
2
0
1
2
1
1
1
1
2
1
2
2
1
3
1
2
1
0
1
2
0
1
1
1
2
2
2
1
1
0
1
2
0
0
2
1
1
0
1
1
1
0
1
1
2
2
1
1
1
1
1
1
0
1
1
1
1
1
0
1
1
0
2
0
1
0
1
1
0
1
2
1
1
1
1
1
2
2
1
2
2
0
1
1
1
2
0
0
1
1
1
2
0
2
1
0
2
1
0
0
0
0
2
1
1
1
1
1
2
0
1
1
0
0
0
1
0
1
2
0
2
1
1
1
1
0
0
0
1
0
2
0
1
1
1
2
2
2
0
2
1
1
2
2
1
1
1
0
0
0
2
0
1
0
0
0
1
2
0
0
1
2
0
1
1
1
1
1
0
1
0
2
1
0
1
0
1
0
1
2
1
0
1
0
1
1
0
1
1
2
0
2
1
5
1
1
2
2
0
2
1
0
2
2
0
1
2
1
1
0
1
1
1
1
0
0
1
2
1
2
0
1
1
1
1
1
0
2
0
2
0
0
0
0
0
1
0
1
2
1
1
0
1
1
2
0
0
0
1
2
1
1
1
1
2
1
1
1
1
2
1
2
1
2
1
1
2
1
1
1
1
0
0
0
1
0
1
1
1
0
0
1
1
0
2
1
2
2
0
2
0
1
0
1
1
2
1
1
0
1
1
1
2
2
1
1
1
0
1
1
0
1
1
1
0
2
1
3
0
0
1
2
2
0
1
0
1
1
1
0
1
2
1
1
2
0
1
0
3
2
0
1
1
1
0
1
0
2
4
1
2
2
2
1
1
1
2
1
0
1
2
2
2
1
1
2
1
0
0
0
1
0
1
1
1
1
1
0
1
0
0
1
1
1
0
1
2
1
0
1
0
1
2
1
1
1
2
2
0
1
4
2
1
1
1
2
1
2
3
1
4
1
1
2
1
1
1
1
1
1
0
1
1
0
4
2
1
1
1
1
0
1
2
1
2
2
1
1
1
0
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
3
0
1
1
0
1
0
2
0
1
2
1
0
0
1
1
1
0
0
2
1
1
0
0
1
1
1
0
0
0
1
0
1
2
1
1
0
1
1
2
0
1
1
1
2
2
0
1
0
1
1
1
3
1
1
3
0
1
2
2
1
1
0
1
0
1
0
1
0
2
1
1
1
1
1
0
2
1
2
1
2
1
0
1
1
1
1
2
2
1
1
1
1
1
1
1
1
2
1
0
2
1
0
0
1
1
2
2
1
0
1
1
1
0
1
1
1
1
0
1
1
1
1
1
0
1
1
1
0
0
1
1
1
2
2
1
2
1
2
1
1
1
1
0
1
0
1
1
1
1
0
2
0
0
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
2
1
2
2
0
1
1
1
2
0
2
1
0
1
1
1
1
1
5
2
1
0
0
0
1
4
1
0
2
2
1
0
1
1
1
0
1
0
1
2
1
1
1
0
0
1
1
1
2
1
1
1
1
0
1
1
1
1
1
2
1
1
0
0
2
1
1
1
0
1
0
1
1
0
1
0
0
3
1
2
1
1
1
0
1
0
1
1
1
1
0
1
1
0
1
1
1
1
2
1
2
2
1
1
1
0
1
0
1
1
1
1
1
0
0
0
1
1
2
2
0
0
2
0
2
1
0
2
1
2
0
1
2
1
1
2
0
1
1
1
0
0
2
1
3
1
1
1
0
2
1
0
1
2
1
1
1
1
2
2
1
1
2
1
0
1
0
1
0
1
0
1
2
1
2
0
1
1
2
2
1
1
2
1
1
1
0
1
1
0
1
2
2
0
1
2
1
1
0
2
2
2
4
1
1
2
0
2
1
1
1
2
1
1
1
1
1
1
0
1
1
0
1
0
1
1
0
2
1
1
1
1
1
0
1
2
1
2
1
1
1
1
2
1
2
0
1
1
2
1
1
0
0
1
2
2
1
1
2
1
1
0
2
3
1
1
2
1
2
0
1
1
0
0
1
0
0
0
1
1
0
2
2
0
2
1
2
2
2
1
2
1
0
1
1
2
1
1
1
1
2
2
1
1
2
1
0
0
1
2
1
0
2
2
1
1
0
1
1
0
0
1
0
0
2
1
1
1
1
1
1
0
1
0
2
2
1
2
2
1
0
1
2
1
0
1
1
1
1
1
2
0
0
1
0
2
2
0
0
0
1
1
1
1
1
1
2
2
0
2
0
0
0
1
1
1
1
1
1
1
1
1
1
1
1
0
1
2
2
2
1
1
1
2
1
2
0
0
2
1
1
2
1
0
2
2
0
2
1
1
0
2
0
1
1
0
1
2
4
1
0
2
0
1
1
1
0
2
1
1
1
0
1
1
1
1
1
2
1
2
1
2
1
0
1
1
2
0
2
2
1
1
1
1
1
0
0
1
0
2
1
1
1
2
0
0
1
1
1
1
1
1
0
1
2
2
1
2
1
1
0
1
0
1
1
2
1
1
1
1
1
1
1
2
1
0
0
2
2
1
1
1
1
1
1
0
1
1
1
1
1
1
0
2
1
1
1
0
1
2
1
1
1
0
1
2
2
1
1
2
1
1
1
0
1
1
0
1
1
1
0
2
1
1
0
1
1
1
0
0
1
0
1
0
1
0
0
1
1
2
1
1
2
2
0
1
0
2
1
1
0
2
2
1
2
2
2
1
0
1
0
2
0
1
1
2
1
0
2
0
1
0
1
0
2
1
2
0
1
0
2
0
0
1
0
2
2
0
0
0
1
0
2
1
1
2
2
1
0
1
1
1
1
1
1
1
1
0
1
1
0
0
1
2
2
2
2
0
0
1
0
1
0
0
0
2
0
2
1
1
1
0
1
0
1
1
1
0
1
2
1
2
1
1
1
0
1
1
0
1
2
1
1
2
0
2
2
0
1
1
0
1
1
1
2
1
2
1
1
0
1
1
2
0
1
0
1
1
1
2
0
1
1
1
2
0
0
2
0
2
1
2
1
1
1
1
1
1
2
1
1
1
1
2
0
0
0
1
1
1
2
1
0
1
4
1
0
1
2
1
1
2
2
0
2
1
0
0
1
2
0
0
0
0
1
1
1
1
1
1
1
1
1
0
2
1
1
0
1
0
1
2
1
1
0
1
1
2
1
0
1
0
0
2
1
1
1
1
2
2
1
1
2
1
2
1
1
2
1
1
1
0
1
1
1
0
0
1
0
1
1
1
1
1
0
0
1
1
1
1
1
2
1
1
0
0
1
1
2
0
1
1
2
1
1
1
0
2
1
2
1
1
0
1
1
1
1
1
2
0
2
1
0
1
1
0
1
1
0
2
2
0
1
2
1
2
1
1
0
1
1
1
2
1
1
1
1
2
1
2
1
1
2
1
0
2
1
1
1
2
1
1
2
1
0
0
1
1
1
1
1
1
1
1
1
1
2
2
3
0
0
1
0
1
0
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
0
1
1
2
0
1
1
2
1
2
1
2
1
0
1
1
0
1
0
0
1
2
1
2
1
0
1
1
0
2
0
1
0
2
2
2
2
0
1
0
0
1
1
1
1
1
0
1
1
0
2
1
1
2
1
0
1
1
1
0
0
1
1
1
0
1
2
0
2
2
1
1
1
1
1
2
1
1
0
1
1
1
1
0
1
0
1
1
0
1
2
1
1
1
1
0
0
1
1
0
0
0
1
2
1
2
1
0
0
1
1
1
0
2
1
1
1
1
0
1
2
1
2
2
0
1
2
1
2
1
2
2
2
1
1
1
1
2
2
1
1
0
1
2
1
1
2
1
2
1
2
1
1
1
0
1
1
1
1
2
1
2
2
2
2
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
2
1
2
1
0
1
2
1
0
1
1
1
1
1
0
2
0
1
0
1
0
1
1
1
1
1
1
0
1
1
0
2
2
2
2
2
1
2
0
2
2
0
1
1
0
1
1
1
1
1
0
1
1
1
1
1
1
1
1
0
1
0
1
0
2
1
0
1
2
2
0
1
2
2
1
1
2
2
2
2
0
0
1
1
1
1
1
0
1
1
1
0
1
0
1
2
2
1
1
0
1
1
1
1
1
1
0
1
1
1
1
2
1
1
1
0
2
2
1
2
0
1
1
2
1
1
0
2
1
1
2
3
0
1
0
1
1
1
2
1
2
2
2
1
0
2
2
1
0
1
1
1
0
1
0
1
2
2
1
1
1
2
1
2
1
0
1
1
0
1
1
1
2
2
1
1
1
1
1
1
1
1
0
0
1
0
0
2
1
2
2
1
1
2
1
0
1
1
0
2
1
1
1
0
1
1
1
0
1
1
1
1
1
0
0
1
2
1
0
1
0
2
1
1
0
2
1
1
0
0
1
2
1
1
1
0
1
1
1
2
0
1
1
1
1
1
1
0
2
1
2
1
1
0
0
2
0
1
1
1
1
0
1
1
1
2
0
1
1
2
1
1
1
1
3
1
2
2
1
1
2
1
1
0
1
1
0
1
0
1
2
1
2
0
1
1
1
2
1
0
1
1
1
1
1
0
1
1
1
0
0
1
1
0
1
1
1
2
2
1
1
0
2
2
1
1
1
2
2
2
2
2
1
1
2
1
2
1
1
1
1
2
2
0
1
1
0
1
2
1
0
1
1
0
0
1
1
2
2
0
3
2
3
0
1
1
1
1
0
2
0
0
0
0
3
0
1
2
1
0
2
1
3
1
1
1
1
1
1
1
1
1
1
1
1
2
1
0
0
1
2
1
1
1
1
1
1
2
1
1
0
1
1
1
1
2
1
1
1
1
0
1
2
3
1
0
1
0
1
1
2
1
1
2
0
2
1
2
1
2
1
1
2
1
2
2
0
2
1
1
1
2
1
1
1
1
0
0
3
0
0
2
0
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
0
1
1
1
1
2
1
1
1
0
0
1
3
0
1
2
2
1
1
1
0
1
1
1
0
1
1
1
2
0
1
0
1
1
2
0
1
0
1
1
1
2
1
1
2
0
0
1
1
0
2
1
1
0
1
2
1
1
0
0
1
1
1
1
1
1
0
2
1
1
2
1
2
0
1
0
1
1
2
0
2
0
1
1
0
1
2
1
1
2
1
1
1
1
0
0
1
1
1
0
1
2
2
2
1
1
0
1
1
1
2
0
1
1
1
1
1
1
2
0
1
1
1
1
0
1
1
1
1
1
0
1
1
0
1
1
1
2
0
1
0
2
2
0
2
3
2
1
2
1
0
2
1
2
1
1
1
2
2
1
2
1
2
0
1
1
0
1
1
1
0
2
1
1
1
2
2
1
0
0
2
2
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
0
1
1
1
1
2
0
1
2
1
2
1
1
1
1
0
1
1
1
1
1
2
1
0
1
0
2
0
0
0
1
0
1
2
2
1
2
0
2
1
1
1
0
1
1
2
0
0
0
1
2
1
1
2
1
1
1
3
1
2
1
0
1
2
1
0
1
0
1
1
0
1
0
2
0
0
3
0
1
0
1
0
0
1
2
2
0
1
0
1
2
0
0
0
0
1
0
0
1
2
0
0
1
1
1
3
2
5
1
0
0
0
1
0
1
2
1
1
2
1
2
1
1
1
0
1
1
1
1
2
1
2
1
1
1
2
1
1
1
0
1
1
1
2
0
0
1
1
1
1
1
1
1
1
3
0
1
1
0
1
0
0
1
1
1
2
2
2
2
0
1
1
1
2
1
1
1
1
0
1
1
2
1
1
0
1
1
1
0
0
0
1
1
2
1
1
2
1
1
1
3
0
1
2
1
1
0
2
1
1
0
3
0
2
1
0
0
1
0
2
2
0
1
2
1
1
1
2
1
2
2
0
1
1
2
0
1
2
2
1
2
1
0
0
0
2
1
1
1
1
1
1
1
1
0
0
0
2
0
1
1
0
0
0
2
1
2
1
2
0
1
1
1
1
1
1
0
2
2
2
1
1
0
2
1
2
1
2
0
2
0
2
1
1
1
0
0
1
0
1
0
1
1
2
1
2
1
1
1
2
1
1
1
1
2
1
1
0
1
1
1
1
2
0
1
2
0
2
1
1
0
0
1
1
1
1
1
0
1
2
1
0
1
1
0
1
0
1
1
1
1
1
1
2
1
0
1
0
1
1
1
1
2
1
0
1
1
2
1
1
2
0
2
2
0
1
0
0
2
2
1
0
0
0
1
0
1
1
1
1
2
0
2
2
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
2
0
1
1
0
2
1
1
1
1
0
0
0
1
2
1
0
1
0
1
1
2
1
1
0
0
2
1
2
1
1
2
1
1
1
2
1
1
1
1
1
0
0
1
0
1
2
2
1
1
1
2
1
2
1
2
1
0
1
1
0
2
0
1
0
1
2
1
2
0
0
1
1
0
1
1
1
0
2
3
1
2
1
2
1
2
2
2
1
1
1
2
0
1
2
2
0
1
1
1
1
1
1
1
2
1
1
0
0
1
1
0
1
1
0
2
0
0
1
2
2
1
1
1
1
1
1
1
1
0
1
0
0
1
1
0
1
0
1
1
1
3
1
2
1
1
1
1
0
1
2
1
0
1
1
0
1
1
1
2
1
0
1
2
2
0
0
0
0
2
0
1
1
2
0
0
1
2
1
0
1
1
0
1
2
2
2
1
1
0
1
0
1
1
2
1
1
1
2
1
1
0
0
2
1
1
1
2
1
0
2
1
1
2
1
1
0
1
1
1
1
1
1
2
1
1
2
0
1
1
0
1
1
1
1
1
2
1
2
1
1
2
0
2
1
0
1
2
2
0
0
0
1
1
1
0
1
1
1
0
1
1
1
0
0
0
1
2
1
1
1
2
2
1
0
1
1
1
2
1
0
2
1
1
2
2
2
1
1
2
1
0
0
0
1
1
1
1
0
2
0
1
1
1
2
2
1
1
1
0
0
2
1
1
2
2
1
1
1
0
1
1
0
1
1
1
1
1
1
1
1
1
2
1
0
0
0
2
0
2
2
1
0
2
2
1
1
2
2
1
1
2
1
0
1
1
1
1
1
0
1
2
2
1
0
2
1
2
1
1
0
0
2
2
2
1
0
1
1
1
1
2
1
0
0
2
2
2
0
2
0
2
1
1
0
2
0
2
1
2
2
1
2
1
1
2
0
0
2
2
1
3
1
0
1
0
1
1
1
1
2
1
2
1
1
1
0
1
2
0
1
2
1
1
2
1
2
1
1
0
0
0
0
1
1
2
1
1
2
2
1
2
1
1
2
2
1
0
0
1
0
2
1
1
1
2
0
0
1
0
2
1
0
2
1
2
1
1
0
0
1
1
1
2
2
2
1
1
1
1
1
1
1
0
1
1
0
1
1
0
0
1
2
0
2
1
1
0
0
1
1
1
2
1
1
1
1
2
2
1
0
0
1
2
1
1
1
1
0
2
1
1
0
2
1
1
1
1
2
0
2
2
1
1
1
3
0
1
1
2
2
1
1
0
1
1
1
2
1
1
2
1
0
0
0
1
2
1
2
1
1
0
2
1
2
2
1
1
2
1
2
1
1
1
1
1
2
0
0
2
2
1
0
1
1
1
1
2
2
2
0
1
1
2
1
2
1
2
2
1
1
0
2
1
0
1
1
1
1
1
0
2
1
1
2
1
1
2
1
1
1
1
2
0
2
1
1
1
1
0
0
0
1
2
0
3
1
1
0
1
0
1
2
2
0
1
1
1
2
1
0
1
1
1
1
1
1
1
2
1
1
0
1
1
2
2
1
0
0
1
0
1
0
1
1
2
1
1
1
0
1
2
0
2
1
1
0
3
1
1
0
0
2
1
1
1
1
1
1
1
0
1
1
0
1
1
2
1
2
0
1
1
1
1
0
1
1
1
1
2
0
2
0
1
2
1
1
0
2
1
1
1
1
2
1
0
0
0
1
1
0
0
1
0
1
1
0
2
0
1
1
1
1
1
3
1
1
2
2
1
2
0
0
8
1
2
0
1
1
1
1
0
1
1
1
2
1
1
1
0
2
1
2
0
2
2
1
1
1
2
1
0
2
0
1
2
0
1
1
1
1
1
1
1
1
1
1
0
1
1
3
1
1
2
0
1
1
2
1
1
0
0
1
2
2
1
1
1
0
2
1
2
0
2
1
1
0
0
0
2
1
0
1
1
1
1
0
2
1
2
0
1
0
1
2
0
1
0
1
1
2
1
1
2
2
1
2
1
2
1
1
2
1
1
1
0
1
1
0
0
1
0
1
0
1
2
0
1
1
2
2
1
0
2
0
1
1
0
0
2
0
1
2
1
0
2
1
1
2
1
1
1
1
1
2
1
2
1
1
1
2
2
1
1
1
3
0
0
2
1
2
1
1
2
1
0
0
0
1
2
1
1
0
2
2
1
2
1
2
2
2
1
0
1
2
0
1
1
2
2
1
1
0
1
1
1
0
1
1
0
2
1
1
1
1
0
2
2
1
2
1
1
1
2
1
1
0
2
1
1
1
2
1
1
3
2
1
1
1
1
1
1
0
2
0
1
2
0
1
1
1
0
2
1
2
1
1
1
1
0
1
0
1
1
1
0
1
2
2
1
2
1
2
0
2
1
1
3
1
0
2
0
0
1
2
1
2
1
2
1
0
1
1
1
0
1
1
1
2
0
1
1
0
1
1
1
2
1
0
0
1
3
2
1
1
1
0
0
0
1
1
1
1
1
1
2
1
1
1
0
1
1
0
0
1
2
2
0
1
1
1
1
0
0
1
1
1
1
1
0
1
1
1
1
0
1
1
1
5
0
2
1
1
1
1
2
2
1
0
1
2
1
0
1
1
2
1
0
2
1
1
1
0
0
3
0
1
1
1
1
0
0
2
2
0
0
0
1
1
1
1
1
1
0
0
0
1
1
1
1
1
0
2
2
2
1
1
0
1
1
0
1
1
2
2
1
1
1
1
1
1
2
0
2
1
1
2
1
0
2
1
0
1
1
0
1
1
0
1
0
1
1
1
1
1
1
2
1
1
0
1
1
1
1
1
1
1
1
1
2
1
1
1
0
2
1
0
1
1
1
1
0
2
1
0
3
2
1
1
2
1
1
0
0
1
1
1
0
0
2
1
2
0
2
1
0
3
1
1
2
2
2
2
0
1
1
2
2
0
1
2
1
1
1
1
1
2
2
2
1
1
1
0
1
1
1
2
0
0
0
1
1
1
1
2
1
1
0
1
2
1
1
1
1
0
1
1
2
1
0
1
1
1
1
1
1
1
1
1
1
2
1
0
1
0
0
1
1
1
2
0
2
1
1
0
1
1
1
1
1
1
0
1
2
1
1
1
2
1
2
1
1
0
0
4
1
2
1
2
2
1
1
0
2
0
1
1
4
2
2
2
0
1
1
1
0
2
2
2
2
2
1
1
1
3
1
1
1
2
2
1
1
1
1
2
2
0
1
0
2
0
2
0
1
1
3
2
1
1
0
0
1
1
1
1
1
2
0
1
1
1
1
1
1
0
2
0
1
0
2
1
2
1
0
3
0
1
0
1
1
1
2
1
1
2
2
0
1
1
1
1
2
1
2
1
1
1
2
1
0
2
2
1
2
0
1
1
2
1
1
2
2
1
0
2
1
1
0
1
2
2
1
1
1
0
1
0
1
1
1
1
2
0
1
1
0
1
1
2
2
1
1
1
1
1
0
2
1
1
0
1
1
0
2
2
0
1
2
0
1
1
1
1
1
0
1
0
1
1
0
1
1
2
1
1
2
0
1
1
0
2
1
0
1
0
1
1
2
2
0
1
0
1
5
1
2
1
0
0
0
2
0
0
2
1
1
0
0
1
1
0
1
1
1
1
0
1
2
0
1
1
0
1
3
2
1
1
2
1
1
0
3
1
2
2
2
0
1
1
2
1
1
1
1
0
1
1
1
1
2
1
1
2
0
0
1
1
1
1
2
0
1
1
0
2
1
0
1
1
1
0
2
1
1
1
2
1
0
2
1
1
2
1
1
0
1
0
2
0
2
0
1
1
1
0
1
2
1
1
2
0
1
0
1
0
0
0
0
1
1
1
0
2
1
1
1
1
0
2
2
0
0
1
1
1
2
0
1
1
1
1
1
0
2
2
1
2
1
1
1
1
2
2
1
1
3
1
1
2
1
1
0
2
0
0
1
1
2
1
1
2
1
1
1
1
1
1
1
2
2
1
1
2
1
1
2
0
1
0
1
1
1
2
2
1
1
0
1
1
2
1
1
1
2
2
2
2
1
2
1
1
2
3
1
1
0
1
1
1
2
1
2
1
1
1
1
0
2
1
0
1
2
2
1
1
2
1
4
0
1
1
1
4
0
0
2
2
1
1
0
1
1
1
0
1
1
1
2
1
2
2
1
1
1
0
2
1
1
1
0
1
1
1
1
1
1
0
1
2
0
2
0
1
2
2
0
0
0
2
0
1
0
0
1
0
2
1
1
1
0
1
1
0
0
1
1
2
3
4
0
3
2
1
1
1
1
1
1
2
0
2
1
0
2
0
1
1
1
1
0
0
1
1
1
0
2
2
0
1
1
0
0
1
0
2
1
1
3
1
2
0
2
1
0
0
2
1
1
1
1
0
1
1
2
2
0
1
0
0
1
1
1
1
1
2
2
1
1
0
1
1
1
1
1
0
0
1
2
1
0
1
2
1
2
2
2
1
2
2
2
2
1
2
1
1
0
1
1
1
2
1
1
1
1
1
0
0
1
2
2
1
1
1
1
1
1
0
0
1
1
1
1
1
1
1
1
0
1
2
1
0
1
1
1
1
1
1
2
0
0
1
1
2
1
2
2
1
3
1
2
1
1
0
1
3
1
1
1
0
0
2
1
1
1
0
0
1
1
2
1
0
1
2
2
1
0
1
0
0
2
1
1
1
1
0
0
1
1
2
1
1
1
1
1
1
1
0
2
1
1
1
1
0
2
1
2
1
1
1
0
1
1
1
1
2
2
1
1
0
0
1
0
1
0
2
1
2
3
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
0
1
2
1
1
1
1
1
2
2
0
0
2
0
1
1
1
2
0
2
1
1
1
1
1
0
2
1
1
1
1
1
1
3
2
1
0
1
1
1
1
0
0
1
0
0
1
1
1
0
2
0
1
1
1
1
0
1
1
1
1
2
1
0
1
0
0
2
0
1
0
1
2
2
1
1
1
1
0
1
0
1
2
1
1
2
0
1
1
2
2
1
1
1
1
0
0
1
0
0
1
1
0
0
2
0
1
0
2
1
0
1
1
1
1
0
0
0
0
0
2
1
0
0
0
1
1
1
2
2
0
0
1
2
2
1
2
1
1
1
1
1
0
0
1
1
2
1
1
1
0
1
1
2
2
1
0
0
0
0
2
2
0
2
2
1
1
2
2
1
1
2
1
2
1
1
2
1
1
0
2
1
1
0
0
1
1
2
2
1
1
2
1
2
0
1
0
1
0
2
1
0
1
1
2
0
1
0
2
1
0
2
2
2
1
0
1
1
0
2
1
1
1
2
1
1
0
1
1
0
1
1
0
1
1
1
2
0
1
2
1
1
1
0
1
1
0
2
1
1
1
1
2
1
2
0
1
1
1
0
1
1
0
0
0
0
1
1
2
1
2
1
1
1
0
1
1
1
1
2
0
1
1
1
2
2
2
1
1
1
1
0
0
1
1
2
0
1
1
2
0
1
1
0
0
1
1
1
1
1
2
1
0
2
1
1
2
0
1
0
2
1
1
1
0
1
1
1
1
1
4
1
0
1
0
0
0
1
1
1
1
0
0
3
1
0
1
1
1
0
1
1
1
2
2
1
1
1
1
1
1
0
1
0
0
2
1
1
1
1
1
1
2
1
1
1
0
2
1
1
1
1
1
1
0
1
1
2
1
1
1
1
1
1
1
0
1
0
1
2
1
2
0
2
3
0
1
1
0
1
1
0
1
1
1
1
1
2
0
1
3
1
1
1
1
0
1
1
1
0
1
0
1
1
0
2
1
1
1
1
0
1
1
1
2
2
1
0
2
2
0
1
2
1
0
1
1
1
1
2
1
1
0
0
0
1
1
1
1
0
2
1
2
1
2
1
0
1
1
2
1
1
2
2
2
1
0
1
1
1
1
1
1
1
1
0
1
1
1
1
1
2
0
1
3
1
0
1
1
1
1
1
1
1
1
2
2
2
2
0
2
1
2
1
2
1
1
1
0
1
1
1
0
0
1
1
2
2
1
0
1
0
0
1
0
2
0
2
1
2
0
1
1
0
0
1
1
0
1
2
1
0
1
0
1
1
1
1
1
1
1
1
1
0
1
0
1
1
2
3
2
1
0
1
2
1
2
2
1
1
0
0
1
2
1
2
1
0
2
1
0
2
1
1
1
1
1
0
1
1
1
1
1
1
1
0
0
2
2
1
1
1
1
1
2
1
1
1
0
1
0
2
1
1
0
1
1
2
1
0
1
1
1
2
1
2
1
2
1
1
0
1
0
0
2
1
2
1
1
1
2
2
2
1
1
1
2
1
1
1
2
1
1
1
1
0
2
1
2
2
1
0
2
2
0
1
0
1
2
1
0
2
1
0
2
1
0
1
0
1
2
2
1
1
1
0
0
1
2
1
1
1
1
0
1
1
1
1
1
1
2
2
1
1
1
0
0
0
1
1
2
2
0
2
1
1
1
0
0
0
0
1
1
0
2
1
0
1
0
1
1
1
2
1
2
1
0
1
0
2
1
4
1
1
1
2
1
1
2
1
0
1
2
1
0
2
2
2
1
1
0
1
2
0
1
1
1
1
1
0
1
1
1
0
0
1
1
0
1
1
2
1
1
0
1
2
1
2
1
2
0
1
1
1
2
1
1
1
2
2
1
1
1
0
0
0
1
2
0
0
1
2
1
0
0
1
1
1
1
1
1
2
1
1
1
1
1
1
2
0
1
1
0
1
2
1
2
1
0
0
1
2
0
0
0
1
1
2
1
0
1
1
2
1
2
1
2
0
1
1
1
1
2
2
1
2
1
2
2
1
2
0
1
1
0
1
0
1
1
1
2
0
0
1
0
0
0
1
1
2
2
1
1
1
1
0
2
1
1
1
1
0
1
2
0
1
0
2
1
1
1
2
0
0
1
0
1
1
1
2
1
1
1
2
1
0
1
1
1
0
0
2
2
1
1
1
1
2
2
0
1
2
0
1
1
1
1
1
1
0
1
1
2
1
1
1
1
1
1
1
2
0
2
1
1
0
0
1
2
2
1
1
2
1
1
1
1
0
2
1
0
1
1
1
0
1
2
0
1
2
1
1
0
1
1
2
2
1
2
2
1
0
1
0
1
1
2
0
4
1
2
1
0
1
0
1
1
2
1
1
0
1
0
1
2
1
1
1
0
1
1
1
0
1
1
1
1
1
1
1
1
0
1
2
1
2
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
0
1
1
1
2
1
0
0
1
0
1
0
1
1
1
1
1
1
1
1
1
2
1
1
1
0
0
0
2
2
1
1
1
0
1
2
1
1
1
1
1
0
1
1
1
0
1
2
1
1
2
0
0
1
0
2
0
1
1
1
1
0
1
1
1
1
1
2
1
1
2
0
2
2
0
1
1
1
1
0
0
1
3
2
1
2
1
1
1
1
1
1
1
0
1
1
1
2
1
2
2
1
1
1
2
1
1
1
1
1
2
0
3
1
1
0
1
2
0
1
1
0
1
0
1
1
1
2
0
0
1
0
0
1
1
2
1
1
1
0
1
0
1
1
0
2
0
1
1
1
0
1
1
2
0
2
2
2
1
0
1
2
2
1
1
2
0
1
1
0
1
1
1
0
1
1
2
2
1
0
3
1
1
1
1
1
1
0
0
1
1
2
1
1
1
1
0
1
1
1
2
2
1
1
1
2
1
1
1
2
2
0
1
1
1
0
0
1
1
3
2
2
0
2
2
1
1
2
0
0
1
1
3
3
1
0
1
0
1
1
0
1
1
0
1
1
1
1
2
1
1
2
1
1
0
0
1
1
1
1
2
1
0
1
2
1
2
0
1
1
2
1
2
0
1
1
1
2
0
2
1
2
0
0
3
1
1
2
1
1
1
2
1
0
0
1
0
2
2
1
0
0
0
2
1
0
1
2
1
1
0
2
1
1
0
0
2
1
2
1
1
2
1
2
1
1
0
1
1
0
1
2
1
0
1
2
2
1
0
1
1
1
1
1
0
2
1
1
1
1
2
2
2
1
2
0
1
0
1
1
1
1
1
1
1
2
2
0
1
1
1
1
0
1
1
0
1
0
1
1
0
2
2
1
1
2
0
1
1
2
1
0
1
2
1
2
0
1
1
1
0
0
2
3
2
1
1
1
0
1
1
1
1
0
1
0
2
1
2
2
0
1
1
1
2
1
1
2
1
1
2
1
1
1
0
0
1
1
0
1
1
2
2
1
2
2
3
1
0
2
2
1
0
2
1
1
1
2
1
1
0
2
0
1
1
1
1
1
2
2
1
1
0
2
1
1
1
1
1
0
1
1
0
1
2
2
1
1
1
0
1
1
2
2
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
2
1
1
2
2
2
1
1
1
1
0
1
1
1
1
1
1
0
1
1
2
0
2
0
3
2
1
1
2
1
1
1
0
1
1
1
2
2
0
0
1
1
1
1
1
1
0
1
1
1
0
1
2
1
1
2
2
1
2
0
1
2
0
0
1
0
1
2
1
0
0
1
0
1
1
2
1
1
1
2
0
0
1
0
1
1
1
1
2
2
2
3
1
1
1
1
1
1
1
2
2
1
1
1
0
1
1
1
2
0
1
1
1
1
2
1
2
1
0
1
1
0
10
1
1
2
1
1
1
1
0
2
1
0
1
0
1
2
1
1
2
1
1
0
0
1
2
1
1
2
1
1
1
2
2
1
0
2
0
1
2
1
1
0
2
2
0
1
1
1
2
2
1
0
1
0
1
1
2
1
0
1
1
0
1
1
1
2
1
2
2
2
1
1
1
1
2
1
1
1
1
1
0
2
1
2
0
1
1
2
1
1
1
1
1
0
1
1
0
1
2
0
2
0
2
1
2
2
2
0
0
0
2
1
1
2
1
1
2
4
0
0
0
0
1
1
1
1
0
2
1
2
2
0
0
1
0
1
3
1
1
0
0
1
2
1
1
1
1
0
1
1
1
2
1
1
1
2
1
1
0
2
0
1
2
1
1
1
1
0
1
0
1
1
1
1
0
1
2
2
1
1
1
0
0
0
0
1
2
1
0
1
1
0
1
0
1
0
1
1
1
2
1
1
2
1
1
1
1
1
2
1
1
1
0
2
0
1
1
2
2
0
1
2
1
1
0
0
0
1
0
2
11
1
0
1
2
1
0
1
2
1
2
0
1
1
1
0
2
1
1
0
1
2
1
1
1
0
2
1
1
2
0
1
0
1
1
2
1
1
1
1
1
0
1
1
1
1
2
1
1
0
0
0
1
1
1
0
3
0
2
2
0
2
1
1
1
0
0
1
5
1
1
1
1
1
1
1
1
1
1
1
0
0
1
2
2
0
1
1
2
0
1
1
2
2
1
1
2
1
1
1
1
0
1
1
1
0
1
1
1
1
0
0
0
2
2
1
1
1
2
0
2
2
2
2
1
1
1
1
1
0
1
1
1
2
1
1
1
0
1
2
1
2
0
0
2
1
1
0
2
1
1
1
1
1
2
2
1
1
1
1
1
2
0
1
1
1
1
2
0
0
0
2
1
1
0
1
0
1
1
1
1
1
1
0
0
0
1
2
2
1
2
2
0
2
1
1
0
2
2
1
1
0
0
2
1
0
1
1
1
2
2
2
1
1
1
1
1
1
0
2
1
2
2
0
1
1
2
1
1
2
1
1
0
0
0
1
2
1
1
2
0
1
1
2
0
1
1
2
2
2
1
1
2
0
2
1
0
1
1
0
1
1
1
1
1
2
0
0
0
1
0
2
1
0
0
1
1
2
1
2
1
1
0
1
0
0
2
1
1
2
1
0
1
1
0
0
1
1
0
0
1
0
2
1
0
1
1
1
0
1
0
1
2
2
1
1
2
1
2
2
3
1
2
0
1
1
2
1
2
1
1
0
0
1
2
0
1
1
1
1
2
1
2
1
1
1
2
0
1
2
0
1
2
0
1
0
1
1
1
2
1
3
0
0
0
1
1
2
2
1
1
1
2
1
0
1
1
1
1
2
1
1
1
0
1
0
1
0
2
1
2
0
1
2
1
1
0
2
2
1
2
1
0
1
2
0
2
2
0
0
2
0
1
1
0
1
1
2
1
0
1
2
1
1
1
0
0
2
1
0
1
0
2
1
2
1
0
1
1
4
1
1
1
1
1
1
2
1
1
1
3
1
1
1
2
1
2
0
2
1
1
0
0
1
2
1
2
1
1
0
0
2
2
2
1
1
0
1
2
0
0
1
2
1
1
0
1
0
2
0
2
1
0
2
2
1
2
1
1
0
0
1
1
2
2
2
0
2
3
1
1
1
3
1
0
0
0
1
0
1
0
1
2
2
2
1
1
0
2
0
1
1
0
0
1
0
1
1
1
2
2
1
1
0
0
2
1
1
1
1
0
1
1
2
2
0
0
1
1
1
0
1
0
0
2
1
1
0
0
1
0
2
2
1
1
0
4
1
1
2
1
2
1
1
1
1
1
2
0
2
2
1
1
1
1
1
2
0
1
0
1
1
1
1
0
1
1
1
0
1
1
2
1
0
1
2
4
1
1
1
1
2
2
2
1
2
1
2
1
0
0
1
1
2
1
1
1
0
2
1
1
1
1
1
2
1
0
1
1
1
1
1
1
2
1
2
0
1
1
1
1
2
1
1
1
1
1
0
1
1
2
1
0
1
2
1
1
2
2
1
1
0
2
1
1
0
0
1
1
2
1
1
0
0
1
0
2
1
1
0
2
1
1
2
0
2
1
2
1
1
0
1
1
0
1
0
2
1
2
1
1
1
0
1
2
2
1
1
3
0
1
1
0
0
2
0
1
2
1
1
2
1
1
1
1
1
1
2
2
2
1
0
1
2
1
1
2
2
1
0
1
1
2
1
2
1
2
1
0
1
1
2
1
1
1
2
0
2
2
0
1
0
1
1
1
2
2
1
1
1
1
2
3
1
2
2
1
0
2
1
1
1
1
1
2
1
5
1
1
1
2
1
1
1
1
1
2
0
3
1
2
0
0
0
1
1
1
1
0
1
1
1
1
2
2
1
0
0
2
1
2
0
1
1
2
1
1
1
2
1
1
1
1
1
2
1
0
1
1
0
0
2
0
1
2
0
1
1
1
1
2
1
0
1
1
1
1
1
0
1
1
1
1
2
0
0
1
1
1
1
1
1
1
0
2
2
2
0
1
1
1
1
1
1
1
1
1
2
1
1
0
1
1
0
1
1
0
0
1
1
1
1
2
1
3
3
2
1
0
0
0
1
1
0
1
1
1
1
1
0
0
1
1
1
1
1
1
0
1
1
1
2
1
1
1
1
0
2
1
1
0
2
1
1
1
1
1
2
1
2
2
1
0
2
4
0
0
1
1
1
1
1
1
1
1
1
0
1
1
0
1
2
2
1
1
1
1
1
0
1
1
1
0
1
2
1
1
2
1
0
2
0
1
0
1
2
1
0
0
2
0
1
2
1
0
2
1
0
1
2
0
1
0
0
1
2
1
1
1
2
1
0
0
2
1
1
1
1
0
1
1
2
1
2
0
2
1
1
0
3
1
0
2
1
0
1
1
1
0
1
1
1
1
1
1
0
1
1
2
2
1
0
0
1
0
0
1
1
0
1
1
2
0
2
2
1
2
1
0
1
0
1
1
1
1
0
0
2
0
1
0
1
0
0
2
0
1
0
2
2
1
0
1
1
2
1
0
1
1
1
0
1
1
0
0
1
0
1
1
1
2
1
2
2
0
2
2
2
1
0
2
2
2
0
1
1
0
1
0
1
1
0
0
2
0
1
2
0
1
1
2
1
1
1
1
1
0
1
0
1
1
1
1
1
1
1
0
1
1
0
2
1
0
1
1
1
0
1
0
0
0
0
1
1
1
2
0
1
1
0
2
0
1
0
2
1
0
3
0
0
1
2
1
0
1
1
1
1
1
0
1
2
0
0
1
1
1
0
2
1
0
1
1
1
2
1
0
1
1
0
2
1
1
1
1
1
1
2
1
0
1
1
1
1
1
0
1
1
3
1
1
2
0
0
1
1
1
0
1
0
0
1
1
2
2
0
2
1
3
2
1
0
2
1
2
2
1
0
2
2
2
1
1
0
0
1
1
1
1
1
0
0
0
0
1
1
1
1
2
1
0
1
2
1
1
2
2
1
2
2
2
0
2
1
1
0
0
2
1
1
0
1
1
1
1
2
1
1
2
1
1
1
1
1
1
0
1
1
0
1
1
0
1
1
0
1
0
2
1
2
1
1
0
2
1
1
2
1
2
1
2
1
0
1
1
0
1
1
0
1
2
0
0
1
1
1
2
2
1
1
2
2
1
0
1
1
1
1
0
2
2
2
2
1
2
0
1
2
1
1
1
1
2
1
3
0
0
1
1
2
0
0
1
1
1
2
2
1
2
1
2
0
1
1
2
0
0
1
2
0
2
1
1
1
1
2
2
2
2
0
1
1
1
1
0
0
1
1
0
1
1
3
2
0
1
2
0
1
1
2
1
1
0
1
0
0
0
1
1
2
1
1
2
1
3
1
1
1
1
1
1
2
1
1
1
1
2
2
0
1
1
1
1
2
1
1
1
2
1
2
0
1
1
1
2
1
2
1
1
1
1
1
0
1
1
2
1
0
1
1
2
1
0
1
1
1
1
1
1
1
1
1
1
1
1
0
1
0
1
1
2
2
1
2
1
1
0
1
2
0
2
1
2
1
1
1
0
1
1
1
0
1
0
0
2
2
1
1
1
1
1
0
1
0
2
3
1
1
1
2
2
1
1
1
1
1
1
0
1
1
0
1
1
3
1
0
1
1
2
1
1
1
1
2
1
1
1
0
1
1
1
1
1
1
0
1
2
1
1
1
1
0
1
0
1
1
1
1
1
1
0
2
1
0
0
2
2
2
2
0
1
1
2
1
0
2
2
1
1
0
0
1
0
1
2
1
0
2
1
1
1
2
2
0
0
2
1
2
0
1
0
0
1
0
2
1
1
1
2
1
1
0
1
1
1
0
1
2
2
2
1
0
1
0
0
0
1
1
2
2
2
1
2
1
2
1
1
0
1
1
2
1
1
2
0
2
1
1
1
1
2
1
0
2
1
1
0
1
0
1
2
0
1
1
2
1
0
1
2
2
0
1
1
2
1
1
2
0
1
2
1
1
1
2
1
1
1
1
2
1
0
0
2
0
0
0
1
2
1
1
2
1
0
1
1
0
0
1
2
0
2
1
2
0
0
1
3
2
1
2
1
1
2
1
1
1
1
1
1
2
0
0
0
1
0
1
2
1
1
1
1
2
1
2
0
0
0
0
1
1
0
2
1
1
1
2
0
1
0
2
1
0
2
0
1
1
2
0
0
0
2
1
0
1
1
1
0
1
1
0
1
1
1
2
2
1
2
1
0
1
0
0
0
2
2
0
1
1
1
1
1
1
0
2
0
1
1
1
2
1
1
1
2
1
2
0
2
1
0
1
0
0
1
1
0
1
1
1
0
2
0
2
1
1
0
1
2
1
1
1
0
1
2
2
0
1
0
1
0
2
0
2
1
0
1
1
2
1
1
1
1
2
1
0
1
1
1
1
1
0
1
0
0
2
1
2
1
1
1
2
2
2
1
2
1
1
0
1
1
1
1
2
1
1
1
0
0
1
1
2
1
1
1
2
1
0
1
1
0
0
1
1
2
6
1
0
1
2
1
2
1
2
2
2
2
0
1
1
1
1
1
1
0
1
0
1
1
1
1
1
2
1
0
2
1
0
3
2
1
1
0
1
0
0
1
1
1
0
2
2
1
1
0
1
1
0
1
2
0
1
2
1
2
2
2
1
1
1
2
1
0
1
0
1
0
1
1
1
1
2
1
1
1
1
1
2
2
2
1
0
1
1
1
1
0
1
2
0
0
0
1
1
1
0
1
1
0
1
1
1
2
1
2
1
1
1
1
1
1
0
1
1
0
1
1
1
1
1
1
2
0
2
0
2
1
1
0
1
1
1
0
2
2
1
1
1
1
1
0
3
0
1
2
1
1
0
2
2
0
0
0
2
1
0
1
1
0
2
1
1
0
1
2
3
1
0
1
1
0
1
1
0
1
0
1
1
2
2
0
1
1
2
1
1
0
2
0
1
2
2
0
2
1
2
2
1
0
0
2
1
1
1
2
2
0
1
0
1
1
2
2
0
2
1
0
1
2
0
2
1
1
2
1
2
1
2
1
1
2
1
1
2
0
1
1
0
1
1
1
2
1
1
1
1
2
1
0
0
1
0
2
2
1
1
1
0
0
0
1
1
2
0
1
1
0
1
1
2
2
0
2
0
2
1
0
2
2
2
1
1
1
2
0
1
3
2
1
1
2
1
1
1
3
0
1
0
1
0
1
1
1
2
1
1
2
2
1
1
1
1
0
1
2
1
2
2
1
3
1
1
1
1
1
0
1
0
1
2
0
1
1
2
1
2
0
0
0
0
1
0
1
1
0
1
0
0
2
0
1
1
1
0
0
0
0
1
1
1
1
1
1
1
1
0
1
1
1
0
0
0
3
0
1
0
0
1
0
0
1
0
2
1
1
0
1
2
0
2
1
2
1
1
1
1
0
1
2
1
1
0
2
1
1
2
1
2
1
0
1
1
1
1
0
1
1
1
1
2
1
1
1
1
1
1
0
1
1
1
1
2
0
1
1
0
0
0
1
2
2
1
1
1
1
1
1
1
2
1
1
1
2
2
1
0
1
0
2
1
1
2
2
2
1
0
2
0
1
1
1
1
1
1
2
1
2
0
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
0
1
1
0
1
0
0
2
1
2
0
1
1
1
1
1
0
2
0
2
2
0
2
2
2
0
1
2
0
1
2
2
2
1
1
2
0
1
0
0
1
2
1
1
1
0
0
1
2
1
0
1
0
0
1
1
1
2
0
2
1
1
1
1
0
1
1
0
1
1
0
2
1
1
1
0
1
1
0
0
0
1
1
0
2
0
1
1
1
2
2
2
0
1
0
1
0
0
0
1
1
1
1
1
1
1
2
0
0
2
0
1
1
1
1
2
0
2
0
0
2
2
1
2
1
1
0
2
0
1
2
1
0
1
1
1
1
1
2
0
1
1
1
1
1
1
1
0
1
0
2
1
1
2
1
2
1
2
1
1
1
2
0
1
1
0
1
2
1
1
2
1
1
0
0
1
1
2
2
0
1
1
2
1
2
2
1
0
1
2
1
1
1
1
1
2
0
1
0
2
1
1
1
2
2
2
2
1
1
1
2
1
2
1
2
0
1
1
1
1
1
1
2
2
2
1
1
1
1
1
2
1
1
1
1
2
1
2
1
1
3
1
1
1
0
1
1
2
1
1
0
1
1
1
1
1
1
1
1
1
0
1
1
1
2
1
2
1
1
1
1
1
1
0
1
1
1
1
2
1
1
2
2
1
1
1
1
1
2
0
1
1
2
0
1
0
1
1
1
1
1
1
1
1
1
1
0
1
2
0
1
1
1
1
1
1
1
2
1
1
4
2
1
0
1
1
0
1
1
1
2
1
1
1
0
0
1
1
0
1
1
2
2
1
0
1
1
1
1
1
0
2
2
1
1
1
2
1
1
1
0
0
0
0
0
1
1
2
1
0
0
1
2
0
2
1
1
0
1
1
0
1
1
2
3
0
0
1
1
2
2
1
0
1
1
0
1
2
2
1
1
2
0
1
1
1
1
0
1
1
0
2
1
0
2
0
1
3
1
1
2
1
0
3
0
2
1
0
1
1
3
1
1
1
1
1
2
0
2
2
1
1
1
1
2
0
2
1
1
1
0
1
0
0
0
2
1
0
0
1
1
2
1
0
1
1
0
0
1
2
1
0
1
2
1
0
0
2
1
1
1
1
2
2
0
0
1
2
0
1
1
1
1
0
1
1
2
1
1
2
1
1
0
2
1
2
1
0
0
1
2
0
0
1
1
0
0
2
1
1
0
1
1
1
1
1
2
1
1
0
1
0
1
2
1
2
1
0
2
1
2
1
0
1
0
2
1
1
1
1
1
1
0
1
1
1
1
2
3
2
1
2
1
1
2
2
1
2
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
0
0
1
0
2
1
1
1
2
1
1
0
0
2
1
1
1
1
1
1
1
1
2
1
0
0
1
1
0
0
0
0
0
1
2
1
0
2
1
1
2
2
2
1
1
2
0
1
2
0
2
1
1
1
1
0
1
1
1
1
0
2
1
1
0
1
0
0
2
3
1
0
2
2
1
0
0
1
2
1
0
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
2
2
0
1
1
1
1
1
0
2
2
1
2
2
2
1
1
2
1
1
2
1
2
1
1
0
2
1
1
0
1
0
1
1
0
2
0
1
1
1
2
0
0
1
1
0
2
1
1
1
2
1
1
0
1
2
1
1
1
1
2
1
1
1
1
0
0
1
1
0
2
1
1
0
1
0
0
0
2
2
0
0
1
1
1
1
2
1
1
2
1
3
1
2
2
1
0
2
1
2
1
0
2
1
2
2
1
1
0
0
0
1
2
0
1
2
1
1
1
2
2
1
1
1
1
0
1
1
1
1
2
1
1
0
1
1
2
1
1
0
1
0
1
1
1
1
0
2
2
1
2
0
0
1
1
1
0
1
2
1
0
0
1
2
2
2
1
1
0
1
1
1
2
1
1
0
0
0
1
2
1
0
1
2
1
1
1
1
2
1
1
1
1
2
1
2
1
2
1
1
0
1
1
2
1
2
0
1
0
1
1
2
0
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
1
0
0
1
1
2
2
2
1
0
2
1
1
1
1
1
0
2
0
0
1
1
0
0
1
1
1
1
1
1
0
1
1
1
2
1
0
0
2
1
1
1
3
0
0
1
1
3
2
0
1
1
0
1
1
2
2
1
0
1
1
0
1
3
0
0
0
0
1
1
2
2
2
1
2
1
0
1
1
1
2
2
1
1
2
1
2
2
2
1
1
1
1
0
0
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
0
1
0
1
1
0
0
0
2
1
0
1
1
1
0
1
0
1
2
1
2
0
0
2
1
0
2
2
2
0
1
1
1
1
0
1
2
2
0
1
2
2
0
1
2
1
1
1
1
0
2
0
2
1
0
1
2
1
0
1
1
1
1
2
0
2
1
1
1
1
1
1
0
3
2
2
2
0
0
2
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
0
1
2
2
1
2
0
2
1
1
1
5
0
4
1
1
1
2
1
2
1
1
1
2
1
2
2
1
0
0
1
2
1
1
2
1
2
0
1
1
1
0
1
1
0
0
1
2
1
2
1
1
0
1
1
1
2
0
1
1
0
1
1
3
1
1
0
1
0
0
2
1
2
0
2
2
1
1
1
1
2
1
1
2
1
1
1
0
2
1
1
1
1
1
1
1
1
1
0
1
2
1
2
1
2
2
1
1
1
0
2
0
2
2
1
1
0
1
0
1
1
0
0
2
3
0
1
2
1
1
1
0
1
1
1
2
2
2
1
1
2
0
1
1
0
2
2
1
2
1
1
1
0
1
1
2
1
2
0
0
1
2
0
0
0
2
2
1
2
1
1
1
1
0
1
1
0
1
1
0
0
1
1
0
1
1
0
1
1
1
2
2
1
1
1
1
0
2
1
2
2
0
0
0
1
2
1
1
2
1
2
1
0
0
1
0
2
2
1
0
0
0
1
1
0
1
3
0
1
1
2
2
0
1
1
1
2
1
1
1
1
0
1
1
0
1
2
0
2
1
1
1
2
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
2
2
1
1
1
0
1
2
1
1
1
1
0
2
0
2
1
2
1
1
0
1
2
1
1
1
1
0
2
2
1
0
2
2
1
0
0
0
2
1
1
2
1
1
1
1
2
1
1
1
0
1
1
1
1
1
1
0
1
0
2
1
2
0
0
0
1
1
1
1
0
0
1
0
0
3
1
0
0
1
0
1
1
0
0
1
2
1
0
2
0
1
2
2
0
0
2
0
1
1
0
2
1
0
2
1
0
1
0
1
0
1
1
2
1
6
0
3
0
0
1
0
0
1
1
2
0
1
1
0
0
2
1
1
1
1
1
1
2
1
1
2
1
2
1
1
1
1
1
1
0
0
1
1
2
0
1
1
1
1
1
2
1
2
1
1
2
1
1
0
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
2
1
1
1
0
1
1
1
1
1
1
1
0
2
2
1
1
1
0
1
1
2
1
1
1
0
1
1
1
2
2
1
0
1
0
1
1
2
1
1
2
0
0
1
1
1
1
2
0
0
1
0
1
2
1
1
2
1
1
1
1
0
2
2
2
0
1
0
2
1
1
1
1
0
2
2
0
2
2
1
1
0
2
0
1
1
1
1
1
0
1
1
1
0
1
1
1
0
0
1
1
1
1
0
1
1
1
1
1
1
0
1
1
1
0
1
1
1
2
1
0
0
0
1
1
3
1
1
2
1
2
1
1
1
1
1
0
0
1
2
1
1
0
2
0
0
0
1
1
1
1
1
2
0
0
0
1
1
2
1
0
1
2
1
1
2
0
1
1
2
1
2
2
1
0
1
1
1
1
1
2
2
1
1
0
1
1
1
2
2
1
0
1
0
1
0
2
1
1
1
1
0
1
0
1
1
1
2
0
0
1
2
2
0
1
1
1
2
1
2
0
0
1
1
2
1
0
2
2
1
1
1
1
1
2
0
0
2
0
0
1
1
1
1
1
1
0
2
0
0
2
1
1
1
2
2
1
2
2
1
1
1
1
2
1
1
0
0
1
0
1
1
1
1
1
0
1
1
1
1
2
1
1
0
1
0
1
0
1
1
1
0
0
0
1
1
1
1
1
2
1
1
2
1
0
2
0
2
1
1
0
1
0
1
1
0
1
1
1
2
1
0
1
1
1
3
2
0
1
1
1
1
1
0
2
2
1
1
1
1
2
0
3
1
1
0
1
1
1
2
1
0
1
2
2
0
1
0
0
1
0
1
2
1
0
0
1
0
1
1
2
1
1
2
1
2
1
1
1
2
2
2
0
0
0
1
1
1
1
1
0
1
1
2
0
1
2
1
1
1
0
2
1
1
2
2
2
0
1
1
2
1
1
2
1
0
2
2
1
0
1
2
1
1
0
1
1
0
1
1
1
0
2
2
1
1
1
2
1
1
0
0
1
0
3
1
0
0
2
1
0
2
1
0
1
1
0
1
0
0
1
1
1
0
1
2
2
0
2
1
1
1
1
1
1
0
1
1
0
1
1
1
1
1
1
1
1
1
0
0
1
2
1
2
0
1
1
1
1
2
2
1
1
2
1
1
1
1
1
2
0
1
0
1
2
0
1
0
1
0
1
2
1
2
0
0
0
1
0
1
2
1
2
0
2
1
2
1
2
0
1
1
1
1
2
1
1
1
1
1
0
0
0
0
1
2
0
1
2
1
1
1
1
1
1
1
1
2
1
2
1
1
2
2
2
1
1
0
1
1
1
1
0
0
0
0
1
1
0
2
0
1
2
1
1
1
2
1
2
1
1
0
0
1
1
0
2
1
2
2
1
1
0
1
2
1
1
0
1
0
1
1
2
0
1
2
2
1
2
2
2
0
0
1
1
1
1
1
2
1
1
0
1
0
1
2
1
1
0
0
1
0
0
0
1
1
0
1
1
1
2
1
1
1
1
0
0
1
2
1
1
1
1
1
0
2
1
0
2
1
2
2
1
1
2
0
0
2
2
1
2
1
1
0
2
1
1
0
1
1
2
1
1
2
1
1
2
2
1
2
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
2
1
1
1
0
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
2
1
2
2
3
1
1
1
1
1
0
1
1
2
1
1
2
0
0
2
1
2
2
1
0
0
3
1
1
6
3
1
1
2
2
1
1
1
1
1
0
0
1
1
0
1
2
0
2
2
1
1
1
0
1
1
1
1
0
1
0
1
1
0
2
1
1
2
1
0
1
1
1
1
1
0
1
2
2
1
1
2
2
0
0
1
2
1
0
1
3
1
1
0
0
1
0
2
1
2
1
1
1
1
0
2
1
1
1
1
0
1
1
1
1
0
1
1
1
1
1
1
2
1
1
1
1
1
0
2
1
1
1
0
0
2
1
0
1
1
1
1
1
1
0
1
1
1
1
1
1
0
2
2
1
1
0
1
0
0
1
1
0
0
0
1
0
0
0
2
0
2
1
1
0
1
1
1
0
1
1
1
1
1
1
1
1
1
1
2
2
0
1
3
1
1
1
1
2
2
1
0
2
1
1
1
1
1
1
1
0
1
0
1
2
1
0
1
1
2
2
2
1
1
1
0
1
1
1
1
1
1
1
2
1
0
0
2
0
1
1
1
2
1
1
2
2
0
1
2
0
1
0
0
2
2
0
0
3
2
2
2
0
1
2
0
1
2
1
1
2
2
1
2
1
0
2
0
2
1
1
1
1
0
1
1
1
1
1
1
2
0
2
1
0
1
1
0
2
1
1
1
1
1
0
2
1
1
1
1
0
1
1
0
1
2
1
1
0
2
0
2
2
2
1
2
1
2
0
1
1
3
1
1
1
2
1
1
1
2
2
0
1
0
1
2
1
2
1
2
0
1
2
0
1
0
0
1
2
2
2
0
1
1
1
0
1
2
1
1
2
1
2
1
1
2
2
2
2
1
1
0
2
2
1
0
0
0
0
2
1
1
1
2
1
1
1
1
0
1
0
2
2
1
1
1
1
0
1
1
1
2
0
0
0
1
0
1
1
1
2
2
1
1
0
1
1
0
2
1
0
1
0
0
1
2
1
1
2
0
1
1
1
1
1
1
1
2
0
2
1
0
0
0
1
2
1
1
1
0
0
1
0
1
2
1
0
2
1
1
1
1
2
2
0
2
1
1
0
1
2
2
1
0
1
2
0
1
2
2
1
1
2
1
1
1
0
1
2
1
2
2
1
2
0
1
0
0
2
2
1
1
2
0
1
1
2
0
1
1
0
0
1
1
1
1
0
2
1
0
1
0
1
1
2
1
0
0
1
1
1
1
2
2
1
1
1
2
1
4
1
1
1
1
1
1
1
0
1
2
1
1
1
1
1
1
1
2
2
1
1
0
1
2
5
1
1
2
1
0
1
2
1
0
1
1
1
1
2
1
1
1
1
1
2
0
1
1
0
0
1
2
1
1
3
1
1
2
1
0
0
1
0
1
1
1
1
2
0
0
0
2
1
1
1
2
1
1
1
1
3
1
1
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
2
1
1
0
2
1
0
1
1
2
1
2
2
1
1
1
1
2
1
2
0
2
1
2
2
1
1
1
1
1
2
1
3
1
1
1
1
2
1
1
1
1
1
1
1
1
1
0
2
3
1
1
0
1
0
1
2
0
2
0
0
0
2
2
1
1
1
1
1
2
1
0
2
1
1
2
1
1
2
2
1
0
2
2
1
2
1
0
1
1
0
1
1
1
2
1
1
1
0
2
1
1
1
1
2
2
1
5
1
1
1
1
0
1
1
0
1
0
1
1
2
1
2
2
0
0
1
1
1
0
1
0
1
1
2
0
1
1
1
1
1
1
1
1
0
0
1
2
2
1
1
0
1
2
1
1
0
1
1
2
0
0
2
0
2
1
2
1
2
1
0
1
2
1
2
2
1
1
1
0
1
0
0
0
0
2
0
2
1
0
1
2
2
1
1
1
1
1
1
1
2
2
0
2
1
1
0
0
1
1
2
1
1
1
1
0
1
1
1
1
0
1
1
1
2
1
1
2
2
0
0
1
2
1
1
1
2
2
1
1
1
1
1
1
2
1
0
1
2
1
1
1
1
0
1
1
0
0
1
0
1
1
1
1
1
1
2
1
0
2
2
1
0
0
1
1
1
0
1
2
0
1
0
2
2
2
1
0
1
0
1
1
1
0
2
1
1
1
2
1
1
1
1
1
0
1
0
1
2
1
1
1
0
1
1
1
2
1
1
2
2
1
1
2
0
1
1
1
1
1
1
0
0
1
1
1
0
0
0
0
1
1
2
2
1
1
0
0
1
1
2
1
1
0
0
1
0
0
0
1
1
0
2
0
2
0
1
2
1
1
0
1
1
0
2
2
1
1
2
2
0
1
0
1
0
2
2
1
1
1
1
2
2
1
1
1
1
2
0
1
0
0
1
0
2
0
3
0
1
0
1
1
1
1
1
0
3
1
0
3
2
0
2
2
2
2
0
0
1
0
2
2
0
1
1
0
1
1
0
1
2
1
1
0
1
1
1
1
1
2
2
1
0
0
2
0
0
1
0
2
1
1
0
1
2
0
1
1
1
1
0
0
1
1
1
1
2
1
1
1
1
1
1
3
1
1
1
2
0
1
1
0
2
0
2
1
1
0
1
0
1
0
0
1
1
1
2
1
0
2
0
2
0
1
1
1
1
0
1
0
1
1
0
1
0
1
1
0
2
1
1
3
2
4
1
1
1
0
1
1
2
2
1
1
1
1
0
0
2
1
0
1
0
2
2
2
3
1
1
0
1
2
1
0
1
1
2
0
0
2
1
1
1
1
1
0
1
2
1
1
1
1
1
1
0
1
1
2
2
0
1
1
2
2
2
0
2
0
1
1
1
1
1
2
0
2
0
1
2
1
1
1
1
1
1
1
0
1
1
1
0
1
0
0
1
1
1
1
1
0
1
1
3
1
2
1
1
2
1
1
1
1
0
1
1
0
1
1
1
0
0
1
1
1
0
1
1
0
1
1
1
1
1
0
1
1
1
1
1
2
1
1
0
1
2
0
1
3
1
1
1
1
0
4
1
0
2
1
1
2
1
2
1
1
1
0
2
1
0
0
3
1
1
2
1
1
2
1
0
2
1
1
0
1
1
0
1
1
2
0
1
1
1
2
1
0
1
0
1
1
2
0
1
1
1
1
1
0
1
1
1
1
1
1
1
1
0
1
1
0
1
1
1
1
1
1
1
0
1
1
1
2
1
1
0
1
2
0
1
1
2
1
2
2
1
2
1
1
1
1
1
1
2
1
2
0
1
1
1
1
1
1
0
0
2
0
1
2
0
1
0
0
0
0
1
1
0
0
0
1
2
0
0
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
0
1
3
0
2
0
2
1
0
2
0
1
1
0
0
1
0
5
2
1
1
1
2
1
1
1
1
2
1
2
1
2
2
2
1
2
1
1
1
1
2
1
1
2
0
1
1
0
2
0
1
1
1
2
1
1
1
1
1
1
0
0
1
1
1
0
1
1
1
1
2
2
2
2
1
1
1
1
2
0
1
1
1
2
1
2
1
1
1
1
1
1
0
1
1
1
1
0
2
0
0
1
1
0
1
1
1
1
1
0
1
0
1
2
1
1
2
2
1
1
1
1
0
0
2
1
1
1
1
1
1
1
2
1
1
0
1
1
1
1
1
0
1
0
0
1
0
0
1
1
2
0
1
1
2
2
1
2
1
1
1
2
0
1
2
0
1
2
1
0
8
1
0
1
2
0
1
1
1
0
1
1
2
3
0
0
1
1
1
2
1
0
2
1
1
0
1
1
0
0
1
1
1
1
2
2
1
1
1
0
1
1
0
0
0
2
2
4
1
1
1
1
1
2
1
1
1
1
1
0
1
1
1
0
1
1
1
1
1
0
0
0
1
2
1
1
1
1
1
0
2
1
1
1
1
0
1
1
1
0
2
1
0
1
1
1
1
1
1
1
2
1
1
0
2
2
1
0
1
1
0
1
0
1
1
2
2
1
1
1
0
2
1
0
2
1
1
1
1
0
1
1
0
1
2
1
1
1
1
1
1
1
1
0
1
1
1
2
2
2
1
1
0
1
2
1
0
1
1
1
1
0
1
1
2
1
1
0
1
0
0
2
0
0
1
1
2
1
0
1
2
1
1
0
1
1
1
1
0
0
1
1
1
1
0
1
4
2
1
2
2
2
0
1
0
1
1
2
1
1
0
1
1
0
2
0
1
1
1
0
1
4
3
1
1
0
0
1
2
1
2
1
1
2
1
2
1
1
2
0
1
1
2
1
0
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
0
2
1
1
1
1
0
4
1
2
1
1
1
1
1
1
1
1
0
1
0
1
0
1
1
1
2
1
0
1
1
1
1
0
0
1
1
0
1
1
1
1
1
1
0
1
2
1
0
1
1
2
0
2
1
1
0
0
0
0
0
1
0
1
2
2
2
2
2
0
1
1
2
1
1
0
1
1
1
2
2
1
2
2
1
2
0
2
1
1
0
1
0
1
0
1
2
2
1
0
1
1
0
0
2
2
1
2
1
1
1
2
1
1
1
1
1
1
2
1
2
0
1
1
0
0
1
1
0
1
0
0
0
1
1
1
2
2
0
1
1
1
2
0
0
0
1
1
0
0
1
1
1
1
0
1
0
2
1
1
2
2
1
0
0
2
0
0
0
1
1
2
1
0
1
1
1
2
1
4
1
1
1
2
1
1
2
0
2
1
1
0
1
1
0
2
2
1
1
1
1
1
2
1
1
0
1
1
2
0
2
1
1
1
1
1
1
1
0
1
0
0
0
0
0
1
2
1
2
1
1
2
1
0
1
1
1
2
1
2
1
1
2
0
1
0
3
1
1
1
1
2
1
1
1
1
1
2
1
0
1
1
0
2
2
1
0
1
1
1
0
1
1
1
1
2
2
2
1
1
1
1
0
2
0
2
2
2
2
2
1
2
0
0
1
0
1
2
0
1
0
1
0
0
2
1
1
2
2
1
1
0
1
1
1
1
0
0
0
0
1
1
2
1
0
1
1
1
3
0
1
1
1
2
0
0
1
1
1
1
1
2
1
0
2
2
2
1
1
2
2
2
0
2
2
1
0
2
1
0
0
1
1
1
1
1
1
5
1
1
1
2
2
1
1
1
1
0
0
1
1
0
1
0
1
1
2
0
0
0
1
2
1
1
0
1
0
1
0
1
1
0
1
2
0
2
1
2
1
2
1
1
2
0
1
2
1
3
2
0
1
1
0
0
0
1
1
1
3
1
0
1
1
2
0
1
2
0
1
0
2
1
2
1
0
1
0
1
0
1
2
1
1
0
1
0
1
1
1
2
0
0
0
1
2
2
1
1
1
1
1
0
0
1
2
1
1
1
1
2
1
1
0
1
2
2
0
1
0
2
0
0
1
2
1
0
0
1
0
2
1
0
2
0
2
1
0
1
1
2
2
1
2
2
1
2
2
0
0
1
1
2
2
2
2
0
1
1
0
0
3
2
1
2
1
2
0
1
2
2
1
1
0
2
2
2
0
1
1
1
0
1
2
1
0
2
1
1
0
1
2
1
1
2
1
1
1
2
2
1
1
2
0
2
0
2
2
1
2
2
2
1
1
2
1
0
1
2
1
1
0
2
1
1
0
0
1
2
1
1
1
0
1
0
0
0
0
1
0
1
1
0
1
1
2
1
0
1
2
0
2
2
0
0
1
0
1
1
1
0
1
2
1
0
1
2
2
1
2
1
2
1
0
1
0
2
0
1
1
1
1
0
2
1
2
2
1
2
1
2
1
1
0
1
1
2
2
1
1
1
2
1
2
2
1
0
0
2
0
1
1
2
1
1
0
1
0
1
2
1
0
1
0
1
1
0
1
1
0
1
1
0
1
0
1
1
1
1
1
1
1
1
1
1
0
1
0
1
0
1
1
0
2
2
1
1
1
2
0
0
1
0
2
1
1
0
2
0
2
1
1
0
1
2
1
2
1
2
1
1
0
1
0
0
1
1
1
2
1
1
1
2
1
1
0
2
0
2
2
2
2
0
0
1
1
1
1
0
1
0
2
2
1
1
2
1
1
0
1
0
0
1
1
0
1
0
1
1
1
1
0
0
1
2
1
1
1
1
1
1
1
1
2
2
1
0
1
1
2
2
0
1
1
1
1
0
1
1
0
1
1
0
0
1
3
0
1
1
1
0
1
1
1
1
0
0
1
1
1
1
0
1
2
2
1
1
2
1
0
1
0
1
0
0
1
1
2
1
0
1
2
1
1
1
0
2
2
1
1
0
0
2
1
1
1
0
4
1
0
0
1
1
0
1
2
2
0
1
2
2
0
1
1
1
1
2
1
0
1
1
3
1
0
2
2
0
1
1
2
1
1
1
0
0
1
2
0
1
1
1
0
1
0
1
2
1
1
0
1
1
1
1
2
1
0
2
0
1
1
1
0
2
1
2
1
2
1
0
1
2
0
1
2
1
1
0
0
1
1
0
1
1
1
2
1
2
1
2
1
1
2
1
1
1
0
2
1
2
1
0
1
1
0
2
1
1
0
2
1
0
0
1
1
1
2
1
1
1
1
2
1
2
2
1
1
0
1
1
1
1
1
1
0
2
1
1
1
2
2
1
1
1
0
1
1
0
1
0
0
1
2
2
1
1
1
0
2
0
2
1
0
1
1
1
0
1
2
0
1
1
1
1
1
0
0
0
2
1
1
0
1
0
1
1
0
1
2
2
1
1
1
1
1
1
1
0
1
2
1
2
1
2
1
2
0
0
1
2
1
1
1
1
2
1
2
2
2
1
2
0
1
2
1
1
2
2
1
0
2
0
1
0
1
0
0
1
1
2
2
1
1
1
2
1
0
1
1
0
1
2
1
1
1
1
2
0
1
0
5
0
2
1
1
1
2
2
2
0
1
1
1
2
1
0
2
0
2
2
1
2
0
1
2
1
2
0
1
1
1
1
2
1
0
1
1
0
2
1
1
1
1
0
2
2
2
1
2
1
1
1
1
1
1
1
1
1
0
1
1
0
1
2
0
1
2
2
1
1
1
1
0
2
1
1
0
1
0
0
1
1
1
2
1
2
1
1
1
1
1
1
0
0
1
2
1
0
2
0
1
3
2
1
1
1
0
2
0
2
0
2
1
1
1
1
2
2
2
1
2
1
0
1
1
1
1
0
1
2
1
1
1
2
0
0
1
1
1
1
1
0
1
1
1
1
2
2
1
1
1
1
1
2
1
1
1
1
1
1
0
1
0
1
1
2
2
2
1
0
0
2
0
1
1
1
2
1
0
1
0
0
1
1
1
1
2
2
1
2
2
1
0
1
0
2
0
0
2
0
1
1
1
1
1
1
1
1
9
1
1
1
1
2
2
1
1
2
0
1
1
1
2
1
2
1
1
1
0
0
2
2
1
0
3
1
1
0
1
0
2
0
2
0
1
2
2
1
1
0
1
0
1
0
1
1
1
1
0
2
2
1
2
1
1
1
1
1
1
1
2
1
0
1
1
1
1
1
1
1
3
1
1
0
0
1
1
0
1
1
1
1
1
1
2
0
1
1
2
1
1
1
1
1
0
1
0
1
1
0
1
1
1
1
1
1
0
2
1
2
0
2
1
2
1
2
1
2
1
0
2
1
1
1
2
1
0
1
1
1
1
1
2
2
1
2
0
1
0
1
1
1
1
1
1
1
0
0
1
2
0
0
1
1
0
1
1
1
1
0
0
1
1
2
0
0
1
1
1
0
1
0
1
2
1
0
0
0
2
2
1
1
1
1
1
0
1
1
1
0
1
0
0
0
2
2
0
1
1
1
1
1
0
1
0
0
2
1
1
1
1
1
2
0
2
1
0
1
0
1
1
2
1
0
1
1
1
1
1
1
1
0
0
2
0
2
2
0
1
1
1
2
1
1
1
0
1
2
1
1
2
2
1
1
2
1
0
2
2
0
2
0
0
1
0
0
0
1
1
0
1
1
1
1
1
1
1
1
1
1
2
1
0
1
2
1
1
1
2
1
2
0
1
2
0
0
1
2
1
1
2
2
1
0
2
1
2
1
1
1
0
1
2
2
0
1
1
0
1
1
2
1
0
1
0
1
1
0
2
1
1
1
1
0
1
0
2
0
2
1
2
1
1
2
2
2
1
1
1
1
1
2
2
1
2
0
1
1
2
1
1
1
1
1
1
1
1
1
1
0
0
1
1
1
1
1
1
1
2
1
3
0
0
1
1
1
0
1
1
1
2
1
2
1
1
0
2
2
0
3
1
1
5
1
0
2
1
1
0
1
2
2
1
0
1
1
2
1
1
1
2
1
1
1
1
2
1
2
1
1
1
2
1
2
1
0
0
2
0
1
1
0
1
0
0
0
1
2
0
0
1
1
1
2
0
0
1
1
1
0
1
0
2
0
0
1
2
1
0
2
1
0
0
0
1
1
1
2
1
2
1
0
2
1
2
0
0
1
1
2
1
1
2
0
2
1
1
2
1
1
0
1
2
1
1
0
2
2
2
1
1
0
1
0
1
1
0
1
1
2
2
2
1
2
1
0
1
2
0
1
2
1
2
0
1
2
2
1
1
1
0
1
2
2
1
2
1
1
0
0
1
0
0
1
2
0
1
0
1
1
0
3
1
1
0
1
0
0
1
1
2
2
1
2
1
0
1
1
1
1
0
2
2
1
1
1
1
2
2
2
1
1
1
1
1
2
2
1
1
1
0
1
0
1
2
2
1
2
2
0
2
1
2
1
1
1
2
1
0
1
1
1
1
1
1
1
0
1
1
2
1
2
1
2
1
1
1
1
0
1
1
1
1
1
1
1
2
1
1
1
1
2
0
0
0
1
0
2
2
1
1
1
1
0
0
1
2
1
1
2
2
1
0
0
1
1
1
1
2
1
2
2
2
1
1
0
1
0
1
0
0
0
1
0
2
1
1
2
2
1
1
1
3
1
2
2
1
1
1
1
2
2
2
1
1
1
2
1
1
1
0
1
1
2
2
1
2
2
1
0
1
2
1
1
1
2
1
2
1
1
0
0
1
1
2
1
0
1
2
1
1
1
0
1
2
1
1
1
0
0
1
1
2
1
2
2
2
2
1
0
1
1
0
1
2
1
1
1
1
0
1
1
2
1
2
1
1
2
2
1
1
1
1
0
0
2
0
1
1
2
1
0
0
1
0
0
0
2
2
1
1
0
0
0
2
1
2
1
2
1
1
2
1
2
1
0
1
1
2
2
1
0
2
0
2
1
1
0
0
1
4
1
0
0
1
2
1
1
2
0
1
2
1
1
1
1
1
2
1
0
2
0
2
1
1
1
1
1
1
0
1
1
1
3
1
1
1
0
1
1
1
1
1
0
1
1
0
2
1
1
1
2
1
2
1
2
1
2
1
1
1
2
1
1
0
1
1
2
2
1
1
1
0
2
1
2
2
2
1
0
1
0
0
0
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
0
0
1
1
2
1
0
0
0
3
0
1
0
2
1
2
1
1
1
1
1
2
1
1
1
1
0
0
1
1
0
1
2
2
2
1
2
2
3
1
1
0
2
1
1
0
0
2
1
1
0
0
1
1
1
1
0
1
2
1
2
1
1
0
0
0
0
0
2
1
2
1
0
0
2
0
2
1
2
1
0
1
2
1
1
2
1
1
2
1
1
1
1
1
0
0
1
1
0
3
1
1
0
0
2
1
1
1
1
2
1
1
0
1
2
1
0
2
0
2
2
1
1
1
2
2
1
1
1
2
0
0
1
1
1
1
0
2
1
1
0
1
2
1
1
1
1
2
1
2
2
0
0
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
3
0
1
0
1
0
2
2
0
0
1
1
0
2
2
2
1
0
2
0
0
0
1
1
2
1
1
1
1
2
2
1
1
1
1
1
1
0
1
0
2
1
1
1
2
1
0
1
1
0
1
0
1
1
1
1
1
1
1
2
0
1
0
3
1
1
0
1
0
2
1
2
1
1
1
1
1
2
2
0
1
1
1
1
2
0
2
1
0
2
0
1
0
0
0
1
2
1
0
1
2
2
1
1
2
1
2
2
0
6
1
1
3
1
1
2
2
1
1
1
1
1
1
1
1
0
1
0
1
1
1
1
1
1
1
0
1
0
1
0
2
1
1
1
2
0
0
0
0
1
1
2
0
1
1
0
2
0
1
1
1
0
1
2
1
1
2
1
0
1
1
1
0
1
1
0
0
1
1
1
2
1
1
1
1
2
1
2
1
0
0
1
0
2
2
2
0
1
0
2
1
2
2
1
0
2
1
1
1
1
1
2
2
1
1
1
1
0
2
1
2
1
0
1
1
1
2
0
2
1
0
1
1
1
2
1
2
1
2
1
0
0
0
2
1
1
1
1
0
1
1
1
2
1
2
1
3
1
0
1
1
2
1
0
1
0
1
1
1
1
1
1
1
2
2
1
1
1
0
1
1
1
1
1
1
0
1
2
2
0
1
2
0
1
2
1
0
2
1
2
1
1
2
2
0
1
1
1
1
1
2
2
1
0
1
1
4
1
0
1
1
2
1
0
1
1
2
1
1
0
1
2
3
0
1
1
1
0
2
1
1
1
0
2
2
0
2
1
2
2
1
1
1
0
1
1
0
0
1
1
1
2
1
2
0
1
1
1
1
0
1
0
1
0
0
1
2
1
1
1
1
2
0
1
1
1
1
1
1
2
2
1
0
1
1
1
1
0
2
3
1
0
0
2
2
0
1
1
2
2
1
2
0
1
0
1
0
1
1
0
1
1
1
0
1
1
1
0
1
1
2
1
1
1
1
1
1
1
1
2
1
0
2
1
0
1
0
1
1
1
2
1
1
1
0
1
1
1
0
1
2
1
1
2
2
1
0
0
1
1
0
1
1
1
1
1
1
1
0
2
2
1
1
2
1
0
1
1
1
0
1
1
2
1
1
1
2
1
2
0
1
1
1
1
2
1
0
2
1
1
1
2
2
1
1
1
2
2
3
1
2
1
1
0
1
1
1
2
0
2
1
0
1
0
1
2
1
0
1
0
0
1
1
1
1
1
0
1
1
1
2
0
1
1
1
1
1
1
1
4
0
2
1
1
0
1
1
1
1
2
1
2
1
1
0
1
1
0
0
2
0
0
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
0
0
2
1
1
0
0
1
1
1
1
2
1
2
2
1
1
2
1
0
0
1
1
0
1
0
1
1
1
2
0
1
0
1
1
1
1
1
3
2
0
2
1
1
1
0
0
1
1
2
0
1
1
1
0
1
0
2
1
1
1
2
1
1
1
3
2
2
1
0
2
1
0
1
2
1
1
0
0
1
1
2
0
1
1
2
1
0
2
1
2
0
1
1
0
1
0
1
2
1
1
2
1
1
1
1
1
1
2
2
1
2
1
1
0
1
1
2
2
2
2
1
1
2
1
1
2
0
1
0
2
0
1
1
1
0
2
1
1
1
1
2
2
1
1
1
0
1
2
0
1
0
2
0
0
0
1
2
2
1
1
1
1
1
0
2
2
2
2
1
0
2
0
2
2
1
1
1
1
2
0
2
0
0
1
1
0
2
1
2
0
1
1
1
1
2
2
1
1
1
2
1
2
2
1
1
0
1
1
0
2
1
1
2
2
1
1
2
1
0
1
0
1
1
2
1
1
2
1
0
2
1
2
1
2
1
0
1
1
2
1
2
1
1
1
1
1
2
2
2
0
1
1
1
0
2
0
1
1
1
0
1
2
2
1
1
0
1
2
1
0
1
1
2
1
1
0
1
1
1
1
1
1
3
1
2
0
1
1
1
2
1
0
1
0
2
1
2
1
0
1
2
2
1
1
2
1
1
2
0
0
0
0
0
0
0
1
1
0
2
1
1
1
2
1
0
1
1
0
1
2
0
0
0
2
1
0
1
2
1
1
1
2
1
1
0
2
0
1
1
2
1
1
1
2
0
1
1
1
1
3
1
0
0
2
4
1
2
1
2
1
1
1
1
1
2
0
0
1
1
1
1
1
2
0
1
1
1
1
0
1
2
0
1
1
0
1
0
2
2
2
2
1
0
1
1
1
2
1
2
0
1
1
0
1
2
2
1
0
2
1
1
2
1
1
2
2
0
0
2
2
1
0
1
0
1
1
0
0
1
0
2
1
1
0
2
1
1
0
1
1
1
0
1
1
1
1
1
1
1
1
0
1
1
2
0
1
1
1
1
0
0
0
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
2
1
1
2
1
4
1
2
2
1
1
0
1
0
1
0
2
1
0
2
1
1
2
0
0
0
1
1
0
1
0
1
1
2
1
1
0
1
1
1
1
1
1
1
2
1
1
0
1
0
0
1
2
1
1
1
1
2
1
0
0
1
1
1
2
1
1
4
1
1
2
0
1
1
1
1
2
1
1
2
0
2
1
1
1
0
1
1
1
1
1
1
1
1
2
0
1
1
2
0
1
1
1
0
2
1
2
2
2
1
0
1
1
1
2
1
1
1
1
0
0
0
0
1
2
1
1
1
1
1
1
0
0
1
1
1
1
1
1
1
0
2
1
1
1
1
2
1
2
1
3
1
1
2
1
2
0
0
1
2
0
0
0
1
2
0
1
1
0
1
0
1
2
1
1
2
1
2
1
0
0
1
2
0
1
1
0
0
1
1
2
1
0
1
3
1
1
1
0
1
1
1
1
0
1
1
0
1
1
2
0
0
1
0
1
1
2
2
1
1
2
2
1
0
1
0
0
0
0
1
0
1
2
1
2
0
1
1
1
2
1
0
1
2
1
1
1
1
1
1
1
1
1
0
2
1
2
2
1
2
1
0
1
1
1
1
0
2
1
1
1
0
0
1
1
0
2
0
1
1
1
1
2
0
2
0
1
2
1
1
0
2
0
0
1
1
2
1
1
0
1
1
1
1
1
0
1
1
1
1
0
2
1
0
0
1
1
0
1
1
1
2
1
0
1
1
2
2
1
0
2
0
0
2
1
1
2
1
3
1
0
1
1
1
1
2
0
2
2
1
2
2
1
2
0
1
2
0
2
1
1
2
0
2
1
2
1
0
1
1
1
1
1
1
1
1
1
2
2
1
0
1
1
0
1
1
0
2
1
0
0
1
2
1
0
0
2
0
1
3
1
1
0
1
1
1
1
2
1
2
1
1
1
1
0
0
0
1
1
1
2
2
1
1
1
0
1
1
1
0
1
1
1
1
1
1
2
1
2
1
1
2
0
1
2
2
2
0
0
0
1
1
1
0
1
1
1
1
1
1
0
0
0
2
0
1
1
1
2
1
2
1
0
0
2
1
1
1
1
0
1
1
0
1
1
0
1
2
0
2
2
1
2
1
1
1
1
2
1
2
1
2
1
2
0
1
0
0
1
1
0
0
3
2
0
2
1
2
1
0
0
2
1
0
0
1
0
1
1
1
1
0
2
2
1
1
2
2
0
2
1
2
0
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
0
1
1
1
1
0
1
2
2
2
2
0
1
1
1
1
2
1
0
2
1
0
2
2
0
0
0
0
1
1
1
0
2
2
2
0
0
1
2
0
2
2
1
1
2
0
0
0
0
1
1
1
1
2
0
2
1
0
0
1
1
1
1
0
2
1
0
1
0
1
0
0
1
1
1
2
1
1
2
0
1
2
1
1
1
1
1
1
1
1
1
0
0
1
0
1
1
2
1
1
1
0
1
0
0
1
1
1
1
2
0
4
3
1
1
0
0
2
2
2
2
1
1
2
2
1
1
0
1
2
3
0
1
0
1
2
0
2
2
0
2
1
1
1
1
1
2
1
0
1
0
0
3
0
1
2
2
1
2
1
0
1
1
1
0
1
2
0
2
1
1
1
0
2
1
3
2
1
1
0
2
2
1
1
1
1
1
1
2
1
3
1
1
0
1
2
2
1
1
1
1
0
1
1
0
3
1
1
3
2
1
1
0
2
0
0
1
2
1
2
1
0
1
1
0
2
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
0
2
1
0
2
1
2
2
2
1
1
1
1
1
2
1
1
1
2
2
1
1
0
1
1
1
1
2
1
1
2
1
1
2
1
1
0
0
1
2
2
1
1
1
0
1
2
0
1
0
1
2
1
0
1
2
3
2
2
1
2
2
0
1
0
0
1
2
2
2
0
1
1
1
1
1
0
1
1
1
1
1
2
2
1
0
2
1
2
2
1
0
1
2
1
2
1
1
1
1
0
1
1
2
0
2
1
1
1
1
1
2
1
1
1
1
0
1
1
1
1
0
0
2
1
1
1
0
0
0
1
2
1
0
1
1
0
1
1
2
0
0
1
1
1
1
1
0
1
1
0
0
1
0
1
0
1
2
1
0
1
2
0
2
2
0
2
1
2
2
0
1
1
1
2
1
1
1
1
0
1
0
1
2
1
1
2
1
1
1
0
1
1
0
0
1
1
0
0
3
1
2
2
2
1
1
0
1
0
1
1
1
1
1
0
1
0
2
1
1
1
0
1
1
2
1
1
1
1
0
1
2
1
1
1
1
0
1
2
1
1
2
1
2
2
2
1
0
1
1
2
1
1
2
0
1
0
1
1
1
0
2
0
1
1
1
1
2
1
1
0
2
1
1
0
1
1
1
1
0
1
2
0
2
2
1
2
1
0
0
1
1
2
1
1
0
2
1
1
2
1
1
1
2
1
1
0
0
2
1
0
2
0
1
1
1
1
0
1
2
0
1
1
1
2
1
3
2
0
2
1
1
1
0
2
1
1
0
1
0
1
0
2
1
1
0
6
1
1
0
2
0
1
1
1
1
1
0
2
1
0
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
2
2
1
1
0
1
1
1
2
0
2
1
1
1
0
1
1
1
2
1
2
2
1
0
0
0
1
0
0
2
1
0
1
2
1
2
1
1
1
0
1
2
0
0
1
2
0
2
1
2
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
2
2
2
1
1
1
1
0
1
1
1
2
0
0
2
0
2
1
1
2
1
2
1
2
0
2
1
2
0
0
0
1
1
1
2
1
0
2
2
1
0
0
1
1
0
1
2
0
0
1
1
1
1
2
1
1
0
1
0
0
2
1
2
1
1
0
1
2
1
1
1
1
1
1
2
1
1
2
0
0
0
1
1
1
2
2
2
1
1
2
1
1
1
1
1
0
1
1
1
0
1
1
0
0
1
1
0
1
2
2
1
1
2
0
1
2
2
1
1
1
1
1
1
1
0
1
0
1
2
1
1
1
0
2
0
2
1
1
1
1
0
0
1
0
0
2
1
1
1
1
2
1
1
2
0
1
1
0
0
0
1
2
1
1
2
0
5
0
1
0
0
1
1
1
1
1
1
1
1
2
1
0
2
1
2
1
0
1
1
1
2
1
0
1
0
1
0
1
0
1
2
1
0
2
0
2
1
0
2
1
1
1
2
1
2
1
2
1
1
0
2
0
1
2
1
3
1
0
0
1
1
1
1
2
1
1
2
2
1
2
2
2
2
1
0
0
1
1
1
1
0
2
1
1
0
1
2
1
2
0
1
1
0
2
1
1
1
1
1
2
2
1
1
1
0
1
1
1
0
0
2
1
2
1
1
1
1
1
1
1
1
2
3
2
1
1
1
2
1
1
1
1
1
1
0
2
1
1
1
2
1
2
1
1
2
0
1
1
0
0
2
2
2
1
2
2
0
0
1
1
2
0
1
1
1
0
1
1
0
1
0
1
1
1
2
2
1
0
0
1
1
1
1
1
1
1
0
0
0
1
1
0
2
1
2
1
1
2
1
2
1
1
2
1
2
2
2
0
0
1
1
0
2
2
1
2
2
1
1
1
1
1
1
1
2
1
1
0
0
1
1
1
1
1
1
0
1
0
2
2
1
1
0
1
1
2
0
2
1
1
1
1
1
1
0
2
0
1
1
1
1
0
2
2
2
2
1
2
1
2
0
2
1
0
2
0
1
2
1
2
1
1
1
2
1
2
2
1
1
1
1
2
1
1
1
1
2
1
3
2
0
1
0
1
0
2
1
2
1
0
2
0
0
1
0
1
1
0
1
1
1
2
1
0
2
1
2
0
1
1
2
1
0
0
1
1
2
1
1
1
1
2
0
1
1
0
2
0
1
1
1
1
1
1
1
1
2
0
0
1
0
1
1
0
1
1
2
0
1
0
1
0
1
0
1
0
2
2
2
1
0
3
1
2
1
1
2
1
1
0
1
2
3
1
2
1
1
0
1
1
0
1
2
0
1
0
0
1
0
1
1
1
1
1
0
0
0
1
1
2
1
1
1
1
1
1
2
0
1
1
1
1
0
0
2
3
1
1
0
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
2
2
2
2
1
2
1
1
1
1
2
2
2
0
1
1
0
1
0
1
0
0
1
2
0
1
1
2
1
2
1
1
2
1
1
2
0
0
2
1
1
1
1
0
0
2
1
1
1
1
2
0
1
1
1
2
1
1
0
1
1
1
1
1
1
1
1
1
0
3
0
1
1
1
0
1
1
1
1
2
2
2
1
2
1
1
1
0
0
1
1
1
1
1
0
0
1
1
1
1
1
1
0
1
1
1
1
2
1
10
2
2
1
1
2
1
4
1
1
1
2
1
1
1
2
1
1
0
2
0
1
1
1
1
2
1
1
2
1
1
2
0
1
1
1
0
0
1
0
0
0
0
1
0
0
0
1
4
1
1
2
1
1
1
2
4
1
1
1
1
1
1
1
1
1
2
1
0
1
1
0
1
0
1
1
2
2
1
1
1
2
0
2
2
1
1
0
1
1
1
1
0
1
1
0
2
2
0
0
1
0
0
1
1
1
2
0
0
1
1
0
1
1
1
1
2
1
1
0
1
1
2
2
1
1
1
0
1
1
1
3
2
1
0
1
1
1
0
1
1
2
2
0
0
1
1
1
1
0
0
1
0
2
2
1
0
0
0
1
1
1
1
0
0
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
2
2
2
0
1
2
1
1
0
1
2
1
1
1
0
1
1
2
0
1
2
1
1
1
0
1
1
0
1
1
1
2
2
1
0
1
1
0
1
0
1
1
1
1
0
1
1
1
4
0
1
1
1
1
1
2
1
0
2
0
1
1
2
0
1
0
0
1
2
0
0
1
2
0
2
2
2
1
1
1
0
2
3
1
2
1
1
1
1
1
2
2
2
0
0
0
1
2
1
1
0
1
1
2
0
0
0
2
1
2
1
2
2
1
1
3
1
1
1
1
1
1
1
0
1
1
2
1
2
0
1
2
0
1
1
0
1
1
1
1
1
0
2
1
1
1
2
1
1
0
1
2
0
1
1
1
1
1
1
1
1
1
0
0
1
2
1
2
2
0
0
1
2
1
2
1
1
1
2
2
2
2
1
0
1
1
2
1
1
1
2
2
0
1
0
2
0
2
1
2
2
1
3
1
0
1
1
0
1
1
2
1
1
0
2
2
1
1
2
0
1
1
0
1
1
1
0
1
1
1
0
2
1
1
1
1
0
2
2
0
1
1
1
1
2
1
0
0
1
1
0
0
3
2
0
0
2
1
1
1
1
1
1
1
1
0
2
1
1
1
1
0
2
0
1
1
2
2
1
2
2
0
0
1
2
1
1
1
1
1
1
1
0
1
3
2
1
1
0
1
1
1
0
0
2
1
1
1
0
1
1
1
1
0
1
1
1
1
1
0
2
0
1
1
1
1
2
1
0
0
1
1
0
1
3
1
1
0
2
2
1
2
0
1
1
0
0
2
2
1
1
0
0
1
2
0
1
2
0
1
2
1
1
1
0
1
2
2
1
1
0
1
1
2
0
1
1
1
0
0
0
2
1
1
1
0
1
0
2
0
1
0
2
1
1
1
1
1
2
1
0
1
1
0
1
2
0
1
1
1
2
1
1
2
1
1
1
0
0
2
0
2
2
1
2
1
2
0
2
1
0
1
1
1
1
1
2
0
0
1
1
1
1
1
2
2
0
1
1
1
1
0
1
1
1
0
1
2
0
3
1
1
1
1
0
1
1
2
1
2
1
0
1
1
1
3
1
1
1
2
3
0
1
1
1
1
1
1
0
1
1
1
1
1
1
1
0
1
1
1
1
2
1
1
1
1
0
2
2
2
2
1
1
1
1
1
2
0
0
1
2
1
2
0
1
0
1
1
1
1
0
2
2
1
2
2
1
1
1
2
0
2
1
1
1
2
0
2
2
1
1
1
1
1
0
1
1
1
0
2
1
2
1
1
1
1
0
1
0
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
1
0
1
1
0
1
2
1
1
1
1
1
0
2
1
0
2
1
1
0
1
0
1
0
1
1
1
1
0
1
0
2
1
2
1
1
2
0
1
0
0
1
1
1
0
1
1
2
1
2
1
1
1
1
0
1
1
2
1
1
2
0
2
0
1
1
2
1
2
0
2
1
2
0
0
2
1
1
1
1
1
2
1
1
1
0
1
2
1
1
0
1
1
1
1
2
1
1
1
2
0
2
1
0
1
0
1
0
0
0
1
1
2
1
1
1
0
2
1
0
2
1
0
2
2
2
2
2
2
1
0
1
2
2
1
1
1
1
1
2
2
1
1
0
0
1
1
1
2
0
0
6
1
0
1
1
1
1
0
1
1
1
2
2
1
1
1
2
1
1
1
1
2
2
1
1
1
0
0
1
1
1
2
2
1
1
2
1
0
2
2
1
1
1
1
1
0
0
0
1
1
1
1
2
1
1
0
0
1
1
1
1
1
0
1
1
1
1
4
0
1
1
2
1
1
2
1
1
1
0
1
2
0
1
1
1
2
1
1
0
2
2
2
2
2
1
1
1
1
2
1
1
2
2
2
0
1
1
0
1
1
1
1
1
1
1
1
0
1
1
2
1
0
1
1
1
2
1
1
1
1
0
1
0
0
1
1
1
1
1
1
0
1
2
0
1
1
2
1
1
0
1
1
1
2
1
0
1
0
1
1
1
2
1
1
1
0
1
1
0
0
1
0
1
0
1
1
0
1
1
2
1
1
1
0
2
1
0
0
1
1
1
1
2
1
1
1
2
1
1
1
0
2
2
1
0
2
1
1
0
0
1
2
1
0
1
1
0
1
0
1
1
1
1
1
1
1
0
1
1
1
1
1
0
1
1
0
1
1
1
2
2
2
1
2
2
0
2
1
1
3
2
1
1
0
1
0
0
1
2
1
1
1
1
1
0
1
1
1
2
2
0
2
3
0
1
1
0
0
0
1
1
1
1
0
2
1
2
0
1
2
1
1
1
1
1
0
0
1
1
1
1
1
0
1
2
1
1
0
2
1
1
1
0
1
1
1
2
0
1
1
2
1
0
1
1
0
1
1
2
2
1
1
0
2
1
2
1
0
1
1
1
1
1
2
1
1
1
1
2
0
1
0
2
1
1
1
1
0
0
1
1
1
0
1
0
0
1
1
1
0
1
2
1
0
0
2
1
1
2
1
1
1
1
2
1
0
1
2
1
2
1
2
2
2
1
1
1
0
0
1
2
0
1
0
2
0
1
1
1
2
0
1
1
0
1
2
1
2
1
0
0
1
0
1
1
0
1
1
0
0
0
1
3
1
1
2
1
1
2
0
1
1
1
1
1
2
1
0
0
1
2
1
1
0
1
1
2
1
2
1
1
1
0
1
2
1
1
0
2
1
0
2
0
4
1
0
2
1
1
0
1
2
2
1
1
0
1
1
1
0
1
1
2
1
1
1
0
1
1
0
1
1
1
1
2
1
1
1
0
2
1
1
0
2
0
2
2
1
1
1
1
0
1
1
1
0
1
1
0
0
1
1
1
0
0
1
1
1
2
1
0
1
1
1
2
1
1
1
2
2
1
1
2
1
1
2
1
0
1
1
1
2
1
2
1
1
1
2
1
1
2
2
1
2
1
1
2
1
1
1
1
0
1
1
1
0
0
1
1
1
0
2
1
1
1
1
3
1
1
0
2
1
1
1
0
1
1
1
1
0
2
1
1
1
1
2
0
1
2
1
1
0
0
1
2
1
2
1
1
2
1
2
2
1
1
0
1
1
1
1
1
1
1
0
1
1
2
2
0
1
2
1
1
0
2
1
2
1
1
0
1
2
1
1
0
1
0
1
1
2
0
1
1
1
2
2
2
1
0
2
1
1
2
2
1
3
2
1
1
0
1
1
1
1
2
2
0
2
0
1
0
1
1
2
1
2
0
2
1
1
0
0
1
1
2
1
0
0
1
2
1
0
2
2
0
2
2
0
1
2
1
1
1
1
1
2
1
1
2
1
0
1
1
1
1
1
0
0
2
1
0
1
1
1
0
0
0
1
1
1
0
1
1
1
1
1
1
0
2
1
0
2
0
0
2
1
0
0
2
0
1
1
1
2
1
1
2
1
1
1
1
0
1
2
1
2
0
1
0
1
1
1
0
1
3
1
1
1
0
0
1
2
0
2
1
0
0
1
1
1
0
2
2
2
0
0
1
1
0
1
2
2
0
1
0
1
1
1
1
2
1
1
0
2
1
2
1
2
0
1
2
2
1
1
0
1
1
0
0
2
1
0
0
0
0
1
1
1
2
2
1
1
2
1
0
1
2
2
1
0
1
2
2
1
0
0
1
2
1
1
1
1
0
1
2
1
2
0
0
0
0
1
0
1
1
0
1
1
2
1
1
2
1
1
1
1
1
0
2
1
2
1
2
1
1
1
0
1
1
1
1
1
2
2
1
1
1
1
1
0
3
0
1
0
2
1
0
1
2
2
2
1
1
1
2
1
2
0
1
1
0
1
0
3
0
0
1
1
0
1
1
2
1
1
1
1
1
1
1
1
0
2
2
0
1
1
0
1
2
1
1
2
2
2
1
1
1
2
0
1
1
1
1
1
2
0
2
2
1
1
2
0
1
1
1
1
1
1
0
1
1
1
1
1
0
1
1
1
2
1
1
1
1
1
2
1
0
0
2
0
2
1
2
2
1
2
2
2
1
1
1
1
1
1
1
1
1
1
0
0
1
1
2
1
2
0
0
2
0
1
1
2
2
0
1
2
1
1
1
1
1
1
0
1
1
1
0
1
1
2
0
1
1
1
1
1
1
2
1
1
0
1
2
1
2
1
1
1
2
2
2
1
0
1
1
1
1
0
1
1
1
1
2
0
1
1
0
1
1
1
1
1
1
2
1
2
0
0
1
1
1
1
1
1
1
1
1
0
1
2
1
1
1
1
2
2
1
2
2
1
1
1
0
1
1
1
0
1
0
0
0
2
2
0
2
1
1
0
1
0
1
2
1
0
1
0
1
1
1
1
1
0
0
1
2
2
0
1
0
1
1
2
1
1
1
0
1
0
0
2
1
1
2
0
0
1
0
2
1
2
1
1
0
1
2
0
2
2
2
1
2
0
1
1
2
0
2
0
1
0
1
0
0
1
1
2
1
0
1
1
1
1
2
1
1
1
1
2
2
0
1
0
1
1
1
2
0
2
1
0
0
0
2
0
1
1
1
2
0
0
1
1
2
0
2
1
1
1
1
1
1
2
1
1
2
2
1
1
0
1
0
1
2
0
2
1
1
1
1
0
1
2
1
0
1
1
1
2
0
1
2
2
1
0
1
1
1
1
1
0
2
2
1
0
0
1
2
2
1
2
0
1
0
1
1
0
2
1
2
2
1
1
1
2
1
0
1
0
0
1
0
1
1
2
0
1
1
0
2
1
1
1
0
0
1
1
1
1
0
1
1
1
1
1
0
1
2
2
2
1
1
2
1
1
1
2
0
1
0
2
2
1
1
0
1
0
0
1
1
1
1
1
1
1
2
0
1
0
1
0
1
1
1
2
1
1
2
1
1
1
1
1
2
2
1
1
2
2
0
0
0
2
1
1
3
0
1
1
1
0
1
0
1
0
1
1
8
2
0
2
1
1
1
2
2
2
2
1
1
1
1
2
2
1
1
0
1
0
0
1
1
1
1
1
1
1
1
2
2
1
0
1
2
1
1
1
2
1
0
1
2
0
2
1
2
1
1
2
1
0
2
1
2
2
2
2
1
1
1
1
1
2
2
1
1
2
1
0
1
1
1
1
0
1
2
2
1
1
0
0
1
1
1
1
2
0
1
1
1
1
2
0
2
0
2
2
1
1
2
1
1
0
2
2
1
1
1
0
1
0
1
1
1
1
2
1
1
0
1
2
1
0
2
2
1
1
2
0
1
0
2
1
0
1
1
1
2
1
0
1
1
1
2
2
2
1
2
1
1
1
1
1
2
2
2
1
1
2
1
1
1
2
1
0
0
2
1
0
0
1
0
1
2
1
1
2
1
1
2
1
0
0
1
0
0
1
2
1
0
2
1
0
1
1
0
2
1
1
2
0
1
1
1
0
0
1
2
1
1
1
1
2
0
1
0
1
1
1
0
0
0
1
2
1
2
2
1
0
1
2
1
2
1
1
0
0
1
2
2
1
1
0
1
1
1
1
1
1
1
0
1
1
1
0
2
1
1
1
2
1
0
0
1
1
1
0
1
2
0
1
2
1
4
1
2
1
1
0
1
0
1
1
0
0
4
0
0
1
1
1
1
2
1
0
1
1
1
0
1
1
0
1
1
1
1
1
1
0
1
1
1
1
1
1
0
0
1
2
2
0
2
1
1
0
1
1
1
2
1
2
1
0
1
1
2
1
1
2
0
1
1
1
1
1
1
0
1
1
0
2
1
0
0
1
1
0
2
0
0
1
0
1
1
1
1
1
1
1
0
1
2
2
1
1
1
0
1
0
0
0
1
0
0
2
1
1
2
1
2
0
0
1
0
2
1
2
1
1
1
1
0
1
2
2
1
1
1
0
2
1
0
1
0
1
1
0
1
1
0
2
0
1
2
0
0
1
0
0
2
1
0
1
2
1
0
1
0
2
2
1
1
1
1
0
1
1
1
1
1
1
1
1
0
1
2
0
1
0
1
0
2
1
1
1
0
2
0
1
2
2
0
0
0
1
1
2
1
0
1
0
0
1
1
0
0
1
1
1
0
2
1
1
1
0
0
2
1
1
2
0
0
1
1
1
1
1
1
2
0
2
0
1
1
1
1
0
1
2
0
0
2
0
2
1
1
1
2
3
0
2
1
1
2
1
2
1
0
1
0
1
0
1
2
0
1
2
1
1
0
2
1
3
1
0
1
1
0
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
2
1
1
1
1
1
1
1
1
0
1
0
1
1
1
1
1
2
1
1
2
1
1
1
0
1
0
1
0
2
1
2
1
0
1
0
1
1
1
2
2
1
2
2
2
0
1
0
1
2
1
2
0
1
1
1
0
1
2
1
1
1
1
2
1
1
2
2
2
1
1
2
0
0
0
2
1
0
0
0
1
2
1
2
1
1
2
1
1
1
0
0
1
1
0
2
1
1
0
1
0
2
0
1
1
1
2
1
1
0
1
1
1
1
0
0
0
1
0
2
2
2
1
2
2
2
2
1
0
1
1
2
1
1
1
1
1
1
1
1
1
0
2
1
1
2
0
1
1
0
1
1
1
1
1
1
2
2
2
2
1
1
1
0
2
1
1
1
0
2
0
1
1
1
1
1
1
0
1
1
1
1
1
0
0
1
2
0
2
1
1
1
0
0
1
2
2
2
1
2
1
1
1
0
1
2
1
1
0
1
1
1
1
1
3
0
0
0
1
1
1
1
0
1
1
1
2
0
1
1
0
1
1
2
1
2
1
1
2
1
1
0
0
2
0
1
1
0
2
1
1
1
2
0
2
1
2
1
1
0
1
1
2
0
1
1
2
1
1
2
1
1
2
2
1
1
2
1
1
1
1
0
1
0
0
3
2
2
1
1
2
0
1
1
1
1
1
1
0
2
1
1
2
2
1
0
0
0
1
2
1
0
2
2
1
1
2
2
2
1
0
0
1
2
1
2
0
0
1
2
1
1
0
0
1
1
1
0
2
1
2
1
1
0
1
0
2
1
2
1
1
2
1
2
1
1
1
0
0
5
0
1
1
1
1
1
2
1
0
2
0
1
1
1
2
0
1
0
1
1
0
0
2
1
1
2
1
1
0
1
1
0
0
0
2
1
0
0
2
0
1
1
1
1
2
0
2
1
2
0
1
1
1
0
0
1
1
0
1
1
2
1
1
1
0
0
0
0
1
1
1
0
1
0
1
2
0
1
1
1
3
1
2
2
0
0
0
0
0
0
2
1
2
2
1
1
1
2
1
2
2
0
2
2
1
1
2
1
0
1
0
0
2
0
0
1
0
2
2
1
0
1
1
1
2
1
1
1
2
1
0
0
1
2
0
1
1
1
0
0
1
0
0
1
2
1
2
1
0
1
0
1
1
2
2
1
0
2
1
0
2
0
1
2
1
2
1
0
1
1
0
1
1
1
1
0
1
2
0
2
2
0
1
1
1
1
0
1
1
2
1
1
1
0
1
1
1
1
0
1
1
0
1
1
1
0
0
2
1
1
2
2
1
1
3
1
0
1
1
1
0
1
1
2
0
2
1
1
2
1
2
1
2
1
1
1
2
2
1
0
1
1
0
1
1
0
1
1
1
1
1
2
1
1
1
1
1
2
2
2
1
0
1
1
1
0
2
1
1
1
1
1
0
1
1
0
1
1
1
1
1
1
0
1
1
0
2
1
0
2
1
0
1
1
0
2
0
3
2
2
1
2
0
0
2
0
0
1
1
1
3
1
2
1
1
0
1
2
0
1
2
2
1
1
1
0
1
2
0
1
1
1
1
2
1
0
2
1
3
0
1
2
0
0
1
2
1
2
0
2
1
2
1
1
1
2
2
2
3
1
0
2
1
1
0
1
0
2
1
1
1
1
1
1
1
1
1
6
2
0
1
1
0
0
1
2
0
0
1
2
1
3
1
1
1
1
0
0
0
1
2
2
0
0
2
1
2
0
1
1
1
1
2
0
1
0
2
0
2
1
0
2
0
1
1
2
1
1
1
1
0
3
2
0
1
1
2
1
1
1
1
1
2
1
1
0
0
0
0
1
0
1
1
1
1
2
1
1
2
2
1
2
2
0
0
2
2
1
0
0
2
1
0
1
0
2
1
2
1
1
0
1
1
2
0
1
2
1
0
1
1
0
1
1
2
0
0
1
2
2
1
2
1
1
0
1
1
1
1
0
1
2
2
1
1
1
1
0
1
1
0
2
0
0
2
1
1
0
1
1
0
1
1
0
2
1
2
1
1
1
2
1
2
1
1
1
1
2
1
1
1
1
1
0
1
0
1
0
0
1
1
0
2
1
1
1
1
1
1
1
2
0
1
0
0
1
2
2
2
0
0
0
1
1
1
1
0
1
2
1
1
2
2
0
2
2
1
1
2
2
1
2
1
0
1
0
1
2
0
1
1
0
1
1
2
1
1
1
1
0
1
1
1
0
0
0
1
1
0
0
0
1
1
0
1
0
1
1
1
0
1
0
0
2
0
2
1
2
2
0
1
1
0
1
1
1
1
0
2
1
1
1
0
1
1
0
1
2
1
2
2
0
0
2
0
1
1
1
2
2
0
0
1
1
1
1
1
1
1
1
2
0
0
2
1
1
1
1
2
1
1
1
2
1
0
1
1
2
1
0
1
2
0
1
1
0
0
0
0
0
1
1
2
0
1
0
0
1
1
1
1
1
0
0
0
0
1
1
1
0
1
1
2
1
1
0
0
1
1
1
2
0
1
1
0
1
0
0
0
1
1
0
2
1
2
1
0
1
2
1
2
1
1
4
1
2
2
1
1
2
1
0
1
1
0
1
1
1
0
1
1
0
1
1
2
1
1
0
1
0
1
0
0
1
2
0
2
0
1
2
1
1
1
0
3
2
1
1
2
1
0
0
1
1
0
1
1
1
1
2
2
0
0
1
2
0
0
0
1
1
1
2
1
1
1
0
2
1
1
1
1
1
2
0
2
0
1
2
2
2
1
2
1
1
1
1
1
1
0
1
2
1
2
1
1
1
1
2
0
1
1
1
2
1
1
1
1
1
0
0
1
2
1
1
1
1
1
1
0
1
2
2
1
0
1
1
2
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
2
1
0
1
1
1
3
1
0
0
0
0
1
1
1
1
1
1
1
1
0
1
1
1
0
2
0
2
2
1
1
2
1
2
1
0
1
0
1
1
1
1
1
2
1
1
2
2
1
1
0
0
0
2
0
1
1
1
2
2
1
1
0
1
1
2
3
0
1
0
1
0
3
1
1
2
1
1
0
2
0
2
1
0
1
2
0
0
1
1
0
1
0
1
1
1
2
0
0
0
1
1
2
2
2
1
1
2
1
1
1
0
0
1
1
1
2
2
1
1
0
2
2
1
1
1
3
2
3
1
0
1
0
1
1
1
0
2
1
2
3
0
1
1
1
0
1
1
1
1
1
2
1
0
0
1
1
1
2
1
1
2
2
1
0
1
1
2
1
1
0
1
1
2
1
1
2
1
0
2
2
0
0
0
1
2
0
2
2
1
1
0
1
1
1
0
1
0
1
2
1
1
1
2
2
1
2
0
2
1
1
1
1
0
2
2
0
1
2
1
1
1
1
1
2
2
2
2
2
1
2
0
1
2
1
0
1
1
2
5
1
1
1
0
2
2
0
1
2
1
2
0
1
1
1
1
1
0
2
1
0
1
2
0
1
1
1
2
0
1
2
1
1
0
1
2
1
1
1
1
2
0
1
2
1
2
2
1
2
1
1
1
0
1
2
1
0
1
2
0
0
1
2
0
1
2
2
1
1
2
0
1
1
0
1
2
1
0
1
1
3
1
1
2
0
2
0
1
0
1
2
1
2
1
1
1
0
1
1
2
1
1
1
1
2
0
2
0
1
1
0
2
2
1
1
1
2
1
0
1
1
1
2
2
1
1
1
1
2
1
1
1
0
1
1
0
1
1
0
1
1
1
1
1
1
1
0
0
3
2
0
1
0
2
2
2
2
1
1
3
1
1
2
1
1
1
3
1
1
2
0
2
0
1
0
2
2
1
1
2
1
2
1
1
1
1
0
1
2
0
1
1
4
1
1
2
1
2
1
0
1
1
1
2
2
2
2
1
1
1
0
1
1
1
3
0
1
0
1
1
1
1
0
0
1
1
0
1
2
1
1
1
0
0
1
0
1
1
1
2
0
0
0
2
2
1
1
2
1
2
1
2
2
0
0
2
1
1
2
2
0
2
1
1
2
1
1
1
1
2
1
0
1
1
1
0
2
1
0
1
0
1
0
0
1
1
1
1
0
2
2
0
1
0
1
1
0
3
0
0
2
0
1
1
1
2
1
2
0
2
1
1
1
1
1
0
1
1
1
0
1
2
2
1
1
1
3
0
1
1
1
1
1
0
0
1
1
0
1
2
2
0
1
0
2
1
2
0
2
0
1
2
2
1
2
1
2
0
1
1
3
0
1
1
1
1
2
1
1
1
2
2
1
0
1
2
0
1
2
1
0
0
1
1
1
2
1
1
2
1
1
0
1
0
1
2
1
1
1
1
1
1
1
0
2
0
0
1
2
0
1
2
0
0
1
0
1
2
1
2
1
1
2
2
1
0
1
0
1
0
1
1
1
0
2
1
0
0
1
1
1
1
1
1
1
0
0
1
0
1
1
0
1
1
1
2
0
1
1
1
1
2
1
1
1
2
0
1
1
1
2
3
0
1
1
0
1
0
0
1
1
1
2
0
1
1
1
1
1
0
0
1
0
0
1
1
1
1
0
1
1
0
1
2
1
1
0
1
2
1
0
0
2
1
1
1
0
1
1
1
2
1
1
1
1
2
1
0
1
1
1
0
2
1
0
0
2
2
2
1
1
2
1
0
2
1
1
1
1
1
2
0
1
1
1
0
1
2
1
1
1
1
1
1
0
1
1
1
1
1
1
0
1
1
1
2
1
0
1
2
1
2
0
2
1
1
1
1
1
1
0
0
1
1
1
1
2
1
1
1
1
0
2
3
1
1
2
0
0
2
1
2
1
1
1
1
1
1
1
1
1
1
1
2
0
0
0
1
1
2
1
1
2
2
2
0
1
2
2
1
1
2
0
1
2
0
1
1
1
1
2
2
1
0
0
1
2
2
0
1
1
1
1
2
2
2
1
2
0
2
0
0
1
1
0
2
1
1
0
1
0
3
1
1
1
0
1
0
1
1
1
0
0
0
1
1
0
1
1
2
2
1
1
0
0
2
0
0
2
2
0
2
0
2
2
2
1
0
1
1
1
1
2
2
0
0
2
2
3
0
1
1
1
1
1
1
2
2
1
0
2
1
0
0
1
2
0
0
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
0
0
2
0
1
0
1
0
1
0
2
0
1
1
1
0
2
1
1
1
1
1
1
1
1
1
1
1
3
1
1
2
1
0
1
0
1
1
1
0
1
0
1
0
1
1
1
1
0
2
2
0
2
1
1
1
0
2
1
1
1
1
1
0
1
1
1
1
3
1
0
4
1
0
0
1
1
2
1
0
1
1
1
1
0
0
1
0
1
1
1
1
2
1
1
2
0
1
1
0
1
1
2
1
1
1
1
0
1
1
1
2
1
1
1
2
2
2
0
0
2
0
2
0
1
1
1
1
2
1
2
1
0
0
2
1
1
1
1
1
0
2
0
0
0
0
1
2
1
0
2
2
1
1
0
0
1
0
1
0
1
2
2
0
1
0
2
0
1
1
0
1
1
2
0
1
0
1
2
1
1
2
0
1
1
2
1
1
1
1
1
1
1
1
0
1
0
1
2
2
1
2
1
0
2
1
0
0
1
1
1
0
2
1
0
1
1
1
1
2
1
2
0
1
2
1
2
1
0
1
1
1
2
1
1
1
1
2
1
2
1
1
0
1
1
1
2
0
1
2
1
2
1
1
0
2
1
3
1
2
1
1
1
0
1
1
1
1
2
1
0
1
1
2
1
1
1
2
1
1
1
1
0
2
1
0
5
1
1
1
2
0
1
1
1
1
2
1
1
0
2
2
1
0
0
1
1
0
0
0
1
0
1
1
1
1
1
1
2
2
1
1
1
2
1
1
1
0
1
1
2
1
2
2
1
0
0
2
2
1
3
0
1
0
1
2
2
1
1
2
2
2
1
1
1
2
2
2
1
2
2
1
1
1
2
0
2
0
1
2
1
0
1
1
1
1
1
2
1
1
0
2
0
1
1
2
0
0
2
1
1
0
1
0
1
1
0
1
1
1
0
2
1
0
1
2
1
1
1
1
1
1
2
3
1
2
1
2
2
0
1
1
2
2
1
1
2
2
0
1
1
1
1
2
0
1
1
2
2
1
0
0
1
2
2
1
1
2
2
0
0
1
0
1
2
1
1
2
1
1
0
1
2
0
0
1
1
0
1
1
0
1
2
0
1
1
1
1
0
1
1
0
1
0
1
0
2
1
1
1
2
1
1
1
0
0
2
1
0
1
0
1
1
1
1
1
1
1
2
1
2
1
2
1
1
1
1
2
1
2
0
1
0
1
2
0
1
1
0
0
1
0
0
2
1
0
1
1
1
1
1
1
1
2
1
0
1
1
1
1
0
2
2
2
1
1
2
1
0
2
1
0
0
0
2
1
1
1
1
2
2
1
2
2
0
1
1
0
2
2
1
2
2
0
0
1
2
2
2
1
1
1
1
1
0
1
1
0
1
2
0
2
2
1
1
0
2
1
1
1
1
1
1
5
2
1
2
0
1
1
1
0
1
2
1
2
1
1
0
1
1
0
2
0
1
1
1
1
1
1
2
0
2
2
2
0
0
1
2
1
0
1
1
1
2
1
0
1
1
0
1
2
1
0
2
1
0
1
1
1
0
1
1
1
1
2
0
2
1
2
1
1
1
1
2
0
2
1
1
1
1
1
1
2
1
0
1
1
2
1
1
3
1
1
1
1
1
1
1
1
1
0
1
2
1
1
2
1
1
2
1
2
1
1
0
1
0
2
2
1
1
1
0
2
2
2
2
2
2
1
1
1
2
1
1
1
0
0
0
1
0
1
0
0
0
1
0
1
1
1
1
1
1
1
2
0
1
1
1
1
1
0
1
1
2
1
0
1
2
1
2
0
1
2
1
2
1
2
1
0
1
2
1
10
1
1
1
1
0
1
0
1
1
1
1
1
0
0
1
1
1
1
1
1
0
0
2
1
1
0
0
0
1
1
0
1
2
1
1
1
0
1
1
0
1
2
1
1
2
2
1
0
1
1
1
1
0
0
1
1
1
0
1
1
1
1
1
0
1
0
1
1
2
0
0
0
1
0
2
1
1
2
2
1
0
1
1
1
1
1
0
1
0
0
1
1
1
0
1
2
2
1
1
2
1
2
1
0
1
2
1
1
0
1
1
1
0
1
1
1
2
1
2
1
2
1
1
2
0
1
0
1
0
1
0
0
1
1
1
1
1
2
0
1
2
1
2
1
0
1
1
1
0
2
1
0
3
1
2
0
0
1
2
1
1
0
1
2
1
2
1
2
0
1
2
1
2
1
0
1
2
2
0
1
0
1
0
1
1
2
1
1
1
2
1
1
1
2
0
1
1
0
1
1
2
0
0
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
0
1
2
1
0
1
5
1
1
0
0
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
0
0
0
2
1
1
1
1
2
1
2
2
1
1
1
1
2
1
1
0
0
1
1
0
1
2
2
1
2
2
1
2
1
1
1
1
2
1
2
1
2
1
1
0
2
0
0
1
2
1
1
1
1
1
1
1
2
0
1
1
0
0
1
2
0
1
0
1
1
1
1
1
1
2
2
1
2
1
2
1
2
0
0
0
2
2
0
1
1
1
1
1
2
1
1
1
0
0
0
1
1
2
1
0
0
1
1
2
0
1
1
0
1
2
1
1
2
2
1
0
0
1
1
1
2
1
1
2
2
0
1
1
1
2
1
0
1
1
0
1
2
1
1
1
0
1
0
1
1
1
1
1
2
1
1
0
1
1
1
1
1
1
1
1
1
2
1
3
1
1
1
1
2
1
0
1
1
0
0
2
1
1
0
1
3
1
2
1
2
2
2
2
0
1
2
0
1
0
1
2
2
1
1
0
1
0
2
1
2
0
1
1
1
1
2
3
1
2
1
2
1
0
1
2
1
1
0
2
1
2
1
0
1
2
1
1
0
2
1
1
0
2
0
1
2
1
1
1
1
1
1
1
1
1
0
0
1
0
1
1
1
1
1
2
1
2
0
2
1
1
1
2
1
1
1
1
1
0
0
1
0
0
1
1
2
2
0
1
1
0
2
1
2
1
0
1
1
2
1
1
0
0
1
1
1
1
2
1
1
1
1
3
2
2
1
1
2
1
0
1
0
1
0
3
1
1
1
0
2
1
2
0
1
1
0
2
0
0
0
1
1
1
1
1
1
2
2
1
2
1
0
1
1
1
2
2
1
1
1
1
1
0
1
2
1
1
1
1
0
2
1
0
0
1
1
1
0
1
0
1
1
1
1
1
2
0
1
1
2
1
0
2
2
2
1
1
0
1
0
0
1
1
0
2
1
1
0
2
0
1
4
1
2
1
1
0
1
1
1
1
2
1
2
1
1
0
0
0
1
3
1
1
0
0
1
1
1
0
2
2
1
1
1
2
2
1
2
2
0
1
1
0
0
0
1
1
1
2
0
2
1
1
0
0
1
1
1
1
1
1
1
0
1
1
0
2
1
2
1
0
1
1
2
1
1
1
0
0
2
1
0
1
1
1
1
2
1
1
2
2
1
1
1
0
1
2
1
0
1
1
2
1
1
2
1
2
0
1
0
0
2
2
2
1
1
2
0
1
1
1
0
1
1
1
1
1
2
2
1
1
0
1
0
0
1
0
1
1
1
0
1
0
1
1
0
1
1
1
0
0
1
2
2
0
0
1
1
0
2
0
0
2
1
1
2
1
1
1
3
1
2
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
0
1
1
1
1
5
0
1
1
0
1
2
2
2
1
2
1
1
0
1
2
2
1
1
1
1
2
2
1
2
1
1
1
1
1
1
0
0
2
1
1
2
0
1
1
1
0
1
2
1
1
1
1
1
0
1
1
1
1
1
0
0
1
1
1
2
0
1
0
2
0
0
0
2
2
1
0
0
1
0
1
1
3
2
0
1
2
2
0
1
1
0
1
0
1
1
1
0
1
2
2
2
0
1
2
1
1
1
1
2
0
2
2
1
1
1
0
1
1
1
1
2
1
1
1
2
1
1
1
4
1
1
2
1
1
1
0
1
1
1
1
0
1
2
1
0
0
1
1
0
0
0
2
1
1
1
1
2
0
0
0
2
2
1
1
1
1
1
2
1
0
0
2
0
1
2
0
1
1
0
1
2
2
2
1
1
2
0
0
2
0
0
2
0
2
2
1
0
2
0
1
0
1
1
1
1
0
1
2
0
2
1
0
2
0
1
1
2
1
2
0
0
1
0
0
1
1
1
2
2
1
1
1
1
1
1
1
1
0
1
1
0
1
1
2
0
2
1
0
2
0
1
1
1
0
2
1
1
3
1
1
1
1
0
1
1
0
1
2
0
0
0
1
1
2
2
3
1
1
1
4
0
0
2
1
1
2
1
0
1
1
2
1
0
2
2
1
2
1
1
2
2
0
1
1
0
1
1
1
0
1
1
0
0
1
1
1
2
1
1
0
1
2
1
2
0
0
1
1
1
0
1
2
0
0
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
0
0
0
2
1
2
1
1
1
0
1
0
1
1
1
1
0
0
1
1
1
2
0
1
1
1
2
1
1
2
2
1
1
1
1
2
0
1
1
1
2
0
1
2
2
1
2
1
2
1
1
1
2
0
1
0
0
1
1
1
0
1
1
0
1
2
2
1
2
1
0
2
1
0
1
0
2
0
0
2
0
0
2
1
1
2
0
1
1
1
2
2
0
1
1
1
2
1
1
1
0
1
2
2
1
1
0
1
2
0
1
1
1
2
1
2
1
1
1
1
0
1
1
1
0
3
0
2
1
2
1
1
1
0
0
2
1
1
0
1
2
2
1
1
0
2
1
0
0
1
2
0
1
1
0
1
0
0
1
1
2
1
1
1
0
0
1
1
2
2
1
2
1
1
1
0
5
1
1
1
0
2
0
1
0
1
0
2
1
0
1
0
1
1
1
1
1
0
2
1
1
1
1
2
3
1
0
0
0
0
1
0
1
1
1
2
0
1
1
1
2
1
1
1
0
1
1
2
0
2
0
1
1
1
1
0
1
1
1
2
1
1
1
2
1
1
1
0
1
1
0
1
2
1
1
2
0
1
2
1
2
0
2
2
2
1
2
1
0
1
1
1
0
1
0
2
0
2
2
1
2
1
0
1
2
1
1
2
1
0
1
1
1
0
2
1
1
1
2
2
1
1
1
0
1
2
2
1
1
1
1
1
1
2
1
0
0
1
1
0
2
2
1
1
0
0
0
1
1
1
2
1
0
2
2
1
1
2
2
0
1
0
0
1
1
1
0
1
1
1
3
1
2
1
0
2
2
0
1
1
0
0
1
1
1
0
1
1
1
0
1
2
1
1
1
1
1
0
1
0
0
2
1
1
1
0
2
0
1
1
2
2
0
1
0
2
2
1
2
1
0
1
2
1
1
2
0
1
1
0
1
2
0
0
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
1
1
0
2
1
1
1
1
2
1
1
2
0
0
2
2
1
1
1
1
1
0
0
1
1
0
1
1
0
2
1
2
0
1
2
2
0
0
1
1
1
2
0
0
1
0
1
0
1
1
0
2
2
1
1
2
1
0
0
1
2
2
1
0
2
0
1
1
1
0
3
1
2
0
1
1
1
2
2
1
1
2
0
1
2
1
1
1
1
1
2
2
1
2
2
0
1
1
1
0
2
1
2
1
3
0
3
1
0
0
1
2
1
1
0
1
2
1
0
1
2
0
2
2
1
1
1
1
1
0
1
1
2
1
1
2
0
1
1
0
0
1
1
1
2
1
1
0
2
1
2
1
0
0
1
1
1
1
0
1
1
1
0
2
1
1
3
1
2
0
0
1
1
2
2
1
1
1
1
1
1
1
0
1
0
2
1
1
1
2
1
0
1
1
1
0
0
2
2
1
1
1
2
2
1
0
2
1
1
1
1
0
2
1
1
2
2
2
0
1
0
2
1
1
1
1
1
1
1
1
2
1
1
1
2
1
0
1
1
0
0
1
0
1
1
1
0
1
1
1
1
2
2
0
1
3
0
1
1
2
1
0
2
0
1
0
1
1
0
0
2
1
1
1
3
1
1
1
2
1
1
2
1
0
2
1
0
1
0
1
1
2
1
1
0
1
1
1
0
3
1
1
1
1
1
1
1
1
1
0
3
1
1
1
2
0
2
3
1
1
0
0
2
1
1
1
1
0
2
1
1
3
1
2
0
0
1
1
1
0
1
1
1
2
1
0
1
2
0
1
0
2
0
2
1
1
2
0
2
1
1
2
1
2
2
1
1
1
1
2
1
2
2
1
1
1
1
1
1
2
1
2
1
2
0
2
2
2
1
1
1
2
1
2
1
0
0
1
2
1
0
1
0
2
0
0
1
0
1
1
1
2
1
1
1
1
0
1
1
1
1
0
2
1
1
1
2
1
2
1
1
0
1
1
2
0
0
1
1
0
2
1
1
0
1
0
0
1
1
2
1
1
1
0
0
0
2
1
0
1
2
1
1
1
1
1
0
2
1
1
1
1
0
0
1
1
2
2
0
1
0
1
1
1
3
1
0
1
1
1
0
1
0
0
1
1
1
1
2
0
1
1
0
1
0
1
1
2
6
1
1
1
1
1
1
1
2
1
1
2
1
1
1
2
1
2
1
2
1
1
1
2
0
1
1
1
1
0
0
1
0
1
0
1
1
0
1
1
1
1
1
0
2
2
0
1
0
1
0
1
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
1
0
1
1
1
0
0
1
1
2
1
1
1
1
1
1
1
1
0
0
1
2
1
1
1
0
0
1
1
1
2
2
1
1
1
1
1
1
0
2
3
1
1
1
1
0
1
2
1
1
2
1
2
1
1
1
1
1
0
2
2
1
1
1
1
1
1
1
1
0
2
1
1
1
1
2
1
0
1
0
0
2
0
1
1
1
1
1
0
1
0
1
2
2
1
0
0
1
1
1
1
1
0
2
1
1
0
1
1
0
2
2
0
1
1
1
1
0
0
1
1
0
1
0
1
1
2
1
0
1
1
1
2
1
1
1
0
0
2
2
0
1
1
1
2
1
0
1
1
1
1
2
2
1
0
1
0
2
2
1
0
1
1
2
1
1
1
2
0
1
0
2
1
0
0
0
2
1
1
1
1
2
1
1
2
2
1
1
1
0
1
0
1
0
1
2
1
0
2
1
1
0
2
1
0
0
1
1
1
1
1
1
1
2
0
0
0
2
0
1
1
2
0
0
0
3
1
0
1
1
1
0
2
0
0
1
0
1
1
2
1
1
0
1
1
0
0
1
2
2
1
1
1
1
0
1
2
1
1
1
1
1
0
2
1
0
2
1
1
1
1
1
1
3
1
0
1
2
1
0
1
1
2
1
0
1
2
2
1
1
1
2
1
1
1
1
0
2
0
1
0
2
0
1
0
0
0
0
1
2
1
1
1
1
2
1
1
1
1
1
2
1
2
1
0
2
1
1
2
1
1
1
1
0
0
0
0
0
2
1
1
1
2
1
1
0
1
0
2
2
0
1
1
1
1
1
0
1
2
1
0
1
0
1
1
2
1
1
0
1
1
1
1
1
0
1
0
0
0
1
1
1
0
1
1
2
2
1
1
1
1
1
1
1
0
0
1
1
2
1
1
0
0
1
1
1
2
1
0
3
2
1
0
2
2
1
0
1
2
1
2
0
1
1
1
1
1
1
1
2
1
1
1
0
2
1
1
1
1
1
0
1
1
2
0
1
1
3
1
2
1
1
1
1
0
2
0
1
1
2
2
1
1
2
0
1
1
0
2
2
0
2
1
0
2
1
1
2
2
1
1
2
1
0
1
1
0
1
1
0
1
1
1
2
0
1
1
2
0
1
2
0
2
1
2
0
1
1
2
0
0
1
2
2
0
1
2
1
1
2
1
2
2
1
0
0
1
1
0
1
1
0
0
1
0
1
1
0
0
1
1
1
1
2
0
1
2
0
1
1
1
2
1
1
1
2
2
2
1
1
1
0
2
1
1
1
0
1
1
0
2
1
0
1
2
1
2
0
1
1
1
1
2
1
2
0
1
0
2
0
1
0
1
2
1
1
2
1
1
1
0
1
2
1
1
1
0
1
0
0
1
0
1
1
1
1
0
0
2
2
1
1
0
1
1
1
2
1
1
1
2
1
0
0
1
2
2
0
1
0
2
0
5
1
1
1
3
2
1
0
1
0
1
1
1
1
0
1
1
1
1
0
1
0
1
2
2
1
1
1
0
2
1
1
1
0
0
1
1
0
1
2
1
2
1
0
1
2
1
1
1
1
0
1
1
1
1
0
0
1
2
1
2
1
2
1
1
1
1
2
0
1
1
1
1
0
1
1
0
2
1
1
2
1
0
1
2
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
0
1
1
1
1
0
0
1
1
1
0
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
0
0
1
1
3
1
0
2
1
0
1
2
0
1
1
1
1
2
1
2
2
0
1
2
1
2
1
1
2
1
0
0
0
1
2
1
1
1
0
1
1
1
2
1
0
4
2
1
1
2
1
1
1
2
0
2
0
2
2
0
1
1
1
1
0
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
0
0
1
1
1
1
0
1
1
2
0
1
2
0
0
2
1
2
0
1
1
1
2
2
2
0
2
0
2
2
2
1
1
1
2
2
1
0
2
2
1
2
2
1
1
0
2
1
1
3
0
1
1
2
1
1
1
2
1
0
2
1
1
2
1
2
1
2
1
0
2
1
1
0
1
1
2
1
1
2
2
1
1
1
1
1
1
1
1
2
0
1
1
2
2
3
2
1
0
0
1
1
0
1
0
1
1
1
2
0
0
2
0
3
0
1
1
0
1
2
1
0
1
0
1
0
0
1
2
0
1
2
1
1
1
1
1
1
0
1
0
2
1
0
1
1
0
1
1
1
2
1
0
0
1
1
3
0
0
0
1
2
2
1
1
1
1
1
1
2
1
0
1
0
0
2
0
0
2
1
1
2
1
0
1
0
1
2
1
0
2
0
1
1
1
1
2
1
1
3
1
1
1
2
1
1
1
2
1
1
2
1
1
1
2
2
2
1
1
0
1
1
0
0
1
1
1
1
1
0
0
1
2
1
0
1
1
1
1
1
1
0
2
2
2
2
1
2
1
2
1
1
0
0
2
2
1
0
1
1
1
1
1
1
1
2
2
1
1
1
1
0
1
1
2
1
1
0
1
1
2
2
1
2
1
1
1
1
0
0
1
1
2
1
1
3
2
1
0
0
1
1
1
1
2
2
0
1
1
0
1
4
1
0
1
1
1
0
1
0
1
2
0
1
1
1
3
2
2
0
2
1
1
0
1
2
1
1
2
0
1
1
1
0
1
1
0
1
2
1
1
0
1
1
1
0
0
2
1
0
0
1
1
1
1
1
1
1
1
1
1
2
1
1
2
2
0
2
2
1
2
0
2
1
0
1
1
2
1
2
1
1
0
1
1
1
1
1
2
0
1
1
0
1
2
1
1
1
0
2
1
1
1
1
1
0
1
1
1
1
1
0
0
1
0
0
1
0
0
0
1
1
1
3
2
0
0
1
1
1
0
1
0
0
1
2
2
1
0
2
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
0
0
1
0
2
0
0
1
0
1
0
2
1
1
0
3
1
2
1
0
1
1
1
1
1
0
1
1
1
1
2
1
2
1
2
1
2
1
1
2
1
0
1
1
2
1
1
1
2
2
2
2
1
1
0
1
1
1
0
1
2
1
2
0
1
0
1
1
2
3
0
1
1
1
0
2
0
0
0
1
0
1
1
1
0
1
1
0
1
1
1
2
1
5
1
2
1
1
1
1
1
0
1
1
2
2
1
2
1
1
0
1
2
2
1
2
1
1
2
1
2
2
1
2
0
3
1
2
1
1
2
0
1
2
1
0
0
0
1
1
1
1
1
1
2
1
0
1
1
1
1
2
1
1
2
0
1
1
1
2
1
0
0
1
2
1
0
1
2
1
0
1
1
1
2
0
1
1
1
1
0
0
1
1
0
0
0
2
1
1
1
1
0
1
1
1
0
1
1
1
1
2
1
1
1
2
1
2
1
1
2
1
0
1
1
1
1
0
1
0
1
1
1
1
1
1
0
0
2
0
1
0
1
2
2
1
1
1
1
1
1
0
1
0
1
2
1
0
2
1
3
1
2
2
2
1
1
2
1
0
0
0
0
0
2
2
0
2
1
2
1
1
0
0
1
2
0
2
1
1
1
2
2
1
1
0
0
0
1
0
1
1
1
1
0
0
1
1
2
1
1
0
2
1
1
2
0
0
0
2
2
0
1
6
1
1
1
2
0
2
0
2
2
1
1
1
1
2
0
2
0
1
1
1
2
0
2
0
1
0
0
0
1
0
1
1
1
0
0
1
1
1
1
2
1
2
1
2
1
0
0
1
0
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
0
1
2
2
1
1
3
1
1
1
1
1
1
0
1
0
0
1
1
2
1
0
0
1
0
2
2
2
2
1
1
1
1
0
2
1
0
1
2
1
1
1
1
1
0
1
2
1
1
0
1
1
2
1
2
1
1
2
1
1
1
1
1
1
0
2
0
0
1
0
0
2
0
2
1
2
1
1
1
1
1
1
1
1
1
2
0
2
1
1
2
3
1
1
0
2
1
0
2
0
0
1
1
1
1
3
1
1
1
2
0
2
1
1
1
1
1
0
1
0
0
1
1
0
0
1
0
1
0
0
1
1
1
2
2
2
1
1
1
0
1
2
2
2
1
1
0
2
1
1
1
1
1
1
3
0
1
1
2
1
1
1
2
2
2
1
2
1
1
1
1
2
1
1
1
1
2
0
0
1
0
2
1
1
1
0
1
1
1
1
1
2
2
2
1
1
1
0
0
1
0
2
1
1
1
2
1
1
3
1
1
1
0
1
1
1
2
0
1
1
1
0
1
2
1
2
1
1
1
1
1
0
1
0
2
0
2
1
1
1
1
2
0
1
1
1
1
1
1
1
1
0
1
1
0
1
2
1
1
1
1
1
2
1
0
2
1
2
2
1
1
1
1
0
0
1
2
1
1
2
1
0
2
1
2
1
0
0
1
1
0
1
1
1
2
1
2
1
3
0
2
1
2
1
1
1
1
2
1
0
0
1
2
0
2
0
1
1
4
1
1
1
0
1
1
2
1
1
0
1
1
2
1
0
2
2
1
1
1
1
1
1
1
1
0
2
1
0
1
2
1
1
2
2
1
2
0
0
1
1
1
0
1
1
0
2
1
0
0
1
0
2
1
1
1
2
0
1
1
1
1
0
1
2
1
1
2
2
0
1
0
1
2
1
1
1
1
1
1
2
0
0
1
0
0
0
0
2
1
0
2
1
1
2
0
1
0
0
0
0
1
1
1
2
1
2
2
1
1
1
2
1
2
1
2
1
1
1
1
0
1
1
2
0
0
1
2
0
1
0
2
0
2
1
1
2
2
0
1
1
1
1
1
1
0
1
1
1
1
2
2
2
1
0
1
1
1
1
2
1
1
2
0
1
1
1
1
0
2
1
1
2
1
2
0
1
0
2
2
1
2
1
1
1
1
3
1
1
2
1
1
2
1
0
1
1
1
0
1
2
1
0
1
1
1
0
0
1
1
1
1
1
0
1
0
2
2
1
2
1
1
1
1
2
1
2
1
0
1
1
1
2
0
1
0
0
0
2
1
0
1
2
2
2
1
1
1
1
0
1
0
2
2
1
2
1
2
1
0
1
0
0
2
0
0
1
1
1
0
0
0
1
1
2
0
1
1
1
1
1
1
0
2
1
2
1
1
1
2
1
1
0
2
1
1
0
1
1
1
0
2
1
1
1
1
1
2
0
1
1
1
0
1
0
1
1
1
1
1
1
2
1
1
1
1
0
1
0
0
1
0
1
1
0
1
2
1
1
1
1
0
1
2
1
1
2
2
2
1
0
1
0
2
0
1
0
1
0
1
1
0
1
1
0
1
0
1
1
0
1
0
0
1
0
0
2
1
2
0
1
2
0
2
1
1
0
1
1
2
1
2
1
0
1
0
1
0
1
1
2
1
2
1
1
2
0
1
1
0
1
1
1
1
1
1
2
1
1
0
2
2
0
2
1
1
1
0
1
0
1
2
2
1
0
0
1
1
3
1
0
1
1
0
2
2
0
1
1
0
2
2
1
0
1
2
2
1
0
1
2
1
0
0
0
1
0
1
0
0
1
2
0
1
1
1
2
0
1
2
1
1
2
1
0
2
1
1
1
0
2
0
2
0
1
1
1
1
1
0
1
1
0
1
1
1
1
2
0
0
0
2
1
1
0
0
1
1
1
1
1
1
1
1
1
2
3
1
0
1
0
1
1
0
1
2
1
1
1
2
2
0
1
2
2
1
1
1
1
1
0
1
1
2
1
1
1
1
1
1
2
1
1
2
0
4
1
2
1
1
0
2
0
2
2
1
0
1
3
1
2
1
0
2
1
1
0
2
1
0
1
1
1
1
1
1
1
1
0
1
1
1
3
1
0
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
2
1
1
2
2
1
1
1
1
1
1
1
1
0
2
2
1
1
1
1
0
1
2
1
1
1
0
1
0
5
1
2
1
0
2
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
0
1
0
1
0
1
2
0
0
1
2
1
1
1
2
1
2
0
1
1
1
0
2
1
0
0
2
1
1
2
2
0
1
1
1
1
1
1
2
1
0
0
1
2
2
1
0
2
1
2
2
1
1
0
0
1
0
0
0
1
1
1
1
0
2
2
2
2
1
1
2
1
0
1
0
1
1
0
2
0
2
0
1
2
2
3
2
2
2
1
3
2
1
1
0
1
2
1
1
0
2
1
1
1
1
1
0
1
1
2
1
1
0
1
2
1
2
0
1
1
1
0
2
0
1
1
2
0
2
0
1
2
1
2
1
0
1
1
2
0
2
0
0
1
0
2
1
2
1
1
1
1
2
1
1
2
1
2
2
0
1
1
0
1
2
0
1
1
1
2
1
2
1
0
0
1
0
1
1
0
1
1
0
2
1
1
0
2
1
2
0
1
0
2
1
1
0
0
3
2
1
1
2
1
1
0
2
0
0
2
1
1
1
1
1
0
1
1
1
1
2
1
0
1
1
1
0
0
0
0
1
0
0
2
1
1
1
1
2
2
1
1
1
1
1
1
0
1
1
3
0
0
0
0
2
1
1
1
2
1
2
3
1
2
0
0
2
0
0
2
2
2
0
1
2
1
1
1
0
1
1
1
1
2
2
0
1
1
0
0
0
2
2
0
1
0
2
1
2
0
1
0
1
1
1
1
1
1
1
2
0
1
1
1
0
1
1
1
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
3
1
1
1
1
1
1
1
1
2
2
1
1
0
2
1
1
1
2
1
0
1
1
2
3
1
1
0
1
2
1
0
1
0
1
1
1
1
1
1
1
2
0
1
1
0
1
0
0
1
2
1
1
0
1
0
2
1
0
2
2
1
1
0
1
1
0
1
1
1
1
1
1
0
1
1
1
2
2
1
1
1
1
1
1
1
0
2
1
0
0
0
0
1
0
0
1
2
2
1
2
2
1
1
1
2
1
1
1
0
1
1
0
1
2
2
1
2
0
1
1
1
1
2
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
2
2
0
0
1
0
2
1
1
1
1
1
1
1
0
1
1
2
0
0
1
1
2
2
0
0
2
1
1
2
1
0
1
1
0
1
2
2
1
0
0
2
0
2
1
2
1
0
0
1
0
1
0
1
2
0
1
1
2
2
2
1
2
0
0
1
1
1
1
1
2
1
2
1
0
3
1
2
0
0
1
2
2
1
1
1
2
0
1
0
1
2
2
2
1
0
1
1
0
1
0
0
1
1
0
1
1
0
1
0
1
2
2
1
2
1
0
0
1
1
1
0
1
2
0
2
1
2
1
1
2
0
0
1
0
2
4
1
2
2
1
1
1
0
1
2
0
1
1
2
2
0
1
0
1
0
2
1
0
0
1
1
0
0
1
1
0
1
1
1
1
1
1
1
1
1
1
2
0
1
4
1
1
1
2
1
2
1
1
1
1
1
1
0
1
0
0
1
1
1
2
2
1
1
1
1
2
1
0
4
0
1
1
2
1
2
1
4
1
0
2
1
0
1
1
2
1
2
1
1
0
1
1
1
2
1
3
1
1
0
2
1
2
2
1
2
2
1
1
1
0
0
1
0
1
2
1
2
1
1
3
1
1
0
1
0
1
1
1
1
1
2
0
0
1
1
0
2
1
0
1
2
0
1
1
0
0
1
0
1
1
1
1
1
1
1
1
1
0
1
2
2
0
0
1
2
2
0
1
0
1
0
1
0
3
1
1
1
1
2
2
0
1
1
2
1
1
1
2
2
0
1
1
2
2
1
2
2
0
2
2
2
1
1
0
1
0
1
2
2
1
2
1
1
1
1
1
2
1
1
1
1
0
1
3
0
2
3
1
1
2
1
1
1
2
0
1
1
2
2
1
0
2
1
0
2
0
0
2
2
2
2
2
1
1
0
2
1
2
1
0
2
1
1
2
2
1
1
2
1
1
1
0
1
1
1
3
0
1
0
0
1
2
1
3
1
0
1
0
1
2
1
1
1
1
0
0
2
1
0
1
2
1
1
1
1
1
1
1
2
1
1
1
1
2
1
2
1
1
1
0
2
0
1
0
1
0
1
1
1
1
0
0
1
1
2
1
2
2
2
2
1
0
1
2
1
0
1
1
1
2
0
1
0
2
1
0
1
1
1
1
2
0
2
1
1
0
1
2
0
2
1
1
1
2
0
1
1
3
1
2
0
2
0
1
1
1
0
1
0
1
1
0
0
1
1
2
0
2
0
2
0
0
1
1
3
1
2
2
1
2
1
2
0
1
2
0
1
1
0
1
1
1
2
1
1
1
1
1
1
1
2
0
2
0
2
1
2
1
1
1
1
2
1
1
1
0
0
1
3
1
0
2
1
0
1
0
1
1
1
1
0
0
0
0
2
1
1
1
1
1
2
2
1
1
0
2
1
1
1
1
1
1
0
1
2
0
0
1
1
2
2
1
1
1
1
0
1
1
1
0
0
2
1
0
1
0
1
1
1
2
2
2
1
1
0
2
0
1
1
1
0
1
0
1
2
1
0
1
0
0
0
1
1
0
1
1
0
1
1
1
0
1
1
0
1
0
1
0
0
1
1
2
1
1
2
1
1
2
0
1
2
1
0
1
2
1
1
0
1
1
1
1
0
0
1
1
1
2
2
0
0
0
1
3
1
1
2
0
2
1
1
0
4
2
2
0
1
0
1
1
1
1
0
1
1
0
0
2
1
1
0
1
1
2
1
0
1
2
1
2
2
1
1
2
1
2
1
2
1
1
1
2
1
1
1
2
1
1
2
1
0
2
1
2
3
1
0
1
0
0
1
1
2
2
1
2
1
2
0
0
2
1
1
2
1
2
1
0
1
1
2
2
2
1
2
0
2
1
1
1
1
1
1
1
2
0
0
1
0
1
0
0
1
2
2
1
0
2
1
0
2
2
2
1
1
0
0
1
1
0
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
2
2
2
2
1
1
1
0
1
2
2
1
0
2
1
0
1
0
1
1
2
1
1
1
1
1
1
1
1
2
1
0
1
1
1
1
1
2
1
1
2
1
1
1
2
1
1
1
1
1
1
2
2
2
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
2
2
1
1
1
0
1
1
1
0
0
1
0
1
2
1
1
1
1
1
2
1
4
1
1
1
0
1
1
1
1
2
1
0
1
2
0
1
1
2
1
1
1
1
0
2
1
2
2
1
1
1
1
1
1
2
1
0
3
1
1
1
0
1
0
1
0
0
1
1
2
0
2
2
2
0
1
1
1
2
2
2
2
1
0
0
2
1
1
1
2
1
2
0
1
1
1
2
2
1
1
1
0
0
1
1
1
0
0
2
1
1
1
2
1
1
1
1
1
1
1
1
0
2
1
1
1
1
1
0
0
0
1
0
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
2
2
1
0
3
1
0
0
1
0
0
1
1
0
1
2
2
1
1
1
0
0
1
0
1
1
1
1
0
2
2
2
1
1
1
2
1
0
1
1
1
0
2
1
2
1
2
1
1
1
2
1
2
1
2
1
2
1
1
1
1
0
0
2
1
1
0
1
0
1
1
2
2
2
1
2
2
0
1
0
1
2
1
2
0
0
1
1
1
1
1
0
1
1
1
2
1
1
2
1
1
1
0
1
1
1
1
2
0
0
1
1
1
2
2
1
1
1
2
1
1
0
1
2
1
1
0
0
3
1
1
1
2
2
2
0
1
0
3
1
1
0
2
1
2
2
1
2
1
0
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
0
1
1
1
1
3
1
1
1
1
1
0
1
1
0
1
2
1
1
0
1
1
2
2
1
1
1
0
1
2
1
0
1
2
0
1
0
2
1
1
0
2
2
0
1
0
2
0
2
1
1
0
1
1
0
0
1
2
1
0
1
1
1
1
1
1
0
2
2
1
2
2
1
2
1
0
0
1
2
1
0
1
0
0
2
2
0
1
1
0
2
1
1
1
1
0
2
2
1
2
1
0
1
1
1
0
1
2
0
2
1
1
1
0
0
1
1
3
1
2
0
0
2
2
0
0
0
1
1
1
1
1
1
1
0
1
1
0
1
0
1
1
0
3
1
1
1
2
1
2
1
1
0
2
1
1
0
1
1
1
0
1
1
1
2
1
1
1
1
1
2
2
1
0
1
1
2
1
0
1
1
2
1
1
1
1
1
2
1
1
1
1
0
0
1
0
2
2
2
1
1
0
0
0
1
0
1
1
0
1
1
1
0
0
1
2
0
1
2
2
1
1
2
0
1
2
1
0
1
1
2
2
2
1
1
0
3
1
2
1
2
2
1
0
1
0
2
1
2
2
0
1
1
1
0
1
1
0
1
2
0
2
1
2
0
0
1
0
1
1
1
1
1
1
1
1
0
2
1
1
0
2
1
1
1
0
2
1
1
1
0
2
1
0
0
0
1
0
0
1
1
1
0
1
0
1
1
2
0
3
1
1
2
1
0
1
1
1
1
1
1
2
1
2
0
0
3
2
0
1
2
1
0
1
1
2
1
1
1
0
2
1
2
0
2
2
2
1
1
1
0
2
1
0
0
1
2
1
1
2
0
1
2
2
1
2
1
1
0
1
2
2
2
1
0
0
1
1
1
1
1
1
1
2
0
1
1
1
1
2
1
1
2
1
2
0
2
1
1
0
1
0
0
1
0
2
1
1
0
1
3
1
2
2
1
1
1
2
0
2
1
1
1
1
1
1
0
1
2
1
1
1
1
0
1
0
1
2
1
1
2
0
1
2
1
0
0
2
2
0
2
1
1
2
1
2
2
1
2
1
1
1
0
1
1
2
1
2
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
0
2
1
2
1
1
1
0
0
2
1
1
0
0
2
1
2
0
1
1
1
1
2
1
1
1
2
1
1
2
0
2
2
1
1
2
2
0
0
0
2
0
0
2
2
1
0
0
0
1
0
2
1
1
0
1
0
0
1
1
0
2
1
0
1
1
1
1
2
1
1
1
0
1
1
1
0
1
1
0
0
0
1
0
1
0
3
1
1
2
0
2
1
2
1
0
1
1
1
1
1
1
1
2
2
2
1
1
1
2
0
1
2
0
0
1
1
0
1
1
1
0
1
2
1
1
1
1
0
1
2
2
1
1
0
1
1
2
0
0
0
1
1
1
3
1
1
2
1
1
0
1
1
2
1
1
1
1
2
1
3
1
2
1
0
2
1
1
0
1
1
2
2
2
1
0
0
1
1
1
1
0
1
0
1
1
2
1
1
2
1
0
0
1
0
1
1
0
1
1
1
1
0
1
1
1
1
0
1
1
2
0
1
1
1
0
0
1
1
1
2
2
1
1
0
1
0
1
0
1
1
1
1
1
1
1
0
2
1
1
1
1
1
0
2
1
1
0
1
2
1
1
1
2
3
0
1
2
0
1
0
2
4
0
1
2
0
0
1
2
0
0
0
1
1
1
1
0
1
1
0
1
1
1
1
1
1
1
1
1
0
1
0
2
2
0
1
0
2
1
1
1
1
1
1
1
1
1
2
2
1
0
2
2
0
0
1
1
1
0
1
0
2
2
1
0
2
1
1
0
2
1
1
1
2
0
1
2
2
1
1
1
1
1
1
1
2
1
1
0
2
0
2
2
0
1
1
0
1
1
1
1
2
0
2
1
1
1
1
0
1
1
0
0
1
1
1
1
2
1
1
2
1
0
1
0
1
1
1
1
2
1
0
1
4
0
1
0
1
1
0
1
2
1
1
0
1
1
1
0
0
1
0
1
2
2
1
1
1
2
0
0
0
2
1
0
2
1
0
0
2
2
1
2
1
1
1
2
1
0
1
1
0
0
2
2
2
0
1
1
1
1
1
1
1
2
1
2
0
1
0
0
1
2
2
1
2
2
1
2
1
1
1
1
1
0
2
0
1
1
0
2
1
1
1
1
1
0
1
1
2
0
1
2
1
1
1
0
1
1
0
0
2
2
1
0
1
0
2
2
2
2
0
0
1
1
0
0
2
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
0
1
1
1
1
1
1
1
1
0
2
0
1
1
2
1
1
2
2
0
0
0
1
1
2
1
1
1
1
0
4
0
2
1
2
1
1
1
1
1
2
2
1
1
3
3
0
1
1
1
2
1
2
0
2
1
0
0
0
0
1
1
0
1
1
1
1
0
1
1
1
2
1
0
1
1
0
0
1
1
1
1
1
1
2
1
2
1
1
1
0
0
0
3
1
1
2
1
0
1
2
0
1
0
2
1
0
1
1
1
2
0
0
0
0
2
1
1
1
0
2
0
0
2
1
0
1
2
1
1
2
1
0
1
1
1
0
1
2
1
0
0
2
1
2
2
2
1
2
0
1
2
1
0
2
1
1
1
1
1
2
1
2
0
2
2
2
1
0
0
1
2
1
1
0
1
1
1
1
2
1
2
3
0
0
0
2
1
0
2
1
0
1
1
1
2
0
1
1
2
1
0
1
1
2
0
2
1
0
1
2
1
1
0
1
1
2
1
0
1
1
1
0
1
1
0
1
2
0
2
1
1
0
1
1
0
0
2
0
1
0
2
1
0
0
2
1
0
2
0
0
2
1
1
1
2
2
0
1
1
0
0
0
1
0
1
1
1
0
1
1
1
2
0
1
0
1
0
1
1
2
2
0
1
1
1
1
2
2
1
1
0
0
1
1
2
0
1
1
1
1
2
0
1
1
2
1
1
1
0
2
1
1
1
1
2
0
1
1
1
2
0
1
1
1
0
1
0
0
1
2
1
1
0
1
2
1
0
1
0
1
1
2
2
0
2
1
1
0
1
1
1
1
1
0
1
1
2
2
2
0
1
1
2
0
4
1
1
0
1
1
2
0
1
1
1
1
0
1
0
1
0
1
2
1
1
1
0
1
0
2
1
1
2
2
1
1
1
1
2
0
0
1
2
1
0
2
1
3
2
2
1
2
1
2
1
1
1
1
2
0
2
1
2
1
2
0
1
1
2
2
0
2
0
1
2
0
0
1
2
1
1
1
1
0
1
0
1
0
2
1
1
2
1
1
1
1
5
1
2
0
1
2
0
2
1
0
1
2
0
1
1
1
0
0
0
2
2
1
1
0
2
1
0
1
1
2
1
1
2
0
2
2
1
1
0
2
1
0
1
1
1
2
1
1
1
1
1
1
0
1
1
2
1
1
2
1
2
0
2
0
1
0
1
1
1
0
2
2
0
1
1
1
2
1
0
1
1
0
1
1
0
2
1
1
0
1
1
1
0
1
2
1
2
1
3
1
2
1
0
2
1
1
1
1
1
1
1
1
0
0
2
2
0
1
1
1
1
0
1
1
0
1
1
1
0
1
1
0
1
1
1
0
1
0
1
1
2
2
2
2
1
1
1
1
1
1
2
1
1
0
0
0
1
1
1
1
0
2
1
1
2
1
1
2
0
0
2
0
2
0
3
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
0
0
1
1
1
1
1
2
1
0
0
2
0
2
1
1
2
1
1
0
1
2
1
2
1
0
0
0
2
1
1
2
1
1
0
1
0
1
0
1
1
2
1
1
2
2
1
1
2
1
1
1
0
1
1
1
1
2
1
0
0
1
0
1
0
0
0
1
2
0
0
1
1
2
2
1
2
2
0
1
2
0
0
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
0
2
0
1
2
2
2
0
0
1
1
0
1
2
1
1
1
2
0
1
2
1
2
0
2
0
0
2
1
0
2
1
2
2
1
0
0
1
1
1
1
2
1
1
1
2
1
0
1
0
0
1
0
2
1
0
1
1
1
0
1
1
2
2
2
0
1
1
1
1
1
1
2
2
0
1
2
0
1
0
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
2
1
1
1
3
1
1
2
0
0
1
2
1
0
1
1
1
2
1
1
0
1
1
1
1
0
1
1
1
0
0
1
0
1
1
0
0
1
1
1
1
0
2
1
2
1
2
2
1
1
0
1
1
0
2
1
1
1
1
0
1
1
1
0
0
1
1
1
2
0
1
1
0
1
1
1
1
0
0
1
2
1
1
1
1
2
1
1
1
1
1
3
0
1
2
2
2
1
0
1
0
2
0
0
1
0
0
0
1
2
1
0
1
0
0
1
0
2
2
0
1
1
1
1
0
2
1
1
0
2
0
2
1
2
1
1
1
0
1
2
0
1
1
1
2
1
2
1
0
1
2
1
0
1
1
1
1
1
1
1
0
1
0
1
2
2
0
2
1
1
0
1
0
1
1
2
2
2
1
0
1
0
0
1
1
1
1
2
1
1
1
1
1
0
1
1
0
0
1
2
0
1
1
1
0
1
1
2
0
2
1
1
0
2
0
1
1
2
2
2
1
1
0
0
1
0
1
3
2
2
1
0
0
1
1
2
1
2
0
1
1
1
1
1
0
1
1
1
2
2
0
2
2
1
2
1
0
1
3
1
1
1
1
2
1
1
0
1
0
1
2
1
2
1
1
1
0
1
0
1
1
2
0
1
1
1
0
1
1
1
1
1
2
0
2
1
0
1
0
1
1
1
2
1
1
1
1
1
2
2
0
1
1
2
3
1
0
1
1
0
1
2
0
2
2
1
1
2
2
0
0
2
1
1
2
1
1
1
3
1
1
1
1
1
1
0
1
2
2
1
0
2
0
1
0
2
2
1
1
1
0
1
2
1
2
1
2
2
1
1
1
1
2
1
2
0
2
1
2
2
1
1
1
1
2
1
0
1
1
1
0
0
1
0
2
2
1
1
1
1
0
1
1
0
2
0
2
0
1
1
0
2
0
2
1
1
1
0
2
1
1
1
0
1
0
2
2
1
0
0
0
1
0
1
2
1
1
1
2
2
2
0
1
1
2
0
1
2
1
2
1
1
4
1
0
0
2
1
1
1
2
1
2
1
2
2
0
1
1
0
0
2
1
0
0
2
1
1
3
0
0
1
1
0
1
1
1
1
0
1
1
1
0
0
2
0
0
1
2
0
1
0
1
1
2
1
2
1
0
1
2
0
2
2
2
2
2
1
2
1
2
1
0
0
0
1
1
1
1
1
0
1
1
0
1
1
0
1
1
1
2
0
1
1
2
2
1
2
1
0
1
1
2
2
0
2
1
1
0
1
2
1
1
2
0
0
1
1
1
1
2
1
1
0
0
2
1
1
0
2
0
1
1
1
1
1
2
2
1
2
1
0
0
1
1
1
1
0
2
2
1
1
2
1
1
1
2
1
0
0
0
1
2
1
0
1
1
2
0
1
1
1
1
1
1
2
2
1
1
0
0
3
0
1
2
1
1
2
1
2
1
2
2
1
1
0
2
1
0
1
1
0
2
0
1
0
3
1
1
1
1
0
2
1
1
1
0
0
2
1
1
1
0
1
2
1
0
1
1
2
1
2
2
1
0
1
1
1
0
0
1
1
2
1
2
0
2
0
0
1
1
0
1
1
1
0
1
0
0
1
1
1
1
2
1
1
1
1
0
1
0
1
0
2
1
0
1
1
0
0
1
1
0
1
1
2
1
1
1
3
1
1
2
0
1
0
1
2
1
1
2
2
1
1
1
0
0
2
2
2
0
1
2
1
0
1
2
1
2
1
2
1
1
0
2
1
1
1
0
0
1
0
0
1
1
1
0
1
2
1
1
1
0
1
1
1
2
0
2
2
1
1
1
1
2
2
1
1
0
0
0
1
0
1
1
1
1
2
2
1
0
0
1
0
1
1
1
1
2
1
1
1
0
2
1
1
1
2
2
1
1
1
1
0
0
0
0
1
1
1
1
2
2
1
2
1
0
0
0
1
1
1
2
1
1
1
2
2
1
1
1
2
0
1
1
2
2
2
1
1
2
2
0
2
2
1
0
0
1
3
2
2
0
1
1
0
2
1
1
1
1
1
1
1
0
1
2
1
0
1
2
1
0
1
0
0
0
1
1
1
2
0
2
1
1
0
1
1
1
1
0
1
2
3
2
0
1
1
1
0
2
0
1
0
2
0
1
0
1
0
1
0
1
0
1
1
0
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
0
1
0
1
2
1
1
1
2
1
3
2
2
1
1
1
1
1
1
1
1
2
0
1
0
1
1
1
1
2
0
2
1
1
2
2
0
1
1
1
1
2
1
0
0
1
1
1
0
0
2
0
2
1
1
0
1
1
1
0
2
1
0
1
0
1
0
0
1
2
1
2
2
1
1
1
1
2
1
1
2
0
2
0
1
1
1
1
1
0
1
0
0
1
2
0
1
1
2
0
2
1
1
1
1
0
1
1
1
0
0
0
2
2
1
1
1
1
1
2
1
0
1
1
2
2
1
1
1
0
2
1
1
1
0
2
1
1
0
2
1
1
1
2
0
2
1
1
1
2
0
1
2
1
0
1
0
0
1
2
1
1
0
1
1
1
2
0
0
0
0
1
1
1
1
0
2
1
0
1
1
1
1
1
2
1
1
1
1
1
1
1
2
0
2
2
0
0
1
1
0
1
2
0
0
0
1
2
0
1
1
0
1
2
0
0
0
1
2
3
2
1
3
0
0
1
1
1
0
1
0
1
1
0
1
2
1
1
0
1
0
1
1
2
2
2
2
1
0
1
1
0
1
1
1
0
1
0
0
1
0
1
1
2
1
1
1
1
1
0
1
1
1
1
1
2
1
1
1
1
1
1
0
1
1
0
1
0
1
0
0
1
0
0
2
1
2
1
1
2
1
1
1
0
0
2
1
0
1
2
1
1
1
2
1
1
1
1
1
1
1
1
0
0
0
1
1
1
0
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
0
2
1
2
1
1
1
0
2
0
1
1
0
1
1
1
0
1
1
1
1
2
2
2
0
1
1
2
1
1
2
3
2
1
2
1
1
1
0
1
0
1
1
2
0
0
2
1
1
0
1
0
0
0
2
2
0
0
1
1
1
1
1
1
0
1
1
1
2
1
2
1
2
0
1
1
0
2
1
2
0
2
1
0
2
2
1
2
1
1
2
0
1
1
2
0
2
1
0
1
0
2
0
1
1
1
0
1
2
0
1
1
1
1
0
1
1
1
1
2
1
0
3
2
1
1
2
1
0
2
1
2
2
0
1
1
1
2
1
1
1
0
0
1
0
1
0
0
1
2
1
1
1
1
2
0
1
1
1
1
1
1
1
2
1
2
0
0
1
1
2
1
0
1
2
1
0
1
1
1
1
1
0
1
2
2
1
1
5
1
1
1
1
1
1
1
2
1
1
1
1
0
1
1
1
2
1
1
1
1
1
2
1
2
1
0
0
1
2
1
1
2
1
0
0
1
0
2
1
0
1
2
0
1
1
1
1
1
0
1
1
2
0
2
1
1
2
1
1
1
1
2
0
0
1
1
3
2
1
0
2
1
2
2
1
2
0
2
1
1
2
1
2
0
1
1
0
1
1
1
1
1
1
0
1
1
2
1
1
1
0
1
1
0
1
1
0
1
2
1
1
0
2
2
2
2
1
1
1
1
1
1
1
4
0
1
2
1
2
1
2
0
1
0
1
1
1
1
2
1
2
0
2
2
1
1
0
1
1
1
2
1
1
2
1
1
2
2
1
0
0
1
2
1
4
1
1
1
1
0
1
2
1
0
1
1
0
1
0
1
0
1
0
0
1
1
2
1
2
1
2
1
0
0
2
2
1
0
1
1
2
1
0
1
1
1
1
0
2
2
2
1
2
1
1
1
1
1
1
0
0
1
1
1
1
1
1
2
2
1
2
0
1
2
2
1
0
0
1
1
1
1
2
1
1
1
1
2
2
1
1
2
1
1
1
1
0
1
2
1
0
0
0
2
0
1
1
2
1
2
0
2
1
1
0
0
1
1
1
0
1
1
1
1
2
0
1
0
0
2
1
2
2
2
0
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
0
2
1
2
1
2
0
0
1
2
0
1
0
0
1
1
1
1
1
1
1
0
2
0
0
1
2
0
1
1
2
1
0
2
0
0
2
2
1
0
2
2
1
2
1
1
0
1
1
1
1
1
0
1
0
1
1
1
1
2
1
2
0
1
2
0
2
1
1
2
0
2
1
2
1
1
1
1
1
1
1
2
0
1
2
1
0
1
0
1
1
4
1
2
2
1
2
2
1
0
0
2
1
0
1
1
1
1
1
1
2
2
0
0
1
2
1
1
0
0
2
1
1
2
1
1
2
0
2
1
1
1
1
2
1
1
1
1
1
0
1
2
0
1
0
1
1
1
0
1
0
1
1
1
1
0
2
1
1
1
2
0
0
2
0
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
2
0
1
1
2
2
1
1
1
1
2
0
0
2
0
1
2
3
0
1
1
2
1
1
1
1
1
2
1
0
2
1
0
1
0
1
1
0
1
1
0
1
0
1
1
1
2
1
2
1
1
0
0
0
2
0
0
1
2
0
1
1
0
1
2
0
2
1
2
1
0
2
2
1
1
1
1
1
0
1
1
2
1
1
1
1
1
0
1
0
0
1
1
1
1
2
2
1
1
1
0
0
1
0
1
1
2
1
1
1
1
1
1
1
1
0
1
0
1
2
1
0
1
1
0
1
2
1
1
1
1
1
0
1
0
0
1
2
1
2
1
1
0
1
1
1
1
1
1
2
1
0
1
1
2
2
1
2
1
0
1
1
1
1
1
0
3
1
0
1
1
2
1
1
1
1
1
0
0
6
1
0
2
0
0
1
1
1
1
2
1
1
0
0
1
0
0
0
2
0
0
0
1
1
1
1
1
2
1
2
1
1
1
0
1
1
2
0
2
1
2
1
1
1
0
1
1
1
0
1
1
0
0
1
1
0
3
1
0
1
0
0
2
1
1
2
1
1
1
1
2
0
1
1
2
0
1
1
0
2
0
1
2
1
0
1
1
1
1
1
0
2
1
1
0
2
1
1
1
3
1
0
1
2
2
1
1
1
2
1
0
1
1
2
1
1
0
2
1
1
0
3
2
0
2
1
0
1
1
1
1
1
0
1
2
1
1
1
0
1
0
1
2
2
0
0
1
1
1
0
2
0
1
1
0
2
0
1
1
1
1
1
1
0
0
1
2
2
2
0
2
1
1
1
1
0
0
2
1
1
1
1
1
0
0
1
0
2
0
0
1
0
0
1
1
1
0
1
1
2
1
1
1
2
1
2
1
0
1
1
1
2
1
3
1
1
1
1
2
0
0
2
1
1
0
2
0
2
2
1
2
0
1
1
1
0
2
0
2
1
0
2
0
0
0
1
1
1
1
1
0
2
2
2
0
1
2
2
2
1
0
0
2
2
1
0
2
1
2
2
1
1
1
1
0
0
1
1
1
1
3
0
0
0
1
1
0
1
1
1
1
0
1
2
0
1
2
0
1
1
1
2
2
1
1
2
1
2
1
2
0
2
0
1
2
1
2
1
2
1
0
0
1
1
1
2
1
2
1
1
1
2
2
2
1
0
1
2
1
2
1
1
1
1
2
0
1
1
1
2
1
1
0
1
0
1
2
1
1
1
1
1
1
2
2
0
0
1
3
1
1
1
1
2
1
1
1
2
2
1
1
0
0
0
1
1
1
1
2
1
0
1
1
1
1
2
2
1
0
1
1
1
0
1
1
0
2
1
2
0
1
1
2
2
1
1
1
0
1
0
1
1
2
1
1
1
1
2
1
2
1
2
0
1
1
2
2
2
0
1
0
1
2
0
0
0
0
2
0
0
1
2
1
1
2
0
1
2
1
1
0
1
0
2
2
1
2
1
2
0
1
1
1
1
2
0
1
1
1
1
2
1
0
2
1
0
0
1
2
1
1
1
1
1
2
1
0
0
1
1
0
1
3
0
1
0
1
0
0
2
1
0
1
1
1
1
0
1
2
0
2
0
1
0
1
1
2
0
0
1
1
1
1
1
0
1
0
0
1
1
2
1
1
1
1
1
2
2
1
1
0
2
2
1
0
0
5
0
2
0
1
1
1
0
0
0
1
0
1
1
0
1
1
0
1
1
1
0
1
1
0
1
1
2
2
1
0
1
1
1
0
0
1
1
1
1
1
0
1
1
1
0
2
0
2
2
0
0
1
0
2
1
1
1
1
1
1
1
2
0
1
0
2
1
0
0
1
0
1
0
0
1
1
5
1
1
2
2
0
2
2
1
1
2
0
1
1
1
1
2
2
1
0
1
0
0
2
0
1
1
1
0
1
1
1
1
1
1
2
1
1
1
1
0
1
2
2
1
1
1
1
1
0
1
1
2
1
2
0
0
2
1
2
0
2
1
1
1
0
1
1
1
0
1
1
1
0
0
1
1
1
0
0
1
1
1
2
2
1
1
1
1
1
3
1
1
2
1
1
1
1
1
0
1
1
0
0
2
2
1
2
1
1
1
2
1
1
1
1
0
1
2
1
1
2
1
1
1
2
1
0
1
2
2
0
1
1
1
2
1
3
1
1
1
0
1
1
1
0
2
1
1
1
1
1
1
0
1
1
0
1
1
2
1
0
0
2
1
1
1
1
0
1
0
1
1
0
1
1
0
0
0
0
2
0
4
0
0
2
1
2
0
0
1
2
2
0
1
2
2
1
2
1
1
2
1
1
0
1
1
1
1
1
2
0
1
1
1
2
1
1
1
2
0
2
1
1
2
2
0
0
1
0
1
0
1
1
2
1
1
1
1
0
1
1
0
0
1
1
1
2
2
1
1
0
0
1
1
0
2
0
2
2
2
1
0
1
1
2
2
1
1
1
1
1
1
2
1
1
2
1
1
1
0
1
0
2
2
1
1
2
1
1
0
1
1
0
1
1
1
1
1
1
1
1
1
2
1
2
0
2
0
2
1
1
1
1
1
2
0
0
2
1
0
2
1
1
1
2
1
1
1
0
1
1
0
1
1
1
1
1
0
1
0
0
1
1
1
1
1
1
2
0
1
1
1
2
1
1
1
1
1
1
1
1
2
2
0
1
1
1
1
1
0
2
0
0
1
1
2
1
0
1
3
0
2
1
1
0
0
1
0
1
2
1
0
0
1
1
2
0
0
3
1
1
1
1
0
1
1
2
2
0
2
2
0
2
2
1
1
0
1
0
1
1
2
1
1
1
1
1
0
3
1
0
2
0
1
0
0
1
1
2
0
2
1
1
0
1
1
1
0
2
1
1
1
0
2
0
1
1
1
0
2
1
1
0
1
0
1
0
2
1
1
1
0
1
2
1
1
0
2
1
2
2
1
1
2
2
2
0
1
2
2
1
2
0
2
1
1
2
1
0
0
1
1
1
1
1
2
0
0
1
2
1
2
1
2
0
2
1
2
0
1
2
1
1
1
1
0
1
1
0
1
1
1
1
1
1
2
1
0
1
1
1
2
1
0
3
0
2
2
1
1
2
1
2
2
2
2
1
1
2
1
0
1
1
1
2
0
1
1
1
1
0
0
2
0
1
2
1
1
1
1
1
0
2
1
0
1
0
1
2
1
1
2
1
0
2
2
2
1
1
2
1
0
1
2
1
0
1
1
2
1
2
1
0
1
2
0
1
1
1
2
1
2
1
1
1
2
1
1
1
1
0
1
1
1
1
1
2
1
1
1
2
0
0
2
0
1
1
0
1
1
0
1
1
1
1
1
1
1
1
1
1
1
0
1
0
1
1
1
2
2
1
1
1
2
2
1
0
1
1
0
1
1
0
0
1
1
1
2
1
2
1
1
1
1
1
1
0
1
1
0
1
2
1
0
1
2
0
0
2
0
1
1
1
2
1
1
1
3
3
0
2
1
2
2
1
0
1
1
1
2
1
1
1
0
3
0
1
2
2
1
0
1
1
2
0
1
1
0
1
1
0
2
0
1
0
1
2
2
0
1
0
2
1
2
0
0
1
0
1
1
1
1
1
0
1
1
0
0
1
1
0
1
1
0
1
1
2
1
1
0
1
2
1
0
1
2
1
1
0
1
0
0
2
2
1
0
1
0
0
1
2
1
1
0
0
2
1
1
0
0
2
1
1
2
0
1
1
0
2
0
1
0
2
2
2
0
2
1
1
1
1
1
2
1
1
1
0
1
1
2
1
2
1
0
1
1
2
2
0
2
2
2
0
3
2
0
1
0
2
1
2
1
1
1
1
1
2
1
1
2
0
1
2
1
2
1
0
0
1
2
2
1
1
0
1
1
1
1
3
0
2
0
2
1
0
1
1
2
1
2
1
1
0
2
2
0
2
2
1
1
0
1
0
1
0
1
0
1
1
1
2
1
0
1
0
1
1
1
0
1
1
1
1
0
2
1
1
1
1
0
0
0
2
1
1
2
0
2
1
1
0
1
0
1
2
2
1
1
1
0
0
1
1
2
2
0
2
1
0
0
1
0
1
0
0
2
1
0
2
2
1
1
2
2
1
0
2
1
1
1
1
0
3
2
1
1
1
0
1
2
2
2
2
1
1
1
1
1
0
2
1
1
0
1
0
3
2
1
1
1
2
2
1
0
1
2
1
1
1
2
2
3
0
1
1
0
2
1
1
1
1
1
1
2
2
3
0
0
1
2
2
2
2
2
2
1
1
1
1
2
0
0
2
1
1
1
1
1
1
0
0
1
3
1
1
2
1
2
1
1
0
1
1
0
0
0
1
2
1
0
2
1
2
1
2
0
0
1
1
1
1
0
2
0
1
2
0
1
1
2
1
0
1
1
2
1
0
1
1
1
0
1
2
2
1
1
0
1
1
1
1
1
0
1
1
2
1
2
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
2
1
1
1
0
1
0
1
0
0
1
1
1
2
2
1
2
1
1
0
1
2
2
1
2
1
2
0
1
1
0
1
0
0
1
1
1
1
2
1
0
1
1
1
2
2
1
1
2
1
1
1
2
2
2
0
0
1
1
2
3
1
1
0
2
1
2
0
1
1
0
1
2
1
1
2
0
1
1
0
1
1
1
1
1
0
2
2
2
0
0
1
0
1
1
1
1
1
2
0
0
0
1
1
2
1
1
1
0
1
2
2
1
1
1
1
1
0
1
0
1
2
1
1
0
1
1
1
0
1
1
1
0
1
2
1
0
2
1
0
0
1
1
2
0
1
1
0
1
0
0
1
0
1
0
0
0
0
2
1
1
1
0
1
1
1
1
0
1
1
1
2
1
2
2
1
0
1
2
0
1
1
1
1
1
1
2
0
2
1
2
1
1
2
0
1
0
1
1
1
1
0
0
1
1
1
1
1
1
2
1
1
0
1
3
1
1
0
0
1
2
0
1
1
0
2
1
2
2
2
1
1
2
2
0
1
0
1
3
0
1
1
1
1
1
2
1
0
0
1
1
1
2
1
0
1
1
0
2
1
0
1
0
1
1
0
1
1
0
0
1
2
2
2
0
0
2
1
1
1
2
1
1
2
0
1
1
1
2
1
1
1
1
2
1
1
1
1
1
0
0
1
1
2
1
0
1
1
1
1
2
1
2
1
2
0
0
2
2
1
3
1
0
0
2
1
1
0
1
0
4
1
0
1
0
1
1
1
1
1
1
2
1
1
0
0
2
1
1
1
2
0
1
1
0
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
2
2
1
1
0
1
1
1
1
0
1
2
1
1
0
1
0
1
0
1
0
1
3
2
0
2
1
0
0
0
1
1
2
0
1
1
1
1
2
2
0
0
2
1
1
0
0
1
1
0
1
1
2
0
1
0
0
1
2
1
1
1
1
2
2
2
1
0
2
1
1
2
1
1
1
1
1
1
2
0
2
0
2
1
0
1
1
2
1
2
2
2
1
2
2
0
2
1
1
2
1
1
1
1
1
1
0
1
2
1
2
2
2
2
1
0
2
1
1
1
0
1
1
2
1
2
2
1
1
0
1
0
2
1
2
1
0
1
1
2
1
2
1
0
2
2
1
2
1
1
0
0
1
1
1
1
1
1
1
1
0
2
1
1
1
1
1
1
0
1
0
0
1
1
0
2
2
2
1
2
1
1
1
1
1
2
1
1
2
1
1
1
1
1
2
2
0
1
1
2
1
1
0
1
0
2
1
1
1
2
1
1
1
1
3
1
1
1
0
0
1
1
0
2
0
1
1
1
2
0
1
1
1
1
0
0
1
2
2
0
1
2
1
2
1
0
0
1
1
1
2
0
1
1
0
1
1
2
2
1
2
1
0
1
2
2
1
2
0
1
0
1
1
0
1
1
1
2
0
1
1
2
1
0
2
0
1
1
2
1
1
0
2
2
0
1
1
2
0
0
0
1
1
1
1
1
1
1
1
1
1
2
2
2
2
2
3
1
2
1
1
0
1
2
1
1
2
1
2
1
3
0
1
0
1
0
2
2
2
0
0
1
1
0
2
1
0
0
2
1
1
2
1
0
1
1
0
2
1
1
0
1
2
1
1
1
1
1
0
2
1
2
1
0
2
1
1
1
2
0
1
1
2
0
2
0
1
1
1
1
2
1
0
1
3
2
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
0
1
1
0
1
1
0
1
0
1
1
2
2
1
1
1
1
0
2
0
1
2
1
2
1
1
1
1
2
2
2
1
0
1
1
1
0
2
1
1
1
1
0
0
1
2
1
1
1
2
1
1
1
1
1
0
1
1
1
2
1
2
1
1
0
1
2
0
2
2
0
1
0
1
1
0
1
1
2
0
2
3
0
1
1
1
0
1
1
0
1
1
0
2
2
2
1
1
0
2
0
1
1
0
1
1
2
0
0
2
1
0
2
1
1
2
1
2
0
0
0
1
0
2
1
1
1
0
2
1
1
2
1
1
2
1
0
1
1
0
0
1
1
1
3
0
1
1
2
1
0
0
3
0
1
1
0
2
2
0
1
0
0
1
1
1
0
1
1
0
1
3
1
1
2
1
1
0
0
0
1
1
1
0
0
2
1
2
1
1
2
0
0
1
0
1
2
1
0
2
0
2
1
1
0
1
1
2
0
1
1
1
1
1
2
1
2
1
1
0
0
1
1
0
0
0
2
1
1
1
1
2
2
1
2
2
1
1
2
0
1
0
1
2
1
1
0
1
1
5
1
1
0
1
0
1
1
1
1
0
1
0
2
1
0
0
2
1
1
1
1
2
0
1
0
0
0
0
1
1
1
0
1
0
1
1
1
1
1
1
0
2
1
1
0
1
1
2
2
2
2
1
2
1
2
0
1
1
0
2
1
2
1
1
0
0
1
0
1
2
2
1
2
1
1
2
0
2
1
2
1
0
1
2
1
2
1
0
2
1
0
1
0
1
1
1
0
1
1
2
1
2
1
1
1
1
1
2
0
0
2
2
1
2
1
1
0
2
0
2
0
1
0
1
2
1
1
0
1
0
1
1
2
2
1
1
2
1
2
1
1
2
2
2
1
2
1
1
1
1
2
1
0
1
2
1
2
0
1
2
1
2
1
1
1
0
1
1
1
1
0
0
0
1
1
2
2
0
1
1
0
2
1
1
2
2
1
2
0
1
2
1
1
2
0
1
1
1
0
1
1
3
2
1
1
2
0
1
2
2
2
0
2
2
2
2
1
1
0
2
2
1
1
0
0
1
0
3
1
1
1
1
2
1
0
1
1
2
1
1
2
1
1
1
1
1
0
0
1
0
2
2
1
1
1
1
3
0
1
2
1
1
1
1
2
1
1
1
0
0
0
0
1
0
2
1
1
2
1
2
3
0
2
1
2
1
2
0
1
1
1
1
1
1
0
1
0
0
2
1
1
2
2
1
1
2
0
1
1
2
1
1
0
1
1
1
1
1
1
1
1
1
1
1
0
1
1
2
1
1
1
2
1
0
2
1
1
2
2
1
1
1
1
2
0
0
1
1
1
2
1
1
1
2
2
0
1
1
1
1
0
1
2
1
1
1
0
1
0
1
1
1
0
1
0
1
0
2
2
1
1
1
1
1
0
1
1
0
2
0
1
1
2
0
1
1
0
1
1
1
1
0
0
1
1
1
2
1
1
2
1
1
2
1
1
0
1
2
1
1
2
2
0
1
0
1
1
0
1
0
1
2
1
1
0
2
1
0
2
2
2
1
0
0
0
1
2
0
1
0
1
1
1
2
1
1
2
1
2
1
1
0
0
1
1
1
1
2
2
2
1
1
2
0
2
0
0
0
1
2
0
2
0
0
0
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
2
0
1
1
2
1
2
1
0
0
0
1
1
2
1
1
1
0
2
2
0
1
1
1
0
0
0
1
1
2
0
1
1
2
2
2
2
0
0
1
2
1
1
1
1
0
1
1
1
2
1
1
0
0
0
2
0
1
1
2
1
0
1
1
2
1
1
0
1
2
1
1
2
2
1
0
1
1
1
1
0
1
1
1
2
1
1
1
1
1
1
0
1
2
1
1
2
2
1
1
1
1
1
1
0
1
1
1
0
0
2
0
2
0
2
1
1
2
1
0
1
1
0
1
1
1
1
1
0
1
1
2
0
0
1
2
1
1
0
1
1
2
2
1
1
1
0
0
2
2
1
1
1
1
0
1
0
1
1
2
1
2
2
1
0
1
1
2
1
2
1
0
0
0
0
2
0
0
2
1
1
1
1
0
1
1
0
1
1
1
2
1
0
0
1
0
2
0
1
2
0
1
1
1
1
0
1
1
1
1
1
1
2
2
1
2
2
0
2
2
0
2
1
2
2
1
1
0
0
2
1
1
1
0
0
1
2
2
0
1
0
0
2
1
1
1
1
0
1
1
1
2
1
2
2
1
1
1
1
1
2
2
2
0
2
1
0
0
2
1
1
2
1
0
1
1
0
0
1
1
1
1
0
1
1
0
1
1
1
3
2
1
1
1
0
2
1
1
0
1
1
1
0
0
1
2
1
0
1
1
1
0
2
1
2
1
2
2
1
1
1
1
1
1
0
2
1
1
1
1
1
2
1
2
1
2
2
1
0
2
2
0
2
1
1
1
1
1
1
1
1
1
0
1
1
2
1
1
2
0
1
2
1
0
1
2
1
1
0
1
1
1
1
1
1
2
2
0
1
1
1
1
1
1
0
2
0
1
0
2
2
1
1
2
2
1
2
1
1
1
1
0
2
0
1
0
0
2
1
1
1
2
2
2
1
2
1
1
0
1
1
2
0
2
0
1
2
1
0
1
2
1
1
2
1
1
2
2
1
1
2
2
0
1
1
1
2
1
2
1
0
1
2
1
2
1
1
0
3
1
0
2
1
0
1
1
0
1
1
1
1
0
2
1
2
1
1
1
1
1
1
3
1
2
2
1
1
2
0
2
1
1
2
2
0
2
1
1
0
2
0
1
0
0
1
1
1
1
1
1
1
1
1
2
1
0
1
0
0
0
1
0
1
1
2
1
1
1
2
1
2
2
1
1
1
1
2
1
1
1
2
1
0
2
2
2
1
1
3
0
2
1
1
2
1
1
0
2
1
1
1
0
1
1
0
0
1
2
1
0
0
1
1
2
1
1
2
0
0
1
2
0
1
2
2
1
0
1
0
1
1
1
1
2
2
2
1
1
1
2
0
1
0
1
1
1
1
1
1
1
3
1
1
1
1
0
1
1
2
1
1
1
2
0
1
0
1
1
1
1
1
1
2
2
2
1
1
1
1
2
2
2
2
1
2
1
1
2
2
1
1
1
1
2
1
2
0
1
2
0
2
1
2
1
1
1
2
0
1
2
0
0
0
1
1
1
2
2
2
2
1
1
2
1
2
2
2
1
1
2
1
0
0
1
0
0
0
0
1
2
0
0
1
1
1
1
2
0
1
1
0
2
0
0
0
1
0
2
3
1
1
1
0
0
2
2
1
0
1
1
0
1
1
0
0
2
2
0
1
2
1
0
1
0
1
1
1
1
0
1
0
0
1
1
1
1
1
1
0
2
2
2
1
2
1
1
1
1
2
0
0
0
1
1
0
0
1
1
1
1
1
2
2
1
2
1
1
2
1
1
1
1
1
1
0
1
2
22
2
1
2
0
0
0
2
2
2
0
1
1
2
1
3
2
1
2
1
3
1
1
1
1
1
1
1
1
2
0
2
1
0
0
1
1
2
1
0
0
1
0
3
1
1
0
1
2
1
1
2
0
1
1
0
2
1
1
2
1
0
1
1
1
1
0
1
2
2
0
2
1
0
1
0
0
2
1
1
0
1
0
0
1
2
3
1
0
0
1
1
0
1
1
0
1
0
2
0
1
1
1
2
0
1
1
1
2
1
1
1
2
1
0
1
1
2
0
2
1
0
1
1
1
2
2
1
1
1
1
1
2
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
0
2
0
1
2
0
2
1
0
1
1
1
2
1
0
1
0
2
2
1
1
1
0
2
2
2
1
1
2
0
2
0
1
1
1
1
1
1
0
2
2
1
1
0
2
0
1
0
0
2
1
1
1
0
1
1
0
0
0
2
2
1
1
2
1
1
1
2
0
2
2
1
2
2
2
1
1
0
1
1
1
1
0
1
0
1
2
1
2
1
0
0
1
0
1
0
0
1
2
0
0
0
1
1
0
1
1
0
1
1
1
1
1
0
1
1
0
1
1
1
1
0
0
0
0
1
1
1
0
0
1
2
2
1
1
1
2
1
1
1
1
2
1
1
0
1
1
1
0
1
0
1
4
1
2
1
1
1
1
2
0
1
1
1
2
1
0
0
0
1
1
1
1
0
1
1
1
1
2
1
2
2
1
1
2
2
2
0
2
0
2
0
0
2
1
0
1
1
1
1
0
1
2
1
0
1
0
2
1
1
1
0
0
2
0
1
2
2
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
0
1
1
1
1
2
2
2
2
2
2
1
0
1
0
0
1
2
1
0
1
1
1
1
2
0
1
0
0
0
0
1
2
1
1
1
1
0
2
2
0
0
1
1
0
1
1
1
1
1
0
0
0
2
1
2
1
3
1
0
0
2
1
0
0
2
1
1
1
2
1
2
1
2
0
0
1
2
2
1
1
2
2
0
2
1
0
0
1
2
1
1
1
1
0
0
1
1
2
0
0
2
3
0
0
2
2
1
1
1
1
1
2
1
1
2
0
0
1
1
2
1
1
1
1
1
1
2
1
2
1
0
1
2
1
1
1
1
1
1
1
1
0
1
1
2
2
0
0
1
1
2
0
1
1
2
1
1
1
1
1
0
1
0
2
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
0
1
0
1
1
1
1
1
2
0
0
2
2
1
2
1
0
2
2
2
1
2
2
1
1
1
1
1
1
1
2
2
2
1
0
1
1
0
2
0
0
0
1
3
2
1
1
0
2
1
1
2
1
0
1
2
0
1
1
2
1
1
0
2
1
1
2
1
0
0
1
1
2
1
1
1
1
2
0
1
1
1
1
1
1
1
1
1
1
2
0
0
1
1
1
0
2
1
1
1
2
2
0
0
0
1
1
0
0
1
1
2
0
1
1
1
1
2
2
0
0
1
1
1
2
0
1
1
1
1
2
1
0
1
2
1
0
1
1
1
1
1
2
1
0
1
2
1
1
0
1
1
2
1
0
2
1
0
0
1
1
2
0
1
1
2
1
0
1
1
1
1
1
2
2
0
1
1
0
1
1
1
2
2
0
1
2
1
2
1
1
1
2
0
0
0
0
2
1
1
0
1
2
1
1
1
0
1
1
1
2
2
0
1
1
2
1
2
0
1
1
1
1
1
1
2
2
0
1
0
1
0
0
1
0
1
2
2
0
0
0
2
3
1
0
1
1
1
2
1
1
1
3
1
1
1
0
2
1
1
1
0
1
1
0
2
0
0
0
1
2
0
1
2
2
1
2
1
1
3
1
3
0
2
1
1
1
1
2
1
1
2
1
1
0
0
2
0
0
2
2
2
2
1
1
1
0
0
1
1
1
1
0
1
1
2
1
2
2
1
0
0
0
0
1
1
0
1
1
0
0
1
1
2
0
1
0
1
0
2
2
2
0
0
0
1
2
1
1
0
1
1
2
2
1
1
0
0
0
2
1
0
1
1
0
2
2
1
1
0
1
1
1
0
1
1
0
0
1
1
1
1
2
1
1
1
1
1
1
2
1
1
0
1
1
1
2
1
1
1
1
1
1
0
1
2
1
2
1
1
1
1
1
1
1
1
1
2
1
2
2
1
2
1
1
0
1
1
1
2
0
1
1
1
1
2
2
1
1
0
1
2
1
2
1
1
1
1
0
0
1
0
0
1
1
2
0
1
0
2
1
1
1
1
0
2
2
0
2
1
1
2
1
1
1
2
1
1
1
1
1
1
0
0
0
0
1
1
0
1
0
0
2
2
0
1
1
1
2
2
1
0
1
2
1
0
1
1
0
0
0
1
2
2
0
1
2
1
1
1
0
1
1
1
2
0
1
2
1
2
1
0
1
1
1
1
2
1
1
2
1
1
1
1
2
0
1
2
1
1
1
2
1
1
0
1
2
1
1
2
2
1
1
1
1
1
2
0
1
2
1
1
2
1
1
1
1
0
2
2
0
1
2
2
1
1
1
1
1
1
0
0
2
1
1
1
1
1
1
0
0
1
2
1
0
2
2
0
2
1
0
1
1
3
1
1
1
1
2
2
1
1
0
0
1
2
1
0
0
1
1
0
0
1
0
1
2
1
2
5
1
0
1
2
1
2
1
2
1
1
1
1
1
1
0
1
1
1
1
0
1
1
2
1
1
2
1
1
1
1
0
0
1
0
1
1
0
2
0
0
0
0
1
1
1
1
0
1
1
0
1
1
2
1
1
0
1
1
0
1
1
2
1
0
2
1
2
2
2
1
2
0
4
1
0
0
1
1
1
2
3
1
0
1
1
0
2
1
0
0
1
0
2
1
2
0
0
1
1
0
2
1
1
1
2
2
0
1
1
1
1
0
1
0
1
2
1
0
1
1
1
1
0
2
1
1
2
2
1
2
0
0
1
1
1
0
1
1
1
1
2
1
1
1
1
1
1
1
0
0
0
0
0
1
2
1
1
2
2
1
1
2
1
1
2
1
2
0
1
1
0
0
1
0
1
0
1
1
1
1
1
0
1
1
0
1
1
1
1
2
0
1
0
1
1
1
1
0
2
0
1
1
1
1
1
1
1
1
2
1
0
1
1
1
2
1
1
1
0
0
1
0
0
1
1
1
1
0
2
1
1
1
0
0
1
1
1
1
0
1
0
1
2
1
1
1
1
1
1
0
1
1
2
2
0
0
0
1
2
1
1
2
1
0
0
0
1
2
2
1
1
1
0
2
1
1
2
0
2
1
1
1
1
1
1
2
0
2
0
0
1
0
1
0
3
1
1
0
2
0
1
1
0
1
1
1
2
1
2
1
1
1
1
2
0
1
1
0
1
1
0
1
1
1
0
2
1
2
1
1
0
0
2
1
0
1
1
1
1
1
0
1
1
1
1
1
1
1
1
2
1
1
2
0
1
1
1
1
1
1
1
1
2
1
1
1
2
0
1
1
1
1
0
1
1
1
2
1
2
0
0
1
1
1
1
0
1
1
0
1
1
1
1
1
1
2
2
1
1
1
0
1
2
2
2
2
1
0
1
1
0
0
0
1
2
1
2
1
1
1
0
1
1
1
0
1
0
0
0
1
2
1
1
1
2
2
0
1
1
0
1
1
1
2
1
2
2
1
1
1
1
2
1
2
2
1
2
1
1
1
2
2
2
2
0
1
1
1
3
1
2
0
1
1
1
0
1
2
1
1
1
1
0
1
2
1
1
1
2
2
1
2
1
0
1
1
1
0
1
1
1
0
1
1
1
1
1
0
0
1
1
2
1
0
2
0
2
2
1
1
1
2
1
1
1
1
2
0
2
1
1
0
1
1
0
1
1
1
1
2
1
1
0
1
0
1
1
2
2
0
1
2
0
1
0
0
2
1
1
0
1
1
1
0
1
0
1
1
3
1
1
2
2
0
1
1
0
1
1
0
1
2
1
0
2
1
1
1
1
1
2
1
1
1
1
2
1
1
2
2
1
1
1
2
2
2
1
2
1
2
1
0
1
1
2
1
0
2
0
0
0
1
1
1
1
2
2
2
1
0
1
0
2
1
1
2
1
2
2
0
1
0
1
1
2
2
1
0
1
0
1
0
1
1
1
1
0
2
2
1
1
1
1
1
2
0
0
0
2
1
1
1
1
2
1
2
2
1
2
1
1
0
1
0
1
0
1
1
1
1
1
1
2
1
1
1
1
1
2
2
2
1
3
1
2
2
2
1
0
2
1
2
0
1
1
2
1
1
0
1
1
1
1
2
1
1
0
0
0
1
1
1
1
1
2
1
0
1
1
1
1
1
1
2
0
1
1
1
2
2
1
1
2
0
0
1
1
0
1
1
1
0
2
1
2
1
1
1
2
1
1
1
2
1
1
2
1
2
0
1
1
1
2
1
0
1
1
2
2
1
1
2
1
1
1
0
1
1
1
1
0
1
2
1
2
2
1
2
1
1
1
1
2
0
2
1
0
1
2
1
2
1
2
2
1
2
0
0
1
1
0
2
0
1
0
1
0
1
2
1
0
2
2
1
2
2
2
1
1
1
1
1
2
1
2
1
1
0
1
0
1
0
1
0
1
0
0
1
1
1
1
0
1
1
0
0
0
1
1
1
1
2
2
2
1
1
2
0
1
0
1
2
0
0
1
1
2
0
0
2
1
1
2
2
2
0
1
0
2
0
0
1
2
2
1
2
1
1
1
0
1
1
1
1
2
1
0
0
2
1
0
0
0
1
2
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
0
1
2
1
0
1
1
0
0
1
1
2
0
0
2
1
1
1
1
0
1
1
0
2
1
1
1
1
1
2
2
1
1
1
1
1
2
0
1
0
1
2
2
2
0
1
1
1
1
2
0
1
0
2
1
0
1
0
1
1
1
2
2
1
0
0
1
1
1
2
1
1
2
1
0
1
1
1
0
1
1
0
1
3
1
1
1
1
1
1
0
1
2
2
1
2
0
1
2
1
0
0
0
1
2
0
1
1
1
2
0
0
0
2
0
1
2
0
0
2
0
2
2
1
1
2
1
1
2
2
1
2
0
0
2
1
1
1
1
0
1
1
1
1
0
1
1
1
0
0
1
1
1
1
0
2
1
3
2
1
2
1
1
0
1
1
0
3
1
1
1
2
0
0
1
1
1
1
1
1
1
1
1
1
0
1
0
1
0
0
0
2
0
1
0
2
2
2
1
1
1
1
1
2
1
2
0
1
2
1
1
0
2
0
1
2
1
2
0
1
1
1
2
0
1
0
2
0
0
1
1
1
1
1
2
0
0
1
1
1
1
1
2
1
2
0
2
1
1
1
2
0
3
1
1
2
1
1
1
1
0
1
2
1
1
2
2
0
1
2
1
0
2
1
2
2
1
1
0
1
2
1
2
1
2
2
1
1
0
1
2
0
0
1
1
1
0
1
2
1
1
0
1
2
1
0
0
0
1
2
2
2
1
1
2
2
0
0
1
0
0
0
2
2
1
1
1
1
0
1
1
2
1
1
1
1
1
1
1
2
0
0
0
1
1
1
0
1
1
1
1
0
1
1
0
1
2
2
1
2
2
1
1
1
2
1
0
1
1
1
2
1
0
1
1
2
0
1
1
0
1
1
1
0
2
0
1
0
1
1
0
1
1
0
0
1
2
1
1
1
0
1
2
1
2
1
1
1
2
1
1
0
0
0
1
2
2
0
2
0
1
2
2
2
2
1
1
1
1
0
0
2
1
0
1
2
1
0
0
0
1
1
2
1
1
0
1
1
1
0
1
0
1
1
1
2
1
1
0
1
1
0
1
0
1
0
1
1
1
0
1
0
0
1
0
1
2
2
1
0
1
1
1
1
0
1
0
0
2
0
1
2
1
0
0
0
1
1
2
1
2
2
1
1
0
0
1
0
0
2
0
1
2
2
0
0
1
0
1
0
2
1
2
1
1
2
2
1
0
2
2
0
1
1
2
2
1
1
1
0
1
1
1
1
1
2
1
3
0
1
1
0
1
1
1
2
1
2
0
1
1
0
2
2
2
0
1
1
1
1
2
1
1
1
1
2
1
2
1
2
0
1
0
0
1
2
2
0
2
2
0
1
1
1
0
1
1
1
0
1
1
2
0
0
0
2
1
1
0
0
0
2
3
1
2
2
1
0
1
1
1
0
0
0
1
0
1
1
0
1
1
1
1
0
1
2
1
1
1
1
1
2
2
1
2
2
2
1
2
0
1
0
1
4
1
0
1
1
1
2
0
1
1
0
0
0
0
1
2
1
2
2
2
0
1
1
1
1
1
2
1
1
1
1
1
0
1
1
1
1
1
2
0
1
2
1
1
1
1
2
2
1
1
1
2
1
1
2
2
1
0
1
0
1
1
1
1
1
1
1
2
2
1
2
0
2
1
1
1
0
1
0
0
2
1
1
2
1
0
1
1
1
0
1
1
0
0
1
1
1
0
1
1
0
1
0
2
2
0
1
0
2
2
1
1
1
1
1
0
1
0
2
2
0
1
1
0
1
0
1
1
3
1
1
1
1
0
2
0
0
1
2
2
0
0
1
0
1
0
0
2
1
1
1
1
0
2
2
0
1
2
1
1
1
1
1
0
2
1
1
2
1
0
0
1
1
1
3
2
0
1
2
1
1
0
0
1
1
1
0
1
2
2
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
0
0
2
1
0
2
1
1
0
1
0
1
0
1
1
2
0
2
0
0
1
1
1
0
1
1
0
1
1
0
2
0
1
1
1
0
1
1
2
0
1
0
1
1
2
2
2
2
1
1
2
2
2
1
1
0
1
1
1
1
2
1
1
1
2
1
1
0
0
1
2
1
0
1
0
2
0
1
0
0
2
0
1
1
1
2
1
0
1
1
2
1
1
0
1
0
0
2
0
2
1
2
1
1
1
0
0
2
1
1
1
2
1
2
1
0
1
0
0
2
1
1
2
3
1
1
2
2
0
0
0
2
2
2
0
1
1
1
0
1
0
0
1
0
1
0
1
1
1
1
1
0
0
1
1
1
1
3
0
1
1
0
0
1
1
1
0
1
2
2
0
2
2
0
1
2
1
1
1
2
2
2
1
2
1
1
1
0
2
1
1
1
1
1
0
0
1
1
2
2
0
2
1
1
1
2
1
1
1
0
2
3
0
1
1
1
1
0
2
1
0
3
1
1
0
1
2
1
2
1
1
0
1
2
1
1
1
0
0
1
0
0
1
1
1
1
1
2
0
2
1
1
1
2
2
1
1
2
0
1
2
2
0
1
2
1
1
2
1
3
1
1
0
1
1
1
2
1
1
1
0
1
1
1
2
1
2
1
1
0
0
2
1
1
2
1
1
0
2
2
1
2
1
2
2
0
0
1
1
0
1
2
1
1
2
0
1
1
1
2
0
0
1
0
1
1
1
1
2
2
0
1
2
1
0
1
0
1
1
0
0
1
1
1
2
1
2
0
1
2
0
1
1
0
2
1
1
2
2
1
1
1
1
0
2
2
2
1
1
1
3
1
1
1
1
1
0
1
2
2
2
1
2
1
0
2
2
1
0
1
0
0
0
2
0
2
0
1
2
1
2
2
1
1
1
1
1
1
1
0
1
1
1
1
2
0
1
1
2
1
2
2
2
0
1
1
1
1
2
1
2
0
1
2
0
2
1
2
2
1
0
2
2
1
1
1
1
0
2
1
0
1
0
0
2
2
1
0
2
2
1
2
0
1
1
1
0
1
1
0
0
0
1
4
1
0
0
2
1
0
1
0
1
2
1
1
0
1
1
2
2
1
1
1
0
2
2
2
2
0
0
1
0
2
0
1
1
0
1
4
1
1
1
1
1
2
2
2
1
2
0
2
0
1
0
0
1
2
1
1
2
1
1
0
1
0
0
1
0
1
0
2
0
1
2
1
1
2
2
0
3
0
1
0
1
1
1
0
1
1
2
1
1
1
1
2
2
1
1
0
0
1
1
2
1
3
1
1
2
2
1
1
0
1
1
2
0
1
2
1
1
2
0
2
1
1
1
0
2
2
1
2
0
0
0
0
0
2
1
1
1
1
1
1
0
1
1
0
2
0
0
1
1
1
2
0
1
3
0
0
2
1
1
3
2
1
1
2
1
1
2
0
1
1
0
2
0
0
1
2
2
2
2
0
0
1
1
1
1
1
1
0
0
0
1
0
1
1
0
1
2
1
0
0
0
2
1
0
1
0
1
1
2
1
1
0
2
0
0
1
2
2
1
1
0
2
1
1
1
1
0
2
2
0
0
0
0
1
0
1
2
1
0
1
0
1
0
0
1
0
1
2
1
0
1
1
1
1
2
1
1
1
1
1
0
1
1
0
1
1
2
2
1
1
0
1
1
1
2
1
0
2
0
1
2
1
0
1
0
1
1
1
2
1
0
2
1
1
2
2
1
0
1
0
0
1
1
2
0
0
1
1
1
0
0
1
0
1
1
1
0
1
2
2
0
1
1
1
2
1
2
1
1
1
1
1
0
1
1
1
2
1
3
0
2
2
1
1
1
1
1
1
0
1
1
0
1
1
3
0
1
2
0
0
1
3
0
1
0
1
1
1
1
0
0
2
2
1
1
1
2
1
1
1
0
0
2
1
2
1
0
0
3
2
0
1
2
1
1
1
1
1
0
1
1
1
0
1
1
1
1
1
1
1
1
0
1
1
1
0
0
1
1
0
1
1
1
2
1
0
0
1
1
2
1
1
1
1
1
0
0
2
0
1
0
0
1
1
0
1
1
2
1
2
2
0
1
2
2
1
2
2
2
1
1
2
1
1
2
0
2
2
0
0
1
1
1
1
1
2
0
2
2
0
2
0
1
2
0
1
1
1
0
1
2
2
1
1
1
2
0
1
1
1
1
1
1
1
2
3
1
2
1
1
1
2
0
5
1
2
2
1
1
1
1
2
4
0
2
2
0
2
2
1
1
2
0
3
1
0
2
1
2
2
1
0
1
1
2
2
1
1
2
0
1
2
1
0
1
1
1
2
0
2
0
0
1
2
1
2
1
0
1
1
2
1
2
2
2
0
1
1
1
2
1
1
1
1
0
1
1
1
0
0
2
0
1
1
0
1
0
2
1
1
0
1
1
0
1
2
2
2
0
1
2
1
0
1
1
2
3
1
1
1
1
1
1
1
0
1
0
2
1
1
0
1
1
1
1
1
0
1
2
0
1
1
0
0
2
0
1
0
1
1
1
1
1
1
0
1
0
1
0
2
1
2
1
1
1
1
2
1
2
1
1
1
0
1
1
1
1
1
2
1
1
0
1
0
0
1
1
1
0
1
0
1
1
1
2
1
1
1
2
1
1
1
0
1
2
1
0
1
1
0
2
0
2
1
2
2
2
1
2
0
1
1
0
1
1
0
1
0
1
1
1
2
1
1
1
1
1
2
2
2
0
1
1
0
2
1
0
1
2
1
1
1
1
1
0
2
2
2
0
1
1
0
1
0
1
1
0
1
1
2
1
0
0
0
1
0
1
0
1
0
1
0
0
1
0
2
1
0
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
0
1
1
1
1
2
2
0
2
2
1
0
0
0
0
0
0
0
0
1
2
2
0
1
1
2
1
1
1
1
0
1
0
5
1
0
2
2
0
2
2
2
1
1
2
1
0
2
0
1
2
0
1
1
4
0
0
0
2
1
0
2
1
1
1
0
1
2
0
0
1
1
0
0
1
0
0
1
2
1
0
2
1
0
1
1
1
1
2
2
2
2
1
0
1
0
0
0
0
1
1
0
2
1
1
2
1
0
2
2
0
1
1
2
1
1
0
0
2
0
2
1
0
1
2
1
2
1
1
2
1
0
2
2
0
1
1
1
1
1
0
2
0
0
2
1
2
1
1
1
1
1
2
1
1
0
1
1
2
0
1
0
1
1
0
1
2
1
2
1
1
1
0
0
1
1
1
2
1
0
2
1
1
0
1
1
1
0
0
1
1
1
2
1
2
1
1
2
1
2
1
0
1
2
1
1
2
1
1
1
2
2
1
0
1
1
1
2
1
0
0
1
1
1
1
1
1
1
1
2
0
0
2
0
0
0
0
2
1
1
1
2
1
0
1
0
1
1
2
2
0
2
1
2
1
1
1
0
1
1
1
0
1
1
1
1
1
1
0
1
0
1
0
0
1
1
1
0
1
2
3
1
1
1
1
0
1
1
1
1
1
1
1
2
0
0
2
1
0
0
2
1
1
1
0
2
0
2
0
2
0
1
2
1
0
1
1
1
1
1
2
0
1
1
0
0
2
1
1
0
0
2
1
1
0
1
1
1
0
2
2
0
2
1
0
2
1
1
2
1
1
1
1
1
0
2
1
1
2
2
1
1
1
0
0
1
0
1
0
1
1
1
0
0
3
1
1
1
1
0
1
1
1
0
1
1
2
0
2
1
1
1
1
1
1
0
2
1
0
0
2
1
2
1
1
1
1
2
1
1
0
1
1
1
1
1
2
1
1
1
1
2
1
1
0
1
1
1
0
2
0
2
1
2
1
0
1
1
1
0
0
1
0
1
2
1
0
2
1
1
1
1
1
1
2
1
0
1
1
0
2
1
1
1
0
1
2
1
1
0
2
1
2
1
1
1
0
0
1
0
0
2
2
2
1
1
2
1
2
1
1
1
0
1
1
1
2
1
1
1
1
1
2
2
1
2
1
1
1
1
0
1
1
2
1
1
1
1
0
0
1
1
1
1
1
2
2
2
2
1
1
0
2
2
0
1
1
1
1
1
1
0
2
1
0
1
1
2
0
1
1
1
1
1
1
2
2
1
1
1
2
0
1
2
1
0
2
1
1
1
1
1
1
1
1
2
2
1
1
0
2
1
2
1
2
2
2
1
1
1
1
2
1
1
0
2
1
2
0
2
1
0
1
2
1
1
2
1
1
0
1
1
1
1
0
2
2
1
0
2
1
1
1
2
1
1
1
1
1
1
0
1
1
2
2
1
1
2
0
1
1
1
0
2
1
3
1
0
1
1
1
1
0
0
0
4
0
0
2
2
1
0
0
2
0
0
1
2
1
2
0
1
1
0
1
1
1
0
1
1
1
0
1
0
1
1
1
1
1
1
1
0
2
1
1
1
2
0
0
1
1
2
1
2
2
1
1
1
1
1
1
1
0
2
0
1
1
1
2
2
1
1
1
1
0
1
3
1
1
1
1
1
1
1
1
1
1
0
1
1
2
2
1
1
1
2
0
0
1
1
0
0
1
1
2
1
1
2
1
1
2
1
1
1
0
1
1
0
2
1
1
2
0
2
1
1
0
2
1
2
2
1
1
1
1
1
1
2
1
1
1
1
0
2
1
1
1
0
1
0
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
2
2
1
1
2
1
0
1
1
0
2
0
2
2
1
0
0
1
0
2
1
1
2
1
2
2
2
1
2
1
1
1
0
0
2
1
1
2
1
1
2
0
2
1
1
1
1
1
1
1
1
1
0
2
1
1
1
0
2
1
0
1
0
1
0
2
1
0
1
0
2
1
1
1
1
2
2
1
0
2
0
1
0
1
1
1
1
0
2
1
0
1
0
2
1
1
1
1
0
1
1
1
0
1
1
1
1
1
2
0
1
1
2
0
2
1
0
1
1
1
2
1
0
1
0
0
1
2
1
1
2
0
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
2
1
0
2
0
2
1
2
1
2
0
0
0
2
2
1
0
1
2
1
1
1
0
1
1
0
1
1
1
0
1
1
1
1
1
1
0
1
2
1
1
0
0
1
2
1
0
1
0
1
2
0
1
1
0
1
2
2
2
2
0
1
2
1
1
1
1
2
1
1
1
1
1
0
2
1
1
2
1
1
0
2
0
1
2
0
1
1
0
2
2
2
0
1
1
0
1
1
1
0
1
1
0
1
0
1
1
1
0
1
1
1
1
1
2
1
1
1
1
0
0
1
0
1
1
2
1
1
0
1
0
1
2
0
0
2
1
1
2
1
1
1
0
1
0
1
1
0
3
1
1
2
1
1
1
0
2
2
2
1
2
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
0
2
1
1
0
2
0
2
1
1
1
2
1
2
2
1
0
2
1
2
0
2
1
1
2
1
1
0
2
1
1
1
0
1
1
2
2
0
1
0
1
1
2
2
1
1
0
1
1
1
0
1
2
2
2
2
1
0
1
1
1
1
0
1
4
1
1
1
0
1
1
2
2
1
1
1
0
1
1
2
1
2
0
1
1
2
0
1
1
1
0
2
1
2
0
1
1
0
1
1
2
0
1
0
1
2
2
2
1
1
1
2
1
1
2
1
1
1
1
1
1
1
0
1
0
2
2
0
2
1
1
1
1
0
1
1
0
1
2
2
1
1
1
0
0
1
1
1
1
0
2
1
2
1
1
0
1
0
1
0
1
0
1
0
1
1
1
1
2
3
1
1
2
0
1
1
2
2
2
0
2
1
1
2
1
1
0
0
0
2
2
1
0
1
1
2
1
1
1
1
1
2
2
1
2
2
2
1
2
2
1
1
1
1
1
1
0
2
1
0
1
2
1
1
0
2
2
1
1
2
2
4
1
1
0
2
0
0
2
2
2
0
1
1
1
1
2
1
0
1
1
0
2
0
1
0
0
0
1
2
2
1
1
1
1
0
1
1
1
1
1
1
1
0
1
1
1
1
4
2
0
1
1
1
1
1
2
1
2
2
1
1
1
1
1
0
1
1
0
0
2
0
0
1
0
1
1
1
1
1
2
1
2
1
1
2
1
2
1
1
2
1
2
2
1
1
1
2
3
1
1
0
2
1
2
0
1
0
2
0
1
0
1
1
1
2
1
2
1
0
0
0
3
1
1
2
2
1
0
1
1
1
1
1
2
0
1
2
1
1
1
1
0
3
1
1
2
1
1
2
1
1
1
2
0
0
2
2
2
1
3
0
1
1
1
2
0
2
1
1
0
1
2
2
1
1
1
2
1
1
1
1
1
0
2
1
0
0
2
0
0
1
0
2
1
2
2
1
1
0
1
1
2
2
1
2
1
0
1
2
1
1
1
1
1
0
1
1
1
0
1
0
1
1
2
1
1
1
1
0
2
0
1
2
1
1
2
1
2
1
0
1
1
1
2
0
1
2
1
1
0
2
1
2
0
2
1
1
1
2
1
1
0
0
1
1
0
1
2
1
2
1
1
1
0
1
2
0
2
1
1
1
1
1
1
2
1
1
2
1
1
1
0
2
1
2
1
2
1
1
2
1
0
1
3
2
2
1
0
2
2
1
0
1
1
2
0
1
1
0
1
1
1
1
0
1
0
0
1
1
1
0
2
2
1
2
0
2
1
1
1
1
1
1
2
1
1
2
1
1
2
2
1
1
1
2
1
1
0
1
2
1
0
2
0
1
1
1
0
0
1
1
3
1
1
2
2
1
0
2
0
2
1
1
1
1
0
0
1
2
1
1
0
1
2
1
1
0
1
1
2
2
1
2
0
1
1
2
0
1
1
1
1
2
1
1
2
1
2
2
0
1
1
0
1
1
0
1
1
1
2
3
1
1
0
1
0
1
2
0
1
0
1
1
1
1
2
1
2
2
0
0
2
1
0
0
1
1
1
1
1
1
1
2
2
1
0
0
0
0
1
2
1
2
0
1
0
1
1
1
2
0
1
1
1
1
2
1
1
3
1
2
2
2
1
1
0
1
0
2
1
2
1
0
2
1
1
1
0
2
2
1
1
0
1
2
0
1
2
1
0
1
1
0
1
1
1
1
3
0
0
2
2
1
1
0
1
1
0
1
1
0
2
1
2
1
1
1
1
1
1
1
2
2
2
0
1
1
1
2
2
1
0
2
1
0
1
0
0
1
1
2
1
1
1
2
2
2
1
0
1
1
2
0
1
1
1
0
0
1
1
2
2
2
2
1
2
1
0
2
0
1
0
1
1
1
1
1
1
1
1
1
1
2
0
2
0
0
2
2
0
1
0
0
1
1
1
1
1
1
2
2
1
0
2
1
2
1
1
1
1
1
0
1
1
0
1
4
2
1
1
2
1
2
2
1
1
1
1
2
0
2
2
1
0
1
0
1
1
1
0
0
1
1
1
0
0
0
0
1
1
1
2
0
1
0
1
1
0
2
1
2
1
2
0
0
2
0
2
1
2
1
1
1
1
1
1
0
1
0
0
1
1
2
1
1
2
1
2
2
1
2
1
1
1
1
1
1
0
0
1
0
1
1
0
2
0
1
1
2
0
1
1
1
0
2
1
1
2
1
1
1
1
3
1
1
2
1
0
1
0
1
1
0
1
1
1
0
0
0
3
1
1
2
0
1
2
1
1
0
2
2
2
1
1
1
1
1
1
1
1
1
1
1
2
0
1
1
2
2
2
2
0
1
1
1
1
0
1
0
1
1
2
0
1
1
1
2
1
0
1
1
1
1
2
1
0
2
1
1
1
2
1
2
1
3
1
1
1
1
2
1
1
1
1
0
1
2
0
0
1
0
2
0
0
1
2
1
1
0
2
2
1
1
0
1
0
0
2
1
2
2
1
0
1
1
2
2
1
0
1
0
2
1
2
3
1
1
1
1
2
1
4
1
2
1
1
1
0
0
0
1
1
1
1
0
0
2
1
2
2
1
1
2
1
1
2
1
1
1
1
1
1
0
1
1
2
1
2
1
2
0
0
1
2
0
1
0
1
2
0
2
2
0
1
1
0
1
1
1
0
0
2
1
1
1
1
1
0
1
1
2
1
0
0
2
0
2
2
2
1
2
2
1
1
2
1
1
0
2
1
1
1
1
5
2
1
0
1
2
1
0
1
1
0
1
1
0
1
0
1
1
1
1
1
4
0
1
1
1
1
0
1
2
0
0
2
1
0
0
1
1
1
1
1
0
1
2
0
1
0
1
1
0
0
0
1
1
2
1
1
0
2
1
1
1
2
1
0
1
1
1
0
1
2
1
0
1
1
2
1
1
2
1
1
1
1
1
1
0
1
1
2
1
1
1
1
2
3
1
1
1
0
1
2
0
0
1
1
2
1
1
1
0
1
1
1
1
0
0
1
2
2
1
0
2
2
1
3
1
0
1
1
1
0
1
1
1
1
1
2
0
1
0
0
1
1
2
2
2
1
1
1
1
0
3
2
0
2
0
1
2
1
1
0
1
2
1
2
4
0
1
0
2
2
1
0
1
1
2
0
1
0
2
1
1
2
1
1
2
1
0
2
2
0
2
2
2
1
1
1
0
0
1
1
2
0
1
0
1
1
1
0
1
1
1
0
1
0
2
1
1
1
1
1
0
0
1
1
1
1
1
1
2
1
1
0
1
1
1
1
1
1
1
2
0
3
2
0
0
2
1
0
2
1
2
0
1
0
0
1
1
0
1
0
1
1
1
1
2
1
1
1
0
1
1
1
1
1
1
2
1
2
1
2
2
0
1
1
1
0
2
0
2
1
1
2
1
2
1
1
1
2
0
2
0
0
2
0
1
1
1
2
1
1
1
1
1
1
1
0
1
1
0
1
1
1
0
2
1
1
0
1
9
1
2
0
0
2
0
1
2
2
2
1
1
0
0
1
2
0
0
1
1
1
0
0
1
1
1
0
1
2
1
1
0
2
2
0
1
0
1
1
2
0
0
1
2
2
2
1
1
1
0
1
2
1
1
0
1
1
1
1
0
0
0
1
0
1
2
0
2
0
1
1
0
1
1
1
3
2
0
1
2
1
2
1
1
1
2
1
1
0
0
0
1
1
1
0
0
0
0
0
1
2
0
0
1
2
2
1
0
1
3
1
2
2
2
2
1
1
2
0
1
1
0
1
1
1
1
1
2
2
1
1
0
1
1
1
1
1
0
1
1
0
1
2
1
2
3
1
2
1
3
2
0
0
0
0
0
1
2
2
1
1
1
1
2
2
4
1
2
0
2
0
2
1
0
2
1
2
2
3
1
1
0
1
1
2
0
1
2
2
1
0
2
0
1
0
1
1
0
0
1
1
1
1
2
1
1
0
0
1
1
1
0
2
2
1
1
3
2
0
0
1
1
1
2
1
1
0
0
1
1
1
1
1
1
2
1
2
1
2
0
0
1
1
1
1
1
1
1
0
1
2
0
1
1
1
0
0
0
0
1
2
2
2
2
1
1
1
1
2
2
1
1
2
1
2
1
1
2
2
2
1
2
2
2
0
2
1
2
2
0
2
2
1
1
1
2
2
1
1
1
0
0
1
2
1
2
1
1
1
1
1
2
0
1
1
1
0
1
1
1
2
0
0
2
1
1
1
1
2
0
2
1
1
1
1
1
1
2
1
1
1
1
0
2
2
2
1
0
2
0
0
0
0
2
2
0
1
3
1
2
1
1
2
1
0
1
0
2
0
0
1
1
2
1
1
1
2
1
2
1
1
0
1
1
2
1
2
1
2
1
2
1
0
0
1
0
2
2
1
2
1
1
2
1
0
2
2
1
1
2
1
2
1
1
0
0
1
1
1
1
0
1
0
1
1
0
2
1
1
2
2
1
0
4
1
0
1
0
0
1
2
1
1
1
1
0
1
1
1
1
0
1
0
1
2
2
1
1
1
1
1
1
1
1
1
1
1
0
1
0
1
1
0
0
2
0
2
0
1
1
1
2
1
1
1
2
1
1
0
1
1
1
2
1
1
2
1
2
2
0
0
0
1
4
2
1
1
1
1
0
1
1
2
1
2
1
1
5
0
2
2
0
0
1
2
2
2
0
1
0
0
2
1
1
1
1
1
2
0
1
2
1
2
0
1
2
1
1
2
0
1
0
2
1
1
1
1
2
1
1
0
0
2
1
1
1
1
1
2
1
1
0
0
1
1
1
1
1
0
1
1
1
0
1
1
2
1
2
3
1
2
0
1
1
0
1
0
2
1
2
1
1
0
1
0
1
1
1
1
2
1
2
3
1
0
2
0
0
1
2
2
1
2
1
1
0
0
1
1
1
2
2
1
1
1
1
2
2
2
2
1
0
2
1
1
0
1
1
1
1
1
1
1
1
0
1
2
2
2
1
1
0
2
2
2
1
2
1
1
1
1
2
2
0
2
0
1
1
2
1
0
1
0
1
1
4
0
0
1
0
1
1
1
2
1
1
0
2
1
1
0
1
1
2
1
1
1
2
0
1
0
2
1
1
1
1
1
1
0
0
1
1
1
3
2
1
1
0
3
0
1
1
1
1
0
2
1
1
1
1
2
1
1
1
1
0
1
0
1
1
1
1
0
2
0
2
1
1
0
1
1
2
0
2
1
2
2
1
2
3
1
2
2
1
0
2
0
0
2
2
1
0
1
0
0
1
1
1
2
1
1
1
2
0
2
1
0
2
2
2
1
1
2
1
1
1
1
1
2
1
1
1
2
2
3
1
1
1
1
0
1
1
1
1
1
2
0
1
3
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
1
0
2
3
1
0
1
3
3
0
1
1
1
1
1
1
1
1
0
1
1
1
1
0
2
0
1
1
3
2
1
1
1
2
1
0
1
0
0
1
2
1
1
0
1
0
2
1
1
1
1
0
2
2
0
0
1
1
0
1
1
2
1
1
1
2
0
1
1
2
0
0
1
1
0
1
1
0
1
1
1
2
1
2
1
3
1
0
2
1
1
2
2
1
0
2
2
0
2
1
2
2
2
2
1
1
1
1
1
1
1
1
1
2
1
1
2
1
0
0
2
1
2
1
0
1
1
2
1
1
1
1
0
1
1
1
9
1
1
2
2
0
1
2
0
0
1
1
0
0
1
0
1
1
1
1
2
0
2
2
0
0
1
1
2
2
1
0
0
1
1
2
1
2
1
0
1
0
2
2
0
1
0
1
2
1
2
1
2
1
1
2
1
2
2
1
1
2
2
0
1
0
1
2
0
1
1
1
1
2
1
0
1
0
1
2
2
1
1
2
1
2
1
1
0
1
0
0
1
1
1
2
2
0
1
1
0
1
2
0
0
0
1
0
1
1
1
1
2
2
1
0
1
1
1
2
0
2
1
1
1
1
1
0
0
1
1
2
2
1
0
1
1
1
0
2
1
1
1
1
2
1
0
1
0
2
1
2
1
0
1
1
0
1
2
1
1
2
0
1
1
0
3
3
2
1
1
2
1
1
1
2
0
1
0
1
1
2
1
2
1
2
1
1
2
0
3
2
1
2
2
1
1
1
1
2
0
1
1
1
0
0
2
1
1
1
1
2
1
2
1
1
1
1
1
3
0
0
1
1
1
1
1
0
1
2
0
1
0
0
0
0
1
1
1
2
2
1
1
2
1
1
1
1
1
2
2
0
1
0
1
1
1
1
1
4
1
1
1
0
1
1
1
0
1
1
2
1
1
1
0
2
1
1
1
1
1
0
1
1
1
0
1
1
1
1
1
0
2
0
1
1
0
1
1
0
1
1
0
1
0
2
0
2
0
1
1
1
0
2
1
2
2
1
0
0
1
0
1
0
2
1
1
1
2
1
0
1
1
1
1
1
1
1
1
2
1
2
1
0
2
1
3
1
1
1
0
0
1
2
1
1
0
2
2
0
1
1
1
1
1
0
2
1
1
1
2
1
1
0
1
0
1
1
0
1
2
1
1
2
0
1
1
0
1
0
2
1
1
2
1
0
1
1
0
1
2
1
2
0
1
2
1
2
1
1
1
1
1
1
2
2
1
5
1
1
2
2
0
2
2
1
2
0
1
1
0
1
1
0
1
1
1
0
1
1
1
1
1
2
0
1
2
0
1
1
1
0
1
3
1
1
0
1
1
1
0
1
1
0
1
1
1
0
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
0
1
2
1
1
1
2
2
0
1
2
2
2
2
0
0
1
2
0
0
1
0
1
1
2
2
2
2
1
0
1
1
1
1
1
1
1
1
0
0
2
1
1
1
1
1
1
1
1
1
1
0
1
0
1
1
0
2
1
2
0
1
1
1
0
1
1
2
0
1
0
1
2
1
1
2
1
0
1
1
2
1
0
3
2
2
0
2
0
1
1
1
1
2
1
0
1
1
2
2
1
1
0
1
1
2
1
2
0
0
0
1
5
0
1
1
1
1
2
1
1
2
2
0
1
1
2
2
1
1
1
1
1
1
1
0
1
0
0
1
0
1
1
2
1
1
2
2
1
0
1
0
1
1
1
0
1
0
1
1
2
1
1
0
1
1
0
0
1
1
1
0
0
2
1
0
2
1
1
1
1
0
0
0
1
0
2
1
1
1
1
2
1
2
1
0
1
2
1
2
0
1
1
2
2
0
0
1
1
1
0
0
1
2
0
1
0
1
1
2
2
1
1
1
1
1
2
2
0
2
1
0
1
1
2
1
2
1
1
2
2
1
0
1
1
1
0
2
2
1
1
2
1
1
1
2
2
0
1
0
1
2
1
1
1
1
1
1
2
2
0
1
1
0
1
0
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
0
1
0
2
1
0
1
0
1
1
1
2
1
1
1
1
2
0
1
2
1
1
3
0
3
1
1
0
2
1
1
0
1
2
0
2
0
2
0
1
1
1
0
1
1
1
0
1
1
1
1
2
1
1
1
2
0
1
1
0
1
2
2
0
1
0
0
1
1
0
0
2
1
2
1
2
1
1
2
1
1
1
0
1
0
2
1
2
1
0
1
2
1
1
2
2
2
0
1
2
0
1
1
1
1
0
1
1
2
2
0
0
0
0
1
0
0
0
1
1
2
2
1
2
1
0
2
2
2
1
0
0
1
1
0
2
1
1
0
1
1
2
1
2
1
1
0
1
2
2
2
1
0
1
1
1
1
2
0
1
2
1
0
1
1
1
1
1
2
0
0
1
1
2
1
1
0
0
1
1
1
1
2
0
1
1
0
0
1
2
1
1
1
1
1
1
1
1
1
0
1
0
0
1
1
1
1
0
1
2
1
1
0
1
1
1
0
0
1
2
1
2
1
2
0
2
2
1
1
2
1
2
0
0
1
1
0
1
1
1
2
1
0
2
2
1
0
1
1
1
2
2
1
1
1
0
3
1
1
1
1
0
1
1
1
1
1
0
1
2
2
1
2
1
1
1
2
1
0
1
1
1
1
1
2
1
1
0
0
2
0
1
1
1
1
2
0
1
1
0
2
1
1
2
1
1
2
0
1
0
1
1
0
1
2
1
1
1
1
2
1
0
3
1
0
1
1
1
2
1
1
0
1
0
1
1
1
1
2
0
1
0
1
2
1
1
1
0
1
1
1
1
1
1
1
1
0
1
1
1
2
0
1
0
3
2
3
0
0
1
1
2
2
1
0
0
1
1
1
0
0
0
2
1
2
1
0
1
1
1
1
2
1
2
1
2
0
1
0
1
0
1
0
2
1
0
1
0
1
1
0
0
0
2
1
1
2
1
1
2
0
2
2
0
1
1
0
1
1
0
1
1
1
3
2
2
1
1
2
0
2
0
0
2
1
2
0
1
0
1
1
0
2
1
1
1
1
1
2
0
0
1
2
1
1
1
1
1
1
2
2
1
1
2
1
2
1
1
1
1
1
0
1
2
1
0
1
2
1
1
2
0
1
1
0
1
1
2
0
0
1
1
1
2
1
2
1
0
0
1
1
2
1
2
2
1
1
1
0
1
1
2
1
1
1
2
0
0
1
2
0
1
2
2
1
1
1
1
1
2
2
0
2
1
1
1
2
2
0
1
1
2
2
0
1
1
1
0
1
0
2
1
0
2
1
1
1
0
1
0
0
2
2
2
2
0
1
0
1
0
1
2
2
1
2
1
0
1
1
0
2
1
1
1
1
0
2
1
1
1
2
2
1
1
1
2
0
1
1
1
2
1
1
1
1
0
1
1
1
0
1
1
1
2
2
2
1
1
1
1
2
0
2
0
0
1
1
2
1
0
2
0
2
2
1
0
1
2
1
0
2
1
1
0
1
1
1
1
0
2
1
1
0
1
1
1
0
1
2
0
0
1
2
2
1
0
0
1
1
2
2
1
1
1
1
1
2
0
1
1
0
2
0
1
0
1
2
0
1
1
0
1
1
1
1
1
1
0
1
1
1
0
0
1
0
0
1
1
1
2
2
1
1
2
0
0
2
1
1
1
1
2
1
0
0
1
0
2
1
1
1
0
1
2
1
1
1
1
1
1
2
2
1
2
0
1
1
0
1
0
2
1
0
1
0
0
2
1
1
1
1
1
0
1
1
1
1
1
0
0
2
0
2
0
0
0
1
2
0
0
1
1
2
0
1
2
1
2
0
1
1
1
1
1
1
1
2
3
2
1
1
2
2
1
1
1
0
1
1
0
1
1
0
1
1
0
0
1
0
1
1
1
0
1
2
1
1
2
2
1
1
1
0
2
0
1
1
2
2
1
1
0
2
1
0
1
2
0
1
2
1
0
1
1
2
0
1
1
2
1
3
0
1
1
2
2
0
2
1
1
1
0
1
1
0
1
0
1
1
0
0
1
1
2
1
1
1
0
1
1
1
0
0
0
1
0
1
1
1
1
0
1
0
0
2
2
0
1
0
1
0
0
2
2
1
2
2
1
0
1
2
2
1
1
0
1
1
2
1
2
2
2
1
1
0
1
0
2
1
1
2
2
1
1
1
0
0
1
2
1
1
2
1
1
2
0
1
0
0
1
1
1
2
1
1
2
1
1
2
1
0
2
1
1
1
0
1
1
2
1
0
0
1
1
2
1
1
0
0
1
1
0
0
1
1
2
1
0
0
1
1
1
1
1
1
0
0
2
1
1
0
1
1
1
1
1
2
1
0
2
3
0
0
1
1
1
1
1
2
1
0
1
1
0
2
0
1
2
2
1
1
1
0
1
3
1
2
2
1
0
4
1
0
0
1
0
2
2
2
1
2
1
0
0
0
0
0
1
2
2
1
2
1
2
1
1
0
2
1
1
1
0
1
0
1
3
1
1
2
1
1
1
1
1
1
1
1
1
0
1
1
1
0
2
1
0
0
0
2
1
1
1
1
1
1
2
1
2
1
1
0
1
1
2
1
1
1
1
1
2
2
1
2
2
0
1
0
1
1
1
0
1
1
1
0
1
1
2
0
1
2
1
1
2
2
2
1
2
0
1
0
1
2
2
1
1
1
2
1
1
2
2
2
1
1
1
1
0
2
1
0
1
0
0
1
1
1
1
1
2
1
2
1
0
1
1
1
1
1
0
1
2
1
0
1
1
0
1
1
1
1
2
1
0
2
1
1
1
0
1
1
0
1
1
2
1
0
3
1
1
2
1
1
1
1
2
1
1
1
1
2
0
0
1
2
2
2
1
2
2
1
1
1
1
1
1
1
1
0
0
0
1
1
1
2
2
1
1
1
1
2
1
2
0
1
0
1
1
1
1
2
3
0
2
1
3
2
1
0
0
2
0
1
0
2
1
1
1
1
0
2
1
1
1
1
2
1
0
1
0
0
2
1
1
1
2
2
1
1
1
0
0
2
8
1
1
0
1
1
1
1
0
1
0
2
2
0
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
0
1
1
1
2
1
0
2
1
2
2
2
1
1
0
0
2
1
1
0
1
0
2
3
0
1
1
2
1
0
2
1
0
1
1
1
2
1
2
1
2
0
1
2
1
2
2
0
1
2
2
0
1
1
1
1
1
0
0
1
1
1
1
0
0
1
1
1
1
1
1
1
0
0
0
2
1
2
0
1
2
1
1
2
1
2
1
1
2
1
1
1
1
2
1
0
1
1
0
1
1
1
0
1
1
1
1
1
1
2
2
1
1
2
1
2
0
2
1
2
1
2
1
2
1
1
0
1
1
0
2
1
0
1
2
0
1
1
2
1
1
2
0
2
0
2
1
1
1
1
1
1
0
1
1
1
1
1
2
2
1
2
0
2
1
1
1
1
0
1
0
2
2
2
1
1
0
2
1
1
1
1
0
1
1
1
2
1
1
1
1
0
1
1
2
2
1
2
0
2
1
0
1
0
1
1
0
0
1
2
2
0
1
1
2
2
1
1
1
0
1
1
0
0
0
0
1
1
1
1
1
1
1
0
1
1
1
1
1
0
1
2
2
0
0
0
1
1
3
1
0
2
2
1
0
2
2
1
1
1
0
1
0
1
1
1
0
0
1
1
2
0
0
1
1
0
2
0
2
1
2
1
1
1
0
1
1
2
0
1
2
0
1
0
1
1
1
1
2
2
1
1
0
0
1
2
2
1
1
0
0
1
3
1
1
2
2
1
1
1
1
1
1
2
2
1
2
1
2
0
1
1
1
1
2
1
2
2
0
1
1
1
2
2
1
1
2
3
0
0
1
0
1
1
1
2
1
0
2
0
1
1
2
1
1
0
1
1
1
0
1
1
1
2
1
1
1
1
1
1
0
2
2
1
0
1
1
1
1
1
0
1
2
1
1
1
1
1
2
1
2
1
1
2
1
0
0
1
0
0
1
1
1
1
2
0
1
1
2
1
1
1
1
2
1
2
1
0
1
0
0
1
0
1
2
0
1
2
0
0
2
1
0
1
1
0
2
1
1
0
3
0
0
2
1
2
2
1
2
0
1
1
1
0
1
1
1
1
1
0
1
1
0
0
1
0
1
1
1
1
1
2
1
1
2
2
1
0
1
1
1
1
1
2
2
1
1
1
0
1
1
1
1
1
1
2
0
1
1
1
0
1
1
1
0
0
1
1
1
2
1
1
0
2
2
1
1
0
1
1
2
2
2
1
1
1
1
1
1
0
2
1
0
2
0
1
1
3
1
1
1
2
2
0
1
2
0
2
1
2
0
0
1
0
1
0
2
1
1
1
2
0
0
1
0
1
0
3
2
3
1
1
0
2
1
1
1
0
1
1
0
1
1
1
2
0
1
1
1
0
1
0
0
1
0
1
2
1
0
0
0
1
0
1
1
1
1
0
1
1
0
1
1
0
1
1
2
0
1
1
1
2
0
1
1
1
0
1
2
1
1
2
1
1
1
1
1
1
1
0
1
1
2
1
1
0
1
1
2
1
2
2
1
1
1
1
1
0
1
1
3
2
0
0
1
1
1
1
0
0
1
1
1
1
0
1
1
1
0
1
2
2
0
0
1
0
0
2
1
1
0
1
1
1
1
0
1
2
1
0
1
2
1
1
1
0
1
0
2
3
0
0
0
0
2
1
0
1
1
1
0
1
1
1
1
3
1
1
1
1
1
2
0
1
0
1
2
1
1
1
1
2
1
2
0
1
0
1
0
0
1
0
0
1
2
2
0
2
1
1
1
1
1
1
1
1
2
1
2
1
1
0
1
1
1
1
1
2
2
2
1
1
1
0
1
1
1
2
2
0
0
1
1
2
2
1
1
1
2
2
1
2
1
2
0
3
1
1
1
1
0
1
1
2
1
1
1
0
1
1
0
1
1
2
2
2
1
1
0
0
1
1
0
0
1
0
1
1
2
2
0
1
1
1
1
0
2
2
1
2
0
1
2
1
1
1
2
1
0
1
1
1
0
1
1
1
1
2
1
4
0
1
1
1
1
1
1
0
1
2
2
1
1
1
0
1
0
1
1
1
1
1
0
0
1
2
1
2
0
1
1
1
0
1
0
0
2
1
2
1
2
1
1
1
2
1
0
1
1
0
1
1
1
0
1
1
2
2
1
1
0
1
2
1
1
2
2
1
1
1
1
0
1
1
2
0
0
1
0
1
2
1
1
0
2
0
2
1
2
0
1
0
1
0
2
2
2
1
1
1
2
0
2
2
1
1
1
2
1
1
1
1
0
2
2
1
2
0
1
1
3
1
1
1
2
1
1
1
0
2
2
1
1
2
1
2
2
1
0
1
2
0
2
0
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
1
0
1
2
1
2
2
1
2
1
1
1
1
1
1
2
1
0
1
0
1
2
0
1
0
1
1
1
0
1
1
1
0
0
1
1
1
1
2
1
2
1
0
1
2
1
1
1
2
1
0
1
1
0
0
2
1
1
0
1
0
0
1
1
0
1
2
0
2
1
2
1
1
1
1
1
1
1
1
2
1
0
0
1
1
1
1
1
1
1
1
1
3
1
1
0
0
1
0
1
1
1
2
1
1
2
1
0
1
0
0
2
0
2
1
1
1
1
2
2
1
0
1
1
1
0
1
1
1
2
2
1
2
0
1
1
1
0
1
2
1
2
0
2
1
2
0
1
2
2
1
2
0
2
1
1
1
1
2
0
1
0
1
1
2
1
1
1
0
1
1
1
1
2
1
1
1
1
0
1
2
1
0
1
2
1
2
0
0
2
1
1
1
1
0
1
2
2
1
2
2
1
2
1
1
1
2
2
1
0
1
0
2
1
1
1
1
1
1
1
1
4
2
1
2
1
0
0
2
1
2
1
0
2
2
0
0
0
1
0
1
2
0
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
0
1
3
1
1
0
1
0
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
0
1
1
0
2
2
1
1
1
0
0
1
1
0
1
1
0
0
1
1
1
2
1
1
0
1
1
1
3
1
0
0
2
1
1
0
2
1
2
0
1
0
1
1
0
1
1
1
0
1
0
2
1
1
2
2
0
0
0
1
2
1
1
2
1
2
1
2
1
1
1
2
1
2
1
1
1
0
1
1
1
1
0
1
2
1
1
1
0
0
1
2
1
0
1
3
0
2
0
1
1
1
1
1
1
0
2
2
1
1
0
0
0
1
1
1
1
2
2
1
1
0
1
1
1
1
1
1
2
0
1
1
0
1
1
1
0
1
0
1
0
0
0
1
1
1
0
1
0
2
1
0
2
1
0
1
2
1
0
2
1
1
0
1
1
1
0
1
0
1
2
1
1
1
2
1
2
1
1
1
1
2
0
1
0
0
1
1
0
1
0
1
0
1
1
1
1
1
0
1
0
1
1
5
2
2
1
0
1
0
2
1
2
1
1
2
1
1
1
2
1
1
0
2
1
2
2
2
0
1
2
1
1
1
1
2
2
1
0
2
1
1
1
2
1
1
1
0
1
1
2
2
1
0
0
1
1
3
2
2
2
0
2
2
2
1
2
2
1
0
0
1
0
1
1
2
1
2
1
0
1
0
1
2
1
1
1
1
2
2
1
1
1
0
2
0
0
1
0
2
1
2
1
1
0
1
0
1
0
1
1
2
0
1
1
0
1
1
2
1
1
1
2
0
1
2
1
0
1
2
3
0
1
1
1
1
2
1
1
1
1
1
1
0
1
2
1
0
1
1
2
0
1
1
0
1
1
1
2
0
1
1
2
1
1
0
2
1
0
0
0
1
0
1
1
1
2
2
0
1
1
1
0
2
0
1
0
2
1
1
1
0
1
1
8
0
1
1
2
0
2
1
3
2
2
2
1
1
1
1
0
0
0
1
0
2
0
1
2
1
2
0
1
1
1
1
1
2
1
2
0
0
1
1
0
1
0
1
1
1
0
0
2
0
1
0
1
2
1
1
1
1
1
1
0
1
0
2
1
1
1
0
2
1
2
0
2
1
1
1
2
1
2
1
0
0
2
2
1
0
1
1
0
2
1
1
1
2
0
1
1
1
2
1
0
1
1
2
1
1
0
1
1
0
2
0
1
1
1
1
2
1
1
1
1
2
0
1
0
2
1
0
1
0
1
1
1
2
1
2
1
1
0
1
0
2
1
1
1
0
2
0
1
1
1
1
1
1
2
2
1
1
0
0
1
1
2
3
1
1
1
3
2
0
0
2
2
1
1
1
2
2
0
2
1
1
2
0
0
1
1
1
2
2
2
1
1
0
2
0
1
1
1
2
2
1
0
2
1
1
1
1
1
1
1
0
2
1
1
1
0
1
0
1
0
1
1
2
1
1
2
0
1
0
1
2
0
1
0
0
2
2
1
0
1
1
1
1
0
1
0
0
0
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
0
2
1
1
1
2
0
0
1
1
1
1
1
1
1
1
1
0
0
1
1
2
0
2
1
2
1
3
2
2
1
1
1
0
1
1
2
2
0
1
1
0
1
1
2
0
0
0
1
0
1
0
2
1
0
2
1
1
2
0
1
1
1
1
2
2
0
1
1
1
2
2
2
1
2
1
3
1
0
1
0
2
1
1
1
1
1
0
0
2
0
0
2
1
0
0
2
1
1
0
0
1
1
2
2
1
1
1
1
1
0
0
1
1
0
1
1
1
2
2
0
1
1
0
1
1
2
2
2
0
1
1
1
0
0
1
1
1
2
2
1
1
2
1
2
1
2
2
1
1
1
1
1
2
0
1
1
1
1
0
2
1
2
1
2
1
1
2
1
1
2
2
1
0
1
0
1
0
2
1
0
1
1
0
2
1
2
0
1
0
0
1
0
1
1
0
0
1
1
1
2
2
1
1
1
1
1
0
1
1
1
2
2
1
1
1
1
1
1
1
1
1
0
1
2
1
1
1
0
1
1
3
1
1
0
0
0
0
1
1
2
2
1
1
1
2
1
0
0
0
1
1
1
0
2
1
1
1
1
1
2
2
1
1
1
2
1
2
1
0
1
1
1
1
1
1
1
0
1
4
1
1
1
1
0
1
1
2
0
1
1
2
1
1
1
1
1
2
1
2
1
2
1
2
1
1
2
1
2
1
0
1
0
1
1
1
0
0
2
0
0
0
3
0
0
2
0
1
1
1
1
1
1
1
1
0
1
2
1
1
1
1
1
1
1
1
0
2
1
1
1
1
1
0
1
0
0
1
1
2
1
0
2
1
1
1
0
2
1
2
0
2
2
1
0
1
0
1
0
1
1
1
0
1
0
0
0
1
1
1
2
0
0
1
0
2
0
1
1
1
1
0
1
2
0
0
1
0
0
2
1
0
1
1
1
1
1
1
1
2
1
1
1
2
1
0
0
1
2
1
1
0
1
1
1
2
0
0
0
0
1
1
1
2
0
1
1
1
1
2
0
1
2
0
1
1
1
1
1
0
1
1
1
1
1
1
1
0
2
1
1
1
1
0
1
1
1
1
0
2
1
2
1
2
0
1
0
0
1
1
1
1
1
1
0
1
0
0
1
1
1
1
1
1
0
1
2
1
0
1
1
0
2
1
0
1
1
1
2
1
1
1
1
0
2
2
0
1
2
2
1
1
0
1
1
1
0
0
1
1
1
2
1
0
2
1
1
1
2
1
1
0
2
2
1
1
1
0
1
2
1
0
0
1
0
0
1
1
1
0
0
1
1
2
1
0
1
1
1
1
2
1
0
2
1
2
1
2
1
1
1
2
0
1
0
1
0
1
1
1
0
1
2
2
1
1
1
2
1
1
2
2
1
1
0
1
1
1
1
1
1
1
2
1
0
0
1
0
1
1
2
2
1
2
1
1
0
1
0
2
2
1
1
0
2
0
2
1
1
1
1
1
1
0
2
1
0
1
1
0
2
1
1
2
1
2
0
1
0
0
2
1
2
0
0
0
0
1
1
1
1
0
0
1
1
2
2
1
1
0
1
2
1
1
2
1
0
1
1
1
1
1
1
1
1
2
1
2
2
0
1
1
0
2
2
1
2
2
1
1
0
0
0
1
1
1
1
1
1
0
2
1
1
1
0
1
1
0
1
2
2
0
1
2
1
1
0
1
0
0
0
0
0
3
2
0
1
2
2
1
1
1
1
1
2
1
1
1
2
1
1
2
1
1
1
1
1
0
1
2
2
1
2
1
3
1
1
0
1
2
1
2
1
1
0
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
0
1
2
1
1
3
0
1
2
1
2
0
1
2
2
2
0
0
1
1
1
1
1
1
2
1
0
1
1
1
1
0
2
1
1
1
2
0
1
0
1
2
0
0
1
1
1
1
2
2
1
1
2
1
0
0
1
1
1
1
1
0
1
2
1
1
1
1
2
0
1
1
1
1
1
0
0
1
0
3
1
1
0
1
1
1
1
2
2
1
0
1
0
0
0
0
1
1
0
2
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
0
2
2
1
1
1
1
2
0
1
1
0
2
1
1
2
1
2
1
1
0
1
1
1
1
0
0
1
1
0
1
1
2
1
1
1
1
0
1
2
1
1
1
1
1
2
1
1
0
1
2
1
1
1
1
0
1
2
1
2
1
1
2
2
1
1
1
0
1
1
1
2
0
2
0
1
1
1
2
1
2
1
2
2
2
1
1
2
1
0
1
2
1
1
1
2
0
1
0
1
2
2
2
1
0
2
1
1
1
2
0
1
1
1
1
0
1
1
1
1
1
0
2
2
1
1
1
2
1
1
1
1
0
1
1
0
0
1
1
1
1
0
0
1
1
1
1
1
1
1
1
1
1
0
0
0
1
1
1
1
1
2
0
1
1
0
2
1
1
1
1
1
1
1
0
1
1
2
2
1
1
1
1
1
1
1
0
1
2
1
1
2
1
1
1
1
1
1
0
1
1
1
0
0
0
1
2
1
1
2
1
0
1
1
1
1
1
0
1
1
1
0
1
1
0
1
1
1
1
2
0
1
2
1
1
1
1
1
1
1
1
2
1
2
1
1
1
0
3
2
0
1
1
2
0
1
2
1
1
1
2
2
0
0
0
1
2
2
2
1
0
1
1
2
0
0
0
2
2
1
2
1
2
2
0
2
1
2
1
1
1
3
1
1
1
0
1
1
1
1
1
0
2
1
0
1
0
0
2
0
1
1
1
1
1
3
1
0
2
2
0
1
1
2
2
2
1
1
1
1
1
2
1
0
0
0
1
2
2
1
1
1
2
2
1
2
0
0
1
1
2
2
1
0
1
1
1
2
1
1
0
2
0
1
1
1
2
1
2
2
0
1
4
1
1
1
2
2
1
1
1
1
0
0
1
0
1
1
1
0
0
0
1
0
1
1
2
1
2
1
2
0
1
2
1
1
1
2
0
3
1
1
1
2
1
1
0
0
1
1
1
0
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
0
1
2
1
1
2
2
1
1
1
1
1
2
0
0
1
1
2
0
2
1
1
1
0
1
1
1
2
0
2
2
1
1
1
2
1
1
1
2
1
1
1
0
3
2
1
0
1
2
2
2
2
1
1
1
1
1
0
0
2
0
1
2
1
0
2
1
1
1
0
1
2
1
2
2
1
1
0
0
1
2
1
2
1
1
1
0
1
0
2
1
1
2
1
1
0
1
2
1
2
2
0
2
0
2
0
2
1
2
2
1
1
3
1
0
0
1
0
1
2
1
0
1
1
1
2
2
2
1
0
1
1
1
1
0
2
2
2
2
1
2
1
2
0
2
1
0
0
2
1
2
2
1
0
2
2
1
2
1
2
0
0
0
2
0
1
1
1
1
1
1
1
0
2
1
2
0
1
0
2
1
1
1
1
1
1
0
1
1
1
1
2
1
1
2
2
1
1
1
1
1
2
2
0
2
1
0
0
1
0
2
0
1
1
0
1
1
2
1
0
1
1
1
1
1
0
2
2
1
2
1
1
0
2
0
1
2
1
0
1
1
0
1
1
1
1
0
1
2
1
1
1
0
0
0
1
1
1
1
1
2
0
1
1
1
0
0
0
0
2
1
1
1
2
1
2
0
2
1
2
2
2
1
1
1
0
2
2
1
0
0
1
2
0
1
1
1
1
2
1
1
0
0
1
2
1
1
1
0
1
1
1
1
1
1
1
0
1
1
0
0
1
0
1
0
1
1
1
1
2
1
0
0
1
2
2
1
2
1
1
2
1
2
1
1
1
1
2
1
1
1
2
2
0
1
1
1
1
0
1
0
1
2
2
2
1
2
1
1
2
0
1
1
1
0
1
1
0
0
2
0
0
0
1
1
0
1
0
0
2
1
2
2
0
0
2
0
1
1
2
1
1
1
2
1
1
1
2
0
1
1
0
1
1
1
2
2
1
2
1
1
1
1
0
1
1
2
1
1
1
0
1
1
2
2
1
1
1
2
2
1
1
1
1
1
1
0
0
2
1
2
2
2
2
1
1
2
0
1
1
1
0
1
1
1
1
2
1
1
1
1
0
0
0
1
0
1
2
1
1
1
1
0
1
1
0
1
1
2
1
0
2
1
1
2
2
1
1
0
1
1
0
1
1
2
1
2
0
2
1
1
1
0
1
2
1
2
2
0
0
1
1
1
1
1
1
1
1
1
1
0
2
1
1
2
1
2
2
1
1
1
1
1
0
0
1
2
0
0
1
1
0
2
2
0
2
0
1
1
1
1
1
1
1
0
1
2
2
1
1
1
0
1
2
2
2
2
1
1
2
0
2
1
1
0
1
1
3
1
1
2
1
2
0
0
1
0
1
2
1
2
1
1
0
2
0
1
2
1
1
1
2
2
1
1
1
1
2
0
1
1
1
0
1
2
0
0
2
1
2
1
1
0
1
1
1
2
0
2
0
2
1
2
1
2
1
0
2
1
1
2
2
1
1
1
1
1
2
1
2
2
1
1
0
1
1
1
1
1
1
0
2
1
2
1
2
1
2
1
0
1
2
0
0
1
2
1
1
2
0
2
1
1
2
2
1
1
1
2
2
1
2
1
1
1
2
1
0
2
0
2
0
1
2
1
1
0
2
1
1
1
1
4
0
1
0
0
1
1
1
0
0
1
1
0
1
1
1
0
2
2
1
2
0
1
0
2
1
2
2
1
1
1
0
1
1
0
1
1
1
1
1
1
1
1
1
2
2
1
1
2
0
1
2
0
1
1
1
2
1
1
1
0
1
2
1
1
0
1
1
1
1
0
0
3
2
1
1
3
2
1
1
1
1
1
2
1
1
1
0
2
1
0
1
1
1
2
1
1
0
0
1
1
0
2
2
2
1
1
0
2
1
1
1
2
1
1
1
1
1
1
0
0
0
2
1
1
2
0
2
0
0
2
1
2
2
1
2
0
1
1
1
1
2
2
1
0
1
1
0
1
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
0
1
0
1
0
1
2
2
1
2
1
0
1
1
2
1
1
1
2
1
0
1
0
0
2
1
1
0
0
1
1
0
2
2
2
2
1
1
1
1
0
1
1
1
1
0
1
2
2
0
0
2
2
0
2
1
0
2
2
2
1
2
2
0
0
1
0
0
1
1
0
0
1
1
2
0
1
1
1
1
1
0
1
1
2
1
3
1
1
1
2
0
2
0
1
1
0
0
2
1
1
1
3
1
1
2
1
1
0
2
0
2
1
1
2
2
1
2
1
2
1
1
2
2
1
2
2
0
1
1
1
1
1
0
1
0
2
1
0
1
0
1
1
2
0
1
1
1
1
2
0
1
1
0
0
1
1
0
1
1
1
2
0
2
2
1
1
2
1
1
0
1
2
1
2
1
2
2
1
5
1
2
1
1
1
2
1
1
1
2
1
2
4
0
1
0
0
1
1
1
1
1
1
2
1
1
2
2
1
0
1
2
2
1
1
2
2
0
1
2
2
2
0
3
2
2
1
2
2
0
1
2
0
0
2
1
2
1
1
1
0
0
2
0
1
1
0
1
1
1
1
1
1
2
1
1
1
0
1
1
0
2
1
1
0
2
1
1
2
3
1
0
1
2
2
1
1
2
0
1
0
1
1
1
1
1
1
2
1
2
1
1
2
0
1
2
0
1
1
2
1
1
1
1
1
1
0
1
1
1
1
1
1
1
2
1
0
0
0
1
2
0
0
1
1
0
2
2
2
2
1
0
1
1
0
1
1
1
1
1
1
1
0
1
1
1
1
2
0
1
1
1
1
0
1
0
2
1
1
1
1
0
0
1
1
0
1
0
1
1
1
2
2
1
1
1
1
1
1
2
1
2
1
0
0
0
2
2
1
1
1
2
0
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
2
2
1
0
2
1
0
2
1
2
1
1
2
0
1
1
1
1
0
0
0
0
1
1
0
2
1
2
0
0
1
1
1
1
2
0
1
2
2
1
1
1
2
0
1
1
1
1
1
2
0
1
0
1
0
0
1
1
1
2
2
1
0
1
1
1
3
1
1
1
1
1
2
1
0
1
1
1
0
2
1
2
0
2
0
1
2
1
2
2
1
1
0
0
1
0
2
0
2
1
0
1
1
1
1
1
1
0
1
0
1
2
2
2
1
0
0
0
1
1
1
2
1
1
2
1
1
1
1
0
0
2
1
1
1
1
1
0
1
1
1
0
1
1
1
1
0
2
2
1
0
1
1
1
1
0
1
1
1
1
1
0
1
1
1
1
1
2
0
1
1
0
1
0
1
0
1
1
1
1
1
3
1
1
1
3
1
2
1
1
0
0
2
1
2
1
1
0
4
1
1
1
1
1
1
1
2
2
2
1
0
1
0
3
1
1
1
2
2
0
1
2
2
3
1
0
1
1
0
2
1
2
2
2
1
0
0
1
2
0
2
0
0
1
2
2
1
2
0
1
2
1
1
1
1
2
1
1
1
0
1
1
1
2
1
0
1
1
1
0
2
0
2
1
1
1
1
0
1
1
1
1
1
0
1
0
1
0
0
1
0
2
1
1
0
2
1
2
2
1
1
1
1
2
1
1
1
0
0
1
0
2
2
0
1
1
1
0
1
2
1
1
1
2
2
2
1
1
2
1
1
0
2
2
0
0
2
1
1
2
1
0
2
1
0
0
1
1
0
2
1
0
1
2
0
0
1
1
2
2
2
1
2
2
2
0
0
0
1
1
1
1
2
1
2
1
2
0
0
1
1
1
0
1
0
1
2
0
2
1
0
2
1
0
0
1
0
2
1
2
0
0
1
1
0
1
1
1
2
1
1
1
2
0
0
0
2
2
1
1
2
0
1
0
0
1
1
1
1
1
2
0
2
0
3
0
1
1
2
1
1
0
1
1
2
0
1
1
1
1
2
0
1
1
1
1
1
1
1
0
1
1
1
2
0
1
1
1
1
1
2
2
1
2
1
0
0
2
1
1
1
1
0
0
1
1
0
0
1
2
1
1
0
1
1
0
2
1
1
2
2
2
1
1
1
3
0
1
1
0
1
1
0
0
1
1
2
2
2
0
1
2
2
1
1
1
0
0
2
1
0
1
1
0
0
0
6
2
0
1
1
2
2
1
1
2
1
2
2
1
2
2
0
1
2
1
1
1
1
2
1
0
0
1
0
1
2
1
1
1
0
1
0
2
0
0
4
1
1
2
1
3
1
1
0
1
0
1
0
1
1
2
1
1
1
1
1
0
0
1
1
2
0
0
1
1
1
1
2
2
1
1
0
1
1
2
0
1
1
0
1
1
1
1
2
2
0
2
0
0
0
0
1
1
2
1
1
2
0
1
2
1
1
1
2
1
1
1
0
0
0
2
2
2
1
1
2
1
0
2
1
1
0
1
1
1
1
1
2
2
2
1
2
2
1
1
0
1
2
1
1
1
1
2
0
0
1
1
2
1
1
0
0
1
0
2
0
1
2
1
1
0
2
0
0
0
4
2
1
2
1
0
1
2
1
2
0
1
1
1
2
1
0
2
2
1
1
1
0
1
1
0
1
1
1
1
0
1
1
2
2
1
1
1
2
0
2
1
1
0
1
1
0
2
1
2
1
1
1
1
1
1
1
0
1
2
2
0
1
1
1
2
0
1
2
2
2
1
1
2
1
1
0
2
0
2
2
1
2
1
1
1
1
0
1
0
0
2
1
1
1
0
1
1
0
2
1
1
1
1
2
1
1
2
0
2
1
2
1
2
1
1
1
1
1
0
1
2
2
0
2
1
0
1
2
1
0
2
1
1
2
2
1
2
1
1
3
1
1
2
1
1
2
1
1
2
1
1
1
1
1
1
2
2
1
0
1
2
1
1
2
1
0
1
2
1
1
0
0
2
1
0
0
1
1
1
1
1
0
2
1
2
1
1
1
0
1
2
2
1
0
1
1
0
2
1
1
2
0
1
2
2
2
2
1
1
0
2
1
1
1
0
2
1
1
0
2
0
1
1
0
1
1
1
2
0
1
2
1
2
2
1
1
0
1
1
1
2
2
1
0
2
1
2
1
1
1
2
1
1
1
1
1
1
1
1
0
0
0
2
1
1
1
1
1
1
1
1
3
1
1
1
1
2
1
1
2
1
0
2
0
1
0
2
1
2
0
2
0
1
1
3
0
4
0
1
2
0
0
1
2
0
2
1
2
0
0
1
2
0
2
2
2
1
0
1
2
1
1
1
1
1
2
1
1
1
0
1
1
0
0
0
0
1
1
1
0
0
2
1
2
1
1
1
1
1
1
2
1
2
1
4
1
2
0
1
0
1
1
0
1
1
0
0
1
1
2
1
0
0
2
2
2
2
1
1
0
1
1
1
1
1
1
2
2
1
0
1
1
1
2
0
1
0
1
1
2
1
0
0
0
1
0
2
2
2
1
1
0
1
1
1
1
1
1
0
1
0
1
0
1
0
2
1
2
1
0
2
1
1
1
0
1
2
1
0
1
1
2
2
1
1
1
1
0
1
1
1
2
0
1
0
0
1
1
1
2
1
0
1
1
1
0
1
0
1
0
2
1
1
0
0
1
1
2
1
1
2
1
1
2
2
2
0
0
0
2
0
0
1
2
2
0
2
2
0
1
0
0
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
3
2
2
3
0
2
1
0
1
1
0
1
0
0
0
2
1
1
0
1
2
2
2
0
1
0
1
0
2
1
0
0
1
2
2
1
0
0
0
1
2
2
0
1
0
1
1
1
1
0
1
1
1
2
2
0
0
1
0
0
2
1
1
0
1
1
2
1
1
2
1
1
2
0
1
1
1
1
1
1
0
1
1
1
1
0
1
1
1
1
0
1
0
0
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
0
0
1
1
1
1
1
0
2
1
0
1
1
1
1
2
2
2
0
1
1
0
1
2
1
0
1
1
2
1
3
3
0
0
1
1
0
2
1
1
1
3
1
1
2
1
1
0
0
1
1
1
2
1
0
1
1
1
2
0
1
0
1
2
1
1
0
2
1
1
2
1
1
1
1
0
2
2
1
1
1
1
2
0
1
2
0
1
1
2
1
1
1
2
1
2
1
1
2
1
1
2
0
1
1
1
0
1
0
1
1
2
1
0
2
1
1
0
1
2
1
2
2
1
2
0
1
1
1
1
2
1
0
1
2
0
2
1
1
2
1
2
1
0
1
2
0
0
2
1
1
0
0
1
1
2
1
1
1
0
1
2
0
1
2
1
3
2
1
1
1
1
1
1
1
1
1
1
1
0
2
1
1
2
1
1
2
1
2
1
2
2
2
1
0
2
1
1
0
1
0
1
0
1
1
1
2
1
1
2
2
1
1
1
1
2
1
1
0
1
1
3
1
1
1
2
0
1
0
3
0
2
1
4
1
0
0
2
0
2
0
2
2
2
1
0
0
1
1
1
1
1
1
2
1
1
1
0
1
2
1
1
0
1
1
1
2
2
0
1
1
0
2
1
1
1
1
1
1
2
0
0
0
0
0
1
1
1
0
1
3
2
0
1
1
0
1
2
0
1
2
2
2
2
0
1
1
0
0
1
1
2
2
1
2
1
1
0
0
1
0
1
1
0
2
1
2
0
1
1
1
2
1
2
1
0
2
0
1
0
0
0
2
0
0
0
1
2
2
1
2
0
2
2
1
1
1
1
1
0
2
0
2
1
2
1
2
1
2
1
1
2
1
1
0
2
1
0
2
1
1
0
3
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
0
1
1
0
0
2
2
1
1
0
0
3
1
0
1
1
1
3
1
1
1
2
2
0
1
0
2
0
1
1
0
2
1
0
1
0
0
1
0
1
1
2
1
1
1
2
1
1
1
1
0
2
0
2
2
0
1
0
2
1
0
2
1
1
2
1
3
0
2
0
1
1
0
2
1
2
1
0
0
1
1
1
0
2
1
1
2
1
1
0
2
1
2
0
1
0
0
2
0
1
0
1
1
1
1
3
1
1
1
3
2
1
1
0
1
2
0
0
0
1
2
1
0
1
2
1
1
0
2
2
1
1
1
1
1
2
0
2
1
0
1
1
1
1
1
2
1
1
1
2
1
0
1
1
1
1
1
1
0
1
1
1
2
1
1
2
1
2
0
1
0
1
1
2
1
2
0
0
2
1
0
0
1
1
1
1
2
1
0
1
1
2
1
0
0
1
0
2
1
1
0
1
1
1
0
2
1
0
0
2
1
0
1
0
1
2
1
1
0
1
2
1
1
1
1
0
0
1
0
1
1
2
1
1
1
0
1
1
5
0
0
1
1
2
2
1
1
1
1
2
1
1
1
0
2
2
0
2
2
0
2
1
0
1
1
1
3
2
1
1
1
1
0
1
0
0
2
0
2
1
1
1
2
2
1
0
1
1
1
1
2
1
1
2
1
1
2
2
0
0
1
0
1
1
1
0
2
2
2
1
1
2
0
1
1
1
1
1
1
0
0
0
1
0
1
1
2
1
1
0
1
1
1
0
0
2
1
1
2
1
0
2
1
0
1
1
1
1
1
1
1
1
2
5
1
1
0
1
0
1
1
0
2
1
1
0
1
2
1
1
1
1
2
1
2
1
0
1
2
2
1
1
0
1
1
1
3
1
1
0
1
1
1
1
0
1
1
1
2
2
1
0
1
1
1
1
0
1
2
3
0
1
1
2
1
0
2
1
2
1
1
0
1
1
1
3
1
1
2
0
1
0
1
1
1
1
0
1
1
0
0
2
2
1
1
1
2
1
1
0
0
1
0
0
1
2
1
0
0
1
2
0
1
0
0
0
1
1
1
2
0
0
1
1
2
1
1
2
1
2
2
1
0
0
0
1
2
2
1
0
2
2
1
3
0
0
0
1
1
0
1
2
1
1
1
1
1
0
0
1
1
1
1
1
2
1
1
0
1
1
1
2
0
0
2
1
1
1
1
1
0
1
2
1
2
1
1
1
0
1
2
1
1
1
1
1
2
1
0
1
2
1
1
1
1
1
2
1
1
1
2
0
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
2
1
2
0
2
1
2
2
3
1
0
0
1
0
1
1
1
1
2
1
1
0
1
0
1
2
1
1
2
1
1
1
2
1
1
1
2
1
1
1
2
1
1
1
2
1
3
1
1
2
1
1
1
1
2
1
1
1
0
1
2
1
2
1
2
1
0
0
2
0
1
2
0
1
1
1
1
0
1
0
0
2
0
2
0
0
1
1
1
1
1
1
0
1
2
0
2
1
0
2
1
1
1
1
1
1
0
1
1
2
1
2
1
1
1
1
1
0
2
2
1
1
1
1
1
1
0
2
1
1
0
1
1
0
1
1
2
2
2
2
1
1
0
2
0
1
1
1
0
1
1
2
0
1
1
1
1
1
1
2
1
1
1
1
1
2
0
1
1
1
3
0
1
0
1
2
1
1
1
2
1
2
2
2
0
2
2
2
1
1
1
1
1
2
2
2
0
1
1
0
2
1
2
1
1
1
1
2
2
1
1
0
1
1
1
0
2
2
1
0
0
1
1
1
2
2
1
2
0
1
1
2
1
1
2
1
1
1
2
0
2
0
2
1
1
2
1
0
2
2
1
0
1
1
0
1
2
1
0
1
1
1
2
0
0
1
1
2
1
1
2
1
1
1
1
2
1
0
2
0
1
2
1
4
0
1
2
1
1
1
1
0
1
1
0
1
1
0
1
1
2
2
1
0
1
0
2
1
2
0
1
1
0
2
0
1
1
0
1
0
1
2
2
4
2
1
1
1
1
2
2
2
0
1
0
1
0
0
2
2
1
1
1
1
0
0
1
2
1
2
1
1
1
0
0
2
0
2
1
0
2
0
1
1
3
0
2
1
0
0
1
2
2
1
1
0
1
2
1
0
2
1
0
1
1
2
2
1
0
1
1
0
0
1
1
2
0
2
2
1
2
2
2
2
1
1
2
2
1
1
1
0
0
1
1
2
0
0
1
2
2
1
0
1
1
2
0
2
2
0
3
1
2
0
2
2
1
0
2
2
1
1
1
0
0
0
1
1
1
1
2
1
1
1
2
1
2
1
1
2
0
1
1
0
1
1
0
1
2
1
1
1
1
0
1
1
1
0
0
1
2
0
1
1
1
2
2
2
1
2
1
2
2
2
2
1
0
0
0
1
1
1
2
1
2
1
1
0
2
1
1
1
2
1
1
1
2
2
1
1
1
3
1
0
1
2
0
1
1
1
1
2
1
1
0
2
1
0
0
1
1
1
2
2
1
0
1
1
1
1
1
1
0
1
1
2
3
1
2
0
0
1
0
1
1
0
1
1
1
2
2
0
2
1
1
0
0
0
2
1
1
1
1
1
1
1
1
0
1
0
1
2
0
2
1
1
0
0
0
1
1
1
2
2
1
0
1
1
1
1
1
1
1
1
1
1
1
2
1
0
0
1
1
0
1
2
1
0
1
0
2
1
2
1
2
1
0
1
0
1
1
1
1
1
0
2
1
3
2
2
1
0
2
2
0
1
1
0
2
1
1
2
1
1
1
1
2
2
2
0
2
1
1
1
1
1
0
1
0
0
1
2
1
2
2
0
1
0
2
2
1
0
1
2
1
1
0
1
0
0
0
1
1
1
2
0
2
1
1
0
1
0
1
1
1
2
0
1
1
1
1
1
2
0
0
0
1
1
2
1
1
2
0
0
0
0
0
1
1
1
0
1
1
1
1
1
1
1
0
1
1
1
4
1
1
0
2
2
2
1
1
1
1
0
1
1
1
0
0
2
1
2
1
1
2
1
2
2
1
1
2
1
1
0
0
1
2
1
1
1
0
0
1
1
1
2
0
1
0
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
0
0
1
2
2
2
2
1
1
0
2
1
1
1
1
1
2
1
1
0
0
2
1
1
2
1
1
2
1
1
1
2
1
1
2
1
2
1
1
2
1
1
1
1
1
0
1
0
1
2
1
1
0
1
2
0
1
1
2
1
2
2
1
2
1
0
1
1
0
0
0
1
0
2
1
1
0
1
2
1
1
2
1
0
0
1
1
0
0
1
0
0
1
1
1
2
2
1
1
1
2
0
1
2
1
2
2
1
0
1
0
2
1
1
1
1
2
1
0
1
1
2
0
1
0
1
1
1
1
1
0
1
0
1
1
1
1
2
0
1
1
0
1
2
1
1
1
1
2
1
0
2
2
2
1
0
2
1
2
1
0
0
0
1
1
1
2
1
1
2
1
1
0
0
0
1
1
1
2
2
2
0
1
1
1
1
2
2
1
1
1
2
0
1
0
2
2
1
0
0
2
0
1
0
0
1
1
1
0
1
1
1
1
1
0
1
0
1
1
1
1
2
0
0
1
2
1
1
1
1
1
1
0
1
0
0
1
1
1
0
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
0
1
1
2
0
1
1
2
1
1
2
1
1
2
0
2
2
1
0
0
0
2
2
2
1
1
0
0
2
3
2
1
1
0
1
1
0
0
2
1
2
0
1
1
2
2
0
1
1
0
0
0
1
1
2
1
2
2
2
2
1
2
0
1
2
1
1
1
1
1
2
1
1
1
1
2
0
1
1
0
1
2
1
2
1
1
1
1
2
2
2
1
1
0
0
1
1
2
1
1
1
1
1
0
1
0
1
0
1
3
1
1
1
2
1
0
0
1
2
0
1
2
1
0
1
1
2
1
0
1
1
0
1
1
1
1
1
2
1
2
1
1
0
2
2
0
1
1
2
1
0
2
1
0
1
0
1
0
1
1
2
2
2
1
2
1
1
1
2
1
1
2
0
1
2
1
1
1
1
1
1
1
2
0
0
2
1
1
1
1
1
2
1
0
1
1
0
2
0
2
1
1
1
1
0
1
2
1
1
0
1
2
1
2
0
2
1
2
1
1
0
0
0
1
1
1
2
1
1
1
0
1
1
2
1
1
0
1
1
1
1
1
1
1
1
1
1
3
2
2
1
0
1
1
0
2
1
0
0
1
0
1
0
2
1
0
0
2
1
0
2
0
1
0
2
1
1
1
1
0
2
1
0
1
1
0
2
2
0
1
0
2
2
1
1
0
1
2
2
1
1
2
1
2
1
1
1
1
1
1
1
1
0
1
1
2
1
0
1
2
1
1
0
2
1
2
1
1
2
2
1
2
1
1
1
2
1
1
2
0
1
1
4
1
1
1
1
1
1
1
1
1
0
1
2
1
1
1
1
0
1
1
0
1
0
1
1
1
0
2
1
0
0
1
2
2
1
1
1
1
1
1
2
2
1
1
2
0
0
1
2
1
0
1
0
1
1
2
3
1
1
0
2
2
1
0
1
1
1
2
1
0
2
1
0
1
0
0
1
1
2
1
1
0
1
0
0
1
1
2
0
2
2
0
2
1
0
1
0
0
1
2
2
2
1
2
0
1
0
1
1
0
0
2
0
2
2
1
2
1
1
0
2
1
1
0
0
1
0
0
1
0
1
2
2
1
1
2
1
2
2
2
1
1
1
1
1
0
1
1
2
2
1
0
1
0
1
2
2
1
2
0
1
1
0
1
1
1
2
2
0
1
1
1
1
1
1
0
2
1
1
1
2
1
1
1
1
1
0
1
1
0
1
1
1
1
1
3
1
2
1
1
1
1
2
0
1
0
2
0
2
2
1
1
0
0
1
2
0
2
1
1
1
1
1
0
1
1
1
0
2
2
1
1
1
2
0
0
2
0
2
1
0
0
1
0
1
1
1
2
0
1
1
1
0
1
2
1
1
2
0
1
1
1
1
0
0
0
1
1
1
1
1
0
0
2
1
1
2
2
0
1
1
2
1
1
1
1
1
1
1
0
1
1
1
1
1
0
1
1
2
1
3
0
1
2
1
1
1
1
2
0
2
1
1
0
1
1
0
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
2
1
1
2
1
1
1
0
0
1
0
0
1
0
1
2
1
1
1
0
1
0
3
0
0
0
2
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
2
1
0
1
2
0
2
1
0
2
2
1
0
2
1
0
1
1
0
1
1
2
1
0
1
1
2
1
2
0
2
1
1
0
0
2
0
2
2
1
2
2
1
2
1
2
0
3
2
1
2
1
0
0
1
2
0
1
1
0
2
0
0
0
0
2
2
1
2
1
2
1
2
1
0
0
0
1
2
1
1
0
1
1
0
0
1
1
0
2
1
0
1
1
2
1
3
1
0
0
1
1
1
1
1
2
1
1
1
1
0
1
0
0
1
0
0
1
1
1
1
1
2
1
2
2
0
1
1
1
1
1
2
2
1
2
1
1
1
2
1
2
1
1
0
0
1
1
1
2
1
1
1
3
1
2
1
0
1
0
0
1
1
2
1
0
0
1
2
1
1
0
2
1
0
0
1
0
1
0
1
2
1
0
0
1
1
0
2
1
0
1
0
0
2
1
1
2
1
1
2
0
1
1
0
0
1
0
2
1
1
1
0
2
1
1
1
0
0
1
1
0
1
1
1
2
2
1
0
0
1
1
1
0
1
2
1
1
1
0
1
1
0
1
1
1
1
2
2
1
1
1
2
2
0
0
1
1
1
0
2
1
1
1
1
1
1
1
1
2
1
0
2
0
1
1
2
2
0
2
1
2
1
0
1
1
2
2
0
1
1
1
1
2
0
1
0
3
1
1
0
1
1
2
1
0
1
0
0
2
1
0
1
2
1
2
1
1
1
1
1
0
1
2
2
2
11
0
1
0
1
1
0
0
0
1
2
0
2
0
1
0
1
0
1
1
1
2
1
1
1
2
2
1
0
2
1
1
1
1
2
1
0
0
0
1
1
1
1
1
1
1
1
0
0
1
1
1
2
2
2
0
1
1
1
1
1
1
2
1
0
1
1
1
1
0
1
0
2
2
0
2
0
0
1
0
1
1
2
1
1
1
1
0
2
1
1
1
1
1
2
1
0
1
1
0
1
1
1
1
0
0
0
2
2
2
1
2
1
2
1
1
2
0
1
1
1
0
0
2
1
1
0
2
1
1
1
1
1
1
0
1
0
1
1
1
2
2
0
1
2
0
1
0
1
1
0
2
1
2
1
1
1
1
1
0
3
1
2
1
1
1
1
2
1
1
1
0
1
0
1
1
1
0
2
0
1
2
1
1
0
0
1
1
1
1
1
1
1
1
1
1
0
1
2
1
0
0
0
2
0
1
0
0
1
1
1
1
0
1
1
1
0
1
1
1
0
2
1
1
1
1
1
1
1
0
2
2
2
2
1
1
2
1
1
1
1
2
1
1
0
1
0
2
2
1
2
0
1
2
1
2
1
0
1
2
1
2
1
1
0
1
1
2
2
3
1
2
1
1
2
1
1
1
0
1
0
0
0
1
1
0
1
1
1
0
2
1
1
0
1
1
1
0
1
0
0
2
1
2
2
0
2
1
1
0
1
1
2
1
0
0
1
2
0
1
0
0
2
1
1
0
1
2
1
1
1
2
0
1
0
2
0
1
1
1
1
1
1
1
1
2
0
0
0
1
0
0
1
1
2
0
1
0
2
1
1
1
1
1
2
1
1
1
2
2
0
1
2
1
0
1
2
1
1
1
1
0
1
0
2
1
1
1
0
0
1
0
2
1
2
3
1
1
2
2
0
1
1
1
1
1
2
1
2
1
1
0
1
0
0
0
0
1
1
1
0
0
1
1
1
1
1
1
2
2
1
0
0
2
2
1
2
0
1
1
0
0
1
2
1
0
0
1
1
1
2
0
1
1
2
1
0
2
2
0
1
1
0
1
0
1
1
1
1
1
0
1
1
1
2
1
1
1
2
2
2
2
0
0
2
2
0
1
0
1
2
1
0
1
1
0
1
1
1
1
1
1
1
1
2
0
1
0
0
1
1
1
1
1
1
1
1
1
0
2
1
0
1
1
1
1
1
1
0
1
0
1
1
1
1
2
1
2
1
0
1
1
1
1
2
1
1
0
1
1
0
2
1
0
1
1
1
0
1
0
1
2
1
1
0
1
0
2
2
3
1
0
2
2
0
1
1
1
2
2
1
0
1
1
2
1
1
0
1
1
0
0
2
1
0
0
1
1
0
0
1
2
3
1
2
2
1
1
0
1
2
2
2
1
0
1
2
1
1
1
0
2
0
1
2
1
1
0
1
1
1
1
1
1
1
1
1
2
0
2
0
1
1
2
1
1
1
1
1
2
1
1
0
1
1
1
1
1
1
1
1
0
1
1
1
2
2
1
0
2
1
2
0
1
1
0
1
1
2
1
1
2
2
1
1
1
2
1
1
3
0
2
2
1
0
2
1
2
0
2
1
0
0
1
2
1
1
0
1
1
2
2
1
1
1
1
1
2
2
0
0
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
0
2
0
1
0
2
1
0
1
1
0
2
1
1
2
1
1
2
0
2
1
0
2
0
1
0
0
1
1
1
2
1
1
1
1
1
1
1
1
0
2
0
1
0
1
0
0
2
2
1
1
0
0
0
1
1
1
1
1
1
2
0
0
0
1
1
1
0
1
0
0
1
2
1
2
1
1
1
2
1
2
1
1
1
1
2
1
2
0
1
1
1
1
0
2
1
1
1
2
1
0
2
0
1
0
0
1
1
1
1
1
1
0
0
1
1
2
0
1
1
1
1
0
1
0
1
1
0
1
1
2
0
1
1
1
0
1
1
1
2
1
1
1
2
0
0
1
1
2
1
1
1
1
1
2
1
1
0
0
2
1
1
0
0
2
1
1
2
2
2
2
2
0
0
2
0
2
1
2
2
1
1
0
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
0
0
2
1
1
2
2
1
1
2
2
0
2
2
0
1
1
1
1
1
1
1
1
1
3
0
0
1
2
0
1
1
1
0
1
1
1
0
0
0
2
1
1
1
0
1
0
1
1
2
1
2
1
0
0
2
1
2
0
1
1
2
2
1
1
1
1
2
2
1
2
1
1
1
0
1
2
1
1
1
1
1
1
1
1
2
0
2
1
1
1
1
1
1
1
1
2
2
1
1
0
2
1
1
2
1
0
1
2
2
2
1
0
1
1
1
1
1
1
0
0
1
1
1
1
1
0
2
1
1
0
1
2
0
1
1
1
2
1
0
2
1
1
1
1
2
0
0
0
1
3
2
1
2
2
1
2
1
0
0
1
0
0
0
1
1
1
1
1
2
0
2
2
0
2
2
1
2
1
1
0
2
2
2
4
2
2
1
0
3
2
1
2
1
1
1
1
2
1
1
1
1
2
1
0
1
2
2
1
0
2
1
0
1
2
2
0
0
1
1
1
2
2
1
1
1
0
2
1
2
1
1
2
1
1
1
1
1
1
1
0
2
0
1
2
2
1
1
0
2
0
0
1
1
2
1
1
2
1
0
1
2
0
0
1
0
0
1
1
2
3
1
2
1
1
1
0
1
1
1
1
1
1
1
1
1
1
2
1
0
2
0
2
1
1
1
1
0
1
2
0
2
1
1
1
1
2
0
2
1
1
1
1
1
1
1
0
0
1
1
2
0
2
1
1
1
2
1
1
2
2
1
1
1
1
1
1
0
2
2
1
1
0
0
1
2
1
2
0
0
2
0
2
1
1
1
1
0
1
2
1
1
2
1
1
1
1
1
0
1
2
1
1
1
1
0
2
1
1
2
2
1
1
0
0
0
0
2
1
1
1
0
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
0
1
1
0
2
2
1
1
2
0
0
1
1
2
0
0
2
0
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
0
0
0
1
1
1
1
2
1
1
0
1
0
2
1
1
0
1
1
2
2
1
1
1
2
1
1
2
0
1
2
1
1
0
2
1
2
0
1
2
1
1
1
1
1
1
0
1
1
1
1
1
0
1
1
2
1
1
0
1
2
1
1
2
1
0
1
0
1
1
1
2
1
1
1
0
1
0
0
2
0
1
0
1
1
1
2
1
1
1
0
2
1
1
1
3
1
0
1
0
2
1
1
1
2
1
1
0
1
1
1
2
2
1
1
1
1
1
0
1
1
0
2
2
1
0
2
2
1
2
0
1
2
1
2
2
2
2
1
2
1
2
1
1
2
2
1
1
2
1
1
1
2
1
1
0
1
1
1
1
2
0
1
2
2
0
2
0
1
1
1
1
0
3
0
2
0
0
1
1
1
1
0
2
1
2
2
1
1
1
1
1
0
2
1
1
1
2
0
1
1
1
0
0
0
1
1
1
1
2
1
1
0
1
1
1
1
0
1
2
2
0
2
1
0
1
1
1
0
0
1
1
2
1
1
1
0
0
0
0
0
1
2
1
2
2
1
0
1
1
0
1
1
1
1
0
0
2
2
0
0
2
1
3
1
1
1
2
1
1
2
0
1
0
1
2
1
1
0
0
1
2
1
1
2
1
0
1
1
1
0
1
1
0
0
0
1
2
1
0
1
1
0
1
2
1
2
1
1
2
1
1
1
1
1
2
1
0
1
1
2
1
1
1
0
2
1
1
1
1
1
1
2
1
2
1
0
1
1
1
1
1
0
1
1
2
1
0
1
0
1
1
1
1
0
0
0
1
1
1
2
1
1
1
0
0
0
1
1
2
0
0
1
2
1
2
1
2
2
1
1
1
2
0
1
0
1
2
1
1
1
2
1
1
2
1
2
1
1
0
0
0
2
2
2
1
1
0
0
1
1
1
1
1
1
1
1
1
2
1
2
1
2
1
3
1
1
0
0
1
0
1
1
0
1
2
1
1
1
1
2
2
2
1
1
2
1
1
1
0
1
1
0
2
2
2
1
2
1
1
2
1
1
0
1
2
0
0
0
1
1
1
0
1
1
2
3
1
2
2
1
1
2
0
1
0
1
0
2
1
1
0
1
0
5
2
0
1
1
1
1
2
0
1
0
3
1
0
1
0
0
1
0
1
0
1
0
0
1
1
0
1
1
0
1
1
1
1
2
2
1
2
1
1
0
1
1
1
1
2
2
1
0
1
2
1
0
1
1
0
2
0
1
3
1
1
1
2
1
1
1
0
1
1
2
1
2
1
1
1
2
1
1
1
1
2
2
1
2
1
1
1
1
1
1
1
3
1
0
2
1
1
0
2
2
1
1
1
3
2
0
0
1
2
0
1
1
2
1
1
1
1
0
1
1
1
2
1
1
0
1
1
1
2
0
2
0
2
2
0
1
2
0
1
1
1
1
1
2
1
2
1
3
1
1
1
2
2
1
0
1
1
1
1
1
0
2
0
2
2
1
1
1
0
1
1
2
2
1
2
2
2
1
0
1
1
1
2
2
0
1
0
2
1
1
0
2
1
1
1
1
1
1
3
0
1
1
1
2
1
0
2
0
1
1
1
0
1
0
0
2
0
1
1
1
2
1
1
1
1
1
1
1
0
1
1
1
1
0
2
2
2
1
0
1
1
0
1
1
2
1
2
2
1
2
2
1
2
1
1
1
2
0
1
1
1
2
0
1
1
0
1
0
0
0
0
0
2
1
1
2
2
2
0
1
1
2
0
2
1
5
1
2
1
2
1
1
0
2
0
1
2
1
1
1
1
1
1
1
0
1
1
1
2
2
1
1
1
0
1
1
2
2
1
2
0
1
1
1
0
0
1
2
0
0
2
1
1
2
1
1
1
1
1
0
1
1
1
0
2
1
2
1
3
2
0
1
1
0
1
0
1
1
1
0
1
2
2
1
1
0
0
0
1
1
2
2
1
1
1
1
1
1
1
4
2
2
2
0
1
1
1
1
0
1
1
2
0
1
1
1
1
2
2
1
0
1
2
0
2
1
1
1
1
2
2
1
2
0
1
2
1
0
2
0
2
0
2
1
2
1
0
1
1
0
0
2
1
1
1
1
1
0
1
0
2
1
1
1
1
2
1
1
0
1
1
0
1
2
1
2
1
1
1
1
0
1
0
1
0
0
0
2
1
1
1
2
1
0
1
0
1
2
1
0
2
2
1
0
0
2
0
2
0
1
1
1
0
1
1
1
1
2
1
0
1
1
0
0
2
1
1
2
0
1
1
0
0
0
2
1
1
1
0
1
1
1
0
2
1
2
2
0
0
2
0
0
2
2
1
2
0
1
3
1
1
1
1
0
1
1
1
2
1
2
1
1
1
0
1
0
1
2
2
1
1
1
2
2
1
1
1
0
0
2
2
1
0
2
0
1
2
0
1
0
2
0
1
1
2
2
1
1
2
1
1
2
1
2
1
1
1
1
2
1
0
0
1
0
1
0
2
3
0
2
1
2
1
1
0
1
2
0
1
2
1
1
1
0
1
1
0
1
0
1
2
2
2
1
1
1
1
1
1
1
0
1
2
1
2
1
1
1
3
1
0
0
0
1
2
0
1
1
2
0
2
1
0
1
2
1
6
2
0
1
2
1
3
0
1
0
1
0
2
0
1
0
1
0
1
1
0
1
1
1
0
0
1
1
1
2
0
1
2
1
1
1
1
2
0
1
1
2
1
2
1
1
1
2
1
2
1
1
1
1
1
1
2
0
1
0
0
1
1
1
0
2
2
2
1
1
0
1
1
1
2
0
1
0
1
1
1
0
1
4
1
2
1
0
1
1
1
1
1
1
1
1
0
0
1
2
1
2
1
1
1
0
0
2
1
2
1
2
1
1
0
1
0
0
2
1
1
1
1
2
0
2
1
1
0
1
0
1
1
1
2
1
1
0
1
1
2
1
0
1
0
0
1
0
0
1
2
0
1
2
2
1
1
2
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
0
1
2
0
1
1
2
1
1
2
1
0
1
1
1
1
2
0
1
0
0
1
1
1
0
2
1
1
1
0
0
0
2
1
1
1
0
1
1
1
1
2
1
0
1
0
1
2
0
1
2
2
1
0
1
1
1
2
1
1
0
1
1
2
0
2
2
1
1
2
0
2
1
0
1
1
2
0
1
2
1
1
2
1
2
2
0
2
1
1
0
2
1
1
1
0
2
1
1
0
3
0
2
1
2
2
2
1
0
2
1
0
2
0
0
1
1
1
1
0
2
1
0
2
1
0
2
0
1
0
1
0
0
1
2
1
0
1
1
2
1
2
1
1
0
1
0
3
1
2
1
1
2
1
2
1
1
1
0
1
0
1
1
0
0
2
1
1
0
1
1
1
2
0
1
1
0
2
2
1
2
0
1
1
1
1
1
1
1
2
0
1
2
1
1
1
2
1
1
1
0
1
1
2
0
1
1
1
2
2
2
1
1
1
0
2
1
1
1
2
1
1
1
1
2
1
2
0
1
2
1
1
0
2
1
1
1
1
1
0
1
1
1
1
1
0
1
2
1
0
1
0
0
1
2
0
0
1
1
1
1
2
0
1
1
2
2
0
1
1
1
0
1
1
2
0
2
0
1
1
1
1
1
0
2
1
1
2
1
1
1
0
1
0
1
2
0
2
1
0
2
2
1
3
0
1
0
1
2
1
1
0
2
2
2
0
1
0
2
0
0
1
0
2
1
0
1
1
1
1
1
2
1
1
1
2
0
2
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
1
0
1
1
1
1
1
1
1
2
0
1
2
1
2
1
1
1
4
1
1
1
0
0
1
0
2
1
1
1
1
1
2
0
1
1
1
1
1
0
0
1
1
1
2
1
1
1
1
1
2
0
1
1
0
3
1
1
1
1
1
1
1
1
0
2
0
2
2
2
1
0
2
0
2
1
2
1
1
0
1
1
2
3
2
1
1
0
1
1
0
0
1
1
1
1
2
2
1
1
0
0
2
1
0
2
1
2
2
0
2
2
1
1
2
1
0
1
0
2
2
1
1
1
0
1
1
0
1
1
0
1
1
0
1
2
2
1
2
1
1
1
0
0
2
1
1
2
1
1
1
2
1
1
1
0
1
0
2
1
1
1
1
1
1
1
1
1
1
1
3
2
1
1
1
2
1
1
0
2
2
0
0
0
2
1
2
1
0
1
1
0
1
0
1
0
1
1
1
1
1
1
2
0
1
1
1
2
1
1
0
1
1
1
0
1
1
2
0
0
2
1
2
2
2
1
0
1
1
2
1
2
1
2
1
2
1
1
0
1
2
1
2
2
1
2
1
3
1
2
0
1
0
2
2
1
0
1
1
0
1
2
1
0
1
1
1
1
1
1
0
2
1
1
0
1
1
1
1
1
0
1
2
1
0
1
1
1
1
2
1
1
1
0
0
1
0
2
0
2
1
1
2
2
0
1
1
0
0
0
2
1
1
1
1
1
1
0
1
1
1
0
1
0
1
0
0
0
1
0
2
1
1
2
0
1
1
1
0
2
1
2
1
2
1
0
0
0
1
1
1
0
1
1
3
0
1
1
2
1
2
0
1
1
0
2
1
1
2
2
0
1
1
1
0
1
1
1
1
2
2
2
1
2
1
1
0
0
1
1
2
1
1
1
1
2
1
1
1
0
2
1
0
1
1
1
1
1
1
2
0
1
1
1
2
1
1
1
1
1
1
2
0
1
1
1
0
0
1
0
1
1
1
1
2
0
1
1
0
0
1
1
1
2
1
0
1
1
1
1
2
2
2
1
1
1
1
1
1
0
0
1
1
2
0
1
2
1
1
2
1
2
1
1
1
0
1
1
1
0
2
1
1
2
0
1
1
1
2
1
1
1
1
1
0
1
1
1
1
0
1
1
1
2
1
2
1
0
1
2
0
1
1
2
1
1
1
1
1
1
1
0
2
1
0
1
1
2
1
2
1
0
0
1
0
1
2
1
1
1
0
0
0
1
1
1
2
0
1
2
2
1
2
1
0
1
0
1
1
0
1
2
2
2
0
0
2
1
1
1
2
2
1
2
0
1
2
1
1
2
1
1
1
1
1
1
3
1
0
0
1
0
0
0
1
1
1
0
0
1
0
1
0
1
0
1
1
0
0
1
1
1
1
0
2
1
0
2
1
2
0
2
1
1
0
1
1
0
0
2
2
0
1
1
1
1
2
2
1
1
1
1
0
0
2
0
1
2
2
2
0
1
2
1
0
1
1
1
1
1
0
0
1
1
1
1
1
2
1
0
1
2
2
2
0
1
1
0
2
1
0
1
0
0
1
2
1
1
1
1
1
2
0
1
1
1
2
1
2
1
2
1
1
0
2
1
1
1
0
1
1
1
1
1
0
1
1
0
1
2
1
0
0
1
2
1
1
0
1
1
1
0
1
2
1
1
2
2
1
1
1
1
2
1
2
1
1
0
1
0
1
1
2
1
1
1
1
1
0
0
1
1
2
0
1
0
0
1
2
1
1
0
1
0
2
2
1
0
2
0
1
2
2
0
1
1
2
0
0
1
0
2
2
1
1
1
1
1
2
2
1
1
1
0
2
2
1
1
1
1
1
2
0
0
1
1
1
1
1
2
1
2
2
1
2
1
1
0
0
0
1
1
0
1
1
1
1
1
0
0
0
1
1
0
1
1
0
0
0
2
2
2
1
1
1
1
0
0
2
1
2
2
0
2
0
1
1
1
1
1
1
1
1
1
2
1
1
1
1
0
1
1
1
1
0
1
0
1
0
0
1
1
0
1
1
0
1
2
1
1
1
1
1
0
1
3
1
0
2
1
2
1
1
2
1
0
1
1
1
1
1
2
0
1
0
0
1
1
1
2
0
1
1
1
2
0
2
1
1
1
1
1
1
1
2
1
1
1
1
0
2
0
2
0
2
0
1
0
1
1
1
1
0
0
1
1
1
1
2
1
1
1
0
1
2
2
0
1
1
0
1
1
0
2
1
1
0
1
0
1
1
2
2
0
2
1
2
0
2
0
0
3
2
1
2
0
1
0
1
1
1
0
2
2
1
1
0
0
0
1
1
1
0
2
0
1
1
1
1
0
1
2
1
1
0
1
2
2
1
1
2
1
0
1
0
1
1
2
2
1
0
1
1
1
1
2
2
0
1
2
2
1
1
2
0
1
2
1
1
0
1
2
1
2
2
1
1
1
2
2
2
2
0
1
1
1
1
1
2
1
0
2
1
1
2
2
1
0
1
1
1
2
1
1
1
1
0
1
2
1
2
1
2
1
0
2
1
1
0
2
1
1
1
0
0
0
1
2
0
1
1
0
1
2
2
1
1
2
2
3
2
2
1
0
0
2
1
1
1
1
0
2
0
1
1
0
1
0
2
1
2
2
1
1
2
1
1
1
0
1
1
2
3
1
2
1
1
2
2
0
0
1
1
0
1
1
0
1
1
2
1
1
0
1
1
0
1
1
0
0
1
1
1
1
1
1
1
1
0
2
0
1
2
1
1
1
1
1
1
2
1
1
0
2
1
1
0
1
0
1
1
1
2
1
1
2
2
0
2
0
0
2
0
1
2
0
1
2
1
0
1
1
0
0
1
1
1
0
1
1
1
1
1
2
1
1
2
1
2
1
2
0
2
2
2
2
0
2
1
1
1
1
1
1
1
1
2
2
2
2
1
2
1
1
3
1
2
1
2
2
1
0
1
1
0
1
2
2
2
0
0
1
1
1
0
0
1
0
1
1
0
1
2
1
1
2
0
1
0
2
2
1
2
2
2
1
2
0
1
1
2
1
0
2
2
2
2
1
1
0
1
2
1
2
1
1
0
1
1
1
1
1
1
0
1
1
2
0
0
1
0
0
1
1
2
1
1
0
1
1
1
2
1
1
1
1
1
0
1
1
1
1
2
0
0
1
0
1
0
0
2
1
2
1
2
2
0
0
2
1
1
2
1
0
1
2
1
0
0
2
1
2
0
0
2
1
0
2
0
2
2
0
1
1
1
0
1
1
1
1
2
1
1
1
1
0
2
2
1
1
1
1
1
1
3
1
0
2
1
0
1
1
1
1
2
0
1
1
1
2
1
1
1
0
1
1
0
1
1
1
0
2
2
2
1
0
2
1
0
1
2
1
2
2
1
0
1
1
0
1
1
1
1
1
2
0
1
2
1
2
0
0
0
1
2
0
1
0
2
1
2
0
0
0
1
2
2
2
2
1
0
2
1
2
1
1
0
1
0
2
0
2
0
2
1
1
1
1
1
2
2
2
0
1
2
1
2
2
1
1
1
2
1
1
0
0
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
0
2
1
0
1
1
0
2
2
0
1
1
1
2
0
1
0
0
2
0
1
1
1
2
1
1
1
1
0
0
1
1
1
0
0
2
1
2
0
2
1
1
1
1
1
0
1
1
1
2
1
2
0
1
1
1
1
4
1
1
1
1
0
1
1
1
1
1
2
1
1
2
1
2
0
1
1
0
1
1
1
2
1
1
0
1
4
0
0
2
2
1
0
1
1
2
0
0
1
2
0
1
0
0
0
0
0
1
1
2
1
2
0
0
1
2
0
1
0
1
1
0
1
1
2
0
1
1
1
1
1
2
0
0
2
2
1
2
2
2
1
1
2
0
2
1
2
0
2
1
1
1
1
1
4
1
2
1
1
2
2
0
2
2
0
1
0
1
0
1
1
0
1
0
1
0
0
0
1
1
1
1
1
1
1
1
1
1
1
1
0
2
1
4
1
2
1
3
1
1
0
1
0
2
0
2
1
1
2
0
2
1
1
1
1
1
1
1
1
0
2
2
0
2
2
1
1
1
1
1
1
0
3
1
1
0
2
1
2
2
0
1
2
1
0
0
0
0
1
1
2
1
1
2
1
2
0
0
1
0
1
0
1
1
1
2
2
0
1
1
1
2
2
1
1
1
2
0
3
1
2
0
2
1
1
2
0
1
2
2
2
1
1
1
0
2
1
1
2
1
1
2
2
1
1
1
1
0
1
1
1
1
1
2
1
2
1
1
0
0
1
1
1
1
2
1
1
1
2
0
1
2
0
2
1
0
1
0
1
0
1
1
2
1
1
1
1
1
0
2
2
1
2
1
1
2
1
1
1
2
1
1
1
1
0
1
1
2
2
0
0
1
0
1
1
2
0
0
2
1
1
2
1
1
0
0
1
2
0
1
1
1
1
2
1
0
1
2
1
1
1
2
1
1
1
2
0
1
1
2
1
1
1
1
0
0
0
1
1
1
1
1
0
1
1
1
1
0
0
0
1
1
2
0
2
0
1
1
2
1
1
1
1
0
1
1
2
1
0
1
1
1
1
1
2
0
0
1
1
1
2
2
0
1
0
1
2
1
1
0
2
1
2
1
1
2
1
1
0
1
0
0
2
0
1
0
0
0
1
1
1
1
0
1
2
1
2
0
1
2
5
0
2
0
2
1
1
1
1
2
1
0
1
1
1
2
1
2
1
0
1
1
1
1
2
2
2
1
1
1
2
1
1
0
2
1
3
1
1
1
2
1
0
0
1
1
1
2
1
2
2
2
1
2
1
1
2
4
0
1
1
1
1
2
2
1
1
1
0
3
0
2
1
2
1
1
1
1
2
1
1
1
1
2
1
2
1
1
2
1
1
2
1
2
2
2
1
2
1
1
2
0
2
1
1
1
1
1
0
1
0
2
0
0
1
2
1
1
0
1
1
0
1
1
0
0
0
2
1
0
1
2
2
1
1
0
1
1
1
0
1
1
2
2
1
1
2
0
1
1
0
1
0
1
1
1
1
0
1
0
2
1
1
2
1
1
1
1
1
1
1
2
0
1
3
2
1
0
2
0
1
1
1
2
1
1
1
2
1
0
1
1
2
0
0
1
1
1
1
2
1
0
1
0
1
2
0
1
2
2
2
1
1
1
1
2
1
1
0
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
0
0
2
1
1
1
2
1
2
1
1
0
0
2
2
1
1
1
0
0
1
2
2
0
1
2
1
1
1
2
2
1
1
0
1
1
1
0
2
1
2
0
1
0
1
1
0
0
1
2
1
0
1
0
1
0
1
0
1
0
0
1
3
1
1
2
0
2
1
1
1
1
1
1
1
1
1
1
0
0
1
2
1
1
1
1
1
1
2
1
1
0
1
2
1
1
1
1
0
1
1
1
1
1
3
2
1
1
1
1
2
1
1
2
2
1
1
2
1
2
2
1
1
1
2
2
2
1
0
1
1
2
1
3
2
2
1
2
0
0
0
2
1
0
1
1
1
1
1
0
1
1
1
0
0
1
1
1
2
0
1
1
1
2
0
1
0
1
7
2
0
1
1
1
0
2
0
2
1
1
2
1
0
1
1
1
1
1
0
0
2
0
0
2
2
0
0
0
1
1
1
1
1
1
1
1
0
1
0
1
1
0
1
1
0
0
1
2
1
1
1
0
2
1
1
2
0
1
2
0
1
1
1
1
2
2
2
0
2
2
0
1
1
1
1
1
1
1
0
2
1
2
1
0
1
1
2
2
1
1
0
0
0
1
1
1
1
1
1
1
1
1
1
1
1
2
0
2
1
2
1
1
0
1
1
1
2
1
0
2
2
1
1
0
2
2
3
2
2
1
0
1
1
2
2
1
0
1
0
1
2
1
0
1
2
1
0
1
1
1
2
1
1
1
1
0
1
1
1
0
2
1
1
2
2
1
2
1
0
0
1
0
2
1
1
1
1
1
1
2
2
1
0
1
2
1
0
2
3
1
2
1
0
1
2
1
2
0
0
0
1
1
2
2
1
1
1
2
1
1
1
1
1
1
0
2
0
1
1
1
1
0
0
1
2
2
0
1
1
1
2
0
0
0
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
2
0
2
1
2
0
3
1
0
2
1
0
1
1
1
2
1
1
1
2
1
1
0
2
1
1
2
1
1
0
0
1
3
1
1
2
1
0
1
0
0
1
0
0
1
1
2
1
1
1
0
0
1
1
1
1
1
2
2
1
1
1
1
0
1
1
1
2
0
1
1
1
2
1
0
0
1
1
0
1
1
1
1
2
0
1
1
2
1
0
0
2
2
0
1
1
1
1
1
2
0
2
1
1
1
1
1
1
0
0
0
1
1
0
1
1
1
0
0
0
1
1
2
1
1
1
1
1
0
1
1
1
2
1
0
1
1
0
2
2
0
1
1
1
0
2
1
2
1
1
1
1
1
1
0
0
0
1
1
0
1
1
1
2
2
1
1
2
2
1
1
2
2
1
0
1
1
0
0
1
1
0
1
1
1
2
1
1
1
1
2
0
1
2
2
1
1
1
2
2
1
1
1
0
1
1
1
1
1
2
1
1
2
1
1
1
2
1
1
1
1
1
0
2
1
1
2
2
1
0
0
1
1
2
1
0
1
1
1
2
1
1
1
0
1
1
2
1
1
0
0
1
1
0
2
1
2
0
1
1
2
2
1
1
1
1
2
2
1
2
1
1
0
1
2
1
2
1
1
3
1
1
1
0
2
1
1
1
1
0
0
2
1
2
0
1
2
0
1
1
2
2
0
2
0
2
1
1
0
1
1
2
1
2
1
2
1
1
1
1
1
0
0
0
2
0
2
1
0
1
1
0
0
1
0
1
1
0
2
1
1
2
1
0
1
1
0
0
2
0
1
1
2
1
2
1
2
1
1
1
0
0
1
1
1
1
1
1
0
2
1
1
0
2
2
0
1
1
0
1
0
1
1
1
2
0
2
1
0
0
1
0
0
1
1
1
1
1
0
1
1
1
1
1
0
1
2
1
0
1
1
2
1
2
2
1
0
1
2
1
1
0
0
1
2
3
1
0
1
2
0
0
0
0
0
1
2
1
1
0
0
2
1
1
1
1
1
1
1
1
1
1
1
1
0
0
1
1
1
1
0
0
2
2
1
2
1
1
0
2
1
2
1
1
1
2
1
2
0
1
1
2
1
1
0
1
2
2
1
2
0
1
2
2
1
1
2
2
0
1
2
0
1
1
1
2
1
1
2
1
2
2
1
2
2
2
1
1
1
1
0
1
0
1
0
2
1
1
1
1
1
2
1
1
0
1
2
0
2
0
1
0
2
1
1
1
0
1
1
1
1
1
0
2
1
0
0
2
0
2
1
1
2
2
1
1
0
0
1
1
1
4
1
1
1
1
1
1
1
1
0
1
0
0
1
2
2
1
2
1
1
0
2
1
0
1
1
1
1
0
1
2
2
2
1
1
0
1
0
1
2
2
1
1
2
1
1
2
3
1
2
1
1
0
1
2
1
1
0
2
1
0
1
1
1
0
1
1
1
1
2
2
1
2
1
2
1
2
2
1
2
2
1
0
1
0
0
0
0
1
0
1
0
2
0
1
1
1
0
0
0
1
2
1
1
0
1
2
1
1
2
1
1
2
2
1
0
2
1
1
1
0
1
2
2
0
1
1
2
1
1
1
0
1
0
1
1
2
2
1
1
1
0
1
0
1
1
0
0
0
2
1
1
0
1
1
1
1
2
1
2
1
1
2
0
0
1
1
1
1
1
0
0
1
0
2
1
2
2
4
0
1
2
0
0
0
2
2
2
1
2
2
2
1
2
1
1
2
1
1
1
0
1
1
0
1
1
2
0
1
1
1
1
1
1
1
1
2
1
1
1
0
1
1
1
1
1
1
1
1
2
0
1
2
1
1
1
1
1
1
2
0
0
1
1
1
2
1
1
0
1
2
0
2
1
1
4
1
1
2
1
2
1
2
1
2
1
1
2
1
1
2
1
1
2
1
1
0
2
2
2
2
2
1
0
2
1
2
1
1
1
0
1
1
1
2
2
2
1
1
1
2
1
0
1
1
2
1
1
1
1
0
1
1
1
1
2
0
2
1
1
2
0
0
0
1
1
0
0
1
1
1
1
0
0
1
2
1
0
1
0
1
2
1
1
2
2
0
0
0
0
0
1
1
1
1
1
0
0
2
0
2
1
0
2
1
2
1
1
2
0
0
1
1
1
1
1
2
2
2
1
1
1
1
0
1
1
0
1
0
1
0
1
2
1
2
0
1
1
1
1
1
1
1
2
1
2
2
1
2
1
1
1
1
1
0
1
0
1
2
1
1
2
1
1
2
1
0
1
1
2
0
0
1
1
1
1
1
1
2
1
1
0
1
0
0
0
1
1
1
0
2
1
1
1
1
1
1
1
1
1
1
1
1
3
1
1
1
1
1
1
1
2
2
1
1
2
0
0
1
1
1
1
1
0
0
1
0
0
0
2
0
1
0
0
0
2
1
1
1
1
1
0
1
0
1
2
1
1
0
2
2
0
5
0
2
0
0
1
1
1
1
0
2
0
2
1
2
2
0
2
1
1
2
1
0
0
1
0
0
0
1
1
1
2
1
1
2
0
2
1
2
1
1
1
1
0
1
0
1
1
1
1
2
1
1
2
1
0
0
1
3
1
1
1
0
1
1
0
2
1
1
1
2
2
1
0
0
1
2
1
2
1
2
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
1
1
0
1
0
1
1
1
0
1
1
0
2
1
1
1
2
1
1
1
2
3
1
1
1
1
1
2
2
0
1
3
0
2
1
1
1
2
0
2
2
1
0
2
1
1
0
3
1
1
1
2
1
1
1
1
1
0
0
1
1
0
0
0
0
1
0
1
1
1
0
2
1
1
2
1
2
1
1
0
1
1
0
0
1
0
0
1
1
1
2
1
2
1
0
1
1
1
1
1
1
1
1
2
1
2
1
1
2
2
0
2
1
0
2
1
1
0
1
0
1
1
1
2
1
0
0
1
2
1
0
2
1
1
0
1
2
2
3
2
0
1
2
2
1
1
3
0
1
0
2
1
2
1
0
1
1
0
1
1
1
1
0
1
1
2
1
1
0
0
1
0
1
1
2
0
1
1
0
1
1
2
0
1
2
0
1
0
1
1
1
2
1
1
1
2
1
1
1
2
0
2
2
0
2
1
0
2
0
1
1
0
1
2
1
1
1
1
1
1
2
1
1
1
0
1
1
0
0
1
2
1
0
1
2
1
2
2
1
0
1
1
1
2
1
1
1
2
2
2
1
2
1
1
2
0
1
0
1
1
1
2
2
1
1
0
2
2
1
1
0
0
2
0
1
1
0
1
2
1
1
3
1
1
0
0
0
1
0
0
1
0
1
1
1
1
0
1
2
1
1
1
1
1
0
0
0
1
1
1
1
1
1
1
1
0
1
2
2
0
1
1
0
1
1
1
2
1
1
1
0
1
0
1
0
3
1
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
1
0
0
0
0
1
0
1
0
0
2
0
1
2
0
1
1
1
2
1
1
1
0
0
0
2
2
1
0
2
1
2
1
2
0
1
2
0
1
1
2
0
1
1
0
1
2
1
1
1
1
2
0
2
1
1
1
0
1
1
1
2
1
2
0
1
0
2
1
1
1
1
1
1
1
0
1
1
1
1
1
0
1
1
2
1
2
1
0
1
1
0
0
1
2
2
1
1
2
2
1
1
1
1
1
2
0
1
1
2
1
2
1
0
0
1
0
2
1
1
3
1
1
0
2
1
1
1
1
0
0
1
0
1
2
1
1
1
2
1
0
1
1
1
1
2
1
1
1
0
1
3
1
1
1
1
0
3
2
1
0
2
1
1
1
1
0
0
2
1
0
0
2
1
1
1
1
2
1
2
1
0
1
0
1
1
2
1
1
1
0
2
2
0
1
0
1
1
0
1
2
1
1
0
1
1
1
0
1
1
1
2
0
1
0
1
1
1
1
2
0
1
1
0
1
1
1
1
1
1
0
1
1
1
2
0
1
1
3
1
2
0
0
1
1
1
1
1
1
2
1
1
2
0
0
1
1
1
1
2
1
2
2
0
1
0
0
1
0
1
1
1
1
1
3
2
1
1
2
1
0
0
1
1
1
2
0
0
0
0
2
0
1
1
1
0
0
0
1
0
1
1
2
1
1
1
1
0
1
0
1
2
0
1
3
1
1
1
0
2
1
2
1
1
1
1
1
1
1
0
0
1
1
0
2
2
0
1
2
1
0
1
2
1
2
0
0
1
1
1
1
2
1
1
0
1
0
1
1
1
1
1
1
1
0
1
2
2
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
0
0
1
2
1
1
0
1
1
1
1
2
1
1
1
1
2
1
0
1
1
0
0
1
3
0
2
1
1
0
2
1
1
1
1
0
0
0
0
1
1
0
2
2
1
0
0
1
1
2
1
1
0
1
1
1
2
0
0
1
0
2
2
1
1
2
1
0
2
1
1
2
2
3
1
2
1
1
1
2
1
2
2
1
1
1
0
2
0
2
1
1
1
0
2
1
0
1
0
2
2
1
0
1
2
1
1
1
2
1
2
0
0
1
1
0
0
1
1
1
2
1
1
1
1
0
0
0
0
1
1
1
1
1
2
2
0
1
1
1
2
0
2
1
2
1
2
1
0
2
1
0
1
3
1
2
1
1
1
2
2
1
1
1
1
2
2
1
1
4
2
1
1
2
0
1
0
1
1
1
1
1
1
1
2
2
1
2
1
2
0
1
1
1
2
1
1
0
2
0
0
1
1
1
0
0
1
1
1
0
1
1
0
1
1
2
0
1
1
2
0
0
1
1
1
1
0
0
1
0
0
1
2
1
1
1
1
1
1
1
1
1
1
0
1
0
0
1
0
1
2
1
1
0
0
0
1
1
1
1
2
1
2
0
1
0
1
2
1
0
1
0
2
1
2
1
3
0
1
0
1
1
1
1
2
1
2
1
1
2
2
0
0
0
1
1
1
1
2
1
0
0
1
1
1
0
1
1
1
2
1
1
0
1
1
1
1
1
2
2
2
1
1
1
1
1
2
2
0
2
1
1
1
1
1
0
2
0
2
1
1
1
1
1
1
1
0
0
1
1
1
0
2
0
1
0
1
0
1
1
0
1
2
1
1
2
1
1
1
0
1
2
1
0
1
0
2
0
1
1
1
2
2
1
1
1
1
1
2
2
0
1
0
2
0
2
2
0
2
2
1
0
1
0
1
1
1
1
0
1
1
3
1
1
1
0
1
2
1
2
1
2
1
6
1
1
3
1
1
3
0
2
1
1
1
2
0
1
1
2
2
1
2
1
1
2
2
0
1
1
1
1
2
1
1
1
1
0
1
1
1
2
1
1
1
2
0
2
1
1
1
2
1
0
0
2
1
1
1
0
2
1
2
2
1
2
2
0
2
1
0
0
2
0
1
2
1
2
2
1
1
1
1
1
2
1
1
1
0
2
0
1
2
1
1
2
1
0
1
1
1
0
2
0
1
0
0
2
0
1
0
1
1
1
1
1
1
1
2
1
1
1
0
1
0
2
0
0
0
1
1
1
2
2
1
1
1
1
1
0
1
1
0
1
1
2
1
1
0
1
2
0
0
1
2
1
1
1
1
1
1
3
1
1
1
2
1
1
0
1
1
1
2
1
0
0
2
1
1
1
3
1
1
2
1
2
0
1
1
1
1
2
0
1
1
2
0
1
1
2
1
0
2
2
1
1
2
2
2
1
2
1
1
1
1
2
1
2
1
1
1
2
1
1
1
2
1
0
1
1
1
1
0
1
0
0
1
0
2
2
2
0
1
1
1
1
1
1
1
0
2
1
1
2
1
2
1
2
1
1
1
1
1
2
3
0
0
0
0
1
1
0
1
1
1
1
1
1
0
2
0
0
2
1
2
2
0
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
0
4
2
2
1
1
1
1
0
1
1
2
0
1
0
1
0
1
2
1
1
0
1
0
1
1
2
2
2
0
1
1
2
1
2
1
1
0
1
0
1
0
1
1
0
2
0
1
1
1
1
2
2
0
1
2
0
1
2
0
1
2
1
1
1
1
1
2
0
1
1
1
2
1
0
2
0
1
1
1
2
0
1
1
2
3
2
1
1
1
2
1
2
1
2
1
0
1
1
1
0
2
0
1
1
1
1
1
1
0
1
2
1
2
2
0
1
1
0
1
0
1
2
0
0
1
1
1
1
2
1
1
1
1
1
1
0
1
0
2
1
1
0
1
2
0
1
1
0
1
2
1
1
1
1
1
0
1
1
1
2
3
1
2
0
1
2
1
1
1
1
0
1
1
1
1
0
2
2
1
0
1
1
1
1
1
1
0
2
1
1
2
1
1
1
2
0
2
1
0
1
1
0
2
0
0
1
1
2
0
1
2
2
1
1
1
0
0
1
1
2
1
2
2
1
1
1
2
0
1
2
1
1
1
1
0
1
1
2
1
1
0
1
1
0
1
2
2
1
1
1
0
1
2
2
2
0
0
1
1
1
0
1
2
1
1
2
1
1
1
0
0
1
2
1
1
1
1
2
1
1
2
0
0
1
1
0
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
2
1
0
0
1
2
0
0
1
2
0
1
1
1
0
2
2
1
1
0
2
1
2
0
2
0
1
1
1
1
1
0
1
2
1
1
0
2
0
0
1
1
2
1
0
2
2
1
1
2
1
1
1
2
1
1
2
1
1
2
0
1
2
0
1
2
2
1
2
1
0
1
1
0
0
1
1
1
2
1
1
1
1
1
2
1
0
1
1
1
1
0
1
1
1
2
2
2
1
2
1
0
1
1
1
1
0
0
0
1
0
2
1
1
0
1
1
0
1
0
1
1
0
1
1
1
1
0
1
2
1
1
2
1
1
1
1
1
1
1
2
1
1
2
0
1
1
0
1
1
2
2
1
2
1
1
1
2
1
2
1
1
0
1
0
1
1
1
1
1
1
1
0
1
2
0
2
0
0
1
1
1
1
1
1
2
0
1
1
1
1
1
1
1
0
2
1
1
2
2
1
1
0
3
2
1
1
0
1
2
0
0
1
1
1
1
2
1
1
0
2
1
1
1
1
1
0
3
1
1
0
1
1
1
2
1
1
2
1
2
1
1
1
2
2
2
0
0
2
1
1
0
1
1
1
2
1
2
1
1
1
1
0
1
1
1
1
1
2
2
1
1
1
1
1
2
2
0
1
0
2
2
2
1
1
0
1
1
2
0
2
0
0
2
1
1
2
1
2
1
0
1
1
1
1
2
2
1
1
0
1
0
1
0
1
1
1
2
1
1
0
2
1
0
2
1
1
0
0
1
2
1
1
2
1
1
1
1
1
1
1
1
0
1
0
0
1
1
0
1
2
2
1
1
1
2
1
1
1
1
0
1
0
1
0
0
1
1
1
0
2
1
0
2
2
0
0
2
0
0
2
0
1
1
1
1
1
0
1
2
2
2
0
2
1
1
1
2
1
1
1
2
1
2
1
2
0
1
2
1
1
2
1
1
0
1
1
1
1
0
0
1
2
0
1
0
2
2
1
1
1
2
1
1
1
1
0
1
1
1
1
0
2
1
1
2
2
0
1
2
1
0
1
1
2
1
0
1
0
1
1
2
1
2
1
0
1
2
1
1
0
1
1
1
1
1
0
1
2
1
2
1
2
1
1
2
1
0
1
2
2
1
2
2
1
0
1
0
0
2
0
1
1
0
2
2
1
0
0
2
2
1
2
2
0
0
0
2
1
2
0
1
1
0
2
1
1
0
1
2
1
1
1
0
1
2
2
0
1
1
2
0
1
2
1
1
1
2
2
2
2
1
0
1
0
1
1
2
2
1
1
1
1
1
1
1
0
2
0
1
1
1
1
0
1
1
1
1
1
1
1
2
0
1
0
1
1
2
2
1
0
1
1
1
2
1
1
1
1
1
0
1
2
1
1
1
1
1
2
1
2
2
2
1
1
1
1
2
1
1
0
0
1
1
1
2
0
1
1
1
0
0
1
1
1
1
1
1
3
2
1
1
1
1
2
1
1
1
1
1
1
1
1
0
1
4
0
0
1
1
2
1
1
2
0
2
2
2
1
1
1
2
0
1
2
1
1
2
1
1
2
1
1
2
1
1
1
1
1
0
0
1
1
0
2
1
0
0
1
2
2
1
1
1
1
1
1
1
1
0
1
1
1
1
0
1
1
1
2
0
0
1
1
1
1
1
2
1
2
0
1
1
1
2
1
1
1
0
1
0
1
1
0
1
1
0
1
1
0
0
0
2
1
1
1
1
2
0
1
0
1
1
1
2
1
1
1
1
1
1
0
1
1
1
1
2
1
1
1
1
2
0
0
2
0
2
1
2
1
1
1
1
2
1
1
2
0
1
1
2
1
2
1
1
2
1
2
2
1
2
2
1
1
1
2
0
0
1
0
0
2
1
0
1
1
1
2
1
1
1
0
4
0
1
1
1
1
1
1
2
2
1
1
1
2
2
1
1
0
1
0
1
1
1
2
0
1
0
2
1
0
1
1
0
1
2
1
0
0
0
1
2
1
1
2
0
1
1
2
2
2
2
1
1
1
0
2
1
0
2
2
1
2
0
2
2
0
1
2
1
1
1
1
2
1
2
2
1
2
2
1
0
1
1
2
1
1
1
0
2
1
1
0
1
1
2
1
1
0
2
2
0
1
1
1
1
1
1
1
1
1
1
1
2
1
0
0
2
0
0
0
1
1
1
0
0
2
2
0
1
2
1
0
2
1
1
0
1
0
1
1
2
0
0
2
1
1
0
1
2
1
1
0
1
1
0
1
1
1
2
1
1
1
2
1
1
1
1
1
1
0
1
1
0
0
1
1
1
0
1
1
1
0
0
1
0
1
1
1
1
1
1
1
1
2
2
0
2
2
2
1
1
1
1
2
1
1
1
1
1
0
1
0
1
1
2
2
2
1
1
2
0
2
1
1
1
2
1
1
1
1
1
2
1
2
0
1
0
1
1
1
1
1
1
1
2
2
1
1
1
1
3
2
0
1
1
0
1
1
1
2
0
1
2
1
1
2
0
1
1
0
1
2
1
2
1
2
2
1
0
1
2
1
1
1
2
1
1
1
0
1
1
1
2
1
0
1
1
1
2
0
2
0
1
1
1
0
2
1
2
1
2
1
1
1
2
0
1
1
1
1
0
0
0
0
1
2
1
1
2
0
1
1
1
2
2
1
1
0
1
2
2
0
1
2
1
1
1
2
0
1
1
1
2
1
1
2
2
1
1
1
0
0
1
0
1
0
1
1
0
0
1
2
2
2
1
3
1
1
0
1
0
1
1
1
1
4
2
1
2
0
1
2
2
0
0
1
1
0
1
0
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
0
1
1
2
0
0
1
0
1
1
1
2
1
1
1
0
1
1
2
1
2
2
1
0
1
1
2
1
1
2
0
1
2
1
2
2
1
1
1
2
1
1
1
1
0
2
0
1
1
1
0
1
1
2
1
1
1
1
3
1
1
0
1
1
0
2
2
1
1
1
1
1
1
0
2
1
1
1
0
1
0
0
2
2
2
2
0
0
0
1
0
0
0
1
1
0
1
1
1
1
1
1
1
1
1
2
1
0
1
2
2
2
2
1
1
1
1
1
0
2
1
2
0
1
0
0
0
2
0
1
2
0
2
1
2
2
1
0
0
1
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
0
1
1
1
1
2
1
1
1
1
0
2
1
0
1
1
0
1
1
1
2
0
1
2
1
2
1
0
2
2
0
1
2
1
2
1
0
1
1
1
1
0
2
0
1
1
0
1
0
1
2
0
1
1
0
1
1
1
1
1
1
1
0
1
1
2
1
1
2
1
1
0
1
1
3
1
1
1
0
0
2
1
0
1
1
2
1
1
2
0
1
0
3
1
1
0
0
1
2
0
2
1
2
0
0
1
2
0
2
2
1
1
0
1
2
1
0
1
1
0
1
0
1
1
1
2
0
0
1
2
2
0
1
1
1
1
0
0
1
1
1
1
1
2
0
1
1
2
0
2
1
2
0
2
1
2
1
0
0
1
0
1
1
5
1
0
0
1
0
2
1
2
1
0
1
2
0
1
2
2
0
1
1
1
1
1
2
1
1
1
0
0
1
2
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
0
2
1
0
1
0
1
0
2
2
2
0
0
1
0
1
1
0
1
1
1
0
0
1
0
1
2
1
0
1
2
1
1
1
1
1
1
2
2
2
1
0
0
1
0
1
2
1
0
1
1
0
0
1
1
2
1
0
2
2
1
1
2
2
1
0
0
0
1
1
1
0
1
1
1
1
2
0
2
1
0
1
1
0
0
2
2
0
1
2
0
2
1
2
0
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
0
2
1
0
0
0
1
1
1
1
2
1
0
2
1
0
1
2
1
0
3
0
1
1
2
2
1
0
1
0
1
1
2
1
2
2
0
2
0
1
0
2
1
0
1
2
2
0
1
1
0
2
2
2
0
0
0
1
1
0
1
1
1
0
0
1
1
0
2
2
1
2
1
1
2
2
1
2
0
1
0
2
1
2
1
0
1
1
0
1
0
1
1
0
2
1
0
2
0
2
1
1
1
2
1
1
1
0
1
1
0
1
0
1
1
1
1
1
1
2
1
2
0
2
1
1
0
0
1
1
1
1
1
1
1
1
0
1
1
1
1
1
0
0
0
0
1
1
1
0
1
1
0
0
2
2
1
0
1
1
1
1
1
1
2
1
0
0
1
1
1
0
1
0
1
1
0
1
0
1
2
0
1
1
2
0
0
2
1
1
1
1
0
1
1
2
0
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
1
1
2
1
2
1
0
1
1
1
2
0
1
1
1
3
1
0
2
2
0
2
2
1
4
0
0
1
0
2
1
2
2
2
1
1
1
1
2
1
2
0
1
1
1
2
0
2
2
0
0
1
0
0
2
1
2
0
1
2
2
0
1
0
2
1
2
0
2
0
0
1
0
1
1
1
0
2
0
1
1
2
2
0
1
1
1
2
2
0
1
2
1
0
1
2
1
1
1
0
1
0
1
1
1
2
1
1
1
1
0
2
1
1
2
2
1
2
2
0
1
1
1
0
1
2
1
1
1
1
1
1
1
2
1
0
0
1
0
2
0
1
1
1
2
1
1
1
0
0
2
1
1
1
2
0
1
2
2
2
2
1
1
1
1
2
0
2
1
0
1
1
0
0
1
1
2
0
1
1
1
1
1
2
2
1
2
2
0
1
2
1
1
0
0
2
0
1
2
2
0
0
1
2
1
0
0
1
1
2
2
2
1
0
1
1
1
1
1
1
2
1
1
0
0
1
1
1
2
2
0
2
0
0
1
0
0
1
1
1
2
0
0
1
1
1
1
0
2
1
1
2
1
1
1
2
0
2
1
1
0
1
1
1
2
1
1
1
1
1
1
0
2
1
1
2
0
1
1
1
0
1
1
0
2
1
1
2
1
2
1
1
1
1
1
2
1
1
1
2
1
2
0
1
1
1
0
2
1
2
1
1
0
0
1
0
2
0
2
1
1
1
1
0
2
0
2
1
2
0
1
1
1
1
2
1
1
1
1
1
0
1
6
1
0
1
1
2
2
1
0
1
1
1
0
1
1
1
1
1
0
2
1
2
1
0
1
1
2
2
1
2
0
2
1
1
2
1
1
0
0
3
1
1
1
1
2
2
1
3
1
1
2
0
1
1
1
1
2
1
1
2
1
0
0
1
2
1
1
2
2
0
1
0
1
2
2
0
2
1
1
0
1
1
1
2
2
1
1
0
1
1
1
0
2
1
0
1
1
0
1
1
1
1
2
1
0
1
0
0
1
1
1
1
1
1
1
0
1
0
1
0
1
1
2
1
1
1
1
1
0
2
2
0
0
0
1
1
1
0
1
1
1
2
1
2
0
2
1
2
1
1
2
1
1
1
1
0
1
0
1
1
1
0
2
2
1
0
1
0
2
2
1
1
2
1
1
0
1
1
1
0
1
2
2
0
1
1
1
0
2
0
1
1
0
1
1
2
1
4
1
1
1
1
1
0
0
1
1
0
1
0
1
1
2
0
2
2
1
0
1
0
1
1
2
1
0
4
1
2
1
0
1
0
0
2
1
0
1
1
1
1
1
1
1
1
0
0
0
1
1
0
1
1
0
0
2
0
1
1
2
1
1
1
1
1
1
2
0
1
0
1
1
1
1
0
0
1
0
1
2
1
1
1
1
1
0
3
0
1
1
1
0
2
1
1
1
1
1
1
2
1
3
1
1
1
1
0
2
1
0
1
0
1
1
1
1
1
1
1
1
0
1
1
0
1
2
1
2
0
2
1
2
2
1
1
2
2
1
0
1
1
1
1
0
0
0
1
1
1
1
1
0
0
1
1
1
0
1
2
1
1
1
0
1
1
2
2
1
2
1
2
2
1
1
1
1
0
2
0
1
1
1
2
0
1
1
1
1
1
0
0
1
1
1
1
0
0
1
0
2
1
1
1
0
1
1
2
1
1
1
2
1
1
0
2
1
0
1
1
2
1
3
1
2
1
1
2
0
1
1
1
1
1
1
1
2
1
2
1
0
1
2
0
1
0
1
0
1
1
0
0
2
1
1
1
0
2
1
1
1
1
1
1
0
1
1
2
0
1
2
1
2
1
2
1
0
1
1
1
0
1
1
2
1
2
2
1
1
1
0
1
2
1
2
1
1
1
1
0
0
1
1
1
1
1
1
2
1
1
0
0
1
0
0
2
1
2
0
1
0
2
1
1
1
1
1
1
2
0
2
2
1
2
2
2
1
1
1
1
1
0
1
1
1
1
1
1
0
1
1
0
2
2
1
1
0
1
1
1
1
2
2
1
1
2
1
1
0
1
1
2
2
0
2
0
0
0
0
0
1
1
0
0
2
1
0
2
1
1
0
1
2
1
1
1
0
1
1
2
0
0
0
2
1
1
1
1
1
1
1
0
1
1
0
4
0
1
2
2
1
1
1
1
1
2
1
1
1
2
2
1
1
2
1
0
0
0
1
1
1
2
2
1
1
1
1
1
1
1
1
0
0
0
0
0
2
1
0
0
1
1
0
1
3
0
2
2
1
1
1
1
0
0
1
0
0
1
0
0
1
2
2
1
1
2
0
1
1
1
1
0
1
1
1
2
1
1
2
2
1
1
1
2
0
0
0
1
1
1
0
2
1
1
1
1
1
2
1
1
1
0
1
2
1
1
1
1
2
2
1
0
1
2
2
1
0
0
0
1
1
1
0
0
2
1
1
1
2
1
2
0
0
1
1
1
1
2
0
0
1
1
1
1
1
0
0
2
1
1
0
1
2
0
0
2
1
1
1
1
0
0
1
1
1
0
1
1
0
2
1
1
1
1
1
0
0
1
2
2
1
1
2
1
2
1
1
1
2
1
1
1
0
1
1
2
1
2
1
2
0
1
2
1
1
0
1
1
1
0
1
1
1
1
0
1
1
1
0
1
0
1
1
1
2
2
1
2
1
1
1
2
2
2
2
2
1
0
1
1
1
0
3
1
1
1
1
1
1
0
0
2
2
2
1
0
1
1
0
1
1
2
1
3
0
1
1
1
2
2
1
1
1
3
1
0
0
0
0
1
2
1
1
1
1
0
1
1
0
1
0
0
1
1
0
1
1
1
1
0
0
0
1
0
1
1
2
1
1
2
2
0
0
2
1
2
1
0
1
0
0
1
2
0
2
2
1
0
0
2
1
1
2
1
2
0
1
1
0
1
0
1
0
0
2
3
1
1
2
2
1
0
1
1
2
1
2
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
0
1
1
0
1
2
0
1
2
1
1
1
2
1
0
1
0
2
0
1
1
1
1
2
0
1
0
0
1
1
0
0
0
1
1
2
1
1
1
1
0
0
1
1
2
1
1
1
1
1
1
2
2
2
0
1
1
1
1
2
2
1
1
1
2
2
1
1
1
1
2
2
1
2
1
2
1
2
1
1
1
2
1
1
1
0
2
1
1
2
1
1
1
1
1
2
2
1
1
0
1
1
0
1
1
0
0
2
1
1
1
1
2
1
1
1
1
1
0
1
1
0
0
2
0
1
2
2
0
1
0
1
0
0
1
2
2
1
1
1
2
2
1
1
2
0
1
2
1
1
1
1
1
1
0
2
1
2
1
0
1
0
1
2
1
1
2
1
2
2
1
2
1
1
1
1
1
0
0
2
1
1
1
1
2
1
1
0
2
0
0
1
2
2
1
2
1
1
0
1
0
1
2
1
1
1
1
0
0
2
1
2
1
2
1
0
0
1
1
1
2
1
0
1
2
1
2
0
0
0
1
1
2
1
1
1
0
1
0
2
1
1
2
1
1
1
2
0
1
2
0
1
2
0
0
1
0
1
0
0
0
1
1
2
0
1
1
1
1
1
0
1
1
2
0
1
1
2
1
1
1
1
1
0
1
1
1
1
1
2
2
1
0
2
1
1
1
0
1
0
0
0
1
0
1
2
1
1
1
2
1
1
2
1
2
1
2
1
2
3
1
1
0
1
0
1
2
1
2
1
1
2
1
0
0
1
0
1
1
1
1
1
1
1
2
1
2
0
1
1
2
1
1
3
1
1
1
1
2
0
1
1
1
1
2
0
3
1
2
1
2
1
2
0
0
0
2
2
0
0
1
1
1
1
2
2
0
1
1
0
0
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
1
0
0
0
0
1
1
2
1
0
1
1
2
2
1
1
0
1
1
1
0
1
1
1
1
0
1
1
0
0
1
1
1
2
1
1
1
1
2
1
2
2
2
1
1
0
0
1
0
2
1
2
2
0
1
1
1
2
1
0
2
1
2
1
3
0
1
1
0
1
2
1
1
0
0
1
1
1
2
2
0
1
1
1
1
1
2
2
2
1
2
1
1
1
1
2
0
1
1
1
3
1
0
1
0
2
0
0
0
1
2
1
2
0
0
2
0
1
2
1
1
0
2
1
2
1
2
1
0
1
1
1
2
0
2
1
1
1
1
0
1
1
1
2
2
1
2
1
1
2
2
1
0
1
1
0
1
2
0
1
1
0
2
0
0
1
1
0
2
2
1
0
2
1
1
1
0
1
0
0
0
1
2
0
1
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
0
2
1
1
1
1
2
2
2
1
1
1
1
1
0
2
1
0
1
1
1
1
0
1
0
1
0
2
1
0
1
1
1
1
1
1
1
1
1
0
1
2
1
1
1
1
0
1
2
1
2
1
1
1
2
1
1
0
1
1
1
2
0
1
2
4
0
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
0
1
0
0
1
1
1
1
0
0
1
1
1
0
0
2
1
1
0
2
1
2
1
0
1
2
2
0
2
2
2
1
1
0
1
1
0
2
0
1
1
1
1
1
2
1
1
1
1
1
1
2
0
2
0
1
2
0
1
0
1
1
1
1
3
1
3
2
1
1
1
1
0
0
0
1
1
2
2
2
1
1
1
2
1
2
2
0
1
0
1
1
1
0
2
1
0
0
0
0
1
2
1
2
1
1
1
1
0
1
1
0
1
2
1
2
2
1
0
0
1
1
1
2
1
1
0
2
0
1
1
1
0
1
1
1
0
2
1
1
0
1
1
1
1
1
1
1
1
2
1
0
2
1
1
0
1
1
0
1
0
1
1
1
2
1
0
1
2
1
1
1
1
2
1
0
0
0
1
1
1
1
2
0
0
0
2
2
1
4
1
0
0
1
1
0
0
1
1
2
1
0
1
2
1
2
3
1
1
1
1
1
2
1
1
2
0
0
2
1
2
2
0
1
0
1
1
0
1
1
1
2
0
1
1
0
0
0
0
0
1
2
0
2
0
2
1
1
2
2
1
0
0
1
1
0
1
1
1
1
1
1
1
2
2
2
0
1
1
1
2
1
2
2
1
1
2
1
2
3
1
1
1
0
0
1
1
1
2
2
2
2
2
2
1
1
0
0
1
1
1
1
1
1
0
1
1
0
1
1
1
2
1
1
1
1
0
1
0
2
1
2
1
0
1
5
0
1
1
1
0
2
1
1
1
1
1
1
0
2
2
0
1
1
2
1
1
0
1
1
1
0
1
1
1
1
2
1
1
1
1
2
0
1
2
0
1
1
2
2
1
3
1
2
0
2
1
0
1
1
2
1
0
2
1
1
1
1
1
1
0
1
1
1
2
0
1
2
2
1
1
1
0
1
0
1
2
3
0
2
2
2
1
2
1
1
0
2
1
2
0
2
1
0
1
1
1
2
0
1
3
1
1
1
1
0
1
1
1
1
1
2
1
1
1
2
0
0
0
1
2
2
2
0
2
0
0
1
1
1
0
0
2
2
1
0
1
1
1
0
1
2
1
2
0
1
1
1
2
1
2
1
2
0
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
2
1
1
1
0
2
1
1
0
2
1
2
2
0
0
1
0
1
1
2
2
1
2
0
1
1
1
1
0
0
1
1
3
1
1
1
1
3
1
2
1
0
1
1
2
1
1
1
1
0
0
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
0
1
1
1
1
0
2
2
2
1
1
1
1
0
1
1
2
2
1
1
0
0
1
1
2
1
1
1
0
0
2
2
1
1
1
1
1
1
1
1
1
0
4
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
0
0
1
1
0
1
1
0
2
0
2
1
1
2
2
2
1
1
2
0
1
0
1
1
2
1
1
2
0
2
2
1
0
0
1
1
2
0
1
1
1
1
1
0
1
0
1
1
1
1
0
0
1
2
1
2
3
0
1
1
1
1
1
1
1
2
0
1
2
2
0
2
2
0
0
0
0
0
1
2
1
0
0
1
1
0
1
1
0
1
0
0
1
0
0
2
1
1
1
1
1
3
2
2
1
0
2
0
1
1
2
0
1
0
1
2
1
0
1
1
1
1
2
0
1
1
0
1
2
1
1
1
0
1
1
1
1
1
1
0
1
1
2
1
2
1
1
0
0
1
1
0
2
2
1
2
1
2
0
2
2
1
1
1
1
1
1
0
2
1
1
2
1
2
1
1
1
1
2
2
1
0
1
2
2
0
1
1
1
1
0
1
1
2
1
1
0
1
1
1
1
1
1
0
1
2
0
1
1
1
2
1
2
2
0
1
1
1
0
0
1
1
1
1
3
1
0
1
1
0
0
2
1
2
2
0
2
1
0
2
1
1
1
2
1
0
1
1
0
1
1
2
2
2
1
2
1
0
1
1
0
0
1
1
3
1
0
2
2
0
1
1
0
2
1
1
1
1
2
0
1
1
1
1
1
2
0
1
2
0
0
1
1
0
0
1
1
1
1
2
1
1
2
1
2
2
2
1
1
0
2
1
0
2
1
1
0
1
2
1
1
0
0
1
1
2
1
0
1
2
1
2
1
1
1
0
1
3
0
1
2
1
1
2
2
1
2
1
0
2
2
1
2
0
1
1
0
0
1
0
2
1
2
3
1
1
1
0
0
1
1
1
1
1
1
1
1
0
2
1
1
1
1
1
1
1
1
1
1
1
1
0
1
2
2
1
2
2
1
0
0
1
1
1
1
2
1
1
1
1
0
2
2
1
1
0
1
1
2
0
1
2
1
0
1
2
0
2
0
1
2
0
0
1
1
1
0
1
2
2
2
2
1
1
1
2
1
0
0
1
2
1
1
1
1
1
0
1
0
1
2
1
1
0
2
1
0
1
1
0
2
2
1
0
2
2
1
1
1
1
2
3
1
0
0
0
0
1
1
1
1
0
1
1
0
1
1
0
2
1
1
2
1
1
2
0
1
1
1
1
1
0
1
1
1
0
1
0
1
1
0
2
1
1
1
1
1
2
0
0
1
0
0
2
1
1
1
2
0
2
2
0
1
2
1
2
1
1
2
0
1
2
1
1
0
0
1
2
0
0
0
1
2
0
1
2
2
1
1
1
1
1
2
1
1
2
0
2
2
1
2
0
1
0
0
1
1
1
1
1
1
1
1
2
2
1
1
2
0
1
1
2
7
1
2
2
0
3
3
2
2
1
2
1
1
0
1
1
1
1
0
2
0
1
0
1
1
1
0
0
1
2
1
1
1
1
0
1
2
2
2
1
1
1
1
1
1
1
2
1
1
2
0
1
1
1
1
1
2
2
2
2
0
1
2
2
0
0
1
1
1
1
1
0
1
1
2
1
1
1
1
1
1
1
1
1
0
2
1
1
1
1
2
1
3
1
2
0
1
1
0
1
1
1
1
0
1
0
1
2
1
1
2
1
1
0
1
2
1
1
1
0
1
1
2
1
1
1
1
2
2
1
0
1
1
0
1
2
0
1
1
1
0
1
0
1
2
0
2
1
1
1
1
1
1
1
0
0
0
1
1
0
1
1
0
1
1
1
1
0
1
1
1
1
0
0
1
1
3
0
1
0
1
0
5
2
1
0
2
1
1
1
2
2
0
2
0
1
1
2
2
2
2
2
1
1
0
0
0
1
0
0
1
0
1
1
1
0
0
2
1
1
1
0
2
1
1
1
2
2
1
0
0
1
1
2
1
0
2
1
1
0
1
1
0
2
2
1
2
1
1
0
0
1
1
1
1
1
1
1
0
1
1
2
0
1
0
2
1
1
0
2
2
1
2
2
1
1
1
1
0
0
1
1
2
1
1
1
1
1
2
1
1
0
1
1
1
2
2
2
1
1
1
0
0
2
1
1
1
1
2
1
0
1
1
0
1
0
0
0
0
1
2
0
1
2
2
2
1
1
0
1
1
0
2
2
1
2
2
2
1
2
1
1
0
0
1
1
0
1
0
2
1
1
0
1
2
1
1
1
1
1
0
2
1
1
0
1
1
1
1
1
1
1
1
2
1
1
2
1
0
2
0
0
1
0
1
0
2
2
0
0
1
1
1
1
1
1
2
1
1
1
2
1
0
1
1
1
1
1
1
2
1
1
1
2
1
0
1
2
1
1
1
0
1
0
0
1
1
2
0
0
1
2
0
1
0
0
2
2
1
2
1
2
1
2
1
1
1
0
0
2
0
1
1
1
1
0
1
0
0
1
0
1
2
0
1
1
1
2
3
0
1
2
0
1
0
1
1
2
1
1
0
1
1
0
2
1
0
1
2
2
2
0
1
2
0
1
1
2
1
0
1
1
2
1
2
1
1
1
0
2
2
1
1
1
0
1
2
2
2
1
1
0
3
0
2
1
0
0
1
0
1
1
0
0
1
1
1
0
1
0
1
2
0
0
1
1
1
1
1
1
1
1
0
0
1
0
1
0
1
0
1
2
0
0
2
1
2
0
2
2
2
1
2
1
2
1
1
1
2
2
1
1
0
3
1
0
1
0
2
1
0
2
2
2
1
1
1
0
1
1
1
2
0
0
1
1
1
1
2
1
0
0
0
1
2
1
2
1
1
2
1
2
0
1
1
2
1
1
2
2
2
0
0
0
1
1
3
1
2
2
2
1
1
4
2
0
2
1
0
1
0
1
0
2
1
1
1
2
0
2
2
1
1
0
0
2
2
2
1
2
2
1
2
1
1
3
0
1
0
1
1
1
2
2
0
0
2
0
1
0
1
1
0
1
2
2
1
1
1
1
0
1
1
0
1
1
1
0
1
1
7
1
0
2
3
1
1
1
0
0
0
2
2
2
2
2
2
1
1
0
1
2
0
1
1
1
1
0
0
0
0
1
1
1
1
1
1
1
1
2
2
2
1
1
1
0
1
1
1
1
1
1
2
2
0
1
1
1
1
1
2
1
1
1
2
2
2
1
1
0
1
1
1
1
1
1
1
0
0
1
0
2
0
1
0
0
1
0
1
1
1
0
1
0
1
1
1
2
1
2
1
1
2
2
1
1
1
2
0
0
1
0
2
2
0
1
1
0
1
0
1
1
0
1
1
2
2
1
2
1
1
1
1
1
0
0
0
1
1
0
1
2
1
0
2
0
0
1
1
1
1
1
1
2
2
1
0
1
2
2
1
0
1
2
1
2
1
3
1
1
1
1
2
0
3
0
1
1
1
1
2
2
0
2
0
2
2
1
1
1
1
2
1
2
0
1
2
0
3
2
1
1
1
1
1
2
2
1
2
0
1
0
0
1
2
0
0
2
1
1
1
0
3
1
2
1
1
1
2
1
1
0
1
2
1
1
0
1
2
1
2
2
3
1
1
0
0
1
1
2
1
1
0
1
3
2
0
0
1
2
1
1
2
1
1
2
2
1
0
1
0
0
1
1
0
1
1
0
0
1
0
2
0
1
0
1
1
0
0
2
1
2
1
1
1
0
1
0
1
1
1
0
1
1
1
0
1
1
2
1
1
2
1
1
1
1
2
0
0
1
1
1
1
1
2
2
1
0
2
2
0
1
0
2
1
1
1
1
1
1
1
0
0
1
2
2
0
1
0
1
0
0
1
2
0
1
1
0
0
1
1
0
1
1
1
2
2
2
1
1
0
0
1
1
1
1
1
1
1
1
0
2
1
2
1
0
1
2
0
1
1
2
1
0
1
1
0
1
1
1
1
2
1
1
2
1
1
0
1
0
1
2
1
1
0
2
1
1
2
1
0
0
1
1
0
2
1
2
2
0
0
0
1
1
1
2
1
1
1
2
2
1
0
0
0
1
1
0
1
1
0
0
2
1
1
1
1
2
1
1
0
1
0
0
1
1
1
0
1
0
0
2
0
2
1
2
2
1
0
2
2
1
1
0
2
0
2
1
1
2
1
2
1
0
1
1
1
0
2
0
1
1
1
1
1
0
1
1
1
1
1
1
1
1
0
1
1
1
1
0
1
1
2
1
1
1
1
1
2
2
1
0
2
2
0
1
2
1
1
2
1
1
1
1
1
0
1
1
1
1
0
2
2
0
1
1
1
0
1
1
1
1
1
0
1
1
0
1
1
0
1
1
2
0
1
0
1
0
1
0
0
1
0
2
1
1
1
1
1
1
0
0
0
2
1
1
1
1
1
2
1
1
0
0
0
0
1
1
2
1
1
1
1
0
1
1
1
2
1
1
0
0
1
1
1
0
1
1
1
2
1
1
2
2
2
1
1
0
1
0
0
2
0
1
1
1
1
1
2
1
1
1
1
1
0
1
1
0
1
1
0
1
2
0
1
2
1
2
3
1
0
2
0
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
4
1
0
0
1
1
1
1
0
2
2
2
2
1
2
1
0
0
1
1
0
2
2
0
0
1
2
2
0
2
1
0
2
1
0
1
1
1
1
0
1
1
1
0
2
0
0
2
1
1
1
2
1
1
2
1
2
1
0
3
1
1
1
2
1
1
0
1
1
1
2
1
1
1
1
1
1
0
1
1
1
0
0
1
1
0
2
2
1
1
2
1
1
1
0
1
2
2
2
0
1
2
1
0
1
1
1
0
1
3
2
1
0
1
1
2
1
2
1
0
0
2
1
0
0
2
0
1
0
1
1
1
1
2
1
2
1
1
1
2
1
1
0
1
0
1
2
1
1
1
0
0
1
1
2
0
2
1
1
1
0
1
2
1
1
1
0
1
1
2
1
1
1
1
0
1
1
1
0
1
2
1
1
1
1
2
1
0
1
2
1
1
1
0
1
1
0
0
1
1
0
1
1
2
0
0
0
2
1
1
1
0
1
2
1
2
1
1
1
2
1
1
0
2
1
1
1
0
0
2
1
1
1
2
2
2
2
2
1
1
2
1
1
1
0
1
0
1
0
1
2
1
1
1
2
0
2
1
2
1
1
1
1
1
2
2
2
1
1
0
1
1
2
2
0
1
0
1
1
1
1
2
1
2
3
1
1
0
1
0
1
1
1
2
0
0
0
1
2
1
3
1
1
0
1
1
1
1
0
1
1
2
0
2
3
1
1
2
0
2
0
1
1
2
2
1
2
1
0
0
1
2
2
1
2
1
1
0
2
2
1
0
1
1
1
1
0
0
0
1
1
1
1
1
2
1
0
1
1
1
1
0
0
1
0
2
2
2
2
2
1
1
0
1
0
2
2
2
2
1
1
0
0
1
1
0
1
1
1
1
1
1
0
0
1
1
1
2
1
0
1
1
3
1
1
1
2
1
1
1
1
1
1
1
1
1
1
0
0
1
2
1
1
1
0
1
0
1
1
0
1
1
0
2
1
1
0
1
0
0
1
1
1
0
1
0
2
2
0
1
2
2
2
1
0
1
1
1
2
1
1
1
1
1
1
2
0
1
2
2
1
2
1
1
1
2
1
0
0
2
0
1
0
2
2
2
1
0
2
0
0
1
3
1
0
1
0
2
1
0
2
3
2
2
2
1
0
0
0
1
1
1
1
1
1
2
2
6
2
0
1
1
1
1
0
1
0
1
0
1
1
1
2
0
1
1
1
2
0
1
1
0
1
2
1
2
3
1
1
1
2
1
0
1
2
0
1
1
2
1
0
2
2
1
1
1
1
0
1
2
0
0
1
1
1
1
1
2
0
0
1
2
1
1
1
0
1
2
2
2
2
2
1
2
2
2
0
1
1
2
1
0
1
1
1
0
2
0
1
1
2
1
0
2
0
1
1
1
0
2
1
1
2
0
1
2
1
1
2
2
1
1
0
1
0
1
1
0
0
4
0
1
1
1
1
1
1
2
2
1
0
1
2
1
1
1
0
1
1
1
1
1
0
2
0
0
1
1
2
0
1
0
1
0
1
3
1
1
1
1
1
3
1
0
0
0
1
1
1
2
0
0
1
2
1
0
1
1
0
1
1
1
2
2
1
2
1
1
1
1
1
1
0
1
1
2
1
2
1
1
1
0
1
1
1
1
0
2
0
1
2
1
0
1
1
1
2
0
2
1
1
2
0
2
1
0
1
2
0
1
1
1
0
2
1
1
1
1
1
0
1
1
0
2
0
0
2
1
1
0
0
2
2
1
0
1
1
1
1
1
1
2
0
1
2
1
0
1
1
2
2
2
1
1
1
1
0
1
0
1
1
1
0
2
1
0
0
0
2
1
1
1
2
1
1
1
0
2
1
2
1
0
1
1
2
1
2
0
2
1
0
1
1
1
2
2
1
0
1
2
1
1
1
1
1
1
1
1
1
1
0
2
1
1
1
1
0
1
0
0
0
0
1
1
1
2
1
2
0
0
1
1
0
1
1
1
1
2
1
2
1
2
1
0
1
2
1
1
0
0
0
2
1
1
1
1
1
1
2
1
2
0
1
1
2
1
0
2
1
2
1
1
2
1
3
2
1
2
0
0
0
2
1
0
1
1
0
0
1
1
0
0
1
1
1
1
1
1
0
1
1
0
1
1
0
0
0
2
2
2
1
1
1
1
1
2
1
1
1
1
2
2
0
2
1
2
1
1
1
1
1
1
1
1
1
1
1
3
2
1
0
1
1
1
2
1
0
0
2
1
1
0
1
1
1
1
1
0
1
0
0
1
2
1
1
2
1
1
1
0
2
1
2
0
1
1
1
2
0
1
0
1
1
1
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
0
1
1
1
2
0
1
1
1
0
0
0
0
1
0
1
1
0
1
1
1
0
0
2
1
1
1
1
1
1
0
2
1
2
2
0
1
2
1
1
1
1
1
0
0
1
0
2
1
2
1
1
0
2
1
1
1
2
0
0
0
2
1
1
1
1
1
0
0
2
2
1
2
0
1
1
0
0
1
0
2
1
1
1
1
2
0
2
1
1
2
0
0
0
2
2
0
0
2
0
1
1
0
1
1
1
2
2
1
1
0
2
2
2
1
1
2
0
0
1
0
0
1
2
1
1
2
8
1
3
1
1
0
2
1
2
2
1
1
0
1
1
1
1
1
0
2
1
0
1
0
2
0
0
1
1
1
2
1
2
1
1
1
0
1
0
1
2
2
1
1
0
1
2
0
1
1
0
2
0
2
2
1
0
1
2
0
1
2
2
1
1
1
0
2
2
1
1
2
1
1
1
0
0
1
1
2
2
0
0
1
1
3
1
1
1
1
1
0
1
1
1
2
1
0
1
2
1
1
0
1
1
0
1
1
2
1
0
2
1
1
0
1
1
2
0
1
1
1
2
1
1
0
2
0
0
2
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
0
2
1
0
0
2
0
1
2
1
1
1
1
0
0
1
0
1
1
1
1
1
1
2
0
2
1
0
2
1
1
2
2
1
1
0
1
1
1
1
0
0
2
2
1
1
1
0
0
2
0
2
2
0
1
1
2
1
2
1
1
1
0
1
2
1
2
1
3
0
0
1
1
1
2
1
0
2
2
1
1
1
1
1
0
1
1
1
1
1
0
1
1
1
1
1
1
1
0
1
0
2
1
0
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
0
1
2
0
2
2
1
1
1
1
2
0
0
1
1
2
1
1
1
1
1
1
1
0
2
1
1
1
1
2
0
2
1
0
1
1
2
0
1
0
2
3
1
2
1
1
0
1
2
1
1
0
1
0
2
1
1
1
0
0
1
1
1
0
0
2
1
2
1
2
2
1
0
1
1
2
0
3
1
0
1
1
0
1
0
2
1
2
1
1
0
1
1
1
1
0
1
1
0
2
1
0
2
2
0
1
1
1
2
0
1
1
0
1
2
0
1
0
0
1
1
3
1
1
1
0
1
1
1
1
1
1
1
3
0
2
1
1
0
0
1
1
1
1
2
1
1
1
1
1
3
1
1
2
0
0
1
1
1
0
2
2
2
1
2
1
0
1
1
1
0
1
0
2
1
1
1
1
2
2
2
1
0
2
1
2
1
0
1
2
2
1
1
1
0
0
1
1
1
0
2
1
0
1
1
0
0
1
2
2
1
1
0
1
0
1
2
1
0
1
1
2
2
2
2
1
1
0
2
1
1
2
0
2
1
2
0
1
1
1
1
1
1
1
1
1
0
1
0
0
1
2
2
1
0
1
0
0
2
2
1
2
1
0
1
0
1
0
1
0
2
1
1
1
1
1
2
0
1
1
0
0
2
1
0
1
2
1
0
1
1
1
1
2
2
1
0
0
1
0
2
1
2
2
1
2
0
1
1
0
1
0
1
0
1
3
1
1
1
1
2
2
2
1
1
2
0
2
2
2
2
1
1
0
1
0
2
2
2
2
1
2
2
1
1
2
1
1
1
1
0
1
1
1
1
0
0
0
2
1
2
0
1
1
0
1
0
1
0
0
1
1
1
1
2
1
1
1
1
1
2
1
1
2
0
1
1
1
1
1
0
0
1
2
2
1
1
1
2
0
1
2
1
1
1
2
0
1
1
0
1
1
2
1
0
1
1
1
1
0
1
0
1
1
0
2
1
2
1
1
1
1
1
2
0
1
2
3
2
1
1
0
1
1
2
1
2
1
1
0
1
0
1
1
0
1
2
0
1
1
1
2
2
2
2
1
1
1
1
2
1
1
0
1
1
1
0
0
0
0
2
2
0
2
2
2
1
1
2
2
1
1
0
1
0
1
1
1
1
2
1
1
1
1
1
1
1
1
1
0
2
1
1
0
0
2
1
2
1
1
0
2
0
0
1
0
1
2
1
1
1
0
1
1
1
0
0
0
1
2
2
1
1
1
1
1
1
2
1
1
2
1
2
2
3
1
2
0
0
1
1
1
1
1
1
2
2
0
0
1
1
1
2
1
1
1
1
0
0
0
2
2
1
1
2
2
2
1
1
0
1
1
1
1
1
1
2
0
1
1
1
1
2
1
2
2
0
1
2
0
1
0
0
1
0
1
1
9
1
1
0
1
1
1
2
1
1
1
2
1
1
1
1
1
1
0
1
0
1
0
1
3
2
0
1
2
1
3
1
1
0
1
2
2
2
1
1
1
1
1
1
1
1
1
2
2
1
0
1
2
1
0
1
2
0
1
2
1
1
1
1
1
1
2
0
1
2
3
2
0
2
0
1
1
0
1
1
1
0
2
1
2
0
1
1
3
1
0
0
0
1
1
2
2
1
1
2
2
1
0
2
0
1
1
1
1
2
0
1
0
2
1
2
1
0
1
2
1
2
2
1
2
1
1
0
0
2
0
0
1
0
0
1
1
1
1
0
2
1
2
2
1
0
0
3
0
2
2
1
1
1
0
1
1
1
0
0
1
0
2
0
2
1
1
0
2
0
2
0
0
1
0
1
1
1
0
0
1
1
1
2
1
2
2
0
1
1
0
1
0
1
1
1
2
2
1
2
1
2
1
1
2
1
1
2
2
1
2
2
1
1
1
1
0
1
0
0
1
1
2
2
0
2
1
1
1
1
2
0
1
2
1
1
1
1
0
1
1
2
0
0
1
0
1
0
2
0
1
0
0
1
0
0
1
0
1
1
0
1
1
1
1
1
2
0
2
1
1
1
1
1
1
0
1
0
1
2
1
1
1
3
1
2
1
1
1
1
1
2
0
1
2
2
2
1
1
0
1
1
0
1
0
1
1
0
1
1
0
2
1
0
0
1
1
1
1
2
0
0
0
1
0
1
1
0
0
2
2
2
1
2
0
1
1
0
0
0
0
0
2
0
1
2
2
3
1
0
0
0
3
2
1
0
2
0
1
0
1
0
1
0
1
0
0
0
3
1
0
0
0
0
0
1
1
0
1
1
0
0
2
1
1
1
1
1
1
2
2
1
1
0
2
0
2
2
1
2
1
1
1
2
2
1
1
1
1
0
2
1
2
1
2
1
1
1
1
1
2
1
2
1
1
1
2
1
2
1
1
1
1
2
1
1
0
1
2
1
2
1
1
0
1
2
1
2
1
1
1
0
1
1
0
1
2
0
2
1
1
1
2
1
0
1
1
1
1
0
1
2
2
2
0
1
1
1
2
0
2
0
0
1
0
2
0
0
1
2
0
2
2
1
0
0
0
2
2
1
2
1
1
1
0
1
1
1
1
1
0
1
0
1
1
2
1
1
2
1
3
1
1
1
1
0
1
2
1
0
2
1
1
1
1
1
0
1
2
2
0
2
1
1
2
1
0
1
1
1
0
0
2
1
2
1
1
1
1
2
2
1
1
1
1
1
0
1
0
0
0
2
1
2
2
1
1
1
2
1
1
3
1
1
1
1
1
1
1
1
0
0
2
2
1
1
1
1
0
1
1
1
1
0
0
1
0
2
1
1
1
2
1
1
1
2
0
0
1
1
2
1
2
2
1
0
2
1
1
1
0
1
2
1
1
2
1
2
1
0
1
1
1
0
1
1
1
1
1
0
1
1
1
1
1
0
1
1
1
1
2
1
0
1
1
1
1
0
2
1
1
2
1
1
0
2
0
1
1
1
0
1
2
1
1
1
1
2
1
1
1
1
1
2
1
1
0
1
1
3
0
1
0
2
1
2
1
1
1
2
1
1
0
1
2
1
2
1
1
1
2
1
0
1
2
1
2
0
0
1
1
1
2
1
1
3
1
2
1
2
1
2
2
1
1
1
2
0
2
2
2
2
1
2
1
0
2
2
1
2
1
0
1
1
2
2
1
1
2
1
1
1
1
2
2
1
0
1
1
1
2
0
1
2
1
2
1
2
1
1
1
1
2
0
0
2
0
1
0
0
2
0
1
2
0
2
1
2
1
1
0
1
1
1
1
1
0
0
2
1
1
0
1
2
2
2
0
1
1
1
1
2
1
1
1
1
0
2
1
0
1
1
0
2
1
1
1
1
0
1
1
1
2
0
2
0
1
2
1
1
0
1
1
0
1
1
0
2
1
1
1
1
2
1
0
0
1
1
2
0
1
1
1
0
0
0
1
1
1
1
0
0
1
0
0
0
1
1
2
0
1
0
1
1
0
1
1
1
2
1
0
0
1
1
0
0
2
1
0
1
1
2
2
1
0
2
1
1
0
1
1
2
1
1
1
0
1
0
0
1
1
1
2
1
2
1
1
1
1
1
0
1
1
1
0
1
1
1
1
2
2
1
2
1
1
2
1
0
1
1
1
1
2
0
1
2
0
3
1
1
1
0
1
1
1
0
0
2
0
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
2
3
1
0
0
1
0
1
0
1
0
1
1
1
0
2
2
2
1
1
1
1
1
2
1
2
2
2
1
1
2
0
1
1
2
2
0
1
1
0
2
1
2
1
2
0
1
1
1
2
1
0
1
1
0
1
2
1
1
2
2
0
1
0
0
1
1
1
2
1
0
1
1
2
2
1
1
1
0
1
1
0
1
1
1
0
0
1
1
1
0
1
1
1
1
1
2
1
0
1
1
2
1
0
1
1
1
2
1
2
1
0
0
0
2
1
1
0
2
1
1
1
1
1
1
1
1
1
1
0
1
1
1
0
1
1
1
1
3
1
1
1
0
1
0
2
2
2
1
1
1
1
0
1
1
2
2
1
0
1
1
1
0
1
0
1
1
1
0
2
1
1
2
1
1
0
1
1
1
1
0
1
2
2
1
0
1
1
1
0
1
0
2
1
1
2
1
0
1
0
0
1
1
1
1
1
2
1
2
0
1
0
1
1
0
0
1
0
1
1
1
0
0
1
1
2
2
2
1
1
1
0
1
1
3
1
1
2
2
1
0
1
0
0
0
2
1
1
1
1
1
1
4
1
1
0
1
2
0
1
1
1
1
1
1
0
0
1
2
2
2
1
2
2
1
2
1
1
1
4
2
2
1
1
2
1
1
0
2
1
0
2
0
1
2
2
0
1
1
1
0
1
2
2
1
0
1
1
1
1
0
1
1
1
1
0
1
1
1
1
2
1
1
2
1
0
2
1
2
1
1
2
0
2
1
1
1
2
1
1
0
1
0
2
0
1
1
1
1
1
1
1
1
1
1
0
2
0
1
0
2
1
1
1
0
3
0
0
0
1
2
1
1
1
0
1
1
1
2
1
2
1
2
1
1
0
1
3
2
1
1
0
0
2
2
2
0
0
1
0
1
1
1
2
1
1
0
0
0
0
1
2
0
0
1
0
1
1
2
1
0
1
2
1
0
2
1
2
1
1
1
0
1
1
1
3
0
0
2
2
1
1
1
0
0
2
1
2
3
1
2
2
1
1
1
1
1
2
1
1
1
2
1
0
1
1
0
0
0
1
1
0
1
1
2
2
2
1
1
0
1
1
1
0
1
1
0
1
0
1
2
1
0
1
0
1
2
0
0
1
1
1
1
0
2
0
1
0
0
1
1
1
0
1
1
2
1
1
1
2
0
2
1
1
2
1
1
0
2
1
1
2
1
0
0
1
2
1
0
0
1
1
1
1
1
1
1
1
1
0
1
0
1
2
1
1
1
1
0
1
4
1
1
1
1
1
1
1
0
1
1
2
1
2
2
0
0
1
1
0
0
3
1
0
1
0
1
1
1
1
1
1
1
0
1
0
1
1
0
0
1
1
1
1
0
2
1
1
1
0
1
0
1
0
1
1
1
0
2
2
0
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
2
1
1
0
2
0
2
0
0
2
1
1
0
2
2
1
1
1
2
1
1
1
1
2
0
1
1
1
1
1
1
1
1
1
1
1
1
0
0
1
1
1
1
2
0
2
0
0
0
0
1
1
1
1
1
1
0
2
2
1
1
1
1
1
2
1
2
2
1
1
0
1
1
2
1
1
1
2
1
0
0
1
1
1
1
2
1
2
2
2
1
1
0
2
1
1
1
1
1
1
1
2
1
1
1
1
0
2
1
2
2
1
1
0
1
2
1
1
1
1
1
1
0
1
1
0
2
1
0
2
1
2
1
1
1
2
0
0
1
2
0
1
0
2
2
0
1
2
2
1
1
0
0
1
1
1
1
0
1
1
0
1
2
2
1
1
1
1
0
1
1
1
0
1
1
1
1
1
1
0
2
2
1
1
2
2
1
1
1
1
1
2
1
1
0
1
1
0
2
0
1
1
2
1
1
1
1
1
2
0
0
1
2
0
1
0
2
1
1
0
2
1
2
1
1
1
1
1
1
1
1
2
1
1
0
1
0
1
0
2
0
1
1
2
2
1
1
1
3
1
1
2
2
1
1
2
0
1
2
1
1
2
2
1
1
0
1
0
2
2
4
0
1
1
2
1
1
0
1
1
1
0
1
2
0
2
0
1
1
1
0
2
1
2
2
1
0
1
1
1
1
1
1
0
0
1
2
0
2
0
2
1
1
1
1
2
1
1
1
2
1
1
0
0
1
2
0
1
1
3
1
0
1
1
1
2
1
1
1
1
1
2
1
1
0
1
0
1
2
1
1
1
2
0
2
1
0
2
1
1
1
1
1
0
3
2
1
0
1
1
2
1
0
1
1
1
1
0
2
1
0
2
1
0
1
0
2
1
1
1
1
0
0
0
1
2
1
1
1
2
2
1
1
1
1
0
1
0
1
1
1
2
1
1
2
0
0
1
0
0
0
0
1
1
0
0
0
1
2
1
1
1
1
0
0
0
2
0
1
0
1
2
1
1
0
1
1
1
1
2
2
0
2
2
1
2
0
1
2
2
2
0
1
1
1
1
1
2
1
1
0
1
0
1
1
1
1
1
2
1
1
3
3
1
1
1
3
1
1
1
1
1
1
2
2
1
1
1
2
1
1
1
0
1
1
1
1
2
2
2
1
1
0
1
0
2
0
0
0
1
1
0
1
0
0
2
1
2
2
1
2
1
1
1
1
2
0
1
1
1
1
1
0
2
1
1
0
2
1
0
2
2
1
1
1
0
2
1
1
1
0
0
1
0
1
1
0
1
1
2
1
2
0
1
1
0
1
1
1
1
1
1
2
0
0
1
1
1
0
2
1
2
2
0
1
2
1
1
1
0
2
1
0
1
1
1
0
1
0
0
1
1
1
1
1
2
1
0
0
0
0
1
0
1
2
1
2
2
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
2
1
1
2
1
1
1
1
1
2
1
1
2
1
2
1
1
1
1
1
0
1
1
0
1
1
1
1
1
2
1
0
2
0
1
2
1
1
1
1
1
0
1
2
1
1
0
0
2
3
1
1
1
1
1
0
2
2
1
1
1
2
2
2
1
1
1
1
2
0
1
0
0
0
1
0
0
0
1
1
2
2
1
0
1
2
2
1
1
2
1
1
1
1
0
1
1
2
1
0
1
1
1
0
1
1
1
1
1
1
1
2
2
1
2
0
1
1
0
2
1
2
0
2
0
2
1
1
0
0
1
2
1
1
1
1
1
1
0
0
2
1
3
1
1
1
0
2
0
1
0
1
0
2
1
2
0
0
1
0
2
2
0
1
1
2
0
2
1
1
1
1
1
1
0
1
2
1
1
0
2
1
2
1
2
1
1
1
2
0
2
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
1
1
0
1
1
0
1
2
0
0
0
1
2
1
0
1
0
2
1
0
2
1
1
0
1
1
0
1
1
0
1
1
1
1
0
1
1
2
2
1
2
2
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
2
0
2
1
1
1
0
0
2
1
2
0
1
1
1
0
2
1
1
0
0
1
1
2
1
1
0
1
2
2
0
2
1
2
1
1
1
1
1
1
1
1
0
0
2
1
1
2
1
2
2
0
0
0
1
1
2
1
2
0
2
0
2
1
2
0
2
1
2
1
1
0
2
0
0
0
2
0
0
0
2
2
0
2
2
1
2
0
1
1
2
2
2
1
2
2
1
1
1
2
1
2
0
0
0
1
1
1
0
2
1
0
2
1
1
2
2
2
0
1
0
2
1
1
0
2
1
0
1
2
1
1
2
1
1
1
0
2
1
0
1
2
2
1
3
1
1
2
2
1
0
0
1
0
1
0
2
1
0
1
1
1
1
1
1
0
1
0
2
2
1
1
0
1
3
2
1
2
2
0
1
1
1
1
1
1
0
1
1
0
1
2
1
1
2
2
1
1
1
3
0
0
1
1
1
2
0
1
1
2
1
1
2
2
1
1
1
1
0
0
1
1
1
2
1
2
0
0
1
1
1
2
1
0
2
0
1
1
1
1
1
2
1
1
0
0
1
2
0
1
1
1
1
1
0
1
1
1
1
2
0
2
0
0
2
2
0
1
1
1
1
1
0
1
1
1
0
2
0
1
0
1
1
0
2
1
0
2
1
1
1
1
0
1
1
0
1
2
2
2
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
0
1
2
0
0
1
1
2
1
1
0
1
1
2
1
2
1
0
2
1
2
1
1
0
1
2
1
0
1
2
0
1
0
0
1
0
0
2
0
0
0
1
2
0
2
1
1
2
2
1
1
0
1
1
1
1
1
1
1
2
0
1
1
0
2
1
0
1
2
1
1
2
1
1
1
1
1
2
1
1
0
0
0
2
1
0
0
1
1
1
0
1
1
1
1
1
1
0
1
0
1
1
2
0
0
2
0
2
1
2
1
1
2
2
2
1
1
1
2
2
1
1
1
0
2
0
1
2
1
1
1
0
1
2
0
0
1
1
2
1
1
1
1
0
2
0
2
3
1
2
1
1
2
0
2
1
1
1
1
1
1
2
0
1
2
1
2
1
1
2
1
2
0
1
2
0
0
1
0
1
2
1
1
0
1
2
1
2
2
2
0
1
2
1
2
2
1
0
0
1
1
0
1
1
1
0
1
0
2
0
1
1
2
1
1
0
1
1
2
1
1
1
0
1
0
0
2
1
1
0
2
1
2
1
2
0
2
1
1
0
1
2
1
1
0
1
1
2
1
1
1
0
0
1
2
0
2
0
1
1
1
1
0
1
1
2
2
1
1
2
1
0
0
1
1
1
3
0
1
1
0
0
2
1
1
0
2
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
2
0
1
1
1
0
2
1
1
1
1
0
1
1
2
2
2
0
2
1
1
2
1
1
1
1
2
1
1
2
2
2
2
1
0
1
2
2
1
1
1
0
2
1
0
2
2
1
1
1
1
2
2
2
2
3
1
2
1
0
2
1
0
0
1
1
1
1
1
1
1
0
0
2
1
1
1
1
1
1
0
1
1
1
1
0
1
0
1
1
2
2
1
0
2
0
0
1
2
1
1
1
0
1
1
2
2
0
3
2
2
1
1
0
2
0
2
1
2
1
0
0
2
1
0
1
2
0
2
0
0
1
1
1
0
0
1
1
1
2
1
2
1
0
1
2
1
0
1
1
1
1
1
1
1
1
0
1
2
1
0
2
1
1
1
0
0
1
2
1
1
1
2
1
1
1
0
1
1
1
1
2
1
1
1
0
1
1
0
3
0
1
1
1
1
0
0
0
1
1
2
1
1
1
1
1
1
0
0
2
0
1
0
1
1
1
2
1
1
1
1
2
0
2
1
1
1
1
1
1
1
0
0
1
1
1
1
0
1
0
2
1
0
0
1
1
2
1
1
1
2
0
1
0
1
2
2
2
2
1
0
1
0
2
1
1
1
0
1
1
1
1
2
0
0
1
2
2
0
1
1
0
1
1
1
1
0
2
0
1
1
2
2
1
2
1
2
1
0
0
1
1
1
2
0
0
1
1
0
1
1
1
1
2
0
1
1
1
2
0
0
2
1
1
1
1
1
2
0
1
3
1
2
0
1
1
0
2
0
1
0
1
1
0
1
1
2
5
0
2
1
0
2
0
1
0
2
1
0
2
1
1
1
2
1
1
1
0
1
0
2
1
1
0
1
1
1
2
2
1
1
1
0
1
1
1
1
1
2
0
0
2
2
1
0
0
1
2
0
0
1
1
0
0
0
1
3
1
2
2
1
1
0
0
1
1
0
1
1
0
2
2
1
2
0
1
1
0
0
1
0
1
1
1
1
1
1
1
2
0
1
1
1
1
1
1
1
1
2
2
4
1
1
1
0
1
0
1
2
0
0
1
1
0
1
2
1
1
1
1
0
0
1
1
1
1
2
0
0
1
1
2
1
1
0
0
1
0
1
1
0
1
0
0
1
1
1
1
3
2
1
1
0
1
2
0
0
0
1
2
1
1
1
1
1
1
0
1
1
1
2
2
1
1
0
1
1
1
2
1
2
1
1
2
2
1
0
2
1
2
2
0
1
1
0
1
1
2
2
2
2
0
1
0
1
1
2
1
0
1
1
1
1
0
2
2
1
1
0
1
1
2
2
2
2
1
0
1
1
1
1
1
1
0
1
0
1
1
1
1
2
0
1
2
2
2
1
2
0
1
1
2
0
0
1
0
2
2
4
3
2
1
1
0
1
2
0
2
1
0
1
0
1
2
1
3
0
1
1
1
0
1
0
1
1
1
2
0
0
1
1
0
1
1
1
2
2
1
1
0
1
2
2
1
1
3
1
0
1
2
0
2
1
1
1
2
2
3
2
1
1
1
1
1
1
0
1
1
1
1
1
2
0
2
1
1
1
2
2
2
1
2
1
1
1
2
1
1
1
2
1
2
1
2
1
2
0
0
2
1
1
0
1
1
1
0
1
2
0
1
2
2
1
1
2
1
2
1
1
0
0
2
0
0
1
1
1
2
0
0
1
1
2
1
1
2
1
1
2
0
1
1
0
2
1
1
2
1
2
2
1
0
1
2
1
1
0
2
2
2
2
1
1
2
2
1
1
1
0
1
1
1
2
1
1
1
0
0
1
1
1
1
1
1
2
2
2
1
1
1
0
2
1
1
1
1
1
2
1
1
1
2
1
0
0
2
1
1
1
1
0
2
0
0
0
0
1
1
0
1
0
0
1
1
1
1
1
2
0
2
2
1
0
1
0
2
0
0
0
0
0
0
2
0
1
4
0
1
0
1
1
1
1
0
0
1
0
1
1
1
2
1
1
1
1
0
1
1
0
0
1
2
1
2
2
0
1
0
0
1
1
0
1
0
0
1
3
2
1
1
1
1
1
0
1
1
1
0
1
1
1
0
1
1
0
0
0
1
1
1
1
1
1
1
1
2
2
0
1
2
0
0
1
1
1
1
0
1
1
1
1
1
1
0
1
0
1
1
0
1
1
0
1
2
1
2
0
0
0
1
0
0
1
1
1
1
0
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
0
2
1
0
2
1
3
0
1
1
1
0
0
0
2
2
1
2
1
1
0
1
0
1
2
2
1
1
1
0
0
2
1
2
1
2
0
0
1
1
0
1
1
2
1
1
1
1
1
1
0
1
15
2
0
1
2
1
2
1
1
1
0
1
1
1
2
1
0
1
1
0
1
0
0
1
1
2
1
1
1
1
2
2
0
1
1
1
0
0
1
1
1
1
0
2
0
1
2
0
1
2
1
2
1
1
2
1
1
2
2
1
2
2
1
1
0
0
1
0
1
1
1
2
0
1
2
0
0
1
2
0
1
0
1
2
1
1
1
1
1
2
1
2
0
1
1
0
1
1
0
1
1
1
1
2
1
2
1
1
0
0
2
1
1
2
1
0
1
1
1
1
1
1
0
2
1
1
1
1
0
0
1
1
2
2
2
2
1
1
1
1
1
0
1
1
1
1
1
1
2
0
2
0
0
0
2
1
1
1
0
1
2
1
1
1
1
1
1
0
0
1
1
0
1
0
1
1
1
0
1
1
3
1
2
0
1
1
1
2
1
0
1
1
1
2
1
2
0
1
2
1
1
1
0
1
3
1
1
1
0
0
1
1
0
1
1
1
1
1
0
0
1
1
1
0
2
1
0
2
2
2
1
2
1
2
1
1
0
1
1
2
2
0
2
1
2
0
2
0
2
1
2
1
1
2
1
1
0
2
1
0
1
1
2
1
2
3
1
0
0
2
1
0
1
0
2
1
1
1
1
1
1
1
1
1
1
2
0
1
1
1
1
0
1
1
0
0
1
2
0
1
1
2
3
0
1
1
2
0
0
1
1
0
1
1
1
0
2
1
1
1
1
1
2
2
2
1
0
1
1
1
2
0
2
1
1
0
0
1
1
1
1
2
3
1
1
0
0
1
0
1
1
2
1
1
2
2
1
2
2
1
1
1
2
1
1
0
0
2
1
0
1
0
1
0
1
1
1
0
1
0
1
1
1
1
0
1
0
1
0
2
0
0
0
2
1
2
2
1
3
2
1
1
2
1
2
1
1
1
0
1
0
1
0
1
2
1
0
2
0
1
0
1
2
2
0
1
1
1
0
1
1
2
0
1
2
0
1
1
2
2
0
1
1
2
1
1
0
2
0
1
2
3
1
1
1
0
2
2
2
1
1
1
1
1
2
0
1
0
0
1
2
0
0
1
1
1
1
2
0
0
2
1
1
1
0
1
0
0
2
2
2
0
1
1
0
2
1
1
2
2
1
1
2
2
1
1
2
0
1
0
2
1
0
4
0
0
1
0
2
1
1
1
2
0
2
0
1
2
2
0
1
2
2
0
1
1
2
0
2
1
1
2
1
1
1
1
0
2
1
2
1
1
0
0
0
1
1
0
1
1
1
1
0
1
2
1
1
2
1
1
1
0
0
2
1
1
1
1
0
2
1
1
1
1
2
1
2
1
2
2
2
1
1
1
0
1
1
2
2
2
0
1
2
0
1
1
1
1
0
0
2
1
0
1
0
1
0
2
1
0
0
1
1
2
0
1
2
1
2
0
1
1
0
0
0
2
2
1
1
1
1
1
1
2
0
0
0
0
0
2
1
2
2
0
1
2
1
1
2
1
1
1
0
1
1
1
1
1
1
2
0
1
2
1
1
1
0
0
1
1
0
1
0
1
0
1
0
2
1
1
1
0
0
3
1
1
1
0
1
1
1
1
1
1
1
1
2
1
1
1
1
0
0
0
0
1
1
2
1
1
2
1
1
0
2
0
1
2
1
1
1
0
2
1
1
1
1
1
1
1
2
1
1
0
1
1
2
0
1
1
1
0
0
1
1
1
2
0
2
1
1
1
1
2
2
3
2
1
0
1
1
2
2
1
2
1
0
2
0
0
1
1
0
2
0
1
1
2
2
1
1
2
1
0
1
1
2
0
1
2
1
1
0
0
0
2
2
1
0
2
1
0
1
0
3
1
0
2
1
1
1
2
1
1
0
1
2
0
1
0
1
1
1
1
2
1
2
1
0
1
0
1
2
1
2
2
2
1
1
1
1
1
2
1
1
1
1
1
2
1
2
1
2
1
1
1
1
2
0
1
1
1
1
0
1
1
1
1
0
2
2
1
1
1
1
1
0
1
1
1
1
1
1
1
2
1
0
2
2
1
1
1
2
0
1
2
1
2
1
1
0
2
1
2
2
0
1
1
1
1
0
1
1
0
1
0
1
2
0
1
1
1
1
1
1
0
0
1
1
1
1
2
0
2
0
1
0
2
2
1
2
1
1
1
0
1
0
1
1
1
2
0
1
1
1
1
1
0
2
0
1
1
1
1
1
1
2
1
0
0
1
1
0
1
1
0
2
0
2
2
0
2
1
1
1
0
1
2
0
1
1
1
3
2
1
0
2
0
0
2
1
1
0
0
1
1
1
1
1
1
0
0
1
0
1
1
1
0
1
1
1
1
1
2
1
2
0
2
2
0
0
2
2
0
2
1
1
0
1
1
2
1
0
2
2
2
2
1
0
1
1
1
1
1
1
1
1
1
0
1
0
2
2
0
1
2
1
0
0
1
2
2
1
1
1
1
1
5
1
3
1
4
0
1
1
1
1
1
1
1
2
1
1
1
1
1
1
0
1
0
1
2
0
2
1
2
0
1
2
2
1
1
2
2
1
1
1
1
3
2
2
0
0
1
2
0
1
1
1
2
2
1
2
1
0
1
1
0
0
1
1
1
1
1
0
1
0
1
1
1
1
3
1
2
0
2
2
1
1
1
1
1
1
0
0
1
0
0
2
0
0
1
2
0
1
1
2
2
1
2
2
1
1
2
1
1
0
0
0
2
1
0
1
0
1
1
1
1
2
1
1
2
0
2
0
2
0
2
1
1
1
1
2
1
1
0
1
2
1
1
0
1
1
2
2
1
1
1
1
1
2
2
0
1
1
0
1
1
2
1
1
1
0
1
1
2
0
0
1
1
2
1
1
0
0
1
1
0
2
0
1
1
0
1
1
2
0
0
0
1
1
0
2
0
2
1
1
0
1
1
1
2
0
0
0
1
1
1
0
2
1
2
0
1
1
1
1
2
1
2
2
2
1
1
1
0
0
1
1
1
0
0
1
1
1
1
5
2
1
0
1
1
1
0
0
1
1
2
1
2
1
2
2
2
0
0
0
2
0
0
0
1
2
0
1
2
1
2
2
1
1
2
0
0
1
1
2
2
1
1
1
2
1
2
2
1
2
1
0
0
0
2
1
1
2
2
0
2
1
1
1
0
1
1
1
2
1
2
1
0
1
1
1
0
1
2
0
2
2
1
0
1
2
1
1
2
2
1
0
2
1
2
1
1
1
0
2
1
1
1
0
1
1
1
1
3
1
0
2
0
0
1
1
1
0
2
1
0
1
2
2
1
2
1
2
0
1
2
0
2
2
0
1
2
1
2
1
0
1
1
1
2
1
1
1
2
0
1
2
1
2
1
1
2
1
1
1
1
0
1
2
2
1
1
1
1
2
1
1
1
0
0
1
1
2
1
1
0
2
1
1
1
1
2
1
1
1
1
2
1
3
1
1
1
1
2
1
2
1
0
1
1
1
2
1
0
1
0
2
1
0
1
1
1
2
2
1
2
1
1
1
0
1
2
2
1
1
1
0
1
1
1
1
1
0
2
1
1
1
2
0
1
2
1
1
1
1
1
1
2
1
2
1
2
1
1
1
1
2
0
1
1
1
1
1
4
1
1
1
1
2
0
1
0
1
0
0
1
1
1
0
1
1
0
2
2
1
0
1
0
2
2
1
1
1
0
1
1
2
1
0
0
0
1
1
2
1
1
1
2
1
1
2
1
0
1
2
1
1
2
1
1
1
0
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
0
1
0
0
1
1
0
0
1
2
1
1
1
2
1
1
2
1
0
0
1
1
0
2
1
2
0
2
1
0
2
1
1
2
1
2
1
1
1
1
0
1
2
1
0
2
1
1
0
0
0
1
1
2
2
1
2
2
2
1
1
1
1
2
2
1
2
1
2
0
0
1
0
0
1
2
2
1
1
0
2
0
2
2
1
1
1
1
3
1
2
0
1
2
3
0
2
0
2
2
1
1
2
0
1
2
2
1
1
2
1
2
2
1
0
3
2
0
0
1
1
1
1
1
1
1
0
0
0
2
2
0
0
1
1
0
2
2
1
1
0
1
0
2
1
1
1
1
1
1
1
2
1
0
1
0
1
1
2
2
1
0
0
3
1
1
1
4
0
0
1
1
1
1
3
1
1
1
0
2
0
2
0
1
2
0
2
1
1
0
0
1
2
1
1
2
0
0
1
2
1
0
1
1
2
1
2
2
0
1
0
2
1
0
1
1
1
2
1
1
1
1
1
2
2
2
1
1
1
1
0
1
0
1
1
1
1
2
1
0
0
1
0
1
1
1
0
1
2
1
1
0
1
1
1
1
0
1
1
1
2
1
1
1
1
0
2
1
0
1
2
1
2
0
1
1
1
1
2
2
0
1
1
0
1
1
1
1
1
1
1
2
1
1
1
1
0
1
2
0
2
1
0
1
0
0
1
2
1
1
1
1
0
1
0
1
1
1
0
2
2
1
1
1
1
2
1
2
1
1
1
1
1
0
1
0
0
0
0
1
1
1
1
0
1
0
1
2
1
0
1
2
1
0
1
2
0
1
1
1
2
1
2
2
0
0
3
1
2
1
1
1
0
1
2
1
0
1
2
1
1
0
0
1
1
1
1
1
1
1
1
1
1
2
0
2
0
1
1
1
0
2
1
1
2
1
1
1
1
0
0
2
0
1
0
1
0
0
1
1
1
0
0
1
0
1
1
1
0
2
0
1
2
0
0
1
1
0
1
1
2
1
1
1
1
1
1
1
1
1
0
0
2
1
1
1
1
2
1
0
1
1
2
2
1
2
1
2
1
2
1
2
1
1
2
2
1
1
1
1
2
1
1
0
1
1
0
1
1
1
2
1
1
2
0
1
1
0
1
2
0
1
0
0
1
2
1
4
2
1
0
0
3
1
2
2
2
2
1
1
1
2
0
2
1
2
1
1
2
0
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
0
1
2
1
2
1
1
1
0
2
1
0
1
1
1
1
1
1
0
1
0
1
2
1
2
1
1
1
1
9
1
2
0
1
1
1
0
1
1
2
0
0
1
1
0
1
1
0
1
1
1
2
1
2
3
1
1
1
1
1
1
2
1
2
2
2
0
0
0
1
2
1
0
2
2
2
2
1
1
1
0
0
0
1
1
0
2
1
0
0
2
0
1
1
0
1
1
2
3
1
1
2
2
1
1
1
0
0
1
1
2
0
1
0
1
1
1
0
1
1
2
0
1
0
0
1
1
1
2
2
2
1
1
1
1
2
1
2
2
1
1
0
1
0
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
0
1
0
0
0
2
0
1
1
2
0
1
1
1
2
1
1
1
0
2
2
2
2
1
3
1
1
1
1
1
0
2
1
1
0
2
1
2
1
1
1
1
1
1
1
1
2
0
0
1
0
2
0
0
1
1
3
1
1
0
2
2
2
0
1
0
1
2
2
2
0
1
3
1
1
2
1
1
1
1
1
0
1
1
1
2
1
0
1
2
1
2
2
1
0
1
0
0
1
2
2
1
1
2
1
1
2
1
1
1
1
0
1
1
2
1
0
2
0
2
2
1
0
2
1
1
1
1
0
0
1
0
1
1
2
1
1
1
2
2
1
2
0
2
2
1
1
2
0
1
1
2
2
2
1
2
1
0
2
1
0
1
1
1
1
2
1
0
1
1
1
0
1
1
1
2
1
1
2
1
2
0
2
1
1
1
1
1
1
1
1
1
1
0
0
2
1
1
0
0
2
0
2
1
1
1
0
0
1
1
2
1
2
2
1
2
1
1
1
1
0
0
1
1
0
1
2
1
1
1
0
1
2
0
2
1
1
1
2
1
1
0
0
6
2
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
0
2
1
2
1
0
0
0
2
1
1
1
1
1
1
0
0
1
1
1
1
0
0
1
2
2
1
1
1
0
1
1
0
2
0
1
2
1
1
1
1
1
0
0
3
2
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
0
1
2
1
0
1
2
0
0
1
1
0
2
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
2
2
2
1
0
0
1
0
1
0
1
0
1
1
1
1
1
1
0
0
2
2
2
1
0
1
1
1
0
1
1
1
0
1
2
1
1
1
0
0
0
0
1
1
2
1
1
1
0
1
0
0
0
0
2
0
0
1
1
1
2
2
1
2
1
1
2
1
0
1
0
2
2
2
1
0
0
1
1
1
1
1
0
0
2
1
2
0
1
0
1
1
1
1
1
1
2
2
1
1
2
1
2
0
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
0
2
2
1
0
0
2
1
1
2
2
1
1
1
1
2
1
1
0
1
1
1
1
1
0
1
1
1
0
2
1
3
1
1
0
1
1
1
1
1
2
2
0
2
1
2
2
2
0
1
7
1
2
1
0
2
4
1
2
2
1
0
1
1
0
0
2
1
1
1
0
2
2
0
2
1
1
0
1
1
2
1
1
0
0
1
1
1
1
2
2
2
0
1
1
1
2
1
1
1
1
1
1
1
0
1
1
0
1
1
2
1
2
2
2
0
0
1
0
1
1
1
2
2
1
1
0
1
1
2
0
2
1
1
1
1
1
2
2
1
1
2
2
0
1
1
0
0
1
0
2
2
1
1
0
1
0
2
0
1
1
1
0
2
1
1
0
1
1
1
2
1
2
1
1
1
1
0
1
0
1
1
2
2
1
0
1
1
1
1
1
2
2
1
0
0
0
2
2
2
0
1
1
0
0
2
1
1
1
1
0
1
1
1
0
2
2
2
1
2
1
2
1
2
0
1
1
1
2
2
0
0
1
2
1
2
2
1
1
2
2
2
3
1
1
1
1
0
2
1
0
1
0
0
0
2
1
1
2
1
1
1
1
1
1
1
1
0
1
1
1
0
1
1
1
0
1
0
1
1
1
2
5
2
1
1
1
1
1
1
1
1
1
0
1
3
1
2
1
1
0
1
1
2
1
0
2
0
1
0
1
2
0
1
0
12
1
1
1
1
2
1
2
1
1
2
2
0
2
2
1
1
0
1
1
1
1
1
2
1
1
2
0
1
1
2
2
2
2
2
1
0
1
1
1
1
1
0
2
1
2
2
1
2
1
1
2
0
2
2
0
2
0
0
1
1
2
2
2
1
1
1
0
0
0
1
1
1
1
0
1
1
0
1
1
3
1
1
1
1
2
0
1
1
1
1
0
1
1
0
0
2
0
2
1
1
1
1
9
1
2
1
0
0
0
2
1
1
1
1
0
1
0
1
1
1
1
2
0
1
1
1
1
1
0
0
1
2
0
2
1
2
2
0
2
1
1
2
1
0
2
2
0
0
1
2
2
1
0
0
1
1
1
1
3
1
2
1
0
2
0
1
1
1
0
1
1
1
0
2
2
0
1
1
1
0
1
1
1
0
1
2
2
0
0
1
1
2
0
1
1
1
1
0
2
2
0
1
0
2
1
0
1
1
1
2
0
0
1
1
1
0
1
1
1
0
0
2
0
1
0
1
2
1
0
1
0
2
1
1
0
2
0
2
1
1
0
1
0
1
0
1
1
1
1
2
1
0
2
1
1
1
1
1
0
0
0
1
1
1
1
1
1
0
1
1
1
1
1
1
3
2
1
1
0
1
1
1
1
0
1
1
1
2
1
0
1
1
3
0
2
1
1
0
2
2
1
1
1
0
1
0
1
1
2
1
1
1
0
1
1
1
2
1
1
0
1
1
1
0
2
0
1
0
1
1
1
1
0
1
1
0
1
0
1
0
2
0
1
1
0
1
3
0
2
1
1
0
0
1
1
0
0
1
1
1
2
0
2
1
1
0
2
0
0
0
0
1
1
0
1
1
2
0
0
1
0
1
0
2
1
1
1
2
2
0
1
1
0
1
2
0
0
2
2
1
0
1
2
0
0
1
0
0
0
2
1
1
1
1
0
2
2
2
1
1
1
2
0
1
1
1
1
2
2
1
0
0
1
2
1
2
1
1
0
2
0
2
1
1
0
0
2
1
1
1
1
1
0
1
1
1
1
1
2
2
0
0
2
0
0
1
0
0
0
1
1
0
1
1
1
1
1
0
1
0
1
0
1
1
1
0
1
2
1
1
0
2
0
1
1
0
2
1
1
1
1
1
1
2
1
1
1
2
0
2
1
1
0
1
1
0
1
2
2
1
1
3
0
1
1
2
0
1
2
1
0
1
1
3
1
1
1
2
1
1
1
0
1
1
1
2
1
2
1
1
0
2
1
0
1
0
2
2
0
1
1
1
1
3
1
1
0
1
0
1
0
1
0
0
1
1
2
1
1
1
1
1
1
1
2
0
0
0
1
0
2
0
0
1
0
2
2
1
0
1
1
2
1
2
1
1
0
0
2
2
1
1
1
0
1
1
0
2
1
0
2
1
1
0
0
2
0
2
2
1
1
1
1
0
2
1
1
2
1
2
2
1
1
0
1
1
1
0
2
0
1
1
1
1
2
1
1
1
1
1
1
2
1
2
2
3
2
1
2
1
1
1
1
0
1
1
1
1
1
0
1
1
2
1
1
2
1
1
1
2
1
2
1
2
1
0
1
1
0
2
1
1
2
1
0
2
2
1
2
3
2
2
1
2
1
1
1
4
0
2
2
0
1
2
1
0
2
0
1
0
1
1
0
1
3
1
1
1
1
1
1
2
1
1
3
0
2
1
1
0
0
2
0
1
0
1
1
1
0
1
1
3
1
1
1
1
0
0
1
2
1
2
1
1
2
0
1
1
1
2
2
2
0
1
1
0
2
1
1
1
1
1
0
1
0
2
1
1
2
0
2
1
1
1
0
1
1
2
1
0
1
1
1
0
1
1
1
1
0
1
1
1
1
1
1
0
0
1
2
1
1
3
1
1
1
1
0
1
4
1
1
0
1
1
0
0
0
1
0
0
2
2
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
2
1
2
1
1
1
1
1
2
2
0
0
1
1
0
3
1
1
0
1
2
2
1
0
1
0
1
1
1
0
3
0
0
0
1
1
2
1
2
1
2
0
0
1
1
0
1
1
2
1
2
2
1
1
1
0
1
1
1
1
1
1
2
0
2
1
1
1
1
1
0
1
1
1
1
1
1
0
0
2
1
0
2
3
1
1
1
1
2
2
1
1
1
1
2
1
2
1
1
0
0
1
0
1
1
2
2
2
0
1
1
1
1
1
0
0
1
1
1
2
2
1
1
2
2
1
2
1
2
0
1
0
1
0
0
1
1
1
1
0
2
1
0
1
0
0
0
1
1
1
1
2
2
1
0
1
1
1
1
1
1
1
1
1
2
1
1
1
0
1
2
1
1
1
1
1
2
2
0
1
2
1
2
0
0
1
1
1
0
2
1
0
0
1
1
1
2
2
1
1
0
2
1
2
1
2
1
2
1
2
1
1
1
2
2
1
1
0
1
1
0
0
1
1
0
0
0
1
2
1
1
0
1
1
0
1
1
0
2
2
0
1
3
0
1
1
2
1
0
0
2
3
1
1
0
2
0
2
0
1
2
0
1
0
1
2
2
0
1
2
1
2
2
1
1
0
1
1
1
2
1
0
1
2
2
1
1
1
0
1
1
0
1
2
1
0
2
3
0
1
1
1
0
1
1
1
2
1
0
1
1
0
1
1
2
1
2
1
1
2
1
1
2
2
1
2
0
1
1
1
1
1
1
2
2
2
0
2
1
0
1
1
1
1
1
0
2
1
2
0
1
1
0
1
1
2
2
1
1
1
1
1
0
1
2
1
1
0
0
0
1
1
1
1
0
2
0
2
2
0
2
1
1
2
2
0
2
3
1
1
2
1
1
1
0
1
0
1
1
1
1
0
2
0
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
0
0
2
2
0
1
1
0
1
1
1
1
2
1
0
0
1
1
2
1
0
1
1
1
1
1
1
2
1
0
0
2
1
2
3
0
2
1
1
0
0
1
1
2
1
0
1
2
1
0
2
2
1
1
2
2
2
1
1
1
1
1
1
0
1
1
1
2
2
1
2
1
1
1
1
1
0
1
2
1
2
1
1
1
1
1
2
2
2
1
1
0
1
0
1
1
2
2
1
0
1
0
1
1
1
1
1
1
1
1
2
0
1
1
1
0
0
2
2
1
2
1
1
1
0
1
1
0
1
1
1
1
1
2
2
1
0
0
1
0
0
1
0
1
2
1
1
1
1
0
0
0
2
2
0
2
1
4
1
1
1
2
1
1
1
1
2
0
1
1
1
2
2
1
2
0
1
0
1
1
2
1
2
1
0
1
0
0
2
2
1
1
1
0
2
2
2
2
2
1
0
1
2
0
0
1
0
2
1
0
0
0
1
2
1
2
2
1
2
3
0
2
1
1
0
0
0
1
1
1
1
1
0
1
0
0
1
2
1
1
0
0
0
1
1
2
2
1
1
1
0
0
2
1
1
0
2
0
2
2
0
1
0
2
2
1
1
0
0
1
1
1
1
1
2
1
1
2
1
1
0
0
2
0
1
1
1
0
1
2
2
0
1
1
0
2
2
0
1
2
0
2
2
2
1
0
0
2
1
2
1
1
0
2
2
0
0
1
0
1
0
1
1
0
1
1
2
2
0
1
2
1
1
1
0
2
0
1
2
0
0
2
1
2
1
2
1
1
0
1
1
2
1
2
2
1
1
1
0
1
1
1
1
1
2
0
2
2
2
1
0
0
1
2
0
1
1
1
1
1
1
2
1
1
1
1
2
1
1
0
0
2
0
1
1
0
1
0
1
1
2
0
1
1
1
2
1
2
1
2
1
1
1
1
1
1
1
1
0
1
1
2
1
1
1
1
1
1
2
1
0
1
2
1
1
1
1
1
0
1
1
1
1
1
1
0
1
1
1
0
1
1
1
1
0
1
2
2
1
0
0
1
2
1
0
2
1
2
1
0
0
1
1
1
0
1
1
1
1
1
1
1
2
0
0
0
1
2
0
2
1
0
1
1
0
1
0
2
1
1
0
0
0
1
1
1
2
1
0
0
1
1
0
1
0
0
1
2
1
1
2
1
0
0
1
1
1
3
1
1
2
0
1
2
1
0
1
2
1
0
1
0
0
1
1
1
0
1
0
0
0
1
1
2
1
1
0
1
1
0
1
2
2
1
1
0
0
0
1
1
1
1
1
1
1
2
1
1
1
1
1
0
0
1
1
2
1
2
2
1
2
1
1
1
0
0
1
1
1
1
0
1
2
1
1
1
1
2
1
1
1
1
2
1
2
1
2
1
1
2
1
1
1
2
1
1
1
1
1
0
2
0
2
2
1
1
1
2
1
0
2
3
1
1
2
2
1
2
1
1
0
0
1
2
0
2
1
1
1
1
1
1
2
0
1
1
0
1
2
1
2
1
5
3
0
2
1
2
2
1
2
1
1
1
2
1
0
0
2
1
0
1
1
1
2
2
1
0
2
0
0
2
2
1
0
1
1
0
1
2
0
1
2
1
1
1
1
1
1
0
0
1
0
1
1
1
2
0
2
2
1
2
1
1
0
2
1
1
1
0
2
1
3
0
1
1
1
1
1
1
0
1
2
1
1
1
1
2
1
1
1
1
2
1
1
0
2
0
1
0
1
2
0
1
0
2
1
1
1
1
1
1
1
1
1
0
0
2
1
1
2
1
0
2
1
1
1
3
1
1
2
2
1
1
1
2
2
1
1
0
0
1
2
0
1
0
1
1
2
1
1
1
1
1
2
0
1
1
2
1
1
1
0
1
0
1
0
1
1
0
1
1
2
1
2
2
1
1
0
0
1
2
1
0
2
2
0
1
2
1
2
0
1
1
1
0
0
1
1
1
2
1
0
1
0
0
1
1
1
2
2
2
0
1
1
1
0
1
1
1
0
1
0
1
1
1
1
1
1
1
1
1
1
2
2
1
2
1
2
2
1
1
2
0
0
0
1
2
1
2
0
2
2
1
3
2
1
0
2
1
1
1
0
0
1
2
1
1
1
2
0
1
1
0
1
1
1
2
0
1
2
1
1
1
1
0
2
0
2
2
0
0
2
1
2
1
1
2
0
2
0
1
2
2
1
1
1
2
1
2
1
0
1
1
0
2
1
1
1
0
1
1
1
1
2
0
1
1
2
1
1
0
0
0
2
2
0
2
2
1
2
1
1
1
2
0
1
1
1
0
0
1
0
2
1
1
1
1
0
1
1
0
1
1
1
0
1
2
0
1
2
0
1
0
0
1
1
1
2
2
2
2
1
1
1
1
0
2
0
1
0
1
2
2
1
1
1
1
2
2
2
0
2
2
2
1
1
1
1
1
1
1
1
0
2
1
0
0
0
0
0
1
1
2
1
1
1
1
1
1
1
0
1
1
2
0
2
0
1
2
1
1
0
1
3
1
0
1
1
1
1
1
1
1
1
2
0
1
1
2
2
0
1
1
1
1
2
1
2
1
1
1
1
2
2
1
1
0
1
2
1
2
1
0
1
1
1
2
1
2
1
2
2
0
2
1
1
1
1
1
1
1
2
1
1
2
0
2
1
1
1
1
0
2
2
2
0
2
0
1
1
1
0
2
0
1
2
2
1
0
1
2
2
1
0
0
1
1
2
0
2
2
1
1
1
1
1
1
1
0
2
1
1
2
1
1
2
0
1
1
0
0
0
1
1
1
0
0
1
2
2
2
1
1
1
1
1
0
2
0
2
2
0
1
0
1
0
2
0
1
2
1
1
1
2
0
1
1
3
1
1
1
2
0
1
0
0
1
2
2
0
1
1
0
1
1
5
0
1
0
1
0
1
0
1
0
1
1
1
1
1
1
2
1
1
1
2
0
1
2
1
2
1
1
1
1
0
2
2
0
1
2
3
1
1
1
1
1
1
1
0
2
1
0
1
0
2
3
2
1
0
0
1
0
1
1
0
2
1
1
1
0
1
1
1
2
2
1
1
2
1
1
1
0
1
1
2
2
2
2
3
2
2
2
1
2
1
1
1
0
2
1
1
2
1
2
0
1
1
2
1
1
1
1
1
1
0
1
1
1
0
0
1
0
1
0
1
1
2
1
2
0
1
1
0
2
2
1
0
1
0
2
1
1
1
1
1
2
0
1
1
1
2
2
0
1
1
2
1
1
0
1
1
1
1
1
0
1
1
1
0
0
1
3
0
1
1
2
0
1
1
1
1
1
2
0
1
2
1
0
0
0
1
1
1
1
2
0
0
2
0
1
2
1
0
1
2
1
1
2
0
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
0
1
1
2
0
1
1
1
1
0
1
1
1
1
0
2
1
1
2
2
4
1
1
1
1
0
1
0
1
1
2
1
1
2
0
1
2
1
0
2
1
0
1
2
1
2
1
1
1
0
2
1
0
1
2
3
1
0
0
2
1
2
1
1
1
1
0
1
2
1
1
0
1
1
1
2
2
2
2
1
1
1
2
0
0
1
1
1
2
1
1
0
1
1
2
0
1
2
2
1
1
2
0
0
2
0
1
1
1
2
2
1
1
1
1
1
1
1
1
0
2
3
2
1
1
1
1
2
1
1
1
1
2
0
1
0
0
1
2
1
2
0
1
0
1
1
1
1
2
2
0
1
1
0
0
1
1
1
1
0
1
2
1
1
2
0
2
0
1
0
1
2
1
2
8
1
0
2
1
2
1
1
1
1
1
1
0
1
1
2
1
1
0
1
1
2
0
2
0
1
2
1
1
1
1
1
1
2
1
1
0
0
2
1
1
1
2
1
2
0
0
0
1
1
1
0
1
0
1
1
1
0
0
1
1
1
0
1
1
1
2
1
1
0
1
1
2
2
2
2
0
1
1
1
2
0
0
1
2
1
1
1
1
0
1
1
0
2
1
2
1
1
2
0
1
1
1
1
2
1
1
1
0
1
2
1
1
1
1
1
1
2
1
2
1
2
1
2
1
3
0
2
0
1
1
1
2
1
0
1
1
1
1
2
2
1
1
0
1
1
1
2
1
1
1
1
1
1
1
1
1
0
0
2
1
2
0
0
1
1
2
1
2
1
1
1
1
0
0
1
1
2
2
0
2
0
2
0
0
1
2
0
2
1
0
2
0
1
0
1
0
0
1
2
1
1
0
0
1
0
1
1
1
0
1
2
1
1
0
1
1
0
1
2
2
1
0
1
1
1
2
1
1
0
1
2
1
3
1
1
1
0
2
0
2
1
1
1
2
0
1
2
2
0
1
1
0
1
1
1
0
0
1
1
1
2
0
1
0
1
1
2
1
1
1
1
1
1
1
2
1
0
1
1
1
3
1
0
1
3
1
1
1
2
2
2
0
1
1
1
0
1
0
0
1
1
2
1
1
2
1
2
2
1
2
2
1
0
0
1
1
2
1
0
0
1
1
2
1
1
1
1
1
1
1
1
0
0
1
1
1
2
0
1
1
1
1
2
2
0
1
2
1
2
0
0
2
1
1
0
1
1
0
2
1
1
1
1
1
3
1
1
1
2
0
1
1
1
1
1
1
1
2
2
1
2
1
1
1
1
1
2
0
1
2
2
2
2
1
1
0
0
1
1
1
0
1
1
1
1
0
1
1
0
1
1
1
1
0
1
2
0
0
2
0
2
0
2
0
2
1
1
1
1
1
1
1
1
1
2
0
1
2
2
1
1
1
1
1
0
1
1
1
1
1
1
1
2
1
1
2
1
1
1
0
1
0
1
1
1
1
1
2
2
2
1
1
1
0
1
1
1
1
1
1
0
0
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
0
1
0
1
2
1
1
1
2
2
0
1
0
1
1
1
1
2
1
2
1
1
0
1
2
0
0
0
1
2
1
1
0
1
0
1
1
3
1
1
1
1
2
0
1
2
2
2
0
2
0
1
2
1
1
1
1
0
0
0
2
1
1
1
1
1
1
2
2
1
2
1
0
1
2
0
1
1
1
2
1
0
1
0
0
2
0
1
0
1
1
1
1
0
1
1
1
1
1
2
1
1
1
2
1
2
0
2
2
1
1
1
0
1
0
1
1
2
0
2
1
2
1
1
1
1
1
1
0
0
1
2
0
0
1
0
2
1
2
1
1
2
0
2
1
1
1
1
2
1
0
2
1
0
1
0
0
1
0
1
1
2
0
1
1
1
1
1
1
1
2
1
0
1
1
1
1
0
1
0
0
1
1
1
1
1
1
1
1
0
1
0
0
0
0
2
1
1
1
2
0
1
0
1
1
1
1
2
1
0
1
1
0
0
0
2
1
2
0
0
2
1
1
1
1
1
2
1
1
1
0
1
1
1
1
1
1
0
2
0
1
1
0
1
1
2
1
2
0
1
1
1
0
1
1
1
1
2
1
1
1
2
2
1
1
1
1
0
0
1
1
0
1
1
1
0
1
1
1
1
0
2
1
1
0
1
1
1
2
2
1
1
4
2
0
1
1
1
1
1
1
1
1
0
1
0
0
2
2
1
1
0
2
1
2
2
1
2
0
1
1
1
2
1
1
1
0
2
1
0
1
1
0
2
0
2
1
1
1
1
2
1
1
1
2
0
0
2
0
0
0
1
0
2
2
1
1
1
1
2
4
1
1
2
1
1
1
0
1
1
2
2
1
1
1
1
2
2
1
1
1
1
2
2
0
0
1
0
0
2
0
2
0
2
0
2
2
0
1
0
1
1
1
1
1
0
1
1
1
2
1
1
1
0
1
0
0
2
1
0
1
1
1
1
0
2
2
1
1
1
1
0
2
1
1
0
1
1
1
2
1
1
0
1
2
1
1
1
1
2
1
1
0
2
0
1
1
2
1
2
1
1
2
1
1
2
2
1
1
1
2
1
2
1
1
2
1
0
0
1
0
1
2
0
1
1
2
0
0
1
2
1
1
2
1
1
0
1
2
1
2
2
1
1
0
0
2
2
1
1
2
1
0
1
1
2
1
1
0
1
1
1
1
0
1
0
1
1
1
0
0
2
1
1
1
1
1
1
2
1
2
1
1
1
3
1
0
0
1
1
3
1
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
0
1
2
0
2
2
1
0
2
1
1
1
2
3
1
1
0
1
1
1
1
2
0
2
0
1
4
0
1
1
0
1
0
1
1
0
1
0
2
1
1
2
1
1
2
1
2
1
1
1
1
0
2
1
1
2
2
1
1
2
2
1
2
1
0
1
1
2
2
1
1
2
2
1
1
1
0
1
1
0
1
1
1
1
0
1
1
0
1
1
1
3
2
1
2
1
1
1
1
0
1
0
1
2
2
1
0
1
2
1
2
0
1
0
2
1
1
1
1
2
1
0
1
2
1
0
1
2
1
1
1
1
0
1
1
0
1
1
0
2
0
2
1
2
1
2
0
0
0
2
1
2
1
2
1
1
2
2
0
1
1
1
0
1
0
2
1
2
1
1
2
0
1
1
2
1
2
1
0
0
2
1
1
0
2
1
1
1
1
1
1
1
1
2
1
0
1
0
2
0
1
2
1
2
2
1
1
1
1
2
1
1
2
1
2
1
2
2
1
0
1
0
1
0
1
0
1
2
2
1
0
1
1
2
0
1
1
1
1
2
1
1
2
1
0
1
0
1
0
1
0
2
2
1
1
1
2
0
0
1
1
2
0
1
1
2
0
2
2
2
1
1
0
0
2
1
1
1
1
1
0
2
0
1
1
2
1
2
0
1
1
1
1
1
1
0
0
2
0
2
0
1
1
0
1
1
1
0
1
1
1
1
1
1
1
2
1
0
1
1
0
2
2
0
1
0
1
2
2
2
2
0
1
1
1
1
1
1
1
2
0
1
2
1
1
1
0
0
1
0
0
0
1
1
1
0
1
2
1
0
2
1
1
2
0
1
1
1
1
0
0
1
2
2
1
1
1
1
1
1
1
0
1
1
1
0
2
1
1
1
1
1
1
1
1
1
0
0
1
2
1
2
1
2
0
1
2
1
1
1
1
2
1
1
1
2
0
1
1
1
0
2
2
2
0
2
2
2
2
2
1
1
0
0
1
1
1
0
0
1
1
2
1
0
2
1
2
2
0
1
1
1
0
1
2
1
1
1
1
1
2
2
2
1
1
1
1
1
2
1
0
1
1
1
0
1
0
2
1
1
1
1
1
2
0
1
2
0
2
0
0
1
1
0
2
0
2
2
0
2
2
0
1
1
0
1
1
2
1
0
1
0
2
1
2
1
1
1
1
1
2
0
1
1
0
1
1
1
0
2
1
1
1
0
2
2
2
1
1
1
1
2
1
2
1
2
1
2
0
2
1
2
0
1
1
0
2
1
1
2
0
1
1
0
0
2
1
0
1
1
0
0
1
0
2
1
1
2
2
2
1
1
1
1
1
1
1
1
1
0
2
1
1
1
2
1
1
1
1
1
1
2
2
0
2
1
1
1
1
1
0
0
1
3
0
1
1
2
0
1
1
2
1
0
1
2
0
2
0
0
1
0
2
0
1
1
2
1
0
1
1
1
1
1
0
0
1
1
1
3
1
1
2
1
1
3
1
0
2
1
1
1
2
1
1
2
2
0
2
2
1
1
1
1
1
2
2
0
1
1
1
1
2
1
1
0
1
1
1
0
1
2
0
1
0
1
2
1
0
0
2
0
1
1
1
1
0
1
1
1
1
1
1
1
0
1
1
1
0
1
2
0
1
0
2
2
1
2
1
1
1
1
1
0
0
1
1
2
1
1
0
2
1
0
1
2
1
1
2
1
1
2
0
2
0
1
1
1
1
1
2
1
1
1
2
2
0
2
2
2
1
1
1
1
2
1
2
1
1
0
0
1
1
1
1
1
1
2
0
1
1
0
1
1
2
1
1
1
1
1
0
2
0
2
1
0
1
0
0
2
0
1
1
0
1
1
0
1
2
1
0
1
1
0
2
0
1
0
2
2
1
1
1
1
0
1
1
0
0
2
2
1
1
2
0
1
2
3
1
1
2
1
0
2
2
0
1
0
1
2
1
2
1
1
2
1
1
1
2
0
0
1
0
1
1
2
1
1
2
1
1
1
1
1
2
2
2
1
0
2
2
1
2
2
2
1
2
1
0
2
2
1
0
0
2
1
1
2
1
0
0
0
0
1
0
2
1
1
1
1
1
1
1
1
2
1
2
1
1
1
3
1
2
2
1
1
0
1
1
0
0
1
1
1
2
1
1
2
1
0
1
1
0
2
1
0
1
3
2
2
3
1
1
1
2
2
1
2
1
0
2
1
1
1
1
2
0
2
1
2
1
2
1
0
2
1
1
1
1
0
1
0
2
1
1
2
1
0
1
1
0
2
1
1
1
1
1
0
2
1
2
2
0
0
1
0
2
0
1
0
1
1
2
1
1
1
1
2
1
1
1
0
1
0
2
1
1
1
1
1
1
0
2
1
0
1
2
1
1
1
0
2
1
1
0
1
1
0
1
1
1
2
1
1
1
2
0
1
1
1
0
1
0
1
2
1
1
1
1
1
0
0
0
1
2
1
1
1
1
0
1
1
1
0
2
2
1
0
1
0
0
2
1
1
1
1
0
0
0
1
2
1
1
2
1
0
1
1
1
1
1
1
1
2
1
1
1
0
0
2
1
0
2
1
1
2
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
1
1
1
0
1
1
1
0
1
0
1
1
0
1
2
1
1
1
1
2
1
0
2
1
1
1
0
1
1
2
1
1
2
0
0
1
1
0
0
1
1
2
1
0
2
2
2
0
1
2
1
1
0
0
1
2
1
1
1
2
1
0
2
2
2
1
1
1
0
1
1
1
2
0
1
1
0
1
0
1
2
0
1
2
0
0
1
2
2
2
0
1
2
2
1
1
0
1
2
1
1
1
2
1
2
1
0
1
1
2
1
1
0
1
3
1
1
1
2
1
1
1
2
1
2
0
1
1
2
2
0
1
0
2
1
1
1
2
2
0
1
1
0
2
1
1
2
1
0
1
1
1
0
0
2
2
0
1
0
1
2
1
1
2
3
1
1
1
1
0
0
1
2
1
0
1
1
2
0
0
1
1
1
1
2
1
1
1
2
0
0
0
1
1
0
1
0
2
2
0
0
1
3
1
1
1
2
1
1
1
0
1
1
3
2
0
2
1
0
1
1
1
1
0
1
0
0
1
0
1
1
2
1
1
1
1
0
1
1
2
0
1
1
1
1
1
0
0
2
2
1
2
0
0
2
1
0
0
1
0
0
2
0
0
0
1
1
1
0
0
1
2
1
1
0
1
2
1
2
2
0
0
2
2
1
1
1
1
0
2
1
0
1
1
1
4
1
1
2
1
2
1
1
1
2
1
1
1
3
1
1
1
1
1
0
1
1
1
0
1
1
1
1
3
1
1
0
2
2
2
1
0
0
0
2
1
1
1
1
1
2
1
2
2
1
1
0
0
1
0
1
0
0
1
1
1
1
1
2
2
1
1
2
0
1
2
1
0
1
1
1
1
1
2
1
0
1
1
1
2
1
1
1
1
0
0
2
1
1
1
1
1
1
1
1
1
1
2
2
0
1
0
0
1
1
2
0
1
0
1
2
2
1
2
0
1
1
1
1
1
1
1
1
1
1
0
2
1
0
1
1
0
2
1
0
1
0
1
0
1
1
1
1
2
1
2
1
1
2
1
1
1
0
0
2
1
0
0
2
1
1
1
1
2
1
6
1
1
1
1
2
1
2
2
2
1
4
2
0
1
1
0
2
2
1
1
0
1
0
1
2
1
2
0
1
0
1
1
1
1
1
1
1
1
0
0
0
1
0
2
0
2
2
0
1
2
1
1
0
0
1
0
1
0
1
0
2
1
1
2
2
1
2
2
2
1
2
2
1
0
1
1
1
3
1
1
1
0
0
2
2
1
1
2
1
2
0
1
0
1
0
1
2
1
2
0
1
2
2
0
1
0
1
0
0
1
1
1
0
1
0
1
2
1
1
0
1
1
2
2
1
2
2
1
2
1
2
1
1
1
1
1
0
0
1
2
1
1
1
1
1
1
0
1
1
2
1
1
1
0
1
1
1
1
1
1
2
1
1
1
1
1
1
1
0
2
1
2
2
0
1
0
1
1
1
1
0
1
1
2
0
1
2
1
0
1
1
1
2
1
0
2
1
1
1
1
2
0
1
1
1
0
0
0
2
1
2
1
1
0
1
2
1
1
1
1
0
1
0
0
1
1
2
2
0
2
2
1
1
1
2
1
0
0
1
2
0
2
1
1
1
1
1
2
1
1
1
1
1
2
2
0
1
2
1
1
1
1
1
1
2
0
1
1
1
0
1
1
2
1
0
0
0
0
1
1
1
0
1
1
1
1
1
0
0
0
1
1
1
1
3
0
2
1
1
0
1
1
0
0
1
0
0
0
0
2
1
1
1
2
1
1
1
1
1
2
2
2
2
2
1
2
1
1
1
0
1
1
1
1
1
2
2
2
2
1
2
1
0
1
1
1
1
0
2
1
1
4
1
0
1
0
0
2
1
0
1
4
1
0
1
0
1
0
0
1
2
1
2
1
1
1
1
1
1
1
1
1
2
2
2
2
1
2
0
1
1
1
2
1
1
1
1
1
0
1
1
1
1
0
1
1
2
1
2
2
1
0
1
0
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
0
1
1
1
1
1
1
1
0
1
2
1
1
1
2
1
0
1
1
2
1
1
1
0
2
0
1
1
1
2
1
1
1
2
0
1
2
0
1
0
1
1
0
1
2
1
1
0
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
0
1
0
2
1
1
1
2
2
0
1
1
1
1
0
1
2
1
1
2
1
1
1
0
0
0
2
1
1
0
1
1
1
1
2
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
0
1
1
1
1
2
1
2
1
0
1
1
1
2
2
2
2
1
2
1
1
1
2
1
2
1
1
0
1
1
1
2
2
1
2
0
1
2
1
0
2
2
1
1
2
2
1
2
1
2
1
1
2
1
2
1
0
1
0
1
1
0
1
1
1
1
0
1
2
0
2
1
1
1
0
1
2
1
1
0
1
0
2
1
1
1
1
1
1
1
1
2
0
0
0
0
1
1
1
1
1
1
2
2
1
1
0
2
1
1
0
1
0
1
2
2
1
0
1
1
1
3
2
2
0
0
1
1
0
0
1
2
1
2
1
1
0
1
1
0
1
2
0
2
1
1
0
3
2
2
2
2
2
0
2
1
1
2
0
0
1
0
1
2
1
2
1
2
2
2
2
1
1
1
1
0
1
0
1
1
0
1
1
3
1
0
0
2
0
1
1
1
0
1
1
2
1
2
1
0
1
0
1
1
0
1
0
1
0
1
1
0
1
1
1
2
0
2
0
1
0
1
0
0
1
1
1
0
2
1
0
0
0
1
1
1
1
2
1
1
0
2
1
1
1
1
1
0
1
0
1
2
1
1
0
1
1
1
1
1
1
0
1
0
2
1
2
0
2
1
1
0
2
1
1
0
2
1
1
1
0
2
1
1
1
0
2
0
1
2
2
2
1
1
1
1
1
0
1
1
1
1
2
2
1
1
1
0
0
0
0
1
2
1
2
0
1
0
0
2
1
2
1
1
1
1
1
0
0
1
2
1
0
0
2
1
0
1
1
1
1
1
2
0
1
1
0
1
1
2
0
1
2
1
0
0
1
2
1
2
2
1
0
1
2
1
0
2
1
0
2
2
1
0
0
0
0
1
0
1
1
0
0
1
1
2
1
1
1
1
1
1
2
0
1
1
1
1
1
1
2
1
0
1
1
3
0
1
1
1
1
1
3
1
2
1
0
1
1
1
1
0
1
1
1
2
0
2
1
1
1
1
1
2
2
1
0
1
1
0
1
1
0
0
2
1
1
2
1
1
1
1
1
0
1
0
0
1
3
2
1
0
1
0
1
1
0
1
0
2
1
0
2
0
2
2
2
2
2
1
1
0
0
1
2
0
0
2
0
1
1
0
0
1
2
2
0
1
1
1
0
0
2
2
0
1
1
0
0
1
3
0
1
2
0
1
0
1
2
1
0
1
0
1
0
1
2
1
1
1
1
1
1
0
0
1
0
0
0
1
1
0
2
0
1
2
1
1
1
1
1
2
1
1
1
1
0
1
1
1
1
1
1
2
0
2
1
0
1
1
1
1
0
1
2
1
1
2
1
2
0
1
2
0
1
0
1
1
1
1
1
1
1
1
1
0
2
1
1
1
1
1
0
1
1
1
1
2
1
0
1
1
1
2
1
1
1
1
1
2
3
1
1
2
1
2
0
2
2
1
0
0
1
1
2
2
1
1
1
1
3
0
1
0
0
1
2
1
0
2
2
2
2
2
0
1
1
1
2
1
0
2
1
1
0
2
1
1
1
0
2
0
2
1
1
0
1
0
1
1
1
0
0
1
0
2
0
1
1
0
0
1
1
1
0
1
1
2
0
2
1
1
1
1
1
1
1
0
1
0
1
1
0
2
1
2
1
1
2
1
1
1
2
1
1
1
1
1
2
0
2
2
1
0
0
1
1
1
1
1
2
1
0
2
1
2
2
1
0
2
1
1
0
0
1
0
0
1
1
2
1
0
2
1
0
0
1
0
0
1
1
1
1
0
2
1
1
1
0
1
1
0
1
1
1
2
1
1
1
1
2
1
1
0
0
1
0
0
1
0
1
2
0
2
1
1
1
1
1
1
2
1
1
0
0
1
1
0
1
2
1
1
2
1
0
2
1
1
1
1
2
0
0
1
1
2
2
0
5
1
0
1
1
0
1
1
5
0
1
2
1
1
1
2
2
1
1
1
1
2
1
0
1
1
0
2
1
2
1
2
1
0
1
0
1
0
1
1
0
1
1
1
0
1
1
0
1
1
1
1
1
1
0
1
0
0
1
1
1
1
1
0
1
1
2
1
1
1
0
2
1
1
1
0
1
1
2
2
2
3
1
1
0
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
2
0
2
2
0
0
2
2
0
2
1
0
1
2
1
0
0
0
0
1
1
0
0
2
2
0
2
1
0
1
2
1
2
1
1
0
2
1
1
1
2
2
0
2
1
0
1
1
1
0
2
2
2
1
3
1
1
1
1
1
1
1
0
1
1
1
2
1
0
2
1
0
1
2
1
1
2
0
3
1
1
1
0
1
1
1
1
0
1
0
1
1
1
0
1
1
0
0
1
1
0
0
1
1
2
1
2
1
1
0
1
0
2
1
1
1
1
0
1
1
2
1
1
2
1
1
0
2
2
1
2
0
2
1
1
1
1
1
0
1
1
0
0
1
0
1
1
1
1
0
1
1
1
1
1
2
2
1
2
1
2
1
1
2
1
1
1
1
2
1
1
1
2
1
1
1
0
0
1
1
1
1
2
2
0
1
0
2
2
2
1
1
0
1
1
2
1
2
0
1
1
1
1
0
0
2
0
1
2
1
0
1
1
1
1
0
1
1
1
1
1
1
2
2
2
1
1
2
1
1
1
0
0
1
2
2
1
0
1
1
1
2
1
2
3
0
2
2
5
1
2
1
1
0
1
1
2
2
0
2
1
2
1
2
1
1
2
2
2
2
1
1
2
1
2
1
2
2
0
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
0
0
0
1
0
2
0
1
1
1
0
1
0
1
0
2
2
0
0
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
1
1
1
1
0
2
1
1
1
1
0
0
1
1
1
1
1
1
1
2
2
1
2
1
1
4
1
1
2
1
0
1
1
2
1
1
2
0
1
1
1
0
2
3
1
2
2
1
2
1
1
1
2
1
1
1
1
1
1
2
3
1
2
2
2
0
1
1
2
2
1
1
2
1
1
1
2
0
1
2
1
1
1
0
1
1
1
2
1
1
2
1
2
1
1
1
2
1
0
1
0
1
1
1
1
2
2
2
1
0
0
1
1
0
0
1
1
0
2
0
1
1
0
1
0
1
1
1
1
0
1
1
0
1
1
1
1
1
1
1
0
1
1
1
1
2
2
2
2
0
1
2
1
2
1
0
0
2
1
1
1
2
2
1
2
0
1
1
2
2
0
1
1
1
0
0
1
1
1
2
1
0
1
1
2
0
1
1
1
1
3
2
1
1
0
1
0
2
1
2
1
1
1
1
1
1
2
1
2
0
2
1
1
0
0
0
1
1
1
0
2
1
2
0
1
1
2
1
0
0
1
1
0
0
1
2
2
2
1
2
2
1
1
1
1
0
0
1
0
1
1
0
0
3
1
2
1
1
0
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
2
1
1
1
1
2
1
1
0
0
2
2
1
0
1
2
1
2
1
1
1
2
1
1
1
1
1
0
2
1
2
1
1
2
1
1
1
1
2
1
1
1
2
1
0
1
1
1
1
1
1
2
0
0
1
2
2
1
1
1
1
2
0
0
1
1
1
1
1
1
1
1
1
0
1
2
1
1
1
2
1
2
0
0
0
0
1
1
1
1
1
1
0
2
0
1
2
0
1
0
0
1
2
1
1
2
2
2
1
0
1
0
1
1
1
1
3
1
1
1
1
2
0
0
1
1
0
1
1
0
1
1
1
0
2
1
1
0
0
0
1
0
2
1
1
2
2
0
1
1
0
2
0
2
0
2
1
1
1
1
0
1
0
2
1
0
1
1
5
1
2
2
0
2
2
0
2
2
1
2
1
0
1
1
1
1
1
2
0
1
1
1
1
2
1
1
0
0
1
1
2
0
0
0
1
1
1
1
1
2
1
0
1
0
0
1
1
2
1
2
0
2
2
1
2
1
1
1
3
2
2
1
2
1
1
1
1
1
1
1
1
1
1
1
0
2
1
0
0
1
1
1
0
1
2
0
0
2
2
1
0
1
1
2
1
1
2
2
1
0
1
1
1
1
1
1
1
1
2
0
1
1
1
1
0
0
0
1
1
1
1
1
0
1
1
1
1
1
3
1
1
1
0
1
1
1
2
2
1
1
0
1
1
1
1
1
1
2
1
2
1
1
0
1
1
1
0
0
2
0
1
1
0
2
1
2
1
1
2
1
0
0
1
1
1
1
1
1
2
0
0
1
1
0
2
0
1
1
1
1
1
1
1
0
1
0
0
2
1
2
0
1
2
1
1
0
0
1
1
1
1
3
0
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
1
2
1
1
2
1
1
1
1
2
1
1
0
1
1
1
1
0
1
1
0
1
1
2
1
1
2
1
1
1
0
0
1
1
0
1
1
1
2
2
0
1
1
2
1
1
0
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
0
2
2
0
1
1
1
1
1
2
2
0
1
1
1
2
3
0
1
1
1
1
1
1
1
0
1
0
1
1
1
1
0
1
2
0
0
1
2
0
0
1
1
0
2
1
1
2
1
0
2
1
1
1
2
2
1
0
1
2
0
2
0
1
2
1
1
0
1
1
1
0
0
1
1
1
1
1
1
2
1
1
0
2
1
1
1
1
1
1
1
1
2
1
0
2
1
1
1
1
1
1
1
0
2
1
1
1
0
1
2
1
0
2
2
1
1
0
0
1
0
2
1
1
2
1
1
1
1
0
1
1
0
2
1
1
2
2
0
2
1
1
1
0
1
1
1
0
2
2
2
2
0
2
3
1
1
2
0
1
0
0
1
0
1
2
1
0
2
2
1
2
1
1
2
0
1
4
1
2
1
0
1
2
1
1
1
2
1
2
0
1
1
2
2
1
0
1
1
0
2
1
0
1
1
1
2
0
0
0
1
1
1
2
0
1
1
1
0
1
1
1
1
0
1
0
2
0
0
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
3
2
1
1
1
1
1
0
1
1
1
1
0
1
1
2
0
1
1
1
2
1
0
0
1
1
1
0
1
1
0
2
3
2
1
1
0
0
2
0
1
3
0
1
5
1
3
1
1
2
1
1
0
0
0
1
1
2
2
1
1
0
1
2
0
0
0
2
2
0
2
1
0
1
1
2
0
1
0
1
2
2
1
0
1
2
1
2
1
1
1
1
1
0
1
2
1
1
1
1
1
1
2
1
1
1
0
1
0
2
0
1
1
0
1
0
1
1
1
1
1
2
1
0
1
2
1
1
1
0
1
0
1
0
1
1
1
1
1
1
0
0
1
2
1
1
1
0
1
1
2
1
2
1
1
2
1
1
0
2
1
1
2
0
0
1
1
1
1
1
1
1
1
0
2
2
1
0
1
0
1
1
2
1
1
0
1
2
0
2
2
1
1
2
1
1
0
0
1
0
2
1
1
1
2
1
1
1
1
1
0
1
1
3
1
0
0
2
1
0
2
2
1
2
1
2
1
2
1
1
0
1
2
1
1
1
1
1
0
0
1
1
0
1
0
1
1
1
1
1
1
2
1
2
1
2
2
1
0
1
1
1
0
1
1
1
1
2
2
1
2
1
1
1
2
2
0
1
1
0
2
2
1
1
2
1
0
0
1
1
0
0
1
1
1
2
1
0
1
2
1
1
2
1
2
0
1
1
1
1
0
1
2
1
1
1
1
0
1
2
1
1
0
2
0
1
1
0
0
2
2
1
1
1
0
0
1
2
1
2
1
1
1
2
1
1
2
1
1
2
1
1
1
2
0
1
0
1
1
0
1
1
2
0
1
2
1
1
1
1
1
1
1
1
1
0
2
1
0
1
1
0
2
2
1
1
1
2
1
0
2
1
0
1
1
3
1
0
1
1
2
1
0
1
0
1
2
0
0
0
1
0
0
1
2
2
0
1
1
1
1
1
0
0
1
1
2
2
2
0
1
1
2
0
0
0
1
1
1
1
2
4
2
4
0
1
0
1
2
1
0
0
1
1
0
1
1
1
1
1
0
1
2
1
1
0
1
1
1
1
1
1
1
0
1
2
2
3
1
1
1
1
1
0
1
1
1
0
2
0
0
0
2
2
1
1
2
1
1
2
2
1
1
0
2
1
0
1
2
2
1
1
2
1
1
0
2
1
1
1
1
2
1
0
1
1
0
1
1
1
0
1
2
1
1
1
1
2
2
0
1
0
1
2
1
2
0
0
1
0
0
2
3
1
1
1
0
0
1
1
1
1
1
2
1
0
1
1
2
1
0
1
1
1
1
0
1
2
1
1
1
1
1
2
1
2
0
0
1
1
1
0
2
2
0
1
0
0
0
1
1
1
2
0
2
0
2
1
0
1
0
2
0
0
2
1
1
2
1
1
1
0
1
1
2
2
1
1
1
1
1
1
1
1
0
2
2
2
1
1
0
2
1
1
0
1
2
2
1
2
1
2
0
1
1
1
1
2
0
2
1
1
1
2
2
1
1
2
2
0
1
1
1
2
0
0
1
2
1
0
1
0
2
0
0
1
2
1
1
0
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
2
2
1
1
3
1
0
1
2
4
2
2
1
1
1
2
1
1
2
2
1
1
2
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
1
1
2
2
1
1
2
4
0
2
0
1
1
1
1
0
0
1
0
0
0
1
1
1
0
1
2
1
1
2
2
1
2
1
1
1
1
2
2
1
1
1
1
1
1
1
1
0
1
2
1
0
1
2
2
0
1
0
0
2
0
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
0
1
1
1
1
0
1
0
0
1
1
1
1
1
1
1
1
0
0
0
1
1
0
1
0
1
1
1
1
1
1
2
0
1
1
0
1
3
6
1
2
0
2
1
0
0
1
1
0
0
0
2
0
1
1
1
1
1
2
0
1
1
1
1
2
1
1
1
1
2
2
1
0
2
1
1
3
0
1
2
1
2
1
1
0
2
1
1
1
1
1
1
1
3
1
1
0
1
1
1
1
2
0
1
2
0
1
1
1
1
1
1
0
1
2
0
0
1
1
1
1
0
1
1
2
1
2
1
2
3
2
0
2
1
1
0
1
1
0
1
1
1
2
1
0
2
2
1
2
0
1
1
2
2
2
0
1
1
1
2
1
1
1
1
2
1
2
1
0
0
2
1
1
1
1
2
0
2
1
1
1
0
1
1
0
1
2
0
0
0
3
1
1
1
2
4
1
2
1
1
2
1
3
2
0
1
0
1
1
2
1
0
0
1
2
1
1
2
0
1
0
1
2
1
2
2
2
1
1
0
1
1
1
1
2
1
2
2
1
2
2
1
0
0
0
1
1
1
1
1
2
2
0
2
0
0
0
1
1
1
1
2
0
0
1
1
1
0
1
0
1
2
1
2
1
2
1
1
1
1
2
0
1
1
1
0
0
1
1
1
1
0
2
2
0
1
1
1
1
2
1
1
1
2
1
0
1
1
2
0
1
3
0
0
2
0
0
1
1
1
2
2
1
1
0
1
2
0
1
1
1
1
0
2
1
2
1
1
1
1
0
1
2
1
1
1
1
1
1
0
2
2
2
1
2
1
0
1
1
0
0
1
2
2
1
1
1
0
1
0
1
1
0
1
0
1
1
1
1
1
0
1
1
1
2
3
2
1
1
1
0
1
2
1
1
0
1
1
0
0
0
1
0
0
2
1
1
2
1
1
0
0
1
1
2
1
1
0
1
1
1
1
1
2
1
0
2
1
2
2
1
2
1
0
0
0
1
1
0
0
0
0
1
0
0
1
1
0
1
1
2
0
0
1
1
2
1
1
1
1
1
1
0
1
1
1
0
1
0
1
1
1
1
0
1
1
0
0
0
1
1
1
0
2
2
2
0
0
2
2
2
1
1
3
2
1
1
1
2
0
2
1
3
1
1
1
0
2
1
2
1
2
1
2
3
2
0
2
2
0
2
0
0
1
0
2
0
1
1
2
2
1
1
2
1
1
2
0
1
1
0
0
2
0
1
1
4
2
1
2
1
2
1
2
2
2
1
1
1
1
1
0
0
1
1
1
2
0
1
1
0
0
0
4
1
1
1
0
1
2
0
0
1
1
1
1
2
1
2
0
2
2
1
2
1
2
0
0
1
1
1
1
1
1
2
1
1
2
1
1
2
2
1
1
0
1
2
2
2
2
1
0
1
2
0
1
1
1
2
2
2
0
0
0
0
0
0
1
2
2
1
2
1
1
2
2
0
0
0
2
1
2
1
1
2
2
1
0
2
1
1
1
1
0
0
2
1
0
1
0
1
2
0
0
1
2
1
1
0
2
1
0
0
0
1
1
2
2
1
1
1
1
2
2
2
1
2
1
1
1
1
0
1
1
2
1
2
1
1
2
1
2
0
2
0
2
1
1
1
1
1
1
1
0
1
2
2
1
2
1
1
1
1
0
1
1
0
1
1
1
0
0
0
1
0
3
1
1
3
0
2
0
1
1
1
2
1
1
1
0
1
1
1
1
2
1
1
0
1
2
1
1
0
1
1
1
1
1
2
0
2
1
1
1
1
1
0
0
1
2
2
1
1
2
1
1
1
2
2
1
1
0
1
0
1
0
1
1
1
1
0
0
0
1
0
0
1
0
2
2
3
1
2
1
1
1
1
1
2
1
1
1
0
2
2
1
0
1
1
1
0
1
1
2
1
0
1
2
1
2
2
0
2
0
1
2
1
1
1
1
1
0
2
2
1
2
1
6
0
1
2
1
2
1
2
2
1
2
1
1
2
0
2
0
2
1
1
1
1
1
1
2
0
2
0
2
1
2
3
0
2
1
0
1
1
2
1
1
2
3
1
1
1
1
1
2
1
1
1
0
0
1
1
1
1
2
0
1
2
0
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
0
3
1
1
2
1
2
0
1
2
1
0
1
1
1
0
1
0
1
1
1
1
0
1
1
0
1
0
1
1
1
1
1
1
1
0
1
1
0
0
1
0
0
1
1
1
1
1
1
1
1
1
1
0
0
1
0
0
1
1
1
2
1
1
1
1
1
1
1
1
0
1
0
1
0
1
1
0
0
1
0
0
1
0
1
1
1
1
2
6
1
0
2
1
2
1
2
1
2
1
1
2
1
0
2
0
1
1
1
2
1
0
1
0
2
0
1
1
1
1
1
1
2
1
1
1
0
1
0
1
1
0
1
1
1
0
0
1
1
2
2
1
0
2
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
3
1
1
1
2
1
0
1
1
1
0
1
1
1
1
2
2
1
0
1
1
2
0
2
1
1
2
2
1
2
0
2
0
0
1
1
2
0
1
1
2
1
1
1
2
1
0
1
0
1
1
1
1
0
2
0
2
2
0
2
0
0
1
1
1
0
1
1
1
1
1
1
1
1
1
2
0
0
1
1
0
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
0
0
1
0
1
1
1
0
2
0
2
0
1
0
1
1
0
1
1
1
1
2
1
1
1
1
1
1
1
0
1
2
1
0
1
0
0
0
2
2
1
1
1
1
2
2
1
1
2
0
0
1
0
0
1
0
1
1
1
1
0
0
2
0
1
0
1
1
0
2
2
0
2
1
1
0
1
1
4
1
1
2
0
2
2
1
2
2
1
1
2
1
1
2
1
2
1
1
2
0
2
0
1
1
0
1
1
1
1
0
2
2
0
0
1
1
2
1
1
0
0
1
2
4
2
2
0
2
2
1
1
0
1
0
1
2
1
1
1
1
2
0
1
1
1
1
1
0
1
1
1
1
2
1
1
1
0
2
1
1
1
1
1
2
0
0
0
0
0
0
1
2
0
0
1
1
1
1
0
1
0
0
2
0
1
1
1
1
1
2
0
2
1
2
0
1
2
1
2
2
0
2
1
1
1
2
2
1
2
1
1
0
1
1
2
2
0
1
0
1
1
1
0
1
0
1
2
1
0
0
1
1
1
3
1
1
2
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
0
1
0
1
1
0
2
1
2
1
0
0
1
0
2
1
0
2
1
1
2
0
1
2
2
1
0
0
1
2
0
2
1
1
1
1
0
1
1
2
1
1
1
2
1
1
2
1
0
1
1
1
1
2
1
0
1
2
1
1
0
1
1
1
2
0
1
1
0
1
1
1
2
1
1
1
1
2
1
0
1
2
2
2
1
1
1
1
0
1
0
2
1
0
1
0
1
0
1
4
2
1
2
0
2
2
1
1
0
1
2
1
1
1
1
2
0
2
2
1
1
2
1
1
0
1
2
1
0
2
2
2
1
1
0
2
2
1
1
1
2
2
1
1
1
0
1
2
1
1
1
1
1
2
1
0
1
1
0
0
1
0
1
1
1
0
0
1
2
1
1
1
0
1
1
1
1
3
1
0
2
1
2
2
1
2
2
0
1
1
1
2
0
2
2
1
2
1
2
1
2
2
0
0
1
2
1
1
0
1
1
2
1
1
1
1
3
0
1
1
1
1
2
0
2
1
1
0
1
1
1
2
1
2
0
1
1
1
2
1
2
1
1
1
1
1
0
2
1
2
1
1
1
1
0
1
1
1
1
2
2
2
0
1
0
0
1
1
2
1
0
1
1
2
1
1
0
1
0
1
1
1
2
2
0
1
1
1
1
1
1
2
2
1
1
1
1
2
1
0
0
1
2
1
1
0
2
1
0
1
1
0
1
1
2
1
0
1
2
1
0
1
0
0
1
2
0
1
1
1
0
2
1
1
1
1
1
3
1
1
2
0
1
0
1
0
1
1
1
2
1
0
2
1
2
0
1
1
0
2
1
2
1
1
1
5
1
1
1
1
1
1
1
1
1
1
0
0
2
1
1
2
0
1
0
0
0
1
1
1
1
0
0
2
2
1
2
1
1
0
1
2
1
1
1
1
1
2
0
2
1
0
1
1
1
1
0
0
1
2
1
1
2
1
1
0
2
1
2
2
1
0
1
0
1
1
1
2
1
1
0
0
1
1
0
1
0
2
1
0
0
2
1
1
1
2
2
1
2
1
0
2
1
1
1
1
0
2
1
1
2
2
1
2
1
1
1
1
0
1
1
0
2
1
1
1
0
0
2
1
1
4
1
1
1
2
1
1
0
1
1
0
1
2
1
1
1
2
0
1
1
0
1
1
0
2
1
1
1
1
1
1
2
1
1
1
1
0
1
1
1
2
1
1
2
1
1
1
1
1
2
0
1
0
0
0
2
2
2
1
1
1
1
1
1
2
1
0
1
1
1
0
1
1
1
1
1
1
2
1
1
0
0
1
1
2
2
1
1
2
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
0
1
1
2
1
1
1
1
1
2
0
1
1
1
2
0
2
1
2
2
1
1
1
1
1
0
1
1
2
0
1
2
2
1
1
1
0
1
1
0
2
2
2
1
1
1
1
1
2
0
0
0
0
2
1
3
1
2
2
0
2
2
1
0
0
1
1
0
0
0
1
0
1
1
2
1
1
1
1
1
1
1
2
1
1
1
0
1
0
1
1
2
1
2
1
1
1
1
2
1
2
1
2
0
1
1
1
1
2
1
0
1
2
0
2
1
1
1
0
1
1
0
2
1
1
0
0
1
1
1
1
0
1
1
1
2
2
1
1
1
1
1
1
0
1
1
0
1
0
1
2
1
1
0
0
3
1
2
1
0
2
1
1
1
2
1
2
2
2
2
1
2
1
1
1
2
2
1
2
1
1
1
1
2
2
2
1
1
1
1
0
1
1
0
1
0
0
1
1
0
1
1
1
1
1
1
1
1
0
2
2
0
0
1
1
1
2
1
1
1
1
0
1
2
1
1
1
2
1
1
0
2
1
2
1
1
2
2
1
1
1
1
1
2
0
1
0
2
1
0
1
0
1
2
2
1
2
1
0
1
1
1
2
2
0
0
2
0
2
1
1
1
1
1
1
1
0
2
0
1
1
1
1
1
0
2
1
0
1
2
1
1
1
2
0
1
1
1
2
1
0
1
0
2
1
1
1
1
0
1
0
2
1
1
2
0
2
0
0
1
1
2
1
1
2
0
1
1
0
1
2
0
1
0
1
1
1
0
2
0
1
3
2
2
2
1
1
1
1
1
1
0
1
2
2
2
1
1
1
0
1
0
1
1
1
1
0
0
1
0
0
1
0
2
0
2
1
1
1
1
0
1
1
1
1
1
0
1
1
2
0
1
1
2
0
0
2
0
1
1
2
1
2
0
0
0
2
2
1
0
2
2
1
2
0
1
1
1
1
1
1
2
1
1
0
1
1
2
1
1
1
2
1
0
2
1
1
1
0
0
2
0
1
1
1
1
1
0
2
2
1
1
1
1
1
1
2
1
1
0
0
1
0
1
1
1
2
1
1
0
0
2
1
2
1
2
1
1
1
1
1
0
0
1
0
0
0
1
1
1
2
1
1
1
2
1
2
0
2
1
1
1
2
2
1
0
1
1
1
1
1
2
1
2
2
2
1
2
2
0
1
1
2
1
2
1
1
1
1
1
2
2
2
1
0
2
2
2
0
1
2
1
2
0
0
0
0
2
1
2
2
4
1
1
1
1
1
1
1
0
1
1
2
1
1
1
1
1
0
0
1
0
1
1
1
1
0
1
1
1
1
3
2
1
2
1
1
1
0
0
0
1
2
1
1
0
2
1
2
1
0
0
0
2
0
1
3
2
0
2
0
1
1
1
2
1
1
1
2
1
0
1
2
2
0
1
2
0
1
1
1
0
2
2
1
1
1
1
1
1
1
2
1
0
1
0
0
1
1
0
1
0
1
1
1
1
1
1
1
1
1
2
1
2
0
1
1
1
1
1
2
2
0
1
0
0
1
2
1
1
2
1
1
0
1
2
1
0
1
1
1
0
1
1
2
1
1
1
2
1
2
1
1
1
2
1
1
1
1
0
0
0
0
1
1
0
1
1
1
2
1
1
1
0
1
2
1
1
2
0
1
2
0
0
0
1
2
1
1
1
0
1
1
0
1
1
1
2
0
2
2
0
0
0
0
1
1
0
1
1
1
1
3
0
1
1
0
1
2
0
1
1
1
0
1
0
1
1
2
1
1
1
1
1
1
2
1
1
2
0
1
1
1
2
1
0
1
0
2
1
1
0
0
2
2
1
0
0
1
2
2
0
1
0
1
0
0
0
0
2
2
1
2
1
2
1
1
1
2
1
1
2
0
0
0
0
1
1
2
2
2
1
2
3
1
2
1
1
1
0
1
0
1
0
2
1
1
2
1
2
2
1
1
1
2
2
1
1
1
1
1
0
2
1
2
2
1
2
1
0
1
1
2
1
0
1
0
2
2
2
0
0
0
1
2
1
1
1
2
2
1
0
0
3
3
2
1
1
0
0
1
2
0
1
0
1
1
0
1
1
0
1
1
1
1
1
1
1
0
1
0
1
1
0
0
2
2
2
1
0
2
0
0
2
0
2
1
1
1
0
0
0
1
1
0
0
1
1
2
1
0
2
1
1
2
1
2
0
1
2
1
0
0
1
1
1
0
1
2
0
1
2
2
0
2
1
2
1
1
2
1
0
1
1
1
2
1
2
2
1
1
0
2
1
0
2
0
1
1
0
1
1
1
8
2
0
1
1
1
1
0
1
1
0
2
1
2
0
1
0
0
0
1
1
1
2
1
1
3
1
1
2
2
1
1
0
0
0
2
1
2
2
1
1
1
1
1
1
1
1
1
1
0
1
0
1
0
1
1
1
1
0
1
0
2
1
0
2
1
1
1
1
1
1
2
1
1
0
2
1
2
2
1
1
1
1
0
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
0
2
0
1
0
2
1
0
2
2
0
1
2
1
1
2
2
2
1
0
2
1
2
1
1
2
1
2
0
0
0
1
0
1
1
1
0
2
0
0
1
1
0
1
0
1
1
1
1
1
1
1
0
2
2
1
1
1
0
0
0
1
1
1
3
1
1
0
4
0
1
2
2
0
1
1
2
1
0
0
1
1
0
0
1
1
0
1
1
0
1
1
1
1
2
1
1
2
2
1
1
0
1
1
2
1
1
2
0
0
2
1
2
2
1
1
1
0
1
1
2
1
1
1
1
1
0
1
1
0
2
1
3
1
1
1
1
0
1
1
1
1
1
2
1
1
1
2
0
1
2
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
2
1
1
2
1
1
1
1
3
1
0
0
0
1
1
2
0
1
0
1
1
2
1
1
1
1
1
2
1
2
1
2
1
1
2
1
0
1
2
1
0
0
1
1
2
0
1
2
1
1
1
2
1
1
0
2
1
2
1
1
1
0
0
0
1
0
0
0
1
0
2
0
1
0
0
1
2
0
1
0
1
1
0
0
1
2
1
0
0
0
1
0
1
1
1
1
1
1
1
1
1
2
1
1
1
0
2
1
1
1
1
2
2
10
1
1
1
0
1
1
0
0
2
2
1
0
1
1
2
1
1
1
2
1
1
2
1
2
2
1
1
2
1
1
1
1
2
2
0
2
1
1
1
2
1
1
1
2
1
1
0
1
1
1
1
0
1
2
2
1
1
1
1
0
1
2
2
1
1
1
1
0
2
1
1
0
0
1
1
1
2
2
1
2
1
1
2
2
1
1
2
2
1
0
1
1
0
0
2
1
1
1
1
2
1
1
1
2
0
1
0
1
1
2
1
1
0
2
1
1
1
2
1
2
2
0
0
2
0
2
1
1
1
1
1
0
1
0
1
1
1
1
2
1
1
0
0
1
1
1
2
0
1
1
1
2
0
2
0
0
1
1
1
1
1
1
2
1
0
1
1
0
1
0
1
2
2
1
0
1
1
1
1
1
2
1
2
0
1
2
0
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
0
1
1
1
0
0
1
2
2
1
0
0
1
1
0
1
1
1
0
2
0
0
2
1
1
1
1
1
1
2
3
1
1
2
2
1
1
0
0
1
2
2
2
1
1
1
1
1
2
1
1
1
2
2
0
2
0
1
1
2
3
0
0
1
0
2
0
0
0
1
1
0
2
1
1
2
2
1
0
1
2
0
1
1
0
1
1
1
1
1
2
1
1
2
1
1
1
1
1
0
0
1
1
1
2
1
2
0
0
1
0
2
2
2
1
1
1
0
1
2
1
1
1
1
2
0
0
2
2
0
1
0
1
0
1
0
2
1
1
1
0
0
1
2
1
1
1
1
0
1
0
1
0
1
0
0
0
1
2
0
2
0
1
1
2
0
1
1
1
1
2
1
0
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
0
2
2
0
1
2
1
2
2
1
1
1
2
0
2
1
2
1
1
1
2
1
2
1
1
1
2
2
0
1
0
1
2
1
0
2
0
2
0
1
1
1
2
1
0
1
1
0
0
1
1
0
0
1
1
2
0
1
2
1
0
0
0
1
1
0
1
0
0
1
1
1
1
1
0
2
2
1
1
1
1
1
2
2
0
2
1
2
1
1
4
0
1
0
1
0
2
0
0
1
1
1
2
1
2
1
0
2
2
1
1
1
1
0
1
1
0
1
1
2
2
1
1
0
2
1
1
1
1
0
1
1
2
1
1
1
1
2
1
2
1
1
2
1
2
1
0
1
1
0
2
1
2
1
1
2
0
1
0
1
1
1
1
1
2
2
1
0
2
1
2
1
2
2
1
1
2
2
1
1
0
0
0
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
0
0
1
1
1
1
1
1
1
1
1
0
0
2
2
1
0
1
0
0
0
2
0
0
0
1
2
1
1
1
1
1
1
1
3
2
2
0
0
1
0
1
1
1
1
1
1
3
1
0
1
1
2
1
1
0
2
2
1
1
1
0
0
0
2
1
1
1
1
0
0
2
0
2
1
1
1
1
1
1
1
2
1
0
1
0
0
1
1
0
2
0
1
1
1
1
2
1
0
2
1
1
0
2
2
1
2
0
0
2
1
1
2
1
1
1
0
1
1
1
0
0
1
3
0
1
1
2
1
1
0
0
1
2
1
1
1
1
0
2
1
1
0
2
2
0
2
0
2
2
0
1
1
1
0
2
2
2
0
2
0
2
0
1
2
0
0
0
1
0
1
1
1
1
1
1
0
0
2
1
1
1
0
1
1
1
0
0
1
1
1
1
1
1
2
1
0
2
1
1
0
2
0
2
2
1
1
1
0
1
1
0
1
0
2
2
1
2
1
0
1
0
1
1
0
0
0
1
2
1
1
1
1
1
1
1
1
2
0
0
1
0
2
1
0
4
0
1
1
1
1
0
0
1
2
1
2
1
1
2
1
1
1
1
2
1
1
2
0
2
2
1
1
2
1
0
1
1
1
0
1
2
2
1
1
1
1
1
1
1
0
0
2
2
0
1
0
1
1
1
2
0
1
1
1
1
2
1
1
0
0
1
1
2
0
2
2
1
1
0
1
1
1
0
0
2
1
2
1
1
1
0
1
1
0
2
2
0
1
1
0
1
1
1
1
1
1
2
1
2
3
0
1
1
1
1
0
2
0
2
1
2
1
2
0
1
1
2
0
0
1
1
0
1
1
2
1
2
0
1
1
1
1
1
1
0
0
0
0
0
0
2
0
1
1
2
0
1
1
0
1
2
1
1
0
1
2
2
1
0
1
0
1
0
1
1
1
2
1
1
1
0
2
1
1
2
1
0
0
2
2
2
5
0
1
1
1
1
2
1
2
1
1
1
1
1
0
1
1
1
1
2
2
2
1
1
1
0
0
1
1
0
2
1
1
1
1
2
0
1
2
1
1
0
0
0
2
1
2
1
1
1
2
0
1
1
2
0
1
0
2
1
1
1
1
1
1
1
1
0
1
1
0
1
0
1
2
1
2
1
0
1
1
0
1
1
0
1
2
1
1
1
2
0
2
1
1
1
1
1
1
1
2
1
0
1
0
1
1
0
1
1
0
0
1
1
1
0
0
1
1
1
2
1
0
2
2
2
1
3
1
1
1
1
0
2
1
1
2
0
1
2
2
1
1
1
1
0
0
0
1
2
2
1
2
1
2
2
2
1
0
0
1
1
1
1
2
2
0
2
1
1
0
0
1
1
1
2
1
1
2
1
1
2
1
1
0
1
2
1
0
2
3
1
2
0
0
2
0
1
0
1
2
0
1
2
1
0
1
2
1
1
2
1
1
1
1
1
2
1
1
2
1
0
1
1
1
1
0
1
1
1
0
1
0
0
1
0
1
1
0
1
1
2
1
0
1
0
1
1
1
1
2
1
2
2
1
1
1
2
1
1
1
1
1
2
0
2
1
2
1
1
0
0
0
1
0
1
0
0
1
2
1
1
1
0
0
1
1
0
1
1
1
0
1
1
0
2
1
0
0
1
1
1
1
1
0
0
2
1
1
0
2
1
1
1
1
1
0
1
1
1
0
1
1
1
2
1
2
2
1
1
1
0
2
2
1
1
1
1
0
1
0
0
1
1
1
1
1
1
1
0
1
1
2
2
1
1
1
1
2
1
2
1
0
0
2
1
1
1
1
1
0
0
1
1
1
1
1
0
1
2
2
1
0
1
3
1
2
2
1
1
1
0
1
1
3
0
1
2
1
1
1
1
0
1
1
1
0
1
1
0
0
2
1
2
1
1
1
1
1
2
0
1
1
2
0
0
1
0
1
1
2
2
1
1
3
1
1
1
2
1
1
0
1
1
0
2
1
1
1
1
1
0
1
2
1
1
1
0
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
0
2
2
0
1
1
1
1
1
1
0
3
2
1
1
1
1
0
1
1
0
1
1
2
1
1
1
0
0
1
2
1
1
0
2
2
1
2
0
2
2
0
1
2
1
0
2
1
1
1
1
1
1
1
0
1
1
1
0
1
2
2
1
1
0
1
2
1
1
2
1
6
1
1
2
1
1
1
0
0
0
0
1
1
2
0
0
1
0
2
1
1
0
0
1
1
1
1
1
2
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
0
2
1
1
0
0
0
1
1
1
0
0
1
1
1
1
2
1
1
2
1
2
2
1
1
2
1
0
2
1
2
1
2
2
0
1
0
0
0
1
1
1
0
1
0
1
1
1
1
0
1
1
2
1
2
1
1
1
0
1
2
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
0
0
0
1
1
1
1
2
2
1
0
1
1
0
1
1
1
1
1
1
2
0
1
1
2
0
1
1
2
1
1
1
1
1
1
2
1
0
2
0
0
1
1
1
2
2
1
1
1
0
0
0
0
1
0
2
1
1
1
1
1
1
1
2
0
1
0
2
1
0
2
1
2
0
0
1
1
0
1
1
0
1
1
2
2
1
1
1
0
1
1
1
1
1
1
1
0
1
1
1
0
1
2
1
0
2
0
1
0
2
0
1
2
1
1
1
0
1
0
1
1
0
0
1
2
1
1
2
0
1
1
1
1
1
1
1
1
2
1
6
1
1
0
1
2
1
0
1
0
2
0
0
1
1
0
1
1
1
1
1
1
1
1
0
1
1
2
0
0
0
1
1
1
2
1
1
0
1
1
2
1
2
2
1
2
1
1
1
0
1
2
1
1
0
1
0
1
1
1
1
0
2
3
1
1
1
1
2
1
0
1
2
1
1
2
3
1
1
0
0
1
1
1
1
1
2
1
1
0
1
0
1
2
2
1
1
2
0
1
1
1
1
1
1
1
1
1
1
0
0
1
0
1
1
2
4
2
1
1
1
0
1
0
1
2
2
1
2
3
2
0
0
1
2
2
1
2
2
1
1
1
1
1
1
1
2
1
1
2
1
2
0
1
1
1
0
1
0
1
4
1
0
1
1
1
2
0
1
2
1
1
0
0
2
2
1
2
1
1
1
1
1
1
0
1
1
0
0
1
2
1
1
0
1
0
0
1
1
1
2
1
1
1
1
1
1
0
0
1
1
1
1
0
1
2
1
1
1
1
1
2
0
2
1
0
1
1
2
1
0
2
1
0
1
2
0
1
1
2
0
1
1
1
0
1
1
1
1
0
1
2
1
1
2
1
2
2
1
2
0
1
0
2
3
2
1
0
2
0
1
1
2
2
1
1
2
0
1
1
1
1
1
0
1
0
0
1
1
1
2
0
0
0
1
0
0
1
0
1
1
1
1
1
1
2
2
1
2
1
1
0
1
1
2
1
0
0
1
1
1
2
1
1
1
0
2
2
2
2
0
0
0
2
2
1
1
1
1
0
1
1
1
1
3
2
0
0
1
1
2
1
0
1
2
2
1
2
1
1
1
1
1
2
1
1
1
0
2
2
0
1
2
2
0
0
2
2
1
2
1
3
1
1
1
0
1
0
2
1
2
1
1
2
1
2
1
0
1
1
1
1
2
2
1
1
2
1
1
2
1
1
2
2
0
0
3
1
1
1
1
1
1
2
1
0
1
1
2
1
0
1
0
2
1
2
0
1
2
2
0
1
0
1
2
1
1
0
0
1
2
2
1
2
1
2
1
2
1
1
0
2
2
0
1
1
1
0
1
1
1
2
2
1
1
2
2
1
1
1
1
1
2
1
0
2
1
1
2
2
1
2
1
1
1
0
0
1
0
0
1
0
1
1
0
0
0
0
1
1
2
2
1
0
1
1
2
0
1
1
1
1
1
2
1
1
1
1
1
1
0
0
1
2
0
0
1
1
1
2
0
0
1
0
0
0
2
0
1
1
2
1
0
2
1
2
1
2
0
2
0
2
0
2
1
1
2
1
2
1
2
1
0
1
0
0
1
0
1
1
1
3
1
1
1
0
0
1
0
1
1
1
1
2
1
1
1
1
1
1
2
2
2
1
0
1
2
1
1
1
2
2
1
0
1
1
1
1
1
1
0
1
0
2
1
3
1
1
1
1
1
0
1
2
0
1
1
1
1
2
1
1
1
1
2
2
2
1
3
2
1
2
1
1
1
0
1
1
0
2
0
2
1
1
1
2
0
0
1
0
1
1
1
0
2
2
1
1
1
2
1
2
0
0
0
2
0
1
1
1
2
1
1
1
1
1
2
1
2
2
2
1
0
1
2
2
1
2
0
1
2
1
1
0
0
1
1
1
2
2
1
0
1
2
1
0
1
1
0
1
2
1
0
2
0
3
2
0
1
0
0
0
2
1
1
0
0
1
2
1
1
0
1
1
0
1
1
0
1
2
1
0
1
1
2
1
1
1
1
1
0
1
1
2
0
1
1
1
0
1
0
2
0
0
0
1
1
0
1
1
2
1
2
0
0
1
2
0
1
1
1
2
2
1
0
1
1
1
2
2
1
1
1
0
0
0
2
1
1
1
1
1
1
1
2
1
0
0
1
0
2
1
1
1
2
2
1
1
1
1
0
1
1
1
2
1
0
1
1
0
1
1
1
1
0
1
1
1
1
1
1
1
2
1
1
0
1
2
1
1
1
2
2
1
1
2
1
1
2
2
2
2
1
2
1
0
2
1
2
2
1
1
1
1
3
0
0
1
0
2
1
0
2
2
2
1
1
2
2
2
1
0
1
2
1
0
2
2
1
1
1
1
1
1
0
1
1
1
1
1
2
2
1
0
0
0
2
1
0
1
2
1
0
2
2
0
1
1
1
1
1
1
2
0
2
2
2
1
0
1
1
1
1
1
1
1
1
0
2
1
2
1
1
2
0
0
1
1
1
1
0
0
2
1
1
0
2
1
1
1
0
1
1
1
2
1
1
0
1
1
1
1
0
2
2
1
1
2
1
2
0
1
1
1
1
1
1
1
2
1
1
1
2
0
1
2
0
1
0
2
1
1
1
1
1
2
0
1
0
2
1
0
0
1
0
1
1
1
2
2
1
1
0
1
1
1
1
1
1
2
1
0
1
1
1
1
1
1
2
2
1
2
2
1
1
2
1
1
1
1
1
1
2
0
1
1
1
1
1
0
1
2
0
1
2
1
1
1
1
1
0
0
2
1
2
1
2
1
2
1
1
1
0
0
1
2
0
2
0
0
1
3
1
1
2
1
2
2
2
3
1
1
0
0
1
2
0
1
0
1
0
1
1
2
1
0
1
2
2
2
1
0
3
0
1
1
2
1
0
1
2
1
1
3
1
1
1
2
1
0
1
2
2
0
1
1
1
1
1
1
1
1
1
1
1
2
0
0
1
0
1
1
1
2
1
1
0
0
1
1
1
1
3
0
1
1
0
1
1
1
2
1
2
0
2
1
0
1
1
0
1
1
1
2
2
0
1
1
1
1
1
1
1
1
0
0
1
1
1
1
0
1
0
1
1
0
2
1
2
1
2
1
1
1
2
1
1
1
1
1
0
1
1
0
1
1
0
1
2
1
2
1
1
1
1
0
1
0
1
1
1
1
0
1
1
1
2
0
1
2
0
0
1
2
1
2
0
2
1
1
2
0
1
1
1
1
0
1
2
2
0
1
2
1
1
1
2
1
0
1
0
1
1
1
1
1
1
0
2
1
1
1
1
1
1
2
1
1
2
1
1
1
2
2
0
1
0
1
0
1
0
1
1
1
0
2
1
2
1
1
1
0
1
1
0
1
2
1
1
1
1
1
2
1
1
0
1
1
1
1
2
0
1
0
1
2
2
1
0
1
0
1
1
1
0
0
1
2
2
1
2
1
1
1
0
2
0
1
2
1
1
1
2
1
1
1
0
1
1
1
1
2
1
2
2
0
0
2
0
0
1
0
1
1
2
1
2
1
2
1
1
1
0
0
1
1
1
0
1
0
1
1
2
1
2
1
2
2
1
2
2
0
1
2
2
1
1
1
2
1
2
2
2
1
3
2
2
2
1
0
1
1
0
1
1
0
1
1
0
1
1
1
2
2
2
1
3
1
1
1
1
2
1
0
1
2
1
1
1
1
1
1
0
0
0
1
1
1
2
2
1
1
2
1
2
1
1
1
2
1
0
0
0
0
0
2
1
1
0
1
1
0
1
2
1
1
1
0
1
1
2
1
0
1
2
1
1
2
0
0
2
1
1
0
0
1
2
1
1
2
1
1
1
2
0
1
1
0
1
1
1
1
1
2
2
1
1
1
0
1
1
0
2
2
0
1
2
1
0
0
2
1
2
0
0
1
1
1
1
2
1
2
1
0
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
2
1
0
1
0
2
1
1
2
1
2
1
1
2
0
1
1
1
1
1
1
1
1
2
0
0
1
1
1
1
1
2
1
0
0
0
2
0
0
0
1
1
3
1
1
1
0
2
0
1
1
0
2
2
2
1
0
0
1
1
1
0
2
2
1
0
0
1
0
0
1
1
2
2
1
2
1
3
1
1
1
1
1
0
1
2
1
1
3
1
0
1
1
1
1
1
0
1
0
1
1
2
1
2
2
1
2
2
1
1
1
1
1
1
1
0
0
1
1
1
1
1
0
0
0
1
0
1
1
1
2
0
1
1
1
1
1
2
1
1
1
1
0
2
0
1
0
1
1
0
1
0
0
2
1
1
0
1
0
2
1
1
1
1
2
0
1
2
1
1
0
2
2
2
1
1
2
2
0
0
1
2
1
1
1
1
0
1
1
1
1
1
1
1
0
0
1
1
2
0
2
0
1
0
1
1
0
1
2
1
1
1
1
2
2
1
0
1
1
0
0
2
0
0
1
1
1
1
0
1
0
1
1
1
1
0
1
0
1
1
1
1
2
1
1
1
2
1
1
1
0
1
1
1
1
0
2
1
1
1
1
1
1
1
0
0
3
0
0
1
1
2
1
2
1
1
2
0
1
1
0
1
1
1
2
1
1
0
1
2
2
1
2
1
0
0
2
2
1
1
0
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
0
1
2
2
1
1
1
1
2
1
1
1
1
1
2
1
1
2
1
2
1
1
1
1
0
1
2
2
1
1
1
1
0
1
1
2
2
0
0
1
0
1
1
1
0
1
2
1
1
1
1
1
0
1
1
1
1
1
1
1
0
1
1
2
2
2
1
1
1
1
1
1
1
3
1
0
1
4
2
0
0
1
0
0
0
0
1
1
1
1
0
0
3
2
1
2
1
1
0
1
1
1
0
1
0
1
0
1
1
1
2
0
1
0
1
2
1
1
0
1
0
1
1
2
1
1
1
2
2
2
1
2
1
0
1
1
0
0
2
0
1
1
1
4
1
2
0
1
1
0
1
1
1
1
0
0
1
1
0
1
1
1
1
1
1
1
1
1
2
2
2
1
1
2
2
1
1
1
1
1
0
1
1
0
1
1
1
0
1
1
2
2
0
0
1
2
1
2
2
0
1
1
1
1
0
1
1
2
1
0
1
2
0
0
1
1
0
1
0
1
1
0
0
0
1
2
1
1
1
1
2
1
2
2
0
0
1
0
2
0
1
1
1
0
0
2
2
1
1
1
1
2
1
1
0
2
1
0
2
0
1
1
0
1
2
1
2
1
0
0
1
0
2
1
1
1
1
1
1
1
2
1
1
1
2
0
2
1
3
1
0
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
0
1
0
1
2
1
0
1
1
2
0
0
1
0
1
3
1
2
1
2
0
0
1
0
1
0
2
1
0
2
1
1
0
2
0
1
1
1
2
1
2
2
1
0
1
2
1
1
0
1
2
2
2
2
1
1
0
1
1
1
1
0
1
0
0
1
1
1
1
1
2
1
1
2
1
1
1
1
1
2
2
1
1
0
1
2
1
1
1
2
0
0
1
0
0
2
1
1
2
1
0
1
1
0
2
2
1
1
2
1
2
1
0
0
3
1
1
1
1
1
1
0
2
0
1
1
1
1
1
2
1
1
2
1
0
0
1
0
2
2
2
1
1
2
1
0
0
1
2
1
1
1
2
0
2
2
0
0
1
1
1
1
2
2
1
1
0
2
1
0
1
1
2
0
0
2
0
1
1
0
1
1
1
1
1
2
1
1
2
1
1
2
0
0
2
2
0
0
2
0
1
0
2
1
1
0
0
0
2
0
1
2
1
1
5
2
1
1
0
2
2
1
2
0
2
0
0
2
1
2
1
3
0
1
2
1
0
0
1
2
2
0
1
2
0
2
2
1
2
1
1
1
1
1
1
0
1
3
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
3
2
1
1
0
2
1
1
1
0
2
1
1
3
2
0
1
1
1
1
1
0
1
2
2
1
1
1
2
1
0
2
1
1
1
2
0
1
1
0
1
0
0
1
1
1
1
1
0
1
1
1
1
0
1
1
1
1
0
1
2
1
0
0
2
1
0
2
1
2
0
2
2
2
1
1
1
1
1
0
1
1
1
1
1
0
1
1
0
1
1
0
1
1
1
1
1
3
0
1
1
0
1
1
0
0
2
0
1
1
1
2
0
0
1
2
1
1
2
2
2
1
2
1
1
2
2
1
1
2
2
2
1
2
1
1
2
1
1
0
1
1
1
0
1
2
2
1
1
1
1
2
2
0
1
2
0
2
1
2
1
3
1
1
0
0
0
1
1
0
1
1
1
2
2
1
2
1
1
2
1
0
2
2
2
1
1
2
1
0
2
0
1
1
2
0
0
2
1
0
1
1
1
0
0
2
1
2
0
2
1
0
1
1
2
1
0
1
1
1
2
1
2
2
1
2
1
1
0
2
1
0
1
1
1
1
1
1
1
2
2
3
1
0
2
2
1
1
2
0
1
1
2
1
1
1
1
1
1
1
2
1
0
0
1
2
0
1
1
1
2
1
1
1
1
1
1
0
2
2
1
0
1
0
2
1
2
1
2
1
1
1
1
2
0
0
1
1
0
2
2
2
1
1
2
0
1
1
1
1
0
0
2
2
2
1
0
1
1
1
1
0
1
1
1
0
2
0
0
2
1
2
2
2
1
1
2
1
1
2
0
2
1
2
1
1
1
1
1
1
1
1
2
2
2
1
0
1
1
2
1
1
0
1
0
2
0
1
1
1
0
2
1
0
2
1
0
2
1
1
2
1
1
1
2
0
1
1
2
0
2
0
1
1
1
0
0
1
1
0
1
2
0
2
0
1
0
2
2
1
1
1
1
1
0
1
0
2
1
1
2
1
1
0
1
0
1
1
1
2
0
1
2
2
1
0
1
1
1
2
2
1
1
1
1
1
2
1
1
1
1
1
3
2
1
2
0
2
0
1
2
1
1
0
2
2
1
0
1
1
0
1
2
0
2
1
0
1
1
1
2
1
1
1
2
0
0
0
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
1
1
0
0
1
1
1
1
1
1
1
0
2
1
0
1
1
2
1
0
0
1
0
1
1
0
1
0
1
2
0
0
1
2
1
0
2
2
0
0
0
1
1
2
1
1
1
1
0
0
2
0
1
1
0
1
3
2
0
1
1
1
0
1
0
0
2
1
0
2
1
1
0
1
2
0
1
0
1
2
2
1
0
1
1
6
0
0
0
1
1
2
0
0
2
2
1
1
0
1
0
1
0
1
1
1
0
0
1
0
5
1
1
2
1
1
2
2
0
0
0
1
1
0
1
1
0
0
2
1
2
2
1
0
1
1
2
1
0
2
0
0
1
2
1
1
2
3
1
1
1
1
0
2
1
1
1
2
1
1
1
2
1
0
1
0
2
2
0
2
2
0
2
1
2
2
1
1
0
0
2
2
0
1
3
2
1
0
1
1
2
0
1
3
2
1
0
1
0
0
0
2
1
2
1
1
1
1
0
1
0
1
1
2
1
2
1
2
0
0
1
2
0
1
1
2
1
0
0
0
0
2
1
1
1
1
1
2
1
0
1
1
0
0
2
0
2
1
1
2
2
0
2
1
1
0
1
1
0
2
1
1
1
0
2
1
0
1
1
1
0
0
3
0
0
2
0
1
1
1
2
0
1
1
1
2
2
1
1
1
0
1
2
1
2
1
1
1
2
0
1
1
0
1
1
1
1
1
1
1
0
0
1
2
2
0
0
2
0
1
1
2
0
1
1
2
0
1
2
2
1
1
1
1
0
1
1
1
1
1
2
1
0
2
2
2
2
1
1
1
1
1
0
2
1
2
0
1
0
1
2
1
1
1
0
2
0
2
1
1
1
1
1
3
0
0
1
1
1
1
2
1
1
1
1
1
1
0
2
1
0
2
1
2
2
1
1
1
2
0
0
2
1
1
1
2
1
1
2
2
2
1
1
1
1
1
2
1
1
1
0
1
2
1
2
1
1
0
0
1
1
2
2
0
1
1
0
2
2
2
0
2
1
2
2
1
1
0
0
2
2
1
1
1
2
0
1
1
1
1
2
0
1
0
2
2
1
1
1
0
2
0
1
2
1
1
0
1
2
2
2
2
2
0
2
1
2
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
0
1
1
1
1
0
1
1
1
0
0
0
1
0
1
1
1
0
1
2
3
1
0
2
2
1
0
2
0
2
1
1
1
2
2
1
0
1
1
1
2
1
1
1
0
1
1
0
1
1
1
0
1
0
1
1
1
0
2
0
1
1
1
2
1
2
1
2
1
0
1
1
2
2
0
1
1
1
1
2
1
0
1
2
1
1
2
0
0
0
2
1
2
2
1
1
1
1
0
1
0
2
1
0
2
1
1
1
1
2
1
1
2
0
1
1
2
1
2
1
1
0
0
1
1
2
0
2
1
1
0
0
1
1
1
0
2
1
0
0
2
2
1
1
1
2
0
1
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
2
1
2
1
1
0
0
1
1
2
1
1
2
0
1
1
1
1
0
0
1
2
1
0
0
1
1
1
4
0
1
1
2
1
1
1
2
1
0
1
1
1
2
1
2
1
2
1
1
0
2
0
1
2
1
1
2
1
1
1
1
0
1
1
0
0
0
0
1
1
1
0
2
1
0
1
0
0
0
2
1
2
1
1
0
2
0
1
1
1
2
2
2
1
0
1
1
1
1
1
0
2
1
1
1
1
1
1
1
1
0
0
2
1
1
1
0
0
1
0
0
1
0
0
1
2
1
2
1
1
1
2
0
0
1
1
2
1
2
3
1
2
1
1
1
0
1
1
2
1
2
1
1
0
1
1
1
1
0
0
2
1
1
0
0
0
0
1
0
2
1
2
1
1
0
1
2
1
1
0
1
1
0
1
1
1
2
0
0
1
0
2
2
1
1
0
2
2
0
1
0
2
0
1
0
0
1
1
1
0
0
1
1
2
1
0
0
2
1
1
0
0
0
1
1
0
1
1
2
1
2
1
0
1
1
0
0
0
1
1
0
1
1
1
1
0
1
1
0
1
1
1
1
1
1
0
2
1
2
1
1
1
1
0
1
0
1
2
1
0
3
0
2
1
0
1
2
1
1
1
0
2
0
1
1
1
1
2
0
0
1
0
1
0
0
0
1
1
0
0
0
2
0
1
1
1
1
1
0
1
1
1
1
1
1
1
2
0
1
2
0
2
0
1
2
2
1
1
1
0
0
1
1
1
1
1
1
0
1
1
1
0
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
2
2
2
8
2
2
0
1
1
0
0
1
1
2
0
1
1
0
2
0
1
1
1
0
1
1
2
1
7
1
1
1
0
1
2
1
1
0
1
1
2
2
1
0
2
0
1
1
2
1
2
1
1
2
1
0
1
1
0
0
1
0
3
2
0
0
2
2
1
1
2
2
2
1
1
1
2
2
0
1
1
0
1
1
1
2
2
1
1
1
0
1
1
4
0
1
1
1
0
0
2
1
1
0
1
2
1
1
1
1
1
1
0
0
2
0
1
1
2
1
1
2
1
1
1
2
0
2
1
1
1
2
1
1
1
1
1
1
1
0
1
1
1
2
0
0
1
1
1
0
1
1
0
2
1
2
2
0
0
2
1
1
1
0
0
1
1
1
0
1
0
2
0
1
0
1
0
1
1
1
1
1
2
4
1
1
2
1
0
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
1
2
1
0
2
1
1
1
1
1
2
1
0
1
1
2
2
0
1
2
1
1
1
1
1
1
1
1
1
1
0
1
1
0
0
0
1
1
2
1
0
2
1
1
0
1
0
2
0
1
2
1
1
1
0
1
1
1
0
1
1
1
1
1
1
0
1
1
1
0
2
2
2
1
1
0
1
2
1
1
1
0
0
1
0
2
1
2
0
2
0
2
1
1
1
0
5
0
2
2
0
0
1
1
0
1
1
1
0
2
2
1
1
1
1
0
5
1
1
1
2
0
1
0
0
1
1
2
0
1
1
1
1
1
1
2
2
1
1
0
0
2
1
0
0
2
2
1
1
2
0
1
0
0
1
1
1
1
1
2
0
2
0
1
1
1
1
1
0
2
1
1
1
2
0
0
2
2
1
2
1
2
0
1
1
1
1
1
0
1
1
0
0
2
1
0
1
1
0
2
1
1
1
1
2
1
1
1
1
2
0
1
2
2
0
1
0
1
0
1
1
1
1
1
1
2
1
1
1
1
0
2
1
0
1
1
1
1
1
1
1
1
1
2
2
1
2
1
1
2
1
1
1
0
1
1
1
1
1
0
0
0
1
1
1
1
1
2
1
0
1
2
1
1
2
1
2
1
2
1
1
1
0
1
0
1
0
1
0
1
2
1
1
2
1
1
2
1
0
1
1
1
1
1
1
1
2
1
1
1
0
1
2
1
1
0
1
2
1
1
0
0
1
0
0
1
2
2
1
2
2
1
1
2
1
1
2
1
1
1
1
1
1
1
1
0
1
1
1
1
0
1
1
2
1
0
2
1
1
1
1
1
3
1
0
1
1
2
0
2
2
1
0
2
1
1
2
0
0
1
0
1
1
0
1
1
1
1
2
2
1
0
0
2
1
2
1
0
1
1
0
1
0
1
0
1
1
0
1
0
1
0
1
2
0
2
1
0
0
1
1
2
1
1
2
1
1
1
1
0
0
1
2
1
0
0
1
1
1
1
1
1
1
0
2
1
2
0
1
1
1
1
1
2
1
1
2
2
0
2
1
1
0
2
1
1
1
1
1
4
2
1
1
3
1
2
1
1
0
2
2
1
2
1
1
2
1
1
0
0
2
1
0
1
0
2
1
2
1
1
2
0
1
0
2
2
0
0
2
2
0
1
2
0
0
1
2
1
1
1
1
1
1
1
1
0
0
1
1
0
2
1
1
2
1
0
2
1
2
1
1
1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
1
1
0
1
0
1
1
1
0
1
1
1
1
1
1
2
1
1
1
1
0
0
1
1
1
0
1
1
4
0
0
1
2
1
0
1
0
1
2
1
1
1
1
1
0
1
2
1
0
1
0
2
1
1
1
1
1
2
1
0
2
1
1
2
1
2
1
1
1
0
1
1
1
1
2
1
0
1
1
1
1
0
1
1
1
1
1
1
1
1
2
0
1
1
0
0
1
2
1
2
0
1
1
2
1
0
1
2
1
1
1
0
2
2
2
2
2
1
0
1
1
1
1
1
1
1
1
1
1
1
1
0
1
0
1
1
1
0
2
1
4
2
2
0
1
0
0
1
2
0
2
2
2
2
1
1
1
1
1
1
0
2
0
0
0
1
2
0
2
1
1
1
1
1
1
1
0
1
1
0
1
1
1
1
2
1
1
1
0
2
0
2
2
1
0
2
1
0
2
2
1
1
1
0
1
1
1
1
1
1
2
1
1
0
2
1
1
1
0
0
1
1
2
1
0
2
0
2
1
0
0
1
2
1
0
1
1
1
0
1
0
0
1
0
2
1
2
1
1
3
1
0
2
1
2
2
1
1
1
1
2
1
1
1
1
0
1
1
0
1
1
1
1
2
1
1
1
1
1
1
0
2
1
0
0
2
2
1
1
2
0
1
1
0
1
2
1
1
1
1
1
1
1
1
1
1
2
2
2
0
1
1
1
1
1
0
1
1
1
2
2
1
2
1
0
0
1
0
1
2
1
0
2
1
0
1
1
1
0
1
2
0
1
0
0
1
2
2
2
2
2
0
2
2
1
1
1
2
3
2
0
2
0
2
0
1
1
1
1
0
1
2
0
1
1
1
0
2
1
2
2
1
2
1
1
1
0
1
0
1
2
2
2
1
1
2
2
1
0
1
1
2
2
2
1
1
2
2
1
1
1
1
1
2
1
1
1
1
0
1
1
0
1
2
1
2
1
0
2
0
1
2
1
0
1
1
0
1
2
0
1
1
1
0
1
1
2
2
1
1
0
2
2
1
1
2
1
1
1
0
0
1
1
1
1
0
2
1
1
1
0
1
1
1
0
1
1
1
1
1
2
0
1
2
1
1
0
1
0
0
1
2
1
2
1
2
0
1
2
1
1
0
0
1
1
2
1
1
2
1
1
2
0
2
1
0
2
1
0
1
1
0
1
1
1
1
1
2
0
2
2
1
0
0
0
1
1
2
2
1
1
0
1
0
1
1
1
0
0
1
0
1
2
0
2
1
1
1
2
1
2
1
0
1
1
1
1
1
0
1
1
1
1
2
1
2
0
0
1
1
1
0
1
1
1
2
2
0
1
1
1
2
1
1
2
0
2
0
2
2
1
2
1
1
0
0
1
1
0
1
1
1
1
1
2
1
1
0
1
1
0
2
1
1
1
0
0
1
2
1
0
1
1
0
1
0
2
1
2
1
1
2
2
1
1
1
2
1
2
0
0
1
1
1
1
0
1
2
0
2
1
1
1
2
2
1
1
2
1
1
2
0
1
1
2
1
2
0
1
1
2
1
0
1
0
1
0
2
1
1
1
0
1
2
0
1
1
1
1
2
0
1
1
0
1
0
1
0
1
2
1
0
0
2
2
0
1
0
1
0
1
1
1
1
1
2
0
0
1
2
2
1
1
1
1
1
0
1
0
0
1
3
1
1
1
1
0
3
1
1
2
0
1
1
1
0
1
0
1
2
0
0
2
1
2
1
2
2
0
1
1
1
1
1
0
1
2
1
1
2
2
1
0
1
2
2
1
1
2
1
2
1
0
1
1
1
1
0
0
1
2
1
0
2
0
1
1
1
2
0
1
2
1
1
0
0
2
0
2
2
1
1
0
3
1
1
0
2
1
0
1
1
1
1
1
0
1
0
1
2
1
0
1
1
1
1
1
2
1
1
1
0
0
1
0
1
1
1
1
0
1
0
0
1
1
1
1
1
0
2
1
1
2
1
1
2
0
1
0
1
0
1
2
1
1
1
1
1
1
0
1
1
1
2
0
2
2
2
2
1
1
1
1
1
1
0
0
1
1
1
0
2
1
1
1
1
2
2
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
2
1
1
1
2
1
1
2
0
1
1
1
2
1
1
1
0
1
2
1
1
2
0
2
2
1
0
2
1
1
1
0
1
0
1
0
1
0
1
2
0
1
2
1
2
1
1
0
1
2
2
0
1
0
1
1
1
2
2
0
1
0
1
0
1
0
0
1
0
1
2
0
0
1
1
1
1
0
0
1
1
0
0
1
0
0
1
1
0
2
1
2
0
2
1
1
1
2
0
0
1
0
0
0
1
1
2
1
1
0
0
0
0
1
1
1
2
1
1
1
2
0
1
1
0
2
1
1
1
1
2
2
0
1
2
1
1
1
1
2
3
1
0
1
0
0
1
1
2
1
1
1
0
1
0
2
0
1
0
1
1
2
1
1
1
0
1
1
1
1
1
1
0
1
1
2
1
1
1
0
2
1
0
2
0
1
1
1
1
1
0
2
2
1
1
0
1
2
2
0
1
1
2
0
1
1
1
1
1
1
1
1
2
0
1
1
0
1
1
1
1
1
1
0
1
1
1
1
1
1
1
0
1
1
1
1
2
1
1
0
2
2
1
1
2
0
1
0
1
1
1
0
1
1
1
2
0
0
1
0
1
0
0
0
1
1
1
2
1
1
2
0
1
1
2
0
1
1
1
2
1
0
1
2
0
1
1
2
1
2
2
1
1
1
0
1
1
1
0
1
1
1
2
0
1
1
1
2
4
0
1
1
2
1
0
0
2
0
1
1
2
1
1
0
1
1
1
1
1
0
1
1
0
1
0
2
2
1
1
1
2
1
1
2
1
0
1
1
1
1
1
1
1
2
1
0
0
1
1
0
2
2
0
1
0
0
1
1
1
0
0
1
0
0
0
0
1
1
0
2
0
0
0
1
1
2
1
2
1
1
1
0
0
1
0
2
1
2
0
0
1
0
2
1
1
1
2
1
3
0
0
1
1
0
1
1
2
0
1
0
1
2
2
1
1
3
1
2
1
1
3
2
1
1
1
1
1
1
1
1
2
1
0
0
0
1
0
0
0
2
1
2
1
1
1
0
1
1
0
2
1
1
2
0
0
0
1
1
2
2
1
1
0
1
2
1
1
1
3
2
1
2
0
2
0
1
1
2
0
0
1
1
1
1
1
1
0
1
1
2
1
1
1
1
2
2
1
1
1
0
1
1
1
1
1
1
1
1
0
0
0
0
0
1
1
1
1
1
1
1
2
2
2
0
1
0
2
2
1
0
1
1
0
2
1
1
0
0
0
1
1
1
0
0
0
1
0
1
0
0
2
0
2
0
1
1
0
1
3
0
0
2
1
1
1
1
1
1
2
1
1
2
2
1
0
0
1
1
1
0
0
1
1
0
0
1
2
2
0
1
1
2
1
0
2
1
1
1
0
1
2
2
1
2
1
2
1
1
2
1
1
0
2
1
1
1
1
1
2
0
1
1
0
2
1
2
0
1
0
1
1
4
2
1
1
2
1
1
1
2
2
0
2
1
0
1
1
1
2
0
0
1
1
1
2
1
2
1
1
1
1
1
1
0
1
2
0
4
1
1
1
0
1
1
1
0
2
1
1
0
0
0
0
0
2
1
1
1
1
2
1
1
1
2
1
1
2
0
0
2
2
1
0
1
2
0
0
1
0
0
1
1
0
1
2
1
1
1
1
2
1
0
1
2
1
0
0
2
1
1
0
1
2
1
2
1
0
2
0
1
0
1
1
1
0
1
2
2
1
2
0
1
0
2
0
0
2
1
1
1
0
1
2
2
3
1
1
2
2
0
1
1
0
2
2
2
0
2
2
1
0
1
1
0
1
1
1
2
2
1
2
1
1
0
2
0
2
0
0
0
1
1
0
0
1
1
2
0
1
1
0
1
2
1
2
1
0
2
0
2
2
1
1
1
1
1
2
1
2
1
2
0
1
1
1
1
2
2
1
0
1
0
1
1
0
0
2
2
2
2
1
1
1
2
0
1
2
0
1
0
1
0
1
0
1
1
0
1
1
1
2
1
1
1
0
0
2
1
0
2
2
0
1
2
0
0
0
1
0
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
0
0
1
1
1
0
1
0
0
1
1
1
1
0
2
1
2
1
2
1
1
0
0
1
1
2
1
1
2
1
1
1
1
1
0
2
1
1
2
0
2
1
2
1
1
1
2
2
1
2
1
1
2
2
2
1
2
1
1
0
2
1
2
2
2
1
1
1
2
1
1
1
1
2
1
1
1
1
1
2
0
1
1
2
1
0
2
1
1
1
1
2
2
1
1
1
2
1
1
2
2
0
2
0
1
1
1
1
2
2
2
2
1
1
1
1
1
2
2
5
0
2
0
1
1
1
1
1
1
0
1
1
0
0
1
1
2
1
1
0
0
1
1
2
1
2
2
0
0
1
2
1
0
2
2
1
1
0
1
1
1
0
1
2
1
1
0
2
1
1
0
1
2
0
1
1
0
0
1
1
2
1
1
1
0
0
1
1
2
2
1
1
2
1
0
1
2
1
0
2
1
1
2
1
0
0
0
1
1
1
0
2
1
0
1
1
1
2
2
0
0
1
0
1
1
1
1
2
1
0
0
1
1
2
2
4
2
0
1
1
1
2
2
1
1
1
2
1
2
0
0
2
1
1
1
2
2
2
1
1
1
2
1
1
1
1
1
1
1
1
0
1
1
1
0
1
1
2
1
1
1
0
1
0
1
0
0
1
1
2
1
0
1
1
2
0
0
1
1
2
1
2
1
1
0
1
2
1
1
2
1
2
0
1
2
0
1
2
0
1
2
1
2
0
1
1
0
1
1
0
2
1
1
0
1
1
1
1
1
0
2
0
0
1
0
0
1
0
1
0
1
1
0
2
2
1
0
1
1
2
2
1
1
0
0
1
0
1
1
1
1
1
2
1
1
1
1
1
0
1
2
2
1
1
1
1
0
1
2
0
0
0
2
0
0
1
2
0
2
1
2
2
0
0
2
0
2
1
0
2
1
0
0
1
2
2
3
2
2
1
2
2
1
0
1
1
2
0
1
1
0
0
0
0
1
1
2
1
1
1
1
0
2
2
1
1
2
1
1
0
1
0
1
1
1
2
2
2
0
2
0
1
2
2
1
2
2
1
2
0
0
1
2
0
1
1
1
1
2
2
2
1
0
1
0
0
1
0
1
0
2
1
2
0
0
1
1
1
1
1
1
1
1
1
4
0
1
4
1
1
1
1
0
2
1
1
0
0
2
1
1
1
1
1
2
1
0
1
1
2
1
1
1
2
0
0
1
0
1
2
1
2
2
2
1
0
1
1
0
2
2
1
1
2
1
1
1
1
1
1
1
1
1
2
0
1
1
1
2
1
0
1
1
1
1
0
1
1
1
0
0
1
3
1
0
1
1
2
1
2
1
1
1
2
1
1
2
2
2
0
1
1
1
2
1
2
1
1
2
2
0
0
2
1
1
1
2
1
2
0
2
1
1
2
2
1
0
1
0
1
1
1
0
1
1
2
2
0
2
1
2
1
2
0
1
1
1
1
0
2
2
1
1
0
1
1
2
0
1
1
2
1
1
1
1
2
1
1
1
1
0
1
2
1
2
1
0
2
1
1
1
1
2
1
0
2
1
1
0
1
0
1
1
1
1
0
2
0
0
1
2
1
2
1
0
0
1
1
1
1
1
1
1
1
1
1
1
2
1
1
0
2
0
2
1
1
0
0
1
1
2
1
1
1
1
0
2
1
1
1
1
1
0
1
1
0
1
1
1
1
0
0
1
1
0
1
0
1
0
1
2
0
1
1
1
1
1
1
2
0
1
2
2
1
1
1
1
0
1
0
2
1
1
1
2
0
2
0
1
1
1
2
1
1
1
1
1
0
0
2
1
2
0
1
1
1
1
1
1
2
1
1
1
2
1
0
1
3
1
2
1
2
1
1
1
1
0
0
2
1
1
1
0
2
0
0
2
1
1
0
1
1
1
1
2
1
1
0
1
1
0
2
2
1
1
1
1
1
1
2
2
1
1
1
0
2
2
1
1
1
2
1
0
2
2
0
1
2
1
2
1
1
1
1
2
1
0
0
2
1
1
1
1
1
2
2
1
1
1
0
2
0
1
1
1
1
0
2
0
1
1
2
0
0
1
2
0
1
2
0
1
1
1
1
1
1
1
1
1
0
1
2
1
0
0
2
1
0
1
0
1
1
1
1
1
1
1
1
2
1
1
0
0
1
2
2
1
2
0
0
2
1
1
1
1
1
2
0
1
1
1
1
2
0
1
2
2
1
1
0
1
1
0
2
2
1
0
0
2
1
2
2
1
1
1
2
2
0
2
1
1
0
2
1
1
0
1
0
1
1
2
0
1
4
1
1
0
1
0
0
1
1
1
1
1
1
1
1
1
1
2
1
2
1
2
1
2
1
2
1
0
1
1
1
2
2
1
1
1
1
0
0
0
1
0
1
1
1
1
1
1
2
0
2
2
1
2
2
1
0
1
1
0
2
0
2
2
0
2
1
0
0
0
2
1
0
1
1
0
0
1
2
1
1
2
1
0
1
1
1
1
1
1
1
0
1
1
1
1
0
0
1
2
1
2
0
4
2
1
0
1
1
0
1
0
1
0
1
0
1
2
1
1
4
1
2
1
0
1
2
2
0
1
1
1
1
1
0
1
0
1
0
2
1
1
0
1
2
2
1
0
0
1
0
0
1
1
1
2
0
0
2
2
1
1
1
0
2
1
0
0
2
1
2
1
1
0
2
0
2
0
1
2
1
1
1
1
1
1
0
1
1
0
1
1
0
0
0
1
2
1
1
0
1
1
1
2
0
1
2
2
1
6
1
1
1
1
0
1
1
2
0
1
1
2
1
1
2
1
2
2
1
0
0
2
1
0
1
2
1
2
2
1
1
1
2
2
2
2
2
1
1
1
1
1
1
2
0
2
1
1
1
0
0
2
1
2
1
0
1
1
1
0
2
0
1
2
0
0
1
1
1
4
1
1
1
2
2
1
0
2
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
2
2
1
1
0
2
1
1
2
0
1
2
1
1
1
2
1
2
2
2
0
1
0
2
0
1
1
1
1
2
0
1
1
2
1
2
2
1
1
1
2
0
0
0
1
1
0
2
1
1
1
2
0
0
2
1
1
1
0
1
1
2
1
2
1
1
1
1
1
2
1
0
0
2
1
2
1
2
1
1
4
0
1
2
1
2
1
1
1
1
0
0
1
0
1
1
0
1
0
2
0
1
1
2
0
1
2
1
1
1
0
2
1
2
2
0
0
0
1
1
1
2
1
1
1
1
1
1
1
2
0
0
0
1
1
2
1
1
1
1
1
0
0
2
0
1
1
2
1
2
1
1
1
0
1
1
1
1
2
0
2
1
1
1
1
1
0
1
1
2
2
0
0
1
2
0
2
1
0
2
1
2
2
1
1
2
1
2
0
0
2
0
1
0
0
1
1
2
1
1
2
0
1
1
2
1
2
1
0
1
2
2
0
0
1
1
1
2
0
1
0
0
1
2
3
0
0
1
0
2
2
2
1
1
0
1
1
2
0
0
0
2
1
0
1
1
0
1
2
1
2
1
1
1
1
1
0
1
2
1
1
0
0
1
1
2
1
1
1
0
1
1
1
1
1
1
1
0
0
0
0
2
0
0
1
1
1
2
1
1
1
1
0
1
0
1
2
1
0
1
1
2
1
1
1
1
2
0
2
1
0
1
1
0
0
1
2
0
1
1
2
1
2
0
1
0
0
2
1
2
1
1
0
1
1
1
0
2
1
2
0
1
1
1
0
1
1
1
1
1
4
0
1
1
1
1
1
0
1
1
1
2
2
1
2
1
0
0
0
2
2
1
1
2
0
1
1
2
0
2
1
0
2
0
1
2
1
2
0
0
1
2
0
1
1
1
1
0
1
1
2
0
1
3
1
2
2
1
1
1
0
0
1
0
1
1
2
1
0
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
0
2
1
1
1
1
2
1
0
0
1
1
2
1
1
0
1
1
2
1
1
2
2
0
0
0
1
0
0
2
0
1
1
1
1
2
4
1
0
2
2
1
1
2
2
2
0
2
0
0
0
0
2
0
1
0
1
1
1
1
0
2
2
0
0
2
1
1
2
2
2
1
1
0
1
0
1
2
0
1
1
1
1
1
0
1
2
1
1
2
1
2
1
2
1
1
1
1
2
1
0
1
1
1
1
2
2
1
1
1
2
1
1
0
1
0
2
1
2
1
2
2
1
0
1
0
1
2
1
1
2
1
2
1
1
2
2
1
2
1
2
1
1
1
1
1
2
1
1
1
1
2
1
2
0
2
1
1
1
2
0
1
1
1
1
1
0
1
1
1
1
0
1
1
1
0
2
1
0
1
1
0
0
1
1
1
1
1
0
0
1
1
1
1
1
2
1
1
2
2
1
1
1
1
1
2
0
2
2
1
0
2
0
2
1
0
1
1
1
1
1
0
1
1
0
1
1
1
1
1
1
1
0
1
1
1
0
1
1
2
1
1
2
1
2
0
1
1
1
0
1
2
2
1
1
2
2
2
2
1
1
1
2
0
1
1
1
1
1
1
2
2
1
0
0
2
1
0
1
1
1
2
2
2
2
2
1
1
1
1
1
1
1
1
0
1
2
1
1
1
1
1
1
1
1
2
0
2
2
1
1
2
1
1
1
1
2
1
1
2
2
0
1
0
2
2
1
1
1
2
2
0
1
1
1
0
1
0
1
2
2
1
1
0
2
0
1
0
1
0
2
1
1
1
1
1
1
1
1
2
2
1
1
1
1
0
2
1
1
1
1
1
1
0
1
1
0
1
0
1
1
0
0
0
1
1
2
2
1
3
1
0
2
0
0
0
2
0
2
2
1
1
0
1
1
1
1
1
0
0
1
0
1
2
1
1
2
1
1
2
1
1
2
1
1
1
1
0
1
0
0
0
1
1
1
1
0
2
2
1
0
1
2
1
1
2
1
2
2
1
1
1
0
0
1
1
1
1
0
2
1
0
1
2
0
0
0
2
0
1
1
0
1
2
1
0
1
1
1
1
2
1
4
2
2
2
1
1
2
3
1
1
2
1
1
0
0
1
1
0
0
2
1
0
1
2
1
0
2
2
1
0
1
0
1
1
1
1
1
0
1
2
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
3
1
0
0
4
2
2
1
1
1
0
2
2
1
1
2
2
1
2
2
2
0
2
1
1
1
1
1
0
2
2
2
1
2
2
2
1
0
0
2
1
1
1
2
1
1
1
1
0
1
0
1
0
1
2
1
2
1
1
0
1
1
2
0
2
1
2
4
2
1
1
0
1
1
1
1
0
0
1
1
1
1
2
1
1
1
0
1
0
0
1
1
1
1
1
0
1
1
1
0
1
1
1
1
2
1
0
0
0
0
1
1
1
2
1
0
0
1
1
2
1
0
1
2
1
1
0
2
2
1
1
1
1
2
0
2
1
1
3
1
1
1
1
0
3
1
0
1
1
1
1
1
1
1
0
1
1
2
1
1
1
1
1
1
1
1
0
1
0
1
1
1
1
1
1
1
1
0
1
1
1
1
1
2
2
1
1
1
2
1
1
3
1
2
0
0
1
1
2
1
1
1
0
0
2
2
1
0
2
2
1
1
1
1
2
1
1
1
0
2
2
1
2
1
1
2
1
1
1
2
0
1
1
0
1
0
1
2
0
0
1
0
0
1
1
0
1
1
1
1
0
0
1
1
3
1
0
2
0
0
1
0
1
2
0
1
2
0
0
2
2
0
2
1
1
1
1
1
1
1
2
1
1
2
1
0
1
1
1
2
2
1
0
0
0
1
1
1
0
2
2
1
1
0
1
2
1
0
1
0
2
2
1
1
1
1
0
1
0
0
1
1
1
2
2
1
1
2
2
0
1
2
0
0
1
0
1
2
1
1
2
0
1
0
1
2
0
0
1
1
1
1
0
1
1
2
2
2
2
0
1
0
1
2
2
1
0
0
0
0
0
1
1
1
1
1
1
2
1
1
1
2
1
0
1
1
0
0
1
1
1
2
1
2
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
0
0
1
1
1
2
1
0
1
2
2
2
0
0
1
1
1
1
1
2
1
1
0
0
1
1
2
0
2
1
2
0
1
1
2
1
0
2
1
1
0
1
1
0
2
1
1
2
2
2
1
1
1
2
1
0
0
2
2
0
0
0
1
1
0
1
0
0
1
0
1
0
1
1
3
1
1
1
1
2
1
1
1
2
2
1
2
1
0
1
1
1
1
1
2
1
1
1
2
0
2
2
1
2
2
1
1
1
1
1
0
1
1
0
2
2
2
1
1
1
0
2
2
1
0
2
1
1
2
1
1
1
0
1
1
1
1
2
1
0
1
0
1
1
1
1
0
1
1
2
1
1
1
1
1
0
1
1
1
0
2
1
3
1
1
1
1
1
0
2
3
1
2
1
2
1
2
1
1
1
1
1
1
1
1
1
0
0
1
1
1
1
1
0
0
2
0
1
0
0
1
2
1
1
0
1
1
0
0
2
1
2
1
1
3
2
0
2
0
0
1
2
0
0
1
1
1
1
2
0
1
2
1
0
1
1
1
1
1
1
0
1
1
1
3
2
2
1
1
1
1
2
1
0
1
2
1
1
1
1
1
1
1
2
1
2
1
0
1
1
1
1
1
1
2
2
2
0
0
2
0
2
0
0
2
2
1
1
1
1
1
1
0
2
1
2
1
2
0
1
1
1
1
1
0
1
1
1
0
2
1
2
2
1
0
1
2
1
2
0
2
0
2
0
1
0
1
1
1
2
1
1
1
1
2
1
2
3
1
1
1
2
2
2
3
1
2
2
0
0
1
0
0
1
2
1
1
1
1
1
1
1
0
0
1
3
1
0
0
1
0
1
1
0
1
0
0
1
1
2
0
0
2
2
0
0
1
1
1
2
1
1
1
0
2
1
2
2
1
0
1
0
1
0
2
2
1
2
1
1
1
1
1
0
0
1
0
1
1
0
1
1
1
1
1
1
1
1
0
2
0
1
2
1
1
0
2
1
1
1
2
1
1
1
1
1
1
1
1
0
1
1
1
1
1
0
1
1
1
1
1
1
0
1
1
2
1
1
1
0
0
1
0
1
1
1
0
1
0
1
0
2
0
2
1
0
1
1
0
1
1
1
0
1
2
1
2
1
2
2
1
1
1
1
3
1
1
1
0
2
1
0
2
1
2
1
1
1
1
1
1
0
1
1
0
2
2
1
0
1
2
2
4
1
1
2
1
0
0
1
1
2
0
0
1
2
1
1
1
2
1
1
2
1
0
1
2
1
1
2
1
2
2
1
0
1
0
1
1
3
1
1
1
1
2
1
1
1
1
0
1
1
1
2
1
1
2
2
0
1
0
1
2
2
0
2
2
1
1
1
1
1
1
2
1
0
0
0
1
1
1
0
2
1
0
1
1
1
2
2
1
2
0
1
1
2
0
1
1
2
1
0
1
1
1
0
2
2
2
1
2
2
2
0
2
2
1
1
2
1
0
2
0
1
1
1
1
2
1
2
0
0
0
0
1
0
1
0
2
2
1
0
1
0
1
0
2
1
1
1
1
0
2
1
2
0
2
2
1
1
0
1
2
0
0
1
2
1
0
2
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
0
2
1
1
1
1
1
2
1
1
0
1
1
1
1
1
0
0
1
2
0
1
2
0
1
1
2
0
1
2
0
1
1
1
1
1
1
1
0
1
0
1
1
2
1
1
1
0
2
1
2
1
0
1
0
0
0
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
0
1
0
2
1
1
1
1
2
0
0
1
0
1
1
1
1
2
1
1
1
0
1
0
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
0
1
0
2
0
0
2
2
1
1
0
2
1
1
1
1
1
0
1
1
1
2
0
1
1
1
1
1
1
1
2
1
0
2
1
0
1
1
1
0
0
1
1
1
1
2
2
1
0
1
0
1
0
1
2
1
0
1
1
0
2
1
0
2
2
0
2
1
0
1
1
1
1
1
1
1
1
0
1
1
1
2
0
1
2
1
1
0
2
1
0
1
0
2
2
0
0
1
1
1
1
1
1
1
1
0
1
2
1
2
1
2
1
0
1
1
1
0
0
2
2
2
1
1
1
1
1
2
2
1
2
1
1
1
0
1
1
1
1
2
0
1
1
0
0
2
1
0
1
1
0
0
0
2
1
1
1
2
2
1
1
1
1
0
2
1
0
1
0
0
1
1
1
0
1
0
2
1
1
2
2
1
1
1
1
1
1
1
1
1
1
0
1
0
1
1
1
1
1
1
1
1
1
1
2
2
2
2
3
1
1
0
1
1
1
1
0
1
1
2
2
1
2
1
1
0
2
0
1
0
0
2
0
1
0
2
1
1
0
1
1
1
2
0
1
0
0
1
2
0
1
2
1
0
1
1
0
1
1
0
1
1
1
0
1
2
1
1
2
0
0
2
1
0
1
2
0
1
2
0
1
2
0
2
2
1
2
0
1
1
1
1
1
2
1
1
1
0
1
1
2
0
0
1
0
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
0
1
1
1
1
1
2
1
1
1
2
2
1
2
1
1
1
1
1
1
0
1
0
1
1
2
2
0
2
2
2
0
1
1
2
1
2
1
2
2
1
1
2
1
1
2
1
1
2
0
2
0
2
1
0
2
1
0
2
1
1
0
1
1
1
1
0
1
0
0
0
2
1
1
0
1
1
2
2
0
0
0
1
2
1
0
1
2
1
1
2
0
1
1
2
1
2
1
2
1
1
1
1
1
1
0
1
0
1
2
1
0
1
1
1
0
0
1
0
2
1
2
1
3
0
1
1
1
1
0
1
1
1
2
1
1
1
0
1
0
1
0
1
1
2
0
0
1
0
1
1
1
0
0
1
1
1
1
0
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
2
1
1
1
1
1
1
0
0
1
1
1
0
0
1
1
2
1
0
1
1
0
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
0
0
1
2
1
1
0
0
1
2
1
2
0
0
0
2
1
0
2
2
2
1
2
0
1
2
0
1
1
1
1
0
2
2
1
0
0
1
1
1
1
2
1
2
1
1
2
2
2
1
1
1
1
0
2
1
1
1
1
2
1
1
2
1
0
2
1
1
2
1
1
0
2
1
1
2
1
2
2
1
1
0
0
1
1
1
1
1
0
1
0
0
0
0
2
2
2
1
0
0
1
0
1
1
1
0
2
0
0
2
2
2
2
0
1
2
0
1
1
2
2
2
2
2
1
0
2
1
1
0
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
0
1
0
1
2
1
1
0
1
2
2
0
1
1
1
2
2
1
2
0
1
1
1
1
1
1
1
1
2
2
0
0
0
0
2
2
2
1
0
2
1
2
0
0
1
1
1
0
1
2
0
1
1
1
1
1
2
1
1
2
0
1
0
1
0
0
0
2
0
1
1
0
1
1
0
1
0
1
1
2
1
1
2
1
2
1
1
0
2
2
1
1
0
1
0
0
1
1
0
1
2
1
2
1
1
1
1
2
1
1
2
1
2
2
0
1
1
2
1
1
1
1
1
1
0
2
1
1
1
1
1
1
1
1
1
2
1
2
2
2
1
1
0
2
0
1
1
1
1
2
0
0
2
1
0
2
2
1
1
3
1
1
2
1
1
1
1
3
1
0
0
2
2
1
2
1
0
3
1
2
2
0
1
0
1
1
1
0
0
2
1
0
0
2
2
2
1
1
2
1
1
1
0
2
1
0
1
2
0
1
1
1
1
1
2
0
0
2
1
1
1
2
1
2
1
2
1
0
1
1
0
2
2
2
0
1
1
1
1
2
2
1
1
0
1
0
1
2
2
1
1
0
1
0
2
1
1
1
1
0
1
2
0
1
1
0
1
1
2
2
2
1
2
0
0
1
1
1
0
1
1
2
0
1
1
2
1
0
1
1
1
0
1
0
2
2
2
1
0
0
1
2
0
1
1
1
1
1
1
1
1
2
1
1
0
0
1
1
2
1
0
0
1
2
1
1
0
1
1
0
1
2
1
1
2
0
0
2
1
2
1
1
1
0
1
2
2
1
3
1
0
1
2
2
1
2
1
2
1
1
1
0
2
1
0
1
0
1
1
0
3
0
1
1
2
2
1
2
1
2
1
1
1
2
1
1
1
2
1
1
2
1
0
2
2
1
0
1
3
1
0
1
2
1
1
1
1
1
1
1
1
2
1
1
2
0
0
1
1
1
2
0
1
1
1
1
1
2
1
1
1
0
1
1
1
1
0
2
1
1
0
2
1
2
1
2
1
1
0
2
1
2
2
0
0
0
2
0
2
0
1
0
1
2
0
1
1
0
1
1
1
1
1
2
1
1
1
1
0
1
1
0
2
1
1
1
0
2
0
1
1
1
0
0
0
1
1
2
2
1
1
1
1
0
0
1
1
1
1
1
2
2
1
1
1
2
1
1
1
0
1
1
0
2
1
1
1
2
1
0
1
1
1
1
1
2
2
2
1
1
1
1
2
1
1
1
1
0
0
2
1
2
0
1
0
1
1
1
0
1
0
0
2
2
1
1
1
1
1
1
1
1
1
1
2
0
2
1
1
2
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
0
0
1
1
1
1
1
2
0
2
1
2
1
1
0
0
1
1
1
1
1
2
1
1
3
1
2
0
0
1
2
1
1
1
0
0
1
1
2
1
0
2
1
1
1
1
1
1
1
1
1
1
0
0
1
1
2
1
1
3
0
1
2
0
2
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
2
0
0
1
0
1
0
2
1
0
1
1
0
2
1
2
1
2
1
0
1
2
1
2
1
1
0
1
1
0
1
1
1
2
0
1
0
1
1
1
1
2
2
1
2
1
0
2
2
0
1
1
1
1
1
2
0
2
2
2
0
1
1
1
1
0
1
1
0
1
1
1
0
1
1
4
1
1
1
1
0
1
0
1
2
0
2
1
1
2
2
1
1
1
1
1
1
2
1
1
2
1
1
1
2
1
2
4
1
1
0
1
1
0
1
1
1
1
0
0
0
1
0
1
0
0
0
1
0
2
2
0
1
2
1
0
0
0
1
1
0
2
1
3
2
1
0
1
1
0
1
2
1
0
1
0
0
2
0
1
1
0
1
2
2
0
1
1
0
2
1
1
1
0
0
1
1
1
1
2
2
2
1
2
1
2
1
1
1
1
2
1
0
0
0
1
2
2
1
2
0
1
1
0
1
1
1
1
1
2
1
2
1
2
2
1
1
1
1
1
1
1
0
1
1
1
1
1
2
1
1
2
1
0
0
0
0
1
1
0
0
1
1
1
1
2
2
0
1
2
1
2
0
1
1
1
0
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
2
1
2
2
2
1
2
1
1
1
1
1
2
1
1
0
1
1
0
2
0
0
1
0
0
2
1
2
1
1
1
2
2
1
1
1
0
1
2
1
1
3
2
1
1
2
2
1
0
2
1
1
0
1
1
2
0
2
1
1
2
1
0
3
1
1
1
0
1
3
2
1
2
0
1
2
0
2
1
1
1
0
1
1
1
2
2
2
1
1
1
2
1
1
0
1
1
1
1
1
1
1
1
0
1
0
2
2
0
1
1
1
1
2
1
0
2
2
1
0
2
1
0
2
1
0
0
1
2
1
2
2
1
0
1
0
1
2
1
1
1
0
0
0
0
0
2
1
2
1
0
0
2
1
2
2
1
1
0
1
2
2
1
2
1
1
4
0
1
2
0
1
2
1
1
1
2
2
1
2
1
1
2
2
2
0
2
1
1
1
2
1
1
1
0
1
1
1
1
2
1
1
2
1
2
3
1
1
0
2
1
1
1
1
2
0
1
2
1
0
2
1
0
1
1
2
1
0
1
0
1
2
1
0
1
1
0
1
1
1
1
1
1
2
0
1
1
0
1
1
1
1
1
1
1
1
2
2
0
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
0
0
2
1
1
2
1
2
1
1
1
1
1
1
0
1
0
1
1
2
1
1
0
2
2
1
1
1
1
1
1
0
2
1
2
2
1
2
0
1
2
2
1
1
1
1
1
2
1
0
1
1
1
1
2
1
1
0
1
1
1
1
1
1
0
0
1
2
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
1
1
1
0
1
0
1
0
1
1
0
1
2
1
1
1
0
1
1
1
0
1
1
2
1
1
2
2
1
2
1
0
2
1
1
0
1
0
0
0
1
2
1
1
1
0
0
1
1
1
1
0
2
2
1
1
1
1
1
2
1
2
2
1
1
1
2
1
1
2
1
4
0
1
0
1
2
0
0
1
0
1
1
1
1
2
1
1
0
0
2
1
1
0
2
2
1
0
1
0
2
2
0
1
0
1
1
1
2
1
0
2
1
2
1
2
1
0
1
1
2
1
0
2
1
0
1
1
1
2
0
1
0
2
1
1
1
1
1
0
0
1
1
1
1
0
2
1
1
2
1
0
0
2
0
1
0
2
0
2
0
2
0
2
2
1
2
1
1
1
1
1
2
2
1
2
1
1
2
1
1
0
1
0
0
2
1
1
0
2
1
0
2
1
0
1
1
0
2
0
1
0
2
1
1
1
0
1
1
1
1
2
1
0
2
2
0
1
1
1
0
1
1
1
0
1
1
0
1
3
1
2
1
0
1
2
2
2
2
0
1
2
1
1
1
1
1
1
1
2
1
2
1
1
0
0
0
1
0
1
1
1
0
2
2
1
0
1
2
1
1
1
1
0
1
1
1
2
1
1
1
1
2
1
2
0
2
2
2
2
1
1
2
2
2
1
1
2
1
1
1
1
0
2
1
2
0
1
0
1
0
1
0
2
2
0
1
0
1
2
2
0
1
2
1
1
1
0
1
2
1
1
1
1
1
1
2
1
3
1
0
1
0
2
1
2
1
1
1
1
0
1
0
1
1
1
0
2
1
1
1
1
0
1
2
0
1
1
1
1
1
1
0
0
1
2
0
0
0
1
1
1
0
1
0
1
1
1
1
1
2
1
0
0
1
0
1
2
0
0
1
1
0
1
0
0
0
1
2
1
1
0
1
1
1
1
1
2
2
1
1
3
1
1
1
1
1
2
1
1
0
1
0
0
1
1
2
0
3
2
2
0
1
2
1
1
0
1
0
1
0
0
1
0
2
2
1
1
1
2
1
0
2
1
1
2
1
1
2
1
1
1
2
0
1
2
1
1
2
1
1
1
1
2
1
0
2
1
1
0
0
0
1
1
2
2
0
1
1
1
0
0
1
0
2
1
1
2
0
1
1
1
0
2
0
1
2
1
1
2
2
1
0
2
1
1
1
1
2
0
0
1
1
2
1
1
1
0
1
1
0
0
0
0
1
1
1
2
1
2
0
0
1
3
1
0
1
1
0
0
2
2
1
1
1
1
1
2
2
2
1
0
0
1
0
1
0
2
0
0
1
1
1
2
1
1
1
2
2
1
0
1
0
2
1
1
2
2
1
0
1
2
1
2
1
1
3
1
1
1
0
1
2
1
0
1
0
1
2
3
1
2
1
1
1
2
2
1
0
2
1
2
0
1
1
2
1
0
0
1
1
1
1
1
1
0
0
1
1
1
1
0
0
1
3
2
1
1
5
0
1
1
2
0
1
1
2
1
1
2
2
2
1
1
1
0
0
1
0
2
1
1
2
1
1
2
2
0
2
2
1
1
1
0
1
1
1
2
2
0
0
2
1
1
1
2
1
1
1
0
1
0
1
2
1
1
0
1
1
2
0
2
1
1
2
2
2
1
1
2
1
1
0
2
1
1
0
0
1
1
0
2
1
1
0
1
1
0
2
0
1
2
2
1
2
1
0
2
1
1
1
2
0
1
1
1
0
2
2
1
1
0
2
0
1
2
1
2
2
1
1
2
1
2
0
0
0
2
2
2
0
1
1
1
1
1
1
2
1
1
1
0
1
2
1
1
1
0
0
1
1
0
0
1
1
1
1
1
1
1
1
1
1
1
2
1
0
1
1
2
1
1
0
0
2
0
2
1
2
1
1
1
1
1
1
1
1
2
1
2
1
2
2
2
2
1
1
1
0
1
1
3
1
1
0
0
0
1
1
0
1
1
0
2
1
1
2
2
1
1
1
0
1
0
1
2
1
2
1
2
1
1
1
0
1
2
2
0
1
1
1
2
0
0
1
1
1
1
0
1
1
2
2
1
0
1
1
2
2
1
1
1
1
0
1
1
2
1
2
2
0
0
2
1
0
2
2
0
2
1
0
1
2
1
1
2
1
1
1
0
0
1
1
1
1
0
0
0
1
1
1
1
2
1
0
1
1
0
1
1
1
0
1
1
1
1
1
1
0
2
1
2
1
1
2
1
1
1
2
0
1
1
0
1
1
1
1
0
2
1
1
1
1
2
1
1
1
1
0
2
0
1
0
2
1
2
1
1
1
1
1
1
2
2
1
0
0
1
6
0
1
0
1
0
1
0
1
1
1
1
0
2
2
0
1
1
1
2
1
1
1
1
2
1
1
2
1
2
1
1
1
0
1
1
1
1
2
1
0
2
2
1
2
1
1
0
2
1
0
1
0
2
1
0
1
0
1
1
2
1
1
2
1
1
1
2
1
1
1
2
0
1
2
2
1
0
2
0
1
1
0
1
0
0
2
1
1
0
1
1
1
1
1
0
1
0
1
2
1
0
3
1
0
0
1
1
0
1
1
1
1
0
0
1
2
1
2
1
1
0
2
2
0
1
1
1
1
1
1
1
2
1
0
0
0
2
1
1
2
2
0
0
2
1
1
1
2
2
1
3
0
1
1
1
1
0
1
3
2
0
1
0
1
1
0
1
2
0
1
1
1
2
0
2
0
2
1
0
2
0
2
2
0
1
1
1
0
1
1
2
2
0
2
0
1
2
0
1
1
0
0
1
0
1
1
1
1
1
2
1
1
0
0
1
2
0
2
1
2
2
0
1
1
1
1
3
1
1
1
1
2
2
2
1
1
1
1
2
1
0
1
1
2
1
0
2
1
1
2
1
1
1
1
0
1
1
1
1
0
0
1
1
2
1
1
2
1
2
0
2
2
2
0
1
1
0
1
1
1
1
2
0
1
2
1
2
0
0
2
1
2
2
0
0
2
1
2
0
2
1
0
1
1
1
0
0
1
1
0
0
1
1
1
0
2
1
1
1
0
2
2
1
1
1
1
1
2
0
0
1
1
0
1
2
1
0
1
1
1
1
1
1
2
1
0
2
0
0
1
1
1
2
1
1
1
0
2
1
0
0
1
1
1
1
2
1
0
2
1
2
0
1
1
2
2
1
2
1
1
1
1
0
0
1
2
0
2
2
2
2
0
1
1
2
2
2
1
1
1
1
2
1
1
1
1
2
1
1
1
3
0
2
1
1
0
1
1
2
1
0
1
2
1
1
0
1
2
1
1
2
0
1
1
1
2
1
1
1
1
2
0
0
1
1
1
0
1
1
2
1
1
1
1
1
2
0
2
0
1
1
1
2
2
1
0
1
2
2
1
1
0
2
0
0
1
0
2
1
1
1
1
1
1
1
0
2
1
1
1
2
2
1
0
2
1
2
1
1
0
2
3
1
2
0
1
2
1
2
1
1
1
1
1
1
1
1
1
1
0
2
2
0
1
1
2
1
1
1
1
2
1
0
1
2
0
1
0
2
0
0
2
2
1
1
1
0
2
2
1
2
1
2
1
1
1
2
1
2
1
1
0
2
0
1
2
2
2
2
1
1
1
0
0
1
1
1
1
0
2
2
1
1
0
1
2
0
1
1
1
1
1
1
0
1
0
2
1
1
0
1
0
1
1
1
0
2
2
1
2
0
1
1
2
0
2
0
2
2
1
2
1
1
1
1
4
1
1
1
2
2
1
0
3
1
0
2
1
2
0
1
1
0
1
1
2
0
1
1
1
1
0
1
2
0
0
2
2
0
1
1
0
1
0
0
0
2
1
2
1
2
1
1
1
2
1
1
1
1
1
3
1
1
0
1
1
2
2
0
0
2
0
1
2
1
1
2
1
2
1
1
0
2
1
0
0
0
0
1
0
1
1
0
0
1
2
1
1
1
2
1
1
1
0
2
2
1
1
0
1
1
0
1
2
1
1
0
1
0
1
1
1
2
1
0
2
2
1
2
1
1
2
0
2
1
0
1
0
0
0
2
1
0
0
1
1
1
1
1
0
2
1
2
2
1
1
0
1
1
2
0
1
1
1
0
1
0
1
2
1
0
1
0
1
0
0
1
0
2
1
1
2
1
0
2
1
2
0
1
1
2
1
1
1
0
1
2
2
2
2
0
0
0
2
2
1
0
1
0
1
1
0
0
2
1
1
1
1
0
1
1
0
2
1
2
2
1
2
0
2
1
2
2
2
0
1
1
1
1
1
1
2
2
1
0
0
0
0
1
0
1
1
1
0
1
0
0
0
1
1
0
0
1
1
1
1
1
1
0
0
2
2
1
1
0
0
1
1
2
0
1
0
1
0
1
1
1
2
2
1
1
0
0
1
1
1
1
1
1
1
0
1
2
1
2
2
2
1
1
0
2
2
1
0
0
1
1
0
1
2
1
1
1
1
2
1
1
1
2
1
2
2
2
1
1
1
0
1
2
1
2
1
0
2
1
2
0
2
1
0
1
1
1
1
2
1
1
0
1
1
1
1
0
1
2
1
1
1
2
1
1
0
1
1
0
0
1
1
0
0
1
1
0
1
2
0
1
0
1
1
1
0
0
1
1
2
1
0
0
2
2
1
0
0
2
1
2
1
1
2
1
1
0
0
1
1
1
1
1
1
2
2
1
0
1
1
1
2
2
1
2
2
2
0
2
2
2
1
1
0
1
2
1
2
1
1
1
0
2
1
0
2
1
0
1
0
1
2
1
1
1
2
1
2
0
0
0
0
1
1
2
1
2
0
2
1
1
1
1
0
1
1
2
2
1
0
1
1
1
6
1
0
1
2
1
1
1
0
0
2
0
1
1
1
1
1
1
0
2
1
1
2
2
2
1
1
1
1
0
1
0
2
0
2
1
1
1
0
1
1
1
1
1
2
0
1
2
1
1
0
1
1
1
1
1
1
1
2
2
0
0
0
0
1
1
2
2
2
1
1
0
2
1
1
1
0
1
1
2
0
1
1
1
0
0
0
1
0
1
2
1
0
1
1
1
0
1
1
1
1
2
1
1
0
0
0
1
1
1
1
1
1
1
1
1
1
0
1
0
1
2
1
0
1
0
2
1
1
2
2
0
1
1
1
1
0
1
1
1
1
1
0
0
0
1
2
2
1
0
2
1
1
2
0
0
1
1
1
1
1
2
2
1
1
0
1
0
1
0
1
1
2
1
1
1
1
0
2
1
0
1
2
1
5
0
1
1
0
2
2
1
1
1
1
1
1
1
0
1
2
1
2
1
2
0
2
1
1
1
2
0
0
1
1
1
1
1
2
1
1
0
1
1
0
1
1
1
2
2
0
0
0
1
2
1
2
1
1
1
1
2
2
0
0
1
2
1
1
1
1
1
1
1
1
1
2
0
1
1
2
1
1
1
1
2
0
2
1
2
1
2
0
1
1
2
1
1
1
1
1
1
1
0
0
1
1
0
1
1
0
2
1
1
1
1
1
0
1
2
2
2
2
1
0
0
0
1
1
2
1
1
1
0
1
1
1
1
1
2
1
1
0
2
1
1
0
1
0
1
1
1
1
0
0
1
1
0
1
0
2
2
2
1
0
0
1
0
2
1
2
1
0
0
1
1
1
0
2
1
2
1
1
1
1
2
1
1
1
1
2
1
0
2
0
1
2
1
2
0
1
1
0
1
3
0
1
0
2
0
1
1
1
2
1
1
2
2
1
1
2
1
2
1
1
2
0
0
1
1
2
0
0
1
1
1
1
1
3
1
1
1
1
0
2
2
1
1
0
0
1
2
0
0
1
2
3
0
2
1
1
1
1
2
1
2
1
2
1
1
1
1
1
1
0
2
1
1
2
1
2
1
1
0
2
0
1
0
1
0
1
1
1
1
0
0
3
1
0
2
1
0
2
0
2
1
0
1
1
1
1
0
2
1
0
1
1
2
0
0
0
0
1
1
1
1
2
0
2
1
0
2
1
1
2
1
1
0
1
2
1
1
1
0
0
0
2
0
2
2
1
1
1
0
1
0
2
0
1
1
0
2
2
2
1
2
1
0
2
2
0
0
0
0
1
2
1
0
0
0
1
1
0
1
1
0
1
2
1
2
1
0
1
1
2
2
1
1
1
1
1
1
1
1
0
1
1
1
2
0
2
0
1
0
1
1
1
2
1
1
1
1
1
2
0
1
0
1
0
0
1
2
1
1
1
1
1
1
2
0
1
0
1
1
1
0
2
1
1
1
2
1
0
1
2
1
1
1
1
2
1
1
2
1
2
1
1
1
1
0
1
0
2
4
1
1
0
1
2
2
0
1
1
1
1
1
0
1
0
1
0
1
1
1
2
1
0
0
1
1
0
2
1
2
1
0
1
1
0
1
0
0
1
1
1
1
0
1
1
1
0
0
1
1
2
1
0
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
0
1
0
1
2
1
2
2
1
2
0
1
2
1
2
0
1
2
1
0
1
2
2
1
2
2
2
2
2
0
2
1
2
2
3
0
0
1
2
0
0
0
0
0
1
1
2
1
1
1
2
1
0
3
1
0
1
3
5
2
1
1
1
1
0
1
0
2
1
1
1
2
1
2
1
1
0
0
0
2
1
3
1
1
2
0
1
2
1
1
1
0
2
1
1
1
0
1
1
0
1
0
2
2
0
1
1
1
5
0
2
1
0
0
1
1
1
1
2
1
1
1
0
1
2
1
2
1
2
0
0
1
1
2
0
0
0
3
1
2
1
2
1
2
1
2
1
1
0
1
0
3
1
1
1
0
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
0
0
1
1
1
1
2
1
2
1
0
2
1
1
2
0
0
2
1
2
2
0
1
2
0
0
0
2
2
2
1
1
1
1
1
1
1
1
0
0
0
0
1
1
1
2
1
1
2
1
2
1
0
1
2
0
1
2
2
6
1
1
1
2
2
1
1
1
1
2
1
0
2
1
1
2
2
1
1
0
0
1
1
1
1
1
0
2
0
0
2
0
3
1
1
1
0
0
1
0
0
1
2
0
0
0
0
2
1
0
1
1
3
2
0
2
2
1
0
2
1
1
1
2
1
1
2
2
1
1
1
0
0
2
0
0
0
0
2
1
2
2
2
3
1
4
1
0
2
1
1
1
0
0
2
1
1
2
1
2
1
1
2
0
1
0
1
2
1
2
1
0
0
0
1
1
2
1
2
1
1
1
2
0
1
1
1
1
1
1
0
1
1
1
1
1
3
1
1
1
2
1
1
1
1
0
2
1
1
1
1
3
0
0
1
1
2
1
1
1
2
1
2
1
0
1
4
1
1
1
1
0
1
0
2
0
1
1
1
2
2
1
1
2
2
1
1
1
2
1
1
1
1
1
2
1
1
0
1
1
1
4
1
0
2
1
2
1
1
1
2
2
2
0
2
1
0
1
0
2
1
1
2
0
1
2
2
1
2
1
2
2
1
1
2
1
1
2
2
2
1
2
1
1
1
1
0
1
1
2
0
1
0
0
0
1
1
1
1
0
1
2
1
1
1
1
1
0
0
1
0
0
1
0
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
1
1
1
1
0
0
1
1
1
1
1
1
1
1
2
0
2
1
1
1
1
1
2
0
1
0
2
1
1
0
1
2
2
0
2
1
2
1
1
0
1
1
1
1
0
2
1
1
1
1
0
1
0
2
2
1
1
0
1
1
1
1
1
2
1
2
1
2
1
1
1
3
1
2
1
1
2
1
0
2
1
1
2
2
1
2
2
1
0
1
2
2
0
1
0
1
1
0
1
2
1
0
2
0
1
1
1
1
2
1
2
1
1
1
1
1
0
2
1
1
0
1
1
1
1
1
0
1
2
1
0
1
4
1
1
0
0
1
0
0
1
0
1
0
1
2
0
1
2
2
0
1
1
0
0
1
2
2
0
0
1
0
1
0
1
1
2
0
1
1
0
1
1
1
1
1
2
1
1
1
2
0
1
1
1
2
0
1
1
1
1
1
2
1
2
1
1
1
1
0
1
1
0
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
0
1
1
1
1
1
2
0
0
3
1
1
1
0
1
1
0
1
1
0
0
1
1
0
1
1
0
1
0
1
1
1
0
0
0
2
1
1
0
1
1
0
1
0
0
1
2
1
1
2
1
1
0
1
2
1
0
1
0
2
0
1
0
0
0
1
1
0
1
1
1
2
2
2
0
1
0
1
0
1
1
2
1
1
2
0
1
0
1
1
1
0
0
2
2
2
1
0
1
1
2
1
2
1
0
1
1
1
0
0
1
0
2
1
0
0
2
1
1
1
1
1
1
0
1
1
0
1
0
2
2
1
0
1
2
0
0
2
1
0
2
1
1
1
1
0
1
0
1
2
1
1
1
1
1
1
0
1
1
1
0
0
1
2
3
1
1
2
1
1
1
1
1
0
1
0
0
1
1
0
1
1
1
0
1
1
2
1
2
2
2
2
1
0
0
0
1
1
1
1
1
2
0
1
3
0
1
1
3
0
1
1
1
1
1
0
1
0
0
2
0
1
0
1
0
2
0
1
0
0
1
1
0
1
0
1
1
2
2
1
1
1
1
1
2
1
1
1
2
0
1
2
2
0
2
2
2
0
1
0
1
1
1
0
2
1
2
1
0
1
1
0
0
1
1
0
2
2
2
2
0
1
1
3
0
2
0
0
0
0
1
2
2
1
1
1
2
1
1
1
2
0
0
1
1
0
1
1
1
1
0
1
1
0
0
0
1
1
0
0
0
2
1
1
2
1
1
1
1
1
0
0
2
1
1
1
3
1
1
0
0
1
2
1
1
1
2
2
2
2
0
1
0
2
1
1
2
1
2
0
0
1
2
1
1
2
1
1
0
1
2
1
1
1
1
1
1
1
3
1
2
1
1
1
2
1
0
1
2
1
0
2
2
0
2
1
1
2
1
0
2
0
1
0
0
2
0
1
2
1
1
2
1
1
2
1
1
0
2
2
0
2
2
2
2
0
1
1
1
1
1
2
1
2
1
0
1
1
2
0
1
1
0
2
2
0
0
2
1
2
2
1
1
1
1
0
2
0
0
1
0
2
0
2
1
2
1
0
1
0
1
1
0
1
2
2
1
0
0
0
1
2
2
0
0
1
1
1
0
0
2
1
2
0
1
1
1
0
1
2
2
2
1
1
0
1
1
1
2
0
0
1
0
2
0
0
1
2
1
2
1
1
2
2
1
2
1
1
1
1
1
2
1
1
2
0
1
1
2
1
0
2
2
1
1
0
1
1
1
0
1
0
2
2
1
0
1
1
0
0
2
0
1
1
1
1
0
1
1
0
2
1
2
0
1
1
1
2
1
1
1
1
2
0
1
2
2
1
0
1
0
0
1
1
2
1
1
1
2
2
1
0
0
1
1
1
3
1
1
1
1
2
2
1
0
0
1
1
1
2
1
1
1
1
1
1
2
1
1
2
0
1
0
1
1
1
0
2
1
2
1
2
1
1
1
0
2
2
1
2
0
0
1
0
1
1
2
2
1
0
1
3
0
1
2
1
2
1
1
1
1
0
1
2
2
0
0
0
1
1
1
1
1
3
1
1
1
1
0
0
1
1
1
1
1
1
1
1
2
1
0
1
1
2
2
0
2
1
2
1
2
1
1
2
2
1
1
0
1
1
0
1
1
0
1
1
1
2
0
2
2
1
1
1
1
1
2
1
1
1
0
0
2
2
0
1
1
0
1
1
1
2
2
2
0
0
0
1
0
0
2
1
0
0
2
1
0
1
0
1
2
1
0
0
0
1
1
2
1
0
1
1
0
1
1
2
1
1
1
1
0
2
0
1
1
1
1
2
1
1
1
2
1
1
2
3
0
0
0
1
1
1
2
2
1
1
1
0
0
1
0
0
1
1
1
1
0
1
2
0
0
0
1
1
1
2
1
1
0
1
2
1
1
1
1
1
3
1
1
2
0
0
2
0
1
1
2
1
1
2
2
2
1
1
1
2
1
2
1
1
1
1
2
1
1
2
2
2
0
1
2
1
2
1
1
0
0
0
1
2
1
0
1
2
2
1
0
1
0
1
1
1
1
1
2
2
1
2
1
0
1
1
2
1
2
1
1
1
0
0
2
1
1
0
1
1
1
1
0
1
1
1
0
1
0
2
1
1
2
0
1
0
0
2
1
1
1
2
2
0
2
2
0
1
2
1
2
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
2
2
2
2
1
1
1
2
0
0
0
0
0
1
0
2
1
1
1
1
0
2
0
1
2
1
0
2
1
1
1
1
0
1
0
1
0
0
1
0
2
0
1
2
1
0
1
1
0
1
1
2
3
1
1
1
0
1
1
1
1
0
1
3
0
1
2
0
0
1
2
1
1
0
1
2
3
1
2
1
1
1
1
1
1
1
0
0
2
0
0
2
1
1
1
1
1
1
1
1
2
0
2
1
0
0
0
0
1
0
1
1
0
2
1
2
1
1
1
1
0
1
1
1
2
1
0
0
3
1
2
1
1
1
1
0
1
2
0
1
1
1
0
1
1
1
1
0
0
1
2
1
1
1
2
1
1
1
1
0
2
1
0
1
0
0
1
1
0
1
0
0
1
1
0
0
2
2
0
1
1
1
2
2
1
2
1
0
1
1
1
2
1
1
1
2
1
0
2
1
1
2
1
0
1
1
1
2
1
1
1
0
2
0
1
1
0
0
1
0
1
2
1
2
1
1
1
0
2
2
1
2
1
1
2
0
2
2
2
2
1
0
1
2
2
2
1
0
1
2
1
2
2
2
1
2
1
1
1
0
0
0
2
0
1
1
1
1
1
0
1
1
1
0
1
1
2
1
1
0
1
1
1
1
4
1
0
1
1
1
1
0
1
2
1
1
2
1
0
1
0
2
1
1
0
1
2
0
0
1
1
1
1
2
2
1
0
1
1
0
1
2
1
1
0
2
1
2
0
1
1
2
3
1
2
1
0
0
1
0
1
2
1
2
0
1
2
1
1
1
1
0
1
0
1
0
1
1
1
2
2
2
1
2
1
0
0
2
0
0
0
1
0
1
1
0
1
1
1
1
1
1
1
2
1
1
0
1
1
2
2
1
2
0
3
1
1
2
1
1
2
1
1
0
0
1
2
1
2
0
2
1
2
2
1
1
1
1
1
1
1
1
1
2
1
0
1
2
1
1
2
1
1
1
2
0
0
1
0
1
1
1
1
1
2
1
0
1
1
1
1
2
1
0
0
1
1
1
2
2
2
1
1
0
1
0
1
1
1
1
0
1
1
0
0
2
1
1
2
1
1
1
2
1
2
0
2
0
1
1
0
2
0
1
1
1
1
1
0
1
1
2
1
1
1
1
0
1
1
0
1
0
1
1
1
2
0
2
1
0
0
1
1
2
1
1
1
1
1
2
1
2
0
2
1
0
1
3
1
1
2
1
1
2
2
2
1
1
2
1
2
1
0
5
1
1
1
2
1
0
1
1
2
2
0
1
1
1
1
1
0
0
0
1
0
0
2
2
1
2
1
0
1
1
2
0
1
2
0
1
1
2
1
0
1
1
1
1
0
2
0
0
0
0
2
2
1
1
2
1
0
2
0
1
1
1
1
2
1
2
1
0
1
1
2
1
1
1
1
0
1
1
1
1
2
1
1
1
1
2
6
1
1
0
1
1
1
1
0
2
1
1
2
2
1
1
1
0
1
1
0
1
1
1
2
1
1
0
0
1
0
0
1
1
1
0
2
1
2
1
1
0
1
0
1
2
0
1
1
1
1
1
1
1
1
1
1
1
1
2
0
3
1
1
1
1
2
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
3
0
2
1
0
1
2
1
1
1
1
1
0
4
2
0
1
2
0
2
0
0
1
2
2
1
1
1
0
1
1
1
1
0
2
1
0
0
2
2
2
1
2
1
1
1
0
1
1
1
1
2
0
1
1
0
1
1
2
0
1
1
1
1
1
0
2
1
1
2
1
1
1
1
0
2
1
1
1
1
1
2
1
1
2
2
1
0
0
1
1
1
1
1
1
2
0
1
0
0
1
1
0
1
2
1
0
1
2
0
1
1
0
2
0
1
1
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
2
0
0
0
2
0
1
0
0
1
1
1
0
0
1
1
1
0
0
1
4
0
2
0
2
1
0
0
1
1
0
2
0
3
1
1
1
2
1
1
2
1
0
0
2
2
0
0
1
0
0
0
1
1
1
1
2
1
1
0
1
2
1
1
1
1
2
0
2
2
2
2
1
0
0
1
1
1
1
1
1
2
1
0
0
1
1
1
1
1
1
2
1
1
1
2
2
1
2
0
0
1
2
1
1
0
1
1
2
1
0
1
1
2
1
0
1
1
2
1
0
0
2
1
1
2
0
1
1
2
4
1
2
1
1
1
2
1
1
1
3
1
1
1
1
1
2
0
1
2
0
1
1
2
1
2
1
4
1
1
1
0
1
1
1
1
0
1
0
1
1
3
2
2
5
0
1
1
1
1
1
0
2
2
2
2
0
1
2
0
2
1
0
1
0
0
1
1
0
0
1
1
2
0
0
2
2
0
3
0
1
0
1
0
1
1
0
1
0
1
0
1
1
1
2
1
1
1
2
1
2
2
2
0
2
2
1
1
1
1
2
1
1
1
0
1
0
1
0
2
2
1
0
0
1
1
2
1
1
2
1
1
2
1
1
1
0
1
1
1
2
1
0
1
1
0
0
1
1
1
1
0
2
1
0
0
1
1
1
1
2
1
1
1
1
1
0
1
1
0
2
2
1
1
1
2
2
1
2
1
1
1
2
1
0
0
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
0
1
1
1
0
1
1
1
2
1
1
2
1
2
1
1
1
2
2
2
1
2
2
1
0
0
2
0
2
0
0
2
1
1
1
2
1
2
1
1
1
0
1
0
1
1
1
0
1
1
1
1
0
1
1
2
1
1
1
0
1
4
1
1
2
2
1
1
0
1
0
1
1
1
2
1
1
2
2
1
2
1
1
1
1
1
1
1
0
1
1
1
1
0
0
0
1
1
2
2
1
1
2
3
0
1
1
1
2
1
2
1
2
2
1
1
1
0
1
2
1
2
1
1
2
2
0
1
2
2
1
0
1
1
0
0
1
2
2
1
1
2
0
2
1
0
1
1
1
1
1
2
2
0
1
1
0
2
1
2
1
1
0
1
1
2
1
1
1
1
1
0
1
1
1
2
1
1
2
1
0
1
0
1
0
1
1
0
1
1
2
2
1
2
1
0
2
2
1
0
2
1
0
1
1
0
2
2
2
1
0
1
1
1
2
1
1
0
1
2
0
2
1
1
2
0
1
1
1
1
1
0
0
1
2
1
1
0
1
1
0
0
1
1
0
2
0
3
2
2
1
1
1
1
2
1
0
1
0
1
2
1
2
1
2
0
1
1
0
1
1
1
1
1
2
2
1
0
1
2
0
1
0
0
0
1
1
1
1
1
1
2
0
2
2
1
1
2
1
2
1
0
2
2
0
1
2
0
2
0
1
1
1
1
1
1
1
1
1
1
2
2
2
2
1
1
2
2
1
1
0
2
1
1
0
1
1
1
1
0
1
1
1
1
1
2
0
0
1
1
0
2
1
1
1
2
0
1
2
1
1
0
1
0
2
0
0
1
0
0
1
1
2
0
1
1
0
0
1
1
1
0
2
1
1
1
1
2
2
0
1
2
1
2
1
1
0
1
0
0
1
1
1
0
1
1
1
2
0
2
1
0
1
2
1
1
2
2
2
2
1
1
1
1
1
1
2
1
2
1
0
1
1
0
0
0
1
0
1
2
2
2
1
2
0
1
1
1
2
1
1
0
0
2
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
0
1
1
1
1
1
2
1
1
2
2
1
1
1
0
2
2
2
1
0
1
1
2
1
2
1
2
1
1
2
1
2
0
1
1
1
2
0
2
2
1
2
1
3
2
1
1
2
0
1
1
2
0
1
1
1
2
1
1
2
1
0
0
1
1
1
0
1
1
1
1
1
0
1
1
2
2
0
1
2
0
1
1
1
2
2
1
1
2
1
1
2
2
1
0
1
1
0
1
2
1
1
2
0
2
1
1
0
1
0
2
0
2
2
2
0
1
2
1
1
1
1
1
2
1
1
0
1
1
0
2
1
0
1
1
1
1
1
2
0
1
1
1
1
1
1
1
2
0
1
0
1
1
1
2
0
0
1
3
1
1
1
1
1
2
2
1
1
0
1
1
2
1
2
1
1
1
1
1
0
0
1
2
1
1
0
2
1
1
1
1
1
1
1
2
1
2
1
1
0
1
1
0
0
1
0
1
1
1
1
1
1
1
1
2
1
2
2
1
1
2
1
1
4
0
0
1
2
1
0
1
2
0
1
2
1
0
1
0
1
1
1
1
0
1
1
2
0
1
0
0
1
1
1
1
0
1
2
0
1
2
1
0
1
1
1
1
1
0
1
0
1
2
1
1
1
1
1
2
1
0
0
2
0
1
2
1
2
1
1
1
1
1
0
1
1
1
0
0
1
2
2
1
3
2
0
1
1
1
1
0
2
1
1
1
1
0
2
2
1
1
1
1
0
2
1
1
0
0
1
1
0
0
1
0
2
2
2
2
2
1
2
1
0
1
0
2
1
1
1
1
1
1
0
1
2
1
1
0
1
0
0
1
2
1
0
1
1
1
2
2
0
1
1
1
2
1
1
2
1
2
0
3
1
1
1
1
2
1
0
0
2
0
0
1
1
1
1
1
0
0
2
1
0
1
2
1
0
2
2
1
1
3
1
0
1
1
1
0
1
1
0
2
1
1
1
1
1
1
1
0
0
1
0
1
2
2
2
1
0
1
0
1
1
1
0
1
1
0
0
0
2
2
1
0
0
1
2
0
1
0
1
4
1
2
2
1
1
2
1
1
2
1
0
1
1
2
0
0
1
1
1
2
2
1
0
0
1
1
1
1
1
1
0
1
0
1
0
0
1
1
0
0
1
1
1
2
1
0
1
2
1
1
0
2
2
1
0
1
1
1
1
0
1
1
2
2
2
2
1
1
2
1
1
2
0
1
0
2
0
0
2
0
1
2
2
0
0
1
0
2
0
0
1
0
0
0
3
1
2
1
2
0
0
1
1
1
1
1
0
0
1
0
2
1
2
1
1
1
1
1
2
1
1
1
1
0
2
1
2
1
1
1
0
1
1
2
1
1
2
2
0
2
1
1
1
1
0
0
1
1
1
0
2
2
2
0
1
1
1
1
1
1
0
0
0
1
2
0
1
2
1
0
2
2
2
0
2
0
1
1
1
1
0
2
0
0
0
1
1
2
0
2
0
1
1
1
1
1
4
1
3
1
1
1
1
1
2
1
2
0
0
0
1
0
1
1
1
2
1
1
1
1
1
1
0
2
1
1
1
1
1
1
0
0
2
4
2
1
1
2
1
0
1
0
2
1
1
1
1
2
1
1
1
0
1
0
0
1
1
1
0
1
1
1
1
1
0
1
2
1
2
1
0
2
0
1
1
1
2
1
2
1
0
1
1
0
1
1
0
2
0
2
1
1
0
0
1
1
1
1
0
2
0
0
2
2
1
1
1
0
2
1
2
2
1
2
1
1
1
0
2
2
0
1
2
1
0
1
1
2
1
1
1
2
0
1
1
1
1
0
1
2
0
2
0
0
0
0
1
0
1
1
1
1
0
1
1
0
2
1
1
0
2
2
2
0
2
1
1
0
2
0
1
2
1
0
1
0
1
1
0
0
0
1
1
0
1
1
2
1
0
1
1
1
0
1
1
2
1
1
0
0
1
1
1
1
1
1
1
2
1
1
0
1
1
1
1
0
0
0
2
2
1
1
2
1
2
2
1
3
1
1
0
0
1
0
1
1
2
1
1
1
1
1
1
2
2
2
0
1
0
0
1
0
1
2
1
0
1
1
2
1
2
1
0
1
1
0
1
1
1
2
0
1
2
0
1
1
1
1
1
1
1
2
1
0
1
0
1
1
1
1
1
1
0
1
1
1
1
2
0
2
0
2
1
1
0
1
1
2
1
1
1
0
1
2
0
2
1
1
0
1
1
1
1
2
2
1
1
2
1
2
2
1
2
1
0
1
2
2
1
1
0
1
0
2
2
1
0
2
0
1
1
0
1
1
1
2
1
1
2
1
1
1
1
2
2
1
0
0
0
0
1
0
1
1
1
1
1
0
2
0
1
1
1
0
0
1
0
2
2
1
1
1
1
0
3
1
2
1
2
1
1
2
1
1
1
0
1
1
0
2
1
1
1
1
1
1
0
1
2
2
0
1
2
0
1
1
3
1
0
2
1
0
1
0
0
0
0
1
1
0
1
0
2
1
1
1
1
2
1
1
2
1
1
2
1
0
1
1
1
0
1
1
2
1
1
2
0
1
0
1
1
1
1
1
1
1
2
0
1
1
0
2
2
1
1
0
1
1
1
1
2
1
0
0
1
1
1
0
0
0
1
3
1
0
1
0
1
2
1
0
1
1
2
1
0
1
0
0
2
0
1
2
1
2
1
1
0
1
1
2
2
1
1
1
1
1
1
0
0
2
0
0
0
0
2
1
2
0
1
1
1
1
1
1
1
2
0
2
0
1
1
1
0
1
1
1
1
1
1
0
1
1
1
1
1
1
2
1
1
1
0
2
2
2
2
2
1
2
1
2
2
1
2
2
1
0
1
0
1
1
0
1
0
1
1
2
0
1
2
1
1
2
1
1
0
0
0
1
2
1
1
2
1
2
2
1
0
0
1
1
1
0
2
1
1
1
1
0
1
2
1
1
0
0
2
1
1
2
2
1
2
1
2
1
1
0
1
3
1
0
1
1
1
0
0
2
2
2
1
2
0
1
0
1
2
0
0
1
2
1
1
2
1
1
1
0
0
1
1
1
2
2
1
0
2
1
2
0
1
0
1
1
1
1
0
0
2
0
1
1
1
1
1
0
1
0
1
0
2
1
1
1
1
1
2
1
2
2
1
1
0
2
1
1
1
1
1
0
1
2
1
1
2
2
2
1
1
0
2
1
0
2
2
1
1
1
1
1
1
1
1
2
1
2
2
1
1
1
0
1
0
1
1
1
0
1
1
1
1
1
0
1
0
1
1
0
2
1
0
1
2
1
0
1
1
0
0
1
0
1
1
2
1
0
1
2
1
0
2
1
1
0
2
0
1
1
1
1
1
1
1
1
1
0
1
1
1
2
0
0
1
1
1
1
2
1
2
1
1
2
1
1
1
1
2
1
1
1
2
2
0
1
1
3
1
1
1
1
1
1
1
1
1
2
0
0
1
1
2
2
0
1
0
1
1
1
2
5
1
1
1
1
1
0
1
0
0
1
1
1
2
0
1
2
1
1
1
1
1
1
1
0
1
1
2
2
2
1
2
1
2
1
1
0
2
1
1
1
0
0
1
0
0
0
2
2
1
0
1
0
1
1
4
2
1
1
0
1
0
1
0
1
1
0
2
2
1
1
1
1
1
1
0
0
0
0
0
2
1
1
1
1
1
2
2
1
2
0
1
0
2
0
1
0
1
1
0
1
2
0
2
1
2
0
1
1
1
2
1
1
1
1
1
1
1
0
1
1
1
1
2
2
1
0
1
1
2
1
2
1
0
0
0
1
1
2
0
0
1
2
0
2
1
1
0
0
1
1
0
0
1
1
0
1
2
1
2
2
1
0
1
0
1
1
1
1
0
1
0
2
1
2
1
1
2
0
1
2
2
2
0
1
1
1
2
0
2
0
2
2
1
1
1
0
1
1
1
1
2
0
1
1
2
0
1
1
0
0
1
0
1
2
1
2
2
2
1
1
1
3
0
2
0
1
1
3
1
2
1
2
0
1
1
1
1
1
2
1
1
1
2
1
2
2
1
1
1
0
1
2
1
0
0
0
1
1
1
0
2
2
1
1
1
1
0
1
1
1
0
0
1
1
0
1
2
1
1
1
2
0
1
2
2
2
1
0
1
1
1
2
0
1
0
1
2
1
1
1
1
1
0
2
0
1
1
2
1
0
1
1
1
0
0
2
1
1
1
1
1
0
0
1
0
1
0
0
1
1
1
2
1
0
1
1
1
0
2
1
2
1
0
1
1
1
1
2
2
1
1
0
1
1
1
1
0
1
1
1
2
0
1
0
0
1
1
1
1
0
1
1
2
2
1
1
0
1
2
1
2
0
0
1
0
1
0
1
1
1
0
1
2
1
1
1
1
2
1
1
2
1
1
1
2
0
1
2
1
0
1
1
1
1
0
1
2
0
1
2
2
1
0
0
1
0
2
0
2
1
1
0
1
2
1
1
1
1
1
2
1
1
0
0
1
0
1
1
2
2
1
2
1
0
0
2
1
2
0
1
2
1
2
0
1
1
0
0
1
2
2
0
1
0
1
1
1
1
1
1
2
0
1
1
1
2
1
2
2
0
1
0
2
0
0
0
1
2
2
1
1
0
0
0
1
1
1
1
1
0
1
0
2
2
1
1
1
2
1
2
2
0
0
1
1
1
1
1
2
1
2
2
2
1
2
1
1
2
2
1
0
1
2
1
1
1
1
1
1
1
1
1
1
1
2
2
3
1
0
1
0
1
1
2
1
2
1
2
2
1
1
1
1
0
2
1
3
2
1
1
1
1
1
2
2
1
1
0
2
0
2
1
1
0
1
1
1
2
1
1
3
0
1
1
2
2
2
2
1
1
1
1
2
1
1
2
3
1
1
0
1
1
2
0
1
0
0
1
0
1
0
1
1
1
1
1
1
2
0
1
2
1
0
0
2
1
2
1
0
1
1
0
3
0
2
0
2
2
0
1
1
1
1
1
1
0
0
1
1
2
1
4
1
1
2
0
1
1
1
1
0
1
2
1
1
1
2
0
0
2
1
2
1
1
1
1
0
1
2
1
1
1
1
0
1
1
0
1
0
2
1
1
0
1
1
1
1
1
0
2
1
0
0
1
1
1
1
2
2
1
0
0
1
1
1
1
2
0
2
2
0
1
0
1
1
0
2
2
1
2
0
2
2
1
7
0
1
0
2
1
1
1
1
1
0
1
0
0
1
1
2
1
1
1
1
0
1
0
1
1
2
2
1
0
1
0
2
1
2
1
1
1
1
1
2
0
2
1
0
1
1
0
1
0
2
0
1
0
1
2
2
1
1
2
2
2
1
1
1
1
0
1
1
1
2
1
1
1
2
1
1
2
1
1
0
0
1
2
2
1
0
1
1
2
1
0
0
1
0
1
1
0
0
1
0
1
0
1
1
0
0
2
1
1
1
1
2
1
0
1
1
1
3
2
1
0
2
1
1
2
1
1
0
1
1
0
0
1
0
0
0
2
1
1
0
0
1
1
0
1
1
2
2
1
1
0
2
0
2
2
2
0
1
2
2
0
1
1
1
1
1
1
1
1
2
0
1
1
2
0
0
1
0
2
1
0
0
1
1
3
0
2
0
0
1
0
1
1
1
1
1
1
2
1
1
1
0
1
0
1
0
0
1
1
1
1
1
1
1
1
1
1
0
1
0
1
0
1
0
2
1
1
1
2
1
0
1
0
0
2
1
0
1
2
1
2
1
1
2
2
1
2
3
2
1
0
1
0
2
1
2
1
2
0
1
1
2
1
0
1
1
1
2
1
2
1
1
2
1
1
0
1
1
0
1
1
0
1
2
0
0
1
1
1
0
2
0
0
1
1
1
1
2
2
1
1
1
1
1
1
1
1
0
0
1
3
1
0
2
1
0
0
1
2
1
0
2
1
1
1
1
1
1
3
1
1
0
2
1
2
1
0
1
2
2
2
0
1
1
0
1
1
1
0
1
1
0
1
1
1
1
1
1
2
2
0
0
2
0
1
1
1
1
2
1
2
1
0
0
2
0
1
1
1
0
2
0
1
0
1
1
0
1
0
1
0
1
1
2
2
0
2
0
2
1
0
1
2
0
1
2
0
1
1
1
1
0
2
0
2
1
2
1
0
0
1
2
1
2
1
1
1
0
1
1
0
1
2
1
1
2
1
0
0
1
2
1
1
1
1
2
1
1
1
1
0
1
1
2
1
2
0
1
1
0
1
2
0
1
0
1
0
1
1
1
1
2
2
1
1
1
2
2
1
0
2
0
1
1
1
2
1
1
1
1
2
1
2
2
2
2
1
2
0
1
1
0
2
0
1
1
1
2
0
0
0
0
0
0
1
1
2
2
0
1
1
1
1
1
1
1
1
0
0
0
1
0
0
1
1
1
1
1
1
2
1
1
2
0
2
2
2
0
1
1
1
2
0
1
1
1
2
1
0
2
1
2
2
2
0
2
2
0
1
0
1
2
1
1
2
0
2
1
0
2
2
1
1
1
1
2
1
0
2
1
0
1
1
2
0
1
1
1
1
1
2
1
0
1
1
1
1
1
1
2
0
1
0
1
1
2
1
1
2
1
1
0
2
0
0
0
0
1
1
1
0
1
1
1
1
1
1
2
2
1
2
0
1
0
1
1
2
1
0
0
1
2
1
1
1
1
0
0
2
1
1
2
2
2
1
1
0
1
2
1
1
2
1
2
1
2
2
1
0
1
0
1
1
0
0
1
0
1
1
1
1
1
1
0
1
2
1
2
2
0
1
1
2
2
0
1
0
2
2
1
0
0
2
0
1
1
2
1
1
0
0
1
1
2
1
1
0
1
0
3
1
1
0
0
1
1
1
1
2
1
0
1
1
0
1
1
1
1
2
1
0
1
0
0
1
1
1
2
2
1
1
0
1
1
1
1
1
1
0
2
1
1
1
1
2
1
2
2
2
1
0
1
0
0
1
0
2
1
0
1
0
2
1
2
0
1
2
1
1
1
1
2
0
1
1
0
1
1
2
1
1
0
2
1
0
1
0
0
1
1
1
1
0
2
0
2
1
1
1
0
2
1
1
1
0
2
2
1
1
2
1
1
1
1
1
0
0
1
0
1
2
1
1
2
2
1
1
0
0
0
1
1
1
2
1
0
0
2
0
1
0
1
0
0
1
2
1
1
1
1
1
2
2
1
0
1
1
1
1
1
0
0
1
0
2
1
0
1
1
2
1
0
1
2
0
0
0
1
1
1
1
1
1
1
1
0
1
2
1
1
1
1
0
1
1
1
2
1
1
1
1
1
2
1
2
1
0
2
2
1
0
1
0
1
1
0
0
1
0
1
2
2
1
0
1
1
0
2
0
1
0
0
1
1
1
0
2
1
1
1
1
2
1
1
1
0
0
1
1
1
2
1
2
1
2
1
2
2
0
0
0
1
1
1
0
1
2
2
1
0
0
1
0
1
1
1
1
1
1
2
1
2
0
2
2
1
0
2
1
1
1
0
1
1
0
1
2
1
1
0
2
1
0
0
0
2
0
2
2
2
4
1
0
1
1
1
2
1
1
2
0
1
0
1
2
1
1
0
2
1
1
1
2
1
2
0
1
2
0
1
0
1
1
2
1
1
1
2
0
1
1
1
0
1
1
1
2
0
1
0
0
0
0
2
1
1
0
1
2
1
1
3
0
1
1
1
1
1
1
2
2
0
0
0
1
1
0
2
2
1
0
1
0
1
1
1
1
1
1
0
0
0
0
2
1
2
0
1
2
0
1
2
1
0
2
1
1
1
1
0
0
1
0
0
1
1
1
0
0
1
1
1
0
1
0
1
1
0
0
1
1
2
2
2
1
1
2
1
1
1
2
1
1
1
1
0
1
2
0
1
2
0
0
1
2
1
2
1
1
1
1
0
1
1
1
0
1
0
2
1
1
1
1
0
1
2
1
2
2
1
2
1
4
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
0
1
0
0
1
1
2
0
2
0
1
1
1
1
1
1
3
1
1
1
2
0
0
0
1
2
1
1
1
2
2
1
1
1
1
1
1
0
1
0
1
1
2
2
1
1
2
0
1
1
1
1
1
1
2
1
0
0
0
1
1
1
1
1
1
0
1
1
2
2
1
1
0
2
2
1
3
2
1
1
0
1
1
0
2
0
1
1
1
1
1
2
0
0
1
1
1
2
1
1
0
2
1
1
1
2
0
1
0
1
1
2
1
1
1
2
1
1
2
1
1
2
2
0
1
2
1
2
0
1
2
0
2
0
0
1
0
2
0
2
1
0
2
1
0
0
1
1
2
1
2
1
1
1
2
1
2
1
1
2
1
0
2
2
1
1
1
1
0
0
2
1
1
2
1
1
2
3
1
1
0
0
1
1
0
1
1
1
1
1
0
0
1
1
0
1
2
2
1
1
1
0
1
2
0
1
1
2
1
1
2
1
1
2
1
2
2
1
1
1
2
2
1
0
1
1
1
0
1
1
0
1
0
0
2
1
2
1
0
0
1
1
1
0
1
0
2
1
1
2
1
0
0
2
0
0
1
1
0
1
1
0
1
1
1
2
0
0
1
1
0
1
1
1
1
1
0
1
1
1
0
0
2
1
1
2
1
1
2
2
1
0
2
1
2
1
1
1
2
0
1
1
0
2
1
1
2
1
0
0
1
1
1
2
1
1
1
1
1
1
2
1
0
0
1
1
0
2
2
1
1
1
2
1
2
1
0
1
2
1
1
2
1
0
0
2
1
0
0
1
1
1
1
0
1
1
1
1
0
2
1
0
1
0
0
1
2
1
1
2
1
1
2
0
0
1
1
1
4
1
1
1
2
1
1
1
1
2
1
1
1
1
1
0
2
1
0
1
1
0
2
0
2
1
2
1
1
2
1
2
1
0
2
1
1
1
2
0
1
2
1
2
1
1
4
2
1
1
2
0
2
2
2
1
1
1
1
1
1
1
1
0
3
0
2
1
2
1
2
2
0
0
0
1
1
1
2
2
2
1
2
1
2
0
1
1
1
2
1
1
1
2
1
1
1
2
1
1
2
2
2
1
1
1
2
2
2
1
0
2
1
2
2
1
1
0
0
1
2
1
1
1
1
1
1
1
1
0
0
1
1
2
1
1
1
1
1
1
0
2
1
0
2
1
2
1
2
2
2
1
1
1
1
3
1
1
2
1
2
0
0
2
0
0
1
1
2
2
0
1
2
1
1
2
0
1
1
2
2
2
0
1
2
0
0
3
1
1
1
0
0
1
1
1
1
1
2
1
2
1
1
2
0
1
0
0
0
1
1
0
1
1
0
1
1
1
2
1
0
1
1
2
3
1
1
1
0
0
1
1
0
2
0
1
1
1
0
1
1
1
2
1
1
2
2
2
1
0
1
1
1
1
1
2
1
2
0
2
1
1
0
0
1
2
1
1
2
2
1
1
1
1
1
1
2
1
0
2
0
2
2
1
0
1
2
1
2
0
1
1
1
1
1
0
1
2
0
0
2
1
0
1
2
0
0
3
0
0
2
0
0
2
1
0
1
0
1
0
0
1
2
1
1
1
0
0
2
1
1
0
1
0
1
1
1
0
0
1
1
1
1
0
1
0
2
1
2
0
0
1
1
1
1
2
1
0
1
2
0
0
0
1
1
2
0
1
1
0
1
1
2
1
0
1
2
1
0
1
0
0
3
1
1
0
0
0
1
1
0
1
1
1
2
1
1
2
0
1
1
1
1
0
0
2
1
1
1
1
1
1
1
0
1
1
1
1
1
0
1
2
6
0
0
2
1
1
2
2
0
1
0
1
1
1
2
2
1
1
1
1
1
1
0
2
0
1
0
1
2
1
0
1
0
1
1
2
2
1
1
1
2
1
1
1
2
1
1
0
0
1
1
1
2
0
0
1
2
0
1
0
2
1
2
1
1
0
1
1
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
2
0
1
0
0
0
1
1
1
1
2
0
1
1
1
0
1
2
1
1
2
0
0
0
2
2
2
2
2
1
0
2
0
1
1
1
1
2
1
2
1
0
0
0
1
1
1
1
2
2
1
2
1
1
1
2
1
1
1
1
0
0
1
1
0
1
2
0
1
1
1
1
2
2
1
0
1
1
0
1
0
1
2
0
1
0
1
1
3
2
3
1
1
1
0
1
0
1
2
2
2
1
0
1
1
1
0
1
5
1
1
1
3
3
2
1
1
0
2
1
2
1
1
1
2
1
1
1
1
1
3
1
0
1
1
1
0
1
1
2
1
1
2
0
2
2
0
1
0
0
2
1
1
1
1
1
0
1
0
1
1
1
0
1
2
2
1
0
2
0
1
0
0
1
2
1
2
3
1
0
0
1
1
1
1
1
1
0
0
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
0
1
1
0
2
1
1
2
1
1
0
1
1
0
2
1
2
1
3
2
1
1
2
1
1
1
3
1
1
0
2
0
0
1
1
1
1
1
1
1
1
1
0
1
0
1
1
1
5
2
0
1
0
0
2
0
0
0
1
1
1
1
1
1
1
0
2
2
0
1
1
2
1
0
1
2
3
1
1
1
2
1
2
1
1
1
0
0
0
2
0
1
1
2
1
0
1
0
1
1
0
0
1
1
0
1
0
0
1
1
1
1
1
1
1
2
2
1
1
2
1
1
2
1
0
1
0
0
1
1
1
1
2
1
0
1
1
0
1
2
2
1
2
1
1
2
1
1
1
1
1
0
2
1
1
1
1
2
0
1
0
1
1
0
0
1
2
1
2
2
1
1
4
1
0
2
1
2
1
0
1
2
1
1
0
1
1
1
2
2
1
1
0
1
2
0
0
1
1
0
0
2
1
0
1
1
0
0
1
1
2
1
1
0
0
1
0
1
0
1
1
1
1
1
2
0
1
1
1
1
1
2
2
1
1
1
0
1
0
2
1
2
1
0
0
2
1
1
1
0
1
1
0
1
0
1
0
2
1
1
2
1
2
2
1
2
1
1
0
1
1
1
0
2
2
1
2
0
1
1
1
1
0
0
0
1
2
1
1
0
2
1
1
1
1
0
1
0
1
2
1
1
1
1
0
0
1
2
1
1
1
0
2
2
1
1
1
1
0
0
1
2
1
0
0
2
1
1
2
0
0
2
1
1
2
0
0
0
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
0
1
2
1
1
1
1
1
2
1
1
1
2
2
2
2
2
3
1
1
0
2
0
0
0
1
1
2
1
0
0
1
1
0
1
1
2
1
0
1
1
1
1
1
2
0
1
1
0
1
2
1
2
1
1
1
0
0
0
2
1
1
1
0
1
2
2
0
2
2
0
0
1
1
1
0
1
2
1
1
1
2
2
2
1
2
1
2
1
1
1
0
1
1
2
0
0
1
0
1
2
0
2
0
2
1
1
2
0
1
4
1
1
2
2
1
0
2
2
1
1
1
1
2
2
1
1
2
0
1
1
1
1
0
1
2
2
1
2
1
0
1
1
0
1
1
1
2
0
2
1
1
1
2
1
1
1
3
2
2
0
2
0
1
0
1
1
0
1
2
1
0
0
1
2
2
2
0
0
1
1
1
1
1
0
0
1
0
1
4
1
2
1
2
1
1
1
1
0
1
1
1
1
3
1
1
2
1
1
2
2
0
1
0
1
0
1
1
2
1
0
2
0
1
2
3
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
0
1
1
1
1
1
1
1
0
1
2
1
1
2
2
1
1
1
1
0
1
1
1
2
0
2
2
0
1
2
0
1
1
1
1
2
0
1
2
2
1
0
2
2
1
2
0
1
1
2
1
1
1
1
1
1
1
1
2
0
1
1
2
2
1
0
1
1
0
1
1
0
2
2
2
0
2
1
2
0
2
0
1
2
2
2
0
1
2
2
0
1
1
1
1
0
0
2
1
0
0
1
1
1
2
2
2
1
1
1
1
1
1
1
2
2
1
0
1
2
1
1
2
1
1
1
1
0
0
3
1
1
1
1
1
2
2
1
0
1
1
2
1
1
0
0
2
2
1
0
1
1
1
0
1
2
1
1
2
1
1
1
0
1
1
2
2
1
2
0
1
1
1
1
2
2
0
1
2
1
3
1
1
1
1
1
2
2
1
1
2
2
2
1
1
1
1
1
1
1
0
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
0
1
2
1
0
1
1
2
2
1
1
0
1
2
0
1
0
0
0
1
2
0
1
2
1
2
2
2
1
0
1
0
1
0
0
2
2
1
1
1
1
1
1
2
1
1
2
2
1
0
1
1
2
1
1
3
0
0
2
1
0
1
0
0
0
1
1
1
0
2
2
1
1
1
1
2
1
1
2
1
0
1
1
1
1
2
0
1
0
2
1
1
1
2
1
2
1
1
2
2
0
1
0
0
1
0
0
2
1
0
1
1
1
1
1
1
0
1
0
1
0
1
1
0
1
1
1
1
0
0
0
0
2
0
1
0
2
1
1
1
1
0
1
2
1
2
0
1
1
1
1
1
1
2
1
1
1
1
2
0
1
1
2
0
1
2
0
0
1
0
0
1
0
1
1
0
1
1
0
2
1
0
1
0
0
1
1
1
1
2
1
1
1
2
1
0
2
1
1
0
1
1
1
1
1
1
1
0
1
0
1
1
0
0
1
1
0
1
0
1
2
2
0
0
0
1
2
2
0
1
3
1
2
0
0
0
1
1
1
0
2
0
0
1
1
2
2
1
1
0
0
1
1
0
0
1
2
1
2
1
2
0
2
1
2
2
1
1
1
1
1
2
1
1
0
0
1
1
0
0
1
1
0
0
2
1
0
0
3
1
1
1
1
4
1
1
0
2
1
1
2
0
1
0
2
0
2
1
1
1
1
0
0
0
1
1
1
1
0
0
1
1
0
2
0
0
0
1
1
1
1
1
1
1
2
2
0
1
1
1
1
0
1
1
2
1
2
0
1
1
2
1
0
0
1
1
2
0
2
1
0
1
1
0
2
2
0
0
0
1
1
1
1
0
1
2
0
0
0
2
1
1
4
2
2
1
1
0
1
1
1
1
1
2
1
1
0
1
2
0
0
1
2
1
1
2
1
1
1
0
1
0
1
1
1
1
1
2
1
0
1
0
1
1
1
0
0
1
2
2
1
0
2
1
3
1
2
1
1
2
1
1
2
1
1
1
1
1
0
0
2
1
1
1
1
0
0
1
1
0
1
0
1
2
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
2
2
1
2
1
2
1
0
1
1
0
2
1
0
1
1
1
2
2
2
1
2
0
1
1
2
2
1
1
2
1
1
1
1
0
1
1
1
1
1
1
0
1
0
2
2
1
1
0
1
2
1
2
1
0
1
1
1
0
0
1
2
1
0
0
0
1
1
1
1
1
2
2
1
1
2
0
1
1
1
2
1
0
2
2
2
1
1
2
1
1
1
1
1
1
4
0
2
0
0
1
1
1
2
2
2
2
2
1
1
0
2
1
2
2
1
0
1
1
0
0
1
1
1
1
1
2
1
1
1
1
1
2
1
0
1
1
1
1
1
1
1
2
2
2
1
2
0
0
2
0
0
1
1
0
1
2
2
1
2
0
1
1
2
0
1
1
1
1
1
1
2
1
2
0
1
1
1
1
0
1
0
1
1
2
1
1
2
0
1
1
3
1
0
0
1
2
1
2
0
1
1
2
0
1
2
2
1
1
1
2
0
2
1
1
1
1
2
1
1
2
2
0
1
2
0
1
1
0
2
0
1
0
1
1
2
2
1
1
2
2
1
2
1
0
0
1
1
1
0
2
1
0
1
2
2
1
2
0
1
0
1
1
0
1
0
2
1
1
1
0
1
1
0
2
0
2
1
1
2
0
1
2
2
2
1
1
1
1
1
1
0
1
2
1
1
2
1
1
1
3
0
2
1
0
2
1
1
1
3
0
1
1
1
0
1
0
1
0
1
2
0
1
2
1
2
1
2
0
1
0
2
1
0
1
0
1
0
1
1
1
1
1
2
1
0
2
1
1
2
1
1
2
1
0
2
0
1
1
1
1
1
1
2
1
1
1
1
0
1
0
1
1
0
1
0
1
1
1
1
1
1
1
1
2
1
1
0
0
2
1
1
1
1
2
2
0
0
1
0
2
1
0
1
2
2
1
2
1
1
1
1
1
1
2
1
2
2
1
2
1
1
0
1
1
0
0
1
2
1
2
1
1
2
2
1
1
1
1
1
2
2
2
1
1
1
2
1
1
1
1
1
1
0
1
1
2
1
1
1
0
1
1
2
0
2
0
2
1
1
0
2
0
1
2
2
2
1
2
1
2
1
1
1
2
2
0
1
2
0
2
0
1
1
0
2
1
2
1
1
0
0
2
2
0
0
2
1
0
1
0
1
1
1
1
1
0
2
2
0
2
0
2
1
1
1
1
0
1
5
2
1
0
0
1
1
2
1
1
1
2
2
1
2
1
0
1
1
1
2
1
1
1
2
0
1
1
0
2
0
1
2
2
0
1
1
0
2
0
1
2
0
2
0
2
0
0
0
1
0
1
2
2
1
0
0
2
0
2
1
1
0
2
1
2
1
1
1
1
1
2
2
2
1
2
2
1
1
1
1
2
0
0
0
2
1
2
1
1
0
2
1
0
0
1
2
0
2
1
1
1
1
1
1
1
1
1
0
1
1
1
0
1
0
0
1
1
1
2
2
1
1
1
1
0
0
2
0
0
1
2
1
2
0
1
0
1
1
1
1
0
1
1
0
2
1
1
1
1
1
2
2
1
2
2
0
1
1
1
1
1
1
1
1
0
0
2
2
0
0
1
1
0
1
1
2
1
1
0
2
0
2
1
1
1
1
0
0
1
1
2
1
1
1
2
0
1
2
1
0
1
1
1
1
1
0
1
0
1
1
1
1
0
1
1
1
1
0
1
0
2
1
1
1
1
1
2
0
2
1
1
1
0
2
1
1
0
1
0
2
2
1
1
0
1
1
2
1
0
0
0
1
1
1
1
1
0
1
1
0
1
1
2
1
0
1
1
2
0
0
1
1
0
1
0
1
1
1
2
2
1
1
1
1
0
0
1
1
0
1
1
1
1
1
0
2
1
1
1
1
0
0
2
1
1
0
1
1
1
2
1
1
2
0
1
2
1
1
2
1
1
1
0
3
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
0
2
1
1
2
1
0
1
2
1
2
1
1
2
0
1
0
0
1
1
1
0
2
1
0
0
2
1
1
0
2
1
1
2
1
1
2
0
2
0
0
2
1
1
1
1
0
2
1
2
1
1
2
1
1
1
0
1
0
1
1
1
2
0
1
3
0
0
1
0
2
1
4
2
1
0
1
2
0
2
1
0
0
1
2
1
0
0
0
2
2
1
2
1
0
0
0
2
0
1
1
1
1
0
2
0
0
2
0
2
1
1
1
1
0
1
1
0
0
1
2
1
0
1
1
2
1
1
1
0
1
1
2
0
2
0
1
0
1
0
0
0
0
1
1
1
2
4
0
1
1
0
1
0
1
1
2
0
1
1
0
0
1
2
1
1
1
1
1
0
0
1
0
1
0
1
1
0
1
0
1
2
1
2
2
2
1
1
0
1
0
2
0
0
0
2
2
1
1
1
0
1
1
1
2
2
0
1
0
1
2
0
0
0
0
2
0
1
1
0
1
0
1
1
0
1
1
1
0
0
1
1
1
1
0
4
0
0
1
2
3
1
2
2
1
1
1
1
0
1
1
1
0
0
2
0
1
1
0
2
0
1
1
1
2
0
0
1
1
0
1
1
1
1
0
1
2
1
1
0
1
1
0
1
1
2
1
0
1
1
1
1
1
1
2
0
0
2
1
1
1
1
2
2
1
1
1
2
2
1
2
2
1
1
0
1
2
2
2
0
2
2
1
1
1
1
1
2
1
1
2
0
2
1
1
1
2
2
1
1
1
1
1
2
1
2
0
1
0
2
1
2
2
0
0
0
0
0
0
0
1
2
1
1
1
1
1
1
1
1
0
1
1
1
0
2
1
0
2
2
2
1
0
2
1
0
1
0
1
1
1
2
1
2
1
1
1
1
2
0
0
1
1
1
0
1
1
1
1
1
0
1
1
1
1
0
2
1
0
1
2
1
1
2
1
0
0
0
0
1
1
1
1
2
4
1
1
0
2
0
0
1
1
1
1
1
2
1
1
0
1
0
0
1
1
0
0
1
0
2
1
0
0
1
1
4
0
1
1
1
1
2
1
0
2
1
0
1
2
0
0
1
1
1
1
2
0
1
1
0
2
2
1
0
1
1
0
1
0
2
2
1
2
1
1
0
1
2
0
2
0
1
0
1
0
1
2
0
2
1
1
1
2
2
0
1
2
1
1
0
0
2
1
1
1
2
1
0
2
1
2
1
0
0
0
1
0
1
1
1
1
2
1
2
1
1
1
0
1
1
1
1
1
2
1
2
0
1
1
2
2
2
1
1
1
2
1
1
1
2
0
1
2
0
1
1
1
1
0
1
2
1
1
0
2
1
0
1
2
0
1
1
1
2
1
2
1
1
1
1
0
1
1
0
0
1
1
2
1
0
1
1
1
0
0
1
1
2
2
1
2
1
2
0
1
1
1
0
0
2
1
0
1
1
1
1
1
1
1
1
2
1
2
2
1
1
1
2
2
2
1
1
0
1
2
2
1
0
2
1
2
0
0
1
1
0
2
1
2
2
0
0
0
1
1
0
1
3
1
1
2
1
1
1
1
1
1
2
0
1
1
1
1
1
0
1
1
0
2
2
1
1
1
2
1
2
1
0
1
1
1
1
1
1
1
1
1
0
2
1
2
0
1
1
1
1
0
1
0
1
2
2
2
1
0
1
1
2
1
0
1
0
1
2
2
1
0
1
2
2
1
2
1
2
1
1
0
0
1
1
0
1
0
1
2
2
2
2
0
1
1
1
0
1
3
1
2
4
1
2
1
1
1
2
1
1
1
1
2
2
1
1
2
1
2
2
0
1
2
1
1
1
1
1
0
1
1
0
1
1
1
1
1
0
0
1
1
1
1
0
1
0
0
1
1
1
0
0
1
1
2
2
0
1
1
1
0
1
1
1
1
2
2
0
1
1
2
1
1
1
0
2
1
0
1
1
0
1
0
1
1
2
0
2
2
1
1
0
1
1
0
1
2
1
1
1
2
1
2
1
4
1
1
1
2
1
0
1
0
2
0
1
1
1
0
0
0
1
1
1
2
2
2
1
1
2
1
2
1
1
1
2
1
1
1
2
1
2
0
1
2
1
0
1
1
2
2
0
1
0
0
2
1
1
2
1
0
1
1
4
2
2
0
0
2
1
1
1
0
1
1
2
1
1
2
0
1
2
0
2
2
0
2
1
1
0
1
1
1
1
2
2
2
1
0
1
2
1
1
1
1
2
0
1
0
1
1
1
0
1
1
1
1
2
1
2
2
2
1
1
0
0
1
1
0
1
0
0
0
1
1
1
2
1
0
1
2
1
0
0
10
1
2
1
1
0
2
0
2
0
2
2
2
1
0
3
1
2
1
1
0
0
0
2
0
0
1
2
2
0
1
2
1
0
0
2
1
0
1
1
1
0
0
1
2
0
2
0
1
1
0
1
0
1
1
1
1
0
1
1
2
1
1
2
0
1
2
0
1
2
0
2
0
1
1
0
0
1
1
0
1
2
2
1
2
1
0
1
1
2
1
1
2
1
0
2
2
0
0
2
1
0
0
1
0
1
1
1
0
0
2
0
2
0
1
2
2
0
2
0
0
0
1
0
1
1
0
1
1
0
1
1
0
3
1
2
2
2
2
1
0
1
1
1
1
1
0
1
1
1
0
0
2
2
2
2
1
0
0
1
1
2
0
1
2
1
1
1
2
3
0
1
0
0
0
0
0
1
1
1
1
1
1
1
0
1
1
1
1
1
0
1
1
0
2
0
1
2
1
1
0
0
1
0
1
2
2
1
1
0
2
1
1
1
1
1
0
1
0
0
1
1
1
0
1
2
1
1
1
0
0
1
1
1
1
1
1
1
1
1
1
0
0
1
1
2
0
1
2
1
1
0
0
0
0
0
2
2
1
1
0
2
0
1
0
2
2
2
1
2
2
1
1
0
0
1
0
1
1
1
1
2
1
1
1
2
0
1
1
1
1
2
1
1
1
1
1
1
2
0
1
2
1
0
1
1
0
1
0
1
1
0
0
1
0
1
0
1
1
2
0
1
1
1
1
2
1
0
1
1
0
2
1
2
1
1
1
2
1
2
1
1
1
2
0
2
1
1
1
2
1
0
2
1
1
1
0
2
0
1
0
1
1
1
1
0
2
1
1
0
0
1
3
1
0
1
1
3
2
1
0
1
0
1
1
0
0
1
1
0
2
1
0
1
2
0
1
2
0
2
1
1
1
1
1
1
0
2
1
1
0
0
1
2
2
2
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
3
1
2
1
1
0
1
2
1
1
2
2
0
2
0
1
0
1
1
0
0
0
2
1
0
1
1
1
2
1
1
1
2
0
1
1
1
1
1
2
1
1
1
2
1
2
0
1
1
1
2
2
1
1
0
0
0
1
1
1
1
1
1
0
1
1
0
2
1
1
1
0
0
2
2
3
1
1
0
0
0
1
0
1
2
0
1
1
1
1
0
1
1
1
1
1
2
1
1
0
1
1
0
0
1
2
1
1
1
1
1
1
1
0
2
0
1
1
1
1
1
1
1
2
1
1
2
0
1
1
1
1
1
1
1
2
1
0
1
2
1
1
1
3
0
0
1
0
4
2
0
1
1
0
1
1
0
2
1
1
1
1
2
0
1
3
1
1
1
1
1
1
0
1
2
1
2
0
2
1
1
1
1
0
1
2
0
2
1
1
1
3
1
1
0
1
0
2
0
0
1
1
0
1
1
2
1
2
1
0
2
0
2
2
1
2
1
1
2
0
0
0
0
1
1
0
0
2
3
0
0
1
1
1
0
2
1
1
0
1
2
1
0
1
2
1
1
2
1
2
0
2
1
0
2
0
0
0
0
1
2
1
1
2
1
1
1
1
0
1
1
2
1
2
1
1
2
1
1
1
1
3
1
0
1
0
1
0
0
1
1
0
1
1
0
1
0
0
1
0
1
0
0
1
0
0
1
2
1
1
0
1
1
1
0
2
0
2
1
0
2
1
2
2
1
1
2
0
1
1
1
1
0
1
1
1
1
1
0
0
1
0
2
2
1
1
1
1
1
0
2
1
1
1
1
1
2
1
2
1
2
1
1
2
1
2
1
1
1
1
0
2
1
2
2
0
2
0
1
2
0
1
1
2
0
0
1
2
0
2
2
1
0
1
2
1
1
2
0
1
2
2
0
0
1
2
1
1
1
1
1
0
0
1
1
2
1
1
1
1
2
1
2
2
2
1
1
2
1
1
1
1
1
0
2
0
1
0
2
0
1
2
1
1
0
1
0
1
1
0
1
0
1
2
2
1
1
1
1
2
1
2
0
2
1
1
2
1
2
1
1
2
1
0
1
2
1
1
2
1
2
1
1
1
0
1
1
0
0
1
0
1
1
0
2
2
0
0
0
1
1
1
0
2
2
1
2
1
0
1
1
2
2
0
1
0
2
2
2
1
0
1
0
1
1
1
1
1
2
2
2
1
0
1
1
1
0
1
2
1
1
2
1
1
2
1
0
1
1
0
1
1
1
0
2
1
1
2
1
1
0
1
2
1
1
2
1
2
1
2
2
1
1
2
1
2
1
1
0
1
1
2
1
2
1
1
1
1
1
1
1
1
1
3
1
1
2
0
0
1
1
1
3
1
2
1
1
1
2
0
2
1
4
1
1
0
0
1
1
1
2
2
1
2
1
0
4
1
2
1
1
0
2
1
1
2
1
1
0
0
1
0
1
1
2
1
0
0
2
1
2
1
1
1
1
1
0
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
0
0
1
0
0
1
0
1
1
1
2
1
0
1
0
1
2
2
0
1
1
0
0
0
0
2
2
0
1
0
0
1
0
2
0
1
1
0
1
1
1
0
2
1
1
1
2
1
2
1
1
1
1
1
1
1
2
3
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
0
1
2
1
1
1
1
1
0
1
1
3
1
1
0
2
1
1
1
2
2
1
1
0
1
1
1
0
0
0
2
1
0
2
0
0
0
0
1
2
1
1
2
1
1
2
1
1
0
0
0
1
1
1
1
0
0
2
2
1
1
0
0
2
1
1
1
2
1
1
1
1
1
1
2
0
1
1
0
0
1
3
1
1
1
0
1
1
1
0
2
0
1
3
2
1
1
1
0
1
1
1
2
0
0
1
1
2
1
1
1
0
0
1
0
1
1
1
1
1
1
1
1
1
1
1
2
0
2
2
1
1
1
2
1
1
1
2
0
0
1
2
1
1
1
1
2
1
2
1
1
0
1
1
1
1
2
2
1
4
1
2
0
1
2
1
2
1
1
2
1
0
0
1
1
0
0
2
1
1
1
1
1
1
1
2
1
2
0
1
1
0
1
1
0
2
2
1
1
2
1
2
0
1
1
0
1
1
1
0
2
1
1
2
1
1
1
2
1
1
1
1
1
0
1
0
1
1
2
1
0
1
2
0
2
1
1
1
1
1
2
1
0
1
1
1
1
0
1
2
2
0
0
1
1
0
2
1
1
2
1
1
1
1
1
1
2
1
1
2
0
1
1
2
0
1
1
0
2
2
1
1
1
1
2
1
1
2
1
1
1
1
0
2
2
2
0
2
2
1
0
1
1
1
1
1
0
0
1
1
2
0
1
0
2
2
0
0
1
1
1
1
0
0
1
1
0
2
1
4
1
1
0
1
1
1
2
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
0
1
0
2
0
1
1
1
1
1
0
0
1
1
0
2
0
2
1
1
2
1
2
1
1
1
1
1
1
1
0
1
1
2
1
1
0
1
0
2
0
2
1
1
0
1
2
1
1
0
1
0
1
1
1
1
0
1
1
1
1
1
2
1
1
1
2
1
0
1
1
1
0
1
1
1
3
1
0
0
1
1
1
0
2
1
2
1
1
1
1
2
2
1
1
2
1
2
2
1
0
1
2
1
1
1
2
1
1
0
1
1
1
0
0
1
2
0
0
1
0
2
2
0
2
0
1
1
2
2
0
1
1
1
1
2
1
1
1
1
2
2
1
1
1
1
1
0
1
0
1
0
0
0
0
1
0
1
1
1
1
0
1
1
1
2
1
1
0
1
1
0
2
1
0
1
1
1
1
1
1
1
2
1
1
0
1
2
1
0
2
0
2
0
2
2
0
1
1
1
2
0
1
1
2
0
1
1
1
0
0
1
1
1
1
1
2
0
0
0
1
2
1
2
2
1
1
2
1
1
0
1
0
1
1
2
0
0
1
1
0
1
1
0
0
1
1
3
1
2
2
1
1
0
0
0
1
1
2
1
2
1
2
1
1
1
2
2
1
2
1
1
1
0
1
1
2
1
1
0
2
0
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
0
2
2
0
1
0
0
1
2
2
2
0
2
1
0
0
1
1
1
2
1
1
1
1
1
1
1
1
2
1
2
1
0
1
1
1
1
1
1
3
1
0
1
1
1
1
0
1
2
1
1
1
1
1
2
1
0
1
1
0
1
1
2
0
2
1
0
1
1
0
1
1
1
1
4
2
1
1
0
2
0
1
1
0
0
1
0
1
1
1
2
1
0
1
0
1
1
1
1
0
2
1
1
1
1
1
2
1
0
1
0
1
1
1
2
1
1
0
2
1
1
1
2
1
1
1
0
1
1
1
2
2
1
1
2
1
1
1
2
2
2
1
1
2
1
2
2
1
2
2
2
0
1
1
1
1
1
1
0
1
1
2
1
1
1
1
2
0
2
2
1
1
1
1
2
1
2
1
2
0
1
1
2
1
1
0
0
2
1
1
3
1
1
1
0
1
1
1
2
2
1
1
2
0
1
2
1
4
1
2
0
1
0
1
1
1
1
2
0
1
1
2
4
1
0
0
2
1
3
0
1
1
1
1
1
0
0
0
1
0
0
1
0
1
0
0
1
1
0
1
2
0
1
1
2
1
1
1
0
0
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
0
0
1
1
1
2
0
0
1
1
1
2
1
1
1
0
1
1
0
1
1
2
0
1
0
1
1
3
1
2
1
2
0
1
1
1
1
2
0
2
1
1
2
1
0
0
4
1
1
1
0
2
0
0
1
1
1
1
1
1
0
1
1
1
0
2
0
1
1
1
1
1
1
1
1
2
1
1
0
1
1
1
0
1
2
1
0
2
1
1
0
1
1
1
2
1
1
2
0
2
1
1
2
1
2
0
1
0
1
2
1
1
1
1
1
1
2
2
0
1
1
1
1
1
2
1
1
1
2
2
1
2
0
1
1
0
1
2
1
2
1
2
2
1
1
1
1
3
2
2
2
2
0
2
1
1
0
1
1
1
1
2
2
2
1
1
1
1
1
1
2
2
2
1
0
1
1
1
0
0
1
2
0
2
2
1
0
2
1
1
0
0
2
1
1
2
1
1
2
1
2
0
1
1
1
2
1
1
2
1
2
0
1
0
1
1
1
2
1
1
2
2
0
2
2
1
1
1
1
0
1
1
1
0
0
6
1
1
1
1
2
2
2
1
1
0
1
1
1
1
1
1
1
2
0
1
1
2
1
1
2
2
1
1
1
1
2
1
1
1
1
2
2
0
1
1
1
2
0
1
2
1
1
1
1
1
1
1
1
0
1
0
1
2
2
0
0
1
2
1
1
1
1
2
1
1
0
1
2
1
1
1
1
1
1
2
2
1
0
2
1
1
1
0
1
1
1
1
1
1
1
3
0
1
1
2
2
1
0
0
1
1
1
0
1
0
1
1
1
2
0
1
1
1
1
1
2
1
1
2
0
1
1
1
2
1
0
1
1
2
1
0
2
2
0
2
1
0
1
0
1
1
0
2
1
2
2
0
1
1
0
1
1
1
1
2
2
1
1
0
0
0
1
1
0
1
1
1
1
1
2
2
2
1
1
0
2
1
2
1
1
0
2
2
1
2
1
2
0
2
1
0
1
1
1
1
0
1
2
1
2
1
0
1
1
1
1
1
2
1
0
2
1
2
2
1
0
1
1
1
1
1
1
0
1
1
1
1
1
2
1
1
2
0
1
1
1
1
0
1
0
4
2
0
1
0
1
0
1
1
1
2
1
1
1
1
1
1
1
2
0
1
1
1
0
1
0
1
2
0
2
1
1
1
0
2
1
1
1
1
2
1
0
1
2
2
2
0
2
1
1
1
1
1
1
1
2
1
3
1
2
2
1
2
1
0
0
2
1
2
2
1
1
2
2
1
1
1
0
3
0
1
1
1
2
1
1
1
1
0
2
0
1
1
1
0
1
0
1
1
0
2
0
1
1
2
1
2
0
0
0
2
0
1
1
2
1
2
2
1
2
1
1
0
0
1
2
0
1
1
1
2
0
1
1
1
1
2
0
0
2
2
1
1
1
0
4
2
1
0
2
2
1
1
0
1
1
2
1
1
0
0
2
1
1
0
2
1
1
0
1
1
0
0
1
1
0
2
1
0
2
2
2
1
2
1
1
1
0
1
1
1
1
1
0
1
1
2
1
1
2
1
0
1
0
0
0
1
1
1
0
1
2
1
1
0
1
2
1
0
2
1
2
1
1
1
2
2
2
2
1
1
1
1
2
1
0
1
1
1
1
0
1
0
2
0
1
2
1
0
0
1
2
0
2
2
0
2
1
1
1
1
0
1
1
2
0
1
0
0
0
2
1
2
1
0
1
1
0
2
1
0
1
1
0
1
0
2
0
1
1
1
1
0
0
1
1
0
2
1
1
1
1
2
0
1
2
1
2
0
1
2
1
1
1
1
0
2
0
1
1
2
2
1
0
1
1
1
0
0
1
1
1
1
0
1
1
2
0
2
1
1
1
0
1
0
1
0
1
2
0
2
1
2
2
1
1
1
1
2
1
2
1
0
1
0
1
0
1
0
1
1
2
1
1
1
2
1
1
1
1
1
1
1
0
2
2
1
0
1
2
1
1
2
0
2
1
1
2
1
0
1
1
0
2
0
0
2
1
0
1
1
1
1
1
2
2
1
1
1
1
0
0
1
3
1
1
0
0
1
0
0
1
0
1
2
1
1
2
1
1
1
1
1
1
1
1
0
1
2
1
1
0
1
1
2
1
0
0
1
0
1
0
2
1
1
0
1
2
1
1
1
0
1
2
1
1
1
1
0
0
1
1
2
1
1
1
0
2
1
1
1
1
2
2
1
1
0
0
2
1
1
0
0
0
1
1
1
0
1
2
1
2
2
1
1
0
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
0
1
2
0
1
1
0
1
2
0
1
1
0
2
1
2
2
0
0
2
1
1
1
0
1
0
2
1
0
0
1
1
0
0
2
2
1
0
1
2
1
2
2
2
1
1
0
1
1
0
0
2
1
1
0
1
2
2
1
1
0
2
1
1
2
1
1
1
2
0
1
1
1
0
0
0
1
1
1
0
0
1
0
2
1
1
0
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
3
1
1
2
2
2
1
2
1
1
2
1
0
0
1
2
1
1
0
1
2
1
1
1
1
1
1
2
0
0
1
2
1
1
2
0
1
2
1
1
1
1
1
1
1
0
1
2
2
1
0
1
2
1
2
1
1
0
1
1
0
0
0
2
0
1
0
1
1
0
1
0
0
1
0
2
0
2
2
0
1
1
1
1
1
2
1
0
1
2
1
2
1
2
0
1
2
1
2
1
1
0
3
1
1
1
1
2
2
0
2
1
2
0
1
1
1
1
0
1
0
1
2
1
0
1
0
2
1
1
2
2
3
2
0
0
1
1
1
1
0
2
1
0
1
0
2
2
0
0
1
2
1
0
1
1
1
0
1
1
1
1
2
1
0
1
1
1
1
1
1
1
1
1
1
0
1
0
1
3
0
1
0
2
1
2
1
2
2
0
1
1
1
2
0
1
1
0
1
0
1
0
1
0
2
1
1
1
1
1
0
0
1
1
1
2
1
0
1
2
2
1
0
1
0
1
1
0
2
1
0
1
2
1
2
2
1
1
2
1
0
1
1
0
2
1
0
1
1
1
1
1
1
0
1
2
2
2
2
1
1
1
0
1
1
1
1
0
1
0
1
1
2
0
0
1
2
1
1
1
1
1
1
1
1
1
2
2
1
1
1
0
2
0
1
0
2
1
1
2
1
2
0
1
1
1
0
1
0
2
1
1
0
1
1
0
2
1
0
2
2
1
1
1
1
1
1
1
1
1
1
1
0
0
1
2
1
1
1
2
2
0
1
1
1
2
1
2
1
1
2
3
1
1
1
2
1
1
1
0
1
1
1
1
1
2
2
1
2
0
1
1
1
0
1
0
1
2
1
0
1
2
1
0
2
1
0
2
2
2
2
0
1
2
1
2
1
0
1
1
1
1
1
1
2
0
1
2
0
2
0
1
1
2
1
3
0
1
0
2
1
1
1
2
1
1
2
1
1
1
2
2
1
0
2
2
3
2
2
0
1
1
1
0
1
0
0
1
1
1
0
1
1
2
1
0
1
1
1
2
0
0
2
1
2
2
0
1
0
1
1
2
1
1
2
0
2
2
2
1
1
2
1
1
1
0
1
1
2
0
2
1
1
3
1
0
2
2
1
2
2
1
0
0
1
0
1
2
2
1
1
0
0
1
0
2
0
1
1
1
1
1
0
1
2
2
2
1
1
0
0
0
0
2
0
1
1
0
1
1
1
1
1
2
1
1
2
1
1
1
2
2
1
1
2
0
1
0
1
0
1
2
1
1
1
0
2
1
1
1
1
2
1
1
0
1
1
2
1
1
1
2
1
0
1
0
1
1
1
1
2
1
2
1
0
1
1
0
2
1
1
1
1
1
2
1
1
0
2
1
0
0
2
0
1
1
2
0
1
2
0
1
1
1
0
1
1
1
1
1
0
0
0
1
2
0
0
2
2
1
1
2
1
2
1
1
1
1
1
2
1
1
0
1
2
1
1
1
1
1
1
0
2
1
0
1
2
0
1
0
1
2
1
1
1
0
1
0
1
1
0
1
2
2
1
0
1
0
0
1
2
1
2
1
1
1
2
1
0
1
1
3
1
4
1
1
0
0
1
0
2
2
2
0
1
1
0
1
2
2
1
1
2
1
2
1
2
0
1
1
1
1
0
2
2
1
1
2
1
0
1
1
2
2
1
0
1
1
1
2
0
2
2
0
0
1
1
0
2
0
1
0
0
1
0
1
1
1
1
1
0
1
1
1
0
1
0
2
1
1
0
1
0
2
1
1
1
1
2
2
1
1
0
1
0
0
1
1
1
0
4
1
1
1
1
1
1
1
2
2
1
0
0
2
1
1
0
1
1
2
0
1
2
1
2
1
0
1
0
1
0
1
1
0
1
1
2
1
1
2
2
0
2
0
1
2
1
2
0
2
0
0
1
1
0
2
2
1
0
2
0
1
1
1
0
2
0
1
1
1
1
0
2
0
2
0
2
1
0
0
2
0
1
1
1
0
0
0
2
0
0
0
1
1
1
0
2
2
2
2
1
1
1
1
1
1
1
2
2
2
1
1
1
1
2
1
0
2
2
2
0
1
1
1
2
1
1
1
0
1
1
0
1
1
1
1
1
1
1
0
1
1
2
2
1
0
1
2
2
3
0
0
1
0
0
2
2
0
2
1
1
1
2
1
1
1
0
0
1
0
1
0
1
1
1
1
0
1
1
1
2
1
1
2
1
1
0
2
1
1
0
1
2
1
1
1
2
1
1
2
1
0
0
2
1
2
2
2
1
1
2
2
0
2
1
1
1
1
4
1
0
2
0
1
2
1
1
1
1
1
1
1
1
2
1
1
2
0
1
1
0
1
1
1
0
1
2
0
1
2
2
1
1
2
2
2
2
2
1
2
1
2
1
0
0
2
1
1
1
1
0
1
0
2
1
1
1
1
1
2
1
1
1
2
1
2
1
0
2
1
0
1
1
0
0
0
1
1
1
1
1
2
1
1
0
1
1
0
0
1
2
0
2
2
2
1
2
0
1
1
1
0
2
2
1
0
2
1
1
0
1
1
1
1
2
1
1
0
1
0
1
1
1
1
1
1
2
1
0
0
1
0
0
1
1
0
1
2
1
1
1
1
1
1
1
1
2
1
0
2
2
1
2
1
1
1
2
1
1
2
1
0
0
1
1
0
1
0
1
2
2
0
1
1
1
1
2
1
2
0
1
1
1
0
0
2
1
1
0
0
0
1
1
1
0
1
0
3
3
2
0
2
1
2
1
1
1
1
1
0
1
1
0
1
1
1
1
1
1
1
1
1
0
0
1
0
1
3
1
2
0
1
1
2
2
2
2
1
2
0
1
0
2
1
2
0
1
0
0
1
3
1
1
0
1
1
1
1
0
1
1
3
1
1
1
1
0
1
1
1
1
1
2
1
1
1
1
2
1
0
0
1
1
1
1
2
1
2
1
0
1
1
1
1
1
0
2
1
0
1
2
1
2
1
1
1
1
1
1
2
1
2
1
0
0
1
1
0
0
1
1
1
0
1
1
1
2
0
1
1
1
1
2
2
1
1
0
2
3
0
1
1
1
1
0
1
1
1
1
1
1
0
1
2
1
0
2
0
0
2
0
1
1
1
0
1
2
0
0
1
2
1
1
1
1
1
0
3
2
1
0
1
1
4
2
1
0
1
1
0
1
1
1
1
2
0
1
1
2
1
1
0
1
1
1
0
1
1
0
0
0
1
0
1
1
0
2
1
1
1
0
1
0
1
0
1
0
1
1
1
1
1
2
1
2
1
1
1
1
0
2
1
0
2
2
1
0
2
1
1
1
0
0
0
1
0
1
1
1
0
1
0
1
0
2
0
1
0
2
0
1
1
0
1
2
1
1
1
0
1
1
1
1
1
0
1
1
1
1
2
0
1
1
1
2
1
1
1
1
0
2
1
2
1
2
1
0
1
0
1
1
1
0
2
1
1
1
1
2
1
1
0
4
1
2
1
2
0
0
1
2
1
0
1
1
0
2
1
1
0
1
0
0
1
1
1
0
1
1
1
1
1
0
2
2
1
1
0
0
1
0
2
1
1
1
1
2
0
1
1
2
0
1
2
2
1
0
1
1
1
0
0
1
1
1
0
1
1
0
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
2
1
1
0
0
1
1
2
0
0
1
2
2
1
2
0
1
1
2
1
1
1
0
1
1
1
2
0
0
2
1
2
2
1
2
1
1
1
1
1
2
2
1
1
1
0
1
0
1
1
0
2
2
0
1
1
1
1
1
1
1
2
1
2
0
0
0
1
1
1
0
0
0
1
1
1
0
1
1
1
2
1
2
0
2
0
1
1
2
2
1
1
2
1
1
1
1
2
0
2
1
1
1
1
0
1
1
2
1
1
2
1
2
2
2
1
1
2
0
1
0
0
2
1
2
0
2
1
2
1
2
1
1
2
2
0
1
1
1
0
1
1
0
2
1
1
1
1
2
0
1
1
2
0
0
0
1
2
1
1
1
1
2
2
1
1
1
1
1
1
0
0
0
0
1
2
0
1
2
1
1
1
2
1
0
2
1
2
1
2
1
1
2
1
1
1
1
1
1
0
1
1
0
2
1
1
1
1
2
1
2
1
1
0
1
0
1
0
2
0
0
2
0
1
2
0
1
1
0
1
0
1
2
0
1
1
0
1
2
1
1
2
1
1
1
0
1
2
1
1
1
1
2
1
2
1
1
1
0
1
1
1
1
0
1
2
0
2
2
1
0
1
0
2
1
3
2
1
1
1
0
1
0
2
1
0
1
1
1
0
1
1
2
1
1
0
1
1
2
1
0
0
1
0
1
1
1
0
0
2
1
1
2
1
1
1
1
1
0
1
2
1
1
1
2
0
2
1
1
1
3
1
2
2
0
0
1
0
2
1
0
1
1
2
1
0
1
2
1
1
1
1
2
2
2
1
1
1
0
0
1
1
1
1
1
0
1
2
2
0
1
1
1
1
1
1
1
2
2
1
2
2
1
1
1
1
1
1
1
0
0
2
1
1
1
1
0
1
0
1
1
2
1
2
0
4
2
1
1
1
1
1
1
2
0
1
1
1
1
1
1
0
0
0
0
0
0
1
1
1
0
1
1
1
1
1
1
2
3
2
0
2
1
1
1
1
0
1
0
1
1
1
1
2
1
1
1
1
1
1
0
1
2
0
0
1
0
2
0
1
0
1
0
0
1
1
1
0
1
1
0
2
1
0
1
1
1
1
1
1
1
1
1
1
1
1
2
0
2
1
0
1
3
2
1
1
1
1
1
1
1
1
1
0
2
2
0
2
2
1
2
1
0
1
0
1
2
2
2
1
0
0
1
1
1
0
0
1
1
0
1
1
1
1
1
1
1
1
1
2
1
0
1
1
0
1
1
1
2
0
0
1
1
1
1
1
1
0
0
2
2
1
0
1
3
0
1
1
2
1
1
0
1
1
1
1
0
1
0
0
1
0
0
2
1
0
1
1
1
2
1
1
1
0
1
0
1
1
1
1
0
2
1
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
0
1
3
1
1
2
0
2
1
1
1
1
1
2
1
2
0
0
0
2
2
0
2
1
1
2
0
0
1
1
0
0
1
1
1
1
1
1
1
1
0
1
0
0
1
1
2
1
1
1
0
0
1
0
0
1
1
2
1
0
1
1
1
1
1
1
1
1
1
0
2
0
0
1
1
0
2
1
2
1
1
1
1
2
2
1
1
2
1
1
2
1
0
1
1
0
0
2
1
0
1
1
1
2
1
1
1
1
1
1
1
1
0
0
2
1
0
1
1
1
0
0
1
1
1
2
1
2
1
1
1
1
1
0
1
0
0
2
1
1
0
0
0
1
1
1
1
2
2
0
2
1
0
1
2
1
1
1
0
1
2
1
1
1
1
0
0
2
0
1
2
1
1
0
1
1
1
1
3
1
1
1
2
1
0
1
1
2
2
1
1
1
1
1
1
1
1
1
2
0
1
1
1
1
1
0
0
0
0
1
5
0
1
2
0
1
0
1
0
0
1
2
2
1
0
2
0
2
1
0
1
1
2
1
1
1
1
1
1
0
0
1
1
2
2
1
3
2
2
4
2
0
1
0
0
1
1
0
1
3
1
0
1
1
1
1
0
1
2
0
1
2
1
2
2
2
1
1
1
1
0
1
1
1
2
1
1
3
1
1
1
1
1
0
2
2
2
2
1
1
2
0
0
1
2
0
1
1
1
1
1
0
0
0
0
0
1
0
0
1
2
0
0
1
1
1
1
0
1
0
0
2
0
1
1
1
1
2
1
1
0
1
1
2
2
1
2
0
1
0
1
2
2
2
1
2
2
0
1
1
2
2
2
1
1
1
2
1
0
2
1
2
1
1
1
1
1
2
1
1
1
0
1
0
1
1
0
2
2
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
2
2
1
2
1
1
1
1
0
1
1
1
2
1
0
0
1
0
0
1
0
1
0
0
0
2
1
2
2
1
0
1
1
0
1
0
0
1
2
1
1
1
0
1
0
2
1
2
1
0
2
2
2
1
0
1
1
1
1
0
1
1
1
2
1
2
2
2
1
1
1
1
0
2
1
1
1
1
0
0
0
1
2
1
1
0
1
1
0
2
0
1
1
1
0
1
2
1
0
1
1
1
4
2
1
2
1
0
1
1
1
2
1
1
0
2
1
1
1
2
1
1
1
1
2
0
0
1
1
1
1
0
1
1
1
2
0
2
2
2
2
1
1
2
1
0
1
0
2
1
0
1
1
0
1
2
0
1
1
3
0
1
1
1
2
1
3
0
1
0
0
1
2
1
2
1
1
0
1
1
0
0
0
1
0
1
1
1
1
1
0
0
2
1
1
1
1
0
2
0
4
1
1
1
2
3
0
1
2
1
0
1
0
2
1
1
1
1
0
1
2
1
1
1
2
1
1
1
1
2
2
1
1
2
1
2
0
1
2
1
1
1
2
1
0
1
1
1
0
1
1
1
0
1
1
0
1
1
1
1
2
0
0
1
1
0
1
2
1
1
2
1
0
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
0
1
1
0
1
1
2
1
1
0
1
1
1
1
0
1
2
2
0
2
1
1
1
2
1
1
0
0
1
1
1
2
2
2
1
2
0
1
0
1
1
1
0
1
2
1
1
2
0
1
1
2
0
1
1
1
1
1
1
1
1
1
1
0
1
0
2
3
1
1
1
2
1
0
0
0
1
2
1
1
1
0
1
1
1
0
1
1
2
2
1
1
2
1
2
1
0
1
1
1
1
2
1
1
1
1
2
0
1
1
1
2
2
2
1
1
1
1
0
1
2
2
0
0
0
5
1
2
1
1
1
2
2
0
0
1
1
0
1
1
0
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
0
1
1
2
1
1
2
1
0
2
3
2
2
1
0
1
0
1
1
2
2
0
2
1
1
1
2
1
0
0
0
1
1
2
1
1
1
4
3
0
0
1
1
0
2
1
1
2
0
0
1
1
1
0
0
1
1
1
1
3
1
0
1
0
2
1
2
1
2
0
0
2
0
3
1
0
2
0
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
2
0
0
2
1
1
1
1
1
0
2
2
1
0
0
2
2
1
2
2
1
1
1
0
0
1
1
1
1
1
0
1
0
1
1
1
1
0
0
1
0
1
1
2
1
1
0
2
1
1
0
1
0
1
0
1
1
1
0
0
2
2
0
1
0
2
1
2
3
1
1
0
1
0
1
0
2
0
0
0
0
1
0
1
1
0
1
1
0
1
2
1
2
1
0
1
1
2
1
1
2
1
2
1
1
2
1
2
1
0
1
1
1
1
1
2
0
0
1
1
1
0
1
1
1
2
1
1
2
1
2
1
1
0
2
0
0
0
1
1
0
1
0
1
1
0
1
1
0
1
1
1
0
1
2
1
2
1
2
1
1
1
1
0
1
1
1
1
1
0
1
1
0
1
1
1
2
1
1
1
1
0
1
0
2
1
2
1
1
1
1
1
1
1
2
2
1
0
1
1
1
1
0
2
0
1
2
2
3
2
2
2
2
1
1
0
1
1
1
2
1
1
2
1
2
1
1
2
2
1
2
0
2
2
2
0
2
1
0
0
0
2
0
0
0
2
1
2
0
1
2
0
1
2
1
1
1
1
1
2
2
2
0
1
0
1
1
1
2
1
2
1
2
1
0
1
2
1
1
1
0
2
0
0
1
0
0
1
2
1
0
2
2
0
0
1
2
1
1
0
1
1
1
1
0
1
1
1
1
1
1
1
0
0
1
0
0
0
2
2
1
1
2
1
1
1
1
2
0
2
2
0
1
1
0
2
0
1
1
0
1
0
0
2
0
1
3
2
1
2
1
2
1
2
1
1
2
1
1
1
0
1
2
0
0
1
1
2
0
1
1
1
2
1
1
2
0
0
0
0
1
1
1
1
0
2
0
1
1
0
1
1
1
1
2
2
2
1
2
1
1
2
1
2
1
1
1
0
1
1
0
1
0
1
0
1
0
2
2
1
2
2
1
0
0
1
1
0
1
1
1
0
1
1
1
1
1
1
1
1
1
0
1
0
1
2
0
1
1
0
0
2
0
0
1
2
1
0
2
1
1
1
1
1
1
2
0
2
1
0
0
1
1
1
2
1
1
2
0
1
1
0
0
1
1
1
0
1
1
1
1
0
1
2
1
0
0
0
2
1
1
0
2
0
0
1
1
0
1
2
1
1
2
1
2
1
1
0
2
1
2
2
1
0
1
1
1
0
1
0
2
3
1
1
1
2
2
0
2
0
1
0
1
1
2
1
1
1
0
1
2
1
0
2
2
0
0
2
2
1
1
2
1
1
2
1
1
1
1
1
1
1
2
2
1
0
1
1
1
1
1
0
2
2
1
2
1
1
0
0
1
0
0
0
1
1
1
1
0
1
1
2
1
0
1
5
0
2
1
1
1
1
1
1
2
1
0
0
2
2
1
1
2
1
1
2
1
1
1
2
1
0
1
1
0
1
2
1
2
2
2
5
1
2
0
0
1
1
1
1
2
2
2
0
1
0
0
2
1
1
0
2
2
2
1
0
1
4
1
0
0
0
1
1
1
1
1
2
1
1
1
2
2
1
0
0
0
0
2
1
1
1
1
1
0
2
1
1
2
1
1
2
1
1
0
1
0
2
1
0
1
2
1
1
1
1
1
2
1
2
1
2
2
3
1
1
1
1
1
2
0
1
1
1
1
2
2
2
0
0
1
1
2
0
1
0
1
1
0
1
1
1
1
1
0
1
1
1
1
1
3
1
0
2
1
1
1
1
1
0
1
0
2
1
0
2
1
1
1
1
1
0
1
0
1
1
0
1
1
1
1
0
0
0
1
1
3
0
1
0
0
1
1
2
2
1
1
1
1
0
1
1
0
1
1
1
1
0
1
1
1
1
2
1
1
0
2
1
1
2
1
1
2
1
1
0
0
0
1
0
1
2
0
0
1
1
1
1
0
2
2
0
0
1
2
0
1
1
2
1
1
2
1
1
1
2
0
1
1
2
1
2
2
1
1
0
1
1
0
1
1
2
1
1
1
0
0
0
0
1
2
2
1
1
0
1
1
0
0
1
1
1
0
0
1
2
2
1
1
1
2
1
1
1
1
0
0
2
0
0
1
0
1
1
1
0
1
1
1
1
1
1
2
1
2
0
0
0
2
0
1
2
0
2
1
1
1
1
1
1
4
2
1
1
1
1
1
2
1
1
1
0
2
1
1
1
1
0
1
1
0
2
1
2
1
1
2
1
1
0
1
1
1
1
1
1
2
1
2
2
1
1
0
1
1
1
1
3
0
0
1
0
2
1
0
2
3
1
2
0
1
0
2
1
2
2
0
1
1
2
0
1
1
2
0
1
2
1
1
1
3
1
0
1
0
1
2
1
0
1
1
1
1
1
1
1
2
1
0
0
0
1
1
0
1
1
1
1
2
1
2
1
0
1
2
2
1
0
2
1
1
0
1
1
1
1
1
0
0
2
0
0
1
1
1
2
1
1
1
1
0
0
1
1
1
1
2
1
1
1
2
2
1
2
1
1
1
0
1
2
1
1
2
1
2
1
1
1
0
2
1
0
2
0
1
0
1
2
1
0
1
1
0
2
1
1
1
1
0
1
1
0
1
0
2
1
2
1
1
2
1
1
1
0
1
1
0
0
1
0
0
0
0
2
1
0
2
2
2
0
1
2
2
2
1
0
0
2
1
1
0
0
1
1
1
2
1
2
0
1
2
2
1
1
1
1
1
2
2
1
1
0
1
1
2
0
2
1
0
1
0
1
1
2
1
1
2
1
1
1
1
0
2
2
1
1
1
1
0
0
0
0
2
1
0
1
1
1
1
2
2
1
2
0
1
0
1
1
1
0
2
2
0
0
0
2
1
1
2
1
1
1
2
1
2
1
1
1
2
1
1
1
1
3
1
1
1
0
2
2
2
0
0
2
1
1
2
1
1
2
0
0
1
2
1
1
1
1
1
1
1
0
1
1
2
2
1
1
0
1
0
2
1
1
1
1
1
0
1
0
2
1
1
2
0
1
0
2
1
4
1
2
1
0
1
0
1
1
1
0
1
1
0
1
1
1
2
0
1
1
1
1
1
2
1
1
1
2
0
2
1
2
1
1
2
1
2
1
1
0
1
1
1
0
0
1
1
1
1
1
1
1
1
1
3
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
5
1
2
0
2
1
1
1
1
1
1
2
1
1
0
1
0
0
1
0
2
0
1
0
1
2
2
0
0
3
2
1
1
1
1
1
0
0
2
1
1
1
2
1
1
2
2
2
1
1
2
0
2
1
2
0
1
2
1
2
2
1
1
2
1
2
1
0
1
2
1
0
2
1
1
1
1
2
0
1
1
1
1
1
0
1
1
1
1
0
1
1
1
0
1
0
1
0
1
0
1
1
1
0
1
0
1
1
1
0
1
1
2
2
0
1
1
1
1
0
1
1
1
2
1
1
2
1
1
2
1
1
0
2
1
0
1
1
1
2
1
1
0
1
1
1
1
0
1
1
1
1
2
0
2
1
1
1
1
0
2
2
1
1
0
2
1
1
1
2
1
1
2
0
0
1
1
1
1
1
0
1
0
1
2
1
1
2
0
1
1
1
2
0
1
1
4
1
1
0
0
2
1
1
0
2
2
1
1
1
0
1
1
2
1
1
1
1
2
0
1
1
1
1
1
1
1
0
1
1
1
1
2
0
0
1
1
1
0
1
2
2
2
1
1
2
1
1
2
0
2
1
1
0
1
0
2
2
1
1
0
0
0
0
0
0
1
1
2
1
1
0
1
2
0
2
1
0
2
2
2
1
2
2
3
0
1
0
0
0
2
1
1
2
1
0
1
1
1
1
1
2
0
2
2
1
0
1
1
1
1
1
2
1
0
2
2
3
1
0
1
1
1
1
1
1
2
1
1
1
1
1
0
2
0
1
0
0
1
0
2
0
0
0
1
1
1
1
2
2
2
1
2
1
0
1
0
2
2
1
1
2
2
1
0
1
1
2
0
2
2
2
0
1
1
1
2
0
1
1
2
1
1
1
1
0
1
0
1
1
0
2
2
1
0
0
1
1
2
2
1
0
1
2
0
1
0
0
1
1
1
2
2
2
1
1
0
1
1
1
1
0
1
1
1
2
1
1
1
0
2
0
1
2
1
1
2
1
1
1
0
2
1
1
1
0
2
1
2
2
0
1
0
1
2
0
1
1
1
0
1
0
2
1
2
1
2
3
1
0
2
1
2
1
1
1
1
1
0
1
0
1
2
1
1
1
1
0
1
0
2
1
2
0
0
2
0
1
1
2
1
0
1
1
1
1
3
2
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
0
2
1
1
1
4
2
0
2
2
2
0
1
1
0
0
2
0
1
2
3
0
1
1
1
1
1
1
1
1
1
1
1
2
2
1
3
0
1
1
1
1
1
1
1
1
1
1
1
0
2
1
1
1
1
1
0
1
2
2
0
2
0
1
1
2
0
1
2
0
2
1
1
2
1
1
0
0
1
1
1
1
2
1
1
1
0
1
1
1
1
2
2
2
1
1
0
1
2
1
0
1
0
1
0
1
1
0
1
1
1
0
0
2
1
2
1
1
0
1
0
0
0
0
0
1
2
2
1
0
1
2
2
0
0
1
1
1
2
1
1
2
0
1
1
1
1
1
0
1
0
0
1
0
1
1
1
1
1
1
2
0
0
1
0
1
0
0
1
2
1
1
0
0
1
0
0
1
1
2
1
2
1
1
0
2
2
0
1
1
1
2
2
2
0
0
1
1
1
1
0
2
1
0
2
1
1
1
0
2
1
0
2
1
0
2
0
1
1
0
2
1
2
2
1
1
0
2
1
2
0
2
1
1
0
1
2
1
0
1
1
1
1
2
0
2
1
0
1
0
0
2
0
1
1
1
1
1
2
1
1
1
0
1
1
1
1
1
2
0
1
0
1
1
1
1
1
2
1
1
1
1
1
0
2
1
1
2
0
1
1
0
1
1
1
0
0
2
1
2
2
1
1
1
1
1
1
0
2
0
2
1
1
2
1
1
2
1
2
0
1
2
1
1
2
1
10
1
1
0
1
2
1
1
1
2
1
1
1
2
0
1
2
2
0
1
2
0
0
1
0
1
0
0
0
1
2
1
0
2
2
1
0
2
1
2
0
0
1
1
1
1
1
2
1
1
1
1
2
1
1
2
2
1
1
1
1
2
1
0
1
0
2
1
2
1
1
1
1
1
0
1
1
0
1
1
0
0
3
2
0
1
2
1
1
2
1
1
1
0
2
0
1
1
1
1
1
0
1
0
1
1
1
1
2
1
0
2
1
1
1
0
1
1
1
1
1
1
1
1
0
2
2
0
1
0
2
2
2
2
0
2
0
2
0
0
1
0
1
2
2
1
2
1
4
1
1
0
1
2
2
0
1
2
0
0
2
1
2
1
1
2
0
1
1
1
2
1
2
1
1
1
1
1
1
1
1
0
2
0
0
2
1
1
1
1
0
1
1
1
1
2
2
1
1
0
1
1
1
0
0
2
1
2
0
1
2
1
0
0
1
1
1
1
1
2
1
1
2
1
2
2
0
2
1
2
0
2
2
0
3
1
1
1
1
1
0
2
2
2
1
2
0
1
1
1
2
1
0
2
2
0
2
0
2
1
2
0
1
1
1
1
0
1
1
0
2
2
2
2
1
1
1
1
0
2
0
2
0
0
1
1
1
1
2
1
0
0
1
2
1
2
1
1
2
2
0
1
2
1
1
1
1
1
1
0
1
1
2
0
2
0
1
1
1
1
1
1
1
1
1
1
0
2
0
1
0
1
0
1
2
2
1
1
0
2
1
1
0
1
1
0
2
0
1
3
2
0
1
0
0
0
2
1
0
2
0
1
0
1
1
1
1
2
2
0
1
0
3
2
0
1
1
2
1
2
2
0
2
1
1
1
2
1
1
1
2
1
1
1
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
0
0
0
0
2
1
1
1
0
2
0
1
1
1
1
2
1
0
1
1
0
1
1
1
1
0
1
1
1
1
1
2
1
0
1
1
2
2
1
1
2
1
2
1
0
1
1
1
1
2
0
1
2
0
0
1
1
1
1
0
1
2
0
0
2
1
2
1
0
1
2
0
0
1
2
1
2
1
2
0
1
2
0
1
1
2
1
1
0
1
1
0
2
1
0
1
1
1
0
0
0
1
1
0
2
1
2
1
1
1
1
0
1
2
1
0
1
1
1
1
1
1
1
0
2
0
1
2
0
1
1
0
1
1
0
1
1
1
1
1
0
1
1
1
1
2
1
1
0
1
1
2
2
2
1
1
1
0
2
0
0
0
1
0
1
1
1
2
0
1
2
1
2
0
1
2
0
1
2
1
2
0
1
1
0
2
0
1
1
1
1
1
0
0
2
0
0
1
0
2
1
0
1
2
0
1
2
0
0
1
1
1
1
1
0
1
1
2
1
0
1
2
1
0
2
1
1
0
0
2
1
0
2
2
1
1
1
1
1
0
0
0
0
2
1
1
2
1
0
1
2
0
1
0
1
0
1
1
0
1
0
1
1
2
1
1
1
1
1
2
1
2
1
1
0
1
1
0
2
1
2
0
1
1
1
1
1
1
2
1
2
1
2
2
1
2
1
1
0
0
1
1
1
0
1
2
1
2
1
1
0
2
0
0
1
0
4
1
0
2
0
2
1
1
0
1
0
2
2
1
2
1
0
2
2
1
1
0
1
2
0
2
1
2
1
1
1
0
1
0
1
1
0
2
3
2
0
0
2
1
1
1
1
1
0
0
2
1
1
1
1
2
2
1
1
1
0
1
1
1
1
0
0
1
2
1
2
1
1
1
1
0
1
1
0
1
3
1
0
2
0
1
1
2
1
2
1
0
0
2
2
1
1
1
1
0
0
1
2
1
1
1
1
1
1
2
2
2
1
0
2
1
2
0
1
1
2
1
1
1
1
0
2
2
1
1
1
1
2
0
0
2
4
1
2
2
1
1
1
1
1
2
1
0
1
2
1
1
1
1
1
1
0
1
2
1
1
1
1
2
0
0
2
1
1
1
1
2
1
1
1
1
2
0
2
2
1
0
0
1
2
1
1
2
1
2
1
2
1
2
1
2
2
1
1
0
1
1
1
1
1
2
2
2
2
2
1
1
1
2
0
2
0
0
2
1
1
0
1
1
2
2
2
0
1
1
2
1
1
2
1
1
2
1
2
1
1
1
2
0
2
1
2
2
1
1
4
0
2
1
1
1
2
2
1
2
0
2
0
0
0
1
2
1
2
1
0
2
1
1
1
1
1
0
1
1
0
1
0
2
1
1
1
2
1
0
1
1
1
0
2
1
0
2
1
2
1
0
0
1
1
2
0
1
1
2
0
2
1
1
1
1
1
0
1
0
1
0
1
1
2
0
1
1
1
2
1
0
1
1
1
1
3
1
1
2
1
1
2
1
2
0
0
1
1
1
1
2
1
0
1
2
2
1
1
1
1
1
0
1
1
0
1
0
0
1
3
0
1
2
2
1
2
1
1
1
2
1
1
0
1
1
1
1
1
1
2
0
1
1
1
2
1
1
0
1
1
1
0
1
0
1
1
1
0
1
1
0
2
2
2
1
2
1
1
1
1
2
1
2
1
1
1
1
0
1
0
2
0
1
2
1
0
1
1
1
1
1
2
1
2
2
1
1
1
0
1
2
1
2
2
2
1
1
0
1
2
2
1
0
1
1
2
1
2
1
0
1
1
2
0
2
2
1
1
1
1
2
0
0
1
2
1
0
1
0
1
2
2
0
1
1
0
2
0
1
1
1
0
2
0
0
1
2
1
1
2
1
1
1
1
1
0
2
1
1
1
1
1
1
0
2
2
2
0
1
1
1
1
0
2
1
1
1
1
1
2
2
1
2
0
1
1
0
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
2
2
2
0
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
2
3
2
1
1
1
0
1
1
0
0
1
2
0
0
1
1
0
0
0
0
1
1
2
0
1
0
0
1
1
1
1
1
0
1
1
2
2
1
1
1
1
0
0
0
1
1
2
1
1
0
2
1
1
2
0
1
1
0
2
1
1
2
2
0
1
1
1
1
1
0
1
1
1
1
0
2
2
0
1
1
2
1
0
1
1
1
1
2
1
1
0
2
0
1
1
1
1
1
1
1
0
2
2
0
1
1
1
1
1
2
1
2
2
1
2
1
1
1
0
1
1
0
1
1
1
1
0
0
0
1
0
1
1
0
1
1
0
1
1
1
3
1
1
1
1
1
0
1
1
1
0
1
1
1
0
1
1
1
1
3
2
1
1
1
1
1
3
2
2
1
2
0
1
1
1
1
2
0
1
0
2
1
0
2
1
0
1
0
0
1
1
1
2
1
1
0
2
2
0
0
2
1
1
0
2
1
1
1
1
1
1
1
1
1
0
1
2
2
2
2
0
0
1
1
2
1
1
2
2
1
2
2
1
0
2
2
1
0
0
1
2
2
1
0
0
1
1
2
2
1
1
1
2
0
2
1
0
1
1
0
0
2
2
1
1
1
2
1
1
2
1
1
1
0
0
2
1
1
2
1
0
1
1
3
1
0
1
2
1
0
1
0
2
1
1
1
0
1
0
1
0
0
1
0
1
1
2
0
2
1
2
2
2
1
1
0
0
1
1
1
1
1
2
0
1
0
0
0
1
0
1
3
2
1
1
2
1
2
0
0
0
1
1
1
2
1
0
1
1
2
2
1
0
0
1
3
1
1
2
2
2
1
0
1
1
0
1
2
1
0
1
2
0
1
1
1
1
1
2
2
1
1
1
1
1
1
3
1
1
1
2
0
0
1
1
2
0
1
2
1
2
0
1
1
1
0
1
1
0
2
2
1
1
1
1
2
1
0
0
2
0
1
2
2
1
1
0
2
0
1
0
1
1
1
0
0
1
2
0
1
1
0
2
1
1
1
1
1
0
1
1
0
0
0
1
0
0
2
1
0
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
0
3
1
2
1
0
1
1
1
1
1
1
1
1
1
1
2
1
0
1
1
1
1
0
0
1
2
1
1
1
1
1
2
0
1
0
0
2
1
0
4
1
2
0
1
0
2
2
1
1
0
0
2
2
1
1
1
0
2
1
1
2
0
0
1
1
2
1
0
2
2
1
1
1
1
2
1
2
2
1
1
1
1
2
0
0
0
1
1
2
1
2
1
1
1
1
2
0
0
1
2
1
1
2
0
1
2
1
2
1
1
2
1
1
0
2
1
1
2
1
0
1
1
0
1
1
1
1
0
1
3
1
2
1
2
1
1
2
2
1
2
0
0
1
1
0
1
2
2
0
0
0
1
2
0
1
0
3
0
2
1
1
1
0
1
2
1
1
2
0
1
1
1
1
0
1
1
0
1
0
1
0
1
2
1
2
1
2
2
0
1
1
1
1
1
1
2
2
1
0
2
1
1
1
1
1
1
1
1
1
0
0
0
1
0
2
1
1
1
0
2
1
2
1
1
2
2
1
2
2
1
2
1
2
1
1
1
0
1
1
2
1
2
1
1
2
1
2
1
2
0
0
1
1
1
1
1
2
2
1
1
1
2
0
1
1
2
1
0
0
1
2
0
1
1
4
1
1
1
0
1
1
1
1
2
0
1
0
1
2
1
0
1
1
2
0
1
0
1
1
1
1
0
1
1
0
1
0
1
2
1
1
0
0
1
1
2
1
2
0
0
2
1
1
2
1
2
1
1
2
1
0
1
1
1
2
1
1
0
1
0
2
1
2
1
1
1
1
1
1
0
1
2
1
0
0
0
1
2
0
1
1
0
1
1
2
2
0
1
2
0
2
1
1
0
1
4
3
2
1
2
1
2
2
0
1
0
2
1
1
1
1
1
1
0
2
0
2
1
0
2
0
1
1
1
1
1
1
1
2
0
1
3
1
1
0
0
1
1
1
1
1
2
1
2
1
2
1
0
1
2
0
0
1
1
1
2
0
1
0
2
0
1
2
1
1
1
1
1
1
0
2
0
1
2
1
0
0
1
1
0
0
1
1
2
2
1
0
2
2
0
1
1
1
0
1
2
1
1
1
1
0
1
0
1
1
0
1
1
1
2
2
1
0
1
2
2
0
1
1
0
2
1
0
1
2
1
1
0
0
0
2
1
0
1
1
1
0
1
2
1
2
0
1
2
1
2
0
0
0
0
1
2
1
0
1
2
1
1
0
0
1
0
0
1
1
1
0
2
0
2
1
1
1
0
2
3
2
1
1
1
1
1
2
1
0
1
0
1
2
2
2
2
2
0
2
2
1
1
1
2
1
0
1
0
0
2
1
1
1
0
1
2
0
1
0
0
1
1
0
0
0
2
1
0
1
0
1
1
1
2
1
1
2
2
1
1
1
1
1
1
2
2
2
0
2
1
0
2
2
1
2
0
1
1
2
1
1
2
0
1
1
1
0
1
2
0
2
1
1
1
2
1
2
0
2
0
1
2
1
1
2
2
1
2
1
1
1
0
1
1
1
0
2
1
1
1
1
2
0
0
0
1
2
2
0
1
1
1
1
2
1
1
0
0
0
0
0
1
0
1
0
2
0
1
1
1
0
1
1
1
1
1
0
2
1
1
0
2
0
0
1
0
2
2
2
1
1
1
0
1
1
1
1
1
1
1
1
0
2
0
0
1
2
2
2
1
1
1
1
1
1
0
1
1
1
1
0
1
1
2
1
1
1
1
2
1
1
1
2
2
0
1
0
0
2
1
1
1
2
1
1
0
1
1
1
2
1
0
1
1
0
1
0
1
1
1
1
1
1
0
0
2
1
2
0
1
2
1
1
1
1
0
1
2
1
1
1
1
0
1
2
1
1
0
0
1
1
1
1
1
1
0
1
1
0
1
2
2
1
1
0
0
1
1
1
0
0
2
1
2
1
0
1
0
1
1
0
2
1
2
2
1
1
2
2
1
1
0
1
1
1
1
2
1
0
1
1
0
0
0
1
2
2
1
1
1
0
1
2
1
1
1
2
1
1
3
1
2
1
2
2
1
2
1
0
1
0
1
0
1
1
2
1
0
0
2
1
1
2
1
1
0
0
0
2
1
0
1
2
1
1
1
0
2
1
2
1
0
1
1
1
1
1
0
1
2
2
1
1
0
3
4
0
2
1
1
1
1
1
1
1
1
0
1
2
1
1
0
0
1
0
1
1
1
1
1
0
0
1
2
1
0
1
1
1
0
1
1
1
1
1
1
0
1
1
1
0
1
0
0
1
1
2
0
2
1
2
1
2
2
1
2
2
0
0
0
1
1
0
0
1
2
1
1
2
1
1
1
1
1
1
1
1
2
0
1
0
0
1
1
0
3
1
1
2
1
2
2
0
1
0
1
1
2
3
1
0
2
1
1
1
1
1
1
0
0
1
1
0
1
1
0
1
2
1
1
2
0
1
1
2
2
1
2
1
1
1
1
0
1
2
1
2
2
1
0
1
1
1
1
0
0
0
2
1
1
1
1
2
0
0
0
1
1
2
2
2
1
0
1
2
1
1
1
2
2
1
1
2
1
2
1
1
1
1
2
1
1
1
1
1
2
2
1
0
1
2
1
0
1
1
0
2
1
0
1
1
1
1
1
1
2
0
1
2
0
1
1
1
1
1
0
2
1
1
1
1
1
1
2
0
1
2
2
1
0
2
0
1
1
2
0
1
2
0
0
1
2
0
1
2
1
2
0
1
1
1
0
1
1
1
1
1
0
1
1
1
1
1
1
1
1
2
2
0
2
3
0
2
1
2
1
1
1
2
1
1
1
1
1
2
0
1
1
2
1
2
2
1
1
1
1
1
1
0
1
0
1
1
1
1
1
0
2
2
1
1
2
0
1
0
1
0
1
0
1
1
1
1
0
0
2
1
1
1
2
2
3
3
1
0
1
0
1
0
1
0
1
2
1
1
0
1
0
2
1
0
2
1
1
0
1
1
2
1
1
0
1
2
1
2
2
1
2
1
1
0
0
0
2
1
0
2
2
2
1
1
1
0
2
1
0
0
0
0
2
0
0
1
2
1
0
0
0
0
2
2
1
1
1
1
2
2
1
1
0
1
1
0
1
2
1
1
2
0
1
2
0
0
2
1
1
1
1
2
2
2
1
1
1
1
2
4
2
1
1
0
0
2
1
0
0
2
1
1
2
0
1
1
0
1
2
1
2
2
1
1
2
0
1
0
2
0
0
1
0
1
0
2
1
0
1
1
1
2
1
1
1
1
0
0
1
1
1
0
1
1
1
1
1
1
1
1
0
1
1
0
0
1
1
2
0
0
2
1
1
1
0
1
2
1
2
1
2
1
1
1
1
2
0
0
1
0
2
1
0
0
1
0
1
1
1
1
0
1
2
1
1
0
0
0
0
0
1
1
0
2
0
2
2
1
0
2
1
1
2
0
1
0
1
1
0
1
2
1
2
0
1
1
1
0
2
1
2
1
1
1
1
0
1
1
1
0
2
2
2
1
0
1
1
2
1
1
0
1
2
1
1
0
0
1
1
0
1
1
1
0
0
2
1
1
0
1
2
1
2
0
1
1
1
1
0
0
1
1
1
1
1
0
1
1
1
1
2
1
2
1
0
2
2
0
1
1
1
1
1
2
1
1
2
0
1
1
2
1
2
2
1
1
0
1
2
1
1
2
1
2
0
0
0
2
1
2
0
1
0
2
1
2
2
1
1
1
2
0
1
1
1
2
1
2
2
0
1
1
1
1
1
1
1
1
1
0
1
1
0
1
1
1
2
1
2
1
1
0
1
2
2
1
1
2
0
2
0
2
1
1
1
1
1
1
1
0
1
1
1
1
1
1
0
1
1
1
2
1
1
0
1
2
2
1
1
0
1
0
1
2
1
1
0
2
0
1
2
0
0
1
2
2
2
2
1
1
0
2
1
2
1
1
1
1
1
2
1
1
1
1
1
2
0
2
2
1
1
2
2
1
1
1
1
1
0
1
2
1
2
2
1
1
1
1
1
2
1
1
1
2
0
2
1
2
0
1
1
1
1
1
1
0
1
1
2
1
1
1
0
1
3
1
0
2
2
2
1
1
1
2
2
0
1
0
1
1
1
0
1
0
1
1
1
2
1
1
1
1
1
1
2
2
2
0
0
1
0
1
2
1
0
1
0
0
1
0
1
1
1
1
1
3
1
1
1
1
2
1
2
1
0
1
0
1
1
1
1
1
1
2
1
0
1
2
1
2
1
2
1
0
1
2
2
1
1
1
0
2
2
1
1
2
1
1
1
2
1
2
2
1
2
0
1
1
1
2
1
0
0
2
1
2
6
1
1
1
0
1
0
1
1
2
1
1
1
1
1
0
0
1
1
1
2
2
0
1
1
2
1
0
1
1
0
1
2
2
0
3
1
1
1
1
2
2
1
1
0
0
1
1
1
1
0
1
1
1
0
0
0
1
0
1
1
1
0
1
1
1
2
1
2
0
2
1
1
0
2
0
0
1
1
1
0
1
1
1
1
2
1
1
0
0
1
1
1
1
1
1
1
0
0
0
0
1
1
0
1
1
1
2
1
2
0
2
2
2
1
1
1
0
1
0
1
1
2
1
1
1
2
2
1
1
0
1
1
1
1
0
1
0
0
0
1
2
0
2
2
0
0
0
0
0
0
1
1
1
2
1
0
0
1
1
0
2
0
2
2
2
0
0
1
0
1
2
0
0
0
1
1
1
1
1
0
2
1
0
4
1
1
1
3
1
1
1
2
0
1
0
1
2
0
2
0
1
2
0
0
1
2
2
1
0
4
0
1
1
1
1
2
0
0
2
1
0
2
1
0
0
0
2
1
1
0
0
1
1
1
0
1
0
1
1
1
1
1
2
1
0
2
1
1
1
1
0
1
0
1
1
1
1
1
0
1
1
1
1
2
2
0
0
0
2
0
1
2
1
1
1
0
1
1
1
1
0
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
0
1
1
0
0
1
2
1
1
0
1
1
1
1
1
1
1
1
1
2
0
0
1
1
1
1
0
1
2
1
1
1
1
2
1
0
1
2
0
2
1
2
1
1
1
1
0
0
0
1
1
1
1
1
0
1
0
0
1
1
2
1
1
1
0
1
0
0
1
1
2
0
2
2
0
1
3
2
1
2
2
1
1
1
2
0
1
0
2
0
1
2
1
2
1
0
2
1
1
2
0
1
1
2
1
1
2
2
1
0
0
1
2
1
2
1
1
0
0
0
1
0
2
2
0
1
1
1
0
0
1
1
1
1
0
1
0
1
0
1
0
1
0
1
1
1
0
1
1
1
1
1
0
1
0
2
1
2
0
0
1
1
1
2
1
2
1
1
0
1
0
1
1
1
2
2
0
0
2
0
1
2
1
1
0
2
1
0
2
1
1
2
1
2
0
1
1
0
0
1
1
1
1
1
1
2
1
2
1
2
0
2
1
1
1
1
0
1
0
2
2
0
2
0
1
2
1
1
1
1
0
1
1
2
0
0
2
2
1
1
0
0
0
1
3
0
2
2
1
1
2
0
3
1
1
0
2
1
1
2
0
1
0
1
1
1
1
2
0
2
1
2
1
0
1
0
1
0
0
0
2
1
2
1
2
2
1
1
1
2
1
2
1
1
3
1
1
1
2
1
1
2
2
1
1
2
0
1
0
1
1
0
1
0
2
1
0
1
1
2
1
1
2
0
1
1
2
2
1
1
1
2
2
1
1
1
1
1
2
1
2
1
1
1
2
1
0
1
1
1
2
2
1
2
2
2
1
2
1
1
1
1
2
1
1
0
1
1
1
0
1
1
0
1
2
1
1
1
0
3
2
0
2
1
1
1
2
0
1
0
2
2
2
2
1
0
1
0
1
0
1
1
1
1
1
1
2
1
1
1
2
1
1
2
1
0
1
1
1
1
1
1
0
2
2
1
2
1
2
1
1
2
2
1
0
2
1
0
1
1
0
1
1
1
1
0
1
1
0
0
2
0
1
0
2
1
2
1
2
2
0
1
1
0
2
2
0
2
0
0
1
1
2
1
1
1
0
2
1
1
0
1
2
1
1
1
1
1
1
1
2
1
2
0
1
1
1
2
1
1
1
2
1
1
0
2
2
2
2
1
2
1
1
1
0
2
1
1
2
2
0
1
2
0
1
8
2
1
2
1
0
1
2
1
2
1
1
0
1
1
1
0
1
1
0
1
1
1
1
1
1
0
1
1
2
2
0
1
1
1
1
1
2
2
0
1
1
0
2
0
1
1
1
2
1
1
1
2
1
0
2
2
1
1
2
1
2
0
1
1
1
0
1
2
1
1
0
0
1
1
0
0
2
1
0
1
0
1
1
0
1
1
0
2
2
1
1
1
1
1
2
0
1
0
1
1
1
1
2
1
2
2
1
1
1
1
2
1
0
1
2
1
2
1
0
2
0
1
2
1
0
0
1
0
0
0
0
1
1
1
2
2
1
1
1
3
1
1
0
2
1
2
0
1
1
1
2
4
0
0
5
1
2
1
0
0
1
1
1
1
1
2
2
1
1
1
1
2
1
2
2
0
1
1
0
1
1
1
1
2
2
2
0
0
1
1
1
2
0
0
1
0
1
0
1
1
0
0
1
1
1
0
0
1
0
0
1
0
1
1
2
1
1
0
1
0
2
0
2
1
2
1
1
1
2
1
2
1
1
2
1
4
0
2
1
1
1
1
2
1
0
1
1
1
2
0
2
1
1
1
1
2
0
1
1
1
0
0
1
1
1
1
0
0
0
1
6
1
2
1
3
1
1
2
1
0
2
2
1
0
1
2
1
2
1
1
2
0
2
0
1
0
1
1
2
0
1
0
1
0
0
0
0
2
2
1
1
1
2
0
1
0
2
1
0
0
1
1
0
1
0
3
1
1
1
1
1
2
0
2
2
0
0
1
0
1
1
0
1
1
0
1
1
1
0
1
1
0
2
1
1
1
2
1
1
0
1
2
1
0
1
0
2
0
1
1
0
0
0
1
0
1
1
1
0
2
2
1
0
1
0
0
1
1
1
0
2
1
1
0
2
1
2
0
1
1
1
1
1
1
1
0
0
1
0
1
1
1
2
2
0
1
1
2
0
0
1
1
1
2
1
1
0
2
0
1
1
0
1
1
0
1
2
0
2
1
1
2
1
0
1
1
1
1
1
0
6
1
1
2
2
1
1
1
1
1
2
0
2
1
1
1
1
2
0
1
0
1
3
2
1
2
2
1
2
0
1
0
1
2
2
1
1
1
4
1
1
1
1
2
0
1
1
1
2
2
2
1
1
1
1
2
1
1
2
1
0
0
0
0
1
1
0
2
0
1
1
1
0
1
0
0
1
2
0
2
2
2
0
2
0
1
0
1
1
1
1
0
3
0
1
1
1
2
2
1
1
1
1
0
0
2
1
1
1
0
1
0
0
2
2
1
0
1
2
2
0
2
1
1
1
2
1
2
0
0
0
1
1
1
1
1
0
1
1
0
1
1
0
1
0
2
2
1
0
2
1
0
1
2
0
1
1
1
1
2
1
0
0
1
0
1
0
1
1
2
1
0
2
0
1
1
1
1
2
0
1
1
0
0
1
2
2
0
1
2
1
1
0
2
0
0
1
1
0
1
2
2
1
1
1
1
2
1
0
0
2
1
1
0
0
0
4
1
1
0
0
2
1
1
0
1
2
0
0
1
1
1
2
0
1
2
2
2
2
1
1
0
1
1
1
2
1
1
2
0
0
0
1
2
1
0
0
0
0
0
2
2
2
1
0
1
1
0
0
1
1
1
1
1
1
1
0
1
2
1
1
2
1
0
1
1
0
1
1
1
1
2
1
0
0
2
1
1
0
2
0
1
0
1
1
1
1
2
2
1
2
0
2
1
1
2
2
1
1
1
1
1
1
1
2
1
0
2
1
1
0
1
2
0
1
1
2
1
2
1
1
1
1
0
1
0
2
0
2
0
1
2
0
1
0
2
1
0
0
1
1
1
1
0
2
0
1
1
1
1
2
1
1
0
1
1
2
1
0
1
2
2
2
1
1
1
2
1
1
2
2
1
1
2
0
0
2
2
0
1
0
1
0
2
2
1
0
1
0
2
1
3
1
1
1
1
0
2
0
1
1
1
1
1
3
0
1
1
1
0
2
1
2
1
0
1
2
1
1
1
1
1
0
2
1
0
1
1
3
1
1
0
1
1
1
0
2
0
1
1
1
1
1
1
1
1
0
1
2
2
2
1
1
1
1
1
2
1
1
1
0
1
1
1
1
2
1
1
0
1
2
2
0
1
2
1
0
2
1
1
1
1
0
1
2
1
1
2
1
1
0
0
1
1
0
2
1
2
2
1
1
0
0
1
2
0
1
1
1
2
2
1
2
2
1
1
2
0
3
1
0
0
1
1
1
2
1
2
2
1
1
1
1
1
0
1
1
1
1
2
1
1
0
1
0
1
1
0
1
0
0
2
1
0
0
0
1
2
2
1
1
2
1
1
1
0
1
1
0
1
1
1
1
0
0
2
1
0
1
1
1
2
0
2
2
1
1
0
1
1
1
1
2
1
1
2
1
1
0
2
0
1
1
1
1
1
0
2
0
1
1
1
1
0
1
1
2
1
0
0
2
2
1
2
1
2
0
0
0
1
0
2
0
1
1
1
0
1
0
1
0
1
2
2
1
1
0
0
1
1
1
1
2
1
0
1
1
1
1
2
2
1
1
0
0
2
2
0
1
0
0
1
2
1
1
1
0
2
1
1
1
0
0
1
0
0
1
2
2
0
1
1
2
0
0
1
1
1
1
0
2
1
1
1
0
0
0
2
0
1
0
1
0
0
0
1
1
1
1
0
1
1
1
1
0
2
2
1
0
1
2
1
0
2
2
1
0
1
1
0
1
1
1
1
2
1
1
2
0
1
1
1
1
1
1
1
2
1
2
2
1
2
2
3
0
1
1
1
1
1
1
1
1
1
1
2
0
1
1
2
1
1
2
3
2
2
1
1
1
2
1
1
0
0
0
2
1
1
2
1
1
2
2
1
0
1
1
1
0
1
1
2
1
3
0
1
0
1
0
0
1
0
2
0
1
2
1
1
1
1
1
0
0
1
0
2
1
1
0
2
0
1
2
1
1
0
2
0
0
1
2
1
0
2
2
2
0
1
1
1
0
1
4
1
1
0
0
1
2
1
1
1
1
1
1
2
0
1
2
1
1
2
0
1
1
2
2
1
2
2
0
1
0
2
0
1
1
1
1
1
1
2
1
0
2
2
1
1
1
1
1
1
2
0
0
0
0
0
0
0
2
0
1
1
1
2
1
2
0
2
0
1
0
2
0
2
1
1
2
0
1
2
1
2
1
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
0
1
2
0
0
2
2
0
1
4
1
2
2
2
2
1
1
0
0
0
0
1
1
2
2
1
1
2
2
1
0
1
0
1
1
1
0
1
0
2
1
2
0
1
1
1
1
2
0
1
1
2
1
2
1
1
1
1
1
1
1
1
0
1
1
0
2
1
1
0
0
1
1
1
1
1
1
0
1
1
2
2
2
1
0
1
1
1
0
1
0
2
1
1
2
2
1
1
2
2
1
2
2
1
1
2
1
1
1
0
1
2
0
1
2
1
1
0
1
2
2
1
0
0
2
0
1
2
1
1
0
0
2
0
0
1
1
2
1
0
0
2
1
0
1
0
0
1
0
2
1
0
0
2
1
1
1
2
0
1
0
1
0
2
1
1
1
1
2
2
2
2
1
1
2
1
1
1
2
0
2
1
2
1
0
0
2
1
1
2
0
0
2
3
2
1
0
0
1
0
1
1
1
0
0
1
1
1
2
0
1
1
0
2
1
2
1
0
1
0
1
2
1
1
2
1
0
1
1
1
0
0
2
0
2
1
2
0
2
0
1
1
2
0
1
1
1
1
2
1
2
0
1
2
0
1
1
1
1
2
1
0
2
1
0
1
1
1
1
3
2
1
0
1
1
1
0
0
0
0
2
1
2
1
1
1
1
1
1
0
1
1
1
0
0
1
1
2
0
0
1
1
1
1
1
1
0
1
2
1
2
0
0
0
0
2
1
0
1
1
1
1
0
1
2
2
2
1
1
1
1
1
1
2
1
2
1
1
1
0
2
0
1
0
1
2
0
0
1
0
1
2
1
2
1
1
1
0
1
1
1
1
1
1
2
1
0
2
0
1
0
1
2
0
2
2
2
2
1
1
2
1
3
1
1
0
1
2
2
1
1
1
1
1
1
0
1
1
2
1
0
1
3
1
1
0
0
0
0
1
2
1
1
1
1
1
1
0
2
2
2
0
1
0
1
2
0
1
1
2
1
2
1
1
1
1
2
1
3
2
7
1
1
0
1
2
1
1
0
1
0
0
1
2
0
2
2
1
1
1
1
0
0
2
1
1
1
1
1
1
2
1
2
1
1
2
1
0
0
4
2
1
1
0
1
2
1
1
1
1
0
1
2
1
0
2
0
0
2
1
1
0
0
1
1
2
0
1
2
0
0
1
2
0
2
1
1
1
1
1
1
0
1
2
1
1
1
1
1
0
2
0
0
2
1
0
0
2
1
0
1
1
1
1
0
2
1
0
1
1
1
0
1
1
1
2
2
0
1
1
0
1
1
2
0
1
1
2
3
0
2
1
1
2
2
1
1
1
1
1
1
0
2
1
0
1
1
1
1
2
2
0
1
1
1
2
1
1
0
1
1
3
2
1
1
0
1
1
1
2
0
1
1
2
1
0
2
1
2
1
2
0
1
2
0
1
1
3
1
0
1
2
1
1
1
1
1
2
1
1
1
0
1
1
2
1
1
1
0
2
0
0
0
2
1
1
1
1
1
1
1
2
1
1
2
0
1
0
1
1
0
0
1
1
0
2
1
2
1
0
0
0
0
0
1
0
2
1
0
1
2
1
2
1
0
2
2
1
0
1
1
1
2
1
3
2
1
1
1
2
2
0
4
1
2
1
0
2
1
1
0
2
1
1
1
1
1
2
0
0
0
1
1
0
2
2
2
1
2
0
1
1
2
1
2
2
1
1
1
2
1
2
1
1
1
0
2
1
1
0
2
1
0
0
1
1
1
1
1
1
0
1
0
1
1
2
1
1
2
1
1
1
1
0
0
0
2
1
1
1
1
1
1
0
1
1
0
0
1
1
0
2
1
1
1
2
1
1
1
1
0
2
2
1
1
1
1
0
1
1
1
0
2
1
1
1
2
0
2
1
1
0
0
1
2
1
0
1
1
0
2
2
0
1
2
1
0
0
1
1
2
1
2
1
1
0
0
1
1
1
1
0
0
1
0
1
1
1
1
2
1
1
2
0
1
0
2
0
0
1
0
0
1
1
1
1
0
1
1
2
2
1
0
0
0
1
2
1
1
1
1
1
1
0
2
2
1
2
1
0
1
1
0
2
1
0
1
1
1
2
2
0
0
2
1
0
0
1
1
1
2
2
2
1
2
1
0
2
2
1
2
2
1
1
0
2
1
1
2
1
0
2
0
1
1
1
0
2
2
1
1
1
1
1
0
1
0
1
1
1
2
1
1
2
0
1
1
1
1
1
2
1
1
1
1
2
1
0
1
1
1
0
1
0
1
1
0
1
1
1
1
1
2
1
1
1
1
0
2
0
0
1
1
2
0
1
2
1
1
2
2
1
0
0
1
1
1
2
2
2
1
2
1
1
1
2
1
1
1
1
1
0
0
0
0
1
0
2
2
1
1
1
1
1
1
1
0
0
0
1
2
2
1
1
1
1
1
2
0
1
2
2
1
1
1
0
1
1
1
1
2
2
2
1
0
2
0
1
2
1
0
1
1
1
1
1
2
0
1
1
2
1
0
1
1
1
0
2
1
2
2
1
1
1
1
2
1
1
1
0
0
1
1
0
1
1
1
2
0
1
0
0
1
0
2
0
1
1
1
1
2
1
1
0
1
1
1
1
3
1
1
1
1
1
1
2
1
1
2
1
0
1
0
1
1
1
0
2
1
2
1
0
1
1
1
2
1
0
1
1
2
1
1
0
2
1
2
1
1
1
0
1
2
1
0
2
1
2
1
2
1
0
0
1
1
1
2
1
1
1
1
0
1
1
1
1
2
2
1
2
1
1
1
1
1
1
2
0
2
0
2
1
0
0
0
1
1
1
1
1
1
1
0
2
1
2
1
1
1
1
1
1
2
2
2
2
1
1
1
2
1
1
1
1
0
0
0
2
0
0
1
1
1
1
2
0
1
1
1
1
1
2
1
0
1
0
2
1
0
2
1
0
2
0
1
1
1
1
1
0
1
2
1
1
0
0
1
1
1
1
1
0
1
0
1
1
1
0
1
1
1
0
1
2
1
1
2
1
1
0
0
0
1
1
2
2
1
1
1
1
1
1
1
2
3
2
1
1
1
1
2
1
1
1
1
1
0
0
1
2
0
0
1
1
1
0
2
2
0
1
0
1
0
2
0
1
1
1
1
2
0
1
1
1
2
1
1
1
2
1
3
2
1
1
1
2
2
1
1
1
2
2
1
1
1
1
1
0
1
1
2
2
2
2
1
2
0
0
1
2
1
3
1
1
1
1
2
1
1
2
0
1
2
2
2
1
1
0
1
0
0
0
1
1
2
1
0
2
1
1
2
0
0
2
2
1
0
1
1
2
2
1
1
2
1
1
2
1
1
1
2
2
0
1
1
1
0
0
1
1
0
1
1
0
0
1
1
1
1
1
1
0
1
1
1
1
0
2
0
1
2
2
2
1
0
2
1
1
1
0
2
2
0
2
2
0
0
0
1
1
0
1
1
1
1
0
2
1
2
0
1
0
1
1
1
3
1
2
2
1
0
2
1
1
0
1
1
1
1
2
2
1
1
3
1
1
1
2
1
1
1
1
2
0
0
1
1
0
2
0
1
1
1
0
2
1
1
0
2
2
0
1
1
1
1
0
1
2
1
1
1
1
1
0
1
1
2
0
2
0
1
2
1
0
2
1
1
0
0
1
1
2
1
2
0
1
1
0
1
1
1
2
1
0
2
2
2
1
1
1
1
2
1
1
1
1
0
0
2
0
1
2
0
2
1
1
1
1
2
0
1
0
1
1
2
0
0
2
1
1
0
1
0
1
0
1
0
0
0
1
0
1
1
1
2
2
1
0
1
1
1
1
1
0
0
1
1
1
2
1
1
1
1
2
2
0
1
2
0
2
2
1
1
1
0
2
0
0
1
1
1
1
0
0
1
1
1
2
1
1
1
0
2
1
2
1
1
1
0
1
1
0
0
1
1
1
1
2
1
1
0
2
1
2
1
1
1
2
1
1
1
1
2
1
0
1
0
1
0
0
1
1
0
1
0
0
1
2
1
1
1
1
1
1
0
1
1
1
0
2
1
1
1
1
1
1
0
0
1
1
1
1
1
2
1
1
2
2
1
1
1
0
0
1
1
0
2
1
1
1
1
0
0
1
1
1
0
0
1
1
2
0
4
2
0
2
2
0
0
1
1
1
1
2
1
1
1
1
2
1
0
1
0
2
2
0
2
1
1
2
0
1
0
2
1
1
1
1
1
1
1
1
1
0
0
0
1
0
2
2
0
2
2
0
0
0
1
1
1
0
0
1
0
2
2
2
0
2
0
1
0
1
1
2
0
1
2
1
2
0
1
1
1
2
1
2
1
2
2
1
2
1
0
0
1
1
0
1
1
1
0
2
2
1
1
2
1
1
1
0
2
2
1
2
0
2
1
0
1
0
1
1
1
1
3
1
0
0
0
1
1
1
0
0
1
1
0
0
1
1
1
0
2
2
2
1
2
1
1
1
2
1
2
1
0
1
1
2
0
1
2
1
1
2
0
2
1
1
2
0
0
2
1
0
1
2
1
0
2
1
1
2
2
2
1
1
2
1
1
1
1
2
2
0
1
0
2
1
2
1
1
1
1
2
0
0
1
1
1
0
2
2
1
2
2
1
1
1
1
0
0
0
2
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
0
2
0
1
1
0
1
1
1
1
2
2
2
0
0
1
2
1
0
0
1
1
1
1
2
1
1
1
2
1
1
0
1
2
0
2
2
1
1
1
2
2
1
0
0
2
1
1
1
1
1
1
1
1
2
1
0
1
2
0
1
1
2
1
1
0
1
0
1
1
1
2
0
2
2
0
2
1
0
0
1
1
0
1
1
2
1
1
1
1
1
2
1
2
1
1
2
0
0
2
1
1
1
1
1
1
1
2
2
2
2
2
2
0
2
1
1
1
1
0
1
0
2
1
1
0
0
1
0
1
2
1
0
0
0
0
0
0
1
1
1
1
1
1
0
1
0
0
1
0
1
1
2
1
2
0
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
0
1
1
2
1
1
2
2
2
1
0
1
1
0
1
2
1
0
1
0
1
0
2
1
1
1
1
0
1
1
2
1
0
1
1
0
1
0
0
1
0
1
1
1
1
2
0
2
1
0
0
0
0
1
1
1
1
1
2
1
1
1
1
1
0
0
2
0
0
0
1
1
1
1
0
2
1
1
2
2
1
0
2
2
0
2
1
1
1
1
1
1
2
3
2
1
2
0
1
2
2
1
1
0
1
1
2
0
1
1
2
4
1
0
1
1
1
1
1
0
3
2
1
0
1
1
1
1
2
1
1
0
0
1
0
0
2
1
1
1
1
1
0
1
0
0
1
2
1
2
2
0
2
1
1
1
0
1
0
1
0
2
2
1
1
1
1
1
2
2
3
0
1
2
2
1
1
1
0
1
2
0
1
0
1
1
2
1
1
2
1
1
1
0
1
1
1
2
1
0
1
1
1
0
0
1
1
2
1
1
0
0
0
2
0
1
1
0
1
0
1
0
0
1
1
0
1
2
0
1
1
2
2
0
2
1
2
2
1
1
2
0
1
2
1
1
2
1
1
8
0
1
1
1
0
3
1
0
0
2
1
1
0
1
0
2
1
0
1
0
0
1
2
1
1
1
1
1
1
2
1
1
0
0
1
1
1
1
2
1
1
0
0
0
1
1
2
1
1
2
0
1
2
1
1
1
1
1
1
1
1
1
0
1
1
2
2
1
0
1
0
1
1
1
1
2
0
1
1
2
0
0
1
1
2
1
0
1
1
1
0
1
0
1
1
1
1
1
1
2
2
1
1
1
0
1
1
1
2
1
0
1
0
0
0
1
1
2
0
2
2
1
0
0
1
1
0
1
3
1
2
1
1
1
1
0
1
1
1
2
1
1
1
2
2
2
0
2
1
1
3
1
2
3
1
1
1
1
0
1
1
0
2
1
2
0
1
1
1
1
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
0
1
2
2
1
0
1
1
1
1
2
2
1
1
1
0
2
1
2
1
2
1
0
2
0
0
1
1
1
2
1
1
1
1
1
0
0
2
1
1
0
1
0
1
1
1
2
0
2
0
2
1
1
1
0
1
1
1
0
1
1
1
2
1
1
1
1
0
1
3
1
1
1
0
1
1
2
0
2
1
0
2
1
2
1
1
1
0
1
0
1
0
1
1
2
2
1
1
2
0
0
1
1
0
1
2
1
0
1
1
1
0
1
1
1
1
1
1
1
1
2
1
1
1
0
0
1
0
1
0
1
1
0
1
1
1
1
0
1
2
2
0
1
1
2
0
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
0
1
0
1
1
1
1
1
1
1
1
1
0
0
0
0
1
1
1
1
1
1
1
1
2
0
1
1
1
1
0
2
1
1
1
1
1
1
1
1
1
0
0
0
2
1
0
0
0
1
1
0
1
0
1
1
1
1
1
1
1
2
0
0
0
1
2
1
1
2
1
1
1
2
1
0
1
0
1
2
2
1
0
0
1
2
2
1
1
0
2
1
3
1
2
1
0
1
0
0
1
1
1
0
1
0
1
0
1
2
1
1
0
2
2
0
1
1
1
2
0
1
1
1
1
1
2
2
1
1
0
1
0
0
1
0
0
1
1
0
1
0
0
1
0
1
0
1
2
1
1
1
0
1
2
1
1
1
1
0
0
1
1
1
1
0
1
2
2
0
0
1
1
1
1
0
1
2
0
2
2
1
1
0
2
1
0
2
2
1
1
0
0
1
1
2
1
2
1
1
2
0
1
1
1
1
1
1
1
1
0
2
1
1
1
0
2
1
1
1
1
0
0
0
2
1
1
1
0
1
2
1
1
1
0
1
1
2
2
1
2
1
1
0
2
1
1
1
1
1
0
2
1
1
1
2
0
2
2
0
1
1
1
0
1
2
1
0
1
2
0
1
0
0
0
0
1
1
0
1
2
0
1
0
1
0
2
1
1
0
1
1
1
1
0
0
1
1
2
2
1
0
1
0
1
1
0
1
2
1
1
1
1
1
1
1
0
0
0
0
2
1
1
0
1
2
0
1
1
0
0
2
1
0
0
1
1
1
0
1
2
0
0
1
0
0
2
1
1
2
0
0
1
2
0
2
1
1
1
1
1
1
0
1
0
1
1
1
0
1
0
1
1
2
1
1
1
1
1
1
1
0
2
4
0
1
1
1
0
2
1
1
1
0
1
0
2
2
2
1
1
0
0
2
2
2
0
1
2
1
1
1
2
0
0
1
2
0
2
2
1
1
0
1
3
1
0
1
1
2
2
1
0
1
1
1
2
0
1
2
1
1
1
0
1
0
1
0
1
2
1
1
2
2
2
1
1
1
2
1
1
1
2
1
2
1
1
1
2
1
2
0
1
0
2
0
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
0
1
1
0
1
2
1
2
2
1
1
2
1
1
1
4
2
2
0
1
1
2
0
2
0
0
0
1
1
1
0
2
0
1
2
2
0
1
0
1
1
2
1
1
2
2
1
1
2
1
1
1
0
1
0
0
1
0
1
1
2
1
2
1
1
0
1
1
1
1
2
0
0
1
1
2
2
1
0
1
2
2
2
2
1
2
0
2
2
0
1
1
2
1
1
1
1
1
0
1
0
0
0
2
0
1
2
0
1
2
0
0
0
2
1
1
0
1
0
1
1
1
1
1
0
1
1
2
0
2
1
2
0
1
2
0
2
0
1
2
1
2
0
1
2
1
0
1
1
2
0
0
0
1
1
1
1
1
0
1
1
1
1
0
1
2
1
1
1
1
1
1
1
0
1
1
1
0
1
1
1
2
1
0
1
2
2
1
1
2
1
2
0
3
0
2
0
2
1
1
0
1
0
2
0
0
2
0
1
1
2
1
1
2
2
1
1
1
2
0
0
1
0
0
0
2
1
1
0
1
0
0
2
0
0
1
0
2
2
2
2
2
1
2
1
1
0
0
1
0
0
1
1
1
0
0
0
1
2
1
1
1
1
2
1
2
1
1
2
3
0
0
1
1
0
2
2
1
2
0
1
0
1
1
1
1
1
0
1
2
0
0
1
2
1
1
2
1
0
1
1
1
1
0
2
0
2
1
0
1
1
1
1
2
1
2
1
2
1
1
1
1
1
0
1
1
1
1
0
3
1
1
1
1
1
1
1
0
1
1
2
1
0
2
1
2
2
1
1
1
1
1
1
1
0
2
1
2
1
0
1
2
1
0
1
0
2
1
1
2
1
1
2
1
0
1
0
0
1
1
2
1
0
1
2
1
1
1
1
0
1
2
1
1
2
1
1
1
1
1
1
0
1
1
1
1
1
2
2
1
2
1
1
1
1
0
0
2
0
1
1
0
1
1
1
2
0
2
1
1
0
1
1
1
1
1
1
1
1
1
0
1
1
1
1
0
2
1
1
1
1
1
1
1
0
0
1
1
1
2
1
2
0
0
1
2
2
0
1
2
1
1
0
1
1
0
0
0
1
0
1
0
0
1
1
2
1
1
2
2
0
1
1
0
0
1
1
1
0
1
2
0
1
1
1
0
1
1
0
1
2
4
0
1
2
1
2
2
1
1
1
1
2
1
2
2
1
2
0
1
2
0
1
2
0
0
0
1
2
0
1
2
2
0
0
0
1
1
1
1
1
1
1
1
1
1
0
1
1
0
1
1
1
2
0
1
2
3
2
0
0
1
1
0
3
0
2
2
1
1
1
1
1
0
2
1
0
0
1
2
1
2
2
1
1
0
0
1
2
1
1
1
0
2
1
0
0
1
1
0
1
1
0
0
1
1
2
1
0
1
1
1
0
2
1
1
2
1
2
2
1
2
1
1
1
2
1
1
1
1
0
0
2
1
2
1
1
0
1
0
0
0
2
1
1
1
0
2
2
2
0
2
2
2
0
1
0
0
1
0
0
2
2
1
1
1
2
0
1
2
1
4
1
1
1
2
1
0
1
1
2
2
1
1
0
1
2
1
0
0
2
0
1
1
1
2
0
1
2
0
1
1
2
1
0
2
1
1
1
1
0
0
2
1
0
1
0
1
1
1
2
1
1
0
2
1
1
1
1
0
0
2
0
1
2
0
1
2
1
1
1
0
1
0
2
1
1
0
0
0
1
2
2
1
0
0
1
1
1
2
1
2
1
0
1
6
0
1
1
1
0
1
1
1
0
1
1
0
1
1
0
1
1
2
1
0
1
0
1
1
2
1
1
0
1
1
1
1
0
0
1
1
1
1
0
1
2
2
1
1
2
1
0
1
1
0
2
1
1
1
1
1
1
2
1
3
2
0
1
1
1
1
0
0
1
1
1
1
0
2
0
2
2
0
0
0
1
1
2
2
1
2
1
1
2
0
1
0
1
1
1
1
1
1
0
1
0
1
2
0
4
2
2
0
2
2
2
2
1
0
0
1
1
1
1
2
1
0
2
1
1
1
1
2
2
1
1
2
2
0
3
1
1
1
1
1
1
2
1
1
1
0
1
1
2
1
0
3
0
0
2
0
0
2
1
1
2
1
0
1
1
1
1
1
0
0
2
1
1
3
2
2
1
1
2
1
2
1
0
1
1
0
0
0
2
1
3
1
1
1
1
2
1
1
1
1
2
2
1
0
1
1
2
0
0
1
2
2
1
1
1
2
1
1
1
2
1
1
0
1
1
1
0
0
2
2
0
0
0
1
0
1
1
1
0
1
0
1
1
1
1
1
0
1
2
1
0
1
1
2
2
2
2
0
0
1
1
2
2
1
1
2
1
1
0
1
0
2
0
0
0
1
4
1
0
1
1
0
1
0
1
2
1
1
1
0
1
1
1
1
2
0
1
1
1
0
0
1
1
2
1
2
1
1
1
1
1
0
0
0
0
1
2
1
1
0
2
0
2
1
0
2
2
1
1
1
2
1
0
1
1
2
0
1
2
0
1
1
1
1
0
2
0
1
2
1
0
2
1
1
1
0
2
1
2
0
1
0
1
1
1
1
2
1
0
1
2
1
1
1
1
0
1
2
3
0
0
0
0
0
2
1
1
2
1
0
2
1
1
2
1
1
1
1
0
1
2
0
1
1
1
1
1
1
2
0
2
0
1
1
2
1
1
2
0
2
2
0
1
0
0
1
0
1
0
0
1
2
1
1
1
0
0
1
1
0
1
2
0
1
1
1
1
0
1
0
1
1
1
2
0
1
1
1
2
1
1
1
0
1
0
1
1
1
1
1
1
1
2
0
1
1
1
2
1
1
2
1
2
1
2
0
2
0
1
2
1
1
0
1
1
2
1
1
1
1
3
1
1
0
1
2
1
1
1
2
0
0
1
1
1
2
1
1
2
1
0
1
1
1
1
1
1
1
0
2
0
2
1
2
0
1
1
1
2
1
1
0
1
1
2
2
0
1
1
1
0
1
0
1
2
1
2
0
2
2
2
1
1
1
1
0
1
1
0
1
1
1
0
1
1
2
1
1
2
2
1
1
1
1
1
1
1
1
0
0
1
1
1
2
2
1
1
1
1
2
0
2
1
0
2
1
1
0
2
1
0
1
2
1
1
1
0
1
0
2
1
1
1
0
1
2
0
1
1
0
0
1
1
2
0
1
1
1
1
1
2
1
1
2
0
1
1
1
2
1
1
2
1
0
1
0
1
2
1
1
2
1
1
0
0
0
2
2
1
1
1
2
1
1
2
0
2
1
1
0
0
0
2
1
1
1
2
1
2
0
0
1
1
1
1
1
0
1
0
2
1
1
2
1
1
1
2
1
2
1
2
1
1
1
2
2
2
1
1
0
0
1
1
1
1
2
1
2
0
1
2
1
1
0
3
1
1
2
2
1
1
0
0
2
2
0
0
0
2
0
1
1
1
0
2
2
2
1
2
1
1
0
1
1
1
1
1
0
2
0
1
2
1
2
0
1
1
0
2
0
2
2
1
1
2
1
0
1
0
1
1
1
1
1
1
1
1
1
0
2
0
1
1
1
0
2
1
2
1
1
0
1
2
1
3
1
1
1
0
2
0
2
2
1
1
0
0
2
0
1
2
2
1
2
1
1
1
2
1
2
1
1
1
0
0
2
1
2
1
2
1
2
2
2
1
1
0
1
1
1
0
1
2
2
2
0
1
1
1
0
2
1
1
2
1
0
1
0
2
0
1
1
1
0
2
1
1
0
1
1
2
0
1
0
1
3
1
0
1
1
0
0
1
1
2
2
0
0
2
2
0
0
1
0
1
0
2
1
1
1
1
1
0
2
1
1
1
0
2
2
0
0
1
2
0
2
1
1
2
1
0
0
0
1
2
1
1
1
1
1
0
0
1
2
2
1
1
2
1
0
0
2
2
0
2
2
2
1
1
2
1
1
0
2
1
2
0
2
1
0
1
1
2
0
2
1
1
2
0
2
2
2
2
1
3
2
0
0
1
2
1
1
2
1
1
1
1
1
2
1
1
2
1
0
2
2
0
1
1
0
0
1
0
1
2
2
1
2
2
1
1
1
1
1
2
0
1
0
4
0
1
1
1
2
0
1
2
0
1
0
0
2
0
0
3
0
1
0
1
0
0
0
0
1
0
1
1
2
1
1
0
1
1
2
1
1
1
2
1
2
1
2
2
1
1
1
1
2
1
0
1
0
0
2
2
2
1
1
1
0
1
1
0
1
1
0
1
2
1
1
1
1
1
1
1
1
1
2
2
2
0
2
1
2
1
2
2
1
1
1
1
0
1
2
2
0
0
1
1
2
1
1
0
0
0
1
1
4
1
2
0
1
2
1
1
1
0
1
0
2
0
1
1
1
2
2
1
1
1
1
1
0
1
2
1
0
1
0
0
2
0
1
0
0
2
0
2
0
2
1
2
1
1
1
2
1
1
1
1
2
1
2
1
2
0
1
2
1
1
2
1
1
2
0
1
1
1
1
0
0
0
1
0
1
0
2
1
1
2
1
1
1
1
1
2
1
1
0
0
2
2
0
1
0
3
2
1
2
2
0
2
1
1
1
1
0
0
1
0
0
2
1
0
0
0
1
1
1
1
1
1
0
0
0
1
1
0
0
2
1
1
1
2
0
1
1
0
1
1
0
0
1
1
0
1
2
2
1
2
1
1
1
1
2
1
2
2
0
1
2
1
1
0
0
1
2
0
1
1
0
0
1
1
1
2
0
0
1
1
1
0
2
2
2
1
2
0
1
1
2
1
2
1
0
1
2
2
1
0
1
2
2
1
1
1
2
1
1
1
1
0
1
2
1
0
1
0
1
1
1
2
1
0
1
1
2
1
1
2
1
2
0
0
1
0
1
2
1
2
2
2
1
1
0
1
1
2
1
0
1
1
0
1
1
0
1
0
1
1
1
1
1
1
0
1
2
2
0
1
0
0
0
2
1
1
1
2
0
2
1
2
1
0
1
1
1
1
2
0
0
0
2
1
1
1
0
0
0
1
1
1
1
3
1
0
0
1
0
1
0
1
2
1
1
1
1
1
0
1
2
2
1
2
1
1
0
1
1
1
0
2
0
1
1
1
1
1
1
1
0
2
2
2
2
1
1
0
1
1
0
0
1
1
2
1
0
2
1
2
0
0
0
1
1
1
0
0
1
0
1
1
1
1
1
1
1
1
1
2
3
1
0
2
2
3
1
1
1
1
1
2
1
0
1
2
1
1
1
1
1
1
1
1
2
1
0
2
0
1
1
2
2
1
0
1
2
0
1
1
1
2
0
1
2
1
2
1
2
1
2
0
0
0
2
1
0
2
1
1
0
0
2
1
1
1
1
1
1
1
1
0
1
0
0
2
0
2
1
0
0
0
2
2
0
1
1
1
1
1
0
2
0
1
1
1
1
1
0
1
1
1
1
2
1
1
1
0
2
1
1
0
2
1
1
0
0
1
1
2
0
1
0
1
1
1
2
1
1
1
1
0
1
2
1
1
4
0
1
0
1
1
1
2
1
1
1
0
0
2
2
0
1
0
2
2
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
2
0
1
0
2
0
2
0
0
1
1
2
1
1
0
1
1
1
2
1
2
2
1
0
1
1
2
1
1
2
0
1
0
2
2
1
2
1
1
1
3
0
2
1
1
0
3
1
2
1
2
1
2
1
0
1
1
0
0
2
0
0
1
0
1
0
1
1
2
0
2
0
1
2
2
1
1
1
1
1
1
1
1
0
0
2
1
1
1
1
2
1
0
1
1
1
0
0
2
1
1
0
2
1
1
0
1
1
1
2
1
1
2
1
1
2
2
1
1
0
1
1
1
1
2
2
0
1
0
1
1
1
0
2
1
1
2
2
0
2
1
0
1
0
2
2
1
2
2
3
1
1
1
0
0
1
2
1
1
0
2
2
1
2
1
0
1
1
1
1
2
2
0
0
1
1
0
2
2
1
1
1
1
0
1
0
2
1
0
1
2
1
1
2
2
1
2
0
1
2
2
1
1
2
1
1
0
1
2
1
2
1
0
2
0
1
1
0
1
1
1
1
1
2
2
1
2
2
2
1
0
1
0
2
1
1
0
3
0
1
2
1
2
2
1
1
0
1
1
1
1
5
1
0
1
1
0
1
1
1
1
1
1
1
2
1
0
2
1
1
0
2
1
2
1
1
1
1
1
1
2
0
1
1
1
1
0
0
1
0
1
1
0
1
2
1
1
0
1
1
2
1
1
1
2
1
1
1
0
0
0
0
0
1
1
1
1
1
1
1
2
2
0
1
1
3
1
2
0
0
1
0
0
1
2
2
0
1
1
2
0
2
1
2
1
0
0
2
1
1
0
1
1
1
1
1
0
1
2
1
1
1
1
1
2
1
1
2
1
1
1
2
1
2
1
0
1
1
1
0
1
0
1
1
2
0
1
1
1
0
2
2
1
2
1
1
1
1
2
1
1
1
0
0
0
1
2
1
1
0
0
1
2
1
0
1
1
1
0
0
1
1
1
2
1
2
0
1
1
1
1
1
2
0
1
0
1
1
1
0
1
2
1
0
2
2
1
2
2
2
1
1
1
2
1
2
1
1
2
2
1
0
1
0
2
0
0
2
2
2
1
1
2
1
0
1
1
2
1
0
0
2
1
0
1
1
2
2
1
1
0
1
1
1
0
1
1
2
1
1
2
1
1
0
0
1
2
2
0
1
1
0
0
0
1
1
1
1
1
1
0
2
2
1
0
2
1
1
0
0
1
0
1
1
1
2
1
0
2
1
1
1
1
0
1
2
1
1
0
0
1
1
1
2
1
1
0
1
1
0
0
1
1
2
1
1
1
1
0
2
2
1
1
1
1
1
1
1
1
1
0
2
0
0
1
2
1
2
1
0
1
1
2
1
2
2
0
1
0
0
1
1
0
1
1
2
1
1
0
1
0
2
2
1
1
0
2
0
1
1
0
1
1
0
1
1
1
0
1
0
1
1
1
1
1
2
1
1
2
0
1
2
1
1
1
2
1
1
0
1
1
1
1
1
1
2
1
1
2
1
2
1
1
1
0
1
1
2
1
1
1
1
1
1
0
1
0
2
2
1
1
1
1
1
2
2
1
0
0
1
1
1
2
1
1
1
2
1
1
1
1
2
0
1
1
1
0
1
0
2
2
0
1
2
0
0
1
1
0
2
4
0
1
2
0
1
2
1
2
2
0
0
2
1
1
1
2
2
0
1
1
2
2
1
1
2
1
0
1
1
2
1
2
0
2
0
0
2
2
0
1
0
1
1
1
1
0
2
1
1
0
1
1
1
1
2
0
1
2
1
2
2
0
0
1
2
0
2
2
2
1
1
0
0
1
1
0
1
1
0
0
1
0
0
1
2
1
1
1
1
2
1
0
1
2
1
1
1
1
0
0
1
1
2
1
1
1
1
3
0
0
0
2
1
1
0
1
0
0
1
1
0
0
1
2
1
2
1
1
2
1
1
0
2
0
1
1
0
1
1
1
1
0
0
1
0
1
1
2
1
2
1
1
1
1
1
1
2
1
1
0
1
2
1
1
2
1
1
1
1
2
2
1
2
2
2
0
0
1
1
1
1
1
0
1
1
1
1
1
2
2
1
1
2
0
1
1
1
1
1
2
1
2
0
1
0
1
0
0
2
1
1
1
1
2
1
1
0
0
3
1
1
1
1
0
1
1
1
1
0
0
2
0
1
0
1
1
1
2
1
2
2
0
1
1
0
1
1
1
1
2
2
0
1
1
2
2
1
1
0
0
1
0
1
1
2
1
2
2
1
1
0
1
1
1
1
0
0
1
1
1
1
1
2
1
2
2
2
1
1
2
0
1
0
0
0
0
1
1
0
0
1
1
1
0
2
1
0
1
2
2
0
2
0
0
1
0
1
2
0
2
2
1
1
2
1
1
0
1
2
0
2
1
1
1
1
1
1
1
1
2
0
1
1
3
2
0
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
0
1
1
1
1
1
2
1
1
0
2
2
1
1
2
1
2
1
2
0
2
1
0
2
0
0
1
1
2
1
1
1
1
1
1
2
0
1
1
2
1
2
2
2
1
1
2
7
0
2
1
1
1
0
1
1
1
1
0
0
2
2
1
1
1
2
1
0
1
1
0
0
0
1
2
1
1
0
2
0
0
1
1
1
1
1
0
1
1
1
1
0
1
2
0
1
0
2
1
1
0
2
1
1
1
0
1
1
0
1
1
2
0
2
1
1
1
1
2
1
1
0
1
2
0
1
1
1
0
1
2
2
0
1
1
1
1
1
1
1
1
1
1
2
1
1
0
0
2
1
1
1
2
0
0
1
2
1
2
0
2
2
1
2
1
0
1
0
0
2
2
1
2
0
1
1
0
1
2
2
1
1
2
0
1
0
1
1
1
1
1
0
1
1
1
0
0
0
1
0
0
1
2
1
1
1
1
2
1
1
0
2
1
2
1
1
1
1
2
0
1
1
1
1
1
1
1
1
0
1
1
2
1
0
1
1
0
2
0
2
1
0
0
0
1
1
1
1
0
2
0
0
1
1
1
0
0
1
1
1
1
1
0
1
1
0
1
0
1
0
0
0
1
0
0
1
1
2
0
1
1
1
0
2
1
1
1
1
0
1
2
1
0
0
2
1
1
0
0
0
1
1
0
1
2
1
2
2
1
0
0
2
1
1
0
1
0
1
1
1
0
1
2
0
1
1
1
0
0
1
1
1
2
2
0
1
1
1
1
1
1
2
1
1
1
1
1
2
1
0
1
4
0
1
1
2
0
2
1
1
2
1
2
0
1
1
2
1
1
0
2
1
1
0
1
0
1
0
1
1
1
1
1
0
2
0
0
2
1
2
1
0
0
2
1
1
1
2
2
1
0
1
1
1
1
2
1
2
1
3
1
0
0
2
1
1
1
0
1
2
1
1
2
0
1
0
0
0
2
1
1
2
1
1
1
0
0
0
2
1
1
2
1
0
1
2
1
3
0
2
1
1
0
1
2
1
1
1
2
1
1
1
1
1
1
2
2
0
1
0
1
1
1
1
1
1
1
0
2
0
1
1
0
0
1
1
1
1
2
0
2
2
1
0
1
1
1
1
2
1
1
1
0
1
2
0
1
1
1
2
0
1
0
3
1
0
0
1
1
1
2
1
2
0
0
1
0
2
2
1
1
1
1
1
2
0
0
1
1
1
2
0
1
1
3
1
0
1
1
2
1
0
1
1
2
1
1
1
1
2
2
1
2
1
2
1
1
2
2
0
2
1
1
1
2
1
1
1
3
1
1
1
0
1
2
2
1
1
0
1
0
0
2
2
2
2
1
2
1
1
1
1
2
0
1
2
1
1
1
1
1
0
2
1
1
2
2
2
1
2
0
1
2
1
0
1
1
1
0
0
1
1
1
0
1
2
0
1
1
2
1
0
1
1
1
1
1
2
2
2
2
1
1
1
0
2
2
2
1
2
0
1
1
1
1
0
2
1
1
1
0
1
1
0
8
1
1
1
2
2
0
2
1
1
1
1
1
1
1
2
1
0
0
0
1
1
1
2
1
1
4
1
0
1
1
1
2
1
1
0
1
4
2
2
2
1
1
1
1
2
0
1
2
1
0
2
0
1
2
0
1
1
0
0
2
0
1
0
0
3
1
1
1
1
2
2
1
1
1
1
3
1
0
0
2
1
2
1
0
1
1
1
1
1
1
0
0
0
1
1
0
2
1
1
1
2
1
1
2
1
2
1
0
2
1
1
2
1
1
1
1
0
1
1
1
1
1
2
1
1
1
1
2
2
1
1
0
2
1
0
0
2
0
2
1
0
0
1
1
0
1
1
1
2
2
0
1
1
0
1
2
0
1
2
1
2
2
1
1
1
2
1
1
0
1
1
1
1
1
1
0
1
0
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
0
1
2
1
1
0
1
2
2
2
0
2
2
1
1
1
1
1
1
2
1
2
2
1
1
2
1
1
1
1
0
0
0
1
1
1
1
1
1
2
0
1
1
0
1
2
1
1
0
2
3
2
2
2
1
2
1
0
1
0
2
0
0
0
1
1
0
0
0
1
1
1
1
2
1
2
1
1
2
1
0
1
0
1
1
2
1
2
1
0
0
1
1
1
1
1
1
1
0
2
1
2
2
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
2
1
0
1
1
1
1
1
0
1
0
2
1
0
0
0
1
1
1
1
1
1
1
2
1
2
1
1
1
1
2
1
0
2
0
0
1
1
0
1
2
2
1
1
1
1
2
2
1
2
1
0
1
1
1
1
1
1
1
1
2
1
1
1
1
2
2
1
0
1
1
2
0
2
2
1
1
0
1
2
0
1
1
2
1
0
1
1
2
1
1
1
2
1
0
0
0
0
1
1
2
1
2
2
1
0
0
1
0
2
0
1
1
1
0
2
1
0
0
1
0
2
0
1
1
1
1
1
1
1
1
0
2
2
1
2
1
1
0
1
1
1
0
0
1
3
1
1
0
1
0
2
1
0
2
0
2
1
2
1
2
1
1
1
1
1
1
1
1
1
4
0
2
0
1
2
1
1
0
1
1
2
1
1
1
1
1
1
0
0
0
1
1
1
1
2
1
1
1
0
0
1
1
1
1
0
2
1
1
0
1
1
2
3
0
1
2
0
1
0
2
1
1
0
1
2
1
1
1
1
0
2
1
2
1
1
0
1
1
0
0
1
0
1
0
1
0
1
0
1
1
1
2
1
0
2
1
0
1
1
1
0
1
1
1
1
0
1
0
1
2
1
0
1
0
2
2
2
1
2
0
0
1
0
0
2
1
2
1
1
2
0
1
2
1
2
1
1
1
1
1
0
1
0
0
2
0
2
1
1
1
2
0
0
2
1
0
1
1
1
0
0
2
2
2
4
1
2
2
0
1
1
1
1
1
1
0
1
0
2
1
0
2
1
1
1
1
1
1
0
1
1
1
2
0
1
0
0
1
1
1
2
1
0
1
0
2
1
1
1
2
2
1
0
0
2
0
0
1
1
1
0
2
1
0
1
1
0
2
0
1
1
1
1
1
0
1
0
1
1
2
1
0
0
1
1
1
1
1
0
1
1
2
1
1
1
0
2
1
1
1
1
1
1
2
0
2
1
2
1
2
1
1
2
1
1
0
2
0
0
1
1
0
1
0
1
1
0
1
2
2
0
0
1
1
0
0
0
0
1
1
2
1
1
2
0
1
1
1
2
0
1
1
1
1
1
1
1
3
0
1
0
1
1
1
1
1
2
0
0
1
1
1
1
1
1
1
1
1
1
3
2
0
2
2
0
2
1
1
0
0
1
1
1
1
2
0
0
4
3
1
0
0
1
2
0
1
0
1
1
1
1
2
0
2
1
0
1
0
1
2
0
0
0
1
1
1
1
0
1
1
0
2
0
1
0
0
1
1
1
2
1
1
1
1
1
2
1
1
1
0
1
1
2
2
1
0
2
0
1
1
0
2
2
2
0
2
1
1
1
0
1
1
1
2
2
2
2
0
2
1
2
1
1
2
1
2
0
1
1
0
1
1
2
2
0
2
0
1
1
1
1
0
1
1
1
2
1
1
1
0
1
1
0
0
1
0
0
1
1
2
1
1
0
1
0
0
1
1
0
2
1
1
1
2
0
2
0
1
2
1
1
1
1
0
2
2
2
0
1
0
1
0
1
0
2
2
0
1
1
1
1
0
1
2
1
1
0
2
1
1
2
2
0
1
0
1
2
2
0
2
1
1
1
0
0
0
1
1
0
2
1
1
2
1
2
1
1
1
1
2
2
1
3
0
3
1
0
1
1
1
1
0
0
1
1
1
0
2
1
2
2
0
1
2
0
1
1
0
1
1
0
1
1
1
1
0
2
2
1
1
1
1
7
1
0
1
2
1
1
1
0
1
1
1
1
0
1
1
1
2
1
1
1
0
0
1
0
1
1
1
2
2
0
1
1
1
0
0
2
2
1
2
2
1
1
2
1
2
1
2
0
1
1
1
1
0
2
0
1
1
1
0
1
2
2
0
1
0
1
2
1
1
2
1
1
2
1
0
0
2
2
2
1
1
1
2
0
1
1
1
1
1
1
1
1
0
1
1
1
1
0
1
2
0
1
0
2
1
1
1
1
0
1
2
1
2
1
1
1
2
1
1
1
1
1
2
1
1
0
1
1
1
0
2
2
1
1
1
2
1
1
0
1
1
2
3
1
1
1
3
1
4
2
1
1
2
0
0
0
0
1
1
0
0
2
1
1
2
0
2
1
1
1
0
1
1
1
1
2
1
1
2
2
1
1
0
1
2
1
1
0
2
1
2
0
2
0
1
0
2
1
2
1
1
1
1
2
1
2
1
0
1
0
0
0
2
2
1
1
2
1
0
1
2
1
1
1
1
1
1
1
2
1
1
1
0
0
1
2
0
1
1
1
0
1
1
1
2
1
0
1
2
0
1
1
1
1
1
2
1
0
1
2
1
1
1
0
2
2
1
2
1
1
1
1
2
1
2
1
1
2
0
2
1
1
1
1
1
1
1
1
0
1
0
0
1
1
1
0
0
2
1
2
1
1
2
1
1
0
2
1
0
2
2
2
1
1
2
1
0
2
2
0
3
2
0
2
1
1
1
0
1
1
1
0
2
1
0
1
1
1
1
1
1
1
1
1
1
1
2
0
1
1
1
0
2
1
1
2
1
1
1
1
1
2
1
1
1
2
0
1
0
1
0
0
1
0
1
0
1
2
0
0
1
0
1
1
2
1
0
0
1
1
2
1
2
1
2
1
1
1
1
2
0
2
1
1
1
2
1
0
1
0
2
1
1
1
0
1
2
0
1
2
0
1
1
0
2
0
1
2
1
2
1
2
1
0
1
0
1
2
0
1
1
2
1
1
2
1
2
1
2
1
1
0
1
0
1
1
1
0
0
1
1
1
1
5
1
1
2
0
0
1
1
2
1
1
1
1
2
1
1
2
1
1
1
0
1
2
1
1
1
0
2
1
0
1
2
0
1
2
1
2
1
1
1
2
0
1
1
0
2
2
0
1
1
2
2
1
2
0
2
1
2
1
1
0
2
1
1
2
2
1
1
1
0
0
2
1
1
3
2
1
1
1
0
1
1
2
1
2
1
1
1
1
1
0
2
2
1
2
2
1
0
2
0
0
2
1
2
1
1
1
0
1
1
1
1
2
1
0
1
0
0
2
1
1
2
2
1
1
1
1
2
0
2
0
0
0
1
1
1
1
0
1
1
0
1
1
1
0
0
1
1
1
1
1
1
1
0
1
1
1
1
1
2
2
1
0
2
0
1
0
0
2
1
1
0
0
1
1
1
1
1
1
2
1
0
1
2
1
0
0
1
0
1
1
1
2
0
1
2
1
2
1
1
1
1
0
2
1
1
2
1
0
1
1
1
1
1
1
1
1
0
1
1
0
1
1
1
2
1
2
1
0
1
1
1
1
1
1
1
2
2
0
1
0
1
1
1
1
2
1
1
2
2
0
1
1
1
1
0
1
1
1
0
2
0
2
2
0
0
1
0
1
1
2
1
0
0
1
1
2
2
0
1
1
1
2
2
0
1
1
0
0
1
0
1
0
2
1
2
2
2
2
2
1
1
0
2
1
1
0
1
1
1
1
1
1
1
1
1
2
0
1
2
2
0
2
1
0
1
0
2
1
1
1
2
1
3
0
1
2
0
1
0
1
1
1
1
0
1
1
0
2
2
2
1
2
1
1
0
1
0
2
1
2
0
1
1
2
1
2
0
0
4
0
1
1
0
0
2
1
1
1
0
1
0
0
0
2
0
1
1
1
0
1
1
1
1
1
1
1
0
2
0
0
2
1
2
0
2
1
1
1
1
1
1
2
0
1
1
0
1
2
2
1
0
1
1
2
1
1
2
1
0
2
2
1
0
0
2
2
1
1
2
1
2
1
1
1
0
0
0
1
1
1
2
1
1
0
1
0
0
1
2
1
2
1
2
1
2
2
0
0
1
2
0
2
0
0
1
1
0
1
1
2
0
2
0
1
1
1
2
1
2
1
2
0
1
1
1
2
1
1
2
2
1
1
1
1
1
1
1
2
1
0
0
1
1
1
1
2
0
1
0
2
1
2
1
1
1
2
2
1
1
1
2
2
2
1
1
1
0
2
1
1
2
1
0
2
1
1
1
1
1
1
1
1
0
1
1
1
1
1
0
1
1
0
1
1
0
0
2
1
1
1
1
0
1
1
0
0
2
1
1
0
1
2
2
1
2
1
1
1
1
0
1
1
1
2
2
1
1
0
0
2
1
0
1
0
1
0
0
2
2
2
1
0
1
2
2
1
1
1
1
0
2
0
3
1
1
0
2
1
2
0
1
0
2
0
1
0
0
1
0
1
1
0
2
0
0
2
1
0
1
0
0
1
0
0
0
2
1
1
1
1
1
1
1
0
1
1
1
1
0
1
2
1
1
0
1
1
0
2
1
2
2
0
1
1
1
1
0
1
0
1
1
1
0
0
0
1
2
1
1
0
1
1
1
1
1
1
0
2
2
1
1
3
1
1
1
0
1
1
1
1
1
0
0
1
0
1
2
0
1
0
2
1
2
1
0
2
1
1
0
1
2
2
2
1
1
1
1
2
1
2
1
1
1
1
0
1
0
1
1
1
1
0
1
1
1
1
2
2
1
2
1
1
1
2
0
2
1
2
1
1
0
1
1
2
1
1
2
1
0
1
2
1
0
1
0
1
0
0
2
1
1
1
0
0
1
0
1
1
2
1
2
0
1
1
1
1
2
1
1
0
1
0
0
1
2
1
1
1
2
1
1
2
0
2
1
2
0
1
1
0
0
2
1
2
0
1
1
2
1
1
1
1
3
1
1
0
1
1
0
0
2
1
2
1
2
1
2
0
1
1
1
2
0
0
0
0
1
0
0
1
1
2
2
1
0
1
0
1
1
1
1
0
1
1
1
1
1
2
0
0
0
1
0
0
2
1
2
2
0
1
1
0
1
1
1
1
2
0
1
3
0
2
1
2
2
2
1
2
1
2
1
0
2
2
1
1
1
1
1
1
0
2
1
1
1
2
1
0
2
1
1
0
2
1
0
2
2
1
1
1
0
1
0
2
1
1
3
0
0
1
0
1
0
2
0
1
1
1
1
1
1
1
0
1
0
1
1
1
1
0
1
1
1
1
1
0
0
1
2
2
1
0
1
2
2
1
1
1
0
1
2
1
0
2
0
2
1
0
2
2
2
0
1
0
1
2
2
0
0
2
2
1
0
1
1
0
2
1
1
0
1
0
1
1
1
2
0
1
1
2
1
1
1
1
0
1
2
0
0
1
1
2
1
0
1
2
1
0
0
2
1
1
1
1
2
1
1
1
1
1
1
1
1
2
0
3
2
1
1
2
2
1
0
1
0
1
1
1
1
0
0
1
1
0
1
1
0
0
0
0
1
0
2
0
0
0
2
1
1
1
2
1
1
2
3
1
1
2
2
1
0
1
1
2
1
1
0
2
1
0
1
0
2
1
1
1
1
1
1
1
2
1
0
0
0
1
2
2
1
0
1
1
1
2
0
1
2
1
1
2
0
2
0
1
2
1
2
1
2
1
0
1
1
1
1
2
0
0
1
3
1
1
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
0
2
2
0
1
1
1
2
1
1
0
2
1
0
0
1
0
1
2
2
1
0
2
0
1
1
2
0
1
0
1
1
1
1
0
2
2
1
0
2
1
0
0
0
1
1
2
1
2
2
0
0
1
2
1
0
1
1
1
1
1
1
1
1
0
2
2
2
1
1
1
1
2
1
2
1
0
1
2
0
0
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
0
1
0
0
1
2
1
2
1
2
0
3
0
1
2
0
1
0
0
0
1
1
1
1
1
2
1
0
1
1
1
1
0
1
1
2
1
2
0
1
1
2
1
0
0
1
2
0
1
1
1
0
0
0
0
1
1
0
1
1
1
1
1
0
1
0
1
2
1
2
1
2
1
1
1
0
2
1
0
0
2
1
0
2
3
2
1
1
1
1
0
1
1
1
2
1
1
1
2
1
1
1
2
0
1
1
1
2
1
1
1
0
1
1
1
1
2
0
0
0
1
1
1
1
0
0
1
0
1
1
0
1
0
2
0
0
1
1
1
1
2
1
1
1
0
1
0
1
2
1
1
1
0
0
1
1
1
2
1
0
1
2
0
1
1
0
2
0
1
2
1
1
0
2
2
2
2
2
0
0
1
1
1
1
1
0
1
0
1
1
0
1
1
2
2
0
1
0
0
1
1
0
2
1
1
1
1
1
2
1
1
1
1
2
1
0
0
1
1
0
1
1
1
2
2
1
2
0
2
0
1
1
0
1
2
1
2
0
1
0
1
0
1
1
1
1
1
1
1
0
1
0
0
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
2
1
2
1
1
0
2
0
2
1
0
0
1
2
1
0
0
1
1
1
1
1
2
2
1
1
1
1
0
1
1
0
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
0
0
1
0
1
1
1
2
1
1
1
2
0
2
0
1
3
1
0
1
0
1
1
0
2
1
1
1
1
1
2
2
2
1
1
1
0
2
2
1
0
2
0
0
1
1
2
0
1
1
1
1
0
1
0
2
1
2
1
0
2
0
1
2
2
0
1
0
3
1
2
1
1
1
1
2
1
1
0
1
1
1
1
1
0
0
0
1
1
1
1
1
2
1
1
1
2
1
1
0
2
1
1
1
0
1
2
2
0
1
1
2
0
2
1
0
1
2
0
2
1
0
0
0
1
1
0
0
1
0
1
1
1
0
2
0
1
1
0
2
1
1
1
1
2
0
1
1
2
2
1
1
2
1
1
1
1
1
2
1
1
0
0
0
1
1
0
1
2
1
3
1
1
2
0
1
1
1
1
2
1
1
2
1
1
2
0
1
1
1
2
0
1
1
0
1
1
1
1
1
1
2
1
1
1
1
1
0
0
1
2
0
2
1
2
1
1
1
4
1
2
1
1
1
1
1
2
2
1
0
1
0
1
2
1
1
0
2
0
1
0
1
0
2
1
1
1
1
2
0
2
1
1
2
2
0
2
2
0
1
1
2
1
2
1
0
1
1
1
1
0
2
0
1
1
0
0
1
1
1
2
2
2
2
1
1
0
0
0
1
2
1
2
1
1
0
1
1
1
1
2
1
2
0
2
1
1
2
1
2
1
0
1
1
1
0
1
0
2
1
1
1
2
1
0
1
1
1
1
1
2
0
1
2
0
1
1
2
1
2
1
2
2
1
1
1
0
2
2
2
2
0
2
1
1
2
1
1
1
3
1
2
2
1
0
2
1
1
1
1
1
2
2
1
0
1
1
0
1
0
0
1
1
1
1
0
0
2
1
1
1
1
1
0
2
2
2
1
1
2
2
1
0
1
1
4
2
1
1
0
1
1
1
1
0
2
0
1
1
1
1
1
1
1
2
1
2
0
1
1
2
0
1
1
0
1
1
3
0
1
0
1
0
0
1
2
1
2
2
1
2
1
1
1
1
1
1
1
0
1
2
1
0
1
1
2
2
0
0
1
1
2
1
0
0
1
3
1
1
1
0
1
1
2
1
1
2
1
2
1
0
1
1
0
2
1
2
1
1
0
2
1
1
2
1
1
2
1
0
2
1
0
2
2
0
0
2
1
1
0
1
1
2
0
1
1
1
0
1
2
0
1
1
1
1
0
0
2
2
0
1
1
0
2
1
2
1
0
0
1
1
1
1
0
2
1
0
1
1
1
2
0
2
1
1
2
1
1
1
1
0
2
1
0
2
1
2
0
0
1
1
1
1
1
0
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
0
2
2
0
1
1
1
1
1
1
1
1
1
0
2
2
2
2
2
2
3
1
0
1
1
1
1
1
1
1
2
1
2
0
0
1
1
1
1
1
1
2
0
1
1
1
0
1
0
0
2
2
1
1
2
1
1
2
1
1
2
0
2
1
1
1
1
1
1
1
1
0
1
1
2
1
1
2
0
2
1
2
1
2
1
1
1
0
0
0
1
1
2
0
2
1
1
1
1
0
2
1
2
1
1
1
1
1
1
2
1
1
0
1
1
2
1
1
1
2
2
0
3
0
1
2
0
1
1
1
1
1
1
2
2
1
0
2
0
1
1
1
0
2
1
1
0
1
2
1
1
1
1
1
1
0
0
1
0
1
2
1
1
0
2
0
0
2
1
2
0
1
0
1
2
1
0
2
0
0
0
1
0
0
1
0
0
1
0
2
1
0
2
2
0
1
1
0
1
0
1
2
0
0
1
1
2
1
1
1
1
0
0
1
2
1
2
0
1
0
1
1
1
2
0
1
2
2
2
1
1
4
2
1
0
2
2
1
2
2
0
0
2
2
1
0
1
1
1
0
2
2
2
1
1
1
1
0
1
0
0
1
2
1
0
1
1
1
1
0
2
1
0
1
2
1
0
1
1
1
0
2
1
1
1
1
2
0
2
1
2
2
0
1
2
1
1
2
2
0
1
2
2
1
1
2
2
1
2
1
2
1
1
2
0
0
0
2
1
1
1
2
0
1
1
2
0
1
0
0
1
2
1
1
0
1
2
1
2
1
3
1
2
3
1
1
1
0
1
1
0
0
2
0
0
2
2
1
1
0
1
1
0
2
1
1
1
1
0
1
1
1
1
2
1
1
1
1
1
0
1
1
0
1
0
1
1
2
2
1
1
1
1
1
1
1
3
2
0
1
0
1
1
1
2
0
0
1
0
1
0
1
1
0
1
2
2
1
1
0
1
1
1
2
2
1
0
2
1
0
1
2
1
2
1
1
1
2
0
3
1
0
1
1
1
1
1
3
2
1
2
0
1
1
2
2
1
1
1
1
0
1
1
1
1
1
1
0
2
2
1
1
1
1
1
1
3
2
0
1
0
1
1
1
0
0
2
1
1
2
1
2
1
2
1
1
1
0
1
1
2
2
1
2
1
0
2
1
1
1
0
1
1
1
1
0
1
1
0
2
1
2
1
0
0
1
2
1
2
1
1
0
2
1
1
2
1
1
0
2
2
1
0
1
2
2
1
1
1
1
1
0
1
1
1
2
1
1
0
1
0
2
1
1
1
1
1
1
0
1
1
2
1
0
1
1
0
1
0
2
1
2
1
0
2
3
0
0
1
1
0
2
1
1
0
1
2
1
1
2
1
1
1
1
1
1
1
2
0
2
2
2
0
1
1
1
1
1
1
1
1
0
0
2
0
2
1
2
0
0
1
1
1
1
0
0
0
1
1
1
0
1
0
1
1
1
0
1
1
0
1
1
1
1
2
0
1
0
1
1
1
0
1
0
1
1
1
0
2
0
2
1
0
1
1
0
1
1
0
0
0
1
1
0
2
0
1
1
1
1
2
0
1
0
1
1
1
0
1
0
2
0
2
2
1
1
0
1
2
1
1
1
1
1
1
1
1
1
1
3
1
0
0
1
1
1
2
1
1
1
1
1
1
1
0
0
1
1
0
1
1
1
1
0
1
1
1
2
1
2
0
0
1
1
1
0
1
0
1
0
1
1
1
1
1
0
0
0
1
1
2
1
1
0
0
1
1
2
1
0
1
1
2
0
2
0
1
1
2
1
0
0
1
1
1
1
0
1
2
1
3
1
0
2
2
0
1
2
0
2
1
0
2
1
0
0
1
1
0
1
1
2
0
1
2
0
2
0
2
0
1
1
2
1
1
0
2
1
1
1
2
0
1
2
1
2
1
0
1
1
1
1
3
2
2
1
1
1
1
1
2
0
0
1
1
1
2
1
1
1
1
0
0
0
2
1
0
1
0
1
1
2
1
1
1
1
3
2
1
1
1
1
1
0
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
0
1
1
1
0
2
1
2
1
1
2
0
1
2
2
0
1
1
0
4
1
2
1
1
0
2
0
1
0
1
1
1
1
2
1
0
1
0
0
1
2
0
1
2
1
0
3
1
2
1
1
0
2
0
2
1
0
2
0
1
2
2
1
1
1
0
0
2
1
1
0
2
1
1
1
1
1
1
1
1
2
1
0
0
0
1
0
1
1
0
1
0
1
2
1
1
1
1
1
1
1
1
0
2
1
0
1
1
2
2
0
0
2
1
0
1
1
1
1
0
1
1
1
2
2
1
0
0
1
0
1
1
2
0
0
1
1
2
1
2
0
1
1
0
2
1
2
1
1
1
0
1
2
2
2
1
2
1
2
2
1
2
2
0
1
1
2
1
1
0
2
1
2
1
1
1
0
1
1
1
1
1
1
1
1
0
1
2
1
2
1
2
1
0
1
1
1
1
1
1
0
1
4
0
1
1
1
1
0
1
1
2
1
1
2
2
1
1
2
2
1
2
1
2
1
1
0
0
0
2
2
2
0
1
0
1
2
1
1
0
0
0
1
1
0
0
1
2
1
0
2
1
1
0
1
2
1
1
2
0
2
1
1
1
2
2
1
1
0
1
0
0
1
2
1
2
1
1
1
2
1
1
0
1
1
1
2
1
1
1
1
2
0
2
0
1
0
1
0
1
0
1
0
1
2
0
0
1
2
0
1
1
0
0
1
0
1
1
2
0
2
2
2
1
2
0
0
0
1
1
2
2
0
1
0
2
0
1
0
2
1
2
1
0
1
1
1
1
0
2
1
3
1
2
2
2
2
0
0
2
0
2
0
1
1
0
1
2
1
1
1
1
1
1
1
0
0
1
1
0
2
1
2
2
1
2
1
0
1
1
0
0
0
0
2
2
1
1
1
1
2
1
1
0
2
1
2
1
1
0
1
1
1
1
1
1
2
1
1
1
1
1
2
0
1
1
1
1
0
2
1
1
0
1
0
2
1
1
1
1
2
2
0
0
0
2
2
0
1
1
0
1
2
2
0
1
2
2
1
2
1
1
1
0
0
0
1
0
1
0
0
2
1
1
1
0
1
1
2
0
0
0
0
0
1
2
1
1
1
2
1
1
0
1
0
2
0
1
1
2
0
1
1
2
1
0
0
1
2
1
0
0
1
0
1
0
1
2
2
0
1
2
2
1
2
1
1
0
1
2
1
1
2
1
1
2
1
0
2
2
1
2
1
1
1
2
1
1
1
1
1
2
2
1
1
2
2
0
1
1
2
1
1
1
2
1
2
1
2
1
1
1
1
1
1
1
0
2
0
1
1
2
1
1
1
1
1
0
1
0
3
2
1
2
1
1
2
1
1
1
0
0
1
1
1
0
1
2
1
2
2
2
3
1
2
2
0
2
1
0
1
0
1
1
1
1
1
0
1
1
1
1
2
2
2
0
2
0
2
1
1
2
1
1
1
0
1
2
2
1
1
1
2
2
1
1
0
0
1
0
0
1
2
0
2
1
2
2
2
1
1
2
1
1
2
1
2
1
1
1
1
2
1
0
0
1
1
2
0
3
1
1
1
1
1
2
1
0
1
1
1
2
1
1
1
0
2
1
1
1
1
1
1
2
1
0
2
1
2
2
1
1
2
1
2
0
1
1
0
1
1
1
1
0
1
2
0
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
2
1
1
2
1
0
0
1
2
0
1
0
2
2
0
0
1
0
1
2
0
0
0
2
1
0
1
0
1
1
1
1
1
1
1
1
1
1
1
2
2
1
0
1
1
3
1
2
1
1
1
2
1
0
2
1
2
0
1
2
1
1
0
2
1
0
2
0
1
1
1
1
1
0
1
1
2
1
0
1
2
2
2
0
0
1
0
1
3
0
1
0
0
1
0
2
2
1
2
2
0
1
1
1
1
2
0
2
1
1
1
1
2
2
0
2
1
1
2
1
0
1
0
1
1
1
1
1
2
1
0
0
1
0
1
1
0
0
2
1
1
1
1
2
0
1
1
1
2
1
1
2
1
0
1
1
0
0
1
1
2
0
0
2
0
1
0
2
0
0
1
0
1
2
1
1
2
2
2
0
2
1
1
2
1
2
3
0
0
1
1
2
1
0
2
1
1
1
1
0
0
2
1
0
1
2
1
2
2
2
0
1
1
2
1
2
1
1
1
0
1
2
2
3
1
1
0
2
1
2
0
2
2
2
1
1
1
1
0
1
1
2
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
0
1
1
1
1
0
0
0
1
0
2
1
1
2
1
2
1
1
1
1
1
1
0
1
3
1
2
1
0
0
1
2
2
1
1
0
2
1
1
2
2
1
0
1
0
1
2
2
0
0
0
1
2
0
0
1
0
0
2
1
0
1
1
2
2
1
0
1
2
0
1
0
0
2
0
1
2
2
1
1
1
1
2
2
0
0
0
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
0
1
1
1
2
0
1
1
2
1
1
2
1
1
2
2
1
1
1
2
1
1
1
0
1
1
0
1
1
2
0
1
2
1
1
1
2
2
2
2
1
1
2
1
0
0
1
2
1
1
2
1
2
1
0
0
1
2
2
2
1
0
1
1
1
1
1
1
0
0
1
1
0
1
1
1
0
2
0
1
1
1
2
1
1
1
0
2
1
0
2
1
1
1
1
3
1
1
1
1
1
1
0
0
2
2
2
1
1
0
0
1
1
0
1
2
2
1
1
0
0
2
2
2
1
1
1
1
1
1
1
1
1
2
1
0
1
2
0
2
0
0
1
2
1
3
0
2
0
1
1
0
1
1
1
1
1
1
1
2
1
1
2
1
2
1
2
1
0
1
1
1
1
0
1
3
0
0
2
1
1
1
1
2
2
2
1
1
0
0
2
0
1
1
1
0
1
1
1
2
1
0
2
2
1
2
1
0
1
2
1
0
1
1
2
2
2
2
1
2
0
0
0
1
1
2
1
3
2
1
1
1
2
1
0
0
0
2
2
1
0
1
1
1
1
0
1
2
0
1
1
1
2
1
1
1
0
2
2
1
0
1
1
2
2
1
1
2
0
1
1
2
2
1
1
1
2
2
1
0
0
1
1
0
1
1
1
1
1
1
0
1
0
1
1
0
3
1
0
1
0
1
0
2
2
0
0
0
1
1
1
1
2
1
1
1
1
1
1
2
0
1
0
1
0
0
0
1
1
1
0
1
1
0
1
2
0
1
1
1
1
0
2
0
1
1
0
1
1
0
1
1
1
1
0
2
1
0
1
0
1
0
2
1
1
1
1
1
0
1
1
1
2
1
2
1
0
2
1
1
1
1
2
1
1
0
1
0
2
1
2
2
1
1
0
1
0
2
2
1
1
1
0
1
2
1
1
1
1
1
0
1
1
1
2
1
1
0
1
2
1
2
0
0
1
0
1
2
0
2
7
0
1
2
1
0
2
0
2
1
2
2
1
1
1
1
0
1
1
0
2
1
1
1
2
3
0
1
0
2
1
0
2
2
1
0
1
2
2
0
2
1
1
1
1
2
2
1
1
0
1
0
0
0
2
1
1
0
2
1
1
2
1
1
1
1
1
2
1
1
1
0
2
2
1
1
2
2
1
1
1
1
0
0
1
1
1
2
1
1
1
2
0
1
1
0
1
1
2
2
0
2
0
0
0
2
1
0
3
2
1
1
1
1
2
1
1
2
1
1
2
2
1
1
1
2
1
2
1
1
1
0
1
2
1
1
1
2
2
2
2
1
0
2
0
0
1
0
1
1
0
2
3
2
1
1
0
1
2
1
3
2
1
0
0
1
1
0
2
1
2
2
2
2
2
1
1
1
1
1
0
1
1
1
1
1
2
0
1
2
2
3
2
1
0
1
2
1
2
1
2
2
1
1
2
1
1
0
1
0
2
1
1
1
1
0
0
0
1
0
1
2
2
0
0
2
1
0
0
1
2
1
0
1
1
1
0
1
1
1
1
2
1
2
0
1
1
2
2
1
1
2
0
1
2
1
1
0
1
1
2
2
1
0
1
2
2
0
1
0
1
0
1
2
1
2
0
2
1
0
1
1
1
2
2
2
2
1
0
1
0
0
1
1
0
1
1
0
0
0
0
0
2
1
0
1
1
1
1
2
1
0
2
0
0
1
1
1
0
2
1
2
1
1
1
2
1
2
0
2
0
0
1
1
1
1
2
1
1
1
1
0
1
2
1
2
1
1
2
1
1
1
0
0
2
1
1
0
2
2
1
1
1
2
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
0
2
1
1
1
0
1
1
2
2
0
2
0
2
2
0
1
3
1
0
2
0
1
1
1
1
2
1
0
2
1
1
0
0
1
1
1
1
2
0
0
1
0
1
1
1
1
0
1
1
0
0
2
1
1
1
1
1
1
2
1
1
0
1
1
1
1
1
0
1
1
1
2
1
2
0
2
1
2
1
1
1
0
1
0
2
1
1
2
0
1
2
1
1
1
1
1
1
0
2
1
1
0
1
0
1
1
1
1
1
1
1
2
1
1
2
0
2
0
2
0
0
1
1
1
2
1
1
2
1
2
1
1
1
3
0
1
0
1
1
1
1
1
2
1
0
1
2
1
1
1
1
1
1
2
1
1
2
1
0
1
1
1
0
1
2
2
0
2
0
2
1
3
0
1
1
0
2
0
0
2
1
1
0
1
1
1
0
1
1
2
0
1
1
0
0
2
1
1
1
0
0
1
1
3
2
1
0
2
1
0
1
0
1
0
1
1
1
1
1
1
1
1
0
0
2
1
2
2
2
1
1
0
1
1
2
1
1
1
1
1
1
6
1
0
2
1
1
1
0
1
0
2
2
2
2
1
2
0
1
0
1
1
1
1
1
0
2
0
1
2
1
1
0
1
0
2
2
1
2
1
1
1
1
1
0
1
1
2
3
1
1
0
1
1
0
0
1
1
1
2
1
1
1
2
1
1
1
2
1
2
1
1
0
1
1
1
1
1
1
2
1
1
0
1
1
0
2
2
1
0
1
1
1
1
1
1
1
0
1
2
2
0
1
2
1
0
1
1
2
2
0
2
0
2
2
2
0
1
1
1
1
2
0
0
1
1
1
2
1
1
1
2
2
1
2
3
0
1
1
1
1
0
1
1
1
1
0
0
1
1
2
2
2
1
2
1
1
1
1
1
1
0
1
1
1
0
2
1
0
2
0
2
2
1
0
0
1
0
1
1
0
1
1
0
0
1
1
1
1
1
2
2
0
1
1
1
1
0
2
2
0
0
1
0
1
1
1
2
1
0
0
1
1
1
1
1
1
1
0
1
1
2
1
2
2
1
1
1
2
2
0
2
2
2
2
1
2
1
1
1
1
0
1
1
0
1
1
0
0
1
1
0
3
1
1
1
1
0
1
0
1
1
1
0
0
1
1
2
2
0
0
0
1
1
0
2
2
0
2
1
1
1
2
2
1
1
1
1
1
0
1
1
1
2
1
0
1
1
2
0
2
0
1
1
2
2
2
0
1
0
1
1
2
2
1
0
2
1
0
0
1
1
0
1
2
0
1
1
0
2
1
1
0
1
1
1
2
1
1
2
0
2
1
2
2
2
0
2
2
1
0
1
1
1
1
2
1
1
2
0
2
0
2
1
1
1
0
0
1
1
2
1
0
1
0
2
1
1
1
1
1
0
1
0
1
2
1
1
1
1
0
1
1
1
1
2
1
0
1
2
2
2
1
2
0
1
2
1
1
1
1
1
1
1
0
1
0
1
1
1
1
1
1
1
1
1
2
2
0
2
1
1
1
1
1
1
1
1
0
1
1
0
1
1
0
2
1
1
0
2
1
1
1
2
1
1
0
0
0
2
1
0
1
1
0
1
1
2
1
1
0
2
0
2
0
2
2
2
2
0
2
1
1
1
2
3
1
0
0
0
2
1
2
0
0
1
1
1
0
1
1
0
1
0
0
1
1
1
2
1
0
2
1
1
2
1
0
1
1
1
0
1
0
1
0
1
0
1
0
1
1
1
1
2
1
0
0
2
1
2
0
1
1
3
0
2
1
0
1
0
1
2
0
1
2
0
2
2
1
2
1
1
1
1
1
2
1
1
0
1
0
1
1
1
1
2
2
4
0
1
1
2
1
2
0
1
2
0
1
1
4
1
0
1
1
2
2
0
1
0
1
2
0
1
1
2
1
1
1
2
1
1
0
1
0
1
1
2
0
1
1
1
0
1
1
0
0
0
1
1
1
1
4
0
1
2
0
0
0
1
0
1
2
0
0
1
1
0
1
1
2
0
1
1
3
1
1
2
2
1
1
0
1
2
0
2
3
0
1
1
1
1
1
0
1
1
1
2
1
0
2
2
1
0
2
0
2
1
1
1
2
1
1
2
1
1
1
1
2
0
1
1
1
0
0
1
1
1
0
1
0
1
1
2
1
1
0
0
1
1
1
1
1
1
1
0
1
1
0
2
0
1
1
1
1
0
2
1
0
2
0
1
0
1
0
0
0
1
2
1
1
2
2
2
1
2
0
1
2
2
0
2
1
0
0
1
2
0
0
2
1
0
1
0
1
1
1
1
2
1
2
1
1
2
1
0
2
0
0
2
0
1
1
1
1
2
1
0
1
1
1
2
0
1
2
2
1
1
1
1
0
0
1
0
1
1
1
1
1
2
2
1
0
0
2
2
2
1
2
0
2
1
1
1
2
1
0
0
1
0
1
2
1
0
1
0
0
0
2
2
1
1
1
1
1
1
2
0
0
1
0
1
1
0
1
2
1
1
2
0
1
2
1
1
1
1
0
0
2
1
2
0
0
2
0
0
1
1
1
2
1
0
1
0
1
0
1
1
1
2
0
1
1
1
2
1
1
1
0
0
1
1
2
1
0
2
0
1
1
0
2
1
0
1
0
1
1
1
1
2
2
1
1
1
0
0
1
0
1
1
0
0
1
1
0
1
1
1
0
1
1
1
1
0
2
1
1
2
0
1
0
2
1
2
1
0
1
0
2
1
1
0
0
1
0
1
2
2
2
0
2
1
2
2
1
1
0
2
0
0
1
0
0
2
0
1
1
1
1
1
1
2
1
2
1
1
2
2
2
1
1
1
1
1
1
2
0
0
2
1
1
1
2
1
0
1
1
0
1
1
2
2
1
0
1
1
0
1
0
0
1
1
0
2
1
3
1
1
1
0
2
1
1
1
1
1
0
0
0
1
1
0
0
1
1
2
0
0
1
2
1
1
2
2
2
1
1
2
0
1
0
3
1
1
1
3
2
1
2
1
1
1
1
0
0
0
0
1
1
2
1
1
1
3
2
0
1
0
1
0
2
2
1
1
0
1
2
1
1
2
1
1
2
2
1
1
0
1
0
2
0
2
1
1
2
2
1
0
2
1
1
1
0
1
1
2
0
2
0
1
1
0
1
1
1
2
1
0
1
1
1
1
1
0
2
1
2
2
1
1
2
0
0
0
0
1
2
1
1
1
1
0
1
1
1
1
2
2
2
0
1
0
2
2
1
2
0
1
1
1
1
1
0
1
2
2
2
2
0
1
3
0
1
0
0
2
0
1
1
1
1
1
1
0
0
1
2
1
1
1
1
1
0
1
1
0
0
1
0
1
1
2
0
1
1
1
2
1
1
0
2
0
1
1
2
2
2
1
1
1
2
2
1
1
0
1
1
1
2
2
2
0
1
2
1
0
0
1
1
1
1
0
2
1
1
2
1
2
0
2
0
1
1
0
0
0
1
2
1
1
1
2
1
1
1
1
1
0
2
0
0
0
1
1
2
0
2
0
1
1
1
2
0
1
1
1
1
1
0
1
1
1
1
1
1
2
1
1
1
1
1
1
1
0
0
1
0
1
1
1
1
1
1
1
1
0
1
1
1
1
2
1
1
0
0
1
1
1
1
0
2
1
0
1
1
1
0
1
1
1
1
2
0
0
0
1
1
1
1
0
1
2
2
0
1
1
0
1
3
2
0
0
1
0
1
1
2
1
2
1
2
2
2
1
0
1
1
1
2
0
1
1
2
1
1
1
2
2
1
0
0
1
2
2
2
1
1
0
2
0
1
0
0
1
2
0
1
1
0
2
0
1
1
1
1
0
2
0
1
2
2
0
0
0
0
0
2
1
1
1
1
2
1
2
1
1
0
1
1
2
1
1
1
2
1
0
1
1
0
2
1
2
1
2
0
1
2
1
1
2
1
0
1
1
0
1
0
0
1
2
1
1
0
1
2
2
0
0
0
1
1
1
1
0
2
2
0
1
1
2
1
1
1
2
1
1
1
1
0
0
2
1
1
1
1
0
2
2
0
1
1
1
2
1
1
1
0
0
2
1
4
2
1
2
1
2
2
1
0
1
1
0
1
1
2
2
1
2
2
2
2
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
2
1
0
0
1
1
0
0
1
1
2
0
0
0
2
1
2
1
0
1
1
1
1
1
1
1
1
1
1
1
0
0
1
1
1
1
0
1
4
2
1
2
2
1
0
1
1
1
1
1
0
0
1
1
2
1
0
0
2
1
0
0
0
0
1
1
2
2
0
0
1
1
0
1
1
1
0
1
0
2
1
2
1
2
1
0
1
1
1
2
0
0
1
2
0
1
1
2
1
2
2
1
1
1
1
1
3
1
0
2
0
0
1
0
1
2
1
1
0
3
1
1
1
2
2
1
2
0
1
0
2
1
0
0
1
0
1
1
1
1
1
3
2
0
2
2
1
0
0
0
0
1
1
0
1
0
1
0
0
2
1
1
1
1
0
1
1
2
1
1
1
1
2
0
0
1
0
0
2
1
1
1
1
1
1
3
1
1
1
1
0
1
1
0
0
2
1
2
1
1
1
2
2
0
1
1
1
0
0
0
0
1
1
1
2
0
1
1
2
1
1
1
1
1
1
1
1
0
2
1
1
1
1
0
1
1
1
0
0
0
0
1
0
1
1
1
2
1
1
0
1
2
0
1
2
1
1
2
1
1
1
2
1
1
1
1
2
1
2
2
1
1
1
1
1
2
2
0
1
1
1
0
0
1
0
1
1
1
1
1
0
1
2
2
0
1
0
2
0
1
0
0
1
1
0
1
0
1
1
1
1
0
0
0
0
0
1
1
2
1
0
1
1
1
0
2
1
1
0
1
2
1
0
1
1
2
1
0
0
1
1
0
1
1
1
1
0
0
0
1
2
1
0
1
0
1
2
0
2
1
1
0
1
1
1
1
0
2
2
1
2
1
1
1
0
1
1
1
1
3
1
1
1
0
2
1
0
1
2
3
1
1
2
1
1
1
1
0
1
0
0
1
1
1
0
1
1
1
0
1
1
1
1
0
0
2
1
0
2
1
1
1
0
1
0
1
2
1
0
1
1
1
1
1
2
1
2
1
1
1
2
1
1
2
2
1
1
2
0
0
2
0
2
1
1
1
0
1
1
1
0
2
1
1
2
1
2
1
1
1
2
2
2
0
1
1
1
0
1
1
0
2
1
1
1
1
1
0
0
1
2
1
3
1
1
0
1
2
1
1
1
1
1
1
2
1
2
2
2
1
2
1
0
1
1
2
0
1
2
2
1
1
1
0
1
1
0
0
1
1
1
2
0
1
2
2
2
1
0
2
1
1
1
3
0
1
0
0
0
1
1
1
2
0
1
1
1
2
1
2
0
1
2
1
1
1
0
2
1
1
1
0
1
0
0
1
1
1
2
0
2
1
0
1
1
0
2
0
2
1
2
1
0
1
0
0
1
2
0
1
1
2
0
1
1
0
1
2
0
1
0
1
1
1
1
1
0
1
2
2
1
2
1
1
1
0
0
0
1
1
0
1
0
0
2
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
2
2
1
0
1
1
3
0
5
0
1
1
1
2
0
1
1
1
2
1
0
0
1
0
2
2
1
1
1
1
0
1
1
0
0
1
1
0
2
1
1
1
0
0
1
2
2
0
2
0
0
2
0
3
0
0
2
2
1
1
1
1
0
1
0
0
1
0
1
1
2
1
0
2
1
2
1
2
1
1
1
1
2
1
1
1
2
0
1
0
2
1
1
2
1
2
1
1
1
0
0
2
0
1
1
0
1
2
1
1
1
0
1
0
1
2
1
0
0
1
2
2
2
2
0
0
1
1
0
2
1
1
1
1
1
0
1
1
1
1
1
0
1
2
1
1
1
0
1
2
2
1
1
0
1
1
0
1
1
1
2
1
0
0
1
3
0
1
1
1
3
1
0
1
2
2
1
2
0
1
0
2
2
1
0
2
1
0
0
2
1
1
0
1
1
1
0
0
1
0
1
1
1
2
1
0
1
2
1
2
2
2
2
8
0
1
0
1
1
2
2
0
0
2
2
1
1
0
1
1
3
0
1
1
1
2
1
0
2
0
0
1
0
1
1
1
1
1
1
2
1
1
0
0
2
2
1
0
0
1
0
2
1
0
0
1
2
1
1
2
0
3
0
0
2
2
0
1
1
1
1
2
2
2
1
2
2
1
1
1
0
1
1
1
1
0
1
1
2
0
0
1
2
1
1
1
2
1
2
1
1
1
0
1
0
1
0
1
1
1
2
1
1
1
1
0
1
2
1
0
1
0
1
0
2
2
1
1
0
0
0
1
0
1
1
0
0
2
1
1
0
0
1
1
2
1
1
0
1
1
1
0
0
0
1
1
1
2
0
2
1
1
0
2
1
1
1
2
2
1
2
1
1
0
1
1
0
0
0
2
1
1
1
0
2
1
1
0
2
1
1
2
2
1
1
2
1
0
0
1
2
1
0
1
1
0
0
2
1
1
0
2
1
0
0
0
1
0
0
1
1
1
0
2
1
0
1
1
1
0
2
1
2
0
1
0
0
2
0
1
1
1
1
0
2
1
2
1
1
2
1
1
1
1
0
1
2
1
1
2
0
1
1
2
1
1
0
1
1
1
1
0
0
2
1
1
0
1
0
2
2
1
2
1
1
2
0
1
1
1
2
1
0
1
2
1
0
2
0
1
0
1
1
1
1
1
1
1
1
1
1
0
4
1
1
0
0
2
1
1
0
2
1
1
1
0
1
1
0
1
1
2
0
0
1
2
2
1
1
0
1
2
2
0
2
1
1
0
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
0
1
2
0
1
2
1
1
1
1
1
1
2
2
2
2
2
2
1
1
1
2
0
1
1
2
1
1
1
2
2
5
0
1
1
0
1
2
1
1
1
1
1
1
1
1
1
1
0
1
2
0
1
1
1
2
2
1
1
0
1
1
0
1
1
1
1
0
1
2
1
1
0
0
2
1
1
1
1
1
1
1
0
0
0
1
2
1
0
2
0
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
2
0
1
0
0
1
2
2
1
2
1
1
2
1
1
1
1
2
2
0
0
2
2
1
1
1
0
0
0
2
0
1
2
1
0
2
1
2
1
1
1
1
1
0
1
1
0
1
0
0
1
2
1
1
2
0
1
1
2
1
0
2
1
1
1
1
2
1
1
1
1
0
1
2
1
1
1
1
1
2
1
2
1
1
1
1
0
1
1
1
1
2
1
2
2
1
1
1
1
3
0
0
1
1
2
1
1
1
1
1
2
1
1
0
1
1
1
0
1
1
0
2
1
1
1
1
1
1
2
1
1
1
1
1
2
0
2
1
1
2
1
0
1
4
0
1
0
1
1
0
1
2
3
0
2
0
0
2
0
1
2
1
0
0
2
0
2
0
0
2
0
0
1
3
2
1
0
1
2
1
1
1
2
2
0
2
1
1
1
2
1
2
1
1
0
2
1
1
0
2
2
1
0
1
0
1
1
1
0
0
0
2
2
1
0
1
1
1
2
2
0
1
2
1
1
1
0
1
0
3
0
1
1
1
0
2
2
0
1
1
1
1
0
0
1
1
1
0
2
2
0
0
1
1
1
0
0
2
2
1
3
2
0
0
1
0
0
0
1
0
1
1
1
1
1
1
1
0
0
2
1
1
1
0
1
1
2
0
0
1
1
1
1
3
1
1
1
2
2
2
2
1
1
1
0
0
1
0
0
2
1
1
0
2
0
0
1
1
0
0
0
1
2
2
1
2
1
1
0
1
1
1
1
1
2
2
1
1
0
2
2
1
1
1
0
1
1
1
1
2
0
1
0
1
1
0
1
1
0
1
1
1
1
0
2
1
1
2
0
1
2
1
1
0
1
1
1
1
0
0
1
0
1
0
0
0
1
1
1
1
1
1
1
0
0
1
1
1
2
1
1
1
1
2
0
0
1
1
2
2
1
1
0
1
1
1
1
0
1
0
2
1
1
1
1
2
1
0
1
1
2
0
0
2
1
1
2
0
0
2
2
1
0
1
1
1
1
2
1
1
0
1
0
0
1
1
1
2
2
1
1
0
2
0
0
2
3
1
1
1
0
2
1
1
0
1
0
1
0
1
2
0
0
0
1
0
0
2
2
1
1
1
2
0
1
1
1
1
2
0
2
2
1
2
0
2
0
1
1
1
1
1
1
1
1
1
2
0
1
0
2
1
1
1
1
1
1
0
2
2
1
0
2
1
1
0
1
1
1
1
2
1
1
0
2
0
2
2
1
1
0
1
1
2
1
1
0
1
0
2
1
1
0
0
1
1
1
2
0
2
1
0
0
0
2
1
1
1
2
1
1
1
1
1
0
1
0
0
0
1
1
1
1
2
0
2
2
1
1
0
2
0
2
3
0
2
0
2
1
0
1
1
1
2
1
2
1
2
0
1
0
2
1
2
2
0
1
2
0
2
3
2
1
1
2
0
0
0
2
0
2
2
2
2
1
1
1
1
1
1
2
0
1
4
1
1
1
16
1
2
2
1
1
1
1
1
1
2
0
0
0
1
0
2
0
1
2
1
2
1
1
1
0
0
1
1
1
1
0
1
1
2
2
1
1
1
0
1
0
1
1
1
1
1
1
0
0
1
1
2
1
1
1
0
0
2
0
1
2
1
1
1
0
1
0
1
2
1
1
1
1
2
1
1
1
2
1
4
1
1
0
0
1
1
1
7
0
1
1
1
0
2
1
2
1
1
1
0
1
0
1
1
1
1
1
1
2
1
1
0
1
1
1
0
0
1
2
2
0
0
1
1
1
0
1
1
0
1
2
1
0
1
1
1
1
0
1
2
2
2
2
2
0
1
0
1
2
1
1
1
0
2
1
2
0
2
1
0
0
0
1
1
0
0
2
2
1
1
1
0
1
0
1
2
3
1
1
0
2
1
1
1
1
0
1
2
1
1
2
2
1
0
2
1
2
1
2
1
1
0
1
0
0
1
0
1
1
1
0
1
1
2
0
0
1
2
1
1
0
0
1
2
1
1
1
1
0
1
1
1
1
2
1
1
1
2
1
0
1
1
2
1
0
0
2
1
1
1
1
1
1
1
0
1
0
2
0
0
2
0
1
2
0
2
0
2
1
1
1
0
1
2
1
1
1
2
1
1
1
2
1
1
0
1
1
2
0
0
1
1
1
0
1
2
0
2
0
0
0
1
1
1
1
1
2
1
1
0
1
1
0
1
1
1
1
1
0
1
1
1
0
1
1
1
1
0
0
0
1
1
1
1
1
0
0
1
1
0
1
0
2
1
0
0
1
1
1
1
1
0
2
1
0
1
1
1
2
0
1
2
1
1
2
2
2
2
0
1
0
1
1
4
1
2
1
1
2
1
2
0
1
1
1
1
0
0
1
3
1
2
1
1
2
1
1
2
0
1
0
1
1
0
1
1
0
2
1
1
1
1
1
1
2
0
1
2
0
1
0
0
2
0
0
3
0
0
1
0
1
1
1
2
1
2
1
2
1
2
0
2
1
1
0
2
1
2
0
0
1
2
1
1
1
1
2
1
1
0
3
1
2
1
2
2
1
0
1
1
1
0
1
1
2
1
1
1
2
1
2
0
1
1
1
2
2
1
1
0
1
2
1
1
1
1
0
1
1
1
1
1
1
2
0
1
1
1
0
2
2
1
1
0
1
1
2
1
1
1
1
2
1
2
1
1
1
1
2
1
0
0
0
1
0
2
1
0
0
1
2
2
0
2
1
1
1
1
1
1
0
1
1
6
1
1
1
1
2
1
1
2
1
0
1
1
0
1
2
1
0
2
1
0
1
1
1
1
1
0
1
0
1
0
1
1
2
1
1
1
1
1
5
2
1
2
2
2
0
2
0
1
1
1
0
1
1
1
2
2
2
1
1
2
1
0
2
0
0
1
2
1
0
0
2
2
3
1
1
1
1
1
2
2
1
0
1
1
2
1
1
1
1
2
0
1
1
1
1
1
1
0
1
1
1
1
2
2
1
2
1
1
0
1
0
1
2
2
2
0
1
2
1
1
2
0
1
0
1
1
0
1
1
2
1
0
0
1
0
1
1
2
2
1
0
2
0
1
3
2
1
1
1
2
3
0
0
1
1
1
0
1
1
1
2
1
0
0
0
0
1
2
0
1
4
1
0
1
1
1
1
1
1
2
0
2
1
1
1
1
1
0
2
1
2
4
1
2
1
1
1
2
2
2
1
1
0
1
0
3
1
2
0
0
1
0
1
1
0
1
0
1
1
1
0
2
1
2
1
1
1
1
1
1
0
1
1
1
2
1
0
0
1
0
1
2
1
2
0
0
1
0
1
0
1
1
0
1
0
2
1
0
0
2
3
0
2
1
1
2
1
0
2
0
4
1
0
3
0
2
0
2
0
1
1
0
1
0
0
0
1
1
2
2
1
2
2
1
0
0
1
0
1
1
0
1
1
0
1
1
0
1
1
0
1
1
1
1
1
1
1
2
1
0
1
1
0
1
1
0
1
1
1
1
2
1
2
2
1
2
0
1
0
1
1
1
1
2
1
1
1
0
1
2
1
2
1
2
1
1
1
1
2
1
1
2
1
1
2
2
2
1
1
2
2
1
0
1
1
2
1
1
2
0
2
1
1
2
1
1
1
1
1
1
1
1
1
0
1
1
0
1
1
1
1
1
1
2
1
0
2
2
1
1
1
1
0
0
1
1
1
4
1
2
1
2
0
0
0
1
0
1
1
1
1
2
1
1
0
0
2
0
1
1
2
1
1
0
1
0
1
1
1
1
2
1
1
2
2
1
1
0
2
2
1
1
1
1
1
0
2
1
1
1
0
0
1
3
2
1
1
0
2
0
2
1
1
0
2
1
1
1
3
1
0
2
0
0
0
0
1
2
1
0
0
1
0
0
1
2
2
1
1
1
1
2
2
1
0
1
1
1
0
1
1
0
1
1
0
2
1
0
1
1
1
1
1
1
0
1
1
0
0
1
1
2
1
2
1
1
3
0
1
1
1
0
1
2
1
1
1
2
1
0
2
1
1
0
1
0
0
1
1
0
1
2
1
2
1
1
0
1
1
1
1
1
1
1
1
0
1
1
1
1
1
0
1
1
1
2
1
2
1
1
1
0
2
1
1
1
1
1
2
2
2
2
3
1
0
0
1
1
1
1
0
0
2
2
2
2
2
2
0
0
1
1
1
0
1
1
0
2
1
2
0
1
0
1
2
2
0
1
0
1
1
2
1
0
0
1
2
1
0
1
1
0
1
1
1
0
1
1
0
0
1
1
1
0
1
2
0
0
1
1
1
2
0
0
0
1
1
1
1
2
2
0
2
0
2
0
1
1
0
1
1
1
3
0
2
2
2
2
0
1
1
1
2
2
1
1
1
1
1
0
1
1
1
2
0
1
2
1
0
1
1
1
1
1
0
2
1
1
0
1
1
1
1
1
1
1
0
0
1
1
0
1
1
1
2
1
2
1
0
1
1
1
2
1
0
0
2
0
1
2
1
0
1
0
1
2
1
1
2
1
0
1
0
1
1
0
0
1
1
0
1
1
0
1
1
1
0
1
1
1
1
0
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
0
2
0
0
0
2
1
1
1
2
2
0
1
0
1
0
1
2
1
0
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
0
1
1
1
2
0
2
2
1
2
0
2
1
2
2
1
1
2
0
1
1
1
1
0
1
2
1
0
1
2
1
1
1
1
2
0
0
1
1
2
2
1
2
0
1
1
0
1
1
1
0
1
1
2
1
0
1
1
1
1
2
0
2
2
1
1
2
1
2
1
1
1
1
0
0
1
1
1
0
1
1
2
2
2
1
1
1
1
2
0
1
1
1
1
2
1
0
1
0
0
2
1
2
1
1
0
2
1
2
1
2
1
2
2
1
1
1
2
2
4
1
1
1
0
0
1
0
1
1
2
0
1
0
1
0
1
1
1
1
1
2
1
1
2
1
1
1
1
1
0
2
2
2
1
1
0
1
2
0
1
1
0
1
1
1
1
1
1
2
1
3
1
1
1
0
1
1
1
1
1
2
2
1
1
1
1
0
0
2
1
1
1
1
1
1
2
0
1
1
1
2
2
0
2
1
1
1
1
1
1
1
0
0
1
1
2
2
0
1
2
1
1
1
2
2
1
1
0
2
2
1
1
1
0
2
1
2
2
1
1
1
2
1
0
2
1
0
1
1
0
0
1
1
2
2
1
0
0
1
1
0
1
1
1
1
0
1
1
2
1
0
0
1
2
2
1
1
1
0
2
2
1
1
1
2
0
3
0
1
2
1
2
1
1
2
1
1
0
1
0
2
2
1
1
2
1
2
2
0
1
2
0
1
2
1
0
2
1
2
1
0
0
0
2
1
1
0
0
1
1
0
0
1
2
2
0
0
1
0
1
1
5
0
3
0
2
1
1
1
1
2
2
0
1
1
1
2
1
2
1
1
1
2
0
0
2
1
1
1
1
2
1
0
1
2
0
0
1
2
0
0
1
1
2
0
0
1
2
2
1
0
0
2
1
1
1
0
1
1
2
1
1
1
1
2
2
2
0
1
3
1
1
1
2
2
2
2
2
0
1
1
1
0
1
1
2
1
0
0
1
1
1
0
2
1
1
0
1
0
1
1
2
1
1
1
0
2
2
1
2
2
0
2
0
1
0
1
1
1
2
0
1
1
1
1
1
1
1
0
2
2
2
1
0
2
2
1
1
1
1
1
1
2
0
1
1
2
2
0
2
0
1
0
1
0
1
2
1
0
1
2
2
1
1
1
1
1
0
1
1
0
2
1
0
1
0
3
1
2
1
2
0
1
1
1
2
1
0
1
2
0
1
1
2
1
1
1
1
1
1
1
1
0
0
1
1
1
1
3
1
0
0
2
0
1
1
1
1
1
0
1
1
2
0
2
2
1
1
2
0
1
1
1
0
0
2
1
2
1
2
0
1
0
0
1
1
1
1
0
1
0
2
2
2
1
0
2
1
0
1
2
1
1
1
2
0
2
0
1
1
1
1
2
1
1
1
1
2
2
2
1
1
1
1
1
0
2
1
3
1
3
1
0
1
1
1
1
1
2
2
2
0
1
1
2
1
1
0
1
2
1
1
1
0
1
0
1
0
1
2
2
2
2
1
2
1
1
1
1
1
3
1
1
0
0
0
2
1
1
2
1
1
1
1
1
0
0
1
1
1
2
0
2
0
1
2
0
2
2
0
0
0
0
0
1
1
1
2
1
1
1
1
1
0
0
1
0
0
1
1
1
0
0
0
0
1
1
1
1
0
2
1
2
1
1
0
2
1
1
1
1
1
2
0
1
1
0
1
2
1
0
1
0
1
1
0
1
1
1
0
2
1
1
1
1
1
0
0
0
2
2
0
0
1
2
0
2
2
1
1
1
1
1
0
2
1
1
1
1
2
1
0
2
0
1
2
1
0
1
0
1
0
0
2
0
2
1
1
0
0
0
2
1
1
0
2
1
1
0
1
1
2
1
2
1
1
2
2
2
1
2
1
2
2
0
0
0
1
1
1
1
1
1
0
3
0
1
1
0
2
2
2
2
1
2
1
1
2
1
1
0
0
0
2
1
1
1
1
1
1
1
0
2
0
1
1
0
1
2
1
0
2
2
1
0
2
2
1
1
1
0
2
1
0
0
1
3
1
0
0
1
2
2
1
0
2
1
0
3
2
2
0
0
1
2
1
1
2
1
1
2
1
1
0
1
1
1
1
0
1
2
2
1
2
0
2
0
2
0
2
1
1
1
1
1
1
1
1
0
2
0
0
1
1
1
2
2
0
0
1
1
1
1
2
1
3
1
0
0
1
2
0
2
3
1
1
0
2
1
1
1
0
2
1
2
2
1
1
1
1
1
1
0
0
1
0
1
1
2
1
1
1
1
0
1
0
1
2
0
1
1
1
1
1
1
2
0
0
2
0
0
1
1
1
0
1
0
2
1
0
2
1
1
1
0
1
1
1
1
0
1
0
0
2
2
2
1
2
0
1
2
1
0
1
1
0
0
2
1
1
5
1
0
1
0
2
1
2
0
0
1
0
1
1
1
0
1
3
0
0
2
2
2
1
1
0
1
1
1
1
2
2
0
1
2
1
1
1
0
0
1
0
1
1
0
2
0
1
1
1
1
1
1
1
0
1
0
0
1
2
0
2
1
1
0
0
1
0
1
1
1
2
1
1
1
1
2
1
0
2
1
0
0
2
1
1
1
1
1
1
0
0
1
1
0
0
2
0
1
1
0
2
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
0
0
0
1
1
1
1
2
2
2
1
0
1
1
1
1
1
1
2
1
1
1
2
1
0
1
1
0
1
1
1
0
0
1
2
0
2
1
2
1
0
0
1
1
0
2
1
1
2
0
2
1
0
1
0
0
1
1
1
1
2
1
2
1
1
2
1
1
2
1
1
1
0
0
1
1
1
1
0
1
2
1
1
0
1
1
0
2
0
2
1
0
2
1
1
2
2
0
2
1
1
1
2
2
2
1
3
2
2
1
1
1
0
0
2
1
0
1
0
1
1
1
1
1
1
2
1
0
1
2
1
1
1
1
1
1
0
1
1
1
2
2
2
1
1
2
1
0
2
0
2
1
1
1
1
1
1
1
1
0
1
1
1
2
0
1
1
1
0
2
0
0
1
1
1
0
0
1
1
1
1
1
2
0
1
1
1
2
1
2
2
1
1
0
1
2
1
1
2
1
1
0
1
2
1
1
1
2
0
0
0
1
1
1
1
1
2
2
1
0
1
1
0
1
1
1
1
1
0
0
1
1
1
1
1
2
0
1
1
4
1
1
1
3
1
2
1
0
1
1
0
0
1
2
0
2
1
1
1
2
2
1
1
1
2
0
0
2
2
1
0
1
1
0
0
1
1
0
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
0
1
0
1
0
1
1
0
0
1
2
2
1
1
2
1
2
1
1
1
1
1
3
2
2
1
0
2
0
1
2
0
1
2
1
1
1
2
1
0
1
1
0
2
2
1
1
1
1
2
2
0
0
2
1
2
2
2
1
1
0
1
1
1
2
2
0
1
0
1
1
2
2
2
2
1
2
1
1
1
0
2
1
1
1
0
2
1
1
1
1
2
4
0
1
1
1
0
0
1
1
1
0
2
1
1
0
1
1
1
1
1
1
1
2
1
1
1
0
1
2
0
1
1
2
0
2
0
1
1
0
0
2
0
1
1
2
1
1
2
0
1
2
1
2
0
1
2
2
0
1
0
1
1
2
1
2
1
2
2
2
1
1
1
2
0
1
1
2
1
2
2
2
1
1
1
0
0
0
1
1
1
2
0
0
2
1
0
0
1
0
1
1
1
1
0
0
0
2
2
2
1
2
1
1
1
2
1
2
1
0
0
1
1
0
1
1
2
1
1
2
1
1
2
1
1
2
1
2
2
1
1
2
1
2
2
0
2
1
0
1
1
2
1
1
1
1
1
1
1
1
1
1
0
0
1
2
2
1
1
1
1
2
1
0
0
0
1
0
2
2
1
1
2
1
1
0
1
1
0
0
1
1
1
1
2
2
1
1
2
1
0
0
2
1
1
1
1
0
0
1
1
1
1
1
2
1
1
1
1
1
1
2
0
0
1
2
0
1
1
1
1
0
2
1
1
0
1
0
2
1
1
3
0
1
0
1
2
0
1
2
1
0
1
1
2
1
1
1
2
1
1
1
1
1
0
1
1
1
1
1
0
0
1
1
1
0
0
0
1
1
2
2
2
1
1
2
1
2
1
0
1
0
0
0
2
1
1
1
1
1
1
1
2
0
1
2
1
1
2
1
1
1
0
1
1
0
1
0
2
2
1
1
1
2
2
0
1
2
2
1
2
0
1
0
1
2
2
1
1
2
1
1
1
1
1
2
1
1
2
1
0
1
2
1
0
1
0
1
1
1
0
1
1
1
1
1
1
1
2
1
1
1
1
0
1
0
2
1
0
1
1
2
0
1
1
1
0
1
1
1
0
1
1
1
1
1
1
1
1
1
2
1
2
0
0
1
2
1
0
0
1
0
0
1
2
1
0
0
1
2
1
1
1
1
2
0
1
1
1
2
1
0
1
1
0
1
0
2
1
1
0
2
1
2
1
1
0
1
0
2
1
1
1
1
1
0
1
1
2
2
1
0
1
2
1
2
0
2
2
2
1
2
1
2
2
1
1
0
1
0
0
1
2
2
0
1
0
0
2
0
1
1
1
0
1
1
0
1
1
1
0
2
1
0
1
1
0
1
1
1
2
0
0
1
2
1
1
1
0
2
0
1
1
1
1
1
1
2
1
1
1
2
1
0
0
2
0
1
1
1
2
3
1
2
2
1
0
1
1
1
1
0
1
0
1
1
3
1
0
0
1
2
1
1
1
1
1
1
2
0
1
1
2
2
1
1
0
1
1
1
1
2
0
2
1
1
1
2
1
1
2
1
1
1
0
1
1
1
2
0
0
1
1
0
0
1
1
0
1
1
0
1
0
1
1
1
0
1
2
1
0
1
1
1
1
1
0
0
1
1
1
1
1
2
1
1
1
2
1
0
1
2
1
0
1
1
1
1
1
0
1
1
0
1
1
2
0
0
1
1
1
0
2
1
1
1
1
0
0
1
1
2
0
2
0
0
1
1
0
1
2
0
1
1
1
2
1
1
2
1
1
1
0
1
1
1
0
1
0
2
2
1
2
3
2
1
0
2
0
1
1
0
1
1
0
1
1
0
0
2
1
1
1
1
1
0
1
2
1
1
0
1
1
1
1
2
2
2
0
0
1
2
1
1
2
0
0
1
1
1
0
0
1
1
1
1
1
0
3
1
1
1
2
2
1
0
1
2
2
1
0
1
2
1
2
0
1
2
0
0
2
1
2
0
0
1
0
1
1
1
1
2
2
2
1
1
0
2
0
2
1
1
2
1
1
1
1
0
1
1
1
1
2
2
0
0
1
2
1
1
2
1
0
1
1
2
0
1
1
2
0
2
3
1
0
1
2
1
3
2
1
1
2
0
1
0
0
1
1
1
2
0
0
0
1
1
1
2
2
1
1
1
2
1
0
1
1
1
1
1
0
0
1
1
1
2
1
2
1
0
0
1
1
1
2
2
1
2
1
0
1
1
1
0
0
1
1
2
1
2
1
2
0
1
0
0
2
2
0
1
0
1
0
1
0
1
2
2
2
1
0
2
2
1
1
1
1
2
2
1
2
2
1
2
2
1
1
2
1
0
1
1
2
3
2
1
1
1
2
1
1
2
1
0
1
1
0
1
0
0
1
1
2
1
1
2
1
0
1
1
2
1
1
1
0
1
1
0
1
1
1
2
1
1
0
1
2
2
0
1
2
0
1
2
2
1
1
1
1
1
2
2
0
1
0
2
2
2
1
0
2
1
2
0
0
1
1
2
1
2
1
1
2
0
2
1
1
1
1
1
0
2
1
1
2
1
1
0
1
0
0
0
2
1
1
1
0
1
0
2
0
1
1
1
1
1
1
1
1
1
1
2
1
1
1
0
2
1
2
2
3
1
1
0
2
2
0
0
2
2
1
0
1
1
1
3
2
0
1
1
2
1
2
2
1
1
0
1
1
0
1
0
1
0
0
0
1
0
1
1
2
0
1
1
1
1
1
2
1
2
6
1
1
0
1
0
0
1
1
1
1
0
2
3
0
1
1
1
1
2
1
1
1
1
0
0
1
0
1
1
1
2
1
2
1
1
0
1
0
0
2
1
2
1
1
1
0
1
2
2
1
0
1
0
2
1
1
1
1
0
1
1
1
0
1
0
0
1
2
1
0
1
0
2
1
1
1
1
0
2
0
1
2
1
1
1
2
0
2
1
1
2
1
1
1
1
2
1
0
1
0
1
1
2
1
1
2
1
0
1
0
1
2
1
1
1
3
0
1
1
1
0
1
1
1
1
0
1
2
0
1
1
1
0
1
1
2
1
2
1
0
1
1
1
2
1
1
1
1
0
0
1
2
2
1
1
1
1
1
1
1
1
1
1
1
2
0
2
2
0
1
1
1
1
1
1
0
1
1
1
3
1
0
1
2
1
1
0
0
2
1
1
1
1
1
2
1
1
1
1
0
1
2
2
1
1
1
1
1
2
1
0
2
2
1
1
1
1
0
2
1
1
2
2
1
0
1
1
2
1
1
2
2
1
1
2
0
2
1
0
1
1
1
1
1
1
1
1
3
2
1
1
2
1
1
1
1
0
1
2
0
0
2
0
0
1
2
2
1
1
0
1
1
1
1
1
2
1
0
1
0
2
1
1
1
1
0
2
1
1
0
2
1
1
1
1
1
0
1
0
1
2
0
1
1
1
0
0
0
2
0
2
0
2
1
1
1
1
2
2
1
1
1
0
0
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
0
1
2
1
0
1
1
1
1
1
1
1
0
2
2
1
1
1
0
2
1
1
0
2
1
2
0
1
1
0
1
1
2
0
1
0
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
0
1
2
0
1
1
1
2
2
2
0
1
1
1
1
2
1
0
0
0
1
2
1
1
1
2
1
1
2
1
0
1
0
2
1
1
0
0
2
2
1
1
2
0
1
0
2
0
1
1
1
2
1
1
1
1
1
1
0
0
1
2
1
1
1
1
0
1
1
1
2
1
0
1
0
1
1
1
1
0
2
1
0
0
0
1
1
1
0
1
1
1
0
0
1
0
1
1
1
1
2
0
1
0
0
1
1
0
2
2
1
2
0
1
1
2
0
2
1
0
0
1
2
2
2
1
0
1
0
1
1
1
1
1
0
1
0
1
1
2
2
2
1
1
2
2
1
1
1
2
1
1
1
1
0
0
0
1
1
1
0
0
1
0
1
0
1
2
0
1
0
2
0
0
0
1
1
2
1
1
1
0
0
1
1
1
1
2
2
2
0
1
1
1
1
2
0
1
0
1
1
1
1
1
0
1
2
2
0
1
0
1
0
1
2
1
1
1
1
1
1
1
1
1
1
0
1
2
1
1
0
0
2
0
1
1
1
2
1
2
1
1
1
1
1
1
1
1
2
1
0
2
1
2
1
0
1
1
1
1
1
0
1
0
1
1
1
1
0
0
1
1
1
2
1
0
0
2
0
2
1
2
0
0
1
1
0
1
1
1
1
1
0
1
2
2
1
2
2
2
2
2
1
1
0
0
1
2
0
1
1
2
3
1
0
2
0
1
1
1
0
1
2
1
0
1
1
2
0
1
1
1
1
1
0
2
1
1
2
1
0
0
1
0
1
0
1
1
3
1
1
1
0
1
2
1
0
2
0
1
1
0
2
0
2
1
1
1
2
2
0
2
1
0
1
2
2
0
2
2
0
1
0
1
2
2
0
0
2
1
1
1
1
1
1
0
0
1
1
0
1
1
1
1
0
1
2
1
0
0
1
1
1
1
1
1
1
1
1
2
0
0
0
1
2
1
1
2
0
1
1
2
2
1
2
2
1
0
2
1
1
0
1
0
0
1
2
0
1
1
1
2
1
1
0
1
2
2
2
0
1
1
1
2
1
0
1
4
1
1
1
1
0
0
1
1
2
1
1
1
1
2
0
1
2
1
0
1
1
0
2
1
1
1
1
1
2
1
1
1
2
0
1
1
0
2
2
0
0
0
2
1
2
3
1
0
0
1
1
1
2
2
0
1
2
1
2
0
2
0
1
2
0
1
1
1
1
1
1
0
1
2
0
1
1
2
1
0
2
2
1
0
2
1
2
1
1
1
0
1
1
1
2
1
1
1
1
1
1
1
1
1
0
1
0
1
1
2
1
0
1
2
0
1
0
1
1
0
2
2
1
1
1
1
2
2
1
0
0
2
1
1
1
1
1
0
2
1
3
1
2
1
0
1
1
2
1
0
1
2
1
1
0
0
0
0
1
0
1
0
1
0
1
2
1
1
0
0
1
3
1
1
2
2
2
1
1
0
0
1
1
0
1
2
1
1
2
2
1
1
1
2
2
2
1
2
1
2
2
1
1
1
0
1
2
2
0
1
2
2
2
0
1
1
1
2
4
2
2
0
2
1
1
2
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
3
2
1
1
0
1
1
2
1
1
1
1
0
1
1
0
1
1
1
0
2
0
0
1
2
0
2
1
1
1
0
1
1
0
2
1
1
0
1
1
0
1
1
1
1
1
2
1
1
1
1
0
1
2
1
2
2
1
0
0
1
2
1
2
1
1
0
1
1
2
1
1
1
1
1
1
1
1
1
0
1
1
1
0
2
0
1
1
2
1
1
1
1
1
1
2
1
2
2
0
2
2
0
0
2
1
1
2
0
1
1
2
1
2
1
2
2
0
1
1
1
0
1
0
0
1
1
0
1
3
2
1
1
1
0
2
2
1
1
2
1
2
0
1
1
1
1
2
1
1
2
2
0
1
1
0
2
2
1
1
1
1
0
1
2
2
1
1
0
1
1
1
1
1
1
1
1
1
2
2
0
1
2
0
1
1
1
0
3
2
1
1
2
2
0
1
1
1
0
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
2
1
0
0
2
0
1
1
2
1
0
2
2
2
1
1
2
1
1
1
0
2
1
1
1
1
1
1
1
2
0
0
2
1
1
2
1
1
2
0
2
0
0
0
3
0
0
0
2
1
1
1
0
0
0
1
0
1
1
2
1
1
2
0
1
1
1
2
1
1
1
1
1
0
0
2
1
2
1
1
1
0
0
1
2
1
2
2
1
0
1
1
2
2
0
1
0
0
2
1
1
0
1
2
1
1
1
1
0
0
0
1
1
0
0
1
0
2
1
1
1
1
1
0
1
1
1
1
1
2
0
1
0
0
1
1
1
1
2
0
1
1
1
2
1
1
1
0
1
1
1
1
1
2
0
1
0
0
2
1
0
2
1
1
1
1
1
0
1
1
2
1
1
1
0
1
2
1
0
2
0
1
1
1
2
2
2
1
1
2
1
1
1
2
2
1
0
1
2
0
1
1
1
1
1
1
0
1
2
0
0
2
0
1
1
1
1
1
0
1
1
1
0
0
2
2
0
0
1
1
2
2
0
2
2
2
1
1
1
1
1
1
2
2
2
1
1
0
1
1
0
1
1
0
2
2
2
1
2
2
1
0
1
0
1
1
1
1
1
0
1
1
1
2
2
0
1
1
1
2
0
1
0
0
0
1
0
1
2
1
2
1
1
0
1
1
0
0
2
0
1
1
1
0
1
1
1
1
2
2
1
0
1
2
1
1
0
2
1
2
1
1
0
0
2
2
2
2
0
0
1
1
0
0
1
0
2
1
1
1
0
2
1
1
1
1
2
0
1
1
2
1
1
0
1
2
1
0
1
1
2
0
0
1
1
1
1
4
0
0
1
2
1
2
1
1
1
0
0
1
1
1
2
1
2
1
0
1
0
2
1
1
2
0
0
1
1
0
0
2
1
1
1
1
2
2
1
0
1
0
1
0
1
3
0
0
1
2
1
2
1
1
1
1
0
1
1
2
0
0
0
2
0
2
2
1
1
2
1
1
1
3
2
0
0
1
0
1
2
1
0
1
1
0
2
0
2
2
1
2
1
1
2
2
1
1
0
1
0
2
1
1
1
1
1
2
1
1
1
2
0
1
1
1
0
2
2
0
1
1
2
2
0
1
1
2
0
1
1
1
2
1
1
1
1
1
1
0
1
2
2
1
1
0
1
2
1
1
1
1
0
0
0
0
0
1
2
1
1
1
1
0
2
0
1
1
0
0
1
2
2
1
1
1
2
0
1
1
0
0
1
0
1
1
1
1
1
2
2
1
1
2
1
1
2
1
1
1
1
0
1
2
0
1
2
2
0
0
0
2
0
2
0
1
0
1
1
1
2
1
1
1
3
2
0
1
1
2
1
0
1
0
2
1
1
2
2
1
2
1
1
0
2
0
2
2
1
1
2
0
2
0
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
0
2
0
1
1
2
1
0
1
1
2
1
1
2
0
1
1
1
1
1
2
0
2
1
1
0
1
1
0
0
2
0
1
0
1
2
1
1
1
1
2
1
0
1
0
2
0
0
1
1
0
1
1
1
0
1
2
2
1
2
2
2
1
1
1
0
1
1
2
1
2
1
1
1
1
1
2
2
1
1
1
2
2
1
1
1
2
3
0
1
1
1
1
1
1
2
1
1
0
1
0
1
0
4
2
2
1
1
0
1
1
2
1
0
1
2
1
2
1
1
1
0
1
1
0
0
1
1
0
2
1
2
0
1
1
0
1
1
1
1
0
1
1
1
2
1
1
2
0
1
1
1
1
0
0
0
1
1
1
1
0
0
1
1
0
2
1
2
2
1
1
2
1
1
1
1
2
0
1
2
1
1
2
0
1
2
1
2
1
1
0
1
1
1
1
0
1
2
2
1
1
1
1
2
1
1
2
1
1
1
1
1
1
0
1
1
1
1
1
1
0
2
0
2
1
1
1
1
1
2
0
2
1
1
1
2
2
1
1
1
1
0
2
0
1
1
2
0
0
1
1
1
1
0
1
1
2
0
2
1
0
3
1
1
1
1
0
1
2
0
0
1
1
0
2
2
0
0
1
2
1
0
1
1
1
1
1
1
2
2
2
0
1
1
1
1
1
1
1
2
1
0
1
0
1
1
2
0
0
1
0
1
1
1
0
1
0
1
0
2
2
1
1
0
1
0
1
1
2
0
0
1
1
1
1
1
1
1
2
0
1
2
0
0
1
1
0
0
0
1
1
1
1
1
1
1
1
2
0
1
1
0
1
1
1
1
2
3
1
1
1
2
1
2
1
1
0
2
1
0
1
1
0
0
2
1
1
1
2
0
2
1
1
1
2
1
1
1
0
1
1
2
0
2
1
0
1
1
2
1
0
1
1
2
1
1
0
0
1
0
2
2
1
0
0
1
1
0
1
2
0
1
1
1
1
2
1
0
1
1
0
2
1
1
0
2
1
1
2
2
0
1
0
1
1
2
1
2
2
1
1
1
2
2
0
1
1
1
1
1
1
1
1
1
1
0
2
0
2
1
0
3
0
1
2
1
2
0
2
1
2
1
1
1
0
1
0
0
0
1
1
1
1
2
1
1
1
1
1
1
1
1
0
1
1
2
1
1
0
1
2
1
1
1
0
1
0
0
2
0
0
0
1
0
1
1
2
2
1
2
1
1
2
2
1
2
3
1
2
0
0
2
2
2
1
1
1
1
0
0
0
1
2
1
2
1
1
0
1
0
0
1
1
1
1
1
1
1
1
1
0
1
0
1
1
0
2
2
2
1
2
1
1
1
1
1
1
2
1
1
0
2
2
1
2
2
2
2
1
0
1
0
1
1
1
1
0
1
0
2
1
2
1
2
1
1
0
2
2
2
0
0
0
2
1
1
1
0
1
0
1
2
1
2
1
1
3
1
2
1
2
2
1
0
0
0
1
1
0
2
1
0
1
0
2
2
0
1
1
1
2
2
1
1
2
0
2
1
1
2
1
2
2
1
1
2
0
2
0
1
1
1
0
1
2
2
0
1
0
1
0
1
2
1
1
1
2
0
1
1
0
2
0
1
0
1
1
0
2
0
1
0
2
1
2
0
1
0
0
0
2
0
0
1
2
1
0
0
0
0
1
1
1
2
1
1
1
1
0
0
1
2
0
2
1
0
1
1
0
1
0
2
1
2
1
1
1
1
2
1
1
1
0
3
1
1
2
1
1
1
0
2
2
1
1
1
1
1
0
1
0
2
1
2
2
1
1
1
2
2
1
0
1
1
2
1
1
2
0
1
2
1
0
1
1
2
1
1
0
2
1
0
2
2
1
2
1
0
1
1
2
1
1
0
2
3
1
1
2
1
2
2
1
1
1
1
1
2
0
1
0
2
1
1
1
1
1
1
0
4
2
1
1
1
2
1
2
2
1
1
0
1
2
0
1
0
1
0
1
0
1
1
1
2
0
1
1
0
0
0
1
1
2
1
1
0
1
2
1
0
1
2
1
1
1
1
1
1
1
1
1
1
1
2
2
0
2
1
1
2
1
1
2
1
1
0
2
2
2
2
1
1
1
0
1
1
1
1
1
1
1
0
2
0
0
4
1
2
0
1
0
1
1
2
2
0
0
1
1
1
0
0
2
1
1
1
1
1
1
0
1
0
1
1
0
2
1
2
1
0
0
2
1
0
0
2
0
2
1
1
2
1
0
3
0
2
2
1
1
2
0
0
1
0
1
1
0
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
0
0
0
0
1
2
0
0
1
0
0
0
2
2
1
1
0
0
1
0
2
1
1
1
1
1
0
1
1
1
1
1
1
2
0
1
1
1
1
1
1
1
1
0
1
1
1
0
1
1
2
1
1
1
1
0
0
1
0
1
1
1
2
2
1
2
2
2
2
1
2
2
1
2
1
2
1
2
1
1
1
1
1
2
1
2
2
1
0
1
0
1
2
1
1
1
1
2
0
1
0
1
1
1
0
1
3
1
0
2
1
2
1
0
0
2
1
2
2
0
2
0
1
1
0
1
0
2
1
2
1
1
1
0
1
0
1
0
0
2
0
2
1
1
1
1
1
2
1
1
2
2
3
0
2
1
2
1
1
0
1
1
1
0
2
2
0
1
0
1
1
2
0
1
1
1
0
1
1
1
1
1
2
0
2
2
1
2
1
0
2
2
1
1
1
0
1
2
1
1
2
1
1
0
0
1
0
2
1
1
0
0
0
1
1
1
1
2
1
1
0
0
0
1
1
1
2
0
2
1
2
0
2
2
1
2
0
0
1
0
2
1
2
1
0
1
2
1
0
0
1
2
2
1
1
1
1
1
2
1
0
2
0
1
1
1
2
2
0
1
1
1
1
2
1
1
2
1
1
1
2
1
1
1
1
0
0
0
1
1
0
1
1
1
0
2
1
2
1
1
1
0
1
0
1
0
1
0
1
2
0
1
1
0
1
1
1
1
3
0
1
2
1
1
0
2
1
0
2
0
0
2
1
2
1
2
1
2
1
1
1
0
1
1
2
1
1
1
1
2
1
1
2
1
2
2
1
2
1
0
1
1
2
1
1
1
2
2
2
2
2
1
2
0
1
1
3
1
1
2
2
2
2
1
1
2
2
2
1
2
1
1
1
0
0
1
1
2
1
0
2
1
1
1
1
2
0
2
1
0
1
1
0
0
1
2
0
1
0
1
1
0
1
0
1
1
2
1
0
1
2
2
2
0
1
1
1
1
3
2
1
1
2
1
1
2
0
2
1
0
1
0
2
1
2
0
2
0
0
0
1
1
2
1
2
0
2
1
0
1
1
2
0
0
1
1
0
0
1
1
2
1
2
1
1
0
2
1
1
1
1
0
1
1
1
0
1
1
0
1
1
1
1
1
1
2
0
0
1
1
0
0
0
1
1
2
2
2
1
1
2
0
1
2
0
2
2
1
0
0
2
1
2
1
2
2
0
0
1
0
1
0
0
0
0
1
2
2
1
1
1
0
1
0
2
1
0
0
0
2
2
1
1
1
4
0
1
2
2
1
1
0
2
2
1
1
1
0
0
1
1
1
1
0
1
1
0
2
0
2
1
6
2
2
1
1
1
1
2
1
1
2
1
1
1
2
0
1
1
2
1
0
1
0
0
1
1
0
3
1
0
1
1
0
2
1
1
0
4
0
2
1
1
1
1
2
1
1
0
3
1
2
1
2
0
1
0
1
1
1
0
0
3
2
1
2
1
1
2
1
2
0
3
1
1
2
1
1
1
1
1
1
1
1
1
0
1
1
2
0
1
1
1
2
2
2
1
1
2
2
1
0
2
0
2
0
0
0
0
1
2
2
3
1
1
1
0
0
1
1
2
0
0
1
1
0
1
1
1
2
1
1
1
1
1
0
0
0
0
1
2
1
2
1
1
0
2
2
2
1
1
0
1
2
2
1
0
0
0
1
1
2
1
2
1
2
3
1
1
2
1
0
2
1
2
1
1
0
1
2
0
0
1
0
1
2
1
2
2
2
2
1
1
0
1
1
1
1
0
1
0
1
0
1
0
1
2
2
2
2
1
0
0
1
1
1
1
2
0
0
2
0
1
1
1
2
1
1
2
1
1
1
1
1
1
2
0
2
1
1
0
2
1
1
1
1
1
1
0
1
2
1
1
1
0
0
0
0
1
1
0
0
1
1
1
1
2
1
1
4
0
1
2
0
2
0
2
1
1
2
2
1
1
6
1
1
1
0
1
0
1
1
2
1
1
1
1
2
0
2
1
1
1
0
2
0
1
0
0
0
1
1
2
1
2
0
0
1
0
1
2
2
0
0
1
1
1
1
1
1
1
0
1
2
1
2
1
0
1
0
1
1
1
1
1
1
1
0
0
2
1
0
0
0
1
2
2
1
0
1
3
1
0
2
2
1
3
1
2
2
1
1
1
2
2
2
1
1
0
1
0
1
1
0
1
1
2
1
1
0
2
2
1
1
0
1
1
0
1
1
0
1
0
1
0
1
1
2
2
2
2
1
0
2
1
1
1
1
0
1
1
1
0
1
0
2
2
0
0
2
0
0
1
2
1
0
0
1
1
1
2
1
1
1
2
0
2
0
1
1
2
0
1
2
1
0
2
0
1
1
2
1
0
2
1
0
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
0
0
1
1
1
1
2
0
0
0
1
1
2
1
0
0
2
1
2
1
1
1
0
1
1
1
1
0
2
1
1
1
0
1
1
2
1
0
0
0
0
1
0
2
2
1
0
1
0
0
1
2
2
1
2
1
0
1
1
1
3
1
2
1
1
2
1
2
0
1
2
3
1
1
1
0
1
1
1
1
1
1
1
0
1
1
0
0
1
2
1
2
0
0
2
1
1
1
1
0
1
2
0
2
1
1
1
1
1
2
0
1
2
2
1
1
1
2
1
0
0
1
1
0
1
0
2
2
1
0
1
1
2
1
2
1
1
0
0
1
2
1
1
0
1
1
2
1
1
1
2
1
0
0
2
2
1
0
2
0
1
1
2
0
1
1
0
2
1
1
0
1
1
1
1
1
1
2
1
1
1
0
1
2
2
1
0
2
0
0
1
1
0
0
0
2
1
1
0
0
1
1
1
1
1
2
0
1
1
1
1
1
1
0
2
1
0
2
1
0
1
1
2
1
0
0
0
1
2
1
2
2
1
1
1
1
1
1
1
2
3
1
3
0
0
1
1
0
0
2
1
2
1
2
1
2
1
1
1
1
1
1
1
1
0
0
3
1
2
0
2
2
0
1
2
1
1
0
1
1
1
0
1
1
1
1
1
1
1
1
2
0
1
1
2
1
1
1
0
1
1
1
1
1
1
1
2
1
0
2
1
2
0
0
1
1
1
1
0
1
0
1
2
2
2
1
0
1
2
1
1
2
2
0
0
1
1
1
1
1
1
1
1
1
1
2
1
2
1
0
1
2
1
0
2
2
1
0
1
2
1
1
2
1
1
1
1
0
1
1
1
1
1
1
2
2
1
1
1
1
2
0
2
1
2
2
1
2
1
0
2
1
1
2
2
1
0
0
2
0
2
1
1
1
1
2
0
0
1
2
1
1
1
2
0
2
1
2
1
1
1
1
2
1
1
0
0
0
1
1
0
2
1
1
1
1
1
0
1
1
1
0
0
0
2
1
2
0
1
0
0
1
0
1
0
1
2
1
1
0
1
2
0
1
0
2
2
1
1
1
1
2
0
1
1
2
1
1
0
1
1
2
1
0
0
1
0
2
1
1
1
1
0
1
0
1
1
1
1
2
1
0
1
1
2
1
1
0
1
0
1
1
1
2
1
1
0
3
0
1
1
0
0
3
2
1
1
0
1
0
1
1
3
2
2
0
1
0
1
0
0
2
1
1
1
2
2
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
0
2
1
1
2
2
0
1
1
1
2
1
0
0
0
1
1
1
1
1
0
1
1
0
1
2
1
1
1
1
1
1
0
0
1
4
1
2
1
2
1
1
1
1
1
1
1
1
0
1
2
1
0
0
1
3
2
0
0
1
0
1
0
1
1
1
0
0
1
1
2
1
1
0
1
1
1
1
2
1
0
2
1
1
2
1
1
1
1
1
1
0
1
1
1
1
2
2
1
2
2
3
1
0
2
2
1
1
1
1
1
1
0
1
1
1
0
1
1
0
1
1
0
0
1
0
1
1
1
1
0
0
0
1
1
1
2
2
1
1
2
0
1
1
2
0
0
1
2
0
0
1
1
2
1
1
1
1
2
2
2
0
1
0
1
1
2
1
1
2
0
1
0
1
0
0
0
1
1
0
1
2
1
0
2
1
1
2
1
1
1
2
0
1
1
0
1
1
2
2
2
1
1
1
0
2
1
1
2
1
1
0
0
1
1
2
1
1
1
1
1
0
0
2
0
2
1
0
1
2
0
1
2
1
2
1
0
2
0
1
1
1
1
1
2
2
1
2
1
2
1
2
1
2
1
2
2
1
1
2
0
0
1
0
2
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
0
2
2
0
0
1
1
1
0
0
1
1
1
0
1
0
1
0
2
1
1
0
1
1
2
1
0
1
2
2
1
2
0
1
2
1
2
0
1
1
1
0
1
1
0
0
1
1
1
1
2
0
0
1
1
1
1
0
0
1
1
2
1
2
1
1
0
1
1
1
1
0
1
1
1
2
1
1
1
1
0
1
2
1
2
2
0
2
1
2
1
1
1
1
1
1
2
1
0
0
1
2
1
1
1
0
0
2
1
1
0
1
2
1
1
1
1
0
1
1
1
0
1
0
0
1
1
1
2
0
1
1
1
0
1
1
1
2
0
1
0
1
2
1
1
1
2
0
1
1
2
0
0
2
0
1
1
1
1
2
2
1
1
1
1
0
1
2
0
2
1
1
1
2
2
2
1
2
0
2
0
2
2
0
1
1
1
1
4
1
2
7
2
1
0
1
1
1
1
1
1
0
1
0
1
1
2
2
0
1
2
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
2
1
2
1
2
0
0
1
1
1
0
1
2
1
1
1
2
0
0
0
1
1
0
1
1
1
2
0
1
1
0
1
1
2
0
0
1
1
1
1
0
0
1
1
0
1
1
0
1
1
1
0
1
0
2
1
1
1
1
1
2
1
1
0
0
0
0
1
3
1
1
2
0
1
1
2
0
2
2
2
1
2
1
0
1
1
2
2
2
2
1
1
2
1
1
2
2
2
1
1
2
0
1
0
1
2
1
1
1
1
1
1
1
1
2
1
0
2
2
0
1
1
1
2
0
1
1
2
2
1
1
0
2
0
0
1
1
1
1
1
1
0
0
1
1
1
2
0
0
0
0
1
1
1
0
1
1
1
1
0
0
1
2
1
1
1
0
1
0
1
1
1
1
1
1
0
1
1
2
1
1
0
2
2
1
3
1
1
2
0
1
1
2
0
1
1
2
2
1
1
1
2
2
2
2
2
1
1
2
1
0
1
1
2
2
1
1
0
2
1
2
1
4
1
0
0
0
0
1
1
2
1
0
0
1
0
2
1
1
0
0
2
1
1
0
2
1
2
0
1
1
2
1
1
2
1
2
2
2
1
0
1
0
2
0
1
0
1
2
1
1
1
0
1
1
1
1
0
1
2
0
2
1
1
1
2
1
0
1
1
0
0
1
1
2
1
1
1
1
2
1
0
1
0
2
1
2
1
1
1
1
0
1
1
0
2
1
0
1
2
1
1
0
1
1
1
1
1
0
2
1
2
1
1
1
0
2
1
0
0
0
1
1
1
0
1
1
2
2
1
2
0
1
1
1
1
0
1
1
0
1
1
2
0
1
2
1
2
1
0
3
1
2
1
1
2
1
0
0
1
2
1
2
0
2
1
1
0
1
1
1
1
0
1
2
1
0
1
1
1
2
2
2
1
1
2
2
2
1
1
1
2
1
1
0
2
1
2
0
0
0
1
1
1
1
0
2
0
1
0
2
1
1
2
1
1
2
1
1
1
1
2
0
1
1
1
0
0
1
1
0
1
1
1
0
2
1
1
2
1
1
1
2
1
1
0
1
0
1
1
1
2
0
1
1
2
1
1
1
2
1
0
2
1
2
0
2
1
0
2
1
1
1
1
1
1
1
0
2
1
2
0
0
1
1
2
2
1
1
1
1
2
2
1
1
2
1
1
1
2
2
0
1
0
1
1
1
1
2
1
1
0
1
2
1
1
1
1
1
0
2
0
0
0
1
1
2
1
2
1
2
0
2
1
1
1
0
1
2
1
1
2
0
0
0
1
1
1
2
1
1
2
1
2
2
1
1
2
1
1
1
1
1
1
0
1
0
0
2
2
2
1
2
1
1
2
2
1
1
1
1
0
1
2
2
0
0
2
1
0
2
1
1
2
1
2
1
2
1
1
0
0
1
1
2
1
1
1
1
1
1
1
1
1
1
0
1
0
2
2
2
0
1
1
2
1
0
2
2
0
2
0
0
1
1
1
0
0
1
0
0
1
0
1
0
1
0
1
1
2
1
1
2
1
1
1
2
1
1
2
2
1
2
1
0
0
1
0
1
1
1
2
0
2
0
2
1
1
0
1
1
1
0
1
1
1
1
1
0
2
2
1
1
2
0
2
0
1
1
1
1
1
1
1
1
1
1
1
2
0
0
2
1
0
1
1
1
2
2
0
2
1
1
1
1
1
0
0
1
1
0
1
0
1
1
1
2
1
1
1
0
2
2
0
2
1
2
2
1
1
1
1
0
1
2
0
1
2
1
1
2
1
1
0
1
2
1
0
1
1
2
2
0
0
2
1
1
0
2
1
0
0
1
2
0
1
2
2
0
2
1
1
1
1
2
1
0
0
1
1
0
1
0
1
1
2
0
1
0
2
0
2
1
0
0
1
1
1
0
0
0
0
5
1
2
0
1
1
2
1
1
2
0
1
1
3
2
1
0
1
1
1
0
0
1
1
1
0
0
1
1
1
1
0
1
1
2
1
0
2
0
1
1
1
0
0
1
2
1
2
2
2
0
0
0
1
2
1
1
1
1
1
1
0
0
1
2
0
0
1
0
0
1
1
2
1
1
2
1
2
1
0
1
1
1
2
0
4
1
1
0
2
1
1
0
3
0
1
2
0
2
2
1
1
1
1
1
0
1
1
1
1
2
0
2
1
1
0
2
0
1
1
2
1
0
0
1
1
1
0
1
1
0
1
1
2
2
1
1
0
1
1
1
1
1
1
1
3
1
1
1
1
1
1
0
0
1
0
1
1
0
0
1
1
0
1
1
1
1
2
1
0
0
1
2
0
1
2
1
1
0
0
1
1
1
2
1
1
1
1
0
1
1
0
1
3
0
1
1
1
1
2
1
0
0
0
1
1
1
1
1
1
2
1
0
1
2
1
2
1
0
1
0
0
0
1
1
1
1
1
1
1
0
0
1
2
1
3
0
1
0
1
1
1
1
1
1
1
1
0
0
2
1
1
1
0
1
1
1
1
1
0
0
2
0
2
2
2
1
1
0
1
2
0
2
1
0
1
0
1
2
1
1
2
2
1
1
1
1
2
1
1
2
1
1
2
1
0
0
1
1
2
2
1
0
1
1
0
1
0
1
1
1
1
2
1
0
1
0
0
1
0
1
2
2
2
1
1
1
1
2
1
0
0
0
0
1
1
2
2
1
1
2
0
1
1
1
3
1
2
1
0
0
1
1
0
1
1
0
0
0
1
2
1
0
2
0
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
0
2
2
1
2
1
1
2
1
1
0
1
2
1
1
0
1
0
1
0
2
1
1
1
1
1
0
2
2
1
0
1
2
2
2
2
1
2
0
1
0
1
1
1
1
1
2
2
1
1
2
1
2
2
1
1
2
1
0
1
0
2
0
0
1
0
1
2
1
0
2
1
1
0
2
1
0
1
0
2
1
2
0
3
1
2
1
1
4
1
1
1
1
0
2
1
2
0
1
1
2
2
0
1
1
1
1
0
1
1
1
1
1
0
0
1
1
0
2
1
0
2
0
1
3
0
2
1
1
2
1
1
0
1
1
1
2
2
1
0
2
1
2
1
2
1
1
2
1
1
2
0
1
1
0
0
1
1
2
1
1
1
1
1
1
0
1
0
2
1
0
0
1
2
2
1
2
1
1
1
1
1
2
1
2
2
1
1
1
0
1
2
1
2
1
0
1
1
1
1
1
2
1
2
0
1
1
1
0
1
1
1
1
0
2
5
1
1
1
0
0
2
1
1
1
0
0
2
1
1
0
1
0
0
0
2
1
1
2
2
0
3
0
0
3
0
2
0
1
1
0
1
1
1
0
0
1
1
1
0
1
2
2
2
2
0
2
1
1
1
0
2
1
1
2
2
1
0
0
1
0
0
0
1
2
1
0
1
0
1
2
1
2
1
2
1
0
0
3
1
2
2
0
1
1
1
1
1
1
0
2
1
1
1
1
1
0
1
1
1
1
1
2
2
1
0
2
2
1
1
2
0
0
1
2
0
1
2
2
2
1
2
1
1
2
1
0
1
1
1
2
1
0
1
1
1
1
1
1
1
1
1
2
1
0
1
1
1
1
0
1
1
1
2
1
0
1
1
0
1
2
0
0
1
2
0
2
0
1
1
1
1
1
0
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
0
2
1
1
1
1
2
2
1
2
0
1
1
0
1
1
1
0
2
0
2
1
0
0
2
2
1
2
1
1
1
0
1
1
1
1
0
1
0
0
1
0
1
1
0
0
0
1
1
0
1
1
1
1
1
0
1
2
1
1
1
1
1
0
2
1
1
0
2
2
2
1
1
1
1
1
1
1
0
0
1
1
2
1
0
1
0
1
2
1
2
1
0
1
2
1
0
1
1
1
1
1
1
1
2
1
2
0
1
2
2
1
1
1
2
1
1
1
1
0
0
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
0
1
1
1
1
1
1
0
1
1
1
1
1
1
2
1
1
1
0
2
2
1
1
1
1
1
1
1
1
0
2
0
0
1
1
1
1
1
1
1
1
1
0
1
1
2
2
1
1
2
1
2
1
1
1
2
2
2
1
1
2
1
1
2
1
1
2
0
1
1
2
1
2
1
1
2
2
2
2
1
1
3
1
1
2
1
1
1
1
1
1
2
2
2
2
1
1
2
0
0
0
0
2
1
0
1
1
1
0
1
0
2
1
2
2
0
1
0
1
2
1
1
1
0
1
1
0
1
0
1
0
1
1
1
2
0
1
1
1
1
2
1
1
0
1
1
2
0
2
0
2
1
0
2
2
1
1
0
1
2
1
2
2
2
1
1
1
2
2
1
2
1
2
1
1
1
2
2
1
0
1
1
2
1
1
2
1
1
0
0
1
1
2
2
2
2
1
0
2
1
1
1
1
2
1
0
0
1
1
0
0
2
0
1
2
2
1
1
1
1
0
0
3
2
0
2
1
1
0
1
2
0
1
2
0
1
1
1
1
1
0
2
1
3
1
1
0
2
1
2
0
0
0
1
1
1
1
0
1
2
1
2
1
1
2
1
0
1
1
2
0
0
1
1
1
2
1
0
0
0
1
1
2
2
2
1
1
3
1
1
0
0
1
1
1
2
2
1
2
2
1
1
2
1
1
1
0
1
1
0
1
1
1
0
2
0
1
2
2
2
1
1
1
1
0
2
1
1
2
1
2
2
2
1
0
1
1
1
1
1
1
2
1
0
1
1
1
1
1
2
1
0
0
1
0
2
0
0
0
0
1
2
1
0
2
1
1
0
2
1
2
1
1
2
0
0
0
2
1
1
2
1
0
1
2
1
1
1
0
1
1
0
0
1
0
2
1
1
1
1
0
1
2
1
1
1
2
1
1
1
1
1
1
1
2
2
0
1
1
2
0
1
0
1
2
0
1
1
1
1
0
2
2
1
2
1
1
2
0
2
2
1
2
0
0
1
2
0
0
0
0
1
0
1
0
2
1
1
1
2
1
2
2
2
1
1
1
0
1
1
0
1
1
2
1
0
0
1
1
1
1
1
1
1
1
1
0
2
2
2
1
0
1
0
2
0
1
1
1
2
1
1
2
0
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
2
1
1
1
2
0
1
1
0
1
1
1
1
1
1
0
2
1
1
1
1
1
1
0
1
1
1
1
0
1
0
1
0
1
1
2
1
1
1
0
0
2
1
1
2
0
0
1
1
1
0
0
1
2
1
1
1
0
0
1
2
2
1
2
1
1
1
1
1
2
2
2
1
1
1
1
0
1
0
1
1
0
0
1
1
1
0
2
1
1
0
2
2
1
0
2
2
2
1
0
1
0
2
0
1
1
1
1
1
2
1
1
1
1
0
1
3
1
1
3
1
1
1
2
1
0
2
0
2
1
2
1
2
1
2
1
1
0
1
0
1
0
2
1
1
1
0
1
1
1
2
1
1
1
0
2
1
0
0
1
0
1
2
1
0
1
2
0
2
2
1
0
1
0
2
1
2
1
0
2
0
1
1
1
1
1
1
1
3
1
1
1
2
3
1
0
1
1
1
0
0
1
0
1
0
1
0
0
1
1
1
1
1
1
1
0
1
2
1
1
1
0
1
1
2
1
1
1
0
1
1
0
1
2
0
1
1
2
1
2
1
2
0
1
2
0
1
0
1
2
2
1
2
0
0
0
1
1
1
1
1
0
0
3
0
1
2
2
0
1
1
2
0
1
1
1
1
2
1
2
1
1
1
0
1
0
2
1
0
1
1
1
1
0
2
2
1
1
1
1
1
1
1
1
2
1
1
2
2
1
0
0
1
0
1
1
0
1
1
0
7
2
1
1
2
1
2
2
0
1
1
1
0
1
1
2
1
1
1
2
0
1
1
0
1
1
1
0
2
2
1
1
1
0
1
1
1
2
1
2
1
1
1
2
1
1
1
2
1
0
1
2
1
2
1
2
1
1
1
1
1
3
1
1
0
1
1
1
1
1
2
1
1
0
1
3
1
1
1
1
1
2
1
2
1
1
1
1
0
1
1
1
1
2
1
1
2
0
1
3
1
2
2
1
0
0
2
1
1
1
1
0
2
2
0
1
0
0
1
2
0
0
1
1
2
1
1
1
0
2
0
0
1
2
0
2
2
1
1
1
2
0
0
0
1
2
0
1
1
0
2
0
1
1
1
2
0
1
1
1
1
1
2
1
0
2
0
1
1
1
1
0
0
1
0
2
0
1
1
2
2
0
0
1
1
1
1
0
1
1
2
1
1
1
1
1
1
0
1
2
0
1
1
1
2
1
2
1
1
1
1
2
2
1
2
2
2
1
1
2
0
2
1
1
0
1
1
1
2
2
1
2
3
2
1
2
2
1
1
1
0
2
1
2
0
1
0
1
1
1
0
0
1
3
0
1
1
0
1
1
1
0
0
0
1
2
0
1
1
2
0
0
1
2
1
1
2
0
2
1
2
2
2
1
1
0
1
1
2
2
1
0
2
2
1
2
2
1
2
1
0
1
1
1
3
2
1
1
0
0
1
1
1
2
2
2
0
2
1
1
0
1
1
0
1
0
0
0
1
1
2
0
2
1
1
0
1
1
0
0
1
0
0
1
1
1
1
0
2
0
4
2
2
1
0
1
1
1
0
0
1
2
0
1
0
1
1
2
1
1
1
0
0
1
2
1
1
1
2
1
2
1
0
1
1
1
0
5
2
1
1
0
2
1
2
1
0
2
1
0
0
1
2
1
0
0
1
1
3
1
0
1
2
1
1
1
0
2
1
1
1
2
1
0
1
1
1
2
0
1
1
1
1
1
1
1
0
1
3
1
0
2
1
1
1
1
0
2
1
3
1
0
1
2
1
0
2
2
2
1
1
0
0
1
1
1
1
0
0
1
1
1
1
2
0
1
0
1
2
1
2
1
1
1
2
1
1
2
2
0
1
0
0
1
1
2
0
2
1
0
1
2
2
0
1
1
1
0
0
1
1
1
1
1
1
0
1
0
1
0
2
1
2
0
0
2
2
0
2
2
1
1
1
2
1
1
0
0
0
3
2
1
1
0
1
1
1
2
1
1
1
0
0
2
2
1
0
2
1
1
2
1
1
1
2
1
2
2
0
1
1
1
1
1
2
1
1
1
1
0
1
0
1
1
0
1
0
1
1
2
0
1
2
2
1
2
1
1
0
0
1
1
1
1
0
1
1
1
0
1
2
0
1
1
0
0
1
2
0
1
1
1
1
1
2
1
2
0
2
0
0
3
2
1
2
2
2
1
1
1
1
1
1
2
0
1
0
2
1
1
0
1
1
1
1
0
0
1
1
1
1
1
1
1
1
2
1
1
2
4
2
1
1
0
0
1
1
1
0
0
1
0
1
1
1
1
1
2
0
1
1
2
0
1
1
2
0
2
1
1
1
2
1
0
1
1
0
1
2
2
1
1
0
1
1
0
1
1
2
0
1
1
2
1
2
1
0
1
1
3
0
0
1
3
2
1
2
1
1
0
0
2
1
1
2
1
1
2
2
2
0
1
2
0
1
2
1
0
2
1
1
2
0
1
0
1
1
1
2
2
0
2
2
0
1
0
1
1
1
2
1
0
0
3
0
1
1
0
1
1
2
1
1
2
1
2
0
1
1
1
1
1
2
1
1
2
0
2
1
1
1
2
1
1
2
1
1
1
2
2
1
1
1
1
0
1
1
0
1
2
1
1
2
1
0
2
1
1
0
1
0
1
2
1
0
1
2
2
1
0
1
0
0
0
2
1
1
1
0
1
1
0
0
1
1
0
0
0
1
1
1
1
1
0
0
0
0
1
1
0
2
2
2
1
0
0
1
0
1
0
0
0
0
0
1
2
2
3
1
1
1
2
0
2
1
1
1
1
1
0
0
1
1
2
1
1
0
1
1
1
1
2
1
1
1
1
1
1
0
0
0
1
1
0
1
0
1
1
1
1
1
2
1
1
0
1
0
1
0
2
1
1
2
1
1
1
0
1
0
1
1
1
1
1
0
1
1
1
2
1
1
2
1
2
1
1
2
2
1
1
1
0
1
2
1
2
0
1
1
2
1
1
0
0
1
1
2
2
0
2
1
1
1
0
1
0
0
2
1
1
0
0
1
1
1
0
2
2
1
1
1
1
1
1
1
1
1
1
1
1
0
2
0
0
1
1
0
1
2
2
1
1
1
0
2
2
0
0
1
1
2
1
1
1
0
1
2
1
1
1
0
0
1
1
0
1
0
1
1
1
1
2
2
0
1
1
2
1
1
2
1
1
2
1
0
2
2
1
2
2
0
2
2
2
2
0
2
1
2
1
2
1
2
1
2
0
1
1
0
2
2
1
1
2
1
0
1
2
2
0
2
1
2
1
2
1
1
0
0
1
2
0
2
2
2
2
1
1
1
2
1
1
1
2
2
1
1
1
1
1
0
0
1
1
2
1
1
1
1
1
1
0
0
0
1
2
2
1
0
2
1
1
2
1
1
1
1
2
1
0
1
0
1
0
1
1
1
1
1
0
1
0
1
3
1
0
0
0
1
1
0
1
1
1
1
1
0
1
1
1
2
2
2
1
1
2
1
1
1
1
2
2
1
1
1
1
0
0
2
0
2
1
1
0
4
1
1
1
2
1
1
1
0
0
1
0
1
0
1
1
0
1
0
1
1
1
0
1
2
2
3
1
2
0
1
2
1
2
1
0
0
0
0
1
2
1
1
2
0
1
1
1
1
1
1
1
1
0
1
1
0
1
0
2
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
0
1
1
0
1
1
1
1
0
0
1
2
1
1
0
0
1
2
0
1
2
1
0
0
0
1
2
0
1
2
2
1
1
0
1
1
1
2
1
1
1
1
2
0
2
1
0
1
1
0
1
1
1
2
1
2
1
1
1
1
1
1
2
2
0
1
1
1
1
0
3
1
1
2
1
1
0
1
2
2
2
2
1
1
1
1
1
1
2
1
1
1
2
1
1
2
1
1
0
1
1
2
1
0
0
1
0
0
2
2
0
1
1
1
1
2
1
2
0
0
1
1
0
0
0
2
1
0
1
1
1
0
2
0
1
1
2
1
1
1
1
1
1
1
2
0
2
1
0
1
0
0
1
1
2
1
0
1
1
0
2
1
2
1
1
0
1
2
2
1
1
2
0
1
0
2
1
2
1
0
1
0
2
1
0
1
1
0
0
1
2
0
0
2
0
1
1
1
2
1
0
1
1
1
1
2
0
1
2
2
0
1
0
1
0
1
1
0
1
2
2
2
1
1
1
1
1
1
1
1
2
1
2
2
1
1
2
1
1
1
2
1
2
0
1
1
2
1
2
1
1
2
1
1
2
1
1
2
1
0
1
1
0
0
3
0
0
2
2
2
0
2
1
3
0
1
0
0
1
0
2
2
2
1
1
0
0
1
1
1
1
1
1
1
0
1
0
1
3
2
0
1
1
1
2
2
1
1
1
1
1
2
0
1
3
2
1
2
2
2
1
1
1
0
1
0
1
2
1
1
2
3
0
1
2
2
0
1
0
2
2
2
1
0
0
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
0
0
2
2
0
0
0
1
1
1
0
2
2
1
0
1
0
2
1
1
0
2
0
2
2
0
1
1
1
0
2
1
0
1
0
1
1
1
1
2
0
1
1
1
1
2
0
2
0
1
1
1
0
0
1
1
2
1
1
0
0
0
1
0
0
1
1
1
1
1
1
0
1
0
1
2
0
1
1
1
2
1
1
1
2
1
0
1
0
2
0
1
2
1
0
1
2
1
0
0
2
2
1
1
1
1
0
0
2
0
0
1
1
2
1
1
2
1
1
1
2
0
2
1
1
1
0
1
1
2
1
4
1
1
0
1
2
1
1
2
1
0
2
1
1
0
1
1
2
0
1
1
1
0
2
0
1
0
1
1
0
1
1
2
0
1
2
1
1
1
1
0
0
1
1
1
1
1
0
1
3
0
1
1
1
1
1
1
1
0
0
2
2
2
1
2
2
2
2
0
0
1
1
1
1
2
3
1
0
1
1
0
1
1
1
1
1
1
1
1
0
0
1
1
1
1
1
1
0
1
1
1
1
2
1
2
1
2
1
3
1
1
2
1
1
2
1
2
1
0
0
0
1
1
1
2
2
1
2
2
1
1
0
1
0
1
0
1
1
1
2
0
1
2
2
0
2
2
1
2
1
1
2
1
2
0
1
0
1
1
1
0
1
0
1
1
1
0
1
1
1
0
1
2
2
1
2
3
1
1
1
1
1
1
1
0
1
1
1
2
0
1
2
0
2
1
0
0
2
1
2
1
1
0
0
1
2
2
1
1
0
1
1
0
1
1
1
1
0
2
1
0
1
1
2
2
0
0
1
2
1
0
0
1
1
2
1
1
2
0
0
0
2
1
1
2
1
1
0
1
0
2
0
2
2
0
1
0
0
2
1
0
0
1
0
1
1
2
1
1
0
2
2
1
1
0
0
1
1
1
2
1
0
2
0
1
0
2
4
0
2
1
0
1
2
1
2
1
1
1
2
2
2
1
0
2
2
0
0
1
0
1
0
3
1
1
2
1
0
1
0
1
3
1
1
0
1
0
0
0
1
2
1
0
1
1
2
1
1
0
0
1
0
1
2
3
1
2
0
1
1
1
1
1
0
1
0
0
1
0
1
2
2
0
1
1
1
1
0
2
1
2
1
1
1
1
0
1
0
1
1
1
1
2
1
1
1
0
0
1
0
1
1
3
1
1
0
1
1
0
1
1
1
2
1
1
1
1
0
0
0
1
2
1
1
1
1
1
0
0
1
0
0
1
1
1
1
1
1
2
1
2
1
1
1
2
0
2
1
0
0
1
0
2
0
2
2
0
1
2
1
1
3
1
0
0
0
0
1
1
1
1
1
0
0
1
0
1
1
1
0
1
1
2
2
2
1
1
1
2
1
1
0
2
1
0
1
1
2
1
1
1
0
1
1
1
1
1
1
1
2
0
1
2
0
1
1
0
1
1
2
2
1
2
1
2
1
0
1
1
1
0
1
0
1
0
2
2
1
2
1
1
1
1
2
0
2
1
0
1
2
0
0
2
2
2
0
1
2
0
1
1
1
2
1
1
2
0
1
0
0
0
1
2
2
0
0
1
1
1
1
1
1
0
1
2
2
1
1
1
1
0
1
3
0
1
1
1
2
1
1
1
1
2
0
1
2
1
2
0
1
1
1
1
2
0
1
1
1
1
2
1
0
1
1
1
0
0
1
1
1
1
0
1
0
1
2
1
1
0
2
0
0
1
0
1
1
1
0
1
2
1
1
2
0
1
1
1
0
0
2
0
1
0
0
2
2
0
1
0
1
1
1
0
0
1
0
1
2
1
1
2
2
1
1
1
0
0
2
0
1
2
1
1
1
1
0
1
1
0
1
1
2
1
1
2
2
2
1
2
0
1
1
0
1
0
1
1
0
2
1
2
0
1
1
0
2
2
0
2
1
1
0
2
1
0
1
2
2
1
3
1
2
0
2
2
1
1
0
1
1
3
1
0
0
1
1
3
2
0
1
0
1
0
1
1
1
2
1
1
2
1
1
2
1
1
1
0
1
1
0
2
0
1
1
2
2
1
2
1
0
1
1
0
0
2
1
0
0
1
2
1
1
2
2
0
1
0
1
1
0
1
2
1
1
2
2
1
1
1
2
1
1
2
0
3
0
1
2
2
2
2
1
0
1
0
2
1
2
2
1
2
1
0
0
0
2
1
1
1
2
1
0
1
2
2
1
1
1
1
2
2
1
1
1
2
0
2
1
1
1
1
1
2
1
1
0
1
2
1
2
1
1
0
0
1
0
1
2
1
1
1
1
0
2
0
1
1
1
1
2
2
0
1
1
0
1
1
0
1
0
1
2
0
0
1
1
1
0
0
0
0
1
1
0
1
2
1
2
1
1
1
1
2
0
1
0
0
0
1
0
0
0
0
1
1
1
2
0
2
0
0
1
1
4
2
0
1
2
1
0
1
0
2
2
0
0
1
0
0
1
0
2
1
2
1
1
1
0
2
1
1
2
1
2
1
1
1
0
1
2
0
1
1
1
1
1
1
0
2
1
1
1
0
0
0
1
1
0
1
1
1
1
2
2
0
1
1
2
1
1
1
1
0
1
0
1
0
2
0
1
2
1
1
2
1
1
1
1
1
1
1
1
3
2
1
0
2
1
1
1
0
1
1
1
1
1
1
0
1
1
1
1
1
0
2
2
1
1
1
2
1
2
2
1
0
2
1
1
2
0
2
1
1
1
1
0
0
0
1
0
2
1
1
1
0
1
2
0
2
0
1
2
2
0
2
2
1
2
1
2
3
0
1
1
0
1
1
2
1
1
0
1
1
1
1
1
2
1
0
2
1
1
1
2
2
1
1
0
0
1
1
1
1
0
1
2
1
1
1
1
1
0
1
1
1
1
0
1
1
0
2
1
1
2
0
2
1
1
1
0
1
2
2
0
0
0
0
1
0
1
1
1
0
1
1
0
1
1
2
2
1
1
1
1
1
0
1
1
1
2
1
1
2
0
2
0
1
2
0
0
0
1
2
1
0
0
1
0
2
0
0
2
0
1
2
0
1
1
1
2
1
1
0
0
1
1
1
1
2
2
2
2
0
1
1
0
2
2
1
0
0
0
0
1
0
0
1
1
0
2
1
1
0
1
0
0
1
1
2
2
0
0
1
2
0
1
1
1
2
1
0
2
1
2
1
1
0
1
0
1
1
1
1
1
2
0
1
2
1
0
2
1
1
2
1
1
2
1
0
1
0
1
1
1
1
1
2
2
1
1
0
2
1
1
0
0
1
0
1
1
1
1
2
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
0
1
1
1
1
2
4
1
2
1
0
0
1
2
0
0
1
1
1
1
2
2
2
1
0
2
1
2
1
1
1
0
1
2
2
1
0
2
0
2
0
2
2
2
2
2
0
1
2
1
2
2
0
0
2
2
2
0
0
0
2
2
0
1
1
1
2
2
2
1
2
1
1
2
0
1
1
2
1
1
1
1
2
1
2
1
3
2
3
2
1
0
1
1
0
1
1
1
0
1
1
3
1
0
1
0
2
1
0
1
0
0
1
1
2
1
1
1
0
1
0
1
2
1
1
1
1
0
1
2
0
2
1
1
1
1
1
0
0
1
1
0
1
0
0
2
1
1
1
1
2
2
1
1
0
2
1
1
1
1
0
1
2
0
1
0
1
0
1
2
1
1
1
1
0
1
2
1
2
2
1
1
1
1
2
2
1
0
1
1
0
1
2
1
1
0
1
1
0
1
1
1
0
1
1
0
1
1
2
1
2
2
1
2
1
1
2
1
1
2
1
2
1
1
1
1
2
2
2
0
2
1
1
0
0
1
0
1
2
1
0
2
1
0
1
2
1
0
1
1
0
0
0
1
2
2
0
1
2
2
2
1
1
2
2
1
1
1
0
1
1
1
0
0
2
1
1
1
1
1
1
2
1
0
1
0
1
2
1
0
2
2
0
2
0
0
1
1
2
0
1
1
1
0
0
2
2
1
0
2
1
1
2
2
1
1
1
1
1
1
0
1
0
0
1
0
2
1
1
1
1
0
2
1
2
2
1
0
2
1
1
0
1
2
2
2
1
2
2
1
1
1
1
2
2
0
1
1
1
1
2
2
1
1
0
2
2
2
1
0
1
1
1
1
1
1
2
0
1
1
1
2
1
1
2
1
1
1
1
2
1
2
0
2
1
1
1
2
0
1
1
2
2
1
1
1
2
1
1
2
1
0
2
0
2
1
1
2
0
1
1
2
0
1
0
2
0
1
1
1
2
1
1
1
1
0
2
2
1
1
0
1
3
1
1
2
0
1
2
0
1
1
1
2
0
2
1
1
0
1
2
1
0
1
0
1
1
1
1
2
1
0
1
2
2
1
1
1
1
1
0
2
1
0
1
1
0
1
1
1
0
0
2
2
1
0
1
1
2
1
1
2
0
1
1
0
3
0
1
2
2
1
1
0
2
2
0
0
1
1
2
1
1
0
1
0
2
2
1
2
2
1
1
1
1
0
1
0
0
1
1
2
1
0
2
0
1
0
0
0
1
0
1
1
2
1
1
1
0
2
2
2
0
2
0
1
0
1
1
1
2
2
1
1
1
1
0
1
1
1
2
0
0
1
1
0
0
2
1
1
2
1
1
0
2
0
1
0
2
1
1
1
0
1
1
2
1
2
2
0
1
1
1
1
1
0
1
1
1
0
2
0
2
1
0
1
0
0
1
0
2
2
1
1
0
1
1
2
2
1
2
3
1
1
2
1
0
0
1
2
2
1
1
1
1
3
1
0
1
2
0
1
1
2
0
1
1
1
1
0
1
2
1
0
0
0
1
0
1
0
1
1
1
1
1
0
2
1
1
2
1
1
0
0
1
1
0
1
1
0
0
1
1
1
1
0
1
1
0
1
1
2
1
0
0
0
1
0
0
2
0
1
1
1
1
0
1
1
1
2
1
1
1
1
1
1
1
2
0
0
0
0
2
1
0
0
1
0
2
1
1
0
1
0
0
1
2
1
0
1
1
1
1
0
2
1
2
0
1
0
0
1
1
2
1
2
1
0
1
0
1
2
0
1
0
3
0
0
1
1
2
0
1
1
1
1
0
0
0
2
1
1
0
2
2
2
2
0
2
1
2
2
0
1
1
0
5
1
2
1
1
1
2
1
1
1
1
1
1
0
2
0
1
1
2
1
1
1
1
2
1
0
1
1
1
1
2
1
1
1
1
1
1
1
0
1
1
0
1
1
0
0
0
1
1
2
1
0
1
2
1
1
1
2
1
1
0
0
1
1
0
1
1
1
3
1
0
0
1
0
1
1
1
1
1
1
1
1
0
0
1
1
0
0
2
0
2
1
1
2
1
0
2
1
0
0
0
1
2
1
0
1
1
1
1
0
1
2
1
0
2
1
2
2
2
0
1
1
1
3
1
1
0
1
1
2
0
1
2
2
0
2
2
1
2
0
3
0
1
1
2
2
1
1
1
1
2
1
1
1
1
1
2
1
4
1
1
0
1
0
2
1
1
1
1
0
1
0
0
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
2
2
0
0
2
0
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
0
1
1
2
1
1
2
2
1
0
1
2
1
2
0
0
0
1
1
1
1
1
1
1
1
1
0
1
2
2
1
1
0
0
1
2
1
1
2
0
0
1
1
2
2
2
2
2
1
2
1
1
0
0
1
1
1
2
0
1
0
1
1
0
1
1
1
0
1
2
1
1
0
1
0
1
0
1
1
0
1
1
0
0
2
0
0
1
2
1
2
1
2
2
2
1
1
1
0
1
2
0
1
0
0
1
1
0
1
1
1
1
1
1
0
1
1
0
1
1
1
0
1
0
1
0
2
1
1
0
0
0
1
0
1
1
2
1
1
1
2
1
1
1
1
1
1
0
0
0
1
1
1
0
1
2
2
2
1
1
2
0
0
1
2
1
2
2
1
2
2
2
2
0
1
1
0
1
3
0
1
1
1
1
0
1
1
1
2
0
2
1
1
1
1
1
2
1
1
0
0
1
1
1
1
1
2
0
1
2
1
1
1
0
0
2
2
2
1
1
0
1
2
2
1
1
1
1
1
1
2
1
1
2
1
1
1
2
2
0
1
2
1
1
1
2
2
1
1
0
1
0
2
1
0
1
1
2
0
2
0
1
1
1
1
2
1
1
1
0
0
0
1
0
2
0
2
1
1
1
1
1
1
2
1
2
1
1
1
1
0
0
1
1
0
2
2
2
0
0
1
2
1
1
1
1
1
1
2
1
1
1
1
0
1
1
1
2
1
0
1
2
1
2
1
1
1
0
2
1
0
1
1
1
1
2
0
1
2
2
0
1
1
0
1
1
0
0
0
0
1
0
0
2
1
0
2
3
1
1
1
2
1
0
0
1
1
1
0
0
2
1
0
1
0
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
2
1
2
0
2
0
0
1
1
1
1
2
1
1
1
1
1
2
2
1
1
1
2
1
0
1
1
0
1
1
1
1
1
1
0
2
0
1
0
3
1
1
2
1
0
1
2
2
1
1
2
0
1
2
1
2
2
1
1
1
1
0
0
2
1
0
0
0
0
2
0
2
1
1
0
0
1
1
1
0
1
1
1
1
1
0
1
0
0
2
1
1
0
1
1
1
2
1
0
1
0
0
1
0
2
1
1
1
2
1
1
1
1
1
1
0
1
0
2
1
2
1
0
1
1
1
1
1
1
1
1
1
1
2
1
1
2
0
1
2
2
1
2
1
2
1
1
1
1
2
0
0
2
0
1
0
1
2
0
1
1
2
2
1
1
1
0
1
1
1
0
2
0
1
1
1
2
1
0
2
2
1
2
1
1
0
2
2
0
0
1
0
2
1
0
2
1
1
2
0
0
1
1
0
0
2
1
2
2
0
1
2
0
2
1
1
0
1
1
2
1
2
0
1
0
0
1
0
1
1
1
1
2
1
0
1
1
1
1
1
2
1
1
0
1
2
1
0
3
0
0
1
0
0
0
2
2
1
2
2
1
1
2
1
0
2
0
1
1
1
2
1
1
1
1
1
1
2
1
0
1
2
1
2
1
1
1
2
2
1
2
1
1
2
0
0
1
1
1
2
0
0
1
2
1
1
1
2
1
1
1
1
0
2
1
1
2
2
1
1
1
2
1
2
1
2
1
0
2
1
1
1
1
1
1
1
1
1
0
2
1
1
1
0
1
0
1
1
0
1
0
1
1
0
1
2
1
0
2
2
1
0
2
0
1
1
1
2
0
2
1
1
2
1
2
2
0
1
1
1
1
1
1
0
3
1
2
0
2
1
1
1
1
1
1
1
0
0
1
0
1
0
2
1
0
0
1
1
1
1
1
1
1
2
1
1
1
0
2
0
0
2
1
2
1
2
2
1
1
1
1
0
0
0
2
0
0
2
1
1
0
0
1
1
1
0
1
1
1
0
1
0
0
1
2
1
1
0
1
2
1
1
1
1
1
0
2
1
0
1
2
1
0
1
2
1
1
1
1
1
1
1
1
0
0
2
1
0
0
1
2
1
1
2
2
1
0
2
2
1
2
2
2
1
1
2
2
1
2
2
0
0
1
0
1
1
2
0
1
2
1
1
1
1
0
2
1
0
2
0
0
1
1
2
1
1
1
0
1
1
0
2
1
1
1
1
0
2
0
1
1
1
2
1
1
1
0
2
1
1
1
1
1
2
1
2
1
0
2
0
2
0
0
2
0
0
1
2
0
1
2
1
2
1
1
2
0
2
1
0
2
0
0
1
2
3
1
1
1
1
1
0
0
1
1
1
1
1
0
1
1
1
2
1
3
0
1
3
2
1
1
1
1
1
0
1
1
2
1
1
1
0
1
1
0
1
1
1
0
1
2
1
0
1
2
2
1
1
1
1
1
1
0
0
1
0
0
0
2
1
1
1
3
1
1
1
2
2
1
2
1
1
2
1
1
2
1
0
1
2
0
1
1
1
1
1
0
0
2
2
1
1
1
1
0
1
0
0
2
1
0
0
1
2
1
1
0
1
1
0
2
1
1
2
1
1
1
2
1
2
1
0
1
0
1
1
0
0
1
1
2
1
1
2
0
1
0
1
1
1
1
1
1
2
0
2
1
0
1
1
1
1
0
2
2
1
2
1
1
1
1
1
1
1
1
0
2
1
1
1
0
1
1
1
1
1
1
1
2
2
0
2
0
1
1
1
1
0
1
1
1
1
0
1
0
0
2
1
2
1
1
1
0
3
2
1
1
1
2
1
0
1
1
0
0
1
0
0
1
0
1
0
1
1
0
1
1
1
1
2
1
1
1
1
0
2
1
2
2
2
1
1
1
1
2
0
2
1
0
1
2
0
2
0
1
2
0
1
0
0
0
1
1
1
2
1
2
1
2
1
1
1
2
1
1
1
1
1
1
1
1
0
0
1
0
2
2
0
1
2
0
1
1
2
1
1
1
0
0
1
1
2
0
0
2
1
2
1
1
1
1
1
0
0
1
2
1
0
1
2
0
0
0
1
1
1
1
1
2
1
1
1
0
2
1
1
2
1
1
0
0
2
1
0
1
1
1
1
1
1
1
2
0
1
2
2
0
1
1
1
0
2
1
1
0
1
2
1
2
0
2
1
1
1
0
1
0
1
1
1
1
1
1
0
1
0
0
0
1
1
1
1
0
1
0
0
1
0
1
2
0
1
0
0
1
2
1
0
1
1
1
0
3
0
0
1
2
0
2
1
1
2
2
1
1
1
0
0
1
2
0
1
0
1
1
1
2
2
2
1
1
1
0
1
1
2
1
1
1
1
0
1
1
4
1
1
1
1
1
0
1
2
2
0
2
1
1
2
1
2
1
1
2
0
1
1
1
2
0
2
2
1
0
2
0
1
1
0
2
1
1
2
1
1
0
1
1
1
2
1
1
1
2
1
1
1
0
1
2
2
0
1
2
2
0
2
1
0
1
1
1
1
2
1
1
1
0
1
0
1
1
0
0
1
1
2
2
2
1
1
1
1
2
2
1
1
0
0
1
0
2
1
1
2
1
1
1
1
1
1
2
1
2
0
2
1
1
2
0
0
2
0
1
1
1
1
2
1
0
1
0
2
2
1
0
2
1
0
2
2
1
1
1
2
1
1
1
0
2
0
1
0
1
1
2
1
2
2
2
0
2
1
1
1
1
1
2
1
1
1
1
0
0
1
1
1
2
2
1
0
2
1
2
1
1
1
1
1
1
2
0
2
2
0
1
1
1
0
1
1
2
1
0
0
0
0
3
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
0
1
1
0
1
0
0
1
1
1
2
1
1
1
2
1
1
1
1
1
0
2
2
1
2
0
1
2
1
1
2
1
2
2
1
0
1
1
1
1
1
0
1
1
2
2
1
0
1
0
4
0
2
1
2
1
1
1
1
1
1
2
1
0
0
2
0
1
1
1
0
1
1
1
0
1
2
1
0
1
2
1
1
2
2
1
0
1
2
1
1
2
2
1
1
1
1
1
1
1
1
2
1
1
1
0
2
1
1
1
0
1
1
0
1
1
2
1
1
1
1
1
1
0
1
2
1
0
1
1
1
1
1
1
1
2
2
4
1
1
1
2
1
2
1
0
1
2
1
0
2
2
1
0
0
2
1
1
0
0
0
1
1
1
2
2
1
2
1
1
1
0
1
1
0
1
1
1
2
1
0
0
2
1
2
1
2
2
1
1
2
1
0
1
1
1
1
0
0
1
1
1
3
0
1
1
0
1
2
1
1
2
0
1
2
1
1
1
1
1
1
1
0
2
1
1
1
0
1
0
2
1
1
2
2
0
1
0
2
1
1
1
1
0
1
1
1
0
0
1
1
1
1
0
1
2
1
1
1
1
2
1
1
1
1
1
2
0
0
0
1
2
1
1
1
2
0
1
1
1
1
0
4
2
1
0
1
2
2
1
1
2
1
1
2
3
2
1
1
1
1
1
0
1
2
1
0
1
1
0
0
1
2
1
1
2
0
0
2
1
1
2
1
1
2
2
2
1
1
1
1
1
1
0
0
1
1
2
1
2
0
1
1
2
1
2
2
1
2
1
0
1
1
1
1
1
1
1
1
2
1
2
0
1
0
0
2
1
1
1
1
1
0
0
1
1
1
2
1
1
1
2
2
2
1
1
2
1
1
1
0
1
1
0
2
2
1
2
0
2
1
1
1
1
0
1
2
2
1
2
1
2
2
0
1
0
1
0
2
1
2
1
2
1
2
1
1
1
1
2
1
1
2
1
1
0
1
1
2
2
0
0
2
0
0
2
1
1
0
2
1
1
1
0
2
0
0
2
1
1
1
1
1
0
2
1
1
1
0
1
1
2
2
2
2
2
1
1
1
2
1
2
1
0
0
0
1
1
1
1
1
1
1
0
1
1
0
1
1
0
1
2
1
0
2
1
1
1
2
1
0
1
1
0
1
1
0
0
1
1
1
1
2
0
0
1
2
1
2
2
0
2
1
1
2
1
2
0
2
1
1
1
1
2
2
1
0
2
1
1
1
1
1
2
0
0
0
1
0
2
0
1
0
0
1
2
2
1
2
1
0
1
1
0
1
0
1
1
0
2
1
1
2
1
2
1
1
0
1
1
1
1
0
2
1
2
0
0
1
1
1
1
1
1
3
3
1
0
2
2
1
2
2
1
2
0
0
1
1
1
1
0
2
0
0
1
2
2
1
1
1
1
1
1
1
1
1
1
2
0
1
0
1
0
1
0
1
0
2
0
1
2
1
1
1
2
1
2
1
1
0
2
1
1
0
0
1
2
0
1
0
0
0
2
2
1
1
2
2
1
0
1
0
1
0
1
1
2
1
3
1
1
0
0
2
0
0
0
1
2
1
2
2
1
1
0
0
1
2
2
0
1
1
1
1
1
1
2
1
1
2
0
1
1
0
0
0
1
1
1
0
1
1
0
1
1
0
1
1
1
2
2
1
1
1
1
1
0
1
1
1
1
1
0
1
1
2
2
1
1
1
0
0
1
1
1
1
1
1
1
0
1
1
2
2
1
1
1
0
2
2
1
0
1
0
2
0
1
1
1
1
1
1
0
1
1
2
2
0
1
0
1
1
1
1
2
1
2
1
1
1
1
1
1
1
2
0
2
2
1
0
1
1
1
2
1
0
2
1
1
1
1
0
1
1
0
1
0
1
1
1
0
0
2
1
1
1
0
1
0
2
1
1
1
1
1
2
2
0
1
1
1
0
2
2
0
1
1
1
0
0
2
2
0
1
1
3
1
1
2
2
0
2
2
1
1
2
1
1
0
1
1
1
2
2
0
0
1
0
2
1
1
1
2
1
0
1
1
1
2
0
2
1
1
2
1
1
2
1
1
0
1
1
0
0
1
1
1
1
0
1
1
1
1
1
0
1
1
1
2
2
0
1
1
2
0
2
1
0
1
2
1
1
1
1
1
2
1
1
1
0
2
1
1
0
2
1
1
2
1
1
2
1
0
0
1
2
1
1
2
1
1
0
0
1
2
0
0
0
2
1
2
0
1
0
1
1
0
1
0
1
1
2
1
1
1
2
1
1
0
1
1
1
1
1
1
2
1
1
1
0
4
1
1
1
3
0
1
0
1
0
1
0
1
1
1
1
1
0
0
1
1
2
0
1
0
1
1
0
1
2
1
2
1
0
2
0
2
1
3
0
0
2
4
0
1
2
1
0
1
1
2
1
1
1
0
1
2
1
1
1
1
2
0
1
1
1
0
1
1
1
0
1
0
0
2
1
1
1
2
1
1
2
1
3
1
2
2
2
0
0
2
1
1
2
2
2
1
0
1
1
0
1
1
1
0
0
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
0
0
1
1
0
2
0
2
2
1
1
1
1
1
2
1
2
0
2
0
1
0
2
1
1
2
2
0
1
2
0
2
0
0
2
1
2
1
0
1
0
1
1
1
0
1
1
0
2
1
1
1
2
2
0
2
2
0
1
0
1
1
1
2
2
0
1
2
0
0
1
0
0
0
1
1
0
1
2
1
0
1
1
1
1
2
1
0
1
0
2
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
2
2
1
1
1
1
1
3
0
1
2
1
2
1
1
1
1
1
0
0
0
2
2
1
2
1
1
1
0
1
1
0
1
0
0
1
2
1
2
1
1
1
0
1
0
1
1
1
0
1
0
1
1
0
0
1
1
1
1
1
1
1
1
1
2
1
1
0
1
0
1
0
1
1
1
2
1
0
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
0
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
0
1
0
1
1
0
0
1
1
1
1
2
3
1
1
1
0
1
0
1
1
1
1
0
1
0
1
0
1
1
2
2
1
1
1
0
1
2
1
0
2
1
0
2
1
1
0
1
1
0
0
2
1
1
1
1
0
1
1
0
1
1
1
1
2
1
1
1
1
1
1
0
2
2
1
1
2
1
1
1
1
1
2
1
0
1
2
1
1
0
1
1
2
2
1
0
1
2
1
1
1
1
1
1
0
0
2
1
1
1
1
0
1
0
1
2
1
2
1
0
1
1
1
0
1
2
2
2
2
0
2
2
2
1
1
1
1
1
2
2
2
0
1
0
1
0
2
2
1
0
1
0
0
0
2
1
2
1
1
2
2
1
1
1
1
1
1
1
2
1
2
2
1
1
2
1
2
2
2
1
0
1
2
0
0
1
1
1
1
0
3
1
1
0
2
1
2
0
1
0
1
1
2
2
1
2
1
0
1
0
1
0
1
1
1
2
1
0
2
0
2
2
1
0
1
1
1
3
1
1
1
1
0
0
1
1
0
1
1
1
0
1
0
1
2
1
0
2
2
2
0
0
2
1
2
0
1
2
2
1
0
2
2
0
1
2
2
2
1
2
0
0
1
0
1
1
1
1
1
1
0
1
1
1
0
1
1
1
1
1
2
2
2
1
1
2
1
1
1
1
0
1
1
1
1
1
1
4
2
1
1
2
1
1
1
1
1
0
1
2
0
0
1
1
1
0
2
1
1
1
1
2
1
1
1
1
0
0
2
1
1
0
2
2
2
1
1
1
2
0
1
0
1
1
1
1
2
2
1
1
1
0
1
2
2
0
2
1
1
1
1
1
0
2
1
1
1
1
1
1
1
1
0
0
0
1
0
0
0
0
1
1
1
0
2
2
0
1
1
1
1
2
0
1
1
1
2
1
2
1
0
1
1
0
0
0
1
1
0
1
2
2
1
1
0
0
0
2
0
0
1
0
1
1
1
0
0
1
1
0
0
1
2
4
2
2
1
1
1
0
0
1
1
2
0
1
1
1
1
2
1
0
2
1
0
1
2
0
0
1
1
1
2
2
0
2
1
2
1
2
0
2
2
1
1
1
2
0
1
0
1
0
2
1
1
1
2
1
0
1
1
1
0
0
2
0
0
0
1
1
1
1
1
2
0
1
1
2
1
0
1
2
1
0
1
0
0
2
1
1
1
2
1
1
0
1
1
1
0
1
2
1
2
1
0
2
1
0
1
2
0
1
1
1
1
1
0
1
1
1
0
0
0
2
1
0
1
0
2
0
0
2
1
1
2
2
1
1
2
0
0
1
0
1
2
1
0
1
1
2
0
0
0
2
1
0
1
1
1
0
2
1
1
1
2
1
1
1
1
1
2
0
2
1
1
2
1
0
2
0
0
0
1
1
2
0
1
0
1
2
2
1
0
1
2
1
1
0
2
0
2
1
1
1
1
0
1
2
2
1
1
2
0
1
0
1
0
1
1
0
1
1
0
1
2
0
2
1
1
2
1
1
1
1
1
1
1
1
0
0
1
2
0
2
3
0
3
0
1
2
1
2
1
1
2
1
1
3
1
2
1
2
2
2
1
1
0
0
1
1
1
1
2
2
2
1
1
0
2
1
0
1
1
1
1
0
1
0
2
1
2
1
2
1
2
1
1
0
2
2
2
2
1
2
1
1
1
0
0
2
1
1
1
0
1
1
1
1
2
1
1
1
1
0
2
1
0
2
1
1
1
1
1
1
2
2
1
1
1
1
2
1
1
2
1
1
1
2
1
1
0
3
0
3
1
2
4
0
1
0
1
2
1
0
1
0
0
1
0
1
1
1
2
1
1
1
0
2
0
0
0
2
0
1
1
1
1
0
1
1
2
1
1
2
1
2
0
1
2
1
1
1
1
1
2
0
2
2
1
1
0
1
1
1
0
2
0
1
1
1
1
2
2
1
2
2
1
0
1
1
1
0
2
1
2
1
1
0
1
1
1
1
1
1
2
0
0
1
0
1
1
2
1
2
1
1
0
0
1
1
1
1
3
2
0
1
0
1
0
2
1
0
0
0
1
2
2
0
0
0
0
1
0
2
2
0
1
1
0
1
2
0
2
2
4
1
1
2
1
1
1
2
1
0
0
1
2
1
1
0
1
1
1
0
0
2
2
0
0
5
1
1
0
2
0
0
2
0
0
1
1
2
2
1
1
2
1
0
0
2
1
0
1
1
1
1
1
2
1
1
1
0
1
1
2
3
1
1
2
0
0
1
0
2
1
1
1
1
1
1
1
2
2
2
1
0
1
1
1
2
1
1
2
2
1
1
0
0
2
2
2
1
1
0
1
1
0
0
1
2
1
2
1
1
2
1
1
3
0
2
1
1
2
3
2
1
2
2
1
2
1
1
0
1
1
1
1
1
2
2
2
2
1
0
1
1
1
3
1
1
1
1
2
0
1
1
1
1
1
0
2
0
1
1
0
2
1
1
1
2
0
1
1
0
1
0
2
1
1
2
2
3
1
2
0
1
0
1
1
1
1
1
1
1
1
1
2
0
1
3
1
1
2
1
1
1
1
1
1
1
1
0
1
2
1
1
0
1
1
0
1
1
0
1
0
0
1
2
1
1
1
1
0
1
2
1
1
0
1
0
1
0
0
0
0
1
2
1
2
0
1
1
0
1
1
1
1
1
1
1
2
0
1
0
1
1
1
1
0
1
1
0
1
1
1
0
0
0
1
0
2
1
1
0
2
2
1
1
2
1
2
1
0
1
1
1
2
2
1
2
1
1
1
2
4
1
0
1
1
3
1
1
1
0
1
2
2
1
1
1
2
1
2
1
1
1
0
2
1
1
2
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
0
2
2
1
1
2
2
0
2
5
1
2
1
1
0
2
1
2
0
2
2
1
1
0
0
1
1
2
1
0
1
2
2
0
0
1
1
2
1
0
1
2
1
1
1
0
1
1
0
0
1
2
1
2
1
2
1
1
0
1
1
1
0
1
1
1
1
1
2
1
1
2
1
1
2
1
1
0
1
0
0
1
1
9
1
2
0
1
0
1
1
0
1
1
1
2
1
0
1
2
0
2
0
0
2
1
2
1
0
2
0
0
0
1
2
1
2
1
0
0
1
2
1
0
1
1
0
1
0
1
3
1
4
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
0
2
2
2
1
2
0
1
2
1
0
1
2
1
0
1
1
2
1
1
1
1
0
2
1
1
1
1
0
1
0
2
0
0
1
1
0
2
2
1
1
1
2
2
1
1
2
3
1
0
0
1
1
1
2
1
0
1
2
2
1
1
1
2
1
1
2
2
1
1
0
0
1
0
0
2
1
1
2
1
1
0
1
1
0
1
1
1
1
2
0
1
1
1
2
0
0
1
1
1
1
1
2
2
2
0
2
1
2
1
0
1
1
1
0
2
1
1
1
0
0
0
1
1
1
1
1
1
1
0
2
0
2
1
1
1
1
2
2
0
1
2
2
0
0
0
1
1
0
1
2
1
1
1
1
0
0
0
2
1
1
0
1
1
0
2
1
1
0
1
0
2
1
1
1
0
0
1
2
2
1
0
1
1
0
2
1
1
0
1
1
2
1
2
1
1
1
2
1
0
1
1
1
1
1
1
2
1
0
2
1
1
2
1
0
1
1
1
0
0
2
0
1
2
1
1
1
1
1
0
0
1
1
1
2
1
2
0
0
0
2
1
2
1
1
0
2
1
1
0
1
2
2
1
1
1
1
2
2
0
1
2
1
1
0
1
1
0
2
1
1
1
1
2
1
0
1
1
0
1
1
2
1
1
0
2
0
1
2
0
1
3
2
1
1
1
1
2
2
1
2
0
1
1
0
1
2
1
0
1
1
0
0
4
1
1
0
1
0
0
1
1
1
2
0
2
1
1
1
1
1
1
0
1
1
0
2
1
1
1
0
2
1
0
0
0
2
1
1
1
0
0
1
0
1
1
0
2
1
1
2
2
1
1
1
2
0
1
1
1
2
1
1
1
0
1
0
1
1
1
0
1
1
1
1
2
2
1
1
1
2
1
1
1
0
3
0
2
1
1
1
1
1
1
1
1
1
0
1
2
1
1
0
0
2
2
1
1
0
1
1
2
0
0
1
3
1
0
2
1
1
1
1
2
2
2
1
1
0
2
0
1
1
1
1
1
2
4
2
1
1
1
1
1
1
1
1
2
0
0
1
2
1
1
1
2
4
2
1
1
1
1
1
1
2
1
0
2
1
1
1
0
0
0
2
0
2
0
1
1
0
1
1
0
1
2
1
2
1
1
1
2
1
0
1
1
1
1
0
1
2
1
1
1
1
1
0
1
1
1
0
1
1
2
1
1
2
2
1
2
1
1
0
1
2
1
1
1
1
0
0
2
1
2
0
2
1
2
1
2
2
0
1
1
1
2
4
2
1
1
2
2
1
1
1
1
1
1
1
3
1
2
1
1
1
2
1
1
1
0
0
0
0
1
1
0
1
1
1
2
1
3
1
2
2
1
3
0
1
0
1
2
1
1
0
1
1
2
1
1
2
2
1
1
1
1
2
0
1
2
0
1
0
2
0
1
1
1
1
1
3
0
0
0
0
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
2
2
1
0
1
1
1
1
1
1
1
2
0
2
1
5
0
1
1
1
1
0
0
1
1
1
1
0
1
1
2
2
0
1
2
1
1
1
2
2
1
1
0
0
1
1
1
0
0
1
2
0
0
2
1
0
1
1
1
0
1
0
0
2
1
1
1
1
1
0
0
1
0
0
5
0
2
1
1
0
1
1
1
2
1
1
1
2
0
1
0
1
0
2
1
1
2
0
1
2
2
2
2
0
2
2
1
0
2
1
2
0
0
2
2
1
1
2
1
1
1
1
2
1
3
2
1
2
0
1
2
2
1
0
0
2
2
1
1
0
0
1
1
2
1
1
0
0
1
1
0
6
0
1
0
0
0
2
1
1
1
0
0
2
1
1
0
2
2
1
1
0
0
0
1
2
2
0
2
1
2
1
2
2
1
1
1
1
1
1
0
1
1
1
2
0
0
1
1
1
0
2
1
2
1
0
1
2
0
1
1
2
0
1
1
0
1
0
2
1
1
1
1
2
1
1
1
1
0
0
1
2
0
2
2
3
0
1
0
0
2
1
0
1
0
2
1
0
2
0
1
2
1
0
1
1
1
1
1
1
1
0
2
1
1
1
0
2
2
2
0
1
2
1
1
1
1
1
0
2
1
3
1
2
1
2
2
1
2
0
1
2
1
1
1
0
2
0
1
1
1
1
1
1
1
1
2
1
1
1
2
1
3
1
1
2
2
1
1
1
1
1
1
1
1
0
2
1
1
1
1
1
2
1
3
1
0
1
1
2
1
1
1
0
2
2
1
1
1
1
1
2
1
0
1
0
1
2
2
1
1
1
2
1
0
1
2
1
1
1
2
1
2
1
1
0
1
1
1
1
2
1
1
1
1
1
1
0
0
2
1
1
1
1
2
1
1
2
2
0
0
1
2
0
1
1
1
0
1
1
2
1
3
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
0
1
1
1
1
1
1
2
1
2
0
0
0
1
2
1
1
0
1
1
0
1
0
1
1
2
1
2
1
0
0
1
2
1
1
1
1
1
1
0
2
2
2
1
1
0
1
1
1
1
1
1
0
1
2
1
1
1
2
1
1
0
0
2
1
1
2
1
2
0
2
1
0
2
1
0
1
1
1
2
2
1
2
0
1
1
1
1
2
0
1
1
1
0
2
1
1
1
1
1
1
2
0
2
2
2
1
0
1
1
1
1
1
1
1
1
1
0
2
0
1
1
1
1
0
1
1
1
1
0
1
1
2
0
1
2
0
1
1
0
0
0
1
0
1
1
1
1
0
2
1
0
2
1
2
1
1
1
1
1
1
1
2
2
1
1
1
0
1
1
0
2
1
1
1
1
2
1
1
1
0
2
2
2
1
1
0
2
2
0
1
1
0
1
0
1
1
0
2
2
1
1
1
0
0
1
2
2
2
1
1
1
1
1
2
1
1
0
0
2
1
1
1
2
1
0
0
1
1
1
2
1
2
0
2
1
1
1
0
0
1
1
1
1
1
2
1
1
0
0
0
0
2
2
2
1
1
2
2
0
1
0
1
1
0
1
2
0
0
1
1
0
1
1
1
1
1
1
1
1
0
1
1
2
1
1
1
1
1
1
1
1
0
0
0
1
1
2
2
0
1
0
1
1
0
2
1
1
1
0
1
1
0
1
0
1
2
0
0
0
0
2
2
0
1
2
0
1
0
1
1
1
0
1
1
1
1
0
1
2
1
1
2
2
0
1
2
1
2
1
0
2
1
1
0
1
1
2
1
1
2
0
2
1
2
1
2
2
0
0
1
1
2
2
0
0
1
1
1
1
1
1
1
1
2
1
1
2
0
0
1
0
2
2
1
0
1
1
2
1
0
0
1
0
1
2
0
1
1
1
1
1
1
1
0
1
1
1
2
0
0
0
2
1
1
2
1
2
2
0
1
1
1
1
1
0
1
1
1
1
1
1
1
2
1
0
1
0
1
1
0
1
0
2
0
1
0
1
1
1
0
0
0
2
0
1
1
1
1
2
1
2
2
3
1
0
2
1
1
0
1
1
0
1
1
1
1
3
1
1
1
1
1
0
1
2
1
1
2
1
0
0
0
6
2
1
1
2
0
1
2
1
2
1
0
2
0
1
0
1
0
1
1
1
1
1
1
1
2
1
1
0
1
0
1
1
1
1
1
1
1
0
1
1
1
0
1
2
2
1
0
2
2
1
1
1
2
1
2
0
0
0
1
2
1
2
1
1
1
1
1
1
1
1
1
1
0
0
0
0
0
1
2
2
1
1
2
2
2
2
1
1
2
2
1
1
1
1
1
1
1
1
2
1
0
0
1
0
1
2
0
0
2
0
1
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
2
1
0
0
1
0
1
1
1
1
1
1
2
0
2
1
0
2
2
1
1
0
1
1
0
0
2
0
1
2
0
1
1
1
0
1
2
0
1
2
1
2
0
1
0
1
2
1
2
1
2
1
1
1
2
1
2
2
0
1
1
1
2
1
1
2
1
0
1
0
1
1
2
0
1
1
2
1
1
2
1
0
1
1
2
1
1
1
1
2
2
0
2
2
2
0
2
1
1
2
0
1
2
3
2
2
1
2
0
1
1
1
0
1
1
1
1
2
2
0
1
2
3
2
1
2
1
1
1
2
0
1
1
2
2
0
1
1
0
2
0
0
2
1
1
1
2
1
0
1
2
2
0
1
0
1
1
1
1
2
0
1
1
1
1
1
1
1
1
2
2
2
1
1
2
1
1
1
1
0
2
2
2
1
0
1
1
2
0
1
0
2
2
0
1
2
0
2
1
0
2
1
2
1
1
0
0
1
1
0
1
0
2
0
1
1
0
1
0
1
1
2
0
2
0
2
1
1
2
2
1
1
1
1
1
2
1
0
0
1
1
1
1
2
1
0
0
0
1
0
2
0
1
1
1
2
1
0
0
1
1
0
1
0
1
0
1
1
1
1
1
1
1
1
1
1
1
0
2
0
2
0
0
2
1
2
1
1
0
2
1
1
0
0
1
1
2
1
1
1
2
2
1
0
2
1
1
1
1
1
2
0
1
0
0
1
0
1
1
0
1
1
1
1
1
1
1
1
1
0
0
1
1
2
1
2
1
1
2
2
1
1
2
1
2
0
1
2
1
1
1
1
1
1
2
0
0
1
1
2
2
1
1
0
1
2
1
2
1
1
1
1
2
1
2
0
1
0
1
1
0
1
0
1
1
1
1
1
1
1
2
2
0
0
1
2
2
1
2
1
2
1
1
0
2
2
1
2
0
1
1
1
0
1
1
0
2
1
2
0
0
1
2
0
1
2
2
1
1
1
2
2
2
0
0
1
1
0
1
0
2
0
1
0
1
0
1
1
2
0
2
0
1
2
2
2
0
1
1
2
0
1
1
1
1
1
0
2
1
1
1
0
0
0
1
1
0
0
2
2
1
1
1
2
1
0
0
0
0
1
1
0
1
0
1
2
1
1
2
2
1
2
2
2
1
0
0
2
1
2
1
1
0
1
2
2
1
1
1
2
0
1
2
1
2
0
0
1
1
2
0
0
1
2
1
1
1
0
2
2
0
1
1
1
1
0
2
0
1
1
2
1
1
1
1
1
0
1
1
2
2
1
1
0
0
1
1
1
0
1
1
1
1
1
1
1
1
1
0
0
0
0
2
1
1
1
1
1
2
2
2
1
0
1
2
0
0
2
0
1
1
0
1
1
1
0
0
1
2
2
1
1
1
1
1
1
1
0
1
0
1
0
1
0
2
2
0
1
1
0
1
1
1
0
2
0
0
1
1
0
2
1
1
1
0
2
2
1
1
1
1
1
1
3
0
2
1
0
1
1
0
2
1
0
0
0
1
2
2
1
2
1
1
1
0
0
0
1
2
2
1
2
1
1
1
1
0
3
1
1
2
0
1
1
1
1
2
2
2
1
0
2
2
2
3
0
0
1
0
0
0
0
0
0
0
1
1
1
1
2
2
1
1
1
1
1
1
0
1
1
0
1
1
1
1
1
1
0
1
1
0
0
2
1
2
1
1
2
0
0
0
1
1
0
1
1
2
1
2
2
1
1
2
1
0
2
2
1
2
0
0
2
1
2
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
0
1
1
1
2
1
1
2
1
2
1
2
1
1
2
0
1
1
2
2
2
0
1
2
1
1
1
1
2
1
0
3
1
0
2
1
0
1
1
2
0
1
1
1
0
1
1
1
2
1
0
1
2
1
1
1
1
0
0
0
1
1
2
1
1
1
1
2
5
1
0
1
1
1
0
1
1
2
1
0
1
1
2
2
1
2
1
1
1
1
1
2
0
2
0
0
1
0
0
1
1
1
1
1
1
1
0
1
1
1
1
1
1
0
0
1
0
1
2
1
1
2
0
1
1
2
1
1
0
1
1
1
0
1
1
1
1
2
1
1
1
1
1
0
2
1
2
1
1
0
0
1
1
1
2
1
2
0
2
0
1
0
1
0
1
2
1
1
2
2
0
1
1
2
2
2
2
1
1
0
1
2
1
1
0
0
2
1
1
1
0
2
2
1
1
1
0
0
1
2
2
1
2
0
1
1
2
1
2
1
2
0
2
0
1
0
1
1
0
1
0
2
0
2
1
1
2
2
2
1
2
1
2
2
1
1
1
2
1
1
1
0
1
4
1
1
1
2
3
1
0
2
0
2
0
1
1
1
0
1
1
1
1
1
1
1
2
1
1
0
1
1
1
0
0
1
1
0
1
2
1
0
2
2
1
1
1
2
1
1
1
1
1
1
1
2
1
2
0
2
1
2
3
3
2
0
1
2
0
0
1
1
1
0
2
3
1
2
1
2
0
0
1
1
2
1
2
2
1
2
0
1
1
1
1
2
1
1
0
2
0
1
1
2
1
2
0
2
1
2
1
1
0
0
2
1
1
2
1
0
2
1
1
2
2
0
1
2
0
2
2
3
1
1
2
1
2
1
0
1
0
1
2
1
0
1
2
1
1
0
1
1
1
1
1
1
1
0
1
1
1
1
1
1
2
1
2
0
1
2
1
1
1
1
2
1
1
2
2
1
0
1
2
1
1
0
1
1
1
1
1
0
1
1
2
1
2
1
2
0
0
1
0
1
1
0
1
0
1
1
1
1
0
1
1
1
1
1
1
2
1
1
1
0
1
1
1
1
1
1
2
0
0
0
2
1
2
2
1
0
2
2
2
2
0
1
0
1
1
0
0
1
1
1
1
1
2
1
1
2
3
1
1
1
2
0
0
0
1
1
1
1
1
1
0
1
0
2
0
1
2
1
3
1
1
1
1
1
1
1
1
1
0
1
1
1
1
4
2
1
2
1
0
1
1
1
1
0
1
2
1
1
1
1
2
1
0
1
1
2
2
0
2
0
0
1
1
1
1
0
1
1
1
1
0
1
1
2
1
1
0
3
1
1
0
2
1
1
1
2
1
1
0
1
0
1
1
2
1
1
1
1
2
1
2
2
2
2
2
1
1
1
3
2
2
1
0
1
0
1
1
1
1
2
0
1
1
1
0
1
0
1
1
1
0
1
1
2
1
1
0
1
1
2
0
1
2
1
1
1
1
1
0
1
1
1
2
1
1
1
1
2
1
2
2
0
1
2
2
1
1
0
1
2
2
0
1
1
2
0
0
1
1
0
1
1
0
0
1
0
1
1
1
2
1
2
1
1
1
1
2
2
2
1
1
1
1
1
1
2
2
1
1
2
0
1
1
1
0
1
2
0
0
1
0
0
2
1
1
1
2
1
1
1
0
0
2
0
1
1
1
1
2
0
1
1
0
2
2
0
1
2
1
0
1
2
1
2
0
1
1
2
0
1
1
1
1
1
1
2
0
1
1
1
1
1
1
1
1
0
1
1
1
1
2
1
0
1
0
1
1
1
1
1
1
2
2
1
1
2
1
1
1
1
1
0
1
2
2
3
1
1
0
1
0
1
1
0
1
1
0
0
1
1
2
1
1
0
1
1
2
2
1
1
1
0
0
2
1
1
1
1
2
0
1
1
1
1
0
1
1
0
1
0
1
1
0
2
2
2
0
1
0
1
0
1
2
0
1
1
1
2
2
0
0
0
1
2
1
1
1
1
1
2
1
2
2
1
2
0
1
0
2
2
0
2
1
1
0
2
1
0
2
0
2
0
2
2
2
2
1
1
2
1
1
1
0
1
1
1
0
1
1
0
1
0
1
1
1
2
1
1
0
1
1
2
0
1
1
1
1
2
2
0
1
2
1
1
2
1
1
1
2
2
2
1
3
1
1
2
1
1
2
1
2
1
1
0
1
0
1
1
1
0
1
1
1
0
0
1
1
1
1
0
0
1
2
0
2
1
1
1
1
1
2
0
1
2
2
2
1
1
1
1
2
0
1
1
1
0
2
1
1
1
2
2
1
1
1
0
1
0
1
2
1
0
2
1
1
2
1
0
0
0
1
1
0
1
2
2
0
1
2
2
0
2
1
1
0
2
0
0
1
0
1
1
2
2
1
1
1
0
1
1
1
2
1
1
1
1
0
0
0
1
1
0
1
0
0
1
0
2
2
1
0
1
2
1
1
0
0
2
2
2
1
1
2
0
1
0
2
1
2
2
0
0
1
2
2
1
0
0
0
1
2
1
1
2
0
0
1
1
1
1
1
0
0
1
1
1
1
2
1
0
1
1
2
0
0
1
1
1
2
0
1
0
1
1
1
1
0
1
1
1
0
1
1
0
2
2
2
0
0
0
1
1
1
0
1
2
1
0
2
2
2
0
0
1
0
1
1
2
1
0
0
2
2
1
1
2
0
1
1
1
1
1
2
1
1
0
1
0
0
0
1
1
1
1
1
0
2
1
1
1
2
2
2
0
0
1
1
2
1
1
2
1
1
1
0
1
0
0
0
1
1
2
2
1
0
1
2
1
2
1
2
1
1
1
0
1
1
1
1
1
2
1
1
1
0
2
0
2
0
1
1
1
2
1
2
0
1
2
1
1
0
2
1
2
1
0
2
1
0
1
0
1
1
2
2
1
1
1
1
2
0
1
1
2
2
1
0
1
1
1
0
0
1
0
1
1
1
0
0
1
0
2
1
2
0
1
2
1
1
1
1
1
2
0
1
1
1
1
1
1
1
0
0
0
2
0
3
1
2
2
2
1
1
1
1
1
1
2
1
1
0
1
0
1
1
0
1
0
1
1
0
0
1
1
1
0
2
1
0
2
1
1
2
2
1
1
1
1
1
1
1
1
1
1
0
1
1
0
0
0
1
1
0
2
1
1
1
2
1
0
0
1
2
1
1
1
1
1
2
0
0
0
1
1
2
0
1
1
1
0
1
1
1
2
2
0
1
1
2
1
0
1
1
2
1
1
1
1
1
1
2
2
2
1
2
1
0
1
0
0
1
1
1
1
1
2
2
1
2
2
1
1
0
0
0
1
1
1
1
1
1
0
1
1
1
0
1
2
1
1
0
1
0
2
1
1
1
2
0
2
0
0
1
1
1
0
1
1
1
1
1
1
1
1
1
1
0
2
0
1
1
1
1
2
2
2
2
0
1
1
1
1
0
2
1
1
1
1
1
1
1
1
0
1
1
2
1
1
3
1
2
1
1
1
1
2
0
0
0
0
1
2
0
1
0
1
1
0
1
1
1
1
1
1
1
0
2
2
0
1
0
0
0
1
0
1
1
2
2
1
0
2
1
1
2
1
1
1
2
0
1
1
1
1
2
2
0
2
1
2
2
2
1
0
0
1
1
1
1
0
1
2
0
1
0
1
1
1
2
1
1
1
0
1
1
1
2
0
2
0
1
2
2
2
1
0
0
1
1
0
0
1
1
2
1
0
1
2
0
1
0
1
0
1
1
1
2
1
2
2
1
1
0
1
1
3
1
1
1
1
1
1
1
1
2
0
2
1
2
1
0
2
2
2
1
1
1
1
1
1
0
1
1
0
2
2
0
1
2
1
1
2
1
0
1
2
1
0
2
0
2
1
1
0
0
2
1
0
2
1
1
2
1
0
1
0
1
0
2
1
1
1
0
3
1
0
1
1
1
0
1
1
2
1
1
1
1
1
2
1
1
1
2
1
3
0
0
2
1
0
2
2
0
0
1
0
1
0
0
1
1
0
2
1
1
1
1
1
1
0
1
1
0
1
0
2
1
1
2
1
1
2
1
2
0
1
1
1
0
0
1
2
1
3
1
2
2
0
1
2
0
0
2
2
1
0
1
1
2
1
1
2
1
0
1
1
1
1
2
1
1
1
0
1
2
1
1
0
1
1
1
1
1
0
1
2
0
1
2
1
1
1
1
0
2
0
1
2
1
0
0
1
1
2
0
1
2
1
0
1
0
0
1
1
2
0
2
1
1
2
1
2
1
1
1
1
1
1
1
0
0
2
1
1
1
2
1
0
1
1
1
1
2
1
2
1
1
2
1
1
1
0
0
1
1
0
1
1
1
1
1
1
1
1
1
1
0
1
0
2
2
1
1
0
1
0
1
0
2
1
2
1
2
2
2
2
1
0
0
0
1
1
0
1
1
0
0
1
1
1
1
1
2
1
1
0
1
1
2
1
1
1
2
2
1
0
1
0
2
2
1
1
1
0
1
2
1
2
2
2
0
2
1
1
0
1
0
2
2
1
0
0
1
1
1
0
0
1
2
1
1
1
1
0
1
1
0
1
2
1
1
1
1
0
1
1
0
1
1
0
0
1
3
1
2
1
0
2
0
0
1
2
1
2
0
1
0
1
2
1
2
1
2
1
2
1
0
1
4
1
1
2
1
1
1
2
1
1
2
1
1
1
2
1
1
2
1
0
2
1
0
2
1
2
2
1
1
0
1
0
2
1
0
0
2
0
0
0
1
1
2
1
2
2
1
0
2
1
2
1
1
1
2
2
2
1
1
0
2
1
2
2
0
1
0
2
2
1
1
1
1
1
4
2
1
1
0
1
1
1
0
1
0
1
1
1
1
0
2
0
0
0
2
0
2
2
1
1
1
2
1
1
1
2
0
1
0
0
2
0
2
0
1
1
0
2
1
2
2
1
0
2
0
1
0
1
1
1
2
0
0
1
0
0
0
0
2
1
1
0
1
1
0
1
0
0
1
1
1
1
2
1
0
1
1
1
2
0
2
1
2
0
2
1
1
1
1
1
1
1
0
1
0
1
1
2
1
0
1
1
0
2
1
1
0
1
1
1
1
1
2
1
2
2
1
1
1
0
2
1
2
1
1
1
2
1
1
1
1
2
0
1
0
0
0
1
1
0
2
1
2
1
1
1
1
0
1
0
2
1
1
0
2
1
1
0
1
1
1
2
0
2
0
2
2
0
2
1
1
2
1
0
1
1
1
1
1
0
1
1
0
1
2
1
0
1
1
2
1
1
1
1
2
1
2
1
1
2
10
1
0
0
2
2
2
1
0
1
1
1
1
1
1
0
2
0
1
0
0
1
1
2
1
1
0
2
1
1
2
1
2
0
0
0
3
0
2
1
0
2
0
2
0
1
1
1
1
1
1
0
1
1
2
1
1
2
1
1
0
0
2
1
2
3
1
2
2
1
0
0
1
1
2
0
2
0
1
2
0
0
0
1
1
1
1
1
0
0
1
0
2
1
0
3
1
1
0
0
0
1
2
2
1
1
0
1
1
1
1
1
1
0
1
0
2
1
1
1
1
2
0
1
1
2
1
0
1
2
2
1
1
2
2
2
1
1
1
1
0
0
2
1
1
1
1
2
0
1
0
2
1
0
1
1
1
1
0
2
1
0
1
1
0
2
2
2
1
1
1
2
1
0
2
1
1
1
2
1
1
1
2
0
1
0
1
0
1
1
1
0
1
2
0
1
2
1
0
1
0
1
0
2
0
1
0
0
0
1
2
2
0
2
1
1
0
1
0
2
1
2
1
1
1
1
0
1
1
0
0
0
1
1
0
1
2
0
0
0
1
1
2
2
1
1
1
2
1
0
1
2
1
0
1
2
1
1
0
2
2
1
2
2
1
1
1
0
0
1
0
1
1
0
1
1
0
0
2
1
1
0
0
2
2
1
1
2
2
0
1
1
0
1
2
1
1
0
1
0
0
0
1
0
1
0
0
1
1
0
0
2
1
1
1
0
1
1
1
1
1
1
2
2
1
1
0
0
1
1
1
2
0
0
1
2
2
1
1
0
0
0
1
1
1
2
0
0
1
1
0
1
1
0
1
0
1
1
1
2
0
3
2
0
2
2
2
2
1
1
2
1
0
1
1
2
1
0
0
1
0
1
0
2
0
1
2
1
1
0
1
1
1
1
0
1
1
1
1
1
2
2
1
0
0
1
2
2
1
1
2
1
1
1
1
2
1
1
2
2
2
1
0
0
1
1
0
1
2
0
0
1
1
1
2
0
1
1
1
1
1
2
1
1
1
1
2
2
1
1
1
1
0
1
2
1
1
1
1
1
1
1
0
0
1
1
0
0
0
1
1
0
1
1
0
1
0
0
1
1
2
1
2
1
2
1
1
1
1
0
1
0
0
1
0
1
2
1
1
1
2
1
1
2
1
2
0
1
2
2
1
1
1
1
2
2
1
1
1
1
1
0
1
0
1
0
0
1
1
1
0
1
1
1
1
1
2
1
1
1
2
0
0
0
0
0
1
1
0
2
0
1
1
1
0
1
2
2
1
0
1
1
0
1
2
0
0
0
0
1
2
0
0
0
2
5
2
1
1
2
1
0
2
0
1
0
1
1
2
1
1
1
0
1
1
1
1
1
2
1
1
1
1
0
1
1
1
2
1
1
0
1
1
1
1
0
0
2
2
2
2
1
1
1
1
2
1
1
1
2
0
0
1
1
2
1
1
1
1
2
3
0
1
2
0
1
2
0
1
1
1
2
1
0
1
0
1
0
1
1
0
3
1
1
0
2
1
2
1
1
1
1
1
0
0
1
2
0
1
2
1
2
1
1
1
0
1
3
1
1
1
1
2
1
0
2
2
2
2
1
2
1
1
2
1
1
0
1
0
1
0
1
1
2
4
0
0
1
1
1
2
0
1
1
1
1
2
1
1
1
2
1
1
1
1
3
1
1
1
0
0
2
1
2
0
1
1
1
0
1
0
2
0
2
1
1
0
1
1
1
2
1
1
2
1
2
1
0
1
0
1
0
2
0
2
2
1
2
0
1
1
1
2
0
2
1
1
1
2
1
0
1
1
2
2
1
1
1
1
2
1
2
1
2
2
0
1
0
0
1
0
1
0
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
2
0
0
2
2
0
0
2
2
1
0
2
0
0
1
1
1
0
0
1
1
1
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
0
0
1
1
1
1
1
2
0
1
2
1
1
1
1
0
0
0
1
0
2
0
1
1
1
1
1
0
0
2
1
2
1
1
1
2
2
1
0
1
2
2
1
0
0
2
2
1
1
2
2
1
2
0
0
2
0
0
2
2
0
1
1
0
2
1
0
1
0
1
1
1
1
1
1
1
1
1
2
0
0
1
2
1
1
1
1
1
1
0
1
1
2
1
1
1
1
1
1
2
0
1
1
3
2
2
0
1
1
2
1
1
0
1
2
0
2
1
1
1
1
2
1
1
1
1
1
2
1
0
1
0
0
0
1
2
2
2
0
0
2
1
0
2
1
1
2
1
1
1
2
0
0
2
1
2
1
2
1
1
1
1
0
0
2
2
1
0
1
2
0
1
2
1
1
1
1
1
2
0
1
0
1
1
1
2
0
0
2
1
1
0
0
1
1
0
1
1
2
0
1
1
2
1
0
1
1
2
0
1
2
1
3
2
0
1
1
0
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
0
2
1
2
0
0
1
0
2
0
2
0
1
1
1
1
1
1
0
1
0
6
1
1
1
1
2
1
2
0
2
1
2
1
1
2
1
1
1
1
1
1
1
1
0
2
2
1
1
0
1
1
1
1
0
1
1
1
0
0
2
1
2
1
2
0
0
1
0
2
1
3
2
1
0
2
1
1
0
1
1
0
0
0
2
2
1
1
1
1
2
0
0
0
1
1
1
1
0
0
2
1
2
2
1
1
2
2
1
2
2
1
2
2
1
0
1
0
1
1
2
1
1
1
2
1
1
1
1
0
1
1
1
3
1
2
1
1
1
1
1
0
1
1
0
1
1
1
1
1
1
2
1
1
0
0
0
2
1
1
0
0
1
1
0
0
0
0
2
1
1
0
0
2
0
1
1
0
1
1
1
0
2
0
1
1
1
2
1
0
1
0
2
4
2
1
1
2
1
1
1
1
1
1
1
1
1
4
0
2
2
1
0
0
1
1
2
2
0
1
1
2
2
2
0
1
5
0
1
1
1
0
1
1
1
1
0
2
1
1
1
2
1
1
1
2
1
1
1
2
0
2
1
1
2
2
1
0
2
0
0
2
0
2
1
0
1
1
2
0
1
0
2
2
1
1
0
0
2
0
0
2
1
1
0
1
1
1
0
2
1
1
2
2
2
0
2
1
2
2
1
0
0
1
1
1
2
2
0
1
0
2
0
0
1
0
0
1
1
1
1
0
1
0
1
1
2
2
1
0
1
1
0
0
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
2
2
1
1
1
1
0
1
1
2
1
0
0
1
1
0
0
1
0
1
1
1
1
1
1
2
1
1
2
2
1
0
0
3
1
1
1
1
1
1
1
1
0
1
0
1
1
2
1
1
1
2
0
0
1
2
2
1
1
0
1
1
0
1
0
1
0
2
1
0
1
1
1
1
2
1
1
2
1
0
1
1
1
2
1
1
2
1
0
1
0
2
1
1
2
1
1
1
1
1
1
0
0
1
2
1
1
1
1
2
0
0
0
1
1
1
1
0
1
1
1
0
1
1
2
1
1
3
1
0
1
1
1
1
0
0
1
2
1
0
0
0
1
0
1
2
2
0
1
2
0
0
0
1
2
2
0
2
1
1
0
0
0
1
1
1
0
1
2
1
2
0
0
2
1
1
0
0
1
2
1
0
0
2
1
1
1
0
1
1
1
2
1
1
1
1
1
4
1
1
2
1
2
1
2
2
1
0
0
2
1
1
1
1
1
1
2
0
1
0
2
1
1
1
1
1
2
2
2
2
1
1
1
2
2
1
2
2
1
1
1
1
2
1
2
0
1
1
1
2
1
1
0
2
1
1
2
1
1
2
2
1
0
0
3
1
2
0
0
2
2
0
1
1
0
1
0
2
1
1
1
0
1
1
2
1
1
3
1
0
1
2
0
1
0
1
1
2
1
0
0
1
1
1
0
1
1
1
4
2
3
2
1
2
1
1
1
2
2
1
1
2
1
0
1
1
0
1
1
0
1
2
1
0
1
1
2
1
2
0
1
1
1
2
2
1
1
0
2
2
2
1
2
1
1
0
1
0
1
1
1
0
1
2
0
2
2
1
2
0
1
2
1
1
1
2
1
0
2
1
1
0
0
1
1
1
0
0
0
1
2
0
1
1
0
1
1
0
1
2
1
2
1
1
1
1
2
0
1
1
1
1
1
1
2
2
1
4
1
1
2
1
1
0
0
1
0
1
0
3
0
1
0
1
1
2
1
1
1
2
2
1
2
0
0
1
1
2
1
0
1
1
0
1
0
1
2
0
0
2
1
0
1
0
1
1
1
1
1
0
1
1
0
1
0
1
2
1
1
1
0
1
1
0
1
0
1
2
2
0
0
2
1
2
0
2
1
0
0
1
2
0
1
1
1
2
1
1
0
0
1
2
1
0
0
1
0
0
0
1
1
1
1
2
0
1
1
1
2
0
1
0
1
1
1
1
1
0
1
1
1
0
2
1
1
1
1
1
1
1
2
0
1
1
1
2
1
1
1
1
2
0
1
1
2
1
0
1
1
2
0
4
0
1
1
0
1
1
1
1
1
1
2
0
1
2
0
1
1
0
2
1
1
0
1
2
1
0
1
1
1
1
2
0
1
1
1
1
2
1
2
0
0
1
1
0
1
0
1
0
2
2
1
1
1
1
0
1
2
1
1
0
0
0
1
1
1
1
2
1
0
1
1
1
1
1
1
1
1
1
1
0
1
2
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
0
2
2
1
2
1
1
2
0
1
0
0
1
2
2
1
1
1
1
2
1
1
1
1
1
1
2
1
1
3
1
0
2
0
1
1
2
1
1
0
1
1
0
0
0
3
0
1
1
1
1
0
1
1
2
0
0
0
1
1
1
2
1
1
0
1
2
1
1
1
2
2
2
0
2
1
1
2
2
1
2
1
0
1
1
0
2
0
2
2
2
1
1
1
0
1
2
2
1
1
2
3
1
1
2
1
0
0
0
1
1
1
2
1
1
1
1
0
1
1
1
1
1
2
0
1
1
1
1
1
1
1
0
1
1
2
1
1
1
1
0
0
1
1
0
1
1
2
1
1
0
1
2
1
1
1
1
2
0
0
0
1
1
2
1
2
1
1
1
3
1
0
0
0
1
1
1
1
2
0
1
2
0
1
2
1
1
1
1
1
1
1
0
1
1
1
1
2
2
1
1
3
0
1
2
1
1
1
1
2
0
2
1
0
1
1
1
0
1
3
1
1
1
1
1
1
1
1
2
1
1
1
1
1
3
1
2
2
2
1
1
0
1
1
1
1
1
1
1
1
1
0
2
1
1
2
1
1
2
2
1
1
1
1
0
1
1
2
2
1
0
1
1
0
0
1
0
1
0
1
0
2
1
1
1
0
1
0
2
1
0
1
1
2
0
2
0
1
0
2
1
1
1
1
1
1
2
1
1
5
1
1
0
1
1
1
1
2
1
2
1
2
3
1
2
0
1
1
1
2
0
1
0
2
1
1
1
0
1
1
0
1
1
1
0
1
1
1
2
2
1
1
2
1
1
1
0
1
1
0
2
1
1
0
1
1
1
1
0
2
0
2
1
1
0
0
0
1
1
1
2
0
1
0
0
0
1
1
2
0
1
1
1
1
2
1
1
1
1
1
2
1
1
0
1
1
0
0
2
4
1
0
1
2
0
1
1
0
2
0
3
2
0
1
0
1
1
1
1
0
2
1
0
1
0
2
0
1
1
2
1
1
0
2
1
0
0
1
2
2
1
1
1
1
1
2
1
2
2
1
1
1
1
1
2
2
1
1
1
1
1
1
1
0
1
1
2
1
1
1
1
1
3
2
1
1
1
2
1
1
1
0
2
1
1
2
1
0
1
1
1
1
1
2
1
0
1
1
1
0
1
0
1
1
1
1
0
1
1
1
0
1
0
0
1
1
2
2
0
0
0
1
0
2
1
0
2
2
1
0
1
2
1
0
2
1
1
2
1
0
2
1
1
1
2
1
1
1
0
1
1
1
1
0
1
1
1
1
1
1
2
2
1
3
1
0
0
1
0
1
1
2
1
0
1
1
1
1
0
1
1
0
0
1
1
1
2
1
2
1
1
1
1
0
1
0
1
2
1
2
0
1
2
1
0
1
1
0
2
0
1
1
2
2
1
1
1
0
2
1
2
0
2
0
1
2
1
1
2
2
1
2
0
1
1
1
1
1
1
2
0
2
2
0
2
2
1
0
1
1
1
0
2
1
2
0
1
0
0
2
2
2
2
1
1
1
1
0
2
1
1
2
1
1
0
1
2
1
0
0
0
0
2
0
1
1
1
0
0
0
1
0
2
2
2
1
1
2
1
2
2
0
1
0
1
0
1
0
1
0
2
0
0
1
1
1
0
2
0
1
1
3
0
2
3
2
2
0
1
1
1
1
1
1
1
2
1
0
1
1
0
0
1
0
0
0
0
2
1
1
1
2
1
1
2
2
2
2
1
0
1
1
2
1
0
1
0
0
2
0
1
1
0
1
1
0
1
1
1
3
0
1
2
2
0
1
0
2
1
0
0
1
1
0
1
0
1
2
1
2
0
1
1
1
1
1
2
2
0
1
1
0
1
2
1
0
1
1
2
1
1
2
1
0
1
1
2
1
2
1
1
0
1
1
1
2
1
2
1
2
2
0
1
1
1
1
0
2
0
1
2
0
1
1
1
1
1
1
1
1
0
0
0
2
2
0
2
0
1
1
1
1
1
0
1
0
1
2
2
1
2
1
2
2
1
2
1
1
2
1
0
0
0
1
1
2
0
0
2
2
1
1
2
2
2
2
1
1
0
1
2
2
1
0
0
0
2
0
0
2
1
1
1
2
3
2
1
1
2
2
2
1
1
1
0
1
1
2
0
0
1
2
1
2
0
0
1
1
2
0
0
2
1
1
1
1
1
1
1
1
2
0
1
1
1
2
1
0
2
0
1
2
0
1
0
1
0
0
1
2
2
0
2
1
1
2
1
0
1
1
0
2
1
1
1
1
2
1
1
3
1
1
1
1
1
1
1
1
0
1
1
2
1
1
0
1
1
1
1
1
2
2
2
2
1
2
2
0
0
0
0
1
1
0
0
1
2
0
2
1
0
1
1
1
1
1
1
1
1
1
2
0
1
1
1
2
3
0
1
1
1
0
1
1
0
2
0
0
1
3
1
1
0
1
1
1
1
1
1
2
2
1
1
1
1
1
1
2
2
1
1
1
0
0
1
1
1
1
2
0
0
1
0
1
2
1
1
1
2
2
3
1
1
0
1
0
1
2
1
1
2
2
1
0
2
3
2
2
1
1
1
1
1
1
1
1
0
1
2
1
0
1
1
2
0
1
2
1
0
1
1
1
2
2
2
1
0
0
1
1
1
1
1
1
2
1
0
1
1
0
1
1
2
1
1
3
1
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
0
1
1
1
0
1
1
1
2
1
0
1
0
1
1
1
1
1
1
1
1
1
2
1
0
1
2
1
0
2
2
1
2
1
1
1
1
1
2
1
3
0
0
1
0
1
1
1
1
1
1
1
2
0
0
1
0
2
1
1
1
1
0
1
2
0
1
1
1
1
0
1
1
0
0
1
0
1
0
1
1
1
1
1
0
0
1
2
2
0
0
4
0
1
0
0
1
0
0
1
1
1
1
0
1
1
1
0
1
1
1
2
1
1
1
1
0
1
0
1
1
1
1
0
1
1
2
2
0
2
1
2
1
2
0
1
1
1
1
0
1
1
1
0
1
0
1
0
2
0
1
2
1
1
2
2
1
2
3
0
1
1
0
1
2
0
1
1
0
2
1
1
0
1
1
3
0
1
2
0
2
0
1
0
1
0
2
1
1
1
0
1
2
1
0
1
1
2
0
1
0
1
1
2
2
1
1
0
1
1
1
1
1
0
0
1
0
1
0
1
1
1
1
0
0
1
2
1
1
1
1
1
0
2
1
2
1
1
1
1
1
3
2
0
2
2
1
1
0
1
1
1
1
1
0
1
1
1
1
1
1
0
1
1
0
2
1
1
1
0
1
1
1
2
1
1
0
1
2
1
1
1
1
1
1
0
1
0
1
1
0
0
1
1
1
1
1
1
1
1
2
2
0
1
0
1
3
1
1
1
2
1
1
2
1
1
2
2
0
1
1
1
0
1
1
1
1
2
1
1
2
0
1
1
1
1
1
0
2
1
1
0
0
0
2
1
2
1
1
2
0
1
1
0
1
0
0
1
2
1
0
1
1
1
1
1
0
1
1
1
1
1
0
1
2
2
2
1
1
1
1
0
1
1
1
1
0
1
1
1
1
1
0
1
1
0
2
1
1
0
2
0
1
2
2
1
3
1
2
2
1
1
1
0
0
1
1
1
1
1
1
1
1
1
2
1
0
1
0
2
1
1
2
1
1
0
1
0
0
0
0
2
2
0
2
1
1
1
1
1
1
1
0
2
1
2
1
0
0
1
2
1
0
0
1
0
1
2
1
1
0
0
1
2
1
0
0
2
1
1
1
1
1
1
1
1
1
1
0
2
1
1
0
0
2
0
1
1
2
0
1
1
2
0
0
1
2
1
0
0
0
0
1
1
0
0
1
2
1
1
1
1
2
1
1
0
1
1
0
2
1
2
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
0
1
2
1
2
1
2
1
0
0
1
1
2
1
0
0
1
2
1
0
2
2
1
1
1
1
1
1
1
1
2
2
1
0
1
2
1
1
1
1
1
1
3
1
2
1
2
1
3
1
2
0
2
2
2
0
1
1
0
2
1
2
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
2
2
2
1
0
0
1
1
0
1
2
2
2
1
1
0
2
2
2
1
0
1
1
1
1
1
0
0
1
2
1
0
0
2
1
1
1
1
0
0
1
1
0
2
1
0
1
1
1
1
0
1
2
1
1
0
2
1
1
0
0
1
1
1
1
1
1
1
2
0
0
1
1
2
1
2
2
2
1
0
2
1
1
2
2
1
0
2
2
1
1
0
1
1
1
0
1
0
0
1
2
0
0
1
1
1
1
2
2
2
2
0
1
0
0
2
1
2
2
2
1
2
1
1
0
1
1
0
1
2
0
0
2
2
1
1
2
1
2
0
1
2
0
1
1
0
1
0
1
2
1
1
0
1
1
2
0
0
0
1
1
1
2
0
1
1
1
1
1
0
0
1
1
1
1
0
1
2
0
2
3
1
2
1
1
0
1
0
1
1
1
0
0
1
1
0
1
1
0
2
3
2
0
1
0
2
1
0
1
1
2
1
1
0
2
1
1
1
3
1
2
0
4
2
1
1
1
1
1
1
1
0
1
1
0
1
0
1
2
1
0
1
2
1
1
2
0
1
1
0
0
1
1
0
0
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
2
1
1
1
2
1
2
0
2
2
1
1
2
2
1
2
1
0
1
2
0
1
2
2
1
2
1
2
1
2
1
1
1
1
2
1
2
0
0
1
1
0
1
0
1
0
0
1
0
1
2
1
1
1
0
0
1
1
1
1
0
0
0
1
2
1
1
2
0
1
2
2
0
1
1
0
0
1
1
0
1
1
1
1
2
2
1
1
3
1
1
1
2
0
0
2
3
1
1
1
1
0
2
0
1
1
1
1
1
1
0
1
2
1
2
1
2
1
2
2
0
2
1
2
1
0
0
1
0
0
2
1
2
1
1
0
0
2
1
1
1
0
1
1
0
1
0
0
1
2
1
1
1
0
0
1
1
2
1
1
0
2
0
0
1
1
3
0
2
2
1
3
2
1
1
0
1
0
0
1
1
1
1
0
0
0
0
0
0
1
1
1
2
2
1
1
0
1
2
0
1
1
2
0
1
1
2
0
1
1
1
0
2
1
0
1
0
1
1
0
1
1
1
1
0
1
1
0
1
0
1
2
1
1
1
1
1
1
1
1
2
2
2
0
0
2
0
2
0
0
2
0
2
0
0
1
0
1
1
0
1
1
2
1
1
1
1
1
1
1
1
1
2
2
0
1
1
1
1
1
1
1
0
0
2
0
1
0
2
2
1
1
2
2
1
1
1
1
2
0
1
0
0
2
1
2
1
1
2
1
1
1
0
1
2
1
0
2
2
2
4
2
1
0
2
0
1
1
2
2
1
1
0
1
2
2
0
2
1
2
1
0
1
0
1
2
1
0
1
3
1
1
0
0
1
1
2
0
1
0
1
0
2
2
1
1
2
1
1
2
1
1
2
1
2
2
1
2
0
1
4
0
1
1
1
0
1
3
0
0
1
1
2
0
1
1
1
1
1
2
0
1
1
2
1
0
1
2
0
1
0
0
1
2
0
0
1
1
1
2
1
2
1
0
0
0
1
0
0
0
2
1
2
1
2
0
1
1
0
0
1
1
1
2
1
0
1
1
1
1
1
1
1
1
0
1
0
1
1
0
2
0
1
2
1
0
2
1
1
1
0
2
1
0
2
2
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
2
1
0
1
0
2
1
2
1
1
1
0
1
0
0
2
2
1
2
0
0
1
1
1
1
1
1
3
0
1
1
0
2
1
0
0
2
0
0
1
0
2
1
2
1
2
0
2
1
4
1
0
0
2
1
2
1
1
0
0
1
1
0
2
1
1
2
2
2
0
2
1
2
1
1
2
0
1
1
1
2
1
1
0
2
1
2
1
0
0
2
1
1
1
1
1
1
0
2
2
1
1
0
2
2
1
2
1
1
1
1
1
0
2
1
1
2
0
0
1
1
0
0
1
2
0
1
2
0
1
1
0
0
1
1
1
2
1
1
1
1
1
0
1
1
0
0
2
0
1
1
0
1
1
0
1
0
1
1
1
1
1
2
1
0
1
1
2
0
0
1
1
0
2
0
1
2
1
1
1
1
2
2
1
1
1
1
1
0
2
0
1
2
2
0
1
1
0
1
1
0
1
0
1
0
1
1
1
1
1
1
0
0
1
1
1
1
1
1
0
0
0
1
1
0
1
2
0
1
1
1
1
0
1
0
1
1
2
1
0
2
0
1
0
1
1
1
2
1
1
1
2
1
2
0
5
1
2
2
1
2
2
1
0
2
1
1
0
2
1
2
1
3
2
1
3
0
0
0
1
2
2
1
2
1
1
1
2
1
0
1
1
1
1
2
1
1
1
2
2
1
1
2
1
2
1
1
1
1
1
1
0
1
2
2
1
1
0
1
0
2
2
2
1
1
1
1
1
2
2
1
2
1
0
1
1
2
2
2
1
0
1
1
1
0
1
1
0
1
1
2
0
0
0
1
1
1
0
2
0
1
2
2
2
0
0
2
0
0
1
1
1
2
0
2
2
0
1
0
2
0
2
1
0
0
0
2
2
1
0
1
1
0
2
1
1
1
1
2
1
2
0
1
1
1
2
1
1
2
1
0
2
1
0
1
1
0
1
0
1
1
1
1
1
2
1
1
1
1
1
0
1
2
2
1
0
0
0
1
1
1
1
0
1
0
1
1
2
2
1
0
1
0
0
2
1
0
1
1
0
2
2
2
1
0
0
0
0
1
1
1
0
1
2
0
1
1
1
0
0
1
1
1
0
1
1
0
1
1
0
1
1
2
0
1
2
2
1
1
2
1
1
2
1
2
1
1
1
2
2
2
2
1
1
1
2
0
1
2
1
2
1
0
2
0
1
2
3
1
2
2
2
1
2
1
1
0
0
1
1
1
1
1
0
0
1
0
0
1
1
1
1
0
1
2
0
1
2
1
2
1
1
1
1
0
1
1
0
2
5
0
1
1
1
1
0
1
2
1
1
2
0
0
2
2
1
1
1
1
1
1
2
1
1
0
1
0
2
1
1
0
1
0
1
2
0
2
2
0
2
1
1
2
2
1
1
1
1
1
1
1
1
2
1
0
0
1
1
0
0
1
1
0
1
1
0
1
1
0
1
0
1
1
0
0
0
1
1
1
2
1
1
1
0
0
1
0
1
1
1
0
2
1
1
1
1
1
0
1
1
1
1
0
2
2
0
0
1
2
2
0
1
1
1
1
0
0
0
1
2
0
1
0
1
2
1
0
2
1
1
1
0
2
2
1
0
1
0
1
2
0
1
0
1
1
2
0
0
1
1
0
1
2
1
2
1
1
0
3
1
1
1
0
2
0
1
0
0
1
1
2
2
2
1
0
0
1
1
1
1
1
0
1
1
1
1
2
1
1
0
1
2
2
1
0
1
1
2
2
1
0
1
1
1
0
1
1
1
2
0
2
0
0
1
0
1
1
2
1
1
1
1
1
0
1
0
2
0
2
2
1
2
0
1
1
1
2
0
1
1
1
0
2
0
1
1
2
1
1
1
1
1
2
1
0
1
0
0
0
2
2
1
2
1
1
1
1
1
0
1
1
0
0
1
0
1
0
0
0
1
2
2
1
0
0
2
1
0
1
2
1
1
1
0
1
1
2
1
1
2
1
2
2
2
1
1
1
2
1
1
2
1
2
0
1
1
1
1
2
1
1
2
1
0
2
0
1
1
1
2
1
1
2
1
0
0
1
1
0
0
2
0
2
1
2
1
1
1
1
1
2
0
1
1
1
1
1
2
1
2
1
2
1
0
2
1
0
2
1
1
0
1
0
1
1
1
1
2
1
3
2
1
1
0
1
0
1
1
2
1
2
0
1
1
0
1
1
0
1
1
0
1
2
2
2
0
0
1
1
1
1
2
0
0
1
1
0
1
1
1
1
1
1
1
1
1
2
2
2
1
1
0
1
0
1
1
1
2
1
1
1
0
1
1
0
1
0
1
2
1
1
1
1
1
1
2
1
1
2
1
0
1
0
2
0
2
0
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
0
2
1
1
2
0
2
1
1
1
1
2
2
1
2
0
2
1
1
1
1
2
1
1
1
1
1
1
2
1
0
1
2
1
0
1
0
2
1
2
0
1
1
0
1
3
1
2
2
1
1
2
1
1
1
1
1
1
2
1
1
1
2
0
2
1
0
0
0
0
1
1
0
2
0
1
1
1
1
0
2
1
2
1
1
1
0
2
2
0
0
1
2
1
1
0
1
2
1
1
1
1
1
2
1
2
1
1
1
2
1
0
1
1
1
0
1
0
2
2
1
2
0
0
0
1
0
2
1
1
1
1
1
3
2
1
0
1
2
1
1
1
1
1
0
1
0
1
0
2
0
0
2
1
1
0
1
1
1
1
1
2
1
0
3
2
1
1
1
2
1
2
1
1
1
0
2
1
1
2
0
1
2
0
1
2
1
1
0
2
0
1
2
0
1
1
1
1
0
0
2
2
0
1
0
0
1
2
0
1
0
2
0
1
0
0
2
0
1
2
1
1
1
2
1
0
2
0
1
1
1
1
1
1
2
1
2
2
0
1
0
1
0
1
1
1
1
0
0
2
2
1
0
1
1
0
1
0
0
1
0
1
1
0
2
1
0
1
0
2
1
2
1
2
1
0
2
2
0
1
2
2
1
2
0
1
1
2
0
2
1
1
1
1
0
1
1
1
1
1
1
0
2
0
0
2
1
1
0
1
1
0
0
0
0
2
0
1
1
1
1
1
2
1
1
0
0
1
0
2
1
1
1
1
0
1
1
1
2
0
1
1
0
0
1
0
2
1
1
0
1
1
0
1
1
0
0
2
0
1
1
2
1
0
1
1
0
1
0
1
2
1
2
0
1
1
0
2
1
0
1
1
2
1
0
1
1
1
2
2
1
2
1
2
2
1
1
2
0
0
1
1
0
1
1
1
2
1
1
1
0
1
0
1
1
1
1
0
0
1
0
0
1
0
1
1
1
1
1
1
2
1
1
0
0
0
0
1
0
1
1
2
1
1
3
1
1
2
1
1
1
3
0
1
1
0
1
2
2
1
0
2
0
1
1
2
1
0
1
0
2
1
2
2
1
1
1
1
0
0
1
2
2
2
2
1
1
1
1
2
1
1
1
1
1
0
1
1
1
2
1
1
0
1
0
1
1
1
0
2
1
1
0
1
1
1
2
1
1
1
2
1
1
0
1
2
2
1
1
2
2
1
2
2
0
2
2
0
1
1
2
2
2
1
2
0
1
2
1
2
2
2
1
0
1
1
1
1
0
0
0
1
1
2
0
1
3
1
1
1
1
0
1
2
0
0
2
1
0
1
2
0
1
2
1
1
1
0
1
0
2
2
1
1
1
1
2
1
0
1
1
2
1
0
1
1
0
1
1
2
0
2
0
1
1
0
1
1
2
2
1
1
1
2
1
0
2
1
2
2
1
1
0
1
0
1
1
1
1
1
2
2
2
2
2
1
1
2
1
2
1
2
1
0
1
1
1
2
2
1
2
1
1
1
0
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
0
2
0
1
0
0
0
1
1
1
1
1
0
2
1
2
1
1
1
0
1
0
1
1
0
1
2
2
0
1
0
1
1
2
1
1
1
1
1
1
1
0
0
0
2
1
0
1
0
0
0
0
0
1
2
1
1
1
1
1
1
0
0
1
2
1
1
0
1
1
1
1
1
1
0
0
1
2
1
2
1
1
2
1
2
0
2
2
2
1
2
2
1
1
1
1
1
2
0
2
1
2
2
3
1
1
1
0
0
1
0
1
1
2
1
0
1
1
0
1
2
1
1
1
2
2
1
1
1
0
1
0
1
1
1
1
1
1
1
0
1
0
2
0
2
1
1
1
1
0
0
2
0
0
2
1
1
2
2
2
1
2
1
1
3
1
1
1
1
1
1
1
0
1
2
1
1
0
1
2
1
0
1
1
1
0
1
1
1
2
0
2
1
1
1
2
1
2
1
0
1
1
2
1
1
2
2
1
2
0
2
0
1
2
0
0
2
0
1
1
1
2
2
1
1
1
1
1
0
1
0
1
1
1
1
0
1
0
1
1
1
2
1
1
0
0
1
0
0
1
1
0
1
1
2
1
1
0
1
1
2
1
1
1
0
1
0
1
2
1
1
0
1
1
1
0
0
1
1
0
0
1
1
0
2
1
2
2
1
1
2
0
2
1
3
1
1
1
0
1
1
1
1
0
2
2
1
1
0
2
1
1
1
2
0
1
2
0
1
2
1
0
1
2
1
2
1
1
1
2
1
1
0
1
2
1
1
1
2
1
0
1
1
1
0
1
1
2
0
0
0
0
1
1
2
0
1
1
1
2
1
0
1
1
1
1
0
2
0
2
1
1
1
0
1
2
1
0
0
1
2
1
2
1
1
1
0
1
0
1
1
1
2
2
2
2
1
1
1
1
1
1
1
0
0
2
2
1
2
0
1
1
1
1
1
0
1
1
1
1
1
2
1
0
0
1
2
0
0
4
0
1
1
1
0
2
0
2
2
1
2
1
2
2
1
2
2
2
1
2
1
1
0
2
1
2
1
1
1
1
2
1
2
0
2
0
1
0
1
1
1
2
0
1
7
2
1
1
1
1
1
1
1
2
2
1
2
2
0
2
1
1
1
1
1
0
1
0
1
1
1
0
2
1
1
1
1
0
1
1
1
1
1
2
1
1
0
1
0
0
1
0
2
1
1
1
1
2
1
1
1
1
0
0
1
1
1
2
2
2
0
1
1
1
2
0
1
2
1
1
0
2
0
1
1
1
2
0
0
0
1
2
1
1
3
1
1
1
2
1
1
2
0
1
2
1
1
2
1
1
2
2
1
0
1
1
3
1
1
2
1
1
0
0
0
2
0
1
1
1
1
1
2
0
0
1
1
2
1
1
0
1
1
0
1
0
1
1
1
1
2
2
0
1
2
1
2
0
1
3
1
2
2
0
1
2
1
2
2
0
1
1
2
1
1
1
0
2
1
1
1
1
1
2
1
1
0
2
1
0
1
2
1
5
2
0
1
2
1
2
1
2
1
1
1
2
1
1
3
1
0
2
1
1
2
1
2
0
1
1
1
1
0
2
1
0
1
2
1
1
0
2
4
1
1
0
1
2
1
1
1
2
2
1
1
0
0
1
0
0
1
0
1
2
1
1
1
2
2
1
0
1
0
0
1
2
2
2
2
1
2
1
1
1
2
1
1
1
0
2
1
1
0
1
1
0
0
1
2
1
1
1
1
1
0
0
1
2
0
0
1
1
2
1
2
1
1
2
1
2
0
0
0
1
2
1
1
1
2
2
1
2
3
1
2
1
1
2
2
0
2
1
2
1
1
0
2
1
2
0
1
0
1
2
1
0
0
0
2
1
1
0
2
0
1
1
1
2
1
2
1
0
0
1
1
1
1
0
1
2
0
2
1
0
2
1
1
2
2
1
0
1
0
1
2
2
0
1
1
0
1
1
1
1
0
2
1
1
2
1
2
1
2
1
2
1
1
1
0
0
1
2
0
1
0
1
1
1
0
2
2
1
1
2
0
1
1
1
0
1
0
1
0
0
0
1
1
2
2
2
1
1
1
1
1
2
0
0
2
1
1
1
1
1
1
2
0
0
1
2
1
0
2
1
1
2
1
2
1
1
1
2
1
2
1
3
1
1
1
2
1
0
0
1
2
1
1
1
0
1
1
0
1
0
0
1
2
1
1
1
0
2
1
1
0
1
1
0
1
1
2
1
0
2
2
2
2
1
0
1
2
1
1
2
0
0
1
1
0
0
0
1
1
1
1
1
1
1
1
1
2
1
1
0
0
2
0
2
2
1
0
0
1
2
0
1
1
1
1
1
0
1
1
1
1
1
1
0
1
1
1
0
0
0
1
2
1
1
1
0
2
1
1
1
0
2
1
2
1
1
1
1
0
1
2
1
2
1
0
1
2
2
0
1
1
1
1
2
1
0
1
0
2
0
1
2
2
1
2
0
1
0
1
0
1
1
1
1
2
0
1
0
0
1
0
1
0
1
1
1
1
2
2
1
0
0
2
0
1
0
2
1
1
0
1
0
1
1
1
1
1
2
2
1
1
1
1
1
3
1
2
0
0
1
0
2
1
1
1
1
0
1
1
2
0
1
1
2
1
1
0
2
1
1
1
1
0
2
2
1
1
2
1
0
0
1
1
1
2
1
1
1
1
1
1
1
2
1
2
2
1
1
2
2
1
0
0
0
1
2
1
1
1
1
2
1
0
1
0
2
0
1
2
1
0
1
1
1
1
0
3
3
1
1
0
1
1
2
1
0
2
2
1
1
1
0
1
0
0
1
0
2
0
1
1
2
1
1
1
0
1
1
1
0
1
1
0
1
0
0
1
1
0
1
0
1
1
0
2
1
1
0
0
1
1
0
0
3
1
1
2
2
1
0
1
1
1
1
2
1
0
1
1
1
1
0
2
1
2
1
1
1
1
0
1
1
0
2
0
1
2
2
2
1
1
0
2
0
1
2
1
1
0
2
1
2
2
2
2
1
1
1
0
1
1
1
1
1
2
1
1
1
0
2
0
1
2
2
1
2
1
1
2
3
1
1
1
1
0
1
2
2
1
1
1
0
1
0
3
0
0
0
1
2
2
1
1
0
1
0
1
2
2
2
1
1
1
1
2
1
1
2
0
1
1
2
1
1
1
0
1
1
1
1
0
1
1
0
0
0
1
1
1
1
1
1
1
2
2
0
1
1
1
0
0
1
1
2
0
1
0
1
2
2
1
1
1
2
1
2
0
2
0
1
0
2
1
1
1
1
0
1
1
2
1
0
1
1
1
1
1
1
0
0
1
2
1
1
1
1
0
2
1
0
1
1
2
1
1
1
1
2
2
1
0
1
1
1
0
2
0
1
1
1
1
1
1
1
0
2
1
1
0
1
1
2
2
1
0
1
2
0
1
0
2
1
1
1
2
0
0
1
0
0
1
1
1
2
1
0
1
1
2
1
0
1
0
1
2
0
2
0
1
1
1
1
0
1
1
1
2
0
0
0
1
1
1
1
0
1
0
1
1
1
2
1
1
2
1
0
1
1
2
2
1
1
0
1
1
0
2
0
1
1
1
2
1
1
0
0
1
0
1
1
1
2
1
1
2
0
1
1
0
0
1
0
1
1
1
1
1
1
3
2
0
1
0
1
1
3
0
2
1
2
1
0
2
2
0
1
2
0
2
1
2
1
1
2
1
1
1
2
1
1
1
1
2
1
1
0
1
0
1
0
1
0
1
1
1
1
0
2
2
0
1
1
1
0
1
0
0
0
1
1
2
1
1
1
2
1
0
1
2
1
2
1
2
2
1
1
1
1
1
1
0
1
0
1
1
2
1
2
2
0
1
0
2
2
0
0
1
0
1
2
1
1
1
0
0
1
1
1
1
0
1
1
0
1
2
1
1
1
2
1
9
0
1
2
1
2
1
1
2
1
0
2
1
1
0
1
1
1
1
0
1
2
1
1
1
2
1
0
1
2
1
0
0
1
2
0
0
1
0
2
1
0
1
1
1
2
1
0
1
0
0
1
2
2
0
1
2
3
1
2
1
1
2
1
1
0
2
1
2
0
2
1
1
1
0
1
0
1
1
1
0
2
0
1
1
1
0
2
0
1
2
2
2
1
1
1
1
1
1
1
0
3
1
1
1
1
1
0
1
1
0
3
1
2
0
1
1
2
5
1
2
1
0
1
0
2
1
2
0
1
2
1
0
1
2
1
2
2
1
1
1
4
1
0
1
2
1
0
1
0
0
0
1
1
2
0
0
0
2
1
1
2
0
2
2
1
1
1
1
1
2
0
1
1
1
0
0
2
2
2
1
2
1
1
2
1
1
1
2
2
0
0
1
2
1
2
2
1
0
1
3
1
1
1
0
2
2
0
1
2
1
0
2
1
1
1
2
1
0
1
1
1
1
1
1
2
1
1
0
1
2
1
2
1
1
1
1
1
1
1
0
1
0
1
1
0
1
1
0
2
1
2
1
2
1
0
0
1
2
1
2
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
0
2
0
2
1
2
0
1
0
0
1
0
2
0
1
0
1
1
0
1
2
1
1
2
0
1
1
0
0
1
0
1
0
0
2
1
1
1
1
1
1
1
0
2
0
1
1
0
1
1
1
1
2
1
1
0
1
1
1
0
2
0
1
2
1
2
1
3
1
1
1
0
0
2
1
1
1
1
2
0
2
0
0
2
1
0
2
1
1
1
1
1
1
0
2
1
1
1
2
0
0
1
1
1
1
1
2
2
1
1
1
0
0
0
1
0
1
0
1
1
1
1
1
2
1
0
1
2
1
1
0
1
1
1
2
1
1
2
0
0
1
2
2
0
2
2
1
2
1
0
0
1
1
2
2
0
1
1
2
1
1
1
1
2
1
0
0
0
1
1
1
1
2
2
1
1
1
2
2
1
1
0
1
2
0
0
2
2
2
0
0
1
1
0
2
0
0
0
0
2
0
2
1
0
1
1
3
1
1
1
0
1
2
1
0
1
3
2
2
1
0
1
1
1
1
1
1
1
1
0
1
2
0
0
1
1
1
1
1
0
2
1
1
1
1
2
1
0
1
1
0
2
1
0
1
1
0
1
0
1
0
2
2
1
0
1
0
0
1
1
0
1
1
1
2
1
0
2
0
1
1
0
1
1
1
0
0
1
0
1
1
1
0
3
0
1
2
0
0
0
1
1
1
1
3
0
1
1
1
0
2
1
1
1
0
0
0
0
1
0
1
1
0
1
1
1
1
1
0
0
1
2
1
1
1
1
1
1
1
2
2
1
2
0
1
2
2
1
0
0
1
2
1
1
0
0
3
1
1
0
1
1
1
1
1
1
0
1
2
1
1
0
1
2
0
2
1
2
2
1
1
1
0
1
2
0
1
1
1
2
0
1
1
1
1
0
1
0
0
1
1
2
2
1
1
1
1
1
0
0
0
1
2
1
1
1
0
1
1
0
1
1
1
1
1
1
1
3
1
1
1
1
2
1
2
1
1
1
2
1
0
1
0
1
1
1
1
1
1
0
1
0
1
1
0
0
2
1
1
2
0
0
2
2
0
3
2
1
1
1
0
0
1
0
2
1
1
1
1
1
1
0
0
3
1
1
1
2
0
1
0
2
1
1
1
1
1
1
0
0
2
2
2
1
1
1
0
2
1
1
2
1
1
1
1
3
1
2
1
1
1
2
0
0
1
1
1
2
1
0
1
1
1
0
1
0
1
1
1
1
2
1
1
1
1
0
2
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
1
2
2
1
1
1
2
1
2
1
1
0
1
1
0
1
1
1
0
0
0
2
0
2
1
1
1
1
1
2
1
1
1
0
1
1
1
1
1
0
1
0
0
1
0
2
1
1
1
2
0
1
0
0
1
2
2
1
1
0
1
1
2
0
0
2
1
0
2
0
0
1
0
2
0
1
1
1
1
1
1
0
0
1
2
0
0
0
1
1
2
2
1
1
1
2
2
1
1
0
1
1
0
0
2
0
0
1
1
1
0
0
1
0
0
1
1
1
1
1
2
1
1
1
1
1
1
1
1
0
2
1
2
0
1
1
1
0
0
2
1
2
1
2
2
0
1
1
1
2
2
1
1
1
1
0
0
1
1
1
2
1
0
1
0
0
1
2
2
1
1
2
2
2
2
2
0
2
0
0
2
1
1
1
1
1
1
2
1
1
2
1
2
0
0
1
1
1
1
1
0
0
2
0
0
1
1
1
0
2
0
1
1
1
1
1
2
1
1
2
1
1
2
2
0
1
0
1
1
1
0
1
0
0
1
2
1
1
0
1
1
1
3
1
1
1
0
1
0
1
1
1
1
2
0
1
0
0
0
1
1
2
1
1
1
1
1
2
1
2
1
2
0
1
0
2
2
1
2
3
1
1
1
1
1
1
1
2
1
1
2
1
1
1
2
2
1
1
0
0
0
0
2
0
0
2
1
0
0
2
1
1
1
1
2
1
0
2
1
0
1
1
1
1
0
1
1
0
1
1
0
2
1
0
1
0
0
1
1
1
0
1
0
0
1
0
0
0
1
1
0
0
1
2
1
2
2
1
2
0
1
2
2
1
1
2
2
1
1
2
0
1
2
1
0
1
1
2
1
2
1
0
0
2
2
0
0
1
1
3
1
0
1
0
0
0
1
2
1
2
1
2
1
1
1
2
2
1
2
1
1
0
1
1
0
1
0
1
0
1
2
2
1
0
2
0
2
0
1
1
1
1
0
0
1
2
2
1
0
1
0
0
0
1
0
1
2
1
1
2
0
1
2
0
1
1
2
1
0
1
1
1
1
2
1
1
2
2
1
1
1
2
0
1
1
1
2
1
2
1
1
0
1
1
2
0
1
0
1
0
1
1
1
2
1
1
0
2
2
3
2
0
1
1
0
2
1
1
1
1
2
1
1
1
2
1
1
1
0
1
1
1
1
0
1
1
1
1
1
0
0
0
1
2
2
1
0
0
1
2
1
1
2
0
1
0
1
1
1
1
1
2
1
1
1
0
1
1
1
0
1
1
2
1
1
0
1
0
3
0
2
0
1
1
2
1
2
0
1
1
2
1
1
1
1
0
1
1
1
0
1
1
0
1
2
0
1
2
1
2
1
1
1
0
1
2
2
1
0
1
1
2
1
1
1
1
0
1
1
1
1
1
2
1
0
1
1
0
2
1
1
2
1
2
1
0
1
1
0
3
0
1
0
1
0
1
1
1
0
0
2
0
2
0
2
0
1
1
0
2
1
0
1
2
0
1
1
0
0
1
1
1
1
1
2
1
2
1
4
2
0
0
1
1
1
1
1
1
0
3
1
1
1
1
1
2
2
2
1
1
0
1
1
0
0
3
2
0
0
1
1
1
2
1
1
0
1
1
1
0
0
1
2
0
1
2
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
5
0
0
2
1
0
1
0
1
1
2
1
2
1
1
0
1
0
2
1
2
1
1
0
1
1
0
0
0
2
1
1
1
1
1
1
0
0
1
1
0
1
1
0
1
1
0
1
0
2
0
1
2
0
1
1
0
0
2
1
1
1
1
1
2
1
1
1
2
0
2
0
1
1
1
1
2
2
2
1
1
1
1
1
3
3
0
2
0
2
0
1
2
1
1
2
1
1
1
2
1
0
1
1
2
1
2
1
0
0
1
1
2
2
1
1
1
1
1
1
2
2
1
1
1
2
1
2
1
0
0
0
1
1
1
1
0
1
0
1
0
1
1
1
1
2
1
1
1
1
2
1
0
0
2
0
2
1
0
1
2
1
1
1
0
1
0
1
0
1
1
0
2
1
1
1
0
0
1
1
1
2
1
1
0
1
1
1
1
2
1
2
1
0
1
1
1
1
0
0
1
2
2
2
1
1
1
1
1
1
0
3
2
1
1
2
1
2
1
1
1
1
0
1
2
2
2
0
1
1
1
2
2
2
1
1
1
0
1
0
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
0
1
1
1
0
0
0
2
1
2
1
1
0
0
1
2
2
1
2
1
1
1
1
1
0
1
1
0
2
0
2
1
1
1
3
2
1
0
0
1
1
1
2
1
2
1
1
2
1
1
1
1
1
1
2
2
1
0
0
2
0
1
2
1
1
1
1
0
1
2
1
2
1
2
0
1
1
3
0
0
1
1
1
2
2
2
1
1
2
1
2
0
0
2
1
1
0
0
2
0
1
0
1
1
2
0
0
1
0
1
1
2
1
2
1
1
1
1
1
1
0
1
0
1
2
1
1
2
0
1
0
1
0
1
1
0
1
0
1
2
1
1
2
2
1
1
2
1
1
2
1
1
1
1
1
1
0
0
1
1
1
4
1
1
0
1
1
1
0
1
0
1
1
2
2
1
1
1
1
1
1
2
1
2
1
1
1
0
1
1
2
2
2
0
1
2
1
1
1
2
2
1
1
1
0
0
1
1
2
1
1
0
1
2
1
1
0
1
2
1
2
1
1
1
1
2
2
1
0
1
1
0
1
1
1
0
2
0
2
2
2
1
1
0
2
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
0
1
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
1
0
0
1
1
1
1
1
1
1
1
1
1
0
1
1
1
0
1
1
1
2
1
1
1
1
3
0
2
2
1
1
0
1
1
1
2
0
0
1
1
0
0
1
1
0
1
2
1
1
0
1
1
0
0
1
1
1
2
0
1
2
0
1
1
2
2
1
0
1
2
1
2
1
1
1
0
2
0
2
0
1
2
1
0
0
2
0
2
2
1
2
1
0
0
1
2
1
1
0
1
2
2
1
0
2
1
1
0
2
0
0
2
1
1
1
0
1
1
1
1
1
2
2
1
1
1
2
1
1
1
1
1
1
0
0
1
2
1
2
1
2
1
2
1
1
1
1
0
2
0
1
1
1
2
0
0
0
1
1
0
1
1
1
1
1
1
1
0
1
0
1
1
1
1
0
0
2
0
1
1
2
1
1
0
0
2
2
0
1
0
1
1
1
1
1
0
1
1
0
1
1
1
0
1
1
1
1
0
0
0
0
2
2
0
1
1
2
2
1
1
2
0
1
1
1
2
0
1
0
1
1
2
1
1
2
1
1
2
2
0
1
2
4
1
1
0
0
2
1
1
2
2
1
2
1
2
1
0
1
2
2
1
1
1
0
0
1
2
1
1
1
1
2
2
1
0
1
0
1
1
1
2
1
2
2
2
0
0
1
1
0
1
2
1
1
1
1
1
1
0
1
1
0
0
2
1
0
2
2
1
1
0
2
2
2
0
1
0
1
0
0
1
2
1
1
0
0
2
2
1
1
2
0
0
2
2
2
1
1
2
1
0
1
1
0
0
1
0
2
1
1
1
0
2
0
1
0
0
1
1
1
1
1
1
0
1
1
1
1
1
1
0
0
0
2
2
2
0
1
0
2
4
2
2
1
0
2
1
2
0
0
1
1
1
1
1
2
1
1
0
1
2
0
1
2
0
2
1
0
1
1
1
1
1
0
1
1
1
0
2
1
0
0
1
2
1
0
0
1
0
0
2
1
1
2
2
1
2
1
0
1
1
1
1
1
1
1
1
2
1
2
0
1
1
1
1
1
1
0
1
1
1
2
2
2
1
1
0
0
1
0
1
1
0
0
0
1
2
1
1
2
2
2
1
0
0
1
0
2
1
0
1
1
3
1
1
1
2
0
2
1
1
1
2
0
1
1
1
2
0
0
0
1
1
1
1
5
0
4
2
1
1
1
3
0
1
0
1
0
1
1
1
2
0
2
1
0
0
1
1
1
0
1
1
1
1
2
1
0
1
2
1
1
2
1
2
1
1
2
0
1
1
1
0
1
1
1
1
1
2
2
1
2
1
0
2
0
1
2
1
0
2
2
1
0
0
2
1
3
0
2
0
1
2
2
1
1
2
0
0
1
1
2
2
2
2
1
0
2
1
2
1
1
1
1
1
1
2
2
2
2
2
0
1
3
2
2
1
1
0
1
0
2
0
1
1
0
0
1
0
2
1
2
2
1
0
2
2
1
1
2
1
1
1
1
2
2
0
1
1
1
1
1
2
1
1
2
2
0
1
0
2
1
1
2
2
1
1
1
1
1
1
0
0
2
0
2
2
2
1
1
1
1
0
1
2
1
1
0
1
1
1
0
1
2
0
1
2
2
1
0
1
1
2
1
1
1
0
0
1
2
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
0
2
0
1
0
0
1
1
1
1
2
2
1
1
1
0
2
0
0
1
2
2
1
1
1
1
1
1
0
1
2
1
0
0
1
2
2
1
2
0
1
1
1
1
1
1
2
1
2
2
0
1
2
1
0
2
1
1
1
0
1
0
2
1
2
1
0
1
1
1
1
2
1
1
0
0
1
1
1
0
1
2
0
0
2
2
1
2
1
1
2
0
1
2
1
1
0
1
0
1
1
0
0
0
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
2
1
0
1
2
1
0
2
0
0
2
2
1
1
2
1
1
2
1
1
1
0
1
1
1
1
2
2
0
2
2
1
1
2
1
1
1
0
2
2
1
1
0
3
2
1
1
0
0
1
1
1
0
0
0
1
1
1
2
0
2
0
1
1
2
1
1
0
1
2
1
2
1
2
1
2
1
0
2
0
1
2
1
1
1
0
1
0
1
1
1
1
2
1
1
2
1
1
0
1
1
1
1
0
0
1
1
2
1
2
1
0
1
1
2
0
1
1
1
1
2
3
0
1
1
1
0
1
1
1
1
2
1
0
2
0
1
2
1
0
2
1
1
1
0
1
0
0
1
1
1
1
0
2
1
1
1
1
1
1
0
2
1
2
0
2
1
1
2
1
1
2
2
1
1
1
2
0
1
1
2
1
1
1
1
1
2
1
2
1
2
2
1
0
1
1
2
2
1
1
1
1
1
1
1
0
1
2
1
2
1
1
1
0
1
0
0
1
2
1
1
1
2
1
0
1
1
1
1
1
2
1
1
1
2
1
2
2
2
1
1
2
0
2
1
1
1
1
1
2
1
2
1
2
1
1
2
2
1
1
1
0
0
1
1
0
0
1
1
1
0
0
2
0
2
2
2
0
1
0
0
1
1
2
2
1
2
0
2
2
2
1
2
1
1
0
2
1
0
1
1
1
0
3
1
1
1
1
0
1
1
1
1
2
2
0
0
1
1
2
0
1
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
0
1
0
1
1
2
2
1
1
2
1
2
1
2
1
2
1
1
2
2
1
1
1
2
2
1
0
1
2
1
1
0
0
1
1
0
0
0
1
1
0
1
1
2
1
1
1
2
1
1
1
1
1
1
0
0
0
0
1
1
1
0
1
1
0
1
0
1
1
0
2
1
1
1
1
2
0
1
1
1
1
1
0
1
1
1
0
1
1
0
0
2
1
0
1
2
0
1
0
1
1
0
1
0
1
1
2
1
1
1
0
2
0
1
1
1
0
1
0
1
1
2
0
1
0
1
0
1
1
2
2
0
2
0
1
0
0
1
0
0
1
0
4
1
2
1
1
1
1
1
0
1
2
0
1
1
2
1
1
1
1
1
0
2
0
1
1
0
0
1
1
1
1
2
1
1
1
0
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
0
0
1
2
1
0
1
0
1
0
1
2
1
2
0
0
1
1
2
1
2
2
0
2
1
1
1
1
1
0
0
0
1
1
1
1
2
1
0
1
1
2
2
0
1
2
1
1
1
0
1
1
1
1
1
2
1
0
1
1
2
1
2
0
1
1
1
0
1
0
1
0
1
0
1
1
1
2
1
0
2
1
1
1
0
2
1
2
0
1
2
1
1
1
1
2
1
0
2
0
0
0
2
0
2
1
1
0
1
1
0
0
2
1
0
1
1
1
1
0
2
1
2
1
0
1
1
1
1
0
2
1
1
1
0
1
2
0
1
1
2
0
1
0
1
2
1
1
1
1
1
1
2
2
1
2
1
1
0
1
0
0
0
1
1
2
1
2
1
0
0
2
1
1
1
2
1
1
1
1
2
0
1
0
1
0
2
2
1
0
1
1
1
2
1
1
1
1
1
1
2
0
1
0
1
1
0
2
1
4
1
1
2
0
1
0
0
1
1
0
1
1
1
2
0
2
0
1
1
0
1
1
1
1
1
0
2
2
0
1
1
1
0
1
1
0
2
1
2
2
0
1
0
2
1
2
2
0
1
1
1
2
1
1
1
2
1
1
1
0
2
0
2
1
0
2
0
0
2
1
1
1
0
2
1
1
2
1
0
1
0
0
2
0
0
2
1
1
3
0
0
1
1
0
0
2
1
2
1
1
1
2
1
0
1
1
1
2
0
0
1
1
0
1
1
1
1
0
0
2
0
1
2
1
1
0
1
3
2
1
1
1
0
1
0
1
0
0
1
1
1
1
2
2
2
0
0
2
1
1
1
0
1
2
2
0
1
1
1
1
0
2
1
0
1
1
0
1
2
2
1
1
1
1
0
1
1
1
2
1
1
1
1
1
0
0
0
2
1
2
0
1
1
2
0
1
1
0
2
1
1
1
1
1
1
1
2
1
0
0
1
1
0
2
1
1
1
1
0
0
0
1
2
1
1
1
1
1
0
1
3
0
1
1
0
0
2
0
0
0
1
2
1
0
0
1
0
1
2
1
0
1
1
1
1
1
1
1
2
1
0
1
1
1
1
2
1
2
1
2
1
0
2
0
2
0
1
1
2
2
1
1
0
1
0
0
0
1
1
1
1
1
1
2
1
1
0
1
0
1
1
0
1
0
2
0
2
0
0
1
1
2
0
1
0
1
1
2
1
2
0
3
1
1
2
0
1
1
1
1
2
1
1
1
1
0
2
1
1
0
0
1
1
0
0
1
0
1
1
1
0
0
2
1
1
0
1
1
0
0
1
0
5
1
1
1
1
1
1
1
1
2
0
0
1
1
1
1
2
0
0
2
1
1
0
1
1
1
1
0
1
0
2
0
1
1
1
0
1
1
0
1
1
2
1
2
1
1
0
2
1
1
2
1
1
2
0
2
1
0
0
1
1
0
1
1
1
1
1
1
2
2
1
1
2
1
0
1
1
2
1
1
1
2
1
1
0
0
1
1
0
0
2
0
1
0
0
0
1
1
0
3
0
1
0
2
2
1
0
0
0
0
2
0
2
2
0
0
1
0
1
2
0
1
3
1
0
1
1
1
0
2
2
1
0
1
1
2
1
1
0
1
1
1
0
0
1
1
1
0
2
2
1
1
0
1
0
2
2
0
1
1
1
1
1
1
1
2
0
1
2
1
2
0
0
0
1
1
1
2
1
2
2
2
0
1
1
1
0
1
2
1
0
1
1
1
0
1
2
2
1
0
0
1
0
3
1
1
0
1
0
1
1
0
1
2
1
1
2
1
2
1
2
1
0
2
2
1
1
1
0
1
2
1
2
0
1
1
1
1
1
1
0
1
1
1
2
2
2
1
1
0
1
1
1
2
1
2
2
1
2
0
1
1
1
0
0
1
1
1
1
1
1
0
2
1
0
1
2
1
1
1
0
2
1
0
0
0
1
0
1
1
2
1
1
2
2
1
2
1
1
1
1
3
2
0
1
0
1
2
0
1
3
1
2
1
2
1
0
1
2
0
0
0
0
0
2
1
1
2
1
0
0
1
0
1
1
1
1
1
1
2
1
0
1
0
1
2
1
1
0
1
1
2
2
1
1
1
1
1
3
1
2
1
1
1
2
2
1
1
1
0
1
1
0
1
2
1
2
1
0
1
2
1
0
1
1
1
1
0
1
2
1
1
1
0
2
1
1
2
0
2
3
0
2
1
0
1
1
1
2
0
1
1
2
0
0
3
1
1
1
0
1
1
1
0
1
2
2
2
2
1
1
2
1
0
1
0
0
2
0
0
2
1
1
0
1
1
0
1
2
1
2
1
0
0
1
1
0
2
1
1
0
0
2
1
1
1
1
0
1
1
0
1
0
1
0
1
1
1
2
1
0
0
0
2
0
1
1
1
1
0
1
1
1
0
2
1
1
2
2
1
1
2
1
1
0
2
2
2
1
1
1
1
0
1
2
1
1
1
1
0
1
1
2
1
1
1
1
1
0
2
0
0
1
0
0
1
1
0
1
1
1
2
0
0
0
3
0
2
0
2
0
1
2
2
2
2
1
2
3
1
2
0
0
1
1
1
2
1
0
1
1
1
2
2
0
2
1
1
1
0
0
0
1
2
1
1
2
1
1
2
0
1
1
1
1
2
1
1
1
2
0
1
2
0
1
0
0
1
1
0
2
2
3
2
0
0
0
1
2
1
1
0
1
0
0
1
1
1
1
0
2
1
2
0
1
1
0
1
2
1
4
0
1
1
1
2
0
1
1
0
2
1
1
1
0
1
1
1
0
1
2
2
1
1
1
0
0
1
0
1
1
1
1
2
1
2
1
2
0
3
0
0
0
1
1
2
2
0
0
2
1
1
1
0
1
1
0
1
1
1
0
1
0
1
1
0
1
1
1
2
1
0
2
1
2
4
1
2
0
0
0
2
1
0
0
0
1
3
0
1
1
2
2
2
0
1
1
0
0
1
0
0
1
2
1
1
1
1
1
2
1
1
1
2
0
1
0
1
1
1
0
1
1
0
0
1
1
1
1
1
1
2
2
2
2
0
1
1
1
1
1
0
0
1
1
1
2
2
0
1
0
2
2
1
1
1
2
1
2
1
1
0
1
1
2
2
1
1
0
1
2
0
1
0
2
2
2
1
2
1
1
1
1
0
1
0
1
1
1
1
0
1
1
1
1
1
0
1
2
1
1
2
1
1
0
2
1
1
1
2
2
0
1
1
3
2
2
0
2
2
0
1
1
2
2
0
1
0
1
0
0
2
0
1
0
0
1
0
1
1
1
0
1
0
1
0
0
1
0
2
1
1
1
0
1
0
1
2
0
0
1
1
1
1
0
1
0
1
1
1
0
1
2
0
2
1
1
0
3
1
0
1
2
2
1
2
1
2
2
0
1
0
1
1
0
1
1
1
0
1
2
1
1
1
1
1
1
1
0
0
1
0
4
2
1
2
1
1
0
1
1
0
1
0
2
1
2
2
2
2
2
1
0
0
1
2
2
1
1
0
1
1
1
1
2
2
0
2
2
0
1
2
1
0
1
1
2
2
1
1
1
0
2
0
1
0
1
1
1
0
0
2
1
0
1
2
1
1
1
1
1
0
2
2
0
2
1
1
2
0
0
1
0
1
2
2
1
1
0
1
1
0
1
1
1
2
1
1
2
0
1
1
1
2
1
1
1
2
0
1
2
0
1
1
2
1
1
0
1
1
0
1
2
1
2
1
0
0
0
1
1
1
1
2
1
1
1
1
1
0
0
1
0
1
0
2
2
2
1
1
1
1
1
1
1
2
3
0
2
1
1
1
2
1
1
1
1
1
1
1
1
0
0
2
1
1
0
2
2
2
0
1
2
1
1
0
0
0
2
1
2
1
1
0
0
0
1
1
0
2
1
6
1
1
2
2
1
1
1
3
1
0
1
1
1
2
2
1
0
0
2
1
0
1
1
0
1
2
1
1
1
0
2
1
1
1
2
2
1
1
2
1
2
2
1
0
0
2
1
0
1
1
1
1
1
0
1
2
0
1
1
1
1
1
0
1
1
1
2
0
0
0
1
0
2
1
1
1
1
2
1
1
0
1
2
1
0
0
1
2
2
0
1
2
0
1
3
2
1
1
0
0
1
1
1
0
1
2
1
2
1
2
0
2
1
2
2
1
2
1
0
1
4
1
1
1
1
0
1
1
1
0
2
1
1
0
1
1
0
1
0
1
2
1
1
1
1
1
2
1
1
1
0
1
1
1
1
1
1
0
1
1
1
1
0
1
0
1
1
0
0
0
1
1
1
3
1
1
1
0
0
1
0
1
2
1
0
1
2
0
3
1
0
2
1
1
2
1
1
1
0
1
0
2
1
1
2
1
1
1
1
2
2
1
0
2
2
1
1
1
0
2
1
1
0
2
1
1
2
1
2
1
1
0
1
1
1
1
0
1
1
2
1
0
1
1
2
2
0
1
1
0
2
1
0
1
0
1
2
1
1
1
2
1
3
1
1
2
0
1
0
1
1
1
2
2
0
2
1
1
1
0
1
2
0
1
2
1
0
2
0
2
2
1
1
2
1
1
1
0
0
2
0
3
1
1
0
1
2
1
1
1
0
1
1
0
1
1
1
1
1
0
1
0
0
0
1
1
1
0
0
1
1
1
1
2
1
1
0
1
1
1
0
0
1
0
1
1
1
2
1
2
1
0
1
0
1
1
2
1
1
0
0
2
1
1
0
0
2
2
1
1
1
1
1
1
2
1
2
0
1
1
1
2
1
0
1
1
0
0
2
0
1
2
1
1
1
1
1
1
2
1
2
1
0
2
1
2
1
0
1
1
1
1
0
1
1
0
1
1
1
1
1
1
1
1
2
2
1
1
2
2
1
1
1
1
2
1
1
0
1
1
0
1
0
1
1
1
1
0
2
0
1
1
2
1
0
1
1
1
1
0
2
1
1
0
1
1
0
1
0
1
1
0
0
0
2
2
1
2
2
0
2
0
1
2
1
1
1
1
0
1
1
1
1
1
0
1
2
1
1
0
1
1
1
2
1
1
1
2
2
1
0
1
2
2
1
1
1
1
0
1
0
2
1
0
1
1
1
1
1
1
2
2
1
2
0
3
0
1
2
1
0
1
1
1
1
0
1
2
1
0
0
2
1
2
0
2
1
2
2
1
0
2
2
1
1
2
2
1
1
1
1
1
0
1
2
1
1
1
1
0
0
1
1
0
1
0
1
2
2
2
1
2
0
1
1
0
1
1
2
1
0
1
1
0
1
1
1
1
1
2
1
2
1
1
1
0
0
0
1
1
1
1
0
1
2
1
0
0
2
1
0
1
1
0
1
1
1
2
0
1
1
0
1
0
1
1
0
1
1
1
1
2
0
1
3
0
1
0
2
1
2
0
1
2
1
0
1
0
1
1
1
3
2
2
0
2
1
2
1
0
0
1
2
2
0
1
1
2
0
0
1
1
0
3
1
1
1
0
1
1
0
1
0
2
1
0
1
1
2
1
1
0
1
1
1
2
1
2
2
2
2
1
1
0
1
2
0
1
2
1
0
0
1
1
1
1
0
2
1
1
0
1
2
0
1
0
1
0
0
1
0
0
1
1
1
1
1
2
1
0
0
1
1
1
1
0
1
0
1
2
0
1
1
1
0
2
1
1
2
0
1
1
0
0
2
2
2
2
2
1
1
2
0
2
2
1
2
0
1
0
2
0
1
1
2
1
0
1
2
2
1
1
0
1
1
1
1
2
1
0
0
1
1
2
1
0
2
0
1
1
2
0
1
1
2
0
1
1
2
0
1
0
1
1
1
2
1
1
1
1
1
0
1
1
1
2
2
1
1
1
1
2
1
1
2
1
1
0
1
0
0
2
0
1
2
1
1
2
2
0
1
2
1
0
1
2
2
2
1
1
1
1
0
0
2
1
2
2
0
1
1
1
1
1
1
1
1
1
1
1
1
0
0
0
2
1
1
1
0
0
2
0
1
1
1
1
1
2
1
1
0
2
2
1
1
1
1
2
0
2
1
2
1
1
0
2
1
1
2
2
2
0
1
0
0
0
0
1
2
2
1
0
2
1
0
1
2
1
0
0
2
2
0
0
1
2
1
0
1
1
1
2
1
1
1
1
0
1
2
0
0
1
1
0
1
2
1
0
2
1
1
1
1
0
1
1
0
0
1
1
1
1
2
1
0
1
0
1
1
0
1
1
2
0
1
1
2
1
1
1
1
0
2
1
0
2
1
0
2
2
1
1
1
1
0
1
1
1
0
1
1
1
2
0
0
0
0
0
2
0
1
2
2
2
0
1
2
1
1
1
1
1
2
0
0
1
1
2
1
1
1
0
2
1
0
1
2
1
1
1
1
1
1
0
1
1
1
2
1
1
1
1
0
2
1
1
1
1
1
1
1
1
1
1
1
0
2
1
1
0
0
2
1
1
3
1
1
2
0
1
1
1
2
1
0
2
2
0
1
1
1
1
1
1
1
2
1
1
2
1
1
1
2
1
1
1
0
1
1
1
1
1
1
1
1
2
0
1
1
2
1
1
1
1
1
1
1
2
2
1
1
2
2
0
1
0
1
0
2
2
0
1
1
0
1
1
1
0
0
1
2
1
1
0
2
1
0
1
2
1
1
1
1
0
1
1
0
1
2
1
2
1
1
1
1
1
0
1
1
1
1
0
1
2
1
2
2
1
0
1
0
3
1
1
2
1
1
2
1
0
2
0
1
1
1
1
1
1
1
1
0
0
0
0
1
1
1
1
2
0
1
0
1
1
1
1
1
1
1
2
2
1
2
0
0
1
2
0
1
2
1
2
1
1
2
1
2
1
1
1
0
1
1
1
1
1
0
1
1
2
1
2
0
1
0
1
3
2
0
2
0
1
1
0
1
2
5
1
1
1
1
1
1
1
1
1
0
1
0
1
2
1
2
1
1
2
1
1
0
3
1
1
1
1
2
1
1
1
1
1
1
0
2
0
2
1
1
1
1
0
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
0
0
1
1
1
1
1
0
1
1
0
0
0
0
1
1
3
1
0
2
1
2
2
2
2
1
1
1
1
1
2
2
0
1
2
1
1
0
1
1
0
2
1
1
1
1
1
0
2
0
0
2
1
1
0
1
1
2
1
1
1
1
1
0
1
1
1
1
0
0
1
1
0
0
1
1
1
1
0
0
1
2
1
0
1
1
1
0
2
1
2
0
1
0
2
0
1
0
0
2
1
0
2
0
1
1
1
1
1
1
1
0
1
0
1
1
2
0
0
1
0
0
1
0
1
1
2
1
2
2
1
1
0
1
1
1
2
0
3
0
1
1
1
1
1
1
2
1
1
2
2
1
0
0
0
1
1
1
0
2
2
2
1
0
0
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
0
1
0
1
0
2
0
0
1
2
1
1
1
1
0
0
2
0
0
1
2
0
2
0
1
1
1
1
0
0
2
0
3
1
1
2
2
1
2
1
1
2
2
0
1
1
1
2
1
1
2
0
0
1
1
1
0
2
2
1
2
3
2
1
0
1
0
2
1
1
0
2
1
1
2
1
1
1
1
1
2
1
2
1
1
1
0
1
1
0
0
0
1
2
1
0
0
1
1
1
1
1
1
1
2
2
1
1
3
2
2
1
2
1
1
1
1
0
0
1
2
0
1
1
2
1
1
1
0
1
1
1
1
1
2
1
0
1
1
2
1
1
1
1
1
1
1
0
1
1
2
2
1
0
0
2
1
1
1
1
4
0
0
1
1
1
1
0
1
1
1
1
1
0
1
2
0
2
1
1
2
2
1
1
1
1
1
2
2
1
2
1
2
0
0
1
3
2
1
0
1
1
0
1
1
2
1
0
1
1
1
2
1
1
1
2
1
0
1
1
1
1
1
1
1
1
2
1
0
1
1
1
3
1
1
0
2
1
2
0
2
0
0
1
1
1
1
1
0
2
1
2
2
0
1
0
1
1
2
1
1
0
1
0
2
1
2
1
1
3
0
1
2
2
0
2
1
1
1
1
0
2
1
2
1
2
0
1
2
1
0
2
0
1
1
1
1
2
0
0
1
0
1
0
1
2
1
1
0
2
2
0
0
1
1
1
3
1
2
1
0
1
1
0
1
1
4
2
2
1
1
1
1
1
1
0
1
2
1
1
0
1
2
1
2
1
1
0
1
1
0
1
0
0
2
1
1
1
1
1
0
1
2
1
1
2
1
1
2
1
2
1
1
1
0
0
1
1
1
1
2
1
1
0
2
2
2
2
1
1
0
0
0
2
0
1
1
1
2
1
0
1
2
1
2
0
1
1
1
0
0
0
2
4
1
1
1
1
1
0
2
1
2
0
1
0
1
0
0
0
0
0
2
2
0
1
1
1
1
0
1
0
2
1
0
2
1
1
0
1
1
0
2
1
1
1
2
1
0
1
1
2
3
1
2
1
2
0
2
1
1
1
1
0
0
1
1
2
2
2
0
1
2
1
1
1
1
2
1
2
1
1
0
1
2
0
0
1
0
1
2
1
1
1
1
0
2
1
1
2
1
1
1
0
1
0
1
0
2
1
0
1
1
2
0
2
2
1
1
2
1
2
0
1
0
1
0
2
2
1
2
1
1
2
1
1
1
0
0
1
2
2
1
2
0
1
2
2
1
2
1
1
0
1
2
2
0
0
1
2
2
1
1
0
2
1
0
1
2
1
1
1
2
1
2
1
0
0
1
1
0
2
0
0
2
1
2
2
1
0
0
0
1
1
1
2
0
2
1
2
1
1
1
0
1
1
1
0
2
1
1
2
0
1
1
2
0
2
0
1
0
4
0
1
0
0
2
0
1
0
1
0
1
2
1
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
2
0
1
1
1
0
1
1
0
0
1
2
0
0
1
1
1
2
1
1
1
2
2
2
1
2
1
1
2
0
2
0
0
1
1
0
2
1
2
0
1
2
1
1
1
1
0
1
2
1
0
1
0
2
0
0
1
1
1
1
2
2
1
0
0
1
1
2
1
1
0
0
2
2
2
1
0
1
1
1
1
1
1
1
2
0
1
2
1
1
0
1
1
0
1
1
0
2
2
2
0
2
0
1
1
0
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
2
0
1
1
2
1
1
2
1
2
0
1
1
0
0
1
1
1
1
2
0
1
1
0
3
1
1
1
1
1
1
1
2
1
1
0
1
1
1
1
1
1
1
1
0
2
1
0
1
1
0
0
0
0
1
0
0
2
2
1
1
1
1
1
3
1
1
0
1
2
1
1
0
0
1
0
1
2
1
0
2
0
0
1
2
2
2
1
2
1
1
1
2
0
1
2
1
1
2
1
0
0
1
0
2
1
1
1
1
0
1
2
2
1
1
0
0
1
0
1
1
0
1
1
0
1
1
1
1
1
0
1
2
1
0
1
0
0
0
0
1
1
4
1
1
1
1
2
1
1
2
0
1
1
0
1
2
1
1
2
2
0
0
1
2
0
1
0
2
1
1
1
0
2
2
2
2
2
1
2
1
1
2
0
1
0
2
2
1
1
1
2
0
2
2
2
1
1
2
1
0
2
1
0
0
0
1
1
2
2
1
1
1
1
1
1
1
1
2
0
2
1
2
1
0
1
0
1
2
1
0
2
0
1
0
0
1
1
2
1
1
1
1
0
0
2
2
2
1
1
2
1
2
1
0
2
1
1
0
2
0
2
1
2
0
1
0
2
1
1
2
1
1
1
1
1
2
1
2
1
1
1
0
1
1
0
1
1
1
1
2
1
0
2
2
1
1
2
1
2
2
1
1
2
1
1
1
2
1
1
1
0
0
0
0
0
1
1
1
1
1
1
1
1
0
2
0
2
0
1
0
1
1
1
1
2
2
1
0
2
3
1
2
1
1
1
2
1
1
1
2
0
1
1
1
1
1
2
2
2
1
1
0
2
0
1
0
1
0
1
1
1
1
0
1
1
1
0
1
0
1
1
1
1
1
1
2
2
2
1
1
0
2
1
2
2
1
1
1
0
0
0
1
2
1
1
1
2
0
0
0
0
1
0
1
1
1
0
1
1
2
0
1
0
1
1
1
2
1
0
1
1
1
2
1
1
0
2
0
1
1
0
1
1
1
2
2
1
2
1
1
1
2
1
1
1
1
2
1
2
1
1
2
1
1
0
1
1
2
1
1
0
0
1
1
0
1
1
1
1
2
0
1
1
2
0
0
2
2
0
1
1
1
1
0
1
0
2
1
0
2
1
0
0
1
1
2
1
1
1
1
0
1
1
2
1
1
2
1
0
1
1
0
1
2
1
1
1
1
2
2
1
0
2
1
1
1
0
1
0
2
2
1
1
1
0
1
0
1
1
1
0
0
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
2
1
1
2
0
0
2
1
1
1
2
2
0
1
0
2
1
0
1
0
0
2
0
0
2
1
2
1
1
1
3
1
1
2
2
2
1
0
1
2
1
2
0
2
1
1
0
0
2
1
2
1
1
2
0
0
0
1
2
1
1
2
0
1
1
1
1
1
1
1
2
3
2
0
1
1
0
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
2
0
1
2
1
0
0
0
1
0
1
1
2
1
0
2
1
2
1
2
1
0
2
1
1
1
2
0
1
2
1
1
0
2
2
1
2
2
1
1
2
2
0
2
2
0
0
1
1
1
2
1
2
1
0
1
1
1
1
0
1
2
0
2
1
2
1
2
1
0
1
1
0
1
1
1
0
1
1
2
0
2
2
1
1
1
1
1
1
2
0
0
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
0
1
1
2
2
1
0
0
1
2
1
0
1
0
1
2
1
0
1
1
1
1
1
0
2
2
1
2
0
0
0
1
0
1
1
0
1
1
1
0
1
0
1
2
2
2
1
2
1
1
2
1
1
1
1
1
1
1
2
1
1
0
1
1
0
2
1
0
2
1
0
2
2
1
3
1
1
2
1
1
2
1
2
2
2
0
1
1
1
1
1
1
1
0
2
0
2
0
1
1
1
1
1
1
1
0
1
0
0
1
3
2
1
1
0
2
2
1
1
1
1
2
1
1
0
1
0
2
2
2
1
1
0
1
2
1
0
0
2
1
0
1
1
1
1
1
0
2
1
0
0
1
1
2
0
1
1
1
1
1
0
1
1
1
2
1
0
2
1
1
1
0
0
2
0
1
1
1
2
1
2
0
0
0
1
0
1
1
1
0
2
1
1
0
1
2
1
1
1
0
0
1
1
1
1
0
1
1
1
1
2
0
0
0
1
1
1
2
1
2
0
1
1
1
0
1
1
1
0
1
1
1
1
1
2
1
1
1
1
2
0
2
1
1
1
0
0
0
1
1
2
1
2
2
1
2
0
1
1
1
1
1
1
1
1
1
1
1
2
0
2
2
2
1
1
0
1
2
0
1
1
2
0
1
1
1
1
1
2
1
1
1
1
1
1
1
2
0
1
1
1
1
0
0
0
2
1
0
1
1
2
1
1
2
2
0
2
1
2
1
1
0
2
2
2
0
0
1
2
0
1
1
2
1
1
1
2
1
1
0
2
1
0
1
0
2
0
1
1
1
2
1
2
0
1
0
1
1
1
0
1
2
1
1
1
1
2
0
2
2
1
2
2
1
2
2
0
0
1
1
1
0
2
2
1
1
0
2
0
1
1
2
0
2
2
1
0
0
1
1
0
1
1
1
0
1
0
2
2
1
1
0
0
2
1
1
1
0
1
2
1
2
1
1
1
2
1
1
0
1
1
1
0
1
1
1
2
2
1
2
0
2
1
1
2
1
2
1
0
1
1
1
1
1
1
2
1
1
2
1
1
1
1
2
1
1
0
1
1
0
2
2
2
1
1
2
1
1
2
1
2
0
1
2
0
1
2
1
0
2
1
0
1
1
0
1
2
1
1
2
2
2
1
2
1
2
0
0
1
0
1
1
0
1
1
1
0
1
0
2
0
2
1
1
1
2
0
1
1
1
1
0
0
2
1
1
0
2
1
1
1
1
1
2
1
2
1
0
0
2
1
2
1
2
2
1
1
1
1
0
1
1
0
2
2
1
2
0
0
1
0
1
2
1
2
1
1
0
1
1
2
1
0
1
1
2
2
1
1
2
2
2
0
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
2
2
2
0
1
0
1
2
1
1
1
0
0
2
0
1
0
2
1
0
1
0
1
2
1
1
0
1
2
1
2
2
0
1
2
2
0
2
1
1
2
1
1
1
1
0
0
1
1
2
1
2
1
1
2
1
0
1
1
1
0
2
2
3
0
0
1
2
1
1
1
2
1
1
1
2
1
0
1
2
1
0
1
1
2
0
0
1
1
1
1
1
0
1
2
0
1
0
1
1
1
2
1
1
2
1
0
1
1
1
2
0
2
1
2
2
0
1
1
1
1
0
2
2
1
1
1
1
1
2
2
1
0
0
0
1
0
1
1
1
2
2
1
0
1
1
1
1
1
2
1
1
2
1
2
1
0
2
2
1
1
2
2
0
2
2
1
1
1
2
0
0
2
1
0
1
1
1
1
2
1
1
1
2
1
2
1
2
0
2
1
1
2
0
1
2
0
1
1
1
0
1
0
0
1
1
1
0
1
1
1
0
1
1
1
2
1
0
0
0
2
1
0
1
1
1
0
1
2
0
2
1
1
1
1
1
1
1
1
0
0
1
2
1
2
1
1
2
0
0
1
2
1
2
0
1
2
0
2
1
2
0
1
1
2
0
2
1
1
1
0
1
2
2
1
1
1
2
1
2
1
1
1
2
2
1
1
0
1
1
2
1
0
0
3
1
2
1
2
1
0
1
1
1
2
1
1
0
1
1
0
2
0
0
2
2
3
2
0
2
1
1
1
2
1
1
0
0
1
0
1
1
1
1
0
1
0
1
1
0
0
0
1
0
1
1
1
0
0
1
1
1
1
3
1
1
1
1
0
1
2
1
1
3
2
2
1
1
2
2
2
1
3
1
1
1
2
1
1
0
2
1
2
2
0
1
1
0
1
1
1
0
1
2
2
0
4
2
1
2
1
2
0
0
0
2
0
1
0
2
1
0
1
1
1
1
1
1
2
0
1
1
0
1
1
1
1
2
1
2
1
1
0
2
0
1
1
1
0
1
2
0
1
2
0
1
1
2
2
1
1
1
2
0
1
2
1
1
2
1
2
1
1
0
0
1
1
1
0
1
1
1
0
1
2
0
2
2
2
1
1
0
2
1
0
0
1
0
1
0
1
1
1
1
1
1
2
2
1
1
1
1
2
2
1
1
2
1
1
1
1
0
1
2
2
1
1
1
1
1
1
2
3
0
1
1
1
0
1
1
1
1
1
1
0
2
3
1
1
1
1
1
1
1
0
1
1
1
1
2
2
2
1
1
2
1
1
2
1
1
1
2
1
1
2
1
1
2
1
2
0
2
1
1
1
2
0
0
0
1
2
1
1
0
1
0
1
1
0
2
1
0
0
1
2
0
1
1
0
1
1
3
1
2
1
1
0
2
0
0
1
1
1
2
0
3
0
1
2
1
0
1
0
1
0
1
1
1
0
0
0
0
2
2
0
1
0
0
0
1
2
1
1
1
3
3
1
0
1
1
1
1
1
3
2
0
1
0
1
1
2
3
1
2
1
0
1
0
0
1
0
1
1
0
1
1
1
1
0
2
0
2
0
0
1
2
2
1
0
1
2
1
1
1
1
1
2
1
1
1
1
0
1
0
1
0
1
1
0
0
2
1
1
1
0
1
1
2
1
1
0
0
1
2
1
1
1
2
1
1
0
1
1
1
1
1
2
0
1
1
1
2
2
2
1
2
2
1
2
1
1
0
1
0
1
0
0
1
1
1
1
0
1
0
2
0
0
2
0
2
0
1
1
1
0
2
1
2
2
1
1
1
1
1
1
0
1
0
1
1
0
1
1
2
1
2
2
1
1
1
2
0
2
1
2
2
2
1
1
0
2
2
1
1
2
1
1
1
1
0
1
1
1
1
2
1
0
1
2
0
2
1
1
0
2
1
1
0
1
2
1
3
0
1
2
1
1
1
1
0
1
1
1
2
1
1
0
1
2
1
1
1
2
2
1
0
1
1
1
1
1
1
0
1
2
2
1
0
0
0
2
0
1
2
1
1
1
0
1
1
1
2
0
2
1
1
2
0
0
1
1
0
1
1
1
1
2
0
2
0
0
0
1
1
1
2
1
1
2
0
1
2
1
2
0
2
1
2
2
2
0
1
1
2
1
1
1
0
1
1
0
2
1
1
0
1
0
1
0
1
1
1
0
1
1
0
1
1
1
0
0
2
0
1
2
0
2
1
0
2
0
0
1
1
1
1
1
2
1
1
1
2
0
2
2
0
2
2
1
1
0
1
4
0
2
1
1
0
1
1
1
0
1
1
0
1
1
2
0
1
0
1
1
2
0
0
1
1
1
1
1
1
1
2
0
0
2
1
0
1
1
1
0
0
1
1
3
0
2
2
1
1
1
1
1
1
3
2
1
1
2
0
1
1
1
1
2
0
1
0
2
1
3
1
0
1
0
2
1
0
0
0
1
0
1
1
1
0
2
1
2
1
0
2
0
0
2
1
1
2
1
3
1
0
0
0
2
0
1
1
0
0
0
2
0
2
1
1
2
2
0
1
1
2
2
1
0
2
1
3
1
0
0
1
1
0
1
1
0
2
1
0
0
2
1
1
0
1
0
1
1
0
1
1
1
0
1
1
2
1
1
1
1
0
1
1
1
1
0
0
4
1
0
0
0
1
1
1
2
1
1
0
1
1
0
2
0
1
1
1
1
2
0
2
1
2
1
1
2
1
1
2
1
1
0
1
2
0
1
1
2
1
3
1
1
1
0
1
2
0
0
1
1
1
0
1
0
2
1
2
1
0
2
1
0
1
2
2
1
2
1
1
3
2
1
0
1
1
1
0
0
0
1
1
1
2
2
2
1
0
1
1
3
1
2
1
1
3
0
0
1
2
0
1
2
1
2
1
1
2
1
1
0
0
2
1
0
1
1
2
2
2
1
1
1
1
1
0
2
1
0
1
1
1
1
0
0
1
1
1
2
0
1
1
1
2
1
1
1
2
1
2
0
2
0
0
0
1
1
0
2
0
1
1
1
0
0
0
2
2
2
1
1
1
1
1
1
0
0
1
1
1
2
0
0
1
1
2
2
1
2
1
1
0
0
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
0
1
2
0
1
1
1
1
1
2
2
1
2
2
1
1
0
0
1
1
1
2
0
2
2
0
1
1
1
1
1
1
1
1
1
0
2
1
1
1
2
1
1
0
1
2
1
1
1
2
1
1
0
0
0
0
1
0
0
1
1
1
1
2
1
2
1
1
0
1
1
1
1
1
1
2
1
0
1
0
1
1
1
2
1
2
2
2
1
1
3
0
0
2
0
1
0
1
1
1
2
1
1
1
1
0
2
1
1
1
1
1
2
0
1
1
1
0
3
0
1
2
2
1
0
1
1
1
2
3
2
2
0
3
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
2
2
2
1
1
1
0
1
1
2
1
1
2
1
0
1
1
0
3
2
0
1
1
3
1
2
0
0
2
1
1
1
1
1
2
2
1
1
1
1
2
0
1
2
1
1
0
1
0
2
1
0
1
2
2
0
0
1
1
0
1
1
0
1
0
0
1
1
1
2
2
1
1
2
1
1
0
2
1
1
0
0
1
1
1
0
2
1
2
1
2
1
2
0
1
1
1
2
2
2
2
1
1
1
0
1
2
1
2
1
0
1
0
2
0
2
0
0
0
2
0
0
0
1
2
2
1
0
2
0
1
1
2
1
0
2
1
0
1
2
1
0
1
1
1
2
2
1
1
2
1
0
2
1
1
1
1
1
2
1
1
1
1
1
1
0
1
0
0
1
2
1
1
1
1
1
0
1
2
1
2
1
0
0
1
0
0
0
0
1
0
1
1
0
0
1
0
1
2
1
1
1
0
2
0
0
2
1
1
1
2
1
0
2
1
1
1
0
1
2
2
0
1
1
0
2
1
0
2
1
0
1
0
1
2
1
1
0
0
1
0
0
2
1
2
3
1
1
1
2
2
2
1
2
0
1
1
1
0
1
2
0
2
1
1
0
2
1
1
2
1
1
1
4
0
1
2
1
1
1
1
1
1
1
1
0
1
1
3
2
0
1
1
2
0
1
0
0
1
1
0
0
1
0
1
1
1
2
1
2
1
1
0
1
1
1
1
3
1
1
2
1
2
1
0
2
2
1
2
1
1
1
0
2
1
1
2
2
1
1
2
1
1
1
0
1
0
1
1
1
1
1
0
0
1
1
1
1
1
1
2
2
1
1
1
0
1
2
0
1
1
1
1
2
0
1
2
2
0
2
1
1
0
1
1
2
2
1
2
0
1
2
2
2
0
1
2
1
1
1
1
0
1
1
2
1
0
0
1
1
2
1
1
1
1
1
2
1
0
1
1
1
2
1
1
1
1
0
2
1
0
1
0
1
1
0
2
1
1
1
0
2
0
3
1
1
1
1
1
2
1
0
1
2
1
3
1
1
1
1
2
0
1
1
1
0
2
1
0
1
2
1
0
1
1
1
2
0
1
0
1
2
1
0
2
1
2
0
1
0
0
2
0
1
1
1
0
1
0
1
1
1
1
2
0
0
1
1
1
2
1
2
0
0
1
2
2
1
1
0
1
1
0
2
1
1
1
1
0
1
2
0
1
1
0
0
1
1
1
1
0
1
2
1
2
0
0
1
0
0
1
1
1
1
0
1
1
2
1
0
1
1
1
0
0
0
1
0
1
2
0
1
0
1
0
1
0
0
1
0
1
1
1
2
1
2
0
2
1
2
1
0
0
1
0
0
0
0
2
1
0
2
1
2
2
1
1
0
1
0
1
1
1
1
1
0
1
2
2
1
1
0
1
2
2
2
1
1
2
0
1
1
2
2
2
0
1
1
2
1
2
1
1
2
1
0
1
2
1
1
1
1
1
2
1
1
0
0
0
1
1
1
2
2
2
2
1
2
1
0
1
1
2
2
0
1
1
0
1
1
1
1
2
1
1
0
0
1
2
1
0
0
1
1
1
0
1
0
0
0
1
1
1
1
1
0
2
1
0
1
0
1
0
0
0
1
1
1
1
0
1
1
1
0
0
3
1
3
0
0
1
3
1
2
2
1
1
1
1
0
1
1
0
0
1
1
1
2
1
1
0
0
2
1
1
0
0
2
1
1
1
2
1
2
1
1
1
1
0
0
1
1
1
1
1
1
0
0
1
2
2
1
1
1
1
1
2
1
2
1
1
0
2
1
2
1
1
2
2
2
1
1
1
1
2
1
0
1
2
1
1
1
1
1
1
1
2
2
1
2
2
1
0
1
1
0
1
1
1
1
0
0
1
0
1
1
2
1
0
2
1
2
0
1
2
0
0
0
1
1
2
1
1
1
1
2
0
2
2
1
0
2
1
1
1
1
1
0
1
0
4
1
0
1
0
1
1
1
1
2
0
1
1
1
1
1
1
1
1
1
1
2
2
1
0
0
2
1
1
1
1
1
1
0
1
0
1
2
0
1
1
1
1
2
1
2
2
1
1
1
1
0
2
0
1
0
1
0
1
1
1
0
1
0
1
0
1
1
1
1
0
0
0
1
2
1
1
1
2
0
0
2
1
1
0
1
2
2
1
0
0
1
1
1
0
2
1
1
2
2
0
1
1
1
1
1
1
2
1
2
0
1
0
1
1
2
1
1
1
2
0
1
1
1
0
1
1
0
1
1
1
1
0
0
1
2
0
1
0
1
1
1
2
0
1
0
1
0
0
0
2
0
0
0
1
1
0
0
1
1
0
1
1
1
0
1
1
1
0
1
1
2
1
1
1
1
0
0
1
1
1
1
1
2
1
0
1
2
1
1
2
0
1
1
2
2
1
0
0
0
0
0
2
1
1
1
0
2
1
1
0
1
0
1
1
1
1
0
1
2
1
0
0
2
1
0
0
1
2
2
1
1
0
1
1
0
1
1
1
0
1
1
2
0
1
2
1
3
2
1
2
1
2
2
1
1
1
2
1
1
2
2
1
2
1
0
0
2
1
2
0
1
1
2
0
0
1
0
1
1
2
1
0
1
1
1
1
1
0
1
1
1
2
2
1
0
0
1
2
2
2
1
2
1
1
1
0
1
1
0
0
1
2
2
1
1
4
1
0
1
1
0
1
1
2
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
1
2
2
2
0
1
2
1
1
0
1
1
1
1
2
1
2
2
1
1
2
2
1
0
0
1
0
1
1
1
0
0
2
1
2
2
1
0
1
2
2
1
1
2
2
1
0
1
2
1
1
1
1
1
2
0
1
0
1
0
0
1
2
1
0
1
2
2
1
1
0
1
2
2
2
1
1
0
1
1
0
1
1
2
0
1
0
2
1
1
1
1
1
2
2
2
0
0
1
0
2
0
1
2
1
3
0
1
1
1
0
0
1
2
0
1
1
2
0
2
2
0
0
1
1
1
0
1
2
1
1
2
2
0
0
1
1
1
2
2
1
0
1
1
2
1
0
1
0
1
1
1
0
2
1
2
1
2
1
0
1
2
1
0
1
2
0
1
2
2
1
0
1
1
2
0
1
1
2
2
1
1
1
0
2
1
2
2
0
0
0
1
1
2
1
0
1
1
0
0
0
1
1
2
2
0
1
1
2
1
0
0
2
0
1
2
1
2
1
2
0
1
1
1
0
0
1
0
1
1
2
0
1
2
2
1
1
1
2
0
1
0
1
1
2
0
1
1
1
0
2
2
2
1
1
1
1
1
0
1
2
2
1
1
1
2
1
3
1
0
1
1
1
2
1
1
1
2
1
1
1
2
0
0
0
0
1
1
1
1
2
2
1
1
1
0
2
4
1
1
0
1
1
1
2
0
1
2
1
1
1
2
1
2
1
1
0
0
1
0
1
0
1
1
1
1
1
1
1
0
1
1
2
1
1
1
1
2
1
2
2
0
1
0
2
0
2
1
1
2
2
0
0
2
1
1
1
1
0
1
2
2
2
1
2
1
1
2
1
1
1
1
2
0
0
0
1
1
1
1
0
1
2
2
1
1
0
1
0
2
3
1
2
0
0
0
1
2
2
1
1
2
1
2
0
1
1
2
0
0
0
2
1
1
1
1
2
1
1
1
0
1
1
1
2
2
2
2
1
1
0
1
1
1
0
1
2
1
0
0
1
1
1
2
1
2
1
1
1
2
0
1
0
1
2
1
2
1
1
1
2
1
1
1
1
0
1
1
1
2
1
1
2
2
4
1
1
1
2
1
1
1
1
1
2
0
1
2
0
1
2
0
0
1
1
1
1
2
1
0
1
2
2
1
0
2
2
2
0
0
0
2
2
2
1
1
1
1
0
0
2
0
1
0
1
1
0
2
2
2
1
1
1
1
1
0
2
1
0
0
2
2
1
2
1
2
2
1
0
1
0
2
0
1
2
1
1
1
0
1
0
2
2
0
1
1
1
0
1
1
1
2
1
2
2
0
0
1
1
2
1
2
1
1
1
0
2
2
0
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
0
1
1
2
1
0
2
1
0
2
1
1
0
0
3
2
0
2
1
0
1
1
2
2
1
2
0
1
1
2
0
2
2
2
1
1
1
0
1
0
2
1
1
1
0
2
1
2
1
1
0
2
1
2
1
1
1
1
0
1
0
1
1
1
1
1
2
1
0
0
0
0
1
1
1
1
1
1
2
2
1
1
0
1
1
1
2
1
1
1
2
0
1
0
1
1
0
1
2
1
0
1
1
2
1
2
0
1
1
0
0
0
1
0
0
2
1
2
1
2
0
2
0
1
1
2
2
0
3
0
1
1
1
1
2
1
2
1
2
0
0
2
1
1
1
0
2
2
0
1
2
2
1
0
1
3
1
1
1
1
1
0
1
0
1
1
1
1
0
1
0
0
1
2
1
1
1
0
1
1
1
2
2
1
1
1
0
2
1
1
2
0
0
2
1
2
1
1
2
1
2
2
2
1
2
1
0
1
2
2
0
1
1
1
0
1
1
1
2
2
2
1
1
2
0
2
2
1
0
2
1
1
0
2
2
2
1
1
1
1
1
1
0
1
0
1
2
2
1
2
1
0
1
1
0
1
1
2
1
2
2
1
1
2
1
0
2
1
1
2
0
0
1
0
2
2
0
0
1
1
0
1
1
1
2
1
1
0
2
0
1
1
2
1
1
0
1
1
0
1
0
1
1
2
1
1
1
2
1
2
0
1
1
0
1
1
1
1
1
1
1
2
1
2
0
1
1
1
0
0
0
1
1
2
0
3
0
1
1
1
1
2
2
1
0
1
1
2
0
2
0
2
1
2
1
1
1
1
2
0
1
0
1
0
2
1
1
1
0
1
1
2
2
1
0
1
1
1
1
1
1
1
0
1
1
0
1
0
1
2
1
2
1
1
1
2
0
1
1
0
2
1
4
0
1
1
1
1
1
1
2
1
2
1
0
1
1
1
1
1
1
2
2
1
1
1
0
2
0
0
2
1
2
2
1
1
2
1
1
1
0
1
1
2
2
1
1
0
0
2
2
0
1
1
0
1
1
1
1
0
2
1
2
1
1
1
1
2
1
0
0
1
1
1
1
1
0
0
0
2
1
1
2
1
1
0
0
2
1
2
0
2
0
0
1
2
2
2
1
2
1
2
2
1
1
2
0
0
1
2
1
2
0
0
1
2
1
2
1
1
0
1
2
3
1
1
1
1
0
2
1
2
2
0
1
0
3
1
1
1
1
1
3
1
1
0
1
1
0
2
1
2
0
0
0
2
0
1
1
2
0
1
2
0
1
1
1
1
0
1
0
1
1
0
2
0
0
0
1
0
1
1
2
2
2
2
0
1
1
1
1
1
0
1
2
2
1
0
0
1
1
1
1
1
0
1
1
2
0
0
2
2
2
1
0
0
1
2
0
1
0
1
1
1
1
1
2
1
6
2
1
0
0
2
1
1
2
1
1
0
2
1
1
0
1
0
2
2
1
1
0
1
1
2
1
1
1
1
1
2
0
2
1
2
1
1
1
1
0
1
0
0
1
1
1
1
2
1
2
1
0
2
1
1
0
1
2
1
2
1
2
1
1
2
0
1
1
2
0
1
1
1
3
1
1
1
1
1
0
1
1
1
1
1
1
2
2
1
0
1
0
1
2
1
1
0
2
2
1
1
1
1
1
1
1
1
0
2
0
1
0
1
1
3
1
2
1
1
0
1
2
1
1
1
1
1
1
1
0
1
1
2
2
0
1
1
2
1
2
0
2
1
2
0
0
2
0
2
1
1
1
0
1
0
2
2
2
0
1
2
1
1
0
0
2
1
0
2
2
1
1
0
2
1
0
1
1
0
1
2
1
1
0
0
1
1
0
2
1
0
1
1
1
1
0
1
2
1
1
1
1
0
1
1
0
0
1
0
2
1
1
1
0
0
1
2
1
1
1
0
0
1
1
1
1
0
2
1
0
0
3
1
1
2
1
1
1
1
0
0
1
2
0
1
2
2
0
1
2
0
1
0
0
0
1
2
0
1
2
1
2
0
1
2
1
2
1
1
0
2
1
1
0
2
0
1
0
1
1
0
1
1
1
1
1
3
2
1
1
1
0
1
2
1
1
1
1
1
1
1
1
2
1
0
0
3
1
0
2
1
2
2
2
0
1
3
2
1
1
0
1
1
0
0
2
1
1
1
2
0
1
0
1
1
0
0
0
0
2
1
1
1
1
1
1
0
1
1
2
0
2
2
2
1
1
1
1
0
1
1
1
1
1
0
2
0
1
1
2
1
1
2
0
2
1
0
1
1
1
3
1
1
1
0
2
1
1
1
1
2
2
2
1
1
1
1
1
2
1
1
0
0
1
2
0
0
2
0
1
0
2
2
0
1
2
0
0
0
1
2
1
0
1
0
1
2
1
2
1
1
1
0
2
1
3
1
1
1
1
1
1
0
2
1
2
2
0
0
1
1
2
1
0
1
1
1
1
1
0
2
0
1
1
2
2
0
1
1
1
0
1
0
2
2
1
1
1
1
1
0
0
1
1
1
2
0
1
1
1
2
2
2
1
1
1
1
1
0
1
1
1
2
1
2
1
1
2
0
1
1
1
0
2
0
1
1
3
2
6
0
1
2
1
1
1
2
1
1
2
1
2
1
1
0
2
2
1
1
2
2
1
0
2
1
2
1
0
0
0
2
0
0
0
0
2
0
1
0
0
1
1
1
2
1
0
0
1
1
0
1
2
0
1
0
0
2
1
0
2
0
1
0
0
1
1
0
0
2
1
2
0
0
0
2
1
2
1
0
1
2
1
1
0
1
1
1
1
1
0
1
0
0
1
1
0
1
1
1
2
2
2
1
0
1
2
2
1
0
1
0
1
0
1
1
1
0
1
0
1
2
1
1
2
1
0
1
1
2
2
1
1
1
1
1
1
0
1
1
1
1
1
2
1
2
1
1
1
2
0
2
1
1
1
0
1
1
1
1
1
1
2
0
1
1
1
0
1
2
2
0
0
0
1
1
0
0
2
1
0
1
1
1
1
1
1
0
0
1
1
0
1
1
2
0
1
1
1
2
0
1
3
1
1
1
2
1
1
1
1
1
1
1
0
2
1
1
1
0
1
2
0
0
0
1
1
2
0
1
1
2
2
2
2
1
2
1
1
1
0
0
0
1
1
1
1
1
0
1
3
0
2
2
0
1
2
1
1
1
0
1
0
0
2
1
1
2
0
3
1
0
1
2
0
2
1
1
1
2
1
1
2
0
1
0
1
0
1
0
0
2
0
0
0
0
1
0
2
1
0
2
2
1
2
2
1
2
1
1
1
1
1
2
0
2
1
2
1
1
2
2
0
1
2
0
0
1
0
1
1
1
0
0
2
1
0
1
2
1
1
2
2
1
0
2
0
1
1
1
0
0
1
1
0
1
1
1
0
1
0
1
1
1
2
0
2
2
1
2
1
2
2
1
1
1
0
0
1
1
5
0
1
0
2
0
1
0
1
1
1
1
2
1
0
1
0
1
2
1
0
1
1
1
1
0
2
1
1
1
1
0
1
1
1
2
1
2
0
1
2
0
0
1
1
0
1
1
1
1
2
1
2
1
1
0
1
1
1
1
1
0
0
1
2
0
2
0
0
1
1
1
2
2
0
1
1
1
2
1
1
1
1
0
1
1
1
2
1
1
1
2
0
2
1
1
1
2
0
1
2
2
1
0
2
1
1
3
2
1
1
1
1
1
2
0
1
1
1
2
1
2
1
1
0
1
1
1
1
0
1
1
1
0
0
1
0
2
2
1
0
1
1
1
1
2
2
1
1
0
1
1
1
0
0
0
1
1
0
2
2
0
1
0
2
1
0
2
1
1
1
0
1
0
1
2
1
1
2
1
1
0
1
1
0
1
1
1
2
1
1
1
1
0
1
1
0
0
0
0
1
1
2
1
0
1
2
2
0
2
0
0
1
2
1
0
1
0
1
2
1
1
1
0
2
2
1
0
1
1
0
1
2
0
1
1
1
1
0
2
2
1
1
1
2
0
1
1
2
1
1
0
1
1
1
1
2
1
1
1
1
1
1
2
1
0
0
0
0
2
0
1
1
1
2
1
0
1
1
0
0
1
1
2
3
0
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
0
2
1
1
2
2
0
2
1
1
2
2
0
1
1
2
2
1
2
4
1
1
2
1
1
0
2
2
1
1
2
1
1
1
0
1
1
1
1
1
2
1
0
1
1
1
2
0
1
1
2
0
1
1
1
2
2
1
1
1
1
1
0
1
0
1
1
1
1
1
1
0
0
1
1
1
1
1
0
1
2
1
0
1
1
1
1
2
0
0
1
1
1
1
0
1
1
2
2
2
1
1
1
1
1
0
1
0
1
1
2
1
1
1
1
2
1
0
1
1
0
2
1
2
0
0
1
2
0
1
1
2
1
0
0
2
0
1
1
1
1
1
2
0
1
1
2
0
1
1
2
0
0
1
1
1
0
0
1
1
1
1
1
0
1
0
1
1
1
1
1
2
0
1
1
3
1
2
1
1
1
9
1
2
0
1
1
1
1
2
2
1
1
0
0
1
1
1
1
1
1
1
1
1
0
1
0
1
1
1
1
2
1
2
1
1
1
0
0
1
0
1
0
1
1
1
1
1
1
1
2
1
0
1
1
1
0
2
1
0
0
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
0
0
0
1
7
2
2
1
0
2
1
2
2
0
1
1
0
0
1
2
0
1
1
1
1
1
0
0
1
2
1
1
1
2
0
0
2
0
1
1
1
1
1
2
1
2
1
1
2
1
2
1
2
2
1
2
2
1
1
1
0
1
1
0
3
1
2
1
1
1
1
1
0
1
2
1
1
1
1
0
0
1
0
1
0
2
0
2
1
0
1
1
1
1
0
2
0
0
2
0
1
1
1
1
1
1
2
0
1
1
1
0
2
0
1
1
1
0
2
2
1
1
0
0
0
1
2
1
1
0
1
1
1
1
1
1
1
1
2
1
2
1
0
1
2
0
1
1
0
2
1
1
1
1
1
1
1
1
2
1
1
1
1
0
2
3
0
0
1
1
2
1
1
0
1
1
1
1
1
1
0
2
2
1
0
0
1
1
1
1
2
1
2
0
1
1
2
1
1
1
0
1
1
1
1
2
1
1
1
1
0
1
2
1
0
0
1
1
1
1
3
1
2
0
0
2
1
1
1
0
1
0
1
1
0
0
0
2
2
0
1
1
2
1
2
1
1
0
1
0
1
1
1
1
1
1
1
0
1
0
1
1
3
1
1
1
1
2
1
2
1
2
2
1
1
1
2
1
2
0
1
2
0
1
1
1
1
1
1
1
1
1
1
0
1
1
1
2
1
0
1
1
1
1
1
0
1
0
2
1
0
2
2
1
1
1
0
2
2
1
2
1
1
1
2
1
1
2
1
1
0
0
0
1
1
1
1
2
0
0
2
1
1
2
1
1
2
2
2
1
1
2
1
0
1
0
1
1
1
1
1
1
1
0
1
0
0
1
0
1
1
1
2
0
0
2
1
0
1
0
2
0
0
0
1
0
1
1
0
0
1
1
0
1
1
2
1
1
1
0
2
2
2
0
1
2
1
1
1
1
2
2
1
1
0
1
1
2
1
1
2
1
0
1
1
1
2
1
2
1
2
1
2
1
1
2
1
0
1
0
1
1
1
1
2
0
2
1
1
1
1
0
1
1
0
2
0
1
1
0
1
1
2
1
1
1
0
3
1
0
1
1
1
2
0
2
3
0
1
1
1
1
0
1
1
0
1
1
0
0
1
0
1
0
1
0
1
1
0
0
0
1
1
1
2
1
1
1
2
2
1
1
2
1
1
2
2
1
0
2
2
2
0
0
2
1
1
1
1
1
2
1
0
2
2
1
1
1
1
1
2
1
1
2
1
2
0
1
2
1
1
1
0
1
1
1
1
2
1
1
2
1
0
1
0
1
0
1
2
1
2
1
2
0
0
2
0
1
2
1
1
2
0
1
1
1
2
1
1
2
1
2
1
1
2
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
2
0
1
1
1
0
1
1
1
1
1
1
0
2
1
1
1
0
1
1
1
1
1
0
1
1
0
1
1
1
2
2
1
1
1
1
2
2
1
2
0
2
1
0
2
1
1
2
1
0
1
2
2
1
2
1
3
1
1
1
1
0
1
1
1
1
1
1
1
1
2
2
0
1
2
2
2
0
1
1
0
1
1
1
0
0
1
1
1
0
1
2
1
0
1
1
1
2
4
1
1
1
1
1
1
2
1
2
0
1
1
2
0
1
1
0
1
1
1
1
2
1
1
2
1
1
0
2
1
0
1
0
2
1
2
2
1
0
1
1
1
0
0
1
1
1
1
1
2
0
1
2
1
1
1
1
0
2
0
0
2
0
0
1
1
2
0
1
1
1
0
0
1
0
0
1
1
2
0
1
1
2
1
1
0
2
1
2
1
3
2
1
2
1
1
1
1
1
1
1
2
2
2
2
1
2
0
1
2
2
1
1
0
2
2
1
1
1
2
1
1
1
2
1
1
0
0
1
1
1
1
1
1
1
1
1
2
1
1
0
0
1
1
2
0
2
2
3
1
1
1
0
1
2
1
0
0
1
1
0
2
1
1
0
0
2
2
2
1
0
2
0
0
1
1
2
0
1
0
0
1
2
1
2
2
2
2
2
0
1
0
0
0
1
0
0
2
1
1
2
1
1
0
2
2
0
0
0
0
1
0
2
2
1
1
0
0
2
1
1
1
1
0
0
0
3
2
1
2
2
1
2
1
1
2
1
0
0
2
1
1
2
2
2
1
2
1
2
0
1
1
1
2
2
0
1
1
0
1
1
2
1
0
1
3
1
0
1
1
1
1
1
1
2
1
1
0
2
0
2
0
0
1
1
1
0
2
1
1
1
0
1
1
2
2
2
2
1
0
0
1
2
0
2
0
1
1
0
0
1
1
1
1
1
0
1
1
0
1
1
1
1
1
2
1
1
0
1
1
1
1
1
1
2
1
1
2
1
2
1
1
1
2
1
1
0
1
1
2
2
2
1
1
1
2
3
1
0
2
1
2
2
0
1
2
1
0
1
1
0
1
1
2
1
1
2
2
1
1
1
1
1
0
1
1
1
1
1
1
1
2
2
1
2
1
0
2
1
1
2
0
0
2
2
2
1
2
2
1
2
0
2
2
1
1
0
1
1
1
1
0
1
1
2
1
1
1
2
1
2
1
1
2
0
0
1
2
1
1
0
1
0
2
1
1
1
2
1
0
2
2
1
0
2
0
0
1
1
1
0
2
1
2
1
1
1
1
1
1
1
2
1
3
0
2
1
1
1
1
1
1
2
0
1
1
2
1
1
2
1
2
1
1
2
0
2
1
1
2
1
0
0
1
1
1
1
1
2
2
1
2
1
1
1
2
1
0
1
1
0
0
1
1
0
2
2
0
1
2
1
2
2
0
1
1
1
0
0
1
1
1
2
2
1
1
1
1
1
0
1
1
2
2
1
1
1
1
2
0
1
1
1
1
1
0
1
0
2
1
1
0
0
0
1
2
0
0
1
1
0
1
2
1
1
1
0
1
1
2
1
1
1
0
1
0
1
2
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
2
2
0
2
1
0
1
2
1
0
1
2
1
1
0
1
1
1
1
1
1
1
1
1
0
1
1
0
1
2
1
0
2
2
1
0
0
0
2
2
1
1
0
1
0
1
0
1
1
1
2
1
1
2
1
0
1
2
2
1
1
2
2
1
2
1
1
2
0
2
0
2
2
0
2
0
1
1
1
1
0
2
0
1
1
0
0
0
1
1
2
1
1
0
1
1
1
2
2
2
1
1
2
1
1
1
2
1
2
1
1
2
1
2
0
1
1
1
2
1
2
1
1
2
2
1
1
0
0
1
1
2
2
2
0
1
4
1
1
2
1
1
2
2
1
1
0
0
2
2
1
0
1
2
1
1
1
0
0
0
2
1
1
1
0
0
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
0
2
1
1
1
2
0
1
0
1
0
1
2
1
1
1
1
2
2
0
0
1
0
1
2
0
1
0
0
1
0
0
0
0
1
1
0
0
2
0
1
0
2
1
0
0
2
1
1
0
1
0
1
0
1
1
1
2
2
1
1
2
0
1
1
1
2
0
2
3
0
1
2
1
2
0
2
1
1
1
1
2
0
0
1
1
1
2
2
1
1
1
1
1
1
1
1
0
1
1
2
2
1
2
1
1
0
1
1
0
0
1
2
2
3
2
1
1
1
1
1
1
2
2
2
1
0
0
2
0
0
2
1
0
1
0
1
0
0
2
1
1
1
2
0
2
0
2
1
1
2
1
1
1
1
1
2
2
0
2
1
0
0
1
1
1
1
2
1
1
0
0
1
1
2
1
0
0
1
1
2
1
2
0
1
0
1
2
1
0
0
0
1
1
1
1
2
1
2
2
1
1
1
2
1
1
0
2
1
1
0
1
1
2
0
2
2
1
1
1
1
0
2
2
1
0
1
0
2
1
0
1
1
0
0
1
0
1
0
1
0
1
1
1
1
1
0
2
2
1
1
1
2
1
2
2
1
1
2
2
1
1
0
2
1
1
1
1
2
1
1
1
2
1
1
2
1
1
2
2
1
1
1
2
0
0
1
2
0
1
0
0
2
2
2
2
0
1
0
1
0
0
1
2
1
1
1
2
2
2
0
2
1
1
1
1
1
1
1
0
0
0
1
1
0
0
1
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
2
1
0
0
1
0
1
1
1
2
1
2
2
1
2
1
2
1
1
2
1
2
1
1
2
1
1
1
0
1
1
0
0
2
1
1
1
2
1
2
1
2
1
1
2
0
1
1
1
1
1
1
1
1
0
2
2
0
1
0
1
2
0
1
1
1
1
1
2
2
1
0
2
1
2
2
1
1
2
0
1
2
1
1
0
0
1
1
2
2
1
2
1
1
1
2
1
1
1
1
2
2
1
1
1
1
1
2
1
0
0
1
2
1
1
1
1
1
2
2
1
1
2
0
1
2
0
1
1
2
1
1
1
1
1
1
0
0
1
1
2
0
0
1
1
1
1
1
2
1
0
1
2
0
2
1
1
2
0
1
2
1
1
1
0
1
2
1
1
0
0
1
1
1
2
1
1
1
1
1
1
1
2
2
2
1
2
1
0
0
2
0
2
1
2
1
0
1
1
2
1
1
1
0
1
1
1
1
1
0
1
1
0
1
2
1
1
2
1
2
2
2
0
2
1
0
2
2
0
1
0
1
1
1
1
0
1
1
1
1
1
1
1
2
1
2
1
2
1
5
2
0
1
0
2
2
1
1
2
1
0
2
2
0
1
1
1
0
1
1
1
1
0
0
0
1
1
1
1
2
0
1
2
1
0
0
2
1
1
0
1
2
1
1
1
1
1
1
0
0
0
2
0
1
2
2
1
1
1
1
2
0
2
0
0
0
0
2
1
0
0
0
0
2
2
0
1
1
1
0
0
0
0
1
0
0
2
2
2
1
2
1
0
2
3
2
2
2
1
0
1
1
1
2
1
1
2
1
0
1
1
1
2
2
0
0
0
0
1
0
0
1
1
2
1
1
1
1
0
0
2
1
1
1
1
1
0
0
1
2
0
2
0
2
2
1
2
0
2
0
1
1
0
1
1
1
0
2
2
1
1
1
1
0
1
0
1
0
2
1
2
1
1
0
0
1
0
0
0
0
0
1
1
1
0
1
1
1
1
1
1
1
2
1
1
1
0
1
1
1
3
1
1
1
2
0
1
1
1
0
2
1
2
0
2
0
1
0
1
1
5
2
1
1
2
1
3
1
1
2
2
2
0
2
1
1
1
0
1
0
1
2
1
2
1
2
1
1
1
1
1
1
1
2
2
1
1
1
2
2
0
2
2
1
1
1
0
1
1
1
2
0
1
1
0
2
2
1
2
1
1
2
1
2
2
2
1
1
1
1
1
1
0
0
1
1
2
2
2
0
1
1
1
0
1
1
1
0
1
1
1
2
2
1
0
1
1
0
1
1
0
0
1
3
1
2
2
1
1
2
0
1
1
1
1
2
1
1
2
1
2
2
1
2
2
1
1
0
2
0
1
1
2
1
1
0
1
1
1
1
1
2
1
0
1
1
1
2
1
1
0
0
1
1
1
0
1
1
0
1
1
0
2
0
3
0
0
2
1
1
1
0
1
0
1
2
1
1
0
1
0
0
1
1
1
1
2
2
2
1
1
2
1
1
1
1
1
1
1
0
2
1
2
2
0
1
1
2
1
1
2
0
0
1
1
2
1
1
1
1
1
0
0
1
1
1
1
0
1
0
0
1
1
0
1
2
0
1
1
1
1
1
1
1
1
0
0
1
1
0
1
2
1
1
0
2
1
0
1
0
1
2
0
0
1
1
0
2
0
1
2
2
1
2
1
1
1
1
1
0
0
1
0
1
1
1
0
1
1
1
1
1
1
1
1
1
2
0
0
0
2
1
1
1
1
2
0
0
0
2
2
1
2
2
2
2
2
1
1
2
1
2
1
0
2
0
1
2
2
1
1
1
1
1
1
0
2
0
1
1
1
0
2
2
1
0
1
2
1
1
1
1
0
1
1
2
0
1
1
1
2
0
2
0
0
1
0
0
1
2
0
2
1
0
0
1
0
0
2
1
2
1
1
2
2
1
2
2
1
0
1
2
1
1
1
1
2
2
1
1
1
0
0
1
0
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
0
0
1
2
3
1
2
1
2
1
1
1
0
2
1
0
1
0
1
2
1
2
1
0
2
0
1
1
0
1
1
2
1
1
1
1
2
1
2
1
0
0
1
1
0
1
1
2
1
1
0
1
0
1
1
1
2
1
2
1
1
1
2
1
1
2
2
1
1
1
1
1
1
2
1
1
0
2
0
1
1
1
1
1
1
1
2
1
1
1
2
0
1
1
1
1
1
1
1
1
1
0
0
0
0
1
1
2
1
2
2
1
0
1
2
1
1
1
1
2
2
1
0
1
1
1
2
1
1
1
0
0
2
0
2
2
1
0
1
0
1
1
1
2
0
0
1
1
1
1
0
1
0
0
1
1
1
2
0
1
1
1
1
1
0
1
0
1
0
1
1
2
0
0
2
1
0
1
2
0
1
1
1
1
0
2
0
1
1
1
2
1
0
1
1
1
1
1
2
0
1
0
1
0
1
1
1
1
1
1
0
1
2
1
1
1
1
1
2
2
0
2
1
1
1
1
1
1
2
0
0
1
2
0
1
2
0
1
1
1
1
2
1
0
2
0
1
1
2
0
1
1
2
0
1
1
0
0
1
2
0
1
1
1
2
2
2
0
1
1
2
1
0
2
0
0
1
1
0
2
0
2
1
1
2
2
1
1
0
2
1
1
2
1
1
1
0
0
0
1
1
1
1
1
2
1
1
1
0
3
1
1
0
0
0
0
1
1
2
1
0
1
1
1
0
6
1
1
1
0
0
2
1
0
2
1
1
1
1
1
0
1
1
2
1
1
0
0
1
1
2
2
1
0
0
0
0
1
0
1
1
1
0
2
0
2
1
0
2
1
1
1
0
2
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
0
1
2
1
1
0
0
1
0
1
0
0
0
1
0
1
1
1
1
2
1
1
1
2
1
0
2
1
1
1
0
2
2
0
1
1
1
2
1
1
2
0
1
0
1
1
1
2
1
2
0
3
1
1
0
0
0
2
1
2
2
1
2
1
2
1
1
1
1
1
2
1
1
2
0
0
1
1
1
0
1
0
1
1
2
2
0
2
2
0
0
2
4
1
2
2
2
1
0
1
2
1
0
2
1
0
1
1
0
1
1
1
1
1
1
1
1
1
1
0
1
1
0
2
1
0
2
1
1
1
1
1
0
0
1
0
0
1
1
1
2
1
0
1
1
2
1
0
1
2
1
1
2
0
2
1
1
1
1
0
1
4
1
2
1
1
1
1
1
2
1
0
1
2
1
0
0
1
1
1
0
0
2
0
1
1
1
1
2
1
1
1
1
2
2
0
1
2
2
2
1
1
2
0
1
1
2
0
2
1
2
9
2
0
1
1
1
0
1
1
1
1
1
0
1
0
2
1
0
2
3
1
2
1
0
1
1
1
2
2
0
1
0
0
1
1
1
1
1
1
1
1
0
0
0
1
1
2
1
0
0
0
2
1
1
2
1
0
0
1
2
1
1
2
2
0
1
1
0
1
0
1
1
1
0
2
1
1
1
1
1
0
0
1
1
1
1
1
0
0
1
2
0
1
1
2
1
0
1
1
1
1
0
1
1
1
1
1
1
0
1
1
1
1
0
1
1
2
2
0
1
1
2
1
1
1
1
1
1
0
2
0
1
1
1
1
1
1
2
2
1
1
1
1
0
1
2
1
0
1
1
2
0
0
1
2
1
1
1
0
2
1
1
1
0
0
1
0
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
0
1
1
0
2
0
1
1
2
1
1
1
0
1
1
1
1
1
2
0
1
1
0
1
1
2
1
1
0
1
1
1
1
0
1
1
0
2
1
0
2
0
2
1
1
2
1
1
1
1
2
2
1
1
0
2
1
1
2
1
2
0
0
1
1
0
2
1
1
1
1
1
2
0
0
1
2
1
2
1
3
1
1
1
0
2
0
2
1
1
2
2
0
0
1
1
2
2
0
1
2
1
1
0
1
1
0
1
0
1
0
2
1
1
0
1
1
2
1
1
1
2
1
0
1
0
1
1
1
0
0
2
1
2
1
2
0
0
0
1
2
1
2
1
1
0
2
2
2
1
0
1
2
1
2
1
0
1
1
3
0
1
2
0
1
1
2
2
0
0
1
0
1
1
1
0
1
2
1
0
1
1
1
1
2
0
0
2
0
2
1
0
2
1
2
0
1
1
2
1
1
2
2
1
1
2
0
1
2
1
1
2
2
1
1
0
1
1
0
1
1
1
1
2
0
1
0
2
1
2
1
1
0
0
1
1
1
1
1
1
2
1
1
1
2
0
1
1
1
0
1
2
1
1
1
1
2
1
0
0
1
1
1
0
2
0
1
2
1
2
1
1
1
0
1
0
0
2
2
1
1
1
2
0
2
0
1
1
0
0
1
1
2
1
2
2
1
1
2
2
1
1
2
1
0
0
1
1
0
2
0
2
0
0
4
1
0
1
1
1
2
0
3
1
0
2
1
3
1
2
1
0
1
2
1
0
1
1
1
2
1
2
1
1
2
0
1
1
0
1
2
0
2
2
1
0
0
1
1
1
2
2
1
1
0
1
0
2
1
0
1
1
1
1
1
0
0
1
1
1
2
1
1
0
2
0
3
1
1
1
1
0
1
0
1
0
1
1
2
0
1
1
0
1
1
1
1
2
1
1
1
1
2
1
0
1
2
1
3
0
2
1
1
1
2
0
0
1
0
1
0
1
2
1
0
0
1
2
1
1
2
1
1
1
1
0
2
1
1
2
1
0
0
1
2
1
1
1
2
0
2
1
2
2
2
0
1
1
1
2
1
1
0
3
1
2
0
2
2
1
1
2
0
0
0
1
1
0
1
2
2
1
1
1
1
2
2
1
0
1
1
1
1
1
1
1
0
1
1
2
1
1
1
1
1
2
2
0
1
1
2
1
0
0
0
0
1
1
1
0
0
2
1
2
0
1
1
1
2
0
1
1
2
1
2
1
0
5
2
1
0
2
1
1
1
0
1
1
2
1
1
1
2
0
1
2
1
1
0
1
0
1
2
1
2
1
0
1
1
0
0
2
1
1
0
1
1
1
1
1
0
1
1
1
1
2
1
2
1
0
1
2
1
1
1
1
1
1
0
1
1
1
1
0
2
1
2
1
0
1
1
1
1
1
1
2
1
2
1
1
0
0
2
2
0
0
1
1
2
0
0
1
1
0
2
1
0
1
1
1
1
2
1
1
0
1
1
2
1
0
1
0
0
0
0
0
2
1
1
1
2
2
1
1
1
1
2
1
2
1
1
0
1
1
1
0
1
1
2
1
1
0
1
1
1
2
1
2
2
1
1
0
1
1
2
1
1
1
1
2
2
1
1
1
2
0
2
1
2
1
2
0
1
1
2
1
1
1
2
1
1
1
2
0
1
1
0
2
2
0
1
2
1
1
2
1
1
1
1
1
1
1
0
2
1
0
1
1
1
2
0
1
0
1
1
1
0
1
1
1
0
0
2
1
2
0
0
2
2
0
1
1
0
1
1
0
1
1
0
1
1
2
2
0
1
2
2
2
2
2
1
0
0
2
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
0
1
1
3
0
1
1
1
1
0
0
1
0
1
1
2
2
1
0
2
2
1
1
0
1
1
1
1
1
1
1
0
1
0
1
0
1
0
0
0
1
1
1
2
0
1
1
2
1
1
0
0
1
1
1
1
1
2
2
1
2
1
1
1
1
1
2
1
2
2
0
2
2
2
2
2
1
1
0
1
1
1
0
2
1
0
0
0
0
1
1
1
1
1
1
0
2
1
2
2
1
1
1
0
1
0
1
1
1
2
2
1
2
2
1
1
1
2
1
0
0
1
1
1
2
1
2
1
0
1
1
2
1
1
1
1
0
0
1
0
2
0
1
0
2
2
0
0
2
2
2
2
1
1
1
0
0
2
1
3
2
1
0
0
2
2
2
0
1
1
1
1
0
1
1
2
2
1
1
2
0
2
1
1
1
1
1
1
2
1
1
1
2
1
1
0
0
2
1
1
2
1
0
1
1
1
0
1
1
1
0
1
2
1
1
1
1
1
1
2
2
1
0
0
0
0
2
0
1
2
1
0
1
0
1
1
1
1
3
1
1
2
2
1
0
0
1
1
1
1
1
1
0
2
1
2
1
1
1
1
1
1
0
2
1
1
2
2
1
1
1
2
1
0
2
0
1
2
2
1
1
1
2
1
1
0
0
2
1
1
1
1
2
1
0
1
0
1
0
1
0
0
1
1
1
2
0
1
0
1
0
1
2
1
1
1
1
2
2
1
1
1
1
2
1
2
1
2
0
0
1
0
1
1
1
1
0
1
1
1
1
0
2
1
2
1
2
0
1
1
0
2
2
1
1
2
0
1
0
2
1
1
1
2
1
1
1
2
1
0
1
0
0
0
0
1
1
1
1
0
2
1
0
1
2
1
1
0
1
1
0
1
0
1
2
1
0
1
2
2
2
1
1
2
1
2
1
1
2
1
1
1
1
1
2
1
2
0
1
1
2
1
0
1
1
1
1
2
1
2
2
2
1
2
1
1
1
1
1
1
0
1
1
1
2
1
1
1
1
1
0
1
1
1
2
1
0
1
1
1
1
1
0
0
0
1
1
0
1
2
1
0
0
0
1
1
2
1
1
2
0
1
2
1
1
0
1
0
0
1
0
1
2
2
1
1
1
2
1
1
1
1
2
1
1
1
1
0
1
1
0
2
1
0
1
1
1
0
1
1
2
1
1
2
2
2
1
1
1
1
1
1
1
1
0
1
1
1
1
0
2
2
0
1
1
1
0
1
1
2
1
1
1
2
0
2
1
1
2
1
0
1
0
1
1
1
0
0
1
1
1
1
0
1
1
0
0
1
0
0
1
2
1
2
1
0
0
1
0
3
2
0
1
0
1
2
1
1
3
0
1
1
0
2
1
1
0
0
1
1
1
2
1
0
0
0
0
2
1
2
2
1
1
1
3
2
0
1
1
2
2
0
1
1
0
0
1
1
2
2
1
0
1
1
1
2
1
2
1
2
1
2
1
1
1
0
1
1
1
1
0
1
1
0
1
1
0
0
1
2
1
1
2
2
1
3
0
1
2
2
2
1
1
2
1
1
1
2
2
1
0
1
0
1
2
1
1
2
0
0
1
1
1
2
2
1
1
1
3
3
0
2
1
2
1
0
1
1
2
2
2
4
2
0
2
2
2
1
1
1
1
1
1
2
0
2
1
2
1
0
1
2
0
1
1
0
1
1
2
1
1
1
1
1
0
2
2
1
1
1
0
1
0
1
1
0
2
1
0
1
1
1
0
1
1
0
0
2
1
1
1
0
0
1
0
1
2
1
2
1
1
1
0
2
1
0
1
0
2
1
2
1
1
1
1
3
0
3
0
1
1
1
1
1
1
1
2
0
1
1
1
1
2
5
2
1
1
2
0
1
1
1
0
1
1
0
0
2
1
1
1
1
1
1
1
1
1
0
1
0
1
0
1
1
0
2
0
1
0
0
2
1
1
2
2
2
2
1
2
1
2
0
1
1
1
2
1
3
1
1
1
0
0
2
2
1
1
0
0
1
1
1
1
0
1
0
0
1
2
1
1
2
2
1
0
1
0
0
1
0
1
1
1
1
1
1
1
0
1
1
1
0
1
1
0
0
1
2
1
1
2
1
1
1
1
2
1
2
1
2
0
1
0
1
1
1
2
1
1
0
0
1
1
0
1
0
1
1
2
1
1
2
1
1
1
1
2
1
2
3
1
2
0
1
1
1
1
0
1
1
2
2
1
1
2
1
2
1
0
1
1
0
1
0
1
1
0
1
1
1
1
1
1
1
2
0
2
1
1
1
1
0
0
1
0
1
0
2
1
1
1
1
1
0
0
0
1
1
1
5
0
2
0
2
2
0
1
2
1
1
1
1
0
2
0
1
1
1
2
2
1
2
1
0
2
1
1
1
1
2
1
2
0
3
1
1
1
0
0
1
1
1
0
2
2
2
1
1
2
1
1
0
1
2
2
2
2
1
0
2
0
1
2
0
2
2
1
1
1
1
1
1
2
1
0
1
2
2
0
2
0
2
1
2
1
1
1
1
1
0
1
2
0
0
1
2
0
2
2
0
1
1
1
1
2
2
0
0
1
1
1
0
2
2
0
1
1
1
2
2
1
0
1
1
4
1
1
0
1
1
0
0
1
0
0
1
0
0
1
2
1
0
0
0
2
1
2
2
1
1
0
2
0
1
1
1
0
1
0
1
0
1
0
0
0
0
0
2
1
0
0
2
1
1
1
2
2
0
2
1
1
1
1
0
0
1
0
2
1
1
1
1
2
0
0
1
0
1
1
2
3
1
1
1
2
1
1
1
1
1
0
2
1
1
1
2
1
2
3
2
1
2
0
1
1
1
1
0
1
2
0
0
2
1
1
2
1
2
1
1
1
2
0
2
1
1
2
2
2
1
2
1
1
0
0
1
1
1
1
1
2
2
2
1
2
1
1
0
1
1
0
0
0
0
1
1
1
1
1
0
1
0
1
1
1
1
1
0
1
1
1
1
1
2
1
1
1
2
1
1
0
2
1
1
1
1
1
1
2
2
0
1
1
1
1
1
2
2
1
1
0
1
1
1
1
1
1
1
1
0
1
2
0
2
1
1
1
1
1
1
1
1
2
1
2
0
0
1
2
2
1
2
1
2
1
0
1
1
0
2
1
0
1
0
2
1
1
1
0
2
2
0
1
2
0
1
1
1
1
1
1
2
1
2
0
1
0
0
1
0
1
2
1
0
0
1
2
1
0
1
1
2
1
0
1
2
1
1
1
2
1
0
0
2
1
0
0
0
1
0
2
1
1
2
1
1
1
0
1
2
1
1
1
3
2
0
1
1
1
0
2
2
1
1
0
2
1
2
2
1
0
0
1
1
2
1
1
1
1
0
0
2
1
1
3
0
3
2
1
1
1
0
1
1
1
1
1
1
2
1
1
1
1
2
2
1
0
1
1
2
1
2
0
0
1
1
0
2
2
0
1
1
2
0
0
1
1
1
0
1
1
2
1
2
2
1
1
1
0
1
0
1
2
1
0
0
1
1
2
1
2
2
2
1
1
0
0
1
2
1
1
1
2
1
2
2
0
0
1
1
2
1
1
0
1
1
0
1
2
1
0
1
1
1
1
0
1
2
1
2
0
2
0
1
1
2
1
1
0
1
1
0
1
1
2
2
0
1
1
2
1
1
1
1
1
0
0
0
1
1
1
1
3
1
2
0
1
0
2
1
1
3
2
2
1
2
1
1
0
1
0
1
0
1
1
2
2
0
1
1
2
1
1
2
1
2
2
1
1
0
1
2
0
1
1
1
1
1
1
0
2
0
0
1
1
0
1
1
1
0
2
0
1
1
1
0
2
3
0
0
0
0
1
1
2
1
1
2
1
2
2
0
0
1
2
1
2
1
1
2
2
1
2
1
1
1
1
1
1
3
1
2
1
0
1
2
1
2
2
0
2
1
2
0
1
2
1
1
1
1
1
2
2
2
0
1
1
1
1
1
1
1
2
1
1
2
1
0
1
1
1
0
2
1
1
2
1
0
1
0
1
1
1
1
2
1
1
1
0
0
2
0
1
1
1
1
2
2
1
1
1
1
0
1
1
0
1
1
1
1
1
4
1
1
1
1
1
0
1
2
0
2
0
0
1
2
0
1
1
1
1
1
2
1
0
1
1
0
1
1
1
1
1
2
2
1
2
2
1
1
1
1
1
1
2
1
3
1
2
2
1
1
2
2
1
2
2
0
1
1
3
0
1
2
2
0
0
1
1
1
1
1
1
0
0
0
2
1
1
1
1
1
0
1
1
0
0
1
1
0
1
0
0
1
0
2
1
1
2
0
0
1
0
0
1
1
1
2
1
0
2
0
1
1
1
1
2
2
1
1
1
1
0
0
0
1
0
1
0
1
1
2
1
1
1
1
1
1
1
0
1
2
2
2
1
0
0
1
1
0
1
1
1
1
0
1
0
0
2
2
1
1
0
0
1
2
0
1
1
1
2
0
0
2
0
1
1
1
0
2
1
1
2
1
1
2
1
1
2
1
1
0
1
2
2
2
0
1
1
3
1
1
0
2
1
2
1
1
0
1
1
1
2
2
2
1
1
0
2
0
1
0
1
1
1
0
2
1
0
0
1
1
2
0
1
3
1
2
2
1
1
0
1
1
0
1
1
1
2
2
0
1
1
0
1
2
1
1
1
1
0
2
1
1
1
0
1
1
1
1
1
1
0
1
1
2
1
1
1
1
0
1
2
1
2
2
2
0
0
1
1
0
1
1
2
1
1
1
1
0
0
2
2
1
1
0
1
1
1
0
1
0
1
1
2
1
1
1
1
1
0
4
0
2
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
1
1
1
1
1
2
1
2
0
0
1
2
1
0
1
0
1
0
1
0
1
0
1
2
0
0
2
2
1
1
2
1
1
1
1
2
1
1
2
0
2
1
1
2
1
2
2
2
1
1
1
1
2
1
1
0
1
1
2
2
1
1
0
1
2
0
0
1
1
2
2
1
1
1
0
1
1
1
0
1
1
1
1
1
1
1
0
0
2
1
1
0
1
2
1
0
0
0
1
1
0
1
2
1
0
1
0
0
2
1
1
1
1
1
2
2
0
1
2
1
1
1
1
0
0
0
1
0
1
0
1
0
1
0
1
1
1
2
1
0
1
0
1
1
1
0
1
1
0
1
1
2
1
1
0
1
1
0
1
0
1
0
2
1
0
1
0
1
1
1
0
0
2
1
2
1
0
2
1
1
0
1
1
2
1
1
1
1
0
1
1
1
2
1
2
1
2
2
2
2
2
1
2
1
0
2
2
1
1
0
1
0
0
0
0
2
0
1
1
2
0
1
1
0
1
1
0
1
1
1
1
0
1
1
2
2
1
2
2
0
0
2
1
1
1
1
2
1
0
0
2
2
1
0
1
0
2
2
0
1
2
0
0
1
1
3
1
2
0
0
2
0
2
1
1
1
1
2
0
1
1
0
2
1
1
2
1
0
1
3
1
1
1
2
1
1
1
1
2
1
0
2
0
1
0
0
2
2
2
0
1
2
1
2
1
0
1
1
1
1
0
0
1
2
2
1
1
5
0
1
1
0
1
2
1
1
1
1
0
0
2
1
0
3
1
1
0
1
1
1
1
1
0
1
1
1
2
1
0
0
1
1
1
0
1
1
0
1
2
1
0
1
0
0
2
1
1
2
2
2
2
2
3
1
0
1
1
0
1
2
1
1
1
1
0
1
2
1
1
1
1
0
1
1
1
2
1
1
1
1
1
1
1
1
0
0
0
1
1
1
0
0
0
1
1
2
1
1
2
2
1
1
2
2
2
0
0
0
1
1
1
3
1
0
2
0
2
2
0
1
1
1
0
1
2
1
2
0
0
1
1
1
0
2
1
2
0
1
1
0
1
2
0
0
1
1
2
2
2
1
1
0
1
0
1
1
2
0
1
1
2
0
1
2
1
1
1
0
2
1
1
0
1
0
1
0
0
1
1
2
0
1
0
2
1
1
3
1
1
2
1
2
1
1
0
0
1
2
2
1
2
1
1
1
0
1
0
1
0
2
0
1
1
1
1
0
1
1
1
2
0
2
1
1
0
0
1
1
0
1
1
0
0
1
1
0
1
1
1
0
1
2
1
0
0
1
2
2
2
1
2
1
2
1
2
0
2
1
0
2
2
1
1
1
1
2
2
1
0
2
0
2
2
1
0
2
2
2
1
2
1
1
1
1
1
1
2
0
0
0
1
1
1
0
1
2
0
2
1
0
1
1
2
0
0
0
3
0
2
1
2
0
0
1
1
1
2
1
1
1
0
1
0
3
1
1
1
0
0
1
1
0
2
1
1
1
1
1
1
1
1
1
0
0
1
1
0
0
2
1
2
0
0
0
2
0
0
1
1
2
0
1
1
2
0
2
2
1
0
2
2
1
2
0
2
1
1
0
0
1
1
1
0
1
1
1
1
1
1
2
2
1
1
0
2
1
1
1
1
1
1
1
0
1
1
1
2
1
1
2
0
2
1
0
1
1
0
1
1
1
0
2
0
0
2
4
1
1
1
0
1
1
2
1
1
1
0
0
1
2
1
2
1
1
1
2
1
1
1
0
2
1
2
0
2
2
0
1
0
1
1
1
1
1
1
1
1
1
0
1
2
0
0
1
2
2
2
1
1
1
2
1
1
2
2
1
0
1
1
1
1
1
2
0
1
0
1
2
0
1
1
1
1
1
0
0
1
1
1
1
0
1
1
0
0
1
1
2
2
1
0
2
1
1
2
2
0
1
0
1
1
0
1
0
2
1
1
2
1
0
0
1
1
2
0
2
1
1
1
1
2
2
1
1
1
0
0
1
0
1
1
1
1
2
1
1
1
1
0
1
1
1
0
0
1
0
2
2
1
1
1
1
2
0
1
1
2
1
1
1
1
0
1
2
1
0
0
1
1
0
0
2
1
1
1
2
1
2
0
0
1
0
1
0
0
2
2
2
1
1
1
1
1
0
1
1
1
2
1
0
0
2
1
1
1
0
1
1
1
0
1
2
0
1
2
1
1
1
2
2
1
3
1
1
0
1
2
1
1
1
2
1
1
1
1
1
1
1
2
2
0
1
2
1
2
3
1
2
0
2
0
1
1
1
1
1
1
3
1
1
1
1
1
1
2
1
1
3
1
1
0
1
1
0
2
1
1
1
2
1
0
2
0
0
2
1
1
1
1
2
1
1
3
1
0
2
1
0
2
2
0
0
1
2
2
3
2
1
0
2
0
1
1
1
2
0
1
1
2
0
0
2
1
1
1
0
2
2
0
1
1
1
2
1
1
2
1
1
2
1
2
1
1
0
1
1
1
2
0
0
1
0
1
0
1
2
1
1
0
0
1
0
0
0
1
1
1
1
2
1
1
1
1
2
0
1
1
1
2
1
0
1
1
0
2
2
2
2
1
2
1
2
1
1
1
1
1
0
1
1
1
1
0
1
2
2
1
1
2
1
1
0
2
3
1
2
1
2
0
1
0
1
0
1
1
1
1
2
1
2
1
1
2
0
2
0
2
1
3
1
1
1
0
1
1
2
1
1
1
1
1
1
2
3
2
1
1
2
0
1
2
1
1
1
1
2
0
1
1
2
0
1
1
0
1
2
0
0
0
1
1
1
0
0
1
1
1
1
2
1
2
0
1
2
1
2
1
1
1
2
1
1
2
1
1
0
0
2
1
1
2
2
1
2
2
1
0
0
2
1
1
0
1
1
2
1
1
2
2
1
1
2
4
2
1
1
1
0
1
0
2
0
0
1
0
1
1
1
0
1
2
1
2
0
0
0
0
2
1
1
1
1
1
1
1
1
1
1
2
0
1
1
1
2
1
2
0
2
2
1
0
1
1
0
2
0
1
0
2
1
0
1
0
2
1
1
0
2
1
1
1
2
2
1
0
2
1
1
1
1
1
2
2
0
0
6
1
0
1
0
1
1
0
2
1
1
1
1
1
1
1
1
1
1
1
1
0
1
0
1
1
0
1
0
1
1
1
1
0
1
1
2
1
1
2
0
1
1
2
1
2
2
1
2
2
2
2
0
0
2
1
0
1
0
1
1
0
0
2
0
1
0
0
1
1
1
1
1
1
1
2
1
0
2
1
1
1
1
1
0
1
1
2
1
2
2
0
0
1
1
2
1
1
2
0
0
1
1
1
1
0
0
2
0
2
0
1
1
2
0
0
2
1
2
2
1
1
1
0
2
1
2
2
2
2
2
1
1
1
1
1
2
1
1
1
2
1
1
2
0
1
1
2
0
0
2
1
2
1
1
5
1
1
1
1
1
1
0
1
2
0
1
2
1
0
1
1
0
2
1
1
2
0
0
0
1
0
0
0
2
0
0
2
1
1
1
0
2
0
2
0
1
2
1
1
1
2
1
1
1
1
1
1
2
0
2
1
1
2
0
1
0
0
1
1
0
2
0
1
1
2
1
2
1
1
1
1
1
1
0
0
2
0
0
0
0
1
1
1
2
1
1
1
0
2
1
3
1
1
2
1
2
2
2
0
3
0
2
1
2
1
1
1
1
1
2
2
1
2
1
1
1
1
2
0
1
0
2
1
1
2
1
1
0
1
1
1
1
1
1
1
0
1
2
0
1
1
1
1
2
1
2
2
2
1
1
2
2
2
0
1
0
0
1
1
1
0
1
0
1
2
2
1
2
1
0
1
1
1
0
2
1
2
0
3
1
2
0
3
0
2
2
2
1
2
1
2
1
0
2
1
1
1
1
1
1
1
0
1
1
0
2
1
2
1
1
1
2
2
0
1
1
1
2
0
2
1
2
0
0
1
0
2
1
2
1
0
0
1
1
1
5
0
1
0
2
1
0
0
2
0
2
0
2
1
1
1
1
1
1
2
0
2
0
1
1
2
0
1
0
2
1
1
1
1
1
1
1
2
2
1
1
2
2
1
0
0
1
2
2
1
1
2
1
0
0
1
2
2
0
3
2
1
1
0
1
1
1
1
1
1
0
1
1
1
0
1
2
3
1
1
1
0
1
1
0
0
1
1
0
0
1
1
0
2
0
1
2
1
1
1
1
1
1
0
0
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
0
2
1
0
1
1
2
2
1
1
2
0
2
1
1
0
0
0
1
1
2
0
0
1
1
2
1
1
2
0
2
1
2
1
2
1
1
0
0
2
2
0
1
2
1
1
2
2
1
1
1
0
1
2
2
1
2
1
1
2
2
1
1
1
1
2
1
1
1
2
1
1
1
0
1
1
1
1
1
1
1
0
2
1
1
0
1
1
0
1
2
0
1
2
1
1
1
0
1
2
2
0
1
0
0
1
2
1
2
2
0
0
2
1
0
1
0
2
2
2
2
0
0
0
1
0
1
1
1
1
0
1
1
0
2
2
2
2
1
1
0
1
1
2
0
3
0
1
1
1
2
0
2
2
1
0
0
1
2
1
1
1
1
1
1
2
0
1
0
1
1
2
2
0
0
1
1
1
1
2
1
1
1
2
1
2
1
2
1
1
1
1
1
0
1
2
1
1
2
0
0
0
2
1
1
2
1
1
1
2
0
1
2
2
2
0
1
0
2
0
2
1
0
1
1
1
0
1
2
2
1
0
0
1
1
3
0
1
1
1
1
1
1
1
1
0
0
1
1
1
0
2
0
0
2
1
1
2
1
1
0
1
1
3
0
1
1
1
0
2
1
2
2
0
1
1
1
0
0
0
0
1
2
1
1
1
0
1
1
1
1
0
1
1
2
1
2
2
1
1
2
1
1
2
2
1
2
0
1
1
1
3
1
2
1
0
0
1
2
1
1
2
1
1
1
1
1
2
1
1
2
0
1
1
0
1
1
1
1
2
1
2
2
1
1
1
1
1
2
1
0
2
0
1
1
1
1
1
2
1
1
2
2
1
0
0
1
0
2
3
1
2
1
1
2
1
1
2
2
0
2
1
1
0
1
1
1
1
4
1
0
1
0
1
1
2
1
2
1
1
2
1
2
0
1
2
2
1
1
2
1
0
1
1
1
2
1
0
1
1
0
2
1
2
0
1
1
0
2
1
1
2
1
1
0
1
2
1
1
1
1
1
0
1
2
1
2
1
0
1
0
3
2
1
0
0
0
1
0
2
1
2
1
1
2
1
1
2
1
2
2
1
1
1
1
2
1
0
1
1
1
1
2
2
1
1
1
2
2
0
1
0
2
0
2
2
2
0
1
1
2
0
2
2
1
2
0
1
1
2
0
2
0
0
1
1
1
2
0
0
1
1
1
2
1
1
1
0
1
2
1
0
1
1
1
2
1
1
1
2
1
2
0
1
3
1
1
1
0
0
1
2
1
1
1
2
1
1
2
0
1
1
2
1
1
0
5
1
1
1
0
1
2
1
0
6
0
0
2
1
1
2
2
2
1
1
0
1
1
0
0
1
1
0
1
0
1
2
2
0
0
1
2
2
2
1
1
1
0
0
0
1
2
2
1
2
0
1
0
1
1
1
2
0
0
2
2
1
1
1
0
1
0
1
1
3
1
0
1
1
0
1
2
1
1
0
1
1
1
2
2
1
2
1
1
2
2
0
0
3
0
0
1
2
1
0
1
1
1
2
2
0
1
0
1
1
0
1
1
1
1
1
1
1
1
1
1
1
0
0
2
2
1
0
1
1
1
2
1
2
3
1
1
0
0
1
0
0
2
1
2
1
3
1
1
1
1
2
1
1
1
1
0
1
1
2
2
2
2
0
2
1
1
0
1
1
1
0
1
1
1
0
1
1
1
2
1
1
2
1
2
0
0
1
1
1
1
0
0
0
0
0
1
1
2
1
1
1
1
2
2
2
0
1
0
1
0
1
0
1
2
1
1
2
1
1
2
1
2
0
1
2
1
1
1
0
2
0
2
1
1
1
3
1
0
1
0
1
1
1
1
1
0
1
1
3
1
1
2
0
2
1
0
0
1
1
1
2
0
0
1
2
1
1
1
2
0
0
1
0
1
1
0
1
2
2
2
2
2
0
0
1
2
1
1
0
1
0
0
1
1
0
1
1
1
0
1
0
1
0
1
1
1
0
1
1
1
1
1
2
0
1
2
0
1
1
1
1
1
1
0
0
1
1
1
1
0
2
1
1
1
0
1
1
1
1
1
2
1
2
2
3
0
1
1
0
2
2
1
1
2
1
2
1
1
0
1
0
0
1
1
1
1
1
2
1
2
0
0
2
2
3
0
1
0
1
1
0
2
1
1
1
2
1
1
1
2
0
1
1
2
1
0
2
2
1
1
1
1
1
2
0
0
1
1
2
1
0
1
2
1
1
2
1
1
2
1
1
1
0
1
0
0
0
2
1
1
2
2
1
1
2
0
0
2
1
0
1
1
0
1
0
1
1
2
1
0
1
1
2
1
2
0
1
1
2
1
0
1
1
1
2
1
1
0
0
1
2
1
1
0
0
0
1
1
0
1
0
0
0
1
0
2
1
1
0
2
0
2
0
2
2
2
2
2
2
1
1
2
1
1
1
2
1
2
2
0
2
1
2
0
1
2
1
2
1
2
1
0
1
1
2
1
1
1
1
1
0
1
0
2
1
1
3
1
2
0
1
2
0
1
1
1
2
1
0
1
1
4
2
1
1
0
2
0
1
1
0
1
0
1
2
2
0
1
1
1
0
0
0
0
2
1
1
1
1
2
1
1
1
2
2
1
1
2
0
0
2
1
2
1
2
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
2
2
0
1
0
1
1
0
1
1
1
0
1
1
2
1
1
0
1
1
2
1
2
2
0
1
1
1
1
1
1
1
1
1
2
2
0
2
1
2
1
0
0
0
1
1
0
0
0
0
1
2
2
2
1
0
1
1
0
0
1
0
2
2
0
1
2
1
1
2
1
1
1
1
2
2
2
1
1
1
1
2
0
1
0
2
1
1
1
1
1
2
1
1
1
1
1
0
1
1
0
0
2
0
1
1
0
1
1
1
2
1
1
2
2
1
1
2
0
1
1
2
1
1
1
0
0
2
1
1
1
0
0
1
1
1
1
1
2
0
0
2
1
1
1
0
1
0
2
1
2
1
1
1
0
1
2
1
1
2
1
0
1
2
1
1
1
2
2
2
2
0
1
1
1
1
1
1
2
2
2
2
1
2
0
0
1
1
1
1
0
1
1
1
2
2
1
1
1
1
0
1
0
1
1
0
1
1
0
2
1
1
2
1
1
2
0
1
0
1
0
1
1
1
0
1
1
1
1
2
1
0
0
1
2
1
1
2
0
2
1
1
1
2
0
2
0
1
1
2
2
1
1
1
1
1
1
1
1
0
1
1
1
0
0
1
1
2
1
0
1
0
2
1
3
1
0
2
2
1
1
0
2
1
0
1
2
1
1
1
1
1
2
0
3
1
1
0
2
1
2
1
1
2
1
2
1
1
2
1
1
1
1
0
0
1
1
1
0
1
0
1
1
1
2
1
1
2
1
1
1
1
1
2
1
0
0
0
1
1
1
2
0
0
0
2
1
1
2
0
1
0
2
2
2
0
0
2
0
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
2
0
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
0
1
1
1
1
0
1
1
1
2
0
0
0
0
0
2
1
0
1
1
1
2
6
1
1
0
1
1
0
2
0
1
1
1
0
0
1
0
1
1
1
1
2
1
1
1
0
1
1
1
2
0
1
1
1
0
1
0
1
0
1
1
0
0
0
0
1
1
1
1
1
1
1
2
0
0
2
1
1
0
1
1
0
2
1
2
0
0
0
2
1
1
2
0
2
1
1
0
1
2
1
1
1
2
1
1
1
1
0
3
1
1
0
1
0
1
1
1
1
0
1
1
2
1
1
1
3
1
1
1
1
0
1
0
2
2
1
1
1
1
0
0
1
1
0
1
1
0
1
1
1
1
1
1
1
1
1
2
2
1
1
1
2
1
2
2
0
2
2
0
0
2
2
0
1
1
1
1
3
2
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
0
1
1
1
2
1
1
1
2
1
2
1
1
1
1
3
0
1
2
4
2
3
1
0
2
3
1
1
1
1
0
0
2
1
0
2
1
2
1
0
2
1
0
0
2
1
0
1
1
1
1
1
2
2
1
0
1
0
2
0
0
2
0
1
1
0
2
1
2
1
0
0
0
1
1
0
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
1
0
1
1
2
1
0
0
0
1
2
1
1
1
1
1
1
1
1
1
1
2
1
5
1
0
1
2
0
0
1
1
1
1
1
0
0
1
2
0
3
0
1
1
1
2
2
1
1
1
1
0
1
1
1
2
2
0
1
2
0
1
0
2
1
1
1
1
2
1
0
1
0
1
0
2
1
1
1
2
4
0
1
1
1
1
2
1
1
1
1
0
0
0
2
2
1
1
1
1
1
0
1
0
1
0
0
0
0
1
1
1
1
1
2
0
1
1
1
0
1
1
1
1
0
1
0
0
1
1
1
0
1
2
1
3
1
2
0
2
2
0
1
1
1
0
2
0
0
1
2
1
1
1
0
2
2
2
1
0
0
1
2
1
1
2
1
1
2
2
1
1
1
1
1
2
1
1
1
2
1
1
0
1
2
1
1
0
1
1
0
1
1
0
0
1
0
1
0
1
1
1
0
2
1
2
2
0
1
1
3
0
1
2
1
0
2
2
2
0
0
2
1
2
1
1
1
1
1
1
0
1
2
0
1
1
1
1
2
1
1
1
0
1
1
1
2
1
2
2
0
3
0
1
2
1
2
1
2
2
0
2
1
1
1
1
1
1
2
0
1
0
1
1
0
1
1
1
0
0
1
1
1
0
2
1
1
1
2
4
2
0
1
1
2
0
1
1
0
0
1
1
2
2
2
2
2
1
2
1
1
1
1
1
1
1
0
1
2
1
0
0
2
2
1
0
1
0
1
0
2
0
0
1
1
0
2
0
0
1
0
2
1
0
2
1
1
0
2
1
0
1
0
2
2
0
2
0
1
0
1
1
1
0
2
0
0
0
2
1
0
1
1
1
2
1
1
1
1
3
1
1
1
1
0
1
1
1
1
1
1
0
1
1
2
1
1
2
1
0
2
1
1
1
0
0
2
1
0
2
1
1
1
2
0
1
1
0
2
1
1
1
1
1
0
0
2
1
0
1
1
2
1
0
2
0
2
1
1
1
0
0
0
2
1
0
2
1
1
1
2
2
2
2
0
1
1
0
2
1
2
0
1
1
1
2
1
2
0
2
0
0
1
1
0
2
1
0
1
1
1
0
0
1
0
1
1
1
1
1
1
2
0
0
1
1
2
1
1
1
1
0
2
0
0
1
2
1
1
1
1
1
1
2
2
0
2
2
0
2
1
1
0
1
2
0
1
1
1
1
1
2
1
1
1
2
2
1
2
1
3
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
2
2
1
1
1
1
0
1
1
1
1
1
1
1
2
0
1
1
0
1
0
0
1
1
1
1
2
1
1
1
1
1
2
1
0
1
1
2
0
1
1
1
0
1
1
1
1
1
1
1
1
0
1
1
1
1
1
0
1
0
1
1
1
1
1
1
1
1
1
1
1
0
0
1
3
2
1
1
2
2
1
2
1
0
1
1
1
1
2
1
2
1
0
1
2
1
1
0
0
1
1
2
1
2
0
1
1
1
2
1
1
1
1
1
1
1
0
1
1
2
2
2
2
0
2
0
1
2
2
1
1
0
2
0
1
2
0
2
2
1
1
1
1
1
1
1
1
1
1
2
0
0
1
1
1
0
2
1
2
2
0
1
2
0
0
1
1
1
2
1
1
2
0
2
1
0
1
0
2
2
1
2
0
1
2
1
1
0
2
2
1
1
1
2
1
1
1
2
1
1
0
2
1
1
1
1
1
1
2
1
1
1
0
2
0
1
1
1
1
1
2
1
0
1
1
2
1
0
1
1
1
1
0
1
1
2
1
1
1
1
3
0
2
1
1
0
1
1
0
1
2
1
1
1
0
1
1
1
1
1
1
0
2
1
2
0
1
1
1
2
2
1
1
1
2
1
0
0
1
1
1
1
0
1
1
1
2
0
2
0
0
1
1
1
2
0
1
1
1
1
0
1
0
0
0
1
1
0
1
1
2
2
1
1
2
2
0
1
0
0
1
1
0
1
0
2
1
2
1
0
2
1
1
1
1
0
1
2
1
0
1
0
1
1
2
1
2
1
1
1
1
2
1
1
1
1
1
0
2
1
1
0
1
0
2
1
1
1
0
0
0
1
0
1
2
2
1
0
1
1
0
0
1
0
0
1
1
1
1
0
0
1
1
1
0
1
1
1
1
2
1
1
1
1
1
1
1
2
0
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
0
3
1
2
2
1
1
0
1
0
1
0
2
0
2
1
1
2
0
2
0
2
1
0
2
1
1
1
1
0
2
1
1
0
1
1
1
0
1
0
1
1
2
1
0
1
1
1
0
1
1
1
0
1
1
1
1
1
1
1
0
1
1
1
1
2
1
0
2
1
2
1
2
0
1
0
1
2
1
0
2
1
2
1
1
2
0
0
1
0
1
1
2
1
1
0
1
0
2
1
1
2
1
1
1
1
1
1
1
0
0
1
0
2
2
2
0
1
1
1
1
2
0
0
0
1
1
2
1
2
1
0
1
0
0
2
2
1
2
1
1
1
1
1
1
1
0
1
1
0
0
1
1
0
2
1
2
2
1
0
2
1
1
1
1
0
0
2
2
1
0
0
0
1
1
1
2
1
1
2
0
0
1
2
0
1
0
1
1
1
0
1
2
1
2
0
1
0
2
1
1
2
1
1
1
1
1
2
1
1
1
3
1
0
1
1
0
2
2
0
2
2
1
2
2
1
2
0
2
1
1
2
0
1
0
1
1
0
0
2
0
2
1
1
1
1
1
1
1
1
1
0
1
2
2
0
1
2
1
1
1
0
1
1
1
0
1
2
2
1
2
1
1
1
1
0
0
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
2
0
1
1
2
1
1
1
1
0
0
1
1
1
1
1
0
0
0
2
0
0
2
0
2
2
2
1
0
1
2
1
1
1
4
1
2
1
1
1
1
0
1
0
1
2
1
3
1
1
1
0
2
1
1
1
1
1
2
2
0
2
1
2
0
0
0
1
1
0
0
2
1
1
1
1
1
2
1
0
1
1
1
0
1
0
1
0
1
1
1
1
2
0
1
2
2
1
2
1
1
1
0
1
1
0
0
1
1
1
1
1
1
0
1
2
1
1
1
1
2
0
2
0
1
1
1
0
1
2
2
1
0
1
1
0
0
1
1
1
0
1
0
1
1
0
1
1
0
1
1
1
0
2
0
2
1
4
1
1
1
2
1
0
0
0
1
1
2
2
1
0
1
1
1
1
2
0
1
4
1
1
2
1
1
1
2
0
1
1
2
2
1
1
1
2
0
1
1
1
1
0
1
0
1
1
1
1
0
1
1
1
1
1
1
1
1
1
2
1
1
1
3
1
2
0
1
2
0
0
1
2
1
0
2
1
0
2
1
0
3
2
2
0
1
0
2
1
0
1
1
1
2
0
1
1
1
1
0
0
1
1
1
1
1
0
1
1
1
3
0
0
1
1
0
1
2
1
0
0
1
0
1
0
1
1
0
0
0
1
1
1
0
0
1
1
0
1
0
1
2
2
2
1
1
1
2
0
1
1
0
2
1
1
0
1
0
1
1
1
1
0
0
1
0
0
1
1
1
1
0
2
1
2
2
1
0
0
1
1
1
1
1
4
1
1
0
1
2
2
2
1
1
1
0
1
0
2
1
0
2
0
0
2
2
1
0
1
1
0
1
2
1
1
1
1
1
0
2
1
1
1
1
2
1
2
1
1
2
2
1
1
1
1
1
1
2
0
0
0
1
0
1
2
1
0
1
1
0
1
2
1
1
5
0
0
0
0
1
1
0
1
1
1
0
0
1
0
1
2
2
0
1
2
1
1
2
0
1
1
2
2
2
2
2
1
0
1
2
1
1
1
1
0
1
2
1
0
1
1
1
1
2
2
2
1
2
1
0
0
1
0
2
1
1
1
2
1
1
1
2
1
0
1
1
0
0
2
0
2
2
1
2
1
0
1
1
1
1
0
1
1
0
1
1
1
1
1
1
2
0
0
2
3
1
1
1
1
2
1
1
1
0
1
1
0
2
1
2
1
0
1
1
2
1
0
1
2
2
1
1
1
1
1
2
0
0
1
0
1
1
0
1
1
1
2
1
2
0
1
0
1
1
1
2
0
1
1
1
2
1
1
0
2
2
2
1
2
1
1
0
2
1
1
0
2
3
1
1
1
1
1
2
1
1
1
2
1
1
1
0
1
0
1
2
0
2
1
1
1
1
1
0
1
1
1
1
1
0
0
1
1
1
1
0
1
1
1
1
0
2
2
0
2
2
2
0
2
2
2
2
1
1
1
1
0
2
0
0
1
0
2
1
0
1
2
0
2
0
1
0
1
1
0
0
0
2
1
1
1
1
2
2
1
1
2
0
1
0
1
1
0
2
1
1
0
0
2
1
0
1
2
1
2
1
1
2
0
2
1
1
0
1
1
2
1
2
1
1
1
0
2
3
1
1
0
0
1
1
1
1
1
0
1
0
1
1
2
0
1
1
0
2
1
1
1
0
1
1
1
0
2
1
2
1
1
2
0
2
2
0
1
1
2
2
1
1
0
2
1
3
1
1
1
1
1
1
0
1
0
1
1
1
2
0
0
1
2
1
0
2
1
1
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
0
0
0
2
0
0
1
1
2
1
0
1
0
1
1
1
0
0
1
2
1
0
1
1
2
0
1
0
1
1
1
1
1
2
0
0
0
1
1
1
1
1
1
1
1
1
2
0
1
1
0
1
1
0
3
1
0
1
2
2
0
0
2
0
2
0
0
3
1
2
0
1
1
2
2
2
0
0
2
1
1
1
2
1
2
0
1
1
2
1
1
0
1
0
2
1
2
0
1
1
0
2
0
0
1
2
1
3
0
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
0
2
2
0
1
1
1
1
1
2
1
1
2
0
2
1
1
2
1
2
1
1
1
0
1
1
0
1
1
1
1
1
3
0
1
2
2
0
2
2
2
0
2
1
1
2
2
1
1
0
1
0
0
1
1
2
1
1
0
1
2
1
1
1
0
0
2
0
1
1
2
1
1
1
0
1
0
1
1
1
0
2
1
0
2
1
1
0
2
0
1
1
1
1
2
2
1
1
1
2
0
1
1
1
1
0
1
1
1
3
2
2
0
0
3
1
1
0
1
1
1
0
1
1
1
1
1
2
1
1
0
1
1
1
1
1
0
2
2
0
0
1
1
0
1
2
2
2
1
0
1
1
0
2
0
1
0
1
0
2
0
1
1
1
1
0
1
2
0
1
1
1
1
2
2
1
1
1
1
0
2
1
2
0
0
1
1
1
0
2
1
1
1
1
1
0
2
1
2
2
1
0
2
0
1
1
0
2
2
0
1
0
2
2
1
1
1
2
0
0
1
1
0
2
2
1
1
1
0
1
1
1
1
2
1
1
1
1
2
3
1
1
1
2
0
1
0
1
1
1
0
1
1
2
1
0
0
1
1
0
1
1
0
0
1
2
1
1
1
0
0
1
2
1
1
1
1
2
0
1
1
0
2
1
2
1
1
1
1
2
1
1
1
1
0
1
1
2
0
0
1
1
1
1
1
0
0
1
2
0
2
3
1
1
1
0
2
0
1
2
1
0
1
1
1
1
1
1
2
0
0
1
0
1
1
1
1
1
2
2
1
1
0
1
1
1
2
1
2
0
2
1
1
2
2
0
2
0
1
1
0
1
2
0
1
2
2
1
0
3
0
1
0
1
1
4
2
1
1
2
0
0
1
1
2
1
0
1
1
1
0
1
1
1
1
0
1
1
1
0
1
1
1
2
1
1
1
0
0
2
1
1
1
1
1
0
2
0
1
0
1
1
0
2
2
1
0
0
1
1
1
0
0
1
1
0
0
1
2
1
0
2
2
0
1
0
1
2
1
1
0
1
1
1
1
1
0
1
2
1
2
1
0
1
0
2
1
1
2
1
2
1
1
0
2
1
1
1
0
1
1
1
2
1
1
1
0
1
1
2
1
0
1
1
1
2
2
1
1
1
2
0
1
1
1
0
1
0
0
1
1
1
1
0
1
1
1
0
1
0
1
2
1
0
2
1
1
1
1
0
1
1
1
2
1
2
2
0
1
2
0
2
0
1
0
1
1
1
2
1
2
1
1
1
2
1
2
2
2
0
0
0
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
0
0
1
0
2
1
0
2
1
1
1
1
1
2
0
2
1
1
1
1
1
1
2
1
2
2
1
2
1
0
1
0
2
0
2
1
0
1
1
1
0
2
1
1
2
1
0
1
1
2
0
1
0
0
1
1
1
1
1
0
1
1
1
1
1
2
1
1
1
2
0
2
1
1
0
1
1
2
0
2
0
1
1
1
2
1
1
1
2
2
0
0
2
1
0
0
2
1
2
1
0
1
1
0
1
1
2
1
1
2
1
1
1
0
2
0
0
2
0
1
1
1
1
1
2
1
0
2
1
1
1
2
1
0
0
2
1
1
1
1
0
1
1
1
1
2
1
1
1
1
0
3
1
1
1
2
1
0
1
1
2
0
0
2
3
1
0
0
1
2
1
1
0
2
0
1
2
1
1
1
1
0
1
1
1
1
2
0
2
1
2
2
1
0
1
2
2
1
1
2
2
0
1
0
2
2
2
1
0
2
1
0
1
1
1
1
0
1
2
0
1
1
1
0
0
2
2
1
1
2
1
1
1
1
1
0
1
2
1
1
1
1
1
0
1
1
2
2
2
2
2
1
0
1
0
2
0
1
1
0
1
1
1
1
2
2
1
0
1
1
1
1
1
2
2
1
1
1
2
2
1
2
1
1
0
1
1
0
0
2
1
0
1
2
1
3
1
1
0
1
0
1
0
0
1
1
1
0
1
2
1
1
1
2
0
2
2
2
1
1
0
1
2
1
2
1
0
0
1
0
0
1
1
1
1
0
2
1
0
1
1
1
2
1
1
0
1
2
1
0
2
1
1
2
1
1
2
0
1
2
1
1
1
1
1
1
0
0
1
1
0
1
1
1
1
2
2
2
1
1
1
1
1
1
2
1
1
0
0
0
0
2
1
1
1
0
1
0
2
0
1
0
0
1
1
1
2
2
1
0
2
1
1
1
0
0
1
1
1
0
0
1
1
2
1
1
0
0
2
0
1
0
2
1
1
0
0
1
3
1
1
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
6
1
0
0
1
1
1
2
1
0
1
1
2
1
1
1
1
3
1
1
1
2
1
1
2
0
0
1
0
1
0
1
1
1
0
2
0
2
1
1
1
1
0
1
0
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
0
1
1
1
0
1
2
1
2
1
2
0
0
1
0
0
2
1
1
2
1
2
1
0
0
0
1
1
1
2
1
0
0
2
0
0
1
0
0
1
1
1
2
2
1
1
0
1
2
1
0
1
2
1
1
1
0
2
1
2
0
1
1
1
2
1
2
1
1
2
0
1
1
4
2
2
1
0
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
0
1
2
0
1
1
1
0
2
2
0
2
1
1
1
1
2
2
1
0
1
1
1
1
2
1
1
0
0
1
4
1
1
1
2
1
0
1
1
1
0
1
1
2
1
1
1
1
2
2
2
1
2
1
0
1
1
0
1
0
1
2
4
2
1
1
1
1
1
0
0
1
1
2
1
0
1
1
1
2
2
2
2
0
1
2
1
2
0
1
0
2
1
1
1
1
2
2
0
1
2
0
1
1
0
1
1
2
1
0
0
1
1
1
1
1
1
1
1
0
1
1
1
1
0
2
1
1
1
1
1
1
1
0
1
2
0
0
1
0
2
1
2
2
2
0
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
2
0
1
2
1
2
1
2
0
1
0
1
1
1
1
1
1
1
0
2
1
1
1
0
0
1
1
0
0
1
1
3
0
2
1
1
1
1
1
1
0
1
0
0
2
2
1
2
1
2
0
0
2
1
2
2
1
1
0
1
2
0
1
1
1
0
0
1
1
3
1
0
2
1
0
0
2
0
2
0
2
0
2
1
1
1
1
1
2
0
0
0
2
1
0
0
1
1
1
0
1
1
2
1
0
2
2
2
2
0
0
2
2
1
1
1
1
0
1
2
1
1
1
1
3
1
0
1
1
2
1
0
1
1
1
0
2
0
2
1
1
1
1
0
2
1
1
1
0
1
1
0
1
2
1
0
2
1
0
0
1
1
3
0
0
1
1
2
1
1
0
1
1
1
1
2
0
1
1
2
1
1
0
0
2
2
1
1
1
1
1
1
1
2
2
1
2
1
2
2
0
0
1
0
2
2
1
1
0
2
0
1
1
1
1
2
3
0
1
1
1
1
2
1
2
1
1
0
1
2
0
2
1
1
1
0
1
0
1
0
0
1
0
0
1
2
2
1
2
1
0
1
0
1
1
1
2
1
1
1
2
1
1
1
0
0
1
0
0
1
2
1
2
2
2
1
1
2
1
0
1
1
2
0
2
1
1
2
1
1
1
2
0
2
0
2
1
1
1
0
1
1
1
1
1
0
1
2
2
1
0
1
0
1
1
2
0
2
1
2
1
2
1
1
1
0
0
2
2
1
0
1
0
1
1
1
1
0
0
1
0
1
0
1
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
0
1
2
1
2
0
1
0
2
2
2
1
1
2
2
1
1
2
2
1
1
1
1
1
1
1
0
1
2
1
0
1
2
1
1
1
0
1
2
1
1
1
0
1
1
2
2
1
1
1
2
1
2
1
1
0
2
1
0
1
1
0
1
0
1
1
1
2
0
1
1
1
1
0
0
1
1
0
1
1
1
1
1
0
1
2
0
1
1
1
2
1
1
0
1
1
0
1
0
1
0
1
0
1
0
0
1
1
0
1
2
1
0
1
1
2
1
1
1
2
1
1
2
1
1
1
1
1
0
2
0
2
2
2
1
0
1
0
2
1
1
1
0
1
1
1
1
0
2
0
2
1
1
1
2
1
1
0
1
1
1
2
2
1
1
1
0
0
1
1
1
0
0
1
0
2
1
1
0
2
1
0
1
1
2
0
1
2
1
2
2
0
1
1
2
0
1
1
1
1
1
1
0
0
0
1
0
0
0
2
1
1
1
1
3
1
0
0
1
1
1
1
2
2
0
0
1
2
0
0
1
0
1
2
1
2
1
1
1
1
2
2
1
1
1
0
2
1
1
1
1
1
1
1
1
0
1
1
1
0
1
1
2
2
1
2
0
1
2
1
2
0
2
1
1
1
1
1
2
1
0
0
2
1
1
1
2
0
1
0
1
1
1
2
1
2
1
0
1
1
1
1
1
1
2
0
1
1
2
1
1
2
1
1
1
1
1
0
2
0
1
1
2
2
0
0
1
1
2
1
0
1
1
0
1
1
2
2
1
1
1
0
1
2
1
0
1
1
1
0
1
1
1
1
0
3
1
1
2
1
2
2
2
2
2
1
1
0
1
0
0
1
1
0
1
4
1
2
1
1
0
1
1
1
1
1
1
0
1
3
1
2
0
1
1
1
2
2
1
1
1
0
2
1
2
1
1
0
1
1
2
2
0
0
0
1
1
0
0
2
1
1
1
1
1
0
1
1
2
1
2
0
1
2
2
0
1
0
2
1
0
0
2
1
0
2
1
1
1
2
1
2
1
1
0
2
2
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
0
1
1
2
0
2
1
1
1
1
0
0
1
0
1
1
1
1
1
0
1
1
2
1
1
0
1
1
2
0
1
1
1
2
1
0
0
2
2
0
2
2
1
1
1
1
1
0
0
1
0
1
2
1
1
0
2
3
1
0
1
1
1
2
1
1
1
2
1
0
1
0
2
2
1
2
1
1
2
2
1
2
0
1
0
0
1
0
0
2
0
1
2
1
1
2
0
1
0
1
1
1
0
1
1
1
1
1
2
1
1
1
1
0
1
1
4
1
0
1
1
1
1
1
0
1
1
1
2
1
1
0
1
0
2
1
1
2
1
1
0
1
0
0
1
0
1
0
1
0
1
1
1
1
1
2
0
2
1
1
1
1
0
2
1
1
0
1
1
1
1
1
1
0
2
1
1
1
1
1
1
2
1
1
2
0
1
1
1
2
0
1
2
1
1
2
1
2
2
1
1
0
0
0
2
0
0
1
0
2
1
1
2
2
1
0
0
0
1
0
0
2
1
1
2
1
0
1
0
1
1
2
0
2
0
1
2
2
1
3
0
1
3
1
1
2
0
1
2
2
1
1
1
1
0
1
0
0
1
0
1
0
1
1
1
2
1
2
0
0
1
2
1
1
1
2
1
1
2
1
1
1
1
0
0
1
1
0
1
2
1
2
1
1
2
2
1
1
2
1
1
1
0
3
1
2
1
0
1
2
1
1
1
1
1
1
0
1
0
1
0
1
2
2
0
1
1
2
0
1
1
1
1
1
1
1
1
1
0
1
2
0
1
0
2
2
1
0
1
0
0
1
1
1
0
0
1
1
2
1
0
0
2
1
2
1
1
1
1
0
0
0
2
0
1
2
0
1
2
0
0
0
0
0
2
2
1
1
0
1
1
1
2
2
1
2
1
3
0
2
1
2
1
1
0
0
1
0
0
0
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
1
1
1
1
0
0
0
1
1
0
0
1
1
1
1
1
1
1
0
2
2
2
1
1
1
2
1
1
0
1
1
1
1
0
0
1
1
2
1
1
1
2
1
2
0
1
1
0
0
0
1
1
1
1
1
1
1
1
1
2
1
1
2
0
1
1
0
1
2
2
1
1
1
1
1
1
1
1
1
2
0
2
1
1
1
1
1
1
1
2
2
1
1
2
0
2
1
1
2
0
1
1
1
1
1
0
1
0
3
2
0
1
1
1
0
0
4
0
1
1
2
2
2
0
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
0
2
0
1
0
2
1
0
1
0
0
2
1
2
1
2
2
0
2
1
1
0
1
1
0
1
1
1
1
1
4
1
1
2
2
1
1
0
1
1
2
1
1
1
0
0
1
1
1
1
1
1
0
1
2
2
1
2
1
1
1
1
1
0
1
1
0
1
1
1
0
0
1
2
1
1
1
0
0
2
1
1
1
0
0
2
1
2
2
1
3
2
1
1
1
1
1
1
1
0
0
1
0
1
1
1
1
0
2
3
1
2
1
1
0
0
1
0
2
0
0
2
1
2
0
0
1
1
0
2
1
0
0
1
1
1
0
0
1
1
1
2
0
2
3
2
1
1
1
2
0
0
1
0
0
1
1
2
0
1
1
0
3
1
1
1
1
1
1
1
0
0
1
0
0
1
3
0
1
2
0
1
1
0
0
1
1
0
1
1
1
0
2
1
1
1
1
1
0
0
0
2
0
0
1
1
0
0
1
1
1
1
1
1
0
1
1
2
0
0
1
1
2
0
0
0
1
2
1
1
1
2
2
1
1
1
1
1
1
0
2
1
1
2
2
3
2
2
2
4
1
2
0
1
0
0
1
1
2
0
1
1
1
1
1
1
0
1
2
1
0
0
0
1
0
2
1
1
2
0
1
0
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
2
1
1
2
0
2
1
1
0
1
1
2
0
2
1
1
1
2
0
2
0
1
2
1
0
2
0
0
1
1
1
1
1
0
2
0
1
1
1
1
2
1
2
1
1
2
3
1
0
1
2
1
1
2
0
1
1
1
0
1
1
1
1
0
1
1
0
0
1
0
0
1
1
1
2
1
0
1
2
0
0
1
2
1
1
0
1
1
0
1
1
2
1
1
1
1
1
1
1
1
0
0
1
2
0
0
1
1
0
3
1
1
1
0
0
0
1
1
1
1
0
1
0
3
1
1
1
1
0
0
0
1
1
1
1
0
2
2
2
0
1
2
1
1
2
0
0
1
0
1
1
0
1
1
1
1
1
1
2
0
2
1
1
1
0
3
1
1
2
1
0
1
1
2
0
1
1
0
1
1
2
1
2
1
1
1
2
2
1
0
1
2
2
2
0
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
3
1
1
2
1
1
2
2
2
0
1
0
0
2
1
1
1
1
2
1
1
1
2
1
1
1
1
0
1
1
1
2
1
1
2
2
1
2
1
1
1
1
1
2
1
2
1
0
0
2
0
0
1
1
1
1
1
1
2
2
0
1
2
2
1
0
1
2
1
2
1
2
0
1
1
1
1
1
1
2
1
2
1
1
2
0
1
0
1
2
1
0
1
1
1
2
2
0
1
3
1
0
1
1
1
0
1
2
2
1
0
2
0
1
0
0
2
1
1
1
0
1
0
0
1
0
1
2
0
1
1
1
0
0
1
1
1
2
1
1
1
1
2
1
2
1
1
1
1
0
0
1
0
1
0
1
1
0
1
0
1
1
1
1
1
1
2
1
1
0
1
1
2
1
1
0
1
1
1
1
1
1
1
0
1
0
1
1
2
2
1
0
1
1
0
0
0
1
0
1
1
1
2
1
1
1
1
1
0
0
0
1
1
1
0
0
1
0
1
0
1
2
2
1
1
1
1
2
2
1
0
1
0
1
1
1
2
0
1
0
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
2
1
1
1
1
1
1
0
1
1
2
1
2
1
1
1
1
2
1
1
2
0
1
2
1
2
0
2
1
1
0
3
1
2
2
2
1
0
0
1
2
1
1
1
1
1
0
1
1
1
0
1
1
1
1
1
1
2
2
0
2
0
0
0
5
1
0
0
0
0
1
0
1
0
0
1
1
2
1
1
1
1
1
1
1
2
0
2
2
1
1
2
1
1
1
1
2
1
0
2
1
1
1
1
2
1
1
1
1
0
1
1
0
0
1
2
1
3
1
2
0
2
0
0
1
2
1
1
1
0
0
2
1
1
0
0
2
1
0
0
0
2
0
1
1
1
0
2
1
1
1
2
1
1
1
2
1
0
1
1
2
1
2
2
0
1
1
1
1
1
1
2
1
2
1
2
1
1
1
1
1
2
0
2
1
2
3
1
1
1
1
1
1
0
2
1
1
0
1
1
1
2
1
0
0
1
1
1
0
0
1
2
0
0
3
1
1
2
1
1
1
2
2
0
1
1
2
0
0
0
1
2
1
1
1
0
0
2
1
1
1
1
1
1
2
1
2
2
1
1
1
1
0
2
1
1
0
2
1
0
0
1
1
1
1
1
1
1
1
1
0
1
0
1
1
1
2
0
0
0
1
0
0
1
2
2
1
2
1
0
1
1
1
0
1
0
1
2
1
1
2
1
1
1
0
0
1
2
1
2
1
1
0
1
2
1
1
1
1
1
0
0
1
4
4
0
0
2
0
1
1
1
0
2
0
0
1
1
0
1
1
2
1
1
1
1
2
1
1
1
0
1
0
1
2
1
1
2
1
2
1
1
0
1
2
1
1
1
3
2
1
0
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
0
1
1
1
1
1
2
0
0
2
0
1
1
0
1
2
0
2
0
1
2
2
1
1
2
0
0
2
0
1
0
2
2
1
0
0
0
0
0
1
1
2
0
1
1
2
0
1
0
2
1
2
0
1
1
1
1
2
1
1
2
1
1
0
1
0
2
0
1
0
1
2
0
2
1
0
1
0
1
1
0
1
2
2
1
3
0
1
2
2
1
0
1
1
0
1
1
2
0
1
2
1
0
0
3
1
1
1
1
1
1
1
1
1
0
1
2
2
1
1
1
2
0
1
2
0
1
1
0
1
2
1
0
1
1
0
1
1
1
0
1
1
2
1
1
0
2
2
1
1
1
1
2
0
2
1
2
0
1
0
0
1
2
1
1
0
2
1
1
1
1
2
1
1
3
1
1
2
0
1
1
1
1
1
2
2
1
1
1
1
1
0
1
1
0
1
1
1
1
1
1
1
1
2
1
1
0
0
1
1
2
1
0
2
1
1
1
1
2
1
1
2
1
1
1
1
1
0
2
1
0
0
1
2
2
2
1
2
0
0
0
1
2
2
2
1
3
1
2
1
2
2
1
1
1
1
2
0
0
1
1
1
0
1
0
1
1
1
0
2
1
1
1
1
1
2
1
0
1
1
1
1
1
0
1
1
2
1
0
1
0
1
1
1
1
1
3
1
1
1
1
1
1
2
1
1
1
1
0
0
2
2
2
1
1
1
1
0
0
4
0
0
0
0
1
2
0
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
2
2
1
0
1
2
2
1
0
1
1
0
1
1
2
1
0
1
1
1
0
1
0
2
1
1
0
0
2
0
2
1
2
1
0
1
1
1
1
0
2
1
0
1
1
1
0
2
2
0
0
1
0
2
1
1
0
0
0
0
2
0
0
2
2
2
0
1
1
1
1
1
1
1
2
1
1
1
1
0
1
2
2
1
1
2
1
2
0
1
0
0
0
1
2
0
2
0
1
2
0
2
1
2
2
0
1
0
0
0
0
0
2
1
1
1
2
1
1
0
0
2
1
0
1
0
2
0
1
1
0
2
1
1
1
2
1
1
1
2
0
1
0
2
0
2
1
0
1
1
0
2
2
1
1
1
0
0
0
2
1
1
2
2
0
1
1
1
5
0
1
1
1
1
0
2
0
1
0
1
1
1
1
1
0
1
0
2
1
1
2
0
0
1
1
2
2
1
1
2
2
2
1
0
1
1
0
0
2
2
1
1
1
1
2
1
1
2
0
1
2
1
1
1
0
1
2
1
1
1
2
1
0
1
1
1
1
1
0
1
1
0
1
1
1
1
1
0
0
1
0
1
0
1
2
1
0
1
0
1
0
2
1
0
1
3
1
0
0
1
1
1
1
1
1
1
2
2
0
2
2
1
2
2
1
0
1
1
1
0
2
2
1
0
0
2
0
1
1
2
0
0
2
0
0
1
1
0
1
2
2
1
1
2
1
1
2
1
2
0
1
1
0
2
0
2
1
0
1
1
4
1
0
1
2
3
1
1
1
0
1
1
1
2
0
1
2
2
1
0
1
1
2
1
1
2
1
1
2
2
1
1
1
1
0
1
1
1
2
2
2
2
1
1
3
1
0
1
4
0
1
2
1
1
2
0
2
2
2
2
1
0
2
1
1
1
0
1
2
3
2
0
1
0
3
1
1
1
0
1
1
2
1
0
0
2
0
0
0
1
1
1
0
1
2
1
1
1
2
0
1
1
1
1
2
0
2
1
3
0
1
1
2
2
1
1
1
1
2
0
0
2
0
2
2
1
1
1
0
2
0
1
2
1
2
2
1
2
1
0
1
1
0
1
0
1
2
0
1
1
0
2
1
0
2
1
1
0
1
2
2
1
2
0
2
1
0
1
0
1
1
1
0
0
0
0
1
1
1
1
0
2
1
1
2
1
2
1
1
1
2
2
1
1
0
0
2
1
1
1
2
1
1
2
0
1
1
1
1
1
0
1
0
2
1
1
1
1
0
1
1
0
2
1
0
2
1
1
1
2
0
2
0
1
0
1
1
0
1
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
1
1
2
1
2
2
1
2
1
0
1
1
1
1
1
2
0
1
1
2
0
1
2
1
1
2
1
1
0
1
1
1
0
1
0
2
0
1
2
2
1
1
1
1
2
0
1
1
1
0
2
2
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
0
2
2
1
1
1
1
1
0
1
1
2
0
1
2
1
0
0
1
1
1
0
2
0
1
1
2
2
2
1
2
1
1
0
1
1
1
2
1
0
0
1
1
2
2
0
2
2
1
2
0
1
1
1
1
0
1
1
1
2
0
2
2
1
1
2
1
1
1
1
1
2
2
0
1
2
2
0
2
1
0
1
1
2
2
2
2
1
0
1
2
1
1
1
0
1
1
1
1
2
1
2
1
1
2
1
2
0
1
1
1
0
1
0
0
0
2
0
1
0
1
1
1
1
1
2
1
1
0
1
2
0
2
1
0
1
1
1
2
3
2
0
1
1
1
2
2
1
2
0
0
1
0
1
0
1
1
0
1
1
1
1
2
2
0
2
1
2
2
1
0
0
1
0
1
1
1
0
1
2
2
2
0
1
1
1
1
0
2
1
1
2
2
2
2
2
1
2
2
2
2
3
1
2
1
1
2
2
1
0
1
1
1
2
1
2
1
0
0
2
1
1
1
2
1
0
1
0
1
2
2
2
1
0
1
2
0
1
1
0
0
1
0
1
0
1
0
1
0
1
1
2
2
0
0
1
2
1
1
1
1
0
1
2
1
0
1
0
1
0
2
2
2
2
1
2
0
1
1
1
0
1
1
1
1
1
1
2
1
2
1
1
1
1
0
2
1
1
0
2
0
0
0
1
0
1
2
2
1
1
0
2
1
2
0
1
1
2
0
0
2
1
1
2
1
0
1
1
1
0
1
1
2
1
2
1
1
2
2
0
1
0
2
1
1
1
0
2
1
2
1
1
1
1
2
2
0
0
0
1
0
2
1
0
1
1
3
1
0
2
1
0
2
2
2
0
0
1
1
1
2
1
1
1
0
0
1
1
1
1
0
1
0
0
1
0
1
1
0
1
0
1
1
1
1
1
0
0
2
2
2
1
1
0
2
2
2
1
0
2
0
2
1
0
1
0
2
2
1
0
1
1
1
1
1
1
1
1
1
0
1
1
1
2
0
2
2
2
2
1
1
0
1
1
0
2
1
1
0
2
0
1
1
1
1
1
1
1
1
2
0
2
1
0
0
0
1
2
0
1
2
2
2
1
0
2
0
0
1
1
1
1
1
1
1
0
0
2
1
0
1
1
0
1
1
1
1
2
1
1
1
2
1
0
1
0
1
1
1
0
2
0
0
1
2
0
0
1
1
1
1
2
1
1
1
1
2
0
0
1
1
2
2
2
0
2
1
1
1
1
0
1
0
1
0
1
2
1
1
1
1
2
0
1
0
1
1
1
1
1
1
0
1
1
0
0
1
2
0
2
2
1
4
1
1
1
1
1
2
0
1
1
1
0
2
1
2
2
2
1
1
2
2
0
0
0
1
2
1
2
0
0
1
0
1
1
0
1
1
1
2
1
2
1
0
1
0
2
1
0
1
2
1
1
0
2
0
0
1
1
1
1
1
1
1
1
1
2
1
1
1
3
1
1
1
2
1
1
0
1
0
1
1
1
1
1
2
1
1
1
1
0
1
1
2
1
1
2
1
1
1
1
1
0
1
1
1
1
1
1
1
2
2
0
0
1
2
1
1
1
1
1
1
0
2
2
0
0
0
1
0
1
0
1
0
0
1
1
1
0
1
0
1
1
1
1
1
0
2
0
1
1
1
1
2
0
2
1
1
0
0
1
1
2
2
1
0
1
1
2
1
1
1
1
2
1
1
2
2
0
1
2
0
0
2
2
0
2
1
1
1
1
2
0
1
0
1
2
2
1
0
1
1
2
1
0
1
1
1
1
1
1
1
1
0
0
2
2
1
0
1
1
2
0
1
2
1
1
1
1
1
1
2
2
0
2
1
1
2
1
1
0
1
2
1
1
2
1
1
1
1
0
1
0
1
1
0
1
1
1
0
1
3
0
2
1
0
2
1
1
0
4
1
1
0
1
1
0
2
1
2
1
1
1
0
1
1
0
1
2
0
2
1
2
2
2
1
1
1
2
1
1
1
0
0
0
1
2
1
1
1
1
2
1
2
0
0
2
2
2
0
1
1
1
2
1
2
2
1
1
0
1
1
0
0
1
0
0
0
2
2
1
1
1
2
1
1
1
0
1
1
1
0
1
2
1
2
1
1
2
1
0
1
0
0
1
2
0
0
1
2
2
1
2
1
2
1
0
1
1
2
1
2
0
1
1
2
1
2
1
1
1
1
1
1
0
0
1
0
0
1
1
1
0
0
1
1
1
0
0
1
0
1
0
1
0
1
0
1
0
0
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
0
1
1
1
1
2
0
0
2
1
1
1
1
1
1
1
0
2
1
1
0
0
2
0
1
0
1
1
0
1
2
1
0
2
1
2
0
0
2
0
0
1
1
1
0
1
0
2
0
1
1
1
2
0
0
1
2
1
2
0
2
0
0
1
0
2
1
2
2
1
1
2
1
3
2
1
0
1
1
2
1
1
1
2
1
1
1
0
1
1
0
1
0
1
2
0
1
1
0
1
0
0
1
1
0
1
1
0
1
0
4
1
2
0
1
1
1
1
2
1
1
1
2
2
1
0
2
0
2
1
2
1
1
1
2
1
1
1
2
2
1
1
1
2
1
1
0
2
0
2
1
1
0
1
1
0
2
0
0
1
2
2
1
0
2
1
1
1
1
0
2
2
1
1
0
2
2
2
0
1
1
0
2
1
1
0
1
2
1
0
0
1
1
1
1
0
1
1
2
1
0
1
1
1
0
0
2
1
2
0
0
2
2
1
2
3
1
1
1
1
2
0
2
0
2
1
2
2
0
2
2
2
0
2
0
1
1
2
2
1
0
0
1
2
2
1
1
1
1
2
2
1
1
0
0
1
1
1
2
1
2
1
0
1
1
2
1
0
1
1
0
1
0
1
0
0
1
1
1
1
1
1
1
0
0
1
1
0
1
1
1
0
1
3
1
0
1
2
2
2
2
1
2
2
1
1
1
2
1
2
1
1
2
1
1
0
2
1
0
1
0
0
0
2
0
2
2
1
1
0
0
1
1
1
0
1
2
1
0
1
1
2
1
0
2
1
1
2
1
2
0
1
2
1
2
1
1
2
1
1
0
1
0
1
1
0
1
1
0
0
1
0
1
2
1
1
2
2
0
1
0
1
0
3
2
1
1
2
1
2
1
1
2
1
0
1
1
1
0
2
1
1
1
1
1
2
0
2
1
0
1
1
1
1
0
1
0
1
2
0
1
0
1
2
1
1
0
1
0
1
1
0
0
1
1
1
1
2
0
1
0
2
2
0
0
2
0
1
1
2
1
1
1
1
0
1
1
0
0
1
2
2
0
0
1
0
1
1
1
1
1
1
1
2
2
0
1
0
1
0
1
0
1
1
0
1
1
1
2
2
2
2
1
1
2
1
1
1
2
1
0
0
0
0
2
1
1
1
0
1
2
1
1
1
1
1
1
1
0
1
2
1
1
2
1
1
0
2
2
2
0
1
1
1
1
1
2
0
1
1
1
0
0
1
2
0
2
0
1
1
2
0
1
1
1
2
1
1
1
1
1
1
0
2
1
1
1
0
1
1
2
1
0
0
0
0
2
2
1
1
1
2
1
1
1
1
1
1
1
2
1
0
1
0
1
2
0
2
2
0
1
1
0
1
1
0
2
1
2
0
1
2
2
1
1
2
2
2
1
0
0
2
1
2
1
1
1
0
2
1
0
2
1
2
0
1
0
0
2
1
1
1
0
0
2
1
1
0
0
0
1
2
0
1
2
1
1
0
1
0
1
0
1
2
1
0
1
0
1
1
0
2
1
1
1
2
1
2
1
2
1
1
2
1
0
2
0
1
1
1
0
0
1
0
0
2
1
1
1
1
0
2
1
1
1
0
1
2
4
1
0
1
1
2
1
1
1
0
2
1
1
2
1
1
0
2
1
1
2
2
1
1
1
2
1
0
1
2
1
1
1
2
0
1
1
2
2
1
1
0
1
0
1
1
1
1
1
2
1
2
0
1
2
2
0
1
1
1
1
2
0
1
0
1
1
2
0
1
1
1
1
1
1
0
1
1
1
2
1
2
1
1
3
0
1
2
0
0
1
0
2
1
1
0
1
1
1
1
1
1
1
2
1
1
2
1
1
1
2
1
1
0
1
0
0
2
0
0
0
1
2
2
0
0
1
1
0
1
0
0
1
0
1
1
0
1
1
1
0
1
1
0
2
1
1
0
1
2
1
2
1
1
2
1
1
1
0
1
1
2
1
1
2
1
0
2
0
2
0
0
2
2
1
0
1
3
1
2
0
1
1
1
1
1
0
1
0
1
1
1
0
0
1
2
1
1
1
2
1
1
1
0
2
2
1
1
1
1
1
1
1
1
1
1
0
2
1
0
1
1
1
1
1
1
2
0
0
1
2
4
2
1
2
1
0
0
0
1
1
2
2
1
1
0
1
0
0
1
1
0
1
0
1
0
0
1
2
0
0
1
1
1
0
2
0
1
0
2
2
2
1
0
0
1
2
2
1
1
1
2
1
2
1
1
2
0
1
1
1
2
1
2
1
1
1
0
1
2
2
1
1
1
2
2
0
1
1
1
2
1
2
1
1
1
1
1
1
2
0
1
2
2
0
2
2
1
1
2
2
0
1
0
0
2
2
2
1
2
1
1
2
1
2
2
0
1
0
2
0
1
1
2
0
2
0
1
2
1
2
2
0
1
1
0
0
0
4
1
0
1
1
1
1
1
0
1
1
2
1
1
1
1
1
2
0
2
0
0
1
2
1
1
1
0
1
1
2
2
0
2
0
1
1
1
0
1
0
0
1
1
2
1
1
1
0
0
1
2
1
0
0
1
1
1
2
1
1
1
2
1
1
1
1
1
2
1
2
0
1
2
1
1
1
1
2
1
0
1
0
2
0
1
1
1
0
2
2
1
1
0
0
2
2
0
1
1
1
0
0
1
1
2
1
1
0
2
1
2
1
1
0
1
0
1
0
1
1
1
0
1
1
2
2
0
2
2
0
1
0
2
1
1
1
2
2
0
0
0
1
1
1
1
1
0
0
2
2
1
1
1
1
2
1
1
1
1
0
2
0
0
1
0
1
2
2
1
1
1
3
1
0
1
2
0
0
0
1
1
2
2
0
0
1
2
1
2
2
0
3
1
1
0
1
1
2
1
2
1
0
1
1
1
1
0
1
1
1
0
2
0
0
1
1
1
2
0
2
0
1
1
1
2
1
1
1
2
2
2
2
2
2
2
1
1
3
1
2
1
1
1
1
1
1
1
1
0
2
0
1
1
1
1
1
3
0
3
0
1
1
1
1
1
0
4
1
1
0
2
0
1
1
1
1
2
1
1
2
2
1
2
2
0
1
1
1
0
0
2
0
1
3
2
1
2
1
1
1
2
1
1
2
0
1
1
1
0
1
2
1
1
1
1
2
1
0
1
0
1
1
1
3
1
1
0
1
1
2
0
1
2
2
1
1
1
0
1
1
1
0
1
1
0
1
1
1
2
2
1
1
1
1
2
1
1
0
1
2
2
3
1
2
1
1
2
0
1
1
2
0
1
2
2
1
1
1
0
1
1
1
1
0
0
2
1
0
0
1
0
2
1
1
2
1
1
2
1
2
0
0
0
0
0
1
1
1
3
0
2
1
0
2
0
0
1
1
1
1
3
1
1
1
2
0
1
0
1
0
1
0
1
2
1
0
2
1
3
2
1
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
0
1
2
2
0
2
0
0
2
2
0
0
0
2
2
1
1
1
1
0
1
1
1
4
1
1
1
0
1
4
1
1
1
1
1
4
1
2
1
0
1
0
0
1
1
1
0
2
1
1
1
2
1
0
0
1
1
3
0
0
0
1
1
1
1
0
1
0
1
1
1
1
1
2
0
1
2
0
1
1
2
2
0
1
1
1
1
2
0
1
0
0
1
0
1
1
0
1
2
1
0
0
1
1
1
2
1
0
1
0
1
2
2
0
2
1
1
1
2
2
2
1
1
2
2
2
2
0
2
1
1
1
1
2
0
2
0
1
1
1
1
2
0
0
2
0
0
1
2
1
1
1
1
1
1
1
1
2
1
1
2
2
1
0
0
1
0
1
1
1
1
1
1
0
0
1
1
1
0
1
0
1
1
2
1
1
1
2
0
1
1
0
2
1
1
1
2
0
1
1
1
0
1
0
2
2
1
1
1
1
0
1
0
0
1
2
0
1
2
1
1
1
1
2
1
3
0
1
1
2
0
1
1
1
1
0
1
1
3
1
0
2
1
1
0
1
1
1
1
1
2
1
2
1
1
1
0
1
1
1
3
1
1
2
0
1
0
1
2
1
1
2
0
1
1
1
1
1
1
1
1
1
0
2
1
1
0
1
1
0
1
1
1
1
1
0
1
1
1
0
1
1
1
1
1
1
1
2
2
2
3
0
1
2
0
1
0
2
1
0
1
0
1
1
0
1
0
2
2
0
1
1
0
1
0
1
1
2
0
0
0
1
1
2
1
1
1
0
0
2
1
0
1
2
1
2
1
0
1
1
1
0
1
1
1
2
2
1
1
1
1
0
0
1
1
1
0
1
0
0
1
2
0
0
2
1
1
0
0
1
1
0
2
1
2
1
2
1
1
1
1
1
2
1
0
1
1
1
0
3
0
1
0
2
1
2
1
1
2
1
2
1
1
1
1
1
1
1
0
0
0
1
1
2
1
1
1
1
2
1
1
0
0
2
1
0
0
2
0
2
1
1
0
1
1
0
1
1
1
1
1
1
1
1
1
1
1
0
1
2
1
1
1
1
1
1
1
4
2
1
0
3
0
1
1
2
1
1
1
1
1
0
0
1
0
1
1
2
1
1
2
1
2
2
1
0
0
1
1
2
1
0
0
1
1
2
1
2
0
1
1
2
1
0
1
1
1
0
1
1
1
1
0
1
2
1
1
1
1
0
0
1
2
2
2
2
1
2
2
0
1
0
1
1
1
2
0
1
1
1
1
1
2
2
3
1
1
2
0
2
2
2
1
1
0
2
1
2
2
1
0
0
1
1
2
2
2
1
1
1
0
1
1
1
1
0
2
1
1
1
0
1
2
1
2
1
1
2
1
1
1
2
2
2
0
2
1
1
1
1
1
1
1
1
0
1
2
1
1
1
0
1
0
1
1
1
0
1
2
0
1
0
2
1
1
2
1
1
1
2
2
2
1
0
2
2
2
1
0
0
1
1
2
1
1
2
1
1
1
1
1
1
1
1
0
1
0
0
0
1
0
2
0
1
0
2
1
1
0
1
2
1
1
1
0
2
2
1
0
1
1
1
2
2
1
2
0
1
1
2
2
1
0
2
2
2
1
1
0
0
1
1
1
1
1
0
1
1
2
1
1
1
0
1
2
1
2
0
1
1
2
1
2
1
1
0
4
1
2
0
2
1
2
1
0
0
1
1
1
0
1
0
1
2
1
2
1
2
0
2
0
1
1
1
1
2
2
0
1
1
0
1
0
1
2
1
2
1
0
0
1
1
1
0
0
1
2
1
1
0
0
1
2
1
0
1
1
1
2
1
0
2
1
0
1
0
1
1
1
2
2
1
0
1
1
0
1
1
1
1
1
1
1
1
2
1
1
2
1
2
2
0
2
0
0
2
0
1
1
1
2
0
2
0
2
2
0
1
0
0
0
1
1
1
0
1
2
0
2
0
0
0
2
2
2
2
2
0
1
1
0
1
1
0
1
1
2
1
1
1
2
0
2
1
1
1
1
1
2
1
1
1
0
0
1
1
0
2
0
0
1
1
1
1
1
3
1
0
2
1
1
1
2
2
2
2
2
1
2
0
0
1
1
1
2
1
1
1
2
1
1
1
0
1
0
0
1
1
1
2
0
1
1
1
0
2
1
1
0
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
1
0
1
1
1
0
2
0
1
0
1
0
2
1
0
0
1
1
1
1
1
1
0
2
0
2
0
0
1
2
1
0
1
1
2
1
0
1
1
1
0
1
1
1
1
2
1
0
1
1
1
2
0
2
0
1
2
1
1
2
1
0
0
1
0
1
0
1
1
1
0
1
4
1
2
2
0
1
1
2
0
1
1
0
1
0
2
0
1
0
0
2
3
2
1
3
2
1
1
1
1
1
1
1
1
1
2
2
0
0
0
1
2
2
1
1
1
2
1
1
1
0
1
2
0
2
1
0
2
0
1
0
0
2
0
1
1
2
1
0
1
0
1
1
1
1
2
1
3
1
0
1
1
0
2
0
1
1
2
1
1
0
1
1
1
1
2
2
1
1
2
1
1
0
1
1
1
2
1
1
1
0
0
2
1
1
0
1
0
2
0
1
0
1
2
1
1
2
2
2
1
0
0
0
1
0
1
0
0
1
1
1
0
1
2
2
1
1
1
2
0
1
1
1
0
0
2
1
1
0
1
2
1
2
1
1
2
1
1
1
1
1
1
2
0
2
0
0
0
0
0
1
0
2
0
0
2
1
2
2
2
2
1
1
0
2
1
1
2
1
0
1
1
1
1
0
1
1
1
0
1
0
1
1
1
1
2
2
1
1
2
1
0
2
1
1
2
0
1
2
1
2
1
1
1
1
1
1
0
2
0
2
1
0
2
2
1
0
1
2
2
1
2
1
1
1
1
0
1
0
1
2
1
2
1
1
1
1
1
1
0
1
1
0
1
0
1
1
2
1
2
1
0
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
2
1
0
1
1
1
0
2
0
1
1
1
0
2
1
1
1
1
0
1
1
1
0
2
0
1
1
3
1
1
0
1
1
3
0
1
0
2
2
1
1
1
0
1
4
2
1
1
1
1
1
0
1
1
2
2
1
1
1
2
0
1
1
2
1
0
2
1
1
2
0
1
1
1
1
1
2
1
0
1
2
1
0
0
1
1
1
2
0
1
0
2
1
1
1
1
0
1
1
1
1
0
0
1
1
0
0
2
0
1
0
2
2
0
1
1
0
1
1
1
0
2
0
2
1
1
2
1
2
2
1
1
2
1
0
0
1
2
1
0
1
1
1
1
1
1
2
1
0
1
1
0
1
1
0
1
1
0
0
1
1
0
1
2
1
1
1
0
2
0
1
1
3
1
1
1
2
1
2
2
1
1
1
4
1
1
2
1
1
1
0
2
0
0
1
2
1
2
0
0
2
2
1
1
1
2
1
1
1
1
1
0
1
1
0
1
2
1
1
1
0
2
1
1
1
1
2
2
1
1
2
0
1
0
1
0
1
0
1
2
1
2
1
1
1
1
0
1
2
1
1
2
1
0
2
0
1
0
1
0
2
2
2
1
1
1
1
1
1
0
1
1
1
2
1
1
2
1
1
0
1
2
0
1
0
2
0
1
0
2
0
2
1
1
2
1
0
0
1
0
0
1
0
1
1
1
1
1
1
2
2
1
1
0
1
1
1
1
1
1
1
0
1
1
0
1
0
1
1
1
1
1
0
0
0
0
1
1
0
1
0
2
1
0
1
1
0
2
0
0
1
1
1
1
2
0
0
1
0
0
1
2
0
2
2
2
1
0
1
2
1
0
1
1
1
2
1
2
2
0
1
2
0
1
1
1
1
2
2
2
1
1
0
2
1
1
1
1
1
2
0
1
2
1
0
1
0
1
1
1
1
1
2
1
1
3
1
1
1
1
1
0
1
2
0
1
2
1
1
1
1
1
1
1
1
1
0
1
0
1
1
1
2
1
1
0
1
1
1
2
1
2
1
1
2
1
0
1
1
0
1
1
1
1
1
2
0
1
1
1
1
0
1
0
1
1
1
2
3
3
2
0
1
2
2
1
1
0
1
2
1
1
2
1
2
1
1
1
0
2
2
1
2
0
0
1
2
1
1
2
2
2
0
0
2
2
1
1
1
0
0
1
1
1
0
1
1
0
0
0
2
0
2
1
1
1
2
1
2
1
1
0
1
0
0
0
2
1
1
0
0
2
2
0
1
1
1
1
1
2
1
0
1
1
1
2
1
2
1
2
0
1
0
1
1
2
1
1
0
1
2
1
1
2
1
2
1
0
1
2
1
1
2
1
0
2
1
1
2
2
2
0
1
0
2
0
0
2
1
1
0
1
0
0
2
1
1
0
0
0
1
1
2
1
2
1
0
1
0
1
2
1
2
0
0
1
1
1
1
1
1
1
1
2
0
1
1
1
2
0
0
0
0
1
1
0
2
1
0
1
2
2
1
1
0
1
0
0
2
1
2
1
1
2
2
1
2
0
1
2
1
1
1
1
0
1
1
1
1
0
1
1
2
0
4
1
1
2
1
1
2
1
1
1
1
1
0
2
0
1
1
1
2
1
1
0
2
0
1
1
0
2
0
1
1
1
1
1
2
1
1
0
1
1
1
2
1
0
1
0
1
2
1
1
2
1
2
1
1
1
2
2
1
0
1
1
1
2
1
2
1
1
1
1
1
2
0
1
0
2
4
1
0
1
1
2
0
1
0
1
1
0
2
1
1
1
2
1
1
2
1
1
0
1
1
2
0
1
0
0
0
1
2
1
0
0
2
0
1
1
1
1
2
1
1
2
0
0
0
1
1
0
0
1
1
1
1
1
1
2
1
1
1
2
2
1
0
2
1
0
1
1
2
0
1
1
1
1
1
1
2
0
0
0
0
1
2
1
0
0
1
1
0
0
0
1
1
2
1
2
0
2
1
0
0
1
1
2
1
1
1
0
1
1
2
1
2
2
1
1
1
2
1
1
1
0
1
1
0
1
0
1
1
1
2
0
0
1
0
0
0
1
1
2
1
1
1
1
1
1
2
1
2
0
1
1
1
1
1
0
0
0
1
0
0
1
1
1
1
0
1
1
1
0
2
1
1
1
2
0
0
2
2
2
0
0
0
0
2
0
1
1
1
2
0
2
2
2
1
1
0
2
0
2
1
0
1
1
1
2
1
2
0
1
0
1
0
1
1
2
1
1
0
2
1
1
2
2
1
1
1
1
0
1
2
0
1
0
1
0
1
1
0
0
1
1
2
1
2
1
2
1
1
1
1
1
2
2
1
0
2
1
1
2
2
1
1
0
1
1
1
1
0
1
0
2
1
0
1
0
1
1
2
0
0
0
0
1
2
1
2
0
1
1
1
0
2
1
1
3
0
1
1
0
1
2
0
0
1
1
1
0
2
0
1
1
1
0
2
1
1
1
1
2
0
1
1
0
1
1
0
1
1
1
1
1
1
1
1
0
2
1
2
0
1
1
0
0
1
2
1
2
1
0
1
0
1
1
0
1
0
1
1
1
1
1
0
0
2
0
1
2
2
1
0
1
1
1
2
0
1
1
0
1
1
2
0
2
1
1
1
1
1
1
1
2
1
0
2
0
0
1
1
2
1
1
1
0
1
2
0
1
0
1
1
0
1
1
0
0
0
1
0
2
1
1
1
2
1
1
2
0
2
1
0
1
1
0
1
2
2
1
1
1
1
1
2
0
3
1
0
0
1
2
2
1
2
2
1
0
0
1
0
2
1
1
1
2
1
1
1
2
1
0
1
0
2
1
2
1
1
2
1
1
1
1
1
2
0
1
1
1
1
1
1
2
1
1
2
0
0
0
1
0
2
1
0
1
1
1
2
0
2
2
1
0
2
1
2
1
1
1
0
0
1
0
0
0
1
1
1
2
0
0
1
1
1
1
2
0
1
1
1
1
0
1
0
2
0
2
1
1
1
0
3
2
2
1
2
1
2
1
1
2
2
0
1
0
1
1
2
1
1
1
1
1
1
1
2
0
0
0
0
0
2
2
1
1
1
0
1
1
1
1
2
2
1
2
0
0
1
2
1
1
0
0
2
1
1
1
1
1
0
0
1
2
0
4
2
0
1
2
2
1
2
1
1
1
1
1
1
1
0
1
1
1
0
1
1
0
1
0
0
2
0
1
1
1
1
2
1
1
1
2
1
1
2
1
2
1
2
2
1
0
1
3
0
1
2
1
1
1
1
1
2
1
0
1
1
1
1
1
0
0
2
1
1
2
2
2
1
0
1
2
0
0
1
1
1
2
6
1
1
2
2
1
2
2
2
2
2
1
2
1
1
2
1
0
2
1
1
1
1
2
2
0
1
1
1
1
0
1
1
2
1
1
1
0
1
1
0
2
1
2
2
1
0
0
2
0
0
1
1
1
2
1
1
1
0
2
1
1
2
1
1
1
1
1
1
2
1
1
2
2
1
1
1
1
2
0
1
1
2
1
0
1
1
1
1
1
1
2
1
0
1
2
1
1
1
0
1
1
0
0
1
0
1
1
7
4
1
1
1
1
1
2
2
2
1
0
1
1
1
1
1
2
2
2
2
0
1
1
1
1
3
1
1
2
1
0
0
1
1
3
2
0
1
1
2
1
2
1
2
0
0
1
2
1
1
1
1
2
2
2
0
1
1
2
1
0
1
1
2
1
0
1
1
0
1
1
1
1
0
1
2
2
1
1
0
1
0
0
1
1
1
3
0
0
0
1
1
0
0
1
2
1
1
2
1
2
0
2
1
1
1
2
0
1
2
1
2
0
0
1
1
1
0
0
1
1
1
0
2
2
1
1
2
2
1
1
0
1
0
0
1
1
2
1
1
1
0
0
1
2
1
0
1
1
2
0
1
1
1
0
1
1
2
0
1
1
1
2
1
1
0
0
1
1
1
1
2
1
2
1
0
2
0
1
1
1
1
1
2
0
1
0
2
1
1
1
1
1
1
0
2
2
1
1
0
0
2
1
1
1
2
0
1
1
1
0
0
3
2
0
1
2
1
0
2
1
1
1
1
1
0
1
1
1
1
1
0
1
2
2
1
0
1
0
1
2
1
1
2
0
2
0
2
0
1
0
2
2
1
1
1
1
3
1
0
1
1
1
2
1
1
1
0
0
1
2
3
1
1
1
0
2
0
1
1
1
2
2
1
1
2
2
0
2
0
1
0
0
2
0
1
0
0
0
2
2
0
1
1
2
1
0
1
0
1
0
0
1
1
1
0
2
1
1
1
2
1
2
1
0
1
1
2
1
0
1
1
1
1
1
1
1
0
2
2
1
2
1
2
1
1
0
1
1
0
0
0
0
1
2
2
1
2
2
1
0
1
0
0
1
1
0
2
2
0
2
1
1
2
2
1
0
1
0
0
1
0
1
0
1
1
0
2
0
0
1
1
2
0
2
1
0
1
0
1
2
0
2
2
2
2
0
2
1
2
0
1
1
1
2
1
1
2
1
1
1
1
1
1
0
0
1
1
0
1
2
0
2
0
0
0
2
2
1
4
0
1
1
1
1
0
0
0
1
0
1
2
1
2
1
0
1
1
1
1
2
1
0
1
0
1
0
1
2
0
1
1
1
1
0
2
0
2
1
2
1
1
0
1
0
2
1
1
2
0
1
1
1
0
0
1
1
1
1
1
1
2
2
1
1
2
1
1
1
1
2
1
0
2
0
1
3
0
1
1
1
0
1
0
0
1
1
0
1
1
1
1
1
2
1
0
1
1
0
0
2
1
2
1
0
0
1
1
1
2
2
1
1
1
0
0
1
0
0
2
2
1
0
1
2
1
1
1
0
1
1
1
1
0
1
1
1
1
1
2
2
1
1
1
1
2
2
1
1
2
0
0
1
2
1
1
1
1
1
0
1
2
1
0
0
0
0
1
1
1
1
2
1
4
1
1
1
1
0
0
2
2
1
1
1
1
1
1
1
1
1
2
1
1
1
3
0
1
0
1
1
1
0
0
1
1
1
1
2
0
1
1
1
0
2
0
2
1
0
1
2
1
1
0
1
0
1
0
1
1
0
1
1
1
1
1
1
0
1
0
2
3
1
1
1
0
3
2
1
0
2
0
0
1
2
1
1
2
1
0
1
1
2
6
1
2
1
1
1
0
1
2
0
1
2
1
1
0
0
2
1
1
1
0
1
0
1
1
2
1
3
1
1
0
1
1
1
2
2
1
0
1
2
1
2
1
0
1
2
1
1
0
1
1
0
2
2
1
1
1
0
1
1
1
1
2
2
2
1
1
1
0
1
0
1
0
1
1
2
2
0
0
2
2
0
2
0
0
2
1
2
0
1
0
1
1
1
1
0
1
1
0
1
1
0
1
2
2
1
1
2
0
2
1
1
1
2
2
1
0
2
2
1
1
1
2
1
1
1
2
0
2
3
1
1
1
1
1
1
1
1
0
2
1
1
1
2
0
1
1
1
2
1
1
0
1
0
2
1
0
2
1
2
1
1
1
0
1
1
1
1
1
2
1
2
0
1
1
0
1
1
1
1
1
1
0
2
2
2
2
2
2
0
0
1
1
2
1
1
1
2
0
1
2
2
1
2
1
1
2
2
1
2
0
1
0
0
1
1
1
1
0
0
1
1
1
3
2
1
1
1
0
2
1
0
1
1
0
2
2
1
1
2
1
2
0
1
1
0
1
0
1
1
1
0
0
1
1
2
2
1
1
1
1
1
2
2
2
0
1
1
0
3
1
1
2
1
1
1
2
1
1
1
1
2
0
0
1
0
1
2
1
1
1
1
0
0
2
0
1
1
2
0
1
0
1
1
1
1
1
2
1
0
0
2
0
1
0
1
1
1
2
0
1
1
2
1
2
1
1
2
1
1
1
1
0
1
1
1
1
1
2
0
0
0
1
2
0
2
3
1
2
1
0
2
1
1
1
1
2
2
2
1
1
2
1
1
1
4
1
1
0
2
1
1
2
1
2
2
0
2
0
0
0
1
1
2
0
1
1
0
0
2
1
1
2
1
1
1
1
1
1
1
1
2
2
0
1
1
0
1
1
1
1
1
2
0
1
1
2
2
0
2
1
0
2
1
2
2
0
1
1
0
1
2
1
2
1
0
1
1
0
1
1
2
2
0
0
2
1
1
1
1
0
1
1
0
1
1
2
1
0
0
0
2
2
1
2
1
0
0
1
1
1
1
0
2
1
0
2
2
1
1
1
1
1
0
0
2
0
1
2
2
0
1
1
1
2
0
0
1
1
0
1
0
0
0
2
1
1
1
1
2
2
1
1
2
1
0
0
2
2
1
0
1
1
2
1
2
1
1
1
1
2
1
2
1
0
2
1
2
1
2
0
1
1
1
1
0
1
1
0
2
1
1
1
2
1
2
2
1
1
0
0
1
1
1
0
1
0
1
1
1
1
1
2
1
1
1
0
1
1
1
1
2
1
0
1
0
1
2
1
1
1
1
2
1
1
2
1
2
1
0
0
2
1
1
1
1
0
1
1
2
1
0
0
2
2
1
1
1
2
1
2
2
0
2
1
1
2
1
0
0
0
2
1
1
0
1
1
1
1
2
1
2
0
2
3
0
0
0
1
0
1
1
0
1
1
1
0
2
1
1
1
0
1
2
2
2
0
1
1
0
1
0
1
1
2
1
1
1
1
1
2
0
1
0
1
1
2
1
1
1
0
0
1
0
2
0
0
0
2
1
1
2
1
1
0
1
0
1
1
2
0
0
1
0
1
0
1
2
0
2
1
4
0
2
2
1
1
0
1
1
1
2
0
1
3
2
1
1
1
1
0
1
2
0
2
0
1
1
1
0
0
0
1
1
1
2
0
2
2
1
1
2
2
2
2
0
0
1
1
1
1
2
1
1
1
1
1
1
0
1
0
1
2
3
2
2
0
1
1
2
1
2
1
0
1
1
1
2
1
1
2
1
2
1
0
2
0
1
1
1
1
0
1
2
1
0
1
1
0
1
0
1
2
1
0
1
1
0
2
2
1
0
1
1
1
1
0
1
2
1
1
0
1
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
2
4
0
1
0
2
1
1
0
1
0
1
0
1
0
2
2
2
1
1
0
2
1
1
1
1
1
0
2
0
2
1
1
1
0
2
1
1
1
1
0
0
2
0
1
0
1
1
0
0
0
1
1
1
1
0
1
0
2
1
2
1
1
1
2
0
1
0
3
2
3
1
0
0
0
0
1
1
2
1
0
2
1
0
2
1
1
3
1
2
0
2
0
1
1
1
0
1
1
0
1
1
1
2
1
1
1
0
0
1
1
3
3
1
2
0
2
1
0
2
1
1
2
1
0
1
1
1
1
1
1
0
1
1
1
0
1
1
1
2
0
1
0
1
0
2
1
1
2
1
0
0
2
0
1
1
1
1
1
3
1
1
0
1
0
2
1
1
2
2
0
1
2
1
2
1
0
1
1
0
1
0
0
1
2
0
0
2
0
2
1
0
1
2
1
1
1
0
1
2
2
1
1
1
1
1
1
1
2
0
1
1
0
1
2
1
1
1
0
2
1
1
1
0
2
2
1
2
2
1
2
0
1
2
0
1
1
0
1
1
1
1
1
1
2
2
1
0
2
0
1
1
1
0
1
2
1
1
1
1
0
1
0
0
1
2
2
1
2
2
1
0
1
0
1
1
1
0
3
0
2
1
0
2
0
2
0
0
1
0
2
1
2
1
2
1
1
2
2
1
0
1
1
1
1
2
2
1
1
2
0
2
1
1
1
2
2
1
0
1
2
1
1
2
1
0
0
0
1
1
0
2
1
1
1
0
1
0
1
1
2
1
1
1
0
0
2
1
2
1
1
1
1
1
2
1
0
1
0
1
2
1
0
1
1
2
1
1
2
1
1
2
2
0
2
1
2
0
0
1
2
1
1
2
0
1
1
1
1
2
2
1
0
0
1
1
1
0
1
1
0
1
2
0
1
1
2
1
0
1
1
1
2
2
0
1
2
1
1
1
1
0
0
1
1
1
0
1
0
1
1
1
2
1
1
1
1
1
2
0
1
1
1
1
1
2
1
1
0
0
0
2
1
2
1
0
0
2
1
1
1
1
0
1
1
2
2
2
0
2
2
1
0
2
1
2
1
2
0
2
2
0
2
0
1
0
1
2
2
0
0
0
1
1
2
0
0
2
2
1
1
1
1
2
1
1
0
0
1
2
1
0
1
2
1
1
2
1
1
2
1
0
0
1
1
1
1
0
2
0
1
2
1
1
1
1
1
1
1
1
2
1
2
0
1
1
1
1
1
2
1
1
2
2
1
1
1
1
1
2
1
1
0
1
0
2
1
2
1
1
0
2
2
1
2
0
1
1
2
0
1
2
0
1
0
1
0
2
1
1
0
0
1
1
2
1
0
0
2
1
1
0
1
1
2
1
1
2
0
1
2
1
1
2
2
0
1
0
1
3
0
0
0
2
1
0
2
1
0
2
1
1
0
6
0
2
1
1
1
0
1
1
2
2
1
1
0
1
1
2
1
1
2
1
1
1
0
2
1
2
0
1
0
0
1
1
0
1
2
1
0
1
1
1
2
1
0
1
0
0
0
2
2
1
1
2
1
2
1
0
1
1
0
1
1
3
0
1
2
1
1
2
1
1
0
1
1
1
1
1
1
0
2
1
1
2
1
0
2
2
1
2
2
0
1
1
1
0
1
1
2
0
1
1
2
1
1
1
1
1
0
2
0
1
1
2
7
1
2
1
2
0
2
2
2
1
1
1
2
0
1
1
0
1
0
1
1
1
1
1
1
2
2
0
0
1
0
1
1
0
3
1
2
0
1
0
2
1
2
2
1
1
2
1
1
2
2
2
1
0
0
1
1
1
1
2
2
0
0
0
2
1
1
0
1
1
1
2
0
1
1
2
0
1
1
1
1
1
1
1
2
2
2
0
2
1
1
0
0
1
0
0
1
2
2
0
0
1
2
1
2
0
0
1
1
1
1
0
0
1
2
1
0
1
1
0
1
1
1
0
1
1
2
1
0
2
1
1
0
1
0
0
0
0
2
2
0
0
2
0
0
0
2
1
0
1
1
2
0
0
1
1
0
0
0
1
0
1
1
2
1
1
1
0
1
1
0
1
1
2
0
1
1
1
0
1
2
0
1
1
1
1
1
1
0
2
2
0
1
2
2
2
1
3
1
2
2
1
1
1
0
0
0
1
1
0
0
0
1
1
0
1
1
1
1
3
1
1
1
0
0
1
0
0
2
1
2
0
1
1
1
1
0
0
2
0
3
1
2
1
1
1
1
2
1
1
0
1
2
1
1
1
2
2
2
1
1
1
1
1
2
2
1
2
1
2
2
1
2
1
1
3
2
0
2
1
1
1
1
2
1
2
2
2
0
1
2
1
2
1
0
1
1
1
1
1
2
2
0
1
2
0
1
1
1
1
1
0
0
0
1
1
2
1
2
1
1
1
1
2
2
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
1
0
0
0
0
1
0
0
1
1
0
2
1
2
2
1
0
1
2
1
1
1
0
2
1
1
2
2
1
1
1
0
2
0
1
0
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
2
1
2
0
1
1
2
1
1
1
1
1
0
1
1
1
1
1
1
1
0
2
1
1
2
1
0
1
1
1
1
1
1
1
2
1
0
2
1
0
1
1
0
0
0
1
0
1
2
1
0
1
1
0
1
0
2
0
2
2
2
1
0
1
1
1
0
1
2
1
1
0
1
1
1
1
0
1
0
0
1
1
1
1
2
1
2
1
1
0
2
1
1
2
1
1
1
1
1
1
2
0
0
1
0
1
2
1
1
2
0
1
0
0
2
1
1
1
2
1
1
1
0
1
0
1
1
0
1
2
2
1
1
1
1
0
0
1
1
1
1
1
1
1
2
0
2
1
1
1
1
1
1
1
0
1
1
1
0
0
2
1
2
2
2
1
1
2
0
3
2
0
1
1
2
1
1
2
1
2
1
1
0
0
0
0
2
1
0
1
1
1
2
0
2
2
1
2
1
1
1
2
0
1
2
1
2
0
1
1
2
2
1
1
1
1
2
1
1
2
0
1
0
0
1
0
1
0
2
1
1
1
0
1
0
2
0
2
0
2
2
2
1
1
0
1
1
0
1
1
1
0
1
1
2
0
1
0
0
0
1
1
0
1
1
0
0
2
2
2
1
0
2
1
0
2
0
2
2
1
0
1
1
0
1
2
1
0
2
1
2
2
1
2
1
2
2
2
2
1
1
4
1
0
1
2
1
1
1
1
0
1
0
1
2
2
1
2
0
1
1
1
1
1
2
0
0
0
0
0
0
2
0
1
1
0
1
0
1
2
1
0
0
2
1
0
1
0
1
0
0
1
1
1
1
0
1
2
1
1
2
1
1
1
1
1
0
1
2
1
1
1
1
1
2
1
0
0
0
2
1
1
1
0
2
0
1
0
1
1
1
0
2
2
0
2
1
1
1
1
0
1
2
1
1
3
0
0
1
1
0
1
1
1
1
2
2
1
1
0
1
1
1
1
2
3
1
0
2
1
2
1
0
1
1
1
0
1
3
1
1
1
1
2
1
1
1
1
1
0
1
1
2
1
2
1
2
2
2
1
2
1
2
0
0
1
0
1
1
2
1
2
1
2
1
1
1
1
0
0
2
0
2
1
2
0
2
2
1
0
1
1
2
1
0
1
1
1
0
0
2
1
1
2
0
0
1
0
2
1
1
0
1
1
0
1
2
1
0
1
1
2
1
1
1
1
1
1
1
1
1
0
2
1
1
1
1
2
2
1
0
1
2
1
0
1
1
2
1
1
1
1
1
0
1
1
1
1
2
1
2
1
1
0
0
1
1
1
2
1
2
0
2
1
1
1
1
1
2
1
1
1
2
1
1
1
0
0
1
0
1
2
2
1
2
1
1
2
0
1
1
1
1
1
0
1
1
1
0
1
2
2
1
1
1
1
2
1
2
1
1
2
2
0
1
2
0
0
1
1
0
1
0
1
1
2
1
1
1
1
1
2
2
0
1
1
1
2
0
0
2
2
1
1
0
1
1
2
1
1
1
2
1
1
2
0
0
0
1
2
1
1
1
1
0
1
0
1
1
0
0
0
1
0
2
0
2
2
0
1
0
0
1
1
1
0
1
1
0
1
1
4
0
2
1
2
1
0
1
1
1
1
0
2
1
1
2
1
1
0
1
0
0
0
0
1
2
0
1
1
1
1
0
1
1
2
1
1
2
1
0
2
1
2
0
2
0
1
2
1
1
0
1
1
1
0
0
1
2
0
1
1
1
1
0
1
1
1
1
0
2
0
1
1
1
0
1
0
1
1
0
0
1
1
1
1
1
0
1
1
1
1
1
2
1
1
0
1
2
1
1
1
3
2
1
2
2
0
1
0
0
1
2
4
2
0
1
1
1
1
1
1
1
2
1
1
2
2
2
1
1
1
1
2
1
1
0
1
1
0
2
2
1
1
1
1
0
1
1
1
1
0
2
0
0
1
0
1
2
4
1
1
0
1
1
1
0
1
2
0
1
0
1
1
1
1
0
1
1
1
2
1
1
0
1
0
1
1
1
0
1
1
2
2
2
1
1
2
0
1
1
0
1
1
1
1
0
1
1
1
1
0
1
1
2
1
2
1
2
1
1
1
2
1
1
0
2
3
1
2
1
2
0
1
1
2
1
1
0
1
1
2
1
2
2
1
1
1
2
2
1
1
1
2
1
1
0
1
1
1
2
0
1
1
0
0
0
2
0
2
0
1
1
2
2
1
2
1
1
2
1
0
1
1
2
1
1
2
0
0
0
1
1
0
2
1
1
2
1
2
0
1
1
1
2
0
1
1
1
2
1
1
1
1
1
1
1
1
2
2
0
1
0
1
2
1
2
1
0
1
1
0
2
2
1
1
1
1
2
2
0
2
2
1
1
2
1
1
1
1
0
0
2
1
2
0
0
1
0
2
2
2
1
2
0
1
1
1
1
1
1
2
1
0
2
0
1
1
2
2
1
1
1
0
1
1
1
0
1
2
1
1
4
0
1
1
2
1
0
0
1
1
1
2
1
2
1
1
1
1
2
2
1
0
0
1
0
2
1
1
1
1
1
1
1
0
2
1
2
1
2
1
2
1
1
1
1
3
1
1
2
1
1
1
2
1
2
0
1
1
0
2
0
2
0
1
1
1
1
3
1
1
0
2
2
1
1
2
1
1
1
0
1
1
2
0
1
1
2
0
1
2
2
1
1
1
2
0
1
2
1
1
1
1
1
2
0
1
1
1
1
1
1
1
2
2
0
1
1
2
2
0
1
2
1
1
1
0
1
0
1
1
2
2
0
1
2
1
1
2
1
1
2
1
0
0
1
2
1
1
2
1
1
1
0
2
1
2
1
0
2
0
1
2
1
1
1
4
0
1
1
2
0
1
1
1
1
0
1
2
2
0
2
1
2
1
1
1
4
1
0
0
1
1
1
1
0
1
1
1
0
1
1
0
1
1
0
0
1
2
1
0
1
1
1
0
0
2
3
0
1
2
0
0
0
1
2
1
1
1
0
1
1
2
1
1
1
0
0
2
1
1
1
1
0
1
1
0
0
5
1
0
1
2
1
1
1
1
1
1
1
1
1
1
2
0
0
1
1
0
1
0
1
1
1
2
1
1
2
1
0
2
1
1
2
0
1
0
1
1
1
0
2
1
2
1
1
0
2
1
1
1
2
1
2
1
0
2
1
1
1
2
1
2
1
1
0
3
3
2
0
0
2
1
1
1
0
1
0
2
2
2
1
0
2
1
0
1
1
1
1
0
1
0
1
2
0
2
0
2
1
1
0
1
1
2
0
1
1
0
2
1
1
0
1
1
0
1
1
0
1
1
1
1
0
2
1
1
2
3
1
1
0
1
1
0
0
0
2
1
1
1
0
2
2
1
0
1
0
1
1
1
2
1
1
1
3
2
1
1
2
0
2
0
2
1
1
0
1
1
0
2
1
0
1
1
1
1
1
1
1
1
1
2
1
0
0
1
2
1
0
1
0
1
0
1
1
2
2
1
0
2
1
2
1
0
2
2
1
1
1
1
1
1
1
1
1
1
0
3
1
4
1
1
1
2
2
1
1
2
2
1
1
2
1
0
1
1
1
1
1
0
2
1
2
0
2
2
1
1
2
1
1
1
3
0
1
2
2
2
0
1
2
0
1
1
2
1
1
1
0
1
1
2
2
0
0
2
0
1
2
1
1
2
2
1
1
1
1
1
0
0
0
1
1
1
2
1
1
1
1
1
1
0
1
0
1
1
1
1
0
0
1
1
1
1
2
2
1
1
1
0
1
1
1
2
1
1
1
2
0
1
0
0
3
2
2
0
2
1
2
1
0
2
0
1
1
1
1
1
0
0
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
3
1
1
0
1
1
2
1
1
1
0
0
1
1
2
0
1
1
0
0
1
1
2
1
1
1
1
2
1
1
1
1
0
1
1
1
1
2
1
2
1
1
0
2
1
2
2
1
1
1
0
2
1
2
1
0
0
0
1
1
1
1
1
2
0
1
1
1
0
1
1
1
2
0
1
0
0
1
1
1
1
1
2
1
0
0
0
1
1
1
1
1
1
1
2
1
2
1
2
2
1
1
1
2
2
2
1
0
1
2
1
1
0
1
2
0
1
1
2
1
2
1
1
1
1
2
1
1
1
1
0
1
0
0
1
1
2
1
1
2
2
2
2
2
2
1
0
1
1
0
2
1
1
1
0
1
1
0
2
1
1
1
0
2
2
1
1
1
2
0
0
0
2
4
1
3
1
1
0
1
2
2
1
1
1
1
2
1
1
2
2
2
1
0
1
0
1
1
1
0
1
1
0
0
1
0
1
2
2
1
1
1
0
1
1
3
0
1
1
1
1
1
2
1
1
1
1
1
0
1
1
1
1
2
1
1
1
2
1
1
2
1
2
1
2
1
1
1
2
1
3
1
2
1
1
1
2
1
2
0
2
1
1
1
2
2
1
1
1
0
0
2
1
1
1
1
1
0
1
2
0
1
0
1
1
1
1
1
2
0
1
1
2
2
1
2
1
0
1
1
1
1
1
2
1
2
2
2
0
1
2
2
0
1
1
2
2
2
1
1
1
2
2
1
1
2
1
1
0
2
1
2
2
2
1
1
2
1
1
1
1
1
1
2
0
2
0
1
2
2
2
1
1
0
0
2
1
2
2
1
1
1
2
1
1
1
1
0
1
0
2
0
1
2
0
1
2
1
1
0
0
2
1
2
1
1
2
1
1
1
1
0
1
1
2
0
2
1
0
1
1
1
1
0
1
2
0
2
2
0
1
1
1
1
1
1
0
1
0
1
1
1
1
1
1
1
1
1
0
2
0
1
0
1
2
2
1
0
1
1
2
1
0
0
2
1
1
1
0
2
2
0
0
2
1
1
2
0
1
1
1
0
1
0
2
2
1
1
1
1
0
1
1
1
1
2
3
0
0
0
1
1
0
1
0
1
1
1
1
2
2
1
2
0
0
1
1
1
0
1
1
0
1
1
1
2
0
0
1
1
2
1
1
0
0
0
2
1
0
0
1
1
1
0
2
1
1
1
1
1
2
1
0
0
1
1
1
2
2
1
1
0
1
1
1
1
2
2
1
0
1
2
0
0
1
1
1
2
1
2
2
2
1
0
1
1
1
2
1
0
1
1
1
1
2
2
1
0
2
0
1
1
1
2
2
1
0
0
1
1
2
0
0
0
1
1
0
2
2
0
2
0
0
1
1
1
2
1
2
2
2
2
1
3
0
1
1
2
1
1
1
2
0
1
1
1
1
1
1
1
2
1
0
2
0
1
1
1
1
2
0
1
2
1
1
2
2
0
0
0
1
3
1
3
0
2
0
0
0
0
0
1
1
1
0
0
0
0
1
1
0
1
0
0
1
1
1
1
1
1
1
0
1
1
0
1
1
1
2
1
0
2
1
1
0
2
1
0
2
1
0
2
1
1
1
1
1
0
0
1
1
0
1
2
0
1
2
1
2
0
1
1
0
1
2
1
2
1
2
0
2
2
2
1
2
2
0
0
1
1
2
1
1
1
0
1
2
1
2
1
1
2
1
1
1
0
0
2
0
1
0
2
2
1
0
1
0
0
0
2
1
1
0
0
1
2
1
1
1
1
1
1
0
0
1
1
2
1
2
0
1
1
2
1
2
1
0
1
1
2
0
1
1
2
0
1
1
1
0
2
1
0
1
2
2
1
1
1
1
1
1
1
0
0
2
0
0
1
0
1
0
2
1
1
0
1
0
1
1
3
1
1
1
0
0
2
2
0
0
2
1
2
1
2
1
1
0
1
0
0
4
3
1
2
1
0
2
0
0
1
1
1
1
1
2
1
1
1
1
1
0
0
0
2
1
2
1
1
0
1
2
2
1
3
1
2
2
1
2
1
2
1
2
1
0
2
0
1
1
1
1
0
2
2
1
2
0
2
1
1
2
1
1
2
1
1
0
2
1
0
1
1
1
2
2
0
1
2
0
1
0
1
1
1
2
0
1
0
0
2
2
2
1
0
2
1
1
1
2
1
1
1
2
1
1
0
1
0
0
1
1
0
1
0
1
0
0
0
0
1
1
2
0
1
0
1
1
1
1
2
1
0
0
1
1
0
1
1
2
2
1
3
1
1
1
1
0
1
1
1
1
1
1
0
1
1
2
1
1
2
2
2
0
1
0
1
1
0
1
1
1
1
2
1
2
1
1
1
0
1
1
0
2
2
1
1
2
0
1
2
1
5
2
2
1
1
0
1
0
1
0
0
0
0
1
1
1
1
2
1
0
1
0
2
1
5
1
1
0
1
0
0
1
1
1
1
1
1
2
1
1
2
1
0
0
0
1
1
2
1
1
1
1
2
2
0
0
0
0
2
1
1
1
1
2
0
1
1
2
0
0
0
0
1
1
0
0
1
1
0
1
1
0
1
1
2
1
0
2
0
2
2
1
1
0
0
1
2
2
0
1
2
2
0
2
1
1
1
0
0
1
1
1
1
1
0
0
3
1
1
1
1
1
0
0
2
1
0
1
2
2
1
2
1
2
2
1
2
2
1
0
1
1
1
0
1
0
0
2
1
1
0
0
1
0
2
0
2
0
0
1
1
0
1
2
1
1
0
2
1
0
1
1
0
1
1
1
2
2
0
1
1
2
1
1
0
0
1
1
1
1
0
0
2
1
0
2
2
2
1
1
1
1
1
2
2
1
2
0
1
2
0
2
1
0
1
0
1
4
1
1
1
0
2
1
2
2
2
1
1
1
0
1
2
0
1
0
1
0
1
2
1
2
0
2
2
1
0
1
1
1
2
1
1
1
1
0
0
1
2
1
2
3
2
0
2
2
2
1
0
1
1
2
2
1
2
1
1
1
1
1
1
1
1
0
1
1
0
1
2
2
1
1
0
0
1
1
1
1
1
1
0
2
1
0
1
0
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
0
1
1
0
1
1
1
2
1
0
2
1
2
0
0
1
2
1
1
0
1
2
1
0
2
2
0
0
1
1
2
0
1
0
2
1
0
1
1
1
1
1
1
2
0
2
1
0
1
2
0
2
0
1
1
0
1
1
0
1
1
1
1
0
0
1
1
1
1
1
1
1
0
1
2
0
2
0
1
1
1
0
1
1
2
1
0
1
1
1
2
1
2
1
2
1
2
1
2
1
1
1
0
1
1
1
1
1
1
0
1
2
1
0
0
0
2
1
2
4
1
1
1
1
1
0
1
2
2
1
1
3
0
2
0
1
1
1
1
2
1
2
2
1
0
1
1
1
0
1
1
1
1
2
1
1
1
0
1
1
0
1
1
1
1
1
0
2
1
1
2
0
1
0
1
2
2
1
2
1
1
2
0
0
2
0
1
0
1
3
1
1
2
2
1
1
1
1
2
2
2
1
1
1
1
1
0
2
1
1
2
1
1
0
2
1
1
1
1
1
0
2
1
2
1
1
1
0
1
0
0
0
0
2
1
2
1
0
1
2
1
1
1
1
1
1
1
1
0
2
2
1
1
2
2
1
0
2
1
0
0
1
1
2
1
0
2
1
0
2
1
1
2
2
1
2
1
1
0
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
1
2
2
1
1
1
1
2
1
2
1
1
1
1
0
1
1
1
1
0
1
2
1
0
0
1
1
1
1
2
1
2
1
1
1
1
2
1
1
3
1
1
1
2
2
1
2
2
1
2
1
2
0
1
1
1
1
1
0
1
2
1
2
1
1
2
0
0
1
1
1
1
0
1
0
2
1
0
1
1
2
1
0
2
1
1
1
1
1
2
1
1
0
1
1
2
2
1
1
0
0
0
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
0
1
0
1
1
0
2
1
1
2
0
1
0
0
1
1
1
0
1
0
2
1
0
1
2
0
1
2
1
1
1
1
1
2
1
1
0
1
0
2
1
2
0
2
0
1
1
1
0
2
1
1
1
0
0
2
1
1
2
1
1
2
2
2
1
0
1
1
1
2
2
0
1
0
0
1
2
2
1
2
0
2
1
1
1
2
0
2
1
2
2
2
1
0
1
2
1
1
1
1
1
0
1
1
0
0
2
2
0
1
1
1
2
1
1
1
1
0
0
2
0
2
0
1
0
1
1
1
2
1
1
0
1
1
1
1
1
1
1
2
2
1
1
1
0
2
1
1
1
1
2
1
1
2
1
2
1
2
1
0
2
1
1
2
2
0
0
1
1
2
2
1
0
1
0
2
2
1
1
0
1
0
0
1
1
0
2
0
1
2
2
1
1
0
0
1
2
1
1
0
3
1
1
0
2
0
0
2
2
2
2
0
0
1
0
1
2
0
1
0
2
1
1
2
1
1
0
2
2
0
0
2
1
0
1
0
1
1
2
1
1
1
0
0
1
2
1
2
1
1
0
1
0
3
1
2
2
0
1
2
2
0
1
2
1
1
2
1
2
2
1
1
1
0
0
1
0
1
1
1
0
1
1
0
1
1
0
1
0
2
1
2
1
1
0
2
1
1
1
1
1
2
2
1
2
1
1
0
0
2
0
1
1
2
1
1
1
2
1
1
2
2
1
2
2
1
1
2
1
1
1
0
1
1
2
1
1
1
1
0
0
0
1
3
2
1
0
1
1
2
1
2
1
2
1
0
1
1
1
0
1
1
0
0
1
1
1
0
2
1
1
0
2
2
2
1
1
2
1
0
1
2
1
0
1
0
1
1
1
1
1
2
1
1
1
5
1
0
0
0
1
2
3
1
1
2
2
2
1
2
1
1
2
1
1
0
0
1
3
1
2
0
2
2
1
0
1
2
1
2
2
1
1
1
2
1
1
0
1
1
1
0
1
1
2
1
1
1
1
1
2
2
0
1
0
1
1
0
3
2
0
0
1
1
1
1
1
0
1
1
1
0
0
0
2
2
1
2
0
1
1
1
1
2
2
2
1
1
1
2
1
0
2
0
0
0
1
1
0
1
2
0
1
0
1
1
1
0
1
1
0
1
1
1
1
2
2
1
0
1
1
1
0
1
1
1
0
1
2
2
1
0
1
1
0
0
1
0
1
2
1
1
1
0
1
2
0
1
1
1
1
2
1
0
1
1
2
1
1
0
0
1
1
0
0
1
1
1
2
0
1
2
1
1
2
3
0
1
1
1
1
1
2
2
2
2
0
2
2
1
0
0
2
0
1
0
1
0
2
0
0
1
0
1
0
1
1
1
0
1
0
2
1
2
2
2
2
1
2
2
1
1
1
0
3
1
2
2
0
2
1
2
0
0
1
0
2
2
1
0
1
1
1
2
1
2
2
0
2
1
0
2
1
2
1
2
2
0
1
0
2
0
0
2
1
1
1
1
0
1
0
1
1
1
2
1
1
1
0
1
2
1
1
0
0
0
0
1
1
1
1
1
0
1
1
1
1
1
1
0
0
0
1
0
1
1
1
0
0
1
1
0
1
1
0
2
1
1
0
1
2
1
1
0
0
2
2
1
1
1
1
1
0
2
1
0
3
1
1
0
1
0
1
2
1
1
1
1
2
1
2
0
1
1
0
1
1
1
1
1
2
1
2
2
1
1
1
0
1
2
2
1
2
1
1
1
2
1
1
2
1
1
0
2
2
1
2
1
0
0
1
1
1
1
1
1
1
0
1
1
0
1
1
1
2
2
0
0
1
2
1
1
1
0
1
1
2
1
1
1
1
3
1
1
0
2
2
2
1
0
1
1
2
1
1
1
1
1
2
0
1
1
1
1
1
3
0
2
2
1
1
1
0
1
2
2
1
1
2
1
0
1
1
0
0
1
2
1
1
1
0
2
1
0
2
0
2
2
0
2
1
1
1
1
2
1
1
2
1
1
0
1
1
1
1
2
0
1
2
1
1
2
1
1
0
1
1
1
2
1
1
2
1
1
2
2
0
2
1
1
1
0
1
0
1
1
2
1
0
1
1
1
0
2
1
2
2
2
1
1
1
0
1
1
1
1
0
1
1
2
1
1
2
1
0
2
1
1
0
1
1
0
2
0
1
2
1
1
4
1
0
2
0
1
1
0
2
0
2
1
1
1
1
0
2
1
1
0
0
1
1
1
0
1
2
2
0
0
1
1
1
1
2
1
0
1
0
1
0
2
1
1
2
2
1
1
2
0
2
0
0
1
0
0
1
2
1
2
2
1
0
0
2
1
1
1
3
2
1
1
1
1
1
1
0
0
1
2
1
2
1
0
1
1
1
1
0
0
2
1
1
2
2
2
1
1
1
2
1
1
1
1
0
0
0
1
1
2
2
0
2
0
1
1
2
2
1
0
1
1
0
1
2
2
2
1
0
2
0
1
1
2
1
1
1
1
1
0
0
1
2
1
2
1
0
1
0
0
2
0
1
2
0
1
2
0
1
0
1
1
1
0
1
0
0
2
1
1
0
1
1
1
1
1
2
0
1
2
0
0
1
2
1
0
0
2
1
1
0
1
1
1
2
2
1
1
0
1
2
2
1
0
2
0
2
1
2
2
2
1
0
2
1
1
1
1
2
1
1
2
2
1
1
1
1
0
0
1
1
1
1
1
1
1
1
1
1
2
0
1
1
1
1
2
1
0
1
2
1
2
1
1
2
2
0
1
1
1
1
2
1
1
2
0
2
0
2
1
1
1
2
0
1
0
1
1
0
1
0
0
1
0
1
0
1
2
1
2
3
0
1
0
1
0
0
1
1
1
2
0
0
1
0
1
1
1
1
2
1
0
1
1
0
0
2
1
0
0
1
0
2
2
1
1
1
0
1
1
2
1
1
1
2
2
0
0
1
1
0
1
1
1
1
0
0
0
2
2
2
1
2
0
2
0
1
0
1
1
2
1
0
1
1
0
1
1
2
1
1
0
1
2
1
0
2
0
2
1
0
2
1
2
2
0
1
0
1
1
2
1
1
1
1
1
1
0
2
1
1
0
1
1
2
2
0
0
0
2
1
1
1
1
1
1
1
1
1
1
1
0
0
1
0
1
2
1
2
1
1
0
1
0
2
1
1
1
0
0
2
1
1
1
0
2
1
0
0
2
2
0
0
1
1
1
1
1
1
1
0
2
1
1
1
1
0
1
0
1
1
1
2
1
1
1
0
0
0
0
2
1
1
0
0
1
0
2
2
1
1
1
1
0
0
0
1
1
1
1
1
1
1
1
1
2
1
1
1
0
1
1
1
1
0
2
1
1
2
1
0
1
2
2
1
1
1
1
1
0
0
2
1
1
1
0
1
2
1
1
1
1
2
2
2
1
1
0
1
1
1
0
1
0
1
1
1
1
2
1
2
1
0
1
0
0
1
2
2
1
4
1
2
1
1
3
1
2
0
1
3
0
1
2
1
1
1
2
1
1
1
1
3
0
1
1
1
0
1
0
2
0
1
1
2
1
1
0
0
1
0
2
1
2
0
1
1
1
2
0
1
2
1
2
1
1
1
0
1
3
0
1
1
2
1
1
0
1
2
1
3
1
2
2
1
2
0
2
1
2
0
1
1
1
1
2
0
1
0
2
0
3
1
1
1
1
0
1
1
1
1
2
2
2
0
0
1
2
1
2
1
1
1
1
1
1
0
1
1
2
1
2
1
6
1
2
1
0
1
1
0
2
1
1
2
0
1
0
1
1
0
0
0
1
0
2
1
2
1
1
1
1
0
0
0
2
1
2
1
0
2
2
1
1
1
0
2
2
1
0
2
2
1
2
0
1
3
1
2
2
0
1
1
2
1
0
2
1
2
1
0
1
1
2
2
1
1
0
1
1
1
0
1
1
0
0
0
1
1
0
1
1
1
1
0
1
1
1
1
2
1
0
1
0
1
1
2
0
1
2
1
0
2
2
0
1
1
1
1
0
0
0
0
1
2
1
0
1
1
1
1
1
2
2
0
2
1
1
1
1
2
2
0
2
1
0
0
2
2
0
2
0
1
2
1
1
2
0
1
2
0
2
1
1
1
2
2
2
0
0
1
2
0
1
2
1
0
1
0
1
1
1
1
1
1
2
0
1
1
1
2
2
0
1
0
0
2
2
2
0
1
1
0
2
2
1
1
1
0
1
0
1
1
1
1
1
1
1
1
1
1
1
0
2
0
0
1
1
1
0
1
0
1
0
2
1
0
1
1
2
0
2
0
1
0
1
0
2
1
1
1
1
0
1
2
1
0
0
1
1
1
1
2
0
1
1
0
1
1
1
0
1
0
2
1
1
0
0
1
0
1
1
2
1
2
2
1
1
0
1
0
1
1
1
1
1
1
0
1
1
2
1
1
1
2
0
1
1
0
1
1
2
1
2
0
1
2
2
1
2
1
2
1
0
1
1
0
0
1
1
2
1
1
1
1
2
2
1
2
1
1
1
2
2
1
0
1
0
0
2
1
1
8
0
1
0
1
1
1
1
0
1
1
0
2
1
2
2
1
0
0
0
1
1
0
2
1
2
1
1
1
1
0
1
1
1
0
1
1
2
0
1
2
1
0
0
1
0
2
2
1
1
1
2
1
0
1
2
1
1
1
0
1
2
2
2
1
2
0
1
1
2
2
1
1
1
0
2
1
0
0
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
0
2
0
1
1
2
1
0
0
2
2
1
1
1
0
0
0
1
2
1
1
1
3
1
1
0
2
1
0
1
0
1
2
2
1
1
2
0
1
1
0
1
2
1
2
0
1
0
1
1
2
1
1
0
0
2
0
0
1
1
0
1
1
2
0
1
1
0
1
1
0
0
1
1
1
1
2
1
2
1
1
1
1
1
0
2
2
1
1
2
0
4
1
1
1
0
1
1
1
1
0
1
0
2
1
1
2
2
1
1
2
0
1
1
0
0
1
1
2
1
1
1
2
1
1
1
0
1
2
1
1
2
1
1
0
2
2
1
0
2
0
0
2
1
0
0
1
0
0
1
2
1
1
1
1
2
1
2
1
1
1
1
0
2
6
1
0
1
0
1
0
1
1
1
1
0
2
1
0
1
2
1
1
1
0
1
0
1
1
1
1
1
1
2
1
0
0
1
0
1
2
1
2
1
2
1
1
0
1
0
1
1
0
1
0
1
1
2
1
0
1
1
1
1
1
1
1
1
1
2
1
0
2
2
0
3
0
1
1
1
1
0
1
1
1
1
1
0
1
1
1
1
0
1
1
2
2
1
1
2
1
1
2
0
2
1
0
1
1
1
2
1
1
1
1
1
0
1
2
2
0
1
0
2
1
1
0
1
0
1
1
2
0
1
2
1
2
1
0
1
1
2
1
1
1
1
0
0
1
1
2
1
1
0
2
1
1
2
1
0
3
2
1
1
1
1
2
1
1
0
0
1
1
2
0
2
2
2
0
2
1
0
1
2
1
1
2
0
8
2
2
1
1
0
2
0
0
1
0
0
2
1
1
2
0
1
1
1
1
1
1
2
0
1
2
1
1
1
1
4
1
0
1
0
0
0
1
1
1
1
1
1
1
2
0
1
1
1
1
2
2
1
0
1
1
1
1
1
1
1
1
0
1
1
2
1
2
1
0
1
1
1
1
2
1
2
1
2
2
0
0
1
1
2
1
2
1
0
1
1
2
1
1
0
1
2
2
0
1
2
2
1
2
1
1
1
2
0
0
0
1
1
1
1
2
0
2
0
1
1
2
1
0
1
1
1
1
2
1
2
1
1
1
4
2
1
0
2
2
1
3
2
1
0
1
1
1
1
2
0
0
2
1
1
1
0
0
1
2
2
2
0
2
1
1
1
1
2
2
1
1
1
2
2
1
1
2
0
1
1
0
1
0
1
1
2
1
0
1
0
1
2
2
0
1
0
1
1
1
1
0
2
2
1
2
1
0
0
1
1
0
2
1
2
1
1
1
1
1
1
1
1
0
1
0
1
1
2
1
1
1
2
0
2
0
2
1
1
4
2
1
1
0
1
2
1
0
1
0
1
1
0
1
0
2
2
1
1
1
2
1
1
1
2
1
2
1
1
2
1
2
2
1
1
0
2
0
1
2
1
1
1
2
1
1
0
2
2
1
1
0
0
0
1
2
0
1
1
1
1
1
2
1
0
1
1
1
1
1
1
1
0
0
1
0
1
1
0
1
1
2
1
1
0
0
1
1
0
1
2
1
1
2
1
2
1
1
1
1
0
0
0
1
1
0
1
0
0
1
3
2
0
1
1
1
1
1
0
2
1
1
1
1
0
2
0
0
1
1
1
2
1
1
1
2
1
0
1
2
0
1
2
2
1
0
1
0
1
0
2
2
1
1
2
0
1
2
1
2
0
0
2
1
1
1
0
1
1
1
0
2
1
0
1
2
0
2
1
2
2
1
2
0
0
2
1
0
1
0
1
1
2
1
0
1
1
1
1
1
0
1
0
0
2
1
0
0
1
2
1
2
1
1
1
1
2
0
1
2
1
1
1
1
2
2
0
1
0
0
2
2
1
1
0
3
2
3
1
1
1
1
1
0
1
0
1
2
1
1
2
0
1
1
1
1
2
1
1
2
1
1
1
0
0
2
1
0
0
2
2
2
2
1
1
2
0
3
1
1
0
1
0
0
0
1
1
0
1
1
1
1
1
1
0
0
0
1
1
1
0
1
1
1
0
2
1
1
1
1
1
1
0
0
1
2
1
1
2
0
1
2
1
1
1
1
1
0
1
2
2
0
0
1
0
2
0
1
1
2
1
1
0
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
2
0
1
0
0
0
1
1
1
0
2
1
1
1
2
1
1
1
2
1
2
1
1
1
0
1
1
1
1
1
1
1
1
0
0
2
0
2
1
1
1
1
1
1
1
0
2
0
2
0
1
1
0
1
1
1
1
0
2
2
1
1
1
2
0
1
0
0
1
1
0
0
1
1
1
1
0
0
1
2
1
2
2
1
2
0
1
2
1
2
2
1
0
1
1
1
1
0
0
1
1
2
2
2
1
2
1
0
1
1
0
2
1
2
2
1
0
0
0
1
2
0
1
2
2
1
1
1
1
0
0
0
2
0
0
1
1
1
2
0
1
2
1
4
2
1
1
1
1
0
2
2
1
1
2
0
0
1
2
1
1
0
2
0
1
2
1
2
2
2
2
1
2
1
0
1
2
1
1
1
1
1
2
1
0
2
2
0
1
1
0
1
0
1
2
1
1
1
0
0
1
1
1
1
1
1
2
1
1
1
2
2
1
0
1
1
1
1
2
0
0
1
0
2
1
1
3
1
2
1
1
0
2
1
1
1
0
0
1
0
1
0
1
1
1
1
2
1
0
1
2
2
1
0
1
2
1
1
0
1
2
1
1
1
1
0
1
1
1
2
1
1
1
2
2
2
1
1
1
1
3
1
0
1
2
0
1
1
2
1
1
2
1
1
2
2
2
1
1
1
1
1
1
0
2
2
1
0
2
1
2
0
0
1
1
1
1
2
1
2
0
1
1
1
1
0
1
1
1
1
2
3
2
0
0
1
1
1
2
1
1
1
2
0
1
1
1
2
2
1
1
1
2
1
0
2
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
0
1
1
1
1
0
0
1
0
2
0
1
1
1
1
2
1
1
1
2
0
1
1
1
1
1
1
1
1
0
2
1
1
0
1
1
2
2
1
1
1
1
1
2
2
2
2
0
1
2
1
1
0
2
2
1
0
1
1
1
1
1
0
1
1
1
1
0
0
1
1
1
1
0
0
1
1
2
1
1
0
0
3
0
1
0
1
0
0
0
0
1
2
0
1
2
2
1
0
1
0
1
1
0
0
0
1
0
0
1
2
2
1
0
1
0
1
1
2
2
1
2
0
0
1
1
2
0
0
1
0
2
0
2
1
2
0
1
2
2
1
1
1
0
2
1
1
1
0
1
0
1
1
0
1
0
1
2
0
0
0
0
2
1
1
1
2
2
1
3
2
1
1
2
0
0
1
1
0
2
0
1
1
1
2
0
0
1
1
1
1
0
0
0
0
1
0
2
1
0
3
2
0
1
1
1
1
1
0
2
2
1
1
1
1
0
1
2
1
1
1
0
1
0
1
1
1
1
0
1
2
1
2
1
1
1
0
2
0
2
2
1
2
2
0
0
1
2
2
0
1
2
2
0
2
1
0
3
1
2
2
2
1
2
1
1
1
2
2
0
2
0
1
0
1
1
2
0
2
1
1
2
2
1
1
2
2
0
0
1
1
2
1
2
1
1
1
1
2
1
0
1
1
0
0
0
1
1
2
0
2
1
1
1
1
1
1
1
1
1
0
1
2
0
2
0
1
1
0
1
1
0
1
0
2
1
2
2
1
0
2
0
1
1
1
1
1
1
2
1
2
1
1
0
1
1
0
1
2
1
1
2
1
2
2
2
1
2
1
1
1
1
5
1
2
1
1
1
1
1
0
0
1
2
2
1
1
1
1
1
1
1
1
2
1
2
1
0
2
0
1
1
1
1
2
0
2
2
1
1
1
1
2
0
0
1
1
1
1
2
1
1
2
2
2
1
1
0
1
0
1
1
1
2
1
0
0
0
1
0
1
1
1
1
1
1
0
2
1
1
1
0
2
0
1
1
2
0
1
1
2
0
0
0
2
1
0
1
1
0
2
1
0
1
0
0
1
2
0
1
2
1
1
1
0
0
1
0
1
1
0
0
1
2
1
1
1
0
0
2
1
1
1
0
1
0
1
1
1
0
1
0
1
1
1
1
0
0
1
2
1
1
1
0
1
1
2
0
2
1
1
0
1
1
3
0
0
1
1
0
2
0
2
0
0
0
1
1
0
1
2
2
2
2
0
0
1
2
1
1
1
1
0
0
2
1
0
2
2
1
1
1
1
1
1
0
2
1
2
2
2
2
0
1
0
0
1
1
1
1
1
1
1
2
0
2
1
1
0
1
1
0
0
2
2
1
1
1
1
0
0
1
1
2
0
0
1
2
1
1
1
0
1
1
2
1
1
1
1
0
1
1
1
0
1
2
1
1
1
2
2
0
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
0
1
2
2
1
0
2
1
1
2
1
1
1
0
2
1
1
2
2
1
2
1
2
1
2
0
0
0
1
0
2
1
1
0
0
0
1
1
0
0
1
1
1
1
2
2
0
1
1
0
1
2
1
1
0
1
1
0
1
1
1
0
1
2
1
0
2
2
2
2
1
0
1
1
0
2
1
2
1
4
1
2
1
2
1
0
1
2
1
1
1
1
2
1
1
2
2
1
0
2
1
1
2
1
2
1
1
1
2
1
1
1
4
1
1
0
1
1
1
2
1
1
0
0
2
2
0
3
1
2
2
1
2
1
0
2
1
2
1
2
1
3
2
0
1
1
2
0
0
1
2
1
1
2
1
0
1
1
0
1
0
2
0
1
1
2
0
1
2
2
1
1
0
2
1
0
1
0
0
0
0
1
1
2
3
1
1
1
0
1
1
2
1
3
1
0
1
1
1
0
1
1
1
2
1
1
1
1
1
1
1
0
1
2
1
1
1
1
0
2
2
2
2
2
1
1
2
1
2
1
1
1
1
1
1
1
1
1
2
2
0
2
1
1
0
1
0
2
1
0
2
1
2
1
0
2
0
0
1
1
1
0
1
1
1
1
1
3
0
1
2
2
0
2
1
2
1
1
2
1
1
2
0
1
2
1
1
0
0
1
0
1
1
1
1
1
1
1
0
1
2
1
0
0
1
1
0
0
1
0
1
1
1
2
0
1
1
1
2
0
1
0
2
1
2
1
0
1
1
0
1
1
0
2
2
1
1
1
1
1
1
0
2
3
1
1
0
1
1
1
0
0
0
1
0
1
2
1
1
0
0
1
1
1
1
0
1
1
1
1
2
1
1
2
1
2
1
1
0
1
2
1
0
1
2
1
1
1
1
1
1
0
0
1
1
1
0
1
0
1
1
2
1
1
1
0
2
1
2
2
0
0
2
2
2
2
2
1
2
1
1
2
1
1
1
2
1
1
1
1
2
0
1
3
1
0
1
1
2
1
2
1
1
2
1
1
1
0
1
0
1
1
2
1
1
1
1
1
1
2
1
3
1
1
1
1
2
0
0
0
1
1
2
2
1
2
2
1
1
0
2
2
2
0
1
2
2
3
2
1
0
1
2
0
1
3
1
1
1
1
2
1
1
0
1
1
1
1
0
1
1
2
0
0
1
0
1
0
2
1
0
1
0
1
1
0
1
1
1
1
1
1
1
1
1
2
1
1
2
0
0
1
2
0
1
0
2
2
2
1
2
1
0
2
1
1
0
1
2
1
0
1
2
1
2
0
3
0
2
1
2
0
0
2
1
1
2
0
1
2
1
0
1
1
0
1
2
0
0
0
2
1
2
2
1
1
1
1
1
1
2
1
1
0
1
0
1
2
2
1
0
0
0
1
0
1
1
2
1
2
2
1
2
2
2
1
2
1
0
1
0
0
1
2
1
1
0
1
1
1
1
1
1
1
0
1
0
2
2
1
0
0
1
1
1
2
1
1
1
1
2
0
1
1
0
2
1
1
1
0
1
1
1
1
1
1
2
2
2
1
0
0
1
1
1
1
0
2
1
1
1
1
0
0
0
2
0
1
1
1
0
1
1
3
0
1
1
2
1
0
1
1
1
1
2
2
1
2
1
0
2
1
2
2
0
1
0
1
0
1
1
1
1
1
1
0
1
2
0
2
1
2
1
2
0
0
1
1
0
1
0
1
2
1
1
1
2
0
0
1
1
2
1
0
2
1
1
1
1
1
1
2
1
3
1
0
1
1
2
0
1
0
1
1
0
0
1
1
1
1
2
1
0
1
0
1
2
1
0
1
2
2
1
10
2
1
1
1
1
0
1
1
1
0
2
0
0
1
1
1
0
1
1
1
1
1
0
1
1
1
1
2
1
1
2
2
2
1
1
0
0
1
1
0
1
1
0
0
2
0
1
1
1
2
1
0
1
1
3
1
1
1
1
1
0
1
1
1
1
1
1
1
2
1
2
4
1
1
2
2
0
1
1
1
1
1
1
1
1
2
2
2
1
1
0
0
0
1
2
1
2
0
0
0
0
1
1
0
0
1
1
1
1
1
0
0
0
2
1
0
1
2
1
0
1
1
1
1
2
0
2
2
2
1
0
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
2
2
2
2
2
0
2
0
1
2
0
1
1
1
1
0
3
0
2
1
1
1
2
1
2
2
0
1
2
0
1
2
2
1
2
0
2
1
0
2
1
1
0
0
0
1
1
1
1
0
1
0
1
1
2
1
4
2
1
1
2
1
1
1
2
0
2
1
2
1
1
0
1
0
0
1
1
3
1
1
0
1
1
1
0
2
1
2
2
1
0
2
1
2
1
2
0
2
2
0
1
1
0
1
0
1
2
1
0
1
2
1
0
0
2
0
0
1
1
1
1
1
2
2
1
1
2
2
2
0
1
0
1
2
1
1
0
1
1
1
0
2
1
2
0
2
1
0
2
1
0
2
2
1
1
1
1
0
0
1
1
1
0
1
1
2
0
2
1
1
1
1
1
0
1
0
1
2
2
1
1
1
1
1
1
1
0
2
2
1
1
3
2
0
0
1
0
2
1
1
1
2
0
2
0
1
1
2
2
1
1
0
1
1
2
0
0
1
1
1
1
0
0
1
1
1
2
2
3
2
1
1
0
1
2
2
1
0
1
1
1
1
0
0
2
1
1
0
0
1
1
1
0
1
1
2
0
1
1
1
2
1
2
0
2
1
2
1
0
0
3
0
1
1
0
1
1
0
1
2
1
1
1
1
1
1
2
1
0
2
1
1
0
2
1
1
0
0
1
1
1
1
0
1
1
1
1
2
1
1
1
0
1
1
1
1
1
0
2
1
0
1
1
1
1
0
1
1
0
2
1
1
1
2
0
2
0
1
1
1
2
1
2
1
1
1
0
0
1
2
0
0
1
2
1
0
2
2
2
1
2
0
1
1
0
1
1
1
1
1
2
0
1
2
1
1
1
2
1
0
0
1
1
1
1
1
2
1
1
0
2
2
0
2
1
1
1
1
0
1
1
1
0
2
2
2
1
1
0
2
1
1
1
1
1
1
0
1
1
1
1
0
2
0
1
2
1
1
1
1
2
0
1
1
0
1
2
2
1
1
1
1
0
3
1
0
0
1
0
2
1
0
1
1
2
2
1
1
4
1
1
1
0
1
1
1
1
1
1
0
0
1
2
0
1
0
0
1
2
1
1
0
1
0
1
1
0
0
1
0
0
2
1
1
2
1
1
1
2
0
1
1
1
2
2
1
0
1
2
2
1
2
2
1
0
0
2
2
2
1
2
1
1
0
2
1
2
1
0
1
1
1
1
2
1
1
1
0
1
0
1
0
2
2
1
1
1
1
1
1
0
2
1
1
1
0
1
0
0
0
0
1
1
1
0
1
2
1
1
3
1
2
2
1
1
1
1
1
1
0
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
1
0
1
1
0
0
0
1
1
2
1
2
1
0
1
1
2
2
0
0
0
1
2
1
1
1
0
1
1
1
1
1
0
1
1
2
1
0
1
1
0
0
1
1
1
1
2
2
0
0
0
0
1
1
0
2
1
1
2
1
0
2
0
0
0
1
2
1
1
0
0
2
0
1
2
0
1
1
2
1
1
0
2
2
0
0
0
4
1
2
1
0
1
1
1
1
2
2
1
1
2
1
0
0
2
0
0
0
1
1
1
2
0
1
1
1
2
2
0
1
1
2
2
1
1
0
1
0
1
0
0
1
1
1
0
2
1
1
1
0
1
0
0
1
1
0
1
1
1
0
0
2
1
0
1
2
1
1
2
2
1
0
1
0
2
0
1
1
1
1
3
1
1
0
1
2
2
1
2
0
1
1
1
0
1
0
0
1
0
1
1
1
1
1
1
1
1
2
2
1
0
1
2
2
1
0
2
0
0
1
3
2
1
0
1
0
1
2
1
1
0
1
1
2
0
1
1
1
2
1
0
1
1
1
1
2
1
0
0
1
0
1
1
1
0
1
1
1
0
1
2
1
1
0
1
1
1
0
2
1
0
1
1
1
0
1
2
0
1
1
1
1
2
1
1
1
1
0
0
2
1
2
1
0
0
1
1
0
2
1
2
1
0
0
2
0
1
0
0
1
0
1
0
1
2
2
0
1
2
1
1
1
1
0
0
2
1
1
0
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
2
1
0
0
2
2
1
1
1
0
2
2
0
1
1
1
1
1
1
0
1
1
1
2
0
1
1
1
2
1
2
1
2
1
0
1
1
1
1
1
1
2
0
2
1
2
1
1
0
1
0
0
1
2
1
1
0
2
2
1
1
1
1
1
1
1
1
0
1
2
1
1
1
0
1
2
1
1
2
1
1
1
1
1
1
2
0
0
2
1
1
0
2
0
1
1
0
0
0
2
1
2
1
0
0
2
1
1
0
1
1
1
2
0
2
1
0
2
0
1
0
2
1
1
0
1
0
0
2
4
1
0
1
1
1
0
2
1
1
2
1
2
1
1
2
0
0
2
1
1
2
3
1
2
0
0
1
2
0
1
0
1
1
0
1
1
2
1
1
1
0
1
2
1
1
1
1
1
1
0
2
1
2
2
2
1
2
1
1
1
1
0
1
0
1
0
1
1
1
1
0
1
0
1
1
1
1
1
1
2
1
0
1
1
1
3
1
1
1
1
2
1
1
1
0
1
0
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
0
1
0
1
1
1
4
2
1
0
2
0
0
1
1
0
1
2
1
0
1
1
1
0
0
1
1
1
1
1
2
1
0
0
1
1
0
0
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
0
1
1
2
1
1
1
2
1
1
0
1
1
0
2
0
2
2
1
2
2
2
1
1
0
0
1
1
1
1
1
1
0
1
0
1
1
0
0
1
2
1
0
1
1
2
1
0
2
1
2
2
1
1
0
1
0
1
1
0
1
1
1
1
1
1
1
1
0
2
0
2
1
1
0
1
1
1
1
0
1
2
1
1
0
1
1
2
2
1
2
0
2
0
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
0
1
0
1
1
0
0
1
1
2
0
2
1
1
1
1
1
1
1
0
1
1
1
2
1
2
2
1
1
0
0
2
1
0
1
0
1
1
1
0
2
1
2
1
0
1
2
1
0
1
1
0
1
1
1
1
0
0
1
1
1
1
0
1
1
1
0
0
1
0
0
1
2
1
2
0
0
2
1
1
2
1
1
1
1
1
2
1
1
2
2
0
1
1
2
0
1
1
1
1
1
1
2
1
2
0
1
1
0
1
1
1
0
1
0
0
1
0
1
2
1
1
2
2
1
0
0
1
1
0
1
1
0
2
0
1
0
1
2
1
0
2
1
1
0
1
1
1
0
1
0
2
1
0
1
0
1
0
2
2
0
0
2
1
1
1
0
2
0
1
1
0
2
1
1
1
1
2
1
2
1
1
9
1
2
0
1
1
2
4
2
0
1
1
1
1
2
1
1
1
1
1
0
1
1
1
0
2
1
1
1
1
1
1
1
0
0
1
1
0
1
0
1
0
2
1
1
1
0
0
1
2
1
1
1
0
0
1
1
1
1
2
2
1
0
2
2
0
0
1
1
2
1
1
1
1
1
2
0
2
1
0
0
1
1
1
1
2
2
2
1
1
1
1
1
1
2
0
1
2
1
1
2
1
2
2
1
2
1
1
1
1
0
1
0
1
2
2
1
2
1
1
1
0
1
1
1
2
2
1
1
1
2
1
1
1
2
1
1
2
2
0
1
1
2
2
2
0
3
1
1
1
2
1
2
1
1
0
1
2
1
1
1
1
1
1
1
2
1
1
1
1
0
1
0
1
0
1
1
1
1
1
2
2
1
2
1
1
1
1
0
2
1
1
0
2
1
2
1
1
0
1
1
1
1
0
0
1
2
2
1
1
1
2
0
1
1
0
1
0
1
2
1
0
1
2
0
0
1
1
0
0
1
1
1
3
2
2
1
0
0
2
2
1
2
1
2
2
1
0
1
2
1
1
2
2
1
2
1
1
1
1
1
1
2
2
0
0
0
1
1
2
1
1
1
1
1
1
0
1
1
0
2
2
1
1
1
1
0
2
1
1
1
1
1
1
2
0
0
1
1
1
1
1
1
2
2
0
0
1
0
1
2
1
1
1
1
0
2
2
2
1
1
2
2
2
1
1
1
1
0
0
0
0
1
1
0
1
0
1
0
1
1
1
1
1
2
1
3
1
3
2
1
2
2
1
1
0
2
0
2
1
1
0
1
2
1
0
2
1
1
2
2
2
0
1
1
1
1
1
2
1
0
1
0
1
1
1
0
2
1
1
1
0
1
2
0
0
2
1
1
0
1
2
1
1
1
1
2
1
1
1
2
1
1
2
4
2
1
2
2
0
1
1
0
1
1
2
1
1
1
1
2
1
2
2
1
0
0
1
0
0
2
3
1
1
0
2
1
2
2
0
0
1
0
1
1
1
0
1
1
0
1
1
2
0
1
0
1
1
2
2
0
0
0
1
1
1
2
1
2
1
1
1
1
0
2
0
1
0
1
0
0
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
2
1
0
1
0
1
1
1
1
1
1
1
1
1
0
1
2
0
0
1
2
1
1
2
0
0
2
2
1
1
1
0
1
1
1
1
2
2
2
1
2
1
1
1
1
0
2
0
1
0
0
1
1
1
0
2
2
1
1
1
1
1
1
1
1
0
1
1
2
0
0
0
0
1
1
0
0
1
2
1
1
1
1
2
1
1
1
0
1
0
1
2
1
0
1
1
3
0
1
2
2
1
0
0
0
2
1
2
0
1
2
1
2
0
0
2
0
2
1
0
1
1
2
4
0
1
0
1
1
0
1
0
2
1
1
2
1
0
1
1
2
3
0
0
1
2
0
1
1
1
1
1
2
1
1
0
2
1
2
2
1
2
0
0
2
2
1
0
2
1
0
1
1
2
1
1
1
0
1
1
1
2
2
1
2
0
1
2
0
2
0
1
2
1
2
1
0
1
1
2
0
1
1
0
1
0
1
1
0
2
0
1
1
1
0
1
2
1
0
1
1
1
0
1
1
1
1
0
0
1
1
2
1
1
1
0
0
1
1
1
2
0
3
0
2
2
1
2
1
1
1
2
2
1
1
0
1
0
0
1
2
0
1
1
2
0
1
1
0
0
1
0
1
1
1
1
2
2
0
2
1
2
1
2
1
0
1
1
2
2
0
0
1
1
0
0
0
2
1
1
1
1
1
0
2
2
2
0
2
0
1
1
1
1
1
2
1
1
0
0
2
1
1
0
1
2
1
1
1
1
1
0
2
1
1
0
1
1
1
1
2
1
1
1
1
1
1
1
2
1
0
0
0
0
1
1
0
1
2
1
1
1
2
0
1
1
0
0
1
1
1
2
1
1
2
0
2
0
2
0
0
1
0
1
1
1
0
2
1
2
1
1
1
1
1
0
2
0
1
2
0
2
0
1
1
1
1
2
2
1
1
1
1
2
1
1
2
2
0
1
2
2
2
1
1
2
2
2
0
1
1
0
1
2
0
2
2
0
1
1
2
1
2
1
1
1
0
1
0
1
1
1
1
1
0
1
1
1
0
1
0
2
2
1
1
1
1
1
1
2
0
1
1
0
1
2
1
2
2
0
1
2
1
1
0
0
1
2
1
0
1
1
1
0
3
2
0
2
1
1
0
2
0
1
2
1
1
1
1
1
1
1
2
0
2
1
1
1
0
1
1
1
1
1
2
0
2
1
2
1
0
1
2
1
0
2
1
1
0
2
1
1
2
2
0
1
2
1
0
1
1
0
1
1
1
2
1
1
1
1
2
2
1
1
1
1
1
1
2
1
1
1
2
1
1
0
1
1
1
1
0
0
1
1
4
0
0
2
1
1
1
1
0
1
2
1
1
1
0
1
1
1
1
1
0
2
0
2
1
1
1
0
1
1
1
1
1
1
1
1
0
1
0
0
0
1
1
1
1
2
1
1
1
0
1
1
2
0
1
2
1
1
1
0
2
0
0
1
2
1
0
1
2
2
1
0
1
1
1
0
1
0
1
1
2
1
1
1
1
1
1
0
2
0
1
1
1
1
2
2
1
0
1
1
0
1
0
2
1
0
1
1
1
1
1
1
0
1
1
1
4
1
0
0
2
1
0
1
1
2
1
0
1
1
2
2
1
0
1
1
0
0
1
1
0
1
1
1
1
1
0
1
2
1
1
1
1
1
1
0
1
1
1
1
0
0
1
1
2
1
1
1
1
1
0
0
1
0
2
1
0
1
1
1
0
1
2
1
0
1
1
0
0
1
1
1
1
0
1
1
2
1
0
2
1
1
3
1
1
1
2
2
1
1
1
0
0
2
1
1
0
0
2
0
1
0
0
1
0
2
2
0
0
0
1
0
2
1
0
2
1
2
1
1
0
0
1
0
1
2
2
1
2
1
0
1
2
6
0
0
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
2
2
1
1
1
2
1
1
1
0
1
0
1
2
1
0
2
1
0
1
1
2
2
1
1
0
0
1
1
2
2
1
1
1
1
1
1
0
4
1
1
1
0
0
2
1
1
1
0
1
2
1
2
1
1
1
2
0
0
1
1
1
1
1
2
0
2
2
2
0
2
1
1
1
1
1
1
1
0
1
1
1
1
1
0
0
1
2
1
0
1
1
0
2
1
2
1
0
3
1
0
1
1
2
3
1
2
2
2
1
1
1
1
2
2
0
0
0
2
1
1
2
2
1
1
1
0
1
0
1
1
1
0
1
1
1
0
1
1
2
1
1
2
2
1
1
2
1
0
2
1
1
1
2
2
1
1
1
0
1
1
2
2
1
0
0
1
0
1
8
0
1
0
0
1
2
2
1
2
0
1
0
1
1
2
3
1
0
1
2
1
1
1
2
0
2
1
0
1
1
0
1
1
1
1
0
1
1
1
1
1
1
1
1
0
0
1
1
0
0
1
3
2
2
1
1
0
1
0
1
1
1
0
1
1
1
0
1
1
0
1
1
2
1
1
0
2
0
1
2
0
1
1
0
2
0
1
0
1
1
2
2
2
3
1
2
1
1
2
2
2
0
2
2
0
1
1
1
0
1
2
1
2
1
1
1
0
1
2
0
1
1
1
1
1
1
1
1
2
1
1
1
2
1
0
2
0
2
2
1
1
2
1
1
2
0
0
1
2
1
1
1
0
1
0
2
1
1
2
2
0
0
2
0
2
1
1
2
2
0
1
2
1
0
1
1
0
1
2
1
2
1
2
1
2
1
1
1
2
2
1
0
1
2
1
1
2
0
1
1
1
2
2
2
0
0
1
1
1
0
0
2
1
1
1
0
1
0
1
1
0
1
1
2
0
1
2
0
1
1
1
2
1
1
1
1
1
0
1
1
1
5
2
1
0
2
0
1
2
1
1
2
1
1
0
1
1
1
1
2
1
1
2
1
2
2
0
1
1
2
1
1
2
0
1
1
0
2
1
0
0
2
0
1
2
1
0
1
1
1
2
1
0
1
1
0
1
1
0
2
1
0
1
1
1
1
1
1
0
1
1
3
0
0
0
2
1
1
2
2
0
1
0
0
0
1
2
1
1
1
2
0
2
0
2
1
2
1
2
2
0
0
0
0
0
1
1
1
1
2
1
2
1
1
1
1
0
0
2
1
2
2
1
0
1
1
2
2
2
0
2
4
1
0
1
1
1
2
1
1
1
1
1
1
0
1
2
0
1
0
2
0
2
0
1
2
1
0
0
2
2
0
1
1
1
2
1
1
0
0
1
1
2
0
0
2
1
1
1
1
1
2
1
1
2
1
0
1
1
1
1
0
2
2
1
0
0
0
2
0
2
0
1
0
2
2
2
1
1
2
0
0
0
1
0
0
2
0
1
0
1
2
2
1
1
0
0
1
1
0
2
1
2
2
0
0
2
1
1
2
2
1
1
2
1
2
1
0
0
1
1
2
1
0
1
1
1
1
0
2
1
0
1
1
1
2
2
1
1
1
0
0
1
1
2
2
2
0
1
2
1
0
0
0
0
1
2
3
0
1
0
1
1
0
0
1
2
1
2
0
1
2
1
1
1
1
2
3
0
2
1
1
0
1
2
2
2
1
0
2
1
1
0
0
1
1
1
1
1
2
2
2
1
1
0
1
1
1
0
1
0
1
2
1
1
1
1
1
0
2
1
1
0
2
0
1
2
0
1
1
0
0
0
1
1
1
1
0
0
1
0
1
1
1
2
0
1
1
2
1
1
1
1
0
2
1
1
1
0
1
1
1
1
2
2
0
0
0
2
1
1
2
1
1
0
1
1
2
1
1
1
0
0
0
2
1
1
0
1
1
1
1
1
1
1
2
1
2
0
2
1
0
0
1
1
2
1
1
1
1
1
1
1
0
2
1
1
1
0
2
0
0
2
1
1
1
1
2
0
1
1
2
1
0
1
1
3
1
1
0
2
0
0
1
1
1
0
1
2
3
0
1
1
2
0
1
1
2
0
1
1
1
0
1
1
0
0
1
1
1
1
1
1
1
0
0
1
0
1
1
1
2
0
1
1
1
2
1
2
1
1
1
1
0
1
2
0
1
1
1
1
1
0
0
0
1
1
1
1
1
1
2
1
1
1
1
0
2
1
0
1
1
0
1
1
1
1
1
0
1
1
0
1
0
1
1
1
1
0
2
1
1
1
1
1
2
2
1
0
1
1
1
1
0
1
1
0
0
2
0
1
1
0
0
0
1
2
1
2
1
1
0
0
1
1
1
2
1
2
1
1
1
0
1
1
1
1
0
0
1
1
1
2
1
0
2
0
1
1
2
1
0
1
1
0
0
1
0
0
0
2
2
2
0
1
1
0
1
1
0
1
2
1
1
2
1
1
2
1
1
0
1
0
1
1
1
3
1
1
2
1
2
1
0
0
1
0
0
2
2
0
0
2
0
1
1
0
2
2
1
2
1
0
2
0
2
1
2
1
1
1
2
1
1
2
1
1
1
2
1
1
2
1
1
1
0
1
1
6
2
1
1
1
1
1
2
2
3
2
1
1
2
0
1
1
1
1
1
1
1
0
1
1
0
1
1
2
1
2
0
0
0
2
0
1
0
2
1
1
1
0
1
0
1
2
0
1
0
2
1
1
2
1
2
1
1
0
0
1
1
0
2
1
0
2
0
1
1
1
1
1
1
1
1
1
0
2
1
1
1
1
1
1
1
1
1
2
0
2
1
0
1
1
2
1
0
2
1
1
0
1
1
1
1
1
2
0
2
1
0
2
1
1
0
1
1
0
0
1
1
0
1
1
1
1
1
0
1
0
2
1
2
0
1
0
1
1
2
0
1
0
2
1
1
0
0
0
1
2
1
2
1
2
2
1
0
1
2
1
1
1
1
1
2
1
0
0
2
1
1
1
0
1
3
2
1
2
0
0
2
0
0
1
1
2
1
1
1
1
0
2
1
1
1
2
0
1
2
0
2
0
1
1
2
0
1
1
1
0
0
2
1
2
0
0
0
0
1
2
2
1
1
0
0
0
1
0
1
1
1
1
1
0
1
1
1
0
1
1
1
1
2
1
1
0
2
1
0
1
1
1
0
2
1
0
1
1
0
1
1
3
1
1
1
2
1
1
2
2
1
1
1
0
0
0
1
2
1
1
1
1
1
1
1
1
0
0
2
0
0
3
0
1
2
2
1
1
1
1
1
1
0
1
0
1
1
1
1
4
0
1
1
0
1
3
2
1
1
0
0
0
1
0
0
2
0
1
1
0
1
0
1
1
1
2
1
0
2
1
1
0
2
2
0
2
2
1
1
0
2
2
0
1
1
1
1
2
2
2
0
1
1
0
1
0
2
0
1
2
1
1
1
2
1
0
0
1
2
0
0
1
1
2
2
0
1
1
1
1
1
2
2
2
1
0
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
0
1
0
1
1
0
1
2
1
1
2
1
1
1
0
2
2
2
1
0
0
1
1
3
2
2
1
1
1
2
0
0
2
1
2
1
2
1
2
2
1
2
2
1
0
0
1
1
1
1
0
1
1
1
1
1
1
0
2
1
1
2
0
2
1
0
1
2
1
1
1
1
1
2
1
0
1
0
1
0
4
3
1
0
0
1
1
1
1
2
1
1
0
2
2
1
1
1
1
0
1
1
2
1
2
1
2
0
0
1
1
1
1
1
1
0
1
1
1
1
1
1
2
1
1
0
0
0
1
1
0
2
1
2
2
2
1
1
1
1
1
1
2
1
1
1
0
2
1
1
0
0
0
0
1
1
0
2
1
0
2
1
1
1
4
1
1
1
1
1
0
2
0
1
0
0
1
2
0
1
1
1
2
0
1
2
1
0
0
1
2
1
1
1
2
1
1
0
1
1
1
2
1
2
0
1
1
2
1
1
0
1
0
1
2
1
2
1
1
1
2
2
0
0
1
0
2
1
1
1
1
2
1
1
0
1
1
0
1
2
0
0
2
2
1
0
1
1
1
1
1
0
0
2
2
1
0
0
2
1
1
2
2
2
1
1
0
1
2
1
1
1
2
1
0
1
0
0
0
1
2
1
1
1
0
1
2
1
2
1
1
0
1
0
0
0
2
2
0
1
1
1
1
1
6
2
1
2
2
1
1
2
1
1
2
1
2
2
1
0
2
1
2
2
1
1
2
0
1
2
1
0
1
0
0
1
0
1
0
1
2
0
1
0
1
2
1
2
2
2
1
1
1
1
3
1
1
2
1
1
1
1
1
1
1
0
1
2
1
0
1
2
2
0
1
1
1
2
1
1
2
1
1
1
0
0
1
1
1
1
0
0
1
2
1
2
2
2
1
2
0
2
0
1
1
1
4
1
1
1
1
1
1
1
0
1
1
1
0
1
0
0
1
0
1
1
0
1
0
1
2
1
0
1
1
0
0
1
1
1
1
1
0
2
1
2
2
0
2
1
0
1
1
2
1
0
1
2
0
0
2
1
1
1
0
1
0
1
1
1
1
2
1
1
1
1
2
1
2
1
0
1
1
0
1
0
2
1
2
1
2
1
2
1
2
1
0
1
2
1
2
1
1
1
1
1
1
1
2
1
0
0
0
1
0
0
1
1
1
2
0
3
1
1
3
1
1
2
2
0
2
2
1
0
1
2
0
1
0
1
1
2
2
2
2
1
1
1
1
2
1
1
1
1
1
1
2
0
1
1
2
1
1
1
0
1
2
0
2
2
2
1
0
1
1
1
2
2
1
2
1
1
0
1
0
1
1
2
2
1
1
2
2
1
0
1
1
1
0
0
1
1
0
1
1
1
1
1
0
1
0
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
2
0
1
1
2
1
0
1
1
1
2
1
0
1
1
1
0
1
0
1
1
0
0
2
2
1
2
1
1
1
0
1
0
1
2
1
2
1
1
1
1
1
2
1
0
0
1
0
0
1
3
1
1
2
1
1
1
0
1
0
0
1
0
0
1
1
1
1
3
2
1
1
1
3
1
2
2
2
1
1
2
2
1
2
1
1
4
1
2
2
1
1
1
2
1
1
1
0
0
1
1
1
0
2
1
2
2
0
1
1
1
2
1
1
1
1
2
7
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
0
2
0
2
1
0
1
1
1
2
1
0
3
2
1
0
1
1
1
2
1
1
1
1
1
1
2
0
1
0
1
1
1
1
0
1
1
1
1
0
0
1
1
0
1
2
1
2
2
2
0
1
0
1
0
0
1
1
1
1
2
2
2
2
1
0
1
0
1
1
1
2
1
2
2
0
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
0
2
1
0
2
2
1
2
1
2
0
1
0
2
0
1
1
1
1
1
1
2
1
1
1
0
2
1
1
1
1
5
1
0
2
1
1
1
3
2
1
1
1
1
1
1
1
0
1
1
1
0
1
2
1
1
1
1
1
1
1
1
2
1
2
0
0
0
0
0
1
0
1
1
2
1
0
1
1
2
1
1
1
1
1
1
1
0
2
1
2
1
1
1
1
2
2
2
1
1
2
1
1
2
1
1
2
1
1
0
0
1
3
1
1
0
2
1
0
1
0
1
2
1
1
0
1
1
1
1
2
1
1
1
1
0
1
1
0
0
1
0
2
1
2
2
1
1
2
1
0
2
1
2
0
1
2
3
0
2
1
0
0
2
1
2
1
0
1
2
2
1
2
2
1
2
2
1
1
1
1
1
0
1
1
0
2
2
0
1
1
1
1
0
0
2
0
1
1
1
1
0
1
1
0
1
1
1
1
2
1
1
2
0
0
0
1
2
1
1
1
0
1
1
0
1
1
2
1
1
0
1
2
1
0
1
2
2
1
2
1
1
2
1
2
1
0
1
2
0
1
1
1
1
1
1
2
1
0
2
1
1
1
1
1
0
1
0
0
1
1
1
0
0
1
2
2
1
1
2
2
0
0
1
1
2
1
1
1
1
1
1
1
1
2
2
0
1
0
1
0
2
2
0
1
1
1
1
1
0
1
1
1
1
1
1
1
2
1
0
1
2
1
1
1
0
0
1
2
2
1
1
0
2
2
0
1
0
1
2
2
1
2
1
0
0
2
2
1
0
2
2
0
1
0
0
1
1
2
2
0
1
1
1
1
1
1
0
1
1
1
1
2
1
0
2
2
1
1
2
2
1
1
1
1
0
1
1
1
1
1
0
2
1
2
1
2
2
2
0
0
1
2
1
1
1
0
0
1
1
0
1
1
1
1
2
0
1
2
2
1
2
2
2
0
1
1
1
1
1
2
1
0
1
0
1
2
1
2
1
1
2
1
2
2
1
1
0
2
0
2
0
1
0
2
1
0
0
1
1
0
1
1
0
1
2
1
0
2
1
1
2
1
1
1
1
1
2
2
1
0
1
2
1
1
2
0
0
2
0
2
1
2
1
0
2
0
1
1
1
1
0
0
0
1
0
1
1
2
1
0
1
1
2
1
0
1
2
2
2
0
1
0
1
1
1
2
1
1
1
1
0
1
1
0
1
1
1
1
0
1
1
1
2
1
0
2
1
0
2
0
1
1
1
1
1
1
1
0
2
1
1
2
2
0
1
2
1
0
1
0
1
1
1
1
0
2
2
1
1
1
1
1
1
1
1
2
0
1
1
1
1
2
2
2
1
1
1
1
1
0
1
1
1
1
1
2
1
1
1
2
1
1
2
2
1
0
2
1
1
0
1
1
1
2
1
0
1
2
0
1
2
0
1
1
1
1
0
2
1
0
1
0
1
2
2
0
0
1
2
1
1
2
1
0
1
0
1
1
0
1
2
1
3
1
1
1
2
1
2
1
1
1
2
1
1
0
1
0
1
1
0
1
0
0
1
1
1
1
1
1
0
1
1
1
2
1
0
1
1
1
1
0
0
1
2
1
1
1
2
2
1
2
1
1
1
0
2
1
1
1
1
1
0
2
2
2
1
0
1
0
2
1
0
1
1
0
0
0
2
0
0
2
2
0
0
0
0
1
1
1
0
0
1
0
0
2
1
2
1
2
1
2
1
1
1
2
1
0
1
1
1
1
1
0
2
1
1
0
1
1
0
1
2
1
2
1
0
1
0
1
1
0
1
1
1
1
0
0
1
1
1
1
2
0
0
1
2
1
2
2
0
1
1
2
2
1
2
5
2
3
1
1
1
1
2
2
0
0
0
2
1
1
1
1
1
0
3
1
1
1
2
2
1
1
2
1
1
1
2
1
1
2
0
2
0
1
0
1
2
1
2
1
1
1
1
0
1
0
1
1
1
1
2
1
1
2
1
2
1
0
0
1
1
0
3
1
0
0
1
2
3
1
1
1
2
1
0
1
0
2
1
0
1
1
3
1
1
1
1
0
1
2
1
1
1
2
2
1
1
1
1
1
0
0
1
1
1
2
1
0
1
0
1
1
2
2
0
0
1
1
1
1
2
1
0
0
1
1
1
0
1
2
1
2
1
0
1
1
1
1
1
0
2
1
1
1
1
1
1
1
1
1
1
1
0
1
1
0
2
1
1
1
3
2
1
1
1
1
0
1
2
2
0
1
1
1
2
1
1
1
2
2
1
0
2
1
0
0
1
1
2
2
2
1
1
2
1
0
1
2
2
1
1
1
0
2
1
0
1
1
1
2
1
1
1
1
2
1
1
2
0
0
1
1
2
0
1
0
2
0
2
2
1
2
1
1
2
2
0
1
1
1
1
0
1
1
3
2
0
1
1
1
2
2
0
0
1
1
1
1
1
0
0
1
1
2
1
1
1
1
2
2
1
0
1
1
1
2
0
1
0
0
3
1
3
0
1
2
0
2
0
2
2
1
1
1
1
1
1
2
1
0
1
1
2
1
1
1
4
1
1
1
1
1
1
2
1
0
1
2
1
2
1
2
1
1
1
0
1
1
0
0
1
0
1
0
1
0
1
1
1
0
1
0
1
1
1
2
2
2
2
2
0
1
1
1
2
2
1
1
1
1
0
1
2
0
1
0
1
2
1
0
1
0
1
0
0
0
1
2
0
1
2
1
1
1
1
1
2
1
0
0
1
0
1
1
1
1
2
0
0
1
1
0
2
1
2
2
0
1
1
1
2
1
2
1
0
1
0
2
1
1
1
0
1
1
1
2
0
2
1
1
1
1
2
2
0
1
1
1
0
1
1
1
1
0
2
1
1
2
2
0
2
1
1
0
0
1
1
1
0
2
2
1
2
1
1
1
0
0
1
1
0
1
0
0
2
0
2
1
2
1
1
1
2
1
1
1
1
4
1
2
2
1
0
1
1
1
2
1
1
1
2
0
1
0
1
2
1
1
2
1
1
2
1
2
2
0
1
1
1
1
1
1
1
2
0
1
2
1
0
1
1
1
0
2
1
0
1
0
0
1
1
2
1
1
2
1
2
0
1
1
2
1
1
1
0
2
1
1
2
1
2
1
0
0
1
1
2
1
0
0
0
0
0
2
0
2
1
1
3
0
1
1
1
1
2
1
1
2
1
1
2
0
1
1
1
0
0
0
0
0
2
1
2
1
1
0
0
1
1
1
1
0
1
0
1
1
1
0
1
1
1
1
1
1
1
2
2
1
1
2
0
1
1
1
1
0
2
0
1
1
0
1
1
1
2
1
1
1
0
1
1
1
1
0
2
0
1
1
2
0
2
1
1
1
1
0
0
1
0
1
1
1
1
1
2
1
0
1
0
1
1
1
0
0
1
1
1
1
1
1
3
0
0
1
0
1
2
1
1
0
0
1
2
1
1
0
2
1
1
1
0
1
2
1
0
1
1
0
1
1
4
0
0
2
1
1
0
1
1
0
1
1
0
1
2
1
2
2
1
1
2
1
0
0
1
1
1
1
1
1
2
2
2
2
2
0
1
1
1
0
1
0
2
2
1
3
1
1
1
1
1
1
1
1
1
1
2
2
2
1
0
2
2
2
2
2
1
2
1
2
0
2
1
1
1
1
1
0
1
1
1
1
1
2
0
1
1
1
1
1
1
2
1
2
1
0
1
0
0
1
0
2
1
1
1
0
2
0
1
2
1
0
1
1
0
1
1
1
1
1
1
1
0
1
1
1
2
3
1
0
1
2
2
2
1
0
2
0
1
0
2
1
0
0
1
0
2
0
2
2
0
1
2
1
1
3
1
0
0
1
2
1
1
1
1
2
1
1
1
2
2
1
0
1
2
1
1
0
0
2
1
1
0
1
2
1
1
1
0
1
1
1
2
2
1
0
1
0
0
2
1
2
1
2
1
2
0
4
1
1
1
1
1
0
2
2
1
1
1
2
1
2
0
0
1
2
1
3
1
2
1
1
1
1
0
1
1
0
1
1
1
1
4
0
2
2
1
1
4
1
1
0
0
1
1
1
1
1
0
1
1
2
1
0
0
1
2
1
1
1
1
2
1
1
0
0
1
1
0
1
1
2
0
1
1
1
1
1
2
0
2
1
1
2
0
1
1
1
2
2
0
1
1
2
0
1
1
2
1
1
1
1
1
2
0
2
1
2
1
0
1
2
0
1
2
0
0
1
1
0
2
1
1
0
1
1
2
0
0
2
1
0
3
0
1
2
2
1
1
1
2
1
0
2
2
3
0
1
0
1
2
0
0
1
2
1
0
1
1
0
0
1
0
1
1
0
1
2
1
1
1
0
2
1
0
2
1
2
0
1
2
1
1
1
2
1
1
0
1
0
3
2
3
1
1
1
1
0
3
0
0
1
0
1
1
2
1
2
1
1
0
2
2
0
1
0
2
0
2
1
1
1
2
1
3
1
1
0
1
0
2
1
0
2
1
2
0
0
0
1
1
1
1
2
1
0
1
0
1
2
1
1
0
1
1
1
1
1
2
2
1
0
2
0
0
1
2
2
1
1
1
0
1
2
2
2
1
1
1
3
1
1
2
1
2
1
0
3
1
1
1
1
2
1
1
1
1
2
1
0
1
0
2
1
2
2
1
1
1
1
2
1
1
1
1
0
1
0
2
1
1
1
1
1
0
1
1
0
1
1
2
0
1
1
4
0
2
1
1
1
2
1
2
0
1
1
0
0
3
1
1
1
1
0
0
0
1
1
1
2
2
1
0
0
1
2
0
2
1
1
2
0
0
0
1
1
2
1
1
1
1
1
1
1
0
1
0
1
0
2
2
0
1
1
1
2
2
1
1
1
1
1
1
0
1
2
1
1
1
1
0
1
1
2
0
1
2
0
1
1
1
2
2
0
1
1
1
1
0
2
0
1
2
0
1
2
2
1
1
2
1
0
1
2
1
2
1
1
1
1
2
2
1
0
0
1
1
1
1
0
1
1
1
2
1
1
1
1
0
2
0
0
1
2
0
2
2
1
2
1
1
1
0
1
1
1
2
2
1
0
0
0
2
1
1
1
2
1
1
1
1
1
3
2
1
2
0
2
2
2
1
1
1
0
1
2
0
2
3
1
1
2
1
0
1
1
0
0
2
2
1
1
2
0
0
2
1
0
0
0
1
1
1
1
1
2
1
1
2
1
1
2
0
0
1
1
1
2
1
1
1
2
0
0
1
1
1
1
1
0
1
1
1
0
0
1
1
1
1
1
1
1
0
1
1
1
2
1
0
0
2
1
1
2
2
0
2
0
0
0
2
0
1
0
1
0
1
2
1
0
0
2
1
2
0
1
0
1
1
2
0
1
2
0
1
1
0
0
1
2
0
1
4
1
0
1
1
0
0
1
1
2
1
0
1
1
0
0
2
1
0
0
2
1
2
2
1
0
2
2
1
1
2
2
3
0
2
1
1
1
2
2
0
1
1
1
0
0
1
1
1
1
2
0
2
1
1
1
1
1
1
1
1
0
2
1
1
1
1
0
1
1
1
2
0
1
2
1
1
2
0
1
1
0
0
1
1
1
2
2
1
0
2
1
1
1
1
2
1
0
1
0
0
2
1
0
1
2
1
1
2
0
0
1
2
1
1
0
1
1
2
0
2
2
0
1
1
0
1
1
1
1
1
0
1
0
2
1
1
1
1
2
3
0
1
1
1
2
2
0
1
1
0
1
1
2
0
2
2
1
1
0
1
1
0
1
1
1
1
0
1
1
0
2
2
1
1
0
1
1
1
2
1
1
1
0
1
2
2
1
0
1
1
0
0
0
1
0
1
0
0
1
1
1
1
0
1
2
1
2
2
2
0
0
0
0
1
2
1
0
2
0
0
1
1
2
2
0
1
1
0
1
1
1
2
1
2
2
1
2
1
0
2
2
1
1
1
1
1
1
2
2
0
1
1
0
0
0
1
1
0
0
2
1
0
0
2
1
1
2
0
1
0
0
1
0
2
1
0
1
2
1
1
1
1
1
0
1
0
1
2
1
1
1
1
1
2
2
1
2
2
1
0
1
0
1
1
1
2
1
1
2
2
1
1
1
1
1
0
0
0
1
1
1
1
2
1
0
0
0
1
1
1
2
1
1
0
2
1
0
1
1
1
1
1
2
1
1
1
0
1
0
2
1
1
1
1
1
0
2
1
0
1
0
0
1
1
1
1
1
2
3
0
1
2
1
1
1
0
1
1
2
0
1
0
1
0
1
1
1
2
1
2
1
1
1
1
0
0
0
2
2
0
1
1
0
2
0
2
0
1
0
1
2
1
2
1
1
1
1
1
2
1
0
1
0
0
1
1
1
1
2
1
1
0
2
1
1
2
1
0
1
1
1
0
1
1
2
2
3
1
2
1
1
2
1
2
0
1
1
1
2
1
3
1
1
2
1
2
0
1
0
0
0
2
1
0
1
1
1
0
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
0
2
1
2
1
1
1
1
2
1
1
0
0
3
1
2
1
0
1
1
3
0
1
1
1
1
1
1
1
1
2
1
2
0
2
1
1
1
0
1
1
0
1
2
1
2
1
0
2
2
2
0
2
3
2
1
2
1
1
1
1
0
2
1
1
2
1
1
0
0
2
1
1
1
1
1
1
1
1
1
0
2
2
1
1
2
0
0
0
1
0
1
2
1
1
0
2
1
2
1
0
1
2
0
1
1
1
2
2
0
1
3
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
0
0
1
1
2
1
1
1
1
0
0
1
2
2
0
2
1
0
1
1
1
1
1
1
2
0
2
0
2
0
1
1
1
1
1
1
2
0
1
1
2
1
1
1
1
2
2
2
1
1
0
1
0
3
2
1
1
1
0
0
1
1
1
2
1
1
0
2
1
1
0
1
1
1
1
2
1
2
1
1
1
1
1
3
1
1
1
1
2
2
1
2
1
1
0
2
2
2
2
2
2
0
1
1
2
0
2
0
2
1
2
1
1
1
1
1
2
1
0
2
2
2
0
2
2
1
0
0
0
1
1
1
2
0
1
1
1
0
2
1
1
1
1
0
1
1
2
1
2
0
1
2
1
1
1
0
1
1
2
1
0
2
0
0
0
1
2
1
1
2
1
2
2
2
1
1
1
2
2
0
1
0
2
0
1
1
0
0
1
2
2
0
1
1
1
2
1
1
1
1
2
1
2
2
0
0
1
0
2
1
2
1
1
0
0
1
1
1
2
1
0
1
2
2
1
1
0
0
1
1
1
1
2
0
2
0
1
1
1
1
1
1
1
1
1
0
1
1
2
1
2
1
1
2
0
4
1
1
1
2
2
2
1
1
1
2
1
1
1
2
1
1
1
1
0
2
0
1
1
0
1
0
2
1
0
1
1
1
2
1
1
1
1
2
1
0
1
1
1
1
1
2
1
0
1
0
1
1
1
0
2
1
1
1
0
2
2
1
0
1
1
1
1
1
0
0
1
0
1
1
1
0
1
2
1
2
0
1
2
1
3
0
2
1
1
0
1
1
1
2
0
1
1
2
1
0
1
1
1
1
1
1
0
2
0
0
2
1
1
1
1
0
1
0
1
0
2
1
1
1
2
0
1
0
0
2
2
0
1
2
1
1
1
1
1
0
1
1
1
1
0
2
0
1
1
1
0
2
2
0
0
1
1
1
2
1
2
2
2
1
1
1
1
0
1
1
2
0
1
0
2
0
1
2
1
0
1
1
1
0
1
0
2
0
1
1
1
1
0
1
2
2
2
1
0
1
1
1
0
1
0
2
1
2
1
1
0
1
1
1
2
1
0
1
0
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
2
1
1
0
2
1
1
1
0
2
1
0
1
1
0
2
0
1
1
2
1
0
1
0
1
1
0
0
0
0
1
2
1
1
2
2
0
0
1
2
1
0
1
1
2
0
1
1
1
1
1
1
1
0
0
1
2
2
2
2
0
0
1
1
1
2
2
1
1
0
1
0
0
1
0
1
1
0
0
1
2
1
1
1
2
1
2
1
1
1
0
1
1
1
0
0
2
1
1
1
1
1
2
0
2
1
1
2
1
0
0
1
0
2
0
1
0
0
1
1
1
2
0
0
1
1
0
1
1
1
1
0
1
2
2
1
1
1
1
1
2
0
4
2
0
0
1
1
1
1
0
1
0
0
1
1
0
1
1
2
0
1
0
1
1
1
1
0
1
2
1
2
2
1
1
0
1
1
1
0
0
1
0
1
1
0
1
0
0
1
1
1
0
2
2
1
2
1
1
2
1
0
1
2
1
0
1
2
1
1
1
0
0
2
1
1
0
2
0
1
2
0
1
1
1
1
1
2
2
2
2
0
2
0
1
2
0
1
1
0
2
1
1
1
1
1
1
1
2
1
2
1
0
1
2
2
0
0
1
1
1
1
1
1
1
0
1
1
0
1
0
1
2
2
2
1
1
1
0
1
1
1
0
1
1
2
1
1
1
1
1
2
0
2
1
0
1
1
0
3
1
1
0
2
1
2
1
0
1
1
1
1
1
1
2
1
1
0
1
2
1
2
1
0
1
1
1
0
0
0
1
1
2
0
0
1
3
0
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
0
2
0
0
1
1
1
1
0
1
2
0
2
1
1
0
1
1
0
1
2
1
2
1
1
1
1
1
1
1
0
1
0
1
2
1
2
1
1
1
1
2
2
1
1
0
0
0
1
0
0
0
1
1
1
1
0
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
0
1
1
1
1
2
1
2
1
0
0
2
1
1
1
0
1
1
1
0
1
0
1
1
1
0
0
0
2
1
0
0
2
1
2
1
2
2
1
1
1
1
1
2
2
2
1
1
1
1
0
1
1
0
1
0
3
1
1
2
0
0
0
0
0
0
1
2
2
1
2
1
0
2
2
0
1
1
0
0
0
2
1
2
1
0
1
0
2
0
0
0
0
2
1
0
1
1
2
0
1
0
0
2
2
1
1
1
2
0
1
1
2
2
2
1
0
1
1
1
1
1
1
1
2
0
2
1
0
1
0
1
1
1
1
1
1
0
1
0
1
1
2
2
0
1
2
3
2
1
1
1
1
1
2
2
0
1
1
0
1
0
2
1
1
1
1
1
2
0
1
0
0
1
1
2
0
0
1
1
2
1
1
0
1
2
1
1
1
1
1
1
1
1
1
0
0
1
1
1
0
1
1
1
0
1
0
2
0
0
1
1
3
2
1
1
1
2
0
0
1
2
0
1
1
0
0
2
1
2
1
2
1
1
1
1
2
0
1
1
1
1
1
0
2
2
2
1
1
1
0
2
0
1
2
0
2
1
0
2
1
2
1
2
1
1
0
2
0
1
1
0
1
3
0
1
1
1
1
2
2
2
1
1
2
1
1
1
0
1
2
1
0
2
0
0
2
0
0
2
1
1
0
1
1
1
0
1
2
0
1
0
2
1
1
2
2
1
1
1
1
1
1
0
1
1
1
0
1
1
1
1
1
2
1
1
0
2
2
2
1
1
2
1
1
2
1
1
1
1
2
1
1
0
2
1
2
1
1
1
1
0
1
2
2
1
1
1
0
1
1
2
0
1
2
0
1
1
1
2
0
1
2
1
1
0
1
2
1
1
2
1
0
1
2
2
1
1
0
2
1
1
0
1
2
1
2
1
2
0
1
1
3
1
0
0
2
0
1
0
2
1
1
2
2
2
1
1
1
1
1
0
1
1
1
2
1
1
1
1
1
0
1
1
0
0
1
1
2
1
2
1
1
1
0
0
1
2
0
1
0
1
1
1
2
3
1
2
1
1
2
1
1
1
2
1
2
1
2
0
1
0
3
0
1
1
2
1
1
0
1
2
0
1
2
0
1
2
2
1
1
1
0
1
1
0
0
2
2
1
2
1
1
1
0
1
0
1
1
1
1
1
0
1
0
1
2
1
1
1
0
2
2
1
1
1
1
0
1
1
0
1
1
2
0
1
0
0
1
1
1
0
2
1
1
0
1
0
1
1
1
2
1
1
1
2
2
0
1
1
1
1
0
1
0
1
2
1
1
1
2
1
0
2
1
0
1
0
1
0
2
0
1
1
0
2
1
2
0
1
0
1
2
2
2
1
0
2
1
1
0
1
2
1
1
1
1
3
1
1
1
2
1
0
1
2
0
0
1
1
1
0
0
1
2
1
1
1
2
1
1
1
2
0
1
2
1
0
1
0
1
0
1
0
0
1
2
2
0
0
1
0
0
0
1
2
1
0
1
1
1
2
0
1
0
1
1
1
1
1
1
1
2
1
1
2
1
1
1
0
0
2
1
1
0
1
1
1
1
2
1
1
1
1
1
2
1
1
3
0
1
2
1
0
1
0
1
1
0
1
2
1
0
1
2
1
2
1
0
1
1
0
1
1
0
0
2
1
1
0
0
1
0
2
0
1
0
0
1
1
0
0
1
1
1
1
2
1
0
1
1
1
1
0
1
2
1
1
2
1
1
1
1
2
1
1
2
0
0
2
0
1
1
0
1
0
1
2
0
3
0
1
1
1
1
2
1
0
1
0
1
0
2
1
0
2
1
1
1
1
1
0
2
1
1
0
1
0
1
1
1
0
0
2
1
1
1
1
0
1
1
0
1
1
1
0
1
2
1
1
1
1
1
1
1
1
0
1
1
1
0
1
2
1
0
1
4
1
1
2
2
1
1
1
0
1
2
1
0
1
2
1
1
1
0
1
1
0
1
0
1
1
1
1
1
0
1
2
0
0
1
1
2
1
2
0
1
2
1
1
1
1
1
0
1
2
0
1
0
1
1
1
0
1
1
1
1
1
2
0
0
2
0
1
0
2
2
1
1
2
2
0
0
1
2
1
2
1
2
2
1
0
1
0
2
2
0
1
1
1
1
1
2
1
0
1
4
1
0
1
2
1
0
0
0
1
1
1
0
0
0
0
1
1
0
1
2
1
1
1
1
1
0
1
0
1
1
1
2
1
1
0
1
1
1
1
1
1
1
1
2
0
2
2
1
1
2
2
1
1
1
1
1
1
0
1
0
0
1
2
1
1
1
1
1
0
0
2
1
1
0
1
1
0
2
1
1
0
1
2
0
0
0
1
1
2
0
1
0
1
1
2
1
2
0
1
0
1
1
2
1
2
1
1
0
1
2
1
1
0
1
0
1
1
1
0
0
0
0
1
0
1
1
1
1
1
1
3
1
0
2
0
1
0
0
1
1
1
1
1
1
2
0
1
0
1
1
1
1
0
1
1
1
1
0
1
0
0
1
1
1
1
1
2
1
2
2
1
1
1
1
1
1
1
2
0
2
0
1
1
1
1
1
0
1
2
1
2
0
1
0
1
1
2
1
2
1
2
0
0
2
1
0
0
2
0
0
1
0
1
2
2
1
0
1
1
1
2
1
1
2
0
0
0
1
1
1
2
0
0
1
1
0
1
2
1
1
2
0
1
1
1
1
2
1
0
0
1
0
0
1
1
0
1
2
1
1
1
0
2
2
0
1
0
1
2
1
2
2
1
0
1
0
1
2
2
1
1
1
2
1
0
2
1
1
1
1
1
2
2
1
2
1
1
1
1
2
1
1
2
2
2
0
0
1
1
1
1
1
1
1
0
1
1
2
1
2
2
1
2
2
0
0
0
0
1
2
1
1
1
1
1
1
1
0
1
1
1
1
2
2
1
1
1
2
0
1
1
1
1
0
1
2
2
1
0
1
1
2
1
1
0
2
2
1
2
2
1
0
2
0
0
1
0
2
1
0
1
2
1
1
1
1
0
2
1
1
0
2
1
0
1
0
1
1
2
1
1
1
1
1
0
0
0
1
1
1
1
1
0
1
1
2
2
0
2
1
2
1
0
1
1
0
1
2
2
1
0
4
1
1
1
2
3
1
1
1
1
1
1
0
0
2
1
1
1
1
1
1
1
2
2
1
1
0
1
1
1
0
1
2
0
1
1
0
0
2
1
1
1
1
2
2
1
1
2
1
0
2
1
1
0
2
2
2
1
1
2
2
1
2
1
1
2
1
2
0
1
0
1
1
1
0
0
1
2
2
2
2
2
1
2
1
1
1
1
2
1
0
0
1
1
0
0
0
1
1
1
1
1
1
1
0
1
1
0
0
1
0
0
1
1
2
1
1
0
1
2
1
0
1
2
1
2
1
1
2
0
2
0
1
1
1
1
0
1
1
2
1
0
2
2
0
1
2
2
1
2
1
1
1
1
2
0
3
1
2
2
1
1
1
1
1
1
0
1
2
2
2
1
2
1
0
1
2
1
2
1
1
1
0
0
2
0
0
2
1
2
1
0
0
2
1
2
1
1
1
2
0
0
0
1
1
0
2
0
1
0
1
1
1
2
1
1
1
0
2
0
1
0
3
1
0
0
1
2
1
1
1
1
1
1
1
2
1
1
0
1
1
0
1
1
0
0
2
0
1
1
1
1
0
0
1
0
1
1
1
1
1
1
1
2
1
1
2
1
1
0
2
1
2
1
1
0
1
2
1
2
3
2
1
1
1
5
2
0
1
1
1
1
0
1
2
2
2
0
1
0
1
0
2
1
1
2
1
1
0
1
1
2
1
1
1
1
1
1
0
1
2
1
2
0
1
2
2
1
1
1
1
1
2
0
0
1
0
1
2
2
1
1
1
2
1
1
2
1
2
3
1
1
0
1
0
2
0
1
1
1
1
0
1
1
1
2
1
1
0
1
1
2
2
2
1
1
1
1
0
2
1
1
2
1
1
2
1
2
0
2
0
1
0
0
2
1
1
2
1
1
2
1
2
1
0
1
0
1
2
1
1
0
0
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
0
1
1
1
0
1
1
1
1
1
0
0
0
1
1
0
0
2
1
0
0
1
0
2
1
1
1
1
0
0
1
2
1
0
0
1
0
1
1
1
1
1
0
1
1
1
2
1
1
2
1
2
1
1
1
0
2
2
0
2
1
1
0
1
1
1
1
1
1
1
2
1
0
0
0
1
1
1
2
1
0
0
1
1
1
0
2
1
1
0
1
0
1
2
2
2
1
1
0
0
1
1
2
1
1
2
0
2
0
2
1
1
1
2
2
2
0
1
1
1
1
2
1
1
3
1
2
1
2
1
1
1
0
2
2
2
1
1
0
1
2
1
0
1
1
1
1
2
0
1
2
1
1
0
1
1
1
2
1
2
0
2
0
1
1
1
1
0
2
1
1
1
1
1
1
0
2
1
0
0
2
2
2
1
0
0
1
1
0
2
2
0
2
0
0
1
1
0
2
3
1
1
1
2
1
1
1
2
0
1
2
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
0
2
1
2
1
0
1
2
1
0
1
1
1
0
0
0
1
2
2
1
2
1
0
1
1
1
1
1
2
0
1
1
1
0
1
1
0
1
1
2
1
0
0
0
0
1
1
0
1
0
1
2
1
1
1
2
1
2
2
1
1
1
1
2
1
2
1
1
0
1
2
1
2
1
1
1
2
2
1
1
1
0
0
0
1
2
1
2
1
1
1
0
1
0
1
2
1
0
1
1
1
1
0
2
1
1
2
1
1
2
0
0
2
1
2
0
1
1
2
1
1
1
2
1
1
2
1
2
1
0
1
2
1
0
1
2
1
0
1
2
1
2
1
1
1
2
2
1
0
1
0
1
2
0
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
2
0
1
1
0
1
1
1
2
1
1
1
0
1
1
3
2
2
1
1
1
1
1
1
0
2
2
2
1
1
1
0
1
1
1
1
1
1
2
2
1
2
2
1
1
1
1
1
1
1
2
2
0
1
1
2
0
1
2
1
1
1
1
0
1
1
1
2
0
1
1
1
1
0
1
0
2
1
0
0
1
0
2
2
1
2
1
1
1
0
2
1
1
1
1
2
1
2
0
1
0
2
0
2
2
2
1
0
1
1
1
1
1
1
0
0
2
1
2
1
1
1
1
1
1
0
1
0
1
0
2
0
0
2
1
2
0
0
0
1
0
1
0
0
2
0
0
2
1
0
2
2
0
2
1
1
1
2
1
3
0
1
2
0
0
1
1
0
1
3
1
1
0
2
1
2
1
0
0
1
2
0
1
1
2
1
1
1
0
1
1
0
2
0
1
1
2
1
2
1
0
1
2
1
2
0
1
1
1
1
1
0
1
1
1
1
1
2
1
1
2
1
2
1
2
1
0
0
1
2
1
0
2
2
2
0
1
1
1
2
2
0
1
1
1
1
0
0
2
1
1
1
1
1
1
0
0
1
1
1
1
0
1
3
0
0
2
1
1
1
2
1
1
1
2
0
0
1
1
1
2
2
1
1
0
1
2
2
1
2
1
1
1
1
1
1
2
1
0
2
1
0
0
1
1
1
1
1
0
0
0
0
2
1
0
1
2
1
1
0
0
1
1
2
1
1
2
0
0
1
0
1
2
0
2
1
1
1
1
2
0
1
3
1
1
2
1
0
1
2
1
2
1
1
1
2
1
1
1
2
1
1
3
0
0
2
1
2
2
2
1
0
1
1
1
2
2
1
0
0
0
1
0
0
2
1
1
1
1
1
0
2
1
1
0
1
1
2
2
0
2
2
1
1
1
1
2
1
0
1
1
1
0
1
0
0
2
2
1
1
2
1
1
1
1
1
1
1
2
0
0
1
0
1
1
2
0
2
0
2
1
2
1
2
0
1
2
1
0
1
2
1
1
2
0
1
1
0
0
2
1
1
1
2
1
1
2
1
2
2
0
0
1
0
2
1
2
0
2
0
1
1
1
1
2
1
0
0
0
0
2
1
1
2
1
0
1
1
1
0
1
1
1
1
1
1
0
1
1
1
1
0
1
0
0
0
0
2
1
1
2
0
1
0
1
2
2
1
0
2
1
2
1
1
1
1
1
0
3
1
2
1
1
2
1
1
1
0
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
3
1
1
1
1
1
0
0
1
1
1
1
1
1
2
1
0
0
1
2
1
1
1
0
0
1
2
1
1
1
1
0
1
1
2
1
1
2
1
2
1
1
0
0
1
1
2
0
1
2
1
0
2
1
1
3
0
0
1
1
0
2
1
0
0
2
1
2
1
1
1
2
1
0
1
1
7
0
2
1
1
1
1
1
2
1
1
4
1
2
0
2
2
1
1
1
0
0
0
1
1
0
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
0
1
1
0
1
1
1
2
0
2
1
1
1
2
1
1
1
0
1
1
1
1
1
1
2
0
1
1
1
1
0
1
1
1
0
14
3
1
2
0
0
1
0
1
2
1
1
2
2
1
1
1
0
0
0
0
0
1
1
1
1
2
2
1
2
2
1
0
1
2
1
1
1
1
1
2
1
2
1
1
1
2
1
0
2
2
0
3
2
2
0
2
1
1
0
0
2
1
0
0
1
0
1
1
1
0
0
1
2
2
0
1
2
0
0
2
1
1
1
2
2
0
1
2
1
0
1
2
1
1
2
1
2
2
1
1
1
1
0
0
1
0
1
2
1
1
0
2
2
0
1
1
1
1
2
2
1
1
1
2
1
1
1
0
2
2
2
0
0
1
0
0
2
1
0
1
0
2
0
1
1
1
1
0
1
1
0
2
0
2
1
2
0
1
2
0
1
1
2
1
1
1
0
1
1
2
1
1
2
2
1
1
1
2
2
3
1
0
0
0
1
0
2
0
1
0
2
1
2
0
0
1
0
1
1
2
1
1
1
0
1
0
1
1
1
1
1
1
1
2
1
1
1
1
0
0
0
2
1
2
1
1
1
2
1
0
1
1
2
2
1
2
1
1
0
0
2
1
0
0
1
1
1
1
0
1
1
0
1
2
2
0
2
1
0
0
2
1
1
1
0
2
0
2
1
1
1
2
2
1
2
0
1
2
1
1
2
1
1
1
1
0
1
2
1
1
1
1
2
0
1
1
1
2
1
1
1
0
2
2
0
1
1
1
1
1
1
1
2
0
0
1
1
1
2
1
2
1
1
2
1
1
1
1
0
0
0
1
1
1
0
0
3
1
1
2
1
1
0
0
2
1
1
0
2
1
2
3
1
0
2
1
3
1
1
1
1
0
1
1
0
1
0
1
0
0
1
4
1
3
2
2
1
1
0
2
1
2
1
0
1
1
1
1
2
1
2
0
2
1
1
1
1
1
2
0
1
0
2
1
1
1
1
1
2
1
1
1
1
1
2
1
0
0
0
2
1
1
0
2
1
0
2
0
2
2
0
1
0
1
2
1
0
0
2
1
0
2
2
3
1
0
1
2
1
2
1
1
1
1
2
1
2
1
0
2
0
1
0
1
1
1
2
1
1
1
1
1
1
0
1
1
1
0
1
1
1
1
1
1
1
1
0
1
2
0
1
1
1
1
1
1
1
1
1
0
1
1
1
0
0
2
2
0
0
1
1
1
2
0
1
1
1
1
1
1
1
2
1
1
2
1
1
1
0
2
1
0
1
2
2
1
0
0
1
0
1
1
0
1
1
2
1
2
2
1
2
0
2
1
1
1
1
1
1
1
2
2
0
1
2
3
2
1
2
0
1
1
1
3
1
1
0
2
2
1
0
0
1
1
2
1
1
0
1
0
1
1
0
1
0
0
0
1
0
1
1
1
1
1
1
1
2
2
0
0
1
1
1
1
0
2
1
1
1
1
2
1
2
1
0
1
1
1
0
1
2
1
1
1
1
1
1
0
1
0
2
1
1
0
1
1
1
0
1
1
1
1
1
0
1
0
2
1
1
2
0
1
3
1
2
2
1
1
1
2
1
2
1
0
1
1
0
1
2
1
1
1
1
1
0
2
1
0
2
0
2
1
1
1
1
1
1
1
1
0
1
2
2
2
1
0
1
2
2
1
1
0
0
2
2
1
0
2
0
0
1
1
1
0
1
1
0
0
1
2
0
0
0
0
1
2
1
1
3
1
1
1
0
1
0
0
1
0
1
1
2
0
0
1
1
1
2
1
1
1
0
1
2
1
2
0
2
1
1
1
0
0
1
1
1
2
2
2
0
1
1
1
0
1
1
1
2
1
2
0
1
0
6
1
1
2
2
2
0
2
0
1
0
1
2
4
0
0
1
1
1
1
2
1
1
2
1
1
1
1
2
0
1
2
2
1
2
1
0
1
1
1
0
2
0
1
1
2
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
2
2
1
1
3
0
2
0
0
1
1
2
2
1
1
0
1
2
1
1
1
1
2
1
2
0
0
0
1
1
1
2
1
1
1
1
3
0
0
1
1
0
1
0
1
1
0
2
0
1
2
1
1
2
0
2
1
1
1
1
1
2
1
0
1
1
1
1
2
1
0
1
2
1
0
1
1
1
0
2
0
1
2
2
1
1
2
1
2
0
1
2
1
1
2
1
1
2
0
1
0
0
1
1
1
0
1
0
2
2
1
1
2
2
0
1
0
0
0
2
0
0
1
2
0
1
1
0
1
1
1
1
0
2
2
1
0
2
2
1
1
1
1
2
1
1
1
2
0
2
1
1
2
1
0
1
1
2
2
0
0
1
1
2
1
1
2
2
1
2
0
0
1
0
2
1
1
0
0
0
0
2
0
1
1
0
1
2
1
1
1
1
2
1
1
0
1
1
1
1
1
0
3
0
2
2
0
1
2
1
0
2
2
1
1
1
1
2
2
1
1
2
1
1
0
1
1
2
1
0
1
2
1
1
0
2
1
1
1
2
1
1
2
0
1
2
1
0
1
2
1
1
0
2
1
1
1
2
2
0
1
0
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
2
1
1
2
0
0
2
0
1
0
1
2
1
2
1
1
1
0
1
1
1
1
0
0
0
0
2
1
2
1
0
0
1
2
1
1
2
1
0
2
2
0
1
2
2
2
1
1
1
2
0
0
1
1
1
0
1
1
2
2
0
0
2
0
2
0
0
1
1
0
2
2
0
1
1
0
1
1
1
1
1
0
0
1
1
0
1
0
1
1
1
1
2
0
2
0
2
1
0
1
0
2
1
0
2
2
2
0
1
2
1
1
2
1
1
1
1
1
1
0
2
2
3
2
2
2
2
0
0
0
2
1
1
1
0
1
1
1
1
1
1
1
1
0
2
1
0
1
2
1
1
1
1
1
1
0
2
0
0
0
1
1
2
1
1
1
2
1
2
1
0
1
1
0
1
2
2
0
1
1
0
2
1
2
1
1
2
2
2
1
1
1
1
0
0
1
1
1
1
1
1
0
1
0
1
1
1
0
1
1
2
0
1
2
1
0
1
1
1
2
1
1
1
2
0
1
1
0
2
1
2
1
0
0
1
1
1
2
0
1
2
1
1
1
1
1
0
2
1
3
1
1
2
0
1
1
1
1
0
1
2
1
1
0
1
2
2
0
1
2
1
1
1
1
1
2
1
2
1
1
0
1
1
0
1
1
0
1
0
0
2
1
1
1
1
1
0
2
0
1
1
1
1
1
1
0
2
0
2
2
1
0
3
1
1
1
1
1
1
1
1
2
0
0
1
0
1
1
2
2
0
1
2
4
1
0
1
1
1
1
1
1
1
1
0
1
1
2
1
1
2
0
2
1
1
1
1
1
1
0
1
0
1
2
1
2
0
2
1
1
1
2
1
0
1
1
1
0
0
2
1
0
2
0
1
1
0
1
2
0
1
0
1
1
1
1
1
1
1
1
1
1
2
1
0
0
0
2
1
1
1
1
2
2
2
2
1
1
1
1
2
2
2
0
1
2
1
1
1
1
0
2
1
0
2
0
1
1
1
0
2
1
2
1
0
0
1
1
1
0
1
1
2
0
3
1
1
0
1
1
1
0
1
1
0
1
0
0
1
0
1
1
1
0
1
2
1
3
1
1
1
1
2
1
1
1
0
0
0
1
0
1
2
3
2
1
2
0
2
1
2
1
1
1
1
1
1
2
1
1
1
0
1
1
2
0
1
1
1
1
0
1
1
1
1
1
0
1
1
1
1
1
1
3
0
1
1
3
1
1
0
4
0
1
1
0
2
0
2
1
1
0
1
1
2
0
1
1
2
0
0
2
1
1
2
1
2
1
1
1
1
0
0
1
2
1
0
1
0
0
3
2
1
1
1
2
1
1
2
2
1
2
1
1
1
0
1
1
1
1
0
1
2
0
1
3
2
2
2
2
1
1
1
1
2
1
1
1
1
5
1
2
1
0
2
1
1
4
2
1
0
0
1
1
1
1
0
1
2
0
1
1
2
0
1
1
1
1
1
1
1
1
0
2
1
1
1
1
1
1
1
0
0
0
1
1
2
2
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
0
1
1
0
1
1
2
1
0
0
1
1
1
1
2
1
1
1
1
1
0
2
1
2
2
2
0
2
2
1
2
3
1
1
1
0
1
3
2
2
0
1
1
2
2
0
0
1
1
1
1
1
1
2
0
2
2
2
2
0
1
2
0
1
0
1
2
1
1
2
0
1
0
1
0
0
0
0
2
0
0
2
1
1
1
1
0
1
2
1
1
1
0
2
2
2
1
1
1
1
1
1
1
1
2
0
1
1
1
2
1
1
0
2
0
0
1
0
0
2
1
2
1
0
1
1
1
2
1
1
1
1
1
1
1
1
2
1
2
0
0
1
0
0
2
1
0
0
2
1
1
1
1
0
1
0
0
2
1
2
1
2
1
1
2
2
2
1
0
0
1
1
0
2
2
1
0
1
0
1
1
1
1
2
1
1
1
2
1
1
1
4
0
1
1
1
0
1
1
0
1
0
0
1
1
1
2
1
1
2
1
0
2
2
0
1
2
1
1
1
0
0
1
0
1
0
2
2
2
1
0
0
1
1
0
1
1
1
0
2
1
1
0
1
1
1
0
0
2
0
1
1
0
1
0
1
1
2
1
1
1
1
1
2
2
2
0
1
0
1
1
1
0
0
1
1
1
1
0
0
0
2
0
0
2
0
2
1
0
1
1
1
0
0
2
1
1
0
1
1
2
0
0
2
1
1
0
2
1
1
1
0
1
1
2
1
1
0
0
1
1
1
1
0
0
1
0
1
2
1
1
2
1
1
1
0
0
2
1
1
2
1
0
1
1
0
2
1
1
0
1
2
2
1
2
0
1
2
1
0
0
2
1
1
1
1
1
1
0
2
1
1
1
1
1
2
1
1
1
0
1
1
0
0
1
0
2
1
1
1
1
2
1
0
1
1
2
2
0
1
1
1
2
5
1
1
1
1
1
1
2
1
2
1
2
1
2
2
2
2
2
1
0
2
2
1
1
1
1
2
0
1
2
2
2
1
3
0
0
0
1
1
1
2
2
0
2
0
1
2
1
2
3
1
1
1
1
0
2
1
1
1
1
2
2
2
1
1
1
2
2
1
1
1
2
0
1
1
1
0
1
3
1
2
1
0
1
1
2
1
1
0
0
1
1
3
2
2
1
1
2
0
2
2
1
2
2
1
0
1
1
1
1
2
1
2
1
0
1
1
1
2
1
1
2
2
1
1
0
0
2
0
0
0
0
1
1
0
1
2
1
1
1
1
1
1
3
0
1
1
1
0
1
0
2
0
1
1
0
1
1
1
2
0
0
0
1
1
0
0
0
1
0
1
1
3
0
1
1
2
1
0
2
2
0
1
2
1
1
1
1
0
1
1
2
1
2
0
1
2
1
1
1
1
1
1
1
1
0
2
3
1
1
0
0
1
1
1
1
2
1
0
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
0
2
1
1
0
0
2
1
2
0
2
2
0
1
1
1
1
1
2
1
1
0
1
2
1
1
2
1
1
1
1
1
2
2
1
1
0
0
0
1
1
0
0
1
1
0
1
2
2
1
1
1
1
2
2
0
0
0
2
1
2
1
1
0
0
1
2
0
1
1
1
0
1
2
1
2
1
1
1
0
1
1
1
0
1
2
1
1
1
1
0
1
1
0
0
1
1
1
1
1
0
1
1
2
1
2
1
1
1
1
1
1
1
3
1
1
2
0
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
0
1
1
0
0
0
0
1
0
2
0
2
2
1
1
2
2
1
0
2
0
2
2
1
2
1
1
0
1
2
1
2
1
1
1
2
0
1
1
0
0
2
2
0
1
1
0
1
1
0
1
2
2
1
1
1
2
3
0
1
1
2
2
1
2
1
2
0
1
2
1
1
1
1
2
2
1
1
0
0
1
1
0
1
2
0
2
2
1
1
2
0
1
2
0
2
1
1
1
1
0
0
1
0
1
1
1
0
0
0
1
1
1
1
1
1
0
1
1
1
1
0
1
1
1
1
2
1
2
2
0
0
2
2
1
1
0
0
0
2
1
0
0
1
0
0
0
0
1
2
1
0
2
0
1
1
1
1
1
2
1
2
2
1
0
2
2
0
1
1
1
1
0
1
1
3
0
0
0
1
0
1
0
1
1
1
3
0
0
1
0
1
2
1
1
1
1
1
2
1
1
1
2
1
1
0
2
1
2
2
1
2
0
1
1
1
2
1
1
0
1
2
1
2
1
0
1
2
1
1
1
2
2
1
0
1
1
0
0
1
1
1
1
1
1
1
2
0
1
0
2
2
1
1
0
1
2
1
0
2
1
0
2
1
1
1
2
1
2
1
1
1
2
1
0
1
1
0
2
2
2
0
1
1
1
1
1
0
1
1
1
0
3
1
1
1
1
0
1
2
0
1
1
2
0
2
2
1
0
1
1
2
2
1
1
1
1
1
1
2
1
1
0
0
0
2
1
0
0
0
1
1
0
1
1
1
1
1
2
1
1
1
1
2
2
1
1
1
3
2
1
1
1
1
0
1
1
0
1
1
1
2
0
1
1
1
1
1
1
0
2
2
1
2
1
0
2
1
0
0
0
2
0
1
1
0
1
2
1
1
1
1
1
1
1
1
1
0
1
1
1
2
2
1
1
2
1
1
0
2
1
0
1
0
0
0
1
1
1
2
2
0
1
0
1
2
1
0
0
0
1
1
0
1
0
1
0
1
2
2
1
1
1
1
1
1
1
1
0
1
0
1
2
1
1
0
0
2
2
1
2
1
2
0
0
1
1
1
0
2
2
0
1
1
2
1
2
2
2
1
1
1
1
1
1
0
2
0
2
1
2
1
2
1
2
1
2
3
1
2
0
0
0
0
2
2
0
1
1
1
0
1
1
0
1
1
0
1
1
1
2
1
0
0
1
1
1
2
0
1
1
1
1
0
1
1
1
1
1
0
1
1
0
1
0
1
2
2
2
1
0
1
0
2
0
2
2
1
0
2
1
0
1
2
0
1
1
1
1
1
0
0
1
2
1
2
0
1
0
1
2
0
0
0
1
1
1
2
0
1
0
1
1
1
1
1
0
2
1
1
1
1
1
1
1
1
0
1
2
1
1
2
2
1
1
1
1
0
2
1
0
0
2
0
1
2
1
1
1
0
1
0
2
2
1
1
1
1
2
2
0
0
1
0
1
1
1
1
0
1
1
0
0
1
1
1
0
2
1
1
0
2
1
1
1
2
3
1
1
0
2
1
1
1
1
1
0
1
0
1
0
0
0
1
2
2
1
1
1
0
1
1
3
1
1
2
2
0
0
1
1
2
1
1
1
0
2
1
1
1
1
2
0
3
0
0
1
1
1
0
1
2
1
1
2
1
2
2
1
1
0
1
1
2
1
1
0
1
1
2
1
1
0
1
0
0
1
1
0
1
2
1
1
2
0
2
1
0
1
1
2
0
1
1
1
2
1
1
0
1
1
2
1
1
0
0
2
1
1
2
0
1
0
1
1
1
2
1
0
0
2
1
0
1
1
2
1
1
1
0
1
1
1
1
1
0
1
0
1
0
1
1
1
0
2
0
1
2
1
1
0
2
0
0
1
2
1
2
1
0
2
1
1
2
1
1
2
1
2
1
1
0
2
2
0
1
1
0
1
2
1
0
2
2
1
2
3
2
1
0
1
0
2
2
2
1
1
2
0
1
2
1
2
2
1
0
1
1
1
1
1
2
2
0
1
1
0
2
1
0
1
2
1
1
1
1
2
1
1
2
0
1
3
2
0
0
1
1
1
2
0
0
0
1
1
0
0
1
1
2
2
0
1
1
1
1
2
1
2
1
2
2
2
1
1
2
1
1
0
0
0
0
1
2
1
1
1
2
2
1
1
1
0
1
1
2
1
1
2
1
1
1
1
0
1
1
2
1
1
2
2
1
1
1
1
1
1
1
0
1
2
1
2
0
1
2
1
1
1
1
0
1
1
2
1
1
1
0
1
2
0
1
1
1
0
0
2
1
0
1
1
1
2
0
2
1
2
1
1
2
1
0
2
1
1
1
1
1
2
1
1
1
2
2
0
2
1
1
2
1
1
1
0
1
2
1
0
1
0
2
1
0
0
2
2
1
1
1
1
1
2
2
1
1
0
1
1
1
1
1
3
0
1
0
1
2
1
2
1
0
2
0
1
0
1
1
1
0
2
2
2
1
2
1
0
1
0
2
1
0
1
2
0
0
0
0
2
1
1
0
0
0
0
1
1
1
0
1
1
0
1
1
1
1
2
2
1
1
2
1
1
1
0
2
2
2
1
1
1
1
1
0
2
1
1
2
1
2
1
1
1
1
0
1
0
0
1
1
0
1
1
1
2
0
1
2
2
1
0
1
1
1
2
1
0
1
1
1
2
2
0
1
2
1
1
2
2
0
2
1
1
0
1
1
1
1
2
1
1
2
2
1
2
1
1
0
0
1
1
1
2
2
1
1
1
1
1
1
1
1
1
2
1
1
1
0
1
2
1
1
1
2
0
1
1
1
1
1
1
2
1
1
1
2
1
0
0
2
2
2
1
1
2
0
0
1
2
2
2
1
1
2
0
2
1
1
1
1
1
1
3
1
1
2
1
1
1
0
0
4
2
1
1
1
1
0
1
2
1
1
1
2
2
0
2
0
1
1
1
2
2
1
1
2
1
1
2
1
0
1
1
0
2
0
1
2
1
1
2
2
2
2
1
2
2
0
1
2
1
2
1
2
1
2
0
1
0
0
2
1
2
2
0
0
0
0
1
1
1
2
0
1
0
2
0
1
0
1
2
1
0
2
1
0
1
0
2
1
1
0
1
2
0
1
2
0
0
2
2
2
1
1
1
1
1
1
2
1
1
1
1
0
0
1
0
1
1
0
2
2
0
1
2
1
1
1
1
0
1
2
0
1
1
1
1
2
1
1
1
2
1
2
1
1
1
0
1
2
1
1
2
1
0
1
1
2
1
1
1
0
1
2
2
1
1
1
2
2
1
3
1
1
1
0
1
0
1
1
1
1
1
1
2
1
2
2
1
0
1
0
2
1
0
0
1
1
0
1
2
1
1
2
0
1
2
2
2
1
1
1
1
1
0
1
3
0
1
1
1
1
1
3
0
1
0
1
0
1
1
0
2
0
2
2
1
1
1
0
0
3
2
2
0
1
2
1
1
0
3
1
1
0
1
2
1
1
1
1
1
1
1
2
1
0
1
1
1
1
2
1
1
0
1
2
2
1
0
1
0
2
0
3
1
1
1
2
2
1
1
1
2
2
0
1
1
2
1
1
1
1
2
1
0
0
1
1
1
1
1
1
0
1
0
0
1
2
2
2
2
0
2
1
1
1
1
2
0
1
0
1
1
1
1
1
1
1
1
2
1
1
2
1
0
2
1
1
1
1
1
6
1
0
0
1
0
1
2
0
1
0
1
1
1
2
0
0
2
1
2
1
1
1
0
0
0
0
2
0
2
1
2
2
2
1
1
0
2
0
1
2
1
2
1
1
0
1
2
1
1
2
2
1
2
1
2
2
1
0
0
2
1
2
1
1
1
1
1
1
0
1
2
1
0
0
0
0
1
1
1
0
1
1
1
0
0
1
1
1
1
2
1
1
2
2
1
2
1
1
1
0
1
2
0
1
2
1
3
1
1
1
1
1
1
1
1
1
1
0
1
1
1
2
1
1
2
1
1
2
2
2
0
0
1
1
0
1
1
2
3
0
0
1
1
1
0
1
2
1
2
1
1
1
2
0
1
1
1
1
1
0
2
2
1
1
1
2
1
2
0
1
0
2
1
1
1
1
1
1
2
2
1
0
1
1
1
1
1
2
1
1
0
1
1
2
1
1
0
1
0
1
1
2
1
2
1
1
2
1
1
1
2
0
2
1
1
2
2
0
1
0
1
0
0
2
2
1
1
2
1
0
0
1
1
1
1
1
1
0
0
2
0
1
1
2
2
2
0
0
1
1
0
1
0
2
0
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
2
0
2
0
1
1
1
1
1
2
2
2
1
0
2
2
1
1
0
0
2
0
1
2
2
0
1
2
1
1
1
1
0
2
1
1
1
1
1
1
1
2
1
2
0
0
1
0
1
2
1
1
0
1
1
1
1
2
2
2
0
0
2
1
0
1
1
2
1
0
1
1
1
1
2
1
1
1
1
0
3
1
1
1
1
0
1
2
2
2
1
0
1
1
2
2
1
1
1
2
1
1
2
1
1
1
1
2
0
1
0
0
2
2
1
0
0
0
1
2
1
2
0
2
2
1
1
0
1
1
1
2
1
1
1
0
0
2
0
1
0
0
0
0
1
1
0
1
1
2
0
0
2
0
1
1
1
1
2
1
1
2
1
1
0
1
1
0
2
0
1
1
1
1
1
2
1
1
1
1
0
0
2
2
0
2
1
0
1
1
2
0
2
1
1
0
3
1
0
1
2
0
1
1
1
1
1
2
1
1
2
0
1
1
2
0
2
1
1
2
1
1
0
1
2
1
2
0
0
1
0
0
1
0
1
0
0
1
2
2
1
1
1
2
2
1
0
0
2
1
1
1
0
0
2
2
1
1
1
1
0
0
1
2
1
0
1
1
0
1
1
0
1
2
0
1
2
2
1
1
2
1
1
2
1
1
1
1
1
1
0
2
2
1
2
0
0
0
1
1
1
1
1
1
0
1
1
2
2
1
2
1
2
1
0
1
0
1
1
1
1
1
0
1
1
1
0
1
1
1
1
3
0
1
1
1
1
1
1
1
1
0
2
2
0
1
3
1
1
1
1
1
1
2
1
1
1
0
2
0
0
2
1
1
1
1
2
0
1
1
1
0
0
1
0
1
0
1
1
0
0
2
0
1
0
1
2
2
0
0
1
0
1
1
1
1
1
1
1
0
1
1
0
1
0
1
1
1
1
2
0
1
0
1
0
2
1
0
2
1
0
1
2
2
1
0
1
0
2
2
1
0
1
1
1
0
0
2
0
1
0
1
1
1
2
2
2
2
1
0
0
2
1
2
1
1
0
0
1
1
0
0
2
1
0
1
1
0
0
0
2
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
2
1
0
1
0
0
0
1
1
0
1
0
0
1
0
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
0
0
1
2
1
2
1
0
0
1
2
1
2
2
1
0
1
2
1
2
1
0
1
1
1
1
1
0
1
1
1
1
0
0
2
2
0
2
2
2
1
3
2
2
2
1
2
1
1
1
1
1
2
0
0
1
1
1
0
0
1
1
1
2
2
1
2
1
1
1
1
1
0
1
2
1
2
0
0
0
0
1
2
0
2
1
0
1
1
1
2
1
1
2
0
1
0
2
2
0
1
1
0
2
2
0
2
0
1
2
1
2
1
1
2
0
0
2
1
1
0
1
1
1
1
2
1
2
2
1
2
0
2
0
3
1
1
2
0
0
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
0
0
0
0
1
1
1
4
2
2
1
1
1
1
2
0
1
1
1
2
0
0
1
1
1
1
2
1
0
0
2
2
1
1
1
0
0
1
2
2
1
2
1
2
0
0
2
1
1
2
2
1
2
1
1
0
1
1
0
2
1
1
0
2
1
1
1
1
1
1
1
0
0
2
1
0
0
1
1
1
2
1
1
0
2
1
1
1
1
0
2
1
0
1
1
1
2
1
0
0
1
1
2
1
1
2
1
1
3
0
1
1
2
1
1
1
1
1
0
1
2
1
1
0
1
0
2
1
1
2
1
0
1
1
0
2
1
1
2
0
1
1
2
2
1
0
1
1
1
0
1
0
0
2
0
2
1
1
1
1
1
1
2
1
0
2
1
2
2
1
0
1
1
2
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
0
1
0
0
0
1
0
1
0
1
1
0
1
2
2
1
2
1
1
1
0
1
1
1
1
0
1
1
2
1
0
1
1
0
1
2
0
2
1
1
0
1
2
0
0
1
0
1
2
1
1
2
1
1
2
2
1
2
0
0
0
2
0
1
0
2
1
1
1
0
1
1
1
2
1
1
0
0
1
0
0
1
1
0
1
1
1
2
2
0
3
1
1
1
1
0
1
1
1
2
1
1
0
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
0
1
1
1
1
1
2
1
1
2
2
0
0
0
1
1
2
1
0
1
1
0
1
0
0
0
2
1
0
2
1
1
1
1
1
1
0
1
0
0
2
1
1
1
2
1
0
1
2
1
1
2
1
2
0
2
1
1
1
1
0
0
2
1
1
1
1
1
1
1
2
1
1
2
2
2
2
1
0
1
0
1
2
1
2
1
1
2
0
1
2
0
1
1
1
1
1
2
0
1
1
1
0
1
1
1
1
1
1
2
1
0
1
0
0
1
1
1
2
1
2
1
0
2
2
2
0
1
1
0
1
1
1
1
1
2
1
2
3
1
2
1
1
2
1
2
1
1
1
1
1
2
1
0
0
1
1
1
1
2
1
2
0
1
1
0
0
4
2
1
0
1
2
0
2
1
0
2
2
1
1
2
2
1
1
1
0
1
1
0
2
2
1
1
1
1
1
0
1
2
1
1
2
1
2
1
2
0
0
2
1
2
1
0
0
1
0
2
1
1
0
0
1
2
1
0
2
2
1
0
2
1
0
1
2
1
2
1
1
1
0
0
2
0
2
0
1
1
0
0
2
1
0
1
0
1
1
1
1
1
1
1
0
2
2
0
0
1
1
2
1
2
1
0
0
0
0
2
0
1
1
1
1
1
0
1
2
0
1
2
1
1
1
1
2
1
1
1
1
2
1
0
2
2
2
2
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
0
0
2
0
0
0
0
1
1
1
1
2
0
0
0
1
1
0
0
1
3
1
1
1
2
0
2
1
1
2
0
1
1
1
1
2
2
1
0
1
1
1
2
0
0
0
1
2
1
2
1
1
0
1
2
1
0
0
0
1
2
1
2
0
2
2
1
1
1
1
1
0
1
2
1
2
1
0
1
0
0
1
0
1
1
1
0
1
0
1
0
1
1
2
0
0
0
1
1
1
0
0
1
1
1
0
2
2
1
1
0
1
1
1
1
1
2
1
1
2
2
2
1
1
1
0
1
1
0
0
1
2
1
0
0
1
0
1
0
1
1
0
1
0
1
1
1
0
1
1
1
1
0
1
1
2
2
1
2
0
1
1
1
1
1
0
2
1
0
1
1
1
1
1
0
1
1
2
0
1
1
0
0
1
1
1
1
0
0
3
0
0
1
1
2
2
2
0
1
0
1
1
2
1
1
0
0
1
1
0
2
0
2
1
2
1
1
2
1
1
0
2
1
0
0
0
1
0
2
0
0
1
1
1
1
0
0
0
1
2
0
0
1
0
1
0
1
2
1
1
0
2
2
2
0
1
1
2
0
0
1
1
1
2
1
0
1
1
0
2
0
1
1
2
1
0
2
1
0
1
0
1
2
2
1
0
1
1
1
1
1
1
1
1
0
0
1
1
1
2
1
1
0
2
1
1
1
1
1
0
1
1
1
1
0
0
0
2
1
1
0
1
1
2
2
0
0
0
0
2
0
1
1
2
2
1
1
0
1
1
2
1
1
2
0
0
0
2
1
1
1
1
1
1
1
2
1
2
1
1
1
2
1
1
1
2
2
0
1
1
0
0
1
2
1
2
1
2
5
1
0
1
1
1
1
0
1
1
2
1
1
0
2
1
2
1
1
0
1
0
1
1
2
2
2
2
3
0
1
1
1
2
0
0
0
2
1
1
1
1
1
1
0
1
1
1
0
1
0
1
2
1
1
1
1
1
0
1
1
1
0
0
1
1
0
0
0
1
1
3
1
1
2
1
1
1
2
0
0
1
1
1
2
0
1
1
0
1
3
0
1
1
0
0
2
0
1
0
2
0
3
0
1
1
1
1
2
1
2
0
1
2
2
1
2
1
1
0
2
0
1
1
0
2
2
1
1
1
1
2
1
2
1
2
2
1
2
1
1
1
0
1
0
2
0
1
1
0
1
1
3
0
1
1
1
2
0
1
2
1
0
1
1
1
1
0
1
0
0
0
1
2
0
1
1
1
2
0
0
1
2
0
1
2
2
1
1
1
1
0
1
1
0
2
1
0
1
1
1
2
1
2
2
0
1
2
1
1
1
1
1
4
1
1
1
1
1
0
2
0
0
1
1
0
1
0
1
1
1
1
2
1
0
1
2
2
0
1
2
1
1
1
2
2
0
1
1
1
0
1
0
1
1
2
1
1
1
3
0
2
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
2
1
0
1
1
2
2
1
1
0
0
0
2
2
1
1
1
2
0
3
0
0
2
0
1
0
0
2
0
0
1
1
1
1
1
1
1
1
0
1
2
1
1
1
0
2
2
2
1
0
0
2
0
2
2
1
0
1
1
0
0
1
1
1
1
1
2
1
0
1
0
1
1
1
1
1
1
1
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
2
2
2
1
1
2
0
1
1
2
1
1
1
2
2
0
1
1
1
1
0
2
1
1
1
2
0
2
1
1
0
1
2
1
1
1
0
2
1
1
0
1
1
0
1
1
1
2
1
1
1
1
1
0
0
1
2
2
1
2
0
0
2
1
0
2
1
1
1
2
1
2
1
1
1
1
0
2
0
1
1
2
0
0
1
1
2
1
1
0
2
1
1
1
1
2
2
1
0
0
1
2
1
1
0
1
0
0
1
3
0
2
2
0
0
2
1
0
0
0
1
1
2
1
1
1
2
1
1
1
2
3
1
1
2
1
2
0
0
0
2
1
0
0
1
2
1
1
0
2
1
1
1
0
1
2
1
0
0
2
1
0
0
2
1
2
0
2
2
2
0
1
1
1
0
0
1
0
1
1
2
0
1
1
2
0
1
0
1
1
1
1
1
0
2
1
0
0
1
0
1
1
2
2
0
1
1
0
1
2
0
1
0
1
0
1
1
2
2
0
1
0
0
2
1
0
2
1
2
0
0
1
1
1
1
0
2
1
1
1
2
1
1
1
0
1
1
1
1
0
1
1
0
1
1
1
2
1
1
0
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
2
1
0
1
2
0
1
1
0
2
1
1
1
1
1
2
1
0
1
0
1
1
2
0
2
1
0
1
1
1
1
1
1
2
0
1
0
1
1
1
1
0
0
2
1
1
1
1
0
1
0
0
2
1
0
2
0
1
1
1
1
0
0
1
2
1
0
1
0
0
0
1
1
1
2
2
2
1
0
0
1
0
2
0
1
1
1
0
1
1
2
0
0
2
2
2
1
0
1
1
1
0
0
2
1
2
1
2
2
2
1
1
1
1
1
1
0
1
2
1
0
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
0
1
1
1
1
1
1
1
2
1
2
1
0
1
1
1
1
1
2
2
1
2
2
0
2
2
1
1
2
1
0
1
0
0
0
1
2
2
1
9
0
2
1
1
1
0
1
1
1
2
2
2
2
1
2
1
1
1
1
1
1
0
1
0
0
0
1
1
1
1
2
0
1
0
0
0
2
1
1
2
0
0
0
2
2
1
2
1
1
0
1
1
1
0
1
0
1
1
1
1
3
0
2
0
1
0
0
1
1
0
1
1
1
1
1
1
1
2
1
1
0
2
2
1
0
1
1
2
1
2
0
1
2
0
1
2
1
1
1
0
0
1
1
1
0
0
2
0
1
1
1
1
1
1
0
2
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
1
0
0
2
1
2
0
0
1
1
2
1
0
2
0
2
0
0
0
2
2
2
0
1
1
1
2
1
0
1
1
0
1
1
2
1
1
2
1
0
2
0
1
2
0
0
1
1
1
2
1
1
2
0
1
1
2
1
2
2
1
2
2
1
2
1
1
1
2
2
2
0
2
2
1
1
2
2
1
2
1
1
0
1
1
1
1
2
1
1
1
0
1
1
2
1
0
0
1
2
1
1
1
2
2
2
1
1
0
2
1
1
1
1
2
0
1
1
0
1
1
1
1
1
2
2
1
2
1
1
1
1
3
1
1
1
1
2
1
1
0
0
0
1
2
1
2
1
1
1
2
0
1
1
0
1
2
0
1
1
2
1
0
0
1
1
1
0
2
1
1
2
1
2
0
1
2
2
1
0
1
0
2
1
1
1
0
1
1
1
2
0
1
1
2
2
1
2
1
0
1
2
1
2
0
1
1
0
2
0
1
1
1
0
0
1
0
2
1
1
2
1
2
1
2
0
1
0
1
1
1
0
1
1
2
0
1
1
1
1
1
1
0
0
0
0
1
0
1
1
0
1
1
0
0
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
0
1
1
1
1
1
0
0
1
0
0
1
1
1
1
0
1
1
1
1
1
1
2
0
1
1
2
1
2
1
1
0
1
1
0
2
3
1
1
1
1
2
1
1
1
1
0
1
0
1
1
2
1
1
1
1
0
1
1
1
1
1
1
1
0
0
1
0
1
2
1
1
1
1
1
2
1
1
1
1
1
1
2
2
0
2
2
2
1
2
1
1
1
2
1
1
1
1
1
2
0
0
1
2
1
0
2
0
2
1
1
1
0
1
1
1
1
1
3
2
1
1
2
2
0
1
1
1
2
1
0
1
0
0
2
2
1
1
1
0
2
1
1
2
2
2
2
2
1
1
0
1
0
1
1
1
1
2
2
1
2
0
1
0
1
1
1
1
1
2
1
1
0
1
1
0
1
1
0
2
2
2
1
1
1
2
1
2
0
1
2
3
1
1
0
2
0
1
1
1
1
2
2
1
2
2
0
2
1
0
1
5
1
1
1
1
0
2
1
1
1
1
3
1
0
1
2
1
1
1
0
0
2
4
2
1
1
2
1
2
1
2
2
1
0
2
1
1
0
1
1
1
2
1
2
1
0
0
0
2
1
1
2
1
0
1
2
1
1
1
0
2
2
1
0
1
1
2
1
1
2
1
1
1
1
2
0
1
0
1
1
1
1
0
1
0
0
1
1
1
1
2
2
0
0
0
1
2
0
1
1
2
2
1
1
1
0
2
2
1
2
0
1
1
2
2
1
2
1
1
1
1
2
1
1
2
0
1
1
1
1
0
2
1
1
1
2
2
0
2
1
1
0
2
2
2
2
0
0
1
1
1
0
2
2
2
0
2
1
1
1
2
0
0
0
1
1
1
0
1
2
1
2
1
1
2
1
1
1
2
1
1
1
1
0
0
2
0
2
1
2
1
2
0
1
1
0
0
1
1
1
1
0
0
1
0
2
0
1
0
1
1
1
1
1
1
1
1
1
0
0
1
2
1
0
2
1
0
1
0
2
1
1
1
0
2
0
1
2
2
0
0
1
1
2
0
1
0
1
0
0
1
0
2
1
2
1
0
2
0
3
2
1
2
1
1
2
1
1
1
0
1
2
1
1
2
1
1
1
1
1
0
2
0
1
2
0
0
0
1
2
0
1
1
1
1
1
1
1
1
0
1
1
1
1
0
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
0
1
1
1
2
2
2
1
0
1
1
1
1
1
0
1
0
0
2
1
2
1
0
1
1
1
1
2
1
1
2
1
1
1
1
1
0
1
2
1
0
1
2
2
1
0
0
1
2
1
2
0
1
1
1
1
2
1
0
0
2
1
2
1
1
2
1
1
0
1
1
1
1
2
1
1
1
0
2
2
2
1
1
1
2
1
0
1
2
2
2
2
1
1
0
1
0
1
1
1
1
1
0
2
2
0
0
2
2
0
0
2
0
1
0
1
1
1
0
2
0
2
1
2
1
1
1
0
1
0
1
1
2
0
0
1
1
0
2
0
1
1
1
1
0
1
2
0
1
1
2
2
2
1
2
1
1
1
1
1
2
2
1
0
2
1
1
1
1
1
1
1
2
1
2
1
1
0
2
1
1
2
2
1
1
1
1
1
0
1
1
2
1
0
0
0
1
2
1
1
2
2
1
0
1
2
1
1
0
0
1
0
1
0
1
1
1
2
1
0
0
1
1
2
1
0
0
1
1
0
0
2
2
0
2
1
1
1
1
1
1
1
0
1
3
2
0
0
2
2
1
1
2
2
1
1
0
2
1
2
1
2
0
2
2
1
0
2
1
1
2
0
2
1
1
2
2
0
1
0
1
1
0
1
1
1
2
0
1
0
0
0
2
1
1
1
1
2
1
1
2
0
2
1
1
0
1
1
1
2
1
1
2
0
0
2
1
1
2
2
1
1
1
1
0
2
1
1
0
1
0
0
2
1
1
0
2
1
1
2
1
1
2
0
1
0
2
0
1
2
1
1
1
1
1
1
1
0
1
1
2
1
1
2
2
0
2
0
1
1
1
1
2
2
2
2
1
0
2
1
1
0
1
2
2
0
0
1
1
2
0
0
1
1
1
1
1
0
1
1
1
0
2
0
1
2
3
1
1
1
1
1
1
0
1
2
0
0
2
1
1
1
1
1
1
1
2
0
1
1
1
1
1
0
1
1
1
1
1
0
2
1
1
2
1
1
2
1
0
1
1
0
2
1
1
2
0
2
0
1
2
0
0
1
1
1
1
1
0
2
2
1
1
2
1
1
2
1
1
0
0
2
1
0
1
1
1
1
1
3
1
2
2
0
1
1
1
1
1
0
1
0
1
1
0
1
0
1
1
0
0
1
1
1
0
2
2
1
2
1
0
2
0
2
2
0
1
1
2
0
0
0
1
1
0
2
1
2
0
2
2
1
2
0
2
1
1
0
1
1
1
2
2
1
0
1
1
1
1
2
2
2
0
2
0
0
0
1
1
2
2
0
0
2
2
2
1
0
0
2
2
1
1
0
1
2
2
1
1
1
1
1
1
1
1
1
0
2
0
1
0
1
2
0
1
1
1
2
1
1
0
1
2
1
1
1
0
2
2
1
1
1
2
1
1
1
0
2
2
0
1
1
2
1
1
2
2
0
2
0
1
1
1
2
1
1
2
1
0
0
1
1
2
2
0
2
1
1
0
0
1
1
1
1
1
1
1
2
1
0
1
0
1
1
2
1
2
1
0
2
2
1
1
1
2
1
2
2
1
3
0
1
1
0
1
0
1
1
1
1
1
1
0
0
0
1
1
1
0
2
1
0
0
1
0
1
1
1
1
0
2
2
2
0
2
1
1
1
1
2
1
2
2
0
2
1
1
2
0
2
1
0
0
1
2
1
0
1
2
0
1
1
1
1
1
2
1
0
2
2
1
0
1
1
1
0
2
2
2
2
1
0
1
2
1
1
0
2
1
1
2
1
1
0
2
1
3
1
1
0
1
0
1
2
1
2
0
1
2
2
0
1
1
1
1
1
3
1
2
0
1
2
1
1
1
1
1
2
2
2
1
2
0
1
1
2
2
2
2
2
1
0
2
1
0
1
1
1
2
0
1
2
1
2
0
2
0
1
0
1
0
1
0
1
1
1
1
2
1
1
2
1
2
1
1
0
2
1
0
1
0
1
2
1
1
1
1
0
1
1
1
1
1
0
0
2
0
0
1
1
1
2
1
1
0
0
1
2
1
1
1
1
2
2
1
1
0
0
0
0
1
0
1
0
2
1
2
2
2
1
1
1
0
2
0
1
1
1
2
2
1
1
1
1
0
0
1
1
0
2
1
1
1
0
1
2
1
2
2
0
1
1
0
1
2
1
1
0
2
1
1
1
1
2
0
1
1
1
1
2
1
1
1
0
2
1
0
1
1
1
0
1
0
2
1
1
2
0
2
1
2
0
0
1
1
1
1
1
1
0
1
0
2
1
1
1
2
2
1
0
0
1
2
1
3
2
0
1
0
2
1
1
1
0
2
0
1
1
0
1
1
0
1
1
1
1
0
0
0
2
1
1
2
1
1
0
2
2
3
2
1
1
1
0
1
1
1
1
2
1
1
1
1
0
1
1
3
1
0
1
0
1
2
1
3
1
0
1
0
2
0
2
1
1
2
1
1
1
1
1
2
1
1
1
1
0
2
0
0
2
0
1
1
1
1
0
1
0
1
1
0
2
1
1
2
3
2
1
0
0
0
2
2
1
1
0
0
2
1
1
1
2
2
1
1
0
1
1
1
0
2
1
1
1
2
1
2
1
2
1
2
2
0
2
2
1
1
1
0
0
1
2
1
1
1
2
1
1
0
1
1
1
1
2
1
2
0
2
1
0
1
1
2
2
1
0
1
3
1
1
0
2
0
1
1
1
1
1
1
2
0
1
1
0
2
2
1
1
1
0
0
0
1
1
0
0
1
1
1
1
1
2
1
1
1
1
0
1
1
1
1
1
0
1
1
0
2
2
1
2
1
1
1
0
2
1
1
2
0
0
1
1
1
0
0
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
2
2
1
3
0
1
1
1
1
1
0
2
1
1
2
0
2
0
1
0
1
0
1
1
1
1
1
0
1
1
2
1
1
1
1
1
1
1
1
1
1
2
0
1
1
2
1
0
2
0
1
1
1
1
2
2
2
1
1
0
0
2
2
0
0
1
1
2
2
1
2
1
1
0
0
1
1
0
2
1
0
0
2
1
1
1
1
0
1
2
0
1
1
1
0
1
6
1
1
2
0
2
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
2
2
1
1
2
1
0
0
1
1
2
2
1
2
1
1
1
1
0
2
2
1
1
0
0
1
1
2
2
1
1
1
1
0
1
0
1
0
2
1
1
2
3
0
2
1
0
0
0
1
0
1
0
1
1
0
1
2
1
1
2
1
2
0
1
1
1
2
0
1
1
1
0
1
1
2
1
2
0
1
1
1
1
1
1
2
1
1
1
1
2
0
2
1
1
1
0
0
0
1
1
2
1
1
1
0
2
0
2
1
0
1
1
1
2
1
1
1
2
1
2
0
1
1
0
1
2
1
0
1
1
2
1
1
1
2
1
2
0
1
1
0
0
2
1
1
0
1
1
2
1
1
1
1
1
2
2
1
2
0
1
2
0
1
2
1
0
2
2
1
1
1
1
1
0
1
0
1
1
0
0
1
2
1
0
2
2
0
1
1
1
1
1
1
4
1
1
0
2
0
1
2
2
0
1
1
2
2
1
1
2
2
0
2
1
2
1
0
2
0
1
2
1
0
1
1
2
1
1
1
0
2
0
1
1
6
2
1
1
1
3
1
0
0
2
1
1
2
1
0
1
1
1
1
2
1
1
1
0
2
2
0
1
1
0
1
1
1
1
2
2
2
0
0
1
2
2
1
2
1
1
1
1
1
2
1
0
1
1
0
1
0
0
2
1
0
1
1
0
1
2
0
0
1
1
1
2
3
2
1
1
1
1
0
1
2
1
1
1
1
1
0
1
1
2
1
1
1
2
1
0
1
1
0
2
1
0
0
1
1
0
1
0
1
0
3
1
2
1
1
1
2
2
1
1
2
1
1
1
0
1
1
1
1
4
1
3
1
1
1
0
2
1
1
1
0
1
2
1
2
1
2
0
0
1
2
0
1
1
0
1
1
1
0
2
1
1
1
2
1
1
2
2
0
1
2
1
1
1
1
1
2
0
1
2
0
1
2
1
1
2
1
2
0
0
0
2
0
2
1
1
0
0
0
0
2
0
1
1
0
1
1
1
1
0
1
0
1
1
1
1
2
1
2
1
2
1
2
1
0
1
1
1
1
2
2
1
1
2
1
1
2
1
1
1
1
1
1
1
1
0
2
1
2
0
1
1
1
1
2
0
2
1
1
1
0
0
1
1
0
1
1
2
1
2
0
2
2
0
1
2
1
0
1
0
2
1
1
1
2
1
0
1
2
2
1
1
1
1
1
1
0
1
1
0
1
0
0
1
1
0
1
2
1
1
1
1
1
1
1
2
1
1
1
0
0
1
0
0
1
0
0
1
0
0
2
2
1
1
0
0
0
1
1
1
1
2
1
1
1
3
1
1
1
1
1
2
1
0
0
1
1
2
1
2
1
0
2
0
1
1
2
1
0
2
0
0
1
1
0
1
1
2
0
2
1
0
1
1
1
1
1
0
1
1
0
1
2
2
2
1
1
1
0
0
1
1
0
1
1
2
0
0
1
2
1
0
1
1
0
2
1
0
2
2
1
1
1
1
1
1
0
1
1
1
2
1
2
1
1
2
2
1
0
1
2
2
1
1
2
1
1
1
1
0
1
0
1
2
1
1
2
1
1
1
0
0
1
2
1
0
2
1
1
2
0
2
1
1
2
2
1
0
0
2
2
3
1
0
1
2
0
2
1
1
1
1
0
1
2
1
2
0
1
2
0
1
0
1
1
2
0
1
1
2
2
0
1
1
1
0
1
1
2
1
0
1
2
0
1
2
0
1
1
0
1
2
2
2
0
1
1
0
1
1
1
1
0
2
1
1
1
1
1
1
1
2
1
2
1
0
0
1
1
1
1
0
1
1
0
1
1
1
2
0
1
1
1
1
1
0
1
1
1
1
1
1
0
1
1
2
1
2
0
1
1
1
1
1
1
2
1
1
2
3
2
1
2
0
2
1
1
2
1
1
2
1
1
1
1
1
3
1
1
1
0
1
1
1
1
0
0
0
1
0
2
1
1
2
1
1
2
2
2
0
0
0
1
1
2
0
1
2
2
1
0
1
0
0
2
1
1
0
1
2
0
0
2
0
1
2
2
1
0
1
2
1
1
2
1
1
1
0
1
1
1
1
1
1
0
1
1
0
1
2
2
0
1
1
1
0
1
2
1
0
1
2
2
0
0
0
1
1
0
1
2
0
1
2
2
0
0
1
1
1
2
1
2
1
1
0
1
1
0
1
2
2
1
0
1
0
1
1
1
1
2
2
2
1
2
0
1
0
1
1
1
0
1
1
0
1
1
0
1
0
1
1
0
1
1
2
1
1
0
1
0
1
1
1
1
1
2
0
0
1
1
1
1
1
1
1
3
0
1
2
2
1
0
1
1
2
0
2
2
0
2
1
1
1
1
1
1
1
0
1
2
1
1
1
0
2
0
1
0
2
2
1
2
2
0
0
0
1
2
0
1
1
1
0
0
1
0
1
0
1
0
1
1
0
1
2
0
1
0
2
1
2
0
0
1
2
2
1
2
0
1
1
1
1
1
0
1
1
2
2
1
1
0
1
0
1
3
1
1
0
0
1
1
1
2
1
1
0
1
1
1
1
2
1
1
1
2
1
0
1
1
1
2
2
1
2
1
0
2
0
1
2
1
2
1
1
2
1
0
1
1
2
1
1
1
1
2
1
2
1
1
2
0
1
2
2
0
1
2
1
0
1
2
0
0
1
0
1
2
2
3
1
1
1
1
0
2
1
0
2
1
1
2
1
1
0
1
1
1
2
1
0
1
2
1
1
0
1
2
0
0
2
2
2
1
1
1
0
1
1
0
0
2
0
2
1
1
1
1
2
1
1
1
0
1
1
0
2
1
0
1
1
0
0
1
1
2
0
1
1
2
1
2
1
0
1
1
1
2
1
1
0
1
0
2
1
0
1
0
2
3
1
0
0
1
1
1
0
0
1
1
2
1
0
2
2
1
1
0
1
1
1
0
0
2
1
1
1
1
0
0
2
1
1
0
2
0
0
1
1
1
1
4
1
1
1
1
1
2
1
2
2
1
1
1
0
2
2
1
0
1
0
1
2
2
1
1
1
1
0
0
1
1
1
1
1
2
2
1
2
1
2
3
1
0
0
1
0
0
2
2
1
1
1
2
2
1
1
1
1
1
0
0
1
0
1
1
1
1
2
1
1
3
1
2
1
2
1
1
1
1
0
1
0
1
0
1
0
0
0
1
1
1
1
1
1
1
0
0
0
1
1
2
0
1
2
1
2
1
1
2
1
1
0
1
1
0
2
1
3
2
1
1
1
1
1
1
0
1
1
1
0
1
0
1
2
1
0
2
0
0
1
1
0
0
1
0
1
1
1
0
1
2
0
1
1
2
1
0
0
1
0
7
2
1
0
0
2
1
2
2
1
0
1
0
2
1
2
0
1
1
1
1
2
1
1
1
0
0
4
1
2
1
2
1
1
0
1
1
0
2
1
1
1
2
1
1
2
0
2
0
0
1
1
1
2
2
1
1
1
2
1
0
0
2
0
1
1
1
1
1
1
2
2
1
1
0
2
1
0
2
1
1
2
0
1
1
1
1
1
1
1
1
1
1
2
1
2
2
0
1
2
0
0
1
2
1
1
1
0
0
1
4
1
1
1
2
0
0
1
1
2
1
2
0
1
1
1
1
1
1
1
3
1
1
1
2
0
1
0
1
2
1
1
2
0
1
0
0
1
1
1
1
0
1
1
0
1
1
0
0
1
1
2
1
1
1
0
2
2
1
2
1
4
1
2
0
1
2
1
2
1
1
1
0
1
2
2
0
1
1
0
1
1
2
0
1
0
1
1
1
2
2
1
2
1
1
0
0
1
0
2
1
0
2
0
0
1
2
2
1
1
1
1
0
0
1
1
1
1
1
1
1
0
2
2
0
0
1
2
1
2
1
1
0
1
2
0
0
1
1
1
2
0
2
0
2
1
1
1
1
1
2
2
1
1
2
1
2
1
1
2
1
1
0
2
2
1
1
0
2
0
1
0
0
1
1
0
1
1
1
1
1
0
1
0
2
2
0
2
0
0
2
1
1
0
1
2
1
2
1
1
1
2
1
1
1
1
1
0
1
1
2
2
2
1
0
1
0
2
0
0
0
1
0
0
1
2
0
1
1
1
1
0
1
0
1
2
1
0
1
0
1
0
1
1
1
1
2
2
1
0
0
0
1
1
0
1
2
1
1
1
0
1
2
1
1
1
1
1
1
1
2
0
1
1
1
1
1
2
0
2
1
1
0
1
0
1
1
1
2
1
0
2
1
0
1
1
1
1
1
3
1
1
1
0
2
1
1
0
0
0
2
1
1
2
1
0
1
2
0
2
1
1
1
1
0
1
1
1
1
0
1
0
0
1
2
1
1
1
1
1
2
2
0
1
0
1
1
1
1
0
0
0
0
0
1
2
0
1
0
2
1
1
2
0
1
1
1
1
2
0
1
1
5
1
1
1
0
2
2
2
0
1
1
1
0
1
2
1
2
1
2
1
1
0
1
0
1
1
1
1
2
1
3
2
2
1
1
2
0
1
1
2
2
1
2
1
2
0
1
2
2
1
1
2
2
2
2
0
1
0
2
1
1
1
1
1
1
1
2
0
0
1
1
2
1
1
1
0
1
0
1
1
2
1
1
1
1
1
1
0
1
1
1
2
2
2
0
2
1
1
0
1
0
1
1
0
1
1
0
1
1
1
1
2
0
1
0
0
1
1
0
1
1
0
0
1
0
0
0
1
1
1
1
1
1
2
1
2
1
0
1
2
1
0
1
0
0
1
2
2
1
2
0
1
1
1
1
2
1
0
2
1
1
0
1
2
1
2
1
0
2
1
2
1
0
2
1
2
2
1
2
1
2
1
0
0
0
1
1
0
1
0
1
0
2
2
0
0
1
2
1
2
1
0
1
1
0
0
1
1
1
1
2
1
1
0
1
2
1
0
0
0
1
2
1
2
0
2
1
1
2
0
0
2
0
1
1
1
1
1
1
1
2
0
1
0
1
1
1
0
0
2
0
1
2
0
1
2
1
0
1
1
1
0
1
1
0
4
2
2
2
1
1
1
1
2
0
1
2
2
2
1
2
1
1
1
2
1
1
1
1
1
1
1
2
2
2
1
1
1
2
1
0
0
1
2
1
1
0
1
2
2
1
1
1
2
1
0
1
1
1
0
2
1
1
2
1
0
1
2
0
0
1
1
0
1
2
2
1
1
0
1
0
1
0
0
0
1
1
1
1
1
1
1
1
1
0
1
1
1
0
1
1
1
0
1
0
1
1
1
1
2
3
0
1
0
0
0
1
0
2
1
0
1
0
0
2
1
2
2
2
1
0
1
1
1
0
1
1
1
1
0
1
1
2
1
2
0
1
0
2
0
0
0
1
1
1
1
0
0
2
1
2
1
1
1
1
1
1
0
2
2
1
1
0
1
1
0
1
2
2
2
1
1
1
1
1
2
1
1
2
2
1
2
1
0
0
2
1
0
2
0
1
0
0
0
1
1
2
1
1
1
2
1
2
1
1
1
2
1
2
1
2
1
1
1
1
1
2
1
2
1
1
2
0
1
0
2
0
0
1
1
1
0
2
1
1
1
1
0
0
0
1
0
1
0
2
2
2
0
1
1
2
1
1
2
2
0
3
1
2
0
1
1
1
1
2
0
2
1
1
1
1
2
1
0
2
1
2
0
0
2
1
0
2
1
2
2
2
2
2
1
0
1
1
2
0
1
1
1
2
1
2
1
1
1
0
2
1
1
1
2
1
1
1
1
0
1
0
3
1
1
1
1
1
1
1
1
0
1
0
1
2
0
0
1
1
1
2
0
0
2
2
0
0
1
1
0
1
2
0
2
1
1
2
0
1
1
2
0
1
1
2
1
1
2
2
0
2
1
2
1
1
1
2
0
1
0
0
1
1
0
1
1
0
1
1
0
3
1
1
1
1
1
1
0
2
2
1
2
2
1
1
1
0
1
1
2
1
1
1
1
1
1
1
0
1
1
2
1
1
2
2
2
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
2
0
1
1
1
1
0
2
2
1
0
0
1
1
2
1
1
0
1
2
1
1
1
1
0
0
0
1
1
2
1
1
0
0
0
1
1
2
1
0
0
0
2
1
1
1
1
0
1
1
1
2
3
0
1
2
2
1
0
0
1
0
0
2
0
1
0
0
1
1
0
2
1
1
0
1
0
2
1
0
1
0
0
0
0
1
2
1
1
1
1
2
1
1
0
1
2
2
1
0
2
2
2
1
1
1
2
1
2
2
1
1
2
2
0
1
4
0
0
1
0
3
1
1
1
1
0
1
2
1
0
1
1
1
4
0
0
0
1
1
0
1
1
2
1
0
0
1
1
0
1
1
1
0
5
0
0
1
1
1
1
0
1
0
1
0
0
1
1
2
1
1
0
2
1
0
1
1
2
0
2
0
2
0
0
1
1
1
1
1
0
2
0
1
2
0
0
0
0
0
3
1
1
0
1
2
1
2
0
1
1
1
1
0
2
1
2
0
1
1
0
1
0
0
1
2
1
1
1
0
1
0
0
1
2
1
0
0
1
1
2
0
2
1
0
0
1
1
1
1
2
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
2
2
1
2
1
1
2
1
1
2
1
0
2
1
1
1
2
1
1
1
1
1
0
1
0
0
1
1
2
2
1
1
1
1
0
0
3
0
1
1
2
1
0
1
1
0
1
0
0
1
1
1
1
0
2
0
0
1
1
1
1
0
1
2
0
1
0
1
2
1
1
1
1
0
1
0
2
1
1
1
1
3
2
0
1
0
1
1
0
2
1
1
1
0
0
2
1
0
2
0
1
1
0
1
1
1
2
1
1
0
0
1
2
1
1
0
1
1
0
1
0
0
1
2
1
0
0
2
2
1
1
2
2
0
1
1
0
1
0
1
1
1
1
2
1
1
1
1
1
1
0
2
2
0
0
0
0
1
2
0
0
2
1
1
1
1
2
0
0
1
1
0
0
1
0
1
0
1
1
0
0
1
2
2
1
6
0
1
1
0
1
2
1
1
3
1
1
2
1
1
0
1
1
2
2
1
1
1
2
1
1
1
0
1
1
2
1
1
1
2
2
1
0
1
2
2
1
1
1
1
1
1
1
1
2
1
2
1
2
1
1
1
1
0
2
2
0
1
1
1
2
2
2
2
1
2
2
1
1
1
1
1
1
1
1
1
1
0
0
1
1
1
1
2
1
0
0
2
1
2
1
0
0
1
2
2
1
1
1
1
2
2
3
1
2
0
2
2
2
1
1
1
1
1
1
0
1
1
0
1
0
1
0
1
1
2
2
0
0
0
2
2
1
1
0
0
1
0
1
0
1
1
1
0
2
1
2
2
1
1
1
2
0
1
0
0
0
1
1
1
2
1
2
1
1
2
1
2
2
1
0
2
0
1
1
0
1
1
1
1
0
2
1
1
2
0
1
2
1
1
2
2
2
1
1
0
2
2
0
1
2
2
0
1
1
1
2
1
1
1
1
1
0
1
1
1
0
0
2
1
2
1
1
1
2
1
0
2
1
1
2
1
2
2
1
1
1
1
1
0
2
1
0
1
1
0
1
1
1
0
1
0
2
1
0
1
1
1
0
0
1
2
1
1
0
1
1
2
2
1
1
2
0
1
1
0
0
0
0
1
1
2
2
0
1
3
0
1
0
1
2
1
0
2
2
1
1
1
1
1
1
0
1
1
1
1
1
1
0
1
1
1
2
1
1
1
0
0
3
1
1
1
1
1
1
1
1
0
1
2
2
0
1
1
1
0
1
0
0
1
2
0
2
1
2
1
1
1
0
1
1
1
0
0
1
1
2
1
0
1
0
1
1
2
1
1
2
1
1
2
0
1
2
1
2
1
1
1
1
0
1
0
1
2
1
2
2
0
1
1
1
1
3
1
0
1
0
2
0
1
2
1
1
1
1
2
1
0
1
0
1
1
1
1
0
0
1
0
1
0
1
1
1
0
1
1
0
1
2
0
0
1
2
2
1
0
1
1
0
1
1
1
0
1
1
1
4
3
1
1
2
1
1
0
1
2
1
1
1
1
2
1
2
0
0
0
1
1
0
2
2
2
1
1
1
1
0
1
1
1
2
0
1
2
1
0
1
2
1
1
0
0
2
0
1
0
1
1
2
0
1
2
1
2
2
2
0
1
2
0
1
1
1
1
1
1
0
1
2
1
2
1
2
1
1
1
3
1
1
0
2
1
2
0
0
1
2
1
1
2
1
1
3
1
2
1
0
1
0
1
1
2
0
1
1
1
1
0
2
1
1
1
1
0
1
1
1
1
0
1
1
0
0
1
1
0
1
1
1
1
2
1
1
1
1
1
1
1
9
0
1
2
2
1
0
1
2
1
2
0
1
1
2
1
0
2
1
0
2
1
1
0
2
2
1
2
1
0
0
0
0
1
1
0
1
1
0
1
1
0
0
2
1
1
1
1
0
1
0
0
0
1
0
0
0
1
0
2
1
2
2
2
1
2
1
1
0
2
1
0
1
1
1
0
0
0
1
0
1
1
1
1
1
1
0
1
1
0
0
1
0
1
1
1
3
1
0
1
1
1
2
2
1
0
0
1
1
1
2
0
0
2
0
1
1
2
2
2
1
2
1
1
1
1
1
1
1
1
0
2
1
0
1
0
0
1
2
0
1
1
1
2
1
2
1
0
1
2
2
1
0
1
1
2
1
2
1
1
2
1
0
2
0
2
0
1
1
1
1
0
2
2
0
2
1
1
2
1
1
1
0
1
1
1
0
1
3
1
2
2
1
0
0
1
1
1
1
2
1
1
0
1
0
2
2
1
0
0
2
1
0
2
2
1
1
0
0
2
2
2
0
1
0
1
0
1
1
0
2
1
2
0
1
1
1
1
1
1
1
0
1
0
1
1
1
1
1
1
0
2
0
2
1
1
1
1
1
1
2
1
0
0
1
1
0
2
1
0
0
2
1
0
2
0
1
0
0
2
1
1
2
0
2
1
1
1
1
1
2
1
1
0
1
0
2
1
1
1
1
0
0
1
2
1
1
1
1
0
1
0
0
1
2
2
1
1
0
1
1
5
1
2
0
1
0
1
1
2
1
0
2
1
2
1
1
1
1
1
0
0
1
1
1
1
0
0
2
0
2
0
0
1
1
0
0
1
0
0
1
2
1
1
0
1
0
1
1
1
1
1
2
1
1
1
2
1
1
2
2
0
2
2
1
0
0
1
1
2
2
0
2
1
1
2
1
1
2
0
3
1
0
1
0
1
0
1
1
0
0
2
1
1
0
1
1
1
1
0
1
1
1
1
1
0
1
0
1
0
1
1
1
2
0
0
0
1
1
0
0
1
2
1
0
1
1
0
1
1
0
1
1
2
1
1
1
1
2
1
2
1
2
1
1
1
0
1
1
0
2
1
2
1
1
2
1
1
1
0
1
0
1
0
2
0
1
1
1
0
0
1
2
1
1
0
1
2
1
1
1
1
1
2
1
1
1
1
1
0
1
0
0
1
1
0
1
2
1
2
0
2
2
2
1
2
1
1
0
2
0
0
1
1
2
0
1
2
1
2
1
1
0
0
1
1
0
1
1
1
1
2
2
1
1
1
1
1
0
1
1
0
0
2
1
0
1
1
1
0
0
1
2
1
1
0
0
2
1
0
0
0
0
1
1
3
1
0
0
0
1
2
0
1
2
0
0
2
1
2
1
0
2
1
1
3
1
3
2
0
2
1
1
0
1
0
1
1
1
1
0
1
2
1
2
1
0
1
2
1
2
1
1
1
2
3
0
1
0
1
0
0
1
0
2
2
2
2
2
1
0
1
0
0
2
0
2
2
2
1
2
6
1
2
1
0
1
0
0
2
2
1
0
2
1
2
2
1
0
1
1
2
2
0
2
1
0
1
1
1
1
2
2
1
1
2
1
1
0
1
1
1
2
1
1
1
2
0
0
1
1
2
1
0
0
2
1
1
1
1
2
2
1
1
0
1
1
1
2
1
0
1
1
1
0
1
1
2
2
0
2
1
1
0
2
0
1
1
2
1
1
3
1
1
1
2
1
1
1
0
1
0
2
2
1
1
1
1
1
1
1
1
1
0
1
2
2
2
2
2
2
1
1
1
0
0
1
1
2
1
1
1
1
2
1
0
2
1
1
0
1
0
1
2
1
1
1
2
1
1
1
0
1
0
1
1
1
0
0
1
2
2
0
1
1
2
1
1
1
0
1
1
2
1
0
1
2
1
1
2
1
2
1
0
2
1
1
0
1
2
2
2
2
1
1
0
1
1
0
2
1
1
1
0
1
1
1
2
0
1
0
1
1
1
1
2
0
0
1
1
1
2
1
1
1
1
2
0
2
1
2
2
0
1
0
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
0
1
1
0
1
1
1
0
2
1
1
0
2
1
2
1
1
0
0
1
2
0
2
1
1
1
1
0
1
2
2
0
1
1
2
1
1
1
0
1
0
0
2
1
1
0
1
0
1
1
0
0
0
1
2
1
1
2
1
2
2
2
0
0
1
1
1
1
2
1
1
0
1
1
1
0
1
2
1
2
0
1
1
0
1
0
1
1
1
1
2
1
2
1
1
0
1
1
1
2
2
1
0
0
1
1
2
1
2
0
2
0
0
2
1
2
1
2
1
2
0
1
1
1
2
1
1
2
1
0
2
1
1
1
1
2
1
1
1
0
2
0
0
2
1
1
1
0
0
2
0
1
1
1
2
2
1
0
1
1
1
2
1
2
1
0
0
0
2
1
0
1
1
0
2
1
2
1
1
1
2
2
1
1
2
0
0
0
1
3
2
2
1
0
0
1
0
0
2
0
2
0
1
1
1
0
2
2
2
0
1
1
1
1
0
1
0
1
1
1
1
0
1
1
1
0
1
0
1
0
1
1
2
1
1
1
0
1
0
2
2
1
1
0
1
2
0
1
1
1
0
0
1
3
1
2
2
1
0
1
2
2
2
1
2
1
2
1
2
1
1
1
0
0
0
1
1
1
1
1
1
2
1
0
2
2
0
2
1
1
0
1
2
1
2
2
1
0
2
1
1
1
1
2
1
1
1
2
0
1
0
0
0
2
0
1
1
2
0
2
2
2
0
2
1
1
2
2
1
1
1
1
0
3
1
0
0
1
0
1
1
1
1
0
1
1
0
1
1
1
0
1
0
1
2
1
1
1
0
1
2
1
2
0
1
0
1
2
1
0
2
1
2
3
0
1
1
2
0
1
1
0
1
1
0
0
0
1
1
1
1
2
1
1
1
0
1
1
2
1
1
0
2
2
1
1
0
1
1
0
1
0
0
1
1
2
1
0
1
1
1
1
1
0
0
2
3
1
0
1
2
0
0
1
0
2
1
1
0
1
1
1
0
1
0
1
1
2
1
0
1
1
1
1
1
0
0
2
1
1
1
1
2
1
0
2
2
1
0
0
2
1
1
1
0
1
1
2
2
1
2
2
2
2
0
1
2
0
2
3
1
1
0
2
1
1
2
2
1
1
2
0
1
1
1
2
1
1
1
1
1
0
2
1
1
1
0
1
1
0
2
3
0
1
0
2
2
0
2
2
1
1
1
0
1
2
1
1
1
0
0
2
2
1
2
2
1
0
0
2
1
0
1
2
1
0
2
1
2
1
1
1
1
0
1
0
1
0
0
1
1
0
1
1
2
0
2
2
2
2
1
1
0
2
2
2
1
2
3
2
2
2
0
1
1
1
1
1
2
1
2
2
1
1
1
1
1
2
1
0
1
1
1
1
1
1
1
1
1
1
0
2
1
2
0
2
2
0
1
1
2
1
2
3
1
1
0
1
2
2
1
1
2
0
1
0
2
0
1
2
1
0
0
1
1
0
3
1
1
1
0
0
2
0
1
1
0
1
1
1
1
2
2
0
1
1
1
1
0
1
0
1
1
1
2
1
1
1
1
1
2
0
1
1
1
1
1
1
0
2
1
0
0
1
2
1
0
2
1
0
1
0
0
1
2
1
0
1
2
2
0
0
1
1
1
1
0
2
0
2
2
3
2
1
0
1
1
1
3
0
1
0
2
1
0
2
0
0
1
1
1
2
0
0
0
1
0
2
2
2
1
1
2
1
1
1
1
2
1
1
1
0
0
1
0
1
2
2
1
1
0
1
1
1
6
1
0
2
1
1
0
2
1
2
2
1
4
2
1
0
2
2
1
1
1
2
0
2
1
2
1
1
1
1
0
1
1
2
1
1
2
2
0
2
1
1
2
2
1
2
2
1
1
0
1
2
0
0
1
2
0
1
0
2
2
1
0
1
1
2
0
2
1
1
1
0
0
1
1
1
2
1
2
1
1
1
0
1
2
0
1
1
1
1
1
1
0
2
1
1
1
2
0
1
1
1
2
1
1
1
1
0
2
0
1
1
0
1
2
2
2
1
0
1
1
1
0
1
1
2
0
1
1
0
1
2
0
1
0
1
0
0
2
1
1
2
1
1
1
1
1
2
2
2
1
1
0
0
1
1
1
2
1
1
1
2
1
1
0
0
1
3
1
2
1
1
1
0
1
2
0
0
2
2
1
0
1
2
1
0
2
1
1
0
0
1
1
1
2
2
2
0
2
1
1
1
1
0
1
1
1
1
2
1
1
0
1
1
1
2
0
1
1
2
2
1
1
1
0
1
1
2
1
1
0
1
1
1
0
1
2
1
1
2
1
1
0
1
2
1
2
1
1
1
0
2
3
2
0
2
1
0
0
1
0
1
0
2
0
2
0
1
2
1
1
1
1
2
2
1
0
2
1
2
1
1
1
1
2
1
1
1
1
1
0
1
1
2
1
2
2
1
1
1
0
1
1
1
0
0
1
2
1
1
0
1
1
0
1
1
2
1
1
0
0
1
0
2
0
1
1
1
0
0
1
1
1
1
1
1
1
1
0
1
2
2
0
0
1
1
1
1
0
1
1
2
1
1
2
2
0
0
1
0
1
1
2
1
0
0
0
1
1
1
1
1
1
1
1
0
2
1
0
0
1
1
1
2
3
2
1
2
1
1
2
0
2
0
0
0
1
1
1
1
1
0
1
1
1
1
1
2
0
2
2
1
0
1
1
1
2
1
0
2
1
1
2
1
1
1
2
1
1
0
1
1
1
0
1
1
1
1
1
2
1
0
0
0
1
1
0
0
1
1
1
1
2
0
1
1
0
1
1
2
1
1
1
1
1
1
1
1
1
1
3
1
1
1
1
2
2
1
1
1
0
1
1
2
2
1
0
1
1
1
0
2
0
2
1
1
3
2
0
1
1
1
2
1
0
0
1
1
1
1
1
1
0
1
0
0
0
2
2
2
1
1
1
1
2
1
1
0
2
1
1
2
1
1
2
1
1
1
1
0
1
1
0
0
1
1
2
1
2
1
1
0
1
0
0
1
1
1
1
2
1
2
1
1
1
2
1
2
1
1
1
1
1
0
1
2
1
1
1
1
1
1
0
0
1
2
0
0
0
1
2
2
1
2
1
1
2
2
0
2
0
2
1
1
1
1
1
1
1
1
1
2
0
1
1
1
0
2
2
2
1
1
1
0
1
1
1
1
0
1
2
1
0
1
2
1
1
0
2
2
1
1
2
1
1
1
1
0
1
2
1
1
2
0
1
1
0
1
0
1
1
0
2
1
2
2
2
1
0
0
1
1
1
1
3
2
1
1
1
1
2
1
0
0
1
1
2
2
0
2
2
2
2
2
1
1
1
2
2
1
1
2
2
1
1
1
4
0
2
1
2
2
1
1
1
1
1
1
1
1
1
2
2
0
1
1
1
1
1
1
2
2
0
4
0
1
0
1
1
2
1
1
1
0
1
1
1
2
0
1
0
0
0
1
2
1
0
1
0
0
1
1
0
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
0
2
2
3
0
1
2
1
1
1
1
3
1
1
0
0
1
1
2
1
1
1
1
1
0
1
1
2
2
1
0
2
1
0
2
2
2
2
1
1
0
0
0
2
1
1
0
1
3
1
1
1
1
1
1
1
1
2
0
1
0
1
0
1
0
1
3
0
1
1
2
1
2
1
0
2
2
1
1
2
1
1
1
0
1
0
0
1
1
1
1
1
0
2
1
1
2
1
1
0
0
2
1
0
0
0
1
1
2
2
1
1
1
0
1
2
1
1
0
2
0
1
2
1
0
2
0
0
0
1
2
2
0
0
0
0
1
1
1
1
1
0
0
1
1
2
0
1
2
1
1
2
1
0
1
2
2
0
0
0
0
1
1
0
2
2
0
1
1
0
1
1
1
1
2
1
0
0
2
1
2
0
2
1
1
0
2
1
1
2
1
0
1
2
0
0
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
0
2
1
1
1
1
0
1
2
1
0
1
1
0
2
2
1
1
1
0
0
2
1
0
1
1
1
1
1
2
0
1
1
0
0
2
0
1
2
0
1
1
1
1
0
1
1
2
0
1
1
1
1
1
2
1
1
2
3
0
2
2
1
1
1
2
0
0
1
2
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
0
1
1
1
1
2
0
0
1
0
2
0
2
1
1
1
1
1
1
1
1
2
1
1
0
2
2
2
1
0
2
1
1
2
2
1
1
2
2
1
0
1
2
1
1
2
1
1
1
1
1
2
2
1
2
1
1
2
2
1
1
2
0
1
2
2
1
1
8
2
2
2
1
0
1
1
1
1
0
0
1
2
0
2
2
1
0
1
0
1
2
2
1
1
1
0
1
2
1
2
1
1
1
2
2
1
2
1
0
0
0
2
1
1
1
0
2
1
2
0
0
1
0
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
0
0
2
2
1
1
1
0
0
1
1
2
1
1
0
1
1
1
1
2
2
1
0
0
0
1
1
0
2
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
2
1
0
1
2
0
1
1
1
0
1
1
2
2
1
1
2
0
2
1
1
0
1
2
1
2
0
1
1
1
1
1
1
2
2
1
2
0
1
3
1
0
0
0
2
1
1
0
0
1
0
2
2
0
1
1
0
0
1
1
1
0
1
1
0
1
2
1
1
1
0
1
1
1
2
2
0
1
0
1
1
2
1
1
1
1
0
2
1
1
2
1
0
0
0
1
1
2
1
1
2
0
1
1
1
3
1
2
1
0
2
2
2
2
0
1
0
2
1
2
1
0
1
0
1
1
0
1
1
1
1
2
1
2
2
0
1
0
0
1
1
2
2
0
0
1
1
0
1
1
1
2
2
1
1
1
0
0
1
0
1
2
0
1
1
0
0
0
1
2
1
1
1
0
2
2
1
1
1
1
1
1
1
2
1
1
0
0
1
1
1
1
1
2
1
1
2
2
1
1
2
1
1
2
0
1
1
0
1
2
1
1
0
0
1
1
2
1
4
1
1
0
1
1
1
1
2
1
4
0
1
1
1
0
1
1
0
0
1
2
1
1
2
1
1
1
1
2
0
1
2
0
1
0
0
0
1
2
1
2
0
0
1
0
1
1
1
1
1
1
1
3
0
0
0
1
2
3
1
2
2
0
1
2
1
1
2
0
0
0
1
0
0
0
0
1
2
0
1
0
1
1
1
1
1
2
1
2
1
1
1
2
2
0
1
1
0
1
2
1
0
1
1
1
1
1
1
0
1
1
1
2
0
1
0
1
1
1
1
2
1
2
1
1
1
0
1
1
1
2
1
1
1
0
1
0
1
1
1
1
1
1
1
1
2
0
0
1
1
0
0
1
1
1
0
2
0
0
2
1
0
1
0
0
2
1
1
0
1
2
1
1
1
1
1
1
1
0
1
2
1
1
0
2
0
0
1
1
1
1
1
0
2
0
0
1
0
1
1
0
1
2
0
1
2
1
1
2
0
1
0
1
1
2
1
1
2
0
1
1
0
0
2
1
1
1
1
1
1
0
3
1
1
0
0
1
1
0
1
2
1
1
1
2
1
0
1
1
2
2
2
1
0
1
0
1
1
1
2
1
1
1
2
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
2
1
1
2
2
0
1
1
1
2
0
0
0
1
2
0
1
1
1
1
1
1
1
0
1
1
1
2
2
0
1
2
2
1
0
1
1
1
0
0
0
1
1
2
1
2
2
1
1
1
1
1
1
1
2
1
0
2
1
0
1
2
3
2
1
0
1
0
2
1
0
1
1
1
1
1
2
2
1
2
0
2
0
2
2
1
2
2
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
0
1
0
1
1
1
2
1
2
1
0
1
1
1
2
2
1
0
0
2
2
0
1
1
2
2
0
1
0
2
2
0
0
1
1
2
0
0
1
1
1
2
1
0
0
2
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
0
0
1
0
1
1
2
0
1
0
1
1
1
0
1
1
1
2
1
1
0
0
1
1
2
2
2
1
1
0
2
0
1
0
1
1
0
1
1
1
1
2
1
1
2
2
0
0
0
1
2
0
1
1
1
1
2
0
1
1
0
2
0
0
2
2
0
1
1
1
1
0
2
0
2
1
1
2
2
2
1
2
1
1
1
2
1
1
2
1
1
1
0
1
1
1
1
1
1
1
0
1
2
1
0
1
1
1
1
0
1
1
0
1
1
1
0
1
1
1
1
1
0
2
1
1
2
2
2
2
1
2
1
1
1
2
2
2
2
1
1
0
2
0
1
1
2
0
0
0
0
1
1
1
0
1
1
1
2
1
0
1
0
1
1
2
1
1
2
1
1
1
0
1
1
0
1
1
0
1
2
1
0
1
2
1
1
1
2
1
2
1
1
1
1
1
1
2
0
1
1
1
2
1
0
1
2
1
0
0
0
1
1
0
1
2
1
2
2
1
1
2
2
2
1
2
1
1
1
1
1
1
0
1
1
0
0
2
1
1
2
2
2
1
1
0
0
0
1
1
0
1
0
0
1
1
1
1
1
2
0
0
2
1
0
1
1
1
1
2
1
0
1
0
1
0
2
0
1
1
2
2
1
2
0
1
2
2
0
1
1
1
0
2
2
1
2
0
0
1
1
0
0
0
2
1
1
2
1
1
1
1
2
1
2
1
1
0
1
2
0
1
1
1
1
2
2
1
1
1
2
1
1
0
1
0
2
1
2
2
0
0
0
1
2
1
0
2
1
0
1
0
2
1
0
2
1
0
5
2
0
1
1
1
1
1
1
2
1
0
1
2
0
1
1
2
0
1
2
1
0
1
0
1
1
0
2
0
1
2
0
1
2
1
1
2
0
2
1
2
1
1
0
0
1
1
2
0
1
3
0
1
0
0
2
1
1
2
0
0
1
2
1
2
1
1
1
0
1
2
3
1
1
0
1
1
1
2
0
1
2
1
0
1
1
1
1
0
0
1
0
1
0
2
1
0
1
0
1
1
1
1
1
1
0
1
0
2
0
1
0
1
0
1
1
0
1
1
0
1
1
1
2
1
1
0
1
0
1
1
1
2
0
1
1
2
0
0
1
1
2
1
1
2
0
2
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
1
0
7
0
1
2
0
1
0
0
1
1
1
1
1
0
2
1
1
1
1
1
1
0
0
2
2
1
0
1
2
1
1
0
1
0
0
1
1
1
0
0
1
1
1
1
1
0
2
3
1
1
2
0
1
1
0
0
1
0
1
2
1
2
1
1
0
1
1
1
1
2
1
1
0
0
2
0
0
1
1
1
1
1
2
0
1
1
1
1
1
1
1
2
0
0
1
2
1
0
0
0
1
0
1
2
1
0
1
2
0
0
1
1
0
1
0
0
1
2
0
2
0
2
1
1
1
1
1
0
1
2
1
1
0
1
2
2
0
1
1
1
1
1
2
0
1
1
1
2
1
0
0
2
1
0
1
0
1
0
2
1
0
1
1
2
1
1
1
1
0
1
1
1
0
1
2
1
2
1
1
0
0
0
1
2
1
1
1
1
1
1
1
2
2
2
0
0
2
2
0
1
2
2
0
0
0
1
0
0
1
0
0
2
1
2
2
1
2
0
0
2
0
1
1
0
1
1
0
0
1
2
0
1
0
1
2
1
0
1
1
2
0
1
1
0
2
0
1
2
1
1
2
0
2
1
1
0
1
2
1
1
0
2
0
1
1
1
2
0
2
1
0
1
1
1
2
0
1
0
2
1
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
0
1
0
0
1
1
2
2
2
2
1
2
1
2
2
1
1
1
0
2
1
2
1
1
1
1
1
1
2
0
1
1
2
2
2
2
1
1
1
1
2
1
0
1
2
1
1
0
1
1
2
2
0
0
1
0
0
2
1
1
1
1
1
2
0
1
1
0
2
1
1
2
1
1
2
1
1
1
1
1
2
1
2
1
2
0
0
1
1
1
1
1
0
1
1
1
2
2
2
2
0
1
1
1
0
1
1
1
2
0
2
0
0
1
1
1
0
0
1
1
1
1
1
3
1
1
2
2
2
1
1
0
0
0
1
1
2
0
0
2
1
1
2
0
0
1
1
2
1
1
1
1
1
2
2
2
0
0
2
1
2
0
1
1
0
1
2
1
1
0
1
0
1
1
1
1
2
2
0
2
0
2
1
0
0
0
2
1
1
2
1
1
2
2
1
1
3
1
1
1
1
1
1
2
1
2
1
1
1
1
0
2
1
1
2
0
1
2
0
0
0
1
2
1
1
1
1
0
1
1
0
0
0
0
2
2
1
0
1
2
1
2
0
1
1
1
1
2
1
1
0
1
2
1
2
2
1
2
1
0
1
1
1
1
1
1
0
0
2
1
1
2
0
1
1
1
1
2
2
1
1
2
1
1
3
1
1
1
0
1
0
1
1
0
1
0
1
1
2
0
1
1
1
1
0
1
1
2
2
1
0
1
1
0
1
0
2
1
1
1
1
0
0
0
2
2
1
1
1
1
1
2
1
1
0
2
1
2
0
2
1
1
1
0
1
1
1
2
0
1
1
2
1
1
1
1
1
2
1
1
0
1
1
0
0
0
1
1
2
0
2
1
1
1
2
2
0
1
0
1
2
1
1
1
0
0
1
1
0
1
2
0
2
1
0
0
2
1
1
1
1
2
1
1
0
2
2
2
0
1
2
1
1
0
0
1
0
1
1
1
1
2
2
0
0
2
2
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
0
1
1
1
0
0
1
2
1
1
2
1
0
0
1
1
1
0
0
1
1
0
1
1
3
0
1
2
0
0
1
1
2
1
0
0
2
4
0
1
1
2
2
0
2
2
1
1
2
1
2
1
1
1
1
1
1
2
2
0
2
1
1
2
1
1
0
2
2
1
1
1
1
1
2
2
2
0
1
1
1
1
1
1
1
0
2
0
1
2
1
1
1
1
0
2
2
0
1
1
1
1
1
1
1
1
1
0
1
1
0
1
1
1
1
2
1
2
1
1
2
1
1
0
1
2
1
1
1
2
0
1
1
1
1
1
1
1
1
1
0
2
1
0
0
1
1
1
1
1
1
1
2
1
0
1
2
1
2
1
1
1
1
2
1
0
1
1
0
2
1
1
1
0
2
1
0
1
1
1
1
1
2
0
1
1
2
1
1
2
0
1
0
0
1
0
1
0
2
2
0
1
1
2
2
1
1
1
0
2
0
1
0
1
2
2
0
1
1
1
1
1
1
0
1
1
1
0
2
0
1
1
2
0
1
1
1
1
1
1
1
1
1
1
1
1
2
0
1
0
2
1
1
1
0
1
1
2
2
0
0
1
0
1
2
1
1
1
1
1
1
1
1
1
1
0
1
1
1
0
1
1
0
0
1
1
2
1
1
2
1
1
0
1
2
0
1
0
2
4
1
1
1
1
2
1
1
1
0
1
1
0
1
2
1
2
1
1
1
2
1
1
0
1
0
1
2
1
6
2
1
2
0
0
1
1
1
2
0
2
1
1
0
1
2
1
2
1
1
1
2
0
0
1
1
2
1
1
2
0
2
1
1
1
2
1
3
2
1
2
2
1
1
1
0
0
0
1
1
1
2
1
2
1
1
2
0
1
1
2
1
1
1
2
1
1
2
1
2
0
1
0
1
1
1
1
2
2
2
1
2
1
1
1
1
1
1
1
1
0
1
1
0
1
1
0
1
1
0
1
0
2
2
1
2
1
2
1
1
1
0
1
1
0
1
1
1
1
2
0
0
1
2
2
2
1
1
1
2
2
1
2
2
1
1
0
2
2
0
0
1
0
1
1
1
0
1
1
1
1
1
1
2
0
1
2
0
1
1
0
1
0
0
1
1
1
2
2
1
2
1
1
1
1
1
1
1
0
0
2
1
0
1
2
1
2
0
0
3
1
0
0
3
0
0
1
1
0
1
1
0
0
2
0
1
1
1
1
2
2
1
2
2
0
2
1
1
1
1
1
1
2
2
2
1
0
1
2
1
1
1
0
2
1
1
0
2
2
1
1
1
1
1
0
4
0
1
2
1
0
1
1
1
0
1
1
1
2
2
1
1
2
2
1
1
1
1
1
1
2
0
1
2
1
1
1
1
1
2
2
2
0
0
1
2
1
1
1
2
3
1
2
1
1
2
2
0
1
1
0
1
1
0
2
1
1
2
1
1
1
0
2
1
0
0
0
2
1
0
1
2
1
3
2
0
1
2
0
0
1
0
1
1
2
1
1
1
1
0
0
1
1
0
1
1
2
2
1
0
1
0
1
1
2
2
2
1
2
1
1
2
1
0
2
1
1
1
1
1
1
1
2
1
1
2
1
0
0
1
3
0
0
1
2
1
1
2
2
1
0
0
1
1
1
0
1
0
2
1
2
0
1
0
1
1
2
2
1
1
1
2
3
1
1
1
1
1
1
0
1
1
1
2
1
0
1
0
1
0
3
1
0
1
2
1
2
2
0
1
2
1
0
2
1
1
2
0
2
0
1
1
0
2
1
2
1
3
2
2
2
0
1
0
1
1
0
2
1
0
1
0
1
1
0
1
0
1
1
1
0
2
0
1
2
2
1
1
2
1
2
1
1
1
2
2
2
1
2
2
1
0
1
1
1
2
0
1
0
0
0
1
1
0
1
2
1
0
1
1
2
2
0
1
1
0
2
1
1
1
1
1
1
1
1
0
2
0
0
1
2
2
1
0
0
2
1
2
1
1
2
1
2
0
1
1
2
0
0
0
1
1
1
1
2
1
0
0
1
2
2
1
2
1
1
0
1
2
2
1
1
1
1
1
1
1
1
1
1
2
0
1
0
1
1
2
0
1
1
1
0
3
1
1
2
1
2
2
1
0
1
1
0
1
1
2
2
1
1
2
2
1
1
0
1
1
1
1
0
1
2
2
2
1
1
1
1
2
1
1
2
1
1
0
1
1
2
0
0
1
0
0
1
1
2
1
1
1
2
1
2
3
0
1
0
0
1
1
2
0
1
2
1
2
1
1
2
1
2
0
1
1
2
0
1
2
0
2
1
1
2
2
1
2
1
1
2
0
1
1
1
0
1
1
1
1
1
1
1
2
1
2
1
2
1
1
0
0
1
2
1
0
2
0
1
0
1
1
1
0
0
1
1
0
1
1
0
1
1
0
0
0
3
1
1
1
0
1
1
0
0
2
1
2
2
1
0
2
2
0
1
1
1
0
1
1
0
1
2
1
2
1
0
2
1
0
1
0
1
1
0
2
1
0
1
1
1
0
0
1
1
1
0
0
0
1
1
1
1
0
1
0
1
1
1
0
1
1
2
2
2
1
1
1
1
1
1
1
2
1
1
0
2
1
1
2
2
0
1
1
1
1
1
2
1
0
1
1
1
1
1
1
2
2
1
0
2
1
1
0
1
2
1
2
1
2
1
1
1
2
0
2
2
1
1
2
1
0
1
1
1
1
1
1
1
1
1
0
0
2
0
1
1
1
3
1
1
0
2
2
1
0
2
1
1
1
1
0
2
0
2
2
1
1
2
2
0
0
1
0
2
1
1
2
2
0
1
1
1
1
1
0
1
2
1
0
1
2
1
1
1
1
2
1
1
2
0
2
2
2
1
1
1
1
1
1
2
2
1
1
2
1
1
2
1
2
1
1
1
3
2
1
1
1
0
2
1
0
1
0
0
1
0
1
0
0
0
1
2
2
2
1
0
1
0
1
0
2
1
1
1
1
1
2
2
2
1
2
0
1
1
1
1
0
0
0
2
1
1
1
2
0
1
2
1
1
1
1
1
0
1
1
0
1
0
2
1
2
1
1
1
1
0
0
2
1
1
1
2
0
0
2
1
1
1
1
1
0
1
1
1
1
2
0
1
2
3
1
0
2
1
0
1
1
1
1
0
2
1
1
1
1
0
2
1
2
2
2
1
1
1
2
1
1
1
0
1
1
4
1
1
1
1
2
1
1
2
1
0
1
0
1
2
1
0
1
1
1
1
1
1
1
0
1
2
1
0
0
1
1
1
2
2
1
1
1
0
1
1
0
0
0
1
1
1
0
2
2
1
1
0
0
1
1
1
0
1
1
2
2
2
1
2
1
1
0
2
2
1
1
1
0
0
1
1
2
1
1
0
1
1
1
2
1
0
0
1
0
1
1
1
1
1
1
2
2
0
2
1
2
2
0
1
0
1
1
0
0
2
1
1
1
1
2
0
2
1
2
1
0
1
1
1
2
1
1
1
0
2
1
2
0
1
1
1
2
0
1
1
2
1
0
1
1
1
0
1
1
1
1
0
1
1
0
1
2
2
1
0
3
1
0
1
1
2
0
2
8
2
1
0
0
1
0
0
1
1
1
1
0
1
0
0
2
0
1
0
1
0
2
0
1
2
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
0
1
1
0
1
0
0
1
1
0
1
2
0
1
1
1
1
1
2
0
1
1
2
1
2
2
1
1
0
0
0
2
1
2
2
1
1
1
1
2
2
2
1
1
1
2
2
2
1
1
2
1
2
1
1
2
1
1
0
0
1
2
2
2
0
2
2
0
1
0
0
1
1
0
2
0
1
1
0
1
0
0
1
1
1
2
1
1
1
1
2
0
0
0
2
0
1
1
0
1
0
1
2
0
1
0
2
1
1
1
0
1
1
1
1
1
2
0
2
0
0
1
1
2
1
1
1
0
2
2
1
2
1
1
0
1
0
1
2
2
1
1
1
1
2
1
1
1
1
0
1
1
1
1
1
0
1
1
1
1
1
1
1
0
1
0
1
0
0
1
1
0
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
0
2
1
1
1
1
1
0
2
1
2
1
1
1
1
1
1
1
2
2
2
1
1
0
1
0
1
1
0
2
2
1
1
0
0
2
1
0
2
1
2
2
2
1
3
0
0
0
0
0
0
2
2
1
1
2
0
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
0
1
1
1
1
0
1
1
1
0
1
0
1
1
1
0
2
2
1
1
1
1
1
0
1
0
0
2
1
1
1
1
2
2
0
1
1
1
1
2
1
3
0
3
1
1
0
1
2
2
1
0
0
1
0
3
2
2
1
1
0
1
1
1
2
1
1
1
1
0
0
1
1
1
1
0
0
1
0
0
0
0
0
0
0
1
3
1
0
0
1
2
1
0
1
1
1
2
1
0
1
1
1
1
1
2
1
0
0
1
2
0
2
1
1
0
0
0
0
1
2
0
2
2
0
0
1
1
1
0
1
1
1
1
1
1
0
2
1
0
2
1
1
2
2
2
1
1
0
1
1
1
1
3
2
0
1
2
1
1
1
1
1
0
0
1
1
1
0
1
1
1
0
0
1
1
1
3
0
1
1
1
1
2
0
0
2
1
1
2
1
2
1
2
0
1
1
0
1
2
2
1
1
0
1
2
1
0
1
2
1
1
1
0
0
0
0
1
1
1
0
1
0
1
2
1
0
0
2
1
1
1
1
0
2
1
0
0
1
2
2
1
1
2
1
0
1
1
2
1
0
1
0
1
1
2
2
2
1
1
1
2
1
1
2
1
1
1
2
0
2
2
1
2
2
0
1
0
2
0
0
1
2
0
1
0
0
0
0
1
1
0
0
0
0
1
1
1
1
1
2
1
2
1
1
1
0
1
0
1
0
1
0
1
1
0
1
1
1
1
2
0
1
1
1
1
2
1
0
0
1
0
1
1
0
1
1
2
1
1
1
1
1
2
2
0
1
0
0
1
2
1
1
0
2
1
2
1
1
2
2
1
1
1
1
1
2
1
0
1
1
2
0
0
0
1
1
1
1
0
2
1
2
2
1
1
2
1
1
2
1
1
1
1
1
0
1
2
0
1
0
1
1
1
1
1
1
1
1
1
1
1
0
0
1
2
0
1
0
2
0
1
2
1
1
0
2
1
1
1
1
1
1
0
1
1
1
1
0
1
1
2
1
1
2
1
0
2
1
0
0
0
1
1
1
1
1
2
0
1
2
1
0
2
0
0
1
0
1
2
1
0
1
2
1
1
2
1
1
1
1
0
2
1
2
1
2
1
2
1
1
0
1
2
0
1
1
1
1
2
1
1
1
0
2
0
1
2
2
1
2
1
1
2
1
2
2
2
1
2
2
1
1
1
1
1
0
1
1
0
1
1
1
2
0
0
1
1
1
0
1
0
2
0
0
1
1
2
0
0
1
1
1
1
1
1
1
0
1
0
0
1
2
1
1
0
1
2
0
1
1
1
0
2
1
1
3
1
1
0
1
1
1
1
1
0
0
2
1
1
2
1
1
0
1
1
1
0
0
0
2
1
1
4
2
1
1
1
2
0
0
0
0
1
2
2
2
1
1
2
0
1
0
1
1
1
1
2
2
2
2
0
2
0
1
0
1
1
0
0
1
2
2
1
2
1
1
1
0
2
0
1
1
1
1
1
1
1
0
2
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
0
1
1
0
2
1
0
2
0
1
0
1
0
2
0
2
2
1
0
0
1
0
2
1
2
1
1
1
2
1
1
1
1
0
0
1
0
1
1
0
3
1
0
1
2
1
1
1
1
1
2
2
1
2
1
0
0
1
1
1
1
0
2
1
0
1
1
1
2
0
1
1
1
1
2
1
0
1
1
2
1
1
1
0
0
0
1
0
0
1
1
1
1
2
0
2
1
2
1
1
0
3
0
1
1
2
0
2
2
0
1
0
0
2
1
1
0
1
0
0
3
1
2
0
1
2
1
0
1
3
2
0
1
1
2
0
2
0
0
1
2
2
1
0
1
0
2
2
1
0
0
1
1
1
1
2
0
1
0
1
1
1
1
1
1
1
1
2
1
0
2
0
2
0
1
1
2
1
2
0
0
0
2
1
2
1
2
1
2
1
1
0
1
2
0
1
1
1
2
1
0
2
1
1
1
2
1
0
2
2
1
2
2
2
2
1
1
0
2
1
1
1
1
1
2
1
0
0
1
1
1
0
1
1
2
0
1
1
2
0
2
1
1
1
2
0
1
2
0
1
1
1
1
1
1
1
1
0
1
0
1
2
2
1
1
1
1
0
1
0
1
2
1
1
2
1
1
1
1
0
1
1
1
1
1
1
1
1
1
0
1
0
1
0
2
1
0
3
1
1
1
1
0
2
1
1
1
1
0
2
2
0
1
2
1
1
1
0
1
0
2
2
1
2
1
2
1
1
0
2
2
1
1
0
2
1
1
2
0
1
1
1
2
0
0
0
1
0
0
0
1
1
0
1
1
0
1
2
1
1
1
2
0
1
0
1
1
0
0
1
1
0
0
1
1
2
1
3
1
2
1
2
0
1
1
2
1
1
2
0
2
1
0
1
1
0
1
1
0
1
0
1
1
1
1
1
1
0
1
0
2
2
1
1
1
0
1
2
0
1
1
0
1
1
1
1
1
1
1
2
0
2
1
1
2
1
1
1
0
2
1
0
1
2
0
1
0
0
2
2
2
1
2
0
1
1
1
1
1
0
1
2
1
0
1
0
2
1
1
2
1
1
0
1
2
2
1
2
1
1
1
1
1
1
1
1
0
0
1
2
0
2
1
0
0
0
2
2
0
2
0
1
0
1
0
1
1
1
1
2
1
2
1
1
2
1
1
1
1
0
1
1
1
1
2
1
1
1
1
2
1
1
1
0
1
2
1
1
1
2
2
2
2
1
1
2
0
1
2
2
0
2
1
0
1
1
0
0
1
1
1
1
2
1
1
0
0
1
1
2
1
0
1
1
1
1
1
2
1
2
1
0
1
1
1
3
2
1
0
1
1
2
5
1
1
1
1
2
1
1
0
2
0
1
0
1
2
1
1
1
2
1
2
1
1
2
0
2
2
1
0
0
1
1
2
1
1
0
2
1
1
1
2
1
1
2
1
2
1
0
0
0
1
2
1
1
2
0
1
0
0
1
0
1
1
0
2
1
1
1
1
1
2
1
2
0
1
2
1
1
1
1
1
1
0
1
1
0
1
1
0
1
1
1
3
1
1
1
2
1
1
1
0
1
0
1
0
1
1
1
2
1
2
1
1
0
1
1
1
1
1
0
1
1
1
1
1
1
1
2
2
1
1
1
0
2
0
0
1
1
1
1
3
0
3
1
0
1
2
0
1
2
0
1
1
2
2
1
0
0
1
1
1
1
1
0
0
0
1
2
1
1
2
1
0
1
0
0
1
0
4
3
1
1
1
0
0
1
1
1
1
1
1
1
1
2
2
2
0
1
1
1
0
2
2
1
1
2
1
1
2
0
2
2
1
1
1
1
0
0
0
1
0
2
1
1
1
2
2
1
1
1
1
0
1
1
1
2
1
2
2
2
1
2
1
0
2
1
0
1
1
1
1
1
1
0
2
2
1
2
2
2
1
1
1
2
0
2
0
1
0
2
1
1
0
0
1
0
0
1
1
4
0
0
1
1
1
0
2
0
2
0
0
1
1
0
1
1
1
0
3
2
2
3
1
1
1
2
2
1
0
0
1
0
1
1
1
1
1
0
2
1
1
1
2
2
2
2
0
1
1
2
0
1
1
1
0
2
2
1
2
1
0
1
1
1
2
0
1
1
2
1
2
1
1
1
1
0
1
1
1
1
1
1
1
2
0
1
0
1
1
0
0
1
0
0
1
1
2
1
1
0
1
1
2
1
1
0
1
1
2
1
1
2
1
1
1
2
1
1
1
1
1
2
2
2
1
1
2
2
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
0
1
1
1
1
1
2
1
1
2
0
2
1
0
2
0
1
1
0
1
0
2
0
1
1
0
1
1
1
2
2
0
0
2
3
1
2
2
2
1
2
1
1
1
1
2
2
1
1
1
1
1
7
1
1
2
1
2
0
1
2
1
2
0
1
1
3
0
0
1
1
0
1
2
0
1
2
2
1
0
1
2
2
0
2
1
1
1
1
1
2
0
2
1
1
0
0
0
0
0
2
1
2
2
0
1
1
2
1
2
1
0
1
1
1
0
1
0
1
2
2
1
1
1
1
0
1
1
1
0
1
1
0
0
1
0
1
1
1
1
1
1
0
0
1
2
1
1
2
2
1
0
1
1
0
2
1
1
0
2
1
0
1
1
1
1
1
2
2
0
1
1
0
1
1
1
2
1
2
2
2
1
1
2
1
2
1
1
1
1
0
0
1
0
0
1
1
1
0
2
1
1
2
1
0
0
3
2
2
1
2
2
1
0
2
1
1
2
0
0
2
1
0
2
2
1
1
0
0
1
2
0
1
0
2
2
2
0
1
1
1
1
1
2
1
0
1
0
1
1
1
2
1
1
2
0
1
0
1
1
1
0
1
2
0
1
1
1
2
0
1
2
1
2
0
2
1
1
3
1
2
2
0
1
1
1
1
1
1
1
1
2
2
1
1
1
1
0
1
1
1
0
0
1
0
1
1
1
2
1
1
0
1
1
0
1
1
0
1
1
1
2
1
1
1
0
0
1
2
1
1
0
1
1
1
1
1
1
1
1
0
1
0
0
2
1
1
1
1
1
1
0
0
0
0
1
1
0
1
2
1
2
1
1
1
1
1
1
2
2
0
0
1
1
2
1
2
2
2
0
0
1
1
0
0
0
1
1
2
2
1
1
1
1
1
1
2
3
1
0
2
2
1
2
1
1
1
1
0
0
1
2
2
1
2
2
1
0
1
1
1
0
1
2
1
1
0
0
1
1
1
2
1
1
0
1
1
1
1
0
0
2
1
1
2
1
0
1
0
1
1
1
1
1
1
0
2
0
1
1
0
1
1
0
1
1
0
1
0
1
1
0
1
1
1
0
0
1
2
0
1
1
2
0
1
1
0
2
2
1
0
2
0
1
1
0
1
0
1
1
1
1
1
1
2
1
0
1
1
1
2
1
1
2
1
2
2
1
1
1
1
1
0
0
1
1
2
3
1
2
1
0
1
2
0
0
1
3
1
1
1
1
1
1
0
2
2
2
2
2
1
1
0
0
0
1
1
1
0
1
1
2
2
1
1
1
2
1
1
1
1
1
1
1
0
0
1
1
1
2
1
1
1
2
2
0
2
2
1
3
0
2
1
0
0
2
0
2
0
0
2
2
1
0
1
1
2
0
1
0
0
1
0
1
2
2
2
1
0
1
1
0
1
1
0
0
0
2
0
1
1
1
1
1
1
1
2
0
1
1
0
0
1
0
3
0
1
1
2
1
1
1
1
2
1
1
2
0
0
0
2
1
0
0
1
1
0
0
2
1
1
1
0
2
1
2
0
1
2
1
2
2
0
0
0
1
1
1
1
2
2
1
2
0
1
2
1
0
1
0
2
1
1
1
0
1
2
1
1
1
1
2
0
2
1
0
0
2
1
2
2
0
2
1
2
1
3
0
1
0
1
1
1
1
2
1
1
1
1
1
1
0
0
1
2
0
2
2
1
1
1
1
2
1
0
1
1
1
1
1
0
1
1
0
1
1
0
0
1
2
1
1
2
0
2
2
1
1
2
1
1
2
0
1
2
0
0
2
0
1
1
1
1
1
1
3
1
0
1
1
2
2
1
1
2
1
1
2
1
1
2
1
2
1
2
2
1
1
0
1
1
2
1
0
1
0
2
1
2
2
1
2
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
2
1
2
2
2
1
0
1
1
1
2
0
1
2
1
0
2
1
2
1
2
1
2
0
1
0
1
2
1
2
1
0
1
2
1
2
1
0
1
1
2
1
1
1
1
1
1
2
0
1
1
1
1
1
1
0
1
0
2
1
1
1
0
2
2
1
1
1
0
0
1
2
2
1
1
0
2
1
0
1
0
1
0
0
1
1
0
1
1
1
0
2
1
1
0
2
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
0
0
0
0
1
1
1
1
2
1
2
0
1
2
0
1
1
1
0
2
1
0
1
1
1
2
2
1
2
0
1
1
1
3
1
1
0
0
0
1
2
1
1
1
0
1
1
0
3
2
0
0
2
0
1
0
2
1
1
1
0
1
3
0
2
1
1
1
2
1
1
0
1
1
1
0
1
0
0
1
1
1
2
1
1
2
1
2
2
1
1
2
1
2
0
1
1
1
2
2
1
1
0
1
1
0
1
0
2
1
1
1
0
1
0
1
2
2
4
2
1
0
1
1
0
0
1
1
1
1
1
2
0
1
0
1
1
1
0
1
1
2
2
2
1
0
0
1
1
1
2
2
2
1
1
2
2
0
1
1
0
1
0
1
1
1
0
1
1
1
2
0
0
1
1
3
1
0
2
2
1
1
0
1
1
0
1
1
0
1
1
1
1
0
1
1
0
0
1
1
0
2
1
0
1
0
1
1
2
1
1
1
2
0
1
1
1
1
0
0
1
1
1
1
1
0
1
1
1
0
1
2
1
1
0
2
0
1
1
1
1
1
1
1
1
1
0
0
1
1
0
1
1
2
2
0
1
1
0
1
0
1
2
1
2
2
2
2
0
0
1
1
1
2
1
1
1
1
1
0
2
4
1
2
1
1
2
0
1
1
1
1
3
1
0
1
1
0
2
1
2
1
1
1
1
2
1
1
1
0
1
1
1
1
2
2
1
1
1
0
2
1
1
2
1
0
2
0
1
0
1
1
3
1
0
1
1
1
2
1
2
0
1
0
1
0
2
1
2
1
1
1
1
2
1
3
2
2
1
0
1
1
1
0
2
1
1
1
0
1
1
0
0
1
1
0
0
2
0
1
0
1
1
1
2
1
1
0
2
2
2
1
0
1
1
2
1
1
2
1
0
0
1
1
0
1
0
1
2
2
0
1
1
1
0
1
2
2
0
0
0
1
1
1
0
1
1
1
2
1
2
0
0
0
1
1
2
1
1
0
1
2
1
0
1
1
1
1
0
2
1
1
1
0
1
1
1
0
1
2
2
1
2
0
1
1
1
1
1
1
2
1
2
1
0
1
2
2
1
2
1
2
2
1
2
2
1
2
0
0
1
1
0
0
1
0
2
0
0
1
2
0
1
1
1
1
1
1
1
1
1
0
1
2
1
2
0
2
1
1
2
1
0
2
0
1
0
1
1
0
1
1
2
1
2
1
1
0
1
1
4
1
0
2
1
1
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
0
1
1
1
1
1
1
1
0
0
1
1
2
1
1
1
1
0
1
1
1
0
1
1
1
0
1
2
2
2
2
1
1
1
2
2
2
2
1
1
2
1
1
2
0
2
1
1
1
2
1
0
2
1
1
1
2
1
0
2
1
1
1
1
0
1
4
1
2
1
1
1
1
1
2
1
0
2
1
2
3
1
2
1
1
2
0
1
1
1
1
2
1
1
1
1
1
2
0
0
1
1
1
2
0
0
0
2
1
2
1
1
1
1
1
0
0
1
0
2
1
1
2
2
1
1
1
2
3
2
3
2
1
2
2
0
2
1
1
0
1
1
1
1
1
1
2
0
1
1
0
1
1
1
1
1
0
1
1
1
2
1
1
0
1
1
0
2
1
1
0
2
1
1
2
2
1
1
1
1
1
0
1
0
1
2
1
1
1
0
0
0
1
0
0
2
2
1
0
2
0
1
2
2
2
1
2
1
1
1
1
1
1
1
0
1
1
1
1
0
1
0
1
0
1
4
0
1
0
1
1
2
1
1
1
2
2
1
1
1
2
1
2
1
0
1
1
1
1
1
0
1
2
1
1
2
2
0
1
2
1
2
2
1
0
1
0
1
2
0
1
2
2
1
1
1
1
0
1
1
1
1
3
2
1
2
0
1
1
1
2
2
2
1
1
1
1
0
1
0
0
1
1
2
1
2
0
0
1
1
1
1
0
2
1
0
0
1
1
2
2
1
0
1
2
1
2
1
1
0
1
0
0
1
0
1
1
1
0
1
1
1
1
1
0
1
1
1
1
1
3
1
2
2
0
0
1
0
0
0
2
1
1
0
1
1
0
1
0
2
0
1
2
1
1
0
1
1
1
0
0
2
1
1
1
1
1
1
1
1
1
0
0
1
1
1
2
0
2
1
1
1
0
1
1
1
1
1
0
1
0
2
0
2
0
1
1
1
1
2
2
0
1
1
1
1
1
1
1
0
3
0
0
1
2
0
1
1
1
1
1
0
1
1
0
0
0
1
1
2
1
1
1
1
1
0
1
1
0
1
1
0
1
1
1
2
0
1
1
1
1
1
0
1
2
2
1
0
1
1
0
0
1
2
1
1
0
2
0
2
1
2
2
2
1
1
2
0
1
1
2
2
1
0
0
0
0
1
1
1
1
1
0
1
0
1
1
1
1
1
1
1
1
0
0
1
0
1
1
1
0
1
1
1
1
1
1
2
0
2
1
1
1
1
1
1
1
1
1
1
1
3
0
1
0
2
2
1
1
2
0
0
1
2
2
1
1
2
1
1
1
2
0
0
1
1
1
1
2
2
1
0
1
1
2
1
1
0
1
1
0
1
1
0
2
1
0
2
0
1
1
2
0
1
1
1
2
3
1
1
2
1
2
0
0
1
0
0
1
0
1
0
1
1
1
1
0
1
1
1
1
1
2
1
1
1
2
1
1
1
2
1
0
1
1
1
2
0
1
0
1
1
1
1
0
1
0
1
1
1
0
0
1
1
2
1
2
0
1
0
0
1
2
2
1
1
1
1
0
2
0
1
2
0
1
1
1
1
1
1
1
2
1
1
0
2
2
0
0
2
1
1
1
0
0
1
1
1
0
1
2
1
1
1
1
1
0
2
3
2
2
1
0
2
2
1
1
1
1
1
0
1
1
1
2
1
1
1
1
1
1
0
12
1
1
2
2
1
1
1
0
1
0
1
2
1
1
0
0
1
1
2
3
1
0
0
0
1
1
1
1
1
1
2
1
2
1
2
1
1
1
2
1
1
1
0
0
1
2
0
2
1
1
1
1
1
1
0
0
2
0
1
1
0
1
0
0
1
0
0
1
0
1
1
1
0
2
1
0
1
0
2
0
1
2
1
1
1
1
1
0
1
1
1
2
1
0
0
2
0
0
0
1
3
1
0
0
0
2
1
0
1
0
1
1
1
1
1
2
0
1
2
1
1
1
1
1
1
1
1
2
1
0
2
0
2
2
1
1
2
1
2
2
1
0
0
1
1
0
0
1
1
1
1
1
1
2
2
0
1
2
0
0
1
0
2
0
0
0
1
1
1
1
2
0
1
0
0
2
2
1
0
0
1
1
1
1
2
0
0
1
2
1
1
0
1
2
2
2
0
1
0
0
2
1
0
1
1
1
1
0
2
0
1
1
1
0
1
1
0
0
0
1
2
3
2
0
0
1
0
2
1
2
0
1
2
1
0
2
2
1
2
2
1
1
1
1
1
2
1
1
0
1
0
1
1
1
0
1
0
0
0
0
1
1
1
1
1
1
0
0
1
1
1
2
0
1
1
1
1
2
1
2
1
1
2
1
1
1
0
1
2
2
0
1
1
1
2
1
2
1
1
1
0
2
1
1
2
0
1
2
0
1
1
2
1
2
1
1
1
1
1
1
1
1
2
0
1
0
0
0
0
1
2
4
0
0
2
1
0
1
2
2
2
0
0
1
1
3
0
2
1
1
1
1
0
2
0
1
1
0
1
1
1
1
1
1
0
1
1
1
0
1
1
1
1
1
3
0
1
0
1
1
1
2
1
2
1
1
1
2
0
1
1
0
1
0
2
0
2
2
2
0
1
1
1
1
1
2
0
0
1
1
1
0
2
1
1
0
1
1
1
1
1
1
2
1
2
2
0
3
0
1
2
1
2
0
1
1
1
1
1
0
1
1
1
1
1
0
1
2
1
0
2
1
0
1
1
2
1
1
2
1
1
2
1
1
0
2
1
1
2
1
1
0
1
1
1
0
1
1
1
2
1
1
2
0
2
1
1
1
1
0
1
1
0
0
1
1
0
2
1
0
1
1
1
0
1
1
1
1
2
0
1
1
1
1
1
1
2
1
1
0
1
2
0
1
1
0
1
0
0
1
2
1
2
1
2
0
1
1
0
0
1
0
1
0
1
0
0
0
1
1
0
1
1
1
0
0
0
1
0
0
1
2
1
1
3
1
1
1
2
1
1
1
0
2
0
1
1
1
0
0
1
1
1
1
1
1
0
0
1
1
2
1
0
0
0
2
1
1
2
1
1
1
1
2
1
2
1
1
0
1
1
2
0
0
2
1
0
0
2
1
1
1
0
1
2
1
1
1
1
0
1
1
0
1
1
2
1
0
1
2
1
1
0
1
1
1
2
0
1
1
1
1
1
1
1
1
0
0
0
0
0
2
0
1
1
0
0
2
0
1
0
0
2
1
0
2
1
2
2
1
1
2
0
0
1
0
0
1
0
1
1
2
2
0
0
2
1
2
1
1
1
1
1
2
0
2
1
2
1
1
2
1
1
2
2
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
0
1
1
0
2
2
0
1
0
1
1
0
2
1
1
0
2
2
0
2
1
0
1
0
1
1
1
1
1
0
1
1
0
1
2
0
1
1
0
2
2
1
1
1
1
0
1
1
2
1
1
2
1
1
1
0
0
2
1
1
2
1
2
2
2
1
2
2
2
1
0
0
1
1
2
1
1
1
0
1
2
1
2
1
0
0
0
1
1
2
1
1
1
1
1
1
1
1
1
0
1
1
0
0
1
2
0
0
2
1
2
1
2
0
1
1
3
2
1
1
1
2
1
1
0
1
1
0
1
0
1
0
1
2
2
2
1
1
1
0
1
0
0
0
1
1
1
1
2
0
1
1
1
2
2
1
0
0
2
1
2
3
1
2
0
0
1
1
0
1
1
0
0
0
2
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
0
1
0
1
1
1
0
2
2
1
1
0
2
1
1
1
1
0
1
0
1
1
1
1
0
1
2
1
1
1
0
1
2
1
1
1
0
1
1
2
2
1
2
1
1
1
1
2
0
1
0
2
2
1
1
0
1
1
2
1
1
0
1
1
1
2
1
2
1
1
0
1
1
2
1
1
1
1
2
2
1
0
1
0
1
1
0
2
0
0
1
0
2
1
0
0
0
2
1
2
1
0
0
3
1
0
1
2
1
1
1
0
1
1
0
0
1
1
0
2
0
1
1
1
0
0
2
1
1
1
2
1
1
1
2
0
1
2
1
1
1
1
1
1
1
1
1
0
0
1
2
1
1
2
2
0
2
0
1
1
1
1
2
1
2
0
1
1
1
0
2
1
0
0
1
1
1
2
1
1
1
1
1
0
1
2
1
0
0
1
1
0
1
0
1
0
2
0
1
0
1
1
1
0
0
1
1
0
1
4
0
1
1
0
1
1
0
2
1
1
0
1
1
1
1
1
1
0
1
1
2
0
1
0
0
1
0
1
1
1
2
1
2
1
1
0
2
1
1
2
1
0
0
1
1
1
2
2
1
0
2
1
1
1
1
1
0
1
0
1
2
1
0
2
1
0
1
1
1
1
1
1
2
1
0
1
0
2
0
0
1
1
2
1
1
2
1
0
1
2
1
2
1
2
1
0
0
0
0
2
1
1
2
2
1
2
1
2
1
1
0
1
1
1
1
1
0
1
1
1
1
0
1
2
1
1
0
2
1
0
1
1
1
1
1
1
1
2
2
0
1
0
0
0
0
1
1
1
2
1
1
1
1
2
1
1
2
2
0
0
1
1
1
2
0
2
2
1
2
2
2
1
1
1
2
1
1
0
2
1
2
0
0
1
2
1
2
1
1
1
0
0
2
1
2
2
0
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
0
1
1
3
1
0
0
2
1
1
2
1
1
0
2
1
3
1
2
1
0
2
1
1
0
1
1
1
0
2
2
1
2
1
1
3
1
1
0
1
1
1
1
1
0
1
2
2
1
2
0
2
0
1
0
1
1
1
0
1
2
2
0
1
1
1
1
0
1
1
1
1
0
0
0
2
1
0
2
2
1
1
1
1
2
2
0
1
1
1
0
1
2
2
2
2
2
1
1
1
1
1
2
0
2
1
1
0
0
1
1
1
1
1
2
2
0
1
2
0
2
1
1
1
0
2
1
1
2
2
1
1
0
1
0
1
2
1
0
1
1
2
2
2
1
1
1
0
1
2
2
1
2
0
0
1
0
0
1
0
1
4
2
1
0
3
0
1
1
2
1
0
1
1
1
1
2
1
0
1
0
1
1
2
1
2
1
1
1
0
2
1
1
1
1
1
1
1
1
1
0
2
0
1
1
0
1
1
2
0
1
1
1
1
1
1
1
0
1
1
1
1
2
1
0
1
1
1
0
1
1
1
0
0
2
2
1
1
0
1
1
2
0
0
2
0
1
1
1
1
1
0
1
2
1
1
1
1
0
2
1
2
2
1
2
0
1
1
1
0
0
0
1
1
2
1
2
2
0
1
1
1
2
1
0
0
1
1
5
0
2
0
0
0
1
1
1
0
1
2
2
0
1
1
0
2
0
2
1
1
0
1
1
0
0
1
1
1
1
1
2
0
2
0
0
2
1
1
2
2
1
1
2
2
0
2
2
0
1
0
1
1
1
1
1
1
1
0
2
1
1
0
0
1
1
2
1
0
0
2
3
0
0
1
2
1
1
1
1
2
0
1
1
1
2
1
1
1
0
1
0
0
1
2
1
2
1
2
1
2
0
1
0
1
3
2
2
1
1
1
1
1
1
1
1
1
1
0
1
1
2
2
1
1
0
2
1
2
0
0
1
1
1
1
0
2
2
1
2
1
0
1
0
1
1
1
2
1
1
1
2
1
2
2
1
0
1
1
1
1
1
0
0
0
1
0
2
1
1
0
1
2
0
1
1
2
2
2
1
1
2
2
1
3
0
2
0
0
0
2
1
1
1
1
1
1
1
2
0
1
1
0
1
1
1
1
2
1
0
1
2
0
1
2
1
1
1
1
0
1
1
0
1
1
1
1
1
1
1
0
2
1
1
1
1
2
0
1
1
1
0
0
2
1
1
1
1
1
1
0
0
1
1
1
2
2
1
1
1
0
0
3
1
1
1
1
1
2
1
0
0
2
0
1
0
1
1
2
1
0
1
1
1
1
1
1
0
1
2
1
0
2
1
1
0
0
2
0
1
0
1
1
2
2
2
2
0
2
2
1
1
2
0
0
2
1
1
1
0
1
1
1
1
1
1
0
1
2
1
2
1
2
1
1
0
1
1
0
2
0
0
0
1
0
1
2
1
2
1
2
2
0
2
1
1
1
2
0
0
1
1
2
0
1
1
1
0
2
0
0
0
1
1
0
1
1
2
2
1
1
2
1
1
1
1
1
0
2
2
1
1
1
1
1
1
2
2
2
2
0
2
1
1
1
2
2
1
2
1
1
2
1
1
0
0
1
1
1
1
1
0
0
1
1
1
1
3
1
0
0
1
0
0
1
0
2
3
0
0
1
1
0
2
1
0
0
0
1
2
2
1
1
0
0
0
2
0
0
1
2
1
1
0
0
1
1
1
2
1
2
1
0
0
1
1
1
1
0
1
1
1
0
0
1
0
2
1
1
1
1
2
0
2
1
1
0
1
0
2
1
0
1
1
1
0
2
2
0
1
1
0
2
1
1
1
1
0
0
2
0
2
2
1
2
1
2
1
1
2
1
1
1
1
0
0
0
0
1
1
1
1
2
0
1
2
0
0
1
1
2
1
2
0
1
2
1
1
1
1
1
0
1
1
1
0
1
1
1
0
1
1
0
0
2
0
2
1
0
0
1
2
2
1
1
2
1
2
1
1
2
2
2
2
2
0
1
2
1
0
3
2
1
1
1
2
2
2
1
1
1
0
1
1
0
1
1
0
2
1
3
0
0
0
1
2
1
2
1
1
1
1
1
0
0
0
0
1
1
1
1
2
1
1
0
2
1
1
1
1
2
2
2
0
1
1
1
1
1
1
0
0
2
2
0
1
1
0
0
1
0
1
1
2
1
1
1
1
0
1
1
1
0
0
1
2
0
2
0
2
1
1
1
1
1
0
0
1
0
1
0
1
1
0
0
1
0
1
1
1
1
1
1
2
1
0
1
1
2
2
2
1
1
2
2
1
1
1
0
1
0
2
2
2
1
0
2
0
1
1
0
1
1
1
1
1
2
1
2
1
0
0
2
1
1
1
1
2
2
1
1
0
1
1
1
2
1
1
2
1
0
1
2
1
1
1
2
0
2
3
0
0
1
1
0
1
2
3
0
2
2
1
1
1
0
1
0
1
2
1
1
2
3
0
1
0
1
0
1
1
3
0
0
1
1
0
0
0
1
2
1
1
1
2
0
2
1
1
1
0
1
1
0
1
1
3
1
1
1
2
1
1
1
2
1
0
1
2
1
1
2
2
1
0
2
2
1
1
1
2
3
2
1
0
1
2
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
0
0
2
1
1
0
1
0
2
2
0
1
1
2
0
2
2
1
1
0
1
1
1
0
0
1
2
1
1
1
2
1
0
1
1
0
1
2
2
1
1
2
1
1
1
1
1
1
1
0
1
0
0
1
1
2
2
0
2
1
1
1
1
0
1
1
2
1
2
2
2
1
1
0
2
0
1
1
0
2
1
1
0
0
1
1
2
0
1
1
0
2
0
1
0
1
0
1
0
0
0
1
1
1
1
2
1
1
0
0
0
1
0
1
0
1
0
2
1
1
1
1
1
1
2
2
1
1
1
0
0
1
1
0
1
2
0
1
1
1
0
1
0
1
1
1
1
1
0
1
1
1
1
0
1
1
2
0
1
2
1
1
2
2
0
1
2
1
1
0
0
0
2
1
1
1
1
1
2
2
1
2
2
1
1
1
0
2
2
1
1
2
0
0
0
0
1
1
0
2
0
2
1
1
1
0
1
2
2
2
2
1
0
2
2
1
0
1
2
2
1
1
0
0
2
2
2
2
1
0
0
2
1
1
1
0
0
0
2
1
2
2
1
1
1
1
3
1
1
1
1
1
1
1
4
1
1
3
1
4
1
1
1
1
1
0
2
1
2
1
1
1
2
0
1
1
1
0
0
0
2
1
2
1
0
1
1
0
1
0
1
1
2
1
1
1
2
0
1
1
0
2
0
2
1
0
2
1
0
1
1
1
1
1
0
1
1
1
0
2
0
2
1
1
1
0
1
2
1
1
1
2
1
1
0
2
2
2
1
2
0
0
2
1
1
2
1
0
1
2
1
1
0
1
0
2
2
0
0
0
1
1
1
2
1
0
1
1
1
3
1
0
2
1
1
1
2
1
1
2
1
2
0
0
1
1
2
1
0
0
2
1
0
0
1
1
0
0
2
2
1
1
2
1
1
1
1
2
4
1
1
1
2
1
1
1
1
0
2
1
2
1
1
1
1
1
2
1
1
1
1
1
2
0
1
0
0
0
0
0
0
1
0
0
1
1
0
1
1
1
2
1
0
0
6
1
0
2
2
0
1
1
0
1
2
1
2
1
2
1
2
0
2
2
1
1
1
0
2
0
0
0
1
0
1
2
2
1
1
1
2
0
1
0
1
1
0
0
2
2
0
1
1
0
1
6
2
3
1
1
1
1
0
1
2
1
2
2
0
1
1
1
0
0
1
1
1
2
2
2
1
2
1
1
1
2
2
0
0
1
1
3
1
1
0
1
1
0
1
1
2
1
1
0
0
1
2
0
1
1
1
0
0
2
1
1
2
1
1
1
1
0
1
2
1
2
0
1
1
1
0
2
0
0
1
0
1
1
0
1
2
0
0
1
1
1
1
1
2
1
1
1
1
1
0
1
1
2
0
1
1
0
1
0
1
0
2
1
0
1
1
1
1
1
1
1
1
1
1
1
0
0
0
1
2
0
1
1
2
0
1
1
2
1
2
1
0
1
0
1
1
0
1
0
1
2
1
1
0
0
0
2
1
1
2
1
1
1
2
1
2
2
1
0
2
2
2
1
1
1
0
2
2
1
3
2
1
1
2
1
1
1
1
2
0
1
2
1
2
1
1
1
1
1
2
2
1
1
1
1
0
1
2
1
1
1
1
0
0
1
2
1
0
1
1
1
1
1
1
2
0
1
2
0
0
1
2
1
2
0
1
2
1
0
1
2
1
2
2
2
1
1
1
2
0
2
1
1
0
2
0
1
1
2
2
1
1
1
2
0
0
0
1
1
1
2
0
2
0
0
1
1
1
2
1
0
1
2
0
0
1
1
2
1
0
2
0
0
1
1
2
2
1
1
1
1
2
0
2
2
1
2
1
1
1
2
1
2
0
1
1
1
0
0
1
0
2
0
0
1
0
2
1
1
2
2
2
1
1
1
1
1
2
1
1
2
1
0
2
0
1
0
1
0
1
2
2
1
2
1
2
1
0
2
1
2
0
1
0
1
2
2
2
2
0
1
2
2
0
0
1
2
1
1
0
1
0
2
1
1
1
1
1
1
1
1
0
1
1
2
0
0
0
1
0
0
1
1
1
0
0
1
2
1
0
0
1
1
1
1
0
1
1
1
2
0
1
1
0
0
2
2
1
2
0
1
1
0
2
1
2
1
1
2
2
1
1
1
2
1
2
2
1
1
1
2
0
1
1
2
1
1
1
2
1
1
1
0
0
0
0
1
1
1
1
1
2
1
1
1
1
2
2
2
2
0
2
2
1
0
0
1
1
1
0
1
2
1
1
1
0
1
1
0
0
1
0
1
0
2
1
1
0
2
1
0
1
2
2
2
1
1
0
1
1
1
1
2
1
0
1
1
0
1
2
1
1
0
1
1
0
1
1
1
1
2
0
1
0
1
2
2
1
1
1
2
0
1
2
0
1
1
1
0
0
0
0
1
1
1
0
1
0
0
2
1
0
2
1
0
1
2
0
1
1
3
1
1
0
2
2
1
1
2
0
1
0
1
0
3
2
1
1
1
1
1
2
1
1
0
1
1
1
0
1
1
2
2
0
1
2
1
0
1
1
0
2
1
1
1
1
0
1
1
0
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
2
1
2
1
2
2
2
2
0
1
1
1
0
0
2
2
2
0
1
1
2
1
0
2
0
0
0
0
3
1
1
1
0
1
2
0
2
1
2
2
0
1
1
1
2
0
2
0
0
0
1
2
1
1
1
1
2
1
1
1
1
3
1
0
1
0
2
0
1
5
0
2
2
0
1
2
1
2
1
1
3
2
1
0
1
1
0
0
1
0
1
1
0
1
2
1
1
1
0
0
1
2
1
1
0
0
0
2
3
2
2
0
2
1
0
1
1
2
1
1
1
2
2
1
1
1
1
1
1
1
1
2
2
0
0
1
2
0
0
0
1
2
1
0
0
1
1
1
0
1
1
0
1
1
1
1
0
2
1
1
2
1
1
1
0
0
2
1
1
0
2
0
2
1
1
1
1
1
1
0
1
1
1
1
1
1
1
2
1
1
1
2
0
1
2
1
1
2
2
2
2
1
0
1
1
0
2
1
2
0
1
1
0
1
0
0
2
2
2
2
1
1
0
0
0
1
0
1
1
2
1
1
1
0
0
2
1
0
1
0
1
1
1
1
0
1
1
1
2
1
0
0
0
0
2
1
0
1
1
2
1
1
0
0
0
0
1
1
1
1
1
1
1
1
1
3
0
1
0
0
1
1
1
1
1
2
1
0
2
0
1
1
2
2
1
0
0
1
0
0
1
1
1
1
2
2
0
0
0
2
0
1
1
1
2
0
0
1
1
1
2
1
2
1
1
2
1
1
1
0
1
1
1
1
1
1
2
3
0
1
1
2
2
0
1
2
2
1
1
1
1
0
0
0
2
1
2
1
1
1
2
1
2
0
0
1
0
1
2
1
1
1
1
1
0
1
2
1
1
2
1
1
2
1
1
1
1
1
2
1
0
1
0
1
1
1
1
1
1
0
1
1
1
2
1
1
1
1
0
1
0
0
0
0
1
1
1
2
1
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
2
1
2
1
2
2
0
0
1
1
1
2
1
2
1
1
1
1
2
0
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
2
1
0
1
2
2
0
0
2
1
2
2
1
2
1
2
2
1
1
2
1
1
1
1
2
0
0
0
1
1
0
0
1
1
0
1
2
1
2
0
1
2
1
1
0
2
1
0
1
1
1
0
1
1
2
1
1
0
2
1
0
1
0
1
1
1
1
1
2
1
1
0
1
0
2
0
1
4
2
0
0
0
1
1
1
0
0
0
2
0
1
0
1
2
0
1
1
0
2
0
2
2
0
0
0
1
0
1
1
1
2
1
2
1
1
1
1
0
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
2
1
2
1
2
1
1
2
2
2
1
1
1
1
1
1
1
1
2
2
1
1
1
0
1
1
2
0
0
2
1
2
1
1
1
0
1
1
2
0
0
0
1
2
1
2
1
2
2
1
1
1
1
0
0
1
0
2
1
1
1
1
2
1
0
2
1
1
1
2
1
1
2
1
0
1
0
1
1
1
0
1
0
2
0
1
1
2
0
1
1
0
2
1
0
0
0
0
1
1
1
0
1
1
1
1
0
0
0
2
1
0
3
0
2
1
1
1
2
1
1
2
1
1
2
1
1
1
1
0
0
0
1
1
1
1
2
1
0
1
1
2
1
1
1
1
0
2
0
1
1
1
2
0
1
2
0
2
1
1
1
1
1
2
1
1
1
1
0
2
0
2
1
0
2
1
1
2
0
1
2
1
2
2
2
0
0
2
1
0
0
1
2
0
2
1
0
2
2
0
1
1
0
1
1
1
1
0
1
1
1
1
1
1
2
2
3
2
1
2
2
0
1
2
1
2
1
1
0
1
1
1
2
1
1
2
1
3
0
0
1
0
0
1
2
0
0
1
1
1
0
1
1
1
2
1
0
0
1
1
1
2
2
1
1
2
1
0
0
2
0
0
0
0
1
0
1
0
1
0
1
1
0
4
1
1
2
1
2
2
1
1
0
2
1
0
1
1
1
0
0
1
1
2
1
1
3
1
3
1
2
1
1
2
1
2
1
1
1
2
0
2
1
1
1
1
2
2
2
2
2
1
2
1
1
0
2
0
2
1
1
0
1
2
1
1
1
2
2
1
1
1
0
1
0
1
2
0
2
0
1
2
0
1
1
0
2
0
0
1
2
1
0
1
0
0
1
1
0
2
1
1
0
0
2
1
2
1
2
1
2
1
1
1
1
1
1
1
1
2
1
2
1
0
1
0
1
2
0
2
2
1
0
0
1
0
0
1
0
2
0
1
1
0
1
0
2
1
0
1
1
2
1
1
1
1
1
0
2
1
3
0
1
2
2
1
0
1
1
2
1
2
1
0
1
1
1
1
2
0
3
2
1
2
2
0
2
2
2
1
2
0
2
1
1
1
1
2
1
1
2
2
2
0
1
0
1
2
1
2
0
1
2
1
1
1
1
1
0
2
2
1
2
0
1
1
0
0
0
1
2
0
0
0
0
1
2
1
1
2
2
0
2
2
1
1
1
1
2
0
2
1
1
2
1
0
1
1
0
1
1
0
2
1
2
1
0
1
1
1
1
0
2
2
2
0
1
2
0
0
1
1
0
1
1
1
1
1
2
1
1
0
1
1
0
1
1
0
1
0
0
2
0
2
1
0
0
0
1
2
1
1
1
0
2
1
0
2
1
2
2
2
1
0
0
2
2
1
2
1
0
1
1
1
2
1
2
1
2
0
0
1
2
1
1
1
1
2
0
1
2
0
1
1
1
2
1
0
1
1
0
0
1
0
1
1
1
0
2
0
1
1
1
2
1
1
0
2
0
0
0
1
1
1
1
2
2
0
0
2
0
0
1
1
1
0
1
1
2
1
1
2
2
1
1
1
1
0
1
0
1
0
1
0
2
2
2
1
1
1
1
1
0
2
1
2
1
0
0
1
1
2
2
0
1
1
0
1
1
2
0
2
0
1
1
0
2
2
3
3
1
2
0
1
1
0
1
0
1
0
1
1
1
1
1
1
0
0
1
1
1
1
1
2
0
1
2
1
2
1
2
2
0
1
0
0
1
1
1
0
0
0
1
1
2
0
1
1
1
0
1
2
1
1
2
0
2
1
0
2
1
1
0
0
1
1
0
1
1
1
1
1
1
1
1
1
1
3
2
1
1
0
2
0
0
0
2
1
1
1
0
2
0
1
3
1
2
2
1
2
1
1
2
0
1
1
1
1
1
2
2
1
0
1
1
1
1
1
0
1
0
1
0
1
1
0
1
1
0
1
1
1
2
2
1
1
1
0
1
1
2
1
1
1
2
1
2
0
1
2
2
1
3
1
0
1
1
2
1
1
1
0
2
2
0
1
1
0
0
1
0
2
2
0
1
1
0
1
0
0
1
0
1
2
1
1
1
2
1
1
2
0
0
1
2
3
1
1
1
1
1
0
1
1
1
1
2
0
2
3
2
1
1
1
1
0
1
2
1
1
1
0
0
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
2
1
1
1
0
2
1
1
2
1
1
1
1
2
1
1
0
1
1
0
1
1
1
0
1
1
1
0
2
1
0
1
1
1
1
1
1
2
1
1
1
0
1
1
2
2
2
1
0
0
1
0
0
1
1
0
2
2
2
1
1
1
0
1
1
0
0
2
1
1
0
2
1
0
1
2
1
0
1
2
1
0
0
1
2
1
1
1
1
1
1
0
2
0
0
1
1
2
0
1
1
1
1
0
1
0
2
2
1
1
1
0
2
1
1
1
1
0
2
1
1
1
2
1
1
0
2
1
0
0
2
1
2
2
1
0
1
1
1
0
1
1
1
2
1
1
0
1
1
1
1
0
1
0
2
1
1
1
1
1
2
1
1
1
2
2
0
1
3
1
1
2
0
0
1
1
0
1
1
2
0
2
0
2
0
1
1
1
1
1
1
1
1
1
1
1
2
1
2
0
2
0
2
1
1
1
1
1
2
2
1
2
1
1
1
1
1
0
2
1
2
1
0
0
1
1
0
0
1
1
2
0
2
1
1
2
2
0
1
2
0
1
0
2
2
1
1
1
0
0
1
1
2
1
1
2
1
1
0
0
4
1
2
1
1
2
1
1
1
1
2
1
2
1
0
1
1
0
2
0
1
1
0
1
0
0
0
1
1
0
2
1
1
0
1
0
0
2
2
0
1
2
1
2
1
1
1
1
1
0
1
0
2
0
1
1
2
2
1
1
1
2
1
1
2
1
0
1
2
1
0
0
2
0
2
2
1
1
1
2
2
0
2
0
1
1
0
1
0
2
1
1
1
2
1
2
2
2
1
1
1
0
1
0
2
1
2
1
3
0
1
1
2
1
0
1
1
2
0
1
1
1
1
0
0
0
1
2
1
2
3
1
1
1
1
1
1
1
2
1
2
1
1
0
1
2
1
1
2
2
2
1
0
1
1
0
1
0
2
2
1
2
2
1
1
2
1
0
1
1
0
1
1
2
1
1
3
0
0
0
2
1
0
1
1
1
1
0
1
1
1
1
1
2
1
1
2
2
0
0
0
2
1
1
2
2
3
2
1
1
1
1
2
0
0
0
1
3
2
2
1
1
1
0
1
1
0
1
2
1
1
1
2
1
1
2
2
0
0
2
0
1
0
1
0
1
1
1
0
2
1
1
1
0
1
0
0
2
1
1
1
1
1
1
0
1
1
1
1
0
2
0
1
1
0
1
2
1
1
0
1
0
1
1
3
1
1
1
1
1
1
1
1
2
2
0
2
0
2
0
1
1
2
1
0
2
1
2
1
2
0
1
1
1
0
1
2
1
1
0
2
0
1
1
2
0
0
1
2
1
1
1
1
2
0
1
0
3
2
1
0
1
2
0
0
0
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
2
1
0
2
1
2
1
1
1
1
0
1
1
1
2
2
1
2
1
2
1
0
2
2
1
0
1
0
1
0
2
0
0
1
1
1
1
1
1
1
1
1
0
2
1
0
2
1
0
0
1
1
1
0
1
1
1
1
2
1
2
0
1
1
1
1
1
1
1
0
2
1
1
2
1
1
2
2
2
2
1
2
1
1
1
1
0
0
2
1
0
1
0
2
1
1
1
1
1
1
2
1
2
1
1
2
2
2
0
0
0
0
1
2
2
0
0
1
0
1
1
2
1
1
1
2
2
0
1
1
1
2
1
1
1
2
1
1
1
2
1
1
2
0
1
0
0
1
1
2
0
1
1
0
1
1
2
0
1
0
1
1
2
1
1
1
1
0
2
1
2
0
1
1
1
0
1
2
0
0
1
1
0
1
1
2
0
0
0
1
1
1
1
0
0
1
2
2
2
1
1
0
2
2
2
0
0
1
1
1
0
0
2
1
1
2
1
1
1
0
4
0
2
1
1
1
0
1
1
2
1
1
1
2
1
1
1
2
1
0
0
1
1
2
0
2
0
1
2
0
1
1
4
1
1
1
2
1
1
2
1
1
0
1
1
2
0
0
2
1
0
1
1
2
1
1
1
0
1
0
1
2
2
1
0
1
1
0
1
1
0
1
2
1
1
2
1
0
0
1
2
0
1
0
0
1
1
1
1
0
2
0
0
1
2
0
1
1
1
1
0
2
1
0
1
1
1
1
1
1
1
1
0
0
2
1
3
1
1
1
2
2
3
1
1
2
0
0
2
0
2
2
1
1
2
1
1
0
2
0
2
0
0
4
0
2
1
2
0
1
1
1
0
2
0
1
2
1
1
2
1
2
0
2
0
1
0
0
2
1
1
2
2
1
1
1
1
1
2
1
1
1
1
1
2
1
2
1
1
0
1
2
0
2
0
0
1
1
1
1
1
1
1
0
1
1
1
1
2
1
2
1
0
1
1
2
2
2
1
2
1
1
1
0
1
1
1
0
1
2
2
0
2
1
1
1
2
1
1
1
2
0
1
0
2
1
0
0
0
1
1
2
1
1
1
1
1
2
1
1
1
1
0
2
0
2
1
1
0
2
1
1
0
0
0
2
1
1
0
2
3
1
1
0
1
1
0
2
2
1
2
0
1
1
2
2
1
1
2
2
2
1
1
1
1
1
1
0
2
1
1
1
1
1
1
1
0
1
1
0
0
0
2
2
1
1
1
1
2
1
1
1
0
1
1
0
2
1
2
1
1
1
0
2
0
1
2
0
0
2
1
1
2
0
1
1
2
1
0
2
1
1
0
0
0
1
2
1
0
0
1
1
1
0
1
0
0
0
2
0
1
1
0
0
0
1
0
2
0
1
1
1
1
1
0
1
2
1
0
1
1
1
2
0
0
1
1
1
1
1
2
0
2
2
1
1
1
1
2
1
1
0
2
1
1
1
1
0
2
2
1
1
1
1
1
1
0
3
2
1
1
1
0
1
1
2
4
2
0
1
1
0
2
0
0
1
0
2
1
0
1
0
2
1
0
1
1
0
2
2
0
1
1
0
1
1
1
0
1
1
1
0
2
1
2
2
0
0
0
2
0
1
0
1
1
1
1
1
1
1
2
0
1
0
2
1
1
0
0
0
1
1
1
1
1
1
1
0
1
0
1
0
2
1
1
0
2
2
2
1
1
1
2
1
1
1
0
1
0
2
2
1
1
0
1
0
1
2
0
1
0
2
1
1
1
0
1
0
2
1
1
1
0
1
0
1
1
1
1
2
0
0
0
2
1
0
1
0
0
1
0
0
1
1
1
2
2
2
2
1
2
0
2
1
1
2
1
1
1
0
2
1
0
1
0
2
0
1
0
0
0
2
1
1
2
2
2
2
1
1
1
0
1
1
1
1
1
0
1
2
2
1
1
0
1
1
1
0
0
0
2
1
1
1
2
2
2
1
0
0
1
1
1
2
1
0
2
2
2
2
1
2
2
1
1
1
0
2
0
0
0
1
2
0
1
1
1
2
0
1
1
0
2
1
1
0
1
2
1
1
0
1
1
2
0
0
0
1
1
1
1
2
1
2
1
1
0
0
2
0
0
2
0
0
2
1
2
1
2
0
2
0
1
1
3
1
1
1
0
1
2
0
2
1
2
1
2
2
0
1
1
1
1
1
2
1
1
2
0
2
1
1
1
1
2
2
1
1
2
1
1
0
2
1
0
1
0
0
2
1
1
1
1
1
3
1
1
2
1
1
2
1
1
1
1
2
0
1
1
1
1
1
1
1
1
2
0
1
0
1
1
1
2
2
2
3
1
1
1
2
1
1
0
0
1
1
1
1
0
1
2
2
1
0
2
0
0
0
2
2
1
1
0
0
1
1
1
0
2
0
0
1
0
1
0
0
1
0
2
1
1
1
1
2
2
2
1
1
1
1
2
1
1
2
2
0
1
2
2
1
0
2
2
1
1
1
2
1
1
1
2
0
0
0
1
1
1
2
1
2
2
0
1
1
0
1
0
1
1
1
1
2
1
1
2
1
0
0
3
1
1
1
2
2
1
0
0
1
0
1
2
2
1
2
1
1
1
0
1
1
0
1
1
0
1
1
1
0
2
1
1
0
1
1
1
0
1
0
0
1
1
1
0
1
0
1
0
1
1
0
1
2
2
0
1
1
0
0
1
0
1
1
1
1
0
0
2
2
2
1
2
0
0
1
0
0
1
2
2
1
1
0
2
1
0
0
2
2
1
1
1
0
0
2
2
1
2
1
1
2
1
1
1
1
1
2
0
0
1
0
1
1
1
1
0
0
2
0
0
2
1
1
1
2
0
1
3
1
1
1
1
1
2
1
2
3
2
1
1
2
1
0
2
1
2
1
4
2
0
1
1
0
1
0
2
0
0
1
1
1
2
2
1
1
2
1
0
0
0
1
1
0
1
1
1
2
1
1
1
1
1
1
1
1
0
2
1
2
2
0
0
0
0
2
1
1
1
1
1
1
0
1
1
0
0
2
0
1
2
1
1
1
1
0
0
2
1
2
1
0
1
2
1
1
2
1
0
2
0
1
2
0
2
3
1
0
1
1
0
1
1
0
1
1
1
1
1
1
2
0
1
1
2
1
0
0
2
0
1
1
1
0
1
1
2
2
0
0
0
0
0
1
1
1
0
1
1
0
0
2
2
2
1
1
1
1
1
0
1
2
1
1
1
1
1
2
1
1
0
0
1
1
1
0
1
2
1
0
1
0
0
1
2
1
0
1
1
1
1
2
1
1
2
1
1
2
2
2
0
0
1
1
1
0
1
1
1
0
1
2
1
0
1
1
1
1
1
3
1
1
1
0
0
1
1
0
1
0
1
1
1
1
2
2
1
2
2
2
2
1
1
1
0
1
1
2
1
0
0
1
2
1
0
2
1
0
1
1
1
1
1
0
0
1
1
0
2
1
0
0
2
2
1
1
1
1
1
2
0
1
2
1
1
0
0
1
1
0
1
1
0
1
0
2
0
0
0
0
1
0
2
2
1
0
0
2
1
2
2
1
1
4
1
2
1
1
0
1
0
1
1
2
2
2
1
1
1
1
2
0
0
2
1
0
1
1
0
0
1
2
1
2
1
1
2
0
0
0
0
0
2
0
1
0
0
0
1
0
2
1
0
1
1
0
1
1
1
1
1
2
0
0
1
2
1
1
1
2
1
1
2
1
1
1
0
1
1
1
2
0
1
1
1
1
1
2
1
1
1
2
2
0
1
2
0
1
1
0
1
1
2
1
1
1
0
0
1
1
1
1
2
2
1
1
0
1
1
0
0
1
2
0
1
2
1
1
2
0
0
1
2
0
1
2
2
0
2
1
2
1
2
1
0
1
2
1
0
1
2
0
2
1
1
1
0
1
1
1
2
1
1
1
1
1
1
1
1
0
1
1
1
0
1
2
1
0
1
1
0
2
1
2
1
1
0
1
1
1
1
0
0
1
0
1
0
1
2
2
0
1
1
0
0
1
0
2
0
0
1
1
0
2
2
0
0
1
1
2
0
0
2
0
1
1
2
2
1
1
1
0
1
1
1
2
1
1
0
1
1
1
1
2
1
2
1
1
1
2
2
0
1
1
0
1
1
1
2
0
0
1
1
1
1
1
1
1
2
0
1
0
0
1
1
1
1
1
0
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
3
1
1
2
1
1
1
1
1
2
1
0
0
1
1
1
0
1
1
1
1
3
2
0
1
0
1
1
1
1
1
0
0
2
2
0
1
2
1
1
1
2
1
1
1
0
1
1
0
1
2
2
1
0
0
1
1
1
1
1
2
0
1
2
0
2
1
1
1
1
2
0
3
1
1
1
1
0
1
0
1
2
1
1
0
1
2
1
1
2
1
2
1
2
2
1
0
1
1
1
2
1
0
2
2
2
1
1
2
2
1
0
1
1
1
2
3
0
1
1
1
1
1
1
1
1
0
1
0
2
2
2
1
2
1
1
1
1
1
0
1
1
1
2
1
2
0
1
1
2
2
0
1
1
1
1
1
1
2
1
1
1
0
1
1
1
1
1
0
1
0
2
2
1
1
2
2
2
0
1
0
0
0
1
1
0
1
0
2
1
2
1
1
1
0
2
0
1
1
1
2
1
0
0
1
3
1
1
0
0
1
2
2
1
2
1
2
2
1
1
0
1
0
0
1
2
1
1
1
2
1
0
1
2
1
1
1
1
0
0
1
1
0
0
2
1
1
1
1
1
2
2
1
0
0
0
2
2
0
0
0
0
2
1
1
2
1
3
1
0
1
1
2
0
1
1
2
1
1
1
0
1
0
1
1
0
1
0
0
1
1
2
1
2
1
0
1
1
2
0
0
2
1
2
2
2
0
2
3
0
0
1
1
0
2
1
1
1
0
1
1
1
1
0
0
1
1
3
1
1
1
1
0
1
1
2
2
0
0
0
1
1
0
1
1
2
1
1
1
1
2
1
0
1
1
2
1
0
1
2
1
1
0
1
1
2
1
0
1
1
2
0
1
2
2
1
1
1
2
1
1
1
1
1
6
1
1
2
1
2
2
2
1
1
1
1
0
0
1
2
2
2
1
0
0
2
0
1
1
1
0
1
1
2
0
2
1
1
1
1
1
2
2
1
2
0
1
2
0
0
1
2
1
1
1
1
1
1
1
0
0
1
1
0
1
1
1
2
1
0
2
0
0
0
1
1
0
2
0
0
0
1
1
0
0
1
1
1
0
0
1
1
1
0
1
2
1
2
1
0
2
1
1
1
1
0
2
0
2
1
1
1
1
0
0
1
2
2
0
1
1
2
1
1
1
1
1
1
2
2
2
1
0
1
0
2
0
1
0
0
1
1
1
2
1
2
1
1
2
2
1
1
0
2
0
1
2
0
0
2
1
0
1
2
2
1
1
0
2
2
2
1
1
1
1
0
3
0
0
1
2
1
0
1
1
1
1
0
1
1
2
1
1
1
1
0
1
1
3
1
3
1
1
2
0
1
1
1
2
1
1
1
1
0
1
2
1
1
1
1
1
1
1
2
1
1
0
1
1
0
1
1
1
0
1
1
2
1
1
2
0
2
1
0
0
1
1
2
1
2
1
1
0
1
1
1
0
2
1
1
1
4
2
0
1
0
1
2
1
1
2
0
1
1
0
1
1
2
2
1
0
1
1
0
1
0
1
1
1
1
1
2
0
1
2
1
1
1
2
1
1
0
2
1
0
1
1
1
1
1
1
1
1
0
2
1
0
2
1
0
1
1
0
1
0
1
1
2
2
0
1
0
0
1
0
0
1
1
1
1
1
1
0
0
1
1
2
1
0
0
2
0
0
1
1
1
0
2
2
1
2
1
1
2
2
0
2
1
2
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
1
2
2
2
1
0
1
0
1
0
5
0
2
2
0
2
1
1
0
1
2
0
2
1
2
2
1
1
3
0
2
1
2
1
0
1
0
2
0
1
2
0
0
1
0
2
1
0
2
0
2
1
0
1
2
0
1
2
1
1
1
1
2
1
1
1
1
3
2
0
0
0
1
2
1
1
2
0
2
2
2
0
1
1
1
2
0
1
0
2
1
1
1
2
0
1
1
1
1
1
0
1
1
1
1
2
0
0
1
1
0
2
2
1
0
1
1
1
1
0
2
2
1
1
1
1
1
1
1
1
1
0
1
0
0
1
1
0
1
0
1
0
1
1
0
1
1
1
0
1
0
2
1
1
1
0
1
1
2
1
2
1
0
2
0
1
0
0
1
2
1
1
1
1
1
1
0
1
0
3
0
0
1
1
0
2
1
1
2
1
1
1
2
2
1
2
1
1
0
0
1
0
0
2
1
1
0
2
1
2
2
2
0
0
2
1
1
2
1
1
0
2
0
1
2
1
0
2
1
2
0
0
1
2
0
1
1
2
2
0
2
1
1
1
0
0
1
1
1
1
1
1
1
1
1
1
1
0
0
0
2
1
1
1
2
0
0
1
1
3
1
1
1
1
1
2
3
1
0
1
1
2
2
1
1
2
1
2
1
1
2
1
1
2
1
1
2
1
0
1
1
2
1
1
0
2
1
0
1
1
1
1
0
0
1
1
0
1
1
1
2
1
1
2
1
1
2
0
1
0
2
1
1
0
2
1
1
1
1
1
1
0
1
1
1
0
2
1
2
1
1
2
0
0
2
1
1
0
0
2
2
0
0
1
2
1
1
0
1
1
1
0
2
2
1
0
0
2
0
1
1
0
2
2
1
1
1
1
1
1
1
1
1
1
0
0
1
3
1
1
1
1
1
1
1
1
1
1
0
0
1
0
2
1
2
0
3
1
1
2
0
1
0
0
1
1
2
2
0
0
1
0
1
0
1
1
1
0
1
1
1
2
2
1
0
0
1
2
2
2
0
0
0
1
0
2
0
1
2
0
1
1
1
2
1
1
2
1
2
2
1
1
1
1
1
1
0
2
0
0
1
0
1
1
2
1
3
1
0
1
1
0
0
1
2
0
2
2
0
1
1
1
3
0
2
0
2
2
2
1
1
1
0
1
2
0
1
1
2
2
1
1
1
1
2
2
1
0
2
3
1
1
1
1
2
0
1
1
2
1
2
2
2
0
1
0
1
1
0
1
0
2
2
0
1
2
1
1
1
2
4
1
1
1
0
1
0
1
1
0
1
1
1
1
0
0
1
1
1
2
0
1
2
1
0
2
1
2
1
1
0
4
1
1
1
2
1
2
0
2
1
1
1
0
2
0
0
1
2
0
1
1
1
1
0
2
1
0
0
0
0
1
2
1
1
2
2
0
1
0
1
1
0
1
1
1
2
1
1
1
0
1
0
1
2
1
1
1
1
1
0
1
1
0
1
2
1
1
2
1
1
2
0
1
2
1
0
0
2
0
2
2
0
0
2
2
1
0
1
1
1
1
1
0
0
1
1
2
0
4
0
1
1
1
1
0
1
2
0
1
0
1
2
0
2
2
1
2
2
1
2
1
1
1
2
1
1
2
1
1
0
1
0
1
1
2
1
2
0
1
0
1
0
1
0
0
0
1
2
1
1
2
1
1
1
2
0
1
2
1
1
2
0
0
1
0
1
1
2
1
1
0
0
1
0
2
0
1
1
2
0
1
0
1
1
1
0
1
0
1
0
1
0
2
1
2
2
1
0
1
1
0
0
1
0
0
2
1
1
0
1
0
1
1
2
0
1
2
1
2
1
1
1
0
2
1
2
2
1
1
1
1
1
1
1
3
1
1
2
1
2
0
2
2
1
1
2
1
2
2
0
1
0
1
1
1
0
0
2
2
2
0
0
1
1
1
0
1
1
1
1
1
0
1
1
0
0
0
0
2
1
1
1
1
1
2
2
1
1
2
2
1
1
0
0
1
1
0
2
2
0
0
2
0
1
1
0
1
1
2
0
1
1
1
1
2
1
0
1
1
1
0
1
1
2
0
1
0
1
1
1
2
1
1
1
1
1
2
1
1
1
0
2
1
1
1
1
0
1
1
0
0
1
1
0
1
0
1
1
2
1
2
2
1
1
1
2
1
1
2
2
1
1
2
1
2
1
1
0
2
2
1
2
0
0
1
1
0
1
1
0
1
2
1
2
2
1
1
2
0
1
0
1
2
0
2
2
1
0
1
0
2
1
1
2
1
2
1
0
3
1
1
1
2
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
2
1
2
1
1
2
1
1
2
1
0
0
2
1
0
0
1
1
0
2
1
1
1
1
0
1
1
1
0
0
2
0
2
1
1
0
1
1
1
0
1
1
1
1
0
2
0
1
0
1
0
1
0
1
2
1
1
1
0
1
2
2
1
1
1
0
0
0
0
1
1
0
1
1
0
1
1
1
2
1
2
1
2
2
2
0
1
0
1
0
2
2
1
0
0
1
2
1
1
0
1
2
1
1
0
2
2
1
0
2
0
1
1
0
1
1
0
3
0
1
1
0
1
2
1
0
2
1
2
2
1
1
1
1
1
1
2
1
0
1
0
2
1
1
2
1
1
2
0
1
0
1
2
2
1
3
1
1
1
0
1
1
1
1
2
2
1
1
1
0
1
2
2
0
1
1
0
1
2
3
2
1
1
1
1
0
1
1
1
0
0
1
1
1
2
1
1
1
1
1
1
1
2
3
1
3
2
2
1
2
1
1
1
1
1
1
1
0
1
1
0
0
1
1
0
2
0
1
0
1
1
1
0
1
0
2
1
1
1
0
1
1
1
1
0
1
0
2
0
2
0
0
1
1
0
2
1
0
1
1
0
1
1
1
0
0
1
0
0
1
1
2
2
1
2
1
2
1
2
1
2
0
0
1
0
0
2
1
1
2
1
0
1
1
0
1
0
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
0
2
2
1
1
1
2
2
2
1
0
1
2
1
0
2
1
2
1
0
1
1
1
1
1
1
1
1
2
1
2
1
2
2
1
2
0
1
1
1
1
1
0
2
0
1
2
1
0
2
0
1
2
2
0
0
1
1
1
0
0
0
1
2
1
2
1
1
0
2
0
2
0
2
2
0
1
0
1
1
2
1
0
2
1
1
1
1
1
0
1
1
0
1
1
1
3
1
2
0
1
1
0
2
0
3
1
2
0
1
1
0
0
1
1
0
0
1
1
1
0
1
1
0
2
2
1
1
0
0
0
1
1
1
0
2
1
1
1
1
2
2
1
2
1
1
0
1
1
0
2
1
1
0
2
1
0
2
1
1
1
2
3
1
1
1
0
2
1
2
1
1
1
1
1
2
1
1
2
1
1
2
3
1
1
2
1
1
1
1
0
1
1
2
1
0
0
0
1
1
2
1
1
2
2
2
1
0
2
1
2
2
2
0
2
0
1
0
1
2
0
1
1
1
2
1
2
1
2
2
1
2
0
0
1
2
1
1
1
1
0
0
1
1
1
0
0
1
1
1
1
2
1
0
1
0
1
2
1
0
1
1
1
0
1
0
2
1
1
1
1
0
0
1
2
2
1
1
0
2
1
1
1
0
1
1
0
1
0
1
0
2
1
1
0
1
1
1
0
1
1
1
1
2
1
2
2
1
2
1
0
1
1
2
1
0
1
1
0
0
2
1
1
1
0
2
1
0
2
1
0
2
1
1
2
2
1
1
2
0
1
1
1
2
1
1
1
2
0
1
1
1
0
2
1
0
1
0
2
2
1
1
2
0
2
1
1
1
1
0
2
1
2
1
2
0
2
1
2
0
1
0
2
1
0
0
1
0
2
2
0
1
2
1
1
1
1
0
2
1
1
2
0
1
1
0
2
2
0
2
0
1
0
2
1
1
0
2
2
1
2
0
2
0
1
2
0
1
2
1
2
1
1
1
0
0
2
2
1
1
2
1
2
1
1
1
0
1
1
0
3
2
1
1
1
1
0
1
1
1
1
1
1
1
1
2
2
0
0
1
2
0
2
2
1
0
1
1
0
1
1
1
1
0
0
0
2
0
2
1
1
2
2
1
2
0
2
0
1
0
1
2
1
0
2
2
1
0
1
2
1
1
1
2
0
1
1
0
0
2
1
0
1
1
2
1
1
2
1
0
1
1
0
1
1
1
2
1
1
1
0
1
1
0
1
0
1
2
0
2
0
0
1
1
1
2
1
1
1
0
1
2
2
0
2
2
2
2
1
2
2
2
2
0
0
2
1
1
0
1
1
0
1
2
0
1
1
2
1
1
1
1
2
0
1
0
0
7
1
1
0
1
1
0
1
1
1
1
2
1
0
2
2
1
0
1
1
2
1
2
1
2
1
2
1
2
2
0
1
1
1
0
1
1
1
0
1
1
0
1
2
1
0
1
1
1
0
2
1
0
0
0
1
2
0
0
1
1
1
2
3
2
2
2
2
0
1
1
1
1
1
1
1
1
2
0
0
1
2
1
1
1
2
0
1
1
1
1
1
1
2
1
2
1
1
2
1
3
0
1
0
1
0
1
2
2
2
0
1
2
0
2
1
1
1
1
1
1
1
2
2
2
1
1
0
0
1
1
1
2
1
2
1
1
1
1
1
0
2
2
1
2
1
2
2
1
1
0
1
0
1
0
0
1
2
2
0
1
0
2
2
1
1
2
1
2
0
0
1
0
1
0
0
2
1
2
1
2
1
0
1
1
1
1
1
0
0
2
1
1
1
0
0
1
1
1
1
1
1
0
3
1
2
0
1
1
1
2
1
2
1
1
1
2
0
2
0
2
2
1
1
1
1
0
1
1
2
0
1
2
0
0
2
0
1
1
2
1
1
1
1
0
2
0
1
2
2
2
1
1
1
1
2
1
1
1
1
3
2
0
1
0
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
0
1
1
1
1
1
2
1
2
1
2
0
1
1
1
1
0
1
1
0
1
0
1
0
1
1
1
2
0
1
1
0
1
1
0
1
1
0
2
1
1
2
1
0
1
0
3
1
1
1
1
1
3
1
1
1
1
0
1
1
1
2
1
1
1
1
1
1
1
1
0
2
1
1
2
1
2
2
1
1
1
0
1
1
2
2
1
1
0
0
2
2
1
2
1
2
1
0
0
1
0
2
0
2
4
1
0
0
0
1
2
1
0
1
0
0
1
1
0
2
2
1
0
1
1
1
3
0
0
1
1
1
1
1
2
2
2
0
1
2
1
2
1
0
0
2
1
1
5
1
1
0
1
1
0
1
2
1
0
1
1
1
1
0
2
0
1
1
2
2
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
2
1
1
1
2
1
2
1
0
1
1
1
0
1
1
0
1
1
1
1
1
2
1
1
1
0
0
1
2
1
1
2
1
1
1
1
2
1
1
2
0
1
1
1
2
2
0
0
1
0
0
1
2
1
0
1
1
1
1
1
1
1
2
1
1
1
3
1
1
1
1
1
0
1
1
1
2
0
2
1
1
1
1
1
1
0
0
0
1
1
1
1
2
1
1
0
1
0
1
1
1
0
0
2
2
1
1
1
0
0
1
2
1
1
1
1
1
2
1
0
2
2
1
0
1
1
2
1
2
0
1
1
0
0
0
1
1
0
1
2
0
0
1
0
0
1
2
0
1
2
0
1
2
1
0
1
1
0
1
1
1
1
1
1
1
0
2
1
2
1
0
2
1
0
1
1
1
2
0
2
1
1
0
1
1
0
1
2
1
3
1
1
1
0
1
1
0
0
1
1
1
0
1
0
1
0
1
1
0
2
1
2
1
1
1
0
2
1
0
1
1
2
2
1
1
1
1
2
1
0
1
1
2
1
2
2
1
2
0
0
0
1
0
1
1
1
1
0
1
1
0
0
1
0
1
1
2
0
1
0
2
1
1
1
1
2
1
2
1
3
0
0
0
1
1
1
1
2
1
0
2
1
0
1
2
2
2
2
1
1
1
1
2
0
0
1
1
2
0
0
1
1
0
1
0
0
2
2
2
2
1
1
0
0
2
1
0
0
0
2
0
1
2
1
1
2
1
0
0
1
2
0
2
2
0
1
1
0
1
1
1
1
1
2
2
0
1
0
0
1
1
0
1
1
0
1
1
2
0
1
2
2
2
1
1
2
1
1
0
0
2
3
0
0
1
2
0
2
2
1
1
1
1
1
2
1
2
0
1
1
0
2
1
1
2
2
3
1
1
1
1
1
0
0
0
2
0
0
2
1
1
1
1
1
2
0
1
1
1
1
2
2
1
1
1
2
2
1
3
1
1
1
1
1
1
2
1
1
1
1
0
1
0
0
1
0
2
2
2
2
2
0
2
1
1
0
2
0
1
2
1
1
2
2
2
2
1
1
1
1
0
1
0
0
0
2
2
1
1
0
0
1
1
2
1
1
1
0
0
1
1
0
1
1
1
1
2
1
1
0
0
1
1
1
1
1
2
1
2
0
2
1
1
3
2
1
2
1
0
2
1
1
2
0
0
1
1
1
2
1
2
1
0
0
0
1
0
2
1
2
1
1
0
0
1
1
0
1
1
0
0
1
0
2
1
1
2
0
0
1
1
0
0
1
0
0
0
1
2
1
0
1
0
1
1
1
2
1
1
0
1
0
2
1
1
1
1
1
1
0
1
0
1
1
2
2
1
1
1
2
1
0
1
2
1
1
1
1
1
1
1
1
0
2
0
0
2
1
0
1
2
2
1
2
1
0
2
0
0
2
1
1
1
1
1
1
2
1
0
0
0
2
1
1
0
2
1
2
2
2
1
0
2
2
1
0
1
0
0
1
1
1
1
0
1
2
1
2
0
0
0
1
0
2
2
1
1
2
0
1
0
1
0
1
1
1
1
1
1
0
2
2
1
2
0
2
1
1
0
1
1
1
2
0
1
1
1
1
0
1
1
1
2
2
2
1
1
1
1
0
1
1
3
1
1
1
2
0
0
0
1
2
2
0
3
1
1
2
1
0
1
0
0
2
2
2
2
0
0
2
1
1
1
1
1
1
1
1
2
1
0
1
1
1
0
2
1
1
1
1
1
1
1
2
1
2
0
2
2
1
2
1
1
0
0
1
2
2
0
1
1
1
0
2
1
1
2
2
1
2
1
1
1
0
2
1
1
2
1
0
2
2
0
1
1
1
1
0
1
1
2
0
1
1
1
0
1
0
0
1
2
0
2
1
1
0
2
1
0
1
2
2
1
1
1
2
0
1
0
1
1
0
1
1
2
1
1
1
3
1
2
1
2
1
0
1
3
4
2
1
2
1
0
1
1
2
1
1
2
2
2
0
1
1
1
0
1
0
1
1
2
1
2
1
1
1
1
2
1
0
1
0
1
1
1
0
1
1
2
0
1
1
1
1
1
2
1
0
0
0
1
1
1
1
1
1
1
1
1
0
1
1
1
1
0
0
1
1
1
2
1
2
2
2
1
2
1
2
2
1
1
1
1
2
2
1
0
1
2
1
2
1
2
2
2
1
1
2
2
1
1
1
2
1
0
2
1
1
1
1
1
2
0
0
1
2
1
2
1
1
1
2
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
2
1
2
2
1
1
2
1
1
0
1
1
1
1
2
2
0
2
2
1
2
1
0
1
1
0
0
2
1
2
2
1
1
1
1
1
0
1
2
2
0
0
1
0
1
1
1
1
2
1
2
1
1
2
0
1
1
1
1
0
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
0
1
0
0
2
1
0
1
0
1
0
1
1
0
2
1
2
1
1
0
2
0
3
1
1
1
1
1
0
2
5
1
0
1
0
1
0
2
2
0
1
1
1
1
1
0
1
1
1
0
1
1
1
1
2
1
2
1
1
2
1
0
0
0
2
1
1
1
1
0
1
0
0
1
0
0
1
1
0
1
2
1
1
2
1
1
2
0
0
1
1
2
1
0
1
1
2
2
1
1
1
1
1
1
1
1
1
2
0
1
1
2
2
2
1
2
1
2
2
1
0
1
1
2
2
2
1
1
1
1
1
2
1
0
1
0
0
1
1
0
1
1
2
2
1
2
0
0
1
1
1
1
1
2
1
1
2
2
0
1
1
0
0
2
2
1
1
0
1
0
1
0
1
0
2
1
1
1
1
1
1
1
1
2
2
1
1
1
0
1
0
1
1
1
2
0
1
2
1
1
1
1
1
1
0
1
1
1
1
1
1
0
1
1
2
0
1
2
1
1
0
1
1
1
1
1
1
0
1
0
1
1
1
1
0
0
1
2
0
1
1
0
1
1
1
0
1
1
1
1
2
1
1
0
0
1
1
0
0
1
2
2
2
0
1
1
0
1
2
1
1
1
0
1
2
2
2
2
1
1
1
1
1
2
1
2
2
2
1
2
2
2
2
1
1
2
2
0
1
2
0
2
1
2
1
0
1
2
2
1
0
1
0
0
1
1
1
1
2
1
2
0
1
1
1
1
0
1
1
1
1
2
2
0
1
2
2
1
0
1
1
1
0
1
1
1
3
1
2
1
1
2
0
1
0
1
0
1
1
1
1
0
0
2
1
2
1
0
2
2
2
1
1
1
0
0
1
0
0
2
1
1
2
2
0
1
2
0
1
0
1
1
1
1
1
2
1
1
1
0
1
0
0
1
2
0
1
1
2
0
1
1
2
2
2
1
1
1
2
0
0
2
1
1
1
1
0
0
1
1
0
1
1
1
1
2
1
0
0
2
0
2
1
2
1
0
1
1
0
1
1
2
1
1
0
0
0
0
0
1
2
1
1
0
2
1
1
1
0
2
1
1
2
2
1
1
1
1
0
0
1
0
1
2
1
1
1
1
1
0
2
1
0
0
1
0
1
1
0
1
1
1
0
1
0
4
2
1
2
0
1
2
1
1
2
0
2
1
1
2
1
1
0
2
1
0
3
2
1
1
2
0
1
1
1
0
2
2
1
1
1
2
1
0
1
1
1
1
1
0
0
1
1
0
1
1
0
0
0
2
1
0
6
1
1
2
1
2
0
0
1
0
1
1
2
2
1
2
0
1
0
0
0
2
1
1
2
0
1
1
1
1
2
0
1
1
1
1
1
0
1
1
1
1
1
2
1
1
2
1
1
2
1
0
1
1
1
1
0
1
0
1
1
0
1
1
1
2
1
2
1
1
0
2
0
1
1
1
1
1
1
0
1
1
1
0
0
3
1
1
0
1
1
3
1
2
1
0
1
1
0
2
0
2
1
0
0
1
1
2
0
0
1
0
1
1
1
2
1
1
1
0
2
1
1
1
1
1
2
2
1
1
1
2
1
0
2
0
1
2
1
1
0
0
0
1
1
1
2
1
1
2
1
2
1
2
2
1
1
1
1
3
1
1
0
1
1
3
0
1
0
1
1
1
2
1
1
1
1
0
0
2
1
1
2
1
1
1
1
3
2
2
0
1
1
1
1
1
1
2
0
1
0
1
1
0
0
1
1
1
1
2
2
1
0
2
1
0
2
1
0
0
0
1
0
1
0
2
1
0
0
2
1
3
1
1
0
1
1
0
0
1
1
2
1
1
0
0
0
1
0
1
0
2
2
2
1
1
0
1
1
1
1
0
2
1
1
0
2
1
0
1
1
2
2
1
2
1
1
1
1
0
1
1
0
2
0
1
0
0
1
2
0
1
0
2
1
1
1
1
2
2
0
1
1
2
1
1
1
0
1
0
1
1
1
1
0
1
1
1
0
1
0
2
1
1
0
1
1
1
0
1
1
1
1
2
1
1
3
2
0
1
2
0
1
1
2
1
0
1
2
1
1
0
1
1
0
2
0
1
0
2
2
1
0
1
0
1
1
2
0
1
1
1
1
1
0
2
1
1
1
0
2
1
1
3
0
2
2
1
3
1
0
2
1
2
1
0
1
1
1
1
0
2
1
2
0
1
0
1
1
1
1
0
2
0
1
1
1
2
1
2
1
2
1
2
0
1
1
1
0
1
1
0
1
1
1
1
1
1
1
2
1
1
1
1
0
2
1
1
1
1
1
1
0
1
3
1
1
1
0
0
1
1
1
2
2
0
0
1
1
1
2
1
2
1
1
0
2
2
1
1
1
0
1
5
1
1
1
2
2
1
2
1
2
2
0
2
1
3
0
0
1
2
2
1
0
2
0
1
0
1
2
2
2
1
1
1
1
1
2
1
1
2
0
0
2
2
0
1
1
1
2
1
1
0
0
0
0
1
2
1
1
0
0
0
0
1
0
1
1
0
2
0
0
2
0
1
0
1
1
1
1
0
2
2
1
0
2
1
2
1
0
1
1
1
1
1
0
1
1
2
1
1
1
2
0
0
0
1
1
0
0
1
0
1
0
1
0
1
0
0
1
1
0
0
2
0
1
0
1
0
1
1
1
0
0
1
0
1
0
0
1
1
1
1
1
1
2
2
1
1
0
1
2
0
1
1
2
2
2
1
1
0
1
0
1
1
1
2
2
1
2
1
1
1
3
2
1
0
0
1
1
0
2
1
1
0
1
1
2
2
1
2
2
2
0
0
1
0
1
2
2
2
1
0
1
1
0
0
1
2
2
1
0
2
2
1
1
1
1
1
2
2
1
1
0
2
1
1
2
0
0
0
2
1
1
1
0
1
1
1
2
1
1
0
2
1
2
3
2
0
1
1
0
0
1
0
0
2
2
2
1
1
1
1
1
1
0
1
3
1
1
0
2
0
0
2
1
1
1
3
1
2
0
2
1
1
0
2
2
1
1
0
1
1
1
2
1
1
2
1
1
1
1
2
2
2
0
1
1
1
1
2
1
1
1
1
1
0
1
2
1
1
0
0
1
0
1
1
1
1
1
1
1
0
1
1
2
2
1
1
1
1
2
0
1
0
2
1
1
2
0
1
2
1
1
0
2
1
1
1
0
1
0
1
2
2
2
1
2
2
1
2
0
1
0
1
2
1
1
1
0
1
1
0
0
1
1
1
1
2
2
1
1
1
2
1
1
1
1
0
2
1
1
2
1
0
3
2
2
2
1
3
1
1
0
0
2
2
0
1
1
1
0
0
1
0
1
1
1
2
2
0
1
0
2
0
1
2
0
2
0
1
1
1
1
0
1
1
0
0
1
1
2
0
2
1
2
1
0
1
0
1
1
1
1
1
2
2
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
0
1
0
0
2
1
0
0
1
2
0
1
1
2
2
2
1
1
2
2
2
2
0
1
2
2
1
1
0
2
0
0
1
0
0
2
0
0
1
0
1
1
1
1
1
1
1
2
0
1
1
0
0
0
1
0
1
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
0
1
2
1
0
1
1
1
1
3
2
0
1
0
4
2
1
0
1
1
1
1
0
0
1
0
1
1
2
2
1
0
1
0
1
1
0
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
0
1
2
2
0
1
1
0
0
2
1
1
1
1
1
1
2
2
1
1
2
1
2
1
1
1
0
0
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
0
1
1
0
0
1
1
2
2
2
2
1
0
1
0
2
0
0
2
1
0
2
2
0
2
0
1
0
1
1
1
1
1
1
1
1
1
0
1
2
2
2
1
1
2
1
2
2
0
1
1
2
1
1
2
2
2
1
1
2
1
0
1
1
2
1
0
1
1
0
0
1
1
1
2
0
1
1
1
1
2
2
0
1
0
0
2
0
1
2
2
1
2
1
1
1
1
2
0
1
2
0
1
1
2
1
1
0
0
1
2
2
2
1
0
1
1
1
1
1
0
1
2
0
1
0
0
2
1
1
1
1
1
1
1
0
1
0
1
2
1
0
1
0
1
1
1
2
0
0
0
2
0
0
2
2
0
2
1
2
2
1
1
1
2
1
3
2
0
3
1
1
2
2
1
2
2
1
2
1
1
1
2
1
2
1
2
2
1
0
0
1
1
2
1
2
1
0
2
1
0
2
0
1
1
0
1
1
1
1
1
1
5
1
2
2
1
2
0
0
1
1
2
1
1
1
1
1
2
2
1
1
0
1
0
1
1
0
1
0
0
1
0
1
0
1
1
1
2
1
1
2
1
1
1
2
0
1
0
1
2
1
1
1
2
1
2
1
2
1
1
1
0
1
1
1
2
1
2
1
0
0
1
0
2
0
2
0
0
1
2
1
2
2
1
1
2
1
1
2
1
3
2
1
1
0
2
2
1
1
2
2
2
1
0
1
2
1
2
1
1
0
0
1
1
1
2
1
2
1
1
1
0
2
2
1
0
1
1
2
1
1
0
0
1
1
0
0
1
0
0
1
1
1
2
2
1
2
0
1
1
1
0
0
0
2
1
2
2
1
0
2
2
1
0
1
1
0
2
2
2
2
1
1
1
0
1
2
0
1
2
1
2
1
1
1
1
0
0
1
1
2
1
1
1
0
0
1
1
1
1
1
1
1
1
0
1
0
2
1
1
1
1
2
1
2
1
0
1
1
0
2
0
1
0
1
1
1
0
1
0
1
0
1
1
1
2
0
1
0
0
2
0
0
1
0
1
0
1
1
0
1
1
0
2
2
1
1
1
1
0
2
0
0
1
1
1
2
2
1
0
0
0
1
1
1
1
1
1
0
1
1
1
0
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
0
2
0
1
0
1
1
2
0
0
1
0
1
0
2
1
0
2
1
2
2
1
0
2
1
0
1
1
2
1
1
1
0
2
1
1
1
0
3
2
1
1
1
1
1
2
1
1
2
2
1
1
2
1
1
2
0
1
1
1
0
2
1
0
1
2
1
1
1
1
0
2
1
1
1
0
1
1
2
2
1
2
0
2
1
1
0
0
1
1
1
1
1
2
1
1
1
2
1
1
1
2
1
1
1
2
2
1
0
0
2
2
1
2
1
0
0
1
2
1
2
0
1
1
0
0
4
2
0
0
2
1
1
0
2
4
0
2
2
0
1
0
2
1
0
2
2
1
1
1
2
1
0
2
0
2
0
1
0
0
1
0
1
2
1
1
1
1
2
1
2
2
1
2
1
2
1
0
1
1
1
0
1
1
2
2
3
1
0
1
0
1
1
2
1
2
2
2
0
2
1
1
2
1
1
1
2
1
2
0
1
1
1
0
1
2
1
1
1
2
2
1
1
1
2
1
1
2
0
1
1
1
2
0
0
0
1
2
2
1
1
0
0
0
1
1
1
0
0
1
1
0
1
1
0
0
1
1
0
1
1
1
1
1
1
3
1
1
1
0
2
1
1
1
1
0
2
0
1
1
2
1
1
1
1
2
1
1
1
1
0
2
3
1
1
1
1
2
1
0
1
2
2
2
0
0
0
2
0
3
2
1
0
0
2
2
0
1
1
2
0
0
1
1
1
2
1
0
1
1
1
0
1
1
1
1
1
0
1
0
0
1
1
1
1
2
1
1
2
0
0
1
0
1
0
1
0
0
1
1
1
1
1
2
1
1
1
1
1
1
0
1
1
1
1
2
1
2
1
2
0
2
2
2
1
2
1
2
2
1
2
1
0
1
1
1
2
4
0
1
1
2
2
2
0
1
1
1
1
0
0
1
0
2
0
1
0
1
1
2
1
1
2
1
1
0
0
1
0
1
2
2
1
1
1
0
2
1
1
0
1
1
1
1
0
1
2
2
0
1
1
1
0
2
1
1
0
1
2
1
1
1
1
2
1
1
0
1
2
0
0
2
1
0
0
1
1
2
1
2
1
1
2
1
1
0
2
0
2
1
2
1
0
1
1
1
2
1
2
1
2
1
2
1
0
1
1
0
1
0
1
1
0
2
2
1
0
1
0
0
1
1
1
1
1
1
0
1
0
2
1
1
2
0
1
2
0
2
2
1
0
0
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
0
1
2
1
0
1
1
1
0
0
1
2
0
2
2
2
1
2
1
0
0
1
1
0
0
1
1
0
1
0
1
1
2
0
2
2
1
1
1
0
1
1
1
1
0
2
1
1
1
0
0
1
0
1
0
1
0
0
1
1
1
2
1
1
1
2
1
1
1
1
0
0
2
2
1
1
0
1
0
1
3
2
0
0
1
2
1
1
2
0
1
1
0
0
1
0
1
2
1
0
1
1
0
1
1
1
1
1
0
1
2
0
2
0
0
1
3
0
0
1
0
1
3
1
1
1
2
1
0
1
1
1
0
1
1
1
0
2
1
2
0
1
1
2
0
1
0
1
0
2
1
1
1
2
0
0
1
0
2
1
0
1
0
1
0
1
1
0
0
2
0
0
1
2
1
1
1
0
1
0
1
0
2
1
2
2
1
1
1
1
2
1
2
2
1
1
2
2
1
1
3
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
2
2
0
0
0
2
0
1
1
1
0
2
1
0
0
1
1
1
1
1
1
1
2
2
1
2
1
1
0
1
2
0
1
0
1
0
1
1
1
1
1
1
1
2
1
1
2
1
2
0
1
0
2
2
2
1
2
2
1
2
1
1
1
1
1
0
1
1
1
2
1
1
0
2
1
2
0
2
0
1
1
1
1
1
1
0
2
1
0
1
1
1
0
3
1
0
1
1
1
2
0
2
1
3
0
1
0
2
0
1
2
2
1
1
1
2
1
2
0
1
2
1
0
1
2
2
0
0
0
1
2
0
2
0
0
1
2
1
1
1
1
1
0
2
1
1
2
3
1
1
0
2
1
0
1
2
1
0
1
1
2
1
1
1
1
2
1
1
2
1
1
2
1
0
2
0
2
1
0
1
0
1
1
2
1
2
2
2
2
1
1
2
1
1
0
1
1
1
2
1
0
0
1
1
0
1
1
1
1
3
2
2
1
1
0
0
2
1
0
2
1
1
1
1
2
2
0
2
1
1
2
1
2
1
2
1
1
1
1
2
1
2
2
0
0
0
1
1
2
0
2
1
1
2
1
2
0
0
1
2
0
0
1
1
1
1
2
1
0
0
1
1
1
3
0
1
1
2
1
3
2
0
1
1
1
0
1
1
2
0
1
0
1
0
1
1
1
1
0
2
2
1
1
1
1
0
1
2
2
1
1
1
1
1
1
1
1
1
1
1
2
2
0
0
1
1
0
1
0
1
1
1
2
2
0
1
2
2
1
1
1
1
1
1
0
1
1
1
0
1
1
1
2
1
1
1
1
1
1
3
0
0
2
2
1
1
2
0
1
1
0
0
1
1
2
1
0
1
0
0
0
1
1
2
2
1
0
1
1
1
0
1
1
0
1
2
1
2
1
1
1
1
0
0
0
0
2
1
2
1
1
1
0
1
2
2
1
1
1
0
1
0
2
0
2
1
1
1
0
0
1
1
0
1
2
0
0
1
1
1
0
1
1
2
1
1
1
2
0
2
1
1
1
1
2
1
0
1
2
2
0
0
1
1
2
0
2
0
0
1
0
0
1
0
1
1
1
1
1
1
2
1
1
1
1
0
1
2
0
0
1
1
1
0
1
1
1
0
1
0
2
0
1
1
3
1
2
1
0
2
1
1
1
2
1
0
1
1
1
1
2
0
1
1
1
0
2
1
1
2
0
2
0
1
3
2
2
0
1
2
2
0
1
0
2
1
1
2
1
2
1
2
1
1
1
1
1
1
0
2
0
1
1
1
0
1
1
1
1
2
2
1
1
0
1
2
2
2
0
2
2
2
1
2
1
1
1
2
2
0
1
1
1
0
1
0
1
0
1
1
0
1
1
1
0
0
1
0
0
1
1
1
1
1
2
1
0
3
2
0
2
1
2
1
0
0
1
1
2
2
0
1
1
3
2
0
2
1
2
0
2
0
0
1
1
1
0
1
0
1
1
2
2
0
1
1
1
1
2
2
0
0
2
1
1
0
1
1
1
1
1
0
1
2
2
1
2
1
0
1
1
1
1
2
2
1
1
1
2
2
1
1
2
1
3
1
0
0
1
2
1
2
1
1
1
1
1
0
2
2
0
1
0
2
1
1
1
1
1
2
1
1
0
1
1
0
2
1
0
1
2
1
1
1
1
2
2
3
0
2
1
2
0
0
1
0
1
1
2
1
2
1
1
1
0
1
1
0
1
2
1
2
2
0
2
1
2
1
1
1
2
0
1
1
2
2
2
1
1
1
1
3
1
1
0
0
1
1
2
0
2
1
2
1
1
1
1
1
1
1
1
1
0
0
1
2
1
2
0
2
2
1
1
1
0
0
2
2
1
1
1
1
1
0
2
2
1
2
1
2
1
2
1
2
1
0
1
1
0
1
2
2
0
1
0
2
1
1
0
2
0
0
0
1
0
1
1
0
2
1
1
0
2
0
1
0
1
0
0
0
1
1
1
1
1
1
1
1
2
1
0
1
1
0
1
2
1
2
1
3
2
1
1
1
2
1
0
0
1
0
0
2
0
1
2
1
1
2
0
0
1
1
2
1
1
2
1
0
2
2
0
1
2
1
0
0
1
2
2
2
0
2
2
2
2
1
0
1
1
0
0
2
0
1
1
1
1
1
0
2
2
1
1
2
0
1
0
1
2
1
2
1
2
0
1
0
3
1
0
1
1
1
1
2
1
2
1
1
1
1
1
1
1
0
1
1
0
0
1
1
1
1
1
2
0
1
2
1
1
0
1
1
1
0
1
2
2
1
2
2
1
0
1
1
1
2
1
0
1
0
1
0
1
0
0
2
1
1
1
2
2
1
2
2
1
1
2
0
1
0
0
0
1
1
1
1
2
2
1
0
0
0
2
1
1
1
1
1
1
1
1
2
1
2
5
0
1
1
0
1
1
1
0
1
0
1
1
0
2
1
1
1
1
0
1
2
1
1
1
1
0
2
0
2
1
1
2
1
1
1
0
0
2
1
1
2
2
1
1
1
0
1
1
1
1
1
0
1
2
2
0
2
1
1
0
2
2
1
0
1
0
1
1
1
1
2
2
0
0
0
1
1
1
1
1
1
0
0
1
1
0
1
2
0
0
1
1
1
1
0
1
1
1
2
1
1
1
1
0
2
0
0
1
1
1
0
2
2
2
2
1
0
1
1
1
1
0
1
1
1
1
2
1
1
2
1
1
2
1
2
1
1
1
2
1
1
2
2
0
1
2
1
0
2
1
1
1
1
1
1
1
1
0
1
0
1
1
1
1
1
1
2
0
0
2
2
1
1
1
1
1
2
1
0
0
1
0
1
1
1
1
1
2
2
2
2
1
0
1
1
1
1
1
1
1
2
0
0
1
2
0
2
0
0
0
1
1
0
0
2
1
1
0
1
1
1
0
1
0
2
2
1
1
1
1
1
1
1
1
1
1
0
2
1
1
1
1
1
0
2
1
1
0
2
2
1
3
2
1
1
1
0
3
0
0
2
1
1
1
0
2
1
0
1
1
1
0
1
0
1
1
1
1
1
1
1
1
1
1
1
1
0
0
0
0
1
1
1
0
0
1
1
1
1
1
0
2
1
1
1
1
1
2
1
2
0
1
1
1
1
1
1
2
2
1
0
2
1
2
1
1
1
2
2
2
2
1
1
2
1
1
0
1
1
1
0
0
2
1
0
0
2
1
1
1
1
2
1
0
1
1
2
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
0
1
0
0
1
1
1
0
2
0
1
0
0
1
0
1
0
0
0
1
1
0
1
1
1
0
2
2
2
5
0
2
1
1
1
1
5
1
1
2
1
1
1
1
2
1
1
0
4
2
1
1
1
1
1
2
1
1
1
0
0
1
1
1
1
1
2
0
1
2
2
2
1
0
1
1
2
1
2
0
1
0
0
1
1
1
1
2
1
1
2
0
2
1
1
2
1
1
0
2
0
0
1
1
1
1
0
2
1
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
0
1
2
1
2
1
1
1
1
2
0
1
2
2
2
2
1
1
2
1
2
0
1
1
1
0
1
1
1
0
1
2
1
0
2
1
0
0
1
0
2
0
1
1
1
2
1
2
0
1
2
1
2
1
1
2
1
0
2
1
1
0
1
1
1
2
2
1
1
1
0
1
1
0
1
1
1
1
1
0
1
1
1
1
2
1
0
0
2
2
0
1
1
1
1
1
0
1
1
0
0
2
1
0
1
2
1
3
2
1
1
2
1
0
0
1
0
1
1
1
1
0
2
2
1
0
0
0
1
1
1
1
1
2
1
1
1
1
0
0
1
1
2
1
2
1
1
0
1
1
2
0
1
1
1
1
1
0
2
1
1
2
1
1
1
1
1
2
0
1
2
0
0
1
0
0
1
1
0
1
1
2
1
1
1
1
0
0
1
1
0
1
1
0
2
2
1
0
2
2
0
1
0
0
1
3
0
0
1
1
1
1
1
2
1
1
0
1
2
1
0
1
1
1
1
1
1
0
0
2
0
1
1
2
2
1
1
1
2
1
1
1
1
0
0
1
2
1
1
1
2
1
2
2
2
0
1
1
1
1
0
1
1
1
1
0
1
0
0
1
1
2
1
1
0
0
0
0
1
1
2
1
1
1
1
1
2
0
1
0
1
1
1
2
1
1
1
1
2
1
0
1
1
1
4
2
1
1
0
0
2
2
1
1
1
2
1
1
2
1
1
2
1
1
1
0
1
1
0
1
0
2
1
1
2
1
0
1
0
1
1
1
0
2
2
1
2
2
0
1
1
1
1
1
1
0
0
1
0
0
0
2
1
1
1
1
1
2
1
1
1
0
1
0
1
0
1
1
0
1
2
0
1
2
0
1
1
1
1
2
2
1
2
2
1
1
2
2
1
0
2
1
1
0
0
2
0
1
0
1
2
0
0
1
1
1
2
1
0
0
0
1
1
0
0
1
2
1
1
2
0
1
1
1
1
1
1
0
1
1
1
1
1
1
1
0
1
0
1
2
1
1
1
1
2
2
0
0
2
0
0
1
2
1
0
1
1
1
1
1
2
2
0
0
1
2
1
2
2
0
1
0
1
2
1
1
1
2
0
2
0
0
1
2
1
2
1
0
1
1
1
1
2
0
1
2
1
0
1
1
0
2
1
1
1
1
0
1
2
0
1
1
1
2
2
2
1
1
2
0
1
1
1
2
1
1
0
1
1
2
0
1
0
2
1
1
1
2
1
1
1
1
1
0
1
0
2
0
3
0
0
1
1
1
0
0
0
1
2
1
1
2
0
2
0
1
0
2
0
1
1
2
1
1
2
1
0
1
1
1
2
0
0
0
4
2
0
2
2
0
0
1
1
1
1
1
1
4
1
2
1
1
1
2
1
1
2
1
0
0
1
1
2
1
1
1
1
1
2
1
1
1
1
0
2
1
1
1
2
1
2
1
0
1
1
0
2
1
2
2
1
1
0
1
2
1
2
2
2
1
2
0
1
1
1
1
0
0
1
1
1
1
1
1
2
0
1
2
0
1
1
0
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
0
2
1
1
1
3
1
1
1
1
2
2
1
0
1
2
1
2
2
2
2
1
0
1
1
1
1
2
1
1
1
1
0
1
2
0
0
1
2
1
3
0
0
1
1
0
0
1
1
1
2
2
2
0
2
2
1
0
0
1
1
1
2
0
1
1
0
2
1
0
1
0
1
0
2
1
2
1
1
0
1
1
1
1
1
1
1
0
2
0
0
0
1
1
1
0
0
2
2
1
1
1
2
1
2
1
1
1
1
0
1
3
2
2
1
2
1
1
2
2
0
1
1
2
1
1
1
0
1
0
1
2
1
1
2
1
0
1
2
2
1
2
2
2
0
1
1
1
2
1
1
2
1
0
2
1
0
1
1
2
2
2
0
1
1
1
1
2
1
1
0
1
1
0
1
0
1
1
1
0
1
0
2
1
1
2
1
0
0
2
1
0
0
1
1
1
2
0
1
1
0
1
1
1
1
1
1
1
1
1
0
0
1
2
1
2
1
0
1
2
1
1
1
1
1
1
0
0
1
0
0
0
1
2
1
2
2
1
1
1
2
1
1
1
3
1
1
1
0
1
1
2
2
0
2
1
2
0
0
2
1
1
1
1
1
1
0
2
2
2
0
1
1
2
1
2
1
1
0
1
1
0
3
1
1
1
2
0
1
2
1
1
0
0
2
1
1
1
2
0
1
0
1
1
2
1
1
1
0
0
0
1
2
1
1
1
1
0
1
1
1
1
2
1
1
0
1
1
1
0
0
1
2
0
0
1
0
1
1
2
1
1
1
0
0
1
1
0
0
2
2
1
1
2
0
1
1
1
0
1
0
1
1
2
1
1
1
0
1
0
1
0
0
0
1
2
2
0
0
2
1
1
2
1
0
1
0
1
1
2
2
1
1
1
1
0
1
0
1
1
1
2
1
1
1
1
0
1
1
0
1
1
0
2
1
1
1
2
2
1
1
1
1
1
2
2
1
0
1
1
1
2
1
2
1
1
2
2
2
1
2
1
0
0
2
2
0
1
1
1
1
1
2
2
0
1
0
1
0
0
1
0
0
2
2
1
0
0
0
1
1
1
1
1
1
1
1
1
1
0
1
0
1
1
1
1
1
1
1
2
2
2
0
1
1
0
1
1
0
0
1
2
2
1
2
0
1
0
2
0
1
1
0
1
2
2
2
1
1
3
0
3
1
1
1
1
0
0
1
3
0
2
1
1
1
0
1
2
1
2
2
1
0
1
1
0
0
1
1
2
1
1
1
3
1
1
1
1
1
1
1
1
1
0
1
2
1
2
1
0
1
0
1
0
0
2
0
1
0
2
1
1
0
1
2
1
2
1
2
1
1
1
1
1
1
1
0
1
2
2
2
1
3
2
0
1
1
1
0
1
2
1
0
0
0
1
1
2
0
0
2
1
1
1
1
1
1
2
1
1
1
0
1
0
0
1
2
1
2
1
1
2
1
1
1
1
1
0
1
2
0
1
1
0
1
1
0
2
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
0
1
1
2
2
0
1
2
1
1
1
1
1
3
1
0
1
1
2
1
0
2
2
1
1
1
0
0
0
0
0
1
0
1
1
0
0
2
1
0
2
2
1
1
1
1
0
1
2
0
1
2
1
1
1
0
1
1
1
2
0
1
1
1
1
2
1
2
2
0
2
1
0
0
1
1
1
0
1
0
1
0
1
2
1
1
1
0
1
2
1
1
1
2
0
0
1
1
1
1
1
0
0
1
0
1
2
4
0
1
1
1
1
2
1
1
2
0
1
2
1
0
0
2
0
0
3
2
1
0
1
1
0
1
0
1
1
1
0
1
2
0
1
1
1
0
1
1
0
1
0
0
2
0
1
0
1
2
1
2
1
2
0
1
0
1
0
0
1
1
2
1
1
0
2
0
0
0
1
0
1
1
1
1
0
0
2
2
1
2
1
0
1
0
1
0
0
1
2
0
0
1
0
0
1
0
1
1
1
1
1
2
0
2
0
1
1
0
1
2
1
0
1
0
1
0
1
1
0
2
1
1
1
0
1
1
1
0
2
0
1
1
0
1
1
0
2
2
1
2
1
0
1
1
0
2
0
1
1
1
1
1
0
1
0
2
1
0
1
0
2
2
1
0
0
2
2
0
0
1
2
1
1
0
2
0
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
0
1
2
1
0
2
1
1
1
3
1
1
1
0
1
1
4
1
0
2
2
2
1
1
1
1
1
0
1
1
1
1
2
1
2
0
2
0
1
1
2
1
2
2
1
1
2
1
1
0
1
2
0
0
0
0
0
1
1
1
2
2
0
1
0
1
2
1
0
1
1
1
1
2
1
0
2
0
1
2
0
1
1
1
1
2
1
1
1
0
2
1
1
1
0
1
1
2
1
1
1
1
2
0
0
2
1
1
1
1
1
3
1
1
1
1
1
1
1
0
2
2
1
0
3
2
0
1
1
2
0
1
0
1
1
1
0
2
1
1
1
1
2
2
1
1
0
0
2
1
2
2
2
1
2
1
2
1
1
1
2
1
1
0
1
2
2
0
1
1
2
2
2
1
3
0
0
1
1
2
0
0
0
1
1
0
1
1
1
0
2
1
1
1
2
0
2
0
2
2
1
0
1
1
0
0
0
1
1
1
0
2
0
0
1
1
2
2
1
1
1
1
1
1
1
1
0
1
0
1
0
2
2
1
1
1
0
2
2
0
2
1
1
1
1
1
1
0
1
1
2
1
2
2
2
2
1
0
2
1
0
1
1
1
1
1
1
1
0
0
2
0
1
1
1
0
2
2
1
1
1
1
1
2
1
1
1
2
0
0
1
0
1
2
0
1
2
2
1
0
0
0
1
0
1
1
1
0
1
1
1
2
1
1
1
1
2
0
1
0
1
1
0
2
2
1
0
1
2
0
1
1
1
1
1
0
1
1
1
2
1
1
1
1
1
2
0
2
1
1
0
2
2
0
1
0
0
2
1
1
1
0
1
1
0
2
1
1
2
1
1
1
1
1
1
0
2
2
1
2
2
1
2
0
2
2
1
1
0
1
1
1
1
0
2
1
1
2
1
1
2
0
1
1
2
1
1
1
1
2
2
2
1
1
1
0
1
1
2
1
0
0
0
1
1
1
1
2
1
2
1
1
1
1
1
1
1
0
1
1
1
2
1
2
2
1
0
0
2
0
1
1
1
1
0
2
1
1
1
1
1
0
0
1
2
2
0
1
1
2
2
2
2
2
2
1
2
0
0
0
1
1
0
2
1
1
1
1
1
3
1
1
1
1
2
1
1
1
1
0
0
1
1
0
1
0
1
1
1
0
0
2
2
1
0
1
2
0
0
0
0
0
1
2
1
1
2
2
0
2
2
1
1
1
0
1
1
1
2
2
1
1
1
1
0
0
0
2
1
1
1
2
1
0
0
1
1
0
1
1
1
0
2
2
1
3
0
1
0
0
2
2
1
1
1
1
1
0
2
2
0
2
1
0
0
1
2
2
1
0
1
1
2
1
2
1
2
1
2
1
0
0
1
2
2
1
2
2
1
2
0
2
2
3
1
0
1
1
1
2
1
0
1
0
2
0
2
1
1
1
1
1
1
1
0
1
1
0
1
1
1
1
1
0
1
0
0
1
1
1
1
1
1
0
1
1
0
1
2
1
0
1
1
1
2
1
2
0
0
1
1
1
1
2
0
0
1
1
0
1
1
0
2
0
1
1
0
0
0
1
0
2
1
1
0
1
2
2
0
1
1
4
1
0
2
1
1
1
1
2
2
1
1
1
2
2
2
2
0
2
1
1
1
2
1
2
1
1
0
1
1
1
1
1
0
0
1
1
1
2
2
1
2
1
0
2
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
0
0
2
0
1
1
1
1
0
1
0
1
2
2
2
1
1
2
2
1
2
0
1
1
1
1
2
1
1
2
0
1
1
0
1
1
1
1
1
1
0
1
0
1
1
1
1
1
1
0
1
1
0
2
1
1
1
0
1
2
1
1
1
2
1
2
0
1
1
2
0
1
2
0
0
3
1
1
1
0
1
1
0
1
1
2
1
1
0
1
0
2
0
1
1
0
0
1
1
0
2
1
0
0
1
2
1
1
1
0
0
0
2
1
2
1
1
2
1
1
1
1
0
1
0
1
2
1
1
2
0
0
1
1
1
1
1
0
1
0
2
1
1
0
0
2
1
1
1
1
1
2
2
1
1
1
3
2
1
2
0
0
1
1
2
2
1
1
1
0
0
0
1
1
1
2
1
1
1
1
1
0
1
1
1
1
0
1
3
1
1
1
2
0
2
1
0
1
1
2
1
1
1
0
1
1
0
1
1
1
1
2
2
1
1
4
2
1
0
0
1
0
2
1
0
0
1
0
1
1
1
1
1
0
2
0
1
2
0
1
3
1
1
2
1
1
1
1
0
1
2
4
0
0
0
1
1
2
2
1
2
1
1
1
1
2
1
1
1
1
0
2
1
1
1
2
1
1
1
0
2
2
2
2
1
1
0
1
1
2
1
1
0
1
1
1
1
1
1
1
2
2
1
1
1
0
0
1
1
0
1
0
2
1
1
1
1
0
1
0
0
1
1
0
1
1
0
1
0
2
1
1
1
1
1
0
2
0
2
0
0
2
0
0
0
1
2
0
0
2
1
2
3
0
1
0
0
1
1
1
0
1
1
1
1
1
1
0
2
1
2
1
1
1
2
1
1
1
0
2
2
0
0
2
2
1
0
2
0
1
1
2
1
1
0
1
1
1
1
2
0
0
0
1
2
2
0
1
1
2
1
1
1
1
1
2
1
2
1
0
0
1
1
1
2
0
1
2
1
0
1
0
0
1
0
1
0
0
1
0
2
1
1
0
1
1
1
1
1
1
3
0
1
1
2
1
1
0
1
2
1
0
2
1
2
1
0
1
1
1
0
1
1
1
0
0
1
1
1
1
2
0
1
2
1
1
0
0
0
0
1
0
0
1
0
2
1
0
1
1
1
0
2
1
1
2
1
0
1
1
2
1
0
1
1
2
1
1
1
1
1
2
2
1
1
0
1
1
0
1
1
1
1
2
1
1
1
1
1
0
2
2
1
1
0
0
0
4
1
1
2
1
1
1
1
1
2
2
1
1
1
0
0
1
1
1
2
2
2
1
1
1
1
1
1
1
0
1
1
2
0
1
1
0
1
1
0
2
1
1
1
1
1
1
1
0
1
1
2
2
1
1
1
1
2
1
2
3
2
1
1
2
0
1
2
0
2
0
0
0
0
3
2
1
1
1
1
2
1
1
2
2
1
1
2
1
2
2
2
2
1
2
1
1
1
1
1
1
1
0
1
1
2
0
0
1
0
1
1
0
3
1
0
1
1
1
1
0
2
1
1
2
2
1
0
2
1
1
0
2
0
1
0
2
1
1
1
0
1
1
1
2
1
1
1
1
0
1
0
1
0
0
1
0
1
1
2
1
0
2
2
1
2
1
1
1
2
1
0
1
1
1
1
1
2
1
0
2
1
0
1
1
1
2
0
0
1
1
2
2
2
0
1
1
1
1
1
1
1
0
1
1
1
1
0
2
0
1
2
0
1
2
3
0
0
1
2
0
1
0
1
1
1
1
2
1
2
0
1
1
1
2
1
2
1
0
1
1
0
0
1
1
1
1
0
1
2
0
0
1
2
2
2
1
1
0
0
1
2
1
2
1
0
1
1
1
1
0
1
2
0
1
1
0
1
0
1
0
1
1
2
1
2
2
1
1
1
1
1
1
1
1
2
2
1
6
0
1
1
1
0
1
0
0
1
1
2
1
1
0
1
2
3
1
1
0
1
1
2
0
2
1
0
1
1
1
1
2
0
2
1
1
1
0
0
1
1
1
0
2
1
0
0
0
1
1
0
1
1
1
1
2
2
1
1
1
2
2
6
1
2
2
1
1
0
1
1
2
2
1
2
0
1
2
0
0
2
1
1
2
1
0
2
0
1
1
2
0
0
1
2
0
0
1
0
0
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
3
1
2
1
1
2
1
4
0
1
1
0
1
0
1
2
1
1
0
0
1
1
1
1
1
1
2
3
1
1
1
1
2
1
1
0
2
0
1
2
1
0
0
1
0
0
1
1
2
1
1
1
2
1
2
2
1
1
1
2
0
1
2
2
1
2
1
1
1
1
0
1
2
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
0
1
1
1
1
2
1
0
1
1
2
1
1
0
1
1
0
2
2
1
0
1
1
1
2
0
1
2
2
0
1
1
2
1
0
1
1
1
2
0
0
0
1
1
1
0
0
1
0
0
0
2
1
0
1
1
1
0
0
0
1
1
1
1
2
1
2
2
1
1
0
1
2
1
1
2
2
0
0
1
1
1
0
0
2
1
0
1
1
1
1
1
1
1
0
0
0
0
1
1
1
0
2
2
1
1
2
1
1
3
2
0
1
1
1
0
2
2
1
1
0
2
1
2
1
1
1
1
2
1
2
0
0
0
0
2
0
0
1
0
0
1
1
0
1
1
1
0
2
1
1
1
1
2
0
0
0
1
2
1
1
2
3
0
0
2
2
2
1
0
0
1
0
2
1
1
1
0
0
1
0
1
2
1
1
2
1
1
0
1
1
2
1
1
2
1
1
1
0
2
0
1
1
0
1
1
2
2
1
2
2
1
2
1
0
0
2
0
0
2
2
1
1
1
2
2
2
2
0
3
2
0
0
1
2
1
1
0
1
1
2
2
1
1
1
0
2
0
1
1
0
1
1
1
1
1
2
2
2
0
1
0
1
2
2
0
2
1
1
2
1
2
0
1
1
1
1
1
1
1
1
0
1
1
1
2
1
0
2
1
1
2
2
2
1
1
1
2
1
1
2
1
1
1
2
2
1
1
0
0
1
1
2
1
1
1
1
1
1
0
0
2
0
1
2
1
0
2
2
1
1
1
2
0
2
2
1
0
1
2
1
1
2
1
1
0
1
1
1
2
0
1
2
2
1
2
1
0
2
1
1
1
0
2
1
2
1
1
2
1
1
0
2
2
1
1
2
1
1
0
1
0
1
1
1
1
2
0
0
0
1
1
0
1
1
1
1
0
1
1
1
0
2
0
1
2
2
1
1
1
1
1
1
0
0
0
2
1
1
0
2
2
1
2
2
1
0
0
1
2
0
2
2
1
2
2
1
2
0
1
0
1
1
0
1
0
0
2
2
2
1
1
1
1
1
0
0
2
2
1
0
1
4
1
1
0
0
2
0
0
1
1
0
1
2
1
1
2
0
1
2
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
0
4
2
2
0
0
1
1
0
1
3
1
1
2
1
1
2
1
1
1
0
1
2
0
1
1
1
0
2
1
1
2
2
1
2
1
0
2
2
1
1
2
1
1
2
1
2
1
1
1
1
1
0
2
0
1
0
2
1
1
1
1
0
1
1
1
1
1
0
1
0
2
0
3
0
0
2
1
0
1
2
1
1
0
0
1
0
0
1
2
1
1
2
1
1
2
2
1
2
1
1
0
0
1
1
1
1
1
1
2
0
2
0
1
2
1
1
1
1
2
1
1
1
1
2
1
2
1
2
1
1
1
2
0
1
1
0
1
2
1
1
1
2
2
1
1
1
2
0
2
1
0
1
1
0
1
1
0
1
1
3
1
2
1
0
0
1
1
1
1
2
1
1
1
2
1
2
1
1
0
0
1
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
2
1
1
1
0
0
2
1
1
0
0
2
2
2
1
1
2
2
1
2
0
1
1
1
0
1
1
0
0
2
0
0
2
0
0
1
1
1
1
0
1
2
2
2
0
0
0
3
2
1
0
1
1
0
0
2
1
1
0
1
1
2
2
2
2
1
0
1
1
1
1
2
2
1
1
1
2
1
0
1
2
0
0
1
0
0
2
0
1
0
1
1
2
0
1
0
0
1
2
2
1
1
1
2
0
1
1
1
1
1
2
1
0
1
0
0
1
0
1
2
1
0
0
1
1
2
2
1
2
2
1
1
1
0
0
0
2
1
1
1
2
1
2
1
1
2
0
1
1
1
1
1
2
1
1
1
2
2
0
0
1
0
1
1
1
1
2
2
1
0
1
2
1
1
1
1
0
1
0
0
1
0
1
3
1
1
2
1
1
0
0
0
2
1
0
1
1
0
1
0
1
0
1
0
1
2
2
1
1
1
1
0
1
0
1
2
2
2
1
0
1
1
2
1
1
1
1
0
1
3
1
2
0
1
1
0
2
1
0
1
0
1
2
1
0
0
1
0
1
0
1
1
1
1
2
1
1
3
2
2
1
1
1
2
2
0
0
1
1
0
1
0
1
1
1
0
1
0
1
2
0
1
1
1
1
2
1
0
1
0
2
2
1
1
1
1
1
0
1
1
1
3
1
2
1
0
2
1
2
1
1
2
2
1
2
1
1
1
2
1
0
2
1
1
1
2
2
1
1
2
1
1
1
1
1
1
0
0
2
2
1
2
0
0
1
1
1
1
0
1
0
2
0
1
2
1
1
0
2
1
2
2
1
1
1
1
0
2
0
2
1
1
2
2
0
2
1
1
1
1
1
2
1
0
2
1
1
1
2
1
1
2
2
1
1
0
1
0
1
1
1
0
1
1
0
2
1
1
1
0
0
1
1
0
0
1
2
0
1
1
3
1
1
1
0
2
1
2
0
2
2
0
1
2
1
2
2
1
0
1
0
1
2
1
0
2
1
2
2
2
1
0
2
1
1
0
1
2
1
1
2
1
0
2
2
1
1
1
0
0
1
1
1
1
1
2
0
1
2
1
1
1
1
1
2
1
0
1
0
1
1
1
1
2
1
0
1
0
1
1
0
2
1
0
2
1
1
1
1
1
0
0
1
1
2
2
1
2
2
1
1
0
0
0
1
0
0
1
1
2
2
1
1
0
2
1
1
1
2
0
1
1
0
0
1
2
0
1
2
1
2
0
0
2
2
1
2
1
1
0
1
1
2
1
0
1
2
1
1
0
2
0
1
0
1
1
1
2
1
0
1
2
1
0
0
2
0
1
0
1
1
1
1
2
1
1
1
0
1
2
1
1
2
1
0
0
2
0
2
0
1
2
1
1
2
2
0
0
0
1
2
0
2
1
0
1
1
0
1
2
0
0
1
0
1
0
2
1
1
2
1
0
0
1
0
1
0
1
1
1
2
0
2
1
1
1
0
0
1
1
2
0
0
1
0
1
1
1
1
1
2
1
1
1
0
2
0
2
1
2
2
2
1
1
4
1
0
1
1
1
1
1
1
0
0
1
2
0
1
1
1
1
0
1
0
0
0
2
0
1
1
2
0
1
2
1
1
1
2
3
1
1
1
1
1
1
2
3
0
1
1
1
1
2
2
0
0
2
2
1
2
1
2
1
1
0
2
1
0
0
1
0
2
1
1
1
2
1
0
0
2
0
0
1
0
2
1
2
1
2
1
1
1
1
1
0
1
2
2
1
0
1
0
1
1
0
1
2
2
1
0
1
1
1
2
0
0
1
2
1
0
1
1
1
0
3
1
1
0
0
0
1
1
1
1
0
2
0
0
1
1
2
0
0
2
0
0
2
1
0
1
2
1
1
2
0
1
1
2
0
0
0
1
1
0
2
1
2
1
1
1
2
0
1
1
1
1
2
2
1
1
0
1
2
2
1
1
0
0
0
0
1
1
0
1
0
2
1
2
1
1
2
2
1
1
2
1
1
1
1
0
0
1
1
1
2
1
1
0
1
0
2
0
2
2
0
0
1
1
2
0
2
1
0
2
2
1
1
1
1
1
0
2
2
2
1
1
0
1
2
1
1
2
2
1
1
2
1
1
1
1
1
0
0
1
1
0
0
0
1
2
1
1
0
0
1
2
1
0
1
1
0
0
2
1
0
1
1
1
1
2
1
1
2
1
1
1
1
1
1
0
1
1
1
1
1
1
0
2
0
1
0
2
2
0
2
1
0
1
1
1
0
0
1
1
2
2
1
1
2
2
0
0
1
2
2
1
1
1
1
1
1
1
1
2
0
1
1
0
1
2
1
1
2
2
2
1
0
2
0
1
1
1
1
0
1
0
1
1
2
2
1
2
1
1
0
1
0
1
0
1
0
0
1
1
1
1
1
2
1
1
1
2
0
0
1
0
0
2
1
2
1
0
1
0
1
1
1
1
0
1
2
1
1
2
0
1
0
2
0
1
6
1
1
2
1
1
0
0
2
1
0
0
0
0
1
0
2
1
1
0
1
0
0
2
0
1
1
1
1
1
1
3
1
1
1
1
0
1
1
1
1
1
2
1
1
2
1
2
1
1
1
2
0
1
1
2
1
2
2
1
0
0
1
2
2
2
0
0
2
2
0
0
1
0
0
1
1
1
2
1
1
2
2
1
2
1
1
1
2
0
2
0
1
1
1
1
1
2
1
3
0
2
1
1
1
1
0
1
1
2
1
1
1
1
2
1
1
3
1
2
1
0
1
1
2
1
1
0
0
1
0
1
1
3
1
0
1
1
1
1
0
2
2
2
1
2
0
2
2
1
0
1
1
1
2
2
1
1
2
1
2
0
1
1
0
0
0
0
0
3
1
2
0
1
2
1
1
0
1
1
1
1
4
3
1
0
2
1
1
1
1
1
1
0
0
0
1
2
1
2
0
2
2
2
1
0
2
1
2
1
0
1
1
0
1
2
1
0
1
1
1
2
1
1
2
2
0
0
0
0
1
2
1
1
2
0
1
1
1
1
1
2
2
1
1
0
3
0
0
2
1
2
1
0
1
0
1
1
0
2
0
2
3
1
0
3
1
0
1
1
1
0
1
0
2
0
1
0
1
1
1
2
0
1
1
1
1
1
2
1
3
1
0
1
2
0
1
2
2
1
1
1
0
2
2
2
1
2
2
0
2
1
1
1
1
0
3
1
1
1
2
1
1
1
1
1
2
2
1
0
2
2
1
1
1
0
0
1
1
0
1
2
1
2
1
1
1
0
0
0
1
2
1
0
1
2
1
1
0
2
0
1
1
2
2
2
1
1
0
2
1
1
0
1
2
2
0
0
0
2
2
1
2
1
1
1
2
1
2
0
1
1
1
1
1
1
0
1
1
1
1
1
0
1
2
0
0
2
1
2
1
1
1
1
1
0
1
1
1
1
0
1
2
0
2
2
1
2
0
0
1
2
0
1
0
0
0
1
0
1
1
2
0
2
1
1
0
1
0
1
0
1
2
2
0
0
0
1
2
1
2
1
1
1
0
2
1
0
0
1
1
1
2
1
1
1
1
1
1
2
0
1
0
1
1
1
2
1
2
2
1
1
0
1
1
2
2
1
1
1
1
0
2
1
1
1
1
1
2
2
1
0
1
1
1
4
1
2
1
0
0
1
3
1
1
2
1
1
2
1
1
1
2
0
1
1
1
2
1
3
1
1
1
1
1
1
1
1
0
1
0
1
2
0
1
1
1
1
1
0
0
0
1
0
1
2
1
2
1
1
0
1
2
2
1
1
0
0
1
2
1
1
1
1
1
1
1
1
2
1
2
1
0
1
1
1
1
1
0
1
1
1
1
0
1
2
1
1
1
0
2
0
0
1
2
0
1
3
0
1
2
2
1
1
0
1
1
3
1
1
1
1
2
0
1
1
1
1
1
1
0
0
0
0
0
2
1
1
1
1
1
1
1
0
1
1
2
1
1
0
1
1
2
1
0
2
2
1
0
1
1
0
1
1
1
1
1
1
1
1
0
0
0
1
1
1
0
1
1
1
1
2
0
2
1
1
1
1
1
1
2
0
0
1
1
1
0
2
2
1
1
2
1
1
0
1
1
1
1
0
2
1
2
2
1
1
2
0
1
2
1
2
2
1
1
2
1
1
2
2
3
2
0
0
2
0
1
0
2
1
1
0
1
2
2
0
0
1
2
2
1
0
1
2
1
1
1
1
2
1
0
1
2
0
1
1
1
1
1
1
1
0
0
0
2
1
2
1
1
1
1
1
1
1
2
1
1
0
3
0
1
2
1
1
1
2
1
2
1
1
0
2
1
2
1
0
1
1
0
2
2
1
1
0
0
3
1
1
1
1
0
1
1
2
1
1
1
0
2
2
1
1
1
2
0
0
0
2
0
1
2
1
1
2
0
1
1
0
0
0
2
1
1
1
0
1
1
1
1
1
0
1
0
0
1
1
1
1
1
0
1
1
0
1
0
0
2
1
0
1
2
1
0
2
2
1
1
0
2
2
1
1
1
0
2
1
1
1
2
1
1
1
1
1
1
2
1
0
1
2
1
1
1
1
0
1
2
1
1
0
1
0
1
0
2
1
0
1
1
1
1
2
1
0
2
2
1
1
1
2
1
0
2
2
1
0
2
1
1
1
0
1
0
1
0
1
2
1
1
2
1
1
1
0
1
1
1
0
0
0
1
1
1
1
0
1
1
0
1
0
1
1
0
2
1
2
1
2
1
1
0
1
1
2
2
1
1
1
1
0
1
1
1
1
2
0
0
1
2
1
1
1
1
0
2
0
1
1
2
1
1
1
0
0
1
1
2
1
2
2
0
1
0
1
0
1
0
2
1
2
2
2
0
2
1
2
1
1
1
0
0
1
1
2
0
2
1
2
1
1
2
1
0
1
1
1
1
1
2
1
1
2
1
1
1
1
1
0
2
1
1
1
1
0
1
0
1
0
2
0
1
2
1
1
1
1
1
1
1
1
2
5
0
0
0
0
0
1
1
1
0
2
1
1
1
0
1
1
1
1
2
0
1
0
0
1
1
1
0
2
1
0
1
1
0
1
1
0
2
1
0
1
1
2
2
1
1
0
1
0
2
1
1
0
0
2
0
2
1
1
2
2
2
0
1
1
2
1
0
2
2
1
2
1
0
0
1
0
2
1
1
1
1
1
1
0
0
0
2
1
0
1
2
1
1
1
0
2
1
0
0
2
1
0
1
1
2
1
1
2
1
2
1
1
1
2
0
1
1
1
2
1
0
1
1
0
1
2
2
1
0
1
1
2
1
1
2
1
1
1
0
0
0
1
0
1
2
2
1
0
2
0
2
1
1
2
1
1
1
0
1
0
0
2
2
1
3
2
1
1
1
1
2
2
2
2
2
1
2
0
1
1
0
0
1
2
2
1
1
1
1
1
1
0
0
0
2
1
1
1
1
1
1
0
1
2
1
1
0
0
0
1
2
1
2
2
2
1
0
2
1
0
1
1
1
1
1
0
2
2
1
2
0
2
1
1
2
1
1
0
2
0
2
1
2
1
0
1
0
1
2
3
1
2
2
2
0
2
1
1
2
2
2
0
1
0
0
1
0
2
1
1
1
1
1
1
1
2
0
0
1
2
2
1
1
1
2
1
1
0
1
1
2
0
0
0
1
3
1
0
1
1
1
2
1
0
1
1
1
1
1
0
1
2
0
1
1
1
2
0
2
1
0
1
1
0
1
1
1
1
0
0
2
2
0
0
1
1
1
1
1
1
1
2
1
1
1
0
0
1
2
0
0
1
1
3
1
1
2
1
0
1
1
0
0
0
1
1
3
2
1
1
1
1
1
2
0
1
1
2
2
1
1
1
1
1
1
2
0
1
1
1
0
1
2
0
2
0
1
1
1
1
1
1
1
0
2
0
0
2
0
1
1
0
1
2
1
1
1
0
1
2
1
2
1
1
1
1
0
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
2
1
2
1
1
1
0
2
1
1
0
0
2
1
1
1
1
0
1
1
0
1
1
2
2
1
1
1
2
2
0
1
1
1
1
1
1
1
2
2
1
1
1
1
0
0
1
2
1
0
1
1
0
1
1
1
1
2
1
1
1
2
0
0
1
1
1
0
0
1
1
2
1
2
1
2
2
1
0
1
0
1
0
0
1
0
0
1
0
0
0
1
1
1
0
1
0
2
1
1
2
1
0
0
1
0
2
0
1
0
1
1
1
1
0
2
1
1
1
1
2
1
1
1
0
2
3
1
2
2
1
2
1
0
1
1
1
2
2
0
2
1
2
2
0
2
1
1
2
1
2
1
4
0
1
1
1
1
1
1
2
1
1
1
0
2
0
1
1
1
1
1
0
0
1
0
1
1
0
1
1
1
1
1
0
2
0
2
0
1
1
1
1
0
1
1
0
0
1
1
0
1
1
2
1
2
2
0
1
0
2
0
1
1
0
0
1
0
1
1
1
0
1
0
1
2
2
0
1
2
0
2
1
1
2
0
0
0
1
1
0
0
1
2
0
0
3
1
2
0
0
1
0
1
2
2
2
1
1
0
1
2
1
0
1
2
1
0
1
2
0
1
0
1
2
1
1
0
2
1
0
0
2
2
1
2
3
3
2
0
2
1
1
2
0
1
1
2
1
2
1
0
1
1
0
0
1
1
1
1
1
2
2
1
1
2
0
1
2
1
1
2
2
1
4
1
1
2
1
0
1
1
1
1
0
2
1
0
2
0
0
1
1
1
1
2
1
0
0
0
1
1
2
0
1
1
2
2
1
2
2
1
0
2
1
1
2
1
1
1
2
1
1
2
1
0
1
1
1
1
2
2
1
0
1
2
0
1
1
0
2
2
0
2
1
0
2
0
2
0
1
2
2
1
0
1
0
2
1
1
0
1
1
1
0
2
2
1
0
0
2
0
1
1
1
1
2
2
1
2
1
2
1
1
1
2
1
0
3
2
0
0
1
1
1
1
0
1
2
1
1
1
1
0
0
1
1
0
2
1
0
1
2
0
1
1
2
1
1
0
1
1
1
1
1
0
1
1
1
0
1
1
0
1
1
2
0
1
1
1
1
0
2
2
2
1
2
1
2
0
1
2
1
1
1
1
0
1
0
2
1
3
2
1
1
0
1
1
0
0
0
2
1
0
1
1
1
2
1
1
1
2
1
1
0
1
2
1
1
0
1
1
1
2
0
0
1
1
0
0
1
1
1
2
0
0
1
1
0
1
0
1
1
2
2
1
1
2
1
0
2
2
1
0
1
2
1
1
1
0
0
0
0
0
1
1
2
2
0
0
2
0
1
1
1
1
0
0
2
1
1
1
1
1
2
1
1
1
1
2
0
1
0
2
1
2
1
2
1
2
2
0
1
1
1
1
2
1
0
2
1
1
1
0
2
2
1
0
1
2
0
1
1
0
1
1
1
3
1
2
2
1
1
1
2
2
1
1
2
3
2
1
1
1
1
2
1
1
1
0
1
1
0
3
2
0
1
1
1
1
1
0
0
1
1
1
2
1
1
1
2
1
1
2
1
1
0
0
2
1
1
2
1
0
1
1
0
2
2
1
1
1
1
1
1
2
2
1
1
1
2
0
1
1
0
1
1
2
0
1
1
1
1
2
2
0
1
0
1
2
1
2
0
1
1
2
2
2
2
1
2
1
2
0
1
2
0
1
1
2
2
1
1
1
1
2
0
0
1
1
1
2
1
2
1
1
0
2
1
1
0
1
0
2
1
0
0
1
0
2
0
1
1
1
2
2
1
2
1
1
1
0
1
1
3
1
2
0
1
0
1
0
1
0
1
1
0
2
1
2
2
0
1
1
2
0
2
0
1
1
2
1
2
2
0
2
1
0
0
1
0
1
2
1
1
1
1
1
0
2
1
1
1
1
0
1
1
2
0
0
1
1
1
1
1
0
0
1
1
0
1
2
1
1
1
0
1
1
0
2
0
1
1
1
0
2
1
1
1
2
1
1
2
1
1
1
1
1
0
0
1
1
1
1
1
1
1
1
0
0
1
0
0
1
1
1
2
1
1
2
1
1
2
1
0
1
1
1
1
0
0
1
1
0
1
0
2
1
1
1
1
1
0
0
1
2
1
2
1
0
0
1
0
0
0
1
1
2
1
1
1
1
1
2
2
1
0
0
1
0
1
0
1
2
1
1
1
0
1
0
0
1
1
0
1
1
2
1
2
2
1
0
0
1
2
1
0
0
1
0
2
1
0
1
1
1
0
0
1
2
1
2
0
2
1
2
1
1
2
1
2
0
1
2
1
0
2
1
1
0
2
1
1
0
1
2
3
0
1
1
0
0
1
0
1
0
2
1
2
2
1
0
1
1
0
0
0
0
0
1
0
2
1
2
1
2
0
0
2
2
1
2
1
0
1
2
1
0
1
1
1
1
2
0
1
1
2
1
1
2
1
0
1
1
1
1
1
2
2
2
0
1
1
2
1
1
2
0
0
0
1
1
0
0
2
0
1
2
2
1
1
2
1
0
0
1
2
1
1
1
1
0
2
1
2
1
0
2
0
1
1
0
1
0
1
0
0
1
2
0
1
2
0
2
2
1
0
0
1
1
1
2
0
1
1
2
0
1
1
0
1
1
1
1
1
1
2
1
1
2
2
0
1
1
1
1
1
1
2
1
1
1
0
2
1
0
2
1
2
1
1
2
0
0
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
0
1
2
0
0
1
1
0
0
1
2
1
1
1
0
0
1
1
0
1
1
2
0
2
1
0
0
0
1
0
1
1
3
1
2
1
2
1
0
1
1
1
1
1
1
1
1
1
1
1
0
1
1
0
2
2
0
1
1
1
1
0
2
1
1
0
3
1
1
0
0
1
1
0
1
0
0
1
1
0
1
0
1
1
2
2
0
1
1
2
1
0
0
1
1
1
1
1
0
2
0
0
1
0
1
0
1
0
0
1
1
1
1
1
2
1
1
1
1
2
2
0
2
1
1
1
0
0
2
1
0
0
1
1
2
0
1
1
2
0
1
0
1
0
0
0
1
2
1
0
1
1
2
0
1
1
0
1
1
1
0
1
0
3
0
1
1
1
0
1
1
1
1
1
1
2
0
1
2
1
0
1
1
1
1
1
2
2
1
2
1
1
1
1
0
0
1
1
2
1
1
2
1
1
1
1
0
0
2
0
1
0
1
1
1
1
1
1
1
1
2
1
2
2
1
0
1
2
1
2
0
1
2
1
0
1
2
2
0
2
1
1
1
0
7
1
0
1
0
0
0
2
1
1
0
1
0
0
0
0
1
0
2
1
3
1
2
2
1
0
1
0
1
0
1
0
2
4
0
1
1
1
1
0
0
0
0
0
1
1
1
0
0
1
0
1
1
0
0
2
1
1
1
1
0
1
1
1
0
1
0
1
1
1
1
1
0
1
0
1
0
0
1
1
2
1
1
1
1
1
1
2
2
2
1
1
0
2
1
1
1
1
3
0
0
1
3
0
2
1
0
2
2
2
0
1
1
1
1
1
0
1
1
0
1
1
1
0
1
1
2
1
2
2
0
0
2
2
1
2
0
0
0
1
1
1
1
1
2
0
0
0
2
1
1
1
1
0
1
2
0
0
1
2
1
1
2
2
0
2
2
3
1
2
1
2
1
1
2
1
0
2
2
2
0
0
0
1
1
2
1
1
1
1
0
2
1
2
1
1
1
1
1
0
0
1
1
2
1
1
0
2
1
2
0
2
1
1
1
11
2
1
2
1
0
2
1
1
2
0
0
2
0
1
0
2
2
2
1
1
0
0
0
1
2
1
1
1
1
0
1
0
2
2
1
1
1
1
2
0
0
1
0
2
1
1
0
1
0
1
0
1
0
1
1
0
0
1
1
1
1
2
1
1
1
2
1
1
1
1
0
2
1
1
1
1
1
1
1
1
1
0
1
2
1
2
1
2
0
2
0
1
0
1
1
1
1
1
2
1
1
1
0
1
1
1
1
4
2
1
0
1
1
1
1
1
0
1
2
1
1
1
0
1
1
2
1
1
2
0
2
1
0
3
1
0
1
1
0
1
2
1
1
1
2
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
2
0
0
1
0
1
1
1
1
1
0
1
2
0
1
1
1
1
1
1
2
0
0
1
1
0
0
1
1
1
2
1
1
0
0
1
2
1
1
2
1
0
1
1
0
1
2
2
1
0
1
0
0
1
0
1
2
1
0
0
0
1
1
1
1
1
2
1
0
1
1
1
1
0
0
0
1
1
0
2
1
1
1
2
1
1
2
1
0
2
1
1
0
1
2
0
1
1
3
2
1
1
1
2
2
1
1
1
0
0
2
0
1
1
0
0
2
1
2
0
1
2
1
1
2
1
1
2
1
1
2
2
1
2
3
1
0
1
0
1
1
1
1
2
1
1
2
1
0
1
2
1
0
0
1
0
1
0
1
2
0
2
1
1
0
1
1
1
0
0
0
2
1
1
0
0
0
1
1
2
1
1
0
1
1
1
1
1
1
1
1
1
0
1
1
2
0
1
0
2
1
1
2
2
1
1
0
2
0
1
2
1
0
2
3
1
1
1
1
0
1
1
1
0
1
1
0
1
1
1
0
1
0
1
1
1
2
1
1
0
0
0
2
0
0
1
2
1
0
0
1
0
2
0
0
2
1
0
1
1
1
1
1
3
0
0
1
1
1
2
3
1
0
2
2
1
2
1
1
0
2
2
0
3
1
0
1
1
1
0
0
1
1
2
1
1
0
1
1
2
1
0
1
3
0
1
1
1
0
1
1
1
1
1
1
1
1
0
0
0
0
0
0
2
1
2
0
1
0
0
1
1
1
1
1
0
1
2
0
1
0
2
0
2
0
2
1
0
1
2
2
0
0
0
1
2
1
2
1
1
1
0
1
1
1
1
1
1
1
3
1
0
1
2
2
2
1
1
2
0
1
1
2
0
2
0
1
2
1
1
1
1
2
1
2
2
1
1
2
1
1
2
1
1
1
0
1
2
1
0
2
0
1
1
2
1
0
1
2
1
1
2
0
0
1
1
0
1
1
1
2
0
1
1
1
1
1
0
0
4
1
1
2
2
1
0
0
1
1
1
1
1
1
0
1
2
0
0
0
1
0
1
0
2
2
1
1
0
0
2
1
1
1
1
1
1
1
2
0
1
1
0
2
1
1
2
2
2
1
1
1
2
2
1
0
0
1
1
1
2
1
1
1
2
1
1
1
0
1
0
0
2
0
0
1
1
1
1
5
1
1
1
1
1
2
1
2
1
1
1
1
1
2
0
1
1
1
1
0
0
2
0
1
0
0
1
1
0
0
1
0
1
1
1
1
2
1
1
1
3
0
1
0
1
0
0
1
1
1
2
1
1
1
2
2
0
2
0
1
0
2
2
2
2
1
0
1
0
3
1
1
1
1
3
1
1
0
1
1
1
1
2
2
0
1
2
1
2
0
0
2
0
3
1
1
1
1
3
1
1
1
0
0
0
2
0
2
1
0
1
1
1
2
0
1
1
0
1
2
1
0
1
0
1
1
0
2
1
1
1
0
2
1
1
1
2
1
0
2
2
2
0
2
2
1
1
1
1
2
1
1
1
1
2
2
1
0
2
1
1
1
0
1
1
2
0
0
2
1
1
1
1
0
0
0
1
1
0
1
1
2
1
1
2
0
4
1
1
2
2
2
1
0
2
1
1
1
1
2
2
0
2
2
2
1
1
1
0
1
0
1
0
1
1
0
1
1
0
1
1
2
1
1
0
1
1
0
1
1
1
1
1
2
1
1
1
1
1
1
0
2
1
1
1
1
3
1
1
1
0
1
0
0
1
2
1
1
1
1
0
2
1
3
1
0
1
1
2
1
1
1
1
1
1
1
1
1
1
1
0
1
2
2
2
1
1
1
0
1
1
1
0
1
2
2
0
1
1
1
1
2
1
0
1
1
1
0
1
1
2
1
1
5
2
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
0
1
1
0
0
1
1
0
2
2
2
1
0
2
2
2
1
0
1
1
1
0
0
0
1
2
2
2
1
1
2
1
0
2
2
1
0
1
2
0
0
2
1
0
1
0
1
2
1
2
1
1
1
2
1
0
0
2
1
1
0
2
0
2
1
0
0
0
2
0
1
1
1
2
2
0
0
1
0
1
0
1
1
0
0
1
2
1
0
1
1
0
1
1
1
1
1
0
3
2
1
2
2
0
2
1
1
0
0
2
1
1
1
0
1
0
1
0
1
1
2
1
0
1
1
2
1
1
1
1
1
1
2
0
1
0
1
0
2
1
1
1
2
2
1
1
1
0
0
2
1
1
0
2
2
1
1
0
1
2
1
1
1
2
2
1
1
2
0
2
0
1
1
0
0
0
2
1
1
1
1
1
2
0
2
2
2
2
0
0
4
0
0
0
1
2
0
1
1
1
1
0
0
1
1
0
1
0
1
1
1
2
2
1
1
1
1
0
1
1
1
1
1
2
1
1
2
1
0
1
1
1
1
0
0
2
1
1
1
1
1
0
1
2
0
1
4
1
1
2
1
0
0
2
2
0
0
2
1
1
0
1
1
0
2
1
2
0
2
2
0
1
1
1
0
1
0
1
1
0
1
1
0
0
1
1
1
1
1
2
1
1
0
1
2
2
1
2
1
0
0
1
0
1
0
2
1
0
0
3
0
1
0
1
1
2
0
1
1
1
1
1
1
0
1
1
0
2
1
1
1
2
1
1
1
1
2
1
2
1
1
0
1
2
0
0
3
2
1
1
1
2
1
1
1
0
1
1
1
1
0
1
1
1
2
0
1
0
2
1
0
2
1
0
0
1
1
1
0
1
1
0
1
1
2
0
1
2
2
0
2
2
1
1
1
1
1
1
0
2
2
1
0
0
2
2
1
1
1
1
0
1
2
3
1
0
1
1
1
1
1
1
2
1
2
1
1
2
1
1
2
0
1
0
2
1
1
1
1
1
2
2
1
1
1
1
2
1
1
0
1
2
1
1
2
0
1
1
1
0
1
1
2
2
1
0
0
0
0
0
2
1
0
2
1
2
1
1
2
1
1
1
1
1
1
1
2
0
1
1
2
1
1
2
2
1
1
1
2
1
1
1
1
2
1
0
1
1
1
1
1
2
0
1
1
1
0
2
1
1
1
1
1
2
1
2
1
2
1
2
0
1
1
2
1
2
2
1
1
1
0
1
1
1
1
0
1
0
0
0
1
2
3
2
1
0
1
1
1
1
2
1
0
2
2
1
1
2
1
1
1
0
1
0
1
2
1
1
2
1
1
1
1
0
1
1
2
0
1
2
1
1
0
2
2
1
1
2
2
1
2
1
2
1
1
1
0
1
1
1
1
0
0
1
0
1
1
1
1
1
1
2
0
2
2
1
1
1
0
0
1
2
1
1
0
1
1
1
2
1
2
0
1
0
1
1
0
1
1
1
1
0
0
2
2
2
0
3
0
2
0
0
1
1
2
1
1
0
0
2
2
2
1
1
0
0
1
2
0
2
2
0
0
2
2
2
4
1
1
4
2
3
2
1
1
1
0
1
1
0
1
2
2
2
1
2
1
2
2
1
1
2
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
2
0
2
0
1
1
2
1
1
1
1
1
1
1
2
0
0
1
0
2
2
1
1
0
1
0
2
1
1
2
0
0
2
0
1
1
1
0
1
1
1
0
1
2
2
1
0
1
1
0
1
2
0
1
1
0
1
1
1
1
0
0
2
0
1
0
2
1
1
1
0
2
0
0
0
1
1
1
1
1
1
1
1
2
0
2
1
1
1
1
1
2
1
1
1
0
1
0
1
1
0
2
0
0
2
2
0
1
1
1
1
0
0
1
1
1
1
2
1
1
0
0
1
0
1
1
1
0
2
0
1
1
1
1
2
1
1
1
1
0
0
0
1
1
1
2
1
2
1
1
1
1
1
0
0
2
0
1
1
1
1
3
2
1
2
2
2
1
0
0
1
2
2
1
1
0
1
1
1
3
2
1
1
2
2
2
1
1
1
1
0
1
1
2
2
1
1
1
0
0
1
1
2
0
1
0
0
0
1
1
2
1
0
1
1
1
1
1
1
1
1
2
1
2
1
2
0
2
1
1
1
0
1
0
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
0
1
1
2
1
1
1
1
1
1
0
1
2
1
2
2
1
2
1
0
1
2
0
0
2
0
0
2
1
1
1
0
1
1
0
1
1
1
0
2
0
2
1
1
1
1
1
1
1
0
1
0
1
1
1
1
1
1
2
1
0
1
1
0
2
1
1
1
0
1
0
1
0
1
1
1
1
2
1
1
1
0
1
1
2
1
1
1
1
1
2
2
2
2
0
1
5
2
2
1
0
1
2
1
0
1
0
1
1
2
2
2
0
0
2
1
1
1
1
1
0
2
2
2
1
1
2
1
1
2
1
1
0
1
0
0
1
2
2
1
2
1
1
1
0
1
1
0
1
2
1
1
2
1
2
0
1
0
1
1
0
2
2
1
1
2
1
2
0
1
1
0
1
0
3
2
0
0
2
1
2
3
2
0
1
1
1
1
1
0
1
1
1
0
1
1
1
1
1
2
1
0
0
2
0
5
0
2
2
1
1
0
0
1
1
0
2
0
1
0
1
1
0
1
0
1
1
1
1
2
0
1
1
0
2
2
1
1
0
0
0
1
1
1
0
1
1
1
2
1
0
1
1
0
1
2
1
1
1
0
1
1
0
1
1
2
0
1
1
1
1
1
2
1
1
1
1
2
1
1
1
0
0
0
2
1
0
2
1
1
0
1
1
1
1
1
1
2
2
2
1
1
2
1
1
0
0
1
1
1
1
0
2
1
1
1
1
1
0
1
1
1
2
1
0
1
1
1
2
1
1
1
1
1
0
2
1
1
2
1
1
1
0
1
2
1
1
1
3
1
1
1
0
0
2
2
1
0
1
0
1
2
1
0
2
0
1
2
1
1
1
1
2
0
0
0
1
0
1
1
0
2
1
1
1
1
2
1
1
1
1
2
1
1
0
2
1
1
0
1
2
1
1
1
1
1
1
1
2
0
1
1
1
1
0
1
1
1
0
2
1
2
1
2
1
1
1
1
0
1
2
1
1
1
1
1
1
2
0
2
0
1
1
0
0
0
0
1
2
1
2
0
0
0
0
1
2
1
0
0
1
1
1
1
1
0
1
1
0
0
0
0
2
2
2
2
1
1
1
0
0
2
0
1
1
1
1
2
1
0
2
1
2
1
1
1
2
1
1
1
1
1
0
1
0
2
0
2
1
2
0
0
1
1
1
0
1
1
1
0
1
0
1
0
1
2
1
1
2
2
0
1
1
2
1
2
1
2
1
1
1
1
1
0
1
0
1
0
1
1
1
1
1
2
1
1
1
0
2
0
0
2
1
1
1
0
1
2
2
0
1
1
2
2
2
1
1
2
1
1
0
1
0
2
0
1
1
1
1
0
1
0
0
2
1
0
2
2
1
1
1
1
1
0
2
1
1
0
2
0
1
1
1
0
1
1
2
0
0
0
1
2
1
1
1
0
2
1
1
0
1
1
0
1
0
0
1
0
1
2
0
1
1
2
1
0
1
1
1
0
1
0
1
0
1
0
1
1
1
1
0
1
1
2
1
0
0
0
3
1
0
1
2
2
1
1
0
1
1
0
1
1
2
0
2
1
2
1
1
1
2
2
2
2
2
1
2
2
2
1
1
2
1
1
1
0
5
0
0
1
2
0
1
1
2
1
1
1
2
1
1
1
2
1
2
2
0
1
1
1
1
1
0
1
1
1
0
1
1
0
0
0
1
1
1
1
1
1
2
1
1
2
1
0
0
1
1
0
2
1
2
1
1
2
2
0
1
1
1
0
0
2
1
1
1
1
1
1
2
4
1
0
2
1
2
1
2
1
0
0
1
2
1
0
0
2
3
0
0
1
1
2
0
1
0
1
1
1
1
1
1
1
1
0
1
1
0
2
1
1
0
1
0
1
0
2
1
1
0
1
2
2
0
0
1
0
3
0
2
0
0
1
2
1
1
0
1
2
2
2
2
1
2
1
1
2
1
1
1
1
1
2
1
1
1
1
1
0
1
1
2
2
1
0
2
1
2
0
0
1
0
2
0
1
0
1
1
1
0
1
2
1
0
1
1
1
1
1
2
2
2
0
1
2
1
2
1
2
1
1
1
0
2
0
1
1
0
0
2
1
2
1
1
0
2
1
2
0
1
1
0
2
1
2
2
1
0
0
1
1
1
0
0
0
1
1
1
1
0
0
1
0
0
1
1
0
1
0
1
0
1
0
3
1
1
0
0
1
1
1
1
1
1
0
0
0
0
2
0
3
1
0
2
1
0
1
1
2
1
1
0
1
2
1
1
2
0
2
1
1
1
0
2
1
1
0
1
1
0
2
1
1
1
2
2
2
0
1
1
0
0
1
2
1
2
1
0
1
1
2
0
1
1
1
1
1
0
0
1
0
2
1
1
1
1
1
1
2
1
1
1
1
0
2
0
0
2
2
2
2
1
0
1
1
1
0
2
2
1
1
3
1
1
1
1
2
1
2
1
2
0
1
0
0
2
3
1
1
2
2
0
0
2
0
0
1
0
1
1
0
1
0
1
0
1
0
1
1
0
2
0
1
5
0
1
1
0
1
0
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
2
1
2
1
2
0
0
2
1
0
1
0
1
1
2
2
1
2
1
1
1
1
2
1
2
1
1
0
1
1
2
2
1
1
2
2
1
1
1
0
1
1
2
0
1
0
1
2
0
2
0
1
1
1
2
1
1
1
1
1
0
0
0
1
2
1
2
1
2
1
2
1
1
2
1
0
1
2
0
0
2
0
2
2
1
2
0
1
2
2
1
1
2
1
1
1
2
0
1
0
1
1
1
1
1
1
1
1
1
1
1
1
2
1
0
0
0
2
0
1
2
1
1
1
1
1
1
1
1
0
1
2
1
2
0
1
1
1
2
1
3
1
1
2
0
1
1
0
1
2
2
0
1
4
2
1
0
0
1
1
1
0
1
2
1
1
1
2
1
0
0
0
1
1
2
1
1
1
1
1
0
3
0
1
1
1
2
0
1
2
2
0
2
1
1
1
1
1
1
2
1
1
2
1
1
1
1
0
0
1
1
1
1
2
2
0
0
0
1
2
0
1
1
0
1
1
0
1
1
1
1
1
2
1
1
1
2
1
1
1
4
2
1
1
2
1
2
0
1
0
2
2
1
1
1
2
1
1
0
0
1
0
2
1
2
1
1
1
1
2
0
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
20
2
0
0
0
3
3
1
2
3
0
2
2
0
2
1
1
2
1
1
1
1
2
1
1
1
1
0
1
1
0
1
1
0
0
2
1
1
0
2
1
1
1
2
0
0
1
0
0
2
2
1
1
1
2
1
2
1
1
1
2
2
1
1
1
1
1
2
1
2
2
0
0
1
1
1
0
0
2
0
1
1
1
1
0
1
1
1
2
1
0
1
1
0
1
1
0
1
1
0
1
1
1
1
0
0
2
1
2
1
1
1
0
1
1
1
0
1
2
1
2
0
1
2
1
2
2
1
1
2
1
1
2
1
0
1
2
1
0
2
1
1
1
0
1
1
0
1
2
1
2
1
1
0
0
0
0
2
1
1
1
0
1
2
1
1
1
1
1
1
1
2
1
0
2
2
2
0
1
2
1
1
0
1
0
0
0
1
0
1
1
0
0
2
0
1
2
1
2
1
1
0
1
0
1
1
2
2
1
1
1
1
1
1
2
2
1
1
2
1
2
1
1
2
1
1
1
1
0
0
0
2
1
0
1
1
1
0
1
2
1
0
1
2
1
2
0
1
0
0
1
2
1
1
2
1
1
0
0
0
0
1
2
1
2
0
0
1
0
1
1
2
0
1
1
2
2
1
1
2
0
0
1
2
0
1
1
1
1
1
1
0
0
0
1
0
1
1
1
0
0
0
0
2
1
2
1
1
1
0
0
1
1
0
1
1
0
1
1
2
1
1
1
1
1
1
1
1
2
2
1
1
2
1
2
0
1
1
1
1
0
2
1
1
2
1
2
0
0
2
1
2
1
1
1
1
1
1
1
1
0
2
0
1
1
1
1
2
2
0
0
2
0
2
0
1
2
2
1
2
0
1
1
2
2
0
2
2
1
2
1
2
2
2
0
0
0
1
2
1
1
1
1
1
0
2
2
2
1
2
1
1
0
0
2
0
1
0
0
1
2
0
0
0
2
2
0
1
0
2
2
1
1
0
1
1
1
1
1
1
1
1
1
0
0
1
1
1
2
0
1
1
1
1
0
1
0
1
1
1
2
1
1
0
2
0
2
1
0
0
1
1
2
1
1
0
1
1
1
1
1
0
1
1
1
2
1
1
1
1
1
3
1
1
0
1
1
1
1
0
1
2
1
1
0
1
1
1
2
1
0
1
1
0
1
2
0
1
2
0
1
0
2
1
1
1
0
1
2
1
1
0
0
1
1
1
1
1
1
1
1
1
1
1
0
1
2
2
1
2
1
1
1
0
0
1
0
0
2
1
2
2
1
1
2
1
2
1
0
2
1
1
1
3
0
2
1
1
1
0
2
0
1
2
1
1
1
2
1
2
2
2
0
0
0
2
1
2
1
1
1
1
1
2
0
1
0
1
1
1
1
1
1
1
1
0
0
0
1
2
1
1
0
1
1
1
1
1
2
2
1
2
1
1
0
2
1
2
0
1
1
1
1
2
2
1
2
2
0
0
1
1
1
2
0
0
1
1
0
2
0
1
1
1
1
0
1
0
1
1
1
1
2
1
2
1
2
1
0
1
2
1
0
1
2
1
2
0
0
1
1
1
1
2
1
0
1
1
1
0
1
1
2
0
2
1
2
1
1
5
1
1
1
2
2
1
1
3
1
2
1
1
0
1
1
1
1
1
1
2
2
2
1
1
1
0
1
1
1
2
2
1
2
1
1
1
0
0
0
0
1
2
2
1
1
1
1
1
1
1
1
0
1
2
2
2
0
1
1
2
2
1
1
1
1
1
2
1
1
1
1
2
1
2
0
1
1
0
1
1
1
1
1
1
0
1
1
1
0
1
1
0
1
1
1
2
1
0
2
1
1
1
0
1
2
2
1
1
1
0
1
1
1
1
1
1
2
1
2
2
0
0
1
2
0
1
0
1
2
1
0
2
1
2
1
2
0
2
0
2
1
1
2
1
2
1
1
0
0
0
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
0
2
2
1
1
0
2
1
1
0
0
0
1
1
1
0
1
2
0
0
1
1
0
2
1
1
1
1
1
1
2
1
0
1
0
1
0
0
1
2
1
2
1
0
1
1
2
0
0
1
1
0
2
2
0
1
2
2
1
1
1
0
1
0
0
1
1
1
1
0
1
1
1
0
2
2
2
2
1
2
1
2
1
0
1
0
1
0
1
1
0
1
0
2
0
0
0
1
2
1
2
0
1
0
0
1
1
1
0
1
1
2
1
1
0
1
2
0
0
1
1
0
1
1
2
2
0
1
1
1
0
0
2
1
1
1
0
0
0
1
4
2
1
1
2
1
2
1
1
0
1
1
0
1
1
2
1
1
1
1
0
1
0
2
1
1
1
0
2
2
1
2
2
2
1
0
0
2
0
2
2
1
0
1
1
2
3
0
1
2
0
1
1
2
0
1
0
1
0
0
1
0
1
0
3
1
0
2
1
2
0
0
1
2
0
0
0
2
1
2
1
1
0
2
1
1
0
1
2
0
0
1
1
2
1
1
2
1
1
1
1
1
1
1
2
0
1
0
1
1
1
1
1
0
2
2
2
2
1
2
1
1
0
1
1
0
1
1
0
0
1
2
0
2
1
1
0
0
1
4
1
1
0
1
2
1
1
1
1
1
1
0
2
0
1
1
1
0
0
2
1
1
1
1
1
0
1
2
0
2
2
1
1
0
1
1
1
2
2
1
2
1
1
1
2
1
1
2
1
0
0
2
1
2
1
2
0
0
2
0
0
0
1
0
2
1
0
1
0
0
0
1
1
0
1
0
1
0
0
2
1
0
1
1
1
1
1
0
0
0
1
1
0
1
1
0
1
1
2
1
1
2
1
2
2
2
1
2
2
2
0
0
0
0
1
1
1
1
1
2
0
0
1
0
1
0
0
1
2
2
1
1
2
2
0
0
2
0
1
0
0
1
1
1
3
5
1
2
0
0
1
1
2
0
1
2
2
1
1
1
2
2
2
2
0
1
1
1
1
0
0
1
0
1
1
2
2
0
0
2
0
2
0
1
1
2
2
1
2
2
2
1
1
0
1
1
1
1
2
2
1
1
1
2
1
2
2
1
1
0
1
1
0
2
1
0
2
1
2
1
0
0
2
0
2
1
1
1
1
2
1
0
1
2
1
1
1
1
1
0
0
0
2
2
1
1
2
0
2
1
1
1
0
0
2
1
0
1
1
1
0
0
1
0
1
0
1
1
1
2
1
0
1
1
1
1
2
0
2
1
1
2
1
3
0
0
1
2
0
1
1
1
1
1
1
1
0
2
0
0
1
2
2
2
1
0
1
1
1
1
0
1
2
1
2
0
0
2
1
1
1
0
2
2
1
1
2
2
1
0
2
2
1
2
0
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
1
2
2
1
2
2
1
1
0
1
1
1
2
1
2
0
2
2
0
3
0
2
0
1
1
1
1
0
1
1
1
2
1
1
2
0
2
1
1
1
2
1
1
0
1
2
1
0
2
1
2
1
0
2
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
0
1
2
1
0
1
1
1
1
1
1
2
1
1
0
1
2
2
0
1
1
1
1
1
1
1
1
2
2
1
1
1
1
0
1
2
3
1
1
1
0
2
1
1
2
1
0
0
1
0
1
1
1
2
1
0
0
2
2
1
2
5
2
1
1
1
1
1
1
2
1
1
0
0
2
2
1
2
1
1
2
4
1
1
2
1
1
1
1
1
1
0
0
0
1
1
1
1
1
2
0
1
3
1
1
0
1
0
0
2
1
2
1
2
2
1
1
1
2
1
0
1
1
1
1
1
1
1
1
0
2
2
1
1
1
1
1
1
1
0
1
1
2
0
1
2
1
1
1
2
1
1
2
1
0
1
1
1
0
2
2
1
1
1
2
1
0
1
2
2
1
0
0
1
0
1
1
4
1
0
1
1
2
1
1
0
1
1
1
1
2
1
2
1
1
1
0
0
2
1
0
2
0
1
7
1
0
0
1
2
0
1
2
1
1
0
1
1
2
0
1
2
1
0
2
1
2
2
1
1
0
0
0
2
2
1
1
1
2
1
0
2
0
1
0
2
0
1
1
0
1
0
0
1
0
1
1
0
0
1
0
3
1
1
0
1
1
0
1
1
1
0
0
1
1
1
1
0
0
1
1
1
1
0
2
1
2
0
0
2
0
1
0
1
1
2
1
2
2
1
1
2
1
1
2
1
1
1
1
0
2
0
1
1
1
1
1
1
2
0
2
0
0
1
2
2
1
1
0
0
1
1
0
2
0
1
2
0
1
1
0
2
1
1
0
0
1
1
1
1
0
0
1
1
2
1
2
0
1
2
1
1
1
1
1
1
0
0
0
1
2
0
1
1
1
0
2
2
1
0
1
0
2
1
2
2
2
1
1
2
2
2
1
1
1
2
2
1
2
0
2
0
1
1
1
1
1
1
0
2
1
2
0
3
0
0
1
2
2
1
1
0
0
2
0
0
1
1
2
1
1
1
1
1
2
0
2
1
2
1
1
1
0
1
1
2
0
2
1
2
1
1
2
0
1
1
2
1
1
1
2
1
1
1
2
0
1
1
1
0
1
0
2
2
1
0
0
1
1
2
2
0
1
1
2
1
2
0
1
1
0
1
2
0
2
1
0
1
0
1
1
1
0
2
1
1
1
0
1
1
2
1
1
2
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
0
2
1
1
2
2
1
1
1
2
1
0
1
1
1
1
0
0
1
1
1
2
0
0
1
2
0
1
2
2
0
1
1
0
1
1
1
2
1
1
1
2
0
1
1
2
0
1
1
1
2
0
2
1
0
1
2
1
2
1
0
0
1
1
1
1
2
0
1
1
1
2
1
2
1
1
1
1
1
0
1
1
0
1
1
0
0
0
1
1
0
1
1
1
1
1
1
2
1
1
1
1
0
0
0
1
1
3
1
1
1
0
1
0
0
1
1
1
2
1
2
1
2
1
2
1
2
1
2
0
1
2
1
1
2
1
1
0
1
1
0
1
0
2
0
1
2
1
0
2
0
2
1
0
2
2
1
0
1
1
1
0
1
1
1
2
0
1
1
3
2
1
1
0
1
1
1
1
2
0
2
1
0
1
1
2
1
1
1
1
1
2
1
1
2
0
1
2
0
1
0
3
0
2
0
1
0
1
1
1
1
0
2
1
2
1
0
0
1
0
2
1
0
0
1
1
0
2
1
0
2
2
1
1
1
1
1
2
0
2
1
1
1
2
0
0
0
1
0
1
0
2
0
2
1
2
2
1
1
1
0
1
1
0
1
0
1
2
1
1
2
1
2
1
1
2
2
1
1
2
2
1
1
1
1
1
0
0
2
0
2
0
1
0
1
1
2
1
1
1
1
2
1
0
1
0
1
1
2
1
1
0
0
1
2
2
2
1
1
1
1
1
1
1
0
1
1
1
2
2
0
2
1
1
1
2
0
1
0
1
2
1
2
2
2
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
0
1
0
0
2
0
2
1
1
1
0
2
0
0
1
2
1
0
1
2
2
0
0
1
1
1
0
1
1
1
1
1
0
0
1
1
2
0
1
0
2
1
2
1
0
1
1
0
1
2
2
2
1
1
2
1
1
1
1
1
0
1
1
1
0
1
1
0
2
2
0
1
0
0
1
1
1
1
1
1
1
0
1
1
1
1
0
1
2
0
1
1
1
1
1
0
2
1
2
1
0
0
2
2
2
1
1
1
0
1
1
1
0
2
2
2
1
1
2
1
0
1
2
0
0
2
2
1
1
1
1
1
1
1
2
2
0
0
1
2
2
1
1
2
0
1
2
2
1
1
3
1
2
0
1
1
1
2
1
1
1
1
2
1
2
0
2
1
2
1
1
1
1
1
1
1
1
0
0
1
0
3
0
1
0
0
1
1
0
1
2
1
0
1
1
1
1
1
3
1
1
2
1
1
1
1
7
1
1
1
0
0
2
2
0
0
1
1
2
1
1
2
0
1
1
0
2
1
1
1
1
1
2
1
2
2
0
0
2
1
2
1
1
1
2
1
1
0
0
1
1
1
1
2
3
8
1
1
1
0
1
0
1
2
1
1
1
1
2
2
1
0
0
1
1
2
2
1
2
1
1
2
1
1
1
0
0
0
2
0
0
2
0
0
1
1
1
0
0
1
1
2
0
2
0
2
1
1
1
2
1
3
1
2
2
1
1
1
0
0
2
2
0
2
0
2
1
1
2
1
1
1
1
1
4
1
1
1
0
2
0
1
1
0
1
1
1
1
1
1
2
0
0
1
1
1
1
1
0
1
0
1
1
0
1
2
1
0
1
0
1
0
0
1
0
2
2
2
1
2
1
1
2
1
1
0
1
1
1
1
0
2
0
0
1
1
1
2
1
1
0
1
1
1
1
0
1
1
0
2
2
2
1
3
0
1
0
0
1
1
1
0
1
1
1
2
0
1
0
2
1
2
0
1
1
1
0
1
2
1
2
0
2
1
0
1
1
2
0
0
1
1
1
0
1
1
0
2
2
0
2
0
0
2
1
1
1
1
1
2
2
2
0
1
1
2
1
1
0
1
1
4
1
1
4
1
2
1
1
1
1
1
0
1
1
2
1
1
0
1
1
1
1
1
0
1
1
1
2
1
1
1
0
2
1
1
0
2
1
2
0
1
2
1
1
2
1
2
1
1
2
1
0
1
1
0
1
0
0
1
2
3
1
1
2
0
0
2
1
2
1
2
1
1
2
2
1
1
1
0
0
1
1
1
1
1
1
1
1
0
2
2
0
1
2
1
1
1
1
1
2
2
1
2
1
0
1
1
2
0
1
1
1
2
1
1
1
1
7
1
1
1
1
1
1
1
1
1
1
0
2
1
1
1
1
2
2
0
2
2
0
1
2
2
1
1
1
0
1
1
1
1
1
1
0
1
2
1
1
0
2
2
1
0
1
1
1
1
1
2
1
2
2
2
1
1
1
1
1
0
0
1
1
1
1
1
1
2
1
0
0
1
1
1
1
1
1
0
0
1
1
1
1
2
0
0
2
1
2
1
1
1
0
1
0
1
2
1
1
0
1
1
1
0
0
2
1
2
1
1
2
1
1
0
1
2
1
1
2
1
1
1
1
0
1
1
1
2
2
0
2
0
1
2
2
0
1
0
1
2
1
1
1
1
0
1
1
1
1
0
1
0
0
1
2
0
1
2
1
0
1
0
1
1
0
0
2
1
0
2
2
2
2
0
2
2
1
0
1
2
1
1
1
0
0
0
1
0
0
1
1
1
1
1
1
0
1
0
1
1
0
1
1
1
0
0
1
1
1
2
1
0
0
0
1
0
1
0
0
1
0
0
1
0
1
2
2
1
0
2
2
0
1
0
0
1
1
2
0
0
1
1
1
1
1
1
1
1
1
2
0
0
1
1
1
0
2
1
0
2
2
2
2
1
0
1
1
1
0
1
1
2
1
1
1
1
0
1
0
0
2
1
0
0
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
0
1
1
0
0
2
0
1
0
0
1
2
2
1
0
1
1
1
1
2
1
2
1
2
1
1
1
2
0
2
1
1
1
3
1
0
1
2
2
1
0
0
1
0
1
1
1
1
2
2
1
1
2
1
1
1
0
0
1
1
0
2
1
1
1
2
3
1
1
1
0
0
0
1
1
1
1
1
0
0
2
0
0
2
1
2
0
2
0
1
2
0
2
1
1
2
0
1
1
2
1
1
2
0
1
1
1
2
1
1
1
1
1
1
1
0
1
1
2
0
1
1
0
1
1
0
0
1
0
1
1
2
1
1
1
1
1
1
0
0
1
0
0
1
1
1
2
2
1
2
1
1
1
1
0
1
1
1
2
1
0
1
1
1
2
0
2
1
0
0
1
0
0
0
2
1
2
1
1
1
1
0
2
1
2
0
1
2
2
1
1
0
0
0
0
1
0
1
1
1
1
1
2
0
0
1
2
0
1
0
1
0
1
0
1
0
1
0
1
1
0
0
2
2
1
1
1
1
0
1
0
1
0
1
1
1
2
0
1
1
0
2
2
3
2
1
0
0
2
1
1
2
1
2
1
1
0
2
2
0
1
0
0
2
0
1
2
1
2
0
0
0
2
1
1
0
1
3
0
1
1
1
1
0
1
0
1
1
1
1
1
1
2
2
1
2
0
1
1
0
1
0
0
2
1
1
1
0
1
1
1
2
0
1
2
2
2
1
0
1
1
1
3
0
2
0
0
1
2
1
0
1
1
1
1
0
1
2
1
0
1
0
2
2
1
2
1
2
1
0
2
1
1
2
0
2
2
0
0
0
1
0
0
2
0
1
0
1
2
0
1
1
2
1
1
0
1
1
1
1
2
1
2
1
1
0
2
1
1
1
1
2
2
1
1
2
2
0
1
0
0
1
2
1
0
1
1
2
1
1
2
1
0
1
0
1
0
1
0
1
0
0
1
1
0
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
2
1
2
1
1
2
0
4
0
0
1
0
1
2
2
2
1
0
1
0
2
2
1
0
1
1
2
1
1
1
1
0
0
0
1
2
1
1
1
0
0
0
0
0
0
0
1
1
2
1
0
0
1
0
1
1
1
1
2
0
1
2
1
1
2
2
2
1
1
1
2
1
0
2
1
1
1
1
1
1
1
0
0
0
1
1
0
1
1
0
0
3
2
1
0
1
1
0
2
1
0
1
1
1
1
2
0
0
2
0
1
0
0
1
0
1
2
1
2
2
1
1
1
1
2
0
2
0
2
1
1
0
1
1
1
2
1
1
0
4
2
2
1
1
0
2
1
1
1
2
0
1
1
1
2
2
0
1
2
1
2
0
1
0
1
1
0
1
0
0
0
1
1
1
2
0
1
2
1
1
1
2
1
1
0
1
1
0
2
1
2
1
2
1
1
1
1
0
1
1
1
1
0
2
2
1
1
1
1
1
2
2
2
1
2
0
0
2
0
1
0
0
2
2
1
1
2
2
1
0
1
0
2
2
2
1
0
1
2
0
0
1
1
2
1
1
1
0
2
0
0
1
1
2
1
1
2
2
1
0
1
0
2
1
2
1
0
2
1
1
0
1
1
1
2
1
0
0
0
1
1
1
0
2
0
1
0
1
2
1
1
1
1
1
1
2
0
2
1
0
4
1
1
1
2
0
2
1
0
0
0
2
1
0
1
1
1
2
0
0
1
1
1
1
0
2
0
1
1
1
2
1
2
1
1
2
2
2
2
1
1
1
0
1
1
1
1
1
1
1
1
2
2
1
1
2
2
1
1
2
1
1
1
1
1
1
1
0
1
0
1
0
0
2
0
0
2
2
1
2
0
2
2
2
1
1
1
2
1
1
1
0
0
1
0
1
1
1
0
1
0
1
1
2
1
0
1
1
2
1
2
2
1
1
1
1
1
0
1
2
1
2
1
1
1
0
1
0
1
1
0
1
1
2
0
1
2
2
1
2
0
1
1
1
1
1
1
3
0
1
1
1
0
1
2
0
1
0
1
1
1
0
1
2
2
0
1
2
2
0
2
2
0
0
1
0
1
2
0
1
1
2
1
2
1
1
1
1
2
1
1
1
0
1
0
0
1
1
2
1
2
1
1
1
1
2
0
1
1
1
1
0
0
0
1
0
0
1
1
1
1
1
2
2
0
1
1
2
1
1
1
0
2
1
1
1
0
1
2
1
1
0
0
0
1
0
1
1
1
1
1
1
0
1
1
2
0
1
0
1
0
1
1
0
1
1
1
2
1
1
1
2
2
1
1
0
1
2
2
1
1
1
1
1
2
0
1
1
2
0
0
1
1
2
1
2
2
1
0
2
0
1
1
1
1
2
1
0
2
0
1
0
0
2
1
2
1
1
2
1
1
1
2
0
0
0
1
1
2
1
2
1
0
0
1
1
1
2
0
0
0
1
2
1
1
1
1
0
2
0
1
1
0
1
1
1
1
0
0
0
2
1
0
2
2
1
0
0
0
1
1
1
1
2
0
1
0
0
2
1
1
1
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
0
1
1
0
0
1
2
0
2
1
2
1
1
0
1
2
0
2
1
1
1
2
0
1
2
1
1
0
1
0
1
1
0
1
1
0
1
1
1
0
2
1
1
2
2
1
0
0
1
0
1
1
2
1
2
2
1
1
2
2
0
1
1
2
0
1
1
1
1
1
1
2
1
1
0
2
0
1
1
2
1
1
0
1
2
1
0
1
1
1
0
1
1
2
1
1
1
1
1
2
1
1
0
2
1
0
3
1
0
0
0
1
1
1
2
0
1
1
0
0
0
0
1
1
1
1
1
2
1
2
3
1
1
1
0
0
1
1
1
1
1
1
2
2
0
0
1
1
1
2
3
1
1
1
2
1
1
2
1
0
0
0
1
1
0
0
1
0
2
1
1
1
1
1
1
1
0
1
1
1
1
4
0
1
2
1
2
1
1
1
1
1
0
1
1
0
2
2
1
0
0
1
1
1
0
1
3
1
1
2
1
1
1
2
1
0
1
1
2
2
2
0
1
1
1
1
1
2
1
2
1
2
0
2
0
1
0
1
2
1
0
1
0
0
2
1
2
1
1
1
1
2
2
1
1
0
1
1
1
1
1
2
0
2
1
0
0
0
0
1
1
0
1
0
1
1
0
1
1
0
1
1
2
2
2
1
0
1
1
1
0
1
1
2
2
1
0
2
1
1
1
2
2
1
1
1
2
1
0
2
0
2
1
0
1
1
1
2
2
2
2
0
3
1
1
1
1
1
1
2
1
1
1
0
0
0
1
1
1
0
1
0
1
1
1
0
2
2
3
1
1
2
1
1
1
2
1
1
1
1
2
0
1
1
1
1
1
1
1
2
1
1
0
1
2
1
1
0
2
1
0
1
2
1
2
2
1
2
1
1
0
0
1
4
2
1
1
1
1
1
1
1
0
0
1
0
1
0
1
0
0
2
1
1
0
1
2
2
1
1
1
1
2
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
0
1
2
1
0
0
1
1
1
1
0
1
2
0
1
1
1
1
1
1
0
1
1
1
2
1
0
1
1
0
1
1
1
2
1
2
2
2
0
2
1
1
1
0
1
1
0
1
1
1
2
0
1
0
1
1
0
1
0
0
0
1
1
2
1
1
1
2
1
1
1
0
1
0
1
3
1
1
1
1
2
1
1
2
1
1
2
0
1
1
1
1
2
0
1
0
0
1
1
1
1
1
1
0
1
0
1
0
1
2
0
1
0
1
2
1
1
1
1
1
1
2
1
1
0
1
1
0
1
2
0
1
2
0
1
3
0
0
1
2
3
0
1
2
2
1
1
3
0
0
1
1
0
2
2
1
2
1
1
1
1
1
0
2
2
1
1
1
0
0
1
1
1
3
2
0
1
1
1
1
2
0
0
2
2
1
1
1
0
2
1
1
1
2
1
0
0
0
2
1
2
1
0
7
1
2
2
0
2
1
0
1
0
1
0
2
2
1
1
1
0
2
1
1
2
1
1
1
2
0
1
1
2
1
1
0
2
0
1
1
2
1
0
0
1
2
0
1
3
1
1
2
2
2
1
1
1
0
2
1
0
2
3
0
1
1
0
1
0
1
0
1
0
1
1
1
0
0
1
1
1
2
0
1
1
0
1
2
1
2
1
1
1
2
1
2
1
1
1
1
2
2
1
1
2
1
1
0
1
0
0
1
0
1
1
2
0
1
1
0
1
2
1
1
1
1
2
1
1
2
1
0
0
0
1
1
0
1
1
1
1
0
2
0
1
1
1
1
1
2
1
1
3
2
1
0
0
1
1
1
0
2
0
1
1
1
2
1
0
3
0
1
0
1
1
1
2
2
2
1
1
2
1
0
0
2
1
1
0
2
1
1
2
1
0
3
0
2
1
1
2
1
1
1
1
2
1
0
0
0
1
0
1
0
2
0
0
1
2
1
0
2
1
1
2
2
1
0
1
1
1
2
1
0
1
1
1
1
1
1
2
2
0
1
2
1
0
1
1
2
1
1
2
1
1
1
1
1
1
2
2
1
1
1
0
1
2
2
1
0
0
1
1
1
1
2
2
1
1
1
2
0
0
1
1
0
0
0
1
0
2
1
1
2
1
1
1
1
2
1
1
1
2
1
0
1
1
1
2
1
0
1
0
0
0
1
1
2
1
1
1
0
0
1
1
1
1
1
2
1
1
1
2
0
1
0
0
1
2
1
1
1
0
1
2
1
0
2
1
1
0
1
0
0
1
1
0
1
1
1
0
2
2
1
1
1
2
0
2
2
1
0
0
2
2
0
1
1
1
1
1
2
1
1
2
1
1
1
1
2
1
0
0
1
2
0
0
2
0
2
2
1
2
1
1
2
0
1
1
1
0
1
2
1
1
1
2
1
0
1
1
0
1
0
0
1
1
0
1
2
1
1
1
0
2
1
0
1
1
0
0
1
0
0
1
1
0
1
2
0
0
1
2
1
0
0
2
2
2
0
0
1
0
1
0
1
1
1
1
1
1
1
2
1
2
1
2
0
0
2
1
1
2
2
1
2
1
1
1
1
2
1
3
0
0
1
0
1
1
1
2
1
1
2
2
1
1
1
2
1
2
1
1
1
2
2
2
1
2
2
0
1
1
1
1
1
0
1
2
2
2
0
0
2
1
2
2
1
1
1
1
1
1
1
0
0
0
2
0
1
2
1
1
1
1
0
1
1
1
1
1
0
0
2
1
1
1
1
0
1
1
3
2
1
2
0
1
1
0
1
1
1
1
1
1
0
1
1
0
0
1
1
0
2
0
1
1
1
1
1
2
1
2
1
1
1
0
2
1
0
1
2
1
1
1
0
2
1
1
1
1
3
0
1
1
2
1
1
2
1
1
1
1
0
2
1
2
1
0
0
1
0
1
1
1
1
2
1
1
1
0
1
0
1
1
1
1
2
1
0
0
1
3
1
1
1
1
1
1
2
2
1
0
2
1
1
0
0
1
1
1
1
1
1
1
0
2
1
1
1
1
0
1
1
0
0
0
2
1
0
0
1
2
1
0
0
1
1
0
1
1
2
1
2
0
0
2
2
0
1
1
1
2
3
2
1
1
2
0
1
0
1
2
0
0
1
1
1
1
1
1
2
0
1
0
0
1
1
2
1
1
1
1
0
2
0
1
1
2
1
1
1
0
0
2
0
0
2
0
2
2
3
1
1
1
2
1
0
2
0
1
2
0
2
2
1
2
0
0
2
1
1
1
0
1
1
1
1
2
1
1
1
0
1
0
1
0
1
0
1
2
1
1
1
0
1
1
2
1
0
0
1
1
0
1
2
2
1
2
2
0
1
1
1
1
0
1
0
2
1
1
1
3
1
0
0
2
1
3
1
0
1
1
2
2
0
1
2
0
1
1
0
0
0
1
1
2
1
0
0
0
2
1
0
1
0
1
1
1
1
1
0
0
0
0
1
1
1
1
1
2
2
0
0
0
1
1
0
0
0
2
1
1
1
0
0
2
1
1
1
2
1
1
1
0
2
2
0
1
0
0
1
1
0
0
1
1
1
2
2
1
1
1
0
0
1
0
0
1
1
1
1
0
1
1
0
0
1
0
1
2
1
1
0
1
2
1
2
2
0
1
1
1
1
1
3
1
1
2
1
1
2
2
1
1
2
1
1
0
0
2
1
1
2
1
2
1
1
0
0
1
1
3
1
1
1
2
1
1
1
1
1
1
0
1
1
1
1
2
1
0
0
1
1
0
1
1
1
1
1
1
1
1
0
2
1
2
1
2
1
1
2
1
1
0
1
3
0
1
1
1
1
1
2
1
1
1
1
0
2
1
1
2
2
2
1
1
0
1
1
1
1
1
2
1
2
0
2
0
2
1
1
0
4
1
0
1
1
2
1
1
2
2
0
0
1
1
0
2
1
2
1
0
1
1
0
0
1
1
1
1
1
2
0
1
2
1
2
1
1
0
1
1
0
1
0
1
1
2
0
2
1
1
1
1
0
0
1
1
1
0
0
1
0
0
1
0
1
2
1
1
1
1
1
1
0
1
1
3
2
1
1
1
0
1
0
1
0
0
1
1
1
0
1
1
1
1
2
2
1
3
1
1
1
1
9
2
1
1
1
2
1
0
1
0
1
2
2
2
1
1
0
1
1
1
0
1
1
0
1
2
1
1
1
1
3
1
2
1
0
1
1
1
1
2
1
2
0
2
2
1
1
1
2
1
3
0
0
1
0
2
1
1
2
1
3
0
1
0
1
1
1
2
1
0
1
0
1
2
1
1
0
1
0
2
1
1
1
0
0
2
0
1
0
2
1
2
1
1
1
0
1
0
1
1
1
2
0
1
1
1
1
0
0
1
0
0
0
2
1
1
1
0
1
1
1
0
2
1
2
1
1
0
2
1
1
1
2
0
1
1
1
2
2
1
2
1
3
1
0
1
0
0
1
1
1
1
0
2
0
1
1
2
0
1
0
0
0
1
0
2
0
0
2
0
2
1
1
1
2
1
1
0
0
2
1
0
1
2
1
1
2
2
1
1
2
2
1
2
1
0
1
0
2
1
1
2
1
1
2
0
1
0
0
2
1
1
1
1
1
0
1
1
1
2
1
1
4
1
2
1
0
1
0
1
0
2
1
1
1
2
1
0
1
1
2
1
1
0
0
0
0
1
1
1
2
0
2
1
2
0
2
2
2
0
1
0
0
1
2
2
2
0
3
0
2
0
1
2
1
1
1
2
0
1
2
1
1
3
1
1
0
2
2
0
0
2
0
1
2
1
1
0
2
0
2
1
1
1
1
2
0
1
2
0
2
2
1
0
1
1
1
1
1
1
1
1
1
2
1
0
1
1
0
1
2
0
0
1
0
1
0
1
1
0
2
0
0
1
1
1
1
1
1
0
2
2
0
1
0
2
1
0
0
0
2
1
1
1
3
1
1
0
0
5
1
1
1
1
1
1
2
1
1
1
1
0
0
2
0
1
1
0
0
1
1
1
1
1
1
1
1
2
2
1
1
2
0
0
1
2
0
0
1
2
0
0
1
2
2
0
0
0
1
3
1
2
1
1
1
1
1
0
2
0
0
0
1
0
0
1
0
1
1
0
1
2
0
0
1
1
0
1
1
1
2
1
1
1
2
2
1
1
1
1
2
2
0
1
0
0
2
0
1
2
1
1
2
1
1
1
0
2
1
1
0
1
1
1
0
0
1
0
1
1
1
0
0
1
2
1
1
2
0
0
0
0
0
0
1
1
1
1
1
1
1
1
0
1
2
1
1
0
1
1
5
1
1
1
1
0
0
1
1
0
0
3
2
1
2
2
1
1
1
0
0
1
0
0
0
1
2
1
1
0
2
1
1
2
0
0
2
0
0
0
0
1
0
0
1
1
1
0
2
1
0
0
0
1
1
2
1
0
0
1
1
1
2
1
0
1
1
1
1
0
0
1
0
1
1
1
2
0
1
1
1
1
2
1
2
1
2
1
0
1
2
1
1
0
0
2
1
0
0
1
1
1
0
1
1
1
2
1
0
1
1
2
2
0
0
0
1
1
0
1
0
0
2
1
1
1
1
1
2
1
1
2
0
0
2
0
2
2
1
1
0
2
1
1
1
1
0
1
2
0
1
2
1
0
1
0
1
0
1
2
0
1
1
2
1
1
1
1
0
1
1
5
0
0
1
0
1
2
0
2
1
2
2
0
2
1
1
2
2
1
1
0
1
0
0
1
1
1
0
1
1
1
2
0
1
0
1
1
0
1
1
2
1
1
0
1
0
0
1
1
1
0
0
2
2
1
1
1
1
2
1
0
1
2
2
1
0
0
2
1
0
1
2
0
2
0
1
1
1
1
2
1
0
0
1
0
0
1
1
1
1
1
0
2
1
2
0
1
0
1
0
2
0
0
1
1
0
1
1
2
1
1
1
1
1
1
1
0
1
1
0
1
1
1
1
2
1
1
0
1
1
0
2
0
2
1
1
0
1
1
2
1
1
1
1
1
2
2
1
1
0
1
0
0
0
0
1
0
0
1
0
1
0
1
1
1
0
1
2
1
3
1
1
0
1
0
1
0
2
1
2
1
0
1
0
2
1
2
1
1
1
2
1
2
1
1
1
1
2
1
1
0
1
1
1
1
1
2
0
2
2
1
1
1
1
2
1
1
1
1
1
1
1
1
0
1
0
0
1
2
1
1
0
1
1
1
2
1
1
0
1
1
1
1
0
2
0
2
1
1
1
3
0
2
1
2
1
1
0
1
0
1
1
1
1
2
1
2
1
1
2
1
1
0
1
2
0
0
0
0
1
0
0
1
1
1
0
1
0
0
0
1
0
1
1
1
1
2
1
1
2
0
1
2
1
0
1
1
2
0
2
1
0
2
1
2
1
0
0
0
2
1
1
1
1
1
1
1
0
1
1
1
1
1
1
2
1
3
0
2
1
0
1
1
0
2
0
2
2
2
1
1
0
0
1
1
0
2
0
0
2
3
2
1
0
0
2
1
1
0
1
0
0
1
0
1
1
0
1
1
1
1
1
1
1
0
1
1
1
1
2
1
1
2
0
2
2
2
1
2
1
2
1
2
2
0
0
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
0
1
1
1
0
1
0
2
0
0
0
1
1
1
1
0
2
0
1
0
1
2
0
2
1
1
3
2
0
1
0
1
1
1
2
1
0
1
0
0
2
1
1
0
0
1
1
1
2
2
1
0
2
1
0
1
1
1
2
0
0
0
1
1
2
1
1
1
2
1
0
2
0
1
1
2
2
1
0
1
1
0
1
1
2
1
1
0
1
0
1
1
2
1
0
1
1
1
2
1
1
2
0
1
1
1
0
0
1
1
1
1
1
0
1
1
1
1
2
1
0
1
0
0
1
1
1
2
1
1
1
1
0
1
1
0
1
0
1
1
1
1
0
2
1
2
0
1
2
1
1
1
0
1
2
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
2
1
2
1
1
0
1
1
0
1
1
1
2
1
2
0
1
1
2
1
0
0
0
1
0
2
0
2
2
1
1
1
1
1
1
2
1
0
0
2
2
1
0
1
1
1
2
1
2
1
2
2
2
0
1
1
1
1
1
1
2
2
1
1
1
1
0
0
2
0
0
0
1
2
1
1
2
1
0
1
0
1
2
1
1
1
0
1
1
1
0
0
1
1
1
0
1
0
1
1
1
2
0
1
1
2
1
1
1
2
2
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
0
1
1
0
1
2
2
1
2
1
1
0
0
1
1
1
6
1
1
0
0
3
1
0
1
0
1
0
2
2
2
1
1
1
1
2
0
0
1
2
0
2
1
1
0
1
2
1
1
2
2
1
2
1
0
2
1
0
0
1
0
0
0
1
2
2
2
1
1
2
0
1
1
0
1
2
1
1
0
1
1
1
1
2
1
1
0
2
1
1
0
1
0
1
1
1
1
0
1
1
1
1
1
0
1
1
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
0
0
0
0
1
2
1
2
1
1
2
1
1
0
0
2
0
2
1
3
1
1
1
1
0
0
2
1
2
0
1
1
1
2
2
1
1
2
1
0
1
2
1
1
1
1
1
1
1
0
0
1
1
1
1
1
1
0
1
1
1
0
1
0
1
1
1
0
1
1
2
1
2
2
1
1
0
1
2
0
1
1
1
0
1
0
1
0
1
1
0
1
0
1
1
1
0
1
1
2
1
1
1
0
2
1
2
2
1
1
1
2
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
0
2
1
1
2
1
1
2
2
1
2
1
1
1
0
0
2
1
0
0
1
0
1
3
1
2
1
0
2
1
1
0
1
1
1
1
0
2
1
1
2
2
0
4
2
3
1
1
2
1
1
0
0
0
1
0
0
2
0
1
1
0
1
0
1
1
1
2
0
0
0
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
0
1
2
0
0
1
2
1
0
1
0
1
1
0
1
1
0
1
0
1
0
0
1
0
2
4
1
1
1
0
0
1
1
1
1
1
1
1
0
1
2
0
1
1
1
0
0
2
0
1
1
2
0
2
3
1
2
1
1
0
1
2
1
1
0
1
1
0
0
0
2
0
2
1
2
0
2
0
1
1
1
0
0
1
0
0
1
1
1
0
1
1
1
1
1
1
2
1
1
0
0
1
1
1
1
1
2
1
2
2
2
1
1
1
2
2
0
0
1
0
0
1
2
1
0
1
0
0
2
2
0
1
0
3
1
2
0
1
1
0
3
0
1
1
2
0
1
1
1
1
0
1
0
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
2
2
2
2
1
1
0
3
1
1
2
2
1
1
1
2
1
2
0
0
1
1
0
1
2
2
1
1
0
2
1
1
1
0
2
0
0
0
0
1
1
2
1
1
0
2
0
1
2
1
0
0
1
0
1
1
2
1
1
2
1
1
0
1
2
1
1
1
1
1
2
3
1
1
1
1
0
1
0
1
0
1
1
1
1
0
2
1
2
1
2
1
2
1
1
1
2
1
0
1
1
1
1
2
2
1
0
2
1
0
2
1
1
1
0
1
1
1
1
1
1
1
1
2
1
0
0
0
1
1
0
1
0
0
1
0
0
2
2
0
1
1
1
0
1
0
1
1
2
1
2
2
1
2
1
2
1
2
1
2
1
2
1
1
0
0
1
0
1
0
1
2
1
1
1
1
1
1
1
1
3
0
0
2
2
1
1
2
1
1
1
0
1
1
1
1
1
1
1
1
2
1
0
1
2
1
2
1
0
1
0
0
1
0
2
2
1
0
2
1
1
1
1
1
0
2
2
0
1
1
1
1
2
1
1
1
0
1
0
0
1
2
0
0
0
2
1
2
1
1
0
0
2
2
1
1
1
2
1
0
1
1
0
1
1
1
0
0
0
2
1
1
1
0
3
0
0
2
1
3
4
0
1
1
1
2
0
1
1
1
2
1
2
1
1
1
2
1
2
0
1
0
1
1
1
0
1
2
2
0
1
1
0
1
1
1
0
3
1
2
1
1
1
0
1
0
2
1
1
1
1
2
1
1
1
1
1
1
0
1
1
1
0
0
2
0
1
1
0
0
0
1
1
0
0
1
1
0
1
1
0
2
1
1
2
0
1
1
3
1
0
2
1
1
0
0
1
1
1
1
1
1
0
1
1
1
0
1
1
0
1
2
2
1
1
1
1
1
2
0
1
2
0
0
1
1
2
0
1
1
2
1
1
2
0
0
1
1
1
2
1
0
1
2
1
2
2
2
0
2
1
2
0
2
2
1
2
1
1
1
0
1
0
2
1
1
1
2
2
0
0
2
1
1
0
1
1
0
1
2
1
1
0
1
2
0
0
0
1
1
1
2
1
1
1
1
2
2
1
1
2
1
2
1
0
1
1
1
1
1
2
0
1
0
0
0
1
2
0
0
1
2
1
0
1
2
2
1
0
2
0
0
1
1
0
0
2
1
1
1
2
1
2
1
2
1
1
0
1
0
1
1
2
1
1
1
2
1
1
1
0
2
2
2
0
0
2
1
4
1
1
0
0
0
2
1
0
2
2
0
2
2
1
1
1
1
1
1
2
1
1
1
1
0
2
2
1
0
0
1
1
1
0
1
1
2
1
1
0
1
2
0
1
0
1
2
2
1
2
0
0
1
1
1
2
2
0
2
0
1
2
0
1
0
1
2
1
1
2
1
1
1
1
2
1
1
0
0
0
1
1
1
1
2
1
1
1
1
2
2
1
1
0
2
2
2
0
1
0
1
1
1
3
1
1
1
1
1
1
2
1
1
0
2
0
1
2
1
1
2
1
1
0
1
1
1
2
1
1
2
2
1
1
2
3
1
2
2
1
2
2
1
1
0
0
1
2
1
2
1
2
1
0
1
0
1
2
1
0
2
1
1
2
1
2
1
2
1
0
1
2
1
2
2
1
1
2
1
1
1
1
0
0
1
1
1
1
1
1
0
1
0
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
0
1
1
1
1
1
2
1
1
2
1
1
1
2
2
1
0
0
1
1
0
1
1
0
1
1
1
2
1
0
1
0
0
0
1
0
1
1
2
1
0
1
2
1
2
0
2
0
1
2
2
1
0
1
2
0
1
0
0
0
1
1
0
2
0
2
1
1
0
2
1
1
1
1
1
1
2
0
1
0
1
0
1
1
2
1
1
1
0
1
0
1
1
1
1
1
0
0
1
1
0
1
2
1
1
0
1
2
2
1
1
2
2
2
1
1
0
1
1
2
1
1
1
0
0
0
1
1
1
1
1
2
1
1
1
1
2
1
0
2
1
1
1
1
1
0
0
2
0
1
1
1
0
0
2
1
0
1
2
0
0
0
2
1
0
0
2
1
1
1
1
0
2
2
1
2
0
1
0
1
0
0
0
2
2
1
0
1
1
1
1
0
1
2
1
0
2
0
2
1
1
2
1
2
2
2
2
1
0
1
1
0
1
2
1
0
1
3
2
1
1
1
1
2
1
0
0
1
1
3
1
1
0
0
1
2
1
1
3
1
2
1
1
1
0
1
1
1
2
0
2
0
1
1
2
0
1
2
0
1
0
2
1
1
1
1
1
1
0
1
1
0
1
1
0
1
1
2
0
2
0
0
2
0
1
1
0
1
1
1
0
0
2
1
1
1
1
0
2
1
1
1
0
1
1
1
0
4
2
2
1
2
1
1
1
1
0
2
1
1
1
2
1
0
1
1
1
1
1
2
2
1
0
0
1
2
0
2
2
1
2
1
1
1
0
2
1
1
1
2
1
2
2
1
1
1
1
0
1
0
0
1
1
2
2
1
2
1
1
2
2
1
1
1
2
0
1
2
0
0
0
1
1
2
1
1
2
0
0
1
2
0
0
1
1
1
1
2
1
2
1
1
1
2
2
0
2
2
0
0
1
0
3
1
1
1
1
1
1
1
1
3
0
0
0
1
1
0
2
0
1
1
1
0
0
0
1
2
1
1
1
0
1
1
2
1
1
2
0
2
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
2
0
1
0
1
1
2
1
1
1
1
0
1
0
0
0
1
2
1
0
1
1
1
1
1
1
1
2
1
2
1
0
1
1
2
1
0
0
2
2
2
1
2
2
2
1
1
0
1
1
1
1
0
1
2
1
3
0
3
2
0
1
1
2
2
1
1
1
1
1
1
0
0
2
2
0
1
0
1
1
4
1
1
0
1
0
1
1
1
0
1
2
0
1
1
0
0
1
1
1
1
1
1
5
0
1
1
0
2
0
2
2
1
0
0
0
1
1
1
0
1
2
1
2
1
2
1
1
1
0
1
1
2
1
1
1
2
0
0
1
1
1
0
0
0
0
2
3
1
1
0
2
2
1
1
1
1
1
0
0
1
0
0
1
1
1
1
1
1
1
1
0
2
1
1
0
1
0
1
1
2
1
0
1
1
0
1
1
1
0
0
1
1
0
0
1
0
0
1
1
0
0
1
2
0
1
1
2
0
3
1
1
1
0
1
1
1
0
0
2
1
2
1
0
1
1
0
2
1
0
1
0
1
1
1
0
2
1
0
0
0
1
2
1
0
1
3
1
2
2
2
1
1
2
1
0
0
1
1
2
1
1
0
1
1
1
2
0
1
2
1
0
0
1
1
2
2
1
1
2
1
1
1
0
2
3
0
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
0
1
1
0
1
1
1
1
0
4
2
2
0
0
1
2
0
2
0
4
1
1
2
1
2
1
2
2
0
0
2
1
0
1
0
1
1
0
1
0
0
0
1
1
1
1
0
2
1
2
2
1
1
1
1
0
1
0
1
2
1
0
1
2
1
1
0
1
1
1
1
2
1
0
2
1
2
1
0
1
1
0
1
1
1
1
1
2
1
1
1
0
1
2
1
1
0
0
0
1
1
1
1
1
2
1
1
0
2
2
1
1
1
2
2
1
0
2
1
1
1
1
1
0
2
0
1
0
1
0
0
1
0
1
2
2
1
1
1
1
1
1
1
0
1
2
1
1
1
0
1
2
0
0
0
0
1
1
1
0
2
2
1
0
0
1
1
1
1
2
1
2
1
1
1
2
2
1
0
2
0
1
4
2
1
2
2
1
0
1
0
0
2
1
2
1
2
0
0
1
2
1
2
1
2
1
2
1
1
1
1
2
2
1
1
1
2
1
2
1
1
0
1
2
1
2
2
1
0
1
1
1
0
1
2
1
2
1
1
1
2
2
0
1
1
2
1
2
2
1
0
1
1
0
1
1
1
1
0
1
0
2
1
0
1
1
0
5
2
2
1
1
0
0
1
2
1
1
1
0
0
1
0
1
1
1
1
0
3
1
0
1
2
2
2
1
1
0
2
1
1
1
1
1
1
2
0
1
2
1
1
1
2
2
1
0
2
1
1
1
0
1
1
0
2
1
1
1
2
1
5
0
1
2
1
0
0
1
0
1
2
1
2
1
1
1
1
2
2
2
0
2
2
1
2
2
2
1
0
1
1
0
1
1
0
1
0
1
0
2
2
1
2
2
1
3
1
0
1
2
0
0
1
0
1
0
1
1
0
1
1
0
1
0
1
1
1
1
1
1
2
1
2
1
2
1
1
1
1
1
2
2
1
1
1
0
0
1
1
0
1
1
2
1
0
1
1
2
0
2
0
1
0
1
1
1
1
2
1
1
1
1
1
1
1
2
1
0
1
2
1
1
0
1
1
1
1
1
1
1
2
0
1
1
0
2
1
1
1
1
1
0
1
2
2
3
1
0
1
0
1
1
1
1
1
2
0
1
1
1
2
2
0
2
1
1
1
1
1
0
1
1
1
1
2
1
1
0
1
1
1
0
2
0
2
1
0
2
1
1
1
1
2
1
1
0
1
1
0
1
1
0
0
1
1
1
0
1
1
1
1
1
1
1
0
1
2
1
1
1
1
1
1
1
0
0
0
1
1
1
0
1
2
1
2
2
1
0
0
1
1
1
2
0
1
2
2
2
1
2
1
1
1
0
1
0
1
1
1
2
1
0
1
0
2
1
0
0
1
1
1
0
0
1
1
3
0
0
1
2
2
0
1
1
2
1
1
2
0
1
1
1
0
0
0
1
0
1
1
1
1
2
2
1
0
0
0
1
0
2
2
0
2
0
1
2
2
2
1
1
0
0
2
1
2
1
0
1
2
1
0
1
0
1
1
1
1
1
0
2
1
1
2
2
1
2
2
0
2
1
1
1
1
1
0
0
2
1
1
0
1
0
0
1
2
1
0
1
1
2
1
0
2
1
1
1
0
1
1
0
1
1
2
1
0
1
1
1
2
1
1
1
1
2
0
1
1
1
1
1
2
2
0
0
1
0
1
0
1
1
2
2
1
1
0
1
1
1
0
1
1
1
2
2
1
1
1
2
1
0
0
1
3
1
2
1
1
1
0
1
1
3
1
1
1
1
1
1
2
2
0
1
1
0
1
1
1
1
0
2
2
1
0
1
1
1
1
1
1
1
1
1
0
2
2
1
0
0
2
2
1
1
1
2
1
1
1
2
0
2
1
1
0
1
1
0
1
0
2
1
0
5
1
1
1
1
1
1
1
5
1
0
2
1
1
1
1
0
0
1
1
1
2
2
2
1
2
1
2
0
0
0
2
1
1
2
1
2
1
1
2
2
2
1
1
2
1
1
0
2
1
0
1
1
2
0
2
1
0
0
1
0
1
0
0
0
0
2
0
1
2
1
1
2
0
1
2
1
0
2
2
2
1
1
1
1
1
1
0
1
1
0
0
2
0
1
0
1
1
2
0
1
1
1
2
1
0
1
1
1
1
1
1
0
1
1
1
1
1
1
0
1
1
0
1
2
1
1
0
0
3
1
1
1
2
2
2
0
1
1
0
2
1
0
0
1
2
1
1
3
1
1
0
2
1
0
1
1
2
0
0
1
0
1
1
2
1
1
0
1
1
1
1
1
1
2
1
1
1
2
0
0
1
1
1
0
1
1
1
0
0
0
1
2
2
1
1
1
0
1
1
0
2
1
0
0
2
1
1
1
1
2
1
0
1
1
0
0
2
1
2
1
1
0
1
2
1
1
1
1
1
2
1
0
0
0
1
1
1
2
2
1
1
2
1
1
0
1
1
1
1
1
1
1
1
1
2
2
1
2
2
1
1
1
0
1
1
2
1
2
2
1
1
1
1
1
0
1
2
0
0
0
0
0
1
2
2
2
1
2
0
1
1
1
0
1
0
1
0
1
1
1
1
1
1
1
1
0
1
1
1
1
0
1
1
2
1
2
0
1
1
1
2
1
1
1
1
2
1
1
0
2
1
1
1
2
2
2
0
1
2
0
2
0
2
2
0
1
0
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
1
1
2
1
1
2
1
2
1
1
1
0
1
1
1
2
0
1
1
0
3
0
1
2
1
1
1
3
1
0
1
2
1
2
1
1
1
2
1
2
0
1
2
1
2
1
2
1
1
1
0
1
0
0
0
1
2
1
1
1
1
1
1
3
1
1
1
1
1
1
2
1
1
2
1
1
2
2
1
1
1
1
1
2
1
1
1
0
0
0
1
0
0
1
1
0
1
1
1
1
0
1
2
2
1
1
2
1
2
0
0
2
1
1
1
2
3
1
1
1
0
0
1
1
1
1
0
1
1
1
2
1
0
1
1
2
2
1
0
2
0
0
0
1
0
0
2
0
1
0
1
1
1
1
1
1
2
0
0
2
1
1
0
2
1
1
0
1
1
1
1
2
1
1
1
0
1
1
1
1
1
0
1
1
0
0
1
1
0
1
1
1
1
1
1
0
2
1
0
2
2
0
1
0
1
0
2
1
1
1
2
2
1
1
1
2
1
2
2
1
0
2
1
1
0
1
2
1
0
1
1
0
2
1
1
0
1
1
0
1
1
2
1
1
0
2
1
2
0
1
1
1
1
1
2
1
1
0
1
1
0
1
1
1
0
2
0
2
0
1
1
0
1
2
0
1
1
2
1
1
1
2
0
1
0
1
1
1
1
1
0
2
1
1
1
1
1
1
2
1
1
1
0
2
1
0
1
0
1
1
1
1
2
1
1
1
2
1
1
0
1
0
3
2
1
1
1
1
2
0
1
2
1
1
1
2
1
0
1
1
2
1
1
1
0
1
0
0
2
1
2
1
0
2
1
1
1
1
2
0
1
0
1
1
0
2
2
0
0
2
1
1
1
1
2
2
2
1
1
1
1
0
0
0
1
1
1
1
1
1
1
1
1
1
0
2
1
1
0
0
1
0
0
2
2
2
1
0
1
0
1
1
1
1
1
1
1
0
1
0
1
0
1
1
0
1
0
1
1
1
0
1
2
1
0
2
1
2
1
2
1
1
2
1
5
1
1
2
2
1
1
1
1
0
2
1
0
1
1
0
1
1
1
1
0
1
2
0
1
2
1
2
1
2
3
1
1
2
0
2
1
1
1
2
0
2
1
1
0
0
1
1
2
1
1
1
1
1
1
0
1
1
1
1
1
3
1
1
2
1
1
1
0
1
1
1
1
1
0
2
0
0
1
1
0
2
2
1
4
1
1
1
2
2
0
1
0
1
2
0
0
2
1
1
1
1
1
2
1
1
1
1
2
1
0
0
1
1
0
1
3
2
1
1
0
2
1
1
0
1
1
1
2
1
1
1
1
2
1
1
2
1
1
0
1
1
1
1
1
2
2
0
0
2
1
1
1
2
0
0
0
2
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
0
1
2
1
1
2
1
1
2
1
1
0
2
1
1
1
2
2
1
0
1
1
2
1
0
0
2
1
2
1
2
1
1
0
1
0
1
0
2
1
0
1
2
2
1
1
3
1
2
2
1
0
0
0
1
2
1
1
1
1
1
0
1
0
0
0
2
3
0
2
1
1
1
1
1
0
1
1
1
2
0
0
0
0
1
1
0
2
0
0
1
1
0
1
1
2
2
2
0
0
1
0
0
0
1
1
1
1
2
1
0
1
1
1
1
0
0
1
0
1
1
2
1
1
2
0
1
1
0
2
1
1
1
0
1
2
1
1
1
1
0
1
2
1
0
0
0
2
0
1
0
1
1
0
1
2
2
1
1
2
1
1
2
0
2
1
0
0
0
0
2
2
2
1
1
1
0
1
0
1
0
1
0
1
1
1
2
1
2
2
1
1
2
2
0
1
0
2
0
2
1
1
2
1
1
1
0
0
0
1
1
2
1
1
1
2
2
1
2
1
1
1
0
1
1
3
0
0
1
2
1
1
1
1
1
2
2
1
1
1
1
1
1
1
0
1
2
1
1
2
2
0
0
2
2
0
2
2
1
0
1
1
1
0
0
0
1
0
1
1
2
1
1
1
1
2
1
1
0
1
0
1
0
1
1
0
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
0
3
1
0
0
2
1
1
0
2
2
2
1
1
1
1
2
2
2
0
0
1
1
2
1
1
1
1
1
1
2
1
1
0
1
2
1
0
1
0
1
2
1
1
1
2
1
0
1
1
1
1
0
0
0
1
1
0
1
2
0
1
2
2
2
2
1
2
1
1
1
1
0
2
2
1
1
1
1
1
1
1
1
1
1
2
0
0
1
1
1
1
2
1
0
1
1
2
1
2
1
1
1
1
1
1
2
1
1
2
1
0
2
1
1
1
0
0
2
1
1
0
1
0
0
1
2
1
2
0
1
0
0
2
1
2
0
0
1
1
2
1
0
2
2
2
1
1
1
1
1
1
1
2
1
2
2
0
1
1
1
1
0
1
0
1
1
8
1
1
1
0
1
1
2
1
1
0
2
1
1
0
1
0
1
0
1
0
1
1
2
2
1
1
1
1
1
2
1
0
1
1
1
1
1
1
0
1
1
2
2
1
1
2
0
1
3
0
2
2
0
2
0
1
0
0
1
0
1
0
1
1
1
2
1
2
1
1
0
2
1
1
1
2
1
1
2
1
2
0
2
1
1
0
1
1
1
1
0
0
1
1
1
1
2
1
0
0
2
1
1
1
1
1
1
0
2
1
1
1
0
1
2
2
2
1
1
1
1
2
1
3
1
0
1
1
1
1
1
1
1
0
1
1
2
1
0
2
0
2
1
1
0
0
2
1
1
1
1
0
0
2
0
0
4
1
1
0
0
1
1
1
1
2
0
1
0
0
1
0
0
0
1
0
1
1
1
2
1
1
0
1
2
1
1
0
1
1
5
1
1
0
1
1
0
0
0
1
1
1
2
2
1
2
0
0
2
2
2
1
1
1
2
0
1
1
2
2
0
1
2
0
1
2
2
2
1
1
1
1
1
1
1
1
2
1
0
1
2
1
1
1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
0
1
2
1
2
0
1
2
1
1
1
2
1
1
1
2
0
1
0
2
1
1
1
0
1
0
0
1
1
2
1
1
1
1
2
1
1
1
0
1
1
0
1
1
2
2
1
2
2
1
2
0
2
1
1
1
1
0
2
1
0
2
2
1
0
1
1
1
0
1
2
1
1
2
2
0
0
1
0
0
1
1
1
1
1
1
2
1
2
1
2
1
1
0
1
0
0
0
2
1
0
2
2
2
1
1
0
1
2
1
1
1
1
0
2
0
0
2
1
1
1
2
1
1
0
0
1
2
1
1
1
1
0
1
0
0
1
2
0
0
1
0
0
1
2
0
0
2
2
2
2
1
0
1
1
0
1
0
1
0
1
2
0
0
2
2
1
2
0
1
1
1
0
0
1
1
1
1
1
1
0
1
0
0
2
1
3
0
0
1
1
1
1
0
2
2
1
0
0
0
2
2
2
1
1
0
1
1
1
1
3
0
2
1
0
2
2
0
1
1
1
2
1
1
0
1
1
2
1
0
1
1
0
0
2
1
2
1
1
1
1
2
0
1
1
1
1
1
1
1
1
1
1
1
0
1
2
1
0
0
1
0
1
1
1
1
2
1
1
1
2
1
1
0
1
1
0
2
1
1
0
1
1
2
0
0
1
1
1
2
2
0
0
1
0
0
2
1
1
1
1
1
1
1
0
2
1
1
0
1
1
1
1
1
0
0
1
1
1
0
2
0
1
1
0
2
1
1
1
0
0
1
1
0
1
1
1
1
1
1
1
1
1
2
1
1
0
0
1
1
0
2
1
2
1
1
2
1
0
1
2
1
1
1
1
0
1
0
1
1
1
2
1
1
2
0
2
2
1
0
2
1
1
1
1
0
1
1
2
1
0
0
0
2
2
1
0
2
1
1
2
1
0
1
0
1
2
0
2
0
1
0
1
1
0
0
4
0
1
1
0
2
0
1
1
0
1
0
0
2
2
2
2
1
0
0
0
2
0
1
1
1
1
0
1
1
1
1
0
3
1
1
1
1
2
0
1
0
1
1
1
1
1
1
2
2
1
1
1
2
1
2
1
0
0
1
1
1
1
1
1
0
1
1
1
1
1
1
0
1
1
1
1
0
1
1
1
0
1
1
0
6
1
0
1
1
2
0
1
1
1
0
0
1
1
2
1
1
2
1
1
1
2
1
0
1
2
1
1
1
2
2
2
1
1
1
2
0
1
3
1
0
1
0
2
1
1
0
1
3
1
1
0
2
1
1
0
1
0
1
0
0
1
1
1
2
1
1
1
2
1
0
1
2
1
1
1
0
0
1
2
1
2
2
0
0
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
2
1
0
1
1
1
1
2
0
1
1
0
1
2
0
0
0
1
2
1
1
1
2
2
0
1
0
0
0
1
1
1
1
1
1
0
1
1
1
1
0
2
2
1
0
1
1
2
0
1
1
0
0
1
2
1
1
1
2
1
2
1
0
2
1
1
1
1
3
0
1
1
2
2
0
1
2
1
2
2
1
1
0
0
1
1
2
2
3
1
1
1
1
1
2
2
1
1
1
2
1
1
1
2
1
0
2
1
1
2
0
1
1
1
2
2
0
0
1
2
1
2
2
1
1
1
1
1
2
0
2
1
1
1
0
2
1
1
0
1
1
1
1
1
1
0
0
1
0
1
1
1
1
1
1
1
1
2
1
1
2
2
0
0
1
3
1
1
1
2
2
2
1
1
1
1
1
1
1
0
1
0
1
0
1
0
1
1
2
2
1
1
1
2
0
3
2
2
1
0
1
1
1
2
1
0
1
1
1
2
2
1
0
2
1
1
1
2
1
1
1
1
1
1
1
3
2
1
1
0
0
1
1
0
0
0
6
1
1
1
1
2
1
2
1
1
0
1
2
1
1
1
2
0
4
1
0
3
2
2
2
1
1
2
1
1
1
2
1
1
0
1
0
0
1
1
0
1
1
1
1
2
1
1
2
2
2
2
2
1
1
2
2
1
1
2
0
2
1
1
0
1
2
2
0
0
1
2
1
1
1
1
1
1
1
2
1
1
1
0
1
1
2
1
1
1
1
1
2
1
1
2
1
1
1
2
1
0
0
2
0
1
0
1
1
1
0
1
1
1
0
1
0
0
2
1
1
1
1
1
1
0
2
1
0
0
1
1
1
1
0
1
1
0
0
2
1
2
0
0
0
1
1
0
0
1
0
2
0
1
0
1
2
1
0
1
1
0
1
2
0
0
2
2
1
0
1
2
1
1
0
1
2
1
1
0
1
1
0
1
1
1
1
0
0
1
0
2
0
1
1
1
1
1
0
1
1
1
1
1
1
2
1
0
0
1
0
2
1
1
1
1
0
0
1
0
1
0
1
1
0
2
1
1
0
2
0
1
1
0
3
1
1
1
1
2
1
1
0
1
1
1
1
1
0
2
2
0
1
2
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
2
0
2
0
2
0
1
1
4
0
1
0
1
1
1
2
1
1
1
2
4
2
1
1
1
1
2
0
1
1
1
1
1
1
2
1
0
1
1
1
1
2
0
1
0
1
1
2
2
1
0
1
1
0
1
1
2
0
1
1
0
1
1
0
1
1
0
1
2
0
2
2
1
0
0
2
1
1
3
1
1
0
1
1
1
0
1
2
0
1
2
2
2
1
1
4
1
0
1
0
1
2
1
1
2
2
0
0
0
1
1
0
2
1
1
1
1
1
2
2
1
2
0
2
1
2
2
0
1
1
1
1
0
1
1
0
0
1
1
0
0
2
1
1
1
1
2
1
0
0
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
0
3
1
2
0
1
2
2
0
2
2
0
0
1
1
0
2
1
2
2
2
0
1
1
2
1
1
0
1
1
1
0
1
1
2
1
0
1
0
0
0
1
1
2
0
0
0
0
1
1
2
0
1
1
1
1
1
0
0
1
1
1
0
0
0
2
0
1
1
1
1
0
2
0
1
2
1
1
2
1
2
0
0
1
1
1
1
1
1
0
1
1
1
0
0
0
0
1
1
1
2
1
2
2
1
1
1
2
1
1
1
5
0
1
2
0
1
1
1
0
2
1
1
1
1
1
2
0
3
1
2
1
2
1
1
0
1
2
1
2
1
1
0
0
1
1
0
1
2
1
2
0
1
1
0
1
1
0
0
1
1
1
1
1
1
2
2
2
1
2
1
2
1
1
2
1
2
1
1
1
0
2
0
2
1
1
1
1
1
2
1
1
0
1
1
2
1
1
0
0
2
0
2
1
1
2
1
1
1
2
0
1
1
0
2
0
1
1
0
0
1
1
0
0
1
1
1
0
1
1
2
1
1
0
2
0
1
1
1
1
2
0
1
1
1
0
0
1
0
0
2
1
2
1
0
1
2
2
0
2
1
1
2
3
0
1
3
1
2
0
0
2
0
1
2
1
1
2
0
0
1
2
2
1
2
2
1
1
2
1
1
1
2
0
2
1
1
1
1
2
1
2
1
2
0
1
0
0
2
1
0
2
1
0
0
1
1
1
0
1
1
0
0
2
0
1
1
1
1
1
0
1
0
1
1
1
0
2
2
0
2
1
1
1
0
2
0
1
1
1
1
2
0
3
2
2
1
0
0
1
1
3
1
1
2
0
0
1
1
0
2
1
0
1
1
2
1
1
2
2
1
1
1
2
1
1
1
1
2
1
0
1
1
1
0
1
0
1
1
1
2
0
2
1
1
1
0
1
0
1
1
1
0
1
2
1
1
2
0
1
0
1
2
0
1
0
2
1
1
0
0
0
1
1
2
1
1
1
0
0
3
2
1
0
1
2
1
1
2
1
1
0
2
1
2
2
0
0
0
1
1
1
1
0
1
1
1
2
1
1
0
0
0
1
1
1
0
0
0
5
1
1
1
1
0
2
0
1
1
0
1
2
0
0
1
1
1
0
0
1
0
3
1
2
1
2
0
2
1
0
1
0
2
0
1
1
0
2
2
1
1
1
1
1
1
1
1
1
2
1
0
2
1
0
2
1
0
1
1
1
1
3
1
1
1
0
1
2
1
1
2
0
0
1
1
0
3
1
1
1
1
1
1
1
2
2
2
2
1
1
1
2
1
0
1
2
2
1
1
1
2
1
2
2
2
2
0
0
0
2
1
1
1
2
0
2
2
2
1
0
1
2
1
1
1
1
1
2
0
1
1
0
1
1
1
2
1
2
1
1
0
0
1
2
2
2
1
2
1
3
0
2
0
0
2
1
0
0
2
1
0
0
0
2
1
2
1
1
0
1
0
2
1
2
1
1
0
2
0
1
1
1
1
1
1
1
1
0
1
1
0
1
1
0
1
2
1
1
0
0
0
1
2
2
1
2
1
2
2
1
1
1
1
0
3
2
1
1
2
1
1
1
0
2
1
1
1
3
0
1
1
2
2
2
1
1
2
0
0
2
1
0
2
2
1
2
0
1
1
2
2
1
1
1
1
1
1
2
1
1
0
1
2
0
1
2
1
1
1
1
1
0
1
0
1
1
1
1
1
1
2
1
0
1
0
1
0
3
0
1
0
1
2
2
1
1
1
1
0
1
1
1
0
0
2
1
1
1
2
1
1
1
1
1
1
1
2
2
2
2
1
1
0
0
1
1
1
0
1
2
1
1
1
0
1
1
0
2
0
1
1
1
0
2
1
0
2
0
1
1
1
1
1
0
1
0
1
0
1
1
1
0
0
1
0
1
2
1
0
1
1
0
1
1
0
0
2
0
1
2
0
1
1
3
0
2
1
1
0
0
1
1
1
1
0
0
0
2
1
2
2
0
1
2
0
0
1
1
1
1
1
1
1
2
1
1
0
2
1
2
1
1
0
1
1
1
1
1
2
0
1
1
2
2
1
1
2
0
1
0
1
0
2
2
0
1
1
1
1
0
1
1
2
1
1
0
1
0
1
1
1
1
1
2
0
3
0
2
0
1
0
2
3
1
0
0
2
1
1
0
1
1
1
1
1
0
2
2
1
0
0
1
1
1
1
1
1
0
2
1
0
1
1
1
1
1
2
1
1
1
1
1
0
1
1
0
2
2
1
0
1
1
1
2
0
1
1
0
1
2
0
2
0
0
1
0
1
1
0
0
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
2
0
2
2
0
0
2
1
1
0
2
1
2
1
0
1
2
1
1
2
2
1
2
0
1
0
1
1
0
1
1
1
1
1
1
0
1
1
2
2
1
1
1
1
1
1
0
2
1
1
1
1
1
2
2
1
0
1
0
0
0
0
1
1
1
0
1
2
1
2
2
0
0
0
1
2
1
1
0
1
2
1
1
1
1
0
2
0
0
2
0
1
2
1
1
2
0
1
2
2
1
2
0
1
1
2
1
2
1
1
2
1
1
1
1
1
1
1
2
1
1
2
1
0
1
1
2
1
1
0
0
1
1
1
0
1
0
1
1
2
0
1
1
2
0
0
1
1
1
2
1
3
0
0
1
0
1
1
0
1
1
2
0
2
1
0
1
2
1
2
1
2
1
1
2
1
2
0
1
2
0
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
0
0
2
1
0
1
1
2
1
0
1
3
2
1
0
1
0
1
0
1
2
0
1
3
1
1
2
1
1
1
0
1
1
1
1
1
1
1
1
1
0
1
0
2
1
1
1
1
2
1
1
2
1
2
2
0
1
1
0
1
0
2
1
1
1
1
1
1
2
1
1
1
0
0
1
1
2
2
1
1
0
2
1
2
1
1
2
2
1
0
1
0
1
1
0
2
2
0
2
1
1
1
2
0
1
0
2
1
0
1
1
2
1
0
1
0
0
1
3
1
0
1
1
1
1
1
1
2
0
1
0
1
2
1
1
0
1
1
1
1
1
2
2
1
0
0
1
1
1
1
2
0
0
1
0
0
1
1
2
2
2
2
2
1
1
1
1
2
2
1
1
1
1
0
2
1
1
0
0
2
2
1
1
1
2
1
0
0
0
2
1
0
0
1
0
1
0
0
1
2
1
2
1
2
1
0
1
1
0
1
1
1
1
2
2
1
1
2
1
1
1
0
1
2
1
1
1
1
1
2
0
1
2
2
2
0
2
2
1
2
0
1
0
2
2
1
1
1
0
2
0
1
0
1
2
0
1
0
1
2
0
1
1
0
1
1
1
0
1
0
0
1
1
1
0
0
1
2
1
0
0
0
2
1
1
1
0
1
0
1
0
1
1
1
0
0
1
1
1
1
0
1
1
2
2
1
1
0
2
1
0
1
1
1
1
1
1
0
2
1
1
0
2
1
1
0
1
1
0
0
1
1
0
1
0
0
0
0
1
1
1
1
1
1
2
2
1
2
1
1
1
1
1
1
0
0
1
1
0
3
1
1
1
2
1
1
0
1
2
0
1
2
1
1
1
1
2
1
0
1
1
0
1
2
2
1
0
2
1
2
0
0
1
1
1
3
0
1
0
2
2
1
2
1
1
1
1
1
0
1
1
0
1
1
1
2
1
1
1
2
0
1
1
1
1
2
1
1
2
1
2
1
2
1
1
1
2
2
1
2
1
2
1
1
2
0
1
0
1
1
0
0
1
1
1
2
2
1
0
1
1
1
1
1
1
1
0
2
1
1
1
1
2
1
1
1
1
1
0
0
0
1
1
1
1
0
1
0
1
1
2
1
1
2
1
2
2
0
0
1
0
1
1
1
1
1
0
1
1
1
1
1
1
0
1
1
1
1
1
0
1
1
0
1
1
2
1
0
0
1
2
2
1
1
1
2
1
2
1
1
2
1
0
1
1
1
1
2
1
2
0
1
0
1
1
1
1
1
1
2
1
0
1
1
2
1
1
1
2
1
2
1
2
2
1
1
2
1
1
2
2
2
1
1
2
2
0
1
2
1
2
1
1
1
0
0
2
2
1
1
0
2
1
1
1
2
1
1
1
0
2
1
1
0
1
1
1
1
2
1
2
0
2
1
3
1
1
0
2
0
1
1
1
2
0
0
0
1
1
2
1
1
1
1
1
1
1
1
2
1
0
1
1
0
1
0
2
1
1
0
1
2
1
2
1
1
2
2
0
1
1
2
1
1
1
1
2
1
2
1
1
1
0
1
1
1
0
0
2
1
1
0
2
2
1
1
1
2
2
1
1
1
2
1
1
1
2
1
1
1
2
1
1
2
1
0
1
1
0
1
1
1
1
2
1
2
1
1
1
2
2
2
1
1
1
2
2
0
1
1
1
1
0
0
2
1
1
0
1
2
0
1
1
1
0
2
0
0
2
0
1
1
0
1
1
2
1
1
1
1
1
2
0
1
1
0
1
1
1
1
1
2
2
1
1
3
2
2
2
0
2
0
1
1
2
2
1
1
1
2
2
0
1
0
1
1
1
2
2
1
1
1
1
1
1
0
1
2
2
2
1
0
1
1
1
2
0
2
2
1
1
1
1
1
1
1
2
1
0
1
0
1
1
0
1
1
1
1
1
1
1
1
2
2
1
1
1
0
0
1
2
1
0
1
1
2
0
1
0
1
2
2
2
1
1
0
1
1
1
2
0
1
1
1
0
0
2
0
0
0
2
2
1
1
1
2
1
1
1
0
1
0
2
1
1
1
1
1
1
0
1
1
3
1
0
1
0
0
1
1
1
1
1
1
1
1
2
0
0
0
1
1
1
2
0
2
0
1
0
1
2
0
1
1
1
0
1
0
2
1
2
0
1
1
2
1
1
0
2
1
1
0
1
1
1
1
1
1
2
0
2
2
1
1
2
1
2
1
2
0
1
1
0
0
0
2
1
0
0
1
0
0
1
1
1
1
1
0
0
2
1
0
1
2
1
0
2
2
1
1
1
2
1
0
2
0
1
1
2
0
2
1
2
1
0
0
1
2
2
1
1
0
2
1
0
1
1
1
0
0
1
0
2
1
1
1
1
0
1
1
1
1
1
1
1
1
1
0
2
2
1
1
2
1
1
1
2
2
0
1
3
1
1
1
1
2
2
2
1
0
2
1
1
2
1
2
1
1
0
1
2
0
1
1
1
1
1
1
0
1
1
0
0
0
1
3
2
0
0
2
2
1
0
1
1
2
1
1
1
2
1
1
0
0
1
2
0
2
0
1
1
1
1
1
1
1
1
2
1
3
1
2
1
2
1
2
1
1
0
1
1
2
2
1
1
1
0
1
1
1
0
1
1
2
2
0
0
1
1
4
2
0
1
1
1
1
1
1
0
2
1
0
0
1
1
1
1
1
1
1
1
1
1
1
0
2
1
1
0
1
2
2
1
0
2
2
0
2
1
2
0
1
1
1
0
2
2
1
1
1
2
1
0
2
1
1
0
1
3
2
1
2
1
2
1
2
2
0
1
1
2
0
1
1
0
2
1
1
2
1
1
3
1
1
1
0
1
1
2
1
1
1
1
2
0
1
0
0
1
1
1
1
1
2
0
1
1
1
0
1
1
1
2
0
1
1
1
2
1
1
1
0
0
2
1
1
1
2
0
1
1
2
1
2
2
0
2
1
1
3
2
1
2
1
1
1
2
1
1
1
2
1
1
1
2
2
1
1
1
2
0
0
2
1
2
1
1
0
1
1
1
2
2
0
0
0
2
1
2
1
1
1
1
1
1
1
1
0
1
0
2
1
1
2
0
1
2
2
0
1
1
1
2
0
1
1
2
1
0
0
1
1
1
0
1
1
1
1
2
1
0
1
1
1
1
0
1
2
3
1
2
2
1
2
1
1
1
0
1
1
1
1
2
1
1
2
2
2
0
0
0
2
0
1
0
0
1
1
1
0
1
1
0
0
1
2
1
0
1
1
1
2
1
0
0
1
0
1
1
1
2
1
0
0
0
0
2
1
1
1
1
2
1
0
1
1
1
1
1
1
1
1
2
0
1
1
1
2
2
1
1
1
1
1
1
1
1
0
2
1
1
2
0
0
1
2
1
0
2
1
1
1
0
0
1
1
1
1
3
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
1
1
2
2
1
1
1
1
0
0
1
0
3
1
1
2
2
1
2
0
0
0
1
1
1
1
1
0
2
1
1
1
2
2
1
1
2
2
1
0
0
3
1
1
1
3
1
1
1
0
0
0
1
0
0
2
0
1
0
1
1
1
1
3
2
1
1
0
1
1
1
1
1
1
1
2
1
2
0
2
1
2
1
1
1
1
2
1
0
1
1
0
0
2
0
0
1
0
1
1
1
1
1
1
1
0
0
0
0
0
2
1
1
1
2
1
1
1
0
0
0
0
0
1
0
1
1
1
1
0
1
0
0
1
1
2
2
1
3
1
1
1
1
0
2
1
1
1
1
2
2
0
1
2
1
0
1
1
2
1
2
2
1
1
1
1
1
1
0
2
0
1
1
1
1
0
1
0
1
1
2
0
0
1
0
1
2
1
1
1
2
2
1
1
2
1
0
1
1
1
0
1
0
2
1
1
1
1
1
2
1
1
0
1
1
2
1
1
2
1
1
0
3
2
2
1
1
1
2
1
1
1
1
0
2
0
2
1
1
2
1
2
1
1
2
2
1
1
1
1
1
1
1
0
0
1
2
2
2
2
0
0
1
1
1
0
2
4
1
2
2
0
1
1
1
0
0
2
1
1
0
0
3
1
2
1
1
1
0
1
0
0
1
2
2
0
2
1
1
2
2
1
1
0
1
0
1
2
0
0
0
1
0
2
2
2
0
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
0
0
1
2
0
1
1
2
2
1
0
0
2
1
2
1
1
0
1
1
2
1
1
0
1
0
0
0
2
1
0
2
1
1
2
0
1
1
2
0
2
0
0
2
1
2
1
1
2
2
1
2
1
2
2
1
1
1
1
1
0
0
1
1
1
0
1
2
2
1
1
1
1
1
2
1
0
1
2
1
1
1
1
1
0
2
1
0
2
0
1
1
1
0
1
0
1
1
1
1
0
2
1
2
1
1
0
1
1
2
1
1
2
1
1
0
0
2
2
1
1
1
1
2
1
1
1
1
0
2
0
0
1
2
1
1
1
0
0
2
1
0
0
0
1
2
2
1
1
0
0
1
1
4
1
2
2
1
1
2
1
1
2
2
1
1
1
2
0
1
1
2
1
3
1
1
1
0
1
2
1
1
1
2
1
0
1
1
1
1
1
1
1
0
1
1
2
1
1
1
0
1
1
0
0
0
0
1
1
1
2
2
2
2
1
1
1
1
1
0
0
2
2
1
1
1
0
2
2
2
0
2
2
2
1
0
3
2
1
1
2
0
1
2
1
2
1
1
1
0
0
1
1
1
1
2
0
1
2
1
0
0
1
1
2
2
1
1
0
1
0
0
0
2
1
1
0
1
2
1
1
1
2
1
2
1
1
1
0
2
1
1
1
1
1
1
0
1
2
0
1
0
0
0
2
1
1
2
1
1
0
1
0
2
1
2
0
0
1
0
0
1
0
2
2
1
1
0
0
1
1
1
1
1
2
1
1
2
1
1
2
0
1
1
1
1
1
0
2
1
0
1
1
2
0
0
1
1
1
0
1
0
1
1
0
2
0
1
1
1
1
0
1
2
2
2
0
2
0
0
0
1
2
1
1
0
0
1
2
0
2
0
0
1
1
1
1
1
2
1
2
0
0
2
1
2
0
1
1
1
0
1
1
0
1
2
1
1
1
0
1
2
1
0
1
2
0
1
3
1
2
1
1
1
1
2
0
1
1
0
1
1
2
0
0
1
0
2
0
1
1
0
4
1
1
0
0
1
2
2
1
1
1
2
2
1
1
2
1
1
0
2
1
2
1
1
1
1
0
2
1
2
1
2
2
1
1
2
2
2
1
1
0
1
0
1
1
0
2
1
1
2
1
1
0
1
1
0
2
0
0
0
1
1
2
0
0
1
1
1
2
1
1
1
1
1
0
0
2
1
1
1
1
1
1
1
0
0
0
1
0
0
1
1
0
2
1
1
0
2
0
0
2
2
1
2
0
0
1
2
1
1
2
1
0
1
1
2
1
1
1
1
1
2
0
0
2
1
1
2
2
0
1
0
1
1
0
0
1
1
1
2
2
1
0
2
1
0
1
2
1
2
1
1
1
1
0
1
1
1
2
2
1
1
2
1
1
1
2
3
1
2
0
2
2
0
1
0
2
1
0
1
1
0
1
1
0
0
2
0
2
2
1
1
2
1
2
1
2
1
0
1
1
2
1
1
1
1
0
0
0
1
1
1
0
1
1
2
1
0
0
0
2
0
1
1
0
1
0
1
1
1
3
1
1
2
1
0
2
1
1
2
1
1
2
0
0
1
1
1
2
0
3
1
1
1
1
1
2
2
1
1
1
1
1
1
0
1
2
1
1
1
1
1
2
3
0
1
2
1
1
1
1
1
2
1
1
0
0
1
1
0
1
0
0
1
1
1
2
1
0
2
1
0
0
1
2
0
1
1
2
1
1
2
0
1
0
1
2
1
0
1
2
0
1
0
2
1
1
0
1
2
2
1
1
2
1
0
2
1
1
1
1
1
1
2
1
0
2
1
1
2
0
2
1
1
0
1
2
2
0
1
1
0
2
1
1
0
1
0
1
2
1
2
1
1
1
1
1
0
2
1
1
1
0
0
1
0
1
1
1
1
1
0
1
1
1
1
1
2
0
1
1
1
1
0
1
2
0
1
1
1
0
0
0
0
2
2
0
0
0
0
1
1
0
1
1
1
1
0
2
2
0
0
2
1
1
1
1
0
1
2
2
1
1
1
1
1
0
1
2
1
0
1
1
0
0
1
2
2
0
2
0
1
1
0
2
2
1
2
1
1
1
1
0
0
2
1
1
2
1
1
1
0
0
2
1
2
0
1
1
1
1
0
2
0
1
2
1
1
1
1
1
1
1
1
0
1
2
0
1
1
1
0
2
2
0
1
0
1
1
1
1
1
1
1
1
1
1
0
0
2
1
1
2
1
0
1
1
1
2
2
0
2
2
1
1
1
0
2
2
2
1
3
0
2
1
1
0
0
2
1
2
0
1
1
1
2
1
1
1
2
0
0
0
1
1
1
1
1
2
0
1
1
2
2
0
0
1
1
1
1
0
1
1
1
1
0
1
2
2
0
3
1
2
1
1
1
1
1
2
0
1
0
2
1
1
2
1
1
1
2
1
1
2
1
0
2
1
1
2
1
2
1
1
1
1
0
0
2
1
2
1
2
0
2
0
2
2
1
0
1
2
1
1
1
2
1
0
3
1
0
1
1
0
0
1
2
1
2
2
0
1
1
0
1
1
1
0
1
1
1
0
1
1
2
1
1
2
1
1
1
0
1
1
0
2
1
1
1
1
1
1
1
1
1
0
0
1
1
1
0
2
1
2
0
1
1
1
1
1
2
2
2
2
1
2
1
2
1
0
0
2
1
1
1
0
1
1
1
2
1
1
0
1
2
1
1
2
1
1
1
0
1
1
1
0
1
3
0
1
4
1
1
2
1
0
0
1
1
1
1
1
1
1
1
1
1
0
1
1
1
0
1
1
1
1
0
0
2
1
2
0
1
2
2
0
1
1
1
0
1
1
0
1
0
1
0
1
0
1
1
0
1
0
0
0
2
1
1
1
0
0
1
0
0
1
0
0
0
0
1
1
2
1
0
1
0
1
1
2
1
0
0
1
0
1
1
1
1
1
1
1
0
1
1
0
1
1
0
1
0
1
1
1
1
2
1
1
0
1
1
1
0
1
1
2
1
1
0
2
0
2
1
0
0
2
1
1
0
2
0
0
1
1
1
1
1
1
1
1
0
2
1
0
0
0
1
1
1
1
0
1
1
1
1
2
1
1
1
0
1
0
1
1
3
2
1
2
1
0
1
2
2
1
0
2
0
1
1
0
1
0
1
1
1
2
1
2
1
0
1
1
1
1
1
1
1
1
4
1
0
2
2
1
1
1
2
1
0
1
1
2
1
1
1
2
1
1
1
0
2
0
1
0
0
1
1
0
0
0
0
0
2
2
1
1
2
1
2
1
1
2
1
2
1
1
0
1
0
2
0
1
2
2
1
2
1
2
0
0
1
1
1
1
0
1
1
0
1
1
1
1
1
0
1
1
1
2
1
2
1
1
1
1
2
2
1
1
1
1
1
0
1
0
1
1
0
1
1
1
0
2
0
0
1
1
1
2
1
2
2
1
1
2
0
0
0
2
1
0
0
2
0
0
1
1
1
1
1
2
1
1
1
1
1
1
1
2
0
1
0
0
1
0
4
0
1
1
0
2
2
0
1
0
2
1
0
2
1
0
1
1
1
1
0
2
1
1
1
0
0
0
0
0
1
0
2
0
2
0
1
1
1
1
1
0
1
2
1
0
0
0
1
1
1
2
4
1
1
0
1
1
1
1
1
2
1
1
1
2
0
2
2
1
1
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
2
0
1
1
1
0
2
0
0
1
2
1
1
0
2
1
0
0
0
1
1
1
1
1
0
0
0
1
0
1
0
1
4
1
1
0
0
1
1
1
1
1
1
0
0
1
2
0
1
1
2
0
1
1
2
0
2
1
1
2
1
1
2
1
0
0
0
0
1
2
1
1
1
1
1
1
1
1
0
1
2
0
1
0
0
0
2
2
2
1
1
2
1
1
0
1
2
1
1
1
1
1
1
0
1
0
2
2
1
0
0
0
0
0
1
0
1
2
1
0
1
1
2
1
0
1
0
1
1
2
0
1
1
0
1
0
1
0
2
1
1
2
1
2
1
1
2
2
0
2
1
1
0
2
1
2
2
2
0
1
1
1
1
1
1
2
2
1
1
1
0
1
2
0
1
1
2
0
1
1
1
1
1
0
0
1
1
1
2
1
0
2
1
2
1
1
1
1
1
1
2
0
0
2
0
1
0
1
0
1
1
1
1
0
0
1
2
0
1
2
1
1
2
1
1
1
1
1
1
0
2
0
1
1
1
1
1
1
0
0
1
1
1
2
1
1
1
2
1
0
0
1
2
2
1
1
1
2
0
0
0
0
1
0
1
0
0
1
0
0
1
2
0
1
0
1
0
1
1
0
2
1
1
0
2
2
1
1
2
0
1
1
1
0
1
2
0
1
1
0
0
1
4
0
1
2
0
2
0
0
1
0
2
1
2
1
0
1
4
1
0
1
0
1
2
1
2
1
1
2
1
1
2
1
1
0
0
1
1
0
1
2
2
0
2
1
1
1
2
0
2
1
0
2
2
1
2
1
0
1
1
1
0
1
1
0
1
1
0
2
1
1
3
1
1
0
0
1
2
1
1
0
1
1
0
1
2
1
2
1
0
1
1
1
2
1
2
2
0
1
0
1
0
1
1
2
3
0
1
0
2
1
1
1
1
1
1
1
1
1
0
0
1
1
1
1
0
2
2
0
2
1
2
2
0
0
1
1
1
1
2
1
1
4
1
0
0
1
2
0
1
2
2
1
2
1
1
1
1
1
1
0
0
0
1
1
0
1
1
1
1
0
2
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
0
1
2
0
0
1
1
0
0
3
1
2
1
1
1
2
2
1
0
1
1
2
1
1
1
1
1
2
0
1
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
0
1
1
0
0
1
1
1
0
1
1
1
1
1
1
0
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
2
1
1
1
0
2
1
1
1
1
1
1
1
1
2
1
1
2
2
0
0
1
2
1
1
0
2
2
2
1
1
0
2
1
1
0
1
2
1
1
1
1
0
0
1
1
2
0
1
0
0
2
2
2
1
1
1
0
1
0
1
0
2
1
1
2
0
1
0
1
1
0
1
2
1
2
1
1
1
0
2
2
1
1
1
1
1
2
2
1
1
1
1
2
2
2
1
1
1
2
1
1
1
2
2
2
2
0
0
1
0
1
1
1
1
1
2
0
0
0
0
1
1
0
0
1
1
1
1
0
1
2
1
1
1
2
0
2
2
1
1
0
0
1
1
1
1
1
1
0
1
1
3
1
2
0
1
0
1
1
1
1
1
0
1
1
0
1
3
2
3
1
2
2
1
1
0
1
0
2
1
1
2
1
1
1
0
1
1
1
0
1
1
0
1
1
1
2
1
0
1
1
1
2
1
1
1
1
2
1
1
1
0
1
2
1
1
1
1
2
0
3
0
1
1
2
1
0
0
1
0
2
1
1
1
2
1
2
3
0
0
1
1
2
2
1
1
0
0
1
2
1
0
1
1
1
2
1
2
1
2
1
1
1
1
2
1
2
1
1
1
1
1
2
0
0
0
1
1
2
1
1
1
0
0
0
1
0
0
1
1
2
1
2
2
0
2
1
1
1
2
1
0
1
1
1
0
0
1
2
1
2
1
1
0
1
1
0
0
1
1
1
1
1
1
0
1
1
1
1
2
1
2
2
1
0
2
2
0
1
1
0
1
0
2
1
0
2
2
1
1
1
0
0
0
1
1
2
0
0
2
1
0
1
1
1
1
1
0
1
2
1
2
1
0
2
1
1
1
2
1
0
1
1
1
2
1
2
0
1
1
0
1
2
1
1
1
0
0
0
1
2
2
1
1
1
1
1
1
1
0
0
2
1
1
1
1
1
1
1
1
0
0
0
2
1
0
1
1
0
1
1
1
0
0
1
0
3
1
2
0
1
2
1
0
1
2
1
2
2
2
2
1
1
1
2
0
1
1
2
1
0
0
1
1
1
1
1
0
1
1
1
0
3
0
2
1
1
1
0
4
1
1
1
1
0
1
1
2
1
0
1
0
1
1
2
0
1
1
1
0
1
1
1
1
0
1
0
0
1
1
0
1
1
0
1
1
3
0
0
1
1
1
1
1
0
1
2
2
0
1
1
1
1
1
1
1
2
0
0
1
2
2
0
1
1
0
1
0
2
0
2
2
1
2
0
0
0
0
0
1
1
1
2
1
1
1
1
2
2
1
1
3
1
3
1
1
1
0
2
1
0
4
1
1
0
0
1
0
1
1
2
2
3
1
1
1
0
1
2
1
1
1
0
0
1
1
0
1
0
1
2
1
0
1
1
0
1
0
2
0
0
1
1
0
1
1
1
1
1
1
0
1
1
2
1
1
0
1
1
0
0
1
2
2
1
1
0
1
1
2
1
1
1
1
1
1
1
1
0
1
1
1
0
2
1
2
1
1
1
1
1
2
1
2
2
1
0
1
2
1
2
1
0
0
2
1
1
0
1
1
1
0
0
0
0
2
1
1
1
1
1
1
0
2
2
0
1
1
0
1
2
1
1
0
1
1
0
1
0
1
2
2
0
1
1
1
0
2
1
1
1
1
1
0
1
1
1
2
1
1
2
1
1
2
1
1
1
2
2
1
2
1
0
1
0
1
2
0
1
2
1
1
1
0
1
0
0
0
2
0
1
1
1
0
1
0
1
1
1
1
2
2
0
1
1
1
1
1
0
1
1
0
1
0
0
1
1
1
2
1
0
1
1
1
1
0
1
1
1
1
1
1
1
1
0
1
2
1
1
0
2
2
0
1
1
2
1
2
2
1
1
0
0
1
1
1
1
2
0
1
0
2
1
0
1
0
0
1
0
1
0
1
1
0
2
0
1
0
1
1
0
1
2
1
1
2
0
1
1
1
1
1
1
1
1
1
2
0
1
0
1
0
0
3
1
1
1
2
1
1
1
1
0
1
1
0
1
0
1
0
2
1
0
1
1
1
1
1
2
0
2
2
0
0
2
0
2
1
1
3
2
1
2
0
1
0
2
0
2
0
0
1
1
1
0
2
1
1
0
0
2
0
2
0
1
1
2
1
1
2
0
0
1
1
1
0
2
0
0
2
2
1
1
1
1
1
1
1
2
1
1
1
2
2
1
2
1
1
2
1
0
1
1
2
0
1
1
1
0
1
1
2
1
2
1
1
1
0
1
1
2
0
1
1
1
0
2
2
0
1
2
2
2
2
1
1
1
1
1
1
0
1
1
0
1
1
1
1
0
1
2
2
1
1
1
0
1
0
2
2
1
1
1
1
1
1
1
1
1
1
0
1
1
1
0
1
1
2
1
1
1
0
0
0
0
1
0
2
2
2
1
0
1
1
1
0
2
0
1
1
1
2
1
1
1
1
1
1
1
1
2
0
2
3
1
1
1
1
0
2
1
1
0
2
2
1
2
2
1
1
1
0
1
0
1
1
0
2
1
2
1
2
1
1
1
1
2
1
0
2
1
1
0
0
1
2
1
1
1
1
1
1
1
0
0
2
2
1
1
1
0
1
2
1
1
0
0
0
1
2
1
0
1
2
1
1
1
1
1
0
1
1
1
1
0
1
0
1
2
1
1
1
1
0
2
0
1
1
0
1
1
1
2
1
1
2
1
1
2
1
2
1
2
0
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
3
1
1
1
1
1
1
1
1
2
0
0
2
1
1
1
2
0
2
1
0
1
1
1
1
1
1
0
1
1
1
0
1
2
1
2
2
1
1
2
0
1
2
2
1
1
0
1
0
1
1
0
1
1
1
4
0
0
0
2
2
1
0
1
0
2
2
0
0
2
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
2
1
1
0
1
2
1
0
1
2
2
0
1
2
1
2
2
1
1
2
1
0
1
2
1
0
1
1
0
1
1
1
1
1
1
0
1
2
1
0
2
0
1
0
0
0
0
2
0
2
0
0
2
1
2
0
0
2
1
1
1
1
1
2
1
0
2
2
1
1
0
1
1
1
2
0
1
1
2
2
1
1
1
1
1
1
0
2
2
1
1
1
2
2
2
1
1
0
1
1
1
1
0
0
0
1
2
1
1
1
0
1
0
0
1
1
1
0
2
0
1
1
2
1
1
2
1
1
2
1
2
1
1
1
1
0
0
1
1
0
1
1
0
0
2
2
2
1
0
0
0
1
1
1
2
1
1
1
0
1
2
1
0
1
1
2
0
0
1
1
1
1
2
1
0
2
0
1
1
0
1
2
2
2
0
2
1
0
1
2
0
0
1
2
1
1
1
1
0
0
0
1
1
0
3
2
0
1
1
1
1
0
1
1
1
2
1
2
1
1
2
1
3
1
1
1
2
0
1
0
2
1
1
0
1
1
1
2
2
2
1
1
1
2
1
0
1
1
1
0
0
2
1
1
1
0
0
1
3
1
1
1
1
1
0
2
0
2
1
0
1
2
1
0
1
1
0
1
1
1
2
1
1
2
2
1
1
1
1
0
1
1
0
0
2
2
1
2
0
1
2
2
1
0
1
0
2
1
1
1
2
1
1
1
1
1
1
1
0
0
1
1
1
1
2
1
0
1
1
0
1
1
2
1
0
1
1
0
2
1
0
2
1
1
2
2
1
2
1
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
2
1
1
2
1
1
1
2
1
1
1
1
0
1
2
1
1
0
0
2
2
1
0
2
1
1
0
0
1
1
3
0
1
1
1
1
0
1
1
1
1
1
1
1
2
1
2
1
1
2
1
1
0
0
1
1
0
0
1
0
0
0
1
0
0
1
1
1
1
1
0
2
1
0
0
2
1
1
0
1
0
2
1
2
1
2
1
0
1
2
0
0
1
2
2
2
0
1
1
1
0
1
1
1
0
1
1
1
1
1
1
1
2
0
2
2
1
0
0
0
0
2
1
1
1
0
2
2
0
2
2
1
1
1
2
0
1
1
0
1
1
1
2
1
2
1
1
0
0
1
1
1
1
2
0
2
1
1
2
3
2
0
1
1
0
1
1
0
1
0
0
0
0
1
1
1
1
2
1
1
1
2
0
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
0
1
1
0
1
1
1
1
0
1
0
0
1
0
1
0
1
2
2
0
0
2
1
1
0
1
1
1
3
0
1
1
0
1
1
2
0
2
1
1
1
1
2
2
2
0
1
1
1
1
1
1
2
2
1
0
0
2
1
1
2
1
1
3
1
1
1
2
0
0
2
1
3
1
4
0
2
2
1
1
1
1
1
0
1
0
2
0
1
1
1
1
1
0
0
0
1
2
0
0
0
0
1
0
1
2
1
0
1
1
1
2
1
2
1
1
1
0
0
0
0
1
2
2
0
2
2
1
0
1
2
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
0
1
0
2
1
1
1
0
0
1
1
1
1
0
1
1
2
0
1
2
2
1
1
2
2
2
2
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
0
1
1
0
2
1
1
1
4
2
2
1
2
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
2
0
2
0
1
0
1
1
1
1
1
1
0
1
2
1
1
0
1
1
0
2
0
2
1
0
2
1
0
2
1
1
0
2
0
2
1
0
1
0
1
1
0
1
1
2
0
1
1
2
1
1
1
1
3
0
0
2
1
0
0
2
0
1
1
1
1
1
2
1
2
1
1
1
2
2
2
1
1
1
1
1
2
2
2
1
1
1
1
0
1
0
0
2
1
0
1
1
0
0
2
0
2
0
0
1
2
1
1
0
1
1
0
2
0
2
1
2
0
0
0
0
2
1
1
1
2
1
1
1
1
1
0
2
0
1
1
2
0
2
0
1
0
1
0
1
1
0
2
1
1
0
0
0
1
0
1
1
1
1
2
1
0
1
1
1
0
0
1
2
1
2
1
2
0
0
1
1
1
2
1
0
2
2
1
1
1
0
1
0
1
2
1
0
2
0
1
2
0
1
1
2
0
1
1
0
2
1
2
2
1
0
2
0
0
1
0
0
0
1
1
1
0
0
2
1
1
1
1
0
3
0
2
1
0
0
2
1
0
2
2
1
0
2
1
1
1
1
2
1
1
2
1
1
2
2
1
0
1
0
0
1
1
1
1
0
1
1
1
1
1
0
1
1
1
1
1
2
1
0
1
1
1
1
1
1
0
1
0
1
1
2
1
2
2
1
1
1
1
1
2
2
2
0
1
1
1
1
1
1
1
0
1
1
0
1
1
1
1
2
2
2
2
2
1
0
1
0
1
1
1
2
2
0
0
2
0
0
1
1
0
1
1
1
0
2
0
1
1
2
1
1
0
1
1
2
1
0
2
0
0
0
1
2
1
1
0
2
0
1
1
1
1
2
0
0
1
1
2
2
2
2
1
1
0
0
0
1
1
2
1
1
2
1
1
2
2
1
0
1
0
0
1
1
0
1
1
1
2
1
1
1
1
1
1
0
1
1
2
2
1
1
1
1
0
1
0
1
1
1
2
0
2
2
1
2
1
0
2
2
2
0
1
0
0
0
1
1
1
2
1
2
1
1
0
1
0
2
1
1
2
1
1
0
1
1
0
2
1
1
2
0
0
0
1
1
1
2
1
1
1
1
1
2
1
1
1
2
2
1
2
1
0
0
1
1
1
1
0
1
0
1
1
1
1
1
1
0
1
1
1
1
0
2
1
2
1
1
1
1
0
1
1
1
1
3
1
1
1
0
1
0
1
2
1
2
1
2
0
1
1
0
1
1
0
1
1
1
2
2
1
1
2
1
1
2
0
2
0
1
1
1
0
1
0
1
1
1
0
2
1
2
1
0
0
2
2
2
1
0
0
0
2
1
1
2
1
0
0
1
1
0
2
1
0
1
2
0
1
1
1
2
0
1
1
0
1
1
1
2
1
1
2
2
0
1
0
1
1
1
1
0
1
1
1
0
0
2
0
0
0
1
2
1
1
0
0
1
1
1
1
1
1
2
0
0
2
1
1
1
2
2
2
2
0
1
1
1
1
0
2
0
2
2
1
1
0
1
2
2
1
1
2
0
1
0
2
1
1
1
1
8
0
2
0
1
1
2
0
1
2
0
1
2
0
1
1
0
2
2
1
1
2
1
0
1
0
2
0
2
1
1
2
1
1
1
0
2
1
1
1
0
1
1
1
0
1
0
1
1
2
2
1
1
2
0
1
1
0
1
2
3
1
1
1
1
1
0
0
1
2
0
2
1
2
1
1
2
2
1
1
2
0
1
0
1
1
1
0
2
1
2
1
1
1
1
2
1
2
0
0
1
0
2
1
2
0
1
1
2
0
1
0
2
1
1
2
1
1
0
1
2
2
0
0
0
1
2
1
1
2
0
1
0
0
3
0
1
1
2
2
0
0
1
2
1
0
2
1
0
0
1
2
1
0
0
1
1
0
1
2
0
2
1
1
3
1
2
0
1
1
2
0
2
1
1
1
0
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
0
0
2
2
1
1
2
0
0
2
1
2
0
1
2
1
1
2
2
0
1
2
0
1
1
0
0
0
1
1
2
2
1
2
2
0
0
1
1
1
0
1
2
3
2
0
0
1
2
1
1
2
0
0
1
1
1
1
1
1
2
0
0
0
1
1
1
0
2
2
2
1
2
1
1
1
1
1
1
1
1
2
1
1
2
0
1
2
1
0
1
1
0
1
1
0
2
0
0
1
3
1
2
2
2
1
0
1
1
0
2
1
2
1
1
1
2
1
1
1
2
0
2
1
0
1
1
1
2
1
2
0
2
2
2
1
1
1
1
1
0
1
2
1
2
1
1
1
2
1
1
1
2
1
1
1
2
2
2
2
1
1
2
1
1
0
1
1
1
1
1
0
1
0
2
1
2
1
1
2
1
1
0
2
0
2
1
0
1
0
1
2
0
1
0
1
3
1
1
1
1
0
2
1
0
1
0
1
1
1
2
1
1
2
2
1
2
2
3
2
0
1
2
1
1
2
0
1
1
1
2
1
0
2
2
1
1
0
0
2
1
1
1
1
1
0
1
2
0
0
1
2
2
1
1
1
0
1
1
1
1
2
0
1
0
1
1
1
0
0
0
0
1
1
2
1
1
2
2
1
2
0
2
0
0
2
1
0
0
0
1
1
0
2
1
1
2
1
0
0
1
1
2
2
2
1
1
1
1
1
1
1
2
0
1
1
1
0
1
1
2
2
1
2
1
2
2
1
1
2
1
1
2
2
1
1
1
1
2
1
2
2
0
1
2
0
1
1
1
0
1
1
1
1
1
2
1
1
1
1
2
0
2
1
1
0
2
1
2
1
1
1
1
1
1
2
1
1
1
2
2
1
1
0
1
0
1
2
1
0
1
0
1
1
1
1
0
1
1
1
1
0
0
1
1
2
0
1
1
0
1
2
1
1
1
1
0
1
2
1
1
1
2
1
1
1
0
0
1
1
1
0
0
1
2
1
1
3
0
1
1
1
1
0
0
0
2
1
0
2
1
1
0
1
2
1
1
0
1
1
1
2
0
1
2
0
2
1
0
0
2
1
0
2
1
1
1
2
1
1
0
1
1
2
1
1
1
0
1
1
2
2
2
1
1
1
0
2
2
2
0
0
1
1
0
2
4
1
1
1
2
3
0
0
1
1
2
2
1
2
1
1
1
2
0
1
2
1
0
1
1
1
1
0
0
0
2
0
3
2
1
2
1
1
0
1
0
1
1
0
1
0
2
2
1
0
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
0
1
1
0
1
1
2
1
1
1
0
2
0
2
0
1
1
1
2
1
1
1
1
1
2
2
0
0
1
1
1
0
1
1
2
0
1
2
1
2
0
0
2
1
2
1
1
2
0
2
1
2
2
0
2
1
0
1
1
2
1
0
0
0
1
1
0
2
0
1
0
1
1
2
1
0
0
1
1
1
1
1
0
1
2
2
1
2
1
2
1
1
1
1
2
0
1
1
1
2
1
0
0
1
2
1
1
1
0
0
0
0
0
2
1
2
2
1
0
0
2
1
2
1
0
1
1
1
0
0
1
1
1
2
0
2
1
2
2
1
1
1
2
0
2
2
1
1
2
1
1
1
0
2
0
0
1
2
0
0
2
2
1
1
1
1
1
2
2
0
2
1
0
3
2
1
1
1
1
1
1
1
1
2
0
2
2
0
2
1
1
0
1
0
0
1
2
2
1
2
0
2
0
0
1
2
1
1
2
1
1
2
2
1
1
2
1
1
1
2
0
2
2
1
8
3
2
1
0
1
1
1
2
1
2
1
2
0
2
2
1
0
1
1
1
2
0
1
0
2
0
1
1
2
2
1
1
1
2
3
0
0
1
0
2
1
2
0
1
2
1
1
1
1
0
2
1
1
1
0
0
1
2
1
1
0
1
2
2
1
1
1
2
1
1
0
1
1
0
1
0
1
2
2
0
2
1
2
2
0
2
1
1
2
2
1
1
1
1
0
1
2
2
1
0
1
1
0
1
1
2
0
1
1
0
1
0
1
1
0
0
1
1
1
1
2
1
1
1
0
0
2
2
2
2
1
2
1
1
1
2
1
1
1
2
2
2
2
2
2
0
1
2
2
0
1
2
1
0
0
1
1
2
0
1
1
1
1
0
0
0
1
1
2
1
1
1
1
1
2
1
0
0
1
1
0
2
1
1
1
0
1
1
0
1
2
2
1
1
1
1
2
2
0
0
2
1
0
1
1
0
0
0
1
2
1
0
1
2
2
0
0
2
0
1
2
1
1
2
0
1
0
0
0
2
0
1
0
1
3
0
1
2
1
0
1
1
1
1
1
1
1
0
1
2
1
1
1
2
2
2
1
2
1
0
1
1
1
1
1
0
1
0
2
1
0
1
0
1
1
0
0
0
1
1
1
1
0
2
2
2
1
1
0
1
1
1
1
0
1
1
3
1
0
1
2
1
1
0
1
0
0
1
2
1
1
1
1
0
1
1
0
2
2
1
1
2
2
0
1
1
0
1
1
1
2
1
1
1
1
0
1
1
1
1
1
0
0
1
1
0
1
1
1
2
1
1
1
1
1
1
0
1
1
1
4
2
2
1
0
1
1
1
1
0
0
1
2
1
1
1
0
2
0
0
0
2
1
1
2
5
1
0
1
1
0
0
1
2
2
0
1
6
2
1
1
2
0
1
1
1
2
1
1
0
0
0
1
1
2
1
1
1
1
1
1
2
0
2
0
1
0
1
1
2
2
2
0
1
0
1
2
1
1
1
1
0
1
2
2
0
1
1
1
2
1
1
0
1
1
0
0
2
1
1
2
1
1
1
0
0
1
2
1
2
1
1
1
0
2
1
0
1
1
2
1
1
1
0
1
1
2
1
1
1
0
1
1
2
2
1
1
0
1
1
0
2
1
0
0
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
0
1
2
1
2
2
2
1
0
1
2
0
1
1
0
1
1
1
1
1
0
0
0
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
2
1
0
2
1
1
2
1
2
1
2
2
0
0
1
2
0
1
2
0
1
2
2
0
2
0
2
1
1
1
1
1
0
1
1
0
2
2
1
1
2
1
0
1
1
1
0
1
1
2
0
2
1
2
2
1
1
1
2
2
1
1
0
0
0
0
0
0
1
2
1
2
2
1
1
2
1
1
1
2
1
0
0
1
1
0
2
0
0
1
2
1
2
0
1
1
2
2
0
1
0
1
1
2
1
1
1
1
1
1
0
1
1
0
1
1
2
2
2
0
1
0
1
0
0
1
2
1
1
1
0
1
2
2
1
0
1
1
1
0
1
1
1
1
1
1
1
1
0
4
1
1
0
2
1
2
0
2
1
1
1
1
0
0
2
1
0
1
1
2
2
0
2
1
1
0
2
2
0
1
0
0
1
2
1
1
0
2
1
1
1
2
1
1
2
1
0
1
0
1
1
2
1
1
2
1
1
1
2
0
1
0
1
1
1
2
2
2
0
1
1
1
0
2
2
0
2
1
0
1
0
1
1
0
2
0
1
0
1
1
0
2
2
2
0
3
1
1
2
1
0
1
1
2
2
1
1
2
1
0
2
1
1
1
3
1
1
0
1
1
1
2
1
1
0
1
1
1
2
1
1
1
1
0
1
1
1
0
0
1
0
1
0
1
1
1
0
2
0
0
0
0
1
0
2
1
1
3
0
1
0
3
1
1
1
1
0
2
1
1
2
2
1
1
2
1
2
0
2
1
1
1
0
1
1
1
1
2
1
1
0
0
1
0
0
2
0
2
1
1
0
1
2
0
2
1
1
2
2
1
0
1
1
0
1
2
0
1
1
2
1
2
2
2
1
0
0
1
2
1
1
1
1
0
1
1
2
0
0
1
1
0
1
1
1
1
2
1
1
1
0
2
1
0
1
0
1
2
1
1
1
1
1
1
2
0
0
1
0
1
1
1
2
1
0
1
1
1
1
2
2
1
2
1
1
1
1
0
1
2
1
0
1
1
1
2
1
1
1
1
1
0
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
0
1
1
2
1
2
0
1
2
1
1
2
2
1
1
0
0
1
0
1
1
1
0
1
2
1
3
0
1
1
1
0
1
2
1
1
1
0
0
2
1
2
3
2
1
1
2
0
0
1
1
1
13
1
1
0
2
0
2
1
1
1
0
3
0
2
2
2
1
1
1
1
1
2
2
1
0
1
2
1
1
1
0
0
0
1
1
1
1
2
1
0
0
2
1
2
1
1
0
1
1
1
1
2
1
1
1
0
1
1
2
1
1
2
1
2
1
3
1
0
1
1
1
1
0
0
1
1
1
2
0
2
1
0
1
2
1
1
0
1
1
2
2
1
1
1
2
1
2
0
2
0
1
0
2
1
2
1
1
0
0
1
2
1
1
0
1
1
1
2
1
1
2
0
1
1
2
1
2
2
2
0
1
1
2
0
2
0
0
1
2
2
1
2
1
5
0
1
1
1
0
1
2
1
0
1
1
1
0
1
0
3
0
1
1
1
1
1
0
1
2
1
1
1
1
1
0
1
0
1
2
0
1
0
1
2
0
1
1
1
0
2
1
0
1
0
1
2
1
0
0
1
1
2
2
2
0
0
3
1
2
0
1
0
1
1
1
2
2
1
0
1
1
1
1
1
0
2
1
2
1
0
0
2
0
1
0
0
1
1
1
2
0
1
1
0
1
2
1
1
0
1
0
1
1
1
2
1
2
1
1
0
2
0
0
2
0
0
1
1
0
1
1
1
2
4
1
1
1
1
0
2
1
2
1
0
2
1
2
0
1
1
0
0
2
1
0
1
1
1
0
0
0
2
2
1
1
2
2
2
0
0
1
0
2
1
1
1
1
0
2
0
1
2
0
1
1
1
1
2
0
1
1
1
1
0
1
1
1
2
1
1
2
1
1
1
1
1
1
1
0
1
1
1
0
1
1
2
1
2
1
1
1
2
0
1
0
1
1
0
1
0
1
0
0
2
0
0
2
0
1
0
1
2
0
1
0
1
1
2
0
2
5
2
1
1
1
0
1
1
1
1
2
1
0
0
1
1
1
1
1
1
1
0
1
1
2
2
1
1
2
0
1
2
1
1
1
0
2
1
1
1
2
2
2
2
2
1
1
1
1
2
2
1
2
1
0
2
0
1
1
1
1
0
1
1
1
2
1
3
2
1
1
3
1
0
0
1
0
3
2
0
1
1
3
1
1
2
1
1
1
2
2
1
1
2
1
2
2
2
1
1
2
0
1
1
1
2
2
0
1
3
1
0
1
2
2
1
1
0
1
1
1
1
1
1
2
1
2
2
2
2
0
2
1
0
2
1
0
1
0
1
0
1
2
1
2
1
1
1
1
2
2
1
1
0
0
3
2
0
1
1
1
1
2
1
1
0
2
1
1
1
1
1
0
1
1
0
1
1
1
2
0
1
0
1
1
0
1
1
2
1
2
0
4
2
1
4
1
1
2
2
2
1
1
1
2
1
1
1
2
0
0
0
0
1
2
1
2
0
1
1
0
0
0
2
0
1
1
1
1
0
1
1
2
1
0
1
1
1
0
1
0
1
1
1
1
1
1
1
0
1
1
0
2
1
1
0
1
1
1
1
2
0
1
1
0
0
0
0
1
0
0
2
1
2
2
0
2
1
0
0
1
1
1
1
0
0
2
1
1
2
1
2
3
1
0
1
0
1
2
1
0
2
0
1
1
1
0
0
1
1
0
1
2
1
1
0
2
1
2
1
0
0
0
1
1
2
1
2
0
1
0
0
2
2
0
1
1
1
2
1
1
0
1
1
0
1
0
2
2
2
0
2
1
1
0
2
1
1
2
2
1
1
0
0
1
1
1
2
1
2
2
2
1
1
1
1
1
1
2
1
2
1
1
0
2
1
0
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
1
1
1
1
0
1
2
2
0
1
2
1
1
1
1
0
2
1
1
1
3
1
1
1
0
1
2
0
1
1
1
0
1
1
0
1
0
0
1
1
1
0
1
1
1
2
2
0
0
2
1
0
2
1
1
0
0
3
1
1
1
6
0
3
1
2
1
1
1
1
2
2
0
1
0
0
1
0
1
1
2
2
0
1
0
1
0
1
1
1
2
0
1
2
0
1
9
0
1
0
0
0
3
1
2
1
1
0
1
0
1
1
1
1
1
2
0
0
1
2
1
1
1
0
2
2
1
1
1
0
0
0
0
1
1
2
2
2
1
1
0
2
0
1
0
2
1
1
1
1
0
1
1
1
0
0
1
1
0
2
2
2
3
1
1
1
0
1
0
1
1
1
1
1
1
1
1
1
1
2
0
2
3
0
1
2
0
1
0
0
1
1
1
1
0
2
1
1
0
2
1
2
2
0
1
2
1
1
1
0
2
1
1
0
1
1
1
0
1
1
1
1
1
1
1
0
0
0
1
1
0
1
1
1
1
1
1
1
2
1
1
1
1
0
1
0
2
2
2
1
1
1
2
1
0
1
1
1
1
1
1
1
1
1
0
1
1
1
2
0
2
1
1
0
1
2
1
2
1
1
1
1
2
1
2
2
0
1
0
1
1
0
0
0
1
0
0
1
0
0
0
1
0
2
1
1
1
1
1
1
1
2
1
1
1
1
0
0
0
1
2
1
1
1
2
1
2
1
2
1
1
1
1
0
1
1
1
1
1
1
1
2
1
1
2
1
0
0
1
1
1
1
2
1
2
2
1
1
3
1
1
2
1
1
0
2
0
2
1
1
3
1
1
2
1
2
1
1
1
1
1
2
1
0
0
2
2
0
2
1
1
1
2
2
1
0
1
0
0
3
0
1
2
1
1
2
1
2
0
1
0
1
1
1
2
0
1
1
1
0
1
0
1
1
2
2
1
1
2
2
1
2
1
0
1
2
0
1
2
2
0
0
1
0
1
1
1
2
1
0
1
0
2
1
0
0
1
1
1
1
1
0
1
1
0
2
1
1
1
1
1
1
2
1
0
1
1
0
1
0
1
1
2
1
2
1
1
0
2
2
0
1
1
0
2
0
0
2
1
1
0
1
2
1
1
1
1
0
1
1
1
1
1
1
1
0
1
1
1
3
1
1
2
1
0
1
0
2
2
1
1
0
1
3
1
0
0
0
0
1
1
1
1
2
2
1
1
2
1
1
1
1
1
0
1
2
1
1
1
2
1
1
1
2
3
1
1
1
2
2
0
1
2
0
2
0
1
0
1
2
0
1
1
0
2
1
2
1
2
2
2
2
0
2
1
1
1
1
1
0
0
1
1
0
1
0
1
1
0
2
1
0
1
0
0
1
0
1
1
2
0
1
2
2
1
1
1
1
2
1
0
1
2
1
0
1
2
0
2
1
2
2
1
0
1
1
0
0
1
1
0
1
2
1
1
2
0
2
0
0
2
1
0
1
1
1
1
0
0
2
1
2
2
0
1
1
1
1
1
1
2
1
1
2
1
1
0
1
2
1
0
1
2
0
0
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
0
0
1
0
1
1
1
2
0
1
1
2
1
1
1
0
1
2
0
0
2
0
2
2
1
2
2
1
1
2
0
0
1
1
3
1
2
1
0
0
1
1
1
1
1
1
1
1
1
3
1
1
0
1
1
0
1
0
1
0
0
0
1
1
0
1
1
2
1
1
2
1
0
0
1
0
1
2
0
2
0
0
0
1
1
2
2
1
0
1
2
2
0
1
1
1
1
2
1
1
0
1
0
1
1
2
1
0
1
3
0
1
0
1
1
1
1
2
4
0
1
2
2
0
1
0
1
0
2
1
1
1
0
0
1
0
0
2
1
1
2
0
1
0
0
0
0
0
1
1
2
2
1
1
1
1
0
0
2
1
1
2
2
1
0
1
1
1
0
0
2
1
2
2
1
2
0
1
1
1
1
0
0
0
1
0
1
0
1
2
1
2
1
0
1
0
0
1
2
2
0
2
2
0
1
1
1
0
1
1
1
0
1
1
2
0
1
2
0
0
1
1
0
1
4
1
2
1
2
0
1
3
0
1
1
1
1
0
1
1
1
1
1
1
0
1
2
2
0
1
2
0
1
2
0
2
0
0
1
1
2
1
1
2
1
1
1
2
2
0
1
1
1
0
0
0
1
1
0
1
0
0
0
1
1
3
1
1
1
1
2
1
0
0
1
2
1
1
2
1
1
0
0
1
1
0
2
0
0
0
2
2
0
1
1
2
1
0
1
1
2
1
2
1
1
1
0
1
1
1
1
1
1
0
1
0
2
1
3
1
0
1
0
1
1
0
1
1
1
1
1
1
2
0
1
0
3
1
2
1
0
0
0
2
2
1
1
2
2
1
2
1
1
1
2
1
1
1
0
1
1
1
0
2
0
2
2
1
0
1
2
2
2
1
1
2
2
2
1
0
1
1
0
2
0
1
0
1
1
2
1
2
1
2
1
1
1
1
1
2
1
1
2
0
0
0
0
2
1
0
2
2
0
2
0
1
1
1
1
2
1
2
1
2
1
1
0
1
1
2
1
0
0
2
2
1
1
2
1
2
0
1
1
1
1
1
2
0
1
2
0
2
0
1
1
1
0
1
1
1
2
1
0
2
1
1
0
2
2
2
1
1
1
0
0
1
0
2
2
0
1
1
1
1
0
1
1
2
2
1
2
0
2
0
2
1
2
1
1
0
1
1
1
0
2
1
1
0
1
0
1
0
1
1
0
0
2
1
1
2
1
2
1
2
0
0
0
0
2
1
1
2
1
1
2
0
1
1
1
1
2
0
0
2
1
0
1
0
2
1
1
0
1
0
0
2
1
1
2
1
0
2
0
0
1
0
2
2
0
1
0
1
1
0
0
1
1
2
2
0
1
1
1
1
1
0
1
0
0
0
2
2
0
1
3
0
1
1
2
0
1
1
2
1
0
0
2
2
1
1
0
1
2
1
1
0
1
1
1
0
1
1
1
1
2
0
1
2
2
1
0
1
0
1
1
2
1
1
0
2
1
1
1
2
2
1
1
1
0
1
0
2
1
1
1
1
2
0
1
1
1
1
0
0
1
0
1
1
1
1
0
2
2
1
1
1
1
1
2
2
3
2
0
1
1
2
2
1
0
1
1
1
2
1
1
2
2
1
1
1
2
0
2
1
1
2
3
1
2
0
2
0
0
1
0
1
1
1
1
2
1
2
0
0
0
0
1
1
1
1
0
0
0
2
0
1
0
0
0
1
1
1
0
0
1
0
1
0
0
1
1
2
1
2
1
1
1
0
1
1
0
1
1
1
0
2
1
1
1
0
1
0
0
1
1
2
1
1
0
1
1
0
1
0
0
2
2
1
2
1
2
2
0
0
2
2
1
0
0
1
0
1
2
0
1
1
0
1
1
1
0
1
0
2
1
1
1
2
0
0
0
2
1
1
1
0
1
2
1
2
1
0
2
0
1
1
2
1
1
1
1
1
2
1
0
1
0
2
2
1
0
1
2
1
0
0
0
2
1
1
1
0
2
2
2
1
1
1
1
0
1
0
2
1
1
0
1
1
2
0
1
1
1
1
2
0
2
1
3
0
0
1
2
1
1
0
1
0
0
1
0
1
1
0
1
1
1
1
1
1
1
1
1
1
2
3
0
0
0
1
1
0
1
2
1
1
1
0
1
1
2
2
1
0
2
2
1
1
1
1
0
2
2
1
1
0
1
2
0
1
1
1
1
1
0
1
1
0
1
1
0
1
1
1
1
1
2
1
0
2
1
1
0
1
2
1
0
2
2
2
1
2
0
1
2
2
0
1
1
0
0
1
1
2
2
0
0
1
1
0
1
2
1
2
1
1
1
0
0
0
0
1
2
1
0
2
2
2
0
2
2
0
1
1
0
1
2
1
0
2
2
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
3
2
0
0
0
1
1
2
2
2
1
1
2
1
1
1
0
2
1
0
0
1
1
0
0
1
1
1
2
1
1
1
2
2
0
1
0
0
1
1
1
0
3
1
0
1
0
1
2
0
1
1
1
1
1
0
1
1
1
0
1
1
2
1
1
1
1
1
1
0
1
0
1
0
0
0
2
0
0
1
1
1
3
1
1
0
1
1
2
1
2
1
1
0
1
1
2
1
1
1
1
2
2
0
1
1
1
2
1
0
0
2
1
2
1
1
1
1
1
0
0
1
1
2
0
2
1
1
1
1
1
1
1
1
2
1
1
0
1
2
1
1
0
1
1
0
1
1
2
1
0
1
0
1
0
2
1
0
1
1
1
1
0
2
1
1
1
1
0
1
1
0
1
1
0
1
2
1
1
1
1
1
0
1
1
2
1
2
2
2
0
0
1
1
1
1
1
1
2
0
1
1
1
0
0
1
1
1
1
1
1
1
1
1
2
1
2
1
0
1
2
0
1
1
2
1
2
0
2
1
1
1
1
1
1
2
2
1
2
1
1
1
0
1
1
1
0
1
0
2
0
0
1
2
2
2
0
0
0
2
1
1
1
0
1
0
2
0
1
1
2
1
1
1
1
1
1
1
1
0
1
0
0
1
2
1
0
1
0
0
1
1
1
0
1
1
2
0
1
2
2
0
1
1
1
1
0
1
1
2
1
1
1
0
0
1
0
1
1
1
0
1
0
1
1
2
1
2
1
0
2
2
2
2
1
1
0
3
0
1
0
1
2
1
2
1
0
1
1
1
2
2
2
1
1
2
1
2
1
1
1
1
1
1
1
2
1
0
1
0
1
2
0
0
0
1
1
2
1
2
1
1
2
1
1
1
1
1
9
1
1
1
0
2
2
2
2
2
2
1
1
0
1
1
1
1
1
0
1
1
1
0
0
2
1
2
0
1
0
1
0
1
2
0
1
1
1
1
1
1
0
2
1
2
0
1
2
0
1
1
1
2
0
1
1
1
2
0
0
0
1
1
1
2
1
1
1
1
1
0
2
2
1
1
2
1
2
0
2
1
1
2
0
2
1
1
2
0
1
0
1
1
1
1
1
2
2
1
2
1
2
1
2
2
2
1
2
3
1
2
1
1
0
1
1
0
1
0
0
1
1
2
1
1
1
1
1
1
1
1
1
0
1
0
1
1
0
1
1
1
2
0
1
1
2
1
1
1
1
0
2
1
1
1
1
0
1
1
1
0
0
2
1
0
1
0
1
1
0
0
1
0
0
1
1
0
2
0
0
2
1
2
1
1
1
1
3
1
0
1
1
2
1
1
0
1
1
0
1
1
2
2
0
0
0
1
1
1
1
1
1
0
1
0
1
0
0
2
1
0
2
2
1
1
1
1
1
0
1
1
0
1
1
1
0
1
2
2
1
2
1
0
2
2
0
2
0
1
0
0
2
1
1
2
1
1
1
0
0
1
2
0
1
1
1
0
1
1
0
1
1
2
0
1
1
1
1
0
1
3
2
1
1
1
1
1
0
1
1
0
1
1
0
1
1
1
2
1
1
1
1
1
2
1
2
2
1
2
0
0
1
1
1
0
2
1
2
2
1
0
1
1
3
2
1
0
2
2
0
0
2
1
2
1
0
1
1
0
1
1
1
2
1
2
1
1
2
1
1
2
2
1
1
1
1
0
0
1
0
1
2
0
1
0
1
1
1
1
2
0
2
0
0
0
2
0
2
1
2
0
1
1
0
2
0
0
1
2
2
1
0
0
0
1
2
0
1
1
2
1
2
1
1
2
0
0
0
2
1
1
1
2
1
1
2
0
2
2
1
1
0
2
2
0
2
1
0
0
2
0
0
1
1
1
1
0
1
1
2
1
2
1
2
2
1
0
1
1
1
1
1
2
2
1
1
0
2
0
1
2
0
0
1
1
1
1
1
1
2
1
2
1
1
2
2
1
2
1
1
1
1
2
1
1
0
2
1
1
1
1
3
1
1
2
0
1
1
0
2
0
1
1
1
0
2
2
0
2
1
1
1
1
2
1
0
0
1
2
0
2
1
1
1
1
1
2
1
1
4
1
1
2
0
0
1
1
2
1
0
1
1
1
1
1
1
1
1
3
2
2
1
0
0
0
3
1
1
0
2
1
0
1
2
0
1
1
1
1
2
0
0
1
1
1
0
0
1
1
0
1
0
1
1
0
1
0
1
0
1
1
1
1
1
2
1
2
0
1
2
1
1
2
2
0
1
2
2
1
1
1
1
2
0
0
2
0
1
0
1
0
0
2
1
1
1
2
0
2
1
2
2
2
2
1
2
1
1
1
0
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
0
1
0
0
0
1
1
1
2
0
1
0
1
2
0
1
1
1
0
1
0
1
1
1
1
1
1
1
2
1
0
1
1
1
1
1
1
1
1
0
2
2
1
2
1
1
2
2
1
1
1
1
1
1
0
1
0
0
1
2
1
1
2
0
1
1
0
0
1
1
1
3
2
2
1
0
0
1
2
2
1
1
0
1
0
1
1
3
1
1
1
1
2
1
2
0
2
0
1
2
1
0
0
1
0
1
0
1
1
1
1
1
1
1
4
0
1
1
1
0
2
1
1
1
1
2
1
2
2
2
0
2
1
2
1
1
1
0
0
1
2
0
1
0
0
2
1
2
1
0
2
1
2
0
1
1
1
0
0
1
1
2
2
1
0
1
1
3
2
2
1
1
1
1
1
0
1
0
1
1
1
2
1
1
1
1
1
1
1
1
2
2
0
1
1
1
0
0
2
1
1
0
1
0
1
1
1
2
1
1
1
0
0
3
1
0
1
2
1
1
0
1
1
0
1
1
2
0
0
2
1
2
1
0
2
2
0
0
1
1
1
0
0
0
1
2
1
2
1
4
1
0
1
2
2
1
1
0
0
1
0
0
0
0
0
1
1
1
1
2
0
0
0
2
1
2
0
0
0
1
1
2
1
0
2
2
2
1
0
1
0
1
1
1
0
1
2
1
1
2
1
2
1
0
2
1
0
1
2
1
0
1
1
0
0
0
2
0
1
2
1
2
2
0
1
1
1
1
1
2
1
2
1
2
0
1
0
2
1
2
2
1
0
0
0
0
1
0
1
1
1
1
1
0
1
2
1
1
2
2
1
0
1
0
2
1
1
1
0
0
1
0
2
1
1
0
1
1
2
1
1
2
2
1
2
1
2
2
1
0
2
1
2
1
1
1
0
0
0
1
1
1
1
2
1
0
1
1
2
2
1
1
1
1
2
1
1
1
0
2
1
1
1
3
2
1
1
0
1
2
2
1
0
0
1
2
1
0
2
2
1
2
2
1
0
1
1
0
1
1
1
1
1
1
2
2
0
1
1
2
2
0
0
1
1
1
2
2
1
1
2
2
2
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
0
2
1
2
1
1
1
1
0
1
2
0
0
1
0
2
2
2
1
0
1
0
0
1
1
0
1
0
0
1
0
1
0
0
1
0
0
1
1
1
1
1
2
2
1
1
2
1
1
0
1
0
1
0
1
2
2
1
1
0
1
2
0
0
1
1
1
1
1
2
2
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
2
1
1
2
0
1
2
1
1
1
0
1
2
0
1
1
0
1
0
1
1
0
1
1
0
0
0
0
1
2
2
1
0
1
1
0
1
0
1
0
0
0
2
1
1
1
2
1
1
0
0
0
0
2
1
0
0
1
2
0
0
1
1
2
1
1
2
1
1
1
0
1
1
2
1
0
2
2
0
2
0
0
1
1
1
2
1
1
1
1
0
1
0
1
2
2
2
2
0
3
2
0
1
1
1
0
0
1
1
1
1
1
1
0
2
0
0
1
1
0
1
2
1
2
1
2
2
1
0
1
1
0
1
1
0
1
0
1
2
0
1
1
2
0
1
1
1
1
1
2
1
1
1
1
1
1
0
0
1
1
0
2
1
0
0
2
1
2
1
1
1
2
1
0
2
0
1
1
0
1
1
1
1
1
2
1
0
0
2
0
1
1
0
1
2
1
1
1
1
1
2
1
1
1
2
2
1
1
1
2
1
1
0
1
1
1
2
0
1
0
1
1
1
1
0
0
1
1
1
1
2
2
0
0
1
1
2
1
1
0
1
0
1
1
1
1
0
2
1
2
1
1
2
0
1
1
1
0
0
2
1
1
0
1
1
1
1
0
2
1
1
0
2
2
1
0
1
0
1
0
1
1
1
2
1
1
2
1
0
0
1
1
1
1
0
0
0
0
1
0
1
2
0
1
1
1
1
1
0
1
1
1
1
2
1
2
2
2
1
1
0
1
0
1
0
0
0
1
1
1
1
1
0
1
1
1
1
0
1
1
1
2
0
1
1
1
2
0
1
1
1
2
3
0
1
1
1
1
1
1
1
0
0
2
1
1
0
0
1
1
1
2
0
1
1
2
0
1
2
1
1
0
1
2
1
2
1
1
1
1
1
0
1
2
1
1
0
1
0
1
1
0
0
2
1
1
0
1
0
2
1
1
1
1
1
1
1
0
1
1
3
0
1
0
1
1
2
1
2
1
1
1
1
1
2
0
1
1
1
1
0
0
1
1
0
1
1
1
0
1
0
1
0
1
1
1
0
0
1
1
2
2
1
1
1
2
1
0
1
1
0
0
1
1
2
0
1
2
0
2
2
2
2
1
1
0
1
1
1
2
2
1
0
1
1
0
1
1
1
2
2
2
0
2
2
2
2
1
1
0
1
1
2
2
0
2
0
2
1
1
2
1
0
0
1
2
1
2
1
2
0
0
1
1
0
2
0
2
1
1
1
1
1
1
1
2
0
0
1
0
1
0
1
1
1
1
2
3
2
0
2
1
1
1
2
0
2
2
1
1
1
1
2
0
1
0
0
1
2
1
1
2
1
1
2
1
1
1
2
0
0
0
1
0
0
0
1
1
0
0
0
1
1
1
1
0
2
0
1
2
1
1
1
1
1
1
2
1
1
1
2
2
2
1
2
1
1
2
2
1
1
2
0
2
1
0
1
1
1
3
2
1
1
2
1
1
2
1
1
0
0
1
1
1
2
1
0
2
2
0
1
0
1
0
3
0
1
2
1
2
2
1
1
1
2
2
2
1
1
1
1
1
1
0
1
1
1
1
2
1
0
1
1
2
0
0
1
1
1
0
0
2
2
1
2
0
2
0
2
1
1
0
1
2
1
1
1
2
1
2
0
1
1
1
1
1
1
0
2
2
1
1
0
1
1
0
2
2
1
1
2
0
2
1
1
0
2
1
2
0
2
1
2
1
1
2
1
1
2
2
1
1
1
1
0
0
0
2
2
0
1
1
1
1
2
2
2
1
1
1
1
2
1
0
1
2
0
2
1
1
1
1
1
2
0
0
2
1
1
2
0
2
0
0
2
1
2
1
1
0
1
1
0
1
1
1
2
2
0
1
1
1
2
1
1
1
1
1
1
1
1
0
2
1
1
0
1
2
2
0
1
2
1
1
1
1
2
0
2
2
1
0
2
1
1
0
1
0
2
0
0
1
1
1
2
1
1
2
2
1
1
0
0
1
2
1
0
1
0
0
2
0
1
0
1
1
1
1
2
0
1
1
0
1
1
2
1
1
1
1
1
0
1
0
0
1
0
1
2
1
1
1
1
2
2
2
2
1
0
1
1
2
1
2
2
1
2
1
1
0
0
1
1
2
1
1
1
1
0
1
1
1
0
1
1
0
2
1
1
1
1
0
1
0
1
1
1
1
1
0
0
1
0
1
1
0
0
1
1
1
1
1
1
1
0
2
1
1
2
0
0
1
0
2
0
2
2
1
0
2
2
1
1
2
1
2
1
1
0
1
1
1
2
1
2
0
0
0
1
2
2
0
1
2
2
1
1
1
1
2
1
1
0
1
0
1
2
1
1
1
0
1
1
3
1
1
2
2
0
1
0
0
1
1
1
1
2
0
1
2
0
2
1
1
1
1
2
0
0
1
1
1
0
1
2
1
1
2
0
1
1
1
2
1
0
2
1
2
1
0
1
1
2
0
0
1
2
1
1
2
1
2
1
2
1
0
1
2
1
1
0
1
2
2
1
1
0
0
1
0
1
1
1
2
1
1
0
2
2
1
1
1
0
2
1
2
1
2
1
1
2
1
1
2
1
1
1
0
0
1
2
1
2
1
1
0
1
2
0
0
1
0
1
0
2
0
0
1
0
2
2
1
2
1
2
2
2
0
0
1
1
1
1
1
0
1
0
1
1
1
1
1
1
0
2
1
1
0
2
1
1
1
1
0
1
1
1
1
1
1
1
0
0
1
2
2
1
1
0
0
2
2
0
1
0
2
0
0
0
0
0
1
0
1
2
1
1
1
0
1
1
0
0
1
2
1
1
2
1
1
1
0
0
2
1
0
1
0
2
2
0
1
0
1
2
1
2
2
0
1
0
0
1
2
0
1
1
2
1
0
0
1
1
0
1
1
0
1
1
0
0
1
1
2
0
1
2
1
1
2
1
0
1
2
1
2
0
1
1
2
1
1
1
1
1
1
0
2
2
1
1
2
2
2
1
2
1
1
0
0
0
1
1
2
1
0
0
2
2
1
1
1
1
0
1
2
1
2
0
1
0
1
1
1
1
0
0
2
2
2
1
0
1
1
1
2
0
0
2
1
2
0
0
1
0
1
0
2
2
0
2
1
2
1
1
1
0
1
1
1
1
1
1
0
2
1
1
0
1
1
2
1
1
2
1
1
2
1
1
0
0
3
1
1
1
1
0
1
1
1
2
1
1
0
2
1
1
1
1
0
1
1
1
1
0
2
1
1
1
2
2
2
1
0
1
1
2
3
0
1
0
1
2
1
2
1
1
1
2
1
1
0
1
1
1
1
1
0
0
1
0
2
0
1
1
0
1
1
0
2
1
3
1
2
1
1
1
1
1
1
0
1
0
2
2
1
0
1
1
1
1
1
0
1
1
0
0
0
2
1
1
2
1
2
1
0
2
0
1
0
2
2
0
1
1
3
1
2
2
1
1
1
1
2
1
0
1
2
2
1
1
1
1
1
0
1
2
1
0
1
2
2
1
2
1
1
1
0
1
2
2
1
2
1
0
1
1
0
1
2
1
1
1
1
2
1
1
1
0
0
1
1
1
1
2
1
0
0
2
0
0
1
1
1
1
3
2
0
1
2
2
0
1
1
0
1
2
1
1
0
1
0
1
1
1
1
1
1
1
2
3
2
1
2
1
0
0
0
3
1
2
0
1
1
0
1
1
2
0
0
2
0
1
1
0
1
1
1
1
1
0
1
1
1
0
1
0
0
1
2
2
1
1
2
1
2
0
0
1
1
1
1
1
0
1
1
1
1
1
2
0
1
2
1
2
2
0
1
0
0
1
1
1
1
1
1
3
2
0
2
2
0
1
1
1
0
2
0
1
2
2
0
2
1
1
2
1
1
2
4
0
0
1
1
1
2
1
0
0
1
0
1
1
2
1
1
2
1
2
2
0
2
1
1
1
1
0
1
1
0
1
2
1
1
2
1
2
0
2
2
2
0
0
1
2
0
1
0
1
2
2
1
2
2
2
1
0
0
1
0
1
2
1
0
2
1
2
1
1
0
1
1
1
2
1
1
1
0
1
1
1
0
1
1
1
3
1
1
1
1
0
1
1
0
0
1
1
1
1
1
1
0
0
0
2
1
2
2
0
2
2
1
1
0
2
1
1
1
2
0
1
0
1
2
2
1
0
0
0
1
1
1
0
1
0
1
2
0
2
1
0
1
1
0
1
2
1
0
0
1
0
1
0
1
1
1
1
1
1
3
1
1
2
1
1
1
2
1
0
1
1
1
1
1
2
1
1
1
1
1
1
1
0
1
3
2
2
1
1
2
0
1
2
2
1
0
1
1
1
0
2
2
2
1
1
1
0
2
2
0
0
0
1
1
1
2
0
0
2
0
0
0
2
2
0
0
1
0
1
2
0
1
0
1
1
1
0
2
0
1
0
1
1
2
0
1
0
1
0
2
2
2
1
0
8
1
2
1
0
0
0
0
1
2
1
0
2
0
1
1
0
1
1
1
1
2
1
0
1
2
1
1
1
1
0
2
2
1
0
1
1
0
0
1
0
1
1
0
1
1
2
2
2
0
1
1
1
1
2
1
1
1
1
0
2
1
2
1
0
0
2
2
1
2
0
0
1
1
1
1
2
1
0
1
1
1
0
1
1
2
1
1
0
1
2
1
2
2
1
1
1
1
1
0
1
2
1
0
2
1
1
2
1
2
2
1
1
2
2
1
2
0
1
2
2
1
1
0
1
1
1
1
2
1
0
1
2
1
1
1
1
1
0
1
1
1
2
0
0
0
0
1
0
1
1
1
1
0
0
2
1
1
2
1
3
1
1
2
0
1
0
1
0
2
2
1
0
2
1
1
1
2
0
1
3
0
1
1
1
0
1
2
2
1
1
0
1
2
1
2
0
0
2
0
1
1
2
1
2
1
0
1
1
0
0
0
0
2
1
0
1
1
1
1
0
0
0
1
1
2
2
2
1
0
2
1
2
2
1
1
1
2
1
2
1
2
0
1
1
1
1
2
0
2
1
1
1
1
1
0
1
0
2
2
2
2
0
0
1
2
2
0
1
1
2
2
1
1
1
1
2
1
1
1
1
2
1
1
0
1
1
0
1
1
1
2
1
0
0
2
1
1
2
2
1
1
1
0
0
0
1
1
1
0
1
0
1
2
1
0
1
0
1
0
1
1
1
1
1
2
0
2
0
1
1
2
1
0
1
1
1
2
1
1
1
1
1
1
0
1
0
1
0
2
0
1
2
2
0
0
2
1
1
0
0
1
1
0
2
1
1
1
1
1
1
2
1
0
1
1
2
1
0
1
2
0
0
1
1
0
1
0
2
1
1
0
1
2
1
0
2
0
2
1
1
2
1
2
1
1
0
2
0
2
0
1
2
2
2
0
1
1
0
1
1
0
0
1
1
5
0
1
2
1
2
2
0
1
1
0
0
1
0
1
1
1
0
1
2
0
3
2
1
2
1
0
1
1
1
1
1
0
1
0
1
0
1
0
1
1
2
1
1
0
2
1
1
1
0
0
1
1
1
1
1
2
1
1
2
2
0
1
1
1
1
1
1
1
0
2
1
1
1
1
1
0
2
0
1
0
1
1
1
1
1
2
1
0
1
1
0
1
1
1
1
2
1
0
1
2
1
1
1
0
1
2
1
0
2
2
1
1
0
2
1
1
1
1
3
2
0
2
1
2
2
1
0
0
0
2
1
0
0
1
1
1
0
0
1
1
0
0
3
2
1
2
0
2
1
0
0
1
1
1
1
1
0
1
1
1
1
1
1
0
1
0
2
0
2
1
1
1
1
2
1
1
1
1
2
2
0
1
1
2
2
1
1
0
1
2
0
1
1
1
2
0
1
0
1
1
0
1
1
1
1
2
1
1
1
2
2
0
1
1
1
1
1
0
0
1
1
2
1
0
1
2
1
1
1
1
0
2
1
1
1
1
2
2
1
1
0
0
0
0
2
2
0
1
0
1
1
1
1
0
1
0
0
1
0
2
1
2
2
0
1
0
0
1
1
1
0
1
0
1
1
2
1
1
1
1
1
0
1
1
1
1
1
0
1
1
2
1
0
1
2
1
2
2
2
0
1
0
2
2
2
1
0
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
0
2
0
1
1
0
1
2
2
2
0
1
1
0
2
0
2
2
0
3
2
0
0
1
0
1
0
0
1
1
2
1
1
1
1
2
1
1
2
1
2
0
1
0
1
1
0
0
1
1
1
1
1
1
1
2
2
1
0
0
1
0
1
4
0
0
2
1
2
1
1
0
1
1
1
0
1
1
1
2
0
3
1
1
1
1
0
1
2
2
0
2
0
0
1
3
0
2
1
2
2
1
2
2
1
1
1
1
0
0
0
1
0
2
1
0
0
1
1
1
1
1
2
1
2
3
0
0
0
1
1
2
0
1
1
2
1
2
2
1
1
1
1
2
0
1
2
0
1
0
0
1
1
0
1
2
1
0
4
1
1
2
2
1
1
1
1
0
1
1
1
0
1
1
2
1
1
1
0
0
0
1
1
1
2
2
1
1
0
0
0
1
0
1
2
1
0
1
1
2
0
0
1
0
1
0
1
1
1
0
1
1
0
1
1
0
1
0
1
1
1
1
0
0
0
2
2
1
0
0
1
1
1
1
1
1
2
1
1
2
1
1
1
1
0
2
1
1
1
2
2
1
0
1
2
1
1
0
1
0
2
0
2
0
1
1
1
1
1
2
1
0
1
2
1
0
1
0
1
1
1
0
0
2
1
1
1
0
1
0
2
0
1
1
2
1
1
0
0
0
2
2
1
2
1
1
2
1
0
1
0
1
2
2
1
2
0
2
2
2
1
1
0
2
1
0
2
1
1
1
0
0
1
1
2
1
2
0
2
0
1
2
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
0
1
1
3
1
2
1
2
1
2
0
0
1
1
1
2
2
1
1
1
1
1
1
1
1
1
2
0
2
1
2
2
1
1
1
2
2
1
1
2
1
1
1
2
0
2
0
3
1
2
0
2
1
1
2
0
1
2
0
2
1
1
1
2
2
0
0
2
1
2
1
1
1
0
1
1
2
0
1
0
1
1
0
1
1
1
2
2
1
0
1
2
1
1
0
1
1
0
1
1
2
0
2
2
1
0
0
2
1
0
2
1
2
1
2
1
1
1
1
3
1
1
1
1
0
2
1
2
1
1
1
1
1
0
2
1
1
0
1
1
1
1
1
0
1
1
0
0
1
0
0
1
0
1
0
1
1
0
1
2
1
0
2
1
1
1
1
2
1
1
1
1
1
1
2
0
1
2
2
1
1
1
2
1
2
1
1
2
0
1
0
1
1
1
0
1
2
1
1
1
0
0
0
1
1
1
2
0
0
1
0
0
1
0
1
2
2
1
1
0
1
2
1
1
1
1
1
0
1
0
0
1
1
0
2
0
0
1
0
1
1
0
1
2
1
1
1
0
1
2
1
1
2
0
2
0
2
1
1
1
0
1
1
2
1
3
1
1
0
1
2
1
2
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
2
1
0
1
0
2
1
0
2
1
0
2
1
1
1
1
2
1
1
1
1
1
0
1
1
2
1
0
6
1
0
2
1
1
2
1
2
1
0
1
2
1
1
1
1
1
1
1
1
0
1
1
1
2
1
1
1
1
1
1
2
2
2
0
2
1
1
0
1
2
1
1
1
2
2
2
1
1
1
0
2
1
0
1
1
2
1
1
0
1
1
1
0
2
1
3
1
0
1
1
1
1
1
1
2
2
1
0
1
0
0
1
0
2
1
2
1
1
2
1
0
1
1
1
2
0
1
0
1
1
1
1
1
0
1
1
1
1
2
1
1
1
2
2
2
1
1
1
2
0
1
1
1
1
0
1
1
0
1
1
1
0
1
1
0
2
1
2
1
1
0
2
0
1
2
1
1
0
2
2
0
0
2
2
1
1
1
1
2
1
0
1
0
1
1
0
1
1
0
2
2
2
2
1
1
1
2
1
1
1
0
0
1
2
2
2
2
1
1
2
1
0
1
0
2
0
1
1
0
1
1
2
1
0
1
1
2
1
1
3
1
2
1
1
0
0
2
0
1
2
1
1
1
0
2
1
0
2
0
2
1
2
1
0
3
0
1
1
2
0
0
1
1
2
1
0
0
2
1
3
1
1
1
1
2
0
0
1
1
1
1
1
2
2
0
1
1
1
1
0
1
1
2
0
1
0
1
0
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
0
1
1
1
1
1
1
2
1
1
0
0
0
1
1
1
0
1
1
2
1
0
2
2
0
2
0
0
1
1
1
1
2
1
1
2
2
1
1
0
0
1
2
2
1
1
1
0
1
1
2
1
1
2
0
0
0
2
1
3
2
0
0
2
1
1
1
2
1
1
1
0
0
1
2
1
0
0
1
1
0
0
1
3
1
1
1
0
1
2
2
2
0
2
0
0
1
0
2
0
1
0
1
0
0
1
2
0
1
1
1
0
0
1
1
1
2
0
2
1
1
1
1
2
2
2
2
1
0
1
2
2
0
1
1
3
1
2
2
1
0
2
1
0
1
1
1
2
1
1
1
1
2
1
1
1
0
2
1
1
1
2
0
2
1
2
2
1
1
2
1
1
1
0
1
1
1
0
2
1
2
0
0
1
1
2
2
1
1
2
1
1
1
1
1
1
0
0
2
2
2
0
0
2
1
0
1
1
1
1
2
2
1
1
1
2
2
0
1
1
0
1
1
2
1
1
1
0
1
0
1
1
2
1
1
1
1
0
1
2
2
1
2
2
1
2
1
2
1
0
2
2
0
0
1
0
1
2
1
1
2
0
1
1
0
1
0
2
1
1
0
2
1
2
2
2
1
1
0
2
1
0
0
0
2
1
2
0
2
3
0
2
2
2
1
1
1
1
1
1
2
0
2
1
1
1
1
1
1
1
1
1
2
0
1
1
1
1
1
1
2
1
1
1
1
0
1
0
1
1
0
0
0
2
1
1
1
0
1
3
0
0
1
2
1
1
2
1
1
1
1
2
1
1
1
1
1
0
1
0
2
0
1
2
1
1
0
2
0
2
1
1
2
1
0
1
1
1
2
0
1
0
2
1
1
1
1
2
0
0
1
1
1
1
2
0
1
2
1
2
2
1
1
2
1
0
1
2
1
1
0
1
1
2
0
1
2
1
1
1
1
1
0
1
1
1
1
0
0
2
2
2
1
1
1
1
2
1
1
2
1
1
2
1
0
1
0
0
2
1
1
2
1
1
1
2
0
0
2
8
1
0
1
1
0
2
1
2
1
1
1
1
1
1
1
0
3
2
0
0
2
0
1
0
2
1
0
1
0
2
1
0
2
2
1
1
0
1
1
1
1
0
1
2
1
2
0
2
1
1
1
1
0
0
2
1
1
1
1
2
0
1
0
2
0
2
1
2
2
1
1
0
1
1
1
1
1
1
1
2
2
0
0
0
1
1
1
1
1
0
1
0
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
2
2
1
1
2
0
2
1
1
1
2
1
0
1
1
0
1
2
2
2
1
2
1
1
2
2
1
0
1
1
2
2
0
0
2
0
2
2
2
2
2
2
2
1
0
1
1
1
2
1
1
2
1
0
1
0
1
1
1
0
1
2
0
2
1
0
1
2
0
1
1
1
1
4
1
1
1
1
1
2
0
1
0
0
1
0
1
0
0
2
2
0
0
2
0
1
1
1
0
1
2
0
1
1
2
1
1
2
1
1
1
2
1
2
1
1
2
2
0
1
2
0
0
0
2
0
2
0
1
2
1
1
1
0
1
0
1
1
1
0
1
0
0
1
1
1
1
1
0
2
1
0
1
0
1
2
1
2
1
1
1
1
0
2
0
1
1
1
1
1
1
2
1
1
0
1
1
2
2
2
0
1
1
0
1
1
1
1
1
2
0
1
2
1
0
1
1
2
1
2
1
0
2
3
1
0
1
1
1
0
2
2
0
0
0
1
0
1
1
3
1
1
1
0
1
1
0
1
2
0
1
0
1
0
0
1
2
1
2
3
0
1
0
1
1
1
2
1
2
1
0
0
1
0
0
1
1
1
0
1
2
0
1
2
1
1
0
0
1
1
2
1
0
1
1
1
0
1
1
2
0
1
0
1
0
1
2
0
1
1
1
0
1
0
1
0
2
1
1
1
1
1
2
0
2
0
0
1
1
1
1
1
1
0
0
1
1
0
1
1
0
2
1
2
1
1
1
1
1
0
1
1
2
1
2
1
1
2
1
2
0
2
1
1
2
2
2
2
1
2
1
1
1
1
1
1
1
1
0
1
2
1
1
2
0
0
1
0
2
1
0
1
1
0
0
1
1
1
1
0
1
0
2
1
0
1
1
1
2
5
0
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
0
1
1
2
0
0
0
1
1
0
1
1
1
1
2
1
1
1
2
0
0
1
2
1
1
0
2
0
0
2
1
1
2
0
2
1
2
2
0
1
1
0
2
1
1
1
1
0
1
2
1
0
1
1
0
2
2
1
2
1
1
1
1
1
1
0
2
1
0
1
0
1
1
2
1
2
1
1
2
1
1
2
1
2
1
1
2
2
2
0
1
2
2
1
1
2
1
1
1
2
0
0
2
1
2
1
3
1
0
1
1
1
2
0
1
1
1
3
1
1
1
0
0
2
1
0
1
1
0
0
1
0
1
1
1
2
1
2
1
1
1
2
1
1
2
0
2
1
1
2
1
1
1
1
1
1
2
1
0
1
1
1
2
2
0
1
0
1
1
0
1
1
0
0
1
1
2
0
0
2
1
0
0
2
0
1
1
0
1
2
1
1
0
1
0
1
1
1
1
1
1
1
0
2
2
1
1
2
1
0
2
0
1
2
2
1
2
0
1
1
1
2
0
1
1
1
1
1
1
0
0
1
1
2
0
0
0
0
1
1
1
2
0
2
1
0
2
1
0
1
1
1
0
0
2
0
1
0
0
2
1
1
0
2
0
1
2
1
1
1
1
1
1
1
2
1
1
0
1
0
2
0
0
1
1
2
0
2
0
1
0
2
1
1
1
2
1
0
2
1
2
0
1
1
1
0
0
0
1
2
1
1
1
1
1
2
0
1
1
0
1
2
0
1
0
0
1
1
1
1
2
1
0
0
2
1
1
2
1
1
3
1
0
2
1
2
1
1
2
1
1
1
1
2
1
1
1
0
1
2
1
1
2
1
1
1
0
1
2
2
1
1
0
2
1
0
1
1
1
1
2
1
1
1
1
2
0
1
1
1
1
1
1
0
0
1
0
1
1
1
1
1
1
1
1
1
2
1
1
0
2
1
2
0
3
2
2
1
2
2
1
0
0
1
1
0
1
2
1
0
1
1
0
0
2
1
1
1
1
0
1
1
1
0
0
1
1
1
1
1
2
1
0
2
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
2
2
3
0
1
0
2
2
1
2
2
2
1
1
1
0
3
2
2
1
1
0
0
1
1
1
0
1
2
0
1
1
1
1
2
2
1
1
0
1
0
2
0
2
2
0
1
2
2
0
1
1
0
1
2
1
0
1
0
1
1
1
1
1
1
2
0
1
2
1
1
2
1
2
1
1
1
1
1
0
0
1
1
0
1
2
1
1
1
2
0
2
1
1
0
1
2
1
1
2
0
1
0
1
2
2
1
0
1
2
1
2
2
1
1
2
1
1
1
0
1
1
1
0
2
0
0
2
2
1
1
2
1
3
0
0
1
1
1
1
1
1
2
0
1
2
1
1
0
0
1
2
0
1
0
3
1
1
1
0
2
1
1
1
1
0
1
1
1
1
0
0
2
1
1
2
0
1
2
0
1
1
2
1
0
1
0
1
1
1
1
0
2
1
1
2
1
2
0
0
0
0
1
1
1
2
0
1
1
1
1
1
1
0
2
0
2
1
1
2
1
1
0
1
1
1
0
3
2
1
2
0
1
1
2
1
1
0
1
2
1
2
2
1
1
0
1
2
0
0
0
1
1
0
1
1
1
2
2
1
2
1
1
1
1
1
2
0
0
1
1
1
1
1
2
0
2
0
0
1
1
2
1
2
2
1
1
1
0
2
2
2
1
0
1
0
2
2
1
1
1
0
1
1
1
1
1
1
2
0
1
1
0
2
1
1
0
3
2
2
1
1
1
2
1
1
2
0
1
2
1
1
2
2
3
0
0
1
0
0
1
1
0
1
1
0
0
0
1
1
1
1
0
1
1
1
1
0
1
2
2
1
1
1
2
0
2
0
1
0
1
0
1
0
1
0
2
0
1
1
1
1
2
1
1
1
1
2
2
1
0
2
2
2
1
2
1
1
1
2
1
1
1
1
0
1
1
2
1
1
0
1
1
1
1
0
2
0
1
0
3
0
1
2
1
2
2
2
2
1
1
1
1
1
1
1
1
2
1
1
1
0
1
2
1
2
1
2
1
1
1
1
1
1
1
1
2
2
1
0
0
0
0
0
1
3
0
1
0
0
0
0
1
2
0
1
1
1
2
1
1
1
1
2
2
0
2
0
0
2
0
1
1
0
1
1
1
1
1
2
2
1
0
1
0
0
1
1
0
1
2
1
2
1
1
0
1
1
1
2
1
1
2
2
1
1
2
2
2
1
0
1
0
1
2
2
1
1
0
0
1
1
1
2
1
0
2
1
2
1
1
2
1
0
0
1
1
1
1
1
2
2
2
1
1
1
1
1
0
0
0
0
1
2
1
1
2
0
2
1
1
1
0
0
1
1
2
0
2
2
1
0
1
2
1
1
2
1
6
0
2
2
1
0
2
0
2
2
1
0
1
2
0
1
0
1
2
1
1
1
0
4
2
1
1
2
1
3
0
1
1
2
0
2
1
1
1
2
1
0
2
1
2
1
0
3
1
1
3
1
1
0
0
1
0
2
1
1
2
1
1
1
2
0
1
1
2
1
1
1
0
1
1
1
1
2
2
0
0
0
0
0
1
1
0
2
0
1
2
0
1
2
1
1
1
2
2
0
1
2
2
1
0
1
2
0
2
1
0
2
0
1
1
1
2
0
2
2
1
0
1
2
0
2
0
1
2
1
1
2
1
1
1
2
0
1
1
1
0
1
1
0
1
1
1
2
1
1
2
1
1
1
1
0
1
1
1
0
0
1
1
1
1
0
1
0
1
0
1
1
0
1
2
1
1
1
2
1
1
1
2
0
2
2
0
1
1
0
2
0
2
1
2
2
1
1
1
1
1
0
2
1
1
1
1
1
2
1
0
1
1
0
1
1
2
0
1
0
1
2
0
0
1
1
0
2
1
2
1
0
0
2
2
1
0
0
1
1
2
2
1
1
1
2
1
2
2
0
2
1
2
1
0
2
0
1
1
0
2
1
1
2
0
1
1
1
2
0
0
1
1
0
1
1
2
1
2
2
2
1
0
2
1
0
1
1
1
1
1
0
2
1
2
0
0
0
0
1
0
1
1
1
0
1
0
0
1
1
1
2
1
2
0
0
1
1
1
1
1
1
1
0
2
2
1
1
1
1
2
1
1
1
2
1
2
2
1
0
1
1
2
1
1
1
1
1
0
2
1
1
0
1
0
1
0
0
1
1
0
1
0
1
1
1
2
1
0
1
1
0
1
1
1
1
0
2
1
1
2
1
1
1
1
1
3
1
1
1
2
1
2
2
0
2
0
3
2
1
1
2
1
1
1
0
0
1
2
0
2
1
2
0
1
1
0
1
2
1
1
1
0
0
1
0
1
1
1
1
2
2
0
0
1
1
1
1
1
1
1
0
1
0
2
1
1
2
1
0
2
0
0
0
1
1
1
1
1
2
1
1
1
1
2
0
0
1
1
1
0
1
1
1
1
1
2
0
0
1
1
1
1
2
1
1
1
1
0
1
2
0
2
1
0
0
0
1
1
1
0
1
1
2
2
0
1
1
1
1
2
1
0
1
2
1
1
2
1
1
0
1
1
0
0
1
0
1
1
1
1
0
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
0
1
0
0
0
1
2
0
0
1
1
1
1
0
1
0
0
1
0
2
1
1
1
1
1
0
1
2
0
1
2
1
0
0
0
1
1
1
0
3
1
1
1
0
0
0
1
1
0
1
1
1
1
1
1
1
0
2
1
1
1
1
1
1
1
1
0
2
1
2
0
0
0
1
1
1
2
2
2
0
1
0
1
0
0
2
1
0
0
1
1
1
2
0
2
1
0
2
2
2
0
0
2
1
2
1
2
2
0
0
1
2
1
2
1
1
2
2
0
2
1
1
1
0
1
2
1
0
1
0
2
1
1
1
1
1
0
1
1
1
0
1
0
0
1
2
1
1
1
1
1
2
1
2
1
0
0
1
1
1
1
2
0
1
2
2
1
0
1
0
1
2
1
0
2
1
1
1
1
1
1
0
0
1
2
1
1
0
2
2
1
1
2
0
1
1
2
1
1
1
1
1
1
2
0
2
1
0
0
1
1
0
0
2
1
0
2
2
1
2
1
1
1
1
2
1
1
2
0
2
2
1
2
1
2
1
2
1
1
1
1
0
0
0
1
2
0
1
1
0
0
2
0
1
1
1
1
0
0
1
1
1
2
1
1
1
1
0
1
1
1
1
1
1
1
1
0
2
1
1
1
0
1
1
1
1
0
2
1
1
1
1
1
1
1
4
2
1
1
2
2
0
2
1
1
0
1
0
1
0
1
0
1
2
2
1
1
0
2
2
2
1
1
1
1
0
1
2
1
2
1
1
2
1
1
1
1
1
2
1
2
1
2
1
1
1
1
0
2
1
1
3
0
1
2
1
0
1
1
1
2
1
1
1
2
2
2
2
0
0
0
0
0
1
0
0
2
1
2
1
2
1
2
1
1
1
1
0
1
1
1
1
1
1
2
1
2
1
1
1
2
1
1
2
2
1
0
0
0
1
1
0
1
0
1
0
1
2
1
1
1
1
0
1
1
0
1
2
1
1
1
1
2
1
1
2
0
1
0
1
1
0
1
2
1
1
1
1
1
0
0
1
1
1
1
0
1
0
1
1
1
0
0
1
0
1
1
0
2
1
2
0
1
1
0
2
2
0
1
1
3
1
1
1
0
1
1
1
2
1
0
0
1
1
0
1
2
1
2
1
1
1
0
0
2
0
1
2
1
1
1
0
1
1
1
2
1
2
1
1
1
1
1
0
0
0
1
1
1
1
0
1
1
1
0
1
2
1
1
0
0
1
0
2
1
0
0
0
2
1
2
1
1
2
1
0
0
1
1
1
2
1
1
1
1
1
1
1
1
0
0
1
1
2
2
1
2
2
2
2
1
2
0
1
1
2
0
2
2
1
1
0
2
1
1
0
0
1
0
1
1
2
1
1
1
1
0
1
1
2
2
1
0
1
1
0
0
2
1
1
1
1
1
2
2
1
0
1
1
1
0
2
0
2
0
1
1
1
1
2
1
1
2
0
1
1
2
0
2
2
2
0
1
0
1
1
1
0
0
0
1
2
1
1
1
0
1
1
2
1
1
0
1
1
1
0
0
1
1
1
1
2
1
1
1
1
0
1
1
2
1
2
1
1
1
2
2
1
0
0
1
1
2
2
1
2
1
1
1
1
1
0
1
1
1
1
1
2
2
2
0
1
1
2
1
0
1
1
2
0
1
3
0
2
0
1
1
1
1
1
1
2
1
0
1
2
1
0
1
1
1
1
1
2
1
1
1
0
1
1
2
1
1
1
1
2
0
1
0
1
1
2
0
0
1
0
0
1
0
2
1
2
1
0
1
0
1
2
0
0
1
2
0
1
2
1
1
0
2
1
1
1
1
1
1
0
1
1
1
2
1
1
1
2
1
1
1
2
2
1
1
1
0
1
0
2
1
1
1
1
2
2
2
1
4
1
1
0
2
0
1
0
1
1
1
1
0
0
0
1
0
0
1
2
2
1
1
2
0
2
2
1
2
1
1
1
0
1
0
1
0
1
0
1
1
2
0
2
1
1
1
2
1
1
0
2
0
0
1
1
3
1
1
1
2
2
2
1
2
2
2
1
1
1
0
0
2
1
2
1
0
1
2
1
0
1
0
0
0
1
1
1
2
1
1
1
1
2
1
1
0
1
1
1
1
1
0
2
0
0
1
1
0
1
1
2
1
0
1
1
0
1
1
0
1
1
2
0
1
2
2
1
1
1
2
1
1
2
1
0
1
1
1
1
1
2
0
1
1
1
1
1
2
1
2
1
2
2
0
2
1
1
0
1
2
1
0
1
1
1
3
1
1
1
0
1
1
1
1
1
0
2
1
0
2
1
1
2
1
1
1
1
4
1
0
1
1
1
1
0
0
1
1
2
2
1
1
0
1
1
1
0
1
1
1
1
1
2
0
1
0
1
1
0
2
1
0
1
0
1
2
1
1
1
1
2
0
1
1
1
1
1
1
2
2
0
1
2
1
1
1
1
1
2
2
0
1
2
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
2
1
1
1
0
0
2
2
2
0
0
0
2
1
0
0
0
1
1
2
1
2
0
0
0
1
2
1
2
2
0
2
1
0
0
1
0
0
2
0
1
1
1
1
2
2
1
1
1
2
0
1
1
0
1
1
1
1
1
1
1
1
0
0
0
1
0
1
1
0
2
1
2
1
2
2
1
0
2
0
1
1
1
1
0
1
1
2
1
0
0
2
1
0
1
2
1
0
1
1
0
2
1
0
2
2
0
1
1
1
1
1
0
1
1
0
1
0
2
2
2
0
1
1
0
0
1
1
1
1
1
1
1
1
0
1
2
0
1
0
0
1
0
1
1
1
1
2
0
1
1
0
2
1
1
1
1
2
1
1
2
2
2
0
1
1
1
2
2
1
1
3
2
0
1
1
1
2
0
0
2
1
0
2
2
1
2
0
1
0
1
0
0
2
3
1
2
1
1
0
0
0
2
1
1
2
1
1
0
1
2
0
1
1
1
1
1
1
1
2
0
2
2
0
1
0
1
2
0
1
2
1
1
0
1
1
2
1
1
2
0
1
0
1
2
1
0
1
1
0
1
1
2
1
1
1
2
0
1
0
1
0
0
2
0
2
0
0
1
1
2
0
1
1
1
1
2
1
1
0
1
2
1
0
0
1
2
2
1
1
2
0
1
2
1
2
0
0
2
0
1
1
2
1
1
1
1
2
0
1
1
1
0
1
1
2
0
2
1
2
2
1
1
2
1
0
0
1
1
1
1
0
1
1
0
2
1
1
0
1
1
1
1
1
1
0
2
1
0
1
0
1
1
2
0
2
2
0
1
1
0
2
1
1
1
1
0
2
1
1
0
1
1
2
0
1
0
1
0
2
0
1
2
1
2
1
2
1
0
1
2
1
1
1
0
1
2
1
0
0
0
1
0
0
1
1
1
2
1
0
2
1
1
0
1
0
1
0
1
1
1
1
2
1
1
1
1
2
1
1
2
0
1
2
1
1
0
2
2
1
0
0
0
0
1
0
1
2
0
2
1
0
1
1
1
2
2
1
1
1
0
1
1
1
0
0
2
0
1
2
1
2
1
1
1
1
1
2
2
1
1
0
2
0
1
1
1
0
2
1
1
1
1
1
2
2
2
2
0
0
1
1
1
1
2
1
0
1
2
1
2
1
1
1
1
2
1
2
1
1
1
1
2
2
2
1
0
1
0
1
1
0
1
2
0
1
1
0
1
1
1
1
0
1
2
0
1
2
1
2
1
1
1
1
0
1
0
1
1
1
1
1
1
1
1
2
1
0
0
1
1
1
1
0
2
1
0
1
1
1
1
0
1
2
1
1
1
0
2
1
2
2
0
4
1
1
0
1
1
1
1
1
0
1
0
2
2
2
2
1
0
2
0
1
1
0
0
1
1
1
0
1
1
1
1
2
1
2
1
2
0
1
1
1
2
2
2
1
0
2
2
2
1
2
2
0
0
2
0
1
2
1
0
1
1
0
0
0
2
1
2
1
0
0
1
1
1
0
0
1
1
1
1
1
1
1
1
1
0
2
1
0
0
0
0
1
0
2
0
1
2
2
1
1
1
1
0
1
2
1
0
1
1
2
1
0
1
2
0
0
2
1
0
0
1
1
2
1
0
2
1
0
0
1
1
1
1
1
1
2
1
1
1
0
1
2
2
2
1
2
1
1
0
0
0
1
1
1
0
1
0
1
1
0
0
2
1
1
1
2
2
0
1
1
1
0
2
1
1
2
4
1
1
1
0
1
2
0
0
1
1
2
1
4
1
0
1
2
0
1
2
1
0
0
1
1
1
2
1
1
1
1
0
1
2
1
1
1
0
2
2
0
1
1
0
1
1
0
1
1
1
1
2
1
0
1
1
2
1
1
0
0
1
2
1
1
2
2
1
2
1
1
1
1
1
0
1
1
1
2
1
2
1
0
0
0
1
2
2
1
1
0
2
1
1
1
1
2
2
0
1
1
2
1
1
2
1
1
1
1
1
2
2
1
0
1
1
1
1
2
0
2
1
1
2
1
1
2
2
2
0
1
0
1
1
1
1
1
1
0
0
0
1
0
0
1
3
0
1
1
2
2
1
0
1
1
1
2
2
2
0
2
1
0
1
0
0
2
1
1
1
0
1
0
1
0
2
2
1
1
1
2
0
0
1
2
0
1
1
0
1
1
0
1
1
1
2
2
1
1
1
1
0
1
1
2
1
0
1
2
0
1
1
0
0
1
1
1
1
2
0
0
1
1
0
1
1
1
2
0
1
1
2
1
2
2
0
1
1
1
2
0
1
1
2
1
2
0
2
1
1
2
1
1
1
1
0
1
1
1
1
1
14
2
3
1
1
1
1
1
1
1
0
1
1
0
0
1
1
1
2
0
2
0
2
0
1
1
1
1
1
1
0
1
1
0
0
3
2
1
1
1
2
1
0
1
1
1
1
1
2
2
1
1
1
2
0
2
1
2
1
1
0
0
1
0
1
2
2
0
0
2
0
1
1
0
1
1
1
2
1
2
1
2
1
1
1
2
1
1
2
0
5
0
2
1
1
1
2
1
2
1
2
1
1
2
0
1
0
0
1
2
0
0
2
1
1
0
1
1
0
0
2
1
1
0
2
1
2
1
0
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
2
1
2
1
1
1
2
2
2
1
1
1
0
1
1
2
0
2
1
2
1
0
1
0
2
1
0
0
1
1
1
1
0
1
1
0
0
2
0
1
2
0
2
0
1
2
2
1
1
1
2
1
1
1
1
1
0
2
2
1
2
1
0
1
1
0
2
1
1
1
0
0
2
1
1
2
2
0
1
1
2
1
1
0
1
0
1
2
1
1
1
1
1
0
1
0
0
0
2
1
1
1
0
1
0
2
2
1
2
1
2
0
0
0
1
2
1
1
1
1
1
1
1
2
0
1
0
1
2
1
1
0
1
0
1
1
1
1
1
2
2
2
0
0
2
1
1
1
1
0
1
1
0
0
0
1
1
2
0
2
1
1
0
1
2
1
0
0
1
1
1
1
1
1
2
1
1
2
1
1
1
2
0
1
1
0
2
2
1
1
0
2
2
0
1
1
1
1
3
1
1
1
1
1
1
0
1
1
2
0
1
0
2
1
1
3
2
0
1
0
1
1
1
2
1
0
0
1
1
0
1
0
1
0
2
1
1
1
2
0
2
2
0
0
1
1
0
3
1
0
0
2
0
1
1
0
1
1
1
0
1
1
1
1
0
2
2
0
1
1
1
0
1
2
1
1
1
2
2
1
1
0
1
1
0
1
1
2
2
1
2
1
0
0
1
1
2
1
1
0
1
0
1
1
1
1
1
1
0
1
1
2
1
0
1
1
1
1
0
0
1
2
2
2
1
1
0
1
1
0
1
1
0
1
1
1
1
1
1
2
1
2
0
1
1
1
1
2
2
1
0
2
0
0
2
1
2
0
1
2
1
0
1
0
1
1
2
2
1
1
1
0
1
4
2
2
1
1
1
0
1
1
1
0
1
1
1
2
2
1
1
1
0
0
2
1
2
2
2
2
0
0
1
0
1
1
1
1
1
0
2
1
1
0
1
1
1
1
0
2
0
0
2
2
1
1
0
2
1
0
1
1
2
1
1
2
1
0
0
2
1
1
0
1
1
1
1
0
1
1
2
0
1
2
0
1
1
1
1
0
0
0
2
1
2
1
0
1
2
1
0
1
1
0
0
1
1
1
1
1
1
1
1
1
0
1
1
2
1
1
1
1
1
0
1
0
0
2
2
1
0
0
1
1
1
1
1
1
1
0
0
1
2
0
0
1
2
1
1
1
0
0
1
4
0
0
1
1
1
1
1
0
0
0
1
1
0
2
1
1
1
1
1
2
0
1
0
1
1
1
2
0
1
1
1
1
1
1
2
2
1
0
1
1
1
1
1
1
1
1
1
2
2
1
1
0
1
0
1
2
0
1
0
1
0
0
2
1
2
2
2
1
1
1
2
0
1
1
2
1
2
2
1
1
1
1
1
0
0
1
2
1
2
0
0
1
0
1
0
1
1
0
2
0
1
2
0
2
1
2
1
1
1
1
1
0
1
2
1
1
1
1
1
1
2
0
1
0
2
1
1
0
1
1
1
1
1
0
2
0
0
1
0
0
2
1
2
0
2
1
1
1
0
1
1
1
1
2
1
1
0
1
2
2
1
1
2
0
0
1
0
2
2
1
1
1
1
0
1
0
1
1
1
1
0
0
0
0
0
3
1
1
3
1
0
2
0
1
1
2
1
1
1
0
1
1
1
1
1
1
0
0
1
1
1
2
1
0
1
1
0
2
2
1
2
1
1
1
1
2
2
3
0
2
1
0
1
1
1
1
0
1
2
1
0
3
1
1
1
0
2
2
0
2
2
1
1
1
2
1
1
0
1
1
0
2
0
1
2
0
1
1
1
2
2
0
0
0
0
1
1
2
1
1
0
1
1
1
0
2
2
0
0
1
2
1
1
2
4
1
0
1
1
1
2
1
1
1
1
0
2
2
0
0
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
2
1
1
0
1
1
1
1
1
1
1
1
1
1
0
0
0
1
2
1
0
1
1
1
0
0
2
0
0
0
1
3
0
1
1
1
0
2
1
1
2
2
1
1
1
1
1
2
1
0
2
0
1
1
2
1
2
0
1
1
1
1
1
1
0
2
2
1
0
7
1
2
0
1
2
0
2
1
1
1
1
1
1
1
2
0
1
1
1
1
2
2
1
1
2
1
0
1
1
1
0
1
0
0
1
1
1
0
1
1
0
2
0
0
1
1
1
1
1
1
1
2
1
0
1
2
0
0
1
0
2
1
1
0
1
1
2
1
1
1
1
1
0
1
0
0
2
2
1
2
1
1
0
1
2
0
2
1
1
1
2
1
1
1
1
0
1
1
1
1
1
1
0
0
1
2
0
1
1
0
1
0
1
1
1
1
4
1
1
0
1
0
2
1
0
0
0
0
1
2
0
0
1
2
0
1
2
2
1
1
0
0
1
1
1
1
1
0
2
1
1
1
1
2
1
1
1
1
2
2
1
1
1
1
0
1
1
1
1
1
2
1
1
0
1
1
1
1
0
1
2
0
1
1
3
2
1
1
1
1
1
1
2
1
1
1
0
2
2
1
0
2
2
2
1
1
0
0
2
0
0
1
1
1
2
0
1
0
1
2
1
1
1
2
0
1
1
1
0
1
0
0
1
0
1
0
1
0
0
1
0
2
1
1
1
2
4
1
1
0
1
1
1
0
0
1
1
2
1
0
0
0
1
2
2
0
2
2
2
2
1
1
1
2
1
1
2
1
0
1
1
1
2
1
0
1
0
1
1
1
0
3
2
1
1
2
1
1
0
1
1
0
2
0
0
1
1
1
0
1
1
0
1
0
1
1
0
1
1
1
2
1
2
0
1
2
0
2
1
2
1
2
0
1
1
1
1
0
1
1
1
0
0
1
1
1
0
0
1
1
1
1
1
1
0
0
1
0
0
1
0
2
1
1
1
2
1
2
1
2
1
1
1
0
2
2
2
1
0
0
0
0
2
1
1
1
1
1
0
0
1
1
1
2
1
1
0
2
1
2
1
1
1
1
1
0
0
1
2
1
1
1
0
1
0
1
0
1
1
1
0
0
0
0
2
1
1
0
1
2
0
1
2
2
1
2
0
2
1
1
1
2
1
0
1
0
1
0
1
2
2
0
1
1
1
1
0
1
0
1
2
1
0
0
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
0
0
1
1
1
2
2
1
1
2
0
1
0
1
2
0
0
1
0
2
1
1
2
2
1
2
1
1
0
1
1
0
2
2
1
2
1
1
1
4
0
1
1
0
0
1
1
1
1
1
1
1
1
1
2
0
0
1
1
1
2
1
1
1
1
0
0
3
1
1
1
1
1
1
0
0
1
2
1
1
0
2
1
1
2
2
1
2
1
1
1
1
1
1
2
1
0
1
1
1
1
7
1
2
1
0
1
1
1
2
2
1
2
1
1
0
0
1
2
1
1
2
2
1
1
1
1
1
0
0
2
1
0
2
1
0
1
1
1
2
1
0
1
0
2
2
0
1
0
1
1
1
1
2
0
1
0
0
0
1
0
1
0
0
1
0
2
0
1
2
1
1
2
1
1
0
1
1
1
2
1
1
2
0
0
1
0
1
0
1
0
2
1
3
1
0
1
1
2
2
1
1
1
2
2
1
1
1
3
2
2
2
1
1
1
2
1
2
0
1
0
0
0
1
1
0
2
0
1
1
0
1
0
1
1
1
2
1
1
2
2
1
2
1
1
1
1
1
1
2
1
2
0
0
2
1
1
0
1
1
1
1
1
0
1
2
1
1
1
0
2
2
2
1
1
2
1
2
2
1
0
2
2
1
0
1
1
1
1
1
1
0
1
1
1
1
1
1
1
0
1
0
1
3
1
0
1
2
0
0
2
0
2
1
1
2
1
2
1
1
3
1
2
1
1
1
2
0
0
0
1
1
1
1
0
1
1
1
0
1
2
0
1
1
1
1
1
1
1
1
1
2
3
0
0
1
1
1
0
1
1
1
1
1
2
1
1
1
2
1
0
2
0
0
1
1
1
1
2
1
2
0
0
1
2
1
1
1
1
1
0
1
1
1
2
0
1
1
1
1
1
1
1
2
2
0
1
0
1
1
1
1
2
0
2
0
1
1
1
0
1
1
2
2
2
2
1
1
2
2
2
1
1
1
1
2
0
1
2
2
0
1
1
1
0
1
2
1
1
0
0
2
1
2
2
1
0
1
1
1
2
2
0
1
1
1
1
0
1
1
1
1
0
1
0
1
2
1
1
1
2
2
1
3
1
0
2
0
1
1
1
1
1
0
1
0
1
1
1
1
3
3
1
1
0
2
1
2
0
1
1
1
1
1
0
1
1
1
0
2
1
1
0
1
1
1
2
0
1
2
1
0
2
1
0
1
1
1
0
1
1
1
2
1
1
0
0
0
1
1
1
0
0
1
2
2
1
1
2
1
1
0
2
1
2
2
0
1
1
1
2
1
0
1
1
1
0
1
1
1
1
2
1
1
1
2
0
1
1
1
0
0
1
1
1
1
2
1
0
2
1
1
1
0
1
1
2
2
0
1
1
1
2
1
0
1
1
0
0
1
1
0
2
0
2
2
1
1
2
0
2
1
1
2
1
2
1
1
1
1
1
0
0
2
2
0
1
1
1
1
1
2
0
2
1
0
1
1
0
2
1
2
0
0
1
0
1
0
1
0
0
0
2
1
2
0
2
1
0
2
1
2
0
0
2
0
2
2
1
0
1
2
0
1
0
1
1
1
3
1
0
1
0
1
1
2
0
1
2
1
2
1
1
1
1
1
0
0
1
0
1
1
1
2
2
2
0
1
1
2
2
1
2
2
0
1
0
1
1
1
1
2
1
2
1
0
1
0
1
1
2
1
2
0
0
2
0
2
2
1
1
1
1
1
1
2
1
2
0
0
1
2
0
0
1
1
2
0
0
0
0
0
1
0
1
1
2
1
0
1
1
2
2
1
2
0
0
1
1
0
1
0
0
0
2
2
2
0
0
0
1
1
1
1
1
1
0
1
1
2
1
1
0
0
2
0
0
1
0
2
1
1
0
2
0
1
0
1
2
0
1
0
0
1
1
1
1
0
0
1
1
3
0
1
0
1
1
0
1
0
2
1
0
0
2
2
1
2
0
1
1
0
0
1
2
1
2
1
1
0
2
2
0
1
1
0
1
0
1
1
1
2
1
1
2
1
2
1
1
1
1
0
1
1
0
0
1
1
1
1
0
2
0
0
0
2
1
1
2
1
1
2
2
0
1
0
2
0
1
1
0
1
2
1
0
0
2
0
1
1
1
1
2
2
2
1
2
0
0
0
1
2
2
1
0
2
1
1
1
2
1
1
1
2
1
0
1
2
0
1
1
2
0
1
0
2
1
1
2
0
0
2
2
0
2
1
2
1
1
0
1
0
2
0
1
1
2
0
0
1
1
2
0
2
0
2
2
0
1
0
2
2
1
0
0
2
2
1
1
1
1
1
1
1
1
2
1
1
1
2
1
2
0
1
0
1
1
1
0
0
1
2
0
0
2
1
2
1
2
2
1
1
1
1
1
1
1
1
0
1
1
1
0
0
0
0
1
0
1
1
2
2
1
1
1
2
1
2
0
1
2
0
1
2
2
1
1
1
1
1
2
1
1
0
1
0
1
1
1
1
1
2
2
1
0
0
0
0
1
1
0
1
0
2
0
2
0
2
0
1
1
1
1
1
1
1
1
0
1
0
0
1
1
0
0
1
1
1
0
2
1
0
1
1
1
1
0
1
1
0
1
0
0
2
0
0
0
0
1
1
1
1
1
1
1
1
1
0
0
1
1
0
1
1
1
0
2
0
2
1
1
1
1
1
1
1
1
2
2
0
0
1
1
2
1
0
1
1
1
1
0
1
3
1
1
0
0
1
1
1
1
1
0
0
0
3
1
1
1
0
0
0
1
2
1
1
2
0
1
1
2
0
1
0
0
2
1
2
1
2
1
1
1
1
0
1
0
1
2
0
0
0
6
1
1
0
0
1
0
1
1
2
1
2
1
1
1
0
1
2
0
1
1
1
0
0
0
1
2
1
2
1
2
1
2
1
1
3
1
1
1
1
2
1
0
0
1
1
1
0
1
0
0
1
1
1
1
4
1
0
0
1
2
2
1
1
2
1
1
1
1
1
0
1
1
0
1
1
2
0
2
2
0
1
2
1
1
1
1
2
2
1
0
2
1
1
1
1
1
1
2
2
0
1
2
0
2
1
2
1
1
0
2
1
1
0
1
0
1
1
1
2
1
1
1
0
1
2
0
2
0
0
1
2
2
1
1
2
0
2
2
0
2
1
1
2
2
2
1
1
2
1
2
1
3
0
2
2
1
2
1
1
0
1
2
1
1
1
1
0
0
1
2
2
0
0
2
1
2
0
2
0
2
2
1
2
1
1
0
0
1
1
0
1
1
1
0
0
2
0
1
2
1
0
1
1
1
0
1
1
2
2
2
1
1
1
1
1
2
0
0
0
1
1
1
0
1
1
1
0
1
1
2
1
2
0
0
1
1
1
1
0
0
2
1
0
1
2
0
0
1
1
1
1
2
1
1
1
0
1
0
1
1
0
0
1
1
2
1
1
1
1
2
1
2
2
1
1
1
1
2
1
1
1
0
0
1
2
2
2
1
1
2
0
1
0
2
1
2
2
1
1
0
1
1
1
0
1
1
2
1
2
1
1
2
1
0
1
1
1
1
2
0
1
1
1
1
2
1
2
1
1
0
1
0
1
2
2
0
1
0
1
1
2
1
0
0
0
1
2
2
1
1
0
1
1
2
1
1
1
1
0
0
1
1
1
0
0
2
1
2
1
1
0
2
0
2
1
0
2
1
2
0
1
2
1
1
1
1
1
0
1
2
1
2
1
1
1
2
2
1
0
1
1
0
2
1
1
1
2
1
0
2
1
1
1
1
1
3
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
2
1
0
0
2
0
1
0
2
1
1
2
1
1
1
0
1
1
0
1
1
1
1
1
1
0
2
1
0
2
2
1
1
1
1
2
1
0
0
1
2
1
2
3
0
2
1
0
1
1
1
1
1
1
1
0
2
1
2
2
2
2
1
0
1
1
1
1
1
4
1
2
1
1
2
1
2
0
1
0
2
1
1
2
0
0
1
1
0
0
1
0
1
2
1
1
0
0
1
1
0
2
1
1
0
2
2
2
1
0
1
1
2
0
1
1
1
2
1
1
1
0
2
1
1
1
1
2
1
0
1
1
1
0
0
1
1
1
1
1
1
0
1
1
2
2
1
1
1
1
1
1
1
0
1
1
1
2
1
1
0
2
1
0
1
2
3
0
3
2
0
1
2
1
2
2
1
1
2
0
1
0
1
2
2
0
2
2
1
1
1
1
0
0
2
2
2
1
2
1
1
0
0
1
2
1
2
2
0
1
1
1
1
2
0
0
2
1
2
1
2
1
2
1
2
1
1
1
2
1
2
0
1
1
1
1
1
2
0
0
0
1
1
1
1
1
1
0
2
1
0
1
1
0
0
1
0
1
1
1
0
1
1
1
0
0
2
1
2
2
1
1
1
0
0
2
1
2
1
1
1
1
1
1
1
1
1
2
2
0
1
1
1
1
1
1
1
1
1
3
0
1
2
1
1
0
1
1
1
0
1
1
2
1
0
1
2
3
1
2
0
1
1
2
1
1
2
2
1
1
0
0
0
1
1
1
2
0
0
1
0
2
1
2
2
1
1
2
2
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
0
1
2
1
2
0
1
1
1
1
1
1
0
1
1
1
1
0
2
1
1
0
2
1
2
0
0
0
3
2
1
2
1
1
1
1
0
0
0
1
0
2
2
2
2
0
2
1
0
2
1
0
1
1
0
1
1
2
3
1
0
1
1
0
1
2
1
1
1
1
2
1
1
1
1
0
0
0
2
1
1
1
1
1
2
1
0
1
1
1
1
1
0
1
0
0
0
1
1
0
0
1
0
2
1
1
1
1
2
1
1
0
2
1
1
2
1
1
0
0
0
1
1
0
1
1
3
1
0
0
1
0
1
0
1
1
2
1
1
2
1
1
1
0
3
1
2
1
1
0
0
1
1
0
1
2
0
2
1
0
0
1
1
1
2
0
1
2
1
2
1
0
1
2
0
1
2
2
1
0
2
0
2
0
1
1
2
2
1
0
1
1
0
1
1
1
1
1
0
0
0
1
1
0
1
2
1
1
2
1
1
1
2
1
0
2
2
2
1
0
1
1
1
1
1
2
0
2
1
2
0
1
1
0
1
2
1
1
2
1
2
1
3
2
1
2
0
0
1
1
1
1
1
0
1
2
2
2
0
1
0
1
1
2
0
1
2
2
1
2
0
1
1
1
1
2
1
0
0
1
1
0
1
0
1
2
0
1
1
1
1
0
2
1
2
1
1
1
0
1
2
3
1
1
2
0
1
0
2
2
2
1
0
1
1
0
0
1
0
2
2
3
2
1
1
2
1
1
1
0
2
0
1
2
0
1
1
1
1
1
2
2
0
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
0
1
0
1
1
0
1
1
0
1
1
0
1
2
1
2
1
1
1
1
1
1
1
1
1
2
2
0
2
2
2
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
0
2
2
1
0
1
1
1
1
1
1
2
1
1
1
2
0
0
1
0
1
1
1
1
2
1
2
0
0
1
2
1
1
0
0
0
1
0
1
0
0
1
2
1
1
1
0
0
0
1
2
0
1
1
1
1
1
2
0
1
1
1
1
1
0
0
2
1
0
2
2
2
1
1
1
0
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
0
1
0
1
0
0
1
1
1
0
3
1
0
1
0
2
1
1
1
2
0
1
0
0
2
1
1
1
0
0
2
1
0
1
1
0
1
1
1
1
0
1
0
0
1
2
2
2
1
1
0
0
2
2
0
1
1
1
0
1
1
1
1
1
2
1
2
1
0
1
1
0
1
1
0
1
2
2
0
1
1
1
0
1
0
1
1
2
1
0
0
1
0
0
1
2
0
1
0
2
1
2
1
0
1
2
1
1
0
0
0
1
1
0
0
2
0
1
2
2
2
0
1
1
0
1
1
1
2
2
2
2
0
2
1
1
1
1
1
1
0
1
1
1
0
1
1
1
1
1
1
0
1
2
0
1
1
1
1
0
2
1
1
1
0
0
0
2
0
2
1
0
1
0
1
1
1
1
0
1
2
2
0
0
1
3
0
1
1
1
2
2
1
0
1
2
1
2
0
2
2
0
0
2
2
0
1
1
1
1
1
1
3
0
1
1
2
1
0
1
1
0
1
0
1
1
2
1
1
1
0
1
0
0
0
1
0
1
1
1
0
0
0
1
0
0
1
1
0
0
0
2
1
1
1
1
2
1
2
0
2
1
1
1
1
0
1
1
2
1
0
2
1
1
1
1
0
1
2
0
1
1
0
1
1
0
1
0
0
0
0
1
0
1
1
0
1
1
2
0
1
0
1
1
2
2
0
1
1
1
2
1
2
1
1
1
1
1
1
1
1
0
1
1
0
0
1
2
2
1
1
1
1
1
2
1
1
0
1
1
1
0
1
0
2
0
1
0
1
1
1
2
1
1
1
0
1
1
2
1
1
0
2
1
2
2
2
0
2
0
1
2
1
1
1
1
1
0
2
0
2
1
1
1
1
1
2
2
1
1
1
2
2
1
2
1
2
2
0
1
2
0
2
0
1
1
0
2
0
0
0
1
1
1
1
0
1
1
0
2
1
0
1
1
1
1
2
0
0
2
1
0
1
1
2
1
1
1
2
0
1
0
2
1
0
2
1
0
0
1
1
1
2
0
0
2
1
2
2
2
1
2
1
1
0
0
1
0
1
0
1
2
1
1
0
1
2
1
1
1
1
0
1
1
1
1
2
1
1
2
1
1
0
2
1
1
1
2
1
1
1
2
2
1
1
1
0
1
1
1
1
1
2
1
2
1
2
1
0
1
0
1
1
1
0
1
2
2
2
0
0
2
2
0
2
1
1
1
1
1
3
1
2
0
1
1
0
2
3
1
2
1
1
1
0
0
1
1
1
1
2
0
1
0
2
1
1
1
2
1
0
1
0
1
1
0
1
0
0
2
1
1
2
1
1
0
1
0
1
1
1
0
1
1
1
0
1
2
1
1
1
1
1
0
2
1
1
1
0
1
0
0
1
1
2
0
1
1
1
0
0
1
0
1
1
1
1
1
1
1
0
0
2
1
2
2
1
1
1
1
0
1
1
2
1
1
2
0
2
1
1
1
2
0
1
2
1
1
1
0
2
1
1
1
1
2
1
0
2
1
2
1
2
1
1
0
2
1
0
1
1
0
2
0
1
1
2
2
0
1
1
1
0
0
0
0
1
3
0
0
1
1
1
2
1
1
2
1
1
1
2
2
3
2
1
1
4
1
1
1
1
0
2
0
1
1
0
2
1
0
1
0
2
0
2
0
1
1
2
2
2
1
1
1
2
0
0
0
1
1
1
1
1
0
2
2
2
1
1
0
1
1
2
1
2
1
0
2
1
0
1
2
2
1
1
1
0
1
1
2
2
1
0
1
0
1
0
1
1
2
0
1
2
1
1
0
2
2
1
1
2
1
1
1
1
1
0
0
0
1
1
1
1
0
1
1
2
1
1
2
1
2
1
1
1
1
0
0
1
1
0
2
1
2
1
1
1
0
1
2
1
0
2
2
2
1
0
1
0
0
1
1
1
1
0
0
2
1
2
2
2
0
0
1
0
0
0
1
0
2
2
1
2
2
1
1
0
0
1
3
1
2
2
2
1
1
1
1
1
1
1
1
1
0
3
1
0
1
0
1
1
1
1
1
1
0
3
0
2
1
1
1
1
1
2
1
0
0
1
1
1
1
1
1
1
2
0
1
1
1
2
2
1
1
1
0
0
0
0
1
0
0
1
2
2
0
1
2
2
2
2
2
0
1
0
0
1
0
2
1
1
0
1
1
2
2
2
1
1
1
1
1
1
0
1
2
1
1
1
1
2
2
0
2
1
0
1
1
2
1
2
2
1
1
1
1
0
0
2
1
0
1
1
1
1
1
1
1
1
0
2
1
2
1
1
3
1
1
1
0
1
0
1
1
1
0
2
1
2
1
1
1
1
2
1
1
0
1
1
0
1
0
1
1
1
0
1
1
2
2
1
0
2
1
1
1
0
2
1
2
2
0
2
1
2
1
1
0
1
1
2
0
1
0
1
0
1
0
0
1
0
2
0
0
1
1
1
0
1
2
0
0
1
0
1
1
2
2
1
2
1
1
1
1
1
1
1
1
0
1
1
1
1
2
1
0
1
1
1
1
0
1
1
1
1
2
1
0
1
1
2
1
1
1
3
1
2
1
0
2
0
0
2
2
0
2
2
1
0
0
1
2
1
1
0
0
0
1
1
2
0
0
1
0
1
3
1
1
1
1
1
2
1
2
1
2
1
1
0
2
1
1
1
0
2
0
1
2
2
1
1
1
2
1
1
0
1
0
0
0
0
2
0
1
1
1
0
1
1
1
1
1
1
0
1
2
0
1
3
1
0
1
1
2
2
0
2
1
2
2
0
1
1
1
2
1
1
1
0
1
1
0
1
1
0
1
1
1
1
1
1
1
0
0
1
1
1
1
0
2
0
0
1
0
1
1
1
1
0
1
0
2
0
1
1
1
1
0
0
1
2
2
1
1
3
1
1
1
0
2
1
2
0
1
1
0
1
1
2
0
1
1
0
1
0
1
1
2
2
1
1
0
0
0
1
0
0
1
2
2
2
1
1
2
2
1
1
0
0
0
2
1
1
0
0
1
2
1
1
2
1
1
2
1
1
1
0
1
0
1
4
0
2
1
1
0
2
0
0
0
2
1
1
1
0
2
2
1
0
1
1
0
1
1
1
0
0
1
0
0
1
0
1
1
0
1
0
1
1
1
1
1
1
0
1
1
0
1
0
1
1
2
1
0
1
1
1
2
1
2
2
1
1
2
1
0
0
1
2
1
2
1
2
1
0
1
1
1
1
0
1
1
2
2
4
3
0
2
1
1
1
1
2
1
0
1
1
0
2
1
2
0
0
2
2
1
0
2
2
0
0
2
0
2
1
1
0
1
2
1
0
1
1
1
3
0
0
2
0
1
2
0
2
0
0
2
0
1
1
1
1
0
1
1
1
1
1
1
2
1
1
1
0
2
1
0
1
1
0
1
1
0
1
1
1
2
1
0
1
1
0
0
1
1
1
1
1
2
1
1
1
1
1
2
1
2
2
2
2
1
1
1
1
0
2
1
1
3
2
0
2
1
2
0
1
1
1
2
1
0
1
1
2
1
0
1
1
1
0
2
1
1
0
1
1
1
0
1
1
1
3
1
2
0
1
0
2
1
1
2
1
1
1
1
1
0
1
1
2
1
1
0
0
1
1
1
2
1
1
1
2
1
1
2
0
2
1
1
1
2
1
2
2
1
1
1
1
1
2
1
2
0
2
1
0
1
2
1
2
1
0
0
2
0
1
1
1
1
0
1
1
1
1
1
1
1
1
2
2
2
0
2
2
1
2
1
2
2
1
0
1
2
0
1
1
2
1
1
1
0
1
0
1
1
2
2
1
1
2
1
2
1
1
2
1
1
0
1
1
1
2
1
1
1
1
0
1
2
2
2
1
1
1
2
0
1
1
1
1
3
1
1
0
1
1
2
1
0
1
1
1
1
1
2
2
1
1
2
0
1
1
1
1
1
2
0
1
1
2
1
1
1
2
2
0
1
3
1
2
1
0
0
0
1
1
1
1
1
2
0
1
1
2
1
1
2
2
1
2
0
1
1
1
1
1
0
0
1
1
0
2
2
2
1
0
0
1
2
1
1
0
1
0
1
1
1
1
1
0
1
2
2
0
1
0
2
1
1
2
1
1
0
1
1
0
2
1
2
2
1
1
2
0
0
0
1
1
0
1
1
0
1
0
1
1
1
1
1
2
2
1
0
3
2
0
1
1
1
1
2
0
1
0
1
1
0
1
1
1
1
1
2
1
1
1
1
0
2
1
0
1
2
2
1
0
0
0
2
2
1
1
1
1
2
1
0
1
1
1
1
1
0
1
1
1
1
2
1
2
2
1
1
1
1
2
1
1
1
1
2
1
0
2
1
0
0
0
2
2
0
1
1
0
2
1
0
0
1
0
2
2
0
1
2
0
0
2
1
1
0
1
2
1
0
0
1
0
3
1
0
1
2
0
2
1
1
1
1
1
2
1
1
1
1
0
1
1
0
0
2
0
0
0
1
2
0
2
1
0
1
0
0
1
1
1
1
1
1
1
1
0
1
1
2
1
1
1
1
1
1
0
2
1
2
0
1
1
1
2
3
1
1
2
1
2
1
2
2
1
1
0
1
1
0
1
0
1
1
1
1
2
1
1
2
1
1
0
1
1
2
2
1
2
1
1
0
1
1
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
0
1
1
1
1
1
2
1
2
0
0
1
1
0
1
1
2
1
1
0
1
1
0
1
1
1
0
1
1
2
0
0
1
1
1
0
0
0
1
0
0
1
1
1
2
2
0
0
1
1
1
2
0
1
1
1
0
0
2
1
2
0
0
2
2
2
0
1
1
1
1
4
2
1
1
0
2
1
0
1
0
1
1
2
1
1
1
0
1
2
1
2
0
1
0
1
1
1
1
2
1
0
1
1
1
1
1
0
1
1
0
1
1
2
1
2
1
1
1
1
1
1
1
1
0
1
1
0
0
2
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
0
1
1
2
0
0
2
1
2
0
0
0
1
1
1
2
1
2
1
0
0
0
0
1
0
1
1
1
2
1
1
1
1
4
1
3
0
1
2
0
1
2
0
1
0
2
1
1
1
0
1
1
0
2
2
0
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
0
1
1
1
1
0
1
3
1
0
1
1
0
1
0
0
2
1
1
1
1
2
0
0
1
1
1
1
2
0
1
1
0
2
1
1
0
1
1
1
1
1
1
2
1
1
0
0
2
0
2
0
1
1
1
1
1
0
1
1
1
1
1
2
2
1
1
0
1
1
1
0
0
2
1
1
2
2
1
0
1
1
1
1
1
0
0
2
1
0
1
0
2
1
0
1
0
1
1
2
1
0
1
2
1
2
1
1
2
1
1
2
1
1
1
1
1
2
1
2
1
2
0
2
0
1
1
1
0
1
1
2
1
1
0
0
2
2
1
1
2
1
2
0
2
1
1
2
1
1
1
2
1
1
1
2
0
1
1
1
1
2
1
0
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
0
1
1
0
1
1
1
1
2
2
1
1
0
1
1
1
1
2
1
1
1
1
1
0
1
1
0
1
1
2
1
2
0
2
2
1
1
2
2
1
0
2
1
2
1
1
0
1
1
1
1
0
0
0
0
2
1
1
0
0
1
0
1
2
2
0
1
1
1
1
1
1
2
1
2
0
0
1
1
3
1
0
1
1
1
1
2
1
0
2
1
2
2
0
2
0
1
0
1
0
1
1
1
0
1
0
2
1
0
1
2
1
2
2
1
1
1
1
2
1
2
2
0
2
2
1
1
1
1
6
2
2
2
1
2
1
1
0
1
1
2
2
2
0
2
0
1
2
1
1
2
1
1
2
1
2
2
2
0
1
1
1
0
0
1
1
1
0
2
1
1
0
1
1
1
1
1
1
0
0
0
0
0
1
0
1
1
0
2
1
1
1
1
1
1
1
0
1
0
0
0
2
1
1
1
0
1
1
3
1
2
2
0
1
0
1
1
2
2
1
2
1
0
1
1
0
2
2
2
0
0
2
1
1
0
0
2
1
2
1
1
1
0
2
1
0
1
0
1
2
1
1
2
1
2
0
1
1
0
2
2
0
2
1
1
1
1
0
3
0
1
1
1
2
2
1
2
2
1
2
1
2
3
1
1
1
1
2
1
0
1
1
2
1
2
1
1
0
0
1
0
0
2
1
1
1
0
0
0
1
1
0
1
1
2
2
1
1
1
2
1
2
2
1
1
2
0
2
0
0
1
0
2
1
1
0
0
1
1
1
1
1
0
1
1
1
1
1
2
1
1
2
0
0
0
1
2
1
1
1
0
1
2
1
1
2
1
1
2
2
2
1
1
0
0
0
0
1
1
1
1
1
1
1
1
1
0
2
1
0
0
0
1
2
1
1
2
1
0
1
2
2
1
0
2
0
1
0
0
0
2
0
1
0
1
0
0
0
1
0
0
0
1
1
2
1
2
1
1
0
1
0
1
1
1
1
1
0
1
1
0
1
2
1
1
1
1
0
1
0
2
2
2
0
0
0
1
1
0
2
1
1
1
0
0
1
2
1
0
1
0
2
0
2
1
1
0
1
1
0
2
2
1
2
0
0
1
0
0
1
0
1
1
1
2
0
1
1
2
0
1
1
0
2
1
1
1
0
1
1
0
1
2
1
2
2
1
0
1
4
1
1
1
2
1
1
1
0
2
1
1
2
1
1
1
2
2
1
2
1
1
2
1
0
2
1
2
2
1
2
2
1
0
2
1
1
1
0
2
1
2
1
1
0
0
0
0
1
1
1
1
4
0
2
1
1
1
1
1
0
1
0
1
2
1
1
1
0
1
1
1
1
0
2
2
0
0
1
0
1
2
2
2
1
2
1
1
1
0
2
1
1
1
2
1
1
1
1
2
1
0
1
1
1
1
2
1
1
1
0
0
1
0
0
1
1
1
0
1
1
1
1
1
1
0
2
2
2
1
1
1
2
1
0
1
1
2
1
2
1
0
2
1
1
2
2
0
2
1
2
1
1
1
2
1
2
1
1
1
1
0
1
1
1
0
1
1
1
1
1
1
1
2
1
2
1
1
0
2
1
0
0
1
1
1
1
0
1
2
1
2
0
1
0
0
0
1
2
0
0
0
1
2
1
1
2
1
1
2
1
1
1
1
1
2
0
2
2
1
2
0
0
1
1
1
1
0
1
2
1
1
1
0
1
1
1
1
1
0
1
2
1
0
1
1
0
0
1
0
1
1
2
1
3
1
0
0
1
1
1
0
0
2
1
1
1
1
0
1
2
1
2
1
0
1
1
1
1
1
1
2
1
1
1
2
1
1
0
0
1
1
0
1
1
1
1
1
0
0
1
1
0
1
0
1
1
1
2
2
1
0
2
1
1
1
2
2
1
2
4
1
1
1
1
1
1
1
1
0
2
0
1
1
1
1
2
0
2
2
1
0
1
1
1
1
1
1
1
2
1
2
0
0
2
2
0
1
5
0
0
1
2
1
1
0
1
1
0
1
2
1
1
1
0
1
1
0
0
1
1
1
0
0
1
2
1
1
1
1
1
0
1
0
0
1
1
0
1
0
1
1
1
2
3
1
0
1
1
3
1
1
2
1
1
2
1
2
2
2
0
0
1
0
0
1
1
1
1
1
1
1
2
1
1
1
1
0
1
2
1
2
0
1
1
0
1
1
1
0
1
3
2
1
1
1
2
1
0
1
1
1
1
1
0
0
1
1
2
2
0
2
1
1
1
0
1
1
1
0
2
1
2
1
1
0
1
1
1
1
2
2
1
0
1
1
2
0
2
2
1
1
1
0
1
1
0
1
1
0
1
1
1
2
2
2
2
1
0
1
0
1
0
0
2
1
1
1
1
2
2
0
1
1
1
1
1
1
0
1
2
2
2
1
2
1
1
0
1
1
1
1
1
1
1
2
2
1
2
1
0
2
1
1
0
1
1
1
0
1
1
2
2
1
1
2
1
1
1
1
0
1
2
1
0
1
0
1
1
1
1
2
1
0
0
1
1
2
1
0
1
0
3
0
1
1
0
2
2
1
0
1
1
1
0
0
1
0
1
1
2
1
2
1
2
0
0
1
0
0
1
0
1
0
0
2
1
2
1
1
1
2
2
0
1
2
0
1
1
0
0
1
2
0
1
1
1
2
0
1
0
0
0
1
0
2
1
1
1
1
2
1
1
5
2
1
1
1
2
1
2
1
1
0
1
2
2
1
0
1
2
1
1
2
1
1
0
1
1
0
1
0
1
1
2
2
1
0
0
1
1
1
0
0
0
0
1
1
0
0
0
0
0
1
1
1
1
2
2
2
1
1
0
1
1
1
1
0
1
1
2
0
2
0
0
2
1
1
1
1
2
2
0
2
1
0
1
2
1
1
1
2
1
1
1
0
0
2
0
0
1
1
1
1
2
0
2
2
2
1
1
2
1
0
2
1
0
0
1
1
1
1
0
0
0
1
2
1
2
1
2
2
2
1
1
1
1
1
1
1
1
0
1
1
2
2
0
2
0
1
1
1
1
1
0
1
1
2
0
0
1
1
4
2
1
1
1
2
1
2
1
0
2
1
1
1
0
0
1
2
0
0
1
1
0
1
2
2
1
2
1
1
0
0
1
1
1
1
1
1
1
1
1
2
1
0
1
1
2
1
1
0
1
1
1
2
0
1
1
0
1
1
1
2
0
1
0
1
0
1
2
1
1
1
0
2
1
1
1
1
0
1
0
1
1
0
2
1
0
4
1
2
1
0
1
0
1
2
0
0
1
1
1
1
2
2
1
2
1
0
1
2
1
2
0
1
1
2
1
0
0
1
1
1
1
1
1
1
1
1
2
1
1
2
0
1
0
1
2
0
1
2
1
1
3
1
0
0
0
1
0
2
1
0
2
1
1
2
1
1
1
0
2
2
1
0
0
2
1
2
1
1
0
1
1
0
1
0
2
1
1
0
2
1
1
2
1
0
0
0
1
1
1
2
0
1
1
2
1
1
0
1
1
1
1
2
1
0
1
1
2
0
0
2
1
1
0
1
1
1
2
0
1
1
1
2
0
1
1
0
1
1
2
2
1
1
2
0
1
0
0
2
1
2
1
1
1
0
1
1
2
2
1
2
1
1
1
2
0
1
0
0
1
0
1
0
2
0
1
0
2
2
1
0
2
1
1
0
1
0
1
2
2
1
2
2
0
1
1
1
1
1
2
0
1
1
2
1
1
1
1
1
1
2
1
1
2
1
0
1
0
1
1
2
2
0
1
2
0
0
1
1
1
0
0
1
2
2
1
0
1
0
2
1
2
1
2
1
0
2
1
1
2
1
1
0
1
2
0
2
1
1
2
1
1
0
1
0
1
1
0
1
1
0
1
1
1
1
0
0
1
1
1
2
1
1
0
2
1
1
1
1
1
2
1
2
1
0
1
1
1
0
0
1
0
2
1
0
1
2
2
2
1
0
2
2
1
2
1
1
0
0
0
0
2
1
3
2
1
2
0
1
1
2
1
1
1
1
1
1
0
0
2
1
1
0
1
2
1
1
0
0
2
1
1
2
2
1
0
1
1
1
0
0
1
0
0
0
1
1
1
1
0
1
1
2
0
2
1
1
2
1
2
2
1
1
1
1
1
1
1
0
2
1
0
0
0
0
2
1
2
1
2
1
1
1
0
0
1
2
2
1
1
0
0
1
0
1
1
2
0
0
0
2
1
1
1
0
1
1
1
2
2
1
1
1
2
2
1
0
0
1
1
0
1
1
1
1
1
0
1
1
1
0
1
0
1
0
1
1
2
0
0
1
2
2
2
1
1
1
1
1
2
1
3
0
0
1
1
2
0
0
1
2
1
1
0
0
0
1
2
1
1
0
1
2
1
1
2
1
1
1
0
1
1
1
1
0
2
1
1
1
2
2
2
1
0
2
0
1
1
3
0
1
2
1
2
2
1
2
1
0
2
1
1
1
0
1
1
1
2
0
1
1
0
2
0
1
0
0
2
1
1
1
1
1
0
2
1
1
0
2
2
2
1
2
1
1
0
1
0
1
2
0
1
1
0
2
1
1
1
1
0
2
6
1
1
2
1
1
2
2
0
0
1
1
1
1
1
0
0
1
1
2
0
1
2
1
2
2
2
2
1
1
0
1
1
1
4
0
0
1
1
1
2
1
1
1
1
1
1
0
0
1
1
0
1
1
2
2
1
0
0
0
0
2
1
0
2
0
2
1
1
0
0
0
1
1
0
2
1
1
1
0
1
2
1
2
0
1
2
1
2
1
0
1
1
1
0
0
2
0
1
0
2
1
1
1
1
1
2
0
0
2
0
1
1
1
2
2
0
0
1
1
2
1
1
0
1
1
0
0
0
1
2
2
1
1
1
1
1
1
0
0
1
0
1
2
1
1
1
1
0
1
1
2
2
0
1
0
1
3
2
0
1
1
2
1
0
2
2
1
2
1
1
0
1
0
1
1
1
1
1
0
1
0
1
0
1
0
2
1
0
1
1
2
2
0
2
1
2
0
1
1
0
1
1
0
1
0
0
1
2
1
1
0
2
2
2
0
1
1
0
1
0
2
2
1
1
0
0
1
1
0
1
0
0
2
1
1
1
1
1
0
0
1
2
0
0
2
1
0
1
2
1
1
0
2
1
1
1
1
1
0
1
1
1
1
0
1
1
1
1
0
1
1
3
2
0
1
0
0
1
0
0
2
1
1
1
2
1
0
2
2
0
0
0
1
1
1
0
1
0
1
1
2
1
1
2
1
0
0
1
1
2
1
1
1
0
1
0
2
0
1
1
1
1
1
0
1
1
2
2
1
1
0
0
1
2
2
1
1
1
1
1
1
1
0
0
1
1
1
1
1
1
1
1
1
1
0
1
1
2
2
1
2
1
2
1
2
1
2
1
1
0
2
0
1
0
1
1
1
0
2
1
0
1
0
1
1
1
1
2
1
1
0
0
1
1
1
2
0
1
1
1
0
2
1
0
0
2
2
1
1
0
1
4
1
1
1
1
0
1
2
1
1
1
1
0
2
1
1
0
0
2
1
2
0
1
1
1
2
1
0
1
1
2
1
1
1
1
0
2
2
1
0
0
0
2
3
1
2
1
1
1
1
2
0
0
2
2
2
2
0
2
0
1
1
1
0
2
1
0
1
2
1
1
1
1
2
1
2
0
1
0
1
1
0
2
1
3
1
1
1
1
0
2
1
0
1
0
1
1
2
0
1
1
2
1
1
1
1
1
1
2
0
1
2
2
1
0
1
0
2
2
0
0
1
2
1
1
0
2
2
1
0
2
2
0
0
1
0
1
1
0
2
2
0
2
2
2
0
1
0
0
2
1
1
1
1
2
1
0
1
1
0
2
0
2
1
1
1
2
1
1
1
1
1
0
1
0
1
1
2
3
1
1
1
1
1
0
2
1
2
1
1
1
2
1
0
0
1
1
0
1
0
1
1
2
0
2
1
1
1
1
1
2
0
2
0
1
0
1
1
1
0
0
0
2
1
1
0
1
0
0
2
4
1
2
1
1
1
1
1
3
1
0
2
1
0
2
0
2
2
1
1
0
1
0
0
0
2
0
0
1
2
1
1
0
1
1
0
0
1
0
2
1
2
1
1
0
0
0
1
2
0
1
0
1
2
0
1
2
1
1
1
0
2
1
2
1
1
1
0
2
0
1
1
0
1
2
1
2
0
1
0
1
2
1
1
0
1
0
1
1
0
2
1
1
1
2
1
1
1
2
1
0
1
1
1
1
1
1
1
1
0
0
2
0
0
1
1
1
1
1
0
1
0
1
0
2
1
1
1
1
2
0
1
0
1
1
1
1
1
1
0
1
1
1
1
1
1
2
1
1
1
1
1
1
0
1
1
1
0
2
1
2
2
1
1
1
1
1
1
2
0
0
0
2
0
2
1
0
1
1
1
2
1
0
0
1
1
0
1
2
2
3
1
0
1
1
1
0
1
1
1
1
1
1
2
1
0
0
2
1
1
1
0
1
0
0
0
0
1
0
1
2
0
0
0
1
1
1
0
1
1
1
1
2
1
1
1
1
1
1
2
1
2
1
0
1
1
2
0
0
1
1
1
2
1
0
1
1
2
1
0
1
2
1
2
2
2
1
1
2
1
1
2
0
1
1
2
1
1
2
0
0
2
1
0
1
1
1
2
1
0
1
0
2
2
1
1
1
1
1
0
1
1
2
3
1
0
1
0
1
0
2
1
1
2
0
1
1
2
0
2
1
2
2
0
1
1
1
1
0
2
2
1
1
2
1
0
1
1
1
2
2
0
2
2
1
1
2
1
1
1
1
1
0
2
0
2
1
0
2
1
0
1
2
2
2
1
1
1
1
1
0
1
2
1
2
0
1
2
2
2
1
1
0
2
1
1
2
1
1
1
1
0
1
1
1
0
2
1
1
0
1
1
0
1
2
0
0
2
0
1
1
1
1
1
1
0
0
2
1
0
2
2
2
1
0
1
0
2
1
2
2
2
1
2
0
2
0
1
0
1
0
2
0
1
1
2
1
1
1
2
1
1
1
1
1
0
0
1
0
2
0
2
1
0
0
2
0
0
0
0
1
1
1
1
1
0
1
0
1
1
0
0
1
1
1
1
0
2
0
0
1
1
0
1
2
3
1
2
1
0
1
0
2
1
1
0
1
2
1
1
2
0
1
2
1
0
0
0
1
1
1
0
1
0
2
1
1
0
0
1
1
1
1
1
1
1
0
0
0
1
1
1
1
1
0
3
1
0
1
1
0
1
1
0
2
2
2
1
1
1
1
1
1
1
1
2
2
0
1
1
2
2
0
1
0
2
1
2
1
0
1
1
1
0
1
1
1
1
2
2
1
0
1
1
1
2
0
2
1
1
0
1
1
1
1
0
1
2
2
1
1
1
1
0
1
1
1
1
1
1
0
2
0
1
2
2
0
1
1
2
2
0
1
1
0
1
0
1
1
1
1
0
1
1
1
1
2
1
2
1
1
2
2
1
1
1
1
2
1
0
1
0
0
1
0
0
2
0
0
0
1
2
1
1
1
0
0
2
1
1
1
1
2
1
0
2
1
1
1
1
2
0
2
1
2
1
0
2
1
1
0
2
0
1
1
1
1
0
1
2
0
1
1
1
1
1
2
1
0
1
0
2
1
2
1
1
2
0
2
1
2
0
0
0
2
1
0
0
0
2
2
0
1
2
1
1
1
2
1
1
1
2
0
2
1
1
1
1
1
2
2
1
0
1
2
0
2
1
1
1
1
1
1
1
2
0
0
0
1
1
1
0
1
2
2
1
1
2
1
0
1
2
1
1
0
1
1
2
0
1
0
1
1
0
2
1
0
2
1
0
1
2
0
1
0
1
3
1
1
2
2
1
2
0
1
1
2
2
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
0
2
1
2
2
0
2
0
1
1
1
0
2
2
1
1
1
1
1
1
1
2
1
1
0
1
1
1
1
1
1
1
1
0
0
0
0
1
1
0
2
1
0
1
1
1
1
1
2
0
1
1
1
1
0
1
0
1
1
1
1
0
1
2
1
2
1
2
1
0
0
0
0
0
2
1
1
2
1
0
1
1
1
1
1
1
2
1
3
0
0
0
2
2
0
1
1
0
1
1
1
0
1
0
2
1
1
1
1
2
2
1
0
0
0
1
1
2
0
1
1
2
2
0
1
0
0
0
1
1
1
1
1
2
1
1
1
1
1
1
0
1
1
1
2
3
1
0
1
0
1
1
0
0
1
1
2
2
0
1
2
1
1
0
2
1
2
2
2
2
2
2
0
2
0
2
1
2
1
1
2
0
0
1
1
1
1
1
1
1
1
1
0
2
0
1
1
1
1
0
1
1
0
2
1
2
2
1
1
0
2
2
0
1
2
1
1
0
2
1
2
1
1
0
1
2
4
1
1
2
2
1
0
0
0
0
1
1
1
2
1
0
2
2
0
1
1
2
0
2
2
1
1
1
1
1
0
0
2
1
1
0
0
1
1
1
1
1
1
0
2
1
0
1
0
2
1
2
0
2
2
1
0
1
2
1
1
0
1
1
0
1
0
1
1
1
1
2
1
1
1
1
2
0
1
1
0
1
1
1
1
0
1
1
2
1
0
2
2
1
1
0
2
0
0
0
1
1
2
0
2
2
1
0
1
2
1
0
2
0
1
0
1
1
1
2
0
2
0
0
2
2
1
1
1
1
2
0
1
2
1
1
1
0
1
2
1
0
1
1
1
1
2
2
2
1
2
2
1
1
0
1
0
0
2
1
1
2
2
1
1
0
1
0
0
0
1
1
0
1
1
1
2
1
1
1
1
1
0
0
0
0
1
0
2
0
1
1
1
0
0
1
0
2
0
1
1
0
2
0
1
0
0
0
1
0
1
1
1
1
0
2
2
1
2
0
2
1
1
1
1
1
2
1
1
1
1
2
2
1
0
0
0
0
2
1
1
1
1
1
2
2
1
1
0
0
2
2
1
0
1
1
2
0
1
1
2
1
1
1
2
1
1
0
1
0
3
0
2
2
2
1
1
1
1
1
2
1
1
0
2
1
1
0
1
2
2
1
2
0
1
1
1
1
3
1
1
2
1
1
1
1
1
0
1
0
1
1
1
2
1
2
1
1
1
1
1
2
2
0
2
0
2
1
1
1
0
1
2
1
0
1
1
1
2
0
0
0
1
1
1
1
2
1
2
1
1
1
2
1
1
1
1
1
2
0
2
1
3
0
1
1
1
1
2
1
1
1
1
2
1
1
0
1
0
2
2
2
1
1
0
1
1
1
0
2
0
1
1
0
1
1
2
1
1
0
0
1
2
1
0
1
1
2
0
2
1
1
1
1
0
2
0
0
1
1
1
0
2
1
2
0
1
1
1
0
1
1
1
2
1
0
1
1
1
2
1
1
2
0
1
0
1
1
0
0
1
1
1
1
1
1
1
2
0
0
0
2
2
1
1
1
0
1
1
0
1
1
1
1
1
1
1
0
0
1
1
2
1
1
0
1
2
0
0
1
1
1
0
2
1
1
2
2
0
2
1
1
1
1
2
1
2
0
1
1
2
0
0
1
2
0
1
1
1
0
1
1
1
0
1
2
1
1
2
2
1
2
0
0
1
1
1
1
1
1
0
1
1
1
1
0
1
1
1
0
2
1
1
1
1
1
0
1
1
1
0
2
2
2
2
1
0
1
1
1
0
1
1
0
2
0
2
1
1
1
1
1
1
1
1
0
1
1
0
2
1
0
0
2
2
0
0
0
0
2
1
2
0
0
0
0
1
0
1
0
2
1
2
1
2
1
1
1
2
1
2
1
0
0
1
1
1
0
1
1
1
1
0
0
1
0
1
2
0
2
2
1
1
2
2
1
1
1
0
1
1
2
0
1
1
1
1
2
2
2
1
0
2
1
1
0
1
0
1
1
1
0
1
1
1
0
1
0
1
1
0
1
2
2
0
1
1
0
1
1
2
1
1
0
1
1
4
0
1
3
1
1
2
1
2
1
0
0
1
2
2
2
0
0
1
1
1
1
1
1
2
1
0
1
2
2
2
1
1
0
2
2
1
0
1
1
1
2
1
0
1
1
1
1
0
1
2
1
0
1
1
0
0
1
0
1
1
1
1
1
1
3
1
1
0
2
1
1
0
1
0
1
0
1
0
2
1
0
0
1
2
0
1
2
0
0
0
1
1
1
0
2
4
0
2
2
1
1
1
0
1
2
1
1
2
0
1
1
1
0
2
1
1
2
1
0
2
1
0
1
1
0
1
1
1
0
2
0
2
2
0
2
1
2
1
1
2
2
1
2
1
2
2
0
2
1
1
1
0
1
1
1
1
0
2
0
1
1
3
1
0
1
1
1
1
1
1
2
0
2
0
0
1
1
2
1
1
2
2
1
0
0
1
1
1
2
2
2
1
1
0
1
1
1
2
1
1
1
1
1
0
0
1
1
2
1
2
2
1
2
2
1
2
0
1
1
1
0
1
1
1
0
0
2
1
2
0
1
0
2
0
0
1
0
1
1
0
1
2
0
2
2
1
1
1
0
2
0
0
1
0
1
0
1
2
1
0
2
2
1
0
1
0
2
1
1
2
0
0
2
1
0
2
1
1
2
1
1
0
0
2
1
2
1
1
2
1
2
0
0
0
1
1
1
0
1
0
1
1
1
2
1
0
2
1
1
0
1
1
0
1
1
1
0
1
1
1
1
2
1
2
1
2
0
0
1
0
1
0
1
1
1
0
2
1
1
1
2
1
1
0
1
1
1
2
1
0
2
3
2
1
2
2
1
0
1
1
1
1
1
0
1
1
1
1
0
2
1
0
1
2
0
1
2
2
1
0
0
1
2
1
1
1
1
1
1
0
2
3
2
1
1
1
0
1
2
0
1
0
1
1
1
1
1
1
1
2
1
2
1
1
2
0
0
1
0
1
1
0
1
1
2
1
1
1
1
2
0
1
1
1
1
0
1
1
2
1
1
0
1
1
2
0
1
1
1
1
2
1
1
1
0
0
2
1
1
0
0
0
1
2
0
1
2
1
2
0
4
1
1
1
0
2
1
0
2
1
1
2
2
0
1
0
1
2
0
0
2
1
1
0
1
0
2
1
2
1
2
0
2
0
1
0
2
0
2
1
2
1
2
1
0
2
0
2
0
1
0
3
2
2
1
0
0
2
0
1
0
1
1
1
1
0
1
0
2
1
1
0
1
0
1
3
1
0
1
0
1
2
0
0
0
2
2
2
0
1
1
2
2
1
1
1
2
2
1
1
2
1
1
1
1
1
2
0
1
1
0
1
1
2
1
2
1
1
1
0
2
0
2
2
0
1
1
1
1
1
0
2
1
1
1
2
0
1
0
1
1
0
0
2
1
2
2
2
0
1
1
1
0
1
0
2
0
1
0
2
0
1
1
2
1
0
0
2
1
0
1
1
1
0
2
1
2
1
1
1
0
1
1
1
2
1
1
1
0
1
1
1
1
1
1
2
0
1
1
2
1
1
0
1
2
1
1
1
1
1
2
0
0
1
0
1
2
1
2
0
2
2
1
1
1
0
2
1
1
2
1
1
1
1
1
2
2
0
1
1
1
2
1
1
1
1
1
0
2
2
1
2
1
2
1
1
2
1
1
2
1
1
1
1
1
1
0
0
1
1
1
1
1
1
1
2
0
3
1
2
1
0
0
1
1
2
1
0
0
2
1
3
2
1
1
1
2
1
0
1
1
0
2
1
2
1
1
1
2
1
0
2
0
4
2
1
2
1
1
0
2
1
1
1
1
1
1
0
0
1
1
0
1
1
1
1
0
1
0
1
2
0
2
1
1
0
1
0
0
0
1
0
2
1
1
2
1
1
1
2
2
0
1
0
0
1
1
2
1
0
1
1
1
1
2
1
2
0
1
1
0
1
0
1
1
2
0
1
2
1
3
1
0
0
1
1
1
1
1
0
1
1
1
1
1
1
0
1
1
0
2
1
2
1
2
2
1
1
1
1
1
0
1
1
1
1
0
2
2
1
0
1
2
1
1
1
1
1
2
1
1
1
2
1
2
1
0
1
2
1
0
0
1
0
1
1
1
1
2
0
2
2
3
0
2
0
1
0
1
1
2
1
2
0
1
1
1
1
0
0
1
1
0
1
2
2
0
1
1
1
1
0
2
1
1
2
2
1
2
1
1
1
1
1
1
2
1
0
1
1
0
1
0
2
1
1
0
2
1
0
2
0
0
0
0
2
2
1
1
1
1
1
2
1
1
0
1
2
2
1
1
1
2
2
1
1
0
1
1
0
1
1
3
1
1
1
1
2
1
0
1
1
1
0
1
2
1
1
2
0
0
1
2
0
2
1
0
1
0
1
2
0
1
1
0
0
0
1
0
1
0
1
2
1
2
1
2
1
1
1
1
2
0
0
1
2
1
0
2
2
2
0
2
0
2
1
2
1
1
0
2
1
0
0
1
2
2
1
1
2
2
1
1
2
1
1
1
1
1
1
1
0
1
0
2
1
2
0
1
1
4
2
0
2
0
2
1
1
2
1
1
1
1
1
0
0
1
1
1
2
0
1
2
1
1
1
1
1
0
0
1
1
0
0
1
1
1
1
1
1
1
2
0
1
2
2
1
1
1
1
0
0
1
1
1
1
0
1
2
0
0
2
1
1
2
3
2
1
1
1
1
2
0
0
2
0
2
1
2
0
1
0
2
3
1
1
1
1
2
1
0
1
1
1
1
1
1
2
1
3
1
2
1
0
1
0
0
1
2
1
1
0
1
1
0
1
0
0
2
1
1
2
1
3
1
1
0
1
1
0
1
1
2
2
2
0
4
1
0
2
2
1
0
1
1
2
1
1
0
0
0
1
1
2
1
1
0
0
4
1
2
1
0
0
0
0
2
2
1
1
0
2
1
1
0
1
1
1
0
0
1
1
1
2
1
1
2
1
0
2
0
0
0
1
2
1
1
2
1
1
2
2
1
2
0
1
2
0
1
1
1
1
0
1
2
0
1
2
1
2
1
0
0
1
0
1
0
1
1
0
2
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
2
2
1
0
1
2
0
0
0
2
2
1
1
1
2
2
1
0
0
1
2
1
2
2
2
0
2
1
1
2
1
1
2
1
2
0
2
1
1
1
1
1
1
0
2
2
1
2
2
1
1
2
2
0
1
0
2
1
0
1
1
1
1
3
2
2
2
2
1
1
1
1
0
1
2
2
1
1
0
2
1
0
2
2
1
2
1
2
1
1
1
1
2
2
1
0
2
1
1
1
0
1
1
1
1
1
0
1
2
0
1
0
1
0
1
0
0
1
2
0
1
0
0
0
0
0
2
1
1
1
2
1
1
2
0
1
1
0
0
1
2
2
2
1
2
0
1
1
1
0
2
1
1
1
2
1
0
1
2
2
0
0
1
0
2
1
1
1
1
1
1
1
1
1
0
1
1
1
2
1
1
1
2
2
1
1
1
1
2
1
2
0
0
0
1
0
1
1
1
2
1
3
0
0
1
0
1
0
2
0
2
0
1
0
0
1
1
2
2
1
1
0
1
2
1
1
1
2
2
1
0
1
0
1
1
1
1
2
2
0
1
0
1
1
2
1
2
1
1
1
0
1
1
2
1
1
1
4
2
2
2
1
1
1
1
1
0
1
1
1
1
1
1
1
0
1
2
1
1
0
2
0
1
2
1
1
2
1
2
2
1
0
1
0
1
0
1
1
1
0
1
1
0
0
0
1
2
2
1
1
0
2
1
0
0
1
0
1
1
1
1
2
2
0
2
2
1
2
1
1
5
2
0
2
1
2
1
2
0
1
1
2
1
2
2
0
1
1
2
1
1
2
0
0
1
1
0
2
1
1
1
2
1
1
0
1
1
0
1
0
0
2
1
1
0
0
1
2
1
1
1
3
2
1
0
0
2
2
1
0
1
2
2
1
2
1
0
1
0
2
2
1
0
1
1
0
1
0
1
2
0
1
1
1
2
1
1
0
0
1
2
1
1
1
1
0
0
0
0
0
2
1
2
1
1
1
2
0
4
0
0
1
1
0
1
0
0
1
2
0
1
1
2
0
1
2
2
1
2
1
0
1
1
1
1
2
2
0
2
2
1
1
0
1
1
0
2
1
1
2
0
1
2
1
0
1
2
1
0
1
2
1
1
1
1
2
2
0
1
1
2
2
1
0
2
0
1
0
0
0
0
1
0
0
1
1
0
1
3
0
0
1
1
0
1
1
1
0
2
1
0
1
1
0
2
1
2
0
2
1
0
1
1
1
2
0
0
2
1
1
1
1
1
0
2
0
0
1
1
0
1
1
2
1
1
2
0
1
1
2
1
1
1
1
0
0
1
1
1
1
1
1
2
0
2
0
2
0
1
1
0
0
1
1
0
1
0
0
1
2
1
1
2
1
1
1
1
0
1
2
1
2
1
1
1
0
1
1
1
3
3
1
2
0
0
1
1
1
1
1
1
0
0
1
1
1
1
2
1
1
1
2
2
0
1
1
1
1
1
1
0
1
2
0
1
0
1
0
2
1
0
1
1
1
0
0
1
2
1
0
1
1
0
1
1
1
1
1
0
1
0
1
1
2
1
0
0
1
1
0
1
1
0
1
1
1
1
1
2
0
1
0
1
2
1
0
1
1
1
1
1
0
2
0
1
1
0
1
0
0
1
0
1
2
1
1
0
0
1
1
2
1
1
1
1
0
1
1
2
1
1
1
2
2
1
1
1
1
1
0
0
2
1
1
1
1
1
1
1
1
0
2
1
1
0
1
1
2
1
1
1
0
2
1
1
2
1
0
1
1
2
0
0
0
1
0
0
1
1
0
1
1
0
2
1
1
0
1
2
1
1
1
2
0
1
2
0
1
1
1
1
1
0
1
1
2
1
0
2
0
1
1
1
2
2
1
2
1
1
1
1
0
1
0
1
1
1
0
2
0
2
1
1
0
0
1
1
2
1
1
1
2
1
2
1
2
1
0
0
1
0
0
0
2
0
1
1
0
2
1
1
2
1
0
1
1
0
0
2
1
0
1
2
1
1
1
1
1
1
0
0
1
2
1
2
2
1
1
1
0
0
2
1
1
1
1
1
2
1
2
0
2
0
1
1
0
2
0
1
1
1
2
1
0
0
1
1
2
1
1
1
1
0
1
1
1
1
2
1
2
1
2
1
2
0
2
2
0
2
2
0
3
0
0
2
2
0
1
1
1
1
1
0
1
0
1
1
1
0
1
2
1
1
2
2
2
1
2
1
0
1
1
0
0
0
1
1
1
1
2
2
1
1
0
0
1
1
0
0
1
0
1
0
2
1
1
1
0
1
2
1
1
1
1
2
1
0
1
0
1
1
0
0
0
1
1
1
2
0
1
1
0
0
1
1
2
0
1
2
0
1
1
1
1
1
0
1
1
1
0
2
0
0
1
0
1
2
2
2
1
2
1
2
0
0
1
0
1
2
1
0
1
0
2
0
1
1
1
1
1
2
3
1
1
1
1
1
2
1
0
1
2
1
2
0
0
10
0
0
2
2
0
2
2
1
2
1
0
1
0
1
1
0
0
1
0
0
1
1
2
2
1
0
0
1
1
0
1
1
1
2
0
1
1
1
2
1
0
1
1
2
2
2
2
0
0
1
1
1
1
2
2
2
1
1
0
1
1
1
0
2
1
1
0
1
3
3
0
1
1
1
1
2
1
2
2
0
0
2
0
0
1
1
1
1
1
1
2
0
2
2
0
0
0
1
2
0
0
1
1
1
2
1
0
2
1
1
1
2
2
1
1
0
1
1
2
1
2
1
1
0
2
0
1
0
0
1
1
1
2
0
2
1
1
1
2
1
0
1
1
1
1
2
2
0
1
1
1
1
2
2
2
1
0
1
1
2
2
0
0
2
1
1
0
1
0
2
1
1
1
0
2
1
0
2
1
1
2
1
0
1
2
0
1
0
0
1
1
1
2
2
1
2
0
2
0
0
2
1
0
2
2
1
1
1
1
0
0
2
2
1
0
0
0
1
1
1
1
2
1
1
1
1
0
2
1
0
1
2
1
0
0
2
0
0
1
0
1
1
1
0
1
0
1
1
1
1
1
1
1
1
0
0
1
1
1
0
1
2
1
1
1
1
0
1
2
1
1
0
1
1
1
2
1
1
2
1
2
1
3
1
0
2
1
2
1
1
1
1
0
0
1
2
1
5
1
1
1
2
1
1
0
1
1
1
1
0
1
1
1
1
1
2
2
2
0
1
0
0
1
1
0
1
1
1
0
2
0
1
0
2
2
0
1
1
1
0
2
2
0
1
1
1
1
1
1
2
0
2
1
2
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
0
1
2
2
1
1
0
1
2
1
2
1
1
1
1
1
1
1
1
0
0
0
1
2
1
2
1
1
0
0
2
1
1
1
1
1
1
2
1
0
2
2
0
1
1
1
1
1
0
0
1
0
0
0
0
1
2
0
1
1
2
3
1
2
1
2
1
1
2
1
1
1
1
0
0
1
1
1
2
0
1
1
2
2
0
1
1
0
1
2
0
1
0
2
1
0
1
1
1
2
1
1
2
2
1
1
0
1
0
1
2
0
1
1
2
1
0
1
1
0
1
2
1
1
1
1
1
1
1
0
2
2
1
1
1
1
1
1
2
1
1
0
1
0
1
0
1
2
0
2
1
2
0
1
2
2
1
1
1
0
0
1
1
0
2
2
1
1
0
0
1
0
2
1
2
1
1
1
2
2
2
0
1
0
1
1
1
1
1
0
1
0
0
0
0
0
1
1
0
2
2
0
1
1
2
2
0
1
1
2
1
1
1
2
1
0
2
1
1
2
1
1
1
1
1
2
0
1
0
1
1
2
0
1
1
0
0
1
1
0
2
0
0
2
0
1
1
0
1
1
0
1
1
0
2
1
0
0
0
2
1
0
2
1
1
0
1
2
0
2
1
1
2
1
1
2
2
1
2
1
0
0
1
2
1
1
2
0
1
0
0
2
1
1
2
1
0
1
0
1
0
1
1
2
1
0
1
1
1
0
0
2
0
4
2
2
1
2
1
0
1
1
1
2
1
1
0
2
1
1
1
2
1
1
1
2
1
1
2
0
0
1
1
1
1
1
2
0
1
1
1
1
1
2
1
0
0
1
1
1
1
1
1
2
1
2
0
2
0
1
2
2
1
1
0
0
1
2
1
1
0
1
2
1
0
0
0
1
3
0
1
0
0
2
0
1
2
1
1
1
1
1
1
0
1
2
2
1
1
1
2
0
1
2
1
0
2
1
2
1
1
0
0
1
3
2
1
2
1
1
2
1
0
1
0
0
0
1
2
0
1
2
0
1
0
1
1
1
0
1
1
0
2
1
0
1
1
0
2
0
2
0
1
0
1
1
0
1
2
0
0
1
1
0
0
1
1
1
1
1
0
2
1
2
1
1
1
1
1
0
2
2
1
0
1
3
3
1
1
1
1
1
1
1
0
0
1
0
0
0
1
1
3
2
0
1
1
1
1
2
0
1
1
1
1
0
2
1
2
2
0
1
1
1
1
0
1
1
0
1
1
2
1
1
0
0
1
0
0
2
1
2
2
0
1
3
1
1
2
0
0
2
1
1
0
0
0
1
0
1
1
1
1
2
2
0
1
1
2
1
2
1
1
1
1
1
1
0
2
1
0
0
1
1
2
2
0
1
0
1
0
1
2
0
1
1
1
0
1
4
1
0
2
1
0
1
1
1
1
1
1
1
0
2
1
2
0
0
1
1
2
1
1
0
1
0
1
0
1
2
2
0
1
2
2
1
0
0
1
1
1
0
0
0
1
1
1
2
0
1
0
1
2
1
0
1
0
2
1
1
1
1
2
0
2
1
0
1
1
0
1
1
1
2
2
2
0
0
1
2
2
1
1
1
0
2
1
0
1
0
0
1
2
2
2
2
1
2
2
2
1
2
1
0
1
1
1
1
1
1
1
1
1
1
1
0
0
0
2
1
1
3
1
1
1
0
1
1
2
0
1
0
2
2
2
1
1
1
1
1
0
0
2
0
0
1
0
1
1
1
1
1
2
0
1
0
2
0
2
1
1
1
2
0
1
1
2
2
1
1
2
1
0
1
1
2
1
0
2
1
1
1
1
1
1
2
1
1
3
2
0
1
1
1
1
2
1
0
2
1
0
2
1
1
0
0
1
0
1
1
0
2
1
0
1
1
1
2
1
1
1
2
3
1
0
2
1
1
2
0
0
1
1
1
0
0
0
1
0
0
2
2
1
1
1
2
1
0
2
3
2
2
1
1
0
0
2
1
1
2
2
1
2
1
1
2
2
2
1
1
2
1
0
1
1
1
1
1
1
1
1
1
0
1
1
1
2
0
0
1
0
1
1
1
1
2
2
0
1
1
0
1
0
1
0
0
1
0
1
1
1
1
1
1
2
1
1
0
1
3
1
3
2
1
0
1
1
1
1
1
1
1
1
0
2
0
1
1
1
1
1
1
1
1
0
0
2
2
1
0
0
1
1
2
1
2
1
1
2
1
1
0
2
1
1
2
2
0
2
1
1
1
1
0
0
0
1
1
1
2
1
0
1
1
0
2
1
2
2
0
0
1
2
1
1
1
0
1
1
1
1
1
1
1
1
2
0
1
3
2
2
1
0
0
2
2
0
1
2
1
1
2
2
2
1
2
0
7
0
1
2
1
1
2
0
1
1
0
1
0
1
0
1
1
2
1
1
0
1
1
1
1
1
2
1
0
2
1
1
1
1
1
2
1
1
1
0
2
0
1
2
0
1
1
2
1
1
2
2
0
1
0
1
1
1
1
3
1
1
1
2
1
1
1
2
0
1
1
1
0
3
1
1
2
1
1
1
0
1
1
1
1
1
2
1
1
0
1
0
1
1
1
1
2
2
0
0
1
1
1
1
1
2
1
0
2
0
1
1
1
1
2
1
1
2
1
1
2
1
0
2
2
1
0
0
1
1
1
1
2
1
0
3
1
0
0
2
0
2
0
1
2
0
1
1
0
1
1
1
0
1
0
1
0
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
0
1
2
1
1
1
1
2
2
1
2
0
1
1
1
1
2
1
2
1
0
0
0
0
1
0
2
0
1
2
2
0
1
1
2
2
2
2
0
1
0
0
1
2
1
1
1
2
3
1
1
1
1
1
0
0
2
1
1
0
1
1
1
1
2
1
2
1
1
0
1
2
1
1
0
0
1
1
0
1
1
1
1
0
1
1
0
2
2
1
0
1
2
1
2
0
2
2
3
1
2
1
0
1
1
0
1
2
1
2
0
1
1
1
1
0
4
1
1
1
1
1
2
1
2
0
1
1
0
1
2
0
1
2
1
0
1
1
1
1
2
0
0
0
1
1
1
1
3
2
2
1
1
1
1
1
2
1
3
1
1
1
0
1
1
0
1
0
2
1
1
0
1
1
1
2
0
1
2
2
0
2
1
1
0
1
0
1
1
3
1
1
1
2
1
0
0
0
2
2
1
0
1
0
2
1
1
1
0
0
2
0
1
0
1
1
2
1
1
1
2
1
2
0
1
1
1
1
2
0
1
1
0
1
1
1
1
0
1
1
1
1
2
2
0
1
1
1
0
2
2
2
1
0
1
1
1
2
1
1
2
1
2
1
0
0
2
1
0
0
1
2
1
0
1
1
0
1
2
2
1
0
0
1
0
1
1
2
0
0
0
1
0
2
2
0
2
1
1
0
0
3
2
0
1
2
1
2
1
1
2
2
2
1
1
2
1
1
2
0
1
1
2
0
0
2
2
2
1
2
2
1
2
0
1
2
1
1
2
0
0
1
0
2
1
2
1
1
2
1
2
1
1
1
0
0
1
0
1
1
1
1
1
1
1
1
1
1
2
1
0
0
1
0
2
0
0
0
1
0
3
1
1
1
2
0
1
1
1
1
1
1
2
1
1
2
1
0
2
1
1
1
1
2
0
0
1
0
0
0
1
2
1
1
1
1
1
1
0
1
1
0
1
1
1
1
2
1
1
1
1
0
2
1
1
1
1
0
1
0
0
1
2
0
1
1
1
1
1
0
1
3
1
1
0
0
1
0
0
1
1
0
0
2
2
2
1
1
0
1
0
1
1
1
0
1
0
1
1
1
2
1
1
1
0
1
1
2
2
1
1
1
1
0
2
2
1
0
1
1
2
1
2
1
1
2
2
1
1
1
0
1
0
1
1
1
1
2
1
1
1
2
0
1
1
1
2
1
2
2
1
1
1
1
1
2
1
1
1
2
1
0
1
1
1
0
1
0
0
2
0
0
1
0
2
1
1
2
1
0
2
2
0
1
2
1
2
0
2
0
0
0
1
1
1
0
1
1
0
1
1
1
2
1
0
1
0
1
2
1
1
0
0
2
1
1
1
2
1
1
2
0
1
1
2
1
1
1
0
1
1
0
1
0
1
2
0
1
1
1
0
1
1
1
2
2
0
2
2
1
1
0
1
1
2
2
0
0
1
1
0
0
1
1
2
2
1
1
1
2
2
1
1
0
1
1
2
0
1
1
2
1
1
0
2
1
1
1
1
2
2
2
0
0
1
3
2
1
2
2
1
0
1
1
0
1
0
0
2
1
1
2
2
1
1
1
1
1
1
0
1
1
1
1
0
1
1
1
1
0
2
1
0
1
2
2
3
1
1
1
1
1
1
1
0
1
1
0
1
1
0
1
1
1
1
1
1
1
1
1
0
0
1
2
2
2
0
1
2
0
1
1
2
1
1
0
0
0
2
0
1
1
0
1
1
1
0
0
2
1
1
1
1
0
1
1
0
2
1
2
1
1
2
1
1
1
1
2
2
1
2
2
1
1
0
1
1
0
1
0
2
0
1
2
0
0
1
1
1
1
2
1
1
0
2
2
1
0
1
1
1
0
1
1
0
2
1
2
1
1
1
1
1
0
2
1
2
1
2
1
0
0
1
2
1
0
1
1
1
2
0
1
1
1
1
1
2
1
0
1
0
0
0
1
1
1
3
1
2
1
1
1
1
2
1
1
2
0
0
0
1
1
1
2
0
1
1
1
1
1
1
2
0
2
0
1
1
1
1
0
0
2
0
0
0
0
1
2
1
1
1
1
2
2
1
0
0
0
1
0
1
1
0
1
0
0
2
1
1
0
2
1
1
1
1
1
1
1
0
0
0
2
2
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
0
1
2
1
0
0
1
0
2
2
0
1
0
0
0
2
2
1
0
0
1
1
1
0
1
1
0
1
0
1
1
1
1
0
1
1
0
2
0
1
2
2
0
0
0
1
1
0
2
2
1
1
1
2
0
2
1
1
1
1
1
1
1
0
2
0
1
1
1
1
1
1
2
2
0
2
1
2
1
1
1
1
1
1
1
0
1
1
2
2
0
2
1
2
0
1
1
1
3
0
1
1
1
2
1
1
1
2
0
1
0
0
1
2
0
2
1
1
2
0
0
0
2
1
0
1
1
0
0
1
0
1
0
1
2
1
2
1
1
1
1
1
0
0
0
2
1
3
0
2
3
0
1
0
2
2
1
1
1
2
1
1
2
2
0
0
0
2
2
1
2
1
2
2
1
0
1
1
1
2
2
2
2
1
1
1
1
1
0
2
2
0
1
1
0
1
2
2
4
1
2
0
2
1
2
2
1
0
1
1
1
1
2
1
1
2
1
1
1
1
1
1
0
0
1
1
1
1
2
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
0
1
0
1
3
1
1
1
1
0
2
0
0
1
1
1
0
0
2
0
0
0
2
2
0
2
2
1
2
1
1
1
0
1
1
1
1
1
1
1
0
1
1
1
0
0
1
0
1
3
1
1
2
1
2
1
0
2
1
1
1
1
1
0
1
1
0
1
1
1
0
2
0
2
1
1
2
1
1
1
1
1
0
2
2
0
0
2
1
1
1
1
1
1
1
1
1
1
1
0
2
0
0
2
0
0
2
1
2
2
1
0
0
0
1
0
1
1
0
1
1
2
1
1
1
2
0
2
0
0
1
1
2
1
0
1
0
2
1
0
2
2
1
2
1
0
0
1
1
2
1
1
1
2
1
2
2
0
0
1
1
1
1
1
1
0
1
0
1
0
2
2
0
1
0
2
1
1
1
1
0
0
2
2
2
1
1
1
1
1
0
2
2
2
3
1
1
0
0
1
0
2
1
0
1
0
2
2
2
2
0
1
1
1
1
2
1
1
1
1
1
0
1
1
1
2
2
1
0
1
0
1
1
1
0
1
1
2
1
1
0
1
2
2
0
0
1
2
1
1
1
2
0
0
1
1
0
2
1
1
1
1
1
2
0
1
1
2
2
1
1
2
2
2
2
1
2
2
1
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
2
1
0
2
2
2
1
0
0
2
1
0
1
0
1
1
4
1
2
1
2
1
2
1
1
1
1
0
0
2
0
1
2
0
0
1
1
0
0
1
0
1
0
1
1
2
2
1
1
1
1
1
0
5
1
0
1
1
1
1
1
2
1
1
1
2
1
1
1
0
3
1
0
1
2
0
0
2
1
1
0
0
1
1
0
2
0
0
1
2
1
2
2
2
1
1
0
1
1
1
0
1
1
1
0
0
2
0
0
1
2
0
1
1
0
2
1
2
1
0
1
1
1
1
2
2
1
2
2
0
1
2
1
0
1
1
1
0
0
0
0
1
2
1
1
1
1
1
0
1
1
1
0
0
2
1
1
1
2
1
2
2
0
3
1
0
0
2
2
1
0
2
1
1
2
1
1
2
1
2
2
1
1
1
0
1
1
1
2
1
3
1
1
1
0
2
1
2
0
1
1
1
1
1
0
1
2
1
1
2
0
1
1
0
0
2
2
1
1
0
0
1
2
0
1
0
1
2
0
0
1
1
1
0
1
0
1
2
0
1
0
1
0
0
0
0
0
2
0
0
1
2
0
0
1
1
1
1
1
1
0
1
1
1
0
2
1
1
2
0
0
2
1
0
0
1
1
2
2
1
1
0
2
0
0
1
2
1
0
2
1
0
2
2
1
2
1
1
1
0
0
0
1
1
2
2
1
1
1
1
1
1
0
2
0
1
1
1
0
0
1
1
1
2
2
1
0
2
2
2
0
1
0
0
1
1
3
1
1
0
0
2
1
1
1
2
2
1
1
2
1
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
1
3
1
1
2
1
1
1
1
1
0
0
1
0
2
1
1
2
1
1
1
0
1
2
0
0
1
1
0
1
1
2
3
1
1
1
2
1
0
0
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
0
1
1
2
3
1
1
0
1
0
1
0
2
1
1
0
1
0
2
1
0
0
2
2
1
0
1
0
1
0
1
2
2
2
1
2
1
1
0
2
0
1
1
0
0
1
1
2
1
2
1
1
0
2
1
1
1
1
0
1
2
1
1
1
1
1
1
2
0
2
1
1
1
0
0
1
1
1
1
2
1
1
1
1
1
2
1
1
0
1
2
2
1
0
1
0
1
1
1
1
0
1
2
1
1
2
1
1
2
1
1
0
0
1
1
1
1
1
0
0
2
0
0
1
0
1
1
1
1
0
2
1
0
1
1
1
0
1
0
0
0
1
1
2
2
1
1
1
0
2
2
1
1
1
1
1
2
2
1
1
1
0
2
1
1
1
1
2
0
1
0
1
1
1
1
1
0
1
1
0
1
1
2
1
1
0
1
1
2
2
1
2
0
1
0
1
2
1
1
1
1
2
1
0
2
1
2
0
0
2
1
1
1
2
0
0
0
2
0
2
1
1
0
1
1
1
1
6
2
1
1
0
2
1
1
2
0
2
0
1
1
0
1
1
1
1
0
2
1
2
1
2
2
1
1
1
2
0
1
0
0
3
3
1
2
2
1
2
0
1
1
1
2
2
0
0
1
0
1
1
1
1
0
2
1
0
1
1
0
2
0
2
2
1
1
1
0
1
2
2
1
0
2
1
1
1
0
0
1
1
1
1
2
0
2
2
1
1
1
1
1
2
1
1
1
1
1
1
0
2
0
1
0
1
1
0
1
1
1
0
1
1
0
1
1
3
1
1
1
1
0
2
2
0
1
1
1
1
0
1
1
1
1
2
2
1
0
1
1
1
1
1
2
2
1
2
0
2
0
2
1
1
2
1
1
1
0
1
0
2
1
1
2
3
0
0
2
1
0
1
1
0
2
1
2
2
1
1
0
1
0
0
1
2
1
1
2
2
1
1
0
2
0
2
1
1
1
0
1
1
1
1
2
2
0
1
1
2
1
1
1
0
1
0
1
2
0
2
1
0
0
2
1
1
2
1
1
1
2
1
0
0
2
2
2
1
1
0
1
1
1
1
1
0
1
0
1
1
2
1
2
1
1
2
1
1
1
1
2
1
1
1
0
2
2
0
1
2
2
1
0
1
0
2
2
0
1
2
2
1
1
1
0
1
1
2
1
1
1
2
1
1
1
1
1
1
1
0
1
1
1
2
2
2
0
2
1
1
1
1
2
2
0
1
1
0
1
1
0
0
2
1
1
1
1
0
2
1
2
2
1
1
1
1
0
2
2
1
0
2
1
2
1
1
0
0
1
0
2
0
0
1
0
2
0
0
0
1
0
1
0
1
1
2
1
1
1
2
2
1
0
0
1
1
0
1
1
1
0
2
1
1
1
0
3
0
1
2
1
1
1
1
1
3
0
2
1
0
1
0
0
2
2
0
0
1
1
1
1
1
1
2
0
1
1
1
1
0
1
2
1
1
1
2
0
1
2
1
1
1
1
1
0
1
1
1
1
1
1
1
1
0
1
0
2
0
2
2
1
1
1
0
1
1
1
1
1
0
1
0
1
0
0
1
2
1
1
2
2
1
1
2
2
0
1
1
0
0
1
2
0
1
0
0
1
1
0
1
1
0
0
0
1
1
1
0
1
0
1
1
0
0
1
2
1
2
1
2
1
0
0
0
1
1
1
1
1
1
1
0
2
1
1
1
1
0
1
0
2
2
0
1
0
1
1
1
0
2
1
0
2
2
1
1
1
2
1
1
1
0
2
1
2
1
0
2
1
2
0
0
1
1
2
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
2
2
1
1
0
2
0
1
1
1
1
4
2
1
0
2
0
2
0
1
0
0
1
0
1
2
1
0
1
0
2
1
0
1
0
0
1
1
1
2
0
1
2
2
1
2
1
1
2
2
0
1
1
2
2
1
3
2
0
3
2
1
1
1
1
1
1
3
1
0
0
2
1
2
2
1
1
1
2
1
0
0
0
3
1
0
1
1
0
1
2
1
1
1
0
1
1
1
2
1
0
0
0
1
1
1
0
1
0
0
1
1
1
1
1
0
2
0
1
0
1
0
0
1
2
1
2
0
2
1
2
0
1
1
1
0
1
1
2
0
1
0
1
2
0
1
2
1
2
1
1
0
1
2
1
0
2
1
1
1
2
0
2
1
2
1
0
1
1
1
1
0
1
1
0
1
1
0
2
1
1
1
1
1
1
1
1
1
1
0
1
2
0
1
0
0
0
1
0
0
1
1
1
1
1
1
1
1
0
1
0
1
1
2
1
1
0
2
1
2
1
2
1
1
2
1
2
0
0
1
2
1
1
0
2
0
1
1
0
0
1
1
0
2
1
0
2
1
1
0
0
0
0
1
2
0
1
0
1
1
2
2
2
0
1
1
1
1
0
2
1
1
1
1
0
0
0
2
1
1
1
0
2
1
1
1
1
2
1
1
2
2
1
1
0
1
1
1
1
1
2
1
1
1
1
1
0
2
1
0
1
2
2
1
1
1
1
0
1
2
1
1
1
0
2
2
0
1
1
0
1
0
1
0
1
2
1
1
1
2
1
0
0
1
1
4
1
1
0
2
2
0
0
1
1
1
1
0
0
2
1
1
2
2
0
0
0
1
2
1
1
0
1
1
0
1
2
2
1
1
1
1
1
1
1
1
3
2
1
2
1
2
1
2
0
1
1
1
0
1
0
1
2
2
1
1
2
0
1
1
1
1
2
1
1
0
1
2
1
1
0
2
2
1
2
0
2
0
1
1
1
2
2
0
0
0
0
1
0
1
1
0
0
1
0
1
0
2
0
1
1
1
0
1
1
1
1
2
0
1
1
0
0
1
0
1
2
2
1
2
1
0
1
2
1
1
1
1
0
2
1
1
0
1
2
0
1
1
1
1
2
1
1
2
1
1
0
1
1
0
2
2
0
0
1
1
2
0
1
1
1
1
1
2
1
1
1
1
0
0
0
2
0
2
1
1
1
1
2
1
0
2
1
1
0
1
1
2
2
0
1
2
1
5
2
0
1
1
0
2
1
0
3
1
0
2
1
1
1
2
1
2
0
1
1
1
2
1
2
1
1
1
0
1
1
1
1
2
1
0
1
3
0
1
0
2
1
1
2
1
1
1
1
0
1
1
2
1
2
0
2
1
2
2
1
0
1
1
0
1
1
1
2
1
1
0
2
0
1
1
1
1
0
4
2
2
2
1
1
1
1
2
2
1
0
0
1
2
1
1
1
2
1
1
1
0
1
1
1
2
2
0
0
1
1
1
1
0
2
2
2
1
1
1
1
1
2
1
1
0
2
5
1
1
1
2
1
1
2
2
1
1
1
1
1
1
1
1
1
0
1
1
0
0
2
1
1
1
0
2
1
3
1
0
1
2
2
1
1
0
1
2
1
1
0
1
1
1
0
1
1
2
1
0
0
1
2
0
1
1
1
0
0
1
1
2
1
1
2
0
0
0
2
1
2
1
1
1
1
0
0
0
0
0
2
1
0
0
0
1
0
1
0
2
2
0
0
2
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
0
1
2
1
1
0
1
0
1
1
1
0
1
1
2
0
1
1
2
0
0
2
1
1
1
1
1
2
1
1
2
2
1
1
1
1
2
1
0
1
1
0
1
1
2
0
2
1
1
1
0
1
1
1
1
2
1
0
0
2
0
1
1
1
2
0
0
0
2
1
1
2
1
1
1
1
1
0
1
1
1
1
2
0
2
1
0
0
1
1
2
2
0
0
1
1
2
0
0
1
0
0
2
1
1
1
1
1
1
0
1
0
0
1
1
1
1
1
1
1
1
2
1
5
1
2
0
1
1
1
0
0
2
2
1
0
0
0
0
1
1
2
1
1
1
1
2
1
1
1
0
2
1
1
1
2
0
2
2
1
1
1
3
1
1
1
0
1
0
1
0
1
1
2
2
1
1
1
2
1
2
0
2
1
1
1
1
1
2
0
4
2
0
1
0
2
0
1
1
0
1
1
1
1
1
1
1
0
2
0
1
2
0
1
1
0
0
2
1
1
1
0
2
2
0
1
0
2
0
1
2
1
0
0
0
1
1
1
1
2
1
2
1
1
1
1
1
1
1
2
3
0
1
1
2
1
2
1
1
0
0
1
1
0
1
0
2
2
1
0
1
1
2
0
1
0
2
2
0
1
1
1
1
2
1
1
2
1
2
1
1
1
1
1
1
0
1
1
2
1
1
1
1
1
1
2
1
2
1
0
1
1
1
1
0
0
1
2
1
1
1
1
1
0
0
1
0
2
1
0
1
0
1
2
1
0
0
1
1
1
2
2
1
1
2
0
1
1
1
1
1
0
1
0
1
0
1
1
2
2
2
0
1
1
0
1
1
0
1
1
1
1
2
0
1
2
0
1
1
1
1
1
0
1
1
0
1
2
1
2
2
2
1
2
1
1
2
1
1
1
2
0
1
0
1
1
1
2
1
2
1
0
1
1
0
1
2
1
1
0
1
2
1
0
1
0
2
1
0
1
1
1
0
1
2
1
1
0
0
1
2
1
1
1
1
1
0
1
3
1
0
0
1
0
0
1
1
0
2
0
1
1
1
2
0
0
1
2
1
0
0
1
1
1
1
1
2
2
1
2
1
1
2
1
2
1
2
0
1
2
0
3
1
1
2
1
1
2
1
1
1
1
1
0
1
1
1
3
2
1
1
1
1
1
1
1
1
1
0
0
2
2
1
1
2
2
1
0
1
1
0
1
0
0
1
2
1
2
1
1
0
1
2
1
1
1
1
1
1
1
3
1
1
0
2
1
1
2
1
1
1
0
1
0
1
0
0
1
1
2
1
2
2
0
1
0
1
2
1
1
0
0
1
1
0
1
2
1
0
1
2
2
16
1
1
2
1
0
1
2
2
1
1
2
2
1
1
1
0
1
1
2
2
0
1
0
1
1
1
1
0
1
2
2
1
0
2
1
0
1
2
1
0
1
1
0
2
1
1
1
2
1
2
0
1
2
1
4
0
1
1
0
1
1
2
0
1
1
2
0
2
0
1
1
0
1
0
2
1
2
1
1
2
1
1
0
1
0
1
1
0
2
2
1
0
0
2
1
1
2
2
2
1
0
2
2
1
1
2
2
1
2
1
2
1
0
0
1
1
1
2
0
1
3
1
2
1
1
1
0
1
0
1
1
0
2
1
0
1
0
2
2
0
1
2
2
2
1
2
2
0
1
2
2
0
3
2
2
1
1
1
0
1
1
1
2
1
1
1
1
1
0
0
0
1
1
1
0
0
2
2
1
0
2
1
2
1
1
1
1
1
1
1
2
2
2
1
1
2
1
1
1
1
2
2
1
2
0
1
1
0
1
0
0
0
0
1
1
1
2
1
1
1
1
2
1
0
2
0
0
2
1
1
0
2
1
1
2
1
1
2
1
1
0
1
2
1
0
1
0
2
1
2
1
1
1
1
1
1
1
2
1
1
0
1
0
2
1
1
0
1
0
1
1
1
2
2
1
2
2
2
2
2
3
1
1
1
0
1
2
0
0
0
2
2
2
2
1
1
0
1
0
2
0
2
2
1
2
2
1
0
2
2
1
0
1
4
2
0
0
2
2
2
1
1
1
1
1
1
1
1
1
2
1
2
0
2
0
2
2
1
0
2
0
1
0
1
1
0
0
1
2
1
1
0
1
0
1
1
1
1
1
2
2
1
1
0
1
0
1
2
2
0
2
2
3
0
0
2
2
1
1
1
2
1
1
0
0
1
0
0
0
2
1
0
1
2
0
2
1
1
1
1
1
1
0
0
0
1
1
1
0
1
0
1
2
1
2
1
0
1
2
1
1
0
1
0
1
2
2
2
1
1
2
1
0
0
1
2
1
2
0
1
2
1
1
0
2
2
0
2
0
1
0
0
1
1
1
1
1
0
1
2
1
0
0
1
1
2
0
0
2
2
0
1
2
0
1
1
1
3
2
2
1
1
2
2
1
0
1
1
2
2
2
1
1
1
1
2
1
1
2
0
1
3
1
1
1
1
4
1
1
0
4
2
2
0
0
1
0
1
0
1
2
2
1
0
0
1
0
1
1
1
2
0
0
0
1
2
1
1
1
0
1
0
0
2
2
0
2
2
1
2
1
1
2
0
1
2
1
1
1
1
1
2
1
0
1
1
0
0
1
1
1
1
2
2
0
0
1
0
1
1
1
1
0
1
1
0
1
1
0
1
2
2
1
2
0
1
0
2
1
1
1
1
1
1
1
0
0
2
1
1
2
2
0
1
0
1
1
2
1
2
0
0
1
1
1
2
2
1
2
1
1
1
0
1
1
1
1
0
2
0
4
1
2
0
2
1
0
1
1
0
1
2
0
1
1
1
2
2
2
0
1
2
0
0
0
2
1
1
0
1
0
1
2
5
1
1
1
1
1
2
1
1
1
1
1
2
2
0
2
2
2
1
1
2
1
2
1
1
0
0
1
1
3
0
0
0
1
0
0
0
1
0
1
1
1
1
1
1
0
1
0
1
0
1
0
1
1
1
0
1
1
2
1
1
2
1
1
1
1
0
1
0
1
1
1
1
1
1
0
1
1
2
1
0
1
0
1
1
1
1
2
0
1
2
1
1
2
1
0
1
1
0
0
1
1
2
1
1
0
0
2
2
2
2
1
1
1
1
2
1
1
1
1
2
1
1
0
0
0
0
0
0
1
2
1
1
2
2
2
1
1
3
1
2
0
0
1
2
1
1
2
0
0
1
0
1
2
2
0
1
0
0
1
1
1
0
0
2
1
1
0
1
2
0
1
1
1
1
2
2
1
1
1
1
1
2
0
2
0
0
1
1
0
2
1
1
0
0
2
1
2
1
1
0
1
1
1
1
1
1
1
2
1
2
1
2
1
1
1
1
1
1
0
0
2
1
2
2
0
0
2
0
2
2
2
0
1
0
1
0
1
1
1
2
1
1
1
2
0
1
0
1
1
0
1
1
2
1
2
1
1
2
2
0
0
1
1
1
2
0
0
3
2
1
1
0
0
2
1
1
2
2
1
1
1
0
0
0
1
2
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
2
2
0
1
1
1
1
2
0
2
0
1
2
1
0
1
1
0
1
1
1
0
1
1
2
1
1
0
2
1
0
0
1
0
2
1
1
1
2
2
1
1
1
1
1
0
1
1
0
2
1
0
2
0
1
0
1
1
1
1
1
1
1
1
0
2
1
0
1
1
3
1
1
0
1
1
1
1
0
2
0
2
0
2
2
0
1
1
2
1
1
1
1
1
2
1
2
0
1
1
0
2
1
0
2
2
1
1
1
0
1
1
1
1
0
0
1
0
1
0
1
1
1
1
1
0
0
1
1
0
1
2
1
1
1
1
1
0
1
1
1
2
2
2
0
1
0
1
1
2
0
2
0
1
0
1
0
1
2
1
0
0
3
0
2
2
1
1
1
0
2
1
2
1
0
0
0
0
2
1
1
2
2
0
2
1
1
1
1
0
1
0
1
3
1
1
0
1
0
2
2
1
0
0
1
2
1
1
1
0
1
1
0
0
1
0
1
2
0
0
1
0
1
0
1
1
1
1
1
2
0
0
4
1
2
1
1
2
0
1
0
1
2
1
1
1
1
1
0
0
1
0
1
1
1
2
1
2
3
1
0
2
0
2
2
1
2
1
1
1
0
1
0
1
1
0
1
1
1
2
0
1
0
0
1
1
2
1
0
3
1
0
0
1
1
1
1
1
1
0
1
4
2
1
1
1
2
1
2
2
2
0
2
1
0
1
1
0
1
1
0
0
0
1
1
2
0
2
0
1
0
2
3
0
2
1
1
1
0
2
1
0
2
1
0
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
0
0
2
1
1
1
0
0
1
1
1
0
0
1
1
1
1
2
1
0
1
2
2
1
1
1
0
0
0
2
2
1
0
0
1
0
2
1
2
0
0
1
1
1
1
1
2
1
1
1
1
0
0
1
2
1
1
2
2
2
1
0
1
1
0
2
1
2
1
0
1
1
0
1
1
1
1
2
2
1
1
1
1
2
1
1
1
2
0
1
2
2
0
2
2
1
1
0
1
1
2
0
0
0
0
1
2
1
0
1
1
2
2
2
2
2
0
2
1
1
2
0
1
0
1
2
1
0
0
1
0
0
1
1
0
1
1
1
2
1
0
1
0
0
1
1
2
1
0
2
1
1
1
1
2
1
1
1
0
1
0
0
0
1
1
1
1
0
1
2
0
2
2
1
0
0
1
0
0
2
2
1
1
1
1
1
1
0
1
0
0
0
0
0
2
1
2
2
1
1
0
1
0
0
1
2
1
1
2
1
1
1
2
1
1
1
0
1
1
1
0
4
2
0
0
0
1
1
1
1
1
2
1
1
0
1
1
2
1
0
1
1
0
2
2
1
2
0
1
1
2
1
1
1
1
1
1
1
0
1
1
1
1
0
1
1
1
1
1
1
2
1
0
1
0
1
1
1
2
1
3
1
1
2
0
2
0
1
2
0
2
1
1
1
2
2
2
1
1
0
1
1
0
1
1
2
1
0
1
2
0
0
1
2
2
2
1
2
0
2
1
1
1
1
0
1
1
2
2
1
1
1
1
0
1
2
1
1
1
1
1
1
2
1
0
2
1
0
1
1
1
0
1
1
1
2
2
2
0
1
2
2
1
2
0
2
1
2
0
2
2
0
0
1
1
1
2
1
2
2
1
2
0
1
1
1
1
1
2
2
0
0
0
0
1
2
0
1
2
1
0
1
1
0
1
0
1
1
0
1
0
0
1
0
0
1
2
2
2
1
2
1
0
0
1
1
0
1
1
0
0
1
0
0
1
2
1
1
1
2
1
2
2
1
1
0
2
0
1
2
1
2
0
0
1
1
1
1
1
1
2
0
1
0
0
1
0
2
2
1
1
1
2
2
0
1
0
1
1
1
1
1
0
1
2
1
0
2
2
0
1
1
1
2
0
1
1
0
2
1
1
1
1
6
1
1
0
1
1
2
1
1
2
1
0
3
2
2
1
1
0
2
1
2
0
1
0
1
1
2
1
1
1
1
1
1
1
1
1
3
1
2
0
1
1
1
0
1
1
1
2
3
1
2
1
2
1
1
1
1
2
0
2
2
0
1
1
2
1
1
2
2
2
0
1
2
1
0
2
2
1
1
1
1
1
0
1
0
1
0
2
0
1
1
0
1
1
0
2
0
2
2
3
0
1
1
2
0
1
1
1
1
1
2
1
1
1
2
0
1
0
0
0
1
0
0
2
1
1
0
0
1
0
0
2
1
1
1
0
1
1
3
1
1
1
0
0
1
2
1
1
2
1
2
1
2
1
2
1
1
1
1
1
0
2
0
1
1
0
2
1
1
1
0
1
0
0
2
1
1
1
1
0
1
0
1
2
0
0
1
0
1
1
0
2
2
1
1
1
0
2
0
1
1
1
0
1
0
1
2
0
2
1
0
1
1
1
1
2
2
1
0
0
0
2
1
1
1
1
1
1
2
0
0
3
0
2
1
1
2
1
1
1
2
1
2
1
0
1
1
1
1
1
0
2
0
2
1
2
1
0
1
1
0
1
1
0
1
1
1
1
2
0
1
1
1
2
1
0
1
1
0
1
2
2
0
1
1
1
1
1
0
3
1
1
1
1
0
0
0
0
2
1
1
2
1
1
1
2
2
0
0
1
1
1
2
2
1
2
1
0
1
2
1
1
1
2
1
1
1
0
1
1
1
1
1
1
0
2
1
1
0
1
1
2
0
2
1
1
0
1
3
0
0
0
1
0
2
1
2
1
4
1
2
0
1
0
0
2
2
2
1
2
0
1
1
1
1
0
1
0
0
1
1
1
2
2
0
1
2
1
2
0
1
0
1
0
0
1
0
0
1
0
2
2
2
2
2
1
0
1
1
1
1
2
1
1
2
1
1
2
1
0
1
1
1
4
1
1
2
2
2
2
1
1
1
0
1
2
2
0
1
0
0
1
0
1
2
1
0
2
0
2
1
1
2
1
1
1
2
2
2
1
0
0
0
2
0
1
0
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
0
2
0
1
1
1
1
0
2
1
0
2
2
1
1
1
0
2
1
1
2
0
0
1
2
2
1
1
2
0
1
0
0
2
0
1
1
1
1
1
1
1
1
1
0
2
2
0
1
2
1
2
0
2
0
2
1
2
1
2
2
1
1
2
2
1
1
2
0
4
1
2
2
1
2
3
0
2
2
2
1
0
1
1
0
1
2
1
0
1
1
1
1
1
1
1
0
1
1
1
2
2
0
2
2
2
1
1
1
0
2
1
1
1
1
1
1
1
1
1
1
1
2
0
1
1
2
1
1
1
1
1
1
2
0
2
0
2
2
1
1
1
1
0
0
1
1
1
1
1
0
4
0
0
1
2
1
2
0
0
1
1
2
1
1
0
1
2
0
2
2
1
1
1
1
1
1
1
2
1
0
1
0
1
0
1
1
0
1
1
1
0
0
0
1
1
0
1
2
1
0
0
1
1
1
0
1
1
1
1
2
2
1
1
1
0
1
1
0
1
1
2
0
1
1
1
0
2
2
1
2
2
1
1
1
1
0
0
2
1
1
1
0
1
0
0
1
1
1
2
1
0
0
1
1
1
0
1
2
2
1
1
0
0
2
1
1
1
1
0
1
1
2
2
0
1
1
2
1
0
2
1
1
0
2
1
1
0
1
1
2
1
0
1
1
1
2
2
1
1
2
0
0
1
0
1
1
1
1
0
1
1
2
1
1
2
1
1
1
2
0
0
1
1
0
0
1
2
1
1
0
1
0
1
1
1
1
1
1
0
2
1
2
2
1
1
1
1
1
1
0
1
1
2
1
1
1
1
1
0
1
2
2
1
1
0
1
1
1
0
1
1
0
1
2
0
1
0
0
0
0
1
0
1
1
0
2
1
1
1
1
0
0
1
2
1
2
0
2
0
1
2
0
0
2
1
1
1
1
2
2
2
1
1
1
3
1
1
2
1
1
1
1
1
1
1
1
1
1
0
1
0
1
0
0
0
1
0
0
0
1
1
0
1
1
2
1
1
1
2
1
1
2
1
0
1
1
1
1
0
0
1
2
2
2
0
1
1
1
0
1
1
1
2
2
0
1
1
1
1
1
1
2
0
2
0
2
2
0
1
1
2
1
2
2
1
2
0
1
0
2
1
1
1
1
1
1
1
1
1
1
0
2
0
0
1
1
1
1
2
1
1
2
2
1
0
1
0
1
0
1
0
1
2
1
1
1
0
1
2
2
1
2
1
2
2
1
0
2
0
1
0
2
2
1
2
0
2
1
1
1
1
1
1
1
2
1
1
1
0
1
1
0
1
5
1
2
2
1
1
1
1
1
1
1
1
0
1
1
2
1
1
1
2
1
1
2
1
0
1
1
2
1
0
2
1
2
1
1
1
1
0
2
1
0
1
1
1
1
0
2
1
2
0
0
1
1
0
1
1
0
1
0
2
1
2
0
1
1
1
0
1
1
0
1
1
1
1
2
0
2
1
1
0
1
1
1
2
0
1
0
1
1
1
0
1
2
1
1
1
1
1
1
1
0
1
1
1
0
0
1
0
0
0
0
1
1
1
1
1
1
0
1
1
1
1
1
2
0
1
1
1
0
0
0
0
2
0
1
1
1
1
1
1
0
1
1
1
2
0
1
2
0
2
0
1
1
3
0
1
2
1
2
2
1
2
1
1
2
1
2
0
1
1
1
1
0
0
1
0
2
1
2
0
1
1
0
2
2
2
0
1
1
2
0
2
2
2
2
1
2
1
2
0
1
1
1
2
2
2
1
2
1
3
1
1
1
2
1
0
1
2
1
1
1
2
0
1
0
1
0
2
1
1
2
1
1
0
2
1
1
2
0
1
0
1
0
0
1
1
0
2
0
0
0
0
1
2
1
0
0
1
0
0
1
2
1
0
1
1
0
1
1
1
2
0
3
1
0
1
0
1
0
1
0
1
0
1
1
1
0
1
2
11
1
1
2
2
0
1
1
1
1
2
0
1
1
0
1
1
1
1
0
1
1
1
0
1
0
2
2
2
0
1
1
1
1
2
0
1
0
2
2
1
1
1
1
1
2
1
1
0
0
0
1
1
1
0
0
0
1
1
1
1
0
0
1
1
1
1
2
0
1
2
1
2
1
2
1
2
1
2
0
0
0
1
1
1
1
1
1
1
1
1
1
0
1
2
0
1
0
1
1
1
1
2
0
0
0
0
2
0
0
1
1
0
1
0
1
0
0
1
1
2
1
2
1
2
1
0
2
0
1
1
1
1
0
2
1
0
2
2
1
0
1
2
1
1
0
1
0
0
0
1
1
1
1
2
0
0
0
0
0
1
2
1
1
1
2
2
1
7
1
1
0
1
2
2
0
0
2
0
2
0
0
1
2
0
0
1
2
1
1
1
1
0
1
1
1
0
1
2
1
1
2
2
0
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
2
2
0
0
0
1
1
1
2
0
2
1
1
2
0
1
1
0
0
2
1
0
2
0
0
1
2
1
0
0
0
2
2
1
1
1
11
1
1
2
1
1
1
0
2
0
2
1
1
0
0
1
1
1
0
1
1
1
0
1
1
1
0
1
1
1
0
0
1
1
2
1
0
1
0
1
1
0
2
0
0
0
0
3
2
2
1
1
1
1
1
1
1
0
1
0
1
1
2
1
0
0
2
4
1
1
1
1
1
1
0
1
1
1
0
0
2
0
1
1
2
1
1
1
2
1
2
2
2
2
1
1
2
1
0
1
2
1
1
0
1
2
1
2
0
1
1
2
0
0
1
1
1
1
1
0
2
1
1
2
1
1
1
1
0
1
0
2
1
2
1
2
2
3
1
2
0
0
1
2
0
0
1
0
0
1
0
1
2
1
1
1
1
1
1
1
1
2
1
0
0
1
1
2
2
0
0
1
0
2
1
0
1
1
2
0
1
2
0
0
2
1
1
1
0
0
2
2
2
2
2
1
1
1
1
1
1
1
2
2
1
0
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
2
1
2
2
0
2
1
2
1
0
1
1
2
2
0
0
1
0
1
0
1
2
1
0
2
1
1
1
0
2
1
0
1
0
1
0
0
1
1
1
2
0
1
0
1
1
1
1
0
2
0
1
2
2
3
1
2
0
2
1
1
1
1
1
2
2
1
0
0
1
0
1
1
0
1
1
1
2
1
2
0
1
0
1
0
1
1
3
0
1
0
1
1
1
0
1
1
1
0
2
1
0
1
1
1
2
1
3
1
2
2
1
2
1
1
1
2
0
2
0
1
1
0
1
2
0
0
0
1
2
1
0
1
1
1
0
1
2
0
1
1
1
0
1
2
1
0
2
0
1
1
1
1
1
2
2
1
1
1
1
1
0
1
0
1
2
0
1
2
1
0
1
0
1
1
2
2
1
1
0
1
1
2
2
2
1
1
2
1
1
1
1
0
0
1
2
0
1
0
1
0
1
1
1
0
1
2
1
1
1
0
0
2
2
1
0
0
1
1
1
1
2
0
1
1
1
1
3
1
1
1
1
1
2
0
1
2
1
1
1
1
1
2
1
1
1
2
1
2
1
1
2
1
1
0
0
1
0
3
0
1
1
0
1
1
2
1
0
1
1
2
1
1
2
1
2
2
1
0
0
1
2
1
0
0
1
1
0
1
2
1
0
1
0
1
2
1
1
1
2
1
0
2
1
2
1
2
1
1
1
1
2
2
1
1
1
2
0
1
1
0
0
1
1
1
2
0
0
1
2
2
1
2
2
2
2
0
0
1
1
2
1
1
1
1
1
1
1
1
0
1
1
1
2
0
1
2
1
1
1
1
1
1
1
2
0
2
0
2
1
2
0
1
0
1
0
1
2
2
1
2
0
1
1
1
0
2
1
0
0
0
1
0
1
0
0
2
1
2
1
1
1
0
1
1
1
3
0
1
1
1
1
1
0
1
1
0
1
2
1
1
0
1
0
1
1
2
0
1
1
1
1
0
2
0
2
2
2
2
2
1
1
0
2
1
1
1
1
1
1
1
1
2
0
1
1
0
0
1
0
1
2
1
1
3
1
2
2
0
0
2
1
2
1
1
1
1
1
2
1
2
2
0
1
0
1
1
1
1
1
1
1
1
1
0
2
2
1
1
1
1
1
1
0
0
2
1
2
1
1
1
1
0
1
1
2
0
1
0
1
1
2
0
1
2
1
0
1
1
2
1
2
0
0
0
2
1
1
1
2
1
4
0
1
0
1
1
0
1
0
0
1
1
0
1
1
2
0
1
2
1
2
1
1
0
2
1
2
1
0
1
1
0
1
1
0
0
1
1
0
1
0
0
0
1
0
0
0
3
1
1
1
1
1
0
1
0
1
2
0
1
0
1
1
0
2
1
1
1
0
1
1
1
1
0
2
1
2
2
1
1
1
1
2
0
0
1
1
1
2
2
1
1
1
0
2
1
0
1
1
0
1
1
1
1
2
0
0
0
1
2
1
0
1
1
2
1
0
1
1
0
1
1
0
1
2
2
0
2
1
1
1
0
3
1
2
2
0
1
1
2
1
2
1
0
1
0
1
1
1
1
2
1
0
0
0
1
1
0
1
0
1
1
1
1
2
1
1
0
1
0
1
0
3
0
0
2
0
1
0
2
0
1
1
1
1
2
1
1
2
1
0
1
1
0
1
1
0
1
1
1
1
3
1
2
0
1
1
2
0
2
1
1
1
1
1
0
1
1
1
0
0
1
1
2
1
2
1
0
2
1
1
2
1
0
0
0
2
1
1
0
1
0
1
1
0
0
1
1
0
2
1
1
1
1
1
0
1
6
0
2
2
0
2
1
0
1
0
2
2
2
3
1
0
1
1
1
1
0
2
1
0
0
1
1
1
1
0
1
1
2
0
2
0
1
1
0
0
1
1
0
1
0
1
0
3
0
1
1
1
1
1
0
1
1
0
2
2
1
1
1
2
1
1
1
2
0
1
0
0
1
2
2
1
1
1
2
1
1
2
2
2
2
1
1
1
1
1
0
1
1
0
1
0
1
1
1
1
2
0
2
1
1
2
0
2
1
2
0
1
1
1
3
2
0
1
1
2
1
1
1
1
1
2
2
1
2
1
1
1
1
1
2
1
1
1
1
1
0
1
1
2
0
2
1
2
1
0
0
1
0
1
1
1
1
1
1
1
0
1
1
1
1
1
0
1
0
1
2
1
1
2
1
1
1
2
1
0
0
4
1
1
1
0
1
2
2
2
1
1
1
1
0
2
2
1
1
1
0
1
0
2
2
1
2
1
2
2
2
0
2
1
1
1
1
0
0
0
2
2
1
2
2
2
1
1
1
0
1
1
1
2
0
2
1
1
0
1
1
0
1
0
2
0
2
2
1
1
2
1
0
1
2
2
1
0
0
1
1
1
0
2
1
2
0
0
1
0
1
1
0
1
1
1
1
0
1
1
0
0
0
0
1
0
1
0
1
1
1
2
0
2
0
0
2
2
1
2
1
2
1
2
1
1
2
1
0
1
0
2
1
1
2
0
1
0
0
1
1
1
1
2
1
0
2
1
1
2
1
2
2
0
1
2
2
2
1
2
1
0
0
1
1
1
0
1
0
1
1
1
1
1
1
0
1
1
0
1
0
0
1
1
1
3
0
0
1
1
2
2
2
0
2
1
1
2
2
1
1
1
1
1
0
0
1
0
0
1
1
1
1
0
0
2
1
1
0
0
1
0
2
1
1
1
1
2
1
5
2
1
1
0
1
1
0
1
1
2
1
2
2
0
0
2
0
1
1
1
1
1
1
1
1
1
2
0
1
0
0
2
1
1
0
2
1
0
0
1
2
0
1
2
2
1
2
1
1
2
1
1
2
2
0
1
2
1
2
1
0
2
1
1
1
1
1
1
1
2
2
1
0
1
1
2
2
1
0
2
1
4
1
2
1
1
1
1
1
1
1
1
2
2
0
1
1
1
0
2
1
1
0
1
0
1
1
2
1
0
1
1
0
0
0
1
0
1
2
2
0
1
1
0
1
1
2
1
1
0
2
2
1
0
1
0
0
1
0
1
0
2
1
1
1
1
2
1
1
1
1
0
1
0
0
1
0
2
2
2
1
0
2
1
1
2
0
1
0
2
1
1
1
1
1
0
1
1
0
0
1
0
1
1
1
2
1
1
1
0
1
0
1
1
2
1
0
2
1
1
0
1
1
2
0
1
1
1
1
1
1
0
1
1
1
1
0
2
2
0
2
1
1
0
0
0
2
0
1
2
2
1
2
1
2
1
1
2
1
2
3
1
1
1
1
1
0
1
2
2
1
1
2
1
3
1
2
1
2
2
0
0
2
0
0
0
2
0
2
2
1
2
2
1
2
1
1
2
2
1
1
1
0
0
0
2
0
2
0
1
3
2
0
2
2
1
2
0
1
1
1
2
0
1
1
0
1
2
1
1
2
2
3
1
1
1
0
1
2
2
1
1
1
0
2
0
3
1
1
0
0
1
1
2
2
0
2
1
2
1
2
1
1
3
1
1
2
1
2
2
0
0
2
1
0
1
1
1
1
2
2
1
0
1
1
1
1
1
0
3
1
2
2
0
1
1
2
0
1
1
1
1
0
0
1
0
1
0
2
0
1
1
1
1
2
1
1
1
0
2
2
1
1
0
1
0
0
1
1
1
1
2
1
2
2
2
1
1
1
1
1
1
1
2
1
0
1
0
0
1
2
0
2
1
1
2
2
0
1
1
1
2
0
2
0
0
1
2
1
0
0
1
1
3
1
1
1
2
2
2
1
2
0
0
1
1
1
1
1
1
1
2
1
1
2
2
0
1
1
2
1
2
2
1
0
2
1
1
1
1
1
0
1
1
2
0
1
0
0
1
1
2
1
1
0
2
1
0
1
0
2
1
1
1
2
1
1
1
1
0
1
1
1
3
2
1
2
1
2
1
0
2
2
1
2
1
0
1
2
2
1
0
2
2
0
2
2
1
1
2
2
0
2
2
2
2
5
1
0
0
1
2
0
0
0
0
0
1
0
1
1
2
0
0
1
1
1
1
1
1
1
1
2
1
2
0
1
1
1
2
1
2
0
1
1
2
0
1
1
0
1
2
0
1
1
1
1
2
0
1
2
1
2
0
2
2
1
2
1
0
0
1
1
1
1
1
0
1
2
1
2
1
1
0
2
1
2
0
1
2
0
0
1
0
1
0
0
7
0
0
0
0
1
2
1
2
1
1
2
1
2
0
3
1
1
2
1
1
2
1
1
1
1
1
2
1
1
1
2
0
1
1
2
0
1
1
2
0
2
1
2
1
1
1
0
1
0
2
1
2
0
1
1
0
0
2
2
1
0
2
1
0
1
1
1
2
0
1
1
1
2
2
1
1
1
0
2
0
0
0
1
1
2
1
2
1
0
2
1
1
1
2
1
0
1
1
1
1
1
0
0
0
1
2
2
1
2
2
1
0
1
0
0
2
0
2
1
2
1
2
2
1
2
2
2
1
2
1
2
2
2
1
2
1
1
2
1
2
1
1
0
2
1
1
2
2
1
0
0
2
1
0
1
1
2
1
1
2
3
0
2
1
1
0
0
1
2
1
2
0
1
2
1
1
1
0
1
1
0
1
0
1
1
1
1
0
0
2
0
1
1
0
1
0
2
1
1
1
2
2
0
1
1
2
1
0
2
1
1
0
1
1
0
1
0
1
2
0
0
2
1
0
2
1
2
1
0
1
0
2
0
0
1
2
2
2
1
0
1
2
2
2
2
1
1
1
0
1
1
0
1
1
2
1
1
0
1
0
0
1
0
1
0
0
1
1
2
1
2
1
2
2
0
1
2
2
0
1
2
1
1
1
2
2
0
0
1
0
8
1
1
1
0
2
1
1
1
0
0
0
2
1
0
0
2
1
1
1
1
4
1
2
2
0
1
2
1
1
0
0
1
0
1
0
2
2
0
2
1
2
1
1
1
1
0
0
1
1
1
0
0
1
1
1
1
0
0
1
0
1
0
1
0
0
1
3
0
1
0
0
2
1
1
1
1
1
1
1
1
1
1
2
2
0
1
1
0
1
1
1
2
2
0
0
0
1
2
0
1
1
1
2
2
1
0
1
1
3
1
2
0
1
1
1
1
1
1
1
1
2
2
1
0
1
1
0
1
1
1
2
2
1
1
1
0
2
1
2
1
0
1
1
0
3
0
2
1
0
1
0
3
1
1
2
0
1
0
2
2
1
0
0
1
1
1
1
1
1
2
1
1
1
1
0
1
0
1
2
2
1
1
0
1
1
2
1
0
0
1
1
0
1
1
2
0
1
2
1
1
1
1
2
1
1
2
2
0
1
1
0
1
1
1
1
1
0
0
1
1
2
1
1
1
2
1
1
2
1
1
0
1
0
0
1
1
1
2
0
1
2
1
1
1
2
2
0
0
1
2
1
0
1
0
1
0
2
1
0
2
0
1
0
1
0
1
0
1
1
1
1
1
0
0
0
0
2
2
1
1
1
0
0
0
0
2
2
2
0
1
2
1
2
0
1
1
0
1
2
2
1
1
0
1
2
1
2
1
1
1
0
1
1
1
1
2
2
2
2
1
3
1
0
1
0
1
0
1
0
1
1
2
1
1
2
1
1
1
1
1
1
3
2
0
1
0
1
1
0
0
2
2
0
2
1
1
0
1
1
0
1
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
0
0
1
1
0
1
0
1
0
1
2
0
2
1
1
2
0
1
0
1
1
1
2
0
2
0
0
2
2
1
1
1
0
1
0
0
0
2
1
1
1
1
1
1
0
1
2
1
0
1
1
1
1
1
1
0
2
0
2
2
3
1
2
0
1
2
1
1
0
1
1
1
0
1
0
2
1
1
1
0
0
2
1
2
1
1
1
1
1
1
2
2
1
1
1
0
1
2
2
0
2
1
1
0
0
1
1
3
0
1
1
1
1
2
1
2
0
1
2
0
1
0
1
0
1
0
1
2
1
2
2
1
1
0
1
1
1
0
2
2
0
2
1
2
0
1
1
1
0
1
1
2
1
0
2
0
1
0
1
1
0
1
1
1
2
0
2
1
1
0
2
1
0
1
1
1
1
0
1
1
0
1
0
1
1
1
3
2
0
0
1
0
0
1
1
0
1
1
1
0
2
1
0
0
1
2
0
1
0
2
2
1
1
1
2
0
0
1
1
1
1
0
1
1
1
2
2
1
1
0
3
1
1
1
0
1
1
0
1
2
0
2
1
2
2
2
2
2
1
2
0
1
1
2
0
1
1
1
1
1
1
0
1
0
2
1
1
0
1
0
1
1
1
1
1
0
2
2
1
0
1
1
1
1
1
1
0
1
1
1
0
2
2
2
1
0
1
1
1
1
1
1
2
1
2
0
1
0
1
1
1
1
1
1
1
0
2
3
0
2
0
1
1
0
1
2
1
1
1
0
1
0
1
2
1
2
2
1
2
1
1
1
1
1
1
0
2
0
0
1
1
0
1
2
1
2
2
1
1
2
0
0
1
1
1
1
1
2
1
2
1
1
1
0
1
2
1
1
1
2
0
1
1
1
2
0
1
2
0
0
0
0
2
1
2
2
2
0
2
1
0
1
1
0
1
1
1
1
1
1
1
0
0
1
2
2
1
1
1
0
0
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
2
0
1
1
1
0
1
0
2
2
2
1
2
1
1
1
1
1
0
1
0
0
2
0
0
0
1
0
0
2
0
1
0
1
1
0
1
0
1
2
1
1
1
1
1
1
2
1
0
0
2
1
1
0
1
0
2
1
1
1
0
1
0
1
1
2
2
1
2
2
2
1
0
1
0
2
1
1
1
2
2
0
0
1
1
1
1
0
1
1
2
0
1
2
1
2
0
2
1
0
2
0
2
1
1
1
1
1
1
2
1
0
1
1
2
1
2
1
1
1
1
2
1
1
0
1
1
1
0
2
0
0
3
0
1
0
1
1
1
0
1
2
1
1
1
0
1
2
1
1
1
1
1
2
1
1
0
0
1
1
1
0
1
1
0
1
1
1
1
3
2
4
0
0
0
0
1
2
1
0
0
1
0
0
1
1
1
1
0
2
0
1
1
1
1
2
2
0
1
1
1
0
0
0
1
1
1
1
2
1
1
1
1
1
1
0
0
1
2
0
0
1
0
1
0
1
2
1
2
1
1
0
1
0
1
2
1
1
1
2
0
2
2
0
1
0
1
1
1
1
1
1
1
0
1
0
0
0
1
0
1
0
0
1
0
1
0
1
1
1
1
1
1
2
1
1
1
0
1
1
1
1
2
0
1
1
1
1
1
0
2
0
2
2
2
2
1
0
2
1
1
0
1
1
1
2
1
1
1
1
1
1
0
0
0
2
1
1
1
1
1
1
1
2
2
0
1
2
0
0
1
1
0
0
1
1
1
1
3
1
2
2
1
1
2
1
2
1
1
2
1
0
0
4
2
0
2
1
0
2
2
0
1
2
1
5
1
0
1
2
1
2
1
2
1
2
2
0
0
0
1
1
1
0
2
0
2
1
1
0
1
2
0
0
2
1
2
0
1
1
2
0
1
0
1
0
0
0
2
0
2
1
0
1
0
0
1
1
1
1
0
0
1
0
2
1
1
1
0
0
1
1
1
1
1
2
0
1
1
1
1
1
2
1
2
0
0
1
1
1
1
1
2
0
1
1
0
0
1
1
2
2
2
0
1
1
1
0
1
1
2
1
0
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
0
1
2
1
1
1
1
1
2
1
0
1
1
0
0
1
1
1
0
1
1
1
2
1
1
1
0
1
1
1
1
1
1
2
2
0
2
1
0
0
1
0
1
2
1
1
2
0
1
1
1
2
0
2
2
0
1
0
2
3
0
1
1
2
1
0
1
0
1
1
2
1
1
1
1
1
0
1
1
2
2
1
1
1
0
1
2
2
1
1
1
0
2
1
2
0
1
1
1
2
2
0
2
1
1
0
2
1
2
0
1
1
1
1
0
0
1
1
1
1
1
1
1
0
2
1
0
2
2
1
1
1
0
2
2
0
1
1
2
0
2
1
0
1
1
1
0
0
1
1
1
0
1
1
0
1
1
1
0
0
1
2
1
0
2
0
1
1
0
1
2
1
2
2
2
2
1
1
1
1
0
0
1
1
0
2
0
1
1
0
1
1
1
1
1
1
2
1
0
2
2
1
1
0
2
2
0
1
0
1
1
2
1
2
1
1
1
2
0
1
2
1
2
2
0
1
0
0
1
1
1
1
0
0
1
2
1
3
0
0
2
2
1
2
1
2
1
1
2
0
1
1
2
0
1
1
0
1
1
1
2
1
1
1
2
0
0
1
0
1
1
1
1
2
2
1
1
2
2
1
0
2
0
0
0
0
0
2
1
1
1
1
2
1
2
1
1
1
0
2
2
1
2
1
2
2
0
2
0
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
0
1
0
2
1
1
1
1
2
1
1
2
2
1
0
2
1
0
1
0
1
1
1
2
1
1
2
1
1
2
0
0
0
1
1
0
1
1
0
0
1
1
1
1
2
2
1
0
0
1
2
2
1
1
1
0
1
1
1
0
0
1
1
0
1
2
1
2
3
1
2
2
2
1
2
1
2
1
1
1
1
1
2
0
0
1
0
1
2
1
2
0
0
1
0
1
1
1
1
0
2
0
2
2
1
1
0
1
1
0
1
2
1
2
1
1
2
2
1
0
2
1
0
1
0
1
1
1
1
2
0
0
0
1
1
1
2
2
1
1
1
1
1
0
1
1
0
0
1
2
1
1
0
1
1
1
3
1
1
1
1
1
0
1
1
1
0
2
1
1
1
1
1
0
1
1
1
1
1
1
1
0
2
1
0
1
2
1
0
2
0
1
1
2
2
0
1
1
4
1
1
1
2
1
1
1
2
0
1
2
1
1
1
2
2
1
0
0
2
0
0
1
0
2
0
0
1
1
2
0
1
0
0
1
3
0
2
1
1
1
0
1
1
0
2
0
1
1
1
0
0
1
1
0
1
1
1
0
2
1
1
0
2
1
1
0
0
1
1
1
0
1
1
0
1
1
1
0
2
1
0
1
1
1
2
0
1
1
1
0
2
1
0
2
0
1
0
1
2
1
1
1
0
0
0
1
1
0
2
2
1
0
1
0
2
2
0
2
1
1
1
2
1
0
1
1
1
0
2
0
1
2
2
1
1
1
0
0
1
1
1
2
1
1
0
0
0
1
1
2
1
0
2
1
0
1
1
1
0
0
0
2
2
1
0
1
2
1
1
1
1
1
2
2
0
2
0
1
0
2
0
0
2
1
1
0
1
0
1
1
0
0
0
0
0
2
0
0
3
2
3
1
1
0
1
1
0
2
1
1
1
0
1
2
2
1
1
1
1
1
1
0
1
1
1
3
0
0
1
1
2
1
1
1
1
1
2
1
1
1
0
1
1
2
1
0
1
1
2
2
1
1
1
1
2
2
2
1
1
2
1
2
1
1
1
0
1
0
1
0
1
1
1
2
1
1
2
1
1
1
0
1
2
2
0
0
2
1
1
0
0
2
1
0
0
1
2
2
1
2
2
1
0
0
2
1
2
1
1
0
2
2
0
2
0
0
1
1
2
1
2
1
0
1
0
1
0
0
1
1
2
1
1
1
0
2
0
1
0
0
0
1
2
1
1
0
1
0
2
1
2
1
2
1
1
1
1
1
0
2
1
0
1
2
1
1
1
2
0
1
1
2
0
1
1
1
1
0
1
0
1
0
1
2
1
1
1
1
1
2
1
1
1
1
1
1
0
1
1
2
1
2
1
1
1
2
1
0
1
1
1
2
0
1
2
0
1
1
2
1
1
1
1
1
0
1
1
0
1
2
2
1
1
0
1
1
2
2
1
1
1
2
1
2
0
0
2
0
1
1
2
1
0
1
0
2
1
0
2
2
1
1
0
0
1
1
0
2
1
1
1
1
0
1
1
2
2
0
1
2
1
2
1
1
2
1
0
1
1
1
1
1
1
2
2
2
1
1
0
1
1
1
1
0
0
1
1
1
1
0
1
1
1
1
0
2
1
2
1
1
2
2
0
3
1
3
2
1
0
1
1
1
1
0
1
0
1
2
1
2
1
1
2
1
1
1
3
1
2
2
1
1
2
1
0
1
0
2
1
0
2
1
1
0
1
0
0
1
1
0
2
2
0
2
2
2
1
2
1
1
1
1
2
1
1
0
0
0
0
1
0
1
1
1
1
0
1
1
1
0
0
2
1
1
1
1
0
0
0
1
2
0
1
1
1
1
0
2
1
0
2
2
0
1
0
1
1
1
0
1
1
1
0
2
1
2
1
0
2
0
1
1
0
0
2
2
1
1
1
0
1
2
1
2
1
0
1
1
1
1
1
1
0
2
1
1
1
0
1
0
1
1
1
1
0
0
2
1
0
1
2
1
1
2
2
0
0
2
1
1
1
1
3
1
1
2
1
1
2
1
0
0
1
1
1
1
0
1
1
0
2
1
1
0
1
2
1
1
1
1
1
1
1
1
0
2
2
2
1
0
1
0
0
1
1
1
1
1
2
0
0
1
1
1
2
2
1
1
2
1
0
2
2
1
1
1
1
0
0
2
2
1
1
1
0
1
1
2
1
0
0
1
2
0
1
1
0
1
0
0
2
1
2
1
1
1
0
0
1
1
1
1
1
1
1
0
1
1
1
2
1
2
1
0
1
1
1
2
0
1
0
1
0
1
1
1
0
1
0
2
2
2
0
1
1
0
0
0
1
1
1
2
1
0
1
5
1
0
2
2
2
1
0
2
1
1
2
2
2
2
1
2
2
1
2
0
1
0
2
1
2
2
2
1
2
2
3
1
3
1
1
0
1
1
1
0
2
2
2
2
1
1
1
1
1
1
0
1
2
1
2
1
1
1
2
1
2
0
0
0
1
0
1
2
1
1
2
0
1
1
2
1
0
2
0
1
2
1
1
0
3
2
1
1
1
1
1
1
3
0
2
1
1
1
1
2
1
1
1
0
1
2
3
1
2
1
1
1
1
1
0
2
2
2
1
1
1
1
2
1
1
0
0
1
2
0
2
1
1
2
1
0
2
1
1
2
1
2
1
1
0
1
0
3
1
1
1
1
1
1
2
2
1
1
0
0
3
1
1
1
1
0
0
4
2
1
2
1
0
1
1
0
1
0
1
1
1
2
0
1
1
1
0
1
2
2
1
0
1
2
2
2
1
1
1
1
1
1
1
0
1
1
3
0
0
1
2
1
0
1
2
0
1
0
1
1
1
2
1
1
2
0
1
1
1
1
2
2
2
1
1
2
1
1
2
1
1
0
0
0
1
1
5
1
0
1
2
1
1
1
2
1
1
2
1
2
1
1
1
1
0
1
0
2
1
0
2
1
1
0
1
1
2
1
2
2
0
2
2
1
0
0
1
2
0
1
1
1
0
1
2
1
1
0
2
1
2
2
1
1
2
1
1
0
1
0
2
1
1
2
0
3
1
1
2
1
1
1
2
1
1
0
0
1
0
0
0
1
1
3
0
1
2
1
0
1
2
2
2
1
1
2
1
1
2
1
2
1
1
1
1
0
1
2
1
1
0
1
1
0
1
2
1
2
1
1
1
0
1
1
2
0
1
1
1
1
0
1
0
1
0
1
0
0
1
1
1
2
1
1
1
0
1
2
1
2
0
2
2
2
1
1
1
0
0
1
1
0
1
2
1
1
2
2
1
1
1
1
1
1
1
1
1
0
0
0
2
1
1
1
0
1
0
1
2
2
0
1
1
1
1
1
1
0
0
1
1
1
1
1
0
1
1
2
2
0
0
2
1
2
1
0
0
1
2
1
1
0
1
2
0
0
0
0
2
1
0
0
2
2
2
2
1
1
1
0
1
1
1
1
1
0
1
1
2
1
0
0
1
1
2
1
1
1
2
1
1
1
1
1
2
1
0
1
2
1
1
0
2
1
2
1
1
2
1
2
0
0
2
1
3
1
1
1
2
2
2
1
1
1
1
1
1
1
1
1
2
0
2
2
2
1
1
1
0
1
1
1
1
1
1
1
1
2
2
0
0
1
0
0
0
1
1
1
1
1
2
0
1
1
2
2
1
0
2
0
1
1
2
2
0
1
0
2
0
1
0
1
1
0
2
1
1
0
0
1
1
2
1
2
1
1
1
0
1
1
1
2
0
2
2
1
0
1
2
1
2
1
2
1
0
1
1
1
0
2
2
2
1
0
1
1
1
1
2
1
0
0
1
2
1
1
2
1
1
1
1
1
3
1
1
2
1
1
2
2
1
0
1
2
0
0
2
0
0
1
1
2
0
0
2
2
1
2
2
2
0
2
0
2
1
2
0
2
1
1
1
1
0
2
1
1
1
1
0
0
1
0
1
1
0
1
1
1
2
0
1
1
1
1
3
2
1
0
0
1
1
1
0
2
0
0
1
1
0
1
0
1
1
1
2
1
1
2
1
1
1
2
1
1
1
2
0
2
0
0
1
1
0
1
0
1
0
3
1
1
1
0
1
1
0
1
0
2
1
2
1
1
2
1
1
2
1
1
1
0
1
0
2
1
1
0
2
1
1
1
1
0
0
2
1
1
0
1
1
0
1
2
0
0
2
2
1
2
0
2
2
2
3
2
1
1
2
1
1
1
4
0
1
1
1
2
2
2
1
2
1
2
0
1
1
1
0
1
1
1
1
0
1
1
1
2
1
2
1
1
0
0
1
2
2
2
2
1
1
2
0
1
1
2
0
0
1
1
2
1
0
2
1
0
1
1
0
2
0
1
2
0
2
0
1
1
2
1
1
1
2
0
1
1
0
2
1
1
2
2
2
0
2
0
0
0
1
0
2
0
0
1
1
0
0
1
0
0
1
4
1
1
1
1
2
1
0
1
2
1
2
0
0
0
2
1
2
0
0
2
0
2
0
3
1
1
1
1
1
0
1
1
0
1
1
0
2
0
0
0
1
0
0
2
0
1
1
1
1
0
0
0
1
0
1
1
2
2
2
1
1
1
1
0
1
1
0
1
1
1
1
1
3
1
2
1
2
2
1
1
1
2
1
0
2
1
0
2
0
3
1
0
2
0
2
0
1
1
2
1
0
1
1
1
0
0
1
1
1
1
1
1
1
1
0
1
1
0
1
1
1
1
2
0
1
1
1
1
1
1
2
1
1
3
0
1
1
1
2
1
1
1
0
1
1
1
0
0
0
2
0
2
1
0
1
0
1
1
2
1
0
1
0
1
0
2
1
0
1
1
1
0
1
0
1
1
1
0
2
1
1
2
1
1
1
2
1
1
2
1
1
2
0
1
0
1
0
0
2
2
0
1
1
1
2
2
0
1
1
1
1
0
1
1
2
2
2
0
1
1
0
1
1
1
2
1
1
2
0
0
1
0
1
2
0
1
0
1
2
1
1
2
1
0
0
0
0
2
0
1
1
1
0
2
0
0
1
2
1
1
1
2
1
1
1
0
0
1
1
2
2
1
0
0
2
2
1
1
3
1
1
2
2
1
1
1
1
1
1
2
1
0
2
3
1
0
1
0
1
0
1
1
0
1
0
2
0
1
1
0
0
2
1
2
1
2
2
2
1
1
1
1
1
1
0
1
1
0
1
1
0
1
0
0
0
0
1
1
2
2
0
1
1
1
2
1
2
1
0
1
0
0
1
1
2
2
0
1
1
1
1
2
1
1
0
2
1
1
2
1
1
0
1
2
1
1
1
2
1
1
2
1
2
0
1
1
0
2
0
0
0
2
0
0
1
2
0
0
0
2
0
1
1
1
0
1
1
1
0
0
1
1
0
1
0
1
1
1
1
2
2
0
0
1
0
2
2
1
1
1
1
2
1
1
1
2
2
1
1
1
1
2
1
1
2
1
1
2
1
1
0
1
0
1
1
2
0
1
1
2
1
1
1
2
2
1
1
1
2
1
0
1
1
1
1
1
2
3
1
0
1
1
2
1
1
1
1
1
0
0
1
0
1
1
1
1
1
1
1
2
1
0
1
2
1
0
1
1
1
0
0
0
1
2
1
1
1
1
1
1
1
0
0
2
1
0
2
0
0
0
0
1
0
2
0
0
1
1
2
1
3
2
0
2
1
2
0
0
3
3
1
2
0
2
2
1
1
1
0
1
2
2
0
1
1
1
1
0
1
1
1
0
2
1
0
2
0
1
1
2
1
0
2
1
0
1
1
1
2
1
1
1
1
1
1
2
1
1
0
1
1
2
0
2
2
1
1
1
1
1
1
1
2
0
0
1
0
2
1
0
1
0
2
1
2
0
1
1
1
0
0
1
2
0
1
1
1
1
0
1
2
2
2
1
1
0
0
2
0
0
2
1
0
1
0
1
2
1
0
1
0
2
1
0
1
1
1
0
0
2
1
0
0
2
2
2
1
1
0
1
0
2
1
0
1
0
1
1
1
1
1
2
2
2
3
1
1
0
1
1
1
0
0
1
0
1
0
1
2
1
1
0
1
2
0
1
2
1
0
4
2
2
1
0
0
1
1
1
0
1
1
1
1
1
0
1
1
2
2
1
4
1
1
1
1
0
2
0
2
2
0
2
1
1
1
1
1
1
1
1
1
2
2
2
2
0
1
2
1
1
1
1
0
1
1
1
1
1
1
0
2
0
1
1
0
0
0
1
1
2
1
2
1
0
1
0
2
1
1
1
0
1
0
1
1
2
2
2
0
0
0
0
0
0
1
1
1
0
2
1
0
1
1
2
1
1
1
1
0
1
0
1
1
0
1
2
2
0
1
1
1
1
1
0
1
1
1
1
2
2
0
1
1
1
0
2
1
0
0
2
2
0
0
1
0
1
1
2
1
1
1
1
2
1
0
1
2
0
1
1
2
1
0
1
0
1
0
1
1
1
0
2
2
2
0
0
1
1
1
0
1
1
1
2
2
1
2
1
1
1
1
1
0
1
2
2
1
1
1
1
2
2
2
0
1
1
1
0
0
1
1
0
2
2
1
1
2
1
3
2
1
1
1
0
2
1
1
2
1
0
1
1
1
1
0
1
0
1
1
0
1
1
1
1
2
1
1
1
1
0
1
2
1
0
0
1
1
0
1
2
2
1
2
1
1
0
2
0
2
1
1
1
0
2
1
1
1
1
1
1
1
0
2
2
1
1
2
1
0
1
1
1
1
0
1
2
2
1
1
1
2
1
0
0
0
0
0
0
1
1
0
1
2
1
1
1
1
1
0
1
2
0
1
0
1
0
0
0
1
2
2
1
2
1
0
1
2
0
1
1
2
1
1
1
1
1
0
0
2
0
0
1
1
2
2
0
2
0
0
2
1
0
1
1
2
1
2
2
0
1
1
1
1
0
1
1
1
2
1
1
0
1
0
0
1
2
0
1
1
1
2
0
1
1
1
2
1
1
1
0
1
1
1
1
1
2
1
0
1
0
1
1
1
1
2
1
0
1
0
1
0
1
1
1
1
2
1
1
1
1
1
0
2
1
1
0
1
0
0
1
1
1
1
2
2
1
2
0
1
1
1
2
1
1
2
1
1
0
0
1
1
1
0
0
0
2
1
1
1
1
1
0
2
1
1
0
0
1
2
2
1
0
1
2
2
0
0
2
1
1
0
1
1
1
1
2
0
0
0
1
2
1
1
2
1
1
1
0
1
1
1
1
1
1
0
0
1
1
1
1
1
0
1
1
1
1
1
1
2
2
1
1
1
1
1
2
1
0
0
1
0
0
1
1
1
2
0
1
2
0
1
0
1
1
1
1
1
1
1
2
1
1
1
1
2
0
1
2
1
0
1
1
1
0
0
2
1
1
1
2
0
2
1
2
1
1
1
0
0
2
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
0
1
1
1
0
2
1
1
0
1
1
1
2
2
2
2
2
1
2
2
0
1
1
2
1
1
1
0
2
1
1
1
2
0
1
1
1
0
1
1
1
1
1
2
1
0
1
1
1
1
0
4
1
2
0
1
1
1
1
3
1
0
0
2
0
2
1
1
1
1
2
1
1
1
2
0
1
1
1
1
1
1
1
0
1
1
0
1
0
1
0
0
0
1
0
0
1
2
0
0
0
1
1
0
0
1
1
0
1
2
1
1
2
1
1
3
2
0
1
0
0
2
1
1
2
1
0
1
1
1
0
2
2
2
0
4
2
1
1
0
0
1
1
2
0
3
2
1
0
2
1
2
1
1
1
2
1
1
1
1
0
1
2
2
2
0
1
1
1
1
1
1
1
1
2
0
1
1
0
1
1
1
2
1
1
0
1
2
2
1
2
1
2
1
0
1
2
1
0
2
3
1
2
1
1
1
0
0
1
0
0
1
2
1
0
2
2
1
2
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
0
1
1
1
1
0
2
4
1
1
2
0
1
1
1
1
0
0
1
0
0
0
0
2
1
1
1
1
1
0
2
1
1
1
1
0
1
1
1
0
1
1
2
1
1
1
1
1
1
1
2
1
1
2
1
2
1
2
1
0
1
2
0
2
1
1
1
0
0
0
0
1
2
1
1
0
1
1
0
0
1
0
0
1
1
1
2
1
1
1
1
1
1
0
2
0
0
2
1
1
1
0
1
0
1
1
2
0
0
1
0
1
2
0
2
1
1
0
1
1
0
0
1
1
1
1
0
1
1
1
2
0
1
0
0
1
1
1
2
1
1
1
1
1
2
0
1
2
2
1
1
1
2
1
1
2
1
1
1
1
1
0
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
0
0
1
0
0
1
1
1
2
0
1
1
2
1
1
1
1
1
1
0
1
1
1
0
1
2
1
2
1
2
1
1
0
0
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
0
1
1
1
0
1
2
1
1
1
1
1
0
1
2
2
2
0
2
0
1
1
0
0
1
1
2
2
0
1
2
0
1
1
0
1
1
2
0
1
1
1
1
1
2
1
1
1
1
1
2
1
2
0
2
1
1
1
0
1
1
2
2
2
1
2
1
1
1
1
1
1
1
2
0
0
1
0
1
2
1
2
0
1
1
0
1
1
0
1
1
2
1
1
0
1
0
0
2
0
1
0
1
2
0
1
2
1
2
1
0
1
1
1
1
1
0
1
1
1
0
1
2
1
1
1
0
0
1
1
0
1
1
1
1
1
2
1
0
1
0
1
1
1
0
2
1
1
0
1
2
0
1
2
2
2
2
1
1
0
1
0
1
1
1
1
2
0
1
1
1
1
0
1
0
2
1
2
1
1
0
1
2
0
1
0
1
0
1
0
1
0
0
1
2
1
1
2
0
0
2
0
1
1
3
2
1
1
2
1
0
1
1
0
1
2
1
1
0
1
1
1
1
1
0
1
2
1
1
1
0
1
2
1
1
1
1
1
0
3
0
0
1
1
0
2
1
1
1
1
1
2
1
0
1
1
3
2
0
1
0
1
1
0
1
2
1
1
0
1
1
0
1
1
1
0
1
1
1
2
1
2
1
0
0
0
1
1
2
1
1
0
0
2
3
0
2
0
0
1
1
0
1
2
2
1
2
2
2
2
1
2
1
1
1
2
1
1
1
0
1
2
1
2
1
2
1
2
1
2
1
1
2
1
0
1
1
2
0
1
2
2
1
1
0
0
1
1
0
1
2
1
2
0
1
1
1
0
0
1
0
1
1
3
1
0
1
1
0
1
0
0
0
0
2
1
0
2
1
1
2
1
0
0
1
1
1
0
0
0
1
1
1
1
1
1
1
0
0
1
2
1
0
1
0
1
2
0
1
1
0
1
1
0
1
1
1
2
1
2
1
2
0
2
2
0
1
0
1
1
2
1
2
4
2
1
1
0
2
1
1
1
2
2
1
1
0
1
1
2
1
1
2
0
0
1
1
0
1
1
1
1
1
0
0
0
0
1
0
2
2
1
0
2
1
2
1
0
1
2
1
1
0
3
1
1
1
1
0
1
1
0
0
2
1
2
1
1
1
2
2
1
4
0
2
1
2
0
1
0
1
2
0
2
2
0
2
0
2
1
1
2
2
2
1
1
1
1
1
1
2
0
0
0
1
1
1
1
1
2
1
1
1
1
1
0
1
1
1
0
2
0
1
1
0
1
0
0
2
1
1
0
2
0
1
0
2
1
1
1
2
0
1
2
0
1
1
0
1
2
1
1
1
0
1
0
1
2
2
2
1
1
1
2
1
1
1
1
2
1
1
0
0
1
3
0
2
1
1
1
2
1
1
0
0
1
1
2
1
2
1
0
1
2
0
0
1
1
2
1
2
1
1
1
1
0
2
0
2
2
1
1
0
0
1
2
1
1
1
2
2
1
1
0
1
0
1
1
1
2
1
1
1
4
1
1
1
2
1
1
0
1
0
1
2
2
1
1
1
1
1
0
1
1
1
1
1
0
0
2
0
1
1
1
1
1
2
1
1
1
2
2
1
1
1
0
0
2
0
1
1
0
2
1
0
1
1
1
1
2
0
1
1
0
1
2
2
1
2
0
2
0
1
1
1
1
0
1
1
2
1
0
1
1
1
1
2
2
2
0
1
1
2
0
1
0
1
0
1
1
1
2
0
2
2
1
2
1
1
2
2
1
0
1
1
2
3
1
1
1
0
1
0
1
1
0
0
1
1
1
1
1
1
0
0
1
2
1
1
1
2
0
0
1
4
2
1
2
0
2
1
0
1
2
1
2
2
1
0
0
1
1
1
1
0
1
1
2
0
1
1
1
1
1
1
0
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
0
0
1
2
2
0
1
0
1
2
1
0
3
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
2
0
1
1
3
0
1
1
2
2
1
1
1
0
0
2
1
1
2
1
1
0
1
1
1
1
4
0
1
2
1
0
2
2
2
2
1
1
2
1
0
1
1
2
1
1
1
0
1
1
2
1
0
1
1
1
1
1
1
0
2
0
0
2
1
1
1
2
0
2
1
1
0
0
1
0
0
0
0
1
0
2
0
2
2
1
2
1
1
1
1
2
1
2
1
0
2
1
1
2
1
2
1
1
1
0
0
2
1
0
2
1
1
1
0
2
2
1
0
2
2
2
1
1
0
1
0
2
2
0
0
1
2
1
2
2
2
1
0
1
2
0
2
2
1
2
0
1
2
2
1
2
0
0
1
1
1
2
0
1
2
1
2
0
1
1
2
2
2
0
0
2
1
1
1
1
1
2
1
1
1
1
1
1
1
0
1
1
1
2
1
1
2
2
1
2
1
2
0
2
2
0
2
0
1
1
2
0
2
0
1
0
1
0
1
3
2
0
1
1
1
1
0
1
1
0
1
2
1
0
0
1
1
0
5
2
1
0
1
1
2
2
2
1
2
1
1
2
1
1
1
2
1
1
2
2
0
1
1
2
1
2
1
0
0
1
1
2
1
1
0
1
2
1
2
1
0
1
1
1
2
1
1
0
2
1
2
2
1
0
1
2
0
1
1
1
1
2
2
1
2
1
1
0
1
1
1
1
2
1
1
1
0
1
1
1
1
1
0
0
2
2
2
0
1
0
1
1
2
1
2
1
2
1
2
1
1
2
1
1
0
0
1
2
1
0
0
2
2
2
0
2
1
2
0
2
1
2
0
1
0
1
1
0
0
1
1
0
0
1
2
2
1
1
1
0
1
0
1
1
1
1
1
0
1
0
1
0
1
2
2
1
1
0
0
0
0
1
2
2
1
2
0
1
0
1
1
1
1
1
1
2
1
0
1
0
2
2
0
2
0
2
1
2
1
2
2
1
0
0
1
1
3
1
0
1
1
1
0
1
2
2
1
1
0
1
0
3
1
2
2
0
0
1
1
1
1
1
1
1
1
1
1
2
1
2
0
2
2
0
1
0
0
0
1
1
0
1
0
1
0
1
0
1
0
1
2
1
0
1
2
1
1
1
1
1
1
1
1
0
1
2
1
0
2
0
0
1
2
2
0
1
2
0
0
1
1
0
2
0
1
1
0
0
1
0
0
1
1
1
1
1
0
1
1
3
2
1
2
1
1
2
0
1
1
1
1
1
0
2
1
2
0
1
1
0
1
1
0
2
1
2
1
2
0
1
2
2
1
1
1
0
2
1
2
1
1
2
1
0
1
1
0
1
0
2
1
2
2
0
1
0
1
1
0
1
1
1
1
1
2
1
0
1
1
2
1
0
1
1
1
0
1
1
1
2
2
0
0
0
2
1
2
2
2
0
1
1
1
2
2
0
1
1
0
1
1
1
2
2
2
1
1
2
2
2
1
1
1
1
1
1
1
1
1
1
2
2
1
2
1
1
1
1
0
0
1
2
1
1
1
1
1
1
0
0
0
2
0
1
1
1
1
1
1
1
1
2
0
2
1
1
0
1
1
2
1
0
0
1
1
0
2
2
2
3
1
3
1
0
1
0
0
2
2
1
1
1
1
0
2
3
2
1
1
0
1
1
1
0
0
3
1
1
1
2
2
1
0
1
1
2
1
2
1
2
1
1
1
1
1
0
0
1
1
0
1
1
1
5
1
2
0
0
1
1
0
1
2
0
0
1
2
2
0
2
0
0
2
0
0
0
1
4
2
0
0
1
1
2
1
2
1
3
1
1
2
0
0
0
1
0
3
1
1
2
1
2
1
1
1
0
0
2
2
4
0
0
0
1
1
0
1
2
1
1
0
2
1
0
1
1
1
1
2
0
1
1
1
1
1
0
1
1
1
1
1
1
2
2
1
2
1
4
2
2
2
1
1
0
1
1
1
1
0
1
1
2
0
1
1
1
2
1
1
2
2
3
0
0
1
1
1
1
2
0
2
1
2
0
1
2
0
1
0
1
1
0
1
2
1
1
1
0
2
1
0
0
1
1
0
0
1
1
1
2
0
1
1
1
1
2
1
0
1
1
1
1
1
3
2
0
2
2
1
1
2
0
0
1
2
1
1
1
1
1
1
1
2
0
0
1
2
2
1
1
1
1
1
0
1
2
1
1
1
1
2
2
0
1
1
1
2
2
1
1
1
0
0
1
0
2
2
1
1
1
2
1
0
1
1
0
1
0
1
0
2
1
1
1
1
1
2
0
0
0
1
1
1
1
2
2
1
1
2
0
2
2
1
0
2
0
2
0
1
1
1
1
0
1
0
2
1
2
1
1
1
0
1
0
0
0
0
1
1
1
1
0
2
1
0
1
2
2
1
3
1
2
2
1
1
2
2
1
1
1
1
0
1
1
1
1
1
1
1
0
1
0
0
2
1
1
1
2
2
1
2
2
1
0
1
1
1
2
3
1
0
2
1
2
1
0
1
1
2
1
0
1
1
1
0
1
1
0
1
2
2
1
0
2
2
1
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
0
2
2
2
2
1
1
1
1
1
2
1
0
1
2
1
1
1
1
1
1
1
1
0
1
1
0
2
2
1
1
2
1
2
0
1
1
0
0
1
1
1
1
1
0
0
0
0
1
1
0
2
1
1
1
1
2
1
0
1
1
1
0
1
0
1
1
1
1
2
0
1
1
0
2
1
0
1
0
2
2
1
2
1
0
1
0
2
1
1
2
1
0
1
3
0
1
1
2
0
2
2
1
2
1
0
3
1
1
0
1
1
2
0
1
0
0
1
0
0
1
0
1
2
0
1
0
1
1
1
1
1
2
2
1
2
1
1
2
0
0
0
0
0
2
1
2
3
1
0
1
1
0
1
1
1
2
1
1
2
1
0
1
1
0
1
1
2
2
1
1
1
2
1
1
2
1
1
1
1
0
1
0
0
1
1
1
1
0
2
1
1
0
2
1
0
0
1
0
1
3
1
1
2
0
0
0
0
0
1
1
1
1
1
0
0
1
0
1
2
2
2
1
0
0
2
2
0
1
2
2
2
1
1
1
1
1
2
1
1
1
0
1
1
2
2
1
2
1
1
5
1
1
0
2
2
1
2
2
1
0
1
2
2
0
1
1
0
2
1
2
1
0
0
1
0
1
0
1
1
0
1
1
2
1
1
2
1
1
1
2
0
0
2
1
0
1
2
0
0
1
1
1
0
2
1
2
1
2
1
1
1
1
1
0
1
1
1
1
2
1
1
1
1
0
1
1
1
2
2
2
3
1
2
0
1
1
1
1
1
1
2
2
1
1
2
0
0
1
1
2
0
1
2
1
1
1
1
0
0
1
1
2
2
3
2
1
0
2
2
3
0
1
1
0
1
2
2
1
0
1
0
2
1
2
1
1
2
1
1
2
0
0
0
1
2
1
2
1
1
1
0
1
1
1
1
0
1
1
2
2
1
2
1
0
1
2
1
1
1
1
2
1
2
0
0
1
2
1
2
0
1
1
2
0
1
1
0
2
1
0
2
0
0
1
1
1
0
1
1
1
0
0
1
0
1
1
0
0
0
2
1
1
0
1
1
0
0
1
0
2
1
1
1
0
1
2
3
2
1
1
1
0
2
1
1
1
0
0
1
0
2
0
0
1
0
1
1
1
1
0
1
2
1
1
0
1
1
1
0
1
2
1
0
0
1
1
1
1
1
0
1
1
0
1
0
1
1
1
1
0
0
2
1
1
0
0
1
2
1
2
1
2
1
0
1
3
2
1
1
1
2
1
1
2
1
0
1
1
1
1
1
0
2
1
2
2
1
1
1
0
1
1
1
0
1
2
2
0
2
0
2
1
2
1
0
0
1
2
1
1
1
1
1
1
1
1
1
2
1
1
0
1
2
1
2
0
2
1
1
1
0
1
1
1
1
1
1
1
1
0
1
1
2
1
2
0
0
1
0
1
2
1
1
1
2
0
1
1
0
0
2
2
0
1
1
0
0
1
1
2
2
1
1
1
1
1
1
0
2
1
2
0
0
1
0
0
1
1
2
2
1
0
1
1
1
0
1
1
1
0
2
1
1
0
2
0
1
0
1
2
1
1
2
2
0
2
2
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
0
0
1
2
2
1
1
0
2
1
1
1
2
1
3
2
1
1
1
1
1
2
1
2
1
0
1
1
1
2
1
1
0
2
1
2
1
1
1
2
0
1
1
2
0
0
2
0
1
1
0
1
1
0
1
2
1
2
2
1
1
2
1
0
2
0
1
0
2
1
1
0
2
1
1
2
0
1
0
0
0
0
0
1
2
1
1
0
2
1
1
1
1
1
2
1
1
0
1
1
2
5
1
1
0
2
2
1
3
1
1
1
0
0
2
2
1
0
0
0
0
1
0
0
1
2
1
1
1
2
1
2
1
1
0
1
1
1
1
1
1
1
1
2
2
2
2
2
1
2
1
0
2
0
1
2
0
1
1
1
1
1
1
2
2
1
1
0
0
1
1
0
1
0
0
1
4
0
2
0
2
1
1
1
0
1
2
0
0
2
1
2
2
1
0
3
2
3
1
0
1
1
2
1
3
1
0
1
1
0
0
2
1
0
2
1
2
1
2
1
2
0
1
0
1
1
1
1
1
2
2
0
0
1
0
1
1
0
1
1
1
0
2
0
2
1
0
1
1
2
2
1
1
1
0
2
0
2
1
1
1
2
3
1
2
2
1
1
0
1
1
0
1
2
1
2
1
2
1
1
1
2
2
1
0
1
1
1
1
1
0
1
3
1
1
2
2
2
0
1
1
0
1
2
0
0
0
0
1
0
1
1
1
1
2
1
0
1
1
2
1
0
0
1
3
0
0
1
1
1
1
2
1
1
1
1
2
0
1
1
0
2
1
0
0
1
0
1
1
0
1
1
0
1
0
2
0
0
2
1
1
1
0
1
0
1
1
1
1
2
1
1
0
2
0
1
0
1
1
2
2
1
1
2
1
1
1
0
1
2
1
2
2
0
0
2
1
1
2
1
1
3
1
1
0
1
0
1
2
1
2
1
1
1
1
1
0
0
1
1
2
0
1
1
1
2
1
0
0
2
1
0
0
1
1
1
0
0
2
1
1
0
0
1
1
0
2
0
1
1
2
1
0
0
1
3
1
2
1
1
1
0
3
1
1
1
1
0
0
1
1
2
0
2
1
1
2
0
1
1
2
1
2
1
0
1
0
1
2
1
1
2
1
0
2
1
1
0
1
2
1
1
1
0
0
1
1
1
1
0
0
0
0
1
0
1
1
2
1
0
1
0
1
1
2
0
1
1
0
1
1
1
2
1
2
1
1
0
1
1
4
1
1
2
1
1
1
1
0
2
1
1
1
1
1
2
1
1
1
2
1
0
0
1
1
1
2
0
2
0
1
1
0
1
0
1
2
1
1
0
0
1
0
1
1
0
2
2
1
2
0
0
2
1
1
1
1
1
2
1
1
2
0
1
1
1
1
2
1
1
1
0
1
1
1
1
1
1
2
0
0
1
0
2
1
1
1
2
0
1
0
1
0
2
0
1
1
0
1
1
0
0
1
1
1
1
0
1
0
1
1
2
2
0
2
1
0
0
2
2
1
2
1
1
0
1
1
1
1
1
1
1
1
0
1
0
1
2
0
1
1
1
0
1
1
0
2
1
1
0
1
1
2
4
1
1
0
1
2
1
0
2
1
1
1
1
2
1
1
1
0
1
1
2
2
0
1
1
0
2
1
0
2
2
1
2
0
2
2
1
2
1
0
0
2
0
2
0
2
1
0
1
0
1
0
1
1
1
1
1
1
1
1
0
1
2
1
0
2
1
1
0
2
1
0
2
1
0
0
0
2
1
1
0
2
1
0
0
2
0
1
2
1
1
1
0
0
1
1
2
0
2
1
0
0
1
2
1
1
1
2
2
0
0
1
1
1
0
0
1
1
2
2
1
0
2
2
1
0
1
2
0
1
1
2
1
0
1
3
2
2
2
1
2
1
1
1
1
0
2
1
0
1
0
2
1
1
1
2
0
0
1
0
2
1
1
2
1
0
1
1
2
2
2
1
1
1
1
0
0
1
1
1
2
0
0
2
1
0
1
2
1
1
0
2
1
0
1
1
0
0
2
2
1
0
1
0
1
1
0
1
4
1
1
1
0
1
1
0
1
1
2
0
2
1
2
0
1
1
1
2
0
1
2
1
0
2
1
1
2
1
1
0
2
2
0
4
2
2
1
2
0
1
1
1
2
1
1
0
1
2
1
1
1
1
2
1
0
1
3
1
1
1
0
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
0
0
0
1
1
2
2
0
1
0
1
0
0
1
0
0
0
1
1
1
1
2
1
0
1
1
2
2
0
1
1
1
1
0
1
1
1
1
1
1
1
1
2
2
0
0
1
0
0
1
0
1
1
3
1
1
2
1
1
2
1
0
1
1
1
1
1
2
1
2
1
1
1
2
1
0
2
1
1
0
1
2
1
1
1
0
1
2
1
0
0
2
1
0
1
0
1
0
1
0
0
0
1
1
1
1
2
1
1
1
1
2
0
1
1
2
0
1
2
0
0
2
1
0
2
1
0
1
0
2
2
2
0
1
1
1
1
0
0
2
0
1
2
1
2
1
1
3
1
2
2
1
1
0
1
1
1
1
1
1
2
1
1
2
0
2
1
0
2
1
2
0
1
1
1
1
1
2
1
2
2
0
1
1
2
1
1
0
1
1
0
2
1
2
1
1
1
1
0
3
1
2
0
0
0
0
1
0
0
0
1
1
0
1
1
3
2
1
2
0
2
0
0
1
1
1
2
1
2
0
1
0
1
1
1
1
2
1
1
2
1
0
1
1
1
1
2
1
0
0
1
1
1
1
1
1
1
2
1
0
0
1
1
1
1
1
1
1
1
2
2
1
2
1
1
1
2
1
2
1
1
1
2
2
0
0
1
0
0
1
2
1
1
0
1
2
0
1
2
1
1
1
1
1
1
1
1
0
0
1
1
0
2
1
2
1
2
1
1
2
1
1
0
1
1
1
1
1
1
1
0
1
1
2
1
0
1
1
1
2
0
0
0
0
2
1
2
2
1
1
2
1
1
2
0
1
0
1
1
1
2
1
0
1
0
2
0
0
0
0
1
1
1
2
0
1
0
0
1
1
2
1
1
1
1
1
2
0
1
1
1
0
1
1
1
0
2
2
2
0
0
0
2
1
2
2
2
1
3
1
0
0
1
0
1
1
1
1
0
2
1
1
2
0
0
1
2
1
1
2
0
1
1
1
1
0
1
0
1
1
1
1
1
0
2
0
1
1
2
0
2
1
1
0
0
1
1
0
1
0
1
1
1
0
1
2
1
0
1
6
1
2
1
2
1
2
2
0
1
2
1
1
1
0
2
0
1
1
1
1
1
1
1
2
1
1
1
0
2
1
1
2
1
1
2
1
1
0
1
2
0
2
2
2
1
1
1
1
1
0
1
0
1
1
2
1
2
1
2
2
2
2
1
1
0
1
1
1
1
2
2
0
2
0
1
1
0
1
1
1
2
1
2
1
1
1
0
2
2
1
1
1
1
1
1
0
1
0
1
1
2
0
1
0
2
1
0
2
2
1
0
1
0
1
0
2
1
1
2
0
1
0
0
1
1
0
2
1
1
1
0
1
2
1
1
0
1
1
1
0
1
2
0
0
1
1
1
1
1
1
0
1
1
0
0
2
1
1
1
2
0
1
1
1
1
1
0
0
0
2
2
2
0
1
0
0
1
1
2
2
1
1
1
1
1
2
1
1
0
1
1
2
2
0
0
2
1
0
1
4
0
0
2
2
0
0
1
0
0
1
1
2
1
1
2
2
0
2
1
2
1
1
0
0
1
1
0
2
1
1
0
1
0
1
2
1
0
0
3
2
1
0
1
2
2
0
0
2
2
1
1
1
2
2
0
1
1
1
2
1
2
2
1
0
1
1
0
1
1
2
0
3
0
0
1
1
0
1
1
2
1
1
1
3
1
1
1
1
0
1
0
0
1
3
1
1
2
0
1
0
1
1
1
0
0
1
2
2
1
2
1
1
0
0
1
2
1
0
2
1
1
1
1
1
1
0
1
1
1
2
2
1
1
2
1
1
1
0
1
2
0
1
1
1
1
1
2
1
0
0
0
1
1
2
1
2
1
2
1
2
1
1
1
2
0
1
1
1
1
0
1
1
0
2
1
1
1
0
0
0
1
1
0
0
2
1
1
1
1
1
0
1
2
0
0
1
2
1
0
2
1
1
1
1
2
2
1
1
0
3
1
0
1
2
1
2
2
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
2
2
1
1
1
1
1
4
1
1
2
2
0
1
1
2
0
0
0
1
1
1
2
1
0
0
2
0
1
1
1
0
1
0
2
2
0
1
1
1
1
1
2
1
2
1
0
2
1
1
1
1
0
1
1
1
0
1
2
1
1
0
1
1
2
1
1
2
2
1
0
2
1
2
1
2
1
2
2
1
1
0
1
1
2
1
0
0
2
1
2
1
1
1
1
1
1
0
2
1
1
0
2
2
0
2
1
0
2
2
2
1
1
1
0
0
2
0
0
1
1
2
1
2
1
2
2
1
0
1
0
1
1
1
1
1
1
1
0
0
1
0
1
1
1
2
1
0
2
1
0
1
1
0
2
1
2
1
1
0
1
1
1
1
1
1
0
2
1
1
2
1
2
2
0
2
0
1
1
1
2
1
1
1
1
2
2
1
1
0
2
0
0
1
0
1
1
1
2
0
1
0
2
1
1
2
0
2
1
2
1
1
0
2
2
1
0
1
1
1
0
1
2
1
1
0
1
1
2
2
1
1
0
0
1
1
1
1
0
0
1
1
1
1
2
0
0
0
1
2
1
1
2
2
1
1
2
2
1
1
1
0
1
1
1
1
1
1
1
1
2
1
0
1
2
1
1
1
0
1
0
0
1
2
1
1
1
1
2
0
1
0
1
0
1
0
1
1
2
1
0
1
2
2
0
1
0
1
2
1
1
2
2
1
0
0
1
2
2
1
0
1
0
1
1
1
0
0
2
1
1
0
1
0
2
1
0
1
2
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
2
0
0
1
2
1
2
0
0
1
2
2
0
1
2
1
1
1
1
2
0
1
2
1
1
1
2
2
0
2
1
1
0
1
1
2
0
0
1
1
1
1
1
2
2
1
1
0
1
2
1
0
0
2
1
1
1
1
1
1
1
1
2
1
2
1
1
1
0
1
2
2
1
1
2
1
1
1
1
0
1
1
1
0
1
0
1
1
1
1
1
0
1
1
1
2
1
0
1
2
1
1
1
1
1
0
1
0
0
0
2
1
2
1
1
1
2
2
1
0
1
1
2
1
0
0
0
1
1
1
2
0
3
2
2
3
1
0
1
1
1
1
1
1
1
1
1
1
1
2
1
0
2
2
0
1
1
2
1
1
0
1
1
0
1
1
0
2
2
1
1
1
2
0
1
1
0
0
1
0
0
0
1
1
2
1
1
1
1
0
0
1
0
1
1
2
2
2
1
0
1
1
0
1
2
1
1
1
2
1
1
1
1
2
2
0
2
1
0
2
0
0
1
2
1
1
0
0
1
0
1
1
0
2
1
0
1
1
1
1
0
0
1
1
1
1
1
1
1
1
1
1
1
1
3
2
0
2
1
1
1
1
1
0
1
1
1
1
2
2
1
2
0
1
2
1
1
1
2
0
0
1
0
1
2
1
1
0
1
0
1
1
2
0
1
1
1
0
0
2
1
0
1
1
2
2
1
1
2
0
1
2
0
1
1
0
1
1
1
1
1
0
1
2
1
1
1
2
1
1
1
0
1
1
0
0
1
1
0
0
1
1
2
1
1
1
0
2
0
1
1
1
0
1
1
1
2
1
2
1
0
1
1
1
1
0
0
1
1
2
1
1
0
1
1
0
2
1
1
1
1
1
1
2
1
0
0
1
0
1
1
2
1
1
0
1
1
0
0
1
1
1
1
1
1
1
1
2
3
1
1
0
1
1
2
1
0
2
0
0
1
1
2
1
0
2
1
0
1
0
2
1
0
1
1
1
0
1
1
0
1
2
0
1
1
0
1
1
0
0
1
0
1
2
0
1
2
1
0
1
1
1
2
1
1
2
0
1
0
1
1
0
1
1
1
0
1
2
0
1
1
1
1
1
1
2
0
2
1
1
1
2
0
1
0
1
1
1
0
1
1
0
2
1
1
0
1
2
2
1
0
1
1
1
1
2
3
0
0
1
0
1
0
1
1
0
2
0
1
0
1
2
2
2
3
1
1
0
1
0
1
0
0
1
1
0
1
1
1
1
0
1
1
0
0
2
2
1
2
1
2
1
1
1
1
2
2
2
1
2
1
2
2
0
0
2
1
1
1
1
1
1
0
0
1
2
1
1
1
0
1
2
2
1
1
2
1
0
0
0
0
0
0
1
0
1
1
1
1
1
1
2
1
2
1
1
2
1
1
0
1
2
1
1
1
1
2
0
1
2
2
1
1
0
1
2
2
1
2
1
1
1
1
1
2
1
1
2
1
1
2
0
0
0
1
2
1
2
1
1
1
1
1
1
0
0
2
2
1
1
0
0
1
1
0
2
1
1
0
0
2
1
0
0
1
1
2
2
0
2
1
3
0
2
2
0
0
1
1
2
0
1
1
2
1
1
0
1
2
1
0
2
0
1
0
0
1
0
1
1
2
2
1
0
1
2
1
2
0
2
1
0
1
2
1
0
1
1
1
2
2
2
2
1
2
1
1
1
1
1
1
0
2
1
0
0
1
0
2
1
0
1
0
2
1
1
1
2
1
0
1
2
2
2
1
0
1
1
1
2
0
2
0
1
2
1
1
0
1
1
1
1
1
1
1
1
0
1
1
1
0
1
1
1
1
1
1
1
1
2
1
2
1
2
1
1
1
2
2
1
2
0
0
1
1
0
1
0
2
2
0
0
1
0
0
0
1
1
1
2
0
0
1
2
1
1
1
3
0
1
1
1
1
0
1
0
2
2
0
2
1
0
2
1
1
1
1
1
1
2
1
0
1
1
2
0
1
1
1
1
1
2
1
1
0
1
2
1
1
1
2
0
1
0
1
0
1
1
1
2
1
2
0
1
2
2
1
1
0
0
1
1
1
2
1
0
1
1
2
1
1
1
2
1
1
1
0
1
1
1
0
0
1
1
1
1
1
0
1
0
0
1
0
2
2
1
2
1
1
2
2
0
2
1
0
1
0
1
2
1
2
3
2
2
1
1
1
0
2
1
0
1
2
2
1
0
1
1
1
1
0
0
1
2
0
2
1
0
2
4
2
0
1
2
0
3
0
1
1
1
0
0
0
1
1
1
1
2
1
0
2
1
1
1
1
0
1
1
2
1
1
1
2
0
2
2
0
2
1
1
1
2
2
2
0
0
1
1
1
1
1
1
1
2
0
0
2
1
0
1
1
1
1
2
1
1
1
0
2
1
0
0
1
0
2
1
2
0
1
1
1
1
2
0
0
0
0
1
1
1
1
1
1
1
1
1
2
0
1
1
1
0
1
1
1
0
0
0
2
1
2
0
2
1
1
0
1
1
0
0
1
1
1
2
0
0
1
1
1
0
0
1
1
1
2
1
2
0
2
2
1
0
1
1
0
1
0
0
1
0
0
2
0
0
2
1
0
2
1
0
0
1
1
0
1
1
1
1
1
2
2
1
1
1
2
1
0
1
1
1
1
0
1
2
1
1
1
1
2
1
0
0
1
1
1
0
1
0
0
2
2
1
1
1
0
1
2
0
1
0
0
2
1
0
1
2
2
1
0
1
1
2
1
2
2
1
0
2
1
0
1
2
1
1
1
1
1
1
1
2
1
1
2
0
1
1
1
0
1
1
1
2
0
0
2
1
1
2
0
1
0
1
2
1
2
0
1
1
2
1
3
0
0
1
0
1
1
0
2
1
1
1
1
0
1
2
1
2
1
0
2
1
2
1
1
0
1
0
0
0
1
1
1
1
1
2
1
1
1
1
1
2
0
1
1
2
0
0
1
1
0
1
1
1
1
1
1
1
0
1
2
0
1
1
0
1
2
1
0
1
2
2
1
1
1
1
0
0
1
2
2
1
2
1
0
1
1
0
2
1
2
0
1
1
1
1
1
1
1
0
0
1
2
2
1
2
0
1
2
1
1
0
3
2
1
1
1
0
1
1
0
0
0
1
1
2
1
1
2
1
1
0
2
0
1
0
1
1
0
1
1
0
1
1
0
1
1
0
1
1
1
1
2
1
0
1
0
1
2
0
0
1
1
1
0
1
0
1
0
0
1
1
0
1
1
1
1
1
1
1
2
2
1
0
1
1
1
0
3
2
1
1
2
1
1
1
1
1
0
1
1
0
1
1
0
0
1
2
1
1
0
1
1
3
1
1
1
0
1
1
1
0
2
2
1
2
1
2
1
2
1
1
1
1
1
1
0
1
1
2
2
0
1
1
1
2
1
1
0
1
2
2
0
1
1
1
1
1
1
2
1
0
2
1
1
1
2
1
1
0
1
2
0
1
2
0
1
0
1
1
1
2
2
1
2
1
2
1
1
0
1
0
1
2
1
1
0
0
1
2
1
3
0
2
1
2
1
2
1
1
1
2
1
0
0
2
1
2
0
0
1
1
0
1
0
1
0
1
1
1
1
1
0
1
1
0
1
1
0
2
1
0
1
2
0
2
4
0
1
2
2
0
1
2
2
1
1
1
1
0
1
0
0
2
0
1
1
1
1
2
1
1
2
2
1
0
0
0
1
1
1
0
2
1
1
1
1
1
1
1
3
2
1
0
1
1
2
0
1
0
1
2
1
1
0
1
1
0
2
0
1
0
0
1
1
2
2
1
0
1
2
0
0
0
0
0
1
0
2
1
1
1
0
2
0
1
2
1
5
0
2
2
1
1
1
1
1
1
1
1
1
1
0
0
0
1
2
1
1
2
1
0
2
1
1
2
1
1
1
0
1
3
0
1
1
1
1
1
1
1
0
2
1
2
0
0
0
2
2
1
2
2
1
2
1
1
0
0
1
3
1
1
0
0
1
2
1
0
1
1
0
0
0
1
1
3
2
0
1
2
2
0
1
1
0
1
1
1
1
0
1
2
1
0
2
1
0
1
1
1
1
0
0
1
1
1
2
0
1
1
2
1
2
1
0
0
0
0
1
0
0
1
1
0
1
1
0
1
1
2
1
1
0
0
1
1
0
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
1
1
0
1
0
2
2
1
2
2
2
2
1
2
0
0
1
0
1
1
1
2
1
1
1
0
0
2
0
1
1
0
1
0
0
1
2
0
1
1
0
1
1
0
1
1
1
0
0
0
1
1
1
1
0
2
1
0
1
1
0
2
1
0
0
1
1
3
1
2
1
2
1
0
1
1
1
2
2
0
2
2
1
1
0
0
1
0
1
2
1
1
0
2
1
1
1
2
2
2
2
1
2
1
1
1
0
1
2
0
0
0
1
1
0
2
1
2
2
1
1
2
3
1
1
2
1
1
0
1
1
1
0
0
1
2
1
2
2
1
1
1
2
1
1
2
1
2
0
1
1
1
0
1
1
2
0
0
0
1
2
1
2
1
2
2
0
1
1
2
1
1
1
1
1
0
1
2
0
1
0
1
0
1
0
0
1
0
2
1
0
1
1
1
2
2
2
2
0
1
2
2
2
1
1
1
0
1
2
1
2
1
0
2
1
1
2
1
2
1
1
1
2
2
1
2
2
0
1
2
1
0
2
2
2
1
1
0
2
0
1
1
0
1
2
0
0
1
0
1
1
1
1
1
2
1
1
2
1
1
1
1
0
0
1
1
2
1
1
0
0
2
2
1
0
0
1
2
1
2
1
1
2
2
2
1
0
0
1
1
1
1
0
1
2
1
1
1
1
2
4
2
0
1
1
1
1
1
1
0
0
1
0
1
1
2
1
0
0
1
1
2
2
1
2
1
0
1
0
2
0
0
1
1
1
2
0
2
1
0
1
1
0
0
0
1
1
2
1
0
0
1
1
2
0
1
1
2
0
0
1
0
1
1
1
1
1
1
1
0
1
1
1
1
0
1
1
2
1
0
0
1
2
1
2
2
2
0
1
1
0
1
0
1
4
0
2
0
3
0
2
1
1
2
1
1
1
1
2
2
1
1
0
0
1
1
1
1
1
2
0
0
1
1
2
2
1
2
1
1
2
2
1
1
1
1
2
0
0
1
1
2
0
2
1
0
1
1
1
1
2
0
1
2
2
0
1
0
2
1
1
1
0
1
1
2
1
1
4
2
1
2
1
1
1
0
0
0
1
2
1
0
1
0
1
1
1
2
1
1
0
1
0
1
1
0
1
2
1
1
1
0
0
1
0
2
1
1
1
0
1
1
1
1
0
1
1
1
2
1
1
1
1
2
1
1
0
1
2
0
1
2
1
0
0
2
1
2
1
2
0
1
1
1
1
2
1
1
0
1
1
1
2
1
0
2
1
1
2
1
1
1
1
1
0
2
1
1
0
2
1
1
2
2
1
3
1
0
1
1
1
0
0
1
1
1
1
2
2
2
1
0
2
2
1
1
1
1
1
0
1
1
1
2
1
1
1
2
0
1
2
1
2
1
1
1
2
0
1
1
3
1
2
2
1
0
0
1
1
1
1
2
1
2
1
2
1
0
0
1
0
1
2
0
1
2
0
1
1
0
1
1
0
1
0
2
1
2
2
5
2
1
1
1
1
0
1
1
2
1
1
2
2
1
1
1
2
0
0
1
1
2
1
1
0
1
0
1
2
3
2
2
2
0
0
1
1
1
1
0
1
1
1
2
0
2
1
1
3
2
1
2
1
1
2
1
0
1
0
1
0
1
1
1
2
1
1
2
2
1
0
1
1
1
1
0
1
1
2
1
1
1
1
1
0
1
1
0
0
2
2
0
1
1
1
0
0
1
4
1
1
1
1
1
0
2
0
1
1
1
2
3
0
0
1
1
0
2
1
1
2
1
1
1
0
1
0
0
0
0
1
1
0
1
2
1
1
0
0
2
1
0
0
1
1
0
1
2
1
1
2
1
1
1
1
1
2
2
1
2
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
0
0
1
1
0
2
1
1
1
2
0
2
2
2
1
1
2
1
1
0
0
0
1
2
11
1
2
1
1
1
1
1
1
0
2
1
1
1
1
0
0
0
1
1
1
2
1
1
1
0
2
0
0
0
0
1
2
1
0
1
1
5
1
1
3
2
1
1
0
0
2
2
2
0
2
1
0
2
1
0
1
0
2
1
1
1
1
1
0
0
2
1
1
1
0
1
1
0
1
1
1
1
1
1
2
0
1
2
2
2
1
1
1
1
1
1
1
2
0
3
1
2
1
1
1
0
1
1
2
2
1
1
1
0
1
1
1
0
1
2
0
2
1
0
0
0
2
0
2
1
1
2
1
2
2
0
1
1
0
1
1
1
1
2
0
0
1
1
2
1
2
1
0
1
1
1
2
0
2
0
1
0
1
1
1
1
1
1
1
0
1
2
1
1
2
2
1
1
3
2
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
0
1
1
1
1
1
1
2
2
0
1
0
0
0
1
1
0
0
2
1
1
1
1
1
1
1
0
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
1
1
9
0
0
1
1
1
2
1
2
0
0
2
0
0
0
1
1
1
0
1
2
1
7
2
1
0
1
2
2
0
2
1
0
1
1
2
0
2
1
2
0
0
1
0
2
1
1
0
0
1
2
1
1
2
1
2
2
2
2
0
1
0
0
2
0
1
0
0
2
1
1
0
0
0
1
1
2
2
2
2
0
2
1
1
2
2
4
0
1
2
0
1
1
2
1
2
1
1
0
0
2
1
1
1
2
2
2
1
2
0
1
1
0
2
1
1
1
2
1
2
3
0
1
1
1
0
2
2
1
1
1
2
1
0
1
2
1
2
1
1
2
1
1
2
2
1
1
0
0
0
2
1
2
0
0
0
1
1
1
1
0
1
1
1
1
1
0
1
2
1
0
0
0
1
1
2
2
2
2
2
1
1
1
1
2
0
0
0
1
0
1
1
1
0
1
2
0
1
2
1
0
0
1
1
2
1
0
0
1
1
2
2
2
2
2
0
2
1
1
1
2
1
0
0
1
2
2
1
2
0
1
1
1
1
1
2
1
1
1
0
0
2
2
2
0
1
0
1
1
0
0
2
1
1
0
1
1
2
0
1
0
1
1
2
1
0
2
0
1
0
1
1
1
1
1
0
1
2
2
1
1
1
2
1
0
1
1
1
1
2
1
1
2
1
2
1
0
0
0
2
1
1
1
1
1
1
0
0
1
1
1
1
5
0
0
1
2
1
0
1
2
1
0
2
1
0
1
1
1
0
0
0
1
2
1
0
3
1
1
2
1
2
1
1
1
0
2
1
2
1
2
1
1
2
2
1
1
0
1
1
2
2
1
1
0
1
1
2
1
1
1
0
1
0
2
1
1
2
1
1
1
0
1
5
2
2
1
1
1
1
1
0
1
2
2
1
1
2
1
1
2
1
0
1
0
1
2
1
1
2
0
1
1
1
0
0
2
0
1
1
1
1
2
2
1
1
1
1
2
1
1
0
1
1
2
2
0
1
0
1
1
1
1
2
1
0
0
1
1
1
0
0
1
1
1
1
1
1
1
1
2
1
1
1
0
1
1
1
1
2
0
2
0
1
0
1
1
1
1
1
2
0
0
1
1
0
0
0
1
2
1
1
0
1
2
0
1
1
0
1
1
0
1
1
1
1
2
2
2
0
0
0
0
1
1
0
1
0
2
2
1
1
2
1
0
1
2
1
2
0
1
1
1
1
1
2
2
0
1
0
1
1
2
1
1
2
2
0
1
1
1
0
1
0
0
1
1
0
1
1
0
2
1
2
1
0
1
1
1
1
1
0
2
0
0
1
1
2
2
2
1
0
1
1
1
1
1
0
1
1
2
0
1
1
3
0
1
3
1
1
1
1
1
0
2
3
0
2
0
1
1
0
1
1
1
0
2
0
0
2
2
1
1
1
2
1
1
1
1
0
1
1
2
1
2
1
1
2
2
1
2
1
0
1
2
1
0
1
1
0
1
1
1
2
1
0
1
2
1
0
0
0
2
1
0
0
1
0
1
2
1
1
1
1
1
2
1
1
1
1
1
1
0
2
1
1
1
1
1
1
2
0
0
1
1
1
1
1
2
1
0
0
1
0
1
1
2
0
1
1
2
1
0
1
2
0
1
1
0
1
1
2
0
0
2
2
1
1
1
2
0
2
2
2
1
2
0
1
1
2
0
1
2
2
2
1
2
1
0
1
1
1
1
1
1
2
0
0
1
0
1
1
2
1
1
1
3
2
2
1
1
0
1
1
0
1
0
0
1
1
2
2
1
0
1
1
3
1
1
1
0
2
0
1
2
0
1
1
0
1
1
1
1
1
2
1
0
1
1
1
1
1
2
1
0
1
2
2
1
1
1
1
0
1
1
1
0
1
1
1
1
2
1
0
1
0
1
2
2
1
1
2
1
0
1
1
2
1
2
1
2
1
2
1
2
1
0
3
1
1
1
1
1
3
1
1
1
2
2
2
1
0
0
1
1
1
2
1
0
1
1
1
1
1
1
2
1
2
1
0
1
1
0
1
1
1
2
2
0
2
1
1
1
2
1
0
1
0
1
1
1
1
1
2
1
2
1
0
0
0
0
0
2
1
1
0
2
1
2
1
1
1
0
0
0
1
1
1
2
1
2
0
1
1
1
2
1
0
1
1
2
1
2
1
2
1
1
0
1
2
0
0
1
2
1
1
1
1
2
1
2
2
1
0
1
0
2
0
0
1
2
0
1
1
1
1
1
1
2
1
1
0
2
2
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
0
3
1
0
0
0
1
1
1
2
1
1
0
2
1
1
1
1
2
1
1
1
0
0
1
1
1
0
1
1
2
0
0
2
3
0
1
1
1
1
2
4
0
1
1
2
1
1
1
1
1
2
2
1
1
1
1
2
0
1
0
1
0
1
1
1
2
2
1
2
2
1
2
2
1
2
1
0
0
0
1
2
2
1
2
0
1
0
2
0
2
1
1
0
1
1
1
1
1
2
1
0
1
0
1
2
1
0
1
2
2
1
0
2
2
0
2
2
2
1
1
2
2
1
1
1
2
0
0
1
1
1
1
0
0
1
0
1
2
1
2
1
1
4
1
1
1
1
0
1
1
2
2
1
1
1
1
1
1
2
1
2
1
2
1
0
1
2
1
2
2
0
2
1
1
0
1
0
0
1
0
2
1
2
2
0
1
0
1
1
1
2
2
1
0
1
2
1
1
0
1
2
1
1
2
2
1
1
1
0
1
2
2
0
1
1
0
0
0
1
0
1
1
2
1
1
2
2
1
1
1
1
1
1
0
1
2
0
1
1
1
0
1
1
0
1
1
0
1
2
2
0
1
0
2
1
1
0
1
2
1
0
1
0
1
0
1
0
0
1
2
2
1
0
0
1
1
2
1
0
1
0
2
0
1
1
1
1
1
1
0
1
2
0
2
2
1
1
1
1
2
0
1
1
1
2
2
1
2
1
1
1
1
2
1
0
0
1
1
2
2
1
1
1
1
1
0
1
1
2
1
1
0
2
0
1
2
1
0
1
2
1
1
1
2
1
0
1
0
1
1
1
1
2
1
1
2
2
1
0
1
1
0
2
1
1
1
1
2
2
1
1
0
1
1
1
1
0
2
1
1
1
2
1
0
0
0
1
1
1
2
1
1
2
1
2
1
1
0
0
1
1
1
0
1
1
0
1
1
1
0
2
1
1
1
1
1
1
0
1
1
2
1
0
2
0
1
1
0
1
1
2
0
1
0
1
0
1
1
0
1
2
2
1
1
3
1
1
0
0
0
2
0
4
1
1
1
2
1
0
1
0
1
1
1
1
0
0
0
1
1
1
1
1
0
2
1
0
2
2
1
2
0
2
0
0
0
1
0
1
1
1
1
1
0
1
1
1
1
2
0
2
2
1
3
1
1
2
1
0
2
1
0
1
1
2
1
1
1
2
0
2
0
2
0
1
0
0
0
1
1
0
1
1
1
1
1
2
1
0
1
1
1
0
2
2
1
0
1
2
1
1
1
0
1
1
1
1
1
2
1
2
1
2
1
1
1
1
2
1
1
1
0
0
1
1
0
0
2
1
1
0
2
2
1
0
1
1
1
1
2
2
1
0
1
1
0
1
1
1
0
0
2
0
0
1
1
2
1
0
1
2
1
1
1
1
2
1
2
1
1
0
0
0
1
1
1
1
1
1
1
2
1
2
2
0
1
1
1
1
2
1
1
0
1
1
0
2
1
2
1
1
0
2
1
0
1
1
1
1
0
1
2
1
2
1
2
1
1
2
1
2
1
0
2
1
1
2
2
1
2
0
0
2
1
0
1
1
2
1
2
0
1
0
0
2
1
2
1
0
2
0
1
0
0
2
1
0
2
1
1
1
1
1
1
1
1
2
2
1
1
0
2
1
1
1
2
1
2
1
0
1
1
2
1
1
1
0
0
1
2
1
1
0
2
0
1
1
0
0
0
1
1
2
1
1
1
0
0
1
1
2
0
2
1
1
1
2
0
1
1
1
1
0
1
1
0
1
0
1
2
3
1
1
2
2
1
3
0
1
2
2
0
1
1
2
1
1
1
1
1
1
0
0
0
1
2
1
1
0
1
1
1
1
2
1
0
0
1
0
1
4
1
2
2
1
1
1
1
1
1
2
0
2
1
1
1
1
2
2
1
1
0
1
1
1
1
1
1
0
2
2
0
1
1
1
0
0
1
0
0
2
1
1
0
1
1
0
0
2
1
2
1
2
1
1
0
0
1
1
1
1
2
0
0
1
0
0
1
1
0
1
1
0
2
1
1
1
1
1
1
1
1
0
1
2
1
0
1
0
1
0
1
1
0
2
0
1
0
2
2
1
2
1
0
4
0
1
1
2
2
1
0
2
2
1
2
0
2
0
1
2
1
2
0
2
1
0
1
1
0
2
1
2
1
1
2
1
1
1
2
3
1
0
1
2
1
2
1
1
2
1
0
2
0
0
1
0
1
1
0
1
0
1
1
1
1
2
1
1
2
2
0
1
1
1
2
1
1
1
1
2
1
2
1
1
1
2
0
2
2
1
1
1
0
0
1
2
0
1
2
1
4
0
1
0
2
0
1
2
2
2
0
0
1
1
1
1
1
0
1
0
0
2
1
2
1
2
1
1
0
0
1
1
2
0
0
1
0
0
1
0
1
1
1
2
1
1
0
0
2
1
1
0
0
2
1
1
1
1
2
1
0
1
0
1
1
2
1
1
1
0
2
1
1
2
1
1
1
1
0
1
1
2
7
1
1
1
0
1
1
1
1
2
1
2
1
0
1
0
1
2
2
2
2
2
0
0
2
1
2
0
1
2
1
0
1
2
1
1
0
1
2
0
2
1
0
0
1
0
0
1
2
1
2
1
1
2
1
0
0
2
0
0
2
0
1
1
2
2
0
1
0
2
1
1
0
2
1
1
1
1
1
1
2
0
1
1
3
2
1
0
2
1
1
1
0
0
0
0
2
1
1
1
2
0
1
1
1
0
1
1
1
0
1
0
2
3
0
0
0
1
0
1
1
0
1
1
2
2
0
1
0
1
1
1
0
1
1
1
1
2
1
0
0
0
1
0
1
2
0
2
2
0
2
1
2
2
1
1
2
1
0
4
2
1
0
4
2
1
0
1
0
2
1
4
0
2
0
1
2
1
1
0
2
0
0
1
0
1
1
1
2
1
0
2
1
1
0
1
1
1
2
0
1
2
2
0
1
1
2
1
1
2
1
1
0
1
0
2
0
1
1
2
1
2
1
1
0
0
1
0
0
2
1
1
1
0
2
1
1
1
1
1
1
2
2
1
0
0
1
0
0
1
2
1
1
2
1
1
2
1
0
2
1
2
0
1
1
2
0
2
1
1
0
0
0
1
1
1
1
0
1
1
1
1
2
1
2
1
2
0
0
1
0
1
0
1
1
1
2
3
2
1
1
0
1
1
1
1
1
0
1
1
0
0
1
1
1
1
2
1
1
1
2
1
1
0
1
2
0
0
0
1
0
0
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
0
1
1
0
1
2
1
2
1
1
1
1
1
1
2
1
2
0
1
0
0
1
2
0
1
2
0
1
1
2
2
0
0
2
1
0
0
2
0
2
2
1
1
1
1
2
2
1
1
1
1
2
2
1
2
0
2
0
2
1
2
0
4
0
2
1
1
1
1
1
1
0
1
1
0
1
1
1
1
0
1
2
0
1
1
2
1
1
0
0
2
1
0
0
1
0
0
1
0
1
3
1
0
1
0
0
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
0
2
0
0
0
1
1
1
1
1
1
1
1
1
1
0
1
1
0
0
1
1
1
1
1
1
1
0
2
2
1
1
1
1
2
2
1
1
0
1
2
1
1
0
1
1
1
1
0
2
0
1
2
1
1
1
1
0
1
1
0
0
0
1
0
1
1
0
1
0
1
0
1
0
1
1
0
1
1
1
0
1
2
0
1
0
2
0
0
2
0
1
1
1
1
0
1
0
0
1
0
1
0
1
1
0
1
1
1
2
1
0
1
1
1
0
1
2
1
1
0
1
0
0
2
0
0
1
2
1
2
1
1
1
1
0
0
3
2
0
0
0
1
0
1
2
2
0
1
2
0
2
1
1
2
1
1
0
2
1
1
0
0
1
1
1
2
1
0
1
0
0
1
0
2
1
0
1
1
3
1
1
0
1
0
1
1
1
1
0
1
2
0
0
1
0
0
1
2
0
1
0
2
0
1
1
1
1
0
6
1
1
1
0
0
1
1
1
1
2
1
1
1
1
1
2
0
1
1
2
1
0
1
0
1
1
1
1
1
1
2
0
1
1
2
1
0
1
1
1
0
0
1
1
1
2
1
2
1
0
0
0
1
1
1
2
1
1
0
1
0
0
1
1
2
1
2
1
0
1
1
1
1
0
2
0
1
1
1
2
0
1
0
2
1
2
1
1
0
0
1
1
1
1
1
0
1
1
2
2
0
1
1
0
0
1
1
1
0
1
2
2
0
1
1
0
2
1
1
2
0
1
0
2
1
0
2
1
1
0
1
1
1
2
0
1
2
1
1
1
1
2
1
0
1
1
2
2
1
2
1
0
1
0
2
0
2
1
1
0
2
2
2
0
0
0
0
2
1
1
0
0
0
2
1
2
2
1
1
1
1
2
2
2
0
1
2
2
1
0
1
0
1
0
0
1
1
0
1
1
1
1
2
2
0
1
1
2
0
2
1
0
0
2
1
0
1
1
2
0
1
1
2
1
1
0
1
1
8
0
1
1
2
1
0
1
1
0
1
2
1
2
1
0
0
0
2
1
1
1
1
0
0
1
2
1
2
1
2
0
1
0
0
2
1
2
2
2
1
1
0
0
1
1
1
2
0
1
1
1
0
2
2
1
1
2
1
1
1
2
0
0
1
1
2
0
1
2
2
1
0
1
2
1
1
1
0
0
0
0
0
1
1
2
1
0
0
1
1
1
1
1
0
1
1
2
2
0
2
1
1
1
1
1
0
1
1
1
0
2
1
0
0
0
1
2
1
1
2
1
1
1
2
1
1
0
1
1
2
1
2
1
1
1
2
1
2
1
1
1
1
1
1
4
0
1
1
2
1
0
1
1
1
1
2
1
1
1
1
0
1
1
2
0
1
1
1
1
1
1
1
1
1
0
1
1
1
0
1
2
3
1
3
0
0
0
1
1
3
1
2
0
1
2
1
0
1
0
2
2
2
1
2
1
0
0
3
1
1
2
2
0
1
1
1
1
1
1
2
1
0
1
1
1
1
1
1
1
1
1
1
1
2
0
2
0
1
1
1
1
2
2
0
0
1
1
1
0
1
2
2
0
1
0
1
0
1
1
1
0
1
1
2
1
0
1
2
1
1
2
2
1
1
1
1
2
2
1
1
1
1
0
1
1
0
0
1
2
0
1
2
2
0
2
1
1
2
1
1
1
2
0
1
2
2
0
1
2
0
2
1
1
0
0
2
1
1
1
1
1
1
1
1
2
0
0
0
1
1
1
0
1
1
1
1
1
0
1
1
1
1
0
0
2
0
1
2
0
1
1
1
0
1
2
2
0
1
1
1
1
0
0
1
1
1
3
2
0
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
0
0
1
1
1
2
2
1
0
1
1
1
1
1
2
0
0
4
1
2
2
1
1
0
0
1
1
1
0
1
1
2
1
0
3
2
1
2
0
2
1
1
1
2
2
1
2
2
2
0
1
1
2
0
0
0
1
0
0
1
0
0
1
1
0
1
1
1
1
2
0
1
1
2
0
1
1
1
1
1
0
1
0
1
2
2
1
0
2
1
0
1
0
1
2
0
0
1
1
2
1
1
1
0
2
1
1
1
1
2
2
1
1
1
1
1
2
1
2
1
1
1
2
1
1
1
0
0
0
1
1
1
0
1
1
2
0
1
1
0
1
1
1
1
1
1
0
2
2
1
1
1
0
1
1
1
0
2
1
1
2
2
0
1
0
2
1
0
1
0
2
1
2
2
0
0
1
1
2
1
0
0
1
2
1
1
0
0
1
1
2
1
1
2
1
0
1
0
1
0
1
1
1
1
1
1
0
1
0
0
2
0
2
1
1
2
0
2
2
1
1
1
1
2
2
0
2
1
1
2
1
1
0
1
1
1
1
0
0
1
2
0
1
0
1
1
2
1
1
0
2
0
1
1
1
0
2
1
1
1
2
1
0
0
0
1
1
1
2
1
0
0
0
1
1
1
0
1
2
1
0
1
1
0
2
1
1
1
1
1
1
1
2
1
1
2
3
1
2
1
1
1
1
1
1
2
3
1
2
1
2
2
0
2
1
1
0
2
0
2
1
1
2
0
1
2
2
1
1
1
1
0
1
1
1
1
1
2
1
1
2
1
2
1
1
1
0
2
1
1
1
1
1
1
2
0
2
1
0
2
2
1
2
1
1
1
0
0
0
0
1
1
1
1
0
1
2
2
1
0
1
2
1
1
2
1
1
0
1
1
1
1
0
1
1
1
2
0
0
0
2
1
2
2
1
0
1
1
1
1
1
1
1
2
0
1
1
1
0
2
0
1
1
2
2
1
1
1
1
2
1
1
1
2
1
2
0
1
1
2
2
1
1
2
0
1
1
1
0
2
1
1
1
2
1
0
1
1
1
0
0
1
0
2
1
1
2
1
2
1
1
1
1
0
0
1
1
2
0
2
1
0
0
1
1
0
1
1
2
2
2
2
1
1
1
2
1
2
0
0
0
1
0
1
1
1
1
1
2
2
0
1
1
1
2
3
1
1
2
0
1
1
2
1
1
2
0
1
0
1
2
0
1
0
1
0
1
0
1
1
0
1
1
0
0
0
1
1
1
1
1
0
1
2
1
2
0
1
1
2
0
1
1
1
2
1
0
2
1
1
0
2
2
1
0
1
1
1
0
1
1
1
0
2
1
1
0
2
1
1
1
0
1
0
0
1
2
1
0
0
0
1
0
3
1
1
1
2
1
1
1
1
1
1
1
0
1
2
1
1
0
1
2
0
0
1
1
1
1
2
1
1
1
1
0
2
1
1
0
0
1
2
0
1
2
2
1
1
2
0
2
0
2
2
1
2
1
0
0
1
2
1
1
0
1
0
1
2
1
2
1
2
1
1
1
0
1
2
2
1
2
1
1
1
2
3
1
0
0
1
0
2
1
1
1
1
0
1
1
2
1
1
2
2
1
1
0
1
3
1
0
2
2
1
0
1
1
1
0
2
1
1
0
1
1
0
2
1
1
0
1
0
1
1
1
1
0
0
1
2
1
1
1
0
1
1
1
0
0
0
2
1
1
0
0
3
1
2
1
1
1
1
1
1
0
1
1
0
0
2
0
2
1
2
1
1
0
1
0
1
1
2
1
1
0
2
1
0
2
0
1
1
1
1
1
1
1
0
0
1
1
0
1
0
1
0
1
1
1
2
1
0
1
1
1
1
0
2
1
0
1
1
0
1
1
0
2
1
1
1
2
1
1
1
1
1
1
0
1
1
2
2
1
1
0
0
1
2
1
3
1
2
2
1
2
1
1
1
0
1
2
2
1
2
0
1
0
2
0
1
1
1
1
0
1
2
1
1
1
0
1
2
0
0
2
1
1
0
1
1
2
0
1
1
1
1
1
1
0
1
0
1
1
0
1
1
1
2
1
1
1
0
2
1
2
0
1
2
1
2
2
1
1
0
2
2
1
2
0
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
0
1
1
1
1
1
0
1
2
1
0
1
1
1
1
2
2
1
2
2
1
0
2
2
1
2
0
3
2
0
1
1
1
0
1
1
0
0
0
2
1
1
1
0
1
2
2
1
0
1
1
1
1
1
1
2
0
1
1
0
1
3
1
0
1
1
2
1
0
1
0
1
0
1
1
1
1
1
1
1
2
1
2
1
2
1
1
1
0
2
2
0
1
1
1
0
0
0
0
1
1
1
0
1
2
1
1
2
0
1
1
1
2
1
0
1
2
2
1
1
2
2
1
0
4
2
1
1
1
1
2
3
1
0
1
0
0
0
0
1
1
1
2
2
1
1
1
0
0
0
1
1
2
0
2
2
1
1
0
1
0
1
2
1
0
2
1
1
2
2
1
1
1
1
2
1
1
1
1
0
1
2
1
1
1
2
1
1
1
0
1
2
1
0
1
0
2
1
1
2
2
0
1
1
2
1
2
1
0
2
0
1
1
2
1
2
1
0
1
0
0
1
2
0
1
2
1
1
1
0
1
1
1
0
2
2
0
2
1
1
0
1
1
1
1
1
1
2
1
1
2
1
0
1
0
0
0
2
1
1
0
1
0
2
1
1
0
0
0
1
1
1
1
1
1
1
0
1
1
2
1
0
1
1
0
2
0
1
1
0
2
1
0
1
0
0
1
0
1
2
1
1
1
1
2
0
1
2
1
2
2
2
0
1
1
1
1
1
1
1
1
2
0
1
1
0
1
1
0
1
0
0
0
0
0
1
1
1
1
1
3
1
1
0
2
2
0
1
1
0
1
0
2
1
0
0
2
1
0
0
0
1
0
1
0
1
1
0
2
1
0
1
1
0
0
1
1
0
0
0
1
2
1
0
2
1
1
1
1
0
1
1
1
1
1
0
0
1
1
0
1
0
0
2
0
1
0
1
1
1
1
2
1
2
1
1
1
1
2
0
0
1
1
2
1
1
1
1
1
0
2
2
0
1
0
0
2
1
1
1
2
2
1
1
1
0
2
1
1
1
0
2
1
1
1
1
1
1
1
1
0
1
0
0
1
1
0
1
0
1
1
0
0
0
1
1
1
2
2
2
0
1
1
1
1
2
2
1
0
2
1
1
1
2
1
1
2
1
2
0
2
1
1
0
2
1
0
2
2
3
2
1
1
1
1
1
1
2
2
0
1
0
1
0
0
2
1
1
2
2
1
1
2
1
2
1
1
3
2
0
1
1
0
0
1
1
0
1
1
1
1
1
1
0
1
2
1
1
1
0
1
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
0
1
1
1
0
1
1
1
1
1
0
1
2
2
2
1
0
1
1
1
0
1
2
1
1
2
1
2
1
1
0
1
1
2
1
1
2
0
2
0
1
2
1
1
3
0
1
1
2
1
1
1
1
1
1
0
0
0
1
0
1
1
1
1
1
2
0
1
0
2
1
1
2
0
2
1
1
1
2
0
1
0
2
1
0
1
1
1
0
1
1
0
1
1
2
0
2
1
2
1
1
1
2
2
0
1
0
2
1
2
2
1
0
2
0
2
1
1
1
1
2
1
1
1
1
3
1
1
1
1
2
1
0
2
0
0
0
1
1
2
0
1
2
0
2
1
1
2
1
1
0
1
0
0
1
1
1
1
0
1
2
0
1
0
0
0
2
0
1
1
1
0
0
0
1
0
2
1
1
1
2
1
0
2
1
1
1
2
1
2
2
1
0
0
0
0
1
1
0
2
0
1
1
2
1
0
2
1
2
0
1
2
0
2
2
0
1
0
0
1
1
1
2
0
1
1
2
2
1
2
2
1
1
0
2
2
0
1
1
0
0
0
1
2
2
0
1
1
1
2
0
1
1
2
1
1
0
1
1
0
1
1
2
1
1
0
1
0
2
0
1
0
1
1
1
1
1
1
2
1
1
0
0
1
0
1
2
0
0
2
2
2
1
1
1
0
1
1
1
2
0
0
0
1
1
0
0
0
1
0
1
0
1
1
1
2
1
2
1
1
0
0
1
1
2
0
0
1
1
1
1
1
1
2
1
1
0
1
2
1
0
1
2
0
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
0
0
1
0
1
0
1
1
0
1
1
2
2
1
1
0
1
1
1
0
1
1
0
1
1
0
1
2
1
2
1
0
1
1
1
1
1
2
0
1
1
1
1
0
1
0
1
0
2
1
1
2
1
1
1
0
2
0
1
0
2
0
2
0
1
1
1
1
1
0
1
0
0
1
0
2
1
0
1
0
1
0
0
1
0
0
1
0
1
1
2
2
2
2
0
0
1
1
2
1
0
2
1
0
1
2
0
1
1
0
2
2
0
1
1
1
1
1
1
2
1
2
0
1
1
1
0
1
1
1
1
2
1
0
1
1
0
2
1
1
2
1
1
0
2
1
1
1
1
1
1
2
2
0
1
1
1
1
0
1
1
1
1
1
1
2
1
1
0
0
2
1
1
1
1
3
1
1
0
1
2
1
0
1
1
1
2
1
0
1
2
0
1
0
2
0
2
2
1
2
1
1
0
0
1
1
0
1
1
1
1
1
1
1
1
1
0
1
2
2
1
0
2
1
2
1
1
1
1
1
1
0
1
1
1
0
0
1
0
0
1
0
1
0
2
1
0
1
2
1
1
1
1
1
1
0
1
2
1
0
0
3
1
0
1
1
0
0
1
0
1
1
1
2
2
4
0
1
1
1
1
1
1
0
1
1
1
1
0
2
1
1
2
1
1
0
1
0
2
2
0
1
1
1
0
1
2
2
2
0
0
1
1
1
0
2
2
1
1
1
0
2
1
1
1
2
2
1
1
1
1
1
1
1
0
1
1
1
2
0
1
1
1
1
2
0
2
0
0
2
2
1
1
2
0
0
1
0
1
1
0
1
1
1
0
2
2
2
1
1
1
1
2
0
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
0
0
1
1
1
1
0
2
1
1
1
2
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
0
1
2
1
1
2
0
1
2
1
1
1
1
1
2
1
1
1
1
1
0
0
1
1
1
1
1
1
1
0
1
2
1
2
2
1
1
1
1
1
1
2
1
0
1
1
0
2
0
0
2
0
2
1
1
1
2
1
1
0
1
1
1
1
2
1
1
0
2
2
2
1
1
1
0
0
1
1
0
1
1
2
0
0
0
1
1
2
0
2
2
1
1
1
1
1
1
1
1
2
2
1
0
0
1
1
1
0
1
2
1
2
2
2
2
1
1
2
1
1
0
1
2
0
1
0
0
0
2
2
1
0
0
0
1
1
1
1
2
2
1
1
1
2
1
1
2
1
2
1
2
0
0
1
1
0
2
1
1
0
2
1
0
1
2
2
1
1
0
1
1
1
2
2
1
2
1
1
0
1
2
1
1
0
1
0
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
2
3
1
1
0
1
0
1
0
1
2
1
1
1
0
1
0
2
1
1
1
1
1
0
0
1
0
1
2
0
1
2
2
1
0
2
0
0
1
0
2
1
0
2
1
1
1
1
1
1
1
2
1
1
0
0
0
2
2
1
1
2
2
1
1
1
2
1
2
1
1
1
1
1
1
1
0
1
2
1
1
1
0
2
1
1
0
2
1
0
2
0
1
2
2
2
0
1
0
1
2
1
1
1
0
1
0
0
1
2
2
2
0
1
1
1
1
1
3
2
0
1
1
2
2
2
1
2
2
1
1
1
2
0
1
1
2
1
1
2
0
1
0
2
0
0
2
1
2
1
0
1
0
1
2
2
0
1
2
1
2
0
1
2
2
1
1
1
0
1
2
1
1
1
1
0
2
1
1
2
2
4
2
1
1
1
2
1
1
1
0
2
2
1
0
1
1
2
1
1
2
0
0
1
1
2
1
0
1
1
1
2
0
1
2
2
0
0
2
1
0
1
2
1
1
1
1
1
1
2
0
1
1
1
0
0
0
1
0
0
1
1
0
0
0
1
1
1
1
2
1
0
2
1
2
1
1
1
2
1
1
1
1
0
1
1
1
1
1
1
1
0
1
1
2
0
1
1
1
1
0
0
2
0
1
0
2
2
1
2
2
1
1
0
1
1
2
1
1
1
2
0
1
1
0
0
1
1
2
1
0
2
1
0
1
1
2
1
0
1
1
1
2
1
1
2
1
1
1
1
1
0
3
2
1
1
2
2
1
2
2
0
0
0
1
0
0
1
1
1
1
1
1
1
0
0
1
1
1
1
2
1
2
1
1
2
1
0
1
1
1
1
1
0
1
0
2
2
1
1
2
2
4
2
0
1
0
2
1
0
1
0
2
0
1
1
1
1
2
2
0
1
0
0
2
0
0
1
1
1
1
1
1
0
1
1
1
2
0
1
1
0
1
1
1
1
1
1
2
2
1
1
1
0
0
1
1
1
2
1
2
1
1
2
0
1
1
2
1
1
0
1
2
2
2
1
1
0
1
2
2
2
1
1
0
2
1
1
1
1
1
1
2
1
2
1
2
2
1
1
1
1
1
0
1
1
0
1
3
0
0
1
2
1
0
2
2
0
1
1
2
1
2
1
1
3
1
1
1
0
1
1
2
2
0
1
2
0
1
1
1
1
0
1
2
0
1
1
2
1
0
2
0
2
0
1
1
1
1
1
1
0
2
0
3
2
1
0
1
1
0
1
1
1
1
1
2
0
1
0
1
0
1
2
1
0
0
1
2
1
1
2
0
1
1
1
1
1
0
2
2
1
1
2
2
2
1
2
2
1
1
2
1
1
1
2
0
1
1
1
0
1
1
0
0
1
0
2
1
1
0
1
0
1
1
3
2
1
2
1
2
1
0
1
0
0
2
1
2
2
0
0
1
1
2
0
1
1
2
2
2
1
1
1
1
2
2
1
1
0
2
1
1
2
1
2
0
2
0
0
0
0
0
0
1
2
1
0
2
1
6
1
0
2
1
1
1
1
2
2
1
2
2
0
2
1
1
1
2
5
1
0
2
2
1
0
2
1
0
1
0
1
1
1
1
2
2
1
2
0
1
2
1
1
1
0
1
2
1
1
1
2
1
2
0
1
1
1
1
2
0
2
0
0
0
0
1
0
0
0
2
0
0
1
1
1
1
1
1
1
2
2
1
3
0
1
0
1
1
1
1
0
0
1
2
1
1
1
1
0
2
1
1
0
1
1
1
1
0
1
3
0
1
0
2
1
0
1
1
0
2
1
1
2
3
2
1
0
1
0
1
1
2
2
1
1
0
1
1
1
0
1
0
2
0
0
1
2
0
2
1
2
3
1
2
2
1
1
1
2
1
1
0
2
2
1
0
0
0
2
2
0
1
1
0
1
0
1
1
1
1
1
1
2
0
2
2
0
0
1
1
2
1
0
1
1
1
0
2
1
1
0
2
0
1
2
2
2
1
1
1
2
0
2
1
0
2
2
0
1
2
0
1
2
0
1
2
1
0
1
2
2
1
2
1
1
1
0
2
0
0
1
1
0
2
1
0
1
2
0
2
1
1
2
2
1
1
1
2
2
1
1
1
1
1
1
1
1
0
0
2
2
1
1
1
1
2
1
0
0
0
1
2
1
0
0
0
0
0
1
2
1
0
2
1
1
2
1
1
1
2
1
1
1
1
2
2
1
1
1
0
0
0
0
2
1
1
0
1
2
1
2
1
1
0
1
0
1
1
2
1
0
1
2
2
2
0
0
2
1
1
0
0
1
0
2
1
1
1
0
1
1
1
2
1
2
0
1
2
1
0
0
1
1
1
0
1
0
1
0
1
0
1
1
0
1
2
1
1
1
1
2
2
0
2
0
2
0
1
1
1
0
1
1
0
1
1
1
2
1
0
1
1
2
2
1
1
1
1
2
1
0
2
0
2
1
1
0
1
0
1
1
1
1
1
2
0
0
1
1
1
2
1
1
1
1
1
2
2
1
2
1
0
1
1
1
0
1
1
1
1
1
1
2
1
0
0
1
1
1
0
2
0
1
1
2
2
0
1
0
1
1
1
0
1
0
2
1
1
0
1
2
1
2
2
2
2
1
1
1
0
0
0
0
0
1
2
1
0
0
0
2
2
0
1
1
2
1
1
1
1
1
2
0
2
0
1
2
0
2
1
2
0
0
1
1
0
0
1
1
1
1
0
1
1
1
2
1
0
1
0
1
0
1
1
1
0
0
2
0
1
0
1
1
0
1
0
1
1
1
1
0
1
1
1
1
1
1
2
2
1
1
1
0
1
1
2
0
2
1
1
1
1
0
1
1
0
1
0
0
1
0
1
0
1
1
1
2
1
0
1
1
1
1
0
2
0
0
1
1
1
1
1
0
2
0
0
1
1
1
1
1
1
2
12
2
0
0
2
0
1
1
0
1
2
2
1
1
1
0
1
1
1
3
0
0
0
1
1
1
1
1
1
1
0
3
1
0
1
1
1
1
1
1
1
2
0
1
2
1
1
0
2
2
2
1
0
1
1
0
1
2
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
3
1
2
0
1
1
1
1
1
1
1
2
1
0
2
0
1
2
1
1
1
2
1
1
0
0
1
1
1
1
1
1
0
2
1
1
0
1
1
1
0
1
1
1
2
2
1
2
1
2
1
2
2
2
1
1
1
1
1
1
1
1
1
1
0
1
0
1
1
1
1
0
2
1
0
2
0
1
1
0
2
2
1
0
1
0
1
1
1
2
1
1
1
2
2
2
1
0
2
1
2
2
1
1
1
1
0
1
1
0
2
1
1
1
0
1
0
1
1
2
2
0
0
1
1
0
2
1
1
0
0
0
1
1
0
1
1
0
1
0
3
1
1
0
1
1
1
3
2
2
1
0
1
1
1
1
2
1
1
0
2
0
1
2
0
1
1
0
1
1
0
1
0
1
2
0
0
0
1
0
0
2
1
1
0
0
1
1
1
1
0
1
2
1
1
1
1
1
0
2
0
1
1
0
1
1
1
1
0
1
1
1
1
1
2
1
1
1
2
2
0
1
2
0
1
1
2
1
0
0
1
1
1
2
1
1
1
2
1
1
1
2
1
1
0
1
2
1
0
0
1
2
1
0
1
0
2
2
1
2
1
1
1
1
2
2
1
1
3
0
1
1
1
1
0
1
1
1
0
1
1
0
1
1
2
2
1
1
0
1
1
0
1
0
2
2
2
1
1
2
0
2
1
2
0
1
0
1
2
1
2
2
0
1
0
1
1
1
0
1
1
1
1
1
1
1
2
0
2
1
2
1
1
2
1
1
0
2
1
1
1
0
1
1
0
2
1
1
1
2
2
1
0
1
2
1
0
2
1
1
1
0
1
1
1
0
2
1
0
1
1
2
0
2
0
2
1
2
0
1
2
0
1
1
2
2
2
0
2
2
1
0
0
2
2
0
0
2
0
2
1
1
0
0
1
0
1
1
1
1
1
1
1
0
0
1
1
0
1
2
2
1
1
1
0
0
1
0
1
1
2
1
0
0
0
1
1
2
1
1
2
1
1
1
1
2
2
0
0
2
1
2
1
2
0
1
0
1
0
2
0
1
0
1
1
1
1
1
0
0
1
1
0
1
1
2
1
0
1
2
0
1
0
0
1
1
1
1
1
1
0
0
0
1
1
1
0
1
1
0
0
1
1
2
2
1
0
1
0
1
0
0
1
2
1
1
0
2
2
1
1
2
1
2
1
1
0
1
1
1
0
2
2
2
2
4
1
2
0
1
1
2
1
1
2
1
0
1
1
1
3
0
2
2
1
2
1
1
0
1
0
1
2
2
1
2
0
1
0
2
1
0
2
1
0
0
1
2
0
0
1
1
1
1
2
1
1
1
1
2
1
2
1
0
0
1
1
2
1
2
1
0
0
2
0
1
2
0
2
2
0
0
0
2
0
0
1
2
0
1
1
1
2
1
1
1
3
2
1
1
0
2
1
1
0
0
1
3
2
1
1
1
1
1
2
1
0
0
0
1
1
1
1
1
2
2
0
1
1
1
1
1
0
2
1
0
1
1
1
0
1
2
0
1
0
2
0
1
0
1
1
1
1
1
1
3
1
1
1
2
1
1
2
0
1
0
0
0
1
1
0
1
1
0
1
0
2
2
1
0
1
1
1
2
2
1
1
0
2
1
1
0
1
1
1
1
2
1
1
0
1
1
1
0
1
2
1
1
1
2
1
0
1
1
1
1
1
2
0
1
1
2
1
1
1
0
2
1
0
1
1
1
1
1
0
0
1
1
1
1
1
0
1
0
2
1
0
0
0
1
0
1
1
0
0
1
0
0
0
1
0
1
0
1
0
1
2
0
2
2
0
1
0
1
0
1
2
0
2
1
1
2
2
2
1
1
1
0
1
2
2
1
1
1
1
1
0
1
1
0
2
2
0
1
1
1
1
1
2
2
1
0
1
2
1
1
0
1
1
1
1
2
1
1
1
0
0
1
1
1
1
2
1
1
1
0
1
1
2
1
1
1
1
1
1
1
1
0
1
0
2
1
1
2
0
0
0
1
1
2
1
2
0
1
0
1
1
2
1
1
0
1
1
0
0
1
1
1
0
2
1
2
1
2
1
1
0
0
1
1
1
2
1
2
0
2
1
0
2
1
1
2
1
1
1
1
0
2
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
2
1
2
1
0
0
1
1
0
0
2
1
0
1
0
1
2
0
1
0
2
1
1
1
2
1
1
1
1
1
1
2
2
0
0
0
1
1
1
1
1
2
2
2
1
1
2
1
1
0
1
2
2
1
0
1
1
0
0
2
1
1
1
1
1
1
0
1
1
1
1
1
2
1
2
2
0
1
1
1
2
0
1
0
1
1
0
0
1
2
0
1
2
0
1
1
2
1
1
3
0
0
1
2
1
0
1
1
1
1
1
1
1
1
2
1
2
0
0
2
0
0
1
1
0
1
1
1
1
0
1
2
1
1
2
0
0
1
1
2
0
2
1
1
1
1
1
1
1
1
1
1
1
1
2
0
1
1
0
1
2
1
3
1
1
1
4
0
0
0
1
2
1
1
1
0
1
1
2
2
1
1
2
1
1
2
1
2
1
2
0
1
1
0
0
0
1
1
1
2
2
0
2
2
1
0
1
1
2
2
1
2
1
2
1
1
2
2
0
1
1
2
2
0
1
1
0
1
1
1
1
2
2
1
1
1
0
0
1
1
1
0
1
0
1
0
2
1
2
1
1
0
2
0
1
1
1
1
0
1
0
2
1
0
1
2
1
1
1
1
1
1
1
0
1
0
0
1
2
2
1
2
2
1
0
0
2
1
1
1
2
1
1
0
1
2
0
2
1
1
0
1
1
1
1
2
1
2
1
0
1
0
1
1
0
0
1
2
0
1
1
1
2
1
1
1
1
2
2
1
1
2
0
0
1
0
1
1
2
0
3
1
0
1
1
1
1
1
0
1
2
1
0
2
4
1
1
0
1
0
0
1
2
2
1
1
2
0
2
0
1
0
2
2
0
1
1
0
1
1
1
1
1
0
1
1
2
0
0
1
1
0
2
1
2
1
1
2
1
2
1
0
1
2
1
1
1
1
0
3
1
1
1
2
1
2
2
3
1
1
1
0
0
2
0
1
1
0
0
2
1
0
0
1
2
1
2
0
1
2
1
2
2
2
1
0
1
0
1
0
2
2
1
1
0
0
1
1
1
1
1
0
2
1
1
1
0
1
2
2
2
1
1
0
0
0
1
3
1
1
2
1
0
1
1
0
1
0
0
1
1
2
1
0
2
1
2
1
2
1
1
2
1
1
1
2
1
0
0
1
2
1
1
1
2
2
1
2
1
1
1
1
1
0
2
1
1
1
1
1
1
0
1
0
2
1
0
0
1
2
0
2
0
1
0
1
1
0
3
0
2
1
1
1
0
2
1
1
0
1
2
0
1
2
1
0
0
1
0
1
1
0
0
1
2
0
1
0
1
0
2
1
2
1
1
1
1
0
1
1
0
2
0
1
2
2
1
0
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
0
1
2
0
1
2
1
1
0
1
1
0
1
1
1
1
1
1
2
0
1
2
1
2
1
1
0
1
2
1
1
1
2
1
2
0
2
1
1
1
0
1
1
1
1
2
2
2
0
2
0
0
2
2
2
1
0
1
2
1
1
0
2
0
0
1
1
1
0
1
1
1
1
2
1
0
1
1
1
2
2
0
1
0
1
1
1
1
0
0
0
2
1
1
1
1
0
2
1
1
0
2
1
2
1
1
0
1
2
0
2
1
1
0
0
1
1
1
0
0
2
0
1
1
1
1
1
1
1
0
0
0
2
0
1
0
1
1
0
2
0
2
0
2
1
1
1
1
2
0
0
1
0
1
1
1
2
1
1
1
0
0
1
1
2
0
2
1
1
1
1
2
1
0
2
1
2
1
1
1
1
2
0
2
0
1
0
0
1
2
1
0
2
1
1
1
1
0
2
2
1
1
1
1
1
2
2
3
2
1
2
1
1
1
0
2
1
1
2
2
1
0
0
0
1
1
1
1
1
1
2
0
1
2
1
0
1
1
2
1
0
1
2
2
1
0
1
0
1
1
2
2
2
1
1
0
2
1
1
0
3
2
1
2
2
1
1
1
0
1
1
1
3
1
1
0
2
0
0
0
1
2
0
2
0
2
1
1
0
0
2
0
2
1
1
2
1
0
0
1
0
1
1
0
2
1
0
1
1
1
0
1
1
0
1
2
0
1
2
0
1
0
2
1
0
2
1
1
1
1
1
1
1
0
1
2
0
0
0
0
1
1
2
1
1
0
1
0
2
1
1
1
1
1
2
2
2
1
1
1
2
1
2
1
1
2
1
2
1
0
2
1
1
2
0
0
0
1
0
1
1
1
1
0
2
5
2
2
2
0
0
0
0
1
1
2
1
2
0
2
1
1
0
1
1
2
0
1
2
2
0
2
0
0
1
1
0
0
2
1
1
1
0
0
1
1
1
1
1
1
1
1
1
1
1
1
0
2
2
1
1
2
2
1
1
2
0
0
1
0
0
0
1
0
0
2
0
1
1
0
2
1
1
0
2
0
2
1
1
1
2
2
1
0
0
1
0
0
0
1
1
1
1
0
0
2
1
1
2
1
1
1
0
1
2
1
2
1
1
1
1
2
0
1
1
1
1
0
1
1
1
2
1
0
2
1
2
0
0
1
2
0
1
3
2
1
1
1
1
3
0
0
0
1
2
0
1
0
0
1
1
2
2
1
2
0
1
1
0
2
0
1
2
2
1
0
0
0
1
2
1
1
1
0
1
2
1
2
0
1
1
1
1
1
1
0
2
1
0
2
1
2
0
2
1
1
0
1
1
0
1
1
1
2
1
1
1
1
1
0
1
2
1
3
1
1
2
1
1
0
1
1
2
0
0
2
1
1
1
0
2
0
1
1
0
1
7
1
1
1
1
1
2
1
2
1
0
0
0
1
0
1
1
1
1
0
3
1
0
0
0
2
2
0
2
2
2
1
1
1
1
1
1
1
1
0
1
0
1
1
1
2
2
1
1
1
0
0
1
0
2
2
1
1
1
2
1
0
1
1
0
2
0
1
2
2
1
3
1
1
0
1
1
1
1
0
1
1
1
2
1
0
2
1
2
1
1
2
1
1
0
0
2
1
1
1
1
0
0
2
1
1
2
1
1
1
1
1
1
0
2
0
2
2
1
0
2
1
0
1
2
1
2
2
2
1
1
1
1
1
1
1
1
0
1
2
0
1
1
1
1
2
0
1
1
0
0
1
1
2
1
2
1
0
0
1
2
1
2
3
2
2
1
2
1
1
1
2
2
1
1
2
1
2
0
2
1
1
1
0
1
1
1
1
1
1
1
2
2
2
1
1
2
0
0
5
0
1
2
2
1
0
2
2
1
1
0
2
2
2
1
1
1
1
2
1
1
2
1
2
3
0
2
1
2
0
1
0
0
1
1
0
2
1
2
2
1
0
1
1
2
0
1
0
1
1
0
0
1
1
0
0
1
0
1
1
1
3
1
1
0
0
0
1
1
1
1
0
1
2
1
1
2
1
2
1
2
2
2
1
1
2
0
1
1
1
0
2
0
1
1
1
0
1
1
1
1
2
1
1
2
1
1
1
2
2
0
1
2
1
1
1
2
1
1
1
1
0
0
2
2
0
1
2
1
1
0
2
1
1
2
0
1
1
1
1
2
1
2
0
0
0
2
1
1
1
2
1
2
1
1
1
1
2
2
1
1
1
0
1
2
1
1
1
1
2
2
0
1
0
0
2
1
0
2
2
2
0
2
2
2
1
1
0
1
0
1
1
1
2
0
1
1
2
1
0
1
0
1
2
2
1
1
2
1
2
2
1
2
1
1
1
0
1
0
2
0
2
1
1
1
2
1
1
1
2
1
1
1
2
1
1
0
2
1
2
0
1
1
2
2
1
0
1
0
1
1
1
2
2
2
1
0
2
1
2
1
1
1
1
0
2
1
2
1
2
2
2
2
1
0
2
2
1
1
6
2
0
2
1
0
1
0
2
0
1
0
1
1
1
0
1
1
1
2
2
1
2
2
1
1
0
1
1
0
2
1
0
2
0
0
1
1
0
1
2
0
2
1
2
3
2
2
1
1
2
0
2
1
1
0
2
1
1
1
1
0
1
1
1
1
0
1
1
0
1
1
0
2
2
0
1
0
2
1
1
2
1
1
1
1
0
1
0
1
1
1
1
1
0
1
1
1
0
1
2
0
0
1
0
0
1
2
1
1
0
0
2
0
0
1
1
1
1
0
1
2
1
2
1
2
0
2
0
1
1
1
2
1
1
1
0
2
2
1
1
1
2
0
1
1
1
1
1
0
2
1
1
1
0
1
1
1
0
2
1
2
1
1
0
2
2
2
2
2
2
2
0
1
1
1
2
1
1
2
0
0
1
0
0
1
2
1
1
1
1
2
0
1
1
1
2
1
2
1
2
2
1
2
1
1
1
1
1
0
2
2
2
1
3
2
1
0
2
1
1
1
0
1
0
1
0
1
2
1
2
0
2
1
1
1
2
0
1
2
0
1
1
0
0
1
0
0
2
1
2
1
1
1
4
2
1
1
1
1
1
1
2
1
0
1
1
1
1
1
1
1
1
1
2
1
1
0
2
0
1
2
0
0
1
1
1
2
2
0
1
1
2
2
1
2
0
1
2
2
1
1
3
1
1
1
2
1
2
1
1
1
0
0
1
0
1
1
1
1
1
1
0
0
1
2
1
2
1
2
1
0
1
1
1
1
0
2
0
0
1
0
1
1
1
0
1
1
1
1
1
1
0
1
1
1
1
1
1
1
0
0
2
1
1
1
0
2
2
0
1
0
1
1
0
0
2
1
2
1
1
1
1
0
2
1
0
1
1
2
0
2
1
1
1
1
1
0
1
1
2
0
4
2
1
0
2
1
2
1
0
2
1
1
0
2
2
1
0
2
0
1
2
0
1
1
3
2
0
1
1
1
1
1
1
1
1
1
2
0
2
0
1
0
2
1
2
2
1
2
1
0
0
2
0
2
1
0
0
2
1
1
0
1
1
1
3
1
1
1
2
1
0
1
1
1
1
0
2
1
2
1
1
1
2
2
1
2
2
0
1
0
1
1
1
2
1
0
1
2
1
0
0
0
1
0
0
1
0
0
1
2
1
1
0
1
2
2
0
0
1
0
2
0
1
1
1
1
1
1
1
2
2
0
2
0
1
1
2
1
2
1
0
1
1
2
2
1
1
2
0
1
1
1
1
1
0
1
0
0
0
1
1
0
1
0
1
1
2
1
1
1
1
0
1
3
0
1
2
2
2
1
2
2
1
1
2
1
1
1
0
1
2
2
2
0
1
1
1
1
3
1
1
1
1
1
1
2
2
0
0
0
1
1
1
2
0
2
1
1
1
0
0
0
0
0
0
2
1
2
1
1
3
1
1
0
0
2
1
1
1
2
0
1
1
1
1
1
1
0
1
2
1
1
1
0
0
0
1
0
0
1
1
0
2
2
1
0
1
4
2
1
1
2
0
1
1
2
1
2
1
1
1
1
1
1
1
0
1
1
0
1
1
2
0
0
1
0
1
1
0
1
3
1
2
2
0
0
2
1
4
1
1
0
1
1
2
2
2
1
0
0
1
1
1
0
0
1
1
1
1
1
2
2
2
1
1
1
1
1
1
0
1
1
1
1
1
2
1
1
1
1
0
1
1
1
2
1
2
1
2
0
0
0
1
0
2
1
1
2
1
2
0
1
1
2
0
2
3
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
2
1
2
2
1
2
2
1
2
1
0
2
2
2
1
0
1
1
1
1
1
1
1
0
1
1
0
1
2
0
2
0
1
1
0
1
1
2
0
2
1
0
1
0
1
1
1
1
0
1
1
0
1
2
2
0
1
2
1
1
2
2
2
1
2
1
1
0
1
1
1
0
1
1
1
1
0
1
0
1
0
1
2
0
0
1
1
0
0
1
1
0
2
2
1
0
1
2
1
0
1
1
1
2
1
1
2
1
1
1
2
2
0
1
1
1
1
0
0
2
0
1
1
2
0
2
1
1
1
1
1
2
1
2
1
2
1
0
0
2
0
1
1
1
1
0
0
0
2
1
0
1
1
1
0
2
1
1
1
1
0
1
0
3
1
1
2
2
1
1
1
1
2
1
0
0
2
1
1
1
2
2
2
1
1
2
1
0
2
1
1
1
0
1
0
1
2
1
2
1
3
2
2
0
0
2
1
1
1
1
2
1
1
2
1
0
1
1
1
1
2
0
1
1
1
1
1
1
2
1
0
6
0
1
1
1
1
3
0
1
1
1
0
1
2
0
1
1
2
1
0
1
1
1
0
1
1
2
1
0
1
1
0
1
1
1
2
3
2
0
0
1
1
0
0
1
4
1
1
1
1
2
1
1
2
1
2
2
1
1
2
1
1
0
0
1
1
1
1
1
2
0
1
1
1
1
1
2
2
0
1
2
2
2
0
1
2
0
0
0
0
1
1
1
3
3
0
0
2
2
2
1
1
1
0
1
2
1
2
2
1
1
2
1
2
1
1
0
0
1
1
2
2
0
1
0
0
2
1
1
1
1
0
1
1
0
0
2
0
1
1
2
0
2
2
2
0
1
3
1
1
1
1
1
1
1
1
2
2
1
1
2
3
1
0
1
2
1
1
1
1
1
1
1
1
2
2
2
1
1
2
1
1
0
1
1
0
1
0
1
0
1
1
2
1
2
2
0
0
1
0
2
1
2
1
2
2
2
0
2
2
0
1
1
0
2
1
1
2
2
1
0
0
2
0
2
0
1
1
0
1
0
2
1
1
2
0
1
0
1
1
1
2
1
2
0
1
1
2
1
0
0
2
1
2
1
0
2
1
2
1
1
1
1
1
1
1
0
2
1
1
1
0
1
0
1
1
1
3
1
1
0
1
0
1
0
2
1
2
0
2
1
1
2
2
1
0
1
1
1
2
1
1
1
1
0
1
1
0
1
1
0
0
1
1
1
1
2
1
0
1
0
1
1
1
0
1
2
0
1
1
1
2
1
2
1
1
1
2
1
0
0
1
1
0
0
1
2
1
1
1
1
0
1
1
1
1
2
1
1
1
1
1
0
0
0
1
0
0
1
0
1
1
2
1
1
1
1
0
0
1
2
2
1
0
2
1
2
1
1
2
1
1
1
0
1
3
1
1
0
0
1
1
1
1
2
1
0
1
0
1
1
1
1
1
1
0
2
1
0
3
1
2
1
1
0
0
1
1
1
2
2
1
1
0
1
1
1
2
1
0
1
0
1
0
0
0
2
0
0
1
2
1
1
1
1
0
1
1
0
1
1
0
0
1
1
2
2
1
1
2
1
2
2
2
2
1
1
1
1
1
0
1
1
1
0
1
1
1
2
2
2
0
1
1
1
2
2
0
1
2
0
0
1
1
2
0
2
1
0
1
1
0
2
0
2
2
1
1
2
1
1
0
1
2
2
2
2
0
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
2
2
1
2
1
1
1
2
1
2
2
1
0
1
2
2
1
0
0
3
1
3
2
1
1
1
2
2
0
0
1
2
1
1
1
1
1
0
1
0
1
1
2
0
1
0
2
1
1
0
1
0
0
1
2
0
1
2
1
1
1
2
0
1
2
0
1
1
1
1
0
1
0
0
2
1
1
1
0
0
1
1
1
1
1
0
1
1
1
1
1
0
0
1
0
2
1
1
0
1
2
0
1
1
1
3
0
1
2
1
1
3
0
2
2
1
0
1
1
2
1
0
1
0
2
3
1
1
1
2
1
1
2
2
2
1
0
2
0
0
2
1
0
1
0
2
1
1
1
1
2
1
0
1
0
0
1
0
1
2
2
1
1
1
1
2
2
2
0
1
2
1
0
1
1
1
2
1
1
2
0
2
1
1
1
1
4
1
2
2
0
1
1
1
1
1
2
1
1
1
0
1
2
1
1
1
1
2
1
1
0
0
1
0
1
1
0
2
2
0
1
1
1
0
2
2
1
2
1
1
1
1
2
1
1
2
0
0
1
0
0
1
1
1
0
2
2
1
2
2
1
1
1
1
0
1
1
1
1
2
0
2
1
1
1
1
0
1
1
1
0
2
0
2
1
2
1
0
2
0
1
2
1
1
1
2
2
1
1
1
0
2
0
0
0
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
2
1
2
0
1
2
2
1
1
1
2
0
2
0
1
1
1
1
1
0
0
1
3
0
1
1
1
1
2
0
2
1
0
1
1
0
1
2
1
1
1
1
0
1
1
1
1
1
1
1
1
2
1
1
2
2
1
1
2
2
0
1
1
0
0
1
1
1
2
2
1
1
3
0
1
1
1
0
1
1
1
1
1
1
2
1
0
1
0
0
0
1
0
2
1
1
1
1
2
0
0
1
1
2
1
0
1
2
0
0
1
1
0
1
0
0
0
1
2
2
0
1
1
1
3
1
1
1
1
1
0
1
0
1
1
1
2
1
1
1
0
1
0
0
1
3
1
1
1
1
1
0
0
1
0
2
1
1
1
1
2
2
1
1
2
1
2
2
1
1
0
1
1
2
1
0
2
0
1
0
0
1
2
1
1
1
2
1
1
0
1
1
2
1
2
1
2
2
1
2
1
0
1
0
1
0
0
1
0
1
1
2
1
0
1
0
1
1
1
0
2
1
1
2
1
2
2
1
1
1
1
1
0
1
1
2
1
1
1
1
0
1
1
1
2
1
3
2
1
0
0
1
2
1
0
1
1
1
1
1
1
2
2
1
1
0
0
0
1
1
1
1
1
1
0
1
0
1
2
0
1
2
0
1
2
0
1
1
0
1
2
2
1
0
1
1
0
1
2
0
2
0
0
0
1
0
2
1
1
1
2
2
1
0
1
0
1
0
0
1
1
0
0
2
1
1
1
1
1
0
1
1
1
2
0
1
1
0
0
0
0
2
1
2
1
1
1
1
3
1
2
1
0
2
3
0
1
1
0
1
1
0
1
2
1
1
1
1
1
1
1
0
0
1
10
0
0
2
0
1
1
1
1
2
1
2
2
2
1
0
2
0
2
0
2
1
2
1
2
2
0
1
1
1
1
1
1
1
1
0
1
1
0
3
0
0
2
1
2
1
2
1
2
1
2
0
0
2
1
0
0
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
0
0
1
1
0
2
1
0
1
0
1
0
1
1
0
0
1
0
0
1
5
2
1
1
0
1
1
1
0
1
1
2
1
1
1
2
1
0
0
1
1
1
1
1
1
2
3
1
2
1
1
2
0
1
2
1
1
2
1
1
2
1
2
1
0
1
1
1
2
1
1
2
1
1
0
1
1
2
2
0
1
1
0
1
0
0
1
1
1
1
1
0
0
2
1
0
1
0
2
1
0
1
1
1
2
0
1
0
1
1
1
2
1
1
0
1
1
2
1
0
0
1
1
1
2
1
1
1
2
2
1
2
2
2
1
0
1
1
1
2
1
0
4
2
2
0
2
1
0
0
2
2
2
1
1
1
1
1
2
1
1
1
2
0
1
2
1
2
1
1
1
1
1
2
2
2
1
2
2
2
0
1
1
1
1
0
2
2
1
0
1
1
1
1
2
1
0
0
1
0
1
1
0
2
2
1
0
1
0
1
1
0
2
1
1
1
1
1
1
0
0
1
0
1
1
2
2
1
0
1
0
2
2
1
1
2
0
0
0
0
1
1
1
1
1
1
2
0
2
0
0
0
1
2
2
1
0
1
1
1
0
2
2
1
1
1
1
1
1
1
2
0
1
2
1
3
1
1
2
3
1
1
2
0
1
1
1
0
0
2
1
1
1
1
0
2
0
2
0
2
0
0
0
1
1
0
0
1
2
1
0
2
1
0
1
1
1
0
1
2
2
0
0
0
1
2
1
2
2
1
1
1
0
0
2
2
2
1
0
1
1
1
0
1
0
0
1
0
0
1
1
1
1
2
1
2
0
1
1
0
0
1
1
2
2
1
1
0
2
1
1
1
0
1
0
1
1
0
1
1
2
2
1
0
1
1
2
0
2
1
0
1
2
1
1
0
2
1
1
1
1
0
1
2
1
2
1
1
0
2
0
1
0
1
2
0
1
1
1
0
1
1
0
0
2
1
0
2
2
1
1
1
1
1
2
1
1
1
1
1
1
3
1
1
0
0
0
1
1
1
1
1
2
0
1
2
1
1
2
1
1
2
1
0
1
1
1
2
1
1
1
1
2
0
0
0
1
1
1
2
1
1
2
1
0
1
1
1
1
1
1
1
2
1
1
0
1
1
2
1
0
1
0
1
0
1
0
2
1
1
1
1
2
1
2
1
1
1
0
1
2
0
2
2
1
1
1
1
2
0
2
0
0
1
1
2
1
0
1
0
0
2
1
1
1
0
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
2
2
1
1
1
1
1
0
1
1
2
2
2
0
1
1
1
0
0
2
0
2
1
2
2
2
2
1
1
1
1
1
1
0
1
1
1
2
1
1
1
1
1
1
0
4
1
1
2
1
1
1
0
0
1
0
2
1
1
2
1
0
0
1
1
1
0
1
1
0
1
1
0
1
1
0
2
1
1
1
1
1
1
1
1
1
2
0
1
1
1
1
3
1
1
4
1
0
1
0
2
1
0
2
2
2
1
0
0
1
3
1
1
1
1
1
1
1
0
2
1
1
1
0
0
0
0
1
2
1
1
1
2
1
1
0
2
2
4
1
2
0
2
1
2
2
1
2
2
2
1
2
1
0
1
1
1
1
1
1
0
0
1
0
0
0
1
2
2
1
1
1
1
1
1
1
1
0
2
1
1
2
4
5
1
2
0
2
0
1
1
0
2
1
1
1
1
2
0
1
2
2
1
2
1
1
1
0
2
0
0
1
1
0
1
1
1
0
2
0
2
1
1
0
2
1
1
0
1
0
0
3
1
1
1
1
1
0
0
1
0
1
1
0
0
0
2
1
1
2
1
1
2
1
1
1
0
0
1
1
2
0
1
1
1
1
1
2
1
1
2
1
0
1
1
1
1
1
1
0
1
0
0
2
1
1
1
1
1
0
1
1
2
0
1
1
1
2
2
0
0
2
2
1
0
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
2
0
1
1
1
1
2
1
1
1
1
1
0
0
1
2
1
0
1
2
1
1
2
1
2
1
0
2
0
1
1
1
1
1
2
0
1
2
0
2
1
1
1
0
2
1
2
1
1
0
2
1
2
1
1
0
1
2
1
1
2
0
1
2
0
1
1
1
1
1
1
2
0
0
2
1
2
1
0
1
2
0
1
1
1
1
2
1
1
1
1
1
1
1
1
0
1
1
2
1
0
0
1
2
0
2
1
0
1
1
2
2
2
0
1
1
1
2
1
2
0
1
1
2
1
2
1
1
1
1
1
1
1
0
2
1
1
2
1
1
1
1
1
1
1
1
1
1
0
0
0
0
1
0
2
2
1
0
1
0
1
2
0
1
1
1
0
1
0
2
1
1
1
0
2
2
2
2
0
0
1
2
1
1
2
2
1
2
2
1
0
2
2
1
1
1
1
1
1
1
1
2
0
2
1
1
1
1
2
0
1
2
0
1
0
1
2
0
1
1
2
1
1
1
2
2
0
1
1
0
0
1
1
1
2
1
1
1
1
2
0
1
2
2
1
0
2
2
1
1
1
1
1
1
1
0
1
1
1
0
1
1
0
1
1
2
0
0
2
1
1
2
2
1
0
0
1
2
1
1
2
1
0
0
1
2
1
0
1
1
0
1
0
2
1
1
0
0
2
2
0
2
1
0
1
1
2
1
0
1
0
1
2
2
1
1
0
0
2
1
0
1
1
2
0
2
1
1
1
2
2
0
0
0
2
1
1
0
1
2
0
1
0
2
0
1
2
2
1
1
1
0
0
1
1
1
2
1
1
0
0
2
1
1
0
1
2
2
1
1
1
0
1
1
3
1
1
0
2
0
2
1
2
2
0
2
0
1
2
0
2
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
0
1
2
1
1
1
1
0
1
2
1
0
1
0
1
0
1
0
0
1
1
2
1
1
3
0
0
2
1
0
0
0
1
1
2
1
1
1
0
2
2
1
0
2
1
1
0
0
0
1
2
0
1
1
1
0
1
1
2
0
0
1
3
0
1
1
1
1
0
1
2
1
0
1
0
1
1
4
0
1
1
0
1
2
2
1
1
0
2
0
2
0
2
2
0
2
0
1
1
1
1
0
0
1
3
3
2
1
2
0
1
1
1
1
1
2
0
1
1
1
1
2
2
1
2
1
1
1
1
2
1
2
1
1
1
1
0
1
1
1
2
1
1
2
1
2
0
1
1
1
2
1
1
2
1
1
2
1
1
1
2
2
0
1
0
0
1
2
1
1
2
2
0
1
0
1
2
0
1
1
2
1
0
1
2
1
1
2
2
1
1
1
1
2
2
4
1
1
1
1
0
2
1
1
1
1
1
0
1
0
1
1
1
0
0
2
1
1
0
0
1
1
1
1
0
1
2
2
1
1
1
1
0
0
1
0
1
1
1
2
1
2
0
1
2
1
1
2
1
0
0
1
1
1
3
1
1
0
2
0
1
1
2
1
1
1
1
1
1
1
2
3
1
1
2
0
2
0
1
1
0
1
1
0
2
1
0
1
1
2
1
1
1
1
2
1
0
2
2
1
0
0
0
0
1
1
0
1
0
1
0
0
1
0
1
1
0
1
2
2
1
0
1
2
1
1
3
0
0
1
1
0
1
2
1
1
1
1
0
1
2
1
1
1
1
2
1
0
2
0
0
1
1
2
0
1
0
2
1
1
1
2
1
0
1
1
1
0
2
1
0
0
0
3
0
2
2
0
2
1
0
2
0
1
1
1
2
0
1
1
2
0
1
1
2
0
0
1
0
1
1
2
2
2
1
1
1
1
1
2
1
0
0
0
2
0
1
1
1
0
2
1
1
1
1
1
2
1
2
2
1
2
0
0
1
0
1
1
1
1
1
1
1
2
1
1
1
1
1
1
0
2
1
1
1
1
1
1
2
0
2
1
2
0
1
2
2
1
0
0
0
1
1
1
1
2
1
0
1
0
1
2
0
0
1
1
3
1
2
1
2
1
1
0
0
2
1
0
2
1
2
0
0
0
0
2
1
1
2
2
1
2
0
1
1
1
2
1
1
1
1
1
1
1
0
0
2
0
1
1
0
1
2
0
2
1
0
1
1
0
3
1
1
0
0
1
1
2
1
0
1
1
1
0
2
2
1
1
2
1
0
1
2
2
0
1
1
0
1
1
1
0
1
1
2
1
1
2
1
1
1
1
1
0
0
2
2
1
0
0
1
2
1
1
1
1
0
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
0
0
2
0
0
1
2
1
1
2
1
1
1
0
0
0
2
1
1
1
1
2
0
1
0
1
0
0
1
0
0
1
2
0
1
0
2
2
1
1
1
2
0
0
1
1
2
0
1
0
0
1
0
1
1
0
0
1
2
1
1
1
0
2
1
0
1
2
2
1
1
1
1
0
0
0
2
0
0
1
1
2
1
1
2
0
1
1
1
1
1
0
2
2
1
0
2
0
0
2
1
1
0
1
1
1
0
0
0
0
1
1
1
1
2
0
1
1
1
2
1
1
1
2
1
0
1
0
1
1
1
0
2
1
2
2
1
0
0
1
2
1
1
1
3
1
2
1
1
1
1
1
1
1
2
0
0
1
1
1
1
1
1
1
2
0
0
0
0
1
0
1
1
1
0
1
1
1
2
0
2
2
1
1
1
2
2
0
1
1
2
0
0
2
1
1
1
1
1
2
1
1
2
1
0
1
0
1
1
1
1
1
2
1
2
1
0
1
0
0
1
1
2
1
2
0
2
1
1
1
1
1
1
2
0
1
1
2
0
2
2
0
0
0
1
1
2
1
2
1
1
2
1
0
1
0
0
0
1
2
1
1
2
1
1
0
1
1
1
0
1
1
1
2
1
1
1
0
1
0
1
2
1
0
0
1
2
2
3
0
1
0
2
0
1
1
1
1
0
2
0
1
1
1
0
0
2
1
1
1
1
0
1
2
0
2
1
1
0
1
1
1
2
1
1
2
1
2
3
1
1
0
1
1
1
2
2
1
0
1
2
1
1
1
1
1
1
1
1
0
1
1
1
2
1
1
1
1
1
2
1
0
1
2
1
2
2
1
1
0
2
1
2
2
2
1
1
1
0
0
2
1
2
0
1
1
2
0
1
1
0
0
6
2
1
2
1
1
2
1
1
1
1
0
0
1
1
1
1
2
1
1
0
0
2
1
0
0
1
2
0
0
1
1
0
0
0
1
1
0
1
0
0
1
2
0
2
2
0
1
1
2
0
2
2
1
0
2
2
1
1
2
1
0
0
2
1
1
1
0
1
1
1
0
1
1
2
1
2
1
1
1
0
1
0
2
1
1
0
1
1
1
3
1
1
1
2
2
0
1
1
1
2
0
1
1
1
2
0
2
1
2
1
1
1
1
1
0
1
2
3
0
1
1
1
1
1
1
2
2
1
1
2
0
1
1
0
1
0
1
0
2
0
1
0
1
3
1
1
1
0
1
0
1
1
2
1
1
1
0
0
0
2
1
1
1
0
0
0
1
2
1
0
1
0
2
1
1
1
1
3
0
1
1
1
0
1
0
1
2
0
0
1
1
0
1
2
0
2
1
2
2
1
1
0
1
0
1
2
0
1
1
1
1
1
1
2
0
2
0
1
1
1
0
0
2
2
1
0
1
1
1
1
1
0
2
0
0
0
2
0
0
1
1
1
2
2
1
1
1
2
1
1
1
2
2
2
1
0
1
1
1
2
1
2
0
2
1
2
2
1
1
3
0
1
1
0
2
0
1
2
2
1
2
2
1
1
2
1
1
1
1
0
2
0
1
4
2
1
0
2
1
0
0
2
2
2
1
1
1
1
1
1
0
1
1
1
0
2
2
1
2
1
0
1
1
0
1
2
1
0
1
2
0
1
0
1
1
1
1
2
2
1
2
0
1
2
0
0
1
1
1
0
1
1
2
2
1
1
0
2
0
0
0
1
0
1
0
1
2
1
2
1
0
1
2
1
1
1
0
0
1
1
1
0
1
2
0
1
1
1
2
1
1
1
2
1
1
0
1
0
1
0
2
2
0
2
1
2
2
1
2
1
0
1
1
1
1
2
1
1
1
2
1
0
2
1
1
1
1
1
1
1
1
1
2
1
1
1
0
1
1
1
1
0
1
0
2
1
1
2
1
0
0
1
0
2
1
1
1
2
0
1
0
2
1
1
1
1
0
0
1
0
2
1
2
1
1
1
1
2
0
0
0
0
1
0
1
1
1
0
3
2
1
1
1
1
0
1
0
0
2
0
1
1
2
2
2
2
0
1
2
2
0
2
2
1
0
2
1
1
2
0
2
4
1
2
1
1
1
1
1
1
0
1
0
1
0
1
0
1
0
1
1
1
2
0
1
1
2
1
0
2
0
0
1
0
0
1
1
1
2
1
1
1
1
1
1
2
2
1
1
2
1
2
0
1
1
1
1
1
1
1
1
0
2
1
1
2
1
2
1
1
2
1
1
1
1
1
2
1
2
2
1
0
1
0
1
1
1
0
1
1
1
0
1
0
1
1
1
2
2
0
0
0
0
0
0
3
1
1
0
1
2
2
0
2
1
1
1
2
2
2
1
1
1
1
1
1
0
0
2
1
1
1
1
1
0
1
1
1
1
1
0
1
1
1
2
1
1
2
3
1
2
2
1
2
1
3
0
1
1
2
1
1
1
2
1
1
1
2
2
2
1
1
1
0
1
2
1
0
1
2
1
2
1
2
1
2
1
1
0
0
1
0
3
1
1
0
1
2
0
2
2
1
0
2
0
2
2
2
1
1
2
0
1
2
0
1
1
0
0
1
1
2
2
1
0
1
1
2
1
2
0
1
1
1
0
3
1
1
2
2
2
1
0
1
0
1
1
0
1
0
2
2
1
2
0
0
1
2
1
1
0
1
0
1
2
0
1
2
2
0
0
0
0
2
0
1
2
2
1
2
2
2
1
0
1
2
2
1
0
2
1
0
2
1
0
1
2
0
1
1
2
0
1
1
1
2
1
1
1
0
2
1
0
1
2
1
1
2
1
0
1
2
1
0
0
1
0
1
1
1
1
0
1
1
0
0
2
0
0
2
1
1
1
1
1
2
2
2
2
0
2
1
1
1
0
1
1
0
0
1
1
1
2
1
1
0
1
1
1
1
1
2
0
1
1
2
2
1
1
1
0
1
2
1
0
2
1
2
0
1
1
0
1
0
2
2
2
2
2
1
1
1
2
1
1
2
0
1
2
1
1
0
1
1
1
2
2
1
1
1
1
1
1
0
2
2
2
1
1
0
1
1
2
1
0
1
1
1
0
1
0
0
2
1
1
2
0
3
1
2
1
2
2
1
1
0
0
1
2
1
1
0
1
1
1
2
1
2
0
1
2
1
0
0
1
1
1
1
0
3
1
1
0
1
1
2
0
1
1
0
1
1
2
0
0
1
0
0
1
0
1
0
2
0
1
1
2
0
1
1
1
0
0
2
2
2
1
1
0
1
0
1
2
1
1
1
1
2
2
2
2
1
1
2
1
0
2
1
1
1
2
0
1
1
2
2
1
1
1
1
0
0
2
2
2
2
1
1
1
2
1
1
2
1
2
2
1
1
2
2
0
2
0
1
2
1
1
0
1
1
0
1
1
0
1
0
2
2
0
1
1
1
0
1
1
0
1
2
1
1
2
0
1
1
2
2
5
0
0
2
2
2
1
0
0
1
1
1
1
0
1
1
1
1
1
2
1
2
1
2
1
2
1
1
0
1
2
0
0
0
0
1
2
1
1
1
1
2
2
2
2
0
1
1
1
1
1
1
0
0
1
2
1
2
2
1
0
1
1
2
1
1
0
1
1
2
0
1
2
1
2
0
1
0
1
2
1
2
1
1
0
1
1
2
0
0
1
1
0
1
1
1
1
1
0
1
0
1
1
2
1
1
1
0
1
2
0
1
2
1
1
0
1
1
0
0
1
1
0
0
2
2
2
1
0
1
2
1
2
0
1
2
2
1
1
1
2
1
0
1
1
1
1
0
2
0
1
1
1
1
1
2
2
2
1
1
1
0
0
0
1
0
1
1
0
1
1
1
1
1
0
1
1
0
1
1
1
2
2
0
0
2
1
1
0
1
1
2
1
0
1
1
1
1
1
2
1
1
0
1
0
3
0
0
1
2
1
2
0
1
0
2
0
0
2
2
2
2
0
0
2
0
2
2
2
2
2
2
1
0
1
2
1
0
0
1
2
2
0
0
2
1
1
1
0
1
0
0
2
2
2
2
0
1
0
1
1
1
1
2
1
1
1
3
0
2
1
2
2
2
1
1
2
1
1
1
0
2
2
0
1
2
1
1
1
1
1
1
0
2
2
1
1
1
1
1
1
1
1
1
1
0
0
1
2
1
0
2
2
1
1
1
2
2
2
1
1
0
2
1
1
0
0
2
1
1
1
1
1
1
1
1
0
1
0
2
1
0
1
2
2
2
1
0
2
2
0
1
1
2
0
0
1
2
2
1
0
2
1
1
1
2
1
2
2
1
1
2
2
1
0
1
1
2
1
1
1
1
1
1
2
1
1
0
0
1
0
1
1
1
2
2
1
2
1
1
1
0
1
1
2
0
1
1
1
1
1
2
1
2
1
1
1
1
1
0
1
2
0
2
2
1
2
1
1
1
0
1
0
1
1
1
1
1
0
0
1
0
0
1
0
0
2
1
1
1
1
1
1
2
0
0
1
0
1
0
1
2
0
0
1
0
1
2
0
1
0
1
1
1
1
1
2
0
1
0
1
0
0
1
1
0
1
1
0
2
1
0
0
1
1
3
1
1
1
1
1
0
0
1
1
0
0
1
1
1
1
2
1
1
1
1
1
0
0
1
0
2
1
1
2
1
1
0
1
2
0
0
0
2
1
0
1
1
0
1
0
1
1
2
1
1
3
0
2
0
2
1
1
0
1
1
0
1
1
1
1
1
1
2
0
1
1
2
0
1
1
1
2
1
1
0
2
1
1
2
2
0
1
1
3
2
2
0
1
2
0
1
1
1
1
1
2
2
1
2
1
0
1
1
1
0
1
1
0
0
2
1
1
1
2
1
0
1
0
0
1
1
1
1
1
3
2
1
2
1
0
0
1
0
2
1
1
1
1
1
2
0
1
1
1
2
1
3
2
0
0
2
1
1
1
0
1
0
1
0
1
1
1
0
0
0
0
1
2
1
1
1
1
2
0
2
1
1
0
1
0
1
1
0
1
1
0
0
2
1
0
3
1
1
1
1
0
2
0
1
1
0
1
1
2
0
1
1
1
3
0
0
1
1
2
1
1
1
1
1
2
1
0
2
1
1
2
1
0
1
1
1
1
1
1
1
1
0
2
1
2
0
1
1
1
2
2
1
0
2
1
0
2
0
1
2
1
2
2
1
0
1
0
1
1
1
1
1
0
0
1
1
1
1
2
1
0
1
1
0
1
1
1
1
1
1
1
2
2
0
2
2
1
1
1
1
2
1
0
1
2
2
1
6
0
2
2
1
1
1
1
1
1
0
1
1
2
2
1
1
0
1
1
0
2
2
1
1
0
1
1
1
2
2
2
0
1
2
1
1
2
1
0
1
0
2
2
1
1
1
3
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
0
0
1
1
1
1
1
1
2
2
1
2
1
1
1
1
1
0
1
4
2
1
1
1
1
0
0
0
2
0
1
1
1
1
1
2
1
1
0
1
0
1
2
0
1
1
0
2
0
1
1
1
2
0
1
1
1
1
2
0
1
1
1
0
1
1
0
1
1
0
1
1
2
1
1
1
1
1
2
0
1
1
0
1
0
1
2
2
1
2
0
0
1
1
0
1
1
1
0
1
0
2
0
1
1
1
1
2
1
1
1
1
1
1
0
0
1
1
1
1
0
1
1
1
2
1
1
1
2
0
0
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
0
1
0
1
2
0
1
2
2
1
1
1
2
1
2
1
2
1
1
1
0
1
1
1
2
1
1
1
1
1
2
0
2
1
1
0
1
0
0
1
0
0
2
0
0
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
0
1
2
1
0
1
1
1
0
1
1
2
1
1
1
0
0
1
1
3
0
0
1
1
2
1
1
1
1
1
1
1
1
1
1
0
1
2
2
1
1
0
1
0
2
1
2
1
2
0
1
1
1
1
1
0
0
0
2
2
1
1
0
1
2
0
1
2
1
1
2
2
0
1
1
1
2
1
0
0
2
1
1
2
1
1
2
1
0
2
1
0
0
2
1
1
2
2
1
1
1
1
0
1
1
1
0
1
1
0
1
2
2
0
0
2
0
2
1
1
1
1
0
2
1
1
0
1
1
1
1
1
1
0
1
0
2
1
2
1
0
0
1
0
0
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
3
1
0
0
2
1
0
1
1
2
2
1
0
1
1
2
0
1
1
2
1
1
1
2
1
1
1
1
0
1
1
1
2
1
3
1
1
1
1
0
1
0
1
0
1
1
3
2
2
1
1
1
1
1
2
2
1
0
1
1
2
2
1
0
0
0
1
1
1
0
0
0
0
0
1
2
1
0
1
1
1
2
0
0
1
1
2
1
2
1
0
1
2
1
1
1
1
2
1
0
2
0
1
0
1
1
1
1
2
2
2
2
1
2
1
1
1
1
1
2
2
1
1
1
1
0
0
1
1
1
1
0
1
1
0
2
1
0
0
2
1
0
1
2
1
1
1
2
2
1
1
1
1
0
2
2
1
1
3
2
1
1
2
1
1
1
1
1
2
1
1
1
1
2
0
0
1
1
1
1
1
1
2
2
1
2
1
0
0
1
1
1
1
0
0
0
1
1
1
2
2
0
1
2
1
2
0
2
1
1
2
1
0
1
1
1
1
1
0
2
1
2
1
2
1
0
2
1
2
1
1
2
1
1
1
1
0
2
0
1
0
1
1
1
1
1
0
2
1
1
1
2
2
1
1
2
0
2
1
0
0
0
2
0
2
2
2
0
1
2
1
1
2
2
0
1
1
1
1
1
0
0
0
0
0
1
0
2
1
0
1
2
1
2
2
3
1
1
0
1
1
1
2
4
0
1
1
2
1
2
2
0
1
0
1
2
1
1
2
1
0
0
1
2
1
1
1
2
1
2
0
1
2
1
2
0
0
2
1
1
1
0
2
0
2
1
1
1
1
1
1
0
1
1
1
2
0
1
1
1
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
0
1
1
1
1
1
2
1
1
0
1
2
4
0
1
2
1
1
0
2
0
2
2
2
0
1
2
1
1
0
0
1
0
1
1
0
1
1
0
2
0
2
1
1
1
1
0
0
0
1
0
2
2
1
2
2
1
1
0
1
1
0
1
1
1
1
2
1
2
2
2
1
1
1
2
1
2
1
0
0
2
2
1
1
1
1
2
1
1
0
1
1
1
1
1
1
2
2
0
1
0
0
1
1
2
1
2
0
0
1
1
0
1
1
1
1
1
1
1
0
2
0
1
1
1
0
0
1
1
0
1
1
1
1
1
1
0
1
1
0
2
1
1
1
1
1
1
1
1
1
0
0
1
2
2
1
2
0
1
0
1
1
0
0
1
1
1
1
1
1
0
1
2
1
2
1
0
1
1
1
1
2
0
0
2
2
2
2
1
0
0
1
2
1
1
2
1
0
1
1
2
2
1
2
0
0
0
2
1
1
1
2
1
1
1
2
1
2
2
1
1
1
2
2
0
1
1
2
0
0
1
5
1
0
2
1
1
2
2
1
1
1
0
0
1
1
0
0
1
1
1
1
1
1
2
3
1
1
0
1
2
1
2
1
0
0
2
1
1
1
1
1
1
1
1
0
1
1
1
2
1
1
2
1
1
1
1
2
2
1
2
0
0
0
0
1
1
0
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
0
2
1
1
0
1
2
2
1
1
0
1
1
1
0
2
0
1
1
0
1
1
1
1
1
1
1
0
1
2
0
1
0
0
1
2
2
0
1
1
1
1
0
1
1
1
1
1
1
2
1
0
1
2
1
0
1
0
1
1
2
1
1
0
1
1
1
0
1
0
1
3
0
1
2
2
0
1
1
2
0
1
1
2
1
2
1
1
1
1
0
1
1
1
2
1
1
0
1
2
2
1
0
0
0
2
2
1
1
1
1
0
1
1
1
0
1
1
1
2
1
2
2
2
0
0
1
2
1
1
1
0
0
3
1
2
0
1
0
1
2
1
2
2
0
1
1
1
1
1
1
2
2
0
0
2
2
1
0
1
0
0
1
1
0
1
2
2
1
0
1
1
1
1
1
1
0
1
1
1
1
1
1
0
0
2
0
2
1
0
1
1
1
1
0
2
0
1
1
3
1
1
1
1
2
2
2
3
0
1
0
2
0
1
1
0
2
1
1
1
2
1
1
2
1
1
1
1
2
1
1
0
1
1
1
2
0
0
1
1
2
2
1
2
1
1
1
1
2
1
1
1
0
1
0
1
1
1
2
1
2
1
1
1
1
0
0
2
1
0
3
1
1
0
1
0
1
1
0
1
2
0
1
0
1
1
2
0
1
0
2
1
1
2
2
1
1
1
0
1
1
0
1
1
1
1
1
1
2
3
1
1
0
1
0
1
1
1
1
0
1
1
2
0
1
0
1
2
1
2
0
0
0
2
1
0
1
1
1
2
1
1
0
2
1
1
0
1
1
2
1
0
1
1
0
1
0
1
0
1
2
0
1
0
0
1
0
1
2
0
0
1
2
1
2
0
1
1
0
0
2
1
0
0
2
0
0
1
0
0
0
2
3
1
0
1
1
1
0
2
1
2
1
1
1
1
1
1
2
0
2
2
1
0
0
2
1
0
1
0
1
0
1
1
2
1
2
0
0
0
0
1
1
2
2
1
1
1
1
2
1
0
2
1
0
0
1
0
2
1
2
0
1
1
1
2
1
0
1
3
1
0
2
1
2
2
2
0
0
2
1
0
0
1
0
0
1
1
0
1
1
0
0
1
0
0
1
1
1
1
0
2
1
1
1
1
0
0
0
1
2
1
0
1
1
1
1
2
1
1
0
1
2
1
1
1
1
1
0
1
1
1
1
1
0
0
1
1
1
1
0
1
1
1
0
1
1
1
1
1
0
1
1
1
2
1
1
0
2
1
0
1
2
1
1
2
2
2
1
1
2
1
1
1
1
1
1
0
1
0
2
1
2
2
0
1
2
1
0
2
1
1
0
1
1
2
1
0
1
1
2
1
1
2
0
2
2
2
1
1
1
1
1
2
1
4
1
1
1
1
1
0
0
1
2
2
2
2
2
1
2
1
1
1
0
2
0
2
0
0
1
1
2
1
2
1
0
2
1
0
1
2
1
1
0
1
1
1
1
1
1
1
1
0
2
2
2
0
2
1
1
1
0
1
1
1
1
0
1
0
1
0
1
1
0
2
2
1
1
1
1
0
1
1
7
2
1
2
1
1
1
1
0
1
1
1
0
1
1
2
0
2
0
1
2
1
2
1
0
1
1
1
1
2
1
1
2
3
2
1
0
1
1
1
1
2
0
1
2
2
1
0
2
1
1
1
1
1
1
2
1
1
1
1
0
1
0
1
1
1
1
0
0
0
1
1
1
2
1
0
1
1
1
1
1
1
0
0
1
1
1
1
1
1
0
1
1
1
1
1
2
1
1
0
0
1
1
0
1
1
1
1
0
1
0
0
1
2
0
1
0
0
1
1
1
0
0
3
0
0
2
0
0
1
2
1
1
2
1
1
1
1
2
1
2
0
1
2
0
1
1
1
1
1
1
2
0
1
1
1
1
1
2
2
1
1
2
1
1
1
1
1
0
2
1
2
1
1
0
1
1
2
0
1
0
1
2
1
2
2
1
1
1
2
1
2
1
0
1
1
1
1
2
2
1
0
0
1
2
1
1
1
2
3
1
0
1
1
1
1
2
1
2
1
0
1
1
1
2
1
0
1
0
1
0
0
1
1
1
0
1
1
2
1
1
2
0
1
0
0
2
0
1
1
0
1
1
0
1
2
2
1
1
3
0
1
0
1
2
1
1
0
2
3
1
2
1
2
1
1
0
2
2
1
1
0
2
2
1
1
1
1
1
1
1
1
1
2
2
1
2
2
1
1
2
1
1
2
1
1
0
0
1
0
1
2
2
1
1
0
2
1
2
2
1
1
0
0
2
1
1
0
0
1
0
1
1
2
1
1
0
1
2
2
1
2
0
0
2
1
1
2
1
0
1
1
1
2
2
2
0
1
2
0
1
2
0
1
1
0
2
1
2
1
1
2
1
1
1
3
2
1
1
1
2
0
1
1
1
1
0
2
3
0
0
1
1
0
3
0
0
1
1
1
1
1
1
2
0
2
1
1
1
1
0
1
1
2
2
2
2
1
0
0
0
1
1
1
1
2
1
1
1
0
1
0
0
2
1
3
0
2
0
0
1
1
1
1
0
0
2
0
0
0
1
1
0
1
1
0
0
0
0
1
1
1
1
1
1
2
0
1
0
1
0
0
2
1
1
0
1
2
2
0
0
0
0
1
0
0
0
1
1
1
1
0
1
0
0
1
1
0
2
0
2
2
1
2
2
1
1
1
1
1
1
1
1
1
0
0
1
0
0
2
0
1
1
0
1
1
1
2
2
1
0
1
1
2
2
1
0
2
1
0
1
0
0
0
1
2
1
1
1
0
0
1
2
1
1
0
1
1
2
1
1
1
1
0
1
2
1
1
0
1
0
1
1
1
0
0
1
0
1
1
1
1
2
1
1
1
1
1
1
1
1
0
1
1
0
0
2
1
1
1
2
1
1
2
1
2
1
2
1
0
1
1
0
2
1
1
2
1
2
2
1
1
1
0
1
1
1
2
1
2
2
1
1
1
0
1
1
1
1
0
1
2
1
1
1
2
1
1
1
0
0
0
0
1
1
1
2
1
0
1
1
1
1
1
2
2
0
0
1
1
1
1
1
1
0
1
1
2
1
2
1
1
2
1
1
1
1
0
2
1
2
1
1
1
1
2
0
2
0
1
0
2
2
1
1
2
2
0
1
1
1
1
0
0
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
2
2
1
0
1
0
2
1
2
1
1
2
1
1
1
0
1
1
0
0
2
1
0
1
2
2
2
1
2
0
2
1
0
1
1
1
1
0
1
1
1
1
1
1
2
2
1
0
2
1
0
12
1
1
1
1
1
1
0
1
0
0
1
1
0
1
1
1
1
0
0
1
2
2
0
1
0
2
1
0
1
1
1
0
2
0
0
0
0
1
1
2
0
0
1
2
1
0
2
0
1
1
1
2
2
0
1
2
2
1
1
1
1
1
1
1
2
1
1
2
2
0
0
1
0
1
1
0
0
0
2
0
1
0
1
1
0
0
0
1
0
1
0
1
0
2
0
1
2
2
1
2
2
1
2
1
2
1
0
0
0
1
1
1
2
1
1
0
2
1
1
0
1
2
2
2
1
0
1
1
1
0
1
0
2
2
1
1
1
1
1
2
1
1
1
2
1
1
1
0
1
0
2
1
1
1
1
2
2
0
1
1
1
1
1
1
1
1
0
1
1
2
3
0
1
0
0
0
2
2
2
1
1
0
0
2
1
1
1
1
1
1
2
1
1
0
0
2
0
2
1
0
0
0
1
2
2
0
0
1
1
1
1
0
1
0
1
0
1
1
1
1
0
3
2
2
0
2
4
1
1
1
1
1
0
1
1
1
1
1
1
0
0
1
0
1
0
1
1
1
0
1
0
1
2
0
1
2
2
2
2
1
1
1
0
1
2
0
0
0
2
2
1
1
2
2
1
2
1
0
1
1
1
1
0
0
1
0
1
0
0
1
2
0
2
1
1
1
0
2
2
0
1
2
1
1
2
1
2
2
1
1
1
0
1
1
1
2
2
1
1
0
0
0
2
0
0
2
1
0
1
1
0
1
0
1
1
0
0
1
2
0
1
1
0
1
1
1
1
0
1
2
1
2
1
2
1
1
1
1
1
2
1
1
1
2
1
0
1
1
0
1
2
1
1
0
0
1
2
1
1
1
0
2
1
1
0
1
2
2
1
1
2
1
1
1
1
2
1
2
2
1
1
1
2
1
1
2
2
2
1
0
0
1
1
1
1
0
1
2
2
1
0
1
1
1
1
2
1
0
0
2
1
2
0
1
1
1
0
1
0
0
1
0
1
1
2
0
0
1
0
1
2
2
1
1
0
1
0
1
2
0
0
1
0
2
2
1
0
0
1
2
1
1
1
1
1
0
2
2
1
0
2
0
1
0
0
1
1
1
1
1
1
0
2
1
1
1
0
1
0
1
1
2
1
0
2
2
1
1
1
1
1
1
1
1
1
2
1
1
0
1
1
1
1
1
0
0
1
2
2
2
1
2
1
1
2
1
1
1
1
0
2
1
2
1
1
1
1
1
1
1
2
1
1
2
2
1
1
2
2
1
1
1
1
0
1
1
0
1
1
1
0
0
2
1
1
2
1
2
1
1
1
1
1
2
0
2
1
0
0
1
0
1
1
1
1
2
0
2
1
1
2
2
1
1
2
1
0
1
1
0
2
1
2
1
2
0
2
1
1
1
2
0
1
1
0
1
1
1
0
1
0
0
0
2
0
0
0
1
0
2
0
1
1
2
0
0
1
0
0
1
0
1
1
1
1
2
1
2
0
1
1
0
1
0
1
1
1
1
1
1
2
0
1
0
2
2
1
0
1
1
1
1
1
0
0
1
0
1
1
0
1
0
1
1
1
1
2
1
1
1
0
1
0
2
1
2
0
0
0
1
1
1
0
0
0
1
2
0
1
0
1
1
1
1
2
1
2
1
2
1
1
1
1
0
1
1
2
1
1
1
1
1
1
1
1
2
1
2
0
1
2
2
1
1
1
0
1
0
1
1
1
1
1
1
1
1
0
1
1
1
1
0
2
1
1
0
2
0
2
0
2
1
1
2
1
0
0
0
1
2
0
2
1
2
0
1
1
1
0
2
0
0
0
0
1
2
1
0
0
0
0
1
2
0
1
1
0
1
0
0
1
1
1
2
0
0
0
0
0
1
1
1
1
1
0
2
2
1
0
1
2
1
1
1
0
1
1
1
1
1
0
1
0
2
1
1
0
1
0
1
1
1
2
0
0
2
1
2
2
1
1
2
1
1
2
1
2
1
1
2
1
1
0
2
2
0
1
1
1
1
0
2
0
0
2
2
0
0
0
1
1
1
1
1
1
0
2
1
1
2
1
0
1
1
1
2
1
1
1
1
0
1
2
1
1
2
1
1
1
0
0
2
1
1
1
1
1
1
1
1
1
1
1
1
0
0
0
1
1
1
0
1
1
1
1
1
2
2
0
1
2
1
1
0
1
0
0
1
0
1
1
0
0
2
0
1
2
1
1
1
2
1
1
2
1
1
1
1
1
1
1
0
1
2
2
0
2
0
1
0
2
0
1
1
1
1
1
1
0
1
0
1
1
0
1
1
1
0
3
2
1
1
1
2
1
0
1
1
2
2
1
1
1
1
2
2
1
1
1
1
1
2
1
2
0
2
1
0
1
1
1
0
1
1
1
1
0
0
1
1
1
0
2
2
0
0
0
1
0
1
0
0
0
1
0
0
0
3
1
1
1
1
1
0
0
1
1
1
1
1
0
0
1
1
0
0
1
2
0
2
1
1
2
1
1
1
1
1
1
1
0
1
1
2
1
1
0
1
2
0
2
2
1
0
1
1
1
1
1
0
1
0
1
1
1
0
1
1
2
0
2
2
0
1
2
1
0
0
0
2
2
2
2
1
1
0
1
1
1
0
0
2
1
1
1
1
2
1
0
0
1
0
2
1
1
1
0
1
1
1
1
1
0
2
0
1
1
1
0
1
1
1
0
0
2
1
1
3
1
1
2
0
1
1
0
0
1
1
2
1
1
1
1
1
0
1
1
1
0
1
0
1
1
1
2
0
1
0
1
1
1
0
1
1
1
0
0
1
0
2
1
1
1
2
0
0
1
1
0
1
1
1
0
1
1
1
0
2
1
1
2
2
1
2
2
1
0
1
1
2
1
2
1
2
1
2
1
1
1
1
0
2
0
1
1
2
0
2
2
0
2
1
1
1
2
1
1
2
1
1
1
0
2
0
1
2
0
0
1
0
1
0
2
1
2
1
0
2
2
2
1
0
2
0
1
1
1
0
0
1
2
1
0
1
1
1
2
1
1
1
2
1
1
0
2
2
0
1
0
1
1
0
1
2
0
1
1
1
1
1
1
1
1
2
1
0
0
1
0
1
1
1
0
1
1
1
1
0
1
1
2
1
0
1
2
0
1
1
1
2
1
0
2
0
2
1
2
0
3
0
1
2
2
0
2
2
1
2
1
0
1
1
0
1
1
2
2
1
1
1
3
1
2
1
2
1
2
2
1
1
2
1
1
1
1
1
1
1
2
0
2
1
1
1
0
1
1
1
1
2
0
1
0
1
0
0
0
0
0
1
1
1
2
1
1
0
0
2
1
2
0
2
1
1
1
1
2
2
2
0
1
1
0
1
1
1
0
2
0
2
0
2
1
2
2
2
1
1
1
1
0
1
0
0
1
0
1
0
1
1
1
2
2
2
1
0
2
1
1
2
1
1
2
2
0
0
1
0
1
1
1
1
0
2
0
1
1
2
2
0
1
2
1
1
1
2
1
0
0
0
2
0
0
1
1
2
1
1
1
1
1
2
1
2
1
1
2
1
2
0
1
2
2
1
2
2
0
1
2
1
1
0
1
1
2
0
0
1
0
1
0
1
2
1
1
1
0
1
2
1
1
1
1
1
0
1
2
1
1
2
2
0
1
1
1
1
0
1
0
0
1
2
0
0
1
2
0
0
0
2
2
2
1
0
1
2
1
2
1
1
1
0
0
1
2
1
1
0
1
1
1
1
1
1
2
2
2
1
1
2
1
1
1
2
1
1
2
1
1
1
1
0
1
1
1
1
1
2
2
1
0
1
0
2
1
1
1
1
2
1
1
2
0
2
2
2
1
1
1
1
1
1
0
2
1
0
0
1
1
1
1
1
2
0
1
1
0
0
2
1
0
1
2
1
2
0
2
1
1
0
1
3
1
1
2
0
2
1
0
2
0
0
1
0
1
1
2
1
0
1
2
0
1
1
1
0
1
0
1
1
1
0
1
0
2
1
1
1
1
1
1
1
0
2
1
0
2
2
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
2
2
0
1
1
1
1
1
2
1
0
2
1
1
1
0
2
1
0
1
2
1
1
2
1
1
0
0
1
1
0
0
2
0
1
3
0
1
1
1
0
1
0
0
3
0
0
1
1
1
1
1
0
1
1
2
0
2
0
2
1
1
0
1
1
1
0
0
0
1
2
1
1
1
1
2
0
0
2
0
1
1
0
2
1
1
0
1
2
0
1
0
1
1
2
1
2
1
0
1
1
0
1
2
2
3
1
1
1
0
1
0
1
1
2
2
1
1
0
1
1
0
2
0
2
1
1
1
1
2
0
1
1
0
1
2
1
1
1
0
2
0
0
2
1
0
0
1
0
1
1
2
1
2
0
1
1
1
0
1
1
0
2
0
1
0
1
1
1
1
1
0
3
0
1
2
0
1
2
0
2
1
0
0
1
1
1
1
1
1
2
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
2
1
1
2
1
1
0
1
1
1
1
1
0
0
1
1
1
0
1
1
1
1
0
0
1
1
0
0
0
0
1
1
2
1
1
1
1
2
0
1
1
0
2
1
2
1
0
1
1
1
0
1
1
1
1
0
1
2
0
1
2
1
1
0
1
1
1
1
2
1
2
1
1
3
0
1
1
1
1
1
1
0
1
2
1
2
1
2
1
1
1
1
2
1
0
1
2
0
0
1
0
1
1
1
1
2
0
0
2
1
1
1
0
1
2
0
2
1
1
2
2
1
1
0
2
2
1
1
0
2
1
2
0
1
0
1
0
0
1
0
0
1
2
1
1
1
1
2
1
1
1
1
0
1
2
2
0
1
1
1
1
0
1
1
0
1
1
0
2
1
0
2
0
1
0
0
1
2
1
1
1
1
1
0
0
1
2
1
0
1
0
1
2
1
1
1
2
2
2
1
1
0
1
0
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
0
1
2
1
1
1
0
1
1
0
2
2
2
2
2
2
1
1
1
1
2
0
2
0
2
1
0
1
2
2
2
2
2
0
1
1
1
1
1
0
1
1
2
0
2
0
1
0
2
0
1
1
1
0
1
2
1
2
1
2
1
2
0
2
1
1
2
1
0
1
0
0
0
2
2
1
1
2
2
1
2
1
1
1
2
0
1
1
0
1
2
1
1
0
0
1
1
1
2
1
1
0
2
1
1
0
0
2
1
1
1
2
0
1
1
1
1
1
2
1
2
1
1
0
1
0
1
2
1
1
0
2
0
1
0
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
0
1
2
0
1
1
2
1
1
2
1
1
0
0
1
1
2
1
1
2
0
0
1
0
0
1
1
2
1
1
2
0
2
0
1
1
1
0
1
0
2
1
1
0
1
1
1
1
1
8
1
1
1
2
2
2
1
1
1
1
1
1
1
1
0
1
2
2
0
0
1
1
2
0
1
1
0
2
1
0
0
0
1
1
2
2
1
1
1
1
1
0
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
0
2
2
1
1
0
2
0
0
1
1
0
1
1
1
1
1
2
2
2
1
0
1
0
0
1
2
0
1
2
1
0
1
1
1
0
1
0
1
2
1
1
1
2
1
3
1
2
1
1
2
1
1
1
1
2
2
1
0
1
1
0
1
2
2
1
0
1
0
1
1
2
0
1
2
1
1
0
1
1
1
1
1
2
2
0
1
0
0
1
1
2
0
2
0
1
1
0
1
1
1
2
1
2
1
0
1
1
1
2
1
1
1
0
1
0
1
2
1
1
1
1
2
0
2
2
1
4
1
2
1
1
0
1
2
1
2
1
0
1
1
0
1
0
1
2
1
0
1
1
0
0
1
0
1
0
1
1
1
2
0
1
1
0
2
0
1
1
1
1
3
0
0
1
1
1
0
2
1
2
2
2
0
1
1
1
1
1
1
0
2
1
1
1
0
2
1
0
1
2
1
1
1
1
0
0
1
1
0
1
1
1
0
1
0
2
1
2
1
2
2
0
1
2
1
0
1
1
1
2
2
1
1
0
0
2
1
1
1
1
1
0
1
1
2
1
1
1
1
1
2
0
2
1
2
0
2
2
0
2
1
1
1
2
2
2
1
1
2
1
1
0
1
1
1
1
1
0
2
0
1
0
1
0
2
1
1
1
1
1
2
3
1
0
1
1
1
2
2
1
0
2
1
2
1
1
1
2
1
0
1
1
0
0
1
0
2
1
1
0
2
0
2
0
0
1
1
2
0
2
1
1
0
0
1
1
0
1
0
0
1
1
1
0
1
1
1
2
0
1
0
1
0
0
1
1
1
1
2
2
1
0
1
0
0
2
0
2
2
1
0
0
1
2
1
1
1
1
1
2
1
1
0
1
0
1
1
0
1
1
2
2
1
1
2
2
1
1
0
2
2
1
2
0
1
2
1
1
0
0
2
0
1
1
1
0
1
2
2
1
1
1
1
2
1
1
0
0
1
1
2
1
1
1
1
1
0
1
1
2
2
2
1
2
2
1
1
1
1
2
1
0
1
2
1
0
1
0
3
1
2
1
1
1
2
1
2
1
0
1
1
0
1
0
2
2
0
1
1
0
1
1
1
1
2
1
1
1
0
0
1
2
1
2
0
1
1
1
1
1
1
1
0
2
1
1
2
2
1
0
1
1
2
2
1
1
0
1
1
1
2
1
2
0
1
0
0
1
0
1
1
2
1
1
0
1
1
2
1
2
1
1
1
0
1
0
1
1
1
1
1
1
0
2
1
0
2
0
1
1
1
1
1
1
2
1
0
2
1
2
1
1
0
0
1
2
0
2
0
1
0
1
1
1
2
0
1
2
1
1
1
0
1
0
1
1
1
1
2
1
1
0
1
1
1
1
1
0
2
1
1
1
2
1
0
1
1
1
1
0
1
2
2
1
1
1
0
1
0
0
2
2
1
1
1
0
1
2
2
1
0
1
1
2
0
1
2
1
1
2
0
0
0
2
2
1
0
2
1
0
2
1
0
1
0
1
0
0
1
0
1
2
0
2
1
2
1
2
1
0
1
1
2
1
1
2
0
1
1
1
0
1
2
1
1
2
1
1
1
0
0
1
0
2
2
1
2
1
2
1
0
1
1
1
1
1
2
1
0
1
0
1
1
1
0
1
1
0
0
1
1
2
0
0
2
1
2
1
1
0
2
0
2
1
1
0
1
0
2
0
0
1
0
2
2
1
1
1
0
2
1
2
0
1
1
0
1
1
1
1
1
1
2
3
2
1
1
1
1
1
2
1
1
1
1
1
1
1
4
1
2
1
2
1
0
1
0
1
1
2
0
0
0
1
2
2
2
0
1
1
0
2
1
2
1
0
1
2
1
2
2
1
1
1
1
2
2
0
0
3
0
1
0
2
1
0
2
2
2
1
2
2
2
0
0
1
2
1
2
1
1
1
1
1
1
0
0
1
0
2
0
2
1
0
1
1
0
0
2
0
2
1
0
0
0
1
1
1
1
1
2
0
2
1
1
0
0
1
1
2
0
1
1
0
0
1
1
0
0
1
1
2
0
0
1
2
2
1
1
1
1
1
1
0
1
2
1
1
0
2
1
1
1
1
0
1
1
2
0
0
2
1
3
1
2
2
2
2
1
1
0
0
1
1
1
0
0
1
1
1
2
1
2
1
1
1
0
2
2
1
1
1
0
2
1
2
0
1
0
2
0
4
1
1
2
2
1
0
0
2
1
1
1
1
2
2
0
1
2
1
1
1
2
0
0
0
1
2
1
1
0
0
2
0
1
2
2
1
1
1
1
0
1
1
1
1
0
1
2
1
2
2
2
0
2
0
1
0
1
1
2
0
1
2
1
2
1
0
1
1
1
1
1
1
2
1
1
1
2
1
0
0
1
0
1
1
0
0
1
2
1
1
1
1
2
0
0
1
0
2
1
0
1
0
1
3
1
1
1
1
2
2
1
1
1
1
2
0
1
1
2
1
2
1
1
2
1
1
1
1
0
2
2
3
1
1
1
1
1
1
1
1
2
0
2
1
1
0
2
2
1
0
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
0
1
1
2
1
2
1
0
1
0
2
1
1
1
2
0
1
1
1
2
1
0
1
1
1
1
1
2
1
2
2
0
0
2
2
2
1
1
1
1
1
2
1
2
1
1
1
0
0
1
0
1
2
2
2
2
1
1
1
2
1
0
0
1
1
1
0
2
1
0
1
0
1
1
0
1
1
1
1
1
0
1
1
1
1
1
2
2
1
2
1
1
1
0
1
1
2
1
1
2
1
1
1
1
0
0
1
0
2
1
1
0
1
0
1
1
1
2
0
0
1
0
1
0
1
1
1
1
1
1
1
0
1
0
1
1
1
1
1
0
1
1
2
1
1
1
0
1
1
1
2
1
1
0
2
1
1
2
1
1
0
1
0
2
2
1
0
1
0
1
1
0
1
1
1
2
2
2
2
2
0
1
0
1
2
0
0
2
2
1
2
1
2
1
1
2
1
1
2
0
1
2
1
1
0
0
0
2
1
2
0
0
1
1
2
1
2
2
1
1
2
2
1
1
1
2
0
2
2
0
1
1
2
1
2
1
2
2
0
1
0
2
1
1
1
1
1
2
3
0
1
2
0
0
0
0
1
0
2
2
2
1
1
0
1
0
2
1
0
0
1
0
2
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
2
2
2
1
0
0
1
2
0
1
1
2
1
2
1
2
2
1
0
1
1
1
0
1
0
1
1
0
0
1
1
1
0
0
2
1
2
0
1
1
2
0
1
1
1
2
2
2
1
2
1
1
2
0
0
0
0
1
1
2
0
1
1
1
1
2
1
2
1
2
2
2
0
1
0
0
1
1
0
0
0
0
1
1
0
1
0
1
1
0
1
1
0
1
2
1
1
1
1
2
1
0
0
0
0
1
1
1
2
1
1
1
2
1
1
0
2
1
1
1
0
1
2
1
1
1
1
0
1
1
0
1
2
1
2
3
2
2
1
0
0
1
1
1
1
2
0
0
1
2
1
0
1
1
1
1
3
1
1
1
1
1
1
0
0
1
2
2
0
1
0
2
1
1
0
1
1
1
0
2
0
1
0
1
2
0
0
0
1
1
1
0
2
0
1
1
1
2
1
1
0
1
0
1
2
2
2
1
1
1
0
0
2
1
0
1
1
2
0
1
1
0
1
2
1
1
0
1
1
1
2
0
1
1
1
0
2
0
1
2
2
1
0
0
0
0
0
0
2
1
2
1
2
1
1
2
1
2
4
0
1
1
2
1
1
2
1
1
0
1
1
2
2
1
0
1
1
1
1
2
1
1
1
1
1
1
1
1
1
0
1
1
1
1
2
2
2
1
2
0
2
1
2
2
1
0
2
1
1
1
2
1
1
2
0
0
1
0
1
2
2
1
1
2
2
1
0
2
1
1
0
1
0
2
1
1
1
1
1
0
1
0
0
1
1
1
0
0
1
0
0
1
0
2
1
1
2
1
2
1
1
0
1
1
1
2
2
2
1
1
1
2
0
2
1
2
0
1
0
2
2
1
2
0
2
1
2
1
1
0
1
1
0
1
1
0
0
1
1
2
7
1
1
2
0
1
1
1
2
1
0
1
1
2
0
1
0
1
1
0
1
1
0
1
1
3
0
0
2
1
1
0
0
1
1
1
2
0
1
1
0
0
1
0
0
1
2
1
1
1
1
0
0
1
2
1
1
1
1
1
1
1
2
2
1
1
0
1
0
1
1
2
2
1
0
2
1
1
1
0
1
1
0
1
2
2
2
1
2
2
2
1
0
1
1
1
2
1
0
1
0
1
0
1
1
1
1
1
0
0
2
0
1
1
0
0
0
1
0
1
1
2
1
0
0
2
2
0
1
1
1
2
2
2
1
1
1
1
1
2
0
2
1
1
2
1
1
1
0
0
1
2
1
1
1
1
4
1
1
0
1
0
1
1
2
2
0
2
0
1
1
2
1
1
0
0
3
1
0
0
1
1
2
0
2
0
1
0
2
2
0
1
1
1
1
0
1
2
1
1
0
1
0
1
2
1
1
2
0
0
1
1
1
1
1
0
1
1
1
1
2
1
0
1
1
1
2
1
1
2
0
1
1
0
2
1
2
1
1
2
2
2
1
0
1
2
1
0
1
0
1
0
1
2
1
0
2
3
2
1
2
1
2
0
0
1
0
0
0
2
2
1
0
0
1
1
1
0
0
0
1
0
1
1
2
2
1
2
1
1
1
0
0
0
2
0
1
0
2
0
1
0
0
1
1
2
1
1
1
3
1
1
1
2
1
1
2
1
1
1
0
1
0
1
2
1
1
2
2
1
1
1
0
0
2
1
1
2
1
2
1
0
0
1
2
1
0
1
1
1
1
2
1
1
1
1
1
0
1
0
1
0
0
1
1
0
1
1
0
2
2
0
2
1
1
0
1
0
0
2
2
2
0
1
0
2
1
2
2
1
2
1
2
1
0
1
2
1
1
1
0
2
2
0
1
0
1
1
2
0
1
2
1
0
1
2
1
0
2
1
1
1
1
2
1
1
1
1
1
0
2
1
2
1
1
2
1
1
0
2
1
1
0
1
0
1
2
1
1
1
0
1
1
2
1
1
0
0
1
1
2
0
1
2
0
1
1
1
1
2
1
1
1
1
0
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
0
0
1
1
1
1
2
1
3
0
1
1
1
2
1
1
1
0
1
2
2
2
0
2
2
1
1
1
2
1
0
1
1
1
2
1
0
2
1
0
2
1
2
1
0
1
1
1
2
1
1
2
0
5
1
1
1
0
1
2
4
1
1
1
0
0
1
0
1
1
1
0
2
1
2
1
1
0
1
3
1
2
2
2
1
2
2
2
0
2
2
0
0
1
2
0
1
0
0
0
0
0
0
2
0
2
0
1
1
1
1
1
1
1
1
1
2
1
0
1
2
2
0
0
0
2
1
2
0
1
1
0
2
0
1
1
1
1
1
0
2
1
2
1
1
1
0
1
2
2
1
0
0
0
2
1
0
0
0
0
2
2
0
1
1
1
2
1
0
1
0
0
2
0
1
1
1
1
1
0
1
1
2
1
2
1
1
3
1
0
1
1
1
4
2
1
1
1
1
2
0
1
1
0
1
0
1
1
1
2
2
2
1
0
1
0
0
1
2
0
0
1
0
2
1
2
0
0
1
0
1
0
2
1
1
1
1
1
2
2
1
0
0
1
1
1
0
1
1
1
0
2
0
0
0
1
1
1
1
1
2
1
1
1
2
0
1
1
1
2
1
0
0
1
1
0
2
0
0
2
1
1
0
1
1
1
2
0
2
0
1
1
0
0
2
0
1
1
1
0
1
0
2
1
1
0
1
1
1
1
0
0
1
1
3
1
2
1
0
2
2
2
0
2
1
1
1
1
1
0
1
2
2
1
1
1
2
1
1
1
1
0
1
1
2
2
2
2
0
1
1
1
1
0
1
0
1
1
0
2
1
2
1
0
1
1
0
2
1
2
1
1
1
1
1
2
2
2
2
1
0
1
1
0
0
1
0
1
2
1
0
1
2
1
1
1
2
2
1
2
2
0
1
1
0
1
1
2
1
0
2
1
0
2
1
1
1
1
1
0
1
1
0
1
0
2
1
0
1
1
1
1
2
0
2
0
0
1
0
0
2
4
1
1
1
0
1
1
1
1
0
2
2
1
2
1
2
0
0
1
1
1
1
1
0
0
0
2
0
1
1
2
2
0
1
0
1
2
1
1
1
2
1
2
1
2
1
1
2
1
1
1
1
1
0
1
1
1
2
1
1
1
1
0
0
1
1
1
1
1
1
0
1
0
2
1
0
1
1
1
0
1
1
2
1
0
1
2
0
2
0
0
1
0
0
2
1
1
1
1
2
1
1
1
1
2
2
1
0
1
1
0
1
1
1
0
0
1
2
2
1
2
0
1
1
1
1
0
1
1
1
1
0
0
1
1
2
1
1
1
0
1
1
2
1
1
2
1
1
2
2
1
1
1
2
1
1
1
0
1
1
0
1
0
1
1
0
2
0
1
1
1
1
1
0
2
0
2
1
1
2
0
2
1
2
1
1
0
1
2
0
2
1
2
0
1
2
2
0
0
1
0
1
1
1
1
1
0
0
2
1
1
1
1
1
1
0
1
1
1
1
2
0
1
2
2
2
0
0
2
0
2
1
0
0
3
2
0
0
0
1
2
2
1
0
1
1
1
0
2
1
1
0
1
0
1
2
1
2
0
2
1
2
1
1
2
2
2
1
1
1
1
1
1
1
2
2
2
0
1
1
0
2
2
1
0
1
1
1
2
0
1
1
2
0
0
1
1
1
2
1
1
1
1
1
0
1
0
1
1
1
2
1
0
2
1
1
1
1
1
1
1
1
2
2
0
0
1
1
1
0
1
2
1
1
2
1
0
2
1
1
2
0
0
1
1
1
3
0
2
0
0
2
0
0
1
2
1
2
1
1
0
0
0
2
2
2
1
1
0
0
2
2
1
1
2
1
1
1
1
0
0
2
1
1
0
0
1
2
1
2
2
2
0
1
0
2
1
0
1
0
2
1
1
0
1
1
0
1
1
2
1
0
1
1
1
1
1
1
0
1
0
1
1
1
2
0
0
0
2
2
0
1
1
0
2
2
1
1
1
1
1
1
1
1
1
1
3
1
1
0
1
0
1
1
1
1
2
2
1
1
1
1
0
1
2
1
1
2
2
1
1
1
1
1
1
0
2
0
1
1
1
1
4
1
1
2
1
2
2
2
0
0
1
1
1
0
0
1
0
1
1
0
1
0
0
1
1
1
0
1
2
1
1
0
1
2
2
1
1
1
2
1
1
1
1
2
1
2
1
1
1
1
2
1
1
2
0
2
1
1
1
2
0
1
1
2
0
1
1
1
2
1
1
0
0
0
2
1
1
1
1
2
1
1
1
1
0
0
0
1
1
1
2
0
1
1
0
1
2
1
2
1
1
1
1
1
2
1
1
1
1
2
2
0
1
1
2
0
0
2
2
1
1
2
2
2
0
2
1
1
0
1
1
2
1
2
2
1
1
1
2
1
2
1
0
1
2
1
1
1
1
1
1
1
1
1
0
0
1
0
1
1
2
1
2
2
1
0
2
1
1
1
1
1
2
1
1
2
1
1
1
4
1
0
2
0
1
2
2
1
0
1
1
1
1
1
1
1
1
2
0
1
1
2
0
2
0
0
1
1
0
0
0
1
1
1
1
1
2
1
1
1
2
1
0
1
0
2
1
1
1
1
1
1
0
2
2
0
1
0
1
1
0
1
0
1
1
2
1
0
1
1
2
0
2
2
1
2
1
0
1
1
1
1
1
0
1
1
0
1
1
1
2
2
1
1
0
2
2
0
0
1
1
0
1
1
2
2
0
1
1
2
0
0
1
1
3
1
0
0
2
1
0
1
0
1
2
0
1
2
2
2
1
0
1
2
0
1
0
3
0
1
1
1
1
0
2
1
1
1
2
0
2
2
1
1
2
0
0
1
2
1
0
2
2
1
0
1
0
2
0
1
2
1
1
1
2
0
1
2
1
2
2
0
1
2
1
1
2
2
2
1
1
0
1
2
1
0
1
1
2
1
1
2
1
1
0
2
1
2
1
1
0
1
1
1
2
2
1
1
0
1
0
1
1
2
1
2
1
1
3
1
2
1
1
1
2
0
0
1
2
0
2
1
1
1
2
0
1
2
1
0
1
2
1
0
1
1
1
1
1
0
1
1
1
1
1
2
1
0
0
1
0
1
1
1
1
1
1
1
1
0
0
1
0
2
2
2
4
1
0
2
1
1
0
1
1
1
1
1
1
2
1
1
2
1
2
2
1
1
2
1
2
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
0
1
2
1
0
1
3
0
1
1
1
1
1
1
0
1
2
2
0
2
3
1
1
1
0
1
1
0
1
0
1
2
2
1
2
0
1
1
1
1
1
1
1
2
0
1
1
0
1
1
0
1
2
1
0
1
1
1
2
1
2
1
2
2
2
1
1
2
2
1
1
1
1
0
1
0
0
1
1
1
1
1
0
1
1
1
2
1
1
1
1
0
1
0
1
1
1
2
2
0
2
2
0
2
2
1
1
1
1
0
1
1
1
1
2
0
2
0
0
1
1
1
1
1
2
1
1
1
1
2
0
3
1
1
0
1
2
1
2
1
1
1
2
0
1
1
1
0
1
1
1
1
1
1
1
1
0
1
1
1
1
0
1
1
0
2
1
1
1
1
0
0
2
0
1
2
1
1
1
1
0
1
0
0
2
1
2
0
0
1
2
1
1
1
1
1
1
1
0
1
1
1
1
2
1
2
1
0
0
0
1
1
1
1
2
1
2
1
1
1
2
0
2
2
3
1
0
1
0
0
1
2
1
2
1
2
2
1
1
1
1
0
2
0
2
0
0
0
1
0
2
1
1
2
1
1
0
1
1
1
1
0
1
1
1
1
1
1
0
2
0
2
0
1
1
1
2
1
1
1
1
0
2
1
0
0
2
1
1
1
2
1
0
1
0
2
1
1
0
1
0
2
1
0
1
1
1
0
1
1
1
2
1
1
1
1
0
1
0
1
1
1
1
0
1
1
2
0
1
1
0
2
1
0
0
1
0
2
2
0
1
0
1
1
1
0
2
0
1
1
2
2
2
2
1
2
1
1
1
1
0
2
1
0
1
2
0
1
0
1
1
2
1
0
1
0
0
1
1
0
1
1
1
1
0
2
1
2
1
2
4
1
1
0
2
0
1
1
1
0
0
1
2
0
0
1
2
1
0
0
2
1
0
1
1
1
0
1
1
1
1
1
2
3
0
1
2
1
2
1
0
2
1
1
2
2
0
1
1
1
2
0
1
1
1
2
1
0
2
1
1
1
0
1
0
1
2
1
0
2
1
1
0
1
2
1
0
2
1
2
1
1
2
2
1
1
1
1
1
0
0
1
2
1
0
1
1
1
1
2
1
1
1
2
1
1
0
1
1
2
1
0
1
2
2
0
1
1
1
1
1
1
1
1
2
1
0
2
1
1
1
0
2
1
1
1
0
2
1
0
1
1
0
0
1
2
2
0
1
1
0
2
1
3
2
1
1
2
0
1
1
0
1
1
1
1
1
0
0
2
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
2
1
0
0
1
1
2
2
1
2
2
1
2
0
1
1
1
1
1
1
1
1
1
1
1
2
1
2
0
2
1
1
2
0
1
1
2
0
1
2
2
1
2
1
0
0
1
1
2
1
0
2
1
3
2
2
0
2
1
2
1
1
1
1
2
2
1
1
1
1
1
0
0
1
0
1
2
0
1
1
1
0
1
1
1
1
0
1
1
0
2
2
0
1
0
2
1
2
0
1
0
1
1
1
2
1
1
1
2
2
0
1
0
1
1
1
0
1
1
1
1
1
1
0
0
2
0
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
3
1
1
0
2
1
0
0
1
0
1
2
2
1
1
1
1
1
0
1
1
1
1
2
1
1
1
2
1
2
1
1
0
0
1
1
1
1
1
2
1
1
0
1
0
1
1
1
1
1
0
1
1
1
0
1
1
2
1
2
0
1
1
0
1
1
2
1
0
2
2
1
1
1
0
0
2
1
1
2
2
1
2
0
1
1
0
2
1
0
1
1
1
1
0
1
1
1
1
2
1
2
1
1
1
1
1
1
1
0
1
1
2
2
0
1
1
0
1
2
0
2
3
1
0
1
1
1
1
1
0
0
2
0
1
1
1
1
1
1
0
2
1
1
1
1
1
2
0
0
1
2
2
1
1
1
1
2
1
1
0
2
1
1
1
0
0
0
1
1
1
1
0
2
1
1
2
0
1
1
1
0
2
0
1
0
2
1
0
0
2
2
2
1
1
0
2
2
2
1
0
0
1
1
1
1
2
2
2
1
1
0
1
0
1
2
1
1
1
0
1
2
2
0
0
0
1
0
0
0
2
2
2
1
3
2
3
0
2
1
0
1
1
0
1
0
1
1
1
2
1
2
2
1
2
1
0
3
1
0
2
1
1
1
1
0
0
2
0
1
2
1
1
1
2
2
0
0
1
0
1
2
1
2
1
1
0
2
2
2
1
2
0
0
0
2
1
1
2
2
0
2
0
1
0
0
1
2
0
0
2
2
1
0
0
1
2
1
1
1
2
1
0
1
1
1
1
1
1
2
0
1
2
1
1
1
1
2
1
1
0
3
1
2
1
2
1
2
0
1
2
0
1
1
0
1
1
0
1
1
1
1
1
0
1
1
1
0
1
2
0
1
0
1
2
1
1
0
1
0
1
0
1
2
2
1
1
1
2
1
1
2
0
1
2
1
1
0
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
1
2
0
1
1
0
0
1
1
2
2
1
2
1
2
2
0
0
1
1
1
1
1
2
0
2
1
2
1
1
0
1
0
1
1
2
2
1
2
1
1
2
2
1
0
1
1
1
0
2
0
2
0
0
1
1
1
1
1
1
2
0
1
1
0
1
1
0
1
1
0
0
0
1
1
0
2
1
2
1
1
1
1
0
0
1
1
1
1
1
0
1
1
1
1
1
0
1
1
0
0
1
0
1
0
1
0
0
1
1
1
1
1
2
0
0
0
1
1
1
1
0
1
0
2
1
2
0
1
1
1
0
0
2
0
1
1
0
0
1
1
1
1
2
0
2
0
1
2
1
1
2
0
1
1
0
2
1
0
0
2
1
0
0
2
1
1
2
0
1
0
1
1
0
0
1
0
0
2
1
1
0
0
0
0
1
0
1
1
4
1
1
1
0
1
1
2
1
2
1
2
1
0
2
2
1
1
12
1
0
2
1
1
0
2
1
0
1
2
0
1
1
2
0
1
1
1
0
2
0
1
2
1
1
0
1
1
1
1
0
2
1
1
1
2
1
1
2
2
1
2
0
3
1
2
0
0
2
2
1
1
1
0
2
1
1
2
2
1
2
1
1
1
1
1
0
0
2
2
0
1
1
1
0
0
2
1
2
2
0
0
1
1
1
1
1
1
1
1
2
1
0
0
1
1
1
1
1
1
1
0
2
1
1
2
1
1
1
1
1
1
1
1
0
0
0
2
1
2
1
1
1
1
1
1
2
1
1
1
1
0
2
1
1
1
2
1
1
1
1
0
1
2
0
1
1
1
1
2
1
2
1
0
1
1
0
1
2
1
2
0
1
1
1
1
1
0
0
2
1
0
0
1
1
1
1
0
1
1
0
1
1
1
2
1
1
1
0
0
1
1
1
2
2
0
2
0
2
1
1
1
1
2
1
1
1
1
1
1
2
0
2
2
1
2
2
2
0
0
1
1
0
1
1
1
3
4
1
1
0
1
1
1
1
1
1
1
0
0
1
3
2
1
2
2
0
0
1
1
0
0
3
1
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
0
1
2
0
1
0
2
1
1
2
0
1
1
0
1
0
1
2
1
2
1
2
1
2
0
1
1
1
0
2
2
0
1
0
2
1
1
1
0
1
2
1
2
1
1
1
1
1
1
1
0
0
1
2
0
1
0
0
0
1
0
1
1
1
0
0
0
0
1
1
1
0
2
1
1
1
1
1
1
2
1
0
1
0
1
2
2
1
1
1
1
0
0
1
1
1
2
1
1
1
1
1
0
1
0
1
2
2
1
2
2
2
1
1
0
1
1
2
1
2
0
1
2
2
1
0
1
2
1
1
2
0
2
1
0
2
1
2
2
1
1
0
1
1
1
1
1
1
0
2
1
1
1
1
1
0
0
0
0
2
0
2
0
1
0
0
1
2
2
0
1
1
1
2
1
0
2
0
0
0
1
2
1
1
2
0
1
1
1
1
0
1
0
1
1
2
1
1
1
0
2
2
2
0
1
2
0
1
2
2
1
1
0
2
2
2
1
2
1
0
1
1
1
1
3
0
1
0
1
2
1
1
1
2
0
1
2
3
1
1
1
2
1
1
1
2
0
2
1
2
0
1
1
1
1
0
1
1
1
2
1
2
2
1
2
1
1
1
2
1
1
1
1
1
2
0
1
2
1
2
2
1
0
1
2
1
0
0
1
0
2
3
2
1
2
2
0
1
0
2
0
2
1
1
0
1
2
0
0
1
0
1
0
1
2
1
1
2
1
0
1
0
1
1
2
1
1
1
1
1
2
2
0
1
0
1
2
0
2
2
1
2
2
2
2
1
1
0
1
1
0
1
1
1
2
0
1
0
1
0
3
1
2
0
1
0
1
0
1
1
2
2
1
0
0
0
2
2
2
1
2
1
1
0
2
2
2
2
0
0
1
2
1
1
2
0
1
2
1
2
0
1
2
1
1
1
2
2
1
1
1
1
0
2
1
1
1
1
1
0
1
1
1
1
1
0
2
1
2
1
3
2
0
1
1
1
1
0
1
2
0
1
2
0
2
2
1
2
1
2
1
0
1
1
1
1
0
0
2
1
3
1
1
0
1
1
0
2
1
0
2
3
2
1
0
1
1
1
1
1
1
1
0
2
1
1
0
2
2
1
1
2
0
1
1
1
2
1
0
0
0
0
0
1
1
2
1
0
0
1
2
1
2
1
1
1
2
1
1
0
1
0
1
1
1
2
1
2
0
0
1
1
1
1
1
2
0
2
0
0
0
1
1
1
1
1
1
0
1
1
1
0
1
2
2
1
1
2
0
2
0
2
0
0
1
1
0
1
0
2
1
2
3
0
1
1
1
1
1
1
1
1
2
2
1
1
0
1
2
1
2
1
2
0
1
1
0
1
0
0
1
1
1
0
1
1
0
2
0
0
1
2
1
1
1
1
1
1
2
1
0
2
1
1
1
1
0
2
1
0
1
1
1
1
1
1
0
1
3
1
0
1
0
0
1
0
2
1
2
2
2
2
0
0
0
2
1
2
0
2
2
1
2
1
0
2
1
2
2
0
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
0
0
1
1
1
1
1
2
1
2
1
1
2
1
1
1
2
0
1
0
1
0
1
1
1
2
2
0
1
0
1
1
0
1
1
1
1
2
1
1
1
1
1
0
1
1
2
1
1
1
2
1
0
2
1
1
0
1
0
1
1
1
1
1
0
0
1
2
0
1
1
2
2
1
0
1
0
0
1
0
1
1
2
0
1
0
1
2
0
2
0
1
2
0
3
2
0
1
0
1
2
1
0
2
1
0
2
1
4
1
2
2
1
1
2
1
2
0
0
2
0
1
1
2
1
2
0
0
0
1
1
2
1
1
1
1
2
0
1
0
2
2
2
1
1
0
0
0
1
2
2
1
1
1
1
1
1
0
1
0
0
2
0
1
1
0
1
1
0
1
1
1
0
0
2
2
1
1
1
0
1
1
0
1
2
2
1
0
2
0
1
2
0
0
1
1
1
0
2
1
0
1
1
1
1
1
1
1
0
0
1
1
1
1
0
1
1
0
1
0
2
1
1
0
1
1
1
1
1
0
1
1
2
1
1
1
1
0
0
1
0
1
2
0
1
1
1
2
1
2
1
2
0
1
0
2
1
1
3
2
1
0
1
1
0
2
1
1
1
2
0
1
1
0
0
0
2
1
1
2
1
0
0
1
1
0
1
1
1
2
0
2
2
0
0
1
1
2
1
1
1
2
2
0
1
1
2
1
2
0
0
1
1
1
1
3
1
2
1
1
1
2
0
2
1
1
1
2
1
1
2
2
1
2
0
0
1
1
0
1
0
2
1
2
2
1
1
2
0
2
2
1
2
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
0
1
2
0
1
2
1
1
1
1
1
1
1
0
0
1
2
0
1
1
1
0
1
1
1
1
0
2
1
1
0
0
0
0
0
0
0
2
1
1
1
1
2
0
2
0
2
1
0
2
2
1
1
1
0
1
0
0
1
1
0
1
1
1
1
0
0
1
1
0
1
0
1
0
0
1
2
0
0
1
1
3
1
1
2
1
1
1
2
0
0
2
1
0
2
2
0
2
2
1
1
1
1
2
1
0
1
1
1
1
1
1
0
2
1
2
1
1
1
0
2
1
0
2
2
0
1
1
0
2
0
1
0
2
1
1
3
1
1
2
0
2
2
0
0
1
1
1
1
1
1
2
1
1
0
2
1
0
2
0
2
1
2
0
1
1
1
1
0
0
1
2
1
1
1
1
2
1
0
1
1
2
1
2
2
1
1
1
1
2
2
1
1
1
2
0
1
2
1
2
0
0
1
0
2
2
1
1
0
1
0
1
1
1
0
1
2
2
1
1
1
2
0
1
1
0
1
1
1
1
0
1
2
2
0
1
1
2
1
1
1
1
2
1
2
2
2
1
0
0
1
1
0
1
0
1
2
2
1
2
1
1
0
1
0
1
1
1
1
4
1
1
0
2
1
1
2
1
1
1
1
1
1
0
2
0
1
2
2
1
1
1
0
1
1
2
2
1
1
1
3
0
1
0
0
1
1
1
0
2
1
1
1
1
2
0
1
1
0
1
1
0
2
1
1
1
1
0
0
1
2
0
1
0
1
2
1
2
1
1
1
1
0
1
1
1
0
2
0
3
2
2
1
2
0
1
2
1
0
2
1
1
0
1
1
1
1
2
0
0
1
0
1
0
1
0
2
0
1
0
2
2
1
2
0
0
0
2
1
1
1
0
1
2
1
2
0
0
2
1
0
1
1
0
1
0
4
1
0
0
0
1
0
0
0
2
2
2
0
0
1
1
0
2
1
2
3
1
2
0
1
2
1
1
0
2
1
1
0
2
1
2
1
2
2
1
2
2
1
1
1
0
2
1
1
1
1
1
2
1
0
2
1
0
0
1
1
2
0
1
1
1
0
0
0
0
0
0
1
1
1
1
1
2
1
2
0
0
2
0
1
0
1
1
0
2
2
1
1
1
2
1
2
1
1
0
1
1
1
2
0
1
0
1
1
2
1
1
2
1
1
0
1
1
1
2
2
1
1
2
0
2
1
2
1
1
1
0
1
2
0
0
2
1
2
1
1
1
2
1
1
0
2
0
0
1
1
0
1
1
0
1
2
1
1
2
1
2
1
1
0
2
1
2
2
1
2
1
0
2
2
1
0
1
2
1
1
1
0
2
0
2
2
1
1
1
1
2
0
2
1
0
2
2
1
1
1
2
0
0
2
1
1
2
0
1
0
1
0
1
1
0
1
0
1
0
1
0
1
1
2
2
2
2
1
2
1
1
1
1
2
2
2
2
2
1
1
1
2
3
1
1
1
0
2
1
1
2
0
1
2
2
0
2
0
1
0
1
1
0
1
2
2
0
1
1
1
1
0
1
2
2
1
1
0
1
2
1
1
1
1
1
0
1
1
1
1
2
1
2
2
0
0
0
2
0
0
1
0
2
1
1
2
1
1
2
1
1
1
2
1
2
1
1
1
0
2
1
1
0
1
1
1
1
0
2
1
0
1
1
1
1
2
0
1
1
1
2
2
1
2
1
1
1
1
1
1
3
1
2
2
0
1
0
2
1
1
0
2
1
0
2
1
1
1
2
1
2
1
0
0
1
0
1
2
2
1
1
0
1
1
2
0
1
1
2
0
2
2
0
1
1
2
2
1
1
2
0
2
1
2
1
2
0
0
2
1
2
0
2
2
1
1
1
1
2
1
1
0
1
2
1
1
1
1
2
1
2
0
1
2
2
2
0
1
2
1
0
1
0
1
1
0
2
2
1
0
1
0
1
1
1
1
0
1
0
1
0
1
1
1
1
1
2
1
2
2
1
1
1
2
1
1
1
2
1
0
1
0
1
1
2
2
0
0
0
1
1
1
1
1
0
1
1
1
1
0
2
1
0
0
1
1
0
1
1
2
1
2
1
2
1
0
1
0
1
0
1
1
3
0
1
1
2
1
1
3
0
0
1
1
1
2
1
1
1
1
0
2
2
1
2
1
1
1
1
0
1
1
1
2
2
1
2
0
0
2
1
0
2
2
2
1
0
2
2
1
2
2
1
4
0
2
2
2
1
1
1
1
1
1
2
2
1
2
0
1
0
0
2
2
2
2
0
0
3
1
1
2
0
1
1
1
0
0
1
1
0
1
2
1
0
0
1
0
2
2
2
1
1
2
1
2
1
0
1
0
2
1
0
1
2
2
1
0
0
1
1
1
2
1
1
0
0
0
2
1
1
2
1
0
1
1
1
1
0
0
2
1
1
2
1
2
0
0
1
1
3
2
0
2
2
0
1
1
1
1
2
1
1
1
2
1
0
1
2
1
1
1
1
0
2
1
1
0
1
1
1
0
0
0
1
1
1
0
1
1
1
1
0
2
2
1
0
0
2
0
1
1
2
1
1
0
1
1
1
1
1
0
1
2
1
0
0
0
1
1
0
1
0
1
1
1
1
1
1
1
1
0
1
2
0
0
3
1
1
1
1
1
1
0
1
1
2
1
1
1
1
1
1
0
0
1
1
1
2
2
0
0
0
2
1
1
2
1
0
1
0
1
0
1
1
1
1
1
1
3
2
2
1
0
1
1
1
1
2
1
2
0
1
1
1
2
2
1
0
1
1
1
2
3
1
1
1
1
1
1
2
0
2
1
1
0
1
1
2
1
1
1
2
1
0
2
1
0
2
1
1
1
2
1
0
1
1
1
1
1
0
0
0
0
1
1
1
1
1
2
2
3
0
0
1
0
1
1
2
0
1
0
2
2
0
0
1
2
1
2
1
1
2
2
2
1
1
1
1
1
1
1
0
1
1
0
1
0
1
1
0
0
1
1
1
0
1
1
1
1
2
1
0
0
1
0
0
2
1
2
1
1
3
1
0
1
2
0
0
2
1
0
1
1
1
1
1
0
1
1
1
0
1
1
1
1
2
1
1
1
0
0
2
1
1
1
3
1
2
1
1
2
3
1
2
1
0
0
0
1
1
1
2
1
1
0
1
1
1
2
0
1
0
1
2
1
0
1
2
1
0
0
2
2
1
1
1
2
1
2
1
1
0
1
1
1
0
1
0
1
0
0
1
2
2
1
2
1
1
2
0
2
0
1
2
2
1
1
1
1
2
2
1
1
2
1
1
1
0
2
1
1
1
2
1
2
0
2
1
1
1
1
1
0
0
1
0
1
1
1
1
1
1
1
0
2
1
1
0
1
0
1
0
0
2
1
1
2
1
0
1
1
0
0
1
1
2
1
1
0
1
0
0
0
4
0
0
2
2
1
2
1
1
1
0
0
0
3
2
0
1
1
1
2
0
2
1
1
1
1
0
2
1
0
2
0
1
2
0
1
1
2
1
0
2
4
1
1
0
1
1
2
1
1
1
1
0
1
1
2
2
1
0
1
2
0
1
1
1
1
1
0
1
1
1
1
3
0
1
1
0
1
1
0
1
2
1
1
1
1
1
2
0
1
0
2
0
2
1
1
1
0
1
2
2
2
1
1
1
1
1
1
2
1
1
0
0
0
2
1
0
1
1
1
1
2
2
1
2
1
0
0
1
1
1
1
1
1
3
1
0
1
0
3
1
1
1
1
2
2
0
0
2
1
1
1
0
1
1
0
1
0
0
0
1
2
1
2
1
1
2
1
0
0
2
1
1
1
2
1
2
1
1
0
2
1
1
1
1
1
1
1
1
2
2
1
1
1
1
2
0
1
0
1
0
1
1
0
2
2
2
1
1
0
0
1
1
0
1
2
1
1
1
0
0
2
0
0
1
0
1
2
1
1
0
1
1
0
2
1
0
1
2
2
2
0
1
2
0
1
2
2
2
2
1
0
1
1
1
1
2
2
0
1
2
1
1
1
0
1
0
1
2
2
1
2
0
2
1
0
1
1
2
1
1
1
1
1
1
2
1
0
2
1
2
0
1
1
0
1
2
2
0
0
2
1
2
1
2
0
2
2
1
1
1
1
2
1
1
1
0
1
1
1
1
1
1
2
1
1
1
2
0
0
1
1
1
0
2
0
0
1
2
1
1
1
1
1
2
1
2
1
1
0
0
2
1
1
0
2
1
2
0
1
1
0
1
0
1
2
1
0
2
0
1
0
1
1
2
2
1
0
1
0
1
0
2
1
1
1
0
1
1
1
2
1
1
1
0
1
1
0
1
1
1
2
0
1
2
1
1
1
0
1
1
2
1
1
2
2
1
1
1
1
1
1
1
0
2
1
0
0
1
1
0
1
1
1
1
1
1
0
0
1
1
1
2
1
0
1
1
0
1
1
2
2
2
0
2
1
1
1
2
2
1
1
2
1
1
0
0
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
0
1
2
2
1
1
2
1
1
2
0
1
2
1
1
1
2
2
0
1
1
0
1
1
1
1
2
1
2
0
2
1
1
1
2
0
0
0
1
1
0
1
0
2
1
2
2
2
1
0
2
2
0
0
1
1
0
0
2
2
1
1
0
1
0
0
2
0
2
1
1
1
1
1
2
2
0
1
1
0
1
0
1
2
2
1
1
1
1
1
0
1
1
2
0
1
1
2
0
0
0
1
1
1
0
1
1
2
0
2
1
1
0
2
0
2
1
1
2
2
1
1
0
1
0
1
1
2
1
0
0
1
0
0
0
0
1
1
1
1
1
1
1
2
0
2
0
1
1
1
1
1
1
2
1
1
1
0
0
1
1
0
1
1
1
2
1
0
1
1
2
1
1
1
0
1
1
1
1
0
2
1
1
0
1
1
0
2
2
0
1
2
1
2
1
0
1
2
3
2
1
0
1
1
2
2
0
0
0
1
1
0
1
1
1
2
1
1
1
0
2
0
0
0
1
2
1
1
2
1
0
1
1
0
1
0
0
2
2
0
2
1
1
2
1
2
1
2
0
0
1
1
0
1
1
0
2
1
1
2
1
2
0
0
1
0
2
2
2
2
0
0
1
1
1
0
0
1
1
1
0
1
0
1
1
2
2
0
1
2
2
2
0
1
2
0
2
1
2
0
1
0
1
0
1
2
1
1
0
1
1
2
1
1
2
0
1
1
2
0
1
0
1
2
1
0
0
2
2
1
0
1
1
1
1
0
1
2
0
0
2
1
3
0
1
1
0
1
0
1
1
1
1
1
0
2
1
1
2
1
2
2
0
2
1
1
1
0
2
2
0
1
1
2
1
1
1
0
1
1
1
0
0
0
1
1
0
2
2
0
0
2
2
0
2
1
1
1
2
1
2
1
0
1
2
1
1
0
0
0
2
2
1
2
1
1
1
2
2
0
2
2
2
0
0
1
1
1
0
1
1
1
0
1
1
1
0
0
0
0
0
1
2
1
2
2
0
1
0
0
1
0
1
0
2
1
0
0
0
2
3
1
0
1
0
1
1
1
0
2
1
2
2
0
1
1
1
1
1
1
0
0
1
1
1
1
0
0
1
1
1
0
1
0
0
2
0
1
1
3
1
1
2
1
1
2
0
0
2
0
1
1
1
0
0
2
1
1
1
1
0
0
0
1
2
1
1
2
0
0
0
0
0
1
1
1
1
1
2
1
1
2
1
1
0
1
0
2
1
1
1
3
1
0
0
2
2
0
1
1
1
1
0
2
1
2
0
3
1
1
1
1
2
1
1
0
2
1
0
2
0
1
1
2
0
0
1
0
1
0
2
0
0
1
0
1
2
0
6
0
0
1
1
1
1
1
2
2
1
1
1
1
2
0
0
1
1
2
1
1
2
1
1
0
2
1
0
2
1
1
1
2
2
1
2
2
0
1
1
2
1
1
0
2
1
1
3
2
0
1
1
0
1
2
0
1
1
1
0
1
0
1
0
0
1
2
1
2
1
1
1
1
1
1
2
2
1
1
2
1
2
1
1
2
1
1
1
1
1
0
0
2
2
1
1
1
1
1
1
1
0
0
1
3
1
2
1
0
1
0
0
0
1
2
0
1
1
2
2
0
1
1
2
1
1
0
0
1
1
1
1
0
1
1
1
3
1
1
1
1
1
2
0
1
0
1
0
0
2
0
0
0
2
1
2
2
2
0
0
0
1
2
2
0
2
0
1
2
2
1
1
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
2
2
1
1
1
1
2
1
1
2
2
1
1
1
2
1
2
1
1
1
2
2
1
2
1
0
2
2
2
1
0
0
0
1
0
0
1
1
0
1
0
1
1
1
1
1
0
2
0
1
2
2
2
0
0
2
0
1
2
1
1
1
1
1
0
1
1
1
1
1
2
1
1
1
1
1
2
0
0
1
2
1
1
0
2
1
2
1
1
2
1
0
1
1
0
0
1
0
2
1
0
1
0
3
0
1
2
1
0
1
1
0
1
1
0
1
1
1
0
0
1
1
2
0
1
1
1
1
1
0
0
1
1
2
2
2
2
1
1
0
1
2
1
2
1
1
1
1
1
2
2
0
1
1
2
1
1
2
1
0
2
1
0
3
1
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
0
0
1
1
1
0
2
1
1
2
2
1
2
2
1
0
1
2
2
2
1
1
1
0
1
1
1
1
2
2
2
1
1
2
1
0
1
2
1
1
1
1
0
2
1
2
0
1
1
2
1
0
1
2
1
0
2
1
1
2
0
2
2
0
1
0
0
0
0
1
1
0
2
0
2
2
1
1
0
2
2
2
1
1
1
1
2
1
1
2
1
0
2
2
0
1
2
1
1
2
1
1
1
2
0
0
2
1
2
0
1
0
1
1
1
1
1
1
1
0
1
1
2
1
1
2
1
0
1
1
0
1
0
2
1
2
1
1
0
3
1
0
1
1
0
1
1
1
1
2
0
1
2
0
1
2
1
0
2
1
1
1
0
0
2
1
1
2
0
2
1
2
0
1
2
1
0
1
1
3
1
2
1
1
1
1
1
1
1
2
1
1
1
1
2
1
0
2
1
0
2
1
1
0
1
1
1
1
0
1
1
2
0
0
1
0
1
2
1
1
1
0
2
0
1
1
1
0
0
1
2
1
2
1
2
0
1
1
2
0
2
0
0
1
2
0
1
1
2
0
0
1
2
1
2
0
2
0
0
1
2
1
0
0
3
1
0
0
0
1
0
2
1
2
1
2
2
1
1
2
0
1
1
2
2
1
0
1
1
1
1
0
2
1
1
1
0
2
1
1
1
1
1
1
1
2
0
1
2
1
1
1
0
1
1
1
1
2
1
2
1
2
1
1
0
2
1
1
0
1
1
1
2
1
0
2
1
1
0
1
1
0
2
0
1
2
1
1
1
2
1
1
0
2
2
4
1
1
1
2
1
2
1
0
0
1
0
0
2
2
1
0
2
0
1
1
0
1
1
1
2
0
1
1
1
0
1
1
1
0
2
2
1
2
1
2
1
2
1
1
2
2
0
1
1
1
1
1
1
1
1
2
2
0
0
0
2
1
0
1
2
0
0
2
1
0
0
1
1
0
1
2
2
1
1
3
2
1
2
2
1
2
1
2
1
2
0
0
2
2
1
0
1
0
0
0
2
1
1
2
1
1
1
2
2
1
2
1
2
2
0
1
2
0
1
2
2
1
0
2
0
0
1
1
2
0
2
2
1
1
1
1
0
1
3
2
1
1
1
2
1
1
1
1
1
0
1
1
2
0
0
2
2
1
1
1
3
1
2
0
2
1
1
1
1
1
0
2
1
1
0
1
0
1
0
1
1
1
2
0
1
1
0
0
1
1
1
2
2
1
0
1
0
1
1
1
1
1
0
0
1
2
1
1
1
2
2
1
1
1
0
1
0
1
1
1
0
0
0
1
1
2
0
0
0
1
1
0
1
1
1
1
2
2
2
2
1
1
0
1
1
1
1
1
2
1
1
2
2
2
2
0
0
2
1
2
2
0
2
2
2
1
1
0
0
0
0
0
1
1
2
2
0
1
1
2
1
2
0
0
0
1
2
0
0
2
1
2
1
2
3
0
1
1
2
0
0
0
1
1
0
2
2
1
0
1
1
0
1
0
0
0
1
1
2
1
2
1
1
1
1
1
1
1
0
2
1
1
1
2
1
1
1
4
0
1
1
0
0
2
2
0
2
1
0
1
1
2
2
1
0
2
0
2
1
2
1
1
2
0
0
2
2
1
1
0
0
1
2
1
2
1
1
2
0
2
2
1
1
1
1
1
1
4
0
1
1
2
0
1
0
2
1
1
2
0
1
2
1
0
1
1
2
1
0
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
2
1
2
1
1
2
1
2
2
1
1
1
1
1
2
2
1
1
0
1
1
1
1
0
1
2
1
1
2
1
0
1
1
1
1
0
0
0
1
1
2
0
1
0
1
1
1
2
2
1
3
1
1
0
1
1
2
1
0
0
1
2
1
1
2
0
0
2
2
1
1
0
1
1
0
1
1
1
1
2
1
2
0
2
1
2
1
1
1
1
1
1
1
2
1
0
0
1
1
1
1
1
1
1
1
1
3
2
0
1
2
1
0
0
1
1
2
1
1
1
1
1
1
1
2
1
1
1
0
0
2
2
0
2
1
1
1
1
0
1
0
1
1
2
1
2
1
1
2
1
1
2
1
2
1
0
2
1
0
2
1
1
1
1
0
1
2
0
0
1
1
1
1
1
1
2
1
1
5
1
2
1
0
1
0
0
1
0
1
0
2
1
1
3
0
0
1
1
1
1
2
1
2
1
0
2
1
2
0
1
2
0
0
1
0
1
1
1
2
1
2
0
2
1
1
1
1
1
0
1
1
1
1
1
2
1
1
1
2
1
1
1
2
2
1
2
1
1
2
1
1
0
0
2
2
1
2
0
1
1
2
1
1
1
2
1
2
1
2
2
2
1
0
1
1
1
1
2
1
0
0
1
1
1
1
2
7
0
2
1
2
2
0
1
1
1
0
1
1
0
1
1
1
0
1
2
1
1
0
1
0
1
2
0
0
0
1
1
2
0
2
1
1
0
2
1
2
2
2
1
2
0
1
1
0
1
2
1
1
0
2
1
2
1
2
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
0
2
1
2
1
1
0
2
1
0
1
1
0
0
0
2
0
2
2
0
0
1
1
2
1
1
1
1
2
1
0
1
0
1
0
1
0
0
1
2
1
2
1
2
0
2
2
1
1
1
1
0
1
1
1
0
2
2
2
1
1
2
1
0
1
2
2
0
2
1
2
1
1
1
3
0
0
0
2
2
1
2
0
1
0
1
2
2
1
0
2
2
2
1
1
1
0
0
0
2
2
3
1
1
2
1
1
2
1
2
1
2
1
2
2
1
2
1
2
0
1
2
1
1
1
2
1
0
1
2
1
2
2
1
2
0
1
2
2
2
2
2
0
1
0
2
1
1
0
0
1
1
1
2
0
0
1
1
1
1
0
1
1
1
1
1
0
1
0
1
1
1
1
1
1
1
1
1
1
0
1
2
1
2
2
2
2
1
2
1
1
0
2
0
2
0
3
1
1
1
2
1
1
1
1
0
1
1
2
1
1
1
1
2
1
2
1
2
1
1
2
1
0
1
2
2
1
2
2
0
1
1
2
1
1
1
2
1
2
1
2
1
1
1
1
1
0
1
1
0
1
0
0
1
0
1
0
1
1
0
0
3
2
1
0
2
1
1
2
2
2
2
1
2
2
0
0
1
1
0
1
2
0
1
1
2
2
1
1
1
1
0
2
1
2
2
1
2
2
2
1
0
1
1
2
0
1
1
2
0
2
0
2
2
2
1
2
1
0
0
1
1
1
1
0
1
0
1
2
1
0
1
2
1
0
0
0
2
1
1
1
1
0
0
2
2
2
0
2
1
1
1
2
2
1
3
1
2
0
1
2
0
1
0
2
0
1
1
1
0
2
1
2
1
1
1
1
1
2
0
2
1
1
1
1
2
2
1
1
1
1
2
1
0
1
0
0
3
2
1
1
2
1
0
2
2
1
1
1
0
1
1
0
1
1
0
1
2
0
2
0
0
0
1
1
1
2
0
1
1
1
2
2
0
2
0
0
1
2
1
2
0
1
1
2
1
0
2
1
0
1
0
1
0
1
2
1
1
1
1
2
0
1
2
0
1
1
1
2
2
2
0
0
1
1
1
1
1
2
1
0
1
1
2
1
1
1
1
0
0
1
1
2
0
0
1
1
2
1
2
0
1
1
1
1
1
0
1
0
0
1
1
0
2
2
0
1
0
1
2
2
0
1
0
1
2
0
0
2
1
3
0
2
1
1
0
0
1
1
1
2
0
2
1
1
2
1
2
1
1
1
1
1
0
3
1
2
1
1
1
1
2
1
0
0
1
0
1
1
0
1
0
2
1
1
4
2
2
1
4
1
0
1
1
1
0
0
1
1
2
1
1
2
2
1
0
0
2
0
1
0
2
1
0
1
0
0
2
2
0
2
1
1
1
2
1
1
1
1
1
2
0
0
1
0
0
1
1
2
1
0
1
1
1
0
1
2
1
2
0
1
2
2
1
0
1
0
1
0
2
0
1
1
2
0
1
1
0
3
1
1
2
2
2
0
1
1
1
1
1
1
5
1
1
1
0
0
0
1
2
2
1
1
2
1
0
2
1
3
0
1
2
1
1
1
1
1
1
0
0
1
1
0
1
0
0
1
1
0
1
1
2
2
1
1
2
1
1
1
1
1
2
1
1
0
0
0
1
0
1
2
1
1
1
2
1
2
1
0
0
1
2
1
2
1
1
1
2
1
2
1
1
1
1
2
2
1
2
2
1
0
0
1
0
2
2
1
1
1
0
2
1
2
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
0
1
2
0
2
1
0
1
1
1
0
0
0
1
1
1
1
1
2
0
1
0
2
0
0
2
2
1
2
0
0
2
1
1
1
1
1
1
2
2
1
2
1
0
1
1
2
1
1
0
3
0
2
4
1
1
2
1
2
1
1
1
0
4
1
1
1
2
1
2
1
0
0
1
1
1
1
1
1
2
0
1
1
1
1
0
1
1
0
0
2
1
1
1
1
2
0
0
1
1
1
1
1
1
3
1
2
0
2
1
0
1
1
1
2
1
0
1
2
0
1
0
1
1
1
1
1
3
2
0
2
0
2
0
1
1
1
2
0
2
0
0
0
0
1
1
1
1
1
0
2
3
1
0
1
0
1
0
2
1
1
1
1
1
1
1
1
1
0
1
1
1
2
0
0
2
1
1
1
1
1
2
0
1
0
2
1
1
0
2
1
0
2
0
1
1
1
1
1
1
2
1
0
2
1
1
1
1
2
2
1
1
2
0
0
1
1
1
1
1
2
1
2
2
1
1
2
2
1
2
2
1
1
1
1
1
1
0
0
1
1
2
0
0
1
0
0
0
0
1
1
1
0
1
1
1
1
1
0
0
2
0
1
0
1
2
1
1
1
2
1
1
2
1
1
0
1
1
1
1
2
2
1
1
1
0
1
1
1
0
0
1
0
0
2
1
2
2
2
2
2
0
0
1
1
2
0
1
0
0
0
1
2
1
1
1
1
1
0
1
2
1
2
0
1
1
0
1
1
1
1
2
1
2
2
2
2
1
1
2
2
0
0
1
1
1
0
1
0
1
1
1
0
1
1
2
1
1
1
2
1
2
1
0
1
2
1
0
1
1
0
0
1
1
1
1
2
2
1
0
1
1
1
7
1
1
1
1
0
1
0
1
0
2
2
1
2
0
0
2
2
1
0
2
2
0
1
1
0
1
1
1
1
2
1
1
0
2
1
2
1
0
1
1
0
1
1
1
0
2
1
0
2
1
1
2
1
0
1
0
1
0
1
0
1
1
0
2
1
1
1
1
2
1
0
1
2
1
1
0
2
0
1
1
2
1
1
2
1
1
1
1
1
1
0
1
1
1
0
1
2
0
1
1
1
1
2
1
0
0
1
1
2
0
0
0
1
1
1
2
2
2
1
1
0
1
1
1
0
1
1
0
0
0
2
0
2
0
0
2
2
1
1
2
1
1
1
0
1
2
1
2
0
0
1
1
0
0
1
1
1
1
0
2
2
1
1
1
1
2
0
2
2
1
1
1
2
2
0
1
1
0
1
1
1
2
2
0
1
0
0
2
1
2
0
1
2
1
1
2
0
1
0
1
0
0
1
0
2
0
2
2
1
1
2
1
2
1
1
0
1
1
3
1
1
0
1
1
0
2
1
1
2
3
2
2
1
1
1
1
1
0
1
2
1
1
1
1
0
1
1
0
0
2
1
0
0
0
0
0
3
2
1
2
2
2
2
1
2
1
1
1
1
0
2
1
0
1
1
1
1
1
1
2
0
1
2
1
0
1
1
1
1
2
1
2
1
1
0
1
1
1
2
1
1
1
1
0
1
1
1
1
1
0
0
2
2
1
1
1
1
2
2
0
0
1
0
0
1
1
0
1
1
1
1
1
0
1
1
1
1
2
1
1
2
1
1
2
1
1
2
0
0
1
1
1
0
1
1
1
1
1
1
0
1
1
1
1
1
1
2
1
1
1
1
2
2
1
2
0
0
1
0
1
0
1
2
1
2
1
1
1
0
1
1
1
2
0
1
1
1
1
1
1
1
0
0
1
2
1
0
1
1
1
0
0
2
1
1
1
0
1
1
0
1
1
0
0
1
2
1
1
1
0
1
2
0
1
1
2
1
1
0
1
0
2
1
1
2
0
0
2
0
1
0
1
2
1
2
0
1
1
2
1
1
1
1
1
2
1
1
2
2
0
0
1
1
1
0
0
2
2
0
0
1
1
1
0
1
2
0
2
2
1
1
1
1
2
1
1
2
2
0
0
2
1
1
0
0
2
0
1
1
1
1
0
1
2
2
2
1
2
1
1
1
0
1
0
0
0
0
0
2
2
0
1
1
1
1
1
1
1
0
2
0
1
1
4
1
1
2
1
2
0
2
1
0
2
0
1
1
0
0
1
1
1
2
1
1
1
1
0
1
0
2
1
1
0
2
1
2
2
0
2
3
0
1
1
1
1
1
1
1
1
2
1
1
1
0
0
2
0
1
1
2
0
1
1
0
1
1
2
1
2
2
0
1
1
1
1
1
0
1
1
2
0
1
0
1
1
2
1
1
1
1
1
0
1
2
1
1
0
1
1
1
1
1
2
1
0
1
1
0
1
1
1
2
2
1
1
1
2
1
1
2
0
1
1
0
1
1
2
0
1
2
0
2
1
2
1
0
2
0
1
1
1
0
2
2
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
1
0
1
1
2
0
2
1
2
1
2
0
1
1
1
0
0
2
2
0
1
1
1
1
1
2
1
1
2
2
1
3
1
1
0
2
1
0
0
2
0
0
2
2
0
1
1
1
1
1
1
0
0
0
0
1
2
1
1
1
2
1
2
1
1
0
2
1
2
2
0
1
1
0
2
1
1
0
1
1
2
0
1
0
0
1
1
1
1
2
2
2
0
0
3
2
0
0
0
0
1
0
1
1
0
3
1
1
0
0
1
1
1
1
0
2
2
2
2
1
1
2
2
0
0
0
1
1
1
0
2
0
0
0
1
1
2
0
1
2
1
1
1
1
2
0
1
0
1
1
1
2
1
1
1
0
1
1
0
0
0
1
1
1
0
2
2
0
2
2
2
2
0
1
1
2
2
1
1
2
2
1
1
1
2
1
2
1
1
0
1
1
0
1
1
0
1
3
1
0
1
1
1
0
1
1
2
1
2
1
1
2
1
1
1
1
1
0
1
1
1
2
1
2
1
1
1
1
2
2
1
2
1
1
2
1
2
2
2
1
0
1
1
2
0
0
0
1
1
0
2
2
0
1
2
0
0
0
1
2
1
1
0
1
3
0
2
0
3
1
1
1
1
1
2
1
1
1
1
0
0
2
1
2
1
0
0
1
1
1
1
1
1
2
2
1
1
2
0
0
1
1
0
1
1
0
1
0
2
1
1
0
1
0
2
2
0
1
1
1
1
1
1
1
1
1
0
1
0
1
2
1
2
2
1
1
1
1
2
3
0
2
1
1
1
1
1
0
0
0
1
1
1
1
2
2
2
1
0
1
1
1
2
1
1
2
2
1
0
0
1
2
0
2
1
1
2
1
2
1
1
2
1
0
1
0
0
0
1
1
1
1
2
1
1
0
1
1
0
1
0
1
1
0
1
2
2
1
1
0
2
2
1
1
0
0
2
1
1
1
2
0
0
2
1
1
2
0
1
1
0
1
0
1
1
0
1
0
1
2
1
2
2
1
1
0
1
1
1
1
1
0
0
0
0
1
2
1
0
0
1
0
1
0
0
3
0
0
1
1
2
1
0
1
1
2
0
1
1
2
1
0
1
1
0
1
1
1
2
1
1
1
1
1
2
0
1
2
2
1
2
1
1
2
1
0
2
1
1
1
0
1
2
2
2
0
2
1
0
1
0
1
1
1
0
2
1
2
1
1
1
1
2
1
1
1
1
2
1
0
2
1
0
1
1
1
1
2
2
0
2
1
2
1
0
2
1
1
1
1
2
2
1
1
1
1
0
1
1
2
2
0
1
0
1
1
0
1
2
2
1
1
0
1
0
1
1
2
0
2
1
1
1
1
1
1
1
2
1
1
2
0
1
1
0
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
0
1
1
2
1
1
2
2
1
1
2
1
1
2
2
1
1
1
0
1
2
1
0
1
0
1
1
0
0
1
1
1
1
0
0
1
1
0
1
1
1
2
1
2
1
2
1
1
1
0
1
0
2
2
1
1
2
0
2
2
0
2
2
0
0
2
0
1
2
1
2
2
0
0
0
1
2
0
1
1
0
0
2
2
1
0
1
0
0
1
1
1
0
1
1
0
1
2
0
2
2
0
0
1
1
2
1
1
1
0
1
2
1
1
1
2
2
1
3
1
2
2
3
2
1
0
1
2
1
0
0
1
1
0
2
2
1
2
2
1
1
1
1
1
1
1
1
2
1
1
1
1
0
0
1
0
1
0
0
2
0
0
1
1
1
1
1
2
0
1
1
0
1
2
0
1
1
0
1
0
2
2
1
2
2
1
1
2
2
2
1
0
0
1
0
0
1
1
1
0
0
1
0
2
1
1
1
1
0
0
0
0
1
2
1
1
2
1
1
0
1
1
2
1
1
1
0
0
1
1
1
2
1
1
1
0
0
1
2
1
2
1
2
1
3
0
1
1
1
2
1
1
1
2
0
1
0
1
1
1
1
1
2
0
1
0
1
0
0
1
2
1
2
0
2
0
0
1
0
2
3
2
0
1
0
1
2
1
2
1
2
0
0
0
0
2
1
1
0
0
1
2
0
0
2
0
0
1
0
1
2
1
0
1
1
1
2
1
1
1
2
1
1
2
0
0
2
2
1
1
2
1
1
0
2
1
1
1
1
1
1
1
1
1
0
1
2
1
4
1
1
1
1
1
1
0
0
2
1
1
0
2
1
1
2
2
1
1
1
0
2
1
0
0
0
1
0
1
1
1
1
1
1
1
1
1
2
1
1
1
0
1
1
2
0
1
1
1
2
1
0
1
0
0
0
1
2
1
0
1
2
1
1
0
1
2
2
2
2
0
1
2
1
2
1
0
1
1
1
1
1
3
1
2
2
2
0
0
0
1
1
1
0
2
2
1
0
1
2
2
1
0
1
0
1
1
1
0
0
0
1
1
2
1
0
2
1
2
0
0
4
1
1
1
1
0
0
0
1
2
1
1
1
6
2
2
0
0
0
0
1
2
2
1
2
0
1
1
1
6
2
4
0
1
1
0
1
0
2
2
0
1
1
1
1
0
1
2
0
1
1
1
1
2
1
2
1
1
2
0
2
2
0
2
0
0
1
2
2
1
1
1
0
2
1
1
0
1
0
2
1
1
1
0
2
2
1
1
2
2
1
1
1
1
1
2
1
0
1
0
2
0
1
0
1
0
1
1
2
1
0
1
1
0
1
2
1
1
1
0
1
2
0
1
0
1
1
0
2
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
2
0
1
1
2
1
3
1
2
1
2
0
1
2
0
1
2
0
1
1
2
0
0
1
1
1
1
1
4
1
2
1
0
1
2
1
1
0
0
1
1
2
2
2
1
2
1
1
1
0
1
1
0
0
1
1
1
1
1
1
0
0
0
2
2
1
2
2
0
1
1
2
1
1
0
2
0
1
2
1
1
1
2
0
0
0
2
2
2
2
2
1
3
1
2
1
2
1
1
1
1
1
0
1
0
1
0
2
1
2
0
2
1
2
1
1
1
1
1
1
2
0
0
1
1
1
1
1
1
0
2
1
1
0
1
0
1
0
0
1
2
2
1
0
1
1
1
2
1
1
1
0
2
1
1
1
1
3
2
0
1
1
2
2
1
1
1
2
1
1
0
2
1
0
1
1
1
1
1
1
2
1
0
2
1
1
1
2
0
1
1
1
1
1
2
1
1
2
2
1
1
2
1
2
0
1
1
0
1
0
2
2
2
1
2
1
1
1
0
0
0
1
1
2
0
0
2
2
0
1
1
1
1
1
2
0
1
2
2
0
1
0
1
1
1
2
2
1
2
1
1
1
1
1
2
0
2
1
1
1
2
1
1
0
1
1
2
2
1
1
1
1
0
1
1
1
2
1
1
2
2
1
2
2
0
1
1
0
1
2
2
0
1
1
1
2
1
1
1
1
1
1
2
0
2
1
2
1
2
2
2
1
1
0
1
2
1
1
0
1
1
1
1
1
1
2
2
2
1
0
1
0
2
2
1
1
1
0
1
2
1
1
0
1
0
2
0
1
1
1
1
1
1
0
0
1
0
1
1
0
1
1
1
1
1
1
0
1
1
2
1
2
1
1
1
1
1
0
1
0
1
1
1
1
1
1
1
0
0
2
1
2
1
0
1
1
2
0
1
1
1
2
1
1
1
1
1
2
1
1
0
2
1
1
1
1
1
1
0
0
1
1
2
2
1
2
2
0
0
1
1
1
1
2
1
1
2
2
1
2
0
1
0
1
2
1
2
1
2
1
0
1
0
0
1
0
1
0
2
0
1
2
2
0
0
0
1
1
1
1
0
0
1
0
1
2
0
1
0
1
1
0
1
1
1
0
0
1
1
1
1
1
1
1
0
0
1
0
1
1
0
1
1
2
0
2
0
0
1
1
1
2
2
0
2
1
0
0
1
1
1
2
1
1
0
1
1
0
1
1
1
1
0
1
1
1
0
2
0
1
0
1
1
1
0
1
1
1
0
0
1
1
1
2
2
1
1
1
0
1
1
2
1
1
0
2
0
1
1
1
1
1
0
1
1
1
2
1
2
2
1
1
2
1
1
0
2
1
0
1
2
2
1
0
1
0
1
1
2
2
0
1
0
1
0
1
1
3
1
1
0
0
2
1
1
1
1
1
2
0
2
2
1
0
0
2
0
1
2
1
0
0
1
1
1
1
1
2
0
0
0
1
1
1
2
0
0
0
1
1
1
2
1
2
2
2
2
2
0
2
1
0
1
1
1
0
0
2
1
0
0
0
0
1
2
1
1
1
2
2
0
1
1
2
0
2
0
1
1
1
1
0
2
1
1
1
1
0
2
1
1
0
1
1
0
1
1
1
1
2
0
1
2
0
2
2
2
0
1
0
1
2
0
2
1
0
1
1
0
0
2
1
1
2
1
0
1
0
1
0
1
1
0
1
1
2
1
1
2
2
0
1
1
2
1
1
0
0
1
0
2
2
1
0
3
1
1
1
1
0
2
0
2
1
1
0
1
1
1
2
2
2
2
1
1
1
0
1
2
2
2
2
1
1
2
0
2
2
0
1
1
1
1
2
1
1
1
0
0
0
2
2
2
2
1
1
0
1
2
1
1
2
2
0
1
1
1
0
1
2
1
0
2
0
1
1
0
1
1
1
1
2
0
0
0
0
2
1
1
1
1
1
0
2
1
1
0
0
0
1
1
2
1
2
1
2
0
0
1
0
1
2
1
1
2
1
1
2
1
1
0
1
1
1
2
1
1
2
1
0
1
1
1
1
1
1
1
2
1
0
0
1
1
0
2
0
2
0
1
1
1
1
1
2
2
1
1
1
1
2
2
1
0
2
1
1
0
0
1
1
1
1
2
0
1
1
1
1
0
1
1
0
1
1
2
2
1
1
1
1
1
1
2
1
1
1
0
0
1
1
0
0
0
2
0
2
0
1
2
1
1
2
1
1
1
1
2
1
0
0
2
0
1
0
0
1
1
1
1
0
0
1
1
0
0
1
1
2
0
1
0
1
2
1
1
1
2
0
2
1
1
0
1
0
2
0
0
2
0
1
0
0
1
2
2
1
1
1
2
1
1
2
1
0
2
1
2
1
1
1
1
2
2
1
2
2
2
1
1
2
2
0
2
1
1
1
0
1
1
1
1
2
0
1
0
1
0
1
1
1
2
1
2
1
1
2
2
1
1
0
1
1
1
0
1
1
1
1
2
1
2
1
1
1
1
1
0
1
1
1
1
1
1
2
1
1
2
1
1
0
3
1
0
1
2
1
0
1
0
3
2
1
1
0
2
1
1
2
3
0
1
1
1
1
1
1
1
0
0
1
2
0
2
1
2
0
0
2
1
0
1
2
1
2
1
0
1
1
1
1
1
2
0
0
1
0
1
0
1
1
1
0
1
1
1
2
0
1
1
1
0
2
1
1
1
1
0
0
0
1
3
1
3
1
1
1
1
0
1
0
1
1
2
2
2
1
1
1
0
1
0
1
0
1
0
1
1
1
1
1
1
0
1
0
0
1
1
1
2
1
1
3
0
1
2
2
2
2
1
2
2
1
1
0
3
2
0
1
1
2
1
0
1
0
0
1
1
1
1
2
1
1
1
1
2
0
2
1
1
1
1
1
1
1
1
1
0
0
0
1
0
0
1
2
0
2
1
1
1
1
2
1
1
2
1
0
0
2
2
2
1
2
1
1
1
0
1
1
2
1
1
1
2
1
0
1
3
1
2
1
0
1
2
1
1
1
2
2
0
2
1
2
1
1
0
1
1
0
1
0
0
2
1
1
1
1
1
1
1
2
1
0
1
2
1
0
1
0
0
1
0
1
1
1
2
1
1
0
1
0
3
1
1
1
1
1
1
1
0
1
1
1
1
2
1
1
0
1
2
2
1
1
1
2
1
1
1
2
2
1
1
1
1
0
1
0
1
0
2
1
1
1
0
0
0
2
0
0
0
2
1
2
0
1
0
1
1
1
1
1
1
0
0
0
1
2
0
0
1
0
1
2
2
1
2
2
0
2
1
1
1
1
2
1
1
2
0
0
0
1
0
0
1
2
1
2
1
1
1
2
1
1
1
1
1
1
2
0
1
1
1
1
1
1
0
1
1
1
0
1
1
1
1
1
1
0
1
1
2
0
1
2
1
1
1
1
1
0
2
1
1
0
2
2
1
0
1
0
0
0
2
2
1
0
1
2
2
1
1
1
1
1
1
1
2
1
2
0
0
0
1
0
2
1
1
2
0
1
2
1
0
1
2
1
1
0
2
2
0
0
1
1
1
3
1
2
1
0
2
1
1
1
1
1
0
0
1
1
2
1
1
1
0
2
1
1
4
1
2
0
0
3
1
0
2
2
2
1
2
0
0
1
1
1
1
1
0
0
1
1
2
1
0
1
1
0
0
1
1
2
1
1
0
0
1
1
1
1
1
0
0
1
1
1
1
0
1
1
1
0
2
1
2
1
0
1
1
2
1
2
1
1
0
1
1
1
1
1
1
0
2
2
0
1
1
2
1
1
1
1
1
1
1
2
0
0
0
0
1
1
1
1
0
2
1
2
1
1
0
1
1
1
2
1
2
1
2
0
2
1
1
1
2
1
1
1
0
1
1
1
1
1
2
1
2
1
0
1
0
2
1
1
0
1
0
1
1
0
1
2
2
2
1
1
0
0
1
0
0
1
1
2
1
1
0
1
1
3
0
1
1
0
2
2
1
0
1
1
2
1
2
1
2
2
3
1
1
1
1
0
1
1
0
1
1
1
2
1
1
1
0
1
1
1
2
1
1
2
1
1
1
1
1
0
1
1
1
1
2
1
1
0
1
1
1
1
1
2
0
1
2
1
2
1
1
2
1
1
1
0
1
1
0
1
1
0
2
2
2
2
0
0
2
2
1
1
1
0
2
0
0
1
1
1
1
1
0
0
1
1
1
0
1
1
0
0
1
0
2
2
1
1
1
2
0
0
1
1
0
0
2
0
1
0
0
1
2
1
1
1
3
1
2
1
1
1
1
1
1
2
1
1
2
0
1
0
0
1
0
0
0
0
1
1
2
0
1
0
0
1
0
1
0
2
0
1
0
2
0
2
1
0
1
2
1
2
2
1
0
2
1
0
1
1
1
1
0
0
1
1
1
1
2
0
2
0
3
2
2
1
1
2
1
1
0
2
1
1
1
1
2
0
1
1
0
2
1
1
0
0
1
1
0
0
2
2
1
0
2
0
1
1
1
2
1
1
0
0
1
1
1
2
1
1
1
1
2
1
1
2
1
0
1
1
1
1
1
2
0
0
2
1
1
1
1
0
1
1
1
1
2
1
2
1
1
1
1
2
0
1
2
1
0
0
0
0
1
1
2
1
2
1
1
1
1
2
2
0
1
0
1
2
1
1
2
1
1
2
0
1
1
2
1
1
1
1
1
2
2
1
1
0
0
2
2
1
2
0
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
0
1
1
1
0
0
0
0
2
2
2
1
2
2
1
1
1
1
2
2
1
1
0
1
0
2
2
3
0
0
1
1
1
0
0
1
1
2
1
1
1
0
1
2
1
1
2
1
1
1
0
1
0
1
0
0
1
1
1
2
2
2
0
1
1
1
1
2
2
1
1
1
3
0
2
0
1
1
1
1
1
1
1
1
0
1
2
1
1
1
0
2
1
0
2
1
0
1
1
0
0
0
2
2
1
2
0
1
1
2
0
1
2
0
1
2
1
1
0
1
0
2
2
1
0
1
1
1
1
2
0
0
2
0
1
0
2
1
1
1
0
1
1
0
1
0
1
1
0
1
0
0
1
2
1
1
1
2
1
1
0
2
1
1
0
1
2
1
1
1
1
2
0
1
1
2
2
0
0
1
1
1
3
1
1
1
1
0
0
1
1
0
1
0
1
1
1
1
1
1
2
2
1
0
1
1
1
0
2
1
0
1
0
2
2
1
1
0
2
1
2
1
1
0
2
1
0
1
0
0
1
1
0
0
1
1
1
2
1
1
1
1
1
0
1
1
1
1
2
1
0
1
1
1
3
1
1
0
2
0
1
2
2
1
0
1
0
2
2
2
1
1
0
1
2
1
1
1
1
0
2
1
1
0
0
1
1
1
1
1
1
1
2
0
1
2
2
1
1
1
0
3
1
1
1
0
1
2
2
1
1
1
1
1
0
0
1
0
1
1
0
2
1
1
0
1
0
1
0
2
2
1
2
2
1
0
1
1
1
1
1
0
2
0
1
1
1
0
2
1
1
1
1
0
1
2
0
0
2
0
2
1
2
2
1
1
1
1
1
1
2
2
1
0
0
1
2
0
2
1
2
1
1
1
0
1
0
1
2
0
1
1
0
1
1
2
2
2
1
1
0
2
1
1
1
1
0
1
2
2
2
0
0
1
0
2
1
2
1
1
1
0
1
2
1
0
0
2
0
1
1
2
0
2
1
1
1
2
2
0
1
0
1
1
1
0
1
2
1
1
2
1
1
1
1
2
2
0
0
1
1
0
1
1
3
1
1
0
0
1
1
0
0
1
1
1
1
0
0
0
1
0
0
1
1
1
2
1
0
1
2
0
1
2
1
0
0
1
0
1
0
2
2
1
0
0
1
2
3
1
2
1
1
2
0
1
0
0
2
1
1
0
1
0
2
1
1
0
1
1
2
0
1
2
2
0
0
2
0
2
0
1
1
0
0
1
1
2
0
1
2
0
2
0
0
1
1
1
1
2
2
1
1
0
1
0
0
2
2
0
1
2
2
2
1
1
1
2
0
2
1
0
2
1
1
0
1
0
1
1
1
0
2
2
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
2
0
3
2
0
1
0
1
1
1
2
0
1
0
2
1
0
0
3
1
1
1
2
1
1
0
0
1
2
1
0
1
1
0
0
1
2
1
0
2
0
1
1
0
1
1
1
1
0
0
1
0
2
0
1
2
0
2
1
0
1
2
2
2
1
2
1
1
0
1
0
1
1
1
1
1
0
1
2
1
1
2
0
0
1
2
1
2
0
1
1
1
1
2
1
2
0
1
2
0
1
1
1
1
1
1
0
2
1
2
1
0
1
1
1
1
1
1
1
0
1
0
1
1
1
1
1
2
1
1
1
1
2
1
1
2
0
1
0
0
1
1
1
0
2
0
1
1
0
0
0
0
1
1
1
1
1
2
1
2
1
1
0
1
1
1
0
1
1
0
1
1
1
2
0
1
1
0
1
1
1
2
1
1
0
1
1
1
2
1
1
1
2
1
0
1
1
1
0
1
1
1
1
0
2
2
3
1
1
1
1
2
2
1
1
2
1
2
0
1
1
0
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
2
2
2
1
1
1
0
1
0
1
0
1
1
0
0
1
2
1
0
0
2
0
1
1
1
1
2
1
2
0
1
2
1
1
0
1
0
1
1
2
2
2
2
0
2
0
1
1
0
1
2
1
2
1
1
2
2
2
1
1
1
0
0
1
1
1
0
0
0
1
1
1
1
1
0
1
0
1
0
2
1
3
0
1
0
1
1
1
0
1
1
0
1
2
1
1
0
1
0
2
2
1
1
1
1
1
1
0
2
1
2
0
2
0
0
1
2
2
1
2
0
1
0
1
2
1
0
0
1
2
1
1
2
2
0
1
1
1
1
1
0
1
1
1
0
1
1
2
1
0
1
1
1
1
1
2
2
1
1
0
1
4
1
0
1
1
0
2
0
0
2
1
2
1
0
1
2
2
1
0
1
0
2
0
1
1
0
2
0
0
1
0
1
1
2
1
1
2
1
0
2
2
1
1
1
1
1
2
2
1
0
0
2
1
2
1
1
2
1
1
0
0
1
1
1
1
3
1
1
2
0
1
2
2
0
2
1
0
1
2
1
1
0
2
0
1
1
0
2
1
1
2
1
1
1
1
1
0
0
0
2
1
2
1
1
1
3
1
1
1
2
1
2
1
1
1
2
2
1
2
1
0
1
1
2
1
1
0
1
1
1
0
1
0
1
1
1
1
0
2
1
1
2
1
0
1
0
2
1
2
1
0
1
1
1
2
0
1
2
0
0
2
1
1
1
0
1
1
1
1
2
2
1
1
4
1
1
1
1
2
2
1
1
2
0
1
1
1
2
1
0
1
1
1
0
1
1
1
0
1
1
1
1
1
0
1
2
2
1
1
1
0
1
1
0
1
1
1
0
1
0
0
0
1
1
1
0
0
1
2
0
1
2
0
1
2
1
2
1
0
2
2
0
1
1
2
1
1
2
2
0
1
0
0
1
1
1
0
0
1
1
2
1
2
2
1
2
1
1
0
1
1
2
1
1
1
1
1
0
0
0
1
1
1
1
1
0
1
1
1
1
2
1
1
1
0
0
1
0
1
0
0
0
0
1
1
1
1
2
2
1
2
1
1
2
0
0
1
1
1
1
1
0
2
1
1
2
1
1
1
2
0
1
1
1
1
1
1
1
0
1
0
0
0
1
1
1
1
2
1
1
1
1
1
0
1
2
1
1
1
1
0
1
2
1
2
1
1
1
1
1
0
0
0
0
0
2
1
1
0
2
1
1
0
1
1
1
1
2
1
1
0
1
1
1
1
2
2
2
1
0
0
2
2
1
0
0
1
1
0
1
2
1
1
0
2
1
0
2
1
1
2
1
0
1
1
1
1
2
0
1
2
1
1
1
1
0
1
2
2
0
1
1
0
1
1
1
2
0
2
1
1
1
1
0
1
2
1
1
0
1
1
1
2
1
0
1
1
1
2
0
1
0
1
1
1
2
0
2
1
1
1
0
1
2
0
1
0
0
0
1
1
1
1
0
1
2
1
1
0
0
1
1
0
1
0
0
1
0
0
1
0
1
6
1
0
0
3
1
2
1
1
0
2
1
1
1
1
1
0
2
2
2
1
2
1
1
1
1
1
2
1
1
0
1
1
2
0
1
2
1
1
2
1
1
0
0
0
0
2
0
0
1
2
2
2
1
1
1
1
2
2
1
1
0
2
1
0
1
0
1
2
0
0
1
1
0
0
2
1
1
0
2
1
1
1
1
2
1
2
1
0
0
1
0
2
0
1
1
2
1
0
1
2
2
1
0
1
1
2
0
1
0
1
2
1
2
0
1
2
1
0
1
1
1
1
0
1
0
2
0
2
2
2
1
0
0
2
0
2
0
1
1
0
0
1
1
1
0
0
2
1
0
0
0
2
0
0
1
1
1
0
0
1
1
0
0
1
2
0
0
2
1
1
2
2
0
0
1
1
1
1
1
0
2
0
0
1
0
2
0
0
0
1
1
2
1
1
0
0
0
1
1
1
1
0
1
1
1
1
0
1
1
2
1
2
0
0
1
1
1
0
2
0
2
0
1
1
0
1
1
1
2
1
1
1
0
1
2
1
1
2
0
0
0
2
0
2
1
1
2
1
1
0
0
2
1
1
2
1
2
2
1
0
1
0
0
2
1
0
1
1
2
0
0
1
1
0
1
1
0
2
2
1
1
0
1
1
1
1
2
2
1
0
1
0
1
0
2
1
1
1
1
1
3
1
1
1
1
1
2
1
1
1
1
2
0
0
0
1
1
0
0
1
1
2
2
1
1
1
0
1
1
2
0
2
1
0
1
1
2
1
1
2
1
0
1
2
1
1
1
1
2
1
1
1
1
1
0
1
1
1
2
2
1
2
1
1
1
0
2
1
2
2
1
0
2
1
2
0
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
0
1
0
2
0
1
0
1
1
1
1
2
1
0
1
1
1
0
1
2
1
1
2
1
1
1
1
1
1
1
0
1
0
1
2
1
1
1
0
2
2
0
2
1
0
0
1
0
2
1
0
1
1
0
1
0
1
0
1
0
1
2
2
1
1
2
1
2
0
1
1
2
2
2
1
0
0
1
2
1
2
2
1
1
1
2
1
2
0
1
0
1
0
1
2
1
2
1
2
2
1
2
1
1
2
1
0
0
1
1
1
1
2
1
1
0
1
0
1
0
0
1
1
0
1
1
1
0
1
0
1
1
0
1
2
1
1
1
1
2
1
0
1
2
2
2
1
0
0
1
1
0
1
0
0
1
0
0
1
1
2
1
1
1
0
1
0
2
1
0
1
2
0
0
2
1
0
0
1
1
1
1
1
0
0
2
1
1
0
2
0
1
2
2
1
1
2
1
1
1
0
2
2
1
1
1
1
0
0
0
0
2
2
2
2
0
0
2
2
1
2
1
1
1
0
1
0
0
0
0
1
0
1
1
1
2
1
1
2
1
1
3
1
0
1
2
1
1
1
1
1
1
1
1
0
0
2
2
0
2
2
2
1
1
2
0
2
2
1
0
2
1
0
1
1
2
1
2
1
1
1
0
1
0
1
2
1
1
2
2
0
1
1
0
1
1
0
0
1
2
1
1
1
0
0
1
1
2
1
1
1
1
0
1
1
1
1
1
1
1
0
2
0
2
2
1
1
0
0
0
1
1
1
2
1
1
1
1
2
2
2
1
1
1
1
0
1
2
0
0
1
0
1
1
2
1
1
2
1
1
2
1
2
0
1
1
1
1
1
0
1
1
1
1
1
1
1
0
1
1
1
1
1
1
2
0
2
1
1
1
1
1
3
1
0
0
0
0
1
1
2
2
1
1
2
0
1
0
1
1
1
2
1
0
0
1
0
0
1
1
1
1
1
0
1
0
0
1
0
1
1
1
1
1
2
1
2
2
1
2
1
1
2
1
1
0
1
2
2
1
1
1
1
1
1
2
1
1
2
1
1
1
0
1
0
1
1
1
2
0
0
1
2
2
2
2
0
1
1
0
2
2
1
1
1
0
0
0
0
1
0
1
1
1
1
0
1
1
2
1
0
1
1
1
1
1
1
0
1
1
0
1
1
3
0
1
1
2
0
1
1
1
1
1
1
1
1
2
1
2
1
0
1
1
1
2
1
1
1
1
0
2
1
0
1
1
1
1
2
0
1
1
2
1
2
1
1
1
1
0
1
1
1
2
1
1
1
0
1
1
2
1
1
2
0
0
1
1
1
1
1
0
2
0
0
2
0
0
1
2
1
2
1
1
2
0
2
1
1
0
0
1
0
2
2
1
1
2
1
2
1
1
0
0
1
0
0
1
1
0
1
1
1
1
2
1
0
1
0
1
0
2
1
2
1
1
1
2
0
2
1
1
2
1
1
0
2
0
0
1
0
1
1
1
1
2
1
1
0
0
1
0
1
2
0
4
2
0
1
0
1
1
1
0
0
1
0
0
0
1
2
2
3
2
2
1
0
0
1
2
0
2
1
1
2
2
2
0
0
0
2
1
1
0
1
0
1
1
3
2
0
1
2
2
1
1
1
2
1
0
1
0
2
1
1
0
0
0
1
1
1
1
1
2
2
0
1
1
1
0
0
1
2
1
1
1
1
2
1
0
1
1
2
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
0
0
1
1
2
1
0
2
2
1
1
1
2
0
2
2
2
1
0
2
1
4
2
0
0
1
0
1
0
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
2
1
1
1
0
0
2
1
2
1
1
0
1
0
1
0
0
1
1
0
1
1
1
0
1
1
1
1
1
0
0
1
1
2
1
1
2
0
1
1
1
0
1
1
0
0
1
1
1
1
1
2
1
2
1
0
1
1
1
1
1
2
1
1
1
1
2
0
1
1
0
2
1
0
1
1
1
1
2
1
2
1
1
1
0
3
1
1
1
0
1
0
1
1
1
1
1
0
1
0
1
1
1
2
3
2
1
2
2
2
2
1
0
0
0
0
1
1
1
2
0
1
0
1
1
1
2
1
1
1
0
1
0
1
1
0
2
1
1
1
2
1
1
2
1
1
1
1
1
0
2
1
2
0
0
1
0
1
1
1
1
1
1
1
0
2
2
0
2
1
0
2
1
1
0
1
1
1
1
1
1
1
2
0
1
1
1
4
0
0
2
1
1
1
1
1
1
2
2
1
1
2
1
0
0
0
1
1
2
1
0
0
1
1
1
1
0
1
0
1
2
0
1
0
0
1
1
0
1
0
4
1
2
1
1
0
0
2
1
1
2
1
1
2
1
1
2
2
0
1
1
0
1
2
1
2
1
0
1
1
1
1
1
1
7
0
0
0
1
1
1
2
1
1
2
1
1
1
2
1
2
1
1
0
2
2
0
1
2
1
2
1
1
1
0
2
0
0
1
1
1
1
1
0
1
2
2
0
2
1
1
1
1
1
1
0
1
2
2
1
1
1
1
1
1
1
0
2
0
1
0
1
1
2
1
3
0
0
2
0
2
1
1
1
0
1
0
0
0
2
0
0
2
1
2
0
2
1
1
1
1
0
0
4
1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
3
2
0
1
1
1
1
2
0
0
2
1
1
1
1
1
2
1
0
0
1
2
1
1
1
1
2
2
1
1
2
2
2
2
0
0
1
1
1
1
0
0
0
1
0
1
1
1
1
1
1
1
0
0
0
1
0
1
2
0
1
0
1
1
2
0
0
0
1
0
2
0
1
1
2
0
1
1
2
0
2
1
1
1
1
1
1
1
0
1
2
2
0
1
1
1
1
2
1
2
1
1
2
1
0
0
2
1
2
1
1
0
1
1
1
1
1
0
0
0
0
1
1
2
1
2
1
0
2
1
0
2
1
1
1
1
2
1
1
0
1
0
0
1
1
2
1
1
1
2
0
0
1
1
2
1
1
1
1
1
1
2
1
1
1
0
1
0
1
1
0
1
1
1
1
1
0
0
1
1
1
0
2
0
0
2
1
1
1
1
2
2
1
3
2
1
2
1
1
1
1
1
2
2
1
1
1
0
1
1
1
2
0
1
1
2
0
1
0
1
1
0
2
1
1
0
1
0
0
2
0
1
2
1
1
1
0
1
0
0
2
1
1
1
1
1
0
3
0
1
1
1
1
1
0
2
1
1
1
0
1
2
1
1
1
2
0
2
1
1
1
1
1
1
0
1
1
2
2
1
1
1
1
2
1
1
1
1
0
0
0
1
1
0
1
0
0
1
1
1
0
1
2
1
0
2
1
2
1
1
0
1
1
0
0
2
4
1
1
1
1
1
0
1
1
1
1
1
2
1
1
0
1
1
1
1
1
1
0
0
1
1
1
1
1
1
1
1
2
2
1
2
0
2
1
1
2
0
1
2
2
2
2
0
0
1
2
1
0
1
1
0
1
0
2
1
2
0
1
1
0
1
0
2
3
1
0
0
0
2
1
1
1
2
1
1
1
1
0
1
0
1
1
1
1
1
1
1
1
2
1
2
0
1
0
1
2
1
1
1
1
1
2
1
1
2
0
2
2
1
0
2
2
1
1
1
2
1
1
0
1
2
1
1
1
2
1
1
1
1
1
2
1
1
2
0
0
1
2
2
1
1
1
1
2
1
1
0
1
1
1
2
1
1
0
2
0
1
2
1
1
1
0
1
1
2
1
1
4
1
0
1
0
1
1
2
1
1
0
0
1
1
2
2
1
0
1
2
1
0
1
0
1
2
0
1
1
2
2
0
2
1
1
0
1
1
2
3
1
2
2
1
0
2
1
2
1
1
1
2
0
0
0
0
1
1
0
2
0
1
1
1
1
2
1
1
0
2
0
1
1
2
1
1
1
1
1
2
1
0
0
1
1
2
2
2
1
0
1
1
1
1
1
1
1
1
1
0
0
0
1
1
3
0
1
2
1
2
0
1
1
2
1
2
1
0
0
1
1
1
1
0
2
1
2
0
1
1
1
0
1
0
1
1
0
1
0
1
0
2
1
2
0
1
2
1
1
1
0
1
2
0
0
0
1
1
1
1
1
0
1
0
2
1
0
2
1
2
1
1
1
1
2
1
1
2
0
1
1
3
0
2
0
0
2
1
0
1
1
1
1
2
0
0
2
0
1
0
1
1
1
2
0
0
1
0
0
2
2
1
0
1
2
1
1
0
0
1
1
1
2
0
1
1
1
2
1
1
1
0
0
2
1
1
2
2
2
1
1
1
0
2
1
0
0
2
1
1
0
1
1
1
1
1
1
0
0
1
1
0
2
0
1
0
2
1
2
1
2
1
0
1
2
1
0
2
1
2
2
1
1
0
2
1
0
1
2
1
2
1
1
1
3
0
0
0
0
1
2
1
1
0
1
2
1
0
0
2
1
2
2
1
0
1
2
2
0
1
1
0
1
0
0
1
1
2
1
1
0
0
1
2
0
1
2
2
1
2
1
1
3
0
1
1
1
2
1
0
1
1
1
1
2
2
1
1
2
1
0
1
1
2
2
0
2
1
1
0
1
1
1
1
1
2
2
1
2
1
1
0
2
1
1
1
2
1
1
1
2
0
2
1
1
0
1
1
2
0
1
2
2
1
1
2
1
1
1
1
2
1
2
1
2
2
1
0
1
1
1
0
0
1
1
1
0
1
1
1
2
0
1
0
2
1
2
0
1
1
2
1
2
1
0
1
1
0
2
1
0
1
0
0
0
1
2
0
0
0
2
1
2
0
1
1
1
1
1
1
2
0
1
1
1
1
1
1
1
1
0
1
0
0
0
2
0
2
0
2
1
2
0
1
0
2
1
0
1
1
1
1
2
0
1
2
1
2
2
1
0
0
2
1
1
1
2
1
0
1
2
2
1
1
2
2
1
0
2
1
1
1
2
1
1
1
1
1
0
0
1
1
1
0
1
1
1
1
1
1
1
0
1
1
2
1
1
0
1
0
1
1
2
2
1
1
2
2
0
1
1
2
2
2
1
2
1
0
2
1
1
1
1
1
1
0
0
0
1
0
2
1
0
2
1
1
1
0
1
0
1
0
1
0
1
1
1
0
2
2
0
1
2
1
1
1
1
1
2
1
1
1
0
0
1
1
1
1
2
0
1
2
0
0
1
0
1
0
1
0
0
0
2
1
0
1
0
0
1
1
1
0
2
0
1
1
1
0
2
1
1
0
1
2
2
0
0
1
1
1
1
1
3
2
0
2
3
0
1
2
1
0
1
0
1
1
1
2
1
1
0
1
1
0
1
1
1
1
2
1
1
2
1
1
1
1
0
2
1
2
2
0
1
2
1
2
0
1
0
2
1
1
1
1
1
2
1
2
2
2
1
1
1
2
1
1
1
2
2
2
1
1
1
2
0
1
0
1
0
1
0
1
2
2
1
1
1
0
2
0
0
1
0
1
2
1
1
1
1
1
2
1
0
2
0
1
1
2
1
2
0
2
1
1
1
1
1
2
1
1
1
0
2
1
0
0
0
0
3
1
1
0
2
2
1
2
1
0
1
2
1
1
1
0
0
2
2
0
1
2
1
1
2
1
1
1
0
1
2
1
1
1
1
0
1
1
2
1
2
1
1
2
0
1
1
1
1
3
0
2
2
1
2
1
0
1
1
0
1
0
2
0
0
3
1
2
2
1
2
0
1
2
2
2
1
1
1
2
1
2
0
1
2
0
1
0
1
1
0
2
2
1
2
0
0
0
1
0
0
1
2
0
1
0
0
2
2
1
1
1
1
1
1
0
0
2
2
0
1
0
3
0
1
3
1
1
1
1
1
0
0
2
1
0
2
0
1
1
1
1
1
2
1
2
1
1
1
1
1
1
0
2
1
2
1
1
1
2
2
1
0
1
1
2
0
1
1
0
1
1
1
0
0
1
0
1
1
2
0
1
1
0
0
0
1
1
0
1
0
1
1
1
1
0
2
0
1
2
0
0
2
0
1
1
2
2
0
3
1
1
2
2
1
0
1
1
1
2
0
0
1
2
1
1
1
0
1
2
1
1
1
1
1
0
0
1
2
2
0
1
0
1
1
2
0
0
1
1
0
1
1
2
2
1
0
1
1
1
1
1
2
0
2
1
2
2
0
1
1
0
1
1
2
2
0
1
1
1
2
1
2
1
1
1
0
0
0
2
0
0
1
1
1
0
1
1
1
0
1
0
1
1
1
1
0
2
0
1
1
1
2
1
0
0
0
1
1
2
2
1
0
0
1
1
1
4
0
2
1
1
0
1
1
0
1
1
2
1
1
0
1
1
1
0
1
1
1
0
1
1
2
0
0
2
1
0
1
1
1
1
2
1
1
1
1
1
1
1
0
2
2
2
1
1
1
2
0
2
2
1
1
1
1
1
1
1
1
2
0
2
1
1
1
1
0
1
2
0
1
0
1
1
2
1
1
1
2
0
1
0
0
2
1
1
0
1
1
0
2
1
1
1
1
1
1
1
2
1
1
1
2
1
1
2
2
2
0
2
2
0
1
1
2
1
0
1
1
1
1
1
1
2
1
0
1
1
1
0
1
0
2
1
1
3
1
1
1
1
2
0
1
1
1
1
1
1
0
1
2
1
0
1
0
2
0
1
0
0
2
1
1
1
2
1
2
0
1
1
1
2
1
1
0
1
1
2
1
2
1
2
1
1
0
1
1
1
1
1
0
2
0
1
0
1
2
2
2
2
0
2
1
1
1
1
2
1
0
1
1
2
2
2
0
1
1
2
0
2
1
0
2
1
2
1
1
1
0
0
1
1
1
2
1
2
2
1
1
2
2
0
1
0
0
0
1
0
2
1
0
1
1
2
0
1
0
2
1
0
1
1
1
1
0
1
1
2
0
1
1
2
1
1
2
1
2
2
1
1
2
1
0
1
0
2
2
0
1
0
1
0
1
1
0
1
2
1
1
2
1
1
1
1
1
0
0
1
1
1
1
1
1
0
0
2
0
1
0
0
1
1
1
1
0
1
1
0
1
0
1
2
2
1
1
1
2
1
0
1
0
2
2
1
1
2
0
1
1
2
1
2
2
0
1
2
2
1
1
1
1
1
1
0
1
1
2
2
2
2
1
1
0
2
1
2
1
1
1
2
2
0
1
0
1
2
0
1
1
1
0
2
1
0
0
1
2
0
0
1
1
1
0
1
1
1
2
0
1
1
2
1
1
1
2
2
1
2
1
0
2
1
0
2
1
1
1
1
0
0
1
2
0
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
0
0
2
2
0
2
1
1
0
2
0
2
1
0
1
2
2
0
2
1
2
0
2
0
0
2
1
1
1
0
1
0
1
1
5
0
1
1
2
0
2
1
0
1
1
1
1
2
0
1
1
1
1
0
1
1
1
1
1
1
3
1
2
1
1
0
1
1
2
0
1
1
1
1
3
1
0
2
1
2
1
1
1
1
1
1
2
2
1
2
2
0
1
0
2
0
0
1
1
1
1
1
0
0
2
2
2
1
1
0
3
1
0
1
1
0
1
1
1
0
1
1
1
2
1
1
1
1
1
1
0
2
1
1
0
2
1
1
1
1
2
0
1
1
1
1
0
2
1
1
0
2
1
1
1
3
1
2
1
1
1
2
0
1
0
1
0
1
1
1
1
0
1
1
1
1
0
2
1
2
2
1
1
0
0
2
1
0
2
1
1
1
1
2
1
1
1
1
2
1
1
0
1
0
1
1
1
1
0
0
1
0
0
1
0
1
1
2
0
1
2
1
1
2
0
0
1
1
1
1
1
0
1
1
1
1
1
0
1
0
1
0
1
0
1
1
1
1
1
0
1
1
1
1
1
2
1
1
1
1
2
1
0
1
0
1
0
1
1
1
1
1
1
0
4
1
0
1
1
1
2
1
1
0
1
2
2
0
2
1
0
2
1
0
1
1
1
1
1
0
1
2
1
2
1
1
1
0
1
1
1
2
1
1
1
1
0
2
0
1
1
1
1
2
2
1
1
0
0
0
1
1
0
0
1
0
2
2
1
2
2
1
1
0
1
1
2
0
1
0
1
2
1
2
3
1
1
1
1
2
2
0
0
2
1
1
2
2
0
1
2
1
0
1
2
0
1
2
1
1
2
2
1
2
2
3
0
2
0
2
2
1
0
2
0
1
1
0
1
0
2
0
2
1
2
2
1
0
1
1
0
2
2
2
0
1
1
2
1
0
2
2
2
1
0
2
1
2
0
1
2
1
1
0
1
1
2
1
1
1
1
2
0
3
1
1
1
0
0
1
1
1
1
1
1
2
1
1
0
1
2
0
1
0
1
0
1
0
1
0
1
2
2
1
2
1
1
1
1
1
2
2
0
2
2
0
1
2
0
2
0
0
2
2
1
0
1
0
2
0
1
2
2
0
1
0
1
1
2
0
1
1
1
1
0
0
1
1
0
1
1
1
1
1
0
1
2
1
1
1
2
2
1
1
0
1
1
2
1
1
1
0
1
1
1
2
1
2
1
2
1
2
2
2
2
1
2
1
2
1
2
2
2
2
2
2
2
1
1
1
1
0
2
0
1
0
0
1
1
0
1
0
0
1
0
1
1
1
1
1
0
2
0
1
0
1
2
2
1
1
1
1
1
1
1
1
0
1
0
1
1
1
1
1
1
1
0
1
1
0
1
2
1
1
0
1
0
0
1
1
1
2
1
0
1
1
2
0
2
0
1
3
1
1
1
0
0
1
1
1
2
0
1
1
2
1
0
0
1
1
0
2
1
1
1
1
0
2
0
0
1
0
0
1
1
1
1
1
1
0
1
1
3
1
1
2
0
0
1
0
1
2
0
2
1
2
0
1
1
1
3
0
2
1
0
0
2
0
2
1
1
1
2
0
1
1
1
0
2
0
0
1
2
1
0
0
2
2
2
1
1
1
1
1
1
2
1
2
1
0
0
0
2
1
2
2
2
1
1
1
1
1
1
1
2
0
1
2
0
0
1
1
2
1
1
1
2
0
2
1
2
1
3
4
1
1
1
2
0
0
1
1
0
0
0
1
1
1
0
2
1
1
1
2
1
2
2
1
1
1
1
2
2
2
0
2
1
0
1
0
1
1
1
1
1
0
1
1
1
1
2
1
1
0
0
1
1
1
1
1
1
2
1
2
0
1
1
1
1
1
1
0
0
2
0
1
1
0
1
1
1
4
1
0
1
1
3
1
2
0
1
1
2
0
0
0
2
1
1
1
1
0
1
2
0
1
2
1
1
1
1
0
1
2
1
0
1
1
1
1
1
1
1
1
1
2
1
0
1
1
1
2
0
2
2
1
1
1
2
1
2
2
1
1
0
1
1
0
0
1
1
1
0
1
0
0
2
2
0
2
1
0
1
2
1
1
0
1
1
1
1
1
1
2
1
2
2
2
2
1
1
0
1
1
0
1
1
0
1
1
1
1
0
1
1
1
0
1
1
0
2
0
1
1
0
1
1
1
0
1
2
1
1
1
1
1
1
1
3
2
1
1
1
1
1
1
0
2
2
0
1
1
1
1
1
0
1
2
0
1
0
1
1
1
0
0
1
1
1
2
0
1
1
2
2
1
2
1
1
0
0
2
0
0
1
2
1
0
2
1
2
0
1
2
1
1
3
1
1
0
2
1
1
1
1
0
1
1
0
0
2
1
1
2
1
1
2
1
0
1
1
1
1
1
1
1
1
2
1
1
1
1
0
0
1
0
1
0
3
1
1
1
2
1
1
0
2
1
0
1
1
2
1
1
2
2
1
0
2
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
0
0
1
1
1
1
1
1
1
0
1
0
2
0
1
2
1
2
2
3
1
2
0
0
1
1
2
1
0
0
1
0
2
1
2
0
2
2
0
0
1
1
1
1
1
1
2
0
0
1
2
1
1
1
0
0
2
1
1
0
1
1
1
0
1
0
1
0
1
1
1
1
2
1
0
1
0
0
1
0
3
2
1
1
1
1
1
2
1
0
1
1
1
1
0
0
1
1
0
0
1
1
2
2
1
1
2
0
1
1
1
0
0
1
0
0
1
1
0
1
2
1
1
1
2
2
1
1
1
1
1
1
1
2
1
2
0
1
2
2
0
1
0
1
1
2
0
0
1
0
1
1
2
1
1
1
2
1
1
2
2
2
2
1
0
3
2
0
0
2
2
1
1
2
0
1
0
2
1
2
1
1
1
2
1
0
4
0
1
1
0
2
1
1
1
0
1
2
1
1
1
1
1
2
0
1
1
2
0
0
2
1
1
1
0
1
2
1
1
2
1
1
1
1
1
0
0
3
0
1
2
1
0
1
1
0
2
2
1
1
1
0
1
1
0
1
1
1
3
1
0
1
1
2
1
1
0
0
1
1
0
0
1
2
2
1
1
1
2
0
3
1
1
1
1
3
1
2
0
2
1
1
0
1
0
1
2
1
2
1
0
1
2
2
1
1
1
2
0
1
2
0
0
1
0
1
1
1
1
0
1
1
1
2
0
1
1
1
0
1
1
1
1
1
1
2
1
2
0
1
1
1
1
1
0
2
2
1
1
2
0
1
1
1
0
2
0
1
1
2
2
1
0
1
2
1
0
1
0
1
1
1
2
2
1
1
0
0
1
1
1
0
2
1
1
0
1
2
0
1
1
1
1
2
1
1
0
2
0
2
1
0
0
0
2
2
0
1
0
0
0
2
0
1
1
0
1
1
2
0
0
1
1
0
1
2
1
0
2
0
2
1
1
1
1
3
1
2
2
0
1
2
3
1
0
1
2
1
1
1
1
2
2
1
1
1
2
1
1
1
2
0
2
1
1
2
1
1
0
1
1
0
2
0
1
1
0
1
1
1
1
0
1
1
2
1
2
2
1
2
2
0
2
1
1
1
0
1
2
1
0
2
1
2
2
0
0
1
1
1
1
1
1
1
1
2
1
1
1
1
2
3
1
0
1
2
1
2
0
1
1
1
1
1
1
0
1
1
1
2
1
1
0
1
1
1
1
1
0
1
2
2
0
1
0
2
0
2
1
1
0
1
1
1
0
1
1
2
1
1
1
2
1
1
1
1
1
0
1
1
1
3
1
0
1
1
2
2
1
1
0
0
0
1
2
2
1
2
1
1
1
0
1
1
1
2
1
1
2
1
4
0
1
0
0
0
2
0
2
0
2
1
2
1
1
0
1
1
0
0
0
1
0
1
0
0
2
1
1
1
1
0
1
2
1
1
0
1
2
1
0
2
1
1
0
1
1
2
1
1
0
1
1
1
1
0
2
0
1
1
0
1
2
0
0
2
1
1
1
1
1
1
2
0
1
2
0
1
0
1
0
2
2
0
0
1
0
1
2
1
1
1
0
1
1
2
3
2
1
0
1
0
2
0
1
1
0
2
2
1
0
0
1
2
1
0
1
0
0
2
1
1
1
2
0
1
0
0
1
2
2
0
1
1
1
1
1
1
1
0
1
0
1
0
1
1
1
1
0
1
1
1
1
1
0
2
1
1
1
1
1
1
2
2
1
3
0
0
1
1
1
1
1
1
0
0
2
0
1
0
0
3
1
0
2
0
2
0
1
1
1
1
1
0
1
1
1
2
1
2
1
1
1
2
0
1
1
0
1
0
1
1
1
1
0
0
2
0
0
1
0
1
2
2
1
0
1
0
1
0
0
0
0
1
1
1
3
2
1
0
2
1
1
1
0
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
0
1
1
1
1
1
1
1
2
1
1
1
1
1
0
0
0
2
1
2
2
1
1
0
1
2
1
1
2
1
1
1
0
2
2
0
1
0
1
2
2
1
1
1
1
0
2
0
1
1
3
2
1
0
0
1
1
1
1
1
2
0
2
1
1
1
1
1
1
1
1
2
1
1
2
1
2
2
0
1
0
0
1
1
0
0
0
1
0
0
0
1
0
2
2
1
1
1
1
2
1
1
2
1
2
1
1
1
1
0
0
1
0
1
2
2
1
1
1
0
1
2
2
1
0
1
1
0
0
0
0
0
2
2
3
1
1
1
3
1
0
1
1
1
2
1
1
1
0
0
1
0
0
2
2
0
1
1
2
2
1
0
2
1
1
1
1
1
2
2
1
1
2
1
0
0
0
0
1
1
0
1
0
1
1
1
1
0
1
1
2
2
1
2
0
1
1
1
1
1
2
1
1
1
2
1
2
1
1
2
0
1
0
1
0
0
1
2
1
1
1
2
1
1
2
0
1
2
0
0
1
1
0
1
1
1
1
0
1
2
1
2
1
1
1
1
2
1
1
1
0
0
2
1
2
1
1
1
2
1
0
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
0
0
1
1
1
0
0
3
0
1
0
4
1
2
0
0
0
1
1
1
2
1
2
0
1
2
0
1
1
2
1
1
1
2
1
1
2
1
1
1
2
1
2
0
1
1
1
0
0
1
1
1
0
1
1
1
2
0
1
0
1
1
1
1
0
1
1
2
1
1
1
0
3
1
0
0
0
2
1
1
1
1
1
0
0
2
2
1
1
1
2
1
1
1
2
1
1
2
2
0
1
2
2
2
1
1
2
1
2
0
0
1
1
0
1
2
0
1
2
1
1
1
1
2
0
1
0
0
1
1
0
1
0
1
1
0
2
0
0
1
0
1
2
2
2
1
2
1
1
1
1
1
1
2
1
1
0
1
0
1
1
0
1
0
2
1
1
1
0
2
1
1
2
0
3
1
1
1
4
0
2
1
1
1
1
2
0
1
1
0
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
0
0
0
2
1
0
2
1
2
2
1
1
0
0
0
2
0
1
0
1
1
1
1
0
0
0
2
1
2
2
0
2
3
1
0
2
2
2
2
2
1
1
0
2
1
2
0
0
1
2
1
1
3
1
1
0
2
1
2
1
0
1
0
1
1
1
1
2
0
1
1
1
1
1
1
4
1
0
1
3
2
1
0
1
1
1
0
0
2
2
0
1
0
1
1
1
0
2
1
1
1
1
1
1
2
1
0
2
1
0
1
1
1
1
0
0
0
1
1
1
1
2
1
2
0
1
0
1
1
0
0
1
0
1
2
1
1
1
1
1
2
1
2
0
1
1
2
1
1
0
1
0
1
1
0
1
1
1
0
2
1
1
0
1
0
0
1
3
2
1
1
0
1
1
2
0
0
0
1
1
1
1
0
1
0
1
0
0
2
1
0
1
1
0
1
1
2
1
0
0
2
1
1
2
2
0
2
1
0
2
2
0
0
1
2
2
1
0
1
1
1
1
2
0
2
1
0
1
1
1
1
0
5
1
1
2
2
1
0
1
0
1
2
2
0
2
1
0
2
1
1
2
1
2
1
2
1
0
1
0
2
1
1
1
2
2
0
0
1
2
1
1
0
1
1
1
2
1
0
1
1
0
1
1
1
1
2
1
0
0
1
1
1
1
1
1
1
1
1
0
1
0
1
0
0
0
2
1
1
1
0
1
1
2
1
2
1
1
0
0
1
0
2
1
2
1
2
1
0
1
0
1
0
1
1
1
1
1
2
2
2
1
1
1
1
2
1
1
2
1
2
1
3
2
0
0
1
1
2
1
1
2
1
1
0
1
1
1
1
0
1
2
2
1
1
1
1
1
1
1
2
1
2
1
1
0
1
1
2
0
0
1
0
1
1
1
2
1
2
1
1
1
1
0
1
1
2
2
1
1
1
1
1
0
1
1
0
1
2
2
1
1
1
0
1
1
1
1
1
0
1
1
2
1
1
0
2
1
2
2
1
2
1
1
2
1
0
2
1
1
1
1
1
1
1
0
1
1
2
1
0
1
1
1
2
0
0
0
1
0
1
0
1
1
2
2
1
1
1
2
1
2
0
2
1
2
1
1
1
1
1
1
2
1
0
0
1
2
2
0
2
2
1
1
0
3
0
1
2
0
1
2
1
1
1
0
1
1
0
1
0
2
1
0
1
1
1
2
1
1
1
0
0
0
1
0
2
1
1
1
2
1
1
1
0
1
2
1
1
1
2
1
2
0
0
2
1
1
1
2
0
0
1
2
0
2
1
1
1
1
2
1
0
0
1
1
0
1
2
0
0
1
0
1
2
0
4
2
0
0
0
1
1
1
0
1
0
1
1
1
0
1
2
1
1
1
0
0
2
1
0
1
1
1
0
0
1
2
1
1
0
2
0
1
2
1
1
2
1
1
2
2
2
1
1
1
0
0
0
2
1
2
0
2
2
1
0
2
1
1
1
2
1
1
2
1
1
1
2
1
1
1
2
0
0
1
1
1
1
1
0
0
3
1
0
0
1
1
1
1
0
2
1
1
1
1
1
1
2
0
1
1
1
0
2
0
1
0
1
1
1
2
2
2
1
0
2
2
1
0
1
1
1
0
0
1
1
1
1
2
1
2
0
1
0
0
2
1
2
1
1
1
1
2
1
1
1
2
2
0
2
1
0
1
1
1
2
1
5
0
1
0
1
1
4
1
2
1
1
1
0
1
0
2
1
1
1
1
1
2
1
1
2
2
1
1
2
1
0
1
2
1
1
1
2
0
0
2
1
1
1
2
1
1
2
1
0
2
1
2
0
0
0
1
1
0
0
1
1
1
1
1
1
0
0
2
2
1
2
2
1
1
1
1
0
1
2
1
2
0
1
1
1
0
2
1
1
1
2
2
2
1
0
1
1
1
2
1
1
1
0
2
2
1
3
2
3
1
2
1
1
0
1
0
1
1
2
1
1
2
0
2
1
0
0
1
1
1
1
2
1
2
0
1
0
0
1
0
1
1
2
1
1
1
0
2
1
3
1
1
2
1
1
1
0
1
0
1
1
1
0
1
2
2
1
2
1
1
0
2
1
1
1
2
1
2
1
1
2
1
2
0
1
1
1
0
0
1
1
2
0
2
1
0
2
1
1
0
1
2
1
2
1
1
0
0
0
2
2
2
0
1
1
1
2
1
1
1
1
1
2
1
2
1
1
1
3
1
1
1
1
1
1
1
2
1
1
2
2
2
0
0
1
1
0
0
1
1
0
2
1
2
0
1
1
1
1
1
2
1
2
1
3
2
0
2
1
1
1
2
1
1
0
0
1
1
0
2
0
0
0
0
2
1
0
0
1
1
1
1
1
0
1
2
1
1
2
1
1
1
1
2
2
1
1
2
0
1
1
1
0
1
1
1
2
1
2
1
1
0
0
1
0
0
2
1
0
1
1
1
1
2
1
1
1
2
1
0
0
1
1
2
1
1
1
2
1
1
1
0
1
0
2
1
2
0
0
1
1
0
1
1
0
0
1
1
0
0
1
2
1
2
1
0
0
1
2
1
1
1
1
1
0
1
1
1
2
1
0
2
2
1
1
0
0
0
1
2
0
2
1
0
2
1
1
0
1
1
2
2
1
1
1
1
1
1
2
0
0
2
1
1
1
1
2
1
0
1
1
1
1
1
1
0
2
2
2
0
2
1
1
2
0
2
0
0
1
0
0
0
1
0
1
1
2
0
1
2
1
1
1
0
2
1
1
1
2
2
1
1
1
1
1
1
0
0
2
1
0
1
1
1
2
0
0
1
2
1
1
1
1
2
1
1
0
1
2
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
2
1
1
0
1
0
0
0
2
1
2
1
1
1
0
1
0
1
1
2
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
0
1
1
2
1
0
1
0
0
1
0
2
0
2
1
0
1
2
1
1
0
0
0
1
1
1
0
1
2
2
1
1
0
1
0
2
1
1
1
1
1
2
1
0
1
1
1
1
0
2
1
1
1
2
1
1
1
1
0
1
1
2
1
1
3
1
2
1
1
0
1
1
1
1
1
1
0
2
1
1
2
2
1
1
1
1
1
1
0
0
1
1
1
2
2
2
1
1
1
2
0
1
2
1
0
2
2
0
0
1
1
1
1
0
1
1
0
2
0
1
1
1
1
2
0
1
1
2
1
1
1
2
1
2
1
2
1
2
0
1
1
2
1
2
1
1
1
0
1
1
1
1
2
2
1
1
1
1
2
0
1
1
1
0
0
0
1
1
1
1
2
1
1
1
2
2
1
2
1
1
0
1
1
1
1
0
1
1
1
2
0
0
1
0
2
2
1
0
2
1
2
2
1
1
2
0
1
0
1
0
0
2
1
3
1
1
2
1
0
1
1
1
0
1
0
2
0
1
1
1
1
2
2
1
1
1
0
2
1
1
0
0
3
0
2
1
2
1
0
1
1
1
1
2
1
0
0
1
1
2
1
1
2
2
0
2
1
2
2
1
2
2
1
2
1
1
0
0
1
2
1
1
2
0
0
1
0
1
2
0
1
1
0
3
0
0
2
0
2
1
1
2
1
1
0
1
0
2
1
1
0
2
2
0
1
1
1
1
1
1
0
1
2
0
1
1
0
2
0
2
0
0
1
1
1
1
1
2
0
0
1
0
1
1
0
0
1
1
1
1
2
1
2
1
1
1
2
2
2
0
2
1
1
1
1
2
2
2
2
1
1
1
1
1
1
2
0
0
1
1
2
1
1
1
0
2
2
0
0
2
0
1
1
2
1
0
2
1
2
0
2
1
2
2
2
1
1
2
0
2
0
1
1
2
1
0
0
1
1
1
0
1
1
1
1
1
1
1
2
2
0
1
2
1
2
2
2
1
1
2
0
0
1
0
1
2
0
1
0
0
0
0
0
2
1
1
1
0
2
0
1
1
1
1
1
1
1
1
2
1
1
1
0
2
0
1
1
0
0
0
1
1
1
1
1
2
0
1
2
0
2
1
1
1
1
2
2
2
2
1
2
1
1
1
2
2
0
2
0
1
1
1
1
0
1
0
1
2
0
1
1
2
1
1
2
1
0
1
1
0
1
0
1
1
1
1
0
1
1
1
2
0
0
2
1
1
0
1
2
2
3
2
1
0
2
1
2
1
1
1
2
1
1
1
1
1
2
1
0
1
1
2
2
2
0
1
1
2
2
2
1
1
2
1
2
1
3
0
0
2
2
2
1
1
3
1
1
2
1
1
1
2
1
2
2
2
2
0
1
1
1
1
1
1
0
0
0
1
1
2
2
1
0
0
1
2
2
2
0
0
2
1
2
0
0
1
1
1
1
2
1
2
0
2
1
1
1
0
2
0
1
2
2
1
2
1
1
0
1
0
1
2
0
2
2
1
1
1
1
1
2
1
0
2
0
1
1
1
1
1
1
0
0
0
2
0
0
1
2
2
0
0
1
1
1
0
1
0
1
1
1
0
1
0
1
0
2
0
1
1
0
1
1
0
0
0
1
1
1
1
0
1
1
1
1
0
0
1
2
1
1
2
0
1
1
1
1
1
1
2
0
2
1
1
1
1
1
1
2
2
0
1
1
1
1
1
2
1
0
1
2
1
1
0
1
2
0
2
1
1
1
2
2
1
1
1
2
1
1
0
1
1
1
1
1
0
1
0
1
1
2
2
1
1
1
2
1
2
1
0
1
1
1
2
0
0
2
1
0
1
1
1
0
1
2
1
1
0
1
1
1
3
1
1
1
1
0
1
0
0
1
1
2
1
0
1
0
1
1
1
1
0
2
1
0
3
2
1
1
1
1
2
1
0
1
2
1
1
1
2
2
1
1
2
2
2
2
1
1
2
2
1
2
1
0
1
2
0
1
1
1
1
2
1
1
0
1
1
1
1
1
0
0
1
1
1
2
2
1
1
3
0
0
3
1
1
1
2
1
1
0
2
1
1
1
0
1
1
2
0
1
1
1
1
1
1
1
1
0
1
0
1
1
0
0
1
1
0
1
0
1
0
1
1
2
2
1
1
0
1
1
2
1
0
1
1
1
0
1
3
1
1
0
1
1
1
4
1
1
1
1
1
0
1
0
0
0
1
2
2
1
1
1
2
1
2
1
2
0
1
2
1
1
4
2
2
1
1
0
1
2
0
0
0
1
2
0
1
0
1
1
0
0
1
2
1
1
1
1
0
0
3
1
1
1
2
1
2
1
1
2
1
2
1
1
1
1
1
1
0
0
1
1
2
1
1
2
1
2
0
1
2
1
1
0
0
0
2
0
1
1
2
2
1
1
2
0
1
2
1
0
2
1
1
1
2
1
1
0
1
1
1
1
1
1
2
1
1
1
1
1
2
0
1
1
0
0
0
1
2
2
0
2
1
2
1
1
0
1
2
1
1
1
1
0
0
0
1
0
1
0
1
0
0
2
2
1
1
1
1
0
1
1
1
1
0
0
0
1
1
2
1
1
2
0
0
2
1
1
2
1
0
1
2
2
2
1
1
1
0
0
1
3
2
0
1
1
0
1
0
1
1
2
1
0
0
1
2
0
1
0
1
2
0
1
1
2
1
1
1
1
2
1
0
1
0
1
1
2
1
0
1
2
2
1
1
1
0
2
1
1
2
1
0
2
0
0
1
4
2
2
1
1
0
2
0
2
0
1
1
1
2
2
2
2
1
1
1
1
1
1
2
1
1
0
1
1
3
1
0
1
2
1
0
1
1
1
1
2
2
1
0
2
0
2
2
0
1
1
1
0
1
1
0
1
1
1
2
1
0
1
1
0
0
1
1
1
1
1
1
1
1
1
0
1
0
0
1
2
1
0
1
2
2
1
0
0
1
0
0
2
1
1
1
0
2
3
1
1
0
3
0
0
0
1
1
0
1
0
2
1
1
1
1
0
2
0
2
1
2
2
1
0
1
2
0
1
1
2
0
1
1
1
2
1
0
0
1
2
2
0
0
1
0
0
1
1
1
0
1
0
1
1
2
2
0
0
2
1
0
1
1
0
1
2
0
0
1
0
1
1
2
1
2
1
0
1
2
3
1
2
2
1
1
1
0
0
1
0
1
2
3
2
0
2
2
1
1
2
0
2
0
0
2
1
1
2
1
1
1
0
2
2
2
3
3
1
1
0
1
1
2
1
2
1
2
0
3
1
1
1
0
0
2
1
0
1
1
1
2
1
1
1
1
1
1
2
2
1
1
0
0
1
0
1
1
0
1
1
1
1
2
1
1
2
0
3
2
0
2
0
0
2
1
0
1
1
0
0
1
1
1
2
1
1
1
1
2
0
0
1
2
2
1
1
1
1
1
1
2
1
0
2
0
1
1
1
2
0
1
2
1
2
1
0
0
0
0
1
2
1
0
1
2
1
1
0
1
0
2
2
1
0
0
0
1
1
1
1
2
1
1
0
1
2
1
2
2
1
1
1
2
1
1
1
0
1
1
0
1
2
1
1
0
2
1
1
2
2
1
2
0
2
1
1
0
1
1
2
2
1
0
2
0
1
1
1
1
0
1
2
1
1
1
2
1
2
1
0
1
1
1
0
1
1
1
1
1
1
3
1
1
1
2
2
1
0
1
0
0
0
1
1
2
1
1
0
1
1
1
0
2
1
1
1
1
2
1
3
1
1
1
2
1
0
0
0
1
1
1
2
2
1
1
0
1
1
2
1
1
1
0
1
1
1
1
0
1
0
0
1
1
1
2
0
2
0
1
2
0
1
1
0
0
1
1
0
1
1
1
1
2
2
1
2
1
2
2
0
2
1
0
1
0
2
0
1
0
0
0
0
1
3
1
2
2
2
1
1
1
0
1
0
1
2
1
2
1
1
1
0
1
0
1
0
1
2
0
2
0
1
1
1
0
1
1
1
2
0
1
0
2
0
0
1
0
1
1
1
1
1
1
2
1
2
1
2
2
1
0
0
1
1
1
0
1
1
2
1
1
1
1
0
1
1
0
0
1
2
0
1
2
2
0
1
2
1
1
1
0
0
1
1
2
1
2
1
2
1
2
1
1
2
1
2
1
1
0
1
0
2
1
0
2
1
2
0
1
1
1
1
2
0
1
2
0
0
1
2
2
1
1
0
1
1
1
1
2
1
2
1
0
1
2
2
2
1
0
2
2
1
2
1
2
1
1
1
1
1
1
2
2
1
1
1
2
1
1
2
1
0
0
0
1
1
1
1
1
1
1
0
2
2
2
1
1
1
0
1
1
1
1
1
0
1
1
1
1
1
1
0
2
1
1
1
0
1
1
2
1
0
2
2
1
1
1
1
2
0
1
1
1
1
1
1
1
1
0
1
1
0
1
2
2
1
1
1
1
1
3
1
1
2
1
2
2
2
2
1
1
1
2
2
1
1
2
0
1
1
0
1
1
1
0
1
1
0
1
1
1
0
1
1
0
1
0
1
2
1
1
2
2
0
0
1
1
1
0
1
1
0
2
1
1
1
1
1
1
2
0
0
0
1
1
0
0
1
2
2
1
1
1
0
2
0
1
1
1
0
1
2
2
2
0
1
1
0
1
1
1
1
0
1
1
1
0
2
1
1
0
2
1
1
1
0
2
0
2
1
0
1
1
1
0
1
1
1
1
3
2
2
0
0
1
1
1
0
1
0
1
2
0
3
1
2
3
2
2
2
2
1
2
2
1
3
0
1
1
1
1
1
1
2
1
1
2
1
2
1
0
0
1
0
2
0
0
0
1
0
2
1
0
2
1
1
0
1
2
1
1
1
2
1
2
1
1
1
1
1
1
2
2
0
1
1
2
1
1
1
1
1
0
1
0
1
2
1
1
2
0
1
0
0
2
1
2
0
0
2
1
0
1
2
2
1
2
1
2
1
0
0
1
1
1
3
0
2
1
0
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
2
0
0
1
2
1
1
0
0
0
2
0
1
1
1
1
1
0
1
1
1
1
0
0
1
2
1
0
1
1
2
0
1
2
4
1
0
1
1
1
2
1
2
1
0
0
1
1
1
3
1
3
0
0
2
0
1
2
1
2
1
2
2
2
1
1
0
0
0
1
2
2
0
0
1
0
1
1
1
0
1
1
1
2
2
1
2
0
0
1
1
1
0
2
1
1
2
2
0
1
2
1
2
0
1
1
2
0
0
0
2
1
0
1
0
1
1
0
0
1
1
2
1
2
1
1
2
1
1
1
1
2
1
1
0
1
1
1
1
1
0
2
1
0
2
0
1
1
1
2
2
2
0
1
0
1
2
1
1
1
1
1
1
1
0
1
1
2
1
0
0
2
2
2
1
1
0
0
1
0
1
1
1
1
0
1
1
0
0
0
1
0
1
1
1
3
0
1
2
2
1
2
2
2
1
1
1
0
1
2
1
1
2
2
0
2
1
1
2
1
1
0
2
1
1
2
1
1
2
2
1
2
1
1
1
2
2
2
0
1
1
1
1
1
0
2
1
0
1
1
2
1
1
1
1
0
1
2
0
0
1
0
2
0
1
1
0
3
0
0
1
1
1
0
2
0
1
1
1
1
1
2
2
1
1
0
0
1
1
0
1
2
2
1
2
1
2
1
0
1
1
0
1
0
0
1
1
1
2
0
0
1
1
2
3
1
0
1
2
2
1
0
0
2
1
1
3
1
1
1
1
1
2
1
2
1
1
2
0
0
2
1
1
2
2
1
1
1
0
1
1
0
1
0
2
2
1
1
0
1
0
2
1
1
1
2
1
2
2
0
1
0
0
0
0
1
0
1
0
0
2
1
2
0
0
2
0
2
0
1
2
2
1
0
1
0
0
1
0
2
2
2
1
0
1
1
1
1
1
1
1
1
1
2
2
2
2
0
1
2
2
0
2
2
2
2
0
1
1
1
2
0
0
1
1
1
1
1
1
0
1
2
1
0
2
0
2
2
1
1
1
1
0
0
1
2
2
1
1
2
1
1
1
2
1
1
0
2
0
1
1
1
0
1
2
1
1
2
1
1
1
4
2
3
1
1
0
1
2
2
1
1
1
1
0
1
0
1
2
0
1
2
0
1
1
1
1
1
1
1
0
1
1
1
0
1
0
1
1
2
1
1
1
0
2
1
0
0
1
1
2
2
1
1
1
1
0
1
0
1
0
0
0
2
1
1
2
1
0
1
1
1
1
1
2
1
1
1
1
1
1
2
2
1
0
0
2
1
2
1
1
1
1
1
2
0
2
2
0
2
2
0
1
1
1
1
1
2
1
1
1
3
1
1
2
1
1
2
1
2
1
1
2
1
1
0
0
1
1
1
1
0
0
0
2
1
1
1
1
0
2
0
1
0
2
1
2
1
1
1
1
2
0
0
1
0
1
1
2
0
1
3
2
0
1
1
1
2
0
2
2
1
1
1
2
1
2
1
1
1
0
2
2
0
0
1
1
1
0
1
0
1
2
0
1
0
0
1
1
1
2
1
1
1
0
0
6
0
2
1
1
1
1
0
1
1
0
1
0
1
0
1
0
1
1
2
2
1
1
1
0
1
2
1
1
1
0
1
1
1
0
0
0
1
1
1
0
1
1
0
1
2
1
1
2
0
1
1
0
0
1
0
1
2
0
1
2
1
1
2
0
1
0
1
1
0
1
2
1
1
1
1
2
1
1
0
2
1
1
1
1
0
0
0
0
1
0
1
0
1
1
1
1
1
2
0
1
0
1
2
0
2
1
1
1
0
1
2
0
0
0
1
1
1
2
1
0
2
1
2
2
1
2
1
1
1
1
1
2
1
1
1
0
1
0
2
0
1
1
2
0
0
1
1
1
1
2
0
0
2
1
2
1
1
2
1
1
0
1
0
2
2
0
2
1
2
1
1
0
2
1
2
0
1
0
1
1
1
2
1
1
2
1
1
0
1
1
0
1
1
0
1
1
0
0
0
1
0
1
1
1
1
0
1
0
1
1
1
2
1
1
0
1
2
0
2
0
0
1
0
2
1
1
1
0
2
1
1
0
1
2
2
2
1
0
1
1
1
1
1
1
2
2
1
1
1
1
2
0
2
1
1
0
1
1
1
1
1
1
1
2
1
0
1
0
1
2
2
2
1
1
1
1
1
1
3
1
2
1
1
2
2
2
1
1
2
1
2
1
1
1
0
1
1
1
2
2
0
0
1
1
2
1
2
1
1
1
2
1
2
0
1
1
0
2
2
1
2
1
1
1
2
1
0
0
2
2
1
1
1
1
1
1
1
2
0
2
1
1
2
0
1
0
2
1
2
1
1
0
0
2
0
1
0
1
0
3
2
1
1
2
1
2
1
0
2
2
0
1
1
2
1
0
0
2
1
0
1
2
0
1
1
2
0
0
0
1
1
1
1
1
1
1
1
0
2
1
1
1
1
0
1
0
1
1
1
1
2
1
1
0
2
1
1
1
1
0
1
0
1
2
2
1
1
2
1
2
2
1
0
2
2
2
0
1
1
1
1
1
1
0
0
1
0
2
1
1
2
2
1
2
1
1
0
0
1
1
1
1
1
1
2
1
0
1
1
1
2
1
0
0
1
1
2
1
1
1
0
1
1
0
1
1
1
1
1
1
1
0
0
2
2
1
1
0
0
1
0
2
1
0
0
0
0
0
1
1
1
3
1
1
1
1
2
2
2
0
1
0
0
1
2
2
2
2
1
3
2
1
2
1
1
0
1
0
0
0
1
2
1
1
1
1
1
0
2
0
2
0
1
2
0
1
1
2
0
1
2
2
1
1
1
1
1
1
1
2
1
2
2
1
1
1
2
2
1
0
1
2
0
0
1
1
0
2
2
1
2
0
0
2
2
2
1
0
2
1
2
1
0
1
2
1
3
1
1
0
1
2
0
0
1
1
0
1
1
2
2
1
1
2
0
1
0
0
0
2
0
3
1
1
0
0
0
0
1
2
0
1
2
1
1
1
1
2
2
2
1
1
0
2
1
1
2
1
0
2
0
2
2
2
2
1
0
1
1
0
0
2
1
0
1
1
1
2
1
1
1
1
1
1
1
1
1
3
2
1
0
2
1
1
2
1
1
2
1
2
2
1
1
1
1
2
1
0
1
1
2
0
2
1
2
1
1
1
1
1
1
1
2
0
1
0
1
2
1
1
1
1
1
1
1
1
1
1
1
0
2
2
2
1
1
2
1
1
0
0
0
1
0
0
1
0
1
0
0
1
2
0
0
1
1
0
2
2
1
1
1
2
0
1
1
1
1
0
1
1
2
0
1
1
1
1
0
0
0
1
1
0
0
0
0
2
1
1
1
1
0
1
1
2
2
1
2
0
1
0
3
0
1
0
2
1
2
0
2
2
2
1
1
1
0
0
2
1
1
1
2
0
1
0
0
1
2
1
1
1
1
0
2
0
2
1
1
2
1
1
1
0
2
0
2
1
1
1
1
2
1
0
1
1
1
0
2
1
2
1
1
1
2
1
2
1
1
2
2
1
0
0
1
1
1
1
1
0
2
0
2
1
0
1
0
2
1
1
0
1
1
2
1
0
1
0
1
0
0
1
2
0
0
1
1
1
0
1
1
2
1
0
1
0
2
1
0
1
1
2
2
0
2
1
1
1
1
1
1
0
1
0
0
1
0
1
1
0
1
3
3
1
1
0
2
2
0
2
1
2
0
1
0
1
1
3
0
2
1
2
1
0
1
1
0
1
1
1
1
0
0
0
1
1
1
0
1
0
2
2
2
1
1
1
4
1
1
2
1
1
1
1
1
2
0
2
1
1
1
1
1
0
1
2
2
0
0
0
2
1
1
0
1
1
1
1
2
0
1
1
2
2
2
2
1
0
1
0
1
0
1
2
1
2
0
2
1
2
1
2
1
2
2
1
1
2
2
1
1
0
2
0
0
1
2
0
1
2
2
1
2
1
1
1
1
1
0
1
1
2
1
1
1
1
0
0
1
2
0
1
0
1
0
1
1
2
1
1
2
2
2
1
1
2
1
1
1
0
1
1
4
1
2
1
0
3
1
1
1
1
1
0
2
1
1
2
1
0
0
0
0
1
1
2
0
2
0
1
1
1
0
2
1
0
1
2
1
2
2
1
1
1
1
0
0
1
1
1
1
1
1
2
0
1
0
1
0
2
0
0
1
0
1
1
1
1
0
2
1
1
1
0
1
0
1
1
2
0
1
2
1
2
1
0
1
0
1
1
1
1
1
1
1
0
0
1
2
0
1
2
1
1
0
0
0
2
1
1
1
1
1
1
1
2
0
1
1
1
1
1
0
2
2
2
1
2
0
2
0
0
2
0
1
2
0
1
1
2
1
1
1
2
1
0
2
1
1
1
0
2
2
1
2
0
0
2
1
2
1
2
1
1
1
2
1
1
2
1
2
2
1
0
0
1
1
1
1
1
1
1
2
1
2
1
2
1
1
1
1
1
1
0
2
0
1
4
1
1
0
2
0
2
0
0
0
1
1
0
1
2
1
2
0
1
0
1
1
1
2
1
1
0
0
1
1
2
2
1
2
0
0
0
0
0
2
0
1
1
1
1
0
0
0
1
1
0
0
1
0
1
0
0
3
0
1
1
1
1
1
1
0
2
2
1
0
1
2
1
2
1
0
0
1
1
1
2
1
1
0
1
0
1
0
1
1
1
0
1
0
1
0
0
1
1
2
2
0
1
1
1
0
2
2
1
0
0
0
1
1
2
1
1
0
1
2
1
0
1
1
1
1
1
1
1
0
1
1
2
1
1
1
1
1
3
2
1
1
1
2
0
1
1
2
0
0
2
1
1
2
2
1
1
1
0
0
0
1
1
1
2
1
1
1
1
1
0
1
0
0
0
2
0
1
1
2
0
2
1
1
1
1
0
1
1
0
2
0
1
1
2
1
1
2
2
1
1
0
1
2
1
1
0
2
0
0
0
2
1
2
1
0
0
1
1
3
1
0
2
2
1
0
1
1
2
2
1
0
0
1
1
1
0
2
1
1
1
1
2
2
1
1
1
2
0
1
0
1
1
1
1
1
1
0
1
1
0
1
1
1
1
2
1
1
2
3
2
1
2
0
0
1
1
1
0
2
0
2
1
1
1
2
2
0
0
1
1
1
2
1
0
0
1
0
1
1
0
1
1
0
0
1
1
1
2
1
1
1
2
2
1
1
1
2
1
1
1
2
1
2
2
2
1
1
1
1
0
2
0
0
2
0
2
1
2
2
2
1
2
1
0
2
1
0
1
1
1
1
2
1
1
0
1
0
0
1
2
0
0
0
1
1
2
1
1
1
1
1
0
0
0
1
0
0
1
0
2
1
1
1
2
0
0
1
2
0
1
1
1
1
0
2
2
0
1
2
1
0
1
1
1
2
1
1
0
2
1
0
1
1
1
1
0
1
2
2
2
0
1
2
1
0
1
1
1
2
1
2
1
1
1
1
1
1
1
2
0
0
1
1
1
2
1
1
1
0
1
0
1
1
1
1
0
1
2
1
0
1
1
2
2
1
1
0
1
1
1
2
0
1
0
0
1
0
1
1
2
2
0
2
0
1
1
2
1
1
2
1
1
2
1
2
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
0
1
2
2
2
0
1
1
2
2
1
0
1
0
0
1
1
0
1
0
1
1
1
0
2
0
1
0
1
1
1
2
1
1
0
1
2
0
0
1
1
0
0
1
1
1
1
1
0
1
1
0
0
1
1
0
1
0
2
0
0
0
1
0
2
1
1
1
2
1
2
0
1
2
0
2
1
1
0
1
1
0
0
1
1
0
2
1
1
1
1
0
1
2
0
1
1
1
2
1
1
0
1
1
1
1
2
2
1
1
1
1
2
0
0
2
2
1
1
2
0
1
1
1
0
1
1
1
2
0
1
2
0
2
2
1
1
1
1
1
0
0
1
1
2
1
1
0
1
2
1
0
1
0
0
1
0
1
0
1
1
0
2
1
1
1
1
1
1
1
1
2
1
2
0
1
1
0
2
1
1
1
1
0
2
0
2
1
1
1
0
2
2
2
1
1
0
0
1
1
1
1
0
0
1
1
0
1
3
0
2
0
1
1
0
1
1
1
1
4
2
1
0
2
2
1
1
1
3
1
1
1
2
1
1
1
1
1
1
0
2
1
0
0
2
1
2
1
2
2
2
1
1
1
1
0
1
1
1
1
1
1
1
1
2
2
2
1
1
1
0
1
1
1
2
0
1
2
1
1
2
2
1
1
2
1
1
0
1
2
0
1
1
1
1
0
1
2
1
0
2
0
2
1
2
2
1
1
0
2
2
1
1
1
0
1
1
0
1
1
1
2
2
0
1
0
2
1
0
1
1
0
0
0
0
1
1
1
1
2
2
0
2
1
0
1
2
2
1
3
1
1
1
2
0
1
0
2
1
0
2
1
1
1
2
2
1
1
0
1
1
2
1
2
1
1
0
1
1
1
1
2
0
1
2
0
2
0
1
1
1
1
0
1
1
1
1
1
1
0
0
1
1
0
0
0
1
1
1
1
1
1
2
1
1
1
0
1
1
2
1
0
0
1
1
2
1
0
1
0
1
0
1
2
2
1
0
0
1
1
1
1
0
0
0
0
2
2
1
0
2
1
2
2
2
0
2
1
0
2
2
0
1
1
0
1
1
0
1
1
2
2
2
1
1
2
0
1
1
0
0
0
0
0
0
2
1
0
2
0
0
1
0
1
2
1
0
1
2
1
1
1
1
1
0
1
1
1
1
2
1
0
1
2
0
1
1
1
0
2
3
1
2
1
1
0
1
1
1
2
1
1
1
1
2
2
3
2
1
1
1
1
1
0
2
1
2
2
1
2
1
1
1
1
1
1
1
2
0
2
1
1
1
0
2
2
2
1
1
1
1
1
1
1
1
1
0
0
1
2
1
1
2
2
0
1
0
2
1
1
0
2
2
2
1
0
2
0
1
1
0
2
1
2
1
1
1
1
2
1
2
1
1
2
1
1
2
2
2
1
2
1
1
1
1
1
1
2
0
1
0
1
0
1
2
2
1
2
1
1
1
0
0
2
2
4
1
1
2
1
1
2
0
1
0
1
2
1
1
1
0
1
2
1
1
2
0
1
1
1
1
1
0
1
2
1
1
1
1
1
1
2
0
1
1
1
2
0
1
1
1
1
1
1
1
2
0
0
1
1
1
2
1
1
1
1
1
0
0
1
1
0
2
1
0
0
1
0
0
1
1
1
0
1
1
0
0
1
1
2
1
1
1
1
0
0
1
3
2
0
0
2
0
0
1
1
1
0
1
2
1
1
1
1
1
1
0
2
2
1
0
1
1
1
1
1
0
1
2
2
1
2
1
1
0
0
0
1
1
1
0
1
0
0
2
1
1
1
1
1
2
1
1
1
1
2
0
0
0
0
1
2
1
0
2
1
1
2
0
2
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
2
1
1
0
1
1
1
2
1
2
1
2
1
2
2
0
2
2
1
1
0
1
2
2
2
0
1
2
1
1
1
1
0
0
1
1
2
1
1
1
1
0
1
1
1
1
0
0
2
2
0
1
1
1
0
2
1
1
1
1
1
0
1
2
1
1
1
0
0
0
2
1
1
1
2
1
1
2
0
2
2
1
1
1
1
1
1
0
1
1
1
3
1
0
2
0
0
1
0
1
2
0
1
0
1
0
1
1
2
1
1
1
1
2
0
2
1
4
1
1
1
1
1
1
1
0
0
1
1
1
0
1
1
0
0
1
2
1
0
2
0
0
1
1
0
0
2
1
0
2
2
1
2
1
1
1
2
1
2
1
1
2
1
2
2
0
0
1
2
1
2
1
0
0
0
2
1
1
1
2
1
2
2
2
1
2
2
1
0
2
0
1
1
1
1
1
0
2
0
1
1
1
1
1
1
1
0
1
2
0
0
2
0
1
0
0
1
1
1
1
1
1
2
0
0
0
1
2
1
2
1
0
2
2
1
1
2
1
1
0
2
0
2
2
2
2
2
1
0
1
2
1
1
0
0
3
1
3
0
0
1
0
0
1
0
1
2
2
1
0
1
1
1
0
1
2
2
0
1
0
1
1
2
0
0
1
1
1
2
1
1
0
0
2
1
2
1
1
1
1
3
1
0
1
1
1
2
0
2
1
1
1
2
0
2
1
1
1
2
1
1
1
1
0
2
0
0
1
0
1
1
1
0
0
0
2
1
2
1
2
1
0
1
1
1
1
2
1
0
1
1
0
1
2
1
2
2
1
1
1
2
1
2
1
1
1
1
1
0
1
1
1
1
1
1
2
0
1
1
0
0
1
1
2
2
0
1
1
1
1
1
1
1
2
2
2
2
0
2
1
2
1
1
1
0
1
0
1
1
1
1
1
2
2
1
2
1
0
2
1
2
2
1
1
0
0
2
1
2
1
1
0
1
0
1
0
1
2
0
2
1
2
2
1
1
2
0
1
1
1
2
1
1
0
1
2
0
1
0
1
0
1
2
2
1
1
0
0
1
1
1
1
0
1
1
2
1
1
1
1
1
1
0
0
1
1
2
3
1
1
1
1
1
2
1
1
1
1
1
0
1
1
1
2
0
0
1
2
1
1
0
0
2
0
1
1
1
1
1
1
1
1
0
2
1
1
1
0
2
0
1
2
1
1
1
0
2
1
2
1
1
1
0
1
0
1
0
1
0
0
1
1
0
0
1
0
1
1
1
2
0
1
0
0
1
0
1
1
1
1
0
0
2
1
0
1
0
1
1
0
1
2
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
0
1
2
1
1
1
0
0
1
0
2
0
3
2
1
0
1
1
1
1
1
1
1
0
1
1
1
1
2
1
1
1
2
2
1
2
0
0
1
2
1
1
1
0
1
0
1
2
1
0
1
1
0
2
1
1
0
1
1
0
0
1
0
1
1
1
3
2
0
1
0
0
1
0
1
1
1
2
2
1
1
2
1
2
1
2
1
1
2
1
0
1
1
1
0
2
1
1
1
2
2
1
1
2
2
2
1
1
2
1
2
0
0
1
1
2
1
1
1
1
2
0
1
2
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
0
1
1
2
1
1
0
0
0
1
0
1
2
2
2
1
2
1
1
1
1
0
1
2
1
1
1
2
1
2
0
1
1
2
1
2
1
2
1
2
1
1
0
0
0
1
3
2
1
2
0
1
2
1
2
1
2
1
0
1
1
1
0
1
2
1
0
2
2
1
1
0
1
2
1
1
1
1
1
2
1
0
0
1
1
1
2
2
0
0
1
2
0
0
1
1
0
1
2
0
1
1
1
1
1
1
2
0
0
2
2
1
1
2
2
1
1
1
1
1
1
1
2
0
1
1
0
2
0
1
0
0
2
1
1
2
1
1
1
2
0
2
1
1
0
1
1
1
2
1
1
1
0
0
1
1
1
1
0
1
2
0
2
2
0
1
1
0
1
1
0
1
1
0
1
1
1
1
1
1
0
1
0
1
2
0
0
2
1
1
1
2
1
1
2
1
1
0
2
2
0
1
0
1
2
0
0
1
1
1
0
2
1
0
1
1
0
1
0
2
1
1
1
1
1
3
0
2
1
2
0
0
1
1
2
1
1
1
2
0
1
0
2
1
1
2
2
1
1
3
1
1
0
0
0
1
2
1
0
0
1
1
0
1
1
2
1
1
1
2
1
1
1
1
2
0
1
2
0
1
1
1
1
1
2
1
1
1
2
0
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
3
2
0
1
1
1
0
0
1
1
1
0
1
0
1
1
1
1
1
0
1
2
1
0
1
2
3
1
0
1
2
0
1
1
2
2
2
2
2
0
1
1
1
2
1
0
1
0
0
1
1
1
0
0
6
0
0
2
1
1
1
1
2
1
1
1
1
1
0
2
2
1
0
1
2
2
0
1
1
1
1
2
1
1
1
1
1
2
1
2
3
3
1
1
1
1
0
1
1
1
1
1
0
1
1
1
2
1
0
2
1
1
0
1
0
1
2
0
1
2
1
0
1
1
1
1
1
2
1
1
2
2
1
1
0
0
2
1
1
1
1
2
2
1
2
2
1
1
1
2
1
1
1
0
1
2
1
1
2
0
2
2
3
1
1
2
1
0
0
2
0
1
1
1
3
2
2
1
1
1
2
1
0
1
1
1
0
2
1
1
1
0
1
1
2
1
1
1
1
0
1
1
1
2
0
2
1
1
1
1
1
2
1
2
1
0
1
0
1
2
1
2
1
1
1
1
2
1
1
4
2
2
2
1
0
0
0
2
1
1
0
2
0
1
1
2
1
2
1
0
1
0
1
1
0
0
1
1
0
2
1
0
1
2
1
1
1
1
0
1
2
1
1
1
2
1
1
0
1
0
0
2
1
1
0
1
1
0
1
2
2
1
1
1
1
2
1
0
1
1
2
1
1
0
0
0
2
1
2
1
1
1
2
2
0
1
1
1
0
1
1
1
1
1
1
0
1
0
2
1
1
1
0
2
1
1
0
0
0
1
0
1
1
0
1
4
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
2
2
1
1
0
1
1
1
1
0
1
1
0
0
0
1
1
2
2
1
1
1
2
1
0
1
1
1
0
2
0
1
1
0
2
1
1
1
2
2
2
0
1
2
2
1
1
1
1
0
2
1
1
1
1
2
1
1
0
0
1
0
3
0
1
1
1
1
1
2
1
0
2
0
0
2
2
0
0
1
1
0
0
0
1
0
1
2
1
1
0
1
2
2
1
1
1
1
1
1
0
0
1
1
1
1
1
2
3
1
1
1
1
1
1
1
1
2
1
2
1
0
1
1
1
2
1
0
0
2
1
2
1
2
2
0
2
1
2
1
1
2
2
0
1
1
1
1
0
0
0
2
0
0
0
3
1
0
1
2
1
1
0
1
0
2
2
0
1
0
2
2
1
0
2
1
2
1
0
1
2
1
3
2
0
1
1
2
0
1
1
1
1
1
0
0
1
2
1
1
1
1
1
1
2
1
0
1
1
1
2
1
1
1
0
2
1
1
0
2
1
0
1
1
1
0
1
2
1
0
2
1
1
1
0
1
0
0
1
1
2
1
0
0
1
1
0
1
1
0
1
1
1
1
0
1
1
1
1
0
0
0
2
0
1
0
1
2
2
0
1
1
1
1
0
2
1
0
1
2
1
1
2
1
2
1
1
0
1
2
0
1
1
1
0
2
1
2
0
0
1
1
1
0
2
1
0
1
1
2
0
2
1
1
1
1
0
0
1
1
1
2
2
1
1
2
1
2
1
1
1
1
1
2
0
1
1
0
1
2
2
0
1
2
0
2
1
1
1
0
1
1
2
1
2
1
1
2
2
1
1
0
1
1
1
1
1
1
2
1
2
1
1
1
3
2
3
0
0
2
0
1
2
2
1
1
1
1
0
1
1
1
0
1
1
0
0
1
1
3
2
1
2
1
0
1
2
0
2
1
1
1
0
1
1
0
1
1
1
1
1
0
1
1
1
1
0
1
1
2
2
1
1
1
2
0
1
1
0
0
2
1
1
1
0
1
1
1
1
0
1
1
2
2
0
3
1
1
0
1
0
1
1
1
0
1
0
1
1
1
1
1
2
0
1
2
0
1
1
0
0
1
1
1
1
1
0
1
0
2
1
1
2
0
1
1
2
2
2
0
1
1
1
2
1
1
2
0
2
1
0
0
1
0
1
1
1
0
2
1
2
0
0
1
0
2
0
1
0
2
2
1
1
1
1
0
1
1
0
0
2
0
1
0
1
1
2
1
1
0
1
1
2
0
0
1
0
1
3
2
1
1
1
0
0
1
1
1
2
1
2
1
1
1
3
1
2
0
1
1
1
0
0
0
1
0
0
1
1
1
2
1
3
0
0
1
1
0
2
0
2
0
2
0
2
3
1
0
0
1
0
0
1
1
1
1
0
0
1
1
1
3
1
1
1
0
1
0
1
1
1
2
1
1
1
0
1
4
1
1
1
1
1
2
1
1
1
1
1
1
3
0
1
1
1
0
1
2
0
1
0
1
2
1
1
2
0
1
1
1
0
0
0
1
1
1
2
2
1
1
1
1
1
1
2
1
0
1
2
1
1
1
1
0
1
1
0
1
1
0
0
1
0
1
2
1
1
1
0
1
1
2
0
1
1
0
1
1
1
1
2
1
1
0
1
1
2
1
0
1
1
0
1
0
2
1
1
1
1
0
2
0
3
2
1
1
0
1
1
1
0
1
1
1
2
0
2
2
2
1
1
1
1
2
0
2
1
1
2
2
1
1
2
0
1
1
1
0
1
1
3
1
2
1
1
0
1
0
2
1
0
2
1
2
1
1
2
1
1
2
1
2
1
1
0
1
0
1
1
2
2
2
0
2
0
1
2
1
1
1
1
1
1
1
1
1
0
1
2
0
1
2
1
0
1
1
1
1
1
1
0
2
0
1
0
2
1
2
1
1
2
0
2
1
2
1
1
1
1
1
1
1
1
2
0
1
1
2
2
0
2
2
0
0
0
0
0
1
2
1
1
2
2
2
1
1
1
1
1
1
0
1
1
1
1
1
0
1
1
2
1
0
1
1
1
1
2
0
1
0
2
0
1
2
1
0
2
1
1
1
2
1
2
1
0
1
2
1
2
1
1
2
1
0
1
1
2
1
1
0
1
3
1
1
2
2
1
0
0
1
0
2
0
0
1
2
0
1
2
0
1
1
1
0
1
1
1
3
2
1
2
1
1
2
1
1
1
2
1
0
0
1
2
2
3
0
0
1
1
0
0
2
1
0
2
0
1
1
0
1
1
0
1
2
1
0
0
0
2
0
1
2
1
0
1
1
0
1
0
2
2
1
2
0
1
1
0
1
0
1
2
1
1
0
1
2
0
0
1
2
0
1
1
2
1
2
0
0
1
1
1
1
2
1
2
1
1
1
2
1
2
0
1
1
0
0
0
1
0
1
1
0
1
0
1
1
3
1
0
0
2
1
1
1
0
2
1
2
1
0
1
0
1
2
0
1
2
1
1
2
1
0
0
2
2
0
0
1
0
6
0
2
2
1
1
0
0
1
1
1
1
0
1
2
0
1
1
2
1
0
2
1
0
0
1
2
2
1
1
2
1
0
2
0
1
2
1
1
1
0
2
2
1
1
1
0
2
2
1
1
1
1
2
0
0
1
1
2
2
0
2
1
1
1
1
1
0
1
1
1
0
1
1
1
1
1
1
0
2
1
1
2
1
0
2
1
1
1
1
2
1
0
2
2
2
0
1
1
1
1
1
0
1
2
1
1
1
1
2
1
1
2
1
5
2
1
2
1
0
1
2
1
1
0
0
2
1
2
2
1
0
0
2
2
1
2
2
0
1
0
1
1
1
0
2
1
1
1
1
1
0
1
2
1
1
1
1
1
1
1
1
1
1
0
2
2
1
1
3
1
2
2
1
1
1
1
1
1
1
2
1
0
1
0
1
1
2
0
1
2
0
1
1
1
0
2
1
2
2
1
2
0
0
1
1
1
1
1
1
2
1
2
1
1
0
0
1
2
1
0
1
1
1
1
2
1
0
1
0
1
2
1
1
1
0
1
1
1
1
1
1
1
0
0
1
1
0
0
1
0
1
2
2
0
1
1
2
2
1
1
0
1
1
0
0
1
1
1
2
1
0
2
1
1
1
1
2
0
1
0
0
1
1
1
2
2
1
2
2
1
2
1
1
0
2
1
2
1
2
0
2
0
1
2
1
1
1
1
0
2
0
0
1
0
1
1
2
2
2
0
0
1
1
0
2
2
2
0
0
0
1
1
2
1
0
1
1
1
2
0
1
0
1
1
1
1
0
1
1
1
1
2
1
1
0
1
1
1
0
2
2
0
0
1
0
2
0
0
0
0
2
0
2
2
0
0
1
0
0
0
2
0
1
0
0
0
1
2
1
1
0
1
1
0
1
0
1
2
0
1
1
2
3
1
0
1
1
1
1
0
1
1
0
2
0
0
1
0
1
0
2
1
2
1
1
1
1
1
2
1
0
0
1
0
0
3
0
1
1
1
1
1
0
1
2
1
0
1
0
2
0
1
1
1
1
1
2
0
0
0
0
1
1
2
1
1
2
1
1
1
2
1
2
1
2
1
2
0
3
1
1
2
0
1
1
0
0
1
1
1
0
1
1
1
1
1
1
1
1
2
0
2
2
1
0
1
0
1
1
1
1
2
0
1
1
0
0
1
2
0
1
1
1
1
1
2
0
2
3
0
2
2
1
0
1
2
1
1
1
1
0
2
1
1
1
1
0
0
0
0
1
1
0
0
1
0
1
1
1
2
2
1
4
2
1
2
0
0
0
2
1
2
2
0
0
1
2
2
2
1
2
1
1
1
1
0
1
1
0
1
1
1
1
0
1
2
1
1
0
1
0
0
1
1
0
1
1
1
1
0
0
0
2
0
2
1
0
2
1
1
1
1
1
2
0
1
0
1
1
1
1
1
2
1
2
1
0
2
1
4
0
1
1
2
1
1
1
0
0
0
1
1
1
1
0
1
2
1
0
1
1
1
1
2
0
2
1
1
1
2
1
1
1
2
1
1
1
1
2
0
1
0
0
6
1
2
1
1
1
0
0
2
1
1
2
1
2
1
1
0
0
2
1
0
0
0
1
1
0
0
0
0
3
2
1
2
1
1
2
1
2
1
1
1
2
1
2
1
1
1
2
1
1
0
1
1
1
1
1
1
1
2
2
1
0
2
2
1
1
1
1
1
2
1
1
2
2
0
2
1
0
2
1
1
1
1
1
1
2
0
2
0
1
1
1
0
0
1
2
2
2
2
0
1
2
1
1
2
1
2
1
1
1
1
1
2
0
0
2
0
1
1
1
1
1
1
0
1
2
1
1
1
2
1
1
2
1
1
0
1
1
0
1
2
1
0
0
0
0
1
1
1
1
3
1
0
2
1
1
1
0
2
1
1
1
1
1
1
1
2
1
0
2
2
2
1
1
3
1
1
2
3
1
1
1
1
2
1
0
1
1
2
1
0
2
1
1
1
1
0
1
2
0
0
2
2
1
1
1
1
2
0
1
0
1
0
2
2
1
1
1
2
2
1
1
0
0
0
0
1
0
1
1
2
0
3
2
1
1
1
2
1
2
1
1
1
0
1
1
1
1
0
1
0
0
2
1
1
1
0
1
1
0
1
2
1
1
2
1
1
0
1
1
2
0
1
2
2
1
1
1
0
1
1
1
0
0
0
2
0
0
1
0
1
2
1
0
1
1
0
2
2
2
1
1
1
0
1
1
2
2
2
1
1
2
0
1
1
1
1
1
0
2
1
0
0
1
1
1
1
1
2
0
0
1
2
1
0
1
1
2
0
0
1
2
1
2
1
0
2
1
1
2
1
1
1
1
1
2
2
1
1
2
0
1
2
2
2
1
1
2
1
0
1
0
2
0
1
1
0
1
1
1
0
1
1
1
1
1
2
1
1
1
1
1
0
1
1
0
1
0
0
1
1
1
2
1
2
0
2
2
1
1
1
0
1
1
1
1
2
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
0
1
1
0
0
0
0
1
0
1
1
1
1
1
1
0
1
0
1
1
0
2
2
2
0
2
1
1
0
1
1
2
1
2
1
0
0
1
1
2
2
5
1
1
1
2
0
0
1
0
1
1
1
0
1
1
1
1
1
3
4
0
1
2
0
1
0
0
1
1
0
1
1
2
1
1
1
2
0
1
1
2
0
0
1
2
0
1
0
1
1
1
1
1
1
0
1
1
2
1
1
1
2
1
2
1
1
0
1
1
1
1
1
0
0
0
1
1
1
0
2
1
1
2
0
2
1
1
1
0
0
0
0
2
1
1
1
0
1
1
2
1
1
0
0
1
0
0
0
1
2
2
1
1
2
1
0
1
0
0
0
2
1
0
2
1
0
1
2
1
1
1
2
1
0
1
1
1
2
1
1
2
0
1
1
1
2
0
0
0
1
2
1
1
1
1
1
0
2
2
0
1
1
1
1
1
1
1
1
0
2
1
0
1
1
1
1
1
1
1
1
1
0
1
2
1
1
1
1
1
1
1
0
0
1
0
1
1
0
2
1
0
1
1
1
1
1
1
1
1
2
1
1
0
1
1
2
1
2
1
0
2
1
2
2
2
1
1
1
1
0
2
2
1
1
2
2
2
1
1
1
0
2
1
1
1
1
2
0
1
1
0
1
2
0
1
1
1
1
1
0
2
2
2
0
1
1
1
1
0
1
1
1
1
2
0
1
2
1
1
2
2
2
1
1
2
1
2
1
0
0
0
0
2
0
1
2
1
1
1
1
1
0
2
1
3
3
1
1
1
1
0
1
1
1
2
1
1
2
0
1
2
1
1
1
0
0
1
1
1
1
1
1
1
0
1
2
0
0
1
1
2
1
1
1
0
1
1
2
1
1
1
1
2
2
2
3
2
1
1
0
2
2
2
0
0
0
1
1
0
1
0
1
0
0
1
0
0
0
1
0
1
1
1
1
2
1
1
1
1
2
1
2
1
2
2
2
1
0
1
1
2
0
1
0
0
0
2
0
1
0
2
0
2
0
0
1
1
0
1
1
1
1
0
1
0
1
0
1
1
1
1
2
0
0
1
0
1
1
0
1
3
1
1
2
2
2
1
0
0
1
1
1
1
1
3
1
0
1
0
1
2
0
1
2
2
1
0
1
1
1
0
2
1
2
1
1
1
2
1
1
2
1
0
1
1
0
1
1
0
0
1
2
1
0
0
2
1
1
2
1
0
1
2
2
0
1
2
1
3
1
1
1
1
2
2
2
0
2
1
1
0
0
0
0
1
2
0
1
0
2
2
1
1
2
1
1
0
1
1
1
1
1
0
2
1
2
1
1
2
1
2
1
0
1
0
0
2
1
0
0
0
0
0
0
0
2
2
1
2
1
1
1
1
1
2
0
1
0
1
1
0
2
1
1
0
1
2
2
2
1
0
1
1
2
1
2
0
1
0
1
1
2
2
0
1
1
0
1
1
1
2
2
2
1
2
0
1
2
0
1
1
1
3
1
1
2
1
1
1
1
1
2
1
0
2
0
1
2
2
1
1
1
2
1
1
1
1
1
2
1
0
0
0
0
1
1
0
1
2
2
3
1
3
2
1
1
0
0
1
1
0
2
2
1
1
1
1
2
0
2
0
1
2
0
1
2
1
0
1
1
1
1
1
1
1
2
2
2
1
1
2
1
1
0
1
1
0
3
1
1
1
0
0
1
1
2
0
1
2
1
1
0
0
2
0
1
2
1
0
1
0
1
1
0
1
1
1
2
1
2
1
1
1
0
1
1
1
0
1
1
2
2
1
1
2
0
2
2
1
0
1
0
1
0
0
2
2
1
1
1
1
2
1
1
0
0
2
1
1
3
0
0
2
0
2
1
0
2
2
0
0
0
1
0
1
0
3
1
1
1
1
2
1
1
1
2
1
0
2
1
2
1
2
1
1
1
1
0
1
0
1
1
2
0
0
0
0
1
2
0
0
0
1
0
1
1
0
2
1
1
1
2
0
0
1
1
0
1
0
1
2
1
1
0
0
1
0
0
1
2
1
1
1
0
1
1
2
1
1
1
1
0
0
1
1
2
13
2
1
3
0
2
2
0
1
1
0
1
0
0
1
1
1
0
1
0
1
0
1
1
1
2
1
2
0
1
1
2
0
1
0
2
1
1
0
1
0
1
2
2
1
1
1
1
1
1
2
0
0
1
1
2
2
0
0
1
2
1
2
2
4
1
2
1
1
1
1
0
1
1
1
1
1
2
2
0
1
1
0
2
1
1
1
0
2
1
0
1
2
1
1
0
0
1
2
0
0
0
0
1
1
1
2
2
1
0
0
1
2
1
1
0
0
2
2
1
1
0
1
2
1
0
1
1
1
1
0
1
0
1
1
2
2
1
1
1
1
0
0
0
1
0
1
0
1
0
1
2
0
1
1
1
0
0
1
2
1
2
1
1
2
1
0
1
1
1
1
1
1
2
0
0
0
0
1
1
6
3
1
1
2
0
2
1
0
1
1
0
1
1
2
1
2
0
2
2
1
1
1
2
0
1
2
1
2
1
0
2
2
1
1
2
2
1
1
0
1
0
1
1
2
0
1
0
2
2
1
6
2
0
1
2
1
1
1
1
1
1
1
1
1
1
1
3
2
0
2
0
1
1
2
1
1
1
1
2
0
3
1
3
1
1
1
2
2
1
2
0
1
0
1
1
2
1
2
2
0
1
0
0
0
2
0
2
2
1
0
0
1
1
2
1
0
0
1
1
1
2
0
1
2
0
1
1
1
0
1
1
2
0
1
1
2
2
1
1
1
1
0
1
2
2
1
1
2
0
0
1
2
1
1
0
2
0
2
1
1
1
1
1
2
2
1
1
0
1
1
1
0
1
1
1
2
1
1
1
0
1
1
1
1
1
0
2
1
1
0
1
0
2
0
1
2
1
2
0
1
1
1
1
1
0
0
0
1
2
1
0
1
1
0
1
2
0
1
0
1
1
1
1
1
0
1
2
2
1
2
1
0
2
1
2
1
1
1
1
1
2
2
0
0
0
2
0
1
1
1
1
1
1
1
1
2
1
0
1
2
1
1
2
1
0
1
1
1
1
1
1
0
0
1
1
1
0
1
1
0
1
1
1
2
0
1
0
1
1
2
0
0
1
1
1
1
1
0
1
3
1
1
1
0
0
2
1
2
1
2
1
0
2
2
2
1
1
3
1
2
1
0
0
1
1
2
0
0
1
1
0
0
0
1
1
2
2
1
1
1
2
1
1
1
0
2
3
1
0
1
1
0
1
1
1
1
1
0
1
2
1
1
0
2
1
1
0
1
0
0
2
0
1
0
1
2
1
2
1
1
2
2
2
1
1
1
0
1
0
2
1
3
2
2
1
1
1
0
1
0
0
1
2
1
2
1
0
2
2
1
0
1
1
1
1
2
0
1
0
0
1
1
2
2
0
1
1
1
0
2
1
1
1
1
1
2
0
2
1
1
0
2
1
0
1
1
1
0
2
1
2
1
0
1
1
2
1
2
0
1
0
1
1
1
0
0
0
0
0
1
1
0
2
0
1
1
1
1
0
2
2
1
2
0
1
0
2
1
2
1
0
1
1
0
2
1
0
1
0
2
1
1
1
1
1
2
1
0
1
1
1
2
1
1
1
2
0
1
1
1
0
0
1
0
0
2
2
1
1
1
0
2
2
1
1
0
1
1
2
1
1
0
0
1
1
2
1
1
1
0
1
1
1
1
1
0
1
2
1
0
1
0
1
1
1
0
1
1
1
1
1
0
0
0
1
0
0
1
0
0
2
0
1
1
2
0
1
2
1
1
3
2
1
0
2
0
0
2
1
1
1
4
0
1
0
0
2
2
2
2
2
1
1
0
2
2
2
1
1
1
0
0
1
1
0
0
1
2
0
0
0
1
1
1
3
1
0
1
0
0
1
1
1
1
1
2
0
1
1
2
0
1
1
2
0
0
2
2
0
1
1
1
2
1
1
1
1
1
0
0
1
1
0
1
2
1
0
0
2
0
2
0
1
1
0
0
2
2
2
2
1
1
1
1
1
0
2
1
2
2
1
1
2
1
1
1
1
2
2
1
0
1
0
3
0
0
1
0
1
1
0
1
1
1
1
1
0
0
0
2
2
1
0
1
0
1
1
0
2
0
1
0
2
1
1
1
0
1
0
1
2
0
1
1
0
1
2
0
1
0
1
1
1
0
1
1
1
2
2
1
1
1
0
2
0
0
2
2
1
1
1
2
1
1
1
0
1
2
1
0
2
2
0
1
1
0
1
2
1
1
1
1
1
2
1
0
1
0
2
1
0
1
4
2
2
2
1
1
1
1
2
1
1
1
0
0
0
1
0
1
2
1
1
2
0
1
1
1
1
1
1
2
1
1
1
0
1
1
1
1
1
1
0
3
0
1
1
1
0
2
2
1
1
1
1
2
1
0
1
2
0
0
1
1
2
1
0
1
1
2
1
0
1
0
2
1
1
1
2
1
1
2
1
1
2
0
1
1
1
1
1
1
2
1
2
0
1
0
1
1
0
0
0
2
1
1
2
1
2
2
1
1
2
1
2
2
1
1
0
2
2
1
1
0
1
0
1
1
1
1
2
1
1
1
2
2
1
1
1
2
0
1
1
0
2
1
1
2
0
0
1
1
1
1
2
1
0
2
1
0
2
1
2
0
1
1
1
0
2
0
0
0
0
4
1
1
1
3
1
0
1
2
1
1
2
2
1
0
0
1
3
2
2
1
1
1
1
1
0
1
1
0
0
1
0
1
1
1
1
2
4
1
1
2
2
2
2
1
2
1
2
0
0
2
0
0
0
2
2
1
1
1
1
0
0
2
2
2
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
2
1
2
0
1
2
1
0
1
1
2
2
1
1
1
1
0
1
2
0
2
1
1
0
0
1
2
1
1
1
1
1
2
2
1
0
1
2
0
1
0
1
1
1
0
1
1
2
1
1
1
1
2
1
1
1
0
1
2
1
1
0
0
1
1
1
2
1
0
0
0
1
1
0
0
0
0
0
2
1
0
1
2
1
0
1
0
2
1
2
1
1
0
1
1
1
1
0
1
1
1
1
0
1
1
1
0
0
1
2
1
2
1
2
1
1
1
2
1
2
1
1
2
1
1
1
0
0
0
0
0
0
1
0
2
1
0
0
0
0
2
1
1
2
1
0
1
1
0
2
1
0
1
0
0
1
1
0
0
1
1
1
1
1
1
0
1
1
1
2
0
3
1
1
0
1
1
1
2
1
2
1
0
0
1
1
1
1
1
2
0
1
2
0
2
1
1
0
1
1
0
2
0
0
2
1
0
1
0
1
1
1
1
0
1
1
0
0
0
1
1
1
2
0
0
1
2
1
1
2
1
1
1
1
1
1
0
2
1
1
1
0
1
2
1
1
1
2
0
1
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
0
1
1
2
0
3
1
1
2
0
1
2
2
1
0
1
0
1
1
1
1
0
1
0
1
1
0
2
1
2
0
0
2
1
1
1
0
0
3
2
1
1
1
1
1
0
0
1
0
1
1
1
1
1
2
1
1
1
1
1
1
1
1
0
0
2
1
1
1
1
1
1
0
1
2
1
2
0
1
2
0
0
1
2
0
1
0
1
1
1
1
1
1
2
0
1
0
2
0
1
2
2
1
2
0
1
0
2
2
1
0
2
0
0
2
1
1
1
1
2
1
1
1
1
0
2
1
1
2
1
0
1
1
2
1
1
0
0
1
2
2
0
2
2
1
1
2
1
1
2
2
2
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
4
0
1
1
0
2
0
2
1
1
1
0
1
2
2
0
2
1
2
2
1
0
1
3
1
1
0
1
1
1
2
0
2
1
0
2
2
0
2
1
1
1
0
0
1
1
1
2
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
0
2
0
1
0
2
1
2
1
1
1
2
1
1
0
1
0
0
1
0
1
1
2
1
1
0
2
0
2
1
2
2
2
0
1
0
2
2
1
0
0
3
0
1
2
1
0
1
0
0
2
0
1
0
1
0
2
1
2
1
2
1
1
1
2
0
2
0
1
1
1
0
1
1
1
1
2
0
1
1
2
1
1
1
1
1
1
1
1
2
1
0
2
0
3
2
1
1
1
1
1
1
2
1
1
2
0
2
0
1
0
0
1
1
0
1
1
0
0
1
2
1
0
1
1
0
0
1
2
0
2
1
1
1
0
1
1
0
1
1
2
1
1
1
2
1
0
2
1
2
1
2
1
1
1
1
1
1
1
0
0
1
1
1
1
1
0
1
0
1
1
0
1
0
2
0
2
0
0
1
1
1
0
1
1
0
1
2
0
1
0
1
1
0
2
2
2
1
2
1
0
2
1
0
1
1
0
1
0
1
0
1
1
1
0
0
2
2
2
1
2
0
1
2
2
0
1
1
1
0
1
1
1
2
0
2
0
1
1
1
2
0
0
0
1
0
2
3
4
2
1
2
1
2
0
1
0
0
1
1
0
1
1
2
2
1
1
1
0
1
1
1
0
1
1
1
0
1
1
1
2
2
2
1
1
0
2
1
0
2
1
1
1
2
0
2
0
1
1
1
0
1
1
1
1
1
0
2
0
0
2
1
2
0
1
1
1
1
1
2
2
1
1
2
1
1
1
0
0
0
1
2
0
1
1
1
1
0
1
1
1
0
2
2
2
1
1
2
1
0
1
2
1
2
0
1
1
2
1
2
1
0
1
2
2
0
0
1
0
1
1
2
1
1
1
1
2
1
2
0
2
1
0
1
2
2
2
2
0
0
0
1
1
1
1
1
2
1
0
1
0
0
0
0
0
0
2
1
1
2
1
1
1
0
1
1
0
0
0
1
2
2
1
0
1
1
0
0
0
2
0
1
1
1
2
2
0
1
1
1
0
1
1
0
1
1
1
0
0
1
1
1
1
1
1
0
0
2
0
2
1
1
1
0
1
1
2
1
1
1
1
0
1
1
1
1
1
1
1
0
1
0
0
0
1
1
1
1
1
0
2
1
2
0
2
1
1
2
1
1
2
0
1
2
0
0
2
2
0
0
0
1
0
1
1
1
1
1
0
0
0
1
1
0
1
0
0
2
1
1
2
1
1
2
1
1
1
0
1
1
1
2
1
1
1
2
2
0
1
1
0
1
1
0
1
3
1
0
0
1
2
1
1
2
1
1
2
1
0
2
2
1
1
2
1
1
1
1
1
1
1
1
1
0
2
1
0
1
1
0
1
0
2
1
0
2
1
1
1
1
1
2
1
2
1
1
2
2
1
2
1
1
1
2
1
0
1
1
2
2
3
2
0
1
1
3
0
2
1
0
1
1
2
0
1
0
2
1
1
1
1
2
0
1
1
2
1
2
1
2
0
1
1
2
1
1
1
1
2
3
2
0
1
1
0
2
0
1
1
1
0
1
1
0
2
1
2
1
0
1
1
2
0
1
2
1
0
2
1
1
2
2
2
1
1
2
1
2
1
1
0
2
1
1
1
1
1
1
0
1
0
2
1
1
2
1
1
1
1
0
2
1
1
0
1
0
2
1
2
0
2
1
0
1
1
1
1
1
1
1
2
1
0
1
1
1
1
0
1
1
0
0
1
1
2
0
0
0
0
1
0
1
1
1
0
0
1
0
1
1
2
2
0
1
1
1
0
1
0
1
0
2
0
1
1
1
1
0
0
1
0
0
1
0
1
2
2
1
2
1
1
0
0
1
0
1
0
2
0
2
1
1
1
1
0
0
1
0
1
1
1
0
1
0
1
1
1
4
1
1
0
4
2
1
1
2
1
1
1
1
1
2
1
1
1
1
1
0
1
2
0
1
1
0
1
0
0
2
1
1
1
1
1
0
0
1
0
1
0
0
1
1
0
1
2
0
1
2
1
1
0
0
2
1
1
0
1
1
0
1
2
0
1
1
1
1
1
1
1
1
2
1
0
2
1
1
0
1
0
1
1
1
0
2
1
1
1
1
0
2
1
2
1
0
1
1
0
1
1
2
2
2
2
1
1
2
2
1
1
1
1
1
0
0
1
0
0
1
2
2
1
1
1
1
1
2
0
0
1
0
0
1
1
2
2
1
0
1
0
2
2
0
0
1
1
1
2
1
1
1
0
1
1
0
1
1
2
1
1
0
2
1
1
0
2
1
1
1
0
2
2
0
2
1
1
2
1
0
0
0
1
1
0
1
1
1
0
1
0
1
0
2
1
1
1
0
2
1
1
2
1
2
1
1
1
1
0
1
0
1
1
1
0
0
0
0
2
1
0
1
0
1
2
2
0
1
0
0
1
1
0
0
0
1
1
1
0
1
1
2
1
1
0
1
1
1
1
1
2
0
1
0
1
1
1
0
1
0
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
0
2
2
2
1
1
1
2
1
2
1
0
1
1
1
0
1
2
1
2
1
0
1
0
1
1
1
1
1
1
0
1
2
2
0
1
1
1
1
1
1
2
1
1
1
1
0
1
2
1
0
1
3
2
2
2
1
2
2
1
2
2
0
1
1
1
0
2
1
2
0
0
0
1
1
1
1
1
0
1
0
0
2
0
0
1
2
1
1
1
1
1
1
1
0
1
2
2
1
0
1
0
1
1
0
1
0
1
1
0
0
0
0
2
2
1
2
0
1
0
1
1
1
0
1
0
1
0
1
1
1
1
0
1
1
0
1
1
1
0
1
2
2
1
1
1
0
0
1
0
0
1
1
1
2
1
1
2
0
0
1
1
2
2
0
1
1
0
1
0
1
1
0
2
1
0
1
1
1
2
1
1
1
1
2
0
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
2
1
1
2
1
1
2
2
1
1
2
2
1
2
1
1
1
1
2
2
1
1
1
1
0
0
1
1
1
1
2
1
1
1
1
1
2
1
2
1
2
2
2
1
1
1
2
2
1
0
1
0
1
0
1
1
1
0
0
2
0
1
1
2
0
1
1
2
2
0
2
2
1
1
1
2
0
0
0
1
1
2
0
1
1
0
2
2
1
1
1
3
2
3
1
1
0
1
1
1
0
1
0
1
1
0
0
2
3
0
0
1
1
0
0
0
0
2
1
1
2
2
2
0
1
1
2
1
0
0
1
1
1
0
0
1
1
2
0
0
1
1
1
1
1
2
0
1
2
1
2
1
0
1
1
2
0
1
0
1
1
1
2
1
1
0
1
1
1
2
1
2
1
1
2
1
1
1
2
1
0
1
0
1
1
1
1
2
2
1
2
1
1
2
1
0
1
0
2
1
1
0
0
1
1
2
0
0
1
2
0
0
1
1
1
2
1
0
1
1
1
3
1
1
1
1
1
1
0
1
0
2
0
1
0
1
0
1
2
0
2
1
1
1
0
1
2
0
0
2
1
0
0
2
1
2
1
1
1
0
2
0
1
1
1
2
1
1
1
2
1
0
1
1
2
2
0
1
1
2
1
2
1
1
0
1
1
1
0
0
2
2
2
1
1
0
0
3
0
1
1
0
1
2
1
1
1
1
0
1
1
1
0
2
1
1
1
1
0
1
1
1
2
1
1
0
1
2
1
0
1
1
0
0
1
1
1
1
2
1
1
1
1
0
0
0
1
0
0
1
1
1
1
2
2
2
1
0
0
0
1
1
2
1
1
2
2
0
3
1
1
1
1
1
0
1
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
0
0
1
1
1
2
1
2
1
1
1
0
1
2
1
1
2
1
0
1
1
1
0
2
1
0
1
2
2
2
2
1
1
0
0
1
1
1
0
2
1
0
1
0
2
1
2
1
3
1
1
0
1
0
0
1
2
1
2
1
1
2
1
1
1
2
0
2
2
1
2
0
1
2
1
1
1
2
0
1
2
2
0
0
2
1
1
1
1
1
0
1
3
1
1
1
2
0
1
1
1
1
2
1
1
2
0
0
1
2
1
0
2
1
2
1
2
2
1
1
0
1
2
1
0
2
2
1
1
2
1
1
1
3
2
1
2
2
0
0
2
0
2
1
2
1
1
1
1
1
1
2
1
1
0
0
0
0
1
1
2
2
1
2
1
0
2
0
1
1
0
0
1
1
0
1
1
1
0
1
2
1
1
0
2
1
1
1
1
1
2
1
0
0
1
1
2
2
1
0
2
1
2
1
2
1
1
1
0
1
0
2
1
2
1
2
2
2
1
1
2
2
0
1
1
1
0
1
1
1
2
1
1
1
0
1
0
2
1
2
2
1
0
0
0
0
1
2
1
1
1
1
0
0
0
2
1
1
0
1
1
1
0
1
2
2
2
1
2
2
1
2
2
1
1
1
2
1
1
2
0
1
0
1
1
0
2
1
0
1
0
1
0
1
1
1
0
1
1
1
0
2
1
2
1
2
1
1
0
1
1
1
2
0
1
0
0
0
1
1
1
1
0
1
0
2
2
2
0
2
2
1
0
2
1
2
1
1
1
1
2
2
2
0
1
1
2
1
2
2
1
1
0
1
0
1
1
1
1
2
1
0
1
1
2
0
1
0
0
1
2
2
0
1
1
2
1
1
1
1
1
1
1
1
4
1
0
0
1
2
2
2
1
0
1
0
1
1
1
2
2
1
2
1
2
1
1
0
2
0
0
1
1
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
0
1
0
1
2
2
1
1
1
1
2
1
2
1
2
1
0
1
1
1
1
1
0
0
1
0
1
0
0
2
2
1
0
1
1
0
1
1
0
1
1
0
0
0
0
2
1
1
0
1
1
1
1
1
1
1
2
2
1
1
1
1
2
1
2
0
3
1
1
1
0
0
2
2
1
1
0
4
1
1
1
0
1
2
0
2
1
1
1
1
1
0
1
0
2
1
0
1
0
1
2
2
0
1
0
1
1
0
1
1
2
2
1
1
1
1
1
0
1
1
1
1
1
0
1
2
0
0
1
1
1
0
2
1
2
1
1
1
1
1
1
2
1
0
1
0
0
2
0
2
2
1
2
1
1
1
1
2
2
0
1
1
1
0
1
2
0
1
3
1
0
1
1
1
1
0
1
2
0
2
1
1
2
0
1
1
1
1
0
1
2
1
1
0
1
1
2
1
0
2
1
1
1
0
2
1
0
1
1
1
1
0
1
0
2
1
0
1
1
2
1
2
2
1
0
1
0
1
1
2
1
2
1
3
1
1
0
1
1
2
1
0
2
2
1
3
3
1
1
1
1
0
1
1
0
1
0
0
1
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
2
1
0
2
1
1
1
0
0
1
2
0
1
0
2
1
1
2
0
1
0
1
2
0
0
2
0
1
0
0
0
1
0
1
2
1
1
0
1
1
1
2
2
1
1
1
1
2
0
0
1
1
0
0
1
1
1
2
1
1
2
1
0
0
1
0
1
1
1
1
1
2
1
0
0
1
1
2
1
2
1
2
2
1
0
0
1
1
1
1
1
2
1
1
1
0
0
0
0
1
2
1
1
1
1
0
2
1
6
1
1
2
1
0
1
0
1
0
0
0
1
1
1
1
0
1
1
0
1
0
1
0
2
0
0
1
1
1
1
0
2
1
1
1
0
1
1
0
1
0
1
2
0
1
1
2
2
0
0
1
1
1
1
1
2
2
1
2
1
1
0
1
0
0
1
0
1
1
0
1
0
1
1
0
5
0
0
1
1
1
1
1
1
1
1
0
1
1
0
2
1
1
2
2
0
2
2
2
1
1
1
1
1
1
1
1
2
2
1
2
2
1
0
1
2
1
1
1
1
1
2
2
1
1
0
2
2
1
1
1
0
1
1
1
1
1
2
2
1
1
2
1
2
1
2
1
2
0
0
1
0
1
1
0
1
2
2
0
1
1
1
2
0
1
1
1
2
1
1
0
1
1
1
1
1
1
0
1
1
2
1
0
1
1
2
1
0
0
4
1
2
2
1
2
0
0
1
2
1
1
1
0
2
2
2
1
1
1
1
1
1
1
1
1
0
0
1
1
1
2
1
0
1
2
2
2
1
1
0
1
1
0
2
1
2
2
0
1
0
1
0
1
1
0
1
0
1
2
0
1
0
0
1
2
1
1
1
1
1
1
1
1
0
1
0
2
1
0
1
1
1
1
2
2
0
0
2
2
1
1
2
2
1
1
1
0
2
0
1
1
1
0
2
1
1
1
1
1
1
0
0
0
1
0
1
2
2
1
1
0
1
2
2
1
2
1
2
1
2
1
1
1
2
0
3
8
1
1
0
1
0
1
1
2
1
1
1
0
0
3
1
0
1
0
0
1
1
0
1
1
1
1
1
0
2
1
1
1
1
1
0
1
2
1
1
0
1
1
1
0
2
0
1
2
1
1
1
1
1
1
0
1
1
1
1
1
1
1
2
1
1
0
2
1
1
1
1
0
1
1
1
1
1
1
1
0
0
0
2
1
0
1
0
2
2
2
2
0
1
1
1
1
1
0
1
0
2
0
1
1
0
1
2
0
1
0
2
2
1
1
1
1
2
2
0
1
2
1
1
2
0
1
1
1
0
0
1
1
1
1
1
2
1
3
1
1
1
0
1
2
1
1
1
2
0
1
1
1
1
1
1
2
1
2
1
1
1
1
2
2
0
0
1
0
1
1
1
0
1
2
1
1
2
0
0
0
1
0
0
2
2
1
0
0
0
1
1
1
2
2
1
1
0
1
0
0
2
1
1
2
2
1
0
1
2
2
1
1
2
2
1
0
1
2
1
0
2
1
1
2
2
0
0
2
1
1
0
1
0
0
2
0
1
1
1
1
1
1
1
2
1
1
1
1
1
1
0
1
1
1
1
0
1
1
0
0
2
2
0
1
1
0
2
1
0
1
1
1
2
1
1
1
0
2
1
1
2
1
1
1
2
0
1
0
1
0
2
2
2
1
2
1
1
1
1
0
2
1
2
0
0
2
1
0
0
1
1
1
2
1
2
1
2
2
1
0
0
1
1
1
1
1
1
2
1
0
0
1
1
1
1
1
1
0
1
2
3
1
0
1
1
1
0
1
1
1
1
1
1
1
0
0
0
1
2
1
1
0
0
1
0
0
2
2
0
1
1
1
2
2
0
2
1
1
1
0
1
0
1
1
1
0
1
2
0
1
1
2
1
2
0
1
1
2
1
0
1
0
2
1
1
2
2
2
0
2
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
0
2
1
1
1
1
2
2
0
1
0
2
1
0
0
2
0
1
1
1
1
0
0
1
0
1
1
1
1
0
1
1
0
0
0
2
0
2
2
1
2
2
1
1
1
1
1
0
1
0
2
1
2
1
2
1
1
0
1
1
1
1
3
1
1
1
1
0
1
2
1
1
0
0
1
1
2
2
0
2
2
1
1
2
1
1
1
2
1
1
1
1
1
1
0
1
1
0
2
1
0
1
1
2
1
1
0
2
1
0
0
1
1
0
2
2
1
2
1
1
1
1
1
0
1
0
4
1
0
1
2
1
0
1
1
1
1
1
1
0
1
1
1
0
1
0
1
1
0
1
1
1
1
2
2
1
1
0
1
1
2
2
1
0
1
1
1
1
0
1
2
1
0
0
2
1
0
2
1
2
1
2
0
1
2
0
1
1
2
1
2
0
1
1
0
1
1
2
1
1
0
1
2
0
0
2
1
1
2
0
1
1
2
1
2
1
1
1
0
2
0
1
1
1
1
2
1
2
1
0
2
1
2
1
1
0
1
1
1
1
2
0
0
0
0
2
1
1
0
1
1
1
0
1
2
1
1
2
0
2
2
1
1
1
2
2
1
1
1
1
2
0
1
0
1
2
2
1
0
2
0
1
2
1
2
0
0
1
2
1
0
0
0
2
2
2
2
1
1
1
1
2
2
1
2
0
0
0
1
0
0
1
1
1
1
0
1
1
1
2
1
0
0
1
0
4
2
1
1
1
1
0
1
2
2
1
0
2
0
2
2
0
2
0
1
1
1
1
2
1
1
2
1
1
2
0
1
2
1
2
1
0
0
0
2
1
1
0
1
4
2
1
0
1
1
1
0
2
1
0
0
1
2
1
1
2
1
0
1
1
0
1
1
2
1
1
1
1
0
3
0
3
1
0
1
2
1
1
0
1
1
1
2
1
0
1
1
1
0
1
1
0
0
2
1
0
2
1
1
0
1
0
1
2
2
1
2
1
0
1
2
2
0
1
2
1
1
1
2
1
0
2
0
0
2
1
1
2
2
1
1
1
1
1
0
1
1
1
2
1
1
2
1
1
1
2
0
2
0
1
1
0
1
1
1
1
2
1
0
2
0
1
0
2
0
0
2
0
1
1
1
0
2
1
1
0
1
1
1
0
1
0
3
1
0
2
0
2
2
1
2
0
1
1
0
2
0
1
0
1
1
2
1
1
1
1
2
3
1
1
1
1
1
1
1
2
0
1
2
0
1
0
1
0
1
2
0
2
1
2
2
2
0
2
1
1
0
1
0
1
1
1
0
0
1
0
0
0
2
0
1
2
1
0
1
2
3
1
2
1
1
2
0
0
0
1
1
1
2
0
2
1
1
1
1
1
1
1
0
0
0
2
1
0
0
0
1
0
0
1
1
2
2
2
1
1
2
1
1
1
1
0
0
1
2
1
2
2
1
1
1
1
0
2
0
2
1
1
1
1
2
1
0
1
1
1
1
1
1
2
0
0
0
0
0
1
1
1
0
1
0
0
2
1
0
2
1
1
0
1
1
0
2
1
1
1
2
2
2
1
0
1
1
0
1
2
1
1
1
1
2
0
0
2
1
2
0
1
1
1
2
0
1
0
1
1
1
1
1
0
0
1
1
1
1
0
2
1
2
0
1
1
1
0
1
0
1
1
1
1
1
1
2
1
2
1
1
3
2
1
1
0
2
1
1
1
2
0
1
1
1
1
1
1
1
1
1
0
0
2
0
0
1
1
1
1
1
2
2
0
1
1
0
1
3
0
1
1
1
0
0
2
1
1
0
1
4
2
2
0
2
1
1
1
0
2
0
1
1
1
1
2
1
1
1
1
2
2
1
1
0
1
0
1
2
1
1
2
0
1
0
0
3
1
1
0
0
2
0
1
1
1
1
0
0
1
1
3
1
1
0
1
2
1
0
0
0
2
1
2
1
0
0
1
1
1
2
0
1
1
0
2
1
2
1
0
0
0
0
1
2
2
1
1
1
2
1
2
1
0
2
2
1
1
0
0
1
1
1
1
1
2
1
3
1
1
1
2
1
2
1
1
1
1
1
0
1
0
1
1
1
1
1
1
2
0
0
1
1
1
0
1
2
1
1
1
2
1
1
0
0
1
1
1
2
1
1
1
0
0
1
2
0
1
0
2
2
1
2
1
1
0
1
1
2
1
1
0
1
2
1
2
0
3
0
2
2
0
1
1
2
1
0
1
2
3
6
1
1
2
1
2
1
0
2
1
1
1
0
0
1
1
1
1
4
1
1
1
1
0
0
1
0
2
1
0
0
1
1
2
0
2
1
1
0
0
1
1
2
0
1
1
1
1
0
1
2
1
0
0
1
1
1
1
1
1
3
2
1
1
1
1
1
0
1
2
1
1
1
2
1
0
0
1
1
0
1
0
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
2
1
2
1
0
5
2
1
0
2
1
1
0
1
1
0
2
1
1
1
1
2
1
2
0
1
0
1
0
1
2
0
1
1
1
1
2
1
1
1
1
3
1
2
0
1
1
1
2
0
1
1
0
0
2
1
1
1
1
1
2
0
1
2
1
0
1
0
0
1
1
1
2
2
1
2
0
0
1
1
2
0
0
0
1
2
1
0
1
1
1
1
1
1
1
1
0
1
1
1
2
1
0
0
1
2
1
1
1
2
2
0
1
2
1
1
0
2
2
1
0
1
1
1
1
2
1
1
0
1
2
0
1
0
1
1
1
1
1
1
1
2
1
0
0
1
2
2
0
2
1
1
1
1
1
1
0
1
1
1
2
1
1
1
0
1
1
2
2
1
1
1
2
1
2
0
2
1
1
2
1
1
1
1
1
0
0
0
0
1
0
2
0
1
0
0
1
2
1
0
1
1
1
2
2
2
2
1
1
2
0
0
0
1
0
1
1
1
1
1
1
1
2
0
2
1
1
4
1
1
1
1
1
2
2
1
1
0
1
1
2
2
1
1
6
1
2
1
0
1
2
1
1
1
2
0
1
1
0
2
2
0
1
1
0
2
2
2
0
1
0
2
0
1
0
0
1
1
2
2
1
1
0
2
0
2
1
1
2
0
1
1
1
1
1
0
1
1
1
2
1
0
0
1
1
0
1
1
1
1
2
1
1
2
0
1
1
0
1
1
0
0
1
2
1
2
1
2
1
1
1
0
0
1
1
0
1
1
1
0
1
1
0
1
2
1
0
2
0
1
1
0
1
2
1
0
1
1
2
1
1
1
1
1
1
0
2
1
1
1
2
0
0
0
1
0
1
2
1
1
0
2
1
4
1
1
2
1
2
1
1
0
0
1
1
2
0
2
0
1
1
2
1
2
1
1
1
1
1
1
0
2
1
0
1
1
0
0
0
0
1
2
1
1
0
2
2
1
1
1
1
0
2
2
2
1
1
1
2
0
0
2
0
1
2
0
1
2
2
0
1
1
1
0
0
0
1
1
1
0
0
2
0
1
1
1
1
0
1
2
2
0
2
1
0
2
0
1
0
0
1
0
1
2
3
2
2
1
1
2
2
1
2
1
0
1
0
1
1
2
0
2
0
1
2
4
1
1
0
1
2
1
1
1
1
1
2
2
1
1
1
1
2
2
0
1
1
0
0
2
1
2
1
0
0
1
0
0
1
2
2
0
0
1
2
2
2
2
1
0
1
0
1
2
2
0
2
1
1
1
1
1
2
1
1
0
0
2
1
1
1
1
2
2
0
0
1
1
1
2
2
1
1
1
2
1
4
0
1
1
0
0
1
0
0
2
1
1
1
2
1
0
2
1
1
1
0
1
2
1
1
1
1
1
0
0
1
0
1
1
1
1
2
0
0
2
0
0
1
2
1
0
2
0
1
1
1
1
0
2
1
2
1
1
2
0
1
2
1
0
0
0
1
1
0
2
0
1
1
1
2
0
1
0
1
1
2
1
1
1
0
0
0
0
2
1
1
1
1
0
1
1
1
1
1
1
2
0
1
2
1
1
1
1
1
0
0
1
2
0
2
0
1
0
1
2
1
1
1
1
1
1
1
1
2
2
2
0
1
1
0
1
1
2
2
2
3
0
1
2
0
1
2
2
1
2
1
2
0
0
2
0
1
1
1
1
1
2
2
1
1
1
1
1
1
3
1
0
1
1
1
1
1
0
1
2
2
1
0
1
1
1
4
0
0
1
1
1
0
1
1
0
0
1
1
1
2
0
2
1
2
2
0
1
1
1
2
1
1
0
1
1
1
0
0
0
0
2
1
0
2
1
1
2
0
1
1
2
2
1
0
2
2
1
0
1
0
1
0
1
0
1
2
1
1
1
0
1
1
1
1
1
3
1
0
1
0
0
1
2
0
2
1
1
0
0
1
0
1
1
2
1
0
1
1
2
0
1
1
1
2
1
1
0
1
1
1
1
1
1
0
0
1
0
0
1
1
0
1
1
1
2
1
1
1
3
0
1
1
2
1
0
1
0
1
0
1
1
0
1
2
0
2
1
1
1
2
1
1
2
2
1
1
1
0
1
1
2
1
1
1
1
2
1
0
0
2
0
1
0
2
1
1
0
1
0
1
1
1
0
2
2
2
1
1
2
1
0
2
1
1
0
2
0
1
1
1
1
1
1
1
1
2
0
1
1
0
0
2
1
2
1
2
1
1
1
0
0
1
0
2
0
1
1
0
1
1
2
1
0
2
2
2
2
1
1
2
1
1
1
1
0
1
1
2
1
0
2
1
2
1
0
1
1
1
0
1
1
0
1
1
1
1
2
1
0
2
2
1
2
1
1
2
0
1
1
0
1
1
2
1
2
1
1
2
2
1
0
3
1
1
1
2
3
1
1
2
1
0
2
0
1
0
1
2
0
2
1
2
1
1
2
0
2
1
1
1
2
0
0
1
0
1
0
1
0
0
1
1
2
1
0
0
2
0
0
0
0
1
1
1
1
1
1
0
1
2
1
2
1
1
1
1
0
1
1
0
0
1
2
1
1
1
2
1
2
1
1
0
1
0
1
1
1
0
1
1
1
0
2
1
2
1
1
2
2
1
0
0
2
1
0
0
1
0
0
2
1
0
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
1
0
1
1
0
2
1
0
0
0
1
1
0
1
1
1
2
0
0
1
1
1
0
0
1
0
1
1
2
1
1
2
2
1
0
0
2
1
0
1
1
1
0
1
1
2
1
1
2
2
2
2
1
1
1
0
0
1
1
1
1
1
1
2
1
6
2
1
2
0
0
1
2
2
1
1
1
2
0
0
1
1
1
0
1
1
2
1
1
2
0
1
1
1
0
1
1
1
1
2
2
0
0
2
1
2
0
1
0
1
1
1
0
0
1
2
0
1
1
1
2
1
1
1
0
1
1
0
1
2
0
2
0
0
0
1
0
1
1
2
1
0
1
0
1
2
1
1
1
0
1
0
0
1
1
1
0
1
0
2
0
0
1
0
0
1
2
1
1
2
1
0
2
1
2
1
0
1
1
1
0
1
0
1
2
0
1
1
0
1
0
0
2
1
1
2
1
0
1
1
0
0
0
2
0
1
0
1
1
1
2
1
1
1
1
1
0
1
0
4
1
1
1
1
0
0
1
0
0
1
1
1
0
0
2
1
1
2
1
1
2
1
1
1
0
2
2
1
2
1
2
0
2
1
2
2
1
1
1
0
0
2
1
1
1
1
1
2
0
1
0
2
1
1
1
1
0
1
2
0
0
0
1
1
4
2
1
2
2
1
0
1
0
2
0
2
1
2
0
1
1
0
1
1
1
0
1
3
0
0
1
1
1
0
1
0
1
2
1
1
0
1
1
0
0
2
0
1
2
1
1
1
1
1
0
1
0
1
1
0
1
1
1
1
0
0
2
3
1
0
2
2
0
1
1
2
1
0
4
1
2
1
2
1
0
1
2
2
2
1
1
1
2
1
1
0
1
0
1
0
2
2
2
0
1
1
1
1
0
0
0
2
1
0
1
1
0
1
0
2
1
0
0
1
1
0
2
1
0
1
4
0
1
1
2
1
2
1
1
1
1
2
2
1
1
2
0
1
0
2
0
1
1
0
1
1
2
2
1
1
1
2
1
0
0
2
0
2
1
1
2
2
1
2
1
2
2
0
0
0
1
1
1
0
0
1
1
0
2
1
1
1
0
1
1
2
2
1
1
0
2
1
1
0
1
2
0
1
1
0
1
0
1
1
1
1
1
1
2
1
0
2
0
0
1
1
2
1
0
0
0
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
0
1
2
0
0
2
1
1
1
2
2
2
1
1
0
1
0
1
1
1
1
1
0
0
1
1
1
0
0
1
1
2
1
1
1
3
0
1
0
0
2
0
1
0
0
2
1
1
1
1
0
1
0
2
1
0
1
1
2
0
2
1
1
2
2
0
1
2
0
2
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
2
0
1
2
1
1
1
0
1
1
0
1
1
2
0
1
1
1
1
0
0
1
2
0
2
1
1
1
2
1
1
0
2
1
1
0
0
1
2
2
1
0
0
1
1
2
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
2
1
2
0
1
2
1
1
0
0
1
1
2
1
1
0
1
0
1
2
2
2
1
0
0
0
0
0
1
1
1
1
0
1
0
1
2
2
1
1
1
0
2
1
1
0
1
2
1
1
1
2
1
2
1
1
0
0
1
0
1
1
0
2
0
0
1
2
1
0
2
1
1
1
0
3
0
1
1
1
1
2
1
1
0
1
1
1
0
1
1
1
2
0
0
2
1
1
1
2
1
1
1
0
2
1
1
1
0
1
1
2
0
1
2
0
2
1
1
0
1
2
1
1
1
2
1
2
1
1
0
1
1
2
0
1
1
1
1
1
1
1
2
1
2
1
1
1
1
2
2
1
1
2
1
1
0
1
1
1
2
1
2
0
1
1
1
1
1
2
0
2
1
1
1
1
1
0
1
0
2
2
1
1
1
0
0
0
1
2
1
6
1
1
2
1
0
1
1
1
0
1
1
2
1
1
1
0
2
1
1
0
1
2
2
1
0
1
1
0
0
0
0
1
1
1
1
1
1
0
0
0
0
0
2
1
2
0
2
2
1
2
1
1
1
1
1
2
2
2
1
0
1
1
1
1
1
1
2
1
1
1
2
0
2
0
1
1
1
1
1
2
1
0
2
1
1
1
0
2
0
1
1
1
1
1
2
1
1
1
0
2
1
1
0
1
1
1
1
2
1
1
1
0
1
2
1
2
2
0
1
1
1
1
0
1
2
1
0
1
1
1
0
2
1
1
1
1
0
1
0
1
0
0
0
0
2
0
1
0
1
2
1
1
1
2
2
0
0
0
1
1
1
1
1
1
1
1
1
1
0
1
0
2
1
1
1
2
1
0
1
2
0
1
1
0
0
0
1
1
1
2
2
0
1
2
1
0
3
1
1
0
0
0
0
2
2
0
1
1
1
2
1
1
0
0
0
1
2
1
2
0
1
0
1
2
1
1
0
2
1
0
6
2
2
0
1
1
1
0
0
1
0
1
1
1
1
1
1
0
2
1
2
1
0
2
0
1
1
1
2
2
1
1
1
2
0
1
1
1
0
1
0
0
1
1
1
2
1
2
2
1
1
0
1
1
2
0
2
1
1
1
1
1
0
0
0
2
0
1
2
1
0
2
2
1
1
0
2
1
0
4
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
0
1
0
2
0
1
1
2
2
1
2
0
0
0
2
0
1
0
2
1
2
0
1
1
0
1
1
1
1
0
2
0
1
1
1
2
0
2
1
0
2
1
1
2
2
1
3
0
0
0
1
0
4
1
1
1
0
1
1
0
1
0
1
2
1
2
1
1
2
1
2
0
1
2
2
0
2
1
0
0
1
2
2
1
1
0
1
1
2
1
1
0
0
1
2
0
2
1
2
0
1
1
0
2
0
1
1
2
1
1
2
0
1
1
1
2
1
1
2
1
1
0
2
0
2
1
0
1
1
0
1
1
0
1
1
0
1
1
2
2
1
2
2
1
0
1
1
1
2
1
2
2
2
1
1
0
0
2
1
1
0
2
2
1
0
1
0
0
0
2
1
1
1
0
1
0
2
1
0
2
1
1
0
1
1
2
1
1
0
1
0
2
0
3
0
1
0
1
1
1
0
1
2
0
2
2
1
0
1
2
2
1
2
1
0
0
1
1
1
0
4
0
2
1
2
1
1
1
1
1
2
1
2
0
0
2
1
0
2
1
0
2
2
0
0
1
2
2
0
0
2
1
1
1
1
2
1
1
0
0
1
2
0
2
1
1
1
0
1
0
2
1
1
1
1
2
2
1
1
1
1
0
1
2
1
0
1
0
1
1
1
1
1
1
0
1
1
1
1
0
1
0
2
2
1
1
2
1
1
1
0
2
1
1
2
0
2
0
2
0
1
1
1
1
1
1
1
1
0
1
1
1
1
1
2
1
0
2
1
2
0
1
0
1
1
1
1
2
2
0
1
2
1
1
0
1
1
2
1
1
1
0
0
0
1
1
1
1
2
0
1
0
1
0
2
0
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
0
1
1
2
1
1
2
1
1
1
1
0
0
1
2
2
2
1
1
1
1
0
1
1
1
2
0
2
0
2
1
2
1
1
1
0
1
1
1
0
2
1
1
1
1
2
1
1
1
0
0
2
1
1
2
1
1
1
0
0
1
0
1
1
0
1
1
2
1
2
1
1
0
2
1
0
2
2
0
0
1
0
1
0
1
1
1
0
2
0
0
2
0
1
0
0
0
1
2
1
0
1
1
1
2
0
1
0
1
0
1
2
1
2
1
1
1
2
1
3
2
1
1
1
0
0
1
1
2
2
0
1
2
1
0
1
1
1
0
0
0
1
1
1
1
1
1
1
0
1
2
1
1
1
2
1
1
1
1
0
1
0
1
1
1
1
2
0
1
1
1
2
0
1
1
1
1
1
1
2
1
1
0
1
1
0
1
0
0
0
2
0
2
2
0
0
1
1
1
1
2
1
0
0
1
1
0
1
1
1
0
1
0
2
0
1
1
1
2
1
0
1
1
1
1
1
1
1
1
1
0
2
2
0
2
2
0
0
0
0
2
0
0
1
2
1
1
1
0
0
1
2
2
0
1
0
0
1
1
1
0
2
1
5
2
0
1
0
1
2
1
1
0
1
1
1
1
1
1
1
2
2
1
1
2
0
1
0
0
1
2
0
2
0
4
1
2
2
1
1
1
1
1
0
2
1
1
1
1
0
1
1
1
1
1
2
1
1
1
1
0
1
1
1
0
0
0
0
1
1
2
1
1
1
0
0
1
0
1
0
0
0
1
1
0
0
1
0
1
1
1
1
0
1
1
1
1
1
0
1
0
1
2
1
2
0
1
2
0
0
0
0
2
0
2
1
1
1
2
0
0
0
0
1
0
1
2
1
1
1
1
2
1
0
1
0
1
0
0
1
1
1
0
0
1
1
1
2
0
1
1
1
2
0
1
1
0
1
0
1
0
1
1
2
2
1
1
1
0
0
0
2
0
1
2
0
1
2
1
1
0
0
1
2
0
0
1
2
2
2
1
2
2
2
1
1
1
1
1
3
1
2
1
0
0
1
0
1
0
2
1
1
1
1
1
0
0
0
2
0
2
1
0
0
1
2
2
2
0
0
1
0
1
1
0
2
0
0
1
0
0
1
0
1
1
0
1
0
0
3
1
1
2
1
0
1
1
0
1
1
0
2
1
1
1
2
2
2
4
0
0
1
0
1
1
2
1
2
1
1
0
2
1
2
0
2
1
2
1
2
1
2
0
2
1
1
2
0
1
0
0
2
1
1
2
1
0
2
0
1
1
1
1
2
2
1
1
0
0
0
0
2
1
0
2
0
1
1
1
1
2
0
0
1
1
1
1
1
2
0
2
1
1
1
1
2
1
0
1
1
1
2
2
1
1
1
2
2
1
0
1
0
0
1
1
1
2
0
1
0
2
2
0
1
2
0
1
2
2
2
1
2
2
1
0
0
1
1
2
1
1
1
1
1
1
0
1
1
1
1
1
2
1
0
0
1
2
1
1
1
2
0
0
2
1
1
1
0
0
0
0
2
1
2
1
0
0
1
1
2
0
0
1
1
1
2
1
4
1
1
0
2
0
2
2
1
1
0
1
0
2
1
2
0
1
1
1
2
0
1
0
1
1
0
0
1
2
1
1
1
1
0
2
1
0
1
0
1
0
1
0
1
1
2
1
1
0
2
0
0
0
0
0
1
1
2
1
2
1
2
1
2
1
2
1
1
1
2
2
1
1
1
0
2
1
0
2
1
1
1
1
1
1
0
2
0
1
1
2
0
1
1
1
1
0
0
1
1
1
0
1
1
1
2
0
2
0
0
0
0
1
1
0
1
1
2
1
2
1
0
1
0
1
0
0
2
0
1
1
2
0
0
2
2
0
0
2
0
0
1
1
1
1
2
0
1
2
0
0
1
0
0
1
1
1
0
1
1
0
1
1
1
1
0
2
2
1
1
0
0
1
1
1
1
1
2
2
0
0
0
1
1
2
1
1
2
1
2
1
2
2
0
0
1
0
2
1
1
2
0
0
2
0
1
1
1
0
1
1
0
1
1
0
1
2
1
1
1
1
0
0
1
2
2
1
1
0
0
1
0
1
2
0
0
1
0
1
2
0
1
0
2
1
0
0
1
2
1
2
2
0
1
1
1
1
1
1
1
1
0
1
1
1
2
1
0
1
1
1
1
1
2
1
1
2
0
1
0
0
1
1
1
1
0
0
1
0
0
1
1
1
1
0
0
1
1
0
1
1
2
1
0
1
1
0
1
0
2
0
2
2
1
1
1
0
1
1
2
1
1
2
1
2
1
1
2
1
1
1
1
0
2
2
3
0
1
1
0
1
1
1
2
1
1
1
1
2
0
1
2
0
2
0
1
1
2
1
1
1
1
1
2
1
2
0
1
2
0
1
1
1
2
0
2
1
1
0
0
3
1
1
1
2
0
0
1
2
1
2
0
1
1
4
1
2
2
1
2
1
0
1
2
1
2
0
0
1
1
1
1
1
2
1
1
0
1
2
1
2
1
1
1
1
1
2
1
0
1
1
1
1
1
1
1
0
1
3
1
1
1
2
1
1
2
1
1
0
1
2
2
2
1
1
0
1
2
2
1
0
2
0
1
1
0
1
2
0
1
2
1
3
2
1
0
2
1
0
1
2
1
1
0
0
1
0
2
2
1
2
3
1
2
0
1
1
1
1
1
2
0
2
1
0
1
1
0
1
1
3
0
0
2
1
1
2
2
1
1
1
1
1
1
0
0
2
2
1
2
0
0
2
1
2
0
2
1
1
1
3
1
1
0
0
1
1
1
1
0
1
2
1
1
1
1
1
0
1
0
1
1
1
1
1
0
0
2
2
1
1
1
0
0
2
1
1
0
1
1
1
2
0
0
1
1
1
2
2
1
2
1
0
2
1
0
1
1
1
2
1
1
0
1
2
0
1
1
1
1
1
1
1
1
2
2
1
1
1
0
1
1
1
1
1
1
0
1
1
0
0
2
1
0
2
2
1
1
1
0
2
0
0
1
1
1
1
0
2
1
1
1
1
0
1
1
0
1
0
1
2
1
0
1
2
0
2
1
1
1
1
2
1
1
2
2
1
1
1
2
0
1
1
2
1
1
1
1
2
2
1
2
2
0
0
1
1
1
1
0
1
1
1
0
1
1
1
1
3
1
2
0
1
2
0
1
1
1
0
1
0
2
1
3
2
0
1
0
1
0
0
0
1
1
1
0
1
1
1
1
0
1
2
1
1
2
1
2
1
1
1
2
2
2
1
1
2
2
1
0
1
0
1
1
1
0
2
2
0
2
1
0
1
2
1
2
1
1
1
1
2
1
1
1
1
1
0
0
0
0
2
1
0
0
1
0
0
1
0
0
0
1
2
1
2
1
1
2
1
1
0
1
1
1
1
1
2
1
1
1
1
2
0
0
1
1
2
1
1
1
1
0
1
1
1
2
2
1
0
2
0
1
1
0
1
0
0
1
1
0
1
1
0
1
1
1
2
1
1
1
1
1
2
1
1
2
1
1
1
1
0
2
2
1
1
1
2
1
0
1
1
1
0
1
0
1
1
0
1
1
0
1
0
1
0
1
1
1
0
3
1
1
1
0
0
2
1
2
2
1
2
1
1
1
1
0
2
0
0
2
1
0
1
1
1
0
2
1
1
1
1
1
1
0
1
2
1
1
1
1
1
2
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
0
2
1
0
0
1
2
2
3
0
2
2
1
2
1
0
0
0
0
0
1
0
0
1
2
2
2
0
1
0
1
1
1
0
0
1
0
1
1
1
2
2
2
1
1
2
0
1
1
0
1
0
0
1
2
1
0
0
0
1
2
1
0
1
2
0
0
1
1
1
1
1
0
2
1
1
1
0
1
2
2
1
1
1
0
0
1
2
1
0
1
1
1
1
1
1
0
0
1
1
0
1
1
1
1
1
2
1
0
1
0
1
1
0
0
3
0
2
0
2
0
1
1
1
1
1
1
0
0
0
1
2
2
1
1
1
2
2
1
1
1
0
2
1
1
0
0
2
1
0
1
0
1
1
1
1
1
2
0
2
2
1
2
2
0
1
0
2
0
2
0
1
1
1
1
0
1
2
0
1
2
1
1
0
1
0
1
1
1
0
1
2
1
1
1
1
1
2
2
0
1
2
2
1
1
3
0
2
2
2
1
1
2
1
0
1
1
0
1
0
1
1
2
1
0
0
2
1
0
1
2
0
2
1
1
1
2
0
1
0
1
0
1
1
2
2
0
3
0
0
1
1
1
0
1
1
1
2
2
0
1
1
1
1
1
2
1
1
0
0
1
1
2
1
0
0
1
1
0
2
1
2
0
0
1
1
1
0
1
1
1
2
1
1
1
0
0
1
2
0
1
0
1
1
1
1
0
0
2
1
1
1
1
0
0
0
2
0
0
1
1
0
2
1
2
1
2
0
2
1
0
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
3
1
1
2
2
1
1
2
1
1
0
1
0
1
2
2
2
1
1
2
1
1
1
0
1
1
1
1
0
0
1
1
1
1
2
1
1
1
1
1
2
0
2
1
1
1
2
1
1
3
1
1
1
2
1
0
3
1
2
1
1
0
0
1
0
0
1
1
2
2
1
1
2
0
1
0
0
0
2
0
2
1
0
0
0
0
1
0
0
0
0
0
1
1
1
2
1
1
1
2
1
1
2
2
1
2
1
1
1
1
2
3
0
1
1
2
0
0
1
1
0
2
2
1
1
1
1
0
0
1
1
2
1
1
2
1
1
1
0
1
1
2
2
1
2
0
2
1
0
0
2
1
1
2
0
1
1
0
2
1
0
1
2
1
1
2
1
2
0
2
1
2
1
1
0
2
0
2
1
2
1
0
1
0
1
1
2
1
0
2
1
1
0
1
2
2
2
1
1
1
1
0
2
2
1
0
1
1
1
0
1
1
1
0
1
4
0
1
2
1
2
1
1
1
0
1
0
1
1
0
1
1
2
2
1
1
1
1
1
0
0
2
0
1
2
1
2
1
0
0
2
1
0
2
2
1
1
1
0
2
1
0
1
1
0
1
2
1
2
2
1
2
1
1
1
1
2
1
1
0
1
0
0
0
1
2
1
1
1
1
1
1
0
2
1
1
1
1
2
2
1
1
1
2
2
1
2
1
1
1
1
1
1
1
2
1
1
0
1
2
1
1
1
1
2
1
1
2
1
2
1
2
1
1
1
1
0
1
2
0
0
0
1
1
0
1
2
1
1
0
0
0
2
1
1
1
2
1
1
1
2
1
1
0
2
1
2
1
1
2
1
1
0
1
2
2
1
1
1
1
0
1
1
1
0
1
1
2
0
1
2
0
1
0
3
1
1
1
0
0
1
0
1
0
0
1
1
1
1
1
1
1
1
1
1
0
0
2
0
1
1
0
0
2
1
1
1
0
2
1
0
0
0
1
0
1
1
0
0
1
2
1
1
0
0
1
0
1
1
2
0
2
1
0
0
0
0
1
1
0
0
2
0
0
2
1
1
1
1
1
2
2
1
5
2
2
0
0
1
1
0
0
1
1
1
1
1
0
1
1
1
2
1
1
0
0
0
0
0
1
1
1
2
1
1
1
2
1
1
1
0
1
1
2
1
1
1
2
2
0
1
2
1
2
0
2
2
1
2
0
2
0
1
1
2
1
1
2
1
1
1
1
1
1
1
2
1
1
2
1
2
1
5
0
1
0
1
1
0
1
1
1
1
1
0
2
1
2
1
0
2
1
0
1
1
1
1
1
1
1
0
1
0
1
0
0
0
1
1
1
2
0
0
1
1
1
2
2
2
2
2
0
0
1
0
0
0
2
1
0
1
3
2
2
2
1
2
2
1
0
1
0
1
1
1
1
2
2
1
2
1
1
1
1
0
0
1
1
1
1
2
0
2
0
2
1
1
2
1
1
2
0
1
1
1
1
1
1
0
1
1
1
0
1
2
0
0
2
2
0
1
0
1
1
1
1
0
1
2
0
1
1
0
0
1
2
1
2
1
0
1
1
1
0
2
1
2
2
0
1
1
0
2
1
1
0
1
1
1
1
0
1
3
1
0
1
2
2
0
1
1
1
2
1
1
1
0
1
1
1
1
2
1
1
2
2
1
2
2
2
0
1
0
0
1
1
1
2
0
1
0
2
1
1
1
1
0
1
0
1
1
2
2
1
1
1
2
0
1
2
2
0
1
1
0
0
2
1
1
1
1
1
1
1
1
1
0
0
1
1
0
0
1
0
1
2
0
1
0
1
2
1
2
1
0
1
2
1
0
2
1
1
2
0
1
1
0
1
1
2
1
1
1
2
0
0
0
1
1
1
0
1
0
1
2
1
1
2
2
2
2
1
3
0
2
1
2
2
0
1
0
0
1
1
1
1
0
0
0
1
0
1
0
1
0
1
1
0
1
1
1
1
1
2
2
1
1
1
0
2
2
1
1
0
2
0
1
1
1
2
1
2
0
0
0
1
1
1
0
1
1
0
0
1
1
1
2
1
1
0
1
1
1
1
0
1
2
0
1
0
0
1
0
1
1
2
1
1
1
1
2
1
1
0
1
2
0
3
1
0
1
2
1
5
2
2
1
1
2
1
1
1
2
1
1
0
2
1
0
1
2
0
3
1
0
1
1
2
1
1
1
0
1
1
0
2
2
0
0
1
0
0
2
1
1
0
0
1
0
0
1
1
2
1
0
1
1
0
1
1
0
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
0
0
0
1
0
2
1
0
1
2
1
0
0
1
1
0
2
2
1
1
0
0
0
1
0
0
1
1
1
1
0
1
1
1
1
0
2
1
0
0
1
1
1
1
2
1
1
1
0
0
2
1
1
2
2
1
2
2
2
1
0
1
2
2
1
1
1
2
1
1
1
1
4
0
1
1
2
1
0
2
2
2
1
1
0
0
1
1
1
0
0
2
1
1
2
1
1
1
2
0
2
1
2
1
1
2
0
2
2
1
0
1
1
2
0
2
0
2
2
1
1
1
0
1
2
1
1
1
1
1
0
1
1
0
1
1
2
0
0
2
1
2
0
1
1
1
1
1
1
1
2
2
1
2
1
2
1
2
1
2
0
1
0
0
0
1
2
1
2
1
1
2
1
1
2
1
1
0
1
0
2
1
2
1
0
2
1
0
1
0
2
2
1
1
1
1
2
1
0
2
2
0
1
2
0
1
0
2
0
1
1
0
0
1
2
1
1
2
1
0
1
0
0
2
0
2
1
1
1
2
0
1
2
2
1
0
0
0
2
1
1
1
1
2
1
2
0
1
0
2
0
1
0
1
2
0
1
2
1
1
0
1
1
0
2
0
0
1
1
1
0
2
1
1
1
0
2
1
0
0
2
1
1
1
2
1
1
1
0
0
1
0
1
1
2
1
0
1
2
2
1
2
0
1
2
0
2
1
2
1
2
2
1
1
2
1
0
0
1
1
2
1
2
1
1
0
0
1
1
1
1
1
2
1
1
1
1
1
1
0
0
2
1
0
0
2
1
1
0
1
3
1
1
0
2
0
1
1
1
1
2
1
1
0
1
1
2
2
2
1
2
2
0
0
1
0
0
1
0
1
2
1
0
0
1
0
1
1
1
2
1
2
0
1
0
2
1
1
1
0
1
0
1
1
1
0
0
1
0
1
2
1
2
1
0
1
1
2
2
2
1
1
0
2
1
1
0
2
2
1
1
2
1
0
1
1
1
1
1
1
0
1
0
1
1
0
0
1
2
1
2
5
0
2
1
1
2
0
1
0
1
2
1
1
1
0
0
1
3
1
2
0
1
2
2
1
0
1
1
1
2
0
1
1
0
2
1
0
1
2
1
0
1
0
1
0
1
2
1
0
1
1
1
0
0
1
1
0
0
1
1
1
1
1
1
2
1
1
1
1
1
1
2
0
0
0
1
0
1
2
2
1
2
2
1
2
2
1
1
1
2
1
1
2
2
1
1
1
2
2
1
1
2
2
1
1
0
0
1
1
1
1
1
1
1
0
2
1
1
1
1
1
1
1
2
0
1
3
0
2
1
1
3
1
1
0
1
1
0
0
1
0
1
1
1
1
1
1
2
2
1
1
1
2
0
0
1
0
0
2
1
1
1
1
1
2
1
2
1
2
0
1
1
0
1
1
2
2
2
1
2
2
0
0
0
1
1
1
1
1
2
1
0
0
2
1
1
2
1
0
0
1
1
1
2
1
0
2
1
1
2
1
0
1
1
2
0
2
1
1
0
2
1
1
2
2
1
1
2
2
1
1
2
2
1
1
2
0
1
0
1
1
1
1
1
1
1
0
0
2
0
1
1
1
1
2
1
0
2
1
1
2
2
1
0
0
2
0
1
1
1
2
1
1
1
1
0
0
2
2
0
1
2
1
1
1
2
1
1
1
0
1
0
1
2
1
1
1
0
0
2
1
1
1
1
4
0
0
1
0
1
1
2
1
1
1
1
1
1
1
2
0
1
2
2
0
1
2
1
2
1
1
0
1
1
0
1
1
1
1
2
0
0
0
1
0
0
1
0
0
1
2
1
1
1
1
2
0
0
1
1
2
0
0
2
1
1
0
1
0
2
1
2
0
1
2
0
2
0
2
1
2
1
1
2
1
1
0
1
2
2
1
1
1
1
3
1
0
1
1
1
1
1
2
2
2
2
0
1
1
1
1
0
2
1
3
1
4
1
1
2
2
0
1
2
1
0
0
1
1
1
2
0
1
1
0
1
1
2
1
1
0
1
2
1
1
2
2
1
1
0
1
1
1
0
2
1
0
0
1
1
4
2
3
1
1
2
0
1
1
0
0
1
1
1
1
1
2
1
2
1
2
0
2
1
1
0
0
1
2
2
2
1
3
1
2
1
0
0
1
2
2
0
1
2
1
1
0
1
1
1
0
1
1
0
1
0
2
2
1
1
1
1
2
2
1
1
1
0
0
0
1
1
0
2
2
1
1
2
0
0
0
0
2
1
0
1
2
2
1
2
1
2
1
1
3
1
1
0
1
2
1
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
0
1
1
0
0
1
1
1
2
2
1
0
0
1
0
2
1
1
1
0
1
1
1
1
2
0
1
2
0
0
2
2
2
1
2
1
2
2
2
2
1
1
1
1
1
0
0
0
1
1
2
1
1
1
0
1
1
1
1
1
0
1
0
1
1
0
1
0
2
0
2
2
0
1
2
1
1
2
1
0
1
1
1
1
1
0
1
0
2
1
1
0
2
1
2
1
0
0
1
0
1
1
1
1
1
0
1
1
1
0
0
1
1
1
0
1
1
1
1
1
0
2
2
2
0
1
0
1
0
1
2
0
1
1
2
1
0
1
1
1
1
2
0
0
0
1
2
2
1
1
0
0
1
1
1
1
0
1
2
1
1
2
3
1
1
2
1
1
0
1
1
1
1
1
1
0
1
0
2
1
1
2
1
1
1
1
1
1
1
2
1
1
2
1
0
2
0
1
1
2
1
1
0
0
2
1
1
0
0
1
0
1
1
1
1
0
1
0
1
1
2
0
1
1
1
0
2
0
1
0
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
0
1
2
2
1
0
1
2
1
0
1
0
1
2
0
1
0
1
2
2
1
0
0
2
1
0
0
1
0
1
2
2
2
2
1
2
1
1
0
1
1
1
0
0
0
2
0
0
1
0
2
1
0
1
1
1
0
1
1
1
1
2
1
1
1
0
2
1
1
2
0
2
1
0
1
1
1
1
2
1
2
1
1
1
1
2
1
2
2
0
0
1
2
0
0
1
2
0
1
0
1
1
2
2
1
1
1
2
0
0
1
1
1
2
0
2
1
0
0
2
1
0
1
2
0
1
1
0
2
0
1
1
1
1
0
0
1
2
2
2
1
0
0
1
2
1
1
1
1
1
2
1
1
1
0
1
2
2
2
3
1
1
0
2
1
1
1
1
1
1
1
1
0
1
1
1
2
1
0
1
1
1
1
0
2
1
1
0
2
1
3
1
0
1
1
1
1
1
1
2
2
1
1
2
1
0
1
1
1
1
4
1
1
1
0
0
2
1
2
1
2
1
1
1
0
0
1
2
2
1
1
1
2
1
0
2
2
2
1
2
1
0
1
1
0
1
2
2
2
2
3
1
2
1
4
1
0
1
0
0
1
0
1
1
2
1
2
1
1
1
0
1
2
1
0
2
1
1
1
1
1
2
1
0
1
2
1
1
1
1
1
0
2
0
1
1
1
1
1
1
1
2
0
1
1
1
1
1
1
1
2
1
1
1
1
2
0
0
1
1
2
1
1
0
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
2
2
1
2
2
1
2
1
1
1
1
1
2
1
1
0
1
0
0
0
1
0
2
0
1
1
2
1
2
1
1
0
1
2
1
2
1
2
0
0
1
3
0
0
2
2
2
1
1
1
0
1
1
1
1
1
1
2
2
0
2
1
1
1
1
1
1
1
2
2
1
1
1
1
2
1
0
1
2
1
1
1
1
1
0
1
0
1
1
1
0
2
1
2
2
0
1
1
1
3
1
2
1
1
0
1
1
1
1
1
2
2
0
1
2
0
1
1
1
1
2
0
1
1
1
1
2
1
1
2
0
1
0
2
1
2
1
1
0
2
1
2
2
1
1
0
1
2
1
1
0
2
1
2
1
1
1
2
2
1
1
2
1
2
2
0
1
1
2
0
1
1
1
1
1
1
0
2
2
1
1
1
1
1
1
1
1
0
1
1
0
1
1
2
1
1
2
3
1
1
1
1
1
0
1
1
1
2
2
0
2
0
1
2
1
0
1
2
2
0
0
2
1
1
1
0
1
1
1
0
0
1
0
1
1
0
2
0
2
1
1
0
2
1
1
1
0
1
2
2
1
0
1
1
1
0
2
0
1
2
1
1
1
1
0
0
0
3
2
2
2
1
0
2
1
0
1
1
1
0
2
1
1
1
1
2
1
0
1
1
1
2
2
0
1
0
1
1
1
0
1
2
1
2
1
1
1
1
2
1
1
2
0
1
2
1
1
0
1
1
1
1
1
1
2
1
1
0
2
1
1
2
2
1
1
2
1
2
1
2
1
1
1
1
1
1
0
0
1
1
0
0
1
0
2
0
1
0
1
0
2
0
2
1
1
1
1
0
2
1
1
1
1
0
1
2
1
1
2
0
1
1
1
1
0
2
1
1
0
1
0
0
1
1
1
1
1
0
1
0
2
2
2
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
0
0
1
1
1
3
2
1
1
0
1
0
2
1
1
1
0
1
2
1
2
0
1
3
1
1
0
1
1
2
1
1
0
1
2
0
0
2
0
1
0
0
0
0
3
0
1
2
1
1
1
1
3
1
1
0
1
1
1
1
1
1
0
1
1
1
1
1
2
1
1
0
1
1
0
2
1
0
1
1
1
0
2
2
0
0
1
3
0
0
1
2
2
1
2
1
1
1
2
1
0
0
1
2
1
1
1
2
0
2
1
2
1
1
1
1
1
1
1
0
1
1
1
1
2
1
1
1
1
1
0
1
1
1
1
1
1
1
0
1
1
1
2
1
1
1
0
1
0
3
1
1
1
1
0
2
1
0
2
1
1
1
2
2
0
1
1
1
2
1
1
1
0
1
0
2
1
1
2
1
2
1
1
1
1
0
0
2
2
0
1
0
2
0
1
2
1
2
2
1
0
0
2
1
0
1
0
1
1
0
1
1
2
3
2
1
1
0
3
1
1
3
1
1
0
1
2
1
1
0
1
2
1
3
2
1
0
1
1
1
1
0
0
1
1
1
0
1
1
1
0
3
0
1
2
1
0
1
2
0
0
1
1
0
0
1
1
0
2
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
2
2
1
1
1
0
1
3
1
1
0
2
2
1
1
0
1
1
1
0
1
2
0
1
1
1
1
1
2
1
1
2
2
0
0
2
1
2
0
0
2
1
1
1
1
1
1
2
0
0
0
1
1
2
1
0
0
2
1
6
1
1
1
0
1
1
1
1
1
2
1
1
0
3
1
0
1
1
1
2
0
1
1
0
1
2
1
1
1
2
1
1
0
0
0
0
1
1
1
0
2
1
0
0
1
0
1
0
1
0
0
0
1
1
2
1
1
0
2
1
1
0
2
1
0
1
1
1
3
1
1
1
2
2
2
1
2
0
1
2
2
1
0
2
1
1
0
1
1
0
0
1
0
1
1
1
1
1
2
0
1
1
0
1
2
1
2
2
2
0
2
1
1
0
0
1
1
2
0
1
1
0
2
1
2
1
0
3
1
1
1
1
2
1
0
0
0
1
1
2
1
1
1
2
1
0
1
1
1
2
0
0
0
1
0
0
0
1
1
1
2
1
2
0
0
0
0
1
1
2
2
2
1
2
1
2
1
2
0
1
0
1
2
1
0
2
1
1
1
0
0
1
1
1
0
1
1
2
1
0
0
1
2
1
1
1
1
1
1
1
2
1
0
2
0
2
2
2
1
1
1
0
0
3
2
1
1
0
1
1
1
0
1
0
1
1
1
2
1
0
1
1
1
1
1
2
1
0
1
1
1
1
0
1
0
0
2
2
1
2
1
2
1
1
1
1
1
1
1
1
4
2
0
1
1
1
1
1
1
2
1
0
1
0
1
2
1
1
0
0
0
1
1
1
1
0
1
1
2
1
1
1
2
1
1
2
2
1
1
2
2
1
2
0
1
1
0
1
1
1
0
2
2
0
2
1
1
1
1
1
1
1
1
1
0
3
3
1
2
0
2
1
1
1
0
1
1
2
0
2
1
1
0
1
0
1
1
2
2
0
1
1
1
2
1
0
1
1
0
0
1
0
0
1
1
1
1
2
1
1
1
1
2
2
2
0
0
0
1
0
0
1
0
0
1
1
1
1
0
0
1
2
2
2
1
0
1
1
0
1
2
2
1
1
1
0
0
2
0
1
0
0
2
1
0
2
1
1
1
1
0
2
1
0
1
2
2
2
1
1
0
1
1
0
1
0
2
1
1
0
2
0
2
0
1
1
0
1
1
2
0
1
0
1
1
1
0
1
0
2
0
1
0
3
1
0
2
1
0
1
0
0
2
0
1
1
2
0
1
1
1
0
2
2
1
2
2
2
2
1
1
1
0
1
0
1
1
2
1
0
1
1
0
2
0
0
1
1
1
0
2
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
0
0
1
1
1
2
1
2
2
0
1
0
2
0
0
1
1
1
2
1
2
1
1
2
0
1
1
2
1
0
1
1
1
0
2
1
1
1
1
1
2
0
2
1
0
1
2
0
2
2
2
2
1
3
2
2
3
2
0
1
1
3
2
2
1
2
1
1
1
1
1
1
0
2
1
2
1
1
0
0
1
1
0
1
0
1
1
0
0
0
1
1
1
1
2
0
1
1
1
0
2
2
2
1
0
2
2
0
2
2
1
2
2
2
2
1
1
0
0
0
0
1
1
1
2
0
1
1
2
1
1
0
2
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
2
1
1
1
2
0
1
1
2
2
1
1
1
1
1
1
2
0
1
0
0
2
1
1
0
2
1
1
2
4
1
1
1
1
1
1
3
1
1
1
2
1
0
1
1
0
0
2
2
0
0
2
1
0
1
0
1
2
3
0
2
2
1
0
1
1
0
2
1
2
1
0
2
2
1
0
2
1
2
2
1
2
1
2
0
1
1
0
2
1
1
1
2
1
1
1
1
1
1
2
0
1
1
1
1
0
1
1
2
1
1
1
2
1
1
1
0
2
0
1
0
2
0
2
1
1
0
2
0
1
1
0
0
1
1
2
1
0
2
2
1
1
1
1
0
1
0
0
0
2
1
1
0
1
1
0
1
1
1
1
0
2
1
1
1
2
1
1
2
1
0
2
1
1
1
2
2
1
1
1
0
0
2
2
1
1
2
1
1
0
1
1
2
0
2
2
1
0
1
1
0
2
2
2
0
1
2
2
1
1
1
2
0
1
2
2
1
1
0
1
1
1
1
1
0
1
1
1
1
0
1
0
0
1
2
1
1
0
2
1
2
0
1
1
1
0
1
1
1
0
3
2
1
1
0
1
1
2
1
3
1
0
1
1
2
1
1
0
1
1
1
2
1
1
2
0
2
0
1
1
0
1
1
1
2
1
2
0
0
2
2
0
1
1
1
1
1
0
1
1
1
0
1
1
1
1
0
2
0
1
1
2
1
1
2
1
2
2
0
2
1
0
1
1
1
2
2
1
1
2
1
2
2
0
1
2
1
1
2
1
2
1
1
1
1
1
1
0
1
1
2
1
1
1
0
1
1
1
1
1
1
0
0
1
1
0
1
1
0
1
0
1
0
0
2
0
2
0
0
1
1
0
2
1
1
0
1
0
1
1
0
1
2
1
0
0
2
0
1
2
2
1
1
0
2
1
1
0
1
0
1
1
1
1
2
1
0
1
1
2
1
1
1
1
1
2
1
2
0
1
0
2
2
1
2
1
1
2
0
1
0
3
1
1
0
2
1
1
0
2
0
2
1
1
2
1
1
2
1
2
0
1
1
1
1
2
0
1
0
1
1
1
0
0
1
1
1
1
2
0
1
1
2
2
1
2
1
1
1
1
0
1
0
1
0
0
2
1
1
0
0
1
1
2
0
1
2
1
1
2
2
2
0
0
2
0
1
0
1
2
2
1
0
1
1
0
1
1
0
2
2
1
1
1
1
2
0
2
1
1
1
0
0
1
1
2
1
1
0
1
2
2
2
3
1
2
1
1
1
1
1
1
0
1
1
0
0
1
1
0
1
0
1
1
1
0
1
2
1
2
2
1
1
1
0
2
1
1
0
2
2
3
0
1
1
2
1
1
1
0
0
1
1
0
1
2
3
0
2
2
0
1
1
1
1
1
1
0
1
0
1
2
0
1
1
1
0
1
2
1
1
1
1
0
2
2
0
0
1
2
1
1
1
0
2
2
1
2
1
2
1
1
1
3
2
0
0
2
1
0
1
1
1
0
1
1
0
3
1
1
1
1
0
0
1
1
1
2
1
1
1
1
2
2
1
2
0
1
0
0
1
1
2
1
1
0
2
1
2
1
1
1
0
1
1
2
0
0
2
1
2
1
1
1
0
1
2
1
1
1
1
1
1
1
2
2
1
0
0
1
0
2
1
1
2
1
2
1
1
1
1
1
2
2
1
1
1
0
0
1
0
2
1
1
0
0
0
0
0
1
0
2
1
2
0
1
2
1
2
1
0
1
0
0
1
1
1
0
1
1
0
1
1
1
0
0
2
1
2
2
1
0
2
1
1
1
0
1
1
1
1
0
1
0
0
1
0
0
0
2
2
1
1
2
2
1
2
2
0
0
0
1
1
0
1
1
1
0
2
0
1
1
1
0
1
1
2
1
2
1
2
1
0
2
1
1
1
2
2
0
0
0
2
3
0
1
1
1
0
1
1
0
1
1
1
1
0
0
1
2
1
2
2
1
1
1
2
0
0
1
1
1
1
0
1
1
2
1
2
0
3
0
1
0
2
2
0
2
0
1
1
1
1
1
2
1
1
1
1
1
2
0
2
0
2
1
0
1
1
1
1
1
3
0
1
1
1
0
1
2
0
0
1
1
1
1
0
2
2
1
1
1
3
1
1
2
1
1
0
1
0
0
1
1
1
2
0
2
2
1
1
2
0
1
1
1
1
1
0
0
0
1
0
1
1
1
1
1
0
1
0
1
0
1
2
1
1
0
1
3
1
0
2
1
2
0
0
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
0
1
1
1
2
1
1
2
1
1
1
1
2
1
1
1
0
1
1
2
0
2
1
2
1
1
2
2
1
1
0
0
2
1
2
3
1
1
2
0
0
1
2
1
1
1
1
2
1
1
2
0
1
1
2
2
0
0
1
2
1
2
2
1
1
1
1
1
0
0
1
0
2
2
1
0
0
1
1
1
0
1
1
1
0
2
0
2
1
1
0
0
1
1
1
1
1
3
1
1
1
2
2
1
1
1
0
2
1
1
1
2
1
1
1
0
0
2
2
1
1
1
2
1
2
2
1
2
1
0
1
0
0
1
1
0
1
1
2
1
2
1
0
1
2
1
1
1
0
2
0
1
2
1
0
0
2
0
1
0
1
1
1
1
1
1
2
0
1
2
2
2
1
0
0
2
1
2
2
1
1
0
0
1
2
1
1
0
1
1
0
1
0
0
2
1
2
0
1
1
2
2
1
1
1
1
2
1
1
1
2
1
0
1
0
1
2
2
1
1
1
1
1
2
1
1
1
1
2
1
0
1
0
2
2
1
2
1
0
1
1
1
1
0
0
1
0
2
0
0
0
0
1
0
1
1
1
2
0
1
1
1
1
1
3
0
1
2
1
2
2
1
0
1
1
1
1
0
2
1
2
1
1
2
1
1
1
0
0
0
0
1
1
1
1
0
2
2
1
1
0
2
0
1
1
0
1
0
0
1
0
0
2
1
2
1
0
0
0
0
1
2
0
2
2
1
1
2
0
0
0
0
2
1
1
2
1
1
1
1
1
0
0
2
2
0
0
1
1
0
0
0
2
1
1
3
0
0
0
0
0
0
0
1
1
1
0
1
1
1
1
1
0
1
2
1
0
1
1
1
1
1
0
0
1
0
0
1
0
1
1
0
0
2
1
0
0
1
2
1
1
0
2
1
0
1
1
1
1
1
0
1
1
1
0
1
2
1
1
1
0
0
0
0
0
0
1
1
1
1
1
2
1
0
2
2
2
2
2
1
1
1
1
1
1
1
2
2
1
2
2
1
1
2
1
1
1
2
2
1
1
1
1
1
0
0
2
1
0
1
0
1
1
0
2
1
0
1
1
2
1
2
0
1
0
1
2
1
2
1
0
1
2
1
1
0
0
0
2
1
0
1
1
2
1
1
4
1
0
0
2
0
1
0
1
1
2
1
1
2
0
1
1
1
1
2
1
2
0
1
2
0
1
0
1
0
1
2
1
2
0
1
0
1
2
1
1
1
1
0
1
1
2
0
1
1
0
1
2
0
0
1
1
1
1
2
2
2
1
1
1
1
1
0
1
0
2
1
0
1
2
1
1
1
0
1
1
2
0
1
1
1
0
0
2
2
1
0
1
2
0
1
1
1
1
1
0
1
2
0
1
0
1
1
2
1
1
1
1
1
1
1
2
1
0
1
1
1
1
1
1
0
1
0
2
0
2
1
0
1
0
0
0
2
2
2
1
1
1
1
0
2
1
1
0
1
1
1
1
0
1
1
0
1
0
1
1
0
0
1
5
0
2
0
0
2
1
1
2
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
3
2
1
2
1
1
0
1
2
2
1
1
1
1
0
1
1
1
2
2
1
1
0
0
1
0
2
0
1
0
1
1
1
1
0
1
0
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
0
1
1
1
1
1
1
0
1
0
2
1
1
1
1
3
1
1
0
0
1
0
2
0
1
1
1
1
0
1
1
1
1
1
1
1
0
1
1
1
2
2
0
2
0
2
0
1
1
2
1
1
1
1
1
1
2
1
1
1
0
0
0
1
0
1
0
1
1
1
3
2
1
1
2
1
0
1
0
1
2
3
1
2
1
0
1
1
1
1
1
1
1
1
0
2
1
2
1
2
2
2
0
1
1
1
0
2
2
0
0
1
0
1
1
1
1
2
1
2
1
1
2
1
1
0
1
1
1
1
2
1
1
2
2
2
1
2
1
0
1
2
0
0
0
1
2
2
0
2
0
2
1
1
2
1
1
2
1
2
0
0
2
2
2
0
2
2
1
2
1
0
0
1
0
1
1
0
2
1
0
2
0
2
1
1
2
0
1
0
3
1
1
0
1
0
2
1
0
1
2
1
2
0
0
1
1
1
1
1
0
1
1
0
3
2
2
1
1
0
1
1
1
1
1
1
1
0
0
1
2
2
1
0
0
1
1
2
0
2
0
2
3
0
2
1
2
1
1
1
1
1
1
2
1
1
0
2
2
0
0
1
1
1
0
0
1
0
1
1
1
1
2
2
1
1
0
2
0
0
0
0
0
1
1
1
1
1
1
1
2
2
1
1
0
2
1
1
0
2
0
1
0
1
1
0
1
1
1
1
1
0
1
1
2
0
0
0
1
1
2
2
2
1
1
0
1
0
1
1
0
2
1
1
2
1
0
1
0
1
2
1
1
1
1
2
2
1
2
2
1
1
1
1
0
2
1
0
1
0
2
0
0
1
1
1
1
1
1
0
0
2
2
1
0
1
0
1
1
1
1
1
2
1
1
1
1
0
1
0
2
1
0
1
1
0
2
2
1
1
0
1
0
1
1
3
0
1
0
1
0
1
1
1
1
0
2
0
0
1
0
2
0
1
0
0
2
1
2
2
0
1
1
2
0
1
1
4
0
2
1
1
2
0
1
1
1
1
2
0
2
1
0
1
1
0
1
2
1
0
1
2
1
0
1
0
0
0
1
1
1
1
1
0
1
1
0
1
1
1
0
0
1
0
2
1
1
2
1
2
1
2
0
0
2
2
2
0
0
1
1
1
2
1
1
0
0
1
1
1
0
1
1
1
0
1
1
1
0
1
0
0
0
0
1
1
0
2
0
0
1
1
2
1
2
2
2
0
1
1
0
1
1
0
0
1
1
1
2
2
2
1
1
0
1
1
0
2
1
0
1
1
1
1
2
0
1
0
0
0
0
1
2
4
0
2
1
0
2
2
1
0
1
0
1
1
2
0
1
2
1
1
1
1
1
1
4
1
0
1
0
1
0
0
1
2
1
1
0
0
0
1
2
1
0
1
2
1
1
1
1
1
0
1
1
1
0
1
1
2
1
1
1
0
2
1
2
1
1
1
1
2
1
3
0
2
1
0
0
1
2
1
0
1
0
1
1
0
1
1
1
2
1
2
1
1
0
1
1
2
2
1
2
1
0
1
1
2
1
2
1
1
0
1
0
1
1
1
0
0
1
2
1
0
0
0
1
0
2
0
1
1
0
1
1
0
1
2
1
1
1
1
1
1
1
1
2
0
1
1
4
0
2
0
1
0
0
0
0
1
0
2
2
0
1
0
1
2
1
0
1
2
3
1
1
0
1
1
0
0
0
2
1
1
0
1
2
2
1
0
2
2
1
1
2
2
0
2
1
1
1
1
0
1
2
2
0
3
1
1
0
0
0
0
1
0
0
0
2
0
1
2
1
2
1
1
0
0
1
2
0
1
0
0
1
2
1
1
1
1
1
1
2
1
2
0
1
1
2
1
0
1
1
1
1
1
1
1
1
0
1
0
1
1
1
1
1
0
1
2
1
0
1
1
1
0
2
1
1
0
1
1
0
1
1
0
1
2
0
0
1
1
0
2
1
0
1
1
2
0
2
1
0
0
1
1
0
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
0
1
2
1
1
0
1
1
1
1
2
1
2
0
1
1
1
1
1
1
0
1
0
1
2
3
1
1
0
1
1
0
2
1
0
1
1
0
1
2
2
1
0
1
2
1
1
1
1
0
2
2
0
1
2
1
0
2
2
1
1
2
1
0
1
1
0
1
1
1
2
2
2
2
1
1
1
0
1
1
2
0
1
5
1
2
1
0
2
2
1
1
0
2
2
1
1
1
0
2
0
1
0
1
2
1
0
0
1
0
0
2
0
1
2
1
1
1
0
0
1
2
2
0
2
2
2
1
1
1
1
1
1
1
0
1
1
1
1
0
1
2
0
1
0
1
1
1
1
2
1
2
0
1
2
2
1
2
0
2
2
1
2
1
1
1
2
1
0
1
0
4
0
1
1
0
0
2
1
2
1
1
2
0
0
1
1
2
0
1
1
1
0
1
1
1
0
0
1
1
2
2
1
1
1
1
1
1
1
0
0
2
2
1
3
1
0
2
1
1
1
0
1
1
1
0
1
2
1
2
1
1
1
0
0
0
1
1
2
1
2
1
1
2
2
0
1
0
0
2
0
0
1
0
0
0
1
0
1
0
1
0
0
1
1
1
1
1
2
1
2
1
1
1
1
1
2
2
1
1
2
1
1
0
1
1
1
1
2
2
1
1
1
0
2
2
2
0
1
0
1
2
1
0
1
1
2
1
1
1
2
1
2
1
1
1
0
2
0
0
1
2
1
1
2
0
1
2
2
1
0
1
0
2
2
0
1
0
2
1
1
0
1
1
1
0
0
1
1
1
1
0
0
1
1
0
2
2
0
0
0
1
1
0
0
1
1
1
0
1
1
0
1
2
1
0
1
2
1
1
0
0
2
0
1
0
1
1
2
2
1
1
0
1
1
0
0
2
1
2
0
1
2
1
0
1
1
2
1
0
2
1
0
1
0
1
1
1
0
2
1
0
2
1
1
1
2
1
1
1
2
2
0
1
2
1
0
1
1
2
1
2
0
1
2
1
1
0
1
0
1
0
1
1
0
2
1
1
0
1
3
1
1
2
0
0
2
1
2
2
1
1
1
1
2
2
0
2
0
2
1
0
1
1
2
1
0
1
0
1
1
2
2
2
0
1
0
0
1
1
2
1
0
2
0
2
0
6
1
1
2
1
2
0
3
0
1
2
1
1
0
0
2
2
1
2
0
1
0
1
2
1
2
1
2
0
2
0
1
0
1
1
2
1
0
1
1
1
1
1
1
0
1
1
0
0
1
1
1
0
4
2
1
1
2
2
0
0
1
1
1
1
0
2
1
1
1
0
1
0
4
0
0
0
0
1
1
1
2
1
1
2
2
0
1
3
1
1
1
0
1
2
0
1
1
1
1
1
1
1
0
1
1
1
1
0
0
0
1
1
0
2
2
1
1
1
0
2
1
0
1
1
2
1
1
2
0
0
2
2
1
1
1
2
1
1
1
1
1
2
2
1
0
0
1
1
1
0
1
2
3
2
1
0
1
0
1
0
1
1
1
0
0
2
0
3
2
2
2
1
2
2
2
2
1
1
1
1
1
2
2
1
2
1
0
2
1
0
1
2
1
2
0
1
1
1
0
1
0
0
1
1
1
2
0
1
1
0
2
1
1
0
0
2
2
2
1
1
1
3
0
2
2
3
1
0
2
2
2
1
2
0
1
1
1
1
0
0
1
1
0
1
0
1
2
0
1
2
2
0
0
1
2
1
0
2
1
1
1
1
1
0
2
2
1
1
0
1
2
1
0
2
1
0
2
2
2
1
1
0
0
1
2
1
2
0
2
0
1
1
1
2
0
2
1
1
0
2
2
0
2
1
1
0
2
7
0
4
1
1
0
1
1
1
2
1
1
2
1
1
1
2
1
1
2
1
1
1
1
2
2
1
1
2
1
1
1
1
1
3
2
1
1
0
1
0
1
2
2
1
2
1
2
0
1
0
1
0
1
0
0
1
1
1
1
1
1
2
2
1
2
1
2
0
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
2
2
0
1
1
0
1
1
2
1
1
2
2
2
1
1
0
1
0
0
0
1
2
2
2
1
0
0
1
1
2
1
1
2
1
0
1
1
2
2
2
2
0
1
1
2
2
0
1
0
1
1
1
1
0
2
0
1
1
1
1
0
0
2
0
1
1
0
0
0
1
2
0
0
1
1
1
1
0
0
2
1
0
1
1
2
1
1
1
1
1
0
1
2
2
1
1
2
1
0
1
0
2
1
0
1
1
1
1
1
1
1
0
2
2
1
2
1
1
2
1
1
1
1
2
2
0
1
1
2
1
0
2
1
0
2
0
1
1
1
1
0
2
2
1
2
1
1
2
0
0
1
2
1
0
2
1
5
0
1
1
1
1
0
5
2
1
1
1
2
1
1
1
1
1
1
2
0
1
1
1
1
2
2
0
1
1
1
1
1
1
1
0
1
0
1
1
1
1
2
1
1
0
2
2
0
2
1
1
1
1
1
0
1
2
0
0
1
0
2
1
1
0
1
2
2
1
0
1
1
1
1
1
1
1
1
2
1
1
0
1
1
1
1
0
1
1
0
1
2
0
2
1
1
1
2
1
1
2
1
1
0
1
2
1
1
1
0
0
1
1
1
0
1
0
2
1
1
0
0
2
0
0
1
0
2
2
1
2
2
0
1
1
2
1
2
2
1
1
1
1
1
0
1
0
2
2
1
0
1
1
2
1
0
1
1
2
2
2
1
1
1
0
0
0
1
2
1
0
1
0
1
0
2
0
0
2
2
0
1
1
1
1
1
2
1
1
1
1
2
0
0
1
1
1
2
1
2
2
0
0
0
1
2
0
2
0
1
2
1
1
1
2
1
2
1
1
1
2
1
1
0
1
1
0
0
1
2
1
1
1
1
1
2
1
1
2
2
1
1
1
0
2
2
1
2
0
1
2
1
1
2
1
0
2
1
1
0
2
1
0
1
1
1
1
1
1
1
0
0
1
1
1
0
1
1
0
0
0
1
2
1
2
2
2
2
1
1
1
2
2
1
0
1
1
1
2
2
0
1
1
1
0
1
1
1
1
1
1
2
2
1
0
0
1
0
1
0
1
2
1
2
1
0
1
1
1
2
0
1
1
0
1
1
0
0
2
1
0
1
0
2
0
2
1
0
1
1
2
2
2
0
1
2
1
0
2
1
0
1
1
0
1
2
0
1
0
2
1
1
0
0
0
1
0
1
1
1
0
1
0
1
1
1
2
0
1
1
2
1
0
1
2
1
2
1
1
1
0
0
1
1
1
0
3
1
1
2
1
0
1
1
0
0
1
1
1
0
1
2
0
0
2
1
1
2
2
2
1
1
1
1
1
2
0
0
1
1
0
1
1
1
1
1
1
1
1
0
2
2
1
1
2
0
2
0
1
0
1
1
2
1
0
0
1
2
2
1
1
1
0
1
0
1
2
0
0
0
0
2
1
1
1
0
0
1
2
2
1
1
0
1
2
0
1
3
1
1
1
1
2
1
0
1
2
0
2
1
1
1
1
1
1
2
0
2
1
2
1
0
0
0
1
1
1
1
1
0
2
0
0
2
0
1
2
1
1
2
2
1
1
1
0
1
2
1
1
1
2
1
1
1
0
1
1
1
0
1
1
2
1
0
1
1
1
2
0
2
1
1
2
1
1
2
0
1
0
1
2
0
2
1
2
0
0
1
2
0
0
1
2
2
0
2
1
0
1
1
0
1
2
1
1
1
1
1
2
2
1
0
2
1
0
1
2
2
1
1
1
1
1
0
2
2
1
2
2
0
2
0
1
1
2
0
2
2
2
2
1
2
2
1
1
1
2
1
0
1
1
2
2
0
1
1
1
1
2
1
0
2
0
2
2
1
2
2
2
1
1
1
0
1
2
2
2
1
1
1
1
1
1
0
1
1
1
2
0
0
2
2
0
0
2
2
1
2
1
2
2
0
0
2
2
2
1
2
1
8
1
0
1
1
0
3
1
0
2
1
0
1
4
0
1
2
0
2
1
1
1
1
2
1
1
1
1
2
1
1
1
0
1
3
0
1
0
1
2
0
2
2
0
1
1
2
1
1
0
2
1
2
1
1
1
0
1
0
1
2
1
1
1
1
2
1
1
1
0
2
1
2
1
0
2
0
1
1
1
1
0
2
1
1
0
1
0
1
1
2
1
2
2
1
1
1
1
2
0
0
0
3
1
0
1
0
1
1
0
0
1
1
1
2
2
2
1
1
0
1
1
1
1
1
1
0
0
0
2
2
0
1
1
1
2
1
1
1
1
1
0
0
1
0
0
1
3
2
2
1
0
0
1
0
1
0
1
1
1
1
2
2
0
0
1
0
0
1
1
0
0
0
1
1
0
2
1
1
1
1
1
1
1
1
2
1
1
2
1
0
1
1
0
0
2
0
2
1
1
2
1
1
0
1
1
1
1
1
0
2
1
2
1
0
1
0
0
1
1
2
0
1
2
2
1
2
2
1
2
1
2
2
1
1
1
1
1
0
1
0
3
1
1
0
1
1
1
2
1
1
0
1
1
1
1
1
1
0
1
2
0
1
1
0
0
0
1
1
0
0
0
1
1
0
0
1
0
2
0
1
1
2
1
0
2
2
2
2
2
2
1
2
1
1
1
1
1
0
0
2
1
0
0
1
1
0
2
1
1
1
0
1
1
0
1
1
0
1
1
1
2
0
1
2
1
0
1
2
1
1
0
1
4
1
1
3
2
1
1
1
1
1
1
1
1
2
2
0
1
1
1
2
1
2
1
1
2
1
2
2
0
0
1
2
1
2
3
1
1
0
0
1
0
0
2
0
1
1
2
1
1
2
1
2
0
2
2
0
0
2
1
0
0
5
0
1
0
1
0
0
1
4
1
2
1
1
1
1
1
1
0
1
2
1
1
1
1
0
1
0
1
0
0
0
1
1
0
1
1
1
2
3
1
1
2
1
1
1
1
1
0
2
2
2
1
0
1
0
0
1
1
0
2
1
0
0
0
0
1
2
1
0
2
2
1
1
1
2
0
2
1
0
0
1
0
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
2
0
0
1
2
2
1
0
2
1
0
2
1
3
1
2
2
1
0
1
0
0
2
1
2
0
1
2
0
2
0
1
1
1
0
1
1
0
1
1
1
0
3
1
0
1
1
2
2
0
2
1
0
2
1
1
0
0
1
1
0
1
1
1
1
2
0
1
2
1
1
1
2
2
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
0
0
2
1
1
0
1
1
2
1
1
1
2
2
2
2
1
1
1
2
2
0
0
2
0
0
0
1
2
1
2
0
1
2
1
1
0
0
1
1
2
1
2
0
1
1
1
1
1
2
1
1
1
1
1
4
1
0
1
2
1
2
2
1
2
2
2
0
1
1
2
1
1
1
0
1
1
1
1
1
1
2
1
1
1
1
1
0
1
2
2
1
0
2
1
1
1
2
0
1
1
0
0
0
1
1
1
3
3
2
3
1
1
2
0
2
1
1
0
2
1
2
0
1
2
2
1
1
1
1
0
1
1
0
1
2
1
0
1
2
2
2
2
1
1
2
0
1
1
1
0
1
0
2
1
1
2
0
0
0
2
2
0
0
1
0
1
1
2
1
1
1
1
1
1
1
0
2
1
1
1
2
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
1
1
1
1
1
0
1
1
2
2
2
2
1
1
1
0
1
1
1
0
1
1
2
1
1
1
1
1
1
1
1
1
2
1
2
0
0
1
0
1
0
2
1
0
2
1
0
1
0
1
0
0
2
0
1
1
1
0
2
0
1
0
1
1
0
1
1
1
1
2
1
1
1
1
1
1
0
2
1
2
0
1
1
1
1
2
0
2
2
0
1
1
2
1
1
2
1
0
2
2
1
0
1
1
1
1
2
2
0
1
1
0
2
1
0
0
0
1
2
0
2
1
0
1
0
1
1
1
0
2
1
1
0
1
1
1
1
2
1
1
1
0
0
1
2
1
1
1
0
0
2
1
1
2
1
0
2
1
1
1
2
1
1
0
1
1
1
1
1
0
1
2
1
1
1
3
1
0
0
2
1
1
1
2
2
2
0
2
1
2
1
1
1
0
2
3
1
2
1
1
1
0
1
1
0
0
0
1
2
1
1
2
1
3
1
1
1
2
1
0
1
0
1
3
1
1
0
1
0
2
1
0
0
1
8
2
1
1
0
2
2
1
1
0
1
0
1
1
0
0
1
1
2
0
0
0
0
1
1
2
1
2
1
0
1
1
0
0
2
2
0
0
0
1
1
1
1
0
0
0
2
1
2
1
2
1
1
1
1
1
1
0
1
0
2
1
1
1
1
2
2
1
1
1
1
1
0
1
0
1
0
1
2
1
1
0
1
1
1
1
0
2
0
2
1
2
2
1
1
0
1
2
1
2
0
1
0
0
0
2
0
1
2
1
1
1
1
0
0
1
1
2
0
1
1
1
1
2
1
2
1
0
1
1
1
2
1
0
1
2
0
1
1
2
0
1
1
1
0
1
1
0
1
2
1
1
2
2
1
2
2
1
0
1
1
0
3
3
0
2
2
1
1
0
1
0
1
1
2
2
2
1
1
1
1
0
1
1
2
2
2
1
0
1
1
0
1
0
1
1
1
1
0
2
0
2
1
1
1
0
0
2
1
0
2
0
1
0
1
0
1
1
1
1
2
1
2
1
1
1
3
2
0
0
1
1
1
0
2
2
0
1
2
0
1
2
1
0
1
1
0
1
1
1
3
1
1
0
1
1
0
1
1
2
0
1
2
2
2
1
1
2
0
1
1
1
1
0
0
1
2
1
1
0
1
1
0
0
1
0
1
2
2
1
1
1
2
1
1
1
1
2
0
1
0
0
1
0
1
0
1
2
1
2
1
2
1
1
2
1
1
1
0
1
0
0
1
2
1
0
1
1
0
1
1
1
1
1
1
1
1
1
0
1
0
1
1
0
0
2
0
0
1
1
1
0
0
1
2
1
1
2
1
1
1
2
0
1
1
0
1
1
1
1
2
1
0
0
1
0
1
1
1
0
2
2
1
1
1
2
0
2
1
1
1
1
1
1
1
1
4
1
1
1
0
1
1
1
2
1
0
2
2
2
1
1
3
0
3
1
0
0
1
1
0
1
2
2
1
1
1
2
2
2
0
2
1
0
1
2
1
1
1
0
1
2
2
2
1
1
2
0
2
0
0
2
1
1
1
2
1
1
1
0
2
1
2
2
2
1
1
2
2
2
0
2
1
1
0
0
1
1
1
1
1
2
1
0
2
1
0
1
1
1
1
1
1
1
2
2
1
0
0
1
1
1
1
2
1
2
1
1
2
1
0
0
1
1
2
0
0
1
1
1
0
3
1
1
1
0
0
1
1
0
2
2
2
1
0
0
2
0
1
1
1
1
0
0
1
0
1
2
1
0
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
0
0
1
0
0
1
1
1
1
2
1
0
1
1
1
0
1
1
1
1
0
0
2
1
2
0
2
2
0
1
0
1
0
1
1
0
2
1
1
1
2
2
1
0
0
0
1
2
2
2
1
2
1
1
1
2
1
1
1
0
0
0
3
0
1
1
1
2
2
0
1
0
1
2
1
0
1
1
0
0
1
1
1
0
2
1
1
1
0
1
1
2
2
2
2
0
2
0
0
0
0
0
2
0
2
1
1
1
0
2
2
1
1
1
1
1
1
1
0
1
2
2
1
1
1
1
1
1
1
0
0
1
1
2
2
0
2
1
1
0
1
1
1
1
1
2
1
2
2
1
0
0
0
1
1
1
0
2
1
2
1
0
2
2
0
0
0
1
0
1
2
1
2
1
2
1
1
1
1
1
1
1
0
0
1
2
1
1
2
1
1
1
1
1
1
1
0
0
2
1
2
1
2
1
0
0
1
1
1
1
1
1
1
1
1
1
2
1
0
1
0
0
1
1
0
1
2
1
2
2
1
0
0
0
2
2
1
0
0
2
1
1
2
1
0
2
2
0
2
1
1
0
0
1
0
1
1
2
1
1
2
1
1
1
1
2
2
2
3
1
0
2
2
1
1
1
1
0
2
0
2
2
0
1
2
2
1
1
1
2
1
1
1
1
1
1
0
2
2
1
0
2
2
1
1
2
2
0
1
0
1
1
1
2
2
1
1
1
1
1
0
0
0
1
1
1
1
1
1
2
1
2
2
1
0
2
1
1
1
1
0
2
1
1
1
1
1
1
1
1
1
0
0
1
0
0
1
1
1
1
0
0
1
0
1
1
1
0
0
1
1
2
2
2
0
1
1
1
1
1
1
1
1
0
1
2
2
2
2
1
1
0
2
0
1
0
1
0
1
2
2
1
0
1
0
1
0
1
0
2
1
0
2
1
0
1
1
0
1
1
0
2
1
1
0
1
0
0
1
0
2
1
1
1
1
0
0
0
2
1
2
2
1
1
2
1
1
1
2
1
1
0
2
2
1
3
1
1
1
0
2
1
1
0
1
0
1
0
1
1
1
0
1
0
1
1
1
0
2
1
1
2
0
1
0
1
0
1
1
1
1
1
2
1
1
1
1
2
2
1
1
1
2
1
0
0
2
0
2
0
1
2
0
1
2
1
1
1
1
1
1
3
0
0
1
1
2
2
1
1
2
2
2
1
1
1
1
1
1
1
0
1
2
2
0
1
1
0
0
0
1
1
1
0
1
1
1
0
0
1
1
1
0
1
1
2
0
1
0
0
1
1
1
1
0
1
1
0
1
1
0
0
1
1
1
0
0
0
0
2
0
2
1
2
2
1
1
0
0
2
1
1
1
0
1
0
2
1
1
1
2
2
1
1
1
1
0
1
0
1
1
2
1
1
0
1
1
2
1
1
1
1
0
1
1
0
2
2
1
1
1
2
1
0
1
2
2
1
1
1
0
1
2
1
1
1
2
2
0
1
1
1
1
1
2
2
1
0
3
0
2
1
0
0
1
3
2
1
0
0
1
1
1
1
2
1
0
1
1
1
1
2
1
1
0
1
0
0
0
1
1
2
0
1
2
0
2
0
1
0
0
1
1
1
2
1
1
1
1
2
1
2
1
1
0
1
1
1
2
2
1
1
2
2
1
0
0
1
2
0
1
0
0
0
1
1
0
1
2
1
2
1
2
0
0
0
2
1
2
1
0
0
1
1
2
0
1
1
0
3
1
1
1
2
0
2
0
1
1
2
3
0
1
0
0
1
1
1
1
2
0
2
1
0
1
1
1
0
2
0
1
2
1
1
0
2
2
2
1
1
2
2
1
1
0
1
1
1
2
1
2
1
0
2
0
1
4
1
2
1
1
1
0
0
1
0
0
2
0
2
0
0
0
1
1
0
0
1
2
1
0
1
0
1
1
3
1
0
1
2
1
1
0
2
0
1
1
0
1
1
2
2
0
2
2
2
0
2
2
0
1
0
2
0
1
2
1
2
1
1
2
0
1
1
2
1
1
1
1
1
0
2
2
0
3
1
1
0
1
2
1
1
1
0
2
1
1
1
1
0
1
6
1
2
2
0
1
1
1
1
0
2
0
1
1
1
1
2
1
2
2
1
0
0
1
0
0
1
1
0
1
1
1
1
1
2
0
2
2
0
2
0
2
1
1
1
0
0
1
1
2
1
1
1
1
2
1
1
2
0
1
1
2
1
1
0
2
1
2
2
1
0
2
1
0
1
1
1
2
2
1
0
0
3
1
1
1
2
1
1
1
2
1
1
0
1
1
1
2
1
1
1
0
2
0
1
1
1
0
2
1
0
2
1
3
2
2
1
0
0
1
1
1
1
1
0
1
0
0
0
1
2
1
1
0
1
2
1
2
1
1
0
1
2
2
2
2
2
1
1
1
1
2
1
1
1
0
1
1
1
1
1
1
1
1
2
1
0
3
1
0
1
2
1
0
1
0
1
1
1
0
1
1
1
0
1
1
1
0
2
0
1
2
1
1
1
2
0
1
1
2
1
0
0
2
0
1
1
2
0
1
1
1
1
2
0
2
1
0
1
0
1
2
0
1
2
2
2
1
1
1
1
1
0
1
1
2
2
1
1
0
0
1
0
2
1
2
2
0
1
1
1
1
2
0
2
0
1
0
0
1
0
1
1
1
0
1
0
0
1
2
1
2
0
1
1
2
1
2
1
1
2
0
1
1
1
0
0
0
1
2
1
1
1
1
2
1
2
0
1
1
0
2
0
1
0
2
1
1
0
1
1
0
1
2
0
2
2
1
1
1
2
2
2
1
1
1
1
1
1
1
1
2
1
1
1
2
2
0
1
1
2
1
1
1
1
2
1
2
2
1
1
1
1
2
2
1
1
2
1
1
2
3
1
2
1
2
0
1
0
1
2
1
0
2
0
1
1
1
1
1
0
2
2
2
1
1
1
1
2
1
1
0
1
1
1
0
1
0
2
0
1
2
0
0
2
0
0
1
1
1
1
1
1
1
2
1
2
0
0
1
1
1
2
1
1
1
2
1
1
1
0
1
1
0
0
1
0
0
1
2
1
2
1
0
1
0
1
2
0
1
2
1
1
1
1
1
1
1
2
1
0
0
0
0
1
1
0
2
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
0
1
1
1
1
1
1
0
1
0
1
0
1
2
1
1
2
1
2
0
2
1
2
2
0
2
1
1
0
0
2
2
1
1
1
2
1
1
1
0
1
0
1
1
1
2
2
2
0
0
1
0
2
1
0
1
2
1
0
1
1
0
1
1
1
1
2
0
0
1
2
1
2
0
2
1
1
1
2
0
1
2
1
3
3
0
1
1
0
1
2
1
1
1
2
2
1
1
0
0
0
1
1
1
1
2
1
2
1
1
1
0
0
0
1
1
0
1
2
1
1
1
2
1
2
1
2
1
1
1
1
2
1
1
0
1
1
0
1
1
1
0
0
1
2
1
1
3
2
1
1
1
0
1
3
2
2
1
1
0
1
0
1
2
1
0
2
0
1
0
1
0
3
1
1
0
0
1
0
2
1
2
0
1
1
1
1
1
0
0
0
1
1
1
0
1
1
0
1
1
0
1
1
3
2
1
1
0
2
1
2
1
1
1
0
2
2
3
1
2
1
2
1
2
0
1
1
1
1
1
0
1
2
1
1
1
0
2
1
0
0
1
1
1
1
1
0
0
0
0
1
0
1
0
1
1
2
0
1
2
1
1
1
1
1
1
1
2
0
1
2
0
1
2
1
1
1
1
0
2
0
0
2
0
1
2
2
1
1
0
2
0
1
1
1
2
2
0
1
1
1
1
0
2
1
0
1
0
0
1
1
2
1
1
3
0
1
3
2
1
2
0
0
3
1
1
1
1
1
0
0
0
2
1
1
1
1
1
2
0
0
0
1
1
1
2
1
1
1
1
0
0
1
1
1
0
0
1
1
0
1
0
2
1
2
1
1
1
1
1
0
1
1
0
2
1
0
0
1
1
1
0
2
0
1
0
1
1
1
0
2
2
0
2
0
1
0
1
1
1
2
1
0
1
1
2
0
2
1
1
1
2
1
0
1
1
2
1
0
1
2
0
0
1
1
1
2
1
1
1
1
2
1
2
1
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
0
1
2
1
0
2
2
0
1
2
1
2
2
2
1
0
1
0
1
1
1
1
1
1
0
1
2
1
0
1
0
1
2
0
1
1
1
1
0
2
2
2
0
1
2
1
0
1
0
1
1
1
0
1
0
0
2
1
1
1
1
1
0
1
1
0
0
1
1
1
1
1
1
0
1
1
2
2
0
0
1
1
1
1
0
1
1
2
2
1
0
2
0
1
1
1
1
3
1
0
2
1
1
1
2
1
2
1
1
1
2
1
1
1
2
1
1
2
0
0
2
1
1
0
1
1
1
1
0
1
0
2
1
1
1
1
1
0
0
1
1
1
1
1
1
1
1
1
1
1
2
0
2
2
1
1
0
1
1
2
1
2
0
3
1
1
2
1
1
0
1
0
0
0
1
1
1
2
1
1
1
1
1
1
2
1
1
1
0
0
1
1
0
1
1
0
2
1
1
0
1
0
1
2
1
1
2
1
0
1
1
1
1
2
1
1
2
2
1
1
1
1
1
0
0
2
2
2
1
1
1
1
2
2
0
1
0
0
0
1
1
2
1
0
0
1
1
1
0
2
3
2
1
1
2
2
1
2
0
0
1
1
1
1
1
1
1
0
0
1
2
2
2
2
1
1
2
1
2
3
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
2
2
1
1
2
0
0
0
0
1
0
0
1
1
1
0
0
1
1
1
2
0
2
2
1
2
2
1
2
3
3
0
0
2
0
1
2
0
1
0
1
1
2
0
2
1
0
1
0
1
1
1
1
0
1
1
2
1
2
1
0
1
1
1
1
1
2
1
0
1
1
2
2
1
2
1
0
1
0
2
2
2
1
2
0
1
1
2
1
2
1
1
3
1
2
1
1
1
0
0
2
2
0
2
1
2
2
0
1
1
1
1
0
1
1
0
0
1
1
0
0
2
1
1
2
0
1
1
0
1
1
0
1
2
0
1
1
1
1
1
2
1
2
1
1
1
1
0
1
2
1
2
1
1
1
0
1
1
1
0
2
0
1
2
0
1
2
1
0
2
2
2
2
1
2
1
1
1
1
2
1
2
0
1
1
1
1
1
1
1
2
1
1
0
0
0
1
1
1
1
3
1
0
1
2
1
0
1
0
1
1
0
0
1
1
1
0
2
2
0
1
3
1
1
0
1
1
1
1
1
0
1
2
2
1
2
0
2
1
0
1
1
1
2
2
1
1
2
0
1
2
1
0
0
0
1
1
1
1
0
0
0
1
1
2
0
1
1
0
1
1
2
2
0
1
2
2
1
1
0
1
0
1
2
1
1
1
2
2
1
1
1
1
2
0
1
0
1
2
0
1
1
1
1
0
1
0
1
2
1
1
2
1
1
2
1
1
2
2
2
1
1
2
1
1
1
1
1
2
1
1
1
0
1
2
0
2
2
2
0
1
1
1
1
2
2
1
1
0
1
2
2
1
1
1
2
0
0
1
1
2
0
2
1
0
0
2
2
1
0
1
1
2
1
0
0
1
1
2
1
2
1
1
1
0
1
0
0
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
0
0
1
1
0
1
2
1
0
0
0
1
0
1
2
2
2
1
1
0
1
2
1
2
1
1
0
1
0
2
2
2
0
1
1
1
1
1
1
1
1
1
1
0
0
1
1
0
0
2
2
0
1
1
1
0
0
0
1
1
2
1
2
1
0
1
1
1
1
0
2
1
1
2
0
2
1
1
2
1
1
1
1
0
0
1
1
1
0
1
2
0
1
0
1
1
0
2
2
0
1
0
1
1
1
1
1
0
1
1
1
1
2
1
2
1
0
0
0
0
1
2
0
2
2
1
0
1
0
1
2
3
1
1
0
2
1
1
1
1
0
1
1
2
1
0
1
1
0
1
2
0
2
2
2
1
2
2
1
0
0
1
1
1
1
1
1
1
0
1
0
1
2
1
2
1
0
1
1
1
0
0
1
1
1
0
1
1
1
0
1
1
0
1
2
2
1
3
1
0
0
2
0
2
0
2
2
1
0
2
1
1
2
1
1
1
0
1
1
2
2
2
0
1
0
1
0
2
2
1
1
1
2
2
1
1
2
1
0
1
2
1
1
0
1
2
2
2
1
1
2
1
1
1
1
0
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
1
1
1
2
1
2
0
1
1
0
1
1
0
1
1
1
0
0
1
2
0
1
1
0
0
1
2
0
1
1
1
2
1
1
1
1
1
2
1
0
1
1
1
0
2
0
0
1
0
2
3
0
1
2
1
1
1
1
1
0
1
1
2
1
1
1
2
1
1
1
0
1
1
1
1
1
1
1
0
0
1
0
2
0
1
0
0
1
1
1
2
1
1
1
2
1
1
1
0
0
1
0
1
1
1
1
2
2
0
2
0
2
1
1
0
2
0
1
1
1
0
1
1
2
1
1
1
1
1
1
2
1
1
0
1
2
0
2
1
1
1
2
1
1
0
1
1
1
1
1
0
1
1
2
0
0
1
0
1
2
1
2
2
1
1
1
2
0
1
1
1
3
1
1
1
2
3
2
2
2
1
1
1
0
2
1
1
1
1
1
0
1
2
2
0
2
2
1
2
0
1
2
1
2
1
1
1
0
1
1
2
1
3
1
1
1
1
1
1
2
1
1
1
2
1
0
1
0
1
2
1
4
7
1
2
1
2
1
1
0
1
0
2
1
1
2
0
1
1
1
1
1
1
0
0
1
1
1
0
1
1
1
1
0
2
1
1
1
2
2
1
0
1
2
2
0
1
2
1
1
1
2
2
1
1
0
0
2
1
0
1
2
0
0
2
2
1
1
1
1
1
1
1
0
0
2
0
2
0
1
1
1
2
1
1
1
1
0
0
0
2
0
1
2
0
1
1
1
2
3
0
0
1
0
2
4
0
1
0
0
1
1
0
0
0
1
1
1
2
0
0
3
2
0
1
1
2
1
0
1
1
1
0
0
1
1
1
0
1
1
1
0
1
0
1
1
0
2
1
0
0
1
1
2
1
1
0
1
2
1
3
1
1
1
0
2
1
2
1
2
1
0
0
2
1
1
0
1
0
0
1
1
0
1
1
1
1
0
1
1
0
1
1
1
2
2
0
2
2
1
0
1
0
1
1
2
2
2
2
2
1
0
1
2
0
1
0
1
1
2
1
1
1
1
1
0
0
0
2
0
1
1
1
0
1
2
2
1
1
1
1
0
2
1
1
1
1
2
2
1
1
2
0
0
1
0
0
2
0
1
1
1
3
1
1
1
1
1
2
1
2
0
1
2
0
1
2
1
2
2
1
2
1
1
1
2
1
1
1
0
1
0
0
2
1
2
1
0
1
0
0
1
0
0
1
1
2
3
1
0
4
0
1
2
1
0
1
0
1
2
0
2
1
0
1
1
1
0
1
1
1
0
1
1
1
2
0
1
0
1
1
0
2
1
1
1
2
1
1
1
1
1
0
0
1
2
2
2
0
1
1
1
0
1
1
1
1
2
1
0
1
1
0
1
1
0
2
1
1
0
1
3
1
0
1
1
0
1
1
1
1
0
1
2
2
1
1
2
0
2
0
1
1
1
1
1
2
0
2
1
1
1
2
0
2
2
1
2
0
1
0
2
1
1
1
1
1
0
1
1
2
1
1
0
1
1
2
1
1
0
1
1
2
0
1
1
1
1
1
1
1
1
1
1
1
1
0
1
0
1
1
0
1
2
1
1
0
0
1
2
2
0
1
1
0
0
1
1
1
1
1
1
1
1
1
1
0
1
1
2
1
1
1
0
0
1
1
1
1
2
0
1
2
1
0
0
2
1
1
2
2
0
1
1
1
1
0
2
2
4
1
2
1
1
1
2
2
1
1
0
2
1
1
0
1
1
2
0
1
0
1
2
2
1
0
2
1
1
2
1
1
2
1
0
2
1
1
1
1
0
1
1
1
0
0
1
1
2
1
0
2
0
1
0
1
2
1
2
1
1
1
1
1
2
1
2
1
2
1
0
0
1
0
1
1
1
2
1
2
0
1
0
0
1
1
0
1
2
0
0
2
1
1
1
1
1
3
1
2
1
2
1
0
1
1
0
1
1
0
2
0
1
0
1
0
0
1
1
1
0
2
1
1
0
1
1
0
1
1
1
1
1
1
1
1
1
1
3
1
1
0
1
1
1
1
0
1
1
2
2
0
1
2
1
1
1
1
2
1
0
0
2
1
2
2
2
2
0
2
1
1
2
1
1
0
0
2
1
2
1
1
0
1
0
1
1
1
1
2
1
0
0
2
1
1
1
0
0
1
1
1
1
1
2
1
0
1
1
1
0
1
1
0
1
1
1
1
0
1
2
1
0
1
1
3
2
0
0
0
1
1
1
0
1
0
2
1
1
1
2
1
1
2
1
1
2
1
1
1
0
1
0
1
1
0
1
1
2
1
2
1
2
1
0
0
0
2
1
0
2
0
2
1
1
1
1
1
0
0
2
1
1
1
1
0
1
1
2
1
1
0
1
0
2
1
2
0
1
1
0
1
1
1
1
2
1
1
2
2
1
1
1
1
2
0
1
1
1
2
1
1
2
2
1
2
1
1
2
0
1
1
1
2
0
1
0
1
2
0
0
1
1
2
2
0
1
2
1
2
1
1
0
1
1
1
2
1
2
1
0
1
1
2
1
2
1
1
1
1
2
1
2
2
1
0
1
0
1
1
0
1
2
1
0
1
0
2
2
0
1
1
2
1
2
0
2
1
1
2
2
1
2
0
1
1
2
1
1
0
2
1
0
1
2
2
2
0
0
0
2
1
2
2
2
1
0
1
2
0
1
0
1
1
2
1
1
2
2
1
0
2
2
1
2
1
0
1
1
1
0
1
1
0
2
0
1
1
2
1
0
1
0
1
2
1
1
1
1
1
2
0
1
1
1
1
0
1
1
1
1
2
1
0
0
1
2
2
0
0
1
0
1
0
1
2
1
1
1
1
2
1
2
0
2
1
1
1
0
1
2
1
1
1
0
1
0
2
1
1
1
0
1
0
0
1
2
2
2
1
1
2
0
0
0
0
0
0
0
2
1
1
1
1
1
0
1
1
1
0
2
2
1
1
2
1
2
1
0
2
2
1
1
1
1
0
1
2
1
1
1
1
1
1
0
2
0
1
1
1
1
2
2
1
1
0
1
0
2
2
1
1
2
1
1
1
1
2
1
1
1
0
1
0
2
1
1
0
0
1
2
2
2
0
1
2
2
2
0
1
1
0
2
0
1
2
1
0
1
1
0
1
1
2
2
2
1
1
2
1
1
0
1
1
2
0
1
0
2
1
2
1
0
1
0
2
2
1
2
2
2
0
0
0
0
1
0
1
0
1
1
2
1
1
0
0
1
1
1
0
1
1
1
0
0
2
2
0
0
1
0
1
1
0
0
2
1
1
4
1
1
2
1
0
1
1
2
1
1
1
1
1
1
2
1
1
1
1
0
2
0
1
1
1
1
0
0
0
2
1
1
1
1
0
0
2
1
0
1
1
1
1
0
1
1
1
1
2
0
1
1
1
1
2
2
0
0
1
1
2
1
1
2
1
1
1
1
0
1
1
1
1
1
2
1
1
1
1
1
1
1
0
0
1
0
2
2
2
0
0
0
0
2
0
1
0
1
1
1
1
0
1
2
2
2
1
1
1
1
1
0
1
2
1
1
0
2
1
0
1
2
1
1
2
1
1
1
2
1
1
1
2
0
1
1
1
1
1
1
1
1
0
2
0
1
1
0
1
2
1
1
1
0
0
2
0
1
1
1
2
0
1
0
0
1
1
2
2
1
1
2
1
1
2
1
1
2
2
2
1
2
1
0
0
2
1
1
1
2
1
2
1
0
3
1
1
0
1
1
2
0
1
1
1
0
1
0
1
1
2
2
1
1
2
1
1
0
2
2
1
0
1
2
1
2
2
2
1
1
1
2
1
2
1
1
1
2
2
1
1
2
1
1
2
1
1
1
1
0
1
0
1
1
1
0
1
0
1
2
0
1
2
2
1
0
1
1
1
0
1
2
1
1
1
1
2
1
0
0
1
1
1
1
1
1
1
0
3
0
1
1
0
1
1
1
1
1
1
2
0
1
1
2
0
2
2
2
1
1
3
2
0
1
0
1
1
1
1
1
3
1
0
2
1
1
1
2
1
2
0
0
2
1
1
0
1
1
0
1
1
1
2
1
2
0
1
1
0
0
1
0
2
1
1
1
1
1
2
3
1
1
2
0
2
1
2
1
1
0
0
1
1
1
0
2
1
0
1
1
1
1
1
2
1
2
1
2
1
1
1
0
0
0
0
1
1
1
0
1
1
1
1
0
1
0
1
0
1
2
1
1
1
2
1
0
0
2
1
1
1
1
1
2
1
1
1
1
0
0
1
2
1
1
0
0
2
2
1
1
0
1
0
0
1
1
1
1
2
1
1
2
1
0
0
0
2
1
0
1
2
1
1
0
0
0
2
2
1
0
1
1
1
2
2
0
1
1
1
1
1
0
1
1
0
1
2
1
2
1
1
1
5
1
1
1
0
2
1
2
2
1
1
0
2
1
2
1
1
0
1
0
1
1
2
1
1
1
1
1
1
2
2
1
2
2
1
0
1
2
1
1
2
1
3
2
1
2
1
3
2
1
0
1
0
0
1
1
0
1
1
1
1
2
2
1
1
1
1
2
1
1
2
1
2
2
1
2
0
0
1
0
1
1
1
0
1
1
1
0
0
1
1
0
2
1
1
1
2
1
2
1
1
2
1
2
1
2
2
0
2
2
0
1
2
0
0
1
2
2
2
1
1
2
0
1
0
1
2
1
1
1
1
3
1
0
1
1
3
1
0
1
2
1
2
1
0
1
2
1
1
2
1
0
1
1
1
1
1
1
0
0
1
0
1
1
1
0
1
1
2
0
1
0
0
0
1
1
0
1
0
1
1
1
2
1
0
0
2
2
1
1
0
3
1
1
0
1
0
1
0
0
2
2
2
0
1
1
0
2
1
0
2
1
1
1
1
0
2
2
0
1
1
0
2
1
2
0
1
2
2
2
1
0
1
1
1
1
2
0
0
1
2
0
1
0
0
0
2
1
1
1
1
1
1
1
1
1
2
3
1
1
0
1
0
1
1
1
1
0
1
0
0
2
2
2
5
1
0
1
2
1
0
1
1
1
1
1
1
1
1
0
1
0
2
1
0
2
0
2
2
0
1
2
1
0
0
2
0
1
0
2
2
1
1
1
1
1
1
2
1
1
0
1
1
1
3
1
2
0
2
1
1
2
2
0
0
1
1
1
1
1
1
1
1
2
1
0
2
1
0
0
1
1
1
1
0
1
1
0
1
0
2
1
0
2
1
1
1
0
2
1
1
1
1
0
0
0
1
2
2
1
1
1
0
1
1
0
1
1
1
0
2
0
0
1
0
1
1
0
0
1
1
0
0
1
1
1
1
2
0
1
0
1
1
1
1
0
0
1
2
1
0
1
1
2
1
1
0
2
1
2
2
2
1
0
0
2
1
1
0
2
1
2
2
1
0
1
1
1
2
0
2
1
1
1
1
0
3
2
1
0
2
2
1
1
1
1
2
0
1
1
2
0
1
2
1
1
0
0
1
0
1
1
2
0
1
2
1
0
0
2
1
2
0
1
0
2
1
1
1
2
1
1
1
1
1
0
3
1
1
2
2
1
1
1
1
1
2
1
0
2
1
1
2
0
1
1
1
1
0
1
1
1
5
2
2
0
1
0
1
1
1
2
0
1
1
2
1
1
0
0
0
1
2
1
2
1
1
0
1
1
3
2
1
0
1
1
2
1
0
1
0
1
1
1
2
1
0
1
0
1
2
1
1
1
1
1
1
1
1
0
1
2
1
1
1
0
1
0
0
1
1
2
2
1
0
1
1
0
1
1
1
2
0
2
0
1
1
2
1
1
1
1
2
1
1
0
1
1
0
0
0
0
0
2
2
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
0
2
1
0
1
1
2
2
1
0
1
1
1
1
1
1
2
1
0
0
2
0
1
1
2
1
1
1
0
0
2
1
2
2
2
0
2
2
1
1
1
1
1
0
1
1
2
1
0
0
1
2
1
1
0
1
2
1
0
0
2
1
1
2
0
2
1
0
2
1
0
0
0
1
0
1
2
0
0
2
1
0
1
1
2
1
1
2
2
0
1
1
1
1
2
4
2
1
1
1
1
1
1
2
1
2
1
1
0
2
1
0
2
0
2
0
3
2
1
2
2
1
2
9
2
2
1
2
0
1
1
2
2
1
0
1
2
1
1
0
1
1
1
0
1
1
2
2
1
0
0
1
1
2
1
1
2
1
1
1
1
0
1
0
2
1
1
1
0
1
2
1
1
1
2
0
2
1
1
1
1
2
2
0
1
1
1
0
1
1
1
1
2
0
2
1
1
1
2
0
1
1
0
1
0
0
0
0
1
1
1
0
1
1
1
1
2
1
1
1
1
0
2
2
1
2
1
1
1
1
1
2
1
2
0
0
1
0
0
2
2
0
1
1
0
1
0
1
0
0
1
1
1
2
1
0
2
2
2
2
1
1
1
1
1
0
1
2
1
0
1
1
2
1
2
1
2
1
2
2
1
2
1
2
2
0
2
1
2
1
1
0
0
0
1
0
0
2
1
1
2
1
1
1
0
1
1
1
0
0
1
0
1
1
0
1
0
0
1
1
1
1
0
0
1
2
2
1
1
2
1
1
1
0
1
0
1
2
1
1
1
2
0
1
2
0
1
2
0
2
1
1
1
1
1
0
1
1
0
1
0
1
1
1
2
1
1
1
2
1
2
1
1
1
1
2
1
2
1
1
1
0
2
0
1
0
1
1
1
0
2
1
1
1
1
0
0
2
1
1
0
0
1
1
1
0
2
2
0
0
1
2
1
1
2
1
1
0
2
2
1
2
0
2
1
1
1
1
1
1
0
1
0
2
1
0
1
2
0
0
2
0
1
2
1
2
1
0
0
2
1
2
0
2
1
1
1
2
0
2
0
1
1
2
0
1
1
2
0
2
2
1
2
1
2
1
1
1
1
2
0
1
1
2
1
2
1
1
1
2
2
1
0
1
0
1
2
0
1
0
2
1
1
0
1
1
1
2
1
1
2
0
2
1
0
1
1
2
0
0
0
2
1
0
3
0
0
2
0
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
0
1
0
0
2
1
0
1
1
1
1
2
0
1
2
0
1
0
1
1
0
1
1
0
0
1
1
1
0
1
2
2
1
1
1
1
2
2
1
1
1
1
1
2
1
0
0
2
1
2
3
1
2
7
2
1
1
1
1
2
0
1
1
0
1
0
2
0
1
1
0
0
0
2
0
2
1
0
1
1
1
0
1
0
1
2
2
1
1
1
1
1
0
0
1
2
0
1
1
1
1
0
1
1
0
1
0
2
1
2
0
2
0
2
2
1
1
0
1
1
2
1
1
0
2
1
0
1
1
1
0
1
1
2
1
2
1
2
0
1
1
1
1
2
0
1
2
1
1
1
1
0
2
2
1
1
0
1
2
0
1
1
2
1
1
1
1
2
1
1
2
1
0
1
1
2
1
0
1
1
2
1
1
0
1
2
1
2
0
1
1
1
1
1
1
1
2
2
2
1
1
2
1
2
1
0
1
0
1
0
2
1
1
1
1
1
0
1
2
1
1
1
1
1
1
1
0
1
2
0
2
0
1
1
0
1
2
0
2
1
1
0
0
1
0
0
1
1
1
1
7
1
0
1
0
2
0
1
1
1
0
0
1
0
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
0
0
1
0
1
2
1
1
2
0
1
1
1
0
1
1
1
1
2
2
2
0
0
2
0
1
1
1
1
0
2
1
2
1
0
1
0
0
1
1
1
2
1
1
0
0
2
1
1
0
1
1
0
2
2
1
0
1
2
1
1
3
1
0
1
1
2
0
2
1
1
0
1
1
1
0
0
1
0
0
2
1
1
2
2
1
1
2
1
1
2
0
1
1
1
4
2
2
2
1
2
1
2
0
2
1
2
1
5
1
1
0
2
1
2
2
1
1
0
0
2
1
1
2
0
0
2
1
1
2
1
0
1
0
1
1
1
2
2
2
0
1
0
1
1
1
0
1
1
2
1
1
2
0
1
2
1
1
1
0
0
1
0
2
2
1
0
1
1
1
1
1
1
2
0
0
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
0
1
0
1
1
1
1
1
1
1
1
2
2
1
0
2
1
2
0
1
2
2
0
2
1
0
2
0
2
0
2
1
1
2
1
1
1
1
0
2
1
1
2
1
1
1
1
1
0
1
0
1
1
0
1
0
1
0
1
1
1
0
1
1
1
1
0
1
1
1
2
0
0
2
1
0
1
1
2
1
0
2
1
2
2
1
1
1
0
1
2
0
0
0
0
1
1
1
0
1
2
1
1
0
0
1
1
0
1
1
1
0
0
1
1
0
1
1
0
0
2
1
2
2
1
1
0
1
2
3
2
1
1
1
2
0
0
1
0
1
0
1
2
0
0
1
2
0
2
0
1
2
0
1
1
2
1
1
1
0
1
0
1
1
1
2
2
0
0
0
1
0
1
1
2
2
2
1
1
0
1
0
0
1
1
0
1
2
1
1
0
2
2
1
0
1
0
1
1
0
0
1
2
0
1
1
2
1
1
0
4
2
2
2
1
0
1
1
2
0
1
1
1
1
1
1
1
1
1
0
2
2
1
0
2
1
0
1
1
1
1
0
2
2
2
1
1
1
1
1
0
1
1
0
1
1
1
1
1
1
0
1
0
2
1
1
1
0
1
1
1
0
1
0
1
2
1
1
0
2
2
0
0
1
1
0
0
2
0
1
2
1
0
1
1
0
1
1
2
1
1
1
0
1
0
0
2
2
0
1
1
1
0
2
1
0
1
0
0
1
0
0
1
1
0
1
1
0
2
0
1
0
1
2
2
0
1
1
1
1
2
0
1
2
0
1
1
2
0
1
1
1
1
1
2
1
0
1
1
1
0
0
0
0
1
0
1
2
1
0
1
0
1
1
2
1
1
1
2
1
1
4
0
2
1
1
0
0
1
2
1
0
1
2
0
0
0
0
1
2
1
1
1
1
0
1
1
0
1
2
1
0
0
1
0
1
1
1
1
2
2
2
3
0
1
1
1
0
1
1
1
2
2
1
2
0
1
1
1
0
2
1
1
0
1
1
1
1
0
1
1
2
0
2
1
1
2
2
1
1
2
2
1
2
1
0
1
1
1
1
0
1
0
1
0
1
0
2
0
2
1
1
2
0
1
1
1
1
1
0
0
2
0
0
0
3
1
0
2
1
0
1
1
0
1
0
2
2
1
1
1
1
2
0
0
1
0
1
1
1
1
1
0
1
2
2
2
1
1
1
2
1
1
0
1
0
1
2
0
0
1
1
2
0
1
1
1
1
0
1
0
1
2
0
1
1
1
1
1
0
1
1
1
1
0
0
1
1
0
2
1
0
1
1
1
2
2
1
1
3
1
0
0
0
1
1
0
2
2
0
0
16
1
2
1
1
1
1
1
2
0
1
2
1
0
1
1
4
1
1
2
1
1
0
2
0
2
2
0
1
1
0
0
2
2
1
2
0
1
0
1
2
1
0
1
0
2
1
1
1
0
1
1
1
1
0
1
1
1
0
1
2
1
1
0
1
1
1
0
2
2
3
1
2
0
2
1
1
1
0
2
1
1
0
1
2
1
2
4
0
1
0
1
1
1
0
2
0
2
1
0
3
2
1
2
2
0
0
1
0
0
0
0
1
1
1
0
2
1
1
1
1
1
0
2
0
1
5
1
1
1
0
1
2
1
2
1
1
0
0
0
2
1
3
1
1
0
1
1
1
1
0
0
1
0
1
1
1
0
1
0
0
1
1
1
1
1
2
1
1
0
0
1
2
1
1
2
1
0
0
1
1
1
2
2
1
2
1
0
1
2
1
0
1
0
1
2
0
0
2
0
1
3
1
1
0
0
1
1
1
1
2
1
1
1
1
2
2
1
1
1
2
2
0
2
0
1
4
1
1
0
3
0
1
0
2
2
2
1
0
1
0
2
1
1
1
1
1
2
2
1
2
1
1
1
2
0
1
1
0
1
0
1
1
1
0
1
1
1
1
2
0
1
2
0
1
1
0
1
1
0
1
0
0
1
0
1
1
0
2
0
2
1
2
1
1
1
2
2
0
0
1
0
1
1
2
0
2
0
2
3
1
2
1
0
2
1
1
0
2
4
2
2
1
1
0
1
1
1
1
0
1
1
1
1
2
1
1
2
0
1
0
2
0
2
1
1
0
2
2
0
1
1
1
1
1
0
1
2
2
2
1
1
1
2
2
1
1
1
1
1
0
1
2
1
1
0
2
1
2
1
1
1
2
1
2
0
1
1
0
0
2
0
2
0
1
1
0
1
1
2
0
2
1
1
2
0
1
2
1
1
1
2
1
1
2
1
1
1
0
2
1
2
1
1
1
2
1
1
0
1
1
1
1
3
1
1
2
2
0
1
2
2
1
1
1
2
1
0
1
1
1
1
0
0
1
1
3
1
0
0
0
2
2
1
1
0
1
1
0
2
2
1
1
1
1
0
2
2
0
0
1
1
0
1
1
1
2
1
1
0
2
1
0
1
1
1
0
2
1
1
1
1
1
0
0
2
2
1
1
1
1
1
0
0
1
1
1
2
1
1
1
1
1
1
1
1
2
0
0
1
1
0
1
0
0
1
1
0
0
2
0
1
1
1
1
0
2
1
1
1
0
1
1
0
2
1
1
1
0
1
1
2
2
2
2
1
2
0
1
1
1
1
1
1
1
0
2
0
2
1
1
2
1
2
1
1
2
0
2
1
1
1
0
0
1
1
0
0
1
1
1
1
1
3
1
1
1
0
1
1
1
2
1
0
1
1
1
1
1
1
2
1
0
1
1
2
1
3
1
0
2
0
2
2
1
1
2
3
1
0
2
0
0
1
0
0
2
1
1
0
0
1
0
2
1
1
0
1
2
0
1
1
2
1
1
1
0
2
2
0
1
0
1
0
0
1
1
1
1
2
0
2
1
1
2
1
1
1
2
2
1
0
1
0
1
1
0
2
1
2
1
0
0
0
0
2
0
1
0
0
1
1
0
1
1
1
0
1
1
2
0
1
2
1
1
1
1
2
0
1
1
2
1
2
1
2
1
0
1
1
0
1
2
0
1
2
3
1
1
1
2
1
1
2
1
0
1
1
2
1
1
1
0
2
0
0
1
2
0
1
1
0
1
2
0
1
1
2
1
2
0
1
1
2
1
0
0
1
2
1
0
1
2
1
1
1
2
1
1
1
0
1
1
1
0
2
2
2
1
0
1
1
1
0
2
1
2
1
0
0
0
0
1
0
1
1
0
1
2
0
1
1
2
2
2
0
0
1
0
0
0
1
2
0
1
1
0
3
2
1
1
1
2
1
2
2
1
2
1
1
2
1
0
0
0
0
1
1
1
1
0
2
1
1
1
0
2
0
1
1
2
2
1
1
0
1
1
2
4
2
1
2
1
2
0
2
1
0
0
1
1
2
1
1
0
1
1
0
1
2
0
1
0
1
1
2
1
1
1
1
0
0
1
0
1
1
2
2
2
0
0
1
1
1
1
1
1
0
0
0
1
1
2
0
2
0
2
2
1
1
1
1
2
0
2
2
1
2
1
0
0
2
1
1
1
1
1
1
0
1
1
2
0
2
0
1
0
1
1
1
1
1
0
1
1
0
1
2
0
1
0
0
2
1
1
1
2
1
2
1
1
1
2
0
1
0
1
1
2
2
1
0
1
1
0
1
1
0
0
1
1
1
1
1
1
1
1
1
0
2
0
0
0
1
2
1
0
1
0
0
0
1
2
2
0
1
1
2
0
2
2
0
1
1
1
0
1
1
2
0
0
1
1
2
1
1
1
1
2
0
1
1
1
2
2
1
1
0
2
0
1
1
0
0
1
0
2
1
2
0
2
0
1
1
1
1
0
1
1
2
1
0
1
0
2
0
1
2
1
0
2
1
1
2
1
1
1
1
0
1
0
2
2
1
1
1
1
2
2
1
0
1
1
0
1
0
1
1
1
2
1
0
2
2
1
1
0
2
0
0
0
1
0
0
1
1
1
1
2
1
1
0
1
0
1
1
2
2
0
1
2
1
2
0
1
1
0
1
2
1
1
1
0
1
1
2
1
1
1
1
1
2
1
0
2
0
2
2
2
2
1
0
0
2
2
0
1
1
1
1
1
1
2
1
2
1
2
0
1
1
2
2
2
0
1
2
1
1
1
0
1
1
1
1
2
2
1
1
0
1
1
0
0
2
2
1
1
0
1
2
2
1
2
1
1
0
1
1
1
1
3
1
1
1
0
1
0
1
1
1
2
1
1
1
1
0
1
1
1
1
1
1
1
0
2
2
1
3
1
2
2
1
0
1
1
1
1
0
1
2
2
2
1
2
1
0
1
0
0
1
1
1
2
2
2
1
2
2
0
1
1
0
1
0
1
1
0
2
1
1
0
3
1
2
4
2
0
1
1
1
1
0
1
2
1
1
1
1
2
1
1
1
0
1
1
0
2
0
1
0
2
0
1
0
1
1
1
2
2
0
1
1
1
1
2
1
1
1
0
2
0
2
1
1
1
1
1
1
1
0
3
1
2
2
1
0
1
1
0
1
0
0
2
1
1
1
1
0
0
0
2
1
2
2
1
1
0
1
0
0
1
0
0
1
1
0
1
1
1
2
1
1
1
1
3
1
0
2
2
2
1
0
1
2
1
0
2
2
1
0
0
2
1
1
2
1
0
0
2
3
1
1
1
2
0
1
1
1
1
1
1
0
1
1
0
2
1
2
0
2
0
3
1
1
1
2
0
1
1
1
1
2
2
2
0
1
1
1
1
0
1
0
1
0
2
0
2
2
1
2
0
0
0
1
1
1
3
0
1
0
1
0
0
2
0
1
1
1
2
2
1
1
1
0
1
1
1
0
0
1
0
1
1
1
2
0
2
2
1
1
0
1
3
0
1
1
0
1
2
1
1
1
1
1
1
2
2
1
1
2
2
2
1
1
1
1
1
1
0
0
3
2
1
1
1
1
0
1
1
2
1
2
1
1
2
1
0
1
0
1
1
1
0
0
0
1
2
2
1
1
1
2
0
2
0
0
1
1
1
0
1
0
0
2
2
1
1
2
0
0
1
1
0
1
1
1
1
0
0
0
1
1
2
0
1
0
1
1
1
2
0
0
1
3
1
1
2
2
0
1
1
1
1
0
0
0
1
0
1
1
1
1
1
2
2
1
1
1
0
2
2
1
1
0
0
0
1
1
1
0
1
1
0
1
2
1
2
1
1
1
1
2
1
3
0
1
1
1
1
1
1
1
1
0
1
1
0
1
1
1
0
1
1
1
2
1
1
1
1
1
1
1
1
1
1
0
1
1
1
2
1
0
1
2
2
0
1
2
1
2
1
1
2
2
1
0
2
0
1
2
1
3
1
1
1
1
1
2
1
1
1
1
1
1
0
1
1
1
2
1
1
2
1
2
0
2
1
1
2
0
0
1
1
2
0
1
0
0
1
1
0
0
1
1
1
0
1
1
0
1
1
0
2
1
1
1
1
0
1
0
2
1
0
1
1
2
1
2
2
1
1
1
1
1
1
2
1
2
0
0
1
1
0
1
2
2
0
1
0
2
2
1
1
0
0
1
0
1
2
1
1
0
1
0
0
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
0
4
1
2
1
1
0
2
2
2
0
1
0
0
0
1
2
1
1
0
1
1
1
2
2
2
2
1
0
1
1
1
2
2
2
0
1
1
0
2
1
1
1
1
0
1
1
1
1
2
1
1
1
0
1
0
1
0
1
1
0
0
0
1
1
2
1
1
2
0
2
1
0
0
1
0
0
2
0
1
2
2
0
1
1
1
1
2
1
2
1
0
1
1
0
2
1
2
1
1
1
1
0
2
0
0
0
0
1
1
1
1
1
0
2
1
0
0
2
1
0
1
2
1
1
1
1
1
1
0
0
0
2
0
1
0
1
1
2
0
1
2
1
1
0
1
0
0
1
1
1
1
1
1
1
2
1
3
2
1
2
1
2
1
2
1
1
1
1
1
2
0
1
2
1
0
2
1
1
2
1
1
2
1
2
0
2
1
1
0
0
1
0
1
2
2
0
1
1
2
1
1
2
0
1
0
1
0
2
0
2
1
1
1
1
2
1
0
1
2
1
2
1
1
2
2
1
1
0
2
1
1
1
0
2
1
2
1
2
1
1
1
1
1
1
0
0
1
1
1
1
0
1
1
1
0
1
1
1
1
0
1
0
2
1
0
1
1
0
2
1
1
2
2
1
1
1
2
2
2
2
1
2
2
2
2
0
1
1
1
2
1
0
1
1
1
1
0
1
0
0
1
0
0
1
1
2
1
2
1
1
0
1
0
1
0
0
0
0
0
0
1
1
1
0
2
1
0
3
1
2
1
1
2
0
2
0
1
2
1
1
1
1
2
1
0
1
1
2
2
1
0
2
1
0
2
0
1
0
0
2
0
1
1
2
0
1
1
2
1
0
1
0
1
0
1
1
1
1
1
0
1
1
2
0
2
0
1
0
0
1
1
1
0
1
2
0
1
2
1
0
4
0
1
1
1
1
1
1
2
1
1
1
0
1
2
0
2
1
2
1
1
1
1
1
2
2
0
0
2
0
1
2
2
1
1
2
2
1
2
0
1
1
1
1
0
0
2
1
0
1
0
1
2
2
1
0
1
1
2
1
2
0
2
1
1
1
2
1
2
1
1
0
2
1
1
2
2
0
1
1
1
1
0
2
1
1
1
2
1
0
1
2
1
1
2
0
2
1
1
1
0
0
2
2
0
0
1
2
2
1
0
1
0
1
2
1
1
1
1
0
1
1
0
0
0
1
1
1
0
1
1
1
3
1
1
0
1
2
1
1
1
1
2
1
0
1
0
0
2
0
1
1
0
1
2
1
1
0
1
2
1
0
1
1
2
1
0
1
1
2
1
1
1
0
2
0
1
1
0
1
2
0
1
1
2
1
1
1
1
0
1
0
2
2
0
1
1
1
1
1
1
1
1
1
1
2
1
0
1
2
2
1
1
1
2
0
2
1
2
3
1
1
0
2
0
1
2
1
1
1
2
9
0
0
2
1
2
3
0
1
1
2
1
1
2
1
1
1
0
0
2
1
1
0
1
1
1
1
1
2
2
2
1
2
1
0
1
1
2
0
1
1
2
0
1
1
0
1
2
0
2
1
0
0
2
1
0
0
2
1
1
1
5
1
1
2
1
1
0
0
1
1
1
0
2
1
2
1
1
2
2
1
2
0
1
0
2
2
2
1
1
0
0
0
0
2
2
1
0
2
2
1
1
0
1
1
0
1
0
2
2
1
0
1
2
0
1
1
0
0
1
1
2
0
1
2
1
1
1
1
2
1
3
2
1
1
1
0
1
1
1
1
0
1
0
1
0
1
0
2
2
0
0
0
0
2
0
2
1
2
1
2
1
3
1
1
1
1
1
2
1
1
2
0
2
1
1
0
2
2
1
1
0
2
2
2
1
2
0
0
1
2
1
0
2
0
0
2
1
1
2
0
0
1
1
2
0
1
0
0
2
2
1
0
3
0
2
1
1
1
0
2
1
4
2
0
0
0
0
1
1
1
0
1
3
2
1
0
1
1
1
0
2
0
0
1
2
0
1
2
0
1
1
0
1
2
0
1
1
1
2
2
1
1
1
0
1
2
1
1
2
0
2
2
1
0
0
2
1
0
1
2
1
1
1
1
1
0
2
2
2
2
1
2
0
1
2
1
0
1
2
2
1
0
2
0
0
0
1
2
1
1
0
2
2
1
1
2
1
1
1
0
0
0
1
1
1
1
1
2
0
1
0
1
2
1
1
1
1
1
0
1
0
1
2
2
1
1
1
0
1
0
2
1
1
1
1
1
0
0
2
0
0
1
1
0
2
2
1
0
0
0
2
1
1
1
1
0
1
2
1
1
0
2
0
1
1
1
1
1
1
1
0
0
0
1
1
1
1
1
0
1
1
2
1
1
1
1
1
0
0
0
1
2
1
1
1
2
0
0
0
1
1
1
1
1
1
2
1
1
1
1
1
1
0
2
1
0
0
0
1
1
1
0
0
1
1
1
2
1
1
1
2
0
1
1
2
1
0
1
1
2
2
1
2
1
2
0
1
1
1
1
1
2
2
1
1
0
1
0
2
2
0
1
2
1
2
0
1
2
1
1
0
1
0
0
2
1
1
1
1
1
1
1
1
0
1
1
0
2
0
1
0
2
1
0
0
2
2
1
1
2
2
0
2
1
1
0
1
1
1
1
1
1
1
2
1
0
1
0
2
0
1
1
1
0
1
0
1
0
1
1
1
1
1
2
0
0
1
2
0
0
0
0
2
2
1
1
1
2
1
1
2
2
1
1
1
1
1
0
1
0
1
1
2
1
1
2
1
0
2
2
0
1
1
1
0
0
1
0
1
0
2
1
2
1
1
1
1
1
1
0
1
1
1
1
0
0
2
1
1
1
1
0
1
2
1
1
0
0
1
0
1
1
1
0
0
2
1
1
1
1
2
0
1
2
1
1
2
1
1
1
1
1
1
2
1
0
2
0
1
0
0
1
1
0
1
2
1
1
0
2
2
2
1
1
2
0
1
1
1
2
1
1
0
1
2
1
1
0
1
1
2
1
1
1
2
0
1
2
2
0
1
1
1
2
1
1
1
1
1
1
1
1
2
2
0
2
1
2
1
1
1
1
1
1
2
1
1
0
1
0
3
0
1
0
1
1
0
0
1
1
1
1
1
0
0
2
1
0
1
2
2
1
1
1
1
1
2
1
1
0
1
1
1
1
2
2
0
1
1
0
1
2
1
1
1
0
0
0
1
1
0
2
1
1
0
1
1
0
1
1
1
1
1
0
1
2
2
2
2
1
2
2
1
2
1
1
1
1
1
0
1
2
0
2
1
1
1
0
2
1
0
1
1
1
1
2
2
2
0
1
0
1
1
1
1
1
1
2
1
0
1
1
1
1
0
1
2
1
2
1
1
1
1
2
1
2
1
2
1
0
1
1
1
1
1
0
1
1
2
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
2
0
0
1
1
0
0
1
1
2
1
0
1
2
2
1
1
2
1
1
0
1
0
1
1
1
0
1
2
0
2
1
1
2
3
2
0
2
1
2
2
0
2
0
1
0
1
0
2
1
1
0
2
1
1
1
0
1
1
1
1
0
1
2
1
0
1
2
1
0
1
2
1
2
1
0
1
0
1
1
1
1
1
0
1
1
1
2
2
1
2
1
1
0
2
1
0
0
1
1
1
2
2
2
2
1
2
1
0
1
1
1
0
0
1
1
1
2
2
1
2
1
1
2
1
2
1
2
1
1
0
2
1
1
0
1
0
1
0
1
0
1
2
1
0
1
0
1
1
2
1
1
1
2
0
1
1
2
0
2
1
2
0
1
1
0
2
1
0
2
1
1
2
0
2
1
0
2
2
1
1
0
1
1
0
0
1
2
1
2
1
1
1
1
2
1
1
0
2
1
1
0
0
0
0
3
0
2
0
1
1
1
1
1
2
0
0
3
0
1
1
2
0
0
1
1
1
0
1
2
1
1
0
2
0
0
1
1
2
2
1
1
1
2
1
2
2
0
0
2
1
0
2
2
0
1
1
1
0
1
2
1
0
1
2
2
0
0
1
1
1
1
1
0
0
2
1
1
1
1
1
1
0
1
1
0
1
1
2
0
1
1
0
1
1
2
2
1
2
2
1
1
1
1
2
0
1
0
3
1
0
0
1
1
1
0
0
0
1
1
0
1
1
2
2
1
0
1
1
1
1
1
1
1
2
1
0
1
2
1
1
1
2
1
0
1
2
1
1
1
2
1
2
2
1
0
0
0
0
1
2
2
1
2
0
1
0
1
0
0
2
2
1
1
0
0
1
1
1
1
1
0
2
1
1
1
2
1
1
1
1
0
1
1
1
1
1
0
1
2
0
1
1
2
2
2
1
1
1
2
1
2
1
1
1
1
3
1
1
1
2
1
5
1
0
1
1
1
1
1
2
0
1
1
1
2
1
0
0
1
0
2
2
0
1
1
1
0
0
1
0
1
1
0
0
1
0
1
1
1
1
1
2
0
1
0
1
0
2
1
1
1
0
1
3
0
0
1
1
1
1
1
1
2
1
1
1
0
1
0
0
1
1
0
0
0
1
1
1
2
0
1
0
2
1
1
1
1
0
1
1
6
0
1
2
1
0
1
1
1
0
1
1
1
1
0
0
1
2
0
0
2
2
0
1
1
0
0
2
1
1
1
0
2
0
1
2
1
2
1
2
1
1
1
1
1
2
2
0
0
1
1
2
1
1
1
1
1
2
0
0
1
1
1
2
2
0
2
0
2
1
2
1
1
1
0
0
1
2
0
2
3
1
1
1
1
1
0
1
1
1
0
1
2
1
0
0
1
1
1
1
1
1
0
1
0
1
2
2
1
1
0
1
1
1
0
1
1
2
1
1
0
0
2
1
1
0
0
0
0
1
1
2
0
2
0
3
2
1
1
2
2
1
0
1
1
1
1
0
0
1
0
0
0
1
0
0
1
1
1
1
1
2
2
2
1
0
1
2
1
1
1
0
2
2
2
0
1
0
0
1
0
1
1
1
2
1
2
1
1
1
1
1
1
2
2
1
2
1
1
1
2
1
1
1
1
1
0
1
0
1
1
1
1
0
1
0
1
1
0
1
0
1
1
1
0
1
0
1
1
1
1
1
2
1
1
1
0
1
1
1
1
0
0
1
1
2
0
1
2
2
0
1
1
0
1
1
2
0
0
2
1
2
1
1
1
1
0
0
0
0
0
0
1
1
1
1
1
2
2
2
2
1
1
1
1
1
1
1
0
1
2
1
1
2
2
0
1
2
0
0
1
0
0
0
0
0
1
2
1
0
1
1
1
1
1
1
1
0
1
1
1
1
1
0
1
0
1
1
2
2
2
2
2
0
1
0
1
1
0
1
1
1
0
1
0
1
2
1
1
2
2
1
1
1
1
1
1
0
1
0
1
1
1
1
1
1
1
1
0
0
1
1
2
1
1
1
3
1
2
0
0
0
1
1
1
1
1
2
1
2
2
1
1
0
0
1
1
0
2
1
0
1
0
1
2
1
0
2
1
1
1
0
1
1
1
0
2
1
1
1
1
2
0
1
1
1
0
1
1
0
1
1
1
2
0
2
1
1
2
1
2
1
0
2
1
0
1
1
1
0
0
1
1
0
1
1
1
0
3
1
1
1
1
1
1
1
1
2
1
1
1
1
0
1
2
1
0
1
1
1
2
1
0
1
1
2
1
1
1
2
1
1
1
2
1
0
1
2
1
0
1
1
2
2
0
1
1
1
1
0
0
1
1
1
2
0
1
1
1
2
1
1
1
0
2
0
1
0
1
2
2
1
1
0
0
1
1
2
2
1
1
1
1
1
1
2
1
0
1
2
1
1
2
1
0
0
2
2
0
2
1
1
1
1
1
1
1
0
1
1
1
2
0
1
0
1
1
2
0
0
2
2
1
0
1
0
1
1
2
2
1
1
2
1
1
0
2
1
2
1
1
1
2
0
0
2
2
1
1
2
2
2
2
1
1
1
0
0
2
1
1
2
0
0
2
0
2
2
1
1
1
2
1
0
1
2
2
0
1
2
1
0
1
2
1
0
1
1
1
1
1
2
1
1
2
2
1
1
1
1
1
2
2
2
2
1
1
1
1
0
2
1
2
2
1
0
2
1
1
0
2
1
1
0
0
0
1
1
1
1
0
1
2
1
1
2
1
1
2
2
1
0
1
1
0
0
2
1
1
1
0
2
1
2
1
1
1
1
1
1
0
0
1
1
1
1
0
1
1
1
0
2
1
0
1
1
1
1
1
2
1
2
1
1
0
1
1
1
0
0
0
1
0
1
1
0
1
2
2
1
1
1
1
0
1
1
1
1
1
1
2
2
0
2
0
0
0
2
1
1
0
2
1
0
1
2
1
1
1
2
2
1
1
1
0
0
1
2
2
1
1
1
1
0
1
1
1
2
1
2
0
0
0
1
2
1
0
2
1
1
1
0
2
1
3
1
2
1
0
0
1
2
0
1
1
2
1
2
0
1
1
2
2
0
2
0
0
2
2
2
1
1
1
2
0
0
1
1
2
1
1
1
2
0
2
0
1
2
1
0
1
2
1
1
1
1
1
0
0
1
2
2
1
0
1
1
1
1
1
1
1
0
2
1
0
2
1
0
0
1
1
1
1
1
0
1
1
1
0
1
1
0
2
1
1
2
0
2
1
1
2
1
2
1
1
1
1
1
1
1
0
2
1
1
0
0
1
0
1
1
1
1
1
1
0
1
3
1
2
1
0
0
1
1
2
1
4
0
1
0
1
2
0
1
2
1
1
2
1
2
1
0
1
1
0
2
1
0
2
2
1
0
2
1
0
1
1
0
1
1
2
1
1
2
2
1
2
0
1
0
2
1
1
2
2
0
2
1
1
0
2
2
2
2
1
1
0
1
1
1
0
1
0
1
1
0
0
1
2
1
0
0
0
1
1
1
1
1
1
0
1
1
1
2
1
0
1
1
1
1
1
1
0
2
0
1
1
0
1
2
1
1
0
1
2
1
1
1
1
2
2
2
2
0
2
1
2
1
2
1
0
1
1
1
2
0
1
0
0
2
2
1
0
1
1
2
2
1
0
2
0
1
2
1
1
1
2
0
1
1
2
2
2
1
1
1
2
1
0
1
0
0
1
1
1
2
1
1
0
2
1
1
1
1
1
0
1
1
0
1
2
2
0
1
2
1
2
1
0
0
2
1
0
1
1
1
1
2
2
0
1
0
1
1
0
0
0
1
1
1
0
1
0
2
1
1
1
1
2
1
0
1
2
1
1
2
2
0
1
1
1
1
0
2
0
0
1
1
1
0
1
1
2
1
1
0
0
2
2
1
2
1
0
1
1
2
2
3
0
0
0
1
2
2
0
0
1
1
0
1
1
1
1
1
1
0
1
1
2
1
3
1
1
0
0
0
0
0
1
1
2
1
1
2
1
1
1
1
0
1
2
1
0
2
1
2
1
1
1
2
2
1
1
1
2
2
1
0
1
1
1
2
1
1
1
1
3
0
2
1
1
1
1
1
1
0
2
1
0
1
1
1
1
1
1
1
2
1
1
0
1
1
2
0
0
1
1
0
2
3
1
1
1
1
1
2
1
1
0
2
2
2
1
1
0
1
0
1
2
0
0
2
1
1
1
1
1
1
1
0
0
1
1
1
0
3
0
0
0
1
1
0
1
1
1
1
1
2
0
1
0
1
0
1
1
3
0
1
1
2
1
0
1
0
2
0
1
2
0
1
1
1
2
1
1
1
1
0
0
0
0
1
1
0
1
0
1
1
1
1
1
2
1
0
2
1
1
0
1
1
1
1
1
1
1
0
0
0
1
1
0
1
2
2
1
0
2
1
2
2
1
1
1
2
0
1
1
1
1
0
0
1
1
1
0
1
0
2
2
0
2
1
1
2
2
1
1
1
0
1
1
2
0
1
1
1
1
1
1
1
0
0
0
0
1
2
0
1
1
1
1
1
2
1
2
1
2
0
0
1
1
0
0
1
2
2
1
0
0
1
2
1
1
0
2
0
1
1
1
2
2
2
1
1
2
2
0
1
1
1
1
1
2
1
1
1
1
1
0
2
1
0
2
2
2
0
1
0
2
1
1
1
1
1
3
1
1
2
0
2
1
1
0
2
1
1
1
2
0
1
2
2
0
1
1
1
2
1
2
0
1
1
0
1
2
0
0
1
0
1
1
2
2
2
2
1
1
1
2
1
1
0
2
1
1
0
3
0
1
2
1
1
0
0
1
1
2
1
0
1
0
1
0
1
1
1
1
2
1
2
2
1
1
1
0
2
1
2
2
0
1
1
2
2
1
2
1
1
1
1
0
1
1
1
1
1
1
2
2
2
1
1
0
0
1
2
1
1
2
0
1
1
0
2
1
1
1
1
0
1
2
2
2
2
1
1
1
1
1
1
0
1
2
1
1
2
1
1
1
2
0
0
1
2
1
1
1
0
1
0
1
2
1
2
2
2
0
1
1
1
1
1
2
1
0
0
0
2
2
1
2
1
1
0
2
2
1
1
2
1
1
1
2
2
1
0
0
1
1
1
1
0
1
1
1
1
1
1
0
2
0
0
2
2
1
1
1
2
0
2
1
2
0
0
3
0
1
2
1
1
0
0
2
1
1
1
1
1
2
0
2
1
2
1
0
1
1
0
1
2
1
0
1
1
2
2
1
1
0
1
0
1
0
2
0
0
1
1
1
3
1
2
2
1
0
3
1
1
1
1
2
0
1
2
1
1
1
0
1
2
0
0
0
1
0
0
3
0
1
1
2
1
0
1
1
1
2
1
1
1
1
2
2
2
2
1
1
1
1
3
1
1
0
2
0
1
2
1
1
0
2
1
1
2
0
3
1
1
2
0
1
2
1
1
0
0
1
0
1
1
1
1
0
2
2
1
1
0
1
1
0
2
2
2
1
1
0
2
1
1
1
1
0
4
2
1
0
2
1
3
1
1
1
1
0
0
1
1
0
0
1
2
1
0
0
0
0
0
1
2
1
2
0
1
1
1
0
0
2
1
0
1
0
1
1
0
1
2
2
0
3
2
1
1
2
1
1
0
1
1
2
2
0
1
1
1
1
1
0
0
1
0
2
1
1
1
1
1
1
1
0
0
1
1
0
0
1
0
1
1
0
0
1
1
0
1
1
1
1
1
0
2
1
0
1
0
0
2
1
0
1
0
1
1
1
1
1
1
2
1
1
1
0
2
2
1
2
2
0
1
0
1
2
1
0
2
0
2
0
0
1
1
1
1
1
1
2
2
1
2
0
2
0
1
0
1
1
1
0
1
0
2
2
2
1
1
0
1
1
1
2
0
1
1
1
1
1
2
1
1
1
0
1
1
1
1
2
0
1
1
2
1
2
1
2
0
1
0
4
2
1
1
0
1
1
1
1
1
1
0
1
0
1
1
1
0
1
0
1
1
1
0
0
2
1
1
0
2
1
0
2
1
1
1
0
2
1
0
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
0
1
1
0
1
1
1
1
1
2
1
0
0
0
1
3
0
1
1
1
1
1
2
1
1
1
1
1
3
1
1
1
1
1
1
2
2
1
0
0
1
0
2
1
2
1
1
2
0
1
0
0
0
2
1
1
1
1
1
1
0
1
0
0
0
1
0
1
2
1
2
0
1
1
1
1
1
1
1
1
2
1
1
1
0
2
1
2
0
1
1
0
1
0
0
1
1
0
1
2
1
1
1
1
1
1
1
1
1
2
2
0
2
1
0
1
0
0
0
1
2
0
0
1
0
1
0
0
1
1
2
0
1
1
1
1
2
1
1
1
0
1
1
1
1
2
0
0
1
0
1
2
0
1
1
1
1
1
1
1
1
1
0
1
1
2
1
1
2
1
1
1
0
2
2
2
0
2
1
1
1
1
0
1
0
1
0
2
1
2
1
1
1
2
1
2
1
1
1
3
2
1
1
1
1
2
0
2
2
1
1
0
1
1
1
1
0
0
2
2
0
1
2
2
1
0
1
2
2
1
0
0
2
1
0
0
2
2
1
1
0
0
3
2
0
1
1
2
1
1
3
0
0
2
1
1
0
1
0
2
0
1
1
0
1
1
1
1
0
0
1
2
0
1
1
1
1
1
1
1
0
2
1
2
1
0
1
2
1
0
3
0
0
2
1
0
0
2
0
1
2
2
2
1
2
0
1
1
1
1
1
0
1
1
1
1
1
0
1
2
2
1
0
1
0
0
1
2
0
2
1
2
1
1
1
0
1
0
1
1
2
1
2
1
0
1
1
1
0
1
1
0
0
0
1
1
0
1
1
1
1
1
1
0
1
0
1
0
1
1
0
2
2
1
0
2
1
1
1
1
1
0
1
1
1
0
0
1
0
1
0
2
1
0
1
1
2
1
1
0
1
1
2
1
1
1
1
2
1
1
1
2
1
1
0
2
2
1
1
0
2
1
1
1
0
1
1
1
1
1
0
2
1
1
1
2
1
0
2
1
1
0
1
0
1
0
1
2
0
0
1
1
2
2
0
2
3
1
1
0
0
1
0
3
2
1
1
1
1
2
1
1
2
0
0
1
1
1
0
1
1
1
1
3
1
0
2
2
1
1
2
1
1
1
1
2
1
1
2
2
1
0
2
2
2
1
1
1
1
0
0
2
2
1
1
2
0
0
1
0
2
0
1
0
1
1
2
1
1
2
1
1
2
2
1
0
0
2
0
2
0
1
1
0
0
1
2
2
1
2
1
1
1
1
1
0
1
0
1
1
0
2
1
0
0
0
1
2
1
1
1
1
0
2
1
2
1
2
2
0
0
0
1
0
1
1
2
1
1
1
0
2
1
1
1
2
0
1
2
1
1
1
1
1
0
0
0
0
2
0
1
1
1
1
2
0
0
2
1
1
0
0
1
0
2
1
0
2
1
2
1
0
0
1
1
0
1
0
0
1
1
2
0
0
1
0
1
1
1
1
2
2
2
1
2
0
1
1
1
1
1
0
1
1
1
0
1
3
1
2
1
2
2
1
1
1
2
0
1
0
0
2
1
1
0
0
2
0
1
1
2
2
0
1
0
2
1
0
1
1
1
0
1
1
0
1
1
1
1
2
1
1
0
0
0
2
2
1
1
2
1
0
1
1
0
0
1
2
1
1
1
1
0
0
1
2
0
2
0
1
0
2
0
1
1
1
2
1
1
1
0
0
2
0
1
2
2
1
1
2
1
1
0
3
0
1
1
0
0
1
1
1
2
0
1
2
2
1
2
1
0
2
1
0
0
1
1
2
2
0
2
0
1
2
0
1
0
1
0
0
1
1
2
1
1
1
1
2
0
1
1
1
1
0
1
1
2
1
1
2
0
1
0
2
1
0
1
2
1
1
0
2
2
0
0
2
1
0
2
2
1
2
1
0
1
1
0
2
1
2
2
0
0
1
2
2
1
0
0
1
0
0
0
0
2
0
1
0
1
1
0
1
1
0
1
1
1
2
1
1
1
0
2
2
1
0
0
2
2
1
0
1
2
0
2
1
0
1
1
0
0
0
1
1
0
1
2
1
0
1
2
2
0
0
0
1
1
2
1
2
1
1
0
2
1
0
1
1
1
0
0
0
1
1
1
0
1
2
1
0
1
1
2
1
1
2
0
1
2
1
1
0
1
2
0
1
2
2
1
0
2
1
2
1
1
0
2
1
1
1
1
0
0
1
2
0
1
1
1
2
1
1
1
1
1
1
2
1
1
2
1
1
1
0
0
2
0
1
2
1
1
1
1
1
2
0
1
1
1
2
2
0
1
1
2
0
2
0
1
2
1
2
2
1
1
1
2
1
1
1
0
1
1
0
1
0
1
1
1
1
1
0
1
1
1
0
2
1
0
2
2
2
1
2
0
1
1
1
1
2
2
2
2
0
0
2
1
0
0
3
1
2
1
2
1
0
1
0
2
1
1
2
1
1
1
1
2
2
1
2
2
0
1
1
2
0
1
3
1
2
1
1
1
1
1
1
0
0
1
1
2
2
2
1
2
1
0
0
0
1
2
1
0
1
1
1
1
1
0
1
1
0
1
0
1
2
2
2
1
1
2
0
0
1
1
0
1
1
2
0
2
1
1
0
1
2
1
1
1
2
1
0
1
0
1
2
1
0
2
0
2
0
0
0
1
1
2
1
1
1
1
1
1
2
2
2
0
0
1
1
2
1
1
0
1
2
2
1
2
0
0
0
0
1
2
0
2
2
0
1
1
1
0
0
1
1
1
2
2
1
2
1
0
2
1
0
1
0
2
0
1
1
1
1
0
1
1
1
0
1
1
1
0
1
1
1
1
1
1
1
0
2
1
1
2
2
3
0
0
1
1
0
1
1
0
1
1
2
2
1
1
1
0
2
2
1
1
1
2
1
2
1
1
2
1
2
0
1
1
1
3
1
2
0
1
2
1
0
1
1
0
2
1
0
1
1
1
0
2
2
1
0
1
1
3
0
2
1
13
1
0
1
1
0
1
1
1
1
1
1
2
1
2
2
0
1
3
1
1
2
2
2
1
1
1
0
1
1
2
0
1
1
1
0
2
2
0
1
0
1
1
0
1
1
0
1
0
0
2
0
1
1
1
1
1
1
1
0
1
2
2
1
2
1
0
0
1
1
1
1
0
0
0
0
1
1
1
1
1
1
1
0
1
2
1
1
1
1
2
1
0
2
1
1
2
1
0
1
2
1
2
0
2
1
0
1
2
2
1
1
1
0
2
1
0
1
1
0
2
0
1
1
1
2
0
2
1
1
2
1
1
2
1
1
0
0
1
0
0
2
2
1
2
0
1
1
0
2
1
1
0
1
2
1
1
1
1
1
2
0
1
2
1
1
2
2
1
1
0
1
1
1
0
1
1
2
1
2
2
1
0
0
1
1
0
1
1
0
1
0
0
2
1
2
1
2
2
1
2
2
2
1
2
1
1
1
1
1
1
2
2
1
2
1
1
1
2
1
1
1
0
1
2
1
1
0
1
2
0
2
1
0
2
1
1
1
1
0
1
1
2
2
1
1
1
1
2
1
0
1
0
1
0
0
1
0
1
1
2
2
0
1
0
1
2
1
1
0
1
1
2
1
1
2
1
0
0
1
1
0
1
1
2
2
1
0
0
1
0
0
2
1
1
2
0
1
1
1
1
1
1
0
0
2
2
2
1
1
2
1
0
0
0
1
1
2
0
0
1
2
1
1
1
2
2
0
1
1
1
0
1
1
1
2
1
2
1
1
1
1
1
1
0
1
1
2
2
1
0
2
1
1
2
1
0
1
1
1
1
2
0
0
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
0
2
2
1
1
0
1
2
1
1
1
1
1
1
0
1
1
2
1
1
0
1
1
1
1
0
1
1
2
2
0
1
1
0
2
2
1
1
2
1
0
2
0
0
1
1
1
1
2
0
1
1
2
3
0
0
1
1
2
1
0
0
1
1
1
0
1
0
0
2
1
1
2
0
0
2
2
1
2
0
0
1
1
2
1
1
2
2
1
0
1
1
0
2
1
1
1
1
2
2
1
2
2
0
0
1
1
1
1
2
3
1
2
1
2
2
2
1
1
1
1
1
0
1
0
1
1
1
2
0
1
1
2
1
1
1
1
0
1
1
1
2
1
3
1
1
2
1
1
0
0
1
2
1
3
1
2
0
0
2
1
1
1
1
1
0
0
0
1
2
2
1
1
1
0
1
0
1
1
1
1
1
0
2
2
2
2
0
2
2
1
2
1
1
2
0
1
2
1
0
0
1
1
1
1
2
0
0
1
1
0
1
1
0
4
1
0
1
1
0
1
0
1
0
1
1
1
0
1
1
2
1
1
0
0
1
0
1
1
1
0
1
0
1
0
1
1
2
2
2
2
0
0
1
0
2
1
1
0
1
1
2
2
1
2
1
1
1
1
1
1
1
1
4
0
1
2
0
1
1
1
1
1
0
1
1
1
1
2
1
1
0
1
1
0
1
0
1
1
0
1
2
1
0
1
1
1
0
0
1
1
1
1
0
2
1
2
1
1
2
1
1
2
2
1
2
1
2
2
1
3
1
1
0
2
0
1
1
1
1
1
0
1
0
2
2
1
1
1
1
1
1
2
2
1
0
2
1
1
0
1
1
1
2
1
1
1
1
1
2
0
1
1
0
1
2
0
1
1
2
1
1
2
2
1
2
1
0
1
1
0
0
1
1
0
1
1
0
2
1
0
1
2
1
1
1
2
2
0
1
1
1
0
0
1
0
1
0
1
2
1
0
1
1
2
1
0
1
3
0
1
1
0
2
2
1
1
0
2
2
0
6
0
2
1
1
0
1
2
0
1
1
1
1
1
1
1
0
0
1
1
2
1
0
0
2
2
1
0
1
2
0
1
1
2
1
2
0
2
1
0
1
1
1
1
2
0
1
1
0
2
1
1
2
2
1
1
1
2
1
0
1
0
1
1
1
1
1
1
2
1
2
2
2
0
2
2
7
2
2
0
0
2
2
0
1
2
2
0
0
0
1
0
1
1
1
1
1
2
0
1
2
1
2
2
2
2
0
1
1
1
0
0
0
0
0
1
1
1
1
1
1
1
0
1
1
1
2
1
1
1
1
0
0
1
0
1
1
1
2
2
1
2
0
2
1
1
1
0
3
2
2
1
2
0
2
2
1
1
1
2
1
2
1
1
1
1
2
2
1
0
2
1
0
1
2
1
0
1
1
1
0
1
1
0
1
0
0
1
0
0
1
1
1
0
1
1
2
1
1
2
1
2
1
1
1
2
1
2
0
1
1
2
1
0
1
0
1
3
1
2
1
0
2
1
2
1
1
1
1
2
1
0
2
1
1
1
1
2
2
1
0
2
0
0
1
1
1
1
1
0
1
2
1
1
1
2
1
2
0
1
2
2
0
1
0
1
1
1
1
2
1
1
0
1
1
1
2
0
0
1
2
1
1
2
1
1
0
1
1
1
2
2
0
0
1
0
7
1
1
1
1
2
1
2
2
2
1
2
2
1
0
0
1
1
0
1
2
0
2
2
0
0
1
1
1
1
2
0
2
2
2
1
1
1
1
1
1
2
1
1
0
1
1
2
1
1
2
2
1
1
0
1
2
0
1
1
2
1
1
0
2
1
1
2
1
0
1
0
2
1
1
1
0
2
1
1
1
1
1
1
0
2
1
1
1
1
1
0
2
1
1
1
0
0
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
1
1
0
1
2
2
0
0
1
2
2
2
2
1
1
0
2
1
1
1
2
1
2
1
2
1
1
2
0
2
1
1
0
1
0
1
1
0
1
1
1
1
1
2
1
1
1
2
1
1
1
2
0
0
0
0
2
0
2
1
0
1
1
1
2
1
1
2
1
2
2
1
2
2
1
1
0
0
2
1
2
1
1
0
1
0
0
0
2
1
2
1
1
1
1
1
1
2
1
1
1
2
1
0
0
1
0
1
0
1
2
1
2
1
2
2
1
2
1
0
1
1
0
0
0
0
2
1
0
1
2
1
1
1
1
1
1
1
2
0
1
1
1
1
0
1
1
1
2
1
1
1
1
1
2
0
2
1
2
0
1
1
2
1
1
0
2
2
1
1
0
1
2
1
0
1
1
1
2
2
0
2
1
1
0
0
0
1
0
1
1
0
1
1
1
1
1
1
1
0
1
1
1
2
1
0
0
1
1
0
3
0
1
1
1
1
1
1
0
0
1
1
2
0
1
2
1
0
0
0
1
0
2
2
1
1
1
3
1
0
1
1
1
0
0
1
2
0
2
0
1
1
0
2
2
1
1
1
0
1
0
1
2
1
1
0
2
1
1
1
2
0
2
1
0
2
0
2
1
2
1
2
2
3
0
1
2
1
1
1
0
0
1
2
1
2
1
1
1
1
0
1
3
0
2
0
1
2
2
0
0
1
0
0
0
2
1
0
1
0
2
2
0
1
2
1
2
1
2
1
1
1
2
1
1
2
2
0
0
1
2
1
2
0
2
1
0
2
0
1
1
2
1
0
0
1
1
2
0
1
1
1
0
1
1
1
2
1
1
1
2
2
1
1
0
1
1
1
1
1
1
1
1
0
0
1
2
1
2
2
1
1
1
1
1
2
2
2
1
3
2
2
1
2
1
1
1
1
1
1
2
2
1
1
2
0
1
1
0
0
1
0
2
1
2
2
2
1
1
0
1
0
1
0
1
0
2
0
2
1
2
2
2
0
1
1
0
0
1
2
0
2
1
1
1
1
2
1
1
1
1
2
0
0
2
1
0
3
1
2
0
1
1
2
0
0
0
1
1
1
1
0
1
2
1
1
0
1
1
0
1
2
2
1
1
0
1
1
2
1
1
0
2
2
2
1
2
1
1
0
0
1
1
2
1
2
2
1
1
0
1
0
1
0
2
2
1
1
1
1
2
1
2
1
1
2
0
0
1
1
1
1
1
2
1
1
0
1
1
1
1
1
2
0
2
0
1
1
1
1
1
1
0
1
0
1
2
1
2
2
1
2
1
2
2
2
1
0
1
0
0
2
1
0
0
1
1
1
1
1
0
1
1
1
1
0
1
2
1
1
1
1
1
1
2
0
2
1
1
1
1
1
0
2
1
1
1
2
1
1
1
0
1
1
2
0
1
1
2
0
0
1
1
1
0
1
1
1
1
1
1
1
3
1
1
0
1
1
1
1
2
0
1
2
1
1
1
1
1
1
2
0
0
0
1
0
1
0
2
1
2
0
1
2
1
1
0
1
1
1
1
0
1
1
1
1
2
2
0
1
1
2
2
1
2
1
0
0
1
1
0
1
2
1
1
2
1
1
1
1
1
1
0
1
2
2
1
2
1
0
1
1
1
0
2
1
1
0
1
0
1
1
1
2
0
0
2
0
2
1
0
2
3
0
1
0
2
1
1
1
1
1
2
1
0
1
1
2
0
0
1
1
1
0
1
1
2
1
2
2
1
1
2
0
0
0
1
1
0
1
0
1
0
1
2
0
0
1
1
0
1
2
2
1
2
1
1
0
2
1
1
1
2
2
1
1
0
1
1
1
1
1
1
1
2
0
2
2
0
2
1
1
1
2
0
0
1
1
1
1
2
2
1
1
1
1
1
0
1
2
2
0
2
1
1
1
2
1
3
0
1
1
1
0
1
0
1
1
2
2
0
2
0
1
2
1
1
1
1
2
0
2
2
1
2
1
0
1
2
0
1
2
0
1
1
1
1
0
0
1
0
0
2
2
1
1
1
2
1
1
1
2
2
2
2
0
1
1
0
0
0
0
1
1
2
1
0
3
1
2
1
1
2
1
1
1
2
1
1
1
0
2
2
2
1
1
2
1
2
1
1
1
1
1
0
1
1
0
0
0
0
2
2
1
0
2
1
4
1
1
2
1
0
1
0
2
1
0
0
1
2
0
1
1
1
1
2
2
1
1
0
1
2
0
0
1
0
1
1
2
1
1
1
1
1
1
1
0
1
0
0
1
2
0
0
2
1
1
0
1
2
1
1
0
0
0
1
2
2
1
2
1
1
1
1
1
1
0
0
2
0
0
1
1
2
4
1
0
1
1
1
2
2
1
0
2
2
4
0
1
1
2
0
1
1
1
2
2
2
1
1
0
1
2
3
1
1
2
1
2
2
0
1
1
1
0
1
0
1
2
0
1
2
2
0
2
1
1
1
1
1
0
0
2
2
1
1
2
2
1
1
2
0
1
1
1
1
1
1
1
0
1
2
1
1
1
0
1
2
1
2
1
2
1
0
0
2
2
0
0
1
0
2
1
1
2
1
2
1
2
0
0
1
0
2
1
0
0
1
2
0
1
2
0
2
1
0
0
1
0
1
0
0
2
1
0
0
0
2
1
0
2
1
2
2
0
1
4
1
1
1
1
1
2
2
2
1
1
0
0
0
1
1
2
1
1
2
0
0
2
1
1
3
0
1
0
1
2
1
1
0
0
1
0
1
2
1
0
2
2
1
2
2
2
1
1
1
1
2
1
0
0
1
1
1
0
0
1
0
2
1
1
2
2
1
1
1
1
2
1
2
0
1
1
0
1
0
2
1
1
0
1
2
2
0
1
2
0
0
1
0
1
2
2
2
0
2
2
1
1
2
0
2
1
1
0
1
2
0
1
0
1
2
1
1
2
1
0
1
0
1
0
1
0
1
1
2
1
1
1
2
1
1
2
1
1
0
1
1
2
0
1
2
0
2
2
0
1
1
2
2
0
2
0
1
2
0
2
1
0
1
2
1
2
1
1
2
0
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
0
1
2
1
2
1
0
2
1
1
2
1
1
1
0
2
1
1
0
1
0
1
1
1
1
1
0
2
1
1
2
2
1
4
5
2
1
2
2
1
1
2
0
0
1
1
1
1
2
1
1
2
1
1
4
0
1
0
2
2
2
1
1
1
0
0
1
1
1
0
2
0
0
1
1
1
1
1
1
1
0
0
0
1
2
0
1
2
1
1
1
1
1
1
1
0
1
1
1
1
1
1
0
3
0
1
1
1
1
1
2
1
2
1
1
0
2
0
1
0
0
0
2
0
1
1
1
1
3
1
1
1
1
2
1
2
0
2
1
0
1
1
0
1
1
2
0
1
2
1
0
1
0
1
0
2
1
1
0
0
1
1
1
2
1
0
1
2
0
1
0
0
0
1
2
1
1
0
1
1
1
1
0
2
2
0
1
2
1
2
1
0
1
0
1
2
1
0
2
1
1
0
1
0
2
1
1
3
1
1
1
1
1
2
1
1
0
1
2
1
1
0
0
1
2
1
1
1
2
1
2
1
2
0
3
1
1
0
0
2
2
2
0
1
2
1
1
2
1
1
0
1
1
1
1
1
1
1
1
2
1
1
1
1
0
1
1
2
1
0
1
1
1
0
0
0
2
2
2
2
1
1
1
1
1
0
0
1
1
1
0
2
1
1
0
2
0
1
1
1
1
0
1
1
1
2
1
1
0
0
1
2
1
2
0
1
1
1
2
1
1
2
1
1
2
0
1
2
1
0
0
2
2
0
1
2
0
0
0
0
1
1
1
1
1
1
0
1
1
1
1
1
0
1
1
2
0
1
2
0
0
2
1
1
0
1
1
2
0
1
2
1
1
0
0
1
1
2
1
0
1
1
0
1
0
2
2
1
1
1
1
2
2
1
1
1
2
1
1
0
1
0
0
0
2
2
1
0
2
2
1
1
1
1
0
1
2
1
1
0
1
0
1
1
1
1
2
2
1
2
0
0
0
1
1
2
1
1
1
1
1
1
2
1
1
3
1
2
0
1
1
1
1
1
1
1
0
3
2
1
1
1
1
2
1
1
1
1
1
1
0
1
0
1
1
1
3
1
1
0
1
1
0
0
1
2
1
1
0
1
1
2
0
1
2
1
0
0
1
1
0
1
1
0
1
0
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
0
1
2
2
0
2
2
0
0
2
0
1
0
0
1
1
1
1
2
1
0
2
0
0
1
2
2
0
2
0
0
1
2
1
1
1
1
0
2
2
0
1
0
0
0
2
1
1
1
2
1
0
0
0
1
1
0
1
1
1
0
1
1
1
1
1
0
2
0
1
1
0
1
2
1
2
2
1
1
0
0
1
1
0
0
1
1
0
2
2
1
1
1
1
1
0
2
1
1
1
2
2
0
1
1
0
2
2
1
1
1
1
1
0
1
0
1
1
1
1
1
1
0
2
1
1
2
2
1
0
1
0
2
2
1
1
0
1
1
1
1
1
1
2
1
0
1
1
0
0
1
0
1
2
2
1
1
1
1
2
0
1
1
1
1
0
1
1
1
1
1
0
2
1
0
1
0
1
2
1
0
1
1
1
0
1
1
1
1
1
2
1
0
0
0
1
2
1
1
0
0
1
1
0
2
0
0
0
1
1
1
1
1
0
1
2
2
1
1
1
1
1
0
1
1
1
1
1
0
1
2
0
2
2
1
1
1
1
2
1
1
2
1
0
1
1
1
1
0
2
0
0
1
1
1
2
2
2
0
2
0
0
1
0
2
1
0
0
0
2
0
2
1
0
0
2
1
2
2
1
1
1
1
2
1
0
1
1
0
0
1
1
1
1
1
1
0
1
1
0
1
1
1
2
1
1
1
2
1
1
1
2
1
2
1
1
2
2
2
2
0
1
1
0
1
3
0
1
0
1
0
1
1
1
2
2
4
2
1
0
0
1
0
1
1
2
0
1
0
1
1
2
1
2
1
1
1
1
1
1
2
1
1
2
0
1
1
1
0
1
1
1
1
1
1
0
0
1
1
1
0
1
1
2
2
0
1
1
2
2
0
2
0
2
1
1
0
0
0
0
2
2
0
1
3
0
3
1
0
1
1
1
1
0
1
2
1
1
1
1
2
1
0
2
1
2
2
1
1
0
1
1
1
1
0
1
1
0
2
0
2
0
2
0
1
1
2
1
1
2
1
0
1
1
1
1
1
0
1
2
2
1
0
0
1
0
1
1
0
1
1
1
2
1
1
2
1
0
1
1
2
1
1
1
0
0
1
1
1
1
0
2
0
2
1
2
0
0
1
1
1
0
2
1
1
0
1
2
1
1
0
1
0
1
2
1
0
2
1
2
2
2
1
1
0
2
1
2
1
1
1
2
0
1
2
2
1
2
1
2
0
0
1
1
1
0
2
4
2
0
2
0
1
1
2
1
1
1
1
1
1
1
1
0
0
2
2
0
1
0
0
2
0
2
2
1
2
1
1
1
0
0
1
0
1
1
2
1
0
1
1
1
1
0
1
1
1
2
4
1
0
1
1
1
0
2
0
1
0
1
1
0
2
1
1
1
2
2
1
1
0
1
2
1
1
0
1
2
0
1
1
1
2
1
0
1
0
0
1
1
0
1
2
1
1
0
2
2
1
2
2
0
2
1
1
1
1
0
1
0
0
0
0
0
1
1
1
1
1
2
1
0
2
0
0
1
2
1
1
1
0
0
1
1
0
1
2
0
1
1
1
2
1
2
1
1
1
1
0
2
1
2
1
1
1
0
1
0
1
1
1
0
2
2
1
1
1
0
0
1
0
2
0
1
2
0
2
2
0
2
1
1
1
1
2
1
2
1
0
1
1
1
1
1
1
0
0
0
1
1
1
1
1
0
0
1
0
1
0
0
1
0
2
1
1
2
1
2
1
2
2
1
1
2
1
0
2
0
1
1
1
2
1
1
2
2
1
0
2
1
1
1
1
0
1
2
0
1
1
2
1
1
1
1
1
0
0
0
2
0
1
1
1
0
3
1
1
1
1
0
1
0
1
0
1
1
0
3
2
1
2
2
0
2
1
1
2
0
1
1
0
2
0
2
1
1
1
1
2
1
2
1
1
0
3
2
0
0
2
1
1
1
1
1
2
2
1
1
3
1
0
0
1
1
1
2
1
0
1
0
1
1
0
0
0
0
1
1
1
2
2
1
1
1
1
0
0
3
2
1
0
1
0
0
2
2
0
1
2
2
1
1
1
1
1
0
0
1
1
0
1
2
1
0
1
1
0
0
1
2
1
2
0
1
2
1
1
1
1
1
1
2
2
2
1
0
1
1
0
1
1
1
1
0
1
0
1
1
0
1
2
0
1
1
1
1
1
1
1
1
1
1
2
0
1
0
2
1
1
2
2
2
1
0
2
2
1
2
0
2
1
0
1
2
2
1
1
1
1
0
1
2
1
1
0
1
1
1
1
1
1
1
0
2
1
1
1
0
2
1
0
1
0
1
1
1
1
1
1
1
2
1
1
1
1
0
1
1
2
1
1
2
1
1
2
1
2
1
1
1
1
2
1
1
1
1
1
0
1
1
1
1
2
0
1
2
1
1
1
3
2
0
1
2
0
1
1
0
0
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
0
2
2
1
1
1
0
1
2
2
1
1
1
1
1
2
2
0
0
0
0
1
2
0
2
2
0
0
0
2
0
0
0
1
0
0
1
1
1
0
2
0
2
2
1
2
0
2
1
2
0
0
1
1
0
1
2
2
1
2
1
1
1
1
1
2
2
2
2
1
0
1
2
2
1
1
1
1
2
1
1
1
1
1
0
1
0
2
1
1
1
0
0
0
2
1
1
0
1
1
1
1
1
2
1
1
0
1
2
0
1
2
2
0
2
0
1
1
2
0
1
1
0
1
1
1
1
2
1
1
1
1
1
1
0
1
2
0
0
1
2
2
1
0
1
0
1
2
2
2
1
2
0
2
0
2
2
1
4
1
0
1
1
1
1
1
0
1
1
0
2
1
1
0
1
1
1
1
1
0
1
2
1
0
0
2
1
0
0
2
0
1
1
1
0
0
1
2
1
1
0
0
1
3
1
2
1
1
2
0
1
2
1
1
2
1
2
0
2
2
1
0
1
1
1
1
1
1
0
0
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
0
2
1
1
1
0
1
1
1
1
1
1
0
1
1
2
2
1
0
1
0
1
2
1
2
1
2
1
1
1
0
1
1
0
1
1
1
2
1
1
1
1
1
1
1
0
1
2
1
1
2
1
0
2
1
1
1
1
1
1
0
0
0
1
0
3
2
1
1
1
1
0
1
2
1
2
3
2
0
0
2
1
1
0
2
0
1
1
1
1
1
1
1
1
1
1
2
1
1
1
0
2
2
0
2
1
0
1
1
2
1
1
1
0
1
1
1
2
2
2
1
1
2
0
2
0
1
2
0
1
1
0
0
0
2
0
1
2
1
2
1
0
2
0
0
2
1
2
0
2
0
1
0
0
1
2
1
1
1
0
0
0
1
1
1
1
2
1
1
2
1
1
1
2
0
1
1
1
2
1
0
1
1
1
2
2
1
1
1
0
0
1
2
0
1
0
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
2
1
0
0
2
1
1
2
2
1
1
2
0
1
2
1
2
1
1
2
1
0
1
2
1
2
1
1
1
0
1
1
1
0
2
0
1
1
0
2
1
1
1
0
1
1
0
2
2
1
0
2
2
1
1
1
1
1
2
0
0
2
0
1
1
1
1
0
2
2
0
0
2
1
2
1
0
1
0
2
2
2
0
1
1
1
1
0
0
0
1
0
2
0
2
0
1
2
1
0
1
1
1
2
1
2
1
1
2
1
1
2
0
2
1
0
2
1
1
0
1
1
1
2
1
2
0
1
2
0
1
1
1
1
1
1
1
2
1
1
1
1
0
0
2
2
1
1
0
1
1
1
1
0
2
2
1
2
2
2
1
0
1
1
1
0
1
2
0
1
1
2
1
1
1
1
1
2
2
2
1
2
1
1
1
2
0
1
1
1
1
1
1
1
1
1
2
0
2
0
1
2
0
1
1
1
1
2
0
1
0
1
0
0
1
1
2
2
2
0
1
1
2
1
1
1
0
1
1
0
1
1
1
1
1
2
1
2
1
1
1
2
2
0
1
1
0
1
1
1
1
0
1
2
0
0
2
2
2
1
1
1
1
1
1
0
1
2
0
2
1
1
1
2
0
2
1
1
1
2
2
1
1
1
1
1
1
2
1
2
0
0
1
1
1
0
0
2
1
2
0
1
1
2
0
1
2
1
1
2
1
2
1
0
2
1
1
2
1
1
0
2
1
1
2
1
1
1
2
2
1
1
1
0
3
1
1
2
2
1
1
2
0
1
2
0
1
1
0
1
1
0
1
1
1
1
1
0
1
1
1
2
1
1
1
1
0
1
1
1
2
2
0
1
0
1
2
0
1
1
0
1
1
2
1
1
1
2
1
2
1
0
1
2
2
1
1
1
2
1
0
2
0
0
1
1
1
0
1
1
1
1
0
2
2
1
1
1
2
1
1
2
0
1
1
0
1
1
0
1
0
0
0
2
0
2
1
2
0
0
1
1
0
2
0
1
0
0
0
1
0
1
1
1
1
1
1
0
1
2
0
0
1
0
0
2
3
1
0
2
2
1
0
2
1
1
2
1
1
1
2
1
1
2
1
1
1
0
1
1
2
0
0
1
1
0
2
2
0
1
6
2
1
0
2
1
1
0
2
1
0
0
1
1
2
2
0
1
0
1
1
1
0
1
1
0
1
1
2
0
2
1
2
1
2
0
1
1
0
1
1
0
0
1
0
1
1
1
1
0
2
1
1
2
1
2
1
1
1
2
1
0
2
1
1
2
0
1
0
1
1
0
2
2
1
2
2
1
0
4
1
0
1
1
1
1
1
0
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
0
0
2
1
2
0
0
1
1
1
0
2
0
1
2
1
2
1
1
1
1
1
1
2
0
2
1
4
1
0
1
2
1
1
1
1
1
0
2
1
1
1
1
1
1
0
1
1
1
1
1
0
1
1
2
1
1
1
1
2
2
2
1
1
2
1
1
1
2
1
1
1
1
2
1
1
0
1
1
1
1
1
1
1
0
1
1
2
1
0
1
1
0
2
1
0
1
0
0
2
2
0
0
1
1
1
1
1
2
1
1
0
1
1
2
1
1
1
1
1
1
0
1
1
0
0
0
2
1
1
0
0
0
2
0
2
1
2
0
1
2
3
1
2
1
0
0
1
2
0
2
1
2
1
2
1
2
0
1
2
1
1
2
0
0
0
1
2
0
0
2
2
2
0
2
1
1
2
1
0
0
1
1
1
1
0
1
0
2
1
1
2
0
3
1
2
0
2
1
1
1
1
1
2
1
1
0
1
1
1
1
1
2
0
1
1
0
1
1
0
2
1
2
0
1
0
0
1
1
2
0
0
0
0
1
0
2
1
0
0
1
0
1
2
1
1
0
1
1
0
1
1
1
0
0
0
2
1
0
1
1
1
2
0
1
2
2
1
1
2
1
0
0
0
1
0
1
1
1
1
1
1
1
1
1
1
1
1
2
2
0
1
1
1
1
1
1
2
0
1
2
1
0
0
1
1
2
1
1
1
2
1
1
2
0
2
1
1
1
2
1
1
1
1
1
0
2
0
2
1
1
0
2
1
1
0
2
2
2
2
0
1
1
0
0
1
1
0
0
1
1
2
3
1
1
2
0
1
2
1
2
1
1
1
1
1
1
1
0
1
1
0
1
1
1
1
2
1
1
1
2
1
1
1
0
1
2
2
1
1
1
1
1
1
1
1
1
1
0
1
0
2
2
1
0
1
1
1
1
1
2
1
0
0
0
1
1
0
0
1
1
1
2
1
2
1
1
1
0
2
1
1
2
0
0
0
1
1
0
1
3
1
1
0
2
2
1
1
2
3
1
2
1
2
0
0
1
1
1
0
1
2
2
2
1
2
1
0
0
1
3
1
2
1
0
1
0
0
3
1
1
1
1
2
1
2
2
1
1
0
1
1
1
2
1
1
1
1
0
2
2
0
1
2
0
1
1
1
1
0
2
0
1
2
0
1
0
1
1
0
1
2
2
2
1
2
1
1
1
1
2
1
1
2
0
2
1
0
1
1
0
0
1
2
1
1
2
1
0
2
0
1
2
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
0
1
1
0
1
0
2
0
2
0
1
0
0
1
1
0
1
3
0
0
1
1
2
1
1
0
1
1
0
2
1
1
0
1
2
1
0
1
2
1
0
1
1
0
0
1
2
2
1
0
1
1
2
1
1
1
1
0
1
2
0
1
1
1
1
0
2
1
2
0
1
1
1
1
1
2
0
1
0
1
1
1
0
1
1
1
2
2
1
2
2
0
2
0
0
2
1
0
3
1
0
1
1
2
1
1
1
1
0
2
2
1
1
1
1
2
1
1
0
3
2
1
1
1
1
1
1
2
1
1
2
1
1
1
0
1
1
1
2
1
2
3
1
1
4
0
1
1
0
2
0
1
2
1
1
4
2
1
1
1
1
0
1
2
1
2
0
1
1
0
1
1
1
1
3
1
2
0
1
2
0
1
0
0
2
1
0
1
1
1
1
1
1
1
0
1
0
1
1
2
1
1
2
0
0
2
1
1
0
1
1
2
0
1
2
1
2
1
1
0
0
1
1
1
2
2
0
1
0
1
0
1
0
0
1
1
1
0
0
1
1
2
0
0
1
1
2
1
1
0
1
1
0
1
0
1
1
0
0
1
2
1
1
1
2
1
1
2
0
1
2
2
0
1
1
1
1
0
1
1
1
3
0
1
2
1
0
1
1
1
1
1
2
2
1
1
2
1
1
0
1
2
0
1
1
0
1
1
1
2
1
1
0
2
3
1
0
1
0
3
2
0
0
1
3
1
1
2
2
2
0
1
1
1
1
0
2
0
3
1
0
2
1
0
1
0
1
0
0
1
0
1
1
1
2
1
1
1
0
1
2
0
0
2
1
1
2
1
2
0
1
1
1
1
0
0
1
1
0
0
2
1
1
0
2
1
0
1
2
1
1
1
2
1
0
1
0
1
2
1
1
1
1
0
2
1
1
1
0
0
2
2
1
0
0
0
0
2
1
0
1
1
1
0
1
0
1
1
1
1
1
2
0
0
2
1
1
1
1
0
1
2
2
1
0
1
1
2
2
0
1
1
1
1
2
2
0
1
1
1
0
0
1
0
0
2
2
2
1
0
0
0
2
1
1
0
1
0
0
1
2
0
2
0
1
1
0
2
1
1
1
1
1
0
1
1
1
1
0
3
1
2
0
1
2
1
0
0
1
0
2
2
1
2
0
1
0
0
0
2
1
1
1
0
0
0
2
2
1
1
1
1
0
3
2
1
0
2
1
0
1
2
0
1
0
1
2
0
1
1
2
1
1
1
1
2
2
1
1
1
0
0
1
5
1
1
2
1
1
1
1
0
2
1
1
1
1
1
0
1
0
2
2
1
2
2
0
0
1
0
1
1
0
1
2
1
1
0
2
1
1
1
1
0
2
1
0
0
2
1
1
1
1
1
2
1
1
1
0
1
2
2
2
0
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
0
1
1
1
2
1
1
1
1
1
2
1
1
1
0
1
2
0
2
1
0
1
1
1
1
2
1
0
2
1
1
1
1
1
1
0
0
1
1
1
1
2
1
1
1
1
1
1
0
1
1
0
2
1
0
1
1
1
1
1
1
0
1
0
2
3
0
1
2
0
1
0
1
1
1
0
1
2
2
1
3
2
1
0
2
0
1
1
4
0
1
1
2
1
1
2
1
2
0
1
1
1
1
1
1
1
2
1
2
1
1
0
1
0
2
1
1
0
0
1
1
0
1
1
0
0
2
1
0
1
1
0
1
1
0
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
2
2
1
1
1
0
1
0
2
5
1
1
1
1
0
1
0
2
0
0
1
0
1
0
0
1
0
1
0
2
0
2
0
1
0
1
1
0
0
2
1
1
1
1
0
1
1
1
1
1
1
1
0
2
1
2
2
1
1
1
0
0
0
1
2
1
1
0
2
1
1
1
2
2
1
1
0
2
2
1
0
2
0
1
1
1
2
1
2
2
0
0
2
2
0
1
2
0
0
1
2
2
1
0
0
1
1
1
1
1
1
2
0
1
0
1
0
1
2
0
2
1
0
1
1
2
2
1
1
0
1
1
1
1
0
1
3
1
1
0
1
1
0
3
2
0
0
1
0
1
1
1
2
1
1
1
1
2
1
1
1
1
0
0
0
0
1
2
1
0
1
2
1
1
1
1
0
0
1
0
1
1
1
1
2
0
1
2
1
1
1
1
3
1
1
3
2
1
1
0
1
1
2
0
2
2
1
1
0
1
0
2
1
2
0
0
1
0
0
2
1
0
2
1
0
1
0
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
4
0
1
1
1
1
1
1
0
2
2
0
0
2
1
0
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
0
2
2
1
1
1
2
2
2
1
1
0
1
1
1
1
2
1
1
1
2
0
2
2
1
0
1
1
1
0
0
1
0
0
2
0
1
2
1
2
1
1
0
1
1
1
1
1
1
0
1
2
1
1
2
1
0
0
0
0
1
1
2
1
0
1
1
0
1
1
1
1
1
0
0
0
1
1
1
1
1
2
0
2
1
0
2
2
0
1
2
0
0
0
1
0
1
1
0
2
1
1
2
1
1
2
0
2
0
2
0
1
2
1
2
2
1
2
1
0
1
0
0
1
1
0
0
1
1
0
0
0
2
0
1
1
2
1
1
0
0
0
1
4
1
1
0
1
1
1
1
0
1
1
1
1
0
0
0
0
2
2
0
0
0
1
1
1
0
1
2
2
1
0
1
0
2
1
1
0
0
1
0
1
1
0
1
2
1
1
0
0
1
1
2
2
1
1
1
0
1
1
2
1
0
1
0
0
1
0
1
1
0
2
1
1
1
1
1
0
1
2
0
1
0
1
1
1
2
1
1
2
1
2
1
0
1
1
0
1
1
0
0
1
0
2
1
0
0
1
0
1
1
1
2
2
1
1
0
1
1
1
1
2
1
2
1
0
0
1
2
1
0
1
1
1
0
0
2
1
2
0
1
2
0
2
2
1
0
2
1
1
1
1
1
0
0
1
1
1
1
0
2
2
2
0
1
1
0
1
2
1
1
0
2
3
1
1
2
1
0
0
1
2
1
0
0
2
1
1
1
1
0
1
1
1
2
0
1
2
1
1
1
1
0
1
1
0
0
1
0
2
1
2
2
2
1
1
1
1
0
2
1
1
1
0
1
1
2
1
0
1
1
1
1
2
2
0
0
1
2
2
1
2
1
1
1
1
1
2
1
1
1
0
1
1
1
1
0
1
0
0
0
1
1
5
2
1
1
1
2
2
1
0
1
1
0
1
1
2
1
0
1
1
1
2
1
0
0
0
1
1
0
1
2
1
2
2
0
1
0
2
0
1
2
4
1
1
1
1
1
0
0
1
1
1
2
1
2
0
1
2
1
1
1
1
1
0
0
1
1
1
1
1
2
1
0
1
1
2
1
1
1
2
2
1
2
0
1
1
1
2
3
0
1
1
0
2
1
2
1
2
0
1
1
1
1
1
1
0
1
1
1
2
2
1
1
1
1
1
1
0
2
0
1
0
0
1
1
1
0
1
1
2
1
0
1
0
0
1
1
1
2
1
0
1
0
0
0
0
1
0
1
1
1
3
1
1
0
1
1
2
1
1
0
2
1
0
1
0
0
1
1
1
1
2
1
1
1
1
0
2
0
0
1
0
0
2
0
2
1
2
1
2
1
1
1
1
1
1
0
3
1
1
1
1
2
0
1
1
1
2
1
1
1
1
1
2
2
0
2
1
2
0
1
2
1
1
0
1
0
1
1
1
1
1
0
2
2
0
0
1
1
1
0
1
1
1
0
1
2
0
1
1
0
1
0
2
1
2
1
3
2
1
1
0
1
0
1
0
1
2
0
1
1
0
2
1
0
0
2
1
1
1
0
0
2
1
1
0
2
1
2
0
1
1
1
1
0
0
1
1
2
0
0
1
2
2
0
1
1
0
2
0
1
3
0
2
1
1
1
0
0
1
2
1
2
0
0
1
1
1
1
0
2
1
1
2
1
0
0
0
1
0
2
0
2
1
1
1
1
1
2
0
2
1
1
0
2
2
2
2
1
1
2
1
2
1
0
0
0
1
0
2
0
0
0
0
2
2
0
1
0
2
2
2
2
0
1
1
3
1
1
1
0
0
1
2
2
1
0
1
1
1
1
1
1
0
1
1
1
1
0
1
0
1
0
0
2
2
0
0
0
1
1
1
0
1
0
0
0
1
2
1
2
1
1
2
0
1
1
1
2
1
2
1
0
2
1
1
2
0
1
2
0
1
0
2
1
1
1
0
0
0
1
1
1
1
1
1
1
1
2
0
0
2
1
2
1
1
0
1
1
1
1
1
2
0
1
1
1
2
0
2
1
1
1
2
1
1
1
1
0
1
0
1
1
2
1
0
2
0
1
2
2
1
1
1
0
0
0
2
1
1
1
1
0
2
1
1
1
1
1
1
1
2
0
1
1
1
1
1
1
0
1
1
0
1
1
0
1
1
2
1
1
1
2
2
1
1
1
2
1
1
1
1
1
0
1
1
1
0
0
0
0
1
1
1
0
2
1
1
1
1
2
0
0
0
1
1
0
1
0
1
1
1
1
0
1
1
2
1
1
1
1
1
2
0
1
1
2
1
0
1
1
0
1
1
1
1
0
0
1
0
1
1
1
2
1
1
1
2
0
1
1
1
2
1
0
1
2
1
0
1
0
0
1
3
2
3
1
1
0
1
1
1
1
3
1
1
1
1
1
1
0
0
0
1
0
2
2
1
1
1
0
0
1
2
1
0
0
1
0
0
1
1
1
0
2
1
0
2
1
2
1
1
1
1
2
1
2
1
1
0
2
2
0
1
2
0
1
2
2
0
1
2
1
1
1
1
1
1
2
1
1
2
2
2
1
1
0
0
1
2
1
1
2
1
1
1
0
0
1
0
1
0
1
1
2
0
3
1
2
1
1
3
1
0
1
0
0
0
1
1
2
1
1
1
0
1
1
1
1
1
2
1
2
2
1
1
1
1
1
2
0
1
2
2
0
1
1
1
1
1
1
1
0
1
0
2
0
3
1
1
1
1
1
1
2
1
1
0
0
1
1
1
0
2
1
1
1
1
1
2
1
1
2
1
0
1
1
2
1
1
0
1
1
0
1
1
1
1
1
1
0
1
1
2
1
1
2
0
0
1
1
0
2
1
1
1
1
1
1
2
1
0
0
0
0
1
1
1
1
1
2
1
2
2
1
1
0
0
1
0
1
1
0
1
1
0
2
0
2
0
0
0
0
0
1
1
2
3
0
1
1
1
2
1
2
1
4
1
0
0
1
2
1
1
1
1
2
1
1
2
1
0
1
0
2
1
1
1
2
0
0
2
2
1
1
1
0
1
1
1
2
0
1
0
1
1
1
2
0
1
1
1
2
1
0
1
1
1
0
0
1
1
2
1
1
1
2
0
1
0
1
1
0
0
2
1
1
0
2
1
1
1
2
1
1
0
0
1
1
1
1
1
1
2
1
0
0
0
0
0
2
1
0
1
1
3
1
1
4
1
2
0
2
2
0
1
0
1
1
1
1
0
1
0
0
2
0
1
2
2
0
1
1
1
3
0
1
2
1
1
1
1
1
1
1
1
1
0
0
1
1
1
0
1
0
1
1
1
0
2
0
0
1
0
0
1
0
1
0
1
0
0
0
1
1
0
1
1
2
2
2
1
2
1
0
1
0
1
1
1
1
1
1
0
0
1
1
2
1
0
1
1
1
1
1
1
0
0
1
1
1
2
0
1
0
1
2
0
1
1
2
2
1
2
1
0
2
1
1
1
1
2
2
1
1
1
1
1
0
1
0
0
1
2
1
0
2
0
1
1
1
1
1
0
1
1
0
0
1
1
1
1
1
1
0
2
0
1
1
1
1
2
1
1
2
0
1
0
1
2
0
1
0
0
0
1
1
2
2
1
0
2
2
2
2
1
1
1
0
1
0
0
2
2
1
1
1
0
1
2
1
0
2
0
1
0
2
0
1
0
2
1
1
1
1
0
0
0
1
1
1
2
0
1
2
1
1
1
0
1
0
0
0
1
2
2
1
2
2
0
1
1
2
1
0
1
2
1
1
0
2
1
0
1
1
1
1
2
1
0
1
2
0
1
2
2
1
1
1
1
1
2
1
2
1
0
1
1
1
1
0
1
0
0
0
1
1
1
2
0
1
0
1
2
0
0
1
1
1
1
0
1
1
0
2
1
1
2
2
2
0
0
0
1
1
1
1
0
0
0
1
0
1
1
1
3
2
2
0
0
0
1
0
1
0
0
1
2
0
1
0
1
1
1
2
1
0
2
1
1
1
0
1
2
2
1
0
2
2
1
1
0
2
1
0
1
1
0
1
2
1
0
1
2
2
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
0
2
2
1
1
0
1
1
0
1
1
1
2
1
1
2
1
0
1
1
0
1
0
1
0
1
1
0
2
1
1
0
1
1
1
2
1
1
1
2
1
0
3
2
1
1
0
1
0
1
2
1
1
1
1
0
2
1
1
1
1
0
1
1
3
1
2
2
0
3
1
0
1
0
0
0
1
0
0
1
2
1
1
0
1
1
1
0
0
1
0
0
4
2
2
1
2
0
2
1
1
0
1
0
0
2
2
0
1
2
1
1
1
1
1
1
1
0
2
0
1
2
3
1
1
0
0
1
0
1
1
1
2
1
0
1
2
2
1
1
1
3
1
0
0
2
1
2
1
1
1
1
1
0
1
1
1
1
1
0
1
1
2
1
1
1
1
2
0
2
1
0
0
0
2
1
0
0
0
1
1
1
1
0
0
2
0
0
0
1
1
2
2
2
0
1
2
1
1
0
1
0
2
1
2
1
1
2
1
2
0
1
0
1
1
1
0
0
2
0
1
1
1
2
2
1
1
1
1
2
0
1
0
1
1
1
0
1
1
1
2
0
1
2
1
0
2
1
1
0
2
0
1
1
1
0
3
0
1
0
2
1
1
0
0
0
2
1
1
0
1
1
1
1
1
0
0
1
2
1
0
2
0
1
2
2
2
2
2
1
1
1
0
1
1
1
2
1
1
1
2
0
1
1
1
1
1
2
1
2
1
2
1
1
1
1
0
1
1
1
4
1
0
1
2
0
1
1
2
1
0
1
1
0
2
1
1
1
1
0
1
2
1
0
1
1
1
1
1
1
2
2
1
2
2
1
0
1
0
1
0
0
1
2
0
1
2
0
0
2
2
1
0
1
1
2
2
2
2
1
1
0
1
1
1
2
1
2
1
1
1
1
1
1
0
1
0
1
1
0
0
0
1
1
1
0
2
0
2
1
2
2
2
1
0
1
0
2
2
0
1
1
2
1
1
2
1
1
1
1
2
4
2
0
1
1
1
2
0
2
1
1
0
1
1
1
1
1
0
1
1
0
1
1
1
1
2
0
1
1
0
0
0
2
1
2
1
1
1
1
1
1
1
1
1
2
0
1
2
1
1
0
1
1
1
1
0
2
2
0
0
0
1
1
1
0
0
2
2
1
1
0
0
0
2
0
1
1
1
0
1
1
2
2
1
0
2
0
1
0
2
0
1
2
1
1
1
1
1
0
3
1
0
2
0
1
0
1
1
1
2
1
2
1
1
1
1
0
1
2
2
0
1
0
1
1
2
1
1
1
2
0
1
2
0
1
0
2
2
0
1
2
0
1
1
1
0
1
1
1
1
1
0
1
2
1
2
0
1
2
0
0
0
2
1
1
1
1
2
1
1
0
1
2
1
0
0
2
2
2
0
1
0
1
2
1
1
1
1
2
1
1
0
0
2
1
1
1
2
1
1
1
1
1
2
1
0
1
0
1
2
2
0
2
1
1
0
1
0
1
1
1
0
1
0
1
1
1
0
0
1
0
0
1
1
0
1
1
0
1
1
1
2
2
0
2
0
0
1
1
1
2
0
1
2
0
2
2
0
1
2
1
0
0
2
2
1
1
1
0
1
1
1
1
0
1
0
1
1
1
2
2
1
0
2
2
1
1
2
1
2
1
2
1
0
0
1
0
2
2
1
1
1
2
1
1
1
1
1
0
2
0
1
1
1
0
1
1
1
1
0
1
2
1
1
0
2
0
0
0
1
1
0
0
1
2
1
2
2
1
0
1
2
1
1
1
2
0
1
1
0
0
1
1
1
1
2
1
0
1
2
0
2
1
0
0
0
0
1
1
1
1
1
2
1
1
1
0
1
1
2
1
1
2
1
2
1
4
2
1
2
1
1
2
0
1
1
1
0
0
1
0
1
0
1
1
2
0
2
0
0
2
1
2
1
1
1
1
0
1
2
0
0
1
1
1
0
0
1
0
1
0
1
2
1
1
0
0
1
0
1
1
2
1
0
1
1
0
1
0
1
1
0
2
0
2
2
2
2
1
2
0
0
1
0
0
1
1
1
1
0
1
1
1
1
2
1
0
2
1
2
0
1
1
2
2
1
2
2
2
1
1
1
2
3
1
1
2
1
2
0
2
1
1
1
1
0
1
1
2
2
1
1
1
0
1
1
0
1
1
0
1
1
0
0
1
1
1
0
1
0
1
1
1
1
1
1
2
1
1
1
1
1
1
2
0
1
1
1
1
0
0
0
0
2
1
1
2
2
1
0
1
1
1
1
1
2
1
0
1
1
1
2
0
2
1
2
1
1
2
1
1
1
2
2
1
1
2
2
0
1
1
2
0
0
2
1
3
0
1
0
0
1
1
0
0
1
1
1
1
0
2
2
1
1
1
1
2
0
1
1
0
2
2
1
1
0
2
1
2
1
1
1
1
1
0
1
1
0
1
3
0
0
1
2
1
1
2
1
1
1
0
1
1
1
1
1
2
0
1
0
2
1
1
2
2
1
0
2
0
2
0
1
1
1
1
0
1
2
1
1
1
1
2
1
1
1
1
1
0
2
1
2
1
0
1
1
1
1
1
2
1
1
1
0
2
1
1
0
2
1
1
1
0
1
0
1
0
0
1
2
1
0
1
2
2
1
0
2
0
0
1
0
2
2
0
1
1
4
1
1
1
1
2
1
2
0
1
2
1
1
1
0
1
1
1
1
2
2
0
2
2
1
0
1
0
0
2
0
1
5
1
1
0
1
2
3
2
1
0
2
1
1
1
2
1
1
2
1
1
1
1
2
1
1
1
1
1
0
0
0
0
1
2
2
0
0
2
2
1
0
1
1
0
1
0
1
1
1
1
0
1
1
1
1
1
0
1
1
1
1
1
2
1
1
1
1
1
1
2
0
1
1
2
0
0
1
1
2
1
2
2
1
1
2
1
1
1
1
2
0
1
1
1
1
1
0
2
0
0
0
2
2
0
1
0
3
0
1
1
1
0
0
1
0
0
1
0
1
1
1
1
1
0
0
1
1
0
1
1
0
0
1
1
2
1
1
2
1
1
1
1
0
2
0
1
1
1
1
1
2
1
0
1
1
1
2
1
2
0
1
0
1
1
2
1
1
2
1
2
0
1
1
1
0
1
1
2
1
1
1
0
1
1
1
0
2
0
1
1
2
1
2
2
1
1
1
1
2
0
2
1
1
1
1
2
1
1
1
0
1
0
2
0
1
1
1
1
0
2
1
1
1
0
2
0
1
0
1
1
0
0
2
2
0
1
1
0
1
0
2
1
1
1
0
2
2
1
1
1
1
2
1
2
1
1
1
1
1
2
2
1
0
2
1
1
1
0
0
2
1
1
1
0
0
2
0
1
1
0
1
0
1
0
1
1
1
0
1
0
1
1
1
2
2
0
0
1
0
2
1
2
1
0
1
1
2
1
0
1
0
3
2
1
0
1
0
1
1
2
0
1
0
0
2
1
1
2
1
0
1
1
1
1
1
1
2
1
1
0
1
1
0
2
1
2
2
0
2
0
1
1
1
2
1
0
1
0
2
0
1
0
3
2
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
0
2
1
1
1
2
1
1
2
1
1
1
1
2
1
1
0
1
1
1
1
2
1
2
0
2
1
0
0
2
1
1
1
0
1
0
0
0
2
1
0
1
1
0
2
2
1
1
2
1
1
2
0
0
0
2
0
1
1
0
1
0
1
0
1
1
1
2
1
0
0
2
1
0
0
0
1
1
1
2
1
2
1
1
0
2
0
1
2
0
2
2
1
1
1
1
1
1
2
0
3
0
0
1
2
0
2
1
0
1
0
1
2
1
2
1
0
2
0
2
1
1
0
2
1
0
1
1
1
1
0
1
1
0
1
2
1
1
2
1
0
1
0
2
1
2
2
1
4
0
1
1
2
0
1
1
0
1
1
1
1
1
1
1
2
1
1
0
2
0
1
1
1
0
0
1
1
1
0
0
1
1
1
1
1
0
0
1
0
2
2
2
1
1
1
0
1
1
1
2
0
1
1
1
1
1
0
1
1
2
0
0
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
0
2
1
1
1
1
1
0
0
0
0
1
1
1
2
1
1
1
0
1
1
2
1
1
2
1
1
1
0
1
1
1
1
0
1
1
1
0
2
0
1
1
2
0
1
1
0
1
2
1
2
0
1
1
1
1
1
1
2
1
2
2
2
1
2
1
1
0
1
1
2
0
0
1
1
1
1
2
1
1
1
0
1
2
2
0
1
1
1
1
1
1
1
0
1
0
1
1
1
1
2
1
2
2
1
1
0
1
2
1
1
0
0
2
1
2
1
2
0
1
1
1
1
1
1
1
2
2
4
0
2
3
1
1
1
2
1
1
1
1
0
2
0
0
0
1
1
2
0
2
1
0
2
2
1
0
0
1
0
2
1
1
1
1
0
1
1
1
1
1
2
0
1
0
0
1
1
2
1
1
1
0
0
1
0
1
1
1
2
2
0
0
2
1
1
2
1
1
1
0
2
1
1
0
2
1
1
0
1
0
1
0
0
0
2
0
1
0
0
1
1
1
1
1
2
2
1
1
1
0
1
1
1
1
1
1
0
2
2
0
2
1
1
1
0
1
0
2
2
1
2
0
0
2
1
1
0
2
1
0
1
1
0
0
1
2
1
1
1
0
1
2
1
0
1
1
1
1
1
0
0
1
0
1
1
1
1
2
2
1
1
2
1
1
1
0
2
1
1
1
1
2
1
0
0
2
0
1
1
2
2
1
1
1
1
2
1
0
1
1
1
2
1
2
1
1
1
1
0
1
1
1
1
2
0
1
0
1
1
2
0
2
1
1
1
2
2
1
1
1
1
2
2
0
1
1
2
1
1
1
0
0
1
1
1
1
2
1
1
1
0
1
1
0
1
0
1
1
1
1
2
1
1
1
0
1
1
1
1
2
1
1
0
1
2
0
1
2
1
1
0
2
1
1
0
1
0
1
1
1
0
1
0
1
1
2
2
2
2
2
0
2
0
1
1
1
1
1
0
1
0
0
1
1
1
1
0
1
2
0
1
2
1
1
1
1
2
2
2
1
1
0
1
1
2
3
1
1
1
1
0
2
2
1
1
1
3
1
1
0
2
1
1
1
1
2
1
0
1
1
1
1
0
1
1
2
2
0
2
1
1
0
1
1
2
1
1
1
0
1
1
2
2
1
2
1
2
2
1
0
1
1
1
0
1
1
2
1
0
1
2
1
1
1
1
1
1
0
1
1
2
1
1
2
1
0
1
1
2
1
1
1
1
1
1
0
2
0
1
2
0
0
0
2
1
0
1
0
2
2
1
3
1
2
1
0
1
2
1
0
0
1
1
1
1
2
1
2
1
1
1
1
2
1
2
1
1
1
0
1
1
1
1
0
0
2
1
1
1
1
0
1
1
1
0
3
1
1
1
1
2
1
2
0
2
3
1
1
0
2
2
2
0
0
1
0
1
1
1
2
1
0
2
0
0
1
1
1
2
2
0
1
1
1
1
1
0
0
2
1
0
0
0
0
1
2
1
1
0
1
0
1
1
1
1
1
1
2
0
0
0
0
1
1
0
0
0
1
1
1
2
1
2
1
0
1
1
2
3
0
1
0
0
0
2
1
2
0
1
2
1
1
3
1
2
1
0
1
1
0
2
2
1
1
1
1
1
1
1
3
2
0
0
2
1
2
1
0
2
1
0
1
0
1
1
1
1
1
1
1
1
2
0
1
2
2
0
1
1
1
1
1
2
2
0
1
1
1
1
1
0
2
2
2
2
1
1
0
2
0
1
2
2
1
1
1
0
1
0
1
0
0
2
1
2
1
1
1
2
2
0
0
0
1
0
2
1
1
1
0
1
1
1
1
0
0
1
1
1
0
4
2
2
2
2
2
2
1
0
2
0
1
2
0
1
1
2
2
0
1
1
0
1
1
0
0
1
1
2
1
3
1
1
2
1
0
1
2
2
1
1
1
1
0
1
2
0
1
1
1
0
1
1
2
1
2
2
2
0
2
1
1
1
0
1
1
2
2
1
2
1
1
2
1
1
1
1
1
2
1
2
1
1
0
1
1
2
0
1
1
2
0
1
2
0
0
1
1
0
1
1
0
1
1
0
1
1
1
0
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
0
0
1
2
0
1
0
1
2
1
2
2
1
1
1
4
1
1
1
1
0
0
1
2
2
1
0
1
1
0
2
2
1
1
0
2
1
0
1
1
1
1
1
1
0
0
1
0
0
1
3
1
1
1
2
1
1
0
1
1
1
1
0
1
1
2
2
2
1
0
2
0
0
1
1
1
1
1
0
1
1
1
1
1
0
1
1
1
0
1
2
1
0
1
2
1
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
2
2
2
0
1
1
1
1
0
2
1
1
1
0
1
1
1
1
1
1
1
2
3
2
2
2
1
1
1
1
0
2
1
0
0
1
2
1
2
1
2
2
1
2
1
1
1
1
1
2
0
1
1
2
0
0
1
2
0
1
0
1
2
2
1
1
1
2
1
0
1
0
0
1
1
0
1
0
1
1
1
1
2
1
2
1
1
2
2
1
0
1
1
0
2
1
1
2
1
1
2
0
0
1
2
1
0
1
0
2
1
1
0
1
0
1
0
0
2
1
0
1
1
2
1
0
1
0
0
2
2
1
1
2
0
0
0
1
0
1
1
1
1
1
0
0
0
1
1
2
0
1
1
3
1
3
2
0
1
2
1
2
1
0
1
0
1
1
1
1
1
1
1
1
0
0
0
1
1
1
1
1
2
2
1
2
2
0
1
2
0
1
1
2
1
1
1
2
1
0
1
1
1
1
1
1
1
1
1
0
1
2
1
0
0
0
0
1
2
2
1
1
3
1
1
0
1
1
1
1
0
2
0
2
1
0
2
1
1
2
0
1
1
0
1
1
1
1
3
1
1
2
1
0
0
1
1
1
2
1
0
0
1
1
1
1
2
2
1
2
1
1
1
1
1
0
2
2
2
2
2
1
2
0
1
0
2
1
2
1
2
1
1
1
0
2
0
1
1
0
0
1
1
1
1
1
2
0
0
0
1
1
1
2
0
1
1
1
0
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
0
0
1
0
1
1
1
0
1
1
0
0
2
1
1
1
0
1
1
1
1
2
1
0
1
1
1
2
1
1
0
2
2
1
0
1
0
0
2
4
1
2
0
0
0
0
0
1
2
1
1
1
1
1
2
1
1
1
4
2
2
1
1
2
1
0
1
1
2
1
1
1
2
1
2
2
0
1
1
1
0
1
1
0
1
2
2
1
1
1
0
2
1
1
1
1
0
1
1
1
1
0
1
1
1
1
1
1
0
2
1
1
1
0
1
1
2
2
1
1
2
3
2
2
1
2
1
2
1
1
2
1
2
2
1
1
1
0
0
1
2
0
1
0
1
1
1
0
2
2
2
1
2
0
1
1
1
1
0
0
1
1
1
0
1
2
2
0
1
1
2
2
0
1
1
1
2
0
2
2
1
1
1
1
1
1
1
1
1
0
0
1
1
1
1
1
1
2
1
0
1
2
2
1
2
1
1
1
1
1
1
0
2
0
0
0
0
2
0
1
2
1
2
0
1
1
0
0
0
1
1
1
1
1
2
0
1
0
1
0
1
0
1
1
1
1
1
2
2
0
1
1
2
1
1
1
0
0
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
0
1
2
3
2
1
0
1
1
0
0
0
0
0
1
0
1
1
1
0
1
0
1
1
1
1
1
1
1
0
0
1
2
0
2
1
1
1
0
1
0
2
0
0
2
1
0
1
2
2
0
0
2
1
1
2
1
2
2
1
2
1
0
2
2
1
2
2
1
0
1
1
0
2
1
2
2
1
2
0
1
1
1
0
1
2
0
1
1
1
1
1
1
1
2
1
2
0
0
1
1
2
0
1
1
0
1
2
1
2
1
0
1
2
1
1
2
0
1
1
1
1
1
1
1
1
0
1
2
1
2
1
1
1
0
1
2
1
2
0
0
2
2
1
1
2
1
1
1
1
0
0
1
1
0
2
2
1
2
1
1
1
1
1
1
2
2
1
0
1
0
1
0
1
1
2
1
0
1
2
1
1
0
1
0
0
1
1
1
0
1
0
1
0
1
1
2
0
1
2
1
2
2
1
1
1
1
1
0
1
1
0
0
1
1
0
1
0
1
2
1
0
1
0
0
1
1
0
0
2
1
1
1
0
0
1
2
1
1
0
1
1
2
0
1
1
2
2
0
1
0
1
0
1
1
2
2
1
0
1
1
1
1
1
0
0
1
1
2
1
1
1
2
2
0
1
0
2
0
0
0
0
0
1
1
1
1
1
2
2
1
2
1
2
1
0
1
2
1
0
1
1
1
1
2
1
1
0
2
2
2
2
2
0
1
2
1
1
1
2
1
1
1
0
1
2
0
1
1
2
1
1
1
0
2
1
2
2
0
1
1
1
1
0
1
0
2
0
2
2
2
2
1
1
1
1
0
2
2
2
0
0
1
1
1
1
2
0
1
1
0
1
2
2
2
1
2
2
2
0
2
1
1
0
0
1
0
0
1
0
1
1
2
0
0
1
1
0
2
2
1
1
1
2
1
0
0
1
1
1
1
1
1
2
1
0
2
1
0
1
1
2
2
1
1
0
1
1
2
1
2
1
1
0
0
1
0
1
1
1
1
0
0
2
1
1
1
0
0
1
1
1
0
1
2
0
1
1
1
0
1
2
1
1
0
0
1
1
1
1
1
2
1
1
1
1
2
1
1
0
0
1
2
1
0
1
2
2
0
1
2
1
1
1
1
1
0
2
2
1
1
0
1
1
0
0
1
1
0
1
0
2
2
2
2
0
0
2
2
1
1
1
1
1
0
2
2
1
1
2
2
2
1
1
1
1
2
2
2
0
0
0
1
1
2
1
1
1
1
0
2
0
0
2
1
1
2
0
1
2
1
2
2
0
2
1
1
0
1
2
1
2
0
1
1
0
3
1
1
1
0
2
2
1
1
1
1
1
1
2
2
0
1
1
0
1
0
2
0
1
1
1
0
1
2
1
1
1
0
1
1
1
0
1
2
1
1
1
2
1
1
1
0
1
1
2
0
0
1
1
1
0
1
2
2
2
1
1
2
1
1
0
1
2
0
1
1
1
1
1
0
0
0
1
1
2
1
1
0
0
0
2
1
1
2
2
1
1
0
0
1
2
2
1
2
1
0
1
0
1
1
1
2
2
2
1
0
0
1
1
1
3
1
1
1
0
1
1
1
0
2
2
0
1
1
1
1
0
2
1
0
0
1
0
1
2
2
2
0
2
1
0
0
1
2
1
1
0
1
0
0
2
0
2
0
1
1
1
0
1
0
1
2
1
1
1
0
1
0
1
1
0
1
1
2
1
2
2
1
1
1
1
1
0
1
1
2
2
1
1
1
0
1
1
1
1
0
1
1
2
0
2
1
0
0
0
1
2
1
1
2
0
1
1
1
0
0
2
1
1
2
1
0
1
3
2
2
1
1
1
2
0
2
2
1
1
1
0
0
0
1
1
0
1
1
1
2
2
1
2
0
2
1
1
0
1
0
1
1
1
1
1
1
1
1
3
0
1
1
1
1
2
2
2
0
0
1
1
0
1
1
2
1
2
1
1
1
1
2
1
2
1
1
1
1
1
0
1
2
1
1
2
1
2
0
1
1
1
2
0
1
0
1
1
2
0
1
1
1
1
2
1
1
2
1
1
1
1
2
1
1
2
1
0
1
0
0
1
1
1
1
0
0
1
1
1
2
0
1
2
0
1
1
0
0
0
0
1
1
1
2
0
3
2
1
1
1
0
0
1
1
1
1
1
0
2
1
2
1
1
1
2
0
0
0
2
0
1
0
2
2
1
2
1
1
1
2
2
1
0
0
2
0
2
1
1
2
1
1
0
1
0
0
1
1
1
2
1
1
1
1
1
1
0
0
1
2
1
2
2
1
0
1
1
1
2
2
1
1
1
1
1
0
2
1
1
0
1
1
2
1
1
1
0
2
0
1
1
1
1
1
1
0
0
0
1
2
1
2
1
1
1
1
1
1
0
2
1
2
0
1
1
1
0
2
2
2
1
1
2
1
1
1
1
2
1
2
2
1
1
2
1
1
1
1
2
1
2
2
1
1
0
1
0
1
2
0
0
0
1
2
2
1
1
1
0
1
1
1
0
0
1
1
0
2
2
1
1
1
1
0
0
2
1
2
2
0
0
0
1
1
0
0
0
1
1
2
1
0
2
1
1
1
1
1
0
1
1
0
1
2
0
1
1
1
1
0
0
1
1
2
1
2
1
1
1
2
2
1
0
1
0
1
0
1
0
1
1
0
2
0
1
0
1
2
0
2
0
1
2
0
1
0
0
2
2
0
0
1
1
1
2
4
1
1
0
2
1
0
1
1
1
2
2
1
1
2
2
1
2
0
1
2
1
3
1
1
0
1
0
1
1
0
1
0
0
2
1
2
1
2
1
3
2
1
1
2
1
1
2
2
0
1
2
2
0
1
0
2
0
1
0
2
1
0
3
1
1
1
0
1
2
2
0
0
1
0
1
1
0
1
2
1
1
1
2
1
1
1
1
2
2
2
1
2
0
1
1
2
0
3
0
1
1
1
0
1
1
1
0
2
1
0
1
2
1
2
2
1
0
0
2
1
0
1
0
1
1
1
1
1
0
0
2
1
2
0
1
1
1
1
1
0
1
2
2
0
2
1
0
1
0
1
1
1
2
1
0
1
0
0
1
1
2
2
1
1
1
2
2
1
1
2
1
1
0
2
2
0
0
0
2
0
2
1
1
2
1
1
2
0
2
2
1
1
0
0
1
1
1
1
2
2
1
0
1
2
1
1
1
0
0
1
0
1
1
4
0
1
1
0
1
2
1
0
2
0
1
1
1
1
2
0
1
0
1
0
0
0
1
0
1
1
1
2
1
2
1
0
2
1
2
1
1
1
2
1
1
2
1
1
2
0
0
0
1
1
1
1
1
0
0
1
1
2
2
0
1
1
0
0
1
1
1
1
0
3
0
1
1
1
1
0
2
0
0
0
1
1
1
1
0
1
2
2
0
1
1
1
0
0
1
1
0
1
1
0
1
0
0
1
1
0
2
1
0
1
0
2
2
0
1
0
2
0
2
1
1
1
1
1
2
1
2
1
1
0
0
1
1
1
2
1
1
1
2
1
1
1
1
0
1
0
2
1
2
1
0
1
2
0
1
1
1
0
1
1
2
0
1
0
2
0
1
1
1
0
1
1
1
2
1
1
1
1
1
1
1
1
1
0
1
1
2
1
2
0
0
1
0
0
1
2
0
1
3
1
1
1
1
0
0
1
1
1
0
2
2
1
1
1
0
1
1
0
1
1
1
2
1
0
0
1
0
1
0
2
1
1
1
1
2
1
1
1
1
1
1
1
0
2
0
0
2
0
1
0
1
0
1
1
0
1
1
2
1
2
1
2
0
2
1
0
1
0
0
1
1
1
1
1
2
0
0
1
1
2
1
2
1
1
0
1
2
1
1
1
0
0
1
1
1
1
1
1
2
2
0
1
1
1
2
1
0
2
2
1
2
0
1
1
0
1
2
1
1
1
0
2
1
2
1
0
2
0
1
0
0
2
1
0
1
0
2
0
1
1
1
1
1
0
0
1
2
1
1
1
1
1
1
0
1
1
2
1
2
1
1
1
1
1
2
1
0
0
0
0
1
2
0
1
2
1
1
2
1
1
1
1
0
0
1
1
1
2
2
1
1
1
1
0
1
1
1
1
0
1
1
0
2
0
2
1
2
0
2
1
0
0
2
1
0
1
2
1
0
1
1
1
2
2
0
1
1
2
0
1
1
1
3
1
1
2
2
3
1
2
0
1
1
0
0
1
2
1
1
1
3
0
1
2
1
0
1
0
1
1
0
1
2
1
0
1
2
1
1
2
1
1
2
1
1
2
2
1
1
1
3
2
1
0
2
1
1
2
2
1
1
1
0
1
1
1
1
2
1
1
0
0
0
1
1
1
1
1
1
0
2
1
1
1
2
1
1
1
1
1
2
1
1
1
2
2
1
1
2
1
1
3
1
1
2
1
1
2
1
2
1
0
1
0
1
1
0
2
2
1
1
1
0
0
0
1
0
2
1
2
1
1
2
0
2
1
0
1
2
0
1
1
1
1
1
2
2
0
2
1
0
1
0
1
0
1
1
1
0
0
0
1
1
2
1
2
1
1
1
3
1
1
1
0
1
2
1
0
1
1
1
1
0
2
1
2
1
2
2
1
1
0
1
1
1
1
0
1
0
1
1
1
0
2
0
2
1
1
2
1
2
1
2
2
2
0
1
2
1
2
0
1
2
1
1
0
2
1
2
1
2
2
2
1
0
1
1
2
1
1
1
3
1
1
2
2
2
0
2
1
2
0
1
1
1
2
0
0
1
2
1
1
1
0
1
2
2
1
1
2
1
1
0
1
0
1
0
1
2
2
1
2
1
1
1
2
1
0
2
0
1
0
1
1
2
0
1
1
2
0
1
0
1
0
2
2
2
0
0
2
1
0
0
0
3
1
1
0
1
2
1
1
1
2
1
0
0
0
0
2
2
1
1
2
1
0
1
1
1
2
1
2
3
1
0
1
0
1
1
0
1
2
1
0
2
1
1
1
2
2
0
2
0
1
1
0
1
2
1
1
1
1
0
2
1
0
0
0
1
1
2
1
1
1
1
0
0
2
0
0
1
1
1
1
1
1
1
1
2
1
0
2
1
0
2
2
1
0
0
1
0
1
0
1
1
2
2
3
2
0
2
0
1
0
0
1
1
2
2
2
2
3
0
2
1
1
1
2
0
1
2
1
1
2
1
1
1
0
1
1
0
3
1
1
0
0
0
1
2
1
0
0
1
1
1
1
2
2
0
2
1
1
0
1
0
1
2
1
1
1
1
2
1
1
1
1
1
2
1
1
2
0
0
1
1
1
1
1
2
2
0
2
0
0
1
1
0
2
0
1
1
1
1
1
2
1
1
2
1
0
1
1
1
1
2
1
1
2
1
1
2
2
1
0
2
1
1
2
0
2
1
1
0
0
1
1
0
2
0
1
1
2
1
1
0
0
2
1
2
0
1
1
1
1
1
1
1
1
1
1
1
1
0
1
2
2
0
2
0
2
0
1
1
1
1
0
1
1
1
2
0
2
1
1
1
0
2
1
1
2
1
2
2
1
1
2
1
2
1
2
3
1
1
1
1
2
0
1
0
1
1
1
1
2
2
1
2
1
1
0
2
1
1
2
2
2
2
1
1
1
1
1
0
1
0
0
0
1
0
2
1
1
0
1
1
0
0
3
1
1
0
1
2
2
0
2
0
2
2
1
0
2
2
0
0
1
0
0
2
1
1
1
0
1
1
1
0
0
1
1
2
1
1
0
1
1
0
0
2
1
1
1
2
1
1
1
0
2
0
1
2
1
0
1
0
2
1
1
1
1
1
0
1
2
1
2
1
1
1
1
1
1
0
1
2
0
1
0
1
0
2
1
1
1
0
1
2
2
1
0
1
1
1
1
2
2
0
1
2
1
0
2
1
0
2
1
1
1
0
2
1
1
1
0
1
1
1
2
1
2
0
1
0
1
1
2
0
1
0
2
1
1
1
1
0
2
1
0
1
0
0
1
2
0
1
1
1
2
1
1
1
1
1
1
0
1
2
1
1
1
1
2
0
1
2
1
2
1
1
0
1
2
2
2
0
1
1
0
1
3
1
1
1
1
1
2
1
1
0
1
1
1
1
1
2
1
2
2
1
0
1
1
1
1
1
3
0
1
1
1
1
2
1
2
2
1
2
1
2
1
0
0
1
2
1
0
1
1
1
1
2
1
2
2
0
0
1
1
2
1
2
1
0
1
2
1
0
1
1
1
1
2
1
2
3
1
2
1
1
0
0
2
1
2
1
0
1
0
2
1
0
1
0
1
2
2
2
1
1
1
1
0
1
2
2
2
1
2
1
2
2
0
1
1
1
1
1
0
1
0
1
0
1
2
1
1
1
1
1
1
1
1
1
1
2
2
0
1
0
2
1
2
1
1
2
0
2
1
1
1
1
2
2
0
0
0
1
0
1
1
2
1
0
1
2
2
1
1
1
1
1
2
2
1
1
1
1
1
1
2
0
1
0
0
1
1
1
2
1
0
1
1
2
2
1
6
1
1
1
1
1
1
0
2
0
1
0
2
0
1
1
2
2
2
1
1
1
1
2
0
2
2
3
1
2
1
0
1
2
1
1
1
2
2
0
2
1
2
1
1
1
2
2
1
1
0
1
2
1
1
1
8
1
2
1
0
1
1
1
2
1
1
1
2
2
1
1
1
1
1
2
1
1
0
1
2
1
2
0
1
1
1
1
1
2
2
1
1
1
1
1
1
0
0
1
1
1
1
1
0
0
1
0
1
1
0
1
0
0
2
0
1
1
2
1
3
1
1
0
1
2
1
0
1
2
1
1
0
1
1
2
2
2
1
1
2
1
2
2
1
2
1
1
0
0
0
0
0
1
1
1
0
1
1
1
0
2
0
1
1
1
2
2
2
2
0
2
1
1
1
1
1
1
1
2
0
2
0
0
0
0
1
0
2
1
0
1
1
0
1
1
0
1
0
0
2
1
1
2
0
1
0
1
1
1
1
2
0
2
0
0
0
0
1
1
1
0
1
1
1
2
1
1
1
0
1
1
1
1
2
1
1
1
1
2
1
2
1
1
0
1
1
1
2
1
0
0
1
0
1
0
1
2
2
2
0
0
1
0
1
0
1
1
1
0
1
1
1
2
1
1
1
1
2
2
2
0
2
1
2
0
1
1
2
1
0
1
1
2
1
0
3
2
0
1
0
1
1
1
1
1
2
0
1
1
1
1
1
1
1
1
2
1
1
0
0
1
1
1
1
1
1
1
1
0
2
0
1
1
1
2
1
0
2
1
1
1
1
1
1
0
2
1
1
2
2
2
2
1
1
2
1
1
2
3
1
0
0
1
0
0
0
1
1
1
0
1
1
1
0
0
2
1
1
0
0
2
0
0
2
2
0
1
1
1
1
1
1
2
2
1
1
1
2
2
2
1
1
1
0
2
2
1
0
1
1
1
1
1
0
2
1
0
0
1
1
1
1
2
0
1
1
0
1
2
0
0
1
1
2
1
0
2
1
1
1
1
0
1
1
1
1
1
2
0
2
0
2
1
0
2
1
0
2
2
2
2
1
1
1
1
0
1
2
1
1
1
1
1
2
0
1
1
1
1
1
1
1
0
2
2
1
1
1
1
2
0
1
1
0
1
0
1
1
1
2
1
1
1
2
1
1
2
1
1
1
1
0
1
1
2
1
1
0
1
0
2
2
2
3
2
0
0
1
1
1
2
2
1
0
1
2
1
1
1
2
2
0
2
1
1
0
1
0
1
0
1
1
2
1
2
0
1
0
2
1
0
1
1
0
0
2
1
2
0
1
0
1
2
0
1
1
1
1
1
2
0
2
1
1
1
1
0
2
1
1
1
1
1
1
1
0
0
2
1
3
1
2
2
0
0
1
1
2
2
0
0
1
1
1
1
2
0
0
1
2
1
1
2
2
2
2
1
1
0
0
2
2
2
1
1
1
0
1
1
2
0
0
0
2
2
1
0
2
0
1
0
1
0
0
1
1
1
2
1
1
1
1
1
1
1
2
0
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
0
1
0
1
1
1
1
2
0
0
0
1
1
3
1
1
1
1
0
2
1
1
1
1
1
1
0
0
1
1
0
1
1
2
0
0
2
1
2
0
0
0
1
1
1
1
1
1
2
1
1
1
1
0
1
1
3
0
2
1
1
1
1
1
1
1
2
1
1
0
2
1
1
1
2
1
1
1
1
2
1
2
0
0
0
0
1
0
1
1
1
1
2
2
1
2
2
1
1
2
0
2
0
0
1
0
2
1
1
0
1
1
1
1
0
3
1
1
0
1
1
1
3
2
1
2
2
1
1
2
0
2
2
0
1
1
1
1
2
1
1
2
1
2
1
1
1
0
1
1
1
1
1
0
0
1
2
1
2
0
1
3
2
0
0
1
2
2
2
1
2
1
1
1
0
2
2
1
1
1
1
1
2
2
1
0
2
0
0
1
1
1
0
1
1
1
1
2
1
0
1
2
0
1
1
0
1
2
1
4
1
2
0
2
1
1
0
1
1
1
1
0
2
1
1
1
1
1
1
2
3
1
1
2
1
0
1
1
1
2
0
0
1
1
2
1
2
2
1
1
1
0
0
2
1
0
0
2
2
1
1
1
2
2
1
2
1
0
2
2
1
1
1
2
0
1
2
1
1
0
0
1
1
2
0
1
1
1
0
1
0
0
2
1
2
0
0
0
1
1
0
1
2
1
2
0
1
1
1
1
1
1
0
0
1
1
2
1
0
1
1
1
0
0
2
1
0
0
2
2
0
1
1
4
1
2
2
0
0
0
0
2
2
2
1
0
1
1
0
1
0
1
1
1
1
2
1
2
1
1
0
1
2
2
2
0
1
1
1
0
1
2
2
1
1
1
2
1
1
0
4
0
2
2
1
1
0
1
1
2
2
1
2
0
1
1
1
2
1
1
0
1
0
0
0
1
1
0
2
2
2
1
2
0
2
1
1
1
2
1
1
2
0
1
2
1
1
0
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
2
1
0
1
2
1
2
1
1
2
1
1
1
0
0
1
0
1
0
1
1
2
3
0
1
2
1
1
2
2
0
1
1
1
1
1
0
1
0
1
2
1
1
2
1
1
1
0
1
2
1
0
0
2
1
0
0
1
0
1
1
1
1
0
1
2
0
1
4
2
1
0
1
2
2
2
1
1
1
2
1
0
1
0
1
0
1
1
2
1
2
2
2
2
1
1
0
2
2
2
1
0
1
1
1
1
1
2
2
1
2
0
1
2
1
1
1
0
2
1
0
0
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
2
1
2
1
2
1
1
2
0
2
1
1
2
2
2
1
2
2
1
1
1
0
2
0
0
2
2
1
1
1
0
1
1
0
1
0
1
1
1
0
1
1
2
1
1
2
0
1
0
2
0
0
1
0
1
1
0
2
2
1
1
1
2
1
1
0
0
1
0
0
0
0
2
1
1
1
0
2
1
1
2
1
1
1
0
1
0
1
2
1
1
2
1
0
1
2
1
1
1
0
2
0
2
1
1
2
1
1
2
1
1
1
2
0
0
1
1
1
1
1
0
1
1
1
1
1
1
0
0
1
1
0
1
1
1
1
1
2
2
1
0
1
1
1
1
1
1
1
1
1
1
1
0
2
2
1
0
2
1
1
2
2
1
1
1
0
2
1
1
1
2
2
2
1
1
2
1
1
1
1
1
1
1
0
0
1
0
1
1
2
2
1
2
2
1
2
1
0
0
2
1
1
1
0
1
0
0
1
0
2
1
1
2
2
0
0
1
0
1
1
2
1
0
1
1
0
0
1
1
2
2
2
1
1
1
2
2
1
1
1
1
0
0
1
1
1
1
0
1
2
1
1
0
1
1
2
2
1
2
2
1
1
1
0
1
1
0
0
1
1
0
1
1
0
2
1
0
1
1
2
1
0
2
0
2
1
1
0
1
0
0
0
1
2
1
1
2
0
1
1
1
2
2
1
1
0
1
1
1
1
2
2
1
0
1
4
0
2
1
0
1
2
1
0
1
1
0
1
1
0
1
2
1
0
1
0
1
2
1
1
1
2
1
2
1
1
1
0
1
1
2
2
2
2
1
2
1
0
1
1
0
1
2
1
1
2
2
1
1
2
1
2
1
2
1
2
1
1
2
1
0
1
1
1
2
1
2
2
0
1
1
1
1
1
1
1
0
0
0
1
1
1
2
2
1
1
0
0
2
2
2
1
2
1
0
0
1
7
0
1
1
1
1
1
2
1
0
1
0
1
0
2
1
0
0
2
1
0
1
1
1
0
2
2
1
0
2
1
2
1
2
2
0
1
2
1
0
0
0
1
0
0
1
2
1
1
1
1
2
0
1
0
1
1
1
1
1
2
1
2
2
2
0
3
2
1
1
2
1
1
1
2
1
0
0
1
1
0
0
8
1
2
1
0
1
2
1
2
2
1
1
1
1
2
0
0
1
0
1
1
2
2
1
1
0
1
1
0
1
1
1
2
1
0
0
2
0
0
1
2
1
1
1
1
1
1
2
0
2
1
2
1
1
0
2
0
1
1
0
1
1
1
1
1
2
1
0
2
1
1
1
1
2
1
1
2
1
1
1
0
1
1
1
1
0
2
1
1
1
0
1
2
1
1
1
1
1
1
0
1
1
2
2
0
0
1
2
2
1
0
1
0
1
0
1
2
2
2
1
1
1
1
2
0
1
1
1
1
1
1
1
1
1
1
1
0
2
1
1
2
2
1
0
3
1
2
2
1
2
2
1
0
1
0
1
2
1
2
2
1
2
1
1
0
1
1
0
1
1
1
2
2
1
0
2
1
2
0
2
2
1
1
2
1
2
1
1
2
0
0
0
0
1
2
1
2
1
1
0
1
1
1
1
0
0
1
2
1
2
1
0
1
0
1
1
1
1
2
1
2
2
1
1
0
0
2
1
0
0
1
1
1
0
2
0
1
1
1
0
0
2
2
1
1
1
1
0
0
1
1
0
2
0
0
2
1
2
2
1
1
0
0
1
2
1
0
1
1
0
2
1
2
0
2
1
1
2
0
0
1
2
1
1
1
2
2
2
0
2
0
2
1
1
1
1
1
1
2
1
1
1
1
1
2
2
1
2
2
0
0
1
1
2
1
1
1
1
0
1
1
2
2
2
1
0
1
1
0
0
2
1
0
1
0
1
1
1
1
0
1
1
1
0
0
0
2
1
2
0
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
2
0
1
0
2
0
1
1
1
1
1
1
2
2
0
0
1
2
1
0
0
1
2
1
1
1
1
1
2
1
1
1
1
2
7
1
1
2
2
1
1
2
1
1
1
1
1
2
0
0
1
0
1
1
3
1
1
1
0
1
0
0
1
1
1
0
1
1
0
0
0
1
1
0
0
2
0
1
1
5
1
0
2
1
0
0
1
1
0
1
0
1
1
1
2
2
1
1
0
0
0
2
1
2
1
0
2
0
1
0
5
1
0
3
0
1
1
2
1
2
0
0
1
0
1
1
0
2
2
2
1
1
2
1
1
0
1
1
1
2
2
0
1
2
0
1
3
1
1
1
1
1
1
1
1
1
1
2
1
0
1
1
2
0
0
0
2
1
0
1
1
1
0
1
1
1
1
0
1
3
0
1
1
1
0
0
1
0
1
1
0
2
2
1
1
6
1
0
2
1
1
0
1
1
1
2
1
2
2
0
1
1
1
1
1
1
1
1
1
0
1
2
0
1
1
2
1
0
1
0
1
1
0
0
1
0
2
2
1
1
1
2
1
0
2
1
0
1
1
0
1
2
1
3
1
2
0
2
0
2
0
1
1
2
0
0
1
1
1
1
1
1
1
3
1
1
1
2
1
1
1
1
1
1
1
1
0
0
1
2
0
1
1
1
1
1
2
2
1
1
2
0
2
1
0
1
1
1
2
1
1
2
0
0
0
1
1
1
0
0
0
1
2
1
2
1
1
1
2
0
2
0
1
1
1
1
1
0
0
1
1
1
1
1
1
1
2
0
2
1
0
1
1
1
2
0
1
1
2
2
0
0
1
1
2
0
1
2
1
1
1
2
2
2
1
1
2
2
1
1
1
2
2
0
2
0
1
1
1
1
0
1
1
0
1
2
1
2
1
2
1
1
1
1
0
1
1
2
2
0
2
1
1
1
1
1
2
1
0
1
1
0
2
1
0
1
2
0
1
1
0
1
1
1
1
2
0
2
2
1
1
1
1
2
1
1
1
2
1
0
0
1
1
1
0
1
1
2
1
2
0
1
1
0
0
1
2
0
2
1
1
0
1
1
1
0
0
0
0
1
1
0
1
1
0
1
1
1
1
1
0
1
0
1
0
1
0
1
2
2
1
1
0
2
2
1
1
0
1
2
0
2
1
2
1
0
1
2
1
1
1
1
1
1
1
1
2
0
0
2
1
0
1
1
1
2
2
1
1
1
2
1
1
1
2
2
1
1
0
1
2
1
0
1
2
0
1
1
0
0
0
2
0
1
1
1
1
0
1
1
1
2
0
1
1
1
2
1
2
3
1
1
2
4
1
1
2
2
2
2
0
1
0
2
2
1
1
1
0
1
0
1
3
1
1
2
1
1
0
1
0
0
2
2
2
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
0
1
1
0
2
0
1
0
1
0
1
1
2
1
2
0
2
1
1
1
2
0
1
1
0
1
2
1
1
2
1
2
0
3
2
0
1
2
1
1
1
2
0
1
1
2
2
0
2
2
0
1
1
1
1
1
1
2
0
1
1
1
2
1
0
0
1
0
0
2
2
1
2
1
1
1
1
1
2
1
1
1
1
1
2
0
1
0
0
2
1
2
1
2
1
2
1
1
1
1
1
2
1
1
1
1
1
0
1
1
2
1
0
1
2
1
1
1
2
1
0
1
1
1
1
1
1
1
0
1
2
1
2
1
0
0
1
1
0
0
1
1
2
1
0
2
0
1
1
1
1
0
1
1
1
2
1
0
1
2
1
2
1
1
0
2
0
0
1
0
2
1
1
0
0
2
2
1
0
2
0
1
0
1
1
0
0
1
0
0
0
0
0
1
0
1
1
0
2
2
1
2
1
1
1
0
0
2
1
1
0
2
1
1
1
1
0
1
1
1
1
1
0
0
0
1
1
2
1
1
1
1
1
1
0
0
1
2
0
0
0
1
0
1
0
2
0
1
0
1
2
1
1
1
2
1
0
0
1
0
1
1
2
1
1
1
1
0
1
1
2
1
2
0
1
1
0
0
1
0
0
2
1
1
1
1
1
0
2
2
1
2
1
2
2
1
2
1
1
1
1
2
0
1
2
0
1
1
1
2
0
1
0
1
1
2
2
1
1
3
1
1
0
0
1
0
2
1
1
0
1
1
2
0
1
0
1
2
2
1
1
2
0
1
1
0
1
0
1
1
2
2
1
1
1
1
1
1
2
1
1
2
1
1
0
1
1
1
1
0
2
2
2
1
1
1
0
2
1
1
1
0
2
2
2
1
0
2
1
1
2
0
1
1
3
2
1
0
0
1
1
1
1
1
2
1
1
1
1
2
1
1
0
1
1
1
1
1
0
1
2
0
1
2
0
1
1
1
0
1
1
0
2
1
2
1
1
1
1
1
3
0
0
1
1
1
1
2
0
0
2
1
1
2
1
1
2
0
0
1
1
2
0
1
0
1
0
0
1
2
1
1
2
1
1
1
0
0
2
0
1
2
1
1
1
1
1
1
1
1
0
1
1
1
1
0
0
1
1
2
1
1
1
1
1
2
0
1
1
1
1
0
0
0
1
2
2
0
1
0
2
1
0
0
0
1
0
1
1
1
2
1
1
1
1
1
0
1
1
1
2
1
0
0
1
1
0
1
2
1
1
1
0
2
1
1
2
1
0
2
1
1
3
0
0
1
2
1
1
1
1
2
0
0
1
0
1
1
0
0
2
1
2
0
0
1
2
2
1
1
2
0
1
1
1
1
1
1
0
1
0
2
1
1
1
0
2
1
1
1
2
2
1
1
1
0
1
1
1
1
1
0
0
0
0
1
1
0
1
2
1
2
1
2
1
1
0
1
0
1
1
1
2
2
2
0
2
1
2
0
1
0
1
1
1
1
0
0
0
2
0
1
2
1
2
1
1
2
2
1
1
0
2
1
1
1
1
1
1
0
0
1
1
0
2
1
1
1
1
1
0
2
1
1
1
0
1
2
0
1
2
3
0
0
1
1
2
1
2
2
1
0
1
1
5
1
1
0
0
1
1
2
2
2
1
1
1
1
2
1
1
1
0
0
0
1
0
2
2
2
0
2
1
0
0
0
1
0
1
0
2
2
1
1
0
1
0
1
0
0
0
1
1
1
2
0
0
0
1
0
2
1
1
2
2
1
1
2
1
0
0
0
1
1
1
1
2
1
2
1
0
0
1
0
1
1
1
0
1
1
0
1
0
2
1
1
1
0
0
1
0
1
2
0
2
1
1
1
1
1
1
2
1
1
0
0
1
0
2
1
2
1
0
2
1
1
1
1
1
0
1
1
2
2
1
2
1
0
0
0
1
0
1
1
1
1
0
1
1
2
0
0
1
1
1
1
1
2
2
1
1
0
1
1
1
1
1
0
2
0
2
1
1
1
1
1
0
1
0
1
1
1
1
1
2
0
1
1
1
0
2
1
2
2
2
1
1
2
2
2
2
1
2
0
2
2
0
1
1
1
0
2
1
1
1
0
1
1
1
1
0
1
0
2
1
2
1
1
2
1
2
1
0
2
1
1
1
1
1
0
0
2
0
1
0
2
3
0
1
1
1
1
2
1
1
1
1
2
1
0
0
0
1
1
2
1
1
1
1
1
0
2
1
0
1
1
0
0
2
1
0
0
1
1
1
1
0
1
0
1
2
1
1
1
1
1
1
0
0
0
1
1
2
0
0
0
1
1
1
0
2
1
0
1
0
2
1
1
2
1
2
0
1
1
0
2
2
1
1
1
0
2
1
1
0
1
1
0
1
0
1
1
1
1
1
0
2
0
2
1
0
1
0
2
1
0
0
0
1
1
1
2
1
0
1
2
2
1
1
2
2
0
1
1
1
1
1
0
0
1
1
0
2
2
1
2
1
1
0
2
2
0
2
0
1
1
1
2
1
1
1
1
2
2
1
0
2
1
2
1
2
1
0
2
1
2
2
0
1
1
1
1
2
1
2
0
1
0
2
1
2
1
1
2
2
1
1
2
1
0
0
2
2
1
1
1
1
1
1
1
0
1
0
0
0
0
2
0
2
1
1
0
1
1
2
1
2
1
1
2
0
0
2
0
1
1
2
2
1
1
1
0
1
1
1
1
2
1
2
2
2
1
1
0
1
2
2
1
0
2
0
1
0
2
2
1
0
2
0
1
1
2
1
1
1
1
0
2
1
0
2
0
0
0
1
1
2
2
2
1
2
1
1
1
1
0
1
1
2
1
0
1
1
2
1
1
2
2
1
1
1
2
1
0
1
2
0
2
1
1
1
0
2
1
1
0
1
0
0
1
2
1
1
1
2
0
0
0
2
1
1
3
1
1
2
0
2
1
1
0
0
0
0
1
1
1
0
0
1
0
1
1
2
1
1
0
1
1
1
0
1
1
0
1
1
0
2
1
1
2
1
1
2
1
1
2
0
2
0
2
1
2
1
1
1
0
2
1
0
0
1
1
1
1
1
2
1
1
1
1
0
0
0
1
1
2
0
0
1
2
2
2
1
2
0
1
0
1
1
1
0
2
1
1
2
3
2
2
2
1
1
2
0
0
1
1
1
1
1
2
1
1
0
1
2
1
0
3
1
0
1
1
1
1
1
0
1
0
0
1
1
2
3
1
1
1
1
1
1
1
2
1
1
0
1
0
1
0
1
2
2
2
2
0
1
1
1
0
1
0
1
1
0
0
2
0
1
0
0
2
4
2
2
1
1
0
0
1
0
1
2
1
0
2
1
2
1
1
1
1
1
1
1
1
1
0
0
1
0
1
0
1
1
1
2
0
2
1
1
0
1
1
1
1
0
2
0
1
1
1
1
0
1
1
1
0
1
1
1
0
2
1
2
1
1
0
1
1
1
2
1
2
1
1
3
1
0
2
1
1
1
1
2
1
1
0
0
0
2
1
1
2
2
1
2
0
0
1
1
1
1
1
1
0
1
2
1
0
1
1
1
2
2
1
1
0
1
0
0
0
0
2
1
1
1
1
2
2
2
2
2
0
2
1
2
0
2
2
1
1
1
1
1
1
0
1
1
1
1
1
2
1
2
1
2
1
1
1
0
1
1
0
1
1
1
2
1
1
1
2
0
1
1
1
1
1
0
1
0
2
1
1
1
1
0
2
0
1
2
1
1
0
1
1
2
1
1
1
2
1
2
1
1
1
0
2
0
1
1
1
0
1
1
2
2
1
0
0
1
0
1
0
0
2
2
1
1
1
0
2
1
0
2
0
2
1
0
0
1
2
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
0
1
1
2
0
0
1
1
1
1
0
2
1
2
0
0
1
1
1
0
1
1
0
1
1
2
0
1
1
1
2
1
0
1
1
0
2
0
1
1
1
1
1
1
1
3
2
1
1
1
0
1
0
1
0
0
1
1
1
1
1
1
0
0
1
2
0
0
1
2
1
1
0
0
1
1
0
0
0
1
0
1
2
0
1
2
0
0
1
1
1
1
2
2
1
1
1
1
0
0
0
1
2
1
2
1
1
2
1
1
2
0
1
0
1
0
1
1
3
1
2
1
1
0
0
1
1
1
0
0
1
1
1
1
1
1
1
0
1
1
2
1
1
1
2
1
1
2
0
0
1
1
1
1
2
2
1
1
1
0
0
2
1
2
0
1
1
0
0
1
0
1
0
1
1
0
1
2
1
2
0
2
1
1
1
1
2
0
0
2
1
0
2
1
2
1
0
1
2
1
1
1
2
1
0
2
0
1
2
1
2
0
0
1
1
1
1
1
1
2
2
1
1
2
2
1
2
1
1
2
2
1
2
3
1
0
3
1
1
1
0
2
0
2
1
1
0
0
0
1
1
1
1
0
2
1
1
1
1
2
2
2
1
2
0
2
0
1
1
1
1
2
1
2
0
1
1
1
1
1
1
1
1
1
0
2
0
2
1
1
1
2
1
0
0
1
1
1
0
1
0
1
0
1
0
0
1
2
1
2
2
0
0
1
0
0
1
1
1
0
2
1
1
1
1
0
2
1
1
1
1
1
1
1
0
1
1
1
0
1
1
2
1
0
1
0
2
0
2
2
1
1
1
1
0
0
1
0
1
0
1
1
1
0
1
1
2
0
1
2
1
1
2
1
1
0
1
0
1
1
1
2
1
2
0
2
0
2
1
0
1
1
1
2
2
0
1
1
2
1
1
1
1
1
2
1
1
0
1
1
1
1
1
0
2
0
2
1
0
1
1
1
2
1
1
1
2
0
2
1
1
1
1
1
0
1
0
1
1
1
0
1
1
1
0
1
0
1
2
1
1
1
1
0
1
2
1
1
0
1
1
0
1
1
1
1
0
0
1
0
2
1
0
1
0
1
0
1
1
2
1
1
1
2
1
2
1
1
1
1
1
0
1
3
2
2
1
2
0
1
2
0
1
1
0
1
1
0
1
1
0
1
1
1
1
1
1
1
1
0
1
1
3
1
1
1
1
0
1
1
1
1
1
1
1
2
2
1
2
1
1
0
1
1
2
1
1
0
2
0
1
1
1
1
1
2
1
0
1
0
1
0
2
2
1
0
0
2
0
2
1
2
1
1
1
0
1
0
1
2
1
2
1
2
0
1
1
1
1
1
2
1
3
1
1
2
1
2
0
1
1
1
2
2
1
1
1
1
1
1
2
1
0
2
1
1
2
0
1
0
1
0
1
1
1
1
1
2
0
1
2
1
1
1
0
0
1
1
1
1
1
1
2
2
2
1
1
1
1
2
0
0
1
2
0
1
2
2
1
2
2
2
1
1
1
0
1
1
1
1
0
1
0
2
1
1
1
1
1
2
1
2
1
0
1
1
4
1
2
1
0
0
2
1
0
0
1
1
1
1
0
0
1
1
0
2
2
1
1
2
1
1
1
0
1
2
1
1
1
1
0
2
1
1
1
2
1
2
1
2
1
2
2
1
1
1
1
2
0
2
2
0
0
0
0
1
1
1
1
1
1
0
0
0
1
0
1
1
0
0
1
2
0
1
1
2
1
1
2
1
0
1
2
1
1
1
0
2
0
1
1
1
2
1
1
0
0
1
2
0
1
1
1
1
2
1
2
1
0
1
2
1
1
1
2
2
1
1
2
1
1
1
2
1
1
1
0
0
0
1
2
1
2
1
1
1
0
0
2
2
2
1
0
1
0
1
1
1
0
1
0
1
1
0
0
0
0
1
0
1
0
0
2
1
2
1
1
1
1
0
1
1
1
1
1
2
0
1
1
0
1
1
0
1
2
1
1
0
1
2
1
1
2
2
2
1
2
2
0
0
1
1
1
1
0
2
0
2
1
1
1
1
2
1
1
0
2
1
0
1
1
1
1
2
0
1
1
2
0
1
1
2
1
0
1
1
1
2
0
1
2
1
1
2
2
1
2
0
0
2
0
1
0
0
0
1
2
0
0
1
1
1
1
1
0
1
1
0
1
1
1
0
1
1
1
0
2
0
0
1
1
2
0
0
0
0
1
0
0
2
2
0
1
1
1
1
2
1
1
1
1
0
1
0
2
1
1
2
1
1
1
0
1
1
0
2
0
1
2
1
1
0
0
1
1
1
0
1
1
0
2
1
1
1
1
1
2
2
1
2
0
1
1
2
0
1
0
0
2
1
0
2
1
1
2
1
0
2
0
2
0
1
1
0
1
0
0
0
0
2
0
0
1
0
0
1
0
0
1
1
2
1
1
2
2
4
1
2
2
1
2
1
0
0
1
1
2
2
1
2
1
1
2
2
1
2
2
1
0
2
1
1
1
1
1
0
1
1
0
1
2
0
1
1
2
1
1
1
1
0
1
1
0
1
1
1
1
0
0
0
1
1
1
0
1
1
1
1
2
0
0
1
1
2
0
1
0
1
1
1
2
0
0
0
2
2
1
2
1
2
0
1
2
1
2
0
0
1
1
1
1
1
2
1
2
0
0
1
1
1
1
2
1
2
1
2
1
2
2
2
1
0
0
1
0
1
1
1
1
1
2
1
2
0
2
1
1
3
0
1
1
0
0
2
1
1
1
0
1
1
1
2
1
1
2
1
1
1
1
1
1
1
2
1
2
0
1
1
1
1
1
1
2
2
1
2
0
1
0
0
0
1
1
0
0
2
2
1
2
0
1
0
1
1
2
2
1
2
0
1
2
1
0
1
1
1
1
1
1
1
1
0
1
1
1
0
1
1
0
1
1
2
1
0
2
1
1
1
0
1
2
1
1
1
3
2
0
1
2
1
1
1
1
0
0
2
1
1
0
2
1
1
2
2
1
1
2
2
0
1
1
2
1
2
1
1
1
2
0
1
1
0
0
1
1
2
0
0
1
0
1
1
1
1
1
1
1
1
1
0
1
1
1
2
1
1
1
2
0
1
1
2
0
1
2
1
0
2
2
0
0
1
0
1
2
1
1
1
2
0
2
1
2
2
1
1
1
0
1
2
1
2
1
1
2
1
1
2
1
2
0
1
0
1
2
0
0
1
1
1
1
1
1
1
1
1
2
2
1
2
1
1
0
1
1
2
2
2
2
1
1
0
1
2
1
0
1
1
1
1
2
0
0
2
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
2
2
0
2
0
0
0
1
1
0
0
1
0
2
0
0
0
1
1
1
1
0
2
1
1
0
1
1
1
0
1
2
1
0
2
0
1
1
0
0
2
0
2
1
1
1
1
0
1
2
1
1
0
2
1
2
1
0
1
1
2
0
1
2
2
1
1
2
1
0
1
1
1
0
0
1
1
1
0
1
2
1
2
1
2
2
1
1
2
1
1
1
0
1
1
1
0
1
2
0
1
1
2
0
1
1
0
1
0
1
2
1
2
1
2
0
1
0
0
0
0
1
0
1
2
2
1
2
1
0
1
1
0
0
1
1
1
2
0
2
1
1
1
1
1
2
1
1
1
1
0
1
0
2
1
0
1
0
0
0
1
2
1
1
2
1
2
2
1
2
1
0
0
1
1
1
1
0
0
1
2
1
1
0
3
2
0
1
0
1
1
1
1
1
1
2
1
1
2
0
2
1
1
1
1
1
2
1
0
1
0
1
2
0
0
1
1
1
0
1
1
1
1
0
2
2
2
3
1
2
1
1
1
1
1
1
0
1
2
1
0
1
1
1
0
2
0
1
1
2
1
1
1
2
1
0
1
1
1
1
1
2
1
2
1
1
0
0
2
1
2
0
1
1
1
1
1
2
0
0
1
2
1
2
1
2
1
1
2
1
2
1
1
1
2
1
1
2
2
2
2
0
1
2
1
2
1
0
2
0
1
1
1
1
1
1
0
2
0
0
1
2
2
0
1
1
1
0
1
2
1
1
1
0
2
1
0
2
1
1
0
1
1
2
1
2
1
0
0
0
0
1
0
0
2
1
1
1
1
1
0
1
0
2
2
1
2
1
1
2
1
2
3
1
0
0
0
0
2
1
1
1
2
1
0
1
1
0
1
0
1
0
1
2
1
1
2
2
3
0
1
0
0
0
0
2
2
2
1
1
2
1
1
0
1
0
1
1
0
2
1
1
1
1
0
0
2
2
2
1
1
1
1
0
1
1
0
2
0
1
0
1
2
1
1
0
2
2
0
1
0
1
2
1
1
1
1
2
2
2
3
1
2
1
2
2
1
0
1
0
1
0
0
1
0
1
1
1
0
1
1
1
1
1
1
1
2
2
1
0
1
0
2
1
1
2
0
1
0
1
1
2
2
1
2
2
1
0
2
2
1
1
1
1
1
1
0
0
0
0
1
1
1
1
1
0
1
0
0
1
1
2
1
1
0
2
0
1
1
1
1
1
1
0
1
1
1
1
0
0
1
1
0
1
1
0
3
0
0
2
1
1
1
1
1
1
3
0
1
0
1
1
0
0
1
1
0
0
0
1
2
1
3
1
1
0
0
1
1
1
1
0
2
1
1
1
1
1
1
1
1
2
1
1
1
0
1
1
1
1
2
1
1
1
1
1
1
1
0
0
1
0
1
2
0
1
1
0
1
1
1
0
1
1
1
1
0
1
1
1
1
1
2
2
0
2
1
2
0
1
1
0
0
0
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
2
1
1
0
1
0
2
1
2
5
1
1
0
1
1
0
0
1
0
1
1
2
0
1
1
2
1
2
0
2
1
0
2
1
1
0
1
0
1
1
1
1
1
1
0
1
1
2
0
2
1
1
2
0
0
1
0
0
1
1
1
0
1
2
0
1
0
1
0
2
1
0
2
1
0
1
0
0
2
0
1
0
0
1
0
1
1
1
0
1
1
1
1
0
1
1
0
1
1
1
1
2
1
0
0
2
1
0
1
1
1
0
1
1
1
0
1
1
1
1
0
3
2
1
0
2
1
1
1
0
1
0
3
2
2
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
0
1
1
1
1
0
0
1
1
1
2
1
2
0
1
1
2
1
1
1
1
0
1
1
1
0
1
1
1
1
1
1
0
2
2
2
1
1
0
0
1
2
1
0
1
0
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
0
1
1
1
1
1
1
1
0
2
1
1
1
1
1
1
1
2
0
0
0
2
1
1
2
2
2
0
0
1
2
0
0
2
1
1
1
2
0
1
2
1
1
0
1
1
1
2
1
2
1
0
2
2
1
0
1
0
0
1
1
1
1
1
1
0
0
1
1
1
0
1
1
2
0
1
0
1
2
2
2
0
1
0
0
1
0
1
1
0
2
1
2
0
0
2
1
3
1
2
1
1
0
1
4
0
1
0
1
1
0
1
0
1
1
0
0
1
1
1
1
0
1
1
1
0
2
1
2
0
1
0
2
1
1
2
1
2
0
2
1
2
0
1
0
1
1
2
2
1
2
0
2
1
1
2
1
0
0
1
2
0
1
0
5
0
1
1
1
1
1
0
0
0
1
1
2
1
1
1
1
0
4
0
1
1
1
2
0
1
1
0
0
0
2
2
2
2
1
2
1
0
1
2
1
1
1
2
1
1
0
2
0
1
0
1
1
0
1
1
0
2
1
0
2
0
1
0
2
1
1
1
1
2
0
1
1
1
2
1
1
1
1
1
1
1
2
2
2
2
1
1
1
3
0
1
3
1
2
1
1
1
0
2
0
1
1
1
1
2
1
1
0
1
2
2
1
1
2
1
1
1
0
1
0
0
0
1
0
2
1
2
1
1
0
1
2
0
2
1
1
2
1
1
0
1
2
1
2
1
1
1
1
1
1
1
1
2
0
2
1
0
1
0
1
2
2
0
0
1
1
1
1
0
1
2
1
0
1
1
1
0
1
1
1
0
0
1
1
1
0
0
1
2
0
0
2
0
0
1
0
1
1
0
1
0
2
2
1
1
0
1
1
0
2
1
0
1
0
1
1
1
1
2
2
0
1
2
0
2
1
1
0
1
1
1
1
1
2
1
0
0
0
2
1
2
1
2
1
2
1
0
0
1
0
3
1
1
1
0
2
1
1
1
1
1
0
1
0
1
2
0
1
2
1
1
2
1
1
0
2
0
2
1
1
1
0
1
1
1
1
0
1
1
1
0
1
1
0
0
1
1
1
1
2
2
1
1
2
1
1
2
1
1
1
0
2
2
1
2
1
1
1
2
1
1
0
0
1
1
1
1
1
2
0
2
1
1
1
2
2
4
2
0
2
1
2
2
1
1
1
2
1
0
0
1
0
0
0
2
2
2
2
2
0
0
2
1
2
1
2
0
0
1
1
1
0
1
1
1
1
2
0
0
1
2
2
2
1
1
2
0
0
0
1
2
2
1
1
2
2
1
2
0
1
1
2
1
0
2
1
0
1
1
1
2
1
2
1
2
1
1
0
1
0
2
1
0
2
1
2
0
2
1
3
1
2
1
1
1
0
1
1
2
0
1
0
0
1
1
1
0
0
1
0
0
1
2
0
1
2
1
1
1
2
1
1
0
1
0
1
1
1
2
1
1
0
0
0
2
1
0
1
1
2
1
0
1
2
2
2
0
1
1
2
1
0
2
1
2
2
2
2
1
1
0
2
6
1
0
1
2
1
1
1
3
0
1
1
0
1
1
0
1
1
0
0
2
0
3
2
1
2
0
1
1
1
1
1
0
1
1
1
2
1
2
1
1
0
0
1
1
0
2
1
0
0
1
1
1
0
3
2
1
2
1
1
1
1
1
1
2
0
0
0
1
1
1
2
2
1
1
1
1
1
2
1
1
2
2
2
0
1
2
2
1
1
1
1
2
1
0
0
2
2
1
2
1
0
0
0
2
1
1
1
1
1
1
0
1
0
1
1
1
1
0
0
1
2
1
1
1
2
1
1
0
0
1
0
0
1
1
1
0
2
2
3
0
1
1
1
1
1
1
1
1
1
2
0
1
0
0
2
1
1
1
1
0
1
1
2
0
0
1
2
0
0
1
0
1
1
0
1
1
0
1
1
1
1
2
1
1
1
0
0
0
0
2
1
1
1
2
1
1
1
0
1
1
2
1
1
1
2
2
1
1
1
1
0
0
1
1
2
1
0
2
2
2
1
1
1
0
1
1
0
2
2
1
1
0
0
1
0
1
1
1
0
0
1
2
1
1
1
0
1
1
1
1
1
1
1
1
0
2
2
2
2
1
1
1
1
0
2
2
1
1
0
2
1
1
2
2
2
0
1
1
0
1
0
1
2
1
2
1
0
1
2
0
1
1
1
2
0
1
1
1
1
2
1
1
2
0
0
1
1
1
2
1
1
0
0
1
1
0
0
2
2
1
2
2
1
0
1
2
1
0
0
1
1
1
1
1
1
1
1
1
1
1
0
0
1
1
1
1
0
2
2
1
2
0
0
1
1
1
1
0
1
1
0
1
1
3
0
1
0
0
1
2
0
1
0
2
0
1
1
1
2
1
0
1
1
2
0
1
2
0
1
1
1
1
0
0
1
1
1
1
2
1
1
2
1
1
2
1
1
0
2
1
1
2
0
1
1
3
1
1
2
1
2
1
2
1
0
1
2
0
1
0
1
1
1
1
2
1
2
0
0
1
1
0
1
0
1
1
2
0
1
1
2
2
1
2
2
1
0
1
1
1
1
2
0
1
0
1
0
1
3
2
1
1
1
1
0
2
1
1
2
1
0
1
2
1
1
2
1
2
0
1
1
2
1
1
1
2
1
2
0
1
1
2
1
1
1
1
1
1
0
1
1
2
1
1
1
1
2
2
2
1
1
2
0
1
1
2
2
2
0
1
1
2
1
1
1
1
2
1
2
1
1
1
2
1
1
1
1
1
0
0
1
1
1
0
0
2
2
2
1
0
0
0
2
1
0
1
1
1
1
1
1
1
0
1
1
1
1
1
1
2
1
1
1
0
1
1
0
1
1
1
2
1
1
0
1
1
1
1
1
2
1
1
1
1
0
2
2
0
1
1
1
0
1
2
1
0
1
1
2
2
0
1
2
2
1
1
1
1
2
0
1
1
0
2
1
2
2
2
2
1
1
1
1
1
2
1
0
0
0
0
0
0
0
1
0
1
1
1
1
2
1
0
0
1
1
2
1
0
1
0
1
1
1
0
1
1
1
0
2
1
0
1
1
1
1
0
0
1
0
1
1
2
1
0
0
1
1
2
0
1
2
1
0
1
2
1
1
2
1
1
2
2
0
1
1
1
0
0
0
1
1
1
0
1
0
0
1
2
2
1
1
2
2
0
0
1
0
2
2
1
1
0
2
1
1
1
0
1
1
1
2
1
1
2
2
0
2
1
0
1
0
1
1
0
1
2
2
1
1
2
2
1
1
2
1
0
2
0
2
0
1
0
0
1
1
1
0
2
2
1
2
1
2
2
0
0
2
0
2
1
1
0
1
1
1
1
2
1
1
2
3
1
2
0
1
1
1
3
2
0
1
0
0
2
2
1
2
1
1
1
0
1
0
2
2
0
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
0
1
0
1
0
0
1
1
1
2
2
2
0
1
1
2
1
2
1
1
0
3
1
1
1
2
2
1
0
1
1
2
2
2
0
0
1
1
1
0
0
1
1
1
2
1
2
0
1
0
2
2
0
1
1
2
1
0
1
1
1
0
1
1
0
1
2
1
1
1
1
1
1
0
2
1
2
1
1
0
2
1
5
1
1
3
0
1
2
1
0
1
2
1
1
1
0
2
1
1
1
1
1
1
1
2
1
1
0
1
2
0
4
1
1
1
1
0
0
0
0
1
1
1
0
1
1
0
0
0
1
1
1
0
1
2
2
1
2
2
1
1
1
0
1
0
2
1
1
0
2
1
1
1
2
1
1
1
1
1
1
2
2
0
2
1
1
2
3
1
2
1
2
1
0
1
1
0
1
1
1
2
1
0
2
2
0
1
0
2
1
0
0
1
1
1
1
1
0
1
1
1
1
2
0
0
1
2
0
0
1
0
2
1
1
1
1
0
1
0
1
1
0
1
0
2
1
1
0
1
0
1
1
1
1
1
2
1
2
2
1
2
1
1
2
1
0
0
0
1
1
1
2
0
0
1
1
1
1
1
1
1
0
1
1
1
0
2
1
0
3
4
2
0
2
1
1
2
2
1
1
0
1
0
2
0
0
2
1
1
1
0
1
0
1
2
0
2
1
2
2
1
0
0
1
1
1
1
0
1
1
1
0
2
1
0
1
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
1
1
0
1
1
0
0
1
2
1
0
1
2
0
2
0
1
1
2
1
1
3
1
1
2
1
1
0
1
0
0
2
1
1
1
1
1
1
0
1
1
1
0
1
2
1
1
1
0
1
1
1
0
1
0
0
1
2
1
1
0
1
1
0
1
1
1
2
1
1
1
0
2
4
2
0
1
3
1
1
1
1
1
1
1
0
2
1
0
0
1
1
1
1
1
1
1
0
1
1
2
2
0
1
1
1
2
1
2
2
1
1
0
1
2
1
1
0
0
2
0
2
0
0
1
1
1
1
2
0
0
1
0
2
0
1
1
1
1
0
3
1
1
0
0
1
0
1
0
1
1
1
1
0
1
1
1
1
1
1
1
0
1
2
1
1
0
1
0
0
0
0
1
2
2
0
1
0
0
1
1
2
1
1
2
0
1
0
2
2
1
0
1
1
1
1
1
1
1
1
0
0
1
0
1
1
0
1
0
1
0
1
2
0
1
1
1
0
0
2
1
0
2
1
0
1
0
1
2
1
0
1
1
1
0
1
1
2
2
1
1
2
0
1
1
0
0
1
1
0
1
0
0
2
1
0
1
1
1
0
0
1
1
1
0
2
2
1
1
1
2
0
1
0
1
2
0
3
1
1
1
0
0
2
0
1
3
1
1
1
1
0
2
2
1
1
2
2
1
0
2
1
2
1
1
0
2
1
0
2
1
1
1
1
1
0
2
2
1
0
1
2
1
0
1
2
1
0
0
2
0
3
1
1
1
1
0
1
1
1
0
2
1
1
1
1
1
1
1
2
1
2
0
1
2
1
2
0
0
2
0
2
2
0
1
2
0
2
1
0
0
1
0
1
0
1
1
2
2
1
1
0
0
2
1
1
1
1
1
1
0
0
1
0
0
1
1
1
3
1
2
1
1
1
1
1
0
1
1
0
0
0
0
2
2
1
2
2
1
0
0
0
1
1
0
0
2
1
2
1
1
1
1
2
1
1
1
1
1
1
0
1
0
1
1
0
1
2
0
1
0
1
2
1
2
2
1
2
2
2
2
0
0
2
1
0
0
1
2
2
1
2
1
2
2
0
2
1
3
1
1
0
0
0
0
0
0
1
2
0
1
0
1
1
1
0
2
0
1
0
1
1
1
0
2
1
1
1
1
2
1
0
1
0
1
2
1
0
0
0
0
0
1
0
2
3
1
0
2
1
1
1
1
0
1
1
0
1
1
0
0
0
1
1
1
0
0
1
0
0
1
0
1
0
0
1
1
1
1
1
2
1
1
2
0
0
0
1
0
1
0
1
0
1
0
0
1
1
3
1
0
1
3
2
0
1
1
1
1
1
1
1
2
1
0
0
1
1
2
1
1
1
0
0
2
2
2
1
1
0
2
2
1
0
0
1
1
1
1
1
1
1
0
2
2
1
1
1
0
1
1
1
1
1
0
0
1
1
1
0
2
1
2
2
0
2
1
1
1
1
0
2
1
1
0
1
4
0
1
1
0
1
0
1
1
2
2
1
2
2
1
2
1
0
2
3
1
0
2
1
1
0
1
1
0
2
1
1
1
1
2
2
1
1
0
1
2
0
2
2
0
2
0
1
1
0
1
2
2
0
2
1
1
2
0
2
1
1
1
1
1
1
1
0
0
1
2
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
2
2
0
1
1
1
0
1
2
1
0
1
1
1
2
0
2
1
1
1
0
0
0
2
2
0
1
1
3
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
0
2
0
2
1
1
1
2
2
0
1
1
0
2
0
0
1
3
2
2
1
2
1
1
2
0
1
1
0
1
1
1
1
2
1
2
0
1
0
1
2
2
1
4
0
1
0
1
2
2
2
1
0
1
1
1
1
2
1
1
1
1
1
1
0
0
1
2
0
1
0
1
1
1
1
0
1
1
1
1
1
0
1
0
2
1
1
0
0
0
0
1
1
1
1
0
0
0
1
1
1
0
0
1
0
1
0
1
0
1
1
0
2
1
1
2
1
1
2
3
0
1
1
2
0
2
0
2
1
2
1
0
1
1
1
1
0
1
1
1
1
1
1
1
1
3
1
2
1
0
1
1
1
2
1
1
1
0
0
0
1
1
1
0
0
2
2
1
0
1
1
1
1
1
2
1
1
2
3
2
1
0
1
1
0
1
2
1
1
2
1
0
0
1
4
0
1
0
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
2
1
1
1
0
0
2
1
1
1
1
1
1
1
1
2
1
1
0
1
1
1
1
2
1
1
5
1
1
2
1
1
1
2
1
2
1
0
2
0
0
0
0
1
1
0
2
1
2
2
1
2
0
1
1
0
0
0
1
1
1
2
1
0
0
0
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
0
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
2
0
1
0
0
0
1
0
2
2
1
1
1
0
2
1
1
1
1
1
1
1
0
1
1
0
0
1
1
2
0
1
1
0
2
1
0
2
2
1
1
3
2
0
1
1
1
1
2
0
1
1
0
2
1
2
1
1
1
1
1
1
1
1
2
1
1
0
1
0
1
1
0
2
0
1
1
0
2
2
1
1
1
0
3
0
1
2
1
0
0
1
2
1
2
1
1
1
1
0
1
1
1
0
1
1
1
1
1
2
0
1
2
1
2
2
1
0
0
0
0
1
1
1
2
3
1
0
0
0
0
0
1
1
1
3
1
4
0
0
2
1
1
1
2
2
4
1
2
0
0
0
1
0
2
1
1
0
2
2
1
2
1
2
0
1
0
0
1
1
1
1
1
1
0
1
0
1
1
0
1
1
2
1
0
1
1
3
2
1
1
2
2
1
1
0
1
1
1
0
2
1
0
2
0
0
1
0
1
1
1
1
0
0
1
1
0
1
1
0
0
0
1
0
1
1
1
2
0
1
0
1
1
2
0
1
2
1
1
0
2
0
1
0
1
2
0
1
1
2
2
1
2
1
1
1
2
5
1
0
2
1
2
1
1
2
2
1
1
0
1
1
2
1
0
3
1
0
1
2
1
1
0
2
0
0
1
2
1
1
0
1
0
1
1
1
1
1
1
1
0
0
2
1
0
2
1
0
1
2
1
2
0
2
1
1
1
0
1
0
0
0
0
1
1
1
1
1
1
1
2
2
1
0
1
1
1
1
1
1
0
1
1
1
1
1
2
1
0
2
1
1
1
1
1
2
0
0
1
1
0
0
1
2
0
1
1
2
1
2
1
1
2
0
2
1
1
1
2
0
1
2
1
1
0
0
0
0
1
1
0
1
0
0
2
2
0
2
1
3
1
1
1
2
2
1
2
2
0
2
3
2
1
1
1
0
1
2
2
1
2
1
0
2
1
1
2
1
1
2
2
2
0
2
1
1
0
1
1
1
1
1
1
0
1
1
2
0
0
1
1
0
1
0
1
1
1
1
2
1
2
1
0
0
0
1
1
1
1
1
1
1
2
2
1
2
0
1
1
0
2
2
1
1
1
1
1
0
2
1
0
1
0
2
1
1
0
1
1
2
1
1
0
1
1
0
2
0
1
1
1
1
0
0
1
1
1
0
1
2
1
1
1
1
0
0
1
2
1
1
2
1
2
0
1
1
1
0
2
2
0
0
0
0
1
2
2
0
0
1
1
2
1
1
2
1
1
1
1
0
0
1
1
1
1
1
1
1
0
1
1
2
0
1
0
1
1
1
2
1
1
0
2
0
1
0
0
2
2
2
1
1
1
1
2
2
1
1
2
0
0
1
1
0
1
1
2
1
0
2
1
2
1
1
0
1
1
2
0
1
1
0
2
0
2
2
0
1
0
1
1
0
1
2
1
1
2
1
0
1
1
1
1
0
1
0
1
0
0
0
0
0
1
1
2
1
2
1
2
1
1
1
0
1
0
1
2
1
1
1
1
2
1
1
1
1
0
1
1
0
0
1
1
1
2
2
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
2
1
0
0
2
0
0
1
1
1
1
1
1
0
1
1
2
1
2
0
0
1
1
4
0
1
1
1
1
1
1
2
3
2
2
0
2
2
1
2
0
1
2
1
1
0
0
1
1
0
1
1
1
0
1
1
0
0
2
1
0
1
1
2
1
1
0
1
0
1
0
2
7
0
2
1
2
1
2
1
2
1
1
0
2
1
0
1
2
0
1
1
1
1
1
1
2
0
1
2
1
1
1
1
0
2
2
1
0
0
2
1
2
1
1
2
1
0
1
1
1
2
0
1
2
2
0
1
2
1
1
1
2
2
0
0
1
1
1
1
1
2
1
1
1
1
1
2
1
1
2
0
1
1
1
1
1
1
0
0
2
0
3
0
1
2
2
2
1
2
1
2
0
2
1
0
0
2
0
1
2
0
1
0
1
1
21
1
2
1
1
1
2
0
2
1
0
0
1
1
1
1
2
1
0
0
0
1
0
1
0
2
0
2
2
0
2
1
0
1
0
0
2
1
1
1
1
1
1
1
0
3
0
1
1
2
1
1
0
1
1
1
1
0
1
1
1
1
0
0
1
1
1
1
0
2
1
1
1
1
2
1
2
1
2
0
2
1
0
0
2
1
2
1
0
1
1
0
1
0
1
2
1
1
2
1
1
1
0
1
1
2
1
1
0
1
1
1
2
2
1
1
0
1
1
0
1
0
1
0
1
1
0
2
1
1
1
2
0
0
2
0
1
1
0
2
1
1
1
0
2
1
1
2
0
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
2
2
0
2
1
0
2
0
2
2
1
2
1
2
1
0
0
0
1
0
1
0
1
1
1
1
1
1
1
2
1
1
1
1
0
1
1
1
1
1
1
2
0
1
0
1
0
1
0
1
3
3
2
1
0
1
0
0
0
2
2
2
2
1
2
1
3
1
1
2
1
0
1
0
1
1
2
2
0
2
1
3
0
1
1
1
1
1
1
1
1
1
0
2
2
1
1
0
1
1
0
1
1
2
1
2
1
2
2
1
1
1
1
1
0
0
1
1
0
1
1
1
2
0
1
1
0
1
1
1
1
1
0
1
1
1
2
0
1
1
1
1
2
0
1
0
0
3
2
1
0
2
3
0
0
1
1
1
1
1
1
1
1
1
1
2
1
0
0
2
2
1
1
1
1
1
0
1
1
2
2
2
0
1
1
1
1
1
2
2
2
0
2
1
1
1
2
1
1
0
2
0
2
1
1
1
2
1
2
1
2
1
3
2
1
1
1
1
0
1
0
1
0
2
1
1
1
0
0
0
2
1
2
0
1
1
3
6
1
1
2
2
1
1
1
1
1
1
1
1
2
2
1
0
4
0
1
1
0
0
1
1
1
1
2
1
1
2
1
0
1
0
0
1
1
1
1
0
2
0
1
2
1
1
2
0
1
0
1
1
0
2
1
1
2
2
1
2
0
2
1
0
1
1
0
1
1
1
1
2
0
1
1
1
0
2
1
1
0
2
0
1
0
1
2
1
2
0
0
1
1
2
0
2
1
2
0
1
1
1
0
0
0
2
0
1
2
2
1
0
2
1
1
1
1
2
1
1
2
0
1
0
1
1
2
0
1
2
1
1
0
2
0
0
2
1
1
0
2
2
0
1
2
2
1
1
1
2
0
2
2
0
1
0
1
2
0
1
2
1
2
1
2
0
2
1
1
2
2
1
2
2
2
0
0
0
0
2
2
0
2
0
1
0
1
0
1
1
1
0
1
2
2
2
1
1
1
0
0
1
1
1
4
1
1
1
0
1
0
1
0
2
1
2
1
0
1
2
1
1
0
1
0
1
0
2
1
1
1
0
1
1
1
1
1
1
0
1
0
1
2
0
1
1
1
0
2
1
2
2
0
2
1
1
2
2
1
1
1
0
0
2
1
1
1
1
0
0
2
1
1
1
0
0
1
2
1
1
2
1
0
1
0
1
0
1
1
1
0
1
1
2
1
3
1
1
1
0
1
2
1
1
0
0
1
1
2
1
1
1
2
0
0
0
1
1
0
1
1
1
2
1
1
2
1
1
1
2
1
2
2
0
2
0
2
1
0
2
2
1
1
1
1
0
0
0
0
2
1
1
2
2
0
1
1
0
1
2
1
1
1
1
2
1
1
1
1
0
1
1
0
1
1
0
1
2
0
1
1
1
2
1
2
2
1
1
1
2
0
1
0
1
2
1
0
0
1
2
0
2
2
2
1
2
0
2
1
1
0
1
1
0
2
1
1
0
0
0
1
0
1
1
2
2
1
1
0
0
1
1
2
2
1
0
2
2
2
0
2
2
1
2
1
1
0
1
1
0
3
0
1
2
1
1
1
0
1
2
1
0
1
1
1
0
2
1
1
1
1
1
1
0
1
0
0
0
0
0
2
0
0
0
1
1
1
1
2
2
1
0
0
1
1
2
1
0
1
0
0
1
0
2
2
0
1
0
1
0
2
1
1
1
2
0
1
1
1
2
0
1
2
1
0
1
1
1
1
1
1
0
1
1
0
0
1
0
1
1
2
1
1
2
1
0
0
0
2
1
2
1
1
2
0
2
2
0
1
2
1
1
1
1
1
0
1
1
1
1
2
0
1
1
2
1
1
2
2
1
1
1
0
0
0
2
1
2
1
1
1
0
0
2
0
1
2
1
1
4
2
1
1
2
2
2
3
1
0
0
1
1
1
0
2
1
0
1
1
1
2
2
0
2
0
2
1
2
2
0
1
2
1
0
0
1
2
0
1
1
1
0
1
0
0
0
2
0
1
1
1
1
1
0
1
1
1
0
1
1
2
1
1
1
0
1
0
1
1
1
0
1
1
1
1
2
2
2
0
1
1
0
2
1
1
0
1
1
1
2
1
0
1
0
1
1
1
2
1
1
2
0
0
2
0
2
1
1
1
1
1
1
1
1
1
0
0
1
2
0
2
1
0
1
2
1
2
1
1
1
1
0
1
1
3
2
1
2
2
1
0
1
1
1
0
1
0
1
1
1
1
1
0
1
2
1
0
1
0
1
1
0
1
0
1
0
1
1
1
1
0
1
2
1
2
1
1
1
1
1
0
1
1
1
1
1
1
2
2
1
1
1
1
3
1
2
1
1
0
1
1
2
0
0
1
1
1
1
0
1
1
0
1
2
1
1
3
2
1
1
1
1
0
1
1
1
1
2
2
2
1
1
1
1
1
0
0
0
2
0
1
0
0
0
1
1
0
1
0
1
0
1
0
1
1
1
2
1
2
0
1
2
2
0
2
1
1
1
2
2
0
2
0
1
1
2
0
0
1
2
0
0
1
1
0
0
0
1
1
1
0
2
1
1
2
0
2
1
1
2
1
0
2
0
1
1
1
1
1
0
0
1
1
1
0
1
1
1
1
0
1
2
0
1
1
1
2
2
2
2
1
1
1
0
1
1
1
1
1
0
1
1
1
0
1
1
0
1
2
1
1
1
1
1
2
0
1
0
0
1
0
1
2
1
2
1
2
2
0
0
1
1
1
1
2
1
2
2
2
1
2
0
2
1
1
2
1
1
1
1
2
1
1
1
0
1
2
1
0
1
1
2
1
2
0
2
2
1
2
0
1
1
0
1
0
2
1
0
0
1
0
1
1
2
2
1
1
0
1
1
0
1
1
2
1
0
2
2
0
1
1
2
2
1
1
0
1
0
0
1
0
1
1
0
1
1
1
1
1
1
1
0
2
1
1
0
1
0
1
1
0
2
1
0
0
0
1
1
1
2
1
2
2
1
1
1
0
2
1
2
1
2
0
1
1
1
1
2
0
1
0
1
4
1
2
1
1
0
1
0
1
1
0
1
1
1
0
0
1
1
2
1
1
0
1
1
1
0
0
0
2
1
0
1
2
1
0
1
0
1
2
1
0
2
2
1
0
1
0
1
1
1
0
1
2
2
0
1
0
1
2
1
0
0
1
1
2
1
1
1
0
0
1
1
2
1
0
1
1
2
2
0
2
1
2
2
1
1
2
2
1
0
2
1
2
2
0
2
1
2
2
1
2
1
0
1
1
1
0
2
1
0
0
1
0
2
1
2
0
1
2
1
0
0
0
2
0
1
2
1
0
0
1
2
1
2
0
0
0
0
2
0
2
1
2
1
1
1
2
1
2
1
1
2
0
0
2
1
2
1
1
1
0
1
1
0
0
1
1
3
1
0
0
1
1
0
0
1
0
0
1
0
1
0
1
2
1
1
2
2
0
1
1
1
1
0
2
0
1
1
1
2
0
2
0
1
2
0
2
1
3
0
2
1
3
2
0
0
0
1
1
2
0
1
1
1
2
1
1
1
2
1
1
2
2
0
0
0
1
1
1
1
1
0
2
1
2
0
0
2
1
1
1
0
2
0
1
2
2
1
1
1
1
1
1
1
1
2
2
1
1
1
1
0
2
1
1
2
2
0
1
1
1
0
1
2
1
2
1
0
1
1
1
1
1
1
1
1
0
1
1
2
1
1
0
2
0
1
0
0
1
0
0
1
2
2
1
1
0
2
1
1
1
0
1
1
0
1
1
2
1
1
2
0
1
1
2
1
0
1
0
2
2
1
1
0
1
2
1
1
1
1
1
2
1
1
2
1
2
2
0
0
1
0
2
1
1
1
1
0
2
1
1
1
0
1
1
2
2
1
0
0
0
2
0
1
0
0
0
1
0
1
1
1
1
1
1
2
1
0
2
2
1
1
0
1
0
1
1
0
1
3
1
0
1
0
1
3
1
1
0
0
0
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
2
2
0
0
2
2
1
2
1
1
2
1
1
2
1
2
1
0
1
2
2
0
0
0
1
1
0
4
1
1
1
0
1
1
1
0
0
2
1
0
0
1
1
3
1
1
0
0
1
2
1
0
1
1
0
0
1
2
1
1
1
1
1
1
1
1
0
0
0
0
1
1
0
2
3
1
2
1
1
1
2
1
1
0
0
1
1
2
2
1
1
1
0
1
1
1
1
0
1
1
2
0
2
1
1
1
1
0
0
0
2
1
3
1
1
1
1
2
0
1
1
2
1
1
2
1
0
0
2
0
0
0
1
1
1
1
1
2
1
1
2
1
2
1
2
2
0
0
4
0
1
1
0
1
1
0
2
1
1
1
0
1
1
1
0
1
1
2
2
1
0
0
1
1
1
1
4
0
2
2
1
2
1
1
1
1
2
1
3
0
1
1
2
1
1
1
0
0
1
2
1
0
0
1
1
2
1
0
2
0
1
1
0
1
1
1
1
1
1
0
1
1
0
1
1
1
1
0
0
0
1
0
0
0
1
0
1
3
0
1
1
2
2
2
2
0
2
1
2
1
1
1
1
1
0
1
1
0
1
0
1
2
2
2
1
2
0
1
0
2
2
0
1
0
0
1
0
1
1
1
2
1
0
2
1
1
1
1
1
0
1
1
1
1
2
1
1
0
0
2
1
1
0
2
1
1
2
0
2
2
1
1
0
1
1
2
2
2
2
2
0
1
1
1
0
1
1
1
1
2
1
1
1
2
2
0
1
2
1
2
2
0
1
2
0
1
1
1
1
0
1
0
1
1
3
1
2
0
1
1
1
2
1
1
1
2
1
3
2
1
1
1
1
0
1
1
2
2
2
0
0
1
1
0
2
1
2
0
1
1
1
1
4
0
1
2
1
1
1
2
1
1
1
2
1
1
0
0
0
1
1
1
1
1
2
0
2
1
2
1
1
1
1
1
1
1
1
1
1
0
1
2
2
1
2
0
1
1
0
1
2
1
0
1
2
1
1
2
1
0
1
0
0
0
1
0
4
1
0
1
2
2
1
0
0
0
0
0
2
1
2
1
0
2
0
0
2
2
2
1
2
1
1
1
1
1
2
1
1
2
0
0
1
2
1
0
1
1
1
1
1
0
1
1
1
1
2
2
2
2
1
2
1
0
2
2
1
1
1
2
2
1
5
0
1
1
1
1
1
2
2
1
0
0
0
2
2
0
1
2
1
0
2
1
1
0
0
2
2
1
1
0
0
1
2
2
1
1
0
1
2
0
1
1
1
1
2
1
0
2
1
0
2
0
1
1
1
1
0
1
1
1
2
1
1
1
1
0
0
0
0
1
2
1
2
1
0
0
2
2
2
1
1
0
1
3
1
0
2
0
1
0
1
1
1
2
1
1
2
1
1
0
1
2
1
1
0
1
2
1
1
1
2
2
0
0
1
0
1
2
2
0
1
0
0
1
0
2
0
0
1
1
1
0
1
0
0
1
1
1
1
1
2
0
1
1
1
0
1
2
1
1
1
1
1
1
0
1
0
1
2
2
0
0
0
1
1
1
1
1
1
0
1
2
0
1
1
2
0
2
0
1
0
1
1
1
0
1
1
1
1
2
0
1
0
2
1
1
1
1
0
1
0
1
1
0
1
0
1
1
1
1
1
2
1
0
2
1
2
1
1
1
0
1
0
1
0
2
1
1
1
0
2
2
2
1
2
1
1
2
1
1
2
1
1
1
1
0
1
2
1
2
2
2
1
2
0
1
1
2
2
1
1
0
1
1
1
2
2
1
2
0
0
0
2
1
1
2
1
1
0
1
0
1
0
1
1
1
1
1
2
1
2
2
1
0
1
2
0
1
1
1
1
2
0
1
2
1
2
2
1
2
0
0
2
2
0
2
1
1
1
2
0
0
0
1
3
1
3
1
1
1
1
1
1
0
1
1
2
1
1
1
1
1
0
2
2
1
0
1
2
1
1
0
0
0
1
2
1
1
0
1
0
0
1
0
2
1
0
0
3
1
2
2
1
1
1
1
1
1
1
1
0
0
0
1
1
1
1
0
0
1
2
1
1
0
0
0
1
1
2
1
0
1
2
2
1
1
1
1
1
1
2
0
2
2
2
1
2
1
1
1
1
1
3
2
1
1
2
0
1
1
1
1
1
3
1
0
0
1
1
1
0
1
0
0
2
1
1
3
1
1
2
0
2
2
0
1
0
1
2
0
0
2
0
0
0
1
1
1
1
1
1
2
1
0
1
1
1
1
1
2
1
1
1
2
0
0
0
1
1
2
2
0
0
1
2
2
1
2
2
1
2
1
2
1
1
1
1
1
2
0
1
2
2
2
1
0
0
1
0
1
1
0
1
1
1
0
2
1
2
1
1
1
1
0
0
1
2
0
1
1
2
2
1
0
1
1
2
2
1
1
0
2
0
1
1
1
1
0
2
1
1
2
2
0
1
1
1
1
1
1
2
1
2
1
1
2
2
1
1
1
1
2
2
1
1
1
1
1
1
1
0
1
0
0
1
0
1
1
2
1
0
0
2
1
2
2
0
1
2
1
2
1
2
2
1
1
0
0
1
1
0
0
0
2
1
1
1
1
0
0
2
2
1
2
1
2
0
1
1
0
1
1
1
1
1
0
2
2
1
2
1
1
2
1
1
2
1
0
2
2
0
1
2
1
1
1
2
2
2
1
1
2
0
1
1
1
2
1
1
2
0
2
1
1
0
0
1
2
0
0
2
1
1
1
1
2
2
1
1
0
0
1
0
2
1
1
1
1
1
1
0
1
1
1
2
1
1
1
2
0
0
1
1
1
2
0
2
1
0
1
3
2
0
1
1
0
0
0
0
2
2
1
2
2
1
1
0
0
2
1
1
2
1
1
2
0
2
2
0
0
1
1
1
3
1
0
1
1
1
1
1
1
0
0
1
1
2
2
2
1
1
2
2
1
1
1
0
1
1
2
2
0
1
2
1
1
1
2
1
1
2
1
1
2
2
1
0
1
1
0
2
1
3
2
1
0
1
1
2
1
0
2
0
2
2
1
1
1
1
0
1
0
1
2
2
1
3
1
1
1
1
1
1
1
1
2
1
0
0
1
2
0
0
2
0
1
1
0
1
2
1
1
0
2
1
1
1
2
1
0
1
0
2
1
1
0
1
1
1
2
2
2
0
1
1
0
2
2
0
1
0
2
1
0
2
1
0
2
1
1
1
2
1
2
0
1
1
1
0
1
1
0
1
1
1
1
0
1
1
1
1
1
2
1
0
1
1
2
1
1
1
1
1
2
1
1
1
0
1
2
1
2
0
0
1
1
1
1
1
2
2
0
2
2
0
1
2
0
1
1
2
1
0
0
0
0
2
0
1
1
1
0
1
2
1
1
1
1
2
1
1
0
0
2
1
1
2
1
2
0
1
1
1
0
1
2
1
0
1
1
0
0
1
2
2
1
2
1
1
0
2
1
1
1
0
1
1
0
2
2
1
0
1
2
0
1
2
0
0
0
1
2
1
1
1
1
1
1
2
1
2
2
0
2
1
0
0
2
0
1
2
0
1
2
2
0
1
1
1
2
1
2
1
1
2
1
1
2
0
1
1
1
1
1
1
1
1
1
1
2
0
1
2
0
1
1
1
1
1
0
0
1
1
2
1
2
1
1
1
0
2
1
1
2
3
2
1
1
1
2
0
1
0
2
2
2
0
1
1
1
2
0
1
0
2
1
1
0
1
0
1
2
1
2
2
1
0
1
1
1
0
2
2
1
3
1
0
1
1
1
1
1
1
1
0
2
1
0
1
2
2
0
1
1
1
1
0
1
1
1
1
1
1
0
1
1
0
0
1
2
0
1
1
2
1
1
0
0
0
1
2
1
2
2
1
1
2
0
2
1
1
1
0
0
0
1
1
1
1
2
1
2
0
1
1
1
0
1
2
2
1
2
0
2
0
1
2
1
1
1
1
1
0
1
2
1
2
1
1
0
0
0
1
2
2
0
0
0
2
1
1
1
0
3
3
1
0
0
0
2
1
1
1
1
2
1
1
2
0
0
1
1
0
0
3
1
1
1
2
1
2
0
2
2
0
1
0
1
2
2
0
2
1
2
2
1
0
1
0
1
1
2
0
0
2
1
1
1
0
0
2
1
1
2
0
0
1
2
1
0
0
1
1
0
1
0
1
1
0
1
2
1
2
0
1
1
0
2
0
1
1
1
2
1
2
2
1
1
1
1
1
1
0
0
1
0
2
1
1
1
2
1
2
2
1
2
1
0
2
0
2
1
1
1
1
0
1
0
0
1
1
2
1
1
1
1
0
0
2
1
1
1
2
1
1
1
1
1
1
1
0
1
1
1
0
0
1
0
0
0
1
1
2
0
1
1
0
1
1
2
1
1
0
1
1
1
1
1
0
0
0
1
1
1
1
0
1
1
1
2
1
1
1
2
2
0
0
0
1
0
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
2
2
1
0
0
1
1
1
1
0
1
1
3
1
1
1
1
1
1
1
1
1
2
1
1
0
1
1
1
1
2
0
1
1
2
0
0
0
1
1
1
1
1
1
2
0
0
2
0
2
2
0
2
1
2
0
2
1
1
1
2
0
0
2
0
1
0
0
1
1
2
2
1
1
1
1
1
1
0
2
1
1
1
1
0
1
0
0
1
0
1
1
1
0
1
2
1
2
2
1
2
0
1
0
1
1
0
2
1
0
1
2
1
0
0
1
1
2
2
2
0
2
2
0
1
1
2
1
0
0
1
1
1
1
1
1
1
2
1
0
0
1
1
0
2
2
0
0
0
1
1
2
2
2
1
1
1
1
1
2
1
2
0
2
0
1
0
2
1
2
1
2
1
1
2
2
2
0
1
1
1
2
1
1
2
1
1
0
1
0
0
1
1
0
0
2
1
1
1
2
0
1
2
1
2
1
1
1
1
1
1
1
0
0
1
1
0
1
2
2
0
1
0
1
0
2
1
0
2
0
2
1
1
0
0
0
1
0
0
1
1
2
2
1
0
1
2
0
1
1
0
1
0
1
0
0
1
1
1
2
2
1
0
0
0
0
1
1
1
2
1
1
1
1
2
2
2
1
1
1
0
2
2
0
1
1
0
0
2
1
1
2
2
2
1
2
2
0
1
1
1
0
1
1
1
0
1
1
1
0
0
1
0
2
1
2
1
2
2
1
1
1
1
2
1
1
1
2
1
2
1
1
0
0
1
1
2
1
2
1
2
0
0
1
2
1
1
2
0
2
1
3
1
1
2
1
1
1
1
1
1
0
1
1
0
1
1
0
1
2
1
1
2
0
1
1
0
1
2
0
1
1
0
1
0
2
1
1
1
1
0
2
1
1
0
1
1
1
2
0
1
1
1
0
1
1
2
0
2
0
2
1
0
1
1
1
1
0
1
1
1
1
1
1
1
2
0
0
2
2
2
0
0
0
0
1
1
2
0
1
3
1
1
0
1
1
2
2
1
1
2
1
0
2
2
1
1
1
1
2
1
1
2
0
1
0
0
1
1
1
0
0
2
1
1
1
2
2
0
1
1
1
1
1
1
0
1
0
1
1
1
1
2
1
1
0
0
2
1
1
1
1
2
1
1
0
0
1
1
2
1
1
1
2
3
0
1
2
1
1
0
1
2
2
1
0
0
1
1
1
1
1
1
0
0
0
1
1
1
1
1
1
1
1
1
1
0
1
1
1
2
1
1
1
1
0
2
0
0
1
1
2
1
1
1
2
2
1
1
1
1
1
1
1
0
2
1
1
2
2
1
0
0
1
4
2
0
0
0
0
1
0
1
2
1
0
1
3
0
1
1
1
1
1
1
1
1
2
2
1
2
2
1
2
2
1
1
1
0
1
1
1
2
1
1
1
2
1
1
0
1
2
1
1
1
1
0
2
2
1
1
1
1
0
1
1
1
1
1
1
1
1
2
1
0
2
2
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
0
0
2
2
1
0
2
2
1
1
1
1
1
0
2
1
1
1
0
1
1
1
1
1
2
1
1
1
0
1
0
1
1
1
0
2
1
1
1
0
1
1
1
2
0
1
2
1
2
0
0
1
2
1
0
1
1
1
2
1
0
2
1
4
1
2
2
1
2
1
2
0
0
0
1
0
1
1
2
2
1
2
0
1
2
0
1
2
0
2
0
1
1
1
2
0
0
2
0
1
1
1
1
1
2
2
1
2
1
0
1
0
1
1
1
0
0
0
1
1
1
0
1
0
1
1
1
1
2
1
0
1
1
0
2
1
2
2
2
1
0
0
0
0
1
0
0
3
1
1
1
2
1
1
0
0
2
1
1
2
0
2
0
2
0
0
1
2
2
1
1
0
1
1
1
1
1
0
1
2
1
1
1
4
0
4
2
2
1
1
1
1
1
0
0
1
2
1
1
0
0
1
1
0
0
1
0
1
1
1
0
1
0
2
1
2
1
2
3
0
1
0
1
1
1
2
1
1
0
0
0
1
1
0
1
0
1
0
1
1
1
1
1
1
2
2
1
2
1
2
1
0
1
1
1
0
1
2
1
1
1
1
0
1
0
3
1
1
2
1
0
2
1
1
0
1
0
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
4
1
1
2
0
1
1
1
0
1
1
1
0
2
1
0
1
1
1
1
1
1
0
2
1
1
1
0
2
1
0
0
1
1
1
1
1
1
1
1
2
0
2
2
1
1
1
1
1
1
1
2
1
1
2
2
1
2
2
2
0
0
1
0
2
1
1
1
1
1
1
1
0
1
1
1
1
1
0
0
2
1
1
1
1
0
1
1
1
1
1
2
1
2
1
2
1
2
1
1
1
1
1
1
0
0
1
1
1
1
2
1
0
1
1
1
0
1
2
2
0
1
1
0
1
2
1
2
0
1
1
1
2
1
2
0
1
1
1
1
2
0
0
1
1
1
1
0
2
1
1
1
2
0
0
1
1
1
0
2
1
1
0
0
1
1
1
2
1
0
1
1
1
1
1
1
1
0
2
1
2
1
1
2
2
1
1
0
2
1
1
2
1
1
2
2
2
1
2
0
2
1
0
1
2
0
1
1
1
0
1
1
1
2
1
1
3
1
1
2
2
0
0
1
0
2
2
1
0
0
2
1
2
1
2
1
1
1
2
4
1
1
0
2
0
0
3
1
2
1
0
2
0
0
3
1
1
2
1
0
0
1
1
1
2
0
1
1
2
1
1
2
2
0
1
1
0
1
1
1
1
2
1
2
1
2
1
2
0
0
0
1
0
1
1
1
0
2
1
2
1
1
1
2
1
0
1
0
1
2
1
0
1
1
1
2
1
0
1
0
1
0
0
2
1
0
1
0
1
0
2
0
1
1
1
1
1
2
0
3
0
1
0
0
0
1
1
1
1
0
5
1
2
2
1
2
0
2
0
1
1
1
1
0
0
1
0
2
0
1
1
1
2
1
1
0
1
0
1
1
1
1
1
0
2
2
1
1
1
1
0
1
2
0
1
1
2
1
1
1
0
1
0
1
1
0
0
0
0
2
2
2
1
1
2
2
1
1
0
2
0
2
1
0
1
2
2
1
1
1
2
1
1
1
0
2
1
2
0
0
0
2
1
0
1
2
1
1
1
1
1
1
2
1
0
0
0
1
2
1
2
0
1
2
2
0
2
1
1
1
0
1
1
0
1
2
1
0
1
0
0
1
1
2
1
2
2
2
2
1
1
2
2
1
2
0
0
1
1
1
2
0
1
0
1
1
2
1
0
1
0
1
2
1
1
1
2
1
0
1
1
1
1
1
2
1
1
2
0
0
0
0
2
0
1
1
1
1
1
0
1
2
1
1
1
1
0
2
1
1
2
1
1
1
2
1
2
1
2
0
1
2
1
0
3
1
1
1
1
0
0
1
1
0
2
0
0
0
2
2
0
1
1
1
1
1
2
2
1
1
2
0
1
1
1
1
0
1
0
1
1
1
0
1
1
1
1
2
0
1
0
2
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
0
1
1
1
2
1
1
2
0
1
1
1
2
0
1
0
0
1
1
1
1
1
1
1
0
1
2
1
1
1
2
2
1
1
1
1
1
1
0
1
1
1
2
2
0
1
2
1
0
1
1
1
1
0
1
0
1
0
2
0
1
1
1
2
1
1
2
1
0
1
0
0
2
1
1
0
1
2
1
0
1
2
1
2
0
2
0
0
1
1
2
1
2
1
1
1
2
1
2
0
0
2
1
1
2
1
1
2
1
0
0
0
0
1
2
1
0
1
1
2
0
2
0
1
2
1
0
0
1
1
0
1
1
0
1
1
1
3
0
2
1
1
1
1
0
1
1
0
1
1
2
2
1
2
1
2
0
1
1
0
1
1
2
0
2
0
1
1
1
0
2
2
1
1
2
2
2
2
1
1
1
1
2
2
0
0
1
0
1
1
1
1
1
1
2
1
1
0
1
1
2
1
0
1
2
1
0
1
2
1
0
1
1
1
1
2
2
1
0
2
1
0
1
2
0
1
2
0
1
0
0
1
2
2
0
1
1
0
1
0
1
1
1
1
0
1
2
0
0
1
2
0
1
2
2
2
0
0
1
1
1
0
0
1
0
1
2
1
2
2
0
1
1
0
1
2
0
2
1
1
1
1
1
1
2
1
2
1
0
2
1
1
1
1
1
1
0
1
0
1
0
1
1
0
2
0
0
1
2
0
2
1
1
2
1
0
0
2
1
1
1
1
1
1
0
2
1
1
0
0
1
0
1
2
1
1
1
1
1
0
0
0
1
0
1
0
1
1
1
2
0
1
0
1
0
0
2
2
0
2
1
1
0
0
0
1
1
2
2
0
1
1
1
1
0
2
0
2
2
1
1
2
0
2
1
2
2
2
2
0
2
2
1
1
0
1
0
2
0
1
2
0
1
1
1
2
0
2
0
2
2
1
1
1
0
2
1
1
1
2
0
1
0
3
1
1
2
1
1
0
2
0
1
2
0
2
1
1
3
1
2
1
2
1
2
1
0
2
0
1
2
0
1
1
1
1
2
0
1
1
1
1
2
0
1
1
2
1
0
1
1
1
2
1
1
3
1
0
0
2
1
2
1
2
0
0
1
0
1
1
1
0
1
2
0
0
0
1
2
1
1
1
1
1
1
0
1
2
0
0
0
2
0
0
1
1
1
1
0
0
2
2
1
2
0
1
1
0
2
2
1
1
1
2
1
1
2
1
2
1
1
1
2
1
1
2
1
0
1
0
0
1
2
1
1
1
0
2
1
1
3
2
0
1
1
1
1
0
2
1
0
2
1
2
0
0
2
2
1
2
1
1
1
0
1
0
2
0
1
1
1
2
1
1
1
3
2
1
1
1
1
1
2
3
1
1
1
1
1
0
1
1
2
2
0
2
1
1
2
1
1
1
2
0
1
2
1
1
1
1
1
2
2
1
1
0
1
1
1
2
2
1
1
2
1
1
1
1
2
1
1
1
0
1
0
0
1
1
1
1
0
0
0
2
2
0
1
0
0
2
1
0
1
0
2
0
1
1
1
2
1
1
1
1
0
1
0
0
0
1
0
1
1
1
1
1
1
1
2
0
0
0
0
1
1
1
1
1
2
0
1
1
1
0
1
1
1
1
1
0
2
1
1
1
1
1
1
2
1
1
1
1
1
1
0
2
1
1
2
1
1
1
0
1
2
0
0
0
2
1
0
2
0
0
2
1
2
1
1
1
1
1
1
1
2
2
1
1
2
0
2
1
0
1
2
1
2
1
1
2
2
1
1
2
1
0
1
2
2
0
2
1
0
1
1
0
1
1
0
0
1
0
0
1
1
2
1
1
1
1
0
1
1
2
1
0
1
1
1
0
2
0
1
1
0
1
1
3
0
1
0
1
0
2
2
1
1
2
0
0
1
0
1
1
0
1
0
2
2
1
0
1
2
2
2
2
0
3
2
1
1
1
0
0
2
0
1
0
1
0
0
0
0
1
2
0
1
0
0
0
1
1
0
2
2
1
2
1
1
1
1
1
1
2
2
2
1
1
1
1
2
1
1
0
1
0
1
1
2
2
2
0
1
1
0
1
0
0
1
0
1
0
1
1
1
2
0
1
2
2
3
0
2
1
2
1
1
0
0
1
2
0
1
0
1
2
1
1
0
1
0
1
2
0
1
1
1
0
1
1
1
1
2
0
1
0
2
1
0
2
0
1
0
1
1
1
1
1
2
1
2
2
0
1
1
1
1
1
3
1
1
3
2
1
0
1
1
1
1
0
1
2
0
0
1
1
0
1
1
2
1
1
1
1
0
1
0
0
1
0
0
1
0
0
0
0
0
2
2
2
1
0
1
1
1
1
2
1
1
1
2
1
0
2
1
1
1
1
1
1
1
2
0
1
0
2
1
1
1
1
3
2
1
2
0
0
1
2
1
1
1
1
1
0
0
1
1
0
0
1
2
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
0
2
1
1
1
1
1
0
2
1
1
1
1
1
0
1
0
1
0
1
0
0
1
0
1
1
1
1
0
0
1
1
0
1
0
1
2
0
1
2
0
0
1
1
2
0
1
0
0
1
2
1
0
1
0
1
1
1
1
2
2
2
0
2
1
1
1
1
1
1
1
2
1
0
1
1
1
1
0
4
0
1
1
2
0
1
1
1
1
1
1
1
2
1
0
2
3
1
2
2
0
2
1
1
3
1
1
0
1
2
0
2
2
2
1
1
1
2
0
1
1
0
1
1
1
2
1
0
2
2
1
0
2
1
1
1
1
2
1
1
1
1
1
1
1
1
0
2
2
2
1
1
0
1
1
1
1
1
1
0
0
1
0
1
1
2
1
0
2
1
0
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
0
0
2
1
1
2
2
1
1
1
0
1
1
0
1
0
1
1
1
2
1
1
0
1
2
1
1
1
1
4
2
1
1
1
1
1
0
1
1
0
0
1
3
2
1
0
1
2
0
0
1
1
0
1
2
2
0
1
1
1
1
2
0
1
0
1
2
1
1
0
0
0
2
0
0
2
1
0
2
2
0
1
1
1
0
1
0
2
2
2
0
2
0
1
1
0
1
0
1
1
1
1
2
0
2
1
1
1
1
2
1
0
2
1
1
2
1
1
0
0
4
2
0
1
1
2
1
2
1
1
1
2
2
0
0
2
1
1
1
1
1
1
1
2
2
2
1
2
1
0
0
1
1
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
3
1
0
1
1
3
0
1
0
0
2
2
0
0
2
1
0
1
0
0
1
1
1
1
2
0
1
1
1
2
0
1
1
1
0
1
1
1
1
1
1
1
1
1
0
2
1
2
2
2
1
0
0
1
2
1
0
2
2
1
2
1
2
2
3
0
1
1
2
1
1
2
1
1
1
1
1
0
2
0
1
0
2
2
2
2
2
1
2
0
1
0
1
3
1
1
1
1
4
1
0
2
1
1
1
0
1
1
1
1
1
2
0
1
0
1
1
2
1
2
1
0
1
0
1
0
0
0
1
2
1
0
2
1
1
0
1
1
1
0
0
1
0
1
2
0
2
1
2
2
0
1
0
0
2
1
0
0
1
1
1
2
0
3
1
1
0
2
1
0
2
0
1
2
2
1
1
1
0
0
1
1
1
1
0
1
2
1
0
2
0
1
0
1
1
1
2
1
1
0
0
2
2
1
2
1
1
1
1
1
0
0
0
2
2
1
0
1
0
1
1
1
1
2
0
1
1
0
2
0
1
1
1
1
2
2
0
1
0
0
2
2
0
1
10
1
1
3
0
0
0
1
1
3
2
2
1
0
1
1
2
1
1
0
1
2
1
2
1
1
0
1
1
1
2
1
0
2
1
1
1
0
0
0
1
1
2
2
1
2
0
1
1
1
2
0
0
2
2
1
1
1
1
1
1
1
1
0
0
2
0
2
1
1
1
1
1
1
0
1
2
2
1
0
2
1
0
2
1
2
0
0
1
2
1
1
1
2
2
0
1
1
2
2
1
0
1
1
0
1
1
1
1
1
0
1
0
0
1
1
1
0
1
1
0
1
0
1
1
0
1
1
1
0
1
1
1
1
0
1
2
1
2
1
0
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
2
1
1
1
2
1
2
1
1
2
2
1
0
1
0
0
1
2
2
0
0
1
1
2
1
2
1
1
0
1
1
2
2
2
1
1
1
2
2
0
1
2
1
2
0
1
1
1
1
1
1
2
1
0
1
1
1
0
0
1
1
1
0
0
0
2
1
2
2
0
1
1
2
1
2
1
1
2
1
1
2
1
1
0
1
1
1
1
2
1
1
1
1
0
2
2
3
0
1
0
2
1
1
1
1
1
1
1
1
3
1
0
1
0
0
2
1
0
1
2
0
2
1
2
2
1
1
2
1
0
1
1
2
3
0
2
1
2
2
0
2
1
1
1
1
0
2
2
2
1
2
0
1
1
0
1
1
1
1
1
0
2
2
1
2
1
0
2
2
0
1
1
1
0
1
1
0
2
0
1
0
1
1
2
2
1
1
0
1
2
0
1
0
1
1
0
1
1
0
1
1
1
0
1
1
2
0
2
1
1
1
1
1
0
1
1
2
1
2
0
2
1
2
1
0
0
0
1
1
2
0
0
1
1
1
0
2
1
0
0
0
2
1
1
2
1
1
1
1
1
1
0
1
0
1
1
1
1
1
2
1
2
1
1
1
1
0
1
0
0
1
0
1
0
2
2
1
2
1
1
1
0
0
2
1
2
1
2
0
1
2
2
0
1
1
1
1
2
0
1
2
1
1
1
1
1
1
0
0
0
0
1
1
1
0
1
1
2
1
2
1
1
0
1
1
0
2
1
1
0
0
2
1
2
1
0
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
1
1
0
2
1
1
0
1
0
1
1
1
0
0
1
1
2
0
1
2
1
0
1
1
1
1
0
1
1
1
2
0
1
1
1
1
1
0
1
0
2
2
2
1
1
0
2
1
1
1
1
1
0
1
1
0
0
1
1
2
1
0
0
1
2
2
1
2
1
1
1
2
0
2
1
1
1
1
0
1
1
0
1
2
1
2
1
1
0
1
1
2
0
1
1
0
1
0
0
0
1
1
2
2
1
2
2
1
1
1
2
1
1
1
2
1
1
2
2
0
1
0
1
2
0
1
1
0
1
2
1
2
2
2
2
1
2
0
0
1
1
1
1
2
1
1
0
1
1
2
0
2
0
2
1
0
0
1
1
1
1
1
2
1
2
1
0
1
1
1
0
0
1
0
0
1
2
1
1
0
1
0
0
0
0
0
0
0
1
1
1
0
1
0
1
1
2
1
3
2
0
0
0
2
0
1
1
2
0
2
1
1
1
1
0
1
1
2
0
2
0
1
0
1
1
1
1
2
2
0
2
2
1
0
1
1
1
1
1
0
1
0
1
0
1
0
0
0
1
1
2
1
1
0
0
0
0
2
0
1
2
2
1
1
1
1
0
1
0
1
2
1
1
0
2
1
2
0
1
1
1
1
2
2
1
2
2
1
1
1
2
1
2
1
1
1
1
1
1
2
0
1
2
1
0
0
0
2
1
1
0
2
2
0
0
1
1
0
1
1
2
1
1
0
1
1
1
1
0
1
1
1
1
2
1
1
2
0
2
2
0
0
2
2
0
1
1
1
1
2
2
0
2
2
1
2
0
2
0
3
1
0
1
1
1
0
1
1
1
1
1
1
0
1
1
1
0
1
2
0
2
1
2
0
1
1
2
0
2
3
1
1
2
0
1
0
0
0
1
1
2
1
1
1
1
2
2
2
1
0
0
1
2
0
1
1
1
1
0
1
0
1
1
2
1
0
1
1
0
0
0
1
1
0
1
1
2
1
1
2
1
2
1
0
1
2
0
0
1
1
0
1
1
0
3
1
2
0
2
1
1
0
1
0
0
2
1
1
1
2
1
0
1
2
1
1
1
0
1
1
1
2
2
1
0
1
1
1
0
2
1
1
1
0
1
0
2
0
0
0
1
2
2
1
1
0
2
0
1
2
1
0
1
1
1
0
2
1
2
3
0
1
1
1
0
0
1
1
1
1
2
0
0
1
1
1
2
1
2
2
0
0
0
0
1
1
1
1
1
0
2
0
1
1
1
1
1
1
1
1
2
1
1
1
2
2
2
1
0
1
1
0
1
2
0
2
1
2
0
2
2
1
1
2
1
1
1
1
0
1
0
1
2
1
1
0
1
0
1
1
0
1
1
0
1
1
1
2
1
0
0
1
1
1
2
1
1
0
0
1
1
1
0
0
1
2
0
0
1
2
0
1
1
2
1
2
1
1
2
1
0
2
1
2
0
1
0
1
1
1
1
2
3
0
2
3
1
1
2
1
0
1
2
1
2
1
1
0
2
0
2
0
0
1
1
2
1
1
0
1
1
1
1
1
1
1
1
0
2
1
2
1
0
1
0
1
1
0
2
0
2
0
0
2
2
1
1
1
1
1
0
1
1
1
2
0
2
1
1
1
0
1
2
1
1
0
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
2
1
1
2
2
2
2
1
2
1
1
0
2
0
0
2
2
1
1
1
0
0
0
2
0
1
1
0
0
1
2
1
1
0
2
1
0
1
1
1
0
1
1
2
0
1
1
1
2
1
2
0
1
2
1
1
1
1
1
0
2
1
1
0
2
0
1
1
0
1
0
0
1
1
2
1
1
1
2
0
1
0
0
0
2
0
1
1
1
2
1
0
0
1
1
1
0
1
0
0
0
2
1
1
2
0
1
1
2
2
2
2
0
1
2
0
2
1
0
0
1
1
1
1
2
2
0
1
1
2
2
2
1
2
0
0
2
1
1
2
0
0
1
1
1
2
0
2
0
1
2
1
1
1
0
2
2
0
1
2
2
0
1
0
1
1
2
1
2
1
0
2
1
1
2
0
1
1
0
2
1
1
2
1
2
1
1
1
1
1
2
1
2
2
1
1
2
2
0
1
1
1
0
2
2
1
1
0
1
1
1
2
0
0
2
1
1
1
2
1
0
1
1
2
0
1
2
0
1
2
0
1
2
1
1
2
1
0
2
1
0
1
0
2
1
1
0
1
2
0
2
1
1
2
3
1
2
0
0
0
0
1
0
0
1
1
0
0
1
1
1
0
1
2
0
2
2
1
2
2
1
0
1
1
2
0
1
1
1
2
2
1
1
1
1
1
2
1
1
1
1
0
1
0
1
1
1
1
0
2
1
1
2
2
1
0
2
0
0
3
1
0
1
1
1
1
0
1
1
1
2
1
0
1
1
1
1
2
1
1
0
1
2
0
1
1
2
0
0
2
0
1
1
1
0
1
0
1
0
1
1
1
1
2
1
1
0
1
1
2
2
0
0
1
1
1
2
1
1
1
1
1
0
1
2
0
1
1
1
1
1
2
1
0
0
0
1
1
2
2
2
0
2
2
0
0
0
0
2
1
1
0
1
2
0
1
2
2
1
1
1
0
1
1
0
2
1
1
1
2
1
0
1
0
1
2
2
0
1
1
2
1
0
1
1
0
0
0
1
1
0
3
1
1
1
1
1
1
1
0
1
1
1
1
0
1
0
1
2
2
1
4
1
1
1
0
0
1
2
1
1
0
2
1
2
1
0
0
2
1
2
0
2
0
2
1
1
0
1
0
0
1
2
1
2
1
1
1
0
0
1
1
0
1
2
1
1
1
2
0
1
1
0
1
0
1
1
0
2
1
1
0
0
0
1
2
1
1
1
2
0
2
2
1
1
2
0
2
1
0
0
1
1
1
2
1
1
1
1
1
2
2
0
1
1
2
3
1
0
2
0
0
1
1
1
1
2
1
0
0
1
1
1
1
0
3
1
2
0
2
1
1
1
1
1
1
2
0
2
1
1
1
0
1
2
1
1
1
2
1
1
2
2
0
1
5
2
1
2
1
0
0
1
1
2
1
0
0
1
1
0
2
2
0
1
1
0
2
0
1
1
0
1
1
1
1
2
1
0
1
2
0
0
1
1
2
2
1
1
1
0
1
1
0
2
1
1
1
1
0
1
1
2
1
2
2
1
2
0
1
3
0
1
1
1
0
1
2
1
1
1
1
1
2
2
2
0
1
1
1
1
1
0
0
1
0
0
2
0
2
2
0
1
2
0
1
2
1
1
1
1
2
1
1
1
1
1
2
2
1
2
1
2
1
0
1
2
1
2
0
0
1
1
1
0
2
1
1
2
1
0
0
1
1
0
1
0
1
2
1
2
1
1
1
1
2
1
0
1
1
1
1
2
0
0
1
1
1
0
1
1
1
1
2
2
0
2
1
2
1
1
2
1
0
1
1
0
1
0
1
0
1
1
2
1
2
1
1
1
1
1
3
1
2
1
2
0
1
1
1
1
0
1
0
1
0
1
1
2
1
0
0
1
1
2
1
0
1
1
0
0
1
1
1
2
1
0
2
0
1
1
2
0
2
1
1
2
2
1
1
0
1
1
1
1
1
0
2
1
1
1
2
2
1
1
0
1
2
1
1
1
1
1
2
1
1
0
1
1
2
1
1
1
1
1
1
1
0
1
1
1
1
1
1
0
2
1
1
1
0
0
3
1
1
1
0
0
0
1
1
0
2
0
1
2
1
1
1
1
1
0
1
1
1
0
1
1
3
1
1
2
0
2
2
1
1
0
2
1
1
1
1
1
2
0
0
2
1
1
1
1
1
2
1
1
2
1
1
0
1
1
0
0
0
0
2
2
1
2
2
1
1
3
0
1
1
1
2
1
1
1
0
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
2
2
1
1
2
1
0
2
0
0
1
0
1
0
0
3
0
1
1
0
1
1
1
2
1
2
4
0
0
0
1
1
2
2
1
0
0
1
1
0
1
1
1
1
1
1
1
2
0
1
1
1
5
1
1
0
0
1
1
2
1
0
0
2
1
1
0
0
1
2
2
0
1
1
0
0
1
1
1
1
2
0
1
0
0
0
0
1
1
1
1
2
2
0
1
1
1
0
2
2
2
1
0
0
0
1
1
4
0
1
2
0
0
0
1
0
1
1
0
0
1
0
1
0
2
0
1
1
1
0
1
1
1
2
1
1
1
2
2
0
2
1
0
2
2
1
1
1
1
1
1
1
1
2
2
1
0
2
1
1
1
1
2
1
2
1
0
1
1
1
1
1
1
1
1
1
1
2
1
1
2
2
1
1
1
0
2
1
0
0
0
2
0
1
2
1
1
1
0
1
2
0
1
1
1
3
1
1
1
0
0
0
1
0
0
2
0
0
1
1
1
0
1
1
1
2
1
2
2
1
2
0
1
2
1
0
1
1
1
0
0
1
1
1
0
1
1
0
0
0
1
1
2
2
2
1
1
0
1
1
1
2
1
2
1
2
1
1
1
1
1
0
1
0
0
3
0
1
0
0
2
1
2
2
1
1
2
1
2
3
1
1
1
2
0
1
1
1
0
1
1
0
2
1
1
2
1
2
0
1
2
2
1
1
1
1
0
1
1
2
1
0
0
2
2
1
1
0
1
1
1
0
1
1
0
1
1
0
1
1
1
0
1
0
0
0
1
1
1
1
1
1
1
1
9
0
1
1
0
0
1
0
1
1
1
1
2
1
2
0
0
0
1
2
1
1
2
0
2
1
0
2
0
0
3
1
0
1
2
1
1
1
0
1
0
2
1
1
2
1
1
2
1
1
2
1
0
2
0
0
0
1
3
2
2
1
0
2
1
0
2
2
1
1
0
1
1
0
2
1
1
2
0
0
1
0
1
1
1
1
2
0
1
1
1
1
2
1
0
2
0
1
1
1
0
0
1
2
1
1
1
1
0
1
1
1
1
0
1
1
1
1
1
1
1
2
1
0
1
2
1
0
1
1
2
1
0
0
1
1
2
3
0
2
0
2
0
1
0
1
1
2
1
1
0
0
0
1
1
1
1
1
1
1
1
1
2
2
1
0
2
0
2
1
0
1
1
0
2
1
1
1
0
1
1
2
0
1
1
0
1
4
0
1
2
0
1
1
2
2
0
2
0
1
2
0
2
1
1
2
2
2
2
2
1
0
1
1
2
0
1
1
0
1
1
1
1
1
1
1
2
1
1
0
0
0
1
1
2
0
0
1
1
0
1
1
2
1
1
1
2
1
1
1
2
0
1
2
1
0
1
0
1
2
0
0
1
1
2
1
1
2
1
0
1
2
0
2
0
1
1
0
1
0
1
0
0
1
2
1
1
1
0
2
1
1
1
1
4
1
1
2
0
1
0
1
0
0
1
1
1
0
1
1
1
1
1
0
1
1
2
2
0
1
2
1
0
1
2
1
0
1
2
0
0
2
0
1
2
2
1
1
1
1
2
0
1
1
1
1
0
1
2
2
0
2
1
0
0
2
1
0
1
2
2
2
1
1
1
1
1
2
1
0
1
1
1
0
1
1
1
1
0
2
0
2
1
1
1
0
2
0
2
1
0
2
1
1
2
1
2
2
0
1
1
2
1
1
1
0
1
1
0
0
2
1
0
2
1
2
1
1
1
1
2
2
2
1
0
1
2
0
0
1
1
0
0
0
1
0
2
0
1
0
0
1
1
2
1
1
1
1
1
1
1
1
1
1
1
0
1
1
2
0
1
0
1
1
1
0
1
1
0
1
0
1
1
0
2
1
1
2
0
2
1
2
2
0
1
1
2
0
2
1
1
1
2
1
0
2
2
0
2
2
2
1
0
1
1
1
3
1
1
2
2
0
1
2
1
1
0
1
0
1
1
2
0
0
0
1
0
1
2
1
2
3
1
1
0
1
0
1
2
1
1
1
1
1
1
0
2
2
1
1
1
1
1
1
1
1
2
1
1
2
1
0
1
2
1
1
1
0
3
1
2
1
0
3
2
1
1
0
2
0
1
1
1
1
0
0
1
1
2
1
1
0
2
0
2
1
1
2
1
0
0
2
0
1
2
0
1
1
1
2
1
0
1
0
1
1
1
0
1
2
0
1
2
1
0
0
1
0
2
1
0
0
1
1
0
6
1
2
0
2
0
2
1
1
0
2
0
0
2
1
1
0
1
0
0
0
0
2
1
2
1
1
0
2
2
1
1
1
1
1
1
1
2
1
1
2
2
1
1
2
0
1
2
1
1
2
1
1
1
1
1
1
1
0
1
1
0
0
1
1
3
0
2
1
1
2
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
2
2
0
1
0
1
1
2
0
1
1
1
1
0
1
0
1
2
1
1
0
2
0
2
1
1
0
1
0
0
1
1
1
0
1
1
1
1
0
2
1
1
0
2
1
1
0
2
2
1
1
0
2
0
0
1
1
1
1
0
1
0
3
0
0
2
2
1
1
2
0
2
1
1
0
1
0
2
0
1
1
1
2
1
2
1
1
1
2
1
1
1
1
0
0
2
1
0
2
2
1
1
1
2
2
2
0
3
1
2
1
1
0
1
1
0
1
0
1
0
1
0
3
1
1
1
2
1
3
1
0
2
2
1
1
2
0
3
1
1
1
2
0
0
1
1
2
0
1
1
0
0
1
0
0
2
2
1
0
2
2
0
1
0
1
1
2
1
2
1
1
2
1
1
1
0
1
1
1
1
1
0
1
18
0
1
0
1
1
1
2
1
2
1
1
1
1
0
1
1
2
1
1
0
0
1
2
1
1
0
2
2
1
0
0
2
1
2
0
1
1
0
0
1
1
0
2
0
1
2
0
0
1
0
1
1
2
1
1
1
1
1
0
1
1
2
1
1
0
0
1
0
0
1
2
1
1
1
0
2
1
1
0
1
2
2
1
0
0
0
0
2
0
1
0
1
1
1
0
1
1
0
2
0
1
1
1
1
2
1
2
0
0
2
1
1
1
1
2
1
0
1
0
1
1
1
0
0
1
2
1
2
1
2
1
2
1
1
1
1
0
1
1
0
1
2
1
1
1
1
1
0
1
0
1
1
1
0
1
1
0
1
2
1
1
2
1
2
1
2
1
2
0
2
1
1
2
2
1
2
0
1
1
0
1
2
0
1
2
1
2
1
1
1
2
2
1
2
2
1
1
2
0
1
0
0
2
1
1
0
0
1
1
1
1
1
1
1
0
2
1
0
0
1
1
1
1
1
0
1
1
1
1
0
1
5
1
1
2
1
0
1
1
2
2
0
0
1
1
2
1
0
0
1
2
0
0
1
0
1
1
1
2
1
1
1
0
2
2
2
0
0
0
1
2
0
1
0
0
1
0
2
1
2
0
1
1
2
1
1
2
1
1
0
1
1
1
1
1
1
2
0
0
2
1
1
0
1
1
1
1
1
0
2
0
0
1
1
2
2
1
0
0
0
1
4
1
1
1
1
0
1
0
1
1
1
0
0
3
1
1
0
1
0
0
2
1
1
0
4
0
1
2
1
0
1
1
2
2
0
2
1
0
1
2
1
0
1
1
1
1
1
2
2
1
1
0
0
1
1
1
3
0
1
1
2
2
1
3
1
0
2
1
1
0
1
0
1
1
2
2
4
2
0
0
1
0
1
0
1
0
1
0
2
1
2
1
0
2
1
1
1
1
1
1
1
0
1
2
1
1
2
1
0
1
1
1
0
2
2
0
2
2
0
0
0
0
1
1
1
1
0
1
0
1
1
2
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
0
3
2
1
1
0
0
2
1
0
2
2
2
0
1
1
1
1
1
1
2
1
1
0
1
0
1
0
1
0
1
1
1
1
0
1
1
2
1
2
1
1
1
0
0
0
1
1
0
0
2
1
1
1
0
0
1
1
0
2
1
0
2
1
1
0
1
1
1
1
1
1
2
0
1
1
2
1
0
1
0
0
1
2
1
1
1
0
0
2
2
1
2
1
2
1
0
1
1
2
1
2
1
0
0
0
1
2
0
1
0
1
2
0
0
0
1
2
2
2
1
2
1
1
2
1
1
2
2
1
1
2
0
0
0
1
1
2
1
1
2
0
3
1
1
0
0
1
0
0
0
0
1
2
0
2
1
0
1
2
1
1
1
1
1
1
1
1
0
2
2
0
2
1
0
1
2
0
1
1
0
1
1
1
1
1
1
1
0
2
1
1
1
0
0
1
1
2
0
1
1
2
1
1
1
1
1
2
0
1
0
1
2
3
2
0
0
1
2
0
2
2
1
2
0
1
2
2
1
0
1
1
1
1
1
1
1
1
0
1
1
1
0
2
2
1
2
1
1
1
1
1
0
1
2
1
2
2
1
1
1
2
1
1
1
1
1
0
1
2
1
1
1
1
2
1
1
1
1
2
1
2
1
0
1
0
0
0
0
1
2
2
0
1
1
1
2
2
2
1
1
0
2
1
0
0
2
2
1
0
1
1
0
1
0
1
1
0
1
1
1
2
1
1
1
1
2
0
2
0
1
1
1
1
2
1
1
1
0
0
1
1
1
1
2
0
1
1
0
2
1
1
2
1
2
2
1
1
0
1
1
1
1
1
1
1
1
1
2
1
1
0
1
1
1
1
1
0
1
1
0
2
1
2
2
1
1
2
0
1
1
2
1
1
1
0
1
1
2
1
2
1
2
1
0
1
1
1
1
0
0
1
0
1
1
1
1
2
1
2
1
1
1
1
0
0
1
1
1
2
1
1
1
2
1
2
1
2
1
1
1
1
2
1
1
2
1
2
1
0
2
0
1
2
1
0
1
1
1
0
1
1
1
1
2
1
0
2
2
0
2
2
1
1
1
1
1
2
0
0
1
1
0
1
1
1
2
1
1
1
1
0
1
2
1
2
0
0
1
0
0
2
1
1
1
1
1
2
2
2
1
1
1
2
1
2
1
1
2
1
1
1
1
2
1
1
2
1
1
1
0
1
1
1
2
1
2
1
1
1
2
1
1
1
1
2
2
2
2
1
1
1
1
3
0
1
1
2
1
2
1
1
0
0
1
1
1
1
1
1
2
1
1
1
2
1
1
1
0
0
1
1
1
1
1
1
1
1
2
1
2
2
0
1
0
1
2
2
1
0
1
0
0
1
2
1
1
2
1
1
1
1
2
1
1
0
2
1
0
2
0
1
1
0
1
1
2
0
1
1
1
1
0
1
1
1
0
0
1
1
1
1
1
1
2
1
2
1
1
2
2
2
1
1
2
2
2
2
1
2
0
2
0
0
0
1
1
0
1
0
1
1
1
0
1
2
2
0
1
0
1
0
2
0
1
1
1
1
1
1
2
0
0
1
1
0
1
1
0
2
1
2
0
1
2
0
1
1
1
0
1
1
0
1
1
1
2
1
0
1
1
1
1
0
1
1
1
0
0
1
4
1
1
0
0
0
0
2
1
1
1
1
0
1
2
0
0
1
0
1
1
0
2
2
2
2
0
2
0
1
0
1
0
1
1
2
1
2
1
0
1
1
2
2
0
0
1
2
0
1
0
1
0
1
1
1
1
0
1
1
1
1
2
1
1
1
3
1
0
2
0
1
1
1
2
1
2
2
2
1
1
2
2
1
0
1
1
2
1
1
1
2
0
0
0
0
1
3
3
1
1
1
1
1
1
2
0
0
1
1
1
0
1
1
1
0
1
1
1
1
2
2
1
1
1
2
1
1
1
1
1
1
1
0
1
1
2
1
1
1
1
2
2
2
2
1
1
2
1
1
2
2
0
1
1
0
1
1
1
2
0
2
1
1
0
2
1
1
1
2
1
2
1
1
1
0
1
1
1
1
1
1
1
1
0
0
0
2
2
2
1
5
1
1
1
1
0
2
1
0
1
2
0
0
0
0
2
2
2
1
1
1
1
1
2
2
1
2
2
2
0
1
0
1
1
1
2
0
1
0
1
1
1
1
1
1
2
2
1
1
2
0
1
2
1
1
1
1
1
2
1
0
0
1
1
0
1
2
1
0
0
2
0
0
0
1
2
0
1
1
2
2
0
2
1
1
2
1
1
1
0
1
1
3
0
1
1
0
1
0
2
0
0
2
0
2
1
1
0
2
1
2
1
2
1
1
0
0
0
1
0
2
1
1
0
2
1
1
2
0
2
1
1
1
2
1
0
1
1
0
2
0
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
1
0
1
1
2
0
0
1
1
2
1
2
2
1
1
1
1
0
1
2
1
2
1
1
1
1
0
0
1
1
2
1
1
1
1
0
1
0
1
0
0
1
1
1
1
0
1
0
1
1
1
2
2
0
0
1
1
0
0
1
1
2
2
1
1
0
2
0
0
1
1
0
0
2
1
1
2
0
1
0
4
1
2
0
0
0
2
2
2
1
0
2
1
0
1
1
1
0
2
1
0
1
2
1
1
2
1
1
1
2
0
1
0
1
1
1
1
1
0
2
2
0
1
1
2
1
1
1
1
2
1
0
1
1
2
2
1
2
1
0
2
2
2
1
2
1
0
1
1
0
2
1
1
1
0
2
1
0
1
1
1
1
0
1
2
1
1
1
1
0
1
0
1
1
2
2
1
1
2
1
1
2
0
1
0
1
0
2
0
1
0
2
1
2
0
2
2
0
2
1
0
1
1
2
1
1
1
0
2
1
0
0
0
1
2
1
1
0
1
1
2
1
1
2
1
2
1
2
0
2
0
0
1
1
1
2
0
1
1
0
1
0
1
1
1
2
1
1
1
1
1
2
1
3
1
1
2
0
1
1
1
2
0
0
1
1
0
0
0
1
0
1
1
0
0
1
1
1
1
1
1
0
1
1
1
1
1
1
2
1
1
0
1
2
1
1
0
2
1
2
1
0
1
1
1
1
1
0
1
1
1
2
0
0
1
1
1
1
2
1
1
2
1
0
1
1
0
0
3
1
1
1
1
1
0
1
1
2
1
1
2
1
1
2
1
2
0
1
1
2
2
0
0
1
2
1
2
1
2
1
2
1
1
0
0
1
1
1
1
1
0
1
1
2
0
0
0
2
1
0
1
0
1
0
1
1
1
2
1
0
2
2
1
0
0
0
0
0
0
0
1
0
1
0
2
1
2
2
0
1
1
1
1
1
2
0
1
2
1
1
2
1
1
0
1
1
2
1
1
1
1
0
2
1
1
0
2
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
3
2
1
1
1
0
2
0
1
0
1
0
2
0
0
0
1
2
0
1
0
1
1
4
0
1
1
1
0
1
0
0
2
1
1
0
0
1
2
1
1
1
1
2
2
2
1
0
2
1
1
2
1
0
0
1
1
1
1
1
2
1
1
1
1
1
0
1
1
1
1
2
1
2
1
1
1
1
1
1
1
0
1
2
2
0
2
2
2
2
1
0
1
0
1
0
3
0
1
1
1
1
1
1
0
1
1
2
1
1
0
2
0
1
1
2
2
0
1
1
2
2
0
1
1
2
0
1
0
1
2
1
0
1
0
2
2
2
1
0
1
1
0
2
2
1
2
1
1
1
1
1
1
1
2
0
1
2
1
2
1
0
0
1
0
1
0
1
6
1
1
1
1
1
1
1
3
1
2
1
0
0
0
0
1
2
1
0
0
1
2
2
1
1
2
1
1
2
1
1
3
0
1
1
0
0
0
1
0
2
1
1
1
1
0
0
2
2
2
2
1
0
1
1
2
0
1
0
1
0
1
1
1
0
1
1
1
1
1
0
0
2
0
1
1
1
1
1
1
1
1
0
0
1
3
1
0
1
1
1
1
1
0
2
2
1
1
2
0
1
2
2
0
2
1
1
1
0
2
1
2
0
1
1
1
2
0
2
1
0
1
0
1
2
1
1
0
1
1
2
1
0
1
1
1
0
2
2
1
2
1
1
2
2
2
2
0
1
1
0
2
1
1
0
1
1
1
1
0
1
2
0
1
1
2
1
0
0
1
0
1
0
0
2
2
1
2
0
1
1
0
1
1
1
1
0
1
3
0
0
1
0
2
0
2
2
1
0
2
0
0
1
1
0
1
1
2
1
2
1
2
1
2
0
0
1
1
1
2
1
1
2
2
2
1
1
1
2
2
1
1
1
1
1
1
1
0
2
1
0
2
1
0
0
0
2
0
1
1
2
1
2
0
1
1
0
1
1
2
1
0
1
1
0
1
0
0
0
1
1
2
1
2
1
1
1
0
1
0
2
1
0
1
2
0
1
1
1
2
0
2
2
2
2
1
0
1
2
0
0
1
1
0
2
1
2
0
1
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
0
1
0
1
1
1
0
2
0
1
2
2
1
1
0
0
2
1
0
1
2
0
4
0
2
1
1
1
1
0
0
0
0
1
2
2
2
0
2
0
2
2
1
0
1
0
1
0
1
2
0
0
0
2
0
1
1
1
1
1
0
0
2
0
0
1
1
1
1
1
2
0
1
1
2
2
1
0
0
0
2
1
1
1
1
1
2
0
2
1
1
1
2
1
1
2
1
2
1
1
0
1
2
2
1
1
1
0
2
1
1
1
1
1
1
1
0
1
2
1
2
2
1
1
2
1
1
2
1
0
1
1
2
1
2
1
1
2
1
0
2
0
1
0
2
2
0
1
1
2
1
1
1
0
2
0
1
1
0
1
1
1
0
0
2
1
1
1
1
0
2
0
1
1
1
1
2
1
1
1
1
1
1
1
0
1
1
1
0
3
1
1
1
1
0
0
2
2
2
0
0
1
1
1
0
2
0
1
2
1
1
1
1
2
1
1
0
0
1
1
1
2
1
0
1
1
1
1
2
0
3
1
1
1
2
1
1
1
1
1
0
1
1
1
1
2
0
0
1
0
1
1
1
1
2
2
0
0
0
0
0
0
1
1
0
1
2
1
2
1
2
2
1
1
1
2
1
2
1
2
2
2
1
1
1
1
1
0
1
1
0
1
1
0
1
1
0
1
1
1
1
0
2
0
1
1
1
1
0
1
0
2
2
1
1
0
1
0
2
1
0
1
1
1
0
2
1
1
1
0
1
1
1
1
1
0
1
1
1
0
2
0
1
0
2
1
0
1
0
1
1
0
1
1
1
1
0
1
1
1
1
1
1
1
1
0
1
1
1
0
1
1
1
2
0
2
2
1
1
1
2
0
0
0
1
2
1
1
2
2
1
2
1
1
1
1
0
1
1
2
0
0
2
1
1
1
1
1
3
0
1
0
0
1
1
1
0
1
1
1
1
1
1
1
2
0
0
1
2
2
0
1
1
0
1
1
0
0
1
1
1
0
1
2
2
1
1
1
0
1
1
1
1
1
2
1
1
2
1
1
1
2
1
2
0
2
0
2
3
0
1
1
2
0
1
2
1
1
1
2
1
0
2
1
1
2
1
0
2
1
2
2
1
0
2
1
0
1
1
2
1
2
0
1
1
1
1
1
0
0
2
0
0
1
1
2
1
1
1
0
2
0
1
0
1
1
2
0
0
1
1
0
0
1
1
0
0
0
0
2
1
0
1
1
1
0
1
1
0
1
1
0
1
1
2
1
0
2
1
1
1
1
2
2
1
3
1
2
1
2
1
3
1
2
2
0
0
2
2
0
1
1
1
0
1
1
1
2
1
2
1
1
0
1
2
1
1
1
1
1
1
0
2
0
0
2
2
0
1
1
0
0
1
1
1
1
2
1
0
1
2
2
0
2
1
1
2
2
1
0
1
1
0
2
1
1
1
2
0
1
0
1
1
1
1
1
0
1
0
0
0
1
1
1
1
1
1
1
0
2
1
0
1
1
1
1
2
1
1
1
2
0
0
2
0
1
2
1
0
2
1
1
2
1
0
1
1
1
1
2
2
1
0
0
1
2
0
1
1
1
2
1
1
1
1
1
1
2
1
4
1
1
1
0
1
0
2
2
0
2
0
0
1
0
1
2
2
2
1
1
1
1
1
1
1
1
0
1
1
0
0
1
0
1
1
1
1
1
2
1
2
2
1
1
3
0
1
1
1
2
0
2
2
1
1
2
1
1
0
2
2
1
1
1
1
1
1
2
1
1
1
2
2
0
1
0
0
0
2
1
2
2
0
1
1
1
1
1
0
1
1
1
0
1
1
2
2
2
1
1
2
1
1
2
1
1
1
1
1
1
1
3
0
1
1
1
0
1
0
2
0
1
1
0
2
1
2
1
2
1
0
2
0
0
0
1
0
0
0
1
0
1
1
1
0
1
1
2
1
1
0
0
0
1
1
0
1
2
0
1
0
1
1
1
0
2
0
0
2
1
0
2
1
1
2
2
2
1
1
1
0
0
1
1
1
0
0
1
1
1
1
0
1
0
1
1
0
1
2
2
2
2
0
2
0
2
1
1
1
1
2
2
1
2
1
1
0
0
2
0
1
1
1
2
2
0
2
1
1
1
2
0
1
1
1
2
1
1
1
2
1
1
2
1
0
1
1
1
1
2
1
1
1
1
2
0
4
0
1
1
1
1
0
2
1
1
2
1
2
2
0
1
2
1
1
2
0
1
0
2
1
0
1
1
1
1
1
2
1
2
0
1
1
0
1
2
2
0
2
1
0
2
2
0
1
1
2
1
2
0
1
1
1
1
1
1
1
2
2
0
0
1
1
2
1
1
1
1
2
2
1
0
2
1
2
1
2
1
1
1
1
1
1
2
1
1
1
0
0
1
0
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
2
1
1
0
2
1
1
1
2
1
0
1
0
1
1
1
2
1
1
1
2
2
1
1
1
0
1
2
1
1
2
1
0
2
1
1
1
2
1
1
1
0
2
0
2
1
1
2
1
1
0
1
1
0
1
1
1
0
2
0
2
1
0
1
1
0
1
1
1
1
0
2
1
1
1
2
0
1
1
1
0
2
0
2
1
0
2
0
0
2
0
1
1
1
1
0
0
0
1
2
1
0
1
1
1
1
1
2
2
2
1
1
1
1
1
2
1
0
1
1
0
1
0
1
1
1
0
2
0
0
1
0
0
2
1
1
1
0
0
0
0
0
0
1
1
2
1
2
1
2
2
0
1
1
1
0
1
0
1
0
1
0
1
0
1
0
0
0
1
0
1
1
0
2
1
0
1
2
2
2
1
1
1
2
0
1
0
1
0
1
1
1
1
1
1
1
1
1
2
1
1
3
2
1
0
1
0
2
2
1
1
1
1
1
2
0
1
1
3
1
1
3
2
0
1
1
0
1
2
0
0
2
1
1
2
1
1
1
1
1
1
0
2
1
0
1
1
1
2
2
1
2
2
1
1
1
2
1
0
2
0
0
2
1
2
2
1
0
1
1
2
1
0
0
1
0
0
0
1
2
1
1
1
1
1
1
2
0
1
1
1
0
1
1
1
1
1
1
1
1
0
1
1
2
1
1
0
0
4
1
1
0
0
2
1
2
1
1
2
2
0
0
1
0
0
0
2
1
1
1
2
1
1
0
2
0
1
2
0
1
0
1
1
1
1
2
1
0
1
1
1
0
0
1
1
1
2
1
1
0
2
0
1
0
2
0
1
1
2
0
2
1
1
1
1
1
0
0
0
1
1
0
1
0
0
1
1
2
0
1
0
0
1
0
2
0
1
0
0
2
0
1
0
1
1
2
1
2
2
2
1
0
1
1
0
1
2
1
2
1
1
1
0
2
0
2
2
1
1
1
0
0
0
0
0
1
0
2
1
1
2
1
1
1
0
1
1
1
1
0
1
1
1
1
2
1
1
0
1
1
1
1
1
1
1
1
0
2
1
2
1
1
2
2
2
1
0
2
1
1
1
0
1
0
0
1
1
0
0
1
2
1
0
1
0
0
2
1
0
1
1
1
0
1
1
1
0
1
2
1
0
0
0
0
1
0
2
0
1
1
1
2
1
1
1
1
1
1
2
2
0
0
1
0
2
0
2
0
2
1
1
1
2
1
0
1
1
2
1
1
2
0
1
0
1
1
0
0
1
0
1
2
1
1
0
1
1
0
0
0
2
2
1
1
2
0
2
1
1
1
1
1
0
0
1
1
1
1
2
2
1
2
0
2
2
1
2
0
1
0
1
1
1
4
1
1
0
2
1
0
2
2
1
0
2
0
1
1
1
2
2
2
2
2
1
1
2
1
1
0
1
0
2
1
2
1
1
0
0
1
0
0
0
1
2
2
1
1
4
1
2
0
1
1
1
1
0
0
2
2
0
0
3
4
0
1
2
0
1
1
1
1
0
2
1
1
1
1
1
1
3
1
0
1
0
1
0
1
1
1
1
1
1
1
0
0
1
1
1
1
1
1
1
0
2
2
1
1
1
1
0
0
1
1
2
1
1
1
2
0
1
1
1
2
1
1
0
0
0
2
2
1
1
1
0
1
1
0
1
1
0
0
1
1
0
1
1
2
0
0
1
0
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
0
1
1
1
0
0
1
0
1
1
1
0
1
0
2
0
2
1
1
2
1
1
1
2
2
1
0
1
1
1
0
2
1
0
0
1
1
1
2
2
0
0
2
1
2
0
0
0
2
1
1
0
2
1
0
1
1
2
0
1
2
0
2
1
1
0
1
2
1
1
2
1
2
1
0
1
0
1
1
1
1
1
1
1
2
2
1
0
2
2
1
1
1
2
1
2
1
2
1
0
0
0
1
1
1
1
0
0
2
1
1
1
2
2
0
1
0
1
3
2
1
1
2
2
0
1
2
1
0
1
2
0
2
0
1
2
0
2
1
1
1
2
2
1
2
1
2
1
1
1
1
1
1
0
2
0
1
2
1
4
0
1
1
0
1
0
2
1
2
1
1
0
2
2
0
1
1
2
1
1
2
1
2
0
0
0
2
0
1
1
2
1
1
1
2
0
1
0
1
0
1
2
1
1
1
2
1
1
1
0
2
1
2
2
1
1
1
1
2
0
2
1
1
0
1
2
2
2
0
1
0
2
0
1
2
0
1
1
2
0
1
3
0
0
2
1
1
2
1
1
2
1
0
1
0
1
1
1
1
1
1
2
0
2
1
0
0
3
1
2
1
1
1
2
2
0
0
1
1
2
1
1
2
0
1
1
1
0
1
0
1
0
2
0
2
2
0
2
2
1
2
2
1
1
2
0
2
1
0
0
1
2
1
2
2
2
1
1
1
1
1
1
1
0
1
2
0
0
1
1
1
1
0
2
2
1
2
1
2
2
1
2
0
1
1
2
2
1
1
1
1
0
1
2
2
1
1
1
3
1
2
1
0
1
1
1
1
1
1
1
1
2
2
0
1
1
1
1
2
0
1
2
1
2
2
1
1
1
1
2
3
0
1
0
0
0
1
1
1
1
1
0
0
1
1
1
1
1
1
2
1
1
1
1
0
1
1
2
1
0
0
0
2
2
1
0
1
0
0
2
1
1
2
0
1
2
0
2
1
2
1
1
1
1
0
1
1
1
2
0
2
2
0
3
1
1
0
1
0
0
1
1
1
1
1
2
2
2
0
2
2
0
0
1
1
2
0
2
1
0
1
1
1
3
0
2
1
1
0
2
0
1
2
1
1
1
0
0
0
3
2
1
1
1
1
1
0
1
0
0
1
2
0
1
0
1
2
1
2
0
2
1
1
1
2
0
2
2
2
2
2
0
2
1
1
2
1
1
2
1
0
0
2
2
0
0
1
2
1
1
1
0
1
1
1
1
2
2
1
1
0
0
1
1
2
1
1
0
1
1
1
2
1
1
1
1
0
0
1
2
0
0
2
1
0
1
1
2
0
1
0
1
2
2
1
3
1
0
1
2
1
0
1
1
0
0
1
0
0
2
2
1
1
0
1
0
1
1
1
1
1
1
0
1
1
1
1
2
2
2
1
2
0
2
0
1
1
1
1
1
2
1
1
1
0
2
2
1
1
1
1
2
1
1
0
1
1
1
2
2
0
1
0
1
1
1
2
2
0
1
1
0
1
1
1
1
1
2
2
0
0
0
1
1
1
2
1
1
0
1
1
1
0
1
0
1
2
2
2
0
1
2
0
2
0
2
1
1
2
1
0
2
1
0
1
0
1
0
0
0
1
1
1
1
2
1
1
1
1
2
2
1
1
1
1
2
0
1
2
1
1
1
1
0
1
1
0
0
0
1
2
2
0
1
0
1
0
1
1
1
0
1
1
2
1
0
2
1
1
0
1
2
0
2
0
1
0
2
0
1
0
1
3
1
0
2
0
0
1
2
2
0
1
1
2
2
2
1
1
2
1
0
2
2
1
2
1
2
1
0
1
0
0
2
0
1
1
2
2
0
0
1
2
2
1
1
1
0
2
0
2
2
1
1
1
2
1
2
2
0
1
2
1
0
0
1
0
0
1
0
1
1
1
1
2
2
2
1
0
1
2
1
1
1
2
0
2
2
1
2
1
1
2
1
2
1
1
1
0
2
1
1
2
1
2
1
1
2
0
1
0
3
1
1
0
1
1
1
0
1
0
0
1
0
0
1
2
1
0
1
2
2
2
1
1
0
1
2
1
1
1
1
1
1
0
2
1
1
1
1
1
1
1
1
2
1
1
1
1
0
0
0
0
1
3
0
0
0
2
2
1
1
1
0
0
0
1
1
1
2
0
1
2
0
2
2
2
2
0
1
0
0
1
0
1
1
1
1
0
0
0
1
2
1
2
1
1
1
1
1
1
2
0
0
0
1
1
1
1
0
1
1
1
0
0
0
0
0
1
0
1
1
1
1
1
1
2
1
1
2
1
2
1
1
2
2
1
1
2
2
1
2
1
0
2
1
0
0
1
1
1
0
2
1
1
1
0
2
0
1
1
0
1
1
3
1
2
1
0
1
1
0
0
1
0
0
2
0
1
2
0
0
0
1
2
0
2
0
1
1
1
2
2
0
1
1
1
2
0
2
0
1
2
1
1
1
0
0
2
2
0
2
1
0
0
1
0
0
2
1
1
0
0
0
1
2
1
0
2
1
0
1
0
1
1
1
0
1
1
1
1
0
1
1
2
0
1
0
0
2
1
1
1
1
1
2
1
1
1
1
1
0
1
2
1
1
2
0
2
0
1
1
1
2
1
1
0
1
0
1
2
0
1
1
1
1
1
1
1
2
2
1
1
1
0
1
0
1
1
1
1
1
1
2
1
1
0
1
2
1
1
0
1
0
1
1
1
1
1
1
1
1
1
0
0
1
1
1
1
1
1
0
1
1
1
0
1
2
1
1
1
0
1
2
1
2
0
1
2
1
0
1
1
2
2
0
2
2
2
0
0
1
1
0
1
3
1
1
1
2
1
2
0
2
3
2
1
0
1
1
1
0
1
1
2
0
1
2
2
2
1
1
2
1
2
1
1
1
1
1
1
0
1
0
2
1
2
0
1
1
2
2
2
1
0
0
1
2
1
0
2
1
1
1
0
1
4
1
1
1
1
4
0
1
0
1
1
1
1
2
1
0
1
1
2
1
1
1
1
0
2
2
1
1
0
1
1
2
1
1
1
1
2
1
1
2
2
0
2
1
1
1
0
1
1
2
2
1
1
0
1
2
1
1
0
2
1
1
1
0
0
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
0
0
1
0
1
0
1
1
2
0
2
1
1
0
0
2
0
1
1
1
2
0
1
1
1
1
1
1
1
1
1
1
1
0
1
1
0
0
2
1
1
0
1
1
2
1
1
1
1
1
0
4
0
0
1
1
1
0
1
0
1
0
1
1
2
1
1
1
1
2
0
1
1
1
2
1
0
0
1
1
0
1
1
2
1
1
2
1
2
2
2
1
2
1
1
1
1
1
0
0
1
1
1
1
1
0
0
1
0
2
1
1
0
1
2
1
1
1
1
1
0
0
0
1
2
1
1
1
0
1
1
1
1
1
1
1
2
1
1
1
1
0
1
2
1
0
2
1
1
1
1
1
0
2
2
1
2
1
2
0
2
1
1
0
1
1
1
0
2
1
0
0
1
0
0
1
1
0
1
1
1
1
1
2
1
1
1
1
2
0
0
0
1
1
1
2
1
2
1
1
2
1
0
1
0
1
0
2
1
1
0
1
0
0
1
2
2
1
0
0
2
1
2
0
0
0
1
2
3
1
2
1
0
1
1
0
2
2
1
2
2
2
0
2
2
1
0
1
1
1
1
1
0
1
2
0
1
0
1
1
0
1
2
1
2
2
1
2
1
0
1
0
1
1
1
1
1
3
1
0
3
1
1
1
1
2
1
0
1
1
1
1
1
3
1
1
2
2
0
1
0
2
2
1
1
1
2
0
2
0
2
1
0
1
1
2
1
0
1
1
1
2
1
1
0
0
2
0
1
1
0
1
1
1
0
2
0
1
2
0
1
1
0
1
1
1
1
1
1
1
0
2
1
2
2
1
1
1
1
1
1
1
2
1
0
2
2
1
1
2
2
1
1
1
2
2
0
1
0
1
0
1
3
0
2
0
2
2
3
1
0
5
0
0
2
1
1
1
2
0
1
1
2
1
0
1
1
1
1
2
1
2
1
1
1
0
2
2
1
1
1
1
1
0
2
2
2
0
0
1
1
1
1
0
1
1
0
0
2
0
0
2
0
0
1
2
1
0
2
1
0
2
1
1
1
1
1
1
1
1
2
1
2
0
2
1
2
1
0
1
1
1
1
1
1
1
1
0
2
2
2
1
1
2
1
0
0
0
1
1
1
0
0
1
0
0
1
0
0
0
0
2
1
1
0
1
2
2
1
1
1
2
0
0
1
2
0
0
2
2
1
1
3
1
0
0
1
1
0
1
1
1
2
1
1
0
1
1
1
1
1
0
1
0
1
1
1
1
1
0
1
1
1
0
1
1
2
1
0
1
0
2
0
1
1
0
1
0
2
0
1
1
2
2
1
2
1
2
2
1
0
3
1
1
0
1
1
1
1
0
1
0
1
2
1
0
1
1
1
2
1
1
0
1
2
1
0
1
2
1
1
1
1
0
1
0
1
1
1
0
1
0
1
1
1
1
0
1
2
2
0
1
1
0
2
1
1
1
0
0
1
1
2
0
1
1
1
1
1
2
1
0
1
1
1
1
2
0
0
2
2
2
0
1
0
2
1
1
1
3
0
1
0
1
1
2
1
1
1
2
0
1
1
0
0
2
0
1
0
1
0
2
2
0
2
2
1
1
1
1
2
1
1
1
0
2
0
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
4
1
1
1
2
0
0
1
0
2
1
0
0
0
0
2
1
0
2
0
1
2
1
1
1
0
1
2
0
1
0
1
1
1
0
1
1
1
3
1
1
2
0
1
1
2
2
2
2
0
2
0
1
1
1
1
2
1
1
2
0
1
2
0
1
1
2
1
0
1
1
1
0
0
2
1
1
2
1
2
2
0
1
0
1
0
1
2
1
1
2
2
1
1
1
1
1
0
1
1
0
3
0
1
1
0
2
0
0
0
1
1
2
1
1
2
1
2
1
1
2
0
1
1
1
1
1
0
1
1
0
4
0
0
1
1
1
1
1
0
1
0
1
1
1
0
1
1
1
0
0
0
2
1
2
0
0
0
1
1
1
1
1
1
1
1
0
1
1
1
1
0
1
1
2
2
1
2
1
3
1
0
1
0
1
1
1
2
1
2
1
0
2
1
1
0
2
1
1
2
0
1
1
2
2
1
0
0
2
0
1
2
0
1
1
0
2
1
2
1
1
0
1
1
1
0
2
1
0
1
0
0
1
1
1
1
2
1
1
0
2
2
1
0
1
2
1
2
2
0
0
1
2
0
1
1
1
0
1
1
1
2
1
1
1
1
2
1
1
0
2
1
0
0
1
0
1
1
0
1
2
0
1
1
1
1
2
1
1
1
1
1
1
1
1
2
0
0
1
0
1
2
0
1
1
0
1
2
0
1
1
1
2
2
1
0
0
1
1
1
1
2
0
1
1
2
1
2
1
0
1
1
1
1
1
1
0
2
1
0
3
2
0
0
1
1
2
0
2
1
1
2
1
2
2
1
1
0
0
1
2
1
0
1
0
0
1
2
0
2
2
2
1
1
2
1
2
0
1
0
1
0
2
0
1
1
1
1
2
1
1
1
4
0
0
1
1
0
1
1
1
0
1
0
1
0
2
0
1
1
1
0
1
2
1
1
1
0
2
0
2
1
1
0
2
0
1
1
2
2
0
2
1
1
1
2
1
1
1
0
1
1
1
0
0
1
2
1
1
0
2
1
1
1
2
2
3
1
1
2
1
0
3
0
0
1
1
3
1
1
2
2
1
1
2
1
0
1
1
1
1
1
1
2
2
1
1
1
0
1
1
0
2
0
1
1
0
1
1
0
1
1
2
2
1
2
1
2
2
1
3
1
1
2
2
2
0
0
0
2
0
1
2
2
1
0
2
0
1
1
1
1
1
1
0
1
2
1
0
0
1
1
1
0
1
1
1
1
1
1
0
0
3
2
0
0
0
2
1
0
0
0
2
2
1
1
2
1
1
2
1
1
1
1
3
1
0
1
0
1
1
2
1
2
1
0
1
0
1
1
1
1
0
1
1
0
1
2
2
0
1
0
1
1
1
1
1
1
2
0
1
0
0
0
1
1
1
1
1
1
1
1
2
2
0
1
0
1
1
2
2
0
0
2
2
2
1
2
1
1
1
0
1
1
0
1
1
0
0
2
1
1
2
1
0
1
3
1
1
1
2
2
1
0
2
1
0
0
0
1
1
1
0
1
2
1
0
0
0
1
1
0
1
1
1
1
1
1
1
0
0
2
1
1
2
1
0
1
1
2
0
2
1
0
2
0
2
1
2
1
0
0
1
1
0
1
1
1
1
0
1
2
1
0
1
2
2
4
2
1
1
1
2
1
0
1
1
0
2
1
3
1
2
1
2
0
2
0
1
1
1
1
1
1
0
0
0
2
1
0
1
0
2
1
1
1
1
2
1
0
1
1
1
1
1
1
1
1
0
1
2
1
1
1
1
1
1
1
1
0
0
2
3
2
2
1
0
1
1
3
0
1
1
0
1
2
1
2
0
2
1
1
0
1
1
1
1
1
1
1
0
1
1
1
1
0
1
1
1
0
1
1
0
1
0
1
1
0
0
1
0
0
1
2
1
2
1
1
2
1
1
0
1
1
2
1
2
2
3
1
2
1
0
1
1
2
0
1
1
1
1
2
2
0
2
0
2
1
2
1
1
1
2
1
1
1
1
0
1
0
2
0
0
1
1
2
1
0
1
1
2
2
2
1
0
2
1
0
0
1
0
1
0
1
1
1
1
1
1
2
2
0
0
2
1
2
1
1
0
1
0
0
2
0
1
1
0
1
0
1
0
2
1
2
1
1
2
0
0
2
1
1
1
0
2
2
1
2
0
0
1
1
1
1
2
1
1
0
1
1
1
1
1
1
0
1
2
1
1
3
2
2
1
1
1
1
1
1
1
1
2
1
1
1
1
2
0
1
1
2
0
0
0
0
0
1
0
0
2
2
1
1
1
1
1
2
0
1
1
1
1
1
2
1
1
1
1
0
2
1
2
1
0
1
1
0
1
1
1
2
1
2
2
1
1
1
0
1
1
1
2
1
2
2
2
1
1
0
1
1
0
2
1
2
2
2
0
1
1
1
1
1
2
0
2
2
1
0
1
1
0
1
0
0
0
0
1
1
1
0
1
2
2
2
1
0
0
0
2
2
1
1
2
2
2
2
0
1
1
1
1
1
1
0
0
2
1
2
0
2
2
1
0
1
0
0
1
0
2
2
1
1
1
1
1
0
1
1
1
1
2
1
2
1
2
2
0
1
2
1
0
1
1
1
0
0
1
1
1
1
1
1
2
1
2
0
2
1
1
0
2
1
2
0
1
0
1
0
1
2
2
0
2
0
1
0
2
1
2
0
1
2
1
1
0
1
1
1
1
1
1
2
0
1
1
1
0
2
1
2
0
2
2
0
2
1
1
2
1
2
1
2
0
2
2
1
0
1
1
2
0
1
1
1
2
1
2
1
1
2
1
2
1
1
1
1
0
1
2
0
0
1
1
1
2
1
0
0
1
0
2
1
1
0
0
0
1
1
2
2
1
0
2
2
2
1
2
1
1
0
1
1
2
1
1
0
1
1
1
0
0
1
2
1
0
1
1
0
2
0
0
2
1
1
1
1
2
2
1
1
0
1
2
0
1
0
0
0
1
1
1
1
1
1
0
1
1
2
1
0
2
1
1
1
1
0
2
0
1
1
2
1
1
2
0
0
1
1
0
1
2
1
0
0
2
1
1
2
1
1
1
1
1
0
1
2
0
1
2
0
1
1
1
1
0
2
2
2
1
0
1
0
0
2
0
1
1
1
1
0
1
1
1
1
2
1
0
1
0
1
0
2
0
1
2
1
1
1
2
1
1
0
0
0
1
1
0
0
1
1
1
2
1
1
2
1
1
2
0
1
1
1
2
1
2
1
1
2
1
0
2
0
1
1
0
0
2
2
0
0
1
1
1
0
1
2
0
0
2
1
1
0
2
1
0
2
1
2
1
1
2
0
1
2
1
1
2
1
1
2
1
1
1
1
1
1
1
0
1
2
1
1
1
1
0
1
1
0
1
1
1
1
2
0
1
1
1
2
2
1
1
0
2
1
1
1
0
1
0
1
0
1
1
1
1
2
1
2
0
3
0
1
1
1
1
1
0
1
1
0
1
1
0
2
1
1
1
0
0
0
2
0
1
0
1
1
2
1
0
0
2
3
1
1
0
0
0
2
1
0
0
1
0
2
0
1
1
1
0
1
1
1
2
1
0
0
1
0
1
1
2
2
2
1
2
1
0
1
2
0
1
0
1
1
2
0
1
1
1
1
2
1
1
1
1
2
1
1
0
0
1
2
1
3
1
1
2
0
1
1
2
0
3
1
2
0
2
1
3
2
2
2
2
2
0
1
2
2
1
2
1
0
2
1
2
2
0
2
1
2
1
1
2
1
1
1
1
1
0
1
0
1
1
1
1
1
0
1
1
2
1
1
1
0
1
0
1
2
2
0
1
0
0
1
1
2
1
0
2
1
1
2
1
0
2
1
2
1
1
2
0
0
0
1
2
1
0
1
1
0
2
1
0
0
1
1
1
2
1
0
2
1
2
1
0
1
0
1
1
0
2
0
2
0
0
1
1
1
2
1
0
0
1
0
2
0
1
0
1
2
1
0
2
1
2
1
1
1
2
0
0
0
2
1
0
1
2
0
1
1
2
1
0
2
1
0
0
2
1
1
2
0
1
1
2
1
0
1
1
1
2
2
0
1
0
0
0
2
1
1
0
2
2
2
1
2
1
1
1
0
1
1
1
1
0
2
2
1
1
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
3
0
0
0
0
1
2
1
1
0
3
0
1
2
1
0
1
1
1
1
1
0
2
0
0
0
1
0
0
0
0
1
0
0
2
0
0
2
0
1
1
1
1
1
2
2
0
1
2
1
0
2
1
1
1
2
1
1
1
0
2
1
1
1
2
1
0
0
1
1
2
2
1
1
1
0
0
0
0
1
1
0
1
0
0
1
1
2
1
1
0
1
1
1
1
1
0
0
1
1
2
1
1
0
1
0
2
0
2
2
2
1
0
1
1
0
1
1
0
2
1
2
2
2
2
0
1
1
0
1
1
1
1
2
0
2
1
2
2
1
0
0
0
3
1
1
1
1
1
1
1
0
1
1
2
1
1
0
0
2
2
2
1
1
1
0
0
1
0
1
1
1
0
0
0
0
0
0
1
1
0
1
1
0
0
2
1
1
0
0
1
1
0
1
1
1
2
1
2
1
1
2
0
1
0
2
1
1
0
0
1
2
2
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
0
1
1
1
2
1
0
0
2
2
1
1
1
1
0
0
1
1
0
1
1
0
2
1
2
1
0
1
1
1
4
1
2
1
2
1
1
1
0
0
0
1
1
1
1
1
1
1
1
1
0
1
3
1
1
2
2
1
1
2
0
0
1
1
0
0
1
2
0
1
2
1
0
0
0
1
1
1
0
2
2
1
2
0
2
2
1
1
1
1
1
1
0
1
2
1
0
0
1
2
0
2
0
1
0
1
1
0
1
0
2
2
2
1
1
2
2
1
1
2
1
1
2
0
2
1
1
1
1
1
1
2
3
1
1
1
2
1
1
1
0
0
1
1
1
1
1
0
0
1
1
1
0
2
2
0
1
1
1
0
1
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
0
1
1
2
1
1
1
0
2
0
1
0
2
1
1
0
1
2
0
2
1
1
2
2
1
1
1
0
1
0
3
1
1
1
1
0
1
2
1
1
2
2
2
0
0
2
1
1
1
1
1
1
2
1
1
2
0
1
1
2
1
1
0
1
0
0
0
0
2
0
1
1
1
0
1
1
0
1
2
1
1
0
1
2
1
1
2
0
1
1
1
1
0
0
0
1
1
1
2
1
1
2
0
0
2
1
1
1
1
1
1
0
0
2
2
1
1
2
2
1
0
2
0
0
2
1
1
2
0
1
0
1
2
0
0
1
1
0
1
1
2
1
2
1
0
1
2
1
2
2
0
1
0
1
1
2
1
2
2
0
2
1
0
0
1
0
1
1
0
1
2
1
2
2
1
1
1
2
0
1
1
1
1
0
2
1
1
1
0
2
2
0
0
0
2
1
0
0
1
1
2
1
1
1
1
1
2
0
1
1
1
1
1
2
2
1
1
0
0
1
1
2
0
2
1
1
1
2
1
1
0
0
2
1
2
0
1
1
1
1
1
2
1
2
0
1
1
1
2
1
1
1
2
1
1
2
1
1
2
2
1
0
2
1
0
0
1
1
1
1
1
1
1
0
0
2
1
1
0
1
2
2
1
1
1
1
0
1
1
1
1
2
1
0
1
1
1
2
1
1
1
2
1
0
1
1
0
1
1
2
0
1
1
1
1
2
0
1
2
1
1
2
2
2
1
1
2
2
2
0
1
1
1
1
1
1
0
1
1
1
0
1
1
0
0
2
3
1
1
0
0
0
2
0
1
0
1
1
2
1
0
1
1
1
0
1
2
1
0
2
1
2
1
0
2
0
0
2
1
2
1
2
2
2
1
0
1
1
2
1
1
1
0
0
1
2
1
0
0
0
2
1
1
1
0
1
1
0
1
0
1
1
1
2
2
1
0
0
1
1
1
1
0
0
1
1
0
1
1
1
1
1
1
1
0
1
2
0
2
0
2
0
2
1
1
0
2
0
2
1
1
1
0
1
1
0
1
0
1
1
1
1
2
1
1
2
0
1
0
1
0
1
1
1
1
1
1
1
1
0
2
0
1
1
1
1
1
2
0
3
0
1
1
1
1
1
3
1
0
0
1
2
1
1
1
1
1
2
2
1
1
1
1
0
1
0
2
1
1
1
0
2
1
0
2
1
0
2
0
1
1
1
1
1
1
1
0
1
0
1
1
1
1
1
1
1
1
1
0
1
2
0
1
1
1
1
1
0
0
2
0
1
2
1
1
1
1
1
1
0
0
0
0
3
2
0
1
0
2
2
1
2
0
1
0
0
0
1
1
2
2
0
0
1
1
2
1
0
0
1
2
2
2
1
2
1
2
1
1
1
1
1
1
0
0
0
1
0
2
1
1
1
1
0
2
1
1
1
1
2
1
0
1
1
0
1
1
1
1
2
1
1
2
1
1
1
0
1
1
0
1
2
2
1
1
1
1
1
1
1
1
3
0
1
1
0
2
1
1
0
0
1
0
1
1
1
0
0
0
1
2
0
0
0
2
1
0
2
1
1
1
1
0
2
1
2
2
1
1
2
2
1
2
1
0
1
0
1
0
0
0
0
1
1
2
1
2
1
0
0
2
1
0
1
0
1
2
1
0
0
1
0
1
1
0
1
0
0
1
2
2
0
1
1
1
0
1
0
1
2
1
0
2
1
2
2
0
1
0
2
1
1
2
0
1
2
2
1
2
2
1
2
1
0
0
0
2
0
1
1
1
2
1
1
0
2
2
1
2
2
1
0
1
0
1
0
1
1
2
1
2
0
1
0
1
0
2
0
2
2
2
1
1
1
1
1
1
1
0
0
1
1
2
1
0
2
1
3
0
1
1
2
2
2
2
1
0
1
0
2
1
0
2
2
1
2
2
0
0
0
2
0
0
1
2
1
2
1
2
2
0
1
1
1
0
1
1
0
1
1
1
1
0
1
2
2
2
2
1
0
0
2
1
0
1
2
1
0
0
1
2
2
2
1
1
1
1
1
2
0
0
1
1
1
2
1
0
1
2
1
2
1
1
0
0
1
1
1
0
0
1
0
0
2
2
1
1
2
2
1
2
0
1
0
1
1
2
1
0
2
1
2
2
0
2
1
1
2
0
2
1
1
1
2
2
2
0
1
1
2
1
2
1
1
1
1
0
1
1
1
2
2
2
1
1
1
2
2
1
1
2
1
1
0
1
1
0
1
2
1
0
1
3
2
2
0
1
1
2
1
1
0
1
0
1
1
2
2
2
2
1
1
1
1
1
1
1
0
2
1
2
1
0
1
1
0
0
2
0
2
0
1
0
0
1
0
2
2
1
1
1
1
2
2
0
1
2
2
1
1
1
1
1
1
1
1
1
1
1
0
2
0
1
0
2
2
0
1
0
0
1
1
2
1
1
1
1
2
1
1
0
2
0
1
1
1
1
1
1
1
2
1
0
0
1
1
1
2
1
0
1
1
1
1
1
2
1
0
1
1
2
1
1
2
0
2
1
1
1
2
1
2
1
1
0
1
1
2
2
1
2
0
1
1
1
1
1
2
1
2
1
0
1
2
1
1
1
2
1
0
2
1
1
0
0
1
1
2
1
0
2
1
1
0
0
1
1
0
1
0
0
2
0
2
1
1
1
1
1
0
1
2
1
1
1
1
2
4
1
0
1
2
1
1
0
2
0
1
0
1
2
1
1
1
0
0
1
1
2
0
1
1
1
2
1
1
2
0
1
0
1
1
0
0
2
1
1
4
0
1
1
1
0
1
1
0
2
2
1
1
1
2
2
0
1
1
2
2
1
1
2
0
0
1
0
2
2
2
1
2
2
1
1
2
1
0
0
2
2
1
0
0
1
1
2
2
1
1
2
0
1
1
0
2
2
1
2
0
2
1
1
1
1
0
1
2
3
1
1
1
1
2
1
1
1
1
0
1
2
1
0
1
2
1
1
4
2
0
1
1
0
1
0
1
1
0
0
2
0
1
1
0
1
1
1
2
0
0
1
1
0
1
1
0
1
3
1
1
1
0
1
1
1
1
1
2
1
1
1
2
1
1
0
0
0
0
1
1
0
1
1
0
0
2
1
1
1
0
0
1
2
0
1
3
1
0
1
1
0
0
0
2
1
1
1
1
1
1
1
1
1
1
2
1
0
1
0
1
2
0
1
0
2
1
2
1
0
2
1
1
1
1
0
1
2
0
1
2
1
1
4
1
1
0
2
3
0
1
1
1
1
1
1
0
2
1
0
1
1
0
1
1
1
1
1
2
2
0
1
0
2
1
1
0
1
0
0
1
1
1
2
1
1
2
1
1
0
2
0
2
2
1
3
0
2
1
1
0
2
2
0
2
2
0
1
2
2
0
2
1
1
1
0
2
0
2
2
1
2
0
1
1
1
1
1
1
1
0
1
0
1
0
2
1
1
2
2
2
1
2
1
1
0
2
1
1
0
1
1
0
1
1
1
2
1
1
2
0
1
1
1
1
0
0
1
2
1
1
0
1
1
1
1
1
2
1
0
1
0
1
1
1
0
2
1
1
0
1
0
1
1
2
0
1
0
1
1
1
1
2
0
1
0
0
1
0
1
1
0
2
1
1
0
0
2
1
1
1
0
0
5
1
1
2
2
1
0
1
0
2
1
1
1
0
1
1
2
1
0
1
2
2
0
1
0
1
0
1
2
0
1
1
1
1
0
1
2
2
2
1
2
2
1
1
0
1
1
1
2
1
1
2
0
1
1
0
1
1
2
2
0
1
2
1
0
2
0
2
2
1
1
1
1
2
1
0
1
1
2
3
2
1
1
1
1
0
2
1
0
1
0
2
1
0
2
1
1
0
1
0
1
0
1
1
2
2
1
1
1
1
1
1
0
1
1
0
2
1
1
2
2
2
1
1
1
1
0
1
2
0
1
1
1
1
1
1
0
0
1
0
1
0
1
1
2
0
0
0
1
2
1
1
1
2
1
1
1
2
1
2
2
1
2
1
2
0
1
2
1
1
1
2
0
0
2
2
2
1
1
2
0
0
1
1
2
1
1
1
2
0
0
1
1
1
2
1
1
1
1
0
1
0
0
1
2
1
0
2
0
0
1
1
0
0
2
1
1
1
2
1
0
0
2
1
0
1
1
1
0
0
1
0
1
0
3
2
0
1
0
1
2
1
1
2
1
0
1
2
1
2
1
1
1
1
1
1
2
1
1
0
0
1
0
0
0
0
2
2
2
1
2
0
1
1
1
2
1
0
2
0
1
0
0
1
0
1
1
1
0
1
1
1
2
1
0
1
1
0
1
1
2
1
1
1
1
1
0
2
0
1
1
1
1
0
2
0
0
1
2
1
0
0
1
0
1
1
1
1
1
0
0
0
1
1
1
1
1
1
0
2
1
1
1
0
0
2
1
1
1
0
0
1
1
1
0
1
3
0
1
0
0
1
0
2
2
2
1
0
1
2
0
1
1
1
0
1
1
1
0
1
0
2
2
1
1
2
2
1
2
0
0
2
0
1
0
2
0
1
1
3
2
0
1
1
2
1
1
1
0
0
1
0
2
1
1
0
2
3
0
2
0
2
0
2
2
1
1
1
1
4
2
1
2
1
0
0
1
1
1
1
0
2
1
1
0
1
1
2
1
1
1
0
1
1
2
0
2
2
1
2
1
1
1
2
2
1
3
0
2
1
1
1
2
1
0
1
1
1
1
1
3
1
2
0
0
1
1
1
1
0
0
1
1
1
1
1
1
1
2
1
0
1
1
2
1
1
1
1
1
1
2
0
0
1
1
1
2
0
2
0
1
1
2
1
1
1
1
2
2
0
1
2
1
0
1
1
1
1
1
1
2
1
2
1
1
0
2
1
0
1
1
2
0
1
2
0
1
1
1
1
0
2
2
1
1
1
0
0
1
0
1
1
2
1
1
2
2
1
1
1
0
1
1
1
2
1
1
1
2
0
0
1
0
1
1
1
0
1
1
2
0
1
2
1
1
1
0
1
0
1
1
2
1
2
1
3
2
2
0
0
1
2
2
1
0
0
1
1
2
0
0
1
0
2
0
1
2
0
1
0
1
1
2
1
1
1
1
2
0
1
1
1
0
2
2
0
1
1
2
2
0
1
1
0
1
1
0
1
2
1
1
2
1
1
1
1
2
1
0
1
1
1
1
2
0
1
1
0
1
1
0
1
1
2
0
1
1
0
1
2
2
2
1
0
1
2
1
1
1
1
0
1
1
1
0
2
1
1
1
1
0
2
1
2
0
2
0
0
0
1
0
1
0
1
0
0
1
1
0
1
1
1
1
1
3
1
2
1
0
2
2
0
2
2
1
1
0
0
1
0
1
1
1
0
2
1
2
0
1
0
2
0
1
1
1
1
1
0
1
1
2
0
1
1
2
1
1
0
2
1
2
1
2
1
0
1
0
2
2
0
2
1
1
1
0
1
1
1
0
1
2
2
2
0
1
1
2
1
1
0
0
0
1
0
2
1
0
0
2
2
1
2
0
0
1
0
1
1
0
1
1
1
1
2
2
1
1
1
1
2
1
2
1
0
0
1
1
0
1
1
0
1
1
1
1
1
1
1
1
2
0
0
1
1
1
1
2
3
0
1
1
2
1
1
2
0
1
2
1
1
3
1
1
0
1
1
0
1
0
2
1
2
1
2
1
0
0
2
2
0
2
0
2
1
1
2
1
2
0
1
0
1
1
1
1
2
1
1
1
0
1
2
1
0
1
2
2
0
2
1
2
1
1
2
0
3
0
2
1
0
0
1
1
2
0
1
1
2
0
0
0
1
3
0
0
0
0
1
1
0
1
0
0
1
0
1
1
1
0
0
2
1
1
1
0
1
2
1
0
2
2
1
1
1
0
1
2
3
0
1
1
1
1
1
1
1
2
1
2
1
0
1
2
1
0
1
1
0
1
1
2
1
1
2
0
1
1
1
1
1
0
1
1
2
1
2
1
1
1
0
0
1
1
1
2
2
1
1
1
1
1
0
1
1
1
1
0
0
1
1
1
0
1
1
3
1
1
1
1
0
0
0
1
4
0
1
0
1
1
1
1
2
2
2
1
1
0
1
1
1
0
1
0
0
0
0
2
0
0
1
2
2
2
0
2
1
0
1
1
2
2
1
0
2
0
0
0
1
1
0
0
1
1
0
2
0
1
1
2
0
2
1
2
0
0
1
1
1
0
1
1
1
1
1
1
1
1
0
0
0
1
0
4
1
1
0
1
0
1
0
1
1
2
1
1
1
1
1
1
1
2
0
1
1
0
1
2
1
1
2
1
1
2
1
2
1
0
0
1
2
0
2
2
2
0
1
1
2
2
0
0
2
2
1
3
1
2
1
1
0
0
0
2
0
0
1
1
0
1
7
0
1
1
1
1
0
0
0
0
1
2
2
0
2
0
0
0
0
1
1
1
1
0
0
2
1
1
0
1
0
2
0
0
1
1
0
0
1
0
1
2
0
1
2
2
0
1
0
2
1
1
0
1
0
1
2
0
0
1
0
0
1
0
2
1
2
1
2
2
0
0
1
0
2
1
1
0
1
2
2
2
0
1
1
1
1
1
1
2
2
1
1
0
2
1
1
2
1
0
1
0
2
1
1
0
2
1
0
0
1
2
2
2
1
2
1
1
2
1
1
0
1
1
1
0
0
1
0
1
1
2
1
1
0
1
2
1
1
1
1
2
1
2
0
2
2
1
1
1
0
1
2
0
1
0
2
1
0
0
2
2
1
1
1
1
1
1
2
2
1
2
1
1
1
2
1
1
1
1
2
2
0
1
1
1
1
2
1
0
1
2
1
2
1
1
1
2
1
0
2
0
1
0
1
1
0
2
1
0
2
1
0
1
1
1
0
2
0
0
2
1
2
2
2
2
2
1
1
2
2
1
2
0
0
0
1
2
0
0
1
2
0
1
1
1
1
1
1
2
1
2
2
1
0
1
1
1
1
0
1
3
2
0
0
1
2
1
1
1
1
1
1
0
0
1
1
0
1
0
0
0
1
1
0
1
1
1
2
1
1
0
1
0
1
1
0
1
3
0
2
2
1
1
0
1
1
1
0
0
0
1
2
1
1
1
1
1
2
1
1
2
1
1
2
0
0
2
1
1
0
1
2
0
1
0
0
0
0
1
0
0
0
1
1
1
1
2
3
1
0
1
1
1
1
1
2
1
0
1
1
1
2
1
0
2
1
0
1
0
0
2
1
0
2
0
2
2
1
0
2
1
1
2
1
1
1
0
2
1
1
0
0
1
1
1
2
0
1
0
1
1
0
1
1
2
1
1
1
0
2
1
1
0
2
1
1
2
1
1
1
1
1
1
1
2
2
3
0
1
1
1
0
0
2
2
1
0
2
1
1
1
1
1
0
0
1
0
2
1
0
1
2
1
2
2
5
1
2
1
1
1
2
1
0
1
1
0
2
0
0
1
2
2
1
1
1
1
1
0
1
1
1
2
1
1
1
0
1
2
0
1
0
2
2
1
1
1
2
0
2
2
0
1
2
2
1
1
2
1
1
0
0
1
0
1
0
1
1
1
0
1
4
1
0
0
1
0
2
0
0
1
0
1
0
1
0
1
1
1
1
0
1
0
2
2
1
1
1
1
1
1
1
0
1
1
0
2
1
0
1
1
0
1
1
1
2
1
1
0
2
0
1
2
2
1
0
2
0
1
2
2
1
2
1
2
1
0
1
2
1
2
1
1
1
1
0
1
1
2
1
1
1
1
1
2
1
1
0
0
2
0
2
1
1
1
1
0
1
0
0
0
0
1
1
1
0
1
1
0
0
0
3
1
1
1
0
1
1
1
2
1
1
1
1
1
2
1
1
1
1
2
0
0
1
1
1
1
1
0
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
0
1
0
1
0
1
1
3
0
0
1
0
1
3
5
1
1
1
1
1
2
1
2
1
1
0
1
2
2
1
1
1
2
0
1
2
0
0
0
1
1
2
1
1
1
0
1
1
2
1
2
0
1
1
1
1
2
0
2
1
1
3
2
1
2
1
1
1
0
1
2
1
2
2
1
0
0
2
0
2
1
0
0
1
2
2
2
1
0
2
1
0
1
0
2
2
2
1
0
1
2
1
1
2
1
1
0
1
1
1
0
0
2
1
0
0
0
2
0
0
1
1
2
1
1
0
0
0
2
2
0
0
1
1
1
1
2
2
1
1
1
0
1
1
2
1
1
2
1
1
1
1
1
1
0
1
2
1
1
2
1
2
2
0
1
1
2
0
1
1
2
1
0
1
0
2
1
1
3
1
1
0
0
2
0
1
1
0
2
2
2
1
0
0
1
3
1
0
1
2
0
2
1
1
1
1
2
1
0
1
1
2
2
1
2
1
1
1
1
0
1
0
0
1
1
1
1
2
1
0
0
1
2
2
0
2
0
2
1
2
1
0
2
0
0
1
1
2
2
1
1
0
0
1
1
0
0
1
1
1
1
0
3
1
2
2
1
1
1
1
0
0
1
1
1
1
0
1
0
2
2
0
1
1
0
3
1
1
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
0
1
1
1
1
0
1
1
2
1
2
1
1
1
1
1
0
2
1
1
1
0
0
1
0
2
1
2
2
1
1
2
1
2
1
1
1
2
1
2
1
1
1
1
0
1
1
0
1
1
1
1
1
0
1
0
1
1
1
2
2
0
2
1
1
1
1
1
0
0
2
0
0
1
1
2
2
2
1
1
0
0
2
1
2
1
1
0
1
1
1
0
1
1
0
4
0
0
2
2
1
0
0
2
2
1
1
1
0
0
2
1
0
2
1
1
1
1
1
1
2
0
1
1
1
0
1
0
1
1
0
1
1
0
0
1
6
0
1
1
2
1
1
2
2
2
1
1
1
2
2
1
2
1
1
0
1
0
2
0
1
1
0
0
1
1
1
1
1
4
1
0
1
1
1
1
1
1
0
0
0
1
1
0
1
1
1
1
1
0
1
0
1
2
1
2
2
1
1
1
2
0
0
0
1
1
0
1
1
1
2
1
1
2
2
0
2
2
0
2
1
0
1
1
1
0
0
0
1
0
0
1
1
1
2
2
1
2
2
1
1
0
1
1
2
1
1
0
0
2
1
0
0
2
1
1
1
1
0
1
1
1
0
1
0
2
0
2
1
1
1
1
2
0
1
1
1
1
1
2
0
1
2
0
0
0
1
1
1
1
2
1
1
0
1
0
1
1
0
0
0
0
1
2
0
1
1
2
0
0
1
0
1
1
1
0
1
2
1
1
2
1
1
0
0
2
0
2
0
1
0
1
1
1
0
4
2
1
1
2
0
1
2
1
1
1
0
1
1
2
1
0
2
0
1
1
1
0
1
2
0
2
2
0
2
1
1
2
1
1
0
1
1
1
1
1
1
1
2
2
1
1
2
1
0
2
2
1
2
1
1
1
2
1
2
0
1
1
1
0
2
2
1
1
0
2
2
1
1
1
0
1
0
1
1
1
1
1
2
2
1
2
1
0
1
0
1
1
1
1
1
2
2
0
1
1
1
0
1
1
1
1
2
1
2
1
2
0
2
1
2
0
0
1
1
0
2
2
1
0
1
1
1
1
0
1
0
2
0
2
0
1
1
2
0
1
1
1
1
2
1
1
0
1
2
1
1
2
1
0
0
2
2
0
2
0
2
0
0
1
0
1
1
1
1
1
1
0
0
1
1
1
1
1
2
2
1
1
1
0
0
1
1
1
1
2
0
2
0
2
0
1
1
1
0
0
1
1
1
2
0
1
0
1
1
0
2
2
3
1
2
2
3
1
2
1
0
2
2
2
2
2
1
1
1
1
1
2
2
1
2
1
2
0
0
1
2
1
1
1
1
1
1
0
0
2
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
3
1
1
0
1
2
1
3
1
0
1
1
1
1
2
1
2
0
1
0
2
2
1
2
1
3
2
1
1
3
1
1
2
2
1
0
2
1
1
0
1
1
1
0
0
0
0
1
2
2
2
0
1
1
1
2
1
1
1
1
1
1
1
1
1
0
1
0
0
1
0
0
1
2
2
3
1
0
0
0
2
1
1
2
0
1
2
1
0
1
0
1
2
1
2
1
1
1
0
2
2
1
1
2
1
1
1
2
0
1
0
0
1
2
1
0
1
1
1
2
1
1
0
1
2
0
2
1
0
1
2
4
1
1
0
1
1
1
2
1
1
0
2
2
0
1
1
1
0
1
0
0
1
1
1
1
1
1
0
2
1
0
0
2
0
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
0
1
0
1
1
0
2
2
0
1
1
1
1
1
1
0
1
2
0
1
1
1
2
1
1
1
0
1
1
1
1
0
1
1
1
1
1
1
0
2
3
2
1
1
1
1
1
1
1
2
1
0
1
1
0
1
2
2
2
1
1
1
1
1
1
1
0
0
1
1
1
1
0
1
0
1
0
1
1
1
2
1
1
1
2
2
2
1
1
0
0
1
0
1
0
1
1
1
1
0
0
1
0
1
1
1
2
1
2
1
4
1
1
1
1
1
1
1
2
1
0
0
2
1
2
1
1
2
0
2
1
0
1
0
0
1
1
2
1
1
0
1
1
2
1
1
2
1
0
1
2
1
4
1
2
1
2
1
1
0
1
2
1
1
2
2
0
2
0
1
2
0
0
1
0
0
1
1
0
2
0
1
0
0
1
0
2
0
1
2
1
1
0
0
2
1
1
1
1
0
2
1
1
2
0
1
0
2
1
0
0
1
1
2
1
1
1
1
1
1
1
2
1
1
1
0
0
2
2
1
1
1
1
0
1
2
0
2
1
1
1
2
1
2
0
1
1
1
1
2
0
0
1
0
1
1
0
1
2
1
2
0
1
1
0
1
1
1
1
1
1
1
2
1
1
0
1
1
1
1
2
1
0
2
2
1
2
1
1
1
1
2
2
0
1
1
2
2
0
2
2
1
0
2
0
1
1
2
1
1
1
2
1
1
0
2
1
0
2
2
0
1
1
1
1
1
0
1
1
1
0
1
2
1
1
1
0
0
2
1
0
1
1
0
0
0
1
2
0
1
0
0
0
1
1
1
1
2
2
0
0
0
2
0
1
2
1
1
1
1
2
0
0
2
0
2
2
2
0
1
2
2
0
1
2
0
1
1
1
0
0
1
2
1
1
0
1
1
0
1
1
1
1
0
1
1
1
2
2
0
0
1
2
1
2
1
0
2
1
1
1
2
0
2
1
2
1
1
2
0
1
2
1
0
1
0
1
1
1
1
2
1
0
1
1
1
2
0
1
3
1
1
0
1
1
0
1
0
1
2
1
0
0
1
0
0
2
1
1
0
1
1
0
0
1
1
1
1
2
1
1
1
1
1
1
1
1
1
0
2
0
1
1
1
1
2
1
1
0
1
1
1
0
1
1
1
1
4
2
0
0
2
0
0
0
2
0
2
2
1
2
0
3
1
2
2
2
0
1
0
1
1
0
2
2
2
0
0
1
1
1
0
1
0
1
1
1
1
2
2
1
1
0
0
0
1
1
1
1
1
0
0
1
1
1
2
1
1
0
1
1
2
0
3
0
1
1
1
2
3
2
0
2
1
1
0
1
1
1
2
1
1
1
0
1
1
1
2
0
1
2
1
1
1
1
1
0
1
1
1
1
1
1
0
1
2
0
1
1
1
0
1
2
0
2
1
1
1
1
0
2
0
0
1
1
0
1
1
2
1
1
1
0
1
2
1
0
2
1
1
0
1
2
0
1
0
1
1
0
0
2
0
2
3
1
0
1
0
2
0
2
1
0
1
1
1
1
2
1
1
1
2
1
2
0
1
1
0
2
2
2
0
0
1
2
1
0
1
1
2
1
0
1
0
0
0
1
1
1
1
1
2
1
1
2
2
1
2
1
2
4
1
0
1
1
1
1
1
1
2
1
0
0
0
2
0
1
1
1
0
1
2
0
2
1
0
2
1
1
1
2
1
1
1
1
0
3
0
1
2
1
2
2
2
0
1
1
1
2
2
1
0
1
1
1
1
2
0
2
1
0
0
1
1
0
1
1
0
1
1
1
1
0
0
1
1
1
1
2
0
0
1
1
0
0
1
1
2
1
1
0
0
2
1
2
0
2
1
1
2
2
1
1
1
1
1
1
1
2
1
0
0
1
1
1
1
1
1
0
2
1
1
0
1
2
2
1
1
1
1
1
1
2
1
1
1
2
1
1
2
0
1
1
1
1
1
0
1
1
1
0
1
0
1
0
1
0
1
0
1
1
0
1
2
0
3
1
0
0
0
3
1
0
1
0
1
1
1
0
1
1
1
2
1
0
0
1
0
2
1
1
1
1
1
1
0
1
1
2
1
2
1
2
0
1
2
0
0
1
1
1
3
1
1
3
1
2
1
0
0
0
0
1
2
1
1
0
0
1
0
1
0
0
1
2
0
1
0
1
1
1
1
2
0
2
2
0
2
0
1
0
1
1
1
0
0
1
2
0
2
0
0
1
2
1
2
1
0
1
0
1
2
0
1
0
1
1
1
0
1
1
1
1
2
1
1
1
0
1
1
1
1
2
0
2
1
1
1
0
1
0
1
0
0
0
2
1
0
1
2
0
0
0
1
1
0
1
2
1
1
0
2
2
0
2
0
2
2
1
2
1
1
0
2
2
1
0
1
0
0
1
1
1
1
0
1
2
0
1
0
1
1
1
0
1
1
0
2
1
0
0
1
1
1
1
0
1
2
0
3
2
0
0
2
2
0
1
1
2
2
0
1
0
1
1
1
2
1
1
0
0
1
1
0
1
1
1
2
2
1
1
3
1
1
2
2
2
0
2
0
2
1
1
1
1
2
2
0
1
1
0
1
2
0
2
1
2
1
2
1
1
2
2
0
1
1
0
1
1
4
1
0
1
2
0
0
0
0
1
0
2
0
1
1
3
1
0
1
2
2
1
2
2
2
0
1
0
0
2
1
1
0
2
1
0
0
1
1
2
2
2
1
2
1
1
2
2
2
1
1
1
1
1
1
1
1
1
2
0
2
1
1
2
1
0
2
0
1
0
2
1
1
1
1
2
1
1
2
0
2
1
2
1
1
1
1
1
1
2
9
1
1
0
2
2
1
0
1
1
1
1
1
1
1
1
1
1
2
1
0
2
0
2
2
2
2
0
1
1
1
2
1
2
1
1
1
1
2
2
0
2
1
1
2
1
1
0
1
2
0
0
0
0
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
0
0
3
1
2
1
1
0
1
0
1
2
0
1
0
1
0
0
1
0
2
2
2
1
0
0
1
1
1
1
1
0
2
1
1
1
0
2
0
1
1
0
0
1
2
1
1
1
1
1
1
1
1
0
2
1
1
2
2
0
1
1
1
2
1
1
1
0
1
0
1
2
1
0
1
0
0
2
2
1
0
1
1
1
0
1
1
1
2
2
2
0
1
1
0
1
1
1
1
1
1
0
2
3
1
0
1
1
1
1
1
1
1
1
0
2
1
1
2
0
1
1
1
2
1
1
1
0
1
0
0
0
1
1
1
0
0
1
1
1
1
1
0
0
1
1
1
1
2
0
0
0
1
2
1
1
1
1
1
0
0
2
3
1
1
2
1
1
1
0
1
0
0
1
1
1
1
1
0
1
1
1
1
1
0
2
1
1
1
2
1
2
2
0
1
2
1
2
1
3
1
1
0
2
1
1
1
2
1
1
1
2
2
0
1
0
0
1
0
0
1
1
0
1
1
0
1
2
1
2
1
1
1
0
1
1
2
1
0
1
2
2
1
1
6
1
0
0
1
1
1
1
1
1
0
1
0
1
1
0
0
1
2
1
1
1
1
2
0
2
1
1
2
1
2
1
1
2
2
0
1
0
1
1
0
1
1
2
1
1
1
1
1
1
0
1
1
2
2
0
2
1
0
3
1
0
1
1
1
1
1
1
1
0
1
1
0
1
0
1
2
1
1
2
1
2
0
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
1
0
1
2
1
0
2
1
1
1
2
2
0
1
0
1
2
1
1
1
0
1
0
1
0
1
1
0
1
1
1
1
1
1
2
2
0
1
1
1
0
1
2
1
1
0
2
1
1
1
0
0
1
1
2
0
1
1
2
1
1
2
1
0
1
1
2
1
0
0
0
1
1
2
1
2
1
1
2
1
1
1
2
1
3
2
0
0
0
1
0
0
1
2
4
1
1
2
1
1
1
0
2
1
0
1
1
1
1
0
1
0
1
1
1
0
0
1
0
2
0
0
1
1
2
1
0
1
2
0
3
2
0
1
0
1
2
1
1
2
2
2
2
0
1
1
1
1
1
0
1
0
1
0
2
0
0
2
2
1
1
2
1
0
0
0
0
0
1
2
1
0
1
1
1
4
2
1
1
1
1
0
0
2
0
1
2
1
1
1
1
2
1
2
1
1
1
1
0
1
1
1
2
1
0
1
1
1
0
0
0
1
1
1
1
1
1
0
2
1
2
0
1
1
1
1
1
1
1
0
1
1
1
2
2
1
1
0
1
1
0
2
2
1
1
1
1
0
1
0
2
1
1
3
1
1
1
1
1
0
0
1
1
1
3
1
2
1
0
2
0
2
1
0
0
0
1
1
1
2
0
0
1
1
1
0
1
2
1
1
0
0
2
2
2
1
2
1
1
1
2
1
1
2
1
1
2
1
1
2
1
1
1
0
1
0
2
1
2
1
0
1
0
1
0
1
1
2
2
1
3
0
1
0
1
0
1
1
0
2
1
1
2
0
0
0
1
0
1
0
0
0
2
1
0
2
1
2
2
1
1
0
1
2
2
1
2
1
1
0
1
2
0
1
2
0
0
1
1
1
1
1
1
0
1
1
1
0
2
2
1
0
1
1
1
1
1
1
2
1
1
2
2
1
1
1
0
0
0
1
1
1
0
0
2
0
1
1
2
1
2
0
1
1
1
0
1
0
2
2
1
2
2
2
0
1
1
1
1
0
0
2
0
0
2
0
0
2
2
0
1
1
0
1
1
0
1
1
0
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
0
2
1
1
1
1
2
1
0
1
0
1
1
2
0
1
0
2
2
2
1
0
1
1
1
2
3
0
2
2
0
0
0
1
1
1
2
1
2
2
1
1
1
0
0
1
1
2
1
1
1
0
2
1
1
1
1
2
0
0
1
2
0
0
1
0
1
1
1
1
2
2
1
1
2
0
1
0
1
0
1
2
1
0
1
0
1
1
0
1
1
0
2
2
1
2
1
1
1
2
1
1
0
0
0
2
1
0
2
1
3
1
2
2
1
2
1
1
1
1
1
2
1
2
0
1
1
0
1
1
0
1
1
1
1
1
2
1
2
2
1
1
1
1
2
1
0
0
1
0
2
1
2
0
2
2
0
1
2
1
0
1
2
1
1
0
1
1
1
1
0
1
0
2
1
1
1
1
1
0
1
1
0
2
1
1
0
2
1
1
0
0
2
1
1
0
2
1
2
1
2
0
0
1
1
1
3
1
2
0
0
1
1
1
1
1
1
1
2
1
1
0
2
2
1
1
2
1
0
2
2
2
1
1
0
0
2
2
1
1
1
1
0
0
2
1
2
0
2
0
0
0
2
1
1
1
1
1
1
2
2
0
0
0
1
1
1
1
1
0
2
0
0
0
1
0
1
1
1
2
1
0
0
2
0
2
2
0
1
2
1
2
2
1
1
0
1
1
1
1
1
0
0
1
1
1
1
1
1
2
2
2
1
1
0
0
2
0
1
1
0
0
1
1
1
2
1
1
1
1
1
2
1
1
1
3
0
1
0
1
1
1
1
1
3
0
1
1
1
1
2
0
1
1
2
1
1
2
2
1
1
0
1
1
1
1
1
2
2
1
0
0
1
1
1
1
0
0
1
1
1
2
1
1
1
1
0
2
2
1
1
1
1
6
1
1
1
2
1
0
1
1
1
2
1
1
2
2
1
1
1
1
0
2
1
2
1
1
1
1
1
2
2
0
1
2
1
0
1
0
1
1
1
0
2
1
1
1
2
2
0
1
2
2
2
1
2
2
0
1
2
2
1
0
2
1
2
1
0
1
1
1
0
2
0
0
1
2
2
1
0
2
0
1
1
1
1
1
2
0
2
1
0
1
1
1
1
0
1
1
1
2
2
1
2
0
1
1
1
0
0
1
1
0
2
1
1
1
1
1
2
1
1
1
0
2
1
2
1
1
0
1
1
2
1
1
1
0
2
1
1
0
1
0
1
1
2
1
0
1
2
2
0
1
0
0
0
0
0
1
2
1
1
1
0
0
1
1
1
4
0
0
0
0
1
1
1
0
2
1
2
1
0
1
1
1
2
0
2
0
0
2
1
1
2
1
0
1
0
0
0
1
1
1
1
2
1
1
2
4
1
0
2
1
1
0
1
1
1
0
1
1
0
2
1
2
0
2
1
1
1
1
2
1
1
1
1
0
1
1
2
1
2
2
0
2
1
0
1
0
1
2
2
1
1
1
1
1
1
1
2
0
0
2
1
0
1
1
1
2
1
1
1
2
1
0
1
0
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
0
2
1
1
2
1
1
1
1
1
2
1
1
1
1
2
2
0
1
1
1
0
1
1
0
1
2
1
0
1
1
0
1
0
1
2
0
1
1
2
1
1
2
2
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
0
1
2
4
2
1
0
0
3
0
2
0
0
1
1
1
0
2
1
1
1
1
1
2
0
2
0
2
2
1
1
1
1
1
1
2
1
0
0
0
3
1
1
2
2
1
2
1
2
1
0
0
1
0
1
1
1
2
0
1
2
1
1
1
1
1
2
1
2
1
0
1
1
1
1
1
1
1
2
0
2
3
2
1
0
1
1
2
1
0
1
0
2
0
0
1
1
1
0
1
2
0
2
1
2
2
0
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
2
1
0
1
1
0
1
0
1
1
1
2
1
2
2
1
1
1
0
1
1
2
1
1
1
1
0
2
1
1
1
0
1
2
1
2
0
1
1
1
1
0
1
1
2
2
0
1
0
1
1
1
1
1
1
0
0
1
2
2
1
1
2
2
1
2
2
1
1
1
2
1
2
1
1
1
0
1
1
1
1
2
2
0
0
2
1
1
1
1
0
2
2
0
2
1
2
1
0
0
1
0
1
2
2
1
1
1
2
1
2
2
0
2
1
1
2
1
0
1
0
1
2
0
2
1
2
1
1
1
1
2
2
1
2
2
2
1
1
1
2
0
1
1
0
1
1
1
2
0
2
1
0
1
1
1
0
1
1
1
1
0
2
2
1
1
1
0
2
0
1
1
2
1
2
1
0
0
1
0
2
0
2
1
0
2
2
1
0
1
1
0
1
1
1
1
0
0
1
0
2
2
1
1
1
0
2
1
1
1
1
2
1
1
2
1
0
1
1
2
1
1
1
2
0
2
2
1
1
0
1
1
1
0
2
1
1
0
1
1
2
1
2
2
1
2
2
1
2
1
1
1
0
1
1
0
1
2
4
2
0
1
1
1
2
0
0
1
1
1
0
0
2
1
2
1
2
1
0
1
1
1
0
0
1
1
1
1
2
1
1
0
1
1
1
1
0
1
1
1
1
0
0
1
0
1
2
1
0
0
1
1
1
1
1
1
2
1
0
1
2
2
0
0
2
1
2
1
1
1
1
1
1
1
1
2
2
2
0
1
1
2
1
0
1
2
2
1
0
2
1
1
2
1
1
1
2
1
1
0
2
0
0
0
2
2
2
0
1
2
1
1
1
0
0
0
2
1
2
1
2
1
0
0
1
1
0
1
1
1
2
1
2
1
2
1
1
0
1
1
1
1
0
2
1
1
0
1
1
1
0
1
1
1
1
1
1
0
1
1
1
1
1
1
1
0
0
0
1
1
1
1
1
1
1
1
2
1
2
1
2
1
1
1
2
0
0
0
1
1
1
1
1
0
0
0
2
2
2
0
0
1
2
1
1
1
1
1
1
4
1
1
1
1
0
0
1
1
1
2
1
1
1
0
2
2
2
1
0
1
0
1
2
1
0
1
0
1
1
1
0
1
1
0
1
0
1
1
2
0
3
0
0
1
0
2
1
1
1
2
1
2
0
2
1
1
1
1
1
1
1
2
2
0
1
1
0
2
0
0
0
0
1
2
1
1
1
1
1
1
0
2
0
1
1
0
1
1
1
1
0
3
1
1
0
0
1
1
0
1
1
1
1
2
2
1
1
2
0
2
0
2
0
0
2
1
2
1
0
0
1
1
1
1
1
1
1
1
1
0
2
3
1
0
0
1
2
0
1
0
1
1
0
0
2
2
1
1
1
2
0
1
1
1
2
2
1
0
1
1
0
2
2
0
1
1
1
2
2
0
0
1
1
2
1
2
1
2
1
2
1
1
0
2
1
1
1
2
1
1
1
0
1
1
0
1
1
1
1
1
1
2
1
1
1
1
1
0
1
2
1
2
0
2
1
1
0
0
1
2
2
1
2
1
2
1
2
1
1
1
1
0
2
1
0
2
2
0
2
1
1
1
0
2
0
1
1
2
1
0
1
0
1
1
2
1
0
2
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
2
1
2
2
1
0
0
0
1
1
1
2
0
0
0
1
1
1
0
0
2
1
0
0
0
1
2
0
0
0
0
0
1
2
2
0
1
1
0
1
1
2
1
1
1
2
0
1
1
2
0
1
2
2
1
1
1
2
0
0
1
1
1
2
0
1
1
1
2
0
2
1
0
0
1
0
2
0
1
1
1
1
2
1
1
1
1
2
1
2
2
1
1
0
1
2
0
1
2
2
0
2
2
2
3
0
0
1
1
2
1
1
1
1
1
1
2
2
2
2
1
2
0
1
1
1
1
1
0
2
2
1
0
1
1
1
1
2
2
1
1
1
2
1
0
1
2
0
2
1
1
0
1
2
2
2
1
0
2
1
1
0
1
2
0
2
2
1
2
1
1
1
1
1
0
1
0
1
1
2
3
1
1
2
0
2
1
1
2
1
0
0
1
1
0
1
1
0
1
2
3
0
1
0
1
3
1
2
1
0
2
1
0
0
2
1
1
1
1
1
0
2
1
2
1
1
1
2
2
1
1
0
1
1
0
1
0
1
1
2
1
1
0
2
1
1
0
1
0
1
2
2
1
0
2
1
1
0
2
1
1
1
0
0
1
2
1
2
1
2
0
2
2
0
0
2
0
1
1
1
0
1
1
1
1
1
0
2
2
1
3
1
1
1
2
2
1
2
0
1
0
2
2
1
1
0
1
1
1
2
1
0
1
0
1
1
1
1
1
2
0
1
0
2
2
1
2
0
1
0
2
1
1
1
1
0
1
1
1
2
1
0
1
2
1
2
2
1
1
0
1
0
1
1
1
1
1
1
1
1
0
2
2
2
2
0
1
2
1
0
0
1
0
1
2
1
0
2
2
1
1
2
1
2
2
0
2
2
1
1
2
3
1
1
2
0
0
1
2
1
0
2
1
2
1
0
2
1
0
1
1
1
1
0
1
0
2
1
0
1
0
2
0
1
2
1
1
2
1
1
1
1
0
1
1
3
1
2
2
0
2
1
1
1
2
1
2
1
1
1
1
1
2
0
2
2
0
1
1
2
1
0
0
2
0
0
1
0
1
1
1
1
0
2
1
1
1
1
2
1
2
2
2
1
0
1
2
1
2
1
1
2
3
2
0
1
2
1
1
1
0
1
2
0
2
0
1
1
3
1
1
1
1
0
0
1
2
1
1
1
4
2
0
2
0
1
2
0
0
1
1
0
0
1
1
1
1
1
0
1
1
1
1
0
1
1
1
0
1
2
1
0
2
2
2
2
0
1
1
1
0
2
1
0
1
2
0
1
0
1
1
1
1
1
2
1
2
1
0
0
1
2
1
1
1
2
0
0
1
1
1
1
1
0
1
1
1
2
1
1
1
1
2
1
3
0
1
2
1
0
1
0
0
0
1
0
1
1
0
1
2
0
1
1
1
1
1
1
0
1
1
1
1
1
1
0
1
0
1
1
1
1
1
2
1
0
1
0
1
1
1
2
1
2
0
2
0
0
1
1
1
1
2
0
1
2
2
0
1
2
0
1
1
1
0
1
2
0
0
1
1
2
0
2
2
1
0
0
2
1
2
1
0
1
1
1
1
1
1
1
1
1
0
2
0
1
1
0
1
1
2
0
0
0
1
1
1
2
2
1
1
1
2
0
4
1
1
1
1
2
0
2
2
2
2
0
0
2
1
1
2
1
1
1
1
1
1
1
3
0
1
1
2
0
1
1
2
1
1
2
1
1
1
2
0
0
1
0
1
0
1
1
0
1
2
2
2
1
1
3
1
1
1
1
1
2
1
1
0
1
1
1
1
0
1
0
1
1
2
1
2
1
0
1
2
1
0
0
2
1
1
1
2
1
1
1
2
0
0
2
1
1
1
1
0
1
1
1
0
1
0
2
0
2
1
1
0
2
2
1
2
2
1
2
1
0
0
1
1
1
1
1
1
2
2
1
1
1
1
1
0
0
0
1
1
0
1
1
2
2
1
2
0
2
0
2
1
0
1
1
1
0
1
1
2
1
2
0
0
1
1
1
2
0
2
0
1
1
1
1
1
1
1
1
2
1
1
1
3
1
2
1
1
2
1
1
0
1
0
1
1
1
1
2
1
0
2
1
0
0
1
3
2
1
0
1
0
2
1
2
1
1
1
2
0
2
1
2
1
0
0
2
1
0
1
0
1
0
1
1
1
1
1
1
1
1
2
1
2
0
0
1
2
1
1
1
1
1
1
2
1
0
1
1
0
1
1
0
2
1
1
1
1
0
2
1
1
1
1
1
1
1
2
1
1
0
0
1
2
1
1
0
1
2
0
1
1
1
1
2
0
2
1
1
0
0
1
0
1
0
1
1
1
1
1
1
0
1
1
1
1
2
2
2
1
1
0
1
0
1
0
1
2
1
1
0
1
1
0
1
2
1
1
1
1
0
0
2
1
0
1
1
1
0
0
0
1
1
1
1
1
1
1
0
1
1
1
1
0
1
2
1
0
1
1
1
0
0
1
0
2
2
2
1
0
1
0
1
2
0
0
1
1
2
1
1
2
0
1
1
1
1
1
1
1
1
2
1
1
0
1
1
2
1
1
1
1
1
0
0
1
0
1
2
2
0
2
1
2
2
1
0
0
1
2
1
0
2
2
1
2
1
1
2
0
1
0
3
0
0
0
1
1
1
1
0
2
1
1
2
1
1
0
4
2
0
1
0
2
0
1
1
1
1
0
1
1
2
1
1
1
0
1
1
1
1
2
0
1
2
2
1
2
0
1
1
1
1
0
0
1
0
1
1
0
1
2
1
1
1
1
2
1
1
1
2
2
0
1
1
2
1
1
1
1
2
1
0
0
3
2
0
2
1
1
3
1
2
0
1
1
0
0
1
1
2
2
2
2
1
1
2
1
1
1
2
1
0
1
1
0
2
1
1
2
1
1
1
1
1
0
1
0
0
1
1
0
1
2
1
1
1
1
0
1
1
2
0
2
2
1
0
0
1
0
1
1
1
0
0
0
1
2
1
0
0
1
1
0
1
2
0
1
1
2
2
2
1
2
1
1
2
2
1
1
1
0
0
1
1
2
1
1
1
1
2
1
1
1
2
0
1
0
0
1
0
1
1
1
1
4
0
1
0
1
2
1
2
0
1
1
0
1
1
2
0
1
0
0
2
1
1
1
0
0
1
1
0
2
2
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
1
1
2
1
1
1
1
2
0
1
0
1
1
2
1
0
2
2
1
1
0
1
0
1
1
2
0
1
1
1
0
2
2
1
1
1
1
0
0
2
0
1
0
0
0
1
0
1
1
0
1
1
2
2
0
1
1
1
1
1
1
1
1
1
2
2
2
1
1
2
1
1
1
0
0
0
1
1
1
1
2
1
1
0
0
1
1
1
0
1
0
1
2
2
1
0
0
1
0
1
1
1
0
1
0
0
2
1
0
0
1
1
2
1
0
2
2
0
2
1
2
1
2
1
0
0
2
0
0
0
1
1
0
1
1
1
0
1
1
1
1
0
1
0
1
2
0
0
1
2
1
2
1
1
1
0
0
0
1
0
1
1
0
2
1
1
1
0
1
1
0
1
1
2
0
2
2
2
2
1
1
1
2
2
1
0
1
1
1
2
1
1
1
1
1
1
2
1
2
2
1
2
1
2
1
1
2
1
3
2
1
2
0
2
1
1
1
1
1
1
1
0
0
0
1
1
0
1
2
1
1
0
1
1
0
1
0
2
2
1
0
1
1
1
1
1
0
1
1
1
1
1
2
0
0
2
0
0
0
2
1
1
1
2
0
1
0
3
1
0
2
1
2
1
0
1
0
2
0
2
2
0
1
0
1
2
2
2
0
1
1
1
2
0
2
0
0
0
0
0
0
1
0
0
2
0
1
1
1
1
1
2
0
1
0
2
1
0
2
1
0
1
1
0
1
1
0
1
0
0
2
1
1
1
2
1
1
1
2
1
2
1
2
1
0
0
1
2
2
1
1
1
0
2
0
2
2
1
1
1
1
1
0
1
2
2
0
0
1
1
1
1
1
0
1
1
1
1
0
2
1
1
2
2
1
1
2
1
0
1
1
0
1
0
1
1
2
0
0
1
0
1
0
1
1
2
3
1
1
1
1
1
1
2
1
1
1
1
2
0
0
0
2
0
0
1
1
1
1
1
1
1
0
1
0
0
2
0
0
0
1
1
0
0
1
1
1
0
2
2
2
2
1
1
1
1
2
2
0
1
1
1
1
2
1
0
0
1
1
0
1
2
2
2
2
1
1
0
0
2
2
1
0
1
1
1
3
1
1
2
1
0
2
0
1
1
0
1
2
1
2
1
0
0
2
2
1
2
2
1
2
1
1
1
2
0
1
1
0
1
0
2
0
2
2
1
1
1
0
0
1
1
1
1
2
1
0
4
0
2
1
1
0
1
0
0
2
0
0
1
2
1
2
2
0
2
1
0
1
0
1
1
1
2
1
0
1
0
1
1
1
1
1
1
1
0
0
2
1
0
1
0
0
0
1
1
1
0
1
1
1
1
0
0
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
2
1
0
2
1
1
1
1
1
0
0
1
1
1
1
1
1
0
2
1
1
0
1
0
1
1
2
1
1
1
1
0
1
1
0
1
1
1
1
0
1
2
1
2
0
1
1
1
0
2
1
0
1
0
1
1
0
1
1
0
1
0
2
2
1
0
1
0
2
1
0
0
0
1
1
0
0
0
1
1
1
1
3
0
0
0
1
0
1
1
1
1
2
0
0
1
1
1
1
2
1
1
2
1
0
0
1
2
0
1
1
0
0
1
0
2
1
0
1
1
0
3
2
1
0
1
2
2
1
1
2
1
2
0
1
2
1
1
1
1
1
1
1
1
2
2
1
0
0
1
1
1
1
1
0
0
1
2
1
1
1
1
0
0
1
2
2
2
0
1
1
2
0
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
0
1
2
1
1
0
0
2
1
1
1
0
1
1
1
2
2
1
1
1
2
2
0
2
2
0
2
1
1
2
0
2
1
1
0
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
0
1
1
2
1
1
1
1
2
1
1
1
1
1
1
2
2
0
2
2
2
1
1
1
2
2
1
1
0
0
1
1
0
0
2
2
1
2
1
0
1
1
1
1
1
0
0
1
1
1
0
0
1
2
1
2
0
1
0
0
1
1
1
1
1
2
2
2
2
0
0
2
2
0
1
2
1
1
1
1
3
0
2
0
1
0
1
1
0
2
1
0
1
1
1
1
2
0
0
2
1
2
0
1
0
2
1
0
2
0
1
2
0
0
1
2
2
0
1
2
1
1
1
1
0
2
2
2
1
1
1
2
2
2
1
1
1
0
1
0
0
1
2
1
1
2
1
2
0
0
2
1
1
2
1
1
2
1
1
0
1
1
2
1
1
1
1
1
0
1
1
1
2
1
1
0
1
2
2
1
1
1
1
1
1
0
1
1
1
1
1
2
1
1
2
0
1
2
0
1
1
1
1
0
2
0
2
1
2
1
1
0
2
1
0
1
0
1
2
2
1
2
1
1
1
2
1
1
1
1
2
1
1
0
0
1
1
2
2
1
1
0
1
0
1
1
2
0
1
2
2
1
1
1
1
1
1
2
1
1
1
0
1
1
2
1
2
1
1
1
1
1
1
1
0
2
1
0
0
0
2
1
2
1
1
2
0
1
1
1
1
1
0
1
1
2
1
0
1
1
0
0
2
1
0
2
1
1
0
2
2
3
0
2
0
1
1
1
2
2
1
2
2
0
1
1
1
1
1
1
1
2
2
0
2
2
1
0
1
1
1
0
0
2
1
0
1
1
1
0
1
2
2
1
1
2
1
1
1
1
1
0
0
1
1
0
0
2
2
0
0
2
2
2
1
1
1
1
0
1
1
2
1
1
1
0
1
2
1
1
2
1
2
1
1
1
0
0
1
2
2
2
0
0
1
1
1
1
1
1
1
0
1
0
1
0
0
1
1
2
0
0
0
0
1
0
1
0
1
0
0
0
1
2
1
0
1
2
1
0
0
0
1
1
0
1
2
1
1
0
2
1
0
1
1
0
1
1
2
1
2
1
1
1
1
2
1
0
1
1
1
1
2
1
0
1
1
0
1
1
2
1
1
2
1
2
1
0
1
0
3
0
2
2
1
2
0
1
0
1
0
1
0
0
1
1
2
1
1
1
0
2
2
2
1
1
1
1
1
0
1
1
1
1
0
1
2
0
1
2
1
1
2
1
1
0
0
0
0
1
1
2
1
1
0
0
1
1
1
1
0
1
0
0
1
1
1
0
1
1
1
2
1
1
1
1
2
4
1
1
2
1
1
2
0
2
0
1
0
0
1
2
0
2
1
1
2
0
1
2
0
2
0
2
1
2
1
0
0
1
0
0
1
0
1
1
2
2
0
1
1
0
0
1
2
1
2
1
2
2
0
2
0
0
0
2
2
1
2
2
1
1
1
1
1
1
1
0
1
2
2
1
2
0
0
0
1
1
0
0
1
1
0
0
0
1
1
1
1
2
1
1
2
1
2
2
1
2
2
1
2
1
1
2
1
2
2
2
1
0
2
0
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
0
0
0
0
1
1
1
0
1
1
0
2
2
0
1
1
1
2
0
1
1
1
2
1
1
0
0
0
0
3
1
1
1
1
1
1
1
1
0
1
1
2
0
0
1
1
1
2
0
1
0
0
2
1
1
0
1
1
0
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
0
0
2
0
1
1
1
0
2
1
1
1
0
0
2
2
2
1
0
0
2
1
1
1
1
1
1
1
0
2
1
2
1
2
1
1
2
1
1
1
1
2
1
1
1
0
1
0
2
1
2
1
2
0
1
1
0
1
1
1
2
1
1
0
2
0
0
1
0
1
2
1
0
1
0
2
1
1
0
2
1
2
0
1
1
1
0
0
1
0
1
0
1
0
1
1
1
1
0
1
0
0
1
1
1
1
2
0
1
2
1
0
2
2
1
1
1
0
2
2
2
2
2
0
0
1
2
1
1
1
0
0
1
1
1
2
1
0
1
1
0
2
2
2
0
1
1
1
2
1
2
1
1
2
0
2
1
0
0
1
1
0
2
0
2
0
2
1
1
0
1
0
2
2
1
0
1
1
2
0
1
0
2
1
1
2
1
1
2
1
0
1
1
1
2
1
1
1
1
1
2
2
1
0
1
0
0
1
0
2
0
1
0
0
2
2
1
2
0
0
2
2
0
1
1
1
1
0
2
1
1
0
2
1
1
0
1
1
0
1
2
0
1
1
0
2
1
0
1
1
1
1
1
1
1
2
0
0
1
1
1
0
1
1
4
3
0
2
1
0
1
1
0
1
0
1
0
0
1
0
1
1
0
0
2
12
0
2
2
1
0
0
0
1
0
1
0
0
2
2
1
1
2
1
1
0
2
1
1
2
0
1
1
1
1
1
2
2
2
0
1
0
2
1
1
0
2
1
0
1
1
1
0
2
0
2
1
1
1
1
0
1
1
2
1
0
0
0
1
1
0
1
1
2
2
1
1
1
0
2
0
0
3
2
0
1
2
1
2
1
1
1
2
2
2
2
2
1
1
2
1
2
0
0
0
2
1
1
1
2
1
1
2
1
1
1
1
0
0
0
1
0
0
0
0
2
2
2
2
1
0
1
0
2
0
2
1
1
2
0
1
0
2
0
1
0
1
1
0
1
1
1
0
0
1
0
2
2
1
2
0
1
2
1
1
1
0
1
0
0
2
2
0
0
2
2
1
0
1
2
1
0
0
0
1
1
0
1
1
1
1
1
2
1
1
0
1
2
1
0
0
1
1
1
0
0
0
1
2
3
0
1
1
1
1
0
0
1
0
1
1
1
1
1
2
2
2
2
0
1
0
1
0
3
0
1
1
1
1
1
1
0
0
2
2
0
1
1
0
2
3
1
1
1
2
0
1
2
2
1
0
1
1
1
1
1
1
2
0
1
1
1
2
2
1
1
0
1
1
1
0
0
0
2
1
0
1
1
1
0
1
1
1
0
1
0
0
2
1
1
2
0
0
1
2
1
2
0
1
1
1
2
0
1
0
1
0
2
1
0
0
1
1
1
2
2
0
0
1
1
1
1
1
1
2
1
0
3
0
1
2
1
0
1
2
0
0
1
1
1
2
2
0
1
1
2
1
0
1
0
1
0
1
1
0
0
1
1
2
1
1
1
1
1
1
0
1
2
2
1
1
0
1
2
1
2
1
1
1
1
1
1
1
1
2
1
1
0
2
1
2
0
2
1
2
1
4
1
1
2
1
1
1
2
1
1
2
0
1
1
2
0
2
2
0
1
0
1
1
2
2
2
1
0
2
1
1
0
0
0
1
1
1
1
2
1
1
1
1
1
0
1
1
1
1
1
2
0
2
2
1
3
4
1
0
0
1
2
0
2
1
3
0
1
2
0
1
1
1
1
0
0
0
2
1
1
2
2
1
1
2
1
2
0
1
1
1
2
1
2
1
1
1
1
1
0
0
2
1
1
1
1
1
0
1
1
1
1
1
1
2
1
1
0
2
1
2
0
1
1
2
2
1
0
0
0
0
1
0
0
1
0
1
0
0
1
0
2
3
1
1
1
2
1
0
1
1
0
1
1
1
1
2
1
1
1
0
1
1
1
1
2
1
2
1
0
2
1
0
1
1
0
1
1
1
1
0
0
1
0
0
2
1
0
1
1
1
1
0
1
2
0
1
1
1
1
2
1
1
0
1
1
1
0
2
0
1
1
0
1
1
0
0
0
1
1
1
2
1
0
1
0
1
1
0
1
1
0
0
2
1
0
0
2
1
2
0
2
1
0
1
0
1
0
1
0
0
2
1
1
1
1
1
1
1
1
1
0
2
1
1
1
1
1
1
0
2
2
1
1
1
1
0
2
2
0
1
1
1
0
3
1
2
1
1
0
2
2
1
2
2
0
0
4
2
0
2
1
2
1
0
2
1
2
2
1
1
0
0
0
2
1
1
1
0
0
1
1
2
1
1
0
1
1
1
1
1
0
0
0
1
0
1
0
0
1
1
1
1
0
1
0
0
2
0
0
1
1
0
1
1
2
1
1
0
0
2
0
1
1
1
1
1
1
0
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
2
1
2
1
2
0
1
1
1
1
1
0
1
1
1
2
2
1
1
1
1
0
0
2
0
2
1
0
1
0
1
1
1
2
2
2
1
1
0
1
1
1
2
1
1
1
2
1
2
1
0
1
1
2
1
0
1
1
1
0
1
1
2
3
1
0
2
1
1
1
1
1
2
2
1
1
0
2
1
1
0
1
1
1
1
1
2
1
1
2
2
0
1
0
0
1
1
1
2
1
1
2
2
2
1
1
2
1
2
0
1
1
2
1
1
2
1
0
2
0
1
1
0
1
1
2
1
1
2
1
0
2
2
1
2
0
1
1
2
0
1
0
1
2
0
0
1
1
0
1
1
1
1
1
1
0
2
0
0
1
1
1
1
1
1
1
1
0
1
1
2
2
0
0
0
1
1
0
2
0
0
1
1
0
2
1
0
0
1
5
3
2
1
1
1
0
0
2
1
1
0
1
0
1
0
1
1
0
0
1
0
2
0
1
1
0
1
1
0
2
0
0
1
2
1
1
0
1
2
2
1
1
1
2
0
2
0
1
1
1
0
0
2
2
1
1
0
1
0
1
1
2
2
1
0
2
2
2
1
1
1
1
1
1
1
1
1
1
0
1
0
1
0
1
3
1
0
0
0
1
2
0
1
1
0
1
2
1
1
2
1
1
2
1
2
1
1
2
1
1
2
2
1
0
1
2
1
0
1
2
1
0
0
2
1
2
1
0
1
2
0
1
0
1
2
2
1
2
0
1
0
1
2
1
1
1
1
1
2
0
0
1
0
2
1
0
0
1
1
1
1
1
0
1
1
1
1
0
1
0
1
1
1
1
1
1
0
1
0
1
1
0
1
1
1
1
0
2
1
2
1
1
1
0
1
0
1
2
1
1
0
0
2
1
1
1
2
1
1
1
1
1
1
1
1
2
4
1
2
0
1
1
1
1
1
1
1
1
1
2
2
2
1
2
0
0
1
2
0
1
0
2
1
1
0
1
1
1
1
1
2
1
2
2
1
0
2
2
0
1
0
1
2
0
0
1
0
2
2
1
1
0
1
1
1
0
1
2
0
0
1
2
1
0
2
1
2
1
2
1
1
1
1
2
1
2
1
0
0
1
0
1
1
1
0
1
1
0
1
2
2
2
1
1
2
0
1
0
1
1
1
0
0
1
0
1
0
1
1
1
1
1
1
1
1
2
2
2
2
1
0
1
1
1
1
1
0
2
0
0
1
2
2
1
1
0
1
1
0
2
2
1
0
0
1
1
0
2
1
1
1
1
2
1
2
1
1
1
0
0
1
1
2
1
1
0
1
2
1
0
1
2
2
1
1
1
1
1
0
1
2
1
2
2
1
2
0
1
0
0
0
1
1
1
1
2
1
2
0
1
2
1
1
0
1
1
1
1
2
0
1
1
1
1
2
1
1
2
1
1
2
1
1
2
0
1
1
1
0
0
1
1
0
1
0
1
1
1
0
0
0
2
1
0
1
0
2
1
1
2
1
2
1
0
0
1
1
0
1
0
0
1
1
0
0
1
0
1
0
2
0
0
1
2
1
1
0
2
1
1
1
1
1
2
2
1
1
1
1
0
2
2
1
1
0
1
1
1
2
1
0
1
2
1
2
2
2
1
0
1
0
2
1
1
1
1
2
2
2
0
1
1
0
1
1
2
1
1
1
1
1
1
1
2
2
0
1
1
1
1
1
2
2
1
1
0
2
1
1
1
2
2
0
2
1
1
2
2
1
0
1
0
1
1
1
0
1
1
1
1
2
2
0
2
1
0
1
1
0
0
0
1
0
1
1
1
1
1
2
0
0
0
2
0
1
1
1
1
2
0
1
2
1
1
1
3
2
1
1
2
2
1
0
0
1
0
1
1
0
0
1
2
1
2
1
1
0
1
2
1
1
0
1
0
0
1
1
0
0
0
0
1
2
1
1
0
1
1
0
1
1
2
2
1
1
0
1
1
1
2
1
0
1
1
1
1
1
1
0
0
2
0
0
1
1
0
1
0
1
0
1
2
1
1
2
2
1
0
1
0
1
2
0
1
1
1
1
1
1
0
0
1
1
0
1
1
1
0
2
10
1
1
2
0
1
2
0
1
1
0
2
2
0
1
1
1
0
0
0
1
0
1
2
2
1
2
2
1
0
1
1
1
1
1
1
1
1
1
0
1
1
1
4
0
0
1
1
1
0
2
1
1
0
2
2
0
1
1
2
2
1
0
0
1
1
1
0
2
0
2
0
1
1
2
1
1
0
0
2
0
1
0
1
1
0
0
2
1
2
1
1
1
1
1
1
0
1
0
2
0
1
0
0
1
1
2
2
0
2
1
1
2
0
0
1
1
0
1
1
1
0
2
2
0
2
1
0
0
1
1
1
1
1
0
2
1
1
1
1
1
2
0
1
1
1
1
0
1
1
1
1
1
1
2
1
2
1
1
1
2
0
0
0
2
2
2
1
0
2
1
2
1
2
1
0
2
1
2
0
2
0
1
0
2
0
1
1
0
2
1
1
0
2
1
0
1
1
0
1
1
0
1
2
1
1
0
1
1
1
1
1
2
1
2
2
0
1
1
0
1
0
1
0
1
0
1
1
2
1
1
2
1
0
2
1
1
2
1
2
2
3
1
2
0
2
1
1
1
1
1
1
0
1
1
1
0
1
1
1
2
0
1
1
0
1
2
2
1
1
1
1
0
1
2
1
1
2
0
1
1
2
3
2
0
0
1
1
1
2
2
1
1
2
1
0
3
1
0
1
0
1
1
1
0
1
0
1
1
0
0
1
1
1
0
1
2
2
1
1
2
3
0
2
1
1
2
2
1
2
0
0
1
1
1
2
2
0
2
0
1
1
1
1
0
1
2
1
1
1
1
1
1
2
1
1
2
1
1
0
1
1
2
2
1
1
1
2
1
2
0
2
1
1
2
2
1
1
1
0
2
1
0
1
0
1
0
1
1
2
4
2
1
1
2
1
2
0
2
0
1
1
1
1
1
2
0
1
1
0
2
1
2
2
1
1
2
1
1
1
1
2
1
2
1
5
0
0
2
2
0
1
2
1
1
1
1
0
1
1
1
1
1
0
2
0
1
0
0
1
1
2
2
1
1
2
0
1
0
0
1
1
1
1
2
0
1
1
1
0
0
1
0
1
1
1
1
2
2
2
0
2
1
1
2
1
2
1
1
1
1
1
2
1
2
0
1
3
0
1
1
1
1
2
0
1
1
1
2
3
1
1
0
1
0
0
1
0
1
1
2
1
1
1
2
2
2
0
1
1
1
2
1
0
0
1
3
0
0
2
1
1
1
0
1
2
0
1
1
2
1
1
1
1
0
1
1
1
2
1
0
0
0
1
1
1
1
1
1
1
1
1
2
1
2
1
0
0
3
2
1
0
1
1
1
1
0
1
0
2
1
1
2
1
0
2
0
1
2
2
1
0
1
1
1
2
0
1
1
1
0
2
0
1
0
2
1
1
1
0
1
0
0
0
1
1
2
1
1
1
0
1
1
2
1
1
1
1
2
1
1
1
1
0
1
1
1
1
2
1
1
0
1
0
0
1
1
3
1
2
0
2
0
0
0
1
2
0
1
0
1
1
0
1
1
0
1
1
2
2
1
1
0
2
1
0
1
1
1
0
1
0
0
0
1
0
1
0
0
1
2
2
1
2
1
1
1
1
1
1
0
1
1
2
0
1
0
3
0
1
1
1
0
2
1
1
1
1
1
2
1
0
3
0
2
1
0
2
0
0
3
0
2
1
0
2
2
1
1
0
1
1
0
2
0
0
1
0
1
1
1
1
1
1
1
1
1
0
3
1
1
1
2
1
1
2
3
2
2
0
2
2
1
1
1
0
1
1
0
1
1
0
1
4
0
1
1
0
1
1
2
1
0
2
0
0
2
0
1
1
2
0
1
1
1
3
1
1
0
2
2
1
1
1
2
1
1
0
0
1
1
1
1
2
1
1
1
0
0
1
1
1
1
2
1
1
2
1
1
2
0
2
1
0
0
1
2
0
1
2
0
1
2
0
1
2
1
1
2
0
1
1
2
0
1
1
0
4
2
0
0
1
2
1
0
2
0
0
0
0
1
1
1
1
0
2
1
1
0
1
1
0
1
1
3
1
2
3
1
2
1
2
0
1
0
1
1
2
1
0
1
1
1
1
1
1
1
0
1
2
2
0
2
2
1
2
1
1
2
1
1
2
2
1
1
1
1
2
1
2
2
1
0
1
1
1
0
1
2
1
1
1
0
1
0
1
1
1
0
1
1
1
0
1
0
0
2
2
2
0
0
1
0
1
0
1
1
0
1
1
1
1
1
0
1
0
2
1
2
1
2
1
0
1
1
1
1
1
0
0
0
2
1
1
1
1
1
1
3
0
1
0
1
1
1
1
2
2
1
2
1
2
1
1
1
1
0
0
2
0
0
2
2
0
0
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
1
0
2
1
1
2
1
1
1
3
1
0
0
2
1
0
1
2
2
0
0
1
1
0
1
1
1
2
1
0
0
1
0
0
2
1
2
2
1
2
0
2
1
0
0
1
0
1
2
1
0
1
2
1
1
1
2
1
2
2
0
0
2
1
3
1
1
1
0
1
1
1
1
1
2
0
1
1
0
2
1
2
0
1
1
1
0
0
1
1
0
2
2
0
1
0
1
0
2
1
0
1
1
2
0
2
0
1
1
1
0
2
2
1
2
0
1
3
0
1
2
1
0
0
0
2
0
1
1
3
1
1
1
0
1
1
1
1
0
2
1
0
2
1
1
3
2
0
1
2
1
2
1
0
2
1
1
1
1
2
2
0
0
0
1
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
1
1
1
0
1
0
1
1
1
2
0
0
1
2
1
1
1
1
2
1
2
1
0
2
0
2
0
0
2
2
1
1
2
2
2
2
1
1
0
1
1
2
1
0
0
0
0
1
1
1
0
1
2
1
1
1
2
1
2
1
1
0
0
0
1
1
1
2
0
0
0
1
0
3
2
1
1
1
2
2
0
1
1
1
0
0
2
0
1
0
0
2
2
1
0
1
1
1
2
1
2
2
1
0
0
0
0
1
0
1
0
1
2
1
0
1
2
0
1
1
0
0
0
1
0
1
1
2
0
1
1
1
1
0
1
2
1
1
1
1
1
2
0
2
0
1
1
0
1
1
2
0
1
0
0
1
1
1
1
2
1
1
0
2
0
1
0
1
1
0
1
0
1
1
1
1
1
0
0
0
2
1
1
1
1
0
2
1
0
1
1
1
2
1
2
3
0
0
1
4
1
1
1
1
1
1
0
1
2
1
0
2
0
2
0
1
2
0
2
1
1
2
2
0
2
1
1
2
1
0
0
1
2
1
1
1
1
1
1
2
1
2
2
1
1
1
0
0
1
0
2
2
1
2
1
2
0
1
1
2
1
1
1
1
2
2
4
1
1
1
2
1
2
1
0
1
0
2
1
1
2
1
2
2
1
1
1
2
1
2
0
1
2
1
2
0
1
0
2
2
1
1
1
2
2
0
1
2
1
0
1
2
1
0
1
2
2
1
1
2
0
1
1
2
1
2
1
1
1
2
1
1
2
0
1
1
2
0
1
2
1
1
1
0
2
1
1
1
2
1
1
1
1
2
1
0
0
0
1
2
1
1
1
1
1
1
1
2
2
1
0
1
2
1
1
1
1
2
1
1
2
1
0
1
1
2
1
1
1
0
0
0
2
0
0
2
0
1
1
1
1
1
2
2
0
1
2
2
1
0
1
1
1
1
2
0
1
1
2
1
1
2
1
1
1
1
0
1
2
1
1
0
0
0
1
0
0
1
0
2
2
0
0
0
1
1
2
1
1
1
0
1
0
1
0
1
2
2
1
0
1
1
1
1
2
1
1
1
1
2
1
1
1
1
0
1
0
11
1
1
1
2
1
2
1
1
0
1
2
1
1
1
1
1
2
3
1
1
1
2
1
1
1
2
0
2
2
2
0
1
1
4
2
1
1
1
1
2
0
0
2
1
1
2
1
1
2
1
2
1
3
2
1
1
2
1
0
1
1
0
1
1
1
0
1
1
1
0
1
1
0
0
1
1
1
2
3
1
2
1
1
1
1
1
1
2
0
0
1
0
1
1
1
1
1
0
0
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
2
0
1
0
1
1
2
0
1
1
0
1
1
0
1
2
1
2
0
1
1
1
1
0
1
1
1
0
0
1
0
1
1
2
2
2
0
0
2
0
1
0
0
0
1
2
1
0
1
1
0
1
1
1
0
1
0
1
1
2
0
1
0
2
1
1
1
0
0
0
1
1
1
1
0
1
1
0
1
1
1
0
1
1
1
1
0
0
1
1
1
1
2
1
2
0
1
1
0
1
1
0
1
0
2
0
1
1
0
0
0
1
0
1
0
1
0
0
2
0
0
1
1
1
1
1
0
2
0
1
1
1
0
1
0
0
2
1
1
1
1
1
2
1
0
1
2
0
0
1
1
1
1
1
0
1
2
1
1
0
1
2
0
0
1
2
1
0
1
1
2
0
1
0
1
0
0
1
2
0
2
1
1
2
1
0
1
0
0
1
2
3
1
1
1
1
1
1
1
0
2
2
2
1
1
2
1
1
1
0
2
0
1
0
0
1
0
1
0
1
2
2
1
1
0
2
1
2
1
0
3
1
1
1
1
0
1
1
1
1
0
0
0
2
2
1
0
1
1
1
0
0
1
0
0
2
2
0
1
1
1
2
1
1
2
2
0
1
1
2
2
1
1
1
0
3
2
0
2
1
1
2
0
2
1
0
1
1
1
1
2
1
2
1
1
3
1
0
2
1
0
1
1
1
1
1
2
0
1
0
1
2
0
1
1
1
1
1
1
0
1
1
0
2
1
1
1
2
1
0
1
1
1
1
0
2
2
1
1
1
1
1
0
1
2
1
1
2
0
1
1
0
1
1
0
2
0
2
0
3
2
1
1
4
2
2
1
0
0
0
0
1
0
2
1
0
1
2
1
0
3
1
2
1
0
1
1
0
0
1
2
0
1
1
1
0
1
1
1
1
1
0
0
3
2
0
1
0
1
1
2
1
2
0
1
1
0
1
1
0
1
1
2
1
1
1
0
1
1
1
1
2
1
1
1
0
2
0
0
1
0
1
1
1
2
0
0
0
0
0
1
1
2
1
0
2
2
0
1
0
0
0
1
1
2
1
1
0
1
2
0
1
1
1
0
2
0
1
0
0
0
1
3
1
1
2
2
1
0
0
1
2
2
1
1
2
1
3
1
1
1
1
1
2
0
0
1
1
1
2
3
1
0
2
1
0
1
0
1
2
2
1
1
0
1
1
1
0
0
2
0
1
0
2
1
1
1
1
1
2
2
2
0
1
1
1
2
1
1
1
0
0
1
1
1
2
1
1
0
1
0
1
0
1
1
2
1
0
1
1
2
0
1
0
2
1
1
1
0
1
1
2
2
1
1
1
0
0
1
0
1
0
1
2
0
2
1
2
1
1
1
2
1
1
1
1
1
2
2
0
2
1
1
0
0
2
1
0
0
1
1
1
0
0
1
1
1
1
1
1
1
1
1
2
0
1
1
2
0
1
0
1
1
3
1
1
1
2
1
0
1
2
1
2
0
1
0
1
1
0
1
1
1
2
1
0
2
2
0
1
1
2
1
1
0
1
0
1
1
2
1
1
1
1
2
0
2
1
1
1
0
2
3
0
0
0
2
0
1
1
0
0
0
1
1
1
1
1
2
1
2
1
1
0
2
1
0
0
1
1
1
2
1
1
0
1
1
1
0
2
0
1
0
1
0
2
2
0
1
1
1
1
0
2
2
1
2
0
1
0
1
2
2
0
0
1
1
1
1
1
0
1
1
1
2
0
1
1
1
1
1
1
0
1
0
0
1
1
1
1
1
0
2
1
0
0
1
0
1
1
1
1
1
1
2
0
1
0
2
2
1
1
1
1
1
10
0
2
2
1
1
0
0
1
1
1
0
1
1
0
1
0
0
2
1
0
1
0
0
1
1
1
1
2
2
1
0
0
1
2
2
1
1
2
2
1
0
1
2
0
0
1
1
0
1
2
0
1
1
0
1
1
1
1
2
1
0
1
0
2
1
1
0
1
1
2
2
0
0
2
1
1
1
1
0
1
1
0
2
1
1
1
1
1
2
2
0
2
0
0
2
1
2
0
1
1
1
1
0
0
0
0
0
1
1
1
0
1
1
2
0
1
1
2
1
1
1
2
1
1
1
2
0
1
1
0
1
0
0
2
3
2
1
1
1
0
0
1
1
1
1
1
0
1
2
1
1
1
1
1
2
1
1
2
0
2
2
0
0
1
1
2
1
0
0
0
1
2
0
4
2
0
0
0
0
2
1
1
1
2
1
1
0
0
2
2
2
0
2
4
1
1
1
1
1
1
0
2
0
1
0
0
3
1
1
1
1
0
1
2
0
1
0
1
1
0
0
2
2
2
0
2
0
1
0
2
0
1
0
2
1
2
1
0
2
2
1
1
1
1
2
0
0
1
1
0
1
2
0
0
1
2
1
0
1
1
2
1
1
1
0
1
0
1
1
2
0
2
0
0
0
1
1
2
0
0
1
0
0
0
0
2
1
2
1
0
0
1
1
0
1
1
0
0
2
1
1
0
1
1
1
0
1
0
2
1
2
1
0
1
0
0
0
1
0
1
2
1
1
1
1
2
1
2
1
1
0
0
0
1
1
1
2
0
1
2
3
1
1
1
1
0
2
1
2
1
1
0
0
1
1
2
1
2
1
1
0
1
1
0
0
2
1
1
1
1
1
1
2
2
2
1
0
1
1
1
1
1
2
1
0
0
0
1
0
1
1
2
1
0
1
1
1
2
1
1
0
0
1
1
1
1
0
2
0
1
1
0
2
2
1
1
2
1
1
0
1
1
1
0
1
2
1
1
1
1
1
1
1
1
1
0
1
2
1
1
1
0
1
1
1
2
2
1
2
2
1
1
0
0
0
0
1
2
0
1
0
1
1
0
2
1
2
0
0
0
2
1
1
1
1
1
1
2
2
1
0
1
1
2
2
2
1
2
0
4
1
1
1
0
1
2
1
1
0
1
1
1
1
0
0
0
2
1
1
1
2
0
1
1
0
1
2
0
2
2
2
2
2
1
1
2
1
1
2
1
0
0
0
1
0
1
0
1
0
2
0
0
1
2
1
0
1
2
0
1
1
1
1
1
2
2
2
1
1
2
1
0
0
1
0
1
2
2
1
2
1
0
1
2
1
1
0
1
1
1
1
1
1
1
2
0
0
0
1
1
1
1
0
1
0
1
1
1
1
0
0
0
2
1
1
1
2
1
2
1
1
2
0
0
2
1
1
1
2
0
1
1
1
0
0
2
2
2
1
1
0
2
1
1
1
1
1
1
0
0
1
0
0
1
1
1
1
0
0
0
1
0
0
0
1
1
0
0
1
1
2
1
2
0
1
2
0
2
1
1
1
2
1
1
0
1
1
1
1
2
0
3
1
0
0
0
2
0
0
0
1
1
0
2
1
2
1
0
1
2
1
1
0
2
0
0
6
1
1
2
1
1
1
1
0
1
1
1
1
1
1
1
3
0
0
1
1
2
1
0
1
1
1
2
2
1
1
1
2
1
2
0
1
0
1
2
0
1
2
1
2
1
2
1
1
2
0
2
1
1
1
0
1
1
1
1
1
2
1
0
1
2
2
2
1
0
1
0
1
2
0
1
1
1
1
1
0
0
0
1
1
2
1
1
2
1
0
1
2
6
1
1
0
0
1
2
1
2
1
1
1
1
2
2
1
0
1
1
1
2
1
1
1
2
1
0
2
2
1
1
2
1
1
0
1
1
1
2
1
0
1
2
1
2
1
1
0
1
1
1
0
1
1
1
0
0
1
1
0
2
2
0
2
1
0
1
1
1
2
1
0
2
1
1
2
2
1
1
2
1
1
1
2
0
0
2
0
2
1
1
2
1
2
1
0
1
0
1
2
0
1
1
0
1
1
1
1
1
1
0
1
2
1
1
2
1
1
1
1
1
0
1
1
0
1
1
1
1
2
2
0
1
1
1
2
1
2
2
1
0
1
1
1
2
1
0
2
0
0
1
1
1
1
1
1
2
1
1
2
0
2
1
2
1
2
2
1
1
1
1
1
0
2
1
0
2
1
0
2
1
0
1
1
0
1
1
2
1
0
2
0
0
1
0
1
2
1
1
1
2
1
2
2
1
1
2
0
1
0
0
1
1
0
0
2
0
1
1
1
1
1
2
2
1
1
0
0
2
2
0
2
2
2
1
1
1
2
1
0
0
0
0
1
0
2
1
1
1
0
2
2
2
1
1
1
1
1
2
1
1
1
1
1
2
1
0
1
2
1
1
0
0
0
1
0
0
1
1
1
0
1
1
0
2
1
1
1
2
2
1
1
1
1
2
1
1
0
0
2
0
0
1
0
1
2
2
1
2
1
0
0
2
1
0
1
1
2
0
1
2
0
2
0
2
1
1
1
1
1
0
1
0
1
0
2
0
1
2
1
1
1
3
1
2
0
2
1
1
2
1
1
0
2
1
1
1
1
1
0
1
0
1
1
1
1
1
0
1
1
0
1
0
1
1
0
2
1
0
1
1
1
0
2
0
2
1
2
1
0
1
1
2
1
0
2
1
2
0
0
0
2
1
0
1
2
1
2
2
1
1
2
1
2
0
1
1
0
1
1
1
0
2
2
0
1
1
0
1
0
1
1
1
1
0
0
1
1
1
1
0
1
0
1
1
2
1
0
1
1
2
0
2
2
1
2
0
2
1
1
1
1
1
1
0
1
1
2
2
1
1
1
2
2
2
1
0
0
2
2
1
1
0
0
1
1
0
1
3
1
2
0
2
1
1
0
1
1
1
1
1
2
2
1
0
2
1
1
2
1
0
0
1
1
1
2
2
0
2
1
1
2
1
1
1
1
0
0
2
0
0
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
0
0
1
2
0
0
3
1
1
1
2
1
1
2
0
2
1
1
2
1
2
1
1
2
0
0
1
2
1
1
1
1
2
3
1
2
1
1
1
0
0
1
2
1
2
0
1
0
1
1
1
1
0
1
0
1
1
2
1
0
0
2
1
1
1
1
2
1
1
0
0
2
1
2
1
0
2
1
1
1
1
1
0
0
2
1
0
1
1
1
2
1
1
0
1
1
1
1
1
0
0
1
0
0
1
1
3
2
2
1
1
1
1
2
1
0
1
0
2
1
2
1
1
0
2
0
1
0
0
2
1
0
1
2
0
1
1
1
1
0
1
2
0
1
1
1
2
1
2
1
0
1
2
0
2
1
2
2
3
0
1
2
1
1
1
1
2
1
1
1
2
0
0
0
1
1
0
1
0
1
0
2
1
1
0
2
1
1
2
0
1
2
2
1
1
1
2
2
1
0
1
1
0
2
1
0
1
0
0
0
0
2
0
0
1
1
1
1
2
0
2
1
1
2
1
1
1
1
0
1
2
1
0
0
1
0
2
1
0
1
2
2
1
1
1
2
1
2
1
2
2
1
1
2
2
2
1
1
2
0
0
1
0
3
1
1
0
0
1
1
1
0
1
0
0
0
2
0
1
2
1
1
1
2
1
1
2
1
1
1
1
1
0
1
1
1
2
1
1
1
1
0
1
0
1
1
0
2
1
1
1
2
2
2
0
1
0
1
2
1
1
0
1
1
2
0
0
1
1
1
1
2
1
1
1
2
1
2
1
0
1
1
1
1
1
1
2
2
1
2
0
0
0
1
1
2
1
0
0
1
1
1
1
1
1
0
1
2
0
1
0
1
1
1
0
1
1
1
1
0
1
2
0
1
2
2
1
1
1
2
1
0
2
1
1
1
1
2
1
0
1
0
1
4
1
0
1
2
2
0
2
1
2
1
1
0
1
2
2
1
0
1
1
1
1
2
1
0
1
1
0
1
1
1
1
1
1
1
1
2
1
0
1
2
2
2
1
1
1
2
1
2
1
1
0
1
0
0
2
1
0
0
3
0
1
1
1
0
1
2
1
0
0
1
2
1
2
1
2
0
1
0
2
1
1
0
0
2
1
2
1
2
1
2
2
1
1
2
1
0
1
1
0
2
2
1
1
2
1
1
0
1
2
2
2
1
1
2
1
1
1
6
0
0
1
2
1
1
1
1
2
1
1
1
0
1
1
1
0
2
0
2
1
2
0
7
0
0
1
1
1
2
1
1
0
1
1
1
1
1
2
0
2
1
1
2
0
1
2
2
1
1
0
2
1
0
2
2
1
1
2
0
0
0
0
1
1
0
1
1
1
0
2
1
1
1
0
1
2
1
0
2
2
1
2
0
2
2
2
1
0
2
0
1
1
0
2
0
1
2
1
1
0
3
1
2
0
1
1
1
1
1
1
1
1
0
1
2
2
0
0
2
1
1
0
1
2
0
2
1
1
2
2
1
1
2
2
2
1
1
2
1
1
0
1
2
2
0
2
2
2
1
2
1
1
1
0
1
1
1
1
1
1
2
0
1
2
1
1
1
1
0
1
2
0
2
2
1
1
2
2
1
1
2
2
1
1
2
1
1
0
0
1
0
1
2
3
0
2
2
2
2
1
2
2
1
1
1
1
1
1
1
0
0
1
2
1
1
0
0
1
1
0
1
1
1
1
1
2
2
2
1
2
1
1
1
0
2
1
0
0
2
1
0
1
0
2
1
1
0
1
2
1
1
1
1
2
1
0
2
1
1
2
1
0
2
1
2
2
2
2
1
0
1
2
2
3
1
1
2
2
1
1
1
1
2
1
1
0
1
1
0
1
2
0
1
2
1
1
1
2
1
1
1
1
2
1
1
0
2
1
2
4
1
2
1
1
2
1
0
0
4
0
1
0
1
2
1
2
1
1
1
0
1
0
1
1
2
1
1
0
0
0
0
0
1
1
0
0
0
2
1
1
0
2
1
1
2
1
1
1
0
1
2
1
1
0
1
1
2
1
1
1
1
1
1
1
1
1
1
2
0
0
1
1
2
0
1
1
1
1
0
1
0
2
1
0
1
2
2
1
2
1
1
0
0
1
1
2
1
2
1
1
1
1
0
0
2
1
1
0
2
2
1
0
1
1
1
1
1
1
0
0
1
1
1
1
1
2
1
1
2
2
0
2
2
2
1
0
0
1
1
0
2
1
1
1
1
1
0
1
1
1
1
1
2
1
0
2
1
1
1
1
1
1
0
0
2
0
1
0
1
0
0
1
2
1
0
2
0
2
1
0
2
0
1
2
1
1
0
2
1
2
1
0
1
1
1
1
0
1
0
1
1
0
1
2
2
0
2
1
2
1
2
0
1
0
1
1
1
0
2
0
1
1
1
1
0
2
1
1
2
2
1
1
1
2
2
0
1
1
1
1
2
1
1
0
1
0
0
1
0
1
0
1
1
1
0
1
2
1
1
1
1
1
2
0
1
2
2
0
0
1
1
0
1
0
1
2
0
2
1
1
0
1
1
1
1
1
1
1
1
1
2
2
0
2
1
2
0
1
1
2
1
0
1
2
1
3
1
2
0
1
1
2
2
2
1
1
1
1
2
1
1
0
0
0
1
1
1
0
1
0
0
2
0
1
0
2
1
0
1
0
1
2
0
1
2
0
3
1
0
0
2
0
1
0
1
1
1
1
1
2
1
0
1
0
0
1
1
1
1
2
1
2
2
1
2
2
1
1
0
1
0
0
1
0
1
1
1
1
2
0
2
0
1
0
0
1
1
2
1
0
2
0
2
1
1
1
0
1
1
2
1
0
0
1
1
1
1
0
1
0
2
1
2
1
0
1
1
0
2
1
1
0
2
1
1
1
1
1
0
1
1
2
0
1
1
1
0
2
1
0
2
0
1
1
2
2
2
1
0
2
1
2
1
1
1
1
2
2
0
1
0
2
1
3
1
0
1
0
0
0
1
2
0
1
0
2
1
1
1
1
1
0
0
1
1
1
0
1
1
1
1
2
1
1
3
2
2
0
1
0
1
0
1
1
0
1
2
1
2
0
2
1
2
0
0
2
0
1
1
0
1
1
0
0
0
1
0
0
2
1
0
1
2
0
1
0
1
1
1
1
0
0
1
1
2
2
1
1
1
0
2
1
0
1
0
1
0
1
0
1
0
1
1
1
1
0
0
1
1
0
1
2
0
2
0
1
0
1
2
0
1
1
1
1
1
1
0
1
1
1
1
1
2
1
2
1
1
1
1
2
2
1
0
1
1
1
0
1
0
2
1
2
0
2
1
1
1
0
1
1
1
1
1
1
2
0
1
1
0
0
2
0
1
1
1
1
2
1
1
1
2
1
0
1
1
1
1
0
1
0
0
0
2
1
1
1
1
1
1
0
1
0
2
1
1
1
1
1
2
0
2
1
2
1
2
0
1
1
1
1
1
1
0
1
1
1
1
0
1
0
1
1
1
1
2
1
0
1
2
0
0
1
2
1
1
1
1
1
1
1
0
1
1
1
2
2
1
0
1
1
1
0
1
1
0
3
4
1
1
1
2
0
1
0
2
1
1
1
0
1
1
1
1
1
0
0
2
0
0
0
1
2
1
1
1
1
2
0
2
1
2
1
1
1
0
0
0
1
0
1
0
1
1
0
1
2
1
1
1
1
0
2
0
2
1
0
1
2
1
0
0
1
2
1
1
2
1
0
1
1
1
0
0
1
1
0
1
0
2
2
1
1
2
0
1
2
2
1
1
1
1
0
1
1
1
1
0
1
1
1
0
1
1
0
0
1
0
1
2
1
1
0
0
1
1
1
0
1
2
1
1
2
1
2
1
1
2
1
2
1
1
1
2
0
0
0
1
1
1
2
2
1
2
2
0
0
1
0
1
0
0
1
1
2
1
0
2
1
2
2
2
0
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
2
0
1
2
1
2
1
1
2
2
0
0
2
0
0
1
0
0
1
2
2
1
2
1
1
2
0
0
0
1
1
2
0
1
2
0
0
1
0
2
1
1
1
0
1
2
1
1
1
1
0
1
0
2
3
1
0
1
2
0
1
1
1
0
1
0
0
1
1
1
2
1
1
0
1
2
0
1
1
2
2
1
2
1
1
0
2
1
2
2
1
1
1
2
2
0
1
1
0
2
1
0
0
1
1
0
2
2
1
1
1
1
2
0
0
0
4
2
1
1
2
1
0
0
1
2
1
0
1
2
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
0
1
2
1
2
1
1
1
1
1
0
2
0
2
1
2
0
1
0
1
1
1
1
0
1
1
2
1
1
2
0
0
2
1
0
0
1
0
2
2
1
1
0
0
0
2
0
1
1
1
0
1
0
0
2
1
2
1
0
1
1
2
1
1
1
0
1
2
0
0
2
1
0
2
1
0
1
0
1
2
1
1
1
1
1
1
2
1
1
1
0
2
0
1
0
0
0
2
1
0
2
1
1
1
0
1
0
1
1
1
2
0
1
0
1
1
1
2
2
0
1
3
0
1
1
2
0
0
2
1
0
0
0
3
1
1
1
2
2
1
1
2
1
1
1
2
1
2
1
2
1
1
0
1
1
1
1
0
2
1
1
1
2
1
1
2
1
0
1
0
1
1
1
0
1
1
0
2
1
1
1
1
1
0
2
2
1
0
1
1
0
0
2
2
2
1
0
1
1
1
0
1
2
1
1
1
2
0
2
1
2
1
1
0
1
2
0
1
2
1
2
1
1
1
2
1
0
2
1
1
0
2
0
2
1
1
1
0
1
2
1
2
1
2
0
1
1
1
0
0
1
1
1
1
1
1
1
0
3
2
1
2
0
2
2
2
2
0
0
0
2
1
2
1
1
1
1
1
0
2
0
0
1
1
0
0
0
1
0
1
1
2
0
0
1
0
1
1
2
1
1
0
0
2
1
1
1
2
0
0
1
2
1
1
2
2
2
0
0
1
1
1
1
1
1
2
1
2
0
1
0
1
0
1
1
1
1
1
0
1
0
1
2
1
2
0
2
1
2
0
0
1
0
1
0
1
1
0
1
1
1
1
1
0
1
1
1
0
0
2
0
0
2
1
1
1
1
1
1
2
2
1
1
1
0
0
1
4
1
0
1
1
2
0
1
1
0
1
1
0
1
1
2
0
1
0
1
1
1
0
0
0
1
0
1
0
0
0
2
0
1
0
1
2
1
0
1
1
0
1
2
0
0
1
1
0
2
1
0
2
1
0
1
0
1
1
2
2
1
1
1
1
1
2
0
1
1
1
1
1
1
1
0
2
1
1
1
1
2
1
1
0
1
2
0
1
1
0
1
2
0
0
1
0
1
0
1
1
1
1
1
0
1
1
1
1
1
1
2
1
2
0
1
0
1
2
0
1
2
3
0
2
1
2
1
2
1
0
1
0
1
3
1
2
0
0
0
2
1
2
1
0
1
2
0
2
1
0
0
2
1
1
0
0
2
1
1
1
2
1
2
2
1
1
1
0
1
0
1
3
0
1
2
1
2
0
1
1
3
1
0
1
2
2
0
0
1
1
2
0
1
1
2
2
2
1
1
2
1
2
0
2
1
1
2
1
1
1
1
1
1
0
2
2
0
1
2
1
0
1
1
1
1
1
1
2
2
2
0
1
1
1
1
0
1
0
0
1
1
1
0
1
1
0
1
1
0
1
1
1
0
0
0
2
0
2
2
1
1
0
0
1
2
2
1
0
1
1
2
0
2
2
1
0
1
1
0
0
1
0
1
2
2
1
2
0
3
0
0
2
1
1
2
0
1
2
2
2
1
2
1
1
1
2
0
1
1
1
1
0
1
2
0
1
2
1
1
1
0
1
0
0
0
1
1
0
1
1
1
2
1
1
1
1
1
1
0
1
0
1
2
2
1
2
1
1
0
0
1
1
2
0
0
1
0
1
1
1
0
0
1
1
1
0
0
1
0
0
1
1
1
0
1
0
1
0
2
1
0
2
1
1
1
1
1
2
1
0
1
0
2
2
1
1
1
5
1
2
1
1
0
3
0
1
2
1
1
2
2
1
1
1
1
1
0
1
0
1
1
0
1
0
0
0
1
1
1
1
1
0
0
1
1
2
1
0
0
1
0
1
0
1
1
1
0
0
0
1
1
2
1
2
0
1
0
1
1
1
1
0
1
1
0
1
0
1
2
0
0
1
1
1
1
0
1
1
2
0
2
1
1
2
1
0
1
0
1
1
2
0
2
1
2
1
2
1
1
1
1
0
2
2
0
1
1
1
1
0
1
1
1
1
1
1
0
1
1
1
1
1
0
1
1
1
1
1
2
2
2
0
0
1
2
1
2
0
1
1
1
1
1
1
1
3
2
0
0
1
0
1
2
1
0
1
1
0
2
2
2
1
2
1
2
0
1
1
2
2
2
1
1
1
0
2
0
1
2
1
1
0
1
2
1
2
2
1
0
2
1
0
0
1
1
1
1
1
1
1
1
1
1
0
1
2
1
2
2
2
1
0
0
0
2
2
2
1
1
1
1
2
0
2
0
0
0
1
1
0
1
2
1
1
1
2
2
1
0
2
1
1
1
1
1
1
2
1
1
1
0
0
6
1
1
1
0
2
2
1
1
1
2
1
2
1
1
2
2
2
2
1
0
2
0
1
0
0
1
1
1
0
1
1
1
1
1
0
1
1
1
1
1
1
2
1
1
0
2
0
0
1
1
2
2
1
0
2
0
2
1
1
1
0
0
0
1
0
1
0
0
1
1
0
0
2
1
1
2
1
2
0
0
1
0
1
1
0
2
0
1
2
0
0
1
1
2
1
1
2
2
0
0
2
2
1
1
3
2
1
1
1
1
2
2
1
1
1
1
2
1
1
2
1
1
4
1
1
1
1
0
0
0
1
0
2
2
2
1
1
0
0
1
1
2
2
2
0
1
0
0
1
1
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
0
2
1
1
2
2
1
0
0
0
1
1
3
2
1
2
2
2
2
0
1
2
3
0
1
2
1
1
2
1
2
2
1
1
2
0
0
0
1
2
2
1
0
1
1
0
2
2
1
0
1
1
1
1
2
1
1
0
1
2
1
2
1
1
1
1
2
1
2
0
1
1
2
1
1
0
1
0
1
1
1
1
1
2
0
1
0
1
0
0
2
2
2
2
2
1
1
1
1
1
0
2
2
0
2
1
1
2
1
1
1
2
1
0
1
1
1
1
0
1
0
0
1
2
2
1
3
1
0
1
0
0
1
2
1
1
2
1
2
1
1
0
2
1
1
0
2
0
1
1
1
2
1
1
1
1
0
0
1
0
2
0
1
1
2
2
2
1
1
1
1
0
0
0
1
1
0
0
1
1
0
1
1
0
2
1
1
1
0
1
1
1
2
1
2
1
1
2
0
2
0
1
1
1
2
1
3
0
0
2
1
1
1
1
0
0
1
1
0
0
0
3
1
0
1
0
1
0
1
1
2
1
1
1
2
2
0
1
0
2
2
2
1
0
1
0
2
1
1
1
1
2
1
2
1
1
1
0
1
0
0
0
2
1
2
1
0
0
1
1
2
1
1
1
1
1
1
0
1
1
0
0
0
1
1
1
1
2
1
1
1
3
2
2
1
1
2
1
0
0
2
1
2
1
1
2
1
0
2
1
1
1
1
0
0
0
0
2
1
1
2
2
1
1
1
1
2
1
0
1
1
2
1
1
2
1
1
1
2
1
1
0
0
1
0
0
1
2
0
2
1
1
0
0
1
2
1
0
1
1
1
0
0
2
1
2
2
3
0
1
2
1
2
1
0
1
1
0
0
1
2
1
0
0
0
1
1
0
1
1
1
1
1
2
1
2
0
1
1
1
0
2
1
0
1
1
0
1
0
1
1
1
1
1
1
1
0
1
2
2
0
1
0
2
1
2
1
2
1
2
2
0
0
2
0
1
1
2
1
0
1
2
0
0
1
0
1
4
0
2
1
0
0
0
0
1
1
1
0
1
1
0
1
0
1
1
2
0
2
0
2
1
2
1
0
1
1
0
2
0
1
1
1
2
1
1
2
2
1
1
2
1
0
0
1
1
1
2
1
2
0
0
1
3
1
1
1
2
2
1
1
2
0
1
0
1
0
2
1
1
0
1
0
0
1
1
2
1
0
2
0
2
1
1
2
1
2
1
1
1
1
2
0
1
2
1
0
2
2
0
1
0
1
0
1
1
1
1
2
0
2
1
0
1
1
1
1
1
1
0
1
1
1
0
2
1
0
1
2
0
0
0
0
1
2
1
1
1
1
0
1
1
1
0
0
0
1
0
0
0
1
1
2
1
1
2
3
0
2
0
2
2
1
0
1
1
1
1
1
1
1
2
0
1
0
2
0
1
1
1
1
1
5
1
2
2
1
1
2
1
1
1
1
0
1
1
2
0
0
2
1
2
2
0
1
2
1
1
1
1
1
0
2
1
2
1
0
2
1
1
1
2
1
2
1
2
0
2
0
2
0
0
0
2
1
0
0
2
0
0
1
2
2
1
1
0
2
0
1
1
2
1
0
0
1
1
0
0
2
1
0
1
0
2
1
1
1
1
1
0
1
2
1
1
1
1
1
1
2
0
2
1
0
1
2
0
1
0
3
1
1
1
1
1
1
1
1
2
0
1
1
1
2
2
1
1
0
2
1
1
2
1
1
1
2
0
1
2
1
1
0
1
2
0
2
2
1
1
1
0
1
2
0
3
1
2
1
1
1
1
0
2
1
1
0
1
0
0
2
1
1
0
1
2
0
2
1
1
0
5
1
1
1
1
0
0
0
2
1
0
2
1
1
3
1
2
1
0
1
1
1
2
1
1
1
1
1
0
1
1
1
1
2
1
0
1
2
1
1
1
2
2
1
1
0
2
2
0
1
1
1
0
2
0
1
1
1
3
1
1
1
1
1
2
1
2
1
0
1
1
1
2
0
1
1
1
2
1
0
2
2
1
1
1
1
1
2
0
1
1
0
1
2
1
2
2
1
1
1
2
1
2
1
1
1
1
2
2
2
2
0
2
1
2
1
1
1
1
1
2
1
0
1
2
2
1
0
1
0
0
1
1
1
2
2
0
2
0
0
2
0
0
2
1
0
2
2
0
0
1
2
1
0
1
1
0
2
1
1
1
0
0
1
1
2
1
2
0
1
1
1
2
1
0
0
2
2
1
1
1
0
1
0
2
0
2
2
1
1
0
0
1
1
1
1
0
2
2
0
0
0
1
4
1
0
2
1
2
2
1
2
1
0
0
0
2
2
2
1
0
0
2
1
0
0
1
1
1
1
1
1
1
1
1
0
2
2
0
1
1
1
1
1
0
1
1
1
1
1
2
2
2
2
1
1
2
1
2
2
1
2
0
2
2
0
1
2
0
2
0
1
1
1
1
1
0
2
2
1
0
1
0
0
2
2
0
1
0
1
0
0
0
2
1
2
1
1
1
2
1
1
1
1
0
0
1
1
1
1
2
1
1
0
1
1
0
2
2
1
1
0
0
1
1
1
1
2
1
1
2
0
1
1
1
1
1
1
1
0
1
0
1
0
1
2
1
1
0
1
1
3
1
1
2
2
0
0
1
1
0
1
0
2
1
2
1
1
1
1
0
1
1
1
1
1
1
0
1
1
2
1
0
0
1
1
1
0
1
2
1
0
2
1
1
1
1
2
0
2
1
1
0
1
1
1
1
0
1
0
1
0
1
3
1
1
0
1
1
2
0
1
1
1
2
1
1
1
0
2
1
1
0
1
1
0
1
1
0
2
1
1
1
1
1
1
1
1
1
1
0
0
0
1
2
2
1
2
2
1
1
1
1
0
2
2
1
0
1
0
1
1
1
0
1
1
1
0
1
0
1
0
1
1
0
1
1
1
0
1
1
1
1
1
2
2
0
0
1
1
1
0
1
1
0
0
1
0
1
0
1
0
1
1
1
2
1
1
1
0
0
0
1
2
0
1
5
0
1
1
1
2
1
1
1
0
1
2
0
1
1
1
1
1
0
1
2
1
1
2
1
1
2
0
1
0
1
2
2
0
1
0
0
0
1
0
1
1
0
2
2
2
0
2
1
2
1
1
0
1
1
1
1
1
1
1
0
2
0
1
2
1
1
1
1
2
1
0
1
5
1
0
1
1
1
0
0
1
1
0
1
0
2
1
0
1
2
0
0
2
1
3
2
2
1
1
1
1
1
1
1
1
1
2
1
1
0
1
1
0
1
1
0
0
0
2
2
0
2
1
1
0
2
0
1
0
2
1
2
1
1
0
1
1
0
0
1
3
1
1
1
1
1
2
1
0
1
0
0
2
2
0
1
1
1
2
1
1
1
0
1
1
0
1
1
2
1
0
1
1
2
1
0
1
0
1
0
3
1
1
1
3
1
2
1
0
2
1
0
1
2
1
0
1
1
1
1
2
1
0
1
0
1
0
0
1
0
0
1
1
2
1
3
1
2
0
1
1
1
0
1
0
1
1
1
0
0
1
1
0
2
0
1
1
2
0
1
1
0
2
2
0
1
1
1
2
1
2
1
2
0
1
0
1
1
1
2
0
1
0
0
2
1
2
1
0
1
2
0
1
2
1
0
1
1
0
0
1
1
1
1
2
1
0
1
1
0
1
0
1
2
0
0
0
1
1
1
2
1
3
0
1
1
1
2
0
0
1
2
1
1
1
1
1
0
0
1
0
2
1
2
1
0
2
2
1
1
2
2
1
1
0
1
1
1
2
1
0
3
2
0
1
1
1
1
0
0
2
0
1
1
0
1
1
1
1
1
1
0
1
2
1
1
2
1
1
0
2
1
1
1
0
1
0
1
0
1
1
2
2
1
1
1
1
1
1
1
2
2
1
2
0
1
1
0
1
0
0
1
0
0
1
1
2
0
1
1
1
1
1
0
0
1
2
1
2
2
1
1
2
0
1
1
1
1
1
1
1
1
2
1
2
1
0
1
1
0
1
0
1
1
1
0
2
1
2
1
1
0
1
1
1
0
1
1
0
1
0
0
1
1
2
2
1
2
2
0
1
2
1
1
0
2
1
1
0
1
0
1
1
0
1
0
1
0
1
0
1
1
0
1
1
1
2
2
0
1
1
1
0
2
2
0
1
1
1
1
0
0
1
1
1
1
1
1
1
1
2
1
1
0
1
1
2
1
1
0
1
1
1
2
2
0
1
0
2
0
2
0
0
0
2
1
1
0
1
1
1
0
2
1
2
1
1
0
1
0
0
1
1
1
1
1
1
0
1
1
0
0
2
1
0
1
0
1
0
0
1
1
1
1
0
1
2
2
2
1
0
1
1
1
1
1
1
1
2
3
1
2
1
3
0
1
1
1
1
1
1
2
0
1
1
1
1
1
0
0
2
0
1
1
1
1
1
1
1
2
1
1
0
0
1
0
2
1
2
2
1
1
0
1
1
0
2
0
1
1
1
0
1
1
1
2
0
1
0
1
1
0
1
0
1
1
0
2
2
1
1
1
1
0
1
0
0
1
0
0
1
2
0
2
1
2
2
1
1
1
1
1
2
2
1
2
2
1
2
1
1
1
0
0
1
1
1
1
0
1
2
1
2
2
1
0
1
1
1
0
1
1
2
2
2
1
1
1
0
1
0
0
1
1
1
2
1
1
2
1
2
1
2
1
2
1
2
0
0
1
1
0
1
2
0
2
0
1
2
1
2
1
1
1
0
2
1
2
2
1
1
1
2
0
0
0
0
1
0
1
1
0
1
1
1
1
1
8
2
2
2
1
0
0
2
0
2
1
1
0
0
0
1
1
1
1
0
2
1
1
0
1
2
2
1
1
2
1
1
0
1
1
0
1
2
1
0
0
2
2
2
0
1
0
2
1
1
2
1
1
1
2
2
0
2
1
0
1
0
1
2
1
2
0
1
2
1
2
2
1
1
1
0
2
1
1
2
0
0
1
1
1
0
1
1
0
2
0
0
2
1
1
2
2
1
1
1
1
1
2
1
0
1
2
1
0
1
1
0
2
1
1
1
1
0
1
1
1
0
1
1
0
1
0
1
1
1
0
1
0
1
1
1
2
2
1
0
1
1
2
1
0
1
2
2
1
1
1
1
2
0
1
1
1
1
2
1
2
1
2
1
1
1
1
2
0
1
1
2
0
2
0
1
1
1
1
1
1
0
0
2
1
2
1
0
1
2
1
0
0
0
1
1
2
0
1
1
2
1
1
0
1
1
1
1
1
2
0
0
1
1
1
2
0
1
1
2
0
2
1
2
1
1
1
1
2
0
1
1
0
2
1
0
0
1
0
1
2
0
0
2
1
1
2
1
0
1
2
1
2
2
1
0
0
2
1
2
1
1
1
2
1
0
1
1
1
0
1
2
2
2
1
1
1
1
1
2
2
2
1
0
0
2
1
2
1
1
0
1
1
0
2
2
1
4
1
0
0
2
2
2
2
1
1
0
1
1
1
1
1
0
2
1
1
1
1
1
2
2
0
2
1
1
2
1
1
2
1
0
0
1
2
0
1
1
0
0
1
0
1
1
0
1
0
1
2
0
0
3
0
2
2
1
1
0
2
1
1
2
1
1
2
1
1
0
1
2
1
0
1
1
0
1
1
1
1
1
2
1
1
2
0
0
2
2
2
0
1
0
0
2
2
1
1
1
0
1
1
0
1
2
0
2
2
1
0
1
2
3
1
1
0
1
1
0
1
1
2
0
1
2
0
1
1
2
1
2
1
1
0
1
0
0
1
2
0
0
2
1
1
2
0
1
1
2
1
0
2
0
1
0
1
2
1
2
0
1
1
0
1
1
1
1
1
1
1
0
0
1
0
1
1
1
0
2
1
2
2
0
1
1
0
1
1
2
1
0
1
0
2
2
2
1
2
0
1
0
2
0
1
0
1
1
1
1
0
1
2
1
2
2
0
2
1
1
1
0
1
2
0
0
2
2
2
0
1
1
0
1
1
2
1
0
0
1
2
1
1
0
1
1
2
3
0
2
1
0
1
1
0
2
1
1
2
2
0
1
3
0
0
0
1
2
1
0
0
0
3
2
2
3
2
1
1
1
1
0
0
1
0
2
1
0
2
1
1
1
1
1
1
1
1
1
1
0
0
0
2
1
1
1
1
1
1
2
1
0
0
0
0
2
0
0
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
0
1
2
2
0
1
2
0
2
0
1
2
2
1
1
0
1
2
1
0
1
1
1
1
0
0
0
0
1
2
0
0
1
1
1
1
0
2
1
0
2
1
1
2
0
1
1
0
1
1
1
0
0
1
0
2
1
2
0
2
1
2
2
1
1
1
1
0
0
0
1
1
0
1
1
0
1
1
1
0
2
1
2
0
2
1
1
1
0
1
1
2
1
2
2
0
1
1
1
2
0
2
1
0
0
2
1
0
1
1
1
0
0
1
0
1
1
0
1
1
1
1
1
1
1
1
1
0
2
2
1
1
2
2
1
2
1
2
0
1
0
0
2
2
0
0
1
1
0
3
2
1
1
1
1
1
1
1
0
1
0
2
2
2
1
1
1
1
2
1
0
1
2
1
0
2
1
1
0
1
1
2
0
1
0
1
0
1
2
1
2
0
2
1
2
1
1
2
0
1
2
0
0
1
1
1
1
1
1
1
1
0
0
2
2
1
0
2
3
0
2
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
0
2
1
2
0
1
2
1
1
1
0
0
0
0
0
1
0
2
0
1
0
2
1
0
0
0
0
3
3
0
1
0
1
0
1
2
2
0
2
1
1
2
1
1
1
0
1
2
1
2
2
2
2
2
1
2
1
1
0
2
2
1
3
0
2
1
1
1
0
0
3
0
1
1
0
1
0
1
1
0
2
5
2
0
1
1
1
2
2
0
2
2
1
1
1
2
0
0
1
1
1
1
1
0
2
2
4
1
0
1
0
1
1
1
1
1
1
2
1
2
1
2
0
1
0
1
0
1
0
1
1
0
1
1
1
0
0
2
1
1
1
0
2
0
0
1
1
0
1
1
1
1
2
1
1
1
1
2
0
0
1
0
1
0
1
1
0
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
0
1
0
1
0
1
0
2
0
1
0
0
1
1
0
0
2
1
2
0
1
1
2
2
1
1
1
3
1
0
0
0
1
2
1
2
1
2
0
1
0
0
1
1
2
1
1
1
1
2
1
1
1
2
1
0
2
3
1
1
1
0
1
1
2
1
1
0
2
1
2
2
0
1
1
1
1
1
0
1
1
1
1
1
0
1
1
1
0
2
1
1
2
1
2
1
2
1
1
1
0
1
1
2
1
1
2
1
1
2
1
0
1
1
1
1
1
1
1
1
1
1
1
1
2
1
0
0
1
2
1
0
2
1
2
2
0
2
2
0
0
0
0
1
1
1
0
1
1
1
2
1
1
0
2
0
2
2
1
0
1
2
2
1
1
1
1
1
1
1
0
1
1
2
0
0
0
1
1
1
1
1
0
1
1
0
1
0
1
1
1
1
1
1
1
1
0
0
1
0
1
1
1
1
1
0
2
1
1
1
1
1
1
1
0
1
1
1
0
0
2
2
1
0
1
2
1
0
1
1
2
2
1
2
1
1
0
0
1
1
2
0
1
0
1
1
2
2
0
1
1
2
0
1
1
0
3
1
1
2
2
1
1
2
1
0
1
1
1
1
2
2
0
1
0
0
2
1
0
0
1
1
1
0
0
1
2
0
0
1
1
1
2
0
1
1
2
0
0
1
0
1
1
1
1
1
1
0
2
1
1
0
0
2
1
0
2
0
1
2
1
2
1
1
1
2
2
1
1
0
1
1
1
2
1
2
1
2
0
1
1
0
1
0
0
1
1
0
0
0
1
0
2
1
2
1
2
1
0
2
1
0
2
1
1
1
1
2
0
1
0
4
0
0
1
1
1
2
1
0
1
1
1
0
0
0
1
1
0
1
1
0
0
1
0
2
0
2
1
0
0
1
1
1
1
1
1
1
1
1
1
1
2
0
2
1
1
0
1
0
0
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
2
0
0
0
1
2
3
2
0
1
2
2
0
0
0
1
1
0
1
1
1
0
2
2
1
8
1
0
1
2
2
1
1
2
0
2
1
0
1
1
2
1
0
1
1
1
2
1
0
2
1
1
0
1
0
2
1
0
0
1
0
1
0
2
0
1
1
1
1
1
1
1
2
1
1
0
2
1
0
1
2
1
2
1
1
1
1
1
2
2
1
2
2
2
3
1
1
1
0
1
0
2
2
0
1
1
1
1
1
1
0
0
0
1
1
0
1
1
1
1
2
1
1
2
1
1
1
0
2
1
1
1
0
2
2
1
1
1
0
2
2
1
2
0
1
2
0
1
0
2
0
2
0
0
1
1
1
0
1
2
1
1
0
0
2
0
2
1
1
1
1
0
1
1
1
0
0
4
1
1
2
1
1
1
0
1
0
1
2
1
2
1
1
1
0
1
1
0
0
2
0
1
1
1
1
2
1
1
1
2
1
1
2
0
0
1
0
2
2
1
1
2
2
1
0
1
1
1
1
0
0
1
2
0
3
0
1
0
0
2
2
0
1
2
1
0
1
2
3
1
0
0
1
1
1
1
1
1
1
2
1
0
2
2
1
1
1
1
1
1
1
1
0
2
1
3
1
1
1
1
2
0
0
1
0
1
1
1
1
0
1
1
0
0
1
0
0
0
2
1
2
2
0
0
0
2
0
0
2
0
0
0
2
1
1
1
1
0
0
0
1
1
1
1
0
1
1
0
0
1
1
2
1
2
2
0
0
2
0
1
0
1
0
2
2
1
1
1
1
1
1
0
0
0
0
1
1
0
2
1
1
1
0
1
2
1
1
1
1
1
2
1
2
2
0
1
0
0
2
1
1
2
1
2
1
1
1
1
1
1
1
1
2
3
1
1
1
0
1
1
1
1
0
3
1
2
1
1
1
1
1
0
1
1
1
2
1
0
1
1
1
2
1
1
0
1
0
1
1
2
0
1
0
1
2
0
2
0
0
1
1
1
2
0
0
2
1
0
0
1
1
0
0
1
1
2
0
1
0
0
1
0
2
1
0
1
2
1
1
0
1
1
1
0
2
2
1
1
1
1
2
2
0
1
1
0
1
1
3
1
0
0
1
1
1
0
0
1
1
0
2
0
1
0
1
1
1
2
2
0
1
0
1
0
1
1
1
1
0
2
1
1
2
1
1
1
1
1
2
0
1
1
0
0
1
1
2
1
1
0
1
2
1
2
2
0
2
1
2
0
2
0
2
1
1
2
1
0
1
0
1
1
1
1
2
0
0
1
0
2
1
0
0
2
0
1
1
2
2
1
0
1
2
1
1
2
1
0
1
1
0
1
1
2
1
1
2
1
1
0
2
1
1
1
2
1
1
1
2
1
0
3
0
1
0
2
1
1
1
1
2
1
1
1
1
0
0
1
0
1
1
1
1
1
1
2
0
0
1
1
1
1
1
0
2
2
1
1
1
1
1
1
2
1
2
1
2
0
1
0
1
0
1
1
0
2
0
1
2
0
1
0
2
1
2
1
1
1
2
1
1
1
0
2
1
1
1
2
2
0
2
1
1
1
3
2
0
0
0
1
1
1
0
0
1
0
0
1
2
1
2
2
1
1
1
2
1
0
1
1
1
1
1
1
1
0
1
2
0
0
2
0
1
1
3
1
1
0
2
0
1
0
1
0
1
0
0
1
2
2
1
1
2
0
1
2
2
1
1
1
1
0
2
2
0
2
1
1
2
0
1
0
1
1
0
0
2
2
1
2
2
0
1
2
2
2
0
0
1
1
1
1
0
0
1
1
1
0
0
0
1
1
1
1
1
2
1
0
0
1
1
1
1
2
1
1
0
1
0
1
1
1
1
1
1
0
2
2
0
0
1
1
2
1
1
2
1
1
1
1
2
1
0
2
2
0
1
1
1
1
1
1
0
1
1
1
1
2
2
2
0
1
0
1
2
2
1
2
2
0
1
1
1
1
1
0
2
1
1
1
1
1
0
1
0
1
2
2
1
1
2
1
1
0
1
1
0
2
2
1
0
1
1
0
0
0
0
2
1
1
1
1
2
1
1
1
1
1
2
1
0
1
2
1
1
1
0
2
0
0
2
2
2
1
1
1
1
1
1
0
2
0
1
1
1
0
0
1
1
2
1
0
1
1
1
1
2
1
0
1
1
1
1
1
1
2
1
1
1
1
1
2
2
0
1
0
1
0
0
2
1
1
2
1
2
0
2
2
2
1
2
1
2
1
1
2
1
0
6
0
2
1
1
1
2
1
2
4
1
1
1
2
3
0
1
1
0
1
1
1
1
2
2
0
2
1
2
1
2
1
0
0
0
1
1
1
2
1
0
1
1
0
1
1
1
2
1
1
1
1
1
1
1
2
2
0
4
2
2
0
3
1
0
1
2
1
0
1
1
1
2
1
1
1
1
1
2
1
1
1
0
0
2
2
1
1
1
1
1
3
1
1
1
1
0
0
1
0
2
2
1
3
1
1
1
1
0
2
1
2
1
2
0
1
1
1
0
1
1
0
1
1
1
0
1
1
2
1
1
1
0
1
1
2
1
1
0
2
1
0
1
0
1
0
1
2
0
1
1
1
1
1
2
1
1
0
1
3
0
1
1
2
0
0
0
1
1
1
1
1
1
1
1
1
0
1
0
0
0
1
0
1
1
1
1
3
0
1
1
0
2
1
0
0
0
1
2
0
0
0
1
1
1
0
1
1
1
1
1
1
0
1
0
0
0
0
1
1
2
2
1
1
1
0
1
1
1
2
2
0
0
1
1
2
1
1
1
2
0
1
1
0
1
0
2
2
2
0
2
1
1
1
1
1
0
1
1
2
1
2
2
0
0
1
1
1
2
1
1
0
1
0
0
0
1
2
2
2
1
1
0
0
1
0
1
1
1
1
1
1
0
1
1
1
0
1
1
2
0
2
2
2
2
0
1
0
0
1
2
0
1
1
1
1
8
1
1
1
1
0
0
0
2
1
2
3
1
2
1
1
2
2
0
0
2
0
0
1
1
1
0
1
1
2
1
2
1
1
2
2
0
2
0
1
1
3
2
2
1
1
1
2
2
0
1
2
1
1
1
1
1
2
1
2
1
1
1
0
2
2
1
0
0
1
1
2
2
2
1
2
1
1
1
1
1
1
0
2
1
1
1
0
1
1
0
1
0
1
1
2
0
1
0
1
1
2
2
1
1
1
1
1
1
0
1
0
3
0
0
1
1
1
0
1
1
0
1
1
0
1
1
1
1
1
1
1
1
1
1
2
1
1
0
1
2
1
1
2
1
1
1
0
1
1
1
2
2
2
0
0
2
1
0
0
1
1
1
2
1
1
0
2
1
1
0
0
1
0
5
1
1
2
1
2
0
1
0
1
3
1
1
1
1
1
1
0
2
1
1
0
0
0
0
0
2
1
0
1
2
1
0
0
0
2
1
0
2
1
1
2
1
1
1
1
2
1
1
0
1
1
1
0
1
2
0
1
1
1
1
1
0
0
2
1
0
0
2
1
0
2
1
1
2
2
1
1
1
2
1
1
0
1
2
1
2
1
2
0
2
0
0
1
0
1
1
0
1
1
0
0
0
0
1
1
1
0
2
0
2
0
1
0
1
1
0
1
2
0
1
1
1
2
1
0
1
0
1
1
2
1
2
1
1
1
0
0
1
1
0
1
2
1
2
0
0
2
1
1
1
1
1
1
2
0
0
1
0
0
2
0
1
1
2
2
1
1
2
2
0
1
2
2
0
1
1
1
2
0
0
1
1
1
1
1
1
2
2
0
2
1
1
2
1
1
2
1
1
0
0
0
1
1
1
2
1
2
0
1
0
1
1
1
2
1
1
1
1
1
1
1
1
1
1
0
1
1
1
0
0
0
1
1
2
2
1
0
2
1
1
0
1
0
1
1
1
1
2
1
2
1
0
0
1
0
1
0
1
0
1
1
0
1
2
0
1
1
1
0
0
1
0
2
1
1
1
1
2
1
0
1
1
1
1
1
2
2
1
0
0
0
0
1
2
2
2
0
0
1
1
0
1
1
1
2
1
2
1
0
2
0
2
1
1
1
1
0
2
0
1
1
2
1
1
0
1
1
1
1
1
2
0
2
1
0
2
1
0
1
1
0
1
1
0
1
2
1
1
0
0
0
1
2
0
1
0
1
1
2
1
0
2
1
1
1
1
0
2
1
0
1
1
1
1
2
1
2
0
1
0
1
1
1
2
1
1
2
1
2
1
1
1
1
2
0
2
1
1
0
1
2
1
2
1
2
0
0
1
1
1
1
1
1
1
2
1
1
1
0
2
1
1
2
2
2
1
2
2
2
2
1
0
1
1
2
2
1
1
1
1
1
1
1
2
1
1
2
2
1
2
1
2
1
0
1
1
2
0
0
1
2
1
1
1
2
0
1
1
3
1
0
1
1
1
0
1
0
1
1
1
2
0
1
1
1
2
1
1
2
1
2
0
1
2
2
1
0
1
1
0
0
2
2
0
0
1
2
0
0
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
0
2
0
2
1
2
2
0
1
1
1
0
0
2
2
1
0
1
1
1
1
0
1
1
2
1
1
0
0
0
0
2
1
0
0
2
1
1
1
0
2
0
0
1
5
2
0
0
1
2
0
0
0
1
1
0
1
1
0
0
0
0
1
0
1
1
1
0
1
2
0
0
1
2
1
0
2
1
1
2
1
0
2
1
1
0
2
0
0
0
0
1
1
0
1
1
0
0
1
2
0
1
2
0
1
1
1
2
1
2
1
1
2
1
2
1
1
2
1
0
2
1
2
1
0
2
2
1
1
2
0
2
1
1
2
0
0
1
1
1
0
1
2
1
1
0
1
1
1
1
0
2
0
2
1
2
0
2
1
2
1
2
1
2
1
0
1
1
1
1
1
0
1
0
2
0
1
1
1
1
2
2
1
2
0
0
1
2
1
0
1
0
0
2
2
1
1
1
1
2
1
1
1
1
1
1
0
2
1
2
2
2
1
1
1
1
0
2
0
2
1
2
1
1
1
0
1
0
1
2
0
1
1
1
1
1
2
2
1
0
1
1
0
1
1
1
1
0
1
1
1
0
1
1
1
1
1
1
1
0
2
1
2
0
2
1
1
0
2
1
1
0
1
0
1
1
1
1
1
1
1
1
1
2
1
2
0
2
1
2
2
1
0
1
1
2
2
1
1
2
2
1
1
0
0
2
0
1
1
2
2
2
1
1
1
2
2
0
1
1
1
2
1
1
1
2
2
1
1
2
1
0
2
2
1
1
0
1
1
1
2
1
0
0
1
1
0
1
0
2
2
1
2
0
0
0
0
0
0
5
1
2
2
2
2
1
1
2
0
1
2
0
1
0
1
0
1
1
1
0
1
1
0
0
2
1
1
1
1
2
2
1
1
0
1
1
0
1
2
2
0
1
1
1
2
1
1
0
2
0
0
0
0
0
1
1
2
1
0
0
1
1
1
1
0
2
1
0
1
0
0
2
1
0
2
1
1
1
2
2
1
1
2
1
1
0
0
1
1
1
1
0
1
1
0
0
2
2
1
3
2
2
1
2
1
1
0
0
2
1
0
1
0
2
1
1
1
2
1
0
2
1
0
1
1
1
1
1
2
1
1
0
1
1
1
1
1
0
1
1
1
1
1
1
2
1
1
0
1
1
1
1
2
1
1
1
1
1
1
0
1
1
0
1
1
0
0
1
0
1
0
2
2
0
1
2
2
1
1
2
1
0
0
1
0
1
1
0
1
2
1
1
1
2
0
1
0
2
1
1
1
2
1
1
0
2
1
0
1
1
0
2
0
1
0
0
1
0
1
1
0
1
1
2
0
1
1
2
1
2
1
1
0
1
0
0
1
2
0
0
0
0
1
0
2
1
0
0
1
1
1
1
0
1
0
1
0
1
1
1
0
1
0
2
0
1
1
2
0
2
0
1
1
1
2
1
1
2
1
2
0
1
2
1
1
0
1
2
2
1
0
1
1
1
2
1
1
0
0
0
1
0
2
1
2
1
0
1
1
2
1
1
1
0
1
1
2
0
2
1
1
0
0
0
1
1
1
0
1
1
1
0
2
1
2
1
2
1
0
1
1
1
0
1
2
1
2
0
0
1
2
1
2
0
0
1
1
0
1
2
2
1
1
0
1
0
1
2
0
0
2
1
1
1
2
0
2
1
1
2
1
1
2
1
0
1
2
1
1
1
1
0
1
1
0
3
0
0
0
1
0
1
0
0
0
0
1
1
1
2
0
2
0
0
1
0
1
2
2
2
1
1
1
2
1
2
1
0
1
2
0
0
1
2
1
1
1
0
0
1
2
1
1
1
1
1
0
1
3
2
1
2
2
1
0
2
1
1
0
2
1
1
1
0
2
1
2
1
0
0
2
1
0
1
0
2
1
0
1
1
1
0
2
2
1
0
1
1
2
0
1
0
1
2
0
0
2
1
1
0
2
0
1
1
2
1
0
0
1
1
2
1
1
1
0
1
0
2
1
0
2
1
1
1
1
1
2
0
1
1
0
2
1
1
1
1
2
0
2
2
1
1
2
1
0
1
0
2
1
0
2
3
1
1
2
0
2
1
0
1
1
0
0
1
2
1
0
1
1
1
1
1
0
1
1
1
2
1
0
2
1
2
2
1
2
0
0
0
0
0
1
2
1
1
2
2
1
1
1
2
1
1
1
2
1
1
1
2
2
2
2
0
1
1
2
2
1
1
1
2
0
1
1
1
1
2
2
0
2
0
1
0
1
1
1
1
2
0
0
0
2
2
2
2
1
0
1
0
2
0
0
1
2
1
2
1
0
1
0
1
2
2
2
1
2
0
0
1
0
1
2
1
0
1
2
1
0
1
0
1
1
1
2
1
1
2
1
1
1
1
1
1
1
0
0
2
0
0
1
1
1
2
1
1
1
1
1
1
3
2
1
1
1
0
2
2
1
1
1
1
0
0
1
0
1
2
1
1
2
2
1
1
0
0
2
1
1
1
0
1
1
1
0
0
2
1
1
1
1
0
1
1
1
2
1
2
0
2
0
1
1
0
2
2
0
2
1
1
0
2
0
1
2
1
3
0
1
1
2
2
1
2
2
1
0
2
1
2
2
1
1
1
0
1
2
2
1
0
0
2
0
1
2
1
0
1
2
1
1
1
1
1
0
2
1
3
1
1
0
1
0
2
1
3
1
2
0
1
1
1
0
0
2
1
1
1
2
5
1
1
2
1
1
1
0
0
2
1
1
1
0
2
0
1
1
1
2
0
1
1
0
1
1
0
2
2
1
0
0
0
1
1
1
1
1
1
4
1
0
0
0
1
1
2
1
2
1
2
3
1
1
1
1
1
0
0
1
0
0
1
0
1
0
0
0
1
2
1
1
0
0
2
1
1
2
1
2
0
1
1
1
2
2
0
2
1
2
1
1
0
1
2
1
1
2
1
0
0
2
1
2
2
1
2
1
0
1
1
2
1
1
1
0
1
1
0
1
2
1
2
1
0
2
1
1
1
0
1
2
0
0
1
1
0
1
2
1
2
1
1
0
1
1
1
1
1
1
1
1
0
1
0
0
1
1
2
2
0
1
1
2
1
1
1
1
2
2
2
0
1
0
1
0
1
1
1
2
2
1
1
0
2
1
0
2
1
0
2
1
1
2
0
1
0
2
0
2
1
0
1
1
1
1
1
0
0
2
0
2
2
0
0
0
1
0
0
1
1
1
0
1
2
1
2
0
1
1
1
1
3
2
1
0
1
2
2
1
2
1
1
0
0
1
1
1
2
1
1
1
0
0
2
2
1
1
1
2
1
1
0
0
2
0
0
1
1
1
1
2
0
1
1
1
2
1
1
0
1
0
1
1
1
2
2
1
0
0
0
2
1
1
2
1
1
1
1
2
1
1
2
1
1
1
2
0
1
0
1
1
2
1
2
1
1
1
1
2
1
1
0
0
2
1
0
0
1
0
0
2
0
1
1
1
1
0
2
2
1
2
2
1
2
1
1
2
0
0
0
1
2
0
1
0
1
1
1
1
0
1
1
1
2
2
2
1
2
2
1
1
1
0
0
0
1
1
1
0
2
1
2
1
1
1
0
1
0
1
1
1
1
1
0
2
1
1
1
0
1
1
1
1
1
2
1
2
0
1
1
1
0
2
3
1
0
1
1
1
2
0
1
1
1
0
0
0
1
1
1
1
1
2
2
2
1
0
2
0
1
1
1
1
0
0
1
0
1
2
0
1
1
2
1
2
2
1
2
0
1
1
0
1
1
1
1
1
1
1
0
1
1
1
1
2
1
2
1
1
0
0
0
0
1
2
2
0
0
2
1
1
0
0
1
1
1
2
1
2
0
0
1
1
1
1
0
2
2
2
1
0
1
1
0
1
1
3
1
0
1
1
0
1
1
2
0
1
0
0
2
1
2
2
2
0
1
2
1
2
1
1
4
2
1
2
1
0
0
1
1
0
0
1
1
1
2
1
2
1
1
0
1
3
1
0
2
1
0
1
2
1
1
1
1
2
0
1
0
2
0
1
1
0
1
2
0
1
1
0
1
0
2
1
1
1
1
1
2
0
0
2
1
0
0
0
1
1
1
1
2
2
1
0
1
0
0
0
2
1
1
1
2
1
0
2
2
1
2
1
1
1
1
1
0
1
1
1
1
3
1
0
2
1
0
1
1
1
1
1
2
2
1
2
1
2
0
1
0
1
2
1
1
1
0
2
1
0
1
1
2
0
0
2
1
2
0
2
1
1
1
1
0
1
1
1
1
0
2
1
2
0
0
1
1
1
0
1
2
2
2
2
2
2
0
0
0
1
2
0
1
2
1
1
1
2
0
1
1
0
1
0
1
1
2
0
1
1
1
1
0
2
2
1
0
1
1
1
1
1
3
2
1
1
2
1
2
2
1
2
1
1
0
1
0
1
2
1
2
1
2
2
2
1
1
1
2
3
1
1
0
1
1
1
1
2
0
1
2
0
0
0
0
1
1
1
1
1
1
1
1
0
0
2
1
2
1
1
0
0
2
2
2
1
1
1
1
0
1
0
2
1
0
1
1
0
6
0
0
0
1
0
1
1
0
0
2
1
1
2
1
0
1
1
0
2
0
2
2
2
1
0
1
1
1
1
1
1
1
1
1
1
1
2
2
0
0
0
1
2
1
2
0
0
0
2
0
2
1
2
1
1
0
1
0
1
0
1
2
2
0
1
2
1
1
2
2
1
1
2
2
0
0
0
1
2
0
1
1
2
1
2
1
1
1
0
1
1
1
0
1
1
1
1
0
1
1
1
1
1
1
1
1
2
1
1
0
3
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
0
1
2
1
1
1
0
1
1
1
1
2
2
0
4
1
1
0
0
1
1
0
2
1
0
2
0
1
1
1
0
1
1
1
2
1
0
0
1
1
0
1
1
2
1
3
1
0
1
1
1
1
1
1
1
0
0
0
0
1
1
1
1
0
1
2
1
0
2
0
0
2
1
1
1
2
0
1
1
2
1
2
1
1
1
2
2
3
2
2
2
1
2
1
1
2
0
0
0
1
1
2
1
2
1
2
1
1
0
1
1
1
2
0
2
1
1
1
1
0
1
0
1
2
1
1
0
1
1
0
2
2
1
1
0
2
1
0
1
0
0
1
1
2
1
0
1
2
1
1
1
1
2
0
0
1
2
1
1
0
1
0
1
1
2
0
0
1
1
2
1
0
2
0
1
0
1
1
0
1
1
1
0
0
1
0
1
1
1
1
1
1
1
0
1
1
1
0
1
1
2
0
1
0
0
2
1
1
0
0
0
2
0
2
2
0
1
2
0
2
1
1
5
0
0
0
1
2
1
1
1
1
1
1
1
1
1
1
1
1
0
0
1
3
1
0
0
2
0
2
2
1
2
1
1
1
1
1
2
0
0
0
1
2
1
0
1
1
1
1
1
1
2
1
0
1
0
0
2
1
2
1
0
2
1
1
2
1
1
1
0
1
1
0
1
1
1
2
1
1
2
1
0
2
1
1
2
0
1
0
1
1
0
2
0
2
1
2
0
0
1
3
0
0
1
2
0
1
0
2
2
1
0
2
1
1
1
1
1
1
1
0
0
0
0
0
2
1
0
1
2
2
0
1
2
1
1
1
0
0
1
1
1
1
1
0
2
2
1
2
1
1
1
1
1
2
1
2
1
2
1
2
1
1
1
1
1
1
2
1
0
0
2
2
1
1
2
2
1
1
0
0
1
1
2
1
2
1
1
1
0
1
1
1
1
1
1
1
0
0
2
1
1
0
1
1
2
1
1
1
2
0
1
1
1
1
1
0
1
2
1
0
2
2
1
2
1
1
2
0
1
1
1
1
0
1
2
0
1
1
0
2
1
2
2
0
1
1
0
1
1
0
2
1
2
1
2
0
1
0
1
1
0
1
1
1
1
1
1
2
0
2
1
4
0
2
1
0
1
2
2
2
1
2
2
0
1
1
1
0
2
0
1
1
1
0
0
1
1
1
0
1
1
2
0
2
1
0
0
0
1
1
1
0
1
2
2
1
1
1
0
1
1
0
0
1
3
1
1
1
2
1
0
1
1
1
1
0
1
0
0
1
2
0
1
1
1
2
1
1
1
1
0
1
1
1
0
1
0
1
1
1
0
1
2
1
2
1
1
0
2
1
2
2
0
2
1
2
1
1
0
2
1
2
2
1
1
0
2
1
0
0
1
0
1
1
1
0
1
1
2
0
2
1
0
1
2
2
1
0
0
2
2
1
0
1
0
1
1
0
1
0
1
1
1
0
2
1
1
1
3
0
1
1
1
1
0
0
1
0
2
1
1
1
3
1
1
1
0
2
2
0
2
2
1
2
1
2
0
1
1
1
1
1
2
2
1
0
1
1
1
1
1
2
0
0
1
2
1
1
1
3
2
0
1
1
1
1
1
1
0
2
1
2
1
1
1
1
1
2
1
0
2
0
1
2
1
0
1
0
2
1
0
0
2
1
3
0
2
1
1
2
1
0
4
2
1
1
2
2
0
2
1
2
1
1
0
1
0
2
1
1
0
0
2
1
1
0
1
2
1
0
1
1
1
1
1
1
2
2
1
1
1
2
1
0
1
1
1
1
2
0
1
1
2
0
2
4
1
0
2
1
1
0
1
1
2
1
0
1
2
1
1
1
0
2
1
2
1
0
0
1
0
1
1
2
0
1
2
2
1
1
1
1
1
0
1
1
1
0
0
2
1
1
1
1
1
0
0
2
2
1
0
0
1
1
1
0
1
1
1
0
1
1
1
1
1
1
2
1
0
0
2
0
2
0
0
1
1
0
1
1
2
2
2
1
1
1
1
1
1
1
0
0
1
0
0
1
1
2
1
0
1
2
2
2
2
1
1
1
1
1
1
1
2
2
1
2
1
1
1
2
1
1
1
0
2
0
1
1
1
1
1
2
1
1
0
1
1
2
0
2
0
1
1
1
0
1
1
1
0
1
1
1
0
2
0
0
1
2
2
1
2
1
0
1
1
0
1
0
0
1
2
1
1
0
1
1
0
0
1
1
2
2
1
1
2
2
1
0
0
2
1
1
2
2
1
2
2
1
1
1
1
1
0
0
1
1
1
0
1
1
1
1
1
1
1
1
0
1
1
1
0
1
2
2
2
0
2
0
1
1
1
1
1
2
0
1
0
1
1
0
0
1
2
1
1
0
1
1
2
1
1
1
2
1
0
1
0
0
1
1
0
1
1
2
1
1
1
2
1
1
2
0
1
1
0
2
1
0
0
2
1
1
1
1
0
0
2
1
1
1
1
1
1
1
1
1
2
0
1
2
0
0
1
1
0
1
1
1
0
1
0
1
1
2
1
1
1
2
0
1
1
1
2
1
1
0
1
0
2
1
1
2
0
1
1
1
0
2
1
2
0
2
1
0
0
2
1
0
2
1
1
4
2
1
0
2
2
1
1
1
1
0
1
1
1
1
2
0
2
1
1
1
0
1
1
0
1
2
1
2
1
1
1
2
2
0
1
0
0
1
1
2
0
1
1
1
1
1
2
0
2
1
0
2
1
1
0
1
2
1
1
0
1
0
1
1
1
0
1
1
1
2
1
1
0
1
0
1
1
0
2
1
2
1
1
1
1
1
2
1
0
0
1
1
2
2
1
1
1
1
1
1
0
1
1
1
1
2
2
1
0
0
1
2
1
1
0
2
1
1
0
0
0
1
1
0
0
1
2
0
1
1
2
1
1
1
1
2
2
1
2
2
0
1
1
1
2
1
0
2
1
1
2
2
1
1
1
0
1
0
1
1
1
2
1
1
1
1
0
1
1
1
1
1
1
1
0
0
2
1
1
0
1
1
1
0
0
1
0
0
1
1
1
1
1
2
0
0
1
1
3
1
0
1
1
0
1
1
1
0
0
1
0
0
0
1
0
1
0
2
2
2
1
1
1
2
2
0
1
2
2
1
1
2
1
2
1
0
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
0
1
0
2
1
1
2
0
0
1
1
1
1
1
2
2
2
1
0
1
2
1
0
1
1
0
0
0
0
1
0
1
1
1
0
1
1
2
0
1
0
1
2
1
1
1
2
1
1
2
2
0
2
2
0
2
0
0
1
1
4
1
1
2
1
1
0
1
1
1
2
2
1
2
1
2
1
0
2
2
2
0
1
1
1
2
1
1
2
0
1
2
0
1
2
1
1
1
1
2
1
0
0
2
0
1
0
2
1
1
1
0
1
1
2
1
0
0
2
1
1
1
1
2
0
1
1
0
2
0
2
0
1
1
2
1
1
1
2
2
2
1
1
1
2
1
1
1
2
1
2
1
0
0
0
1
2
0
0
1
2
1
0
1
2
2
2
1
1
2
3
2
2
1
1
1
2
0
1
1
1
2
1
1
2
2
2
0
2
2
0
1
2
3
1
2
1
2
1
1
2
1
1
0
1
1
1
0
0
1
0
0
0
0
1
2
1
2
1
1
1
1
1
2
0
0
1
1
1
2
0
1
2
1
1
2
1
0
2
0
0
2
2
2
1
0
1
0
1
1
1
1
0
1
1
1
2
2
2
2
2
1
1
2
1
1
0
2
0
0
1
0
1
1
1
1
1
1
1
1
2
1
1
1
1
0
0
2
1
0
1
2
1
1
1
0
1
2
1
2
0
1
1
0
1
0
1
1
1
1
1
1
1
1
0
1
2
0
1
2
1
1
1
0
1
2
1
0
1
1
1
2
1
1
1
1
1
1
2
1
1
2
0
2
0
1
1
1
3
3
1
2
2
2
0
3
6
3
1
0
0
0
2
2
1
1
1
1
2
0
0
1
1
0
1
0
1
0
0
1
2
1
1
2
0
2
1
0
1
0
1
1
1
2
2
1
2
1
2
1
1
2
1
1
1
2
0
1
2
2
0
1
0
1
0
1
3
1
1
1
0
1
0
1
1
1
1
2
2
1
1
0
0
1
1
2
1
0
1
1
1
1
1
2
1
0
1
2
2
1
2
2
0
1
0
1
0
1
1
0
2
1
0
2
1
2
0
1
1
1
1
2
1
0
1
0
1
1
1
1
1
1
1
1
2
1
1
1
1
0
0
0
1
1
1
1
0
2
2
1
2
0
0
1
1
1
1
1
0
1
1
0
2
1
1
0
0
1
1
1
1
1
1
1
1
2
0
1
1
1
0
0
1
2
1
2
0
0
2
0
1
1
1
0
1
0
2
2
2
0
1
0
2
0
1
2
1
1
2
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
0
1
1
0
0
1
1
1
2
1
0
0
1
2
0
1
0
3
0
1
1
1
1
1
0
1
0
1
1
1
0
1
1
0
0
1
1
1
5
1
1
2
0
1
1
1
1
1
1
1
1
2
1
1
2
2
1
1
0
1
0
0
1
0
0
2
1
1
1
2
0
1
2
0
1
2
1
0
1
0
2
1
0
1
1
2
1
0
1
2
0
2
1
1
1
1
1
1
0
1
1
0
2
2
2
2
1
2
2
2
2
1
2
2
1
1
1
2
0
1
1
0
0
0
0
2
1
2
1
1
1
1
0
2
1
1
1
1
1
2
0
1
0
1
0
2
1
1
2
0
0
0
2
0
0
0
2
1
1
1
0
1
1
2
1
0
1
2
1
0
0
0
0
2
1
2
2
1
1
1
2
0
1
1
0
1
1
1
1
2
1
1
1
0
1
1
1
1
1
0
2
0
2
2
1
1
0
1
0
1
2
1
0
1
1
1
1
1
0
0
1
0
2
1
2
2
0
1
1
1
1
2
1
1
1
1
1
1
2
0
0
1
1
0
0
2
1
1
1
1
1
2
1
0
1
0
1
1
0
0
0
0
1
1
1
1
1
2
2
1
0
1
2
0
2
0
1
1
1
1
2
0
2
0
0
2
1
0
1
2
1
0
2
3
1
1
2
1
2
0
0
0
1
0
1
1
1
1
3
1
1
1
1
0
1
1
2
1
1
1
0
1
0
0
1
2
1
1
1
1
1
1
2
2
1
0
2
1
1
2
1
0
1
1
1
2
1
1
2
0
2
1
2
1
1
2
0
1
0
1
0
0
2
1
2
0
0
1
1
1
2
0
1
1
1
0
1
0
2
0
1
1
1
1
1
2
1
1
0
1
2
1
1
1
3
1
2
2
2
1
1
1
2
1
1
0
2
1
1
2
0
1
1
1
1
2
2
0
1
0
1
2
0
0
2
1
3
1
2
1
1
1
1
1
0
0
0
0
1
0
1
1
2
0
2
2
1
1
1
1
1
1
1
1
1
2
1
1
0
1
2
0
1
0
1
2
1
1
1
0
0
2
2
1
1
0
1
0
1
1
1
1
0
1
2
1
0
1
2
2
1
1
0
2
1
1
2
1
0
1
0
1
2
1
1
1
2
2
2
2
1
1
0
2
1
1
1
5
1
1
0
1
1
0
1
1
2
2
0
2
1
0
1
2
1
1
0
0
0
1
2
1
1
0
2
1
0
0
1
1
0
1
1
2
1
0
1
0
2
1
2
2
1
1
0
0
1
1
2
1
1
1
0
1
2
1
0
2
2
0
1
2
0
0
1
0
1
0
1
0
2
0
1
0
1
2
0
2
0
0
1
0
0
1
1
1
1
0
1
1
0
1
1
0
2
1
2
2
1
1
2
1
0
1
2
1
1
0
1
2
1
1
2
1
3
1
1
0
2
1
1
1
0
1
2
2
2
2
0
1
0
0
1
1
0
1
0
2
1
0
1
2
1
1
1
1
1
1
2
2
2
2
1
1
1
1
1
1
1
2
0
1
0
0
1
0
1
1
0
2
1
1
0
0
2
2
1
1
1
0
2
1
2
1
2
1
0
1
1
1
1
1
0
1
1
0
0
1
2
1
1
0
1
1
1
1
1
0
1
1
1
0
1
0
1
1
0
2
0
2
1
1
1
1
2
2
2
1
1
2
2
1
1
0
1
1
1
0
2
1
2
2
1
2
1
1
2
0
2
1
2
1
1
2
2
1
2
1
1
1
2
1
1
1
1
0
0
1
1
2
0
1
0
0
0
0
1
1
1
1
0
1
2
2
1
1
1
0
1
1
1
0
1
0
1
2
0
1
1
2
1
1
1
2
0
1
1
2
1
1
0
2
1
1
2
0
2
1
0
0
1
1
1
1
1
2
1
1
1
1
0
1
2
1
2
1
1
1
1
2
2
0
1
2
1
1
2
2
2
1
0
1
1
1
1
2
1
1
0
1
1
1
2
1
0
1
1
0
1
1
0
1
2
0
1
1
1
0
1
1
1
2
1
1
0
0
1
0
0
0
2
2
1
1
1
1
0
2
0
2
2
0
2
2
1
1
1
0
1
1
1
2
1
1
2
1
2
2
2
2
1
1
1
2
1
0
1
1
1
0
1
2
0
0
1
0
0
0
0
1
1
1
1
0
2
1
1
1
1
1
2
2
1
1
0
1
2
1
1
1
1
2
2
1
0
1
2
1
1
1
2
1
0
1
0
1
1
1
0
1
1
3
2
2
0
0
0
1
0
1
1
1
1
2
1
2
0
0
0
1
1
1
2
1
0
1
1
1
1
1
1
0
1
1
1
1
1
1
3
1
3
2
1
0
1
2
2
1
0
0
2
1
2
1
0
2
1
2
0
1
2
2
1
0
2
0
1
1
0
1
2
1
1
2
0
2
1
1
1
1
1
1
0
0
1
0
1
1
0
1
0
1
0
1
2
2
1
1
1
1
0
1
1
1
1
0
1
0
2
1
0
1
0
3
1
0
0
1
4
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
2
1
1
2
0
2
1
0
1
2
1
1
2
2
1
0
2
1
0
1
2
1
1
1
1
1
1
0
0
1
0
0
1
0
0
1
1
2
2
1
1
1
2
1
1
1
1
2
0
1
1
1
0
1
1
1
1
1
0
1
0
2
1
0
2
1
2
2
1
2
1
0
1
1
2
1
0
1
0
0
1
1
2
1
2
2
0
2
1
0
1
0
1
0
4
1
0
1
1
2
0
1
2
0
0
0
2
1
0
1
1
1
2
2
1
0
2
0
0
1
1
0
2
2
2
0
1
1
0
2
1
1
0
0
1
2
1
2
1
0
1
1
1
0
2
0
0
2
1
0
1
0
2
2
1
0
1
0
1
0
0
1
1
1
0
2
0
1
2
1
2
0
0
1
1
2
0
1
0
1
1
0
0
2
0
0
0
1
0
1
0
1
1
1
0
1
1
1
2
0
1
1
2
2
1
3
1
1
0
2
1
0
1
3
1
0
1
0
1
2
2
2
2
0
0
0
1
1
2
0
1
0
1
1
2
2
1
2
2
0
2
1
1
1
0
0
1
1
0
1
0
2
2
1
2
0
0
1
1
1
1
1
0
2
1
0
1
1
1
2
2
0
0
2
2
1
2
0
1
1
0
1
0
0
1
1
0
2
1
0
1
1
0
1
2
1
1
1
2
1
0
0
1
1
2
1
0
2
1
0
2
1
1
0
0
1
0
1
1
2
1
1
0
1
1
0
0
1
2
0
1
1
1
1
2
1
1
2
1
1
2
2
1
0
0
1
7
2
1
1
0
1
2
2
0
2
2
1
0
1
2
1
1
0
1
1
1
1
1
0
0
0
1
1
1
1
0
2
1
0
2
1
1
0
1
2
1
1
2
1
1
1
1
1
1
1
0
2
0
1
2
4
1
2
2
1
1
2
1
1
0
2
1
1
2
2
2
1
2
1
1
1
1
1
1
2
0
1
2
0
1
0
0
2
0
0
0
1
1
1
0
2
1
2
0
2
0
1
0
2
1
1
2
1
1
1
1
1
2
1
1
1
2
1
2
2
1
3
1
1
1
0
1
1
3
1
1
2
2
3
1
1
1
0
1
1
1
0
1
1
1
2
1
2
1
0
0
2
1
1
1
2
0
1
1
1
0
2
1
0
2
1
2
0
1
1
0
2
1
2
1
1
1
2
1
1
1
2
1
2
1
0
1
0
0
0
1
1
2
1
1
1
1
1
1
1
1
1
3
1
4
0
0
1
1
1
0
3
1
0
1
1
0
0
2
0
1
1
1
3
0
1
1
1
0
1
1
1
1
2
0
1
1
2
1
3
1
2
1
0
0
2
1
1
1
0
1
1
2
0
0
1
2
1
2
2
2
2
1
2
0
1
1
2
1
1
1
1
1
1
1
1
2
0
1
1
2
1
1
2
1
0
1
0
1
1
1
2
1
1
2
2
1
0
2
0
1
1
1
2
0
2
1
1
1
1
1
0
1
1
1
1
1
1
0
1
0
2
2
2
1
2
1
0
1
0
1
1
2
0
2
1
1
0
2
0
0
0
1
0
1
2
0
2
2
1
0
2
2
2
1
2
1
1
0
1
1
1
1
1
2
2
0
1
0
2
1
2
0
1
2
2
0
1
1
1
0
1
1
1
1
1
0
0
1
1
1
2
1
1
1
1
1
0
1
2
1
1
0
0
1
0
0
1
2
2
1
1
0
0
0
1
1
1
3
0
1
2
1
1
1
1
1
0
2
1
1
2
2
0
1
1
1
2
2
2
0
1
0
1
0
0
1
2
1
1
1
1
0
1
1
2
2
1
0
0
2
5
1
0
1
1
0
0
1
0
1
1
0
1
1
1
1
1
1
2
1
1
1
1
1
0
1
1
2
0
0
3
1
2
2
1
1
2
2
1
1
1
2
1
1
0
1
0
1
1
1
1
1
1
0
0
0
1
2
1
1
1
2
2
2
1
0
1
1
1
0
0
1
1
1
2
1
0
1
1
1
1
1
0
2
1
1
2
1
1
2
1
3
1
2
1
1
0
0
1
0
1
1
1
1
1
1
2
1
1
0
1
0
2
0
1
0
1
2
2
1
1
2
1
2
2
1
1
1
1
3
1
1
1
2
1
0
2
1
0
0
1
1
0
0
1
2
0
2
1
1
0
1
1
0
1
1
1
0
0
2
0
0
2
2
0
2
1
1
0
0
2
0
1
1
2
2
2
3
2
1
1
0
1
1
1
2
0
0
1
1
1
1
1
2
1
0
3
2
0
1
1
0
1
1
1
3
1
1
2
1
1
1
0
1
0
1
1
1
1
1
1
1
1
1
2
1
1
0
1
1
1
1
1
0
0
1
1
1
3
1
1
2
2
1
1
2
1
2
0
1
1
0
1
1
1
2
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
0
0
1
1
2
1
0
2
2
0
2
1
1
0
1
2
2
0
0
1
0
1
1
2
0
1
0
1
0
1
0
0
1
0
3
1
0
2
3
0
0
2
1
2
2
0
3
1
2
1
2
2
1
1
1
1
1
0
1
2
1
1
2
0
1
1
2
1
0
1
1
0
1
1
1
3
2
2
1
1
0
0
1
0
0
1
0
2
1
0
2
1
1
1
2
2
2
1
2
1
2
1
1
2
1
0
1
0
1
1
1
0
0
1
1
1
1
0
1
1
2
2
0
0
2
1
0
2
1
0
0
0
1
1
1
1
1
2
2
2
1
1
1
1
0
1
2
2
2
1
1
1
1
2
2
1
2
0
0
1
0
1
1
1
1
1
1
0
0
0
1
2
2
3
0
1
1
2
0
1
1
1
1
1
1
0
1
0
1
2
1
1
1
1
1
2
0
1
2
1
1
0
1
2
2
1
2
0
1
2
2
1
0
2
1
2
1
1
1
2
2
0
0
0
1
1
1
0
1
1
1
1
2
1
2
1
1
0
0
1
1
2
1
0
2
1
0
1
2
2
2
0
1
1
0
1
0
1
2
0
1
0
1
1
1
1
2
2
0
0
1
0
1
0
1
1
0
1
1
1
2
2
1
1
1
2
0
1
2
0
2
2
1
1
2
0
2
0
1
2
2
0
0
1
1
0
2
0
2
0
1
0
1
0
3
1
3
1
0
1
1
0
1
1
0
1
1
2
0
2
1
0
1
0
1
2
1
2
0
2
1
2
0
0
2
1
0
2
1
1
0
2
0
1
1
1
1
1
2
0
0
1
2
2
1
0
0
1
1
1
0
1
1
0
1
0
1
1
3
0
1
2
1
1
0
1
1
0
1
2
2
0
2
4
2
1
1
0
2
1
1
1
0
1
1
0
1
1
0
1
2
1
2
2
1
1
1
0
2
1
2
1
1
1
0
1
2
2
1
1
2
1
2
0
1
2
1
2
1
1
3
0
0
1
2
3
1
1
1
1
2
1
2
1
1
0
1
1
1
1
0
1
1
2
1
1
2
1
0
0
2
0
2
2
2
0
0
0
1
1
1
1
1
1
1
1
2
1
2
2
1
0
2
0
0
1
1
1
1
2
1
1
1
0
1
0
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
2
1
1
1
1
1
1
0
1
0
0
1
1
2
2
1
0
0
0
0
1
0
2
1
0
2
1
0
1
0
2
2
1
1
2
0
2
1
1
1
1
1
1
0
0
1
1
2
1
1
1
1
1
1
0
1
2
0
2
2
2
1
2
0
1
1
1
2
0
1
1
1
0
1
1
0
1
2
2
0
1
1
1
1
1
1
2
0
0
0
1
1
0
1
1
1
1
2
1
1
1
1
2
0
1
1
0
0
1
2
1
2
1
2
1
1
1
1
1
2
1
2
0
1
1
1
1
1
1
0
1
2
1
2
1
0
1
1
1
1
1
2
0
2
0
0
2
1
0
0
2
0
1
0
1
0
2
1
1
2
3
2
1
1
0
1
1
1
1
1
1
2
2
2
1
2
1
2
2
1
1
1
1
0
1
2
1
2
0
1
1
0
0
0
1
0
1
0
1
0
1
1
0
2
1
1
1
2
1
0
0
1
1
1
1
0
0
1
0
2
1
1
1
0
2
1
1
1
1
2
0
0
3
2
1
1
1
0
1
1
1
1
0
1
2
1
1
1
1
1
3
1
0
2
0
1
1
1
0
1
1
0
1
1
2
1
2
0
0
2
1
2
1
1
1
1
1
0
0
0
1
2
1
0
1
1
1
0
1
1
1
1
1
1
2
0
2
0
1
0
0
0
1
1
0
1
1
2
0
0
0
0
1
1
2
2
1
1
2
2
1
2
0
0
1
1
2
0
1
0
1
0
0
1
1
0
1
2
2
0
2
1
1
0
0
2
2
0
1
1
1
1
0
2
2
1
1
1
1
1
0
2
2
0
1
1
1
2
2
0
2
2
0
2
2
1
1
2
0
5
2
0
1
0
1
2
2
0
1
1
1
1
1
0
1
1
1
1
2
1
1
1
2
1
1
1
0
6
1
1
1
2
1
2
0
0
0
0
1
2
2
0
0
0
1
1
1
1
1
2
1
1
2
2
1
0
1
1
1
0
1
1
0
0
2
0
0
1
1
0
0
0
0
2
1
1
2
0
1
0
1
0
1
1
1
0
1
0
1
2
1
1
0
1
1
2
1
1
0
1
0
2
0
0
2
0
1
0
2
0
2
2
1
0
0
1
1
0
0
2
4
1
2
2
1
1
0
2
0
0
2
2
1
2
2
0
1
1
0
2
1
1
1
2
1
1
1
2
1
1
1
0
1
2
1
1
2
1
0
2
1
2
2
1
1
1
1
0
1
2
0
1
1
2
1
1
1
2
1
0
1
1
2
1
1
1
2
2
2
1
1
1
1
0
0
1
2
1
0
1
1
1
2
2
1
2
2
2
1
0
2
0
1
2
1
1
0
1
1
0
0
1
0
1
2
1
1
2
1
1
1
1
0
1
4
0
1
1
1
1
1
1
0
2
1
0
1
0
0
2
2
0
1
1
1
2
2
1
1
1
1
1
1
0
0
2
0
1
1
2
1
1
0
0
1
2
1
2
0
1
2
1
0
0
1
1
1
2
1
1
1
1
0
1
1
0
1
2
0
1
1
1
2
1
3
1
2
0
1
1
0
1
1
1
1
1
1
1
1
1
1
1
0
2
0
2
1
1
0
0
1
1
0
1
1
0
2
0
0
1
0
2
1
1
1
0
2
1
0
1
2
0
1
1
1
0
1
1
1
1
0
2
2
1
0
1
1
0
1
0
1
1
2
1
0
1
1
0
1
1
0
0
0
1
0
1
1
1
0
2
2
0
1
1
2
1
1
1
0
2
1
1
0
1
2
0
1
1
0
1
1
2
0
3
1
0
1
0
0
4
1
0
0
1
1
2
1
1
2
1
2
1
1
0
0
1
2
1
2
1
1
2
1
0
1
2
2
0
1
1
1
1
0
0
0
1
0
1
1
2
1
2
1
0
1
1
0
0
2
1
1
0
0
1
1
0
1
2
1
1
1
1
0
0
0
1
1
0
1
0
2
1
0
0
2
0
1
1
0
1
1
1
1
0
0
1
1
0
2
1
1
1
3
0
1
1
1
1
2
3
2
1
1
1
1
1
2
2
1
1
1
1
2
2
2
1
1
2
0
1
1
2
0
1
0
1
0
1
1
1
1
2
1
2
0
0
1
1
0
1
0
1
2
1
2
1
0
0
1
1
1
0
1
0
1
0
2
1
0
2
2
2
2
0
2
1
1
2
2
2
2
1
0
2
2
1
2
0
2
0
1
1
0
1
0
1
1
1
1
0
1
1
1
0
1
0
1
0
0
2
0
1
1
1
1
0
2
0
0
3
0
0
1
1
1
1
0
1
1
1
1
1
0
2
1
0
1
0
2
2
1
1
0
2
0
2
0
2
2
1
1
0
1
0
1
2
0
1
0
0
1
0
1
1
1
0
0
1
2
2
1
1
2
1
0
0
1
2
1
1
0
1
0
1
2
1
0
0
2
2
1
2
1
0
1
1
1
1
1
0
1
2
2
2
1
0
1
0
1
0
1
0
1
1
2
1
1
0
0
1
1
1
1
1
1
1
0
0
1
1
1
1
0
0
0
1
1
1
1
1
1
1
1
2
2
0
1
0
0
0
1
1
0
1
0
1
0
2
1
1
1
1
2
1
1
2
2
1
1
1
0
2
1
1
0
0
1
1
1
1
0
1
1
0
0
1
2
2
2
0
0
0
0
1
1
0
0
1
0
0
1
1
0
0
1
1
1
1
2
2
0
2
1
1
2
1
2
0
1
1
2
1
2
1
2
1
1
1
1
0
1
2
1
0
0
1
1
2
1
1
1
1
1
2
1
0
2
1
2
2
1
0
0
2
1
1
1
1
2
1
1
0
0
1
1
1
1
2
1
2
1
1
0
1
1
1
1
0
1
1
0
7
0
1
0
2
2
2
2
1
0
1
1
1
3
1
1
1
1
1
1
0
1
2
2
2
0
0
0
0
0
1
1
1
1
1
2
1
1
1
0
2
2
1
1
0
1
1
0
2
2
1
1
1
1
0
0
2
1
0
0
0
1
1
0
1
1
1
1
2
2
1
1
2
1
2
1
2
1
1
1
1
1
1
2
1
1
0
1
3
1
0
2
1
1
2
2
1
0
0
0
1
1
0
1
2
2
1
2
1
1
0
1
0
2
1
1
0
1
2
2
0
1
1
2
1
0
1
0
0
1
0
1
2
1
1
0
1
1
1
2
0
1
2
1
3
1
1
1
2
1
0
1
1
1
0
1
1
1
0
1
1
1
1
1
1
2
1
0
1
0
0
1
0
1
2
0
0
2
0
1
2
1
0
0
1
0
1
1
0
1
2
1
1
1
2
1
1
1
1
1
1
2
0
1
1
2
2
2
1
2
0
1
1
2
3
0
2
0
0
0
1
1
3
1
1
0
1
1
1
2
1
0
1
1
2
1
4
1
1
2
0
1
2
1
1
2
0
0
0
1
2
2
1
1
1
1
1
1
2
0
1
1
1
1
2
1
1
1
1
2
0
1
1
2
1
1
2
0
1
1
1
0
1
1
0
1
1
1
0
1
1
1
2
2
1
0
1
2
1
1
1
0
1
2
0
0
2
2
0
1
1
1
2
1
0
1
1
0
0
2
0
2
2
1
1
0
2
1
0
2
1
1
1
2
1
1
0
1
1
0
1
2
1
2
1
1
2
3
1
1
1
2
1
1
1
3
0
1
1
0
2
1
1
1
2
2
0
2
1
1
1
0
2
2
0
1
0
0
1
1
0
1
1
0
1
1
1
1
0
1
2
0
1
0
2
2
2
1
2
2
1
2
0
0
1
1
2
1
1
1
1
1
2
0
2
0
0
1
1
0
0
0
0
0
2
2
1
0
1
0
0
0
2
1
1
1
1
0
1
1
1
2
0
1
2
0
0
1
1
1
0
0
0
2
1
2
2
1
4
1
1
1
1
1
1
0
2
2
2
2
0
1
1
1
1
1
0
1
1
1
0
1
1
1
1
1
0
1
1
1
0
0
0
2
1
1
0
1
0
0
1
1
2
1
0
0
3
0
1
0
1
1
0
0
1
1
1
1
0
1
1
1
1
2
0
0
0
2
0
1
1
2
1
1
1
0
2
0
1
1
0
0
1
2
3
1
1
2
2
1
1
1
2
1
1
1
0
2
2
2
2
1
1
2
0
1
0
1
1
2
1
1
1
0
0
1
1
1
1
1
1
1
1
1
1
0
0
1
0
1
0
0
0
1
1
1
1
0
0
0
2
1
0
1
1
2
0
1
1
1
1
1
1
1
1
2
1
0
2
2
0
1
2
1
2
0
2
0
1
1
1
2
1
1
0
2
1
2
1
1
2
1
1
2
1
0
1
2
1
1
0
1
1
0
2
1
1
1
0
0
0
1
2
2
1
1
2
1
0
1
2
1
1
2
2
0
1
1
1
1
1
1
1
1
1
0
2
0
2
1
2
1
2
0
2
1
0
0
1
1
1
2
1
1
2
1
1
1
1
1
0
1
0
1
1
2
1
0
1
1
1
2
0
1
1
1
1
0
1
0
2
0
1
0
0
0
1
2
1
2
1
2
1
0
2
1
1
1
2
2
1
0
0
0
2
0
1
1
2
0
2
1
1
1
1
1
2
0
0
1
2
1
1
1
1
1
0
0
1
1
1
2
1
1
0
1
1
1
1
1
0
0
3
2
1
2
1
1
1
1
0
2
1
1
1
1
0
1
0
1
2
2
1
2
0
0
0
1
0
0
2
1
1
1
0
1
0
1
1
2
1
0
0
2
2
1
1
1
1
0
2
1
1
0
1
1
1
0
2
1
2
2
1
2
1
1
2
2
1
1
1
2
1
0
2
2
1
1
1
1
1
2
0
1
0
2
1
1
1
1
0
1
1
0
1
0
1
1
2
0
1
1
1
0
1
0
0
0
1
2
1
2
0
1
1
0
1
2
1
1
0
1
2
1
1
1
0
1
2
2
1
1
2
3
2
1
1
0
1
2
1
1
1
0
0
1
2
2
1
0
1
1
1
0
0
1
0
1
1
0
1
0
0
0
0
1
1
1
2
1
0
0
1
2
1
0
1
1
1
2
0
1
1
1
1
1
1
1
1
2
1
1
1
1
2
2
2
1
2
0
2
1
0
2
2
1
2
1
1
0
1
1
2
0
1
2
0
0
1
1
1
0
1
1
0
1
1
1
1
1
2
0
0
1
0
1
0
1
0
2
2
1
1
1
0
1
1
1
1
1
1
1
1
1
0
1
0
1
2
0
1
0
2
1
0
2
1
1
1
2
2
0
1
1
0
1
0
1
1
1
0
2
1
1
2
1
1
1
2
1
0
2
1
2
2
1
2
2
1
1
0
1
2
0
1
1
1
1
1
1
0
1
0
3
1
1
0
0
1
2
2
1
2
2
2
0
1
1
1
2
1
1
2
1
2
1
2
1
0
2
1
2
1
1
1
0
1
1
1
1
1
2
2
2
0
2
1
1
0
1
1
2
1
1
2
1
1
0
3
1
0
0
2
1
2
0
1
2
0
1
0
1
1
1
2
0
1
2
0
1
2
0
3
0
1
1
3
2
1
1
1
1
1
1
0
2
1
0
2
0
1
1
0
2
1
2
1
2
1
2
1
2
0
1
1
0
0
1
0
1
1
1
0
1
1
1
2
0
2
1
1
0
1
1
1
1
1
2
1
1
1
1
1
1
0
1
0
1
0
0
2
1
1
0
0
2
1
2
0
0
2
2
2
1
0
0
1
0
2
1
1
2
0
1
1
1
1
0
1
2
1
2
2
0
1
0
1
2
0
2
1
0
0
1
1
1
1
2
1
0
1
2
2
1
1
0
0
1
1
1
2
1
2
1
0
2
1
2
0
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
0
1
1
2
1
1
1
2
1
1
1
5
0
1
1
2
2
0
2
0
1
1
2
0
2
1
1
0
0
1
1
1
0
2
1
0
2
1
2
2
0
2
1
5
2
0
1
0
2
0
1
2
1
1
0
1
0
1
3
2
0
0
2
1
2
1
0
1
2
2
0
0
0
2
1
1
1
2
0
2
2
2
0
1
2
1
0
0
0
1
3
0
1
1
2
1
1
1
2
1
1
1
1
1
0
1
1
1
2
2
2
2
2
0
2
2
1
0
2
1
1
1
1
0
0
2
0
1
1
0
0
0
1
1
1
1
1
1
1
1
0
1
0
2
1
0
3
1
1
1
2
0
1
1
0
1
0
2
3
0
1
2
0
1
0
0
2
1
0
1
2
1
1
1
0
2
1
0
1
1
2
1
0
0
0
0
0
2
1
1
1
2
2
1
2
1
1
1
0
1
2
2
2
0
2
0
2
0
0
1
0
1
1
2
0
1
1
0
0
1
1
1
2
0
2
1
3
1
0
2
1
1
2
1
0
2
1
0
2
0
1
1
2
0
0
1
1
1
1
1
2
1
0
0
2
1
0
1
0
2
1
2
0
0
1
1
0
0
1
1
1
1
1
2
1
2
0
1
1
1
1
2
1
1
2
1
2
1
1
1
1
1
1
0
2
2
1
1
0
1
2
0
1
0
2
1
2
1
0
2
1
2
2
1
1
1
1
1
2
1
1
1
1
1
0
1
1
1
1
0
2
0
2
0
1
0
0
1
0
0
1
1
0
0
1
2
1
2
1
2
1
1
1
1
2
1
2
0
0
2
2
1
1
1
2
2
0
2
1
0
1
1
1
2
1
1
1
1
1
2
1
3
0
0
1
0
2
1
1
1
1
1
0
1
1
4
1
0
1
2
2
1
2
1
1
0
0
0
0
0
1
1
1
0
3
1
0
1
2
2
1
1
1
1
1
1
2
1
2
1
0
1
1
1
0
2
1
1
1
2
1
1
0
0
2
0
1
0
1
1
1
1
1
0
1
1
1
1
4
0
1
2
0
2
0
2
0
1
1
0
1
1
2
2
1
1
2
1
1
1
1
0
1
2
1
2
1
1
1
0
1
1
1
1
2
2
1
2
2
3
1
1
2
1
1
1
2
0
0
1
2
1
2
2
0
1
1
2
1
1
1
2
1
2
1
2
1
1
2
0
1
1
0
0
0
0
4
1
1
0
1
2
0
0
1
2
1
1
1
2
0
1
1
0
1
1
2
1
2
2
2
1
0
1
1
2
0
2
1
0
0
2
0
1
2
1
1
1
1
1
2
2
3
0
1
1
2
0
1
2
2
2
0
0
2
2
1
1
3
1
1
1
0
2
1
1
0
0
2
1
1
0
2
1
3
1
1
1
1
0
1
1
1
1
2
0
1
0
1
1
2
1
0
1
0
1
1
0
0
2
1
0
1
1
2
1
1
0
2
1
2
1
0
1
0
1
1
2
2
0
1
1
3
1
1
1
0
1
0
0
2
1
0
1
1
1
1
0
2
1
0
1
0
1
1
1
0
1
0
1
2
3
1
2
0
2
1
1
0
1
1
0
0
1
0
1
2
1
1
2
0
0
1
2
1
2
2
1
1
0
0
1
1
0
2
1
2
1
2
2
1
1
1
2
1
0
2
1
1
2
2
1
0
0
2
1
1
0
1
1
2
1
1
1
1
2
0
1
0
1
1
1
2
1
3
1
1
0
0
2
1
1
1
2
3
0
1
1
1
1
1
1
1
2
0
1
0
2
0
0
1
2
1
1
1
1
1
1
2
1
1
2
1
1
1
0
1
1
1
1
3
1
1
2
1
1
1
0
1
1
1
0
2
2
1
1
2
2
1
2
1
1
1
1
1
1
1
0
1
2
1
1
1
3
1
1
0
1
0
1
0
2
0
2
1
0
0
2
1
1
0
1
1
1
3
2
0
1
1
0
1
2
1
1
1
1
1
1
1
1
0
0
0
1
1
1
2
1
0
0
0
0
2
2
1
0
1
0
1
2
0
0
1
1
1
2
1
1
1
1
1
2
0
1
1
0
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
1
2
0
0
1
0
0
1
0
1
2
2
1
2
1
0
2
1
0
2
1
1
1
2
2
1
1
2
2
0
1
2
2
1
2
1
1
0
3
1
0
1
1
1
1
0
1
1
2
1
1
0
0
3
2
0
1
1
0
0
2
1
1
1
1
0
0
1
0
1
0
1
0
1
1
3
1
1
3
1
1
1
0
1
2
1
2
3
0
2
2
2
1
0
2
1
2
0
2
2
0
1
1
0
3
2
3
2
0
1
1
0
1
1
1
2
1
1
1
1
0
0
1
0
1
0
1
0
1
1
2
1
1
1
1
1
1
1
1
0
1
1
2
0
1
0
1
1
1
1
1
0
1
0
0
0
1
0
1
0
2
2
2
0
1
1
2
1
1
1
1
1
1
2
2
1
2
1
3
1
1
0
1
1
0
1
0
1
1
1
1
0
0
1
1
0
2
1
1
0
2
1
2
1
0
1
1
2
1
2
2
1
1
1
1
1
0
1
1
1
1
0
2
1
1
1
1
2
1
5
1
3
1
1
1
1
0
0
1
1
1
1
1
2
1
0
2
0
1
1
1
0
1
2
2
1
1
0
2
0
0
1
2
1
0
0
1
1
1
2
0
1
1
1
1
1
0
1
1
1
1
0
0
1
0
2
1
2
1
1
1
1
0
1
1
0
0
2
1
2
1
2
2
1
0
1
2
0
1
2
2
1
2
2
1
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
1
1
1
0
0
2
1
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
0
2
0
1
1
0
2
6
0
1
1
0
2
1
1
1
1
0
0
2
2
1
0
2
2
1
1
3
1
0
1
1
0
1
0
2
1
0
2
0
1
2
1
0
0
1
1
1
1
1
1
1
1
1
1
2
2
0
1
0
1
0
1
0
1
1
0
2
1
1
1
1
0
2
0
2
1
0
2
2
0
2
2
2
0
0
2
1
1
0
0
0
1
0
2
1
1
1
1
1
0
0
0
2
1
0
0
2
2
2
1
1
1
1
2
1
1
0
0
2
0
2
1
1
0
1
1
2
1
1
1
0
1
0
1
0
0
2
1
1
1
1
1
0
1
1
0
1
0
1
1
1
1
1
2
2
0
1
1
1
1
0
1
0
0
2
2
1
1
2
2
0
3
2
1
2
1
1
0
1
0
1
1
3
0
1
0
0
1
2
2
2
1
1
2
0
1
2
0
0
1
1
0
1
2
1
2
0
1
1
2
1
1
1
2
1
1
2
1
1
2
1
1
0
0
1
2
1
0
1
2
1
1
1
0
1
1
0
1
1
2
2
1
0
0
0
1
1
0
2
1
1
1
0
2
1
2
1
2
1
2
1
1
1
0
2
0
1
1
1
2
0
1
2
2
0
2
1
0
0
1
0
0
2
2
0
1
1
1
1
1
1
1
1
0
3
2
1
1
0
1
1
2
2
2
1
1
0
0
0
1
1
1
0
2
1
0
1
2
1
1
0
1
2
0
1
1
2
1
2
0
1
1
1
1
0
1
1
1
1
1
1
2
0
0
1
0
0
1
1
2
2
0
0
0
1
2
2
2
1
2
2
1
0
0
0
1
2
0
2
2
2
0
2
1
2
1
1
0
0
2
1
3
0
1
2
0
0
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
2
1
0
2
0
0
1
2
2
0
0
0
0
1
1
1
0
1
1
1
2
6
1
1
1
1
0
1
1
0
0
3
0
1
1
1
1
2
1
1
1
2
0
1
0
2
1
1
1
0
2
2
1
1
0
1
1
1
1
2
0
2
1
2
1
1
0
1
1
1
0
0
1
1
1
1
2
1
1
2
1
1
2
1
1
0
1
1
0
3
1
2
1
1
1
0
1
1
0
1
2
1
2
2
0
2
1
1
0
1
0
0
0
1
0
2
0
2
1
0
1
2
1
1
2
2
1
2
1
1
1
0
1
2
1
1
0
2
1
1
1
1
1
0
2
2
2
1
2
0
2
0
1
0
1
0
1
1
0
2
1
1
1
2
2
2
2
1
0
0
1
2
1
0
1
2
2
1
2
1
1
1
0
0
1
2
0
1
1
1
2
1
1
1
1
1
0
1
2
1
2
2
2
2
1
0
2
1
1
0
2
2
1
3
1
1
1
1
1
1
1
1
2
1
1
1
0
1
2
2
0
2
1
0
1
2
1
1
1
0
1
0
1
2
1
1
0
1
1
1
1
1
0
1
1
0
0
2
1
0
2
1
2
1
0
1
2
0
2
0
0
1
1
0
1
1
2
1
1
1
1
0
1
1
2
0
1
1
1
1
1
1
2
1
1
1
1
1
2
2
1
1
1
1
2
0
2
0
1
2
1
1
1
0
1
0
1
1
1
2
1
2
2
2
2
1
1
1
1
0
0
1
1
1
0
1
1
0
1
2
1
1
2
1
1
1
1
1
1
0
0
0
1
1
1
1
1
1
1
1
2
1
0
1
1
2
1
0
1
1
2
0
1
1
1
1
0
2
1
0
1
1
1
1
1
1
0
2
1
2
2
0
2
1
1
2
1
0
1
1
0
1
1
1
1
1
0
1
1
1
2
2
1
1
2
2
1
0
1
1
2
1
1
6
2
1
1
2
2
0
0
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
2
2
1
2
1
1
1
1
2
1
0
2
0
2
1
2
0
0
2
1
2
2
1
1
0
1
0
1
1
1
1
1
1
1
0
1
0
2
1
1
1
1
0
1
2
1
0
0
2
1
0
1
1
2
2
1
1
1
0
2
0
2
2
2
1
1
2
0
1
1
0
1
1
1
1
0
1
0
2
0
0
2
0
0
0
2
1
1
0
0
0
1
1
0
0
1
1
1
1
0
0
1
1
0
1
0
2
1
1
1
0
1
0
0
1
1
2
0
2
1
1
1
1
1
1
1
1
2
1
1
1
2
0
1
1
0
0
1
1
0
2
0
1
2
2
0
1
1
1
1
1
1
1
1
2
0
2
2
1
0
1
0
1
0
1
1
2
1
2
1
0
1
0
2
1
2
0
1
1
1
1
1
0
2
0
1
1
1
1
2
1
1
1
2
1
0
1
0
1
1
0
0
1
1
1
2
1
1
1
1
1
2
0
1
1
0
2
1
1
2
1
2
1
2
2
1
0
0
2
1
1
0
1
0
1
1
1
0
1
0
2
1
0
1
2
1
2
1
1
1
0
0
2
1
1
1
1
1
0
1
0
1
0
1
1
1
1
1
0
1
0
0
1
2
0
0
1
0
1
1
1
1
1
0
0
0
0
1
2
1
1
1
2
1
1
1
2
1
1
0
0
1
1
1
2
1
1
1
1
2
1
0
0
1
1
0
1
1
1
0
1
0
0
2
0
1
1
1
0
2
1
0
1
1
1
2
0
0
1
2
0
1
2
0
1
1
0
2
1
1
1
1
1
2
1
1
1
1
1
1
0
1
2
1
1
1
0
0
3
1
0
0
1
2
1
0
1
2
1
1
1
2
2
2
1
0
1
0
1
2
1
2
4
0
1
1
1
1
1
1
0
1
0
2
1
1
2
0
1
2
0
0
1
3
0
1
0
0
1
0
2
1
0
1
1
0
2
2
2
1
2
1
2
1
1
0
0
2
1
1
0
0
0
0
1
3
1
1
0
0
1
1
1
1
1
0
0
1
0
2
1
0
1
3
0
1
0
0
1
2
1
2
1
0
2
1
0
1
1
1
0
1
0
1
1
1
1
1
1
0
0
0
1
1
1
1
0
2
1
2
1
0
1
0
0
1
1
1
1
1
1
2
1
1
0
2
2
0
1
1
1
1
2
2
1
1
1
2
1
2
2
1
1
2
1
2
0
2
1
1
2
1
1
1
0
1
2
2
2
1
2
2
1
1
1
2
1
1
2
0
1
3
1
0
1
2
2
2
0
0
1
1
1
1
0
1
1
1
0
1
0
0
1
0
0
0
2
1
1
1
2
2
1
0
2
1
2
2
2
1
0
1
4
2
1
1
1
2
2
0
1
2
0
0
1
1
1
0
3
1
1
0
1
2
0
1
1
2
2
1
1
1
1
1
3
0
1
1
0
2
0
0
1
1
0
2
1
1
2
0
1
0
2
0
0
1
1
0
2
1
2
0
2
1
2
1
2
0
0
1
1
1
1
0
3
1
0
0
1
1
2
1
1
2
0
1
1
1
2
2
1
0
1
1
1
1
1
1
1
0
0
1
1
2
2
2
0
1
0
1
1
0
2
1
3
2
1
2
0
2
1
1
1
2
1
0
0
1
2
1
0
2
1
1
1
1
1
1
0
0
1
2
2
1
1
2
2
1
0
1
1
1
0
1
1
0
2
1
1
0
1
1
2
1
1
0
1
2
1
1
2
0
0
1
2
1
3
2
0
0
1
5
1
0
2
1
1
1
1
1
0
0
1
0
1
1
0
1
1
1
0
1
0
1
1
1
1
1
0
2
0
0
2
0
2
0
1
0
1
0
0
1
2
1
0
1
1
0
0
0
1
2
0
1
1
1
0
1
1
4
1
1
1
0
0
1
2
1
1
2
1
0
2
1
1
1
0
1
2
0
1
1
0
1
1
0
2
1
0
1
2
1
1
1
1
1
0
1
1
1
1
2
2
0
0
1
1
0
3
0
1
1
1
1
0
1
0
1
1
1
0
0
2
0
2
0
0
1
1
2
1
1
0
1
1
1
1
2
1
2
2
0
0
0
1
1
2
2
1
0
1
0
1
1
1
1
2
1
0
1
1
0
1
1
1
1
0
1
0
2
1
1
1
1
1
2
1
1
0
1
0
1
2
3
2
0
1
1
2
1
1
0
0
1
2
2
1
1
2
1
2
0
1
0
1
1
0
1
1
1
2
2
1
1
1
1
1
1
1
0
1
1
1
2
0
1
2
1
1
1
1
3
1
0
0
1
1
1
2
2
0
2
1
1
1
1
0
1
1
2
2
1
3
0
0
0
1
0
1
0
0
1
2
1
1
1
1
1
1
1
2
1
1
0
0
1
1
1
1
1
1
2
1
1
0
0
1
2
2
1
0
1
2
1
0
1
2
1
0
2
2
1
0
1
3
1
1
0
1
2
0
0
2
0
3
0
1
1
1
1
0
1
1
2
1
1
1
2
3
1
0
1
1
1
2
1
1
2
3
0
0
1
1
2
1
0
1
2
1
1
0
3
1
2
0
2
1
0
1
1
2
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
0
1
1
1
0
1
1
1
1
1
0
1
1
1
1
2
1
1
2
0
0
2
2
1
2
0
1
0
1
1
1
1
0
1
1
0
1
0
0
1
0
1
2
0
0
2
1
1
1
0
4
0
0
1
2
1
1
2
1
0
1
1
0
0
2
1
1
1
2
2
1
1
1
2
1
0
1
0
1
1
1
2
1
1
0
0
1
0
0
0
1
1
2
2
1
1
0
1
0
2
2
0
0
1
1
1
2
2
2
0
0
1
1
0
1
2
0
1
2
0
2
1
1
1
1
0
1
0
0
2
2
1
1
0
0
1
1
1
1
3
1
1
1
1
0
2
0
1
0
1
0
1
1
1
1
1
1
1
1
2
1
1
0
0
1
0
0
2
2
0
0
2
0
0
1
0
2
2
1
0
1
1
1
1
0
1
0
1
0
0
1
1
0
2
0
2
1
1
1
2
2
1
0
1
0
1
0
2
2
0
1
0
2
1
1
0
1
1
0
0
1
2
1
0
0
1
2
1
1
1
2
1
0
1
1
1
2
1
1
2
0
2
1
1
1
1
1
2
1
2
1
0
1
1
0
1
2
2
1
1
0
1
0
0
1
1
0
0
0
0
0
2
1
1
1
1
2
0
2
1
1
2
1
2
2
2
1
0
1
0
1
1
2
1
1
1
1
0
2
1
2
1
1
1
1
1
0
1
1
0
1
1
2
2
1
1
2
2
0
1
1
2
1
0
1
2
0
2
1
1
1
0
1
1
1
1
1
0
0
1
1
1
0
1
1
0
2
0
1
0
1
0
1
2
1
1
1
1
1
1
1
1
0
0
1
1
1
1
1
1
0
2
1
1
1
1
0
2
2
2
1
0
1
0
1
2
2
0
1
1
1
0
1
1
1
1
1
0
1
0
1
0
2
2
2
1
0
2
0
1
2
0
0
2
2
0
2
1
0
1
1
1
0
1
0
2
0
0
1
0
1
0
2
1
1
0
2
1
0
0
1
2
2
1
2
1
2
1
1
2
0
2
2
2
0
1
2
1
2
1
2
1
2
0
1
0
1
2
1
0
1
0
0
1
0
1
2
0
1
1
1
1
1
1
0
0
0
1
1
2
1
1
1
1
2
2
1
1
1
1
0
2
0
1
1
1
1
0
2
1
2
1
0
0
1
2
0
2
1
1
2
0
1
1
1
1
0
0
1
2
0
1
1
2
1
0
0
2
0
0
0
1
2
2
2
1
1
0
1
1
2
0
1
0
1
2
1
1
1
1
2
1
2
0
2
1
2
1
2
1
0
0
0
0
1
1
2
1
1
1
0
2
1
1
2
0
2
1
1
1
0
2
1
2
1
1
0
1
0
0
1
1
1
1
1
1
2
1
1
0
0
0
1
2
1
1
1
1
1
2
2
2
2
1
1
1
1
1
1
0
1
2
1
1
0
1
0
4
1
0
2
0
2
1
2
1
0
1
2
2
2
1
1
0
1
1
1
1
1
2
0
1
2
2
2
1
1
0
2
1
1
0
2
1
1
0
2
2
0
1
0
0
1
2
1
1
1
0
2
2
2
0
1
2
1
0
2
1
0
0
1
2
0
0
0
1
1
1
0
1
1
1
0
0
0
0
1
2
0
0
1
2
1
1
1
1
1
0
1
1
1
0
2
1
2
1
1
2
2
1
0
1
1
0
1
2
1
0
1
1
1
1
1
1
1
2
0
0
0
1
1
1
1
1
2
1
1
1
0
0
1
2
2
2
1
1
0
1
2
2
0
2
1
1
1
1
1
2
0
2
1
1
1
0
0
0
1
1
1
1
1
1
1
0
2
1
2
1
2
1
1
0
1
2
2
1
1
1
2
1
0
1
1
1
1
1
0
1
1
1
0
0
1
0
2
2
1
1
1
0
0
0
0
0
1
0
1
1
1
1
1
0
1
1
1
1
0
0
1
1
1
2
2
1
1
0
2
1
0
1
0
0
2
2
1
1
2
1
1
1
0
0
1
1
2
1
0
0
1
2
1
2
1
1
1
1
1
1
1
1
2
0
1
1
1
1
1
0
0
1
1
1
1
0
1
1
0
1
0
0
2
0
4
1
0
2
0
2
2
2
2
2
1
1
0
1
1
1
1
2
1
0
1
2
0
0
1
0
2
1
1
2
1
1
1
2
1
3
1
1
1
1
0
0
1
0
1
2
3
1
1
0
1
1
0
2
1
1
1
0
1
1
1
1
1
1
1
1
0
2
1
1
0
2
2
1
0
1
0
1
0
2
2
2
1
1
1
2
0
0
1
2
1
1
2
0
0
1
1
1
0
0
2
2
1
2
1
0
1
1
2
0
1
0
2
1
1
2
0
2
1
0
1
1
0
1
1
1
0
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
0
1
1
1
1
1
1
1
2
1
0
1
2
0
1
1
2
0
0
2
2
2
1
2
2
0
1
2
2
1
2
1
0
0
2
2
1
2
1
0
1
1
2
2
1
2
1
2
1
1
0
1
2
0
2
2
1
1
2
0
1
0
1
1
2
0
1
1
1
2
1
2
1
1
1
0
2
0
1
1
2
0
1
1
1
2
2
1
1
0
1
0
0
0
1
1
1
2
1
0
1
1
0
1
0
2
2
2
0
0
0
0
2
1
0
0
2
2
0
1
1
1
1
0
1
0
1
1
1
1
2
1
0
2
2
0
1
1
2
1
1
1
1
1
1
1
2
1
0
3
2
1
1
1
0
0
1
1
0
1
1
0
1
1
1
2
0
0
1
1
0
1
1
2
0
1
1
1
0
1
1
1
0
1
2
1
0
0
0
1
2
2
2
0
1
2
1
1
1
0
1
1
0
1
2
2
2
1
2
1
1
1
2
1
0
2
1
2
1
0
1
1
1
0
2
1
1
1
2
1
0
1
1
0
1
1
0
0
1
1
1
1
2
1
0
0
0
1
2
2
2
1
2
3
1
0
1
1
3
2
1
1
1
1
1
0
1
0
2
2
2
1
1
0
0
2
1
1
2
0
0
0
2
1
0
1
0
1
1
1
0
1
0
1
1
1
0
2
0
1
0
1
0
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
2
2
1
2
1
1
1
1
1
4
1
1
1
1
0
1
1
1
1
1
1
1
1
0
1
0
0
2
1
0
1
1
1
1
1
2
2
1
1
1
0
2
1
1
1
0
1
0
1
0
1
0
0
1
0
1
1
1
0
1
2
0
2
1
1
2
0
1
2
2
1
1
0
1
0
2
1
0
0
1
3
2
0
2
0
1
1
2
1
3
1
1
1
1
1
0
0
1
1
1
0
1
1
2
1
0
0
1
2
1
1
2
2
1
2
1
0
1
1
1
0
2
0
0
1
2
1
1
1
1
1
1
1
2
0
1
1
0
1
0
1
0
2
2
2
0
0
1
2
1
1
1
1
2
1
0
1
0
1
2
1
0
1
1
0
1
0
2
1
0
0
1
2
0
1
1
0
1
1
1
0
1
0
0
2
2
1
0
1
1
0
1
2
2
1
2
1
1
2
1
2
2
2
0
2
2
1
0
1
1
1
1
0
1
0
0
0
1
1
1
0
1
0
2
2
1
1
2
2
1
1
2
1
1
2
2
2
2
0
0
0
1
2
1
1
2
0
0
1
1
0
1
1
2
0
2
1
2
2
2
2
0
1
1
2
1
1
1
2
0
2
1
1
0
2
1
1
1
2
1
1
0
1
0
2
1
0
0
1
2
1
1
0
0
1
1
2
2
2
1
1
1
0
0
1
0
2
1
0
2
2
1
1
2
1
1
1
2
0
2
3
1
1
2
1
0
2
0
0
0
1
1
1
1
1
2
2
2
0
0
1
0
2
1
1
0
2
0
0
0
0
2
2
0
0
1
1
1
1
1
1
1
2
1
1
1
1
0
0
1
1
1
0
1
1
1
1
1
1
2
2
1
2
1
1
1
1
1
0
2
1
4
1
1
1
2
1
1
1
2
0
2
1
0
1
1
1
0
1
0
1
0
1
1
1
1
0
1
1
1
1
2
0
2
1
2
1
0
1
1
1
1
1
1
1
2
2
1
1
1
0
2
1
0
1
1
1
1
2
1
1
1
0
0
1
1
2
1
1
0
0
1
2
1
1
0
0
0
2
1
1
0
1
1
2
1
4
1
1
1
2
2
0
1
1
1
2
2
1
0
2
0
2
3
2
1
1
1
0
2
1
0
1
1
0
1
1
1
1
1
2
0
1
2
1
0
1
1
0
1
1
1
1
1
2
0
0
1
1
1
0
1
1
2
2
1
1
0
1
0
1
0
0
2
1
0
1
1
1
1
1
2
0
2
0
1
2
1
1
1
1
1
1
1
1
0
1
0
2
0
0
2
1
1
1
2
1
0
2
0
1
1
1
0
1
0
4
0
2
2
0
1
2
1
1
2
2
0
2
1
1
1
1
1
1
1
2
2
0
1
1
1
1
0
1
1
1
2
0
1
2
0
1
0
0
1
1
2
2
1
1
0
1
1
1
1
1
1
2
1
2
2
2
1
0
0
1
1
1
1
0
1
2
0
1
0
0
0
1
0
1
0
1
1
1
2
0
2
1
0
0
0
0
0
0
1
2
0
2
1
1
1
0
2
2
1
1
1
1
0
1
1
1
1
1
1
1
1
0
1
2
2
2
2
1
0
0
1
3
0
0
2
1
1
1
1
1
1
2
1
2
1
0
1
1
1
2
0
1
2
1
1
1
1
2
1
2
2
1
1
4
1
1
2
0
1
1
2
1
1
2
0
2
1
1
2
1
1
0
1
0
1
1
1
0
1
0
1
0
0
0
0
0
1
1
1
0
1
2
0
0
1
0
1
2
1
1
1
1
1
1
0
1
2
0
2
1
1
1
1
0
2
1
0
1
0
1
1
2
2
1
1
2
2
2
1
1
1
1
1
1
2
0
1
1
1
0
2
0
1
1
1
2
1
1
0
1
1
1
0
2
2
0
1
1
1
0
1
1
1
1
0
0
1
1
1
1
1
1
1
2
1
1
2
1
2
2
1
0
1
1
0
2
0
1
2
1
0
1
0
1
1
2
2
1
0
1
2
1
1
1
2
1
1
1
1
0
2
0
1
1
1
1
2
0
2
0
1
2
0
2
1
0
2
3
1
1
0
0
0
1
2
0
1
1
0
0
1
1
1
1
2
2
0
1
1
2
1
1
0
0
2
0
1
0
1
1
1
1
2
1
0
1
0
1
2
1
0
1
1
1
0
1
2
1
2
2
1
0
0
1
1
2
1
1
1
1
2
1
1
1
3
0
2
0
1
2
0
1
2
1
1
2
1
2
2
0
1
0
1
1
1
2
1
2
1
1
0
1
1
1
4
1
0
1
1
1
1
2
0
0
1
0
1
1
1
2
2
0
2
1
0
1
1
1
1
0
1
0
2
2
0
1
1
1
0
0
1
2
1
1
2
1
1
1
1
2
0
0
0
1
1
1
0
1
1
1
1
2
0
0
1
1
1
1
1
1
0
2
0
1
2
1
0
1
2
1
0
1
2
1
1
1
1
1
1
0
0
1
0
2
1
0
0
1
1
0
1
0
2
1
2
1
1
1
1
1
1
2
0
1
0
1
2
0
2
2
1
0
0
1
1
1
2
2
1
1
1
1
0
1
0
1
1
1
1
1
1
1
1
0
1
1
1
1
1
2
0
2
2
2
1
1
0
2
2
2
2
1
2
1
1
1
1
0
0
0
0
2
2
0
2
2
2
0
1
1
2
0
1
2
0
1
1
1
1
2
0
1
0
1
1
1
1
1
2
1
1
1
2
0
1
1
1
0
2
0
1
3
1
1
1
0
0
2
2
1
2
2
0
1
0
1
1
1
2
1
0
2
0
1
5
1
1
1
2
0
1
1
1
1
1
1
2
1
0
1
1
0
2
0
1
0
0
0
2
1
1
0
2
1
1
1
2
2
0
1
1
0
2
1
0
0
3
2
1
0
1
1
1
0
0
1
2
0
1
0
1
0
1
1
1
1
1
2
1
1
1
1
0
2
0
1
1
1
1
1
0
1
1
2
0
1
1
1
2
1
2
2
1
2
1
2
2
0
2
1
1
0
2
1
0
1
2
3
2
2
4
1
1
1
2
1
0
0
1
1
1
0
1
1
3
1
2
0
2
1
2
1
1
1
0
0
1
1
0
1
1
1
0
0
1
2
0
0
1
0
2
1
2
1
0
0
0
2
2
1
1
1
1
0
1
2
1
4
2
2
2
2
1
1
0
0
2
2
2
0
1
2
2
0
1
0
1
1
1
1
1
2
1
1
1
1
1
1
1
2
3
0
2
2
0
1
1
0
1
1
2
1
0
0
2
1
1
0
0
3
1
0
2
1
1
2
2
0
0
1
0
0
1
2
1
2
1
0
0
1
2
0
1
0
1
2
2
1
1
1
1
1
1
2
1
0
1
1
1
1
1
1
1
0
3
1
1
0
1
2
1
1
1
1
2
1
0
2
1
0
1
1
1
1
1
1
0
1
1
2
1
0
1
2
2
2
2
1
0
2
1
1
1
0
4
0
1
2
1
2
1
0
2
1
2
1
2
1
2
1
1
2
1
1
1
1
1
1
1
0
2
1
2
2
0
2
0
1
1
1
2
1
1
0
1
1
0
0
1
1
1
0
1
1
1
5
1
0
1
0
0
0
2
2
1
2
0
1
1
1
2
1
0
0
1
1
1
2
1
1
2
2
1
0
0
1
0
2
1
1
2
1
2
1
1
0
1
0
1
2
2
1
1
1
1
1
0
1
1
4
1
1
1
1
1
0
2
1
2
1
1
0
2
3
0
1
0
1
3
2
1
1
0
1
1
1
1
1
2
1
0
1
1
1
0
1
1
2
2
1
2
0
2
1
1
2
2
0
1
1
1
2
1
1
1
1
2
0
1
1
1
1
1
0
1
2
0
1
1
0
3
0
2
1
0
0
2
0
0
1
0
1
1
2
1
1
0
1
1
1
0
0
1
1
1
1
2
1
2
2
2
1
1
1
2
2
1
0
0
1
1
1
1
0
0
0
1
0
2
0
0
1
1
1
1
2
0
1
1
0
0
0
3
2
1
1
2
1
1
0
0
1
1
0
2
1
1
1
1
2
2
1
1
0
1
3
0
1
2
1
1
1
0
0
1
1
1
1
2
1
0
0
0
1
1
1
1
0
1
1
1
1
2
2
1
1
2
1
2
1
2
2
0
2
1
1
1
0
1
1
2
1
0
2
0
2
2
1
0
1
1
0
1
2
1
0
1
1
1
1
1
1
1
1
1
1
1
0
0
2
2
2
1
0
1
1
1
2
1
1
2
1
2
1
1
1
1
0
2
1
1
1
0
2
1
1
0
2
1
1
3
1
2
2
2
1
1
1
1
1
1
3
1
1
1
1
1
2
1
0
2
1
0
1
1
0
1
0
1
2
1
0
0
0
1
1
0
2
1
2
0
1
1
0
1
0
2
1
2
0
1
2
1
2
0
2
1
1
1
1
0
2
1
1
0
0
1
1
1
1
0
1
0
2
1
1
1
1
4
1
1
1
2
2
1
2
2
0
2
1
2
2
1
0
1
1
2
1
1
1
1
2
1
2
2
2
1
0
0
1
2
2
2
0
0
0
0
0
2
2
1
1
0
1
1
0
0
1
2
2
1
0
1
0
1
2
2
0
2
1
0
1
0
0
1
1
0
0
2
1
1
0
2
0
1
1
1
0
0
1
0
0
1
1
0
1
2
2
2
2
1
2
1
0
1
0
0
3
1
1
1
1
1
2
2
2
1
0
1
0
0
7
0
0
2
1
0
1
1
1
2
1
0
0
0
1
1
0
1
1
1
1
1
1
0
1
0
2
1
1
2
1
1
1
1
1
2
1
1
1
2
1
0
1
0
1
1
1
2
1
1
0
0
2
1
1
1
1
1
2
1
1
0
2
1
1
2
2
1
0
1
1
1
1
2
0
1
2
0
1
1
1
0
1
1
2
0
1
1
0
1
1
1
0
1
2
1
1
1
1
2
1
1
1
0
1
0
1
0
2
2
0
1
1
0
2
0
1
0
2
2
1
0
2
1
0
2
1
2
2
1
2
1
0
1
1
2
0
1
0
0
1
1
2
1
2
2
0
0
1
1
1
1
1
2
0
1
0
0
2
1
1
2
1
2
1
1
1
0
0
2
1
2
0
1
0
2
0
1
0
1
1
0
2
1
0
2
1
1
1
2
1
2
2
1
1
0
1
1
4
1
2
1
1
0
1
1
2
1
2
1
1
1
0
1
1
1
2
1
0
1
1
1
1
1
1
1
1
1
1
0
0
1
1
1
2
1
1
2
0
0
1
1
2
0
1
2
0
1
2
2
1
1
1
1
0
2
0
2
2
3
1
2
1
1
1
0
2
1
1
1
2
0
2
1
0
1
0
0
3
1
1
0
1
0
0
2
1
0
2
1
0
1
2
0
1
1
0
1
2
0
0
1
0
1
1
2
0
1
1
0
1
1
0
1
3
0
0
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
2
0
1
2
2
2
1
0
2
0
2
2
1
1
1
2
1
1
1
1
1
2
0
1
1
2
1
1
1
3
2
1
1
2
1
0
2
1
1
1
1
0
1
2
0
1
1
1
2
1
1
2
1
1
1
1
2
3
0
1
1
1
1
1
1
2
1
1
0
2
1
1
1
1
2
2
1
2
1
1
0
1
1
1
1
1
1
1
0
1
0
0
1
1
0
1
1
1
1
0
2
2
1
1
0
2
1
0
0
2
0
1
1
1
0
0
1
1
2
2
1
1
3
2
1
0
0
1
1
1
0
1
1
0
1
2
1
0
1
0
1
2
1
0
1
2
1
0
2
2
1
0
1
1
1
1
2
1
2
1
2
1
3
2
1
1
1
0
1
1
1
1
1
1
0
1
1
2
1
1
1
3
1
0
1
1
1
1
1
0
0
1
0
0
1
0
0
0
1
1
0
1
1
1
1
1
1
1
2
1
2
1
2
1
1
0
0
1
1
0
0
1
0
1
1
2
1
1
0
1
0
1
1
2
1
1
1
1
0
0
1
2
2
1
1
2
2
1
2
1
0
1
1
0
1
4
1
1
1
0
1
2
1
0
1
0
1
1
1
2
1
1
2
2
1
1
1
0
1
2
2
1
0
2
0
2
0
0
2
2
1
2
2
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
0
0
1
1
1
0
1
1
2
1
1
1
1
0
1
1
1
0
2
1
2
0
1
1
1
1
1
1
1
0
1
1
0
1
0
0
1
1
1
0
2
1
2
1
2
2
0
0
1
2
2
1
0
0
0
1
1
1
2
0
0
2
1
1
0
1
1
0
2
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
0
1
1
2
1
1
1
2
0
1
0
2
1
0
1
2
1
0
0
2
1
0
1
1
2
1
1
1
2
1
3
2
0
1
1
0
0
1
0
0
1
1
2
0
2
1
2
2
0
0
1
1
1
1
2
1
0
1
0
1
2
0
1
1
1
0
1
0
1
1
1
1
1
0
1
2
1
1
1
2
2
1
1
1
1
1
2
0
1
2
1
0
1
1
1
0
1
2
1
1
0
2
1
1
1
0
2
2
2
1
2
0
1
2
1
0
2
1
2
1
0
1
0
1
1
1
1
1
0
1
2
0
2
0
0
2
1
2
1
0
2
0
0
2
2
1
1
2
1
1
1
1
1
1
1
0
1
0
1
1
0
1
1
0
1
0
1
0
2
2
1
1
0
1
2
1
3
0
0
1
1
0
0
1
3
0
1
1
1
1
0
1
1
0
1
0
0
1
0
1
1
1
2
1
2
2
1
2
1
1
0
1
1
0
0
0
2
1
1
1
0
2
2
1
1
1
1
1
1
1
2
1
1
2
1
1
2
1
0
0
2
1
1
2
1
1
1
1
0
2
1
2
2
1
1
0
1
1
0
1
1
1
0
1
2
1
0
1
2
1
1
1
0
1
1
2
1
2
1
0
1
1
0
2
2
0
0
1
1
1
1
1
1
1
2
0
1
2
0
1
1
0
0
1
0
1
1
1
1
1
1
2
2
1
2
0
1
0
0
1
2
1
1
1
0
2
2
1
0
2
2
0
1
1
0
3
1
0
1
1
1
0
2
0
2
1
2
1
1
2
2
0
1
1
1
1
1
1
1
0
1
2
2
1
0
1
1
2
0
1
0
1
1
1
1
2
1
1
1
0
0
1
1
1
0
2
1
1
0
1
1
2
0
1
0
1
1
0
1
1
2
1
2
0
2
1
1
1
1
2
0
0
1
1
0
1
1
1
0
1
0
1
1
1
1
1
0
1
2
1
1
0
2
2
1
1
2
1
2
0
1
1
1
1
1
1
1
1
0
1
0
0
1
1
2
1
1
0
0
1
2
0
1
0
2
2
1
2
2
0
2
1
2
1
2
0
2
0
0
2
1
1
2
0
0
2
1
3
1
1
1
1
3
1
1
0
1
0
2
0
1
1
0
1
1
0
0
1
1
1
0
2
1
1
1
0
2
2
0
1
0
2
2
2
1
1
1
1
1
1
1
1
0
1
2
1
1
1
0
1
0
1
2
1
1
1
1
2
0
2
0
2
1
2
1
1
1
0
1
1
1
0
1
1
2
2
2
2
2
1
1
0
1
1
1
2
0
2
1
1
0
1
1
2
0
1
2
1
1
1
1
0
1
1
1
2
1
1
1
1
0
0
2
0
1
0
2
1
2
1
2
0
2
2
1
0
1
0
1
1
2
1
2
1
0
0
1
1
0
1
0
0
1
0
1
2
0
2
1
1
1
1
0
1
1
0
1
2
0
1
1
1
2
2
1
2
1
2
1
0
0
1
1
0
1
2
1
1
2
0
2
2
1
0
0
0
1
1
0
1
0
1
0
0
2
2
0
1
1
1
0
1
1
1
2
0
1
0
0
1
1
1
1
0
2
2
1
0
2
0
2
2
1
3
0
1
1
1
2
1
2
1
2
1
2
1
1
1
0
0
0
1
1
2
2
1
2
2
1
0
1
2
1
0
1
1
0
1
2
1
0
0
0
2
1
0
3
1
2
0
0
1
0
2
1
2
1
1
1
0
0
1
1
0
1
1
0
2
1
1
1
1
0
1
1
2
1
5
1
0
1
1
1
1
1
2
1
1
1
1
1
0
2
1
0
1
1
1
1
1
1
1
1
0
1
1
1
1
2
2
0
1
2
1
2
1
1
0
1
1
2
0
2
0
1
1
1
0
1
1
1
1
0
2
1
2
1
0
1
0
1
2
1
1
1
0
1
1
0
1
1
1
1
2
0
0
1
1
2
1
1
1
1
2
1
1
1
1
2
1
0
2
0
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
2
0
0
0
1
1
0
1
2
1
1
2
0
1
1
0
1
2
0
1
1
1
1
0
1
2
0
0
0
1
2
1
0
2
0
1
1
0
0
2
1
0
1
1
1
1
1
2
0
2
2
2
1
1
1
1
1
1
1
1
0
0
2
2
1
0
0
1
1
1
0
1
2
0
1
1
1
1
0
2
1
1
0
1
1
2
2
0
1
1
0
0
0
1
0
0
1
1
1
1
2
1
1
0
1
0
1
1
1
1
1
1
1
2
2
2
1
0
0
1
0
1
1
0
0
1
1
1
1
1
1
1
1
2
0
1
1
1
3
2
1
1
0
0
1
1
2
0
0
1
1
1
2
0
2
1
1
2
2
1
2
1
0
1
1
2
1
2
1
0
1
0
1
1
2
1
1
1
1
0
2
1
1
1
0
0
0
0
1
0
0
1
0
2
2
2
2
1
1
0
2
1
2
2
1
1
0
1
1
1
1
1
1
1
0
2
2
1
1
0
1
1
1
0
2
2
1
1
1
0
0
0
2
2
0
2
1
1
0
1
0
0
2
2
0
0
1
1
2
0
1
2
2
1
1
1
1
1
0
1
1
1
0
2
0
1
2
1
1
2
1
1
1
1
1
1
1
1
2
2
1
1
1
0
1
1
1
0
2
0
1
0
1
1
2
0
1
1
1
1
1
1
1
0
1
1
1
0
1
1
1
0
0
1
2
1
1
0
1
1
1
1
0
2
1
0
1
0
1
1
1
2
1
1
1
0
0
1
1
0
1
1
1
0
2
0
1
0
0
2
1
0
1
2
0
0
0
1
1
1
0
2
1
2
1
0
1
1
1
0
2
2
1
2
0
1
1
1
1
1
0
1
1
1
2
0
1
0
0
0
1
1
2
1
1
0
0
1
2
1
0
0
1
2
1
1
0
0
2
1
1
1
0
2
0
2
1
2
1
0
1
1
1
1
2
0
1
2
2
1
1
0
1
1
1
1
1
2
1
2
2
1
1
0
1
2
1
2
1
0
0
1
1
1
1
2
2
1
1
1
1
1
1
1
0
2
2
0
2
3
1
0
0
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
0
1
2
2
1
0
0
1
0
2
1
0
1
0
1
2
1
0
1
0
2
1
2
1
2
1
1
0
1
0
1
2
1
1
2
1
2
2
1
0
1
1
1
2
0
1
0
2
2
1
1
1
1
0
1
0
1
1
1
0
1
0
2
1
2
0
2
1
1
2
0
1
1
1
1
1
1
3
0
2
0
1
1
1
2
1
1
1
1
1
0
0
1
1
0
1
1
2
2
0
0
1
0
1
2
2
0
1
0
1
3
1
2
1
1
2
1
1
0
1
1
0
1
0
0
2
1
2
1
0
1
0
1
2
2
2
0
1
1
1
0
0
2
0
2
1
2
0
1
0
2
0
1
0
2
2
1
1
1
1
1
0
0
0
2
0
0
1
1
1
1
1
0
1
0
1
1
0
2
0
1
2
2
1
0
1
1
1
0
0
1
0
1
0
2
0
1
1
0
1
1
1
2
2
0
1
2
1
1
1
2
0
1
2
1
1
1
1
1
2
1
0
1
1
1
3
1
1
1
1
3
1
0
1
2
1
1
2
2
1
1
2
1
0
2
1
2
1
1
1
1
0
1
0
2
0
2
2
1
1
1
2
1
2
1
0
1
1
1
2
1
2
1
1
1
1
0
1
2
0
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
0
2
1
1
1
1
1
2
1
1
1
0
0
1
1
0
1
2
0
2
1
1
2
1
1
0
1
0
1
1
0
1
1
0
1
1
1
1
2
0
1
1
2
1
0
1
2
2
2
1
0
1
0
2
0
0
0
2
2
2
1
1
2
1
2
2
1
0
1
0
1
2
2
3
1
1
1
1
3
1
2
1
1
0
2
1
2
1
0
1
1
0
1
0
1
1
1
1
2
1
1
1
2
1
1
2
1
1
1
1
2
0
0
0
2
0
4
1
1
2
1
1
1
2
1
1
1
1
0
1
1
1
0
0
0
0
0
1
1
1
0
2
2
1
1
0
1
1
1
0
1
0
2
1
0
0
1
1
0
0
1
1
1
1
0
0
1
1
2
2
0
1
1
1
1
0
1
1
2
0
2
1
1
2
2
1
1
0
2
0
2
2
1
2
0
0
0
0
0
1
0
1
1
0
1
0
1
1
2
1
1
0
0
1
1
1
0
0
1
0
0
0
1
0
3
2
2
0
1
1
1
1
1
0
0
1
0
2
0
1
1
1
2
0
1
0
0
0
1
0
1
1
1
1
1
0
1
1
1
1
2
0
0
1
1
1
2
1
0
1
0
1
1
0
1
0
1
0
1
1
0
2
1
1
1
1
2
1
1
2
2
2
1
0
1
1
0
2
0
1
2
0
2
1
3
0
2
1
1
1
2
1
1
3
0
2
2
2
0
1
2
1
0
1
0
3
0
1
1
1
0
2
0
1
0
1
1
1
2
1
2
1
1
1
2
0
2
1
1
1
1
1
0
2
1
2
1
2
2
1
1
1
1
1
1
0
2
2
1
1
0
1
0
1
1
1
1
0
1
2
0
0
1
1
0
2
0
1
2
1
1
1
2
2
1
2
1
1
0
0
1
1
1
1
1
1
2
1
1
2
2
1
2
1
2
0
1
0
1
1
1
1
1
1
1
1
1
0
1
1
1
2
1
1
1
2
1
2
2
1
0
2
2
2
1
1
1
2
1
1
1
1
1
2
3
0
1
1
1
1
2
0
1
1
1
2
1
1
0
0
2
1
1
1
1
1
1
2
2
2
1
1
3
0
2
2
2
0
1
0
1
2
1
1
2
0
1
1
2
2
1
1
2
1
1
1
1
0
2
2
3
1
2
1
1
2
2
1
2
1
0
2
1
0
1
1
2
1
2
0
2
0
1
1
0
1
1
1
1
0
1
2
0
2
0
2
2
1
1
1
0
0
1
1
0
2
1
0
1
2
1
1
0
2
1
1
0
0
0
0
2
1
0
1
0
1
2
0
1
1
2
2
2
1
1
1
1
0
1
1
0
2
1
1
1
2
1
1
0
2
2
1
1
3
0
1
2
0
1
0
1
1
1
2
2
0
1
1
1
0
1
1
2
0
1
0
2
2
1
2
0
1
2
0
2
1
2
1
0
2
1
1
0
2
0
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
0
1
1
1
0
1
0
1
1
0
1
2
1
0
0
1
1
2
0
0
1
1
2
0
1
1
1
1
2
1
2
2
1
2
0
0
1
1
1
0
1
2
1
2
0
1
1
0
0
1
1
0
2
2
0
1
1
1
3
1
1
1
0
0
1
0
1
0
0
1
1
2
1
0
1
2
0
1
2
1
0
0
0
0
0
0
0
1
1
2
2
1
0
1
1
0
0
0
1
1
1
5
1
0
0
2
1
1
1
1
1
1
1
0
2
1
2
1
0
1
2
1
1
1
1
1
0
0
2
0
2
0
1
1
1
1
1
1
0
1
1
0
1
2
1
0
1
1
1
1
1
1
1
0
1
1
0
0
1
1
0
1
2
2
1
0
0
0
1
0
2
1
1
1
2
1
1
0
1
0
1
0
1
1
0
2
1
1
2
0
1
1
0
1
1
1
2
2
1
1
2
1
0
1
1
2
1
0
0
1
1
2
2
1
1
1
0
0
0
2
1
1
1
1
2
1
3
1
0
2
1
2
1
1
2
1
1
1
2
0
1
2
0
2
2
2
1
1
0
1
1
1
1
1
1
1
1
0
1
0
2
1
1
1
1
1
0
2
1
1
1
0
2
1
0
0
1
1
2
1
1
3
1
2
2
0
0
2
0
2
1
1
1
2
0
0
0
1
1
1
0
1
2
1
1
1
1
1
1
0
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
0
3
0
0
2
0
0
1
2
0
1
1
1
1
2
1
1
0
2
0
2
1
1
1
2
2
2
1
1
1
0
1
2
0
2
1
1
0
2
1
1
2
1
2
0
0
2
1
0
1
2
1
3
0
1
1
0
0
1
1
0
2
1
1
1
1
1
1
1
2
1
1
1
2
0
1
1
0
1
1
0
0
1
1
0
0
1
0
0
1
1
0
1
1
2
1
2
0
1
2
1
1
0
1
1
1
1
2
0
0
1
1
4
2
2
2
1
0
2
1
1
1
1
1
1
0
2
1
1
1
2
1
0
1
1
0
1
0
1
0
1
1
1
0
1
1
2
1
2
0
0
1
1
1
2
1
0
0
2
0
1
1
0
1
2
1
0
0
1
0
0
1
1
1
1
2
0
1
1
2
0
0
0
0
1
2
0
1
2
0
1
1
5
1
1
2
1
0
2
0
0
1
1
1
2
1
1
0
0
1
2
1
1
1
1
0
1
0
2
1
2
1
2
2
1
1
0
0
1
2
2
1
1
2
0
2
0
1
2
1
1
1
0
0
2
0
1
1
1
0
1
0
1
1
1
1
0
0
1
1
2
2
1
2
2
2
0
0
1
3
2
1
2
0
0
1
0
4
2
2
0
1
0
1
0
2
2
0
1
1
1
1
1
1
1
2
0
1
1
1
0
1
2
0
1
2
0
1
0
0
2
0
1
0
1
2
2
2
0
2
1
0
2
0
1
2
2
1
2
1
0
2
1
0
1
0
2
1
1
1
0
0
2
0
0
4
1
1
0
3
0
2
2
0
1
0
0
1
0
1
1
1
0
2
2
1
1
1
2
1
1
1
1
0
0
1
1
1
0
0
2
0
1
0
2
1
1
1
0
1
0
1
1
1
2
1
1
1
1
2
1
2
0
1
1
2
2
1
1
1
1
1
0
2
1
1
1
2
1
2
0
0
0
1
1
1
1
1
1
0
0
2
1
0
1
1
1
1
2
1
2
1
0
1
1
0
3
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
0
2
1
1
1
1
1
1
2
1
1
2
1
1
1
1
0
2
2
0
2
0
2
2
2
2
0
1
1
0
1
0
1
2
0
1
1
1
2
1
1
1
2
1
1
2
0
1
1
1
1
2
0
1
0
1
1
1
3
2
1
1
1
1
1
0
1
0
1
2
2
2
1
1
1
1
1
1
1
0
1
1
0
1
1
0
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
0
0
0
0
0
1
1
0
0
1
1
0
1
2
0
1
0
2
1
0
0
0
2
1
2
1
1
1
1
1
1
1
1
1
1
1
2
2
0
1
1
1
0
1
2
0
0
1
1
1
2
2
1
1
0
1
0
1
1
2
2
0
2
1
1
1
2
0
0
1
2
0
2
1
1
0
1
2
0
0
1
1
1
0
1
2
1
1
1
1
2
1
2
1
0
2
1
2
1
1
1
0
1
1
1
2
2
2
3
1
4
0
2
0
2
1
0
1
1
2
1
1
1
2
1
0
1
2
2
1
1
0
1
1
2
1
2
0
2
0
1
2
2
1
1
1
2
1
1
2
1
1
1
0
1
1
2
1
0
2
1
2
1
2
0
1
2
0
1
2
1
1
1
1
1
0
1
1
1
0
2
2
0
2
1
2
2
1
1
1
2
1
0
0
1
1
1
2
1
1
2
1
2
1
2
1
1
1
0
0
2
2
1
0
2
0
3
0
1
2
2
2
0
2
1
1
0
1
0
1
1
1
0
0
1
2
0
2
2
0
0
4
0
0
0
0
0
1
0
0
1
2
0
1
2
1
1
0
1
1
0
1
0
1
1
0
0
1
1
2
0
0
1
1
1
2
1
0
1
1
0
1
1
1
1
2
0
1
1
0
1
1
1
0
2
2
2
0
0
2
2
1
2
1
1
0
1
1
1
1
1
0
0
0
0
1
0
1
1
1
2
0
1
2
1
2
1
1
2
1
1
0
1
0
2
2
0
0
1
1
2
0
0
1
1
1
2
1
1
1
1
0
0
0
2
1
0
1
0
2
1
0
1
0
1
1
1
1
1
1
2
0
1
1
0
1
0
0
2
1
2
0
1
1
1
2
0
0
0
1
1
0
1
2
1
0
1
1
1
1
1
2
1
0
1
2
0
1
1
0
0
2
0
0
3
1
1
1
0
1
1
1
1
1
1
2
2
2
2
0
1
2
1
1
1
1
1
0
2
1
1
2
0
1
2
1
2
1
0
1
1
2
0
4
0
1
1
1
0
1
0
2
1
2
1
1
1
2
1
0
1
0
1
2
1
1
2
1
1
1
1
1
1
1
0
1
2
0
1
2
1
2
1
2
1
1
0
2
0
1
1
1
2
1
1
1
1
1
0
2
1
1
2
0
2
1
0
1
1
1
2
2
0
1
1
1
2
2
1
0
1
1
1
1
2
0
1
1
2
1
1
1
1
0
0
1
2
1
0
1
0
2
0
1
0
1
1
1
1
1
1
0
1
0
1
2
1
1
0
2
0
1
1
1
1
1
1
1
0
1
0
1
1
1
2
2
2
1
0
2
1
0
1
1
1
1
2
0
1
1
1
0
1
1
0
0
1
1
2
0
2
0
2
0
2
0
1
1
1
2
1
2
2
1
3
0
1
1
1
2
0
0
1
2
1
0
0
1
2
0
2
1
1
1
2
0
1
0
1
2
0
1
1
1
1
2
0
2
2
0
0
1
1
2
1
2
1
0
1
1
1
1
0
1
1
0
0
1
2
1
2
1
2
2
1
0
2
0
2
0
1
0
1
2
0
1
2
2
1
1
1
0
1
1
2
3
1
0
2
1
2
1
2
1
0
2
1
0
0
1
1
0
0
0
2
0
1
1
1
0
1
1
1
2
2
0
2
0
0
0
1
1
1
2
2
1
1
1
0
0
1
1
1
1
1
1
1
1
1
1
0
0
0
1
2
0
0
1
1
2
2
0
0
0
1
1
0
1
0
1
0
4
0
1
0
1
0
1
2
2
1
0
1
2
1
1
1
1
1
1
1
1
1
1
1
0
1
0
1
0
1
1
2
0
1
1
1
0
1
1
2
2
0
1
1
1
1
1
1
2
0
1
0
1
1
0
1
0
0
0
1
1
0
0
1
1
1
1
2
1
1
1
1
0
1
1
1
1
1
0
1
1
1
0
1
1
1
0
2
0
2
2
3
2
2
1
1
2
2
2
0
4
1
2
1
1
1
1
0
2
1
1
1
1
0
2
0
1
2
1
1
0
1
1
2
0
0
1
1
1
1
0
1
0
1
2
1
1
1
1
1
1
1
1
1
1
0
1
2
2
1
1
2
1
1
1
2
0
1
0
0
1
2
2
1
2
1
1
0
1
0
2
1
1
2
2
1
1
2
1
1
0
0
1
1
1
0
2
0
0
2
0
2
2
2
0
1
1
0
1
1
2
1
1
2
1
1
2
2
0
1
2
1
0
2
1
0
1
1
1
1
2
1
1
0
2
1
3
1
2
1
0
0
1
0
1
1
1
2
1
0
1
0
1
1
1
1
1
2
1
0
1
1
0
1
1
2
1
0
1
1
1
1
2
0
0
2
1
2
1
2
1
2
0
2
0
1
2
1
1
0
2
1
1
1
1
0
0
0
0
1
0
2
0
0
1
2
0
1
1
2
1
2
1
1
1
1
2
1
1
1
1
0
2
0
0
1
1
1
1
2
1
0
2
0
2
0
2
1
1
1
1
1
1
2
0
1
1
1
0
1
1
2
1
1
2
1
1
0
0
0
1
1
0
1
1
2
2
2
2
0
1
0
2
0
1
0
1
0
1
0
1
1
0
0
1
1
0
0
1
2
1
1
2
1
1
2
2
1
0
2
2
1
0
1
1
1
0
1
1
0
2
2
2
2
0
1
0
1
1
0
1
1
0
0
1
0
1
2
1
0
1
1
1
0
1
1
1
0
1
1
1
1
1
1
1
1
0
2
0
1
1
0
0
1
1
1
3
2
1
0
0
2
2
0
1
2
2
0
1
1
1
2
1
0
2
0
1
1
1
2
1
1
1
1
0
1
1
1
0
1
1
0
1
0
0
1
2
1
2
1
2
1
2
1
2
1
1
2
1
2
0
2
1
1
1
0
1
1
1
0
1
0
1
1
1
2
1
2
2
2
1
1
2
1
0
2
2
1
0
1
1
1
0
1
1
1
1
2
2
1
2
0
1
0
1
1
2
1
1
3
2
2
1
1
1
2
1
2
2
1
2
3
0
1
2
0
2
1
2
1
0
4
1
1
0
1
1
1
1
0
2
1
0
1
1
1
1
1
2
0
1
1
1
2
1
1
0
0
2
0
0
1
1
2
2
1
1
1
0
1
1
2
2
0
2
1
2
1
2
1
0
1
1
1
1
1
2
1
0
0
1
2
1
1
1
1
0
1
1
2
1
1
0
1
1
2
2
1
2
1
1
1
2
1
0
1
1
0
1
1
2
0
1
1
1
1
2
1
1
1
2
1
1
0
1
1
1
1
0
1
0
1
1
2
1
2
1
1
1
2
1
1
1
0
1
2
1
1
1
0
1
2
0
2
0
2
1
2
2
0
1
1
2
1
1
0
1
2
1
2
1
1
2
0
1
2
1
1
0
1
2
2
1
2
1
1
1
1
1
1
2
1
1
1
1
0
1
1
1
2
1
1
1
1
1
0
1
0
1
1
2
1
0
2
2
0
1
1
1
0
1
1
1
1
1
1
2
1
2
2
1
1
0
2
1
0
0
1
2
2
0
1
1
0
0
1
0
0
0
2
2
0
0
1
1
1
1
1
1
2
0
1
1
0
2
2
1
0
1
0
1
1
1
1
1
1
1
1
0
1
0
0
2
1
0
1
0
1
1
0
2
0
1
2
2
0
1
1
1
0
1
2
0
1
1
2
0
1
1
0
2
1
1
1
1
1
0
0
0
0
2
1
1
0
1
0
0
0
0
1
1
1
2
1
1
2
0
0
1
2
0
1
1
0
1
1
1
1
1
1
1
2
1
1
1
1
0
1
1
2
2
2
1
0
1
1
2
2
1
1
1
1
1
1
1
2
2
1
2
2
1
1
0
0
0
0
0
1
0
1
1
0
1
0
1
2
1
1
0
0
0
0
2
0
1
2
0
2
2
2
0
1
2
0
0
1
1
0
1
1
2
2
1
1
0
0
2
2
1
1
2
1
2
2
1
0
2
2
1
1
1
0
0
2
2
1
2
1
0
0
1
0
1
1
1
1
0
0
3
0
2
2
1
2
1
0
1
0
7
2
0
0
3
0
1
1
1
2
1
1
2
0
0
0
1
1
0
0
2
2
2
0
2
2
1
2
0
0
1
1
1
1
1
0
2
2
1
1
1
1
0
0
2
1
0
1
0
2
1
4
1
2
1
1
1
0
2
1
1
1
0
1
1
0
0
1
3
1
2
1
1
2
0
1
0
1
0
0
2
2
0
0
1
1
2
1
2
2
2
2
0
1
2
1
0
2
1
1
1
2
1
1
0
2
1
2
1
1
1
1
3
2
0
1
2
1
1
2
1
2
2
1
1
5
1
1
0
1
1
0
1
1
1
0
1
1
2
2
0
1
0
1
0
1
2
1
1
1
1
1
1
0
2
2
2
2
1
0
2
2
1
1
1
1
1
1
1
0
0
1
1
2
1
0
0
1
2
1
0
1
1
1
1
1
1
1
2
1
1
2
0
1
0
2
2
2
0
0
2
2
0
1
0
1
0
1
3
1
0
1
2
0
0
1
0
0
1
2
1
1
1
2
1
0
1
0
2
0
1
1
0
2
0
2
0
1
1
1
1
2
1
1
1
1
1
1
1
1
0
0
1
1
2
0
1
1
2
2
1
1
2
2
1
1
2
1
0
1
1
2
2
0
0
1
0
2
0
1
2
1
1
1
0
0
0
1
2
1
1
0
1
1
2
1
2
0
0
2
1
1
1
1
1
1
3
0
0
1
2
1
1
1
1
0
1
2
0
1
1
0
1
1
0
0
1
1
1
0
1
1
1
1
2
0
1
1
0
1
2
1
2
1
0
1
1
2
1
1
2
0
0
1
1
1
1
1
0
1
1
0
1
0
0
1
2
2
0
1
1
2
2
0
1
1
1
1
1
1
1
0
2
2
0
1
1
0
1
1
1
1
2
2
1
1
2
2
1
2
0
2
1
1
1
2
2
2
1
0
0
1
1
0
1
0
2
1
2
0
2
1
1
1
2
0
1
1
1
1
1
0
2
0
0
2
0
1
1
1
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
0
1
1
2
1
2
0
1
2
0
1
2
0
1
1
1
2
0
1
3
1
2
4
1
1
0
1
1
1
0
1
1
1
1
1
0
2
2
1
2
1
1
1
2
1
1
1
1
0
1
1
2
2
1
1
1
1
2
1
2
0
1
0
1
1
2
2
1
1
1
0
1
1
1
2
1
2
1
1
0
0
1
1
0
1
0
1
1
1
0
2
1
1
2
1
0
1
1
0
4
2
0
2
2
1
0
0
1
1
1
1
1
0
1
1
2
1
0
1
1
1
1
1
1
2
2
0
1
2
0
0
0
0
1
0
0
1
1
1
1
0
2
2
0
1
1
1
1
2
1
1
2
1
1
1
2
2
2
1
0
2
0
1
2
0
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
2
1
0
0
1
0
2
1
2
1
1
2
0
1
1
0
0
2
1
2
2
2
0
1
0
0
1
1
0
1
0
0
2
1
1
1
0
1
0
1
0
2
1
2
2
0
4
2
1
2
1
1
0
1
1
1
0
1
2
1
1
1
2
1
0
0
1
1
2
2
1
2
1
1
1
1
0
2
0
1
1
0
1
0
0
1
2
1
3
1
0
0
0
0
1
1
1
0
2
0
3
0
1
0
1
2
1
3
1
1
1
0
2
1
0
1
2
1
0
0
0
1
2
1
0
0
2
1
2
1
0
2
0
2
1
1
1
1
1
2
0
0
2
0
0
3
0
2
0
2
1
1
0
0
1
1
1
0
2
1
3
1
1
1
0
2
4
1
1
2
0
2
1
2
2
1
2
0
0
0
1
2
1
1
1
1
0
0
0
1
0
1
0
1
2
2
0
1
1
1
1
2
1
1
1
1
1
4
0
0
0
0
1
1
0
1
1
1
1
1
1
1
1
2
0
3
0
1
1
1
1
0
3
1
2
1
1
1
1
2
0
1
2
2
1
1
1
3
0
1
2
0
0
1
1
1
1
0
0
0
0
1
2
2
2
2
2
1
1
0
1
2
3
0
1
2
1
1
1
6
1
2
0
1
1
2
0
0
1
0
1
1
0
2
2
1
1
1
0
1
1
1
1
1
1
2
2
2
1
0
2
1
0
1
0
0
1
2
1
1
2
1
2
1
2
0
0
0
1
1
2
2
2
2
2
1
1
1
1
0
2
1
1
1
2
0
2
1
1
1
0
1
1
1
1
1
2
1
1
2
0
1
1
2
2
1
1
1
1
2
2
2
1
1
1
1
1
1
0
0
2
0
0
0
1
0
1
1
1
1
0
0
1
2
2
1
1
0
2
2
1
2
1
2
1
1
2
1
1
1
1
2
0
1
1
1
1
1
1
1
0
1
0
1
1
1
1
2
0
0
0
2
2
2
1
1
1
1
0
3
1
0
1
1
1
0
0
1
2
2
3
1
1
0
0
0
1
1
1
0
2
1
2
1
1
1
2
1
1
1
1
0
1
2
2
0
1
1
1
1
0
2
2
0
0
0
2
1
0
0
1
1
1
1
1
1
2
0
1
1
2
1
2
1
0
0
1
2
0
0
0
1
1
1
2
1
1
0
1
2
1
0
1
1
1
1
1
0
1
0
0
1
1
1
0
0
2
1
0
1
1
1
1
0
0
0
1
2
1
2
1
1
2
1
1
1
1
1
1
1
0
0
1
0
1
0
1
1
2
0
1
1
0
1
1
2
1
1
1
0
0
1
2
2
1
3
1
0
2
1
0
2
2
1
1
1
1
1
0
1
1
1
0
0
1
1
2
1
1
1
1
0
1
2
1
0
0
2
0
0
1
0
1
2
1
1
0
2
1
1
0
1
2
0
1
1
0
2
1
1
2
0
0
1
1
0
1
0
0
1
1
0
0
0
0
1
0
1
1
0
1
0
0
1
0
1
0
0
1
2
1
1
1
1
2
0
1
1
1
0
0
1
2
1
0
0
1
0
0
0
0
1
1
0
0
0
1
2
1
0
2
1
1
1
2
1
1
1
1
0
2
1
1
0
1
1
1
1
2
2
0
1
2
1
1
1
0
1
1
1
1
1
2
1
2
0
0
0
1
0
0
0
1
0
0
1
1
2
2
1
1
2
1
2
1
1
2
1
1
1
1
2
1
2
2
1
2
0
1
2
2
1
1
0
0
0
1
1
1
2
1
2
2
0
2
1
1
1
1
2
1
0
1
1
1
1
0
2
1
2
1
1
1
1
1
0
2
1
1
2
0
2
2
2
2
0
1
0
1
1
1
0
1
1
0
1
2
2
1
0
1
1
1
0
1
1
1
0
1
1
1
1
2
1
2
2
2
2
0
0
0
1
1
1
1
1
0
1
1
1
2
1
2
1
1
1
0
1
0
1
1
1
1
1
1
0
1
0
1
2
0
1
1
1
0
0
1
0
1
0
0
1
1
0
0
0
1
0
0
0
0
7
1
1
0
1
2
1
0
2
1
0
1
1
1
1
1
1
0
1
1
1
1
2
2
1
2
1
2
0
2
1
1
1
0
1
2
0
0
1
0
1
3
1
2
1
3
1
1
1
1
2
2
1
0
0
1
2
2
2
0
1
1
0
0
1
1
0
1
1
1
1
1
1
1
2
1
1
1
1
1
1
0
1
1
2
1
1
1
1
1
1
2
2
1
4
1
1
1
1
1
1
0
1
1
2
1
0
2
0
0
2
1
1
1
1
1
1
2
2
0
1
1
1
0
1
1
1
2
0
1
0
1
3
1
1
0
2
1
1
2
1
1
0
1
2
0
1
2
1
2
1
1
1
1
2
2
1
2
1
0
1
1
1
0
0
0
0
1
2
0
0
1
1
0
1
2
1
1
1
1
1
0
1
2
1
2
3
0
0
1
1
1
2
1
0
0
1
2
1
0
1
0
1
1
2
0
1
1
1
2
0
3
2
1
0
0
1
0
0
0
1
1
1
0
0
1
1
0
1
1
0
1
1
0
0
2
2
1
1
0
1
1
1
2
2
1
0
0
1
1
1
2
2
0
1
0
0
1
1
0
2
1
2
0
1
1
0
1
0
2
3
0
1
1
2
2
2
0
0
0
0
1
0
0
0
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
0
1
0
1
0
0
1
0
1
0
1
0
1
1
1
2
1
1
0
1
2
1
1
1
1
1
0
1
0
0
1
1
0
1
1
1
2
2
2
1
1
3
1
0
0
1
2
0
0
7
1
1
2
0
2
0
1
0
1
1
0
1
0
1
1
1
1
0
1
2
1
2
1
1
1
2
0
2
2
1
0
0
0
2
1
1
2
1
1
2
1
0
0
1
2
1
1
1
0
1
1
0
2
0
1
1
0
2
1
0
2
1
2
1
1
1
1
1
0
1
1
1
2
7
1
0
2
1
2
0
3
0
2
2
2
1
0
1
0
1
1
1
2
1
2
1
2
1
0
1
1
2
1
1
1
0
1
1
0
1
2
1
1
2
1
1
0
2
1
2
1
2
2
0
1
1
1
2
1
2
1
1
1
0
2
0
1
0
0
2
0
0
1
2
1
2
0
1
1
1
1
2
2
1
1
0
0
0
0
2
1
2
2
0
2
1
2
1
1
1
1
1
0
1
1
1
1
1
0
1
2
1
1
1
2
0
0
2
2
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
0
2
0
1
1
1
0
0
1
1
1
2
1
0
0
0
1
1
0
2
1
2
0
2
1
0
1
1
1
1
0
1
1
0
1
1
1
2
1
1
1
1
2
1
2
1
2
2
2
2
0
1
1
0
1
0
0
1
1
1
0
1
1
0
2
1
1
1
0
1
1
0
1
1
0
0
0
0
0
0
1
2
1
1
1
1
2
1
2
0
1
1
1
1
1
0
1
1
0
0
1
2
0
1
1
2
2
1
1
1
0
1
1
1
1
2
2
0
2
0
2
1
2
1
1
1
1
1
1
1
1
0
1
2
1
0
1
0
0
1
0
2
1
1
2
1
1
12
1
1
1
2
1
1
1
1
1
1
1
2
0
1
1
0
1
0
1
1
1
2
2
1
2
2
1
2
2
1
1
0
2
1
1
1
1
2
1
0
1
2
1
1
1
1
1
2
2
1
1
1
2
2
1
0
0
1
1
2
1
2
1
1
0
1
1
1
2
0
1
2
1
2
0
2
2
1
2
0
1
0
0
1
1
1
1
1
1
1
2
1
2
1
1
2
1
0
1
0
2
0
2
1
2
1
1
0
2
1
2
1
1
2
0
1
1
2
1
1
1
1
2
0
0
1
1
0
1
1
0
0
1
1
1
1
0
1
2
1
2
0
1
1
1
1
2
1
1
1
1
2
2
1
0
2
1
1
0
1
1
1
1
1
1
2
0
1
1
1
1
2
1
0
2
1
1
1
2
1
0
0
0
0
0
1
1
1
0
1
1
0
0
0
1
2
1
2
2
1
0
1
2
0
1
1
1
1
2
1
2
1
1
1
1
2
0
1
1
3
1
1
1
1
1
1
1
0
2
1
2
0
1
1
1
1
2
1
0
0
0
2
1
1
0
0
1
1
0
0
0
1
1
1
0
0
2
1
1
0
0
2
1
0
1
2
2
1
0
1
0
1
2
1
2
0
0
2
1
0
2
1
1
0
1
1
0
2
1
1
1
1
2
2
1
1
2
3
0
0
1
0
1
1
2
2
2
0
0
1
0
1
2
2
1
1
1
2
0
1
0
1
1
1
1
2
1
2
1
1
0
0
1
1
1
1
1
1
1
0
1
2
1
0
2
1
2
1
1
2
0
0
1
1
1
1
1
0
2
1
2
0
1
0
0
1
1
1
0
1
0
0
1
2
1
2
0
3
2
2
1
0
0
1
0
2
1
0
1
2
1
0
1
1
1
2
0
0
1
1
1
1
1
1
2
0
2
1
2
2
1
0
1
1
1
0
1
2
1
2
2
1
1
0
1
2
1
2
1
0
1
0
1
2
1
1
0
1
1
2
0
1
0
2
0
1
2
0
0
1
0
1
2
1
0
0
1
1
1
2
1
0
0
0
1
2
1
1
1
1
1
1
1
1
2
1
2
1
1
2
0
1
1
1
0
0
1
1
1
0
1
2
1
1
1
1
1
2
1
1
2
1
1
1
1
0
0
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
0
1
0
2
1
1
1
0
1
1
1
1
1
1
1
2
1
1
1
0
1
0
0
0
1
2
0
2
1
0
1
1
2
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
2
0
1
2
0
1
1
1
1
1
2
1
0
1
1
1
2
0
1
1
2
1
0
1
1
1
2
2
1
2
1
1
0
0
2
1
1
0
0
2
1
0
1
0
1
2
0
1
1
0
1
0
1
0
2
1
0
1
1
1
0
1
1
0
1
0
1
1
0
2
0
2
0
2
0
1
1
0
0
0
0
2
0
2
0
2
0
2
1
1
1
1
1
0
2
1
1
2
0
1
0
1
2
1
1
0
0
6
1
0
1
1
2
0
0
1
1
0
1
1
1
0
1
1
1
2
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
2
1
2
2
0
2
2
0
1
0
2
1
0
2
2
1
0
1
1
2
1
0
1
1
1
1
0
1
1
1
1
1
1
2
1
1
1
0
2
1
2
2
2
0
1
1
1
1
0
1
1
1
1
1
0
0
2
1
1
1
1
1
2
1
0
1
2
1
0
1
1
1
0
1
2
1
1
1
1
0
1
2
2
1
0
1
0
0
0
1
0
2
1
1
1
0
1
1
1
1
3
1
0
2
1
2
1
2
1
0
2
1
0
0
1
0
0
1
1
1
1
0
1
0
0
0
1
2
2
1
0
1
1
1
1
0
0
2
1
1
0
1
1
1
1
0
1
0
2
0
0
2
1
2
0
0
0
2
2
2
1
0
1
1
0
0
1
1
1
1
0
1
1
1
0
1
0
1
1
0
1
1
0
0
0
0
1
1
1
2
1
1
1
2
1
2
1
1
2
1
1
1
3
2
2
0
0
1
1
1
1
1
2
0
1
1
1
0
1
1
1
1
0
1
0
1
2
1
1
1
0
2
2
2
0
1
1
1
1
0
4
1
1
0
2
1
1
1
1
0
0
1
0
1
1
1
0
0
1
1
1
0
2
0
1
1
1
1
1
1
1
2
2
0
0
0
1
2
2
1
1
1
1
1
0
2
0
0
1
1
1
0
2
1
0
2
1
1
1
0
1
1
1
0
0
1
1
1
1
2
0
1
1
4
1
2
0
2
1
0
2
1
1
1
2
2
1
1
0
1
0
2
0
2
1
0
0
1
1
1
1
0
1
1
1
1
0
1
1
1
1
0
2
1
1
1
2
0
1
1
2
2
0
1
0
1
0
2
1
1
1
1
1
0
2
1
1
2
1
3
0
1
0
1
1
2
1
1
1
2
0
0
1
2
1
0
0
0
1
2
0
1
1
2
0
1
1
1
1
0
2
1
1
0
2
1
2
1
1
0
1
2
1
1
1
1
0
1
0
1
1
1
2
0
1
0
1
0
1
1
2
1
1
1
2
1
0
1
1
1
1
2
1
0
0
0
1
1
1
1
0
2
1
2
1
1
2
2
2
1
1
2
1
2
1
0
3
2
0
1
2
0
2
1
0
2
1
1
2
1
3
0
1
0
1
0
1
0
1
1
0
2
2
0
1
1
2
1
1
1
2
1
1
1
0
1
1
2
1
1
2
0
2
1
1
2
0
1
1
0
1
2
0
1
1
4
1
2
1
1
0
2
2
1
2
2
4
0
1
1
2
1
1
0
1
0
1
0
1
1
1
1
1
1
0
1
0
2
2
1
0
1
2
2
1
1
0
1
0
2
0
2
1
2
0
2
0
3
1
1
1
1
1
1
2
0
0
0
1
2
1
1
0
0
1
1
0
0
2
1
0
0
1
2
1
0
1
1
1
0
1
2
2
0
1
1
1
2
2
1
2
1
2
1
1
0
0
0
1
1
1
1
1
2
0
1
1
0
0
0
2
1
2
1
2
1
1
1
0
1
0
2
1
1
2
1
1
0
2
0
1
0
1
0
1
0
1
1
2
1
2
0
1
1
3
0
2
0
0
1
0
2
2
1
0
1
1
2
2
2
0
2
2
1
0
1
1
1
2
2
2
2
1
1
0
1
1
1
1
0
1
1
1
1
0
0
1
2
1
1
0
2
1
0
1
0
0
1
0
0
2
1
1
2
0
1
0
1
1
1
1
0
0
2
1
2
0
1
0
0
1
1
0
1
1
2
1
1
1
1
0
1
2
1
2
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
0
0
2
1
1
2
1
1
2
0
0
1
0
1
2
1
0
1
2
2
0
1
0
0
1
1
1
1
1
1
2
1
2
1
1
2
1
2
1
1
2
0
2
1
0
1
2
2
0
1
0
1
2
1
2
0
2
0
0
0
2
1
1
2
1
0
0
1
0
2
0
1
1
0
1
2
1
1
0
0
1
1
1
2
0
0
1
1
1
1
0
1
1
2
1
1
1
1
0
2
1
1
1
0
1
2
2
2
2
2
2
0
1
1
2
1
1
2
1
2
1
1
2
1
2
1
1
0
2
1
2
1
1
0
2
1
1
1
2
1
0
1
1
1
0
2
1
0
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
0
0
1
1
1
1
1
0
0
0
0
0
1
1
1
0
0
1
1
1
0
1
1
1
2
2
1
1
0
1
0
2
1
2
2
1
2
1
1
2
1
1
2
1
1
1
2
1
1
1
0
1
1
1
0
2
1
1
4
1
1
0
1
1
2
1
1
0
3
4
2
1
0
0
1
0
1
0
1
1
2
0
1
1
1
1
1
0
1
2
1
1
1
2
2
2
1
1
2
1
0
1
2
2
1
1
1
1
1
1
0
1
1
2
2
1
1
1
1
1
2
0
1
1
1
1
2
1
2
0
1
2
0
1
2
0
2
2
1
0
1
0
1
1
2
2
1
0
2
0
0
0
0
0
2
0
1
1
2
2
1
0
1
0
1
1
1
2
2
1
2
0
1
1
0
0
2
0
1
0
1
1
2
2
2
3
2
1
1
0
0
1
1
1
0
1
1
0
1
0
1
2
1
1
2
1
1
2
0
2
0
1
1
0
2
1
1
1
1
1
1
1
0
0
1
0
0
1
5
0
2
1
0
0
1
1
2
2
1
1
1
1
1
1
1
1
1
2
0
1
1
1
1
2
0
2
1
0
1
1
1
1
2
2
0
1
2
0
1
0
1
2
0
0
1
2
0
1
1
1
2
2
2
1
1
0
1
0
2
1
0
1
2
2
1
1
1
2
1
1
1
2
1
1
0
0
0
2
1
1
1
0
1
1
1
1
1
0
0
0
1
0
0
1
0
0
1
1
2
1
0
1
1
0
0
2
0
2
1
1
1
2
2
1
2
0
1
1
2
1
2
1
2
2
1
0
2
0
1
1
1
0
3
1
2
1
1
0
0
1
0
1
1
1
1
2
0
1
1
1
2
1
1
1
2
1
1
2
1
0
2
1
1
1
1
0
2
0
1
1
1
2
1
0
1
1
0
1
1
2
0
1
2
0
2
0
1
0
2
1
0
2
2
1
1
1
2
1
0
0
0
1
1
1
2
0
2
1
1
1
2
0
1
1
0
1
0
1
1
1
1
1
1
0
1
1
2
0
1
0
1
2
0
1
1
1
0
1
1
2
0
2
2
1
1
1
1
0
1
1
1
1
0
1
0
0
0
1
2
2
0
1
1
2
1
1
1
0
1
1
1
1
0
1
0
0
1
0
0
0
0
0
1
1
1
0
0
2
1
1
0
0
1
0
2
1
1
2
1
1
0
2
0
1
0
2
0
2
1
1
0
1
0
0
0
0
0
1
1
1
1
1
1
1
0
0
1
1
1
1
2
1
2
2
0
2
1
2
2
0
2
1
1
2
0
1
1
1
0
1
0
1
1
1
2
2
2
0
0
1
1
0
2
1
1
0
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
1
2
1
0
2
1
1
1
1
0
2
0
1
2
1
1
1
1
2
2
1
1
2
2
1
1
2
1
1
1
0
2
0
1
1
1
1
1
1
0
2
1
0
2
1
1
0
1
1
1
0
0
1
1
1
1
1
1
0
2
1
2
1
1
1
1
1
2
1
1
1
1
1
0
1
2
0
1
2
1
1
1
1
0
1
1
2
1
1
1
2
0
1
1
2
1
1
0
0
0
2
2
0
0
1
1
3
0
2
1
1
0
1
2
2
1
1
1
1
0
0
1
1
3
1
1
2
1
0
2
0
1
1
1
1
2
2
1
1
0
1
0
1
1
0
1
1
1
1
0
1
0
1
1
1
1
0
0
1
1
2
1
0
0
1
0
2
2
2
0
1
1
1
1
1
2
1
0
1
1
0
1
0
1
0
0
1
0
2
1
0
0
2
2
0
0
1
1
0
2
1
1
1
1
2
2
0
1
1
1
1
1
2
1
2
1
1
1
2
2
1
1
2
2
2
1
2
1
1
1
1
1
0
1
2
1
2
1
2
1
2
1
1
1
1
1
1
1
1
0
2
1
1
3
1
1
0
0
0
2
1
1
0
1
0
1
2
1
0
1
1
1
2
2
1
0
2
2
1
0
2
1
0
2
0
1
0
2
1
0
2
0
1
1
0
1
1
1
1
0
0
1
1
2
1
0
2
1
1
1
1
0
1
2
1
1
1
0
1
1
2
2
2
1
1
0
1
1
1
2
0
0
1
0
1
0
1
0
0
0
1
2
1
1
2
1
0
2
1
1
0
0
1
2
0
0
2
0
0
2
2
0
1
1
1
1
2
0
1
1
1
1
1
0
2
1
2
1
0
0
2
1
0
1
2
0
1
1
0
1
2
2
2
0
1
1
2
1
2
1
0
2
0
1
1
0
0
1
2
0
2
1
1
0
2
1
0
1
0
0
1
1
0
1
1
1
1
1
1
1
1
1
2
1
2
1
0
2
1
1
2
1
1
0
1
1
1
1
1
1
1
1
0
1
1
1
2
1
2
0
1
0
2
1
2
1
0
2
2
1
1
1
1
2
2
1
1
0
1
1
1
0
0
2
0
1
1
1
2
1
1
2
1
0
1
2
1
0
1
1
1
1
2
2
1
1
1
0
1
1
1
0
0
0
1
1
1
1
2
1
0
0
2
1
2
1
1
2
0
0
1
1
0
0
1
0
1
2
1
2
1
0
0
1
1
1
1
0
1
0
0
1
2
1
2
1
1
1
0
3
0
0
2
0
2
4
1
2
2
1
0
2
0
2
2
1
1
2
1
1
1
0
0
1
1
0
1
2
1
1
1
1
0
1
0
0
1
1
2
1
0
0
2
1
1
2
0
1
1
1
2
1
2
1
1
0
1
0
0
1
2
2
2
1
0
3
1
1
2
1
2
2
1
1
2
1
0
2
2
0
1
2
4
1
1
1
1
1
2
1
1
0
2
1
1
2
0
1
1
1
0
1
1
2
2
1
3
1
2
1
1
1
0
1
1
2
2
0
1
1
2
2
0
1
2
1
1
1
0
2
2
1
0
0
1
1
0
0
1
2
0
0
2
2
1
2
2
0
2
0
1
2
1
0
1
1
0
2
1
1
2
0
0
0
1
1
2
2
1
1
1
2
0
0
0
2
1
0
1
2
2
0
1
2
2
1
1
2
3
1
1
1
1
0
2
1
1
2
2
2
1
1
0
2
0
0
2
1
1
1
1
0
1
1
2
1
1
0
2
0
0
1
0
1
1
0
1
1
2
1
2
0
0
0
1
1
2
1
1
1
2
2
1
1
0
1
1
1
1
1
1
2
1
0
0
1
2
1
1
1
0
1
1
1
2
1
2
1
1
0
1
1
1
0
1
2
1
0
1
1
1
0
2
0
2
1
0
0
1
2
0
1
2
0
1
1
1
2
1
2
2
1
2
0
1
0
1
1
1
1
0
1
2
0
0
2
0
3
2
2
0
1
2
2
2
1
0
2
0
0
0
1
1
1
2
1
1
2
1
2
1
0
1
2
1
0
0
2
2
1
0
0
1
1
1
0
1
0
1
2
0
1
2
1
0
1
0
1
1
1
0
0
2
1
1
1
1
2
1
1
0
1
1
2
0
2
1
2
1
2
1
1
2
1
0
0
1
1
1
0
1
1
2
1
1
1
2
1
0
2
1
1
0
1
1
2
0
2
0
1
2
1
0
1
1
1
2
0
1
0
1
0
0
1
1
1
1
1
1
3
1
1
1
0
0
1
0
0
2
0
2
1
1
1
3
0
1
0
2
1
2
0
2
2
1
2
0
1
2
0
0
2
0
2
0
2
1
1
2
1
1
1
0
1
2
1
1
1
2
2
1
2
2
2
1
0
1
0
1
2
2
1
3
1
2
1
1
1
2
1
1
1
2
1
1
1
2
1
1
2
1
2
2
1
1
1
1
1
1
2
0
2
0
2
0
0
0
2
1
1
2
0
1
2
1
1
1
2
2
0
1
1
1
2
1
2
1
1
3
1
0
2
2
2
0
0
2
1
1
1
0
1
1
1
0
2
1
1
2
0
2
1
1
2
0
0
0
1
1
2
1
1
1
2
1
0
2
2
2
1
1
2
1
1
1
0
1
0
1
0
1
0
0
2
2
2
2
1
1
1
1
2
0
1
0
0
1
1
2
1
0
1
1
0
1
3
1
1
1
1
2
1
2
0
0
2
2
0
2
1
0
1
1
3
0
2
1
1
0
1
2
0
1
1
1
1
2
1
0
0
1
1
0
1
2
0
1
1
1
2
1
1
1
2
1
1
0
1
1
2
0
0
1
2
1
1
0
2
2
1
1
1
0
0
1
2
1
1
0
1
0
1
2
1
2
2
0
2
0
2
0
2
1
1
1
1
1
0
1
2
1
0
1
1
1
1
0
0
0
1
2
1
1
2
1
1
3
2
2
1
1
1
1
1
1
2
1
0
1
0
1
1
2
1
1
1
2
1
1
2
1
1
2
1
2
2
2
2
2
1
1
2
1
2
1
1
1
2
0
2
2
1
0
1
0
0
2
1
1
0
2
2
1
1
2
1
1
1
2
1
2
2
1
2
0
1
0
1
2
4
0
2
0
2
1
1
1
0
1
2
2
1
1
1
1
2
1
1
2
1
0
1
1
0
1
3
1
1
1
0
2
0
1
0
1
1
1
1
1
0
2
1
0
1
1
1
2
0
1
1
1
0
0
1
2
0
3
2
1
1
1
1
1
0
1
0
0
0
1
1
1
1
1
2
2
2
1
1
0
1
1
1
1
0
0
1
1
0
0
1
2
2
0
1
0
1
1
1
2
0
1
0
0
1
1
1
1
2
0
0
2
1
1
0
2
1
1
0
1
2
1
2
1
1
0
2
1
1
1
1
1
1
1
1
1
0
9
0
1
1
0
1
0
2
2
1
0
1
0
1
1
2
2
1
1
0
1
1
0
2
2
1
1
1
2
0
1
1
2
1
2
1
0
1
1
1
0
1
0
2
1
1
0
1
0
1
1
0
1
2
1
0
2
0
2
1
1
0
2
1
2
1
1
1
1
2
1
0
1
2
1
2
0
2
1
1
1
0
1
1
0
2
1
1
1
0
1
0
1
1
1
0
1
1
0
1
0
0
0
2
2
1
1
1
0
0
1
1
1
1
2
0
1
1
1
1
1
1
1
1
1
2
0
2
1
0
1
1
1
1
1
1
1
0
1
1
0
1
1
0
0
1
1
1
2
0
1
2
0
1
1
1
1
2
0
2
0
1
8
2
1
2
2
2
2
0
1
2
1
0
2
1
1
0
1
1
0
1
2
1
1
0
2
2
0
1
1
1
1
1
2
1
1
0
2
1
0
0
2
1
1
1
0
1
2
1
0
1
0
1
1
2
0
1
1
0
0
1
2
1
0
1
1
1
0
1
0
2
1
1
1
2
0
1
0
2
0
1
0
1
0
1
2
0
1
1
2
1
2
0
2
1
1
1
0
1
0
1
0
1
2
1
0
1
1
1
2
1
1
1
1
1
1
0
1
1
1
0
2
0
1
1
1
0
1
1
0
1
0
1
0
1
1
2
2
0
0
1
1
0
1
1
0
1
0
0
1
1
1
0
2
1
1
1
0
0
1
2
3
1
0
1
2
1
0
0
0
1
1
1
1
1
1
0
0
1
2
2
1
1
2
1
0
0
2
1
1
0
2
1
2
1
1
1
2
0
2
2
1
2
2
0
0
1
2
1
0
0
1
1
0
2
2
1
1
1
0
1
2
1
2
1
1
1
1
1
1
1
1
1
1
0
0
0
0
1
0
1
0
2
0
0
2
0
1
2
1
1
1
2
0
1
1
2
1
2
0
2
1
1
0
2
1
4
2
1
0
1
0
2
1
2
1
2
1
1
2
2
1
0
1
1
0
2
1
0
1
1
0
0
0
1
0
1
1
1
1
2
0
0
3
1
1
1
2
2
3
1
1
2
1
3
1
1
0
2
0
1
1
2
1
0
1
1
0
1
2
1
1
0
1
0
1
2
1
1
0
1
1
1
0
1
1
1
2
2
0
1
2
1
1
2
2
1
0
2
0
0
1
1
0
1
2
2
1
3
0
0
0
2
1
1
1
1
2
2
0
1
0
0
0
2
2
2
1
1
1
1
0
2
2
1
2
2
0
1
1
1
1
2
2
1
0
1
2
2
0
0
0
1
1
1
0
1
0
1
1
1
0
2
2
1
0
2
1
0
1
2
2
2
0
0
0
1
0
2
1
1
1
2
1
1
0
2
2
1
1
1
1
1
1
1
2
1
1
0
2
0
0
1
2
1
1
1
2
1
1
1
2
1
1
0
1
1
1
1
2
1
1
1
1
1
1
1
1
3
0
1
1
0
1
1
1
0
1
1
0
0
1
0
0
2
0
0
1
1
1
1
1
2
1
1
1
2
2
1
1
0
1
2
1
0
1
0
1
1
2
0
1
1
1
1
1
1
1
1
0
1
1
0
1
1
1
1
1
1
1
1
0
0
1
1
1
0
1
2
2
2
1
1
0
1
1
0
0
2
2
1
1
1
0
0
1
1
1
1
1
1
0
1
1
1
2
1
2
1
1
3
1
2
1
1
0
2
1
0
1
1
1
2
2
0
0
0
2
1
0
1
2
2
1
3
1
0
1
1
1
1
1
0
6
0
1
1
0
1
0
1
0
0
2
2
0
1
0
2
1
0
3
0
1
1
0
1
0
1
0
2
1
0
0
1
1
2
1
1
0
2
0
0
0
1
2
1
1
1
2
1
1
1
4
1
1
1
1
1
1
2
4
1
1
1
1
1
0
0
1
1
2
1
1
1
2
2
0
1
0
0
0
0
0
0
0
0
0
1
2
1
1
1
1
1
1
1
1
1
1
0
0
1
2
1
0
2
0
2
2
1
2
0
0
1
1
2
2
2
1
0
0
1
0
1
0
1
1
2
2
1
3
1
1
1
1
2
2
0
0
1
0
1
1
2
1
1
1
1
0
2
1
0
0
1
1
1
0
2
0
2
1
1
0
1
1
1
0
1
2
2
2
1
1
1
1
1
1
0
1
2
0
1
1
1
1
0
1
1
1
1
2
0
1
0
1
1
0
1
1
2
1
1
1
1
2
2
1
0
0
0
1
1
1
1
2
0
1
2
1
2
2
1
1
1
1
2
1
1
1
2
2
1
1
1
1
2
0
1
3
2
1
1
1
1
1
0
1
1
1
2
0
2
2
0
2
2
1
0
0
0
0
1
1
0
1
0
0
1
2
2
0
2
1
1
1
0
1
1
0
1
0
1
0
1
2
1
0
1
1
2
1
1
0
1
1
2
1
1
2
1
0
1
1
1
2
0
1
1
0
0
2
0
2
0
1
2
1
1
2
1
2
1
0
2
1
1
1
1
1
1
1
0
0
1
2
1
2
1
1
0
1
1
1
0
1
2
1
0
2
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
0
1
1
1
1
1
2
0
2
1
0
1
1
1
0
2
1
0
0
1
2
1
1
1
1
1
1
2
2
1
1
0
2
0
2
0
1
0
1
0
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
0
2
1
1
2
1
0
2
1
1
1
2
1
0
2
1
0
1
1
2
3
0
0
1
0
1
0
2
1
1
1
1
2
0
1
0
1
2
2
0
1
2
1
0
0
0
2
1
1
1
1
0
2
0
2
1
1
0
1
1
1
0
1
0
1
2
0
1
1
1
1
1
2
1
1
1
0
1
1
1
1
0
0
1
1
2
1
0
1
1
2
1
0
1
1
1
1
0
2
2
0
0
0
1
1
2
1
1
2
2
2
2
1
0
2
1
0
1
0
1
2
2
2
1
2
0
1
0
0
0
1
1
0
1
5
2
0
0
1
1
2
2
1
1
1
0
1
0
1
1
1
1
2
0
0
1
2
0
0
1
0
1
2
2
2
3
1
1
2
1
1
3
1
2
1
1
1
2
1
0
1
1
1
0
8
2
1
1
0
1
1
2
2
0
0
1
2
0
1
0
0
0
1
0
0
0
1
0
1
2
0
2
0
0
1
1
1
1
2
2
0
0
1
1
0
0
2
2
1
2
0
1
0
1
1
0
1
1
1
0
1
1
0
2
0
1
1
2
1
0
1
0
0
1
2
1
1
0
1
1
1
1
1
1
1
1
0
1
0
1
2
1
2
2
1
2
0
1
1
0
0
1
1
1
1
1
1
1
1
1
1
0
2
0
0
1
1
1
0
2
1
0
2
1
0
0
0
1
0
0
1
1
0
0
0
1
1
0
2
2
1
1
0
1
2
0
1
1
1
1
0
0
0
0
1
1
1
1
1
0
2
1
0
1
0
2
0
1
1
0
1
1
1
1
2
0
1
0
2
1
1
1
1
1
1
1
0
2
1
1
0
2
1
1
1
2
1
0
2
1
0
1
1
1
2
2
1
1
1
1
1
1
0
1
2
2
0
1
0
1
1
2
0
1
1
2
2
0
2
5
1
2
2
1
2
1
2
2
1
1
1
1
1
0
1
1
0
0
2
0
2
0
1
1
2
0
0
1
2
0
1
0
1
0
2
0
1
0
2
3
1
1
0
0
1
2
2
1
1
1
1
0
0
0
1
1
1
0
0
2
1
0
1
0
1
2
1
1
1
2
2
1
0
0
1
1
3
0
2
1
0
0
1
1
1
1
2
1
0
0
2
4
0
2
1
1
0
0
1
1
1
1
1
0
1
1
2
1
0
1
0
3
0
1
0
1
1
1
1
1
0
0
1
2
1
1
1
1
2
1
2
1
1
1
1
3
1
1
2
2
1
0
2
1
0
0
1
1
2
1
0
0
1
1
2
0
0
1
1
1
1
1
0
1
1
1
0
2
1
1
1
0
0
1
1
1
1
2
1
0
1
2
0
2
2
2
0
1
1
2
1
0
0
2
1
0
1
1
1
1
2
0
0
0
0
2
1
1
0
2
1
1
1
0
1
0
1
2
2
0
1
0
2
1
1
1
1
0
1
1
1
1
0
2
1
1
2
0
0
1
1
1
1
0
2
1
1
2
1
1
0
0
1
0
1
1
1
2
1
1
0
1
0
4
1
0
1
0
1
0
1
0
1
1
2
1
0
1
0
2
1
1
1
1
0
0
1
1
2
1
1
2
0
2
2
0
2
1
2
1
0
1
0
1
1
2
1
1
0
0
1
2
1
1
1
0
0
1
0
0
2
1
2
1
0
1
1
1
0
1
1
0
1
2
0
2
1
0
1
1
1
1
1
2
1
1
1
0
0
1
1
1
1
0
0
1
2
0
0
0
1
2
1
1
3
1
2
0
0
1
1
0
1
0
1
1
2
0
2
2
1
1
0
2
1
1
1
1
1
2
2
0
1
1
2
1
0
1
1
1
3
1
1
1
1
1
0
0
1
3
0
1
0
0
0
2
0
0
0
1
2
2
1
0
1
1
1
1
0
1
1
2
2
3
1
1
1
2
2
0
0
0
0
0
1
1
2
1
1
2
1
1
0
0
0
1
0
2
1
0
1
0
2
5
2
2
2
1
1
2
1
1
0
1
2
0
2
2
1
1
1
1
2
1
1
0
2
2
1
1
1
1
1
0
1
1
1
1
1
1
1
0
2
1
1
0
0
1
2
1
1
1
0
2
1
1
2
3
2
0
1
1
1
0
1
2
1
0
1
0
1
2
1
1
0
2
2
1
1
1
2
0
1
1
2
0
1
1
1
1
5
1
0
1
1
2
1
2
0
1
1
1
0
1
0
1
2
1
1
1
1
0
1
1
1
1
0
1
2
2
0
1
0
0
2
1
1
2
1
1
0
2
0
1
1
1
0
2
1
0
1
0
2
1
1
0
1
2
0
2
2
1
2
3
0
1
0
1
0
1
1
1
0
1
0
0
1
1
1
0
1
1
1
1
0
1
1
0
0
1
2
2
1
0
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
1
0
1
0
1
0
1
0
1
1
1
1
1
1
1
1
1
2
0
1
0
0
1
1
1
1
2
2
2
0
1
1
1
1
1
1
2
0
1
0
3
1
0
2
1
0
1
2
2
2
1
0
1
2
1
1
2
1
1
0
1
2
1
1
1
2
1
1
0
1
1
1
1
1
1
1
0
2
0
0
0
1
1
1
1
1
1
2
2
1
2
1
1
0
1
0
1
2
2
2
1
1
1
1
1
1
2
1
1
1
1
1
0
2
1
1
0
1
1
0
1
1
0
1
1
1
1
0
1
0
2
0
1
1
2
0
1
1
2
1
1
2
0
2
0
1
3
2
2
1
1
1
1
1
1
1
2
1
1
2
1
0
0
1
1
2
1
0
1
2
1
1
1
0
2
2
0
2
2
1
1
3
1
1
0
1
1
2
2
1
1
1
2
1
1
1
0
2
1
1
1
1
1
0
1
1
2
2
2
1
1
1
1
0
1
0
0
1
1
1
2
1
1
1
1
1
1
0
0
1
1
1
0
1
2
2
0
1
1
1
1
1
1
1
1
0
1
0
1
0
2
1
2
2
1
1
1
0
1
0
2
0
1
1
2
2
1
1
1
2
1
1
2
0
1
1
1
1
0
1
0
1
1
1
0
2
1
0
0
1
0
0
3
1
0
1
0
2
1
1
1
2
1
1
2
1
1
1
1
2
0
1
2
1
1
1
1
1
1
1
0
0
1
0
0
1
1
0
1
2
0
0
1
0
1
1
1
1
0
1
1
0
2
1
2
1
2
1
1
0
0
2
1
2
2
0
2
2
1
1
1
1
1
0
1
0
2
0
1
1
1
1
1
1
0
1
1
1
0
1
1
0
0
1
1
0
1
2
0
0
1
2
1
0
1
1
0
0
1
2
1
1
1
1
1
1
1
2
2
0
0
0
1
2
0
1
1
2
0
0
1
0
0
0
1
0
1
1
1
0
0
2
0
1
0
0
1
0
0
1
2
2
1
0
1
1
2
0
0
2
1
2
0
1
1
0
1
2
1
1
2
0
1
0
1
1
1
1
0
1
2
1
0
3
1
0
0
1
1
1
2
2
0
1
2
1
1
1
1
0
2
1
0
1
0
1
2
3
0
1
1
1
1
2
1
1
2
3
1
0
0
2
0
2
1
2
0
1
0
1
1
0
1
2
0
2
1
1
1
1
0
1
1
1
1
1
0
1
1
3
1
1
1
1
2
1
1
0
2
1
1
1
2
2
1
1
0
3
1
2
1
0
2
1
1
1
2
0
1
1
1
1
2
2
1
1
1
2
1
0
1
0
2
1
0
1
2
0
1
1
1
1
1
1
1
0
0
0
1
2
1
0
2
0
1
0
0
1
1
2
1
2
2
0
1
1
2
1
0
1
1
1
0
0
2
1
0
1
2
1
2
0
1
1
2
1
1
0
0
0
1
1
1
2
1
2
2
1
1
1
0
1
0
1
0
1
0
0
0
2
0
0
1
2
2
0
1
1
0
1
1
1
2
0
1
1
1
0
0
1
1
1
0
1
0
0
1
0
0
4
2
0
1
1
1
1
1
1
1
2
1
1
0
1
1
2
2
1
1
1
1
0
1
1
1
3
2
1
1
1
1
2
1
2
1
1
1
0
1
2
0
1
0
0
1
2
1
1
2
0
1
0
1
2
1
0
1
2
1
1
2
3
1
2
2
0
1
0
1
1
1
1
1
2
1
1
1
2
2
0
2
2
1
1
1
1
1
1
1
0
0
1
0
0
1
2
2
1
1
1
1
1
0
1
1
0
1
1
0
0
1
1
1
1
0
2
0
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
1
1
2
1
0
0
0
1
0
1
1
1
1
1
0
1
1
0
0
2
0
1
1
2
2
1
1
1
1
0
1
2
1
2
1
1
1
1
1
1
1
2
1
2
1
0
1
1
2
2
0
1
0
1
2
1
1
1
0
0
0
2
0
1
1
0
3
2
1
1
1
1
5
2
2
1
2
2
1
2
1
2
2
1
1
0
1
1
1
2
2
1
1
1
1
1
2
0
1
2
1
1
1
0
1
2
1
2
0
0
0
2
1
1
2
0
2
1
1
1
1
1
2
2
1
1
1
0
0
0
1
1
1
2
1
0
1
0
2
1
2
2
2
1
0
1
1
0
2
1
0
1
0
2
0
0
2
4
1
2
1
1
1
1
1
0
1
0
1
1
1
0
1
0
0
0
0
0
2
2
1
2
2
0
1
0
1
2
0
1
0
1
1
1
1
2
0
0
1
3
1
1
1
1
2
2
1
1
2
0
0
2
0
1
1
1
0
0
1
2
2
1
1
0
0
1
1
0
0
0
1
1
2
1
2
0
1
3
1
2
1
1
1
0
1
1
1
0
0
1
1
2
2
1
2
0
0
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
0
1
0
1
1
0
1
1
0
1
2
0
2
1
4
2
0
1
1
7
0
1
1
2
1
0
1
0
0
1
1
2
1
1
1
2
1
0
1
1
1
0
2
1
2
0
1
1
1
1
1
0
1
2
0
0
1
0
2
2
0
2
1
1
1
0
1
0
0
2
1
2
1
2
1
2
1
1
1
2
2
0
1
0
1
2
1
0
2
0
2
1
1
0
2
1
2
1
0
0
1
2
1
1
0
0
1
0
1
2
1
0
1
0
1
1
2
0
1
0
0
0
1
0
1
1
0
2
1
0
1
0
1
2
2
2
1
0
2
1
2
0
1
1
1
1
2
0
2
1
1
0
0
1
1
1
2
1
0
1
1
2
1
0
1
1
1
1
0
1
2
0
1
1
1
1
1
0
1
1
1
1
0
2
1
1
1
0
1
1
2
1
0
2
0
1
1
1
2
1
0
2
1
1
1
2
0
1
0
0
1
1
1
1
0
2
0
2
2
1
1
1
2
1
1
2
0
0
1
0
1
1
1
1
2
2
1
2
2
0
1
1
0
0
2
1
0
0
1
1
2
1
0
1
0
0
0
2
1
1
1
2
1
1
1
1
0
1
1
0
1
1
1
2
2
1
1
2
1
2
0
1
2
1
0
2
0
2
2
1
0
2
0
0
1
2
0
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
0
1
1
2
1
1
1
1
0
2
1
1
0
1
1
1
2
1
4
1
1
0
2
1
1
1
1
1
1
1
0
0
0
1
1
0
1
1
0
1
1
1
0
1
1
2
1
1
2
1
0
2
1
0
1
2
1
1
1
2
2
0
1
1
2
1
1
1
1
1
1
1
1
0
0
2
3
0
1
1
0
1
1
2
1
0
2
3
2
1
2
2
1
0
2
1
1
1
1
0
0
2
2
2
2
1
0
1
1
1
1
0
1
1
1
1
1
1
0
1
1
2
2
2
1
1
1
2
1
1
1
1
0
1
2
0
2
2
1
2
1
1
1
2
1
1
1
0
1
1
1
1
1
2
1
1
2
1
2
2
2
1
2
1
2
1
0
1
1
1
1
1
0
0
2
1
1
1
1
1
0
1
1
1
1
1
2
0
2
1
1
2
1
2
0
1
0
2
0
2
1
1
1
1
1
2
0
1
0
2
2
1
1
0
0
1
0
2
2
1
1
0
2
0
2
1
1
0
1
0
1
1
1
0
2
1
1
1
4
0
1
1
1
1
2
1
2
1
1
1
1
1
0
1
3
0
1
1
1
0
2
1
1
1
1
1
1
1
1
3
1
1
1
2
1
1
1
0
1
0
1
2
1
2
2
2
1
0
1
0
0
1
0
1
1
0
0
0
0
1
1
1
1
0
0
1
1
1
0
2
1
0
1
2
1
2
2
2
2
1
0
1
1
1
2
1
1
1
1
1
0
1
2
1
1
1
1
1
1
1
2
1
1
0
0
1
2
0
2
0
2
1
1
2
1
2
1
1
1
0
0
1
1
2
0
1
1
1
0
2
1
1
2
2
1
1
1
1
2
1
1
2
2
2
1
1
1
1
1
1
1
2
1
1
1
0
1
1
1
1
1
2
2
1
1
0
0
0
1
1
1
0
3
1
0
1
2
1
0
1
1
2
1
0
1
0
1
2
1
1
1
1
1
5
1
1
0
1
1
2
0
2
0
2
1
1
3
1
1
1
2
1
0
1
1
2
1
1
0
1
1
2
0
0
1
0
0
1
1
0
2
2
1
1
1
1
1
0
1
0
2
0
1
1
1
1
0
2
2
1
2
1
1
0
1
1
1
1
1
1
0
1
1
1
1
0
0
0
1
2
0
1
1
0
2
0
3
1
1
0
0
2
0
1
1
2
1
0
1
1
1
1
1
1
1
1
1
2
0
1
1
1
2
2
0
0
1
1
1
1
2
1
0
1
1
1
1
1
2
1
1
1
0
2
2
1
0
0
0
2
2
2
0
0
2
1
1
1
0
3
0
2
1
2
0
0
1
1
2
1
2
0
1
2
2
0
0
1
1
1
2
1
0
1
1
1
2
2
1
1
0
2
2
2
2
2
1
2
1
2
0
2
2
1
1
3
0
0
1
1
1
2
1
1
1
2
1
0
1
0
1
2
2
1
2
2
2
1
0
1
0
1
0
2
1
2
2
1
1
1
2
0
2
1
0
1
1
1
0
1
0
2
1
2
1
1
2
1
1
1
1
0
1
1
2
1
1
1
1
0
1
1
2
2
1
1
0
0
2
0
1
1
2
1
0
0
0
1
1
0
1
1
2
1
3
1
2
2
1
0
0
1
2
1
1
1
1
2
3
1
1
0
2
1
0
2
2
2
0
0
0
2
1
1
0
0
1
1
0
2
1
0
1
2
1
0
1
2
1
1
0
1
2
1
2
1
1
2
1
1
1
2
0
2
1
1
2
2
1
1
1
0
0
2
1
0
1
1
0
1
3
1
2
2
1
2
1
1
1
1
1
1
2
0
2
1
1
1
0
1
1
1
2
1
1
3
1
2
1
1
2
1
1
0
1
0
2
0
1
1
2
2
1
1
2
2
2
0
1
1
1
1
0
1
1
0
2
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
0
1
2
2
1
1
2
1
2
1
0
0
1
2
1
2
1
1
1
0
1
1
2
0
1
0
0
0
0
1
1
0
1
0
1
1
0
0
1
0
0
1
0
1
2
1
0
2
1
1
1
1
1
1
1
0
2
1
0
1
1
1
1
1
0
1
0
0
1
3
1
1
1
1
1
2
1
2
1
0
0
1
1
1
1
2
2
1
7
1
1
0
1
1
2
1
1
0
0
2
0
0
0
1
2
1
0
0
0
2
1
1
1
1
1
1
2
2
1
0
0
0
0
2
0
1
0
0
0
0
1
2
2
1
1
0
0
1
2
2
0
2
0
1
1
1
1
1
2
1
1
1
1
1
1
1
0
0
1
2
1
2
1
1
1
1
2
0
0
1
1
1
2
1
2
0
1
2
0
1
0
1
0
1
1
1
1
0
1
1
0
1
1
0
1
2
1
1
2
2
1
0
0
0
1
1
1
1
0
0
1
1
3
1
1
0
1
1
2
0
0
0
1
1
2
2
1
1
1
1
1
0
1
1
2
1
2
1
1
1
0
1
1
0
1
1
1
0
1
0
1
0
1
1
2
1
2
0
2
2
0
0
2
1
0
1
1
2
1
0
1
2
0
1
1
0
0
0
2
1
1
2
1
1
1
1
1
1
0
1
0
1
1
1
1
0
1
2
1
0
0
0
1
1
1
2
2
1
1
1
0
2
2
1
0
1
2
2
1
2
0
0
0
0
0
1
1
1
0
0
0
1
0
2
2
1
1
0
2
1
2
1
1
0
1
1
1
1
1
2
2
0
1
0
2
1
1
1
2
2
2
1
1
1
2
1
1
0
1
1
1
0
1
1
2
1
0
0
0
1
1
0
1
1
1
0
1
2
0
1
1
1
1
1
2
1
1
3
2
1
0
2
1
1
2
0
1
0
2
2
1
0
1
1
1
0
3
1
2
0
1
1
1
1
1
1
1
2
2
0
1
1
1
0
0
0
1
1
0
0
0
0
0
2
2
2
0
0
1
1
1
2
1
0
0
1
1
0
2
1
1
1
2
0
1
2
1
1
1
0
2
0
1
1
4
1
1
0
0
0
1
0
0
1
1
1
0
1
0
1
1
1
1
0
1
0
1
1
1
0
1
2
1
1
2
2
1
0
2
0
0
0
2
1
2
1
1
0
0
1
0
1
0
2
0
2
0
1
1
2
0
1
1
0
0
1
1
0
0
1
2
0
1
0
4
1
1
0
0
0
2
0
1
1
1
0
0
1
1
0
1
0
1
1
1
2
1
1
1
2
1
1
1
0
1
0
2
1
0
1
1
0
0
0
0
1
1
1
2
1
1
0
0
1
2
0
1
2
1
0
1
1
2
1
1
1
1
2
2
0
2
2
0
0
0
1
0
1
3
1
1
1
2
1
2
1
1
0
0
1
2
0
0
1
1
2
3
3
1
0
1
1
1
2
1
0
1
0
0
1
1
2
0
0
1
0
2
1
0
1
2
0
1
0
1
1
2
2
1
1
2
0
2
1
1
1
1
1
1
2
1
1
1
1
1
1
0
1
0
1
0
1
1
1
1
2
1
1
2
0
2
1
1
2
1
1
1
2
1
0
0
0
1
2
0
3
0
1
1
1
2
1
1
0
1
1
1
1
1
0
0
1
1
2
1
1
2
1
0
1
1
1
1
0
2
0
1
1
2
0
0
2
1
0
1
2
0
1
0
1
1
2
0
1
2
2
1
2
0
2
2
2
2
1
1
0
1
2
0
0
1
0
2
1
2
1
1
2
0
1
2
1
0
1
0
0
1
1
1
1
0
0
0
1
1
2
1
2
1
0
0
0
2
1
0
2
0
2
1
1
3
1
1
0
0
0
1
0
1
0
0
2
1
2
1
1
1
1
1
0
1
1
2
1
1
1
0
1
2
1
2
1
0
1
1
1
1
0
1
2
2
1
1
2
0
0
1
1
1
2
0
1
1
1
1
0
5
2
1
1
1
1
1
0
1
1
0
1
1
2
1
1
2
0
2
1
0
1
1
1
0
1
0
1
1
1
1
1
0
1
0
2
1
1
0
1
1
0
1
1
1
1
4
1
1
1
1
2
1
0
1
2
1
1
1
0
1
0
1
0
2
1
2
0
3
1
0
2
1
0
1
1
1
1
1
2
1
0
0
1
1
1
0
1
1
1
2
1
1
2
0
1
1
1
0
1
1
0
1
0
0
1
0
1
0
0
1
0
1
0
1
1
0
1
1
1
1
1
0
2
0
0
1
1
0
1
1
2
1
2
1
2
2
1
2
1
1
1
1
1
2
1
2
1
1
1
0
0
1
0
1
1
0
1
1
0
2
1
1
1
0
1
1
0
1
1
1
1
2
2
1
1
1
0
2
2
1
0
0
2
1
1
2
2
1
0
1
0
0
1
1
1
1
0
1
2
0
1
0
1
1
1
2
1
2
1
0
1
1
1
1
2
0
2
2
1
1
1
0
2
1
1
1
2
1
1
1
0
1
2
3
0
0
1
1
3
2
1
1
0
1
0
1
1
1
0
1
2
0
0
1
0
0
1
2
1
1
0
2
1
1
1
2
2
1
1
1
1
0
2
0
2
1
2
1
0
1
1
2
1
1
2
1
2
2
1
0
1
1
0
1
1
2
0
2
1
1
1
1
0
1
2
0
1
1
0
1
0
2
2
2
1
0
1
2
0
0
0
1
1
1
0
1
1
2
4
2
0
1
1
0
1
1
1
1
2
2
1
2
1
2
1
2
0
0
2
2
1
0
1
1
1
1
0
1
1
0
1
1
0
0
0
0
1
0
0
0
1
1
1
3
1
0
2
1
1
0
0
1
2
1
1
2
1
0
2
1
1
1
0
0
2
1
2
1
1
2
0
1
2
0
1
1
1
0
1
2
2
1
2
2
2
1
1
1
2
1
1
0
1
0
0
2
1
2
1
1
0
0
1
0
1
1
2
0
0
1
0
1
0
1
1
0
0
0
2
0
1
1
2
1
2
0
1
1
0
2
1
1
1
1
1
2
1
1
0
0
0
1
2
1
1
0
0
2
2
1
1
1
0
2
1
1
1
1
1
0
0
0
1
2
2
1
2
1
1
1
0
2
0
0
1
0
1
2
2
2
2
2
2
0
1
1
2
0
2
2
1
1
1
2
0
1
1
2
0
2
1
0
0
3
1
2
1
0
1
1
1
1
0
2
0
1
1
0
1
1
1
2
1
1
2
1
1
2
1
1
0
1
1
1
1
1
2
2
1
1
0
0
1
1
1
1
1
0
1
2
1
3
2
1
0
2
1
0
1
3
3
0
1
0
1
1
1
3
2
0
0
1
0
1
1
1
2
1
0
0
1
2
0
0
1
0
1
1
1
1
2
0
2
0
2
1
0
0
2
1
1
0
1
0
1
2
2
1
1
1
1
0
1
0
1
1
1
1
2
0
2
1
0
2
2
1
1
2
1
1
1
0
2
1
1
0
2
0
2
0
1
1
2
0
1
1
2
0
1
1
1
1
0
2
0
1
1
2
0
0
1
1
1
1
1
0
1
1
1
2
2
0
1
1
0
0
1
2
1
2
1
2
1
1
1
2
2
1
2
1
1
0
1
1
1
2
1
2
1
1
1
1
2
1
2
2
1
1
2
2
2
2
2
1
1
0
0
1
2
1
1
0
2
0
2
1
1
1
1
1
0
2
1
2
0
1
1
2
2
1
1
1
1
2
1
1
1
2
1
3
0
0
0
0
1
1
1
0
1
2
0
0
1
1
1
1
1
1
2
1
1
3
1
1
1
1
2
1
2
1
1
0
0
1
1
2
1
2
1
1
2
1
1
0
1
1
0
1
1
0
1
1
1
2
1
0
0
1
2
1
1
1
1
2
0
1
0
0
0
1
0
1
1
1
0
0
2
1
0
0
1
0
0
0
2
1
0
1
1
1
2
2
1
1
1
1
0
2
1
1
1
1
1
1
1
0
1
1
1
1
1
0
1
1
1
0
1
1
2
2
1
0
1
1
1
1
1
1
1
0
1
1
2
2
1
1
1
1
0
2
1
1
1
2
1
2
0
0
0
1
0
2
1
1
0
1
1
1
1
1
0
0
0
1
1
1
1
1
0
2
1
1
0
1
1
2
1
2
2
1
0
2
2
2
0
1
1
1
1
0
2
0
1
0
1
1
0
2
1
1
2
1
2
0
1
1
1
1
1
2
0
1
1
0
0
1
2
1
0
1
1
1
2
1
0
0
1
2
1
0
2
1
1
1
1
0
1
1
2
1
2
0
1
1
1
1
0
0
0
0
2
0
1
0
2
1
1
0
1
1
1
1
0
0
1
2
2
2
2
2
1
0
2
1
1
0
1
1
0
2
3
1
2
1
0
1
0
2
2
0
1
1
1
1
1
2
1
1
2
0
1
2
1
1
1
0
1
1
0
2
2
3
2
1
2
1
0
0
1
4
1
0
1
1
1
1
2
0
0
2
0
2
1
1
1
1
0
1
1
1
2
0
1
1
1
2
0
1
1
0
1
0
0
1
2
1
0
1
2
2
2
1
2
1
2
1
2
2
1
1
2
1
2
2
1
0
1
1
1
2
1
2
1
1
1
1
2
1
2
1
1
1
0
1
1
2
2
2
0
2
0
2
1
5
1
0
2
1
1
1
1
0
2
1
1
1
2
1
0
2
0
2
1
0
1
2
1
1
1
2
1
1
1
2
1
0
1
1
1
0
2
2
1
0
0
2
0
2
2
1
1
1
1
1
1
2
1
0
1
2
1
1
1
1
0
0
1
0
1
1
2
1
1
1
1
0
1
1
1
1
1
1
1
0
3
0
0
1
2
1
2
1
1
0
2
0
2
1
1
1
0
2
1
2
1
1
3
1
1
1
1
2
1
1
1
0
1
0
1
2
1
1
1
1
2
1
2
2
0
0
1
1
0
1
1
1
2
0
0
0
1
1
1
1
2
1
2
1
1
1
1
2
2
1
1
1
1
0
2
1
2
1
1
1
0
1
1
1
1
1
1
3
1
2
1
0
1
1
1
1
1
1
1
0
0
1
2
0
2
0
0
0
1
1
0
2
1
2
0
2
0
1
0
1
1
3
1
1
0
1
3
1
1
0
1
0
0
1
0
0
2
1
1
2
0
2
1
2
1
0
1
1
1
1
2
1
1
1
1
0
1
2
0
0
2
2
1
1
0
0
1
1
0
1
0
0
0
0
1
1
2
1
0
0
0
1
0
1
1
0
1
1
1
2
0
0
0
1
1
0
1
4
1
1
2
1
0
2
1
1
2
1
2
1
1
1
0
2
1
2
1
0
2
2
1
1
0
1
2
1
1
1
0
1
1
1
0
2
1
1
2
1
2
2
0
2
2
0
0
0
1
1
0
0
1
1
2
1
1
1
1
1
2
2
1
1
2
0
0
1
1
1
0
0
0
1
2
1
1
2
1
0
2
1
2
0
1
2
1
1
1
2
1
3
1
0
1
1
1
1
1
2
3
1
1
1
2
2
2
1
1
1
1
1
2
0
1
1
1
2
0
0
1
0
1
0
1
0
1
2
2
2
0
2
0
1
1
1
0
2
1
1
1
1
1
1
1
0
1
0
0
0
0
1
0
1
1
0
2
1
1
1
1
1
2
1
2
0
2
2
1
1
1
1
1
0
0
1
2
1
2
0
1
0
1
0
1
1
1
1
2
0
1
1
1
1
1
0
1
1
1
0
0
2
0
1
1
0
2
0
2
1
1
2
2
1
1
0
1
0
2
2
0
1
2
2
1
1
0
1
1
1
1
1
1
1
1
1
0
1
1
1
2
1
1
0
2
0
1
0
1
1
2
1
1
1
0
0
1
1
1
1
0
1
1
2
1
1
1
1
0
0
1
1
3
2
0
1
2
1
1
1
2
2
0
1
2
1
0
1
0
2
1
1
1
1
1
2
2
1
0
0
1
0
0
0
2
1
1
0
1
1
2
3
1
1
1
1
1
0
1
1
2
1
2
1
0
0
2
1
2
0
1
1
2
1
1
1
1
1
1
0
1
0
2
1
0
1
2
1
2
2
1
2
2
0
1
1
1
1
0
3
1
0
0
1
2
0
2
0
1
1
1
0
0
0
2
1
1
1
1
1
1
0
1
0
1
2
1
1
2
1
1
1
2
1
0
2
1
2
0
1
2
1
2
0
2
0
0
2
1
3
1
1
1
1
2
2
1
1
1
1
1
1
1
0
1
0
0
0
1
0
1
1
2
0
0
1
1
0
1
1
1
1
5
2
2
0
0
0
1
0
2
1
1
0
0
2
0
1
1
1
1
2
1
0
0
1
2
0
2
1
2
1
2
0
1
2
2
1
1
1
0
1
2
1
1
2
2
0
0
1
3
0
1
2
1
1
0
1
2
1
1
1
2
2
2
1
2
1
1
1
1
0
1
1
1
1
1
1
0
0
1
1
0
1
0
1
1
1
1
1
0
0
0
1
2
1
0
1
0
1
2
0
1
2
1
2
0
1
0
1
1
1
1
1
2
1
2
1
0
1
1
0
2
1
1
0
1
1
1
1
2
1
0
0
2
2
1
1
0
1
1
0
0
1
1
0
1
1
1
2
0
0
0
1
0
0
2
0
1
2
0
0
1
1
1
1
1
1
1
0
1
2
0
1
0
1
1
1
1
0
1
1
1
1
0
2
1
2
0
2
1
0
2
1
1
1
1
2
2
1
1
0
0
2
1
0
0
0
1
2
2
0
2
1
1
0
3
1
2
1
0
1
0
2
1
0
0
1
2
1
0
1
1
0
1
1
0
1
0
1
1
1
0
1
1
1
1
1
1
0
0
0
0
1
1
1
1
0
0
1
1
1
0
1
2
2
1
1
2
1
1
2
1
1
2
2
1
2
1
1
1
1
3
2
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
0
2
0
1
1
2
1
0
1
2
1
1
1
2
1
1
1
0
2
1
1
1
0
0
0
0
1
2
0
0
1
1
0
2
0
0
1
1
1
1
0
2
1
2
0
0
1
6
1
0
1
2
1
1
0
1
1
1
1
1
1
1
0
0
1
2
1
1
0
1
1
0
2
1
1
1
1
1
1
1
2
0
2
1
1
1
2
2
0
1
3
1
2
1
2
0
2
0
1
2
2
0
1
1
1
1
0
2
2
1
0
0
0
1
2
0
1
1
1
1
0
1
1
1
1
1
1
1
2
2
2
0
1
1
2
2
1
1
1
1
2
1
0
2
1
0
1
1
2
0
1
1
0
0
0
1
2
1
0
2
1
1
1
1
0
0
2
2
2
1
1
0
1
1
2
1
1
2
2
1
1
2
1
1
2
0
2
2
2
2
1
0
0
1
1
0
1
0
1
1
2
1
1
1
2
1
1
0
1
2
1
1
1
1
1
2
1
1
1
1
2
1
2
0
1
1
2
1
1
1
0
1
0
1
2
0
2
1
0
2
2
0
1
1
1
2
0
2
2
1
0
1
1
0
0
1
1
2
1
0
1
0
0
1
3
1
1
1
1
2
2
1
1
1
1
2
0
1
1
0
1
2
1
0
1
1
1
0
0
1
1
0
1
1
1
1
1
1
0
1
1
0
1
2
1
1
1
1
0
1
1
2
0
2
1
1
1
2
1
1
1
0
1
1
0
1
0
0
2
1
0
0
1
1
1
1
0
0
1
2
1
0
1
2
0
1
1
2
2
2
1
0
1
0
2
2
0
1
2
0
2
1
1
1
2
0
0
0
3
1
2
0
2
0
1
0
1
1
0
0
1
0
2
1
0
1
2
1
1
1
0
1
0
1
2
1
1
1
2
1
0
0
1
1
1
1
0
1
1
1
1
1
1
0
0
2
1
1
2
0
1
0
1
1
1
0
1
1
1
1
1
1
1
2
0
2
1
2
0
1
1
1
2
1
0
0
1
1
1
0
2
3
1
2
0
0
0
1
1
1
1
1
1
0
1
1
1
0
0
1
1
2
0
1
2
1
1
1
2
2
1
1
0
0
2
1
2
1
1
2
1
0
1
0
1
1
0
1
1
2
1
2
2
1
1
1
2
1
1
1
0
1
0
1
0
1
2
0
1
1
1
0
0
1
1
1
1
2
3
1
0
1
1
1
0
1
0
1
0
0
1
1
1
2
1
3
1
1
0
1
0
2
1
1
2
1
3
1
0
1
1
1
1
1
1
1
0
2
0
1
0
0
2
1
0
0
1
0
4
1
2
0
1
2
2
1
1
1
2
2
1
1
2
1
1
0
1
0
1
1
0
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
0
1
1
2
1
2
0
1
1
1
1
1
1
1
2
1
1
2
1
1
0
2
1
1
1
2
1
1
1
1
2
1
1
1
1
0
0
0
1
1
1
1
1
0
1
0
0
1
1
0
1
2
1
2
0
0
1
1
1
1
2
2
2
1
1
1
1
0
1
2
1
2
1
2
0
3
0
0
0
2
1
1
0
1
1
0
2
1
1
1
2
1
1
0
1
1
0
1
0
1
0
1
0
1
1
2
1
0
1
2
1
2
2
2
1
2
1
1
2
1
2
2
1
0
0
1
2
1
0
1
1
2
2
1
0
0
1
1
1
1
2
1
1
0
2
1
2
0
2
0
1
0
1
3
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
0
0
1
1
1
2
1
1
1
1
2
1
0
0
1
1
1
1
2
0
2
0
2
1
1
1
1
0
0
1
2
1
1
1
1
1
0
2
1
2
2
1
0
1
2
1
0
2
0
1
1
0
1
1
2
1
1
0
1
0
1
1
0
0
1
0
2
1
1
2
1
1
0
0
2
1
3
0
0
1
1
1
0
0
0
1
1
2
1
1
0
2
2
0
0
1
3
1
0
2
2
0
1
0
1
3
0
1
1
0
1
2
1
0
2
0
1
2
0
1
0
0
1
2
1
0
1
2
2
1
1
0
1
1
0
1
1
2
1
2
1
1
0
1
1
1
0
1
0
0
1
1
1
1
2
2
2
0
2
1
1
1
0
1
1
2
1
2
0
1
2
2
2
1
0
1
1
0
1
0
1
1
0
1
2
2
0
2
1
1
0
0
1
0
1
2
0
0
1
0
2
1
2
0
0
0
0
1
1
3
2
1
1
2
1
0
1
2
1
3
1
2
1
1
0
2
0
1
3
0
3
0
1
1
1
1
2
2
0
0
1
1
0
1
2
0
1
1
2
1
1
0
1
1
2
1
0
1
2
1
1
0
2
1
1
1
2
1
2
2
2
2
0
1
0
0
1
2
1
1
1
1
0
1
2
2
0
1
1
1
1
1
1
0
1
1
2
0
1
1
1
1
1
1
1
1
0
1
0
1
1
1
1
0
2
1
1
0
1
2
1
0
1
2
2
1
1
2
0
2
1
1
0
1
2
1
0
1
1
2
1
2
1
5
1
2
0
1
1
0
1
1
1
1
1
0
1
1
1
1
2
0
0
1
1
2
1
0
1
1
2
0
0
1
0
1
1
2
1
1
0
1
0
2
0
1
2
1
2
1
2
1
1
1
0
2
1
1
1
0
1
2
1
1
0
1
1
1
0
1
1
1
2
1
1
1
1
1
2
2
1
1
1
0
0
1
1
1
1
0
1
1
1
1
1
1
1
0
1
1
1
1
2
1
0
2
0
1
2
2
1
2
1
1
0
1
0
1
1
1
0
1
0
1
2
2
1
2
1
1
1
1
4
2
1
1
0
0
0
1
1
1
1
1
0
1
1
2
0
2
1
1
0
1
2
0
1
2
1
1
0
2
1
1
1
1
1
2
1
2
0
1
1
1
0
1
0
1
2
2
1
1
0
2
1
0
2
0
0
1
0
0
1
1
2
0
1
0
2
2
0
1
2
1
1
1
2
1
1
0
1
0
1
3
0
2
2
1
1
1
2
1
0
1
1
1
0
1
1
0
1
0
0
1
2
1
0
1
0
1
2
1
1
2
1
1
1
1
1
1
2
0
2
1
1
1
2
1
1
2
0
0
0
1
0
2
1
2
1
3
0
0
2
0
0
1
0
1
1
3
1
0
1
1
1
0
1
2
2
1
1
1
1
1
1
2
2
1
1
1
2
1
1
0
1
2
1
1
2
1
1
2
0
1
1
2
1
2
2
2
1
1
1
1
1
1
0
0
1
1
3
0
1
2
0
1
1
1
1
1
2
1
2
0
1
2
1
0
2
0
1
1
0
1
1
1
0
0
0
2
1
1
1
0
2
1
2
1
0
2
1
1
1
1
0
0
2
1
1
0
1
1
1
1
0
1
2
1
1
1
2
1
0
2
0
2
2
2
2
0
1
0
1
1
1
1
2
1
1
2
2
1
0
1
2
0
1
0
1
2
0
2
1
2
1
1
1
1
1
1
2
1
1
1
0
2
1
1
2
2
1
0
2
2
0
2
0
1
1
0
1
1
2
0
0
1
2
0
1
1
1
0
1
1
1
0
0
1
1
1
1
1
1
1
2
1
3
1
3
1
0
1
1
0
1
2
0
1
2
1
0
1
0
1
0
1
1
1
0
1
1
0
2
1
1
1
2
0
1
1
0
2
2
0
1
1
1
1
0
2
1
0
0
2
1
2
0
2
1
2
1
1
1
1
0
1
0
1
1
1
0
2
0
0
0
1
1
1
0
1
1
2
1
1
1
1
1
1
0
0
1
0
0
1
1
1
0
1
1
1
0
1
1
1
1
0
2
1
1
2
0
1
1
1
0
1
0
1
0
1
2
1
1
0
1
0
1
1
0
1
2
1
0
1
2
0
1
1
1
1
1
2
1
2
2
2
2
1
2
1
1
2
1
1
1
3
0
1
1
1
1
1
2
1
1
1
0
1
1
2
0
1
0
1
2
1
1
1
1
1
2
0
1
0
2
1
2
0
2
0
1
3
4
1
1
0
1
2
2
1
1
0
1
2
1
1
1
2
1
1
1
0
2
2
1
0
1
1
2
1
2
1
1
1
0
0
1
2
1
1
1
2
1
2
1
2
1
1
1
0
1
0
2
1
2
1
2
0
0
1
0
1
0
0
1
2
1
1
1
1
2
2
1
1
0
1
1
4
1
1
2
1
1
2
0
0
1
2
1
1
2
2
0
1
2
2
1
0
1
2
1
1
1
1
1
0
1
1
0
1
1
2
0
0
1
2
1
1
0
1
1
1
1
1
0
0
2
1
0
1
1
0
0
2
1
0
0
1
1
0
1
0
0
0
1
0
1
1
1
1
1
1
1
1
1
2
0
0
0
0
1
2
1
1
0
2
1
1
0
1
1
0
0
0
1
1
2
0
1
2
1
0
1
0
2
2
0
1
2
1
1
2
1
1
1
1
1
0
1
2
2
1
0
1
1
1
2
1
1
1
2
0
0
1
1
1
1
0
1
1
1
1
2
0
1
0
2
2
1
1
1
2
1
1
1
0
1
0
0
1
1
1
1
0
1
2
2
1
2
2
2
0
1
1
0
0
0
1
0
2
1
0
1
1
1
1
1
1
0
2
1
1
2
0
2
0
1
1
1
2
1
1
1
0
1
0
0
0
4
1
13
0
2
1
1
1
2
1
1
0
2
1
1
1
1
1
1
0
0
1
2
0
1
2
0
1
1
0
1
1
2
0
2
1
1
2
1
1
1
0
1
1
1
0
2
1
2
1
1
2
1
1
2
0
2
1
2
1
0
0
1
1
1
0
2
1
2
1
0
0
0
1
2
1
1
2
0
0
2
1
1
1
2
2
2
0
1
1
0
0
0
0
0
1
1
0
1
1
0
2
1
2
0
1
0
0
1
1
2
2
1
0
1
0
0
1
0
1
2
2
0
0
1
1
1
2
1
1
0
2
1
1
1
1
2
1
1
2
2
2
1
0
1
2
2
0
1
2
2
1
1
1
2
1
0
4
2
3
1
1
2
0
1
2
0
2
0
1
0
1
1
1
2
1
0
1
1
1
2
0
0
1
0
0
1
1
1
1
2
1
1
1
3
1
1
1
0
1
1
2
1
1
1
2
1
1
1
0
1
1
8
2
0
2
1
1
0
1
0
0
1
1
1
2
1
2
1
1
1
1
1
2
1
2
1
1
1
1
2
3
1
2
1
0
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
0
0
1
0
1
0
3
1
0
1
0
1
1
0
1
1
1
1
1
1
1
0
1
2
1
1
1
0
1
0
1
1
1
2
1
1
3
1
1
1
0
1
0
1
2
1
2
0
0
1
2
1
0
1
1
1
1
1
1
1
1
0
1
1
1
0
1
2
0
5
2
1
1
0
1
2
1
1
2
2
1
2
1
1
0
1
0
0
2
2
0
1
0
0
1
2
1
1
0
1
2
0
0
0
0
3
1
2
2
1
1
1
0
1
1
1
2
1
2
1
1
0
5
1
2
0
2
2
1
1
1
1
1
0
0
0
2
1
1
1
1
4
1
1
1
0
2
0
1
1
0
2
2
1
1
1
1
1
1
0
1
0
0
1
1
1
2
6
1
2
2
2
1
1
1
1
0
1
1
0
2
2
1
1
1
1
1
0
2
2
2
0
0
1
1
1
2
1
1
2
1
1
0
1
1
2
2
1
0
1
2
0
1
1
1
0
1
2
1
1
3
2
0
1
0
0
1
0
2
1
1
1
0
0
1
1
1
1
0
1
1
1
1
0
0
1
1
0
1
1
2
1
0
1
1
1
1
0
1
1
0
1
0
2
1
2
0
1
1
1
2
2
1
1
1
1
0
1
1
2
1
1
1
1
0
0
0
0
1
1
2
2
2
2
2
2
3
1
1
0
2
1
2
1
0
1
2
0
0
1
1
1
1
0
1
1
1
1
2
2
2
1
0
0
1
1
2
2
1
2
1
1
1
1
1
2
0
1
0
1
0
1
0
2
2
0
2
2
1
1
2
0
1
2
1
1
0
1
0
1
1
0
1
2
1
1
1
1
0
0
0
0
1
1
1
1
1
0
1
2
2
1
0
0
1
0
1
2
2
1
0
1
2
2
0
2
0
0
1
0
1
0
1
0
2
1
1
0
1
1
1
2
0
1
2
1
1
2
1
1
2
2
0
1
2
1
0
1
0
0
0
1
1
0
0
1
1
1
1
0
1
2
0
1
0
1
0
1
1
2
1
1
2
0
2
1
1
1
1
0
1
1
1
0
1
1
2
2
1
1
1
2
1
1
1
1
0
2
2
1
0
1
1
1
2
2
1
1
0
0
0
2
2
1
3
0
0
0
1
1
2
0
1
1
1
1
2
1
0
1
2
0
2
1
2
1
1
2
2
0
0
1
1
1
1
1
1
2
1
3
1
1
2
1
0
2
3
1
1
2
1
1
1
2
0
1
1
2
0
1
1
1
1
2
2
2
1
0
1
0
1
0
2
1
1
2
0
2
1
0
0
0
1
1
2
0
1
1
2
1
2
0
1
1
0
1
1
1
0
1
1
2
2
1
1
2
1
1
0
2
1
1
1
1
2
0
0
1
1
2
1
1
0
1
2
0
1
1
2
1
2
1
0
2
1
1
1
2
0
2
1
1
1
1
2
0
2
1
2
2
1
1
1
1
1
1
0
1
1
2
1
0
0
1
2
0
1
1
1
1
2
1
1
0
2
1
0
1
0
1
2
1
0
1
1
0
1
0
2
1
1
2
1
2
1
1
1
1
1
1
1
0
2
1
0
1
2
0
2
1
0
1
1
0
1
2
1
1
0
1
0
1
1
1
1
1
2
1
1
0
2
1
0
0
1
2
1
2
1
0
0
1
1
0
2
2
0
0
2
1
1
1
1
0
2
2
1
1
1
0
0
1
0
2
1
1
1
1
1
2
1
0
1
2
1
1
0
0
2
2
1
0
0
3
2
1
1
1
1
1
0
1
1
1
1
1
0
1
1
1
1
1
1
1
2
1
0
1
0
0
2
1
0
0
3
0
2
1
1
1
2
0
1
1
0
0
1
0
1
2
1
1
1
1
1
0
1
0
1
2
0
1
1
4
0
2
1
2
1
1
0
1
1
1
1
0
2
0
1
1
1
1
0
2
0
0
1
1
1
1
0
0
2
1
1
1
1
2
1
1
1
0
1
0
1
1
2
0
2
2
2
1
1
1
1
2
1
0
1
0
0
2
1
0
1
3
0
0
1
1
1
1
1
2
2
0
1
1
1
2
1
2
1
2
1
2
1
2
0
0
2
2
1
1
1
1
1
1
2
2
2
1
0
1
0
2
1
1
1
1
1
1
1
2
0
2
1
1
5
0
1
2
1
1
2
1
1
1
1
1
0
2
0
1
0
1
2
2
0
2
0
2
1
2
1
1
1
1
1
1
1
0
3
1
1
0
0
1
1
1
0
1
1
1
0
0
0
1
1
1
2
1
0
2
0
1
1
1
2
0
1
1
2
1
1
0
0
1
0
1
1
2
1
1
1
2
2
1
1
2
0
1
1
0
1
2
2
1
1
1
1
1
2
0
1
1
1
1
1
0
2
2
1
0
0
0
1
2
1
2
1
0
2
2
2
6
1
0
1
0
1
0
1
1
2
0
2
2
0
1
0
0
0
3
1
0
1
0
1
1
1
1
2
1
1
2
1
1
1
3
0
2
0
1
1
0
1
1
1
2
1
1
2
1
2
0
0
1
1
1
1
2
1
1
1
1
2
0
1
0
1
2
1
1
0
1
1
1
3
1
1
1
1
1
2
2
1
6
2
2
2
0
1
2
1
0
2
1
2
2
1
2
0
1
1
0
1
0
1
1
0
1
1
1
1
3
1
2
1
0
1
2
1
1
1
0
1
1
1
1
2
0
1
1
0
1
1
1
2
1
1
1
1
1
0
0
1
0
1
1
0
1
1
2
2
2
0
1
1
1
0
0
0
1
1
1
1
0
2
0
1
1
1
2
0
1
2
0
0
0
1
1
1
2
2
2
2
0
2
1
1
0
0
1
0
2
1
1
1
1
1
0
1
0
0
2
1
1
2
1
0
2
1
0
2
1
0
2
2
1
1
1
1
2
1
1
2
1
0
1
1
1
1
1
1
1
1
1
0
1
0
0
2
2
1
2
1
2
2
2
2
1
1
0
1
0
0
3
1
1
2
1
1
1
1
2
2
1
1
2
1
1
1
0
1
2
1
1
2
0
1
2
2
0
1
1
1
1
1
1
0
1
0
1
0
0
1
2
2
1
1
2
1
1
1
1
1
2
1
1
1
0
2
1
1
2
1
1
1
0
1
1
2
0
3
0
2
1
1
2
1
1
1
2
1
2
0
0
1
1
2
1
1
1
0
2
1
1
1
1
1
2
2
0
0
1
1
0
1
1
1
2
0
1
1
1
1
0
1
1
1
1
2
0
1
0
0
1
0
1
2
1
0
2
2
1
2
1
1
0
1
1
0
2
1
2
1
2
0
1
1
1
1
2
0
0
2
1
1
1
0
1
1
0
1
1
1
1
1
1
1
1
1
1
1
0
1
1
2
0
1
1
2
1
0
1
1
1
0
1
0
1
1
0
1
0
1
2
1
1
0
1
2
1
1
1
0
2
1
1
2
1
1
2
1
0
2
2
1
0
0
2
0
1
0
2
1
1
1
1
1
1
1
1
1
2
0
1
2
1
1
2
0
2
0
2
1
1
0
2
0
1
5
1
1
1
1
1
0
0
1
0
1
0
1
1
2
5
1
0
0
0
0
1
0
1
0
0
4
1
1
1
0
0
1
1
2
1
0
0
2
0
0
0
1
2
1
1
1
1
1
0
1
1
2
1
1
2
2
1
2
1
1
2
2
1
1
1
1
1
2
2
0
2
1
1
1
2
0
0
1
1
2
1
1
1
1
0
1
1
0
1
0
1
1
0
1
0
1
1
1
2
1
1
1
2
0
2
0
1
0
1
1
0
1
1
1
1
1
1
0
0
0
0
1
0
1
1
1
0
2
2
2
1
1
0
1
1
1
1
1
2
1
1
1
0
0
1
1
1
1
0
1
1
2
0
1
2
3
1
1
1
0
1
2
1
1
1
2
0
1
0
1
0
0
1
0
2
0
0
0
0
1
1
1
0
1
2
2
0
2
2
1
1
0
0
1
0
0
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
2
0
2
1
2
1
1
1
2
1
1
1
0
0
1
0
0
2
1
2
1
1
1
0
1
1
2
0
1
2
1
2
0
1
2
1
2
1
1
1
2
2
0
0
1
1
2
1
2
1
1
2
0
1
2
0
0
1
0
1
1
2
1
0
1
1
4
1
1
1
1
1
2
0
1
2
1
2
1
1
0
2
0
1
2
1
1
1
2
3
1
0
1
1
2
1
2
1
0
0
0
0
2
1
2
1
0
2
0
1
1
2
0
1
1
1
2
2
2
0
1
0
1
1
2
1
1
0
1
1
1
1
2
1
2
0
0
1
0
1
2
1
1
1
1
1
2
1
0
1
0
1
0
2
2
1
1
2
1
1
1
0
1
1
1
0
2
1
1
0
1
0
2
1
1
1
1
1
2
0
0
0
2
1
1
1
1
0
2
2
2
1
1
1
1
1
0
1
0
1
0
1
1
1
1
1
0
2
2
1
1
1
0
2
0
1
1
2
1
0
1
1
2
1
1
0
1
1
2
0
1
1
2
2
1
1
1
0
2
0
1
2
1
2
1
2
0
1
2
0
0
0
0
2
1
1
0
1
1
1
2
1
1
0
2
1
3
0
1
1
0
1
1
2
1
1
0
2
1
1
1
1
1
1
1
1
0
1
1
1
0
1
2
1
1
2
1
1
1
1
0
2
2
2
1
1
1
1
1
0
0
0
1
1
0
0
1
0
2
1
2
1
0
0
1
1
4
0
1
0
2
2
1
1
1
2
2
1
2
2
1
2
0
0
0
1
2
0
2
0
2
1
0
2
0
1
0
2
1
1
0
0
0
1
1
2
0
1
0
0
2
0
1
1
1
0
1
1
1
3
1
1
2
2
1
0
1
1
2
1
1
0
1
0
1
0
2
1
1
1
2
1
1
2
3
2
2
2
2
0
2
1
2
1
1
1
0
0
0
1
1
2
1
0
1
1
1
0
2
2
2
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
1
1
2
0
2
0
2
0
2
1
1
2
1
1
1
2
1
0
1
1
0
1
2
1
1
0
1
1
1
1
1
1
2
2
2
0
2
0
1
2
0
3
1
1
1
1
2
1
1
1
2
0
0
1
0
1
2
2
1
1
1
1
0
2
1
1
0
1
1
0
1
1
1
2
1
1
1
1
1
1
0
1
0
0
0
1
1
1
1
2
1
2
1
2
1
1
0
1
1
1
2
1
1
0
1
1
2
0
2
1
0
1
0
1
1
2
1
0
2
2
0
0
1
2
0
1
0
2
1
2
0
1
1
0
1
2
1
1
1
1
0
0
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
0
2
1
0
1
2
1
2
1
1
2
0
2
2
0
2
1
0
2
1
0
1
0
2
0
1
2
0
1
1
1
1
0
0
1
1
1
0
2
1
2
0
1
1
2
1
2
0
2
1
0
2
2
0
1
1
0
2
1
1
0
0
2
2
1
2
1
0
1
1
0
1
0
1
1
0
0
1
0
1
0
2
2
2
1
2
1
1
1
1
0
2
1
1
1
1
1
0
0
0
1
2
1
1
1
0
1
1
0
0
0
2
1
2
1
0
0
0
0
2
2
0
1
1
1
1
1
0
1
1
0
1
1
1
0
1
0
1
1
1
1
2
1
1
1
2
1
2
2
1
0
1
1
0
0
0
0
1
1
2
1
2
1
1
0
2
0
1
0
1
2
2
1
0
0
0
0
1
0
1
1
1
0
1
1
3
0
2
1
1
3
1
2
1
0
1
0
2
1
1
2
1
1
1
0
2
1
1
1
2
1
1
0
0
1
2
0
1
1
2
1
1
0
1
2
1
2
0
1
1
0
1
0
0
1
1
0
1
0
2
1
1
1
1
1
1
1
1
2
0
1
0
1
0
2
1
1
2
0
1
1
1
2
1
2
0
1
1
1
0
0
0
2
1
1
0
1
2
1
0
0
2
1
2
2
1
2
2
1
1
0
1
0
1
1
1
0
0
2
0
1
0
2
1
1
1
1
1
1
1
0
1
0
1
1
1
2
1
0
1
1
1
1
1
1
2
2
1
1
0
1
1
1
2
1
2
1
1
2
1
1
2
0
2
1
1
2
0
2
2
2
0
0
3
1
2
1
1
0
1
1
1
0
1
0
1
1
0
1
1
1
2
2
1
1
1
0
2
1
0
1
1
1
1
2
1
2
0
1
2
0
3
0
0
1
1
1
1
1
1
2
1
0
1
1
1
1
1
1
2
1
1
1
1
1
1
0
0
1
1
1
0
1
1
0
1
2
2
0
1
3
1
1
2
1
1
1
0
0
1
2
1
0
0
1
2
2
2
1
0
0
1
1
2
1
0
1
1
2
1
1
2
1
0
1
0
0
1
0
1
1
1
1
1
1
0
2
1
0
2
2
1
1
2
1
1
1
1
1
2
1
1
2
0
1
2
1
1
2
1
2
1
0
0
1
0
1
2
1
2
2
0
0
2
2
0
2
2
1
0
2
2
1
1
0
1
1
1
1
1
1
0
1
1
1
1
1
1
1
0
2
1
1
0
1
1
1
1
2
0
1
1
0
1
1
1
1
0
2
1
2
2
1
2
1
1
1
1
1
1
2
0
1
1
1
1
1
1
0
1
1
2
0
0
2
1
0
1
0
1
0
1
2
1
0
2
1
1
1
1
1
1
1
1
0
0
2
1
1
0
0
0
0
2
1
2
1
1
1
1
1
0
1
1
0
1
2
1
2
0
0
0
1
1
1
1
2
1
1
1
1
0
1
1
2
1
1
1
2
1
1
0
1
2
0
2
0
1
1
0
1
2
0
2
1
1
1
2
1
1
1
0
0
0
2
2
2
1
1
1
0
1
0
2
0
1
1
1
2
2
2
0
1
1
0
2
2
1
0
1
1
1
0
2
1
2
1
0
1
2
1
1
1
2
0
0
0
2
1
0
0
0
1
1
1
1
2
0
1
0
1
0
1
2
1
2
1
2
1
1
1
2
2
1
2
0
0
1
2
0
1
1
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
0
0
0
0
1
0
0
1
0
0
0
1
1
0
1
1
1
0
1
0
1
0
2
2
2
1
1
0
0
0
0
1
1
1
1
1
0
2
1
1
1
0
1
0
1
0
0
1
0
3
0
0
1
1
1
1
1
0
0
0
0
1
3
0
2
0
0
1
1
1
1
1
1
1
2
0
1
0
2
1
0
2
2
2
1
1
1
0
5
1
3
1
0
1
2
0
1
2
1
2
1
1
1
0
1
2
0
0
1
1
1
1
1
1
2
1
1
1
2
2
2
1
1
1
2
0
2
1
0
0
1
1
0
1
1
1
1
1
0
2
1
1
1
1
0
0
2
0
1
1
1
1
1
0
0
2
1
1
1
1
1
2
1
1
0
1
0
0
0
0
1
1
1
1
1
1
1
0
1
2
1
0
1
1
1
2
1
0
1
1
1
1
1
0
1
1
1
0
2
1
2
1
2
1
1
2
1
1
2
1
2
1
0
1
2
1
1
0
1
1
1
1
1
4
1
1
1
2
1
2
1
1
1
1
1
0
1
1
2
2
1
2
0
1
1
1
4
2
1
1
0
1
1
0
1
1
1
1
1
2
1
2
0
1
0
1
0
1
0
2
1
2
2
2
1
1
1
1
1
0
2
1
1
1
1
1
0
1
1
0
2
0
1
0
1
2
0
0
2
1
1
0
1
1
0
2
1
1
1
1
2
1
1
2
1
1
1
0
1
1
1
1
1
2
1
2
0
1
2
1
0
1
1
0
1
0
0
1
0
1
0
0
1
1
1
1
0
2
1
1
1
2
2
1
1
0
0
2
1
2
0
0
1
1
1
2
1
1
1
1
2
1
1
1
0
1
1
1
1
0
1
1
3
0
1
1
1
0
1
3
1
2
1
0
0
0
1
2
1
1
0
1
0
1
2
1
0
1
0
1
1
1
0
1
1
0
1
0
1
1
1
2
1
1
2
2
1
2
1
2
2
1
0
0
1
1
0
1
2
1
1
2
0
0
0
1
1
1
1
0
1
2
0
0
0
1
1
1
2
0
1
1
1
1
1
0
0
0
2
2
1
2
1
0
1
1
2
0
2
1
1
2
1
2
1
0
1
1
2
1
1
1
2
2
0
0
1
1
2
1
1
0
0
0
1
0
1
1
2
1
0
1
1
1
1
1
2
1
1
2
1
2
1
2
2
2
1
2
2
0
0
2
1
0
1
1
2
2
0
0
1
2
1
1
0
1
1
1
2
0
1
0
0
1
1
1
1
2
1
0
1
0
1
0
1
1
2
1
1
1
0
2
1
2
1
2
0
1
1
1
0
0
0
2
2
0
1
1
0
1
2
2
1
1
2
1
1
1
1
2
0
1
0
2
0
1
1
0
2
0
0
2
1
1
1
0
0
3
1
1
0
1
1
1
1
1
1
1
0
1
1
2
0
1
2
1
1
2
1
1
0
2
2
0
0
1
2
1
1
1
2
1
1
1
1
1
1
1
1
0
1
2
0
0
1
1
0
0
1
2
1
1
0
0
2
1
1
1
0
1
0
1
0
1
2
0
1
1
0
0
3
1
1
1
2
1
2
1
1
2
1
1
1
1
1
1
0
1
1
3
2
1
2
1
1
0
1
2
1
1
0
2
1
0
2
0
2
1
1
2
2
2
1
1
2
0
0
2
1
0
2
1
2
1
1
0
1
2
0
2
1
0
0
0
1
2
1
1
2
1
1
0
1
4
0
2
1
1
0
1
2
0
0
1
1
1
1
1
1
1
2
1
1
1
2
1
3
1
2
2
0
0
2
0
2
1
1
1
1
3
1
0
1
2
1
0
0
1
1
1
1
2
0
1
1
0
1
2
1
1
2
2
1
0
1
2
0
2
1
0
0
1
2
0
1
1
1
1
1
1
0
0
0
1
2
0
1
0
1
0
0
4
0
1
1
1
1
1
1
1
1
1
2
2
0
1
2
1
1
0
0
0
1
1
2
1
2
0
0
0
2
0
2
0
0
1
1
2
1
1
1
2
0
0
1
1
0
0
2
1
2
3
0
1
1
1
1
2
1
0
0
1
1
1
0
2
3
1
1
1
0
1
0
0
1
2
2
2
1
1
0
1
0
1
1
2
1
2
1
1
1
1
2
1
3
0
1
1
0
0
2
1
1
1
1
1
2
1
1
2
1
0
1
3
1
1
1
1
1
1
1
1
2
0
2
1
1
1
0
1
1
1
0
2
1
0
0
0
1
1
1
1
2
2
0
0
0
0
1
1
1
0
2
1
1
2
1
2
1
2
1
2
0
0
1
0
0
0
1
2
0
3
2
0
0
2
1
1
1
1
1
1
0
2
0
2
3
3
1
1
1
1
2
1
1
0
1
2
1
2
1
0
1
2
0
1
0
2
1
1
1
1
1
1
1
1
1
2
0
1
1
1
0
1
1
1
1
1
0
3
1
1
2
2
0
1
1
2
2
0
0
1
1
1
2
0
1
1
1
1
1
0
1
1
1
0
1
1
0
0
2
0
0
2
1
1
1
1
1
2
0
1
1
2
0
1
0
1
1
1
1
1
2
2
1
1
1
1
1
0
2
2
1
1
1
1
0
2
1
1
0
0
1
0
1
2
2
0
1
1
1
1
1
2
1
1
3
1
2
1
2
2
0
1
1
1
1
0
1
2
2
1
1
0
0
2
1
1
2
1
0
1
1
0
2
0
0
0
2
1
0
1
0
1
1
2
1
0
0
0
1
2
2
1
1
1
2
1
1
3
1
1
1
2
1
1
0
0
1
0
1
1
1
1
0
1
1
0
0
0
2
1
1
1
1
2
2
1
1
1
1
1
0
1
0
2
0
1
2
1
1
2
0
3
2
1
2
1
0
0
1
1
1
1
1
1
0
2
2
2
1
1
1
1
1
2
0
1
0
0
2
0
0
1
2
1
1
1
0
2
2
1
0
1
1
0
0
1
2
2
0
0
1
1
4
1
1
1
1
1
1
1
1
0
0
4
1
0
0
2
0
0
1
0
1
1
0
1
1
0
2
0
2
2
1
1
0
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
0
1
1
2
1
2
1
0
2
2
2
1
0
1
2
2
0
1
1
1
0
0
1
2
1
1
0
1
1
0
2
0
1
1
1
2
1
1
0
2
1
0
1
1
0
1
2
2
2
1
0
1
0
1
1
1
1
1
0
0
0
1
1
0
1
0
1
0
1
1
2
0
0
2
3
1
0
1
1
1
1
0
0
0
0
1
1
0
1
2
1
1
1
1
1
1
1
1
1
2
1
0
1
0
0
1
1
2
1
2
0
1
2
1
1
2
1
1
1
2
1
1
1
0
2
1
2
1
1
1
2
1
2
1
0
2
1
1
1
0
2
1
2
0
1
1
0
0
0
1
1
0
1
2
1
1
1
1
1
2
2
0
0
1
0
2
1
1
2
0
0
1
1
1
1
1
1
1
0
2
1
1
2
1
1
2
1
0
2
0
2
1
2
0
0
1
1
0
1
1
0
1
1
1
0
2
1
0
1
2
1
1
1
0
2
2
0
0
1
1
1
1
1
0
1
2
1
1
1
0
2
0
1
0
1
2
0
2
1
2
0
1
1
0
1
1
1
0
2
1
1
1
1
0
2
2
1
1
1
2
1
1
1
0
1
1
1
0
1
1
0
1
1
0
2
0
1
0
2
1
1
1
0
1
1
1
1
0
1
1
0
2
1
2
1
2
0
0
1
1
2
2
1
2
1
1
0
1
1
1
2
0
1
0
1
2
1
0
1
2
0
1
1
1
0
2
2
0
0
0
1
2
0
1
2
1
1
1
1
1
0
0
1
1
0
0
2
1
1
1
0
1
1
1
0
1
1
1
0
1
1
1
1
1
0
0
1
0
1
1
0
2
0
1
1
1
1
1
2
0
2
0
2
2
0
1
1
1
0
1
1
1
0
1
1
2
2
1
1
3
2
1
2
1
1
2
1
2
2
1
1
1
1
0
0
0
2
2
0
4
1
0
1
0
0
0
1
1
2
1
0
1
1
2
1
1
1
1
1
3
1
2
2
1
1
1
1
1
2
1
2
1
0
1
1
0
1
1
1
1
1
2
1
1
2
1
1
2
0
0
2
2
1
1
2
0
2
1
1
2
2
1
1
1
1
1
1
1
2
2
1
2
1
1
2
1
1
1
1
1
2
2
1
2
1
2
1
0
1
1
1
1
0
1
2
1
0
1
0
0
0
0
1
1
1
1
1
1
0
1
1
0
1
1
1
0
1
1
2
0
0
2
1
1
1
1
1
1
0
0
0
1
0
1
2
1
1
1
0
2
1
1
2
1
1
2
1
0
1
1
1
2
1
1
1
2
1
0
1
0
1
2
1
1
2
1
1
2
2
2
3
1
2
2
0
0
1
1
0
2
1
1
1
0
1
1
1
1
2
1
0
1
0
2
1
2
0
1
1
1
1
1
2
0
1
1
2
2
1
1
2
1
2
1
1
2
1
1
0
1
1
2
1
1
2
1
0
2
1
0
1
0
1
2
1
0
2
0
2
1
2
2
2
1
2
2
2
2
2
1
0
2
1
1
2
1
1
1
1
0
0
1
1
2
2
0
1
1
1
2
2
1
0
1
1
1
1
1
1
2
1
1
0
2
1
1
1
0
0
0
0
0
1
2
1
2
1
1
0
2
2
1
1
1
3
1
0
0
1
1
3
1
1
1
1
2
0
2
0
1
1
0
2
0
0
1
2
2
1
3
1
1
1
0
0
0
0
2
0
1
2
2
2
1
2
1
1
1
1
0
2
2
1
0
1
1
2
1
2
1
1
1
0
1
0
0
0
0
1
1
1
2
2
1
1
1
1
1
1
1
0
0
2
3
0
2
1
3
1
1
2
1
2
1
2
0
1
2
2
1
1
1
0
1
1
0
1
1
2
2
1
4
2
1
1
2
0
0
1
0
1
2
0
0
1
2
1
2
1
2
2
2
1
1
1
1
2
0
2
0
2
1
2
1
1
1
2
1
0
0
1
1
1
2
1
1
1
2
1
0
2
1
2
1
1
0
0
2
2
1
2
1
0
1
1
1
1
2
1
1
2
1
1
2
0
1
1
1
1
2
1
0
1
2
0
1
0
1
2
1
1
1
1
1
2
0
2
1
1
1
1
2
0
1
2
1
2
3
2
1
1
1
1
1
1
1
0
0
1
2
1
1
1
0
1
0
2
2
1
1
0
0
0
1
1
1
0
0
0
1
1
1
1
2
1
0
2
0
0
1
0
2
0
0
1
1
0
1
1
2
0
1
1
1
1
1
1
2
1
0
2
0
0
1
0
0
1
0
1
1
2
1
2
1
0
0
0
2
0
1
0
0
1
1
2
1
2
1
1
1
0
1
2
1
1
1
1
2
0
2
2
1
0
1
1
0
2
1
1
1
1
1
1
2
2
1
2
0
1
1
1
1
0
1
1
1
0
0
2
0
3
1
2
4
1
2
1
2
3
1
1
0
1
2
1
1
0
1
2
1
2
0
0
1
2
1
1
0
0
0
2
2
0
2
3
1
2
1
1
1
2
1
1
2
0
0
0
1
1
1
1
1
2
1
1
1
0
1
1
2
1
1
1
0
1
0
1
2
1
3
0
1
1
1
2
1
1
1
1
0
1
0
1
0
2
2
1
1
0
1
1
0
1
1
1
1
2
1
1
0
1
1
0
1
2
1
1
0
1
1
1
1
1
1
2
0
0
1
0
1
1
1
1
1
1
0
0
1
1
0
1
0
0
0
1
0
0
1
1
1
0
2
2
1
1
1
1
2
0
1
1
1
0
1
1
0
2
0
1
2
2
0
0
1
0
0
1
1
0
0
0
0
0
2
2
0
0
2
0
1
2
2
1
0
1
1
2
2
1
2
0
0
0
0
1
0
1
0
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
0
0
1
0
1
1
1
1
2
1
0
1
1
0
0
1
0
1
1
1
1
2
1
1
0
0
1
0
1
0
1
1
0
1
1
1
0
1
2
0
1
2
1
1
2
2
0
0
1
0
1
2
2
0
1
0
0
1
2
0
0
0
0
1
2
0
0
2
0
2
1
1
1
2
1
1
1
1
0
1
1
0
2
1
0
0
0
0
1
0
2
2
1
1
0
1
1
2
2
1
1
1
1
1
1
1
0
0
1
1
1
2
1
0
0
1
1
1
1
4
2
1
1
0
1
1
1
2
0
1
1
1
0
2
1
1
0
2
2
1
2
0
0
2
1
2
2
1
0
1
1
0
1
0
1
2
1
0
3
1
0
2
0
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
0
1
1
0
1
1
1
2
2
2
1
0
1
2
1
1
1
1
0
1
0
2
0
1
1
2
1
1
2
1
1
0
6
1
1
1
1
1
1
1
1
2
1
2
3
1
1
2
1
0
1
1
2
1
2
1
2
1
1
1
2
1
1
1
2
2
2
1
0
2
1
1
1
0
1
0
0
1
0
2
0
1
1
1
0
2
2
1
2
1
1
2
1
1
1
2
1
1
1
0
1
1
1
0
1
1
2
1
1
1
1
2
0
1
0
2
0
1
1
1
0
1
1
1
1
1
1
1
0
2
0
0
3
1
0
1
2
2
1
1
2
2
1
1
0
1
1
1
0
1
0
0
1
1
2
1
2
1
1
0
1
2
1
1
0
0
2
2
1
2
2
2
0
1
1
1
1
1
0
0
0
2
1
2
1
0
1
1
2
0
2
1
1
1
0
1
0
0
2
1
1
1
1
1
1
2
1
1
1
1
0
0
1
1
1
1
1
0
0
2
2
2
3
0
2
0
0
0
1
2
0
2
1
0
0
1
1
1
0
1
1
1
1
1
0
1
2
1
1
1
0
0
2
2
1
2
2
1
1
1
2
1
1
1
0
2
1
1
1
1
2
1
0
1
2
1
0
0
2
0
2
0
1
0
1
1
1
0
1
2
0
1
0
1
1
1
1
2
2
1
0
1
0
1
0
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
0
1
2
0
2
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
0
1
1
1
1
0
2
1
1
1
1
0
1
1
0
1
0
2
1
2
2
1
1
2
1
2
2
1
0
0
1
2
0
0
1
1
0
1
2
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
3
1
1
1
2
1
1
1
0
1
1
1
1
1
1
2
0
0
1
0
0
1
1
2
0
1
0
1
1
1
2
2
1
0
2
1
1
1
1
0
1
0
1
1
2
1
0
0
2
2
3
0
2
1
2
0
2
0
1
1
2
1
1
1
1
0
1
2
2
1
2
1
1
0
1
2
1
1
2
1
1
1
1
1
0
0
0
1
2
1
1
2
1
1
7
0
1
1
1
1
0
1
1
1
1
0
1
2
1
2
1
1
1
0
2
1
0
1
1
2
1
0
0
1
1
0
2
1
2
2
1
1
1
1
2
1
2
2
1
1
1
0
0
1
1
1
1
0
2
0
2
1
1
1
1
1
1
0
3
2
1
1
0
0
2
1
0
0
1
1
1
1
0
1
1
2
1
1
0
1
1
2
0
0
0
1
2
0
0
0
1
2
1
0
1
0
1
1
0
1
1
0
1
0
1
0
1
0
1
1
0
1
0
1
2
0
0
0
2
3
1
1
0
1
2
0
2
2
0
0
2
1
2
2
1
0
2
2
1
3
2
0
1
2
0
1
0
1
2
2
1
1
1
0
2
1
1
0
1
0
0
1
1
1
2
0
0
1
0
2
1
1
2
2
1
0
1
1
1
1
0
1
1
1
0
0
0
1
2
2
2
2
2
1
1
2
1
1
2
0
2
0
0
0
1
1
0
2
1
0
0
1
1
2
1
1
1
1
2
0
1
1
1
2
0
2
1
0
1
2
1
0
2
2
2
1
0
1
2
1
1
1
1
1
0
1
1
1
0
1
1
0
1
2
1
1
0
1
1
2
2
0
0
0
0
1
0
1
1
2
0
1
1
0
1
0
1
1
0
1
1
0
1
2
1
1
0
2
1
1
2
0
2
1
0
1
0
1
0
2
1
1
1
1
2
1
0
1
1
0
1
2
1
2
0
1
1
2
0
1
2
1
3
1
1
1
0
2
1
0
0
0
1
0
1
0
2
2
0
0
1
1
3
1
2
1
1
1
1
0
0
0
1
1
1
1
1
2
0
1
2
0
1
0
2
1
1
1
1
2
2
1
1
2
1
1
0
2
1
0
1
1
0
0
3
2
1
2
0
0
0
0
1
0
2
2
1
1
1
1
1
0
1
1
0
1
1
1
0
1
1
0
1
1
2
2
1
3
1
0
1
0
1
1
2
0
2
1
1
0
1
0
1
2
2
1
0
1
1
1
1
2
0
1
1
0
2
0
0
2
2
2
1
0
0
1
1
2
2
1
1
1
0
1
1
1
2
1
0
2
1
1
2
2
1
1
0
2
1
2
0
2
1
1
1
1
2
2
1
0
1
1
2
0
1
1
1
1
2
1
1
2
2
1
1
3
6
1
0
1
0
1
1
0
2
2
2
2
1
0
1
1
0
3
1
1
1
1
1
2
1
0
0
1
0
1
0
1
1
1
1
1
0
1
2
0
1
0
1
1
1
1
1
1
0
2
1
0
0
0
1
0
1
0
1
2
1
1
0
3
2
0
2
2
0
0
1
1
0
0
0
1
0
2
2
1
2
0
1
1
1
1
1
1
1
0
0
2
1
0
1
1
0
1
1
1
0
1
1
2
2
1
0
1
0
0
0
1
1
1
0
2
2
1
1
1
1
1
0
0
2
1
2
1
0
1
2
1
2
1
2
2
1
2
1
1
1
1
1
1
2
2
1
1
0
0
1
1
1
1
0
1
1
1
1
1
1
0
1
1
1
1
2
1
2
0
1
1
1
1
1
0
0
1
0
2
2
1
1
1
1
1
0
1
0
1
0
1
2
1
1
1
1
1
1
0
2
1
0
0
2
1
1
1
1
2
1
1
0
0
1
1
2
0
0
1
1
2
1
1
1
1
1
2
0
1
1
0
0
1
0
1
2
1
1
1
2
1
2
1
2
0
1
0
0
1
1
0
0
1
0
0
0
1
1
1
2
1
0
2
0
0
1
1
1
1
0
1
1
1
1
1
1
3
2
0
2
1
1
0
1
1
1
1
1
2
1
2
0
1
1
0
0
2
0
0
0
0
0
1
1
1
1
1
0
1
1
0
0
1
1
1
0
0
0
2
1
1
2
1
1
0
1
2
1
1
2
1
2
0
1
0
1
0
1
1
0
1
2
2
0
1
0
0
1
2
2
0
2
2
1
2
1
1
0
0
1
1
1
2
1
1
1
1
2
1
1
3
1
0
0
1
1
0
1
1
0
1
1
0
2
1
1
1
1
1
2
1
1
1
1
0
2
1
1
0
1
1
1
2
2
1
0
1
1
1
2
2
0
1
0
1
1
0
2
2
1
1
1
1
2
0
1
1
1
1
2
1
0
0
0
0
1
0
2
1
0
0
1
2
1
1
0
2
0
1
1
0
1
0
0
0
0
0
1
1
1
1
0
0
1
1
0
1
0
1
1
2
0
1
0
1
0
1
0
2
1
1
0
0
2
2
1
2
0
1
2
1
2
2
0
0
2
1
1
1
1
1
0
0
1
1
0
1
1
0
2
2
0
2
1
1
1
2
1
1
1
2
1
1
2
2
0
1
1
1
1
1
2
1
1
2
1
0
0
1
2
1
2
1
1
2
2
2
1
0
1
0
1
1
0
1
1
1
2
0
0
2
1
2
2
0
1
0
1
2
1
1
0
0
1
1
2
0
2
2
1
0
2
2
1
2
2
1
1
1
2
0
0
1
1
2
0
0
1
1
2
0
2
0
0
0
1
0
1
1
1
1
0
0
1
1
2
1
1
1
1
1
1
1
0
0
1
2
1
1
2
2
1
1
2
2
1
1
0
2
1
1
1
1
1
1
0
0
1
1
2
1
3
0
0
0
2
2
0
1
1
2
1
1
2
1
1
0
2
0
1
1
1
1
0
0
2
1
2
2
0
1
2
2
2
0
2
2
1
0
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
0
2
2
0
0
2
1
1
1
0
1
1
2
1
2
2
2
2
1
0
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
0
0
2
0
2
1
1
2
1
2
1
1
2
1
1
0
1
0
1
1
1
1
0
1
0
0
2
1
1
0
1
1
1
2
2
1
0
1
0
2
0
2
0
2
1
1
0
0
1
0
2
1
0
1
1
1
0
1
1
1
0
0
1
1
0
0
0
1
1
2
2
0
0
0
2
1
0
2
0
1
2
0
1
1
1
2
1
1
1
0
2
1
0
2
1
0
2
1
1
2
0
1
1
0
0
0
2
1
1
0
1
0
2
1
1
1
1
1
1
2
1
1
2
2
1
0
1
1
2
2
1
1
1
1
1
1
0
2
0
2
0
2
0
1
2
0
1
1
0
1
1
1
1
3
1
1
0
0
1
0
1
1
2
0
0
1
2
1
2
0
1
1
1
0
1
1
1
1
1
0
1
1
2
2
1
1
1
1
0
1
1
2
0
2
1
1
2
1
1
0
1
1
2
1
1
0
1
1
0
0
1
0
1
0
1
1
0
2
1
0
0
2
1
1
0
0
1
1
0
1
1
1
2
1
1
1
0
0
1
1
0
2
1
1
1
1
0
0
0
1
1
1
0
1
1
1
0
2
2
2
1
0
2
2
2
2
2
0
2
1
2
1
2
2
0
2
1
1
1
0
1
2
1
2
0
1
1
0
1
1
0
2
0
1
1
2
1
2
0
1
1
0
1
5
1
2
2
1
1
2
1
0
2
1
1
1
1
0
1
1
11
2
1
2
2
1
1
0
0
0
1
1
1
1
2
1
1
1
2
1
2
1
2
1
2
1
1
1
2
0
2
1
0
0
1
2
0
0
1
2
1
2
0
1
2
1
0
0
0
1
0
1
2
0
1
1
2
2
2
1
1
1
0
1
1
1
0
2
1
1
0
1
1
2
0
1
2
0
0
1
0
2
1
2
0
0
0
2
1
1
1
1
2
0
1
1
1
1
2
1
2
2
1
1
2
1
1
2
1
1
1
2
0
2
1
1
1
1
1
1
1
1
1
1
0
0
2
2
2
0
2
1
1
1
2
0
1
1
0
1
0
1
2
0
1
2
1
0
2
1
2
2
1
2
2
1
1
2
1
1
0
1
0
1
1
2
1
1
1
1
0
1
1
1
2
2
1
1
1
0
1
1
1
1
0
1
2
2
1
0
2
1
2
2
1
0
1
1
1
2
1
2
1
3
0
3
1
1
0
0
1
1
3
1
1
2
1
2
0
1
1
1
1
2
2
1
1
1
1
2
0
1
1
0
1
0
1
2
1
0
2
0
0
2
2
1
1
1
2
1
1
2
2
2
0
1
0
1
1
2
1
1
1
0
1
1
1
2
1
0
1
1
1
2
1
0
0
0
1
1
1
1
2
2
1
1
1
3
0
1
0
1
1
1
2
2
1
0
2
2
1
1
0
0
2
2
1
1
1
1
2
1
1
0
2
2
1
0
1
2
0
2
1
0
1
1
1
1
1
1
1
1
2
0
0
0
1
0
0
0
2
2
1
1
1
1
1
0
2
1
0
2
1
2
1
0
1
2
2
0
1
1
1
2
0
1
2
2
2
1
0
1
0
1
1
3
1
0
0
2
1
2
1
1
0
0
2
2
0
0
2
1
1
1
0
1
2
1
2
2
0
1
1
2
1
2
0
0
1
0
0
1
2
2
0
1
0
1
0
1
2
0
1
1
2
1
2
1
0
1
2
1
0
0
1
0
2
1
1
1
1
1
0
0
1
1
1
1
1
1
1
0
1
2
1
1
1
0
1
2
2
0
2
1
1
1
0
2
0
0
1
1
1
1
1
1
1
2
2
1
1
2
0
1
1
1
1
0
1
0
1
0
2
1
2
1
0
1
1
2
1
1
2
1
2
1
1
1
1
1
2
1
0
0
1
1
1
1
2
0
0
1
0
1
1
1
1
2
2
1
0
1
1
0
0
1
1
0
1
0
0
1
0
0
1
0
2
1
1
2
2
2
1
1
1
0
2
1
1
2
0
0
1
1
0
1
0
2
0
0
1
1
2
1
2
1
1
1
0
2
1
1
1
0
1
1
0
2
2
0
0
0
1
2
2
2
1
1
1
2
0
2
0
2
1
2
1
2
1
1
0
1
1
2
0
1
1
2
1
1
2
2
1
2
1
1
1
1
1
0
0
2
1
1
1
1
1
2
1
0
1
0
1
2
2
2
0
2
0
1
2
1
1
1
1
1
1
0
0
1
1
1
1
1
2
1
2
1
1
2
0
1
1
2
1
1
1
0
1
1
1
1
1
0
2
2
0
2
1
0
2
1
1
0
0
3
0
2
1
1
1
1
0
1
0
2
1
0
2
2
1
1
0
0
1
0
1
0
0
1
1
1
1
0
0
1
1
1
3
1
1
1
2
1
2
0
1
2
0
0
1
2
2
1
1
6
0
1
1
1
2
2
0
0
1
1
1
1
0
1
1
1
1
1
1
2
2
1
2
0
1
1
1
0
0
2
0
1
1
1
1
1
2
1
1
0
1
1
1
1
1
1
0
0
0
0
0
1
0
2
1
1
2
2
1
0
1
1
1
0
1
1
3
2
2
0
1
0
0
6
2
1
1
2
1
1
2
1
0
1
0
1
1
1
0
2
1
1
1
2
1
1
1
1
2
1
1
0
2
1
0
1
1
1
1
0
1
1
1
1
4
2
1
1
1
0
0
2
1
0
1
0
0
0
1
1
0
3
2
1
0
0
4
2
0
1
2
1
1
1
2
2
4
0
0
1
1
2
0
0
0
1
1
1
1
0
1
1
1
2
1
2
2
1
0
2
1
1
1
0
1
2
1
2
1
1
1
2
2
2
1
1
2
1
1
2
2
1
0
1
0
2
1
0
2
2
1
1
1
1
1
0
1
1
0
1
1
1
0
1
2
0
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
0
2
0
1
1
2
0
0
1
1
1
1
1
1
0
1
1
1
2
1
1
0
2
1
1
0
1
0
2
1
2
1
2
0
1
0
2
2
1
0
0
1
0
1
2
0
3
0
1
0
1
2
1
1
2
1
0
1
2
1
2
0
0
2
0
0
2
2
1
1
0
1
2
0
1
0
2
0
0
1
0
0
0
1
0
1
1
1
1
2
0
2
1
1
1
1
0
0
0
2
1
1
0
0
1
1
1
1
1
1
0
2
1
2
0
2
1
0
1
1
1
1
1
1
2
0
1
1
0
0
2
0
2
2
1
1
2
1
0
1
0
2
1
1
2
1
1
2
1
1
2
1
2
0
1
0
1
1
0
0
0
1
2
2
0
2
1
1
1
1
0
1
1
1
0
1
2
0
1
1
0
1
1
1
0
1
1
1
1
2
2
1
1
2
2
1
1
1
1
1
0
1
1
1
1
1
1
0
2
1
1
1
0
0
0
1
1
1
2
1
1
1
2
0
1
0
1
0
0
0
1
1
1
0
2
1
2
1
1
2
1
1
0
1
0
2
1
1
0
1
1
1
0
0
0
0
1
1
1
0
1
1
2
1
0
1
1
2
2
0
0
1
0
1
1
0
0
1
1
2
1
1
1
0
1
1
1
2
1
1
1
1
2
1
1
1
0
0
1
1
2
1
0
2
0
2
1
2
0
1
1
1
0
1
1
2
1
1
0
0
1
2
1
1
1
1
1
1
1
1
1
0
2
1
1
1
3
2
1
0
1
1
1
0
1
1
0
2
2
1
1
2
2
0
1
2
2
1
1
1
0
2
1
0
1
0
1
0
1
1
1
1
1
3
1
0
2
0
1
1
1
2
0
0
2
1
1
1
1
0
1
0
0
2
1
0
2
1
2
3
2
0
1
1
2
2
1
2
1
1
1
1
1
1
1
1
0
1
1
1
1
0
1
1
1
1
2
1
2
0
1
1
0
0
0
1
2
2
2
2
2
2
1
1
2
1
1
1
0
0
1
1
1
0
1
1
1
2
2
1
1
1
0
1
1
1
1
0
1
1
2
1
2
1
1
1
1
1
0
1
0
0
1
1
1
1
0
1
1
1
1
2
0
1
0
1
0
0
0
1
0
1
1
1
2
1
2
2
1
1
1
2
1
0
0
1
1
1
0
2
0
2
2
1
1
1
1
1
0
0
1
4
1
1
1
1
4
2
1
0
0
2
1
2
1
1
2
1
1
2
0
0
1
1
1
1
2
1
2
0
1
2
1
1
0
0
2
1
0
1
2
2
1
1
0
1
1
0
0
1
0
2
1
1
1
1
1
2
2
1
1
1
1
1
1
1
0
0
2
0
1
1
0
1
0
1
0
0
1
0
1
2
1
1
0
1
1
1
1
1
1
0
1
0
2
1
1
1
3
0
1
1
0
1
1
0
2
1
1
2
1
1
2
2
1
2
1
1
1
1
1
0
1
1
2
1
1
1
1
0
2
1
1
1
1
3
0
2
2
1
1
1
1
2
2
0
2
1
0
2
0
2
1
2
2
0
1
1
0
1
1
0
1
1
1
1
1
1
1
1
1
2
2
1
1
0
2
0
1
1
1
0
2
0
0
1
1
2
0
1
0
0
0
1
0
1
3
1
1
0
1
1
1
2
0
0
1
1
1
0
1
2
1
2
0
2
0
1
2
1
0
0
2
1
1
1
3
1
1
1
2
1
0
1
1
0
1
1
0
1
1
0
2
0
1
1
0
2
0
1
1
1
1
1
1
1
1
1
0
0
2
1
0
0
2
1
2
2
1
0
1
0
1
0
1
2
1
1
2
1
0
2
1
1
2
2
2
1
1
1
1
1
2
2
0
1
1
0
2
1
1
1
2
1
0
0
1
1
1
2
2
1
0
1
1
1
2
2
0
2
1
1
2
1
1
1
1
0
2
1
1
1
0
1
1
1
2
1
1
1
1
0
1
1
1
1
2
1
0
1
0
2
1
0
1
0
1
1
2
1
2
2
1
1
1
2
2
0
2
0
1
1
1
1
1
2
0
1
2
1
1
1
2
0
1
2
1
1
0
2
0
0
1
1
1
0
0
1
1
0
1
0
1
2
1
1
1
2
2
1
2
0
0
0
1
1
2
2
2
2
1
1
1
0
1
2
1
0
1
1
1
2
1
0
1
0
1
1
1
0
0
1
1
0
1
0
2
0
2
2
0
1
1
0
2
0
1
1
1
1
1
2
1
2
2
2
2
3
1
1
1
0
1
0
0
1
2
1
1
0
1
0
1
1
1
0
1
1
0
1
0
0
3
1
3
2
1
1
1
2
0
1
0
2
0
2
0
0
2
2
1
0
1
2
1
2
1
0
1
1
1
1
1
1
0
0
1
1
2
1
1
0
1
1
0
1
1
1
1
2
1
1
1
1
2
1
0
1
0
1
2
1
1
1
2
1
1
1
0
0
0
1
1
0
1
1
1
1
1
1
1
1
0
0
0
2
1
0
1
0
2
0
1
1
1
1
0
0
1
1
1
2
1
0
2
1
1
2
0
1
2
1
1
0
1
2
2
1
1
2
2
1
1
1
1
1
2
2
0
1
2
1
1
1
1
2
0
1
0
1
1
1
0
0
1
1
0
1
1
2
1
2
1
1
2
0
0
1
0
0
1
1
0
1
1
1
1
0
2
2
2
1
0
1
1
1
1
3
0
1
2
1
1
1
1
0
1
0
1
1
1
0
0
1
0
0
1
1
1
0
0
1
1
2
0
1
1
1
0
2
1
1
1
1
1
1
1
0
0
0
1
1
1
1
1
1
1
1
1
0
0
2
2
1
1
2
1
1
2
1
1
1
0
1
0
1
1
1
1
1
0
2
1
1
2
2
1
0
2
2
0
1
1
0
2
1
0
1
1
0
1
1
0
2
0
0
0
0
0
0
1
2
0
0
1
0
1
1
1
1
2
1
1
1
0
1
1
2
1
0
1
1
0
1
2
0
0
0
1
2
1
2
0
0
1
1
2
2
1
1
1
2
0
0
1
0
1
0
1
0
0
0
1
1
2
1
2
2
1
2
2
1
2
1
4
1
1
1
0
2
1
2
1
0
2
2
1
2
2
1
0
1
1
0
2
1
1
1
0
2
0
0
2
0
2
1
2
1
2
1
1
1
1
1
2
0
0
1
2
1
0
1
1
2
0
1
1
0
1
1
0
2
1
1
1
2
1
1
0
1
1
0
1
0
2
2
0
0
1
1
1
1
1
1
0
1
0
1
0
1
1
0
0
1
3
0
0
1
1
1
1
2
1
0
1
0
3
2
1
0
2
0
1
1
1
1
1
2
1
1
2
1
2
1
1
1
1
1
1
0
2
1
0
1
2
2
1
0
0
1
1
0
1
1
2
2
0
1
1
0
1
1
2
2
2
1
0
1
1
1
1
2
2
2
4
0
0
0
1
2
0
2
1
1
1
2
1
2
2
0
0
1
1
1
0
1
1
1
1
1
3
0
2
1
1
2
2
1
0
1
2
1
1
1
1
2
1
2
1
1
1
2
2
0
2
2
1
1
1
1
1
2
2
0
4
0
2
1
1
1
1
1
1
1
1
2
2
1
0
1
1
1
2
1
1
1
1
1
1
0
1
1
0
1
1
1
0
2
1
1
2
0
2
1
2
0
2
1
0
1
0
1
2
2
1
1
0
2
1
1
1
2
1
1
1
1
1
1
1
2
1
2
2
2
2
1
2
0
0
1
1
1
1
1
0
2
4
0
0
0
4
1
0
2
1
3
1
0
0
1
1
0
0
1
1
2
0
1
1
2
1
0
1
1
2
1
1
1
2
2
0
2
2
1
0
1
1
1
2
1
2
1
1
1
0
2
1
0
1
0
0
1
0
1
1
1
1
0
0
1
2
1
2
1
1
1
1
1
0
0
0
0
1
1
3
1
1
2
1
0
0
1
0
1
1
2
2
0
1
1
1
1
1
1
1
1
2
1
1
2
0
1
1
2
1
1
1
1
1
1
0
2
0
2
1
0
1
0
1
3
0
1
1
2
1
2
2
1
2
1
1
2
1
1
1
0
0
1
2
0
1
2
1
2
1
1
1
1
1
1
1
1
0
0
1
1
0
1
1
0
0
1
0
1
2
1
1
2
2
0
1
1
2
1
0
1
2
1
1
1
2
3
1
2
0
0
1
0
0
2
2
1
0
0
1
1
1
1
1
2
0
0
1
1
1
2
2
1
1
1
0
0
1
2
1
1
1
2
2
0
1
1
1
3
1
1
2
1
1
0
2
2
1
2
0
1
0
1
2
0
1
1
2
0
1
1
2
0
2
1
0
1
0
1
1
1
0
0
0
1
2
1
1
1
2
1
1
1
2
0
0
1
1
0
0
1
1
1
0
1
1
2
1
1
2
1
1
3
1
0
2
1
2
2
1
0
2
2
1
1
2
1
1
0
2
2
1
0
0
1
0
1
1
1
2
0
1
0
1
0
1
1
1
1
0
2
2
2
0
1
1
0
1
1
1
1
1
0
0
1
1
0
2
1
2
1
1
1
1
2
1
1
1
0
1
0
1
1
1
0
1
1
2
0
1
1
0
1
1
0
1
0
0
1
1
1
1
1
1
1
2
2
1
2
2
1
0
1
1
2
0
1
0
0
2
2
1
1
0
1
1
1
0
1
1
0
1
1
2
2
2
0
0
0
4
2
1
1
1
0
1
1
2
1
0
1
3
1
0
1
0
1
0
2
0
1
1
1
2
1
0
0
1
1
1
0
0
0
3
0
1
1
0
1
0
2
2
1
2
1
2
1
1
1
0
1
1
1
1
0
1
2
1
2
1
0
2
1
1
2
1
2
2
1
0
0
1
1
0
1
1
1
1
2
1
1
2
1
0
0
1
0
1
1
1
0
2
1
0
1
1
0
0
0
2
2
1
2
1
1
1
2
1
0
0
0
1
1
1
0
1
1
0
2
2
1
1
1
1
2
0
1
1
1
1
1
2
0
1
1
2
1
0
0
1
1
1
1
1
1
1
1
1
1
2
1
1
2
2
1
2
0
2
2
0
2
1
2
2
1
1
1
1
0
0
1
1
1
2
1
0
1
1
0
1
0
1
2
2
0
1
1
0
1
1
1
0
1
1
1
0
2
1
1
1
0
1
1
2
1
0
1
1
0
1
2
1
1
1
0
1
1
2
2
1
1
1
1
1
1
2
2
1
1
1
2
1
2
1
0
1
2
2
2
1
1
1
2
1
0
0
1
1
1
0
2
0
0
0
1
0
1
0
2
2
2
1
1
1
0
1
1
1
0
1
0
1
0
1
1
0
1
1
1
3
1
0
1
2
1
1
1
1
1
1
2
0
2
2
0
0
1
2
1
0
0
0
2
0
1
2
1
1
0
1
0
2
1
1
0
1
0
1
1
1
0
2
0
1
2
0
0
1
1
1
1
1
1
0
2
2
0
1
1
0
1
0
1
1
0
1
0
0
1
1
0
1
1
1
1
2
0
1
0
1
1
2
2
1
0
0
2
2
1
1
1
1
1
1
1
1
0
1
2
1
1
1
2
2
2
1
2
2
1
1
1
1
0
1
2
0
1
0
2
1
1
2
2
2
2
1
1
2
2
2
1
1
2
1
0
1
0
1
1
2
0
2
1
0
2
1
1
0
0
1
0
2
1
1
2
1
2
1
1
0
1
2
0
0
0
2
1
0
1
1
1
0
1
0
1
1
1
2
1
2
0
0
1
1
1
0
0
1
1
1
1
2
2
1
2
1
1
1
0
1
2
0
2
2
2
1
2
1
1
0
2
1
2
0
0
1
1
1
0
1
1
0
1
0
1
1
0
2
1
1
1
2
1
0
1
2
0
1
0
1
1
1
1
1
0
1
1
1
2
0
1
2
1
2
2
3
1
1
1
0
3
2
1
2
1
2
0
1
0
1
2
1
1
1
1
1
0
1
2
2
2
2
2
0
1
0
1
1
0
0
0
2
0
2
0
2
1
0
1
1
1
2
1
1
2
1
0
1
1
2
1
1
0
0
0
0
0
2
2
0
1
1
1
0
1
1
1
1
2
1
1
0
2
1
1
1
0
2
0
2
2
1
1
1
1
0
1
1
1
1
1
2
0
0
1
0
1
1
1
0
0
1
2
2
1
0
2
3
1
0
1
2
0
2
1
1
2
1
2
0
1
1
1
1
2
0
0
1
1
1
1
1
0
0
0
0
1
1
2
1
1
2
1
1
0
1
1
2
2
1
1
1
2
1
1
2
2
1
1
1
1
2
1
2
0
2
2
1
1
1
2
1
1
1
1
1
3
1
2
2
1
1
1
1
1
2
1
0
1
1
1
2
0
1
0
1
1
2
2
0
1
0
1
1
0
0
2
1
1
2
1
2
1
2
2
1
2
0
1
2
1
0
1
1
2
1
2
2
0
1
0
1
2
1
1
1
0
0
1
1
2
0
0
1
2
1
1
1
2
1
2
2
1
1
0
1
1
1
1
0
2
0
1
1
3
0
2
1
1
1
2
0
2
1
0
1
2
1
1
1
0
1
1
2
2
1
0
1
0
2
0
2
1
1
0
1
1
1
0
2
1
2
0
1
2
2
0
0
2
2
1
2
2
1
1
2
0
1
0
0
2
1
1
2
1
1
2
1
1
2
1
0
1
0
1
1
0
0
1
1
0
1
1
2
1
1
0
0
2
0
1
1
1
0
2
1
2
2
1
1
1
2
1
1
2
1
2
1
0
0
0
1
1
1
0
0
1
0
0
2
2
1
1
1
1
1
1
1
1
3
1
1
1
0
1
1
3
1
0
0
1
0
2
1
0
2
1
1
2
1
1
1
1
0
0
1
0
0
1
2
0
1
2
1
1
0
1
1
1
0
0
2
1
2
1
0
1
1
1
1
1
1
1
1
1
1
0
1
0
2
1
1
1
1
1
0
0
1
2
1
1
1
1
2
2
1
1
1
0
0
0
1
1
0
1
0
0
0
2
2
2
1
1
0
0
0
2
1
0
1
1
1
0
0
1
2
1
1
1
1
1
0
0
0
0
1
2
0
0
1
1
1
0
0
0
1
1
1
1
1
0
0
1
0
1
0
0
1
2
0
1
1
2
0
1
2
0
0
2
1
1
0
1
1
1
1
1
2
1
2
0
2
2
2
1
1
1
1
2
2
0
2
1
1
1
2
1
1
2
1
0
0
1
0
1
2
1
1
0
2
1
0
2
1
1
1
1
1
1
0
1
1
1
1
1
1
1
0
2
0
2
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
1
1
2
2
0
2
1
2
0
1
0
1
1
1
0
2
1
2
1
2
1
1
1
1
1
2
1
2
1
1
1
0
2
2
0
2
1
1
0
1
0
0
2
1
2
0
2
1
1
1
2
2
1
1
0
1
0
0
1
1
2
1
2
0
0
1
1
1
0
1
1
1
1
2
1
1
0
2
1
1
1
1
1
0
1
2
1
0
2
2
1
2
1
0
1
1
2
1
1
1
1
1
0
1
1
4
1
1
2
2
2
1
1
0
0
0
1
1
1
1
1
2
1
1
1
1
1
2
1
0
0
1
2
1
1
1
2
0
2
1
1
1
0
2
2
1
0
0
2
1
0
1
1
0
0
2
1
1
1
1
0
2
1
1
1
1
0
1
1
0
0
0
1
0
1
1
2
2
1
1
0
1
1
1
0
1
4
1
0
1
0
0
0
0
0
0
0
0
2
1
1
2
0
2
1
2
1
2
1
0
0
1
1
0
1
0
2
1
0
1
0
0
0
1
0
1
1
0
2
1
1
0
0
1
2
1
0
1
1
1
1
0
1
1
0
1
2
1
1
4
0
2
0
0
1
1
1
1
1
1
1
1
0
1
1
1
2
1
1
2
2
0
2
2
0
1
1
1
1
0
2
2
0
0
0
2
1
0
0
1
1
1
1
0
1
1
0
2
0
1
1
0
0
1
1
1
0
1
1
0
0
1
2
1
1
1
1
1
0
2
1
1
1
1
2
1
2
1
0
1
1
1
2
3
1
0
2
0
2
0
1
1
1
1
2
1
1
2
0
0
1
1
1
2
1
0
0
2
2
1
1
0
0
0
1
1
3
0
1
2
2
1
0
2
1
1
0
1
0
1
1
1
0
0
1
2
1
2
2
2
0
1
2
1
1
2
0
2
1
1
2
1
2
1
0
0
1
1
2
1
1
1
0
2
0
2
1
1
1
1
1
0
1
2
1
1
0
2
1
2
1
2
1
2
1
0
1
2
1
1
0
2
0
2
1
2
1
1
1
0
0
2
1
1
1
0
1
2
2
2
1
2
0
1
0
2
1
1
2
1
1
1
0
0
0
1
0
0
1
2
2
0
1
1
1
1
1
2
1
1
0
2
2
1
2
1
1
0
0
0
1
1
1
1
2
2
0
1
1
1
1
1
0
1
0
1
0
1
1
0
1
2
1
1
0
0
1
1
2
0
1
2
1
2
1
1
2
2
2
1
2
2
1
2
1
2
0
1
1
1
1
0
0
1
2
1
1
1
0
2
2
1
2
0
0
2
0
1
1
1
1
2
1
2
1
1
1
0
0
1
1
0
2
1
0
1
1
2
0
1
1
1
0
1
0
1
1
0
0
1
1
2
1
1
1
1
1
1
1
1
1
2
1
2
2
1
1
2
1
1
0
0
1
1
2
0
2
1
0
1
2
1
1
1
1
1
1
1
1
1
0
2
2
1
1
0
1
1
1
2
2
1
1
1
1
1
0
1
0
1
1
0
1
1
2
1
0
0
2
1
2
1
0
1
0
0
1
1
1
1
0
1
2
1
2
1
1
1
1
0
1
1
0
0
1
2
1
1
1
0
2
2
1
1
0
0
0
0
1
0
1
3
3
2
1
0
1
1
1
1
1
1
2
2
0
1
2
2
1
1
1
1
0
1
1
1
1
1
1
1
0
1
1
1
1
1
1
2
1
0
2
1
1
0
0
2
1
1
0
2
1
1
0
1
1
1
1
1
1
0
2
1
0
1
0
1
2
0
0
1
2
0
1
1
1
3
1
2
0
0
1
0
1
1
0
1
2
0
2
1
1
3
0
1
0
1
1
1
0
1
1
1
0
1
1
2
1
1
2
0
1
1
1
0
2
2
2
2
1
1
1
1
0
1
1
1
0
1
1
0
1
1
1
0
0
1
2
1
0
2
1
1
1
1
2
2
2
1
0
1
1
1
0
0
0
0
2
1
0
0
0
1
1
2
1
1
0
1
1
2
0
1
0
1
1
1
1
2
1
0
1
2
2
1
0
1
1
1
1
0
0
1
0
1
2
2
1
1
1
1
0
1
1
1
1
0
1
1
1
0
2
1
0
2
0
2
1
2
1
2
1
2
1
2
1
1
2
1
1
1
1
0
2
1
2
2
1
2
1
1
2
0
0
2
2
2
1
1
1
1
2
1
0
2
1
2
2
0
1
1
1
1
1
2
1
1
1
1
1
2
1
0
1
1
2
0
1
0
1
0
0
0
2
2
1
0
0
1
1
1
0
2
0
1
2
1
1
1
1
2
1
2
1
1
3
1
2
0
1
0
2
1
2
2
2
0
0
1
1
1
1
1
0
1
0
1
1
0
0
1
2
1
0
0
1
0
1
0
1
0
0
1
1
1
2
1
2
1
2
1
1
1
1
1
1
0
1
1
1
2
2
1
0
1
1
0
0
1
0
0
1
1
0
1
1
2
2
2
1
1
2
2
1
1
2
1
1
1
0
0
0
0
1
1
1
0
2
0
2
1
1
1
1
0
0
1
1
1
2
1
2
2
0
1
1
0
2
1
1
1
3
2
1
1
2
1
0
1
1
0
1
0
1
0
1
1
0
0
1
0
1
2
1
0
1
2
0
0
0
1
4
1
1
2
3
3
1
1
2
2
1
2
0
1
1
1
0
0
2
0
2
1
2
0
2
1
0
2
1
5
1
2
2
1
0
1
0
1
1
1
1
0
1
2
1
0
1
1
0
0
2
2
1
0
1
0
1
1
1
1
1
0
1
0
0
2
0
0
0
2
2
0
2
1
1
1
1
1
1
1
0
0
0
1
1
2
2
1
0
1
1
1
1
1
1
0
1
1
1
1
0
1
2
1
2
0
1
1
1
0
0
0
2
2
1
1
2
1
0
0
0
0
1
1
0
1
0
2
1
1
1
0
2
2
1
3
1
0
1
1
1
0
1
1
0
1
1
1
1
1
0
1
1
1
2
1
1
1
1
1
0
1
1
2
1
0
1
1
1
0
1
1
1
2
1
0
1
0
1
1
1
1
0
0
2
1
1
0
1
1
1
1
1
1
3
0
2
1
0
1
0
2
2
1
0
1
2
1
0
1
1
1
1
1
1
1
2
0
2
1
2
1
1
1
1
1
1
0
1
1
1
1
1
1
0
2
1
2
2
1
2
2
1
1
0
0
1
1
0
2
1
2
2
1
2
0
1
2
0
1
1
0
0
2
1
1
0
1
1
1
1
1
0
0
1
2
0
2
0
2
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
2
1
1
3
1
0
1
1
0
1
1
1
0
2
2
1
1
2
2
0
1
1
2
1
0
1
1
2
2
0
1
1
0
1
1
2
1
1
1
1
2
0
2
0
0
0
0
0
1
1
0
0
0
0
1
1
1
0
1
1
0
0
1
1
2
1
1
0
1
0
1
2
1
0
2
0
0
1
1
1
1
0
1
1
1
2
1
1
1
1
0
1
0
0
1
2
1
0
1
0
0
2
2
0
2
1
1
1
2
1
1
1
1
1
0
1
1
0
2
1
1
2
1
1
1
1
2
1
2
2
1
0
1
0
1
0
1
0
1
0
2
0
1
1
0
1
0
0
1
1
1
2
1
1
1
1
1
0
2
2
0
2
1
1
0
2
1
1
1
7
2
1
1
0
0
1
1
1
0
1
1
1
1
1
0
0
1
0
0
0
1
1
1
1
2
0
1
2
0
0
1
2
1
1
1
1
0
1
2
1
1
1
0
0
0
1
1
1
0
1
0
1
0
0
1
2
2
2
1
3
0
1
0
1
0
1
1
2
0
0
2
0
0
0
2
1
2
2
1
0
1
0
1
2
1
2
0
1
1
2
1
2
1
2
1
1
1
1
0
1
1
1
2
2
2
2
0
1
0
0
0
1
1
1
0
2
1
1
0
0
1
3
3
1
1
1
1
1
1
1
1
3
1
2
1
1
1
1
2
0
0
0
2
6
0
0
0
1
0
1
1
1
1
0
2
1
0
1
1
1
1
2
1
1
2
1
0
1
1
2
0
2
2
2
0
2
1
1
1
1
0
1
1
1
1
1
1
2
2
1
1
1
1
0
1
0
1
2
1
2
1
1
1
1
1
1
0
1
0
2
1
1
1
2
0
1
2
0
2
2
1
0
1
1
1
1
0
1
2
1
1
1
1
0
0
0
0
2
0
0
1
1
1
4
2
1
2
0
1
0
1
1
1
1
1
0
1
1
0
1
2
1
1
1
0
1
1
0
2
2
1
2
1
1
1
1
1
1
1
1
1
0
1
1
1
1
0
1
2
1
0
1
1
2
1
1
2
0
0
1
1
1
1
1
1
1
1
2
1
1
1
0
2
0
1
3
0
1
0
2
1
0
1
1
1
1
1
0
0
1
1
1
1
1
0
1
2
1
2
0
0
0
1
2
0
1
2
2
1
1
1
1
1
1
0
0
0
2
2
1
1
1
1
1
0
1
2
0
1
1
2
0
2
0
1
1
0
1
0
1
0
0
1
1
2
2
1
1
1
1
1
1
1
0
1
0
2
0
2
1
1
0
0
0
0
0
1
1
0
2
1
2
1
1
2
0
2
2
2
1
1
0
1
0
1
1
1
2
1
2
1
2
0
1
1
1
1
1
2
1
1
0
0
1
1
2
0
1
2
1
1
2
2
1
1
1
1
1
0
0
1
0
1
1
4
1
0
0
1
2
0
1
1
1
2
1
2
0
1
1
1
1
1
1
1
1
1
2
0
2
0
1
2
0
2
3
1
1
1
1
0
0
2
1
0
1
1
2
0
0
1
1
0
1
0
1
1
2
2
1
1
1
1
0
0
3
1
1
2
2
1
1
1
1
1
2
1
1
1
1
2
1
1
0
1
0
0
1
2
0
1
1
0
1
0
2
2
0
1
1
0
2
1
2
1
1
0
0
1
2
0
2
2
1
1
2
1
1
2
1
0
2
2
1
1
0
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
0
2
2
0
1
1
0
0
0
0
2
2
1
0
0
1
1
0
2
0
1
1
1
1
1
0
1
1
1
2
0
0
1
1
0
0
2
0
1
1
2
2
2
0
2
2
1
1
0
1
2
2
0
0
0
1
0
1
2
0
1
2
1
0
1
1
2
1
1
0
0
0
2
0
0
1
2
0
1
1
2
2
1
1
1
1
0
0
1
0
1
0
1
1
0
1
1
1
1
0
0
1
1
2
1
1
0
1
1
0
1
2
2
1
2
1
2
1
1
1
1
0
0
2
1
2
1
0
0
1
1
1
1
0
1
1
0
0
1
1
0
0
2
1
2
0
1
1
0
1
2
0
0
2
0
2
0
1
2
1
1
1
1
1
1
1
1
1
2
0
0
0
1
1
1
0
1
1
1
1
0
1
1
1
0
0
1
2
1
1
1
1
0
1
1
1
1
1
0
2
1
1
2
1
1
1
0
2
0
1
1
1
0
6
2
1
1
0
1
0
1
2
1
0
2
0
0
2
1
1
0
1
1
2
1
2
2
1
2
1
2
1
0
1
2
1
0
0
2
1
2
0
1
0
1
1
2
0
0
1
0
4
0
1
1
2
0
1
1
2
1
2
2
1
2
0
1
1
2
3
0
1
2
1
2
1
0
3
1
0
0
1
1
2
1
1
0
2
1
2
2
2
1
2
1
0
1
0
0
1
1
0
0
1
0
1
1
2
1
1
1
0
0
0
0
1
2
1
2
1
2
0
2
1
1
2
2
1
2
1
3
1
1
0
0
1
1
2
0
1
1
1
2
1
1
1
1
1
1
1
1
1
1
0
0
1
0
0
2
1
1
1
1
0
1
1
1
1
1
1
0
0
1
1
1
1
2
1
2
0
1
1
0
0
1
1
1
0
0
0
1
1
2
0
2
1
2
2
2
1
0
2
1
2
1
1
2
1
2
2
0
1
0
1
1
1
1
1
2
1
2
0
1
0
2
0
0
1
2
1
0
1
1
1
1
1
2
2
1
2
0
0
0
2
0
1
1
1
0
1
1
1
1
0
1
1
2
0
1
1
1
1
2
1
0
1
1
0
1
1
2
1
1
1
2
1
1
4
1
1
1
1
1
1
2
1
1
1
1
1
0
0
0
2
1
0
2
0
0
0
2
2
2
1
2
1
0
1
1
1
2
2
1
1
1
1
1
3
0
0
0
1
0
2
0
1
1
1
1
0
1
0
1
0
1
1
0
2
1
1
2
1
1
1
1
1
2
2
2
0
1
1
0
1
3
0
0
2
1
0
0
1
1
1
0
0
2
2
1
2
0
0
1
1
1
2
1
1
1
2
0
2
1
2
2
1
1
2
1
1
0
1
0
1
1
2
1
2
0
1
2
2
1
1
1
0
0
1
1
0
1
1
1
0
1
1
1
1
1
1
2
1
2
1
0
1
1
0
0
1
2
1
2
1
2
0
1
1
0
1
0
2
1
2
0
2
0
0
2
1
0
1
0
1
1
1
0
2
1
1
0
0
0
1
1
1
1
0
2
0
1
0
1
1
1
1
1
1
1
2
0
1
0
2
0
1
1
1
1
0
2
2
0
1
1
1
0
1
1
2
0
1
1
2
1
1
1
1
0
2
1
1
1
0
1
1
0
1
1
1
2
0
1
1
1
2
2
1
0
2
2
1
1
1
0
0
1
0
1
1
0
1
1
1
0
2
0
2
0
0
1
1
2
0
1
1
1
1
1
2
1
0
1
0
0
0
1
1
1
1
2
1
1
1
2
1
1
1
1
0
0
0
1
1
0
2
1
1
1
2
2
1
1
1
0
0
1
1
0
0
2
1
1
1
2
0
1
1
1
0
2
1
0
1
2
1
0
0
0
1
1
2
1
1
2
1
1
0
1
2
0
1
1
2
1
0
1
1
1
0
2
0
1
2
1
0
1
1
0
1
2
0
2
1
1
1
0
2
2
0
1
2
2
2
1
0
1
1
0
2
1
1
0
1
3
0
0
1
1
1
2
0
2
1
2
1
2
1
1
1
0
0
1
2
1
1
1
3
0
1
2
0
0
0
1
2
1
1
2
1
0
2
2
0
2
1
1
1
1
1
1
0
0
1
1
0
0
1
1
2
1
2
0
1
0
1
2
2
1
0
1
1
5
2
2
0
1
1
2
2
1
0
2
2
3
2
1
2
1
2
1
2
1
0
2
0
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
2
1
0
1
0
1
1
1
0
1
1
1
0
1
1
1
1
2
0
0
1
1
0
2
1
0
1
2
1
2
1
0
1
2
1
0
1
2
0
3
1
3
1
0
0
1
2
2
3
1
1
1
2
2
0
0
2
1
0
0
2
0
1
1
2
2
0
1
2
0
2
1
1
2
1
2
1
1
0
2
1
2
1
1
1
2
1
2
2
0
2
0
1
2
1
1
1
1
1
1
2
1
0
1
0
2
1
0
1
1
2
2
0
0
2
1
0
1
2
2
3
0
2
0
1
1
1
1
1
1
0
1
1
2
2
1
1
1
1
1
1
2
1
1
2
1
3
0
1
0
1
1
1
2
2
0
0
0
0
1
1
1
1
2
0
0
0
3
1
1
1
1
0
1
1
1
1
2
1
1
0
2
1
2
1
2
0
0
1
0
0
1
1
1
1
2
1
1
1
0
0
2
1
2
1
1
1
1
0
2
1
0
1
0
0
2
1
0
0
1
1
1
0
1
0
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
0
1
1
2
1
2
1
1
1
1
1
0
1
1
2
1
0
1
1
0
0
1
1
1
1
1
1
1
1
0
1
0
1
1
1
1
0
1
2
0
1
0
1
1
1
0
1
2
1
2
2
0
1
2
2
1
3
1
1
2
1
1
2
0
2
2
3
1
1
1
0
0
2
1
1
1
2
1
1
0
2
1
1
1
1
2
1
1
0
1
0
1
1
1
1
1
0
1
1
1
1
1
1
0
1
1
1
2
0
2
2
1
1
2
2
0
2
2
2
1
1
0
2
1
1
1
0
1
1
1
2
0
0
2
2
1
0
1
0
1
1
1
1
1
0
2
0
1
0
1
2
2
1
1
1
1
1
1
1
1
2
0
0
0
1
1
1
1
2
1
2
2
1
4
0
1
1
1
0
1
1
3
1
2
2
1
1
1
1
1
0
1
1
4
2
0
0
0
1
1
1
2
2
0
2
2
1
1
0
2
1
1
1
2
0
1
0
2
1
0
0
1
1
1
2
2
1
0
1
0
1
2
2
1
1
1
0
0
2
1
1
1
0
0
1
1
1
0
0
0
0
1
2
0
2
1
1
0
1
2
1
1
2
1
1
2
0
1
2
1
1
1
0
2
1
1
1
2
1
1
2
1
0
1
1
1
1
1
1
1
0
1
2
1
1
0
1
0
1
1
0
0
0
2
1
1
1
2
1
1
2
0
2
0
1
1
0
3
1
1
2
1
0
1
1
0
2
1
2
1
0
1
1
0
0
2
1
2
1
1
1
1
0
0
1
0
2
1
2
1
2
1
0
0
1
1
0
0
0
1
1
2
0
1
0
1
0
0
1
1
0
1
0
1
0
0
0
2
1
2
2
1
1
1
1
0
0
1
2
1
0
1
2
1
0
1
2
1
0
2
1
2
0
0
1
1
1
1
1
1
1
1
1
0
2
0
1
1
1
0
1
1
1
1
1
1
0
1
0
1
1
0
2
1
0
1
0
1
1
1
1
0
1
0
1
1
1
1
2
1
2
0
1
0
0
1
0
0
2
2
0
1
2
1
1
2
1
1
1
1
2
1
0
2
1
1
2
2
0
1
2
2
2
1
2
1
0
0
2
2
2
2
2
0
1
0
0
1
0
1
1
0
1
1
0
0
0
1
2
1
1
1
0
0
0
1
1
1
0
1
0
2
1
1
0
1
1
1
1
1
0
1
2
1
1
0
0
1
0
1
0
0
2
0
0
1
0
2
1
0
1
1
2
0
3
1
1
0
2
2
2
2
1
0
1
1
0
0
1
1
2
2
1
0
1
2
0
1
1
1
2
2
2
1
0
0
1
1
0
1
2
2
2
2
2
2
1
1
0
1
1
1
1
1
0
0
2
7
1
1
2
1
2
2
1
0
2
1
1
1
0
0
0
1
0
3
2
1
0
2
2
2
1
0
0
1
1
1
1
1
0
1
1
1
0
2
1
2
1
1
2
1
1
1
0
0
1
1
0
1
0
1
1
1
0
0
1
0
1
0
1
0
1
1
0
1
2
2
1
2
1
1
1
1
0
0
1
1
1
1
1
2
0
2
1
2
3
1
0
1
0
1
1
1
1
0
1
0
0
0
0
0
1
1
1
1
2
1
2
1
2
0
1
2
1
0
2
1
0
1
0
1
1
1
2
0
2
2
1
1
1
1
1
3
2
1
2
0
1
1
2
1
2
1
0
3
1
0
1
2
2
2
2
2
0
0
1
2
0
1
1
0
1
0
2
1
1
0
2
0
0
1
1
1
1
1
1
2
1
2
1
1
2
1
0
1
1
0
1
1
1
0
0
1
0
0
2
1
0
0
0
1
2
1
2
1
2
0
1
1
0
3
1
1
1
1
2
1
1
1
2
0
0
0
1
1
1
1
2
1
1
1
0
0
1
1
1
1
1
1
1
0
1
2
2
1
1
1
0
2
1
1
2
2
1
1
1
3
1
0
1
1
0
0
2
0
1
1
1
2
0
1
1
1
0
2
1
1
1
2
0
1
1
2
1
2
0
0
1
0
2
1
1
0
3
1
2
0
1
1
0
2
0
2
1
2
1
1
1
1
1
2
1
0
2
0
1
2
2
0
0
1
0
1
1
1
1
1
0
1
1
0
0
3
1
1
0
1
1
1
1
1
3
0
1
0
1
1
2
1
2
1
1
0
1
0
2
0
1
1
1
1
0
1
2
2
1
1
1
1
2
1
0
2
1
1
1
1
1
1
3
0
2
1
2
1
0
2
2
1
1
0
1
0
2
2
1
0
0
0
1
1
0
1
0
1
2
1
1
1
1
0
1
1
2
2
1
1
1
1
1
0
1
1
1
1
2
1
1
0
1
0
0
2
1
1
0
1
1
0
1
1
0
0
0
1
1
1
2
0
0
2
2
1
1
0
0
2
0
0
1
0
0
1
2
1
2
2
1
2
0
1
2
2
1
0
1
1
2
2
0
1
1
1
2
2
0
1
0
1
2
1
0
1
1
2
1
1
2
1
1
1
0
1
0
0
1
1
1
0
0
0
0
2
0
1
1
2
2
0
0
1
1
2
1
1
2
1
1
0
2
0
1
1
1
1
0
0
1
2
1
1
1
0
1
1
1
1
1
0
1
0
1
1
1
1
1
1
1
1
1
1
0
2
1
2
1
0
2
1
2
2
0
1
2
2
1
1
2
1
1
0
2
1
2
1
2
1
1
1
1
1
1
1
1
1
0
0
2
2
1
1
1
1
1
2
2
1
0
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
0
1
2
2
1
0
0
1
2
1
1
1
0
2
1
1
0
1
2
1
1
1
1
1
2
2
0
1
1
2
1
0
2
1
2
1
1
2
2
1
1
1
1
2
1
1
1
0
1
0
2
1
0
2
2
1
1
0
2
2
0
1
0
2
2
0
1
2
0
1
0
1
2
1
0
1
1
1
1
1
2
1
0
1
0
1
1
1
1
1
2
2
0
0
0
0
1
1
1
1
2
1
0
0
0
0
2
0
1
0
2
0
0
1
0
1
1
1
1
2
0
0
1
0
2
1
0
1
1
1
1
0
2
1
0
1
1
2
1
2
1
0
0
2
2
0
0
2
1
0
0
1
1
0
2
1
1
0
0
1
2
0
2
1
1
1
1
2
0
1
1
1
1
0
1
2
0
3
1
1
1
0
2
2
0
1
2
0
2
0
2
0
1
1
2
1
1
1
1
1
1
1
0
0
2
1
2
1
1
1
2
1
1
0
1
1
1
1
0
0
0
1
1
0
0
2
1
1
1
1
2
2
2
0
1
1
0
2
1
1
1
0
0
0
2
1
1
0
1
5
2
1
1
0
0
1
1
2
0
2
0
1
1
0
2
1
1
0
3
0
1
1
2
0
1
1
0
1
0
2
1
0
1
0
1
1
2
1
4
0
1
1
1
2
2
1
0
1
1
1
0
0
1
1
1
1
1
2
0
1
2
0
0
2
0
1
1
0
1
2
1
0
1
2
0
1
1
1
1
1
1
1
2
1
2
1
1
2
1
0
1
1
1
1
0
1
0
1
1
2
2
2
1
1
2
1
1
2
0
2
1
0
1
1
1
1
1
0
0
1
2
1
1
1
2
0
1
0
0
1
0
0
1
1
1
1
0
1
1
1
2
1
1
1
1
1
0
0
1
0
2
0
1
0
0
0
1
1
2
1
1
1
2
2
2
1
1
1
1
2
1
0
1
2
1
1
0
0
2
0
2
1
2
1
1
2
1
1
2
0
3
2
0
0
1
0
1
2
2
1
1
1
2
1
0
2
1
2
1
1
2
1
1
1
0
2
0
1
1
0
1
1
1
1
2
0
1
1
1
1
1
1
2
0
1
2
2
0
1
3
2
1
1
2
1
0
0
1
1
1
1
1
0
0
2
0
0
0
0
2
2
1
1
1
0
1
1
0
1
2
0
2
1
1
2
0
0
1
2
0
1
2
1
0
1
1
2
2
1
0
0
0
1
1
1
1
1
1
2
2
1
1
1
2
1
1
1
2
0
1
2
1
1
0
1
1
0
2
1
1
1
0
1
1
3
2
1
2
1
2
0
1
1
0
2
1
1
1
0
1
2
1
1
0
1
2
1
1
0
1
1
1
1
1
1
1
0
0
0
1
0
1
2
1
0
1
0
0
0
1
0
1
0
1
2
2
2
0
0
0
1
1
2
0
1
0
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
0
0
1
0
1
1
0
1
2
1
2
0
1
1
1
2
2
0
2
1
1
0
2
1
1
0
1
1
1
3
1
1
2
1
2
1
2
1
1
1
1
1
2
2
2
0
0
1
1
2
1
1
1
0
1
0
1
0
1
0
0
1
0
1
1
2
2
2
0
1
1
1
2
1
1
3
1
0
1
1
1
1
1
2
1
1
1
1
0
1
2
2
1
0
1
1
1
0
2
4
2
1
1
1
2
1
1
0
2
0
2
1
0
0
1
1
1
2
1
0
1
0
1
2
1
0
1
1
3
1
0
2
1
2
1
0
1
2
1
1
2
0
1
0
2
1
1
0
1
1
0
1
1
1
2
2
1
1
0
1
1
2
6
1
1
0
1
1
1
1
1
1
2
1
2
2
0
1
2
1
0
2
0
0
1
1
1
1
0
1
1
0
2
1
0
1
0
1
0
1
2
0
2
1
0
1
1
0
1
1
1
1
2
1
0
2
1
1
1
1
1
4
0
0
1
2
2
1
0
2
1
0
1
1
1
2
1
1
2
1
2
2
0
0
2
1
1
1
0
1
0
1
2
1
1
0
1
1
0
1
0
1
0
2
1
2
0
0
2
1
0
1
2
1
0
1
2
1
1
1
1
1
2
1
0
1
1
2
0
5
0
1
1
1
0
1
0
2
1
0
2
1
0
2
0
1
0
1
2
1
0
1
0
2
2
1
1
2
1
0
1
1
2
1
0
2
2
0
1
2
2
1
1
1
2
2
1
1
1
1
0
1
2
1
0
1
1
1
0
2
2
0
2
0
1
1
1
1
2
1
1
0
2
2
1
2
1
2
1
1
1
1
1
0
1
2
1
1
0
2
1
1
1
0
1
2
2
1
1
0
1
1
1
0
1
1
2
1
2
1
1
2
0
2
1
0
1
1
0
1
0
2
1
0
1
2
1
2
1
1
1
1
1
1
2
0
2
1
1
0
1
0
0
1
0
2
1
0
1
2
1
0
1
1
0
1
1
1
1
2
1
1
0
1
1
1
2
1
1
0
2
0
2
1
0
2
2
1
1
2
2
0
1
0
1
1
1
1
1
1
2
1
2
0
0
0
0
0
1
2
2
0
1
1
2
1
0
0
0
1
2
0
1
1
2
1
2
0
1
0
0
1
2
2
0
1
1
1
1
1
1
0
0
1
0
0
1
1
1
1
2
0
1
1
0
1
0
1
2
0
1
1
2
1
1
1
0
1
0
1
0
0
1
1
1
3
2
0
1
1
1
1
1
2
1
0
1
0
1
2
0
1
1
0
1
7
0
1
2
1
1
0
1
1
0
2
1
0
1
1
0
1
2
1
1
2
1
0
1
0
1
1
1
1
1
1
0
1
1
1
0
0
3
1
1
0
0
1
1
0
1
1
2
3
2
2
2
1
2
1
2
1
1
1
0
1
1
1
0
1
2
0
1
1
2
1
1
1
0
1
1
1
1
1
1
2
0
0
1
1
2
1
2
1
2
1
1
1
1
1
0
0
1
1
2
1
1
1
1
0
2
0
2
1
1
1
1
1
0
1
2
1
2
1
1
0
2
1
3
1
1
1
1
0
1
2
2
2
1
1
0
1
2
2
2
2
1
2
1
0
1
0
1
0
2
1
1
0
1
1
0
1
1
0
2
0
2
1
1
1
2
0
1
2
0
1
1
1
1
1
2
0
1
0
0
2
0
2
0
0
1
1
1
2
1
2
1
1
0
1
1
2
1
2
2
2
2
1
1
1
1
1
2
0
1
2
1
0
1
1
1
1
1
0
0
3
1
1
2
2
2
1
0
2
0
1
0
2
1
1
1
0
0
2
2
0
1
0
1
1
0
1
1
0
1
1
1
1
1
0
0
0
1
1
2
1
1
2
1
2
1
0
1
0
1
2
1
1
0
2
2
2
1
1
1
1
0
0
0
2
1
1
2
1
0
1
2
1
1
2
1
1
1
2
1
2
2
1
1
1
2
0
1
1
2
1
1
1
1
1
0
1
1
1
2
1
1
1
0
2
0
1
1
0
1
1
1
2
2
1
0
0
2
0
1
0
1
0
2
1
2
2
1
1
1
1
1
1
1
0
0
1
1
0
2
2
1
1
0
1
0
1
2
1
2
2
0
1
2
1
1
1
1
2
1
2
2
0
0
1
0
0
0
0
0
1
1
0
1
1
2
2
1
1
2
1
1
1
0
1
1
0
2
1
0
1
0
1
1
1
1
2
1
1
2
2
0
1
1
2
2
1
2
1
1
1
2
1
1
0
0
0
1
1
1
1
1
2
1
1
2
2
0
2
1
1
0
1
1
2
1
1
2
2
1
2
1
2
1
1
1
1
1
1
2
1
0
0
0
0
2
1
1
1
1
0
1
0
0
1
1
1
1
2
1
2
2
2
0
2
2
1
0
1
1
1
0
0
3
0
1
0
1
2
1
1
0
0
0
2
1
2
1
3
1
1
0
2
2
0
1
1
2
1
2
1
1
1
0
2
0
1
1
1
0
1
1
2
1
0
1
1
2
1
1
1
0
1
0
3
4
2
2
1
1
0
0
2
1
1
1
2
1
1
1
1
1
0
0
2
1
2
1
1
2
1
1
1
1
2
2
1
2
1
1
1
1
0
1
1
0
1
0
0
0
0
1
1
1
1
1
1
2
2
0
2
1
1
0
1
2
0
1
2
1
0
1
2
0
1
2
1
0
0
1
1
1
1
1
1
1
2
0
1
2
2
0
3
2
1
1
1
2
1
1
1
0
0
0
1
0
1
1
1
1
1
1
0
1
1
2
1
1
1
1
0
1
0
0
2
1
2
1
1
1
1
0
1
1
1
1
1
0
0
1
1
2
1
1
0
1
0
1
0
1
1
1
0
1
2
1
1
3
2
2
2
2
0
1
0
1
1
1
2
1
0
1
1
1
1
0
1
2
1
2
1
1
0
1
2
1
1
1
1
1
1
1
1
0
1
0
1
1
1
1
2
2
1
1
1
1
1
1
2
1
1
1
2
8
1
1
1
1
2
0
0
1
1
1
1
1
0
1
1
1
1
2
0
1
1
1
1
2
2
1
2
1
1
1
0
1
0
1
0
2
2
2
1
2
1
1
0
0
2
0
1
1
1
0
1
1
0
0
1
1
0
1
0
1
1
2
0
1
1
0
1
0
1
2
0
1
2
1
1
1
1
1
1
1
1
3
1
1
1
2
1
1
3
2
1
0
2
1
0
0
0
2
1
1
1
1
2
1
1
1
0
1
1
1
1
1
1
1
1
2
1
0
2
1
1
2
1
1
1
0
1
0
2
0
2
2
1
1
1
2
1
1
0
1
1
2
2
1
1
2
0
0
1
0
0
1
1
0
1
1
0
0
0
2
2
1
1
1
1
0
2
1
1
1
1
2
1
1
1
1
2
0
1
0
0
1
1
0
2
2
1
1
0
1
0
0
0
0
0
1
0
1
0
2
2
0
0
1
1
2
0
1
1
1
2
1
1
0
0
2
1
2
3
0
1
1
3
0
1
0
1
0
1
0
2
0
1
0
1
0
1
0
1
0
1
1
2
2
1
2
1
0
1
0
1
1
1
1
1
1
0
0
2
1
1
2
1
1
2
0
1
2
1
2
1
1
1
1
0
1
0
0
0
1
0
1
1
2
1
0
2
0
2
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
0
1
0
2
1
1
1
0
1
1
1
0
0
2
0
0
1
0
2
1
1
2
2
0
1
2
2
2
1
0
0
2
2
1
2
0
1
1
2
2
1
0
1
2
1
2
1
0
1
0
1
1
2
1
1
0
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
3
1
1
2
0
0
1
1
2
0
1
1
1
1
1
1
1
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
0
0
1
0
0
1
2
0
0
0
2
1
1
0
0
0
0
2
1
1
1
1
2
1
0
1
2
2
1
1
1
1
1
1
1
2
1
0
1
1
2
2
0
2
1
0
0
2
0
2
1
1
1
1
2
2
1
1
1
1
2
0
1
2
1
1
0
1
1
0
0
2
1
1
0
1
2
2
1
1
1
1
4
1
1
2
0
1
0
0
0
1
1
2
1
2
0
2
1
2
1
1
1
1
1
0
1
0
2
1
2
1
1
1
1
0
1
1
1
1
0
2
1
0
1
1
2
1
0
2
0
1
1
0
0
1
1
1
2
1
0
1
2
1
0
0
0
1
2
0
2
1
0
0
2
2
0
0
1
1
1
2
1
1
2
2
1
1
1
1
0
1
0
1
2
0
2
0
1
1
1
2
1
2
1
1
0
2
2
1
1
2
1
2
1
3
2
1
0
1
1
0
0
2
1
1
2
1
2
1
0
1
2
0
1
1
1
3
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
0
1
2
1
1
1
1
2
1
0
1
0
2
1
2
0
1
1
1
0
2
1
1
1
1
1
1
1
1
0
0
2
0
0
0
2
0
0
1
1
0
1
2
1
2
0
1
1
1
1
2
0
1
1
1
1
1
0
1
1
2
1
1
2
1
2
1
0
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
2
2
2
2
2
0
1
2
1
0
0
0
0
2
2
1
2
2
1
1
2
1
1
0
2
1
0
2
0
1
0
0
0
2
0
2
1
1
0
3
0
1
2
2
0
2
2
1
1
1
2
0
1
0
0
0
0
2
1
1
1
2
2
1
1
1
0
1
0
0
1
2
0
0
1
0
2
2
2
2
1
1
1
0
1
1
1
1
2
2
2
2
1
1
1
2
2
0
1
1
0
1
1
0
0
0
1
2
1
2
2
0
1
1
1
1
0
0
2
1
0
1
2
0
1
1
0
0
1
1
1
1
0
2
1
0
0
1
0
0
1
1
0
1
0
1
1
1
0
1
1
2
2
1
1
1
2
0
1
1
1
0
0
1
1
0
2
0
0
2
2
1
1
2
1
0
1
0
0
0
2
2
1
2
0
1
0
0
0
1
2
1
2
0
0
2
1
1
2
1
1
2
2
1
1
1
1
1
2
1
3
0
1
1
1
1
1
1
2
2
2
1
1
1
1
2
1
0
2
2
1
1
1
1
1
1
2
0
2
2
1
2
0
1
2
1
2
0
0
1
1
2
2
1
0
0
1
2
0
1
2
0
1
1
2
1
2
0
1
1
1
1
1
1
1
2
1
1
0
1
1
1
1
0
2
0
2
2
1
1
1
1
0
2
1
0
1
1
1
1
0
2
2
0
2
1
2
1
2
1
1
1
2
1
1
1
1
1
2
1
1
0
0
1
2
1
1
1
0
2
2
1
0
1
1
2
1
0
2
0
3
2
2
1
1
0
1
2
2
0
1
1
1
3
0
1
1
1
1
1
0
2
1
0
0
1
0
1
0
0
1
0
2
0
1
0
1
1
1
1
1
0
0
1
1
1
1
1
1
0
1
1
2
1
0
0
1
1
1
1
0
1
1
2
1
1
1
0
2
1
1
1
1
1
0
2
1
0
1
2
2
0
2
0
1
1
0
2
0
1
0
1
1
2
1
2
2
1
1
1
1
1
1
1
2
0
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
0
1
1
1
0
0
1
0
1
1
2
2
0
2
0
2
1
1
1
1
2
0
1
1
2
1
2
2
0
0
2
2
2
1
2
2
1
2
0
1
1
1
2
0
1
1
2
1
2
1
1
0
1
0
2
2
0
3
2
0
2
2
1
1
0
1
1
1
1
2
1
2
0
0
1
1
1
1
2
1
1
1
1
1
2
1
1
1
0
0
0
1
1
0
2
1
1
1
1
0
1
3
0
1
2
2
1
1
0
1
1
1
3
2
1
0
2
2
0
2
1
1
1
0
2
0
0
1
1
1
1
1
2
1
1
0
1
1
1
0
2
2
1
0
0
1
1
1
0
0
1
2
1
0
1
0
2
2
0
2
1
0
1
2
2
2
1
1
1
2
0
2
1
2
1
0
1
2
1
2
1
0
2
1
1
0
1
1
0
0
0
1
2
1
1
2
1
2
1
1
0
2
1
2
1
0
0
2
2
1
1
1
2
1
1
1
0
0
0
0
1
1
2
1
2
1
1
1
2
1
2
0
0
2
1
0
1
1
1
1
1
0
2
1
2
1
1
2
0
3
2
2
1
1
1
1
1
0
0
0
1
2
2
0
1
3
1
1
1
1
2
1
1
0
2
1
1
1
1
1
1
1
1
1
0
1
1
1
0
1
1
0
0
0
1
1
2
1
1
1
1
1
1
1
2
1
1
0
1
1
0
1
0
1
2
0
1
0
1
1
0
1
2
2
1
2
1
2
1
0
1
1
2
0
1
1
2
0
0
0
0
1
2
1
1
1
1
1
1
1
1
2
1
1
1
0
1
1
0
2
1
1
0
0
2
1
2
0
1
1
0
1
1
0
0
2
1
1
1
2
2
0
2
1
0
1
1
1
1
1
1
0
1
1
2
1
1
2
1
1
1
2
3
1
2
0
3
1
1
2
2
1
1
1
1
0
1
1
2
0
0
1
0
0
1
1
2
1
0
1
1
1
1
4
1
1
2
3
0
0
1
0
2
0
1
0
1
0
1
1
2
1
1
1
1
1
2
2
1
2
1
2
1
0
1
2
2
2
2
1
1
2
1
1
0
0
1
1
1
1
1
2
0
0
2
0
1
1
1
0
1
0
1
1
1
1
1
1
1
1
1
2
1
0
1
0
0
1
1
1
1
1
1
1
0
0
0
0
2
1
0
0
0
1
1
2
1
1
1
1
2
1
2
0
1
1
1
0
1
0
1
1
1
1
1
1
1
0
1
1
0
2
1
0
0
1
0
0
1
4
1
0
1
1
1
1
1
1
2
1
1
1
1
1
1
1
0
1
0
1
1
1
0
0
1
2
1
2
0
2
1
1
2
0
1
2
2
1
2
0
1
2
2
2
1
1
0
0
1
1
1
1
1
1
0
2
1
1
1
0
3
1
0
1
2
0
2
1
2
1
2
1
1
0
2
1
0
0
1
2
2
2
1
2
1
1
1
1
0
1
1
0
2
1
1
1
1
1
1
1
1
1
2
1
1
2
2
1
2
0
1
1
2
2
1
1
1
0
1
1
2
2
2
0
1
0
1
2
0
2
1
0
1
1
1
1
1
0
1
1
1
2
0
1
0
1
3
2
0
1
1
1
1
1
0
2
1
0
2
1
0
1
1
2
0
2
1
1
1
1
1
1
1
0
2
2
0
2
2
1
1
1
1
1
1
0
1
1
1
1
3
1
1
2
1
1
0
1
1
0
0
1
1
2
1
1
1
0
1
0
3
0
1
1
1
2
2
1
0
2
1
1
1
1
0
1
2
0
0
0
1
1
0
1
1
0
2
2
0
0
1
0
1
1
0
2
1
1
1
0
0
1
1
0
1
2
2
1
2
1
1
1
1
1
2
2
1
0
1
1
1
1
0
1
2
0
0
3
2
0
1
1
1
0
1
1
0
2
1
0
1
1
1
0
1
1
0
1
1
1
1
0
1
0
2
0
1
1
1
1
0
0
1
1
2
2
1
2
0
1
2
1
0
2
2
2
1
1
0
1
1
1
1
0
1
0
1
0
1
1
0
0
0
1
2
2
1
1
0
0
1
0
1
1
1
1
1
0
2
1
1
1
0
1
2
2
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
0
1
0
2
1
2
0
0
0
1
2
1
0
2
1
0
2
1
1
1
2
2
1
0
1
0
1
0
2
0
2
0
1
1
1
2
1
2
1
1
2
1
2
1
0
0
3
1
2
2
2
0
2
2
0
2
1
1
1
0
2
0
0
1
0
1
1
0
1
0
1
1
0
2
2
1
1
0
0
1
1
1
1
2
2
0
2
0
1
0
1
1
0
1
2
1
0
1
0
0
1
1
1
1
1
0
1
2
1
1
1
0
1
0
1
1
0
0
0
0
1
0
1
1
2
1
1
0
0
0
2
1
1
1
0
2
0
2
3
1
0
2
1
1
0
1
2
1
1
1
2
1
1
0
1
0
2
1
1
0
0
0
0
2
1
2
1
0
1
0
0
1
1
0
0
1
1
1
2
1
0
0
2
0
1
1
1
1
0
1
2
0
1
2
1
1
2
1
1
1
1
2
1
4
2
0
1
1
1
1
1
2
2
1
1
1
0
2
1
1
0
1
1
1
1
0
2
1
1
0
0
1
1
1
2
1
1
0
2
1
1
0
0
2
1
1
0
1
1
2
1
0
0
1
1
1
0
0
1
1
1
1
0
0
0
1
1
0
1
2
1
1
2
1
1
1
1
1
1
1
0
0
1
1
0
1
0
1
2
0
0
1
1
1
1
1
0
1
0
2
0
1
1
2
1
1
1
0
2
1
2
2
1
1
2
1
1
1
0
1
0
1
2
1
0
1
2
1
2
2
0
0
1
1
2
0
1
2
1
1
1
1
2
0
1
0
1
1
1
1
2
1
1
1
0
2
1
0
1
1
1
2
1
1
1
1
2
2
3
0
1
1
0
1
2
1
0
0
1
1
1
1
1
2
1
0
1
1
2
1
1
0
2
1
2
1
1
1
1
1
2
0
2
2
2
1
0
2
1
2
0
2
1
2
1
1
0
2
1
0
3
0
1
1
2
1
1
2
1
1
1
0
1
2
1
2
0
1
0
2
0
0
2
0
0
1
0
0
2
1
1
2
1
0
1
1
2
0
2
0
2
1
0
0
0
0
2
1
1
1
1
1
0
2
1
1
2
1
0
1
2
1
1
1
1
2
0
1
1
0
1
1
2
0
2
1
1
2
1
1
0
2
1
1
0
0
2
1
1
0
1
1
1
2
0
2
0
2
1
1
1
1
1
0
0
2
2
0
0
1
2
1
1
0
0
1
1
2
1
2
0
0
1
0
2
0
1
1
2
0
1
1
1
2
0
0
0
0
1
1
0
1
1
1
1
1
1
0
0
0
0
1
1
1
1
0
1
1
1
0
1
2
2
2
0
1
1
2
1
1
1
1
2
0
1
0
1
1
2
2
0
0
2
1
0
1
2
1
1
2
1
2
2
1
2
2
1
2
1
1
2
1
0
2
0
2
1
1
1
1
0
4
0
1
0
1
1
1
0
1
1
0
0
0
1
2
0
1
1
1
0
1
1
1
1
1
0
0
1
1
1
1
1
0
1
0
1
1
0
4
0
0
0
1
1
2
1
1
0
1
1
1
2
2
1
1
2
0
1
2
1
2
2
2
1
2
0
2
1
1
0
2
1
0
2
1
1
1
0
1
1
1
0
2
2
0
1
1
1
1
2
3
2
1
1
1
1
1
2
2
1
2
2
2
0
1
3
1
1
1
2
2
2
1
1
1
1
0
1
1
2
0
1
2
0
2
1
2
2
1
2
1
5
2
2
2
2
2
2
2
1
0
1
2
2
1
0
0
0
1
1
2
2
1
1
0
0
0
1
2
1
1
1
1
0
0
1
2
0
1
1
1
1
0
0
1
2
1
0
2
1
0
1
0
1
1
1
0
0
0
1
1
1
1
1
0
1
0
1
0
1
0
0
0
2
0
2
1
0
2
1
1
0
0
1
1
2
0
0
1
1
1
0
1
0
1
0
2
1
1
2
1
1
3
1
0
1
1
2
1
2
1
0
2
1
2
1
2
1
0
0
1
1
1
0
1
2
1
2
1
1
1
2
0
0
1
1
1
1
0
0
2
0
1
0
1
0
1
0
1
0
2
1
0
0
1
2
1
0
1
1
1
1
2
1
2
1
1
1
2
2
0
2
0
0
1
2
0
1
1
0
1
1
3
1
1
2
2
1
1
0
0
1
0
0
0
1
1
1
1
2
1
1
1
2
0
0
1
1
2
1
1
2
0
0
1
1
1
2
1
1
0
1
0
1
1
0
2
2
1
1
0
1
1
1
0
1
0
1
1
2
1
2
0
1
1
1
1
1
1
1
0
1
0
2
1
1
0
1
1
1
0
2
3
1
0
1
1
1
1
0
0
1
0
0
2
0
1
0
1
2
0
0
1
0
1
1
1
1
0
0
1
2
1
0
1
2
0
0
1
0
1
2
1
1
1
1
2
0
1
2
1
0
2
0
0
1
0
1
0
2
1
0
1
1
0
1
0
1
0
1
1
1
2
2
1
1
0
1
1
2
1
0
1
1
1
0
1
1
1
2
2
2
0
1
1
0
0
0
0
0
1
0
0
1
1
0
2
0
1
2
1
2
0
0
1
1
1
1
1
1
1
2
2
2
2
0
1
2
2
1
1
2
1
0
1
2
3
0
1
0
0
1
1
1
1
2
2
1
1
1
2
1
2
1
2
1
0
0
0
2
1
3
0
2
1
1
1
0
1
1
1
0
0
1
0
2
1
0
0
0
1
0
2
1
1
2
1
1
1
1
1
0
1
1
1
1
1
0
0
0
1
2
0
1
1
1
2
2
0
0
1
0
0
1
2
1
0
1
1
1
1
2
1
2
1
4
2
0
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
1
1
0
1
1
2
0
1
2
0
1
0
1
1
0
0
1
0
2
0
1
1
1
2
1
2
1
1
1
1
0
0
1
0
2
1
0
0
0
1
1
2
1
1
0
1
2
2
1
1
2
0
1
1
1
1
0
1
2
1
2
1
0
0
1
0
1
1
1
0
1
0
2
1
2
2
1
1
2
0
1
0
1
0
1
0
1
2
0
0
1
2
1
2
1
0
1
0
2
1
0
2
2
1
1
2
1
1
0
2
1
1
1
0
3
2
1
1
1
0
1
1
0
1
0
1
0
1
2
1
0
2
0
0
1
2
1
0
3
0
1
1
1
1
1
1
1
1
1
1
0
2
0
1
1
2
1
0
1
1
2
2
2
1
1
2
1
1
1
0
2
1
1
2
0
1
1
1
0
0
0
2
1
0
1
1
0
6
1
1
0
0
0
1
0
2
1
1
2
2
2
0
1
0
1
1
0
1
2
1
1
1
2
1
1
0
0
1
1
1
0
0
2
1
2
0
1
1
2
2
1
1
2
0
1
1
0
2
2
2
2
2
0
0
1
1
1
0
1
1
1
1
0
1
1
0
1
0
1
0
2
1
2
2
1
2
1
1
0
1
1
2
0
0
2
1
0
1
1
2
1
2
1
2
1
2
1
1
1
1
2
0
2
2
2
2
1
1
0
8
2
1
1
3
0
1
2
1
2
1
2
1
1
3
2
0
1
0
0
2
1
0
1
1
1
0
1
1
0
1
1
2
1
1
1
0
1
0
0
2
2
2
1
3
0
1
1
2
2
1
0
1
1
0
2
0
0
1
0
1
1
2
3
2
0
1
0
1
1
0
1
1
2
2
1
0
1
1
0
1
1
0
1
1
0
1
2
1
1
0
1
0
1
0
0
2
1
2
0
2
2
1
1
0
0
0
2
2
7
2
1
0
1
2
2
2
1
0
2
1
1
0
1
1
1
2
1
1
0
0
1
2
1
1
2
0
1
0
1
1
0
1
0
1
1
1
1
1
2
0
2
2
1
1
1
1
1
1
1
1
3
1
1
1
1
0
2
0
1
1
1
1
1
0
1
1
1
1
0
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
2
0
2
1
0
1
2
1
1
1
1
2
1
1
2
1
2
2
1
1
0
0
2
1
1
1
2
1
2
0
1
0
0
0
1
0
0
1
1
1
0
2
1
1
1
2
2
2
2
1
2
1
1
0
0
0
1
1
1
1
0
2
1
1
0
1
0
1
1
1
2
2
1
2
0
0
0
1
2
1
1
1
1
2
2
1
1
2
1
1
2
1
2
0
2
1
1
1
2
0
2
0
0
1
0
2
1
1
2
1
2
1
1
1
2
0
2
1
0
1
2
0
0
2
0
1
1
1
0
0
1
0
0
1
0
2
1
1
2
0
2
1
1
1
1
1
1
1
2
0
2
1
1
1
1
1
1
1
2
0
0
1
0
1
2
2
0
2
2
1
0
1
2
1
1
1
2
2
1
0
2
1
0
1
1
1
2
1
1
1
1
0
0
1
1
0
1
1
1
2
2
1
1
1
1
1
1
1
2
2
1
0
1
2
0
0
0
1
2
1
1
0
1
1
2
1
0
2
0
2
1
1
1
1
1
0
1
0
0
1
0
0
2
2
0
1
1
1
1
0
1
0
1
1
1
1
1
1
1
0
2
2
1
1
1
0
1
0
1
0
1
1
1
2
0
0
1
1
0
1
1
2
0
0
0
1
2
1
2
1
1
0
0
0
0
2
0
2
0
2
0
1
0
1
2
0
1
2
1
1
1
1
1
2
0
1
1
1
1
1
2
2
0
1
1
1
0
0
2
0
2
1
1
1
1
2
1
2
2
2
2
1
0
2
0
2
1
1
0
1
1
2
2
1
1
1
1
1
2
1
0
2
2
1
2
1
0
1
1
0
0
0
0
1
0
1
1
1
0
1
0
0
1
0
2
1
1
1
1
1
1
2
2
1
1
1
1
0
0
0
2
2
2
2
1
1
1
1
1
1
1
0
0
2
2
1
1
0
2
2
3
1
0
0
0
0
0
2
1
1
1
1
1
1
1
2
1
1
1
0
0
0
1
1
0
1
1
1
1
1
1
2
2
0
1
1
1
0
0
1
2
2
0
1
0
1
2
0
1
1
1
0
0
1
0
0
0
1
1
1
1
2
1
2
0
1
1
1
2
1
0
4
1
0
1
0
2
2
1
1
2
1
1
0
1
1
1
1
0
1
1
2
2
2
1
1
1
1
1
1
0
1
1
1
1
0
1
0
1
0
0
2
1
0
1
0
1
1
0
1
0
2
0
2
1
1
0
1
1
0
0
1
2
2
1
2
2
1
1
1
0
1
1
0
1
1
1
1
1
1
1
1
1
1
1
0
0
1
1
0
1
0
1
2
1
0
2
1
1
1
2
1
1
1
1
1
0
2
2
1
2
1
0
1
2
2
1
1
1
1
2
0
1
1
2
0
1
1
1
2
1
1
1
1
1
1
0
1
1
4
1
0
0
1
1
1
1
1
1
1
1
2
0
0
2
1
0
1
0
1
1
1
0
1
1
2
2
1
1
1
0
0
2
1
2
1
1
0
1
0
1
2
1
0
1
1
0
1
1
2
1
1
2
0
2
1
1
1
2
1
1
1
0
2
1
1
0
0
1
2
2
1
1
1
1
1
0
1
1
1
1
1
1
2
0
1
2
1
1
0
0
1
2
1
1
0
0
1
1
1
2
0
1
1
1
0
0
1
0
0
1
2
1
1
1
6
1
2
0
1
2
1
2
1
0
0
0
0
0
0
1
1
0
1
2
0
2
1
1
1
0
1
1
2
1
2
2
2
1
2
0
1
1
1
2
0
1
1
0
1
1
1
0
0
0
1
0
0
0
1
2
1
1
1
2
1
1
2
0
0
1
0
1
1
0
1
0
0
2
1
1
1
1
0
0
2
1
2
1
1
2
0
2
2
2
1
1
2
0
2
1
1
2
0
2
0
1
1
0
0
1
2
2
1
1
1
1
1
1
2
2
2
1
2
0
1
2
1
1
2
1
1
0
2
1
2
2
1
1
1
1
0
0
1
1
1
0
1
1
2
1
0
2
1
1
1
0
2
0
2
1
1
0
0
1
1
1
1
1
1
2
0
0
1
1
0
0
2
0
1
1
0
2
1
2
1
0
1
1
1
0
2
0
0
1
1
1
0
0
0
0
3
1
0
1
0
0
1
1
2
0
1
1
2
1
1
2
2
0
2
2
1
0
1
1
1
2
0
2
2
1
1
1
1
1
1
1
1
1
2
0
2
0
1
0
3
1
1
1
1
1
1
1
0
1
1
1
1
1
3
2
1
1
1
0
3
2
1
0
1
2
1
1
0
1
1
3
2
2
0
1
1
0
2
1
0
0
1
1
1
1
1
0
1
0
2
1
0
0
1
0
0
2
0
1
1
1
0
1
0
0
1
2
0
0
0
1
0
1
1
2
1
0
1
1
1
1
1
2
1
1
0
0
1
2
0
2
0
0
1
1
2
1
1
1
1
0
2
1
1
1
2
2
1
1
2
1
0
2
2
1
1
0
0
2
2
1
0
0
0
2
1
1
1
1
0
2
1
1
1
1
2
1
1
0
2
2
1
2
0
2
0
1
2
1
2
2
1
1
2
1
0
1
1
0
1
1
1
2
1
2
1
0
1
1
1
1
2
2
1
1
2
2
1
2
1
0
1
0
0
1
0
0
2
1
2
1
1
1
1
1
1
2
0
0
2
2
2
2
1
1
1
1
2
1
1
1
0
1
2
0
1
0
2
1
1
1
2
2
1
0
1
0
1
1
0
1
0
1
0
0
2
1
1
1
1
2
2
0
0
0
2
1
0
1
1
0
1
1
2
1
1
2
2
1
0
1
1
1
1
2
2
0
0
1
1
1
1
1
1
1
1
1
1
1
1
0
1
2
2
1
1
0
0
0
2
2
0
1
2
1
0
2
0
1
1
2
1
1
1
0
0
2
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
0
2
2
2
2
1
2
0
2
0
1
2
1
2
2
2
2
2
0
2
1
0
0
2
0
1
0
1
0
1
1
0
0
0
1
1
1
0
2
2
1
1
0
0
0
0
0
1
0
1
0
1
2
1
0
1
3
1
2
1
1
1
2
0
1
2
1
1
0
0
0
2
0
0
1
1
1
1
1
1
1
0
1
0
1
1
2
1
2
2
3
1
1
0
0
1
1
1
1
1
2
0
0
1
1
1
1
0
0
2
2
0
2
2
2
1
0
1
1
0
1
1
1
2
2
0
1
1
2
1
0
0
0
0
2
2
0
1
2
1
1
1
1
2
1
0
1
1
1
1
2
2
1
1
0
0
2
2
1
1
1
1
1
0
0
1
0
2
1
1
1
0
0
1
2
0
1
3
0
0
0
0
1
1
0
2
1
1
0
0
2
1
1
2
2
1
1
1
1
0
1
0
1
2
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
0
1
2
0
1
1
2
1
1
2
2
1
1
2
2
1
2
3
0
1
1
2
1
1
1
2
0
1
2
1
0
2
1
1
2
1
1
1
1
1
2
2
1
0
0
1
2
0
0
1
0
1
1
1
1
1
0
1
2
0
0
1
0
0
1
1
1
1
1
2
1
1
1
2
1
1
2
5
2
0
1
1
0
1
0
1
1
1
1
1
1
2
0
3
1
1
1
2
1
1
0
0
1
2
1
1
1
0
0
1
2
1
1
2
1
2
1
0
1
2
1
1
1
2
2
1
2
1
0
0
1
1
2
0
1
2
1
1
1
1
2
1
1
1
1
0
0
1
2
1
1
2
0
1
1
1
2
1
2
1
1
1
1
1
1
0
1
1
1
1
1
1
2
0
2
1
2
0
1
0
1
1
1
0
1
0
2
1
1
1
2
1
2
2
2
1
2
1
1
1
1
1
2
1
1
0
1
2
1
1
0
2
0
1
1
1
1
0
3
2
2
1
1
1
2
2
2
2
1
2
1
2
1
2
1
1
1
1
2
1
1
1
0
1
0
1
0
1
1
2
0
1
1
1
1
2
1
1
0
0
1
2
1
2
0
1
0
1
1
1
1
1
1
2
1
0
0
2
2
1
2
2
0
1
2
0
2
2
1
2
1
2
1
1
0
1
1
2
1
0
1
0
0
1
1
1
1
0
2
4
2
0
0
2
1
1
1
0
1
0
1
1
1
0
3
2
0
1
1
1
1
1
1
1
0
1
1
1
1
2
0
2
1
2
1
2
1
2
0
1
1
1
1
1
2
1
1
1
1
0
2
1
3
0
1
1
0
1
1
1
0
1
1
2
1
0
1
1
1
1
2
2
2
0
0
0
1
2
1
1
1
1
1
1
1
1
0
1
0
1
1
1
1
0
1
0
2
1
0
0
0
1
1
0
0
0
1
0
2
2
2
2
0
1
2
2
2
2
1
2
0
1
1
1
0
0
1
2
1
1
1
0
2
0
1
1
2
1
1
1
1
0
1
1
2
2
2
1
2
1
1
0
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
1
0
1
0
2
1
2
1
1
2
0
1
2
1
1
2
1
2
1
1
1
0
0
2
0
1
3
1
1
2
2
1
2
2
2
1
0
1
1
1
2
1
1
0
1
1
0
1
1
1
0
2
1
2
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
2
0
1
1
2
2
0
2
1
2
1
2
1
2
0
1
2
0
0
1
1
0
2
1
0
1
1
1
1
1
1
1
1
1
1
1
2
0
2
2
1
1
1
0
0
1
1
0
0
0
2
1
0
0
2
1
1
1
1
1
0
2
2
1
2
0
1
1
1
0
0
1
1
1
1
1
1
0
2
0
2
1
2
2
1
0
2
1
1
2
0
0
1
1
1
1
2
0
1
2
1
2
1
2
1
0
0
0
1
1
1
0
2
2
1
2
1
1
1
1
1
1
2
2
1
2
1
0
1
0
1
2
2
2
2
1
1
1
1
1
1
0
1
1
1
1
0
1
1
1
0
2
1
1
2
2
1
2
1
1
1
1
1
1
0
1
1
1
1
2
1
1
1
0
2
1
0
2
0
0
1
2
0
1
1
1
1
2
2
0
1
1
1
1
1
1
1
1
0
1
1
1
1
1
2
2
2
1
3
1
2
2
0
1
2
0
0
1
2
2
1
1
0
2
0
2
0
1
1
1
1
2
1
1
1
1
2
0
1
0
1
0
0
0
2
1
1
1
0
1
1
3
2
0
1
1
1
1
1
1
2
2
1
1
0
2
2
2
0
0
1
1
0
0
1
1
1
3
2
2
0
1
1
1
1
2
2
1
0
0
2
1
0
0
1
0
1
0
1
1
0
1
1
2
1
2
1
1
0
1
1
1
2
1
1
0
1
1
0
1
1
1
0
1
1
1
1
1
0
2
1
0
1
2
0
1
0
1
0
2
1
1
1
1
0
0
1
0
1
1
0
2
1
2
3
2
0
1
0
1
1
2
2
1
2
0
1
2
1
1
1
1
2
1
2
1
2
2
1
2
1
1
1
2
2
0
0
1
1
0
2
1
1
2
1
1
0
1
2
0
1
1
1
1
1
0
0
0
1
1
2
2
2
1
2
2
0
1
1
0
2
2
1
0
2
1
2
1
1
2
0
2
2
2
1
3
1
2
0
1
2
2
1
0
1
1
1
0
1
1
1
1
2
1
1
2
0
1
1
1
1
0
2
0
0
1
1
1
2
1
1
1
0
1
0
1
1
2
0
1
1
2
3
1
0
1
1
1
1
2
1
2
1
2
1
2
1
0
1
0
1
0
0
1
1
3
0
2
4
1
1
0
1
1
1
1
2
1
1
0
1
2
1
2
1
1
1
2
0
1
2
1
2
1
0
2
1
2
1
2
1
1
2
0
0
1
1
1
2
1
1
1
1
1
1
1
0
1
0
1
1
1
1
0
1
0
1
0
0
1
2
2
1
0
1
0
0
1
1
0
2
1
1
0
0
1
1
2
2
2
2
1
2
2
2
1
1
0
1
2
2
2
0
1
2
0
1
1
1
1
0
0
1
1
1
0
2
2
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
0
0
1
1
0
1
2
0
2
2
2
3
2
3
2
1
2
2
0
2
1
1
1
1
1
2
0
1
0
1
0
2
0
0
2
1
1
1
2
2
0
1
1
0
0
1
1
1
0
2
1
1
0
1
0
0
1
0
2
2
0
2
1
1
1
0
2
0
2
2
1
1
1
2
0
0
1
0
0
1
0
1
1
1
2
2
2
2
0
0
1
1
1
1
1
1
0
2
1
3
1
1
0
0
1
2
1
2
1
0
1
1
1
1
1
1
1
0
0
2
1
1
0
1
2
2
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
0
1
1
1
2
1
1
0
2
2
2
2
1
1
2
1
2
1
1
1
0
1
1
0
1
1
1
1
2
1
1
0
0
1
1
1
1
2
2
1
0
0
0
2
1
1
1
0
0
2
3
1
2
1
0
1
2
0
1
1
0
0
0
2
1
0
1
0
1
0
2
1
1
0
1
2
1
2
1
0
1
1
2
1
0
0
2
1
2
1
1
2
1
2
0
0
1
0
1
0
1
1
1
0
0
1
0
1
1
1
0
1
1
1
1
2
3
0
1
0
2
2
0
2
2
2
1
2
1
1
1
2
2
1
3
1
0
1
1
0
1
1
1
0
2
2
1
2
2
0
1
0
1
1
1
1
3
0
1
1
2
0
2
1
1
2
1
0
2
1
0
1
1
4
0
0
1
1
1
0
2
1
0
1
0
0
1
0
1
1
0
0
0
0
1
0
0
1
1
2
1
1
2
1
1
2
1
1
1
0
2
1
1
1
2
1
1
2
2
1
0
2
4
1
1
0
1
2
1
0
1
1
1
1
1
0
0
1
1
1
1
0
2
1
1
0
1
1
1
0
1
1
1
0
2
0
2
1
1
1
1
1
2
2
1
0
0
1
0
1
0
1
1
0
2
1
1
1
1
1
1
2
2
1
1
2
1
2
2
1
1
1
1
1
0
2
1
1
1
1
1
0
1
2
1
1
2
2
0
0
1
0
0
1
1
2
0
1
1
2
0
1
1
2
1
1
2
0
2
1
1
1
2
1
2
1
2
1
1
1
0
0
1
1
1
4
1
1
0
0
1
1
1
1
1
1
1
2
0
2
0
0
1
0
0
0
2
1
1
1
1
1
1
0
1
2
0
2
0
0
0
1
1
1
1
1
1
0
0
2
2
2
1
2
0
1
0
0
2
0
4
1
2
0
1
1
2
0
2
0
1
1
2
0
2
1
1
1
2
2
2
0
2
1
2
1
2
0
2
0
1
0
0
2
1
0
1
1
1
1
1
1
1
2
1
0
2
1
1
1
2
2
2
0
1
0
1
0
1
2
1
1
0
0
2
1
1
0
0
1
1
1
0
1
1
1
0
0
0
1
2
1
1
0
1
0
0
1
1
1
3
1
1
2
1
1
0
2
1
2
0
1
1
1
1
0
0
1
1
1
3
1
2
1
1
1
1
1
1
1
1
0
1
2
0
1
0
2
0
2
1
1
0
1
0
1
1
2
1
1
1
0
1
1
2
1
0
2
2
2
2
1
1
1
1
2
0
1
1
2
1
1
2
1
0
1
1
0
2
1
1
1
1
1
1
1
1
0
1
0
2
1
1
1
1
1
0
1
0
0
0
2
1
2
1
2
1
1
1
1
1
2
1
1
1
0
1
2
1
1
2
1
3
1
1
0
1
1
1
1
2
0
0
2
1
1
2
1
1
1
2
0
0
0
0
1
0
1
2
0
1
2
1
1
2
0
1
1
0
0
1
2
2
0
1
1
1
2
0
1
1
1
0
1
1
1
1
0
1
1
1
1
2
1
1
1
1
1
2
1
2
0
2
1
0
1
0
1
1
1
1
2
1
0
1
1
2
1
1
0
1
1
1
2
1
1
2
1
0
1
2
0
0
1
1
2
1
0
2
1
1
2
2
2
1
1
1
0
2
1
0
0
1
0
0
0
1
1
1
1
0
1
1
1
2
0
1
1
1
1
1
1
1
0
1
1
1
0
1
2
1
2
0
1
1
2
2
2
0
1
1
0
0
2
2
2
1
2
2
2
1
1
1
1
1
1
1
1
2
0
1
2
2
1
0
1
1
1
1
0
1
1
1
1
1
0
1
1
1
1
2
1
0
1
1
0
2
0
2
1
0
1
1
1
0
1
1
1
1
1
1
1
2
1
2
1
0
1
1
1
2
1
2
1
1
2
1
1
1
1
1
2
0
1
1
1
1
1
1
0
1
1
2
1
1
0
2
1
0
1
1
3
3
1
0
2
1
1
0
1
0
1
2
1
1
0
2
1
0
0
0
1
0
1
0
2
0
1
0
1
1
0
1
1
1
1
1
1
2
1
0
1
2
2
1
0
0
0
0
1
1
1
0
1
1
2
1
1
0
0
0
1
1
1
0
2
0
1
0
1
1
3
1
0
2
1
2
1
1
2
1
1
0
1
1
0
2
1
2
1
2
1
1
1
0
1
2
1
2
2
2
0
1
1
2
0
1
3
2
1
1
1
0
1
1
1
1
2
0
1
1
1
1
1
2
0
0
2
1
1
0
1
2
2
2
1
2
1
2
2
2
2
1
1
0
1
1
1
0
1
1
1
1
0
1
0
1
1
1
0
0
1
1
0
2
1
1
2
1
2
1
2
1
1
2
1
0
1
1
0
2
1
1
1
1
1
2
2
1
1
1
1
0
1
0
2
2
0
1
1
1
2
1
0
0
1
0
2
1
2
2
0
0
0
1
3
1
1
2
1
1
1
2
1
2
0
0
0
2
0
2
0
2
1
1
1
1
1
2
1
0
0
1
2
0
1
2
0
2
1
0
2
0
2
1
1
0
0
1
2
0
2
1
0
1
1
0
0
1
1
0
1
1
2
1
1
1
0
1
0
1
1
0
2
1
2
2
1
1
1
2
1
0
0
1
0
0
1
1
1
1
2
0
2
2
1
0
1
1
2
0
1
1
1
2
0
0
2
1
1
1
1
1
0
1
1
0
1
1
1
0
1
2
1
1
0
1
1
1
1
2
1
2
2
1
0
2
3
0
1
0
1
1
0
2
3
1
2
0
1
0
1
0
1
2
1
1
1
1
2
1
1
1
1
1
1
1
0
1
1
1
0
1
1
1
2
1
1
0
1
2
0
1
2
1
0
1
1
2
0
1
1
1
0
3
2
2
1
0
1
2
1
0
0
2
0
0
1
0
1
1
0
0
1
1
1
0
1
1
1
2
1
2
2
0
1
1
0
1
2
2
0
1
1
1
1
2
1
1
0
1
0
1
0
0
0
1
2
1
2
0
1
1
1
1
1
1
1
1
1
1
2
0
0
2
1
0
1
2
0
0
0
1
1
2
1
1
1
2
3
0
1
1
2
2
0
0
1
1
1
0
1
1
2
0
1
1
0
1
0
2
0
2
2
0
0
1
2
1
2
0
1
0
0
2
1
1
1
2
0
1
1
1
0
2
0
1
1
1
0
1
2
1
1
2
1
1
0
1
1
0
2
1
1
2
2
1
1
2
1
2
0
1
1
1
0
1
1
2
0
1
1
0
1
1
1
0
0
1
1
1
1
1
2
1
0
2
2
1
1
1
1
1
0
0
1
1
3
1
2
1
0
0
0
1
1
0
1
1
2
1
1
0
1
2
1
2
2
0
1
0
1
0
1
1
0
0
1
0
0
1
1
1
0
1
0
1
1
0
1
0
2
1
1
0
1
2
1
0
1
1
2
1
1
0
1
2
2
1
3
1
0
0
2
1
0
1
1
1
0
1
1
1
1
0
0
1
2
1
1
1
0
1
2
2
1
1
2
1
1
1
1
2
1
0
1
1
0
1
1
1
2
0
0
0
0
0
2
1
2
1
0
1
1
2
0
0
1
0
2
2
2
0
1
0
1
1
2
0
2
0
1
2
1
1
1
0
2
1
1
1
1
1
0
1
1
1
1
0
1
1
0
2
1
1
1
1
3
1
3
1
0
2
1
1
2
1
0
1
1
1
1
2
0
1
2
0
1
2
1
0
1
1
1
1
1
1
1
0
0
1
0
0
1
1
1
1
1
1
1
1
1
1
1
1
0
1
0
2
2
2
1
1
1
1
1
1
1
0
0
1
1
1
0
1
1
0
1
0
1
0
2
0
2
0
2
2
1
2
0
0
1
1
1
1
0
1
2
1
0
0
0
2
2
0
2
1
0
2
0
1
2
1
2
0
1
0
1
1
1
2
1
1
1
0
2
3
0
2
1
1
0
1
1
0
2
1
1
2
0
1
1
0
0
2
1
1
1
1
0
1
1
1
1
0
1
1
0
0
1
0
1
2
0
0
2
1
2
0
1
0
2
2
0
0
1
1
0
1
0
0
1
2
0
1
0
1
2
1
1
0
0
0
1
1
2
2
1
2
2
1
1
2
1
1
1
0
1
1
0
1
1
1
2
1
2
2
1
1
1
1
2
1
2
0
2
0
1
1
1
1
1
0
2
1
1
2
2
1
1
2
1
2
1
2
0
1
1
2
1
1
1
0
2
1
1
1
2
0
1
1
1
1
1
0
2
1
2
0
0
1
2
3
1
1
2
0
1
2
1
1
1
1
1
2
1
1
1
0
2
1
1
2
2
1
1
1
2
1
1
1
2
2
0
1
1
2
1
1
1
2
2
0
1
0
2
1
1
0
1
1
1
0
1
1
2
2
1
0
1
2
1
1
2
2
0
1
0
1
0
1
2
2
1
0
1
1
1
2
1
0
2
0
0
1
2
1
1
1
1
2
1
2
2
0
2
1
1
1
2
1
0
1
1
1
1
1
1
1
2
1
2
1
0
0
0
1
1
1
2
1
1
1
0
2
1
1
1
0
0
2
2
1
1
1
1
1
2
1
2
0
1
1
1
2
0
1
0
1
1
4
2
2
0
2
0
1
1
1
0
1
0
1
2
1
1
1
0
1
1
1
1
2
0
2
0
1
1
1
0
1
0
1
1
1
0
0
1
1
1
2
0
1
1
1
2
2
0
1
0
0
1
1
0
0
1
1
1
2
1
2
1
1
1
1
1
1
1
0
2
1
0
2
1
2
0
0
1
1
2
1
2
2
2
2
0
1
2
0
1
1
1
1
0
3
0
1
3
0
2
1
1
0
0
1
0
1
2
2
0
2
1
0
0
1
2
1
1
2
0
2
2
2
1
1
1
1
1
1
2
1
2
1
0
1
2
0
1
2
2
1
2
0
1
2
1
0
1
2
1
0
2
1
1
0
2
1
1
0
0
2
0
2
1
0
1
2
1
2
1
2
1
1
1
1
1
2
1
1
0
1
1
1
1
2
0
1
0
1
1
1
0
1
1
2
0
0
0
0
1
1
1
1
0
2
0
0
1
1
0
2
1
0
1
0
1
2
3
1
3
2
1
1
1
1
0
0
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
0
2
1
1
1
2
0
1
1
2
1
0
1
1
1
1
2
0
0
0
1
2
0
3
1
1
0
1
1
0
2
0
1
2
1
0
0
1
1
1
1
1
1
1
1
0
1
1
1
1
1
2
2
1
2
0
1
1
0
1
0
2
0
3
1
1
1
1
2
2
1
1
0
2
0
1
1
1
1
1
0
1
1
0
1
0
2
1
1
1
0
0
1
0
1
1
1
0
2
1
1
0
1
2
0
2
1
1
2
2
0
0
1
0
1
0
2
1
2
0
2
1
1
1
1
0
1
2
1
1
2
1
1
2
0
0
0
1
0
1
0
1
1
1
2
0
1
1
0
1
1
1
2
1
2
1
1
0
1
0
1
0
1
2
0
0
2
2
2
2
1
2
0
2
0
0
2
0
1
0
1
1
1
2
1
2
1
1
1
0
1
1
0
2
0
1
1
0
1
2
2
0
1
2
1
1
1
2
1
0
0
1
2
0
1
1
1
2
1
1
0
2
0
2
2
2
2
1
0
1
0
1
1
1
1
0
1
2
1
0
1
1
2
1
1
1
1
1
1
0
1
1
0
1
1
0
2
2
2
2
0
1
1
1
0
1
1
1
1
1
1
0
1
0
0
2
0
1
1
0
0
0
2
1
1
1
1
1
2
1
0
1
1
2
1
2
2
0
0
1
0
2
0
1
0
1
0
1
1
1
0
1
2
0
1
0
0
2
0
1
0
1
1
1
0
1
1
1
2
1
0
1
0
1
2
3
1
1
1
1
2
2
2
0
0
2
2
2
0
0
3
1
0
1
2
0
1
1
2
2
1
1
1
1
1
1
1
2
0
1
0
1
2
2
1
2
1
2
1
0
1
0
1
2
1
2
0
2
0
1
1
1
1
1
1
2
1
0
1
1
2
3
2
0
0
2
2
1
2
1
0
2
2
2
2
1
0
0
1
0
1
1
2
2
1
0
2
1
2
0
2
1
2
0
2
0
1
1
1
1
2
1
1
0
2
2
1
0
0
1
0
1
1
2
2
1
1
0
0
2
0
0
1
0
0
0
1
2
0
1
1
1
1
0
1
0
3
1
1
1
1
2
1
1
0
2
2
0
2
1
2
2
2
1
2
1
1
1
0
2
0
0
1
1
1
2
1
0
1
1
2
1
2
1
0
1
1
0
0
1
1
1
1
1
1
1
0
1
1
1
1
1
1
0
1
0
1
0
1
2
2
1
1
1
2
1
0
1
0
0
0
1
0
5
1
0
0
1
1
1
0
1
2
1
2
1
0
1
1
1
1
0
1
0
1
0
1
0
0
0
1
2
0
1
0
0
2
1
2
2
1
1
5
2
2
2
2
1
0
1
1
1
0
1
0
1
1
1
1
1
1
1
1
0
1
2
1
0
2
2
1
0
0
1
1
0
1
1
0
0
0
2
0
1
1
1
2
1
2
2
0
2
0
1
0
0
1
1
2
1
0
1
1
2
0
3
1
0
1
1
2
1
1
2
1
1
1
0
1
1
0
1
2
0
1
0
1
2
1
1
1
2
2
1
1
1
1
2
0
2
1
2
2
1
1
2
1
1
2
1
0
1
0
0
2
2
1
2
0
1
0
4
1
1
2
1
1
0
1
1
0
2
1
1
1
1
1
1
1
1
1
1
1
1
0
1
2
0
1
0
0
0
2
0
1
1
2
1
1
0
2
2
2
2
1
0
1
1
2
2
1
0
2
0
2
1
1
1
1
1
1
1
1
1
1
0
2
0
2
1
1
0
1
1
2
0
0
2
1
2
0
0
1
3
1
1
2
1
1
1
2
0
3
0
3
0
1
1
1
2
1
0
1
1
0
1
1
0
1
1
1
1
0
1
1
0
1
1
2
1
1
2
1
1
1
1
2
1
1
2
1
1
2
2
1
0
2
1
1
1
0
1
0
1
0
2
0
1
2
2
2
1
1
1
0
1
1
1
1
0
0
1
2
1
1
1
0
0
1
1
1
2
0
1
2
2
1
0
0
1
1
2
1
0
2
1
1
0
1
0
1
1
0
0
2
1
2
1
0
1
1
1
1
0
0
1
2
1
1
1
2
0
0
1
1
0
0
1
2
1
2
0
2
1
1
2
1
0
1
1
1
0
1
2
1
1
0
2
0
2
0
0
1
0
0
0
1
2
1
0
1
1
1
0
1
0
2
1
2
2
1
1
1
1
2
2
2
1
2
1
0
0
0
2
1
2
1
1
2
2
1
1
1
2
1
1
1
2
1
1
2
1
1
0
1
1
2
1
2
1
1
1
2
0
2
2
2
1
1
1
1
2
0
0
0
1
1
0
2
1
1
1
2
1
1
0
1
2
1
1
0
1
0
1
1
3
0
1
1
1
1
2
1
1
0
1
2
0
0
2
1
1
1
2
1
1
1
1
1
0
1
1
2
3
1
1
1
1
2
1
1
0
1
1
1
0
2
1
1
1
2
0
0
1
1
0
1
2
1
1
0
0
2
1
0
2
1
1
0
1
1
1
0
1
1
0
2
2
2
1
1
2
1
2
0
0
1
2
1
1
1
3
2
2
2
1
1
2
2
1
0
2
2
0
1
1
1
1
1
1
1
0
1
1
1
0
1
1
0
2
1
2
1
2
1
1
0
0
2
1
1
1
2
1
1
1
0
1
1
1
1
0
2
0
1
1
2
1
0
1
2
1
1
1
2
2
1
1
1
1
1
2
3
0
0
1
1
0
1
1
2
2
2
2
0
2
1
2
1
0
2
0
2
1
1
1
1
1
0
1
2
2
0
2
0
0
0
1
0
2
1
1
1
1
2
1
0
2
1
1
1
2
1
2
1
1
1
1
2
0
2
0
0
0
1
1
2
1
2
1
1
1
1
2
1
1
0
1
0
1
0
0
1
2
1
0
2
1
0
1
1
1
2
2
1
0
2
0
2
1
1
0
1
0
2
1
1
1
2
1
1
1
1
0
1
1
0
1
1
0
0
0
1
1
5
1
2
0
1
1
2
1
1
1
1
2
1
1
1
1
1
0
0
0
2
1
0
2
2
0
1
0
0
2
8
2
1
1
3
2
1
2
2
1
1
0
1
2
1
1
1
1
0
0
2
0
0
1
1
1
2
1
0
1
1
2
1
0
2
1
1
0
1
2
1
1
2
1
1
1
2
1
2
1
0
0
2
1
1
1
1
1
1
0
1
2
0
1
0
1
1
0
0
0
1
2
1
2
1
2
1
2
2
0
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
2
0
0
1
2
1
3
2
1
1
2
1
1
1
1
1
0
2
0
1
1
1
0
0
2
0
2
0
0
1
0
0
1
1
0
1
2
1
3
1
0
1
0
0
1
1
0
0
1
1
0
1
1
0
1
1
2
0
0
1
1
2
0
1
0
1
2
1
0
2
1
1
2
2
0
1
1
1
1
1
3
2
1
1
1
1
0
1
1
1
1
1
1
1
1
2
3
1
0
1
2
1
1
1
2
1
2
1
1
2
1
1
0
0
1
1
1
1
1
1
3
0
1
1
0
1
1
0
0
1
1
1
1
3
0
1
2
1
2
1
1
1
1
1
0
2
2
1
0
0
0
1
1
0
2
1
0
1
0
1
0
1
1
1
2
3
1
1
1
2
1
0
2
1
2
1
2
1
1
1
2
0
1
1
2
1
1
1
2
1
1
1
1
1
0
2
6
1
1
0
0
0
2
1
1
0
0
1
1
0
0
2
1
0
0
1
2
1
1
1
2
1
2
1
0
0
1
1
1
0
0
1
0
1
1
2
2
1
0
2
1
0
1
2
2
1
0
2
2
2
1
3
2
1
2
1
2
1
1
1
2
1
1
1
1
2
1
0
0
1
1
0
0
1
0
1
1
1
0
2
1
1
0
1
1
1
2
1
1
1
2
0
1
1
1
2
0
1
0
2
0
1
1
0
0
1
0
2
2
1
1
1
1
2
0
1
0
1
2
2
1
1
1
1
1
2
1
1
1
1
2
1
2
1
0
1
1
1
1
0
1
1
1
2
1
0
2
0
2
2
1
2
1
0
6
1
2
2
1
2
1
1
2
0
1
1
1
0
1
1
0
1
3
1
1
1
2
0
2
2
0
1
1
1
1
1
1
0
0
2
0
0
0
2
1
1
1
2
1
1
0
0
1
0
1
1
0
0
2
0
3
0
2
0
1
1
0
1
1
3
1
1
1
1
1
1
0
2
1
1
1
1
1
1
1
2
0
2
0
2
1
1
1
1
1
1
0
0
0
0
1
1
1
1
0
1
0
1
1
1
1
0
0
2
2
1
2
2
1
1
1
0
0
1
2
2
1
0
0
2
1
2
4
2
2
0
1
2
1
0
0
0
1
1
0
1
1
1
1
2
1
1
0
2
2
0
1
0
2
0
1
1
1
1
1
1
1
1
1
2
0
2
1
2
1
2
1
1
1
1
1
1
1
0
2
2
1
1
0
2
2
1
2
1
1
1
1
1
0
2
0
0
1
0
1
1
1
1
0
1
1
2
0
2
2
1
2
2
0
1
2
1
2
3
2
1
1
3
2
5
0
2
1
0
6
2
1
2
2
0
0
1
1
1
1
2
2
1
0
0
0
1
1
1
1
1
1
2
1
0
1
0
1
1
0
1
1
1
0
1
1
1
1
1
1
0
2
1
1
2
1
0
0
2
0
1
1
2
2
1
1
2
1
1
1
1
1
1
1
0
3
2
0
2
0
1
1
2
3
2
1
1
1
0
1
2
2
1
0
0
1
2
1
2
1
2
6
1
0
0
2
1
3
1
1
1
1
1
1
1
1
1
0
2
1
2
0
1
1
2
3
1
1
1
0
1
1
2
1
2
0
0
1
1
0
2
0
0
2
1
1
1
0
1
2
3
0
0
1
1
0
1
0
0
2
1
1
2
1
1
1
3
1
1
2
1
1
0
1
1
1
1
1
1
2
1
0
3
1
1
2
0
2
1
1
1
0
0
2
0
1
1
0
1
0
1
1
1
1
1
0
0
1
1
1
1
2
2
1
1
1
1
1
1
2
0
0
5
1
0
2
1
0
1
1
1
1
1
0
1
2
2
1
1
1
2
1
2
0
1
0
0
0
0
1
2
1
0
0
1
1
0
2
0
2
1
1
0
1
1
0
1
1
2
2
1
1
2
0
0
1
1
1
0
2
0
0
1
0
2
2
0
2
1
0
1
2
1
2
1
1
1
1
0
1
1
1
1
0
2
1
1
0
0
3
2
2
0
1
0
2
1
2
1
1
2
0
1
1
1
1
1
1
1
0
2
1
0
3
1
0
1
1
2
0
1
0
2
1
1
2
0
1
0
1
1
1
0
0
1
0
1
2
0
1
2
1
2
1
1
1
1
1
1
1
0
1
2
0
0
2
1
1
0
1
0
1
1
3
2
1
2
1
1
1
1
2
1
1
2
1
0
2
0
0
1
0
1
1
0
2
0
1
1
0
1
1
1
1
0
1
1
1
1
2
1
0
1
2
2
1
0
2
1
0
2
2
0
1
1
1
0
0
1
0
2
0
1
2
1
1
1
1
1
0
0
1
1
1
0
1
2
0
1
1
0
0
1
1
1
1
1
1
1
2
1
1
1
0
0
2
2
3
1
1
0
1
1
0
0
1
0
0
3
1
0
1
1
1
2
1
1
1
2
1
1
1
0
2
1
0
2
0
1
1
1
1
1
1
0
0
1
0
1
1
2
0
2
1
2
2
0
1
2
1
0
1
1
1
1
1
1
1
1
1
3
2
1
0
0
2
2
2
1
1
2
0
1
1
2
1
0
1
1
1
1
1
2
0
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
0
2
0
1
0
2
0
1
1
2
1
1
2
0
1
0
1
1
1
2
1
1
1
0
2
0
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
0
2
1
1
1
1
0
2
1
2
1
1
2
2
1
1
2
2
2
0
2
1
0
1
1
1
0
2
1
0
0
2
0
0
1
2
2
1
1
1
0
1
0
1
1
0
2
1
2
1
1
2
0
3
0
2
0
1
1
1
0
1
1
1
1
2
1
0
1
1
1
1
0
2
2
1
1
0
0
0
1
1
1
1
1
0
1
0
0
1
1
1
1
1
1
1
1
2
2
2
1
0
1
2
0
1
3
1
2
0
1
1
1
1
1
0
1
1
1
0
1
1
1
1
2
2
0
2
1
1
1
1
0
1
1
1
1
1
2
1
1
1
2
0
1
1
1
1
1
0
2
1
0
0
2
2
2
1
1
2
1
1
0
1
1
1
1
3
2
0
2
1
0
1
1
0
1
0
2
2
2
1
0
0
0
0
0
1
2
3
0
3
1
2
0
2
0
2
1
0
0
0
0
2
2
0
1
1
2
0
0
1
0
1
1
1
1
0
1
1
0
1
1
1
1
1
0
1
1
1
1
2
0
1
1
1
1
2
1
1
1
1
0
1
2
2
1
1
0
2
1
0
1
1
0
0
1
0
1
1
1
1
2
2
2
1
1
1
2
0
1
1
1
2
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
2
1
1
1
1
1
2
1
0
1
4
1
0
1
0
1
1
1
2
1
1
1
0
0
2
2
1
2
1
1
0
2
1
2
1
0
1
1
1
1
1
1
2
1
1
0
1
1
0
1
1
1
0
2
2
1
1
1
0
0
1
1
1
1
1
1
0
1
2
0
1
1
1
1
1
1
2
0
0
1
1
1
0
2
1
0
0
1
2
0
2
0
0
2
1
2
1
1
1
0
0
1
1
1
0
0
1
1
1
1
0
0
0
1
2
1
0
2
1
2
2
0
1
0
1
1
1
0
1
2
1
2
2
2
1
1
1
1
0
0
1
1
0
2
1
0
0
2
2
0
1
0
1
0
1
2
1
0
1
1
1
1
1
2
1
1
1
0
0
2
2
0
1
2
1
1
1
1
1
0
1
0
1
2
1
1
1
2
1
0
0
1
1
1
0
1
2
1
0
2
2
1
1
1
0
1
1
1
1
1
1
0
0
1
0
0
1
1
1
2
1
2
2
1
2
1
1
1
2
2
1
1
1
2
1
1
1
2
0
1
1
2
1
1
1
1
1
0
1
1
2
2
1
1
2
0
1
0
1
0
1
0
1
1
3
0
0
2
2
1
0
1
1
2
1
1
1
1
1
1
1
0
1
1
1
2
3
2
1
1
1
1
0
2
1
1
2
0
0
2
1
1
1
0
0
2
1
0
2
1
0
1
2
1
0
1
0
1
3
1
1
1
1
1
2
1
2
0
2
1
2
2
0
2
0
1
2
1
1
0
1
2
0
2
0
0
0
0
0
1
1
1
1
1
0
1
1
1
1
2
2
3
1
1
1
1
1
1
1
2
1
0
1
2
2
0
1
2
1
0
1
1
2
2
2
1
1
2
0
1
1
1
0
1
1
0
1
3
1
1
0
1
2
0
1
1
1
1
1
1
1
0
1
2
1
2
1
1
0
2
1
0
1
0
1
1
1
1
1
0
1
0
1
1
1
1
2
1
1
0
2
0
2
0
1
1
2
0
1
1
2
1
1
1
1
2
1
1
1
0
0
2
3
1
1
1
2
2
2
1
1
0
1
0
1
1
1
1
1
1
2
0
0
1
2
0
0
1
2
1
1
2
1
0
1
1
1
1
1
0
1
1
1
1
0
1
0
0
1
0
0
0
0
1
1
1
2
0
1
2
2
0
2
2
1
1
1
0
2
0
0
2
2
1
1
1
0
1
0
2
0
2
1
1
0
1
1
1
1
2
0
2
2
1
0
0
2
0
0
1
1
0
2
2
2
0
1
1
1
2
1
0
1
1
1
1
1
1
2
2
1
0
1
1
1
1
1
0
1
1
0
1
2
3
1
0
0
1
0
2
1
1
1
2
0
0
1
1
1
1
2
1
1
1
0
2
1
1
1
1
4
0
2
2
1
1
1
1
0
1
1
0
1
1
0
0
1
0
1
2
1
2
2
0
0
1
1
1
1
0
2
2
1
1
0
0
1
1
1
0
2
0
1
0
2
1
0
0
1
0
0
0
1
2
2
1
1
1
1
2
0
0
2
2
2
1
0
1
0
1
1
1
0
1
0
1
1
2
1
1
0
1
1
0
1
2
1
1
0
1
1
1
0
0
0
1
0
2
2
0
1
2
1
0
1
1
0
2
2
1
1
1
2
2
0
1
1
1
1
2
1
1
1
1
3
1
1
1
0
1
0
1
0
1
1
1
1
1
1
0
0
1
0
0
0
1
2
1
1
2
1
1
0
1
0
1
1
0
1
1
1
2
1
2
1
1
1
1
1
2
1
0
2
1
0
2
2
2
2
1
1
2
0
2
0
0
0
1
1
2
1
0
1
2
1
1
0
2
2
0
2
1
0
2
0
2
0
2
2
0
1
1
1
0
0
2
1
0
2
2
1
1
2
0
0
1
2
1
0
1
1
2
0
0
1
1
2
0
0
0
2
1
1
1
1
0
1
2
1
2
1
1
0
1
0
1
1
0
0
2
1
1
2
1
2
0
1
1
1
1
0
2
2
1
2
1
1
0
0
1
1
1
1
0
1
1
0
0
2
1
0
2
2
0
0
0
1
1
1
0
1
2
0
2
0
0
1
1
2
1
0
1
2
1
0
0
1
0
2
0
1
1
1
2
1
0
1
1
1
0
1
1
0
0
1
0
0
2
1
1
0
1
1
0
0
1
0
1
0
1
0
1
1
2
0
0
2
1
1
2
1
1
1
1
0
1
0
0
3
1
0
0
1
2
1
1
0
1
1
1
2
1
0
1
1
2
1
1
0
1
0
2
1
1
0
1
1
1
1
1
1
0
0
1
0
0
1
2
1
0
2
2
1
1
0
0
0
1
1
1
1
2
1
1
2
2
1
1
2
1
1
2
1
1
0
1
0
2
2
0
1
2
0
1
1
2
1
0
1
2
1
2
1
0
1
1
0
1
0
3
3
1
0
0
1
1
1
1
2
2
2
1
0
1
0
0
0
1
1
0
2
2
1
1
2
2
1
0
1
1
2
0
1
1
1
2
0
2
1
1
1
1
2
0
1
2
1
1
1
1
1
0
1
1
0
0
1
1
1
0
1
1
1
1
0
1
2
1
1
1
1
2
0
1
1
1
1
2
2
1
0
0
2
2
0
1
0
0
0
1
0
0
1
1
1
1
2
1
1
0
1
0
1
1
2
1
0
1
1
1
2
0
1
1
0
2
1
1
0
2
1
1
1
1
1
5
1
0
2
1
2
1
2
1
1
1
2
2
1
1
2
2
2
1
0
2
1
1
2
2
3
1
1
1
1
1
1
1
2
0
0
0
1
1
0
1
1
2
2
0
0
1
1
2
1
1
2
2
1
1
1
0
0
1
3
1
1
1
1
1
2
2
2
1
0
1
1
1
1
1
1
1
1
1
0
0
1
2
1
1
1
0
1
1
0
1
1
1
0
1
2
1
1
0
2
1
0
0
1
1
0
1
1
2
1
0
1
0
1
1
0
0
0
2
0
1
0
2
1
1
1
2
0
1
1
1
2
1
0
1
1
2
2
2
1
2
1
0
1
1
0
1
1
1
1
2
1
2
1
1
1
0
1
2
0
1
1
1
1
0
1
1
0
2
1
1
1
1
2
1
1
1
2
0
0
1
1
1
2
1
0
0
1
1
1
1
1
0
2
0
1
0
1
2
1
0
1
1
1
1
0
1
0
0
0
1
1
0
2
1
1
0
0
2
1
0
2
2
1
0
1
0
1
1
1
1
0
0
2
1
1
2
1
1
1
1
1
2
0
1
1
2
1
1
2
1
1
1
1
2
1
2
1
1
1
1
2
1
1
2
2
1
1
1
0
1
2
1
2
1
1
2
1
2
1
1
0
1
1
1
2
1
1
1
1
1
2
1
1
1
1
0
0
1
1
2
2
0
1
1
1
2
1
0
1
1
1
0
0
0
1
1
0
1
0
1
1
1
0
1
1
1
1
1
0
1
5
0
2
1
1
0
1
1
0
0
0
2
1
0
1
2
1
1
1
0
0
0
1
1
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
0
1
2
0
1
0
2
1
2
1
1
1
0
0
1
0
2
0
2
1
0
2
2
1
2
1
1
1
1
2
1
0
1
3
0
2
2
2
0
1
0
1
1
2
2
1
2
2
1
1
0
0
0
7
0
1
1
0
1
1
1
1
1
0
1
1
2
1
1
1
1
2
2
0
1
2
1
0
1
2
1
2
1
1
2
1
2
0
1
1
0
1
1
0
0
1
1
0
2
0
1
2
1
0
2
1
1
0
1
1
1
0
1
0
1
1
0
2
1
1
0
1
1
1
0
0
0
0
0
2
2
1
1
1
2
1
2
1
0
0
0
1
1
1
1
1
1
1
0
1
2
0
1
1
2
0
2
1
1
1
1
0
1
2
1
1
2
2
1
1
2
2
2
2
1
1
2
1
1
1
3
1
1
2
1
1
1
2
0
0
0
2
2
1
1
1
1
0
1
1
1
1
0
1
1
2
1
1
2
0
2
2
0
1
1
3
2
1
1
1
2
0
1
1
1
2
0
1
1
0
1
1
2
1
1
1
0
1
1
0
2
2
1
1
1
1
1
0
1
2
0
1
0
1
1
1
0
0
2
0
1
1
0
1
0
1
1
0
1
1
2
1
1
0
2
0
1
0
2
1
2
2
0
2
2
1
1
2
1
0
2
2
0
2
0
0
3
0
1
2
1
0
0
1
1
0
2
1
2
0
1
0
1
1
2
1
1
2
0
2
1
2
1
0
2
2
1
2
1
1
1
1
1
2
3
2
1
1
2
2
1
0
0
1
0
1
0
0
0
0
1
2
1
2
0
2
0
0
1
1
1
2
2
2
1
0
1
0
1
1
1
2
1
1
0
1
2
1
0
2
1
0
1
1
2
1
0
1
0
1
2
1
0
1
2
1
0
1
1
1
1
2
2
0
1
1
2
1
1
1
1
1
2
0
0
1
1
0
2
1
1
1
2
1
1
0
2
1
1
2
1
1
1
0
1
1
2
0
1
1
2
1
1
0
1
0
1
1
0
0
1
1
1
2
1
1
1
1
2
1
0
1
1
1
1
2
2
0
1
2
1
0
1
1
1
1
2
0
1
0
0
1
1
1
1
2
1
0
2
0
2
0
2
1
0
2
1
0
0
2
1
1
2
0
0
2
1
0
0
1
1
0
2
0
0
0
1
1
1
2
2
2
1
1
3
1
2
2
2
1
2
0
1
1
1
0
2
0
0
1
1
1
0
1
1
1
1
1
0
1
1
1
1
0
1
0
0
1
1
1
1
1
1
1
0
1
1
1
0
0
0
1
2
1
1
1
1
1
2
1
2
2
1
0
1
0
1
0
0
0
1
1
1
1
2
1
0
0
0
1
1
2
1
0
0
0
1
0
0
1
0
2
0
1
0
0
0
1
1
1
1
2
2
1
0
1
2
1
1
1
1
0
1
1
1
1
0
1
1
1
0
0
0
1
2
0
2
0
1
1
1
2
1
1
2
1
1
2
0
0
1
0
1
1
1
0
2
1
2
1
1
1
2
2
1
2
1
0
2
1
0
2
1
0
0
1
0
0
2
0
1
1
0
1
0
3
1
2
1
0
1
2
1
0
1
1
2
1
1
1
0
4
2
0
2
2
1
1
0
1
1
1
2
0
1
1
1
2
0
1
1
1
0
0
0
1
1
1
1
3
1
2
0
2
1
1
1
0
1
1
1
1
1
1
2
1
1
2
1
1
1
2
1
2
2
0
0
1
2
1
1
0
2
1
0
2
1
1
2
0
2
0
1
1
0
1
0
2
1
0
2
1
1
2
1
1
1
1
0
1
1
0
0
0
0
1
2
1
1
3
2
1
2
2
1
1
0
2
2
2
1
1
1
1
1
1
1
0
1
1
1
0
0
1
1
2
1
1
2
1
2
0
2
1
1
2
0
2
1
1
1
1
2
1
2
1
0
1
1
2
1
2
2
2
1
0
2
0
1
0
1
1
0
1
0
1
1
0
2
1
1
0
0
1
2
2
1
1
1
1
1
2
0
1
0
1
0
1
1
2
1
1
0
0
0
1
2
2
2
1
2
0
1
1
0
2
3
2
1
1
2
0
1
1
1
0
1
1
1
1
1
2
1
1
2
2
1
0
2
1
1
1
0
2
1
2
2
1
2
1
2
1
2
1
0
1
1
0
1
2
0
2
1
1
1
2
0
1
1
1
0
2
0
1
1
1
2
0
1
3
1
0
1
2
0
2
1
1
0
0
1
1
1
1
1
2
1
0
0
0
1
0
1
1
1
0
2
1
1
0
2
0
2
0
1
0
2
1
1
0
0
1
2
0
1
2
2
1
0
1
0
1
0
1
1
1
2
1
2
1
2
1
0
1
0
1
1
1
1
1
1
1
1
1
0
2
1
1
1
2
1
0
1
2
1
1
1
2
1
2
1
1
0
1
1
2
1
1
2
2
0
1
1
1
1
1
2
1
0
1
1
0
1
1
2
1
2
1
2
0
3
1
0
2
0
2
1
2
1
1
1
2
0
1
0
0
1
1
1
1
1
0
0
1
1
2
0
1
1
1
2
0
1
1
2
1
1
1
1
0
1
1
1
3
1
1
0
0
1
0
0
1
0
2
0
1
1
1
2
2
1
0
1
1
1
1
0
0
1
1
1
0
0
1
0
1
1
1
2
1
1
1
0
1
2
1
0
0
0
0
1
0
0
1
1
2
1
1
0
1
1
1
1
2
1
1
1
1
0
2
0
2
0
0
2
2
1
0
1
0
2
0
1
1
1
1
2
3
2
0
0
2
2
2
0
2
0
1
1
2
0
1
1
0
1
1
0
0
2
0
2
1
1
1
1
0
1
1
0
2
1
2
1
2
1
1
0
1
2
1
1
1
1
1
0
0
1
1
1
1
1
2
1
2
1
1
2
2
0
0
2
1
2
2
2
2
1
2
2
1
1
0
0
1
1
0
2
1
2
1
1
0
1
2
0
2
1
0
2
1
0
2
1
0
0
1
1
1
1
0
2
1
1
2
1
1
1
1
4
1
2
1
2
1
1
0
1
1
2
1
1
0
1
2
2
1
0
2
1
1
0
0
1
1
1
1
0
1
2
1
0
0
0
0
1
0
1
1
1
0
2
1
2
1
0
1
0
1
1
1
1
0
1
2
1
1
2
2
0
1
0
1
1
0
1
1
2
1
1
0
2
1
2
0
2
1
0
0
0
2
1
1
1
2
1
0
3
0
1
1
1
2
0
2
2
1
1
2
3
0
1
0
1
1
1
2
3
1
0
1
1
1
0
2
1
1
1
2
1
0
0
1
1
1
1
0
1
2
1
2
1
0
0
1
1
1
1
2
0
0
0
1
2
1
1
0
1
2
1
1
1
2
1
1
1
2
0
0
0
1
1
1
1
1
0
1
2
1
1
1
1
2
0
0
2
1
1
2
1
0
1
0
1
1
1
0
0
0
1
0
1
2
0
0
2
1
1
1
2
1
1
1
1
1
0
2
2
0
1
1
2
1
0
1
2
1
2
0
1
2
0
1
2
1
0
0
1
0
2
1
1
1
0
1
2
1
0
1
1
1
0
1
0
0
1
1
1
2
0
1
1
1
1
1
1
2
0
1
1
0
1
1
2
0
1
1
1
1
0
1
2
1
1
2
1
0
1
2
1
0
0
0
1
1
1
1
1
0
1
0
1
2
2
0
0
1
0
1
2
2
1
0
1
0
1
1
1
0
1
1
2
1
1
2
1
1
0
2
1
1
1
1
2
1
2
1
0
1
0
0
2
1
1
0
1
1
1
2
0
1
1
1
2
1
1
0
0
1
1
1
2
1
2
0
0
1
2
0
0
1
1
0
1
2
0
0
1
2
0
1
1
1
0
1
2
1
1
2
0
0
1
1
0
1
1
0
1
1
1
1
1
0
0
0
0
1
1
1
2
2
0
2
1
2
1
1
2
1
0
1
0
0
1
1
0
1
0
1
1
1
2
2
1
1
2
1
1
1
0
3
1
1
0
0
1
1
1
1
1
0
1
2
2
1
0
2
1
2
2
0
2
2
1
1
1
2
2
1
1
1
2
1
0
1
2
1
1
0
0
0
2
2
2
1
0
2
2
1
1
1
1
2
1
0
1
0
1
2
1
1
1
0
0
0
1
1
2
0
0
0
2
0
1
0
1
0
0
1
1
1
2
2
1
1
1
1
0
1
1
1
2
2
0
0
0
1
0
1
1
1
1
2
1
1
1
2
1
0
2
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
0
1
1
1
0
0
1
0
1
3
2
1
0
2
1
1
3
4
1
1
1
1
1
2
1
0
1
2
1
0
1
1
2
1
1
1
1
1
0
1
0
1
1
2
1
1
2
1
2
1
1
0
0
2
1
1
2
1
1
1
2
1
1
1
0
0
1
2
2
2
2
1
3
1
1
1
1
1
2
0
0
1
0
2
1
1
1
2
1
2
1
1
0
1
1
0
0
1
1
0
1
1
0
2
1
2
2
1
0
0
0
1
0
0
2
1
2
0
2
1
0
0
1
1
1
2
0
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
2
2
1
1
1
1
2
0
1
1
0
0
0
2
1
1
0
1
1
0
0
1
1
0
1
0
0
2
2
0
1
0
1
1
1
3
1
0
1
0
1
1
0
1
1
0
1
2
1
2
1
0
2
0
0
1
0
1
2
1
0
2
0
1
1
1
1
2
1
2
0
1
1
1
0
1
2
1
1
2
1
1
1
0
1
0
0
0
1
1
1
1
0
0
1
1
0
0
1
2
1
1
1
1
1
1
0
0
1
2
1
1
0
1
2
2
0
1
2
1
2
0
2
1
1
1
2
1
1
1
2
1
1
1
1
0
1
0
1
0
2
1
0
2
2
0
2
1
2
0
3
0
0
1
1
1
0
1
1
1
1
1
1
1
1
1
2
0
0
1
1
2
0
2
1
0
0
2
2
0
1
0
2
0
0
1
1
1
1
1
2
1
1
0
1
2
2
1
1
0
1
2
1
0
0
0
1
0
2
2
1
2
2
0
2
0
1
1
1
1
0
2
1
0
2
1
1
0
1
1
1
0
1
0
0
2
1
1
1
0
0
1
2
0
3
1
1
1
1
1
1
1
2
1
1
0
1
0
2
2
2
1
2
1
1
0
1
1
2
1
1
1
1
1
0
0
1
1
1
1
1
1
1
1
2
1
0
1
2
0
2
0
1
2
1
1
1
0
1
1
2
0
0
0
0
2
1
1
2
0
1
0
1
1
0
1
1
1
1
2
0
1
1
2
0
1
2
1
0
1
0
1
2
0
2
2
2
1
1
0
1
1
1
1
1
2
2
1
1
1
1
1
0
1
1
0
1
1
1
1
1
0
1
0
0
2
1
0
1
1
2
1
1
1
0
2
1
2
0
2
0
2
1
2
1
0
1
1
0
1
2
2
1
1
0
1
1
1
1
1
1
3
2
0
0
1
1
1
2
1
0
0
1
1
1
1
1
1
0
0
0
1
1
1
1
1
1
2
2
1
0
0
1
2
0
1
0
1
2
1
0
2
1
2
2
0
1
1
1
1
1
1
1
0
1
0
1
1
2
1
2
1
0
1
2
0
1
3
1
0
0
1
0
1
1
1
2
1
0
1
1
2
1
0
1
1
2
0
2
2
1
1
1
2
1
2
2
1
1
1
2
0
1
1
1
1
1
1
0
3
1
0
2
1
1
1
0
1
1
0
0
0
1
2
1
1
2
2
1
2
1
0
1
0
1
2
1
2
0
2
1
2
0
2
2
1
1
1
1
2
2
0
1
1
0
0
0
0
1
1
2
0
0
1
0
1
1
1
1
1
2
1
2
1
0
2
1
1
0
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
0
0
2
1
2
1
1
0
2
0
1
1
2
0
1
1
1
1
1
1
2
0
2
2
1
1
1
0
2
0
0
0
1
2
1
2
1
0
0
0
2
2
0
0
2
2
0
0
1
1
1
1
0
1
1
2
0
0
2
1
1
0
2
0
0
1
1
0
1
0
0
1
1
4
0
1
1
2
3
1
1
1
1
0
0
2
1
1
1
0
1
0
1
0
2
1
1
1
2
1
1
1
0
3
2
2
1
0
1
1
1
1
2
2
0
1
0
1
2
1
0
2
2
0
0
2
1
1
1
1
0
1
2
0
1
1
1
2
1
1
1
2
2
1
2
2
0
0
2
0
1
0
2
1
1
1
1
1
1
0
1
0
2
1
0
2
1
1
2
3
1
1
1
1
1
2
1
0
2
1
0
2
1
0
1
1
0
0
1
0
2
1
0
2
1
1
0
0
2
0
1
1
1
0
0
0
0
0
0
2
1
1
0
1
2
1
3
1
1
0
1
1
1
1
1
0
1
1
1
1
1
0
0
1
1
2
1
0
1
2
0
0
0
1
2
2
0
1
1
1
1
0
2
2
2
0
1
1
0
0
1
1
1
2
0
1
1
1
0
2
1
1
1
2
0
2
1
0
1
1
1
1
1
1
0
0
1
1
1
1
1
1
1
1
2
1
1
1
0
1
1
1
0
1
1
2
2
1
2
1
1
2
0
0
2
0
1
1
2
0
2
1
2
0
2
1
0
0
1
0
2
1
1
2
0
1
1
1
0
2
1
2
2
2
1
1
2
1
0
1
1
0
0
1
2
1
0
0
0
0
0
0
0
1
0
1
1
0
0
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
0
1
2
2
1
2
1
1
2
0
1
1
0
2
2
1
1
0
1
1
1
0
0
0
2
0
0
1
0
1
1
0
1
1
1
1
1
0
1
2
1
1
1
0
1
0
0
1
1
0
0
2
2
1
1
2
0
1
1
1
1
1
1
2
3
2
0
1
0
2
1
0
1
0
1
1
1
2
2
2
0
1
2
2
2
1
2
2
2
2
0
1
0
1
2
0
0
0
1
1
2
1
1
1
0
1
0
1
1
1
0
1
1
1
2
1
0
0
0
0
1
2
1
2
0
0
1
2
0
0
0
1
0
0
1
1
2
1
1
2
0
0
1
2
0
0
2
1
0
0
1
0
1
1
2
2
1
1
1
1
1
2
1
1
1
0
2
0
2
3
1
0
1
1
2
1
0
2
2
1
2
2
2
0
2
0
1
1
2
1
1
1
1
1
1
2
1
1
1
0
2
2
2
1
1
1
1
1
2
1
1
1
1
1
1
0
1
4
1
2
2
1
2
2
1
0
0
0
1
1
2
2
2
0
1
1
1
1
1
1
0
1
2
0
0
1
0
1
1
0
2
1
0
0
0
2
2
0
2
1
1
0
0
0
0
1
1
1
2
0
1
1
0
1
2
1
1
1
2
2
3
1
2
1
1
0
0
1
0
1
1
2
1
1
1
0
2
2
1
1
1
1
2
1
1
1
0
1
0
1
1
2
0
1
1
2
0
1
1
1
2
0
1
1
2
0
0
2
0
0
2
1
1
2
2
1
0
0
1
1
1
0
1
0
1
1
1
0
2
1
0
2
1
1
1
1
0
1
2
2
2
0
1
0
2
1
1
0
1
1
1
1
0
1
1
0
1
1
0
0
1
1
1
1
0
1
1
1
1
1
0
0
1
1
1
1
1
1
1
0
2
1
1
1
0
1
1
1
0
2
1
0
2
1
0
1
0
2
0
0
2
0
1
1
1
2
1
2
1
0
1
2
1
0
2
2
1
2
1
0
0
1
1
0
1
0
1
1
1
1
2
3
2
2
0
2
2
2
1
2
1
1
0
1
1
0
2
1
2
1
0
0
1
0
0
0
0
0
0
2
0
1
1
1
1
1
1
0
0
0
1
2
1
1
1
0
2
1
0
1
1
0
1
1
2
1
1
2
1
1
1
1
1
1
0
1
1
1
0
1
1
1
2
2
1
0
2
1
2
0
0
0
0
0
1
2
1
1
1
0
1
1
1
0
0
1
0
1
0
1
2
1
0
1
1
2
0
1
0
1
1
1
1
2
1
1
1
2
0
2
2
1
1
1
1
1
0
2
1
1
2
0
1
1
1
1
1
1
2
3
2
1
1
2
1
1
3
1
0
2
0
1
1
3
0
1
1
1
2
2
2
2
1
1
2
4
1
1
0
1
1
1
2
2
0
0
1
1
1
0
0
0
2
2
1
1
1
2
0
2
2
2
0
2
2
2
0
0
1
1
1
1
1
2
0
0
2
1
0
0
2
2
0
1
1
1
0
0
0
1
1
0
1
1
2
1
0
2
1
1
1
1
0
1
2
1
1
2
0
0
2
1
1
1
2
1
1
0
1
2
2
1
0
2
0
1
0
1
1
2
2
1
1
1
1
1
1
0
2
1
1
2
3
1
0
2
0
2
1
1
1
1
1
1
0
0
0
1
1
0
1
1
2
0
0
1
1
2
1
2
4
1
2
2
1
1
2
1
1
1
0
0
1
1
0
1
1
1
1
0
2
0
1
0
1
0
2
1
1
0
1
1
0
1
0
1
0
1
1
0
0
1
1
0
1
2
1
2
2
1
2
0
1
1
2
1
1
1
2
2
1
1
2
2
1
0
1
1
1
0
2
1
1
0
1
1
1
1
1
0
2
2
1
1
2
2
0
1
0
2
0
2
1
0
0
1
1
1
1
0
1
1
1
0
1
2
1
1
1
1
1
2
3
2
0
0
2
0
2
0
1
2
0
0
1
1
0
1
0
1
2
0
1
0
1
0
1
2
1
2
2
0
1
2
0
1
1
1
2
0
0
0
1
2
1
2
1
1
0
0
2
1
1
2
0
1
1
0
1
0
1
1
1
1
1
2
0
0
2
1
1
2
3
3
1
1
2
0
1
3
1
0
1
1
2
1
2
1
2
1
2
1
0
2
1
1
1
1
2
1
1
1
1
2
0
2
0
0
2
1
1
2
1
1
0
1
0
2
1
1
1
0
2
2
2
1
1
1
1
2
1
1
1
2
2
1
1
0
2
1
2
1
2
0
2
1
2
1
1
1
1
1
2
2
1
2
1
1
0
1
1
1
1
2
1
2
1
1
1
2
1
2
1
1
0
1
2
2
1
1
1
1
1
1
2
1
2
0
1
2
1
2
0
1
1
2
0
1
0
1
0
1
1
1
2
1
2
2
0
1
1
0
2
1
0
1
1
2
0
2
1
1
1
1
1
1
1
1
0
1
1
1
1
0
2
0
1
1
0
1
0
1
2
0
1
0
1
1
1
0
1
1
1
1
1
3
2
1
1
2
1
1
1
1
2
1
1
1
2
1
0
0
0
1
1
2
1
2
2
0
1
0
1
1
2
0
0
1
2
0
1
1
1
2
2
1
2
1
0
2
2
1
2
0
1
2
1
2
2
1
1
1
1
1
1
1
2
1
1
2
2
2
1
0
0
1
1
1
0
1
0
1
1
1
0
1
1
1
1
1
2
1
2
0
1
1
2
2
1
1
2
0
2
2
0
1
0
1
1
1
1
0
0
0
1
1
2
2
1
1
2
1
1
2
1
0
1
1
2
0
0
0
1
2
1
1
0
2
1
1
2
0
2
1
0
1
1
0
1
1
0
1
1
1
1
3
1
0
1
0
1
1
1
0
1
1
1
1
1
1
1
0
1
1
2
1
0
2
1
1
1
1
2
1
1
1
2
0
1
2
1
1
0
1
0
0
1
1
2
0
1
1
1
2
2
1
1
2
2
2
2
1
1
1
1
2
1
2
0
1
0
2
1
2
1
0
1
0
1
1
1
0
0
1
3
1
0
1
1
2
0
0
2
1
1
1
1
0
0
0
0
1
1
0
1
1
2
0
1
2
0
0
1
1
3
1
1
0
1
2
1
1
0
1
1
0
2
2
0
1
1
1
1
1
1
0
1
2
1
1
0
1
1
0
1
1
1
1
1
0
1
2
1
1
1
1
0
1
0
2
1
1
1
1
1
1
2
1
1
0
1
2
1
1
1
1
1
0
1
1
1
1
1
1
1
1
2
1
1
1
0
2
1
2
2
1
0
2
1
0
2
1
2
2
1
0
1
0
0
1
1
1
1
2
1
0
2
2
2
1
1
2
1
0
0
1
2
2
1
0
1
0
1
1
0
2
2
0
2
1
1
1
0
1
2
1
0
1
1
1
1
2
2
1
1
1
1
0
1
2
2
2
0
0
1
1
1
2
1
2
1
2
0
2
0
1
1
0
1
1
2
0
1
1
1
2
0
0
2
1
1
3
2
0
2
0
2
0
0
1
0
2
0
0
0
1
2
2
1
1
1
1
1
1
0
0
0
1
1
0
2
1
1
1
1
2
1
0
1
1
1
1
1
1
2
1
1
1
0
1
2
1
0
1
0
1
0
2
1
1
0
0
2
0
2
1
1
2
1
1
2
1
0
2
1
0
1
0
1
1
0
0
1
1
2
1
1
1
1
2
1
0
0
1
1
2
2
1
1
1
0
1
1
2
0
1
1
1
1
1
0
1
2
1
1
0
2
1
1
1
0
0
0
1
1
1
2
1
1
2
1
2
1
1
2
2
1
1
1
0
1
0
2
1
0
0
0
0
2
1
1
1
1
1
1
2
1
2
0
1
1
1
1
0
1
2
1
2
0
1
2
2
2
0
0
0
1
1
2
1
1
0
1
1
1
1
2
0
1
1
0
2
0
0
2
1
1
1
2
2
1
2
3
0
1
0
1
0
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
0
0
1
1
1
1
2
2
0
2
1
2
1
1
1
1
1
2
2
0
2
1
2
1
0
2
2
1
0
2
0
1
0
1
1
2
0
2
1
1
2
1
1
0
0
1
1
1
1
2
1
2
2
1
1
1
0
1
2
0
2
1
2
0
2
1
0
2
1
0
2
0
0
0
1
0
0
0
1
1
1
1
1
1
0
6
1
2
0
1
1
2
1
0
1
0
2
0
0
1
1
1
1
0
1
1
1
1
1
1
1
1
0
2
1
1
0
1
1
1
0
1
2
2
1
2
0
1
1
0
0
1
1
1
0
1
2
0
1
1
1
2
1
1
1
1
1
1
1
1
0
1
0
1
2
0
2
2
1
2
1
1
0
1
0
3
1
0
1
2
0
0
0
0
1
0
1
0
1
1
1
2
1
1
2
1
0
0
2
2
1
1
2
1
1
1
1
1
1
1
0
1
1
1
2
0
1
2
2
2
0
1
0
0
2
0
2
1
1
0
0
0
1
1
1
1
2
2
1
1
2
1
2
1
0
1
0
1
0
1
1
2
2
1
1
0
1
1
0
1
0
1
1
0
1
1
0
0
2
0
2
1
1
1
0
1
2
1
2
2
0
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
2
1
0
1
3
0
1
0
2
1
0
1
3
1
2
0
0
1
2
0
1
1
2
0
2
0
1
1
1
0
1
1
0
0
2
0
1
2
1
1
1
1
0
1
2
3
1
0
1
1
1
2
1
1
1
1
2
1
2
2
2
1
1
1
0
0
0
0
1
0
1
0
2
2
1
2
0
2
1
0
2
1
2
1
0
1
0
1
1
0
1
2
0
2
1
2
2
1
0
1
2
1
0
1
1
1
2
1
2
1
1
1
0
1
1
0
1
1
0
1
2
1
0
1
0
0
1
0
1
1
1
1
1
1
1
1
0
2
2
1
1
1
0
2
1
1
1
1
1
0
1
1
2
1
1
1
2
1
2
1
1
2
0
0
1
1
0
0
0
0
1
2
1
1
0
1
0
2
0
1
0
2
2
1
0
0
1
1
1
4
1
1
2
2
0
1
1
2
1
1
1
1
1
0
1
1
0
0
0
1
1
1
1
1
1
1
1
1
1
0
2
0
2
1
1
1
2
2
1
0
0
0
0
1
2
1
0
1
1
0
1
2
1
0
0
2
2
0
0
1
1
1
1
2
1
2
2
2
0
1
0
1
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
2
1
1
2
2
2
1
1
0
1
2
1
4
1
1
1
1
2
0
2
1
2
0
0
1
2
2
0
1
0
1
1
0
0
1
1
2
4
1
1
2
0
0
2
3
1
0
1
2
1
1
1
0
0
1
1
0
1
1
1
0
1
1
2
0
0
1
1
2
1
3
0
1
0
1
1
1
1
0
2
2
0
1
0
0
2
1
1
1
1
1
2
0
0
1
2
1
2
0
1
1
2
1
1
3
0
1
1
0
1
1
2
1
2
1
0
0
2
0
0
1
0
1
0
1
1
1
2
1
1
1
1
2
1
1
0
0
1
1
0
1
2
2
0
1
1
1
0
2
1
0
2
1
1
1
1
1
0
1
1
1
1
1
1
0
0
1
1
0
0
0
2
1
0
1
2
0
1
2
1
0
1
1
2
1
0
1
1
0
0
1
1
1
1
0
2
1
0
1
1
1
1
1
0
0
1
2
2
1
1
0
1
0
2
1
1
1
0
0
0
2
1
0
2
2
0
1
1
2
1
1
0
1
2
1
1
1
0
0
0
1
1
1
1
0
0
2
1
2
1
1
1
0
2
1
1
1
2
2
1
2
2
1
2
0
1
1
0
0
2
0
0
1
1
0
2
1
1
1
1
2
2
0
2
1
1
3
1
1
1
2
0
0
1
2
2
2
1
1
0
1
1
2
1
0
1
2
1
1
1
1
2
1
2
4
1
2
1
1
2
2
0
0
2
1
2
1
1
0
2
1
1
0
2
1
1
0
1
1
1
1
0
1
1
1
1
1
1
1
1
1
0
1
1
0
1
3
0
0
1
2
0
0
1
1
2
0
1
1
1
0
5
1
0
0
0
2
1
2
0
1
1
1
1
2
1
1
1
1
2
0
0
2
1
2
0
1
0
2
2
2
1
1
0
1
1
1
0
0
0
1
1
2
2
1
1
1
2
2
2
1
2
0
2
1
1
1
1
2
2
1
0
2
0
1
1
1
1
0
1
1
2
1
0
1
1
1
2
0
0
1
0
0
0
2
1
1
1
1
1
1
0
2
0
1
1
1
1
2
0
2
0
1
3
0
2
0
2
0
1
0
3
1
1
2
1
0
2
0
1
2
1
2
2
2
1
5
1
1
1
0
1
1
1
1
1
1
0
2
2
1
0
0
2
0
0
2
1
2
2
2
1
0
1
1
2
2
0
0
1
1
1
2
1
0
1
1
1
0
0
1
2
0
2
1
2
1
0
1
2
1
0
1
2
1
1
1
1
1
1
0
0
1
1
0
2
0
1
0
2
1
0
0
5
1
2
1
2
1
1
4
0
2
2
0
0
0
0
2
1
0
1
1
2
1
2
1
0
0
1
1
2
1
1
1
1
1
1
0
2
1
1
1
1
1
1
0
2
1
1
2
0
2
1
1
2
2
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
0
1
1
1
1
1
1
1
0
2
0
0
1
0
1
0
0
1
1
1
0
1
2
2
0
1
1
1
0
2
1
0
1
1
1
1
1
0
1
0
1
1
1
0
1
1
2
1
1
2
0
1
0
0
1
1
0
1
1
1
1
1
0
0
1
1
0
0
1
2
1
1
2
2
1
0
1
1
1
1
2
1
1
0
1
0
1
1
1
1
2
0
1
1
1
1
2
1
1
1
1
1
3
1
0
0
2
1
0
1
2
2
2
1
1
1
2
1
1
1
1
1
1
0
2
2
1
1
0
1
1
0
1
2
1
1
0
1
1
2
1
1
2
0
0
1
1
1
1
1
1
1
1
0
1
1
1
1
1
0
1
1
0
1
1
0
0
0
1
0
2
0
1
2
0
2
1
1
2
0
0
2
0
1
1
2
0
0
2
2
1
2
5
1
3
1
0
3
1
0
2
0
1
1
1
1
1
0
1
1
1
0
0
2
1
1
1
0
0
1
1
2
1
1
1
2
2
1
0
2
1
1
0
2
1
0
0
1
0
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
0
2
3
2
1
1
0
1
2
3
0
1
1
1
0
1
1
1
0
0
0
1
1
0
1
0
1
2
1
1
1
0
3
2
1
1
2
2
1
2
1
2
1
0
0
1
1
1
1
1
0
1
2
1
0
1
0
2
2
2
1
1
1
0
1
1
1
0
1
2
0
2
0
1
0
2
2
1
2
1
1
1
1
1
1
2
1
1
2
1
1
1
1
0
0
2
1
0
1
1
1
1
2
2
1
0
2
0
2
1
1
1
1
1
1
1
2
0
1
0
0
1
1
0
1
2
1
0
1
1
1
0
0
1
1
1
0
0
1
0
0
1
1
1
2
1
0
1
1
1
2
1
1
1
2
0
0
1
0
1
2
1
1
1
0
0
0
2
1
0
2
2
1
0
2
1
0
2
2
2
1
1
1
0
2
1
0
1
1
0
1
1
2
2
1
2
2
1
2
0
1
1
1
1
0
2
1
2
0
1
1
1
1
0
0
0
0
1
2
2
2
1
0
1
0
1
1
1
1
1
0
0
1
1
0
1
1
2
1
1
2
1
1
0
1
1
1
1
1
3
1
1
1
0
0
1
0
1
1
2
2
0
1
1
0
2
2
2
0
1
2
1
2
1
1
1
1
1
2
0
1
0
0
1
2
1
2
0
0
1
1
1
1
0
1
0
0
1
1
0
1
0
1
0
1
0
2
2
2
0
1
0
0
1
1
1
1
1
2
2
1
1
2
1
2
1
1
2
0
2
1
2
1
0
2
0
1
0
0
1
1
2
0
1
0
1
1
1
2
0
1
1
0
2
1
1
1
2
1
1
0
1
1
2
1
2
1
1
1
0
1
0
0
1
2
0
1
0
1
2
0
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
2
1
0
1
0
2
2
0
0
1
0
1
1
0
2
3
0
0
1
1
1
1
1
1
0
1
1
1
0
1
2
1
2
1
2
1
4
1
1
1
2
1
0
2
0
0
2
0
1
1
1
1
2
1
0
1
1
0
1
2
1
1
1
0
1
1
1
0
1
1
2
0
1
0
1
1
0
0
2
1
1
1
1
2
1
1
1
1
0
2
1
1
1
3
0
1
2
0
2
1
2
1
0
1
0
2
0
1
0
1
1
0
2
1
2
1
1
1
1
1
1
2
2
2
1
0
1
1
1
1
1
0
1
1
0
2
1
0
2
0
1
1
1
1
2
1
0
1
2
1
1
1
3
1
1
1
1
0
0
1
1
0
2
0
1
1
0
1
1
1
1
1
1
2
0
2
1
1
0
1
2
1
1
2
0
2
1
2
1
1
1
0
1
1
1
2
1
2
2
2
1
1
1
1
2
2
1
2
0
1
0
0
2
0
1
0
1
1
1
1
1
1
1
1
1
2
1
1
3
0
5
1
1
0
2
2
0
2
2
1
3
1
1
2
1
1
1
0
0
2
2
1
1
1
0
1
0
1
1
1
1
0
1
1
0
0
2
1
1
1
2
1
1
0
1
2
0
1
0
0
1
2
2
2
0
0
2
1
0
1
0
1
0
1
1
0
0
0
1
2
2
0
2
1
1
0
0
0
0
1
1
1
0
1
1
0
0
3
1
0
0
1
1
2
0
2
1
0
1
2
1
1
0
1
1
0
1
1
1
1
1
1
1
1
2
2
1
2
2
2
1
0
1
1
2
1
0
1
0
0
0
0
0
0
1
0
0
2
0
1
1
0
1
2
1
1
0
1
1
0
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
0
1
1
2
1
2
2
1
0
1
1
2
2
0
2
1
0
1
2
1
1
1
1
0
2
1
1
0
2
1
1
1
1
1
2
1
0
0
1
2
1
1
0
1
0
0
2
1
1
1
2
0
1
0
2
1
0
2
1
2
0
1
1
7
2
0
0
2
0
1
2
1
2
1
1
2
1
0
1
1
1
2
1
2
0
0
1
0
1
2
1
1
0
2
1
1
0
0
0
1
1
1
1
0
1
1
1
1
0
1
3
4
0
1
1
1
1
1
1
1
0
2
2
1
1
0
1
1
0
1
2
0
1
2
1
0
1
2
0
1
2
0
2
0
0
1
1
1
1
1
0
2
0
1
1
1
1
1
2
2
1
0
1
2
1
0
1
1
0
1
2
0
0
1
1
1
1
1
0
0
0
2
1
0
2
2
2
2
1
0
1
1
2
0
1
1
2
2
1
1
2
1
1
1
0
0
1
0
2
1
1
0
0
1
1
2
0
1
1
0
1
3
1
0
1
1
1
0
1
0
1
0
1
2
1
1
1
0
1
1
1
3
1
1
1
2
1
0
2
1
0
0
0
1
2
1
1
1
1
1
2
1
2
1
1
1
1
0
1
3
0
1
1
0
2
1
1
1
1
2
1
1
0
2
1
1
0
2
0
2
0
2
1
1
1
1
0
1
1
1
1
1
2
1
2
0
2
1
1
1
1
1
2
0
2
1
1
1
0
1
1
1
0
2
0
1
0
1
3
1
0
2
2
3
0
2
1
1
1
2
2
2
0
1
0
1
1
0
2
2
2
1
1
1
0
1
1
1
1
1
1
2
2
0
0
0
2
0
2
2
2
1
1
1
2
1
1
0
1
1
1
1
1
1
1
1
0
0
1
1
1
2
2
2
0
1
1
1
2
2
1
1
1
1
2
0
2
0
1
2
1
0
0
1
1
1
0
0
1
1
1
1
1
2
2
1
2
0
1
1
1
1
1
1
1
1
1
2
1
2
0
2
0
0
1
1
1
1
0
0
1
1
1
1
0
1
2
1
1
0
1
1
0
2
2
1
2
2
1
2
0
2
1
1
1
1
1
2
2
0
2
0
1
1
2
0
0
0
0
0
1
0
1
0
0
2
0
1
2
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
0
1
0
2
1
1
2
0
1
1
0
0
0
1
1
2
2
0
1
0
1
2
1
1
0
0
2
0
2
0
1
2
1
2
1
0
0
1
1
2
2
0
1
1
1
1
0
1
0
2
0
2
0
1
1
1
2
0
1
2
1
1
1
2
1
0
1
1
2
2
1
1
2
1
2
0
4
0
1
1
2
1
1
1
0
2
2
2
1
1
1
2
2
1
1
1
1
0
2
1
1
0
2
2
0
1
1
0
2
2
2
0
1
1
0
0
1
1
1
1
0
1
2
0
0
0
0
1
2
1
1
0
1
0
1
1
0
1
0
2
1
1
1
0
0
2
2
2
1
2
1
1
0
1
0
1
1
2
0
0
1
3
0
0
1
1
1
0
2
0
0
1
0
1
1
2
1
1
1
2
1
1
0
2
2
1
0
0
1
1
2
1
0
2
0
1
1
0
0
1
0
1
2
0
1
1
1
1
1
1
1
2
2
2
2
0
0
0
1
2
2
2
0
0
0
1
2
0
1
1
0
2
2
2
1
2
2
2
0
2
2
0
0
1
1
1
0
0
0
1
1
1
1
1
1
1
1
1
0
2
2
1
2
1
1
1
0
2
0
1
1
1
1
2
1
3
0
1
2
1
1
2
1
1
0
1
0
1
1
1
0
1
2
1
1
2
2
1
2
1
1
0
1
0
1
4
0
1
1
2
2
2
1
2
0
0
1
2
0
1
1
2
0
1
1
1
2
2
0
1
0
1
2
1
2
1
0
0
1
0
2
0
1
2
1
1
2
1
1
1
1
1
1
0
1
2
0
1
0
2
1
1
1
0
0
1
1
1
1
0
0
2
1
1
1
1
2
2
0
2
2
1
1
0
1
1
1
1
2
1
1
2
2
2
1
0
1
1
1
1
2
2
0
1
1
1
1
1
1
1
2
0
0
4
1
2
1
2
1
1
1
0
1
1
2
1
0
1
0
2
0
0
1
1
1
1
1
1
1
0
1
0
2
1
1
1
0
1
1
2
1
0
2
2
2
0
1
1
0
4
2
1
1
1
1
1
1
2
2
1
1
1
0
1
2
1
1
1
2
2
0
1
0
1
1
0
1
2
1
1
1
2
1
1
2
1
1
1
0
0
0
1
1
1
1
1
0
1
2
1
2
2
0
0
1
0
1
1
1
1
1
0
1
2
0
0
0
1
0
0
0
0
1
2
1
1
1
2
0
0
1
2
1
2
0
1
1
0
0
2
2
1
1
0
3
0
0
1
1
2
1
1
2
2
2
1
1
0
2
1
0
0
0
2
2
1
1
1
0
1
0
1
0
1
1
1
1
1
0
1
1
2
0
0
1
2
2
0
0
1
1
0
2
1
1
0
2
1
0
0
1
2
1
1
2
1
2
1
1
1
2
1
0
1
0
1
1
1
1
1
1
0
2
1
0
2
0
1
0
2
0
1
1
1
1
1
0
1
1
2
0
1
1
1
0
0
1
0
1
1
1
1
2
2
0
1
0
0
1
1
2
2
1
1
1
1
1
0
0
0
1
1
2
2
1
1
2
0
2
1
2
1
0
2
1
1
2
2
1
0
1
1
1
1
2
0
2
0
2
1
1
1
0
1
1
2
2
0
2
1
0
2
1
0
1
1
1
2
0
2
1
1
1
2
2
1
1
1
0
0
1
0
2
0
1
0
1
2
2
2
1
0
1
4
1
0
1
2
2
0
1
2
1
1
1
1
1
1
1
0
1
2
1
2
0
1
2
1
2
1
2
0
0
1
1
2
2
1
1
1
1
0
1
2
1
2
2
1
2
2
1
1
1
1
5
1
1
2
1
2
1
2
0
2
1
1
2
1
1
0
1
0
1
2
1
0
1
1
2
1
0
0
2
2
1
2
0
0
1
2
0
1
0
1
1
2
1
0
0
1
1
1
1
1
0
2
0
1
0
2
0
0
1
2
2
0
2
1
1
1
1
1
2
1
1
0
0
1
1
1
2
1
1
1
2
0
1
1
2
2
1
0
2
2
1
2
1
1
1
0
0
0
1
1
2
2
2
0
2
0
1
0
1
2
1
0
2
0
1
1
2
0
0
1
0
1
2
0
0
1
2
0
1
1
1
1
1
2
1
1
1
1
4
2
1
1
1
0
1
1
1
1
0
1
2
1
2
1
0
1
2
1
2
1
2
2
1
2
1
1
1
1
0
0
1
0
1
1
2
1
0
1
2
0
1
2
1
1
1
2
2
2
1
1
2
1
1
0
0
0
1
1
0
1
1
1
0
2
0
0
2
1
2
1
1
1
1
0
1
2
2
1
1
1
2
0
1
1
1
0
0
2
1
0
1
1
1
1
1
3
1
1
1
1
1
1
1
0
1
1
2
1
2
2
3
0
1
1
0
2
2
0
0
2
1
2
1
1
0
0
0
1
1
2
2
1
1
1
1
1
1
1
2
0
2
1
2
2
1
2
1
2
2
1
1
1
1
1
3
1
1
2
1
1
0
1
2
2
0
0
1
1
1
1
2
1
1
1
3
0
2
1
2
2
0
1
1
1
1
0
0
1
2
2
0
2
0
1
1
1
0
1
0
2
0
0
1
0
1
2
0
2
0
0
1
2
2
1
1
1
1
0
0
1
2
1
0
1
0
1
1
1
1
1
1
0
1
0
1
1
0
0
3
1
1
1
0
1
1
0
0
2
1
0
1
0
2
0
0
2
1
0
1
2
2
1
2
1
2
1
0
0
0
1
1
2
0
1
2
2
2
1
2
1
1
2
3
1
0
1
1
1
1
1
0
2
1
0
0
0
2
1
0
2
3
0
1
1
2
1
1
0
1
0
0
0
1
2
1
1
1
1
1
1
0
1
1
2
2
2
2
2
1
1
2
1
0
1
0
0
1
2
1
0
1
0
0
1
0
1
1
0
1
0
0
1
1
1
1
2
1
1
0
2
2
0
2
1
0
2
1
1
1
2
1
1
0
0
1
0
1
2
1
1
0
2
0
0
2
1
1
0
1
0
0
0
1
1
1
2
0
0
2
1
1
0
0
2
1
1
2
0
0
2
1
0
2
0
0
1
1
1
1
1
1
0
0
2
2
1
0
1
0
1
1
0
1
2
0
1
0
1
1
1
0
1
1
1
1
1
1
0
1
2
0
1
1
1
2
2
2
1
1
2
1
0
2
1
1
1
0
1
5
1
1
1
1
0
1
1
1
1
1
1
1
0
1
1
1
0
1
2
1
1
1
1
1
0
1
1
1
1
1
1
1
2
1
1
1
0
3
2
1
1
0
1
1
3
1
1
0
2
1
2
1
1
1
1
2
1
3
1
1
2
0
1
2
1
0
1
1
1
2
1
1
1
1
1
1
0
0
1
0
1
1
1
0
1
1
0
2
1
1
1
1
1
1
1
1
0
1
1
2
1
2
0
1
1
2
1
1
0
0
0
1
0
1
1
1
1
1
1
1
0
2
1
1
1
2
2
0
2
0
1
1
1
0
2
1
0
1
1
2
0
0
0
0
1
1
2
1
1
0
2
2
2
0
1
1
2
2
1
2
0
2
2
1
0
0
1
2
0
2
2
1
1
2
1
1
1
0
1
1
1
1
2
2
1
1
0
1
0
1
1
1
1
1
2
2
1
0
2
0
1
1
1
2
2
0
1
1
1
2
1
0
2
1
2
1
1
0
2
1
0
0
1
1
1
2
2
1
1
1
1
0
1
3
2
0
0
0
2
1
1
1
0
1
0
1
1
2
0
1
2
1
1
1
1
1
2
1
0
0
1
1
1
1
2
2
1
2
0
1
0
1
0
0
2
1
2
1
1
1
1
2
1
0
1
1
1
2
0
1
1
0
1
0
0
1
0
1
2
0
2
1
1
0
0
0
1
1
0
0
2
1
0
1
0
2
0
1
1
1
1
1
0
1
0
0
2
1
2
2
2
1
2
1
1
1
2
1
1
2
1
0
2
1
2
0
1
0
2
1
1
2
2
1
0
1
0
1
1
1
1
1
3
0
0
1
0
1
2
1
1
1
3
1
2
1
1
1
0
1
1
2
0
2
1
2
1
0
0
1
1
1
0
1
0
0
0
0
1
0
2
1
1
1
1
2
1
0
1
0
2
0
0
0
1
1
1
1
1
2
1
1
2
1
1
1
1
0
2
1
2
1
1
1
2
1
3
0
1
1
1
1
0
1
2
1
0
1
0
1
1
1
1
1
5
2
0
0
0
1
1
1
0
0
1
1
2
1
1
2
0
2
1
0
1
2
1
0
1
0
1
1
1
0
2
1
2
1
1
1
0
1
1
1
1
1
0
1
2
1
1
1
0
0
1
3
0
0
0
1
0
1
0
2
0
1
3
0
1
1
2
2
0
2
0
2
0
2
2
1
1
1
1
0
1
1
0
0
1
1
1
1
2
1
2
1
1
2
0
0
1
1
1
1
0
0
2
0
2
0
1
1
0
1
2
0
1
1
0
1
1
1
2
1
2
1
1
0
1
2
1
1
1
1
1
0
1
0
2
0
1
0
1
0
0
1
1
2
2
2
2
2
0
0
1
1
1
2
0
1
2
1
0
0
0
2
1
0
0
1
2
0
0
1
3
1
1
0
1
1
1
0
2
2
2
1
0
1
1
1
1
0
0
1
1
0
1
2
0
1
1
0
1
1
1
1
2
2
0
0
2
1
1
2
0
0
2
0
2
0
0
1
1
1
1
1
0
0
0
1
1
0
2
1
1
1
1
1
1
1
1
2
1
1
2
0
1
0
1
0
0
0
2
0
2
0
0
1
2
1
1
2
1
2
1
0
2
3
1
1
1
0
2
0
0
1
2
1
1
3
1
1
2
1
1
1
0
1
2
1
0
0
1
1
1
2
1
2
1
1
2
2
0
1
0
0
0
1
1
2
2
0
1
1
0
1
4
2
2
1
1
0
1
1
1
1
2
0
0
1
2
1
2
2
1
2
1
2
1
1
0
1
1
1
2
2
2
1
1
1
1
1
1
0
1
0
2
0
1
1
1
1
0
1
0
0
0
0
2
1
1
1
1
1
0
1
1
3
1
1
1
0
2
1
0
1
1
1
0
2
1
0
0
0
1
0
2
3
0
1
1
2
1
1
1
1
2
1
1
1
0
1
0
0
0
2
1
2
1
1
0
0
2
1
1
0
1
0
1
2
2
2
2
1
1
0
0
1
1
2
0
0
1
0
2
1
0
2
1
1
4
3
0
0
1
1
1
1
1
2
1
1
1
0
1
1
2
1
0
1
1
1
1
0
2
2
1
1
1
0
1
1
0
0
2
2
0
1
0
1
1
1
1
0
0
1
1
1
1
0
0
1
1
2
0
1
2
2
1
0
1
1
1
2
2
2
0
2
1
1
1
1
1
2
0
0
1
1
0
1
2
1
0
1
2
1
1
1
1
1
1
0
0
1
1
1
1
1
2
1
1
0
1
1
1
0
0
1
1
0
2
2
1
1
1
2
0
1
0
1
1
1
1
1
2
0
1
2
1
1
2
1
1
1
1
2
1
0
0
1
1
2
1
1
1
2
0
2
2
0
1
0
1
2
0
0
1
2
0
1
0
0
2
1
1
1
1
0
1
1
0
1
1
1
2
1
1
1
2
1
1
1
1
0
1
2
2
0
1
1
2
1
0
1
1
1
1
1
1
2
1
1
1
1
2
1
1
3
0
1
1
1
1
1
0
1
2
1
1
2
1
0
1
1
1
1
0
1
1
1
2
2
2
2
0
1
2
1
0
1
0
0
1
5
2
2
1
2
1
0
0
1
0
2
1
1
0
0
1
1
2
0
1
1
0
1
2
1
0
0
2
1
1
2
2
0
0
1
1
0
2
0
1
1
1
1
1
1
0
1
2
0
1
1
1
1
3
2
2
1
1
2
0
1
1
0
1
1
1
1
1
0
1
0
0
1
1
1
1
2
1
2
1
2
2
1
1
0
1
1
1
1
0
0
0
1
0
1
2
1
1
1
1
0
0
0
1
0
1
1
2
1
0
0
1
1
1
1
1
1
1
1
0
0
1
1
1
2
1
0
0
1
2
2
1
1
1
1
2
1
1
1
0
0
1
0
1
1
1
2
1
1
1
0
2
0
0
0
2
1
2
2
1
1
0
2
1
1
2
0
0
2
1
1
0
2
1
1
0
0
1
1
2
1
1
1
0
0
1
0
1
0
1
0
2
1
0
0
1
2
0
1
1
1
1
1
1
0
0
1
2
1
1
1
1
1
2
1
1
0
0
2
1
1
1
6
1
1
2
1
2
2
1
3
1
0
1
2
1
1
1
1
1
2
1
1
1
2
0
1
0
0
0
0
0
2
1
0
0
2
0
0
1
2
1
1
1
1
1
2
1
1
0
1
0
2
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
2
1
2
0
1
1
0
1
1
1
1
1
0
1
0
0
1
1
0
1
0
2
0
0
1
1
1
2
2
1
0
1
0
2
1
1
0
1
2
1
1
2
2
1
0
0
2
1
2
1
1
1
3
0
1
1
2
2
1
1
1
2
0
2
1
2
0
1
1
0
2
2
1
1
1
2
2
1
0
1
1
1
0
1
2
2
0
2
1
0
0
2
1
1
0
1
0
0
0
1
2
2
1
0
1
0
0
1
0
1
1
2
0
2
2
0
1
1
1
1
0
1
1
0
1
0
2
1
1
1
2
0
2
0
0
1
1
0
2
2
0
1
0
1
2
0
1
1
1
1
1
0
1
1
1
1
2
0
0
1
1
0
1
1
1
0
2
0
1
1
2
1
1
0
2
2
0
0
2
2
1
1
0
1
2
0
0
0
0
1
0
1
1
1
0
1
0
1
2
0
1
1
1
0
0
1
1
1
1
1
1
1
1
0
2
2
1
2
1
1
1
1
1
1
1
1
1
0
0
1
2
0
0
2
2
2
2
0
1
2
0
0
1
1
0
1
1
2
1
0
0
1
1
1
0
1
0
1
1
1
1
2
0
1
1
2
0
2
0
2
0
2
0
1
2
1
1
1
1
2
1
1
1
0
1
0
1
0
1
1
1
1
1
2
1
1
1
0
1
2
1
0
1
1
3
0
1
1
0
2
2
1
2
2
1
1
0
1
1
0
1
1
2
0
1
1
0
0
1
1
2
0
1
1
1
1
0
2
0
1
1
0
1
1
0
1
0
0
1
0
1
2
1
1
0
1
0
2
3
2
1
1
1
1
1
1
3
1
1
1
0
0
0
1
0
0
1
1
1
2
1
1
0
2
0
1
0
2
0
1
0
0
1
0
0
2
1
1
1
1
0
1
1
1
1
1
2
1
2
1
1
1
2
1
1
1
1
0
2
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
0
1
2
0
1
1
2
1
1
1
0
1
0
1
2
1
0
1
1
1
2
0
2
1
2
2
2
0
1
2
0
1
0
2
1
1
2
2
1
0
1
0
3
2
2
0
1
1
0
1
2
2
1
2
2
1
2
0
1
1
1
1
1
0
0
1
1
1
0
1
2
1
2
1
1
1
2
0
3
2
2
1
1
1
2
1
3
0
2
1
0
1
0
2
1
1
1
2
0
1
0
0
1
0
1
0
1
2
2
0
2
2
1
0
2
1
1
2
0
2
2
1
0
2
1
2
1
1
1
1
0
1
0
1
1
1
1
1
2
1
1
1
1
1
1
2
1
0
0
1
2
0
1
1
2
0
2
1
2
2
1
1
1
0
1
2
1
1
1
1
0
2
2
2
4
2
2
1
0
1
2
1
0
1
1
1
0
0
1
1
0
1
1
2
1
1
1
1
1
1
1
2
0
1
1
0
2
1
2
1
2
1
1
1
1
1
2
2
1
2
1
1
1
1
0
0
0
1
2
2
0
2
0
2
1
1
0
1
1
0
0
1
1
0
1
1
0
0
2
1
0
4
2
2
1
3
1
2
1
1
2
1
1
0
0
2
2
0
2
2
0
1
1
1
1
0
1
1
1
1
1
0
0
0
0
2
2
0
1
1
0
3
1
1
1
2
0
2
2
2
2
1
2
1
2
2
2
1
1
0
1
1
1
1
2
0
1
0
2
1
0
1
1
1
2
1
1
0
0
1
1
1
0
1
1
0
1
1
1
1
0
1
2
1
1
2
1
1
2
1
1
1
0
1
1
1
2
0
2
1
1
0
2
1
2
1
1
1
2
1
2
0
0
0
1
2
2
1
0
1
1
1
0
1
1
0
0
1
0
0
2
1
1
0
2
1
1
1
1
2
1
1
0
1
0
1
2
1
2
2
0
0
1
0
0
1
2
2
1
2
1
1
1
1
2
2
0
2
1
1
2
2
1
1
2
1
1
0
1
0
1
0
2
0
1
1
1
0
1
1
0
2
0
1
1
1
0
1
1
1
1
1
3
0
1
2
0
1
1
1
1
3
1
1
0
1
0
2
3
1
1
1
0
0
1
1
2
1
0
0
0
2
1
2
1
6
1
1
1
3
0
1
2
1
1
1
0
0
1
0
0
2
1
0
1
1
2
2
1
1
0
1
2
0
1
0
0
0
1
1
1
1
1
1
0
0
1
2
1
0
1
1
0
1
1
1
2
0
2
0
2
0
1
1
0
0
2
0
0
1
1
1
2
1
2
1
0
1
2
1
1
0
0
3
1
2
1
0
2
2
1
1
2
2
0
0
0
0
2
1
2
0
1
0
2
1
1
1
1
1
1
2
1
1
1
1
2
1
0
1
2
0
0
1
1
0
1
1
2
0
2
2
2
0
1
1
2
2
1
2
2
1
1
1
2
1
1
2
1
0
1
1
1
0
1
0
0
2
1
2
0
0
1
1
2
2
2
2
2
1
2
1
1
1
3
2
2
1
1
0
1
1
2
0
0
1
1
1
0
2
1
0
2
3
0
1
1
1
0
2
1
1
1
1
1
0
1
0
2
1
1
0
1
1
2
1
2
1
0
0
2
1
2
1
2
2
1
2
1
2
1
1
2
0
2
2
0
0
0
2
1
1
1
0
1
1
0
0
3
1
1
1
1
0
2
1
1
1
2
0
1
1
1
0
1
1
1
2
1
1
1
1
0
0
1
2
0
0
1
2
0
2
2
1
0
1
1
1
2
1
0
2
1
2
2
0
1
1
1
2
2
0
1
0
2
0
1
2
0
0
1
2
1
1
1
2
1
1
1
2
0
1
0
1
0
1
0
2
1
0
2
1
1
0
0
2
1
1
1
2
1
4
0
0
0
1
1
1
0
0
1
0
1
1
2
1
1
0
0
1
1
1
1
1
1
1
0
1
2
0
2
0
0
2
1
1
2
1
1
2
0
2
0
1
0
2
2
1
2
1
0
2
2
0
1
1
2
1
1
3
0
0
1
2
0
1
0
0
0
1
1
1
0
0
1
0
0
2
2
1
0
1
1
2
2
1
1
2
2
0
1
1
0
1
1
1
1
0
1
0
1
1
0
1
1
0
1
2
2
2
1
2
2
1
0
2
2
0
0
1
1
1
2
1
2
2
1
0
0
1
1
1
0
1
0
1
2
2
2
0
1
1
0
2
0
1
0
1
1
1
2
0
1
2
3
2
1
1
2
1
1
1
2
0
1
0
1
1
0
1
0
0
0
0
1
1
0
0
2
0
0
1
1
2
0
1
0
1
2
1
1
0
0
1
1
1
0
1
1
2
0
0
2
0
1
1
0
1
1
2
0
0
1
2
1
1
0
0
1
2
1
1
1
2
0
1
1
1
2
0
2
1
1
0
0
1
1
2
0
1
2
1
1
2
1
0
1
2
0
0
0
1
1
1
0
1
1
1
1
1
1
2
2
0
0
1
1
0
0
0
0
1
2
0
1
1
0
1
0
0
2
2
1
1
0
2
2
0
2
1
2
1
2
2
2
1
3
1
1
2
1
1
1
1
3
1
2
1
1
2
0
1
1
1
1
1
2
1
1
1
2
0
2
2
1
0
1
0
0
0
1
1
0
0
0
1
1
1
0
2
1
0
1
1
1
2
1
1
0
1
2
1
1
0
0
1
1
1
2
2
0
0
1
2
2
1
3
0
1
1
0
2
1
1
1
0
2
1
2
1
1
1
2
1
0
0
0
1
1
1
0
0
1
1
4
0
2
1
0
1
1
1
0
2
1
0
0
2
1
1
2
1
0
0
1
1
1
2
1
0
1
1
1
1
1
0
1
1
1
1
0
2
0
1
1
0
1
1
1
0
1
0
1
1
0
1
1
1
0
1
1
2
2
1
0
1
1
0
1
2
1
1
1
1
1
1
2
1
1
1
0
1
1
1
0
0
1
1
0
1
0
0
1
1
1
1
1
1
2
0
0
2
0
1
1
0
0
1
0
1
2
1
1
1
2
1
1
1
1
0
2
1
1
0
0
3
2
1
1
2
2
1
0
0
1
1
1
1
1
2
0
0
0
1
1
1
2
1
2
2
1
1
1
1
1
2
1
1
1
2
0
2
0
1
0
0
0
0
2
1
0
0
1
1
1
0
1
1
1
0
0
1
0
1
1
0
1
2
1
1
0
2
1
2
2
1
0
0
1
0
1
1
1
2
2
0
2
1
1
0
1
2
2
1
0
2
0
1
0
0
0
1
2
0
2
1
1
1
1
2
1
1
1
2
1
2
2
2
1
2
2
1
1
0
1
1
2
1
2
0
2
0
1
0
0
1
1
0
0
2
1
0
2
0
1
2
1
2
1
1
1
1
0
0
0
1
1
0
0
1
1
1
1
1
3
0
4
2
1
1
1
1
0
1
1
2
0
0
1
2
2
2
1
1
0
1
2
0
1
2
2
2
1
0
2
2
0
2
1
2
1
1
1
1
0
1
0
0
0
2
1
1
1
2
0
1
2
2
1
0
1
0
1
0
0
1
1
0
1
0
2
0
1
2
2
2
0
1
0
1
1
1
0
1
1
0
1
0
1
2
1
2
1
1
0
1
1
0
0
2
1
2
1
1
1
1
0
1
2
0
0
0
2
1
0
1
0
1
2
1
1
1
2
1
0
1
1
1
1
0
0
0
1
1
1
1
1
1
1
1
0
1
2
1
2
0
1
2
1
2
1
0
0
1
1
1
1
1
1
1
1
2
1
0
0
1
1
1
1
1
1
0
2
2
1
1
1
2
1
1
2
1
0
1
2
1
2
2
0
1
0
1
0
0
1
1
0
0
1
0
2
1
1
1
2
2
1
2
0
1
0
1
1
1
1
1
2
0
0
1
0
2
1
1
1
1
0
1
1
1
1
1
2
1
1
0
1
1
0
1
1
0
0
0
1
1
2
2
0
0
1
2
2
4
0
1
1
1
2
1
2
1
2
2
0
1
1
1
1
1
0
1
1
0
2
1
1
2
0
0
0
1
0
1
1
0
0
1
2
1
2
1
1
1
1
1
0
0
0
1
1
2
1
2
1
1
2
2
1
1
1
1
1
0
2
1
0
2
1
1
1
2
1
0
7
0
0
0
0
0
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
0
0
2
1
1
1
0
0
1
1
2
2
2
2
1
2
1
1
2
2
1
0
0
1
2
1
1
1
2
1
2
1
2
2
0
0
1
1
3
0
1
1
1
1
1
2
1
2
1
1
1
1
0
0
0
2
0
1
0
2
0
1
1
1
1
1
1
1
2
0
2
2
2
0
0
1
1
2
1
2
1
1
1
1
0
1
1
1
1
1
1
1
0
0
1
1
2
2
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
2
2
1
0
1
0
2
1
1
2
1
1
1
2
1
2
1
2
1
1
2
1
1
1
1
1
0
0
2
1
1
1
2
0
0
1
1
0
2
1
0
1
0
1
1
2
1
0
0
0
0
2
1
0
2
0
1
1
1
1
1
2
4
1
1
2
0
0
1
1
2
0
4
0
2
0
1
2
1
1
1
1
0
2
2
2
2
1
2
0
1
2
2
1
0
1
2
1
1
2
1
2
1
1
0
1
1
2
1
1
2
0
2
2
1
2
1
1
0
1
1
1
1
1
1
1
2
0
2
0
0
2
2
1
2
1
2
1
1
0
1
1
2
0
1
1
0
1
1
0
1
0
0
0
1
2
2
0
0
2
2
1
0
1
2
2
2
2
1
0
0
0
0
2
1
2
1
2
2
2
1
0
2
0
2
1
1
1
1
1
1
2
1
1
1
1
2
2
1
1
0
1
2
1
1
1
1
1
1
2
1
0
1
4
2
2
0
1
1
0
1
2
1
1
1
1
2
1
0
1
2
2
0
1
2
0
1
0
1
2
2
1
0
1
1
1
2
0
1
0
1
0
0
1
2
1
1
1
1
0
0
1
1
0
0
1
1
1
1
2
1
0
0
1
1
0
0
2
0
1
0
1
0
2
1
1
1
0
0
0
1
1
1
1
1
0
1
1
1
2
1
2
2
1
0
2
0
0
2
1
0
0
1
0
1
1
0
1
1
1
1
1
2
0
3
1
1
0
5
2
0
2
1
1
1
1
1
1
1
1
2
2
2
1
2
0
1
1
1
2
1
1
1
1
0
1
1
1
2
2
2
1
1
1
0
2
1
1
1
1
1
2
1
1
1
0
1
2
2
2
2
1
1
2
1
0
1
1
0
2
1
1
0
2
0
1
1
0
1
1
1
0
1
2
0
1
0
0
1
1
0
0
2
2
0
2
2
1
0
1
1
0
0
2
0
0
1
1
1
0
1
0
0
2
1
1
0
1
0
1
1
1
1
1
2
1
1
1
1
1
1
1
1
0
2
0
1
2
0
1
0
2
2
1
1
0
0
2
2
1
1
1
0
0
1
1
0
1
1
0
0
0
1
1
3
2
0
0
2
0
0
0
1
1
0
2
1
1
1
0
1
1
1
2
1
0
2
1
1
1
1
1
1
0
2
0
1
1
1
1
0
2
0
0
2
1
0
1
2
0
1
1
1
1
2
1
1
1
1
1
3
1
2
0
2
0
0
1
1
1
2
2
1
2
1
1
1
2
2
1
0
1
2
1
1
1
1
1
1
3
1
1
2
2
1
0
0
2
0
0
2
0
1
1
1
3
1
0
3
1
1
0
2
1
0
1
1
0
1
2
0
1
1
0
0
1
0
2
0
1
1
1
1
2
2
0
2
1
1
1
1
1
0
0
2
2
0
2
1
0
0
2
0
2
0
1
1
1
1
2
1
0
0
1
1
1
1
1
2
0
1
2
2
1
0
1
1
2
2
1
1
1
2
1
1
1
2
0
1
2
1
0
1
1
0
2
2
2
1
1
2
0
2
1
1
1
1
0
0
1
1
5
0
2
1
1
1
0
2
2
1
1
1
1
0
1
1
0
1
1
0
2
0
1
2
1
1
1
0
1
2
1
0
1
0
1
2
1
0
2
0
0
1
2
1
1
2
1
1
1
0
1
2
2
0
0
0
2
1
1
1
0
1
0
0
1
1
1
0
1
1
2
0
1
0
0
1
2
3
1
1
1
0
0
1
2
1
0
0
1
0
2
0
0
2
2
1
1
1
1
1
0
2
1
2
1
1
0
1
1
2
2
1
0
1
2
0
2
1
0
1
0
0
2
1
1
2
1
1
1
1
1
0
0
0
1
1
0
2
1
0
1
0
1
1
1
1
0
1
1
0
1
1
1
1
1
2
1
1
2
1
0
1
0
0
0
2
1
1
2
2
1
0
1
1
0
1
0
0
2
2
1
0
2
1
2
1
1
1
1
0
1
0
1
1
0
1
1
0
0
1
0
1
2
1
1
3
2
1
0
3
3
2
2
1
0
1
2
1
0
2
1
0
0
2
0
1
0
0
2
1
0
1
1
0
1
1
0
2
2
1
1
2
0
2
1
0
1
1
1
2
2
2
1
2
0
0
2
2
1
1
1
2
1
2
1
1
1
1
0
2
1
1
1
2
1
0
2
2
2
1
0
1
1
0
1
0
2
0
1
1
0
1
0
1
2
1
1
0
1
1
1
1
1
1
1
2
2
1
0
1
2
2
0
0
1
1
0
0
0
0
0
0
2
0
2
1
0
1
1
0
1
1
1
3
1
1
0
2
0
1
1
0
0
2
0
0
0
1
1
1
1
2
2
0
1
1
2
2
1
1
1
1
0
0
0
2
1
0
1
0
0
0
1
2
1
1
2
1
1
2
1
1
0
2
2
2
1
1
1
1
1
1
1
1
0
1
0
1
1
1
2
1
2
0
1
2
2
1
2
2
2
1
1
1
1
1
0
0
1
1
1
0
0
0
0
0
1
2
1
2
2
0
1
0
0
1
0
1
0
0
1
1
2
1
1
1
2
1
1
1
1
2
0
3
1
0
0
0
1
0
1
1
0
1
1
4
0
2
1
2
1
1
1
1
0
1
1
1
0
1
1
1
2
0
0
1
1
6
1
0
2
1
0
2
0
0
0
0
1
1
1
0
1
1
2
0
2
2
1
1
2
3
2
1
1
1
2
1
0
1
0
2
0
0
1
0
1
1
0
1
1
0
2
0
2
1
2
0
1
0
2
1
2
0
1
2
1
2
0
0
1
1
1
0
1
2
1
2
2
0
1
2
1
0
2
1
1
1
0
2
1
1
1
0
1
1
1
1
0
1
0
0
1
0
1
1
0
1
0
1
2
3
0
1
0
2
0
2
1
0
0
1
0
1
1
0
0
1
2
1
1
2
1
1
4
1
0
1
1
1
1
1
0
0
1
1
0
2
2
0
0
1
0
1
1
1
1
2
2
0
1
2
1
1
2
0
1
2
2
0
1
0
0
2
0
0
2
0
0
1
2
1
2
2
1
1
2
2
0
1
0
1
0
2
1
1
2
1
0
1
2
1
1
1
0
0
0
1
1
1
1
2
0
2
1
1
2
1
2
1
0
0
1
1
1
2
2
0
2
1
0
1
0
1
2
1
0
1
1
2
1
1
1
1
2
0
3
2
1
2
0
0
1
1
1
0
0
0
1
1
1
2
1
0
1
1
1
2
0
1
1
0
2
1
2
1
2
0
2
0
1
0
1
0
0
1
1
1
1
0
2
0
1
1
2
1
1
1
2
1
2
2
2
1
1
1
0
1
1
2
0
2
2
2
0
0
0
0
1
1
0
1
0
1
0
1
1
1
1
0
0
0
1
1
0
1
1
1
0
1
0
1
1
0
0
1
1
0
3
1
0
1
0
0
4
3
0
1
2
1
1
1
0
1
0
1
1
0
0
1
2
1
2
0
1
1
1
1
2
2
1
1
2
0
0
0
0
1
1
2
1
2
1
2
1
0
1
0
2
0
0
0
0
1
1
1
1
1
2
2
0
1
1
2
1
1
1
1
1
0
1
1
0
0
2
2
1
1
1
0
0
0
1
2
2
0
1
1
1
0
1
1
1
2
2
1
0
0
1
1
1
1
2
1
0
1
0
1
2
0
1
1
1
1
0
1
1
2
2
1
0
1
1
1
0
1
1
2
1
2
1
1
1
2
1
1
4
2
2
0
0
0
0
1
2
0
2
0
3
1
2
2
2
2
1
0
2
1
2
1
1
1
1
1
2
1
1
0
0
1
0
1
0
1
1
2
1
1
1
2
0
1
1
1
2
2
2
2
2
1
0
0
1
2
2
1
1
0
0
0
1
1
1
0
2
1
0
1
1
0
1
1
1
1
2
1
1
0
1
1
1
1
0
1
1
2
2
2
1
0
0
0
1
0
0
2
1
1
1
4
2
1
0
1
0
2
1
1
1
2
1
0
1
0
2
2
1
1
1
2
1
1
1
2
2
0
1
1
1
2
1
0
0
1
1
1
2
2
1
1
1
1
0
2
2
1
1
0
1
0
1
2
1
2
0
1
0
2
0
0
2
0
0
2
1
1
1
1
2
1
1
1
2
2
0
0
4
0
2
1
0
2
1
1
1
1
2
1
2
1
0
0
0
2
2
0
2
1
0
0
3
2
0
2
0
0
1
0
3
0
0
0
1
1
0
1
0
1
1
1
0
2
1
0
2
1
1
1
1
0
1
1
2
1
1
1
1
1
0
1
1
1
1
0
1
2
1
2
1
1
1
1
0
0
1
1
1
1
2
2
1
1
0
1
0
1
2
1
0
0
1
0
1
2
2
1
0
0
0
1
1
1
1
1
2
1
2
2
1
1
2
1
0
1
1
0
0
2
1
2
2
0
1
2
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
0
1
1
0
1
1
2
0
1
1
1
1
1
1
1
1
1
2
0
2
1
1
2
1
2
1
2
1
0
1
1
0
0
2
2
0
0
2
1
0
1
0
0
1
0
2
1
2
0
0
1
1
1
1
1
1
2
2
1
1
2
1
2
2
2
0
0
1
4
0
2
0
0
1
1
0
0
1
2
2
1
1
1
0
1
1
2
1
0
0
2
3
1
0
1
1
0
1
0
2
0
1
2
1
1
1
0
1
0
1
0
2
1
1
0
0
1
1
0
2
1
0
4
1
2
2
0
0
1
1
1
0
2
1
1
1
1
1
1
1
0
2
0
2
0
2
0
1
1
3
0
2
1
2
2
2
1
0
0
1
4
1
1
0
1
1
1
1
2
1
1
0
2
0
1
1
2
1
1
1
0
0
0
1
1
0
1
1
2
1
1
1
0
1
2
0
1
1
0
2
1
0
1
0
2
0
0
1
0
1
0
0
1
1
1
1
2
1
1
0
1
0
1
1
2
1
2
1
0
1
1
1
1
1
1
1
2
0
1
0
2
0
1
1
1
0
1
1
2
1
2
0
1
1
1
0
1
2
0
2
1
3
0
2
1
2
1
1
1
2
0
1
0
2
1
0
2
1
2
2
1
2
2
1
1
0
1
0
1
2
1
1
1
1
1
0
1
1
1
2
1
1
1
0
0
1
1
2
1
1
2
1
2
1
0
0
1
1
1
0
1
1
1
0
1
2
0
1
0
1
2
2
1
1
1
1
1
0
1
1
1
1
1
1
1
2
1
1
2
2
1
1
1
0
0
1
0
0
1
1
1
1
1
2
0
3
0
1
2
2
1
1
2
1
1
2
1
0
1
2
1
1
1
1
2
2
1
1
1
1
1
1
2
0
1
1
0
1
1
1
1
0
1
1
0
1
2
0
1
0
1
1
1
1
1
2
0
0
2
2
0
0
0
2
1
2
2
0
1
0
1
0
1
3
2
2
1
1
1
1
1
1
1
2
1
1
2
0
1
1
1
0
0
0
2
1
1
1
2
2
2
0
0
1
1
1
2
0
2
0
1
1
0
1
0
0
2
2
0
1
1
2
1
0
1
1
1
2
2
1
2
1
0
1
1
2
1
1
1
2
0
2
0
0
1
1
0
0
1
2
1
1
1
1
1
0
1
1
0
1
2
1
1
1
1
1
2
2
1
2
1
3
0
1
2
1
1
1
1
2
2
1
1
1
2
0
2
2
1
1
1
0
5
0
1
2
1
1
0
1
1
0
0
0
2
0
1
1
1
0
2
1
1
0
0
1
1
0
1
1
1
1
0
0
1
0
0
1
0
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
2
2
0
1
0
2
0
1
1
2
0
0
2
1
1
2
0
1
1
2
0
2
1
2
2
1
0
1
1
0
0
1
1
1
2
0
1
1
1
0
1
0
0
1
0
0
2
0
2
1
1
1
0
2
2
0
2
1
2
0
2
0
1
2
2
1
2
0
1
0
1
0
1
1
0
0
1
1
1
1
0
1
2
2
2
2
1
2
1
1
1
2
1
1
0
1
2
1
1
0
1
1
2
2
0
2
0
1
1
1
2
1
1
1
1
0
0
1
1
1
1
1
1
1
1
0
0
1
0
1
0
1
1
0
1
1
1
2
1
0
2
0
1
1
1
1
2
2
1
1
0
0
2
0
2
1
1
1
1
1
1
1
1
1
0
2
1
1
1
1
2
0
1
1
2
0
2
0
1
1
1
0
2
2
0
0
1
0
1
0
2
1
0
1
1
1
1
0
2
1
2
1
0
0
1
2
2
0
1
3
1
0
1
0
1
2
0
1
1
1
0
1
2
0
1
1
1
2
1
0
1
1
2
2
0
2
1
0
1
2
0
1
1
1
1
1
2
2
1
0
2
1
1
1
2
0
0
1
2
1
1
1
1
1
1
0
0
1
1
1
1
2
2
1
2
1
2
1
1
1
1
0
1
1
1
1
0
2
1
1
1
0
1
2
1
1
1
1
0
1
0
1
2
2
1
3
2
1
2
1
1
2
1
0
0
1
2
1
2
1
2
0
1
2
1
1
1
2
1
2
1
2
1
0
1
1
0
1
1
0
2
0
1
1
1
0
0
1
0
1
0
0
1
2
0
2
2
1
1
1
1
1
1
1
1
2
3
1
2
2
0
2
0
1
1
1
1
1
1
1
0
0
1
0
1
0
2
1
0
2
0
3
1
0
1
1
1
2
3
1
0
2
0
0
2
0
1
1
1
1
1
0
2
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
2
1
0
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
0
0
1
1
1
1
2
1
2
0
1
1
2
1
0
2
1
2
0
1
1
2
1
0
2
1
1
1
1
1
0
0
1
2
0
0
1
0
1
2
1
1
1
1
0
2
1
0
2
1
1
1
2
1
0
1
0
1
1
2
1
1
0
0
2
0
0
1
0
0
0
0
2
2
0
1
1
0
0
2
2
1
1
1
1
2
1
2
2
0
1
0
1
2
2
1
1
1
1
1
1
0
1
1
1
2
0
1
0
0
1
1
1
1
2
1
0
1
1
1
1
0
1
0
0
2
1
1
1
2
1
1
2
1
1
1
1
0
0
1
0
2
1
0
1
1
1
0
1
2
1
1
2
1
0
1
2
0
2
1
1
1
1
1
0
0
0
0
2
1
1
0
2
1
1
0
0
1
1
1
1
1
0
0
1
1
1
1
0
1
2
0
0
1
3
0
1
2
0
2
1
1
1
0
1
1
0
1
1
0
1
0
0
1
0
2
0
2
1
2
2
2
1
0
1
0
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
2
1
1
0
1
2
0
1
1
1
1
1
1
0
1
1
1
1
1
1
2
1
0
1
1
2
1
1
2
1
2
1
1
1
1
2
2
0
1
1
2
1
1
1
2
1
1
0
1
1
0
2
2
1
1
0
0
1
1
1
1
1
1
1
2
1
1
2
1
1
1
0
0
1
1
1
1
0
1
2
0
1
0
2
1
1
2
0
1
1
1
1
1
1
0
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
5
2
1
1
2
3
0
2
0
0
1
2
1
0
1
3
0
1
1
0
1
1
0
0
1
1
1
2
1
1
0
2
1
1
0
0
1
0
2
1
2
1
2
1
1
1
1
1
1
0
1
1
1
2
0
2
1
0
0
0
1
1
1
0
2
1
1
2
2
2
2
2
2
1
1
1
1
2
2
0
0
1
2
2
0
1
0
1
0
1
1
0
1
1
0
1
0
2
1
1
1
2
1
2
0
2
0
1
0
2
1
2
1
2
0
1
1
0
1
1
1
1
0
1
1
1
1
0
0
0
1
2
1
1
1
1
2
2
0
1
1
1
0
1
0
1
1
1
2
0
1
1
1
2
1
0
0
1
1
0
1
1
1
1
2
2
1
1
1
1
1
1
2
2
1
2
0
0
1
1
0
0
1
1
0
2
1
1
0
1
0
2
1
0
1
1
1
2
3
1
1
1
1
1
2
1
0
2
1
1
0
1
0
0
1
1
0
2
1
2
1
0
2
2
0
1
1
1
1
2
1
1
1
1
0
2
1
1
1
1
2
1
0
0
1
1
1
1
2
2
1
2
0
1
1
1
2
0
1
2
2
3
1
1
2
0
1
1
0
1
1
0
1
0
0
1
2
0
1
3
2
1
2
3
0
2
1
0
2
1
0
1
1
1
1
0
2
1
1
0
1
1
0
0
0
1
0
2
2
0
2
1
0
1
2
1
1
1
2
0
0
1
1
2
2
0
1
1
1
1
1
3
1
2
2
0
1
0
1
1
1
1
2
1
2
1
4
1
1
1
2
0
0
0
1
1
1
0
1
1
1
1
2
1
1
0
0
0
2
1
0
1
1
2
0
2
2
0
2
1
2
1
1
2
1
2
1
1
2
1
1
1
1
1
2
2
2
1
2
1
1
2
1
1
0
1
1
0
1
1
0
1
1
1
0
0
1
0
1
0
2
0
2
1
1
2
1
1
0
2
1
1
3
2
2
1
1
1
2
2
0
2
1
2
1
2
1
1
0
2
0
2
1
1
1
1
1
1
2
1
1
1
1
0
1
1
2
0
2
1
2
0
0
2
0
2
0
2
1
0
2
1
1
1
1
1
1
0
0
2
1
1
0
1
1
2
2
1
0
1
2
1
2
1
1
2
1
1
2
0
1
2
1
1
1
2
1
1
0
2
2
0
2
1
2
2
1
1
2
1
1
1
2
1
2
1
1
0
2
0
1
2
1
0
3
2
1
1
0
1
2
2
1
1
0
0
2
1
0
2
2
1
0
2
1
1
2
2
1
0
1
1
1
1
2
1
1
2
0
1
0
2
1
0
2
1
1
4
0
1
2
1
2
1
1
0
1
1
1
0
0
2
2
0
1
0
1
0
0
0
2
3
1
2
0
0
2
0
1
1
1
0
2
1
2
2
2
1
0
1
1
1
1
1
2
2
0
2
2
2
1
1
1
2
0
0
1
1
1
1
2
0
2
0
1
1
1
0
2
1
0
2
0
0
0
1
0
1
1
1
0
0
1
2
1
0
1
1
1
0
0
2
1
0
0
0
0
1
0
1
1
2
2
0
0
2
1
1
1
1
1
2
1
2
0
1
2
1
0
0
0
1
0
1
1
2
1
0
1
0
1
2
1
0
1
0
1
1
2
1
1
1
1
1
1
0
4
1
2
0
1
1
1
1
1
1
1
2
0
0
1
1
1
1
1
1
1
0
0
0
2
0
0
1
1
1
1
0
1
1
0
0
0
1
1
1
1
0
2
0
2
0
1
0
0
0
1
1
2
2
1
1
0
0
1
0
0
1
1
2
0
0
1
1
1
0
0
2
2
2
0
2
1
2
1
2
1
1
1
0
2
0
1
1
1
1
1
1
0
1
1
2
1
0
0
2
1
0
0
1
0
0
2
0
2
2
0
1
0
2
1
1
1
1
1
1
1
0
1
1
0
0
1
1
2
1
1
2
1
1
1
0
1
0
1
0
1
1
1
1
1
1
2
1
0
0
1
0
1
1
0
1
1
2
1
2
2
2
2
1
1
1
1
1
1
3
2
1
2
1
0
1
0
0
2
1
1
1
1
0
1
1
0
0
0
0
1
2
1
1
2
1
1
1
0
2
1
0
0
0
1
1
1
1
1
2
0
4
1
0
0
0
0
1
2
1
0
0
0
2
0
1
0
1
1
2
1
1
0
1
1
1
1
2
1
1
1
1
0
1
1
1
2
0
1
1
2
4
2
1
1
1
2
0
1
1
0
1
1
1
2
0
2
0
1
1
1
1
2
1
2
2
1
0
1
0
1
1
1
2
0
1
0
1
0
1
1
0
1
1
2
2
2
1
1
1
1
2
0
0
1
2
1
2
0
1
2
0
1
2
2
1
1
1
1
0
2
0
1
1
1
2
1
1
1
0
0
0
1
2
1
1
1
1
1
2
1
1
1
2
2
1
1
2
1
1
1
1
2
1
2
1
0
2
1
1
1
1
1
1
1
0
0
0
1
1
1
0
1
2
2
2
1
1
0
0
1
0
1
1
2
1
1
0
1
1
0
2
1
1
1
1
1
2
1
1
0
4
0
1
1
0
0
1
1
2
1
1
0
0
2
1
1
1
1
1
1
1
0
1
1
2
1
1
2
2
2
1
1
1
0
0
3
2
2
1
1
1
0
1
0
2
0
2
2
1
0
2
1
2
1
1
1
1
0
2
2
2
1
1
0
0
2
2
2
1
1
1
0
2
1
1
1
2
1
2
2
1
1
1
0
1
1
2
2
1
0
1
1
2
1
1
1
0
1
1
1
1
1
2
0
1
1
2
3
1
1
2
1
1
1
0
1
1
1
2
1
2
0
1
1
1
0
0
0
2
1
1
1
2
1
2
1
2
0
2
1
0
1
2
2
1
1
2
2
1
1
0
1
0
2
1
2
1
0
1
1
1
1
1
1
1
1
1
0
2
1
1
1
2
2
1
2
1
1
1
1
1
0
0
1
1
1
1
1
2
1
0
2
1
0
2
0
1
2
1
0
1
1
2
0
1
2
2
1
2
0
1
1
2
1
2
2
1
1
1
2
1
0
1
1
0
2
1
3
0
1
0
1
2
1
1
1
0
1
0
0
2
2
1
2
1
1
2
1
0
2
0
0
0
2
1
1
1
1
1
0
1
2
1
2
1
1
0
0
2
1
0
1
1
0
1
2
1
1
1
0
2
2
1
1
1
1
1
1
2
1
1
0
1
1
1
3
2
1
1
1
1
0
0
0
1
1
2
0
1
0
0
0
2
1
0
2
1
0
1
1
2
0
0
1
1
2
2
1
2
1
1
2
2
1
1
1
2
2
1
2
0
0
1
0
0
1
0
1
1
0
0
0
1
1
0
1
2
0
2
1
0
0
1
0
2
2
0
1
1
2
0
0
2
1
1
0
2
2
2
1
0
0
1
0
1
1
1
1
1
1
2
2
1
1
1
0
1
2
1
0
1
1
1
1
1
1
0
1
0
1
1
2
2
0
2
1
0
1
1
2
1
1
1
0
2
1
2
1
0
2
1
1
0
1
2
1
1
3
0
1
1
2
1
0
1
1
2
1
1
0
2
2
0
1
1
1
1
2
2
1
1
1
0
0
1
1
1
1
1
0
0
1
0
2
2
1
1
1
0
2
1
0
2
1
1
0
2
0
1
1
1
1
1
2
2
1
1
2
1
1
1
1
0
2
0
0
2
2
0
1
2
2
1
0
1
0
1
1
1
1
1
0
2
2
1
1
2
1
2
1
0
2
2
1
2
2
1
0
2
2
1
1
1
1
0
0
3
1
1
2
2
2
0
1
2
1
0
0
2
1
1
0
2
2
2
0
2
1
2
2
0
1
1
1
1
1
0
2
1
1
1
0
1
2
2
1
1
0
1
1
1
1
1
2
0
0
1
1
0
1
2
1
0
1
1
2
0
1
0
1
1
1
1
1
0
0
0
1
1
1
1
0
0
2
0
0
1
2
2
1
0
1
2
2
0
1
2
0
0
1
1
3
1
1
2
0
1
2
1
0
1
1
1
2
1
1
1
0
1
0
0
1
2
0
2
1
2
0
1
2
1
2
1
2
0
1
1
1
1
0
1
2
1
2
1
1
1
4
1
1
1
1
1
1
1
1
0
1
2
0
0
1
0
0
1
1
1
1
1
1
1
0
0
0
0
1
1
1
0
2
2
0
0
1
0
1
1
1
1
1
0
1
1
1
1
1
0
2
2
2
1
1
2
0
1
1
0
0
1
1
2
2
2
1
1
2
0
2
0
2
0
1
1
1
2
1
1
1
2
1
1
1
1
1
1
0
1
1
1
0
2
2
0
1
1
4
2
1
1
1
2
0
1
1
0
0
2
1
2
1
1
2
2
1
1
1
1
1
1
1
2
1
0
2
2
2
0
1
1
2
1
1
1
3
1
1
1
0
2
0
0
0
1
1
0
0
1
2
0
0
1
0
1
2
1
0
1
2
2
0
2
2
2
2
1
1
0
2
1
2
1
2
2
0
0
0
1
2
1
0
1
1
2
1
0
0
2
2
2
2
0
1
1
0
1
2
1
1
2
1
0
2
1
1
1
3
2
1
1
1
1
1
1
1
0
0
1
1
1
1
2
0
2
1
0
1
2
1
0
1
1
2
0
1
1
1
1
0
1
2
1
1
1
0
0
0
1
1
1
1
0
1
0
1
2
2
1
1
1
0
1
2
2
0
0
0
1
0
2
0
2
2
0
0
1
0
1
1
2
0
2
2
2
0
0
0
0
2
1
1
1
0
1
0
2
2
0
1
1
2
1
2
1
1
2
1
0
0
2
1
1
1
1
1
1
1
2
1
0
0
1
1
2
2
2
1
0
2
0
1
0
0
1
1
0
2
2
0
1
0
1
1
0
0
1
0
1
1
1
1
0
1
2
2
1
1
1
2
2
1
3
1
1
2
2
1
1
0
1
0
0
1
2
0
1
1
0
2
1
1
2
0
0
1
1
0
1
1
0
2
1
1
1
1
1
0
1
1
1
1
1
1
0
1
1
0
1
0
1
0
2
2
1
1
1
1
1
1
1
0
2
1
0
1
2
0
0
1
1
2
1
1
1
1
1
1
1
0
2
2
1
0
0
1
0
1
1
1
2
0
1
2
1
2
1
1
1
2
0
1
0
0
0
1
2
0
2
1
1
0
1
2
1
2
1
2
2
2
1
0
0
2
0
2
1
1
1
1
1
2
1
0
2
2
5
0
1
1
1
2
0
0
1
2
2
0
1
1
2
1
0
1
1
1
2
0
0
1
1
1
1
1
1
1
2
2
1
0
1
0
1
1
1
1
1
0
1
0
1
1
2
0
0
0
0
1
1
2
1
0
2
1
1
1
2
1
0
1
1
2
2
1
1
1
1
0
1
0
1
2
1
2
0
1
1
1
1
1
1
2
2
0
1
3
2
1
1
3
2
1
0
0
1
0
2
1
0
2
1
0
1
1
1
1
1
6
0
1
2
1
1
0
1
1
1
1
2
1
0
1
1
1
1
0
1
0
1
1
1
0
1
1
2
1
0
1
1
2
1
0
1
0
1
1
1
1
0
0
1
1
1
2
0
2
2
1
1
0
0
1
0
0
1
1
2
1
0
1
0
1
2
1
1
0
0
0
2
2
2
1
1
1
2
1
1
1
1
2
1
1
0
1
1
2
2
1
2
2
1
1
0
1
1
2
1
1
1
1
1
3
2
1
0
1
0
2
2
1
0
1
1
1
1
1
2
0
1
2
1
1
0
0
1
1
1
1
0
1
0
1
0
0
0
1
0
0
1
1
1
0
0
1
0
1
2
0
3
0
0
1
1
1
1
1
2
1
1
0
0
1
2
1
0
0
1
1
2
0
0
2
1
1
2
1
2
0
1
2
2
2
2
1
1
1
0
1
1
1
1
0
0
1
0
3
2
2
0
0
2
1
1
0
0
2
2
1
2
1
1
1
1
1
0
0
1
1
1
1
0
0
2
2
1
0
3
1
1
1
1
0
1
1
1
1
1
0
0
0
2
1
2
1
0
1
1
1
0
1
2
2
2
1
1
0
0
0
1
1
0
2
1
2
1
2
1
0
2
1
1
1
2
0
0
1
0
0
1
2
1
1
1
2
1
1
1
2
2
0
1
1
2
1
1
0
1
1
2
1
1
2
1
2
2
2
1
1
0
0
4
1
0
2
0
1
0
2
1
1
0
2
1
1
1
0
1
2
1
0
0
0
0
1
2
1
1
1
0
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
2
0
0
1
0
2
0
0
0
1
0
1
2
1
2
1
2
1
2
1
1
0
0
2
0
0
1
1
1
0
1
1
2
0
0
1
1
1
0
1
0
1
0
1
1
1
1
1
1
1
1
1
2
0
0
2
1
0
2
3
0
1
0
1
0
1
0
0
1
0
2
2
1
2
1
0
0
0
1
1
1
2
1
2
1
1
2
2
1
1
1
1
1
1
0
1
2
1
0
1
1
1
0
0
2
1
4
1
2
2
1
0
1
1
1
0
1
1
1
1
1
0
1
1
1
0
1
0
1
1
0
2
2
1
0
1
0
1
2
1
0
1
1
0
1
0
2
0
2
1
1
2
2
1
1
0
2
0
1
2
0
2
1
1
2
1
1
1
1
2
1
0
1
1
3
0
0
2
2
3
3
1
1
1
0
1
1
1
2
2
0
0
2
0
0
1
0
1
1
1
0
0
2
3
0
1
1
0
0
0
1
2
0
1
2
1
1
1
1
1
1
0
2
2
1
1
1
1
2
0
1
2
2
1
0
1
1
0
1
1
0
1
1
1
0
1
0
1
1
1
1
2
1
1
0
1
2
2
1
0
1
1
0
2
1
1
1
1
2
2
1
2
1
1
1
1
0
0
0
1
1
0
1
0
1
0
1
1
1
0
1
1
1
2
1
1
0
0
1
2
1
2
1
2
0
1
1
1
0
1
0
1
1
1
1
1
1
0
2
1
1
1
1
1
2
2
1
1
1
1
1
2
1
0
1
1
2
0
1
0
2
1
2
0
2
0
0
1
2
1
1
1
0
0
1
1
2
1
0
1
2
1
2
2
1
1
1
1
1
0
2
2
0
1
1
2
2
1
0
2
1
1
0
0
0
1
1
1
1
0
2
0
0
1
1
1
1
1
2
1
0
1
1
1
0
0
2
0
1
1
1
1
1
2
0
0
1
2
0
1
1
0
2
0
0
2
1
2
1
1
0
1
1
1
1
2
1
1
2
1
1
1
1
1
1
0
0
1
0
0
1
0
1
1
2
1
0
1
1
2
1
2
2
0
2
1
0
0
1
2
0
1
2
1
0
2
2
2
0
1
1
0
0
1
2
1
0
0
1
1
1
2
1
0
0
1
3
1
1
1
2
2
2
2
1
0
2
1
1
1
1
1
1
2
1
1
1
2
1
1
0
0
0
1
2
0
1
1
1
1
1
1
1
2
1
0
1
1
1
1
0
2
2
1
2
2
2
0
2
1
1
1
1
2
1
2
0
2
1
1
2
2
1
1
2
1
1
2
0
2
1
1
1
2
1
2
1
0
1
1
1
1
2
6
1
0
2
1
1
1
1
2
2
1
0
0
2
1
1
2
1
0
2
1
0
2
1
0
1
2
2
2
2
2
0
0
1
1
1
1
1
1
1
1
0
1
0
0
0
2
0
1
2
1
1
0
1
1
0
1
0
1
0
1
1
0
0
2
0
1
2
1
1
2
1
2
2
2
1
2
1
1
2
1
2
0
2
2
1
1
1
1
2
0
1
1
0
2
1
1
1
1
1
1
0
1
0
1
2
1
1
1
1
1
0
1
2
1
1
1
0
1
2
0
0
1
0
2
0
2
1
2
1
2
2
0
0
1
1
1
1
0
1
3
0
1
1
0
1
1
2
1
1
1
1
1
1
1
1
1
1
0
1
1
0
1
1
2
0
2
2
2
0
1
2
2
2
1
1
0
0
1
0
1
2
2
1
1
2
1
1
1
2
0
2
1
2
2
2
0
1
1
0
1
0
1
2
2
1
2
0
2
0
1
2
3
1
1
1
0
2
0
0
1
2
1
0
2
1
1
0
1
0
0
1
2
1
0
1
1
0
3
0
0
1
2
1
1
0
1
1
2
2
1
0
1
2
1
0
1
3
0
1
0
1
1
1
0
1
0
1
2
1
1
1
1
1
1
0
1
1
2
2
2
0
1
0
1
0
1
0
1
0
0
2
1
1
2
1
1
1
1
0
1
1
2
1
1
0
1
2
1
1
0
1
0
1
1
2
1
1
2
1
1
1
0
2
1
1
1
0
0
1
1
2
1
0
2
2
1
1
2
2
1
1
2
0
1
2
2
0
1
1
0
1
2
0
1
0
1
2
0
0
1
2
2
2
2
2
0
0
1
4
0
0
1
2
1
1
1
2
1
2
1
1
1
2
0
2
2
1
3
2
0
0
1
1
1
1
0
0
1
2
1
2
2
1
1
0
0
1
2
1
1
0
3
0
2
2
2
1
0
0
1
1
0
1
3
1
1
0
2
3
2
1
2
1
2
1
1
0
0
2
0
1
2
2
2
0
0
0
1
0
2
2
1
0
1
1
2
2
1
0
1
1
4
0
0
1
2
1
1
2
1
0
2
1
1
0
0
0
0
0
1
2
1
1
2
1
2
2
1
1
1
3
2
2
2
2
1
5
2
2
1
1
0
1
1
1
1
2
1
1
1
1
1
1
1
1
2
0
1
0
0
1
1
1
0
1
1
0
2
0
0
0
2
2
3
2
1
2
1
2
1
0
2
1
1
0
2
2
2
1
1
1
1
1
0
0
2
0
0
1
1
1
0
1
0
0
1
1
1
2
1
1
1
0
1
2
2
0
1
0
1
0
0
1
0
2
0
0
2
1
2
1
0
0
2
1
0
2
0
0
1
1
1
1
1
1
1
1
1
0
0
1
1
0
1
1
1
1
1
1
1
2
1
2
1
2
2
1
1
1
1
2
1
0
0
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
3
0
2
1
0
0
0
1
1
1
2
1
1
2
0
0
1
0
1
1
2
2
1
0
1
1
0
1
1
1
1
3
0
1
0
0
2
0
0
0
1
2
0
0
2
0
0
1
2
1
1
1
1
1
1
1
2
1
1
2
0
1
0
1
1
1
0
2
2
1
2
1
0
1
1
1
1
2
1
2
2
1
1
1
0
1
1
1
1
3
1
3
2
0
0
1
0
1
1
3
0
0
0
2
1
3
1
2
1
0
2
0
1
2
2
1
2
1
0
1
0
1
1
2
0
1
1
2
1
2
0
2
0
0
0
2
2
1
1
1
0
2
1
2
1
2
2
0
3
1
1
1
0
1
0
1
1
1
0
2
1
1
0
0
0
2
1
2
1
1
1
0
2
1
0
0
1
1
1
1
2
0
0
2
1
1
1
0
1
1
1
1
1
1
0
1
2
1
0
0
1
2
0
1
0
2
0
2
2
1
1
1
3
0
1
0
2
1
0
1
1
1
1
1
1
1
1
1
2
0
0
1
0
1
1
1
3
1
1
1
1
1
1
1
1
0
1
1
2
1
1
0
0
0
0
1
2
1
0
1
1
2
0
0
1
1
1
1
0
1
1
1
0
2
1
1
1
2
1
2
1
0
1
1
2
0
2
0
2
1
1
1
1
1
2
1
1
0
2
0
0
0
1
0
0
1
0
0
1
1
1
1
2
0
1
1
1
2
2
1
0
1
0
1
2
2
0
1
1
1
0
0
0
1
1
0
0
1
1
0
0
0
0
0
1
1
1
1
1
1
2
1
1
2
0
0
1
0
1
1
0
0
1
1
1
0
1
0
1
0
2
0
2
1
1
0
2
1
1
1
1
2
0
0
0
1
0
1
2
1
0
0
1
0
1
0
1
0
0
0
1
1
1
0
1
1
0
0
1
1
1
1
2
2
0
2
1
2
1
2
0
0
1
1
2
0
0
1
1
0
1
2
2
0
1
0
0
0
0
2
0
1
1
2
2
1
1
1
0
2
2
0
0
1
0
2
0
1
1
2
0
1
0
1
1
1
1
1
0
2
2
1
1
0
0
2
0
0
0
1
1
2
0
2
1
3
0
1
2
2
2
1
2
0
1
1
0
2
0
1
2
0
1
2
0
1
0
1
2
2
1
2
1
0
0
1
0
1
2
0
0
1
2
0
0
1
0
1
1
1
1
1
2
2
2
2
1
2
2
1
2
2
1
2
1
0
1
0
1
1
2
2
1
1
0
0
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
0
1
1
2
1
0
1
4
2
0
1
1
1
0
1
1
2
2
1
0
3
0
1
2
0
1
2
2
1
1
1
0
1
1
2
1
1
0
0
2
0
1
1
1
0
1
1
2
0
0
1
0
1
1
1
0
1
2
0
1
2
1
1
1
1
1
1
1
1
2
2
1
1
1
0
1
1
1
1
1
0
2
1
1
1
0
1
1
0
1
1
0
0
1
0
2
1
1
2
2
2
0
1
1
1
1
1
1
1
1
1
1
0
0
1
2
2
0
1
1
1
1
0
0
1
1
1
1
1
0
2
1
1
0
2
1
1
1
1
2
1
1
0
1
1
1
1
1
1
0
1
0
1
2
1
0
1
1
1
1
0
1
0
1
1
1
0
1
2
1
0
2
0
0
2
1
2
1
1
1
0
0
0
1
0
0
1
2
3
1
0
1
1
2
1
1
1
0
1
0
1
2
1
2
0
1
1
0
3
1
0
0
0
1
1
2
0
0
2
2
0
2
1
2
1
1
1
1
2
1
1
0
2
0
1
2
2
1
1
1
1
2
3
1
2
1
1
0
1
1
1
0
0
1
1
0
1
2
1
2
1
0
1
1
1
0
0
0
1
1
1
1
0
0
1
1
0
1
1
0
0
0
2
0
1
0
1
1
0
2
0
1
0
1
1
0
2
1
0
2
2
0
1
1
0
1
1
1
0
0
2
1
1
1
0
1
1
2
1
2
1
0
2
1
2
2
1
1
1
3
1
1
0
2
1
0
1
1
0
1
0
1
1
0
0
1
1
1
1
0
2
1
1
1
1
1
0
1
1
1
1
0
0
2
1
0
1
2
0
1
1
1
0
1
1
0
2
0
2
1
2
0
0
2
1
1
0
0
0
1
1
1
2
0
2
1
1
0
2
2
2
2
1
1
2
2
1
2
1
1
0
2
0
1
0
0
1
2
0
0
1
1
1
1
1
1
1
0
0
1
1
1
1
0
3
1
1
0
1
1
2
0
0
1
1
1
1
2
0
2
1
1
2
1
1
1
0
0
2
1
0
1
2
0
0
1
1
1
2
1
1
1
2
1
1
1
2
1
0
2
1
0
1
2
1
2
1
2
2
2
1
1
2
2
1
1
2
2
0
1
2
0
2
2
0
1
1
0
0
2
2
0
1
1
2
2
1
1
1
2
1
1
1
0
1
1
1
1
1
0
0
0
1
0
1
1
0
1
1
0
1
1
0
1
2
0
0
2
2
1
0
1
2
1
0
0
0
2
3
1
0
1
1
0
0
0
0
1
0
2
1
1
2
1
1
1
2
0
1
2
1
2
0
1
2
0
1
1
0
1
0
2
0
1
1
0
2
1
2
2
2
0
0
1
2
1
1
0
1
1
1
1
1
0
2
1
1
2
0
2
0
1
1
1
1
1
1
2
0
2
2
2
2
1
0
0
1
1
1
2
2
1
2
1
2
1
1
1
1
1
0
0
1
1
2
1
1
0
0
1
1
1
2
2
1
1
1
2
1
1
1
2
0
1
2
1
1
0
1
1
2
2
1
1
1
1
1
2
4
0
1
1
1
1
2
2
2
0
1
1
1
1
1
0
1
1
1
2
2
1
2
1
0
1
2
0
1
1
0
0
0
1
2
1
1
0
0
2
0
1
1
1
0
0
1
0
0
0
1
1
2
2
1
2
1
1
1
1
2
0
2
3
1
2
1
1
0
1
1
2
1
0
0
3
2
0
1
2
1
2
1
1
1
1
2
0
2
1
1
1
1
2
0
2
0
1
0
2
2
1
1
1
2
0
2
0
3
1
0
1
0
2
2
1
2
1
0
1
1
2
5
1
2
1
0
1
1
2
2
2
1
1
2
1
1
1
2
2
2
2
0
0
1
1
1
2
2
2
1
0
1
1
0
1
1
0
0
2
2
0
2
2
1
0
0
1
2
1
2
1
1
0
1
0
2
2
1
0
2
1
2
1
2
1
1
1
1
1
1
1
1
0
1
0
1
1
0
1
1
1
0
1
2
1
1
2
1
0
1
0
2
1
1
0
1
0
0
0
2
0
1
0
1
1
2
1
0
1
1
0
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
0
1
0
1
1
0
0
1
0
2
1
1
1
1
1
1
2
2
1
1
0
0
0
2
2
1
1
1
1
1
0
1
2
2
3
2
1
1
1
1
2
1
2
1
0
0
0
1
2
1
4
1
1
1
0
0
2
0
1
2
1
3
2
2
1
0
0
0
1
1
0
1
1
0
0
1
1
2
0
1
0
1
0
1
1
0
0
2
0
1
0
2
0
0
0
1
0
1
2
1
0
1
2
0
1
2
2
0
2
1
1
0
1
2
0
1
1
1
0
2
1
1
3
0
0
0
0
0
0
1
1
2
1
1
1
0
0
2
2
0
1
0
2
2
1
2
2
1
1
2
1
1
0
1
0
1
0
1
0
1
8
1
2
2
1
0
2
2
1
1
1
1
1
1
0
0
2
1
0
1
2
1
1
1
0
1
0
1
2
1
0
0
1
1
2
2
2
0
0
2
2
1
2
1
1
1
0
1
1
2
1
1
7
2
2
1
1
0
1
2
1
2
2
2
0
1
0
1
2
1
3
0
0
2
1
0
0
2
1
1
1
1
2
1
0
1
0
0
1
0
2
1
1
1
1
0
0
3
1
1
1
2
1
1
2
2
1
1
1
2
0
1
1
1
1
2
1
1
1
1
1
0
2
1
1
1
1
2
0
1
1
2
0
2
1
2
0
2
2
1
0
1
1
0
0
2
2
1
1
1
0
1
0
2
1
0
2
1
0
1
2
1
1
1
1
2
1
0
0
1
0
0
1
0
1
1
2
1
0
0
1
2
0
2
1
1
0
1
1
2
1
1
0
0
0
0
2
0
0
1
1
2
1
2
1
0
1
1
0
1
1
0
2
0
1
1
2
0
1
0
3
0
2
1
1
2
0
1
0
1
2
1
2
1
1
2
2
1
1
1
1
0
1
1
1
2
0
2
2
1
2
0
2
2
1
2
0
2
0
0
0
1
1
1
13
1
1
1
1
1
0
0
0
1
2
0
1
2
1
1
1
2
1
1
1
1
1
2
1
1
1
0
1
1
0
1
0
1
2
1
1
1
1
1
1
0
1
1
1
1
0
1
0
0
0
2
1
2
1
0
1
0
2
1
1
1
0
0
2
1
3
1
1
2
2
1
0
2
1
0
0
1
0
0
1
1
1
0
1
1
2
1
1
1
2
1
1
1
2
0
1
5
1
1
0
2
1
1
1
2
0
1
0
1
1
1
1
1
1
1
2
1
1
0
0
1
0
0
0
1
2
1
1
1
1
1
2
2
2
2
2
0
2
1
1
1
2
1
0
2
1
1
2
2
0
1
1
1
0
1
0
1
0
1
2
2
1
0
0
0
1
1
0
1
0
1
3
1
2
1
1
1
0
1
2
2
1
1
1
2
0
1
2
0
2
1
2
1
1
2
2
1
0
2
0
1
3
2
1
1
0
2
0
1
1
1
0
0
0
1
0
1
1
1
1
1
2
1
0
0
1
2
2
2
0
0
1
1
1
0
1
1
2
0
1
0
2
2
1
0
1
2
2
1
2
1
2
2
2
1
0
1
0
1
2
1
1
2
2
1
2
2
1
1
0
0
1
1
2
1
1
0
1
1
1
2
1
4
2
1
1
1
1
2
1
2
1
1
0
1
1
1
1
0
1
1
2
1
1
2
0
0
1
0
1
1
1
1
2
1
1
1
1
1
0
0
1
0
0
1
1
1
0
1
1
0
1
2
0
1
2
2
1
2
2
1
1
1
1
0
0
1
0
2
0
1
0
1
2
1
2
1
1
2
1
1
0
0
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
0
1
0
0
2
1
1
2
0
0
1
0
2
0
0
2
1
1
1
2
0
1
0
1
0
1
1
3
1
2
1
0
1
1
2
0
0
0
1
2
1
1
1
1
0
0
2
0
2
1
2
1
2
2
2
1
1
1
1
0
1
0
2
1
1
2
0
1
2
1
0
1
1
1
1
1
0
0
1
2
0
1
2
2
2
0
1
0
1
2
1
1
1
1
0
2
2
1
0
1
1
1
1
1
0
1
1
2
2
1
2
0
1
1
2
1
2
2
2
1
2
0
2
0
2
1
1
1
0
1
1
1
1
2
2
1
0
1
1
1
0
1
1
2
1
1
1
2
1
0
1
1
2
0
0
1
2
1
1
2
2
1
1
0
2
1
0
1
0
1
0
1
0
2
1
1
1
2
1
0
1
1
2
0
1
1
1
2
0
1
2
1
1
1
1
1
0
0
1
0
1
1
0
1
0
1
2
1
1
1
2
0
0
1
0
1
1
1
2
0
1
0
1
0
1
1
0
0
1
2
0
1
0
0
1
2
1
0
1
1
1
1
1
0
2
2
0
1
1
1
1
1
1
0
1
1
0
2
0
2
1
2
2
1
1
0
1
2
1
1
2
1
0
1
1
4
1
1
2
1
2
0
1
1
1
1
4
0
1
1
0
5
1
1
1
2
2
1
0
1
0
0
1
1
2
1
0
0
2
1
0
1
0
1
0
1
1
2
1
2
2
0
1
1
1
1
2
0
0
1
2
0
0
1
1
2
1
0
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
0
1
1
1
0
1
1
0
1
0
1
2
2
1
1
1
0
1
0
1
1
2
1
1
1
1
1
2
2
2
2
0
2
0
1
1
2
0
1
1
1
1
2
1
1
0
2
0
0
2
1
0
2
1
1
0
1
1
0
1
1
0
1
0
0
0
1
2
0
1
0
0
1
1
0
1
2
0
1
1
2
1
0
1
1
1
1
1
2
2
1
1
1
2
0
1
1
1
0
1
2
1
0
0
2
2
1
1
1
1
2
1
2
0
0
1
0
2
1
2
2
2
2
1
2
1
1
1
0
0
0
1
1
1
1
1
1
1
0
1
1
1
0
1
1
1
2
1
0
0
2
2
2
0
2
0
0
1
1
0
1
2
2
2
0
2
1
2
1
2
1
1
1
1
0
1
2
2
1
1
1
0
0
1
1
1
1
1
1
1
1
2
2
2
1
0
2
1
1
1
1
1
1
1
2
2
0
1
2
1
0
1
0
1
1
2
1
1
2
2
1
1
0
0
1
1
0
1
1
2
1
0
1
2
1
2
0
0
1
0
2
2
1
2
1
1
1
1
1
1
2
1
1
1
2
2
0
2
0
0
1
0
1
3
1
1
1
1
0
1
1
1
2
1
1
2
0
2
1
2
2
0
0
1
0
0
0
0
2
1
2
2
2
0
1
0
2
2
1
1
1
0
2
1
1
1
1
1
1
1
0
1
1
1
1
1
2
1
0
0
0
2
2
1
2
0
1
0
2
2
2
1
0
1
1
2
1
1
1
1
1
0
0
1
1
0
1
1
2
0
1
2
1
1
1
0
1
0
0
2
1
1
1
1
0
1
0
2
1
2
0
2
0
0
1
0
2
0
1
0
1
1
1
1
1
2
1
1
1
2
1
0
2
1
1
1
1
2
1
2
2
1
0
1
1
0
2
2
1
1
1
1
0
0
1
2
2
1
1
0
0
0
2
1
1
1
2
1
1
1
1
1
2
1
1
1
0
0
1
1
1
0
0
1
1
2
2
2
0
1
0
1
3
1
1
1
1
1
1
1
0
2
1
1
1
1
0
2
1
2
2
2
1
1
2
1
1
1
0
1
3
0
0
2
1
1
1
2
1
0
1
1
0
0
0
2
1
2
1
1
1
0
1
0
2
1
1
1
1
0
1
2
1
0
1
2
1
0
1
1
0
1
2
0
1
2
0
1
1
2
1
2
1
0
5
1
0
1
0
2
3
2
2
1
1
0
2
0
1
1
1
0
1
1
1
0
1
1
0
1
2
1
1
2
1
1
1
0
0
0
2
2
1
1
1
1
0
1
2
1
1
0
1
1
0
1
1
1
1
0
1
1
1
0
1
0
1
1
1
0
1
0
2
2
1
2
0
1
1
1
1
1
1
1
1
0
1
2
1
1
0
0
0
1
2
1
2
1
1
1
2
0
1
0
1
0
1
1
0
0
1
1
1
1
1
1
1
1
1
1
0
3
1
1
1
1
0
1
1
1
0
0
3
2
0
0
0
2
1
1
1
1
1
1
1
1
1
0
0
1
0
1
1
2
0
1
1
2
1
0
1
2
1
1
2
2
1
1
0
1
1
0
1
1
1
0
2
0
0
0
3
0
2
1
0
1
2
1
1
0
1
1
1
0
2
0
0
1
2
1
1
2
0
1
1
1
2
0
2
2
0
2
1
1
1
1
2
2
2
1
2
1
0
1
2
0
1
1
2
2
1
1
1
1
1
0
1
1
1
2
2
2
1
0
2
2
1
0
0
1
1
1
2
0
2
1
0
0
1
2
0
1
1
1
0
0
1
3
0
2
2
1
1
1
0
0
1
1
0
1
0
0
0
1
1
0
0
0
0
2
1
1
0
1
1
0
1
1
0
1
2
0
1
1
1
0
0
1
1
1
1
2
1
1
0
1
2
2
1
1
1
1
1
1
1
0
1
0
1
1
1
1
1
1
2
1
1
1
0
0
2
1
0
1
2
1
1
1
0
1
2
2
0
2
2
0
1
1
2
1
2
1
0
1
0
0
2
1
1
1
1
0
1
0
2
1
0
1
1
2
1
0
1
0
0
2
0
1
1
0
1
1
2
1
0
0
1
2
1
0
0
1
1
0
2
1
0
0
1
1
1
2
0
2
2
1
1
1
0
1
0
1
1
0
2
0
1
1
0
2
2
2
1
0
0
1
1
0
3
1
1
1
2
1
0
1
1
1
1
1
1
1
1
1
2
1
2
2
1
0
1
1
1
1
1
0
1
1
1
2
1
0
0
1
0
0
1
1
1
1
0
0
1
1
0
0
0
1
1
0
1
1
1
1
0
2
1
0
2
2
1
1
1
0
2
0
1
2
0
2
0
1
0
0
2
1
2
1
1
1
1
1
1
1
1
1
1
0
0
0
1
0
1
1
3
1
1
1
2
0
1
0
1
1
1
2
1
0
2
2
2
1
1
2
1
1
0
2
2
2
1
1
1
0
1
2
1
0
1
1
1
1
1
1
1
1
0
0
2
1
1
1
1
2
0
1
1
1
2
1
0
1
0
1
1
1
1
0
0
1
2
1
0
0
2
2
0
1
1
1
1
0
1
1
1
1
1
0
1
2
2
1
1
1
2
1
0
0
1
1
1
1
1
1
2
1
1
1
1
0
1
0
0
0
2
1
0
0
1
1
4
0
2
1
1
1
1
1
0
1
2
1
2
0
1
1
2
1
0
1
2
2
1
1
2
1
0
0
1
1
0
1
1
1
1
1
1
1
2
1
1
0
1
1
1
1
0
1
1
1
2
1
1
2
1
1
2
2
1
1
1
2
2
0
2
1
0
1
0
1
0
2
2
0
0
1
2
0
2
0
1
1
0
2
0
1
1
2
1
1
0
2
1
1
0
1
2
1
1
1
2
1
1
1
1
1
0
2
2
0
1
0
0
1
2
1
1
1
0
1
0
0
2
1
1
1
1
1
1
2
2
1
2
0
0
1
1
7
1
1
0
0
0
1
2
2
1
1
2
0
1
0
1
0
1
0
1
2
1
0
1
1
1
2
2
0
2
1
1
2
0
0
1
0
1
0
1
1
0
1
1
1
1
1
1
0
0
1
1
2
1
1
1
0
0
1
1
1
2
1
0
0
2
0
0
1
1
1
0
1
9
2
1
0
1
1
1
1
1
1
1
0
0
1
1
1
1
1
0
0
1
1
2
0
2
1
0
2
1
1
1
1
1
2
1
1
1
0
0
1
0
0
1
2
0
0
1
1
1
1
2
2
1
1
1
1
2
3
1
2
1
0
0
2
0
1
1
2
1
0
2
2
0
1
1
1
2
0
1
1
1
2
2
2
1
1
1
0
0
1
1
0
1
0
1
0
1
2
1
1
0
0
2
0
3
2
0
2
1
2
1
2
1
1
1
0
0
0
0
2
1
2
1
0
2
1
2
1
2
1
1
1
1
1
1
1
0
1
2
1
2
0
2
1
2
1
0
2
0
1
1
1
0
0
2
1
1
2
1
2
1
1
0
1
1
2
0
1
1
1
0
1
0
2
1
2
1
1
2
0
0
1
0
1
1
1
1
1
0
1
1
0
3
1
2
1
0
1
1
1
0
1
1
0
1
1
1
2
1
1
1
1
0
1
1
1
0
0
2
1
1
1
1
1
1
1
1
1
1
0
1
2
2
0
1
2
0
2
2
2
0
1
1
1
1
2
0
2
1
1
0
1
0
1
1
0
1
0
0
2
0
1
0
1
2
0
1
0
1
1
1
2
1
0
0
1
1
1
1
1
1
2
2
1
1
0
1
2
2
0
1
0
0
1
0
1
1
2
1
1
1
0
1
1
0
0
0
0
1
1
1
2
2
1
1
1
2
1
2
1
2
0
2
1
1
2
2
1
1
1
0
0
0
1
2
1
1
0
0
1
2
0
2
1
0
1
1
1
1
1
2
1
1
3
2
2
2
2
1
1
1
1
2
1
0
2
1
0
1
1
0
0
0
1
1
2
3
1
1
2
1
1
1
0
2
1
1
1
0
2
1
0
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
0
1
1
1
2
2
2
2
0
2
0
2
1
1
3
1
0
1
0
2
2
2
1
1
1
1
0
2
2
1
1
1
1
2
1
0
1
1
1
0
1
1
1
0
1
1
0
0
1
2
0
1
0
1
1
2
0
1
1
1
1
1
1
1
0
0
1
1
1
2
1
0
1
2
0
1
2
1
0
1
2
1
0
3
1
0
1
1
1
0
1
1
3
2
0
0
3
1
2
0
0
1
1
1
2
0
0
2
1
1
1
0
0
0
1
2
1
0
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
0
1
0
1
2
2
0
1
0
0
1
2
0
0
1
0
0
1
1
0
0
2
0
0
0
0
1
0
1
1
1
0
1
1
1
2
0
2
2
0
1
0
0
0
0
1
2
1
1
0
0
2
1
1
2
2
1
1
1
1
2
0
0
1
1
2
2
2
1
1
0
1
0
1
1
1
2
0
0
2
1
1
1
2
0
1
2
1
0
1
2
0
1
1
1
0
2
0
1
2
1
1
2
2
1
1
0
0
2
1
0
2
1
1
2
2
1
0
0
1
1
0
1
1
0
1
1
2
1
2
1
2
2
2
2
1
2
1
0
1
1
2
2
2
0
2
2
1
1
1
1
1
1
0
1
1
2
1
2
1
1
0
2
2
1
2
0
1
0
0
2
1
0
2
0
0
1
0
1
1
1
1
1
2
2
0
1
0
1
2
1
1
2
1
1
0
1
1
1
2
1
1
2
0
1
1
2
1
2
0
2
0
3
2
1
2
0
2
2
1
1
1
0
1
2
0
1
2
0
1
0
1
0
2
0
0
1
1
0
0
1
1
1
1
1
1
2
1
2
0
1
1
1
1
1
0
2
2
0
2
0
2
1
1
2
2
2
2
0
2
0
2
1
1
1
0
0
1
2
0
1
1
2
2
1
1
1
0
1
1
1
1
0
1
0
1
1
1
2
1
0
1
2
1
2
0
2
2
4
1
2
0
1
0
0
1
1
0
0
1
1
0
2
1
2
2
1
0
0
0
0
1
1
0
0
2
1
1
1
1
1
2
1
0
1
2
2
2
1
2
0
1
0
1
1
1
1
1
0
1
0
2
1
1
2
3
2
2
1
1
2
1
1
2
0
0
0
1
0
0
0
1
1
0
0
0
1
1
1
0
1
1
1
1
0
1
0
1
1
1
2
2
2
1
1
0
1
1
1
1
2
1
1
0
0
0
1
1
1
0
1
0
1
1
2
1
2
2
2
1
0
0
1
1
1
2
1
1
1
2
1
1
1
0
2
1
1
1
0
1
1
2
2
1
1
0
1
1
1
1
1
1
1
2
1
1
2
0
0
1
0
4
0
0
0
1
2
1
1
0
0
1
1
1
1
0
3
2
0
1
0
3
0
1
0
1
1
1
1
2
2
0
1
1
1
0
1
1
1
2
1
0
0
0
0
4
2
1
0
0
1
1
0
0
1
1
2
1
0
2
2
1
1
1
0
1
1
0
1
1
0
0
2
0
1
1
0
2
2
1
0
1
1
1
1
0
2
1
1
1
2
1
1
1
1
1
0
2
0
0
2
1
2
0
0
0
1
2
0
0
0
1
0
0
1
0
0
1
1
2
1
0
1
0
1
1
2
0
1
0
2
1
1
1
1
0
1
1
1
1
1
0
2
2
1
0
1
1
0
0
0
0
2
1
2
0
0
2
1
2
1
1
1
1
1
0
2
0
1
1
2
0
1
2
0
1
2
0
1
1
2
1
1
0
1
1
1
1
1
0
2
1
0
2
2
1
1
0
1
1
1
0
1
2
2
1
1
0
1
1
2
1
0
1
0
1
1
2
0
2
2
1
1
1
0
2
2
0
2
0
2
1
3
1
1
2
0
1
0
1
1
0
1
2
2
1
1
1
1
1
1
2
0
3
1
0
1
1
0
0
1
0
1
1
0
1
1
1
2
2
1
1
1
2
1
1
1
1
0
0
2
0
1
1
2
0
0
1
2
2
2
1
1
2
1
0
2
1
0
2
0
1
1
0
2
1
0
1
2
0
1
0
2
1
0
1
1
1
1
0
2
1
1
1
2
1
2
2
1
1
1
0
0
1
2
1
1
2
2
1
1
1
6
0
0
2
0
1
0
2
0
1
1
1
1
1
4
0
1
0
1
1
0
1
1
1
0
1
2
2
2
1
1
0
1
1
0
0
1
0
1
1
2
1
1
0
1
0
0
1
2
0
1
1
0
1
1
1
1
0
2
1
2
1
1
0
1
1
2
0
1
1
2
1
2
1
0
1
1
1
1
0
1
1
2
0
1
1
1
1
1
1
1
1
1
1
1
0
0
1
1
1
0
1
2
1
1
2
1
1
1
1
0
0
1
2
2
2
1
0
1
2
1
1
0
1
2
2
1
1
0
0
0
1
1
2
1
0
2
0
1
3
2
1
1
1
2
1
0
1
0
2
1
1
2
1
0
2
1
1
0
1
1
0
1
1
1
0
0
1
2
1
1
0
2
1
0
2
1
1
1
1
1
1
2
0
1
2
2
1
1
2
1
0
1
2
2
0
0
0
2
2
0
0
1
1
0
2
1
1
0
0
2
1
1
1
1
1
0
2
0
0
0
0
0
1
1
0
1
1
2
0
0
2
1
2
1
2
1
1
0
1
2
1
2
1
1
2
2
0
0
2
2
0
2
0
1
2
1
1
1
0
0
2
1
1
2
0
0
1
1
1
1
2
1
2
2
1
0
2
1
1
1
1
1
2
0
1
1
1
1
1
1
1
2
0
1
2
1
1
2
1
2
1
2
1
1
2
1
2
1
1
1
1
0
1
1
0
1
2
1
1
1
0
0
0
1
1
1
0
2
2
2
2
2
2
0
1
1
1
1
2
1
1
1
2
2
1
1
0
0
1
1
0
1
1
0
0
0
1
2
0
0
1
0
1
0
0
2
1
1
0
1
2
1
1
1
1
2
1
2
2
1
1
0
1
1
0
2
0
1
0
2
2
1
2
2
2
1
1
1
0
1
0
2
1
1
2
2
2
1
2
1
0
2
1
1
2
1
2
1
1
1
1
1
2
1
1
1
2
2
3
1
2
1
0
0
1
1
1
0
0
0
2
2
1
0
1
1
1
0
1
2
1
1
1
1
1
1
1
2
1
1
2
2
1
2
2
0
1
1
1
1
2
1
1
1
1
2
1
2
0
1
2
0
0
2
2
0
1
2
2
1
2
0
1
0
1
1
1
2
1
1
2
1
1
1
1
1
1
2
2
1
3
1
0
2
2
1
1
1
1
0
1
0
1
0
1
0
1
1
0
2
0
1
2
0
1
1
1
1
1
0
1
0
1
1
1
2
2
0
0
2
1
0
1
1
0
1
0
0
2
0
1
1
2
1
2
1
0
1
2
2
0
5
1
1
2
0
1
1
0
1
1
0
1
0
1
2
1
0
0
0
1
0
0
1
2
1
0
0
0
1
1
1
1
1
1
2
2
0
2
1
1
2
1
1
1
2
2
0
1
0
2
0
2
1
1
2
0
1
1
1
1
2
1
1
1
1
2
3
1
1
1
1
0
0
0
1
2
1
2
0
1
2
1
1
2
1
1
1
1
0
2
1
1
0
2
1
2
2
0
1
2
0
1
0
1
1
1
0
1
1
1
1
2
1
2
2
1
1
1
2
1
1
2
1
2
2
1
1
1
1
1
1
2
0
1
2
1
2
1
1
1
1
2
0
1
1
1
1
2
1
1
0
2
0
1
1
2
2
0
1
1
1
1
0
0
1
1
0
2
0
1
1
1
1
1
3
1
2
0
2
3
2
1
0
1
2
1
1
1
2
1
1
1
0
2
1
0
1
1
1
1
1
1
1
1
2
1
2
0
2
2
1
0
1
1
1
0
1
0
0
1
0
1
1
3
0
1
2
1
1
1
2
1
1
4
1
2
1
1
1
0
0
1
1
2
1
2
1
1
2
1
2
0
0
1
1
1
1
2
2
0
1
0
0
1
0
1
1
1
0
1
1
1
1
1
1
1
0
0
2
0
0
1
2
4
1
1
2
2
0
1
2
1
1
1
1
1
0
0
2
1
0
2
1
0
1
1
1
1
2
1
0
2
1
0
2
0
1
1
0
1
1
2
1
0
1
1
1
1
1
1
0
2
1
0
0
1
1
2
1
1
1
0
2
1
1
0
1
1
0
1
2
1
0
0
1
1
2
2
1
1
2
1
2
1
1
0
0
2
1
0
1
0
0
2
2
1
3
1
2
0
1
0
1
1
0
1
1
1
0
1
0
2
2
1
0
1
0
2
0
2
2
2
0
0
1
3
2
1
0
1
0
1
0
1
1
1
0
0
0
1
0
0
1
1
1
2
1
0
0
1
2
2
1
1
1
3
1
1
1
0
1
1
2
1
1
0
0
1
1
0
0
1
1
0
2
1
0
0
1
0
1
1
1
1
1
0
1
2
1
2
1
1
0
2
1
0
2
0
1
0
0
1
2
2
1
0
1
1
2
2
1
1
0
1
2
1
2
1
1
3
0
1
1
2
3
0
0
1
1
2
1
1
1
1
1
1
0
0
1
1
0
0
1
2
0
1
2
0
1
1
1
1
2
1
2
0
2
1
1
1
1
2
2
0
1
2
2
1
1
1
1
1
1
2
1
1
1
0
1
2
1
0
1
1
2
0
1
2
1
1
1
0
2
2
1
1
2
0
3
0
2
0
0
1
2
1
2
2
1
1
1
1
1
1
1
0
1
2
0
0
2
1
2
1
2
2
0
0
0
1
1
1
0
1
2
0
2
1
1
1
0
1
1
2
0
2
1
1
0
2
1
1
1
2
0
1
1
2
0
0
2
0
2
1
0
2
1
1
2
1
0
1
0
1
0
1
1
1
0
0
0
1
2
1
0
1
1
1
2
2
0
1
2
1
1
0
2
1
1
1
1
0
0
0
1
1
0
1
1
2
1
1
1
2
2
1
1
2
1
1
2
1
1
1
1
0
0
1
1
0
0
0
2
2
0
0
1
0
1
2
3
1
0
2
1
2
1
1
2
1
1
2
1
0
2
0
1
2
1
1
1
1
2
1
1
1
1
0
2
0
0
2
0
1
1
0
2
1
1
0
1
1
2
1
0
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
0
1
1
1
1
1
1
2
1
1
1
0
2
0
0
1
1
1
2
1
1
1
1
2
1
1
1
2
1
0
1
1
0
1
1
2
1
0
1
0
1
0
1
1
1
1
1
2
0
2
1
2
0
2
0
1
1
2
1
4
1
1
2
2
3
0
2
1
1
1
2
2
0
2
0
1
0
0
1
1
1
0
1
2
1
0
1
2
1
1
1
0
4
2
1
0
0
1
1
1
1
1
1
0
1
1
1
2
1
0
1
0
1
1
2
1
2
2
1
2
1
1
2
2
2
0
0
2
0
1
1
1
1
1
2
0
2
0
1
2
1
2
1
2
1
2
1
0
0
0
2
0
1
1
0
2
1
1
0
1
1
1
1
0
1
1
0
0
1
2
1
0
0
0
0
2
1
1
1
1
0
2
1
2
1
0
1
1
1
1
1
2
0
1
0
1
1
1
1
5
0
1
1
0
1
1
0
1
1
0
2
1
1
1
0
0
1
1
2
1
1
0
2
1
1
1
1
1
1
2
0
1
2
0
1
1
1
1
1
1
0
1
2
2
0
1
2
0
1
1
1
2
2
2
1
0
1
1
2
0
1
1
1
1
2
2
1
0
1
1
1
1
0
0
1
0
1
1
1
1
1
0
1
0
1
0
1
0
1
1
1
0
2
1
1
1
1
0
2
2
2
0
2
1
0
1
0
1
1
0
0
1
1
0
1
1
1
1
0
1
1
2
0
1
0
2
1
0
1
0
1
0
2
0
2
1
1
1
2
1
2
0
1
0
2
2
1
1
0
2
1
1
2
0
2
0
1
1
2
0
0
1
2
2
1
3
0
2
0
0
1
2
0
1
1
2
1
0
0
0
1
0
1
1
0
0
0
2
1
1
1
0
0
1
2
1
2
2
2
1
2
0
2
1
1
1
1
0
0
0
1
1
1
1
1
1
0
1
1
1
0
1
1
2
1
1
2
0
2
0
1
0
2
0
0
1
0
1
1
2
0
1
0
1
0
1
1
3
1
0
1
1
1
1
1
0
1
1
1
1
1
1
1
2
1
0
1
0
2
0
2
0
2
1
1
1
0
2
1
0
0
2
1
0
1
2
0
4
1
1
2
1
1
1
1
0
1
1
2
1
2
1
1
0
0
1
1
1
2
0
1
1
2
0
1
0
1
2
1
1
1
2
0
1
2
0
0
0
1
2
0
0
1
1
1
1
0
0
2
1
1
1
2
0
1
2
2
1
1
1
0
1
0
1
0
2
1
1
1
0
2
0
1
0
1
2
1
0
1
2
1
1
0
0
1
2
1
1
1
0
0
0
1
1
1
0
0
1
1
1
1
1
2
1
1
0
1
2
1
2
0
2
1
0
1
1
1
2
1
0
0
2
1
1
1
2
0
1
2
1
1
1
2
1
0
1
1
0
1
1
1
1
1
1
1
1
1
0
1
0
0
1
0
0
1
1
1
1
0
2
1
1
2
1
1
1
1
0
2
1
1
1
2
1
2
0
0
0
0
1
1
0
0
0
1
1
1
2
0
1
0
1
2
1
2
2
0
1
0
0
1
1
1
1
1
0
0
1
1
1
2
1
1
0
1
0
2
2
0
1
1
2
0
0
2
0
1
0
1
0
0
1
2
2
2
0
1
1
1
1
0
1
1
1
2
2
1
1
1
1
2
2
0
2
1
0
1
1
0
0
0
1
1
2
1
1
2
0
2
0
1
1
2
0
0
1
1
1
0
0
1
0
1
1
2
1
1
2
2
0
2
2
2
1
1
1
1
2
0
0
0
1
1
1
0
0
1
1
1
1
1
0
2
1
0
2
2
0
1
0
1
1
0
1
0
1
1
1
0
2
1
1
1
2
1
1
1
1
1
2
2
1
1
2
1
2
2
0
0
1
1
0
1
0
1
0
0
2
1
0
1
1
2
1
0
1
0
2
0
1
1
1
0
1
2
1
1
1
1
1
0
2
2
2
1
2
1
1
2
1
2
1
1
1
1
1
0
2
2
1
0
0
0
1
1
1
1
0
0
0
1
1
1
1
1
0
1
2
0
0
2
1
1
1
1
2
0
1
0
2
2
0
0
1
2
1
1
1
0
1
2
1
0
0
2
2
1
1
0
1
2
1
2
1
0
1
1
1
0
2
1
1
0
1
0
1
1
1
1
2
0
0
1
0
0
0
1
1
1
0
0
1
0
1
0
1
0
1
1
1
1
2
0
1
1
0
1
1
1
1
1
0
0
2
1
0
1
2
2
1
1
2
1
0
2
1
0
1
0
1
2
2
2
0
1
1
1
0
1
0
1
2
1
2
3
1
1
1
1
0
2
1
2
1
0
1
1
2
4
2
0
0
1
1
0
2
1
0
2
0
0
1
2
2
2
0
1
1
0
1
2
0
2
1
2
1
1
1
1
0
1
1
1
1
1
1
0
0
1
2
1
1
2
2
1
0
1
1
1
1
2
2
1
2
2
1
1
0
1
1
1
1
1
1
1
0
1
1
2
1
0
0
1
2
1
0
1
0
1
1
1
2
1
1
2
0
0
2
1
1
1
0
0
0
0
2
1
0
1
1
1
0
0
0
1
2
2
0
0
0
1
1
2
0
1
0
1
2
2
0
1
0
0
1
1
1
2
1
2
1
2
1
2
1
1
2
1
2
2
0
2
0
3
1
1
1
0
1
1
1
2
0
3
1
2
0
1
1
0
1
0
1
0
2
0
1
1
2
1
2
0
1
1
1
1
2
1
2
1
1
1
2
1
2
1
1
1
1
0
2
1
1
0
0
0
1
1
0
1
1
1
2
1
0
1
2
0
0
1
0
1
0
0
2
0
1
3
1
0
0
1
1
1
1
2
2
1
1
1
0
0
1
0
0
1
1
1
2
1
3
2
1
0
1
2
1
0
2
1
2
0
2
0
2
2
1
0
1
2
1
2
1
0
0
2
1
0
2
0
1
1
1
1
1
1
0
2
1
0
0
2
1
2
0
1
0
1
2
0
1
2
2
1
1
1
0
1
0
1
1
1
2
0
1
1
1
1
0
0
2
0
2
1
1
0
1
1
2
2
2
1
1
1
1
1
1
1
1
1
1
0
2
0
1
2
2
2
0
0
1
2
1
0
1
3
0
0
1
1
1
2
1
0
1
1
2
0
0
2
2
0
0
1
2
0
0
1
1
1
2
1
1
1
1
1
2
1
1
1
1
2
0
0
1
1
2
1
0
2
1
1
0
0
0
2
0
1
1
0
1
1
1
1
1
1
1
1
1
2
2
2
1
0
0
1
2
0
1
2
1
1
0
2
1
1
1
2
1
2
2
2
1
0
0
2
0
0
2
1
0
0
0
0
0
1
2
1
0
2
1
2
1
0
1
1
0
1
1
0
2
1
1
0
1
0
0
0
2
1
0
1
0
2
1
1
0
1
1
0
0
1
0
1
1
1
1
1
2
1
0
0
1
2
1
2
1
1
1
1
0
1
2
2
1
1
2
1
0
2
1
2
1
0
1
0
1
0
2
1
0
0
1
0
2
2
1
1
1
1
2
1
0
0
1
1
1
2
0
2
1
1
1
0
2
2
0
0
1
1
2
1
1
2
2
1
1
1
1
2
0
1
1
2
1
1
1
3
1
0
2
2
1
2
1
2
2
2
2
2
0
0
0
1
1
1
1
0
2
2
0
1
1
0
0
0
1
1
1
1
2
1
0
0
1
2
1
0
1
1
1
1
0
1
1
0
1
2
2
1
2
2
0
1
0
1
1
2
0
2
1
3
0
1
2
2
1
1
1
0
1
1
0
1
1
3
2
0
1
1
1
1
0
1
1
0
1
1
2
2
2
1
0
1
1
1
0
2
1
0
1
1
2
1
0
0
1
0
1
1
0
2
2
2
0
1
2
2
0
1
2
0
0
1
1
1
2
0
0
0
2
1
1
1
1
1
1
1
1
0
1
1
0
1
0
0
0
1
0
1
1
1
0
1
1
1
1
1
1
0
2
2
0
1
1
1
1
1
2
2
1
0
1
2
1
1
1
1
1
2
1
0
1
0
2
1
0
1
3
0
1
0
1
0
1
1
0
1
1
1
1
1
0
1
2
0
1
0
0
0
0
1
0
2
0
2
1
1
1
4
1
1
2
1
1
1
1
2
1
2
0
1
1
0
2
0
0
0
1
2
2
2
1
0
0
1
1
2
1
1
1
1
1
1
2
0
0
1
2
1
1
1
2
0
0
1
0
0
1
1
1
1
2
1
0
1
0
1
1
1
1
1
1
1
2
0
1
1
1
3
2
0
0
1
1
1
1
0
1
1
1
1
0
2
1
1
2
1
2
2
2
0
1
2
2
2
1
0
1
1
0
1
0
1
1
2
1
1
0
1
1
1
1
0
1
1
1
0
0
1
1
1
1
2
2
1
0
1
2
1
2
0
2
0
0
2
0
1
2
2
1
2
1
0
1
1
1
0
2
1
1
1
1
2
3
0
1
1
0
1
2
0
2
1
0
1
0
1
2
2
1
1
1
0
1
1
1
2
0
2
1
1
1
1
0
0
2
2
0
0
1
1
0
1
2
2
1
1
1
1
1
2
0
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
0
2
0
1
1
1
1
1
1
0
1
0
1
1
1
1
1
2
1
1
1
2
2
1
1
0
1
2
1
1
1
1
2
1
0
0
2
0
1
1
1
0
0
0
1
2
2
1
0
1
2
2
1
1
0
2
0
1
2
1
1
1
2
0
0
1
2
0
1
2
0
0
1
0
1
1
1
1
0
1
1
1
0
1
0
1
1
1
1
0
0
2
1
1
2
0
1
1
2
0
2
1
0
1
1
2
1
1
2
1
1
1
0
2
3
1
1
1
0
2
1
0
1
1
2
1
1
1
1
0
1
2
1
1
0
0
1
0
1
0
1
1
1
1
2
0
1
0
1
3
3
0
0
1
2
1
0
1
1
1
0
0
1
1
1
3
1
0
1
1
2
1
2
0
1
0
0
2
0
2
1
1
2
1
0
1
2
1
1
3
1
0
1
0
1
0
0
1
1
1
2
0
1
2
0
1
1
1
0
1
0
1
2
2
1
1
1
1
1
1
2
1
1
1
1
2
1
0
1
1
1
1
1
1
1
0
0
1
2
1
1
0
1
2
2
2
2
1
0
2
2
0
2
2
2
0
0
1
2
1
1
1
0
2
2
1
2
2
0
1
2
0
1
1
0
1
1
1
2
1
0
1
2
1
1
1
1
2
2
1
1
1
1
1
2
1
1
1
0
1
1
1
0
2
0
1
1
2
0
1
0
2
1
1
1
1
1
0
2
1
1
2
1
1
1
1
1
2
1
1
0
1
1
1
1
0
2
0
1
1
0
1
2
1
1
1
1
1
1
0
1
1
2
1
2
2
2
1
1
0
1
0
1
2
1
1
0
1
1
2
2
1
2
0
1
1
1
1
2
0
2
3
0
1
1
1
1
1
1
1
1
1
1
0
0
1
0
1
1
0
1
2
2
1
1
1
2
1
0
1
2
1
1
1
0
0
1
2
0
1
2
1
1
0
1
1
1
1
2
1
1
0
0
1
0
2
2
3
1
2
1
2
2
2
0
2
2
2
1
1
1
2
1
0
0
1
0
1
1
1
1
1
1
1
1
1
1
0
0
2
2
1
0
1
1
1
2
1
0
4
1
1
1
2
0
1
1
2
1
0
2
1
0
1
1
2
1
1
1
2
1
1
1
0
0
0
0
1
1
1
1
1
1
2
2
1
0
1
1
2
1
0
0
2
0
2
2
1
1
1
1
1
1
1
1
0
1
1
1
1
0
1
1
1
2
1
0
0
1
1
2
0
2
0
2
1
0
1
1
1
0
1
1
1
2
1
1
1
1
1
0
1
1
0
0
1
1
1
1
1
1
1
1
0
1
3
1
2
2
1
0
1
0
1
0
1
1
1
1
2
1
0
3
1
0
1
1
2
0
0
2
1
1
0
1
2
1
0
2
0
3
1
1
1
1
1
1
0
1
1
2
1
1
1
1
1
0
2
0
1
0
1
2
1
0
1
1
2
1
1
0
1
2
2
1
1
0
1
1
1
1
0
1
1
1
1
0
2
2
1
1
2
1
0
0
0
0
1
1
1
1
2
0
0
1
1
2
0
2
1
1
1
1
2
1
1
1
2
1
0
0
1
2
2
2
1
1
1
1
2
2
0
1
2
1
0
1
1
1
1
1
2
2
2
1
0
0
1
0
2
1
1
1
0
2
1
0
2
1
0
1
1
2
0
1
1
1
1
2
2
1
0
1
2
2
1
1
1
2
0
0
0
1
2
0
0
0
0
0
1
0
2
1
2
1
1
1
2
0
1
1
1
0
0
0
1
1
1
1
2
1
0
1
1
1
0
1
2
1
2
1
2
1
1
1
0
1
1
1
0
1
2
2
0
2
1
1
1
1
1
1
0
1
1
1
0
1
1
1
2
1
0
2
0
1
1
0
1
2
0
1
1
1
1
1
2
0
0
1
1
0
2
2
1
1
2
1
1
0
3
0
1
1
2
1
1
1
1
2
2
1
0
2
2
1
0
2
0
0
2
2
1
0
1
0
2
2
1
1
1
0
0
2
2
1
2
0
2
0
1
2
1
1
0
1
0
1
0
0
1
0
1
2
1
2
1
0
1
0
0
1
1
1
0
0
1
1
1
1
0
1
1
0
0
2
2
0
2
1
1
0
3
2
1
1
1
0
1
0
1
1
1
0
1
1
0
0
1
1
1
0
0
0
1
0
1
1
2
1
1
1
0
0
1
1
2
0
1
1
1
1
0
1
1
2
2
2
0
1
0
0
2
1
1
1
0
1
0
0
1
0
2
1
2
2
1
1
0
2
1
1
1
2
0
1
2
0
0
2
1
2
2
1
1
0
1
0
2
0
1
0
1
1
2
1
0
1
1
2
2
1
0
2
1
1
1
1
2
1
0
3
1
0
4
1
1
2
2
1
0
0
0
2
1
0
1
1
2
0
2
0
1
1
2
1
1
2
1
1
1
2
2
1
1
2
1
1
0
1
1
1
0
0
2
1
2
0
1
0
1
1
0
0
1
0
1
0
1
1
1
3
1
0
1
0
1
1
1
0
1
1
1
0
1
1
1
1
2
0
1
1
1
1
1
1
0
1
1
0
1
1
1
1
1
2
3
2
1
0
2
2
2
1
1
3
1
2
0
0
1
1
0
2
0
1
1
0
1
1
1
2
1
1
1
0
4
1
2
2
2
0
2
0
1
1
2
0
1
0
2
0
0
2
1
2
1
2
2
1
1
1
1
0
1
1
2
1
0
2
1
1
1
2
1
2
2
2
1
0
2
0
2
1
1
0
1
0
1
2
1
2
2
1
0
0
2
1
2
1
1
1
0
0
3
2
0
1
0
1
1
1
1
1
1
1
2
0
1
2
1
1
1
1
0
2
2
3
1
2
2
1
0
1
1
0
2
0
1
0
0
1
0
1
0
2
0
1
1
1
1
0
2
1
1
1
1
1
1
1
1
1
1
2
2
2
0
1
1
1
1
2
1
1
1
1
1
2
1
0
1
2
1
0
1
1
1
2
1
1
0
1
1
0
1
1
0
1
2
2
0
0
1
2
2
1
1
2
1
0
1
1
0
2
2
1
2
1
1
0
0
1
2
1
1
1
1
1
1
1
1
1
0
0
2
1
2
0
1
0
1
0
1
1
1
0
1
1
1
2
1
0
2
2
0
1
1
1
0
0
1
1
2
1
0
1
0
1
1
0
2
0
1
1
1
1
0
1
2
1
1
1
0
1
3
1
1
1
1
0
2
0
0
2
1
1
0
0
0
1
2
2
1
1
1
0
2
2
0
0
2
1
2
0
1
1
1
1
2
1
1
0
1
1
1
0
1
1
0
1
2
0
1
1
0
1
1
2
1
1
1
2
1
1
1
2
2
1
1
1
0
2
0
1
2
1
2
2
1
2
1
1
0
1
0
1
1
1
2
1
2
2
1
1
0
1
2
2
2
0
2
1
1
0
2
2
1
2
2
0
1
1
1
0
2
0
2
5
1
0
0
1
1
2
1
0
2
1
2
1
1
1
1
1
0
0
1
2
2
0
1
0
1
1
1
2
2
1
2
2
1
1
1
2
3
1
1
1
0
0
1
0
2
1
0
2
0
2
0
3
1
2
0
0
0
1
2
1
1
1
1
0
0
2
2
1
1
0
1
3
2
1
0
0
1
0
1
0
1
1
1
2
0
0
2
2
2
1
1
1
2
1
2
1
1
1
2
2
1
0
1
1
1
0
1
0
1
1
2
0
2
1
1
1
1
1
1
1
0
1
1
2
1
1
1
1
1
1
1
0
0
1
1
1
1
2
0
1
1
1
2
1
0
1
2
1
1
0
1
0
0
1
0
1
2
2
0
1
1
1
0
0
2
1
1
0
1
2
1
1
1
1
2
2
1
0
1
1
1
1
1
2
2
2
0
1
1
1
0
0
1
1
1
1
1
0
3
1
0
0
2
0
1
1
0
2
2
3
1
0
1
0
2
1
1
0
1
1
2
1
0
1
0
2
1
2
2
0
0
1
0
1
0
0
1
1
1
0
2
1
2
0
1
0
0
1
0
2
0
2
1
0
1
0
1
2
1
2
4
1
0
0
0
2
0
0
2
1
2
1
0
1
3
1
0
0
0
1
1
0
1
1
1
1
1
2
1
1
2
1
0
0
1
2
0
1
2
1
0
1
1
1
1
1
2
1
0
0
2
1
1
1
0
1
0
2
1
1
1
1
1
2
2
0
0
1
1
2
0
1
0
1
1
1
1
1
0
1
1
1
0
1
2
2
1
1
1
0
2
2
1
1
1
1
2
0
1
1
2
1
2
1
1
0
2
1
0
2
0
0
2
2
0
1
1
0
1
1
2
1
2
0
1
1
2
0
2
0
0
0
1
2
1
1
1
1
1
1
0
1
1
0
1
1
0
1
0
1
1
1
1
0
1
0
1
1
0
0
0
1
1
1
1
1
2
1
1
1
0
2
2
1
0
0
0
0
0
1
1
1
1
2
0
2
1
1
2
0
0
0
1
1
1
2
1
1
2
0
1
2
1
2
0
1
2
2
1
0
0
2
1
2
1
1
1
2
1
2
0
0
0
2
3
1
2
1
1
1
1
1
1
1
2
1
1
0
0
1
1
2
1
1
0
1
2
1
2
1
1
0
1
1
1
0
1
2
2
2
2
2
2
1
0
1
0
1
0
0
2
1
1
3
1
1
0
0
0
1
1
2
1
2
1
1
1
2
0
1
1
0
1
2
2
1
1
1
0
1
0
0
1
1
4
0
0
1
1
1
0
1
1
1
0
1
1
0
1
0
1
1
1
1
6
1
2
1
0
1
1
0
1
2
1
0
1
2
1
0
1
1
0
0
1
1
1
0
0
0
1
0
2
0
1
3
1
0
1
1
1
1
2
1
2
2
2
2
1
1
2
2
1
2
1
1
2
1
0
2
1
1
1
1
0
0
0
1
1
2
2
2
0
1
1
1
1
1
1
1
1
1
1
1
1
2
2
0
0
1
0
1
2
2
1
1
1
0
2
2
1
2
0
0
1
2
1
1
0
1
1
0
0
1
2
2
1
0
1
2
1
1
2
2
0
1
2
0
2
2
1
1
1
0
2
1
0
1
0
0
1
0
0
0
1
1
0
2
1
1
2
1
1
1
0
2
1
0
1
1
2
1
1
1
2
1
0
1
1
1
1
2
1
2
1
2
0
1
1
0
2
1
0
2
1
0
0
1
0
2
2
0
1
1
1
1
1
2
1
1
2
0
0
1
1
1
1
1
1
2
0
1
1
0
2
2
1
1
2
1
0
0
1
1
2
2
2
1
1
2
0
0
0
0
2
0
2
1
1
0
1
1
1
0
2
1
1
0
2
0
0
0
1
1
1
1
1
1
1
2
1
1
1
2
0
1
1
0
0
0
0
1
1
0
1
1
0
1
2
1
2
1
0
0
2
1
0
0
2
1
2
1
1
1
0
0
0
1
1
1
2
1
1
1
0
1
1
1
2
1
0
0
1
2
2
1
0
1
2
1
2
1
2
1
1
0
1
2
1
3
2
1
2
1
1
1
1
0
1
1
1
1
1
1
0
1
2
1
0
1
2
1
0
1
0
1
2
1
0
2
1
1
1
2
1
1
1
3
2
2
1
1
3
1
0
2
2
0
1
2
2
2
1
0
1
1
1
0
1
2
0
1
2
0
1
1
0
0
1
1
1
0
1
1
1
1
3
1
2
2
2
2
0
1
0
1
2
2
2
0
0
0
0
0
0
1
1
2
1
1
2
1
0
2
0
1
0
0
1
1
1
2
1
0
0
1
0
0
0
1
1
2
2
0
1
1
1
1
1
1
0
1
1
2
1
2
1
2
1
1
1
0
4
1
1
0
1
1
2
1
2
2
0
1
2
0
0
2
1
0
1
2
3
1
2
1
1
0
1
0
1
1
0
1
1
0
3
1
1
0
2
1
2
1
0
2
1
1
2
0
1
0
1
1
1
1
1
1
1
1
0
1
1
2
0
0
1
0
1
0
1
1
2
2
0
2
1
0
0
1
1
2
2
1
0
1
2
2
1
0
1
2
0
1
2
1
0
1
0
2
1
1
1
2
0
1
1
1
1
13
0
1
1
2
0
1
1
0
0
0
0
2
0
1
1
3
2
1
1
1
0
1
1
0
1
2
0
2
2
0
1
0
0
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
2
2
2
2
1
2
0
1
1
1
2
2
1
1
1
0
1
0
0
1
0
1
1
2
1
0
0
2
2
1
2
1
1
0
2
2
2
0
1
0
1
0
0
2
0
2
1
0
2
1
0
1
1
0
0
1
2
1
2
1
1
1
1
1
1
1
1
1
0
1
2
2
0
1
2
2
1
1
1
1
2
1
2
1
1
0
1
1
0
2
0
1
1
1
1
0
2
2
2
1
1
1
0
1
2
0
2
2
2
4
1
1
0
2
0
0
1
1
1
0
1
2
0
1
0
2
2
1
1
1
1
0
1
2
2
2
0
2
1
1
0
1
1
1
1
1
1
0
2
0
2
1
1
0
2
1
1
1
1
1
1
1
1
1
1
1
2
1
0
1
0
2
1
0
1
1
0
2
2
1
1
2
2
1
1
2
2
1
1
0
1
1
2
1
1
2
1
1
1
1
0
1
0
2
1
0
1
1
0
1
2
1
1
1
1
0
1
2
1
0
1
0
1
1
1
1
1
2
2
2
2
0
0
1
2
0
2
0
1
0
3
1
3
1
1
0
2
0
1
0
0
2
0
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
0
1
2
1
0
0
1
1
1
1
1
1
0
2
2
1
0
0
0
1
2
1
2
0
1
0
3
1
0
1
1
2
0
0
0
1
3
2
1
1
1
2
1
1
1
1
2
2
1
0
1
1
1
1
1
1
2
1
0
1
1
1
0
1
2
1
1
0
0
1
0
4
2
1
2
17
1
1
1
2
0
1
0
1
0
1
2
1
1
0
2
2
1
1
1
2
2
1
1
2
2
2
1
1
2
1
1
0
0
1
1
0
0
1
0
2
1
0
0
1
1
0
1
1
1
1
1
1
0
1
0
2
2
0
1
1
1
1
2
1
1
1
0
0
1
2
1
0
0
2
1
1
1
0
0
2
2
2
0
2
1
2
2
2
2
1
2
1
2
1
0
0
1
1
1
1
1
1
0
0
1
1
1
0
1
3
0
0
1
1
1
0
1
2
0
2
2
2
1
2
0
1
1
2
1
0
0
0
0
1
1
1
1
1
1
1
0
1
1
0
1
1
0
1
0
1
1
0
0
1
1
2
0
1
1
1
1
1
2
1
0
1
0
3
0
1
1
1
0
0
1
0
1
1
2
2
1
0
1
0
1
1
1
2
0
0
1
1
2
0
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
2
2
1
0
1
2
1
2
2
0
0
0
1
1
1
1
2
2
2
1
3
0
1
0
1
0
0
1
1
2
2
0
0
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
0
2
0
1
0
0
0
0
1
1
1
2
0
2
2
0
1
2
1
2
2
1
1
2
1
1
0
1
1
1
1
1
1
1
2
0
0
1
1
1
1
1
0
1
1
0
2
1
1
1
1
1
1
1
0
2
2
0
1
2
2
2
1
0
2
1
1
0
0
1
2
1
0
1
0
1
1
0
1
1
2
2
1
2
1
1
1
2
1
1
2
1
0
0
1
1
1
1
1
1
1
1
0
0
1
1
1
1
1
2
1
2
0
1
2
1
1
0
1
0
0
2
1
0
1
1
2
1
1
0
0
2
1
1
1
1
1
2
1
0
0
1
2
0
1
2
0
2
1
1
1
2
0
0
0
0
0
2
1
1
1
0
0
2
1
1
1
1
1
1
2
0
0
1
2
0
2
0
0
0
1
2
2
0
2
0
0
2
2
1
2
1
1
1
1
1
1
1
1
2
0
2
0
1
1
1
2
0
0
1
0
1
0
1
0
2
1
1
1
0
1
1
0
1
1
2
1
1
1
2
1
1
1
0
2
1
0
1
1
2
0
2
0
1
2
1
1
1
1
0
0
1
2
0
0
0
1
1
1
1
2
2
1
1
0
0
2
1
0
2
2
1
0
1
2
1
0
2
0
1
1
2
1
1
0
1
0
1
2
0
0
0
1
1
0
0
2
0
0
1
1
1
0
2
0
0
1
0
1
2
1
2
1
1
1
0
1
1
0
1
1
2
2
2
1
0
1
1
0
1
0
0
2
1
1
0
0
1
1
1
2
1
1
0
1
1
1
1
1
1
1
1
1
2
0
1
1
0
3
0
1
0
0
1
1
0
1
1
1
1
1
0
1
1
1
0
1
1
1
1
1
0
1
1
0
4
2
1
1
0
0
1
0
0
2
1
1
1
1
1
0
0
1
0
1
1
1
2
1
1
1
1
1
0
1
1
2
1
1
1
2
1
1
0
1
2
1
1
2
1
2
1
1
0
1
2
1
0
1
1
1
1
1
0
1
2
0
2
0
1
1
1
1
2
2
1
0
0
2
0
0
2
0
1
1
1
0
1
1
2
1
1
0
1
0
0
1
1
2
2
1
1
0
1
2
1
0
1
1
1
1
2
0
0
2
1
3
2
1
0
0
1
1
1
0
0
1
2
1
1
1
1
2
2
1
2
0
2
1
1
0
1
0
0
1
2
0
2
1
1
2
0
2
1
1
0
1
2
1
1
2
2
2
1
2
2
2
2
1
1
0
1
1
1
0
1
2
1
1
2
1
1
0
1
1
0
1
0
0
1
2
1
2
2
0
2
1
2
1
1
2
0
1
1
0
2
1
1
1
1
2
1
0
1
1
2
1
2
0
1
2
0
0
0
1
1
1
2
1
1
0
1
1
0
1
1
1
1
2
2
2
1
2
0
2
1
1
0
1
1
2
1
1
0
2
1
0
0
0
1
2
1
1
0
2
0
1
2
1
1
1
2
1
1
2
0
1
2
1
0
1
2
1
2
1
1
1
1
1
2
1
0
1
0
0
2
0
1
2
0
0
1
2
1
1
2
1
2
2
0
0
1
1
1
1
1
2
2
1
1
0
0
1
2
1
1
2
1
0
2
1
1
2
1
1
1
0
1
2
1
2
0
1
2
2
2
2
3
2
1
1
0
1
1
0
1
2
0
1
2
1
0
1
1
0
0
1
1
1
1
1
1
1
2
2
0
2
2
1
1
0
1
1
0
2
1
0
1
1
0
0
1
1
2
1
0
1
2
1
1
1
0
1
2
1
1
1
1
1
0
0
0
0
1
0
5
1
0
1
0
0
2
0
2
1
1
0
1
1
1
0
1
0
1
1
1
1
0
1
2
0
0
2
0
0
2
0
1
0
1
0
1
0
2
0
1
0
1
2
0
2
0
1
1
0
2
1
0
2
0
2
1
1
2
1
1
1
1
1
2
1
2
1
1
0
1
2
0
2
2
0
1
1
1
0
1
2
5
1
1
1
1
1
2
0
0
0
0
1
1
1
1
0
2
1
2
0
1
0
1
2
1
0
1
2
0
2
2
0
1
0
2
2
1
1
1
0
1
1
2
0
1
1
0
1
1
1
1
1
1
0
2
1
3
2
0
2
0
1
1
2
1
1
2
1
2
2
1
1
2
0
0
1
1
1
1
1
1
1
0
1
2
1
1
2
1
1
1
1
1
1
0
0
1
2
1
0
0
1
1
1
1
0
0
0
1
1
1
2
0
1
1
0
0
0
2
1
1
2
0
1
2
0
0
1
1
1
0
0
0
1
1
0
1
2
1
2
2
0
2
0
1
1
1
1
0
2
2
0
1
0
1
2
1
2
0
1
1
0
2
1
2
1
2
1
2
1
0
1
0
0
3
1
1
1
0
1
1
1
1
2
1
2
1
1
0
1
0
0
1
2
1
1
1
1
2
2
2
1
1
2
1
1
2
1
1
2
1
0
1
1
0
1
2
1
0
1
0
1
1
1
0
2
1
2
1
2
2
1
0
1
0
1
0
1
0
0
0
1
1
0
2
2
0
1
0
1
1
2
1
1
2
1
2
2
0
1
2
1
2
1
2
2
1
1
2
1
0
1
1
1
1
1
2
1
2
0
1
1
1
0
2
1
1
0
1
0
1
1
4
1
0
2
2
0
1
1
1
1
1
1
1
0
1
1
0
1
1
1
1
1
0
0
1
1
0
1
1
2
1
0
1
1
1
2
1
2
0
1
0
1
2
1
1
2
0
1
1
1
2
1
1
0
2
1
0
1
2
2
0
2
0
0
2
1
1
1
0
1
1
1
0
1
3
0
1
1
1
1
2
1
2
0
3
1
1
1
2
0
1
1
0
1
0
2
2
0
2
1
2
1
1
1
0
2
2
0
1
1
1
1
0
2
1
2
1
1
1
0
2
1
1
1
1
0
0
1
1
0
2
2
0
1
1
1
0
2
3
2
1
0
0
1
1
0
0
1
1
1
1
0
0
0
0
2
0
1
1
1
1
0
2
0
0
1
0
1
0
0
2
0
1
0
3
0
0
1
1
1
1
3
1
1
0
1
0
1
1
3
0
0
2
1
1
2
2
1
2
0
0
2
1
1
1
0
1
1
1
1
2
0
1
1
2
1
1
0
1
2
0
1
0
2
2
1
1
1
1
2
1
1
2
1
1
1
0
1
1
1
0
1
2
1
2
1
1
1
0
2
1
0
1
2
2
1
0
0
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
0
2
1
1
0
2
0
2
1
1
1
3
1
1
0
0
2
1
3
2
1
2
2
1
0
0
1
1
1
0
1
1
1
1
1
0
0
1
1
2
1
2
1
0
1
1
1
2
0
0
1
2
1
2
0
2
1
1
0
1
1
0
1
0
1
0
1
1
0
0
2
1
1
1
1
1
0
1
1
0
5
0
1
0
1
2
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
0
0
2
0
2
1
3
0
0
2
1
0
0
1
2
2
1
1
2
2
1
0
1
4
1
0
0
1
1
1
2
1
2
1
4
1
1
1
0
0
1
0
1
2
1
2
0
1
0
1
1
0
1
0
2
1
2
1
1
1
1
2
0
1
2
1
2
2
2
1
1
1
1
1
2
0
0
0
0
2
3
0
0
0
1
2
1
1
2
1
1
1
2
2
1
1
1
1
0
1
1
2
2
0
1
0
0
0
2
0
1
1
0
1
0
2
2
2
3
1
2
1
1
2
1
0
1
1
1
1
1
1
0
2
2
0
1
0
3
1
1
0
1
1
0
2
0
1
0
1
1
2
1
0
1
1
1
0
2
1
2
1
2
2
0
0
1
1
1
1
2
2
2
0
2
1
1
1
0
1
0
1
1
2
0
0
1
2
2
1
1
1
1
0
1
2
2
1
0
1
1
1
0
0
0
0
1
2
1
2
1
1
1
1
1
1
1
2
0
0
1
0
2
1
0
1
1
1
1
2
1
2
2
1
2
1
0
0
1
0
1
1
2
0
2
1
1
1
1
2
2
1
1
1
0
1
1
0
0
1
0
1
0
0
1
1
1
2
1
2
1
1
1
0
1
1
3
1
1
1
1
2
2
1
0
0
0
1
0
2
1
1
1
1
2
1
1
1
0
2
1
0
1
0
0
0
1
2
1
2
0
1
2
0
2
1
0
3
0
1
2
1
2
1
0
1
1
1
0
1
0
1
2
1
2
1
2
1
1
0
0
1
1
1
2
1
1
2
0
0
1
0
0
2
2
1
1
0
0
1
1
0
1
0
0
1
0
1
1
1
3
1
1
1
0
1
1
0
1
2
1
0
2
1
0
2
1
1
0
1
1
0
0
0
1
1
2
2
2
3
2
2
0
0
0
1
0
1
1
1
1
3
1
0
2
0
0
1
1
1
1
2
2
1
3
2
1
0
1
1
1
2
2
0
1
2
1
2
2
1
1
1
2
1
1
1
2
1
1
0
4
1
1
1
1
0
1
2
1
1
0
1
2
2
1
1
2
0
1
1
1
1
1
1
1
2
1
1
2
1
1
2
1
1
2
3
1
0
0
1
1
1
2
2
0
1
2
1
0
1
1
1
0
2
1
0
1
0
1
1
1
1
1
1
1
0
2
2
1
1
2
0
1
2
2
2
0
1
1
2
1
0
1
0
1
1
2
1
1
1
1
1
1
0
1
1
2
1
1
2
1
2
0
1
1
2
0
0
1
1
0
0
2
1
0
2
2
0
1
1
0
0
0
0
1
1
1
1
1
0
2
0
1
1
2
1
1
2
0
1
2
1
1
0
0
0
2
1
0
1
0
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
3
2
1
1
0
1
1
1
1
0
1
0
0
0
2
1
1
0
1
1
1
1
0
1
0
0
1
2
1
1
2
1
1
0
1
1
1
1
1
2
1
0
1
1
0
1
1
0
1
1
1
1
0
1
1
1
1
2
1
0
1
2
1
1
0
1
0
1
0
0
1
2
1
1
1
1
1
1
0
0
1
1
2
1
0
2
2
0
1
1
1
1
1
2
1
1
1
2
2
1
0
1
1
1
0
0
1
1
1
1
0
1
1
1
2
1
1
1
0
1
2
1
1
1
1
0
1
1
2
1
1
1
1
2
2
1
1
0
0
1
1
0
1
0
0
1
1
1
1
0
1
0
1
0
1
1
1
2
3
1
1
0
1
1
0
0
1
0
1
2
1
1
1
2
2
1
0
1
3
1
1
1
2
1
2
2
1
2
0
2
0
2
1
2
1
0
2
1
1
1
2
2
1
2
1
0
2
2
1
0
2
2
1
0
0
1
1
2
2
1
1
1
0
0
1
2
1
2
0
2
1
0
1
1
2
1
2
1
1
2
0
0
1
2
0
1
2
0
1
1
1
1
2
1
1
2
0
2
2
1
1
1
2
0
1
1
0
2
2
0
0
1
2
0
1
1
0
0
2
2
0
2
1
1
1
2
2
1
2
2
1
2
0
0
1
1
1
2
1
1
1
1
1
2
0
2
0
1
1
2
1
0
2
1
1
1
2
2
1
1
1
2
0
2
0
0
0
1
0
1
1
2
2
0
1
0
2
0
0
2
1
1
0
1
1
1
0
1
2
2
0
1
0
1
2
1
0
1
1
1
1
1
1
1
0
0
0
1
2
1
2
1
1
1
0
1
1
1
0
1
2
1
1
1
2
1
0
1
1
0
1
1
0
4
1
1
1
0
1
1
1
0
2
2
0
1
0
1
2
1
1
1
2
1
1
0
0
1
1
0
1
1
1
2
0
0
1
1
0
0
0
4
1
2
1
1
1
0
2
2
0
1
1
1
1
1
1
0
0
0
2
1
2
1
0
0
0
2
0
1
1
0
1
1
2
0
0
1
1
1
1
2
1
0
0
2
2
1
1
1
2
1
0
0
1
1
1
1
1
0
1
2
1
1
0
1
1
1
1
1
1
1
1
1
2
1
0
0
2
1
0
2
0
2
1
1
1
1
0
1
0
0
1
0
0
2
1
1
2
0
2
2
1
2
1
1
0
1
0
0
2
1
1
1
0
1
0
1
2
1
2
1
0
0
0
0
1
1
1
1
1
2
2
1
0
1
0
2
2
2
1
0
1
1
0
1
0
2
0
0
4
2
0
0
0
1
0
1
1
1
1
0
1
0
1
1
1
1
0
1
1
1
0
1
0
0
1
1
2
0
1
0
2
1
1
0
2
1
0
1
2
1
1
1
1
1
1
1
1
1
1
1
0
1
1
2
0
1
1
1
1
1
1
0
1
0
1
1
1
0
1
1
0
1
2
1
0
1
0
1
1
2
0
1
0
1
1
2
1
2
2
1
1
1
1
0
0
1
0
2
1
0
1
1
1
0
2
1
1
1
2
0
1
0
1
2
1
1
1
2
1
1
1
1
2
2
2
1
1
2
1
0
1
1
1
1
0
1
1
1
1
1
2
1
0
1
2
2
0
2
1
0
0
0
1
1
0
1
1
2
2
1
1
2
2
1
1
1
0
1
1
1
1
1
2
1
0
1
1
2
1
0
0
2
1
1
0
0
0
1
1
1
1
1
1
0
1
2
1
1
0
1
2
1
0
0
1
0
1
0
1
7
1
0
2
0
2
1
3
2
1
2
1
1
1
0
6
1
2
1
1
1
0
0
1
1
0
1
0
1
1
2
2
1
1
2
1
0
0
2
2
2
1
1
1
2
1
2
1
1
1
1
0
2
1
1
1
2
1
1
1
2
1
1
2
2
2
1
1
3
0
1
2
2
0
0
2
0
2
1
2
1
1
0
1
1
1
1
1
1
1
0
1
1
0
2
1
1
0
1
1
1
0
2
0
0
1
1
1
1
1
2
3
0
1
1
0
1
0
2
1
1
0
2
1
2
0
1
1
0
1
0
2
0
2
0
1
1
0
2
1
1
1
1
2
1
1
1
2
1
2
1
1
0
1
1
1
0
1
2
0
3
0
2
1
1
2
1
1
1
1
1
2
2
2
0
2
2
1
1
1
0
0
2
1
1
0
1
1
1
0
0
1
1
1
1
4
0
1
1
0
1
1
1
0
1
1
1
1
0
0
1
0
1
1
1
1
0
2
2
1
1
1
0
1
1
1
1
0
3
2
1
2
1
0
0
0
1
0
2
1
1
1
1
1
1
2
1
1
1
0
0
1
2
1
0
1
0
1
0
1
1
1
1
1
2
1
1
1
2
0
1
0
1
1
2
1
0
1
1
0
0
0
1
0
2
1
1
0
1
1
1
0
1
2
1
2
1
0
0
1
1
1
1
2
2
1
2
2
2
1
1
1
1
2
0
1
2
0
0
1
2
1
0
2
0
2
1
2
1
0
2
1
2
1
0
1
1
1
1
1
0
0
0
1
0
2
2
1
1
3
1
0
0
1
2
1
0
1
0
1
0
1
1
1
1
0
1
0
1
0
1
0
1
1
1
1
2
1
1
1
1
1
0
1
1
1
0
1
0
0
0
1
0
1
0
2
2
1
1
1
1
0
0
0
2
0
1
0
0
1
0
2
2
1
1
0
1
1
2
0
0
0
1
1
0
0
1
0
1
2
1
1
1
0
1
2
2
1
2
0
1
1
1
1
1
1
1
1
0
2
1
1
1
1
1
0
1
0
0
2
1
0
1
1
0
0
1
1
1
1
1
1
2
0
0
0
2
1
2
1
1
1
0
0
2
1
1
0
1
2
3
1
1
1
1
1
2
1
1
1
0
1
1
1
0
1
2
2
1
1
0
1
1
1
0
2
3
1
1
1
2
1
1
1
1
0
1
0
1
2
1
0
2
0
2
2
1
1
0
1
1
1
1
0
1
2
1
2
2
2
1
2
2
2
2
2
1
1
1
1
2
1
0
2
0
1
1
1
0
1
1
1
1
1
1
1
2
1
2
2
1
1
0
1
1
1
0
1
0
0
2
1
0
0
1
2
1
1
1
1
1
1
0
1
1
2
1
3
0
1
1
1
1
2
1
0
2
0
0
1
2
0
2
2
1
1
1
0
0
1
0
1
1
2
2
1
1
1
1
1
2
1
2
1
1
1
0
1
1
2
1
1
1
0
0
2
1
0
1
0
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
0
1
0
1
1
1
1
1
3
0
0
1
1
0
0
0
3
0
2
0
1
1
1
1
2
1
0
1
1
0
1
0
0
0
1
0
2
1
2
1
2
2
0
1
2
0
0
1
0
0
2
1
1
1
1
0
0
2
0
2
1
1
2
0
2
1
1
0
3
2
0
1
1
2
2
0
2
1
1
1
0
0
0
0
2
1
0
2
2
1
2
1
1
2
1
1
2
1
1
1
1
4
2
2
1
3
1
1
2
1
2
2
1
2
1
2
1
1
2
1
2
2
0
1
0
1
1
2
2
1
1
0
1
1
2
0
1
2
0
1
0
0
1
2
0
2
0
1
1
2
1
0
1
1
1
1
2
1
0
1
1
1
0
0
0
0
0
1
1
0
1
1
1
1
1
1
1
0
2
0
1
2
0
1
0
1
1
0
0
2
0
2
0
1
1
1
1
1
2
0
1
1
1
1
1
1
1
2
2
1
2
1
1
0
1
2
0
1
2
0
1
1
1
2
0
0
1
0
0
0
2
1
0
0
0
0
1
0
0
1
1
1
2
0
1
0
2
1
0
2
1
2
1
2
1
1
2
0
1
1
1
1
1
0
1
0
1
0
0
0
1
0
1
2
0
1
2
0
1
0
0
1
3
1
0
5
1
2
0
1
0
1
2
1
1
0
1
1
1
1
2
0
0
0
1
1
1
1
1
2
0
2
0
1
1
1
0
2
1
1
1
0
0
1
0
1
1
1
1
2
1
2
1
1
2
1
2
1
0
1
2
1
0
1
0
0
1
1
1
2
2
1
1
1
1
3
1
0
1
0
2
0
2
1
1
0
0
1
1
1
1
2
2
1
2
2
1
2
1
0
1
0
2
1
2
1
1
1
4
1
1
3
1
1
0
1
2
0
0
0
1
1
1
2
1
2
2
1
1
2
0
2
1
0
2
0
3
1
2
1
2
1
0
1
1
2
1
1
2
1
0
1
1
0
2
1
0
1
0
2
2
1
1
1
1
1
1
1
2
0
1
2
1
2
1
1
1
1
0
1
1
1
1
1
0
1
1
0
1
2
1
2
1
1
0
1
2
2
2
1
1
3
2
2
2
1
3
1
0
1
0
0
2
1
0
0
2
3
2
1
1
0
1
0
0
1
1
1
1
0
1
2
2
1
1
1
0
1
1
1
1
2
0
0
0
0
1
1
1
0
2
1
1
1
0
0
1
1
0
2
2
1
3
1
2
1
3
1
2
2
0
2
1
1
2
1
1
2
0
1
2
1
2
2
2
1
1
0
1
0
1
0
1
2
2
1
0
1
1
1
1
2
1
0
0
2
0
0
1
0
1
2
1
0
0
1
0
0
2
2
0
2
1
2
1
0
2
0
0
2
1
2
1
1
1
1
1
1
2
1
0
1
1
2
1
2
1
1
1
1
2
1
1
2
1
1
1
0
0
0
0
3
0
1
0
2
0
2
1
1
0
2
1
1
2
1
1
1
1
1
1
2
2
1
1
1
2
1
1
1
0
2
1
1
2
1
1
2
1
0
0
1
2
2
1
1
1
0
0
1
1
0
1
1
1
0
1
1
0
1
1
1
0
2
2
1
1
1
2
1
1
0
1
1
1
1
2
3
2
1
2
2
1
1
0
0
0
1
2
1
1
1
0
1
0
0
2
1
0
2
2
2
2
1
2
0
1
2
1
2
2
0
0
1
2
2
2
2
2
0
0
1
1
1
1
0
1
1
2
2
1
3
2
2
1
0
1
2
1
2
1
1
2
0
0
1
1
1
0
1
0
0
0
1
1
2
1
1
1
2
0
0
1
1
2
0
0
1
1
2
0
1
1
2
1
1
1
0
1
0
0
0
0
2
0
0
1
2
0
1
1
1
0
2
0
0
0
1
0
1
2
1
1
1
1
1
2
1
2
0
0
1
0
1
1
2
1
1
1
0
1
1
1
0
2
0
1
1
0
0
0
2
0
1
2
1
1
0
0
1
1
1
1
0
2
1
0
0
0
0
1
0
0
2
0
1
1
2
0
1
1
2
1
1
1
2
2
1
2
0
1
1
0
1
1
1
1
1
1
1
0
2
0
1
1
1
2
0
1
0
1
2
1
2
1
1
1
1
1
1
1
1
1
1
0
1
0
1
1
0
1
1
1
1
1
1
1
2
2
2
2
1
2
1
2
1
0
0
1
1
2
2
2
1
1
0
1
1
1
1
2
0
0
1
1
0
0
2
0
0
0
1
2
1
1
1
1
1
0
0
2
1
1
0
1
0
0
0
2
0
2
3
1
1
1
0
1
1
1
1
1
1
0
1
0
2
1
2
1
0
1
1
1
1
1
1
0
1
2
1
1
1
2
1
2
1
0
1
1
2
1
1
1
0
2
0
1
0
2
2
2
1
0
1
2
0
0
1
1
0
1
1
0
0
1
0
1
2
1
2
1
0
1
1
0
0
0
1
2
1
2
1
0
0
1
1
1
2
1
2
2
1
5
1
2
3
0
1
1
1
1
2
1
2
1
0
2
0
0
0
1
1
2
2
1
2
2
1
1
1
0
1
0
2
1
1
0
4
2
1
1
1
1
1
2
0
1
0
1
1
1
2
1
0
1
0
1
1
1
2
1
1
0
0
2
2
0
2
1
0
1
1
1
1
0
1
1
1
1
1
1
1
2
1
2
0
0
2
2
1
1
1
1
1
1
0
1
2
1
1
0
1
1
1
1
2
0
1
2
2
1
1
2
0
1
1
2
0
0
1
0
1
1
2
1
0
1
0
1
0
2
1
1
1
0
1
1
1
1
1
0
1
1
1
1
1
0
0
0
1
1
1
2
1
1
1
2
2
0
0
1
1
0
2
0
2
2
1
2
3
0
1
1
1
1
0
1
0
1
0
2
2
1
1
1
2
2
1
4
1
1
1
2
2
1
1
2
0
0
1
1
1
1
0
1
1
2
0
0
1
1
1
2
0
1
2
1
2
1
1
1
2
1
2
2
1
2
1
0
1
1
1
2
1
1
1
2
0
2
1
1
2
1
1
0
0
1
1
0
1
1
2
0
0
2
1
1
1
2
0
1
1
1
2
1
1
1
1
0
0
2
1
2
0
1
1
2
1
1
1
1
0
1
2
2
1
2
2
1
0
1
2
1
1
2
1
1
1
1
1
0
1
0
2
1
1
2
1
1
2
2
0
1
1
1
0
1
0
0
2
2
1
1
1
0
2
1
2
2
1
2
1
1
1
0
2
1
1
1
1
1
0
2
2
1
2
1
1
0
1
0
0
0
1
2
0
0
1
1
1
0
2
0
3
1
1
0
2
1
1
1
0
1
1
1
0
0
0
0
2
1
0
2
1
0
0
2
2
1
1
0
1
0
1
1
2
1
2
1
1
1
1
3
2
2
1
1
0
1
1
2
1
1
0
1
1
1
2
1
1
1
2
1
1
0
1
1
1
0
1
0
1
2
1
1
1
1
1
1
2
0
1
0
1
2
1
1
0
1
2
1
0
1
3
2
1
2
1
1
1
0
2
2
0
0
1
0
1
0
2
1
0
0
0
1
0
2
0
0
3
1
2
4
1
1
0
1
1
1
0
0
2
1
0
2
0
2
1
2
0
1
2
2
1
2
0
1
1
1
0
0
2
0
1
1
2
0
2
2
1
1
2
3
0
1
1
0
0
0
1
2
1
1
1
1
2
1
1
1
1
2
2
0
1
1
1
0
0
0
1
0
1
0
1
2
2
2
1
0
1
0
1
0
2
1
2
1
2
1
1
1
1
0
2
2
0
2
1
0
2
2
1
1
0
0
1
1
2
1
0
0
1
1
1
4
2
0
1
2
0
1
0
0
1
0
0
1
1
1
0
2
2
1
2
2
0
0
0
1
1
0
1
2
1
0
1
1
0
1
1
1
0
2
1
2
0
1
0
1
1
0
1
1
1
1
1
0
1
1
1
2
1
1
1
2
1
1
0
2
1
2
1
1
0
0
2
0
0
2
0
1
2
2
1
2
0
1
1
1
1
1
1
0
0
0
1
1
1
1
2
0
1
1
2
3
1
2
1
1
6
1
2
0
1
1
0
0
1
1
2
2
3
1
1
2
1
1
1
0
1
1
0
1
2
2
2
1
0
1
1
2
2
0
1
1
1
1
1
2
1
1
2
1
1
0
0
2
1
0
1
1
1
2
0
1
1
1
1
0
1
2
2
1
2
1
1
1
1
1
1
1
2
2
1
1
2
1
1
2
0
1
0
2
0
0
1
2
2
2
0
1
1
1
2
1
1
0
3
0
1
0
1
1
1
0
2
1
0
0
0
1
0
2
1
0
0
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
0
0
1
0
1
1
1
1
2
2
2
2
0
1
1
0
1
1
1
0
0
1
2
1
1
1
2
1
1
0
1
1
0
0
1
1
0
0
1
0
0
2
1
1
1
1
2
2
1
1
0
2
1
0
1
0
1
3
1
2
2
0
2
2
2
1
1
1
1
0
1
1
1
0
1
1
0
1
0
2
1
2
2
2
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
2
0
1
1
2
0
1
1
1
2
0
1
0
1
1
2
1
1
0
2
1
0
1
1
2
1
2
0
3
2
1
1
0
1
0
2
0
1
0
1
1
1
1
0
0
2
2
1
1
0
0
1
1
1
1
2
1
1
0
0
2
1
1
1
0
1
2
1
1
0
0
1
4
1
1
1
2
1
1
2
2
1
1
0
1
0
0
1
1
1
0
2
1
0
1
2
0
1
0
0
2
3
2
1
2
0
2
2
0
1
2
1
0
0
1
0
1
2
0
2
1
2
1
0
2
1
1
0
1
0
1
1
0
1
2
3
0
2
2
1
1
1
0
1
1
0
2
2
2
1
0
1
0
1
0
1
1
1
1
1
2
1
1
2
0
1
0
1
1
1
0
1
1
1
4
1
0
0
0
1
0
1
0
0
1
0
2
1
0
1
2
2
2
2
1
1
1
0
0
1
0
2
1
1
1
1
1
2
0
1
0
1
2
1
1
2
0
1
1
1
1
1
1
2
4
1
1
0
2
1
0
2
0
2
1
1
1
2
1
1
1
0
0
0
1
1
1
1
1
2
1
0
1
1
0
0
1
1
0
1
1
0
2
0
1
1
0
0
1
2
1
2
1
2
1
1
1
0
1
1
1
0
1
1
0
1
1
1
0
1
3
2
1
0
0
1
1
2
1
1
2
0
1
0
1
1
1
1
0
3
1
1
2
1
1
0
2
3
1
1
2
2
1
1
1
1
2
0
1
1
2
1
0
0
1
0
1
0
1
1
2
1
2
1
2
1
1
2
0
1
1
1
1
0
1
1
0
1
0
1
0
1
0
0
2
2
0
2
2
0
2
1
1
1
1
2
0
2
0
1
1
1
1
1
2
0
1
1
0
2
2
1
4
2
1
1
0
1
1
0
1
0
0
1
0
1
1
1
2
2
1
0
1
2
1
1
2
1
0
1
2
0
1
1
0
1
1
0
1
0
2
0
1
0
1
0
1
1
0
1
1
1
1
1
0
2
1
0
1
1
2
1
0
1
2
0
1
0
1
0
1
1
2
1
0
0
2
1
3
1
1
1
2
1
1
0
2
1
1
0
1
0
2
1
1
2
1
1
0
1
1
1
1
1
1
1
1
1
1
0
0
0
0
1
2
2
1
1
2
1
0
1
1
1
1
2
1
1
1
1
0
1
1
1
1
1
1
1
2
0
1
1
1
0
2
0
1
2
2
2
1
0
2
1
1
0
0
1
2
1
1
1
2
1
1
1
0
1
1
1
3
1
1
0
0
1
2
1
1
1
1
0
1
1
0
1
0
1
1
1
1
2
1
1
2
0
2
1
1
2
1
1
0
2
2
0
1
2
1
1
1
0
2
0
1
1
1
1
1
2
2
2
2
1
0
0
1
2
0
1
0
2
0
2
2
1
1
1
0
0
0
0
1
0
1
1
1
1
1
3
2
1
0
0
1
0
0
0
2
1
1
1
1
2
2
1
2
1
0
1
1
1
1
1
1
0
1
0
1
1
1
1
0
1
1
0
2
1
0
1
1
1
1
3
2
1
1
1
1
2
1
1
1
2
0
1
2
1
1
1
2
1
1
1
1
1
1
0
1
1
1
2
2
1
1
2
1
2
2
1
1
1
2
1
0
1
2
0
3
1
1
1
1
3
1
1
0
0
2
1
2
1
1
0
1
0
1
2
1
0
1
1
2
1
1
0
2
2
1
0
1
2
1
0
1
1
2
1
0
1
2
0
2
1
1
0
2
0
1
1
2
0
0
0
1
1
2
1
0
0
0
2
1
2
3
1
0
1
2
2
0
0
2
1
0
0
1
2
2
1
1
0
2
1
1
0
1
2
2
1
0
0
0
0
2
1
1
1
0
1
3
1
1
0
1
1
2
1
2
0
2
0
0
1
1
2
1
1
1
2
0
1
2
2
0
1
1
2
2
1
1
0
1
1
2
1
1
1
1
2
1
0
2
2
1
1
1
0
1
1
1
2
2
1
0
1
1
2
0
0
0
0
1
2
2
1
1
2
1
0
0
1
0
2
2
1
1
1
5
1
1
1
0
1
1
0
0
1
1
1
1
1
2
0
1
1
2
2
2
1
0
1
1
1
2
2
0
1
1
0
2
1
0
0
1
1
1
2
1
2
2
2
1
1
1
0
1
2
1
0
1
1
0
1
1
2
0
1
2
0
0
0
1
0
2
1
0
1
1
0
0
2
1
1
2
2
0
2
0
0
1
1
2
1
2
1
1
1
2
1
0
0
1
1
0
0
1
1
1
1
0
2
2
2
2
1
1
4
2
0
1
1
1
1
1
1
1
0
2
2
1
1
0
1
2
1
1
1
1
0
2
0
1
2
1
1
1
2
1
0
1
0
1
2
0
0
1
2
2
1
1
1
1
0
0
0
0
2
2
2
0
0
2
0
1
1
0
3
1
1
1
1
1
2
0
1
0
1
1
2
1
0
1
1
1
1
2
2
0
2
1
0
2
1
1
0
2
1
0
1
1
2
1
1
2
1
1
0
1
1
0
2
1
1
1
2
0
1
1
1
1
1
1
1
1
2
0
2
1
1
1
1
2
1
2
1
1
2
1
0
1
0
1
2
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
0
1
1
1
1
0
1
1
1
1
1
0
1
0
1
2
2
1
1
0
1
0
2
1
1
1
1
0
1
1
1
2
1
1
2
1
1
1
1
1
2
0
1
1
1
0
0
0
1
0
1
1
0
0
2
1
0
1
1
2
1
1
1
0
1
1
1
1
1
1
1
0
1
0
1
0
1
1
2
1
1
0
1
2
1
3
1
1
0
0
1
2
1
1
1
3
1
0
0
2
1
0
1
2
2
1
1
1
2
2
2
2
1
1
1
2
1
1
1
1
2
1
1
0
1
1
2
0
0
2
1
1
1
1
0
1
1
1
0
1
1
1
0
1
1
0
1
1
1
2
2
0
1
2
0
0
0
1
1
0
2
0
0
1
1
2
1
0
1
1
0
0
1
1
1
2
1
1
2
1
2
0
1
1
0
0
2
2
0
1
1
2
0
2
0
1
0
1
1
1
2
1
1
1
1
1
1
1
1
2
2
1
0
1
2
1
2
1
0
1
2
0
2
2
1
1
0
1
1
0
1
1
2
0
1
2
0
2
0
0
2
0
1
1
1
0
0
0
2
1
0
2
1
1
1
0
1
1
2
2
1
1
0
1
1
1
1
2
1
1
1
0
1
2
1
2
0
2
1
2
2
2
2
1
1
1
1
1
1
0
1
1
1
1
1
0
2
0
1
1
2
1
1
2
0
1
2
0
2
1
1
1
0
1
2
1
1
1
0
1
2
1
1
0
2
0
1
1
1
1
2
0
2
1
2
1
1
1
1
1
1
1
1
1
0
0
1
1
0
1
0
1
1
0
1
2
0
1
0
1
0
1
1
1
1
0
1
0
2
2
0
0
2
0
1
0
1
1
0
1
1
0
0
1
1
2
0
1
1
0
1
1
1
1
0
0
1
0
1
1
0
0
0
2
1
0
2
1
2
0
1
0
0
1
1
2
2
0
1
0
0
0
2
1
1
1
1
1
1
1
1
0
1
0
1
1
2
2
1
0
2
1
1
1
0
1
1
2
0
1
3
1
0
2
0
0
0
1
2
1
1
2
0
2
2
1
1
1
2
0
2
1
2
1
1
1
0
1
1
0
1
1
1
1
1
1
1
1
0
1
2
2
1
1
1
2
1
1
2
2
1
2
1
0
0
0
2
2
0
1
1
1
1
1
2
2
1
2
0
1
1
2
1
1
2
0
1
0
2
4
1
1
2
0
0
1
0
1
1
1
0
1
1
2
1
0
1
2
0
1
2
1
2
1
0
1
1
1
1
0
0
2
2
0
2
1
2
0
0
0
2
1
1
0
2
0
2
1
2
1
0
2
0
1
0
0
1
1
1
2
1
0
1
1
1
2
2
1
0
1
1
2
0
2
1
1
2
1
1
1
1
1
0
0
1
2
2
1
2
1
2
1
1
2
1
2
1
3
1
0
1
0
1
0
1
1
2
2
1
1
0
1
0
2
1
2
1
0
0
1
1
1
1
1
0
1
1
0
1
0
0
2
0
0
2
1
0
1
1
1
1
1
1
0
2
1
2
0
1
0
0
1
1
1
0
1
2
2
1
1
1
1
1
0
0
0
1
1
0
0
1
0
1
0
1
1
2
1
0
1
1
1
1
1
2
1
1
0
1
1
0
0
1
1
0
2
1
1
1
2
0
0
2
1
2
2
1
2
2
1
1
0
0
0
2
1
2
1
1
2
1
1
2
0
0
1
0
2
0
1
0
2
0
1
2
0
2
0
2
0
0
1
0
1
0
1
0
0
2
1
1
2
2
1
1
0
2
1
1
1
1
0
0
1
0
2
1
2
1
1
1
1
0
0
0
2
0
4
2
1
1
1
0
1
2
0
1
0
2
0
1
1
1
2
0
2
1
3
2
1
1
0
2
1
0
2
2
1
1
0
0
1
0
1
1
2
1
0
0
2
0
1
2
1
1
2
0
0
1
2
1
1
2
0
1
1
2
0
1
2
1
2
2
1
2
0
0
0
1
2
1
2
2
1
2
1
0
1
2
2
1
0
1
0
0
2
0
0
2
1
1
0
0
1
1
2
1
2
0
2
2
1
2
3
1
0
1
2
1
1
1
0
1
1
0
1
1
0
1
0
1
0
1
1
1
1
2
1
2
1
2
0
1
0
1
1
1
1
2
1
2
2
2
2
0
1
0
2
1
0
1
1
1
1
0
1
1
2
1
1
1
1
0
2
0
0
1
0
0
1
1
1
1
2
0
1
2
1
2
1
1
1
1
1
3
0
0
1
1
1
2
1
1
2
0
1
0
2
1
0
2
0
1
0
1
2
0
1
1
0
1
0
1
0
0
1
1
2
1
1
0
0
1
2
0
1
1
2
0
1
1
1
1
0
0
0
2
1
0
0
1
1
1
1
1
1
1
2
2
1
0
0
1
1
1
1
1
1
2
0
0
1
0
1
1
1
1
0
1
2
1
1
2
0
1
2
1
0
1
1
0
0
1
1
1
1
1
0
2
1
0
2
1
0
1
1
1
1
1
1
1
1
0
1
1
1
0
0
1
1
1
1
0
1
0
0
1
1
2
1
1
1
1
0
1
1
1
1
1
1
2
2
0
0
0
1
1
1
1
1
1
1
1
0
1
1
1
2
1
1
2
0
1
1
1
1
0
1
1
1
2
1
2
0
0
1
1
2
1
0
2
2
2
1
2
0
2
2
1
1
1
0
1
1
0
0
1
1
2
0
2
1
1
0
1
2
2
2
1
0
1
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
0
1
1
0
1
2
1
1
1
1
1
0
2
0
0
2
2
1
2
1
0
1
1
2
1
1
1
0
2
1
0
1
1
1
1
1
1
1
0
1
10
1
1
1
2
1
3
1
1
2
1
2
2
1
2
0
0
1
1
0
1
1
0
1
1
2
1
1
1
1
1
0
1
0
2
1
0
2
2
1
1
1
0
0
0
2
0
1
1
1
1
1
1
2
2
2
1
0
1
1
1
0
1
2
1
2
1
2
2
1
1
2
1
1
2
2
0
2
2
1
0
0
1
0
0
2
1
1
2
2
1
1
1
2
1
2
2
1
0
1
1
1
0
2
1
1
0
1
0
0
1
1
1
1
1
1
0
2
1
1
1
1
1
2
1
0
0
1
1
1
0
1
1
0
1
0
2
1
2
2
0
2
1
0
1
1
0
0
1
1
1
2
0
2
1
1
1
0
1
1
2
2
1
1
1
2
2
0
1
2
2
2
1
1
1
2
1
1
2
0
1
1
1
1
0
0
2
0
0
2
1
2
1
2
0
1
2
1
0
2
1
0
2
1
2
1
1
1
1
0
1
2
1
1
1
2
0
1
2
0
1
1
0
0
0
0
0
1
0
2
1
0
1
2
2
1
0
0
1
0
1
0
1
1
2
1
1
0
0
0
2
2
0
1
2
1
1
0
1
1
1
2
1
2
2
2
0
0
1
1
0
1
1
2
1
3
0
2
1
2
1
0
1
1
0
1
2
0
0
1
1
1
0
1
2
1
2
1
1
1
1
1
2
1
0
2
1
0
0
1
2
1
1
2
1
1
1
2
1
1
1
1
0
0
1
1
0
1
1
2
1
1
2
0
2
1
1
0
2
0
1
0
1
1
0
0
2
2
1
1
1
1
0
2
2
2
1
1
0
1
1
0
1
2
1
2
0
2
2
1
1
1
1
2
1
1
2
0
1
1
1
1
1
1
1
1
0
1
1
1
0
2
1
2
1
1
2
1
1
2
1
1
2
1
2
0
1
2
0
1
0
1
1
4
0
1
0
1
0
1
1
0
2
2
0
1
2
2
2
0
1
0
3
1
0
0
2
0
1
1
1
1
0
2
0
1
1
1
2
1
1
1
0
1
1
0
1
1
1
1
2
1
0
1
2
1
1
1
0
1
1
0
1
1
1
2
1
1
1
2
1
1
2
2
1
0
0
1
2
2
0
2
1
1
1
1
1
1
2
1
1
1
0
1
1
0
0
0
0
1
0
1
2
2
2
2
1
2
1
0
1
1
2
1
1
1
1
1
2
1
1
0
2
2
1
0
1
2
2
1
0
2
0
1
2
1
1
1
1
0
1
1
2
3
1
0
1
1
0
3
1
2
1
0
1
1
1
1
1
1
0
1
0
0
1
1
1
0
2
0
1
1
0
2
0
0
0
1
1
0
1
1
0
0
1
0
2
1
0
1
1
2
1
0
1
0
1
0
1
1
2
1
0
3
1
1
2
0
1
1
1
0
0
0
0
1
0
1
1
1
1
2
2
0
2
0
1
4
1
1
0
1
1
1
2
2
0
1
2
1
2
1
1
1
2
2
1
0
1
0
0
2
1
1
0
1
1
1
1
0
2
1
2
1
0
0
1
1
0
2
1
1
0
1
1
2
2
1
2
2
1
6
1
2
0
1
2
0
1
1
1
0
1
1
0
0
2
1
1
0
1
1
1
0
2
1
0
1
1
0
1
2
1
2
1
1
1
0
1
1
1
1
0
1
3
0
1
1
2
2
0
2
1
1
0
2
0
0
2
0
1
1
0
1
1
1
3
2
1
1
2
1
0
0
2
1
0
1
1
1
1
0
0
2
2
1
0
2
2
0
1
2
1
0
0
0
2
2
2
0
0
1
2
0
1
0
1
1
1
1
0
1
1
0
2
0
1
0
1
1
2
0
1
0
1
2
1
2
0
0
0
1
1
1
1
1
1
1
2
2
1
1
1
1
2
0
2
1
2
1
0
1
2
1
1
0
1
1
1
1
1
2
1
0
1
1
1
2
0
1
1
1
0
1
1
3
1
0
2
2
1
3
1
0
1
0
0
1
1
1
1
2
1
1
1
1
1
0
1
0
2
1
1
1
0
1
0
1
2
0
0
2
0
1
1
2
1
1
1
1
0
0
1
2
2
2
0
2
3
0
2
1
0
0
1
1
0
1
0
1
1
0
0
1
1
1
1
1
2
1
1
0
0
0
1
1
1
2
1
1
1
0
1
0
2
0
1
2
1
1
1
0
0
1
2
1
1
0
1
1
1
2
2
1
2
1
1
2
1
1
1
3
0
1
0
0
1
2
1
1
2
0
1
2
1
1
0
1
1
1
1
2
1
1
2
2
2
1
2
2
2
0
1
1
2
2
1
1
1
0
0
0
0
1
0
0
2
1
0
3
1
1
2
1
1
1
0
1
1
1
0
1
1
0
1
1
2
2
1
1
2
1
2
1
0
0
1
0
1
1
1
1
1
1
1
1
1
0
2
1
1
1
1
1
1
0
0
2
1
1
1
1
0
1
1
2
1
2
1
1
0
0
2
1
1
1
1
0
1
1
1
0
1
1
1
1
1
1
1
1
0
1
2
1
1
1
2
1
1
0
2
1
2
0
2
1
1
1
1
1
3
0
1
1
1
1
1
0
1
0
0
0
1
0
1
0
0
1
0
1
1
1
2
2
1
1
1
1
1
0
1
1
2
1
1
2
0
2
1
0
1
0
1
1
0
2
2
1
0
1
0
0
0
2
0
1
1
1
3
1
1
2
1
2
1
0
2
1
2
0
1
0
0
1
0
2
1
1
1
1
1
1
2
0
0
1
1
1
2
1
2
2
1
2
1
0
0
0
1
1
1
1
1
0
2
0
1
1
1
1
1
2
1
0
1
2
1
1
1
2
2
0
1
0
0
0
0
1
0
0
2
0
1
0
1
1
1
2
1
1
2
1
0
0
3
1
0
0
0
1
1
1
1
0
0
0
0
0
1
0
0
2
2
1
1
2
1
1
2
1
0
1
1
1
1
1
0
0
1
1
1
1
1
1
1
1
1
0
2
1
1
1
2
1
1
0
1
1
1
3
2
2
1
2
1
2
2
0
1
1
1
1
2
2
2
0
2
1
1
1
2
1
1
1
1
2
1
1
2
0
0
2
0
1
1
1
0
0
0
1
0
1
1
0
1
0
0
0
1
0
1
0
1
1
2
1
0
1
1
1
2
1
2
2
2
1
0
1
1
1
1
1
1
0
1
0
0
1
2
0
1
1
2
1
2
1
1
2
1
2
0
0
0
0
1
2
1
2
1
1
1
0
0
0
0
1
1
2
2
1
2
1
1
0
1
1
2
2
2
1
2
2
1
0
1
2
0
1
0
1
1
1
1
1
2
2
1
1
0
0
1
2
2
2
2
2
0
2
1
1
1
0
1
2
2
2
0
0
1
2
0
1
1
0
2
2
0
0
2
1
1
0
1
2
2
1
1
0
1
1
0
2
1
1
1
2
0
0
1
1
3
2
0
1
0
1
2
1
1
1
1
1
1
1
0
2
1
1
2
0
1
1
2
3
1
1
1
1
0
0
0
2
0
1
1
1
0
1
1
1
1
2
2
1
0
1
0
1
1
1
2
1
2
1
2
1
0
1
1
1
0
2
1
0
2
1
1
0
0
2
1
0
1
3
2
2
0
0
0
1
1
1
1
2
0
0
1
0
1
0
2
0
1
2
1
1
1
0
2
1
1
1
0
1
1
1
2
0
0
1
0
1
1
2
2
2
3
0
1
1
1
0
0
0
2
1
2
1
0
0
0
2
2
1
0
1
1
2
0
0
1
1
1
1
1
1
1
1
1
0
1
1
2
1
1
1
1
0
0
0
1
2
1
1
0
1
1
2
1
1
1
2
0
0
1
0
1
1
1
1
1
1
0
1
0
0
0
0
1
2
1
2
1
1
2
2
0
2
7
1
1
1
1
1
1
0
0
1
1
1
1
2
1
1
0
1
1
1
1
1
0
0
2
1
0
0
1
1
3
2
1
2
1
2
1
1
1
1
1
1
2
1
2
1
0
0
1
1
0
0
1
1
1
0
2
1
0
1
1
1
1
1
2
0
1
1
1
1
0
1
0
1
2
0
0
2
0
1
2
1
2
2
1
1
0
1
2
1
1
1
2
2
2
2
3
1
2
1
1
1
0
0
0
1
2
1
1
1
1
1
2
2
0
0
0
2
1
1
1
1
0
1
0
2
0
1
1
1
1
1
1
1
1
1
1
1
0
1
2
2
0
0
0
0
0
2
2
1
1
1
1
0
0
1
0
0
0
1
1
2
0
1
0
1
2
1
1
0
1
0
1
3
0
1
0
2
2
2
1
0
2
1
0
2
1
0
1
2
1
0
2
1
1
1
2
1
1
4
0
2
1
0
1
0
0
1
0
1
1
1
0
0
1
0
2
1
0
1
1
1
1
2
0
2
1
1
1
0
1
2
2
1
0
1
1
0
1
2
0
1
0
1
1
1
2
1
2
1
2
2
1
1
1
1
0
1
1
0
2
2
0
0
1
1
1
1
0
2
0
1
2
2
2
1
1
0
2
1
0
1
1
0
0
1
0
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
0
1
1
2
0
1
1
2
0
0
2
1
1
1
1
2
2
1
1
1
1
1
1
2
0
2
2
1
1
2
0
1
0
2
1
1
1
0
1
1
0
0
1
1
1
0
2
1
2
1
0
1
1
1
1
1
2
2
1
1
1
1
0
1
1
2
1
0
2
1
0
1
1
0
1
1
2
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
2
1
0
1
0
1
0
1
0
1
0
1
1
0
1
2
1
1
1
2
1
1
1
1
0
2
2
0
1
2
1
2
0
2
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
0
1
1
1
0
0
1
1
1
0
0
1
1
2
1
0
0
0
2
0
1
1
2
1
2
1
0
1
0
1
1
1
1
2
0
1
0
1
1
1
1
2
1
1
1
0
1
2
1
0
1
1
1
2
1
2
0
0
1
1
1
0
0
1
2
0
2
1
2
2
1
1
0
0
1
2
2
1
1
1
1
2
1
2
1
1
1
1
0
2
1
0
1
0
1
1
0
0
1
2
1
3
1
1
2
1
1
0
1
1
1
0
0
1
1
5
2
1
1
0
2
1
0
2
2
2
0
0
0
0
1
1
1
0
0
2
1
2
3
2
0
1
1
2
2
1
1
1
1
2
2
1
2
2
1
3
1
1
1
1
2
1
1
0
2
1
1
0
1
1
1
1
1
1
1
1
0
1
1
1
1
1
0
1
2
1
1
1
0
2
1
1
1
0
1
0
0
1
0
1
1
1
1
1
1
1
1
0
1
1
1
2
0
1
0
1
1
2
1
1
1
2
1
1
1
1
0
1
1
2
2
1
1
0
1
0
1
1
1
1
0
1
1
1
0
0
2
1
2
0
1
2
2
1
2
1
2
1
1
1
1
0
1
1
1
1
2
0
0
2
2
1
1
0
2
0
0
2
1
1
1
1
2
1
2
1
0
2
1
1
1
1
1
0
2
1
1
1
0
2
2
0
1
2
0
1
1
0
2
0
1
2
1
1
1
1
1
2
1
1
2
1
1
0
1
1
2
0
1
2
2
0
2
0
1
1
1
1
1
1
1
1
1
0
0
0
2
1
1
0
2
0
1
1
1
1
0
1
2
1
1
2
0
0
1
2
1
1
2
1
0
0
0
1
1
1
0
1
1
2
1
0
1
1
3
0
1
1
0
1
2
0
1
1
2
1
2
0
0
2
0
1
1
1
1
2
2
1
1
1
1
0
2
2
0
0
0
1
2
2
0
0
0
1
1
1
2
0
0
0
0
1
1
1
1
2
2
2
2
0
1
1
1
1
1
1
2
0
2
1
2
0
2
1
2
0
2
0
1
2
0
1
2
2
2
2
1
0
1
3
2
1
1
0
1
2
1
0
1
2
0
1
1
0
0
1
2
1
1
1
1
1
1
3
1
0
1
0
2
1
2
1
2
0
1
1
1
2
2
1
1
1
2
0
1
2
1
1
0
1
0
2
2
1
1
1
1
0
1
2
0
1
1
2
0
1
2
1
2
2
1
1
0
1
1
1
1
1
0
1
2
1
1
1
1
2
2
2
2
1
2
2
1
1
1
1
2
0
1
1
1
1
2
1
1
2
0
1
1
0
0
2
0
0
1
1
1
2
2
1
0
1
1
1
0
1
0
2
1
1
0
0
2
0
2
1
0
1
1
1
1
2
2
1
1
1
0
1
1
0
2
1
1
2
2
0
2
1
2
1
0
0
0
2
2
0
2
3
1
2
1
0
0
1
2
1
1
1
1
1
0
1
2
1
1
0
1
0
0
0
2
0
0
0
1
1
0
0
0
1
1
0
1
0
1
0
0
1
2
1
0
1
1
2
1
2
1
1
2
0
1
0
1
1
2
1
2
0
1
1
1
1
0
1
1
1
2
1
0
2
1
2
0
0
1
2
2
1
0
2
0
1
1
1
0
0
1
1
1
2
1
1
2
1
1
1
0
0
1
1
1
1
1
1
2
0
1
1
1
1
2
1
1
0
1
1
0
0
0
1
0
0
1
1
1
0
0
0
0
2
1
1
1
1
1
1
1
2
1
1
2
1
2
2
0
0
1
0
1
0
1
0
0
1
1
1
0
1
1
1
1
2
0
2
1
1
1
0
1
1
1
0
1
1
1
0
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
2
0
2
2
1
2
0
1
0
0
2
0
1
1
1
0
1
2
1
1
0
2
0
2
0
1
1
1
1
2
0
1
1
1
1
1
2
2
0
0
0
1
0
1
0
1
0
0
2
1
1
0
1
1
1
1
1
2
1
1
1
0
0
2
1
0
1
1
1
0
2
4
0
2
0
1
2
1
2
1
1
0
1
3
0
2
0
1
1
0
1
2
0
1
0
1
0
3
2
0
1
0
1
1
0
0
2
1
0
1
0
1
1
2
1
2
1
1
2
2
1
0
0
1
0
4
0
2
2
1
1
1
1
1
0
1
0
1
1
2
1
1
1
1
2
2
2
0
2
1
1
1
1
1
1
1
1
1
2
1
1
0
1
2
1
2
1
0
1
1
1
1
2
1
1
1
2
0
1
1
1
0
0
2
0
1
1
1
2
2
0
0
0
1
2
1
1
2
0
2
1
2
1
1
2
0
0
1
1
0
2
0
1
2
0
2
0
0
1
0
0
2
1
1
1
1
2
4
0
2
0
1
1
0
0
0
0
4
1
2
2
1
1
0
1
1
1
0
1
1
2
2
1
1
1
1
1
0
1
1
0
1
2
1
1
1
2
1
2
1
1
1
1
1
0
0
1
0
1
0
1
1
1
0
0
0
0
2
0
0
1
2
1
1
1
2
1
1
0
0
2
1
2
1
1
0
2
2
2
1
1
1
1
0
2
0
0
2
1
2
0
1
0
1
1
1
1
0
2
1
0
1
1
1
0
1
2
1
2
2
0
0
1
1
2
0
1
1
1
1
2
1
1
2
1
0
0
2
0
2
1
2
2
1
0
1
0
1
1
0
2
1
0
0
0
1
0
1
2
1
1
0
1
1
0
1
1
1
0
1
2
3
1
1
0
0
1
1
1
1
1
0
1
1
1
1
1
1
2
2
2
1
1
1
1
2
1
0
2
2
1
0
2
0
0
2
0
1
1
1
1
1
1
1
2
0
0
1
2
1
1
0
1
0
0
2
0
1
1
1
0
0
1
2
1
0
0
0
1
2
0
4
1
1
2
2
1
1
1
2
1
0
0
2
1
1
1
1
1
1
0
0
1
0
1
1
1
2
2
1
2
1
1
1
1
1
1
0
1
1
1
1
1
0
1
2
2
1
1
0
1
0
1
3
1
0
1
0
3
0
2
1
2
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
0
1
0
0
0
1
2
0
1
0
1
0
2
2
2
1
0
2
0
2
1
1
1
1
1
1
2
1
1
0
1
1
1
1
1
1
2
2
1
2
1
2
2
1
1
0
1
1
1
0
1
1
0
2
1
1
1
0
2
0
1
0
0
1
1
2
0
0
0
1
0
1
1
1
0
0
1
1
0
1
1
1
0
0
0
1
0
1
2
1
2
1
1
2
2
0
0
0
1
0
0
2
2
1
2
2
2
1
2
1
1
2
1
1
0
0
1
2
2
2
1
2
1
1
1
1
1
2
1
1
1
2
1
0
2
1
1
1
1
1
1
0
1
2
1
1
1
3
2
1
0
2
1
2
1
1
0
2
1
0
1
2
2
2
1
1
0
0
1
2
1
0
1
0
0
1
2
1
1
1
1
1
1
1
1
1
1
0
2
1
1
2
1
1
1
1
1
2
0
1
2
1
2
0
1
1
1
1
1
1
2
1
2
2
0
2
0
0
1
0
0
2
1
2
1
1
1
2
0
1
0
1
0
0
0
0
1
1
2
0
0
1
2
0
1
1
2
1
1
1
1
1
0
1
0
1
1
1
2
1
2
1
1
4
2
3
1
1
1
2
0
1
1
0
2
3
0
1
2
2
1
1
2
2
0
1
1
0
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
0
1
2
1
1
1
1
1
0
1
1
3
1
2
1
0
0
0
2
1
3
1
1
1
0
0
0
1
1
1
1
0
1
1
2
0
0
0
1
0
1
0
1
0
2
3
1
2
1
2
2
1
2
2
1
3
1
1
2
2
1
1
1
1
1
0
1
1
1
2
1
1
1
1
1
1
1
0
0
2
0
0
2
1
1
1
1
1
1
1
0
1
2
1
0
1
0
0
1
1
0
0
2
1
1
1
1
1
1
2
1
0
0
1
2
1
0
1
1
0
1
2
1
1
1
0
1
1
2
1
1
1
1
1
0
1
1
0
0
2
1
0
0
0
2
2
0
1
1
0
1
0
1
1
1
0
1
2
1
0
0
0
1
1
0
1
1
0
1
2
0
1
1
1
1
0
1
1
2
0
1
1
2
1
1
2
1
0
0
1
2
0
1
1
2
1
0
2
1
0
0
1
0
1
1
1
1
1
2
1
2
1
1
1
0
0
2
1
1
2
0
1
2
2
1
0
1
3
0
1
2
1
1
1
1
0
1
1
2
0
0
1
2
1
2
0
0
1
0
2
1
1
1
0
1
2
0
2
1
1
2
0
2
1
0
0
1
2
1
2
1
0
0
0
1
1
0
1
2
2
2
0
2
2
1
1
1
2
1
1
0
1
1
1
1
0
0
0
2
1
0
0
1
2
2
1
3
0
1
1
1
1
2
1
2
0
1
1
1
0
2
1
1
2
0
0
1
1
2
2
2
2
1
0
2
1
1
1
0
0
0
1
1
1
1
1
1
0
1
1
2
1
1
0
2
1
1
1
0
0
2
1
1
1
1
1
0
1
2
1
1
2
0
1
0
1
0
2
1
0
1
1
1
2
1
1
1
3
1
2
1
4
3
1
0
0
0
0
1
2
2
1
0
1
2
1
1
2
2
0
1
1
0
1
0
1
0
1
1
0
1
2
2
2
1
2
0
0
1
0
1
3
1
5
2
1
1
1
0
0
0
0
1
2
0
0
1
1
0
1
2
1
1
2
0
1
1
0
1
1
0
0
1
1
1
1
2
1
1
0
0
0
1
0
0
1
2
2
1
1
2
1
1
2
1
1
0
2
0
0
0
1
1
1
1
0
2
1
1
0
3
0
1
1
3
1
2
1
1
1
2
1
1
1
0
1
0
0
1
1
0
1
1
0
0
2
2
1
0
1
0
1
1
1
0
1
1
1
1
2
1
1
5
1
0
0
2
2
2
0
0
0
1
2
2
1
0
1
1
1
1
1
0
2
1
1
1
0
2
1
1
1
0
2
1
1
2
1
2
1
0
1
0
2
2
1
2
0
1
1
2
1
0
1
3
1
16
0
1
0
2
2
1
2
1
1
0
0
1
1
0
0
1
2
1
1
0
1
0
0
2
0
0
0
0
1
1
0
2
0
0
2
1
1
0
0
2
0
1
1
2
1
2
1
1
2
0
1
0
2
2
1
0
1
0
1
1
1
1
1
0
0
1
2
2
1
1
1
1
2
1
1
0
1
2
2
0
1
1
1
1
1
1
1
0
2
1
1
1
1
1
1
1
1
0
1
2
1
0
0
0
1
0
1
0
1
0
0
1
1
2
0
2
1
1
1
0
0
2
2
1
1
1
1
1
0
0
0
1
1
1
1
1
2
0
2
1
1
1
1
1
0
1
2
3
0
0
1
1
1
1
0
1
0
1
2
0
1
1
1
1
1
0
2
1
1
1
1
1
1
0
0
2
1
1
2
0
1
1
1
2
2
1
1
1
0
1
2
1
1
2
1
1
2
1
1
0
1
0
0
1
1
1
1
2
1
1
0
2
0
2
1
2
1
2
0
0
1
1
2
1
1
0
0
1
1
1
0
1
2
0
1
1
0
2
2
2
1
1
2
0
2
0
2
3
1
1
1
1
1
2
1
0
1
1
1
1
0
0
0
1
0
2
1
1
1
1
2
0
2
0
1
1
0
2
0
1
0
1
0
2
2
2
2
0
1
2
0
2
1
1
2
1
2
1
2
2
2
0
1
2
2
1
2
1
0
1
2
1
1
1
0
1
1
1
2
1
1
1
1
1
2
1
1
1
1
2
2
2
2
1
2
1
1
1
1
1
0
0
1
0
0
0
0
2
1
1
2
0
1
1
1
2
1
2
2
3
1
2
1
0
2
1
2
0
0
2
1
0
1
2
1
0
1
1
1
1
0
0
1
1
2
1
1
0
1
0
1
1
0
2
1
0
1
1
1
2
1
0
1
0
1
2
0
1
0
1
0
0
2
1
1
1
0
0
2
2
1
0
1
1
2
2
1
1
1
1
0
1
0
1
1
1
1
0
1
2
1
0
1
1
1
1
2
2
0
1
1
1
1
1
1
3
1
0
2
1
1
0
0
2
1
1
1
2
1
1
0
1
1
0
1
1
0
1
1
1
1
1
0
2
2
1
2
2
0
1
1
1
2
0
1
1
1
1
1
1
1
0
0
2
1
1
1
1
1
1
1
2
1
2
0
1
1
2
1
1
1
1
0
1
1
1
0
0
1
0
2
1
0
2
0
0
3
1
0
1
1
3
0
0
1
1
0
1
1
0
1
2
1
0
0
1
1
0
1
2
1
1
1
0
2
2
1
1
1
2
0
1
1
1
0
0
0
2
0
1
1
2
0
0
2
1
0
0
1
1
0
1
0
1
2
0
0
1
1
1
1
0
0
1
0
1
2
1
1
0
1
0
2
2
0
0
1
0
1
2
0
0
0
7
1
1
2
1
2
1
2
1
2
1
1
0
2
1
1
1
1
0
1
0
1
0
1
1
1
0
2
1
0
1
1
1
2
2
1
2
0
1
2
1
1
2
3
1
0
0
1
3
0
1
1
1
1
1
1
0
0
1
1
2
1
0
0
2
0
1
1
1
2
0
2
0
1
2
2
1
2
1
0
0
1
2
0
0
1
1
2
1
1
2
1
1
0
1
0
1
2
2
1
0
0
1
0
0
3
2
0
1
1
0
0
1
1
3
1
1
2
0
2
0
2
1
1
2
3
2
1
2
0
0
0
1
2
2
2
0
0
1
0
2
1
1
0
1
1
2
0
0
0
1
1
2
1
1
2
1
2
1
1
0
1
0
1
1
0
0
2
0
2
1
0
0
1
1
2
1
1
1
1
1
4
0
1
1
1
0
0
1
1
2
1
1
0
2
0
2
1
2
1
1
2
1
2
2
2
2
0
1
2
2
2
1
1
2
2
1
1
1
1
2
0
0
1
1
2
1
0
1
0
1
1
2
1
2
1
0
2
0
1
1
2
0
1
1
1
1
0
1
0
2
2
1
2
0
1
1
0
1
1
1
0
1
2
1
1
1
1
2
1
0
0
1
0
1
1
2
2
1
1
1
0
0
2
1
1
0
1
0
1
1
3
1
1
1
1
1
1
0
2
1
0
0
0
1
0
1
2
1
1
0
2
1
1
0
2
0
0
2
1
2
4
1
0
0
1
1
0
1
0
2
2
1
1
1
1
1
1
0
2
1
1
0
1
2
2
2
3
1
1
2
0
2
2
3
2
1
0
2
0
2
2
2
0
0
1
1
1
1
1
1
1
1
0
1
1
1
0
0
1
1
1
2
0
1
0
2
1
0
1
0
1
1
1
1
1
0
2
0
0
2
1
1
1
2
0
1
0
0
2
2
1
1
0
1
0
1
2
1
2
1
0
1
2
1
0
0
0
2
1
1
0
0
0
1
1
0
0
0
1
1
2
1
1
1
1
1
2
1
2
2
0
1
2
1
2
0
2
1
0
1
1
1
0
1
0
0
1
1
2
0
0
2
1
0
2
1
1
1
0
1
1
1
0
1
1
1
1
1
0
1
2
1
1
0
0
2
1
1
1
0
0
0
1
1
1
1
1
2
2
1
0
1
1
1
1
1
2
1
2
0
2
1
1
1
0
1
1
0
1
1
0
2
1
0
1
0
1
2
1
1
0
2
2
2
0
2
0
1
0
2
0
0
2
0
1
0
2
2
0
0
1
1
2
1
1
2
2
2
1
1
2
1
1
1
0
1
2
1
1
1
1
1
0
1
1
1
2
2
1
1
0
1
1
1
0
1
1
2
2
0
2
1
0
1
1
1
0
1
2
1
1
1
2
1
1
1
0
1
2
1
0
0
0
0
2
1
1
1
1
1
2
2
2
1
1
1
2
0
0
2
0
1
1
0
1
1
1
2
0
1
1
2
0
1
2
0
1
1
0
0
1
1
2
1
1
1
2
0
1
1
0
0
1
0
1
1
2
0
1
2
1
0
1
0
2
1
0
2
1
1
1
0
0
1
3
2
2
0
1
1
1
1
1
1
0
2
0
2
1
2
1
2
1
0
2
1
1
2
2
0
1
1
0
1
0
1
1
0
0
2
1
0
0
1
1
1
1
0
1
2
2
2
0
4
1
1
1
1
1
1
1
0
1
1
1
1
1
2
1
0
1
0
1
1
0
1
2
1
1
0
2
1
1
0
1
4
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
2
2
0
0
1
1
1
1
1
2
1
0
0
1
1
1
2
1
0
1
2
1
0
0
1
0
0
0
0
1
1
2
0
0
2
1
1
1
1
2
0
0
0
1
1
0
1
2
2
1
1
2
1
2
2
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
0
1
1
1
1
1
0
1
2
2
0
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
0
1
1
2
2
2
1
2
2
1
1
3
0
1
2
1
2
1
0
2
1
2
0
2
1
0
1
1
2
1
0
0
0
0
0
0
1
2
1
2
1
1
2
1
0
2
0
0
0
1
2
2
1
1
1
2
0
0
0
1
2
0
0
2
1
1
1
1
2
1
0
2
0
1
1
1
0
1
0
0
1
2
0
1
1
1
2
1
1
2
1
0
1
1
0
2
3
0
1
1
1
0
1
1
1
0
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
0
0
0
1
2
0
1
1
1
1
2
0
2
0
0
1
0
0
1
0
1
1
1
1
1
0
1
1
0
1
0
3
2
2
0
2
1
1
0
1
1
2
2
1
1
0
1
1
1
2
1
0
2
1
0
1
0
0
2
1
2
1
1
0
1
1
2
1
1
1
1
2
2
2
0
1
2
1
0
1
0
0
0
2
0
1
0
1
1
2
0
2
1
1
1
2
1
0
0
1
2
1
2
0
0
1
1
1
2
1
1
1
2
2
1
0
2
1
1
1
0
1
0
1
1
1
0
1
1
0
1
1
2
1
1
2
2
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
0
1
2
3
1
1
0
1
2
1
1
1
1
1
0
1
2
0
0
0
0
2
0
2
1
0
1
1
1
1
1
2
2
1
2
0
0
1
0
0
1
0
1
1
0
1
0
1
0
1
1
1
1
0
2
1
1
2
2
0
1
1
1
0
0
1
1
1
1
2
1
1
1
1
2
1
2
2
2
2
2
2
1
2
1
0
0
1
1
2
1
1
2
2
1
0
2
0
1
1
1
1
0
1
0
2
0
1
1
1
1
1
1
2
1
1
1
1
2
2
1
1
0
1
1
1
1
0
1
0
1
1
1
2
1
0
1
1
1
1
5
2
0
2
0
1
2
1
0
1
0
1
0
1
0
0
1
0
1
2
1
1
2
1
1
1
1
1
2
2
1
0
0
1
2
1
1
1
2
1
1
1
2
2
1
1
0
1
1
1
1
0
1
1
1
0
3
1
1
1
1
1
0
1
1
1
1
1
0
2
1
1
0
1
0
1
2
1
2
1
2
1
1
1
0
1
2
1
1
0
1
0
0
0
1
2
1
2
1
2
1
1
1
1
1
1
2
0
1
1
1
1
1
1
1
1
1
0
2
0
0
0
0
2
2
0
2
0
1
1
1
0
1
1
1
1
2
1
2
0
0
0
1
1
1
2
1
2
2
1
1
0
1
2
1
1
1
2
1
1
1
1
1
1
2
1
3
1
1
0
0
1
0
1
0
2
1
0
1
1
2
0
1
2
1
1
2
0
1
2
1
2
2
0
1
0
2
0
0
0
1
2
1
1
1
1
4
2
2
2
1
1
0
1
1
2
2
1
3
2
1
1
2
1
1
1
2
1
0
0
2
1
1
1
1
1
2
1
2
2
2
1
1
1
0
0
1
2
0
1
1
1
2
2
0
2
1
1
2
0
0
1
1
0
1
0
1
1
1
1
0
0
0
4
1
2
0
1
1
2
0
0
1
2
1
1
0
1
2
0
0
1
1
0
1
1
0
0
2
1
1
1
1
1
1
2
2
2
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
0
2
1
1
1
2
1
1
1
0
2
2
2
1
1
1
2
1
0
1
1
1
0
1
1
0
1
2
1
1
1
2
1
0
0
0
2
0
1
3
1
1
1
1
1
1
0
0
1
0
1
0
0
1
1
1
1
0
0
2
1
0
1
1
0
2
0
3
1
1
1
1
2
2
0
0
1
0
1
1
1
1
0
0
2
2
1
1
0
1
0
0
0
1
0
1
0
1
2
2
1
0
0
0
1
0
2
2
1
1
1
2
1
0
0
2
1
0
1
0
2
2
0
2
2
2
0
0
2
1
0
2
2
0
1
1
1
1
1
0
1
1
1
1
1
2
1
1
2
1
1
0
2
0
2
1
1
2
2
1
1
2
2
1
2
0
0
1
2
0
0
1
2
1
2
2
2
2
1
1
0
0
0
2
1
2
1
1
1
1
0
0
1
0
1
1
0
0
1
1
1
2
0
1
0
1
1
0
1
0
1
2
1
3
2
2
2
1
2
0
1
1
0
2
1
1
1
0
0
1
2
1
1
0
0
1
1
2
0
1
1
2
1
1
1
2
1
1
1
0
1
1
2
2
1
0
1
0
0
1
0
1
1
1
1
0
1
0
3
1
0
1
1
1
1
0
1
0
2
0
1
1
1
0
2
1
0
1
2
0
1
1
1
0
2
1
0
0
1
1
1
1
0
0
0
2
0
2
1
0
3
2
1
1
3
2
1
0
2
1
0
1
1
2
1
1
1
0
0
1
2
0
0
0
0
1
1
2
2
0
1
1
1
2
1
2
0
1
1
1
1
0
3
1
2
2
1
1
1
2
1
1
0
1
1
1
2
0
1
1
1
0
1
0
0
1
1
1
1
1
2
2
1
1
0
1
1
1
0
0
2
1
1
1
1
1
1
1
1
0
1
0
0
0
1
0
2
1
0
2
0
1
0
2
1
1
1
2
0
1
2
2
0
1
1
0
0
1
1
1
1
1
2
0
2
0
1
0
2
2
0
2
2
1
1
0
1
1
0
1
1
2
0
1
0
1
1
1
2
1
1
0
0
1
0
2
1
1
0
0
2
1
1
1
1
1
1
1
1
0
1
0
2
1
1
2
2
1
0
1
0
1
1
0
1
0
1
1
3
0
2
1
2
1
1
1
1
2
1
1
0
0
1
1
1
1
2
1
0
0
0
1
1
1
1
0
1
2
0
2
2
1
1
1
1
1
0
2
0
0
0
2
1
0
1
1
1
0
1
1
1
4
0
2
1
1
2
1
1
2
0
2
1
2
0
1
1
0
1
2
0
2
1
2
2
0
0
1
1
1
1
2
1
0
2
1
1
0
1
0
1
1
1
1
2
0
1
0
1
2
1
1
1
1
2
0
1
1
2
1
0
1
1
0
1
0
1
0
0
0
0
2
0
1
0
2
0
0
2
0
1
2
1
1
1
0
2
0
0
0
0
1
2
0
1
0
1
1
1
0
2
1
2
0
1
0
0
1
0
1
1
1
0
1
0
0
1
1
2
0
0
1
2
1
1
0
0
0
1
1
3
1
1
1
1
2
1
0
1
1
2
1
2
2
1
2
1
1
2
2
1
0
0
2
1
1
0
1
1
1
2
3
0
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
0
2
0
1
2
2
1
0
1
0
0
1
1
0
0
1
1
3
0
1
2
2
0
1
1
2
1
2
2
1
2
1
0
1
0
1
1
1
2
1
1
0
1
0
1
0
1
0
0
2
1
2
0
3
2
0
1
1
1
1
1
0
1
2
1
2
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
1
2
1
0
0
0
2
1
1
0
0
0
0
2
2
0
2
1
1
2
1
1
1
2
2
1
1
2
1
2
0
2
0
1
1
1
1
1
1
1
0
1
0
1
1
2
0
0
1
1
1
1
2
1
2
1
1
1
1
1
2
0
1
0
1
1
2
0
1
0
0
1
0
1
1
0
2
2
1
1
1
0
2
1
2
2
0
1
1
1
1
1
2
1
1
0
2
1
1
2
1
0
2
0
0
1
2
2
1
1
1
0
0
2
1
1
0
1
0
1
1
1
0
4
1
1
1
1
1
1
1
1
0
0
2
1
2
1
1
0
1
0
2
0
1
1
1
1
1
0
2
1
1
1
0
1
1
1
1
0
0
1
1
0
1
1
1
1
0
0
1
1
1
1
2
1
1
2
2
2
0
0
1
1
0
2
0
1
1
1
1
1
1
1
1
0
1
0
1
1
0
1
0
2
1
2
3
2
0
2
1
1
1
0
0
2
1
1
1
1
0
1
2
0
0
1
2
1
1
1
1
1
1
1
1
2
2
1
1
2
1
0
0
1
0
0
0
2
1
1
1
2
2
1
1
1
0
0
2
2
2
2
1
2
1
0
1
0
1
0
2
2
1
4
0
1
2
1
2
1
1
1
1
1
1
0
1
1
1
0
1
1
1
0
0
1
1
2
1
2
2
0
1
0
0
1
1
0
0
1
0
2
0
2
0
0
1
1
1
2
1
1
1
2
1
2
1
1
1
0
1
0
2
1
0
1
1
1
1
0
0
2
1
1
0
1
1
1
1
0
1
0
0
1
2
1
1
1
1
2
1
0
2
0
0
1
2
1
0
0
0
1
1
1
0
1
1
2
2
1
0
1
2
2
1
2
2
1
1
1
2
0
1
0
0
3
2
0
0
0
1
1
0
0
0
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
2
1
2
1
1
1
0
1
0
1
1
1
2
2
1
2
2
2
1
1
1
2
2
1
0
0
0
0
0
1
1
1
1
2
1
1
1
1
1
2
1
1
1
0
1
1
1
1
1
1
2
2
1
1
2
1
1
1
0
1
2
1
1
1
1
1
1
2
1
1
2
2
0
1
1
3
1
1
1
0
0
1
1
0
0
2
2
1
1
1
1
1
0
1
1
1
0
1
1
1
1
1
1
3
0
0
0
1
1
1
1
0
1
2
1
0
1
1
2
1
1
1
1
1
0
2
1
0
2
1
0
2
2
2
1
1
0
1
1
1
2
1
0
1
1
2
1
2
1
2
1
1
1
0
1
1
1
1
0
2
0
1
1
1
1
1
2
1
1
2
1
0
2
2
1
1
2
2
0
0
1
1
2
1
0
2
2
1
1
2
1
0
1
1
1
0
2
2
0
0
1
2
0
1
1
1
2
1
1
1
0
2
2
1
0
1
2
1
2
1
1
2
1
1
1
1
1
0
1
2
1
0
2
2
2
2
0
0
1
1
2
1
3
1
3
0
1
1
0
1
1
2
1
1
0
1
1
1
1
2
1
0
0
0
1
1
1
2
1
2
1
1
2
1
1
0
1
1
2
1
1
2
1
2
1
1
2
2
1
1
0
1
0
1
2
1
1
1
1
1
1
1
0
2
0
1
2
2
1
1
0
1
0
2
1
1
2
1
1
1
2
1
1
0
2
2
1
1
1
2
0
0
1
1
1
1
2
0
2
1
0
2
1
2
1
0
5
0
1
0
1
1
0
1
1
1
2
0
0
0
1
2
4
1
1
0
0
1
0
0
1
1
1
2
1
1
1
2
1
1
2
2
1
1
1
1
1
1
1
0
1
0
0
0
1
1
2
1
2
2
1
1
2
2
1
1
2
2
1
1
1
0
1
1
0
1
2
1
1
1
1
1
1
0
2
1
1
2
2
1
1
2
2
1
1
0
1
1
1
1
2
1
0
0
1
0
2
1
0
2
0
1
2
1
0
1
2
0
0
0
0
1
0
1
0
0
2
2
1
1
1
1
0
2
2
1
1
0
0
1
0
1
1
2
0
0
1
0
2
1
1
1
1
1
1
0
0
0
1
1
1
0
2
0
1
1
2
0
0
1
1
0
0
1
2
1
3
1
1
1
1
1
1
0
0
0
1
1
1
1
1
0
1
1
2
0
2
1
0
1
0
2
1
2
1
0
0
1
1
1
0
1
2
0
0
1
1
1
1
1
2
2
1
1
1
1
1
2
2
0
0
1
2
2
0
1
1
0
0
1
1
1
1
2
1
1
1
1
0
0
1
1
0
0
1
1
2
1
1
0
2
0
0
1
1
2
2
1
2
1
3
1
1
1
1
0
1
6
1
1
1
1
1
2
0
1
1
1
1
1
1
0
1
1
1
1
1
1
0
0
0
0
1
1
0
2
2
2
1
1
1
0
1
1
0
1
1
1
1
1
2
1
0
1
1
2
1
1
1
1
1
0
1
3
1
1
1
1
2
1
1
1
0
1
1
1
1
1
2
1
0
1
1
1
1
1
1
1
0
0
1
1
1
1
1
0
1
2
2
1
1
0
1
1
1
2
2
2
2
0
1
0
2
2
0
0
2
1
2
0
2
1
0
0
0
1
1
3
2
1
0
1
1
1
1
1
1
0
2
2
1
2
1
1
1
1
1
1
1
2
0
1
2
0
1
1
0
1
0
0
2
1
1
2
0
0
0
0
2
1
2
1
2
0
1
2
0
1
1
1
0
6
1
0
1
1
1
2
2
1
1
2
0
1
1
0
1
0
0
0
1
2
1
0
2
1
1
0
1
1
1
0
1
2
1
1
1
1
3
2
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
0
2
1
2
1
2
2
1
2
0
1
2
2
1
0
0
1
1
2
1
2
1
1
1
2
2
0
0
0
0
2
1
3
2
2
2
1
2
1
1
2
0
1
2
1
1
0
1
0
1
1
1
2
2
2
1
1
1
1
0
1
2
1
1
0
1
0
1
0
1
1
0
0
1
2
1
2
1
1
0
1
0
1
1
1
1
1
1
2
1
1
1
1
1
0
1
1
0
1
1
1
0
2
1
2
1
1
1
0
1
1
0
0
1
1
1
0
2
2
0
1
3
2
2
1
1
2
1
2
1
1
0
1
1
1
1
0
1
1
1
1
1
2
1
1
1
1
1
1
0
0
1
0
0
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
0
2
1
1
1
2
2
1
1
2
1
0
1
0
1
1
2
0
0
1
0
2
1
2
1
1
1
0
2
1
0
2
0
0
1
1
2
2
1
1
2
1
1
2
0
1
1
1
1
1
1
1
2
0
2
2
2
0
1
2
1
0
0
1
1
0
1
2
1
1
1
2
0
1
1
2
0
0
0
2
1
2
1
1
2
1
2
1
1
0
2
1
1
0
0
0
1
1
0
1
0
2
1
0
1
0
1
2
0
2
1
0
1
1
1
2
1
1
1
2
1
1
1
1
1
2
1
0
1
1
1
2
2
1
0
0
1
0
1
1
1
4
0
2
1
1
2
1
0
1
1
2
1
1
0
2
1
2
1
1
1
1
0
1
1
3
1
1
0
1
1
1
1
2
1
1
2
2
1
0
1
1
2
2
0
1
2
2
0
0
1
2
1
0
0
2
1
1
2
1
0
1
2
0
1
1
1
1
2
2
1
0
1
0
1
1
1
1
1
2
2
0
1
2
2
1
1
0
1
2
1
1
0
0
0
2
0
1
0
1
1
1
0
1
1
1
0
0
0
0
2
1
2
1
0
1
0
2
1
2
2
2
1
1
1
1
1
2
1
1
2
0
1
1
2
0
0
0
1
1
1
0
1
1
2
1
2
1
2
1
1
1
2
1
1
2
1
1
0
2
1
2
1
0
1
1
0
1
3
2
3
1
2
1
1
0
1
0
1
1
1
0
0
0
1
1
1
1
0
2
2
2
0
1
2
0
0
2
1
1
1
1
2
1
2
2
1
1
0
1
0
1
1
0
1
0
1
3
1
1
2
1
1
0
1
2
1
1
1
0
0
1
0
1
0
1
1
1
1
1
1
1
1
1
0
1
2
0
0
1
1
0
1
0
1
2
1
2
2
0
1
0
0
0
5
0
1
1
0
1
1
1
0
2
1
1
2
1
0
1
2
1
2
2
1
1
0
1
1
1
0
1
1
2
1
0
1
0
1
2
0
0
1
3
2
1
1
0
1
2
1
1
2
1
1
0
1
0
0
1
0
1
0
2
1
0
1
2
1
0
0
1
1
1
0
0
1
2
1
1
0
0
1
0
1
2
1
1
1
0
1
1
1
2
1
0
2
0
2
1
1
1
0
0
2
0
2
1
2
1
2
0
1
2
1
1
0
0
0
1
1
1
0
2
0
2
2
2
1
1
1
2
1
1
2
1
0
2
2
0
1
1
1
1
1
2
1
1
2
1
1
1
0
1
0
0
1
2
1
1
2
0
2
2
2
0
1
1
2
2
1
0
1
2
2
0
1
0
1
0
1
1
2
1
1
2
1
1
2
2
0
2
1
2
0
2
1
1
0
1
2
0
1
1
0
1
1
1
1
0
2
0
0
2
0
1
1
0
2
1
2
1
1
1
1
0
2
1
1
2
0
0
0
1
0
3
1
2
2
1
2
0
2
1
1
0
0
1
0
1
2
0
2
0
0
0
1
1
0
2
2
0
0
1
1
0
2
1
1
1
1
2
1
1
1
2
3
1
1
1
0
1
2
0
1
2
1
1
1
2
1
1
1
2
1
1
1
1
1
2
2
1
1
1
1
2
1
1
0
2
1
2
1
0
1
2
1
0
1
2
1
2
2
1
0
2
2
0
1
1
1
1
2
1
0
0
2
0
2
2
1
1
0
0
1
1
1
1
2
2
1
1
1
1
1
0
1
1
2
1
1
1
2
1
1
1
1
0
1
0
1
2
1
4
0
1
2
1
0
1
1
0
1
2
2
1
1
1
0
1
1
0
1
2
0
3
0
4
1
0
1
1
0
1
1
1
0
1
0
0
0
1
1
1
1
1
0
5
2
2
1
0
0
1
1
0
1
1
2
0
2
0
0
2
1
1
2
1
1
2
1
0
1
1
0
2
0
0
1
1
2
1
1
1
1
2
1
0
0
1
0
1
1
0
1
1
0
0
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
0
1
1
0
1
1
1
1
0
2
2
0
0
1
2
1
1
1
0
1
2
2
0
2
1
2
1
0
2
2
2
0
1
1
1
2
2
0
1
1
0
0
1
2
1
2
2
1
1
1
1
1
1
1
1
2
1
1
0
1
1
0
1
2
1
1
0
1
0
2
1
2
2
1
0
0
1
2
0
1
2
1
2
1
2
2
1
0
0
0
1
1
0
1
0
0
2
0
2
2
1
1
1
2
2
1
4
1
1
1
0
2
1
0
1
2
1
1
0
1
2
0
0
1
0
0
0
2
2
1
1
1
0
0
2
1
0
1
1
0
2
2
0
1
1
3
1
1
0
2
1
0
1
1
1
1
1
0
1
0
0
1
0
1
1
2
0
0
1
1
0
1
2
1
0
0
1
1
1
1
2
0
1
1
2
1
1
1
1
2
1
2
1
0
2
2
1
1
0
1
1
1
1
1
1
3
2
1
0
0
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
0
1
1
2
2
0
0
1
0
1
1
1
1
1
1
1
1
0
0
1
0
1
1
0
2
1
2
2
1
2
0
2
1
2
1
1
0
0
2
1
1
1
2
1
0
1
1
2
1
3
1
1
2
0
1
0
2
1
1
1
0
1
1
1
1
1
2
0
2
1
1
1
1
2
1
1
2
0
2
1
0
0
1
2
1
1
2
1
1
1
2
1
2
2
2
1
0
2
1
1
0
1
1
1
1
1
0
1
0
2
1
0
0
1
1
1
2
0
0
0
1
2
1
1
1
0
0
1
1
1
1
1
0
3
1
2
1
1
1
0
1
2
2
1
1
0
0
1
1
1
1
0
1
2
0
2
0
1
2
0
1
1
2
1
1
1
1
2
0
0
1
1
1
2
1
1
0
1
1
2
1
1
0
0
1
1
1
2
1
1
1
1
1
0
2
0
2
1
1
1
0
0
1
1
1
1
0
1
1
1
1
1
0
1
1
1
1
1
1
2
1
1
1
0
2
0
1
1
1
1
1
1
1
1
1
2
1
0
1
1
1
0
1
0
1
0
1
1
2
0
1
1
2
1
1
1
1
2
0
2
1
0
1
1
2
1
1
1
0
1
2
2
1
1
1
1
1
1
0
1
1
1
1
1
0
2
2
0
1
0
0
2
1
1
1
1
1
3
1
0
1
1
2
0
0
0
1
1
1
0
1
0
1
1
2
0
1
2
1
1
1
3
1
1
0
0
1
2
0
1
1
2
2
1
1
2
2
0
0
1
1
2
1
1
1
0
1
2
1
1
0
1
1
0
2
0
1
2
0
0
1
1
1
0
1
1
0
1
1
2
2
2
1
0
1
0
1
1
0
1
1
1
1
0
2
1
2
1
1
0
1
0
1
1
1
0
2
2
1
2
1
1
0
1
1
1
0
2
0
2
0
2
1
1
1
2
0
2
1
0
1
4
1
0
1
0
1
2
0
1
2
1
1
1
2
1
1
0
1
1
1
0
0
1
0
2
1
0
0
2
1
2
1
2
1
1
1
0
0
1
1
1
2
1
1
1
0
2
0
1
1
0
2
2
2
0
0
1
1
1
0
1
0
0
2
2
0
0
1
2
1
1
1
0
1
2
1
1
0
2
1
2
1
1
1
1
1
1
1
2
2
1
2
0
1
0
0
1
0
1
3
1
2
1
2
2
1
2
2
2
2
0
1
1
1
1
1
1
0
0
2
1
1
0
0
1
1
0
1
1
1
1
1
1
1
1
1
1
1
2
0
2
0
1
1
1
0
0
1
1
1
2
0
0
1
1
1
1
0
1
0
1
1
1
2
1
0
1
1
2
2
3
2
0
0
2
1
2
1
2
0
2
1
1
1
1
1
0
0
2
0
1
2
2
2
0
1
0
0
1
0
1
1
2
0
0
2
1
0
2
2
1
1
1
0
0
2
1
2
0
2
2
3
3
1
0
1
2
2
0
0
1
1
0
2
0
0
0
1
2
0
1
2
1
2
0
1
2
1
4
0
1
1
1
0
1
0
1
1
0
1
1
2
1
1
0
1
1
1
0
1
3
1
2
2
1
1
1
2
2
2
2
0
0
0
2
1
1
1
0
1
2
1
0
0
0
1
1
1
1
1
0
1
0
2
0
1
1
1
1
1
2
1
1
2
0
1
2
0
2
2
1
1
1
0
0
1
0
2
1
2
1
1
1
2
1
2
1
2
1
0
1
1
2
1
0
0
1
1
0
0
0
2
2
1
1
1
0
1
0
1
2
1
1
1
0
1
0
1
2
1
1
1
1
0
1
1
0
3
1
1
1
1
1
1
2
1
1
0
2
2
2
0
2
2
1
0
0
2
1
1
0
0
2
1
1
2
1
1
2
0
1
2
1
1
1
0
1
1
0
0
0
0
1
1
1
0
2
1
2
1
1
0
0
1
2
1
1
0
2
1
1
1
2
1
2
1
1
1
0
1
1
1
2
1
1
1
1
1
1
1
2
2
1
0
1
0
1
2
2
0
1
0
0
0
2
2
0
1
1
0
1
1
1
1
2
1
1
0
1
1
0
1
1
1
1
0
1
2
1
1
0
1
0
1
0
1
1
1
0
1
1
0
1
2
0
1
1
0
0
0
2
1
0
0
1
2
0
0
0
4
2
2
2
2
1
1
1
1
2
0
1
1
1
1
0
1
2
1
1
1
2
1
1
2
2
1
1
1
1
2
1
2
2
1
2
0
1
0
1
2
1
0
1
1
0
0
0
1
1
0
1
0
2
2
1
2
1
1
1
1
0
1
1
1
1
0
1
1
0
0
0
1
0
1
1
2
2
1
1
1
0
2
2
2
1
1
2
2
0
1
0
1
2
4
0
0
1
2
0
1
0
1
0
0
0
2
1
0
0
1
1
1
1
2
1
2
1
2
1
1
1
1
1
1
1
0
1
1
2
2
1
1
1
2
0
1
1
1
2
1
1
1
1
1
0
5
2
1
2
1
2
2
2
0
1
1
0
2
2
1
1
0
1
1
0
2
1
0
1
2
1
1
0
1
1
1
2
0
1
1
1
2
2
0
2
2
0
0
1
2
1
1
2
0
0
1
1
0
1
2
3
3
0
0
1
2
0
2
1
1
2
1
1
0
1
2
1
1
1
2
2
1
1
1
1
2
1
1
1
0
0
1
1
0
0
0
1
0
1
1
2
2
1
0
0
0
2
1
1
0
0
2
1
1
1
1
2
1
1
0
0
1
2
1
1
1
0
0
1
0
2
1
0
0
0
1
0
0
2
0
1
1
2
0
0
2
2
2
1
0
1
1
1
1
0
2
1
2
1
1
1
2
1
0
0
1
1
1
1
1
0
1
1
0
0
1
1
1
1
1
0
0
1
0
1
2
1
1
1
2
1
0
2
0
1
1
1
0
0
1
1
1
1
1
2
1
1
1
0
2
0
0
1
2
2
1
2
1
1
1
2
0
0
1
1
1
0
2
0
0
1
0
1
1
1
2
0
0
2
1
2
0
1
1
2
2
0
2
0
1
1
1
0
1
1
1
1
1
1
1
1
1
1
0
1
1
2
1
2
2
0
1
1
1
2
1
1
1
1
1
1
0
1
1
2
1
1
0
1
1
1
1
1
1
0
1
2
1
2
2
1
1
1
1
1
0
1
1
0
2
2
1
2
1
0
1
2
0
1
2
2
2
2
1
0
1
1
1
1
1
1
2
1
1
2
0
0
2
1
0
1
1
2
1
1
2
2
1
0
0
2
1
1
0
3
1
1
1
1
2
2
0
0
1
0
1
1
0
0
0
1
1
1
0
2
1
1
0
1
0
2
1
1
1
1
1
0
0
1
1
1
1
1
2
1
1
2
1
1
2
2
1
1
1
0
0
2
2
0
2
2
3
2
0
2
2
1
2
0
1
1
1
1
0
1
1
0
3
1
1
2
1
1
1
0
0
2
1
1
1
1
2
0
1
1
1
2
0
0
1
0
0
1
1
2
2
1
1
1
0
1
0
0
1
0
0
0
2
2
1
1
1
1
1
2
2
2
3
1
0
2
0
0
2
1
0
1
2
1
0
1
1
1
1
0
1
1
2
1
0
1
1
2
1
1
2
1
2
0
2
0
2
0
1
1
1
2
0
1
2
1
0
1
0
1
1
2
1
1
1
1
1
0
1
1
2
0
1
1
2
1
1
2
2
0
1
2
2
1
1
1
1
0
2
0
1
1
1
1
1
1
2
0
1
1
2
1
1
2
1
1
2
0
1
1
0
1
0
1
1
2
2
1
2
1
1
2
0
2
0
1
1
1
1
1
0
1
0
0
0
0
2
1
0
1
2
1
1
0
1
1
1
1
1
1
2
1
2
1
1
1
1
2
2
1
0
2
1
1
1
0
1
1
0
1
0
2
1
2
0
1
1
1
2
1
1
0
0
0
2
1
2
2
1
1
0
1
0
0
1
2
0
2
1
0
1
0
0
2
0
1
2
1
1
0
3
0
1
0
0
2
0
1
0
1
2
1
1
1
1
0
1
1
1
1
1
1
1
2
0
2
1
1
1
2
0
1
0
0
1
0
0
1
2
1
1
1
2
2
0
1
1
0
2
2
0
0
0
2
2
1
2
2
1
1
2
1
2
0
2
2
1
1
1
0
0
1
1
1
2
0
2
2
1
1
0
1
0
1
1
1
0
1
2
1
1
1
2
2
1
2
1
1
1
1
3
0
1
2
1
1
1
2
2
3
1
1
1
0
0
1
1
1
1
0
1
0
1
1
0
0
1
1
1
2
1
2
1
1
1
1
1
2
1
0
0
0
0
1
1
0
1
1
1
0
2
1
0
1
1
2
0
1
1
2
2
1
0
1
1
1
2
0
0
2
1
1
2
0
1
0
1
1
1
0
1
1
0
0
1
1
1
0
2
1
2
1
1
3
2
2
2
1
2
0
1
1
4
1
0
2
2
0
1
1
1
2
1
1
0
1
1
1
1
0
1
2
0
1
1
1
1
0
2
0
2
1
0
1
1
0
1
0
3
1
1
2
2
1
0
2
0
1
1
1
2
0
1
1
0
2
0
2
1
1
1
2
1
1
2
1
1
1
0
1
1
1
1
1
2
0
1
1
1
1
0
1
2
1
0
0
1
2
1
0
1
0
0
2
0
4
1
1
1
1
0
0
1
2
1
0
0
2
1
2
1
2
0
2
1
0
1
2
0
1
1
1
2
0
1
2
2
1
2
1
1
1
4
2
1
0
0
1
1
2
1
1
1
0
1
0
0
2
1
1
0
1
1
2
1
1
1
0
2
2
1
1
1
1
1
0
1
2
0
3
1
1
1
1
1
1
1
0
1
0
1
0
1
1
2
2
2
1
0
2
1
1
2
1
1
0
1
1
1
1
0
1
1
3
0
0
1
1
2
1
1
2
1
0
2
1
0
1
2
2
1
1
0
2
1
0
1
1
1
1
0
1
0
2
1
1
2
1
1
1
1
2
1
2
0
2
1
1
1
2
1
2
1
2
1
2
1
1
0
2
1
2
1
1
2
1
1
2
1
1
2
1
2
1
2
1
1
2
0
1
0
1
0
1
1
2
1
1
1
2
1
2
1
1
1
2
1
1
1
0
1
0
2
0
2
5
1
1
0
1
1
1
1
1
1
1
0
1
2
0
1
0
1
2
0
1
1
0
1
0
1
1
0
0
1
0
1
0
2
1
0
0
2
0
1
2
0
1
4
0
1
1
1
0
0
0
0
1
2
0
1
0
2
1
0
1
1
1
1
1
1
0
1
0
1
0
2
0
0
2
1
1
2
1
0
1
2
1
1
0
1
2
2
0
1
1
1
1
1
1
1
0
0
1
3
0
0
1
1
0
0
1
0
0
2
1
0
1
0
1
1
1
0
2
0
1
1
1
1
1
3
2
1
3
1
1
1
0
0
0
1
2
2
1
1
0
2
1
2
0
1
1
2
1
1
2
1
2
1
0
1
1
1
0
0
2
2
1
0
2
0
1
2
0
1
0
1
1
2
0
2
2
2
0
0
2
1
0
1
1
1
1
1
1
0
1
1
0
3
2
1
0
0
2
2
1
2
2
2
1
2
1
1
0
1
1
0
1
0
0
1
0
1
2
0
1
2
2
1
2
1
1
1
1
1
1
2
2
1
1
1
2
1
1
0
0
1
2
1
2
3
1
1
1
2
1
4
1
2
1
1
0
2
2
0
1
1
0
1
1
2
1
3
2
0
2
1
1
2
0
2
1
1
0
2
0
0
1
1
0
0
1
1
1
2
1
1
1
0
1
2
1
0
1
2
0
0
1
1
2
2
1
1
1
2
2
2
2
0
1
1
2
1
1
1
1
0
1
1
5
0
1
1
1
2
1
1
2
1
0
1
1
0
2
1
2
2
1
0
0
0
0
2
1
1
0
1
1
0
2
0
2
2
2
2
2
1
1
0
1
0
2
0
1
1
1
1
0
1
2
2
1
1
0
1
0
0
1
0
0
1
0
0
2
1
1
1
1
0
0
1
1
2
1
1
1
2
2
1
1
1
1
1
0
0
1
2
0
1
0
0
2
0
0
1
2
1
1
2
1
1
1
1
0
0
1
2
2
1
1
1
0
0
1
1
1
1
1
1
2
1
1
1
1
2
2
1
1
0
1
1
0
1
1
0
1
0
1
0
1
3
0
0
1
1
1
2
2
1
0
0
0
1
0
2
0
1
1
2
1
1
1
1
0
0
0
1
1
1
1
2
1
0
1
0
0
1
1
1
1
2
0
0
2
1
1
1
1
1
1
2
2
1
1
2
2
1
1
1
1
0
3
1
1
0
2
1
0
1
1
0
2
0
2
1
1
2
1
2
1
1
0
1
2
1
1
1
1
1
1
1
1
1
1
2
0
1
1
0
0
1
0
0
2
0
1
1
2
1
1
1
1
0
2
0
0
1
1
1
1
1
0
1
0
2
2
2
2
1
1
1
0
1
1
1
1
1
2
0
2
0
2
1
1
0
1
1
1
1
1
1
1
1
1
1
0
2
2
1
1
1
1
1
1
2
2
2
0
2
1
1
1
2
2
2
1
0
0
1
0
0
1
1
0
0
1
2
1
1
1
5
1
1
1
2
0
1
2
1
1
0
1
0
1
2
2
0
2
2
2
1
1
0
0
2
0
0
2
0
2
0
1
2
0
1
2
0
0
0
0
1
1
1
2
1
0
1
1
1
2
1
0
1
1
1
1
0
1
1
1
1
0
2
1
2
1
2
1
1
2
2
1
0
2
1
0
1
2
1
2
0
0
1
1
1
0
2
1
0
1
2
1
1
0
1
0
1
2
2
1
1
1
2
2
1
1
3
1
0
0
1
0
0
1
2
0
1
1
1
1
1
0
1
0
0
2
0
1
1
0
0
1
1
1
2
2
1
1
1
1
1
2
3
1
0
0
0
0
1
0
1
1
0
1
1
1
1
2
1
1
2
0
2
2
0
1
0
2
2
0
1
1
0
0
2
0
1
1
1
2
1
1
0
0
2
1
0
1
1
1
1
1
1
1
1
1
0
1
1
2
0
1
2
1
0
1
1
1
1
2
1
0
1
1
2
1
1
1
1
0
1
0
1
2
1
1
2
2
1
1
1
1
1
1
2
2
1
2
1
1
2
2
1
1
0
0
2
2
2
1
0
0
1
2
4
1
1
0
1
1
0
0
0
1
0
0
0
0
0
1
1
1
0
1
1
1
1
0
0
0
1
1
3
1
1
1
1
1
2
0
1
2
1
1
0
2
1
1
1
1
1
0
1
1
0
0
1
0
1
0
0
1
1
1
1
1
1
1
1
0
0
1
2
2
0
2
2
1
1
1
0
0
1
1
1
1
2
0
1
0
1
0
2
2
0
2
2
1
0
0
1
0
2
1
1
2
0
0
1
1
2
0
2
2
1
1
2
1
1
0
1
1
2
1
0
2
0
1
1
2
2
1
2
0
2
1
1
0
1
1
1
3
1
2
1
1
1
1
1
0
2
1
0
1
1
0
2
2
2
0
2
1
2
1
2
1
1
1
1
1
1
1
2
1
1
2
2
1
1
0
1
1
2
0
1
2
1
2
1
1
1
2
0
2
0
1
1
0
1
0
2
2
1
2
1
1
2
0
1
2
1
1
2
1
1
1
2
2
1
1
2
1
2
2
0
1
0
1
1
1
0
1
1
1
0
2
1
1
1
1
0
1
1
2
0
1
1
0
1
0
0
2
1
1
1
1
1
0
0
1
2
1
1
1
2
2
1
2
2
1
1
1
1
1
1
2
1
0
0
2
1
1
1
1
0
1
1
1
1
2
1
1
0
1
1
2
2
1
0
0
1
1
2
1
0
0
1
1
1
2
1
0
2
1
1
0
1
0
1
2
2
1
2
2
1
4
1
1
2
0
2
2
0
1
0
0
1
2
1
1
1
1
1
1
0
1
1
0
1
0
2
1
0
1
1
1
1
0
1
2
2
2
1
1
2
0
1
1
1
1
0
1
2
2
1
1
1
1
1
1
0
2
3
0
1
1
1
1
0
0
1
1
1
0
2
2
0
1
0
0
0
0
0
1
1
1
1
2
1
1
2
1
0
1
1
1
1
2
1
0
2
2
0
1
1
1
2
1
1
1
1
2
1
0
1
1
1
0
2
1
1
0
0
1
0
2
2
1
1
0
2
1
1
1
0
0
2
2
2
1
1
2
1
1
1
1
2
2
0
1
0
1
1
3
0
1
0
1
0
1
2
2
0
0
1
1
2
1
1
2
0
0
1
1
1
1
1
1
2
1
2
2
0
0
1
1
0
1
0
2
1
0
0
2
1
0
1
2
0
2
1
0
1
1
1
1
1
1
0
1
2
2
1
1
1
2
1
0
1
0
0
1
2
1
0
2
1
1
1
1
0
1
2
0
1
2
0
1
2
2
0
2
1
2
1
2
1
0
2
2
0
2
0
1
2
0
0
0
1
1
1
1
1
1
2
0
1
1
2
0
2
0
1
1
0
1
1
1
1
1
1
1
1
0
0
0
2
2
0
2
1
1
1
2
0
1
2
1
1
1
1
1
2
2
0
0
2
2
1
1
1
1
1
0
1
0
2
1
0
1
1
1
1
1
1
1
1
1
2
2
2
1
1
0
0
2
1
1
2
0
3
0
0
1
1
2
1
1
2
1
2
1
2
2
1
2
0
2
1
1
0
0
0
0
1
0
3
0
1
1
1
3
2
2
0
1
0
0
1
2
0
1
2
2
1
2
1
1
1
0
0
0
2
1
2
1
1
1
0
0
1
0
1
1
1
2
1
0
0
0
1
2
1
0
0
1
1
0
2
1
1
1
1
1
2
0
1
1
0
1
4
0
1
0
0
2
2
0
1
0
0
1
1
1
1
1
1
1
1
1
0
0
0
0
1
1
0
0
1
1
1
1
1
1
2
2
0
0
1
0
2
2
1
2
1
2
1
1
0
2
2
0
2
0
1
2
1
1
2
1
1
0
1
1
2
2
0
2
1
1
1
0
1
1
2
1
1
0
1
1
1
1
2
1
0
2
1
2
0
1
0
1
0
1
0
2
1
2
0
0
1
0
1
1
0
0
2
0
1
1
0
0
1
0
2
2
1
1
1
1
1
2
1
2
0
1
1
1
2
1
1
1
2
2
1
1
1
1
0
1
0
2
2
1
1
0
0
1
1
1
1
1
1
1
0
1
2
1
2
2
0
1
1
2
0
2
0
1
1
1
1
0
0
1
1
1
0
2
2
0
0
2
1
0
1
0
1
3
0
2
0
1
0
1
1
0
0
1
1
2
0
2
2
2
2
0
1
1
1
1
1
2
0
1
2
1
0
1
0
1
1
0
1
0
1
1
0
2
0
0
1
1
1
1
2
2
1
1
0
1
1
1
1
1
1
1
1
1
1
0
0
0
0
2
0
1
0
1
0
1
2
0
1
1
1
1
2
0
1
2
0
0
0
1
0
1
0
0
0
1
1
1
1
1
0
1
1
2
2
1
0
1
2
1
1
1
1
1
2
1
1
0
1
2
0
1
3
2
1
2
1
2
1
1
1
1
1
2
0
0
2
0
1
1
2
1
1
0
0
1
2
1
3
1
0
1
1
0
0
1
1
2
3
2
1
0
1
0
1
1
1
0
2
1
1
2
1
1
0
1
0
2
0
0
2
0
1
1
0
1
1
1
1
2
1
2
1
1
0
0
0
1
1
2
1
1
1
1
1
2
2
1
1
1
0
1
2
1
2
1
0
1
2
0
1
1
2
1
1
1
1
1
1
0
1
0
1
1
1
1
0
0
2
1
2
1
1
1
0
1
2
2
1
0
1
1
3
0
1
1
2
1
1
2
1
1
1
1
1
0
1
2
1
1
1
1
0
0
0
0
0
1
1
1
0
1
0
1
1
2
1
0
0
0
0
1
1
0
0
1
0
1
1
1
1
1
2
0
1
0
2
1
2
1
1
0
0
1
1
0
2
2
1
1
1
1
1
0
1
0
1
1
1
0
0
1
1
2
0
1
0
0
0
2
2
1
1
1
2
0
1
0
1
1
2
0
0
1
1
1
1
2
0
1
0
1
1
2
1
1
2
0
2
1
1
1
0
0
0
2
2
1
0
1
2
1
1
2
2
1
1
2
1
0
1
1
1
1
1
1
1
1
0
1
1
3
1
1
0
1
2
1
1
1
1
1
1
1
1
2
3
2
1
1
0
1
2
0
1
0
1
2
1
0
0
1
1
0
2
1
0
1
2
1
0
2
2
1
1
0
1
2
1
2
1
0
0
1
1
2
2
1
1
0
1
0
2
0
1
2
1
1
1
0
1
1
1
2
1
0
0
1
1
1
0
0
0
1
1
0
1
1
0
2
1
1
1
1
3
2
1
1
1
0
1
1
0
0
0
0
1
1
0
0
2
2
1
1
1
2
1
3
1
1
1
0
2
2
0
1
0
1
1
2
1
1
1
2
1
1
0
1
0
1
1
2
1
1
0
0
0
1
1
1
1
1
0
0
1
1
0
1
1
1
2
1
2
2
1
1
1
1
0
1
1
1
1
1
1
1
2
1
0
1
2
1
1
2
1
1
2
1
0
1
0
2
1
1
1
1
1
1
1
1
1
1
1
0
0
2
0
1
0
1
1
1
2
2
1
1
1
1
0
1
1
0
1
1
0
2
1
1
2
1
1
1
0
0
0
1
1
0
2
1
0
1
1
0
1
2
1
3
2
0
1
2
1
1
2
1
1
0
2
0
1
1
0
1
1
1
2
3
1
1
2
0
0
0
2
1
1
0
1
1
2
1
1
1
2
0
1
0
2
2
1
2
2
0
1
0
1
1
1
1
1
2
2
2
0
0
2
2
2
0
1
1
0
0
1
1
1
2
0
1
2
0
1
1
0
2
1
0
1
1
2
1
0
1
1
1
0
1
1
1
0
1
0
1
0
1
2
2
0
1
1
1
0
2
1
0
1
2
1
1
0
0
0
1
2
2
2
2
1
0
1
1
2
1
2
2
3
0
1
0
2
1
0
2
1
0
0
1
1
1
1
2
0
2
1
2
1
1
1
0
1
1
2
2
1
2
0
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
0
2
1
2
1
2
2
1
2
2
0
0
1
0
0
1
1
1
2
2
1
0
1
0
1
1
1
1
1
1
1
2
1
1
0
1
1
1
2
2
1
2
1
2
0
1
2
1
2
1
2
1
1
2
1
0
1
0
1
1
0
0
0
1
1
2
1
0
3
0
1
1
1
2
0
1
0
2
2
1
1
0
0
0
0
1
1
1
1
1
1
1
0
2
1
1
1
2
1
0
1
0
2
2
1
2
0
1
2
1
1
1
1
2
1
1
0
1
1
1
2
0
1
1
1
0
1
0
1
1
1
0
0
0
0
1
0
2
1
0
1
2
2
1
1
1
2
0
1
2
2
1
1
1
1
0
1
1
2
1
2
0
2
1
0
1
5
1
2
2
0
1
1
1
1
1
1
1
1
2
0
1
2
1
1
0
0
0
1
1
0
1
1
1
0
0
1
1
1
2
2
1
0
2
1
0
0
0
0
1
1
0
1
1
1
0
2
1
0
0
0
2
0
0
1
1
1
0
0
2
0
1
0
0
1
2
2
1
1
1
0
1
0
1
2
2
1
0
2
1
1
2
2
0
0
1
1
0
1
2
1
2
1
1
1
1
0
1
2
1
1
2
0
0
1
0
0
1
1
0
2
1
2
2
2
1
2
1
1
0
2
1
0
0
1
1
0
2
0
1
0
1
0
1
1
0
1
0
0
1
1
0
2
0
0
1
0
1
2
2
1
2
2
0
0
4
0
1
0
1
1
1
1
1
0
0
2
1
2
2
0
1
2
2
2
1
1
1
1
1
2
0
1
2
2
1
0
1
1
1
1
0
1
1
0
0
2
0
1
0
0
1
1
1
0
0
0
2
1
2
1
1
0
1
0
1
3
0
1
1
1
1
1
1
1
2
3
0
1
1
1
1
1
2
2
2
1
1
0
1
2
0
1
0
0
1
1
2
1
2
1
1
0
0
1
0
1
1
0
0
1
0
0
1
1
1
2
1
0
1
2
1
1
1
1
1
1
1
0
0
2
1
1
0
2
1
2
1
0
1
1
1
0
1
0
1
1
1
0
1
1
1
1
0
0
1
1
1
1
2
1
1
2
1
2
0
0
2
1
2
0
0
2
0
1
0
1
2
1
1
0
1
0
1
2
1
2
0
2
3
0
1
0
2
2
1
0
1
2
2
1
1
2
10
1
0
2
2
2
1
0
1
1
2
2
0
0
2
1
1
0
0
1
1
2
2
1
1
0
1
1
1
2
1
1
1
1
0
1
1
1
1
1
1
1
1
1
2
1
0
1
0
0
1
1
1
1
1
1
2
0
1
1
0
0
1
0
1
1
1
2
1
2
1
0
1
0
0
2
1
1
1
1
2
0
1
1
2
1
1
2
1
0
1
1
2
2
0
2
1
0
1
1
1
0
1
1
1
3
0
1
0
1
1
2
3
0
1
0
1
1
1
1
0
0
2
0
1
0
1
1
1
0
0
1
1
0
2
1
1
2
2
2
1
2
0
0
1
0
2
1
2
1
1
1
1
0
0
1
1
0
0
1
0
1
1
1
2
0
2
1
1
1
1
0
1
1
1
0
2
0
1
1
1
1
1
1
3
1
0
1
1
1
1
1
1
1
1
0
2
1
0
1
1
1
2
1
0
1
1
0
0
0
0
1
2
1
0
1
0
1
2
1
1
1
1
0
1
2
1
0
1
2
1
1
1
2
2
0
1
2
2
2
1
2
0
2
0
0
5
0
2
2
0
2
1
1
2
2
1
1
1
2
1
0
0
0
0
0
0
1
1
1
0
1
1
1
1
0
3
2
0
1
2
2
2
1
2
1
1
2
0
1
1
1
0
2
0
0
1
0
2
1
2
2
0
1
1
1
2
0
2
1
1
0
1
1
2
1
1
1
0
1
1
1
1
1
1
1
1
0
0
0
1
0
1
1
1
1
0
2
1
1
1
0
0
1
1
1
1
0
1
0
1
1
2
1
1
2
0
1
2
0
1
1
1
1
1
0
0
0
1
1
0
2
1
0
0
1
1
1
1
1
1
1
2
1
0
1
1
1
0
2
1
1
3
0
1
1
3
0
0
0
1
0
0
1
2
0
1
0
0
2
0
0
1
0
1
1
0
2
0
1
0
0
1
2
1
3
0
0
1
1
1
1
1
1
4
1
1
2
0
1
0
1
1
2
1
0
1
1
1
2
1
1
1
2
0
1
1
2
0
2
1
2
2
2
1
0
1
2
1
1
1
2
1
1
0
0
1
2
1
0
0
0
1
0
1
2
1
1
0
1
0
1
1
0
1
2
1
0
2
0
1
2
1
0
2
0
2
0
1
1
0
1
2
2
2
0
1
1
2
0
1
1
1
2
0
0
1
1
0
1
1
1
1
0
1
0
1
1
1
2
0
2
0
0
1
1
1
2
1
0
1
0
1
0
1
1
1
1
1
0
1
1
1
1
1
1
1
1
2
1
1
0
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
0
1
1
0
1
2
1
2
2
1
1
1
1
2
2
2
0
1
0
1
1
1
1
2
1
1
0
0
1
1
0
0
1
0
2
0
1
0
0
0
2
1
1
1
2
1
0
1
0
1
1
0
1
1
0
1
1
1
1
2
0
0
1
1
1
2
0
1
1
1
1
0
0
2
1
1
1
1
2
0
1
1
1
1
1
0
1
2
0
1
1
0
2
2
2
1
2
0
2
0
0
1
1
1
2
1
2
2
1
1
1
1
1
2
1
1
2
0
1
2
1
1
1
1
1
2
1
0
0
2
1
1
1
0
1
0
1
0
2
2
1
2
1
0
1
1
1
1
2
1
2
0
1
1
1
2
1
2
2
0
0
1
0
1
1
2
0
0
1
2
1
0
1
2
1
1
2
1
0
2
2
0
1
2
2
1
1
1
2
1
1
1
0
1
1
1
0
2
1
2
1
1
2
1
0
1
0
1
1
0
1
2
0
1
1
1
1
2
1
2
1
0
1
1
2
1
2
1
0
1
1
1
1
1
1
1
1
1
1
1
2
0
1
1
1
1
0
1
1
0
1
2
1
1
2
1
1
1
0
1
2
1
0
1
1
1
1
0
2
1
1
2
1
0
2
1
1
1
1
1
0
2
0
1
1
1
1
1
2
1
1
3
1
1
2
2
1
1
1
0
1
1
1
1
0
2
1
0
0
0
0
2
1
2
1
1
1
0
1
0
1
1
0
2
1
0
1
1
2
2
1
0
1
1
0
1
0
2
2
2
2
1
2
1
0
1
0
1
1
1
1
1
1
1
2
1
2
1
0
2
1
2
0
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
2
1
1
1
0
0
0
2
2
2
1
1
1
0
1
0
2
1
1
2
0
1
2
1
0
2
1
0
0
1
0
1
1
0
1
1
1
2
1
0
3
1
2
1
2
1
2
1
1
2
2
1
1
1
1
1
1
2
1
2
1
1
2
0
1
0
2
0
1
0
0
1
0
2
2
0
0
1
0
0
0
1
3
0
0
1
1
2
1
0
1
2
2
1
2
2
2
1
0
1
1
1
1
1
0
1
2
2
2
1
0
2
2
1
0
1
2
2
1
2
1
2
0
0
1
0
2
2
1
0
1
1
1
1
0
1
1
2
0
0
2
1
1
0
2
2
0
0
2
1
0
3
2
2
2
1
0
1
1
2
0
2
0
1
1
0
0
1
1
1
1
1
2
1
1
0
1
1
2
5
1
2
0
2
1
1
0
0
2
1
1
1
1
0
1
1
0
1
0
2
0
1
0
2
0
2
1
1
0
2
0
1
2
1
0
1
1
0
0
2
2
0
2
0
1
1
1
1
1
1
1
1
1
1
1
0
2
0
1
0
0
1
2
2
0
2
0
1
1
0
0
3
1
2
1
0
2
1
0
2
1
0
2
1
2
1
1
2
1
1
0
1
0
2
3
1
0
1
0
2
1
1
1
1
0
1
0
2
1
0
3
1
2
0
1
1
2
1
2
1
0
1
1
1
1
1
2
1
0
1
1
2
1
1
0
1
4
2
1
0
1
1
2
0
1
2
1
1
1
0
1
1
1
1
1
1
1
1
1
1
2
0
1
1
1
2
1
0
2
0
1
2
0
0
2
1
1
1
1
1
1
1
2
0
0
0
2
2
0
2
0
1
1
0
1
1
2
2
1
0
1
1
1
0
1
0
2
1
1
1
1
1
1
2
2
0
1
0
2
3
0
1
0
0
1
2
0
1
1
1
0
2
1
0
2
2
1
1
1
1
1
2
1
2
1
1
0
1
1
2
4
2
2
1
2
2
1
1
0
1
1
1
1
2
2
2
0
2
1
2
0
2
1
2
0
1
1
0
0
0
2
0
1
0
2
1
0
1
2
0
2
0
1
1
2
2
1
1
1
1
2
1
1
2
1
1
0
1
2
2
0
0
2
1
1
1
0
2
1
2
0
0
1
1
0
1
1
1
0
1
2
2
2
2
1
1
1
0
1
0
1
1
1
1
1
0
1
2
1
2
0
1
1
1
1
1
1
0
1
1
1
2
1
1
0
2
1
2
1
1
2
1
1
2
0
1
2
1
0
2
1
2
0
2
1
1
1
2
5
2
0
1
2
0
0
1
1
2
2
1
1
1
1
2
0
1
2
2
1
1
2
1
1
2
0
1
2
1
1
1
1
1
1
2
2
2
1
1
1
1
0
2
0
1
1
1
0
1
1
0
0
1
2
0
2
2
1
1
1
2
1
0
1
1
1
1
0
2
1
1
2
0
1
2
1
2
2
1
1
2
0
1
2
0
1
1
2
0
1
1
1
0
2
0
0
0
0
1
2
0
2
0
0
3
1
1
1
1
1
1
1
0
2
1
1
1
1
1
2
2
1
1
2
1
2
1
2
1
0
1
1
0
3
1
1
1
1
1
4
0
1
2
1
2
2
0
1
0
1
2
1
0
1
2
1
0
1
1
1
0
1
2
0
1
1
0
2
0
2
2
1
1
1
2
1
2
1
1
0
1
1
1
2
0
1
1
2
1
0
0
1
1
3
0
0
2
0
0
2
2
2
0
0
1
1
1
1
2
2
1
1
1
1
0
1
1
1
1
2
0
1
1
0
0
0
2
1
0
1
1
1
1
1
1
3
1
1
1
0
0
2
0
0
2
1
1
1
1
1
2
1
1
3
1
0
2
0
0
0
2
1
1
0
2
0
1
1
2
1
1
2
0
1
2
0
2
1
0
2
0
1
1
1
1
0
1
2
1
0
1
0
2
2
2
2
1
1
0
0
1
1
2
1
0
1
2
1
2
0
1
1
1
0
1
1
0
1
1
1
2
0
0
1
2
1
1
1
0
2
2
0
0
1
2
1
1
2
2
2
0
0
4
0
2
2
1
0
1
2
2
0
0
2
1
0
1
1
0
1
0
1
0
1
2
0
0
1
1
1
2
0
2
1
1
0
0
2
1
1
1
0
1
1
1
1
1
2
2
1
2
1
1
1
0
0
1
0
0
2
2
0
1
2
1
2
1
1
1
1
0
1
2
1
0
2
1
1
0
1
2
1
1
0
1
1
0
1
1
0
2
0
2
0
1
1
2
1
1
2
1
1
0
0
1
1
1
0
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
2
1
0
1
1
0
1
1
2
1
0
1
0
0
2
1
2
1
0
2
1
1
1
2
0
1
1
2
0
1
1
0
0
1
0
1
1
1
1
1
1
0
1
0
0
0
1
1
1
1
2
0
2
0
1
0
0
1
1
1
1
2
0
2
1
5
0
1
1
0
1
1
0
2
1
2
1
0
2
1
2
0
1
2
1
1
1
1
2
2
1
2
0
1
1
2
0
2
2
2
2
1
1
1
1
1
1
1
1
2
2
0
0
2
1
1
0
0
2
1
0
1
1
1
1
0
1
1
2
0
2
0
3
0
2
2
1
0
0
1
0
2
2
0
1
0
0
1
2
0
2
1
1
0
1
1
1
1
2
2
0
0
1
0
0
0
2
1
1
0
2
1
1
1
1
0
1
1
0
2
1
1
1
1
1
2
0
0
1
0
2
1
1
2
2
0
0
1
2
1
0
1
2
0
1
1
0
1
1
2
0
1
0
1
1
1
1
1
0
1
0
1
1
1
0
0
2
1
1
0
1
1
1
0
1
1
1
1
2
1
0
1
1
0
1
1
1
0
0
2
1
1
1
0
1
1
2
2
1
1
1
1
1
0
1
0
2
1
2
1
1
2
2
1
1
2
1
2
0
0
2
1
1
1
2
1
1
2
0
1
1
2
2
1
1
1
1
2
1
1
1
1
2
1
0
0
1
1
1
1
0
1
1
2
2
1
2
2
2
1
0
1
2
2
1
0
0
1
0
0
1
0
1
0
1
2
2
2
1
3
0
1
0
1
0
1
2
0
1
1
1
1
1
1
1
0
1
0
1
2
2
0
1
0
2
2
1
1
0
0
1
1
0
1
1
1
2
1
1
1
1
1
1
1
1
0
1
1
0
0
0
1
1
0
1
0
2
1
2
1
0
1
2
2
1
0
1
1
2
2
2
1
0
2
2
2
1
1
1
1
0
1
1
1
1
1
2
0
0
1
2
1
2
2
1
1
0
1
2
0
1
2
0
2
1
0
0
0
0
2
1
0
2
2
1
0
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
0
0
2
0
1
1
2
1
1
0
1
0
2
1
1
1
0
1
1
2
0
1
0
1
0
0
0
1
1
1
1
1
1
0
1
1
2
2
2
1
1
0
2
0
0
1
0
1
0
2
0
1
0
1
0
1
1
0
2
2
0
1
0
1
2
2
0
1
1
1
2
3
0
1
2
0
1
2
1
2
1
2
1
4
0
1
2
0
0
1
2
1
1
1
2
1
1
1
3
2
1
0
1
0
1
1
1
0
0
1
2
1
1
0
0
1
0
2
3
1
2
2
2
3
1
0
0
1
1
1
1
1
1
1
1
1
0
1
0
2
1
1
1
2
0
1
1
2
1
1
1
2
1
0
1
0
2
2
1
1
1
2
2
1
1
2
2
1
2
2
1
2
2
2
1
2
1
0
2
1
1
1
1
1
1
1
2
0
2
1
1
1
0
0
1
2
2
1
1
0
1
1
0
1
1
1
1
1
0
1
1
1
2
1
1
1
1
1
0
0
0
1
0
1
0
0
2
1
1
0
1
1
1
1
4
1
1
1
0
2
2
2
1
1
1
0
1
1
0
0
1
1
1
1
1
0
0
1
0
1
1
1
1
2
0
0
1
1
1
2
1
2
0
1
1
1
0
0
2
0
0
0
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
0
2
1
1
2
2
1
1
2
1
1
1
1
0
2
0
1
2
1
0
3
1
2
1
0
2
1
1
1
1
2
2
2
1
2
2
1
2
1
1
1
1
1
1
2
0
1
2
2
0
1
2
0
1
0
1
2
1
2
1
1
0
0
2
1
1
1
1
1
0
0
0
0
3
2
1
0
2
2
1
1
2
0
0
1
2
1
1
1
0
0
1
1
1
1
1
1
2
1
2
1
2
1
0
1
1
1
1
2
0
0
2
1
1
2
1
0
1
1
2
1
0
0
2
1
1
2
1
1
1
1
2
2
1
1
0
0
1
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
2
1
1
0
2
1
1
2
1
2
1
1
1
2
1
2
0
2
0
0
1
1
2
1
1
1
1
1
1
1
0
2
1
1
2
1
5
1
1
1
2
0
1
0
0
1
1
1
1
1
1
2
1
1
0
2
1
1
0
0
1
0
1
0
1
1
0
0
2
1
1
0
1
1
1
2
0
1
1
0
1
1
1
1
0
1
0
0
1
2
1
1
0
1
2
1
0
0
2
1
1
1
0
0
1
0
1
1
2
2
0
1
1
0
0
1
1
0
1
1
0
2
2
0
1
1
0
1
0
0
1
2
1
2
1
2
2
1
2
0
1
0
1
1
2
1
1
1
1
1
1
1
0
3
1
0
2
0
1
2
1
1
1
1
1
0
1
1
2
1
2
2
1
2
1
0
1
1
0
0
1
1
1
0
1
2
5
1
2
2
1
1
1
2
2
1
2
1
1
0
2
1
1
0
1
1
2
1
1
0
1
1
1
0
1
0
1
1
0
2
1
0
1
2
2
1
0
1
1
1
1
0
0
2
3
1
1
0
1
1
0
2
2
1
0
0
0
1
1
0
0
2
1
1
2
1
2
2
1
1
1
2
1
1
2
1
1
1
1
3
1
1
2
0
1
1
1
0
1
0
0
0
0
1
1
1
2
1
2
2
2
2
2
0
1
2
0
0
1
1
1
1
0
1
1
1
1
2
1
2
1
2
3
2
0
2
2
0
1
0
1
2
1
2
0
1
0
1
2
1
1
0
2
0
0
2
1
1
0
0
1
1
0
2
1
1
1
1
0
1
1
3
0
0
0
1
2
1
1
2
0
0
0
0
0
0
1
1
2
1
2
1
1
1
1
0
0
1
2
2
1
2
1
2
2
1
1
1
1
1
2
1
1
0
1
0
1
1
1
0
1
0
2
0
0
1
0
0
1
1
2
1
1
0
2
0
0
2
1
1
1
0
0
1
0
0
1
1
1
1
1
1
0
2
1
1
0
1
2
1
0
1
2
1
1
2
2
1
1
1
2
1
2
1
2
0
0
0
1
1
0
2
1
2
0
1
2
2
1
0
1
0
1
1
0
1
2
2
1
0
0
0
1
1
2
2
2
1
1
1
1
1
1
2
0
0
0
2
0
1
1
1
0
2
2
2
2
2
1
4
0
1
1
2
1
1
1
1
0
0
2
0
2
1
1
1
0
0
1
1
2
1
1
1
1
1
1
1
1
2
1
0
1
2
0
0
0
2
1
1
1
1
1
1
0
0
1
1
1
1
1
0
0
2
0
0
0
0
1
1
1
1
1
2
1
1
0
1
0
0
2
2
1
2
0
1
1
1
1
0
1
1
2
1
0
0
1
1
0
2
1
2
1
0
0
1
0
2
1
1
0
1
2
1
2
2
1
1
1
1
1
2
1
1
1
0
1
1
1
1
1
1
1
0
0
0
0
1
0
2
0
1
0
0
1
0
2
0
1
1
1
1
1
1
0
1
2
1
1
1
2
1
1
0
1
1
2
0
1
0
1
1
0
1
2
1
1
0
0
1
0
1
0
2
1
1
1
1
0
1
0
1
1
1
1
0
1
1
1
1
2
2
2
1
1
0
0
1
0
1
0
1
1
0
1
1
2
1
2
0
1
1
1
2
0
0
1
1
1
0
1
1
1
1
2
1
1
1
1
1
0
1
1
1
2
1
1
2
2
1
2
1
1
0
1
1
1
1
1
1
1
2
0
1
1
0
1
1
1
1
1
1
1
1
1
1
1
0
3
1
1
1
0
1
1
2
1
1
2
2
1
0
0
1
1
0
0
1
1
0
2
1
0
1
2
2
0
0
2
1
1
1
1
1
1
0
1
1
2
1
0
2
3
1
1
0
1
0
2
1
1
1
1
2
1
1
0
1
2
1
1
2
1
2
1
1
1
2
1
1
0
0
1
0
1
1
2
2
1
0
0
1
0
0
1
2
1
2
1
1
2
1
1
0
1
1
1
1
1
0
1
2
2
0
1
1
0
2
1
0
0
0
1
0
2
1
2
1
0
0
1
1
1
1
1
1
0
1
2
2
2
2
1
2
1
1
0
0
1
1
0
0
2
0
1
1
1
0
0
2
2
1
1
1
0
2
1
1
2
1
1
2
1
1
0
1
0
1
0
1
1
0
1
1
1
2
1
1
1
1
1
1
1
0
0
3
0
1
1
1
1
1
1
1
2
0
0
0
1
1
1
1
0
2
2
2
0
1
1
1
1
1
2
1
1
1
2
2
2
0
1
2
1
1
1
1
0
1
2
1
1
2
1
1
1
2
1
1
2
0
1
1
1
1
2
1
0
1
2
1
0
2
4
0
1
1
0
0
1
0
1
1
1
1
2
0
1
1
1
1
0
2
0
0
1
1
1
0
1
0
1
0
1
2
2
1
0
2
0
0
2
1
1
1
1
1
0
0
2
1
0
1
1
1
2
2
0
0
1
2
0
1
1
1
1
1
1
0
1
0
2
0
1
0
1
2
1
0
0
1
1
1
0
2
2
1
2
2
1
0
4
2
0
4
1
1
0
2
1
1
0
1
2
0
1
1
1
1
1
1
1
0
1
1
2
1
1
1
1
1
2
2
0
1
1
2
0
2
2
0
2
0
1
1
0
1
1
0
2
0
1
1
2
0
1
1
1
0
1
2
2
2
0
1
0
1
2
2
1
0
2
2
1
0
1
2
2
1
0
0
2
1
1
0
1
1
0
1
1
1
1
1
1
1
1
1
1
1
0
1
2
0
1
1
1
1
1
1
2
1
0
1
2
1
1
0
2
1
1
0
1
0
2
1
1
1
2
1
1
1
1
1
1
1
0
2
1
0
1
0
2
1
1
0
0
1
0
1
1
0
3
1
1
1
1
0
1
1
1
2
1
1
1
1
0
0
2
2
1
0
1
1
1
0
1
2
1
1
0
1
1
0
1
1
0
1
0
1
1
1
0
2
1
1
2
2
1
0
1
2
2
1
2
0
1
2
1
0
0
0
1
0
1
1
0
1
1
1
1
0
1
0
1
2
1
1
1
0
1
0
1
0
1
0
2
1
0
1
0
0
0
2
0
0
1
0
2
1
1
0
0
2
2
2
1
0
1
0
2
0
0
1
1
1
1
1
1
2
0
2
2
0
1
1
1
0
0
2
1
1
2
1
1
1
1
1
0
1
1
0
2
0
0
2
1
1
1
1
0
2
1
0
0
2
1
1
1
1
0
2
1
0
1
2
1
0
1
0
0
1
1
0
1
1
1
2
1
0
0
2
0
1
3
0
1
1
0
0
0
1
0
1
0
0
1
1
2
2
2
0
2
2
0
0
2
0
2
1
0
0
1
1
1
1
1
1
0
1
0
2
1
2
1
1
1
1
1
1
1
2
0
1
0
1
1
1
1
1
1
0
2
1
2
1
2
0
1
1
0
1
1
1
0
0
1
1
1
1
1
1
1
1
1
2
2
2
1
1
2
0
1
0
1
0
0
1
0
1
1
1
1
0
0
2
1
1
1
2
0
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
0
1
2
1
1
1
0
1
1
1
0
2
2
1
1
2
2
2
1
1
1
2
2
1
0
1
2
1
0
1
1
0
1
1
2
1
1
0
1
1
1
0
1
2
2
1
1
1
0
1
0
1
1
1
0
0
2
1
2
2
2
2
1
0
0
1
2
2
0
2
1
1
1
1
0
1
1
0
1
0
1
2
1
0
1
2
1
0
2
0
1
0
1
1
0
2
2
1
1
2
1
1
1
2
1
2
0
1
1
2
1
2
2
1
1
2
0
1
0
0
2
0
2
2
0
1
2
1
1
1
0
0
1
1
0
1
1
1
3
0
2
0
0
2
1
1
0
1
1
1
2
0
1
1
2
0
1
1
0
1
0
1
2
0
1
1
1
1
1
0
1
0
1
2
2
1
0
2
1
1
1
1
0
1
2
1
0
1
2
1
2
0
1
0
2
1
1
1
2
1
1
1
1
1
1
2
1
0
1
1
1
1
1
0
0
1
2
1
1
1
1
1
0
1
1
1
1
0
1
2
1
1
2
1
0
1
0
1
1
1
0
0
1
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
2
2
2
2
1
0
1
0
1
1
2
1
1
0
3
1
0
2
2
0
0
0
1
0
0
1
1
2
1
2
1
1
1
2
1
2
2
0
1
1
6
1
0
1
0
1
2
1
2
2
2
2
2
1
1
1
2
3
0
0
1
6
2
1
0
1
1
0
1
0
1
1
2
0
0
1
0
1
2
2
1
1
0
1
1
1
1
2
0
0
1
0
1
2
1
2
2
1
2
1
2
1
0
1
2
1
1
1
1
2
1
1
1
2
2
1
2
0
2
2
0
0
2
1
0
0
2
2
1
0
1
1
2
2
1
0
0
1
0
0
2
1
2
2
1
0
0
0
1
1
0
1
1
1
1
0
1
1
1
2
0
1
1
2
2
2
1
1
1
1
0
1
1
1
1
1
0
1
0
0
2
1
1
1
0
0
1
1
2
1
0
2
1
2
2
0
1
1
1
2
1
2
2
1
0
0
1
1
0
1
2
1
0
0
1
1
1
0
1
1
2
0
2
0
2
1
0
1
0
1
1
2
1
2
1
1
2
1
0
2
0
1
0
0
0
1
1
1
0
0
1
0
2
1
1
0
1
0
2
0
1
2
1
1
2
1
1
2
2
0
2
1
0
1
1
2
1
0
1
0
1
2
1
2
1
1
1
0
2
1
0
2
1
1
1
2
1
0
2
2
1
1
2
2
1
1
0
2
0
1
0
1
0
0
1
1
1
1
1
0
2
1
0
1
1
0
1
1
1
1
2
2
1
1
1
0
0
1
1
1
0
1
2
1
2
2
1
1
1
0
0
0
0
1
0
2
0
1
0
1
1
1
1
0
1
2
1
2
2
1
1
0
0
1
1
2
1
0
0
1
1
2
2
1
1
1
0
1
1
1
0
2
1
0
1
1
1
2
1
0
0
1
1
1
2
1
1
1
1
1
1
1
1
2
1
0
2
2
2
1
0
2
1
0
1
1
1
2
2
2
2
0
1
1
1
1
2
2
1
1
2
2
0
0
2
2
0
2
1
2
0
1
2
1
1
2
0
2
1
1
1
1
0
1
2
1
0
1
1
1
0
0
1
1
1
1
1
2
1
0
1
1
1
1
1
2
1
1
1
2
2
1
0
0
2
0
1
2
1
1
1
2
1
2
2
0
1
1
2
3
0
2
1
1
1
2
1
1
0
1
2
0
1
1
2
2
0
1
1
0
1
1
2
1
2
3
1
1
0
0
2
0
2
1
1
0
1
1
1
1
2
0
1
1
1
1
0
1
1
1
2
1
1
0
1
1
1
2
1
1
1
1
0
1
1
0
1
1
2
2
0
0
1
1
1
2
0
1
1
0
1
1
0
2
2
0
0
0
1
1
1
0
2
2
1
0
1
1
1
2
0
2
1
1
0
1
1
0
1
1
0
2
1
2
1
0
0
2
0
2
1
1
0
2
1
1
1
2
1
0
0
1
0
0
1
2
0
0
1
2
0
0
1
0
1
0
1
0
0
1
2
1
0
1
1
1
1
1
0
1
1
1
2
1
0
1
0
1
1
0
1
3
0
1
1
2
1
2
0
1
1
2
2
1
1
2
1
2
1
1
0
0
0
0
2
1
1
0
2
0
1
3
2
2
1
2
1
1
2
1
1
0
2
2
1
1
1
1
0
1
2
1
0
1
0
1
0
0
0
1
2
0
2
1
2
1
0
0
1
1
1
1
2
0
0
0
1
1
1
1
1
1
1
1
2
2
1
1
2
0
1
1
0
0
2
2
0
1
1
2
0
3
1
2
2
2
1
1
1
1
0
2
0
1
1
1
1
1
1
1
2
0
1
1
1
0
0
2
1
1
1
0
0
0
2
1
1
1
2
0
1
0
0
1
2
1
2
2
1
0
0
1
1
0
1
1
1
2
1
1
1
1
1
1
2
0
2
1
1
1
1
1
0
1
1
3
1
1
1
1
1
1
2
0
2
2
0
2
1
3
1
2
1
1
1
1
1
1
2
1
0
2
1
0
2
0
1
0
1
2
2
1
0
2
1
0
1
1
0
0
1
1
1
1
1
2
2
1
0
0
2
1
1
1
2
1
0
0
1
1
1
1
1
2
0
1
1
1
1
2
0
1
1
2
0
1
1
1
1
1
2
2
0
0
1
1
0
2
2
0
0
1
2
1
0
1
1
1
2
0
0
1
1
0
1
0
1
1
0
1
1
1
2
0
0
1
0
2
1
3
2
1
1
1
1
1
0
1
1
2
1
1
1
1
2
1
0
0
2
1
0
3
0
1
1
1
0
0
0
1
1
2
2
0
1
1
0
0
1
2
0
2
1
0
2
0
2
1
0
2
0
1
1
0
0
1
0
2
1
1
0
0
0
2
0
1
1
1
0
1
1
0
1
0
0
1
0
0
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
0
1
2
0
0
1
1
1
1
0
1
0
0
1
2
1
2
2
2
1
1
2
2
2
0
2
1
1
0
2
1
1
1
2
2
2
1
0
1
1
1
1
1
2
1
1
4
3
1
1
2
2
0
2
2
1
0
1
1
0
0
2
0
0
1
1
2
0
1
0
1
2
1
1
1
2
1
1
0
0
2
1
1
0
1
1
1
1
2
1
1
2
1
0
1
1
2
1
0
1
1
1
1
1
2
2
1
1
2
0
2
1
2
0
1
0
2
1
1
2
1
2
0
0
1
1
1
1
1
1
0
0
0
0
1
1
1
2
2
1
2
0
1
1
0
2
0
1
0
0
1
1
1
1
1
0
2
1
1
2
1
1
1
1
0
2
0
1
2
2
1
3
1
2
1
0
2
1
2
0
1
2
1
1
1
1
1
2
1
2
2
0
2
1
1
1
2
1
0
0
0
1
1
1
0
1
0
2
1
0
1
0
1
0
1
0
1
2
1
0
0
1
1
0
2
1
4
2
2
0
1
2
1
0
2
1
1
1
2
1
1
1
1
1
1
2
1
1
2
0
1
0
1
0
1
2
2
0
0
1
0
2
2
1
2
1
1
1
2
1
2
1
1
1
1
1
1
1
1
0
0
0
0
1
1
1
1
1
0
1
2
1
0
1
1
1
1
2
0
1
0
1
1
0
1
1
3
2
1
1
1
0
1
1
1
2
1
1
0
0
1
0
1
1
2
1
1
0
0
1
1
1
1
1
2
0
1
1
0
2
1
1
2
0
1
2
2
1
1
1
0
1
1
2
0
1
1
2
2
1
1
1
0
0
0
1
1
2
3
0
0
1
1
1
1
0
1
1
1
0
1
1
0
2
2
1
1
1
1
0
1
1
0
1
2
0
0
0
2
0
1
0
1
1
1
0
2
1
2
0
0
2
1
2
1
0
1
1
1
2
0
0
1
2
1
0
1
0
1
0
0
2
1
1
1
1
1
0
0
1
0
1
1
0
1
1
1
0
1
0
1
1
1
1
0
1
2
1
0
1
0
1
2
0
2
1
2
2
0
0
1
1
2
0
0
0
2
1
2
1
1
1
1
0
0
1
1
1
2
1
1
1
1
1
0
0
1
1
0
2
1
1
2
0
0
2
1
0
1
2
2
1
1
1
0
2
2
1
2
0
1
0
1
1
1
0
0
0
1
5
0
2
2
0
1
1
1
2
1
0
1
1
1
1
1
1
1
2
2
0
2
1
0
3
2
2
1
2
1
1
1
4
1
2
0
1
0
1
1
2
1
1
1
1
0
2
0
2
0
2
1
1
1
1
2
1
0
1
1
1
1
0
0
1
0
1
1
2
0
2
2
2
0
1
1
1
1
1
0
1
1
1
1
0
1
0
2
1
1
1
2
0
1
1
0
1
1
1
2
1
2
1
1
1
2
0
1
1
0
1
1
1
0
2
0
0
1
2
2
1
1
1
0
1
0
1
1
3
1
1
0
1
1
1
2
1
2
2
1
1
1
0
1
4
1
3
1
0
1
0
1
1
0
2
1
2
2
1
2
0
0
1
1
1
1
0
1
2
1
1
1
1
1
0
1
0
0
0
0
1
1
1
1
0
1
1
1
1
2
0
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
0
2
1
1
2
0
1
0
2
1
0
1
0
0
0
0
1
0
1
1
2
1
1
2
1
1
1
1
0
0
2
1
1
1
2
1
0
1
1
2
1
1
2
2
0
1
1
2
2
1
1
2
0
1
0
2
0
0
2
1
0
1
1
2
0
1
0
0
0
0
1
2
2
1
1
2
2
1
2
2
2
1
2
1
1
1
0
1
1
1
0
0
0
1
1
1
1
1
1
2
0
1
1
2
1
0
1
0
2
1
1
0
1
1
2
1
2
0
1
0
1
1
1
2
1
1
2
0
0
1
0
0
1
0
1
2
1
1
1
1
2
1
1
1
1
0
1
1
1
2
2
2
1
1
0
2
0
2
1
0
1
1
0
1
1
1
1
1
2
2
1
0
1
0
2
1
1
1
0
2
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
2
1
3
1
1
1
0
0
0
1
2
1
0
1
2
1
1
1
0
2
1
1
1
0
3
2
1
2
1
1
0
1
1
1
1
1
1
0
2
1
0
1
2
1
0
0
1
1
1
2
0
0
1
0
2
0
2
0
3
1
1
2
1
2
1
2
1
1
1
1
2
1
2
1
3
2
2
1
1
0
1
0
0
1
1
1
1
2
0
0
2
1
1
0
0
0
1
1
1
1
1
1
1
2
3
1
1
2
1
0
0
1
1
1
1
0
1
2
1
1
1
1
1
0
2
2
0
1
2
1
0
0
0
0
1
1
1
2
1
1
1
1
1
0
1
0
0
0
0
0
1
2
1
1
3
0
3
1
0
1
1
1
0
1
1
2
2
0
2
2
0
1
1
0
2
1
0
0
1
1
1
2
2
2
1
0
0
2
2
1
1
2
2
2
1
2
1
2
0
1
1
2
0
1
1
1
1
1
1
0
2
1
0
1
1
1
2
2
2
2
1
2
1
0
1
3
1
0
1
1
1
2
1
0
4
1
1
1
1
0
0
1
1
1
2
1
1
2
0
1
1
1
1
1
1
1
0
0
0
2
0
1
1
2
1
0
1
1
1
1
2
1
1
1
0
2
1
1
0
2
1
1
2
1
0
2
1
2
2
1
0
2
1
1
1
1
2
0
1
0
1
1
1
1
1
0
1
0
0
1
2
0
2
1
1
1
2
5
0
1
1
1
0
2
2
1
1
1
1
2
0
1
1
1
1
0
1
1
2
2
1
2
1
2
2
1
0
2
1
0
2
1
2
2
0
2
0
1
1
0
1
1
0
0
2
1
0
1
1
1
1
0
0
1
1
1
1
0
0
2
0
2
1
1
1
0
0
2
1
1
0
2
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
0
1
1
2
1
1
2
0
1
0
1
2
1
0
1
1
0
0
1
0
2
0
1
1
2
1
0
1
1
0
0
1
1
0
1
0
0
3
1
0
1
0
2
0
1
1
1
1
1
0
2
0
2
0
1
1
2
0
1
0
1
1
2
0
2
2
2
2
0
0
1
1
1
1
1
0
2
1
0
2
1
2
1
1
1
1
1
0
1
1
0
1
1
0
1
0
2
2
0
0
0
1
2
2
2
0
0
1
0
2
1
0
2
2
0
1
0
1
1
1
2
1
0
1
1
1
1
1
1
0
1
0
0
2
0
1
1
1
1
1
1
1
0
0
0
1
0
0
1
1
1
0
1
1
1
0
2
1
2
2
0
1
1
0
1
1
1
2
2
1
2
1
0
1
0
1
1
1
1
2
1
1
0
2
1
1
2
2
2
2
1
1
1
0
1
1
1
0
2
2
1
1
0
0
0
1
1
1
1
2
1
1
0
2
0
1
1
1
1
1
1
0
1
1
0
1
0
1
2
0
2
0
1
2
0
1
1
1
2
0
1
2
1
0
1
0
1
1
0
2
0
1
1
0
1
1
1
2
0
1
2
1
1
2
1
1
1
1
2
1
0
1
1
2
1
1
1
0
1
2
2
1
1
1
1
1
2
1
0
2
1
1
2
1
1
0
0
1
1
0
2
0
1
0
1
2
2
2
1
2
1
1
1
0
2
0
1
0
0
2
2
1
0
1
1
1
0
2
1
2
2
2
1
1
2
0
1
2
1
1
2
0
1
1
1
1
0
1
2
0
2
1
2
1
5
0
1
1
1
1
1
1
1
1
1
2
1
2
0
0
1
0
1
0
1
2
0
1
0
0
1
0
0
0
1
0
1
1
1
1
2
1
0
2
1
2
2
0
0
1
1
1
1
1
1
1
2
1
3
0
1
2
1
1
2
0
0
2
1
1
1
0
1
2
1
2
1
0
1
1
1
0
1
1
1
1
1
0
2
0
2
2
1
0
1
0
0
1
1
1
0
0
1
2
0
0
1
0
2
0
1
0
0
2
1
1
1
2
0
2
1
0
1
0
2
1
0
0
1
0
0
1
2
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
0
0
2
1
2
1
1
1
1
1
1
1
2
1
1
1
0
1
1
2
2
0
0
2
2
1
1
0
2
1
1
1
1
1
1
0
1
1
0
1
1
2
2
1
0
1
2
1
0
1
1
1
1
3
2
1
1
1
1
1
0
0
0
2
2
1
1
2
1
1
0
2
2
2
2
2
1
3
0
2
1
0
2
1
2
1
1
0
1
1
1
1
1
1
0
1
0
1
0
1
1
0
1
2
1
0
1
1
1
2
0
2
1
1
1
1
0
1
1
1
0
1
1
1
1
1
0
1
0
0
0
1
2
1
2
1
2
0
2
4
1
0
1
1
1
0
1
0
2
0
2
1
0
1
1
0
2
2
2
1
1
2
0
1
1
2
1
2
0
1
1
1
2
2
1
1
0
2
1
1
2
0
2
1
0
1
1
2
1
1
1
0
1
1
1
0
1
0
1
1
1
0
2
1
1
1
0
1
0
1
0
1
0
1
1
4
1
1
2
2
1
0
1
2
0
1
1
1
0
0
0
0
2
0
1
1
2
1
1
2
0
1
0
0
0
1
1
1
0
0
1
1
1
2
1
0
0
2
1
2
2
1
1
2
1
0
0
1
1
1
1
1
1
0
1
0
1
1
1
0
0
2
2
1
0
0
1
1
1
0
2
2
0
1
1
0
0
0
1
1
1
0
1
1
2
0
1
1
0
1
0
0
2
1
1
1
1
1
0
1
1
1
1
1
1
2
2
1
0
1
1
0
1
2
1
1
1
2
1
0
2
1
2
2
2
2
1
1
0
1
2
1
2
0
1
1
1
2
2
1
1
1
1
0
0
2
2
1
2
1
0
1
0
2
1
1
1
1
0
1
1
1
1
0
0
0
1
0
0
1
1
0
1
1
1
2
0
1
2
1
1
2
2
0
1
0
0
1
1
0
1
0
0
0
0
0
2
0
1
1
1
2
0
1
2
2
1
1
2
1
0
0
1
1
1
1
1
0
1
0
2
1
0
2
1
0
1
1
0
1
1
0
0
0
1
1
1
2
2
1
1
0
1
1
0
1
0
1
2
1
1
1
1
1
1
1
1
0
1
1
1
1
2
0
1
0
1
1
1
0
3
1
1
1
0
2
0
2
1
1
1
1
1
1
2
2
1
2
2
1
2
1
2
2
1
0
1
2
1
0
2
1
0
1
1
1
1
2
1
1
1
1
3
2
0
0
0
0
1
2
1
2
2
1
1
0
1
2
1
0
1
1
1
1
2
1
1
2
2
1
2
1
0
1
2
0
1
1
1
1
2
1
1
0
1
2
0
0
1
0
1
1
1
1
0
1
0
0
1
1
0
1
2
0
1
1
0
1
1
0
1
1
0
1
1
1
1
1
1
1
1
0
0
2
0
1
0
2
1
1
2
0
0
0
1
1
1
0
3
1
1
1
1
0
1
2
0
0
1
2
1
2
0
1
0
1
2
1
1
1
1
0
1
1
0
2
0
1
1
1
2
1
1
1
0
1
2
0
0
0
0
1
1
2
1
1
1
2
0
1
2
2
1
0
0
1
1
2
1
1
2
1
1
1
0
0
0
1
0
1
2
2
1
2
2
2
0
1
0
0
1
0
1
0
1
3
0
2
2
0
2
1
1
0
3
1
2
1
1
0
1
0
2
0
1
2
1
0
1
1
1
1
1
1
1
1
1
2
2
1
2
2
2
1
2
1
0
1
1
1
1
0
1
1
1
1
1
2
1
1
0
1
2
1
1
0
1
1
1
2
1
1
2
1
1
1
2
2
2
1
1
1
1
0
0
1
1
0
0
1
1
0
1
0
0
1
0
1
2
2
2
1
1
2
1
0
2
2
1
1
0
0
0
1
1
2
1
1
1
1
1
2
2
2
1
1
1
0
2
1
2
1
1
2
2
2
1
0
1
2
1
1
1
3
0
1
1
1
0
1
1
2
3
1
2
1
1
0
1
1
1
2
1
2
1
0
2
1
1
0
1
0
0
0
1
2
2
1
2
1
1
3
1
0
0
1
1
1
0
0
0
2
2
2
1
1
1
1
1
3
1
1
1
0
1
2
1
2
1
0
2
1
1
5
1
1
2
2
1
0
0
1
0
1
0
0
2
0
1
1
1
1
1
0
0
1
1
2
1
2
2
0
2
0
1
0
1
0
2
1
1
0
2
1
0
1
1
1
2
1
0
1
1
0
1
1
2
1
0
0
0
0
1
2
2
0
1
2
1
1
2
0
1
1
1
1
1
2
1
1
0
2
0
2
0
1
1
2
0
1
0
2
1
3
2
0
1
0
0
1
0
1
0
1
2
1
1
0
2
3
2
1
0
1
0
0
1
1
1
1
1
1
0
0
2
0
1
0
2
0
1
2
1
1
1
2
1
2
0
1
1
1
1
0
2
0
1
1
2
2
0
1
0
1
1
0
1
0
1
1
0
1
2
1
1
0
1
1
1
1
0
1
1
1
1
2
0
1
0
1
2
1
0
2
0
1
0
3
1
1
0
0
1
2
1
0
0
2
1
1
1
1
2
0
1
0
1
2
2
2
2
1
2
1
1
1
2
0
1
0
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
0
1
0
0
0
1
1
2
1
2
1
1
1
1
0
0
1
0
0
1
2
2
0
1
1
2
1
1
1
1
2
1
2
1
1
1
0
0
1
0
2
2
1
1
2
1
1
0
1
1
1
1
2
1
1
1
0
1
0
1
0
0
0
2
2
0
2
2
2
1
0
0
1
1
0
0
0
1
0
1
1
2
1
2
1
1
0
1
0
1
2
1
0
1
1
0
0
0
1
0
1
1
2
0
2
1
1
3
1
1
1
1
1
1
1
2
2
1
0
1
1
0
0
0
2
1
1
0
0
1
1
0
0
0
1
0
1
1
2
1
1
1
2
2
1
1
1
0
2
4
1
2
5
0
1
1
2
1
1
18
2
1
1
0
1
2
2
0
1
1
1
0
1
1
2
0
1
1
0
1
0
2
0
2
2
1
1
2
2
0
1
0
1
1
2
1
2
2
1
1
2
1
2
1
1
1
1
1
1
2
2
2
1
0
1
1
1
1
0
1
1
2
1
1
0
1
1
1
2
1
2
0
1
1
1
0
0
1
0
1
1
1
0
1
1
1
1
0
1
1
2
1
1
0
2
2
1
0
2
1
1
0
1
1
2
1
2
1
1
2
1
0
1
1
0
1
0
1
0
1
1
2
2
0
1
2
0
1
2
1
0
1
0
0
1
1
1
0
1
0
0
0
1
1
2
1
1
1
2
2
1
0
2
0
1
1
1
1
1
1
2
1
2
0
2
1
0
1
1
2
0
1
0
1
1
2
1
0
2
1
1
1
0
1
2
0
1
1
1
1
1
1
1
1
1
1
1
0
1
2
0
1
1
1
0
0
0
0
2
2
1
0
2
1
1
2
1
1
1
3
2
0
2
2
0
3
1
1
0
0
1
2
0
2
0
3
2
1
1
0
2
1
1
1
2
1
1
1
2
1
2
2
2
0
1
2
1
0
0
1
0
0
1
2
1
1
1
2
2
1
1
2
2
0
0
1
0
1
1
0
1
1
0
0
1
1
0
1
2
1
2
1
1
1
1
1
2
0
0
1
0
2
0
1
0
0
1
2
1
1
1
1
1
1
1
2
0
1
2
1
1
1
0
2
1
1
1
2
0
0
1
1
3
0
2
1
1
0
0
1
2
1
2
0
2
1
0
0
1
0
2
1
2
1
2
0
0
0
2
2
5
1
3
0
1
1
1
1
1
1
1
2
1
1
0
1
1
1
1
1
0
1
1
1
2
1
2
2
1
0
1
1
2
2
2
1
1
2
1
0
2
1
1
2
2
0
1
0
2
0
1
1
0
1
1
1
1
1
2
0
2
2
0
1
2
2
0
1
1
1
2
0
0
1
1
3
1
1
0
1
1
1
2
1
0
1
1
1
2
1
1
1
0
1
1
1
1
1
1
1
2
0
2
0
1
2
1
2
1
1
1
1
1
2
1
0
0
1
2
2
2
1
0
2
1
1
0
2
1
2
0
1
1
2
2
1
1
1
0
1
1
0
2
1
1
0
4
0
1
1
1
0
2
0
1
1
2
1
1
1
1
3
0
1
1
1
0
0
1
1
0
1
2
1
1
0
2
2
0
2
1
1
0
0
2
1
2
0
1
2
2
0
2
1
1
1
1
1
2
0
0
1
1
1
1
1
2
1
2
2
0
0
2
0
0
1
1
1
1
1
1
0
0
2
1
1
1
2
1
0
1
0
1
1
0
2
1
2
1
1
1
1
1
0
0
1
2
1
0
1
0
0
3
1
1
0
1
0
3
2
2
2
0
0
0
2
1
1
0
1
0
1
1
1
1
1
1
1
0
0
1
1
1
2
1
3
0
1
1
1
1
1
1
0
2
1
0
0
1
2
1
2
0
1
1
0
1
1
1
1
0
1
1
1
1
1
0
2
2
2
0
0
1
1
1
2
1
0
2
1
1
0
0
1
1
0
1
2
1
1
0
1
2
1
0
1
1
1
2
1
1
0
1
0
0
0
1
2
1
1
2
1
2
1
1
0
2
2
0
1
1
2
2
1
2
2
1
2
1
0
1
1
2
1
0
2
1
0
4
0
1
1
0
1
0
1
0
2
0
1
1
1
1
1
2
1
1
2
0
0
1
1
2
0
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
0
1
0
1
2
0
0
1
1
1
1
1
2
1
1
1
1
1
1
1
0
1
0
0
0
1
1
0
0
2
1
1
1
2
0
1
1
1
0
1
1
1
1
1
1
0
1
1
1
1
0
1
1
1
1
2
1
0
1
0
0
2
1
1
1
1
1
2
0
1
1
1
0
0
1
1
1
2
0
3
1
1
3
2
0
1
0
1
2
2
1
1
1
2
1
2
1
1
1
0
1
1
0
1
0
1
1
0
2
2
1
0
0
2
1
1
2
1
1
0
0
2
1
0
0
1
1
1
0
0
1
1
1
1
1
2
1
2
0
0
1
1
0
1
1
1
0
1
1
1
1
2
1
1
1
0
1
0
1
0
1
1
1
1
2
3
1
1
0
1
3
2
0
1
1
2
1
1
1
1
1
0
1
1
0
1
0
0
2
2
2
1
0
1
1
0
1
1
1
0
0
0
2
1
0
1
1
0
2
0
2
0
1
1
2
0
1
1
1
1
1
2
1
0
0
1
0
0
0
0
1
1
1
0
1
1
1
1
2
1
2
2
1
0
1
0
2
1
1
1
1
1
0
1
1
2
2
2
2
1
1
0
2
0
2
1
0
1
0
0
1
1
2
1
0
1
1
0
2
1
0
0
0
1
1
1
1
1
0
1
2
2
1
1
1
2
1
2
1
2
1
1
0
0
0
1
1
0
1
1
2
1
1
2
1
1
0
2
1
1
1
0
2
2
1
1
2
1
1
0
2
0
1
0
0
2
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
0
2
1
1
1
0
1
2
2
3
1
2
1
0
1
0
2
0
1
1
1
2
2
1
0
2
1
3
2
0
1
0
0
1
1
2
0
1
0
0
2
0
1
1
1
2
1
0
1
1
2
0
2
1
2
1
1
1
1
0
0
0
1
2
2
1
2
1
2
1
0
1
1
0
2
0
1
1
1
2
1
1
2
2
1
1
1
1
8
2
0
1
1
1
0
2
2
1
1
0
1
2
2
0
1
1
1
1
0
1
1
1
1
1
1
0
0
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
0
1
1
2
2
0
1
0
2
1
1
1
1
2
2
1
0
2
1
1
1
2
2
1
2
1
1
0
1
0
2
0
1
1
0
1
1
1
0
1
1
1
1
2
1
1
2
2
1
2
2
1
2
1
0
1
1
2
1
1
1
1
0
0
1
1
2
1
0
1
1
1
2
2
1
1
1
2
1
0
1
2
1
1
1
1
1
0
1
1
0
2
1
1
1
1
3
1
1
1
1
1
2
1
1
0
0
2
2
2
1
1
0
1
1
0
1
1
1
1
0
1
0
0
1
2
0
1
0
2
0
1
1
1
0
2
1
0
0
0
1
2
2
1
0
4
1
1
1
1
0
1
1
4
2
0
1
0
0
0
0
1
1
1
1
0
2
1
1
1
1
2
2
0
1
1
1
1
1
1
1
1
1
2
0
1
0
1
1
1
2
1
0
1
0
2
1
1
1
2
1
3
2
1
1
0
1
0
1
0
1
0
0
1
0
2
1
1
0
0
1
1
1
1
0
2
0
0
1
1
1
1
2
2
1
1
0
2
2
1
1
0
1
2
1
1
2
1
1
1
1
1
1
2
1
2
2
0
0
0
1
1
1
0
0
0
2
1
0
2
0
1
1
2
2
1
2
2
1
1
2
0
1
1
1
1
1
1
0
1
1
2
1
1
0
1
2
0
1
1
0
0
2
0
2
0
1
2
0
1
2
2
2
1
0
1
1
0
1
1
1
1
1
1
1
1
0
2
2
1
0
1
2
0
2
1
2
3
2
2
2
0
0
1
1
0
0
1
0
0
0
0
1
0
0
1
3
0
2
0
1
1
0
1
1
0
0
0
2
2
0
1
1
0
0
2
1
0
0
2
1
0
1
1
1
1
1
2
1
2
1
0
0
0
0
1
0
2
2
0
0
2
0
0
1
1
1
1
2
1
2
1
1
1
1
1
1
0
1
0
0
2
1
1
0
0
1
1
2
1
1
1
1
1
2
2
1
1
1
1
2
0
0
1
0
1
0
1
1
1
1
0
1
1
0
0
0
1
1
1
1
2
1
0
1
1
1
1
2
1
1
0
0
2
1
1
2
1
1
1
1
2
2
1
0
1
1
1
1
1
1
2
0
0
2
1
0
0
1
2
1
1
1
0
2
0
1
1
0
1
0
1
0
1
1
0
0
2
1
0
1
2
1
1
1
1
1
1
0
2
1
1
0
1
1
0
1
1
0
1
0
1
1
2
2
1
0
1
2
1
1
2
0
1
0
1
0
1
1
1
1
1
1
1
2
2
2
1
1
2
2
2
0
1
1
1
2
0
0
2
1
0
1
1
0
0
0
0
1
1
1
2
1
1
1
1
0
1
1
1
1
1
1
1
0
0
1
1
1
1
1
0
1
1
1
0
0
1
2
0
0
2
1
1
1
2
2
2
0
0
0
2
1
2
1
2
1
0
2
1
1
1
0
2
1
1
2
0
0
0
2
2
1
0
1
0
2
0
2
1
1
0
1
1
1
3
1
0
1
1
1
0
1
1
2
1
1
1
0
0
2
0
0
1
1
1
1
1
2
2
1
1
1
2
2
1
1
1
0
2
0
2
0
0
1
1
1
0
0
1
2
2
1
1
1
0
0
1
1
2
1
2
1
1
1
2
1
1
1
1
0
2
1
2
1
1
1
0
2
1
0
0
1
1
1
1
0
1
1
0
0
1
0
1
2
2
0
2
1
2
1
1
1
0
1
1
1
1
0
1
2
2
0
2
0
1
1
1
0
1
1
2
1
2
0
1
2
1
0
0
1
2
1
0
2
1
1
2
1
1
0
2
1
1
1
2
2
2
2
0
1
2
0
1
2
1
0
2
2
0
0
2
2
0
2
2
1
2
1
0
1
1
0
1
0
1
0
0
1
2
1
1
1
0
1
1
1
1
2
1
1
1
3
1
1
1
1
0
0
2
0
2
1
1
0
0
1
1
1
3
1
1
1
1
1
0
0
1
2
1
0
2
2
1
1
1
1
1
1
1
1
2
1
0
0
0
0
0
1
0
1
0
1
1
1
1
1
1
2
1
0
1
1
0
2
1
1
1
0
1
1
0
1
1
0
0
2
2
0
1
1
0
1
1
0
1
2
1
1
2
0
0
1
1
1
2
0
2
0
2
1
1
0
1
1
0
0
2
1
2
1
1
2
1
0
2
1
2
2
1
1
2
0
1
1
1
1
2
1
1
2
2
1
2
0
1
0
2
1
0
0
1
2
1
1
0
1
1
0
2
2
1
0
2
2
1
0
1
1
0
1
1
1
2
1
1
0
1
1
1
1
0
2
0
1
2
0
3
1
0
2
1
1
0
2
1
0
1
2
0
0
0
1
1
1
1
0
1
0
2
1
2
2
1
1
0
1
0
0
2
1
1
1
0
1
1
0
1
0
2
2
0
1
0
2
1
0
2
1
0
1
1
1
2
0
1
2
0
0
1
0
2
2
1
0
0
1
1
2
1
1
1
2
1
1
1
1
1
1
2
1
2
0
2
1
2
0
2
0
1
0
1
1
2
0
1
1
1
1
0
2
1
1
2
1
1
1
1
0
1
1
2
1
1
2
1
1
1
1
1
2
0
1
2
1
0
1
1
0
2
1
2
2
1
2
0
1
2
2
0
0
0
2
1
1
1
1
2
1
2
1
0
0
1
1
2
1
2
1
0
1
1
1
2
2
1
1
0
1
1
2
1
2
1
2
1
0
1
1
1
1
1
1
0
0
2
0
1
0
0
0
2
1
0
2
1
2
0
0
2
1
1
0
0
1
2
2
0
1
0
1
0
0
1
1
2
0
0
1
2
1
0
1
1
1
1
0
1
1
2
1
1
1
3
0
1
1
1
0
1
1
1
1
1
1
2
1
1
2
3
0
0
1
0
2
2
2
1
1
2
0
4
1
0
2
1
1
2
1
0
0
1
0
1
0
0
1
2
1
2
2
1
1
1
1
0
2
0
1
0
2
0
1
1
0
0
2
0
2
2
2
1
1
1
1
2
0
0
1
1
1
1
1
1
1
1
1
2
0
1
1
2
2
1
2
1
2
0
0
1
2
1
1
1
2
1
0
1
1
1
0
0
0
1
1
2
1
1
0
0
1
1
0
0
2
1
1
1
0
2
1
2
0
1
2
1
1
2
1
1
1
1
1
1
0
1
0
0
2
1
0
1
2
0
1
1
2
1
1
1
0
0
0
1
0
1
1
1
0
2
1
1
1
1
2
1
0
1
1
1
0
1
1
1
1
1
1
1
2
0
1
1
0
0
0
1
1
1
1
2
1
1
1
0
2
1
0
2
2
1
0
1
1
1
2
2
1
1
1
0
4
7
2
1
2
1
1
0
2
0
1
2
0
1
1
1
1
1
1
1
1
0
2
2
1
1
1
1
0
1
0
1
2
2
1
1
1
0
1
1
1
3
1
1
0
1
2
0
2
1
1
1
1
2
1
3
5
1
1
0
1
1
0
1
1
1
0
2
0
1
1
1
0
1
2
1
0
2
1
1
1
1
1
0
1
1
1
1
2
2
1
1
0
1
1
1
1
1
1
1
2
1
1
1
2
1
2
0
0
0
0
0
2
2
1
2
1
0
1
0
0
1
1
1
1
0
1
1
0
1
1
1
1
1
1
1
2
2
1
1
1
2
1
0
0
2
1
1
0
1
2
1
1
2
0
0
0
1
2
0
2
1
2
2
1
0
1
1
1
1
2
1
2
1
1
1
0
0
1
2
0
0
0
1
1
0
1
0
2
2
0
1
1
1
1
1
1
1
1
2
2
1
1
0
1
0
0
0
2
1
2
1
1
0
0
1
1
1
1
0
2
0
1
2
2
0
2
0
2
1
1
2
1
0
2
0
0
0
0
2
2
2
0
1
1
2
1
0
1
1
1
1
1
1
1
0
0
1
2
1
2
1
1
2
1
1
0
2
1
1
1
0
1
0
1
0
0
1
1
2
2
1
1
1
0
2
1
1
2
1
2
1
0
0
0
0
0
0
2
2
1
0
2
1
1
1
0
1
1
2
1
2
1
0
0
2
0
1
2
1
1
1
0
1
1
2
0
1
1
1
0
1
1
1
1
0
0
2
1
1
1
0
1
2
0
1
1
1
0
1
2
1
1
0
1
0
2
2
2
1
2
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
1
1
2
1
3
2
0
0
0
1
2
1
0
1
1
1
1
2
1
1
0
2
1
0
0
1
2
1
0
1
1
1
2
0
2
1
1
2
1
1
1
1
1
1
1
2
2
0
1
0
1
0
2
1
1
2
0
1
2
1
1
2
0
1
1
1
2
0
1
1
1
1
2
2
2
1
1
1
0
1
1
2
0
1
0
1
1
2
0
1
6
0
2
1
1
1
1
0
0
1
0
1
1
1
1
0
2
0
0
1
1
2
1
2
2
1
2
0
2
1
1
1
1
0
0
0
1
1
0
2
2
1
0
0
1
2
1
1
0
1
0
1
1
1
1
1
1
0
0
2
2
2
1
1
1
1
1
0
1
0
0
0
0
1
1
0
2
0
1
1
2
0
2
0
1
3
0
2
0
1
0
1
1
1
1
2
0
1
1
0
1
1
0
1
2
1
0
1
1
1
1
0
1
1
2
1
1
1
0
2
0
2
1
1
1
2
2
2
1
1
2
0
0
0
1
0
1
0
1
0
1
1
1
1
1
1
1
3
0
0
1
0
0
0
1
1
1
2
1
1
1
2
1
1
0
1
1
1
2
1
0
1
2
1
1
1
0
1
0
0
2
2
2
2
0
1
1
2
1
1
0
1
2
2
0
1
2
0
1
2
0
0
2
0
1
1
0
1
1
1
2
1
1
2
0
1
2
1
1
1
1
0
2
1
2
1
1
2
1
1
0
2
1
2
1
0
2
0
1
1
2
1
1
1
1
0
2
1
1
0
1
3
1
1
3
2
2
0
1
1
0
0
0
2
1
0
1
2
0
2
1
0
1
0
1
1
1
1
0
0
1
2
1
1
2
1
3
1
0
1
0
0
1
2
0
1
1
0
2
2
1
1
1
0
2
2
0
1
1
1
1
1
1
0
1
3
1
0
0
1
2
2
2
0
1
1
1
1
0
3
0
2
0
2
1
1
2
2
1
0
1
1
2
2
2
1
0
1
0
1
2
1
1
1
1
0
1
0
2
1
2
0
1
2
2
1
0
1
1
1
1
0
1
0
2
0
2
2
1
1
2
1
2
1
1
1
0
1
2
1
0
1
1
2
2
1
0
1
0
0
1
0
1
1
0
2
1
1
0
1
2
1
1
2
1
1
1
0
1
2
1
1
1
1
0
2
1
2
1
0
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
0
0
1
1
2
2
1
1
1
1
2
2
1
0
1
1
0
1
1
2
1
2
0
0
2
1
0
1
0
0
0
0
1
0
1
1
0
1
1
2
0
1
2
2
1
2
2
1
0
2
1
1
2
0
1
1
1
1
1
2
1
1
1
0
2
0
1
0
2
2
1
0
1
2
2
0
1
1
1
0
1
0
1
1
0
0
0
0
2
2
0
1
0
1
1
0
1
0
2
1
1
1
1
0
1
1
1
1
2
0
0
0
1
2
0
1
0
2
1
1
1
0
2
1
1
1
1
1
1
0
1
2
2
2
1
1
0
1
0
1
1
2
1
2
2
1
0
1
1
1
1
0
1
0
1
1
1
1
2
1
2
0
0
2
1
1
1
2
1
1
0
1
1
1
1
2
2
1
1
0
1
0
0
1
1
1
0
1
1
0
1
0
3
0
1
2
0
1
2
2
0
0
2
1
0
1
1
1
1
0
1
1
1
1
0
0
2
0
2
1
0
0
0
1
1
1
1
1
2
2
2
0
1
0
0
2
0
1
0
0
2
2
1
0
2
2
2
2
1
1
1
2
1
0
1
1
1
0
1
1
1
1
1
0
8
0
0
2
0
0
0
1
1
1
1
2
2
1
0
1
0
2
2
2
1
0
2
1
1
1
2
1
0
1
1
1
1
1
2
1
1
0
0
0
2
1
0
1
2
1
1
2
1
1
2
1
1
1
1
2
1
0
0
2
1
1
1
2
1
0
0
0
1
1
2
1
1
2
2
1
1
1
0
2
2
1
2
1
1
2
1
1
0
1
0
1
1
2
2
2
1
0
1
1
0
2
0
0
2
1
2
0
1
1
1
2
1
1
2
2
2
1
1
2
1
0
1
2
1
1
2
0
1
1
0
1
2
0
2
1
0
2
1
1
1
2
2
1
1
1
1
0
2
2
1
1
2
0
1
2
1
1
2
1
0
0
1
0
2
0
1
0
0
2
0
1
1
1
0
1
1
1
1
1
0
1
1
1
1
1
0
1
2
3
0
1
2
1
1
1
1
2
1
1
0
1
2
1
1
0
1
1
0
1
1
1
1
1
1
1
1
0
1
1
1
1
0
1
2
1
1
1
0
0
1
2
1
1
1
1
1
1
1
0
2
2
0
2
1
1
1
1
0
0
2
3
1
2
0
2
2
1
2
1
0
0
1
1
1
2
1
1
0
2
0
1
1
1
2
1
1
1
1
1
1
0
1
0
2
1
0
0
1
1
1
1
0
1
1
1
0
1
2
1
1
1
1
1
1
0
1
0
1
1
2
1
2
2
2
2
2
1
3
1
2
1
2
2
2
1
2
0
1
1
1
0
0
1
1
1
1
1
1
2
1
1
0
1
2
1
0
1
1
0
1
0
1
1
0
2
2
1
1
1
2
0
1
1
1
2
1
1
0
2
1
1
2
1
1
0
0
0
0
0
1
0
1
0
1
1
1
1
0
0
2
1
2
1
0
0
1
0
1
2
1
2
1
3
1
1
2
2
1
1
1
2
1
1
1
1
0
1
1
0
0
0
1
0
1
0
1
2
0
0
1
1
0
1
1
0
1
1
0
0
1
1
1
1
1
0
2
1
0
1
2
0
0
1
1
0
0
2
1
1
2
2
1
1
2
3
2
2
1
0
2
0
2
2
0
0
1
1
1
1
1
0
2
2
0
1
1
2
2
2
2
1
2
1
0
1
0
1
0
2
2
2
2
1
0
1
2
1
2
1
2
0
1
0
1
1
1
1
1
1
1
0
0
1
1
0
0
1
1
1
3
0
0
0
2
1
1
1
1
2
0
1
0
2
0
0
0
1
1
2
1
2
0
1
2
3
3
1
1
0
1
1
1
2
2
1
2
2
1
1
0
1
1
1
1
1
0
1
0
0
1
0
1
0
1
1
2
2
2
1
1
0
1
0
0
1
1
1
0
2
1
2
1
2
1
1
2
1
3
2
1
0
0
5
1
0
1
1
0
0
0
1
2
1
1
1
1
0
1
0
1
0
2
2
1
1
2
1
2
0
0
2
1
2
3
1
1
1
1
0
2
1
1
2
0
1
1
2
2
1
2
0
1
1
0
2
2
2
0
1
0
2
2
2
1
1
0
2
0
0
1
1
1
0
1
2
0
1
0
2
1
2
0
0
0
1
2
0
1
0
0
0
1
1
0
1
2
1
1
2
1
1
0
1
1
1
1
1
2
2
0
1
0
2
1
2
3
0
1
1
1
1
1
1
1
0
1
1
1
0
1
0
1
1
1
1
1
1
0
1
2
0
1
1
0
0
0
1
1
1
1
0
2
1
2
2
1
1
0
1
1
2
1
0
0
0
1
2
2
0
1
1
1
1
1
2
0
2
1
1
1
1
0
1
2
2
1
2
1
1
1
2
1
1
1
0
0
1
1
1
2
1
1
1
0
1
0
2
1
0
1
2
0
1
1
1
1
0
1
0
1
0
0
1
1
0
0
1
2
0
0
2
1
3
1
0
0
2
2
1
1
0
2
1
0
1
0
1
1
1
1
1
2
1
1
1
1
1
0
1
1
0
1
1
2
0
1
2
1
1
1
2
1
1
1
0
2
2
2
1
0
0
1
0
2
2
0
2
1
2
1
3
0
0
2
1
0
0
1
1
1
2
0
1
2
2
0
1
1
1
1
2
0
1
0
0
1
2
0
1
0
0
1
1
1
0
0
0
2
2
0
1
1
0
1
2
1
0
2
1
1
2
1
1
1
1
1
0
0
1
2
1
0
1
2
1
0
2
0
2
1
2
2
2
1
0
1
1
1
1
1
0
1
0
1
1
2
1
1
1
1
2
0
1
2
1
3
1
2
0
1
0
1
1
2
1
1
0
0
2
0
1
0
1
1
1
0
3
1
2
2
2
1
2
1
2
1
1
2
1
1
1
0
0
1
1
0
1
1
1
0
1
1
0
1
1
1
1
1
0
2
1
1
0
1
1
1
1
1
2
1
1
2
0
1
2
1
1
2
1
1
1
1
0
1
2
2
1
2
1
1
0
3
1
2
1
0
1
1
1
1
1
1
1
2
1
2
2
1
0
1
1
0
1
2
1
1
1
1
1
2
2
2
1
1
0
1
1
1
1
0
1
1
2
0
0
1
1
2
2
1
2
0
1
2
1
1
1
1
1
0
1
1
0
1
1
1
0
2
2
1
1
1
1
1
1
1
2
1
0
0
1
1
1
2
2
0
1
0
2
1
1
1
1
1
1
1
1
2
2
1
1
0
1
0
2
0
1
0
0
2
0
0
0
1
1
2
0
1
1
1
1
1
1
0
0
0
1
2
2
2
1
1
1
1
0
1
1
1
1
2
2
1
1
0
1
0
0
0
1
1
1
1
0
0
0
1
1
2
2
1
2
0
2
1
2
0
0
2
0
1
1
1
1
1
1
1
1
0
0
2
2
2
0
0
1
1
2
0
1
2
1
0
0
2
1
2
2
1
1
0
1
1
2
2
2
1
0
1
0
1
1
1
1
0
0
1
2
1
2
1
1
2
1
1
0
0
1
1
1
1
1
1
1
0
2
2
1
2
0
0
1
2
2
2
2
1
1
0
1
1
0
1
1
1
0
0
1
1
1
2
1
1
0
1
0
2
1
0
2
0
1
1
2
2
2
1
2
1
0
2
2
1
0
1
1
1
1
2
1
2
1
0
1
2
0
1
1
1
1
0
2
2
0
0
1
0
1
1
1
0
2
1
0
1
1
1
1
2
0
1
3
1
1
1
1
0
1
1
1
0
2
0
0
2
1
0
0
1
2
0
1
1
0
2
2
1
0
2
2
2
2
1
1
1
0
1
0
0
1
1
0
1
1
1
1
1
1
0
1
0
2
1
0
1
0
1
1
2
1
1
1
0
0
0
1
2
1
1
1
1
1
0
0
0
1
1
1
1
1
1
1
0
0
1
1
2
2
2
0
2
1
0
2
2
1
1
1
0
1
0
2
2
2
1
0
1
1
0
1
1
1
1
1
2
1
1
1
2
0
1
1
2
1
0
1
1
0
1
1
2
1
1
1
1
2
1
0
1
2
2
1
0
0
2
1
2
0
1
0
0
1
1
1
1
1
2
0
1
1
2
2
1
0
0
0
1
2
1
1
1
1
0
1
0
2
2
1
2
0
0
1
1
2
0
2
1
1
2
0
1
0
2
1
0
1
2
0
2
2
1
2
1
1
1
1
1
0
1
1
1
1
0
1
0
1
1
2
1
2
2
2
1
1
0
2
2
1
1
1
0
2
1
1
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
1
1
1
0
1
2
1
2
1
1
0
1
2
1
2
1
1
0
1
0
1
1
0
0
2
1
0
2
0
1
1
2
2
0
1
0
2
2
2
0
0
1
1
1
1
1
0
2
0
0
0
1
5
1
2
2
0
1
2
0
0
2
1
1
1
1
0
1
0
1
2
0
1
1
1
0
0
2
0
1
1
0
1
1
3
1
0
1
1
1
2
1
2
0
1
1
1
1
1
2
0
0
1
2
1
0
1
0
0
1
1
1
1
2
1
0
0
2
0
4
1
1
2
2
1
1
2
1
2
1
2
1
0
1
1
2
0
0
1
0
1
0
1
1
2
2
1
0
1
0
0
1
0
1
1
0
1
0
1
0
2
1
2
1
2
1
1
0
2
1
1
2
1
1
1
2
1
1
2
0
0
2
1
1
1
1
1
1
0
1
2
1
2
3
2
2
2
1
0
2
2
1
2
2
0
1
2
0
1
1
2
0
1
1
1
1
1
1
1
0
1
2
2
1
1
1
0
1
0
0
0
1
0
2
0
0
0
1
1
0
0
2
0
0
1
1
1
1
2
0
1
1
0
0
2
1
0
2
1
1
0
1
2
0
2
1
1
0
1
0
1
1
1
1
1
0
1
1
1
2
0
0
2
1
2
0
1
1
0
0
4
0
1
1
1
1
2
1
0
0
1
1
1
1
2
1
2
1
0
1
0
0
2
0
0
1
2
0
2
0
0
1
2
0
1
0
1
2
0
1
1
0
0
1
0
1
1
0
2
1
2
1
0
2
1
2
1
1
0
1
2
0
1
1
1
2
1
2
0
2
1
1
1
1
0
1
2
1
1
0
1
2
1
0
1
2
2
2
2
0
1
1
1
1
0
2
2
1
1
2
1
2
1
2
0
1
2
2
2
2
0
0
1
4
1
1
1
1
1
1
2
1
1
0
1
0
0
1
1
0
2
0
2
2
1
1
1
2
1
2
0
2
0
0
2
1
1
0
0
0
1
1
1
1
1
0
1
2
1
2
1
2
2
1
1
2
0
1
1
1
1
1
1
1
2
0
1
2
1
1
2
1
1
1
1
3
0
3
1
1
1
2
1
0
0
1
1
2
2
0
2
0
1
3
0
2
0
0
2
1
1
1
2
2
0
0
1
2
1
1
2
0
1
0
1
1
1
2
0
0
0
0
0
1
1
1
0
0
1
0
0
1
0
1
2
1
1
1
2
1
2
0
0
0
1
1
1
1
5
0
2
1
2
1
0
1
1
0
2
1
0
2
2
1
1
0
2
0
2
1
2
1
0
1
1
2
2
1
0
1
0
2
1
1
1
1
0
1
1
0
1
0
0
0
1
2
2
0
1
1
2
0
1
2
2
0
2
1
1
2
2
1
2
2
0
1
1
1
1
1
1
1
0
0
2
2
4
0
2
1
0
2
0
1
1
1
0
1
3
0
1
1
2
0
0
2
1
2
0
1
2
1
0
2
1
1
0
0
1
0
1
1
1
1
2
0
1
1
0
2
1
1
1
0
1
1
1
0
1
1
2
3
1
1
1
1
0
1
2
0
0
1
0
1
1
0
1
2
1
0
1
1
1
1
1
2
0
1
0
2
1
1
2
1
2
1
0
1
2
1
2
1
1
0
1
0
1
0
1
1
1
0
0
1
0
1
0
1
1
1
1
0
2
1
0
0
1
0
0
0
1
1
2
1
0
2
1
1
0
2
1
1
1
1
1
1
1
1
2
0
3
0
1
1
1
1
0
1
1
2
1
1
1
2
1
0
0
1
1
1
0
1
1
3
1
0
0
1
0
1
2
1
1
1
1
0
0
0
1
2
0
2
1
0
1
1
0
1
2
1
1
1
0
1
0
1
0
2
0
2
0
1
1
1
1
2
0
0
1
0
1
1
0
2
0
1
1
1
1
2
2
1
1
1
1
2
2
1
1
0
1
0
2
1
1
0
1
0
3
0
1
1
1
0
1
0
1
1
2
2
0
1
1
2
0
0
1
2
1
2
1
2
2
1
2
1
2
2
0
2
2
1
2
2
2
1
0
2
0
1
2
0
1
1
0
1
1
1
1
1
1
1
2
2
1
0
2
2
1
1
1
1
0
2
1
0
1
0
1
0
0
0
0
1
2
1
1
1
2
1
2
1
1
1
2
1
2
0
2
1
1
1
1
1
1
1
1
1
0
1
1
1
0
2
2
3
0
0
1
1
1
0
2
1
1
1
1
1
0
2
1
0
1
2
1
0
0
0
1
0
1
2
0
1
1
1
0
0
1
1
1
1
1
0
1
0
1
1
1
1
1
1
1
1
3
1
1
1
0
0
0
1
1
2
1
1
5
1
1
2
1
2
1
0
0
1
1
2
0
2
1
0
1
0
1
2
0
2
1
2
1
1
1
1
1
2
1
2
1
1
1
0
0
0
0
2
0
2
2
0
1
1
2
1
1
1
2
1
1
0
1
1
0
0
2
2
1
1
0
1
1
1
1
1
0
0
1
1
2
1
1
2
1
0
2
0
2
1
3
1
1
0
0
2
0
1
1
1
1
2
0
2
0
2
1
1
1
2
0
2
0
0
2
0
1
1
2
2
1
0
0
1
1
1
1
1
0
0
2
1
2
1
1
1
1
1
0
1
1
0
2
1
1
2
1
1
1
2
1
0
0
2
2
1
2
2
1
0
2
1
0
1
2
1
2
1
1
1
1
1
3
1
1
0
0
1
2
2
2
1
1
2
1
1
1
1
1
1
1
1
2
0
1
1
1
1
0
0
1
0
0
1
1
1
2
2
2
1
1
0
0
1
1
1
1
2
0
1
0
1
0
0
1
0
2
2
0
1
2
1
0
2
0
1
1
0
0
0
1
1
0
1
2
0
1
0
1
0
1
2
1
1
2
2
1
2
1
1
1
5
0
1
1
1
1
2
1
1
2
2
2
2
0
3
1
0
1
2
1
1
1
2
2
1
0
1
1
1
1
0
1
1
0
0
2
2
0
1
2
1
2
2
0
0
0
1
1
2
1
1
1
1
0
0
1
0
0
1
0
1
1
0
2
1
2
1
1
2
2
1
0
1
1
1
4
3
3
1
1
0
1
2
1
1
2
0
0
2
0
1
1
1
0
0
2
1
1
1
1
0
1
0
1
1
1
2
1
0
1
1
1
2
1
2
1
1
0
2
1
1
1
2
1
2
1
1
1
1
0
1
2
1
1
2
1
1
2
0
1
1
0
0
1
0
1
0
1
0
0
1
1
2
1
0
1
1
1
3
0
0
1
0
0
1
0
1
1
2
1
1
2
1
1
1
2
1
2
1
1
2
0
2
0
1
0
2
1
1
1
1
1
2
2
1
0
0
0
1
1
1
1
1
1
1
0
0
1
1
1
1
1
1
1
2
1
0
1
1
0
1
1
1
0
1
1
1
2
0
2
0
1
1
1
2
1
1
1
1
2
1
0
2
2
3
2
1
2
1
2
1
0
1
1
0
2
1
2
1
2
2
0
1
1
1
2
2
1
2
0
2
1
2
0
2
1
2
2
0
0
1
1
0
0
1
1
1
0
2
1
2
1
1
0
1
1
0
0
1
0
1
1
1
1
1
0
1
2
1
1
1
2
1
2
1
1
1
2
1
0
2
2
1
2
0
0
1
0
1
0
0
1
1
2
1
0
1
0
1
1
0
2
1
1
1
1
1
1
0
2
1
2
0
1
0
1
0
1
2
1
1
1
2
1
1
0
2
1
2
1
2
1
1
0
1
2
0
0
1
2
2
1
2
1
1
0
1
2
1
0
1
0
2
2
2
1
1
2
1
2
1
0
0
0
2
0
2
1
1
0
2
1
2
0
1
0
1
2
0
1
2
1
1
0
1
2
1
1
1
0
1
1
2
0
1
1
2
1
1
0
1
1
1
0
2
2
1
1
2
0
1
2
1
0
2
2
1
2
2
1
0
2
0
0
2
1
1
1
1
2
1
2
1
1
0
0
0
1
1
0
0
1
1
2
0
0
2
0
1
1
0
2
1
0
1
2
0
2
2
1
1
1
0
0
2
0
2
0
0
1
1
0
1
1
2
0
1
1
0
1
1
1
0
1
3
0
0
2
1
1
1
1
1
1
1
1
1
1
1
0
2
1
1
1
1
2
1
0
2
1
2
1
2
1
1
1
0
1
1
2
1
0
0
1
2
1
0
2
2
0
1
1
1
2
0
0
0
3
1
1
1
1
1
2
3
1
2
1
0
1
2
2
2
2
0
1
0
1
0
1
3
1
1
0
0
1
1
1
0
0
1
2
1
0
1
1
1
0
1
1
0
0
0
0
1
0
2
1
0
1
2
1
0
1
1
0
0
2
2
1
1
1
2
1
1
1
1
1
0
0
1
1
2
2
2
1
0
2
1
1
1
0
1
1
1
0
1
1
0
2
1
0
1
2
1
2
1
1
1
2
2
1
1
1
1
0
0
1
1
1
1
1
1
2
1
1
0
1
2
0
0
1
1
1
0
1
0
0
1
1
1
1
1
2
2
2
2
2
1
2
1
2
0
0
1
1
2
2
0
1
2
2
0
2
1
0
0
1
0
2
1
1
0
1
2
1
1
1
1
1
2
1
2
0
0
1
0
0
1
2
1
0
2
2
2
1
1
1
0
1
2
0
0
1
1
2
1
1
1
2
1
0
1
1
1
1
1
1
1
0
1
1
0
0
2
0
1
1
1
1
2
2
1
1
0
1
0
1
1
1
0
1
2
1
2
2
1
1
1
1
1
0
2
1
0
2
2
2
2
2
1
1
1
0
1
0
1
2
0
1
0
1
1
1
2
1
1
1
1
2
2
2
1
1
1
1
1
2
2
0
1
1
1
0
1
1
0
0
1
1
0
1
1
0
1
1
1
1
2
0
1
0
2
1
1
1
0
0
2
1
1
0
1
1
0
0
1
1
1
2
0
0
1
2
1
2
1
1
1
1
2
1
2
1
1
1
1
2
1
1
1
2
1
1
1
7
2
1
2
0
0
1
3
3
1
1
2
0
0
1
2
2
1
1
4
1
1
1
2
0
2
0
1
2
0
1
0
1
1
1
0
1
2
1
1
1
1
1
1
1
0
1
1
1
1
1
1
0
1
1
1
2
1
0
2
1
1
1
0
1
1
1
1
1
0
1
2
2
1
1
2
2
1
0
1
1
1
1
3
1
0
1
2
0
1
1
0
1
1
1
0
1
1
1
0
2
2
1
0
2
2
1
1
1
2
2
1
1
1
1
0
2
2
2
0
1
1
2
1
2
1
2
1
0
1
0
1
1
0
1
2
0
1
0
1
0
2
1
2
2
1
0
1
1
1
1
2
0
1
1
1
3
0
1
0
1
0
1
2
2
1
1
1
1
0
1
2
0
0
1
2
1
1
0
1
1
1
0
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
3
1
1
1
0
2
2
2
0
0
0
1
1
1
2
1
0
0
1
1
2
0
1
0
1
3
0
0
1
2
2
1
0
0
0
2
1
1
2
2
0
1
0
1
2
0
2
1
1
2
0
4
1
1
2
0
0
2
1
0
1
0
1
0
1
0
2
0
0
2
2
1
1
1
1
2
1
1
1
0
1
0
1
2
0
2
1
2
2
1
1
1
1
2
1
2
2
2
1
0
1
1
1
1
1
1
1
1
2
1
1
2
0
1
2
1
0
1
2
1
2
0
1
2
1
2
0
0
2
1
0
0
1
0
3
2
2
0
2
2
1
1
0
2
0
1
2
1
0
0
0
0
0
2
1
2
1
0
1
0
1
0
1
0
0
1
1
1
0
1
2
1
0
0
1
0
0
0
1
2
1
1
1
1
0
2
1
1
0
3
1
1
0
1
1
1
1
2
2
2
1
1
1
0
1
2
0
1
0
1
1
1
1
1
1
0
1
1
1
2
1
0
1
1
1
1
1
0
2
2
0
1
1
1
0
0
1
1
0
1
2
1
0
1
2
0
2
1
1
1
2
0
1
0
1
1
0
2
1
1
1
1
1
2
3
2
0
1
1
0
3
2
1
2
2
2
1
1
0
2
1
1
1
0
0
0
1
1
2
0
2
1
1
1
2
0
1
1
1
0
1
1
1
1
1
1
0
1
0
2
1
2
1
2
1
1
0
2
1
1
2
1
1
1
0
1
1
2
1
1
1
0
1
2
1
2
1
1
1
2
1
1
1
0
1
2
0
1
0
2
2
2
1
0
1
1
1
0
1
0
1
0
5
0
0
0
2
1
1
0
2
2
1
0
0
1
0
1
0
1
1
0
1
2
2
2
1
1
1
2
0
0
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
0
2
1
0
2
0
0
0
1
1
2
0
1
1
2
2
2
1
0
1
1
2
0
2
1
0
1
0
3
1
1
1
1
0
0
1
2
2
2
1
1
1
0
1
2
2
1
2
2
0
0
1
2
2
2
1
1
0
1
0
1
1
1
2
1
2
0
2
1
2
1
1
1
1
1
0
0
1
0
1
2
2
0
0
1
0
0
1
2
1
1
0
1
2
1
1
1
0
1
2
1
2
1
0
1
1
2
1
2
0
1
1
1
0
0
2
1
1
2
0
2
3
1
1
2
1
1
0
2
0
1
2
2
2
2
2
1
2
2
2
0
1
0
1
1
1
1
1
1
2
0
2
1
0
2
1
0
0
0
0
1
1
0
1
1
1
1
1
1
0
1
2
0
2
0
1
0
2
0
0
0
0
2
1
0
2
1
1
1
0
2
1
1
0
1
2
2
0
0
0
0
1
1
1
1
0
0
1
0
0
1
1
0
2
2
0
1
1
0
0
2
0
0
1
1
1
0
1
1
0
1
1
0
1
1
0
2
2
1
2
1
1
2
0
1
2
1
0
1
2
1
2
1
0
0
1
0
1
1
0
2
0
0
0
1
1
0
1
1
1
2
1
0
1
0
1
0
1
1
1
0
1
2
3
1
1
1
1
1
1
1
0
1
2
2
2
3
1
1
1
2
1
1
1
2
1
2
1
0
1
1
0
0
1
2
1
1
1
1
2
0
0
1
1
0
1
2
1
2
1
1
2
2
2
0
1
0
0
1
0
1
0
1
1
1
2
0
0
2
0
1
2
0
1
1
1
2
2
0
1
1
1
0
2
1
1
1
2
2
1
1
0
2
2
1
0
1
2
3
2
1
1
1
1
2
0
1
2
2
1
1
0
2
2
1
0
1
0
0
1
1
0
2
1
1
1
1
2
1
2
1
1
0
0
2
1
0
0
1
0
1
1
0
0
0
2
1
1
1
0
0
1
0
1
0
2
1
1
1
1
0
2
1
0
2
0
1
1
1
0
1
0
1
0
1
1
1
2
0
2
2
1
1
0
0
0
2
1
1
2
1
1
1
1
0
1
1
2
2
1
1
1
0
1
1
1
3
1
0
0
1
2
1
1
0
1
1
1
3
0
1
1
1
2
0
1
0
0
1
1
1
0
1
0
1
0
2
1
2
0
1
0
2
0
1
1
1
2
2
0
0
1
2
2
2
2
1
1
0
1
1
0
1
1
1
1
2
1
1
1
1
1
1
0
1
1
1
1
1
2
0
2
1
2
1
1
1
1
1
1
0
0
0
0
0
1
0
1
0
0
2
1
0
1
0
2
1
1
1
1
1
1
0
1
1
1
0
0
2
1
2
2
4
2
1
1
1
1
1
2
0
2
1
1
1
1
1
1
1
1
1
1
0
1
0
0
2
1
1
1
0
1
1
1
1
0
0
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
3
2
1
1
2
1
1
1
1
0
1
0
1
1
0
1
2
1
1
1
0
2
2
2
0
1
2
0
0
1
1
1
0
1
1
1
0
0
2
1
2
1
1
1
2
1
0
1
2
1
0
1
1
2
0
2
0
2
2
2
1
1
2
1
2
2
0
1
1
0
2
1
2
2
2
1
0
2
0
2
1
1
1
2
1
1
2
0
1
1
1
2
1
0
0
1
2
2
1
2
0
2
0
2
1
1
1
0
2
3
2
2
2
0
2
1
1
1
1
2
1
1
2
0
1
1
1
1
2
2
0
1
0
1
1
0
1
1
0
1
1
1
0
1
2
1
1
1
1
1
2
0
1
0
0
3
1
1
3
0
1
1
0
0
6
1
1
2
1
1
2
0
1
0
2
1
0
1
1
0
1
1
2
2
1
0
1
1
1
2
0
2
1
1
1
2
1
2
0
2
1
0
1
0
1
0
3
1
0
2
1
2
1
1
1
1
0
1
1
1
2
1
1
1
0
0
0
1
1
0
2
1
1
1
2
0
1
2
1
2
2
1
1
1
0
1
0
1
1
0
0
1
1
3
2
1
1
0
0
1
2
2
4
0
0
2
2
1
1
1
2
1
1
2
0
0
1
0
1
0
0
1
1
1
2
2
1
2
1
1
0
1
1
1
1
1
1
0
1
2
1
2
1
1
0
1
1
2
2
0
1
1
1
1
2
2
0
1
1
0
0
1
1
1
1
1
2
1
1
1
0
2
1
0
1
2
1
0
2
1
0
3
0
1
0
1
0
2
1
1
2
1
2
2
1
1
1
1
2
1
2
2
0
1
1
1
1
1
1
0
0
0
1
0
1
2
1
3
1
0
0
2
2
1
0
2
1
3
0
1
2
1
1
1
2
2
1
1
1
2
1
1
1
2
2
1
0
0
1
1
0
1
1
1
1
3
1
1
2
0
1
1
1
1
1
1
0
0
2
2
0
2
1
0
0
1
1
0
1
0
1
0
2
1
1
1
1
1
1
0
1
2
0
1
2
0
1
2
1
1
1
1
0
2
0
2
1
2
1
1
0
1
2
2
2
0
0
1
1
1
0
2
1
1
1
1
1
2
0
1
1
0
1
0
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
0
1
1
2
1
1
1
0
1
1
1
1
1
1
0
2
2
2
1
1
2
1
2
2
2
1
1
2
1
1
2
1
2
2
1
1
1
2
0
1
0
1
2
1
1
1
2
0
0
0
0
2
1
1
1
2
2
0
2
1
1
0
1
0
0
0
1
2
1
2
1
2
0
2
1
1
1
1
0
2
2
0
1
2
1
2
1
0
1
2
1
1
0
1
0
0
2
2
1
0
1
2
0
0
1
2
1
2
1
1
1
1
0
1
1
0
0
1
2
1
1
1
1
0
2
1
0
1
0
5
1
2
2
1
0
0
2
1
1
1
0
2
0
1
1
1
1
1
0
1
1
1
2
1
0
1
1
0
2
1
0
2
2
2
0
0
1
1
3
2
1
2
1
1
1
2
0
1
0
2
0
1
1
0
1
2
0
0
2
1
1
1
0
2
1
2
1
1
0
0
1
1
1
1
1
0
0
1
1
0
1
0
1
2
1
2
1
1
2
1
1
2
0
0
1
0
1
2
1
2
1
1
1
1
1
1
0
2
1
2
0
1
2
0
2
1
1
1
0
0
0
1
2
1
2
2
1
1
1
0
0
0
1
1
1
1
2
0
1
2
2
1
1
1
0
1
1
1
0
2
1
1
1
1
2
1
2
1
2
2
1
1
1
1
1
1
0
1
1
2
1
1
0
1
1
2
1
2
1
2
1
1
0
2
2
2
1
0
1
3
1
1
0
2
0
0
2
2
0
1
0
2
2
2
2
0
1
2
0
0
1
1
2
1
0
0
0
2
1
0
1
1
0
2
1
2
1
0
2
1
0
0
1
1
2
2
1
1
0
1
0
0
0
1
0
2
1
1
1
1
1
1
1
1
0
2
1
2
1
0
1
0
0
0
1
2
1
0
1
1
1
0
1
1
1
1
2
0
0
1
2
0
1
1
2
1
1
0
1
2
0
1
1
1
0
1
2
2
0
0
1
1
1
0
2
0
1
1
2
2
1
0
2
1
2
1
1
1
1
1
0
0
2
1
1
1
1
0
1
1
0
1
1
1
1
1
0
2
1
2
1
0
1
0
1
1
2
1
0
2
1
1
0
1
1
2
0
2
1
1
1
1
0
1
1
1
2
1
2
0
1
1
1
1
2
1
2
0
1
0
2
0
1
1
1
1
1
1
1
0
1
1
2
1
1
1
0
0
1
0
1
0
1
0
2
1
0
0
1
2
2
2
0
1
1
2
0
2
2
2
0
1
2
2
2
0
0
2
2
1
1
0
1
1
0
1
2
1
2
1
1
0
0
1
1
0
1
2
1
1
2
1
2
5
0
2
1
2
1
1
1
1
0
2
2
1
2
1
2
0
2
1
1
0
1
2
0
0
0
0
0
0
0
3
2
1
1
0
1
2
2
2
1
2
0
1
2
2
1
1
1
1
1
1
0
1
2
2
2
1
0
1
1
0
2
2
2
0
1
2
2
1
0
1
2
2
2
1
0
2
2
2
0
1
1
0
0
0
1
2
2
0
2
2
0
2
2
2
1
0
1
0
1
0
1
1
1
2
0
2
0
2
1
0
1
0
0
0
1
2
1
1
1
0
1
1
0
1
1
0
1
0
2
1
0
1
1
2
1
2
1
0
1
1
0
0
1
1
2
2
1
1
1
1
2
1
2
1
2
1
0
2
1
0
1
1
2
2
0
1
2
0
1
1
0
2
1
1
1
0
1
1
1
2
0
1
1
1
1
1
1
0
2
1
1
1
1
2
0
1
1
2
0
2
2
1
1
1
2
2
2
1
2
2
2
1
1
2
1
0
2
1
1
2
0
1
1
1
0
2
1
0
0
1
0
0
1
2
1
1
0
2
1
0
2
1
1
1
1
5
1
1
0
1
0
0
1
1
1
1
0
1
1
1
0
1
2
1
0
0
1
3
2
2
2
1
1
1
1
1
0
2
1
2
0
0
2
0
2
0
0
3
2
1
0
1
1
0
1
1
0
1
1
1
1
1
0
2
2
2
1
0
2
1
0
1
1
1
2
2
1
1
1
1
2
1
1
1
0
2
1
1
1
2
1
0
0
3
1
1
1
0
2
2
1
2
2
0
1
1
1
1
1
4
1
1
2
1
1
2
2
2
0
1
2
1
0
1
2
1
1
0
1
0
0
1
2
2
2
2
2
1
1
0
1
2
0
3
1
2
1
2
2
1
1
1
1
0
1
1
0
1
1
2
1
1
1
1
0
0
1
1
0
1
2
0
3
1
1
1
1
1
0
0
1
2
1
0
1
1
2
1
1
1
1
1
1
1
2
2
1
1
0
1
1
1
2
0
1
2
0
1
2
2
2
2
1
1
2
1
2
1
2
0
0
1
0
0
1
1
2
1
2
2
0
0
2
0
2
1
1
1
0
1
2
0
2
2
2
1
1
1
1
1
1
1
1
2
0
1
1
1
0
2
0
1
1
2
0
1
2
1
2
0
1
1
2
2
1
1
1
2
0
2
0
1
1
1
2
1
1
0
0
1
0
1
1
2
0
1
0
1
1
2
1
1
2
1
3
2
0
0
1
0
0
1
1
0
2
1
0
2
1
0
1
0
0
2
2
1
1
1
1
0
1
1
1
2
1
2
1
1
0
1
0
0
2
1
1
2
1
0
0
1
0
1
0
1
1
1
1
0
0
1
1
1
0
0
0
1
0
2
1
0
0
1
0
1
1
1
0
1
1
0
1
1
1
1
2
1
1
0
0
1
1
0
1
0
0
1
1
1
0
2
0
0
1
1
1
1
1
2
2
0
2
0
2
0
1
2
0
1
1
2
1
1
1
2
1
0
2
1
1
1
1
0
1
2
2
0
0
1
1
1
1
1
0
2
1
1
2
0
0
1
2
0
1
1
0
1
1
1
0
2
1
0
1
1
2
0
2
1
2
1
0
2
1
1
0
0
1
0
1
2
1
2
1
1
1
0
1
1
2
0
2
1
2
0
1
0
1
0
1
0
0
1
0
0
0
2
1
1
2
1
1
1
0
0
0
2
1
2
1
3
1
2
1
0
1
0
2
2
1
2
1
0
2
1
0
0
0
0
0
1
0
1
2
2
2
1
1
2
1
0
0
2
1
1
1
1
2
1
2
2
1
2
0
2
0
2
0
0
2
1
0
0
2
1
2
1
2
1
1
1
1
1
1
1
1
0
2
1
1
0
0
1
1
0
2
1
0
1
1
2
0
2
0
0
1
2
0
1
1
1
0
2
1
1
1
0
2
2
1
0
1
0
1
0
0
1
1
0
1
1
1
0
0
1
0
1
1
1
1
1
1
0
0
1
1
0
1
2
1
1
2
1
0
2
0
0
2
0
2
1
1
2
0
0
1
0
1
2
2
0
0
0
1
1
1
2
0
2
1
1
1
0
2
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
2
0
1
2
1
1
1
2
2
2
1
1
1
1
0
1
1
1
0
2
0
1
2
1
2
2
1
2
1
1
1
2
1
1
1
0
0
1
1
0
2
0
0
1
2
0
2
0
0
2
0
0
1
1
0
1
1
1
1
1
2
0
0
1
2
1
1
0
2
0
0
0
0
0
0
1
1
1
0
0
1
0
1
1
0
0
1
0
1
1
2
2
1
0
1
0
1
0
1
1
0
1
2
1
1
0
1
1
0
1
0
3
1
0
0
2
1
1
1
2
0
1
0
0
1
0
2
0
3
2
1
0
2
2
1
0
1
2
0
0
0
1
1
2
1
0
0
1
0
2
1
1
2
1
0
0
2
0
0
2
2
2
1
0
0
1
1
1
1
1
0
0
1
1
1
0
0
2
0
3
1
1
2
2
0
2
1
1
1
1
1
1
1
0
1
2
1
0
0
1
1
2
1
1
2
3
0
1
0
1
0
1
3
2
1
1
1
3
2
0
1
1
1
0
2
0
1
0
0
1
1
1
1
1
1
0
1
2
1
1
1
1
1
1
1
2
0
2
1
1
1
0
0
1
1
1
0
1
1
0
1
2
0
0
0
1
0
2
2
2
1
0
1
0
1
1
1
0
2
1
2
1
2
1
1
1
1
1
2
0
2
2
0
1
2
1
2
1
3
1
2
1
0
1
1
1
1
1
2
2
0
1
1
1
0
1
1
0
0
2
0
2
0
1
1
1
1
1
0
1
1
0
1
1
0
1
1
1
0
0
0
1
0
1
1
0
0
1
1
2
0
1
0
1
2
2
1
1
1
0
2
1
1
1
1
1
2
2
1
2
1
0
0
1
1
2
1
1
1
1
1
1
0
1
2
1
0
1
1
2
1
1
1
1
1
0
0
2
1
1
1
1
0
1
1
1
0
1
0
1
0
0
2
1
0
1
0
2
1
1
0
1
1
1
2
0
2
1
2
1
1
1
0
2
2
0
2
1
0
1
0
0
1
0
0
1
0
2
1
1
0
0
2
2
0
1
0
2
1
1
0
2
1
1
2
1
1
1
0
2
1
0
3
2
2
1
2
0
1
0
0
2
1
1
0
0
2
1
0
1
1
2
2
0
1
1
0
0
1
0
1
1
2
0
0
2
1
0
1
2
1
1
0
1
1
1
1
1
0
2
1
1
1
1
1
0
2
0
1
0
1
1
0
2
1
1
2
2
0
1
2
2
0
0
1
1
1
1
0
1
1
0
2
1
0
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
0
0
2
1
1
1
1
2
0
2
2
1
1
0
0
2
0
1
0
1
0
2
1
1
1
0
0
2
2
1
1
1
1
1
1
0
0
3
0
0
1
1
2
1
0
0
0
0
0
2
1
2
0
1
1
1
1
1
1
1
1
2
2
2
1
1
2
1
0
0
1
0
1
1
0
0
2
1
0
1
0
2
1
1
2
2
1
2
0
0
2
2
1
1
1
0
0
0
1
1
1
0
0
2
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
0
0
0
1
1
1
0
5
2
0
0
2
0
2
1
1
1
2
0
0
1
0
1
1
2
0
1
1
1
1
1
0
1
2
1
1
1
1
1
1
2
1
1
1
0
1
2
1
0
1
2
1
2
0
1
1
1
1
2
1
0
2
1
2
1
0
0
2
0
2
3
1
0
0
1
1
1
1
1
1
2
1
0
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
2
1
1
0
1
1
0
2
1
1
1
1
2
2
2
1
1
1
2
1
2
0
1
0
0
1
1
1
2
2
1
2
2
1
2
2
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
1
2
0
0
0
0
0
1
0
2
1
2
1
1
1
1
0
1
1
1
1
0
1
1
2
0
0
2
0
1
0
0
1
1
0
0
1
0
1
2
2
1
0
1
1
1
1
1
0
1
2
1
1
1
1
1
0
1
0
3
2
2
1
2
1
0
1
1
1
0
0
2
1
1
1
0
2
2
0
1
0
1
0
1
2
0
1
1
0
2
2
1
1
1
2
1
0
1
1
1
2
1
1
1
0
2
1
1
2
1
1
1
0
1
1
1
1
1
0
1
1
1
1
2
1
2
1
3
1
1
0
1
0
0
2
2
1
1
2
0
1
2
0
1
2
0
1
1
1
1
2
1
0
1
2
1
1
1
1
1
1
1
2
2
2
1
1
1
0
2
2
0
2
1
0
1
1
0
0
2
0
1
1
4
1
0
2
0
0
1
0
2
1
1
2
0
1
1
0
0
1
1
2
0
1
1
1
1
1
1
1
1
2
0
1
2
1
0
1
2
2
0
1
1
0
1
0
2
1
0
2
0
1
1
1
1
1
0
0
1
0
1
1
1
0
0
0
1
1
2
1
0
1
0
0
1
2
0
1
0
2
1
2
1
1
1
0
1
0
1
0
2
0
1
2
2
1
0
0
1
2
2
2
1
1
1
1
0
0
1
1
1
2
1
1
0
1
1
2
2
0
1
1
1
0
0
1
0
0
2
1
1
0
0
1
1
2
0
2
2
2
1
2
1
0
2
1
0
1
0
1
2
0
1
2
1
2
1
1
1
1
2
1
2
2
2
1
1
2
1
0
2
0
1
1
1
2
2
1
2
0
0
1
2
2
2
0
1
1
1
1
2
1
1
2
1
0
1
2
1
0
1
1
0
1
1
2
1
1
0
1
1
0
1
1
1
0
0
1
1
3
2
0
1
1
1
0
2
0
1
0
1
1
1
0
1
2
0
1
2
1
2
1
0
0
1
1
1
1
2
1
3
1
1
0
0
0
2
1
0
1
1
1
0
0
1
1
0
1
1
0
0
1
0
1
0
1
0
0
1
2
0
1
0
0
0
2
1
2
2
1
2
2
1
1
1
1
0
0
0
1
2
1
2
0
0
1
1
0
1
0
2
2
1
1
0
0
1
1
2
1
1
1
1
0
1
0
0
1
2
0
1
0
1
0
0
0
1
1
1
1
1
1
1
0
1
2
2
0
2
1
1
1
1
1
1
2
1
0
2
1
0
0
1
1
2
2
1
2
2
0
1
0
0
1
0
1
2
0
1
1
1
2
1
1
1
1
0
1
0
1
1
1
1
1
0
1
2
2
1
2
0
2
2
1
1
1
0
1
0
1
0
2
1
1
2
3
2
0
2
1
0
1
0
0
1
1
1
1
1
1
1
0
1
1
2
2
0
0
1
1
1
1
0
0
1
0
1
2
0
2
1
0
0
2
0
3
1
0
1
1
2
2
2
1
0
2
1
0
2
0
1
1
0
0
1
2
2
1
0
1
1
1
1
1
1
1
2
2
1
1
0
2
0
1
1
1
1
1
0
1
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
0
1
1
1
0
1
2
0
2
1
1
1
1
1
0
0
1
2
1
1
2
1
2
2
1
0
1
1
1
1
1
2
1
2
1
1
0
0
1
1
1
1
0
2
1
0
2
1
0
0
0
2
2
1
2
1
2
2
1
2
0
1
0
1
1
0
2
1
3
1
2
1
0
2
2
0
0
1
0
1
1
1
0
1
2
2
2
0
2
2
0
1
1
1
1
2
1
1
1
1
1
2
0
2
2
1
1
2
2
0
1
2
0
1
1
1
1
0
1
1
0
0
1
1
0
0
2
0
2
1
2
1
1
1
1
3
2
1
1
1
2
0
1
1
2
1
0
1
1
0
1
1
0
1
1
0
1
2
2
1
1
1
1
2
1
0
0
0
2
0
1
1
0
1
1
1
1
0
2
0
1
1
2
1
1
0
0
2
1
0
1
1
1
2
1
1
2
0
1
1
1
1
2
2
2
1
1
1
1
1
2
1
0
1
1
1
2
1
1
1
1
4
2
2
0
0
0
0
1
1
0
1
1
1
1
1
1
0
1
0
2
2
1
0
2
1
1
0
1
1
2
2
2
1
1
1
1
2
1
0
1
0
1
1
1
1
1
1
1
2
1
2
1
0
0
1
0
1
0
2
1
2
2
1
2
1
0
1
0
1
0
0
0
0
2
0
1
1
1
1
0
2
1
1
0
0
1
0
1
2
0
2
2
2
1
1
1
2
0
1
1
4
1
2
1
0
1
0
0
0
2
2
1
2
3
2
1
1
0
1
2
0
2
1
2
2
0
1
2
4
1
1
2
1
0
0
0
2
1
1
1
0
2
1
2
2
0
0
1
1
1
1
1
1
1
0
1
1
2
2
0
1
1
2
3
0
1
0
1
1
2
2
0
1
1
0
1
1
1
2
0
1
2
1
0
1
2
1
2
1
1
1
2
0
1
1
2
0
2
0
1
0
2
1
0
2
1
1
1
0
1
0
0
2
1
0
1
0
1
1
2
2
2
2
1
1
1
2
1
2
3
0
1
2
1
1
1
1
1
1
0
1
2
1
0
5
0
1
1
1
2
3
1
0
0
1
1
2
1
2
0
1
1
0
1
1
1
1
1
0
2
1
4
1
2
1
0
0
1
0
2
1
2
2
1
2
1
1
1
0
1
1
1
1
0
2
1
1
1
2
1
1
0
0
1
1
1
1
2
1
4
1
1
0
1
0
2
1
3
0
0
0
0
0
0
1
2
1
0
2
0
2
1
2
2
1
1
1
0
1
2
2
1
0
2
1
2
1
1
1
1
1
1
0
1
2
2
1
2
0
2
1
0
2
1
1
0
1
2
2
0
0
0
1
2
0
1
1
1
1
1
1
1
1
1
2
0
0
0
1
0
2
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
0
1
0
1
1
2
0
1
2
2
2
2
1
1
0
1
0
2
1
0
1
1
1
1
0
2
2
1
1
0
1
1
1
0
2
1
2
2
0
1
1
1
1
0
1
1
1
0
1
1
1
1
0
1
1
2
2
1
0
2
1
2
1
0
0
2
0
1
1
0
1
1
1
0
2
0
2
1
1
1
1
0
1
1
1
1
0
1
2
1
0
1
1
0
1
1
1
0
1
1
1
0
0
1
2
1
2
1
0
2
0
1
2
1
1
0
1
0
1
1
1
0
0
2
1
1
2
1
2
1
0
1
1
1
1
1
0
2
1
2
1
1
1
2
0
1
0
1
0
0
1
1
2
2
1
2
0
1
1
1
2
1
0
0
1
2
5
0
1
1
0
0
1
1
1
1
1
2
0
2
1
2
0
2
2
1
2
1
0
0
0
1
0
1
0
1
1
1
2
1
1
1
1
1
2
0
1
1
1
1
0
1
0
0
0
1
2
1
1
0
1
0
0
1
2
1
2
0
1
0
1
1
2
2
0
0
2
1
2
0
3
0
2
2
1
2
2
1
1
2
1
1
1
1
0
0
1
1
0
0
1
1
1
2
1
1
1
0
1
2
1
1
1
2
2
0
0
1
1
1
2
1
1
0
1
1
1
0
1
0
0
1
2
1
1
0
0
1
1
1
1
1
1
1
0
0
0
1
1
3
1
1
1
1
2
0
1
1
1
1
1
1
2
1
1
1
1
2
0
2
1
1
1
1
1
2
2
1
2
1
1
1
2
1
0
1
0
1
3
1
1
1
1
2
1
1
2
1
0
1
1
0
3
1
1
2
1
0
0
0
0
2
1
0
0
0
2
1
0
2
0
0
2
1
1
1
1
0
2
2
2
1
1
0
0
2
1
1
2
1
0
1
1
1
1
2
1
0
2
0
1
0
1
1
2
1
1
1
0
1
1
2
0
1
1
0
2
2
1
1
0
1
2
2
1
3
1
1
0
2
2
0
1
0
2
1
1
0
2
1
2
2
2
1
2
1
1
0
0
2
1
2
2
0
1
0
2
1
1
1
1
1
0
1
3
2
1
1
1
0
1
1
1
0
2
1
0
2
2
0
1
1
2
2
0
2
1
1
0
1
1
0
0
1
1
1
2
1
0
2
1
1
1
0
2
1
0
1
1
1
2
1
1
2
1
1
0
1
1
0
1
0
1
2
2
2
1
1
0
2
1
1
0
1
2
1
2
1
0
0
1
0
0
1
1
1
0
1
0
0
0
1
0
1
1
0
1
1
1
1
1
2
0
0
1
1
2
1
1
2
2
1
1
1
1
2
1
0
1
1
2
1
2
1
1
1
2
1
1
1
1
1
0
2
2
0
1
1
1
2
2
1
1
1
0
2
0
2
0
2
1
0
2
1
0
0
0
1
0
1
0
2
0
1
1
2
2
2
2
0
0
2
2
1
2
2
1
2
2
2
2
1
2
1
0
1
1
2
1
1
1
1
2
1
1
0
2
1
0
0
2
1
2
0
0
1
1
1
0
0
1
2
2
2
1
0
0
1
2
1
2
2
1
2
1
2
2
2
1
1
2
1
1
1
2
0
1
1
0
1
0
1
2
0
2
1
0
1
1
1
2
1
1
2
0
0
1
2
1
1
1
0
1
2
1
1
1
2
1
0
2
2
0
2
1
1
1
2
1
1
2
1
2
2
0
1
0
2
1
0
0
1
0
1
1
1
0
2
1
2
1
0
1
2
1
0
1
1
1
2
1
1
0
1
1
0
0
1
0
2
1
1
1
1
0
1
1
0
2
0
1
1
1
1
1
1
1
2
2
1
1
1
1
1
0
3
1
0
2
0
1
1
2
0
0
2
0
1
1
2
1
0
1
1
1
1
1
1
0
1
1
0
1
1
1
1
4
0
1
2
1
0
1
1
0
1
0
0
1
0
0
1
2
2
1
1
2
1
0
1
2
1
0
2
2
1
1
2
1
2
1
1
0
1
0
1
0
0
0
0
1
1
0
0
2
2
1
1
1
1
1
2
3
1
0
0
2
2
1
2
2
1
0
0
0
2
1
2
2
2
1
0
0
0
2
0
2
1
1
3
1
1
1
1
2
2
1
2
1
1
1
0
1
1
1
0
0
1
0
1
1
2
2
1
2
1
1
2
1
0
0
2
1
2
1
2
1
1
0
1
0
1
2
1
1
1
1
0
2
1
0
1
1
1
0
2
1
1
2
1
1
0
1
2
1
1
0
1
2
0
2
2
1
1
2
1
0
2
2
0
1
1
1
0
2
0
1
1
0
2
1
1
2
1
2
0
1
0
1
2
1
1
1
2
3
2
2
0
1
2
1
1
1
2
1
1
0
0
1
2
0
2
2
1
2
1
0
0
0
0
1
0
2
1
2
1
0
2
0
0
1
3
2
2
3
1
1
0
0
1
1
1
1
1
1
0
1
0
1
0
0
1
1
1
2
0
1
0
1
1
0
1
0
1
1
0
1
1
1
1
1
0
0
1
2
1
1
0
0
2
1
0
0
1
0
2
1
2
0
1
1
1
2
1
0
1
0
0
0
1
1
1
2
1
2
1
0
0
1
1
2
1
1
0
0
1
2
2
2
0
0
1
2
2
0
1
0
1
1
1
0
1
2
1
1
1
2
1
1
2
0
0
2
2
0
1
1
2
1
0
1
1
1
1
1
1
1
1
1
1
0
1
0
1
1
0
0
2
1
2
2
2
1
1
2
1
1
1
1
0
0
2
2
3
2
2
0
1
0
0
2
1
4
1
1
0
2
2
2
0
2
1
2
2
2
1
0
0
0
2
2
1
1
2
1
1
2
1
1
1
1
1
0
2
1
0
1
2
1
1
0
2
0
2
1
1
1
0
1
1
2
0
0
1
1
2
1
0
1
1
0
9
1
1
0
1
0
1
0
2
2
1
2
1
0
2
0
0
1
2
0
0
0
0
0
0
2
0
1
0
0
0
1
1
0
1
1
1
2
0
1
2
0
1
1
2
0
1
1
2
2
0
1
2
0
0
1
1
2
0
1
1
1
1
1
1
0
1
1
1
2
0
1
0
1
2
1
0
1
0
1
1
2
1
1
0
1
2
4
1
1
0
0
0
1
1
2
2
0
1
1
1
1
1
1
2
1
1
1
2
2
0
0
1
1
1
1
2
1
2
0
0
1
2
1
2
1
0
1
0
1
0
1
1
0
2
1
1
2
2
2
1
2
1
1
1
1
1
1
1
2
0
1
1
0
0
0
1
0
1
1
0
1
0
0
0
1
2
2
1
0
1
1
1
1
1
1
1
0
2
1
1
2
2
0
1
1
1
1
0
1
0
1
1
0
1
4
2
2
1
0
2
2
2
1
1
0
0
2
0
0
1
2
2
2
2
2
0
1
0
1
1
1
0
1
1
1
1
2
1
1
2
2
1
1
0
2
1
1
1
1
2
1
1
1
0
1
1
1
1
0
2
2
1
1
0
1
1
1
2
2
1
1
0
1
1
1
1
1
0
2
1
0
0
2
2
0
2
2
1
2
0
1
0
1
0
1
1
1
1
0
0
1
1
1
0
0
2
0
1
1
0
1
1
1
0
0
0
2
1
0
0
1
1
1
0
1
1
0
1
0
1
1
1
1
2
0
2
0
1
2
1
1
0
1
2
2
2
1
1
2
1
0
1
1
2
1
1
0
1
1
0
2
1
1
1
0
2
1
2
1
2
2
2
1
1
2
1
1
0
0
0
2
2
0
0
2
1
0
2
1
1
1
2
0
0
2
1
1
0
2
1
0
1
1
2
0
2
1
1
1
2
0
0
1
1
2
0
2
1
1
0
1
1
1
1
2
1
0
1
0
1
1
1
1
1
1
1
1
1
0
1
0
2
0
2
3
1
1
0
1
0
1
0
1
1
1
1
0
1
1
1
0
1
0
1
0
1
2
0
1
0
2
1
1
1
1
1
1
0
1
1
0
2
0
1
0
0
0
0
1
1
1
2
0
0
1
0
0
2
1
1
1
0
1
0
1
2
1
2
3
2
1
1
2
1
1
0
0
0
1
1
1
2
1
2
0
2
1
2
0
2
1
1
0
2
2
1
2
2
0
1
0
1
0
0
1
1
1
0
2
0
1
0
0
1
1
1
1
2
1
1
2
0
1
1
2
1
1
0
0
2
1
0
0
1
2
1
1
1
0
2
1
1
1
1
0
1
2
0
2
1
1
1
1
1
1
1
1
2
0
0
1
0
1
1
2
2
0
2
0
1
1
0
1
2
1
1
0
2
1
2
2
0
1
1
1
1
2
0
1
1
2
1
1
1
0
1
1
2
0
2
0
1
1
1
2
1
2
2
1
1
1
1
1
2
2
0
2
0
1
0
1
1
2
2
1
1
0
0
0
1
0
2
1
2
1
0
1
1
0
1
0
0
0
1
2
0
2
1
2
1
0
1
2
1
2
1
2
1
0
2
2
0
2
0
0
2
1
1
1
1
1
0
0
1
1
2
1
2
2
1
1
0
1
0
1
1
1
2
1
0
2
1
1
0
1
1
0
1
1
1
2
0
1
0
0
0
0
1
1
2
1
2
1
1
0
1
1
0
1
2
1
0
1
0
1
2
1
2
1
0
1
2
1
1
0
0
2
1
2
2
2
0
1
1
0
1
1
2
1
1
1
1
2
1
2
1
1
1
1
2
0
0
1
0
1
5
1
0
1
1
1
2
1
2
1
2
1
0
1
0
2
0
1
1
2
0
0
3
2
1
0
1
1
1
2
3
1
0
1
0
0
0
1
1
2
1
1
1
0
2
0
0
1
1
1
1
1
1
0
1
1
2
0
1
0
1
1
1
1
2
0
1
1
1
1
2
1
1
1
2
1
1
1
0
0
0
1
2
0
0
1
2
2
0
1
2
2
2
0
1
2
1
1
2
1
1
0
1
1
1
2
0
1
1
2
0
2
1
0
1
0
1
1
0
1
1
1
1
1
0
1
1
0
0
1
0
2
2
2
1
0
1
1
2
1
2
2
1
1
2
0
1
2
1
1
2
2
1
1
1
1
0
1
2
1
2
1
1
1
0
1
1
1
1
0
1
1
0
2
1
1
3
1
1
0
2
1
1
1
0
0
0
1
0
1
2
1
0
0
2
0
1
1
2
0
2
1
1
0
2
1
1
2
1
1
1
1
2
1
1
1
1
0
1
1
1
2
1
0
2
1
2
3
1
2
1
1
0
1
0
2
0
1
1
1
2
1
1
1
1
1
1
1
0
3
1
1
1
0
1
1
1
1
1
1
0
1
0
1
0
2
2
1
1
1
2
1
1
0
1
0
1
2
1
1
1
1
0
0
1
0
1
1
1
2
1
1
2
0
0
1
0
0
2
2
1
1
2
1
0
1
1
1
1
1
2
1
1
2
1
0
0
1
1
2
2
1
1
1
1
2
1
2
1
1
2
0
0
2
1
0
0
1
1
1
1
1
1
0
0
2
0
1
2
1
1
1
0
1
1
1
1
1
1
1
0
2
2
1
0
0
1
0
1
0
1
2
0
0
1
1
1
1
2
1
1
0
1
0
1
0
1
2
2
1
1
1
1
2
1
1
1
1
1
1
0
0
2
1
1
0
0
1
1
3
0
2
1
2
0
1
1
2
1
0
2
1
1
1
2
1
0
1
0
0
2
1
2
0
1
0
2
1
2
2
1
1
0
2
2
1
1
1
1
2
0
1
0
1
1
2
2
0
1
0
2
1
2
1
2
2
1
1
0
2
2
2
1
2
1
2
0
2
0
2
1
0
1
2
2
2
3
1
1
3
1
2
2
2
1
0
2
1
2
1
1
2
1
2
1
0
2
3
2
1
0
2
2
1
1
0
1
1
1
2
0
0
1
0
1
1
0
0
1
1
2
0
1
1
0
1
1
2
1
1
1
2
1
1
1
1
1
3
2
1
2
1
2
1
1
1
1
1
0
0
2
1
2
2
1
1
2
1
1
1
0
1
2
1
1
1
1
2
1
1
3
2
1
1
1
2
1
0
1
0
1
2
2
1
1
1
1
0
1
1
1
1
1
2
1
0
0
2
1
1
0
1
0
2
1
0
0
2
0
1
0
0
3
2
1
0
2
1
1
0
1
1
2
0
0
0
0
1
0
1
1
1
1
1
2
2
0
3
0
1
1
2
1
0
1
0
3
1
1
0
1
1
1
1
2
0
2
0
0
1
1
2
0
1
1
2
0
2
1
1
1
0
1
1
1
0
1
1
2
1
1
0
1
0
3
1
2
1
1
1
1
0
1
0
1
1
1
1
1
1
1
0
0
1
1
0
2
1
1
1
1
0
1
2
1
1
0
1
2
1
0
1
3
1
1
0
1
0
2
1
0
1
1
0
1
1
1
2
1
0
1
1
1
2
0
2
1
1
0
0
0
1
0
2
1
0
1
0
1
2
2
2
0
1
1
2
1
1
0
1
2
0
2
1
2
2
0
2
0
0
3
1
2
0
1
1
1
1
1
0
0
0
0
0
0
0
0
1
0
1
2
1
1
0
1
1
2
1
2
1
0
2
0
2
1
1
1
2
1
1
0
1
1
0
1
1
0
0
2
0
1
1
2
1
0
0
1
0
0
2
3
1
1
1
1
0
0
0
2
1
2
1
1
2
1
2
2
1
2
2
2
1
2
0
1
1
0
1
2
2
0
0
1
1
1
0
0
1
3
0
1
0
0
1
0
0
6
2
0
1
0
0
0
0
2
0
0
0
1
1
0
0
1
1
1
1
1
1
2
2
1
0
1
1
2
2
0
2
1
1
1
1
1
0
1
1
1
1
2
2
1
1
2
2
1
0
0
0
0
2
1
2
0
2
1
2
1
0
3
1
1
1
1
0
0
0
1
1
0
2
2
0
2
0
0
0
1
1
1
1
2
1
1
2
0
0
0
1
1
1
0
0
1
1
2
2
2
0
1
0
1
1
0
2
0
0
2
1
1
0
1
0
4
1
1
1
1
1
1
2
2
1
1
1
2
1
1
1
0
1
1
1
1
1
0
1
1
0
1
0
1
3
1
1
0
0
2
1
0
0
1
1
1
3
2
1
1
0
1
2
1
1
2
0
0
1
1
2
1
1
0
0
0
2
1
1
0
1
0
1
1
1
2
5
1
2
2
1
1
1
0
2
2
1
1
1
1
2
2
2
0
1
0
1
2
1
2
0
1
1
0
0
1
1
2
1
1
2
0
0
1
1
1
2
2
1
1
1
1
2
1
1
2
1
3
2
1
0
1
0
0
1
0
0
1
0
0
1
0
1
1
0
1
1
1
0
0
0
1
1
1
1
2
2
1
1
0
1
2
1
0
1
1
0
2
1
1
0
2
0
1
1
1
0
0
1
1
0
1
1
1
0
2
1
1
0
2
1
3
0
0
0
0
2
2
0
0
2
1
1
1
0
0
1
2
2
0
0
1
1
0
1
0
0
2
1
1
1
2
1
0
1
1
1
3
2
0
0
2
1
2
2
1
1
1
1
1
2
1
1
2
2
2
0
1
2
1
0
0
0
0
0
2
1
2
0
1
0
1
2
1
1
2
2
1
1
0
0
2
0
2
1
1
2
0
1
1
1
1
1
0
0
2
2
1
1
0
1
1
0
1
2
1
2
2
1
2
2
0
1
2
2
1
1
2
2
1
2
2
2
1
0
2
1
1
1
0
2
0
1
0
1
1
1
0
1
2
1
0
0
0
1
0
2
1
0
0
2
0
2
0
1
2
0
0
0
1
2
1
1
0
4
1
1
1
2
1
0
2
1
2
1
1
0
3
3
1
1
1
1
1
1
2
2
0
1
0
2
0
0
0
2
0
0
1
1
0
0
0
1
2
1
1
1
1
2
2
0
0
1
1
0
0
1
1
0
2
0
0
0
0
2
2
0
1
0
1
1
0
0
2
0
0
0
1
1
2
1
1
1
1
1
1
0
2
1
0
1
2
2
1
0
1
2
2
0
1
1
1
2
1
1
0
1
1
1
1
1
1
2
1
1
2
2
2
1
0
1
1
0
1
0
1
2
1
2
1
2
2
2
1
1
1
1
1
1
1
1
1
2
1
1
3
1
2
0
1
0
3
0
2
1
1
2
2
1
1
1
0
0
1
0
1
0
1
0
0
1
2
1
1
2
1
1
2
0
1
0
1
1
1
1
0
1
0
0
2
0
2
2
1
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
2
2
1
2
0
1
0
1
0
1
1
0
1
0
1
0
1
1
2
1
1
1
1
1
1
1
0
2
0
2
0
1
1
0
1
1
1
1
1
1
2
0
0
2
1
0
0
0
2
1
0
1
1
0
1
1
1
1
2
0
0
1
1
1
0
1
2
1
1
2
0
1
1
1
2
1
1
1
1
0
1
0
2
1
1
2
1
1
1
1
1
1
1
1
1
0
0
0
0
2
2
5
1
1
0
0
1
1
1
8
1
0
0
1
0
4
1
1
0
1
1
0
0
1
1
0
0
1
1
1
1
0
1
0
1
2
2
1
2
1
0
2
1
0
1
2
2
2
2
0
2
2
0
1
2
1
1
1
1
0
0
0
0
2
1
0
1
1
1
1
2
0
2
0
1
2
1
1
2
2
2
0
1
1
1
2
2
0
1
1
2
1
1
2
1
2
2
1
1
1
0
2
2
2
0
1
1
2
2
1
2
1
1
0
2
1
1
1
0
1
0
1
0
1
2
0
0
0
1
0
1
1
1
1
2
1
0
1
1
0
0
1
1
1
1
0
2
2
1
1
0
1
1
0
0
1
1
1
1
2
2
1
1
0
0
2
0
1
1
0
1
1
0
1
1
2
1
1
1
1
1
1
0
1
1
0
0
1
0
1
1
2
0
0
2
2
2
2
1
1
0
2
1
2
2
1
1
1
1
1
2
1
0
0
0
1
1
2
2
1
1
0
1
0
1
1
2
1
0
0
1
1
1
0
1
1
1
1
0
1
1
1
2
1
0
1
2
1
1
2
2
0
1
1
0
1
0
2
1
1
1
1
2
1
1
1
1
1
3
1
1
1
1
1
1
1
1
0
1
1
2
2
1
2
0
1
2
1
0
2
0
1
1
1
2
1
2
0
1
1
0
0
0
0
2
1
0
1
1
1
0
0
0
2
0
2
0
2
1
0
1
1
1
1
1
1
1
2
1
1
1
1
0
2
2
2
0
0
2
1
1
1
1
1
1
1
1
1
1
2
1
2
0
1
1
1
0
0
0
1
1
2
1
1
0
1
0
1
1
2
1
0
2
0
2
2
0
0
0
0
1
1
1
5
1
0
0
1
1
1
1
0
1
1
1
0
1
0
0
1
1
0
1
0
1
1
1
1
2
4
1
1
1
2
0
1
1
1
2
0
0
0
0
1
0
1
0
1
0
0
2
1
1
1
0
0
1
2
2
1
1
1
1
0
1
1
0
1
1
1
1
0
0
0
1
2
0
2
1
0
1
1
1
1
1
0
1
1
1
0
1
1
1
0
0
0
0
0
1
2
0
1
1
0
2
0
1
2
1
0
0
0
0
1
0
1
1
1
1
1
0
0
0
1
2
1
0
2
1
1
0
1
1
2
0
1
2
2
0
1
1
1
1
0
2
0
2
2
0
2
1
0
1
1
1
1
1
1
1
2
2
0
2
2
1
0
0
2
1
1
2
0
1
1
0
1
1
1
1
0
1
1
0
2
2
1
0
1
0
0
1
1
1
1
1
1
2
0
0
1
1
1
2
0
0
2
0
1
1
1
1
1
2
1
1
1
0
2
0
1
1
0
1
1
1
1
0
1
1
1
1
0
0
2
1
1
0
0
1
2
1
0
0
0
1
0
1
1
2
1
0
1
0
0
2
0
0
1
2
1
0
1
1
2
1
1
1
2
1
2
1
1
0
2
0
1
2
1
1
0
1
0
2
0
2
1
1
1
0
1
1
0
2
2
1
1
0
2
3
2
0
0
1
0
1
0
1
2
2
1
0
0
1
2
1
1
1
0
1
0
2
1
0
0
1
1
1
1
0
0
0
2
1
2
2
0
2
0
1
2
1
1
1
0
0
1
1
2
1
1
1
1
1
0
1
3
0
1
1
1
1
1
2
0
1
1
1
0
1
0
1
1
2
2
1
1
1
1
1
2
1
0
0
2
0
2
2
0
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
2
2
1
1
0
1
1
0
2
2
1
1
1
1
0
1
2
1
1
1
0
0
0
1
0
2
1
1
1
1
0
2
1
1
1
0
1
1
0
1
1
0
1
1
0
1
5
0
0
0
2
1
2
0
2
0
1
1
2
2
0
0
1
0
1
1
1
6
0
0
1
0
1
1
1
0
1
0
1
0
1
3
2
1
1
2
0
2
1
1
2
2
1
1
0
0
1
1
1
2
0
1
0
1
2
1
0
1
2
2
3
2
1
1
2
2
1
1
0
0
0
1
0
2
1
1
1
1
1
0
2
2
1
1
1
1
1
0
0
0
1
1
0
2
1
2
1
1
1
1
0
1
1
1
2
1
0
2
1
0
1
1
1
0
2
2
0
0
0
1
2
1
1
3
0
2
1
1
1
0
0
2
2
0
2
3
1
2
0
1
2
1
1
0
2
1
2
0
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
0
2
2
1
2
0
0
2
1
0
2
1
1
0
1
2
1
1
0
2
1
0
0
1
1
0
1
1
2
1
1
2
2
1
0
1
2
1
1
1
1
0
0
1
1
1
0
1
1
1
2
1
1
2
1
0
2
0
1
2
1
0
1
2
1
1
2
2
0
2
2
1
1
0
1
0
1
2
1
1
0
0
1
2
2
2
1
1
2
1
2
1
1
0
1
0
2
1
1
1
0
1
0
2
1
2
1
1
2
0
1
2
1
1
1
0
1
2
1
0
1
0
2
1
1
1
1
2
1
1
1
1
1
0
1
1
1
0
2
2
2
2
2
2
0
0
2
2
0
0
2
0
2
0
1
2
1
0
0
1
0
1
2
2
0
1
0
2
0
1
1
1
1
1
0
1
1
0
1
1
0
2
0
0
1
1
0
1
1
2
0
1
0
2
1
1
0
0
1
2
0
1
0
0
1
0
0
1
1
1
1
2
1
2
1
1
1
1
0
0
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
0
3
2
2
0
1
2
0
2
0
2
1
1
2
0
0
1
0
0
2
0
1
1
1
2
0
2
1
0
1
1
0
1
0
2
0
1
1
2
1
1
0
1
4
0
1
0
1
0
1
0
1
1
0
1
2
2
0
1
1
1
1
1
0
1
0
2
1
0
1
1
1
1
1
0
1
1
2
0
1
1
1
2
1
2
1
1
1
0
0
0
1
1
1
1
0
1
1
2
1
1
1
1
1
1
0
2
1
0
1
1
1
2
2
2
1
1
1
1
1
0
1
2
2
2
1
0
0
1
0
1
2
1
2
1
2
1
1
1
1
1
2
2
0
0
1
2
1
0
0
1
1
1
1
3
2
1
1
1
1
1
2
0
1
1
1
0
1
1
0
2
2
2
1
1
0
2
0
1
0
0
2
2
1
0
1
2
1
1
1
1
0
1
1
0
1
0
2
1
1
1
1
0
1
2
2
2
1
1
1
0
0
1
2
1
1
1
1
0
1
1
1
1
0
2
1
2
1
0
1
1
1
1
1
0
2
1
0
1
1
1
1
0
2
1
2
0
0
1
2
0
0
1
0
1
0
2
2
1
0
0
0
0
1
1
2
2
2
1
3
1
0
0
1
2
1
1
0
1
1
1
0
1
1
2
0
1
2
1
2
1
0
0
2
1
0
1
1
1
1
1
1
1
1
0
1
1
1
2
1
2
0
1
2
1
0
1
1
2
2
1
1
0
1
0
1
1
1
1
1
0
1
2
1
1
0
1
0
1
0
0
1
1
2
1
1
1
2
0
1
3
1
1
2
0
1
2
1
1
1
1
1
1
2
1
1
1
2
0
1
0
2
0
0
1
2
1
1
1
0
1
0
0
2
2
1
2
0
0
1
2
1
1
2
0
0
1
1
0
1
2
1
2
0
2
1
0
2
1
1
0
2
1
1
1
0
1
1
1
0
2
1
2
0
0
0
2
2
4
2
1
2
2
1
0
1
1
1
0
1
1
1
1
2
1
0
3
1
2
2
0
1
1
2
1
1
2
2
1
1
1
1
1
2
2
0
1
2
2
0
0
2
1
2
1
1
1
2
2
1
2
1
0
1
1
1
1
1
0
1
1
2
0
1
0
1
1
1
1
1
0
2
1
1
0
0
1
0
0
2
1
0
1
2
1
1
1
2
2
0
1
1
1
1
1
2
1
1
2
2
0
0
0
1
1
3
1
0
0
1
1
2
1
0
0
1
2
0
1
1
2
1
0
1
1
0
0
1
0
0
0
0
2
1
1
1
1
2
1
0
0
0
1
2
0
1
0
1
2
1
2
2
0
1
2
2
1
1
1
1
0
0
1
0
0
1
2
2
2
1
0
0
0
2
1
1
1
2
1
0
1
0
2
1
1
1
1
2
1
2
1
0
1
1
0
1
2
3
0
1
1
2
1
1
2
1
1
1
1
1
2
1
1
1
1
1
0
2
1
0
0
1
0
0
2
0
0
1
0
2
3
0
0
2
1
2
1
0
1
0
0
1
1
1
1
1
1
1
2
1
1
2
0
1
0
0
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
2
1
2
1
1
0
0
1
0
1
2
1
1
1
1
1
1
1
0
1
1
2
1
0
0
1
1
2
1
1
2
1
1
1
1
1
1
2
2
1
0
2
1
0
1
1
1
1
0
2
1
1
2
1
2
1
0
1
0
0
1
1
0
2
2
2
1
2
2
1
0
1
1
2
1
2
2
1
1
1
1
1
0
2
0
1
1
2
1
1
2
0
2
1
2
1
2
0
0
0
2
0
2
0
0
1
0
0
1
2
0
1
2
1
1
1
1
2
0
1
2
1
1
1
1
0
1
1
2
1
1
0
1
1
1
1
2
1
1
1
0
1
1
0
1
2
2
0
1
0
0
1
1
0
1
0
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
0
2
1
1
1
1
3
2
0
1
1
0
0
0
1
1
1
0
1
1
1
2
0
3
1
2
1
1
2
1
1
2
0
1
0
1
0
1
1
1
2
0
1
1
0
2
1
0
2
2
1
1
0
1
1
0
2
1
0
1
2
1
1
1
0
1
0
1
1
1
1
1
1
0
1
1
2
1
1
0
0
0
1
0
1
1
0
1
1
3
1
2
2
1
1
1
2
2
1
1
1
0
1
2
1
1
1
1
0
0
1
1
4
2
1
0
1
0
2
1
1
0
0
1
2
2
1
2
0
1
1
1
0
0
1
1
1
2
1
2
0
1
2
2
0
0
1
1
1
1
0
0
0
3
1
2
1
1
1
0
1
1
0
2
2
2
1
1
1
1
0
1
1
1
1
1
1
1
0
1
2
1
1
1
0
1
2
1
2
1
1
2
1
2
1
1
2
0
2
1
0
1
1
2
1
1
0
1
2
0
2
0
2
2
2
0
2
2
1
1
1
0
1
0
1
0
1
2
0
2
0
1
1
1
1
1
0
0
1
1
1
0
2
1
2
0
2
1
1
2
1
1
1
2
0
1
1
1
2
1
2
1
2
0
2
1
2
1
2
0
1
1
1
3
1
1
1
1
0
1
4
2
6
2
1
1
0
2
0
1
2
0
1
1
0
1
1
2
0
0
1
2
0
0
1
0
2
1
1
1
1
1
0
0
2
2
1
1
0
1
1
1
0
1
2
2
0
1
0
1
0
0
0
1
1
2
0
1
1
0
0
1
0
1
2
1
0
2
1
1
0
2
0
2
1
1
1
0
1
0
2
1
1
2
1
2
1
1
1
1
1
0
1
1
1
1
1
0
0
1
1
0
2
0
1
2
1
0
1
2
0
2
2
3
0
1
0
1
2
0
0
0
0
0
2
0
0
1
2
1
2
0
0
1
1
2
1
2
1
1
0
0
0
1
2
1
1
2
1
1
2
1
2
1
1
2
2
2
1
1
1
1
1
1
0
0
1
1
2
1
1
1
3
1
1
2
1
1
2
1
2
2
0
1
1
2
0
1
1
1
1
1
1
0
0
1
1
1
2
1
0
0
1
0
0
0
0
2
1
2
2
1
1
0
0
1
1
1
1
2
2
1
1
1
2
0
1
3
2
0
1
2
1
1
1
2
0
1
1
1
1
1
2
2
1
0
0
0
0
2
1
2
2
3
1
1
1
1
2
2
0
1
1
1
1
2
1
2
1
0
0
1
0
2
0
1
2
1
0
1
1
2
1
1
1
1
1
2
1
1
1
1
0
2
1
0
0
2
1
2
2
1
0
2
0
0
1
1
1
2
1
2
0
1
1
0
0
2
0
1
1
1
2
1
2
1
2
1
1
1
1
1
2
1
2
2
2
1
1
1
1
0
0
1
1
1
2
0
2
2
1
2
1
2
1
2
1
1
2
1
0
1
1
2
1
2
0
1
1
1
1
2
1
2
1
1
0
1
3
1
0
0
3
1
1
1
0
0
2
0
1
2
1
1
2
0
1
1
0
1
2
3
0
1
1
1
1
0
1
2
1
0
1
0
1
0
1
2
0
1
1
1
1
3
1
1
0
1
0
1
2
1
1
1
1
2
0
2
0
2
3
1
2
0
1
1
1
1
0
0
0
2
0
0
0
1
2
1
2
1
2
0
2
1
0
0
0
1
1
2
0
2
0
2
0
0
1
1
0
1
0
2
1
1
0
2
0
1
1
1
1
0
0
1
1
2
1
1
1
1
1
1
0
1
0
1
1
2
1
1
2
1
1
0
1
0
1
1
2
1
1
1
1
0
1
1
1
1
2
1
1
0
1
1
2
1
1
1
1
1
0
0
1
1
2
1
1
1
1
1
0
2
2
0
1
0
0
2
1
1
0
1
1
1
1
0
2
1
0
1
0
1
1
0
2
1
2
2
0
2
0
2
0
1
3
1
1
1
1
1
2
2
0
0
2
0
1
0
0
2
0
2
1
2
1
0
1
1
1
1
2
0
1
0
0
2
1
1
1
1
0
1
1
2
1
2
2
1
0
1
1
1
1
2
0
0
2
0
0
1
1
1
1
2
2
1
1
1
1
1
1
0
1
1
2
2
0
0
0
2
1
0
0
1
1
1
2
2
1
0
0
1
1
0
1
0
2
1
1
1
1
0
1
1
1
1
2
1
1
1
1
1
1
0
2
1
1
1
0
3
1
2
0
0
1
2
2
1
2
0
2
0
1
2
1
1
2
0
2
0
0
0
0
2
1
1
2
0
0
1
1
0
1
1
0
1
1
1
0
0
1
1
1
2
0
1
0
1
1
1
2
1
2
1
1
1
0
0
1
1
2
2
2
0
1
2
1
1
0
1
1
0
1
1
1
0
1
1
1
2
1
2
0
1
2
1
0
1
1
2
0
1
1
0
0
1
2
1
1
1
1
1
1
1
2
0
1
0
1
0
1
1
1
2
0
1
2
1
1
1
2
1
2
2
1
0
1
0
1
1
1
0
0
1
0
1
0
1
5
2
1
1
0
2
1
0
0
1
2
1
1
1
1
1
1
1
1
1
0
0
2
2
3
0
1
0
1
0
2
0
0
0
0
1
1
0
0
2
0
1
1
1
0
0
2
1
1
0
1
2
1
0
1
2
1
0
2
1
1
2
1
1
2
2
1
1
0
1
1
1
1
1
1
1
1
0
1
1
2
1
0
1
0
1
1
0
0
1
1
0
0
0
0
0
1
1
1
2
1
2
1
0
1
1
1
1
1
0
0
2
0
0
0
0
2
1
1
1
3
1
2
0
1
1
2
2
0
1
0
3
0
1
1
1
1
1
1
2
1
1
1
0
1
0
0
1
1
1
0
1
1
0
2
0
1
0
2
2
2
1
2
2
1
1
0
2
1
1
0
2
1
0
0
1
2
0
1
0
1
0
1
0
1
2
2
0
1
1
1
2
1
1
2
2
1
0
1
2
0
1
0
1
1
1
0
1
0
1
2
1
0
1
2
1
1
1
2
1
0
1
0
1
2
1
3
1
1
1
1
0
0
2
2
2
1
1
1
1
1
2
1
1
0
1
0
2
1
1
0
1
1
1
1
0
1
1
0
1
0
1
0
1
2
0
2
2
1
1
1
1
2
1
1
0
1
1
1
1
1
1
0
1
1
1
1
1
1
1
2
1
2
3
1
0
1
2
1
0
0
1
0
2
2
0
3
1
1
1
1
1
2
2
1
1
1
1
1
0
0
1
1
1
2
1
2
1
2
1
1
1
1
2
1
1
2
0
1
2
1
1
1
1
2
0
3
0
2
1
2
0
1
1
1
1
1
1
0
1
1
1
1
1
1
2
0
0
1
0
1
1
0
1
2
1
1
0
1
1
1
0
1
1
2
1
1
0
1
0
2
2
1
1
1
0
1
3
0
2
1
1
1
1
2
0
1
0
1
1
1
2
1
1
2
2
0
2
0
1
1
1
1
2
0
2
0
1
0
1
1
1
1
1
1
0
1
1
1
1
2
0
0
0
0
1
1
1
1
1
1
1
2
1
2
2
0
2
2
1
1
1
0
2
2
2
1
1
0
2
0
0
1
1
0
1
1
0
1
1
1
1
2
1
1
0
1
1
2
0
1
1
1
1
1
1
1
1
2
2
1
1
1
1
0
0
0
1
1
0
1
1
0
0
0
1
0
0
1
1
2
1
1
1
1
1
2
1
1
2
0
1
0
1
1
1
1
1
1
2
1
1
0
4
0
2
1
1
1
2
1
1
2
2
0
1
2
0
0
0
0
0
0
1
1
2
1
0
1
0
1
0
1
2
0
1
1
1
0
1
1
1
1
0
1
0
3
1
1
1
1
1
1
1
1
2
1
1
0
0
1
1
2
1
1
1
0
1
1
2
2
1
2
1
0
1
2
1
2
2
1
0
2
0
1
0
0
1
1
2
0
0
1
2
2
0
0
2
1
1
1
2
0
1
1
0
3
0
2
1
2
2
2
1
0
1
1
1
0
1
0
1
0
0
1
0
2
2
1
1
1
0
2
0
0
0
1
0
1
1
1
0
0
1
1
2
1
0
0
1
1
1
2
1
1
0
0
2
0
2
1
0
1
1
0
2
1
2
0
0
1
1
0
1
0
1
0
1
1
1
0
1
1
1
1
2
0
1
1
0
1
1
0
0
0
2
0
0
1
1
0
1
1
2
1
0
2
0
1
2
0
0
1
2
2
1
1
0
1
1
1
1
1
1
0
1
1
0
1
1
1
1
1
0
1
1
1
1
1
0
1
1
0
0
0
1
1
2
2
2
2
0
1
0
2
2
1
2
0
1
1
1
1
2
1
0
0
1
2
1
1
1
1
1
2
1
0
1
2
1
1
1
1
1
2
1
1
2
0
2
0
1
1
1
1
1
1
0
1
1
2
2
0
0
0
2
2
1
1
2
2
0
1
1
0
1
0
2
1
0
1
1
2
1
0
1
1
1
0
0
1
2
1
1
1
2
1
1
1
1
2
1
1
2
1
2
0
0
0
1
1
1
2
0
1
0
0
1
1
2
2
0
1
0
1
0
1
0
1
2
1
1
0
1
0
1
1
0
0
2
0
1
0
1
0
1
2
1
2
2
1
1
1
0
0
1
2
0
1
2
0
1
2
1
1
0
1
1
2
1
1
2
2
1
1
0
0
1
0
1
1
1
1
0
0
1
1
2
1
0
1
1
2
1
0
1
0
1
2
2
0
2
1
2
0
2
1
2
1
2
1
2
1
2
0
2
1
1
1
1
2
2
1
1
2
2
1
1
1
2
1
2
1
0
1
0
1
1
1
2
1
1
1
0
2
1
3
2
1
1
1
1
0
2
1
1
1
2
0
1
1
1
1
1
1
1
0
1
1
1
1
2
3
1
2
1
1
2
1
2
0
1
0
0
1
3
1
1
1
1
0
1
0
1
1
1
1
0
0
0
1
1
1
2
1
0
1
1
0
1
1
0
1
1
1
1
1
1
2
0
0
1
0
1
2
0
2
1
1
0
1
0
1
1
0
1
1
0
1
1
0
1
1
0
0
0
0
1
2
0
2
1
1
1
1
1
1
2
0
1
0
2
1
1
2
1
1
0
0
2
1
1
0
0
1
2
0
2
0
2
1
2
1
0
1
1
1
0
1
0
0
0
1
1
1
1
1
1
2
1
2
0
0
0
1
0
1
1
1
1
0
2
0
1
2
1
0
2
1
2
1
1
1
2
0
2
0
1
0
1
1
2
1
1
1
1
1
0
1
1
2
2
2
1
0
1
0
0
2
1
2
1
0
0
2
1
1
0
1
2
0
1
2
2
0
0
0
1
1
1
0
2
1
0
1
3
2
0
0
2
2
2
1
1
0
1
1
1
2
0
0
1
1
2
1
1
1
1
1
1
0
1
1
1
1
1
1
0
0
1
2
1
1
2
1
1
0
0
0
1
0
0
2
1
1
0
1
1
2
2
1
1
1
0
0
2
1
1
1
1
1
1
2
2
1
0
1
2
2
1
1
1
1
0
1
1
2
0
0
1
2
1
0
1
0
2
1
1
1
1
2
0
2
2
1
1
2
0
2
1
3
1
3
1
1
2
1
2
1
1
1
1
2
1
0
1
1
2
0
1
1
1
0
1
1
0
0
0
1
1
2
1
1
0
4
2
1
0
2
1
1
1
1
0
1
1
1
1
0
1
1
0
1
1
1
0
1
1
0
1
0
1
1
2
0
0
0
2
2
1
1
1
1
2
1
2
1
1
1
0
0
0
0
1
2
1
0
1
0
1
1
0
1
0
1
0
0
1
1
0
1
2
1
1
0
0
1
2
2
2
0
2
2
1
0
1
2
1
1
0
1
1
1
1
2
1
2
1
1
0
1
1
0
1
1
0
2
1
1
1
1
2
1
1
1
1
0
1
1
2
1
0
2
1
2
1
2
1
0
0
2
1
1
1
1
0
1
3
1
0
1
0
0
0
2
2
1
0
1
1
1
1
0
2
2
1
2
1
1
1
0
1
1
1
1
1
1
0
1
1
1
0
1
1
1
1
0
2
1
1
2
1
1
1
0
2
2
1
0
2
1
0
1
1
1
1
0
2
1
1
1
1
1
0
1
0
1
1
0
1
0
1
2
1
2
1
2
2
0
1
2
1
1
1
2
2
2
1
2
2
0
1
0
1
1
0
1
2
2
0
0
1
1
1
2
2
0
0
1
1
0
1
1
1
2
1
1
1
2
1
1
1
1
0
0
1
1
1
0
1
1
2
0
1
1
0
1
1
2
2
2
1
0
0
1
0
2
1
2
0
1
1
1
2
0
0
0
0
0
1
1
2
0
1
1
1
2
1
1
0
1
1
0
1
2
1
1
0
1
0
1
1
0
1
1
1
1
0
1
2
1
1
1
1
1
0
0
1
0
0
2
1
1
1
2
4
1
1
2
0
4
1
2
1
1
1
1
1
1
1
2
1
1
0
1
0
1
1
1
0
2
0
0
0
1
2
1
1
2
2
1
1
2
1
1
0
0
1
1
1
1
0
1
0
1
1
1
1
2
1
2
0
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
0
1
1
2
1
1
1
0
0
1
0
1
0
1
1
1
1
1
1
0
1
2
2
1
2
0
2
2
1
1
1
1
1
0
1
2
2
2
2
2
1
1
2
1
0
1
1
2
1
1
1
2
1
1
1
1
1
2
0
1
1
1
1
0
1
1
1
2
1
1
1
0
3
0
1
1
1
1
1
0
2
1
1
0
0
1
0
1
1
1
1
0
0
1
1
0
1
0
2
2
1
2
2
1
1
0
1
0
2
0
2
1
0
0
3
0
1
2
1
0
1
1
1
1
0
1
1
1
0
1
0
1
0
2
1
1
0
1
0
0
1
0
1
1
0
0
0
0
1
2
1
1
1
1
1
1
1
1
3
2
1
2
1
1
2
1
1
0
0
1
1
2
1
2
1
1
0
0
1
2
0
2
0
0
1
1
1
2
0
1
2
1
1
1
2
0
1
2
2
0
1
0
1
1
0
1
0
0
0
0
1
0
1
1
1
0
0
1
1
0
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
0
1
2
1
0
2
1
1
1
1
1
0
1
0
0
2
2
1
2
1
1
1
1
1
0
1
1
2
0
1
2
2
2
0
1
2
0
1
2
1
1
1
0
0
1
1
1
1
1
2
0
0
0
0
0
2
1
2
2
2
2
2
2
1
0
0
1
1
0
0
1
1
1
1
1
1
1
1
2
1
1
1
2
1
0
1
0
2
1
1
0
2
2
1
1
1
2
1
1
2
2
0
1
0
0
0
0
2
1
0
0
1
2
2
2
1
0
1
1
3
1
0
1
2
1
1
1
0
1
1
2
1
1
2
1
2
1
2
1
0
1
2
0
0
1
1
0
0
1
0
3
2
1
2
0
1
1
1
2
1
3
0
0
1
1
1
0
1
1
2
11
1
0
1
2
2
1
2
2
1
1
1
1
2
1
0
2
1
0
0
1
1
1
0
1
0
1
1
1
2
1
1
1
1
1
0
0
0
1
1
1
0
1
1
4
1
2
0
1
0
2
0
0
2
1
1
1
1
1
2
1
1
2
0
1
1
1
2
1
1
2
0
1
1
1
0
1
0
1
1
0
1
1
2
1
1
2
0
0
0
1
0
0
1
1
1
0
2
0
0
0
2
2
0
2
1
1
3
1
1
2
1
1
1
1
2
0
2
2
2
1
1
2
0
1
1
0
2
2
0
1
1
1
0
0
0
1
1
2
1
0
0
1
1
0
0
1
0
1
1
1
0
1
1
2
1
1
2
0
1
0
1
1
1
1
1
0
0
1
0
2
2
1
2
1
1
1
1
0
0
1
1
0
2
2
2
2
1
0
1
2
2
1
0
1
1
1
0
1
1
1
2
1
1
1
0
1
1
1
1
1
0
1
1
2
1
1
2
1
1
1
1
1
0
1
0
2
1
0
2
1
1
2
2
1
1
1
0
1
1
1
0
2
1
0
1
2
1
2
0
0
0
1
1
1
1
2
1
1
1
0
1
1
0
0
0
2
1
1
1
1
1
1
1
2
1
1
1
0
0
1
1
2
0
2
0
0
1
1
2
1
2
0
1
0
1
0
1
1
0
1
1
1
1
1
2
0
1
2
1
0
1
2
1
1
1
0
1
1
2
1
2
1
1
2
2
2
1
1
1
2
1
0
0
2
1
1
1
0
0
1
1
2
1
0
1
1
1
2
2
1
0
2
1
0
2
2
1
1
1
1
1
0
0
0
1
1
2
1
1
1
1
0
1
1
0
1
2
1
2
1
0
0
1
2
1
0
2
0
1
1
2
0
1
0
0
1
1
1
2
2
0
1
2
1
2
0
2
2
1
1
2
2
1
1
2
2
2
1
1
1
1
2
0
1
1
1
1
0
1
1
0
0
0
1
0
1
1
1
2
1
1
2
1
2
1
1
4
1
1
0
2
0
0
1
1
2
1
1
0
2
2
0
0
0
1
1
2
1
1
2
1
0
0
1
1
1
2
2
1
0
0
1
0
1
0
1
2
1
1
1
2
1
1
1
1
1
0
1
2
1
2
0
1
2
0
0
1
1
0
0
1
2
1
2
1
1
2
1
1
1
2
1
1
1
2
2
1
2
0
1
1
0
2
0
0
1
1
3
1
0
0
1
1
0
1
1
0
1
1
1
1
1
1
2
2
0
1
2
1
2
2
1
1
0
1
0
0
1
0
1
1
0
1
2
1
0
1
1
0
0
1
0
1
0
2
3
1
2
1
1
0
1
0
2
2
0
2
1
0
1
1
1
1
0
1
0
1
0
1
0
1
1
2
1
1
0
0
2
0
0
2
0
1
2
1
1
1
1
0
0
1
1
2
1
1
1
2
1
1
1
3
2
0
2
1
2
1
1
1
1
1
0
1
2
0
2
2
1
0
2
1
2
1
1
1
1
0
1
1
0
0
0
1
0
1
2
1
1
1
1
1
1
1
1
0
2
1
1
1
1
0
0
1
1
1
1
1
2
0
1
2
1
1
0
0
1
1
2
2
2
1
0
1
1
2
0
2
0
1
1
2
0
1
0
1
1
1
0
2
2
1
1
0
1
1
1
1
2
1
0
1
0
2
0
0
0
0
1
1
0
1
2
2
0
1
0
0
1
0
2
2
0
1
2
1
0
1
0
0
1
1
0
0
1
1
0
2
2
1
1
2
2
0
0
1
0
2
2
1
2
1
2
2
2
1
1
1
1
1
1
2
2
1
1
1
1
1
2
1
0
0
1
1
1
0
1
0
1
1
1
2
1
0
1
1
0
0
2
1
2
0
1
1
2
1
0
1
1
0
1
1
0
1
0
1
0
1
0
2
1
1
0
2
0
0
2
2
1
2
2
1
2
1
1
0
1
2
1
1
1
0
0
1
0
0
1
2
2
1
2
0
1
0
1
1
2
2
2
0
0
0
0
3
1
2
1
1
1
1
1
1
1
0
0
0
1
2
1
0
0
3
2
0
1
1
2
0
0
1
1
2
1
0
1
0
0
1
0
2
0
0
2
1
0
1
1
1
0
1
2
3
0
1
0
1
0
0
1
0
1
1
0
1
0
1
1
2
1
1
2
1
2
2
1
1
1
2
1
2
2
0
0
0
1
0
2
2
0
1
0
1
1
0
4
0
0
1
2
1
1
3
1
1
1
1
0
1
1
0
1
0
1
0
1
2
3
2
1
1
1
1
1
1
2
1
1
0
2
0
2
0
1
1
1
1
1
0
0
0
1
2
1
0
1
2
2
1
1
0
0
2
0
1
0
1
0
2
2
1
1
1
0
1
3
1
0
3
1
1
1
0
1
0
1
1
1
1
2
1
1
1
1
1
1
1
0
1
1
1
1
1
1
2
1
0
0
1
1
1
0
2
1
1
2
2
1
0
1
2
2
0
1
0
2
1
2
1
1
2
2
0
0
0
2
0
1
0
1
2
2
2
1
0
1
1
1
1
2
1
1
2
1
1
0
3
1
1
2
1
0
2
1
0
2
2
2
0
1
2
2
1
3
2
1
2
0
2
2
0
2
0
0
1
1
1
0
1
1
0
0
0
0
1
2
1
0
1
1
0
1
0
0
1
0
1
2
2
1
2
0
1
1
0
1
1
1
0
1
0
2
1
1
1
1
2
1
2
1
1
1
2
2
1
1
1
1
1
0
2
1
2
1
1
1
0
2
0
1
0
2
1
1
2
1
2
1
0
0
1
1
0
1
2
0
1
1
0
2
1
1
1
0
1
1
0
1
1
1
1
1
0
2
2
2
1
2
2
1
1
1
1
1
1
2
1
1
2
2
2
1
1
1
2
1
2
1
2
1
0
2
1
2
1
2
1
0
2
2
1
1
1
0
1
0
1
1
0
1
1
0
2
0
2
1
1
1
0
1
1
1
1
0
1
0
0
0
1
1
2
1
0
1
0
2
2
1
0
2
0
1
1
0
1
1
0
0
1
1
1
2
2
1
2
2
2
2
1
2
1
1
0
0
3
0
2
1
0
1
1
1
2
1
0
0
0
1
1
0
1
1
0
1
0
0
2
2
1
0
1
1
1
1
0
2
1
2
2
2
1
1
1
2
2
0
1
3
4
1
2
1
1
0
1
2
1
1
1
1
2
2
1
0
1
1
0
0
1
1
1
0
1
1
0
4
0
1
0
0
2
1
1
1
0
0
0
1
2
1
2
1
0
0
0
1
2
0
0
0
2
2
1
0
1
0
2
1
0
0
1
2
2
0
2
0
1
2
1
2
1
1
1
1
2
1
1
0
0
1
1
1
0
2
0
1
1
1
0
0
1
1
0
2
1
0
1
2
2
2
0
1
1
1
1
1
2
1
0
1
1
2
1
1
3
2
0
2
1
2
1
4
0
2
0
1
0
2
2
0
1
1
1
0
1
0
1
0
1
1
1
2
0
1
1
0
1
2
1
1
2
0
1
2
0
2
2
2
1
2
2
1
1
2
4
2
0
1
0
2
2
0
1
2
1
1
1
2
2
1
0
1
0
0
2
0
3
0
1
2
3
2
1
1
1
1
1
0
1
1
1
0
0
0
2
1
1
1
2
0
3
0
1
1
1
2
2
1
2
0
1
0
1
1
0
1
0
1
0
2
1
0
1
1
2
0
1
0
2
1
1
1
1
0
0
1
0
1
1
1
1
2
0
1
0
1
1
0
0
0
2
0
1
0
1
0
1
1
1
1
1
0
0
0
1
1
0
1
1
0
1
1
2
2
1
2
1
2
1
0
0
1
0
1
1
1
1
1
0
2
1
1
2
0
1
1
2
0
2
2
0
0
1
2
1
1
2
1
0
0
0
1
2
0
1
2
1
1
1
1
1
1
1
0
1
1
1
2
1
1
1
2
1
0
1
1
2
1
0
1
1
1
1
1
1
1
1
1
1
0
2
2
1
1
1
1
0
2
1
1
0
0
1
1
1
1
1
0
0
1
2
1
0
1
1
1
1
2
1
2
2
2
1
2
2
1
1
1
0
1
0
1
1
0
1
0
2
1
2
0
1
0
0
1
0
0
1
1
1
0
0
0
0
1
2
1
1
1
1
0
2
1
0
2
1
1
1
2
1
2
0
0
2
0
1
2
1
1
1
1
1
2
1
1
2
2
1
1
1
1
0
0
0
0
0
1
2
1
2
1
1
0
1
1
1
2
1
2
2
0
1
1
1
1
0
1
1
1
2
1
1
0
1
0
1
1
1
0
2
0
1
0
1
0
1
3
1
1
1
1
2
1
1
1
1
1
1
1
2
1
0
0
0
0
0
1
1
1
1
1
0
0
1
0
3
1
2
1
2
2
1
1
2
0
0
2
1
1
1
2
1
1
1
1
1
1
1
0
1
1
2
0
0
1
2
2
1
1
1
1
1
1
2
1
1
2
1
0
0
0
1
1
2
0
2
1
0
1
1
0
1
0
3
0
1
2
1
1
1
0
2
1
1
1
1
1
2
1
1
1
3
2
1
1
0
3
1
1
0
1
1
1
1
1
1
1
1
1
0
2
1
1
2
2
0
1
1
1
0
1
1
1
2
1
0
1
1
1
1
0
0
0
1
1
1
2
1
1
1
2
0
0
0
1
1
0
0
0
1
1
1
1
1
2
0
1
2
0
0
2
2
1
1
2
1
2
0
2
1
1
1
0
0
2
2
1
2
0
2
0
2
2
2
2
2
1
2
2
1
2
1
0
1
1
0
1
1
2
0
1
1
1
1
1
2
1
2
1
1
1
2
0
0
2
2
1
0
1
0
1
1
1
2
2
2
0
0
0
1
1
1
0
1
2
2
2
1
0
1
1
1
0
2
1
1
2
1
1
2
1
1
1
1
1
2
3
1
1
1
0
2
1
1
1
2
1
1
1
1
1
1
0
2
2
1
1
1
0
1
2
1
0
1
1
0
0
1
2
1
0
0
1
1
1
0
1
0
0
2
0
1
1
1
1
0
1
2
1
1
1
0
0
1
0
1
1
0
2
1
1
0
2
2
1
1
1
2
0
1
2
1
0
0
1
1
1
1
1
1
0
0
0
2
1
1
1
0
0
0
0
1
1
0
0
0
1
1
0
1
0
0
2
1
0
1
1
1
1
1
2
1
1
2
1
2
1
1
0
1
1
1
0
2
2
0
2
3
2
1
1
1
1
0
1
0
1
1
1
1
1
1
2
1
1
2
1
0
2
1
0
1
2
2
2
2
0
2
1
1
0
1
0
1
2
0
0
1
1
2
2
1
0
0
2
1
1
2
0
2
1
1
1
2
0
1
0
1
1
1
1
0
1
1
1
0
1
1
1
1
2
0
1
1
2
1
2
1
1
1
0
1
0
1
0
2
0
1
0
1
1
1
2
2
1
1
0
2
0
1
2
3
1
1
0
0
1
1
0
0
1
0
2
1
1
1
0
1
2
2
0
2
1
1
1
2
0
1
1
2
3
1
2
0
2
1
2
0
1
0
1
1
1
2
2
1
1
1
1
0
0
0
1
1
1
1
1
0
1
1
1
0
0
0
2
0
2
0
1
2
2
1
2
2
1
2
1
1
0
0
1
0
1
2
1
2
0
0
1
1
1
0
2
2
1
1
1
1
0
1
2
1
1
1
0
2
0
2
1
1
2
1
0
1
1
0
1
2
1
0
2
2
1
0
1
2
1
0
0
0
1
2
1
2
1
0
2
3
1
1
3
2
3
1
1
2
1
0
2
1
2
1
1
1
0
1
2
2
1
0
2
1
0
1
1
1
0
2
1
1
3
1
2
1
2
0
2
1
1
1
2
2
1
2
0
1
1
0
1
0
1
1
1
0
1
1
0
1
2
2
1
1
2
1
1
1
2
0
1
1
0
1
2
1
2
2
5
0
1
1
1
1
1
0
2
1
1
1
1
1
0
1
1
1
1
2
1
1
1
1
0
1
1
0
1
1
1
2
0
2
1
1
0
1
1
1
1
1
0
1
1
2
2
0
2
1
2
0
2
2
1
0
1
0
1
1
2
1
2
1
0
0
1
2
1
1
2
1
0
1
0
0
1
0
1
1
2
0
1
0
0
0
2
2
2
1
0
2
1
2
1
1
1
1
1
1
2
0
0
1
1
2
0
0
1
2
1
1
0
0
1
2
1
0
2
1
3
1
1
2
1
1
1
1
1
1
1
1
2
1
1
0
2
1
0
1
1
0
2
2
1
0
0
1
2
2
2
1
0
2
0
1
0
0
1
0
1
2
2
1
2
2
0
1
2
0
0
2
1
1
2
3
1
2
1
2
2
2
1
0
1
1
0
2
1
1
2
1
2
2
0
2
0
0
1
0
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
2
2
0
0
1
0
1
1
0
1
1
1
0
0
1
2
1
1
1
2
1
2
1
1
2
0
1
2
2
1
1
0
1
1
1
0
2
1
2
1
2
0
1
4
1
0
1
0
1
2
1
1
1
0
0
0
0
1
0
1
0
1
2
1
2
0
1
1
1
1
1
1
2
1
0
1
1
1
0
1
2
1
1
2
0
0
1
0
2
1
1
0
1
1
2
2
1
1
1
0
1
2
1
2
1
0
1
1
0
0
3
0
2
2
1
1
1
1
3
2
1
1
1
0
2
0
0
2
4
1
0
2
2
1
1
2
2
1
0
0
1
0
2
1
1
2
2
2
2
0
2
2
1
1
0
1
1
1
1
1
1
1
1
0
0
2
1
1
1
1
2
1
1
1
1
0
1
1
2
2
2
1
0
1
0
1
1
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
2
1
0
1
1
1
0
1
1
1
1
2
1
0
1
1
1
1
1
1
1
0
0
1
0
2
0
1
1
1
1
0
1
2
3
1
0
1
1
1
1
1
1
1
1
1
0
0
1
0
1
1
1
1
1
1
1
1
2
3
1
1
1
1
0
1
1
1
1
1
1
2
1
1
2
0
0
0
2
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
1
1
1
2
0
1
2
1
1
0
1
1
2
0
0
0
0
2
0
1
2
1
1
1
2
0
1
1
1
3
0
1
1
0
2
0
1
1
1
0
2
0
1
1
2
0
1
0
1
1
1
0
1
1
1
2
1
2
0
1
2
2
2
2
2
1
0
2
1
2
1
2
2
1
0
2
0
0
1
1
1
0
0
2
0
2
0
0
1
1
0
2
1
1
1
1
2
1
2
2
2
0
0
0
2
1
1
2
1
2
2
1
2
0
2
1
1
1
1
1
2
1
2
1
1
1
0
1
1
2
1
1
0
1
1
1
1
1
1
0
1
1
1
2
0
1
1
1
1
0
0
1
1
1
1
0
0
2
1
1
1
1
0
1
1
2
1
1
0
0
1
2
1
1
1
1
1
0
2
1
0
1
0
1
1
0
1
1
1
1
0
0
2
2
1
1
1
1
1
2
1
2
1
0
0
0
0
0
2
1
2
2
0
1
1
1
1
1
0
1
1
0
2
0
2
2
2
0
2
1
0
0
0
2
2
0
0
1
1
1
0
0
0
1
1
0
1
1
1
0
1
1
1
2
1
2
1
1
1
0
1
1
1
0
2
1
1
1
1
0
0
0
2
0
0
1
2
1
1
1
1
1
1
1
1
2
1
2
0
1
1
2
1
0
1
0
1
1
1
1
0
0
0
1
1
1
1
0
0
1
2
0
1
1
0
1
1
0
2
1
2
1
1
2
1
2
1
1
1
1
2
1
1
1
1
2
2
0
1
0
2
2
1
1
1
1
1
1
2
2
4
1
0
2
1
1
2
1
1
1
1
0
0
1
1
1
2
1
0
1
2
1
1
1
1
0
0
0
1
1
2
0
1
1
4
1
0
2
1
2
1
2
0
0
1
2
2
1
0
1
2
0
1
0
0
0
1
2
2
1
2
1
1
2
2
1
0
0
1
0
1
2
1
0
1
1
1
0
2
1
2
2
1
1
2
2
1
1
1
0
1
1
1
1
1
1
1
1
0
1
0
2
2
1
1
2
1
1
1
0
1
0
0
1
2
1
1
0
0
1
1
2
0
2
0
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
2
1
2
0
2
1
0
0
0
0
1
1
1
1
0
1
1
2
1
1
1
1
1
0
1
0
1
1
0
0
1
1
0
1
1
1
0
1
1
1
1
1
0
1
1
0
0
0
0
2
2
2
0
1
2
2
2
1
0
1
2
0
0
2
0
2
0
1
1
1
0
0
0
1
2
1
1
1
1
1
0
0
0
2
0
0
0
1
1
1
2
1
1
1
1
1
0
1
2
2
1
1
0
1
0
1
1
1
1
0
2
2
2
0
0
2
1
0
0
1
2
1
0
1
0
2
1
0
1
0
0
1
1
1
2
1
1
1
1
1
1
1
0
1
1
1
1
2
1
0
2
0
1
1
1
0
2
1
1
0
2
1
1
0
1
2
0
2
3
2
1
1
1
1
2
0
1
1
1
1
1
0
1
0
3
1
1
0
0
1
3
0
0
1
1
1
1
1
1
1
0
0
1
0
0
1
1
1
2
2
1
1
0
0
1
1
1
0
1
1
0
1
2
0
0
1
2
1
2
1
1
0
2
2
0
1
1
1
3
0
2
0
1
1
0
1
1
0
0
1
1
0
0
1
1
2
2
1
1
2
1
1
0
1
3
1
0
1
1
2
1
1
1
1
2
1
0
0
1
2
2
1
0
0
1
2
2
1
1
0
1
0
2
2
2
1
1
1
1
1
1
1
0
2
0
2
1
1
2
2
0
0
0
1
1
1
1
1
1
1
1
1
1
1
0
2
1
1
2
0
1
0
1
1
2
2
2
1
2
1
0
1
1
0
0
1
1
1
1
0
1
1
0
0
1
0
2
2
1
1
0
2
0
0
0
1
0
2
0
2
2
2
1
1
1
1
1
0
1
1
1
0
1
2
1
0
1
1
1
1
1
1
1
0
2
1
2
2
2
1
1
0
0
0
1
1
1
1
0
0
1
0
1
1
1
1
0
1
2
1
1
1
1
2
1
1
2
1
0
2
1
2
2
1
1
2
0
1
0
1
1
1
1
0
1
1
0
2
1
1
0
0
1
1
1
2
1
4
2
0
0
1
0
1
1
0
1
1
2
1
2
0
2
1
1
1
2
2
1
1
0
0
0
1
2
2
1
1
1
1
0
9
2
1
1
1
2
1
1
1
0
1
2
2
2
1
1
2
1
2
1
1
2
0
2
1
0
2
2
0
1
1
1
1
1
2
2
2
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
0
1
0
1
1
0
1
0
2
2
1
0
2
2
1
1
2
1
2
0
2
1
1
0
0
2
2
1
1
0
1
0
0
2
1
1
1
2
0
1
0
1
1
1
0
0
3
1
1
0
1
1
2
0
1
0
1
2
0
1
0
1
1
0
1
3
1
1
1
1
2
1
2
1
1
0
1
0
0
1
5
2
1
0
1
0
1
1
2
0
2
0
2
1
1
2
1
2
0
1
2
0
1
2
1
0
2
2
1
2
2
2
2
1
1
0
1
1
0
1
1
3
1
1
1
0
0
0
2
2
2
0
0
0
1
2
1
1
1
1
2
0
1
1
1
0
0
1
1
1
4
0
0
1
0
0
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
0
1
0
1
1
0
1
0
1
0
0
2
1
0
1
0
0
2
2
2
3
1
1
0
1
0
1
0
0
2
1
0
2
0
2
1
0
1
1
2
0
0
1
1
1
1
2
1
1
0
0
1
0
1
0
0
2
1
0
0
0
1
1
1
0
2
1
2
1
1
1
0
0
2
2
1
1
2
2
1
1
1
1
1
1
1
1
1
0
0
0
0
1
0
0
1
0
1
2
1
1
1
0
0
1
1
1
2
0
1
0
2
1
2
2
0
1
2
2
0
1
0
2
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
2
2
1
2
1
2
2
1
1
1
0
0
2
1
2
1
1
1
0
0
0
0
1
1
1
1
1
1
1
1
2
1
0
2
0
0
0
0
1
1
1
0
2
2
1
1
1
0
2
0
1
1
1
1
1
1
1
1
2
1
1
1
0
0
1
1
0
0
4
1
1
1
0
1
1
0
1
2
1
1
1
0
2
1
1
1
1
1
2
1
1
1
2
1
1
1
0
1
1
1
0
1
2
0
2
0
2
2
1
1
2
2
0
1
1
0
2
0
2
1
1
1
1
1
1
0
0
1
1
1
2
1
1
1
1
1
3
2
2
2
4
1
1
1
2
0
1
0
1
1
3
1
1
2
2
1
1
0
2
0
0
2
1
1
1
0
1
1
2
2
0
2
0
0
0
1
0
1
1
0
0
1
2
1
2
1
0
0
1
1
0
0
1
0
1
1
1
1
0
1
0
2
0
1
0
2
0
2
1
1
0
0
1
2
1
2
1
1
2
1
0
0
1
1
1
1
1
1
2
1
0
1
0
0
0
0
1
1
2
0
3
2
2
2
0
2
0
1
0
1
0
1
1
0
0
2
1
0
0
1
1
4
2
1
1
0
2
2
1
1
1
1
1
2
0
2
0
0
1
1
2
1
1
0
1
2
1
0
1
1
2
2
1
0
0
1
1
0
0
1
2
1
1
2
0
0
1
1
1
1
2
2
2
1
0
0
1
1
1
0
0
2
1
0
1
2
1
0
2
2
0
0
1
1
2
1
2
2
1
1
1
1
1
1
0
0
1
1
1
2
1
4
2
2
1
0
0
0
0
1
0
2
1
2
0
1
0
1
2
1
1
1
0
0
0
0
1
1
1
0
0
1
1
1
2
0
2
1
1
1
2
1
1
1
1
2
1
0
1
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
1
0
2
2
0
2
0
0
2
0
1
2
1
1
1
1
1
0
1
2
0
1
0
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
1
1
0
2
1
1
0
1
1
1
1
0
0
0
1
3
0
2
1
1
1
2
2
1
0
2
1
0
2
2
1
0
0
0
2
0
1
2
0
0
2
1
2
0
2
0
1
1
1
2
1
0
1
1
1
0
2
2
2
2
1
1
1
0
2
1
2
2
1
1
1
1
0
2
1
1
1
0
1
0
2
1
1
1
1
1
1
0
2
1
2
1
1
0
1
2
0
0
2
1
1
2
1
2
1
1
1
0
0
2
2
2
0
1
0
1
1
0
1
0
0
2
2
0
1
1
1
2
2
1
2
2
2
1
0
2
2
0
0
2
2
1
1
1
2
1
1
2
1
1
0
0
0
1
1
1
3
2
1
1
1
1
1
1
2
1
2
2
1
0
3
1
1
0
0
1
1
2
0
0
1
2
0
1
1
1
0
1
0
1
2
1
0
1
1
1
2
0
1
1
1
2
1
2
0
1
0
1
3
2
1
1
0
2
2
1
1
1
0
1
1
1
1
0
0
2
2
4
0
1
1
1
1
1
1
0
0
0
2
0
2
1
2
1
2
2
2
0
1
0
3
1
1
0
0
2
2
2
1
0
1
1
2
1
0
1
1
1
0
1
1
0
2
1
0
1
0
0
1
1
1
1
0
0
1
1
0
1
2
2
0
1
1
1
0
0
0
2
0
2
0
1
0
0
1
1
2
1
0
0
2
2
0
1
0
1
0
1
1
1
2
0
0
1
2
1
2
1
2
1
1
1
0
1
2
0
1
1
0
1
1
1
0
2
0
0
1
2
0
1
1
1
1
1
1
2
0
0
4
0
0
1
1
2
0
2
0
1
2
1
1
1
0
1
0
1
1
2
1
2
2
1
1
0
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
0
1
0
0
1
0
0
0
1
2
0
1
2
1
0
1
1
0
2
1
1
1
1
1
1
1
1
1
1
0
1
1
2
1
0
0
2
2
2
1
1
1
2
1
2
1
1
1
1
2
1
0
0
1
0
1
1
0
2
2
0
1
2
1
1
1
1
0
2
1
1
0
0
2
1
1
1
0
0
1
1
0
2
0
1
1
2
1
1
1
0
1
1
1
1
2
1
1
2
0
0
1
0
2
2
1
0
2
0
0
1
2
2
1
1
2
1
1
0
1
1
1
1
1
0
1
1
2
0
0
2
0
2
2
0
2
0
2
1
0
2
1
1
0
1
2
1
2
2
2
0
2
1
1
1
2
1
2
0
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
0
1
0
1
2
2
1
2
1
0
0
1
1
1
1
1
0
2
2
1
0
0
1
0
1
0
2
1
2
1
2
1
1
0
1
1
1
2
1
0
1
2
2
2
0
2
2
2
1
2
1
1
2
0
1
0
1
0
0
1
2
1
1
2
0
0
2
1
1
1
1
0
2
3
0
1
2
2
1
1
1
1
2
1
2
0
0
1
1
2
2
1
1
1
2
1
1
0
0
0
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
0
1
1
1
1
1
1
0
2
0
1
2
1
1
2
0
2
0
1
2
2
0
1
2
1
1
1
1
2
2
0
0
2
0
1
2
1
1
1
1
2
2
1
2
1
1
1
1
1
1
0
0
1
1
1
1
0
1
2
1
1
1
1
0
1
1
0
0
1
2
1
0
2
2
1
1
1
2
1
1
1
0
2
1
1
1
1
1
0
2
1
1
2
0
0
1
2
0
2
1
1
1
0
2
2
1
0
1
1
2
1
2
1
2
2
1
0
0
0
2
0
2
1
2
2
1
0
1
2
2
1
1
0
1
0
1
0
0
1
1
0
2
1
0
1
1
2
1
1
1
1
0
1
0
0
0
2
0
1
1
0
1
2
2
1
1
1
0
1
1
1
1
2
1
1
1
0
1
1
1
2
0
0
2
1
2
0
2
0
0
0
0
1
2
1
1
2
1
2
1
1
1
0
1
1
2
1
1
0
2
0
0
0
0
1
1
1
1
2
1
1
0
1
2
1
1
2
1
0
2
1
1
2
0
1
2
0
0
1
1
0
2
2
1
0
1
0
0
0
1
0
1
0
1
1
0
0
1
1
0
0
2
1
1
1
2
1
1
1
2
0
2
3
2
2
1
0
2
1
0
1
1
1
2
0
1
1
1
2
1
1
1
0
0
0
1
0
1
1
1
0
1
1
2
1
1
1
2
1
0
2
0
2
1
1
0
1
2
1
1
1
1
0
0
0
2
1
0
1
0
1
1
1
1
0
1
0
1
0
2
1
0
0
1
2
1
1
3
2
1
2
0
1
1
1
1
1
0
1
0
1
1
1
2
0
1
1
1
0
1
1
1
0
0
1
1
0
1
3
0
0
1
1
2
1
0
1
1
1
1
1
1
1
1
2
1
1
0
2
0
1
0
2
1
2
0
1
0
1
1
1
2
1
0
2
2
0
1
1
0
0
2
1
1
1
0
0
1
2
2
1
2
2
4
1
1
0
0
0
1
1
1
2
0
0
1
1
0
1
2
1
0
2
1
0
0
1
1
2
1
1
1
2
1
1
0
2
2
1
1
1
2
1
0
1
1
2
1
1
1
1
2
1
1
0
1
1
1
1
0
2
0
2
1
1
1
0
2
2
0
2
1
0
0
1
0
0
2
2
1
2
0
2
2
0
2
3
2
2
1
1
0
0
1
1
1
2
1
0
0
1
2
1
0
1
1
0
0
2
2
0
1
0
0
0
1
2
1
2
2
0
2
0
1
1
2
2
1
1
0
1
1
1
1
1
1
1
0
1
2
0
2
1
1
0
1
1
0
1
2
1
1
1
1
1
2
0
1
0
1
0
0
2
1
1
1
1
2
1
1
1
1
1
1
2
0
2
1
0
1
2
1
1
0
1
1
1
1
2
1
0
1
0
2
0
1
1
1
1
0
1
1
2
2
0
1
1
2
0
2
1
0
1
2
1
1
3
0
0
0
2
1
1
0
2
0
2
1
1
2
0
0
1
1
1
1
1
1
0
3
1
2
0
0
2
1
1
0
0
1
0
1
1
0
1
2
1
2
2
1
1
1
0
0
2
2
1
0
2
0
1
0
1
0
2
1
1
1
1
1
2
1
2
0
2
2
2
0
0
2
0
1
0
1
1
2
2
0
2
2
0
0
1
0
1
1
1
3
1
1
0
1
2
1
1
1
1
1
1
2
2
1
2
1
2
0
2
0
1
1
1
0
0
1
0
1
0
1
2
1
1
1
2
2
0
1
2
1
1
2
1
1
1
2
1
1
2
2
0
0
1
1
0
2
1
2
0
0
0
1
1
0
1
2
1
1
2
1
1
1
1
2
2
2
2
0
0
1
2
1
1
1
0
1
1
1
1
2
0
2
1
1
0
0
1
2
0
1
0
1
1
0
1
1
1
1
1
0
0
0
0
0
0
0
0
1
1
1
0
1
2
0
0
0
0
1
0
1
1
0
2
1
0
1
2
2
0
1
1
0
0
0
1
1
1
3
0
2
2
1
1
1
0
1
1
1
2
1
2
4
1
1
0
1
0
1
0
0
1
0
1
2
0
1
1
1
0
1
1
2
1
1
1
1
1
0
0
2
3
0
0
1
1
0
0
1
2
0
1
0
0
3
1
2
2
2
1
1
1
2
0
1
1
1
2
0
0
1
2
1
1
0
2
1
0
1
2
1
0
1
2
0
2
1
1
2
2
1
2
1
0
1
1
2
1
1
2
1
1
0
2
3
1
1
0
2
1
1
0
0
1
2
1
0
1
1
1
2
0
3
1
0
1
1
0
0
0
1
1
1
1
2
0
1
0
1
0
0
0
1
0
2
2
0
1
2
1
5
0
1
1
2
1
2
0
1
0
2
0
0
1
3
0
2
1
0
1
2
0
0
0
1
1
2
0
1
1
2
0
2
1
0
0
1
1
0
1
1
1
1
0
0
0
2
2
1
1
1
0
1
1
1
1
0
1
2
1
1
1
1
1
0
1
2
1
2
0
0
0
1
0
0
0
1
2
1
1
1
2
1
2
0
1
0
1
1
2
3
2
0
2
2
1
0
1
1
1
1
1
2
0
0
1
1
1
2
0
2
1
2
1
1
1
1
1
1
1
1
1
2
1
0
1
0
1
1
2
1
0
0
1
0
0
1
1
2
2
0
4
1
0
2
1
2
0
0
1
1
1
0
2
1
0
0
1
0
0
1
2
1
1
1
2
1
1
0
0
0
2
1
1
2
0
1
1
1
2
1
0
1
1
2
0
1
1
2
1
2
1
1
0
1
0
2
1
1
0
0
1
1
1
0
0
1
1
1
2
3
0
1
1
0
1
1
0
0
0
2
1
0
1
0
1
0
2
1
1
0
1
1
1
1
0
2
0
1
2
2
0
0
1
3
0
0
1
1
0
0
2
2
0
0
1
0
1
1
1
1
0
1
0
1
1
1
1
2
1
0
1
1
1
2
1
1
1
1
1
0
1
0
1
1
0
1
2
2
1
1
0
1
2
0
2
1
1
1
0
2
2
2
2
0
1
2
1
1
0
1
0
1
1
1
1
1
1
2
1
1
0
2
0
2
1
0
1
2
0
2
0
0
0
1
0
1
1
1
0
2
1
0
2
0
1
2
2
1
1
0
1
2
1
2
2
1
2
0
1
0
2
1
2
1
2
1
0
0
0
2
1
0
0
2
1
1
0
1
0
1
0
0
1
1
1
0
1
2
2
0
2
1
1
0
1
2
2
2
2
1
1
1
0
2
1
1
0
1
2
1
0
1
1
1
1
1
0
0
0
1
0
1
1
2
0
1
1
0
1
1
1
2
0
0
2
2
0
2
2
1
1
1
0
1
2
0
1
2
1
1
1
0
1
1
2
2
1
1
0
2
0
0
2
0
2
1
2
0
2
0
1
1
1
1
2
0
0
1
0
2
2
1
0
1
2
2
1
2
1
2
1
1
1
2
1
0
1
1
1
2
1
0
2
0
1
0
1
0
1
1
1
1
0
1
1
1
2
2
2
0
2
0
1
0
1
0
1
1
0
1
1
0
2
1
0
1
1
0
1
0
2
0
1
1
1
1
1
1
1
1
0
1
1
0
2
1
0
0
0
0
1
0
1
0
1
1
0
0
1
1
0
2
2
2
2
1
1
1
0
0
1
1
1
2
0
1
1
1
0
1
1
1
3
0
0
1
0
0
1
0
2
2
0
0
2
0
1
0
1
1
0
0
1
1
2
1
0
0
1
2
2
2
2
2
1
1
2
0
0
2
1
2
1
1
0
1
2
1
2
0
1
1
2
0
1
1
1
0
1
1
0
1
1
0
2
1
1
2
0
1
2
1
2
0
1
1
2
2
1
1
1
1
0
2
1
2
1
1
1
0
2
0
1
1
1
0
1
1
1
1
1
0
2
1
1
0
2
1
1
1
1
1
1
1
1
2
0
1
2
1
0
0
1
0
0
1
0
1
1
1
2
2
0
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
0
1
0
1
1
0
2
0
1
1
2
0
1
5
1
0
1
1
1
2
1
2
1
1
1
2
1
1
1
0
1
1
0
0
1
1
1
1
2
1
1
1
1
2
0
1
1
1
0
0
0
0
1
2
1
1
0
0
1
1
1
0
0
1
0
0
1
1
1
0
1
1
2
0
1
1
1
1
4
0
2
1
1
0
0
2
1
1
1
1
1
0
2
2
2
1
1
1
0
2
1
0
0
1
1
2
2
0
2
1
0
1
1
0
2
0
0
0
1
1
0
0
1
1
1
1
2
0
0
0
1
2
2
0
2
0
0
2
1
1
1
0
1
2
1
1
2
1
1
1
1
2
0
0
2
1
1
1
1
1
1
0
1
0
1
1
2
1
2
2
0
1
1
1
1
2
0
3
2
1
2
1
2
1
1
0
1
2
1
1
2
2
1
1
1
1
2
0
1
1
0
1
1
1
2
1
2
1
0
1
0
1
2
2
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
0
0
1
2
1
1
1
1
0
1
0
1
0
0
2
0
1
1
0
0
1
0
2
1
2
2
0
2
0
0
0
1
1
0
2
1
1
2
1
1
0
1
1
0
2
2
0
1
1
1
1
1
0
1
1
1
1
0
2
2
1
1
3
1
0
0
0
2
1
0
1
3
1
2
1
1
1
0
1
1
2
2
0
0
1
0
0
1
2
0
0
0
0
1
1
1
0
1
0
1
2
2
1
1
1
0
0
2
0
1
1
1
1
1
0
1
2
1
1
0
1
0
1
2
1
1
2
1
1
1
1
0
1
1
0
1
2
2
0
1
1
1
1
1
2
1
0
2
1
0
1
1
2
2
2
1
1
1
1
1
1
1
1
1
0
0
0
2
1
2
0
2
1
1
0
2
0
1
1
2
1
1
1
1
1
0
0
2
1
0
1
0
1
1
1
1
0
1
1
1
1
0
2
0
1
0
1
1
0
0
1
0
2
2
1
0
1
1
1
2
2
2
1
1
2
2
1
1
0
2
0
1
1
1
2
1
2
0
1
1
1
2
0
1
2
2
1
2
1
1
1
1
2
0
0
0
0
2
2
2
1
0
1
2
1
1
1
2
0
2
0
2
1
1
2
0
0
1
1
1
2
3
0
2
1
1
1
2
1
0
1
2
0
1
1
1
0
1
0
2
0
2
0
0
0
1
1
0
1
1
1
1
0
1
1
1
1
1
1
1
1
0
1
1
3
1
1
1
1
1
2
0
1
2
0
1
2
1
1
2
0
2
1
0
1
1
1
1
1
1
0
1
0
2
3
2
0
1
1
1
2
2
2
1
1
0
0
2
1
0
2
0
0
2
0
1
1
1
1
2
1
1
2
2
1
2
1
1
1
1
0
1
1
1
1
0
0
1
0
2
1
0
0
0
2
1
1
1
1
1
0
2
2
0
0
1
1
2
1
1
1
0
1
2
1
0
2
1
2
1
0
1
0
1
2
1
2
2
2
0
0
1
0
2
1
1
0
0
1
0
1
2
2
1
1
0
1
1
1
1
1
0
2
2
1
2
1
2
1
2
2
1
0
1
0
1
2
0
1
2
1
1
1
0
1
2
0
2
0
0
1
1
1
1
0
0
0
1
2
1
1
1
1
1
2
1
2
1
1
1
2
1
0
2
1
2
1
1
2
1
0
0
1
1
2
3
0
0
1
0
1
1
1
2
2
2
1
1
1
1
1
1
1
0
2
1
0
1
0
0
1
1
2
1
0
1
0
1
1
1
1
2
1
1
1
0
1
1
0
1
2
2
0
2
1
1
0
1
2
2
0
1
1
1
1
1
2
0
0
1
0
0
0
0
1
1
1
0
0
1
3
2
1
1
1
0
3
0
1
0
1
0
0
1
1
2
0
2
1
1
0
0
2
1
2
1
0
0
1
1
2
1
1
1
0
0
1
2
0
1
1
1
1
1
1
0
1
1
1
2
1
2
0
2
0
2
0
0
2
2
1
0
1
0
0
2
1
1
1
0
1
1
1
2
1
1
2
0
1
1
1
1
1
1
1
2
1
1
0
0
1
1
1
1
1
1
1
1
0
2
1
1
0
1
2
2
1
2
0
0
1
0
0
1
2
0
1
1
1
1
0
0
0
0
1
2
0
2
1
1
1
4
0
1
0
0
2
1
1
2
0
1
1
2
0
1
1
2
1
1
0
1
1
1
2
1
1
2
1
1
1
0
2
1
0
1
1
0
2
1
1
0
2
0
1
1
0
2
2
1
1
0
2
2
2
2
0
1
1
2
1
0
1
2
2
0
1
1
1
0
1
2
0
1
2
2
1
2
1
0
2
0
0
1
1
1
1
2
1
1
0
1
1
1
2
2
1
0
2
0
0
1
1
1
0
0
2
1
1
1
1
1
1
2
0
1
0
2
1
1
1
1
1
2
1
0
0
2
1
0
1
0
1
1
1
1
1
0
1
2
1
1
1
0
0
2
1
1
1
0
2
2
0
1
0
2
2
0
1
1
5
1
1
0
1
1
1
1
1
0
0
1
0
0
1
1
1
1
2
1
1
0
1
0
0
1
1
0
0
1
0
2
0
1
2
1
2
1
1
1
1
0
1
2
0
0
1
2
2
1
1
1
0
2
1
1
1
2
1
1
1
0
2
0
1
2
2
2
2
1
0
2
1
1
1
0
1
1
2
1
1
0
2
2
0
0
1
0
0
2
1
1
2
1
0
0
2
1
1
0
2
1
1
1
1
1
1
0
1
0
3
1
0
1
2
0
1
1
1
1
1
1
1
1
2
2
2
1
2
1
1
1
1
0
1
1
1
2
2
2
2
0
1
2
0
1
0
1
1
1
2
2
0
1
2
1
1
1
0
0
1
1
0
0
1
0
1
0
0
2
2
1
1
1
2
1
1
1
2
1
1
1
1
0
1
0
1
0
0
1
0
1
1
1
2
0
1
2
1
1
1
1
0
1
1
2
1
1
0
1
2
1
0
3
0
1
0
0
2
1
1
1
1
1
1
1
1
0
2
1
0
1
1
1
1
0
1
1
1
1
1
0
1
1
1
1
0
1
1
0
3
2
0
1
1
0
2
2
0
1
1
0
1
1
1
2
0
2
0
2
2
1
2
0
1
1
1
1
1
3
1
2
1
1
2
1
1
1
0
2
2
1
1
0
1
2
0
1
1
0
1
0
1
0
2
1
0
0
2
1
3
2
1
0
0
1
1
0
2
2
1
1
1
1
0
0
1
2
0
1
2
1
2
2
0
2
0
0
1
1
0
3
2
2
1
1
0
1
2
1
1
2
1
1
0
0
0
1
0
1
2
1
1
1
2
1
0
1
1
2
0
2
2
1
1
1
0
0
0
2
1
2
0
1
2
2
0
0
0
1
1
1
0
1
0
0
1
0
2
0
1
0
1
1
1
1
2
2
1
1
1
2
1
1
2
0
1
0
0
2
1
2
1
4
1
0
0
2
1
1
0
1
0
1
0
1
1
0
1
3
0
1
0
1
2
1
0
1
1
0
1
1
1
1
0
2
2
2
0
1
1
0
2
1
1
1
1
1
1
1
1
0
0
2
2
2
0
2
0
2
0
0
0
0
0
2
2
0
1
1
0
1
2
2
1
2
1
1
0
2
1
2
2
2
2
1
1
2
2
0
1
2
2
1
2
1
0
1
0
2
2
1
1
2
0
2
2
0
0
2
1
1
1
1
0
0
0
2
1
0
1
0
0
0
2
1
0
3
1
1
1
1
1
2
0
1
3
0
0
2
1
0
1
1
1
1
1
1
1
2
0
1
0
2
1
0
2
1
2
1
1
2
1
2
1
1
2
0
1
1
0
2
1
0
0
1
1
1
0
1
1
1
2
1
2
1
1
1
0
1
1
0
2
0
2
2
1
1
2
0
1
1
1
1
1
1
1
0
1
1
0
0
2
2
1
1
0
0
0
1
1
2
1
2
2
0
1
2
1
2
2
2
1
1
1
1
0
1
1
1
1
1
2
2
1
2
1
1
1
0
1
0
1
1
0
2
2
1
1
3
0
1
2
1
2
1
1
1
2
1
1
0
1
0
1
1
1
0
0
0
2
1
1
2
1
0
1
2
1
2
0
0
0
0
0
2
2
2
1
1
2
1
0
2
1
1
2
3
0
1
1
2
1
0
0
1
0
1
1
1
1
1
1
1
0
2
1
2
0
2
1
2
1
1
0
3
1
0
1
1
1
1
0
2
1
0
1
0
1
0
1
2
1
0
1
0
1
2
2
0
1
1
0
1
0
1
1
1
1
1
1
1
1
1
0
1
0
0
1
2
2
1
0
0
2
1
1
1
1
2
0
1
0
1
1
1
2
2
1
1
2
1
0
1
2
1
2
1
0
1
2
1
1
0
2
1
0
0
1
1
1
2
0
0
1
1
2
1
1
2
2
0
1
1
1
1
1
0
1
1
1
1
0
1
1
1
1
1
1
2
0
2
1
1
1
0
1
0
0
1
1
0
1
1
1
1
1
1
1
1
0
1
1
2
1
0
1
1
0
1
0
1
1
2
0
2
1
1
1
0
0
2
1
0
1
2
1
1
0
1
2
1
0
1
1
1
2
1
2
2
1
0
1
0
1
0
2
2
1
1
0
1
1
0
1
1
0
1
2
0
1
2
0
1
2
1
2
2
0
0
1
1
2
2
0
1
1
1
0
1
2
2
2
2
1
1
0
1
0
1
1
1
2
1
0
0
1
1
2
1
1
1
1
0
2
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
3
2
1
1
1
1
2
0
1
1
1
0
0
1
0
1
0
1
0
0
2
2
0
1
0
1
0
2
1
0
2
0
1
1
2
2
2
2
2
0
2
1
1
1
0
1
0
1
2
0
1
0
1
0
2
2
1
0
1
1
2
1
1
2
0
0
1
2
0
1
1
1
1
2
0
0
1
0
2
1
1
2
0
2
2
1
2
1
1
2
1
3
1
2
1
1
0
2
0
1
0
1
1
1
1
2
1
1
1
1
1
1
2
0
1
0
1
1
1
0
2
1
2
2
1
0
0
1
0
1
0
2
2
0
0
0
2
1
0
0
0
2
2
1
1
1
0
1
0
2
2
2
1
0
1
0
2
0
0
1
0
1
1
2
2
1
0
0
1
0
1
1
1
0
0
1
1
1
0
1
1
2
2
2
2
1
4
1
1
1
1
1
0
2
0
1
1
1
2
2
0
0
0
1
1
0
1
1
0
1
4
1
1
1
1
1
0
1
0
0
1
0
1
1
1
2
1
0
0
1
1
1
0
1
2
1
1
0
2
3
1
2
1
2
1
0
1
2
0
0
0
2
1
2
1
1
2
1
1
1
1
1
0
1
1
1
2
2
1
1
0
1
0
0
2
1
1
0
0
0
1
1
2
1
2
3
1
1
0
0
0
0
1
2
0
1
2
2
1
0
2
2
1
2
2
1
1
0
2
2
2
2
2
0
1
0
0
1
1
0
0
0
1
1
2
1
1
0
1
0
2
1
3
1
0
1
1
0
1
1
2
2
1
1
0
1
2
0
1
1
1
0
1
0
0
1
2
0
1
1
1
0
1
2
1
0
0
0
0
1
3
0
1
2
3
0
0
0
1
0
1
2
0
1
1
2
2
1
1
0
2
1
1
0
2
1
1
1
1
1
1
1
1
0
1
0
2
2
1
1
1
0
1
1
2
1
1
1
0
1
1
0
1
2
0
1
0
1
0
1
1
2
0
1
0
1
1
0
0
0
2
1
1
0
1
1
0
0
1
1
0
1
1
1
1
2
1
2
0
0
1
1
0
1
1
1
1
0
0
2
0
1
1
1
1
1
1
2
2
1
1
0
1
2
1
1
1
1
1
1
2
2
1
0
0
1
1
0
1
0
1
1
1
0
1
0
1
0
4
0
0
1
1
1
2
1
2
0
2
2
1
0
2
2
0
2
1
1
1
2
1
1
1
1
2
0
1
1
2
0
2
1
1
1
1
0
1
1
0
1
1
1
1
1
2
1
2
0
1
1
2
0
2
2
1
0
1
0
2
1
0
1
2
2
0
1
1
2
0
0
0
2
1
1
0
0
0
2
1
2
1
0
1
0
1
1
1
1
1
1
1
1
1
1
0
2
0
1
1
2
1
2
1
3
1
2
0
1
1
1
0
1
1
1
0
2
1
0
2
2
0
1
1
1
1
0
0
0
1
0
2
2
1
1
1
1
1
1
1
2
2
1
1
1
1
3
2
0
0
0
1
1
1
1
0
2
1
1
1
1
1
1
0
0
0
2
1
1
1
1
0
1
2
0
1
1
1
1
0
1
1
2
1
0
2
1
2
1
0
1
1
2
1
1
1
2
0
1
1
1
0
0
1
0
2
1
1
1
1
2
1
1
2
1
1
1
0
2
1
2
1
0
0
1
0
1
1
2
2
2
2
0
1
1
1
2
0
0
0
0
1
0
1
1
1
0
1
1
1
1
1
1
0
2
1
2
1
2
2
2
2
2
1
0
0
1
1
1
2
2
1
1
1
1
0
1
1
0
1
1
1
1
2
2
2
1
1
1
0
1
1
1
2
2
2
0
0
1
1
1
0
1
1
1
1
1
1
2
0
0
3
1
1
1
0
0
1
2
0
2
1
0
1
1
0
2
2
1
1
1
2
1
0
0
1
1
0
1
0
0
1
0
0
1
2
2
2
1
0
1
0
1
0
1
1
2
1
1
1
1
0
0
1
2
4
2
0
0
0
1
0
2
1
2
1
1
1
1
1
2
1
1
0
2
1
1
1
1
0
1
2
1
1
2
1
0
1
2
1
0
2
1
2
0
0
1
1
1
1
0
0
1
1
1
1
1
2
0
1
1
1
1
1
0
1
1
0
1
1
1
2
2
1
2
1
0
0
2
2
2
0
0
2
0
1
0
0
1
1
1
1
0
1
1
0
1
0
0
1
1
2
1
1
1
2
1
1
1
2
1
1
0
1
1
1
1
1
2
1
0
2
1
0
1
2
1
2
1
1
1
1
1
1
2
1
0
1
2
2
2
1
2
0
2
1
1
1
2
0
1
1
1
1
1
1
1
0
1
1
2
1
0
1
1
2
2
0
0
2
1
2
1
1
0
1
1
1
1
1
1
1
1
1
0
1
0
1
1
0
1
1
1
1
2
0
1
1
1
0
2
1
2
1
1
1
1
1
2
2
1
0
2
2
1
1
0
1
0
0
1
2
1
2
2
1
2
1
1
1
1
1
2
1
0
1
1
1
1
1
0
2
1
0
1
1
1
1
1
1
1
2
0
1
2
1
0
1
2
3
2
1
0
2
1
2
1
0
1
1
2
0
0
0
0
2
0
0
2
1
1
1
2
1
1
2
1
0
1
1
0
0
1
1
1
3
2
1
0
1
1
1
0
2
2
2
1
1
1
1
1
1
1
0
2
2
1
3
1
2
0
2
2
0
1
0
1
1
1
2
1
1
0
2
1
2
1
1
1
1
1
1
2
1
1
0
2
0
2
1
0
0
0
1
1
1
2
0
0
0
2
1
0
0
1
2
0
0
1
3
1
1
1
2
0
1
0
1
1
1
1
1
1
1
2
0
1
1
4
1
0
2
1
1
1
2
1
0
0
0
1
1
0
1
1
2
2
1
2
2
1
1
1
0
1
0
0
2
2
1
2
1
1
0
0
1
0
0
1
2
1
0
1
1
2
1
2
0
0
1
0
1
1
0
1
1
2
2
1
1
1
1
0
1
0
1
2
1
0
2
1
1
2
2
1
3
1
0
1
2
1
0
1
1
0
1
1
1
1
1
1
2
0
1
0
1
0
0
4
0
1
1
1
0
1
1
1
1
1
2
1
1
1
1
0
0
1
0
1
2
1
1
1
1
1
1
1
2
3
2
1
1
1
3
1
1
2
3
0
1
1
0
1
1
0
2
2
2
1
1
0
2
1
2
1
1
0
1
1
0
0
1
1
1
1
1
0
2
1
1
2
1
1
1
1
0
1
1
1
3
0
0
5
2
0
3
1
1
0
1
1
1
1
1
1
0
1
2
1
1
1
0
0
0
1
0
2
1
2
2
1
2
1
0
1
1
1
2
1
0
0
2
1
1
0
0
1
0
1
2
1
0
2
1
1
0
1
2
2
1
0
1
1
2
0
1
1
1
1
0
1
0
2
1
1
1
2
1
1
0
0
1
2
1
1
0
0
1
1
1
1
1
1
0
1
0
1
2
1
0
2
0
1
0
1
2
1
1
1
0
2
2
1
0
0
2
1
1
1
1
0
1
0
1
1
1
1
1
1
1
2
2
1
1
0
0
1
1
0
1
1
1
1
1
2
1
0
0
1
1
2
0
2
2
0
1
1
1
2
2
1
2
1
0
1
2
2
1
1
1
1
1
1
0
1
1
1
1
1
0
1
0
3
1
1
2
1
1
1
0
0
0
1
2
2
2
0
2
0
1
1
2
2
1
0
2
0
1
0
0
1
1
2
1
1
1
2
1
1
1
1
1
1
2
1
0
2
1
1
2
0
2
1
1
1
1
1
0
1
1
0
1
1
1
2
1
2
1
0
0
0
2
3
0
0
1
1
1
1
1
0
0
1
2
2
1
1
2
1
0
0
0
0
1
1
2
1
0
1
2
1
1
1
1
0
1
0
1
1
1
1
0
1
1
1
1
1
1
1
2
1
1
2
1
2
2
1
1
2
2
2
1
1
1
0
2
0
0
2
1
1
1
2
1
2
0
0
0
2
0
0
1
0
0
2
0
2
1
1
1
1
0
2
0
0
0
2
0
1
2
1
2
2
1
2
1
1
0
2
2
1
0
1
1
0
0
1
2
1
0
0
2
1
0
0
0
2
0
1
0
2
1
1
1
0
1
1
1
1
1
0
0
1
1
1
2
0
0
1
1
1
1
1
0
0
1
1
1
1
2
0
2
2
1
1
0
1
1
1
1
1
1
2
1
2
0
0
1
1
2
1
2
0
1
1
2
0
1
2
1
2
0
3
1
0
1
2
1
2
1
0
0
0
1
0
0
0
0
1
0
1
1
1
1
1
1
1
0
0
2
0
2
0
1
1
1
1
0
2
1
1
1
0
1
1
0
2
1
2
1
1
1
2
0
1
3
2
1
1
1
2
0
1
1
0
1
0
0
1
1
1
1
1
1
0
0
2
1
2
2
2
1
1
1
1
1
0
0
0
0
1
2
0
1
1
1
2
1
1
0
1
2
0
0
2
2
1
2
0
1
0
1
2
0
1
1
0
1
2
0
0
1
1
1
1
1
1
0
0
0
1
1
1
1
1
1
1
0
0
1
0
2
0
2
1
1
1
2
0
1
1
1
1
1
0
0
1
0
1
1
1
1
1
0
2
1
1
1
1
2
1
2
1
1
0
1
1
2
2
2
0
1
1
1
1
1
0
0
1
2
0
2
1
1
1
2
1
0
1
0
1
0
1
0
0
1
0
1
0
1
1
1
2
1
1
2
1
0
2
0
1
1
1
2
1
1
2
1
2
1
2
1
1
2
0
1
1
1
0
0
2
2
0
1
1
1
0
1
1
1
0
1
1
1
0
1
2
1
1
0
0
1
1
1
1
1
2
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
2
3
2
1
0
2
0
2
2
1
1
0
0
2
0
1
1
2
0
0
0
1
0
0
0
2
1
0
1
1
1
0
2
1
1
0
0
1
1
1
2
2
1
1
1
2
0
0
1
2
0
1
2
0
1
0
0
1
1
0
1
0
0
2
2
1
0
0
1
1
2
0
1
1
1
2
1
2
1
0
1
1
1
2
2
2
2
2
0
2
2
1
0
1
1
1
1
1
1
1
1
2
0
1
2
2
1
0
2
1
1
3
0
1
2
0
2
0
0
1
1
2
2
1
1
0
2
0
2
0
0
2
1
1
2
1
1
1
0
2
1
1
0
2
1
0
1
2
1
2
1
1
2
1
1
0
2
1
0
0
0
0
0
1
0
1
1
0
0
1
0
0
1
0
2
1
1
1
0
0
0
0
3
2
1
1
1
1
1
1
0
1
0
1
1
0
1
0
1
1
1
1
0
1
2
0
1
1
2
1
1
0
0
2
2
1
1
0
1
0
1
1
0
1
0
1
0
1
1
1
1
1
1
1
1
0
0
2
1
1
1
1
0
2
0
1
1
2
0
1
3
1
1
2
2
1
1
1
1
1
1
1
1
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
2
2
1
2
1
1
0
1
2
0
0
1
1
2
2
0
0
1
1
1
1
2
1
1
0
1
1
0
0
1
1
0
1
1
0
1
0
2
4
1
1
1
0
0
1
1
1
0
2
0
2
1
2
2
2
0
2
1
1
2
1
1
1
1
2
1
0
1
1
1
1
1
1
0
1
1
0
0
0
2
1
2
0
1
0
2
0
2
0
0
0
1
1
0
1
1
0
0
2
2
0
2
1
2
2
1
0
1
2
1
1
0
1
1
0
2
2
2
1
2
1
1
1
3
1
0
2
0
2
0
2
1
1
2
0
1
0
2
2
0
0
0
1
1
1
0
0
2
1
0
1
2
1
1
1
1
1
0
3
2
1
1
1
1
0
1
2
0
2
0
0
2
0
1
1
0
1
2
0
0
2
1
0
1
2
1
2
1
2
0
2
0
2
1
1
2
1
0
2
1
0
1
0
2
0
1
1
1
1
2
2
1
1
2
1
0
0
0
2
0
0
1
2
0
1
1
2
1
2
1
2
1
1
0
1
2
2
1
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
1
0
0
1
1
1
1
2
1
1
0
1
1
0
1
1
2
0
1
1
2
1
0
1
1
1
2
2
2
1
1
0
1
0
2
1
0
2
0
2
1
1
1
2
0
2
1
1
1
0
1
1
0
2
1
0
2
1
2
1
0
2
0
0
1
1
2
2
1
1
0
2
2
2
0
0
1
0
0
1
0
2
1
1
2
1
1
1
1
1
2
2
1
1
0
2
0
1
1
2
1
1
0
1
2
1
1
1
1
1
2
1
0
2
2
1
1
1
1
2
1
0
1
2
0
2
2
1
1
2
2
0
0
1
0
1
1
1
0
1
0
2
2
2
1
1
1
3
2
2
0
0
1
1
1
1
2
0
1
1
1
0
1
1
1
2
0
1
2
1
1
2
0
1
0
0
0
2
0
3
0
0
1
1
1
0
2
2
2
1
1
1
2
2
1
1
1
2
2
0
1
1
1
1
0
1
1
2
0
0
1
0
1
1
1
2
1
0
1
0
0
1
1
2
1
1
0
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
0
1
2
0
1
0
0
1
1
1
1
3
1
1
1
1
1
0
0
1
1
1
1
0
0
1
0
2
0
1
0
1
2
1
0
2
1
1
1
1
1
1
2
0
1
0
0
1
0
1
0
1
2
2
0
0
1
1
2
0
2
1
0
0
0
1
1
1
0
0
1
1
1
0
2
0
1
0
1
0
2
1
1
1
1
0
2
1
1
1
1
1
1
2
1
0
2
1
2
1
1
2
1
0
1
1
1
2
3
2
0
1
0
1
1
1
2
1
0
2
2
0
1
0
0
0
2
0
2
1
1
0
1
0
1
2
2
0
1
1
1
0
0
1
2
2
0
1
0
1
1
0
0
1
1
1
0
2
1
0
1
2
2
0
1
0
0
1
4
0
0
1
0
0
2
0
1
2
1
1
0
1
2
1
1
0
1
1
1
2
1
1
0
0
0
1
1
1
1
1
0
0
1
1
1
1
1
0
2
1
0
1
0
1
1
0
1
2
1
1
0
0
0
1
0
1
2
1
1
1
1
1
2
0
2
0
0
2
0
1
1
1
0
1
1
1
1
2
0
1
0
0
1
0
1
2
2
2
2
0
3
1
0
1
1
1
0
0
1
1
0
1
1
1
2
0
0
1
1
2
0
0
1
1
1
2
1
1
1
1
1
1
0
2
1
0
1
1
2
1
0
1
1
2
1
0
1
1
1
2
0
2
0
2
2
0
1
1
1
1
1
1
0
2
1
0
1
1
0
1
1
2
1
1
2
0
0
2
2
1
1
0
1
2
2
1
1
0
0
1
0
1
2
1
1
0
1
1
1
2
0
0
1
1
1
1
1
0
1
0
1
1
0
0
2
2
1
2
1
0
2
1
1
2
2
1
0
1
1
1
1
2
0
1
0
1
2
1
1
0
2
1
2
1
1
2
0
0
2
1
1
1
0
0
1
0
2
1
0
1
2
1
1
0
0
2
0
1
1
1
1
1
0
0
1
1
0
2
1
1
1
2
1
0
1
0
1
2
2
1
1
1
1
2
0
2
2
0
1
1
1
1
1
0
0
1
2
2
1
1
0
2
1
1
0
0
1
0
1
1
0
0
1
0
0
2
1
1
3
0
0
1
1
0
1
1
1
0
2
0
2
2
2
1
1
0
0
0
1
2
1
1
1
0
2
1
1
0
2
1
1
5
1
1
1
0
1
1
1
0
1
2
1
0
1
0
1
1
2
2
3
1
0
1
2
0
1
0
1
2
2
2
1
1
0
0
1
0
2
1
0
1
2
1
1
0
0
2
1
0
1
1
0
1
0
1
1
1
0
1
1
1
1
0
2
0
1
1
1
1
1
1
1
1
0
1
1
1
1
2
1
2
0
1
1
1
1
2
1
0
2
1
1
1
0
1
1
0
0
0
2
1
0
2
1
0
0
1
2
1
1
0
1
1
2
0
0
1
0
1
0
2
3
1
2
0
2
2
1
2
1
3
2
1
2
1
0
1
2
1
0
0
0
1
0
1
1
2
1
1
1
1
0
1
2
2
1
2
1
1
1
1
2
0
2
2
0
2
0
1
2
0
2
1
0
0
1
1
1
0
0
1
1
1
1
0
1
1
1
1
1
1
1
0
2
2
0
0
0
0
2
0
1
2
0
0
2
0
1
2
1
1
1
0
1
1
2
2
0
1
1
1
2
2
1
1
1
2
0
2
4
1
0
2
1
1
2
1
1
1
1
1
2
2
1
1
1
1
0
0
1
1
0
0
2
1
1
0
1
1
0
1
1
2
0
2
1
0
0
1
0
2
0
2
1
1
1
0
1
2
1
1
0
2
1
1
1
1
0
1
1
1
1
1
0
1
2
1
5
1
2
1
0
1
5
1
0
1
1
1
0
0
0
3
0
1
1
1
0
2
1
1
1
0
0
1
1
1
1
1
1
3
2
2
1
2
0
1
1
1
0
2
2
2
0
0
1
2
2
1
1
0
1
1
2
2
2
1
1
1
0
1
1
0
0
1
1
1
1
2
2
1
2
0
1
0
1
1
0
1
1
1
2
2
1
1
0
2
1
0
2
2
2
1
2
2
1
1
2
2
0
0
1
1
1
1
1
0
1
2
0
1
1
1
1
1
1
0
1
1
2
0
1
2
1
2
1
1
0
0
1
1
1
0
2
1
2
0
0
0
1
2
1
1
0
1
2
1
1
1
1
2
1
1
1
2
2
1
2
1
1
1
1
1
2
1
1
2
1
2
1
1
2
2
1
3
2
2
3
0
1
0
2
2
2
1
3
0
0
2
0
1
2
2
1
3
2
1
1
1
2
1
2
0
1
1
1
2
0
2
1
0
1
2
1
1
1
1
2
1
1
2
2
0
0
0
2
1
1
2
1
1
1
0
0
1
0
0
1
2
1
0
1
1
1
1
2
0
1
3
1
1
0
2
1
1
2
0
1
1
1
1
2
2
1
1
0
0
0
0
2
1
1
1
1
0
0
1
1
1
0
2
2
1
1
2
2
0
0
0
0
1
1
0
1
0
1
0
0
1
0
1
0
2
0
0
1
2
1
1
2
1
0
1
1
2
0
1
2
1
1
1
1
1
1
1
0
2
2
1
1
1
1
2
2
2
1
1
1
0
1
1
0
1
2
0
1
2
1
0
2
0
1
2
2
2
0
2
1
1
1
1
1
2
2
1
0
1
2
1
1
0
1
1
1
0
1
1
1
1
2
1
0
1
0
0
2
0
1
1
1
1
2
1
1
1
2
1
2
1
2
1
1
1
1
1
1
0
2
1
0
1
2
0
1
1
1
1
0
1
0
0
1
1
0
0
0
1
2
1
2
2
1
0
1
1
1
2
0
1
1
1
0
1
1
0
1
1
1
1
2
0
1
1
0
1
0
0
0
1
0
1
1
0
3
1
1
1
1
2
0
1
1
0
2
1
0
1
0
0
1
1
0
1
1
1
0
2
1
1
1
2
0
2
0
0
0
2
2
6
0
0
2
1
2
2
1
0
1
1
1
1
0
0
2
1
2
0
1
0
1
1
0
2
0
0
1
1
0
0
2
1
1
0
1
0
1
0
0
1
1
2
2
1
1
1
1
1
2
1
0
1
0
2
2
1
1
0
0
0
1
1
0
1
2
1
2
0
0
1
2
0
2
0
0
0
0
0
1
0
1
2
0
1
2
2
0
1
0
2
2
2
1
0
1
2
2
6
1
1
1
1
0
1
1
1
1
2
1
0
2
0
1
3
1
0
2
2
1
0
0
2
2
0
2
1
1
1
0
1
1
1
0
0
0
2
2
1
1
2
1
2
1
1
6
0
1
1
1
2
0
1
2
2
1
1
1
2
1
0
1
0
2
2
1
0
1
2
1
2
2
1
1
1
1
1
2
0
1
1
1
2
0
1
1
2
2
1
1
0
1
1
1
0
1
1
2
2
1
1
0
1
1
0
0
1
1
1
2
0
1
0
2
1
1
1
0
1
1
1
2
0
2
0
1
0
0
0
1
0
2
1
2
1
1
1
0
2
2
1
2
0
1
2
0
0
1
0
0
1
1
1
1
2
1
1
1
1
2
0
1
2
1
1
1
0
1
1
1
1
2
2
1
1
0
1
1
0
1
2
1
2
0
2
3
0
1
2
2
2
2
0
1
1
1
1
2
0
1
1
2
2
0
0
1
2
1
1
1
1
0
1
1
2
1
0
0
1
1
2
0
2
0
0
0
2
0
0
1
1
2
1
1
2
1
1
1
1
0
1
2
0
1
1
1
1
1
1
1
1
1
0
0
2
1
0
2
1
1
1
0
1
0
1
1
0
1
1
1
0
1
2
2
2
1
0
0
2
0
0
1
0
1
1
2
3
1
1
1
0
0
1
1
1
1
1
1
2
2
0
2
1
1
2
1
2
1
3
1
0
0
2
0
0
1
1
2
0
0
1
0
1
0
0
1
0
2
1
1
0
1
1
2
1
0
0
1
2
1
1
0
1
0
1
1
1
2
0
1
1
2
2
0
1
1
0
1
0
2
0
2
0
0
2
2
0
1
0
1
2
1
1
2
0
1
0
1
1
1
2
0
2
1
1
1
2
1
1
2
1
1
2
1
1
2
0
0
1
2
2
2
1
1
2
1
0
1
2
1
2
1
0
0
1
0
2
0
1
1
2
0
1
1
1
1
2
0
1
0
2
1
1
2
2
2
1
0
1
1
1
2
1
0
0
0
0
0
1
2
1
1
1
2
1
0
0
0
0
1
1
0
1
2
1
1
0
2
0
0
1
1
1
1
1
1
1
1
0
1
2
1
2
0
1
1
1
1
1
1
0
1
2
0
1
2
1
0
1
2
1
0
1
0
1
0
2
1
0
2
3
1
0
0
0
1
0
0
2
1
2
2
0
1
2
1
1
0
0
2
0
1
1
1
1
2
2
0
1
1
2
1
0
0
0
0
1
0
0
1
1
1
1
1
1
1
1
1
0
0
0
0
2
1
3
2
2
1
1
1
1
1
1
0
2
1
0
1
2
0
1
2
1
0
0
1
0
0
1
0
1
1
2
0
1
1
1
1
0
0
1
0
0
2
1
0
2
1
0
2
2
0
1
0
0
1
0
1
0
1
1
1
1
2
1
2
1
0
1
0
2
0
1
1
2
2
0
1
0
1
1
1
1
1
2
0
0
0
1
1
2
0
2
1
1
1
0
1
1
0
2
2
1
0
2
1
2
1
0
0
0
0
1
1
1
1
2
0
1
1
1
1
1
1
0
0
0
2
0
1
1
1
0
0
0
1
0
1
1
2
1
1
2
2
0
1
1
0
3
2
1
1
1
1
0
1
0
0
1
1
1
1
1
1
2
1
1
0
0
1
0
1
1
1
1
2
0
0
0
2
1
1
1
0
2
1
1
1
1
2
2
2
0
1
1
2
1
0
1
3
1
2
1
1
0
1
2
0
0
0
1
1
1
2
1
1
1
0
2
1
0
1
0
1
1
0
1
2
0
0
0
0
1
0
0
0
2
1
1
2
2
2
2
1
1
1
1
1
2
1
1
1
1
2
1
1
1
0
1
2
1
1
0
2
1
0
1
1
1
1
0
2
1
1
1
0
2
0
1
2
1
1
1
0
1
1
1
0
2
2
1
1
0
1
1
1
2
1
1
0
1
1
1
1
1
2
2
1
1
0
1
2
0
1
2
2
1
2
1
1
0
2
0
0
2
1
1
0
1
1
0
2
1
1
1
1
0
1
1
0
2
1
0
0
1
1
1
2
2
1
1
1
0
0
1
2
0
1
1
0
1
4
2
1
2
1
2
2
0
0
1
2
1
1
2
0
0
2
1
0
1
0
2
1
2
1
0
1
1
1
0
0
1
2
1
2
2
0
1
0
2
0
0
1
2
0
1
1
2
1
1
1
1
0
1
0
1
0
2
1
2
1
1
0
1
0
2
0
2
1
1
0
0
0
1
1
0
1
1
1
1
0
2
0
0
0
0
2
2
0
1
1
1
0
0
1
0
1
0
1
1
2
2
1
1
1
2
0
2
1
0
1
1
0
1
2
1
0
1
1
2
1
0
0
0
2
0
2
1
2
2
1
0
1
2
2
0
1
0
1
0
1
1
0
1
2
2
3
0
1
0
1
2
1
0
1
2
1
1
0
0
1
1
1
1
1
1
1
1
0
0
0
2
1
0
1
0
1
0
1
1
2
2
0
2
0
1
1
2
0
2
2
2
2
0
2
1
2
0
1
0
1
0
0
0
0
1
0
0
1
2
1
1
0
1
1
0
0
0
1
2
1
1
1
2
1
0
1
0
1
1
1
1
0
1
1
1
1
1
2
0
0
2
1
0
1
1
1
1
2
1
2
1
2
1
1
0
1
1
2
0
0
1
1
0
0
0
1
1
2
1
2
1
2
1
1
1
1
1
1
2
1
2
2
0
0
1
1
1
0
1
1
0
1
0
0
2
2
1
1
1
1
0
2
1
1
0
0
1
0
1
1
0
2
0
1
1
2
1
1
0
0
1
2
2
2
0
0
1
1
0
1
1
1
2
1
1
1
1
1
1
1
4
1
1
1
1
1
1
1
2
1
1
1
0
1
1
1
0
1
1
1
0
1
1
1
0
1
0
1
0
2
1
1
1
1
0
1
1
0
1
1
0
1
2
0
0
2
1
1
1
2
2
0
0
0
2
1
0
0
1
2
0
1
2
1
0
1
1
0
1
0
1
2
1
1
2
0
0
0
1
1
2
1
1
0
1
1
1
0
1
0
0
1
1
1
1
0
1
1
2
0
1
0
1
1
1
1
2
1
1
1
0
0
1
3
1
2
1
1
1
1
1
1
1
1
1
0
1
0
1
1
0
0
0
2
1
2
0
0
1
1
1
1
1
1
1
1
0
1
0
2
1
1
0
0
1
1
2
3
1
1
1
2
2
1
1
1
0
0
1
1
2
1
2
2
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
0
0
2
1
2
0
2
2
1
0
2
1
1
1
1
1
1
1
1
3
1
0
1
0
0
2
0
1
1
1
0
0
1
1
2
1
1
2
1
2
1
1
1
1
2
2
2
1
0
1
1
0
0
0
0
1
1
1
1
0
1
2
2
0
1
2
0
2
1
1
1
1
1
2
1
1
0
2
0
1
1
1
1
0
0
0
2
2
2
1
1
0
2
1
1
0
1
1
1
2
1
1
2
1
0
0
1
2
1
2
1
2
2
0
0
0
0
2
0
0
1
1
0
2
2
1
1
1
4
0
2
0
0
1
0
2
3
1
2
0
1
1
1
1
2
0
0
1
1
1
0
0
2
1
1
1
1
1
1
0
0
2
2
0
1
0
1
1
1
1
1
0
0
1
1
0
0
1
2
1
0
1
2
1
0
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
0
1
2
1
1
2
0
1
2
1
1
0
0
2
0
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
0
1
1
0
1
0
2
0
1
0
2
2
2
2
0
1
0
1
1
1
0
1
2
1
1
2
2
2
2
2
2
1
0
1
1
1
0
1
2
1
1
1
1
0
1
0
2
1
1
0
1
2
1
1
0
1
0
1
1
2
2
1
2
1
0
1
0
1
1
0
2
0
0
2
1
1
1
1
2
2
1
2
2
2
0
1
0
1
1
1
2
2
1
1
2
0
1
2
0
1
2
2
0
1
1
1
0
0
1
0
1
1
1
1
1
2
1
1
1
1
0
0
1
0
0
2
0
1
1
1
0
1
2
1
1
1
1
0
1
1
1
1
1
2
2
1
2
1
2
1
1
1
1
1
1
0
0
0
1
2
0
2
1
1
1
2
2
1
1
1
0
1
0
0
0
0
2
1
0
2
1
1
1
1
2
1
1
1
0
1
2
1
1
1
0
0
0
0
1
1
0
0
1
1
1
0
1
1
1
0
1
1
1
1
0
0
2
1
1
2
2
0
1
1
0
0
2
1
2
0
2
0
0
0
1
2
1
0
0
1
2
0
0
1
2
1
2
0
0
1
1
0
1
0
2
0
1
0
2
1
1
1
0
1
1
1
2
1
1
1
1
1
1
1
1
1
0
1
1
1
3
0
0
0
3
1
2
2
1
0
0
2
0
0
1
0
1
0
1
0
0
0
1
2
1
1
0
1
2
1
2
0
2
1
2
1
1
1
0
1
2
2
1
1
0
1
2
1
0
0
0
1
0
2
1
1
1
1
1
1
0
1
2
1
1
1
2
2
2
1
0
0
0
1
1
1
0
1
1
0
0
1
0
1
1
2
0
1
0
0
1
1
0
1
0
1
0
0
2
1
2
2
0
1
0
1
2
1
1
1
0
2
0
0
0
2
1
0
0
1
1
0
1
1
0
1
0
1
0
2
1
1
0
1
1
1
2
0
0
1
0
1
1
1
0
1
1
2
0
0
0
1
2
1
1
2
2
0
2
1
1
0
1
1
0
0
0
1
1
4
0
1
0
2
1
1
2
1
1
0
1
2
1
2
0
0
1
1
2
1
1
0
0
2
2
1
0
2
1
1
0
1
2
1
0
2
1
1
2
3
0
1
2
1
1
0
1
1
1
1
1
2
61
1
0
2
2
1
1
1
2
0
1
1
1
2
1
1
2
0
1
1
0
1
1
1
2
1
0
1
1
1
1
2
1
0
2
2
1
1
2
0
0
1
0
1
2
1
1
1
2
3
1
2
0
0
1
1
1
2
2
1
1
1
1
1
0
0
1
1
0
1
1
0
1
2
2
0
2
2
3
1
2
2
0
0
0
0
2
1
1
0
1
2
1
0
1
0
1
1
2
2
0
1
1
1
0
1
1
1
0
1
1
2
2
2
1
2
1
1
1
1
2
1
1
1
0
0
1
2
1
0
0
0
1
1
2
2
1
1
1
0
1
1
2
2
0
0
3
1
0
1
2
1
1
1
1
2
0
1
1
1
1
1
1
1
2
1
1
0
1
1
1
2
0
1
1
2
1
0
1
0
1
2
0
1
0
2
1
0
0
1
1
0
1
1
1
1
2
1
2
1
1
1
1
0
2
0
2
1
0
1
1
1
1
2
1
1
2
1
2
1
0
2
2
0
0
1
0
2
0
1
1
1
0
1
1
1
0
0
1
2
1
1
1
1
1
1
1
0
2
1
1
0
2
1
2
2
2
2
2
1
1
1
0
0
1
1
0
1
1
2
1
1
1
2
1
1
1
1
1
0
2
1
1
2
0
1
1
0
1
1
1
1
1
0
1
0
2
2
0
1
1
1
1
0
2
2
1
4
0
0
2
1
0
0
1
2
0
2
4
0
1
2
1
0
2
1
1
1
1
1
0
2
0
1
2
0
2
1
2
2
1
2
0
1
2
1
0
0
1
2
1
1
1
1
2
2
0
1
1
2
1
2
0
2
2
1
2
1
1
0
1
1
1
0
0
1
1
2
0
0
1
1
0
1
0
1
1
1
1
0
1
2
0
1
1
1
2
1
1
1
2
0
1
0
1
2
1
1
1
1
1
2
1
1
0
1
1
3
2
2
0
2
0
1
1
1
2
1
0
1
2
1
0
1
0
1
0
1
2
0
3
1
1
0
1
1
0
1
1
2
0
0
2
1
2
0
0
1
1
1
0
2
1
0
1
2
2
1
0
1
0
1
1
1
1
2
1
1
0
0
1
2
0
0
1
1
1
1
0
2
1
0
1
1
2
2
1
1
1
1
0
0
0
0
0
1
1
1
0
2
1
1
1
2
0
1
0
0
1
0
2
1
1
1
1
0
1
2
2
1
0
1
2
0
2
1
1
2
0
1
1
2
1
1
1
0
1
1
0
1
1
1
1
0
0
2
1
2
1
1
0
1
1
2
0
1
1
2
2
1
1
1
1
0
0
0
1
0
2
1
1
1
1
1
1
2
2
1
0
1
0
1
1
1
1
0
1
1
1
2
0
2
0
1
1
2
0
0
1
1
1
2
3
0
0
1
0
1
1
0
7
0
2
0
0
1
0
2
0
2
0
1
2
1
2
1
1
1
0
1
1
1
1
1
1
2
1
1
0
0
0
0
1
1
1
2
2
2
1
1
1
1
2
1
1
1
2
1
0
1
1
0
1
1
1
0
1
1
1
1
0
1
1
2
1
1
1
2
1
1
1
1
2
1
2
2
1
2
0
1
1
1
0
0
1
2
1
2
0
0
2
2
0
1
3
0
1
1
1
1
1
1
1
1
1
1
2
2
0
1
1
0
1
1
0
1
1
2
0
1
1
0
2
2
1
1
1
0
1
1
0
1
1
1
1
0
0
1
0
1
0
2
0
1
0
1
1
1
1
1
2
0
1
1
1
0
1
1
2
2
2
2
0
1
2
1
1
1
2
1
0
1
2
1
1
1
1
2
1
0
1
0
1
0
1
1
2
0
1
1
0
1
0
0
2
1
2
1
1
1
1
1
1
0
1
1
1
1
2
2
1
0
0
0
0
0
0
1
1
0
0
1
1
0
1
0
1
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
1
2
1
1
0
1
2
2
2
1
1
2
2
2
1
1
0
2
1
1
1
2
1
2
0
1
2
2
1
1
0
1
2
1
2
0
1
1
0
2
0
1
1
0
1
1
1
2
1
1
0
1
1
1
0
1
2
0
1
1
0
0
2
1
0
1
1
1
2
2
1
2
0
2
2
1
2
2
0
2
1
1
1
0
1
0
2
0
1
1
0
0
1
3
1
0
0
0
1
2
1
1
1
1
1
1
1
1
1
1
2
0
1
2
0
1
0
1
1
2
1
1
2
1
1
0
0
0
2
0
1
2
1
0
1
0
1
0
1
2
2
2
1
3
2
2
0
1
0
0
1
0
1
1
0
1
2
2
0
0
1
1
0
0
1
0
1
1
1
2
0
0
0
0
2
0
2
1
1
1
0
1
2
0
2
1
1
1
2
1
1
2
1
2
0
2
1
1
1
0
2
0
0
1
1
1
1
0
0
0
0
1
0
0
0
1
1
1
2
0
1
1
2
2
0
0
1
0
2
0
1
1
1
1
1
1
1
1
0
1
1
0
2
2
2
1
1
1
2
0
1
1
1
0
2
1
1
0
2
1
1
1
0
1
0
0
2
1
1
2
0
1
1
0
1
0
0
3
1
1
1
1
1
0
0
1
1
1
1
0
1
0
1
1
0
1
1
0
2
1
0
1
1
1
1
1
1
2
1
0
2
2
1
0
2
2
0
1
1
1
1
2
2
1
1
0
2
1
1
0
2
1
2
1
1
0
1
1
1
1
1
1
1
1
0
1
2
0
2
1
1
1
2
1
1
0
1
1
1
2
1
0
1
1
0
1
1
0
0
1
0
0
1
0
1
2
2
0
1
1
3
1
0
1
0
1
2
2
0
0
1
1
2
2
1
2
0
2
2
2
1
1
2
0
1
2
1
1
2
0
0
0
1
0
1
2
1
2
2
1
1
2
2
1
1
1
0
0
2
0
0
1
1
0
0
2
2
2
2
1
1
1
1
2
1
1
0
2
0
2
1
2
1
0
2
0
0
0
0
1
1
0
1
1
1
1
1
2
1
1
2
1
2
1
1
2
0
2
1
1
2
2
0
2
0
2
0
2
0
1
1
1
1
0
2
1
2
1
2
1
0
1
1
2
0
2
1
2
1
1
0
1
0
0
1
1
2
1
0
2
1
1
1
0
0
1
1
1
1
0
1
2
0
1
1
1
1
1
2
0
1
1
2
0
2
0
2
2
2
1
1
1
1
2
1
2
0
1
1
2
1
1
1
1
1
1
1
1
1
0
0
1
2
0
1
1
2
1
1
2
1
0
1
1
0
1
1
0
0
1
2
1
1
1
1
0
0
1
2
2
0
2
1
0
0
1
1
1
2
1
1
2
0
1
1
1
1
1
1
2
1
1
2
1
0
2
1
2
1
2
1
1
0
1
1
1
1
2
1
1
1
1
0
2
1
1
1
1
2
1
1
1
1
2
1
2
0
0
0
1
2
0
2
1
0
0
1
0
1
2
0
0
0
1
0
1
1
1
2
0
0
1
1
2
0
2
1
1
1
1
0
1
0
2
2
1
2
0
1
1
1
2
0
1
0
2
2
0
2
1
1
1
1
1
1
0
1
0
2
1
1
1
1
1
0
1
0
1
0
2
1
1
0
1
1
1
2
0
1
1
2
1
2
1
1
0
2
2
1
0
2
2
0
1
2
0
2
2
0
2
1
2
1
1
1
2
0
2
1
0
0
1
2
1
1
1
0
1
2
0
1
1
0
2
0
0
0
1
2
1
1
1
2
0
2
1
0
1
0
0
1
1
1
1
2
1
0
1
1
1
0
1
1
1
1
0
2
0
1
1
2
1
1
2
1
1
1
0
0
2
1
0
1
2
0
0
0
1
1
0
4
2
2
0
1
1
0
1
1
1
0
1
1
1
2
1
0
1
1
1
0
1
1
2
2
2
1
1
1
2
1
0
1
1
0
1
1
1
1
2
1
0
1
1
1
1
1
2
0
1
1
2
1
0
1
0
1
2
0
0
2
0
2
2
2
2
3
0
0
0
1
1
0
1
1
0
0
0
1
1
1
1
0
0
0
0
1
0
2
1
0
2
2
2
1
1
0
1
1
0
0
0
2
1
1
1
1
1
2
1
1
1
2
1
2
1
0
1
1
1
1
2
1
1
0
2
1
2
0
1
0
0
1
2
1
0
1
1
1
1
0
2
1
2
1
0
2
1
2
0
1
3
2
1
1
0
1
2
1
0
2
2
2
1
1
1
1
0
1
2
0
1
2
1
1
1
1
2
0
1
1
1
1
1
2
2
1
1
2
1
1
0
1
0
0
1
0
0
1
1
1
1
1
2
0
1
0
0
1
0
1
1
1
0
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
3
2
1
2
2
0
0
1
3
1
2
2
1
0
1
1
0
0
0
2
0
1
2
1
2
1
1
1
0
2
1
0
1
1
3
0
1
0
1
1
1
1
0
1
0
0
1
0
1
2
1
2
1
1
1
1
2
2
2
0
1
2
0
1
0
1
0
2
0
1
2
4
1
2
1
2
0
1
1
2
0
1
0
1
0
0
1
3
0
2
0
0
0
1
0
1
0
2
0
1
2
1
1
0
2
2
0
1
2
1
1
0
2
1
0
0
0
1
0
2
0
1
1
1
0
2
1
1
2
1
2
1
1
1
0
1
1
1
2
2
1
0
1
1
0
1
1
2
2
2
2
1
1
1
1
1
0
1
1
0
1
0
1
1
0
1
2
2
2
1
1
1
2
2
1
2
2
0
1
1
1
1
1
1
1
1
2
2
0
0
2
0
1
2
2
1
1
2
0
1
1
0
2
1
2
1
0
2
2
1
1
1
0
0
2
1
0
1
0
1
0
1
0
1
1
1
2
2
3
2
0
2
0
0
1
1
1
2
2
1
2
1
2
0
0
2
1
2
2
3
0
0
2
2
0
1
2
2
1
1
0
0
1
0
0
1
1
1
1
1
1
1
2
0
3
2
2
0
0
2
0
0
1
0
1
2
0
0
2
1
1
1
1
0
0
1
1
1
4
1
0
1
1
2
1
1
1
1
2
2
2
1
1
2
1
1
2
1
0
1
0
1
2
1
2
0
1
0
1
1
0
2
0
1
2
2
1
1
1
2
1
2
2
0
2
2
1
0
2
2
1
1
0
1
2
1
1
2
1
0
0
1
1
1
0
0
2
0
0
1
2
1
0
0
1
1
1
0
1
2
0
1
0
2
1
1
0
1
0
2
4
1
1
0
1
2
0
1
1
2
1
2
1
1
1
1
2
2
1
2
0
1
1
0
1
0
2
1
1
1
2
2
2
1
4
1
0
1
0
1
0
0
1
1
1
3
1
1
0
2
1
2
1
1
0
1
1
0
2
1
1
2
0
1
2
0
1
0
2
1
2
1
0
1
1
2
0
0
0
1
1
1
1
1
2
2
2
0
1
1
0
1
2
0
1
1
1
2
0
1
1
1
2
0
0
1
1
1
2
0
1
1
1
1
0
1
0
0
1
1
0
1
2
1
0
1
0
2
1
2
0
2
1
1
2
1
2
1
1
1
1
1
1
0
1
1
1
1
0
1
1
1
1
4
1
0
1
2
1
0
0
1
1
1
0
1
0
1
1
0
2
2
1
2
0
1
1
1
1
3
0
1
2
0
0
1
1
2
0
0
0
0
0
2
0
0
1
1
1
1
1
1
1
1
0
1
1
0
0
2
1
1
1
1
1
1
1
2
0
0
1
1
2
1
1
1
1
0
1
1
1
2
1
1
1
1
2
1
2
1
1
2
2
1
1
2
1
2
1
2
2
2
0
1
1
1
1
1
1
1
1
1
1
1
0
2
1
1
0
1
1
1
1
1
2
1
2
1
1
0
1
1
2
2
0
1
1
1
0
1
1
2
0
2
1
0
1
0
0
1
1
2
1
0
1
1
1
2
1
1
2
1
1
1
1
1
1
0
2
2
2
0
1
2
1
0
2
0
1
0
2
2
2
1
1
1
0
1
1
3
1
1
0
1
2
0
1
1
4
0
2
1
1
1
0
0
0
2
1
1
0
0
2
4
1
0
1
1
2
1
1
1
1
0
2
1
2
1
1
1
1
0
0
2
1
3
3
0
0
1
1
0
2
0
0
0
2
0
1
1
1
1
2
2
3
1
1
1
1
1
0
0
0
1
2
1
1
0
2
0
2
2
2
1
2
2
0
2
1
1
1
1
1
1
1
2
2
2
1
2
1
1
1
1
1
1
2
1
2
1
1
2
1
2
2
1
0
2
1
1
2
1
0
2
0
2
0
0
0
2
1
1
0
1
1
0
2
0
0
0
0
1
0
1
2
1
2
2
1
1
2
1
2
1
0
1
0
1
1
1
1
2
1
1
2
1
0
0
1
0
1
1
2
1
0
1
1
1
1
1
0
1
0
0
1
0
2
1
0
2
1
1
2
0
0
2
1
1
0
0
1
1
2
1
0
1
0
0
1
1
0
0
2
2
2
1
0
2
2
1
1
1
1
2
0
2
1
2
0
0
1
2
1
1
1
1
1
1
1
0
1
2
2
0
1
0
0
0
1
1
0
0
1
1
2
1
2
2
1
0
0
0
1
1
1
2
0
1
1
0
0
2
1
0
1
0
0
1
0
1
2
1
0
1
1
0
2
2
1
1
1
0
1
2
1
1
2
1
2
1
1
1
0
1
1
1
1
0
1
1
2
1
0
1
2
1
1
1
1
1
1
2
1
1
0
0
1
1
1
1
1
1
4
1
1
0
1
1
1
0
0
0
2
1
1
1
0
0
1
0
0
1
1
1
1
1
2
0
1
0
0
2
1
1
0
0
1
1
2
1
1
1
1
1
1
0
1
0
1
0
0
0
0
2
1
0
1
1
0
1
1
1
0
1
0
2
2
2
0
1
1
1
0
1
1
0
0
1
2
1
2
1
2
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
0
1
1
0
0
1
0
1
1
0
2
1
2
1
1
1
1
1
1
2
1
0
1
1
0
2
1
2
2
1
1
2
2
1
0
1
2
1
2
1
1
1
2
1
0
1
0
1
1
2
2
0
2
1
1
1
1
1
1
0
2
1
2
1
1
1
0
1
1
0
0
1
0
2
1
1
1
1
2
2
0
2
1
1
0
1
0
3
1
0
1
1
1
1
1
1
0
1
1
2
1
2
0
1
2
1
1
1
1
2
1
2
1
1
0
0
1
1
1
0
1
1
2
1
0
2
1
0
0
2
2
2
1
1
1
1
0
0
0
0
1
2
1
1
2
1
1
1
1
1
1
1
1
0
2
1
0
2
3
0
1
1
2
1
2
1
1
1
0
1
1
0
1
1
4
0
2
1
1
0
1
1
0
0
1
2
2
1
1
1
2
1
2
2
0
0
1
2
1
1
2
1
1
2
0
0
1
2
1
1
1
1
2
1
1
2
1
1
1
2
1
1
0
0
1
0
1
0
0
2
1
0
0
2
0
0
1
1
0
0
1
2
1
1
1
1
1
1
1
1
1
2
0
1
1
0
0
1
1
2
1
0
2
1
1
1
2
0
0
0
1
1
1
0
2
1
1
1
2
1
1
0
1
0
1
0
1
1
1
2
1
1
0
0
1
1
2
1
1
0
0
2
2
1
1
1
1
2
1
1
1
1
2
1
0
2
1
0
1
1
0
2
2
1
1
0
1
1
1
1
2
1
2
1
2
0
1
1
1
0
3
1
1
1
2
1
1
1
0
0
0
2
0
1
0
0
1
1
1
1
0
2
0
1
0
0
1
1
1
0
1
1
1
1
1
1
1
2
3
1
1
2
1
0
1
1
1
1
1
0
0
2
1
0
1
2
1
1
1
1
0
2
1
2
2
1
2
1
2
1
1
1
0
1
2
1
2
1
1
0
0
1
2
0
0
1
1
1
2
0
0
0
2
0
2
1
0
1
0
2
1
1
0
1
1
1
2
1
0
1
1
1
1
1
1
1
2
1
1
1
0
1
1
1
1
1
0
2
1
2
1
1
0
1
2
1
0
0
1
1
0
1
0
1
1
0
0
2
0
1
0
1
2
0
0
1
0
1
0
0
0
1
0
3
3
2
0
1
0
2
1
2
2
0
0
1
1
3
2
0
1
0
1
1
2
1
1
1
1
2
2
1
0
1
1
1
2
1
1
2
2
1
1
1
1
1
1
1
0
0
1
1
0
1
1
1
2
1
1
2
1
1
0
2
0
0
1
1
2
1
2
1
1
0
1
1
1
2
1
0
1
1
1
1
4
1
1
2
1
4
1
1
0
1
2
0
0
2
2
0
1
1
0
1
1
1
2
1
1
1
2
1
1
1
1
1
0
2
2
0
1
1
1
1
0
0
1
0
2
2
1
1
1
2
2
1
1
0
2
1
0
1
0
2
2
1
1
0
1
1
1
1
0
0
1
2
2
1
1
0
0
2
1
1
2
1
1
1
0
1
1
1
0
1
1
1
2
0
1
1
1
2
0
1
1
0
0
2
1
1
2
0
1
1
0
2
2
2
1
1
1
1
2
2
0
0
0
1
1
1
1
1
1
0
1
1
2
1
1
1
1
1
1
2
1
1
0
2
0
2
1
1
1
1
2
0
3
1
1
1
1
2
1
1
0
2
1
1
1
1
2
1
1
0
0
1
1
1
1
1
3
0
1
2
1
2
1
0
2
1
1
1
1
0
1
0
1
1
1
0
1
1
1
1
1
1
1
1
1
1
0
0
2
0
0
0
1
0
0
1
1
2
1
1
0
1
1
1
0
1
1
0
2
0
1
1
1
0
1
1
1
0
0
0
1
0
0
2
1
0
2
0
2
1
0
1
2
1
1
1
1
1
2
0
0
2
0
1
1
0
0
2
2
1
1
1
1
0
0
1
1
1
1
2
0
1
2
1
0
0
2
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
0
1
0
1
0
1
1
0
0
1
1
1
0
1
1
1
1
1
1
3
0
1
1
2
2
0
1
2
1
0
0
1
0
2
1
2
2
2
0
0
2
2
1
0
0
1
2
2
1
2
1
1
2
1
1
1
2
2
1
1
1
0
2
0
0
0
1
2
0
1
0
2
0
0
2
0
0
1
2
1
1
1
0
2
1
1
2
1
2
1
1
3
1
2
1
1
1
1
1
2
2
2
1
2
0
1
1
2
2
1
2
0
1
1
1
1
1
1
2
2
1
2
1
1
1
1
0
0
0
1
2
1
2
2
2
3
2
1
0
2
1
0
0
2
0
3
1
1
2
0
1
1
1
0
2
1
1
1
0
0
1
0
1
2
1
1
1
0
1
1
1
1
1
1
1
1
0
1
1
0
0
1
1
1
1
1
2
1
1
1
0
2
1
1
1
0
1
0
1
2
2
1
1
0
1
1
1
1
2
0
1
1
0
0
1
1
1
1
0
1
0
1
2
1
1
2
0
2
1
1
1
1
2
1
0
1
1
3
0
1
0
1
0
0
0
1
1
1
1
2
0
1
0
1
0
1
1
1
2
0
2
1
0
0
0
1
0
1
1
0
2
2
1
1
1
0
0
0
1
2
0
0
1
1
1
1
1
2
1
2
2
1
1
2
2
1
0
0
0
1
1
1
1
1
1
1
1
2
1
2
1
2
1
0
1
2
1
1
0
0
1
1
1
2
1
2
1
2
0
1
2
1
2
1
0
1
0
1
2
0
0
1
1
1
2
2
2
1
2
0
0
0
2
1
1
1
1
1
1
1
1
1
0
1
0
0
1
1
2
1
1
1
2
1
2
1
1
0
1
0
1
1
1
3
1
0
1
2
0
1
1
0
1
1
1
0
2
0
1
1
0
0
1
1
1
1
1
1
2
1
1
2
2
0
1
0
1
1
1
2
1
1
0
0
2
2
1
1
1
2
1
2
2
1
1
1
3
2
2
1
2
2
1
0
1
1
2
2
0
0
2
1
0
2
3
1
1
0
2
1
1
2
1
0
0
2
2
1
1
1
2
1
0
0
1
2
0
1
0
0
1
1
0
0
2
1
0
2
1
1
1
1
0
1
1
2
1
1
1
1
1
2
1
1
1
1
1
0
1
0
0
0
0
1
1
1
1
2
1
1
1
1
1
1
1
1
0
0
1
0
1
1
0
1
1
1
1
1
1
1
2
1
2
0
0
1
0
2
2
1
2
1
1
0
1
2
1
1
1
1
1
0
1
1
1
1
0
0
1
1
1
2
1
2
0
0
1
1
1
2
1
1
1
2
2
1
2
2
0
1
0
1
0
1
1
2
1
2
1
1
2
1
2
2
1
0
1
0
2
1
1
1
0
0
1
2
1
2
1
1
1
2
1
0
2
0
2
1
0
1
2
0
1
2
1
2
1
1
0
2
1
1
0
0
1
1
1
0
1
1
1
2
2
2
2
0
1
2
0
1
1
1
2
2
1
1
0
0
0
2
2
0
0
0
1
0
0
1
1
1
1
0
2
0
1
3
2
1
1
2
0
1
2
2
1
1
1
1
1
1
1
0
2
1
0
0
1
1
1
0
0
0
1
1
1
1
1
2
0
3
2
2
2
1
0
1
3
1
1
0
1
0
0
0
1
0
1
1
2
1
2
1
1
2
1
1
0
1
2
0
0
1
1
0
1
0
1
1
1
0
1
0
1
2
0
0
1
1
0
1
1
1
1
2
2
2
0
0
2
1
1
1
1
0
1
1
1
0
0
1
1
2
1
0
1
2
1
0
2
0
1
0
1
1
1
1
2
1
1
1
0
2
1
2
0
0
2
2
1
2
0
1
0
0
0
1
2
1
2
1
0
1
1
5
0
2
1
1
2
2
0
0
2
2
1
1
2
2
1
0
0
1
2
1
0
1
2
0
1
0
1
0
1
1
2
1
0
1
0
2
1
2
1
1
2
1
0
1
1
0
2
6
4
1
1
1
1
0
2
1
0
1
1
1
1
0
1
1
2
0
1
1
0
1
1
0
1
1
1
1
1
1
2
0
0
2
0
2
2
1
1
1
1
1
1
0
0
0
1
1
1
1
1
0
0
1
1
1
1
1
0
2
1
0
1
1
1
0
1
1
1
1
1
2
0
2
2
1
0
1
1
1
1
1
1
0
1
1
1
1
1
0
1
0
1
1
2
0
2
1
1
0
1
1
1
1
1
0
0
2
1
0
0
1
2
2
2
2
0
2
1
1
0
2
1
1
2
2
1
1
0
0
2
1
1
1
1
1
1
0
1
2
0
2
1
0
0
1
1
2
1
1
1
1
0
1
1
2
0
1
2
0
1
1
1
1
0
0
1
1
1
1
1
1
0
1
1
1
1
1
0
0
0
1
0
1
2
1
1
0
0
0
2
0
1
1
1
0
1
1
2
1
1
1
2
0
1
2
0
1
1
1
1
2
2
0
0
0
2
1
1
2
0
2
0
1
2
1
0
5
2
1
2
1
0
1
2
0
0
0
1
1
0
0
1
1
0
0
1
1
0
0
1
1
0
1
1
1
1
1
1
2
0
0
2
1
0
1
0
1
0
1
0
1
1
0
1
0
1
2
1
1
0
0
2
1
2
1
0
0
1
2
1
1
1
1
1
1
1
1
0
1
3
1
1
0
0
2
1
2
0
1
1
1
1
2
2
0
0
1
1
0
2
0
1
2
1
2
1
2
0
4
1
1
1
1
1
1
0
2
1
2
0
2
1
0
1
1
0
0
1
0
0
1
2
1
1
1
2
1
2
2
1
1
0
1
1
1
1
2
1
1
1
0
1
1
1
2
1
0
1
0
1
1
1
1
2
0
1
1
1
2
1
0
1
1
0
0
2
1
2
1
0
0
1
0
0
1
1
0
1
0
1
1
2
1
0
1
0
0
1
0
0
1
0
2
0
0
0
1
1
1
0
2
0
0
2
1
2
2
1
0
0
0
2
2
1
2
2
2
1
1
1
2
1
1
1
2
0
1
0
0
2
2
0
1
1
2
2
0
0
2
0
1
2
0
2
1
1
1
0
1
1
1
1
1
1
1
0
0
1
1
1
1
1
1
1
1
1
1
0
1
2
2
1
1
1
0
0
1
1
0
1
2
0
1
1
2
2
1
0
0
0
1
1
0
2
2
1
2
1
1
0
2
1
1
1
1
2
1
1
2
2
0
1
1
0
2
1
2
0
2
0
1
1
2
3
1
1
1
2
0
1
1
1
0
2
2
1
1
1
1
1
1
1
1
1
0
2
1
2
0
2
1
2
2
1
1
2
2
1
1
1
1
0
2
1
0
0
1
2
0
1
1
0
0
0
0
0
1
2
1
1
1
1
1
0
1
1
1
1
0
0
2
1
1
0
1
1
1
1
0
1
1
0
0
3
1
3
1
1
0
2
1
1
2
1
1
2
1
1
1
1
0
0
1
1
0
2
1
0
1
1
0
1
1
2
1
1
1
2
1
2
0
2
1
1
0
1
2
1
1
1
1
1
1
1
1
1
2
0
2
1
0
1
1
2
1
1
0
1
1
2
0
3
1
0
1
1
2
2
2
0
0
0
2
1
1
1
0
0
1
0
1
0
0
2
0
0
1
1
1
0
2
1
1
2
0
1
1
0
0
2
0
1
1
2
0
0
2
2
1
1
1
1
1
1
0
1
2
1
1
2
2
2
2
0
1
0
1
0
2
0
1
2
1
0
2
1
0
2
0
2
1
2
1
2
1
0
1
0
0
0
1
1
1
1
2
1
1
2
2
1
2
1
1
1
1
3
1
0
1
0
0
1
0
1
0
1
1
1
0
2
1
0
0
1
0
2
1
0
1
0
1
1
2
1
2
1
2
0
1
0
0
1
1
1
2
1
1
2
0
1
0
0
2
1
0
1
2
2
2
1
1
2
1
2
1
2
2
1
1
0
0
2
1
1
1
0
1
1
0
1
2
2
1
0
0
1
1
2
1
1
1
1
1
0
0
2
1
1
1
1
1
2
1
2
0
2
2
0
0
1
1
0
1
1
2
1
2
1
0
2
1
0
2
0
0
1
0
1
0
1
1
1
1
1
3
0
1
1
0
1
1
2
10
1
1
1
1
0
0
1
1
1
1
0
2
0
2
0
1
2
0
0
1
1
1
1
1
1
1
2
2
2
0
0
1
1
0
1
1
0
2
0
1
1
1
1
0
1
1
1
1
0
1
0
1
1
1
1
1
1
1
1
2
1
2
1
1
2
2
1
1
1
1
1
1
2
2
0
1
2
1
2
1
3
1
2
1
2
1
1
1
1
0
2
1
0
2
2
0
1
0
1
1
2
1
0
0
1
0
1
1
1
0
1
1
1
0
1
1
2
2
0
2
1
2
1
0
0
2
1
0
0
2
1
1
1
0
0
1
2
1
1
2
2
0
2
2
2
1
0
1
0
1
1
1
1
2
0
2
1
1
1
1
1
0
1
1
0
0
2
1
1
1
1
2
2
1
1
1
0
2
0
1
2
2
1
0
0
2
2
1
1
2
2
1
1
2
2
1
2
1
1
0
2
0
1
2
2
1
3
1
1
0
2
1
2
2
0
2
0
0
1
0
1
1
1
2
0
0
0
1
1
2
1
1
1
2
0
1
1
1
2
0
0
0
1
0
1
2
2
0
1
2
1
1
0
1
0
2
2
1
1
1
2
1
0
2
1
0
1
1
0
2
1
0
1
1
2
1
3
1
0
1
1
2
2
1
1
1
1
0
0
2
1
1
1
1
1
1
2
1
0
1
0
1
0
2
1
1
1
0
0
1
0
1
1
1
1
1
0
0
0
1
0
2
1
1
1
1
0
1
0
5
2
0
2
1
1
1
1
0
1
1
1
0
1
2
0
1
0
2
2
1
0
2
1
1
1
1
1
0
1
1
1
1
2
1
1
4
1
0
0
1
2
0
1
1
1
0
1
1
2
0
0
1
1
0
1
2
0
0
1
0
1
2
1
1
1
2
0
0
1
1
3
0
1
0
1
0
1
0
2
1
1
1
1
1
2
1
1
1
2
0
0
2
0
2
3
2
1
1
1
1
0
2
0
0
1
0
1
1
1
0
2
1
1
1
1
0
6
1
0
1
2
1
2
1
1
1
0
2
1
1
1
0
2
2
0
1
1
1
1
1
2
1
1
1
0
2
1
2
1
2
1
2
2
0
0
1
0
1
1
0
1
2
1
1
1
2
1
1
1
0
2
1
2
2
1
2
1
2
1
0
1
1
1
1
2
2
1
0
1
0
1
0
1
2
1
1
1
2
1
1
4
1
0
2
1
2
1
0
2
1
1
1
2
1
1
1
1
2
1
1
1
1
0
1
1
2
0
0
0
1
2
2
0
1
2
2
1
1
1
1
1
1
1
1
1
2
0
1
2
2
1
2
2
1
1
0
0
1
2
0
2
1
1
1
2
0
1
0
1
1
1
1
1
0
1
1
0
0
1
1
2
1
1
1
1
0
1
1
0
1
1
2
1
3
2
2
2
1
0
7
1
0
1
1
2
2
0
2
0
2
1
1
0
1
0
1
1
0
1
0
1
1
1
1
1
2
1
1
1
1
0
0
1
3
0
0
2
1
2
0
1
1
2
1
1
0
2
1
1
1
1
1
1
1
1
0
1
0
1
1
2
1
1
1
2
0
2
2
0
1
0
1
0
2
1
0
2
0
0
1
1
1
0
1
2
2
2
0
1
1
1
1
0
1
2
0
0
2
1
1
3
0
0
0
2
1
1
0
0
0
1
2
0
1
1
0
0
2
1
3
1
0
1
0
0
1
1
2
1
1
0
1
2
1
0
2
1
1
1
1
1
0
1
2
1
0
1
1
1
1
1
1
0
1
0
1
1
1
1
1
2
1
0
2
1
0
0
1
1
0
1
2
1
1
1
1
1
1
1
1
1
2
2
0
1
1
2
1
1
0
1
1
2
2
1
0
2
1
1
1
1
1
1
0
2
0
1
1
1
2
1
0
1
2
1
2
1
1
1
2
0
1
1
2
1
0
2
1
1
0
1
0
0
1
1
2
1
1
1
0
2
0
0
2
2
2
1
0
1
1
2
1
1
2
2
1
0
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
0
0
1
2
1
1
2
1
2
2
0
1
15
1
2
0
2
0
1
1
0
0
1
1
1
0
1
1
1
1
1
0
0
1
1
2
0
1
1
0
2
2
1
1
1
2
1
0
0
1
0
1
1
2
2
1
2
0
1
0
1
1
1
2
0
1
1
0
2
2
2
1
2
0
1
0
0
1
2
0
0
2
1
1
1
2
1
0
0
0
1
1
2
1
1
1
1
1
1
1
0
0
1
0
1
0
2
1
0
1
1
2
1
0
0
1
2
1
0
1
1
0
0
0
2
2
2
0
1
1
0
1
2
2
1
1
1
1
1
1
1
1
1
2
0
1
1
2
1
4
0
1
0
1
0
1
2
1
0
1
2
2
2
2
0
0
1
1
1
1
1
2
1
3
2
1
1
0
0
1
0
2
1
1
1
1
2
1
0
1
1
2
0
0
3
1
1
0
1
0
0
1
2
0
1
1
1
1
0
1
1
0
1
0
1
1
1
2
0
2
1
1
1
1
2
2
0
1
1
2
1
2
1
1
2
2
1
1
3
1
0
1
2
0
1
1
1
1
1
1
1
1
0
2
1
0
1
2
1
0
2
0
1
1
1
1
1
1
0
1
1
1
0
2
1
1
0
0
2
0
1
2
0
1
1
2
0
0
1
0
1
1
0
1
1
2
1
1
2
1
1
1
1
1
1
1
2
1
1
1
0
0
1
1
1
1
1
1
0
2
1
0
1
1
1
1
1
1
0
2
1
1
1
0
4
1
1
2
2
0
0
1
1
2
0
2
0
2
0
1
1
2
1
2
2
3
0
1
2
2
2
0
1
2
1
1
1
0
1
1
1
0
1
1
2
2
4
1
1
1
1
0
0
2
2
0
1
0
1
1
1
1
2
1
2
2
1
1
1
1
1
2
2
1
2
0
0
1
2
0
2
2
1
2
0
1
1
1
1
2
1
1
1
2
0
1
0
1
0
1
2
2
0
1
1
1
2
2
1
1
2
0
1
0
1
0
1
0
2
0
0
2
1
1
2
1
1
0
1
1
2
0
1
0
1
1
1
0
0
1
0
2
1
0
1
1
2
0
1
1
0
0
1
4
1
1
1
2
2
1
2
1
1
2
1
2
1
1
0
0
2
2
0
0
1
1
0
1
0
1
2
1
1
1
1
2
2
1
2
0
2
1
1
0
0
1
1
1
1
2
1
2
1
1
2
1
0
1
1
1
1
0
2
1
1
2
1
1
1
3
2
2
2
1
1
1
1
1
2
1
1
1
0
1
0
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
2
1
2
1
1
2
0
1
0
0
2
1
1
0
1
1
1
1
1
0
2
1
1
1
1
1
1
1
1
0
2
1
2
2
0
1
1
2
2
2
0
1
1
0
0
1
1
1
0
1
2
1
0
2
0
0
2
1
0
1
2
2
2
0
2
0
1
1
1
0
1
2
0
0
1
1
0
1
1
1
1
1
2
0
1
2
2
0
0
2
2
1
0
2
1
2
1
1
2
1
2
2
1
1
1
1
0
2
2
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
0
0
0
0
1
1
1
2
1
1
2
0
2
1
0
2
1
1
2
0
1
1
0
2
0
2
0
0
2
1
1
1
2
1
1
2
1
2
0
0
2
1
1
2
2
0
2
0
0
0
0
0
1
0
1
0
2
1
0
1
1
0
1
2
1
1
1
1
2
0
0
2
1
0
2
1
1
0
0
2
2
0
0
1
1
3
2
1
2
2
0
2
0
0
1
1
0
1
1
0
2
0
1
1
1
0
0
2
1
0
1
0
3
1
1
1
2
1
2
0
0
1
1
0
1
0
0
1
2
2
0
2
1
2
0
1
1
1
0
0
1
0
1
3
0
5
1
1
0
1
0
0
1
1
1
0
1
1
1
1
0
1
1
2
2
2
1
0
1
1
1
1
1
1
1
2
1
2
2
4
0
2
1
0
1
0
1
0
1
1
0
2
1
1
1
0
1
2
1
1
1
2
1
0
0
1
1
1
0
1
2
1
2
1
2
1
2
1
0
1
1
2
1
1
2
1
0
2
0
0
1
1
1
1
0
1
1
1
0
1
1
2
0
1
0
0
1
1
1
2
1
0
1
0
0
3
2
1
1
0
0
0
2
1
1
0
1
2
1
0
0
0
2
1
1
0
1
1
2
2
1
1
1
1
1
1
1
2
0
0
1
1
3
1
1
0
1
2
2
2
1
2
2
2
1
0
2
1
1
1
0
1
1
2
2
2
1
1
0
2
0
0
1
0
1
1
1
2
2
0
2
2
1
0
1
1
2
0
1
1
1
0
1
0
1
1
2
0
1
1
1
0
1
2
1
1
2
3
2
1
0
0
1
1
1
2
0
2
1
1
1
2
1
0
1
1
1
3
1
0
0
0
0
1
0
1
1
1
1
1
1
2
1
0
1
1
1
1
2
1
0
1
1
1
2
1
0
1
1
1
2
1
1
1
0
2
1
1
1
0
0
0
0
1
1
1
1
1
1
3
3
0
1
1
1
1
0
1
1
1
1
2
1
0
1
1
1
1
1
1
2
0
1
1
0
1
1
0
1
1
0
1
0
0
1
2
1
2
2
1
1
1
1
1
1
2
2
1
0
1
0
1
0
0
1
2
1
0
2
1
0
1
0
0
2
1
1
1
2
2
0
0
2
2
0
0
1
2
2
1
2
0
2
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
2
0
1
1
2
2
2
2
2
2
1
1
1
2
0
1
1
1
0
1
1
0
0
1
1
1
2
1
0
1
1
1
1
1
1
1
2
1
1
1
0
2
1
2
1
1
1
1
2
0
1
2
1
0
1
1
2
0
0
1
1
1
1
0
1
0
2
1
0
0
2
1
2
1
0
2
0
1
0
1
2
1
0
1
1
2
0
0
3
0
1
1
1
1
2
0
1
2
1
2
1
1
2
1
0
0
2
1
1
1
3
1
1
2
0
2
0
1
2
1
2
1
1
0
1
2
2
0
1
0
2
1
0
0
0
0
1
0
0
1
5
2
2
2
1
0
1
1
0
1
1
2
0
3
5
2
1
2
0
0
1
0
1
0
0
0
4
0
1
5
1
2
1
1
0
0
1
1
0
1
2
2
1
1
0
0
1
0
1
2
1
1
1
1
1
2
0
1
2
1
1
1
1
1
1
2
1
0
1
0
1
1
1
2
0
2
2
0
0
0
1
2
1
1
0
1
0
1
2
0
2
2
1
1
1
2
1
1
1
1
2
1
1
0
1
2
1
1
0
1
0
2
2
2
2
1
1
0
1
1
0
1
1
1
0
0
3
1
2
0
1
1
1
0
2
0
2
0
1
2
1
1
1
2
2
2
3
1
2
0
2
1
1
1
1
1
1
1
3
2
1
1
0
1
1
1
2
2
0
1
1
2
0
1
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
2
1
2
1
2
1
1
1
0
1
1
1
1
1
1
0
1
2
1
1
2
0
2
1
1
1
1
1
0
0
1
2
1
1
2
1
2
1
2
1
2
1
2
1
1
0
1
1
1
2
1
1
0
0
2
0
1
1
0
1
1
1
1
1
2
1
2
2
1
1
1
0
1
1
1
2
1
0
2
0
1
0
1
1
2
1
2
1
2
0
1
2
0
1
1
2
1
1
1
1
2
1
0
1
0
2
1
2
1
1
2
1
0
2
1
1
1
1
2
0
1
1
1
1
0
1
1
1
0
0
2
1
2
0
1
0
2
1
0
2
2
0
1
0
1
1
1
2
0
2
1
2
2
1
1
3
1
1
1
0
1
2
2
1
1
1
1
0
0
0
1
1
2
1
0
1
1
1
2
1
0
0
2
1
1
2
2
2
1
2
2
1
1
1
1
1
0
1
2
2
1
2
1
1
0
1
2
2
0
0
0
0
1
0
1
1
1
2
2
0
2
2
1
1
3
2
0
1
0
1
1
2
0
1
1
0
2
1
2
1
1
1
2
2
0
1
0
2
1
1
1
1
0
0
0
2
1
1
1
2
0
2
1
2
0
1
1
1
1
1
2
1
0
1
2
1
1
0
0
1
1
1
1
0
1
0
1
1
1
1
2
0
2
1
1
2
1
0
1
1
1
2
1
0
0
1
2
1
2
1
1
1
0
0
2
2
2
2
1
1
0
1
1
0
1
1
1
0
2
0
1
0
0
0
1
2
0
1
1
0
2
1
2
1
2
1
1
1
1
2
2
1
1
1
0
0
0
2
1
1
2
1
2
1
1
1
1
2
1
1
1
1
1
0
2
2
0
1
1
2
1
1
1
1
2
0
0
2
1
2
2
1
1
1
1
1
0
1
1
0
2
1
1
1
1
2
1
1
0
0
0
0
2
1
0
0
2
2
2
1
1
1
1
0
2
2
2
0
0
1
1
5
1
0
3
1
0
1
2
0
1
0
0
1
1
2
1
1
1
1
1
1
1
2
1
0
0
1
1
2
2
1
2
1
1
2
2
2
2
0
2
2
2
1
0
0
1
1
1
1
1
1
2
1
1
0
2
0
0
0
1
0
1
0
1
1
0
2
1
1
1
1
1
1
1
2
0
1
1
0
1
0
3
1
1
1
1
0
0
1
1
1
1
1
1
1
1
1
2
2
2
0
1
1
1
1
0
0
1
1
1
0
1
1
1
1
1
1
1
1
0
0
1
1
2
0
2
0
0
1
2
0
1
1
0
2
1
3
0
1
1
1
1
0
1
1
1
0
1
0
1
1
1
1
0
1
1
1
0
1
0
1
1
2
0
2
1
1
2
0
2
2
1
1
2
0
0
1
1
0
1
0
0
0
2
1
1
1
1
0
2
2
1
2
1
1
1
2
0
1
1
1
0
2
0
0
2
1
1
1
2
1
2
2
1
2
1
2
1
2
1
1
0
1
1
2
2
2
1
0
1
1
1
0
1
1
1
1
0
0
1
0
0
1
0
2
0
2
1
1
2
1
1
2
1
0
2
0
2
0
1
0
1
1
1
1
1
1
1
1
0
1
0
0
0
0
2
1
1
2
1
1
2
2
1
1
1
2
0
2
1
1
0
0
1
1
0
2
2
2
0
2
0
2
0
2
1
0
1
1
1
1
1
1
1
0
0
2
1
1
1
2
1
1
1
1
1
1
1
1
2
1
0
2
1
2
2
0
1
0
0
1
1
2
1
1
1
1
2
1
1
1
1
0
1
0
1
0
1
0
1
2
1
2
2
0
0
1
2
0
1
1
0
1
1
1
1
1
1
1
3
1
2
1
0
1
0
1
0
1
1
3
2
1
0
2
0
2
1
1
1
1
1
0
0
0
2
1
1
1
1
0
2
1
0
1
0
1
1
1
2
1
1
1
2
2
2
1
1
1
1
0
0
1
0
1
1
1
1
1
0
2
1
2
2
0
1
1
2
2
1
0
1
0
0
1
1
1
0
2
0
2
0
0
2
0
2
0
1
1
1
0
1
0
2
1
2
0
1
0
1
1
0
1
0
2
0
0
0
1
0
0
1
2
0
1
1
0
5
0
1
1
2
0
1
1
2
1
2
1
0
1
0
2
2
2
1
0
1
0
1
0
2
1
1
2
2
0
1
2
2
0
2
1
1
1
1
1
0
1
1
2
2
1
0
0
1
0
1
5
1
1
2
0
1
0
2
1
1
1
2
3
0
1
1
2
1
2
2
1
2
0
2
1
1
1
1
1
0
1
2
2
1
1
0
1
0
1
1
1
0
1
2
0
1
1
2
1
0
1
0
1
1
1
1
1
0
0
2
0
0
1
1
2
2
1
0
0
1
1
1
1
0
0
1
0
2
1
2
1
0
1
1
0
0
0
2
1
0
0
0
1
2
1
0
1
1
0
2
0
0
0
2
0
2
1
1
0
1
1
1
1
2
1
0
1
1
2
2
2
1
1
1
2
0
1
1
1
0
1
0
1
1
3
1
0
1
2
0
0
1
0
1
1
1
1
2
2
0
1
0
0
0
2
2
1
1
2
0
0
2
2
1
1
1
1
1
1
1
1
2
0
1
1
1
1
0
1
1
1
1
1
0
1
3
1
1
1
0
0
0
1
1
0
1
1
1
1
0
0
2
1
1
1
1
0
1
1
0
1
1
0
0
0
1
0
1
2
1
1
2
1
1
0
0
0
0
1
1
0
1
0
2
1
1
2
2
1
2
1
2
1
0
1
1
1
1
0
1
2
1
0
1
0
0
2
1
0
1
2
1
0
1
1
1
1
1
1
2
1
0
2
1
0
2
1
0
1
1
1
0
2
2
2
0
1
0
0
0
1
1
1
1
2
1
2
3
0
1
2
2
1
0
1
2
1
1
1
1
1
1
2
1
1
2
1
1
2
2
2
2
0
2
0
1
0
1
1
1
0
1
0
0
3
1
1
2
1
0
1
0
1
1
1
1
1
1
2
2
1
2
0
1
2
1
1
1
1
1
1
2
1
0
1
2
0
2
0
1
3
1
0
1
0
2
1
2
1
1
2
1
2
0
1
0
1
2
1
0
1
1
2
1
0
2
0
1
0
1
1
0
1
1
1
2
1
2
1
1
2
1
0
1
0
0
1
1
1
0
0
2
2
2
0
2
1
1
2
1
1
2
0
2
1
0
2
2
1
1
0
1
1
1
1
1
0
2
1
1
1
1
1
0
1
2
1
0
1
0
1
0
1
2
2
1
1
0
0
1
2
1
1
2
0
2
1
2
0
2
0
1
1
1
2
1
0
1
1
0
2
1
0
1
1
0
1
1
1
2
2
2
1
1
1
2
0
1
1
1
1
1
2
0
0
1
0
0
1
2
1
1
2
2
1
0
1
0
1
2
0
0
1
2
1
1
2
2
1
1
1
2
0
1
0
1
1
1
0
1
0
1
1
1
1
2
1
2
1
1
2
1
0
1
1
1
1
0
1
1
2
1
0
2
0
1
0
1
1
1
1
2
0
1
0
1
1
4
1
2
0
1
1
1
1
2
2
2
1
0
0
0
0
1
2
1
0
1
1
1
2
1
1
1
0
1
1
1
1
1
1
0
1
1
1
2
1
1
0
1
1
1
1
1
1
1
3
0
1
0
1
2
2
0
0
1
1
1
2
2
0
0
1
1
2
0
1
1
1
1
0
1
1
2
1
1
0
0
1
0
2
1
1
2
1
2
1
2
0
2
0
0
1
1
1
1
2
0
1
0
0
1
0
0
1
1
2
0
2
1
1
1
0
1
1
1
0
2
1
1
2
1
1
1
1
3
2
2
0
1
2
1
1
0
2
2
0
1
0
1
1
1
1
1
1
1
2
1
1
0
1
1
1
2
2
2
2
1
1
0
0
0
0
2
0
2
1
1
1
1
0
1
1
1
1
1
0
0
1
1
1
0
1
2
1
2
1
1
1
1
2
1
0
1
0
1
2
2
1
2
0
0
0
0
1
2
0
0
1
1
0
1
0
0
0
1
2
0
2
1
0
1
0
2
1
1
2
1
1
2
0
2
1
1
1
1
0
0
0
0
2
1
1
0
1
3
0
1
2
1
1
0
1
0
1
1
1
0
1
2
0
1
0
3
1
1
1
1
1
2
1
1
1
1
1
1
0
2
1
1
1
1
1
1
1
1
1
2
0
1
0
2
0
2
1
2
1
1
3
0
2
1
1
1
2
1
0
1
1
1
1
0
2
1
0
1
1
2
0
2
1
2
2
1
1
2
1
0
0
1
1
0
1
1
1
0
0
0
0
2
0
1
1
0
2
0
1
1
2
1
0
1
3
1
1
1
2
0
0
1
0
1
1
1
0
0
1
1
1
2
1
1
0
1
1
0
0
1
1
0
0
0
1
1
1
0
3
0
1
0
2
0
0
2
1
1
1
1
0
0
0
1
1
2
0
1
0
2
1
2
1
2
1
1
1
0
0
1
2
2
0
0
0
1
0
0
1
0
1
1
1
1
1
2
2
0
1
0
1
2
0
2
1
0
2
0
0
1
1
1
1
1
1
2
2
1
1
1
1
0
1
2
1
1
0
1
1
1
0
1
2
0
1
2
2
1
0
0
1
2
1
2
0
2
1
0
0
1
2
1
1
1
0
1
1
2
0
1
1
1
1
0
1
0
2
1
1
1
0
1
2
0
0
1
1
1
0
1
0
0
2
1
1
0
1
2
1
0
1
1
1
0
1
1
0
1
1
1
2
1
0
2
2
0
2
2
0
1
1
1
0
2
1
1
1
2
0
1
1
1
0
1
2
2
1
1
2
2
2
2
1
2
0
2
2
0
1
1
2
1
1
1
2
1
1
1
1
1
2
2
1
2
2
1
2
0
1
1
0
2
2
0
2
1
0
1
2
1
2
2
2
0
2
2
1
1
1
0
0
1
1
1
0
1
1
2
1
1
1
1
1
1
1
1
2
0
2
2
0
0
1
2
2
2
2
1
2
2
1
1
1
1
1
0
1
1
0
1
0
1
0
1
1
0
1
2
0
2
0
1
2
0
2
0
0
2
0
1
0
0
2
2
0
1
1
1
1
1
1
1
1
1
1
0
0
1
0
1
2
1
0
1
2
0
0
1
2
1
1
1
2
0
0
1
1
1
1
1
1
4
0
2
1
0
0
1
1
1
1
2
1
1
2
1
1
1
1
0
1
1
0
2
1
1
2
1
0
0
0
1
2
1
1
2
3
1
1
1
1
1
0
1
1
1
1
2
1
1
2
1
1
1
1
2
0
0
0
1
1
2
2
0
2
0
1
1
3
1
0
0
1
1
1
1
0
3
1
1
1
0
0
2
0
1
1
1
0
2
1
1
1
0
1
1
2
0
2
2
1
2
1
1
1
0
0
1
1
0
2
2
1
1
0
1
0
2
2
2
2
0
2
1
0
1
1
0
2
1
1
1
0
2
2
3
1
1
2
0
1
1
0
1
0
0
0
0
1
1
0
3
0
2
2
1
0
2
1
1
1
1
2
2
1
0
0
1
1
2
1
1
1
0
2
1
1
0
1
1
0
1
1
1
1
1
1
2
1
0
0
1
2
1
2
1
1
0
1
1
1
1
0
0
1
1
2
2
2
1
1
2
0
0
1
1
0
2
0
1
1
1
1
1
0
1
1
1
1
1
1
0
1
1
1
1
1
1
1
0
1
1
0
1
1
1
1
0
1
0
2
1
0
1
2
1
2
0
2
1
1
1
2
2
2
0
0
1
1
0
1
1
1
2
0
2
1
1
0
1
1
0
2
1
0
1
0
1
1
2
1
0
1
1
0
0
0
1
1
1
1
0
2
0
1
1
1
1
2
2
1
0
0
1
0
1
2
1
1
1
2
1
1
1
0
1
0
1
1
1
1
1
1
0
1
1
0
1
0
1
1
1
0
2
1
1
0
3
0
2
1
1
0
1
1
2
1
0
2
0
1
1
2
0
0
1
1
1
1
1
1
1
2
0
1
2
2
1
1
1
1
1
0
1
1
1
1
2
1
2
1
0
1
0
0
2
1
1
1
1
2
1
1
0
2
2
2
2
1
2
1
2
1
1
0
1
1
2
0
0
1
1
3
1
1
1
0
2
1
1
1
2
0
2
1
2
1
1
0
2
0
2
2
1
1
2
2
1
1
2
0
1
2
2
1
2
0
0
0
1
1
2
0
1
2
1
1
0
1
1
1
1
0
1
0
2
2
1
1
0
1
0
2
1
0
2
0
1
0
2
1
2
2
2
1
0
2
1
2
1
1
1
1
2
2
1
1
0
1
0
1
0
1
1
0
1
1
0
0
1
1
0
1
1
2
3
0
1
1
1
0
1
1
0
2
0
1
2
0
1
0
1
1
1
1
0
0
0
1
2
1
1
1
0
1
2
1
1
1
1
2
1
1
1
2
0
1
1
0
2
0
2
1
0
0
1
0
1
0
1
1
1
1
1
0
0
1
1
2
2
0
1
2
2
1
1
1
1
0
4
0
0
1
2
1
1
0
1
0
1
1
2
1
0
0
2
1
1
1
1
1
1
0
0
1
2
0
1
1
0
1
0
1
0
1
2
0
1
1
1
1
2
1
1
1
1
0
0
0
1
2
0
1
1
1
2
0
1
0
0
0
1
0
2
0
2
2
1
0
0
1
1
0
2
0
1
1
1
1
0
3
1
1
1
1
2
1
1
2
0
1
1
0
0
1
0
0
2
1
2
1
1
1
1
1
1
0
1
0
0
0
2
2
1
1
2
0
1
0
0
1
0
0
2
2
1
1
1
2
2
2
1
1
0
0
2
0
0
0
1
1
2
1
1
1
1
1
1
1
1
1
0
1
2
1
2
1
1
2
1
1
1
1
2
1
1
2
0
0
2
0
1
1
2
3
0
3
1
1
1
1
1
1
2
1
0
2
1
1
2
0
1
0
1
0
2
1
0
1
1
2
2
2
1
1
1
2
0
1
2
1
0
2
1
0
2
2
1
1
1
0
2
1
1
2
0
1
1
1
0
0
1
1
1
1
1
0
1
2
2
2
0
1
2
0
0
0
1
1
1
0
0
9
1
2
0
0
2
1
0
0
1
2
1
1
1
1
1
0
0
1
1
1
1
1
1
1
2
0
1
1
2
1
1
1
0
1
2
0
1
1
1
2
2
2
0
1
2
1
0
1
0
0
1
1
2
1
1
0
1
0
1
1
1
0
1
1
0
2
1
2
1
2
1
0
1
1
0
3
1
0
0
2
0
0
1
0
1
2
1
1
0
1
2
0
1
1
1
2
1
1
0
1
1
1
1
1
2
0
1
0
2
0
1
0
0
1
2
0
2
1
2
0
1
1
2
1
1
1
0
1
0
1
1
1
1
1
1
2
0
2
0
1
2
1
1
2
0
1
1
2
2
0
2
0
0
2
3
1
2
0
1
1
1
1
1
2
1
1
1
2
1
0
1
0
0
0
1
0
1
1
0
0
0
1
1
3
1
1
0
2
2
0
0
1
1
1
1
1
0
1
0
2
1
0
1
2
1
1
2
1
2
0
1
0
0
2
0
1
2
1
0
1
1
1
0
2
0
0
2
1
0
2
0
0
2
1
2
0
1
0
1
2
1
1
2
1
2
2
1
2
1
0
0
1
1
1
2
2
1
0
2
1
2
2
1
0
1
2
1
0
2
1
1
1
1
2
0
2
1
0
1
0
0
1
1
1
1
2
2
0
1
1
2
1
0
0
2
1
0
1
1
1
0
0
1
1
1
2
1
1
1
0
2
1
0
0
1
1
1
1
0
3
1
0
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
0
2
1
1
3
2
2
1
1
1
1
2
0
1
0
1
2
0
2
1
1
1
0
1
1
0
1
2
1
2
1
1
2
1
1
1
0
1
0
1
0
0
1
2
1
1
2
1
1
1
2
2
2
4
2
1
0
2
0
2
2
1
0
0
1
2
2
1
1
0
1
1
2
1
1
2
0
1
0
1
0
2
3
2
1
0
0
0
0
1
2
1
1
1
1
1
1
2
1
1
0
1
1
0
1
0
1
1
1
0
0
1
1
2
1
1
3
0
0
0
2
1
1
1
0
1
1
2
0
1
1
1
1
2
1
2
0
1
1
1
1
1
1
1
1
0
2
1
0
1
1
1
1
1
0
1
2
1
1
0
1
1
0
2
1
1
1
1
2
2
0
1
0
1
1
0
2
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
3
0
1
1
1
1
2
0
1
1
1
0
0
0
1
1
0
2
2
1
1
1
1
1
1
1
1
0
1
2
1
1
1
1
1
0
2
1
1
1
1
0
0
1
1
0
1
0
1
2
0
2
1
1
2
1
0
1
1
1
1
2
0
1
0
0
2
2
2
1
1
1
1
2
1
1
1
0
1
2
0
2
0
1
2
1
1
1
0
3
2
1
0
0
1
1
2
2
0
2
1
2
2
0
1
2
1
1
1
0
1
2
1
0
0
1
1
1
1
0
0
0
1
0
1
1
1
1
0
1
4
1
1
1
0
2
1
2
1
0
0
1
0
1
1
1
1
0
1
1
1
1
0
2
1
1
0
0
0
1
1
1
0
1
1
1
1
1
0
1
1
1
3
1
2
1
1
1
2
1
1
1
2
0
2
1
1
0
0
1
1
2
0
2
1
0
0
1
3
1
1
0
1
2
2
1
2
1
0
0
1
1
1
0
1
0
1
0
1
1
0
1
1
1
0
2
2
2
3
1
1
0
1
1
0
1
2
1
0
2
0
0
1
2
1
0
0
0
1
1
1
1
0
2
2
1
1
1
1
2
0
1
2
0
2
2
1
2
1
1
1
1
1
0
0
0
1
0
1
1
1
0
2
0
1
1
1
0
2
2
0
8
1
0
1
2
1
0
0
2
1
0
1
2
0
2
1
0
2
0
0
2
1
1
1
1
1
0
2
1
1
2
1
1
2
2
1
1
1
1
0
1
1
1
1
0
1
0
2
1
0
1
1
1
0
0
2
1
1
1
1
2
0
2
1
1
0
1
2
0
1
1
0
1
1
0
1
0
0
1
0
0
0
1
1
1
1
1
2
1
1
1
1
1
0
2
1
1
2
1
0
0
0
0
1
1
1
0
1
2
1
1
0
2
1
0
0
1
1
1
2
1
2
1
1
1
1
1
2
2
1
0
1
1
1
2
1
2
2
0
1
0
0
2
1
1
0
0
1
1
1
2
1
3
1
2
1
2
1
0
1
2
0
1
1
1
2
2
2
2
1
1
1
2
1
2
1
0
2
1
2
0
2
0
0
0
1
0
0
1
0
1
1
2
0
0
1
1
1
0
1
0
1
1
1
1
0
1
3
1
1
1
1
2
0
0
1
1
0
2
0
1
1
1
1
0
0
2
0
1
1
2
1
1
0
1
1
1
0
0
1
0
1
1
1
1
1
1
0
1
1
1
1
2
1
2
0
1
1
1
1
2
1
1
1
2
2
0
0
2
1
1
2
1
2
1
1
0
0
2
1
1
2
1
1
1
1
0
0
1
1
0
1
1
1
0
1
1
1
1
0
1
2
1
1
1
1
1
0
0
1
0
2
1
1
2
0
1
2
1
3
1
2
0
1
2
1
1
0
1
0
0
0
1
2
0
1
1
1
1
1
2
2
2
1
1
0
1
1
0
2
1
2
0
1
2
1
1
0
1
0
1
1
2
0
1
2
1
0
1
1
0
1
1
0
1
2
2
0
1
0
1
1
1
1
1
1
1
0
0
0
1
0
1
2
1
0
1
1
1
0
1
1
2
1
2
0
2
1
1
1
1
2
0
0
0
1
0
1
0
1
1
1
0
1
0
1
0
1
1
0
0
1
2
0
1
0
2
1
2
1
2
2
1
1
0
1
1
2
2
0
0
1
2
2
3
1
1
0
2
1
2
0
1
1
0
2
1
1
0
2
1
1
0
1
1
1
2
0
1
1
2
2
1
2
1
1
0
0
1
0
1
2
0
1
0
1
2
2
1
1
1
1
1
0
1
2
1
2
1
1
1
2
0
1
1
2
2
1
2
1
2
0
0
0
1
2
1
2
1
0
0
0
2
2
1
0
1
1
0
1
0
2
0
1
1
1
0
2
0
1
1
1
1
1
1
0
0
1
1
1
1
1
0
2
0
1
0
2
1
1
1
3
1
1
0
0
0
0
1
1
3
1
1
1
1
1
0
1
1
1
0
2
1
1
2
1
0
1
0
1
1
1
1
1
0
1
1
1
1
1
2
0
0
1
1
1
1
0
1
1
0
2
0
0
0
1
1
1
1
3
1
1
1
1
0
1
0
1
2
0
0
2
1
0
0
0
1
2
2
0
1
0
1
1
1
1
1
0
0
2
2
0
1
1
1
0
2
1
1
1
1
0
3
0
1
1
0
0
1
1
0
0
1
1
1
1
2
1
1
1
0
0
1
0
2
0
2
1
0
1
0
1
1
1
2
1
0
0
1
1
2
1
2
1
1
1
1
1
1
2
2
1
2
0
0
1
1
1
1
0
1
2
0
2
2
0
1
2
0
2
2
2
0
1
0
1
2
1
2
0
2
1
2
1
1
2
0
0
1
1
0
1
2
1
0
1
1
1
1
0
1
1
2
1
0
2
1
2
1
1
1
2
0
1
0
0
1
2
1
1
2
1
2
1
1
0
1
2
2
0
1
0
0
1
1
2
1
1
0
1
0
1
1
1
1
0
1
1
2
1
1
0
2
0
1
1
1
0
2
1
2
1
1
1
1
1
1
1
0
0
1
1
1
1
0
2
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
0
1
3
1
1
1
1
0
0
1
1
1
1
2
1
1
1
1
1
1
0
0
2
0
2
2
2
0
1
1
1
0
2
1
2
0
1
0
2
2
2
2
2
2
1
2
0
1
0
2
1
1
1
2
2
0
1
1
1
0
1
0
1
0
0
1
0
0
1
0
1
2
2
2
1
0
2
2
1
1
1
1
1
1
1
1
2
0
1
2
0
0
0
2
2
1
1
0
1
1
1
2
1
0
0
1
1
1
0
2
1
1
1
0
0
2
0
1
1
2
1
5
2
0
1
0
1
0
0
0
0
1
2
0
2
2
1
1
2
2
0
1
0
2
1
1
1
0
2
0
1
1
0
1
2
1
2
0
0
1
1
1
1
1
0
1
2
1
1
0
1
0
2
2
1
2
1
0
0
1
2
0
0
1
0
0
1
2
2
2
0
1
1
0
1
2
1
1
2
3
0
0
1
2
0
1
1
1
1
2
0
2
0
1
2
1
1
2
0
1
0
1
1
1
0
1
0
1
1
2
1
2
2
1
1
0
2
0
1
3
1
0
1
2
0
2
0
1
0
1
1
2
1
2
0
1
2
0
1
0
1
0
1
2
1
1
0
1
2
2
2
0
1
1
1
0
1
1
2
1
0
0
1
1
0
1
1
0
0
0
0
0
0
2
2
2
1
2
1
3
0
0
2
0
0
0
2
2
1
1
1
1
2
0
1
2
1
1
0
1
0
1
1
2
0
0
0
1
1
1
0
1
2
0
0
1
1
2
1
1
0
1
1
1
0
1
0
0
1
0
1
2
1
1
1
0
2
2
0
1
2
0
2
2
1
3
1
1
2
1
1
2
1
1
1
1
1
1
0
1
1
2
1
1
1
0
0
2
2
1
0
0
2
1
0
1
1
1
1
1
2
1
0
2
1
1
1
0
0
2
1
2
1
1
2
0
0
1
1
2
2
2
1
1
0
1
1
1
0
5
1
1
1
1
1
1
2
2
1
0
1
1
0
0
1
2
1
0
1
1
2
0
1
1
1
1
1
2
1
0
1
1
1
0
1
1
0
2
0
1
1
1
0
1
1
1
2
2
2
2
2
1
0
1
2
0
1
1
0
1
0
1
2
1
1
2
1
0
0
2
1
2
1
1
0
2
0
0
2
2
1
1
2
1
1
1
1
1
1
1
0
1
1
0
1
2
1
0
0
0
1
1
2
1
0
0
1
1
1
0
1
0
0
0
1
1
2
2
1
1
0
0
1
0
1
0
0
2
1
1
3
1
0
1
1
1
2
0
1
1
0
1
1
1
2
1
1
1
2
0
1
0
2
0
0
0
2
1
2
1
0
0
0
1
1
1
0
1
12
1
0
0
0
2
0
1
1
1
1
0
1
0
0
1
2
0
1
1
1
0
0
2
1
0
1
0
1
1
0
1
1
2
0
1
0
0
2
2
0
1
1
2
0
2
1
1
1
1
1
1
2
2
0
2
1
1
0
1
1
1
1
1
1
1
1
1
0
1
1
1
0
0
1
1
1
1
1
1
2
2
0
0
3
0
2
0
10
2
0
1
1
1
2
0
0
2
1
0
1
1
0
1
1
3
1
0
1
0
0
1
0
2
0
2
1
1
2
1
2
1
1
1
0
0
2
0
1
1
1
1
1
0
0
1
1
2
0
2
1
1
1
1
1
0
2
0
1
0
1
1
1
1
1
0
1
1
2
1
2
0
0
1
1
2
0
1
2
2
1
2
2
2
0
1
1
1
1
0
0
2
1
2
1
1
1
1
1
1
0
0
1
2
0
1
1
2
1
2
2
2
1
3
1
0
1
0
0
1
1
2
0
1
1
2
2
0
1
1
2
2
1
1
2
0
1
2
1
0
1
0
1
2
2
1
1
1
1
1
1
0
1
0
2
1
2
2
2
1
2
0
2
1
0
1
2
0
2
1
1
1
1
2
0
0
1
0
1
1
0
1
2
2
0
1
3
0
1
1
1
1
1
1
0
0
1
0
2
1
1
1
1
1
2
0
1
1
1
1
1
2
1
1
1
1
2
0
1
2
1
2
1
1
1
2
1
1
0
1
2
0
0
2
1
0
0
1
2
1
2
0
1
0
1
0
0
1
1
1
2
0
1
1
1
0
1
0
1
0
1
1
1
1
1
0
0
1
1
1
1
1
0
0
1
2
1
0
1
1
1
2
2
1
2
0
1
0
1
1
2
2
2
2
1
0
1
2
0
2
1
1
1
1
1
1
0
1
1
1
1
2
1
1
1
0
1
1
4
1
1
0
2
1
0
3
0
1
2
1
2
1
1
2
2
1
1
0
2
1
0
1
2
2
0
2
1
2
2
2
0
2
0
1
1
1
1
1
0
1
1
0
2
2
0
0
1
0
2
0
0
2
1
2
0
1
1
2
0
1
1
3
2
0
0
1
1
1
1
1
1
1
0
0
1
0
0
1
1
1
1
0
0
2
2
1
1
0
1
2
1
1
1
1
1
1
0
1
1
0
0
1
2
1
2
1
0
1
1
0
1
1
1
0
0
1
2
1
1
1
2
2
2
0
1
1
0
1
1
1
1
2
1
1
1
2
0
1
1
0
2
1
1
1
1
1
1
2
5
1
1
0
1
1
2
1
1
1
0
0
0
0
1
1
1
2
1
1
0
0
1
3
1
1
1
1
0
0
1
1
2
1
2
0
1
1
2
1
1
1
2
1
2
1
2
1
2
1
1
1
1
1
2
1
2
0
0
1
1
1
2
2
1
1
2
2
1
1
1
1
0
1
4
1
0
0
1
1
0
1
0
2
2
1
1
1
1
2
1
1
0
1
1
0
1
1
1
0
2
0
0
0
1
1
1
1
0
2
2
1
1
1
1
1
1
1
1
1
1
0
1
1
0
2
1
1
1
0
1
1
0
2
0
1
2
1
2
1
0
1
2
2
1
1
1
1
1
2
1
1
1
1
0
0
0
0
1
1
0
0
0
2
0
2
1
0
1
0
1
0
0
1
2
1
1
1
0
2
0
0
1
0
1
1
1
1
2
0
1
0
1
2
1
0
2
0
2
1
0
1
1
1
1
0
0
1
1
1
1
0
1
1
2
0
1
2
2
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
2
1
1
1
0
2
0
2
1
1
1
4
0
0
1
2
1
1
0
0
2
2
1
1
0
1
1
2
1
1
1
2
1
1
1
1
0
2
1
1
0
0
0
0
0
1
0
1
0
1
1
1
1
1
2
0
1
1
1
1
1
1
1
1
0
2
0
2
2
1
0
0
2
2
1
1
1
2
0
2
1
1
0
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
2
1
1
2
1
0
1
0
0
1
0
1
0
2
2
2
1
1
1
0
1
1
2
2
1
1
0
0
1
2
1
2
1
0
2
1
0
1
1
1
2
1
2
1
1
1
1
2
1
1
1
2
1
1
1
1
0
1
1
2
1
1
2
2
0
1
0
1
1
1
1
1
0
0
0
1
0
0
0
2
1
1
1
1
1
2
2
0
1
1
1
0
2
0
1
1
1
1
2
1
1
1
2
2
1
1
2
1
1
0
2
1
0
1
0
1
1
0
1
1
1
1
1
2
1
1
2
0
1
2
2
0
0
1
1
0
2
1
2
0
2
0
1
2
2
1
2
1
0
1
1
0
1
1
2
1
1
0
1
0
1
1
2
1
2
1
1
1
2
0
0
2
0
1
1
1
2
1
1
1
1
2
1
2
1
1
1
0
1
1
1
2
1
2
0
3
2
1
2
1
1
1
0
0
1
1
2
1
1
2
2
1
2
1
0
2
1
1
2
2
2
2
1
1
0
1
2
0
2
1
1
1
0
1
2
0
1
1
1
1
1
2
1
0
0
1
1
1
2
0
2
1
1
0
1
2
0
1
2
0
2
2
1
1
2
2
1
1
2
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
0
0
0
1
1
1
0
1
1
1
2
3
1
1
0
1
1
0
1
0
0
2
1
2
3
1
2
0
1
1
1
2
1
1
2
0
2
0
2
1
0
1
0
2
0
0
1
1
6
1
1
1
1
0
2
1
2
1
0
2
1
1
1
2
1
2
1
2
0
1
1
1
1
2
1
1
0
1
1
1
1
2
1
1
1
0
1
0
0
1
1
0
1
0
1
1
1
0
0
1
1
1
0
2
1
1
1
1
1
1
2
1
2
0
2
1
1
1
2
2
0
2
1
1
2
0
1
1
3
1
1
1
0
1
1
0
1
2
2
1
2
1
0
1
0
0
1
1
1
1
1
1
2
3
1
0
1
0
2
1
1
1
1
2
1
1
0
2
1
0
1
0
1
1
1
1
1
1
1
0
1
1
1
0
1
1
0
2
1
1
1
1
1
1
0
1
0
2
2
0
1
2
1
0
0
0
3
1
2
7
0
1
1
0
1
0
1
0
1
1
2
2
1
1
1
0
1
3
0
1
1
1
1
1
2
1
1
1
1
2
1
1
2
2
0
1
0
1
2
2
2
0
1
0
2
1
1
1
2
2
1
1
1
1
1
1
1
2
0
1
1
2
0
1
1
2
3
1
1
1
1
1
1
2
0
0
0
2
2
1
2
1
1
2
1
2
1
0
1
2
0
0
0
1
1
2
1
0
1
2
1
0
1
2
0
1
0
1
1
1
1
2
2
1
2
0
1
0
2
1
1
3
1
0
1
2
0
2
1
1
0
1
0
1
1
0
1
0
0
1
1
1
1
1
1
0
1
2
2
1
1
0
1
0
2
1
0
0
2
0
1
2
0
1
2
0
0
1
1
0
1
2
1
1
2
0
2
2
1
2
0
2
1
1
0
1
1
2
1
2
2
1
2
1
1
1
1
1
2
1
0
1
1
2
2
2
1
2
0
1
2
0
0
1
1
1
2
1
0
1
1
0
0
1
2
1
0
1
1
0
1
1
2
0
2
1
1
2
1
2
2
0
2
0
1
1
1
1
1
1
0
1
1
0
1
3
2
1
0
1
1
1
1
1
1
1
1
2
0
0
1
0
2
1
2
1
2
1
1
1
0
0
1
1
0
1
2
1
1
2
1
1
1
1
3
2
1
1
0
1
2
1
1
2
2
0
0
1
1
1
1
0
1
2
1
2
1
1
1
1
0
1
0
1
2
1
1
3
1
1
1
0
1
0
2
0
0
2
1
1
2
0
0
0
1
0
2
0
0
1
1
1
1
1
1
1
0
0
2
0
1
2
0
2
1
0
0
1
1
0
1
1
0
1
1
1
2
2
1
1
0
1
1
0
1
0
2
2
2
1
1
0
0
2
1
1
2
0
0
1
0
2
1
2
1
1
0
0
3
0
1
1
2
0
1
2
1
1
1
1
2
2
1
1
0
1
0
1
1
2
2
2
1
1
1
1
1
1
0
0
0
0
1
1
0
1
1
1
2
0
1
0
1
2
1
1
1
1
1
2
0
1
2
1
2
1
0
0
1
1
2
1
1
0
1
1
1
2
2
1
1
1
1
1
0
1
1
1
1
1
2
1
0
2
0
1
2
1
1
1
1
1
0
2
2
1
0
1
0
1
1
1
0
2
1
1
1
2
1
1
1
1
1
1
1
0
1
1
1
1
2
1
2
1
2
2
0
1
0
2
1
1
1
1
0
1
1
0
1
0
0
1
0
1
2
1
2
1
1
0
1
2
0
2
1
2
1
0
1
0
1
2
0
2
1
0
4
1
1
2
2
2
1
1
2
2
1
2
1
1
0
0
1
0
1
1
0
0
1
2
1
1
0
1
1
1
1
2
3
2
1
0
0
1
0
2
1
1
2
1
0
1
1
2
1
1
1
1
0
1
0
0
1
1
0
0
0
1
2
2
1
0
2
2
0
2
2
1
1
1
1
1
1
0
1
1
0
2
1
1
1
0
2
0
1
2
0
1
0
1
1
1
1
1
0
1
2
2
0
1
1
2
2
1
0
2
2
1
0
2
0
1
1
0
0
0
2
0
2
1
2
0
2
1
2
1
1
1
2
0
0
1
2
1
1
2
1
0
0
1
1
1
1
0
0
2
0
0
1
1
1
1
0
1
1
1
2
2
0
0
0
1
0
1
0
1
2
1
1
0
1
3
1
0
1
1
2
1
0
1
2
1
1
1
1
1
1
0
1
2
0
1
0
1
2
1
1
2
1
1
1
1
1
1
1
1
0
1
2
2
1
1
2
1
2
1
1
1
1
0
2
1
1
2
2
2
0
0
1
0
2
1
0
1
1
2
1
0
2
2
3
1
1
0
1
2
0
0
0
0
1
1
1
1
3
1
2
3
0
1
2
2
1
1
2
2
1
1
1
1
1
1
1
1
0
1
1
1
1
0
1
2
1
1
0
0
1
1
1
0
0
2
1
0
2
2
0
1
0
1
0
0
1
1
1
1
1
1
2
0
1
0
2
0
2
1
1
1
1
1
1
0
1
2
1
0
2
0
0
0
1
1
1
1
1
1
2
1
2
1
2
1
2
0
1
2
1
1
1
1
1
0
1
1
0
2
1
2
1
1
1
2
3
1
1
0
1
1
2
1
1
0
0
2
1
1
2
1
2
1
2
1
6
0
2
0
1
1
0
0
1
2
0
1
0
1
0
0
0
1
0
1
1
1
1
2
1
2
0
2
2
2
2
1
1
1
1
0
0
0
1
1
1
1
1
2
0
1
0
0
2
2
0
1
0
2
0
0
0
0
1
1
2
1
2
1
0
0
2
1
1
1
0
1
0
1
2
1
1
2
2
1
1
0
0
0
1
2
1
1
1
1
1
2
2
1
2
1
0
2
2
1
1
0
2
1
1
2
1
1
2
1
1
0
3
2
2
2
2
1
1
1
2
1
1
0
1
0
2
1
1
2
0
2
2
1
1
1
1
0
0
0
1
1
1
1
0
0
0
1
2
1
2
1
1
0
2
0
2
1
1
0
0
0
2
1
2
1
1
0
5
1
1
0
0
1
3
1
1
2
0
1
1
1
5
1
0
2
1
1
0
0
0
1
1
1
2
1
1
1
2
0
2
1
1
0
0
0
1
0
1
1
2
0
0
2
2
1
2
2
2
2
2
1
1
2
1
1
0
2
0
2
1
1
3
2
0
2
1
2
1
2
1
0
2
1
1
2
1
2
1
1
0
1
1
2
1
3
0
1
1
0
1
2
1
2
0
2
1
1
0
1
2
0
0
1
0
1
2
2
2
1
0
1
1
0
2
1
1
3
1
1
1
1
4
0
2
2
1
1
1
2
1
0
2
2
2
1
0
1
0
1
2
0
1
2
1
1
1
0
2
1
1
2
1
2
0
1
1
0
1
1
0
1
2
1
1
1
0
2
0
1
3
0
1
1
1
1
1
1
1
1
1
0
2
1
1
1
1
1
0
0
1
2
1
2
2
1
0
1
0
2
1
1
0
2
2
0
1
0
1
2
1
0
1
2
1
0
1
0
2
0
1
1
2
0
0
0
2
1
1
1
0
1
1
1
1
0
0
0
1
2
1
0
1
1
0
0
0
1
1
0
1
2
1
1
1
1
2
1
2
1
1
2
0
1
1
2
2
1
1
1
0
0
0
1
1
0
1
1
2
1
1
1
0
1
1
2
0
2
0
1
0
0
0
0
1
1
1
2
2
1
0
0
1
1
2
1
0
2
1
2
1
1
0
1
2
0
0
2
2
1
1
1
2
1
1
1
0
2
1
1
1
1
1
1
2
0
0
1
0
1
1
2
0
2
0
1
1
2
1
1
0
1
1
2
0
0
0
0
1
1
0
0
1
1
1
3
2
1
1
1
1
2
1
0
2
1
1
2
0
1
1
1
1
1
1
2
1
0
0
0
0
0
1
1
2
1
1
1
1
2
0
0
1
2
2
1
0
0
2
0
0
0
2
1
0
2
1
1
0
2
2
2
1
2
1
2
2
0
1
2
2
1
1
1
0
2
1
1
2
2
2
2
0
1
1
2
1
0
1
1
2
1
0
1
1
2
2
0
2
0
0
1
1
1
1
0
1
0
2
1
2
1
2
1
1
2
1
1
0
0
3
1
1
0
2
2
0
0
2
0
1
2
1
2
0
2
2
1
1
1
2
1
2
0
0
1
1
1
1
0
1
2
0
1
1
2
0
1
1
1
0
1
0
0
1
1
2
2
0
1
0
1
1
1
1
1
1
2
1
1
2
0
0
1
2
1
0
1
0
1
1
0
2
0
0
2
1
1
0
0
1
1
0
1
1
1
1
1
0
0
1
1
1
0
0
1
1
1
1
1
0
0
1
1
1
1
0
2
0
2
1
0
2
0
2
1
1
1
0
1
1
2
1
0
1
0
0
2
1
2
2
1
1
1
1
0
1
1
0
2
1
1
1
1
0
0
1
1
1
1
2
1
3
0
1
3
1
1
0
1
0
2
0
1
1
1
1
1
0
1
2
1
1
2
1
1
1
0
1
2
1
0
1
1
2
1
1
1
0
2
1
1
1
2
1
0
1
0
0
1
1
2
1
2
1
1
0
1
2
2
2
2
0
0
1
1
1
2
1
2
1
2
1
1
2
2
0
1
1
2
1
1
1
2
2
1
0
1
1
1
2
1
1
1
2
0
1
2
2
1
1
1
1
1
1
1
1
1
0
2
0
1
0
1
2
2
1
0
1
2
0
0
0
1
1
1
1
2
2
0
0
3
1
0
1
1
1
1
0
1
1
1
1
0
1
2
2
0
1
1
2
0
1
2
0
1
1
1
1
0
0
1
1
0
1
1
1
0
0
1
2
1
1
2
1
1
1
1
0
1
0
2
1
1
1
2
1
1
1
2
1
0
4
0
2
0
1
1
2
0
1
0
1
2
0
0
0
0
2
0
2
0
1
1
1
1
0
1
2
2
0
0
2
2
1
0
2
0
0
1
4
1
2
0
0
0
1
1
0
1
1
2
1
2
0
1
1
1
1
2
1
2
1
1
1
1
2
0
1
1
2
1
1
1
2
0
2
0
1
0
0
1
1
1
2
1
1
1
1
1
1
1
0
0
1
0
1
1
1
0
1
2
0
0
1
2
0
1
0
2
0
0
1
1
1
0
1
1
2
1
0
1
2
1
2
0
2
2
2
1
1
1
1
1
1
0
1
2
0
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
2
1
1
2
1
1
2
1
1
0
1
0
0
2
1
1
1
1
1
1
0
1
2
1
1
1
1
0
1
0
1
1
1
0
1
2
1
0
1
1
1
0
0
2
2
0
1
1
0
1
1
0
1
0
1
5
1
0
1
2
1
1
0
1
1
0
1
1
1
2
1
2
2
1
2
2
1
1
1
0
2
0
2
1
1
0
1
2
1
0
0
1
2
0
1
1
1
0
1
1
1
1
1
1
0
1
1
0
2
0
0
1
1
0
1
1
2
1
1
1
2
2
2
2
1
0
2
1
1
3
0
1
1
0
1
1
1
1
1
0
3
2
0
0
1
1
1
1
1
0
0
0
1
1
0
1
0
1
1
1
0
1
0
1
2
0
0
2
1
0
0
1
1
1
2
0
1
1
0
1
2
0
0
1
1
0
1
0
1
0
1
1
1
1
2
1
0
0
1
1
1
2
0
0
0
0
0
1
0
1
0
1
1
1
3
1
1
1
0
1
0
1
0
1
2
1
0
1
1
0
2
1
1
1
1
0
0
2
1
1
1
1
1
0
1
1
1
2
1
1
1
0
2
1
1
1
1
0
1
2
1
1
1
2
1
1
0
2
1
0
1
1
1
1
1
1
1
0
0
2
0
1
0
0
2
1
0
0
2
1
1
0
1
0
2
1
0
0
1
2
0
0
1
2
2
2
0
1
0
2
0
0
1
2
1
0
2
1
1
1
2
1
1
3
1
1
1
1
1
2
0
1
1
0
0
2
1
0
1
0
1
1
2
1
1
1
2
0
1
1
1
0
0
2
1
1
1
2
1
1
1
1
1
0
1
0
0
2
1
1
0
1
2
2
1
1
1
1
0
1
0
0
2
1
1
1
0
0
1
0
1
2
1
2
1
1
1
1
1
1
1
1
2
2
0
1
0
2
3
1
1
2
2
1
1
1
0
0
0
2
0
2
1
1
0
2
2
1
0
0
0
2
2
0
1
0
1
0
2
4
1
1
2
1
1
2
2
1
1
1
1
2
2
0
2
0
2
1
1
0
1
1
0
2
1
2
2
2
1
2
1
1
0
1
1
1
2
0
0
1
1
2
1
1
1
0
0
0
2
1
1
1
1
1
1
0
1
1
1
0
1
1
1
1
1
1
0
0
1
0
0
0
1
1
1
1
1
1
1
1
1
2
0
1
2
0
1
0
2
0
1
1
1
1
1
2
2
1
1
0
1
1
0
1
0
1
0
0
1
2
0
1
1
1
1
2
1
0
1
1
1
0
2
0
0
1
1
2
2
0
2
1
0
1
1
0
0
1
0
1
1
1
2
1
1
0
1
2
1
2
1
1
1
0
0
2
1
1
2
1
2
0
1
4
1
1
1
0
1
2
1
0
1
2
0
0
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
5
2
1
1
2
1
2
0
1
1
0
1
0
2
1
0
0
0
2
2
1
0
2
0
1
0
0
0
0
1
1
1
1
0
1
0
1
2
0
2
2
0
1
0
1
2
1
1
0
1
1
0
1
1
1
1
1
2
0
0
0
2
1
0
1
0
1
0
1
2
0
1
2
1
1
0
0
1
1
2
1
1
0
1
2
1
0
1
2
0
2
0
2
2
1
1
0
1
1
0
0
0
1
0
2
3
0
2
0
2
2
2
0
0
2
2
1
2
1
1
1
1
0
0
2
1
2
2
2
1
1
2
2
1
2
2
2
1
1
2
1
0
2
1
2
0
1
1
1
1
0
0
1
1
1
1
1
2
2
1
0
1
1
1
1
2
1
1
1
2
2
1
1
1
0
1
1
2
1
1
0
2
1
1
2
1
1
2
1
2
1
1
1
1
0
1
0
1
1
0
1
0
1
1
2
1
1
1
1
2
1
1
0
0
1
0
1
1
1
0
3
1
1
1
2
1
1
0
1
1
1
0
1
5
2
1
1
1
2
1
2
0
2
1
1
3
0
1
2
1
1
1
0
1
0
1
1
1
1
1
2
0
1
2
0
2
1
2
1
2
2
1
1
2
2
1
0
0
1
0
0
1
0
1
1
1
0
0
4
1
1
0
1
2
1
2
0
1
2
1
0
1
0
2
2
1
2
1
0
1
1
1
1
0
2
2
2
1
1
1
1
1
1
2
2
1
1
2
1
1
2
1
1
1
0
0
1
2
2
1
1
1
0
1
1
1
0
1
0
2
1
1
1
2
0
0
2
2
1
1
1
2
1
0
2
1
2
0
1
1
0
2
1
1
1
1
2
1
1
1
1
0
1
0
1
2
0
0
1
1
1
0
1
1
1
1
1
2
0
0
1
0
1
0
1
2
1
1
2
1
1
2
1
0
0
1
2
0
0
1
0
0
1
1
0
1
2
1
0
1
1
2
0
2
0
1
1
1
2
1
1
1
1
1
0
0
1
1
1
2
1
1
0
1
6
1
0
0
1
1
1
1
1
2
1
2
1
1
2
1
2
2
0
1
2
1
0
1
0
1
0
1
0
1
1
1
1
1
0
2
5
1
0
2
0
2
2
0
1
0
0
1
1
0
1
1
0
1
1
0
1
0
1
1
0
1
2
2
0
1
2
1
1
2
1
1
1
1
1
1
1
3
0
2
1
0
0
1
1
1
0
1
0
0
1
2
0
0
2
0
1
1
1
1
1
0
1
2
2
2
1
4
1
1
1
2
0
1
0
0
1
1
2
2
1
1
2
2
2
2
1
0
2
1
2
2
2
1
2
0
1
1
1
1
1
0
2
1
0
2
2
1
4
0
1
2
1
1
1
0
2
1
1
0
0
0
1
0
0
3
1
3
2
1
0
2
1
1
0
0
1
1
1
1
1
0
0
1
1
2
0
2
2
2
0
1
1
1
1
0
1
1
1
0
2
3
1
2
1
0
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
2
1
0
0
0
1
1
0
1
1
2
2
1
0
0
0
2
1
1
1
1
1
1
0
1
0
0
2
0
1
1
1
1
2
2
2
2
1
0
0
2
0
2
1
1
1
0
0
0
2
0
2
2
2
0
0
1
0
1
2
0
0
1
2
2
1
1
2
3
2
1
1
2
0
0
2
0
1
1
0
0
1
0
1
1
1
1
2
0
2
2
2
1
1
0
1
0
2
0
0
1
0
2
1
1
1
2
0
2
0
0
1
1
0
1
2
1
0
1
0
1
2
0
1
1
0
6
2
0
2
2
0
1
2
2
0
1
2
1
1
1
2
1
1
2
1
2
2
0
1
1
1
1
1
0
1
1
2
0
0
1
1
0
0
1
2
0
1
2
2
0
1
0
2
0
0
2
1
1
1
1
0
1
1
0
2
0
1
1
0
1
0
1
0
1
1
1
2
1
2
1
2
0
1
1
2
0
1
2
0
1
2
1
1
1
2
2
2
1
1
1
0
0
0
2
1
1
1
1
1
2
1
0
0
1
2
1
0
1
1
1
2
1
1
0
1
1
0
1
2
0
1
1
1
1
2
2
1
1
1
0
1
2
1
1
1
1
1
1
1
1
1
1
2
1
0
1
0
0
0
1
0
1
1
1
1
1
1
1
0
1
1
1
1
2
2
2
2
0
0
1
1
1
2
1
0
0
1
1
1
1
0
1
2
1
1
1
0
2
2
0
2
0
1
1
1
1
0
1
2
2
1
1
1
2
0
1
2
2
1
1
2
1
1
1
0
0
1
2
1
0
1
0
0
1
2
2
0
2
3
1
2
2
1
2
2
2
2
1
1
1
0
1
1
0
1
1
1
0
1
0
1
1
2
0
2
2
0
1
1
0
1
2
1
1
1
1
0
5
0
1
2
1
1
2
1
1
2
1
1
1
0
1
1
1
1
0
1
2
1
1
2
0
2
2
1
1
2
1
1
2
1
2
1
0
1
1
1
2
1
0
2
1
0
0
1
1
0
1
0
1
2
2
2
1
2
2
1
0
1
2
0
1
0
1
2
1
2
1
1
1
0
0
1
2
2
1
1
1
1
1
1
1
2
1
0
1
0
1
2
2
1
0
0
1
0
2
0
0
1
1
2
2
0
1
1
2
0
2
1
1
1
0
0
1
0
0
1
2
2
1
1
0
3
1
2
0
1
2
1
0
2
2
0
1
0
1
1
1
1
1
2
1
2
0
0
1
0
0
1
1
0
2
1
1
0
0
1
1
1
1
2
1
1
0
1
0
1
1
2
1
1
0
1
1
0
1
1
1
0
2
0
0
2
0
1
1
1
1
1
1
2
2
1
0
1
0
1
0
0
1
3
1
1
1
2
1
0
2
1
1
2
0
1
2
1
0
1
2
1
2
1
1
0
1
1
1
2
1
0
1
0
1
1
0
2
0
1
2
1
2
2
1
1
1
2
0
0
0
1
2
1
1
1
1
0
1
1
1
1
1
0
2
0
1
1
1
1
0
2
0
2
0
1
0
1
0
1
0
1
0
2
1
1
2
0
1
1
0
1
0
0
1
0
2
1
1
0
2
2
1
1
0
0
1
0
2
1
0
2
1
1
1
1
1
1
1
2
1
1
0
1
1
1
1
2
1
2
1
2
0
1
2
2
1
1
0
2
0
2
2
0
0
0
1
1
0
1
1
1
1
2
1
1
0
1
0
1
1
1
1
0
2
1
1
0
0
1
1
1
1
1
1
1
1
1
2
0
0
0
1
2
1
1
2
0
2
0
3
1
0
2
0
1
5
1
0
2
1
1
0
2
0
2
1
1
1
2
2
1
0
1
1
1
1
0
1
1
1
1
1
1
1
1
1
0
2
2
0
0
1
0
1
0
1
2
2
1
1
1
0
1
2
0
1
2
0
2
0
2
2
0
1
0
1
1
1
2
2
1
2
0
2
1
1
0
1
0
1
1
2
0
1
1
0
2
0
1
1
2
0
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
2
0
1
1
1
1
0
1
2
1
1
1
2
0
2
2
2
0
2
0
1
1
2
3
2
2
0
1
3
0
0
1
2
0
0
2
1
0
2
0
0
0
1
1
1
0
6
1
1
1
0
0
2
1
1
1
0
0
2
0
1
2
1
1
1
0
1
0
0
1
1
1
1
1
1
1
1
1
0
1
1
0
1
2
1
0
0
1
1
0
2
0
1
0
1
1
1
1
0
1
0
0
2
1
2
0
1
1
1
0
1
1
1
0
1
2
1
1
1
0
1
1
2
0
1
1
1
2
1
0
0
2
2
1
1
1
1
0
1
0
1
2
1
2
2
0
2
0
0
2
1
2
2
0
0
3
0
2
2
1
1
1
1
1
1
2
1
1
1
0
0
1
0
1
0
1
1
0
1
1
0
1
1
1
1
2
1
1
1
2
0
0
0
2
2
2
2
2
1
1
0
0
1
2
0
1
1
2
1
1
0
2
0
1
1
2
2
0
0
1
2
1
0
0
1
2
2
1
1
2
1
1
2
0
1
2
1
1
1
1
1
0
1
1
2
0
0
0
0
0
1
1
1
0
1
3
0
1
1
1
1
0
0
1
2
1
2
1
1
2
1
1
0
0
0
0
2
1
1
1
0
0
1
1
1
2
0
1
1
1
1
1
1
1
2
2
0
1
2
1
1
0
1
1
0
0
1
0
1
1
1
2
1
0
1
1
2
2
1
1
1
1
0
1
0
1
2
1
2
1
1
1
0
0
0
0
1
1
1
1
1
1
2
2
1
2
2
1
0
0
2
1
1
1
1
2
1
1
1
2
2
1
2
1
1
2
4
1
1
0
3
1
1
1
2
1
1
2
2
2
0
1
0
1
0
2
1
1
0
0
0
1
0
0
1
0
0
2
1
2
2
1
1
2
0
1
1
1
0
1
1
0
0
1
1
2
0
1
3
2
1
2
1
1
2
1
1
1
1
0
0
1
0
1
1
2
1
2
1
1
1
1
0
2
2
1
1
0
1
0
2
1
1
1
1
0
1
2
0
0
3
2
1
0
1
2
1
1
1
1
2
1
0
2
0
2
2
1
1
3
1
1
1
0
1
1
0
1
2
1
0
1
1
0
0
1
1
1
1
2
1
2
2
2
1
2
2
0
1
2
1
1
1
0
1
0
2
0
1
0
1
0
1
1
1
1
0
2
1
1
1
1
0
1
1
0
1
1
1
2
1
1
1
2
2
0
2
2
1
1
2
0
1
0
1
1
0
2
1
1
1
1
1
1
0
1
0
2
1
2
0
1
1
0
2
1
1
1
1
1
1
0
1
1
1
0
2
2
1
2
1
0
2
2
1
1
1
0
2
0
2
1
1
1
2
1
0
1
2
1
2
0
2
1
1
2
0
2
1
1
1
1
1
0
1
2
2
1
0
1
1
2
0
1
0
0
0
1
2
0
0
2
1
1
0
2
1
1
1
0
1
1
0
0
1
0
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
1
2
1
0
1
1
1
1
1
0
1
1
0
1
0
2
2
1
2
0
1
0
0
1
1
1
0
2
1
0
0
1
2
2
1
1
2
0
2
1
2
1
0
0
1
1
2
1
0
0
1
1
0
1
1
0
1
0
1
2
1
1
1
0
1
2
1
1
0
0
0
0
1
2
0
0
0
1
0
1
1
1
0
3
1
2
2
2
1
0
2
1
0
1
1
1
0
1
1
0
0
2
2
1
1
0
1
1
1
1
0
1
1
0
1
2
2
1
2
1
1
0
1
1
2
1
0
0
0
1
1
2
2
1
1
0
1
0
1
1
2
1
1
1
1
0
2
2
1
2
1
2
1
1
1
2
2
0
3
0
2
0
0
2
1
2
0
1
2
0
1
2
1
1
1
0
1
1
2
2
0
1
1
1
2
1
1
1
2
2
1
1
1
1
2
1
1
1
2
1
0
2
1
0
1
1
2
2
0
0
1
1
1
0
1
1
1
2
2
2
0
0
1
1
0
0
1
0
2
1
1
2
1
2
0
2
1
1
0
0
0
3
1
1
1
0
1
1
2
0
1
0
1
1
2
1
0
1
0
0
1
0
1
1
0
1
1
2
2
2
1
1
1
1
1
1
1
1
1
0
2
2
1
1
1
1
1
6
1
1
0
1
2
1
1
0
0
1
2
0
2
2
2
1
1
1
2
2
1
1
1
2
1
1
0
1
0
1
0
2
1
2
1
1
1
1
0
0
2
1
1
2
2
1
0
1
2
2
1
1
0
1
0
1
1
0
0
1
2
1
1
0
0
2
0
1
1
2
2
1
0
1
1
0
1
0
1
1
1
1
2
2
1
1
3
0
1
0
2
0
1
1
0
1
1
2
0
1
1
0
1
1
2
0
1
0
1
1
1
0
1
0
1
1
2
1
0
1
0
1
0
2
1
1
2
2
0
1
1
1
2
1
1
2
0
1
0
1
0
0
1
1
2
2
0
1
1
0
1
2
2
0
1
0
1
1
0
0
1
1
0
2
1
2
1
1
1
1
2
2
1
2
0
1
1
2
0
1
1
1
1
2
1
0
0
1
0
1
1
1
1
0
1
1
0
0
1
0
1
0
1
0
0
2
1
1
0
1
0
0
0
1
1
1
0
1
2
0
2
1
2
2
0
1
1
3
0
2
1
2
0
2
1
1
1
1
0
1
1
1
1
0
1
0
1
3
1
1
2
2
2
2
1
1
0
1
1
1
0
1
2
1
2
0
1
3
1
1
1
1
1
1
0
2
2
1
2
1
1
1
1
0
2
1
1
1
2
2
1
0
2
1
0
2
1
1
0
1
2
1
0
1
2
1
0
2
1
1
0
1
1
2
2
2
1
2
1
2
1
0
1
2
0
2
2
1
0
1
0
1
1
0
0
2
1
0
2
0
1
1
1
1
2
1
0
2
0
0
2
1
1
1
2
2
0
0
0
0
1
1
0
1
1
1
1
1
2
0
1
0
1
1
2
1
0
1
0
1
2
1
1
2
2
1
0
1
1
0
2
0
1
1
0
0
0
0
1
1
1
2
0
2
1
1
1
1
0
2
1
2
1
1
1
0
2
1
1
1
1
0
1
0
1
1
1
1
1
1
1
0
2
0
1
2
1
2
1
2
0
1
0
1
1
0
1
2
2
1
1
0
0
1
0
1
1
2
0
1
1
1
0
2
2
1
0
0
1
1
2
0
2
2
2
2
1
1
2
3
1
1
1
0
1
1
2
0
2
1
2
0
2
0
1
0
1
0
0
1
2
1
2
2
0
0
1
0
1
1
1
1
1
1
1
2
0
0
1
1
2
0
1
0
1
1
0
2
0
2
0
2
1
1
0
2
0
1
1
2
0
1
1
1
2
2
2
2
1
0
1
0
0
1
1
0
1
2
0
1
1
3
0
0
0
2
1
1
1
1
0
2
2
1
2
0
1
0
1
0
1
1
0
1
1
1
0
3
0
0
1
1
1
1
1
0
2
2
1
1
1
0
1
0
1
1
1
1
1
2
1
2
1
2
3
0
2
2
0
1
1
1
1
0
2
2
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
2
0
0
0
1
0
1
0
1
1
0
1
1
0
1
0
1
1
2
1
2
2
1
2
0
0
0
1
1
2
0
1
1
1
1
2
3
1
1
2
2
1
0
0
1
0
3
2
2
3
2
2
1
1
3
1
2
2
2
1
1
2
2
0
1
1
4
2
1
2
0
1
1
1
1
1
2
2
1
0
1
2
2
1
1
1
1
0
0
0
1
2
0
0
1
1
1
1
2
4
2
1
1
1
1
1
1
5
2
1
1
2
1
1
1
2
2
0
1
0
1
1
1
2
0
1
0
1
1
0
0
1
1
1
1
1
2
1
1
1
0
1
1
1
1
0
0
0
1
1
2
3
0
0
1
1
2
1
1
1
1
0
1
1
1
0
1
1
2
1
1
2
2
0
1
4
1
1
1
1
2
1
1
1
1
0
1
1
1
1
2
1
1
1
1
2
2
1
1
1
1
0
1
1
1
0
0
1
0
2
1
1
1
1
2
2
2
1
2
1
1
0
1
2
1
0
1
2
1
1
2
2
1
0
2
1
1
0
2
1
0
0
1
2
2
1
1
1
1
0
2
1
2
1
1
1
2
1
1
2
1
0
2
0
2
1
1
0
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
0
0
1
1
0
1
1
1
1
1
1
0
1
1
0
1
0
1
2
0
1
0
1
1
1
1
1
1
3
0
2
1
1
0
2
1
1
2
1
0
0
1
2
2
1
3
1
2
2
2
1
2
1
0
1
1
1
1
3
1
0
0
0
1
1
2
1
2
1
1
1
0
0
1
1
1
1
1
1
1
0
0
1
0
1
2
1
0
1
2
2
1
2
1
2
1
1
2
1
1
2
1
2
2
2
1
1
2
1
1
2
2
1
1
0
1
2
0
1
2
1
1
0
1
2
2
2
2
2
0
1
0
0
2
0
1
1
0
1
1
1
2
0
1
0
1
1
1
1
1
1
2
1
2
0
1
2
2
0
0
1
0
1
2
0
1
1
0
0
0
0
1
2
0
1
0
2
1
1
0
1
0
1
2
1
1
0
1
1
1
1
0
1
1
1
0
1
1
1
1
1
2
1
1
0
2
1
0
0
2
0
0
1
1
0
2
2
2
2
1
2
2
1
0
2
2
1
1
0
0
1
0
1
1
0
0
2
2
1
0
1
0
1
1
1
2
2
1
1
0
1
2
1
0
1
2
1
1
0
0
0
2
1
2
2
0
1
0
2
1
2
1
0
1
1
1
1
1
1
0
1
1
0
0
1
1
1
2
1
1
1
2
2
1
1
0
2
2
0
1
2
2
0
1
2
2
1
0
0
1
1
1
1
1
1
1
1
3
2
2
2
2
0
1
1
0
1
0
0
2
1
2
1
1
2
1
1
2
0
0
2
1
0
0
1
0
0
2
1
1
1
1
1
1
1
1
0
0
1
1
2
1
0
0
1
0
0
2
1
0
1
1
1
1
1
0
2
0
2
0
1
3
1
1
0
1
1
1
2
2
2
1
1
1
1
0
1
1
0
0
1
2
0
1
2
3
2
0
2
0
1
1
0
1
0
2
1
0
0
0
1
1
1
1
0
2
1
2
2
2
2
1
1
1
1
1
2
1
2
2
1
1
0
2
1
0
0
0
2
1
0
1
0
2
2
2
1
2
1
1
0
1
0
1
0
1
2
1
1
2
2
1
1
2
0
1
1
1
1
1
2
4
1
2
1
1
2
1
2
0
2
0
0
1
1
0
2
0
2
0
1
1
2
1
1
1
1
2
2
0
2
1
0
0
0
4
0
1
1
2
2
1
1
0
2
2
1
1
1
2
0
2
1
0
1
2
1
2
1
0
2
1
0
1
1
0
3
1
1
1
0
0
1
2
1
0
1
1
2
1
2
1
1
0
1
1
1
1
0
1
1
1
1
1
2
1
1
1
1
1
1
2
0
1
1
1
2
1
0
0
2
1
1
1
2
0
2
0
0
0
1
1
2
1
1
1
2
0
1
1
1
0
1
0
0
1
1
2
2
1
0
1
2
2
1
1
1
1
1
2
2
1
0
0
1
0
0
1
1
1
1
1
1
2
3
1
1
1
0
0
1
1
1
1
0
2
2
1
1
1
0
1
0
1
1
1
2
1
1
1
1
1
1
2
2
1
0
2
0
1
0
0
1
1
1
0
2
2
0
1
1
1
2
1
0
1
0
2
0
0
0
1
3
0
1
0
1
1
1
2
1
1
2
2
1
2
1
0
0
0
2
1
1
1
0
1
2
1
2
1
0
1
2
0
1
1
0
2
0
1
0
2
2
1
1
0
2
1
2
1
0
2
1
0
1
1
0
1
2
0
0
1
0
3
1
1
1
0
1
0
1
0
1
1
0
1
2
0
1
0
1
0
1
1
1
2
0
2
2
1
0
0
1
2
1
0
2
0
1
2
2
1
1
0
0
1
0
0
2
1
0
1
0
0
1
1
2
1
0
2
0
1
1
2
0
1
0
1
0
0
2
1
0
2
0
1
2
1
0
1
1
1
1
2
1
1
2
0
1
1
2
1
1
0
0
1
1
1
2
1
1
0
1
1
1
0
2
1
0
0
1
2
0
0
1
1
1
0
0
0
2
1
1
1
1
1
1
2
0
0
1
1
2
1
1
1
1
0
2
1
1
2
1
1
1
1
2
1
2
1
0
1
1
2
0
2
0
2
2
1
1
2
1
1
0
0
2
2
1
1
1
1
0
2
1
0
2
1
1
2
1
2
0
1
1
1
2
0
1
1
1
0
2
1
0
0
2
1
7
1
1
0
1
1
0
1
3
2
1
1
1
1
1
1
1
1
0
0
2
2
2
2
2
0
1
2
1
1
1
0
0
1
1
2
0
0
2
1
2
1
0
1
1
1
1
2
2
1
2
0
3
1
2
1
1
1
0
2
2
1
1
1
1
0
1
1
1
0
1
1
1
2
2
1
1
1
0
1
2
1
0
0
1
1
1
2
1
1
2
1
1
1
0
1
2
2
0
1
1
0
1
1
0
1
0
0
0
2
1
0
0
2
2
2
1
1
1
1
2
0
1
0
1
1
1
1
0
0
1
1
1
1
1
0
2
1
1
2
1
1
2
1
1
2
0
1
1
0
0
1
1
0
1
1
1
1
1
2
0
1
1
0
1
0
2
1
1
4
1
2
0
2
0
1
0
1
2
1
1
1
2
0
1
0
1
2
2
1
1
1
1
0
2
0
2
1
1
1
1
0
2
0
1
1
2
1
1
1
1
2
0
0
2
1
0
0
0
1
1
1
1
2
0
2
2
1
1
1
0
0
1
2
1
1
2
1
0
0
2
0
2
0
1
1
2
1
1
2
1
2
1
1
1
0
2
2
1
0
0
0
1
0
0
0
0
1
0
2
1
0
2
2
1
1
1
1
1
2
1
0
1
1
0
1
1
0
1
1
2
1
1
2
1
0
8
1
0
2
2
2
0
0
1
1
4
1
1
0
1
1
0
2
1
1
0
0
1
1
1
1
0
1
1
1
1
1
0
2
1
1
2
1
0
0
1
1
0
1
0
2
1
1
1
0
0
1
1
0
1
1
0
2
0
2
0
1
0
1
1
2
0
1
1
0
1
2
2
1
1
1
1
2
1
1
0
0
1
1
2
2
1
1
0
1
2
1
1
1
1
2
0
1
2
0
0
1
1
1
2
1
0
1
2
2
2
0
0
2
1
1
1
1
1
0
2
1
1
0
1
2
0
1
2
2
1
1
1
2
0
1
1
1
1
1
1
2
1
2
2
4
1
0
1
2
1
0
1
1
2
0
0
1
1
1
1
0
1
0
1
0
1
1
1
1
1
1
0
1
0
1
0
1
0
0
1
1
0
2
1
1
1
1
1
2
1
1
2
1
2
1
1
1
0
0
2
0
0
1
2
1
1
2
0
1
1
1
1
1
0
0
1
1
1
1
1
1
1
0
1
0
1
1
1
1
0
2
1
0
1
1
2
0
1
1
1
2
2
1
1
1
0
1
2
2
1
1
1
2
1
0
1
0
1
2
1
0
1
1
4
1
2
0
1
0
0
0
1
2
1
1
1
2
0
1
1
1
1
0
2
1
0
1
1
1
1
1
1
1
2
0
1
1
1
1
1
1
1
1
1
2
0
1
2
1
1
0
1
1
2
1
0
1
1
1
1
0
0
1
1
1
0
0
1
1
2
1
1
1
1
0
1
2
2
2
2
1
0
1
2
2
1
0
1
1
1
0
0
2
1
0
2
1
0
2
1
2
1
1
2
1
0
1
1
0
1
2
1
2
1
2
0
1
2
1
2
1
1
1
2
1
0
0
2
1
0
1
1
1
2
1
2
0
2
1
0
2
0
1
2
1
1
0
1
1
2
0
0
1
1
2
2
1
0
1
0
1
1
0
2
1
1
0
1
1
1
0
1
1
2
1
2
0
1
1
1
1
1
1
1
1
0
1
1
0
1
1
1
1
0
1
1
2
2
1
2
1
0
2
0
1
1
1
1
2
0
0
1
2
1
2
1
1
2
0
1
2
1
1
1
1
1
0
1
0
0
1
0
0
1
1
1
1
1
1
2
1
0
1
2
2
1
2
0
0
1
2
2
1
0
2
0
1
1
2
2
1
0
1
1
1
0
1
0
2
0
1
2
0
0
1
2
2
0
1
1
2
1
0
1
1
1
1
1
1
1
1
1
1
1
0
1
2
0
1
1
1
2
1
1
1
1
0
2
0
1
0
0
1
1
1
0
1
1
1
2
1
1
0
0
1
0
1
1
0
1
1
1
5
0
1
0
2
1
1
1
2
2
2
2
1
1
3
2
1
1
0
1
0
1
1
1
1
1
1
1
1
1
1
1
0
2
2
1
2
1
2
1
1
0
0
1
0
0
1
2
1
1
0
0
1
2
2
0
2
2
1
1
1
1
4
1
2
2
1
1
2
1
2
0
1
2
1
2
2
2
0
0
1
1
1
2
1
0
2
1
1
2
2
2
1
0
1
2
0
1
1
0
1
0
2
1
1
2
8
2
0
1
0
1
1
1
2
1
0
1
1
1
0
1
1
1
1
1
1
0
2
1
0
1
4
3
0
1
1
0
0
1
0
0
1
1
1
2
0
1
1
2
0
1
1
0
2
1
0
1
1
0
2
0
0
1
2
0
0
2
1
1
0
1
1
0
1
4
2
0
2
0
1
1
1
1
0
0
1
2
2
0
1
0
2
0
0
1
1
2
0
1
0
2
0
0
2
1
0
2
0
2
0
1
4
1
1
2
2
3
0
1
1
0
1
1
1
1
0
0
0
2
1
1
1
0
1
1
0
1
1
2
0
1
1
4
2
2
1
0
0
1
0
0
2
2
1
0
1
2
0
1
2
1
1
1
2
1
1
2
1
1
1
1
1
1
0
1
0
1
0
2
1
1
2
2
1
2
1
1
1
1
1
1
1
0
1
1
0
0
1
1
1
2
2
2
0
1
2
1
1
1
1
0
1
1
0
0
0
2
1
0
0
0
0
2
1
1
0
2
3
0
1
1
0
1
0
2
1
1
1
1
3
1
1
1
1
0
2
0
0
2
2
2
0
0
2
1
1
0
1
2
2
2
1
0
2
2
1
2
1
1
1
0
1
1
1
3
0
2
1
1
2
1
1
1
1
1
1
1
1
3
1
2
0
2
2
1
1
1
1
0
2
1
0
1
1
2
1
1
0
2
1
2
2
0
1
2
0
0
0
1
1
1
0
5
2
2
0
0
2
1
2
2
1
0
1
2
1
1
2
1
2
2
0
1
0
1
0
2
1
2
1
1
1
1
2
1
1
1
0
2
1
1
2
1
5
2
0
0
1
1
1
0
1
0
1
1
0
0
0
1
1
1
1
1
0
1
2
1
1
2
2
1
0
1
0
0
2
1
0
1
1
1
0
1
1
1
1
2
1
1
1
1
1
0
1
1
1
1
1
1
1
2
1
1
1
2
1
0
1
0
1
0
0
2
2
2
0
1
1
1
1
1
1
2
1
0
1
0
1
0
2
1
2
1
2
0
1
2
0
0
1
0
0
0
0
1
2
2
1
0
0
1
2
2
0
2
1
2
2
2
1
0
1
0
2
1
1
1
1
2
1
1
1
2
0
2
1
1
1
0
1
0
0
1
1
1
0
1
2
0
1
1
1
0
1
1
2
1
1
0
1
0
0
1
1
1
1
1
1
2
0
1
2
1
1
1
0
2
2
2
1
1
1
1
2
2
0
2
1
1
1
1
1
2
1
2
2
1
2
0
1
1
2
0
0
0
2
0
0
1
1
2
0
1
1
1
2
1
1
0
1
1
0
1
2
0
2
1
0
1
1
1
2
2
0
2
3
1
2
1
1
0
2
1
1
2
0
2
1
5
0
3
0
1
1
1
1
2
0
0
1
1
2
1
1
1
1
3
1
1
0
2
2
1
1
0
0
0
0
1
1
1
0
1
1
2
1
2
2
2
0
2
1
2
2
0
1
0
1
2
0
1
2
1
2
1
1
1
1
1
0
1
2
1
0
1
0
1
1
0
1
0
2
1
0
1
2
0
0
0
1
0
2
0
2
2
1
1
0
1
1
1
0
1
2
1
2
1
2
1
1
1
2
0
2
1
2
2
1
0
0
2
2
1
1
2
2
2
0
0
0
1
0
1
2
1
1
1
1
0
1
0
1
1
2
1
1
1
2
2
1
1
1
1
2
0
1
0
0
0
1
2
1
0
1
1
1
1
1
0
1
1
1
0
2
0
1
1
0
1
1
1
1
1
1
2
1
0
1
2
1
1
1
0
1
2
1
1
1
2
1
1
2
1
1
1
2
0
0
0
1
2
2
2
1
2
4
1
1
1
1
1
1
1
1
1
2
0
1
2
2
1
1
0
1
0
0
2
1
1
2
0
2
1
0
1
2
1
1
0
0
1
1
2
2
0
1
0
1
1
1
1
2
2
1
0
0
1
2
1
1
0
0
1
1
1
1
1
0
1
1
0
0
1
4
1
1
1
0
1
1
1
2
1
1
1
1
1
2
2
1
1
1
1
1
1
2
2
2
1
1
2
1
0
1
1
1
1
1
1
1
1
1
1
0
1
1
0
1
1
0
0
1
2
0
1
1
1
1
0
1
2
1
1
1
1
1
2
0
2
1
1
1
1
0
0
1
2
2
1
0
1
2
1
1
1
2
2
0
2
1
0
2
0
1
1
0
0
1
1
1
1
2
1
0
1
1
2
1
2
2
1
1
0
1
1
1
1
1
1
1
0
2
0
1
1
0
1
2
1
0
0
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
3
1
1
1
0
0
1
2
1
2
2
1
2
1
1
2
0
0
1
3
0
1
0
1
2
2
1
1
1
0
1
1
1
1
1
0
2
2
1
1
2
0
0
1
0
1
0
2
1
1
1
1
1
1
1
1
0
2
1
1
1
0
1
2
0
1
2
1
1
2
2
3
1
2
1
0
1
1
1
0
2
0
1
1
1
0
0
2
2
1
1
1
1
1
2
2
0
0
1
0
1
1
0
1
0
1
1
2
1
0
2
1
2
1
0
1
2
1
2
1
0
1
1
0
1
2
1
0
1
1
2
1
1
1
1
1
4
2
2
1
2
1
2
1
1
1
2
1
1
2
1
1
1
2
1
1
1
1
0
2
1
1
1
2
2
0
1
2
2
2
1
1
2
2
1
1
0
1
1
1
0
1
2
1
2
1
0
0
1
2
1
2
0
0
2
2
1
1
0
1
1
1
1
0
1
0
0
2
2
1
1
1
1
1
0
0
2
2
0
0
2
1
2
2
2
0
0
1
2
2
1
0
1
1
1
1
1
1
0
1
2
0
2
1
2
1
1
2
0
2
1
1
1
2
0
0
1
0
1
1
0
2
2
1
0
2
2
2
1
1
1
1
1
2
0
2
0
2
0
4
1
0
1
0
1
2
0
1
2
2
0
1
0
1
2
1
1
2
2
1
2
1
3
2
1
0
1
0
1
1
1
0
1
1
1
1
1
2
2
1
1
0
2
1
1
0
1
0
0
1
0
1
2
2
1
0
1
1
1
1
1
1
1
2
1
0
1
1
1
2
0
1
2
1
0
1
0
1
2
1
1
2
0
1
0
1
0
1
0
0
2
1
1
2
0
0
1
2
1
2
1
1
2
1
1
0
1
2
0
0
1
0
1
0
0
1
0
1
2
1
1
2
2
1
0
1
1
1
0
1
1
1
2
0
0
1
1
0
0
1
0
1
0
1
1
0
0
1
1
1
2
2
1
1
0
0
0
0
2
1
2
1
1
2
1
2
1
2
2
0
2
1
0
1
0
1
2
1
1
2
1
1
1
1
1
1
2
2
0
1
1
0
2
0
0
1
1
1
0
1
2
1
1
0
2
1
1
1
0
1
1
2
0
0
1
0
1
1
1
1
1
3
1
1
2
1
1
1
1
0
0
1
0
1
1
1
2
0
1
0
1
0
1
0
1
1
0
1
1
1
1
2
1
1
2
1
0
1
1
1
1
1
2
1
0
0
2
2
0
1
1
1
2
1
2
0
2
1
1
2
2
1
0
1
0
0
1
2
0
2
0
2
2
0
0
0
1
1
2
0
1
2
1
1
1
1
2
1
1
0
3
2
1
2
1
1
1
1
2
1
1
0
0
2
0
0
2
1
0
2
4
1
0
0
1
0
1
1
1
1
0
0
0
3
1
1
2
1
2
1
1
1
2
0
0
1
1
0
0
1
1
2
0
0
0
1
1
1
1
1
1
1
1
1
0
2
0
1
2
1
1
0
2
1
2
1
2
0
1
1
2
0
1
1
1
3
1
1
0
0
0
2
1
0
0
0
1
1
0
1
2
0
1
2
1
1
1
1
1
0
2
0
0
0
1
4
1
0
1
1
1
1
1
1
1
1
3
2
1
1
1
1
0
1
1
1
2
2
1
2
1
1
1
1
1
2
1
0
1
1
1
1
1
1
2
2
0
1
1
1
2
0
0
1
1
1
0
2
1
0
2
1
2
1
1
1
1
1
1
1
1
1
1
2
0
1
2
1
2
1
2
0
1
2
0
0
1
0
1
2
1
1
1
1
2
1
2
0
1
1
2
3
1
1
2
1
1
0
1
1
1
1
2
1
1
1
2
1
1
0
1
1
2
2
0
1
1
2
1
1
1
1
1
0
0
2
0
0
2
0
0
2
1
0
1
1
1
2
2
0
1
0
1
1
0
2
0
2
2
1
1
1
0
1
1
2
0
1
1
2
0
0
2
2
1
0
2
0
0
1
1
2
0
0
2
1
2
2
0
2
1
0
2
2
2
1
0
1
1
0
1
1
1
0
0
1
1
2
2
0
0
2
4
1
1
1
2
0
2
1
1
1
1
2
2
0
0
1
1
1
1
0
0
1
1
0
1
2
1
1
1
0
2
1
1
0
1
1
2
2
2
1
2
1
1
2
0
2
1
0
1
0
0
1
1
1
1
1
2
0
2
2
1
1
1
0
1
1
1
1
3
1
1
1
1
1
1
2
1
0
2
2
1
2
1
0
0
2
0
0
1
1
0
2
1
0
1
1
0
1
1
2
0
2
2
1
1
0
1
1
3
2
1
0
2
0
1
1
2
1
0
0
1
1
1
0
1
1
1
1
1
1
0
2
1
1
2
1
2
1
2
1
2
1
0
1
1
1
1
2
0
0
1
2
1
1
0
1
1
1
1
1
2
1
0
1
0
2
1
1
2
2
1
0
0
1
1
0
2
2
1
0
1
1
1
0
1
0
0
1
0
2
1
0
1
0
1
0
1
1
0
2
2
1
0
0
4
0
1
2
0
1
1
1
0
0
2
0
2
1
1
1
1
1
1
1
1
1
2
1
0
0
2
2
0
1
0
1
2
2
1
1
2
1
2
0
1
1
2
1
2
1
1
0
2
1
2
1
0
1
1
1
1
1
0
1
3
1
1
1
2
1
2
1
1
1
1
0
0
1
1
0
0
0
2
1
0
2
1
2
1
1
2
1
1
0
0
0
2
0
1
1
0
1
0
1
2
1
1
1
0
1
1
1
0
1
2
3
1
2
2
1
2
0
2
1
0
2
1
1
2
1
0
1
1
0
1
1
1
2
2
0
2
0
2
2
1
0
2
0
0
1
2
0
1
0
1
2
1
0
0
1
1
1
2
0
0
1
1
2
1
1
1
1
1
1
2
3
0
2
0
0
1
1
1
2
1
1
1
1
1
0
1
0
2
2
1
1
1
0
1
1
0
1
4
0
1
2
1
2
1
2
1
1
0
0
1
0
1
1
0
1
1
2
1
0
0
1
2
0
1
2
2
1
0
1
1
1
2
0
0
1
0
1
1
1
0
2
0
2
0
1
2
0
2
0
2
1
1
0
0
1
2
1
1
1
1
1
1
0
1
1
1
0
1
0
1
2
1
1
1
1
1
2
2
1
1
2
2
1
1
0
1
2
2
0
1
1
0
1
1
0
1
0
2
0
1
1
1
1
0
2
2
0
0
1
0
0
2
2
1
1
2
1
0
0
2
1
2
1
1
0
1
0
2
1
1
2
1
0
1
2
0
1
1
1
1
1
2
1
2
0
2
0
1
2
1
1
1
0
1
2
0
0
1
1
0
0
2
1
1
1
0
2
2
1
2
1
1
2
2
2
1
1
0
1
2
1
1
0
2
1
1
3
2
0
0
0
0
0
1
1
1
1
0
0
1
2
0
2
2
2
3
1
1
1
0
0
1
0
1
0
1
1
2
2
1
1
2
1
1
0
1
1
0
1
1
1
0
1
1
1
1
2
1
0
0
2
1
1
0
1
1
1
1
0
0
2
1
0
1
0
1
2
1
1
2
0
1
2
1
0
1
0
0
1
0
1
1
1
0
1
1
1
1
2
0
1
2
2
2
1
0
1
0
2
1
1
1
0
1
2
1
0
2
2
1
1
0
2
1
2
1
0
2
1
1
2
1
1
2
1
1
0
0
1
1
2
0
1
1
2
1
2
1
1
0
2
0
2
2
0
0
1
0
2
1
1
2
0
1
1
3
2
0
1
0
1
2
2
1
1
1
2
1
1
0
1
1
2
0
3
1
1
1
2
1
1
2
1
1
1
2
2
1
2
1
0
0
0
2
1
1
0
0
0
1
1
0
1
0
2
1
1
1
1
1
1
1
0
2
2
2
0
1
1
0
1
1
1
0
1
1
0
0
1
1
0
0
1
1
1
0
2
1
2
0
1
2
1
0
0
2
1
2
1
1
2
1
1
0
2
1
1
1
2
1
0
0
1
2
0
1
0
0
1
0
1
0
2
1
1
1
1
0
1
2
1
2
1
0
1
2
1
2
1
1
1
0
1
1
2
1
1
0
1
1
1
1
1
1
2
1
1
1
1
1
2
1
0
0
1
1
1
1
2
2
2
2
1
1
0
0
0
1
1
1
2
2
0
1
0
2
1
2
1
1
2
0
1
2
1
2
2
1
1
1
1
1
1
1
2
1
2
0
0
1
1
1
1
2
2
2
2
2
1
1
2
1
1
2
2
1
1
1
0
1
1
2
0
0
1
2
2
0
2
0
2
1
0
0
0
0
0
0
0
0
2
0
1
1
1
1
1
1
2
1
1
0
1
1
1
2
1
1
0
1
0
0
1
0
0
2
1
0
0
1
1
2
1
2
2
2
0
1
1
1
0
2
1
0
2
0
1
2
0
1
1
1
1
2
0
0
1
0
1
1
0
2
1
1
1
2
2
2
2
2
1
1
1
1
0
1
1
2
1
2
0
2
1
0
1
0
1
0
1
2
1
0
1
1
1
1
0
0
2
0
1
1
1
1
0
1
1
1
0
2
1
1
1
1
0
1
2
2
1
0
1
0
2
2
1
1
0
0
1
0
1
2
0
0
2
1
1
2
1
0
0
1
2
0
1
2
0
1
1
1
1
1
2
0
1
2
0
1
1
1
1
1
0
0
0
1
0
0
3
1
1
1
2
1
2
0
1
1
2
2
1
2
0
1
0
1
0
0
1
1
0
2
2
2
1
0
1
0
1
1
2
0
0
1
1
2
1
2
0
2
1
1
0
0
1
1
1
1
0
1
2
1
1
2
1
1
1
1
1
0
1
1
0
0
1
0
0
1
1
1
1
1
0
1
1
1
1
2
1
1
1
2
0
1
1
1
1
1
2
2
2
0
1
1
1
0
2
1
1
1
1
1
1
1
2
2
1
1
1
0
1
0
1
2
1
0
2
2
1
1
1
1
1
1
0
0
0
1
1
1
1
2
0
0
1
2
0
0
0
2
1
1
1
2
1
0
4
1
1
1
1
0
1
1
1
1
0
1
1
2
1
2
2
1
0
0
1
0
0
0
0
1
1
1
1
1
2
0
1
0
1
2
1
2
1
1
2
2
0
2
2
0
1
2
1
0
1
0
2
2
1
0
2
1
1
2
1
2
1
1
0
1
2
2
0
1
0
1
2
0
1
1
1
0
1
1
1
1
2
1
2
1
1
0
1
1
2
1
4
1
0
1
1
1
0
1
1
1
1
1
2
0
1
1
1
1
2
2
1
1
0
2
2
0
0
0
1
1
0
1
0
1
0
1
1
1
0
0
2
1
0
1
0
1
2
2
2
1
2
2
0
1
0
0
0
2
1
1
1
1
1
1
1
2
1
2
1
1
0
2
2
0
3
0
0
0
1
0
1
1
2
0
1
1
1
1
2
1
1
2
2
1
2
1
1
2
1
2
1
2
2
1
2
1
2
0
1
1
2
1
1
1
2
2
1
0
1
1
2
1
0
1
2
1
0
2
0
0
0
2
2
2
2
1
0
2
2
1
0
0
1
1
2
2
2
0
2
0
1
2
0
1
0
1
2
2
1
2
0
1
1
2
1
1
1
2
1
0
1
1
0
0
2
1
1
2
2
2
1
1
1
1
2
0
1
1
0
2
2
1
0
0
0
1
0
2
2
1
2
1
2
1
2
2
0
1
1
1
1
2
0
1
1
1
1
0
1
1
2
0
0
1
2
1
2
2
0
1
0
0
0
2
0
2
1
1
1
1
2
2
1
1
1
1
1
0
1
0
0
2
1
2
1
1
0
0
0
2
1
2
1
2
2
1
0
0
1
1
1
1
0
0
0
1
2
1
1
0
3
1
1
1
1
1
1
1
1
2
2
1
0
2
2
0
1
1
1
3
1
2
2
2
1
0
1
2
1
2
2
1
1
1
2
1
0
2
1
2
1
1
1
1
1
1
0
0
1
1
0
0
1
0
2
2
1
1
1
0
0
1
1
2
1
1
1
1
1
1
2
0
1
1
1
2
1
0
1
2
1
1
1
1
2
2
2
0
1
1
1
1
1
0
2
0
1
1
1
2
2
1
1
0
2
2
1
0
2
2
2
0
0
1
1
2
1
1
2
1
2
1
0
1
2
1
1
2
2
0
2
2
0
2
0
2
1
1
1
2
2
1
0
0
1
1
0
1
0
2
0
1
2
0
1
1
0
2
0
2
1
1
1
2
0
0
1
1
1
1
2
1
2
3
0
1
0
1
2
0
1
1
1
1
3
1
1
1
0
3
2
2
2
1
1
1
1
0
2
1
2
1
0
1
1
0
1
1
1
0
0
1
2
1
2
1
0
1
1
1
1
1
1
0
0
2
1
2
3
1
1
1
1
1
1
0
1
3
1
2
1
1
0
2
1
1
0
1
0
2
2
1
2
1
1
0
1
2
0
0
1
2
0
1
1
1
2
1
2
2
1
2
0
1
0
1
1
0
1
2
1
0
2
1
0
1
1
1
1
0
1
2
1
1
1
1
1
0
0
1
2
1
0
0
1
2
0
1
1
1
1
1
0
0
0
0
2
3
2
1
1
1
2
2
1
1
2
0
0
0
0
1
0
1
1
1
1
2
2
1
0
1
2
1
1
0
0
3
2
2
1
2
2
1
1
1
1
1
2
1
1
2
0
1
2
1
1
0
1
1
1
1
2
1
1
1
0
1
0
0
1
1
1
1
0
2
1
1
3
1
1
0
0
2
2
0
2
2
0
2
1
0
1
0
1
1
1
0
1
2
0
1
0
1
1
1
1
1
0
0
2
1
2
1
0
1
1
1
1
0
2
0
2
0
1
0
1
1
1
2
2
2
2
2
1
0
2
0
1
0
0
2
1
0
0
2
2
1
2
0
0
0
1
2
1
2
1
1
1
0
1
1
0
0
1
1
1
2
1
2
2
1
2
1
1
0
0
2
2
0
1
1
1
1
1
0
0
1
0
1
0
0
0
1
2
0
1
1
1
0
1
1
0
1
1
0
1
1
2
1
1
0
1
0
1
1
2
1
1
0
1
2
0
1
1
0
0
2
1
1
2
2
4
1
1
1
1
2
0
2
0
0
2
0
1
0
1
1
1
0
1
2
2
1
1
2
1
1
0
0
2
0
1
2
0
1
1
1
1
2
1
1
1
2
2
1
1
1
0
0
1
0
1
1
2
0
1
2
0
0
1
1
1
0
1
0
0
1
2
1
1
2
1
0
3
2
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
0
0
2
2
1
2
1
1
1
2
2
0
1
1
0
0
1
1
1
0
1
1
3
1
2
0
2
1
1
0
1
1
1
0
1
2
1
1
1
2
2
2
2
2
1
1
1
0
2
2
1
1
1
1
2
1
2
1
1
0
1
0
1
0
1
2
0
0
2
1
1
1
2
2
3
1
1
2
1
1
2
1
1
1
1
0
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
2
0
0
0
1
2
0
1
0
1
0
1
3
1
1
2
0
1
2
0
1
0
1
2
0
2
2
1
0
0
1
1
1
1
1
1
1
1
1
1
1
0
1
1
0
1
2
2
4
1
0
1
1
1
1
2
0
2
2
2
1
0
0
2
1
0
1
0
1
0
0
1
1
1
0
2
1
2
0
1
1
1
0
1
1
2
2
2
1
2
1
0
0
1
0
0
1
0
0
1
0
1
0
1
0
1
0
0
0
1
0
1
1
1
1
1
1
0
1
3
1
0
0
0
0
1
1
2
1
0
1
1
2
0
2
2
2
0
1
1
2
0
0
0
0
2
0
2
1
1
0
1
1
1
1
0
0
1
1
2
0
0
1
1
0
2
2
0
1
0
0
1
2
1
1
0
0
2
2
0
2
0
0
1
1
2
2
1
1
1
3
1
1
2
1
1
1
1
0
2
1
0
1
1
1
1
1
1
0
2
1
1
1
1
0
1
0
1
1
1
1
4
2
1
1
1
1
1
1
0
1
0
0
2
1
0
1
1
1
1
1
1
1
2
0
2
1
1
0
1
0
0
2
0
2
1
1
1
0
0
1
1
0
0
1
2
1
1
2
2
1
1
0
1
1
2
0
0
0
2
1
0
0
0
1
0
2
1
1
1
0
1
1
1
0
1
0
2
0
0
1
1
1
1
3
1
0
0
1
1
1
1
1
4
0
1
1
1
1
1
1
0
2
1
1
2
0
0
1
1
1
1
0
2
1
1
1
0
1
0
1
2
1
2
1
2
2
1
0
1
1
1
1
1
1
2
1
1
1
2
0
1
2
1
1
0
1
0
1
1
1
2
1
0
0
1
1
1
2
1
1
0
2
0
1
2
1
1
1
2
1
1
2
3
2
0
0
0
2
1
1
1
2
1
0
1
2
1
0
4
2
2
0
1
2
2
1
0
0
0
1
2
0
1
1
2
1
0
1
0
1
2
1
2
1
2
1
1
1
2
1
1
1
1
1
1
2
1
1
2
1
0
1
0
1
1
0
1
1
2
1
1
1
1
0
1
0
2
2
0
1
0
0
2
1
1
1
1
1
1
2
1
0
2
0
1
1
1
1
1
1
1
0
2
2
0
1
1
1
1
2
1
0
0
1
1
0
1
0
2
2
0
1
1
1
1
2
0
2
3
1
0
1
0
1
1
1
2
1
1
1
0
2
1
1
0
1
2
1
1
2
0
0
1
1
1
2
1
1
1
1
2
1
1
1
0
0
0
1
1
2
2
1
1
1
1
2
0
1
1
1
2
1
2
2
1
1
1
1
1
0
1
1
1
1
1
2
1
2
1
1
1
1
2
2
1
2
1
0
1
1
0
0
1
1
1
1
1
0
1
1
0
4
0
2
1
0
1
0
0
2
4
2
1
1
0
1
2
2
1
1
0
2
1
2
2
1
0
1
0
1
1
0
0
0
2
1
2
1
1
2
1
1
1
0
1
2
1
2
1
1
1
1
1
1
0
2
1
2
1
1
1
1
0
0
1
1
1
0
2
1
0
1
1
0
2
1
0
1
2
1
1
1
0
0
2
0
0
0
1
1
1
0
1
1
0
0
1
1
1
1
1
1
2
1
1
2
0
1
1
0
0
0
2
2
1
0
2
2
1
2
0
0
0
0
1
0
1
1
2
0
1
1
1
2
1
1
1
0
1
1
0
0
0
1
1
0
1
0
1
1
2
2
1
2
0
1
1
2
0
1
1
1
1
2
2
1
0
2
1
1
1
1
1
0
1
2
1
1
1
1
1
0
2
2
0
0
0
1
2
1
1
2
1
1
0
0
2
1
0
2
0
1
0
1
2
1
1
3
1
1
1
1
2
2
1
1
2
1
2
1
2
1
0
1
0
2
2
1
2
1
0
1
1
1
1
1
1
0
0
1
1
0
1
0
1
1
2
1
1
1
1
1
2
1
0
1
3
1
2
0
0
1
0
2
1
1
0
2
1
2
0
1
0
1
1
0
1
1
0
0
0
1
0
0
1
1
2
0
1
1
1
1
1
1
1
2
1
2
1
0
2
1
0
2
1
0
1
1
0
1
1
1
0
0
2
1
0
0
1
0
2
1
2
2
1
2
2
0
3
1
1
1
0
1
0
1
0
1
0
1
3
1
1
2
1
1
0
0
0
1
2
0
1
1
1
0
0
2
1
0
1
0
1
1
1
1
2
2
1
0
1
1
1
1
1
0
0
1
2
1
1
0
2
1
1
0
1
1
0
2
0
1
2
4
1
0
1
1
1
0
1
0
0
1
1
1
2
1
3
1
1
3
2
2
1
0
1
1
0
1
1
1
0
0
1
2
0
1
2
2
0
0
1
1
0
1
2
1
2
1
0
1
1
0
1
0
2
2
1
1
0
1
2
1
1
2
2
1
0
1
0
1
2
1
2
0
2
1
0
0
0
2
1
1
2
1
2
2
1
1
1
1
0
0
2
2
0
0
1
0
2
1
1
0
2
1
1
1
1
1
0
1
1
0
1
1
0
1
0
1
1
2
2
1
2
2
0
1
1
2
1
0
0
1
1
2
1
1
2
1
1
0
1
0
1
1
2
1
0
1
1
0
2
0
2
1
2
1
1
1
0
1
2
1
1
2
0
2
2
1
1
1
0
2
1
1
0
1
1
0
1
1
5
0
2
1
0
2
2
1
1
2
2
2
1
1
2
0
0
1
2
2
1
1
1
0
1
1
1
1
0
0
1
0
1
2
2
2
2
1
1
1
1
1
1
1
2
0
1
1
3
1
1
2
2
0
1
1
1
1
2
3
1
2
1
1
1
1
2
2
0
1
0
1
0
2
1
2
1
1
1
0
1
0
2
0
0
1
1
1
1
0
0
0
0
1
0
1
2
1
0
0
1
1
1
0
1
1
2
2
1
0
1
1
1
1
2
0
1
2
3
1
1
1
1
1
2
1
1
2
1
1
1
0
1
2
2
0
0
1
0
1
1
1
2
2
1
2
0
1
0
0
0
1
1
1
1
2
1
0
1
1
2
0
0
1
1
0
0
1
0
1
5
1
2
1
2
1
1
1
1
1
1
1
1
0
1
2
1
1
1
1
0
1
1
2
1
0
2
0
1
1
1
2
2
1
1
0
1
2
0
1
1
1
0
1
0
1
1
0
1
0
1
2
1
1
1
1
2
1
2
1
2
1
1
1
1
1
1
2
0
1
1
1
2
1
1
1
2
1
2
0
1
0
2
1
1
0
0
1
1
2
2
2
1
1
1
1
1
0
0
0
1
1
1
1
2
1
0
2
2
0
4
1
2
1
0
0
0
1
1
0
2
1
1
2
1
0
1
0
1
0
0
2
2
1
1
0
0
1
0
2
0
1
1
1
1
1
1
1
1
2
1
0
1
0
1
0
0
1
3
2
1
2
2
2
0
2
1
0
1
1
2
2
1
0
1
2
1
2
0
0
2
1
2
2
2
1
0
2
1
1
1
1
2
1
1
2
1
1
1
0
1
2
2
0
1
1
2
0
1
1
2
2
1
1
1
1
1
0
1
1
1
1
2
1
1
1
2
2
1
2
0
1
0
0
1
1
1
1
0
1
1
0
1
0
1
0
1
0
1
1
1
0
2
0
0
2
2
2
0
1
2
1
2
1
1
1
1
2
0
1
1
1
1
2
0
0
2
0
0
1
1
1
0
0
2
1
1
1
0
1
1
0
2
1
1
1
1
0
1
1
0
1
1
1
1
1
1
0
2
1
1
2
0
1
1
2
0
2
1
1
0
1
2
2
0
2
1
0
1
0
2
0
1
2
1
0
1
1
2
1
0
1
2
1
2
0
1
1
2
1
2
1
0
0
2
2
1
1
2
0
1
2
2
0
1
0
1
4
0
0
2
1
1
1
2
0
2
0
2
1
1
2
1
1
1
1
1
0
1
1
1
1
2
2
2
4
2
0
2
1
0
1
1
0
2
1
0
0
1
1
1
0
1
1
2
2
2
1
0
2
1
0
1
10
1
0
1
1
0
1
1
1
1
0
1
1
2
1
1
1
2
0
2
2
0
0
1
1
1
0
1
1
1
1
1
0
2
1
2
1
2
0
1
1
0
0
1
1
0
1
0
0
1
1
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
2
1
1
0
1
1
1
1
0
0
1
0
2
2
2
1
1
0
1
2
1
1
0
1
0
1
1
2
2
1
1
2
2
1
5
2
2
1
4
2
1
1
1
2
1
3
2
1
0
1
0
1
1
0
1
0
1
2
2
1
1
2
2
1
2
1
2
1
1
2
1
1
1
0
0
0
0
1
0
1
1
0
0
0
1
2
1
1
0
1
0
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
0
1
1
1
0
1
1
1
0
1
0
0
1
0
0
1
1
2
2
2
1
2
2
1
2
1
0
2
1
1
1
3
1
0
2
1
0
1
2
2
1
1
0
1
2
3
2
1
1
0
2
1
1
1
1
2
1
0
0
1
1
2
1
1
1
1
1
0
0
1
1
1
0
1
1
0
1
2
0
1
2
1
1
1
1
2
5
1
0
1
1
1
2
1
0
0
1
1
0
1
1
1
0
2
1
2
1
0
1
1
1
1
0
1
1
0
1
3
1
1
1
1
0
1
2
0
1
0
1
1
1
2
0
0
1
2
2
0
2
1
0
1
1
1
2
1
2
2
0
1
1
1
1
0
1
1
2
1
1
0
1
1
1
1
1
1
1
2
0
1
0
1
1
1
1
0
1
1
1
0
1
1
0
1
1
1
0
1
1
1
1
0
1
0
1
1
2
0
1
0
1
1
1
1
1
1
0
1
1
2
1
0
5
2
1
1
2
1
0
2
1
1
1
2
0
0
1
1
1
1
1
1
1
1
1
0
1
1
1
1
2
1
0
1
1
0
1
0
2
1
1
0
1
1
1
1
1
1
0
0
0
0
4
0
0
2
1
1
1
0
1
1
0
1
0
0
1
0
2
1
1
1
0
1
0
1
1
1
2
1
2
2
0
1
1
1
0
0
2
1
3
0
2
1
0
2
0
1
1
0
0
1
1
2
0
1
1
1
0
1
0
2
0
1
2
2
1
2
0
1
1
0
0
1
0
1
2
1
0
0
2
1
2
1
2
1
0
1
1
1
0
0
1
2
2
0
1
0
0
0
0
2
2
1
1
1
0
0
0
1
1
2
2
1
1
1
2
1
0
2
1
0
2
2
0
2
0
1
2
1
1
0
1
1
1
0
1
0
1
1
2
1
2
2
1
1
1
1
2
2
1
1
1
1
0
0
1
1
1
1
2
2
2
0
1
1
1
1
1
1
2
1
2
2
0
1
1
1
0
1
1
1
1
1
1
1
2
1
0
1
2
0
0
2
1
1
0
1
1
1
1
1
2
2
1
0
0
1
2
1
2
1
0
0
1
1
2
1
2
1
1
1
1
1
0
2
1
0
1
1
0
0
1
2
1
0
2
1
1
2
0
0
0
1
1
1
3
2
1
1
2
0
0
0
0
1
0
1
1
1
1
1
2
1
1
1
1
1
0
0
0
0
0
1
1
2
1
0
1
0
2
1
1
1
0
1
0
1
1
2
0
0
2
1
1
1
1
0
0
0
1
1
1
1
0
1
0
3
2
1
0
2
1
1
1
1
1
1
1
1
2
1
0
1
1
1
1
1
1
0
2
1
2
0
0
1
1
1
2
2
1
0
1
1
1
1
2
2
1
1
1
2
1
1
0
2
1
1
0
2
0
1
1
0
1
0
1
0
2
0
2
1
1
1
1
2
0
3
1
0
2
0
1
1
0
0
1
1
1
1
1
1
1
2
1
0
2
2
2
2
0
2
1
1
1
1
1
1
1
3
1
1
1
1
1
1
1
0
1
0
1
1
1
0
1
2
1
1
1
1
0
0
2
1
1
1
1
1
0
2
1
0
2
1
2
0
2
2
0
1
0
1
2
0
0
2
1
1
0
1
1
2
0
1
1
1
2
1
1
1
1
2
1
1
1
0
2
1
1
3
1
0
1
0
0
1
1
2
0
2
0
1
0
1
1
0
1
1
2
2
1
1
0
2
1
1
0
1
1
0
1
1
0
2
1
1
2
2
1
1
1
1
1
1
1
1
2
0
1
2
0
0
1
0
2
1
0
0
1
1
1
2
1
2
1
0
0
1
1
1
0
1
1
0
1
2
0
1
2
1
0
1
2
1
1
1
1
2
1
2
1
0
1
1
1
2
1
2
1
1
0
0
1
2
1
2
0
1
1
2
0
1
1
2
0
0
2
1
1
0
0
0
2
1
2
1
0
1
1
0
1
1
0
1
1
0
0
1
3
1
1
1
1
1
1
0
1
2
1
1
1
2
1
4
1
1
1
0
0
2
1
1
1
0
1
2
1
1
0
0
1
2
0
1
2
1
0
1
1
2
2
1
2
2
1
2
0
1
0
0
2
1
1
1
2
0
1
1
1
1
1
2
1
0
0
2
1
1
1
1
1
2
1
1
1
2
0
1
1
1
1
1
1
1
1
1
2
0
0
2
1
1
2
1
1
1
2
1
1
1
0
0
0
1
1
0
2
1
0
1
1
1
1
0
1
2
0
1
1
2
0
1
0
1
0
1
2
0
1
2
1
1
1
1
0
1
1
1
1
1
0
2
0
1
1
1
1
2
2
2
2
2
2
2
2
2
1
1
1
0
1
1
1
0
2
1
2
2
1
1
0
0
1
0
0
0
1
0
1
1
1
0
1
2
1
0
1
1
0
2
1
1
0
1
1
1
0
1
3
2
1
1
0
1
0
0
1
1
1
1
1
1
2
1
1
1
1
2
0
2
1
0
0
2
0
0
1
2
1
2
2
0
0
2
0
1
1
0
0
1
2
0
1
1
0
1
1
1
1
1
0
1
1
2
1
1
1
2
2
1
1
1
2
0
0
1
1
0
1
2
1
0
1
1
0
2
1
1
1
2
2
1
2
1
1
1
0
2
1
1
0
0
2
2
2
1
1
1
1
1
2
1
1
2
2
2
1
1
2
1
1
1
2
2
2
0
2
0
1
3
1
1
1
2
1
1
1
1
0
1
1
2
2
1
2
2
0
1
1
2
1
2
2
1
1
2
1
1
1
0
0
2
2
1
0
0
0
0
1
1
2
0
0
2
1
1
1
1
1
1
2
1
0
2
0
1
0
2
1
1
2
1
1
0
2
0
1
2
1
1
1
1
1
1
1
1
2
2
2
1
0
0
1
0
2
0
2
0
1
1
0
1
0
2
1
1
1
1
0
1
0
2
0
0
1
1
1
2
1
1
0
0
1
2
1
2
0
1
2
1
1
2
1
2
1
1
0
0
1
2
1
2
1
1
1
0
2
1
0
2
1
0
2
0
1
1
1
0
1
1
1
1
0
0
1
1
0
1
0
1
0
1
1
1
2
0
0
1
0
1
1
3
1
1
2
4
0
1
0
1
1
0
1
1
1
0
1
3
0
1
1
2
2
1
1
1
1
0
0
1
2
2
0
2
1
2
2
1
0
1
0
0
0
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
0
1
1
1
2
1
1
0
2
1
1
2
0
0
1
0
1
3
1
1
1
1
1
1
1
0
0
1
1
1
2
1
0
2
1
0
0
0
2
2
2
1
1
1
1
0
2
1
1
2
0
1
1
0
0
2
1
1
1
1
0
0
0
0
2
1
1
1
1
1
0
2
1
2
1
0
1
0
1
0
1
0
2
2
1
1
2
1
1
0
1
1
0
8
1
2
0
1
0
1
1
0
1
1
1
1
1
1
1
1
1
1
0
1
0
0
1
1
1
2
1
1
1
0
1
2
2
1
2
1
1
0
1
2
1
2
0
1
1
1
1
0
1
2
0
0
1
0
2
1
1
1
0
1
1
1
0
2
1
1
1
0
0
1
2
1
1
1
0
0
2
1
1
2
1
1
1
0
1
0
0
2
1
0
2
1
0
2
0
2
1
2
0
0
1
2
1
1
0
0
0
1
1
1
1
1
0
1
1
0
0
1
0
1
0
0
1
2
1
0
1
2
1
2
1
2
2
0
0
1
1
0
1
2
2
1
0
2
1
1
2
1
0
0
1
0
0
1
0
1
0
1
1
2
1
1
0
1
1
1
2
1
2
0
1
1
1
1
1
2
1
1
1
2
0
1
2
1
2
1
1
1
1
2
1
1
2
2
1
2
2
3
2
1
2
0
1
2
2
1
0
1
0
0
1
2
1
0
0
0
1
1
2
1
1
0
2
0
0
1
0
1
3
1
2
1
2
1
1
0
1
1
1
0
2
2
1
0
1
1
1
0
1
1
0
1
1
0
2
1
1
1
1
2
2
1
1
0
2
1
2
2
1
0
1
2
0
2
1
1
4
1
1
0
0
1
1
1
1
1
2
1
1
4
1
2
2
1
1
2
2
1
0
1
2
0
1
1
1
0
0
1
0
2
0
0
2
1
1
0
0
0
0
1
1
0
1
1
0
0
0
2
1
0
0
2
1
0
1
2
0
2
2
1
1
1
1
1
1
1
0
2
1
2
0
1
0
1
2
1
2
2
2
0
1
0
2
2
1
0
2
1
0
0
1
1
1
1
1
0
0
2
2
1
2
3
3
0
1
1
2
1
1
2
0
1
0
1
0
2
2
1
1
1
1
1
0
2
1
0
1
1
0
1
1
2
1
2
1
0
1
2
1
1
1
2
2
1
1
0
2
1
0
1
1
2
0
0
1
1
1
1
1
1
2
1
1
1
1
2
0
1
0
0
2
1
1
1
0
0
0
1
0
0
1
0
2
0
1
0
0
2
1
2
2
1
1
2
2
1
1
1
0
1
1
1
1
0
1
1
2
1
2
0
0
2
1
2
0
1
0
0
0
3
1
0
1
1
0
2
0
0
2
0
0
1
2
2
1
1
2
2
1
1
2
0
0
1
1
0
1
1
1
1
2
2
1
2
2
1
0
0
0
0
1
1
1
1
1
1
1
1
2
2
2
1
1
0
1
2
2
1
1
2
1
1
1
1
1
2
1
2
2
2
1
0
0
0
1
2
1
4
2
0
1
0
2
1
1
1
2
1
1
0
0
1
0
0
0
1
0
0
1
1
1
2
1
2
2
1
2
0
1
0
0
1
1
1
2
2
0
0
1
1
2
2
0
1
2
1
2
0
0
1
1
2
0
0
1
1
1
0
2
0
1
1
1
2
0
1
1
0
1
0
0
1
1
1
2
0
2
1
1
0
1
1
2
0
0
0
0
1
0
2
1
0
2
2
2
2
2
0
1
1
1
1
1
2
0
2
0
2
1
1
1
1
1
1
2
1
0
1
1
1
1
1
2
1
1
1
1
1
2
0
1
1
2
1
1
1
1
1
1
0
0
2
1
1
3
1
1
1
2
0
1
1
1
2
2
1
3
2
1
1
1
1
0
1
2
0
4
0
0
1
0
1
0
2
1
0
1
2
1
1
1
1
0
1
0
1
2
0
1
1
1
0
0
1
1
0
1
0
0
1
1
1
1
0
2
2
1
2
1
1
1
2
1
1
0
2
0
0
2
1
1
0
2
1
0
0
2
1
1
0
1
1
1
1
2
1
0
1
1
2
1
1
2
2
0
0
1
1
0
1
0
2
2
1
2
2
2
0
1
1
1
1
1
1
1
1
0
2
1
1
2
2
2
1
1
0
0
1
1
1
1
0
1
1
1
3
1
2
1
1
1
2
0
1
2
1
2
0
0
1
1
1
1
0
2
1
1
1
1
2
1
1
1
0
3
1
2
1
1
2
1
0
1
3
0
0
1
0
0
1
0
2
0
0
1
1
1
0
0
1
1
1
0
0
1
1
1
0
1
1
0
0
2
1
1
1
1
2
1
1
1
1
2
2
0
1
2
2
2
0
2
1
1
0
0
2
1
1
1
1
1
1
1
1
2
1
1
1
1
0
1
1
1
2
2
1
1
0
1
0
0
1
1
1
1
1
0
0
1
0
1
1
1
1
0
2
1
1
2
0
1
0
1
1
1
1
1
0
1
0
0
1
2
1
1
0
0
1
1
0
0
1
2
1
1
1
1
2
1
0
1
1
0
1
1
2
1
1
0
2
1
0
1
1
1
0
1
1
0
2
1
0
1
1
1
1
1
0
1
1
1
0
1
2
0
1
0
1
2
2
2
1
1
1
0
1
2
2
2
1
1
1
0
2
0
1
1
1
0
1
1
1
1
1
1
2
1
0
5
1
1
2
0
0
0
1
1
0
1
1
1
0
0
0
1
1
2
1
1
1
0
0
1
2
1
0
0
2
2
1
0
2
2
2
0
2
0
1
1
1
0
2
1
1
0
0
0
1
0
1
1
0
1
1
2
1
1
1
2
2
1
1
1
1
1
1
2
0
1
1
1
2
1
1
1
2
1
2
0
1
2
1
1
2
1
2
2
1
1
3
1
1
1
1
1
2
2
1
2
1
2
1
0
2
1
0
1
1
2
1
0
1
1
2
2
1
2
1
1
1
0
1
1
1
0
1
2
2
1
1
0
1
1
1
0
1
1
0
1
2
1
0
0
1
1
1
3
1
2
1
1
1
2
0
1
1
0
0
0
1
1
1
2
1
1
1
0
1
0
1
2
2
2
1
1
1
1
2
0
0
1
1
1
2
0
1
1
1
1
1
1
0
1
1
2
1
1
2
2
2
1
0
1
1
1
1
1
2
0
2
1
1
0
1
2
1
1
0
2
1
2
1
0
1
0
1
2
2
1
1
2
1
0
1
2
2
1
2
0
0
1
0
0
1
1
2
0
1
0
1
0
1
1
0
3
1
1
2
1
2
2
1
2
1
2
0
0
2
0
0
0
1
1
1
1
2
0
1
2
1
2
1
1
1
0
2
1
0
1
0
2
2
0
1
1
1
1
0
1
1
0
1
1
2
1
1
1
1
0
1
1
0
2
0
2
0
0
1
1
1
1
1
1
0
1
2
0
1
1
0
0
0
1
1
2
0
1
1
0
2
2
1
0
0
1
2
1
1
1
1
0
1
0
0
1
2
2
0
1
0
0
2
0
1
1
0
1
1
1
0
0
1
1
0
0
1
0
2
2
1
2
1
1
1
1
2
0
1
1
1
1
1
2
2
1
0
1
1
1
2
0
2
1
2
0
1
1
1
0
6
0
0
2
1
0
0
1
1
1
1
2
1
2
1
0
2
0
1
1
2
1
2
1
1
1
2
2
0
1
2
1
1
1
1
1
1
2
0
2
1
0
0
1
1
1
0
1
0
1
2
1
1
0
1
1
0
1
1
2
1
1
1
0
0
2
0
0
1
1
1
1
0
1
1
0
2
1
1
0
1
0
1
2
1
0
1
1
0
1
0
0
2
0
2
1
1
1
2
1
0
1
1
2
1
1
0
0
1
1
1
0
2
1
1
1
1
1
2
2
2
2
0
2
3
1
2
1
1
1
1
2
2
3
1
0
1
0
2
1
2
0
1
1
0
1
1
2
0
1
0
1
1
1
1
1
0
1
0
0
0
0
0
1
2
1
0
0
1
0
2
0
2
1
1
1
1
2
1
1
1
1
2
2
3
0
1
2
1
1
2
1
2
1
2
1
4
0
2
1
1
1
2
2
2
1
1
1
0
0
1
2
2
1
0
2
1
2
1
1
0
1
0
1
1
1
1
0
0
0
1
1
0
1
0
1
1
1
1
3
0
1
2
1
1
1
1
0
1
2
0
1
2
1
1
2
1
1
1
1
1
0
1
2
1
1
1
0
1
1
2
1
0
2
0
1
1
0
1
1
1
0
0
1
1
1
0
1
2
1
1
2
3
0
0
0
1
2
1
2
0
0
0
2
1
1
1
1
1
1
1
0
1
2
2
1
2
1
1
2
1
1
2
2
0
1
1
2
1
2
1
0
0
2
1
1
1
1
1
1
0
1
0
1
2
0
0
1
1
1
2
0
1
1
1
1
1
0
1
1
2
1
2
2
2
0
1
1
2
1
1
1
0
0
1
0
1
1
1
1
2
1
2
2
1
0
0
0
1
2
1
1
2
2
0
0
1
1
2
0
1
1
1
1
1
1
1
1
1
1
1
0
2
1
1
1
0
1
1
1
1
0
0
0
0
2
1
0
1
0
2
2
0
0
3
1
2
1
1
1
2
1
0
1
2
2
0
2
0
1
1
1
0
1
1
0
0
1
1
0
1
1
1
1
2
1
4
2
1
1
0
0
0
1
2
1
1
0
2
0
1
1
0
1
0
2
0
0
1
1
0
2
1
2
1
2
2
1
2
2
2
1
0
0
1
2
2
1
1
0
0
4
1
3
0
0
0
2
2
1
0
0
1
0
1
1
1
1
1
2
1
1
0
2
1
2
1
1
1
2
1
1
1
2
1
1
1
0
1
1
1
1
2
2
2
1
1
0
2
1
1
2
1
0
0
0
2
1
0
1
1
2
1
1
1
0
1
0
0
1
1
1
1
0
2
1
2
1
1
1
1
1
0
0
1
1
1
2
1
1
1
1
1
1
0
2
1
1
1
1
1
0
2
2
2
0
1
1
0
2
2
1
1
1
0
0
2
1
1
1
2
2
1
2
1
0
1
1
1
1
1
0
0
2
1
1
0
0
1
0
0
1
1
0
1
0
1
2
1
2
1
1
0
1
1
1
1
2
1
2
0
0
0
1
0
1
1
1
1
1
0
2
0
1
1
0
2
1
0
0
2
1
1
1
2
0
0
1
1
1
0
1
1
2
0
1
1
1
0
0
2
0
3
2
1
2
1
2
1
0
1
0
1
1
2
1
1
1
0
2
0
2
1
1
2
1
1
2
0
1
2
2
0
0
1
0
1
1
1
1
2
1
0
2
1
2
1
0
2
2
1
0
1
0
0
0
1
2
1
1
2
1
1
0
1
1
1
2
1
2
0
1
0
0
1
1
0
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
2
0
1
1
0
0
1
1
2
0
1
1
2
1
1
2
1
1
2
2
1
1
2
1
2
1
2
0
2
1
2
0
1
0
1
1
1
2
1
0
2
1
1
2
2
2
2
2
1
1
1
0
1
0
0
0
2
1
0
1
0
0
0
1
0
1
0
1
0
0
1
0
1
1
2
0
1
1
1
1
1
0
0
2
1
1
1
2
1
0
0
2
1
1
2
0
0
0
0
0
0
1
1
1
1
2
1
1
2
0
0
1
1
1
2
2
2
2
2
1
1
1
0
1
1
1
1
2
1
0
1
2
1
1
1
0
0
0
1
1
2
1
0
1
1
1
0
0
1
1
2
1
0
1
1
0
1
0
2
0
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
0
2
1
0
1
1
1
0
1
1
0
0
0
0
1
2
1
1
1
0
1
2
0
0
1
0
1
2
2
1
1
1
1
1
0
0
2
2
2
1
1
1
1
1
1
0
0
1
0
1
2
1
1
1
1
2
1
0
0
1
2
0
1
1
2
2
1
1
0
1
1
2
0
2
2
1
1
0
1
1
1
1
1
2
0
1
0
1
1
1
1
1
2
1
2
0
1
1
0
0
1
1
1
0
2
2
0
2
0
1
1
0
2
2
1
1
2
2
2
1
0
2
0
1
0
1
1
1
2
1
0
2
2
0
2
1
1
1
1
1
0
2
1
0
1
2
0
1
1
2
1
1
0
2
0
1
0
1
2
1
1
1
2
1
0
0
1
1
1
1
1
1
1
2
1
0
1
0
0
1
2
1
1
1
1
0
1
1
1
1
1
2
1
0
1
0
1
0
0
0
0
1
2
2
1
0
2
0
1
1
0
2
1
1
2
1
0
1
2
1
0
1
2
1
1
1
1
0
2
2
1
1
2
2
1
1
0
1
0
2
0
0
1
0
0
1
1
1
1
2
0
1
2
1
0
2
1
2
2
1
1
2
1
2
1
1
1
2
0
1
0
1
1
1
1
1
2
2
1
1
1
1
1
0
1
1
1
1
1
0
1
1
0
2
0
2
1
1
2
2
1
1
2
1
0
1
1
1
1
2
2
0
2
0
1
1
2
0
2
1
1
1
1
1
1
2
0
2
2
0
0
1
0
2
0
0
3
0
1
1
1
0
1
0
0
0
1
1
1
2
1
0
1
2
1
1
0
1
5
1
2
2
1
1
1
2
0
1
2
1
1
2
2
1
1
0
1
2
2
0
2
2
1
0
2
1
1
1
1
1
1
0
1
1
2
1
1
0
1
1
1
0
1
2
4
1
1
2
1
0
1
1
2
0
1
0
2
1
1
2
1
2
2
0
2
1
1
1
2
2
2
1
1
2
2
0
1
2
0
0
1
1
2
1
1
1
2
1
2
1
1
0
0
1
0
0
2
2
2
0
1
1
2
1
2
0
1
1
1
1
1
1
0
1
1
0
1
1
2
0
2
0
0
2
1
1
0
2
0
0
1
5
2
1
2
2
0
0
1
0
1
2
2
1
0
1
1
2
1
2
1
0
1
0
0
1
1
2
2
0
0
4
2
1
0
1
1
0
0
1
1
1
1
0
0
1
2
1
1
1
2
2
1
1
0
0
2
1
1
0
1
1
1
1
1
0
1
0
2
1
0
1
1
0
0
2
1
1
1
1
1
2
2
2
2
0
1
1
1
1
1
1
0
0
1
2
1
1
1
0
1
1
2
1
1
1
0
0
1
1
1
0
0
1
1
1
2
1
1
1
1
0
1
0
0
0
0
2
1
2
2
1
3
2
1
0
2
1
0
0
1
1
1
1
1
0
0
1
1
2
1
1
1
1
1
1
0
1
1
1
1
1
1
0
0
1
1
2
2
1
0
0
0
0
1
2
0
1
1
2
1
0
0
1
2
2
1
1
0
1
0
1
2
1
1
2
1
1
0
0
2
1
0
2
1
0
0
0
2
2
1
0
2
1
1
0
2
1
1
2
2
1
1
1
1
1
2
1
0
1
2
0
1
1
1
0
1
0
1
1
1
1
2
2
1
0
2
2
2
1
0
0
2
1
1
1
2
1
2
2
0
1
0
0
2
1
2
1
1
0
0
0
1
1
2
1
0
1
1
0
1
1
2
1
1
1
0
1
1
1
1
2
1
2
0
0
2
2
1
1
2
0
1
1
0
1
2
1
1
1
2
1
1
1
0
2
2
0
0
1
1
0
2
0
1
1
1
1
2
2
1
1
1
2
1
0
0
0
1
1
0
2
1
0
1
0
1
1
1
0
0
2
2
2
1
0
0
0
2
0
1
1
1
0
2
2
1
1
2
1
1
1
2
1
1
2
1
1
2
2
1
1
1
1
1
1
1
0
1
0
6
2
1
2
1
1
1
0
0
2
1
0
0
2
1
1
0
2
2
1
0
1
2
1
0
1
2
2
0
0
0
1
1
1
2
1
0
1
1
0
3
2
0
2
0
1
1
0
0
1
1
0
1
0
2
1
1
1
0
2
1
1
0
2
1
0
1
1
1
1
0
0
1
0
0
2
1
1
1
1
1
1
1
0
0
2
0
1
1
2
2
0
2
2
0
1
1
1
0
0
1
0
1
2
0
2
1
1
2
2
1
1
1
1
0
2
1
1
0
2
0
0
0
1
1
1
1
2
0
1
2
0
1
2
0
2
1
1
1
0
0
1
0
0
2
1
4
1
1
1
1
1
0
1
0
5
2
1
0
1
0
0
1
1
1
2
2
1
0
1
1
0
1
2
0
1
1
1
0
1
0
1
0
1
1
1
1
1
2
2
1
1
2
3
1
2
1
1
0
2
0
1
0
1
1
1
2
2
0
0
1
1
1
1
2
1
1
0
2
2
1
0
0
2
1
0
0
1
2
1
1
2
1
1
1
0
2
1
1
0
0
2
1
2
0
1
0
1
0
2
0
1
1
2
1
0
0
1
1
1
1
0
1
1
1
2
0
0
1
0
0
1
1
2
1
0
1
1
1
1
1
2
1
2
1
2
1
0
1
0
2
1
2
0
1
1
1
0
2
2
0
2
1
1
1
1
1
1
2
1
1
0
1
2
1
1
2
1
1
1
2
1
1
1
1
0
1
0
1
1
1
1
1
0
2
1
0
1
1
1
0
0
1
2
1
1
1
1
1
0
0
1
1
1
1
0
1
2
1
2
1
0
1
0
0
1
1
1
2
0
1
1
2
1
2
2
0
1
1
1
1
1
1
0
2
3
1
0
1
1
2
1
1
1
1
2
1
0
1
0
0
1
1
1
1
1
1
0
1
0
1
1
0
1
1
1
1
1
0
0
1
0
1
1
1
0
1
1
2
0
2
1
1
1
2
1
0
0
1
0
1
1
0
1
1
2
1
2
0
1
1
1
0
2
1
1
1
1
0
1
0
0
0
1
1
1
1
0
1
2
0
2
0
2
3
1
1
1
0
1
0
2
1
1
1
1
1
0
1
1
2
2
1
2
1
2
1
2
1
2
1
1
3
2
0
2
1
1
3
0
0
2
0
0
2
0
0
0
1
0
1
1
0
1
1
0
1
2
1
1
1
0
0
2
1
2
2
0
1
1
1
1
2
2
1
1
1
2
2
1
0
2
1
1
2
1
1
0
1
1
1
1
1
1
2
1
2
0
2
2
1
1
0
1
1
1
2
1
1
0
2
1
0
0
1
1
0
0
1
2
2
0
2
0
0
1
2
0
1
0
1
1
1
1
1
2
1
1
0
1
0
1
1
1
1
1
0
1
1
0
1
1
0
0
0
2
2
1
1
1
1
2
0
2
1
0
1
1
1
1
2
1
2
2
1
2
1
1
1
1
1
2
2
1
2
1
1
0
1
0
1
0
1
2
0
0
1
2
2
1
1
1
2
1
2
2
1
2
0
2
3
0
2
2
1
0
0
2
0
1
1
1
1
2
1
0
0
1
0
1
1
1
1
1
0
1
1
0
1
0
0
2
1
1
2
1
1
1
0
1
0
1
2
2
0
1
1
1
1
1
0
2
1
2
2
1
1
1
1
2
0
1
2
1
1
0
1
0
2
0
2
2
0
1
1
0
0
2
2
1
1
2
0
1
1
0
2
2
1
0
1
0
2
1
2
2
1
1
0
1
1
0
1
3
0
1
0
1
1
2
1
2
1
2
1
1
1
1
1
0
1
1
1
2
0
1
2
0
2
1
0
1
1
1
1
1
0
1
2
1
0
2
1
0
1
1
0
1
1
0
0
1
0
1
1
1
2
0
2
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
2
1
0
1
1
1
2
1
1
1
1
2
1
0
0
1
0
1
0
1
1
2
1
1
1
2
1
2
2
0
2
1
1
2
2
1
1
0
2
1
1
1
2
1
2
0
2
3
1
0
2
2
1
1
0
1
1
1
2
2
1
1
0
0
0
2
2
1
1
1
1
2
1
1
1
1
1
2
1
2
1
1
0
2
2
1
2
1
2
2
1
2
2
1
1
1
0
1
0
1
2
1
1
0
1
1
2
1
1
1
0
2
0
1
1
0
2
0
0
0
2
1
1
0
2
0
2
1
1
0
1
2
2
1
1
2
1
2
1
1
0
1
1
0
1
0
1
0
0
1
2
0
1
2
1
2
0
0
1
1
1
0
2
1
1
1
1
1
0
2
1
1
1
1
0
0
1
2
1
2
3
2
1
1
1
0
1
0
0
1
2
0
1
1
0
1
1
3
1
0
1
1
1
0
0
1
1
2
1
0
2
1
1
0
1
0
2
1
1
2
1
1
1
0
2
0
1
1
1
1
0
1
1
1
0
0
1
1
1
1
1
0
2
0
1
0
1
1
1
1
1
0
1
2
0
2
0
1
1
0
2
2
1
1
1
1
0
2
2
2
1
3
2
0
0
1
2
1
1
0
0
1
1
1
1
2
0
1
1
2
1
1
1
1
0
1
1
0
1
0
0
1
2
1
1
0
1
0
0
1
2
1
1
0
1
1
1
1
0
1
0
1
1
0
1
1
0
0
2
1
0
0
1
1
2
3
1
1
1
2
1
1
0
0
2
1
1
0
0
2
1
1
1
0
2
2
2
1
1
2
1
0
2
2
1
1
0
1
1
1
2
1
1
1
2
2
1
1
2
1
2
2
2
2
0
0
2
0
1
0
0
2
1
2
1
1
1
1
2
1
1
0
1
1
1
2
1
1
1
2
2
2
0
1
1
0
2
1
1
0
2
1
0
1
1
0
0
1
3
0
1
1
0
1
1
1
1
1
0
0
1
0
1
1
0
1
0
2
2
1
1
1
1
0
0
1
2
1
1
1
1
0
1
2
0
0
1
1
1
1
1
1
2
1
1
1
1
0
0
1
1
1
2
1
1
0
1
0
1
3
1
0
2
1
1
2
1
1
1
2
0
1
0
0
2
0
0
1
1
0
1
0
0
1
2
2
2
1
1
1
1
1
1
2
1
2
0
0
1
0
2
0
1
1
0
1
1
2
1
1
1
2
1
1
0
1
2
1
2
1
0
0
1
0
1
0
1
2
1
1
2
2
1
1
1
2
2
0
0
2
1
1
0
1
0
1
2
0
0
0
1
0
1
2
1
1
1
1
1
1
2
0
0
1
1
2
2
1
1
0
0
1
2
0
2
1
2
1
1
2
0
2
0
1
0
2
2
0
1
2
1
1
1
1
1
1
1
0
1
0
1
1
1
1
0
0
1
0
2
0
1
1
0
1
2
0
2
0
0
1
1
0
2
2
1
1
1
1
0
1
1
2
0
2
0
1
2
2
0
2
1
0
0
1
1
1
1
1
1
2
0
2
1
2
1
1
1
1
2
1
2
1
2
2
1
0
1
0
1
2
1
1
0
0
0
1
1
1
0
0
1
0
2
1
2
2
1
1
1
1
1
1
1
1
0
0
1
0
1
1
1
0
1
2
1
1
1
1
0
1
0
1
0
2
1
2
1
1
2
2
2
0
2
1
2
1
1
1
1
1
2
0
0
1
1
1
1
1
0
1
2
1
2
1
1
1
1
1
1
2
2
1
0
1
2
0
0
1
0
0
3
1
1
1
1
1
0
0
0
1
2
2
0
2
0
1
0
2
1
1
3
1
0
1
1
1
0
1
1
1
0
2
1
0
0
0
1
2
0
0
0
1
1
1
2
1
3
0
0
2
1
2
1
2
1
1
2
2
1
2
1
1
1
1
2
3
2
1
1
2
1
0
2
1
0
2
0
1
0
0
1
0
2
1
0
2
1
2
1
1
2
0
2
1
1
1
1
0
2
1
1
0
1
2
0
1
2
1
1
0
1
2
1
1
0
1
0
2
1
0
1
2
1
1
1
2
1
1
1
2
1
0
1
0
1
1
1
1
2
2
1
0
1
0
1
2
2
2
2
1
2
0
1
1
0
1
0
0
1
0
1
0
1
3
1
1
2
1
1
2
0
0
1
1
0
2
1
0
1
1
0
0
1
0
1
0
1
1
0
1
1
0
0
1
0
0
1
2
0
1
2
1
1
1
1
1
2
3
0
2
1
1
1
0
1
1
0
1
1
1
0
0
1
1
1
0
1
0
0
1
1
1
1
1
2
2
1
0
1
1
2
0
1
1
2
1
1
2
2
0
1
0
2
1
1
0
1
1
1
1
2
1
0
1
1
1
0
0
1
1
1
1
1
2
1
2
2
0
1
0
2
2
1
1
2
2
0
1
2
1
1
2
2
0
1
1
2
2
0
1
1
0
1
0
0
1
1
1
2
1
1
2
1
0
0
0
1
2
1
2
2
2
0
0
1
1
1
1
1
1
1
1
1
0
0
1
1
2
2
1
1
1
1
0
0
2
0
1
2
2
1
1
1
1
1
1
1
1
1
0
0
1
2
1
1
2
1
2
1
2
0
2
1
2
1
1
2
3
1
2
1
2
1
1
1
1
1
1
1
1
2
1
1
2
2
0
1
0
0
1
1
1
0
1
0
2
2
1
1
0
1
1
1
2
1
0
0
1
1
1
2
0
1
0
0
2
1
1
1
1
2
2
1
2
2
2
1
1
1
1
1
3
1
1
1
0
2
1
1
2
0
0
0
2
1
1
1
2
1
0
2
1
1
0
1
2
0
1
0
0
1
1
1
1
2
0
1
2
0
2
1
1
1
2
0
1
1
1
2
1
1
1
0
0
0
1
2
0
1
2
1
1
0
1
1
2
2
0
2
1
2
1
1
1
1
1
0
1
1
1
0
1
1
1
1
1
4
1
1
1
1
1
1
2
2
0
1
1
1
0
0
1
1
1
2
1
2
1
1
1
2
1
1
1
1
2
2
2
0
0
0
0
2
1
1
1
2
1
0
0
2
1
1
1
1
1
1
2
0
0
2
2
1
0
0
2
2
2
0
1
1
1
1
1
2
1
2
2
2
1
1
1
1
1
2
0
1
1
1
2
1
1
2
1
0
0
1
1
0
1
1
1
1
1
2
1
0
2
1
1
1
0
1
0
1
0
2
0
1
1
1
1
2
1
0
1
1
2
2
0
0
0
4
1
1
2
0
0
2
1
0
1
2
1
0
0
1
2
1
1
1
2
1
1
0
0
1
2
1
1
1
1
1
1
2
2
2
0
2
0
0
2
1
4
0
1
0
1
2
1
0
1
0
2
1
1
1
1
0
2
1
1
1
1
1
1
1
0
1
0
1
1
1
1
1
1
1
0
1
2
1
1
1
1
1
1
1
1
1
2
1
0
0
2
1
1
0
0
1
1
0
1
2
1
0
2
0
0
1
0
2
2
1
1
1
1
1
1
0
2
1
1
2
0
1
1
1
2
2
1
1
2
1
1
2
0
1
1
1
1
2
1
0
0
1
1
1
1
0
1
1
2
2
1
1
0
1
2
0
1
1
2
0
3
0
0
1
1
1
2
2
1
0
0
0
2
0
1
0
1
0
0
0
1
1
2
0
1
1
2
1
1
2
0
1
2
0
0
1
1
1
1
1
2
0
1
1
1
0
0
0
1
1
2
1
2
0
1
1
0
1
0
1
1
2
1
1
1
1
1
0
1
2
1
1
1
1
2
1
1
1
1
1
0
1
1
0
1
0
0
0
2
1
2
5
2
2
1
2
1
2
0
1
2
1
0
1
0
1
1
1
1
2
2
2
0
0
1
0
1
0
2
2
0
2
1
1
1
2
2
1
0
0
1
1
2
0
2
2
0
0
2
0
1
1
1
0
1
2
0
1
0
1
0
0
0
1
2
0
0
1
1
1
1
1
2
1
0
1
1
1
1
0
1
0
1
0
1
1
2
2
1
0
0
1
0
0
2
1
2
1
1
2
1
1
2
1
1
1
2
2
2
0
0
1
1
2
1
1
1
1
1
0
1
1
1
2
1
2
0
2
1
1
2
1
1
0
1
0
1
1
1
1
1
1
0
1
0
1
1
1
0
1
1
2
1
0
0
2
0
0
1
1
1
1
2
1
1
1
0
1
1
2
1
1
0
1
2
2
1
0
1
1
0
2
1
1
2
1
0
2
1
0
2
1
1
0
0
1
2
0
1
1
2
1
1
1
1
0
1
0
1
1
2
1
1
2
1
2
1
1
1
2
1
0
1
0
0
1
1
2
2
2
0
1
0
0
1
1
0
1
1
1
0
1
2
2
1
1
2
1
1
1
2
1
1
2
1
1
1
1
1
2
2
1
1
1
1
1
1
0
2
0
1
1
0
2
2
0
1
2
1
2
0
1
1
2
1
1
1
0
2
2
2
1
0
0
0
1
0
0
0
1
0
1
0
2
1
1
1
2
1
1
0
1
0
2
1
1
1
1
1
1
2
0
0
1
0
0
1
1
2
2
1
1
1
2
2
2
1
2
2
1
1
0
2
3
1
0
0
0
1
2
1
1
0
0
0
0
1
2
1
1
1
2
0
1
2
2
1
1
1
1
1
0
2
2
1
1
1
1
1
1
2
0
0
1
0
1
1
1
1
0
0
1
0
1
1
1
2
1
2
1
2
1
2
2
1
0
2
0
1
1
1
1
0
1
1
0
0
1
2
1
1
2
1
0
1
2
1
1
2
2
1
2
1
1
0
1
0
1
1
1
2
0
1
0
0
1
1
1
1
1
0
1
0
0
2
2
0
2
1
1
0
2
1
0
2
1
0
0
0
0
0
1
0
2
1
2
1
2
0
1
1
1
1
2
1
2
0
0
0
2
1
1
0
1
2
0
1
1
1
1
1
1
0
1
1
0
1
2
1
2
1
1
1
1
1
0
1
1
0
1
1
1
2
1
1
1
0
1
2
2
1
1
1
1
1
1
1
0
0
2
1
1
1
1
1
2
1
3
1
1
1
0
1
0
1
1
0
2
0
0
2
1
1
1
1
0
0
1
1
0
0
1
1
1
1
1
2
0
1
1
0
2
0
0
0
2
2
2
1
2
1
1
1
2
1
0
1
2
2
0
2
0
1
2
0
1
0
2
1
1
0
1
2
1
1
0
0
0
1
2
0
1
1
1
0
1
2
1
1
2
2
0
1
1
1
2
0
1
2
0
0
0
1
1
1
2
0
0
1
0
2
0
1
1
1
0
1
2
1
1
1
0
1
2
1
2
1
0
2
1
2
1
1
1
1
2
1
1
1
1
2
1
0
1
0
1
1
1
1
1
2
1
1
1
1
1
2
1
1
0
1
2
1
2
0
0
1
1
1
2
1
0
0
1
1
1
1
2
1
1
0
1
2
1
1
2
1
1
1
0
2
1
0
1
0
0
1
0
1
1
1
2
0
0
1
2
2
0
1
2
0
2
2
0
1
2
0
0
1
1
1
2
1
0
1
1
1
0
2
0
1
1
1
2
1
0
0
2
0
1
2
1
0
2
1
1
1
2
2
1
1
0
1
2
1
1
1
1
1
1
1
0
1
1
1
0
1
1
1
0
1
2
1
1
3
2
1
2
0
1
1
1
1
1
0
1
0
1
0
1
2
1
2
2
0
0
1
1
2
1
1
1
1
2
1
0
0
1
0
0
2
1
2
2
0
0
1
1
0
1
0
1
3
2
0
2
2
1
0
1
1
0
0
1
1
2
2
1
1
0
2
1
1
2
1
0
0
2
1
1
1
1
0
1
2
2
1
1
2
3
0
1
0
1
2
2
1
2
1
1
2
1
1
0
1
0
1
1
0
2
0
1
0
1
0
1
2
1
0
1
1
0
0
2
1
0
0
0
1
1
2
0
1
1
1
0
1
1
0
2
1
2
1
1
2
1
1
2
1
1
1
0
2
2
1
0
1
0
1
0
0
1
0
1
2
1
1
1
0
1
0
0
0
2
1
1
1
1
0
2
0
2
1
1
0
0
2
1
1
1
2
2
2
2
1
2
1
0
1
2
1
1
2
0
2
1
3
1
2
1
1
1
1
1
1
1
0
1
2
1
1
0
0
2
0
2
0
1
1
1
2
1
0
1
1
2
1
1
1
1
2
2
0
2
2
1
1
3
2
2
0
1
0
2
1
1
1
0
2
1
2
3
2
0
1
1
2
1
1
1
0
2
1
2
1
1
0
1
1
2
2
2
1
2
0
1
1
1
0
2
2
1
1
0
0
2
1
2
1
1
0
2
2
1
1
0
0
1
2
2
1
1
0
0
1
2
1
2
0
1
0
1
2
3
0
1
0
0
0
0
1
1
0
1
1
1
1
2
1
1
1
1
2
1
3
1
1
2
2
2
1
1
2
1
0
1
1
0
0
1
1
1
1
0
2
1
1
2
1
1
1
0
2
0
0
1
2
0
1
1
1
0
1
2
1
0
2
2
1
1
2
1
0
1
1
1
1
2
2
1
1
1
2
0
1
1
0
1
1
2
1
0
0
0
0
0
1
1
1
0
1
2
2
1
2
1
1
1
2
1
1
0
1
2
0
2
1
1
1
1
0
1
1
1
2
1
0
0
1
1
2
0
2
1
1
1
1
1
1
1
0
2
0
2
2
2
1
1
1
0
1
2
1
1
1
1
1
1
0
1
0
1
1
1
3
0
2
1
2
1
1
1
1
1
0
0
1
0
2
1
1
1
2
1
3
1
1
1
2
3
0
2
1
1
1
1
2
2
2
1
1
0
1
1
1
1
2
1
2
2
1
2
1
0
2
1
1
1
2
1
0
1
1
1
1
1
0
1
1
1
0
3
1
1
0
1
2
0
2
2
1
1
2
1
0
2
1
1
0
1
1
1
0
3
1
0
2
0
0
1
1
1
1
2
0
0
2
1
0
0
1
2
1
0
0
2
0
1
0
1
1
0
1
2
0
1
1
0
2
1
0
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
0
1
1
1
1
1
1
1
1
1
2
1
1
1
2
0
2
0
0
1
1
1
1
2
2
1
2
2
2
1
2
1
2
1
2
0
1
1
3
0
1
1
1
1
0
1
2
2
1
0
1
2
1
2
1
1
1
1
1
1
1
2
0
0
1
1
0
1
1
2
1
0
2
0
2
2
1
1
1
2
1
1
2
0
1
2
1
1
0
2
1
1
0
2
1
0
1
4
1
1
1
1
0
1
2
0
1
0
2
1
2
1
1
1
1
1
0
0
0
1
0
1
1
1
2
0
2
0
1
1
2
2
1
0
2
0
1
1
1
0
1
1
0
2
1
2
2
1
0
2
1
0
2
1
1
0
2
0
2
1
1
1
1
0
1
1
2
2
2
2
2
2
0
0
1
1
1
1
2
1
1
0
0
1
1
1
2
1
1
2
1
1
2
0
0
1
1
1
1
0
2
1
1
0
0
1
1
0
1
1
2
1
1
1
1
0
0
0
1
1
0
4
2
1
1
1
1
1
1
1
1
0
1
2
2
0
3
1
0
0
1
2
2
1
0
1
2
2
1
0
1
0
0
1
1
3
1
0
1
0
1
1
0
1
2
0
1
2
1
1
1
1
0
0
1
0
1
2
0
1
1
2
1
1
2
1
2
0
1
1
2
0
2
0
1
0
1
0
1
2
0
2
2
2
0
2
2
1
1
1
1
1
1
1
0
2
1
0
1
1
1
1
2
1
2
2
2
1
1
0
2
1
1
1
1
1
2
1
1
2
2
2
1
1
1
0
1
1
1
1
1
1
1
1
1
1
2
0
1
0
2
2
0
1
2
1
1
2
0
1
0
1
2
0
2
0
1
0
2
2
1
1
1
0
1
0
0
1
0
2
2
1
2
2
1
0
0
0
1
2
2
1
1
1
1
2
1
0
0
1
1
1
1
1
2
0
1
1
1
2
1
1
0
2
1
0
1
1
1
0
2
0
0
1
1
2
0
1
1
1
1
1
2
0
0
0
2
2
1
0
1
1
1
1
0
1
2
1
2
0
1
0
0
1
1
0
1
1
0
2
0
1
1
2
1
1
2
2
1
2
1
1
0
1
1
2
2
0
1
2
1
1
1
1
1
0
2
1
0
2
1
1
0
1
1
0
2
2
1
2
1
1
0
2
2
0
1
1
0
2
1
2
2
1
0
1
1
2
1
0
1
1
1
2
1
2
1
0
2
2
1
1
2
1
1
1
0
0
2
0
1
0
2
0
0
1
1
1
1
1
2
2
1
1
1
1
1
0
0
1
1
1
1
2
3
0
1
3
0
2
1
2
1
0
1
0
2
0
1
1
1
0
0
2
0
2
0
1
1
1
1
0
1
1
0
0
1
2
1
0
1
1
1
1
2
1
0
0
2
0
1
1
1
1
1
1
1
0
1
0
1
2
2
2
2
1
0
1
0
1
1
1
2
0
1
0
1
1
1
0
2
1
2
1
1
2
2
0
1
1
4
0
0
0
1
1
2
1
1
0
0
1
1
0
1
2
0
1
1
1
1
0
2
1
0
1
0
1
1
1
2
1
1
0
2
0
1
1
1
0
2
2
1
1
2
1
1
1
1
0
1
1
1
0
2
1
1
2
1
1
1
2
1
1
0
2
0
0
1
0
1
1
1
0
2
0
1
2
1
0
0
2
1
1
0
0
1
1
2
0
1
1
1
1
2
1
2
1
0
1
0
1
0
1
1
2
0
0
2
0
1
1
1
1
0
1
0
0
1
1
1
1
0
1
1
0
2
1
1
1
0
1
4
0
0
1
0
0
1
1
1
1
1
1
1
1
1
0
1
1
0
1
1
0
3
0
0
0
1
1
1
1
0
1
2
1
0
0
0
1
2
2
0
1
0
0
2
1
1
1
1
1
2
2
1
2
1
1
2
1
1
1
0
0
1
2
2
1
1
1
1
1
1
0
1
1
2
0
0
0
1
1
2
1
1
1
1
0
1
2
2
1
2
1
1
1
0
0
2
1
0
1
0
1
0
2
1
1
1
1
1
1
2
2
2
0
1
0
0
1
1
0
1
1
0
1
1
2
0
2
0
1
1
1
2
2
1
1
1
2
2
0
1
0
1
2
1
0
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
0
2
0
1
1
1
0
1
1
2
2
0
1
0
0
2
2
1
1
2
0
1
1
1
2
0
2
2
2
1
2
1
2
1
2
2
2
1
1
0
1
1
1
2
1
1
1
2
2
1
1
2
0
2
1
2
0
1
0
1
0
1
1
1
1
2
2
1
2
1
1
1
0
0
2
0
1
2
1
2
1
1
1
2
1
1
0
1
1
1
1
3
1
1
1
2
2
1
0
2
2
1
1
0
2
1
0
1
1
0
1
1
4
0
0
2
1
1
1
2
1
1
1
2
2
1
0
2
2
1
0
0
1
1
1
0
1
0
0
1
1
2
1
2
2
1
1
1
2
1
2
2
3
1
0
2
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
2
1
0
1
1
1
2
2
2
0
1
1
1
2
1
2
1
1
1
1
0
0
1
0
1
1
1
1
2
1
5
0
2
1
3
0
1
1
1
2
0
1
1
2
1
1
1
0
0
0
1
1
1
1
2
1
0
0
1
1
0
1
1
0
0
2
0
1
2
2
1
1
1
0
1
1
0
0
0
1
1
0
1
0
2
1
0
1
2
1
1
1
1
0
1
2
2
2
0
2
2
0
2
0
2
1
2
0
1
1
0
0
0
1
0
2
2
2
2
2
2
0
1
1
2
1
1
0
1
1
1
0
1
2
2
0
1
1
2
2
0
2
2
1
2
1
1
1
2
1
1
1
0
1
1
1
1
2
1
1
0
2
2
0
1
2
1
0
1
0
2
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
2
1
2
2
1
2
2
0
0
2
1
1
2
1
0
0
2
1
1
1
2
2
1
0
1
2
0
1
0
0
1
1
1
1
1
1
0
1
0
0
0
2
2
0
1
0
1
1
1
0
1
1
1
0
0
0
2
0
1
0
0
1
1
2
1
1
1
2
2
1
1
2
1
2
0
1
1
1
2
0
2
1
1
1
0
0
1
2
1
2
2
1
1
1
1
0
1
1
2
1
0
1
1
1
2
1
1
0
1
2
1
1
0
0
2
1
1
1
1
2
1
1
0
2
1
0
1
1
1
0
1
1
0
1
0
2
0
1
0
0
1
0
0
1
0
1
1
1
1
2
0
2
1
2
0
1
1
0
1
2
1
0
1
0
1
2
2
1
0
3
1
1
1
1
1
1
2
1
1
2
1
1
1
0
1
2
1
0
0
2
1
2
2
1
2
1
2
1
2
1
0
1
2
0
1
1
0
0
1
1
2
2
2
2
1
0
2
0
2
1
0
1
1
0
2
0
0
1
2
1
0
0
2
0
0
2
2
1
2
0
1
1
2
2
1
0
2
2
2
1
1
1
2
1
1
2
2
0
1
1
0
1
1
0
1
1
1
1
1
1
1
1
0
1
2
1
1
2
1
3
1
1
2
0
2
1
2
1
2
0
1
2
1
1
0
1
1
1
1
1
0
1
1
1
2
1
2
0
1
1
1
2
2
1
0
2
1
2
1
2
1
1
1
1
1
3
1
2
1
2
1
2
0
1
1
2
0
0
1
0
0
1
1
0
1
1
0
1
0
2
1
1
1
1
1
1
1
2
1
1
0
0
1
1
2
0
1
0
0
1
1
1
2
1
2
0
0
2
1
0
1
0
1
1
0
1
1
3
2
2
2
1
1
2
0
0
1
0
3
1
2
0
1
1
0
1
1
2
1
1
1
1
1
1
1
0
1
0
0
1
0
0
1
1
1
2
1
1
1
1
0
1
0
1
1
1
1
2
1
1
1
1
0
1
2
1
2
0
1
2
2
1
0
2
0
0
0
1
0
2
1
0
1
0
1
0
1
2
0
2
0
1
1
1
2
0
1
2
1
0
2
1
1
2
2
1
1
2
1
0
2
2
1
2
0
0
2
2
2
1
2
2
1
0
1
2
1
2
0
1
1
0
1
1
1
1
1
1
1
1
0
0
3
1
1
1
1
2
1
2
3
1
0
1
1
1
1
1
1
0
0
1
1
0
2
1
1
2
0
1
1
0
1
2
1
0
1
0
2
1
0
1
1
1
2
1
0
1
0
0
1
2
1
2
2
2
1
0
1
1
1
1
2
3
1
0
0
0
2
1
1
1
1
0
2
1
0
0
1
0
0
1
1
1
1
1
1
0
0
2
2
1
0
0
1
1
0
1
0
0
1
1
1
1
1
0
2
1
2
1
1
1
0
2
1
0
1
0
0
1
0
1
1
1
1
2
0
1
1
0
0
2
2
1
1
1
2
0
1
1
1
0
1
0
1
2
0
1
2
1
2
1
0
0
2
1
1
2
2
1
0
0
1
0
0
0
2
1
1
3
1
0
2
2
0
1
1
0
0
1
1
1
1
1
2
0
1
0
2
2
1
0
0
0
1
1
1
0
1
1
0
0
1
1
1
1
1
0
1
1
1
1
1
0
1
1
1
2
1
1
1
1
2
2
0
1
1
1
0
1
1
1
1
1
1
1
1
0
0
1
0
1
1
1
2
1
0
2
2
1
2
1
0
0
0
0
1
0
1
2
1
2
0
2
1
0
1
0
0
0
0
1
2
1
0
2
0
1
1
1
0
0
0
0
1
1
0
0
1
1
0
1
1
2
1
0
2
0
1
0
1
1
1
2
1
2
2
1
1
0
2
1
0
2
1
2
1
1
1
1
2
0
2
2
1
0
1
1
1
2
1
1
1
1
1
2
1
2
0
1
1
2
0
0
1
2
1
2
1
1
2
1
1
1
0
0
1
1
1
2
0
1
1
0
0
0
1
2
1
0
1
1
1
1
2
1
0
1
1
0
1
1
2
0
1
0
0
2
2
1
1
0
1
0
1
0
1
1
0
1
1
1
0
0
2
1
1
0
2
1
1
1
1
1
2
1
1
2
1
1
2
1
2
1
1
2
0
1
0
0
2
1
2
1
0
0
1
1
1
1
1
2
1
0
1
1
1
0
1
0
1
2
1
2
2
2
1
0
2
1
1
1
3
1
0
1
1
0
1
1
1
1
0
1
1
1
0
1
2
0
1
0
0
1
1
3
0
0
0
2
1
1
1
2
2
1
2
2
1
2
1
2
0
1
2
0
1
2
2
0
1
2
1
0
1
1
0
0
1
0
1
1
2
1
1
0
2
1
1
1
2
2
0
0
1
1
1
2
1
2
1
2
1
1
1
2
1
1
2
1
0
1
1
0
1
0
1
2
0
2
2
1
2
1
0
2
1
1
2
1
1
1
1
0
2
0
1
2
0
1
0
0
0
1
1
0
2
0
1
0
0
1
2
1
1
0
0
1
1
1
1
1
1
1
2
1
0
3
0
1
0
1
2
0
1
0
2
0
3
1
0
0
2
1
0
1
0
1
1
0
0
1
2
1
1
2
1
1
1
1
1
1
0
0
1
2
0
1
0
1
0
1
0
1
1
0
1
2
0
0
0
1
2
1
1
2
2
2
2
2
2
0
0
3
1
0
1
1
1
1
2
0
0
1
2
2
2
0
0
1
0
1
2
1
1
2
0
2
1
1
2
0
2
2
1
0
2
0
2
1
0
1
1
1
2
2
0
2
1
2
1
0
0
1
2
2
1
2
1
1
1
1
1
0
1
0
0
1
2
1
2
0
0
0
1
1
0
1
0
1
0
1
0
2
1
1
0
1
0
2
1
2
1
0
2
2
1
0
1
0
1
1
1
1
1
3
1
2
1
1
1
1
1
2
1
1
0
0
0
0
1
1
1
2
1
1
0
1
1
1
1
2
2
1
0
1
1
1
1
2
0
1
4
2
1
1
2
1
2
1
2
0
1
0
2
1
0
2
1
1
1
1
2
1
2
0
1
1
2
1
2
1
1
0
1
2
1
0
1
1
1
0
0
1
1
2
1
2
1
0
0
0
1
0
1
2
1
1
1
2
0
1
1
2
1
0
1
1
1
1
2
1
0
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
0
2
2
2
3
2
1
0
1
1
1
0
2
1
2
1
1
2
2
2
1
1
1
2
2
0
0
1
1
1
0
1
1
1
1
2
1
1
0
1
1
1
0
0
0
0
1
1
2
1
1
1
1
0
2
0
1
2
1
0
0
0
1
1
0
1
1
0
1
1
1
2
2
1
0
3
1
0
1
0
1
1
0
1
0
2
1
1
0
1
1
2
2
2
2
0
1
0
1
1
0
1
3
1
1
1
1
0
0
1
1
1
0
1
2
2
2
0
1
0
0
2
1
0
1
2
1
1
1
1
1
0
1
1
0
2
2
1
0
1
1
2
0
1
2
1
1
1
1
0
1
2
1
1
0
1
1
1
1
1
0
0
1
2
1
1
0
0
0
1
2
1
0
1
1
0
1
1
1
1
2
1
0
2
0
2
1
1
1
0
0
0
2
2
0
1
1
1
2
2
1
1
1
1
1
1
0
0
0
1
0
0
0
0
0
1
1
1
0
1
1
1
2
1
0
2
2
1
0
1
1
0
1
2
0
0
1
0
1
0
0
1
1
1
1
1
0
3
0
2
0
0
0
1
4
2
1
2
1
1
0
1
2
1
2
1
1
1
1
2
1
1
2
2
1
2
0
1
1
1
2
2
2
1
2
1
3
0
1
2
0
1
1
2
0
2
2
1
1
0
0
1
0
0
2
0
2
2
1
1
0
2
0
2
1
1
1
2
1
0
2
2
1
0
0
1
1
1
0
2
0
0
0
1
0
2
2
1
2
1
1
1
1
0
2
1
1
2
1
2
1
1
1
2
1
1
0
0
1
2
1
1
1
1
1
0
1
1
2
1
2
0
2
0
0
1
0
1
1
1
2
1
1
2
1
1
0
0
1
2
1
2
2
0
1
1
2
1
1
0
0
0
1
1
0
3
2
3
0
2
0
1
1
1
0
0
1
1
1
2
1
2
2
0
0
2
2
0
1
2
2
0
1
2
0
1
0
1
1
2
1
2
1
1
1
0
1
1
0
1
2
0
1
2
1
0
1
1
1
1
0
1
1
2
1
0
2
1
1
2
0
2
0
1
1
2
1
0
0
2
1
1
1
2
2
1
2
0
1
0
1
2
2
1
2
0
0
1
1
1
1
1
2
2
2
1
2
1
1
1
1
0
2
1
2
0
2
0
1
0
1
0
0
2
2
0
1
2
1
1
0
2
2
1
2
1
1
1
1
1
1
2
1
2
2
0
2
1
2
1
1
1
0
1
2
0
1
1
0
2
0
1
2
1
1
1
1
1
1
1
1
2
1
1
0
2
0
1
1
1
1
1
0
1
1
2
0
2
0
2
1
1
1
0
0
1
2
1
0
0
1
0
1
1
1
0
6
0
1
1
1
2
1
1
0
0
1
1
1
2
1
1
0
1
1
2
1
0
1
1
0
1
1
1
2
1
1
1
2
2
0
1
0
1
1
1
1
1
2
2
0
1
1
2
0
4
0
1
1
1
2
0
1
1
0
1
1
1
1
1
1
1
0
0
1
0
0
1
2
1
2
2
0
0
1
2
1
1
1
0
2
2
0
0
0
2
0
1
1
1
3
2
0
2
0
2
2
0
1
2
0
1
0
0
1
1
0
0
1
1
0
1
2
2
0
1
2
1
1
1
2
1
2
1
1
1
1
1
2
1
2
1
0
1
0
1
0
0
1
0
0
1
0
2
1
1
0
0
0
1
2
1
0
1
0
1
1
1
1
2
1
0
1
1
0
2
2
2
2
2
1
0
1
1
0
1
1
1
0
0
1
0
0
1
2
0
1
1
2
1
1
1
0
1
0
2
1
1
1
1
2
1
0
2
2
0
1
1
0
0
1
1
1
1
0
1
1
2
1
1
0
1
1
0
0
1
0
1
1
1
1
1
1
1
1
2
2
1
2
1
0
1
1
1
0
1
2
2
2
0
0
2
1
1
1
1
1
1
0
0
0
2
2
1
2
1
2
2
0
2
2
0
1
1
1
1
1
1
1
0
0
2
1
2
1
0
0
1
1
1
1
1
1
1
1
2
2
2
1
2
1
1
1
0
0
1
1
2
1
0
2
1
0
1
1
2
1
0
0
2
0
2
2
1
1
0
1
0
1
0
0
2
1
1
2
0
0
1
0
2
2
1
1
1
2
2
0
0
1
4
2
1
0
1
0
1
0
1
1
0
1
0
0
2
0
1
0
1
1
1
1
1
1
1
1
0
2
1
1
1
0
0
1
0
1
1
2
1
1
1
1
1
0
0
0
0
0
0
1
1
0
2
2
1
1
1
1
1
1
1
1
1
2
1
2
1
2
2
1
0
1
2
2
1
0
0
0
1
1
1
1
1
1
0
2
1
1
1
1
1
0
1
0
3
0
2
0
1
1
2
1
2
2
1
0
0
2
1
1
2
2
2
2
0
1
1
0
2
0
1
1
1
1
2
0
1
1
1
2
1
1
0
1
1
1
2
1
0
1
1
0
1
0
0
1
0
0
0
1
1
2
1
0
1
1
2
1
1
0
2
0
2
2
1
1
1
2
1
0
2
3
0
1
0
0
2
1
0
1
1
1
2
2
0
1
0
2
0
1
1
2
1
1
0
0
1
1
2
2
1
2
1
1
0
1
1
2
1
1
2
1
2
2
0
1
1
2
1
2
1
0
2
0
1
2
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
2
1
1
1
1
1
0
2
0
1
1
1
2
1
1
1
2
0
2
1
2
1
2
1
1
1
1
0
0
2
1
1
0
1
1
0
0
1
0
0
1
2
2
2
0
1
2
1
1
0
2
1
1
1
1
1
0
1
0
0
1
2
1
2
0
0
1
2
0
0
1
1
1
0
0
1
1
1
2
0
2
1
1
0
1
1
1
1
1
2
1
2
0
1
2
2
1
0
0
0
1
1
1
1
1
1
1
0
2
2
0
1
1
2
2
0
2
2
1
0
1
2
1
0
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
0
1
1
1
1
1
1
0
1
2
0
1
2
1
0
1
1
1
2
2
2
2
0
0
1
1
2
1
0
1
2
0
1
2
2
2
2
1
2
1
1
2
0
2
1
1
0
2
1
1
1
2
0
0
0
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
1
1
1
2
1
1
1
1
1
0
1
0
0
1
0
0
1
1
0
0
1
1
0
1
1
1
1
1
0
2
1
1
0
1
1
0
1
0
1
1
1
1
1
0
2
1
2
1
0
1
1
1
1
1
2
1
2
0
1
1
1
0
1
1
1
1
0
1
0
2
0
1
2
0
2
1
1
1
0
0
2
0
1
0
1
2
1
0
0
1
1
1
0
1
0
1
0
0
1
0
1
0
1
0
0
2
0
0
1
1
0
0
3
1
1
1
1
1
1
0
1
1
1
1
2
0
3
2
1
1
1
2
2
0
1
2
0
0
1
2
1
1
1
1
1
2
0
1
1
1
2
0
2
1
2
2
1
1
1
1
0
2
1
1
1
1
1
1
2
1
0
0
1
2
0
1
2
1
1
1
1
1
0
0
2
1
1
2
1
0
0
1
0
0
0
0
2
0
0
2
1
1
0
0
1
1
0
1
0
0
2
0
1
2
1
0
1
1
1
0
1
1
0
1
1
2
1
3
2
1
0
0
1
2
1
0
0
1
1
1
2
1
1
2
0
1
1
0
1
1
1
2
2
1
2
2
1
1
2
1
1
1
0
1
1
1
0
1
0
0
1
1
1
1
1
2
1
2
0
1
2
1
1
1
1
0
2
1
0
0
2
1
2
0
0
1
0
0
0
2
3
1
1
1
0
0
1
0
0
1
0
1
2
1
2
1
0
1
1
2
0
2
2
2
1
2
1
1
1
1
1
2
0
2
2
1
1
2
1
0
2
0
1
2
1
1
1
1
1
1
1
0
0
2
0
2
1
4
1
0
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
0
2
0
1
0
2
2
1
0
1
1
1
1
2
1
0
0
1
1
0
1
1
2
0
0
2
1
1
1
1
1
1
1
1
1
1
2
0
0
1
2
0
1
0
2
2
1
1
0
0
1
2
1
0
0
1
2
0
1
0
0
0
1
1
0
2
1
1
1
1
0
1
1
1
0
1
0
1
1
0
2
0
1
0
0
2
2
0
1
0
2
2
1
1
0
2
1
1
1
0
1
2
2
1
1
0
1
2
1
1
1
2
1
2
1
2
2
1
0
1
2
1
2
0
1
1
2
1
1
1
0
1
1
2
1
0
2
2
1
1
1
2
2
1
1
1
2
1
1
1
1
1
1
0
1
1
1
2
0
1
1
2
2
0
0
1
0
1
2
0
0
1
0
2
1
0
1
1
0
1
0
1
0
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
0
2
1
3
0
0
1
1
1
1
2
0
2
2
1
0
2
1
1
1
0
2
1
4
2
1
1
0
1
2
0
1
1
1
1
1
0
2
2
1
0
1
1
2
0
1
1
0
2
0
1
2
1
1
2
1
0
0
1
1
2
0
0
1
2
1
0
2
0
0
0
1
0
1
0
1
0
1
1
1
2
1
0
0
1
2
0
0
1
1
1
1
1
1
1
0
0
2
1
1
1
2
1
1
1
1
2
2
1
0
2
1
0
1
2
1
1
2
1
2
2
1
1
1
2
0
1
0
0
0
0
1
0
0
1
1
1
1
2
1
0
0
1
0
1
0
1
0
1
1
2
3
1
1
2
2
2
2
2
2
8
0
1
0
1
1
0
1
1
2
1
1
2
2
1
0
0
1
2
1
1
0
1
1
0
1
0
1
0
0
1
1
1
1
1
2
0
1
1
0
2
1
0
1
0
0
1
2
0
1
1
1
0
0
2
0
0
1
1
0
2
1
2
1
0
1
2
1
0
1
0
0
1
0
1
1
2
0
1
2
2
0
0
2
1
1
2
2
1
1
2
0
2
0
1
1
2
0
2
0
1
1
1
2
2
0
1
1
1
0
1
0
2
1
1
1
1
1
0
1
0
1
2
0
3
0
1
1
1
0
1
2
0
1
0
1
0
1
0
1
0
1
2
1
1
0
5
1
0
0
2
1
1
1
1
1
2
1
1
0
0
1
2
1
1
1
1
1
1
2
1
0
1
0
2
2
2
1
1
0
1
3
1
1
1
1
1
1
2
1
1
1
1
0
1
1
1
2
1
1
2
2
1
1
2
0
1
1
1
2
1
1
1
0
2
0
1
1
1
0
0
2
0
2
1
2
2
1
1
1
0
1
1
0
1
1
1
2
2
0
1
1
1
2
1
1
1
2
2
2
2
0
1
0
1
0
1
0
0
2
0
0
0
3
1
1
2
0
1
2
3
0
1
1
0
0
1
1
1
1
1
0
2
0
2
2
1
1
1
1
1
1
0
1
1
1
2
1
2
1
1
1
1
2
0
0
0
1
1
1
1
1
2
2
1
1
1
1
0
1
0
1
3
2
1
2
1
0
1
1
1
0
1
1
2
1
1
1
1
0
1
0
2
1
1
2
2
1
1
2
1
1
1
0
2
1
1
1
0
1
0
1
2
1
1
0
1
1
1
0
2
1
1
0
2
0
0
1
1
1
1
0
0
1
0
0
1
0
1
0
2
1
1
2
2
0
0
1
2
2
0
2
2
2
1
1
2
1
0
1
1
1
1
2
1
1
0
0
0
1
2
1
0
2
2
1
1
2
0
1
1
1
1
1
0
1
1
1
1
0
0
0
1
2
1
0
1
1
1
0
1
1
2
2
2
1
1
1
1
1
2
0
1
1
1
1
1
2
0
1
0
0
1
1
0
2
1
1
2
1
1
1
1
0
0
2
1
1
2
1
0
1
1
2
1
2
1
2
1
1
1
2
1
0
1
0
1
1
1
1
1
0
2
2
1
3
0
2
1
1
2
1
2
1
2
2
0
0
1
0
0
1
1
1
1
1
1
0
2
1
0
1
0
0
0
2
1
1
1
1
1
0
2
0
2
1
0
1
1
0
1
1
2
1
2
1
1
1
1
0
0
0
2
1
2
0
1
1
1
1
1
1
1
0
1
2
1
1
2
0
1
2
0
1
2
1
1
1
0
1
0
0
0
3
0
1
0
1
2
1
2
1
1
2
1
0
1
0
1
1
2
1
0
1
1
2
0
1
2
1
0
1
1
0
2
2
1
1
1
2
2
1
1
2
1
0
2
2
2
1
0
0
2
2
0
1
1
0
1
1
0
2
1
0
1
1
0
1
0
1
7
0
2
2
1
1
1
1
1
0
1
1
1
0
0
2
2
1
1
2
1
0
2
1
0
1
4
0
1
2
1
1
1
2
0
1
1
1
2
1
1
2
2
0
1
2
1
1
2
2
1
1
0
1
1
2
0
1
1
1
2
1
0
2
2
1
0
0
0
1
2
2
1
1
0
0
1
1
1
1
0
1
1
0
1
1
1
1
2
1
0
2
2
1
1
3
2
1
0
1
0
2
1
1
1
3
0
1
1
0
1
1
1
1
1
2
0
0
0
1
2
1
1
1
1
1
0
0
3
2
1
2
0
0
0
0
1
1
1
0
0
0
0
3
0
1
2
0
0
1
1
2
0
1
1
1
4
2
1
2
0
1
1
1
2
1
2
1
2
2
0
2
0
1
1
2
1
2
1
1
0
0
0
1
0
1
0
1
1
1
1
1
2
0
0
1
2
1
1
1
1
1
0
3
2
2
0
1
2
1
0
1
1
1
0
0
2
1
1
0
2
0
0
1
1
1
1
1
0
1
0
1
1
0
2
0
2
1
0
1
1
1
1
2
2
1
1
1
1
1
0
1
1
1
0
2
1
2
2
0
1
1
1
2
0
2
2
1
1
0
3
0
1
2
1
3
0
0
2
1
0
1
0
1
1
0
1
0
1
1
1
2
1
1
0
1
1
0
1
2
1
1
1
0
1
0
2
1
0
0
1
1
1
1
1
1
1
0
0
1
1
1
2
2
1
0
0
1
1
1
0
1
0
0
0
1
1
0
2
2
2
1
1
0
2
1
0
2
2
0
0
1
0
1
1
2
1
0
1
1
0
1
2
1
2
2
0
1
0
2
0
1
1
1
2
1
1
2
1
2
1
1
0
0
0
1
1
1
1
1
2
1
0
1
0
0
1
0
2
1
1
2
1
2
1
1
2
2
1
1
2
0
1
0
0
1
1
1
1
1
3
0
2
1
0
1
1
1
1
2
0
0
0
0
1
2
2
3
1
0
1
0
1
0
2
2
1
1
1
1
1
1
2
0
1
0
0
1
1
1
3
2
1
0
1
1
2
2
0
2
1
0
1
1
1
2
1
1
0
2
2
0
1
1
0
0
1
0
2
0
0
0
2
1
1
2
1
0
1
1
0
1
2
1
2
1
1
0
1
0
2
1
2
0
0
2
0
1
2
1
0
0
1
2
0
0
0
0
1
1
1
1
1
4
1
2
1
2
2
1
1
1
0
2
0
1
1
1
1
0
1
1
2
1
2
2
1
1
1
0
1
0
1
1
0
2
1
1
0
1
2
2
0
0
1
2
1
0
1
1
1
0
0
2
1
2
0
1
1
1
1
1
3
1
1
0
2
1
1
2
1
1
2
1
0
1
1
1
1
0
0
1
1
0
0
1
1
1
1
1
2
0
1
0
1
3
2
1
1
1
1
1
1
1
2
2
1
0
0
1
0
1
1
1
1
1
1
1
1
1
0
1
0
0
0
1
2
2
0
1
2
1
2
2
2
2
1
1
0
0
0
0
1
1
1
1
1
0
0
1
0
3
1
1
1
1
0
1
0
1
1
1
2
0
1
1
1
0
1
1
1
1
1
1
1
1
2
1
1
0
1
1
0
0
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
3
1
0
1
0
2
1
1
1
1
1
0
1
1
2
0
2
0
1
0
2
0
0
1
1
1
1
0
0
1
1
0
2
0
2
1
0
1
1
1
1
1
2
1
0
0
0
1
1
1
2
2
1
1
1
0
2
1
2
1
2
1
1
1
1
1
1
1
1
2
1
0
1
1
0
1
0
1
1
2
1
1
0
1
0
0
1
2
2
1
0
2
1
1
0
0
1
1
2
1
1
1
1
0
1
2
2
0
0
2
1
0
1
1
1
1
0
0
1
0
0
1
2
2
0
1
1
2
1
1
1
1
2
1
1
1
0
1
1
1
1
0
1
1
0
0
1
2
2
0
1
0
1
2
1
1
2
1
1
1
2
2
1
0
1
2
1
0
0
2
1
1
1
1
1
1
1
0
1
1
0
1
2
1
2
0
1
0
0
0
1
1
0
1
0
1
1
1
0
1
2
1
1
2
2
0
1
1
1
1
1
0
0
1
0
0
0
0
1
1
1
0
1
3
1
1
1
1
1
2
0
0
1
0
0
0
0
1
0
1
0
0
1
2
1
1
0
1
1
2
2
1
0
2
1
1
0
2
2
0
0
2
1
1
1
2
1
2
0
1
0
2
1
1
2
1
1
2
1
0
0
2
1
2
0
1
1
1
1
1
1
0
1
1
2
0
1
1
2
0
2
3
2
1
1
1
1
1
1
0
1
1
1
0
1
1
1
1
1
1
0
2
1
1
1
3
1
1
2
1
2
1
1
0
1
2
0
2
1
0
1
0
1
2
1
2
1
1
1
0
1
1
0
1
2
2
1
0
0
0
0
1
1
0
1
1
1
1
2
0
1
0
1
1
1
1
2
2
1
1
0
0
0
1
1
1
1
2
1
0
2
1
0
2
1
0
2
1
1
2
1
1
0
0
0
1
1
1
2
0
1
1
1
1
1
2
2
2
2
0
1
1
2
3
1
0
2
2
0
2
0
1
0
1
0
1
2
0
2
1
1
2
1
2
0
1
1
1
1
0
0
2
0
0
1
1
1
1
0
0
1
0
1
0
0
1
1
2
0
2
0
1
0
1
2
1
0
2
0
2
1
1
1
1
2
0
0
2
0
0
2
0
1
1
1
1
2
0
2
2
0
0
2
1
1
0
0
0
2
1
2
1
1
1
0
1
0
1
1
1
1
0
1
1
1
1
0
1
2
1
0
1
1
0
2
1
2
1
1
1
0
1
0
0
2
1
1
1
1
0
0
2
1
2
0
1
1
1
1
1
2
2
2
0
1
2
1
1
0
1
1
1
2
0
2
1
1
1
1
0
1
1
1
1
1
0
0
1
1
1
2
1
1
0
0
2
0
1
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
0
0
2
0
1
1
0
0
1
1
1
0
0
1
2
1
2
1
1
1
1
1
1
1
0
1
1
2
1
1
1
0
1
1
2
1
2
1
1
2
2
0
1
1
1
1
1
1
1
2
1
1
2
1
1
1
2
1
1
1
1
1
1
2
0
1
1
2
1
0
0
1
1
1
1
0
1
1
1
1
0
0
0
2
1
2
1
0
1
1
1
2
1
1
2
1
2
2
1
1
2
0
0
2
1
1
0
2
1
0
2
1
1
2
2
1
2
2
1
1
1
2
1
1
1
0
0
1
0
0
0
2
2
1
1
1
1
1
2
2
0
1
1
1
1
1
0
0
1
0
1
1
1
1
1
2
0
1
2
1
2
1
2
1
1
0
1
1
1
3
1
1
0
0
2
0
1
2
0
0
0
1
2
1
1
1
2
0
0
0
0
0
0
1
1
1
1
0
1
0
0
1
0
2
0
2
1
1
0
1
1
1
1
1
1
1
1
1
0
0
0
0
0
2
2
1
0
2
1
1
2
1
1
0
0
2
1
0
1
1
1
0
1
0
0
2
2
1
2
0
1
2
1
1
2
0
1
1
1
1
2
1
1
2
2
2
2
0
2
2
2
2
1
1
1
0
1
1
0
0
1
0
0
1
2
2
1
1
1
1
2
2
1
2
0
0
2
0
2
1
1
1
1
1
0
1
1
1
0
1
1
1
0
2
0
0
2
0
1
0
1
1
0
0
1
0
2
2
2
1
0
3
0
0
1
0
1
0
2
1
0
1
2
2
1
1
0
0
0
2
0
1
1
1
1
0
2
2
1
1
1
1
0
2
1
1
2
2
2
1
1
2
1
1
2
0
0
3
0
2
1
1
0
0
0
2
1
0
1
1
0
0
1
1
1
2
1
2
2
2
1
0
1
0
2
1
1
1
1
1
1
2
0
2
1
0
1
1
2
0
1
1
2
1
1
1
0
2
0
1
0
1
1
1
2
0
1
0
1
1
0
1
0
0
0
0
1
2
1
3
2
2
0
1
1
0
1
1
1
1
0
1
1
0
0
0
1
0
0
2
0
2
1
0
2
1
1
3
1
2
0
1
1
0
1
1
1
1
2
2
1
2
2
2
1
0
1
1
2
1
2
1
1
0
2
2
0
2
2
0
3
0
1
1
3
1
2
1
1
2
1
1
0
1
1
0
1
2
0
1
2
2
1
0
1
1
1
0
2
2
2
0
1
1
0
4
1
1
0
1
1
1
1
1
0
1
1
0
1
1
2
0
1
1
1
0
2
0
1
0
1
1
1
2
1
2
0
1
2
1
1
2
2
0
0
0
1
2
1
1
2
0
0
2
0
1
1
2
1
3
1
1
1
2
1
1
1
0
2
1
0
0
0
2
1
1
1
1
1
2
1
1
0
2
0
1
1
2
1
1
2
0
1
1
2
0
0
2
1
1
0
1
2
2
2
1
2
1
0
0
0
2
1
0
1
0
2
1
0
1
2
1
1
1
0
1
0
2
1
0
1
1
0
1
1
0
1
1
1
1
1
1
1
1
1
2
0
1
2
2
0
2
2
1
1
0
0
2
1
2
1
0
1
2
1
1
1
2
2
1
0
1
1
1
2
1
2
1
1
1
0
1
1
1
1
1
3
0
1
0
1
1
0
1
0
1
2
1
1
1
2
0
2
0
1
1
1
1
1
0
1
1
1
1
1
1
1
1
2
1
2
1
2
1
3
2
0
1
0
0
1
2
1
1
1
2
2
1
0
1
2
0
1
2
1
0
1
1
0
2
1
1
0
1
1
0
1
1
1
1
1
0
1
1
1
2
0
0
1
1
1
1
2
1
0
1
0
2
1
2
0
2
2
2
2
1
0
1
2
0
0
1
1
0
1
1
1
1
1
1
1
1
2
0
1
0
2
1
0
1
0
1
0
1
0
1
1
0
0
2
0
2
0
2
1
3
0
1
0
2
1
1
1
1
0
0
0
3
0
1
1
0
1
1
1
2
2
2
1
2
1
0
0
2
0
1
2
2
1
2
2
1
1
1
1
0
0
3
0
1
1
1
2
2
0
1
1
2
2
2
0
2
1
1
0
1
1
0
1
0
2
1
1
0
1
1
2
2
0
1
2
2
0
1
0
0
2
1
0
1
1
1
2
1
2
1
1
1
0
1
0
1
2
2
1
1
1
2
1
0
1
1
0
1
1
1
2
2
1
2
1
1
2
1
0
1
2
1
1
1
1
2
1
0
2
0
1
1
2
1
2
2
0
0
1
1
2
1
1
2
1
0
2
1
0
0
0
1
1
1
1
1
1
1
2
3
2
2
2
1
0
2
2
1
2
1
1
1
1
0
2
1
2
0
1
1
1
0
2
1
0
2
0
1
2
0
2
1
0
2
1
1
1
1
2
0
1
1
0
1
2
0
0
0
1
1
1
1
1
2
1
1
1
3
2
1
1
1
3
1
0
0
2
1
0
0
1
0
1
1
1
0
1
1
1
2
1
1
0
1
1
1
1
0
1
1
1
0
1
4
2
1
1
2
2
1
2
2
1
0
0
2
1
2
3
0
1
2
1
1
1
1
1
1
1
0
0
1
1
1
1
1
0
0
2
2
0
1
0
1
0
1
2
1
0
1
0
0
1
2
2
0
1
2
1
0
3
1
1
2
1
2
1
0
1
0
1
2
1
1
1
1
1
0
0
1
2
0
1
1
1
0
1
1
1
1
1
0
0
0
0
0
2
1
0
0
1
2
1
0
1
2
1
0
2
1
0
0
1
0
1
2
1
3
0
0
0
1
1
2
1
2
1
0
0
1
1
2
0
1
0
0
1
1
1
1
1
1
1
1
1
0
0
1
1
2
1
2
2
2
2
1
2
1
0
1
0
2
1
2
1
1
0
1
0
1
0
1
1
1
1
1
0
2
2
1
2
0
1
1
0
3
2
0
1
1
0
1
1
1
1
2
1
0
1
0
2
2
1
2
2
0
0
1
1
0
1
2
1
0
1
1
1
1
0
0
1
1
0
1
0
1
1
2
1
1
2
1
2
2
1
1
2
1
1
0
2
0
0
1
1
1
2
0
1
1
1
1
0
0
0
2
1
2
1
1
2
0
1
0
1
0
0
1
1
1
2
1
2
1
1
1
2
1
2
1
0
1
2
1
1
1
1
1
2
1
2
0
1
1
1
1
1
2
1
2
1
2
1
1
1
1
0
1
1
2
1
1
1
2
0
1
2
0
2
1
1
1
0
1
2
1
1
0
0
0
1
1
0
1
1
9
0
12
0
0
2
2
1
2
1
0
0
1
1
0
0
2
2
1
0
2
2
2
1
0
1
1
1
1
1
0
2
1
1
2
2
0
1
1
1
1
0
1
2
1
1
1
1
1
1
0
0
2
2
0
2
1
1
0
0
1
1
1
1
0
1
1
1
0
1
2
1
2
1
1
2
1
2
1
1
1
2
2
1
0
0
1
1
2
1
0
3
1
0
0
2
2
1
2
2
1
0
1
0
1
2
0
1
1
0
2
0
0
0
1
2
1
0
0
0
1
1
0
1
0
1
0
2
0
1
0
1
1
1
2
1
2
1
1
1
0
0
1
0
2
1
0
0
0
0
2
1
1
1
1
1
1
1
0
2
1
1
1
0
0
0
1
1
0
1
1
0
2
2
1
2
1
1
1
2
0
1
1
0
1
1
0
1
1
0
2
0
1
1
1
2
1
2
0
1
1
0
0
1
0
1
0
2
1
1
1
0
3
0
1
1
1
1
2
0
0
1
0
1
1
1
1
1
1
1
1
1
0
1
3
1
1
2
2
1
1
1
0
2
0
1
1
2
1
1
2
1
1
0
1
0
1
0
0
0
1
1
1
1
0
2
0
1
1
0
0
2
2
0
1
1
0
2
2
0
1
2
2
1
1
0
1
1
1
0
2
2
0
1
1
0
1
1
1
0
1
2
0
0
3
1
1
1
0
1
2
1
0
3
1
1
1
2
1
1
2
2
2
2
1
2
1
2
1
2
2
1
2
1
0
1
2
1
1
2
1
2
1
1
1
0
0
1
1
0
2
1
0
1
1
2
0
1
1
0
1
2
1
1
1
2
1
1
0
1
1
1
0
1
2
1
1
1
2
1
1
0
0
1
1
1
2
2
0
1
1
1
1
1
1
0
1
1
1
1
1
1
0
1
0
0
2
0
1
0
0
2
1
0
0
0
1
2
2
0
2
1
1
1
1
1
2
1
0
1
1
2
1
1
1
1
0
2
1
1
0
1
1
1
2
2
1
3
1
2
0
2
0
2
1
2
0
2
1
1
1
2
2
1
1
2
1
1
1
2
1
2
1
1
0
2
2
1
1
0
4
2
2
1
1
1
2
1
0
0
1
2
0
1
1
1
1
2
1
0
1
1
1
2
1
1
0
0
1
4
1
2
1
2
1
2
1
1
1
0
1
2
2
1
3
2
0
0
0
1
2
2
0
1
2
1
2
1
2
1
1
2
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
2
2
2
1
1
0
1
1
1
1
2
2
0
1
0
1
2
1
1
0
0
0
1
2
1
0
1
2
1
1
1
1
1
1
1
0
1
2
1
0
1
0
0
1
2
1
1
3
0
0
1
2
1
2
2
1
1
1
1
1
1
2
1
0
1
0
0
1
1
1
1
1
2
1
2
1
0
1
1
1
1
2
0
1
2
1
2
2
1
0
1
0
1
1
1
1
1
1
0
1
0
1
2
2
2
1
2
0
1
0
1
2
1
2
2
1
2
1
1
1
0
2
1
1
1
1
1
0
2
1
1
2
1
1
1
0
1
1
1
0
1
0
1
1
0
2
1
1
2
1
2
0
1
1
1
1
1
1
0
0
1
1
1
0
2
0
1
1
1
1
2
2
2
2
1
2
1
1
1
1
0
0
2
1
1
1
1
1
0
1
2
1
1
1
1
1
1
1
2
0
2
1
1
2
0
0
1
0
1
1
1
2
2
1
2
2
2
0
2
2
2
2
1
2
1
0
0
1
0
2
1
0
0
2
0
0
0
2
1
1
2
1
2
2
0
1
1
0
1
1
1
1
2
1
1
1
0
0
2
0
1
0
1
1
2
1
2
2
0
2
1
1
0
0
0
1
1
0
0
1
1
1
1
1
2
2
1
1
1
1
1
1
0
1
1
1
1
1
1
1
2
1
1
1
1
0
0
1
0
1
0
0
1
1
1
1
2
2
2
0
0
2
3
1
2
1
0
0
1
2
1
2
1
1
0
1
0
0
1
1
2
2
1
1
1
2
1
1
1
2
0
1
2
1
1
1
1
0
2
3
2
0
1
1
3
2
2
0
3
1
1
2
1
0
1
0
1
1
1
1
2
0
1
1
2
1
0
0
2
2
0
0
1
1
0
0
2
2
0
1
1
1
1
1
0
2
0
0
2
2
0
2
1
1
0
1
1
2
2
2
1
1
1
1
1
1
0
1
1
2
1
2
3
2
1
2
1
0
0
0
2
1
2
2
2
0
1
0
0
1
0
1
1
2
1
2
1
1
1
1
1
0
1
0
1
2
1
1
3
0
1
2
1
1
1
2
1
0
1
2
2
2
1
2
2
2
1
0
1
0
1
2
0
0
1
1
1
0
1
1
1
2
1
1
0
0
3
0
1
1
0
1
0
1
0
2
1
1
1
1
1
1
2
1
1
0
1
1
1
0
2
1
2
1
1
2
2
2
2
1
1
1
2
1
0
1
1
1
1
2
1
1
0
1
1
0
0
1
1
2
1
2
0
0
2
1
0
1
0
2
1
0
0
1
0
1
2
1
1
2
0
1
0
1
1
1
1
1
1
0
0
1
1
2
0
2
2
0
0
1
1
1
0
2
1
2
1
1
1
1
1
0
0
1
2
1
0
1
0
1
0
1
2
1
0
2
2
1
1
1
0
1
1
0
1
1
2
1
1
1
2
0
1
1
1
1
0
0
1
2
0
0
1
2
1
2
2
0
1
1
1
0
0
2
2
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
0
0
1
1
1
1
0
2
0
1
1
2
1
0
2
0
1
1
1
0
1
1
1
0
1
1
1
1
2
1
0
1
0
1
2
1
2
1
0
1
0
1
2
0
1
1
2
2
1
1
1
0
2
2
1
1
3
1
1
1
2
0
0
1
1
1
1
2
2
1
1
0
2
1
2
1
1
1
0
1
0
0
1
1
1
0
2
1
0
1
1
2
1
1
2
1
1
2
1
2
0
1
0
1
1
0
1
1
0
1
1
1
1
0
1
2
1
0
1
1
1
1
2
2
2
1
2
1
1
1
2
1
2
2
2
0
1
2
1
2
2
0
0
0
1
0
1
1
1
1
1
1
3
0
1
1
0
2
1
1
0
2
0
1
1
1
0
1
1
0
1
2
2
0
1
0
1
2
1
0
0
1
0
1
1
1
2
2
1
1
2
1
2
1
1
0
2
1
0
1
0
0
1
2
1
0
0
1
1
1
1
2
1
1
1
0
1
1
1
1
3
2
1
1
1
2
0
1
1
1
2
1
2
0
0
0
1
0
1
1
1
1
1
2
2
1
0
0
1
1
0
1
2
0
1
1
1
1
2
1
2
2
2
1
0
1
2
1
0
2
1
1
1
0
2
1
1
0
0
0
1
0
1
2
1
1
1
0
2
2
1
1
2
1
0
1
2
1
2
1
2
2
1
1
1
0
2
0
0
1
0
2
3
1
1
0
1
1
1
1
2
1
0
2
2
0
1
2
0
2
0
2
3
1
1
1
1
2
2
1
0
1
1
2
1
2
1
1
1
1
1
0
0
0
0
1
1
0
0
1
1
1
2
1
2
1
1
2
1
1
1
2
1
1
1
1
0
1
0
0
0
0
1
2
1
2
1
0
0
0
2
0
1
1
0
1
2
1
1
2
2
0
1
2
1
0
1
0
0
0
2
1
0
0
2
0
1
0
2
2
1
1
1
2
0
2
2
1
1
1
0
2
1
1
0
2
0
0
1
1
1
1
1
0
1
0
2
0
1
0
2
0
2
0
1
2
1
2
1
1
1
1
1
1
0
0
1
2
1
2
2
1
1
1
1
1
1
0
0
2
1
1
1
0
0
0
1
0
1
1
2
1
0
1
1
3
1
1
0
1
0
2
1
0
0
2
2
1
2
0
1
2
2
2
1
2
1
1
1
1
1
2
1
1
1
1
2
4
1
1
2
2
1
1
1
1
0
0
0
1
2
1
1
1
2
0
1
0
1
1
2
2
3
0
0
0
0
0
1
1
1
1
1
1
0
0
1
1
1
0
0
1
1
1
0
1
1
2
1
0
2
1
1
2
2
0
1
2
0
0
1
2
0
2
1
1
0
0
2
2
0
1
0
1
0
1
1
2
2
1
0
1
0
1
0
2
2
1
2
2
2
1
1
1
1
2
1
1
1
2
1
1
1
2
2
1
1
2
1
0
1
1
2
0
1
0
2
0
1
1
1
0
0
1
1
0
1
2
1
2
1
1
1
2
0
1
2
1
0
0
1
0
0
0
2
1
1
1
1
0
1
1
2
1
2
1
2
2
1
1
1
0
1
1
1
0
2
0
0
2
0
1
1
0
2
2
0
0
0
1
1
1
1
1
2
1
0
1
1
1
1
0
2
2
1
1
1
1
1
2
1
1
1
2
1
1
2
0
0
1
2
1
2
1
0
1
2
1
0
0
1
2
2
1
1
1
1
1
0
1
1
0
1
1
1
1
0
2
2
1
1
2
1
0
2
1
2
2
1
1
1
0
1
2
1
0
1
1
0
2
1
1
0
0
0
2
1
2
1
2
2
2
1
0
1
0
1
0
1
2
2
1
0
0
2
0
1
2
2
2
1
2
1
1
2
2
2
1
0
1
1
0
0
1
2
1
2
2
0
1
1
1
3
1
1
1
2
1
2
1
0
1
1
1
1
1
1
0
1
1
1
1
0
1
1
0
0
1
0
1
1
1
1
2
2
1
1
0
1
0
2
1
1
1
1
2
0
0
1
0
1
2
0
0
0
0
1
1
1
2
2
1
0
1
1
1
2
2
1
0
0
0
2
1
0
2
1
2
2
1
2
0
2
0
0
1
1
1
0
0
1
1
1
0
0
1
1
0
1
1
0
1
2
1
0
0
1
1
2
1
2
0
1
2
1
1
1
0
2
1
2
1
0
1
1
1
1
0
1
1
0
0
2
2
1
0
1
1
0
0
1
0
0
2
1
0
1
0
1
1
1
0
1
0
1
1
1
1
1
2
0
1
1
1
1
1
0
1
0
2
1
1
1
0
2
2
0
2
0
0
1
0
1
1
1
0
0
2
1
0
1
1
2
1
1
2
1
1
1
2
0
1
1
0
1
2
2
2
1
0
1
0
2
1
1
1
1
1
1
1
1
2
1
0
1
1
1
2
0
1
0
1
4
2
1
2
2
1
1
1
0
1
1
1
2
1
1
1
1
0
0
1
1
1
2
0
1
1
2
1
2
0
1
0
0
0
2
2
1
2
1
2
1
1
1
2
0
0
0
1
2
1
1
1
1
1
2
0
1
0
1
1
1
0
2
1
1
2
2
1
1
0
1
2
2
1
1
0
1
2
2
0
1
0
1
0
1
1
2
1
2
1
1
0
1
1
0
0
0
0
1
1
1
0
1
1
0
2
1
1
3
0
0
1
0
2
2
0
0
1
2
1
1
1
2
2
1
0
1
1
2
2
1
2
0
1
1
1
2
1
2
1
0
0
1
0
1
1
0
2
1
1
1
1
0
1
1
2
0
1
1
1
1
0
1
2
0
2
1
0
0
1
1
4
0
2
2
0
2
1
1
1
0
0
0
0
1
1
2
1
1
0
0
1
0
1
0
2
1
0
1
0
0
1
1
1
1
1
2
1
0
1
2
2
1
0
1
1
1
2
1
1
1
1
1
0
1
1
1
0
1
1
0
1
0
1
1
0
2
2
1
1
2
2
1
0
2
0
0
1
2
0
1
1
2
0
1
1
2
1
1
1
2
1
2
1
2
1
0
1
1
1
1
2
0
1
2
2
0
0
1
2
2
1
1
2
2
1
2
2
1
1
0
1
2
2
0
1
1
0
2
0
1
0
1
1
2
0
1
2
1
1
1
1
1
1
0
1
0
1
1
2
1
0
1
1
0
3
1
0
2
2
1
0
2
1
1
1
1
0
1
1
1
0
1
2
1
1
0
0
1
1
0
1
1
0
3
2
1
2
1
0
1
1
0
1
2
0
1
1
2
2
1
0
1
0
1
1
1
1
0
1
1
2
0
0
0
0
1
1
1
0
4
0
2
0
1
2
0
0
1
1
1
2
0
5
1
1
1
0
1
2
2
1
1
2
1
0
2
1
2
0
0
0
1
0
1
0
2
1
2
1
0
0
0
2
3
0
2
1
1
0
3
0
1
2
0
1
1
1
1
0
2
1
0
1
1
1
1
1
0
0
1
2
2
1
2
1
2
1
0
2
0
1
1
3
2
1
1
1
1
1
1
2
1
0
1
0
1
1
2
0
2
2
1
1
2
0
1
2
1
2
0
1
1
2
1
0
1
1
1
1
2
1
0
1
0
0
0
1
1
1
1
1
1
1
1
0
0
1
0
2
1
1
1
1
1
0
1
1
1
1
1
2
0
1
1
1
1
1
1
0
1
1
1
2
0
1
1
2
1
1
0
1
1
2
2
2
2
1
1
0
1
1
0
2
1
2
2
1
1
1
1
2
0
0
1
1
2
1
2
0
0
1
2
1
1
0
1
1
0
1
1
1
0
1
2
1
2
1
0
0
0
0
1
1
0
0
2
1
2
1
2
1
3
2
2
6
1
1
2
1
2
2
2
0
0
0
1
1
0
1
3
2
1
1
2
1
0
2
1
0
1
2
1
1
0
1
2
1
1
1
1
1
0
2
1
0
1
1
1
2
1
1
1
0
1
2
1
2
1
1
1
1
0
1
1
1
1
2
1
1
0
2
0
0
1
1
0
0
0
1
1
0
1
1
1
1
2
0
1
0
0
5
1
0
1
1
2
1
1
1
0
1
0
0
1
1
0
2
1
1
0
0
1
1
2
2
0
0
1
1
0
0
2
1
0
2
1
1
1
1
1
0
2
1
1
1
1
1
2
1
1
1
0
2
1
0
1
0
1
0
0
1
1
0
1
0
1
1
1
2
4
2
0
2
1
0
1
2
1
1
0
0
2
0
0
1
1
2
0
1
2
0
1
1
1
2
1
0
1
2
0
1
2
1
1
1
1
0
1
2
2
1
1
2
2
0
0
2
1
1
1
1
1
1
1
1
1
0
0
2
1
0
1
1
1
1
0
2
0
1
1
0
1
1
0
1
1
0
1
0
2
1
0
2
1
1
1
2
1
1
1
1
1
2
0
1
2
2
1
2
0
0
2
2
2
2
2
1
0
1
0
2
1
0
1
1
1
1
2
1
1
1
1
0
0
0
0
1
0
2
0
2
2
1
1
1
1
0
0
2
1
2
0
1
2
2
0
2
0
1
2
1
0
0
1
1
0
2
2
1
0
1
2
0
1
0
2
2
0
1
1
0
1
1
0
0
2
2
1
0
0
2
2
1
2
0
1
2
1
1
0
2
0
1
1
1
1
1
1
1
1
0
0
1
0
2
1
2
0
2
2
0
2
2
0
1
2
1
2
2
0
1
1
1
1
1
1
1
2
0
1
2
1
2
0
1
1
0
0
0
0
0
1
1
0
2
1
1
1
1
3
1
1
1
1
1
1
0
0
2
1
0
0
1
2
1
1
1
0
1
0
2
0
0
1
1
1
2
1
1
2
1
2
0
0
2
1
1
0
1
1
0
2
1
2
0
1
2
2
1
0
3
2
0
0
1
2
1
1
1
1
1
1
1
0
1
0
1
1
1
0
0
2
1
0
1
0
2
0
1
1
0
1
1
1
1
1
1
1
2
1
2
1
1
1
1
0
1
1
0
0
0
2
2
2
1
1
1
0
1
1
0
1
1
0
0
2
0
2
1
1
2
1
0
1
1
1
1
2
2
1
1
1
1
0
1
0
1
0
1
1
0
1
2
2
1
1
2
2
1
1
0
1
0
2
2
1
0
2
1
0
1
1
1
1
1
0
2
2
2
0
2
1
1
1
2
0
1
0
1
0
1
1
1
0
1
0
0
2
1
1
1
1
1
1
1
2
1
1
0
2
1
1
1
1
1
1
2
1
0
0
2
1
0
1
2
1
1
0
1
0
0
1
2
2
2
2
1
1
0
2
1
1
1
0
0
2
1
2
1
1
0
1
0
1
1
0
1
2
1
2
0
1
1
1
2
1
1
0
1
1
0
0
1
1
1
0
2
2
2
3
2
2
0
0
2
0
0
2
0
0
0
1
1
1
2
0
1
2
1
1
1
2
1
1
0
0
0
2
0
2
1
1
1
2
0
0
1
0
1
1
2
1
1
0
0
0
2
0
2
1
0
0
1
2
1
1
1
2
1
2
2
1
0
2
0
3
2
1
1
1
0
1
1
0
1
2
2
1
1
2
1
2
2
0
0
0
1
1
0
0
0
0
0
2
2
1
2
0
0
2
0
1
2
1
0
0
0
1
1
2
0
0
1
1
1
1
1
1
1
0
1
0
2
1
1
1
1
1
1
2
1
1
2
2
2
1
0
1
1
0
1
1
1
0
1
0
0
0
1
2
0
2
0
0
0
1
2
1
0
2
0
1
1
0
2
1
0
2
1
1
1
1
0
1
2
2
0
0
1
2
1
1
0
0
1
0
0
2
0
1
0
0
1
2
0
0
1
2
3
1
2
0
0
1
1
1
2
1
1
0
1
0
0
1
1
2
1
0
2
1
0
1
2
0
1
0
1
1
1
1
1
1
1
2
1
0
1
0
2
2
1
1
2
1
2
1
2
0
1
1
1
1
1
1
0
1
0
1
2
0
1
1
2
0
3
0
1
1
1
0
0
4
1
2
1
2
0
2
2
1
2
1
0
1
0
1
1
1
1
0
0
0
1
2
2
2
2
2
2
1
1
1
2
1
2
2
0
0
1
1
1
1
0
0
1
1
1
2
0
0
0
1
1
0
1
2
0
0
1
0
1
1
1
2
0
0
1
1
0
0
0
1
1
1
0
2
2
1
2
1
1
0
2
1
1
1
2
0
2
0
1
1
1
0
1
1
1
1
1
2
0
1
2
1
0
1
0
1
0
0
1
1
2
0
1
1
1
1
1
2
1
1
1
0
0
1
0
1
0
1
0
2
0
0
1
0
1
0
2
0
0
1
1
1
0
1
1
1
1
1
2
1
1
1
1
0
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
0
1
0
0
2
1
1
1
1
0
1
2
0
1
0
1
1
0
2
1
1
1
1
0
1
1
1
1
1
1
1
1
3
1
1
1
1
0
1
0
0
1
1
1
1
1
1
1
1
1
1
1
0
1
0
1
0
0
1
1
0
2
0
2
0
0
1
1
2
1
1
1
1
2
2
0
0
0
1
0
1
1
3
1
2
1
1
0
0
1
0
1
2
0
1
0
2
1
1
0
1
0
1
0
2
1
1
0
0
1
1
1
1
1
2
0
1
1
2
1
1
0
0
2
1
2
1
0
1
1
1
1
1
1
1
1
1
1
0
1
1
2
1
2
1
1
0
1
0
0
1
1
0
1
1
1
0
1
0
0
1
1
0
1
0
0
2
1
2
0
3
1
1
0
1
0
3
0
1
1
1
0
2
2
1
1
1
0
0
2
1
1
1
1
1
1
0
1
1
1
1
0
2
1
2
0
1
1
1
2
2
1
1
1
0
2
1
2
1
2
2
0
0
0
0
3
1
2
0
1
0
0
1
2
1
1
0
3
2
0
0
1
1
2
1
1
1
0
1
0
1
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
0
1
1
0
0
0
0
2
2
0
1
2
0
1
1
1
0
2
0
1
1
1
0
1
1
1
1
1
1
1
5
1
1
0
1
1
1
0
0
0
1
2
0
0
1
0
1
1
2
1
1
0
0
1
0
0
1
1
2
1
1
1
0
1
2
2
2
0
1
0
4
1
0
1
1
1
0
0
1
1
0
0
1
0
0
0
1
1
1
1
0
1
1
0
1
1
1
2
0
2
0
0
1
2
2
1
0
1
0
1
1
1
1
1
1
0
0
1
0
1
1
0
2
0
1
0
1
1
1
1
0
0
2
2
2
2
1
2
2
1
1
1
0
1
1
0
1
2
1
1
0
2
0
2
1
1
0
2
0
0
1
0
1
1
2
1
2
1
1
1
1
1
0
2
1
0
0
1
1
3
1
2
1
3
0
0
1
1
1
2
1
0
1
1
0
0
1
1
0
2
1
1
1
1
0
1
2
0
2
1
1
2
1
1
1
2
0
1
1
0
0
0
1
1
0
0
2
0
1
2
1
1
1
1
1
1
1
1
1
1
0
0
1
1
3
1
1
1
2
1
2
0
1
1
1
1
2
1
1
1
2
1
0
2
1
2
1
1
1
0
1
2
1
0
1
1
1
0
1
1
0
0
0
1
1
1
1
1
1
2
0
2
1
0
1
2
2
1
0
2
0
2
1
2
1
2
2
1
1
2
1
1
1
1
1
2
1
1
0
2
2
0
1
2
1
1
0
1
0
1
1
1
1
0
2
1
1
2
2
1
0
1
1
1
2
2
1
2
1
0
1
0
0
1
0
1
0
0
1
1
0
2
2
2
1
0
1
0
1
2
0
2
1
1
2
2
2
0
1
0
2
1
2
1
0
0
1
2
1
3
2
2
2
1
2
2
2
0
2
0
2
1
2
0
0
1
0
0
1
0
1
2
2
1
1
1
1
1
2
2
1
1
0
8
1
1
1
1
0
0
0
0
1
0
2
1
1
1
1
0
2
2
0
2
1
0
1
0
0
1
0
1
1
0
2
2
1
1
1
1
1
0
2
1
2
1
0
2
1
1
1
0
1
1
0
2
2
2
1
0
2
1
1
1
1
1
0
2
1
1
0
0
0
0
2
1
1
2
1
1
0
0
1
0
1
1
0
1
1
1
0
1
0
1
1
0
1
2
1
1
0
1
1
1
1
1
1
0
1
2
1
1
2
1
1
2
1
2
0
0
1
1
0
1
0
1
1
0
1
2
1
2
0
0
2
1
2
1
0
2
2
0
1
1
2
2
1
0
2
1
1
1
0
1
1
1
1
1
1
0
1
2
1
1
1
2
1
2
0
1
0
1
2
0
0
1
2
1
0
0
1
0
1
1
1
1
1
0
2
1
1
1
1
2
1
0
0
1
1
1
1
1
0
2
1
1
0
0
1
2
1
0
1
2
1
1
0
0
0
3
1
1
0
2
0
1
0
1
1
1
1
0
1
1
1
0
0
2
2
0
0
0
2
0
0
0
1
0
1
0
1
1
0
2
1
0
1
2
1
1
1
1
1
2
1
2
1
1
1
0
1
1
1
2
1
1
1
2
1
2
2
0
2
2
2
1
1
2
1
0
1
2
1
1
2
1
1
5
2
0
1
2
0
1
1
1
0
2
2
0
2
1
1
0
0
2
1
2
0
2
3
0
1
0
0
0
2
0
0
0
0
0
0
0
1
1
0
1
0
1
1
1
1
2
0
1
2
2
0
0
1
2
1
2
2
2
0
0
1
1
1
1
1
0
1
2
1
2
1
1
0
0
2
2
3
1
1
2
0
1
0
0
2
1
0
0
1
1
2
1
0
2
0
0
2
2
2
1
1
2
2
1
1
1
0
1
0
1
0
1
0
1
1
2
1
2
0
1
0
1
1
2
1
0
2
0
0
1
1
1
1
1
1
1
0
1
0
0
1
0
1
2
3
1
0
2
3
2
1
1
1
1
1
1
0
1
1
1
0
0
3
1
0
1
2
1
1
1
0
0
2
0
1
0
2
1
0
2
0
2
1
0
0
0
0
1
2
1
2
1
0
1
2
0
1
1
1
1
0
1
1
1
1
4
1
0
0
1
1
0
1
1
2
1
0
1
1
1
2
1
1
1
1
2
1
1
1
2
1
0
0
1
1
1
0
0
0
2
0
1
0
2
0
0
2
1
0
1
1
2
1
1
0
0
1
0
1
1
1
0
0
0
1
1
2
0
2
1
0
1
1
1
2
2
2
0
0
2
1
1
1
1
0
1
1
0
0
2
1
0
0
1
1
1
1
1
1
1
1
1
1
1
0
0
2
2
1
1
1
2
1
2
2
0
2
1
1
0
1
1
2
1
0
1
1
2
1
0
1
2
2
0
1
0
0
2
0
1
1
2
1
2
2
0
2
1
1
1
1
2
1
1
0
1
1
2
1
0
0
1
1
0
1
2
2
1
1
2
1
1
0
1
1
1
2
1
1
1
1
1
0
0
1
0
1
0
2
1
1
1
1
1
2
1
1
2
2
0
1
4
1
1
0
1
1
2
2
1
1
1
1
1
1
1
1
0
0
2
1
1
0
0
2
1
0
1
2
1
1
2
0
2
2
0
0
1
1
0
0
0
2
1
0
1
2
1
0
1
0
2
0
0
2
2
2
1
1
3
0
2
2
1
0
1
1
0
1
0
2
0
0
1
1
1
1
1
2
1
0
0
1
0
1
0
0
2
1
1
2
0
0
2
1
2
2
1
0
1
1
1
2
0
1
2
0
1
0
2
1
0
2
0
1
0
2
0
1
0
1
1
2
1
1
1
0
1
1
2
2
2
1
1
1
1
1
0
1
1
1
1
1
0
2
2
0
1
2
1
1
0
1
0
1
1
2
1
1
2
0
1
0
2
2
1
2
2
0
1
1
2
1
0
1
1
1
2
1
2
0
2
1
2
0
0
1
0
1
0
2
0
0
2
0
2
1
2
0
1
0
1
2
1
2
0
0
0
0
0
1
2
1
1
0
2
0
1
1
2
1
1
0
1
1
1
1
0
1
0
2
0
1
1
1
3
2
1
0
1
2
2
1
2
2
1
1
1
1
1
1
0
1
1
0
2
0
0
1
1
2
1
1
2
1
1
0
1
2
1
2
1
1
1
1
2
2
1
0
1
1
1
0
0
0
2
2
0
1
2
1
1
1
1
1
0
1
3
0
2
1
1
1
1
0
1
1
1
1
0
1
1
1
1
0
0
2
1
1
2
0
0
2
1
0
2
1
0
0
1
2
1
1
0
2
2
2
0
1
1
1
0
1
0
0
1
2
1
2
1
2
1
1
0
0
1
0
1
1
1
1
1
1
1
0
2
1
0
1
1
1
1
0
1
1
3
0
1
1
2
1
2
2
1
1
1
1
0
1
1
1
1
1
2
1
1
0
1
0
1
1
0
1
1
1
1
1
0
0
1
1
1
1
1
1
0
1
1
1
0
1
1
1
0
2
0
1
2
1
1
2
2
0
1
0
0
1
1
2
2
0
1
1
1
1
2
0
2
0
2
1
2
2
1
1
0
2
1
1
2
0
1
1
2
1
1
2
0
1
0
1
1
1
0
0
1
1
1
2
1
1
1
0
1
2
2
1
0
1
1
2
0
2
0
1
0
0
1
0
0
1
2
1
1
0
1
1
1
1
2
2
0
1
0
1
1
1
1
2
1
3
0
1
2
1
1
0
1
1
1
0
1
0
1
0
1
1
1
0
1
1
1
1
1
1
0
0
2
1
1
0
0
2
0
0
0
1
1
1
1
1
0
0
1
1
1
2
1
1
0
1
1
2
1
1
2
0
1
1
0
2
1
2
2
0
0
2
0
1
1
2
1
1
1
0
1
0
1
0
1
1
2
2
1
1
2
1
2
0
1
1
1
1
2
1
1
1
1
0
1
1
2
2
2
1
1
2
0
2
1
2
0
0
0
0
2
1
1
2
1
1
1
2
0
1
0
2
0
2
0
0
1
1
1
2
1
0
1
2
2
0
1
2
0
0
1
1
2
2
2
1
1
1
2
0
1
1
1
0
1
2
4
0
0
1
0
1
1
0
1
1
0
1
0
1
2
1
2
1
0
2
0
2
0
0
1
1
1
2
2
2
0
2
1
1
4
1
1
1
1
1
1
2
1
1
1
1
0
0
0
1
3
1
0
1
0
2
1
1
1
1
1
0
0
1
2
1
1
2
1
0
0
0
2
2
1
2
4
2
2
7
1
1
1
2
1
1
1
2
2
2
2
2
1
2
0
0
2
1
1
1
0
1
1
0
0
1
1
0
1
1
2
0
0
1
0
1
2
1
0
2
0
1
1
1
2
1
2
1
1
1
0
1
1
1
1
1
0
0
0
2
1
1
1
1
1
2
0
1
1
1
0
1
0
1
0
1
1
1
1
1
2
2
2
2
1
1
0
0
1
1
0
0
0
2
2
0
2
2
1
0
1
1
1
1
4
1
0
2
1
1
1
1
2
2
2
0
2
2
0
1
0
0
0
1
1
0
1
0
1
0
1
2
1
1
2
1
0
0
2
1
0
1
2
1
0
0
1
1
0
2
1
0
2
1
2
0
1
1
1
2
1
0
1
2
0
1
1
2
1
0
0
1
2
2
2
2
1
1
1
0
1
1
1
1
0
0
1
0
1
1
1
1
1
1
1
0
1
1
2
1
1
0
1
1
1
2
2
0
2
0
2
2
2
0
1
1
1
4
1
1
1
1
2
1
1
0
1
1
0
1
2
1
1
1
1
1
1
2
1
1
0
0
1
2
0
1
0
0
2
1
0
2
2
0
1
1
1
0
1
2
0
2
0
1
1
0
0
0
2
1
0
0
0
1
1
2
1
1
1
0
2
1
1
1
0
1
1
1
2
1
1
1
0
0
1
2
0
1
1
1
1
0
1
1
1
1
2
0
2
0
1
1
1
2
1
1
1
2
1
1
1
0
1
2
1
1
1
0
0
1
0
1
2
1
0
1
1
2
0
1
2
1
1
1
0
0
1
1
0
0
0
0
1
1
1
0
0
1
1
2
1
1
0
1
1
2
0
2
2
1
0
0
0
1
2
1
0
1
1
0
1
0
1
1
1
2
0
1
0
0
1
1
1
0
2
1
2
0
1
0
1
1
2
0
2
1
0
1
1
1
2
0
2
1
1
0
2
1
2
0
1
0
1
1
0
2
1
2
2
3
2
1
1
1
1
1
2
0
0
2
0
2
2
0
0
0
1
2
0
2
1
1
1
1
3
1
0
2
1
0
1
0
1
1
1
1
2
2
2
0
1
1
0
1
0
1
1
0
2
1
1
0
1
1
2
1
2
0
1
1
0
1
1
2
1
0
1
1
1
1
0
1
1
1
3
1
1
1
0
2
1
0
0
1
1
1
1
2
1
1
2
1
2
0
1
2
2
1
1
1
1
1
1
2
0
1
2
1
1
0
2
0
1
1
2
1
0
1
2
4
1
0
2
1
2
1
2
2
2
1
1
2
1
2
1
1
1
1
1
0
2
1
0
1
0
0
2
2
1
1
1
0
1
1
2
0
2
1
1
1
1
2
2
1
1
2
2
1
0
1
0
1
1
2
2
2
1
2
0
0
0
1
2
0
1
1
1
1
2
0
1
2
1
1
1
0
1
1
1
2
1
1
1
2
0
2
0
1
0
0
1
0
1
0
0
2
2
0
0
1
1
1
2
0
2
1
2
1
1
0
1
1
3
0
1
1
1
1
1
1
1
0
1
2
1
0
1
1
2
0
1
1
2
2
1
0
0
0
2
3
2
1
1
1
2
1
0
1
1
1
2
2
0
2
0
1
1
2
2
1
1
0
1
1
1
1
1
1
1
1
2
2
1
1
1
0
2
1
0
1
1
0
1
0
0
1
1
0
1
1
1
0
0
0
1
1
1
2
2
1
2
2
1
1
2
0
0
0
1
2
0
2
0
1
0
0
0
2
1
2
0
1
0
1
0
0
3
1
0
1
1
1
1
1
1
1
1
1
0
1
2
0
2
2
1
1
1
1
1
2
0
0
0
2
1
0
1
1
0
1
2
2
1
0
1
0
1
1
1
1
1
1
1
1
1
0
1
0
0
0
2
1
1
1
1
1
2
0
0
1
1
1
1
1
2
0
1
1
1
1
1
1
1
1
2
1
0
1
1
1
2
2
0
1
1
3
0
0
2
1
1
2
0
2
0
0
1
1
1
0
0
0
0
1
1
2
2
1
2
0
1
1
1
2
2
1
0
1
0
1
2
2
0
1
2
0
1
1
2
1
1
0
1
0
1
0
1
1
1
0
1
3
0
1
2
1
1
1
0
1
1
0
2
1
0
2
0
1
1
2
1
1
1
1
1
2
1
1
2
0
0
1
1
1
0
1
1
2
0
0
1
0
1
1
1
1
0
1
2
1
2
2
1
1
1
1
2
1
1
2
1
1
1
1
0
1
1
1
0
1
1
1
2
1
1
0
1
1
2
1
1
1
1
1
1
1
2
0
2
1
1
0
0
0
2
0
1
1
0
1
1
0
0
0
0
0
1
0
1
1
0
1
0
0
2
1
0
1
2
1
1
1
1
1
3
0
0
2
2
0
1
1
2
1
2
0
0
1
1
1
2
0
2
0
1
1
1
1
0
1
1
1
1
1
0
1
0
1
1
1
1
1
2
0
2
2
1
2
2
3
1
2
0
1
0
0
2
2
1
2
0
1
2
2
1
1
2
1
2
2
1
2
1
0
2
1
2
2
1
2
0
1
1
1
0
1
1
0
6
0
1
1
1
1
1
0
0
1
1
1
1
1
2
0
1
1
0
1
1
2
2
2
1
0
1
0
1
0
2
1
2
2
0
0
1
1
2
1
1
1
1
1
2
1
3
1
1
1
0
1
2
1
1
1
1
2
1
0
0
1
2
1
1
1
1
1
0
1
1
1
2
0
0
0
1
2
1
1
1
1
1
3
1
1
1
0
2
1
1
1
0
2
2
1
0
0
4
1
2
0
2
2
2
0
1
1
1
2
1
0
0
2
1
1
2
0
0
1
1
2
1
2
1
0
1
2
0
2
1
2
1
1
0
1
0
1
1
2
1
2
2
0
1
0
0
0
0
0
1
2
2
0
0
2
2
1
0
0
0
1
2
0
1
2
1
1
0
0
4
0
1
1
1
1
2
1
2
1
2
1
1
0
1
1
0
1
1
2
0
2
1
2
2
1
1
1
1
2
2
0
1
0
0
2
1
1
1
1
2
0
2
1
1
2
1
1
1
1
1
1
0
2
0
2
0
1
2
1
1
3
1
2
1
1
1
1
2
7
2
0
2
1
1
1
1
2
0
0
2
1
2
1
0
0
0
1
1
1
1
1
1
1
2
2
1
2
1
2
1
1
0
1
1
1
0
0
0
0
1
1
1
1
1
0
1
0
0
1
1
1
2
0
1
0
1
1
2
2
1
2
0
1
2
2
1
1
0
0
1
0
0
2
2
1
1
1
1
1
1
1
0
1
1
1
1
1
2
0
1
1
2
0
1
1
1
2
0
1
1
0
1
1
1
1
2
1
1
0
1
1
0
2
2
1
2
1
3
1
0
2
0
1
0
1
2
1
1
1
0
1
0
1
1
1
1
1
1
2
1
1
1
1
2
1
0
1
1
0
0
2
1
1
1
2
1
2
1
2
1
2
0
1
1
1
0
1
1
1
1
1
0
1
0
2
1
2
0
2
0
1
1
2
0
1
1
1
0
0
1
0
0
0
1
2
1
1
2
2
1
2
1
1
1
1
2
1
0
0
0
0
1
0
1
0
0
0
1
2
2
1
2
0
1
2
1
2
3
2
1
1
0
1
0
0
2
2
0
1
2
2
2
1
1
0
2
1
1
1
4
1
0
0
1
1
2
1
1
1
2
1
2
1
2
2
1
1
0
1
2
0
2
1
1
0
1
1
0
1
1
0
1
2
1
1
0
1
1
0
2
2
0
1
1
1
1
1
0
0
1
1
2
0
1
2
2
1
0
1
2
1
1
1
2
1
1
1
1
2
1
0
0
1
0
1
2
0
1
1
1
1
0
0
1
0
1
0
0
2
1
2
1
1
1
5
1
1
0
1
0
2
0
2
2
0
2
0
2
2
1
1
2
1
1
1
1
1
0
2
1
1
2
2
2
1
1
1
1
0
2
1
0
1
3
1
2
0
2
0
2
1
2
0
2
1
1
2
2
1
1
2
1
0
0
2
1
1
1
0
1
1
1
0
1
1
2
1
1
1
2
1
2
0
0
1
0
2
1
3
1
1
1
0
1
1
1
1
2
0
2
2
1
1
1
1
2
1
0
1
2
1
0
1
1
1
1
1
0
2
1
1
1
1
0
1
1
1
2
1
1
0
1
1
2
1
1
1
1
0
1
1
0
0
1
2
2
1
1
2
1
1
1
0
2
0
5
1
1
2
0
0
3
2
1
0
0
1
2
1
1
1
1
1
1
1
1
3
2
1
1
2
0
1
1
1
1
1
1
1
1
2
0
2
1
0
1
1
1
2
1
0
2
2
0
2
1
1
1
1
1
4
0
1
1
0
1
0
1
1
1
2
1
1
1
1
0
1
1
0
2
2
1
1
0
1
2
1
1
2
1
2
0
1
1
1
1
2
0
0
1
2
1
1
1
0
2
1
0
2
0
1
1
1
1
2
0
1
1
1
1
0
1
0
1
1
2
2
0
2
0
2
1
2
1
0
0
1
0
1
1
0
2
3
0
2
1
1
1
1
1
1
1
1
0
0
1
1
1
2
1
0
1
1
2
1
0
0
1
0
0
1
1
2
1
0
2
0
1
1
1
2
0
1
2
1
0
1
1
0
1
2
2
1
1
1
1
2
1
0
0
1
0
1
2
1
2
1
0
1
1
1
0
0
2
1
1
1
1
1
1
2
1
0
0
1
0
0
0
0
1
1
1
1
1
1
1
1
0
0
1
0
1
1
1
1
1
1
1
0
1
1
1
2
1
2
1
0
1
1
1
1
1
1
2
1
1
2
2
0
2
0
5
1
0
2
1
1
2
0
1
2
1
1
1
1
0
2
0
1
0
1
2
2
1
1
1
0
0
0
1
1
1
0
1
0
1
2
1
1
1
0
2
1
2
1
1
0
1
1
2
1
0
2
0
2
2
1
1
1
1
0
1
1
0
2
1
1
2
2
4
2
1
0
2
1
1
1
1
1
1
1
0
1
2
0
1
1
0
1
0
2
1
1
0
1
0
1
2
1
1
1
1
0
1
1
2
1
0
0
0
1
2
2
2
0
0
0
1
0
1
0
2
2
1
3
0
1
1
1
2
0
2
1
2
0
0
1
2
2
1
0
1
0
2
2
1
2
2
0
0
1
2
1
0
2
0
1
1
0
1
1
0
0
2
1
1
0
1
2
1
0
0
2
2
3
2
4
2
0
1
0
1
2
0
0
1
0
1
2
2
1
0
1
1
0
0
0
1
1
1
1
0
1
0
2
2
1
2
0
1
2
2
2
1
1
0
1
0
2
1
0
1
2
1
0
1
2
0
1
2
0
2
1
2
0
1
1
1
2
1
1
1
2
1
1
0
1
2
0
1
1
1
1
1
2
0
1
1
1
1
1
2
2
0
1
1
2
0
0
1
0
1
1
1
0
2
1
1
1
2
1
1
1
1
0
2
1
1
1
1
1
1
2
1
1
1
0
1
0
0
0
2
1
0
1
2
2
1
1
0
1
2
1
1
1
0
1
0
0
1
0
0
1
2
1
1
2
0
1
1
0
1
0
1
1
1
1
2
1
1
0
1
1
1
0
0
0
1
1
1
1
1
2
1
2
2
2
2
0
0
0
0
1
0
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
2
1
1
2
0
1
1
2
2
1
1
1
1
2
1
0
2
1
2
2
0
0
1
0
2
1
1
1
1
1
1
1
0
1
1
0
1
1
1
1
1
2
1
0
1
1
1
0
0
1
0
2
1
0
1
1
1
1
1
1
1
1
1
1
0
1
2
2
1
1
1
1
1
1
2
1
0
1
1
1
1
2
0
1
1
0
1
0
2
1
1
1
1
0
1
2
0
2
1
1
1
1
0
1
0
0
0
0
1
0
0
2
0
1
1
1
2
2
1
1
2
1
2
2
1
1
0
2
1
1
3
1
0
0
1
0
2
1
0
1
2
1
1
1
2
0
2
0
0
0
1
1
2
1
1
3
0
1
2
2
1
2
1
1
1
1
1
2
2
0
2
1
0
1
2
1
1
1
1
1
1
0
1
1
1
2
0
0
1
1
1
1
2
1
0
1
1
1
0
2
0
1
3
0
1
0
1
1
1
2
0
1
0
2
0
1
2
1
1
0
0
0
2
0
1
0
1
2
1
0
1
1
0
0
1
0
1
0
1
1
0
0
1
0
1
1
2
1
1
1
1
2
1
1
1
1
0
0
2
1
2
1
0
1
1
1
1
0
1
2
1
0
1
2
0
2
2
1
1
1
2
1
1
1
0
1
1
1
1
0
1
2
1
0
2
1
0
0
0
2
1
2
2
2
1
1
0
0
2
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
0
2
2
1
1
0
2
2
0
1
3
1
1
1
2
1
0
2
1
2
2
1
1
1
0
1
2
1
2
0
0
1
0
0
1
2
1
1
2
2
1
1
2
1
1
1
1
1
0
1
1
1
1
1
1
1
2
2
1
1
1
1
1
0
1
2
1
0
1
1
2
0
0
0
2
2
1
1
1
1
2
1
2
1
2
2
1
2
2
0
2
0
0
0
1
3
1
1
1
2
1
0
1
1
2
1
0
0
2
1
1
1
0
0
1
0
1
1
1
0
2
1
1
0
0
0
5
1
2
0
1
2
2
0
1
2
1
2
2
1
0
2
1
1
0
1
1
2
1
0
1
1
1
4
1
1
2
1
2
2
1
0
1
1
2
2
1
1
1
1
1
0
2
0
1
2
1
1
1
1
2
1
1
1
0
1
0
1
1
1
0
1
1
0
1
1
1
0
1
0
2
1
1
1
0
1
2
2
1
1
0
0
1
0
1
3
1
1
1
0
1
2
1
1
1
0
1
1
1
1
1
0
1
2
1
1
2
1
1
1
0
1
2
0
1
2
0
2
1
2
2
1
1
0
1
2
1
2
1
1
1
1
0
1
1
1
0
1
2
2
1
0
2
1
0
2
2
1
1
1
1
1
0
1
2
1
1
1
1
1
1
1
1
1
1
2
0
3
2
1
1
1
0
0
1
0
2
2
1
0
1
1
1
0
1
1
0
2
1
1
0
0
1
1
1
0
1
1
0
1
0
1
0
0
1
1
0
0
1
2
1
1
1
0
1
2
2
1
1
1
2
2
1
1
2
1
0
1
1
2
1
2
0
0
2
0
2
1
0
0
2
1
1
1
1
1
1
0
1
0
2
1
1
1
2
0
0
1
0
0
0
0
1
0
1
1
1
1
3
1
1
1
1
2
0
2
2
2
1
0
1
0
1
1
0
1
1
1
0
1
1
1
1
1
1
1
0
1
0
1
1
0
2
2
2
1
2
1
1
0
0
1
2
2
1
1
2
1
1
1
0
1
1
1
1
1
1
0
0
1
1
0
1
1
1
0
1
1
0
1
2
0
1
1
1
0
0
2
1
1
2
0
1
3
2
0
2
1
0
1
1
0
0
2
0
1
0
0
1
1
0
2
2
0
1
2
2
1
0
1
1
2
0
0
1
1
0
1
2
1
2
1
1
2
1
1
3
1
0
1
1
2
1
1
1
2
1
2
2
1
0
0
2
1
1
1
3
0
1
1
1
1
1
0
1
2
1
1
1
1
0
0
1
2
1
1
1
1
1
0
1
1
2
0
2
0
1
1
0
1
1
2
1
1
0
1
1
1
1
2
1
2
1
0
1
2
1
1
1
1
2
2
0
2
0
2
1
1
0
1
1
0
0
1
1
0
1
1
0
0
0
2
1
1
1
1
1
2
0
1
2
2
1
1
0
2
0
1
1
0
1
0
1
1
0
1
1
1
2
0
1
1
2
2
2
1
0
1
0
1
1
1
1
1
2
2
0
1
0
3
1
0
1
1
2
2
1
0
1
0
0
1
2
2
0
1
2
1
2
3
1
1
1
1
0
1
0
1
1
2
2
1
0
1
0
1
0
0
1
0
1
1
3
1
1
0
1
0
2
0
1
1
0
1
1
1
1
0
1
0
1
1
1
1
1
1
1
2
1
0
2
1
1
1
0
1
0
0
0
0
1
1
0
0
1
1
1
2
1
1
0
1
2
1
1
1
0
0
1
1
1
1
1
1
0
1
1
1
2
0
0
0
0
4
2
1
2
1
1
2
0
1
1
2
2
1
1
1
0
4
1
1
1
2
2
1
2
1
0
1
1
0
1
0
1
2
1
1
0
2
0
2
0
1
1
0
0
1
1
0
0
1
0
0
0
1
1
2
1
1
1
1
2
2
1
1
1
0
2
0
2
2
2
1
0
0
1
2
2
1
2
1
2
2
1
1
1
0
1
2
2
1
0
1
1
2
1
2
0
2
1
1
2
2
1
4
2
1
2
2
1
2
1
1
2
4
1
1
2
0
0
2
1
1
0
1
1
1
1
1
1
1
2
0
1
1
0
0
1
0
1
0
1
1
2
2
1
1
0
0
1
0
1
2
2
1
0
1
1
3
0
1
1
2
1
1
0
1
0
0
2
2
1
0
1
0
0
0
2
0
1
1
2
1
0
1
2
0
1
0
1
1
1
1
2
0
1
1
2
1
1
1
1
1
0
1
2
1
0
1
2
1
1
0
1
2
0
1
0
1
1
1
1
1
1
0
1
1
0
0
1
1
1
1
1
4
0
2
2
1
1
1
1
1
1
1
0
2
2
1
1
2
1
1
1
1
1
1
0
0
0
1
2
1
1
2
1
1
0
0
1
3
1
1
1
1
2
2
1
0
1
1
0
1
1
2
1
2
1
2
1
2
2
1
1
0
1
1
0
0
1
0
2
2
0
1
1
1
1
1
1
0
1
1
0
2
1
2
2
2
2
2
0
2
2
1
2
0
1
0
1
1
0
1
1
1
0
1
2
0
0
1
1
2
2
1
1
1
0
0
0
2
1
0
0
1
1
2
0
1
1
0
1
1
2
2
2
1
1
2
0
1
1
1
1
1
0
1
1
1
1
0
2
2
1
1
1
1
1
0
1
1
1
1
1
1
0
0
0
1
1
0
2
2
0
1
0
1
1
1
1
0
2
1
0
2
1
1
1
2
1
1
2
1
1
0
2
2
1
2
1
4
0
2
0
1
2
1
1
1
1
1
2
1
0
0
0
1
0
1
0
1
2
1
0
1
1
1
0
1
1
0
1
0
1
1
0
1
0
0
1
0
1
2
1
2
1
1
0
1
1
2
1
1
1
1
2
2
0
1
1
1
0
1
1
2
0
1
0
0
0
0
0
1
1
1
1
1
2
1
1
2
1
0
0
2
1
0
0
0
0
2
1
1
0
0
2
0
2
0
1
2
3
1
1
2
0
0
1
0
1
1
1
0
0
0
2
0
1
1
0
1
1
0
1
1
1
1
0
1
1
2
0
1
2
1
2
0
2
1
1
2
2
1
1
2
1
0
2
1
3
0
0
2
1
1
0
1
1
1
0
0
2
2
0
1
0
1
1
1
1
0
1
0
2
2
1
1
1
2
2
2
0
1
2
0
1
0
0
2
1
0
2
2
1
2
0
1
1
1
2
0
1
0
0
0
2
2
1
1
0
1
1
2
0
1
1
1
1
2
0
1
1
0
2
2
2
1
1
2
1
1
2
1
1
1
2
1
1
1
2
0
0
1
2
1
1
1
0
1
0
1
1
1
1
1
2
1
2
1
0
1
0
0
1
1
2
2
1
1
1
2
1
1
2
0
1
1
0
0
2
1
2
1
0
1
0
0
1
1
1
1
1
1
2
1
1
1
1
1
2
0
3
1
0
1
1
1
0
3
1
0
1
0
1
1
2
0
0
1
1
1
0
1
0
3
1
2
2
2
2
1
0
0
1
1
1
1
1
2
2
0
1
1
0
2
0
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
2
1
0
1
1
1
1
0
1
2
2
1
0
0
1
0
2
2
1
2
1
2
1
1
0
2
1
0
2
1
1
1
2
0
1
1
1
0
1
1
0
2
2
2
2
2
1
2
1
0
1
0
2
1
0
2
1
1
2
1
2
1
1
3
1
1
1
1
3
1
1
1
1
1
1
0
1
0
2
2
2
0
1
2
1
1
1
0
1
0
1
0
1
2
1
2
3
1
1
0
1
1
2
0
1
1
1
1
1
1
0
2
2
1
0
0
1
1
2
1
0
1
1
1
2
2
1
1
0
1
0
0
1
0
1
1
0
1
1
1
0
2
0
1
1
1
1
0
1
1
1
1
0
2
1
1
1
1
1
1
1
0
1
1
1
0
0
3
1
0
1
0
1
2
1
0
0
1
2
1
1
2
1
0
1
1
2
1
2
2
0
1
1
1
0
0
1
1
0
1
2
0
0
0
2
1
1
0
1
1
2
1
0
2
2
0
1
2
1
1
1
2
1
0
1
2
1
1
1
2
2
2
1
1
1
2
1
1
0
2
0
0
1
1
0
1
1
1
1
1
1
1
1
0
2
0
1
0
0
2
1
0
1
1
1
0
2
0
0
0
1
3
1
2
1
2
1
2
2
1
4
2
1
1
2
2
1
0
0
1
0
1
2
1
0
1
1
2
1
2
1
0
2
0
1
2
0
1
1
1
1
0
1
1
3
1
1
1
2
2
1
2
1
1
0
0
1
1
0
2
1
1
0
1
1
2
1
1
1
1
1
1
2
3
1
1
0
0
2
1
1
2
0
1
1
2
1
1
0
1
1
1
2
1
0
1
0
2
1
0
1
2
1
1
1
1
1
1
1
1
2
2
1
1
2
1
0
0
2
1
1
1
0
2
0
2
2
1
1
0
1
1
1
1
2
0
0
0
1
0
1
2
1
1
0
2
2
2
2
1
0
1
1
2
2
0
1
1
1
2
1
0
1
2
1
2
0
1
1
0
0
1
1
0
0
1
0
2
0
1
0
1
1
2
1
1
0
0
1
0
0
1
1
1
0
1
0
0
0
0
1
2
2
0
1
1
1
0
1
1
0
0
2
1
0
0
2
1
1
1
2
2
0
1
3
2
0
2
1
1
1
1
0
1
1
1
1
1
1
3
2
1
0
0
0
0
1
1
1
2
1
1
1
0
1
1
1
2
2
1
0
0
1
0
1
2
1
0
0
1
1
1
2
1
1
0
2
1
2
1
1
1
0
1
0
0
1
1
0
0
2
1
2
1
1
2
1
0
0
0
1
0
1
1
0
0
0
0
2
2
1
1
0
1
2
2
3
0
0
1
1
1
0
1
1
1
0
0
0
1
1
2
0
1
1
0
1
0
1
0
1
1
1
1
0
1
2
0
0
1
1
0
1
2
1
0
1
2
1
1
1
2
1
1
0
1
1
0
1
2
1
1
0
2
1
1
0
2
0
2
1
2
2
1
2
1
1
1
0
0
1
2
1
0
1
2
2
1
1
1
2
2
0
1
0
1
1
0
1
1
1
0
1
1
1
2
0
0
0
1
1
0
1
1
1
1
0
1
1
0
1
2
2
1
1
0
2
0
1
2
1
1
1
1
0
1
0
2
1
1
1
1
1
1
1
0
1
0
1
1
2
2
1
0
1
1
1
2
1
1
1
1
2
1
1
0
1
2
1
0
2
2
1
1
2
0
2
1
0
1
1
1
0
1
2
2
0
0
0
2
2
1
1
1
0
2
1
1
0
2
0
1
2
1
1
1
2
1
1
1
2
1
1
2
1
1
2
0
1
1
1
1
0
1
2
2
1
0
1
1
0
0
1
0
1
2
1
2
1
1
1
1
0
3
1
1
0
1
1
0
2
0
2
1
2
1
1
0
2
1
1
2
1
0
1
2
1
1
1
1
0
0
0
2
2
2
1
0
1
1
1
1
0
1
1
1
2
1
2
2
2
0
2
2
1
1
2
1
2
1
1
1
1
3
1
1
2
0
1
1
1
2
0
1
1
1
2
0
3
1
1
1
1
0
0
3
1
1
1
1
1
2
1
2
1
1
0
1
1
1
1
2
1
1
1
0
1
1
1
1
1
1
1
1
2
1
1
2
1
2
0
0
1
1
1
0
1
1
2
0
1
1
0
1
0
1
2
1
0
0
0
0
2
1
1
1
1
1
1
1
1
2
0
1
1
2
3
2
1
2
2
2
1
2
1
1
1
0
0
1
0
0
1
0
1
1
2
1
1
1
0
0
0
0
2
0
2
1
2
1
1
2
2
2
1
0
0
1
1
0
1
3
1
1
1
0
2
0
1
0
2
0
0
1
1
2
1
1
1
1
1
0
0
1
0
1
0
1
2
0
1
1
3
1
1
1
1
0
2
1
1
2
0
1
1
2
0
0
1
0
1
2
1
1
1
1
0
2
1
0
2
1
1
0
2
1
1
1
0
2
2
1
1
0
1
0
2
0
0
1
0
2
3
0
0
0
1
1
2
0
1
2
1
2
0
2
2
2
1
1
0
1
1
1
2
2
1
1
0
1
0
3
0
0
1
2
2
0
2
2
2
1
1
1
0
0
1
1
1
1
1
1
1
0
1
1
2
1
1
1
2
1
0
0
1
1
1
1
1
1
0
1
2
1
2
2
0
2
1
1
1
0
1
0
0
2
0
0
1
1
1
1
1
1
1
0
0
0
1
1
2
0
1
1
1
1
1
1
1
2
0
2
0
2
1
0
1
1
1
3
2
0
2
1
1
1
1
0
0
1
2
0
0
1
1
2
3
0
2
1
0
1
0
0
2
1
0
1
0
2
0
1
2
2
0
1
1
2
0
1
1
1
0
1
0
2
0
2
1
3
1
2
2
1
2
1
1
1
1
0
1
2
2
0
0
0
0
1
1
1
1
3
1
0
2
4
0
2
0
2
1
1
1
1
1
2
0
1
2
1
1
1
1
0
0
1
1
1
0
2
1
1
0
1
2
1
2
1
1
0
0
1
0
1
1
1
2
2
1
2
1
2
1
2
1
2
1
1
1
1
1
1
2
1
2
1
1
0
1
1
1
0
2
1
1
1
0
1
0
0
0
1
1
1
0
2
1
1
1
0
1
0
0
2
1
2
0
2
1
1
1
1
2
1
2
1
1
2
1
1
2
0
2
0
2
2
2
1
1
0
1
0
2
1
2
3
1
1
1
1
0
1
1
1
1
2
1
1
2
2
1
2
2
1
1
1
2
1
1
1
2
1
0
2
0
1
1
1
0
2
1
2
2
1
2
0
0
0
1
1
5
1
0
1
0
0
1
1
2
1
1
1
0
1
1
1
1
0
2
2
1
2
0
1
1
0
1
2
1
1
1
1
2
1
1
1
0
2
1
3
1
1
2
1
1
0
1
2
1
0
0
1
0
1
1
2
0
2
1
1
0
2
1
1
1
1
1
0
1
1
0
1
1
1
1
2
1
2
2
1
1
1
1
1
1
1
0
1
1
2
1
1
1
2
0
1
1
1
1
1
0
0
0
1
2
1
1
0
0
2
1
1
0
1
1
1
1
1
0
0
1
1
2
2
2
1
1
1
1
1
2
1
1
1
1
1
0
2
2
0
1
1
1
0
1
1
0
2
1
1
0
0
0
1
0
0
1
2
1
1
1
2
2
2
1
2
0
1
2
2
1
2
1
0
1
1
0
2
1
0
0
0
1
1
2
1
0
1
1
0
1
1
1
1
1
2
0
1
0
1
0
0
1
0
1
0
2
0
1
1
1
1
2
0
2
1
0
2
1
2
1
0
1
2
1
0
0
0
0
2
0
0
1
1
1
2
2
2
2
1
1
1
2
1
1
2
2
1
2
1
1
2
1
0
1
1
2
1
1
2
1
1
1
1
2
0
0
0
0
0
1
0
2
0
1
1
1
2
2
1
0
1
2
2
0
1
0
0
0
1
1
1
1
1
1
0
3
1
2
1
1
0
1
1
0
1
0
1
2
1
1
1
1
1
1
2
1
0
2
1
1
0
0
0
2
0
0
1
0
1
1
0
0
1
1
1
0
0
0
0
0
0
1
1
0
1
2
1
0
0
2
0
1
1
1
1
1
1
2
1
1
0
0
1
2
1
1
1
1
0
1
1
1
0
1
1
2
2
0
2
1
2
1
1
1
0
0
1
1
2
2
1
1
3
1
2
1
2
1
1
1
2
0
0
1
1
1
1
1
0
2
0
1
2
1
1
1
3
2
1
0
1
0
2
0
1
1
3
1
1
0
1
1
1
5
0
1
0
1
2
0
1
1
1
0
0
1
0
1
0
2
2
1
2
0
1
1
2
0
0
1
2
2
0
1
0
0
1
0
1
0
1
0
1
3
1
0
0
0
1
1
1
2
0
2
1
0
1
2
3
0
0
1
1
0
1
1
1
0
2
1
1
0
1
0
1
0
1
0
2
1
1
2
1
1
1
0
0
0
1
3
1
1
1
0
1
0
1
1
2
1
1
0
3
0
1
1
2
0
2
1
1
1
0
1
1
1
1
1
1
1
1
1
2
0
1
1
1
1
1
2
0
2
2
2
1
1
1
1
1
1
2
1
2
1
1
1
1
2
2
1
0
2
1
1
0
2
1
0
2
1
1
1
0
0
0
2
0
1
1
1
2
1
1
2
0
1
1
0
1
1
1
2
1
0
0
2
0
0
1
1
2
2
1
0
0
2
2
1
2
0
1
0
1
2
1
0
0
0
1
0
2
1
1
2
2
1
1
2
0
2
1
1
1
2
1
2
1
0
1
2
1
2
1
2
2
0
1
1
1
0
0
0
2
1
1
1
1
0
1
1
2
0
1
2
1
0
1
3
1
1
1
1
2
1
2
0
0
1
1
1
1
1
1
1
1
1
0
1
1
1
1
0
2
1
0
0
0
1
1
1
1
0
0
1
1
2
2
1
1
0
1
0
1
1
3
1
0
1
1
0
1
1
0
1
2
0
1
2
1
2
0
0
1
2
1
2
1
2
0
0
1
2
1
1
1
0
1
0
1
1
0
0
0
1
0
1
1
2
0
1
0
1
2
1
0
0
1
0
1
2
1
1
1
1
3
0
1
1
1
0
2
1
1
2
1
2
0
2
2
0
1
2
1
2
0
0
1
1
0
0
1
1
2
2
0
0
1
1
2
0
1
0
1
1
1
2
0
0
2
2
1
2
1
0
2
0
1
1
1
1
1
1
0
1
1
2
2
2
1
1
1
0
2
1
1
0
1
1
1
2
0
0
0
1
2
2
2
1
1
0
1
2
1
2
1
1
1
1
0
0
0
0
1
1
1
1
2
2
2
2
3
2
0
1
1
2
1
1
1
1
1
1
1
1
1
1
0
1
1
1
0
1
0
1
1
1
1
2
0
1
0
2
2
0
1
1
1
0
0
2
1
1
1
0
1
1
1
2
0
0
0
0
0
1
0
1
2
0
0
1
1
0
2
1
1
2
1
1
2
0
1
1
1
2
2
0
1
2
0
1
1
3
1
1
1
1
2
1
1
1
2
2
0
0
0
1
1
1
1
2
0
1
1
0
2
1
0
1
0
1
1
1
0
2
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
0
0
1
0
0
1
0
1
1
2
1
0
1
1
0
0
0
1
1
0
0
2
1
1
1
2
1
2
0
1
1
1
1
0
1
0
1
2
0
1
1
1
2
1
1
1
1
0
1
1
0
0
1
1
0
1
0
1
1
2
2
2
0
1
1
0
1
2
1
2
1
1
0
0
1
0
2
1
1
1
1
0
1
0
0
1
1
2
1
1
0
2
0
2
2
2
2
1
1
2
0
2
0
1
0
2
1
0
1
2
2
0
1
1
2
0
2
1
0
0
2
0
1
1
2
1
0
1
1
1
0
0
2
0
1
1
1
0
1
1
2
1
1
0
0
0
1
1
1
2
2
2
1
1
2
0
0
1
1
0
2
1
2
2
1
1
1
1
0
2
2
1
1
2
1
2
1
0
1
1
2
1
1
1
1
1
0
1
2
1
1
0
1
2
1
0
0
0
0
1
1
0
1
1
2
1
1
0
2
2
0
0
4
1
1
1
0
1
1
0
1
0
1
2
2
1
1
0
1
1
0
2
1
0
0
1
1
0
0
1
0
1
1
0
1
2
2
1
1
0
1
1
1
1
1
1
1
1
0
1
2
1
0
0
1
0
0
1
2
2
1
1
0
1
0
1
1
2
1
0
1
0
0
1
1
0
1
1
1
1
1
1
0
0
2
1
2
1
0
1
1
2
0
1
1
1
0
1
1
0
0
1
0
1
1
0
0
2
1
0
3
2
1
1
2
0
1
1
0
0
1
0
1
1
1
0
0
2
0
1
1
0
1
2
1
1
2
2
0
1
0
0
2
1
2
2
1
2
1
1
2
1
0
1
1
0
1
1
1
2
1
2
1
1
2
0
1
1
0
1
0
1
1
1
0
1
0
2
1
0
0
1
2
1
0
1
2
1
1
1
1
0
0
1
0
1
1
0
1
2
1
2
0
1
1
2
0
1
2
0
1
1
2
2
1
2
0
1
0
1
2
2
1
1
0
1
2
1
0
0
0
1
0
1
1
2
0
1
1
1
2
1
1
1
2
0
2
2
2
1
1
2
0
1
1
0
0
2
1
1
1
1
1
2
1
1
1
2
1
2
1
2
0
1
1
0
1
1
1
0
0
1
1
1
0
0
1
2
2
1
1
1
2
1
0
0
2
2
1
2
0
1
1
0
1
0
0
1
2
2
0
1
1
2
1
0
1
1
0
1
1
2
1
2
0
1
1
2
0
0
0
1
2
0
0
1
2
1
1
1
0
1
0
1
0
1
1
1
1
0
0
1
0
1
1
1
1
1
0
1
2
0
2
1
2
0
1
0
2
1
2
0
0
0
0
0
2
2
1
2
2
1
0
2
1
1
2
0
1
0
1
1
2
0
1
1
0
1
2
0
1
1
1
1
0
1
1
2
1
1
1
0
2
1
0
0
0
0
2
2
1
1
1
1
1
1
1
0
0
1
0
2
1
1
1
2
1
2
0
0
1
0
0
1
2
0
4
1
0
0
0
0
2
1
0
2
1
1
1
2
1
1
1
1
1
1
1
0
1
0
2
1
2
0
2
1
0
1
0
0
1
1
0
2
1
1
1
1
1
0
1
1
0
2
2
0
2
0
0
2
1
1
2
0
0
0
0
2
1
1
1
1
2
0
2
1
2
2
0
1
1
0
2
1
1
1
1
0
0
1
1
1
1
1
0
0
2
0
2
0
0
0
2
1
1
2
1
0
1
2
2
2
2
0
1
0
0
0
2
1
0
2
1
1
0
2
1
0
1
0
1
1
1
1
0
1
1
0
2
1
1
2
1
0
1
1
1
0
1
0
0
1
1
2
2
2
0
2
0
0
1
0
1
3
1
1
1
1
0
0
0
2
0
0
1
1
1
1
1
2
1
1
0
1
1
1
2
0
1
3
2
1
1
1
0
1
1
1
2
0
1
1
1
1
1
0
1
1
2
0
1
1
1
2
2
2
1
1
2
1
1
2
2
1
1
1
1
2
1
0
1
2
2
1
2
1
0
1
1
0
0
1
1
1
1
1
1
0
1
0
2
2
2
1
1
2
1
1
0
1
1
1
0
0
2
0
1
0
0
1
0
2
2
1
1
1
1
0
1
1
1
2
1
2
2
1
1
2
1
0
0
2
2
0
2
0
1
2
1
0
1
2
1
0
2
0
1
2
2
0
1
1
1
2
2
2
1
0
2
0
2
2
2
1
1
2
2
1
0
0
1
0
0
2
0
0
3
0
0
1
1
2
1
2
2
1
1
1
0
1
2
2
1
1
1
2
1
1
1
2
0
0
0
1
1
1
1
1
0
1
1
1
1
0
0
2
2
1
2
0
0
0
2
1
1
1
0
1
1
1
1
0
1
0
2
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
0
1
0
2
1
1
1
1
1
0
1
1
2
1
1
2
0
0
0
1
1
2
2
0
2
1
1
1
1
2
1
1
1
1
0
2
1
2
1
1
0
1
1
1
1
1
1
2
0
1
0
0
1
2
1
1
2
1
1
2
0
2
2
0
1
0
1
1
2
1
0
1
2
1
2
1
1
2
1
2
1
2
0
0
1
0
0
2
1
1
1
2
1
1
1
0
1
0
2
1
1
2
1
1
1
0
0
0
1
1
0
1
0
0
1
2
2
1
1
0
0
1
2
1
1
2
2
1
1
1
1
1
1
0
0
0
1
2
0
1
0
1
2
2
1
1
0
0
1
0
0
2
1
0
0
1
2
1
0
1
2
0
0
1
1
2
1
1
1
0
1
1
2
0
2
0
0
0
1
1
0
1
2
1
1
1
2
0
0
1
1
1
1
0
1
0
2
2
1
2
1
1
1
1
1
2
0
1
1
2
0
2
0
1
1
1
2
1
1
2
1
1
1
2
0
2
0
0
0
1
1
1
0
1
0
1
2
1
1
1
1
2
1
1
2
2
1
0
2
1
2
1
1
0
0
2
2
1
1
0
1
2
2
1
2
1
1
0
1
0
1
1
0
1
0
0
2
1
1
1
2
1
1
2
1
2
2
0
1
2
2
0
1
0
2
2
1
0
2
2
2
0
0
1
1
1
0
0
1
1
1
1
1
2
0
1
0
2
2
2
1
2
1
1
0
2
2
2
2
1
1
0
4
1
1
1
2
2
1
1
1
1
2
0
1
0
2
1
1
1
2
1
1
2
0
1
1
1
1
1
0
2
0
1
0
2
1
1
0
1
1
0
1
1
1
2
0
2
0
1
1
1
1
2
1
2
0
1
0
1
2
1
1
1
1
1
0
1
1
2
2
2
1
1
1
1
1
1
1
0
1
1
0
0
2
3
2
0
1
1
0
0
1
1
1
1
1
0
1
1
0
1
1
0
1
2
1
0
1
1
1
0
1
1
2
2
0
2
0
1
2
1
2
1
1
1
1
1
2
1
1
2
0
1
1
0
1
1
1
0
0
1
0
2
3
4
1
1
2
3
1
1
1
0
1
0
1
1
1
1
1
1
1
1
1
3
2
1
1
0
2
2
1
1
1
1
1
1
2
0
0
1
2
1
2
1
1
1
1
2
0
1
1
1
0
1
1
1
2
0
1
0
1
0
1
1
1
1
2
1
2
1
1
1
0
1
1
0
0
2
2
1
1
1
2
1
2
0
1
2
0
2
2
2
1
1
1
0
1
1
1
1
1
2
0
1
0
0
2
1
1
1
2
1
0
1
1
0
2
0
2
1
1
0
0
1
1
0
0
2
1
2
2
1
0
2
0
1
1
0
0
0
1
2
1
2
1
1
0
1
3
2
1
3
0
1
2
1
2
1
1
1
2
0
0
0
0
0
0
1
1
0
1
0
1
1
1
1
1
1
0
2
1
2
1
0
1
0
1
0
1
0
0
1
1
1
0
1
1
1
1
2
1
2
1
1
2
1
1
0
2
1
1
1
1
0
1
6
0
2
2
1
0
0
1
1
1
1
1
2
1
2
1
1
2
1
0
1
0
1
0
1
1
1
1
2
1
1
2
1
1
2
2
1
1
0
1
0
1
1
1
0
2
1
2
0
2
0
1
2
1
1
0
2
0
1
0
0
0
0
0
2
1
1
0
2
2
0
2
0
0
1
2
1
0
0
1
0
1
0
2
0
2
1
1
1
1
0
2
0
2
1
0
1
2
1
0
1
1
2
1
1
1
1
0
1
1
1
1
1
2
2
1
1
1
1
1
1
1
0
0
0
1
1
1
1
1
2
1
1
0
1
1
0
1
1
0
1
1
1
1
2
2
0
2
1
0
0
1
1
1
0
0
1
2
2
1
1
1
0
2
1
1
0
1
1
1
1
1
0
2
0
1
1
2
1
2
1
1
1
1
2
0
1
1
2
1
1
1
0
1
1
1
2
0
1
1
1
0
2
2
1
1
1
2
2
1
2
2
0
0
2
1
0
1
2
1
1
0
0
2
2
2
0
1
1
0
0
0
1
0
1
2
0
0
1
1
1
1
2
1
0
1
1
0
0
0
1
2
3
0
2
1
1
2
1
1
1
0
0
2
1
0
1
1
1
2
2
0
2
2
1
2
1
0
2
2
1
1
2
1
1
1
1
2
2
1
1
1
0
2
1
2
2
4
2
1
1
2
1
1
1
2
1
0
2
2
1
1
1
0
0
0
1
2
1
0
1
1
2
1
1
2
1
0
1
1
1
1
0
0
2
0
1
1
1
1
2
2
2
1
1
2
1
0
0
1
0
1
1
0
1
1
0
1
0
2
2
1
1
1
1
1
1
2
2
1
2
1
1
2
2
2
2
1
1
1
1
2
2
1
1
1
0
1
0
1
1
1
3
2
0
0
1
1
0
1
2
1
0
1
1
1
1
0
0
0
1
1
1
1
1
1
0
0
1
1
0
1
3
2
1
2
0
0
1
2
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
0
1
2
2
2
1
2
0
1
0
1
2
1
1
4
1
0
0
0
2
1
2
0
1
1
1
1
2
1
1
1
3
1
2
2
0
0
2
1
0
1
1
1
0
1
1
1
1
0
1
1
1
1
1
2
1
0
1
1
2
1
0
0
0
1
2
1
1
1
2
1
1
3
0
2
1
0
0
1
0
2
1
2
1
1
1
2
0
0
0
0
2
1
2
2
1
1
1
1
0
0
1
0
1
0
1
1
1
1
0
2
0
1
1
0
2
0
2
1
1
1
4
2
1
1
1
2
1
1
2
0
2
1
1
0
2
1
0
1
1
1
2
1
1
0
0
1
0
0
1
1
2
0
3
1
1
1
1
0
0
1
0
2
1
0
0
1
2
1
0
4
1
0
1
0
2
3
0
1
1
1
0
1
0
1
2
2
0
2
0
0
2
0
0
1
2
2
3
1
2
1
2
1
1
0
5
2
1
0
2
1
1
1
1
1
1
1
1
1
2
1
1
0
2
1
3
1
1
0
1
1
1
1
1
2
1
2
1
0
2
0
1
1
1
2
0
0
2
0
1
0
1
1
1
0
1
2
1
0
1
2
1
2
2
1
1
1
2
2
1
1
0
1
0
0
1
2
3
1
1
1
1
2
1
0
1
1
1
1
2
0
0
1
1
0
0
0
1
1
2
2
4
0
0
0
1
2
1
2
0
1
1
1
0
1
1
2
1
1
1
1
1
1
1
1
0
1
0
1
1
1
2
1
1
0
0
1
0
1
1
1
1
2
1
1
0
0
0
1
1
2
0
1
1
2
2
1
2
1
0
2
0
2
1
2
1
0
1
1
1
1
1
0
1
1
2
2
2
0
1
0
1
1
1
0
1
1
1
1
1
0
2
0
2
2
0
1
1
0
1
1
1
0
1
1
1
2
1
1
1
1
0
1
1
1
2
1
2
1
0
1
0
2
2
2
1
2
1
1
1
1
1
0
1
1
1
1
1
2
0
2
2
0
2
1
1
1
2
1
2
0
1
0
1
1
2
0
1
0
2
3
1
1
1
1
2
0
1
3
0
1
1
0
1
1
1
2
1
2
0
1
1
1
1
1
1
2
0
1
1
2
1
1
1
0
1
1
1
1
0
2
5
2
1
1
1
1
1
0
0
1
1
1
0
1
2
1
1
0
1
2
0
1
0
1
2
1
0
1
1
0
2
1
1
0
2
1
1
2
1
1
1
1
2
1
0
0
2
2
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
0
1
2
0
3
1
1
1
0
2
1
1
1
2
1
0
1
2
5
1
1
1
0
1
1
1
1
0
0
2
1
1
1
1
1
1
1
0
1
1
1
0
2
2
0
1
1
1
1
0
1
1
1
2
1
0
1
1
1
0
1
1
1
2
1
0
1
1
1
0
1
1
0
2
1
0
1
1
1
2
1
1
2
1
1
2
1
2
1
1
0
0
2
0
2
1
1
1
1
0
2
0
0
1
1
1
2
0
0
1
1
1
2
0
1
1
2
0
1
2
1
1
1
2
0
1
1
1
1
1
1
1
0
1
1
0
0
2
1
2
0
1
1
0
1
0
1
2
1
0
1
2
1
1
1
0
1
1
1
1
1
1
1
1
1
1
0
0
1
1
0
2
1
0
1
1
1
0
2
1
1
1
1
1
1
0
0
2
1
0
0
0
1
0
1
0
1
1
1
1
1
1
0
1
2
2
0
1
2
2
0
2
1
1
1
1
1
1
0
2
2
1
1
0
0
2
0
1
1
1
0
0
1
2
1
0
1
1
2
1
0
1
2
1
0
2
0
0
0
1
1
0
0
0
0
1
1
2
0
1
0
1
1
1
1
1
1
2
0
2
2
1
0
1
0
0
1
1
2
1
0
0
2
0
1
0
1
1
0
0
1
1
1
1
0
1
0
0
1
1
1
1
0
1
0
1
2
1
1
1
2
1
2
1
2
0
2
1
2
2
0
2
1
0
0
1
1
1
2
1
1
1
0
1
2
2
0
1
1
2
1
2
2
0
1
2
1
1
2
2
1
1
1
2
1
2
1
2
2
1
1
2
1
1
2
1
2
1
1
1
1
0
1
0
0
1
1
2
1
1
3
1
0
0
2
1
1
0
1
1
2
0
1
0
0
1
1
0
0
1
1
1
1
0
0
1
0
0
2
1
1
0
1
2
1
1
1
1
1
0
0
0
1
0
1
0
1
1
1
0
0
2
1
2
2
1
1
2
1
0
0
1
6
1
1
2
0
2
1
2
1
1
0
1
1
1
1
2
1
0
2
1
1
2
1
0
1
0
1
1
1
0
1
1
1
2
1
3
1
1
2
0
1
1
0
0
1
0
0
1
1
2
2
1
0
1
0
1
1
1
1
1
3
0
3
1
1
2
1
2
1
1
2
2
0
0
1
1
1
1
1
1
0
2
2
1
1
1
0
0
1
0
1
0
2
2
0
1
1
1
2
1
1
1
1
1
0
1
1
0
2
1
0
0
2
1
1
0
1
1
1
0
2
0
0
0
1
1
0
2
1
1
0
1
2
1
1
1
0
1
1
0
2
0
1
1
2
2
2
1
0
0
1
2
1
0
2
2
2
1
1
2
0
0
0
1
1
1
1
1
1
1
1
1
2
0
0
2
2
0
0
1
1
1
1
2
1
0
1
1
1
1
1
1
0
1
1
2
2
1
1
1
2
0
1
1
2
1
1
1
4
1
2
1
0
1
0
2
0
1
1
0
2
0
1
1
0
0
1
1
2
0
0
0
1
1
1
2
1
0
1
0
2
1
0
1
1
2
2
0
1
1
0
0
0
1
1
0
0
0
2
1
1
1
1
0
1
0
0
1
1
2
1
1
2
1
2
0
1
1
1
0
0
0
1
2
1
1
1
0
0
1
0
0
0
2
1
1
0
1
1
1
1
1
1
1
1
1
1
1
0
1
1
2
1
1
1
1
0
1
1
1
1
1
1
1
0
1
1
1
1
2
1
1
1
0
0
1
1
1
1
1
2
1
0
2
1
2
2
1
2
2
0
1
0
1
1
0
1
1
1
1
1
1
1
1
1
2
2
0
1
2
0
1
0
1
1
0
1
1
1
1
1
0
2
2
2
2
1
2
0
2
1
1
2
1
0
1
0
0
1
2
1
1
1
2
2
2
1
0
1
1
0
1
1
1
1
1
2
1
1
2
2
2
2
1
1
1
0
2
0
2
2
1
0
1
1
1
0
2
2
1
2
0
1
1
1
1
0
2
1
1
1
1
1
0
2
1
1
1
1
5
1
1
0
0
0
0
1
1
1
1
0
0
1
1
1
0
1
1
1
1
2
1
1
1
2
1
1
0
3
0
2
2
1
2
1
1
1
2
0
0
2
1
1
1
2
2
1
1
1
1
1
1
2
2
2
3
2
1
1
1
0
1
1
2
1
1
1
2
0
1
1
2
0
1
2
2
1
1
0
0
1
1
1
2
2
1
1
1
0
1
2
0
1
3
1
1
0
0
0
0
1
1
0
2
0
1
2
1
1
0
1
1
1
0
1
2
1
2
1
0
1
2
0
0
2
2
1
1
0
0
2
1
1
1
1
1
1
4
1
1
1
1
1
0
1
1
1
1
1
1
2
2
1
1
1
2
1
1
0
1
1
1
1
2
2
1
2
1
0
2
1
1
1
0
0
1
2
0
1
2
1
2
0
2
1
0
0
1
1
1
1
2
1
1
1
0
2
1
1
2
2
0
1
1
1
0
1
0
0
0
0
0
0
1
1
1
1
1
1
1
0
2
1
1
1
1
1
1
0
1
1
1
1
1
2
1
1
1
1
1
2
1
3
1
1
1
2
1
2
2
2
1
1
0
1
1
1
2
1
0
1
0
2
1
1
1
1
1
1
1
0
1
1
1
0
1
1
1
0
1
0
2
2
2
3
0
1
0
0
2
2
1
1
1
1
0
0
2
1
2
1
2
1
2
1
0
0
2
1
1
1
1
1
0
1
3
0
1
1
0
1
0
0
1
1
2
2
1
1
1
2
0
1
0
0
1
2
0
1
0
1
0
2
2
2
1
1
2
1
2
0
0
1
0
0
1
1
0
0
1
1
0
1
1
1
0
1
0
2
1
1
2
1
1
1
0
1
2
2
1
1
0
2
0
1
0
2
2
1
1
2
0
2
2
2
0
1
0
1
0
2
2
1
1
1
2
0
2
0
1
0
2
1
1
2
1
1
2
1
1
1
1
0
2
0
1
2
1
2
0
2
1
3
0
0
2
1
1
0
1
2
1
0
0
1
7
1
1
2
2
1
0
0
2
1
1
0
1
2
1
2
1
1
0
1
1
1
1
0
1
3
2
2
1
1
1
1
2
1
1
2
1
1
2
2
2
1
0
1
1
1
0
0
0
1
0
2
2
1
1
3
0
5
1
1
2
1
0
2
2
1
2
1
1
1
0
1
1
1
0
0
0
0
0
1
2
1
1
1
2
1
1
1
2
1
0
1
1
1
1
1
0
1
1
1
2
1
1
0
0
2
1
0
0
2
2
1
0
0
2
2
0
1
2
1
0
0
1
1
0
0
0
2
1
1
1
0
1
2
1
1
0
1
2
2
0
1
1
2
2
1
1
0
1
0
2
1
1
1
1
0
2
1
2
2
1
0
2
1
0
0
1
1
0
2
1
1
1
0
0
2
2
1
1
0
1
1
1
1
4
1
3
2
0
0
1
1
1
2
0
2
0
1
0
1
2
2
1
1
1
0
1
1
1
1
0
0
1
1
1
0
0
1
1
2
1
1
1
0
1
0
0
0
1
2
1
1
2
1
1
1
1
1
0
1
0
1
2
1
1
0
1
1
1
2
1
2
1
1
1
1
1
1
1
0
1
1
0
1
3
0
1
1
0
0
1
1
1
1
1
2
1
0
1
2
1
1
1
2
1
1
1
1
1
1
0
1
1
1
0
2
1
0
0
1
1
1
2
0
1
4
2
1
0
1
0
2
1
1
1
1
1
1
0
1
2
2
1
2
1
0
1
1
1
0
1
2
1
1
1
0
1
1
0
1
1
1
2
1
0
0
0
1
2
0
1
0
0
1
1
2
2
0
0
0
1
2
2
1
2
0
1
2
1
2
0
0
1
1
1
2
2
0
1
1
1
1
0
0
1
0
1
0
1
1
2
0
1
1
2
1
1
2
0
2
1
1
1
0
0
2
0
0
0
1
0
1
1
0
1
1
1
2
0
2
1
1
1
1
1
1
2
1
1
0
0
1
1
0
0
0
1
0
2
1
1
1
1
1
1
1
1
1
0
1
1
0
1
2
1
1
1
0
1
2
1
0
1
1
1
0
1
1
1
1
0
2
0
1
2
1
2
2
0
0
1
1
1
0
1
3
1
1
0
0
2
2
1
2
0
2
0
1
0
1
2
1
0
1
1
1
0
0
1
2
2
2
0
1
0
1
1
2
1
0
1
1
2
0
1
0
0
1
1
0
1
1
1
1
1
0
0
2
2
0
2
1
0
1
1
2
0
1
1
3
1
1
2
2
2
0
0
2
1
0
2
1
2
2
1
1
1
1
2
1
1
2
1
0
1
2
1
1
0
1
0
0
0
1
0
0
2
1
0
0
1
2
2
1
1
2
2
2
2
1
1
2
1
0
1
1
1
1
1
1
1
0
1
1
2
0
0
1
1
1
1
1
0
1
0
1
0
2
0
1
1
2
1
1
2
0
0
0
0
1
0
1
0
1
1
2
1
2
1
1
1
1
2
1
0
1
1
3
2
1
1
2
1
1
0
1
0
1
1
2
5
1
0
0
0
1
2
2
0
1
1
1
1
1
1
1
0
0
0
0
1
1
0
1
0
0
1
1
0
0
1
0
0
0
0
1
1
2
0
1
1
1
1
2
1
1
1
1
1
0
1
2
1
1
2
2
1
1
1
2
0
2
1
0
2
0
1
0
2
1
1
1
1
1
0
1
0
1
2
1
0
1
1
1
0
1
1
1
1
2
0
1
1
0
1
1
1
0
0
1
1
1
2
1
1
1
1
0
0
0
0
2
1
2
1
2
0
1
1
1
2
0
1
1
1
1
0
0
2
1
2
0
0
0
3
2
1
0
1
1
1
0
1
1
1
1
1
1
1
0
2
0
0
0
1
2
1
2
0
1
0
3
2
2
0
1
1
1
0
0
1
1
0
0
0
0
1
1
2
2
1
0
0
1
2
2
2
1
1
1
1
0
0
1
1
0
0
1
0
1
2
1
1
2
0
0
1
0
0
1
1
0
2
1
0
1
1
1
0
1
0
2
1
0
2
3
0
0
0
1
0
0
1
1
0
1
2
1
2
2
0
1
1
1
1
0
0
1
1
1
0
0
1
1
0
1
1
1
0
2
1
1
2
1
1
0
1
2
2
0
1
2
2
1
1
0
1
1
1
0
1
0
3
0
1
1
2
1
1
1
1
1
1
1
1
0
1
1
2
0
1
0
2
2
2
0
0
1
1
0
2
1
1
1
0
0
2
1
1
1
1
1
0
0
1
1
0
1
0
0
0
2
2
2
1
0
2
0
0
1
2
1
0
0
2
1
1
1
1
1
1
1
0
1
0
0
1
2
0
1
0
0
2
1
0
0
1
2
1
1
1
0
2
0
0
0
1
2
2
0
1
0
2
1
0
1
2
1
2
2
2
1
1
2
0
1
0
0
2
0
0
1
1
0
1
1
0
1
1
1
1
2
1
1
2
1
1
1
2
1
1
2
0
0
1
2
1
1
1
2
1
0
1
1
1
2
2
0
1
0
2
1
1
1
0
1
2
0
0
2
2
1
1
1
2
1
0
0
2
2
1
1
1
1
0
1
1
0
0
2
2
2
1
1
1
0
0
1
1
0
3
1
2
1
0
0
0
1
1
2
1
1
1
2
2
2
2
1
1
0
2
2
2
0
0
2
1
1
1
0
0
0
1
1
1
1
1
0
1
3
1
1
1
1
0
1
1
0
1
2
1
1
2
0
1
1
1
1
1
2
1
1
2
1
1
1
1
1
0
0
3
1
1
1
1
0
1
1
0
1
1
1
1
1
0
2
0
2
1
2
1
2
1
0
2
1
2
1
1
1
0
1
2
2
2
1
1
1
2
1
1
2
0
0
1
2
1
1
1
1
0
1
1
1
1
1
0
0
0
1
1
0
1
0
1
2
1
2
1
1
1
0
0
2
2
0
0
0
1
0
0
2
0
2
0
0
1
1
1
1
2
1
1
2
0
1
2
0
2
1
0
2
0
1
1
0
1
2
1
1
1
3
1
0
1
2
2
1
2
2
0
1
2
1
2
0
0
1
1
2
1
1
1
1
1
2
2
0
1
1
0
2
0
2
1
2
1
0
1
1
0
1
1
1
1
0
1
0
1
1
1
1
1
0
0
2
0
1
1
1
1
1
1
2
2
2
1
1
0
1
1
1
1
1
1
0
1
1
0
1
1
1
1
1
1
1
1
1
0
0
0
2
1
0
0
1
0
1
1
1
1
2
0
1
1
0
1
2
1
0
1
1
0
1
0
0
2
1
0
1
0
1
0
1
2
0
1
1
0
1
0
2
1
0
1
2
2
2
1
2
2
2
1
0
1
2
1
2
1
1
1
0
1
1
1
1
2
2
1
0
1
1
2
0
1
1
2
2
1
1
1
0
1
0
2
1
2
0
0
2
0
1
1
0
1
1
1
2
0
2
2
2
2
0
1
1
0
0
0
0
0
0
2
1
0
1
1
2
1
1
1
1
1
2
1
2
0
0
0
1
0
2
0
2
0
1
1
2
0
2
0
1
1
0
2
1
2
1
1
2
1
1
0
2
1
2
1
1
2
1
2
1
1
2
1
0
0
1
0
2
1
1
1
3
2
1
1
1
0
2
2
1
1
0
1
1
1
1
2
1
1
0
1
1
1
0
0
1
1
1
0
2
0
1
0
0
3
4
1
2
1
1
1
1
0
0
0
0
0
1
1
0
1
2
2
0
2
1
1
1
1
2
1
1
1
0
0
2
0
1
1
1
1
0
0
1
2
0
0
0
1
2
1
1
1
0
0
0
1
2
1
1
1
1
0
1
2
0
1
1
1
0
0
2
1
1
0
1
1
0
1
2
1
0
1
0
2
2
0
0
1
2
2
1
1
1
2
2
3
1
1
0
1
1
0
1
0
1
2
1
1
1
1
0
1
2
1
0
0
1
2
1
1
2
1
1
2
0
1
1
0
1
2
0
1
1
1
1
4
1
1
2
0
1
1
1
1
1
1
1
2
2
1
2
1
1
1
1
0
1
1
2
2
1
2
2
2
2
0
0
2
2
1
0
1
0
1
1
0
0
1
0
1
1
1
2
2
2
0
2
2
2
0
0
3
1
1
1
0
1
1
1
1
1
1
0
2
1
1
0
1
0
1
1
1
1
1
2
1
2
0
2
1
1
0
0
0
1
1
2
2
1
2
1
1
1
2
1
1
1
2
1
0
0
1
1
0
1
1
0
2
0
0
1
2
2
1
1
1
0
1
2
2
1
1
0
1
0
1
1
1
1
0
1
0
1
0
1
0
2
1
2
1
1
1
2
2
1
0
0
1
1
1
1
2
2
2
1
1
1
0
1
0
1
1
0
1
1
1
1
0
1
0
0
0
1
1
0
1
1
1
1
1
0
1
1
2
0
1
0
1
1
2
1
1
0
0
1
2
1
0
1
0
2
1
1
0
3
1
1
0
1
2
1
1
1
1
2
0
1
1
2
0
1
1
0
0
1
0
1
1
0
1
0
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
0
1
3
1
0
2
1
0
0
0
1
0
0
1
1
0
1
0
2
0
1
0
0
0
1
2
1
1
1
1
1
1
1
1
1
1
4
0
1
1
2
0
1
2
2
1
2
1
0
1
0
1
0
1
1
2
1
0
0
1
0
1
3
1
1
1
1
2
1
1
1
0
3
1
1
0
0
1
2
0
1
1
0
1
1
0
2
1
0
1
2
2
0
1
0
3
0
2
1
0
0
1
1
2
1
1
0
2
0
1
1
1
1
1
1
0
1
1
0
0
1
3
1
0
1
1
1
2
0
1
0
1
0
1
2
0
2
1
3
0
2
2
2
2
1
2
2
1
0
0
1
2
1
1
0
2
0
0
1
1
0
0
2
1
0
1
0
1
1
1
1
1
1
1
1
0
2
1
0
1
1
2
0
0
1
1
2
1
1
2
1
2
2
2
2
1
0
0
0
1
1
2
0
2
1
0
1
2
1
1
2
1
2
3
1
1
1
0
2
1
1
2
1
1
1
1
0
1
1
0
1
1
1
0
1
1
0
1
2
1
0
0
1
1
1
0
0
1
2
2
0
1
1
1
0
1
2
1
2
1
0
1
2
0
1
1
2
2
1
2
1
1
1
1
0
2
0
2
3
1
2
1
0
0
2
0
2
2
0
2
1
0
0
2
3
2
1
0
1
0
2
1
1
0
1
1
0
1
0
2
1
1
1
2
1
0
1
1
1
1
1
1
0
1
1
1
1
0
1
2
0
2
3
0
0
2
1
2
2
1
1
1
0
2
2
0
1
2
1
1
0
2
0
1
1
2
0
1
0
2
3
0
4
1
2
2
0
1
1
1
3
2
1
1
1
1
1
1
1
1
2
0
0
2
1
1
1
1
0
0
1
1
0
2
2
1
1
1
0
1
1
1
2
4
0
1
1
3
2
1
1
2
1
0
1
1
1
1
1
1
1
0
0
1
2
0
1
1
3
1
1
1
2
1
2
2
1
1
0
1
0
0
1
1
1
1
1
1
0
2
2
1
1
2
0
0
1
0
1
1
1
1
2
1
0
1
2
1
2
1
0
1
2
0
1
1
1
0
0
2
1
1
1
1
1
1
0
2
2
0
1
0
0
1
1
0
1
2
0
0
1
0
1
1
1
0
0
0
0
2
1
1
0
1
1
1
0
1
2
0
1
3
1
0
1
1
1
1
1
0
2
1
1
1
2
1
2
1
2
1
0
1
1
0
1
2
1
0
0
3
2
0
0
2
1
2
2
0
1
0
2
1
1
0
2
1
1
2
1
0
0
1
1
2
1
1
1
2
1
2
1
1
1
1
1
2
2
1
0
1
0
0
1
1
1
0
2
1
1
1
2
1
1
1
1
1
0
4
2
1
2
2
1
0
0
1
4
0
0
1
1
1
1
1
1
2
2
2
1
1
1
1
0
1
0
0
0
1
1
1
1
1
1
0
0
2
1
0
1
0
1
1
1
1
2
1
2
1
1
0
1
1
1
1
0
0
2
2
1
1
1
1
1
2
1
0
3
0
1
0
1
0
1
0
1
1
2
1
1
1
1
1
1
1
1
0
1
0
1
0
1
1
1
0
1
1
1
2
2
1
0
1
1
1
1
1
1
2
1
0
1
2
0
2
1
2
0
2
0
0
0
2
1
1
0
1
1
2
1
1
0
1
1
1
0
0
1
1
2
1
1
0
1
0
1
1
1
0
0
1
1
1
0
1
0
1
2
1
2
0
1
0
2
2
1
2
2
1
1
0
1
1
2
2
1
1
1
2
2
0
0
1
2
1
1
1
2
1
1
1
0
1
1
0
1
1
0
0
2
2
0
2
1
2
2
0
2
2
1
2
1
1
1
2
1
1
1
1
1
1
0
1
1
1
0
1
1
1
0
0
1
2
0
1
0
1
1
2
1
1
0
1
3
1
1
2
2
2
0
2
1
0
2
1
1
2
0
1
1
1
1
1
0
1
0
0
0
1
2
1
0
0
0
1
0
0
2
1
2
0
1
1
2
1
1
2
1
1
1
1
2
0
1
1
0
1
1
2
1
1
1
1
1
2
1
1
2
1
1
1
2
1
0
2
1
1
1
1
0
0
0
1
0
1
2
2
1
1
1
1
1
2
2
2
1
1
2
1
1
1
0
0
2
0
2
1
2
0
0
1
1
0
1
1
1
2
0
2
1
1
0
0
1
1
2
1
1
1
0
1
0
0
1
2
0
0
0
2
0
0
2
1
0
1
2
7
1
0
1
2
0
2
1
0
1
2
0
0
1
0
0
2
2
1
0
0
1
1
1
2
2
1
1
0
1
1
0
0
1
1
0
2
0
2
1
1
1
2
1
0
2
2
1
0
0
1
1
1
0
0
1
0
0
0
1
3
1
0
1
1
2
1
0
2
1
1
1
0
1
1
1
0
2
1
2
1
2
1
0
0
1
0
1
2
1
2
1
2
2
2
1
1
1
1
2
2
1
0
0
1
1
1
0
1
1
1
0
0
1
1
0
2
0
2
0
2
1
0
1
2
1
2
1
2
1
1
2
0
1
1
1
2
0
1
2
1
1
1
0
1
0
1
1
1
1
1
0
1
2
0
2
2
1
1
2
2
1
1
1
1
2
0
2
1
2
1
0
1
0
1
0
1
1
1
0
2
1
0
1
1
1
1
0
1
1
0
1
0
1
1
0
0
0
1
0
1
1
1
1
0
1
0
1
1
1
2
0
1
1
1
2
1
0
1
0
1
2
1
2
1
2
0
2
1
1
1
1
2
1
0
2
0
1
2
1
0
0
1
1
0
1
1
0
2
1
1
0
1
1
1
0
1
1
0
1
1
1
1
1
1
2
1
1
0
1
0
2
1
1
1
0
2
0
1
1
2
2
1
2
0
1
2
2
2
1
1
1
2
2
3
1
0
1
1
1
1
0
1
2
0
0
0
1
1
1
1
0
0
1
2
1
1
2
0
1
2
2
1
2
1
1
1
1
0
0
0
2
2
0
1
0
1
1
1
1
1
2
1
1
1
0
0
0
0
2
0
0
1
0
0
1
5
0
1
2
1
1
0
1
1
1
0
2
0
2
1
0
1
0
0
0
2
0
2
2
1
0
2
0
3
4
2
2
1
1
0
1
0
0
2
0
2
1
0
1
0
0
1
1
2
2
0
2
1
0
1
0
1
1
1
1
2
0
2
1
1
1
0
1
0
0
1
0
1
1
1
1
2
2
1
0
0
1
1
0
1
1
0
1
2
1
2
0
3
1
1
1
0
0
2
1
1
0
1
1
2
0
0
1
0
2
1
0
0
1
1
1
1
1
2
0
1
0
1
0
2
2
1
2
0
0
1
0
1
2
2
0
2
1
1
2
1
2
0
1
0
2
1
0
2
1
0
0
0
1
1
1
1
0
0
0
2
1
0
1
1
1
1
0
0
0
1
1
0
2
0
0
1
1
1
1
2
0
1
1
1
0
2
1
2
1
1
1
2
2
2
2
1
2
0
2
2
1
1
1
2
1
0
1
1
1
1
3
2
1
0
0
1
1
1
1
1
1
1
1
2
2
0
1
2
1
1
1
1
1
1
1
1
1
2
2
0
1
1
1
0
1
1
1
1
0
1
0
0
1
1
2
1
1
1
2
2
1
2
3
0
1
1
0
3
0
1
1
1
1
0
2
1
0
1
2
1
1
2
1
1
0
1
1
0
0
0
0
0
1
2
1
1
0
2
1
1
0
1
0
1
0
1
0
1
0
1
1
1
2
1
0
1
1
1
0
1
1
2
0
2
1
1
1
1
0
1
0
0
1
1
1
0
1
0
0
1
1
0
1
0
1
1
0
1
2
0
2
1
0
2
1
1
2
2
1
0
1
1
1
0
0
1
0
1
2
0
1
2
2
1
0
0
1
0
0
1
0
0
2
2
0
0
1
2
1
1
0
1
1
1
0
2
1
1
2
1
0
0
1
1
1
0
1
2
2
1
1
1
1
0
1
1
2
2
1
1
2
1
1
0
0
1
2
1
1
2
2
0
2
1
2
1
0
1
2
2
1
1
0
1
1
0
2
1
1
1
1
1
2
1
2
1
2
1
1
0
0
1
1
0
1
0
1
1
1
1
1
1
1
2
0
2
1
0
2
1
1
0
1
2
0
1
2
1
1
0
0
0
1
1
1
1
1
0
1
0
2
2
1
1
2
2
2
1
0
0
0
1
1
2
1
1
1
1
1
1
1
0
2
0
1
1
1
1
3
1
1
2
2
1
0
2
1
1
0
0
1
1
1
0
0
1
1
1
1
1
1
0
2
1
0
0
1
0
0
1
0
1
1
1
2
1
2
1
2
0
1
1
1
1
1
1
1
1
1
1
0
2
0
1
2
2
1
2
0
1
2
2
0
2
2
1
1
2
1
1
1
1
1
0
1
0
1
1
1
0
1
0
1
1
2
1
2
2
0
0
2
1
2
1
2
1
0
2
1
0
3
0
0
1
1
1
0
0
1
0
1
0
0
0
1
1
2
1
0
2
1
2
2
1
1
2
0
0
1
0
0
1
1
1
1
1
1
1
0
0
1
1
1
0
1
0
2
1
1
1
0
0
2
0
2
1
1
1
2
0
2
1
1
0
1
2
1
1
2
2
1
1
1
1
2
2
2
1
1
1
2
1
0
2
1
1
0
0
1
0
3
1
0
1
1
1
2
1
0
1
2
1
2
1
1
0
1
2
0
1
0
1
1
2
1
2
0
2
2
0
1
2
0
2
1
1
0
1
1
1
1
2
1
1
0
0
0
2
2
1
0
2
2
1
1
0
2
2
1
3
1
0
1
1
1
1
1
1
2
1
1
0
1
1
2
1
2
2
1
0
2
1
2
1
1
2
1
0
2
2
0
1
0
1
1
1
1
1
2
2
0
0
1
1
0
0
0
1
1
1
1
2
2
1
1
1
2
1
0
2
1
0
2
1
1
2
1
2
1
2
0
0
2
1
0
0
0
0
1
2
1
3
0
1
0
1
2
2
0
2
0
2
2
1
1
0
0
1
1
2
1
1
1
1
1
1
1
1
0
1
1
1
0
1
1
1
2
1
1
1
1
0
2
1
0
0
0
0
0
2
0
2
1
3
0
1
0
1
2
2
0
1
1
3
1
1
1
0
0
2
1
0
2
2
1
1
0
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
0
0
1
0
1
1
2
0
1
1
1
0
1
1
1
0
0
0
0
0
2
2
1
0
0
1
1
1
0
0
1
0
0
1
1
3
0
1
2
1
0
2
1
1
0
1
0
2
0
1
1
1
0
1
2
0
1
1
1
2
1
1
1
1
1
0
0
0
3
1
2
0
0
1
0
1
2
0
1
1
3
0
0
1
0
1
0
0
1
1
1
1
1
1
2
2
2
3
1
0
0
2
0
1
0
1
1
0
1
2
1
0
1
0
1
1
2
2
0
2
0
2
1
0
0
1
1
1
3
1
1
1
1
0
1
1
1
1
1
0
1
1
1
1
0
1
2
2
2
2
0
1
0
1
2
0
0
0
0
1
2
1
3
2
0
1
1
2
1
1
0
1
0
1
1
1
1
1
2
0
0
0
1
1
2
0
1
2
1
0
1
0
0
1
2
1
1
2
2
2
0
2
0
2
1
0
1
0
1
2
1
0
0
0
2
1
1
2
1
2
3
2
1
1
0
1
0
1
1
0
2
0
1
0
1
2
1
0
0
0
1
0
1
1
2
1
0
1
0
1
0
2
2
1
2
1
1
1
1
0
1
2
1
1
0
1
1
1
0
0
1
1
2
1
1
2
1
1
0
1
0
1
0
1
2
2
1
2
2
0
2
1
5
2
1
1
1
2
1
0
1
1
2
2
1
1
1
1
1
0
2
0
1
1
0
2
0
0
0
1
1
1
1
0
0
1
1
1
0
2
1
1
1
3
1
1
1
0
0
1
0
1
0
1
1
0
1
1
2
1
1
1
0
0
1
1
1
1
1
0
1
1
2
1
1
1
2
1
0
3
1
1
2
1
1
1
0
2
2
1
2
2
2
1
1
0
0
0
0
3
1
1
0
0
2
1
2
1
2
0
1
1
2
2
1
1
1
1
0
0
1
1
1
1
1
2
2
0
1
1
2
1
2
1
1
1
2
1
1
1
2
2
2
1
2
1
1
0
1
0
0
1
0
1
1
0
1
1
1
1
2
1
1
2
0
1
1
2
1
1
1
2
1
0
1
0
0
2
2
1
1
0
0
1
1
1
0
0
1
1
0
1
2
0
2
1
2
0
0
2
1
2
1
0
1
1
0
1
0
2
0
2
1
0
1
1
1
1
1
1
1
0
1
1
2
1
0
1
2
0
1
1
0
0
2
1
2
2
1
1
1
1
1
1
0
1
1
1
0
1
2
1
1
2
1
1
1
1
1
0
0
1
1
1
1
0
2
1
0
1
0
0
0
2
1
1
2
0
2
0
0
2
1
1
0
1
1
2
2
1
1
2
1
2
1
2
0
1
1
0
2
1
1
1
2
1
1
1
0
1
1
2
1
1
1
1
2
1
1
1
1
2
0
2
0
0
1
2
1
1
1
0
0
1
0
1
1
2
1
1
1
1
0
1
0
1
0
1
2
1
1
2
1
1
1
1
0
1
1
1
0
2
1
0
1
1
1
1
0
1
1
2
0
1
2
0
1
1
0
0
1
1
1
1
1
0
2
1
0
2
1
1
1
1
1
1
1
1
2
0
1
2
2
2
2
1
1
1
1
2
1
2
1
1
1
2
2
2
1
1
1
2
1
1
1
2
0
0
1
0
0
2
1
0
0
1
1
0
0
1
0
1
1
0
3
1
1
1
1
1
2
0
1
1
1
1
1
1
1
0
1
2
2
2
2
1
2
1
1
2
1
1
1
1
1
0
1
1
1
1
2
1
0
2
2
1
1
1
0
1
2
0
1
1
1
1
1
2
1
0
0
1
1
0
1
0
0
1
1
1
1
1
0
1
1
2
1
1
0
0
1
0
1
1
1
1
0
2
2
1
0
1
2
1
0
0
0
1
0
3
1
1
2
2
2
1
0
0
0
1
0
2
0
2
2
3
0
2
2
1
1
2
1
2
2
1
1
1
1
1
1
1
2
0
2
2
1
0
0
1
1
0
3
1
0
1
1
2
1
1
1
0
1
1
0
2
3
4
2
2
1
0
1
0
2
0
2
1
2
1
2
0
1
1
0
1
0
0
1
0
2
1
0
0
1
0
1
0
0
2
1
1
1
0
0
1
0
2
1
0
2
1
2
2
2
1
1
3
1
2
5
1
0
1
1
1
1
0
0
2
1
2
1
0
2
1
1
1
0
1
1
0
0
0
1
1
0
2
0
1
1
2
1
1
1
1
1
0
1
1
2
1
0
0
1
0
2
2
1
0
1
0
1
1
0
1
1
1
0
2
1
0
0
1
1
1
2
1
1
1
1
0
2
1
1
1
2
2
1
1
0
1
0
0
1
1
1
1
1
1
2
0
1
0
1
1
2
0
0
2
1
1
0
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
0
1
2
2
0
1
0
0
0
1
1
1
1
1
2
0
2
1
2
0
1
1
2
0
0
1
1
1
0
0
1
1
0
3
0
0
1
1
0
0
1
2
1
1
1
1
1
1
1
1
2
0
1
2
1
2
0
0
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
2
1
2
0
1
0
1
1
0
1
1
2
2
1
2
2
1
2
0
1
1
2
2
0
2
1
0
1
1
1
0
1
1
1
1
0
1
1
1
1
1
0
0
0
1
0
1
0
0
1
2
1
1
1
2
1
2
1
0
1
2
1
1
1
2
1
0
1
1
1
1
1
0
0
2
1
2
1
1
1
3
0
0
1
1
1
0
1
0
1
1
1
0
1
1
0
1
2
2
0
1
1
1
0
0
0
2
1
2
1
1
0
1
2
1
2
1
1
1
1
2
2
1
1
1
2
2
2
1
1
1
0
0
1
1
1
1
1
1
0
1
0
2
1
0
1
1
1
0
2
2
0
0
1
1
1
2
1
1
1
0
0
1
1
1
2
1
1
1
2
1
0
0
1
0
2
2
0
1
0
0
1
2
1
2
2
0
1
0
1
0
1
0
1
2
1
1
0
2
0
1
0
0
2
1
1
1
1
0
1
1
2
1
1
1
3
0
1
2
0
0
0
2
1
1
2
0
2
1
1
0
0
0
2
1
2
0
0
1
1
0
1
1
1
1
1
2
1
0
2
0
0
1
2
1
2
1
1
0
1
1
0
1
1
1
1
0
1
1
1
1
2
1
0
0
1
2
1
0
1
0
1
1
0
2
2
0
0
2
2
1
2
2
1
1
2
2
1
1
1
1
0
1
0
2
0
1
2
0
0
1
1
1
2
0
2
2
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
2
0
1
0
1
1
1
1
1
0
0
1
1
1
1
0
1
2
2
0
2
0
0
0
1
0
2
0
1
1
1
1
1
0
0
1
0
0
1
1
1
0
1
1
2
1
1
1
0
0
1
1
1
1
2
1
1
0
0
0
1
1
1
2
1
2
0
1
1
1
0
2
0
1
1
2
1
1
0
2
0
0
1
2
2
0
1
1
1
1
0
2
0
0
1
1
1
1
1
1
1
1
2
1
1
1
1
0
1
1
0
2
2
1
1
0
0
1
1
1
2
1
2
1
1
0
0
1
1
0
1
1
2
0
0
1
1
2
0
2
1
1
1
0
1
1
1
2
1
1
1
1
1
0
1
1
1
0
2
1
0
1
1
1
1
2
1
1
2
2
1
0
1
2
2
1
2
2
1
2
3
1
1
0
2
0
2
0
1
1
1
0
2
1
1
1
1
1
2
0
0
1
0
1
0
2
1
0
1
1
1
2
1
0
1
1
2
0
1
1
1
1
1
1
0
2
2
2
0
2
2
1
1
0
0
1
1
1
0
2
0
1
1
2
0
1
2
1
1
1
2
1
1
1
1
0
1
2
1
1
1
1
1
1
1
0
0
1
0
1
2
1
1
2
2
0
1
0
1
1
1
1
1
1
1
1
0
2
2
1
2
1
1
1
2
1
0
0
2
2
1
1
1
1
2
1
0
1
2
2
1
1
2
1
2
1
1
1
1
1
1
0
0
1
1
0
1
1
0
1
1
2
2
1
1
1
1
2
1
1
0
1
2
1
2
1
2
1
2
1
0
1
0
2
2
1
1
1
2
1
0
0
0
0
1
1
3
1
2
1
1
0
1
1
1
2
1
0
0
0
1
1
1
0
1
0
0
1
1
2
0
0
1
2
1
0
0
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
0
1
1
1
2
1
2
1
1
0
1
1
1
1
2
0
1
0
1
0
3
0
1
1
0
0
1
1
1
1
0
0
0
1
1
1
1
1
2
0
1
0
0
0
0
2
0
1
1
1
2
1
0
1
0
1
0
0
1
1
2
2
1
1
0
1
0
1
1
0
1
1
2
1
1
1
0
0
1
2
1
1
1
2
2
0
1
1
1
1
0
0
1
0
2
1
2
3
0
0
0
1
1
0
1
1
0
2
1
1
0
0
1
1
0
1
2
0
1
1
2
0
1
1
1
1
2
0
2
0
2
1
1
1
0
2
0
1
0
0
1
1
0
1
1
0
1
0
1
0
0
1
1
1
1
0
3
1
1
1
1
2
1
1
0
1
2
6
0
1
2
1
2
1
1
1
1
1
1
2
1
0
1
2
1
0
1
1
0
2
1
1
2
1
1
0
2
2
0
1
2
1
1
0
2
1
1
0
0
1
2
1
1
1
1
0
0
0
2
1
0
2
1
0
1
1
0
0
1
1
1
1
0
0
1
1
1
1
1
1
2
1
1
1
0
0
1
1
1
1
2
1
2
0
1
0
1
2
1
1
1
1
0
0
0
1
1
0
0
2
1
2
0
0
1
2
2
1
0
0
0
1
2
1
1
2
1
1
2
0
1
0
0
2
1
1
1
1
0
2
1
0
1
0
0
2
1
1
0
1
2
3
1
2
1
0
0
2
2
0
1
2
1
2
1
0
1
2
0
2
1
1
1
2
0
1
2
0
1
2
0
1
2
1
1
0
0
1
1
1
0
2
1
1
1
1
1
1
0
0
1
1
1
1
1
1
2
2
1
2
2
1
1
1
2
0
1
0
0
1
1
1
0
0
1
2
1
1
2
2
1
0
2
1
1
0
0
0
0
1
1
1
1
1
1
0
1
2
1
1
2
1
1
0
0
0
1
2
1
1
1
0
1
1
2
2
0
1
1
0
0
1
0
2
0
1
1
1
1
1
2
0
0
3
1
1
2
1
1
0
0
1
1
2
2
1
1
1
2
1
1
2
0
2
2
1
2
0
1
1
1
2
1
1
2
2
0
1
2
2
0
1
1
1
0
1
0
1
0
1
2
1
1
0
0
1
0
0
0
1
1
1
2
0
1
0
2
2
0
2
1
1
1
2
1
2
1
1
0
2
1
1
1
0
0
2
1
1
2
0
1
0
0
0
1
1
1
1
2
2
1
2
0
2
1
1
1
1
0
2
1
2
1
0
0
0
2
1
0
1
1
1
2
1
2
1
2
2
1
0
2
0
1
1
0
1
0
1
1
1
0
2
1
1
1
1
0
0
0
2
2
1
1
1
1
1
0
1
1
2
0
1
3
2
0
1
1
1
1
1
1
0
1
2
1
4
1
1
0
1
0
1
1
2
2
0
1
2
1
0
0
1
1
0
1
1
1
0
1
2
1
0
1
1
1
1
1
0
1
0
1
1
1
1
0
0
1
0
1
0
2
2
2
1
1
2
1
2
1
0
0
1
0
1
2
2
0
1
3
0
0
2
2
0
1
0
0
0
2
1
1
0
1
1
1
2
1
0
2
1
0
0
0
1
2
2
1
0
1
1
2
0
1
1
1
2
2
2
1
2
1
1
1
1
0
0
1
1
0
1
0
2
3
0
0
1
1
0
0
1
1
2
1
1
1
2
1
0
0
1
0
1
1
1
1
1
0
2
1
1
2
0
1
1
2
1
0
1
2
0
0
2
1
1
1
1
1
2
0
1
1
2
1
2
0
1
0
1
1
2
0
1
1
1
1
7
1
0
1
0
1
1
2
1
3
1
1
0
1
1
0
0
2
1
0
0
1
0
2
1
0
2
0
1
1
0
2
1
1
0
0
1
1
0
0
2
1
2
2
0
0
0
1
0
1
0
0
1
0
1
1
1
1
1
1
1
0
1
0
2
0
0
0
0
1
2
1
1
1
1
1
0
1
0
1
2
0
2
1
0
1
1
0
2
2
0
1
1
0
1
1
0
1
2
1
0
0
0
1
1
1
2
1
1
2
0
2
2
2
2
1
1
2
2
1
1
1
1
0
2
0
1
0
2
1
2
2
1
1
0
0
0
0
1
1
1
0
2
1
1
2
1
2
2
1
2
1
1
1
0
0
1
1
1
2
0
1
1
1
1
2
1
1
2
1
1
1
1
0
1
0
0
2
1
2
1
1
1
0
2
1
1
1
0
3
1
1
1
1
1
1
1
1
3
0
1
1
1
1
1
2
2
1
0
0
0
0
1
1
1
0
1
2
2
2
2
0
1
0
1
1
1
1
2
1
1
0
0
0
2
1
1
1
2
1
0
1
1
2
2
1
1
2
1
1
1
1
1
0
0
0
0
1
1
1
1
0
2
1
1
1
1
1
0
0
1
1
0
1
0
0
1
1
3
1
1
0
1
0
1
2
2
1
0
0
2
1
1
2
0
1
1
1
0
0
0
0
1
2
2
2
1
2
2
2
1
1
1
2
2
0
2
0
0
2
1
1
0
0
1
2
2
1
1
1
0
1
1
1
4
2
1
0
1
2
1
3
0
2
0
2
1
0
1
1
0
0
0
0
0
1
0
2
0
1
1
0
1
0
1
1
1
1
1
1
0
1
1
0
1
5
1
2
0
1
2
0
2
1
0
1
0
0
2
0
1
2
1
2
1
2
1
1
2
2
1
1
1
0
1
0
1
1
1
1
1
1
1
2
1
0
0
1
1
1
1
1
1
1
1
0
1
1
0
2
2
1
1
2
2
0
0
0
1
1
2
1
2
0
1
0
2
2
2
2
1
2
2
2
0
1
1
1
1
1
2
1
2
0
1
2
0
2
0
1
1
1
1
1
0
0
1
0
1
0
2
1
1
2
1
0
0
0
1
0
2
1
1
1
0
1
1
1
1
1
1
0
2
1
1
0
1
1
0
1
1
2
0
1
0
0
0
0
1
2
1
1
1
2
0
0
1
0
0
1
2
1
1
1
0
1
0
0
1
1
1
1
0
1
2
1
0
1
1
0
0
1
1
1
2
1
1
0
1
0
1
0
1
2
1
1
0
0
2
1
1
0
5
1
0
1
1
0
1
1
1
1
2
0
1
1
1
0
1
1
2
0
1
1
2
0
1
0
1
0
2
0
1
1
1
1
1
1
2
1
0
0
2
1
2
0
0
1
2
1
0
1
0
1
1
1
0
0
2
2
1
1
1
2
1
1
2
0
0
1
1
1
0
1
1
2
0
1
1
0
0
1
1
1
1
1
1
1
1
0
1
0
1
1
0
1
1
0
0
1
1
0
2
1
2
1
1
1
1
1
1
0
0
0
1
1
1
1
1
0
0
1
0
2
1
1
1
1
1
2
1
0
1
2
1
1
2
0
1
2
1
2
1
1
2
1
1
0
2
0
1
2
0
2
1
1
0
0
2
1
1
2
0
0
1
2
0
1
1
2
1
1
1
2
1
1
1
1
1
0
1
1
1
0
1
1
0
2
2
0
0
1
2
1
1
2
1
1
2
1
1
1
1
1
1
2
0
0
1
3
0
3
1
1
0
1
1
1
2
2
1
1
0
1
0
2
1
2
1
0
1
0
2
1
2
1
0
0
1
0
1
1
0
1
1
1
2
2
1
0
1
1
2
2
2
0
1
1
0
1
1
1
1
1
2
0
1
0
0
0
0
0
1
2
2
0
1
2
1
0
1
1
0
1
1
0
2
0
1
0
0
1
1
1
2
1
1
1
1
1
1
2
0
1
0
0
1
0
0
0
1
1
1
0
1
0
1
2
1
0
0
0
1
1
1
1
3
2
1
1
2
0
2
1
0
0
1
1
0
1
1
1
0
0
1
1
1
2
0
0
0
1
1
1
0
0
1
1
0
2
0
1
1
0
0
1
1
1
1
1
1
2
2
0
1
0
0
0
1
1
1
1
0
1
3
1
0
1
1
1
2
1
1
1
1
1
1
1
2
1
3
1
0
0
1
1
0
1
2
0
2
2
1
1
0
1
1
1
0
1
2
1
2
1
1
2
1
1
1
1
2
1
0
1
0
0
1
2
2
1
1
1
2
1
1
2
2
2
2
1
2
1
1
2
2
2
1
1
1
1
2
1
1
1
0
0
2
3
0
0
1
0
1
1
1
1
1
1
1
1
1
2
1
2
1
2
1
1
0
2
1
0
2
1
0
1
1
2
0
2
2
0
0
1
1
1
1
1
0
1
1
0
0
1
1
1
0
1
1
1
0
0
1
1
1
1
2
2
2
1
1
1
2
2
2
1
2
1
1
1
0
0
1
1
1
0
0
1
2
1
1
1
2
0
0
1
0
2
2
2
1
0
1
0
3
2
0
0
0
2
0
1
2
1
1
0
1
1
2
1
1
1
1
1
0
1
1
0
1
1
1
1
0
0
1
1
1
0
2
1
0
0
2
1
0
1
2
0
0
1
0
0
2
0
1
1
0
0
1
2
1
1
1
0
1
1
1
2
0
1
0
0
1
2
0
2
1
2
0
1
0
1
0
2
0
0
1
0
1
1
1
2
2
1
1
2
0
1
1
1
2
0
1
1
0
1
1
0
0
0
1
1
2
1
1
1
1
1
3
1
1
1
2
1
0
1
1
0
2
0
0
1
2
0
1
0
1
1
1
0
1
3
1
0
1
1
1
1
1
0
2
1
0
1
0
2
0
1
1
0
0
0
1
0
0
2
1
1
1
1
0
0
2
1
1
1
0
2
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
0
0
0
1
1
1
1
2
1
1
1
1
1
1
0
1
1
2
1
2
0
0
1
2
2
0
3
1
1
1
1
1
0
1
0
1
2
2
0
1
2
2
1
1
1
1
0
0
2
1
1
1
1
0
2
1
1
1
1
0
2
1
0
2
0
1
1
0
0
2
2
1
2
1
0
1
0
1
2
2
2
1
0
1
1
1
1
3
0
1
2
1
1
1
2
0
1
2
1
0
0
1
2
1
2
1
1
1
1
0
0
2
0
0
0
1
1
0
2
0
2
0
1
3
2
1
1
0
0
1
0
1
2
0
1
1
1
1
0
1
1
1
2
0
1
1
1
1
2
2
1
1
1
2
0
1
1
0
0
1
0
1
2
1
0
1
1
1
1
0
1
1
0
0
1
0
2
0
1
1
1
2
1
2
1
1
1
5
1
1
1
1
2
2
1
0
2
1
1
2
1
1
2
1
1
1
2
1
1
1
0
1
2
0
0
1
1
1
1
0
1
0
0
0
1
0
0
2
1
1
2
1
2
1
1
1
2
0
2
2
1
1
0
0
2
2
1
1
2
2
2
1
1
0
1
0
1
1
1
1
1
1
1
2
2
2
0
1
2
1
1
1
2
0
2
1
2
1
1
1
0
1
1
0
1
0
2
1
0
1
1
0
0
0
1
0
0
1
2
2
0
0
2
0
0
1
1
0
1
2
1
1
1
1
1
1
0
1
0
1
1
0
0
1
0
0
1
2
1
1
1
1
1
1
0
1
0
0
2
2
0
0
0
1
1
1
0
1
2
1
2
0
1
1
0
0
1
0
1
1
2
1
1
0
0
1
1
0
1
1
0
1
1
1
1
0
1
1
0
1
0
1
1
1
1
1
1
2
1
1
2
0
1
1
0
1
2
1
1
1
1
2
1
1
1
1
1
1
1
0
2
2
2
0
2
0
1
1
1
0
0
1
1
1
1
2
1
2
0
0
1
1
2
2
1
1
0
1
0
1
1
1
0
2
0
2
1
1
1
0
1
2
1
0
1
1
0
0
1
1
1
0
0
2
2
2
2
1
1
1
1
0
0
3
1
0
1
1
1
2
1
1
1
0
2
2
1
1
0
1
1
1
1
0
2
0
1
1
0
0
0
1
0
2
1
1
1
3
1
3
1
2
2
2
1
0
1
2
1
1
1
1
1
2
1
1
2
1
0
0
0
2
2
0
9
0
2
1
2
0
0
0
2
0
0
1
1
1
1
1
1
2
1
0
1
2
1
1
3
1
2
0
1
0
0
1
1
0
1
0
1
0
1
0
0
0
0
1
1
1
0
2
1
2
1
0
2
0
1
1
3
0
1
1
1
2
1
1
2
1
0
0
0
1
1
1
0
0
1
0
0
1
3
0
2
1
0
2
1
1
1
1
1
0
1
0
1
0
1
1
0
1
2
2
0
1
1
2
0
0
0
0
2
1
0
0
0
2
0
1
1
1
1
1
1
0
0
1
3
1
2
1
1
2
3
1
2
1
1
1
0
1
0
1
2
1
1
2
1
0
1
2
0
1
0
2
3
2
1
0
1
0
0
2
1
2
0
1
0
2
2
1
2
0
1
1
1
2
2
1
1
0
1
2
1
2
1
1
0
1
0
1
2
0
2
1
1
1
2
0
1
2
2
1
1
2
2
1
1
0
1
1
1
3
2
1
2
1
1
1
1
2
0
0
1
0
1
1
1
1
1
2
1
1
1
0
1
1
0
1
2
1
1
1
2
2
1
1
0
0
1
2
1
2
1
1
0
1
2
2
1
1
1
1
2
1
0
1
2
0
0
0
1
1
1
0
1
0
1
1
1
0
0
0
2
0
2
1
1
1
2
0
1
2
1
1
0
1
1
0
0
2
0
1
2
1
0
1
1
2
0
0
0
2
1
1
1
1
1
2
0
1
1
1
2
1
1
2
2
2
0
1
1
1
1
0
1
1
1
0
0
0
1
2
1
1
1
1
0
2
2
0
1
2
0
2
1
0
0
1
2
2
2
3
0
1
1
1
0
1
1
1
0
1
0
1
2
1
1
2
0
1
0
2
1
1
0
0
1
1
0
1
1
1
1
2
0
2
0
0
1
1
1
2
3
0
1
2
3
0
0
1
0
1
1
0
2
1
1
1
1
0
0
2
1
0
0
1
0
0
2
1
0
1
1
1
1
1
2
1
0
1
1
1
2
1
2
1
0
2
0
1
1
1
2
0
1
1
1
0
1
0
0
1
0
0
1
2
1
1
1
1
1
1
2
1
1
0
2
1
0
1
1
1
1
1
0
1
2
1
0
1
0
1
0
1
0
0
2
1
1
1
1
2
2
1
1
1
0
0
1
0
2
1
1
2
2
0
1
0
1
2
2
1
2
1
2
1
1
1
2
2
2
1
1
1
1
0
2
2
1
2
2
1
0
0
0
0
1
2
1
1
1
0
1
2
1
1
2
2
0
1
1
2
3
0
0
1
0
1
2
2
1
0
1
1
2
2
0
1
0
1
0
2
0
1
0
0
1
1
0
0
1
0
1
1
0
2
1
2
2
2
0
1
2
0
2
2
1
0
2
2
1
2
0
1
2
1
0
2
1
2
0
2
2
1
2
0
1
1
0
1
2
0
1
0
0
2
1
2
0
1
1
1
1
0
0
0
0
2
1
1
1
1
0
2
0
1
0
1
1
2
1
0
2
0
1
2
1
1
0
1
1
1
0
0
1
1
1
0
1
1
2
1
1
1
2
0
0
1
1
2
1
0
1
1
1
1
1
2
0
1
2
0
2
1
1
2
1
2
2
0
2
1
0
1
2
2
0
1
1
1
2
1
1
1
0
2
1
0
1
1
1
1
0
1
0
2
1
0
2
0
1
1
0
1
0
1
0
0
2
1
1
0
1
1
2
1
2
1
2
0
1
1
0
0
1
0
0
0
0
1
2
1
0
1
0
2
1
0
1
2
1
0
1
2
1
1
1
1
1
0
1
0
1
2
1
2
2
2
0
2
1
2
1
2
1
0
1
0
1
0
1
1
1
1
2
2
1
1
1
2
1
1
1
1
0
1
1
1
2
0
2
2
0
2
1
1
2
1
2
1
1
1
1
2
2
0
0
1
2
1
1
0
1
0
1
2
0
1
1
1
2
2
1
1
1
2
2
1
1
1
0
2
1
1
1
1
1
1
1
0
1
0
0
0
1
1
2
1
1
0
1
1
2
0
2
1
0
2
1
1
1
1
2
1
1
1
1
2
1
2
0
2
0
0
1
2
1
1
0
0
1
1
1
2
1
0
1
1
0
2
2
3
0
0
1
0
1
1
0
1
0
1
0
2
2
1
1
2
1
0
2
1
2
1
0
0
1
1
1
1
1
1
1
0
1
0
2
0
2
0
1
2
0
0
3
1
1
1
1
1
0
1
1
1
1
1
1
1
2
0
1
2
1
0
0
2
2
2
2
2
2
1
1
1
1
0
0
1
0
0
1
1
1
1
1
0
1
2
0
1
1
1
0
1
1
1
1
0
0
1
1
2
0
1
0
0
2
0
2
1
1
0
0
1
1
1
0
1
2
0
1
2
0
1
1
1
0
2
0
0
2
0
0
1
1
1
1
1
2
1
1
2
1
1
0
0
1
1
0
2
1
0
1
2
1
0
0
2
2
1
1
0
0
1
0
1
1
0
2
1
1
1
0
0
2
1
2
1
1
0
0
0
1
2
1
1
1
0
0
2
1
1
2
0
1
1
1
0
1
1
1
1
0
1
2
0
1
1
1
1
1
2
1
2
1
0
1
1
1
1
0
3
1
1
1
0
0
2
1
1
0
2
1
1
1
1
2
1
0
0
1
0
1
1
1
0
2
1
1
1
1
1
2
0
2
1
2
1
1
1
1
1
1
0
1
0
1
0
1
1
1
3
2
1
1
0
1
0
2
1
2
3
1
1
1
1
0
1
2
2
1
2
1
0
1
2
0
1
0
1
0
1
0
1
0
1
0
1
0
0
0
2
1
4
0
1
0
1
2
2
2
1
1
1
1
1
0
1
2
1
2
0
1
1
1
0
1
1
2
0
1
1
1
1
1
1
1
1
1
1
1
0
1
2
1
1
2
1
1
1
1
1
1
2
1
1
0
1
1
2
2
4
0
1
1
1
1
0
1
0
1
0
2
1
1
1
1
1
1
2
0
1
1
1
1
1
2
2
1
0
0
1
1
1
0
2
1
1
0
0
1
1
3
2
1
1
2
0
1
1
2
2
0
1
1
1
1
1
3
0
2
1
1
1
1
1
1
0
1
0
2
1
0
1
0
2
1
0
1
0
0
1
2
0
1
2
1
0
2
2
1
1
2
1
1
0
1
3
1
1
1
1
0
1
0
1
0
1
0
1
0
1
1
0
1
1
1
1
1
1
2
1
1
1
1
1
1
0
2
1
0
0
1
1
2
1
1
2
1
1
2
1
1
2
0
1
0
1
1
1
1
0
1
0
2
1
2
2
1
2
1
1
1
3
1
1
0
1
1
1
1
2
0
2
2
0
0
2
2
1
3
1
2
2
0
0
0
2
1
1
1
1
1
2
2
1
0
0
1
2
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
1
0
0
0
1
2
1
1
1
1
1
0
1
2
2
1
1
1
0
1
1
1
3
0
0
1
2
1
0
1
0
1
0
0
0
1
1
1
1
0
1
1
0
1
2
1
1
2
1
0
1
2
1
0
1
1
1
0
2
2
2
2
1
1
1
0
2
1
0
2
0
0
1
1
1
1
1
1
1
1
0
0
1
1
1
1
1
0
1
1
2
0
1
1
1
0
1
2
1
1
2
1
2
0
1
1
1
1
0
1
0
2
1
2
1
0
2
1
0
2
1
2
0
0
0
1
1
1
2
1
1
1
1
0
1
1
1
0
1
0
1
1
1
1
0
1
1
2
1
2
2
2
1
0
1
1
2
3
1
0
2
1
0
1
2
2
1
1
0
1
1
2
1
0
2
1
1
2
1
1
0
1
2
2
2
0
0
1
1
3
1
2
2
1
1
0
3
1
1
1
1
1
1
2
1
0
1
1
2
1
1
1
1
2
0
2
0
1
1
2
1
2
2
1
1
1
0
2
1
0
1
1
1
0
0
1
0
1
1
1
1
1
1
1
1
0
2
0
1
1
1
1
2
1
1
1
2
1
1
0
2
2
0
3
1
0
0
1
0
1
1
2
1
1
0
2
1
2
0
2
0
2
2
0
0
1
1
2
1
1
1
1
2
2
1
0
1
1
0
1
1
0
2
1
1
0
1
0
0
0
0
0
1
2
0
0
1
2
0
0
1
0
1
1
2
1
1
2
2
2
1
1
0
0
2
0
2
1
2
0
1
2
0
3
0
1
0
1
1
1
0
0
2
1
1
1
1
1
0
2
1
2
1
1
2
2
2
1
2
3
1
2
1
2
1
1
0
1
2
1
2
1
0
1
2
1
1
0
2
1
1
1
1
0
1
2
0
2
0
2
1
0
1
1
1
2
0
1
1
1
1
1
1
2
1
1
1
1
0
0
1
1
0
1
1
3
1
0
1
0
0
1
0
0
0
1
0
2
0
1
1
2
2
2
2
2
1
1
1
1
2
1
1
2
0
2
0
1
1
0
2
0
0
1
0
1
2
0
2
2
1
2
1
2
0
0
0
1
2
2
1
1
2
1
1
1
1
1
1
1
0
0
2
1
0
1
1
1
0
0
2
1
1
1
0
1
2
1
1
1
1
2
1
1
2
1
1
1
0
1
1
1
2
1
2
0
1
1
2
2
2
5
0
1
0
1
2
2
1
0
1
1
1
0
1
0
0
2
0
0
2
1
1
1
0
1
1
0
1
0
0
1
1
1
0
2
1
0
1
1
1
1
0
0
1
1
1
2
1
1
1
2
0
1
0
0
0
1
1
1
1
1
1
1
2
0
0
1
1
1
0
0
1
1
0
0
2
2
2
1
2
2
1
0
1
2
1
1
1
1
0
1
1
1
1
2
0
0
1
1
1
1
1
0
0
1
2
1
2
1
1
1
1
0
0
1
2
1
1
1
1
1
0
0
1
1
2
0
1
2
2
2
1
0
1
0
0
1
0
1
0
1
1
1
1
0
1
0
1
1
1
1
1
0
1
2
2
1
0
1
0
1
1
1
1
1
1
2
2
1
1
2
1
1
1
2
2
2
1
2
0
1
2
2
0
0
0
1
1
1
1
1
0
2
0
1
0
0
2
2
1
1
1
0
2
0
0
2
2
1
1
2
1
1
1
1
1
0
1
0
1
1
1
3
0
1
0
1
1
1
2
1
1
1
1
0
1
0
1
0
1
1
0
0
2
1
1
2
1
0
0
1
2
1
1
1
1
0
2
1
1
1
1
0
1
1
2
0
1
0
1
1
1
1
1
1
1
0
2
2
1
1
2
0
0
0
0
2
1
0
0
8
1
0
1
2
0
2
1
2
1
1
0
0
1
1
1
0
1
1
2
0
2
0
1
1
1
1
1
0
0
2
1
2
1
0
0
1
2
1
2
1
1
0
2
2
2
2
1
0
1
1
1
1
2
4
0
1
1
1
1
2
0
1
0
1
2
1
1
1
1
2
1
2
1
1
1
1
1
2
1
0
1
0
0
2
2
1
1
1
1
1
0
1
1
2
1
0
1
1
2
1
1
0
1
2
1
2
2
2
1
1
0
1
0
1
2
2
0
1
1
1
1
1
0
0
2
1
1
0
0
2
1
1
1
1
1
1
1
0
2
0
1
0
1
1
1
1
2
1
3
0
0
1
2
0
2
1
2
2
2
0
1
2
1
1
2
2
0
2
0
0
2
0
0
0
1
1
1
1
0
0
0
1
1
1
2
1
0
1
0
1
1
1
1
1
1
2
0
0
1
1
2
0
0
1
1
4
1
1
1
2
2
1
1
1
1
0
1
0
2
2
0
1
2
0
2
0
0
1
1
0
1
1
1
0
1
0
1
1
1
1
2
0
1
0
2
0
0
2
1
2
0
0
2
0
1
2
2
0
2
0
1
1
1
1
1
0
1
2
1
2
2
1
1
2
1
4
0
1
2
2
1
1
2
1
0
1
2
2
1
2
0
2
2
0
1
1
1
1
1
0
1
1
2
0
1
0
2
1
2
1
1
2
2
0
2
1
0
0
0
0
1
1
3
0
0
1
1
1
1
0
2
1
1
2
1
2
1
2
1
1
1
2
1
1
0
1
1
2
2
2
0
1
2
2
0
2
1
0
1
1
0
2
1
1
2
2
1
2
1
2
1
1
1
1
0
2
0
1
1
2
0
1
0
1
0
0
0
0
0
1
0
1
2
2
2
1
1
1
0
1
1
1
1
1
1
1
0
1
2
1
1
1
0
1
0
1
0
1
0
2
1
1
1
1
1
0
0
1
0
1
0
1
1
0
1
1
2
0
0
0
1
0
1
0
2
1
1
0
1
1
0
3
1
0
2
2
2
0
0
0
2
1
1
3
0
1
0
2
2
1
1
2
0
0
1
1
1
2
1
1
0
2
2
1
2
0
2
1
1
0
1
2
1
1
1
1
1
1
1
2
1
2
2
1
0
1
4
0
1
1
0
1
1
0
1
1
1
1
1
1
2
1
2
1
0
1
2
2
2
2
2
1
2
1
2
1
1
1
1
0
1
1
0
2
1
0
1
0
1
2
1
1
1
3
2
1
1
1
0
2
0
3
1
1
2
1
0
2
1
1
0
1
1
3
1
0
0
1
1
2
1
1
0
2
0
2
1
2
0
1
1
1
1
0
1
0
0
1
2
1
0
1
1
2
2
1
3
2
1
1
2
0
1
0
1
4
1
0
1
0
2
2
3
1
0
0
0
1
1
1
1
1
1
2
0
1
1
2
1
2
1
1
2
0
1
1
1
1
1
2
0
1
1
0
2
2
0
2
1
1
1
0
1
0
1
1
1
2
1
1
0
1
1
0
0
0
0
2
1
0
0
2
1
1
0
2
0
1
0
1
0
1
1
0
1
1
0
1
1
3
1
2
1
0
1
1
1
1
1
0
1
1
1
0
2
0
1
1
1
1
1
1
0
2
1
1
1
2
1
1
1
2
2
1
2
0
2
2
1
0
1
2
1
1
3
1
0
1
1
1
0
2
0
1
0
1
2
1
0
1
0
0
3
2
1
2
1
1
2
1
2
0
0
1
1
1
3
1
1
0
2
1
1
2
0
1
2
0
0
2
1
2
0
1
2
0
2
2
1
1
1
0
2
1
0
1
1
1
2
1
1
0
0
2
1
3
0
1
0
1
0
2
2
1
0
0
1
2
0
2
2
0
1
0
0
0
1
2
1
1
0
0
1
2
0
0
2
1
1
2
2
0
0
2
2
0
2
2
1
1
0
0
0
1
2
0
0
1
1
2
1
0
0
0
2
1
1
2
1
1
1
0
0
4
1
1
1
1
2
1
2
1
2
0
1
1
1
0
0
2
0
1
1
0
1
1
1
1
0
0
1
2
1
3
0
2
2
1
1
0
1
0
0
1
1
1
1
1
0
2
0
0
2
0
1
0
1
1
1
1
1
1
0
0
0
1
1
0
1
1
0
2
1
1
0
1
1
1
2
1
0
2
1
1
1
2
2
1
2
2
2
1
2
2
0
0
1
2
1
0
1
1
1
0
1
0
1
2
0
0
1
1
1
1
1
1
0
2
1
1
0
1
1
1
2
1
0
0
2
1
1
1
1
1
1
1
1
2
0
0
1
1
0
0
0
1
2
1
1
1
1
1
1
2
1
1
1
3
1
0
0
1
1
0
1
0
1
2
0
1
1
0
2
2
2
1
2
1
0
1
1
2
2
1
1
1
0
0
1
2
1
2
1
1
2
3
2
2
2
2
1
1
1
2
3
2
1
1
0
2
2
1
1
1
1
0
0
1
1
1
0
2
0
2
1
1
2
2
1
1
1
0
2
2
1
0
0
0
1
0
0
1
0
2
0
1
1
1
2
1
1
1
0
2
0
0
0
1
2
1
0
1
1
0
1
2
0
2
1
1
2
2
1
2
0
2
1
1
0
0
1
0
1
2
1
1
0
1
0
1
0
0
0
0
2
1
1
1
0
1
0
1
1
2
2
0
1
1
0
1
2
1
1
1
1
1
1
1
1
1
0
0
0
0
1
1
2
1
1
0
2
2
1
0
2
0
1
1
1
1
2
1
0
2
2
1
2
0
2
1
0
0
0
1
0
2
0
1
1
2
2
1
1
1
2
2
1
0
1
2
1
0
1
1
1
1
0
1
0
0
0
2
2
1
1
1
2
2
2
0
0
2
0
0
0
2
1
1
0
0
1
1
1
2
1
1
1
1
0
0
1
2
2
1
1
2
1
0
2
1
1
1
1
2
1
0
1
1
1
1
1
0
1
2
2
1
1
2
2
1
1
1
1
1
2
0
2
0
2
0
0
0
1
1
0
2
1
1
0
0
1
0
1
2
1
1
2
1
1
0
1
0
0
1
2
2
1
0
2
1
2
1
0
1
1
0
1
1
1
1
2
1
1
2
0
2
0
1
0
2
0
2
2
2
2
2
1
1
0
3
1
1
1
1
3
1
1
1
1
2
1
2
0
1
0
1
0
2
1
1
2
1
0
0
0
1
2
2
1
1
0
1
2
2
1
1
0
1
2
1
1
1
1
1
1
0
0
2
1
0
1
1
1
1
1
0
1
0
2
0
2
2
2
1
2
1
1
1
1
0
1
2
2
2
1
1
2
1
0
2
1
1
1
2
1
1
1
4
1
2
1
0
1
1
1
1
2
2
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
0
2
2
2
1
1
2
2
1
2
1
3
1
2
2
2
2
0
1
1
1
1
1
1
0
2
2
0
1
1
2
0
1
2
1
1
2
2
1
1
1
0
1
1
0
1
0
2
0
1
1
0
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
0
2
1
2
1
1
0
2
1
1
0
1
0
0
0
1
1
1
0
0
2
0
0
2
1
1
0
1
0
1
1
0
2
0
2
1
1
1
0
1
1
1
0
0
1
1
1
0
0
1
1
2
1
2
1
1
0
0
1
2
1
1
0
1
1
1
0
2
2
0
1
1
1
0
0
2
0
2
1
1
0
1
1
1
1
1
0
0
1
0
2
2
0
1
1
0
0
1
2
1
0
0
1
1
0
0
2
2
1
1
1
0
1
1
1
2
0
1
1
1
1
1
2
1
2
0
2
2
0
1
1
1
1
1
1
2
1
1
1
1
2
2
1
2
1
1
1
0
1
1
2
2
1
2
1
0
1
1
1
2
2
1
1
2
1
0
1
1
1
0
0
2
0
0
1
1
1
0
0
2
0
0
1
2
1
0
2
2
1
0
2
1
0
0
1
1
1
0
1
1
1
0
1
1
1
1
1
1
2
1
1
2
1
0
1
2
1
1
0
1
2
2
2
2
1
0
1
2
2
2
2
1
0
1
2
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
2
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
0
2
1
1
0
0
1
0
0
0
2
2
2
1
0
2
1
1
2
1
1
1
2
1
1
2
2
1
1
0
1
1
0
0
2
2
1
1
2
1
1
2
0
1
2
1
1
2
0
1
1
1
0
1
1
2
1
1
0
2
2
2
1
0
0
0
1
2
1
2
2
2
0
0
2
2
1
1
0
0
1
1
2
1
0
1
1
1
1
1
1
1
0
1
0
0
2
1
1
1
0
0
1
0
1
1
0
0
0
0
2
1
0
0
0
2
1
1
1
1
1
2
2
1
0
2
0
0
1
1
1
0
1
0
1
1
1
1
0
1
2
1
2
1
1
2
2
1
2
0
1
0
1
1
1
1
1
0
0
0
1
1
1
0
1
2
0
0
0
0
0
1
1
1
3
2
2
1
1
2
0
0
0
0
0
2
1
1
1
4
1
1
1
0
1
1
1
1
1
1
2
0
2
0
1
1
1
0
1
0
1
1
2
2
1
0
0
1
0
2
2
1
2
2
1
1
1
1
1
1
1
2
1
1
1
2
1
1
0
1
2
2
1
1
2
2
1
0
1
1
1
2
2
2
0
0
1
1
0
1
0
1
0
2
0
0
0
0
1
2
1
1
2
1
1
1
2
3
1
0
0
1
1
0
1
1
1
1
1
0
2
1
0
1
0
0
0
0
0
2
1
1
1
0
1
0
1
2
1
1
2
1
1
0
1
1
1
1
1
1
1
1
0
1
0
1
1
2
1
2
1
3
0
0
2
1
1
2
1
1
1
1
2
0
1
0
1
0
2
2
0
0
2
1
1
0
1
2
0
0
2
1
1
0
1
1
0
2
1
1
1
1
2
1
1
0
0
1
1
0
1
2
2
1
0
1
2
1
0
1
1
2
1
0
1
1
1
0
1
0
2
1
1
0
0
2
1
0
0
1
2
0
1
0
0
1
1
1
2
1
1
1
2
1
1
1
1
1
0
1
1
2
1
2
1
1
0
1
2
0
2
1
1
1
1
0
1
1
2
0
1
1
2
1
1
2
1
0
2
1
2
1
1
1
2
1
1
0
2
2
1
1
1
0
2
2
0
0
2
1
0
2
1
1
0
1
1
2
2
1
1
1
1
0
2
2
0
1
1
2
2
2
1
1
1
1
0
1
1
0
0
1
1
1
0
1
1
0
1
0
1
1
2
3
1
0
1
2
1
1
0
0
1
0
1
0
1
1
1
2
1
1
2
2
1
1
1
1
2
1
2
0
1
1
1
2
2
1
2
0
1
1
1
1
0
0
2
1
2
1
1
1
0
2
3
0
1
0
1
1
2
0
1
1
0
0
2
1
1
1
1
0
1
1
0
1
1
2
1
1
1
0
1
0
1
1
0
0
2
1
1
1
1
2
0
0
2
1
1
1
1
1
1
1
1
1
1
1
1
2
0
1
1
2
1
0
2
1
1
1
1
1
0
0
1
1
1
1
1
0
1
1
0
0
0
1
1
2
0
1
1
1
0
1
1
2
0
1
2
1
0
2
0
0
1
1
1
1
2
2
1
0
2
1
0
1
0
1
1
2
2
1
1
1
0
1
1
0
0
1
1
1
2
1
1
0
1
1
1
0
2
1
0
1
1
1
2
0
0
2
0
0
0
0
0
1
1
1
2
1
1
1
2
1
0
0
1
0
2
1
1
1
2
1
0
1
1
0
1
0
1
1
1
0
2
1
0
1
1
1
1
1
1
1
2
1
0
1
2
2
0
1
1
1
1
1
2
2
0
2
2
2
1
0
1
1
2
0
2
2
2
2
1
1
0
2
0
1
0
0
1
3
1
2
1
1
1
2
0
1
1
1
0
2
1
2
1
1
1
2
0
1
0
0
2
0
2
1
1
1
1
1
0
0
1
0
2
2
2
2
1
2
1
0
1
0
1
1
1
1
2
1
1
2
2
3
1
0
1
1
1
1
1
1
2
0
1
1
0
2
2
1
1
1
1
1
2
1
0
2
1
1
1
0
1
1
1
2
1
0
1
0
0
1
1
1
2
1
1
1
1
0
6
1
2
1
1
1
1
2
0
1
2
0
1
1
1
1
1
1
0
0
1
1
1
2
2
0
0
1
1
0
1
2
0
2
1
2
1
1
1
2
1
1
1
1
0
2
1
0
0
0
2
1
2
2
0
1
2
1
1
0
2
2
1
2
1
1
0
1
2
2
0
2
1
1
1
0
1
0
2
1
1
2
0
1
1
0
1
2
1
0
1
0
1
1
1
0
1
2
1
1
1
0
0
2
0
1
1
2
1
1
0
0
0
0
1
0
2
1
1
1
1
1
0
0
1
0
0
1
1
2
2
0
1
1
2
0
0
0
0
2
1
0
2
2
1
1
1
1
2
0
1
0
0
1
0
1
0
1
2
1
2
1
1
1
0
1
1
2
2
0
0
1
1
0
2
1
2
1
0
1
2
0
2
1
0
0
2
0
0
0
2
1
1
1
1
0
1
2
1
0
2
1
2
0
1
1
1
2
1
1
1
1
0
0
1
1
0
1
1
1
0
2
2
1
2
1
1
0
1
2
1
2
0
1
1
1
1
1
1
1
1
1
2
0
1
1
1
1
1
1
1
1
2
1
0
1
1
0
0
2
2
1
1
1
1
2
1
1
1
0
1
1
1
1
2
0
0
0
0
0
2
1
0
1
1
0
2
1
2
1
2
1
2
1
1
1
1
0
2
1
1
1
1
1
0
1
0
1
1
2
1
1
1
2
1
1
1
1
0
1
1
1
1
1
1
1
2
0
1
0
1
1
1
1
1
0
0
1
1
1
1
0
2
1
1
0
1
0
0
1
1
0
1
1
0
0
2
2
0
1
1
1
0
1
1
0
1
1
3
1
1
1
1
1
1
1
1
3
1
0
1
1
1
2
0
2
0
1
1
1
1
0
1
0
1
1
0
1
1
1
2
0
1
1
1
1
1
1
2
2
1
1
1
0
0
2
2
2
1
1
1
2
0
2
0
0
2
0
2
1
1
2
0
0
2
1
1
2
1
0
1
2
0
6
1
5
0
0
1
0
1
2
1
2
2
2
0
1
1
1
0
2
1
2
0
1
0
0
2
0
1
2
2
1
1
0
1
1
1
1
2
0
0
1
1
0
0
0
1
0
1
0
2
1
2
2
2
0
0
1
2
1
1
2
0
1
0
1
1
1
1
1
1
1
2
0
2
1
2
1
1
1
1
2
2
1
1
1
0
0
1
0
2
1
2
2
1
1
1
0
1
1
1
2
1
1
1
1
1
0
0
1
2
2
1
1
1
0
1
2
1
0
1
3
2
1
1
1
2
1
1
0
0
1
0
0
1
1
1
1
1
1
1
2
1
1
1
2
1
1
2
0
1
2
1
1
0
1
0
1
1
1
1
1
3
1
1
0
2
0
1
1
1
0
2
0
1
1
1
1
1
1
0
0
1
1
1
1
0
1
1
1
0
1
1
1
0
2
2
0
2
1
1
1
0
0
1
0
2
1
1
1
0
1
0
2
1
0
0
1
2
0
1
2
2
0
2
0
1
0
1
2
0
0
1
2
1
0
2
1
0
1
0
0
1
1
2
2
1
2
1
1
2
1
2
1
1
2
0
1
2
0
0
0
2
3
2
0
1
2
1
0
1
2
1
1
1
1
0
2
2
0
1
0
2
1
0
0
1
1
1
1
1
1
1
1
1
1
0
0
2
2
0
1
0
2
0
0
1
1
1
0
2
1
1
1
1
1
1
1
1
1
2
2
2
1
1
0
2
2
0
1
1
1
1
2
1
1
1
0
0
1
0
2
1
1
0
1
0
0
2
2
1
1
0
3
1
1
0
0
1
2
2
1
1
0
0
1
0
2
1
1
2
1
1
1
4
2
1
1
1
0
0
1
1
1
0
1
2
2
1
1
1
1
2
2
0
2
1
0
1
0
1
1
0
1
1
2
2
2
2
0
0
1
1
1
1
0
1
1
0
2
0
0
2
0
0
1
0
0
2
2
2
0
2
1
1
1
1
1
1
2
1
1
0
2
2
2
1
1
0
1
2
1
0
0
0
0
0
2
1
2
1
0
1
2
1
1
1
2
1
2
1
1
1
2
1
2
1
0
2
2
1
2
1
0
0
0
0
0
0
1
1
0
0
1
0
1
0
1
1
1
0
1
1
2
0
2
1
2
0
1
1
0
0
0
1
1
1
2
2
0
1
2
2
1
1
0
1
1
2
1
1
2
1
1
1
1
2
1
0
1
2
1
2
2
1
1
0
1
2
2
1
1
1
1
0
1
0
1
1
2
1
1
1
1
0
1
0
1
1
0
1
1
0
1
1
2
1
1
0
2
1
0
0
2
1
1
0
1
1
2
1
0
0
1
1
0
0
1
0
5
2
0
1
1
1
1
0
0
0
0
1
0
2
0
1
2
3
2
0
1
1
1
0
2
1
2
0
2
2
1
1
0
1
1
0
0
1
1
2
1
1
1
1
0
1
1
2
0
2
1
0
1
1
0
1
2
1
1
2
1
1
1
2
1
2
1
1
1
0
1
0
0
2
0
0
2
0
1
1
1
0
1
2
1
1
2
1
2
0
1
1
1
0
2
0
1
1
1
1
1
1
1
0
1
2
2
1
0
1
2
1
1
0
1
0
1
1
1
1
0
0
2
0
1
2
0
2
1
0
2
1
2
1
1
2
1
1
1
1
1
1
1
1
2
0
1
2
1
2
1
1
1
2
1
1
1
1
0
1
3
0
1
1
0
1
1
0
1
1
2
0
0
2
0
1
0
1
2
2
0
3
1
2
1
2
1
1
1
1
0
2
2
1
0
1
2
0
1
0
0
0
1
0
2
0
2
0
1
3
1
1
1
2
2
0
0
1
1
1
1
1
1
1
1
1
0
0
1
1
1
1
1
1
2
1
1
0
1
2
2
2
2
2
1
1
1
1
1
1
0
2
1
2
2
1
1
1
0
1
0
1
0
0
1
0
1
0
1
1
1
2
1
2
2
0
2
1
1
1
1
0
0
0
1
1
2
1
0
2
0
0
1
1
1
1
1
2
0
1
1
2
1
3
2
0
1
1
0
1
2
1
2
1
1
2
0
1
1
0
2
1
1
1
2
1
0
2
2
2
1
0
2
2
1
0
1
0
0
1
2
1
2
0
1
2
1
1
2
1
0
1
1
1
0
0
2
1
1
0
1
2
1
1
1
2
1
0
1
0
2
1
0
1
1
0
1
1
2
1
1
0
2
1
2
2
0
0
2
2
1
0
1
1
0
2
1
1
2
0
0
0
1
1
1
0
1
0
2
0
1
1
0
1
1
1
0
1
1
0
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
2
1
2
1
1
2
0
0
1
2
0
1
1
1
1
1
2
1
2
0
1
0
0
1
0
0
2
1
2
1
0
2
1
1
1
2
2
2
1
2
2
0
1
1
1
1
2
1
1
2
0
2
1
1
1
2
0
1
0
2
2
1
0
0
1
0
0
1
1
1
0
0
1
1
1
1
1
1
0
1
1
0
1
2
1
0
1
1
1
1
1
2
1
0
1
1
1
1
1
1
1
0
0
0
1
1
1
3
0
2
1
1
0
1
2
2
1
1
0
0
1
1
1
1
0
0
1
2
2
1
1
2
0
2
1
2
2
0
1
2
2
1
0
2
1
1
1
1
1
0
1
0
1
1
1
0
2
1
0
1
1
0
0
1
2
1
0
2
0
2
2
1
1
1
1
1
0
1
0
1
0
1
0
2
2
1
2
1
1
1
0
0
1
2
0
2
1
1
1
1
1
0
1
1
0
1
1
2
1
1
1
2
2
1
1
1
2
1
0
1
2
1
1
2
1
2
1
2
2
2
2
1
0
2
1
2
0
1
1
0
1
1
1
1
2
0
1
0
0
1
1
1
1
1
0
2
1
2
0
0
0
0
0
2
1
1
2
1
1
1
1
2
0
0
0
1
2
1
1
1
1
1
1
1
1
1
1
0
1
1
2
2
0
0
2
1
1
2
2
1
2
1
0
2
1
1
2
1
1
1
1
1
1
1
1
0
1
1
1
2
0
1
1
1
0
3
0
1
1
1
1
2
2
0
0
1
2
1
1
1
1
1
0
1
1
1
0
0
1
1
1
0
0
2
0
2
1
1
0
1
1
1
1
1
1
0
3
2
0
1
0
0
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
0
1
1
1
1
0
2
2
2
1
1
0
2
1
1
1
0
1
1
0
1
0
1
0
0
2
1
2
0
1
1
1
0
0
2
1
1
1
1
2
1
1
0
1
1
1
1
1
2
0
2
2
0
1
1
1
4
2
1
2
0
0
1
1
2
1
3
2
0
1
1
1
2
1
0
1
2
2
2
2
1
1
1
1
1
0
2
1
1
0
1
2
0
1
1
1
2
2
1
1
2
0
1
0
1
0
0
0
0
1
0
1
1
1
2
1
1
1
1
1
0
2
1
0
0
2
2
1
0
1
1
1
0
0
3
1
0
0
4
0
2
1
2
1
3
1
2
1
1
0
0
1
0
2
0
1
2
1
0
2
1
1
0
1
1
1
0
1
2
1
2
1
2
2
1
1
1
1
2
1
1
1
2
1
0
1
1
0
1
2
1
0
0
0
1
1
1
2
2
1
1
1
1
1
2
2
1
0
1
0
1
1
0
1
1
1
1
0
1
1
0
0
1
1
1
2
1
0
1
2
0
2
1
4
0
2
3
2
0
2
1
0
2
1
0
0
0
2
1
1
0
2
1
1
1
2
2
1
0
1
1
2
1
2
0
1
2
2
0
1
2
1
1
2
0
0
1
0
0
1
2
1
2
2
1
0
2
0
1
0
2
0
1
0
0
1
2
1
2
1
1
0
2
1
1
2
2
0
1
0
1
1
2
1
1
2
1
0
0
1
2
1
1
1
1
0
1
0
2
0
1
0
1
1
1
0
0
0
1
0
1
0
0
1
0
2
0
1
2
1
1
2
2
0
1
1
2
2
1
1
0
1
1
2
1
0
1
0
1
1
2
1
1
0
1
1
1
2
0
2
1
1
1
1
0
1
0
0
0
1
0
0
1
1
1
2
1
1
0
2
1
2
1
2
0
1
2
0
0
1
1
1
0
3
0
0
1
2
1
1
1
2
0
1
1
0
0
1
1
0
1
0
2
2
1
1
0
1
2
2
1
2
1
1
0
2
1
2
2
1
0
1
2
2
0
1
2
2
2
2
2
2
1
1
0
2
2
2
1
1
0
1
6
2
0
1
1
2
0
1
1
1
1
2
0
1
1
2
2
2
1
0
0
1
2
1
1
1
2
1
1
1
1
2
1
1
1
1
0
1
1
1
0
1
2
0
1
0
1
1
1
0
1
1
1
2
2
1
1
1
1
0
1
1
1
1
1
2
1
2
0
1
6
1
0
0
0
1
1
0
2
1
2
1
2
1
1
1
1
0
1
0
0
1
1
1
1
0
0
1
2
1
1
2
2
0
1
1
1
2
1
1
2
0
2
1
2
1
1
2
1
2
1
1
0
0
0
1
0
11
1
2
2
2
0
0
1
1
0
1
2
1
1
1
2
1
2
1
1
0
2
0
0
1
1
2
1
0
1
0
0
1
2
1
1
0
0
1
0
2
2
2
1
1
1
1
1
0
0
1
0
2
1
1
1
0
0
1
2
1
0
0
1
0
1
1
1
1
3
0
0
1
0
2
2
0
1
0
1
1
1
2
0
1
1
1
1
1
1
0
1
1
0
2
4
2
2
0
2
0
0
1
1
1
1
0
1
2
1
0
0
0
1
1
0
1
1
1
0
1
2
2
1
0
0
2
1
2
0
1
3
1
0
1
1
1
0
2
1
1
1
0
0
1
1
0
1
1
0
1
1
1
1
0
1
2
1
1
0
2
1
1
1
1
1
0
0
1
1
0
1
2
0
1
2
1
1
0
1
1
0
0
2
1
1
1
0
0
2
2
1
0
0
0
1
0
1
1
1
1
2
2
1
1
0
1
0
0
0
1
1
1
0
1
1
0
2
1
0
1
1
1
2
0
1
2
1
1
1
0
1
0
0
2
1
1
1
1
1
0
0
1
1
0
2
2
2
1
2
2
2
0
2
0
1
1
3
1
0
0
1
1
0
1
0
1
1
0
1
1
2
1
1
1
1
1
1
1
2
1
1
2
2
0
1
0
1
1
0
2
0
1
1
1
1
1
2
0
1
0
0
1
1
2
1
1
0
1
1
1
3
2
1
1
0
1
0
2
1
1
1
1
1
2
1
1
1
1
1
0
1
2
1
2
1
2
3
1
0
0
1
1
0
1
2
0
1
2
1
0
1
1
2
2
1
1
0
1
1
2
2
2
2
0
1
2
0
1
2
1
0
1
1
1
2
2
1
2
2
0
0
2
1
0
2
2
1
1
2
0
1
1
1
1
2
0
1
2
2
2
0
1
1
2
2
1
2
1
1
1
2
1
0
0
1
1
1
0
1
2
0
1
0
2
1
0
1
1
1
0
1
1
1
2
1
1
1
2
1
0
1
1
2
1
2
1
2
1
1
2
1
1
0
1
2
0
1
1
1
1
0
0
2
1
1
1
1
1
1
0
1
1
0
1
2
2
1
0
1
1
0
2
0
2
0
2
1
1
1
0
0
0
1
0
1
1
1
1
1
0
1
0
1
1
1
2
0
1
0
1
1
1
2
2
2
1
1
2
0
1
1
1
1
1
1
1
0
2
0
1
1
1
1
1
2
2
0
1
2
1
1
2
2
1
1
1
0
0
0
1
2
2
2
1
2
1
1
1
1
1
2
1
1
1
1
2
1
1
1
0
0
1
0
2
1
2
1
2
2
1
1
1
1
2
0
1
1
1
0
1
1
1
2
1
1
1
0
0
3
2
1
1
0
1
2
0
1
1
0
0
1
1
1
1
1
1
0
1
1
1
2
1
0
2
0
0
1
2
1
0
1
2
0
1
0
1
0
0
1
1
1
0
1
2
1
1
2
1
1
2
0
1
1
2
1
2
1
1
1
1
0
0
0
2
1
1
0
1
1
1
1
1
2
1
1
2
0
0
2
2
1
2
0
2
0
1
0
1
1
1
1
1
1
0
1
2
2
1
0
0
1
0
1
1
1
0
2
1
1
1
1
0
1
1
1
1
1
0
1
1
1
1
0
2
1
1
1
1
0
0
2
1
0
1
1
0
1
3
1
2
0
4
3
1
1
2
1
2
0
2
0
2
1
2
2
2
1
1
1
0
2
1
0
2
1
0
1
1
2
1
1
2
1
0
1
2
1
1
1
0
2
1
1
2
2
0
1
1
1
1
2
1
2
2
1
2
1
1
1
1
1
1
1
0
2
1
1
1
0
1
1
1
1
0
1
0
1
1
1
2
0
0
2
0
0
0
1
2
1
2
1
0
1
1
3
0
0
1
1
2
1
2
0
2
2
0
0
2
1
2
1
1
1
2
0
2
1
1
1
1
0
0
1
1
0
1
1
1
1
1
0
2
1
2
1
0
1
0
1
2
0
2
1
2
0
1
0
2
0
1
1
2
0
1
2
1
0
0
1
1
2
1
2
0
1
0
1
1
2
1
1
2
1
1
0
0
1
2
1
1
3
1
1
0
1
1
0
1
1
1
2
1
1
0
1
0
0
2
1
2
1
1
1
1
1
1
1
1
2
0
0
2
1
1
0
2
2
0
0
1
1
1
0
0
1
1
1
1
2
1
1
1
1
1
1
0
0
1
2
2
1
2
0
1
1
1
1
0
0
0
1
1
1
1
2
0
2
1
1
0
2
0
1
2
1
0
0
0
2
1
1
1
2
1
1
0
0
2
1
1
1
2
2
1
2
2
1
1
2
0
0
0
0
2
1
1
1
0
0
2
0
0
1
1
1
1
0
1
1
1
1
2
0
1
1
1
1
0
1
2
1
0
1
0
1
1
1
1
2
0
2
1
0
0
2
1
1
0
1
0
1
1
0
2
1
1
0
2
1
1
5
2
0
1
1
1
0
1
1
0
0
1
2
0
0
1
1
0
0
1
1
1
2
1
1
1
0
2
0
1
0
1
0
1
1
0
0
0
1
2
1
0
1
1
0
0
1
0
1
0
0
1
2
1
1
1
1
2
0
0
1
1
1
2
1
2
0
0
1
2
3
1
0
1
1
0
0
0
1
1
0
0
0
1
0
1
0
2
1
0
1
1
0
1
2
1
1
2
0
1
1
2
1
1
1
1
1
1
1
1
0
1
1
0
2
0
2
1
1
0
1
0
0
1
1
1
0
1
2
1
1
1
2
1
1
1
1
1
0
2
2
1
1
2
1
0
1
0
0
2
1
1
2
1
1
2
1
1
1
2
1
1
1
1
2
0
1
1
1
1
1
2
2
2
2
1
1
0
1
1
0
1
0
2
1
0
1
0
0
0
1
2
1
0
1
1
1
1
1
2
1
1
1
1
1
1
2
0
2
2
1
2
2
1
1
1
1
0
0
0
1
0
0
2
2
1
1
2
2
0
0
0
2
1
1
1
2
1
0
0
1
1
1
1
1
1
1
0
0
1
2
1
1
1
3
1
1
2
1
0
1
0
1
1
1
1
2
1
0
2
1
0
1
1
1
0
1
1
1
1
1
2
0
2
1
1
2
0
0
0
0
1
2
0
0
2
2
1
1
1
2
1
1
4
1
0
0
1
2
1
0
2
2
0
1
0
1
1
0
2
2
0
1
1
1
1
1
1
1
1
1
1
1
1
1
0
2
2
1
0
2
0
2
1
3
1
0
0
1
2
0
0
1
1
1
1
0
1
1
1
0
2
1
1
2
2
1
1
2
1
1
1
1
2
1
1
1
2
0
0
0
0
0
2
2
0
2
1
0
1
2
0
2
0
0
0
1
0
1
1
0
0
1
0
1
1
1
1
0
1
2
0
1
1
1
1
1
1
2
1
1
1
0
1
0
0
0
2
1
1
1
2
1
1
1
1
2
1
1
0
0
2
1
0
0
1
2
2
1
1
1
1
1
1
0
1
1
1
0
0
1
2
1
1
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
2
0
0
1
2
1
2
2
0
2
2
0
2
2
1
1
2
1
1
0
1
1
2
1
1
0
1
1
2
1
2
1
1
0
1
0
1
1
1
1
1
0
1
0
1
1
1
2
1
1
1
1
1
0
2
0
1
1
0
1
0
2
1
1
0
1
2
1
2
1
0
1
0
2
0
0
0
0
2
1
1
0
1
1
0
1
1
1
0
1
0
2
0
2
1
1
2
2
1
1
1
2
1
2
1
2
1
2
2
1
2
2
2
0
1
2
0
1
3
2
2
1
1
1
0
0
1
0
2
1
1
1
3
1
2
0
1
2
0
2
1
1
0
0
1
1
1
1
1
0
1
2
1
1
2
2
2
0
1
1
0
0
1
0
2
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
2
2
0
2
1
1
2
1
1
0
1
1
3
0
1
0
0
2
1
1
2
1
0
0
1
3
1
1
1
1
1
0
1
1
2
1
1
0
0
0
1
1
0
0
2
1
0
1
2
1
0
1
2
2
1
0
1
0
0
0
1
0
3
2
1
1
0
1
2
0
1
1
1
2
1
1
1
0
2
4
0
0
0
1
0
1
1
1
1
0
1
0
1
1
3
1
1
1
1
0
1
1
0
1
1
1
0
1
1
1
1
1
1
0
2
1
2
2
0
0
1
2
2
0
2
1
1
1
1
1
2
1
0
1
1
1
2
2
1
2
2
0
0
2
1
2
1
2
0
0
1
1
1
2
1
1
2
2
1
1
0
1
2
0
0
1
1
2
1
0
1
1
0
1
1
1
1
2
1
1
1
1
1
2
2
1
0
1
2
2
1
1
1
2
2
1
1
1
0
1
1
0
0
1
1
2
2
0
1
1
1
1
1
1
1
1
2
2
2
2
2
1
2
1
1
1
1
2
1
1
1
1
1
0
0
2
1
1
1
0
2
0
2
0
2
2
0
1
0
3
0
1
0
1
0
1
2
2
1
2
1
1
2
1
0
0
1
2
1
0
0
1
1
2
0
1
2
1
1
1
2
2
0
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
0
1
2
1
1
2
2
1
1
1
0
1
1
0
0
1
2
0
0
1
1
0
0
2
2
0
1
1
2
0
1
2
0
1
1
1
2
2
0
2
2
1
1
1
1
0
0
1
2
1
1
1
1
1
1
0
1
0
0
1
2
2
0
1
1
2
0
0
1
1
1
1
2
2
0
0
1
1
1
1
2
1
2
1
1
2
1
1
1
0
1
1
1
2
2
0
1
1
1
1
2
2
1
0
1
1
1
1
1
1
0
1
1
1
1
1
2
1
0
1
1
2
0
1
1
0
1
1
2
1
1
1
1
2
1
1
2
1
2
0
0
0
1
1
0
1
1
0
2
1
0
1
0
1
1
0
1
1
2
2
2
0
1
1
1
0
3
0
1
1
2
2
1
0
0
0
2
0
2
1
2
0
2
2
1
2
1
1
1
1
2
2
1
1
2
1
0
2
1
2
1
1
1
1
1
1
1
0
0
2
2
2
2
1
0
2
2
2
1
1
1
1
1
0
2
2
1
2
2
1
1
1
1
2
2
1
2
1
1
1
0
1
0
1
1
1
1
1
0
0
2
2
0
1
1
1
2
0
0
2
1
2
2
1
1
1
1
1
1
1
1
0
1
0
1
0
1
0
1
1
2
0
0
0
1
1
0
2
1
1
2
0
1
0
1
1
0
1
1
1
2
0
2
0
1
2
1
2
1
1
1
1
2
0
1
2
0
1
0
1
2
1
1
0
1
1
1
1
0
2
2
1
1
1
1
1
2
1
1
0
1
1
2
2
0
0
1
0
1
3
1
1
1
0
0
1
3
0
0
2
1
1
2
1
0
0
0
1
0
1
2
2
2
1
1
1
1
1
2
0
1
1
1
1
2
1
0
0
0
1
1
1
1
4
1
0
1
0
1
1
1
1
1
0
2
1
0
2
0
2
0
1
0
1
0
0
0
1
1
1
1
2
2
2
0
0
1
1
1
2
1
1
0
0
0
1
1
1
0
1
1
2
2
2
1
0
2
0
2
1
2
1
1
0
1
1
2
0
0
1
0
1
1
1
1
1
0
1
1
4
0
1
2
1
1
1
1
1
1
1
2
1
1
0
2
1
0
2
0
1
0
1
1
0
1
2
0
2
1
0
1
2
0
1
1
0
0
0
2
2
0
1
0
0
1
2
0
2
0
1
1
3
1
1
0
2
1
2
0
1
2
1
1
0
0
1
1
0
0
0
0
0
0
2
1
1
1
1
1
0
0
2
2
0
1
1
1
1
2
0
0
1
1
1
2
2
0
0
1
0
1
1
1
1
0
1
0
2
1
1
2
1
1
0
1
0
0
1
0
1
1
0
0
1
0
2
0
2
2
1
1
2
1
1
0
0
1
1
0
1
1
1
1
1
1
0
1
1
1
0
1
2
2
0
0
3
1
1
1
2
0
0
2
1
1
1
1
0
1
1
1
0
1
1
1
2
1
0
0
1
1
1
1
1
0
1
2
3
1
0
1
1
1
0
1
1
0
1
2
2
1
1
1
0
0
1
1
2
0
0
0
1
0
1
2
2
0
1
2
1
1
2
1
0
1
1
0
0
1
0
0
1
1
2
1
2
2
0
2
0
0
2
1
2
1
1
1
1
1
2
1
1
1
1
2
1
0
1
1
1
1
1
2
1
1
2
1
0
1
0
2
1
2
1
1
1
1
2
6
2
0
2
0
1
1
0
0
0
1
1
0
1
1
1
0
0
1
1
0
0
1
1
1
1
0
1
0
1
0
0
1
1
2
0
1
1
2
0
1
1
0
1
1
1
1
1
2
1
1
1
3
0
2
2
1
2
2
1
0
1
2
2
1
1
0
0
0
1
1
1
2
1
2
2
1
1
1
2
2
1
1
1
1
1
0
1
2
1
1
2
2
0
0
1
1
1
0
2
1
1
0
1
1
2
0
2
1
1
1
1
2
1
2
0
2
1
1
1
1
1
0
2
2
2
1
2
4
1
1
1
0
0
1
1
1
0
1
2
1
2
1
1
0
2
1
1
1
1
1
0
1
2
1
0
1
0
0
1
1
1
0
2
0
1
1
1
1
2
0
0
0
1
1
1
0
0
1
2
2
0
0
1
1
0
1
1
1
0
0
4
1
1
1
1
2
2
1
0
1
1
1
1
1
1
1
0
0
1
1
1
1
0
0
0
4
1
1
0
1
1
1
1
1
0
1
2
1
1
0
2
1
1
1
0
0
1
0
2
2
1
0
1
1
1
1
0
1
2
2
1
1
1
0
0
2
2
2
1
1
1
2
1
0
3
1
0
1
1
0
2
1
1
1
1
0
2
1
0
2
2
1
1
2
1
0
2
1
3
2
1
0
0
1
1
1
0
1
1
1
1
0
2
0
3
1
2
1
0
2
0
2
1
1
1
1
0
2
0
0
1
1
1
3
1
0
0
1
0
1
1
0
2
0
0
2
1
1
2
1
1
1
1
1
2
1
1
0
1
1
1
2
1
0
1
2
2
1
2
1
1
1
0
0
2
1
0
1
0
2
1
1
1
1
1
1
2
1
1
1
0
0
1
0
1
2
1
0
0
1
2
1
0
1
0
2
2
1
1
1
0
1
1
1
1
3
1
1
2
1
1
1
1
1
2
1
2
0
1
1
0
1
2
0
1
2
2
0
1
0
0
2
1
1
0
0
2
2
1
1
0
0
1
0
2
1
2
1
1
1
1
1
0
2
1
1
2
1
0
0
1
1
1
1
1
0
1
0
0
1
2
1
1
0
2
1
1
2
1
0
1
1
1
2
1
0
0
0
1
2
0
1
0
1
0
0
1
1
1
2
1
1
1
1
1
0
1
1
1
0
0
2
2
2
1
2
1
1
1
1
2
0
1
1
1
2
0
1
2
0
4
2
1
0
1
1
0
2
1
2
1
1
1
2
2
1
2
0
1
1
0
0
1
1
1
1
1
1
1
1
1
0
1
2
1
2
1
1
1
1
1
0
1
1
1
1
0
2
0
1
0
1
1
2
0
0
1
1
1
1
0
0
1
1
2
1
2
0
0
2
2
2
1
1
1
0
0
0
1
0
1
1
2
0
1
0
1
0
0
1
3
2
1
1
2
1
0
2
2
0
1
1
0
0
1
2
1
0
1
1
0
1
0
0
0
1
1
0
1
1
1
2
0
1
1
0
1
2
0
0
2
2
1
0
1
1
0
1
0
1
1
1
1
0
2
2
1
1
2
0
0
0
3
1
2
1
0
1
1
2
1
0
0
0
3
1
3
1
1
2
0
1
0
1
0
2
2
2
0
1
0
2
2
1
0
0
2
1
1
0
1
1
4
2
0
1
2
1
0
0
1
0
1
1
0
1
1
0
0
1
0
0
0
1
1
1
0
0
1
2
3
2
2
1
0
1
1
1
2
1
0
1
1
1
2
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
0
1
2
1
0
0
0
1
1
1
1
0
1
1
0
2
0
1
0
1
2
1
0
2
0
2
2
0
0
1
1
1
2
2
1
1
0
1
0
1
1
0
0
1
1
1
0
0
1
0
1
1
2
2
1
1
1
0
1
1
2
1
1
0
0
1
2
2
2
2
2
0
1
2
0
1
0
2
1
1
0
1
0
1
1
0
0
1
1
0
1
0
2
1
1
1
0
0
2
0
2
2
1
2
5
1
0
1
1
0
1
1
0
0
2
1
1
2
1
1
2
0
2
1
1
0
5
1
1
2
1
2
0
0
0
1
1
1
0
1
1
1
1
2
1
1
1
2
1
1
0
1
0
1
1
1
0
0
1
3
0
1
2
2
1
1
1
1
0
0
0
1
1
1
2
1
1
0
2
1
0
0
0
1
1
1
0
3
1
0
2
0
1
1
2
1
1
0
2
1
2
0
0
1
1
0
0
0
2
1
2
0
2
0
2
2
2
1
0
1
1
1
1
0
0
0
0
1
1
1
2
1
1
0
1
1
0
1
3
1
2
0
1
0
0
0
0
1
1
0
1
1
1
1
1
2
0
2
1
1
2
2
1
1
1
0
1
1
1
1
2
0
1
2
1
2
2
2
1
1
1
1
0
2
0
0
0
1
1
0
0
2
1
1
0
2
0
0
1
1
1
1
2
0
1
0
1
1
1
1
2
1
1
0
1
1
2
2
1
1
2
0
1
1
1
2
1
0
1
1
1
2
1
0
1
1
0
1
2
1
2
1
1
0
0
2
0
2
0
1
1
2
1
0
0
1
1
2
0
0
0
0
0
0
1
1
0
1
0
1
1
0
1
1
1
0
1
1
0
1
1
1
0
1
1
1
1
0
1
2
1
0
0
1
1
1
1
1
1
1
1
0
0
2
1
1
2
2
1
1
0
2
1
0
0
1
1
1
0
1
2
1
1
1
0
1
0
1
1
1
1
1
1
1
1
1
0
1
1
3
1
0
1
2
0
2
0
0
0
0
1
2
1
0
1
2
1
1
1
2
0
2
1
1
0
1
1
0
1
1
1
2
0
1
2
1
1
2
2
2
1
1
1
1
1
0
2
1
2
1
2
1
1
2
1
0
1
1
1
1
0
1
1
0
1
1
1
1
1
0
1
1
1
0
2
1
1
1
0
2
1
1
1
0
1
1
1
1
1
1
0
2
0
0
0
0
0
1
2
1
1
0
0
1
1
1
1
1
1
1
2
1
2
1
1
1
2
1
1
2
2
1
2
1
1
2
1
0
1
1
0
1
2
0
1
1
1
2
4
0
1
1
1
1
1
1
2
0
1
1
1
2
0
2
1
1
1
1
3
1
2
1
2
0
0
1
1
0
2
2
0
0
1
1
0
1
0
1
0
2
1
2
2
1
1
1
0
1
1
2
0
0
2
0
0
1
1
1
1
2
1
0
2
1
1
1
1
3
0
1
2
0
1
0
1
1
1
1
1
1
2
1
1
1
0
1
0
1
1
0
1
2
1
0
1
2
0
1
1
1
1
1
1
1
1
0
1
1
2
2
2
1
1
2
0
1
1
1
0
1
1
1
1
2
0
0
1
2
2
1
0
2
0
1
0
2
0
0
1
1
2
1
0
1
0
3
1
1
1
1
1
0
1
1
2
1
1
1
1
0
0
1
0
1
1
1
1
1
1
0
1
1
0
1
1
2
0
2
1
2
1
2
0
1
1
1
0
0
1
2
1
1
1
1
1
1
1
0
2
1
1
1
0
1
1
1
0
1
1
0
1
1
1
0
1
1
1
2
1
1
1
1
0
2
1
1
0
2
1
1
0
1
1
0
1
2
2
0
1
1
2
0
1
0
0
0
2
0
0
2
2
0
0
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
0
0
1
1
0
0
1
0
1
1
1
2
1
1
1
1
2
1
1
1
0
1
2
1
0
1
0
1
1
2
1
2
2
2
0
1
0
0
1
2
0
1
2
2
1
2
1
1
0
1
0
1
1
2
1
0
1
2
2
0
1
1
2
0
1
1
2
1
1
0
1
0
1
2
0
2
1
2
1
0
1
2
2
1
1
0
2
0
1
0
0
1
1
1
0
1
2
1
0
0
1
1
2
2
2
1
2
1
2
1
1
2
0
2
0
1
0
0
1
1
1
1
2
1
1
3
0
1
2
1
2
2
1
2
1
1
2
3
1
0
2
1
2
1
2
1
2
1
1
1
0
2
1
1
1
1
2
1
0
1
1
1
0
1
2
1
1
0
1
1
0
1
1
1
1
0
1
0
1
2
1
1
1
1
1
1
1
1
0
0
0
1
1
1
1
1
0
0
1
1
1
1
1
0
2
2
0
0
2
1
1
2
0
1
1
2
1
1
1
1
1
0
2
1
0
1
1
0
0
1
0
1
0
3
2
0
1
0
1
0
2
0
0
0
1
1
2
1
1
1
1
1
1
2
0
1
1
2
1
0
1
1
1
0
1
1
0
1
0
1
1
0
3
1
1
0
1
2
1
1
2
1
0
1
1
1
1
1
2
2
0
1
2
1
0
1
1
1
1
0
0
0
0
1
1
2
2
0
0
0
1
1
2
0
1
2
0
2
1
1
1
2
1
1
2
1
1
2
0
1
1
1
1
1
0
1
0
1
1
0
2
1
1
0
1
4
1
0
0
1
2
1
0
1
2
2
1
1
1
2
1
2
0
1
2
2
0
2
1
1
1
2
2
2
1
0
0
1
1
1
1
2
1
1
1
2
1
1
1
0
1
0
0
0
1
1
1
2
1
1
1
1
1
1
1
1
0
1
1
1
0
1
1
1
2
3
1
1
0
2
0
0
2
1
2
1
0
1
0
2
1
0
1
2
1
0
2
1
1
1
2
1
2
2
1
1
1
1
0
2
1
0
2
1
0
1
0
1
3
2
2
0
1
0
2
1
2
1
1
1
1
1
1
1
0
1
0
0
2
0
1
0
2
1
2
0
2
0
1
3
0
1
1
0
1
1
1
0
1
1
2
0
1
1
1
2
1
1
2
1
1
0
1
0
1
0
3
1
2
1
1
1
2
1
0
2
0
2
0
2
1
0
1
0
1
0
1
0
1
1
1
0
0
1
1
1
1
1
1
1
0
2
1
1
1
1
0
1
1
1
2
1
2
0
1
1
1
2
1
1
0
1
2
2
0
1
1
2
1
1
1
1
1
2
1
0
0
1
0
0
3
1
1
1
0
1
1
2
1
1
0
0
0
2
1
1
1
1
1
1
1
0
2
1
0
0
1
1
0
1
0
0
2
1
1
2
0
1
1
1
1
1
0
1
1
1
0
0
1
1
1
0
0
0
0
0
1
0
1
2
0
0
0
1
0
2
2
0
1
1
1
1
1
1
1
1
1
1
2
0
1
1
1
1
1
1
1
1
1
0
1
0
1
0
1
2
0
1
1
1
1
0
1
1
2
2
1
1
2
1
1
0
1
1
2
1
2
1
1
1
2
0
1
1
1
1
2
2
1
1
1
2
0
1
2
1
1
2
0
1
1
1
1
1
0
0
0
2
1
1
2
1
1
1
0
1
0
0
1
0
0
2
0
0
1
0
1
0
1
0
1
2
2
1
1
1
1
0
1
1
0
0
1
1
2
2
1
0
1
1
2
0
0
1
1
1
1
1
0
2
0
0
0
1
0
1
1
1
2
0
3
0
0
1
2
0
1
0
1
1
1
1
2
2
1
1
1
1
1
2
1
1
0
1
0
1
0
0
1
1
2
1
0
2
0
1
1
0
0
1
1
0
1
1
2
1
1
2
1
0
0
0
0
1
1
1
0
1
2
1
1
0
1
1
0
1
1
1
1
2
1
0
1
1
0
2
1
0
2
0
0
0
1
0
0
0
1
1
1
0
2
1
1
0
1
2
1
4
2
0
0
0
0
1
0
0
1
0
1
1
1
0
0
1
2
1
2
0
0
1
1
1
2
1
1
2
2
1
2
1
2
1
1
1
1
0
0
1
1
1
0
1
1
1
1
0
0
1
1
1
2
2
1
3
1
1
1
1
2
1
1
1
1
0
1
1
0
1
1
1
0
0
1
2
0
2
1
1
0
1
0
1
0
1
0
1
0
2
1
1
1
1
0
2
2
1
1
0
2
1
1
1
0
1
2
1
1
1
0
1
2
0
2
0
1
1
1
0
1
1
0
0
0
0
1
1
2
1
1
1
2
0
2
0
1
1
2
1
2
2
1
1
1
2
2
1
3
2
2
1
1
0
1
0
2
0
1
2
2
1
2
1
1
2
0
1
3
0
1
1
1
1
0
1
3
1
0
2
2
0
1
2
2
0
1
1
0
2
0
1
2
1
1
0
1
1
0
0
1
1
0
0
1
1
1
1
0
0
2
1
1
2
2
0
0
2
0
1
2
1
0
2
0
1
1
2
1
1
1
1
0
2
1
1
1
0
1
0
0
0
1
2
0
0
1
1
0
2
3
0
1
2
1
0
1
1
0
1
0
0
0
3
0
1
1
1
0
1
1
1
2
1
1
2
2
2
0
1
2
1
1
1
1
0
1
1
0
1
1
1
0
0
2
1
1
1
1
1
0
1
1
0
1
0
1
2
0
0
2
2
0
0
2
3
1
2
0
2
1
2
1
1
1
1
1
1
1
0
1
1
1
0
1
2
2
1
1
1
0
0
2
1
1
1
1
1
2
0
0
1
1
0
2
0
2
1
1
1
0
0
2
2
0
2
2
1
1
1
2
0
0
2
2
1
0
0
1
1
0
0
1
1
2
1
2
0
1
0
0
1
0
2
1
1
2
1
2
2
2
2
1
1
2
1
1
2
2
1
1
0
1
0
1
1
0
1
1
2
2
1
1
0
1
2
2
1
0
0
1
1
1
2
0
1
1
1
1
1
1
1
1
1
2
4
2
0
1
1
2
0
0
1
0
1
0
2
0
1
2
2
0
1
1
1
0
1
2
0
2
1
0
2
2
2
1
1
2
1
0
1
0
2
1
0
1
1
2
1
0
0
1
2
0
0
1
1
2
1
2
0
1
1
0
1
1
2
1
2
0
1
2
1
1
0
1
1
0
0
2
1
0
2
1
1
1
0
2
1
2
1
1
0
2
1
1
2
0
1
2
1
2
1
0
1
2
1
1
1
1
1
1
1
1
0
0
0
2
0
1
2
1
1
0
2
1
0
2
0
0
1
1
1
0
1
1
0
1
0
1
1
1
0
1
1
0
0
3
0
1
2
1
0
0
2
1
2
0
1
1
0
2
0
1
1
1
2
1
3
0
1
1
1
0
1
2
1
1
1
1
0
0
1
1
1
1
2
0
1
0
1
1
1
1
0
3
1
1
0
2
0
1
0
1
1
0
1
1
1
2
2
0
1
2
1
0
1
1
1
0
0
1
2
0
0
1
1
0
3
1
0
1
1
1
0
1
0
2
1
1
1
1
2
1
1
1
1
1
0
0
2
1
2
0
0
2
2
1
1
2
0
1
0
2
1
1
0
1
2
0
1
0
1
3
1
1
0
2
2
1
0
0
1
0
0
2
1
1
1
2
2
2
1
3
1
1
1
2
0
0
3
0
1
1
1
1
1
1
1
1
2
1
1
1
2
1
0
1
0
1
1
1
1
2
1
0
1
0
1
2
1
1
2
0
1
2
1
0
1
0
2
0
1
0
1
0
1
0
1
0
2
0
1
1
1
1
0
1
2
1
0
0
0
1
2
1
2
2
1
1
1
1
1
2
0
1
1
1
2
1
1
0
0
0
0
2
2
0
2
1
2
1
1
2
0
1
1
2
2
1
1
1
1
1
2
1
1
1
1
2
2
1
2
1
1
1
0
0
0
1
1
1
0
1
2
1
2
2
1
2
1
0
0
0
1
1
1
1
0
1
0
1
1
0
1
1
1
1
0
1
2
2
1
0
2
1
1
1
1
0
2
0
1
1
1
2
0
2
0
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
0
0
0
1
0
1
2
1
2
2
1
0
1
2
0
1
0
0
0
0
1
0
2
1
0
2
1
1
1
2
2
1
2
0
1
1
2
2
0
0
2
2
1
1
1
1
2
1
2
1
0
2
1
1
1
1
1
1
2
1
1
2
2
2
0
1
1
1
1
2
1
2
1
1
1
1
1
2
2
1
2
1
2
1
0
1
1
2
0
0
2
1
0
1
0
1
1
2
0
2
1
0
1
0
2
0
0
0
1
1
1
2
1
2
0
0
1
1
2
1
0
0
2
1
1
1
2
2
0
2
0
1
0
0
0
2
1
1
1
2
1
2
1
1
1
2
1
1
2
0
1
1
0
0
2
1
2
2
1
1
1
1
1
0
2
1
1
1
1
1
0
2
0
2
1
2
1
1
0
2
2
1
1
0
0
1
1
1
2
1
2
1
2
2
0
1
1
1
0
0
0
1
2
2
1
1
2
0
1
1
0
1
1
2
1
0
1
0
1
1
1
2
1
1
1
2
1
1
1
1
0
1
2
1
0
1
0
1
1
0
1
1
1
2
0
2
1
0
1
0
1
1
1
1
0
2
0
1
0
2
3
1
1
1
0
1
1
1
2
0
1
1
0
1
0
2
1
1
1
1
0
1
1
1
0
1
2
2
1
2
0
1
1
3
1
1
2
1
1
2
1
1
1
0
1
1
1
2
1
2
0
1
1
2
1
1
1
2
2
2
0
0
0
0
1
1
1
1
0
0
1
1
0
1
1
2
0
2
1
2
1
0
1
1
1
2
1
0
0
2
1
2
0
1
1
1
1
1
1
0
0
1
1
1
0
1
2
2
1
0
0
2
0
1
2
1
1
1
5
1
1
2
2
1
1
0
1
1
1
0
1
2
2
1
1
2
0
1
0
1
1
1
0
1
2
1
1
1
1
2
1
1
2
1
0
1
1
1
1
1
1
1
1
1
1
0
1
1
0
0
0
1
0
0
0
0
2
1
1
3
0
1
2
0
1
0
1
0
0
0
2
0
0
2
1
2
1
1
1
2
0
2
0
0
0
1
2
1
1
2
2
2
1
2
1
1
1
1
1
0
0
1
0
1
1
1
2
2
2
1
1
0
1
0
2
1
1
1
0
1
0
1
0
2
1
1
3
2
1
1
0
1
2
1
0
1
1
0
1
1
2
2
2
1
2
0
2
2
0
2
1
2
1
2
1
0
0
0
0
0
1
1
1
1
1
2
2
2
1
1
0
1
0
1
0
1
0
0
1
1
0
0
1
1
2
0
1
1
1
1
0
0
1
1
1
1
2
0
0
1
1
0
2
1
1
2
2
1
1
0
2
1
2
1
0
0
2
1
1
0
1
1
1
0
1
1
0
1
0
0
0
1
1
0
0
1
1
2
3
1
0
1
0
1
0
1
0
0
1
0
0
1
0
2
1
0
0
1
2
1
0
1
1
0
2
1
1
1
1
1
1
1
1
1
0
0
1
0
0
1
0
1
0
1
1
2
1
2
1
0
1
0
0
0
1
0
2
1
1
0
2
1
0
0
1
1
1
1
1
1
0
1
1
2
1
0
1
1
1
0
0
0
1
1
1
1
1
1
0
2
1
1
0
2
1
1
1
2
0
1
0
1
2
1
2
1
1
0
1
1
1
1
2
0
1
1
1
2
1
1
0
1
0
2
1
2
1
1
0
0
2
2
1
1
1
2
1
1
1
0
0
2
1
2
2
1
0
2
1
1
1
1
1
0
1
2
2
1
1
1
1
0
1
0
0
1
1
1
0
0
0
1
1
0
2
1
0
2
1
2
0
0
1
2
0
2
1
0
0
2
2
2
1
0
1
0
1
1
2
2
1
1
2
0
2
1
2
0
2
1
1
1
0
1
0
1
0
1
1
1
1
1
1
2
2
3
1
1
1
0
0
1
0
1
1
0
1
1
1
0
0
1
1
0
0
2
1
1
1
2
1
1
1
1
2
0
1
2
1
0
1
1
2
0
1
0
2
1
1
1
1
1
1
0
2
1
0
0
1
1
2
1
1
1
1
1
2
0
1
1
2
1
0
2
1
2
0
0
1
2
2
1
1
1
0
1
2
1
1
1
1
1
0
0
1
1
1
1
1
1
0
1
0
1
1
1
2
2
2
1
0
1
2
2
1
1
0
2
2
1
2
0
1
1
1
2
1
1
1
2
1
1
4
2
1
1
1
1
2
0
1
1
2
0
1
0
1
0
2
0
1
1
2
0
1
1
2
2
1
1
1
1
1
0
1
1
2
0
1
0
0
3
1
1
1
1
1
1
0
0
0
0
1
0
0
1
2
1
0
0
1
1
0
1
0
1
1
2
1
2
1
1
0
0
1
1
1
2
1
0
4
1
1
1
2
1
1
1
1
1
0
1
1
3
2
2
2
1
2
1
1
1
1
2
0
0
1
2
0
1
2
1
2
1
1
1
1
1
2
1
1
0
2
0
1
1
1
0
1
1
1
1
0
1
2
0
2
1
1
1
0
1
2
1
0
1
1
0
2
0
1
1
2
0
2
1
0
0
1
0
0
0
1
1
2
1
2
1
1
1
0
1
1
2
1
2
2
2
2
2
1
0
0
0
1
1
1
0
1
0
0
1
1
1
2
0
0
0
0
1
1
2
0
2
2
2
1
2
1
2
1
1
1
0
0
1
0
1
1
1
2
0
2
0
0
1
1
1
1
2
1
1
0
1
2
1
1
1
0
1
1
2
1
1
2
1
1
1
2
1
2
1
1
2
1
1
1
2
1
0
2
1
1
1
1
0
1
2
0
1
1
0
2
1
0
0
2
1
1
1
1
2
1
0
0
1
2
1
0
1
1
1
1
0
1
1
0
1
0
1
1
0
0
1
1
0
1
0
1
1
0
1
1
1
1
0
1
1
1
0
1
0
1
1
1
1
1
1
0
1
2
0
1
1
0
0
1
1
2
2
1
0
2
1
1
1
2
0
0
1
2
1
0
2
2
0
0
1
1
1
1
1
0
1
2
2
2
0
1
1
1
1
2
0
1
1
0
0
2
1
0
0
1
1
1
0
1
0
1
1
1
1
1
2
0
2
1
0
1
3
1
1
0
1
1
2
0
2
1
1
1
0
1
1
1
1
2
2
0
2
1
2
0
3
1
2
2
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
2
2
0
1
1
1
2
2
0
2
1
0
0
1
0
1
0
1
0
2
0
1
1
1
1
0
1
0
1
2
0
2
0
2
2
1
6
0
0
1
1
1
1
1
1
2
1
1
0
0
1
1
0
0
0
1
2
0
1
2
1
2
1
0
1
0
3
1
0
2
0
2
0
1
1
0
2
1
2
0
2
0
1
2
1
1
1
2
2
1
0
1
2
1
1
0
1
2
1
2
2
1
1
1
1
2
1
0
1
1
1
1
1
0
1
1
1
1
1
1
2
0
0
1
2
2
1
1
0
1
2
1
2
2
1
0
2
1
1
2
1
1
0
0
1
1
0
1
0
1
1
0
1
0
1
1
1
0
0
2
1
0
1
2
1
2
1
2
2
1
1
2
2
0
1
0
1
2
0
1
1
2
2
2
2
0
0
0
1
1
2
1
0
2
0
1
0
0
1
2
1
1
0
0
1
1
0
2
2
1
1
0
1
1
1
1
1
0
1
1
1
1
1
0
1
2
0
0
0
1
1
0
0
1
1
1
2
1
0
2
1
2
1
0
1
1
1
1
0
2
1
1
1
1
2
1
2
0
1
2
2
0
1
0
1
0
0
0
1
2
1
0
1
0
1
0
2
1
1
1
2
1
1
2
1
1
2
1
1
1
0
2
0
2
1
0
1
2
1
0
1
0
0
2
1
1
0
2
1
0
1
0
2
0
0
0
2
2
2
0
1
0
2
0
0
2
1
1
1
2
2
1
0
2
2
2
1
0
0
1
2
1
1
2
2
1
1
1
1
1
1
1
2
2
0
0
0
2
1
2
1
1
1
2
1
1
2
1
1
0
2
1
1
1
1
0
0
2
0
3
2
2
0
2
1
1
0
0
1
3
1
1
0
0
1
2
2
0
0
1
1
1
0
2
1
0
1
1
2
1
0
1
2
0
0
1
1
1
1
1
2
1
1
2
2
0
2
1
1
2
0
0
1
1
1
2
0
2
1
1
0
0
0
0
0
2
1
1
2
0
1
0
1
3
1
1
1
1
0
1
2
0
0
0
0
1
1
1
1
3
1
1
1
0
0
2
1
2
2
2
2
0
1
2
1
1
1
1
1
1
1
2
1
0
1
0
2
2
0
1
1
0
1
1
0
1
2
1
2
1
1
1
0
1
2
1
1
0
1
1
2
1
2
1
2
0
1
2
2
2
1
1
1
0
0
0
1
1
0
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
0
1
1
2
1
0
0
1
1
1
1
0
1
1
0
1
2
1
0
0
0
1
0
1
1
1
1
2
3
1
1
0
1
1
1
0
1
0
2
1
1
0
2
2
0
2
0
1
1
1
1
1
2
2
0
2
1
0
0
1
2
1
1
1
0
1
0
0
1
1
1
0
1
1
1
1
2
0
1
0
0
2
0
1
1
0
1
1
1
1
1
2
1
1
2
2
1
1
1
1
2
1
1
1
2
0
1
1
1
1
1
1
2
2
1
2
1
2
1
1
0
1
0
1
1
1
1
1
0
0
2
1
2
0
1
2
1
0
1
1
0
0
0
1
0
1
0
2
1
1
1
1
1
1
1
1
0
1
2
6
1
2
1
0
2
1
2
1
2
2
2
0
1
1
2
2
2
2
2
0
2
1
1
0
1
1
1
1
1
1
0
1
2
0
2
1
2
2
1
1
2
1
2
2
1
1
2
1
0
0
2
0
1
2
1
3
1
1
2
0
1
1
1
1
3
2
2
0
0
1
0
2
1
1
2
1
0
2
0
0
1
1
1
1
1
0
2
2
1
2
1
1
2
1
2
2
1
1
0
0
1
0
0
1
1
0
1
0
1
1
1
1
1
2
2
1
1
1
2
1
3
2
0
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
2
0
1
0
1
3
1
2
0
2
1
1
2
1
1
2
0
1
1
0
2
1
5
0
1
1
1
0
2
2
1
2
1
1
2
1
2
2
1
1
1
2
0
1
0
2
1
1
1
2
1
1
1
2
1
2
2
1
1
1
2
1
2
1
1
2
1
0
1
1
2
4
0
1
1
1
0
0
0
1
0
3
0
1
1
0
0
1
0
1
1
0
1
2
2
1
1
1
1
5
1
0
1
0
0
1
2
0
1
1
2
1
2
1
0
1
1
1
2
1
0
0
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
2
1
1
0
1
1
3
0
0
1
0
0
2
1
1
2
2
1
1
0
0
1
2
2
2
1
1
4
2
1
2
1
1
1
1
1
1
1
0
1
0
1
2
2
0
1
1
1
1
2
1
1
2
1
0
1
1
2
1
1
0
1
2
0
1
0
1
1
1
1
2
0
1
1
0
1
0
0
1
1
2
1
1
1
1
0
2
0
2
0
1
1
3
1
1
2
1
1
1
1
1
1
2
1
1
2
0
1
1
0
0
1
0
0
1
1
0
1
2
2
1
0
2
0
2
1
0
2
0
3
1
0
2
1
2
0
2
2
0
1
0
1
1
1
1
0
1
0
1
2
1
0
0
1
1
1
2
2
0
1
0
1
2
1
0
0
1
1
1
0
1
2
1
0
1
1
2
1
2
1
1
2
1
1
2
0
2
2
1
1
2
0
0
0
1
2
0
0
2
1
1
0
1
0
1
1
2
1
0
1
1
0
1
1
2
1
1
0
1
1
0
2
2
1
1
1
1
0
1
2
0
1
1
1
2
1
1
1
1
1
1
0
2
1
0
1
1
1
2
1
0
1
1
1
2
0
0
1
1
1
1
1
0
2
1
1
0
1
1
1
1
2
0
1
0
2
1
3
1
1
2
0
1
1
0
1
1
2
1
2
2
0
1
1
2
1
0
1
1
0
1
2
0
1
1
1
1
2
1
1
1
1
0
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
2
1
1
0
1
1
1
2
2
1
0
2
1
0
0
0
1
1
1
2
2
0
0
2
1
1
0
1
2
1
2
0
2
1
1
2
1
2
1
1
0
1
1
2
1
0
1
0
0
1
1
0
1
0
1
0
1
2
0
1
0
2
1
2
1
2
0
1
1
1
0
0
1
0
1
2
0
2
0
2
1
1
1
0
1
1
2
1
0
2
1
2
1
2
1
0
1
2
0
1
1
0
3
0
0
1
1
0
1
2
2
1
1
2
0
1
2
1
0
1
1
1
0
1
1
1
1
0
1
1
1
1
1
0
1
0
1
2
2
1
2
0
1
2
0
0
0
1
0
1
1
1
0
1
0
1
2
1
1
1
2
1
0
2
0
1
1
1
0
2
0
0
1
2
0
0
0
0
0
1
0
1
0
1
1
2
1
0
1
2
1
0
0
1
0
2
1
2
0
2
1
1
0
1
1
2
2
0
2
1
2
1
0
0
0
2
1
1
0
0
1
1
0
0
0
1
1
2
2
0
0
1
2
0
1
1
1
1
0
0
2
2
1
2
0
1
2
1
0
1
1
1
1
1
0
1
2
1
1
1
1
2
1
1
1
1
1
0
2
1
0
0
0
2
1
2
0
2
2
0
1
1
2
2
0
0
1
0
2
1
1
1
0
1
0
2
1
1
2
2
2
1
1
1
1
1
1
0
0
0
1
2
1
1
1
1
1
0
1
1
0
2
0
2
1
0
0
1
2
1
2
2
1
4
1
1
1
1
0
2
2
2
1
2
0
1
2
1
2
0
1
2
1
1
1
0
1
1
0
0
2
2
2
1
1
2
0
1
2
1
2
1
0
1
1
2
0
1
2
2
0
0
1
2
0
1
1
0
1
1
1
0
2
1
1
0
1
2
2
1
1
1
1
1
1
1
1
2
1
2
2
1
0
1
0
0
2
1
1
1
2
1
1
1
1
1
1
1
2
0
1
0
0
2
1
1
1
2
1
2
2
0
0
2
0
1
1
1
1
0
2
1
2
0
1
2
1
1
0
2
0
3
0
1
2
2
1
2
1
1
1
1
1
1
1
2
2
0
1
2
2
6
1
2
1
0
0
0
0
1
1
1
2
1
1
1
1
1
1
2
1
1
1
0
0
1
1
1
1
6
1
1
1
1
1
1
1
2
1
0
1
1
0
1
0
1
0
2
1
1
1
1
1
1
1
0
0
0
1
1
1
1
1
1
1
2
0
2
1
0
0
0
0
2
0
0
1
0
1
1
0
2
0
0
0
0
2
1
1
1
2
1
0
0
1
2
1
1
1
1
0
2
3
1
3
0
1
2
2
0
1
1
2
1
1
1
1
1
1
1
0
0
1
1
1
1
2
1
1
1
1
1
1
1
1
0
1
0
1
1
2
0
2
0
1
1
1
1
0
2
1
2
2
1
1
2
1
0
0
0
2
0
1
1
1
2
1
2
1
1
1
1
2
0
0
1
0
2
1
2
0
1
1
1
0
0
1
1
2
1
0
1
2
1
1
2
2
0
0
2
2
1
0
1
1
1
1
2
1
1
2
2
2
0
0
1
2
1
0
1
0
1
1
2
1
2
1
1
1
1
1
0
0
2
1
1
1
1
1
1
1
2
2
0
2
1
1
1
1
0
1
1
0
0
2
0
0
0
1
1
0
0
2
1
2
1
2
1
1
1
0
0
0
1
2
0
1
1
1
1
1
1
0
0
1
0
0
1
1
0
0
1
1
0
1
2
2
1
1
1
1
0
1
0
1
0
3
0
1
1
1
1
2
1
0
0
2
1
0
1
2
2
1
0
1
0
1
0
1
1
2
1
0
1
1
1
1
0
2
0
0
1
1
1
1
2
2
1
2
2
1
0
1
0
0
1
1
1
0
2
2
1
1
2
1
1
0
1
2
1
1
1
2
1
1
1
0
1
0
1
2
2
1
1
1
1
0
1
1
1
1
1
0
2
0
3
0
2
0
1
2
1
0
1
0
0
2
1
3
1
1
2
1
1
0
1
2
1
1
1
1
1
1
1
2
0
1
1
1
1
1
2
1
0
0
0
1
0
1
0
1
1
0
2
1
0
1
1
1
2
1
1
1
0
1
1
2
0
1
0
2
0
2
2
2
1
0
0
1
0
1
1
0
0
1
2
2
1
1
2
1
0
1
1
0
0
2
2
1
1
1
1
1
1
2
0
1
2
2
1
2
1
0
1
2
1
0
2
1
2
1
1
1
0
1
1
0
1
1
0
0
1
1
1
0
1
2
1
2
1
0
1
1
2
1
2
0
0
1
0
1
1
0
2
1
0
1
1
1
1
1
0
1
0
2
2
1
1
2
1
2
1
1
1
1
1
2
1
0
2
2
0
0
1
1
1
1
0
0
1
2
0
0
0
0
2
2
0
1
1
0
0
3
2
1
1
2
0
1
1
2
1
1
2
2
1
1
2
0
1
1
1
0
0
2
2
1
1
2
1
2
1
1
1
1
1
1
0
1
0
1
2
1
1
1
0
1
1
0
1
1
1
0
2
1
2
0
2
1
1
2
1
0
0
1
1
1
1
2
2
1
0
1
1
2
1
1
1
0
1
2
2
0
1
1
2
0
0
0
2
1
1
1
4
1
1
2
1
2
1
1
1
0
2
1
2
0
0
0
2
1
0
1
1
1
1
0
1
1
0
1
1
1
1
2
1
2
1
2
2
1
2
0
1
0
0
2
1
0
1
1
2
0
1
0
1
1
2
2
1
1
2
2
1
2
1
1
1
2
0
1
0
2
1
0
1
1
2
1
1
0
0
0
1
2
1
2
1
0
2
0
0
1
0
1
1
2
0
0
1
0
1
1
1
2
0
1
0
1
0
1
2
2
2
1
1
1
1
1
0
1
0
0
2
1
1
1
2
1
0
1
2
0
2
1
0
1
1
1
0
0
2
1
1
0
1
1
1
1
1
0
0
1
0
0
1
2
1
1
2
0
1
0
2
1
0
2
1
1
1
1
1
0
2
1
0
1
2
0
0
0
2
2
1
1
1
0
0
0
1
2
0
1
0
1
0
0
1
1
0
1
1
0
0
2
2
0
2
1
1
0
1
2
1
1
0
2
1
1
0
1
1
2
2
1
1
1
1
1
1
1
2
2
1
1
1
2
1
2
0
2
1
1
1
3
1
2
1
1
2
2
1
1
1
1
1
1
1
1
1
2
0
1
1
1
0
1
2
1
2
1
1
1
2
0
0
1
1
1
1
1
2
1
2
1
1
0
1
0
1
2
2
1
1
2
2
0
1
0
1
2
0
1
2
1
0
0
2
0
2
0
0
5
1
0
2
2
1
1
1
2
0
1
0
1
1
1
0
1
2
1
0
1
1
1
2
2
1
0
0
1
0
0
1
0
1
0
2
2
2
1
0
2
1
1
1
1
2
0
1
0
1
1
1
1
2
1
0
0
1
1
1
0
2
2
1
1
0
2
2
0
0
2
1
2
3
1
1
2
2
1
1
2
1
2
0
2
2
2
2
1
2
2
1
1
1
0
1
2
2
0
1
1
0
0
0
1
1
1
1
2
1
0
1
2
0
2
1
1
0
0
1
1
0
1
0
1
1
0
0
1
1
2
1
2
2
0
0
3
1
1
1
2
2
2
0
0
2
2
1
1
2
1
1
0
1
0
2
0
2
0
1
0
0
1
0
1
0
1
2
1
0
1
1
2
1
1
1
1
1
1
1
2
1
2
1
2
1
2
1
2
0
2
0
2
0
2
2
2
2
2
0
0
0
4
0
0
0
1
1
0
1
2
1
1
1
1
1
1
0
2
2
1
2
0
1
1
1
1
1
1
1
1
2
1
2
1
0
0
2
2
1
0
1
2
1
0
2
1
2
0
1
1
0
1
1
0
2
1
1
2
0
2
2
0
3
1
1
1
1
0
2
0
1
1
2
1
0
2
2
1
2
0
0
0
1
1
1
2
1
2
1
2
0
1
2
1
1
1
1
0
1
1
1
2
1
0
1
3
1
0
0
2
0
1
1
1
2
2
2
1
1
1
0
1
1
1
2
0
0
0
2
1
1
2
0
1
1
0
0
1
1
1
1
0
1
0
0
1
2
0
1
2
1
1
3
2
1
1
1
1
1
4
1
0
0
2
2
1
1
2
1
1
0
0
0
1
2
1
2
0
1
1
1
1
1
0
1
2
1
1
1
0
0
2
0
1
1
1
1
2
2
0
0
1
1
0
0
0
0
2
0
0
1
2
1
1
2
1
2
0
1
1
1
1
2
1
1
1
1
1
0
0
1
1
0
1
1
0
0
0
1
2
0
1
0
2
2
1
2
0
1
1
2
1
2
1
1
1
0
0
1
1
2
1
0
0
0
1
1
1
2
1
0
1
0
0
1
2
1
1
2
1
0
2
1
2
0
2
2
1
0
1
1
1
1
2
0
2
1
0
2
2
2
2
1
1
1
0
0
1
0
0
2
1
1
1
0
2
1
0
1
1
1
0
0
2
1
1
1
0
1
1
0
1
0
1
1
1
1
1
2
1
2
1
2
1
2
0
0
1
1
1
1
1
1
1
0
1
1
2
2
1
1
0
1
1
1
0
0
0
2
2
0
0
2
1
0
0
0
1
0
0
1
1
0
1
0
2
2
2
1
2
2
1
1
0
2
0
2
1
1
2
0
1
2
1
1
1
1
1
3
4
1
2
1
1
0
2
0
2
2
2
1
0
1
1
2
2
0
1
1
1
1
1
0
1
2
1
1
1
1
1
0
1
1
1
1
2
1
1
2
0
1
1
0
1
0
0
3
0
1
1
0
1
1
1
0
2
0
2
1
1
0
1
1
2
0
3
0
1
1
1
2
0
0
2
0
1
0
1
1
1
0
2
0
2
1
0
0
1
1
1
1
2
2
2
0
2
1
2
2
0
0
1
1
1
1
1
1
1
1
1
1
1
2
1
0
0
1
1
1
1
0
2
4
1
1
1
1
1
2
1
1
1
5
1
2
0
1
2
1
2
1
0
2
1
1
1
0
1
1
1
1
2
1
1
1
2
2
2
1
0
2
0
1
0
2
0
1
1
0
2
1
2
0
1
0
2
2
1
2
0
1
0
1
3
1
1
2
1
1
0
0
1
2
0
1
1
2
0
2
2
1
1
2
1
0
1
1
1
1
2
1
1
2
0
2
1
1
1
2
0
0
0
1
2
1
0
1
0
1
2
1
1
1
2
1
0
1
1
1
1
0
2
1
0
2
1
1
1
2
0
0
0
2
1
2
2
0
1
1
0
2
2
0
0
2
1
2
1
0
1
0
1
0
2
1
1
0
0
2
2
0
0
1
1
1
0
0
0
0
2
0
1
1
0
2
0
0
0
0
1
1
1
1
2
2
0
1
1
1
1
0
1
1
0
0
2
1
1
2
2
2
2
0
1
1
1
1
2
0
0
2
1
1
1
1
0
1
0
1
1
1
0
1
3
3
1
0
1
1
0
1
1
2
1
2
1
1
0
2
2
1
1
0
0
1
1
2
0
1
0
1
1
1
0
0
2
1
0
1
0
1
0
1
0
1
1
2
1
0
2
1
1
0
1
0
1
0
1
1
1
2
1
2
2
1
0
0
2
1
1
2
1
1
1
0
1
1
1
1
2
2
0
0
1
1
1
0
2
0
0
1
0
1
2
2
0
1
1
1
1
2
1
1
1
1
0
1
1
1
0
2
1
1
1
2
0
0
0
1
2
1
1
2
2
1
1
2
1
1
0
3
1
1
1
1
1
1
1
1
1
0
1
0
1
1
1
1
2
0
0
2
1
1
1
1
2
1
1
1
0
1
2
1
1
2
1
2
1
0
2
0
1
1
1
1
0
1
1
0
1
1
1
0
0
1
2
1
1
2
1
2
1
0
1
1
3
0
1
2
0
0
1
0
2
1
1
2
2
1
1
1
2
0
1
0
2
1
0
2
0
1
1
1
1
1
2
1
0
0
1
2
2
1
1
0
0
1
1
2
1
0
2
1
1
1
1
2
1
0
0
1
2
1
1
1
1
0
2
1
1
2
2
1
0
2
0
2
1
2
1
0
2
1
0
1
1
1
0
2
3
0
1
2
0
2
1
1
1
2
0
0
0
1
1
0
1
2
0
0
1
5
1
1
1
0
1
1
1
1
1
1
1
0
2
1
2
2
0
2
1
1
0
1
1
1
1
1
0
1
2
0
1
1
1
0
2
2
1
1
1
1
0
1
0
1
3
0
2
1
1
1
1
2
3
0
1
2
1
1
1
0
0
0
1
1
1
2
3
1
1
1
0
0
0
1
1
2
1
1
2
0
2
1
2
0
0
2
2
1
2
1
2
1
1
2
1
1
0
1
1
1
0
1
1
1
0
1
1
2
1
1
0
0
1
0
0
1
1
1
1
0
1
2
0
2
1
0
0
1
2
1
0
0
1
2
2
0
0
1
0
0
1
1
2
1
1
1
0
1
0
1
1
4
1
0
1
3
2
0
1
2
1
3
1
0
1
2
1
1
1
2
2
2
1
0
1
2
0
1
3
1
2
0
1
1
1
2
1
2
0
1
1
1
1
1
0
0
1
2
0
0
2
1
0
2
1
1
1
0
0
1
2
2
2
3
1
0
1
0
0
0
1
1
1
1
2
1
1
1
3
1
2
1
2
0
1
0
0
2
2
1
1
1
0
0
1
0
1
1
1
1
1
0
1
2
2
1
3
1
2
1
0
2
2
1
2
2
0
0
1
1
2
1
0
2
0
0
1
1
1
0
1
1
1
3
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
0
0
1
0
1
1
1
1
1
1
0
2
1
0
2
1
1
1
1
2
1
2
1
2
2
1
1
1
2
1
0
2
0
1
0
1
1
1
0
1
1
1
1
1
2
2
1
2
1
1
1
2
2
1
0
0
2
0
0
0
2
1
0
0
0
4
2
2
3
0
0
2
1
1
1
1
1
1
2
1
1
1
0
1
0
1
1
0
1
0
2
1
1
0
1
1
1
1
1
1
1
2
1
1
0
1
0
0
2
1
0
0
1
0
0
2
2
1
0
1
0
1
1
0
1
1
0
0
0
1
1
1
1
1
1
0
0
1
0
1
1
0
2
0
1
2
2
1
1
1
1
1
2
1
1
0
2
1
1
1
0
1
2
1
2
1
2
2
1
0
1
0
0
3
0
2
0
2
0
0
0
2
0
0
0
0
1
1
1
1
1
1
1
0
1
1
1
2
0
2
1
2
0
0
1
1
0
1
2
1
0
1
1
0
0
0
0
0
1
0
1
1
1
1
0
1
1
1
0
1
0
1
1
4
2
1
2
0
0
1
1
0
1
1
1
0
2
1
1
0
2
1
1
2
1
2
1
0
0
1
1
1
0
1
1
0
1
1
1
1
1
2
1
2
0
1
2
1
2
2
1
1
2
1
2
1
1
1
1
2
1
2
1
1
1
1
0
2
1
1
0
2
1
1
1
1
2
0
0
2
0
0
0
0
2
1
2
0
1
1
1
0
1
0
1
1
0
1
0
2
1
2
5
0
0
2
0
1
2
0
1
0
0
1
1
1
1
0
1
1
1
0
1
1
1
1
1
1
2
2
2
1
2
0
0
1
0
3
2
1
1
0
2
0
2
0
2
0
2
0
1
1
2
2
1
2
1
1
1
2
1
0
0
0
0
0
1
1
0
2
1
1
1
2
0
1
1
1
0
1
0
1
1
1
1
2
1
2
1
1
1
0
2
2
1
1
0
1
0
0
2
2
1
1
2
1
2
2
1
1
1
0
2
1
1
1
1
2
1
1
1
0
1
0
1
1
1
1
1
2
1
1
0
2
1
0
0
2
1
2
1
0
2
1
2
2
2
0
0
2
0
2
1
1
1
0
2
2
1
1
2
0
2
1
2
1
0
2
1
2
2
1
1
0
1
0
0
2
2
1
1
1
2
1
1
1
0
2
1
0
1
1
2
3
1
0
0
0
0
1
1
2
1
1
0
1
1
1
0
0
1
0
0
2
0
1
1
1
1
1
1
0
2
1
0
1
1
0
1
1
1
1
1
1
1
2
1
3
2
0
1
1
2
2
1
1
1
1
1
1
2
1
1
2
2
1
1
0
2
1
0
2
2
2
1
2
1
1
0
2
3
1
2
0
2
2
1
2
2
2
1
0
1
1
2
2
0
2
0
1
1
1
2
1
1
1
1
1
0
2
0
1
1
1
0
0
0
1
1
1
1
1
0
1
1
1
1
1
1
0
2
0
2
1
1
2
1
1
0
0
1
0
2
2
1
0
0
1
1
1
2
1
2
2
2
1
2
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
0
0
1
1
1
0
1
1
1
1
2
1
1
1
3
1
1
0
1
2
0
0
0
1
0
1
1
1
1
0
1
0
1
0
0
3
2
1
1
0
1
1
1
0
1
1
0
2
1
1
0
1
0
0
2
1
1
1
0
1
1
1
0
0
1
1
2
0
1
0
2
2
1
0
1
2
1
1
1
2
0
0
1
1
2
1
2
0
2
2
0
1
2
2
1
0
0
3
1
0
0
1
1
1
0
1
0
1
0
2
1
1
2
0
1
0
0
0
0
1
1
0
1
1
1
2
0
1
2
1
1
0
0
2
1
1
1
1
0
1
1
1
1
1
3
1
1
1
1
1
2
0
0
1
0
1
1
1
2
1
2
1
2
0
1
1
0
1
1
2
1
2
0
1
0
1
1
1
2
0
1
1
0
1
2
1
1
1
1
1
0
2
1
0
1
1
1
2
0
2
0
0
1
0
1
1
1
2
1
2
0
2
1
2
1
1
2
2
1
1
1
2
1
2
1
2
1
2
2
2
0
1
1
2
2
1
1
1
1
2
0
0
2
2
1
2
1
1
2
1
1
1
0
1
1
1
0
0
1
0
0
1
0
2
0
0
0
0
1
2
0
1
1
1
1
1
1
1
1
1
1
0
2
1
1
2
2
1
2
0
1
1
0
0
0
0
1
1
1
1
0
0
1
1
0
0
0
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
0
0
2
1
0
0
2
1
0
0
0
0
0
2
1
1
1
2
1
0
1
1
1
0
2
2
1
0
0
0
1
1
1
0
1
2
0
0
1
1
2
0
2
2
1
1
0
2
1
0
0
1
1
2
0
1
1
1
0
1
0
1
1
1
2
1
1
1
0
1
2
0
0
1
1
1
1
0
1
0
1
1
0
1
1
0
1
0
0
2
1
1
1
1
2
0
1
0
2
1
1
1
2
1
2
1
1
0
2
2
0
2
2
1
2
1
0
0
1
1
2
1
0
1
2
1
1
1
1
0
0
1
1
1
1
1
2
1
1
1
1
1
1
0
1
2
1
1
1
0
1
1
0
1
2
1
1
0
1
1
2
0
0
1
2
1
1
1
2
0
1
0
1
1
1
1
1
1
1
0
2
2
1
1
2
1
0
0
0
0
2
0
0
1
2
1
1
2
1
2
1
2
2
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
0
1
2
1
0
1
1
1
0
1
1
2
1
0
0
1
2
1
1
1
2
2
1
2
0
1
0
1
1
2
1
0
0
0
1
0
0
1
1
1
1
0
1
2
1
1
1
1
3
0
0
1
1
2
2
0
1
2
1
2
1
1
1
1
2
1
0
1
2
1
1
1
1
1
1
1
1
3
1
1
1
1
4
1
1
1
0
1
0
2
2
2
1
1
2
1
2
2
1
0
1
0
2
1
1
1
0
2
1
0
0
2
2
0
1
2
1
1
2
1
1
0
1
0
1
2
1
1
0
2
1
2
2
1
2
1
1
2
1
1
1
2
0
1
1
1
0
2
3
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
0
1
1
1
0
2
1
1
1
0
1
0
1
1
0
1
0
1
1
1
1
1
1
1
2
1
0
2
1
2
1
1
2
0
1
1
0
1
2
1
0
1
1
2
2
1
2
1
2
1
1
2
2
0
1
1
1
2
2
1
1
1
0
1
1
0
1
1
1
2
0
1
2
1
1
2
1
1
1
2
1
0
1
1
1
1
1
0
0
0
1
1
1
0
1
1
2
0
0
1
1
0
1
1
0
1
3
0
2
1
2
1
1
2
0
2
0
2
0
0
2
0
1
2
2
0
1
0
0
1
0
2
2
0
2
1
1
2
1
0
2
1
1
0
0
0
0
0
1
1
1
1
2
1
1
1
0
1
2
2
2
1
1
0
1
1
1
1
1
1
1
2
0
1
0
2
1
1
2
2
1
2
1
0
1
1
1
1
0
2
2
2
1
2
1
2
0
2
1
1
2
0
1
1
2
1
1
1
2
1
2
1
0
0
0
0
1
1
0
2
0
1
1
2
2
1
0
0
1
1
2
1
2
1
0
1
2
2
2
2
2
1
0
2
0
1
2
0
0
1
1
0
1
2
1
2
0
0
1
0
2
0
1
1
2
2
0
1
1
0
3
0
2
0
0
0
0
2
1
2
0
1
1
1
1
1
1
1
1
0
0
1
1
0
2
1
1
1
2
0
0
2
1
0
1
1
1
1
2
1
1
1
2
1
1
0
2
2
2
1
2
1
2
6
1
2
1
0
1
1
1
1
0
0
1
1
2
1
1
1
1
2
1
0
1
0
0
0
0
2
0
1
0
1
1
2
1
2
0
1
0
0
2
1
1
0
1
1
0
0
1
0
2
1
1
0
0
1
1
1
0
0
1
1
0
1
2
1
2
1
0
0
2
2
0
1
1
2
1
1
0
2
1
2
0
1
1
1
0
0
2
1
1
1
1
0
1
2
3
1
1
1
1
1
1
1
2
1
0
1
1
0
1
2
0
1
1
1
1
1
1
1
1
0
1
2
1
1
2
0
1
2
1
1
0
2
1
1
1
1
2
1
0
1
1
1
2
1
1
0
0
0
0
1
1
1
1
0
1
0
1
1
2
1
1
0
1
0
1
1
2
1
1
1
2
2
1
2
0
1
0
2
1
1
1
1
1
1
1
1
2
0
0
2
1
2
1
2
2
1
1
1
0
1
2
1
1
2
1
1
1
1
2
2
1
1
1
0
1
0
2
2
1
1
0
0
2
0
1
1
2
0
2
1
1
2
1
2
1
1
2
1
4
1
0
1
2
1
6
1
1
1
2
1
2
1
2
1
1
2
0
3
1
1
0
1
1
2
1
1
1
2
2
0
0
1
1
1
2
1
1
1
2
0
1
0
2
0
1
1
3
1
2
1
2
1
0
1
0
2
1
1
1
1
0
1
1
1
1
0
1
2
1
1
2
1
1
1
1
0
2
0
1
0
1
2
1
1
0
1
1
2
1
1
0
1
1
0
0
2
1
1
1
1
2
1
1
1
1
1
1
0
2
0
2
0
1
1
1
1
1
2
1
1
1
0
2
2
1
1
1
2
0
1
2
1
1
1
2
2
1
0
1
1
1
1
0
1
1
1
1
0
2
0
2
1
2
1
1
1
0
1
1
1
1
3
1
1
1
0
2
0
0
1
0
0
0
0
2
2
0
1
0
0
1
2
1
1
1
3
1
1
2
1
0
0
1
1
2
1
1
0
1
1
1
2
0
1
1
2
2
0
0
1
2
2
2
1
0
0
1
1
2
1
1
0
2
0
1
1
0
1
1
1
1
0
1
1
2
1
2
2
1
2
0
1
0
2
2
2
0
1
0
2
0
1
2
1
2
1
0
0
3
1
0
1
2
1
0
2
2
0
0
1
1
2
1
2
1
1
0
2
1
1
1
2
2
2
0
1
0
1
1
1
1
0
1
1
2
1
0
1
2
0
1
1
0
0
1
0
1
0
1
2
1
2
0
2
2
1
1
2
1
2
0
0
1
1
2
1
1
1
1
0
1
0
1
1
1
2
1
1
1
1
1
0
0
1
1
2
0
2
0
0
0
1
2
0
1
0
1
2
2
1
1
1
0
1
2
1
1
1
1
2
1
1
3
2
1
0
1
0
1
2
1
1
0
1
1
1
2
0
1
1
1
1
1
0
2
0
1
2
1
2
1
1
2
1
1
0
1
1
1
1
0
2
0
1
1
1
1
3
1
2
2
0
0
1
0
2
2
2
1
1
1
1
0
0
1
1
1
2
0
2
1
0
3
1
0
1
1
1
0
1
1
1
2
2
3
1
2
1
1
2
1
1
1
1
1
0
0
1
1
0
0
1
0
1
1
1
1
1
0
2
1
1
1
0
1
2
1
2
1
1
1
2
2
1
2
2
1
0
1
0
2
0
2
1
1
1
1
0
1
0
0
0
1
1
1
1
2
2
2
1
1
1
1
2
0
2
2
2
1
1
2
1
1
1
1
2
1
1
1
2
5
2
2
0
1
2
1
1
2
1
0
2
2
2
1
1
2
2
1
1
2
1
1
1
3
0
1
2
1
1
1
1
2
1
2
0
1
2
1
1
1
2
1
1
0
2
1
2
2
2
0
1
1
1
2
1
1
0
2
1
1
1
0
0
1
1
0
1
1
1
1
1
0
1
2
2
2
1
0
1
0
1
1
1
1
1
1
1
0
3
1
0
1
1
0
1
1
0
0
2
1
0
0
2
1
0
2
0
1
0
1
0
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
0
0
2
1
2
1
0
1
2
0
2
2
0
2
1
1
1
0
2
0
1
1
1
2
2
2
1
1
1
1
1
1
0
0
1
1
0
1
2
1
2
0
1
1
2
1
1
1
2
0
1
0
1
0
0
1
0
1
2
0
1
0
2
2
2
0
1
0
0
0
1
0
0
0
1
1
1
1
1
2
0
0
1
0
1
0
0
1
1
1
2
1
1
1
1
1
0
1
1
1
0
0
1
1
1
2
1
2
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
0
0
2
1
1
1
1
2
1
0
1
2
1
1
4
0
0
1
1
0
2
1
1
0
1
0
2
0
0
1
1
1
1
0
1
2
0
0
0
2
2
1
1
1
0
1
1
2
0
1
1
0
0
1
1
1
1
1
1
1
2
0
1
2
1
1
2
1
1
1
1
2
1
0
1
0
1
1
1
1
1
0
0
1
0
0
1
1
0
2
0
1
0
2
1
0
1
1
1
2
1
1
0
2
1
2
1
1
2
1
2
1
1
0
0
1
1
2
1
0
1
1
2
1
2
1
1
2
2
1
1
0
0
1
1
2
2
0
1
0
1
2
1
1
1
2
2
2
1
2
1
1
1
1
1
0
0
1
0
1
1
0
2
0
2
1
1
0
1
1
1
1
1
1
1
2
1
2
2
2
1
1
1
1
1
1
1
0
2
0
0
1
2
2
0
2
1
1
1
0
1
0
1
1
2
2
1
1
1
2
1
1
1
0
0
0
0
2
1
1
1
0
3
1
1
1
1
0
1
0
1
0
2
1
1
2
1
1
2
0
1
1
0
1
2
2
2
0
0
1
0
0
1
2
2
1
2
1
1
0
1
1
2
0
2
1
1
1
1
1
2
1
0
1
2
1
1
0
0
2
1
0
1
3
0
1
0
1
1
1
1
2
1
1
1
0
1
2
0
0
0
1
2
1
2
1
1
1
0
1
2
1
0
1
1
0
1
1
1
1
2
1
0
0
0
1
1
1
2
1
2
1
2
1
1
1
0
2
0
1
2
2
1
1
2
2
1
1
1
2
0
3
0
2
1
2
2
1
0
0
0
1
0
1
0
0
2
2
1
0
1
1
0
1
1
2
0
0
0
1
1
2
1
1
1
0
1
1
1
2
0
1
2
1
1
1
1
2
1
0
2
1
1
0
1
2
1
2
2
1
1
1
1
0
1
2
0
1
1
0
0
1
1
0
1
1
2
0
2
1
3
0
1
2
1
2
1
1
1
2
1
1
1
1
1
2
0
1
1
0
0
1
1
2
1
1
1
2
1
0
2
1
2
1
0
1
2
2
0
1
1
1
2
1
0
2
1
2
2
2
1
1
1
1
2
0
0
1
1
1
0
1
1
1
0
1
1
1
1
2
2
1
1
1
1
2
0
1
0
1
1
2
0
1
0
2
2
2
1
1
1
2
1
2
0
0
0
1
2
1
1
0
1
0
1
1
2
2
1
1
1
1
0
1
1
0
1
2
0
1
0
2
1
1
1
0
1
2
1
1
2
1
1
1
0
2
1
1
1
0
0
0
1
2
2
2
0
1
1
0
0
0
1
2
0
1
0
1
1
0
1
1
1
1
1
0
0
1
1
1
1
0
1
1
2
2
1
1
0
1
1
2
2
0
1
1
0
0
0
1
1
1
1
0
0
0
0
1
2
2
1
2
2
0
1
1
1
1
1
0
2
0
1
0
1
1
1
0
1
1
1
1
0
1
1
0
1
1
2
2
1
0
1
2
0
1
1
2
1
0
1
1
1
0
1
1
0
1
0
0
2
1
2
1
0
1
2
1
0
1
0
1
1
0
0
1
0
1
2
1
1
1
1
1
2
1
1
1
1
0
1
1
1
1
1
2
1
0
2
1
0
0
0
1
1
2
1
1
0
2
2
2
0
1
0
0
1
2
0
1
3
3
0
0
2
0
0
1
2
0
1
0
0
1
0
1
0
1
2
1
1
2
1
1
1
1
1
2
1
2
0
1
1
1
1
1
1
2
1
0
2
1
1
1
1
2
1
2
1
0
2
2
0
1
2
0
1
0
2
0
1
1
0
1
1
0
1
0
1
1
1
1
2
0
1
0
1
2
1
1
2
1
2
1
1
2
2
0
1
0
2
1
0
0
1
4
2
1
1
0
2
11
0
2
1
2
1
0
1
1
2
0
1
1
0
2
0
1
0
2
2
0
2
1
0
1
1
2
1
0
1
2
0
1
1
1
1
1
2
1
1
1
1
0
2
1
2
1
2
0
1
1
0
2
1
1
2
2
1
0
1
1
0
1
0
1
1
1
1
2
1
1
1
1
1
0
2
0
0
2
1
1
2
1
2
0
2
0
1
2
0
2
1
1
1
2
7
2
1
1
0
2
1
0
2
2
1
1
1
1
1
1
1
1
1
2
1
2
0
1
1
1
2
0
1
2
1
1
1
1
1
0
0
0
1
1
1
2
2
1
1
1
2
2
2
1
2
1
0
2
0
1
0
0
1
1
1
1
0
0
2
0
1
2
0
2
1
2
1
0
0
2
1
1
1
1
1
1
1
1
0
1
1
2
2
2
2
0
1
1
1
1
2
2
4
1
1
0
1
2
2
1
0
1
0
1
1
2
1
1
0
1
2
1
2
0
2
1
0
0
0
2
1
1
1
1
2
2
1
1
1
2
1
1
1
1
1
0
2
0
6
1
0
1
1
2
0
0
1
1
0
0
1
1
1
1
2
0
1
1
0
2
1
1
1
1
1
1
2
2
0
1
1
0
1
0
1
1
1
0
1
2
2
1
0
1
2
1
1
2
1
1
1
2
0
1
1
1
0
2
0
2
0
2
1
0
1
2
2
0
0
1
1
2
0
1
0
1
0
0
1
2
1
2
1
0
0
0
1
1
0
0
0
0
1
2
2
2
1
1
0
0
1
1
1
0
1
1
1
0
1
1
1
1
2
1
2
1
1
0
1
1
0
1
0
1
1
0
0
2
1
1
0
2
0
0
2
0
1
0
1
1
1
0
1
0
0
0
2
1
1
1
0
1
1
1
1
2
1
1
2
1
0
0
0
2
1
0
1
1
0
2
0
1
2
0
0
0
1
1
0
1
1
1
2
2
1
2
1
1
0
1
1
1
2
1
1
0
0
1
0
1
0
1
0
1
1
2
1
0
0
1
2
1
1
1
2
0
2
0
1
4
0
1
1
1
0
2
1
1
2
2
1
0
1
1
1
0
2
0
1
2
1
2
1
0
2
2
2
1
0
0
0
0
1
1
2
0
1
0
1
1
0
0
0
1
2
1
1
2
1
1
1
0
2
2
0
1
1
0
0
1
0
1
1
1
1
1
1
1
1
1
0
0
1
0
1
1
3
2
2
1
2
1
0
2
2
1
0
2
2
1
1
1
2
2
1
2
2
1
1
1
0
1
0
2
1
1
1
1
1
0
1
2
1
1
2
1
1
1
2
1
1
0
1
1
0
2
1
1
2
2
1
1
0
2
0
1
0
0
1
1
0
1
2
0
1
1
0
1
1
1
0
1
1
1
2
1
0
2
0
1
0
1
1
1
2
1
0
1
1
1
1
1
1
0
1
0
1
0
1
1
2
2
1
0
0
1
0
1
0
1
1
1
1
1
1
1
2
1
0
1
1
1
1
2
0
0
2
1
1
3
1
2
1
2
1
2
0
0
1
1
1
1
0
1
1
2
0
2
1
1
0
1
1
0
1
0
0
0
1
1
2
1
0
1
1
1
0
1
1
0
0
0
1
0
1
1
1
1
1
0
1
1
0
2
1
1
2
0
0
1
0
0
2
1
1
1
1
0
1
1
0
0
1
1
1
1
1
1
0
0
0
2
0
2
1
0
2
1
1
1
0
1
0
1
1
1
1
1
1
1
2
2
0
0
1
1
1
0
0
2
1
0
2
1
1
2
2
0
2
1
1
1
1
0
1
2
1
1
2
1
1
1
1
1
1
1
1
2
2
1
1
0
2
1
0
1
2
1
1
1
0
2
1
2
1
2
0
2
1
0
1
0
1
0
1
1
1
2
1
0
2
1
0
1
0
0
2
1
1
1
1
0
1
1
1
2
2
1
2
1
1
1
1
1
0
1
1
1
1
0
0
1
1
2
0
1
0
1
1
0
0
1
0
0
4
2
1
2
0
1
2
1
1
0
1
2
1
0
0
2
1
2
1
1
0
1
0
2
0
0
1
1
1
1
2
1
1
1
1
1
2
2
2
0
2
1
0
1
1
1
1
1
0
1
1
1
2
1
2
0
3
2
0
0
3
0
1
1
1
2
1
0
0
0
1
1
2
1
0
1
2
0
2
1
0
1
1
2
2
2
1
1
2
0
1
1
2
1
1
1
0
1
1
1
1
1
0
1
2
1
1
1
1
2
2
1
0
0
2
2
1
1
1
1
2
1
2
1
1
1
2
2
1
1
1
1
0
0
1
2
2
0
0
1
2
0
0
2
2
3
2
2
1
1
0
2
1
1
1
2
1
1
1
0
1
1
1
2
1
2
0
1
0
1
1
1
2
1
2
1
0
0
1
1
2
2
0
1
2
0
0
1
1
1
2
2
2
2
0
0
0
0
1
1
1
0
3
2
0
2
2
2
0
1
1
2
2
1
0
1
1
1
1
0
1
2
0
1
1
2
1
2
0
1
2
2
0
0
1
1
1
0
2
1
3
0
1
0
0
0
1
1
2
2
1
1
1
1
0
1
2
1
0
0
1
0
1
0
1
2
1
1
0
2
1
1
1
1
1
1
1
1
1
0
0
0
1
2
1
0
1
2
1
0
1
2
1
2
1
2
1
1
1
2
2
0
0
0
0
1
1
1
1
1
1
0
1
1
0
1
1
1
2
1
2
1
0
1
0
1
1
1
1
2
1
1
1
1
1
0
1
1
1
1
0
0
0
2
0
1
1
1
0
0
2
0
0
1
0
0
2
1
1
2
1
0
2
1
0
1
1
1
1
0
1
1
0
2
0
2
0
1
2
1
1
2
0
1
2
2
1
1
1
1
1
1
0
1
1
3
1
0
2
2
2
2
2
2
0
0
0
1
1
1
0
0
2
1
1
2
3
1
1
1
1
1
1
1
0
1
2
1
2
0
1
1
1
0
1
1
1
1
0
1
1
2
0
1
0
1
0
2
1
1
2
1
1
1
2
1
1
2
1
1
1
0
0
2
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
0
1
2
0
1
4
0
0
1
0
1
2
2
1
2
2
1
1
0
2
1
1
1
1
1
1
0
0
1
1
0
1
0
1
0
1
2
0
1
0
0
2
2
1
2
2
1
1
0
2
2
1
2
1
0
0
1
1
1
2
1
2
1
0
1
0
0
1
1
1
1
3
1
1
0
1
2
2
1
1
1
1
0
1
1
1
0
1
1
1
1
1
0
0
0
1
1
0
1
1
1
2
0
2
2
2
1
2
1
1
0
3
0
2
2
0
2
0
1
1
0
1
2
1
1
2
0
1
1
0
2
2
1
0
2
2
2
2
1
0
0
1
1
1
0
0
2
0
1
0
0
1
1
0
1
0
1
0
0
2
2
2
0
0
0
2
0
1
1
0
2
0
1
1
2
1
2
0
0
1
1
0
0
1
1
0
1
2
1
0
1
0
1
2
1
1
1
1
1
1
1
0
1
1
1
1
0
0
1
1
1
1
0
1
1
0
0
4
1
2
0
2
1
1
0
1
0
1
1
1
1
0
0
0
1
2
1
1
0
1
0
1
1
0
1
2
1
1
1
1
0
0
1
2
2
1
1
0
0
4
0
1
1
1
0
0
2
1
1
1
0
2
0
1
2
1
2
1
1
2
1
1
2
1
2
0
2
1
3
2
1
2
2
2
0
2
2
1
1
1
2
0
1
2
0
0
1
0
2
2
1
1
0
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
0
1
1
1
1
0
2
1
1
0
2
2
1
1
1
2
2
0
1
1
1
1
1
0
2
0
0
1
1
2
1
1
0
1
2
1
1
1
1
0
0
1
1
1
0
0
1
2
1
2
2
1
1
2
2
1
1
1
2
1
0
1
2
1
1
2
1
1
1
0
0
1
0
1
0
2
1
1
2
1
2
2
0
1
1
0
1
1
0
1
1
1
0
1
1
1
1
2
1
1
1
1
0
1
0
1
1
1
2
1
0
0
0
0
1
1
1
1
0
1
0
0
1
2
1
2
2
1
1
2
1
0
2
1
0
2
1
1
2
2
0
1
0
0
1
1
1
0
1
1
1
2
2
1
1
1
1
1
1
1
1
0
1
2
1
0
1
1
2
1
1
1
1
1
1
1
1
1
1
0
2
1
2
1
2
0
1
0
2
2
1
1
0
0
1
1
1
1
1
1
1
2
0
0
0
0
1
2
1
1
2
0
0
3
1
1
1
0
0
1
1
0
1
1
1
1
1
0
0
1
2
0
0
1
1
0
1
2
1
1
1
1
1
3
1
1
1
1
0
1
2
1
2
1
1
2
1
1
0
1
0
1
2
2
2
0
1
0
1
1
1
0
0
1
1
0
0
0
1
0
1
1
0
1
0
0
1
1
2
1
1
2
0
1
1
0
1
1
1
1
0
0
1
1
0
2
1
1
1
1
0
2
0
2
1
1
1
2
0
1
1
0
2
2
2
1
2
1
1
0
1
0
3
2
2
1
0
0
1
2
1
1
1
2
0
0
1
1
2
1
1
1
2
1
2
1
0
1
1
1
1
1
1
0
1
1
1
2
0
0
1
1
1
0
1
1
0
1
0
2
0
3
0
1
0
1
2
2
0
1
0
2
0
0
1
1
4
1
1
1
0
0
2
1
1
0
2
2
1
2
0
2
2
1
2
2
2
1
1
0
2
1
0
2
1
0
1
1
0
0
1
1
1
2
1
0
0
1
2
1
1
1
1
0
1
2
2
2
0
1
1
3
0
1
1
1
2
1
2
1
0
2
0
0
1
2
1
1
1
1
2
1
2
1
0
0
1
1
2
1
2
2
2
0
1
1
2
1
1
1
1
0
1
1
0
0
0
0
0
2
1
1
0
1
1
1
0
1
1
4
1
1
2
1
0
1
0
1
3
1
1
0
1
2
1
1
0
1
2
1
0
1
1
0
1
0
0
1
0
0
1
1
0
1
1
1
0
1
1
1
2
0
2
2
1
2
1
1
1
1
2
1
1
2
1
0
1
1
1
1
1
1
0
2
2
1
1
1
2
1
1
6
1
1
0
1
1
0
1
0
0
1
0
1
1
1
2
2
1
1
3
0
0
1
1
1
2
1
0
1
0
1
1
1
1
1
0
0
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
0
1
1
1
1
1
1
2
0
1
1
2
0
1
1
2
2
1
3
2
1
1
1
1
1
1
0
0
0
1
1
0
2
1
2
2
2
2
1
1
1
1
2
2
1
0
0
1
1
0
3
2
1
1
1
2
0
0
0
0
0
1
1
1
1
2
1
2
0
1
1
0
1
0
1
0
1
1
1
0
0
1
1
1
1
0
1
1
1
1
1
2
2
1
1
0
1
1
1
2
1
1
2
6
1
0
0
2
1
1
1
2
2
0
1
1
1
1
1
1
1
2
1
0
1
2
1
0
2
0
0
2
0
2
1
1
1
0
1
0
2
1
2
1
2
2
2
2
2
1
1
1
1
1
1
0
1
1
0
1
2
2
1
1
2
1
1
1
0
2
2
1
1
1
1
0
2
1
1
1
1
0
0
0
2
1
2
1
1
2
0
1
1
2
2
0
2
1
0
1
0
1
1
1
1
0
2
0
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
0
0
1
2
2
0
0
1
1
2
1
0
0
0
1
1
2
0
2
1
2
1
2
1
1
2
1
1
1
1
0
1
1
0
1
0
1
1
1
0
1
1
1
1
1
1
4
0
2
0
2
0
1
0
0
1
1
1
1
0
1
1
0
1
1
1
0
2
0
1
1
1
1
1
2
1
1
0
1
1
2
2
1
1
0
1
1
0
0
1
2
0
1
1
1
0
1
1
1
1
1
0
0
1
1
1
1
1
2
0
1
4
0
1
0
1
0
1
1
0
1
0
1
0
1
1
0
1
1
0
2
0
1
3
2
0
1
0
1
1
1
2
1
2
1
2
2
0
1
0
1
1
2
1
1
2
3
1
1
1
1
1
1
1
2
1
1
0
1
1
1
2
1
1
1
1
2
1
0
2
1
1
0
1
1
2
1
2
1
2
1
1
1
0
2
0
1
2
1
1
0
2
1
1
0
0
1
1
1
1
0
2
1
1
1
1
0
2
1
1
2
1
0
0
1
3
1
1
1
1
1
1
2
1
0
1
1
2
2
1
1
1
0
1
1
2
0
2
0
0
1
1
1
0
1
2
0
1
1
0
0
1
1
2
1
0
1
0
1
1
1
1
1
1
3
1
1
1
1
0
1
2
1
1
0
1
0
1
0
2
1
0
1
0
1
1
1
2
1
1
2
0
2
0
1
2
1
1
1
0
2
1
2
1
1
2
2
0
0
1
0
0
1
2
0
2
0
1
2
1
1
2
1
1
1
1
1
2
1
1
1
0
1
2
0
2
0
2
1
2
2
1
2
0
1
1
0
1
6
2
1
1
1
0
1
1
2
1
0
0
1
1
1
0
1
0
0
0
0
2
1
1
1
1
0
1
1
1
2
0
0
2
1
0
0
0
0
1
0
1
1
1
1
2
1
0
2
1
2
1
1
1
0
0
0
1
1
1
2
1
1
1
2
1
0
2
1
0
0
0
1
2
1
1
1
0
0
1
0
1
0
0
2
2
2
1
0
2
0
1
0
2
1
1
0
1
1
2
1
1
1
1
0
1
0
2
1
1
0
2
1
1
0
1
0
1
1
0
1
0
2
2
0
2
1
1
1
2
1
1
2
0
2
1
2
1
1
1
1
2
1
0
1
1
0
1
0
2
2
0
1
1
1
2
2
2
1
0
1
1
0
1
0
1
0
1
1
0
1
1
1
1
0
2
1
1
1
0
1
2
1
1
0
1
2
2
2
1
0
0
1
1
2
0
1
1
1
2
1
1
0
2
2
1
1
0
0
0
0
0
0
0
0
1
1
0
1
1
1
1
1
0
1
0
1
1
1
0
0
1
0
1
2
1
1
0
2
1
2
0
1
1
1
1
1
0
0
2
1
1
1
1
1
1
1
0
1
0
1
1
0
1
1
2
2
1
1
0
1
0
2
3
2
2
0
2
0
2
2
1
1
1
2
1
3
1
0
0
0
0
1
2
2
1
0
2
0
1
1
0
1
1
2
4
2
0
0
1
0
1
1
1
2
1
1
1
0
1
0
1
1
1
0
1
0
0
0
2
1
0
0
2
3
0
1
2
1
2
1
0
1
0
1
1
1
0
1
1
2
2
1
1
1
0
0
1
2
1
2
1
2
0
1
2
2
2
1
1
1
0
1
0
2
1
2
1
2
1
1
1
2
1
0
1
1
1
0
1
1
1
1
1
0
1
1
0
1
1
1
2
0
2
1
2
2
0
2
1
0
2
1
2
1
0
1
2
2
2
1
0
1
2
0
0
0
1
0
1
2
0
1
1
0
0
2
0
3
1
1
1
0
1
1
0
1
1
1
0
1
1
2
2
1
2
1
2
2
0
2
0
1
1
0
0
0
0
1
1
1
1
0
0
1
0
1
2
1
1
1
0
2
3
2
2
1
1
0
1
0
0
0
1
2
1
0
1
2
0
1
1
0
1
2
0
1
1
1
2
0
0
1
2
1
2
1
1
1
1
2
0
0
1
1
2
1
0
1
1
1
1
2
2
1
0
2
1
1
0
1
1
0
1
1
1
2
2
2
1
1
1
2
1
2
1
1
1
0
2
1
1
2
2
2
1
1
1
1
1
1
0
1
1
2
1
1
2
1
0
0
0
1
1
1
2
2
0
2
1
0
1
0
1
0
1
0
1
0
1
2
1
1
1
3
0
1
0
0
1
1
2
2
2
1
1
0
0
0
0
1
0
1
0
1
1
0
2
1
1
2
1
0
2
1
1
1
1
1
1
2
1
2
1
2
1
1
2
1
1
1
1
1
0
0
2
2
1
1
2
1
1
1
2
1
0
1
2
1
0
1
1
2
2
1
1
0
1
1
1
2
2
1
0
1
3
1
1
0
1
1
0
1
1
1
1
2
1
1
1
1
1
1
2
1
2
1
0
0
0
0
2
0
1
1
1
0
1
0
1
0
0
0
1
1
1
1
0
0
0
1
0
0
0
0
2
2
1
1
2
1
1
0
2
1
0
1
0
2
1
1
2
1
1
1
0
2
1
1
3
0
1
0
0
2
1
0
1
2
2
1
1
0
1
1
1
0
1
0
1
0
1
1
1
0
0
2
1
1
1
1
1
0
0
0
1
2
1
2
1
1
1
1
2
0
1
1
1
1
1
0
1
0
1
1
1
1
0
2
0
1
1
1
1
0
0
1
1
2
1
1
2
1
1
2
0
2
0
2
2
0
1
0
1
1
1
2
0
1
1
2
1
2
1
1
1
1
0
1
1
0
0
2
2
1
1
2
0
2
1
1
2
1
2
2
1
3
1
1
1
1
1
0
0
1
1
0
0
2
1
0
0
0
1
2
1
1
2
1
0
1
0
1
0
2
1
1
1
1
1
2
1
2
1
0
1
2
2
2
1
0
1
1
1
0
0
1
2
2
0
1
0
1
2
2
1
0
1
2
1
1
0
1
2
1
1
2
2
1
0
1
0
0
1
2
1
2
1
0
1
1
0
0
1
1
1
1
4
2
1
2
2
1
1
0
1
1
1
2
0
1
1
1
0
2
1
1
1
1
1
1
1
1
0
0
0
0
1
2
0
0
1
0
2
2
1
1
1
1
0
1
0
1
2
1
1
1
1
2
2
2
0
2
0
1
1
1
0
0
0
0
1
0
0
1
1
2
0
1
1
0
1
2
1
1
1
1
1
2
1
0
0
1
1
1
2
1
0
1
0
3
1
1
1
2
1
0
2
1
0
2
0
1
3
1
1
0
1
1
1
2
2
1
0
1
0
0
1
0
1
0
1
1
1
1
1
1
3
1
1
0
2
0
1
0
1
1
1
1
2
0
1
0
0
1
1
1
1
1
1
1
0
0
0
1
1
0
1
1
1
0
2
2
0
1
0
1
2
0
2
0
1
2
0
1
1
1
0
2
0
1
1
0
2
1
2
1
1
1
1
1
1
0
0
1
1
1
1
0
1
1
1
0
0
1
0
1
0
2
0
1
2
2
0
1
1
2
1
1
1
2
1
0
1
1
1
0
0
1
0
2
2
0
1
1
2
2
1
1
0
0
1
0
2
2
0
1
1
1
0
0
0
1
1
0
0
0
0
4
2
1
0
1
0
1
0
1
2
0
2
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
1
3
1
2
1
0
0
0
1
1
0
1
1
1
1
1
1
2
1
1
0
1
0
2
1
1
1
0
1
2
1
2
1
2
1
1
0
1
2
1
1
2
0
1
1
2
2
1
1
1
0
1
3
1
1
2
2
2
1
0
1
0
0
1
1
1
1
0
0
1
1
1
0
1
0
0
1
0
0
2
0
2
1
1
0
0
1
0
1
1
1
1
0
0
1
0
1
0
0
1
1
0
1
0
0
2
1
0
1
2
1
1
1
2
1
1
2
1
0
2
3
2
1
1
1
1
1
2
2
1
1
1
0
0
1
1
1
0
1
0
2
2
1
1
1
0
1
1
0
0
2
2
0
0
0
0
1
0
2
1
0
0
2
3
1
1
1
0
1
2
1
0
0
0
1
2
0
1
2
1
1
1
1
1
0
2
1
1
1
0
2
1
0
1
1
0
0
1
2
0
0
0
2
1
1
1
0
2
2
1
0
1
1
1
1
1
0
1
1
0
2
2
0
1
2
0
0
1
1
1
1
0
0
2
1
1
1
1
1
0
0
1
0
3
1
0
1
1
0
1
1
0
2
2
1
1
1
1
0
1
0
1
1
1
0
1
0
2
0
2
2
1
0
1
0
0
0
1
0
2
1
1
1
2
0
1
0
1
1
0
1
1
2
0
1
1
1
1
2
1
1
0
1
1
2
1
1
1
1
2
0
0
2
0
1
0
3
1
1
1
1
1
2
2
1
0
0
2
1
2
1
0
1
1
1
2
0
2
1
1
0
1
0
0
2
2
2
0
1
1
2
1
0
1
0
1
0
1
1
2
1
0
0
1
0
2
2
2
1
2
1
0
1
0
0
1
1
1
1
1
0
0
2
1
0
1
1
1
2
2
1
0
1
1
1
2
2
1
2
0
0
0
1
1
0
1
1
2
1
2
1
1
1
1
2
1
0
1
0
2
1
1
0
2
0
2
0
0
1
0
1
2
0
2
0
0
1
1
0
1
1
2
0
0
2
1
1
1
1
1
2
2
1
1
2
0
1
1
1
0
1
2
2
0
1
1
2
1
0
2
2
2
1
1
2
2
0
1
0
1
1
1
0
2
1
0
1
1
1
1
1
0
1
2
0
1
1
1
0
2
1
1
1
3
1
1
1
0
0
1
1
2
0
2
0
1
1
2
1
2
2
0
0
1
1
2
1
2
0
0
1
1
1
1
1
1
2
0
1
1
1
1
1
0
1
0
1
1
2
1
0
1
0
1
2
1
0
1
1
1
2
0
1
1
1
1
0
1
0
0
0
2
1
1
2
2
2
1
2
0
0
2
2
3
1
1
1
2
1
1
1
1
1
3
1
1
1
0
1
0
2
2
0
0
1
1
0
1
2
2
1
0
2
1
2
0
1
0
0
0
1
1
2
1
0
2
0
1
1
2
2
1
1
1
1
0
2
0
2
2
2
0
0
0
2
2
0
1
0
2
1
0
0
1
1
0
1
1
0
1
1
0
1
0
1
2
1
2
1
1
2
2
1
0
0
1
1
0
0
1
1
2
2
1
1
0
1
1
2
0
0
1
1
0
0
3
1
0
1
3
0
1
0
1
0
1
0
1
2
1
1
1
3
1
1
0
0
2
1
0
2
0
1
0
1
0
2
2
0
1
1
0
0
2
0
2
0
0
2
1
0
1
1
2
1
1
1
1
0
0
1
0
0
1
1
1
1
2
2
0
0
0
1
0
0
1
1
1
0
1
2
1
1
2
0
2
0
1
1
1
0
1
2
1
1
2
1
2
1
2
1
2
2
3
1
1
1
0
2
0
0
1
0
1
0
1
2
2
1
0
0
1
0
1
0
2
2
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
0
1
1
1
1
2
1
1
1
2
4
2
0
2
1
0
1
1
2
2
0
1
0
2
0
1
0
1
0
0
1
0
2
1
1
2
0
1
1
1
0
2
1
2
0
0
1
1
0
1
0
1
0
1
0
1
0
2
2
1
0
2
1
2
1
1
1
2
1
1
1
0
2
0
2
0
1
1
1
0
1
2
0
0
1
0
1
1
0
2
1
1
0
1
1
1
1
1
3
1
1
0
1
1
2
1
1
1
1
1
0
0
2
1
1
1
0
1
0
1
0
1
0
1
2
1
1
1
1
2
2
2
2
1
1
0
1
1
1
2
1
0
0
1
1
1
0
0
1
1
1
2
3
1
1
0
2
1
1
3
2
1
1
2
1
2
1
1
0
0
2
0
2
1
1
1
2
0
2
2
1
2
1
0
1
1
0
0
1
0
0
1
0
0
1
2
2
2
0
1
2
1
1
1
1
1
1
1
0
1
1
0
1
1
1
0
1
1
0
0
2
1
0
0
1
0
1
0
1
0
2
1
1
1
2
0
1
1
0
1
0
0
0
1
1
1
1
1
1
1
1
0
2
2
1
2
1
2
2
0
1
2
0
1
1
1
0
0
1
1
0
1
0
1
1
1
1
1
1
1
2
0
0
1
2
1
0
1
1
0
0
0
1
1
1
0
1
0
1
2
0
1
2
2
2
1
0
1
1
2
0
2
3
0
1
1
1
1
1
1
1
2
1
1
1
1
0
1
1
1
0
1
2
0
0
1
0
2
0
1
0
2
2
1
1
2
1
0
0
1
1
0
2
2
0
1
1
2
1
0
0
0
2
2
1
2
1
0
2
1
0
2
0
2
2
0
2
0
1
1
1
0
2
1
1
1
1
0
1
2
2
2
1
1
1
0
2
1
0
0
0
0
0
1
0
1
2
2
1
2
2
0
1
2
0
1
0
0
0
2
2
1
1
0
0
1
1
0
1
2
0
0
2
2
1
0
2
1
2
1
1
1
0
1
1
1
0
0
1
0
0
2
2
0
0
0
2
2
1
1
2
1
0
1
1
1
1
1
0
1
1
1
3
1
2
1
1
0
2
2
1
0
0
2
1
1
2
0
2
2
1
1
1
1
0
0
1
0
1
2
1
1
1
2
2
1
1
2
0
3
1
1
1
0
1
1
0
1
1
0
0
1
2
1
2
0
1
1
1
2
2
0
1
0
0
0
1
0
1
1
0
0
0
1
0
1
2
1
1
1
1
1
1
1
1
1
1
1
0
0
1
2
0
0
1
1
2
1
1
2
0
1
2
1
0
0
1
1
0
0
0
0
2
1
2
1
0
0
0
1
0
1
1
0
1
1
0
1
2
4
1
2
2
1
0
0
1
1
1
0
0
1
1
2
0
1
2
1
1
1
1
2
2
1
0
0
1
1
1
2
0
2
2
1
0
2
1
1
1
1
1
1
1
2
1
1
1
2
1
1
0
2
2
0
1
4
0
2
2
1
1
1
1
0
1
0
1
1
2
0
1
2
2
1
2
2
1
0
1
1
0
1
1
0
0
0
1
1
1
1
2
0
0
1
1
2
1
1
1
1
0
1
1
2
1
0
1
3
1
1
1
0
2
2
1
1
1
1
0
1
1
1
1
1
1
1
2
0
2
1
1
1
1
1
1
0
0
1
2
1
1
1
1
1
2
0
1
0
0
1
1
0
0
0
0
2
1
0
1
2
0
2
1
0
0
1
0
1
0
2
0
1
2
0
2
1
1
2
0
1
1
2
1
0
1
1
2
1
0
2
2
0
2
1
0
0
2
1
0
2
0
2
1
1
2
1
2
2
3
0
1
2
2
0
2
1
2
1
1
0
0
2
1
1
0
0
2
1
2
2
1
1
2
1
1
1
1
0
2
2
1
1
0
2
1
1
3
1
2
1
0
1
2
1
2
2
0
0
2
1
1
1
0
1
2
1
2
0
1
0
1
2
1
1
0
1
0
3
0
1
1
0
0
0
0
0
0
1
1
1
1
1
1
0
1
1
1
1
0
0
1
1
0
2
1
0
1
2
1
2
1
1
0
0
2
2
1
1
0
1
1
0
2
2
1
1
1
1
1
2
2
1
2
1
0
1
1
0
1
2
2
2
2
1
0
1
0
1
1
2
1
2
0
1
0
0
1
1
1
1
1
1
1
0
1
1
2
1
1
1
1
2
0
2
1
2
2
0
0
1
1
0
1
0
2
1
1
1
1
0
0
0
0
2
1
2
3
1
1
1
0
0
1
1
0
0
1
2
2
1
0
0
1
2
1
2
1
1
2
1
2
1
0
1
1
1
0
2
2
1
0
2
1
0
1
1
0
1
0
0
1
2
2
2
0
0
1
1
1
1
1
1
1
2
0
0
1
1
2
1
0
1
0
1
0
1
2
1
0
1
0
1
1
1
0
1
0
1
1
1
1
2
1
1
2
1
2
1
1
0
2
1
1
0
0
0
2
1
1
1
1
1
1
1
2
0
0
1
1
2
0
0
0
1
1
1
1
1
0
1
0
1
2
2
2
1
1
2
2
0
0
1
1
2
1
1
2
2
2
2
0
0
0
1
1
0
2
1
1
2
2
0
1
0
2
1
2
1
0
1
1
0
1
3
1
1
0
0
1
1
2
1
1
1
2
2
0
2
2
1
1
1
1
0
1
1
2
1
0
3
0
0
1
1
1
1
0
0
2
1
0
1
1
2
1
0
0
1
1
0
1
1
2
2
2
1
2
2
1
1
1
2
0
1
0
1
1
1
2
0
0
2
0
0
0
2
0
1
1
1
2
0
1
1
1
2
3
1
0
0
2
0
1
0
2
2
1
1
1
0
1
1
1
1
1
2
1
1
0
0
2
1
1
1
1
0
0
2
2
1
1
1
1
2
1
0
1
1
1
1
1
1
1
1
1
1
0
1
1
0
2
0
1
1
2
0
0
1
1
2
1
2
1
1
0
0
0
1
1
1
0
0
1
1
1
2
1
2
2
0
2
1
1
0
2
1
1
1
1
0
1
1
1
1
0
0
0
2
1
2
2
1
2
1
2
0
1
2
0
1
1
1
1
1
0
1
1
0
1
1
1
1
2
2
0
1
2
0
1
2
1
2
0
1
3
2
0
1
2
0
0
0
1
0
1
1
0
0
1
0
2
1
2
1
0
1
2
0
0
0
1
2
0
2
1
0
2
1
1
2
0
0
2
0
1
2
2
2
0
1
1
1
1
0
1
1
2
2
1
1
1
2
0
3
1
2
1
1
1
1
2
1
1
1
2
1
2
1
1
2
9
1
0
0
2
1
1
2
1
0
0
2
1
2
0
0
1
1
0
2
1
1
1
1
0
0
1
1
1
1
2
1
1
1
2
1
1
0
3
1
0
2
1
1
0
0
2
1
1
2
1
1
1
1
2
1
1
1
1
1
2
1
2
0
1
2
1
1
1
0
2
0
1
0
1
1
1
1
0
1
1
1
2
0
2
2
0
2
0
2
1
1
1
2
1
1
0
2
1
1
2
0
1
2
2
0
1
1
1
1
2
1
0
1
1
2
1
0
1
1
1
1
1
1
1
1
0
1
1
1
2
1
10
0
1
1
2
1
2
0
2
1
1
2
0
1
0
2
1
0
1
1
1
2
1
1
2
2
1
1
2
1
1
2
1
1
1
1
1
1
0
1
2
0
1
2
3
0
2
1
1
1
1
1
0
1
1
0
1
2
1
1
1
1
2
1
2
1
1
2
1
1
0
0
1
1
1
1
1
2
1
1
1
0
1
1
2
1
0
1
1
1
1
1
2
1
0
1
0
0
1
1
1
1
2
2
1
2
1
5
1
0
0
1
0
2
2
0
2
1
1
1
1
1
2
0
1
3
1
1
1
1
1
1
0
1
2
0
0
0
1
2
0
0
1
1
1
1
2
0
1
1
0
2
2
1
0
1
1
0
2
0
1
1
1
2
4
1
1
0
1
2
1
1
2
1
2
1
1
1
1
1
0
0
1
1
1
1
1
0
3
1
3
1
1
1
1
0
2
0
1
0
2
2
1
1
1
1
0
1
1
0
2
1
0
1
1
2
1
0
0
0
0
0
2
1
2
2
1
1
2
2
1
0
2
0
1
2
1
2
1
2
1
2
1
1
1
0
0
1
1
1
1
1
1
0
0
1
1
1
1
1
2
0
2
3
1
0
2
0
1
1
0
1
0
1
0
1
1
1
1
2
0
0
2
0
0
0
2
0
1
0
0
0
1
1
1
1
1
1
2
1
1
2
1
1
1
1
0
0
2
0
2
1
1
2
1
0
2
2
1
2
1
0
2
1
1
0
1
1
0
0
0
0
0
2
0
2
2
1
1
1
2
2
1
1
0
1
1
0
2
2
1
1
0
1
1
1
1
1
1
0
2
2
2
0
0
0
0
1
0
1
0
1
1
0
0
1
1
1
1
0
0
1
1
0
2
0
2
1
2
0
1
1
1
1
2
2
0
1
2
1
0
0
0
1
1
2
1
0
1
1
2
2
1
2
2
1
1
1
0
1
1
0
2
0
0
2
0
1
1
2
0
3
2
0
1
1
2
2
1
1
0
1
0
1
2
1
1
1
1
0
2
2
2
1
2
1
1
0
0
0
1
1
0
0
0
0
1
1
2
2
1
0
1
1
0
2
1
1
2
2
1
1
1
1
0
2
2
1
0
0
0
1
1
2
2
0
0
1
0
0
2
1
2
0
2
2
2
0
1
1
1
1
0
1
1
1
2
1
1
2
2
2
1
1
1
2
1
1
0
1
1
1
1
0
0
0
1
1
1
1
0
1
1
2
0
0
1
3
1
0
1
1
0
2
1
1
0
0
2
1
1
1
0
1
0
1
2
2
1
1
1
1
2
0
2
2
1
2
0
1
1
2
0
1
1
1
0
0
1
2
1
1
1
2
1
1
1
0
1
1
0
1
2
1
1
2
0
1
1
1
2
1
1
1
0
1
1
1
0
1
1
2
2
1
1
1
1
1
1
1
0
1
1
1
1
1
1
0
1
2
1
0
2
1
1
1
1
1
1
2
1
1
1
1
2
1
0
0
1
1
1
1
1
1
1
1
1
1
2
0
1
1
0
2
1
1
0
1
1
1
0
1
1
1
1
0
1
1
1
2
2
2
1
1
1
0
2
2
1
1
2
0
1
2
0
1
0
1
2
1
1
1
1
1
1
0
1
0
2
1
1
0
0
1
1
1
2
2
1
0
1
1
1
0
1
2
1
1
1
1
2
1
1
0
1
2
2
1
2
1
2
0
0
0
0
2
2
2
1
0
8
1
1
0
1
1
1
1
2
2
0
1
2
1
0
1
1
0
1
2
1
0
1
0
1
0
1
1
0
0
1
1
2
1
1
1
1
1
1
1
2
0
2
1
0
1
1
0
0
0
0
1
1
0
0
1
1
1
1
1
1
1
1
1
1
1
0
0
2
2
2
1
1
0
1
1
1
0
1
1
0
2
2
1
1
2
1
2
1
0
1
0
1
1
1
1
0
1
1
1
0
2
0
2
0
2
1
2
1
1
1
0
2
0
2
0
1
0
1
0
1
0
1
1
1
2
1
2
1
1
0
0
2
0
0
0
1
0
0
1
1
0
0
0
0
1
1
1
0
2
1
2
1
1
1
1
1
1
1
2
1
1
1
0
0
0
1
0
1
1
1
1
1
2
0
1
2
1
3
1
0
2
1
1
0
0
2
1
2
1
1
1
1
1
1
1
2
2
0
1
1
1
1
1
2
0
1
0
1
0
1
0
2
1
1
2
2
0
5
1
0
1
1
0
1
0
0
2
0
1
1
1
0
0
1
1
1
0
0
3
2
2
1
0
2
2
1
4
1
1
1
1
1
1
2
0
1
1
1
1
1
2
1
0
1
1
2
0
2
0
1
0
1
2
1
2
1
2
0
2
1
0
0
1
0
2
0
2
0
2
1
0
0
1
1
0
0
2
1
0
1
1
1
0
2
0
1
3
2
3
1
0
1
1
1
1
1
0
2
1
0
0
1
1
1
2
1
0
1
2
1
0
0
1
0
1
1
2
0
0
1
1
1
1
1
0
2
1
1
1
0
0
0
0
0
2
1
2
0
2
1
1
1
0
0
2
1
1
2
1
1
2
0
1
0
2
2
1
1
0
1
1
1
2
2
1
3
1
1
1
1
0
1
2
2
2
1
1
2
1
1
1
1
0
1
1
2
1
1
1
1
1
0
2
2
1
1
1
0
1
1
0
2
1
1
0
2
0
2
1
1
0
2
2
1
0
0
0
1
1
1
1
1
1
1
1
1
1
1
0
1
1
0
2
1
2
1
1
1
1
0
2
0
1
1
1
1
0
1
1
2
0
1
1
2
0
1
1
1
2
1
1
2
1
1
0
1
1
1
1
1
1
2
1
1
0
1
1
1
1
1
1
1
1
0
0
2
1
0
1
1
0
1
0
2
0
1
3
2
4
1
2
2
1
2
0
1
1
1
1
1
0
0
1
0
1
1
0
1
1
1
1
2
2
1
0
1
0
0
0
0
0
1
2
1
1
2
1
1
1
1
1
0
2
1
0
1
1
0
1
1
1
1
2
0
1
0
1
1
0
1
2
2
2
0
1
0
2
1
0
1
1
2
1
2
1
2
1
1
2
0
1
1
1
1
1
0
0
0
0
2
1
0
0
2
1
2
0
1
0
1
2
0
0
1
2
0
2
1
0
1
0
1
2
1
0
0
1
1
0
0
1
1
1
0
1
1
1
2
2
0
0
1
2
1
2
0
2
1
1
2
1
1
1
1
0
0
0
2
1
0
1
1
1
1
0
2
1
0
1
1
1
0
2
0
0
1
1
2
0
1
1
0
1
1
1
1
2
1
1
1
2
0
0
0
1
3
1
0
0
2
0
1
1
2
2
1
1
1
0
1
1
1
0
1
0
1
1
1
1
1
2
1
1
1
1
1
2
2
0
1
0
2
1
1
0
2
1
1
0
1
1
2
1
0
1
1
1
2
1
1
2
1
0
1
1
0
1
2
1
2
1
1
2
1
1
1
0
1
1
0
1
0
1
0
1
1
1
2
0
0
2
2
1
1
2
2
1
0
0
2
2
0
1
2
0
1
1
0
1
1
2
1
1
1
2
1
2
1
1
2
1
1
0
1
1
0
1
0
1
2
1
1
1
1
1
2
1
0
0
1
3
0
1
1
1
2
1
2
2
2
1
1
1
0
1
1
1
2
1
1
2
1
0
0
1
1
1
1
0
1
2
0
1
1
1
4
1
1
1
2
0
1
1
0
1
2
2
2
1
0
0
0
0
1
1
0
6
1
0
1
0
1
1
1
0
2
0
1
1
1
0
1
0
0
0
1
1
1
1
0
1
2
1
2
1
0
1
1
1
2
0
2
2
1
2
1
1
0
1
2
0
2
1
1
1
1
0
1
1
0
1
1
1
2
1
0
1
1
0
2
1
1
1
1
0
1
1
2
1
1
2
1
0
0
1
1
2
1
0
1
0
1
1
1
0
2
0
1
2
3
0
1
2
1
1
1
2
2
1
1
0
0
1
0
1
0
2
2
1
0
1
1
1
2
1
2
0
1
1
2
0
1
1
1
1
1
1
2
0
0
2
2
1
1
0
2
2
1
1
1
2
0
0
1
2
2
1
2
2
1
0
0
0
2
1
1
1
1
2
2
1
0
1
0
2
1
1
1
6
1
1
0
1
0
0
0
1
1
1
1
2
2
1
1
1
0
1
1
2
0
1
2
0
1
1
2
0
1
1
2
0
1
2
0
0
1
1
1
1
2
1
1
1
0
1
2
1
1
1
0
2
2
2
2
1
1
0
1
0
1
0
0
0
0
2
0
0
2
2
0
1
1
2
0
0
1
1
2
0
2
1
1
0
0
1
1
0
2
2
1
1
2
1
0
1
2
1
1
1
1
1
1
1
2
2
2
0
1
0
0
0
1
2
1
1
2
0
0
1
1
1
0
2
1
2
0
0
1
2
1
1
0
1
1
2
2
1
1
0
1
1
0
1
1
1
0
2
1
0
1
0
0
1
1
2
1
1
2
1
0
0
0
1
1
2
2
1
2
1
1
2
1
2
2
2
2
2
1
1
3
0
1
1
2
1
1
3
1
1
2
0
3
1
2
2
0
0
1
2
1
1
2
1
1
1
1
1
0
1
1
1
2
0
1
0
0
0
0
0
1
2
2
1
1
1
1
0
1
2
1
0
1
1
0
1
1
1
1
1
1
2
0
1
0
1
0
1
1
2
1
0
0
1
0
1
1
2
0
1
1
0
1
0
1
2
1
1
2
1
0
2
0
0
2
0
0
1
0
1
1
2
1
2
1
1
1
1
0
0
1
2
2
0
0
1
0
2
0
1
1
0
1
2
1
2
0
2
1
0
1
1
1
2
2
1
1
1
1
1
1
1
2
0
2
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
2
0
1
0
1
2
1
1
1
0
2
0
1
1
1
1
1
2
0
1
1
0
0
0
1
2
1
0
0
0
1
1
1
1
0
1
1
0
1
1
2
3
2
0
2
2
1
1
1
0
1
1
1
1
0
1
1
2
0
1
1
1
2
1
2
1
0
1
0
4
1
0
1
1
0
1
0
1
0
1
0
2
0
0
1
1
1
0
2
1
1
1
0
0
0
1
0
1
1
1
0
3
1
0
0
0
2
1
1
1
0
3
1
1
0
1
2
1
2
1
2
1
1
0
1
0
1
0
2
1
1
0
0
1
0
0
1
1
1
0
1
1
0
0
1
0
1
0
1
2
1
0
2
1
2
0
0
1
1
1
0
1
1
0
1
0
1
1
0
1
2
1
0
1
1
1
2
2
1
1
1
0
0
0
0
0
2
0
1
1
1
0
1
2
0
1
1
0
2
2
1
1
1
0
0
1
0
0
1
1
1
1
1
0
0
2
1
1
0
1
1
1
1
1
1
1
1
1
2
1
0
1
0
0
0
1
0
0
2
1
2
1
0
0
1
1
1
1
0
2
0
1
0
1
0
2
1
1
1
0
0
2
0
1
1
0
0
1
1
1
1
0
2
0
1
1
0
1
0
0
0
1
1
2
2
0
1
2
1
1
2
1
1
1
1
2
2
0
1
2
1
2
1
2
1
0
1
1
1
1
1
2
1
2
1
1
1
1
0
1
2
1
0
1
0
0
1
0
0
0
1
1
2
1
1
0
1
1
1
1
2
1
1
3
1
2
2
1
1
1
0
1
0
1
2
1
1
2
0
2
2
1
1
2
0
2
2
0
0
2
0
0
1
1
1
0
1
1
0
1
1
1
0
0
1
1
1
1
2
1
1
0
1
2
1
3
1
1
0
1
1
1
2
1
1
1
1
1
1
0
1
1
0
1
0
1
2
0
2
2
1
1
2
0
1
2
1
0
1
0
2
2
1
1
1
1
1
2
1
0
2
0
1
1
2
1
2
1
1
2
2
1
2
1
1
2
0
1
2
0
1
0
2
1
0
0
1
1
1
1
1
2
0
2
1
1
1
0
0
1
1
1
1
1
1
2
1
0
2
1
0
1
0
1
2
0
0
1
1
1
2
2
1
1
0
1
1
1
1
1
0
2
1
1
1
1
1
1
0
1
0
2
1
1
1
2
0
1
0
1
2
0
2
2
1
2
2
0
1
1
1
0
2
1
2
3
0
1
2
0
0
0
1
2
2
0
1
1
1
2
2
1
0
2
1
2
2
0
2
0
1
1
0
1
0
2
1
0
1
1
2
1
2
2
1
1
1
0
0
2
0
1
1
1
0
2
1
2
2
0
0
2
1
0
1
0
1
2
1
2
0
1
1
0
0
0
1
0
0
2
0
3
1
1
0
1
1
1
1
1
0
2
1
1
0
1
1
2
2
1
1
1
2
2
1
1
0
2
1
0
1
1
0
0
1
2
1
1
0
2
2
2
1
0
0
2
0
1
0
1
1
0
0
0
1
1
0
2
1
1
1
1
2
2
2
1
1
0
1
1
0
1
0
2
1
1
1
1
1
1
1
1
0
2
0
2
1
1
0
2
0
0
0
1
1
0
2
1
1
2
1
0
2
1
0
1
1
1
0
1
1
2
1
0
1
2
0
0
1
1
1
2
0
0
0
2
1
1
1
1
2
2
0
1
1
1
0
1
0
2
1
0
0
2
0
0
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
0
1
2
1
3
1
0
2
0
1
1
1
1
0
1
1
0
0
1
2
0
1
1
1
0
1
0
0
1
0
3
2
1
1
1
1
1
1
0
1
1
2
1
1
2
1
2
1
1
0
0
2
0
1
0
1
0
1
1
1
1
2
1
1
1
0
1
1
1
1
1
1
0
2
0
1
1
0
1
1
2
1
1
1
1
1
2
0
0
0
0
1
0
1
1
1
1
0
1
2
1
0
3
2
0
0
1
1
1
0
1
1
2
0
0
1
0
2
2
1
2
1
2
1
2
2
0
2
0
1
2
1
1
2
1
2
1
1
2
1
1
1
2
2
0
0
2
1
2
1
1
2
0
1
1
1
2
0
0
2
1
2
1
0
1
1
1
2
1
1
0
1
2
1
1
1
1
1
1
1
1
2
2
1
2
1
0
1
1
1
4
0
2
1
0
0
1
0
1
0
1
2
0
1
1
1
0
1
1
1
1
0
1
1
1
0
1
2
1
1
0
0
1
1
0
2
1
2
1
1
2
1
1
0
1
0
1
1
2
3
1
0
2
1
2
1
0
1
0
1
1
2
1
1
1
3
1
2
1
1
1
1
1
2
1
0
1
2
1
2
1
1
0
2
1
2
1
0
1
1
2
2
2
1
1
2
1
1
0
2
2
0
0
1
1
1
2
0
0
1
0
1
0
1
0
0
1
0
3
1
0
3
1
1
2
1
0
3
1
1
1
2
0
1
1
1
1
0
0
1
1
0
1
1
0
1
1
1
0
1
0
0
0
1
1
2
1
2
0
1
2
1
1
1
1
1
1
1
5
1
1
2
0
0
1
0
1
2
2
2
0
1
0
1
1
1
0
1
2
1
3
1
0
3
1
2
2
0
2
1
1
1
1
0
1
2
1
0
1
1
1
2
2
1
2
2
1
1
1
1
1
1
0
0
1
0
0
2
2
1
1
1
1
1
1
0
1
1
1
1
1
0
1
1
1
1
0
1
1
0
0
0
2
0
1
1
1
0
1
1
1
1
2
2
1
2
3
0
1
1
2
0
0
0
0
2
2
1
1
2
2
0
0
1
2
0
1
2
1
2
1
0
1
0
1
1
1
1
2
2
1
1
1
1
1
1
2
1
0
1
2
1
0
1
0
1
1
0
1
1
0
0
2
2
0
3
1
1
1
1
1
1
1
1
2
0
1
1
2
0
1
1
1
1
1
1
1
2
1
1
0
1
2
1
0
1
2
1
0
1
1
1
0
1
0
2
0
1
1
1
1
2
1
1
1
1
1
0
1
1
2
2
2
0
1
1
1
1
2
1
2
2
2
1
1
2
4
1
1
1
0
1
2
1
0
1
2
1
1
1
1
1
0
1
2
0
1
0
0
1
1
0
1
1
0
0
0
1
1
2
2
0
1
1
1
1
1
1
1
1
0
2
1
0
1
1
0
1
1
0
1
2
1
0
1
1
2
4
2
2
1
1
1
2
2
0
1
0
1
0
2
2
1
1
1
1
0
0
0
0
1
0
1
1
1
1
2
1
0
2
1
2
1
2
0
1
2
1
1
0
1
1
2
2
1
0
0
2
1
1
2
2
2
1
2
1
2
1
0
1
1
2
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
1
1
1
1
1
1
0
1
2
1
0
2
0
3
1
0
1
0
1
1
1
2
1
1
0
1
1
2
0
1
2
1
0
0
1
1
1
0
2
0
0
1
1
2
0
0
1
0
1
1
0
1
0
2
2
2
0
0
1
1
0
1
1
1
1
2
1
1
0
1
2
1
1
1
1
0
1
1
0
1
0
1
1
0
2
2
1
2
1
1
1
1
0
0
1
0
0
1
1
4
1
2
2
0
2
1
0
2
0
2
1
1
0
0
1
2
1
2
1
1
1
0
0
0
1
2
1
1
2
0
1
0
3
1
0
1
1
1
0
1
1
2
0
2
1
1
0
0
1
2
2
1
2
1
1
1
1
1
1
1
0
1
1
5
2
1
0
1
2
1
2
1
1
2
1
1
0
1
1
2
1
1
0
0
2
0
2
1
2
0
1
0
1
2
1
0
1
1
1
1
2
1
3
2
2
2
1
0
1
1
0
0
1
0
0
1
1
1
1
2
1
1
0
1
1
1
0
0
0
1
0
0
2
1
1
1
0
0
2
0
0
0
2
1
0
1
1
1
0
1
4
1
1
0
1
2
0
1
2
2
1
1
0
0
1
2
2
1
1
1
0
1
0
1
2
1
1
2
1
1
1
1
0
1
0
2
0
1
1
1
0
3
1
0
2
1
1
1
0
0
1
2
0
0
1
1
0
1
0
2
1
1
1
2
1
1
1
0
1
2
1
1
1
1
2
0
2
1
2
2
1
2
1
2
1
1
1
0
1
1
2
1
1
1
0
0
1
1
0
1
1
3
2
2
0
2
1
1
1
0
1
0
1
2
0
2
1
1
1
2
2
1
0
1
1
0
1
1
2
1
1
1
1
0
2
0
1
1
2
1
0
2
0
0
0
2
1
0
1
0
0
0
0
0
1
1
1
0
1
2
1
1
0
1
0
1
1
1
2
2
1
0
0
0
1
1
2
1
1
2
1
2
1
2
2
1
0
0
2
0
2
1
2
2
1
0
1
1
1
1
2
1
1
2
1
0
1
1
1
2
2
0
1
0
1
1
2
1
0
2
2
2
1
0
1
0
1
2
1
2
1
2
2
2
1
1
0
1
1
2
1
1
1
0
1
0
0
1
5
1
2
0
2
1
1
2
1
1
1
2
1
2
2
2
2
1
1
0
1
0
1
1
1
2
0
2
1
1
1
0
2
2
0
1
1
1
1
1
0
1
1
1
1
0
0
1
0
2
1
0
1
1
1
0
1
0
2
2
0
0
0
4
1
1
1
1
2
1
1
1
1
0
1
1
0
1
1
1
1
1
1
0
2
0
0
1
1
0
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
2
2
2
1
1
1
1
0
1
1
2
1
1
1
2
2
1
1
1
1
2
2
1
1
2
2
2
0
1
1
1
2
1
2
1
2
1
0
1
0
1
2
3
2
1
1
1
1
1
1
1
2
1
1
1
0
1
0
1
2
0
2
0
1
1
3
1
1
1
2
0
0
2
0
1
0
2
2
2
1
1
2
0
0
1
1
0
2
1
0
0
1
1
1
2
2
1
0
1
0
1
1
1
0
2
0
0
1
0
1
2
0
1
2
1
2
1
0
2
0
0
1
1
2
1
0
1
0
0
2
0
0
1
1
1
2
0
0
1
1
2
1
2
4
0
2
0
2
1
1
2
2
2
1
2
2
1
0
2
1
1
0
1
1
0
1
2
1
1
0
3
2
1
2
0
0
2
2
1
1
2
0
2
2
1
0
0
2
0
0
2
1
2
2
1
1
1
0
2
1
1
0
0
1
2
0
1
1
1
1
1
1
1
1
1
0
0
1
2
0
0
2
0
1
2
1
1
0
2
1
1
2
2
1
1
1
0
1
0
0
1
0
2
2
1
1
0
0
1
1
0
1
2
1
1
2
2
0
1
0
2
0
1
0
1
1
2
1
2
1
1
1
1
2
1
1
1
1
0
1
1
1
1
1
1
1
1
2
2
2
1
1
0
1
1
0
1
2
1
1
1
1
1
1
1
1
1
2
0
1
2
2
0
1
0
1
2
1
1
0
0
1
1
1
0
1
0
1
1
1
1
1
1
1
0
0
2
1
1
0
0
2
1
1
1
0
2
3
1
1
1
1
0
1
0
2
0
0
1
1
1
2
2
1
0
2
2
2
2
1
1
1
0
1
0
1
0
0
1
0
0
0
1
1
0
0
2
1
0
1
0
1
1
1
1
1
0
1
0
0
0
2
1
1
3
1
2
1
2
1
2
0
1
1
1
1
2
0
1
1
0
2
0
2
2
0
1
1
1
2
2
1
0
0
1
1
0
1
1
0
0
2
1
1
0
1
0
0
1
1
2
1
1
1
1
1
1
2
1
0
1
1
1
2
2
1
0
1
1
1
1
1
1
2
1
0
2
1
1
2
2
1
0
2
1
0
1
1
2
0
0
1
0
1
0
0
0
1
1
2
2
0
1
0
2
0
2
1
1
0
2
1
1
1
1
1
1
1
1
1
2
0
1
1
1
1
0
1
2
1
1
2
1
2
1
0
0
1
1
1
2
1
1
2
2
0
1
0
1
0
1
1
1
1
0
0
1
1
2
0
1
1
2
1
1
1
2
1
0
1
2
1
0
0
1
1
1
1
2
0
0
2
0
1
2
1
2
2
0
0
2
0
0
0
0
2
2
1
1
1
0
2
0
2
1
2
2
2
1
1
2
0
0
0
0
0
1
2
0
0
0
1
1
0
1
1
0
0
2
0
2
1
1
1
0
1
2
1
0
0
0
0
0
1
0
1
2
2
1
2
1
0
1
1
0
1
1
2
2
0
0
1
0
1
0
2
0
2
1
2
1
2
0
2
2
0
2
0
1
1
1
2
2
1
2
2
1
2
1
1
0
0
1
1
1
2
0
1
0
0
2
0
1
1
2
1
2
1
0
1
1
1
1
1
0
0
2
0
0
1
0
0
0
2
1
2
2
2
2
1
1
0
2
1
1
2
1
2
0
1
1
0
1
2
1
1
2
0
1
1
0
1
1
2
1
1
0
1
0
1
1
1
2
0
2
1
2
1
1
0
0
1
2
2
2
2
1
1
1
2
0
1
1
2
0
2
2
1
1
1
1
2
0
1
1
1
1
2
0
1
1
1
2
0
1
1
1
2
1
1
1
2
0
1
2
1
0
1
0
1
2
1
1
1
1
0
1
1
1
2
1
1
1
0
0
1
1
0
1
2
1
1
1
1
1
0
1
0
2
1
0
1
1
2
1
2
0
1
1
0
2
1
2
1
2
0
1
1
2
1
2
1
1
1
2
1
1
1
1
2
2
1
1
1
1
1
0
1
1
0
1
0
1
1
1
0
1
0
2
1
0
0
0
1
1
1
1
2
1
1
1
0
3
1
2
0
1
3
1
2
1
1
1
2
0
0
0
1
1
1
1
1
1
1
2
0
0
2
1
2
2
0
1
1
2
2
1
0
1
2
1
1
1
2
2
0
1
1
1
2
1
1
0
2
1
1
1
0
1
1
1
2
0
1
2
0
1
1
0
2
0
0
2
1
0
0
4
1
1
1
1
2
1
1
0
1
0
1
1
0
1
1
0
1
1
0
1
2
0
0
2
1
0
0
0
1
2
1
1
2
1
2
1
2
2
1
0
1
0
2
1
1
1
1
1
1
0
1
2
2
2
0
4
0
2
2
1
1
0
0
0
0
1
2
0
1
1
2
1
2
1
1
0
2
1
1
1
1
2
0
0
1
2
1
0
2
0
1
1
0
2
0
0
1
1
1
2
1
1
0
1
2
4
0
1
1
1
2
1
2
2
1
0
1
0
1
1
1
1
1
1
1
1
0
1
2
2
1
1
2
1
0
1
1
1
1
0
0
1
0
1
2
2
2
1
1
1
1
1
2
1
2
0
2
1
0
0
1
1
0
0
0
1
1
0
1
1
1
1
0
1
1
2
1
1
1
2
0
2
1
0
1
0
0
1
0
1
0
0
0
0
1
0
0
1
2
0
1
2
2
1
1
0
1
1
1
0
1
1
1
1
0
1
2
2
2
1
1
2
2
2
1
2
1
1
1
1
1
1
1
1
2
0
0
1
2
1
1
1
0
0
2
1
2
2
1
1
1
2
1
1
1
0
1
1
0
1
2
2
3
1
2
1
1
0
2
0
2
1
1
2
2
0
0
0
1
1
1
0
0
0
0
1
0
1
1
0
0
1
2
1
2
0
0
2
1
2
1
0
1
1
1
2
0
0
2
0
1
0
0
2
2
2
1
0
0
0
1
1
0
1
0
0
1
2
1
2
0
2
0
0
1
0
2
1
2
2
1
1
2
0
0
0
0
1
1
1
1
1
1
1
1
0
2
0
0
1
0
8
1
2
1
1
1
1
0
0
1
1
2
2
1
1
1
0
0
2
1
1
1
1
1
2
0
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
2
1
1
1
1
1
1
1
1
1
1
1
1
0
2
2
2
1
0
2
2
0
1
1
2
2
1
2
0
1
2
1
0
2
2
2
1
0
1
2
2
1
0
1
2
1
2
1
1
1
0
1
2
1
0
2
2
2
1
2
0
1
1
1
0
1
1
1
1
6
2
1
3
1
1
1
2
0
1
1
2
1
0
2
2
0
1
1
2
1
0
2
0
0
2
1
1
0
0
1
1
1
1
1
2
0
1
1
2
0
2
0
1
0
0
1
2
1
2
0
2
2
0
0
2
2
1
1
1
1
1
0
1
2
1
1
1
1
1
2
0
1
1
1
0
1
0
0
2
1
1
1
0
2
1
1
2
1
1
2
0
2
1
1
1
0
1
0
1
2
1
1
0
0
0
2
3
1
1
1
1
1
1
0
0
1
1
2
1
1
2
1
0
1
1
2
1
1
2
1
0
1
2
0
1
1
1
1
1
0
1
0
2
0
1
1
2
0
2
1
1
0
1
2
1
2
2
0
2
2
1
1
1
1
2
2
0
2
0
1
2
0
0
2
1
2
0
1
2
1
0
2
1
0
1
1
1
1
2
1
2
1
1
1
1
2
2
0
1
1
0
0
1
0
0
1
1
2
2
2
1
0
1
1
1
1
1
1
2
1
1
1
1
0
2
1
1
2
2
1
2
0
2
1
1
0
0
0
1
1
0
1
0
1
2
0
2
1
1
0
1
1
1
0
1
0
1
1
1
0
1
1
3
2
1
2
2
2
1
0
1
3
1
1
1
1
2
1
2
2
2
1
2
1
1
1
0
1
0
0
2
0
1
1
1
2
2
2
1
1
2
0
0
1
2
1
1
1
0
1
0
0
1
2
0
1
1
2
1
1
0
0
0
1
1
1
1
1
1
2
1
1
0
2
2
1
0
1
0
1
0
1
1
1
1
0
1
1
0
0
1
0
1
0
1
1
0
1
0
1
0
0
0
0
2
2
0
1
0
0
0
0
1
1
2
1
1
0
0
1
2
0
1
0
2
1
1
0
2
1
1
1
0
1
1
1
1
0
1
0
1
0
2
2
1
2
2
1
1
0
0
1
0
2
2
0
0
0
2
1
1
2
0
1
1
1
0
2
1
4
1
2
1
2
0
3
0
0
1
1
2
0
0
2
0
0
1
2
1
2
1
2
0
1
0
1
2
1
1
1
1
0
3
0
2
0
0
1
0
2
1
1
0
1
2
2
2
1
0
0
1
1
2
0
1
3
2
2
1
2
1
1
2
2
2
2
2
1
0
1
1
2
1
0
2
0
0
2
1
0
2
1
0
0
1
0
1
1
2
1
1
2
0
1
0
2
0
2
0
2
1
2
2
1
1
1
2
0
0
1
2
2
0
0
0
1
0
3
1
1
0
0
0
2
1
2
1
0
0
1
2
1
1
0
0
2
1
1
0
0
2
1
1
2
2
1
1
0
0
2
1
1
0
0
0
1
0
1
2
0
1
1
2
1
1
1
1
0
2
2
0
0
2
1
1
2
1
1
1
1
0
2
1
2
0
1
1
2
0
0
2
2
1
2
1
0
0
2
0
2
2
2
4
0
0
1
1
1
1
1
1
0
1
1
2
1
1
1
0
1
0
1
2
2
1
1
1
0
2
1
0
2
1
2
0
0
2
0
0
1
2
1
0
1
1
1
1
1
2
1
1
0
0
2
1
3
1
2
1
2
2
1
2
1
1
1
0
0
2
2
1
1
1
2
1
0
0
0
0
1
2
1
0
1
0
1
1
1
1
1
1
1
2
1
0
1
2
1
1
1
0
1
2
2
1
2
1
0
1
2
1
2
2
0
2
2
3
1
1
2
1
2
1
1
1
1
1
1
0
0
2
1
2
2
1
0
1
1
1
0
0
1
0
1
2
1
1
1
0
0
1
0
1
1
1
1
1
1
1
1
1
2
0
1
1
2
1
1
2
1
0
1
1
0
2
0
1
1
0
0
1
1
3
1
2
0
1
1
0
1
0
1
1
1
0
2
0
0
1
1
1
1
1
0
1
2
1
2
0
0
1
1
2
2
1
1
2
2
0
0
0
2
2
1
1
1
1
2
0
0
0
2
1
1
0
1
0
1
1
1
1
0
1
1
0
1
0
1
0
2
0
1
1
1
2
1
1
1
0
1
0
1
1
0
1
1
1
1
0
1
1
0
1
1
1
0
0
1
1
1
1
1
1
0
1
1
1
1
1
1
1
2
0
2
2
1
1
1
1
1
1
1
1
0
1
0
1
2
0
1
1
1
1
0
1
1
1
1
0
2
1
1
1
1
1
0
2
1
0
2
0
0
0
1
1
1
1
0
1
1
2
2
2
1
1
1
0
0
0
0
0
1
1
2
2
0
2
1
0
1
1
1
2
0
0
0
0
1
2
0
0
1
1
0
2
1
2
2
2
1
1
1
1
2
2
1
1
1
1
0
1
2
0
1
2
1
2
1
1
0
1
1
0
1
2
1
0
1
1
0
1
0
1
1
1
1
1
2
0
1
0
0
1
1
1
1
0
1
1
1
2
1
1
2
2
1
5
1
1
1
1
1
0
1
0
1
1
0
1
0
2
2
1
0
0
1
2
0
2
1
1
1
1
0
1
0
1
1
1
0
1
1
2
2
2
1
2
1
1
0
2
0
0
1
1
1
1
0
1
2
0
2
1
1
1
0
1
1
0
1
2
1
2
0
1
1
1
1
2
1
1
2
1
1
1
1
0
1
3
0
1
1
0
0
0
0
0
2
0
0
1
1
1
1
0
1
1
0
0
0
0
1
1
1
1
0
0
1
1
0
1
0
1
1
0
0
1
0
0
0
1
1
0
2
1
2
0
1
2
1
2
0
1
0
1
1
1
1
1
1
1
1
2
0
1
1
1
2
1
1
0
1
0
0
1
2
2
2
1
0
0
1
1
1
1
1
0
1
1
1
2
1
0
1
4
0
1
2
1
1
2
1
2
0
1
1
2
1
1
2
1
1
2
0
1
1
0
2
0
1
2
1
1
2
0
1
1
0
1
1
0
0
0
1
1
0
1
1
1
2
0
1
1
1
0
1
2
1
2
1
1
1
1
1
2
2
0
0
1
0
0
1
1
1
1
2
2
2
1
1
0
2
1
2
2
2
1
0
2
1
1
0
1
1
2
2
0
2
1
0
1
1
0
0
1
1
2
1
1
0
2
0
1
0
1
1
2
2
0
0
1
2
0
0
0
1
0
2
0
0
2
1
1
2
1
1
0
1
1
0
1
0
1
1
0
1
0
1
2
1
1
1
1
1
2
1
1
1
1
0
1
1
0
1
4
2
2
0
0
1
1
2
1
1
3
1
0
1
2
2
0
1
1
0
0
0
0
0
1
1
0
1
1
1
1
2
0
0
0
1
1
2
1
0
0
2
0
0
1
1
1
1
2
1
1
1
4
2
1
0
0
1
2
1
0
0
1
1
1
1
2
0
2
2
2
1
0
0
0
2
2
2
1
1
1
2
2
1
0
1
0
0
1
1
0
1
1
0
2
3
2
2
1
0
1
1
2
1
0
3
0
2
1
1
1
1
1
0
1
1
0
2
2
2
0
1
1
1
2
1
2
1
1
1
0
1
2
0
0
1
1
0
0
0
1
0
2
1
2
0
0
2
1
2
0
1
0
2
1
1
1
1
1
2
0
1
0
1
1
1
2
0
2
2
0
1
0
0
2
1
0
2
0
2
1
1
1
3
2
0
1
0
1
0
1
1
0
2
1
0
1
2
1
0
2
1
1
3
2
1
2
2
1
1
0
1
1
2
2
1
0
1
1
1
1
1
1
1
0
2
1
0
1
0
1
0
2
1
2
1
1
0
1
0
1
2
0
0
0
2
1
0
0
0
1
1
0
1
1
1
2
2
2
1
1
6
2
0
2
0
1
1
1
1
2
0
1
0
1
1
2
1
1
1
1
0
1
1
1
1
1
1
1
2
1
1
1
1
2
1
2
1
1
0
0
1
0
1
0
2
0
1
1
1
0
1
1
1
0
1
1
1
0
2
1
1
3
1
0
1
0
1
1
1
2
0
1
0
0
1
1
1
1
0
1
2
1
1
1
1
1
0
1
1
1
0
1
2
1
1
1
1
0
1
0
1
1
1
1
1
1
1
2
2
1
0
3
1
2
1
0
1
1
1
4
1
1
1
0
1
1
1
1
0
1
0
1
1
1
2
1
2
1
2
1
0
1
1
1
1
1
2
1
0
1
0
1
1
1
2
0
1
1
1
2
2
1
2
2
1
1
1
1
1
1
1
1
2
1
1
1
0
1
1
1
1
2
1
1
0
1
0
1
2
2
1
1
1
1
2
0
0
1
1
1
1
0
1
1
1
0
2
1
1
1
1
1
1
1
2
0
0
1
0
0
3
3
0
1
1
0
0
1
1
2
0
1
1
1
2
0
0
1
1
1
1
0
2
1
1
2
1
1
1
1
1
1
1
0
0
2
1
1
1
1
2
2
1
1
1
2
1
1
2
2
1
1
2
0
0
2
0
1
2
0
2
1
1
2
2
1
1
0
1
2
1
2
1
2
2
2
1
2
1
1
1
0
1
1
1
1
0
2
2
1
0
0
1
2
0
7
0
0
1
0
0
1
1
2
2
0
1
1
0
1
1
1
2
1
1
2
2
0
2
1
1
1
1
1
1
0
1
2
1
1
0
1
1
2
0
0
1
1
1
1
1
6
1
2
2
1
1
1
2
0
1
2
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
2
0
1
0
2
0
3
0
1
0
0
0
1
1
0
1
1
0
0
1
2
3
1
2
1
1
2
2
1
3
1
1
0
2
1
2
3
1
1
1
1
1
2
2
1
1
1
1
2
1
0
0
0
1
0
1
0
1
1
1
2
2
0
1
1
0
0
1
1
1
2
1
1
1
0
0
1
0
1
1
2
1
1
2
1
1
1
0
2
0
1
0
2
2
0
0
2
1
1
1
1
1
0
1
0
1
1
1
2
2
1
0
0
1
1
1
0
1
2
3
0
1
2
2
0
2
1
0
0
0
1
1
1
0
1
1
1
2
0
0
1
1
1
0
2
2
1
1
0
0
1
1
0
0
2
0
0
1
1
2
1
1
1
1
1
0
0
2
1
4
2
1
2
2
1
0
0
0
1
1
2
0
1
2
0
0
0
0
1
1
2
0
0
0
2
2
1
0
1
2
1
2
0
0
0
1
1
1
0
1
0
1
2
1
0
2
2
1
1
1
2
0
2
1
0
0
0
1
2
1
1
1
2
1
0
0
1
1
1
1
1
1
1
0
2
1
0
1
1
1
2
0
1
2
1
1
1
1
1
1
0
2
1
2
1
2
0
1
1
2
0
0
2
1
1
1
1
1
1
1
1
1
0
1
1
0
1
1
2
0
2
0
1
3
1
1
1
1
0
1
3
2
0
1
2
0
1
1
1
0
1
0
1
1
2
1
3
1
1
1
3
1
1
0
1
1
1
1
2
1
0
0
1
1
1
0
1
1
2
2
1
1
1
1
0
1
1
1
0
1
0
1
1
2
0
0
1
0
2
1
2
0
1
0
2
0
2
2
2
0
1
2
1
1
1
1
1
1
1
0
0
1
2
1
1
1
0
1
1
1
2
1
4
2
1
0
0
2
0
0
1
2
1
3
2
0
1
0
1
0
2
1
0
0
2
1
1
0
0
1
2
1
1
0
2
1
1
2
0
0
1
1
1
1
0
2
0
1
2
1
2
1
0
1
0
1
1
1
2
1
0
1
0
2
0
1
1
1
1
1
2
3
2
1
0
1
1
1
2
1
2
0
0
0
1
1
2
2
1
0
0
1
0
0
2
1
2
0
1
1
0
1
2
1
1
0
0
1
0
1
2
1
0
1
0
1
1
1
2
1
1
0
0
1
2
2
1
0
0
1
2
1
0
1
1
2
2
1
1
0
2
1
2
0
2
1
1
1
2
1
1
0
1
0
1
2
0
0
0
2
0
1
0
1
0
1
0
1
1
0
1
0
1
0
2
0
2
0
2
2
1
2
1
0
1
1
1
1
1
1
1
1
0
1
0
0
0
1
0
2
1
0
1
1
2
1
2
1
2
2
1
0
1
1
2
1
1
0
1
1
2
2
0
1
1
1
1
2
0
1
1
1
1
1
0
1
2
1
1
1
1
2
1
1
1
1
1
2
1
1
0
1
1
1
2
1
1
1
0
1
1
2
0
1
1
1
2
2
1
2
1
1
1
1
2
1
1
0
1
1
1
1
2
1
0
1
2
2
1
0
2
2
0
1
1
2
2
0
1
1
1
1
2
1
0
1
2
0
2
2
1
1
1
0
2
1
1
0
0
2
1
1
1
1
2
0
1
1
1
2
1
0
1
0
0
1
1
1
2
0
1
1
0
2
0
0
1
0
0
1
0
0
1
3
1
2
1
2
2
1
1
2
2
1
0
0
0
2
2
2
2
0
1
0
1
2
2
1
1
2
1
0
2
1
2
2
1
1
1
1
1
0
2
1
1
2
2
1
2
2
2
0
0
1
0
1
2
1
1
0
1
1
1
1
2
1
1
1
0
1
1
1
0
2
2
2
1
1
2
2
1
1
0
0
1
1
1
1
1
2
2
2
0
1
1
1
0
2
1
0
0
1
0
1
1
1
0
3
0
1
1
1
2
1
1
0
2
2
1
0
1
0
1
3
1
1
2
1
1
1
2
0
0
1
1
2
0
1
1
1
2
2
2
1
0
0
1
0
1
0
1
2
2
1
1
2
0
1
2
2
2
1
1
0
2
1
1
1
1
1
1
1
1
1
2
1
0
2
1
2
1
1
1
0
2
2
1
2
1
1
1
0
1
2
2
2
2
2
1
1
0
1
2
1
1
0
1
1
2
1
1
2
3
2
0
0
0
0
0
1
1
1
1
0
0
1
1
2
2
0
0
2
1
0
2
1
1
4
0
1
1
1
2
2
0
1
1
1
0
2
2
1
1
1
1
1
0
1
1
1
1
1
1
1
0
1
2
1
1
1
1
1
1
2
1
0
2
1
1
1
1
2
1
0
1
0
1
2
1
1
3
1
0
1
0
0
0
2
0
1
1
2
2
1
1
0
0
1
1
1
1
1
1
0
2
1
3
1
0
1
0
1
2
1
0
1
1
0
2
2
1
1
0
2
2
1
1
1
1
2
2
1
0
1
2
1
2
1
2
2
2
1
1
1
1
1
1
1
1
0
1
2
1
1
1
1
1
2
1
1
0
0
1
1
1
1
1
0
2
0
1
1
0
1
0
2
1
1
0
1
2
0
0
2
1
0
1
1
1
2
2
0
1
1
1
2
0
2
1
0
1
0
0
2
0
1
0
2
0
1
2
1
1
0
0
1
0
2
1
1
2
2
0
0
1
1
2
1
1
0
1
1
0
1
0
0
1
1
1
2
1
1
1
0
1
1
0
1
2
1
1
1
1
1
0
2
1
1
1
1
1
1
0
1
1
1
2
2
1
1
0
1
2
1
1
1
2
1
0
1
2
1
1
2
4
2
0
1
1
1
0
1
0
1
0
1
1
1
0
2
1
1
1
1
2
2
0
1
0
1
1
0
1
2
1
1
1
0
1
1
1
0
0
0
1
0
1
1
2
2
1
0
0
0
1
0
2
2
1
1
0
2
2
2
0
2
0
0
0
1
1
1
1
1
1
1
2
1
1
0
0
0
1
2
1
1
2
1
2
3
1
2
1
1
1
1
1
1
1
0
0
2
1
1
1
0
0
0
1
2
2
2
1
1
2
0
1
0
0
0
0
0
1
0
0
1
0
1
1
1
2
1
1
1
2
0
2
0
1
1
0
1
0
1
1
1
1
2
2
1
0
0
1
1
1
1
1
0
1
1
2
2
1
2
1
0
2
0
2
0
1
1
0
2
0
1
1
2
0
1
0
1
1
2
1
2
2
1
1
1
1
0
2
1
0
1
2
1
0
0
2
2
1
1
1
1
1
2
1
2
0
0
0
0
1
2
0
1
1
1
0
1
0
1
2
1
1
2
1
2
0
2
1
0
1
1
0
0
1
1
1
2
1
1
1
1
0
2
0
2
1
2
0
1
1
0
1
0
0
1
1
2
1
2
1
0
0
1
0
1
1
0
0
1
1
1
1
1
1
2
0
0
1
0
3
2
2
1
1
0
2
1
1
0
1
2
0
2
0
1
0
0
2
1
2
1
1
2
1
1
1
0
1
2
0
1
1
1
1
1
2
1
1
1
1
1
0
1
2
1
0
1
2
1
0
2
0
1
1
1
0
2
1
1
1
2
2
1
1
0
1
1
2
1
2
2
1
0
1
2
0
1
1
1
1
2
2
1
0
1
1
0
1
1
0
1
3
1
1
1
1
2
0
1
2
1
0
1
1
3
1
1
1
1
0
2
0
0
2
1
0
1
0
1
1
0
1
1
0
0
2
1
1
1
0
0
2
0
1
2
1
1
4
0
0
0
1
1
1
0
1
1
1
1
3
1
1
1
0
0
1
1
1
1
1
1
0
1
0
0
1
1
2
0
1
3
1
1
1
0
0
2
2
1
1
2
0
1
0
2
0
1
0
2
2
1
2
0
2
1
1
1
0
2
1
1
3
1
2
1
0
1
0
1
1
1
2
1
2
2
0
0
0
1
1
1
0
1
2
0
1
1
1
1
1
1
2
0
1
2
1
0
1
1
1
1
1
1
0
1
0
1
1
1
1
0
2
1
0
2
1
1
1
2
1
1
1
1
0
1
2
2
0
1
1
1
1
1
0
1
1
1
2
1
2
1
1
4
1
0
2
0
0
0
2
1
0
0
1
0
1
2
1
3
1
2
2
0
1
1
1
2
0
1
2
1
1
1
2
1
0
0
1
1
2
1
0
0
2
1
0
2
0
2
1
2
1
1
1
1
0
1
1
3
2
0
1
1
0
1
2
2
2
1
3
1
1
1
1
2
1
1
0
2
0
0
1
1
0
1
1
1
1
2
2
1
0
2
0
1
1
2
0
1
1
1
1
0
1
1
1
0
1
1
1
1
2
1
1
1
0
1
1
0
2
0
2
2
0
0
2
1
0
1
0
1
1
0
1
0
1
1
1
1
2
1
2
2
1
0
1
2
0
0
0
2
0
1
1
0
1
1
1
0
2
1
1
1
1
1
1
0
1
1
1
2
0
1
1
1
1
1
2
2
1
1
1
1
1
0
0
1
0
0
1
1
1
1
0
2
1
1
1
1
1
2
2
2
0
1
0
1
1
1
2
0
0
1
2
1
1
0
1
0
2
1
0
0
1
0
0
1
1
1
1
1
0
2
1
0
0
1
1
1
1
2
1
1
0
2
1
1
0
0
1
1
2
0
0
2
1
1
1
0
1
2
2
1
1
1
0
0
0
2
1
1
0
1
2
1
1
0
2
0
1
1
2
1
0
2
1
2
0
0
2
1
0
1
1
2
1
1
1
2
2
1
1
1
2
1
1
0
2
0
0
1
1
2
1
2
0
1
2
1
1
1
0
2
1
0
1
1
2
1
1
0
1
2
0
1
1
0
0
1
0
0
2
1
0
1
1
1
1
1
1
1
2
2
2
0
1
1
2
0
2
1
1
1
1
1
1
3
1
1
1
1
0
1
1
2
0
0
2
1
2
0
2
2
0
2
2
1
0
1
2
2
1
1
0
1
1
1
0
2
0
1
2
1
2
1
0
2
1
1
0
0
2
1
1
2
2
0
1
0
2
0
0
0
1
1
1
2
1
0
0
1
2
0
1
2
2
3
1
1
1
0
1
2
1
1
1
1
2
2
2
0
1
0
1
1
1
0
0
1
1
2
1
2
1
1
1
1
0
1
0
1
0
2
1
1
1
1
2
1
2
2
0
1
2
1
1
2
0
1
0
0
0
0
0
1
1
1
0
2
2
1
1
0
1
2
0
1
2
2
2
1
2
1
2
2
2
1
0
1
0
1
1
2
0
1
1
1
0
1
1
0
1
2
1
1
2
2
2
0
1
2
2
0
3
1
1
1
2
2
0
1
0
1
3
2
2
1
0
1
1
2
0
1
1
0
0
1
1
0
2
0
1
1
2
1
1
0
2
1
0
2
2
1
1
1
1
1
1
1
1
2
2
0
1
2
2
1
1
0
1
1
0
0
1
1
0
1
1
0
1
0
1
1
0
0
0
2
2
1
2
1
1
1
0
0
0
1
1
2
0
2
2
0
1
1
1
0
1
1
1
0
0
1
1
1
0
1
1
0
1
1
0
2
1
2
2
1
1
0
1
0
0
0
1
1
1
2
1
1
2
1
1
3
0
0
1
1
1
1
0
1
2
1
2
2
0
1
2
1
0
1
2
2
0
2
1
2
2
1
1
1
1
2
1
1
0
0
0
0
2
1
2
1
1
1
0
1
1
2
2
1
1
0
1
2
2
0
1
1
0
1
0
0
1
1
2
1
0
1
1
1
1
1
1
0
1
1
3
1
1
1
2
1
2
0
1
1
0
0
1
0
1
1
2
1
0
1
0
0
2
0
1
1
1
1
2
1
0
1
1
1
2
1
1
1
1
1
0
2
1
0
0
1
1
1
1
2
1
2
1
0
0
2
0
1
0
0
1
0
1
1
1
1
2
1
2
0
1
2
2
1
1
1
1
0
1
2
1
0
0
2
0
1
2
2
0
1
1
2
2
1
2
2
1
0
1
2
1
2
2
1
1
0
2
0
1
0
0
2
0
1
1
0
0
1
1
1
0
1
1
6
2
1
1
2
2
1
1
0
2
0
1
1
2
1
2
1
2
0
1
0
2
1
2
1
1
0
0
1
1
2
1
2
1
1
2
1
0
1
0
1
1
1
0
1
1
0
0
2
1
2
1
1
2
1
1
0
1
1
1
0
0
0
2
0
1
1
0
1
1
1
1
2
1
1
1
1
1
1
0
2
1
1
0
2
2
1
1
0
1
2
1
1
0
1
2
0
0
2
1
2
1
0
2
0
2
0
1
1
1
1
1
1
0
0
0
1
1
1
0
0
0
0
2
1
1
0
2
1
2
2
1
0
1
2
0
1
1
1
1
1
0
1
2
0
1
0
1
2
0
0
2
2
2
0
1
1
1
2
0
1
1
1
1
0
1
1
0
2
2
2
1
1
1
1
0
0
1
1
1
1
2
3
1
1
0
2
0
1
0
1
1
1
2
2
0
1
2
1
2
2
0
1
0
2
1
0
0
1
0
2
0
2
1
1
0
0
2
1
1
0
1
2
1
0
1
1
1
2
1
0
1
1
0
1
2
2
2
2
0
2
1
2
1
2
1
1
2
1
1
0
1
0
1
1
1
1
1
1
1
1
1
0
1
1
1
2
0
0
1
1
1
0
1
2
0
2
2
1
0
1
1
2
2
1
1
2
1
2
0
1
1
1
0
2
1
1
2
0
0
1
1
1
1
2
1
1
1
1
0
0
1
1
1
0
1
1
1
2
2
0
0
1
0
0
2
0
1
0
0
2
0
1
2
2
2
1
1
0
1
1
1
2
1
1
1
0
1
1
0
3
0
2
0
2
0
0
2
1
1
1
1
2
0
1
1
1
1
2
2
1
0
1
0
1
1
1
1
1
2
1
2
1
2
2
1
2
1
0
1
0
0
1
0
1
1
2
0
1
1
1
2
1
0
2
1
1
0
0
1
1
1
1
2
0
2
2
2
2
1
1
1
0
0
0
1
1
0
1
1
1
2
1
1
1
0
2
1
2
1
1
0
0
1
2
1
1
1
0
2
1
1
2
2
1
1
2
0
1
2
1
1
1
1
1
2
1
0
1
2
0
0
1
2
2
1
0
6
0
2
2
3
2
1
0
1
1
1
1
1
0
1
0
1
1
0
1
1
2
1
2
0
1
1
0
1
1
2
2
1
1
1
1
2
0
0
1
1
1
1
0
0
0
2
0
1
1
1
1
1
0
0
3
1
0
1
1
1
1
1
1
1
1
2
2
1
1
2
0
2
1
4
2
2
0
2
0
0
2
2
1
2
2
0
1
0
1
1
1
0
0
0
0
1
2
2
1
2
1
1
0
1
1
1
2
2
1
1
0
2
1
0
0
2
1
2
1
1
1
1
2
1
2
0
0
2
0
1
2
1
1
1
2
1
1
0
0
2
0
0
2
0
1
2
2
1
1
1
0
0
1
0
0
2
2
0
1
0
0
1
1
3
2
1
1
1
1
0
0
2
0
1
2
2
2
2
0
1
0
1
1
1
1
1
2
1
2
2
1
1
1
1
0
1
2
0
0
1
2
0
3
2
1
2
2
1
1
1
1
1
2
1
1
1
1
1
0
0
1
2
1
0
2
2
2
2
0
0
1
1
0
0
0
1
1
0
1
2
2
0
0
1
0
1
0
1
1
1
3
0
1
1
2
3
1
1
1
1
0
0
1
1
1
2
1
1
1
1
1
1
1
0
0
1
1
1
1
0
1
1
1
1
1
1
2
1
0
1
1
1
1
1
1
1
0
1
1
0
2
1
0
1
1
2
0
1
0
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
2
0
1
1
2
1
2
0
2
1
1
2
1
1
1
1
0
1
0
0
0
1
0
0
1
0
1
1
0
2
0
0
2
0
2
1
1
1
1
2
2
1
1
2
1
1
2
1
1
1
1
1
2
1
1
1
1
1
0
1
1
0
0
1
1
1
2
1
2
1
1
1
0
2
0
1
2
0
0
2
0
2
2
0
2
1
1
1
1
1
1
0
3
1
1
1
1
0
1
2
0
0
1
0
1
0
0
0
1
1
1
1
1
1
0
2
0
2
1
1
0
1
1
1
2
1
1
1
1
0
1
0
0
1
1
2
2
2
0
0
2
1
1
1
2
0
0
1
1
1
0
0
1
1
1
2
1
0
1
0
0
2
1
0
2
0
1
1
1
0
0
1
0
1
0
1
1
1
1
2
1
0
1
2
1
2
0
1
0
0
1
0
0
0
1
0
0
0
0
2
0
1
1
2
2
1
0
1
1
1
1
0
2
1
2
1
0
0
2
0
1
0
1
0
1
1
0
0
2
0
2
1
0
2
0
1
0
0
1
1
1
1
0
1
1
1
2
1
2
0
1
1
1
2
1
1
2
0
1
2
2
2
2
1
1
2
0
1
1
1
1
0
0
2
2
0
2
0
0
2
1
1
1
0
0
2
0
1
1
1
0
1
0
0
0
0
0
1
0
1
1
1
1
1
1
1
2
1
1
0
2
0
1
0
1
0
1
2
1
2
1
1
2
1
1
0
0
1
1
1
1
2
1
1
1
2
1
1
1
1
2
1
0
0
1
1
1
2
1
0
1
1
2
1
0
2
2
2
2
1
1
1
1
2
1
0
0
1
2
0
2
1
0
1
0
0
1
1
2
1
1
0
1
0
1
0
1
1
2
2
1
0
1
1
0
2
1
1
1
2
0
2
1
1
0
2
0
1
0
1
0
1
1
2
0
2
0
1
1
1
1
1
1
1
1
1
0
1
1
1
1
0
5
2
0
0
0
1
0
0
1
1
1
1
1
0
2
2
0
1
2
1
1
2
1
0
2
0
2
1
1
2
1
2
0
1
1
0
0
2
1
1
0
1
1
0
2
2
1
1
1
0
1
0
1
1
1
0
0
1
2
1
2
0
2
0
0
1
0
1
1
2
0
2
2
0
1
0
1
0
1
1
1
0
0
1
1
1
1
1
1
0
1
0
1
1
1
0
1
3
0
0
1
0
1
1
1
3
1
1
0
0
0
2
2
2
2
1
0
0
0
1
1
0
0
0
1
2
2
1
2
3
1
1
0
1
3
1
0
0
0
1
2
1
1
1
1
1
1
0
1
1
2
1
0
1
1
1
2
1
1
0
1
1
1
0
2
1
1
1
2
1
2
0
2
2
2
1
1
1
1
0
1
1
1
0
1
6
2
2
1
1
1
1
1
1
0
2
2
2
2
0
1
1
1
2
0
1
1
1
1
2
2
0
1
1
1
0
0
1
1
1
1
2
4
1
2
2
0
1
2
1
0
0
2
1
0
2
2
1
0
0
1
0
1
1
1
0
1
1
0
1
2
1
1
1
1
1
0
2
1
1
2
1
0
2
1
1
0
1
2
2
1
1
1
2
0
0
1
0
0
0
1
0
0
1
1
2
1
2
1
1
2
1
1
2
2
2
0
2
1
2
2
0
0
0
2
2
0
0
1
0
1
0
0
0
2
2
2
0
1
1
2
0
2
0
1
1
1
1
0
1
1
2
1
2
1
0
0
1
1
1
2
1
1
1
1
4
1
1
1
1
1
1
1
1
1
1
0
1
0
2
1
1
1
1
1
0
1
1
1
2
0
1
0
1
1
2
2
1
0
0
0
1
0
1
1
1
0
1
2
1
1
2
1
1
0
0
2
0
1
0
1
0
1
2
0
1
0
1
1
1
0
1
1
1
0
2
1
1
0
0
1
2
0
1
1
1
2
1
0
1
2
1
1
0
1
1
1
1
1
2
1
1
2
1
0
1
1
1
1
0
1
1
0
1
1
1
1
1
1
1
0
1
0
1
0
2
0
0
1
1
0
1
2
1
2
2
1
1
0
2
1
0
1
1
0
2
1
0
0
2
1
1
2
2
0
1
1
2
1
1
0
1
3
1
0
3
0
0
0
1
0
1
1
1
1
2
1
1
2
1
2
0
2
0
2
1
0
0
0
1
2
0
1
2
2
0
0
0
2
1
1
1
1
2
1
0
2
0
2
1
1
1
0
1
1
1
1
1
0
1
0
1
1
0
1
1
1
1
2
2
0
1
0
1
0
2
0
1
1
1
2
2
1
1
0
1
2
1
1
0
0
0
1
5
1
1
2
1
2
0
2
0
1
1
0
1
2
1
1
1
2
1
1
0
0
2
0
1
1
1
1
2
1
1
1
0
2
1
3
1
1
1
0
0
0
2
1
0
3
1
2
1
1
1
1
0
0
1
0
0
1
1
1
1
1
0
1
1
0
2
1
3
1
1
1
1
1
0
1
1
0
2
0
1
1
1
2
0
0
0
1
1
1
1
1
1
1
1
1
2
1
2
1
2
0
0
0
2
1
1
0
1
1
2
0
2
1
0
2
1
2
1
1
2
0
1
0
2
1
1
2
1
1
2
1
1
1
1
1
0
0
1
1
0
1
1
1
1
1
0
0
1
1
2
2
0
1
0
2
0
2
2
1
0
1
1
0
0
1
2
1
2
1
1
1
1
1
2
1
1
0
0
0
2
2
1
1
3
1
1
1
2
1
1
1
1
1
1
1
2
2
1
2
1
0
1
1
1
0
0
0
1
1
1
2
0
1
1
2
1
0
1
2
2
0
1
2
1
1
1
1
1
1
3
1
1
1
1
1
0
2
2
1
2
1
1
1
2
2
1
1
1
1
1
1
0
1
1
0
1
3
2
2
2
2
3
1
1
1
0
0
1
1
1
1
1
2
2
1
1
1
0
1
0
1
0
1
0
1
1
0
2
1
3
2
1
1
2
1
1
1
0
2
0
0
1
1
0
1
0
1
0
1
0
1
0
0
3
0
1
0
0
2
2
0
2
2
0
2
0
1
0
1
0
0
0
1
2
3
2
0
1
0
1
1
0
1
2
1
1
0
0
1
1
0
1
1
1
0
1
2
2
0
1
2
1
1
1
1
1
1
1
1
1
1
0
2
0
2
0
1
2
1
1
2
2
1
2
1
1
3
1
1
2
1
0
0
2
1
1
2
1
1
0
1
1
0
2
2
1
1
1
1
0
1
1
1
1
1
2
1
1
1
3
1
2
0
1
0
0
2
1
1
0
1
1
1
0
1
2
1
1
1
0
0
1
0
2
0
1
1
0
0
1
1
0
1
2
0
0
1
2
0
1
0
1
2
1
1
1
2
1
0
1
2
1
1
1
0
0
2
0
2
0
0
0
2
1
3
1
1
0
1
1
0
2
0
2
2
0
1
1
0
0
2
2
1
1
0
0
1
0
3
1
1
1
2
1
1
1
1
1
1
1
0
1
2
1
0
0
0
1
0
1
2
1
2
0
0
1
0
1
1
2
0
0
1
1
1
1
2
1
2
0
1
2
1
1
0
1
0
2
0
2
1
1
1
2
1
2
0
2
0
2
1
1
2
2
0
0
0
1
1
1
1
1
1
1
2
2
0
0
1
0
1
0
1
1
1
1
0
2
7
0
2
1
1
2
0
2
1
1
1
1
1
1
1
2
0
1
0
1
2
2
1
2
1
0
1
2
0
1
1
0
1
0
1
1
1
2
0
0
1
2
2
1
2
1
0
2
1
2
2
1
0
2
1
2
1
1
1
1
2
2
1
1
2
0
1
0
1
2
0
0
1
0
2
1
2
1
0
0
0
1
2
2
2
1
0
1
1
0
1
1
0
1
0
2
1
0
0
1
1
1
1
1
1
1
3
1
0
0
0
0
0
1
1
1
0
2
1
2
1
0
0
1
0
2
2
1
0
1
1
2
2
0
1
2
1
1
1
2
2
2
1
2
1
2
1
1
1
0
2
0
0
2
0
1
2
2
1
1
1
2
1
1
0
0
1
1
0
1
1
1
1
2
0
1
1
1
2
0
0
2
2
1
1
1
0
2
1
0
0
2
1
1
1
2
0
1
1
1
0
2
2
2
2
1
0
1
1
1
1
1
1
1
2
0
1
0
1
1
1
0
2
1
2
0
1
1
0
0
0
1
0
2
1
1
2
0
1
0
1
2
2
0
1
1
1
0
0
2
0
1
1
1
1
1
2
0
0
1
1
1
2
0
1
2
1
1
1
0
2
0
1
0
0
1
1
1
2
1
2
2
2
0
1
2
1
1
1
2
2
0
1
1
2
1
1
0
0
2
2
1
0
0
1
0
0
0
2
1
1
0
0
0
1
1
2
2
2
2
0
0
2
2
2
0
1
1
1
1
0
1
0
0
0
1
1
1
1
0
1
1
1
2
0
0
1
0
1
1
1
3
1
1
2
0
1
0
1
1
2
0
1
2
0
1
0
1
2
1
0
2
1
2
0
2
1
1
1
1
0
1
2
2
1
1
1
2
0
0
1
1
1
0
1
1
2
2
2
1
1
2
1
1
1
1
2
1
1
0
0
2
0
1
2
2
0
1
1
2
1
0
1
2
0
2
1
1
0
2
0
0
2
1
2
0
1
1
0
1
1
1
0
1
2
1
0
1
1
1
0
1
0
0
2
0
1
2
2
0
1
2
1
1
0
1
2
2
0
1
0
1
1
1
2
0
1
2
2
1
2
0
2
1
0
1
2
0
1
2
0
2
2
2
1
0
0
1
2
1
1
2
0
1
1
0
1
1
0
2
3
0
1
1
1
1
1
0
1
1
2
0
1
2
1
3
2
1
0
1
1
1
2
1
0
2
1
1
1
1
0
1
2
2
1
1
1
1
1
0
2
1
1
1
0
1
0
1
0
1
1
2
0
1
1
1
0
3
1
1
1
1
1
0
0
0
1
1
0
1
1
0
1
1
1
2
1
1
2
1
1
1
1
1
1
2
0
1
1
1
2
0
1
1
1
1
1
2
1
1
1
1
0
2
1
1
0
0
1
0
1
0
1
0
1
1
0
2
1
0
1
1
2
1
1
2
1
1
1
0
2
1
0
1
1
0
2
1
0
1
0
1
1
0
2
0
1
2
0
1
1
1
2
1
0
1
2
1
0
1
2
2
2
1
0
0
1
0
1
1
0
1
0
2
0
1
1
1
1
1
1
0
1
0
1
2
2
1
1
1
0
1
1
2
1
2
1
0
1
1
1
1
1
1
1
1
0
1
0
2
1
1
1
0
2
0
1
0
1
0
1
2
1
2
0
2
0
1
1
1
2
0
0
0
2
0
0
0
0
1
1
1
0
2
2
1
0
0
2
0
2
1
1
0
0
1
0
0
1
0
0
0
1
0
1
0
1
2
0
1
0
1
1
0
0
1
2
0
1
1
2
2
0
1
2
0
1
1
1
2
0
2
2
1
2
0
2
1
0
0
1
0
1
1
1
1
1
1
1
0
1
0
2
1
1
1
1
2
1
1
1
0
0
2
2
0
1
2
1
0
1
2
1
1
0
0
1
2
1
0
0
1
0
0
1
1
0
1
1
2
1
2
1
0
0
2
2
1
2
2
1
0
0
2
1
0
1
2
1
1
1
0
1
2
2
0
1
0
0
1
2
0
0
2
0
1
3
1
1
1
1
0
1
1
1
1
1
0
1
1
0
0
1
0
2
1
2
2
1
1
2
1
1
0
1
0
0
1
1
1
0
0
0
1
1
1
1
0
0
2
1
1
1
4
1
0
1
2
2
1
1
1
1
0
1
2
1
1
1
0
0
1
1
1
2
1
2
1
1
0
4
2
2
1
1
1
1
1
0
2
1
1
0
0
1
1
1
0
1
1
1
1
1
2
0
1
1
1
0
2
1
0
2
1
1
1
1
0
0
2
1
2
1
0
1
0
1
2
1
0
2
1
1
1
1
0
1
2
1
1
0
0
1
0
1
1
1
0
1
1
2
1
0
0
3
1
1
0
1
5
0
1
0
1
3
0
1
1
1
1
1
2
0
1
1
2
0
1
2
1
2
1
0
1
1
1
0
1
0
1
2
1
1
0
1
0
1
1
2
0
5
2
2
0
1
1
1
1
1
2
1
3
0
1
1
0
1
0
1
0
2
1
0
1
1
1
0
1
1
1
1
0
1
1
1
1
3
2
0
1
0
1
2
1
1
0
1
2
1
1
2
2
1
1
3
0
1
0
0
1
1
1
1
2
1
1
0
1
1
2
1
1
0
1
0
1
1
1
2
3
2
1
0
2
1
1
0
0
2
0
2
0
0
2
0
0
1
1
1
0
1
1
1
1
1
2
1
2
1
0
1
1
2
0
2
0
2
1
1
1
1
1
0
0
2
1
1
1
1
2
2
1
1
0
1
2
1
2
2
2
2
1
1
0
1
2
1
1
0
1
0
2
1
1
0
0
1
0
1
2
0
2
1
0
0
0
1
1
2
1
1
1
0
2
1
1
0
0
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
0
2
1
1
1
1
1
0
1
2
0
1
0
0
1
1
2
0
1
1
2
1
2
2
1
1
0
1
1
1
0
0
1
0
1
1
2
1
0
2
1
1
1
2
0
1
1
1
2
0
0
2
1
1
1
1
0
1
1
1
0
1
0
0
2
1
1
0
1
1
1
1
1
1
2
0
0
3
1
0
2
2
2
1
1
1
1
2
2
0
2
0
1
1
1
2
1
0
0
0
0
1
1
2
1
1
0
1
1
1
1
1
1
1
1
0
1
2
2
1
1
3
2
1
1
1
0
0
1
0
1
1
2
0
0
1
1
1
0
2
1
1
1
0
2
2
2
2
0
1
2
1
0
2
0
2
1
1
1
1
1
1
0
1
1
1
1
1
1
1
2
0
1
1
2
0
1
0
0
1
1
1
0
2
1
1
0
0
0
2
1
2
1
0
0
2
1
1
1
1
1
2
1
0
2
1
0
0
0
0
2
1
1
1
1
1
1
2
0
2
1
1
0
1
0
2
1
1
0
2
1
2
1
1
0
1
1
1
3
1
0
0
1
1
2
2
3
1
0
2
1
0
0
1
0
0
1
1
1
1
1
2
1
0
1
0
1
1
0
1
0
2
1
2
2
1
1
1
2
1
1
1
2
1
0
0
1
0
1
1
1
0
2
0
1
1
0
0
1
2
1
0
1
1
1
1
1
2
0
2
0
1
2
2
1
1
2
1
2
0
1
1
1
1
2
1
1
0
1
2
0
1
1
1
2
1
0
2
1
0
2
1
1
1
1
2
2
1
1
0
1
1
1
2
1
2
1
1
0
1
0
2
0
2
1
1
1
1
1
1
0
0
0
2
1
1
0
2
2
0
1
2
1
2
1
2
0
1
1
0
1
0
0
1
1
0
0
1
1
0
0
1
0
1
1
1
1
1
2
1
2
1
1
1
1
0
0
1
1
0
2
0
0
1
1
0
1
1
1
1
1
2
0
2
1
1
1
1
1
1
2
2
1
2
1
2
1
2
0
1
1
2
2
0
0
0
1
1
1
2
1
2
1
1
1
0
0
1
0
1
1
1
0
2
1
2
2
2
0
0
1
2
1
0
0
0
1
1
1
2
1
2
0
1
1
1
1
1
0
1
1
1
2
1
0
1
0
1
1
0
0
1
1
0
0
0
1
1
1
2
1
0
1
1
1
1
1
0
1
2
1
1
1
1
1
1
1
0
2
2
3
1
1
1
0
1
2
0
0
1
1
1
1
1
1
2
1
1
2
0
2
1
0
1
1
1
0
1
2
1
1
0
1
0
1
1
1
2
1
0
1
1
1
1
1
2
1
1
1
0
1
1
1
0
1
1
0
1
2
1
2
0
1
0
1
1
0
1
1
0
1
1
0
1
1
2
1
2
0
2
0
1
0
1
2
1
1
0
2
1
2
1
2
0
1
1
1
2
2
2
1
1
1
0
1
1
1
1
1
1
0
1
1
0
2
1
0
1
1
0
2
2
2
2
1
1
1
1
0
0
2
1
0
0
1
0
1
1
2
1
2
1
1
2
1
2
0
1
0
4
2
1
2
1
0
1
1
1
0
1
0
0
1
1
0
1
1
1
0
1
1
1
1
0
0
1
0
1
1
1
1
1
1
1
2
1
0
2
2
1
1
1
1
2
0
1
1
0
2
1
0
1
2
1
2
0
0
1
1
1
0
0
1
1
2
2
2
2
1
1
1
0
1
1
1
0
2
1
2
1
1
2
1
0
1
1
1
1
0
1
1
1
1
1
2
1
0
0
1
2
1
2
1
0
1
0
1
2
1
1
2
1
1
0
1
2
1
2
2
2
1
1
1
2
11
2
1
1
0
1
1
1
2
1
0
1
1
1
1
1
1
1
1
1
2
1
3
1
0
1
1
2
1
0
1
0
1
0
1
2
2
1
0
1
0
0
2
1
1
1
0
1
0
1
0
1
0
1
1
1
0
1
1
1
1
1
2
0
1
1
1
1
1
1
2
0
2
2
2
1
1
2
1
0
1
0
0
0
2
0
1
1
1
2
0
1
1
0
1
0
2
1
1
0
1
0
0
2
1
1
2
2
1
1
0
0
2
0
2
1
1
0
0
2
0
0
1
1
1
1
1
0
1
1
1
0
1
2
0
1
1
0
0
1
2
2
0
2
2
1
2
1
1
0
1
1
1
0
1
1
2
0
1
1
2
2
1
1
1
2
0
0
0
1
1
0
1
2
2
1
0
2
1
1
1
1
1
1
0
1
1
1
1
1
0
2
2
0
1
1
2
1
0
0
2
0
2
2
0
1
0
2
1
1
2
2
0
0
1
2
1
1
0
1
0
1
2
2
1
0
1
1
1
1
1
1
0
1
0
1
1
1
1
1
2
0
1
1
1
0
0
1
1
2
2
3
1
1
1
1
1
1
2
1
1
1
2
1
2
2
1
2
1
0
2
2
1
2
0
2
2
2
1
0
1
2
0
2
1
0
2
1
1
1
0
1
4
2
1
0
2
1
0
1
0
1
0
0
0
2
0
0
2
1
1
3
1
2
1
1
2
1
1
1
1
3
0
0
1
1
1
1
2
0
0
0
1
0
0
1
1
2
1
0
2
2
0
1
2
1
2
0
0
0
1
2
0
2
0
0
0
1
1
1
1
0
1
1
1
1
2
1
1
1
0
0
1
0
0
1
0
1
0
1
0
1
1
1
1
1
1
0
1
1
2
1
1
2
1
0
1
1
1
1
0
1
0
1
0
0
1
1
0
1
1
0
0
1
1
0
2
0
2
1
1
0
0
2
2
1
1
0
1
1
1
1
0
1
1
2
2
1
1
1
1
0
0
2
0
2
1
0
2
1
1
0
1
2
1
1
1
0
1
1
1
0
1
1
1
1
2
2
1
2
1
1
2
0
2
1
3
1
0
0
1
1
2
1
0
0
1
1
1
1
2
1
0
1
1
1
1
1
1
1
2
0
0
0
1
1
1
1
0
1
2
1
0
1
2
1
0
2
2
0
2
0
2
1
1
1
0
0
1
1
1
2
0
1
1
1
2
1
1
0
2
1
1
2
1
1
1
0
0
1
1
1
2
1
1
1
1
0
1
1
2
1
1
0
1
2
3
1
1
1
0
0
2
2
1
0
1
1
1
2
2
1
2
1
3
0
0
0
1
1
0
1
1
0
1
1
2
2
2
0
2
1
2
0
1
0
1
0
1
1
1
3
1
0
0
0
2
2
1
1
2
1
1
0
1
0
0
1
0
0
2
0
0
2
0
0
4
2
1
0
1
0
1
1
2
0
2
1
1
2
1
1
2
4
0
0
2
1
1
0
2
1
1
1
1
0
1
1
1
2
1
2
1
1
0
1
2
0
1
1
2
0
3
1
1
2
1
1
2
2
2
1
0
3
1
0
1
1
0
1
1
1
1
1
0
2
2
1
1
0
1
1
0
1
1
0
2
1
1
1
1
0
1
1
0
2
0
1
0
2
2
0
2
0
2
2
2
1
0
1
2
1
1
1
1
1
0
1
1
1
1
1
1
2
2
1
0
1
1
1
2
0
1
0
1
1
1
1
0
2
0
1
0
1
1
1
1
1
0
1
0
1
1
1
1
1
0
0
1
2
2
1
1
1
2
1
2
1
2
0
1
1
1
4
1
1
1
0
0
1
0
1
1
1
0
1
0
1
0
0
1
1
1
0
0
1
2
0
2
1
0
1
0
1
0
0
2
1
2
2
1
2
1
1
1
1
1
1
1
1
1
1
1
0
0
1
0
1
0
0
1
2
1
1
1
1
2
1
1
2
1
1
1
0
1
1
0
2
2
1
0
1
1
2
1
1
1
1
1
2
0
3
1
0
1
1
1
2
0
1
2
1
0
2
1
1
2
2
2
1
2
1
1
2
1
2
2
1
1
1
2
2
1
0
2
2
0
1
0
1
1
2
1
1
0
0
0
2
1
1
1
2
2
2
1
2
2
1
1
1
1
2
1
1
2
0
0
0
0
1
0
1
1
2
1
1
1
1
1
1
0
1
0
1
3
1
1
1
1
1
0
1
1
0
1
1
2
0
2
2
0
1
1
0
0
0
2
1
1
1
2
1
2
2
1
0
0
0
2
2
1
1
1
0
0
2
1
1
1
1
0
1
1
2
1
0
0
1
2
0
1
2
2
0
0
2
2
0
0
2
1
1
2
2
1
2
1
0
0
1
1
1
1
2
1
4
0
1
0
1
0
1
0
1
1
2
2
1
1
2
0
2
1
0
1
1
1
7
1
2
1
2
2
0
1
1
1
1
1
1
0
1
2
0
2
0
0
1
1
2
1
2
1
1
1
0
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
0
1
0
1
0
1
1
1
1
2
2
0
1
2
1
1
0
0
0
0
0
1
0
1
1
0
2
2
1
1
2
1
2
1
2
0
1
1
2
2
1
2
2
0
1
1
0
0
0
0
1
2
1
2
1
0
0
1
0
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
0
1
1
0
2
1
1
1
1
0
0
1
0
1
1
2
1
2
0
0
0
0
0
0
1
0
1
1
1
2
1
1
0
0
2
1
1
1
1
0
0
1
1
1
0
1
1
1
2
2
2
1
1
1
1
0
2
0
1
1
1
1
0
0
1
2
0
2
0
0
2
1
1
1
0
1
1
1
2
0
1
1
0
2
2
0
1
0
2
2
0
1
1
1
1
1
1
1
1
1
2
1
0
2
1
1
2
2
1
2
1
2
0
1
1
2
1
1
2
0
1
1
1
2
0
1
0
0
2
1
1
4
0
1
1
0
1
0
1
1
1
0
0
1
0
2
1
1
0
1
0
0
2
1
1
3
1
1
1
2
0
1
1
1
1
2
1
0
1
3
1
1
2
1
0
1
2
1
1
2
1
2
0
1
2
0
1
0
2
1
1
2
1
2
2
1
0
2
1
2
2
0
0
2
2
1
0
1
1
2
1
1
1
2
1
1
2
0
1
0
1
0
1
1
1
2
1
1
0
1
1
0
2
2
1
0
1
1
0
0
0
2
1
1
0
1
0
2
1
0
1
2
0
0
1
0
0
0
1
2
1
1
1
3
2
1
2
1
2
1
1
0
2
1
2
1
1
2
2
0
0
1
1
2
1
1
2
1
1
2
2
2
1
3
0
1
2
0
1
1
1
1
0
1
1
1
1
1
0
0
1
2
1
2
2
1
0
1
1
2
2
1
1
1
0
1
1
2
0
1
1
1
1
2
2
2
1
0
0
2
1
2
2
1
2
2
0
1
1
1
1
1
1
1
0
1
2
1
2
0
1
2
1
1
0
1
2
1
0
0
2
0
1
2
1
2
1
2
1
1
1
1
2
2
1
0
1
2
1
2
1
1
1
0
2
1
1
0
1
1
1
1
0
0
1
1
1
1
1
0
1
1
1
0
1
2
0
1
0
1
1
1
1
1
1
0
3
0
1
0
1
0
2
1
1
2
0
1
1
1
1
1
0
1
0
2
1
0
1
0
0
1
1
2
1
1
1
1
1
0
2
2
1
1
0
2
1
1
1
2
1
1
2
1
2
1
2
1
1
1
2
1
0
0
1
1
2
1
2
2
0
1
1
0
2
1
0
0
0
2
1
1
0
0
0
0
1
2
1
2
0
2
1
1
1
0
1
2
0
0
0
2
1
1
2
1
2
1
1
2
0
0
1
2
1
0
1
1
2
0
1
1
1
2
1
1
1
0
0
1
1
0
0
0
1
1
1
1
0
0
1
1
1
1
2
1
1
2
2
2
1
1
0
2
0
1
0
1
2
1
1
2
1
0
0
0
3
1
2
0
1
1
1
2
2
2
0
3
1
0
0
1
1
1
1
1
0
0
0
1
0
2
1
1
0
2
0
0
0
2
1
1
0
2
0
1
0
1
0
1
2
1
2
1
0
1
2
1
1
1
0
1
1
0
2
2
0
0
1
2
2
0
2
0
1
2
1
1
2
1
0
1
1
2
1
0
2
0
1
1
0
0
1
1
2
0
1
1
1
1
1
1
0
0
3
0
0
1
2
2
0
0
1
1
0
0
0
0
1
1
2
0
1
1
1
2
2
1
1
0
1
1
1
0
0
1
2
0
1
1
1
1
1
2
1
0
1
1
1
2
0
1
2
2
1
0
2
1
1
0
0
1
1
0
1
1
0
1
2
1
0
0
3
1
1
0
0
1
3
2
1
0
0
1
1
0
1
0
1
1
1
1
0
2
0
0
1
2
1
2
1
1
0
2
1
3
1
1
1
1
0
2
1
1
1
3
0
1
1
1
1
1
0
1
1
1
2
1
1
1
4
0
1
0
2
0
0
1
0
2
1
2
0
1
1
2
0
0
1
0
1
0
0
2
1
3
2
2
1
1
0
1
2
0
0
1
2
0
0
2
1
2
1
1
0
1
1
2
0
0
1
0
1
0
1
0
0
1
1
2
2
1
1
1
0
1
0
1
0
1
1
2
1
1
1
1
1
1
0
1
1
1
2
1
1
1
2
1
1
0
1
1
2
1
1
1
2
1
2
1
1
0
1
0
0
1
1
2
1
1
2
2
1
2
2
0
2
1
0
0
1
1
1
3
1
1
2
1
1
1
0
1
0
2
0
1
0
1
0
2
2
1
1
2
0
1
2
1
1
2
0
1
1
1
1
1
1
2
0
2
0
0
0
1
1
1
1
0
0
0
0
0
1
1
2
1
2
2
2
1
1
0
0
0
1
0
0
2
2
1
2
0
1
2
2
1
0
2
1
1
0
0
2
2
1
0
1
2
2
1
7
1
3
1
3
2
1
0
1
1
0
0
1
2
1
2
2
1
1
0
1
1
1
1
2
1
1
1
2
1
1
2
1
0
0
0
1
1
1
0
1
1
1
1
0
0
1
1
1
0
0
2
1
1
1
1
1
1
1
0
1
2
1
1
1
2
1
1
1
1
0
2
1
1
1
1
0
1
0
2
1
0
0
1
0
1
1
0
0
1
0
0
1
1
1
1
1
1
2
1
1
0
2
1
1
0
0
1
1
1
1
0
1
2
1
1
1
1
2
2
1
1
1
1
0
1
1
1
0
1
2
2
1
2
1
2
2
1
1
2
1
2
1
2
0
0
0
1
1
1
1
1
1
0
2
0
2
3
0
1
2
1
1
1
2
2
0
0
1
1
1
2
1
0
2
2
0
0
2
1
2
1
1
0
1
1
0
0
1
0
1
0
1
5
1
0
1
2
2
1
0
0
2
1
1
0
0
2
0
1
2
1
1
1
0
2
1
1
1
2
2
0
1
1
2
1
1
2
2
0
0
0
1
2
1
1
2
1
2
2
0
1
1
1
1
1
0
2
1
1
0
2
2
1
1
0
1
0
0
1
1
2
2
1
1
1
0
1
1
2
2
1
1
2
2
1
0
2
2
0
0
2
1
2
0
1
0
2
1
1
2
2
1
1
0
1
0
0
0
2
1
2
1
0
0
1
1
0
1
1
1
1
1
1
1
1
1
1
0
0
1
1
1
2
1
0
2
0
2
1
2
1
1
2
1
1
1
2
0
2
1
0
2
1
1
1
1
0
1
1
1
2
1
0
0
0
1
1
1
1
1
2
1
2
1
1
0
1
1
1
0
1
1
1
1
0
1
1
0
1
1
1
0
1
2
0
1
2
1
1
1
0
1
0
2
1
0
0
0
1
1
0
1
1
0
1
0
1
1
0
1
1
0
2
2
2
2
1
1
1
0
1
1
1
2
0
1
1
2
0
2
2
1
2
2
0
1
0
1
1
1
1
0
1
1
0
2
0
1
0
0
0
1
1
0
1
1
1
1
0
1
0
1
1
0
1
2
1
0
0
0
0
1
1
2
2
2
1
1
0
2
1
0
0
1
1
2
1
1
0
1
0
1
1
2
0
2
0
1
1
1
1
2
1
1
0
1
0
1
1
1
1
1
0
2
0
0
2
1
2
0
1
0
0
2
1
0
0
2
0
0
0
1
1
1
1
1
1
1
1
1
1
1
2
2
0
0
2
1
1
1
1
2
0
1
1
0
2
0
1
2
0
0
1
2
1
1
2
2
1
1
2
1
1
1
3
1
0
1
1
0
2
1
2
0
3
1
1
2
1
2
1
1
1
7
1
0
4
0
2
0
1
1
1
1
1
1
1
0
1
1
0
2
1
2
0
1
1
1
0
1
1
1
1
1
0
1
1
0
1
1
3
1
2
1
2
2
1
1
0
1
0
1
2
1
1
2
0
1
0
2
1
1
0
1
2
0
1
1
1
0
1
2
1
1
2
2
1
2
1
0
1
1
2
3
1
1
1
0
1
1
1
0
1
2
2
0
1
0
1
1
2
1
0
1
2
2
0
2
0
2
1
1
0
1
0
1
1
1
1
1
2
1
2
2
1
1
1
1
1
2
0
2
0
1
1
2
2
2
1
1
2
1
1
2
2
1
1
0
0
0
1
3
1
1
1
2
1
0
0
1
1
1
1
0
2
2
1
1
1
2
0
1
0
1
1
1
1
1
0
1
0
0
1
1
2
2
0
0
1
1
1
1
0
1
1
2
0
1
0
0
0
2
0
1
1
2
1
2
0
2
0
2
2
2
0
2
1
0
1
0
3
1
1
2
1
1
1
1
1
0
1
2
0
1
1
3
1
1
0
2
2
1
0
1
1
1
2
3
2
1
2
0
1
0
0
0
1
1
0
1
1
1
1
0
1
1
1
0
0
1
1
2
0
0
1
1
1
1
2
1
1
1
1
0
3
2
1
0
2
2
1
1
0
1
3
0
0
1
1
0
1
0
1
0
0
2
1
1
1
0
1
2
0
1
1
0
2
2
1
1
1
1
1
2
1
2
1
0
1
1
1
2
2
1
1
1
2
1
1
1
1
0
1
1
1
0
1
1
0
2
1
1
0
0
1
1
1
1
2
0
1
1
0
1
1
2
1
1
0
2
1
1
1
0
1
0
1
0
1
1
1
0
1
1
0
1
0
1
1
0
3
1
1
1
1
0
1
2
1
1
1
0
0
1
0
1
1
1
0
1
2
1
1
0
2
1
0
1
0
0
2
2
1
2
1
1
1
0
1
1
2
1
1
0
3
2
0
1
2
2
2
2
0
1
1
0
1
1
1
1
1
1
2
1
1
1
1
1
1
1
0
1
1
0
1
0
0
2
1
0
0
2
1
2
2
1
1
1
2
1
2
1
2
0
3
1
2
2
2
0
1
0
0
1
0
0
1
2
1
2
1
1
2
1
1
1
1
1
1
1
2
1
1
3
0
0
1
2
1
1
1
1
1
1
0
1
1
1
0
1
2
0
1
1
0
1
1
1
1
1
2
2
1
0
0
1
1
2
1
0
1
1
2
1
0
1
2
1
1
1
0
1
0
1
0
2
0
1
1
1
1
1
1
2
0
1
0
0
2
1
1
1
1
1
0
1
1
1
1
0
1
2
2
1
1
2
0
1
2
1
1
2
2
0
1
1
2
1
0
1
0
0
1
1
1
1
2
0
2
0
2
1
0
0
1
1
0
1
2
1
2
0
1
1
1
0
3
1
1
1
1
1
1
2
1
1
0
1
1
1
3
0
1
1
2
2
1
2
0
1
0
2
1
1
1
0
1
0
1
0
1
1
1
1
0
0
2
1
2
2
1
2
2
0
1
1
2
1
1
0
0
0
2
1
1
0
0
2
1
1
0
2
1
1
0
0
2
1
0
1
1
0
2
1
2
1
2
0
1
1
1
1
2
1
1
1
1
1
2
1
2
1
1
1
0
0
1
1
0
0
2
1
1
1
2
1
0
0
1
0
0
1
0
0
1
2
1
1
1
1
1
1
1
1
1
2
2
1
0
1
1
3
0
1
0
1
1
0
2
2
1
1
1
2
1
2
2
2
1
1
0
1
1
2
2
0
1
0
1
0
1
0
0
1
0
1
2
1
0
1
1
2
0
0
1
0
1
1
0
1
0
1
2
1
1
1
2
0
1
0
2
1
1
1
0
2
2
1
2
1
1
0
1
1
0
1
1
2
1
1
1
2
3
2
0
1
2
2
0
2
0
2
1
1
0
1
1
1
1
1
1
0
1
1
0
2
2
2
0
2
0
0
0
2
1
1
1
0
1
2
1
1
2
1
0
1
2
0
1
1
2
1
1
0
2
2
0
0
1
1
2
2
1
1
1
1
0
1
1
1
2
0
0
2
1
2
1
2
1
1
1
1
1
1
2
0
1
2
0
2
2
1
1
1
5
0
1
1
1
1
1
1
1
0
0
1
2
1
1
0
2
1
2
1
1
1
1
1
2
2
0
1
1
1
1
2
1
0
0
2
1
2
2
1
1
1
1
0
1
0
0
0
1
1
1
2
1
1
1
2
1
1
2
1
0
0
1
0
1
1
1
2
1
0
1
2
0
2
2
1
1
1
2
0
0
0
1
1
0
0
2
1
2
1
2
0
1
2
1
1
0
0
2
0
1
1
1
0
0
0
1
2
2
1
0
1
2
1
0
2
0
1
1
2
1
1
1
1
0
3
1
1
1
1
2
2
1
1
1
2
1
1
1
13
1
1
2
1
1
1
2
1
2
1
0
1
0
1
1
2
0
2
1
2
0
1
2
1
1
2
1
1
1
0
1
1
2
1
1
2
0
1
1
2
1
1
0
2
0
3
1
0
0
1
1
2
1
1
1
1
1
1
1
1
1
2
2
0
1
0
0
2
1
2
1
1
2
1
0
0
1
4
1
1
2
1
1
1
1
0
1
0
1
1
0
1
0
1
2
0
2
1
0
0
2
1
2
0
0
1
1
0
2
0
0
2
2
1
1
0
1
2
2
2
2
1
1
0
0
2
0
1
2
1
1
1
1
2
1
1
1
0
0
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
0
1
2
0
1
1
1
1
0
1
2
0
1
0
1
1
1
1
1
1
2
0
2
1
1
1
0
2
0
0
0
2
1
1
1
0
1
0
0
0
1
1
2
1
0
1
1
1
0
0
2
0
1
1
1
1
1
2
1
0
2
2
2
1
0
2
2
1
1
1
0
0
1
1
1
1
1
0
1
2
2
1
1
1
2
0
0
1
2
2
1
1
1
2
2
1
0
0
1
1
0
1
1
0
2
1
2
2
1
1
0
1
2
1
1
1
1
1
1
0
1
1
1
2
1
4
1
2
0
0
0
1
1
1
1
1
1
1
1
0
2
2
1
0
1
1
1
1
2
0
1
1
2
0
1
2
0
2
1
2
1
0
1
0
0
0
1
1
0
1
1
1
1
1
1
2
2
1
1
2
2
1
0
2
1
1
1
1
0
1
1
1
0
1
1
2
1
1
2
2
1
1
0
0
0
2
2
0
1
0
1
1
2
1
2
1
1
0
1
1
1
0
1
3
2
1
0
0
1
2
2
0
1
0
1
1
1
1
1
1
1
1
1
2
2
0
0
0
0
1
3
0
0
1
1
0
4
1
1
1
1
1
0
1
0
2
0
1
1
0
2
1
0
1
1
1
1
1
1
2
0
1
2
0
2
1
1
3
1
0
2
1
1
1
2
1
1
0
1
1
2
0
1
1
2
1
0
1
0
1
2
0
1
2
0
0
1
1
1
2
1
1
0
1
1
2
0
0
2
1
1
2
1
0
1
1
0
2
1
2
2
0
1
1
1
1
1
1
3
1
2
0
2
0
0
1
0
2
1
1
1
1
1
1
2
1
1
1
1
2
1
2
1
1
2
1
1
1
1
1
1
3
1
2
1
1
1
0
2
2
1
2
1
2
1
2
1
1
1
1
1
1
0
0
0
1
2
0
1
0
0
0
1
1
0
0
2
1
0
2
0
0
2
0
1
1
2
1
0
1
1
1
2
2
1
1
0
1
0
1
0
2
0
1
2
2
0
1
1
0
0
0
1
1
1
2
0
0
0
1
0
2
2
2
0
2
1
1
1
1
2
0
0
1
2
2
0
0
1
1
1
1
1
1
2
1
0
1
0
1
1
0
1
1
0
1
0
1
1
0
1
0
1
0
0
2
1
2
0
0
0
1
1
2
1
0
1
1
1
1
2
0
1
1
1
1
2
1
0
2
0
2
1
0
2
1
1
0
1
1
1
1
2
1
1
0
1
0
1
0
0
0
1
1
1
2
1
1
1
0
2
2
1
4
1
0
1
1
1
1
0
1
2
0
1
1
1
0
1
2
1
1
1
0
1
0
0
1
0
1
0
2
0
1
1
1
0
0
2
2
1
1
1
1
1
1
0
2
1
1
0
0
1
0
2
2
1
0
1
0
1
0
0
2
1
1
1
2
5
1
0
1
1
0
0
0
1
0
1
1
1
1
1
0
1
1
2
2
0
1
1
0
1
1
1
0
0
1
1
1
0
2
1
1
1
1
1
1
0
1
1
1
2
0
0
1
2
1
2
3
0
0
2
1
1
0
0
0
2
2
2
1
0
0
1
2
2
1
2
0
2
2
0
0
1
0
2
0
2
0
0
2
1
1
1
1
0
1
2
1
1
0
2
1
1
0
0
0
1
1
0
1
1
0
1
0
1
1
0
1
1
1
2
2
0
1
2
1
1
0
2
1
0
1
1
1
1
1
1
1
0
0
2
1
1
1
1
0
1
2
1
1
1
1
0
1
0
0
2
0
0
1
0
2
0
1
1
0
2
1
1
1
0
2
2
1
1
1
0
0
0
1
1
0
1
2
0
3
2
0
2
2
1
1
2
1
0
4
1
0
1
1
0
1
1
0
2
1
1
2
1
1
1
1
2
1
0
2
2
1
1
0
1
0
1
1
1
2
1
1
1
2
0
1
1
1
1
0
2
0
0
0
1
0
1
1
1
1
2
0
2
2
1
1
1
1
1
2
0
1
1
1
1
2
1
2
1
0
1
1
2
1
1
1
0
1
1
0
1
2
1
1
1
1
1
2
1
2
1
0
2
1
0
2
1
1
1
2
2
0
1
1
2
1
0
1
2
1
2
2
1
1
2
2
1
1
0
1
1
1
0
2
2
1
0
1
2
1
0
1
0
1
2
1
0
1
2
1
1
1
1
1
0
1
1
0
0
1
1
0
1
0
1
0
0
0
1
1
1
0
1
0
1
1
1
2
1
2
0
1
2
0
3
1
0
1
3
1
1
1
1
1
0
0
1
0
1
1
0
0
0
2
0
1
1
1
1
1
1
0
0
1
1
1
1
2
0
1
1
1
0
1
1
0
1
1
1
1
1
2
0
2
1
0
2
0
1
1
1
0
2
1
0
2
0
0
1
0
0
0
1
2
1
2
2
2
2
1
1
1
1
1
1
1
1
1
1
0
2
1
1
1
1
1
1
1
1
1
0
0
1
1
1
0
2
0
0
1
0
1
1
1
2
1
2
0
1
1
0
0
1
2
0
2
1
1
2
1
2
3
0
1
2
1
1
2
0
0
1
1
0
1
0
1
0
1
1
1
1
1
1
2
1
1
1
1
0
1
1
2
0
1
1
1
1
0
0
5
1
1
0
1
0
0
0
2
1
1
1
2
1
1
1
1
1
1
2
1
1
0
1
1
1
2
2
1
1
1
1
0
1
2
0
1
1
0
2
2
0
2
0
1
2
1
0
0
2
1
0
2
2
0
0
1
1
1
1
2
2
0
0
1
1
2
2
1
2
2
0
1
0
2
1
2
2
1
2
0
1
0
1
2
1
0
1
0
2
1
1
2
0
1
0
1
2
1
0
0
0
0
2
2
1
0
0
0
2
1
1
2
1
0
1
2
1
1
1
1
1
1
2
1
2
1
2
1
1
0
1
1
1
2
0
2
1
0
0
0
1
1
2
0
2
1
1
0
1
1
1
2
1
2
2
1
0
0
1
3
1
1
2
1
0
0
1
1
1
0
1
0
0
1
1
1
0
0
0
1
1
2
0
2
1
2
1
1
2
1
2
1
2
2
1
1
2
2
0
1
1
1
2
0
0
1
0
1
0
1
2
2
1
2
2
1
1
1
1
2
0
1
1
1
2
1
1
0
1
1
0
1
1
2
1
0
0
0
2
0
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
0
1
0
2
0
2
1
2
0
1
1
2
1
1
0
1
2
2
1
1
2
2
2
2
1
2
1
1
1
2
2
1
2
0
0
1
1
2
2
1
1
0
0
1
1
2
0
2
2
1
2
0
1
1
1
1
2
1
1
3
2
1
1
2
1
1
1
1
1
1
0
1
1
2
2
0
1
0
3
1
1
1
1
2
0
2
2
0
2
0
2
1
2
1
0
1
1
2
0
1
0
1
1
2
1
2
1
1
0
1
1
0
0
0
2
1
1
0
0
2
1
0
2
1
2
1
1
2
0
1
2
1
1
0
1
2
1
1
0
0
1
1
2
1
1
0
0
0
1
0
1
2
0
1
1
1
0
2
2
1
1
1
1
1
1
1
0
1
1
2
0
1
0
1
1
0
2
1
1
1
3
0
1
2
1
1
2
0
1
1
0
2
1
2
2
0
2
1
2
2
2
1
2
1
1
1
1
0
1
1
0
2
3
1
0
1
1
1
2
1
1
1
1
0
0
2
3
1
2
1
2
1
0
2
0
1
2
0
0
1
1
2
1
2
1
0
2
2
1
0
0
1
2
1
1
0
2
2
1
1
0
2
0
1
1
0
1
1
0
2
1
1
1
1
0
0
0
0
1
1
1
1
2
1
0
1
0
1
1
1
0
2
1
1
2
0
1
0
0
1
2
1
1
1
1
2
1
1
2
0
1
1
1
1
1
1
1
1
2
1
2
0
0
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
2
0
1
0
1
1
0
1
0
0
1
2
0
2
1
2
2
0
2
1
1
1
0
1
0
1
1
0
0
1
1
1
0
1
0
1
1
2
2
0
0
2
2
1
1
0
1
1
1
0
1
1
0
1
1
1
1
1
1
1
0
1
0
1
1
0
1
1
1
2
2
2
2
1
0
1
0
2
1
1
1
1
0
3
0
0
2
0
2
1
2
1
0
0
0
1
0
1
1
0
1
2
0
2
1
1
2
0
0
0
0
2
0
0
0
0
1
2
2
0
2
2
2
1
1
0
1
1
1
0
1
3
1
1
0
1
2
1
1
1
1
1
2
0
1
1
1
0
1
0
1
0
0
2
1
1
1
0
1
2
1
1
0
0
1
2
2
0
1
1
2
2
2
1
0
0
1
0
0
1
0
1
0
1
1
2
1
1
1
2
1
0
1
1
2
1
1
1
2
0
0
1
0
0
2
1
0
1
2
2
1
1
1
0
1
0
1
1
1
1
1
2
4
2
2
1
1
0
1
1
1
1
0
1
0
1
2
2
1
1
1
1
0
1
0
1
1
1
1
1
0
0
1
1
1
1
1
2
1
0
1
1
2
2
2
0
0
3
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
0
1
1
0
1
0
2
2
1
2
2
2
1
0
1
0
2
1
0
1
1
1
2
2
1
1
1
1
2
1
2
0
1
1
0
2
1
1
2
1
0
1
2
9
0
0
0
2
1
0
0
1
1
2
2
1
0
1
0
1
0
0
1
2
0
0
0
0
0
1
1
1
0
1
0
1
0
1
0
4
0
1
2
1
1
1
2
0
1
0
0
1
1
1
2
1
1
1
1
1
2
1
1
1
2
0
2
1
0
1
0
1
1
2
1
1
0
0
1
1
2
1
2
0
1
2
0
2
3
0
1
0
0
1
2
1
1
2
3
1
0
0
1
1
1
1
2
2
0
1
2
1
1
1
1
1
2
1
2
1
1
0
2
1
1
1
2
2
1
0
1
2
1
1
1
0
1
2
0
1
0
0
2
2
0
1
0
1
0
1
1
0
2
1
0
2
0
1
1
0
1
1
0
1
1
2
1
1
1
1
0
1
2
1
1
2
0
1
0
1
1
1
1
0
1
2
2
1
1
0
1
1
2
0
1
1
1
0
0
2
0
2
0
1
1
2
2
1
1
2
0
2
1
1
0
0
1
1
0
1
2
1
2
1
2
1
0
0
1
1
1
0
1
2
2
2
1
2
0
1
0
1
1
1
2
2
0
1
1
2
1
1
1
1
3
0
1
2
1
0
0
2
0
1
1
0
1
0
0
1
1
1
1
2
1
1
0
0
0
1
0
2
0
1
1
1
1
1
2
2
2
2
2
1
1
2
1
1
0
1
1
1
0
1
1
1
2
0
2
0
2
0
1
1
1
1
2
1
2
1
2
1
2
1
2
1
2
2
1
0
1
1
0
0
1
0
1
1
2
0
1
1
0
2
0
1
0
1
1
2
2
0
1
0
0
0
1
1
1
1
1
2
1
0
0
1
1
1
0
1
1
1
0
0
2
0
2
1
2
1
1
2
1
1
0
1
1
0
1
0
1
1
0
2
1
1
1
1
0
2
1
2
1
1
1
0
2
2
1
1
0
2
0
0
1
2
2
1
2
1
1
1
1
0
1
0
2
0
2
0
0
1
2
0
1
2
3
2
1
0
1
1
2
2
1
2
0
3
2
1
0
2
1
2
0
0
1
3
0
1
1
1
0
0
1
0
1
1
0
1
1
1
1
3
0
0
0
0
0
1
2
1
0
1
1
0
1
2
1
1
1
1
1
0
0
2
1
0
1
2
1
1
1
2
1
1
1
1
0
2
0
1
0
1
1
0
0
1
1
2
1
2
1
0
1
0
0
2
2
1
1
2
1
1
0
1
1
1
0
1
1
0
1
1
1
1
2
0
1
2
2
1
0
1
1
0
1
1
1
2
1
0
0
2
1
2
1
0
1
2
1
1
1
2
1
2
1
1
0
1
1
2
2
0
2
1
2
1
1
0
1
1
1
2
1
1
2
3
1
0
2
2
0
0
0
1
0
1
1
1
1
1
1
2
1
1
1
1
1
3
0
1
0
1
0
1
1
1
1
2
0
0
2
1
1
0
1
2
1
0
1
0
1
1
1
1
0
2
1
1
2
2
1
1
0
2
1
0
1
1
1
1
1
2
2
2
0
1
1
0
0
0
1
1
1
0
2
0
1
1
1
1
2
0
1
1
1
0
1
2
0
1
2
1
1
1
0
1
1
1
2
1
0
0
0
1
2
2
2
2
1
0
1
0
3
2
2
1
1
1
2
1
2
2
1
2
1
2
1
2
1
1
0
2
3
2
2
1
2
1
2
2
0
1
1
0
1
1
0
1
1
0
0
2
1
1
1
0
2
1
1
2
2
1
2
1
1
1
0
2
1
1
1
1
2
0
2
0
2
0
0
2
1
0
2
2
0
1
0
4
1
0
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
0
1
1
2
0
2
0
1
1
1
1
1
1
1
0
1
1
1
0
0
2
0
1
1
1
2
1
2
0
1
1
0
2
1
1
2
2
1
1
2
0
1
0
2
1
1
0
1
3
1
1
1
2
1
1
0
0
0
1
0
2
1
0
0
1
0
2
1
1
1
0
2
1
1
2
2
1
2
2
0
1
0
0
0
2
1
2
0
1
1
1
1
1
0
1
1
0
2
1
1
1
0
1
1
1
0
1
1
2
1
1
1
0
1
1
0
1
1
1
2
1
2
1
1
0
1
1
2
2
1
1
0
1
1
2
2
1
1
1
2
0
1
1
1
2
1
1
1
1
2
2
1
1
1
0
1
1
2
2
2
1
3
1
1
1
1
1
2
1
2
0
0
1
1
2
1
1
2
1
1
1
2
0
1
1
1
0
2
2
1
1
2
3
1
1
0
0
0
1
1
0
1
1
1
2
0
2
0
1
1
1
1
0
1
2
0
1
3
2
1
1
2
1
1
2
1
0
1
1
1
0
0
1
0
1
1
1
1
1
1
2
0
0
0
0
0
2
1
1
1
0
1
2
0
1
1
1
1
1
2
1
2
0
1
2
1
0
1
0
1
0
1
0
2
1
1
1
1
0
2
2
1
2
0
1
1
1
0
0
1
1
1
1
1
2
1
2
1
1
2
1
0
1
1
1
1
1
0
0
2
2
1
0
1
1
1
1
1
2
0
1
2
0
1
1
0
1
1
2
2
1
2
2
1
2
1
2
1
0
1
1
2
1
1
0
1
0
1
2
0
2
0
0
1
0
0
2
1
0
0
0
1
1
2
2
1
2
1
1
1
2
1
0
1
0
1
0
1
0
1
1
0
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
0
1
1
1
0
1
2
1
2
0
0
1
1
2
1
2
2
2
1
1
2
0
0
1
1
2
1
0
1
0
1
0
2
1
0
1
1
1
1
1
0
2
1
1
0
1
1
1
2
0
1
0
2
0
1
1
0
0
1
1
1
2
2
1
1
1
1
0
0
1
1
1
0
0
1
1
0
1
1
0
0
0
2
0
2
0
2
0
0
1
1
1
1
0
0
0
0
2
1
1
0
1
2
1
2
1
1
2
1
2
0
2
1
0
0
1
0
1
0
1
1
1
2
0
2
2
0
1
1
0
1
3
1
2
2
1
1
2
1
1
0
1
3
1
0
1
2
1
2
3
1
2
1
1
0
1
2
1
1
0
0
1
1
0
1
0
1
1
0
2
1
1
1
0
1
1
2
1
0
1
2
1
2
1
0
2
1
1
2
0
1
2
2
1
2
2
2
1
0
1
2
2
0
0
2
1
0
1
1
0
0
1
1
1
2
1
2
1
1
0
0
2
1
0
0
1
2
3
2
0
0
2
1
0
0
2
2
1
1
0
2
1
1
2
2
2
3
1
2
1
2
0
1
0
0
0
1
1
1
1
1
0
0
0
0
1
1
2
0
1
1
1
2
1
1
1
0
0
1
2
1
1
1
0
0
1
1
1
1
0
1
0
1
0
1
1
1
2
2
1
1
0
2
1
1
0
0
2
0
0
1
0
1
1
1
1
2
0
1
1
1
1
0
2
0
1
1
1
2
2
0
0
2
0
0
2
1
1
1
1
0
0
0
0
2
2
1
3
1
0
0
1
2
2
2
2
1
1
1
2
0
0
1
1
1
1
0
1
0
0
1
2
2
1
0
1
1
1
1
1
1
0
1
0
1
1
1
0
2
0
1
1
3
0
1
1
2
0
1
1
2
1
1
1
1
1
0
0
2
1
0
1
0
0
1
1
1
2
1
1
1
0
0
0
1
2
1
1
0
1
1
1
1
0
1
0
3
2
0
1
1
1
1
0
1
2
2
1
1
2
9
1
1
1
1
0
0
0
1
1
1
1
2
1
2
0
0
2
1
0
1
1
1
2
1
1
1
1
1
2
2
0
0
2
2
1
1
1
1
0
1
1
1
1
2
1
0
0
2
1
2
1
1
1
0
1
1
2
1
2
0
1
1
0
1
1
0
0
3
1
1
1
2
2
0
1
1
2
2
1
1
2
1
2
0
2
2
2
1
0
1
1
0
1
1
1
1
1
1
0
1
1
1
1
1
1
3
1
1
2
0
1
1
1
1
0
1
1
1
2
1
0
1
2
0
0
2
1
0
0
1
1
1
1
0
2
0
2
0
1
1
1
1
1
0
2
1
2
1
0
0
1
1
1
1
1
2
0
1
2
0
3
1
0
2
1
1
1
0
1
1
0
0
1
1
1
1
1
0
1
1
1
1
0
1
2
1
1
2
1
2
1
1
1
1
2
1
2
1
0
1
1
2
2
2
1
1
0
1
2
0
1
2
1
1
1
0
0
1
1
1
0
1
1
0
2
1
1
1
1
1
1
1
0
0
2
1
2
1
0
2
2
1
2
1
1
1
0
1
2
2
1
2
1
2
1
1
2
1
1
1
1
0
0
2
1
1
1
3
0
1
0
1
1
1
0
1
2
1
1
1
0
1
1
1
1
2
1
2
2
0
2
1
1
0
2
1
2
0
1
1
3
1
0
2
1
0
2
1
3
1
1
0
1
1
1
1
1
2
1
1
0
1
2
2
1
1
2
1
2
1
0
0
1
2
1
2
2
0
0
0
1
0
1
1
2
1
1
0
1
1
0
0
1
2
2
1
1
1
1
1
1
1
0
2
1
1
0
1
1
2
1
1
1
1
1
1
0
0
1
1
1
0
1
0
2
2
2
0
2
1
1
1
1
1
1
1
1
0
2
1
2
1
0
2
1
1
1
2
2
4
1
2
0
0
1
2
1
2
1
2
3
2
1
1
0
1
1
1
1
2
0
2
1
1
0
2
2
2
1
1
1
1
1
2
1
2
0
1
1
2
1
0
1
2
0
1
1
0
1
1
1
1
1
1
0
1
1
1
1
2
1
1
2
1
1
1
1
1
2
0
2
1
0
1
0
2
1
0
1
0
2
1
1
1
1
2
1
2
1
1
1
1
1
1
0
2
1
1
0
0
0
1
2
0
1
1
1
1
1
1
0
1
2
1
1
0
0
0
2
1
0
1
1
2
1
2
0
1
2
1
1
0
1
1
0
1
2
1
2
2
1
0
2
0
1
2
1
0
2
0
1
0
1
0
1
0
2
1
2
0
2
1
2
1
1
1
0
2
1
1
1
1
2
1
1
1
1
1
1
1
0
2
2
1
0
1
4
2
0
1
1
0
0
0
2
1
1
0
0
0
2
1
1
1
1
2
1
0
2
0
1
1
1
1
2
2
1
0
0
0
0
2
0
1
1
1
1
1
1
1
2
1
1
2
2
0
0
0
0
1
1
1
2
1
2
1
2
0
2
3
0
0
1
1
3
2
1
1
0
1
0
0
2
2
2
2
0
1
1
6
1
2
1
1
2
1
1
1
1
0
3
0
1
2
1
1
2
0
0
0
2
1
2
0
1
2
1
1
1
0
2
1
2
1
1
1
1
1
1
0
2
1
0
2
2
0
2
1
2
0
1
0
1
0
0
0
2
1
1
0
1
1
0
0
1
1
2
1
0
1
0
1
1
1
0
1
2
3
1
1
1
1
1
1
0
1
0
2
1
1
2
1
1
1
0
1
2
2
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
2
1
0
2
2
1
1
1
1
1
1
2
1
1
1
1
0
1
1
1
1
0
2
1
1
2
1
1
1
0
1
1
1
3
1
0
0
1
2
1
0
1
1
1
0
0
0
1
1
1
2
2
0
0
1
2
1
2
2
0
1
1
0
2
2
1
1
1
2
2
1
2
2
1
1
1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
2
0
0
2
1
1
2
1
2
1
2
0
1
1
1
0
1
1
0
2
2
1
2
1
1
0
1
1
1
2
1
1
1
1
0
0
1
1
2
3
0
1
0
0
0
2
2
2
0
1
0
1
2
1
1
0
1
1
2
1
0
1
1
2
1
0
1
1
1
2
0
0
0
2
0
0
1
0
1
2
2
1
1
1
1
1
2
1
1
0
0
2
0
1
0
0
0
1
1
0
0
1
0
2
2
1
1
2
1
1
2
1
1
0
0
1
0
1
1
1
1
1
0
2
2
0
2
0
0
3
0
0
1
2
1
1
1
1
2
0
0
0
1
2
0
1
2
1
2
1
1
0
2
2
0
1
1
1
1
0
1
1
1
2
1
2
1
0
2
1
2
0
0
0
2
1
0
1
0
2
1
2
0
0
1
0
2
2
2
0
1
0
0
1
1
1
0
0
1
1
1
0
1
1
1
1
0
0
2
1
0
2
0
0
2
1
0
2
2
1
1
0
1
1
1
0
1
1
1
2
3
2
2
1
1
1
1
2
2
2
1
2
2
1
1
0
0
1
1
0
3
0
1
1
1
1
0
0
0
1
1
2
1
1
0
2
0
0
1
0
0
1
1
0
1
1
2
0
1
0
0
1
0
0
2
0
1
1
1
2
1
1
1
1
2
1
1
2
1
1
0
1
1
0
0
1
1
2
1
1
1
0
0
2
2
1
1
1
1
5
0
0
1
0
0
1
1
1
0
1
1
1
2
1
2
2
1
0
1
1
2
1
2
0
2
1
1
1
0
2
0
0
1
0
1
1
0
0
1
1
2
1
1
0
3
1
2
2
2
1
1
1
1
0
0
0
1
1
0
2
0
1
0
0
1
2
3
0
1
2
1
0
1
1
1
2
1
1
0
1
0
1
0
1
2
2
1
1
1
1
2
1
1
0
0
0
0
1
2
1
1
0
2
0
0
1
1
1
1
0
2
1
1
1
1
1
2
0
1
1
0
2
2
1
0
2
1
1
1
1
1
1
1
1
2
2
0
1
1
1
1
2
1
2
1
1
1
1
0
1
1
3
0
1
0
1
1
0
0
0
0
2
2
1
1
1
1
0
1
1
1
1
1
1
1
2
2
1
2
1
1
0
1
0
1
2
0
1
1
1
1
1
1
0
0
2
1
1
2
2
1
1
1
0
1
1
1
1
2
0
1
1
2
0
1
1
1
1
1
2
1
0
0
2
1
1
0
1
1
2
0
0
0
1
1
1
1
0
1
0
0
1
2
0
0
0
2
1
1
1
1
2
0
1
1
0
0
1
1
0
0
0
1
1
1
1
0
1
0
2
1
1
2
1
1
2
1
2
3
0
0
0
0
2
0
1
1
0
2
0
1
0
0
0
1
1
2
2
2
2
0
0
2
1
1
1
1
1
2
0
1
1
2
2
1
1
1
1
0
1
0
1
1
0
1
2
2
0
2
1
0
1
1
1
1
1
1
1
1
0
2
1
1
1
1
1
1
1
1
0
0
2
2
1
1
1
0
1
0
1
1
2
1
1
1
0
1
0
1
1
1
1
1
2
1
1
1
0
0
0
2
1
1
2
0
0
2
2
0
2
0
2
0
2
1
1
1
1
0
1
0
2
1
0
1
1
1
1
1
0
0
1
1
0
1
0
3
0
1
0
1
2
0
2
1
1
1
0
0
0
2
2
1
1
1
1
1
1
1
0
2
1
1
3
1
0
1
1
1
1
1
0
1
1
2
1
3
0
2
1
1
1
2
1
1
1
0
2
1
1
1
1
1
0
2
0
2
1
0
1
1
0
1
0
1
1
1
1
1
2
1
0
1
1
2
1
1
2
0
1
2
1
2
0
2
1
0
0
0
2
0
0
0
1
0
1
0
2
1
1
2
1
0
2
1
0
1
1
2
2
2
0
1
1
2
1
0
1
1
2
1
1
1
1
1
3
1
1
2
1
1
0
1
0
0
3
0
1
0
2
1
1
1
0
1
1
2
1
1
0
0
2
1
2
1
2
2
1
1
1
0
2
2
1
1
1
1
2
1
0
1
1
0
2
0
1
1
1
1
1
2
1
0
1
1
1
2
1
1
0
1
1
3
2
1
2
2
0
1
1
2
1
1
2
0
1
0
0
1
2
1
1
1
1
2
0
1
0
0
1
1
2
2
2
2
2
2
1
1
1
0
0
0
2
1
1
1
1
1
1
1
1
0
1
2
1
0
0
1
0
2
1
1
0
1
1
1
1
1
0
1
0
2
2
0
1
1
1
1
1
1
1
1
0
1
2
1
1
2
0
1
1
1
0
1
1
1
1
1
1
1
1
0
2
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
2
0
0
1
1
1
0
1
2
0
1
1
1
0
0
0
1
0
0
1
2
2
2
1
2
0
1
1
2
1
2
1
0
1
1
0
1
2
2
2
1
2
1
2
2
1
1
1
2
1
0
1
1
1
1
2
1
0
1
0
1
1
1
1
3
1
2
1
1
1
1
0
1
0
0
1
1
2
0
0
1
2
1
1
0
1
1
1
1
0
2
1
1
2
1
1
1
1
1
1
1
0
2
0
1
1
1
0
0
2
1
1
2
0
2
1
0
2
2
0
0
2
2
0
2
1
1
1
0
0
1
1
1
1
1
1
2
0
0
0
2
0
0
1
2
1
2
1
1
1
2
0
1
1
1
1
1
2
2
0
1
1
1
1
1
1
1
1
1
0
0
1
2
2
1
1
2
0
1
1
1
1
2
0
1
1
3
1
2
0
1
1
2
1
1
2
0
0
1
0
0
1
1
1
1
0
0
2
1
1
0
0
0
1
2
1
0
1
1
0
2
0
1
1
2
2
0
1
1
1
2
0
2
3
1
1
0
0
1
0
1
2
1
0
2
2
1
0
1
1
2
0
1
1
1
0
0
1
1
1
0
0
3
0
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
2
1
0
2
0
1
1
1
1
2
0
1
2
2
2
0
1
1
0
1
1
1
1
1
0
2
1
1
2
0
1
2
2
0
1
0
2
1
1
0
0
0
0
0
1
2
1
1
1
1
1
1
0
2
1
0
2
1
1
2
1
1
1
1
2
1
1
0
2
1
1
1
0
1
2
2
1
0
2
0
1
1
0
1
1
2
2
1
2
0
1
1
1
1
0
1
1
1
1
1
1
2
1
1
1
1
1
0
1
1
1
2
0
1
1
1
1
2
1
1
0
0
0
0
0
2
2
1
1
1
1
0
0
2
1
2
1
0
0
0
1
1
1
2
1
1
0
0
0
2
2
1
1
1
3
2
1
0
2
1
0
1
1
0
0
0
1
2
2
0
0
1
1
1
1
1
2
1
0
4
1
2
1
2
0
0
0
1
0
1
1
0
1
1
0
2
0
2
0
1
1
1
1
2
1
2
2
2
1
0
2
0
2
2
1
1
1
0
0
2
2
0
3
2
1
0
1
0
1
1
1
1
1
2
0
2
1
2
1
0
2
0
0
0
1
0
2
2
0
0
1
2
1
1
1
2
1
2
1
1
1
1
1
0
0
1
1
1
1
1
1
1
1
2
1
1
1
0
2
0
1
0
1
1
1
1
3
1
1
1
1
1
1
1
0
2
1
1
1
1
1
1
1
1
2
1
0
1
0
1
0
1
1
2
1
0
1
1
1
1
1
0
1
2
1
1
0
2
2
1
1
0
0
1
1
0
1
1
1
1
1
2
1
0
1
2
0
2
1
0
1
0
0
1
1
0
2
1
2
1
1
1
1
1
1
2
2
0
1
1
1
1
1
2
1
0
0
2
1
1
1
2
0
1
3
1
1
0
1
1
0
2
2
1
1
1
0
0
0
2
0
1
1
1
0
1
1
2
2
1
2
0
0
1
1
1
2
0
0
1
0
1
1
1
2
1
0
0
1
1
0
2
1
1
2
0
2
2
0
0
1
2
1
0
1
0
1
1
1
1
0
0
6
1
0
1
1
1
1
2
1
1
1
0
1
1
2
0
1
1
1
1
0
2
1
2
2
0
2
1
0
1
1
0
0
0
1
2
2
0
1
1
1
0
1
1
0
0
4
1
0
4
1
0
1
1
0
1
1
2
0
2
1
1
0
3
1
1
2
2
2
0
1
2
1
1
1
1
2
2
0
2
1
0
1
1
1
1
2
1
4
0
0
1
7
1
1
1
2
1
1
0
2
2
0
1
1
0
1
1
1
1
2
0
0
1
1
0
0
2
0
2
2
2
0
1
2
0
0
2
1
0
1
1
2
2
1
1
1
2
1
1
1
1
0
1
0
2
0
0
2
0
0
1
0
1
1
2
2
1
0
1
1
2
1
0
0
1
0
0
1
0
0
1
1
2
2
2
0
1
0
0
1
1
4
1
1
2
2
0
0
2
0
1
0
2
1
3
0
2
2
2
2
0
0
0
1
1
1
1
1
1
0
1
0
2
1
0
1
1
1
1
1
2
0
1
0
2
1
2
2
0
1
1
1
1
2
1
1
0
2
0
0
2
1
2
1
1
0
1
1
1
0
0
0
2
2
1
1
1
2
0
1
0
1
1
2
1
0
2
1
1
1
0
2
1
1
2
1
2
1
1
1
2
0
1
0
1
1
1
1
1
1
1
1
0
1
0
0
1
2
1
2
1
1
1
2
1
1
1
1
0
1
1
1
1
1
2
2
2
0
1
1
1
1
1
1
2
2
1
1
1
2
1
1
2
0
1
1
1
2
2
0
1
1
0
2
0
0
1
1
0
2
2
0
1
1
0
1
1
1
1
1
2
1
0
0
2
1
0
1
2
0
1
1
1
1
1
0
1
1
2
2
0
0
1
1
1
1
1
1
0
2
0
1
1
2
0
0
1
0
0
1
1
1
1
2
3
1
1
2
0
1
0
2
0
0
0
0
1
1
2
0
1
0
1
0
1
0
1
0
1
0
0
0
0
1
1
1
1
0
2
1
1
0
1
1
2
1
1
1
1
1
1
2
0
1
1
2
1
0
1
2
2
1
1
0
1
2
2
1
1
1
1
1
1
1
2
1
1
2
2
1
1
0
1
2
1
0
2
2
1
1
1
1
2
1
0
0
1
1
1
1
1
2
0
2
1
1
0
3
0
0
0
0
1
1
0
1
1
2
0
1
0
1
0
1
1
1
1
1
1
1
1
1
0
2
0
1
2
1
1
1
0
2
2
1
0
2
2
1
1
1
0
0
0
1
0
1
1
1
2
0
1
2
2
0
1
1
1
1
0
0
2
1
0
0
1
0
0
1
1
0
0
0
1
0
0
1
1
1
0
1
1
1
0
0
1
1
1
2
1
0
2
0
2
0
1
1
2
2
1
1
1
1
1
2
1
1
1
1
1
2
2
2
0
1
1
1
1
2
1
1
1
1
2
0
1
1
1
0
0
2
1
1
1
2
0
1
1
2
2
1
1
0
2
2
1
2
2
3
2
1
0
1
0
2
1
1
1
1
1
1
0
3
1
1
1
1
1
1
1
1
1
2
1
0
2
1
0
1
2
2
0
0
1
1
2
0
1
1
0
1
0
1
1
0
0
1
0
1
1
0
0
1
1
1
1
2
1
0
1
1
1
1
0
1
1
1
2
0
1
0
0
2
2
1
2
1
2
1
1
2
2
0
1
0
1
1
1
0
2
1
2
1
1
2
2
1
1
1
1
1
1
0
2
0
2
2
0
0
1
1
3
2
1
1
1
0
1
0
2
1
1
0
0
1
1
1
0
2
0
1
2
0
1
1
0
2
1
1
0
1
2
1
0
1
2
1
2
1
1
0
1
0
0
2
1
0
1
1
2
1
2
0
2
0
1
1
1
1
0
0
1
1
1
1
2
1
1
1
1
1
1
0
1
3
2
2
0
2
1
1
0
1
1
2
1
2
1
0
1
0
2
0
2
2
1
1
1
2
0
0
0
0
2
1
0
2
0
2
1
1
1
1
2
2
0
2
0
2
1
0
1
2
1
1
0
1
1
1
0
2
1
3
1
1
1
2
2
1
1
1
1
0
2
1
0
0
2
0
1
0
0
2
1
2
1
2
1
1
2
1
1
0
1
0
1
1
2
1
1
1
0
1
1
2
2
1
1
1
1
1
1
1
1
1
0
0
1
0
1
2
2
2
2
1
2
0
1
3
1
1
3
1
0
1
1
2
2
1
1
0
1
0
1
2
2
1
1
0
1
1
0
1
1
0
0
2
0
1
2
1
0
0
1
1
2
2
2
1
1
1
1
0
0
1
2
1
0
1
1
1
1
1
1
0
1
1
0
1
1
0
2
1
1
1
1
0
0
1
2
1
1
1
0
0
1
2
0
1
1
1
2
1
2
2
0
1
1
1
2
1
1
1
1
0
0
0
2
1
1
2
1
1
2
1
2
0
1
2
2
0
1
2
1
0
0
0
1
0
1
2
1
0
2
0
2
0
0
1
1
0
0
0
1
1
2
1
1
2
1
1
2
1
1
2
0
1
1
1
1
0
0
1
0
0
0
0
1
1
2
1
1
1
0
0
2
1
0
1
0
1
1
1
1
1
0
2
1
0
0
1
1
1
2
1
0
1
1
2
2
0
0
2
0
0
2
0
2
1
2
0
1
1
1
0
0
1
2
0
2
1
1
0
0
1
2
1
1
1
0
1
2
1
2
0
0
2
1
1
1
2
1
0
0
1
1
2
0
0
0
0
1
0
2
1
0
1
1
0
0
1
1
1
0
0
0
1
1
1
0
2
1
1
0
1
0
1
1
1
0
1
1
1
1
0
1
1
0
1
2
1
1
2
2
1
1
0
1
2
2
3
1
1
1
1
2
1
2
0
2
0
1
1
1
1
0
1
4
1
1
1
1
1
2
2
0
1
0
0
0
2
1
0
0
1
1
1
1
0
1
0
1
1
0
0
1
1
1
1
2
0
1
0
1
2
1
1
0
1
1
0
1
2
1
1
1
1
1
2
1
1
1
0
1
0
0
2
2
0
1
2
2
1
2
1
0
0
1
1
1
0
1
2
0
1
2
0
1
1
2
1
0
2
1
0
1
1
1
2
0
1
2
1
1
1
1
2
2
0
1
2
1
2
1
1
0
0
1
1
0
1
0
1
1
0
1
0
1
1
2
5
1
1
1
1
0
0
1
2
2
0
1
1
1
0
0
2
0
1
0
0
1
0
1
2
0
0
1
1
0
1
3
1
1
3
2
2
1
1
2
1
1
2
1
1
1
1
1
2
0
2
0
0
0
0
2
1
1
1
1
1
2
2
1
0
0
1
0
1
2
0
2
2
1
1
1
6
0
1
1
2
2
0
1
0
1
0
1
1
2
1
2
1
2
2
0
2
1
1
0
1
2
2
1
2
2
1
1
2
2
0
1
1
1
1
1
0
2
1
0
1
2
1
1
1
2
1
2
1
2
2
0
1
1
1
2
1
1
1
1
1
0
2
1
0
1
1
1
1
0
2
0
1
1
0
1
2
1
1
2
1
2
1
0
0
0
1
1
0
1
1
1
2
1
2
1
2
0
0
2
2
1
1
1
2
2
2
2
1
0
2
0
2
0
1
2
1
1
1
2
1
1
1
0
1
1
1
1
2
2
1
1
1
1
2
3
0
1
1
1
1
2
1
0
1
1
0
1
2
2
0
1
1
0
1
1
1
2
0
1
0
0
1
1
0
1
2
0
2
2
2
1
1
0
2
1
1
0
2
1
0
1
0
0
1
1
1
2
1
0
1
0
1
1
0
2
1
1
2
0
1
1
1
0
1
2
2
2
2
0
1
1
1
2
1
1
0
1
1
1
0
2
0
2
0
1
1
2
1
2
0
1
0
1
0
1
1
1
1
0
1
2
1
1
2
0
1
0
1
2
2
1
1
0
1
1
0
2
1
0
2
2
0
1
2
0
2
0
0
2
0
1
0
0
1
1
1
0
1
1
1
1
1
1
0
0
1
0
0
1
1
1
0
3
2
0
1
0
2
2
1
1
1
0
2
1
1
1
2
2
2
1
1
2
0
2
1
0
1
1
2
0
0
3
2
1
1
1
0
0
0
1
0
0
1
1
1
0
2
1
1
0
0
0
0
2
1
1
1
1
1
0
0
1
1
1
2
0
1
1
1
1
1
0
1
0
1
0
1
2
0
0
1
1
0
8
1
1
4
1
0
2
3
2
1
1
2
1
1
1
1
3
0
1
1
2
2
1
1
1
2
1
2
2
1
1
0
1
0
0
5
1
1
1
1
1
1
1
1
0
1
1
1
0
0
0
1
2
1
0
0
0
1
0
0
1
1
1
2
0
0
1
1
1
1
1
1
1
1
2
0
0
2
2
0
1
2
2
1
1
0
2
0
1
0
1
0
0
2
1
2
0
1
2
1
0
0
2
1
2
1
0
0
0
2
0
1
2
1
1
0
1
0
0
1
1
1
1
2
1
0
1
1
1
0
0
1
2
2
2
1
1
0
1
0
1
1
2
1
2
1
1
1
1
1
1
2
2
1
1
2
1
1
1
2
1
1
1
2
1
0
1
0
0
0
1
0
2
1
1
2
1
0
2
0
1
2
2
2
1
2
1
0
2
1
2
2
0
1
0
1
0
1
0
1
1
1
2
0
2
1
0
1
1
1
1
1
0
2
1
1
0
1
1
1
1
2
2
2
1
1
0
0
2
2
0
1
1
2
1
1
1
1
0
0
0
1
1
1
1
2
0
1
1
3
1
1
2
0
1
0
2
0
2
0
2
1
4
1
1
1
2
1
1
1
2
1
1
0
1
0
1
1
2
1
1
1
1
1
0
0
0
0
1
1
0
1
1
0
4
0
1
1
1
1
2
0
1
0
1
2
0
1
0
2
2
1
0
1
0
0
1
2
1
0
1
1
0
1
0
2
1
1
1
0
0
2
2
1
2
0
1
1
1
1
1
0
1
1
1
0
0
0
0
0
0
2
1
0
2
1
1
1
2
1
2
2
1
0
1
0
1
1
1
0
0
1
1
1
2
2
1
1
1
1
0
0
2
2
2
2
0
2
2
1
1
2
1
0
2
1
2
0
0
2
0
0
2
1
3
0
2
2
1
1
2
0
1
0
1
1
1
2
2
1
1
0
2
1
2
0
2
2
0
2
1
0
2
1
0
1
1
1
1
1
1
0
1
1
1
2
2
1
2
1
1
1
0
1
0
0
1
1
0
1
2
1
1
2
2
1
2
1
2
1
1
2
2
1
0
1
1
1
1
1
2
0
0
0
1
0
1
2
0
2
1
2
0
0
0
2
2
1
1
0
0
1
2
1
1
2
1
1
1
0
1
0
0
1
2
1
0
0
2
1
1
1
1
0
1
2
0
1
0
1
1
3
1
1
1
0
1
0
1
1
1
1
0
2
1
1
1
1
0
0
1
1
1
4
1
2
1
0
0
0
1
2
2
0
1
1
1
0
2
1
1
3
0
1
1
1
2
0
2
2
0
1
1
0
2
1
2
0
0
1
1
4
1
1
1
2
0
2
1
0
1
0
1
2
2
0
2
1
0
1
1
0
1
2
2
1
1
0
2
1
1
1
2
1
2
0
1
1
1
2
0
1
1
4
1
1
0
1
3
1
1
0
1
1
1
1
1
1
1
1
2
1
0
1
0
1
4
1
1
1
1
0
2
2
0
2
1
0
0
1
1
0
1
2
1
2
1
1
2
1
1
2
1
2
1
1
0
1
1
2
0
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
0
0
1
1
1
2
2
1
2
1
1
1
0
0
1
1
2
1
1
1
1
1
2
2
1
0
0
2
0
0
0
1
1
0
1
0
0
1
2
1
0
0
1
0
0
1
1
1
1
2
2
1
1
2
0
0
2
1
1
1
1
0
2
0
2
2
2
1
1
1
2
0
1
1
1
0
1
1
1
2
0
0
0
3
2
0
1
1
2
1
1
1
2
1
0
1
1
1
1
0
0
1
2
1
2
0
2
2
1
1
1
0
1
2
1
0
1
1
1
2
0
2
2
0
0
0
1
2
0
0
2
2
1
0
1
0
3
1
1
0
1
2
1
0
1
1
1
1
2
2
2
1
0
1
0
2
1
1
1
0
1
1
1
1
2
1
1
1
1
2
0
0
1
1
0
1
1
1
1
2
2
0
1
1
1
0
2
2
0
2
1
0
1
1
1
1
2
1
1
0
2
1
0
1
2
1
1
1
0
0
0
2
2
0
2
1
1
0
1
2
2
2
0
0
1
1
1
1
1
0
0
1
0
1
2
1
1
1
0
1
2
2
1
1
0
2
2
1
1
2
1
1
0
1
1
1
0
1
1
0
0
1
1
1
2
1
0
2
2
1
2
1
1
2
2
1
1
2
1
2
1
0
0
0
0
1
2
1
2
1
1
1
1
1
1
1
1
2
1
2
1
2
2
1
2
1
1
0
1
2
1
3
2
1
3
1
2
2
1
1
1
0
1
0
2
0
3
0
0
0
1
1
1
1
2
1
1
1
1
1
2
1
1
1
0
1
1
1
1
0
1
1
1
0
1
0
1
1
2
2
0
0
2
1
2
1
2
1
0
0
1
1
1
0
1
0
0
1
1
2
0
1
2
0
1
1
1
0
1
1
1
1
1
0
1
0
1
2
1
2
0
0
0
1
1
1
2
2
0
0
1
2
3
1
1
2
0
0
1
1
1
0
2
1
2
0
2
1
1
1
2
0
0
0
0
2
0
1
2
1
2
1
1
0
1
1
0
1
2
2
0
0
1
0
3
1
2
1
0
1
1
1
1
1
0
2
1
1
0
0
1
1
1
2
1
1
2
0
2
1
1
1
2
1
2
1
0
2
1
2
1
1
1
1
1
1
0
2
1
0
2
0
1
1
2
2
2
0
0
0
1
1
1
1
1
0
2
0
1
1
0
0
2
1
1
1
1
1
2
0
2
1
0
1
1
3
2
1
1
1
1
0
0
2
0
1
1
1
1
0
1
2
1
1
1
1
1
1
0
0
1
1
2
1
1
1
0
1
1
2
1
0
1
1
2
1
2
1
2
1
1
3
2
0
1
0
1
0
1
1
1
1
2
0
2
1
1
1
2
1
1
0
1
1
2
1
1
0
2
1
0
2
1
1
1
2
1
1
2
0
0
2
0
2
2
1
0
0
0
2
1
2
1
2
1
1
1
1
2
1
0
1
0
1
0
2
1
0
2
0
0
1
1
1
1
0
1
1
1
0
1
0
0
1
1
0
2
1
2
1
1
0
2
1
0
2
1
0
1
1
1
1
0
1
1
1
2
0
1
1
1
1
2
1
1
1
1
1
2
3
2
1
0
1
1
2
1
1
1
2
2
1
1
1
1
1
1
2
0
1
1
2
0
0
0
2
1
0
0
1
1
1
4
1
1
1
3
0
0
1
0
2
1
1
2
0
1
1
0
1
1
1
0
1
1
1
0
1
1
1
1
1
1
1
1
0
0
1
1
3
2
1
2
1
1
2
1
2
1
1
1
2
1
1
1
1
2
0
0
1
1
2
0
1
1
0
1
2
2
1
0
1
1
1
1
1
2
1
1
0
1
1
1
0
0
0
1
0
3
0
1
0
0
1
1
0
0
1
2
0
2
0
1
1
1
1
0
1
3
2
0
2
1
2
0
1
0
2
1
1
1
0
3
0
1
0
1
2
1
2
0
0
1
1
1
1
1
2
1
1
0
1
0
1
1
2
1
1
1
1
0
1
1
3
1
1
1
1
1
1
0
0
0
1
0
1
0
2
2
0
2
1
1
0
1
1
1
1
1
1
0
0
1
1
1
3
1
1
0
1
1
2
1
1
1
1
1
0
0
1
1
2
2
0
0
7
0
2
1
2
0
2
0
1
1
2
1
2
1
2
1
0
1
1
1
0
0
2
0
2
1
0
1
0
2
2
1
0
1
1
1
1
2
1
2
1
0
1
1
1
1
1
2
2
1
1
0
2
0
1
1
1
1
1
1
0
1
0
0
1
0
1
1
0
2
1
0
0
0
2
0
1
1
1
1
1
0
0
2
1
1
0
2
2
1
2
1
0
0
0
1
2
0
1
1
1
0
1
1
1
1
1
1
0
2
3
1
1
2
1
0
1
1
0
1
1
1
1
0
0
0
1
0
0
0
2
2
2
1
1
2
1
0
0
0
1
0
1
2
1
1
2
2
2
2
2
0
0
0
1
0
1
1
2
2
1
2
1
0
1
1
0
1
1
1
1
1
1
2
0
1
1
2
2
1
1
1
0
1
2
1
1
2
2
0
1
2
0
0
0
1
0
1
0
1
1
0
0
2
1
0
1
0
1
1
2
1
0
1
0
1
1
0
1
2
1
1
2
2
0
1
2
3
0
0
0
2
0
1
2
1
2
0
0
2
1
2
1
0
2
1
1
1
1
2
1
1
2
1
2
1
1
0
1
0
0
2
2
0
0
2
2
1
0
0
3
2
1
0
1
1
0
2
1
0
1
1
0
1
1
2
1
0
1
2
1
1
0
1
0
1
1
0
2
2
1
0
1
1
0
1
2
1
0
0
1
1
2
1
1
1
2
3
0
2
0
1
2
1
1
1
3
0
1
1
0
1
1
2
2
2
2
1
1
1
1
1
1
0
0
1
1
1
2
3
1
1
0
1
2
1
0
1
1
1
2
0
1
1
1
1
1
0
2
2
1
1
2
1
2
2
1
2
0
1
1
1
1
1
1
2
2
0
1
0
1
1
1
0
1
2
2
2
1
2
1
2
0
0
0
1
0
0
1
0
1
0
1
1
2
2
0
0
0
1
0
1
4
1
2
0
2
1
2
1
1
1
1
1
2
0
1
1
1
1
0
2
1
2
1
1
1
0
0
0
2
2
0
0
1
1
0
2
0
0
1
1
1
1
1
2
0
2
1
2
2
1
2
2
1
1
1
0
1
1
2
0
1
0
1
1
2
1
1
0
1
1
0
0
0
0
1
1
0
2
2
1
2
1
0
1
1
2
1
1
1
1
3
0
2
0
0
0
1
0
1
0
1
0
1
1
0
2
2
0
1
1
2
0
2
1
1
2
1
1
0
0
3
1
1
0
1
1
1
1
2
1
2
1
1
2
2
1
2
0
0
1
1
1
1
1
1
0
2
0
0
1
1
2
0
1
1
1
1
1
0
2
1
1
0
1
1
1
1
0
2
1
0
1
1
0
2
2
1
0
2
1
2
2
0
2
1
0
1
2
1
1
1
0
1
0
2
0
1
1
2
1
0
2
1
1
0
2
0
2
2
2
1
0
1
1
0
1
1
0
1
1
0
0
2
1
1
1
0
1
1
0
1
1
1
0
1
0
0
0
0
1
0
1
1
1
2
0
1
0
1
1
0
1
2
1
2
1
2
0
1
1
1
0
1
0
2
2
2
2
1
1
2
1
2
1
0
2
2
2
2
1
2
0
2
0
1
1
2
7
0
2
2
2
1
1
1
1
1
1
1
1
1
0
1
2
1
1
0
1
2
2
2
1
2
1
1
1
0
2
1
1
2
2
0
0
1
1
1
2
1
1
0
2
1
0
2
1
0
0
1
1
1
1
2
1
1
2
1
1
1
1
0
1
0
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
0
0
1
0
0
2
1
1
0
0
1
1
1
0
0
1
0
0
1
2
1
2
0
1
2
1
1
0
1
0
1
1
2
1
1
1
2
0
1
2
1
2
1
1
0
1
2
0
1
0
1
2
1
2
1
1
2
1
1
2
0
3
1
1
1
1
1
2
0
0
0
1
0
2
1
0
2
0
0
1
1
1
1
0
2
1
1
1
2
0
1
0
2
0
1
0
1
2
0
2
0
2
1
0
1
2
1
2
2
1
1
1
2
2
1
2
0
2
0
0
0
1
1
2
0
1
1
2
1
1
0
2
0
0
0
2
1
1
0
1
0
1
2
1
1
0
1
1
1
0
1
1
1
1
1
0
0
2
1
2
1
0
2
1
0
0
0
0
1
2
1
2
1
0
2
1
2
1
1
0
2
0
1
0
1
1
2
1
1
1
0
1
2
1
1
1
1
1
0
0
1
0
2
1
1
0
0
1
2
1
1
2
2
1
0
0
2
0
1
1
1
1
0
2
1
0
1
1
2
1
1
0
0
2
1
1
0
1
0
1
1
0
1
1
0
1
1
2
0
2
2
0
0
0
0
1
2
1
1
2
1
1
2
1
2
0
1
2
1
0
0
0
0
2
1
0
0
2
1
1
0
0
1
0
1
1
1
1
1
0
0
0
1
1
1
1
1
0
1
2
1
2
2
0
0
0
1
0
1
1
1
2
0
2
1
2
1
1
0
2
2
0
1
0
2
1
0
2
0
0
2
0
1
0
1
0
1
0
0
1
1
1
1
1
0
1
1
0
0
2
1
1
0
1
0
0
1
0
2
1
1
2
1
1
2
0
2
1
0
0
1
0
1
1
0
2
0
0
0
2
0
0
1
1
1
2
1
1
1
2
2
1
0
1
1
0
1
2
0
0
2
1
0
0
0
2
0
2
1
0
2
2
1
0
1
1
0
0
2
1
2
1
0
2
0
1
1
0
0
1
2
2
2
0
1
1
1
0
1
2
1
0
0
1
0
2
1
1
0
1
1
1
3
1
1
1
1
1
1
1
0
1
2
0
2
0
2
1
1
0
1
0
1
1
1
1
1
1
1
1
2
2
3
0
2
3
1
1
1
1
0
1
1
2
1
1
1
2
1
0
1
1
2
2
1
1
0
2
2
2
0
2
1
1
1
1
1
1
1
1
2
1
0
0
1
2
0
1
0
2
1
1
0
0
1
1
2
1
1
1
3
2
1
0
0
1
1
0
1
1
0
0
1
1
2
1
1
2
1
1
1
1
1
0
0
1
0
1
2
2
2
2
0
1
1
1
2
1
0
1
1
0
2
1
0
0
1
1
1
1
1
1
0
1
1
2
1
1
0
0
0
0
2
0
2
1
1
0
1
0
1
1
1
2
1
0
0
0
0
2
0
1
2
1
1
1
2
2
1
1
2
1
2
2
2
1
2
1
2
1
0
2
1
0
0
1
0
2
0
2
1
1
1
1
1
0
2
1
1
1
1
2
1
2
0
1
1
1
1
1
1
1
0
1
0
0
0
1
1
2
1
0
0
1
1
2
1
1
1
1
1
1
1
1
2
1
2
1
1
1
2
1
2
1
1
2
1
1
1
1
1
1
0
1
1
1
0
1
0
2
2
2
2
1
1
1
1
0
1
1
2
0
2
1
1
1
1
1
1
1
1
2
0
0
0
1
0
0
0
5
2
1
1
1
1
1
1
2
1
0
1
1
0
0
1
1
0
1
1
1
2
2
1
2
2
0
0
1
1
2
1
0
0
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
0
0
1
1
1
1
0
1
1
1
2
1
1
2
1
2
1
1
2
1
1
1
1
0
0
1
2
0
2
4
2
2
2
3
1
1
0
1
1
2
1
1
0
2
2
1
2
2
2
1
1
1
0
0
1
1
0
0
2
1
0
2
2
2
1
2
2
0
2
0
1
2
2
0
0
2
2
1
1
1
1
2
1
1
1
1
2
1
2
2
1
1
1
2
0
2
0
1
1
0
1
2
0
1
1
0
1
0
2
4
0
0
0
2
0
2
1
1
1
0
1
1
1
1
2
2
2
1
4
1
1
2
2
1
0
1
1
2
0
1
1
0
0
2
1
1
2
0
1
0
1
2
2
1
2
2
1
0
1
0
0
2
2
2
1
1
1
2
0
1
0
0
1
1
0
0
1
1
1
1
1
2
1
1
1
1
1
1
0
1
0
1
2
1
0
1
1
1
1
1
0
1
2
0
2
2
1
0
1
0
2
1
2
1
1
1
1
1
1
1
0
1
2
1
1
2
0
0
1
2
2
2
0
1
0
1
1
0
0
1
1
1
0
2
0
1
1
1
1
2
0
1
2
1
1
0
1
2
1
1
1
2
2
2
0
1
1
1
1
1
2
0
0
1
0
2
1
1
2
1
1
0
1
0
2
2
0
1
0
1
1
2
0
2
2
1
1
2
1
1
2
2
0
1
1
0
1
1
1
1
2
1
2
2
0
2
1
1
2
1
1
1
1
0
1
2
0
0
1
0
0
1
1
0
1
1
1
1
1
2
0
0
1
0
1
1
2
0
1
0
1
2
0
2
1
0
0
0
2
0
1
2
1
1
1
1
0
1
2
1
1
0
1
1
0
0
1
0
0
0
0
1
1
1
1
2
0
1
1
0
0
2
0
1
1
1
1
0
2
1
0
2
2
0
0
1
2
1
1
2
2
1
1
1
2
1
2
0
0
1
1
0
1
2
3
0
1
1
1
2
0
1
0
1
1
0
2
0
3
1
2
1
0
1
2
1
1
0
1
1
2
2
2
1
1
1
4
1
2
1
0
2
1
1
1
1
2
1
2
1
1
0
0
0
1
1
2
1
0
0
1
2
2
0
1
1
1
3
1
2
2
1
1
1
1
1
1
1
1
1
1
1
0
0
0
1
0
0
1
2
0
2
1
1
0
1
1
1
2
2
1
1
1
1
1
0
1
0
1
1
2
1
1
1
1
0
1
2
1
1
1
1
2
1
0
1
2
3
1
0
1
1
1
0
1
1
0
2
1
2
0
2
1
2
1
0
1
1
1
0
0
1
0
2
2
1
2
1
1
2
1
2
1
2
0
2
1
2
1
3
1
1
2
1
2
0
1
1
0
1
1
0
0
2
2
1
1
2
1
0
1
1
1
2
1
0
1
2
1
0
1
0
1
1
1
1
1
2
2
0
1
1
1
1
0
0
2
1
2
1
1
1
0
1
2
1
0
1
2
1
0
1
2
0
0
1
2
1
0
0
1
0
1
2
1
1
0
2
1
1
0
0
1
1
2
0
0
1
2
0
1
1
1
1
0
2
1
0
1
1
0
2
0
2
1
1
1
1
1
1
1
1
1
0
1
1
0
2
1
0
2
0
1
0
1
1
2
2
1
1
0
2
2
1
0
1
1
2
0
1
1
0
0
0
0
0
1
0
2
0
0
2
1
1
2
2
1
0
1
2
1
1
1
1
2
1
2
0
0
1
1
1
1
2
1
0
1
1
0
0
0
1
2
1
1
1
1
2
1
0
1
1
2
1
0
1
1
2
0
2
1
0
0
1
1
1
1
2
1
1
0
1
0
1
1
1
1
0
0
1
2
0
0
1
2
1
0
2
1
1
1
1
1
1
0
1
0
0
0
1
2
2
0
2
1
1
1
1
0
1
2
1
2
1
2
1
0
1
0
1
1
0
1
1
1
1
1
1
1
1
2
1
1
2
0
0
1
0
2
1
0
1
1
1
1
0
1
0
1
1
1
1
0
2
1
1
1
2
1
1
1
1
2
2
2
1
0
0
2
1
1
0
2
1
1
1
2
3
1
0
2
1
1
1
0
1
1
1
1
0
1
1
1
1
1
1
1
1
1
3
1
1
2
0
1
0
2
1
0
1
0
2
1
0
1
1
1
1
1
1
1
1
0
2
2
0
2
2
1
0
1
1
1
1
1
0
2
2
1
1
1
1
1
0
1
1
1
1
1
2
0
1
1
0
0
2
1
1
0
1
1
1
2
2
1
0
1
1
1
0
2
3
0
0
1
2
0
2
1
1
1
1
1
1
2
2
0
1
0
1
1
2
1
0
2
1
1
2
1
1
1
2
0
1
0
2
0
1
1
2
0
2
1
1
1
1
1
1
1
1
1
1
0
1
2
0
1
0
3
1
1
1
1
1
0
2
0
0
1
1
0
2
1
1
1
0
1
1
2
2
1
1
2
0
0
2
2
1
1
1
2
2
0
1
2
1
1
1
1
1
0
0
2
1
2
1
1
1
2
1
1
2
1
1
2
0
0
1
2
1
2
2
2
0
0
2
0
1
1
1
0
1
1
0
1
1
0
0
0
0
1
1
1
3
1
1
2
1
1
1
1
1
1
2
1
2
2
1
1
2
0
1
2
0
1
0
1
1
2
1
2
0
2
1
1
2
1
0
1
2
1
1
0
0
1
2
1
1
1
2
1
2
1
1
0
1
0
1
1
5
2
0
0
0
1
1
2
1
1
1
1
0
2
0
2
1
1
0
0
1
0
1
1
1
0
0
1
2
0
0
1
0
1
1
2
1
0
2
0
1
0
1
2
1
1
1
1
1
1
1
1
3
1
0
0
0
1
2
2
2
1
1
2
2
1
1
0
2
1
0
2
1
0
2
2
2
1
1
2
0
2
0
3
2
1
0
0
1
1
2
1
1
1
1
0
2
1
2
1
1
1
2
0
1
1
1
1
1
1
0
1
0
0
2
2
0
0
1
2
1
0
1
1
1
1
1
0
2
1
1
1
0
0
1
1
0
0
1
1
0
1
0
0
2
1
0
2
2
2
1
0
1
0
1
2
1
0
1
1
2
2
1
0
2
1
0
1
1
1
1
2
0
2
1
1
1
0
1
0
1
0
2
1
0
2
0
0
1
1
2
2
1
1
1
1
1
0
1
2
1
2
1
1
1
0
1
0
1
1
1
1
2
1
2
1
0
0
1
1
2
1
1
1
1
1
1
1
2
0
1
1
0
1
1
1
1
1
0
0
0
2
1
1
1
0
2
1
0
0
1
0
0
1
1
2
1
1
2
1
1
2
1
1
2
1
1
0
1
0
0
1
2
2
1
1
1
0
1
2
2
1
0
1
1
0
0
1
0
1
2
1
1
1
0
0
0
0
1
1
1
0
1
1
0
1
2
1
1
0
1
0
0
2
1
0
1
1
1
1
0
1
1
1
2
1
1
1
1
1
1
0
1
2
2
2
1
2
1
2
1
1
1
0
1
1
2
1
2
1
1
0
2
0
2
0
0
0
2
1
0
0
1
2
1
1
0
1
1
0
1
1
1
0
3
1
2
1
1
0
1
0
2
0
2
1
1
1
2
3
0
1
0
1
2
1
2
1
1
2
1
1
0
2
2
1
0
1
1
0
0
1
1
2
1
0
1
0
1
1
1
0
2
1
0
1
2
1
1
0
2
1
1
2
1
0
1
1
1
0
1
0
0
2
2
2
1
0
2
1
1
0
2
1
0
1
1
1
1
0
1
1
0
1
1
0
1
1
0
1
2
1
1
1
2
2
1
1
1
0
1
1
2
1
1
1
0
0
1
2
1
1
1
2
1
0
0
0
0
4
2
1
1
1
0
1
2
1
2
1
2
2
0
0
2
0
2
1
0
0
1
1
0
2
1
1
1
0
2
1
2
2
1
1
2
0
2
2
2
1
1
1
0
1
0
0
1
1
2
2
1
1
2
1
1
2
1
1
0
0
2
2
2
0
2
2
0
1
0
0
2
0
2
1
2
1
1
0
2
0
1
0
1
2
1
1
2
1
1
1
1
2
2
1
2
1
1
1
0
1
4
0
0
0
1
0
0
1
1
2
1
1
0
1
1
1
0
0
1
2
3
1
1
1
2
1
2
1
1
2
2
1
2
1
1
2
1
1
0
1
0
1
1
1
2
2
1
1
2
0
1
1
3
0
1
1
1
0
1
4
1
2
2
2
0
1
1
0
0
0
0
0
1
1
2
1
1
1
1
1
0
2
1
1
1
2
2
0
1
1
1
1
1
0
1
2
0
1
1
0
1
1
2
1
0
0
1
1
1
0
0
0
1
2
1
0
0
0
2
1
6
3
0
0
1
1
1
1
1
2
1
0
2
1
0
1
1
0
2
1
0
0
2
1
0
0
0
1
1
1
0
2
2
0
0
1
1
1
2
1
1
1
1
1
1
0
0
1
1
2
1
1
1
0
0
2
2
1
1
0
0
0
0
2
1
0
2
1
1
1
1
2
0
0
1
0
1
1
2
2
2
1
1
2
0
1
1
2
1
2
1
1
1
1
1
1
0
1
1
2
1
1
1
0
0
1
2
0
0
2
1
0
1
0
0
2
1
1
0
0
2
2
1
1
1
0
1
1
0
0
1
0
0
2
1
2
0
0
2
2
2
1
1
2
1
1
0
0
1
2
1
2
0
1
1
1
2
1
2
2
0
1
0
1
1
2
2
1
0
1
0
0
0
0
2
0
0
1
0
2
2
1
2
0
1
1
0
1
2
2
1
1
2
1
1
2
0
0
1
1
0
1
2
2
2
1
1
0
1
0
0
1
2
1
0
1
1
1
0
1
1
1
1
1
2
2
2
2
1
0
0
1
2
0
1
0
1
2
2
2
2
1
1
0
2
2
0
1
1
2
0
1
0
1
0
2
1
2
2
1
1
0
0
1
0
0
2
0
1
1
1
1
1
2
1
0
0
1
1
1
1
1
2
0
2
1
1
0
2
0
2
0
2
2
2
1
1
1
1
1
0
0
0
2
0
1
1
1
1
2
1
2
2
1
2
5
1
2
0
0
0
1
1
1
1
0
2
1
0
2
1
2
2
0
2
1
1
0
1
1
1
1
1
2
1
1
0
1
1
2
2
1
0
1
0
1
0
1
1
1
2
1
1
1
1
0
2
0
2
1
0
0
1
0
1
1
1
0
1
1
2
2
1
1
1
1
0
1
2
1
1
2
1
1
1
2
1
0
0
0
1
1
2
1
2
2
1
1
0
1
1
1
0
1
0
1
0
1
1
1
0
0
1
1
2
0
0
2
2
1
1
1
1
1
1
1
0
0
0
0
1
0
1
3
1
0
1
0
1
0
1
0
1
1
1
2
1
0
0
0
0
1
1
1
0
2
1
1
0
0
1
1
1
0
2
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
0
2
1
1
1
1
1
2
1
1
0
2
0
0
1
1
2
1
1
1
1
1
2
0
0
2
2
1
0
2
1
0
0
1
1
2
0
0
2
1
0
1
0
1
2
1
2
2
0
1
2
1
1
1
0
1
1
0
0
2
1
2
1
1
1
1
2
1
1
1
0
1
1
2
1
1
1
1
1
0
1
1
0
1
1
0
1
0
2
1
1
2
1
0
2
2
1
2
1
2
2
1
1
1
1
1
2
0
2
0
0
0
1
3
1
0
2
0
0
2
0
0
1
0
0
1
1
1
0
1
0
1
0
1
2
1
0
1
1
2
2
0
1
2
1
1
0
2
1
1
1
1
2
1
2
1
0
1
2
1
1
2
2
2
0
1
2
1
1
1
1
1
1
1
0
1
1
1
0
1
1
1
0
1
1
1
2
1
0
1
0
1
2
1
1
0
2
2
1
0
1
1
1
0
0
2
1
2
1
1
1
2
1
1
4
1
2
0
2
2
1
1
1
0
2
0
0
1
0
1
1
0
1
0
1
1
0
0
0
1
0
1
0
1
1
2
1
2
0
1
1
0
2
2
2
1
1
1
2
1
1
2
3
2
0
2
2
1
0
2
1
2
1
0
0
2
1
1
2
2
1
1
2
2
1
2
1
0
1
1
1
1
0
1
2
2
0
0
0
2
1
2
1
1
0
2
2
1
1
1
2
2
1
0
0
1
1
0
2
0
2
1
1
1
1
1
1
1
0
0
1
1
1
1
1
1
2
0
0
0
1
0
1
1
1
0
1
2
1
1
0
2
1
0
0
1
1
1
1
1
1
0
1
0
1
1
1
0
1
2
3
0
0
0
1
1
2
0
1
0
2
1
1
0
1
1
0
0
1
1
0
0
2
2
0
2
0
1
1
1
2
2
1
1
0
2
0
0
1
1
0
1
1
1
0
0
0
2
1
1
1
1
1
1
0
1
1
0
0
0
1
0
0
1
0
0
1
3
0
2
2
1
1
1
1
0
1
2
1
2
1
0
1
1
1
0
1
1
1
0
1
0
1
0
1
2
1
1
2
1
1
1
1
1
1
1
0
1
3
1
0
1
1
0
0
1
2
1
2
1
1
1
1
1
1
2
1
1
0
0
1
1
0
3
1
2
1
1
0
1
1
1
1
0
0
0
1
1
0
1
2
0
1
1
2
1
1
1
0
2
1
1
0
1
1
0
0
1
0
1
1
2
1
0
1
1
1
0
1
0
1
0
2
0
0
1
1
0
2
2
1
1
0
1
1
2
1
0
1
2
2
0
1
1
1
1
1
1
1
1
2
1
5
1
1
1
1
2
0
1
1
2
1
0
0
1
0
1
1
1
0
0
0
1
2
2
0
0
2
2
1
0
1
1
2
2
2
2
2
1
0
1
2
2
1
1
2
1
0
0
2
1
0
1
1
1
2
1
0
2
2
0
2
1
0
0
2
0
1
0
1
1
0
2
2
1
1
1
1
0
1
0
1
2
1
2
1
2
2
0
0
0
0
0
0
0
0
1
1
1
1
1
1
0
2
1
0
1
1
1
1
0
0
1
0
1
0
1
2
1
1
0
1
2
0
1
1
0
1
0
1
1
1
1
0
1
0
1
0
1
0
2
1
0
1
2
2
1
0
1
2
1
0
1
1
0
0
0
1
2
1
1
2
2
0
0
1
0
0
1
1
0
0
1
2
0
1
2
1
2
3
0
1
1
0
1
2
0
0
1
1
1
0
0
1
0
2
0
1
1
2
1
1
2
1
1
0
0
1
1
0
2
1
0
1
0
2
0
1
1
1
1
1
1
1
1
1
0
2
1
1
1
1
1
2
1
1
1
0
1
1
1
0
1
1
0
1
0
2
1
3
1
1
1
1
2
1
0
0
0
1
1
0
2
1
1
1
2
1
1
1
1
0
1
0
1
1
0
0
1
0
1
1
2
2
0
1
2
0
0
1
1
0
1
2
1
2
2
2
1
2
2
2
0
1
1
0
1
0
0
1
2
2
2
1
1
0
1
2
0
0
1
1
0
1
0
2
2
2
0
1
2
2
1
4
0
1
1
1
2
1
0
1
0
0
1
1
1
1
1
1
1
1
0
2
1
1
1
0
1
0
2
0
2
0
1
0
1
1
2
1
0
1
0
2
0
0
0
1
1
0
1
0
2
1
0
1
0
0
2
0
1
1
1
1
1
1
0
1
1
1
0
2
1
1
1
2
1
1
0
2
1
1
0
1
1
0
2
0
0
1
0
0
1
0
1
2
2
0
1
1
1
1
1
1
1
1
1
1
1
2
1
2
0
2
3
0
2
1
2
1
1
1
1
0
0
1
1
0
2
1
2
2
1
1
2
3
2
1
1
2
1
2
0
1
0
2
1
1
1
1
1
1
2
1
2
2
1
0
1
0
0
1
0
1
2
1
0
0
1
1
0
0
1
2
1
1
1
0
2
0
0
0
1
1
2
2
0
0
1
1
0
1
2
1
1
0
1
0
1
2
1
0
1
1
1
0
1
1
0
1
1
2
1
1
1
1
0
1
1
0
2
1
1
2
2
0
1
1
0
0
2
2
2
1
4
1
0
2
1
1
1
1
1
1
0
1
2
2
1
1
1
1
0
1
2
1
1
2
2
1
1
1
1
2
0
1
0
1
2
1
0
0
1
1
0
1
0
1
2
1
1
1
1
0
1
0
1
1
2
2
1
2
0
0
1
0
1
2
0
1
0
0
1
1
1
1
1
0
0
0
2
0
0
2
0
1
0
2
2
2
1
1
1
0
1
2
2
0
1
2
1
0
2
2
1
0
1
0
1
1
1
0
1
1
1
0
2
0
0
2
0
2
0
2
1
0
1
1
2
2
0
2
1
0
1
4
2
0
0
1
2
2
2
0
1
1
1
0
1
0
1
2
0
2
0
1
1
1
2
0
0
1
0
1
1
0
1
0
1
1
1
2
1
1
1
2
1
0
0
0
2
1
0
1
0
2
1
1
1
0
1
1
1
1
2
1
1
1
2
1
1
0
2
1
1
0
1
1
1
1
0
1
1
0
0
1
0
1
0
1
0
1
2
1
0
0
1
2
1
0
0
1
0
2
0
1
2
0
1
0
0
1
1
1
1
2
0
0
1
0
0
0
1
1
1
0
0
0
1
0
1
2
1
2
2
2
0
1
1
0
2
1
1
2
1
0
0
0
1
1
1
1
1
1
2
1
1
1
0
0
1
2
0
0
0
0
0
0
2
3
2
1
0
0
1
1
2
1
2
1
1
0
1
0
0
0
1
1
0
0
1
2
0
1
1
1
2
1
1
1
1
0
1
0
0
1
0
2
1
1
0
1
2
1
2
0
1
2
1
1
1
1
1
1
2
1
1
1
5
2
1
1
1
1
1
1
2
0
2
2
0
1
2
1
0
0
0
1
0
0
0
2
1
1
2
2
2
1
0
0
0
1
1
0
1
1
0
0
1
2
1
0
1
1
2
2
1
1
1
1
1
0
1
2
1
1
1
1
1
1
0
0
2
1
1
2
0
1
0
1
2
1
2
0
2
1
1
1
1
1
1
1
0
1
1
1
2
1
2
1
0
1
2
1
6
1
2
0
0
2
0
0
0
1
0
0
1
4
0
1
0
1
0
1
1
2
1
0
0
0
0
0
3
1
1
0
0
1
2
2
1
1
2
1
2
2
2
2
2
1
2
0
1
2
0
0
1
1
2
2
2
1
1
1
1
1
1
1
2
1
2
0
1
1
1
1
2
1
0
2
2
1
1
1
1
1
1
0
0
1
0
1
0
1
0
1
1
1
1
1
1
1
1
1
1
0
2
1
2
1
1
2
1
1
2
2
0
1
2
0
2
1
0
2
0
2
1
0
2
1
1
1
2
1
1
2
2
1
2
2
1
0
0
0
0
1
2
1
1
1
2
1
2
2
2
1
0
1
2
1
1
0
0
1
0
0
0
1
1
2
2
1
1
0
0
0
0
1
2
2
0
2
0
2
1
1
1
0
0
1
1
0
2
2
1
1
2
2
2
2
2
0
1
1
1
1
0
2
1
0
1
2
0
0
2
2
0
1
0
1
0
3
0
1
0
2
0
0
1
1
1
1
1
2
0
1
2
2
2
1
1
0
1
1
1
0
1
1
2
0
2
0
1
2
0
1
2
2
0
2
0
1
1
0
0
1
2
0
1
1
0
1
0
1
1
0
1
0
1
1
0
2
1
1
1
1
1
0
2
1
1
1
1
1
2
1
0
0
1
1
0
0
1
1
2
2
0
1
1
0
1
3
1
1
1
2
1
1
2
2
0
1
0
2
0
1
1
2
1
2
0
2
0
2
0
1
2
0
1
1
1
1
1
0
1
1
1
2
1
0
2
1
0
1
2
0
0
1
1
1
1
1
1
0
0
2
1
0
1
0
0
1
0
1
1
1
0
1
1
3
1
0
1
1
0
1
1
2
2
2
1
1
2
0
2
1
1
3
2
0
0
0
2
1
1
2
1
0
1
0
1
1
1
1
2
1
1
0
2
1
2
2
1
0
2
0
1
0
1
1
1
1
1
1
1
2
0
1
1
1
0
0
0
1
1
0
1
0
1
0
0
0
1
0
1
0
0
1
0
1
1
1
1
1
0
0
0
0
0
1
1
1
2
1
2
2
1
1
1
2
0
1
1
2
2
2
1
2
1
3
1
1
1
1
1
0
1
1
3
1
1
2
1
0
1
1
1
1
1
0
1
0
0
0
1
1
1
2
1
2
7
2
1
1
2
2
2
0
2
1
3
2
1
0
1
1
0
1
2
1
0
1
0
0
1
0
2
2
1
0
1
2
1
2
2
2
1
1
2
0
0
1
0
0
1
1
3
1
2
1
1
1
1
3
2
1
1
0
2
1
1
1
1
0
2
2
1
2
2
1
1
1
1
0
2
2
2
1
0
0
2
1
0
0
1
1
2
1
1
2
1
1
1
0
0
2
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
2
0
2
1
0
2
0
1
1
1
1
0
1
2
0
0
0
1
1
1
0
1
1
0
1
1
0
1
1
1
1
1
2
0
1
1
1
1
1
3
1
0
1
2
2
1
1
1
1
1
1
2
0
1
1
1
1
1
0
2
1
1
1
2
2
1
0
1
2
1
1
1
1
1
0
0
1
2
1
1
1
1
1
1
0
1
1
1
0
2
2
1
2
0
1
2
1
2
2
1
2
1
2
1
0
0
2
1
1
1
1
0
2
0
1
2
1
1
2
1
1
2
1
0
0
2
1
1
1
1
1
0
2
2
2
1
1
0
1
1
1
1
1
1
2
1
1
0
1
1
1
0
2
0
0
1
1
1
0
2
0
2
1
1
0
1
1
0
1
2
1
2
0
3
1
0
2
1
2
0
0
1
1
1
1
1
0
1
0
0
0
1
0
1
1
1
2
1
1
0
2
2
1
2
0
2
2
1
1
1
1
1
0
0
1
2
1
0
1
0
0
1
1
0
1
0
1
1
2
1
1
0
1
2
2
1
1
0
0
1
2
1
1
1
1
0
0
1
2
1
0
1
1
2
1
1
2
2
1
1
1
2
2
0
1
1
1
0
1
1
3
0
2
1
1
0
2
1
2
0
1
2
2
0
1
1
1
3
2
0
1
1
1
0
1
2
1
2
2
1
2
3
2
2
1
1
0
0
1
1
2
2
0
0
0
1
2
1
2
1
1
2
1
2
1
1
2
1
1
1
2
1
0
1
0
1
2
2
2
0
2
2
1
1
1
0
1
1
1
1
2
2
1
1
1
1
1
0
1
2
1
0
1
1
1
1
0
1
1
2
2
0
1
1
2
1
2
1
1
1
1
1
1
2
0
2
0
1
1
2
1
1
1
0
0
1
2
1
2
1
1
1
1
1
1
1
2
1
1
0
0
0
1
1
2
1
1
1
2
2
1
1
1
1
0
1
0
1
2
0
1
0
2
0
1
2
2
2
2
1
1
1
1
1
1
1
1
2
0
0
0
1
0
1
2
0
1
0
0
2
1
0
1
2
2
1
1
1
1
1
1
2
1
1
1
2
0
1
1
1
1
0
1
1
1
1
1
1
0
0
1
1
1
1
0
0
2
1
1
1
0
1
1
1
0
1
1
1
1
0
2
1
2
1
1
0
0
0
1
1
1
0
0
1
0
0
1
1
1
1
1
1
1
1
0
1
1
2
0
0
1
2
2
1
2
2
2
2
1
0
0
1
1
3
1
1
1
0
1
0
0
0
1
0
0
0
1
2
1
1
0
1
1
1
1
1
1
0
0
1
1
2
1
0
0
0
1
0
1
0
2
1
1
1
1
2
0
1
1
1
2
2
1
1
0
1
0
0
1
0
2
1
2
1
0
1
1
1
0
1
0
0
1
1
1
1
1
1
0
2
1
1
0
2
1
0
1
0
1
1
1
0
0
0
1
1
0
1
3
2
2
1
1
0
2
1
1
1
1
3
1
0
2
1
2
1
0
1
1
1
0
0
0
1
1
2
1
1
1
1
0
1
0
0
0
1
1
1
1
1
1
1
2
2
0
0
0
2
0
0
0
1
1
0
1
2
1
1
0
0
0
3
2
0
2
1
1
0
2
1
2
1
0
0
1
0
1
1
0
1
1
0
1
1
1
2
0
1
1
2
1
1
0
1
1
0
1
1
0
1
4
1
0
2
0
1
2
1
0
2
1
2
2
1
0
2
1
1
0
1
2
0
3
1
2
2
1
0
1
1
1
1
2
1
1
2
1
0
1
1
0
1
1
1
2
2
0
0
1
1
1
0
1
2
1
2
1
1
0
2
0
0
1
0
1
2
1
2
0
0
2
0
1
1
1
1
1
1
0
1
0
0
0
2
0
1
0
1
1
2
2
1
0
0
1
2
2
0
1
1
1
0
1
1
1
2
1
0
1
3
0
1
2
2
0
0
1
0
1
1
1
1
0
1
1
1
1
2
1
2
1
1
0
0
1
2
0
2
1
1
2
0
2
0
2
1
1
1
1
0
1
0
2
1
1
0
2
1
1
0
1
0
1
1
0
2
2
0
2
1
0
1
1
0
0
1
1
1
0
0
0
1
0
0
1
2
2
2
2
1
1
2
0
0
2
1
1
2
1
1
1
0
1
2
1
1
0
0
1
1
1
1
1
2
0
1
1
0
1
1
2
0
1
1
2
2
1
1
0
0
0
1
2
1
1
1
0
0
1
1
1
1
0
1
0
0
2
2
1
1
2
1
0
2
1
0
1
0
0
2
1
2
1
1
1
1
2
1
2
0
0
0
2
2
1
1
1
2
0
1
2
1
1
1
0
2
1
1
0
0
1
1
1
1
1
1
1
0
1
1
0
1
0
0
2
2
1
1
2
0
0
1
2
0
2
1
1
0
0
2
2
2
1
1
0
1
0
1
1
2
1
0
1
1
1
1
1
1
0
2
2
2
1
1
2
2
0
0
1
1
0
1
1
1
1
1
1
0
1
1
2
1
0
1
2
0
1
1
1
1
0
0
1
1
0
2
1
2
1
1
2
0
0
0
0
0
4
1
2
1
1
2
2
1
1
0
1
0
1
0
2
1
0
0
1
1
1
1
1
0
0
2
1
1
0
0
0
0
0
1
0
1
0
1
0
0
1
1
0
1
0
1
1
2
0
2
2
0
1
0
1
1
1
1
0
1
2
1
1
1
2
1
1
1
1
1
1
1
1
0
1
0
0
1
2
1
1
1
1
2
2
1
1
1
1
2
1
0
2
1
2
1
0
0
1
1
2
1
1
0
1
2
1
0
0
1
2
0
0
1
1
0
1
1
1
1
2
0
0
1
1
1
0
1
1
1
1
0
1
0
4
1
0
1
1
1
1
0
2
0
1
1
2
2
1
0
2
1
0
1
0
1
0
1
1
1
1
2
0
0
1
0
0
2
0
1
0
1
1
1
1
1
4
0
1
1
2
0
1
1
1
1
2
2
1
1
0
2
1
1
0
2
2
0
0
3
1
0
1
1
1
0
1
1
1
0
1
1
0
1
0
1
1
1
1
1
0
5
1
1
0
1
0
0
1
2
1
1
1
2
1
2
1
2
1
1
2
1
1
1
1
0
0
1
0
1
1
0
1
1
0
1
2
1
1
1
1
3
2
0
1
2
0
0
1
2
2
1
2
2
3
1
1
2
0
1
1
1
1
0
1
1
0
1
2
1
0
1
2
2
2
1
0
1
1
0
1
1
0
1
1
0
1
1
1
0
1
1
0
2
1
1
1
0
2
3
2
1
1
0
0
1
2
1
2
0
1
2
2
0
0
0
1
1
1
0
0
1
0
0
2
0
2
1
0
0
1
1
2
0
1
0
2
2
2
1
0
1
1
2
1
0
2
1
2
1
1
1
0
0
1
3
1
0
0
1
1
0
0
0
0
1
2
2
1
2
1
0
0
2
2
2
1
0
1
1
1
1
1
0
1
2
1
2
1
2
1
1
0
0
1
1
1
1
1
1
1
1
1
1
0
1
0
2
2
1
2
1
1
1
1
2
1
1
0
1
2
2
1
0
2
1
1
1
1
2
1
1
1
1
2
2
0
1
1
0
0
2
1
1
2
1
0
2
0
2
1
1
2
1
1
0
1
2
1
0
0
1
1
0
2
2
0
1
4
1
2
2
0
0
2
2
0
1
1
2
0
0
2
0
0
1
0
2
1
1
2
2
1
2
1
1
0
1
2
0
2
1
1
0
0
1
0
1
1
1
0
1
4
0
1
2
1
0
0
1
0
0
0
1
1
2
2
0
2
2
2
2
1
1
1
1
2
1
0
0
4
1
1
0
0
1
1
2
0
1
1
1
1
1
1
0
0
1
0
0
1
1
0
1
0
4
1
1
0
0
0
1
1
0
0
1
1
1
0
1
1
2
1
2
1
0
0
0
1
1
1
1
1
0
1
1
1
1
1
0
0
1
0
0
0
1
1
2
0
1
2
2
1
1
2
1
0
1
1
2
0
2
1
2
2
0
1
0
1
0
0
1
1
0
2
0
1
0
0
1
2
1
5
0
2
1
1
1
0
1
0
2
1
0
1
2
1
0
1
1
1
1
0
1
1
0
1
0
2
0
0
1
1
2
0
1
1
1
0
2
2
0
1
1
1
0
2
1
1
2
1
0
1
1
1
2
1
1
1
0
1
1
0
0
0
2
1
0
1
1
2
0
3
0
1
1
2
1
1
1
2
0
1
0
1
1
2
1
1
1
1
1
0
2
2
0
0
2
0
0
0
1
1
1
1
1
0
2
1
2
0
1
1
2
0
2
0
3
2
0
1
0
2
2
0
1
1
1
1
0
2
2
1
1
0
0
1
0
2
0
0
1
1
1
2
1
1
1
4
3
1
1
1
1
1
3
1
0
0
2
1
1
1
2
1
2
1
1
2
0
2
2
1
2
1
0
0
0
1
2
0
1
1
0
1
1
2
1
2
0
0
0
2
0
1
2
3
1
1
0
2
1
1
1
1
1
1
2
1
1
0
0
0
1
2
2
0
2
2
1
0
1
0
0
1
0
2
1
2
2
0
1
0
0
0
2
0
0
1
2
1
1
0
1
1
0
2
2
1
1
2
1
2
1
1
1
0
1
1
1
1
1
2
2
2
2
1
1
2
2
1
1
0
0
1
1
2
2
1
2
2
1
1
1
0
1
1
0
1
0
1
1
0
0
2
2
1
1
0
1
1
1
1
1
1
2
0
2
0
0
1
1
1
0
1
2
1
1
0
0
0
2
1
1
1
1
0
2
1
1
1
2
1
1
0
2
0
2
1
2
1
1
1
1
0
0
2
1
2
2
0
1
0
0
1
1
2
1
0
2
0
1
1
1
0
1
1
2
0
1
2
1
1
1
1
2
0
1
0
1
2
1
0
1
1
0
0
2
1
2
2
1
1
2
1
0
0
0
1
0
0
2
2
1
2
1
2
0
0
1
1
1
0
0
0
1
1
1
1
1
2
1
2
2
1
1
1
1
1
2
1
1
0
1
1
1
0
2
2
1
0
0
1
1
1
1
2
1
2
0
1
0
2
3
0
0
2
0
0
2
1
1
1
1
2
1
0
0
1
0
1
1
0
1
1
2
0
1
1
1
1
0
1
1
0
1
0
0
2
1
1
1
1
1
1
2
0
2
1
1
1
2
2
2
1
1
0
2
0
0
1
0
0
1
1
0
1
0
0
0
2
1
2
2
1
0
1
1
1
1
2
2
1
1
1
0
1
0
2
1
1
2
2
0
2
1
0
2
2
1
2
1
1
1
1
0
0
2
2
2
1
0
2
2
0
2
0
1
1
1
1
1
1
1
0
0
2
1
0
1
1
0
1
0
1
1
1
2
0
0
1
1
1
1
1
2
1
0
1
5
1
1
1
1
0
1
0
0
1
1
1
0
0
1
1
0
2
1
1
1
2
1
0
2
2
1
1
1
1
1
2
2
1
0
2
1
0
1
1
0
1
0
1
2
1
1
0
1
1
2
1
2
2
2
1
0
1
1
0
2
1
1
1
0
1
1
1
2
1
0
1
1
1
1
1
1
2
1
0
0
1
2
2
2
0
0
0
1
1
2
2
1
1
1
0
1
0
2
1
2
1
0
1
1
1
1
1
2
0
2
1
1
0
2
0
1
1
1
1
1
2
2
2
1
2
0
1
1
1
2
1
1
1
2
2
0
0
0
3
1
1
0
1
2
2
1
1
1
1
1
2
1
2
0
1
1
1
1
0
1
1
1
1
0
1
1
0
2
1
1
1
1
0
2
1
2
1
1
2
0
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
0
2
1
2
1
1
0
3
1
1
2
1
2
1
2
1
1
1
1
0
2
1
0
1
1
2
2
2
0
0
0
1
1
1
0
0
1
2
2
0
1
2
1
1
2
1
0
1
1
2
2
0
1
0
1
1
1
0
1
1
1
2
2
1
1
2
1
1
1
0
1
2
1
1
1
1
1
0
1
1
1
0
1
1
1
1
2
3
1
0
2
0
1
1
1
1
0
2
1
2
0
1
0
1
2
1
0
1
2
1
2
2
0
1
1
1
1
0
1
2
1
0
0
1
1
0
1
1
1
1
2
1
1
0
2
2
0
0
0
1
0
1
1
0
1
0
1
2
1
0
0
1
1
0
2
2
0
1
1
2
1
1
0
1
2
2
0
0
1
1
0
1
1
0
1
0
2
1
2
3
0
1
0
0
1
0
1
0
1
1
0
2
1
0
1
2
1
2
2
1
2
1
1
1
0
1
1
0
1
1
0
2
1
1
1
0
0
1
2
0
1
2
2
2
0
2
1
2
2
1
1
0
1
1
1
1
0
1
0
1
1
1
0
1
0
1
1
1
2
1
0
0
1
1
1
1
0
0
1
1
2
2
0
1
1
1
1
0
0
1
1
2
2
2
0
1
2
1
1
0
2
1
1
1
2
1
1
1
1
1
0
0
2
0
1
1
1
0
1
1
1
1
1
1
1
0
1
2
2
1
1
3
1
2
2
0
0
1
0
2
1
0
2
0
2
1
1
1
3
2
2
2
1
1
1
0
1
2
1
1
1
1
2
1
0
1
1
1
0
0
1
2
2
1
1
2
2
1
0
1
1
2
0
2
1
1
3
1
1
0
0
1
1
1
1
0
1
0
1
1
1
2
1
2
0
1
1
0
1
1
0
1
1
1
0
1
0
2
1
1
1
1
1
1
1
2
2
2
2
1
1
0
1
1
1
0
1
0
2
1
1
1
0
1
1
1
1
1
2
1
0
2
1
1
0
1
1
1
0
1
0
1
0
1
0
1
0
1
0
0
0
1
0
2
1
1
1
0
0
0
1
1
1
2
2
3
1
2
1
2
2
1
2
1
1
1
1
1
0
2
1
0
2
1
0
2
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
2
2
0
0
2
2
2
1
1
1
0
1
2
2
0
0
0
0
1
1
1
0
0
1
1
0
1
1
1
1
1
1
1
1
1
2
1
0
1
1
1
1
1
1
1
1
1
1
1
0
2
1
0
0
2
0
1
0
0
1
1
0
0
2
1
1
2
2
0
1
1
1
0
2
0
1
1
2
0
1
1
1
1
1
1
2
1
2
1
2
0
2
2
1
1
2
2
1
1
1
1
0
1
2
1
1
1
0
0
1
0
2
1
1
0
1
1
3
2
1
0
0
0
1
1
2
1
1
1
1
0
1
0
3
1
1
2
2
1
1
2
0
2
0
1
2
1
2
0
1
1
2
1
1
0
1
1
1
1
1
0
1
2
2
2
0
1
1
1
1
0
1
3
1
0
1
4
1
2
1
0
2
2
0
0
1
0
1
2
1
1
1
0
1
0
1
1
1
1
2
1
1
1
1
1
1
1
1
1
0
1
1
2
2
1
2
0
2
2
1
1
1
1
1
1
1
1
1
1
2
0
2
1
1
0
1
2
1
0
0
0
1
1
0
0
2
1
1
1
1
2
1
0
1
2
0
1
0
0
0
1
1
1
1
0
1
2
2
1
2
0
1
0
1
0
2
1
1
2
1
1
0
1
1
1
1
1
0
2
0
1
1
1
0
0
1
1
0
2
0
1
0
2
0
0
1
1
1
1
2
2
2
1
0
1
0
1
0
1
1
1
1
2
2
0
1
1
1
0
0
0
2
2
1
2
1
1
1
0
0
1
0
2
1
0
9
2
0
0
2
2
1
1
1
1
1
1
2
1
1
1
0
1
1
0
2
2
2
1
1
0
1
2
0
1
0
1
1
1
1
1
1
1
2
2
0
2
0
1
1
2
1
1
0
0
1
1
0
2
2
1
0
2
1
1
2
0
0
1
0
1
2
1
1
0
1
1
2
1
2
0
2
0
2
1
1
0
1
1
1
1
1
0
1
1
2
2
0
1
2
2
1
1
2
0
1
0
2
2
2
0
0
0
0
1
1
1
2
1
2
2
2
1
1
0
3
0
0
2
1
1
2
2
1
1
1
1
1
0
2
0
2
0
2
2
1
1
2
0
0
2
1
2
2
1
2
1
2
1
1
2
0
1
1
1
1
1
3
1
1
0
1
2
1
2
1
0
1
0
2
0
1
1
1
1
0
0
1
1
1
2
2
0
1
2
1
0
0
1
1
2
0
2
1
1
0
0
1
0
1
1
0
1
1
1
0
1
0
0
0
2
2
0
1
1
0
1
2
1
1
0
0
1
1
1
1
1
1
2
0
2
0
0
1
1
0
1
1
1
2
0
2
1
2
1
2
1
0
0
1
1
1
1
1
0
2
0
0
1
1
1
0
1
1
1
0
0
1
2
0
0
1
0
2
0
1
1
0
1
3
1
1
2
0
0
0
1
1
2
1
2
0
0
1
1
1
2
1
0
2
2
2
0
1
1
0
0
0
2
1
0
1
2
0
0
0
2
0
0
1
0
0
1
2
1
2
0
1
1
1
2
1
1
0
0
1
0
0
1
1
1
1
2
0
0
1
2
1
1
2
1
0
1
1
1
1
1
1
1
2
1
1
1
0
2
0
1
1
0
1
0
1
1
0
0
1
1
2
1
1
0
1
0
1
0
0
1
2
1
1
0
2
1
0
1
1
2
0
2
0
2
2
1
1
0
0
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
2
1
0
1
1
2
1
0
1
1
1
1
2
1
0
1
1
0
1
1
0
1
1
0
1
0
1
1
0
2
0
1
0
1
0
1
1
2
0
1
2
1
2
1
0
1
1
1
1
2
1
1
1
1
2
1
1
1
1
0
1
1
0
0
1
1
1
2
1
1
1
2
1
1
0
1
0
2
0
0
0
1
1
1
1
1
1
1
1
1
1
2
1
2
1
0
0
0
0
0
2
2
0
1
2
2
0
1
2
1
1
0
0
1
1
3
1
1
1
0
0
0
2
0
1
2
2
1
1
1
2
1
0
1
1
1
2
0
1
2
0
1
0
18
1
1
1
1
0
1
0
0
2
1
0
0
0
0
1
2
1
1
0
0
0
0
1
1
1
1
1
2
1
1
1
2
1
1
1
1
0
2
2
0
1
1
0
2
0
0
1
1
0
1
1
2
2
1
1
0
2
2
1
1
1
0
1
1
0
1
0
2
0
2
0
2
2
1
1
1
0
2
0
0
1
1
1
1
1
1
3
0
1
2
2
2
1
1
1
1
1
1
0
1
0
0
1
1
1
2
1
0
1
1
1
0
0
2
1
0
2
2
0
1
2
1
1
2
0
0
1
1
1
0
1
1
1
2
1
0
1
2
2
1
1
1
1
1
1
1
0
1
1
1
7
1
1
1
1
1
0
1
2
0
1
1
0
2
1
1
1
1
1
1
1
1
0
2
2
1
1
1
0
1
1
1
1
1
1
0
0
2
2
1
0
1
1
2
0
1
1
1
1
1
1
2
1
1
2
1
0
1
1
0
1
0
2
2
0
1
1
1
2
1
1
0
1
1
1
0
0
2
1
2
1
0
0
0
1
1
1
0
1
2
1
2
1
1
1
2
2
1
1
1
1
0
1
1
1
1
1
1
2
1
0
1
1
1
1
0
1
1
0
2
1
2
2
1
1
0
2
0
2
1
0
2
2
1
1
0
0
0
2
0
1
1
1
2
0
1
3
0
1
0
1
1
0
2
0
0
2
1
1
1
2
2
1
1
0
0
2
2
1
0
1
1
1
1
1
0
1
1
2
0
1
2
1
1
3
0
1
1
1
0
1
1
1
2
2
2
1
0
0
1
1
2
1
1
1
0
2
0
1
1
1
1
1
2
0
1
0
1
0
0
0
1
1
1
1
3
0
1
2
1
1
0
0
1
1
1
1
2
2
0
1
0
1
0
1
1
1
1
1
2
2
1
1
0
0
1
2
1
1
2
0
0
0
0
0
1
1
0
2
1
2
0
0
2
0
0
1
1
2
1
1
1
1
1
0
1
0
1
2
1
1
1
1
1
1
1
2
0
1
1
1
1
1
0
0
1
1
0
0
1
0
0
3
2
1
1
1
2
1
2
1
1
2
0
1
1
0
1
1
1
2
1
0
1
0
1
1
2
2
2
0
0
1
0
2
2
1
2
1
1
2
0
1
0
0
1
2
0
1
2
1
1
1
1
2
0
0
1
1
1
1
2
0
2
1
1
1
0
1
2
1
1
1
1
1
1
1
1
0
1
0
2
1
1
1
2
2
2
2
0
1
2
2
0
0
1
2
1
1
0
1
1
2
1
2
1
0
0
1
1
2
0
0
0
2
2
2
1
1
1
1
0
1
1
2
1
1
0
0
2
1
1
0
1
1
0
1
1
0
1
1
1
1
0
1
1
1
1
2
0
0
2
1
2
0
1
1
2
1
0
0
0
1
0
2
0
2
0
2
0
1
1
0
2
1
1
2
1
0
1
1
1
1
1
1
0
1
1
2
0
0
1
1
1
0
1
1
0
2
2
2
0
2
1
2
1
1
0
1
1
1
1
1
1
1
2
0
1
1
1
2
1
2
1
0
2
1
2
1
1
1
2
1
0
0
0
0
2
1
1
1
2
0
1
1
2
0
2
0
2
2
2
1
0
1
1
2
2
1
0
1
1
2
2
2
2
0
1
0
1
1
0
0
1
2
0
1
1
1
3
2
1
2
1
1
1
1
1
1
1
1
2
1
0
2
1
1
1
0
1
1
1
2
1
0
2
0
0
0
0
0
0
1
1
1
3
1
0
1
2
0
1
0
2
1
1
1
1
1
0
1
0
1
1
1
1
2
1
1
1
2
1
1
0
1
0
1
3
2
1
2
1
2
1
2
2
1
1
1
1
2
0
1
1
0
0
1
1
1
1
0
2
1
2
1
0
1
2
2
1
1
2
2
1
1
1
0
1
1
1
1
1
1
1
0
2
1
1
1
1
0
1
1
1
1
1
1
2
2
1
0
1
0
1
1
1
0
1
1
2
0
1
0
0
1
1
2
1
1
2
0
1
1
0
1
1
1
0
2
1
1
1
1
1
1
1
2
1
1
1
0
1
2
1
1
2
1
2
3
1
0
1
0
0
1
0
0
1
0
0
1
2
1
3
2
2
2
0
2
0
1
0
1
1
1
1
0
1
0
0
1
0
2
1
0
2
1
0
2
1
1
0
0
0
0
1
1
2
1
2
2
1
2
1
2
1
0
1
1
1
1
0
1
1
1
1
0
1
2
2
0
0
1
0
1
0
1
1
1
0
1
1
0
1
1
1
1
2
1
2
2
1
2
1
0
1
2
1
1
1
1
0
1
1
2
2
2
2
2
1
1
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
2
1
1
0
0
0
3
1
1
0
1
1
2
1
1
2
1
1
1
1
0
1
1
1
1
1
2
0
1
1
2
1
2
0
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
3
1
1
0
0
0
1
1
3
0
0
1
1
0
0
1
1
2
1
1
1
2
0
1
2
2
0
2
1
1
2
2
1
0
1
1
1
1
1
1
0
0
1
0
1
0
2
1
1
0
1
0
1
0
2
0
0
0
1
2
0
1
1
2
1
1
1
2
1
1
1
1
1
0
2
1
2
4
1
2
0
0
1
1
2
1
1
1
1
0
2
2
1
1
2
1
1
1
2
1
1
2
1
0
1
1
1
1
1
2
0
0
1
1
0
1
2
1
2
1
1
1
1
2
1
1
2
2
0
0
2
1
1
1
1
2
1
1
0
2
1
1
2
1
1
0
1
1
0
1
1
1
2
0
0
0
0
2
2
1
2
2
1
2
1
0
1
1
2
0
0
2
1
1
2
0
0
1
1
2
1
1
1
1
0
1
0
1
1
2
1
1
1
0
0
0
0
1
2
0
2
1
1
0
2
0
1
2
2
1
2
2
1
1
2
1
0
1
2
1
2
1
1
1
1
1
1
1
0
0
1
1
1
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
0
1
1
1
1
1
0
1
2
1
1
2
1
1
1
0
1
0
1
2
1
1
1
1
1
1
2
0
1
0
2
1
1
1
2
1
1
1
1
1
2
2
0
2
0
2
0
2
2
0
1
2
1
0
1
2
0
0
0
1
2
0
1
0
0
2
2
1
1
0
1
2
2
1
2
1
0
1
0
2
2
1
1
1
2
1
1
0
2
1
0
1
1
1
1
0
1
1
1
1
2
2
1
1
1
0
2
1
1
1
0
0
1
1
0
0
0
1
2
1
0
0
0
2
1
1
0
0
1
2
2
0
0
2
0
2
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
2
1
2
0
0
1
2
1
1
2
1
1
0
1
0
1
1
1
2
1
0
2
1
1
2
1
1
1
1
0
2
1
0
1
1
0
1
2
1
1
1
1
0
0
1
1
2
1
1
2
2
1
2
2
2
1
2
1
1
1
1
0
1
0
0
1
0
1
1
1
0
2
1
0
1
1
0
2
1
0
0
0
0
2
2
0
2
2
1
1
2
0
2
1
0
0
1
0
1
1
2
1
1
0
2
1
2
1
1
0
0
1
0
1
1
1
1
1
1
0
0
1
0
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
0
0
1
1
1
1
1
1
1
0
1
1
0
2
1
1
0
1
0
1
1
1
1
1
1
1
1
1
1
2
0
0
2
2
1
2
3
2
2
0
1
1
1
0
1
1
0
1
1
0
2
2
0
2
1
1
1
0
0
1
1
0
1
0
0
1
1
1
1
2
0
1
1
1
2
2
0
0
1
1
1
1
2
1
1
1
1
0
1
0
0
1
2
0
1
1
1
0
1
1
1
0
1
2
0
1
1
2
1
0
1
1
1
2
0
2
2
2
1
2
1
0
1
1
2
0
1
1
2
1
2
0
1
1
1
0
0
1
0
1
0
0
2
1
0
1
2
1
1
0
1
0
2
1
1
1
1
2
1
0
1
1
0
2
1
0
2
0
1
1
1
1
1
1
0
1
0
1
0
1
1
1
0
0
0
0
1
1
1
2
5
1
1
2
1
2
2
1
1
1
1
1
2
1
1
1
1
0
0
1
0
1
1
1
1
1
1
2
1
0
0
1
1
1
0
0
1
2
2
0
2
2
1
1
2
0
1
0
0
1
0
1
2
1
1
0
1
0
1
1
1
1
0
0
0
2
1
1
1
2
1
1
0
1
1
0
0
2
1
1
1
1
1
1
0
1
1
0
2
1
1
1
0
1
1
2
2
1
1
0
1
1
2
0
1
0
1
1
2
0
1
2
2
1
2
1
0
1
2
1
1
1
1
2
0
1
0
1
2
0
1
1
0
1
0
1
1
1
2
0
2
1
1
1
1
3
1
1
1
3
2
1
1
1
2
1
1
0
1
0
1
1
0
0
1
1
0
1
2
0
1
1
1
1
2
1
1
1
1
0
2
0
1
1
2
2
1
1
3
7
2
0
1
1
2
0
1
0
0
1
2
1
0
0
1
0
1
2
0
2
2
0
2
1
0
2
1
2
1
1
2
1
0
1
1
1
2
2
1
0
0
1
1
1
0
1
2
1
0
2
0
1
1
2
0
0
0
2
1
0
0
2
1
0
1
1
1
1
1
0
1
1
1
1
0
1
1
2
3
1
1
1
1
0
0
3
3
2
0
1
1
2
2
1
1
1
0
0
0
0
0
2
1
1
1
1
0
1
2
1
1
1
1
0
2
2
1
1
1
1
1
2
2
1
2
1
1
0
1
1
1
0
2
2
1
2
2
1
2
1
1
1
2
1
1
1
1
1
1
6
2
2
0
1
1
0
2
0
1
0
1
0
2
1
0
0
1
1
1
0
0
2
1
1
2
0
1
1
1
2
2
2
1
0
1
1
4
2
1
2
1
0
1
1
2
2
1
1
2
2
1
0
0
1
0
1
0
1
1
0
1
1
2
2
0
0
1
1
1
1
1
0
2
1
1
0
2
1
2
1
0
0
2
3
1
2
2
2
0
1
1
2
1
1
1
0
0
2
2
2
2
2
1
1
1
2
2
1
0
0
2
1
2
2
1
0
1
2
1
2
1
1
1
1
0
2
2
3
1
1
2
1
0
1
1
0
1
0
1
1
1
1
1
0
1
0
0
0
0
0
2
1
0
0
1
1
1
3
2
2
2
1
1
0
2
2
2
2
0
1
2
1
0
1
0
1
1
1
1
2
0
1
1
0
1
0
1
0
2
2
1
1
1
0
0
0
1
0
0
0
2
1
0
0
1
1
1
1
1
2
0
0
0
2
1
1
1
1
2
1
1
2
1
1
0
1
1
0
1
0
1
0
2
2
0
1
1
0
1
2
1
0
1
1
2
1
2
1
0
1
0
2
0
2
1
0
0
1
1
1
2
1
0
1
1
2
1
2
1
1
1
1
1
2
1
1
1
1
1
2
1
2
0
1
2
1
0
0
1
0
0
1
1
0
1
1
1
1
0
1
1
0
1
1
0
1
1
1
0
2
0
2
0
1
1
1
2
0
1
1
1
0
1
1
1
1
1
1
0
1
1
1
1
1
1
3
0
1
1
2
1
2
0
1
0
1
0
1
1
2
1
1
0
1
0
1
2
0
1
0
1
0
1
1
0
0
1
1
0
1
2
1
1
1
1
1
2
1
0
1
2
1
0
2
0
2
0
1
2
1
1
2
3
0
1
1
0
1
2
1
0
0
1
1
0
2
0
1
1
2
1
1
1
1
0
1
1
1
0
1
1
2
1
1
1
1
2
1
0
1
2
0
2
2
1
1
1
2
0
1
2
1
0
2
1
1
0
0
1
0
0
0
1
0
2
2
1
2
1
1
0
1
1
0
1
2
1
1
2
1
0
1
0
1
0
0
1
1
1
1
1
1
2
0
1
0
1
1
2
2
0
0
2
3
2
2
1
1
1
2
1
0
0
1
2
1
1
1
1
2
0
1
0
0
0
0
1
0
1
1
1
1
2
1
1
1
1
1
2
0
2
0
0
1
1
0
1
1
1
1
1
1
0
2
2
0
1
1
2
2
0
2
2
0
1
1
0
1
0
1
1
0
1
1
0
2
0
1
1
1
1
2
1
1
1
1
1
1
1
0
0
1
1
2
0
1
0
1
0
1
1
1
1
0
0
1
1
0
1
1
1
1
2
1
1
1
2
1
0
0
0
1
1
2
0
1
2
0
1
1
2
2
0
1
1
1
2
1
1
0
1
1
1
2
0
2
1
1
2
3
1
1
0
1
1
1
0
0
0
0
1
1
1
1
1
1
0
2
0
0
1
2
1
1
1
2
0
1
0
0
2
1
2
0
0
0
1
2
2
1
0
2
0
1
1
0
0
1
1
1
1
0
1
1
1
1
0
1
0
2
1
2
1
2
1
1
0
1
1
0
1
2
1
2
3
2
1
1
2
0
0
2
0
1
1
2
1
2
0
1
1
1
1
1
1
1
1
1
1
2
0
1
1
2
1
1
1
0
0
2
1
0
1
2
1
0
1
2
0
1
1
1
0
1
2
0
1
1
0
1
1
0
1
1
1
1
1
3
1
2
0
2
0
0
1
3
0
0
2
1
0
2
2
1
1
0
0
1
1
1
1
1
1
1
0
1
1
2
2
2
1
1
1
2
2
1
1
1
1
1
0
0
2
1
2
0
1
2
1
1
2
1
1
0
1
1
0
1
0
0
2
0
0
1
1
2
0
1
0
1
0
1
1
1
0
1
2
1
1
0
0
1
1
1
0
1
0
0
0
1
0
1
2
0
0
1
1
1
2
1
2
2
1
1
0
1
0
2
2
1
2
1
1
0
1
1
1
2
3
1
1
0
1
0
0
0
1
0
1
1
0
2
0
1
1
0
0
0
1
2
1
1
1
1
2
2
2
1
1
0
1
1
1
1
0
0
0
1
0
1
1
1
1
0
2
1
2
1
2
1
0
0
1
2
0
0
0
1
1
1
0
1
2
2
1
1
0
2
0
2
1
0
1
1
2
1
1
1
2
2
1
2
2
1
1
0
0
0
1
0
1
2
0
0
3
1
0
1
2
2
2
2
2
1
1
2
2
1
0
1
1
0
1
0
1
1
0
0
1
1
2
2
1
0
1
0
1
2
0
1
2
2
1
2
1
1
0
1
2
1
1
1
0
1
1
1
2
1
1
1
0
2
1
0
1
1
1
0
1
0
1
1
0
0
1
1
0
3
1
1
0
1
1
1
1
1
0
1
0
2
1
2
2
2
1
0
1
2
2
1
1
1
1
2
2
1
0
1
2
1
0
0
0
0
1
0
0
0
1
1
0
0
1
1
1
1
2
1
1
1
1
1
0
2
1
0
1
1
0
1
1
1
1
2
1
2
0
1
1
1
1
1
1
0
1
2
2
0
1
1
1
1
1
1
2
0
0
2
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
0
1
1
0
2
5
1
1
2
1
2
2
1
1
1
0
3
1
1
1
1
1
0
0
2
1
1
2
2
1
1
1
0
2
2
2
0
0
2
1
0
0
1
2
0
1
2
0
1
0
0
0
0
0
2
0
0
0
1
1
0
0
2
2
1
2
1
0
0
1
2
0
1
2
2
2
0
1
4
1
0
0
1
1
1
1
1
1
2
1
0
2
2
0
1
1
1
1
0
1
0
0
0
1
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
0
0
1
0
2
0
1
0
0
0
0
3
0
1
4
1
1
0
1
1
1
0
0
2
1
0
2
0
0
0
1
2
2
0
2
2
2
1
2
2
0
1
0
2
1
0
1
1
0
1
1
0
2
2
0
1
1
1
1
2
2
0
1
1
0
1
1
2
2
3
2
0
1
0
0
1
2
2
1
0
0
1
1
1
1
2
0
1
1
0
1
2
1
1
2
2
1
1
0
0
2
2
0
2
1
2
2
0
0
0
1
1
1
2
2
1
1
0
1
0
0
1
0
1
1
1
1
2
1
0
1
0
2
0
0
2
1
0
3
0
1
1
1
1
2
0
1
2
2
1
0
0
1
1
1
1
1
0
0
1
1
0
0
2
4
1
0
1
0
1
0
0
2
2
2
1
1
2
1
0
2
0
1
3
0
2
1
1
0
2
1
0
1
2
1
1
0
1
1
1
1
1
0
2
1
2
1
1
0
0
0
1
2
2
0
2
2
2
1
0
0
2
1
0
1
1
1
0
2
1
0
1
1
1
1
2
0
2
0
0
1
0
1
2
0
1
2
0
1
1
2
1
0
1
0
0
1
1
0
1
0
1
0
1
1
1
1
1
1
0
1
0
1
1
3
0
1
1
2
0
1
0
1
1
1
0
2
0
1
1
0
0
1
1
0
0
0
2
1
1
1
1
1
0
1
1
0
1
0
0
0
1
1
0
1
1
1
2
1
1
0
1
1
1
1
1
1
1
2
1
2
2
1
1
0
1
2
1
1
2
1
1
1
1
0
1
0
1
1
2
1
1
0
1
0
0
1
1
1
1
2
0
1
1
2
1
1
1
1
1
1
1
0
2
2
1
1
0
2
0
2
0
1
1
0
2
1
1
2
1
1
0
1
2
1
2
0
1
1
1
2
1
2
2
0
0
2
0
0
1
2
1
0
0
2
1
1
0
1
1
0
2
0
1
0
1
1
0
0
4
1
1
1
1
1
2
1
2
1
0
1
1
1
1
2
2
1
0
1
1
0
2
0
2
1
2
0
0
1
1
0
0
1
1
1
1
2
1
1
1
1
2
0
2
1
2
2
1
2
1
2
2
2
1
1
1
1
2
1
0
0
1
3
0
1
2
1
0
2
0
0
1
1
2
1
1
2
1
1
0
1
1
0
2
1
0
2
2
1
1
2
0
1
2
1
0
2
1
0
1
2
1
0
1
2
0
1
0
0
0
2
0
2
0
0
0
1
3
1
2
1
0
0
1
0
0
1
1
1
2
0
2
2
2
1
0
1
0
1
0
0
1
1
1
2
1
0
0
2
1
0
1
1
1
2
1
1
1
1
0
1
0
1
1
1
0
1
2
1
1
1
1
0
2
1
0
1
0
2
1
2
0
0
0
1
2
1
1
1
0
2
1
1
0
1
0
0
3
1
1
1
1
2
1
0
2
0
1
1
1
1
1
0
1
2
0
0
1
1
0
1
2
1
1
1
1
0
0
1
0
0
1
1
1
2
1
1
1
1
1
1
1
2
1
0
1
1
1
1
1
2
2
1
2
2
2
2
2
2
1
2
1
1
1
2
0
1
2
0
1
1
1
1
1
0
1
2
0
1
2
2
1
3
1
0
1
2
2
1
1
1
1
1
1
2
1
0
1
1
0
1
1
1
2
1
1
1
0
1
1
0
1
1
2
2
0
0
0
1
2
2
1
0
1
1
1
1
1
2
2
1
0
1
2
1
2
2
0
1
2
2
0
2
1
0
2
1
0
1
1
0
2
2
1
1
1
0
0
2
2
1
0
1
2
1
1
1
2
1
1
2
1
0
0
0
1
2
0
2
1
0
2
1
1
2
1
2
1
1
1
1
2
0
1
0
0
1
0
1
2
2
1
1
1
2
1
0
0
0
1
1
0
1
1
0
1
2
0
2
0
1
1
0
0
0
1
1
1
0
1
2
1
2
1
1
0
2
1
1
1
0
1
0
2
2
1
1
1
0
0
2
1
0
1
0
0
1
1
1
1
1
1
3
5
0
1
1
0
1
1
1
1
2
1
3
0
0
1
1
1
1
3
1
1
1
1
2
1
1
2
2
1
0
1
0
1
0
0
1
2
1
1
0
1
1
2
2
2
0
0
0
1
1
1
0
1
1
1
2
1
1
1
1
1
3
1
2
1
1
2
1
2
1
1
0
1
1
0
1
1
1
1
2
2
1
1
1
0
2
0
1
1
0
2
1
0
1
0
1
1
0
0
1
1
1
1
0
0
1
1
1
1
1
2
0
0
1
1
1
0
2
1
0
0
0
1
0
2
2
1
0
2
2
1
1
1
0
2
1
1
1
2
1
1
0
1
1
1
0
1
0
1
2
2
1
2
1
0
2
2
2
2
0
1
1
1
2
1
0
1
2
0
1
0
1
0
0
0
0
2
1
0
3
1
0
1
1
1
1
1
2
0
0
1
2
1
1
0
1
2
1
0
1
1
2
2
1
1
2
1
1
0
2
0
1
2
0
1
1
2
0
1
1
0
2
1
2
2
2
0
1
1
0
2
2
1
2
1
0
1
0
1
0
1
2
1
1
0
2
2
2
0
1
1
0
2
1
1
0
1
1
0
0
1
1
2
1
1
0
1
1
2
1
1
0
2
2
1
1
1
1
0
2
0
0
1
1
1
1
1
0
1
2
1
1
1
0
0
0
2
1
0
0
1
1
1
1
1
1
2
2
1
1
0
1
1
0
2
1
1
2
0
0
1
0
2
1
1
2
1
1
1
1
1
1
1
0
1
1
0
2
2
2
1
1
2
1
1
0
1
0
0
0
2
1
2
0
0
2
1
2
1
1
1
0
1
1
1
1
2
1
0
2
3
2
1
0
1
0
0
0
0
1
0
0
1
1
1
2
1
1
2
1
0
0
1
2
0
1
1
1
2
1
0
2
1
2
1
2
0
0
0
2
0
0
0
2
2
0
1
1
2
0
2
0
1
1
0
2
1
1
1
1
1
1
0
1
1
0
1
1
1
1
1
1
1
1
1
1
0
2
1
0
1
1
0
1
1
2
1
1
1
0
1
0
0
1
0
1
0
2
0
2
1
0
1
2
1
2
0
1
1
0
1
0
0
2
2
0
1
2
0
1
2
1
1
1
1
0
1
1
2
0
1
0
2
0
2
1
1
2
1
0
0
0
1
1
0
0
2
2
1
1
0
2
1
2
1
2
0
1
2
0
3
1
1
0
1
3
1
1
0
1
0
1
2
2
1
1
2
0
1
0
1
1
2
1
1
1
0
2
0
2
1
0
0
1
1
1
2
2
1
1
2
2
2
1
0
0
1
1
1
0
2
1
2
1
0
1
2
2
0
0
2
2
0
0
2
0
2
2
2
1
1
0
1
1
1
1
1
2
1
0
0
1
0
1
0
1
1
1
3
0
1
1
0
2
1
1
0
0
0
0
0
0
0
1
1
1
1
1
3
0
0
0
2
2
1
0
1
1
1
0
2
1
0
2
1
2
2
1
2
0
2
3
0
0
1
1
0
1
2
1
0
1
1
1
0
0
0
1
1
1
1
2
1
1
2
2
0
1
0
1
1
1
1
1
1
1
1
1
0
0
0
2
0
1
0
1
0
1
1
0
0
1
0
1
1
1
1
1
1
1
1
2
0
2
2
0
1
2
2
0
0
2
1
3
0
1
1
1
1
0
0
4
0
1
2
2
1
1
1
1
1
1
2
0
1
2
0
1
1
1
1
0
1
2
1
1
0
1
0
1
2
2
2
2
2
1
1
1
1
0
2
2
1
1
1
0
1
0
1
0
2
2
1
1
1
1
1
1
0
0
1
0
1
0
1
0
1
0
1
1
1
1
2
0
1
1
1
1
0
3
2
0
1
1
0
1
1
0
1
0
1
1
0
0
1
2
0
1
1
2
2
0
0
1
2
0
1
1
0
0
1
1
2
0
2
1
0
2
1
2
1
0
1
1
2
1
1
0
1
0
0
1
1
1
1
2
2
1
1
1
0
1
1
0
1
2
1
1
1
0
1
0
1
1
2
0
1
1
1
1
1
1
1
0
0
0
1
0
1
1
1
1
1
2
3
2
1
1
1
1
1
1
1
1
1
1
1
0
1
3
2
0
2
1
2
2
1
1
1
1
2
1
1
1
0
1
1
1
0
1
0
0
1
2
1
1
1
1
1
1
2
0
1
1
0
2
2
0
0
1
2
2
1
1
0
2
3
1
1
1
1
0
1
0
4
2
1
0
2
0
1
1
0
1
1
2
1
1
1
1
0
1
1
2
1
1
0
2
1
1
0
1
0
1
0
0
1
0
2
0
1
0
1
0
1
0
1
2
1
1
1
0
2
5
0
1
0
1
1
2
0
2
1
1
0
0
1
1
2
2
2
2
0
1
1
1
1
1
0
2
1
0
0
0
0
1
1
1
0
2
4
2
1
2
0
0
1
1
1
1
2
1
1
0
1
0
1
1
0
2
1
1
1
0
1
2
1
2
1
1
0
1
1
1
0
0
1
1
1
2
1
2
1
0
1
0
1
1
0
1
2
1
1
1
1
1
1
0
0
2
1
1
0
1
1
1
2
1
0
2
1
0
2
0
0
0
1
0
1
1
1
1
1
1
2
2
2
1
2
2
1
1
1
0
0
0
0
1
0
0
1
1
1
0
1
2
1
1
1
0
1
0
0
1
1
2
1
1
0
2
1
0
0
0
2
1
1
0
2
0
1
1
1
1
1
1
1
1
0
1
1
1
0
0
2
0
0
2
1
0
1
0
2
1
2
0
1
1
1
5
1
1
1
0
1
2
0
0
1
2
2
1
0
1
2
0
1
1
0
0
1
0
1
1
1
0
2
2
1
2
1
1
0
1
1
0
0
0
0
1
1
1
1
1
1
1
1
1
1
2
0
1
2
2
1
0
2
2
0
1
0
1
2
2
3
2
1
1
1
1
2
1
1
3
1
1
1
2
0
0
0
0
1
2
1
0
2
2
1
0
0
2
2
0
1
2
1
2
1
1
2
1
0
1
1
0
1
1
1
0
1
1
1
1
0
1
1
1
2
1
2
2
0
2
0
1
0
1
0
1
0
0
1
0
2
2
0
1
1
1
1
1
1
1
1
1
2
1
0
2
2
2
2
1
1
2
0
1
1
1
1
0
1
1
1
0
0
0
1
0
0
1
2
0
1
1
0
0
1
2
0
2
1
2
1
1
2
0
0
2
1
2
1
1
2
2
2
1
1
1
1
0
1
2
1
1
2
1
2
0
2
1
1
1
1
1
1
1
2
1
1
1
1
0
2
1
1
1
1
0
1
0
1
1
1
1
0
0
1
1
2
0
2
1
1
1
1
1
1
1
1
2
0
2
1
0
1
1
1
0
0
1
2
2
2
2
0
0
1
0
1
0
1
0
1
1
0
0
1
1
0
2
2
1
2
1
1
0
0
2
0
2
1
1
2
1
1
2
0
0
0
1
1
2
1
0
0
1
2
1
1
0
1
1
1
0
2
1
2
2
0
1
1
0
0
1
2
0
2
2
2
0
1
0
2
0
1
2
1
1
0
2
1
1
1
2
1
1
2
1
0
0
1
0
0
2
0
0
0
1
1
0
1
0
1
0
1
1
2
1
1
1
2
1
1
0
1
0
0
0
1
1
2
1
1
1
1
1
0
1
2
2
1
1
1
2
1
1
2
1
0
2
1
0
2
1
2
2
1
1
1
0
2
0
2
1
1
1
1
0
2
0
0
1
1
3
0
1
1
1
0
2
1
0
0
2
1
2
1
0
1
0
1
0
3
1
1
1
2
1
1
0
2
0
1
0
2
0
0
0
2
1
0
1
0
2
1
1
1
0
1
1
0
1
1
2
1
2
0
1
1
1
1
1
1
1
1
2
1
0
1
1
0
1
0
1
0
2
1
1
0
1
1
1
1
1
2
1
2
2
0
0
0
2
1
1
1
1
1
2
1
1
1
1
1
0
1
1
1
0
0
2
2
1
0
1
1
0
1
0
1
1
2
2
2
0
0
2
2
1
1
0
1
1
1
0
1
1
1
1
1
1
1
1
0
1
1
2
1
1
2
1
0
1
0
1
1
1
1
1
1
1
1
2
2
2
1
1
1
2
2
1
0
1
2
1
1
2
1
0
0
0
1
0
1
0
1
2
1
2
1
1
0
0
1
0
1
0
2
1
1
1
1
2
1
1
1
3
0
1
0
2
0
0
1
0
1
1
2
1
0
1
1
1
0
2
1
2
1
1
1
1
2
1
1
1
2
1
2
1
2
2
2
2
1
1
1
1
1
1
0
0
2
0
1
3
2
1
1
1
1
0
1
1
1
1
1
0
1
1
0
2
0
0
0
0
1
1
1
0
2
1
1
2
3
0
0
1
0
1
1
0
1
0
1
0
2
0
1
1
2
1
1
2
0
2
0
0
1
2
1
1
1
2
2
0
2
1
0
1
1
0
1
1
1
3
0
0
1
1
1
0
0
1
1
0
1
0
0
1
0
1
1
1
0
2
2
1
1
1
2
1
1
2
1
1
1
1
1
2
1
1
4
1
0
0
0
2
2
1
0
1
1
1
2
2
0
1
2
2
1
1
0
0
0
0
1
1
1
0
1
0
2
2
1
1
2
2
1
1
1
1
1
2
1
0
1
0
0
2
0
1
1
1
2
1
2
0
1
1
1
1
1
1
1
0
1
0
0
1
1
1
1
1
1
2
3
1
0
0
1
1
2
1
0
0
2
0
1
1
2
1
1
1
1
1
2
0
2
1
2
1
0
0
1
0
2
1
1
1
2
3
1
2
1
2
1
1
0
0
0
1
1
0
0
1
2
1
1
1
0
1
2
1
1
2
1
1
1
0
2
1
4
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
0
2
1
0
1
1
0
1
1
2
0
2
3
2
1
1
1
1
2
0
1
0
0
2
1
2
3
0
3
1
0
1
3
0
2
1
2
1
0
0
2
2
1
1
1
1
0
0
1
1
2
1
0
1
1
2
1
0
1
3
0
0
1
2
0
1
1
1
0
1
1
0
0
0
1
0
2
1
2
1
2
2
0
0
1
0
0
1
1
0
2
1
1
2
1
1
1
1
1
2
2
1
0
0
0
0
0
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
2
0
1
0
1
1
1
1
0
1
1
1
0
1
1
2
0
0
2
2
2
0
0
1
0
2
0
1
2
1
1
0
1
1
1
0
0
0
2
1
1
0
1
1
0
0
2
0
0
0
1
2
2
1
1
2
1
2
1
1
0
0
1
1
2
0
1
2
1
0
0
2
1
2
2
1
1
2
1
1
1
0
1
1
1
2
3
0
0
1
2
2
2
1
1
1
1
0
3
2
0
1
1
2
0
1
0
1
0
0
2
2
1
0
2
1
0
1
1
0
2
1
0
1
1
1
1
0
1
0
1
1
2
1
0
1
2
1
0
0
1
0
1
1
2
1
2
2
2
0
1
0
0
2
0
2
0
1
1
0
1
1
0
1
1
2
0
1
0
2
0
1
0
0
0
0
1
0
0
2
1
2
1
0
1
1
2
2
1
1
0
1
0
1
0
1
1
0
2
1
1
1
1
1
0
2
0
1
0
1
0
0
0
1
1
1
0
0
0
1
1
1
0
1
2
1
1
1
0
1
1
1
5
2
1
0
0
1
1
0
0
1
0
1
1
0
0
0
1
1
1
1
0
0
0
1
1
0
1
2
2
1
2
1
0
1
0
1
1
1
0
0
1
0
0
2
1
2
1
1
1
0
0
3
1
2
2
2
1
1
0
1
0
0
0
2
2
1
1
2
2
2
0
2
1
2
1
1
0
2
1
1
1
0
1
1
0
1
1
0
0
1
1
1
2
0
2
0
1
1
1
0
0
0
1
1
1
1
2
2
0
1
2
3
2
2
0
1
2
1
1
2
1
0
1
2
1
1
0
2
1
0
1
0
1
1
1
1
2
1
1
2
2
1
1
0
0
0
2
1
2
1
1
0
0
0
0
1
1
1
1
1
0
1
1
1
2
1
1
1
2
1
1
0
0
1
1
2
1
0
0
0
0
0
1
1
1
1
1
2
1
1
1
1
1
2
0
1
1
1
1
1
1
2
1
1
0
1
1
1
1
0
2
2
1
1
0
0
0
1
1
1
0
1
1
1
2
1
0
0
1
1
0
0
0
2
1
1
2
1
1
0
1
0
0
2
1
0
1
0
1
1
1
1
1
0
1
1
2
1
0
0
3
2
1
2
1
1
1
3
1
2
1
0
2
1
1
1
2
1
1
2
0
2
1
2
0
1
1
1
1
0
0
1
1
1
0
1
1
2
1
0
2
1
1
0
0
1
0
1
0
1
2
1
1
1
1
0
0
0
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
2
1
2
2
1
0
1
1
1
1
0
0
1
0
2
2
0
1
2
0
1
0
4
1
2
1
2
1
0
2
1
3
0
2
2
1
2
0
1
1
2
0
1
1
2
1
2
1
0
1
0
1
1
0
1
0
0
1
1
1
2
1
0
1
1
1
1
0
0
0
0
1
2
0
2
2
1
0
0
0
0
1
0
2
1
2
0
1
1
1
0
0
2
0
1
1
1
1
0
1
0
1
1
1
2
1
1
0
0
3
0
0
1
1
2
0
0
0
2
0
1
1
1
0
4
0
0
1
1
1
0
0
1
2
2
0
1
1
1
1
1
0
0
1
1
0
0
0
1
1
2
1
0
1
1
1
1
1
2
2
2
1
2
1
2
0
1
2
1
1
1
1
1
2
2
1
0
1
1
1
0
1
1
1
0
1
0
2
1
2
2
1
1
1
0
1
1
0
1
0
1
1
1
1
1
0
2
0
2
0
2
1
0
1
1
0
2
1
2
2
0
1
1
0
1
1
1
1
0
1
0
1
0
2
0
1
0
0
1
1
0
1
2
0
2
2
1
1
1
2
0
0
2
2
1
1
1
1
1
0
1
0
2
2
2
0
1
1
1
0
1
0
2
0
2
0
1
1
0
0
2
0
1
1
1
0
0
1
2
1
1
1
1
1
0
2
2
1
1
1
0
1
1
0
1
2
1
2
3
1
2
1
1
1
2
2
0
0
1
2
2
1
2
1
1
0
0
1
0
0
1
1
1
1
1
1
1
0
2
0
1
0
1
0
1
0
1
2
2
2
0
0
1
1
0
1
2
1
1
1
0
1
1
1
1
2
0
1
0
0
1
1
0
1
2
2
2
0
0
1
1
1
0
1
0
1
2
0
2
1
0
1
1
1
1
2
1
2
1
1
1
1
2
0
2
1
2
0
1
2
1
1
0
3
0
1
1
1
1
1
1
1
0
2
2
0
0
2
1
1
1
1
0
3
0
2
2
0
0
1
1
2
0
1
1
1
0
0
1
1
0
1
1
1
2
1
1
1
1
1
0
2
1
0
1
1
2
0
1
2
1
0
1
0
0
1
2
0
2
2
1
1
0
1
1
0
1
1
2
1
0
1
2
1
1
2
2
1
1
1
0
1
1
0
2
0
1
2
1
2
0
0
2
1
2
2
1
0
1
2
2
1
1
1
2
2
0
0
2
1
1
1
1
0
1
0
0
2
1
1
1
0
1
2
2
1
0
0
1
0
2
1
0
1
2
0
1
2
1
1
1
2
2
2
1
1
2
2
1
0
0
0
2
2
2
2
1
1
0
0
0
1
2
1
1
2
1
0
1
1
2
1
2
1
2
1
1
2
1
1
2
1
1
0
2
0
0
1
2
0
0
1
0
2
1
1
1
2
0
2
2
1
2
1
0
2
1
1
2
0
1
2
1
1
2
2
1
2
1
2
2
1
0
0
1
0
0
2
0
1
0
1
1
1
2
2
1
0
0
1
1
1
0
0
1
1
0
1
1
0
0
1
0
0
0
1
1
1
0
2
0
2
2
1
0
1
2
0
1
1
0
0
1
2
0
3
1
2
1
1
1
1
0
2
1
1
1
0
1
1
0
0
2
2
1
0
0
2
1
1
1
1
2
1
2
1
1
1
1
1
0
2
1
1
0
2
1
0
2
2
2
2
1
2
2
1
0
1
2
0
1
2
1
1
2
0
1
1
0
0
0
0
2
1
2
1
1
1
1
0
0
1
1
1
1
1
0
1
0
1
0
1
0
0
0
1
0
0
2
0
1
2
2
1
1
0
0
0
1
1
1
1
1
1
1
1
0
2
1
1
1
1
1
1
0
3
0
1
1
1
1
1
0
0
0
1
0
1
0
0
1
0
1
1
1
0
0
1
2
1
1
1
1
2
0
1
0
2
0
1
0
1
1
0
1
1
0
0
1
0
1
1
1
0
1
1
1
0
1
2
1
2
2
2
1
2
0
1
0
0
0
2
1
0
2
1
1
1
1
1
0
1
1
0
0
1
0
0
1
1
1
2
0
2
1
2
1
1
0
2
1
1
2
1
1
1
0
1
1
1
1
0
1
2
0
1
1
2
2
1
1
0
1
1
0
1
1
1
2
2
1
0
3
2
1
0
1
0
1
1
2
1
1
2
1
2
1
2
1
1
2
1
2
1
1
1
1
1
0
1
1
1
1
1
0
0
0
1
1
2
1
1
1
1
1
1
2
2
0
1
0
1
1
0
1
2
1
1
1
1
1
1
1
1
1
2
2
2
1
2
1
2
2
3
1
1
0
0
1
1
1
2
1
1
2
0
0
1
1
2
0
1
1
1
2
1
1
0
1
1
1
1
0
1
1
1
1
1
1
0
1
0
1
1
0
2
1
0
0
1
0
1
1
0
2
1
1
1
0
1
2
2
0
2
1
1
1
1
2
0
4
1
2
1
1
1
0
0
1
1
0
1
2
1
2
0
0
0
2
0
0
0
2
0
1
1
1
0
1
1
1
3
2
0
1
1
0
2
1
1
2
1
0
1
2
2
1
0
0
0
1
0
1
2
0
2
1
2
2
1
1
0
0
2
0
1
1
1
1
0
1
1
2
2
1
0
0
3
1
0
2
1
1
2
0
1
2
0
0
1
1
1
1
1
1
0
1
0
1
1
1
1
1
1
0
0
2
0
2
1
0
2
0
1
0
1
1
0
1
2
1
0
1
1
1
1
2
1
1
2
1
1
2
1
1
2
0
0
1
1
1
0
1
1
1
1
0
2
1
1
0
0
2
1
2
1
1
1
0
0
1
0
1
1
2
1
0
1
1
0
2
0
0
0
2
0
1
1
0
1
1
1
0
1
1
0
1
1
0
1
1
0
1
1
1
1
1
1
1
1
0
1
0
2
1
1
2
2
2
1
2
1
1
1
1
1
2
1
1
1
2
0
1
1
1
1
1
1
1
1
0
1
1
1
2
0
1
0
0
1
1
2
1
2
2
1
1
0
1
1
2
2
0
2
0
2
0
2
1
1
1
1
1
1
0
0
1
1
1
1
1
0
1
1
1
0
1
1
1
0
1
2
2
2
2
1
0
2
0
2
0
1
1
1
0
1
1
2
1
1
0
0
2
1
0
0
0
1
0
0
2
1
0
1
0
0
2
1
0
2
1
2
0
1
2
0
1
1
0
2
1
2
1
1
1
1
0
1
1
3
1
2
1
2
1
2
1
1
2
1
1
0
1
1
1
0
1
2
2
0
0
0
0
1
1
1
3
3
2
0
1
2
0
0
0
1
1
2
0
0
0
2
0
0
1
1
1
2
1
0
1
1
1
1
0
2
0
1
2
1
2
2
1
0
2
1
0
0
2
1
1
1
0
2
2
1
0
2
0
2
1
2
0
1
1
2
1
1
1
1
1
1
0
0
0
1
0
1
1
2
1
0
2
0
0
1
1
1
1
1
1
1
1
1
1
1
3
0
3
1
2
2
1
0
1
1
0
0
2
1
0
1
0
2
1
2
0
0
1
1
1
1
0
2
0
1
1
1
0
0
1
0
1
1
1
1
2
1
1
2
1
2
0
1
2
0
2
1
1
2
1
0
2
1
1
2
1
0
2
0
0
0
1
1
1
0
0
0
0
1
1
2
1
1
0
0
2
1
0
0
1
1
0
0
1
1
1
1
1
1
1
2
0
1
0
1
0
1
2
1
1
2
1
1
1
2
2
0
0
0
0
2
2
1
2
1
1
2
2
0
0
1
1
1
0
2
0
2
2
1
1
2
2
1
1
1
1
1
2
1
1
0
1
2
0
1
0
2
0
1
2
2
1
2
0
1
1
1
1
2
1
2
0
0
0
1
0
0
1
0
1
1
1
0
1
1
2
1
0
2
1
1
0
2
0
1
2
1
0
1
1
1
0
2
0
1
0
0
2
0
2
1
0
1
0
1
2
0
1
1
1
1
0
2
1
1
1
0
1
2
1
0
1
1
2
1
2
0
1
1
1
1
2
2
1
1
0
0
2
2
2
0
1
1
1
1
1
1
2
2
1
2
1
0
1
0
1
1
1
2
1
2
0
1
0
0
0
0
1
0
1
1
1
1
1
0
0
1
0
2
0
2
2
2
1
1
2
1
1
1
1
0
1
1
2
0
1
0
2
2
1
1
0
1
1
0
1
2
2
0
1
2
0
0
2
2
1
2
1
0
1
1
2
0
0
0
1
1
0
2
1
2
1
1
2
1
1
2
2
1
2
1
0
0
1
1
0
0
1
0
0
1
1
1
0
0
1
2
1
1
1
1
1
1
2
1
1
2
1
2
0
1
1
1
1
0
2
1
0
1
0
1
2
0
1
0
1
1
0
1
1
1
1
0
1
1
0
2
1
2
2
2
0
0
0
2
1
1
0
1
1
1
0
1
0
1
2
0
1
1
0
1
0
1
2
1
1
1
1
1
0
2
0
1
1
2
1
1
0
1
1
1
1
2
3
0
1
1
2
0
1
2
1
1
1
1
0
1
0
1
0
1
2
1
1
1
2
2
0
1
1
1
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
0
1
1
0
1
2
2
1
1
1
1
1
1
0
0
1
2
2
1
1
0
1
1
1
1
2
1
2
1
1
0
1
1
1
2
0
0
1
2
0
1
1
1
2
2
1
1
1
0
2
1
1
2
2
2
1
1
3
1
1
1
1
0
1
2
4
0
0
0
0
1
2
1
1
1
2
1
1
1
1
1
2
1
2
1
2
1
0
1
1
2
0
0
1
2
0
2
2
1
2
2
1
0
1
1
2
1
1
0
2
0
1
1
1
2
2
2
1
1
1
1
1
1
1
1
1
2
1
2
0
2
0
0
0
2
1
1
2
0
1
1
1
1
0
1
2
1
1
2
1
0
0
1
1
1
1
1
1
1
0
0
0
1
1
1
2
1
2
2
0
0
1
1
0
1
0
0
2
1
2
0
2
0
1
1
0
0
2
1
0
1
0
0
0
2
1
0
0
1
1
2
1
0
0
0
0
1
0
2
0
0
1
0
1
1
1
1
1
2
1
2
1
4
2
1
1
0
2
0
1
1
2
2
2
1
0
3
0
1
1
1
1
1
2
1
1
1
2
2
0
1
2
1
1
2
1
0
1
2
2
0
0
1
1
1
2
0
1
2
0
1
1
1
1
1
2
0
1
1
0
0
0
1
0
0
1
1
1
1
1
0
2
0
1
1
1
1
1
2
0
0
1
0
2
0
0
1
0
0
5
1
1
0
1
0
2
2
1
1
1
2
2
1
1
1
0
1
1
1
0
1
0
0
1
2
1
1
1
1
0
1
1
0
2
1
1
1
1
3
1
1
1
0
0
2
0
1
1
1
0
1
1
0
1
0
1
2
1
0
0
1
1
1
1
0
2
0
2
1
2
2
1
0
1
0
2
1
0
2
1
1
0
1
0
1
1
1
1
1
1
0
2
1
2
1
2
2
2
0
0
1
1
2
1
1
0
0
1
0
0
1
0
2
0
2
2
2
0
1
0
1
1
1
0
1
1
0
0
1
1
1
1
1
1
0
2
2
2
0
1
0
0
2
2
1
1
1
1
2
1
1
1
0
0
2
3
1
0
1
1
2
0
2
1
1
1
1
0
1
1
1
0
2
0
0
1
1
1
0
2
0
2
2
2
0
0
1
1
0
0
1
3
1
3
3
0
1
2
2
0
2
2
1
0
1
1
0
1
1
2
0
0
1
2
1
1
1
1
1
2
1
1
1
2
1
0
1
2
0
1
2
0
1
0
1
0
1
0
2
2
0
0
1
2
0
0
1
2
1
1
2
1
2
1
0
2
1
1
2
1
1
0
0
0
1
0
1
1
1
1
1
1
0
2
0
0
2
1
3
2
2
0
1
1
1
1
1
1
1
1
0
1
1
2
0
3
0
2
1
1
0
1
1
1
0
1
1
2
1
1
1
1
2
0
1
1
1
0
1
1
2
2
1
2
2
1
2
1
0
1
1
1
1
1
1
2
1
1
1
1
1
0
0
0
1
1
0
0
1
0
0
1
1
0
1
2
2
1
1
2
1
2
0
0
0
0
1
1
2
2
0
1
0
1
0
2
0
0
0
0
1
1
2
1
1
2
2
1
2
1
1
1
0
0
0
0
0
0
1
1
1
1
0
0
1
1
1
0
2
2
0
0
1
1
1
0
1
1
1
1
1
2
2
0
0
0
2
2
1
1
2
4
1
1
2
0
1
1
1
1
2
0
2
1
1
1
0
1
0
1
1
0
1
1
1
0
1
0
2
1
1
2
0
1
1
0
1
1
2
1
1
2
1
1
0
1
1
0
1
2
0
1
1
0
1
1
1
2
1
1
1
2
1
0
1
2
2
0
1
2
1
2
2
1
2
2
1
0
1
1
0
1
2
1
2
1
1
1
0
2
0
1
1
1
1
1
1
2
2
2
0
1
1
0
2
1
1
1
0
1
1
1
1
0
1
0
2
0
0
1
2
1
0
2
1
1
1
1
0
1
2
0
0
0
1
1
1
2
1
1
1
1
0
1
2
2
1
0
1
0
2
0
1
1
0
1
1
1
1
1
2
1
1
0
1
0
2
1
1
0
0
1
2
1
1
0
1
2
2
0
1
1
2
0
2
1
2
1
1
2
1
1
1
1
1
3
0
0
1
1
0
1
1
0
0
2
1
1
2
1
2
2
2
2
1
0
2
1
1
0
1
1
0
3
1
1
2
1
2
2
1
0
1
2
1
2
0
1
2
2
1
0
2
0
0
1
1
2
1
1
0
0
1
2
0
0
0
1
2
2
1
1
1
2
1
1
0
1
0
0
0
0
0
2
1
2
1
1
1
1
1
1
1
1
1
1
0
2
2
1
0
1
1
1
1
0
0
1
1
1
1
1
1
0
1
4
1
2
1
2
1
1
1
0
1
1
2
0
0
1
0
1
1
1
0
1
1
0
1
1
2
1
2
2
2
0
0
0
1
1
2
0
0
1
2
2
2
2
0
1
2
1
0
1
0
1
1
1
0
1
1
1
2
1
1
0
1
2
1
1
1
1
2
1
1
1
1
2
2
2
0
1
1
1
1
2
1
0
0
1
6
1
1
0
1
1
1
2
1
1
1
2
2
1
0
0
1
1
1
1
0
1
1
1
1
1
2
1
4
1
2
0
2
1
2
0
2
0
2
2
1
1
1
0
1
1
0
2
0
1
1
0
2
0
1
2
0
1
0
2
2
1
1
0
1
1
1
1
0
1
0
1
0
1
0
1
1
1
1
0
1
1
1
2
2
1
2
0
0
1
2
1
0
0
0
0
1
1
1
1
1
2
2
2
1
0
0
2
1
1
1
1
1
1
0
0
1
0
1
1
1
2
0
0
1
0
1
1
1
2
1
0
2
1
0
1
2
2
0
0
0
1
0
0
0
1
2
2
2
2
1
2
2
0
1
1
0
1
1
1
0
0
1
1
1
0
2
2
2
1
1
2
1
2
1
1
1
2
0
1
0
2
1
0
1
1
2
1
0
1
1
1
1
1
0
2
1
0
1
1
2
0
1
1
1
0
2
1
1
10
1
2
1
1
1
0
1
0
1
2
0
1
2
1
2
1
1
1
2
2
0
1
1
1
1
0
1
1
1
0
1
1
1
1
2
1
1
1
2
0
1
0
2
1
1
0
1
0
2
1
0
2
0
1
0
1
1
4
0
0
1
1
1
1
1
1
1
1
0
2
0
1
0
2
1
2
1
1
1
2
2
1
1
2
1
1
0
1
1
0
0
1
2
1
2
0
2
1
0
0
1
1
0
1
2
1
1
2
1
0
1
1
1
1
0
0
0
1
1
2
1
1
1
1
1
1
1
1
2
2
0
1
1
1
3
1
2
2
1
0
2
2
0
0
1
1
2
1
1
1
1
1
2
1
0
1
1
1
1
1
0
0
1
1
1
1
0
1
1
2
1
1
1
1
0
0
1
1
1
1
0
1
1
2
1
1
1
0
1
1
0
2
0
0
1
1
2
2
1
1
1
2
0
2
1
1
0
1
1
0
0
1
1
1
1
2
0
1
2
1
2
1
1
0
1
0
1
0
0
0
1
1
0
0
2
2
1
0
1
1
1
2
2
1
0
1
0
1
0
2
2
1
1
1
1
1
2
1
2
0
1
1
0
2
0
0
1
1
1
0
1
1
1
1
2
1
1
2
1
1
1
0
0
1
1
1
2
1
1
1
0
1
0
0
2
1
0
0
2
1
2
0
1
1
1
1
2
0
1
1
2
2
1
0
0
2
1
1
1
2
1
1
1
0
1
1
1
1
0
1
2
1
1
1
2
1
1
1
2
2
1
1
2
1
1
1
1
2
1
1
1
1
1
1
3
1
1
2
2
1
1
1
0
2
2
2
1
0
2
1
6
2
2
1
1
1
1
1
2
1
0
1
1
1
1
0
1
0
1
1
1
2
0
0
0
0
1
1
0
0
0
3
2
2
0
2
1
2
0
2
2
0
2
2
1
0
0
1
1
1
0
1
1
1
0
2
2
0
1
2
1
1
1
1
1
2
1
1
1
1
2
1
2
1
0
1
2
1
1
1
1
1
0
1
2
1
1
1
0
0
0
0
2
1
2
1
1
1
0
0
1
2
1
0
1
1
1
1
4
1
1
2
1
0
0
1
0
1
1
2
1
0
1
1
0
1
1
2
2
1
1
2
0
1
2
1
2
0
1
2
1
1
1
2
0
1
1
2
2
1
1
0
2
1
1
1
0
0
1
1
1
2
0
1
1
1
1
1
1
1
0
2
0
1
1
2
2
0
1
1
1
0
0
0
1
1
0
0
0
1
1
1
2
1
1
1
0
0
1
1
1
2
1
0
0
1
3
1
2
2
1
1
1
1
1
1
2
2
1
2
0
1
1
0
1
1
0
2
1
0
0
1
1
1
0
1
0
1
1
0
2
0
1
1
1
0
1
2
0
0
1
2
1
1
2
1
0
0
1
0
0
0
0
1
0
1
1
1
0
0
2
2
1
0
0
0
2
1
2
2
1
1
1
1
1
2
1
2
0
1
1
1
0
0
2
1
2
0
0
2
0
1
0
2
2
2
1
0
0
2
2
1
2
1
1
1
0
2
0
1
1
2
1
0
2
1
1
0
1
1
1
0
1
2
0
1
0
0
1
2
0
0
1
1
1
0
0
1
0
0
1
1
0
2
0
1
1
1
2
1
1
1
1
2
1
1
2
1
1
3
1
1
2
0
1
2
2
0
1
3
0
1
1
0
1
1
1
2
3
2
0
2
1
0
1
1
1
1
1
0
1
1
1
0
2
1
2
1
1
0
2
0
0
1
0
1
1
2
1
0
2
1
1
0
1
2
1
1
1
2
0
0
1
2
1
2
1
1
0
0
1
1
0
0
0
2
0
1
2
1
0
2
0
2
1
1
1
0
2
0
1
1
2
2
1
0
1
2
1
2
2
1
2
1
2
1
1
0
1
0
2
2
1
1
1
1
1
0
1
1
1
1
1
1
4
2
1
1
2
1
0
2
1
1
1
1
1
2
1
1
1
2
1
1
1
0
2
1
1
0
1
0
1
1
0
1
2
0
0
1
1
2
0
1
2
1
1
2
1
1
1
0
2
1
1
2
0
2
1
2
1
0
1
1
1
0
2
2
1
1
0
0
2
1
2
1
2
2
1
0
0
0
1
1
0
1
1
1
1
0
2
1
2
2
1
0
1
3
1
1
2
1
1
1
1
0
1
1
1
2
1
0
1
0
0
1
0
1
0
1
1
0
1
0
1
0
1
1
1
1
0
0
1
2
1
0
0
1
0
1
2
1
2
1
1
1
2
2
1
1
1
1
1
1
1
0
1
1
2
1
1
2
1
1
0
1
0
0
1
1
4
1
1
2
0
0
0
1
0
2
1
0
2
0
1
1
0
2
1
1
2
2
1
0
1
1
2
0
1
1
1
1
2
0
1
2
2
2
1
1
1
1
1
2
2
1
1
1
1
2
1
1
0
2
1
0
0
1
2
1
2
1
1
1
0
0
1
1
2
2
0
2
2
1
1
0
0
0
1
1
1
2
1
1
1
1
2
1
2
0
1
2
2
1
1
1
1
2
1
2
0
1
1
1
1
1
2
1
0
0
3
1
1
1
2
1
1
1
0
1
0
2
1
1
2
1
1
1
0
1
2
2
1
1
0
1
0
0
1
1
1
2
2
2
2
2
1
1
1
2
1
1
1
1
1
2
1
1
2
1
1
0
2
0
0
2
0
0
1
1
0
2
2
1
2
2
2
1
2
2
1
0
0
1
1
2
1
2
1
2
1
0
1
0
1
0
0
1
2
1
0
0
1
1
1
0
1
1
1
2
1
1
0
1
1
1
1
1
2
2
1
0
0
0
1
0
2
1
1
0
2
2
1
1
1
1
1
0
2
2
1
2
0
2
2
1
0
1
2
1
0
2
1
2
0
2
0
1
2
2
2
0
1
1
1
2
2
2
1
1
1
0
1
1
1
1
0
1
2
1
1
1
1
1
0
1
1
1
0
2
1
1
1
0
1
1
2
1
1
1
0
1
0
1
1
1
2
1
1
1
2
0
1
1
1
1
0
1
1
1
1
1
1
1
0
1
1
0
1
2
2
2
1
0
2
0
1
1
3
0
1
1
0
0
2
2
0
1
0
1
0
0
1
0
0
0
0
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
0
1
1
1
1
0
1
1
1
0
0
1
0
0
1
0
1
0
1
1
1
1
1
1
2
2
1
0
0
0
0
1
4
0
2
2
1
0
1
2
1
0
1
2
0
1
1
1
0
2
1
1
0
0
1
0
2
1
0
2
1
0
1
1
1
1
2
1
0
1
1
1
1
1
1
2
1
1
3
2
1
0
0
0
1
1
0
1
1
1
2
0
1
1
1
1
1
1
1
2
0
1
1
2
2
0
1
2
2
2
0
1
0
1
0
2
1
1
1
2
1
1
2
1
1
1
0
1
2
1
2
1
1
2
1
1
0
1
1
1
0
1
1
1
1
0
2
1
0
2
1
2
1
1
0
1
0
2
2
2
0
0
1
1
1
0
0
1
2
1
1
1
1
1
1
1
1
2
1
1
0
1
1
0
1
2
1
1
1
0
0
2
2
0
0
2
1
0
2
2
2
0
1
0
0
2
1
1
2
1
1
0
1
2
1
1
0
0
2
1
1
1
1
1
0
0
1
0
0
2
1
1
0
0
1
2
0
1
1
0
0
0
1
2
1
1
2
0
1
1
0
1
1
0
2
0
1
1
1
1
1
1
0
0
1
1
1
0
2
1
1
3
1
1
1
1
0
2
1
1
1
0
0
1
1
2
1
1
1
1
1
1
0
1
1
2
2
1
0
0
0
1
2
1
1
1
1
1
0
1
0
0
0
0
1
1
0
1
1
2
1
1
0
0
2
2
2
1
0
1
1
2
2
3
1
0
1
0
1
1
1
2
0
0
1
2
2
3
0
1
5
2
1
1
1
0
2
2
1
1
2
1
1
0
1
1
2
0
0
1
0
1
1
4
0
1
2
1
1
1
1
1
1
1
2
0
1
1
2
1
1
1
1
1
1
1
1
1
2
0
3
0
0
1
1
0
0
1
2
0
1
1
1
1
2
2
3
0
4
1
0
2
1
2
1
1
1
1
1
1
2
1
1
1
2
2
2
0
1
0
1
2
1
2
1
2
1
1
2
1
0
2
1
2
0
1
0
1
1
1
2
0
1
0
1
1
1
0
1
0
1
2
0
1
1
2
0
2
0
0
0
0
0
0
0
1
1
2
1
0
0
1
1
3
1
2
2
1
0
1
1
1
1
0
1
0
0
1
1
2
1
1
0
2
2
1
0
1
2
1
1
1
2
1
1
2
2
1
1
2
0
0
2
1
1
2
0
1
2
0
2
0
1
1
1
1
1
2
2
2
1
0
1
2
2
0
0
0
1
1
1
0
1
0
1
1
1
1
2
0
1
1
2
0
2
2
2
0
0
2
1
1
1
0
1
1
2
0
0
0
2
2
1
0
1
0
0
1
1
1
1
1
1
0
2
1
1
1
1
1
0
0
0
1
1
1
1
2
0
1
2
1
2
1
1
0
0
1
1
1
1
0
2
1
0
1
1
1
1
0
0
0
1
0
1
1
0
2
0
2
1
1
1
1
1
2
1
0
1
2
1
1
2
1
1
0
1
2
0
1
2
1
0
1
2
1
1
1
2
1
1
0
1
0
1
0
1
0
1
1
0
1
2
2
2
1
1
1
1
0
1
2
1
1
2
1
0
1
1
0
0
1
1
1
1
0
0
0
0
1
1
0
0
1
2
1
1
2
0
1
1
0
2
1
1
1
2
2
0
2
2
0
1
0
2
1
1
1
1
2
2
2
0
2
1
1
1
1
1
2
1
2
0
2
0
2
1
1
1
0
2
1
0
2
1
2
2
2
1
1
0
1
1
1
2
0
1
1
1
1
2
1
1
1
0
0
2
0
1
0
0
4
1
1
1
1
1
2
0
1
2
2
2
0
2
0
2
1
1
2
1
1
2
1
1
0
1
0
1
1
0
2
0
1
1
2
0
0
0
1
0
1
1
0
1
2
1
1
0
1
2
1
2
2
1
1
1
1
1
1
0
1
0
1
0
1
1
0
1
2
3
1
1
1
0
1
0
1
0
1
1
0
1
1
1
2
2
0
2
1
1
1
0
1
0
0
1
1
1
2
0
1
2
1
1
1
1
1
1
2
0
1
1
2
1
1
1
1
0
2
1
0
2
1
0
2
0
2
2
1
0
0
0
2
1
0
2
2
0
2
0
2
1
1
1
1
2
1
1
6
0
0
1
1
1
1
1
1
0
2
1
0
1
0
0
0
2
0
1
1
2
0
1
2
0
1
0
1
3
1
1
1
1
1
1
2
0
1
1
1
1
0
2
1
1
0
1
2
1
3
1
2
1
1
2
1
0
0
1
0
1
1
0
2
1
1
0
0
0
1
2
2
2
2
1
1
1
0
2
1
2
2
0
2
0
1
1
1
2
0
2
1
1
1
0
0
0
0
2
2
2
1
0
1
1
2
1
2
1
0
1
1
1
2
1
1
3
0
2
0
1
0
0
1
1
0
1
1
1
0
0
2
2
1
0
1
1
1
1
0
3
1
1
2
0
1
2
2
0
1
1
2
0
1
0
2
0
1
2
0
2
1
2
1
1
2
1
2
1
1
0
2
2
3
2
0
0
1
2
1
0
0
1
2
1
3
1
1
1
0
0
1
2
1
2
0
1
0
1
0
2
1
1
1
1
1
2
0
1
1
0
1
1
0
0
2
0
1
1
2
2
1
1
0
0
1
2
2
1
1
1
1
1
3
1
2
0
2
1
0
0
1
2
3
1
1
1
1
3
2
1
2
0
4
0
0
1
1
3
1
1
0
0
0
0
1
0
0
1
1
0
2
2
0
0
1
1
1
1
0
1
2
2
0
1
1
1
1
0
0
1
0
0
1
0
1
1
1
1
1
1
2
0
1
1
1
1
0
2
1
2
1
1
2
1
2
1
1
1
0
1
1
2
0
1
1
2
0
1
1
1
2
2
1
1
1
0
2
1
0
1
2
2
0
1
1
1
2
0
2
2
0
1
0
2
1
2
0
1
1
0
2
2
2
2
1
1
1
1
1
1
0
2
1
1
1
1
0
0
2
2
1
3
1
1
1
1
1
1
2
1
1
1
2
0
1
2
1
1
0
0
0
2
1
1
0
0
1
1
2
1
1
2
1
2
0
2
1
0
0
1
1
1
3
1
1
1
2
2
1
1
2
2
2
1
2
0
2
1
1
1
1
0
1
1
0
1
3
1
0
1
1
0
0
0
2
1
1
0
0
1
1
1
0
2
0
1
1
0
1
1
1
1
1
1
0
0
1
0
2
1
1
1
0
1
1
1
0
1
1
0
2
1
0
1
0
1
1
2
0
0
1
1
1
1
1
0
1
1
0
1
0
0
1
1
3
0
1
2
1
0
1
1
1
0
1
1
1
2
1
1
1
1
1
0
2
1
1
1
1
2
1
2
1
1
3
2
2
1
2
0
1
1
1
1
1
1
0
1
1
1
1
2
2
1
1
0
1
1
2
2
1
1
3
0
2
1
1
2
1
1
2
1
1
1
0
0
1
1
1
2
0
0
0
1
2
0
1
0
0
1
1
1
1
1
0
2
0
1
0
1
1
1
4
1
1
0
1
1
1
0
2
0
0
1
0
1
1
1
2
1
1
1
1
0
2
0
1
0
0
0
2
1
1
0
0
0
2
0
0
1
0
0
1
1
0
3
1
1
1
1
0
0
2
1
2
0
0
1
0
1
2
2
1
0
1
3
1
0
0
0
1
1
1
1
0
1
0
1
1
1
2
1
1
3
2
0
2
0
1
1
1
1
1
0
1
0
0
0
1
0
2
0
1
1
1
1
1
0
2
2
1
0
1
1
1
1
2
1
1
3
2
1
2
1
1
2
1
2
2
0
0
1
1
1
1
1
0
1
2
0
2
1
1
1
2
1
2
1
1
0
2
1
1
0
1
1
2
1
2
1
0
1
2
1
1
1
0
0
3
1
0
1
0
0
1
1
1
1
1
2
0
1
1
0
1
1
0
0
1
2
1
0
0
0
2
2
0
1
0
2
1
0
2
1
1
2
2
2
2
0
1
1
0
1
1
1
2
0
1
0
2
3
1
1
0
3
0
0
1
1
1
0
2
0
1
1
1
1
1
1
1
0
1
1
1
2
1
1
1
1
1
1
0
2
1
2
1
0
1
1
2
1
1
1
0
1
1
0
0
1
0
1
1
2
1
1
1
0
1
2
1
2
2
1
1
1
0
1
1
1
1
1
0
0
1
2
1
1
0
0
1
1
2
1
0
0
2
1
0
2
0
1
1
0
1
1
1
1
1
1
0
0
1
0
0
1
1
1
0
1
1
0
1
1
1
1
0
1
1
1
1
1
0
0
1
1
2
2
1
1
1
1
1
2
1
1
0
1
2
0
2
2
2
0
0
2
2
0
1
1
1
1
1
0
1
2
1
0
0
0
0
3
0
0
1
0
1
2
1
1
0
1
1
1
1
0
1
2
2
2
0
1
2
2
1
2
1
0
1
2
2
2
0
0
0
1
0
2
2
1
1
1
0
0
0
2
0
1
1
2
1
2
1
0
1
1
2
1
1
0
1
1
2
1
1
1
2
1
0
2
0
1
1
1
1
0
1
0
0
1
1
1
1
0
1
1
0
2
1
1
1
1
0
2
2
2
1
2
0
1
1
1
0
0
1
1
2
1
2
0
1
0
1
1
2
0
0
1
0
0
0
1
0
2
1
0
1
0
0
1
0
1
1
1
1
0
1
0
1
0
2
0
1
1
0
2
0
0
0
0
2
2
1
0
1
2
0
0
1
1
1
1
0
1
0
2
0
1
0
0
2
1
1
1
0
2
1
1
0
0
1
1
1
0
0
1
0
0
1
1
3
2
2
2
1
1
1
2
2
1
2
2
0
1
0
2
2
0
0
1
0
3
1
0
2
1
0
2
2
1
0
1
0
1
1
0
1
1
0
0
1
1
0
0
1
1
0
0
0
1
0
0
1
2
0
0
1
1
1
1
0
0
2
1
0
3
1
1
1
1
2
2
2
1
2
0
1
0
2
1
1
0
1
1
1
1
0
1
0
0
2
1
0
0
0
1
1
2
0
1
0
2
1
2
1
2
0
2
1
1
0
0
1
1
1
2
2
1
0
0
1
0
1
1
0
0
0
2
1
0
2
1
2
1
0
1
2
1
2
1
0
1
1
1
1
1
0
1
0
2
2
1
0
2
2
0
1
2
0
1
1
1
1
1
2
1
0
0
2
2
1
1
1
1
1
1
2
0
2
0
1
1
1
2
1
1
0
0
0
1
0
1
1
1
1
1
1
1
1
0
1
0
1
1
0
0
1
2
1
1
1
2
2
1
2
1
0
1
2
1
0
1
0
1
1
1
1
1
2
1
0
1
2
1
1
0
0
1
0
1
0
2
1
0
2
0
3
1
0
0
0
1
1
1
1
0
1
1
1
1
0
1
0
2
1
2
1
2
1
1
1
1
0
2
0
1
0
0
1
3
2
2
1
1
1
2
0
0
2
1
1
2
0
0
1
1
1
0
0
1
1
1
2
2
0
0
0
0
1
1
1
1
1
1
0
1
2
1
0
2
1
1
0
2
2
1
0
2
1
0
1
0
0
1
0
0
2
1
1
0
1
1
1
2
1
1
1
1
2
1
1
1
1
0
0
0
1
1
1
0
1
1
1
1
0
2
1
1
2
1
0
1
0
1
1
1
2
1
0
0
1
0
0
1
1
1
1
1
0
2
1
1
1
1
0
1
0
0
1
0
2
1
1
2
0
0
1
0
2
0
1
2
1
1
0
0
1
2
1
2
2
1
1
1
1
0
0
2
2
1
1
1
1
1
2
2
1
1
1
2
1
1
0
2
2
0
0
0
0
0
1
1
2
0
0
1
2
1
0
2
0
1
1
2
1
2
1
1
0
1
1
1
0
0
3
1
1
1
0
2
2
1
1
1
0
1
1
2
0
1
1
1
2
0
1
1
2
1
1
2
1
1
2
2
1
1
1
2
2
1
1
1
2
1
1
1
1
1
1
1
1
0
1
2
1
1
2
0
2
1
1
1
1
0
0
1
2
1
1
2
1
1
2
2
1
0
1
2
1
2
1
1
2
1
1
1
1
2
1
0
1
1
1
0
0
0
1
1
1
2
1
2
0
1
1
0
2
1
0
2
1
1
2
1
2
1
0
1
1
0
1
1
1
2
1
1
1
2
0
1
1
1
1
1
0
1
0
2
1
1
1
1
1
1
2
1
2
2
1
0
2
1
0
1
0
0
1
0
2
1
2
1
2
0
2
1
0
2
0
1
1
0
1
0
0
2
0
1
1
1
0
1
2
1
1
2
1
0
1
2
1
1
2
1
0
1
2
1
1
2
2
0
1
1
2
1
2
1
0
2
2
0
1
1
1
1
1
1
1
1
1
0
1
0
1
0
1
1
1
1
0
1
1
0
0
1
1
0
1
1
2
2
1
0
1
1
1
1
1
2
1
1
2
1
1
2
1
0
0
2
2
0
2
1
1
1
2
2
1
0
1
0
2
1
1
1
1
2
0
1
1
1
1
1
1
1
0
1
0
0
0
2
1
0
1
2
1
1
0
0
0
1
2
1
1
1
1
0
1
1
1
1
1
0
2
0
1
1
0
1
1
1
1
4
0
2
0
2
0
1
2
1
0
2
1
1
1
1
0
0
0
2
1
0
1
1
1
1
2
0
0
2
1
2
1
0
0
1
1
0
1
1
0
1
2
1
2
0
1
2
0
0
0
2
0
1
0
0
2
0
2
1
0
3
1
2
1
1
2
0
0
1
1
1
1
2
2
1
2
1
0
1
1
1
0
2
1
2
1
1
2
0
2
1
0
2
1
0
1
1
1
1
1
0
1
0
2
1
1
1
2
2
1
2
1
0
1
0
1
1
1
0
1
1
0
1
0
1
2
2
2
2
1
2
1
2
2
0
1
1
2
1
0
0
0
0
2
1
2
0
1
2
2
1
0
1
1
1
0
1
1
1
2
2
0
1
1
2
1
1
1
1
2
0
1
1
2
3
1
0
1
1
0
0
2
1
1
2
1
1
1
1
0
0
0
0
0
2
1
1
0
1
2
1
1
1
2
1
1
1
1
2
1
1
2
0
1
1
2
0
2
2
1
1
0
1
0
0
1
1
1
1
0
1
1
1
0
1
2
1
1
2
1
1
1
1
1
0
0
1
2
0
1
2
1
0
1
0
1
2
1
1
1
1
1
0
1
1
1
1
1
1
1
1
2
0
1
1
0
1
1
0
1
1
1
1
2
2
1
0
1
1
1
2
0
1
2
1
0
1
2
0
1
1
0
1
0
1
1
0
1
1
1
1
1
0
0
0
0
0
0
0
1
1
1
1
1
1
1
2
0
0
1
1
1
1
2
1
0
2
0
1
1
1
1
1
0
0
1
1
2
1
2
0
1
1
1
1
0
1
1
1
1
1
1
1
1
1
0
3
1
0
2
1
2
2
1
1
1
2
2
1
1
1
1
1
1
2
1
0
1
2
2
1
1
1
1
1
0
1
1
1
0
1
1
1
1
1
1
1
0
1
1
3
0
1
1
1
0
0
2
2
2
1
1
2
0
1
1
2
1
2
1
2
1
0
1
1
2
1
0
1
0
0
0
1
1
2
2
1
1
0
2
0
2
2
1
1
1
2
1
2
0
2
0
2
0
1
2
0
0
1
1
2
2
2
1
1
1
1
0
0
0
1
1
0
0
0
1
2
1
1
2
2
2
1
1
1
2
2
1
0
1
2
1
2
1
0
2
1
0
0
1
1
0
2
2
0
1
1
1
1
1
2
1
1
0
2
0
0
0
1
2
2
1
0
1
2
0
2
2
0
1
1
0
0
1
2
1
2
1
2
1
0
1
2
2
1
1
1
2
0
1
2
2
2
0
1
2
2
0
1
0
1
0
2
1
2
0
0
2
1
1
0
1
1
1
1
2
1
4
2
1
1
1
1
0
1
1
2
2
1
1
1
1
1
2
0
1
1
1
1
2
2
1
2
2
0
1
1
2
0
1
1
1
1
1
1
1
1
1
1
0
0
1
2
1
1
1
1
1
1
1
1
1
1
0
3
0
2
2
1
1
2
1
1
2
1
2
3
1
0
1
1
2
1
1
1
2
2
1
1
1
3
1
1
0
0
1
1
1
1
1
1
2
1
2
0
2
0
0
1
1
0
1
0
0
1
1
1
0
1
1
1
0
2
2
1
1
2
0
1
1
1
2
1
1
1
2
1
0
0
0
1
1
1
0
0
1
2
1
1
1
1
1
1
1
3
1
1
0
0
0
1
1
1
2
0
0
1
1
0
0
2
1
2
0
1
1
2
0
1
0
1
0
1
1
1
1
2
1
1
2
1
1
2
2
1
0
2
1
2
0
2
1
0
1
2
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
1
1
0
0
1
1
1
1
1
1
2
0
1
1
2
1
1
1
2
1
0
1
4
1
1
2
2
0
1
2
1
1
0
0
0
0
1
1
1
1
1
0
1
0
0
1
1
0
1
0
2
2
2
0
1
1
1
0
2
2
1
1
0
0
2
2
0
2
2
0
0
2
0
1
1
0
1
1
1
1
1
2
2
0
0
1
1
1
1
1
2
1
1
1
1
1
0
0
0
1
1
1
2
1
2
0
0
1
1
1
2
1
0
0
0
0
0
0
1
1
2
2
1
0
2
2
1
0
2
1
1
1
0
1
1
0
1
1
0
0
0
2
0
1
1
0
1
0
2
1
0
2
0
1
1
2
1
0
1
2
0
1
3
1
1
2
1
1
1
1
1
1
0
1
0
1
1
0
0
1
2
4
1
0
0
1
0
0
1
1
1
0
1
2
0
0
0
2
0
1
3
1
0
2
1
1
0
0
1
0
2
2
3
0
1
0
2
0
0
1
1
0
1
2
1
0
0
0
0
1
0
1
1
1
0
1
1
2
1
1
0
0
0
1
0
2
1
1
0
0
2
4
2
0
2
1
1
0
2
0
2
2
1
1
0
1
0
1
1
0
0
1
0
0
0
0
0
0
2
1
0
2
1
2
1
2
0
2
0
1
0
2
1
0
1
1
1
1
1
3
1
0
2
1
0
2
1
0
0
1
2
0
1
1
0
2
1
1
2
0
0
0
2
1
0
0
1
1
2
1
1
1
1
1
1
1
1
1
0
1
2
1
2
0
0
1
1
1
1
1
0
0
2
2
2
1
2
2
1
0
0
0
1
1
1
0
1
1
1
2
2
0
0
1
1
0
1
1
1
1
1
1
0
1
1
1
1
1
1
0
0
2
1
1
1
1
0
1
1
1
1
2
3
1
0
1
0
2
1
1
1
0
0
0
1
1
1
1
2
2
1
2
2
0
2
0
1
2
2
1
0
0
1
1
0
1
1
1
1
1
1
1
0
1
2
2
2
2
0
2
1
0
1
0
2
2
1
2
1
2
1
0
1
1
1
1
1
1
1
2
1
1
1
2
1
1
3
2
1
1
1
1
1
1
1
0
1
2
0
1
1
1
0
0
1
1
1
1
1
1
1
1
1
1
2
0
1
2
1
0
0
0
1
0
1
1
1
2
2
0
2
1
0
1
2
2
1
1
1
1
1
2
1
1
1
1
0
2
1
2
1
1
1
2
1
1
2
1
1
2
1
1
1
1
1
1
1
1
2
0
1
2
1
1
1
1
1
1
2
0
0
1
0
1
1
1
1
0
2
1
0
0
1
2
1
0
2
1
1
0
2
2
0
0
1
2
1
1
0
1
0
1
2
1
2
1
1
1
2
2
0
2
0
0
2
1
0
1
1
1
1
1
1
1
0
1
1
1
1
1
0
1
1
1
0
2
0
1
2
1
0
1
1
2
1
2
1
1
0
1
1
1
0
0
0
2
1
1
1
2
1
1
1
0
1
1
5
1
1
1
1
1
1
1
0
1
1
2
0
1
1
2
1
0
0
1
0
1
1
1
3
1
1
1
2
2
1
1
1
0
1
0
0
1
0
0
3
1
1
0
1
1
1
1
1
1
1
1
0
2
2
2
1
0
1
0
1
1
2
0
1
3
0
2
1
1
1
1
0
2
1
1
2
2
1
2
1
2
1
0
1
1
2
1
1
0
1
2
2
1
0
2
0
0
1
0
1
1
1
2
0
1
1
1
1
1
1
0
0
1
0
1
0
1
0
0
2
1
1
2
0
2
0
0
1
1
0
0
0
2
2
2
1
2
2
1
0
0
1
1
2
1
1
0
1
2
0
1
1
1
1
1
1
1
1
2
0
2
2
1
1
1
1
0
1
0
2
1
2
1
1
0
2
1
1
3
0
0
1
2
1
2
1
2
1
2
1
3
1
1
2
1
1
1
0
1
4
1
0
1
0
0
1
1
0
1
2
2
3
0
0
0
1
1
1
1
0
2
1
0
1
2
2
0
2
1
2
1
0
1
2
1
1
1
1
1
1
1
1
0
1
1
1
0
1
1
2
0
2
1
1
0
0
0
1
0
2
0
1
0
3
0
2
1
0
0
1
1
1
0
1
0
1
0
2
1
1
2
0
2
1
1
0
0
1
0
1
2
1
0
1
1
1
0
1
1
2
1
1
0
0
0
0
1
1
1
1
1
1
0
1
1
2
2
1
0
1
1
1
1
1
0
1
1
2
1
1
1
1
0
1
1
1
1
1
2
1
1
2
0
1
0
1
0
2
1
2
1
2
1
1
1
1
1
0
1
1
1
0
0
0
2
1
1
1
0
1
1
1
1
2
2
1
0
1
1
1
1
1
1
3
1
1
0
1
1
1
0
1
2
1
1
2
0
1
0
1
1
2
0
1
0
0
1
2
1
0
0
2
1
2
0
1
0
0
0
2
2
2
1
1
0
1
0
0
1
2
2
0
2
1
0
1
2
1
1
2
0
0
1
1
0
0
0
2
0
1
1
1
0
1
1
1
1
0
2
1
0
1
1
2
0
1
2
1
1
1
0
1
2
1
1
0
1
0
1
1
0
1
0
2
0
0
0
0
1
1
0
1
0
1
1
1
0
1
1
1
1
3
1
0
0
1
0
0
1
1
2
1
1
1
1
1
0
1
2
1
1
0
1
0
1
3
0
1
2
1
1
1
1
1
2
1
2
0
1
1
1
0
1
1
0
1
1
1
2
0
2
2
1
1
1
0
2
1
1
1
0
1
1
1
1
0
0
1
0
2
1
1
1
2
2
0
2
1
0
2
1
1
0
1
1
1
1
0
1
1
0
2
1
2
2
1
1
1
1
2
1
2
0
0
2
0
0
2
1
1
2
2
0
1
1
0
1
1
1
1
2
2
1
2
2
1
2
1
0
5
1
1
0
0
1
2
0
0
1
0
1
1
0
1
0
2
1
2
0
2
0
1
2
2
1
1
1
2
1
0
0
1
0
2
2
1
1
1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
0
2
0
0
1
1
1
0
1
2
0
0
1
2
0
0
1
0
1
1
2
2
1
1
0
0
2
1
0
1
2
0
1
1
1
0
0
1
1
1
1
0
0
0
0
1
2
2
1
0
1
1
0
1
2
1
0
1
1
1
0
1
0
0
1
0
2
2
2
1
0
0
2
1
4
1
1
0
1
2
1
1
1
1
2
1
2
1
1
1
1
2
1
0
1
0
2
2
1
8
1
2
0
1
2
1
1
0
1
2
0
1
1
2
0
2
0
1
0
1
0
1
1
1
0
0
0
1
0
1
1
2
1
1
2
2
0
1
2
0
1
1
0
1
0
1
0
1
1
2
0
0
1
0
1
1
1
0
0
2
2
1
0
1
2
0
1
2
2
2
0
2
1
0
1
1
0
0
1
1
1
1
1
1
0
1
1
1
0
0
1
1
1
1
0
2
0
2
1
0
2
1
1
1
1
1
1
0
2
0
0
1
1
0
0
0
1
0
0
1
2
1
1
2
1
0
2
2
2
1
0
1
1
0
1
1
1
1
0
1
0
1
2
0
1
2
1
1
1
0
0
1
0
1
1
1
0
1
0
2
1
1
0
1
1
1
0
1
2
0
0
0
0
2
1
1
1
1
1
1
0
1
1
0
1
1
2
1
1
1
1
1
0
2
1
1
0
0
0
2
0
1
1
1
1
0
1
1
0
2
1
1
1
1
1
0
0
1
0
1
0
1
0
1
0
1
1
1
1
1
0
0
1
0
1
1
2
2
2
2
1
0
1
1
1
2
1
2
2
2
1
1
2
1
0
0
1
1
0
0
1
2
1
1
1
1
2
1
2
2
1
0
2
0
1
0
1
2
1
2
2
1
1
1
0
0
1
1
1
1
2
0
1
2
1
1
0
1
1
2
2
0
1
1
0
2
2
1
0
1
2
0
2
0
1
2
1
2
1
0
1
0
2
1
2
2
0
2
1
1
1
1
0
0
1
0
1
0
0
1
1
2
2
1
2
1
0
1
1
3
0
2
1
2
1
1
1
0
2
1
1
2
1
1
0
2
0
0
1
1
1
1
1
0
1
0
0
0
2
0
1
1
0
1
0
0
1
1
1
0
0
2
2
1
2
0
1
2
1
2
2
2
1
0
0
1
1
1
0
4
1
1
2
1
1
1
1
3
1
1
1
1
2
2
1
0
2
1
1
1
0
1
1
1
1
2
0
2
0
1
1
2
2
1
1
1
2
1
1
0
1
2
0
1
0
1
2
2
1
0
2
1
1
0
0
1
1
1
0
0
1
2
1
2
1
1
1
1
2
1
0
1
0
2
1
1
0
0
1
1
3
0
2
2
0
2
1
2
1
0
0
0
1
0
1
1
1
1
1
0
2
0
1
1
0
0
1
2
1
1
1
0
1
2
1
1
0
1
1
0
1
0
2
1
0
1
0
1
1
0
0
0
1
1
0
0
2
0
1
0
2
2
0
2
1
0
2
1
2
2
2
1
1
2
2
1
1
1
0
1
0
1
4
1
0
2
1
1
0
0
2
1
1
0
0
1
1
1
0
2
1
3
2
2
1
1
2
0
1
1
1
2
0
2
0
1
2
0
1
2
3
2
1
0
1
1
0
1
0
2
0
0
1
0
0
0
2
0
0
1
2
2
0
2
1
1
3
2
2
1
1
0
1
1
2
2
1
2
0
0
1
1
3
1
0
1
1
0
2
1
1
1
1
1
0
0
1
0
0
1
0
1
1
8
0
0
1
2
0
2
1
2
1
0
1
0
0
1
0
1
1
2
3
1
0
1
0
1
1
0
0
1
0
1
0
1
2
2
0
0
2
2
1
1
2
0
2
1
0
1
1
2
1
1
1
1
1
2
1
0
2
0
0
1
0
0
1
2
1
2
1
2
1
0
0
1
2
2
1
1
2
0
0
1
1
1
1
0
2
1
1
1
2
1
2
1
0
1
2
0
1
0
0
1
2
1
2
0
1
2
1
0
2
0
1
1
1
1
1
0
0
1
1
1
2
1
1
1
1
0
0
2
1
1
1
2
1
2
1
2
0
1
2
1
1
1
1
1
0
2
1
1
1
2
1
2
2
1
1
1
2
1
2
1
1
1
1
2
1
1
1
0
1
2
1
1
0
0
0
1
1
1
0
0
1
1
1
2
0
1
0
1
2
1
1
1
0
1
1
2
1
3
1
1
1
2
0
2
1
1
2
0
0
2
0
3
1
1
0
0
1
0
1
2
0
1
1
1
1
1
0
2
1
1
0
1
1
2
1
1
0
1
2
1
0
1
1
0
1
0
2
0
0
2
1
2
2
0
1
1
1
1
0
2
2
2
2
2
2
1
2
2
1
2
0
1
1
0
1
2
2
1
1
1
1
0
0
1
1
2
2
1
2
1
0
1
2
1
0
1
1
2
1
1
2
1
2
0
0
1
1
1
1
1
0
1
4
1
1
2
1
1
2
0
0
2
2
0
0
0
1
2
0
1
1
1
2
2
1
1
1
0
1
0
2
1
1
0
1
1
2
2
1
1
1
0
0
0
2
1
1
0
0
2
1
1
1
1
0
1
1
1
1
1
0
1
0
0
1
0
1
2
0
1
2
0
2
1
0
1
1
1
1
1
2
0
1
0
0
1
2
0
1
1
0
1
2
1
1
2
0
1
0
0
0
0
0
1
2
0
2
2
1
2
1
1
0
1
1
1
0
0
0
1
0
3
0
1
1
0
1
1
2
1
2
2
1
2
1
1
1
1
1
0
0
0
2
1
0
3
1
0
0
1
0
1
0
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
0
1
1
1
1
0
2
1
2
1
2
1
0
2
0
1
1
0
1
2
0
1
1
0
0
2
3
0
2
1
0
1
1
1
1
1
1
0
1
2
1
2
1
1
1
1
1
2
0
1
0
1
2
1
1
0
0
1
0
0
1
1
1
1
1
2
4
1
1
1
1
2
0
0
1
1
1
1
1
2
2
2
1
0
2
0
0
1
0
1
1
1
1
2
0
2
2
2
1
1
2
2
1
1
1
2
0
0
1
1
1
2
1
0
0
1
2
1
1
1
1
2
1
0
0
1
2
1
1
1
1
0
1
2
1
0
1
0
1
1
2
0
0
0
1
1
1
0
1
1
0
0
1
1
1
0
2
1
1
1
1
0
1
0
1
1
0
2
1
0
1
1
1
0
0
0
0
1
1
1
2
1
2
1
0
2
2
2
1
0
2
1
1
2
1
0
0
2
2
1
1
1
2
2
0
1
0
2
2
2
2
1
3
2
1
1
3
2
1
1
0
2
1
1
1
0
1
1
2
0
1
0
1
1
2
1
1
2
1
2
1
1
0
0
1
3
2
0
0
1
2
0
2
0
1
0
1
1
1
1
1
0
0
1
1
0
1
1
1
0
0
2
0
0
0
1
0
1
1
0
1
0
0
2
1
0
1
0
3
0
1
1
2
0
2
0
1
1
0
0
1
1
0
1
1
0
1
0
1
1
0
1
1
1
1
1
2
0
1
3
2
1
1
2
1
1
2
0
1
2
2
1
1
1
1
2
1
1
1
1
0
0
1
1
1
0
0
2
1
2
2
1
0
1
0
1
1
1
0
2
2
1
0
1
0
1
1
1
0
0
0
1
1
0
1
0
0
0
1
3
1
0
1
2
1
1
1
2
0
1
1
1
1
0
2
2
1
1
2
2
1
0
1
1
2
1
0
0
0
2
1
1
1
2
1
0
0
2
2
1
1
1
0
0
2
1
1
2
0
2
0
1
1
2
2
0
1
1
0
1
1
2
1
1
1
0
1
1
1
1
2
1
1
1
0
1
1
1
2
1
1
2
0
1
2
2
1
1
2
1
1
1
1
0
1
0
2
0
1
1
3
1
2
1
0
4
2
1
0
0
2
2
1
1
1
0
2
0
0
1
0
1
2
1
1
1
1
2
1
1
1
1
2
2
2
0
1
0
1
0
0
1
2
2
0
1
1
0
1
1
1
2
2
2
2
1
1
2
1
1
1
2
2
2
0
1
0
0
5
2
1
1
1
1
2
1
1
0
1
1
2
1
1
2
0
1
2
2
1
1
1
1
1
0
1
0
0
2
1
1
2
1
1
0
1
2
2
1
1
1
1
1
1
1
1
0
0
1
1
2
1
1
1
1
2
1
1
0
0
1
1
1
1
1
0
1
2
1
0
0
2
1
0
1
1
1
2
0
2
1
3
0
1
0
1
1
2
0
1
1
2
2
0
0
1
2
0
1
0
0
1
0
0
2
1
0
1
1
2
1
2
5
0
1
0
1
0
1
1
2
0
1
1
2
2
1
2
0
1
2
1
1
3
1
0
1
0
0
1
2
2
1
0
1
2
1
0
1
2
0
1
3
0
1
1
0
2
1
2
1
1
1
0
0
1
0
1
2
0
1
1
0
2
2
2
2
1
0
2
0
2
2
0
2
3
1
1
0
1
2
1
1
0
0
2
1
2
0
2
1
0
2
0
1
1
1
2
0
0
1
1
2
1
1
1
1
1
1
1
1
0
0
1
1
2
1
1
2
1
0
0
2
1
0
1
0
0
1
2
1
1
0
0
2
1
2
1
0
0
1
0
0
1
1
1
1
0
1
1
2
0
1
0
1
1
2
1
2
0
1
2
2
1
1
1
2
0
0
0
1
2
1
1
1
0
2
0
1
1
2
0
2
1
2
1
0
1
0
0
1
2
1
1
1
1
1
0
0
0
1
0
1
2
2
1
1
1
0
2
1
1
1
1
1
0
2
0
1
2
1
1
0
0
1
0
2
2
0
0
1
2
0
2
1
2
1
2
0
1
1
1
1
1
1
0
1
1
1
0
0
3
2
2
2
1
1
0
1
1
0
2
1
1
1
1
0
1
0
2
6
2
1
1
0
2
2
1
0
1
0
2
1
0
0
0
1
1
0
0
2
0
2
1
1
2
0
1
0
0
0
1
1
2
1
0
1
1
1
0
2
1
2
1
2
2
1
1
0
0
0
1
1
1
1
3
2
0
1
0
1
1
0
2
1
1
2
1
1
2
1
1
1
1
0
1
1
2
1
0
2
2
1
2
1
1
2
1
1
1
5
2
0
0
0
0
1
1
1
1
2
1
1
1
1
2
1
0
1
1
0
2
1
2
1
2
1
1
1
1
0
1
0
1
1
1
1
1
1
1
1
0
2
1
2
1
2
2
2
1
1
1
1
1
1
0
1
1
1
0
1
1
1
1
0
1
1
0
1
2
1
1
0
1
7
1
1
1
1
0
1
1
2
2
0
0
1
1
0
1
1
1
1
1
2
0
0
1
1
2
1
0
1
2
2
1
1
0
2
0
0
1
1
0
0
1
2
0
1
0
0
0
2
1
2
2
1
2
1
0
1
1
1
2
1
1
1
1
1
0
1
2
1
1
1
1
1
0
2
1
0
1
1
3
1
1
0
1
0
2
1
2
0
1
2
0
1
3
1
1
0
1
1
1
2
0
1
2
1
1
2
0
1
1
2
2
0
1
0
2
2
1
1
2
0
1
1
1
2
1
1
2
1
1
2
0
1
1
1
1
1
1
0
0
2
0
1
2
0
2
0
1
0
0
1
2
2
2
0
1
1
1
1
0
1
1
1
0
0
2
1
1
1
1
1
0
0
1
2
1
0
0
2
0
1
1
1
1
1
1
1
1
0
2
1
0
0
0
1
0
1
1
2
2
0
1
2
1
1
2
0
2
1
0
2
1
1
0
1
1
0
1
0
1
1
2
0
1
0
3
1
2
1
0
1
0
2
2
2
2
1
1
2
1
2
0
1
1
1
0
1
0
1
0
1
0
4
1
0
1
1
1
0
2
0
0
1
1
1
1
2
2
1
1
1
0
1
2
0
0
0
1
0
1
0
1
2
1
2
0
2
1
1
1
1
1
0
1
0
0
0
0
0
2
2
0
1
1
1
0
1
2
1
0
1
0
1
1
0
1
2
1
2
2
1
2
0
1
0
0
1
2
1
2
1
1
1
1
1
1
1
3
1
1
1
2
1
2
2
0
1
1
1
1
1
1
1
0
1
1
1
2
3
0
1
0
0
1
1
1
1
1
0
1
2
2
1
0
1
1
2
1
2
0
0
1
1
1
1
0
1
1
1
1
0
1
1
1
1
0
1
1
0
0
1
2
2
2
1
2
2
1
2
0
1
1
2
1
1
1
1
1
2
1
0
1
1
1
2
1
1
3
1
0
0
1
1
1
1
1
0
1
1
1
1
1
1
1
1
0
2
2
1
0
1
2
0
1
2
2
1
1
1
2
1
0
1
1
2
1
1
1
0
0
1
0
1
1
2
0
1
0
2
0
0
2
1
2
2
2
0
1
1
1
0
1
2
1
1
1
0
2
1
2
1
1
0
1
2
1
2
1
1
1
0
2
0
1
0
2
2
1
0
0
1
1
2
0
2
1
1
1
1
1
2
1
2
1
1
0
1
2
1
1
1
1
1
2
1
2
1
0
1
2
2
1
1
0
3
1
1
1
1
2
0
1
2
1
1
2
0
1
1
1
1
2
1
0
0
1
2
0
1
1
0
0
1
2
0
1
0
0
1
1
2
2
0
1
1
2
2
0
0
2
0
2
0
1
1
1
2
0
1
1
1
0
0
0
1
1
2
0
1
1
2
0
1
0
1
0
1
0
0
0
2
2
0
0
1
1
1
1
1
0
1
1
0
1
0
1
0
1
1
2
1
2
1
0
1
0
1
0
0
0
1
1
1
2
2
1
1
0
2
0
2
2
0
1
0
1
0
1
1
1
1
0
0
2
1
0
2
2
0
1
1
2
1
1
2
2
2
1
1
1
2
1
2
1
2
1
0
2
1
0
0
0
1
0
0
1
1
1
2
1
0
1
2
0
2
1
1
2
1
1
2
2
1
1
1
2
0
1
0
1
2
0
1
1
0
1
1
2
0
2
1
1
0
1
2
1
1
1
1
0
1
0
1
1
0
1
2
1
2
1
0
1
0
2
2
1
2
1
1
0
1
1
1
1
1
1
0
1
0
1
0
0
2
1
1
0
1
2
0
2
1
2
1
2
0
0
2
1
0
1
0
2
1
0
1
1
0
2
1
0
1
0
1
2
1
0
3
0
0
1
1
1
1
1
0
2
1
1
2
2
1
2
1
1
1
0
1
1
1
2
1
2
0
1
1
1
1
1
0
2
0
2
1
0
1
1
1
0
0
2
0
2
1
0
0
1
1
0
1
3
2
0
0
0
0
1
1
1
3
1
0
0
2
2
2
1
2
0
0
2
2
1
0
2
1
0
0
0
0
2
1
1
2
1
0
1
1
0
0
1
0
1
0
2
1
2
1
2
2
1
3
0
1
1
1
0
2
2
1
1
0
0
1
0
0
1
1
1
1
1
1
1
0
1
0
1
0
2
0
2
1
1
2
0
2
1
7
0
1
0
1
1
1
2
1
0
2
2
1
2
1
2
1
0
1
1
2
1
0
1
1
0
1
1
2
2
1
2
0
1
1
1
1
1
1
0
0
0
0
0
1
2
1
2
1
2
2
1
1
0
1
0
1
1
1
2
1
2
1
0
2
0
1
2
1
2
1
1
1
0
2
1
2
2
1
0
1
2
1
2
1
2
1
1
0
2
0
1
2
0
1
1
1
0
0
1
0
1
1
1
1
1
1
1
1
0
1
2
0
2
1
0
1
1
1
1
1
1
2
0
1
1
2
1
0
2
1
1
2
4
0
0
3
0
2
2
1
1
1
0
1
1
2
1
1
1
1
0
1
0
1
2
0
2
0
1
1
2
2
0
2
1
1
1
0
2
2
0
1
1
0
1
1
0
1
0
1
1
0
0
2
2
1
2
0
1
1
1
2
0
1
1
1
1
0
0
1
2
2
2
2
2
2
2
0
2
1
1
0
2
0
2
0
2
2
1
1
1
0
1
0
2
0
1
0
3
1
2
2
0
1
0
1
1
1
0
1
2
1
0
1
0
1
0
0
2
0
1
1
1
0
1
2
2
0
1
2
1
1
0
2
1
1
2
1
1
0
0
0
1
0
1
1
1
2
1
0
1
0
0
0
0
1
2
0
1
2
1
2
3
0
1
0
1
1
1
0
1
2
2
1
0
0
1
0
1
1
0
1
1
2
2
1
0
0
2
1
2
1
2
0
2
0
3
2
1
0
2
2
0
2
1
0
1
1
1
2
2
1
1
1
0
1
0
1
1
0
2
1
0
2
1
1
1
0
1
0
0
0
1
0
0
0
1
0
2
1
1
1
0
1
0
1
0
0
1
1
2
0
1
2
1
1
1
1
0
0
0
0
1
2
0
1
1
1
3
0
0
1
1
0
1
3
1
1
0
2
1
2
1
1
2
0
1
1
2
0
0
0
0
0
0
1
0
1
0
1
1
2
0
2
2
1
2
2
0
1
1
0
1
1
2
1
0
2
1
1
1
1
0
1
1
0
2
0
0
0
2
1
1
1
0
0
1
2
0
1
0
0
1
0
1
1
1
1
1
0
2
2
0
2
2
1
1
1
0
2
0
2
1
1
1
2
1
2
1
2
1
0
0
1
0
2
2
1
1
1
0
1
2
0
1
0
2
1
1
0
2
1
2
1
0
1
2
2
1
1
0
1
0
1
2
0
0
2
0
1
0
0
1
0
1
1
2
1
1
1
0
0
1
1
1
1
0
2
0
1
1
1
1
0
1
2
0
0
3
1
1
3
0
1
1
1
0
0
2
1
2
0
1
1
0
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
0
1
2
1
1
2
2
0
1
0
2
0
0
1
0
1
1
1
1
0
0
0
2
2
2
0
1
1
0
1
1
2
1
0
1
0
2
1
0
1
0
2
1
1
1
0
2
1
1
1
1
2
2
1
0
1
2
1
1
1
1
1
1
0
0
1
2
1
1
0
2
0
2
2
1
0
0
1
0
1
1
0
0
0
1
1
1
1
1
1
2
0
2
1
0
2
0
0
10
2
0
0
2
1
2
1
1
2
1
1
1
1
1
1
1
0
0
0
2
0
2
1
1
0
2
1
1
1
1
1
1
2
0
1
2
2
0
0
1
1
0
0
0
1
1
0
0
1
1
3
2
2
2
1
1
0
2
2
2
0
1
1
1
1
1
0
0
1
0
1
1
0
2
0
1
1
0
0
0
0
1
0
1
0
1
1
1
2
1
2
1
1
1
1
1
1
1
2
2
1
1
1
3
2
1
1
1
2
2
0
0
2
1
0
2
1
0
2
0
0
0
0
1
2
1
1
1
1
1
1
1
1
1
2
0
2
1
2
1
1
1
0
1
1
1
2
1
2
2
1
1
0
0
1
1
1
0
1
1
1
1
1
1
2
1
1
0
0
1
0
1
0
1
1
1
2
0
1
1
0
1
1
1
3
1
1
0
1
1
1
0
1
1
1
3
1
0
0
0
1
1
1
2
0
0
0
1
0
0
1
0
1
2
2
1
1
2
2
1
0
1
0
1
2
0
1
1
1
1
1
2
1
1
0
1
1
2
1
0
3
1
1
0
0
2
1
1
0
2
1
0
0
1
1
1
1
2
0
2
1
2
1
1
2
2
1
1
1
1
1
1
0
2
1
1
0
2
1
1
3
2
2
1
1
1
2
1
1
1
2
0
1
2
0
1
2
1
1
1
1
0
2
0
1
1
2
2
1
0
1
2
0
1
2
1
1
2
2
1
2
1
1
2
1
1
0
1
1
2
0
1
1
2
1
1
1
1
1
2
1
0
2
2
1
1
1
1
0
0
0
1
2
1
2
1
0
1
1
0
0
0
1
1
0
0
1
0
3
1
0
1
2
2
1
1
1
0
0
1
1
0
1
1
0
1
9
2
0
2
1
0
2
0
1
1
1
2
1
2
2
1
0
0
2
2
2
1
1
1
0
2
1
1
2
2
1
3
2
1
0
1
1
2
2
2
1
1
1
0
1
2
1
1
1
0
1
2
0
0
1
1
2
2
1
1
1
0
1
2
1
0
1
1
0
1
2
1
1
1
2
0
0
1
1
1
2
1
2
1
0
0
0
2
1
2
0
0
2
0
1
0
1
1
0
0
1
2
1
1
0
0
2
0
1
2
1
0
0
0
1
1
0
1
1
0
1
1
1
1
1
1
1
1
1
2
0
2
2
1
1
1
1
1
0
0
0
0
2
2
2
1
2
1
2
0
1
1
1
0
0
2
0
0
2
1
1
1
0
1
1
2
1
1
1
2
1
0
0
1
0
1
1
1
1
1
2
2
1
0
1
0
0
1
1
2
0
0
0
2
1
2
2
1
1
2
2
0
3
2
1
1
2
1
0
0
1
1
0
1
1
1
1
1
0
2
1
0
1
0
2
2
1
1
1
1
1
2
2
1
0
0
1
1
2
1
0
2
0
1
0
1
1
1
1
1
0
0
0
2
1
2
0
1
1
1
0
2
0
1
1
0
1
1
0
3
1
1
1
2
0
1
1
1
1
0
0
1
1
0
0
1
1
0
1
1
0
0
0
1
2
2
1
2
0
1
0
1
0
1
0
1
1
1
0
1
1
1
0
1
1
1
1
1
2
1
0
1
2
1
0
1
2
0
2
1
1
1
0
1
0
1
1
1
1
1
1
1
1
2
0
1
0
0
2
1
1
1
2
1
1
1
1
0
1
2
1
3
1
1
2
1
2
1
2
0
1
2
1
1
1
1
1
2
1
1
1
1
0
1
1
3
1
2
0
0
1
2
1
1
1
1
1
2
1
1
2
1
1
1
3
0
1
2
0
1
1
1
0
0
1
1
2
1
1
1
1
1
0
1
1
2
1
1
1
1
0
1
1
0
0
1
2
1
0
0
2
2
2
2
1
0
1
1
1
1
0
1
2
1
1
1
0
1
2
1
0
1
1
0
5
1
2
1
1
1
1
1
1
0
2
1
2
0
1
0
1
1
2
1
1
2
2
0
2
0
0
1
1
2
1
1
1
1
0
1
1
1
2
1
1
1
0
1
2
0
1
2
0
1
0
3
2
2
4
1
0
1
1
0
0
0
1
2
0
2
1
2
1
1
1
1
1
2
2
1
1
0
2
1
1
1
1
1
2
2
2
0
2
0
0
1
2
1
3
2
1
2
2
1
1
1
2
1
0
1
1
1
2
2
1
1
1
0
1
0
2
0
1
0
1
2
1
2
1
1
0
2
0
0
1
1
1
0
1
2
1
1
2
0
0
1
2
1
1
2
0
1
2
1
2
0
1
1
2
1
1
0
0
2
1
1
1
0
2
1
2
0
1
1
2
2
0
1
1
0
1
1
0
0
2
1
0
3
2
1
1
1
1
2
0
1
1
1
1
0
1
0
1
0
1
1
0
1
0
1
2
3
1
2
1
1
1
2
1
0
1
1
1
0
2
2
0
1
2
0
2
1
2
2
0
1
0
3
1
0
1
0
2
1
2
1
1
0
1
2
2
2
2
1
2
0
2
2
0
0
1
2
1
1
0
1
1
1
0
2
1
0
2
2
4
0
1
1
0
1
0
2
2
0
1
1
1
1
0
0
1
4
0
1
2
1
1
1
0
1
0
0
0
2
1
2
0
1
1
1
1
2
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
2
2
0
1
1
2
0
2
1
1
1
1
0
0
2
1
0
0
1
2
0
1
1
1
1
1
1
1
0
0
1
1
1
2
0
1
1
0
2
0
1
0
1
1
2
2
1
2
1
0
2
2
1
2
1
0
0
1
1
0
1
1
1
1
1
1
2
1
0
1
0
1
1
1
0
1
1
1
1
1
2
0
1
1
0
1
1
1
0
1
2
2
1
1
1
0
1
0
1
2
2
1
1
1
0
1
1
1
1
2
1
1
2
0
1
1
2
0
2
2
0
2
1
1
2
1
0
1
0
2
1
2
0
1
0
1
0
0
1
0
0
1
2
1
2
2
2
1
0
1
0
2
1
1
2
1
0
2
1
1
0
1
1
0
1
2
1
2
1
0
2
1
0
1
2
1
1
1
1
1
1
1
0
0
1
0
0
2
2
2
0
1
0
2
0
1
1
1
1
0
0
1
2
3
1
0
1
1
1
1
1
0
2
1
1
1
1
2
1
1
1
0
0
2
1
0
0
0
0
0
0
0
1
2
1
2
1
1
2
1
2
1
0
1
2
0
1
1
1
1
2
2
0
1
2
0
2
2
2
1
1
2
0
0
1
3
1
2
2
1
1
2
0
1
0
1
1
1
1
2
1
0
1
2
1
0
2
1
1
1
2
0
1
1
0
2
0
2
1
1
0
1
1
1
2
0
2
1
1
1
0
2
3
1
1
2
0
1
2
1
0
1
2
2
0
1
1
0
2
1
0
0
1
0
1
2
1
2
0
0
2
1
1
0
2
1
1
2
1
1
1
0
1
2
1
1
0
2
1
1
2
3
1
0
2
2
2
2
1
1
1
1
1
0
2
0
2
0
1
1
2
1
0
1
1
0
1
1
1
2
0
1
0
1
1
2
1
0
2
1
1
1
2
0
2
2
1
1
1
1
1
0
0
1
1
0
2
1
2
1
1
1
1
1
1
1
1
1
1
0
1
1
2
1
1
1
0
0
1
0
1
1
1
1
1
0
1
1
1
0
1
0
2
1
0
1
1
0
0
1
2
0
2
3
1
1
2
2
1
1
0
1
1
1
2
2
2
1
1
2
0
2
1
1
1
0
2
1
1
2
1
1
1
2
1
1
1
2
1
1
2
2
1
1
1
2
0
2
1
0
2
3
0
0
2
2
1
1
2
1
0
2
1
0
2
1
1
0
2
1
0
0
1
1
1
2
1
1
1
1
1
1
0
1
0
1
1
0
2
1
1
1
1
2
2
1
1
0
1
1
2
0
1
1
1
1
1
0
0
1
2
2
1
0
1
1
1
1
1
0
1
0
0
2
1
1
1
1
2
0
2
1
1
1
0
1
0
1
1
1
1
1
0
1
0
1
1
1
0
1
1
2
2
2
1
0
1
0
1
0
1
0
1
0
0
1
1
1
1
1
1
2
1
1
1
0
1
1
1
0
1
1
0
1
1
0
1
0
1
1
1
0
1
1
1
1
0
0
1
1
0
2
2
1
0
2
0
1
2
2
0
1
1
0
0
2
1
1
1
0
1
0
0
0
0
1
1
0
1
0
1
2
0
1
1
1
1
0
1
1
1
1
2
1
2
0
1
1
2
1
2
0
2
0
0
2
1
1
2
0
0
1
0
2
1
1
1
1
2
2
1
1
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
1
2
2
1
0
2
2
2
0
0
0
2
1
0
2
2
1
1
1
2
2
1
1
1
1
1
0
0
1
1
1
1
2
1
0
0
1
0
1
2
1
1
1
0
1
1
0
0
1
1
2
1
2
1
1
1
1
1
1
0
1
0
1
1
0
2
0
1
1
1
0
1
2
2
2
0
1
1
2
1
2
1
0
1
3
0
2
2
1
1
2
1
1
1
0
1
1
1
1
1
2
1
1
1
2
0
1
0
1
1
0
1
1
1
0
0
1
1
1
1
0
1
1
2
2
1
1
14
2
0
0
2
1
1
1
1
1
0
0
1
0
1
2
1
2
2
1
1
1
1
1
1
1
1
0
1
2
1
0
0
1
1
1
1
1
1
1
0
1
2
0
0
1
0
1
2
1
1
0
1
1
2
1
2
2
1
2
1
1
1
0
1
0
2
0
2
1
1
0
2
3
2
1
1
0
1
1
1
0
0
2
1
1
2
2
0
1
1
1
1
1
0
1
1
0
1
2
1
1
0
0
1
0
1
0
3
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
0
1
0
1
0
0
2
0
1
1
0
2
0
0
2
1
1
1
2
0
0
0
1
1
0
2
1
2
2
2
1
1
1
1
0
1
0
0
1
1
0
1
1
0
1
0
2
0
1
0
1
1
1
1
1
1
2
1
1
0
2
1
0
0
0
1
0
1
1
1
0
0
0
0
1
2
2
1
2
1
1
2
0
2
0
0
2
1
0
2
1
1
1
1
2
0
1
2
1
1
2
1
1
1
1
0
1
1
1
0
1
1
2
1
2
0
1
1
1
2
1
1
1
1
0
1
1
2
1
1
2
0
2
1
1
1
0
2
1
2
1
1
0
0
0
2
2
0
2
0
2
2
1
0
2
0
1
1
1
1
2
0
2
2
2
1
1
1
0
1
0
1
2
2
2
0
2
1
1
1
1
1
0
0
0
1
0
0
1
1
2
0
0
1
0
1
1
1
0
0
0
0
1
0
1
1
1
1
1
1
1
1
1
0
1
2
0
1
2
2
1
1
2
0
0
0
1
0
0
1
1
2
1
1
1
2
0
1
1
2
0
1
2
0
2
1
1
0
1
1
2
2
1
1
1
2
1
2
2
1
2
0
2
2
0
1
1
1
2
1
0
1
0
1
1
1
0
0
2
0
2
0
0
1
0
1
1
1
1
1
0
0
0
3
0
0
0
0
0
1
2
2
0
0
1
0
2
1
0
1
1
1
1
1
1
1
1
2
1
0
0
1
0
0
0
1
0
0
0
2
2
1
0
1
2
0
1
1
0
2
1
0
0
2
1
0
1
2
1
0
1
2
1
1
1
1
0
1
1
1
1
1
1
2
0
1
0
1
4
0
1
1
2
1
1
1
2
0
1
2
2
1
1
1
3
2
0
1
1
1
2
1
2
1
4
0
2
2
1
1
1
2
2
1
1
0
1
1
1
2
1
1
2
1
1
1
1
1
1
0
0
1
1
1
0
1
1
1
0
1
1
2
1
1
1
1
3
1
0
0
1
0
1
2
1
2
2
1
1
1
2
2
1
1
1
2
2
1
0
1
2
1
2
0
1
0
1
2
2
1
0
1
0
1
2
1
3
0
0
1
1
1
4
1
0
0
0
1
1
2
2
1
1
1
1
2
0
2
2
2
1
1
1
0
1
1
2
0
0
2
1
0
1
1
1
1
2
1
1
1
2
0
0
2
0
2
2
0
1
1
1
2
1
2
2
0
2
1
1
1
0
1
3
2
0
2
1
1
0
0
2
2
0
0
1
1
2
1
2
1
2
0
1
0
0
1
0
1
4
0
2
0
1
0
1
0
1
2
0
1
1
0
2
0
3
1
0
0
1
1
0
0
1
1
1
0
1
0
1
1
1
0
1
0
0
1
1
2
1
1
1
0
1
1
2
1
1
0
1
2
2
1
2
2
1
1
2
2
0
3
2
0
1
1
1
0
1
1
1
1
1
2
1
2
1
1
0
1
2
1
0
1
1
1
2
2
1
1
1
0
2
0
0
2
1
0
1
1
0
2
1
1
1
0
1
0
0
0
1
1
2
2
0
2
1
0
0
2
1
2
0
0
0
2
1
2
1
1
1
2
1
0
1
1
2
1
1
1
2
2
2
1
0
1
0
0
1
2
1
0
1
1
2
1
0
0
2
1
2
1
1
1
1
1
1
1
1
4
1
2
1
2
2
2
0
1
0
1
1
1
1
1
1
1
1
1
2
0
1
1
2
1
1
0
1
1
1
1
1
1
0
2
1
0
2
2
2
1
2
2
1
2
0
1
1
2
1
1
1
1
0
1
1
2
2
1
2
1
2
0
1
0
1
1
1
1
1
0
0
1
0
1
2
1
1
1
1
0
1
0
1
1
1
1
1
0
0
1
0
2
2
1
1
2
2
0
0
1
1
1
1
1
2
1
6
2
1
1
0
0
0
2
0
1
2
1
0
0
2
2
0
2
0
1
1
1
1
1
1
1
2
3
1
2
1
0
1
1
1
1
0
2
1
1
1
1
1
1
2
1
0
0
1
0
2
1
0
2
0
0
1
2
1
0
2
2
2
2
1
1
3
1
1
0
0
1
1
1
1
1
0
0
0
0
2
1
2
2
1
1
1
1
0
2
3
2
0
0
1
1
2
1
2
2
0
0
0
1
2
1
0
1
1
0
1
2
1
1
1
1
2
0
2
0
1
0
2
1
1
1
1
2
1
0
0
3
2
1
1
1
1
1
1
1
2
0
0
0
2
2
1
1
1
0
0
2
2
2
2
2
2
2
1
2
0
1
2
2
1
1
2
1
1
0
1
2
2
1
0
1
2
1
2
0
2
0
1
1
0
1
1
1
1
1
1
1
0
1
0
0
2
1
1
1
0
1
1
2
1
0
0
1
0
2
0
1
1
0
3
1
1
1
0
0
0
1
2
2
1
0
1
2
1
1
0
0
0
1
2
0
1
1
0
1
0
4
1
1
2
2
2
0
0
2
1
0
0
1
1
1
1
0
0
0
1
1
0
1
0
2
0
0
2
0
1
1
0
0
1
0
1
0
1
2
2
2
0
2
1
2
2
2
0
0
1
1
1
1
0
0
0
1
2
0
0
1
1
1
1
0
0
2
1
2
1
1
1
1
1
0
2
2
2
1
4
2
1
0
0
2
3
1
1
1
2
0
1
2
1
1
1
1
1
2
1
1
1
1
1
1
2
0
2
0
1
1
1
0
1
2
2
1
2
2
1
1
0
0
1
1
2
0
1
1
0
2
0
0
1
2
2
2
1
2
0
1
0
1
1
1
1
2
1
0
1
0
2
0
2
1
1
1
1
1
1
0
1
1
0
1
0
2
1
1
1
1
1
1
0
2
1
1
2
1
1
1
1
2
1
2
0
2
1
2
1
2
1
1
2
0
0
1
2
1
1
0
2
1
1
2
2
1
0
1
0
0
0
1
1
1
1
1
0
1
0
0
1
2
1
0
1
1
0
1
2
1
4
1
0
2
0
1
2
0
1
1
1
1
1
1
1
1
0
2
0
1
0
1
0
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
0
2
0
1
1
2
2
1
1
2
0
2
2
1
0
1
1
1
2
0
3
1
1
2
8
1
0
2
1
1
1
1
2
1
1
1
1
1
1
0
0
1
1
1
0
2
1
2
2
1
0
2
2
0
1
1
2
1
1
2
2
0
1
0
1
2
1
1
0
2
1
2
1
0
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
0
0
1
1
1
2
1
1
1
1
1
1
0
2
0
1
1
2
1
1
1
2
2
1
1
1
1
1
0
1
2
1
1
0
1
1
0
1
0
1
0
0
1
0
2
1
0
1
2
1
1
2
3
2
1
1
0
1
0
0
2
1
2
1
0
1
3
2
1
1
1
1
1
1
1
0
0
0
2
1
2
0
0
1
0
0
3
1
0
2
0
2
2
2
2
2
1
2
2
0
0
1
1
1
1
0
1
2
1
1
2
1
1
1
0
0
1
1
1
2
1
1
0
1
1
2
1
1
0
2
2
1
0
1
1
1
1
0
1
1
3
1
2
2
1
1
1
1
1
0
1
1
0
1
0
1
1
1
2
2
1
0
1
1
0
1
0
1
1
0
1
3
2
1
1
1
2
1
0
2
1
0
1
2
1
2
1
1
1
0
1
1
2
0
0
0
0
1
1
1
0
0
0
2
1
0
1
2
0
0
1
1
1
1
1
1
1
0
2
0
1
1
0
0
0
1
1
0
2
1
0
0
2
2
1
0
1
1
0
1
3
2
1
2
1
1
2
3
2
3
2
2
1
0
0
1
1
1
2
2
0
1
1
0
0
2
2
2
1
1
0
1
0
1
1
1
1
2
0
0
1
1
1
0
1
1
1
1
1
1
1
0
2
1
0
0
1
2
1
2
0
1
1
1
2
0
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
2
1
1
2
2
1
1
1
0
1
1
1
1
0
0
1
2
1
0
2
2
1
1
1
0
1
0
0
1
2
1
0
1
1
1
1
1
1
2
1
1
2
1
0
1
2
0
1
1
1
1
2
1
2
1
1
1
0
1
0
1
1
2
1
1
0
1
0
1
1
2
2
0
1
1
1
1
0
0
1
0
0
1
1
1
1
0
1
1
1
1
1
0
0
1
0
2
1
1
1
0
1
1
2
0
0
1
1
1
1
1
1
2
2
0
1
1
1
1
0
2
0
1
1
1
3
1
1
2
0
1
1
1
2
1
2
1
2
2
0
2
1
1
1
1
2
1
2
1
2
1
0
2
2
1
1
1
2
0
1
1
2
1
0
0
1
0
2
1
2
1
1
0
1
0
1
2
1
1
2
1
0
2
0
1
1
0
1
1
1
2
2
1
1
2
0
0
1
0
1
1
1
1
1
1
0
1
1
1
1
1
2
0
1
2
3
2
1
1
2
1
1
1
1
1
0
1
1
1
0
2
1
0
0
2
2
3
0
1
1
1
1
1
0
1
0
2
0
0
2
1
1
0
1
0
0
0
1
1
1
1
2
0
0
3
1
0
0
1
2
1
1
1
1
1
1
1
2
1
2
1
2
0
1
2
1
1
0
0
1
0
2
1
1
1
0
0
1
0
2
1
1
2
0
0
0
0
1
2
0
1
1
2
0
2
0
1
1
0
0
1
0
1
1
1
1
1
2
1
1
0
0
1
0
2
1
1
0
1
2
1
0
1
1
1
0
1
1
0
0
2
1
0
1
1
1
1
1
1
2
2
2
1
2
2
0
1
0
1
0
1
1
2
1
1
1
2
0
2
0
1
0
0
1
1
1
0
1
1
1
1
1
1
1
1
1
2
1
0
1
2
1
0
1
1
2
1
1
2
1
2
1
1
0
2
1
0
2
0
1
0
1
1
1
0
2
1
0
1
0
3
0
1
1
0
2
1
1
1
1
1
1
2
1
1
2
1
0
2
1
1
1
2
0
1
1
1
0
2
2
1
1
1
1
1
0
1
2
1
1
1
1
0
1
1
0
2
0
0
2
1
2
1
0
1
0
1
2
1
2
1
1
1
1
1
1
0
1
0
1
1
1
0
1
1
2
1
1
2
2
1
2
0
1
2
1
1
0
0
0
1
0
1
1
2
1
1
0
1
1
0
1
1
1
1
1
0
2
1
2
2
1
0
1
0
1
0
1
1
1
1
0
1
0
1
2
1
1
2
1
0
2
2
1
0
0
1
0
1
2
2
1
2
0
2
0
1
1
0
1
2
1
0
1
0
0
1
0
1
2
1
0
1
2
0
1
1
0
2
2
1
1
1
1
3
1
2
1
0
1
1
1
1
1
2
1
1
1
1
0
1
0
1
2
2
1
3
0
2
1
1
2
0
1
2
1
0
1
2
1
2
1
1
1
0
1
1
1
1
0
0
1
1
1
0
0
1
2
1
2
2
0
1
0
0
1
0
1
0
1
0
0
0
1
0
1
0
1
1
1
0
2
1
1
2
1
1
1
1
2
0
1
1
1
1
1
1
1
2
1
0
1
1
1
0
1
0
1
0
2
1
1
2
0
1
1
0
1
2
1
1
1
0
1
1
0
1
1
1
1
3
1
0
1
1
2
0
2
2
1
2
1
3
1
2
0
1
1
0
1
1
2
1
2
0
0
2
2
2
1
1
1
0
1
2
2
1
2
0
1
2
1
2
2
1
2
0
2
1
0
1
3
0
0
1
1
0
0
1
2
1
0
1
1
1
2
1
2
1
1
1
2
1
1
1
1
1
0
1
1
1
1
1
1
1
1
0
1
1
1
2
0
0
2
0
0
2
1
2
1
1
0
1
1
1
1
3
2
1
1
1
1
1
0
1
0
2
2
0
1
1
0
2
1
0
0
1
2
1
3
1
2
1
1
1
1
1
1
0
1
1
1
0
0
2
1
1
1
2
0
0
1
2
2
1
0
2
0
0
1
0
2
1
2
1
1
1
2
0
1
0
1
2
1
1
0
1
1
1
1
2
2
2
1
1
0
1
1
3
0
0
1
1
1
1
1
0
1
1
2
1
1
1
0
1
2
1
2
1
0
1
2
0
0
2
0
0
2
0
1
0
1
1
1
2
2
1
1
0
1
1
2
0
1
0
0
1
1
2
1
3
1
1
0
0
2
2
0
1
0
0
0
1
1
0
1
1
1
1
2
0
1
2
2
0
0
2
0
1
0
0
3
2
0
1
1
2
1
1
2
2
0
0
2
1
2
0
1
2
0
1
2
0
0
1
1
1
1
1
0
1
1
2
1
0
0
0
2
1
1
0
0
0
2
1
0
1
1
1
1
0
0
1
1
1
1
0
2
2
0
1
0
1
0
0
2
1
0
0
2
0
1
3
2
1
2
1
2
1
1
5
2
0
1
1
3
1
1
0
1
1
2
1
1
0
1
2
1
1
2
0
2
0
2
1
2
2
0
0
2
0
0
0
2
1
1
1
1
1
0
1
0
2
0
1
0
2
1
2
1
1
1
0
1
1
2
1
0
1
0
2
0
1
0
1
1
1
1
1
1
1
1
1
0
1
0
1
2
2
1
0
2
1
1
1
2
4
2
0
1
1
0
2
1
1
1
1
3
1
0
1
1
0
1
1
1
2
1
2
1
1
2
0
2
2
0
1
2
2
0
1
2
2
1
2
0
1
1
1
1
1
2
1
1
1
1
0
2
1
0
0
2
1
0
0
2
0
1
2
1
1
1
0
1
2
1
1
1
0
2
0
1
2
2
2
0
1
0
2
1
0
0
0
1
1
1
1
0
1
1
1
1
0
0
1
1
0
2
1
0
1
0
2
4
1
0
1
1
1
1
2
1
1
0
2
0
0
0
2
1
1
2
1
1
0
1
2
2
2
2
1
1
1
2
1
2
0
2
2
2
2
0
2
1
2
0
2
1
1
1
0
1
0
2
0
0
1
1
0
0
0
0
0
1
0
1
1
1
1
1
0
0
1
2
0
1
2
1
2
2
1
1
2
1
0
2
1
1
0
1
1
2
1
0
2
0
1
2
1
2
1
1
1
1
1
1
1
0
0
1
1
1
1
1
0
0
1
0
1
2
1
1
1
0
0
1
0
0
2
1
0
0
0
3
0
1
1
0
1
2
0
1
0
0
2
2
1
0
1
0
2
1
0
1
1
0
1
1
2
1
1
1
1
2
3
2
3
2
1
2
2
2
1
3
0
1
1
1
2
2
0
0
3
1
1
1
2
1
2
1
1
0
1
0
1
0
2
2
0
2
0
2
1
0
2
1
0
1
0
1
0
0
2
1
1
1
1
1
4
0
1
1
3
1
1
1
0
0
0
2
1
1
0
1
1
0
2
1
1
1
3
1
1
0
2
1
0
2
2
0
1
1
0
0
1
2
0
2
0
1
2
1
1
1
1
2
1
1
2
0
2
2
1
1
0
2
1
0
2
2
2
1
1
1
2
1
2
1
8
1
2
1
2
2
2
1
1
1
0
2
1
2
1
2
1
1
2
1
2
2
1
0
1
1
0
4
0
2
1
2
1
1
2
2
2
1
0
0
0
1
1
2
2
0
2
1
1
1
1
2
2
1
2
0
0
2
1
1
1
2
1
1
2
1
0
1
1
1
1
2
0
1
1
1
1
1
1
2
0
1
2
2
1
0
0
0
2
2
1
1
2
0
2
1
0
0
1
1
1
1
1
0
2
1
4
1
3
1
2
2
1
1
1
1
1
1
0
1
2
1
1
1
0
0
1
2
1
0
1
2
1
1
0
0
1
1
0
2
1
0
2
2
1
1
1
0
1
2
1
2
0
1
2
2
0
1
2
1
1
1
0
1
2
0
1
0
1
1
0
1
1
1
0
1
1
0
2
1
1
2
1
1
1
1
1
2
1
0
1
0
1
2
1
1
0
2
0
1
1
0
1
1
1
2
0
1
2
1
1
1
2
0
1
2
2
2
0
1
2
1
1
0
1
1
1
1
1
2
2
0
1
0
2
0
0
0
2
0
1
0
0
1
1
1
1
0
0
1
2
1
1
0
1
1
1
1
1
1
1
0
1
2
1
1
1
1
0
2
2
1
0
1
1
1
0
1
1
1
2
1
2
0
2
1
2
1
2
2
1
1
2
1
1
0
1
0
2
0
2
1
1
1
0
1
1
2
2
0
0
1
1
1
1
2
1
2
2
1
1
1
1
2
1
1
1
1
1
0
1
1
0
1
1
1
2
1
1
1
0
1
2
2
1
1
1
1
1
1
1
0
1
2
1
0
3
2
1
1
0
2
1
0
1
1
1
1
2
0
1
1
0
1
1
1
1
0
1
1
2
1
3
1
1
1
1
2
1
1
0
2
1
1
0
0
3
0
2
2
1
0
1
0
1
0
0
1
0
2
1
1
1
2
1
1
2
2
3
0
1
1
2
1
1
0
1
0
2
1
1
2
2
1
2
1
1
1
1
0
2
1
2
0
1
0
0
2
0
0
0
1
1
0
1
2
3
1
1
1
1
0
1
1
1
1
0
1
0
0
0
1
2
1
0
2
1
2
0
2
1
1
1
1
2
1
0
1
1
1
2
0
1
2
1
1
1
1
0
1
1
1
0
1
2
2
1
1
1
1
0
1
1
2
2
1
1
1
1
2
1
0
2
1
1
1
0
1
1
1
1
1
2
0
1
1
0
1
2
1
2
2
3
2
0
0
1
2
1
2
1
1
1
1
3
1
1
1
0
2
1
2
1
1
0
1
0
1
2
2
1
2
0
1
2
0
1
1
1
2
1
1
0
1
1
0
1
2
1
1
1
1
1
1
1
2
1
2
1
1
0
0
0
1
1
1
2
0
2
0
1
1
0
1
1
2
0
1
2
1
0
0
0
2
2
1
2
0
0
1
1
0
4
0
1
1
0
1
1
1
0
2
1
1
3
1
2
1
1
0
2
1
1
4
1
0
0
0
0
1
2
2
1
2
0
1
0
2
1
0
2
1
2
0
0
1
1
3
1
0
0
1
1
1
1
1
0
1
2
2
0
0
1
1
1
1
2
1
2
1
0
0
1
1
0
0
2
0
1
2
1
2
1
1
0
0
1
2
1
1
0
1
0
0
2
1
2
0
1
1
1
1
1
1
1
1
2
0
1
0
1
1
3
0
2
0
2
1
0
1
1
2
1
1
1
1
2
0
0
2
0
1
1
1
1
1
0
2
1
1
1
0
4
1
2
2
1
1
2
2
1
1
0
1
2
1
0
1
1
1
1
1
1
1
0
1
1
1
2
1
0
0
1
2
1
0
1
1
0
2
1
1
2
0
0
0
1
1
0
1
2
1
2
1
1
1
2
3
1
1
1
0
1
1
1
2
1
1
1
2
1
1
1
2
0
1
1
1
1
1
0
0
2
0
1
2
2
1
0
0
1
2
1
0
0
0
1
0
1
2
2
2
2
1
1
1
1
1
0
0
1
1
1
0
1
0
1
1
1
1
1
0
1
1
2
1
1
2
1
0
0
1
0
1
0
0
2
1
2
1
0
2
0
2
2
1
1
2
0
1
1
1
4
1
1
2
0
2
0
0
1
2
1
1
1
2
0
1
0
1
1
0
1
0
0
1
2
1
0
1
1
0
1
0
1
13
0
1
1
1
1
1
3
1
2
0
1
2
0
1
2
1
2
0
2
0
0
0
1
0
2
2
2
0
1
0
1
1
3
1
2
1
0
1
1
1
1
1
0
1
1
1
2
1
2
2
2
2
0
0
0
1
1
1
0
1
3
1
1
2
2
1
2
2
2
2
0
0
1
0
2
1
0
3
0
1
1
3
1
2
0
2
0
1
0
1
0
0
1
2
1
0
2
2
2
1
2
2
1
1
1
0
1
1
1
2
0
1
1
1
1
0
1
2
0
1
1
1
0
0
2
1
1
1
1
1
0
2
0
1
2
0
1
1
1
2
1
2
0
2
1
1
2
1
0
2
0
0
1
0
1
1
0
2
1
1
1
1
1
1
0
0
0
1
1
1
1
0
1
2
0
0
1
1
0
1
1
1
2
2
2
1
1
1
3
1
0
2
1
0
1
1
1
0
2
1
1
0
1
2
0
1
4
0
0
0
0
0
1
1
1
1
1
1
2
1
2
0
0
2
0
2
1
1
1
1
1
2
2
1
1
1
1
1
0
0
0
1
0
0
1
2
1
1
1
1
1
1
1
0
0
2
1
1
1
1
1
0
1
1
1
0
1
1
1
1
1
2
0
0
1
2
2
1
0
1
1
0
0
2
2
2
1
2
2
0
2
2
0
2
1
1
1
1
0
2
1
1
0
1
0
0
2
1
1
2
2
2
0
1
1
1
2
2
0
2
1
1
2
0
1
0
1
0
1
0
1
1
0
2
2
2
1
2
1
0
1
0
1
1
1
2
1
0
1
1
2
1
1
0
0
1
1
1
1
0
0
1
1
1
0
1
1
1
0
1
1
1
0
1
0
1
0
2
0
1
2
1
1
1
1
0
1
0
1
1
2
1
0
1
2
1
0
1
2
1
1
2
1
2
2
2
0
1
2
1
0
1
2
0
2
0
1
1
0
1
0
1
1
0
0
0
2
1
0
0
1
1
1
1
2
1
2
1
0
2
2
0
1
1
1
6
0
1
0
2
0
1
1
0
0
1
2
1
0
1
1
2
1
1
1
1
1
1
1
2
0
1
2
2
0
1
2
1
1
0
0
0
0
0
1
1
1
2
2
0
1
2
0
1
5
0
2
0
1
0
1
1
1
1
1
0
0
0
1
1
1
0
0
0
3
1
0
1
1
2
1
1
1
2
2
1
2
2
0
1
0
1
2
2
1
1
0
2
0
1
2
1
2
1
2
2
0
1
2
1
1
0
1
1
1
0
1
1
2
1
1
0
1
1
1
2
1
1
1
1
2
1
1
1
0
1
1
1
1
0
1
2
1
1
1
0
3
0
0
1
0
1
1
0
1
0
0
0
0
0
1
0
1
0
1
2
2
1
2
1
1
0
1
1
1
1
2
1
1
0
0
1
1
1
0
2
2
2
0
1
2
2
2
0
1
2
1
1
2
1
1
1
1
2
1
2
0
1
0
1
0
2
0
0
2
0
1
2
1
1
1
1
0
1
2
1
0
0
1
2
0
0
0
0
1
1
1
2
1
1
2
2
1
0
0
1
0
2
2
1
1
2
0
1
2
2
1
1
1
1
1
0
0
1
0
2
2
1
2
1
0
0
0
3
0
0
2
1
1
1
1
1
0
0
2
1
2
0
1
2
1
1
0
0
1
1
1
1
1
1
1
0
1
1
0
2
1
0
1
1
1
2
1
0
1
0
3
1
0
0
2
3
4
1
1
1
1
2
1
1
0
1
1
1
1
2
1
1
1
0
1
0
1
0
1
1
0
1
2
1
0
1
1
1
1
0
1
1
1
0
1
1
1
1
1
0
1
1
1
1
2
1
2
1
2
1
0
1
2
0
1
0
1
0
0
1
1
0
1
0
1
2
0
2
2
1
1
2
2
1
0
1
0
1
2
1
2
1
0
1
1
1
0
1
1
1
1
1
0
2
1
0
0
1
0
0
1
1
2
1
1
1
1
0
2
0
0
2
2
0
1
2
0
0
2
1
1
1
1
0
0
2
1
1
2
2
0
0
1
0
2
1
1
1
1
1
2
2
1
1
0
2
1
0
1
0
1
2
1
3
0
0
1
0
1
1
2
2
2
1
0
2
0
0
1
2
2
0
1
2
2
1
2
1
0
1
0
1
2
0
0
1
2
0
1
2
1
2
1
0
2
1
1
1
0
2
1
2
2
1
1
1
1
1
2
3
0
0
1
1
0
1
1
2
0
2
1
1
1
1
1
0
1
0
1
1
1
2
2
0
1
1
0
0
1
1
0
0
0
0
0
1
0
2
1
0
0
1
1
0
0
1
2
0
2
1
1
0
2
1
2
0
1
0
2
0
0
1
0
1
1
0
1
0
2
1
1
1
1
1
1
0
0
1
1
1
0
0
1
1
1
1
0
1
0
1
2
1
2
1
1
1
0
2
0
1
1
0
2
1
1
1
0
1
2
1
1
1
2
2
1
2
1
0
0
1
2
1
0
1
0
2
1
1
1
0
1
1
0
1
3
1
0
1
0
1
1
0
1
2
1
2
2
1
1
1
0
1
1
2
0
2
0
0
0
1
0
1
1
1
2
0
0
1
1
0
0
0
1
2
0
0
1
1
1
1
1
3
1
2
1
0
0
2
1
0
3
2
0
1
0
2
1
0
0
2
2
1
1
0
2
1
1
1
3
0
1
1
1
2
0
1
2
0
0
0
2
1
1
1
2
2
2
2
1
2
0
1
1
1
1
2
0
1
0
1
0
1
0
2
1
1
1
0
2
3
2
1
2
1
1
1
1
1
2
2
2
1
1
2
1
1
1
1
1
0
1
1
0
1
0
1
1
0
2
0
0
0
0
1
1
1
2
2
2
0
2
2
1
1
1
1
3
1
1
1
1
2
1
0
1
1
1
0
0
1
0
2
0
0
1
1
0
1
1
2
0
0
2
0
0
1
0
2
1
1
1
1
0
1
2
1
0
1
1
1
0
0
1
1
1
1
1
2
2
1
2
1
2
2
0
1
0
2
1
0
0
1
1
1
1
2
0
0
1
1
2
1
2
2
0
1
2
2
2
1
1
1
1
3
2
1
1
0
1
1
1
1
0
1
0
1
0
2
5
0
0
1
2
1
2
1
1
1
0
1
2
0
1
1
0
1
2
1
1
2
0
1
0
1
1
1
2
1
1
2
1
1
0
0
1
1
1
2
1
0
1
1
2
1
0
1
1
1
2
2
2
1
2
0
1
2
1
1
1
1
1
1
1
2
1
0
0
1
1
1
0
1
1
2
1
2
0
2
1
0
1
0
1
0
1
0
0
1
0
1
1
2
1
1
4
2
0
1
1
1
0
1
1
1
1
2
0
2
1
1
1
2
1
2
1
1
2
1
1
2
1
1
2
1
2
2
2
2
2
0
2
0
0
2
0
1
1
2
1
2
0
1
1
1
2
2
1
0
0
1
0
1
0
0
1
1
2
1
2
1
2
2
1
1
1
1
2
1
1
1
1
0
0
2
1
1
2
0
2
1
1
2
0
0
0
1
2
2
2
0
1
1
1
0
0
1
2
1
0
2
1
0
0
1
1
1
0
2
1
1
1
2
0
2
1
0
1
1
1
2
1
0
0
1
1
2
2
0
1
1
2
1
1
0
2
2
0
1
1
2
2
1
1
2
1
2
1
0
1
1
1
1
1
1
1
1
0
2
0
0
2
2
0
1
1
2
1
0
1
0
1
1
1
1
0
1
1
0
0
1
0
0
2
2
2
2
1
1
1
1
0
1
1
1
2
1
2
0
0
2
2
2
0
0
1
0
0
2
1
0
1
2
1
1
2
1
2
2
1
0
2
1
0
2
0
0
3
0
1
2
1
0
1
0
1
0
0
2
1
1
0
2
1
1
1
2
0
1
2
1
2
2
2
0
1
1
2
0
1
1
1
1
2
1
1
0
2
1
2
2
2
1
1
2
1
0
1
0
1
2
0
1
0
0
1
1
1
1
0
0
0
1
1
1
1
1
1
1
0
1
0
2
1
1
0
2
0
1
1
1
0
2
1
1
1
2
1
1
0
1
0
0
2
2
1
0
0
2
1
2
1
1
1
1
0
2
0
0
1
0
2
0
1
2
1
3
2
1
2
1
2
2
1
0
0
1
2
1
0
0
1
1
2
1
1
3
0
1
1
1
1
0
1
1
2
1
1
2
2
0
1
0
0
1
1
2
1
1
1
1
1
0
2
2
0
1
2
0
1
1
2
1
1
0
0
1
0
2
1
2
1
1
0
1
2
0
2
0
2
1
0
1
0
2
2
0
1
2
2
2
1
1
2
0
0
1
0
1
1
2
2
1
1
1
1
2
1
1
0
0
2
1
2
2
0
0
1
1
1
1
1
2
1
0
0
1
2
0
1
2
1
1
1
0
1
0
2
0
0
2
1
1
0
1
1
1
2
2
1
0
1
2
1
1
2
1
2
1
0
1
1
1
1
0
2
1
0
1
0
2
2
1
2
2
2
1
1
1
1
2
0
1
2
2
1
0
1
1
2
1
0
1
1
2
3
1
2
0
2
1
0
1
2
0
1
2
1
1
1
0
1
1
1
1
2
0
1
2
1
2
1
2
0
0
1
1
1
2
0
0
0
1
0
1
1
1
0
2
1
2
0
1
0
0
1
1
0
1
1
0
0
0
1
1
1
1
0
1
1
2
0
1
1
1
1
1
1
1
1
1
1
4
2
1
1
1
0
1
0
1
2
2
1
0
0
1
0
0
1
1
2
0
2
1
0
1
1
1
1
1
1
1
0
1
2
1
1
2
0
1
1
1
2
1
1
1
1
1
1
1
1
2
0
1
0
2
2
0
1
0
1
1
2
1
1
0
2
1
0
2
1
1
1
1
1
1
1
1
2
2
1
1
1
1
0
1
0
1
1
0
1
2
1
1
2
0
0
0
0
0
1
1
1
2
1
2
1
1
2
1
2
2
2
0
1
1
0
1
1
3
2
2
2
0
2
2
0
2
2
1
0
2
1
0
1
1
0
0
1
0
2
2
1
1
2
0
1
1
2
2
0
1
1
2
2
1
1
0
2
0
1
1
1
1
2
1
2
1
1
1
1
1
2
0
0
2
0
1
2
2
2
1
0
2
2
2
1
1
1
1
1
1
1
2
2
0
2
1
1
1
1
0
1
1
0
1
0
0
1
2
0
1
2
0
1
1
0
0
1
2
1
1
0
2
2
0
1
0
1
2
1
0
0
2
2
1
1
1
1
2
1
0
0
1
1
1
0
0
0
2
0
2
1
0
2
2
2
0
2
2
2
0
1
0
1
0
0
1
1
2
1
0
2
1
1
1
1
1
1
0
1
1
0
0
1
1
1
2
1
2
2
2
2
1
2
2
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
2
0
1
0
0
1
1
1
1
2
1
1
1
0
2
1
1
1
1
0
1
1
2
2
1
2
1
0
0
0
1
1
0
1
1
2
0
0
2
0
1
1
1
1
2
1
0
0
2
0
0
0
1
2
0
1
2
0
0
1
0
1
1
1
1
0
2
1
2
2
0
0
1
1
0
1
2
0
1
1
2
2
1
1
2
2
0
0
0
0
0
1
1
1
1
1
0
2
1
1
2
0
0
1
1
0
2
2
1
0
1
0
1
0
1
2
1
1
1
1
2
0
1
1
0
1
1
1
0
1
0
2
0
2
1
1
1
3
0
1
2
0
3
1
1
1
0
1
0
0
1
1
1
1
0
1
1
2
1
1
2
1
2
0
0
1
1
2
1
1
2
1
0
1
2
1
0
1
0
1
1
1
2
0
2
1
2
1
0
1
0
0
0
0
0
1
2
1
2
0
2
1
1
2
1
1
1
1
1
0
2
2
1
1
2
1
2
0
2
1
1
1
0
1
1
1
0
0
1
1
0
2
1
0
2
1
2
0
1
1
1
1
0
1
1
4
1
1
2
2
1
2
2
1
0
0
2
1
1
2
0
1
0
1
1
2
2
1
0
1
1
1
1
1
0
0
0
1
0
2
1
0
1
1
2
1
0
2
1
1
1
1
2
1
0
0
1
1
0
1
2
0
0
2
1
2
1
2
1
0
1
1
0
0
2
0
0
2
1
2
2
1
1
0
0
2
1
1
2
2
1
1
1
0
1
1
2
2
0
1
1
1
2
1
2
1
2
1
2
1
1
0
0
2
1
2
1
1
0
1
1
1
1
2
0
2
1
0
0
1
1
2
0
1
0
0
0
1
1
2
1
1
2
2
1
0
1
2
1
0
1
0
1
2
0
0
1
1
1
1
1
1
1
0
1
1
1
2
1
0
1
1
2
0
2
1
1
2
2
1
1
1
1
1
0
0
1
1
1
0
3
0
0
2
2
2
0
2
1
1
1
0
0
0
2
1
1
0
1
1
2
1
0
1
0
0
1
0
1
1
0
1
3
1
2
1
2
1
1
1
1
0
1
1
1
1
0
0
1
1
0
2
0
0
1
1
1
2
5
1
0
2
0
0
2
0
0
1
0
1
1
1
0
0
1
1
1
0
0
1
1
1
1
1
1
0
0
1
0
1
1
1
0
1
0
1
2
1
1
2
0
1
1
1
2
2
1
1
2
1
1
2
1
2
3
0
2
2
2
1
1
2
0
2
1
1
1
1
2
0
2
1
0
0
1
1
1
2
1
1
2
0
1
2
1
1
2
1
1
0
2
2
1
2
1
1
2
1
1
2
2
0
1
1
1
1
0
1
1
0
2
1
1
1
0
0
0
1
0
0
1
0
1
1
1
1
2
1
1
1
1
1
3
1
0
1
0
1
1
1
2
0
1
1
1
1
1
0
0
2
0
2
2
1
1
1
0
1
2
0
1
1
0
0
1
1
1
0
1
0
2
0
0
1
0
1
0
0
1
1
2
0
2
2
1
2
0
1
2
0
2
1
1
0
2
1
2
0
1
2
2
1
0
0
2
1
0
1
1
1
1
1
0
1
1
1
1
1
1
2
1
2
1
1
0
2
1
0
2
0
1
1
2
1
0
1
1
0
0
2
0
1
2
0
2
2
1
0
1
1
0
0
0
2
3
1
0
1
0
1
2
0
1
1
1
2
1
1
1
2
1
2
2
2
1
0
1
0
0
1
1
4
1
1
2
1
0
1
1
0
1
0
2
0
0
2
0
0
1
0
0
2
2
2
0
1
1
1
1
1
1
1
1
0
0
1
0
1
1
1
1
0
2
3
0
1
0
0
1
1
1
0
1
1
2
1
1
1
1
2
1
1
2
0
1
1
1
1
1
1
2
0
1
2
2
2
2
1
0
2
2
2
2
1
2
1
0
1
0
0
1
2
0
2
1
1
1
0
2
0
1
1
1
1
1
1
0
1
2
1
2
1
0
2
1
2
1
1
1
0
0
1
0
2
0
0
0
1
1
0
1
0
1
2
2
1
2
1
0
1
0
0
2
2
3
1
0
0
1
1
2
1
0
0
2
1
0
1
1
1
1
0
0
1
0
0
1
2
0
1
0
1
0
2
2
2
0
0
1
2
2
1
1
2
0
2
2
1
1
1
0
0
2
2
1
2
1
1
1
1
2
1
1
1
2
2
2
2
0
1
1
1
1
1
2
0
1
1
0
0
1
1
1
1
1
2
2
2
1
2
2
1
1
1
0
1
1
1
1
0
1
1
1
1
2
1
1
1
0
1
0
1
1
2
1
1
1
1
1
1
1
2
0
1
2
1
2
3
0
2
0
1
1
0
1
0
1
1
1
1
2
1
1
1
0
2
0
1
2
2
2
0
1
0
0
2
1
1
1
1
2
1
0
2
0
1
1
1
1
0
0
1
0
0
2
2
3
1
2
1
0
0
0
2
2
0
1
0
1
2
0
2
1
1
1
2
2
1
1
1
0
2
1
1
2
1
0
1
2
1
1
2
1
0
0
1
2
1
1
1
1
0
0
0
1
2
2
2
0
0
1
2
1
1
1
2
1
0
1
1
1
0
1
1
0
1
1
1
3
1
1
1
0
1
0
1
2
2
2
1
1
1
0
1
2
0
0
2
0
2
0
1
1
3
0
0
0
1
1
1
0
1
1
1
0
1
2
0
1
2
1
0
1
0
2
1
3
1
0
1
3
1
1
2
2
0
1
1
2
2
1
3
2
1
0
1
0
0
0
1
0
1
2
0
0
1
1
1
1
1
1
1
0
1
0
2
0
1
2
0
1
1
1
2
3
0
0
2
1
1
1
1
0
1
2
1
0
0
0
1
1
1
1
0
0
2
2
1
0
2
2
0
1
0
2
1
0
1
0
2
2
1
2
0
1
0
1
1
1
1
0
2
1
2
1
1
2
2
2
2
1
2
0
1
0
2
0
1
1
1
1
0
1
2
0
1
1
2
1
1
0
0
0
1
0
1
1
1
2
2
3
1
2
2
1
2
1
1
1
1
2
0
0
0
1
0
2
1
0
2
1
1
2
0
0
0
1
2
1
0
1
0
2
0
2
0
1
1
0
1
2
2
1
2
1
0
0
0
1
2
1
0
2
1
1
1
1
2
1
2
0
0
1
1
2
1
1
0
1
1
1
1
2
1
1
0
1
2
0
0
1
2
0
2
2
1
0
2
0
1
0
1
1
1
1
1
1
0
1
3
2
1
1
2
2
1
0
1
1
3
1
1
1
0
1
2
1
1
2
0
1
0
0
0
1
1
2
3
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
0
2
1
0
1
1
0
0
1
1
1
1
0
5
1
0
0
2
2
1
2
2
1
1
0
0
1
1
1
1
2
2
1
0
1
1
0
2
0
1
1
0
2
2
1
1
1
1
5
1
1
2
2
1
0
1
0
0
0
2
2
1
0
0
0
1
1
1
0
1
2
0
2
0
2
2
1
1
0
0
2
2
2
1
1
1
0
1
1
1
1
2
1
0
2
0
1
1
1
1
2
0
1
0
1
2
1
0
0
0
0
2
4
1
2
1
1
1
0
1
1
2
2
2
2
1
0
1
0
0
1
1
1
1
0
0
0
1
2
2
1
1
1
1
2
1
1
1
2
0
0
1
2
1
1
0
1
1
1
1
1
0
1
0
0
1
2
0
1
2
1
2
1
1
2
0
1
2
2
1
1
1
0
2
0
0
1
0
0
1
1
1
0
2
0
1
1
1
1
1
1
1
0
1
0
1
2
1
1
2
0
1
1
1
1
2
2
0
1
1
0
2
0
0
0
1
0
0
1
1
2
1
1
2
0
0
0
2
2
0
1
2
2
2
1
0
1
1
2
0
2
1
1
2
1
2
0
1
0
1
1
0
1
1
1
1
0
1
1
1
1
1
0
3
1
1
2
1
0
2
1
0
0
1
0
1
1
1
1
1
2
0
2
2
2
2
0
1
1
1
2
1
2
0
2
1
2
1
1
1
1
1
1
1
0
1
1
1
1
2
0
2
2
2
1
1
1
2
1
0
2
1
0
1
0
0
1
1
0
1
1
0
3
1
2
0
2
1
1
2
0
1
1
2
2
1
1
1
0
1
1
1
1
0
1
1
2
1
1
1
1
1
1
1
1
1
1
0
0
1
2
1
1
3
0
1
0
1
0
0
0
2
1
0
2
0
1
2
0
1
2
1
1
1
1
1
1
0
1
0
1
1
2
1
1
0
1
2
0
2
3
0
0
1
0
1
1
1
1
1
0
1
1
1
0
0
2
2
1
1
1
1
1
1
1
2
1
0
0
1
0
0
2
0
1
2
0
2
1
1
1
0
0
1
1
1
1
0
0
2
1
1
1
2
1
1
1
0
2
0
1
1
1
0
1
2
2
1
2
1
1
1
1
2
1
0
2
0
1
1
1
1
1
1
2
1
1
0
0
0
0
2
0
1
0
0
0
1
1
0
0
0
1
2
1
2
2
0
3
1
2
1
0
2
0
0
0
1
0
1
1
1
1
0
1
2
0
2
1
0
1
2
2
1
2
1
1
1
1
2
1
2
1
2
1
1
1
2
2
1
1
3
1
1
3
0
2
0
1
0
1
1
1
1
1
0
1
1
1
0
2
0
1
1
2
2
2
0
1
0
1
2
1
0
1
2
1
2
0
2
1
0
2
1
1
2
1
1
0
1
2
1
2
2
1
1
1
2
1
2
1
1
1
1
1
1
1
2
2
2
1
1
1
0
1
1
1
0
1
0
1
2
1
2
2
1
2
1
1
2
3
2
1
1
0
2
1
1
1
1
1
1
1
1
2
0
1
1
1
1
2
0
1
0
1
1
0
1
0
0
1
2
2
2
5
1
1
2
0
1
2
2
1
1
1
1
1
1
1
1
1
0
1
2
0
1
1
0
1
1
1
0
2
2
1
0
0
1
1
1
2
0
1
2
1
1
1
0
1
1
0
2
2
1
2
0
1
0
0
1
1
0
1
1
0
2
1
0
1
0
1
2
0
2
1
1
1
1
1
0
1
1
1
1
1
2
0
2
2
0
1
0
2
1
0
1
0
1
1
1
0
1
1
1
1
1
2
1
0
1
0
1
0
0
2
1
0
1
1
1
1
0
2
1
0
1
2
1
1
1
1
1
1
1
0
0
1
1
0
0
2
1
2
2
1
2
1
2
2
1
2
2
1
1
1
1
1
0
0
1
1
0
1
0
0
2
1
0
1
0
1
1
1
1
1
2
2
1
1
2
1
2
2
2
1
1
1
1
0
0
0
1
1
1
0
1
3
2
2
0
1
1
0
1
1
2
0
1
2
0
1
0
1
2
0
1
1
1
1
2
1
0
1
1
1
2
2
0
1
0
1
1
1
1
1
1
1
0
1
2
2
2
1
1
1
2
0
1
0
0
0
3
2
2
2
1
1
1
0
1
1
0
1
0
1
1
1
1
2
1
0
1
1
1
0
2
1
1
1
1
2
1
1
1
0
3
0
1
1
1
2
3
1
1
1
1
2
1
1
0
1
2
1
0
1
1
1
1
1
2
1
1
0
0
2
1
1
1
0
1
1
1
2
1
2
0
1
1
2
1
2
1
1
1
1
2
1
1
2
0
1
1
1
1
1
1
1
1
2
1
1
2
2
1
1
1
2
1
2
1
0
2
2
2
2
2
2
2
0
1
1
0
2
1
1
0
0
1
1
2
1
0
2
0
0
2
2
1
1
1
1
1
1
1
1
1
2
0
1
1
1
1
1
0
1
2
3
1
1
2
1
2
0
1
2
1
1
1
1
1
0
1
1
1
3
1
1
1
1
0
0
1
1
2
0
1
0
0
1
0
2
0
1
0
0
1
0
1
2
2
1
1
1
0
0
2
1
1
1
0
1
0
1
1
1
0
1
2
0
1
1
0
1
1
2
0
2
2
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
1
0
1
1
2
0
0
1
2
1
0
0
1
1
1
2
1
0
2
1
0
1
1
0
1
2
1
1
2
0
1
2
0
2
0
2
1
1
2
1
1
0
0
1
2
0
1
1
0
2
2
1
0
1
2
0
2
2
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
0
2
2
1
1
2
0
1
1
1
1
1
2
0
2
2
0
2
1
0
1
1
2
2
1
2
0
2
2
1
1
1
1
0
1
1
1
2
1
0
1
1
1
2
2
2
1
1
1
2
0
1
2
2
0
1
1
2
1
0
2
1
1
0
1
1
1
1
1
1
1
0
1
3
0
1
0
1
0
0
1
2
1
2
2
1
2
1
2
2
1
0
2
1
3
2
1
1
1
0
2
1
1
1
1
1
2
0
0
0
2
0
1
1
1
0
2
1
2
0
1
1
0
2
1
2
2
2
2
1
1
1
1
1
0
1
2
0
0
1
0
1
0
1
1
2
0
1
2
0
2
1
2
1
1
2
2
0
0
1
1
1
0
2
1
1
1
1
0
0
1
1
0
2
1
3
1
3
3
1
0
0
1
1
0
3
0
2
0
1
1
1
2
1
2
1
3
0
1
0
0
1
1
0
1
0
1
2
1
2
1
2
0
1
2
2
1
0
0
1
1
0
9
1
1
1
2
1
1
2
4
1
1
1
1
2
0
0
1
1
0
1
2
1
1
1
2
1
1
1
0
1
2
1
2
1
1
0
1
1
0
0
1
1
1
0
1
2
1
1
2
0
1
0
2
1
2
1
1
1
2
1
1
2
1
2
2
0
1
1
1
0
2
1
1
1
1
1
1
2
2
0
1
0
2
1
1
0
2
0
1
1
1
1
2
1
0
1
0
1
1
2
0
2
0
1
1
1
1
0
2
2
1
0
0
1
0
2
1
1
2
1
1
0
0
1
1
1
1
1
1
1
0
0
2
0
1
0
0
1
0
1
1
1
2
0
0
2
2
1
0
0
0
1
2
0
0
1
1
1
3
1
1
2
2
1
1
1
0
0
0
1
0
1
0
0
1
2
2
1
0
2
3
1
2
1
1
1
0
0
1
1
0
1
1
0
1
1
1
0
2
0
1
0
0
1
1
0
1
2
0
2
1
1
0
1
3
1
1
1
1
1
0
0
2
1
1
0
2
0
0
1
1
2
2
0
2
1
1
2
1
2
1
1
3
1
1
1
1
0
1
1
1
2
0
1
1
1
1
1
1
0
0
1
0
1
2
1
1
1
2
2
0
1
1
1
2
0
2
1
0
2
2
1
1
1
3
0
1
1
1
1
0
2
2
0
1
1
1
1
1
0
1
0
2
1
2
1
0
0
0
2
1
1
2
1
0
0
1
2
1
1
2
1
2
0
1
2
1
1
1
0
1
1
0
2
1
1
2
1
0
1
0
1
1
1
2
1
2
1
0
1
1
1
2
1
2
2
2
2
0
2
0
0
1
2
2
2
1
1
1
1
1
2
1
0
0
2
1
1
1
1
1
2
1
0
1
0
1
2
0
1
1
1
1
1
1
2
2
2
0
2
2
0
1
0
0
1
1
2
0
1
1
2
3
1
2
0
1
1
1
2
1
1
1
1
1
1
2
0
2
0
0
2
0
1
2
2
0
1
1
1
1
2
2
2
2
0
1
1
1
1
1
0
1
0
1
1
0
1
2
0
1
1
1
1
1
0
2
0
1
2
1
0
0
1
1
1
0
0
0
0
2
1
1
0
1
1
1
0
0
1
0
3
0
2
0
1
2
1
0
0
1
1
1
1
1
0
1
0
1
1
2
2
1
0
2
1
1
2
2
0
2
0
0
1
1
2
0
2
0
0
0
2
2
1
1
1
1
1
1
1
2
0
2
3
2
1
1
3
1
1
0
1
1
0
0
1
1
2
1
1
0
0
2
3
1
1
0
0
2
1
2
0
1
2
1
0
1
2
1
1
2
2
2
1
1
0
2
2
1
2
1
0
1
1
1
1
1
0
1
1
0
1
0
3
1
0
0
0
1
1
2
1
2
0
0
1
1
1
1
1
1
1
2
1
1
1
1
0
1
2
1
1
1
1
0
2
1
1
1
0
1
2
1
0
1
0
1
1
2
1
0
1
0
1
0
3
0
2
1
0
2
0
1
0
0
0
2
1
0
1
3
2
2
1
0
0
1
1
1
0
0
3
1
1
0
2
2
0
1
2
0
0
1
0
1
0
2
3
1
1
2
2
2
0
2
0
1
0
0
0
0
0
2
1
2
1
1
1
0
0
2
1
2
1
1
0
1
1
1
1
1
1
1
2
1
1
0
1
0
1
1
0
1
2
2
2
1
1
1
2
1
0
2
1
1
0
0
0
1
1
2
1
1
0
0
1
1
0
2
1
2
4
0
0
0
2
1
1
1
1
2
1
2
1
2
0
2
1
1
1
2
2
1
0
2
0
1
0
1
0
2
1
1
0
1
2
1
1
1
1
1
0
1
1
0
1
1
2
0
1
1
1
1
1
2
2
1
0
1
1
0
1
1
0
0
0
2
1
1
1
1
1
1
3
0
1
1
2
1
1
1
0
2
0
2
1
2
1
1
2
1
1
2
2
2
1
0
1
0
1
1
1
1
1
1
1
1
2
0
1
2
1
1
1
1
0
0
2
1
1
1
2
0
2
1
0
2
0
1
1
2
1
1
2
2
1
0
1
1
1
1
1
2
2
1
0
1
1
1
0
1
0
1
2
1
1
0
1
1
1
1
1
2
1
2
2
1
0
0
0
1
1
1
1
0
0
2
1
2
0
0
1
1
0
0
0
0
1
0
0
2
0
0
0
1
1
3
1
1
1
1
2
2
0
0
1
2
1
2
1
1
0
1
0
1
0
1
1
1
1
1
1
1
0
1
0
1
2
0
1
1
2
1
1
1
2
1
1
0
0
3
0
0
1
0
0
1
1
1
1
1
1
2
1
0
0
0
3
1
0
2
2
1
0
0
0
2
0
0
2
1
1
2
1
0
2
1
0
0
1
1
0
1
0
0
0
1
2
1
1
1
1
0
0
1
2
0
2
1
1
1
1
1
0
2
1
2
1
1
1
1
1
2
1
1
0
0
2
1
1
2
2
0
1
1
0
0
2
1
1
1
1
0
2
1
2
1
1
1
0
1
0
1
1
1
1
1
0
0
0
2
0
1
0
1
2
1
1
1
1
1
0
1
2
0
2
1
1
1
1
0
0
2
1
1
2
1
1
2
1
1
1
0
0
1
1
1
1
1
1
1
0
0
1
2
0
1
1
1
1
1
1
3
2
0
2
3
1
1
1
1
0
1
1
1
2
2
1
2
0
1
0
0
1
0
0
1
2
1
1
1
1
2
0
1
2
1
2
2
2
2
0
1
1
0
3
2
1
1
0
0
2
0
1
2
1
0
2
1
1
0
1
1
0
1
1
2
0
0
2
1
0
2
0
1
0
1
1
1
1
0
2
1
2
0
1
0
1
1
0
1
0
1
0
1
1
1
0
0
0
1
1
1
0
1
2
2
1
1
1
1
0
2
0
1
0
2
1
1
2
1
0
1
2
1
2
1
1
2
2
1
1
3
1
0
1
0
1
2
1
1
5
1
0
2
1
1
1
0
1
1
2
1
2
0
0
1
1
1
1
0
1
1
1
1
1
1
1
1
1
0
1
0
1
1
1
0
1
0
1
1
1
0
0
2
0
1
0
2
2
1
0
1
2
2
1
1
2
2
2
1
1
1
1
2
1
1
3
0
2
0
3
0
1
2
1
1
1
1
1
1
1
2
0
0
1
1
1
2
0
1
1
0
2
1
1
1
2
0
0
1
2
1
1
1
0
1
2
0
1
0
0
1
1
0
0
1
2
1
1
0
1
2
2
1
1
1
1
0
1
1
1
2
0
0
2
1
1
1
1
0
2
1
2
1
1
0
1
2
1
2
1
0
1
2
1
1
1
1
1
0
2
1
1
1
2
0
1
1
1
0
1
1
1
0
1
0
0
1
2
2
1
1
2
1
3
1
1
1
1
1
1
2
2
0
0
1
1
1
2
0
1
1
2
0
0
2
1
0
0
2
1
1
1
1
2
2
1
1
2
1
1
1
0
0
1
1
2
1
0
2
1
2
1
0
3
1
0
2
1
1
0
2
0
1
0
0
1
1
1
2
1
1
1
1
1
0
0
1
0
0
1
1
1
0
3
1
2
1
1
2
2
1
0
1
0
2
1
1
0
0
1
1
1
0
1
0
1
2
1
0
2
1
1
1
1
1
1
0
1
1
0
1
1
1
1
2
0
1
0
0
1
1
2
0
2
2
1
2
1
1
2
0
1
0
1
1
0
2
0
0
1
1
1
1
1
2
1
0
1
1
1
2
1
1
2
0
2
0
1
1
1
1
0
1
1
1
1
0
1
1
1
0
1
1
1
1
0
1
1
1
0
0
2
1
1
2
0
2
1
2
0
1
1
0
1
2
1
1
1
0
0
0
1
0
1
1
1
1
1
1
0
1
0
2
1
1
0
0
0
1
1
1
0
1
0
1
0
1
0
1
1
1
0
2
1
2
2
1
1
1
1
2
2
1
0
1
2
1
2
1
0
0
2
0
0
1
1
2
1
2
1
2
1
1
1
0
2
1
0
2
2
0
0
2
1
1
0
1
1
1
1
0
2
1
0
1
2
0
2
3
0
0
1
0
0
1
0
1
0
0
2
0
1
1
0
2
0
0
0
1
2
0
0
1
0
1
0
1
2
1
2
2
1
1
1
1
1
0
1
0
0
1
0
1
1
1
3
1
0
1
1
0
1
3
1
2
2
1
0
1
1
1
2
0
1
1
2
2
0
1
2
2
1
1
1
2
0
0
1
1
1
0
1
1
2
1
2
1
2
1
0
2
1
1
1
1
0
1
0
0
2
0
1
1
2
1
0
2
1
1
0
1
1
0
1
0
0
3
0
0
2
1
1
1
0
1
1
1
2
1
1
1
1
2
1
2
1
0
1
0
0
0
1
1
2
1
1
0
0
1
1
1
1
3
0
0
0
0
2
1
0
1
1
1
1
0
1
1
2
1
0
1
1
1
1
3
1
1
1
0
1
1
1
2
0
0
1
1
1
1
1
1
0
1
1
1
2
2
2
1
1
1
0
2
1
1
1
2
1
1
0
1
2
0
1
0
0
0
0
1
1
2
0
2
0
0
2
0
1
0
2
1
2
1
0
1
1
1
1
2
2
1
0
0
1
2
0
1
2
0
2
2
1
2
1
0
1
1
1
1
1
0
1
1
1
0
2
0
1
1
0
2
0
1
1
0
1
0
0
0
2
1
0
0
2
1
1
1
0
1
2
0
0
1
1
1
1
2
2
0
1
1
1
1
2
1
2
0
2
2
0
1
1
0
0
1
2
0
1
1
1
1
2
1
1
1
0
1
0
1
1
0
1
1
0
1
3
0
1
0
1
1
1
1
1
1
0
0
1
1
1
2
0
0
2
0
1
1
1
0
1
2
1
0
2
1
1
0
1
1
1
0
0
0
1
0
1
1
1
0
0
1
0
1
1
2
1
1
1
0
2
3
0
0
0
1
0
0
1
1
0
1
1
1
2
0
1
1
0
0
0
1
0
1
2
1
0
2
2
0
2
0
2
1
1
0
2
2
1
2
0
1
0
0
0
0
1
2
1
0
2
1
0
1
1
0
1
2
2
1
1
0
0
2
2
0
2
1
2
1
1
1
1
1
2
0
0
1
1
1
1
2
1
1
1
1
1
2
1
2
1
1
0
0
1
1
1
0
1
1
1
0
2
1
0
2
0
1
1
1
0
1
1
1
1
0
0
1
2
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
0
1
2
1
1
2
0
1
1
2
1
0
1
1
0
2
0
0
0
1
2
2
1
1
2
1
0
2
1
0
1
0
1
0
1
2
1
1
1
0
1
1
2
0
0
3
0
2
1
0
1
1
0
1
1
0
1
2
2
1
0
1
1
1
2
1
0
1
0
2
1
1
1
1
1
0
0
0
1
0
1
1
2
1
1
1
1
2
1
1
2
0
0
1
0
1
2
1
0
1
1
0
2
1
2
1
3
1
1
0
1
0
1
2
1
1
1
0
0
1
2
1
4
1
0
1
1
2
1
1
1
0
0
1
2
2
3
0
0
1
1
2
2
1
1
2
1
1
2
2
1
1
0
0
1
1
1
1
1
1
1
0
1
2
0
0
0
0
1
1
1
1
0
1
0
2
0
2
2
0
1
3
1
1
0
2
1
1
1
1
1
1
2
1
1
2
1
2
2
0
1
1
0
0
1
1
1
0
0
0
0
2
1
0
1
2
0
2
2
1
0
1
0
0
2
2
1
0
0
2
1
1
2
1
1
2
1
0
0
0
2
2
0
0
1
0
1
1
1
1
1
1
1
1
1
1
0
1
1
2
0
2
2
1
0
1
2
1
1
1
2
1
2
0
0
0
1
0
2
0
0
2
2
1
0
1
2
1
1
1
1
2
0
1
1
5
0
2
1
0
0
0
0
0
1
1
1
0
1
0
0
2
0
1
0
0
1
0
0
0
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
0
1
1
0
1
0
2
1
1
1
1
1
1
0
1
1
0
1
0
1
2
2
0
0
2
1
2
0
1
1
1
1
2
2
0
1
0
1
1
1
1
1
1
1
1
0
0
1
1
1
3
0
1
2
2
1
1
1
1
1
2
0
2
2
1
1
2
0
1
0
2
1
1
0
1
1
1
1
0
0
0
0
1
1
1
0
1
0
2
0
0
0
1
1
0
1
1
1
1
1
0
2
1
0
1
0
1
1
0
1
0
0
1
0
2
2
0
2
0
1
0
1
1
1
2
1
0
1
0
1
0
2
1
1
0
1
1
0
0
1
1
0
1
2
1
0
2
0
0
1
1
2
0
1
2
2
1
1
1
0
1
2
2
2
1
1
3
2
2
1
1
0
1
1
0
2
2
2
1
1
0
0
2
1
1
0
1
2
1
3
0
1
1
0
1
1
1
1
2
1
2
0
2
1
0
0
0
1
0
0
1
2
0
1
2
1
2
0
1
1
1
2
1
1
1
2
2
0
1
2
1
1
0
0
1
1
0
0
2
1
1
1
0
2
0
1
1
2
2
2
1
0
2
1
0
2
0
1
2
0
2
0
2
1
2
1
1
1
1
1
1
3
1
0
1
1
0
0
0
1
0
0
2
0
0
0
1
0
1
2
1
1
1
2
1
1
1
1
0
1
1
1
1
1
1
1
0
0
0
0
1
1
0
2
1
0
0
0
2
1
1
1
1
0
2
0
1
1
2
0
2
1
1
1
1
2
1
0
1
1
1
1
1
2
0
1
1
0
0
2
0
1
1
0
0
1
1
1
1
1
1
1
2
1
1
1
0
2
1
1
0
0
2
0
0
1
1
0
1
2
0
1
0
0
1
1
1
1
1
2
1
0
0
1
0
1
2
2
2
0
2
1
1
0
0
2
2
1
0
1
0
1
1
2
2
2
2
1
0
2
1
1
2
1
1
1
2
2
1
0
0
1
1
1
2
1
1
0
0
0
0
0
2
2
0
1
1
1
1
2
1
1
1
2
1
0
1
1
1
2
1
2
2
1
1
1
0
1
2
0
0
2
1
1
0
1
1
1
1
0
0
1
2
0
2
1
1
1
1
0
0
1
1
2
1
1
1
0
1
2
1
1
1
1
1
2
1
2
1
1
1
0
2
2
1
0
2
0
1
1
2
1
0
1
1
3
1
0
0
0
1
1
1
1
0
1
1
0
0
1
1
1
1
2
1
2
1
0
1
1
1
2
2
2
1
1
1
0
1
2
0
2
0
0
1
0
0
1
0
1
0
0
1
2
1
1
1
0
1
1
2
2
2
1
1
1
1
1
1
0
1
2
2
1
0
2
2
0
0
2
1
2
2
0
1
1
0
0
1
0
1
0
2
1
2
0
1
0
1
1
1
0
1
0
2
1
1
0
1
1
1
2
1
1
1
1
2
0
1
0
2
1
1
0
2
1
1
3
2
1
2
1
2
1
2
1
1
1
2
0
2
1
0
1
0
1
2
0
0
0
0
1
1
1
1
1
0
1
2
1
1
0
0
0
0
2
0
1
1
1
0
0
2
0
0
1
1
1
2
1
0
1
1
1
1
2
1
1
1
2
0
1
0
0
0
2
0
2
1
1
0
0
0
1
2
0
1
0
1
0
0
1
1
1
3
1
1
2
0
2
2
1
3
2
1
1
0
2
1
1
1
2
0
1
1
1
2
2
2
2
1
0
1
1
1
1
1
1
2
2
1
2
2
2
1
1
2
0
1
1
0
0
1
0
2
2
1
0
1
0
1
1
1
0
1
0
2
1
1
1
1
1
1
1
0
1
0
0
2
2
2
0
1
1
1
1
1
1
2
1
0
1
1
0
1
1
1
2
1
0
1
1
2
0
0
0
1
1
1
1
1
2
1
0
1
0
1
1
1
1
2
1
1
1
1
3
1
1
1
2
2
1
0
1
0
1
0
1
1
2
1
2
0
0
0
0
1
1
1
0
2
0
0
1
0
1
2
2
1
2
1
2
2
0
1
0
1
2
2
1
0
0
1
0
0
1
1
1
0
1
1
0
2
0
1
1
1
2
0
1
0
1
0
2
2
1
3
0
1
1
1
1
2
0
1
0
0
1
2
1
1
1
2
1
2
0
1
0
1
0
1
2
1
1
2
0
1
0
1
1
2
1
1
1
2
0
0
1
0
2
1
1
1
1
2
1
0
1
1
0
1
1
0
0
1
0
2
1
2
1
1
0
1
0
2
2
1
0
0
2
2
0
1
1
1
0
1
1
0
0
1
1
1
0
1
2
2
0
2
1
2
1
1
0
2
2
0
2
0
0
0
0
1
2
1
1
2
0
1
0
2
2
0
0
0
1
0
1
1
0
2
0
1
1
1
2
1
1
1
0
1
1
2
1
1
0
1
1
1
2
2
1
2
0
2
1
2
2
1
1
0
1
1
1
1
2
1
2
0
0
1
2
0
3
1
0
1
2
1
2
0
2
1
0
1
0
1
2
1
1
0
1
2
1
1
0
1
1
1
1
1
0
2
2
1
1
0
0
1
4
2
2
2
1
0
1
1
2
1
2
2
2
1
0
0
0
0
1
1
1
1
1
2
2
2
0
1
0
3
2
1
0
0
1
2
1
0
0
2
0
1
1
2
0
0
1
1
2
0
0
1
2
1
2
2
0
1
2
2
2
1
2
2
1
1
2
1
1
1
2
0
1
1
0
2
0
0
1
1
1
1
0
1
1
1
0
2
2
1
1
1
0
1
1
0
2
1
0
0
2
3
1
1
1
0
1
1
2
1
0
0
1
1
0
1
2
1
0
0
2
1
0
1
1
1
1
3
2
0
1
2
2
1
2
1
1
0
1
1
2
0
1
1
1
1
1
0
0
0
1
1
1
0
1
1
0
1
2
2
1
1
0
1
1
1
1
2
1
1
2
0
0
3
2
1
0
1
1
0
1
1
0
0
2
2
0
1
1
0
2
0
2
2
2
0
0
1
1
1
1
2
0
1
1
0
1
1
1
2
1
0
1
1
1
1
2
1
1
1
0
0
2
2
2
2
0
1
0
1
0
2
0
0
0
0
1
0
1
1
0
1
1
1
2
1
1
0
1
1
1
3
1
1
1
1
0
2
1
2
2
1
1
1
1
1
0
0
1
3
0
2
1
1
0
1
1
1
2
1
2
0
1
1
4
1
1
1
0
1
1
2
1
0
1
2
2
0
2
2
2
1
1
0
1
0
0
2
1
1
1
2
2
3
1
0
2
1
1
0
0
0
1
1
1
0
2
2
1
2
1
2
2
0
1
1
2
1
0
1
0
1
2
0
0
1
1
1
0
1
0
1
0
1
1
1
1
1
1
1
0
1
1
0
1
1
2
1
0
1
2
1
1
2
0
1
0
0
1
1
1
2
1
2
0
0
2
2
2
1
2
1
0
1
1
1
1
1
1
0
1
0
1
2
1
1
2
2
1
0
2
2
0
0
1
1
0
1
1
0
1
0
2
0
0
2
1
2
0
1
1
0
0
2
1
1
2
1
1
0
2
0
1
2
1
2
1
0
1
1
1
2
2
0
0
0
1
1
1
1
0
0
1
2
1
1
3
1
2
2
1
2
1
1
1
1
1
2
0
2
0
0
1
1
0
1
0
1
0
1
1
1
0
1
2
0
0
0
0
0
2
1
0
0
2
0
2
1
2
1
1
2
2
2
0
0
0
2
0
1
0
1
1
2
0
2
1
2
1
0
0
0
1
1
2
1
2
2
0
2
2
1
1
1
1
1
1
0
1
1
2
0
1
1
1
1
0
0
0
2
2
2
2
0
2
2
1
1
1
1
1
2
2
1
1
1
2
1
1
0
1
2
1
1
0
1
1
0
1
1
1
1
2
2
1
0
1
1
2
0
1
0
1
0
1
0
1
0
2
0
1
0
1
1
2
0
1
1
2
0
0
2
0
2
1
1
0
0
1
4
1
1
1
1
1
0
1
2
0
0
0
0
2
1
0
0
0
1
1
0
1
1
2
1
0
0
1
1
1
1
1
1
2
1
3
2
2
0
1
1
2
2
0
2
1
1
1
0
1
0
2
2
1
1
1
1
0
1
1
1
1
1
0
1
0
1
1
2
1
1
3
1
1
0
2
1
0
1
0
1
0
0
2
1
1
1
2
0
0
0
0
2
1
2
0
2
1
1
1
2
1
1
0
0
0
1
0
1
1
0
1
1
0
1
0
0
2
1
1
1
2
1
2
2
1
1
0
0
0
1
1
2
2
1
0
0
1
1
1
0
1
0
2
1
0
1
1
2
1
1
2
0
0
1
0
1
0
1
0
2
1
1
0
1
1
2
1
2
2
1
2
1
1
1
0
1
1
0
2
0
2
2
2
0
0
1
1
0
2
0
2
1
0
0
1
1
1
1
1
1
2
1
0
2
1
0
0
0
1
2
1
2
1
0
0
1
2
2
2
1
0
1
0
1
1
1
1
2
1
0
0
1
0
1
0
1
0
1
2
2
2
2
0
1
1
0
1
0
2
2
1
0
1
1
1
2
1
1
1
0
1
0
1
2
1
0
1
0
0
1
2
1
1
1
1
2
0
1
1
1
1
1
0
1
1
0
1
0
2
0
0
0
1
2
1
0
0
1
0
0
0
1
1
0
0
2
0
2
0
0
1
0
1
0
1
2
1
2
1
1
0
0
1
1
6
1
2
1
0
1
0
2
2
0
1
1
1
1
1
0
0
1
1
1
1
0
1
2
0
2
1
2
0
1
0
1
0
1
0
0
2
1
1
0
1
0
1
0
1
0
1
1
1
0
1
0
0
0
1
0
1
0
1
1
1
1
1
1
1
0
0
2
1
1
1
0
0
3
2
0
1
1
2
1
1
0
2
0
1
1
2
1
0
2
1
0
0
1
1
0
0
1
0
2
1
0
1
0
2
1
1
1
0
0
2
1
1
1
2
0
1
0
0
0
1
2
0
0
1
1
1
1
0
0
1
2
0
3
0
1
1
1
0
1
1
1
2
0
1
1
0
2
2
2
0
2
1
0
1
1
1
1
2
0
1
0
2
2
0
1
1
1
0
1
0
1
1
1
1
1
0
2
1
0
0
2
1
1
1
2
0
2
0
2
1
2
2
3
1
0
1
3
1
0
1
1
0
0
1
0
1
0
1
0
0
0
1
1
2
1
1
2
0
0
2
2
0
2
2
1
1
2
1
7
1
1
0
2
1
1
0
2
0
1
1
1
1
1
2
2
1
1
1
1
1
2
1
0
0
1
2
1
1
1
1
1
2
1
2
1
0
2
2
1
0
1
2
1
1
0
1
2
1
0
1
1
1
0
1
1
1
1
2
1
1
0
0
1
1
2
0
0
0
0
0
1
0
1
0
1
0
0
2
0
0
1
1
0
0
2
3
1
2
2
0
0
2
1
1
1
1
2
2
1
1
0
1
1
1
1
1
0
1
0
0
0
1
1
2
1
2
1
1
1
1
1
1
1
0
2
1
1
0
1
2
1
2
1
0
2
1
1
1
2
0
1
2
0
1
1
1
0
0
0
1
1
1
1
1
1
2
0
1
1
2
0
1
2
2
0
0
2
1
0
1
1
1
1
1
2
0
2
0
1
1
0
1
0
1
1
1
1
1
0
1
1
1
2
0
2
0
1
0
1
1
1
1
1
2
1
1
0
0
2
0
1
0
1
0
1
2
0
0
1
2
1
2
1
2
1
1
2
2
2
1
2
2
2
2
1
1
0
0
2
1
1
0
2
0
3
2
1
2
0
2
1
2
1
1
1
2
1
2
1
1
1
0
1
2
1
1
1
2
1
1
1
1
0
1
2
2
1
1
1
1
2
2
1
0
0
1
1
1
1
0
0
2
2
1
0
2
1
1
1
0
2
0
0
2
3
1
0
2
2
1
0
1
0
2
0
0
0
1
0
1
1
0
1
0
1
1
1
1
1
1
1
1
1
2
0
2
1
1
2
0
1
1
1
1
2
0
1
1
1
1
2
2
0
0
0
1
1
1
1
0
1
0
1
1
1
0
1
1
1
0
1
0
1
1
1
0
1
1
1
0
1
1
0
1
1
1
2
1
0
0
2
1
1
1
2
1
0
0
1
1
1
2
0
1
0
0
0
2
0
1
1
0
0
1
2
2
0
1
0
2
1
1
0
1
1
1
2
0
0
2
0
0
0
1
1
1
1
1
1
0
1
2
1
1
2
1
1
1
0
1
0
0
2
1
0
1
1
1
1
1
0
1
2
2
0
1
1
2
1
1
1
1
1
0
1
0
0
1
1
1
2
1
1
2
0
1
2
1
2
2
1
1
2
2
1
1
0
1
2
2
0
0
0
1
0
1
1
1
1
1
1
1
1
1
1
1
0
0
2
1
2
2
1
1
1
1
1
2
0
1
1
0
2
1
2
1
1
1
0
0
0
2
1
1
1
0
1
0
2
1
1
0
2
1
3
1
1
1
2
2
2
2
1
1
1
0
2
1
1
1
1
1
0
1
0
1
1
2
1
1
0
0
1
1
2
0
2
0
1
1
1
2
2
1
0
2
1
0
1
1
0
0
2
1
1
1
1
0
2
2
1
1
2
2
1
1
0
1
0
2
3
1
0
2
2
2
1
2
1
1
1
1
2
3
2
1
2
1
1
1
0
0
1
1
1
1
0
1
0
1
0
1
1
1
2
1
0
2
1
2
1
2
0
1
1
1
2
3
0
1
1
1
2
1
1
2
1
1
1
1
0
2
2
0
0
1
0
1
1
0
2
1
1
0
1
2
1
1
2
0
1
1
2
0
0
1
1
0
0
2
0
0
1
2
1
0
0
2
0
0
1
0
0
2
0
0
0
4
1
1
1
1
0
1
1
3
1
1
1
1
0
1
0
1
1
1
1
0
1
1
1
1
2
2
1
2
2
1
1
2
0
1
1
2
1
0
0
0
1
2
1
1
2
0
2
1
1
0
1
2
0
2
5
1
1
2
0
1
0
1
2
0
2
0
1
1
1
1
0
0
1
2
1
1
0
1
0
0
1
2
1
1
0
1
1
0
1
0
0
1
1
2
2
2
1
1
0
1
2
1
0
1
2
1
2
0
2
2
1
1
2
1
2
0
2
2
1
1
1
2
0
1
1
1
0
1
1
0
1
1
1
3
1
1
1
2
1
1
1
1
2
1
1
0
2
1
1
1
0
1
0
0
0
1
1
2
0
0
2
1
0
1
2
0
1
0
2
1
1
0
1
2
1
2
1
0
0
1
1
1
1
1
0
1
1
1
1
1
0
0
1
0
0
2
0
1
0
1
1
1
1
1
2
0
2
0
1
1
0
1
1
1
1
1
2
0
1
1
2
1
2
1
3
0
2
1
1
2
1
1
1
1
1
0
0
1
1
1
0
1
0
0
0
0
0
1
1
1
2
1
0
1
1
0
1
1
2
1
1
1
1
0
2
2
1
1
1
0
0
1
1
0
1
2
1
1
1
1
1
0
1
0
2
1
1
2
1
1
2
0
1
2
1
1
1
2
1
1
1
1
1
0
0
1
1
0
1
1
1
1
1
1
2
0
1
0
1
0
2
1
0
0
0
1
0
1
2
0
1
1
1
1
1
1
0
2
0
0
0
0
1
2
2
0
0
1
0
1
1
1
1
1
1
2
0
1
1
1
2
1
1
1
0
0
0
2
0
2
1
2
2
0
0
0
0
1
0
1
2
1
1
2
0
1
1
1
2
1
0
1
0
1
0
2
1
0
0
2
3
1
1
1
2
0
1
0
1
1
1
1
1
1
2
2
0
3
1
1
0
1
0
0
0
1
1
1
0
0
1
1
1
1
2
2
2
0
0
2
2
0
1
1
1
0
2
2
2
2
1
1
1
1
2
1
1
1
0
1
1
1
2
1
0
1
1
2
0
2
1
1
2
1
1
0
0
1
1
1
1
1
0
0
0
1
1
1
1
2
1
1
1
0
2
2
0
0
1
1
1
2
2
1
1
0
2
3
2
0
2
1
2
2
0
1
1
1
3
1
1
0
1
1
0
0
0
1
1
1
1
2
2
0
0
1
1
0
0
1
1
1
0
2
2
1
1
1
2
0
1
1
0
1
1
1
1
0
1
4
1
1
1
1
0
0
1
1
1
1
2
0
2
2
0
0
2
1
1
1
2
0
1
0
1
2
1
0
1
1
2
3
0
0
1
2
0
1
1
1
1
2
1
0
1
1
1
0
2
0
2
1
0
1
1
0
2
0
1
1
1
1
1
1
0
1
1
1
2
0
1
2
1
1
0
1
1
0
1
2
2
2
2
1
1
1
2
2
2
0
1
1
1
1
2
1
2
0
0
1
2
1
0
1
2
0
1
1
1
2
1
2
0
0
1
1
0
0
1
2
0
0
0
1
1
2
2
0
1
1
1
1
1
1
1
0
1
1
0
1
1
1
0
1
1
1
1
0
0
2
1
1
1
2
0
1
2
1
1
1
1
0
1
1
2
0
1
1
2
2
2
1
0
1
0
1
1
1
2
0
0
0
1
1
0
1
2
1
1
1
1
1
0
0
2
1
0
1
1
1
1
1
1
3
2
1
2
0
1
0
2
0
0
0
1
1
1
1
0
0
0
1
1
1
1
1
1
1
1
0
2
1
1
2
2
1
1
2
1
1
2
1
1
0
1
1
0
2
0
1
2
1
2
0
1
0
0
0
1
1
0
1
1
1
0
1
2
1
2
1
0
2
2
2
1
3
2
1
1
1
1
1
1
1
0
1
1
0
1
1
0
1
0
0
1
0
0
0
2
0
1
1
1
1
0
1
1
1
1
1
0
1
1
1
2
2
1
1
1
1
1
0
2
0
0
0
0
1
2
1
1
1
0
1
0
2
1
1
1
2
0
1
2
1
1
1
1
1
1
2
2
2
1
2
1
1
0
1
1
2
1
0
1
0
1
1
0
2
1
1
0
0
0
1
1
1
1
1
1
1
0
0
1
1
2
0
0
2
1
2
1
1
1
1
2
1
1
2
1
1
1
2
2
1
0
1
1
1
1
1
1
1
0
2
1
1
1
0
0
0
1
1
1
1
0
2
1
1
1
0
4
0
1
0
1
2
1
0
1
0
2
2
1
2
0
1
1
1
1
1
1
2
0
0
1
0
1
0
1
0
2
1
3
1
2
1
1
1
1
0
2
1
0
1
1
1
0
0
1
1
0
1
2
1
0
1
1
0
1
1
1
1
1
0
2
1
1
2
1
1
1
1
1
2
1
1
1
0
1
1
1
1
2
0
1
1
1
0
1
2
1
1
2
1
1
1
0
0
0
0
0
1
1
1
0
1
1
1
2
1
1
2
1
1
1
1
1
1
1
0
1
1
0
2
0
1
0
1
1
1
1
2
0
0
3
1
1
1
1
2
2
2
1
1
0
1
0
2
1
0
1
1
1
1
1
0
0
2
1
1
1
1
1
0
0
1
1
1
2
0
1
1
1
0
1
3
4
1
0
1
2
0
0
0
2
1
0
1
0
1
1
0
1
1
1
1
1
1
1
0
0
0
1
1
2
2
0
0
1
2
1
1
1
1
2
0
1
1
1
1
1
2
1
0
1
2
0
1
0
1
1
1
1
1
1
1
0
2
3
1
2
2
0
1
1
1
1
1
1
0
1
1
2
2
0
2
1
1
1
0
3
1
0
2
1
1
2
2
0
2
1
0
1
2
0
1
1
1
2
0
0
1
1
2
1
1
1
0
1
1
0
1
2
1
2
2
1
1
1
1
0
1
0
2
1
2
2
2
1
1
0
2
2
0
1
0
1
0
0
0
1
2
1
0
1
1
0
0
0
0
1
1
3
2
2
0
0
1
0
0
1
1
1
2
1
1
1
2
2
1
0
2
1
1
1
2
0
0
1
2
1
1
1
0
1
1
1
2
1
1
2
1
2
1
1
2
1
1
1
2
1
1
1
1
0
0
1
1
1
1
2
1
1
0
2
1
1
1
1
0
1
0
1
1
1
1
2
1
0
1
1
0
1
0
2
1
1
1
2
1
0
3
1
0
1
1
1
1
1
1
0
1
0
1
1
1
2
2
1
1
1
1
1
0
1
2
2
2
1
1
0
0
0
2
2
1
1
2
0
2
1
3
1
1
1
2
1
1
1
1
0
0
1
1
0
0
0
0
0
1
1
0
0
1
0
2
3
0
0
2
2
0
2
2
1
1
1
0
2
1
2
0
2
1
1
2
0
1
1
0
0
1
0
2
1
0
0
1
0
2
1
0
1
0
3
1
1
0
0
1
2
0
1
3
1
0
2
2
1
1
2
1
0
2
1
2
1
0
2
0
1
2
0
0
0
1
2
1
0
0
1
1
0
2
1
0
1
1
2
1
2
1
1
0
1
0
2
1
1
1
0
1
0
1
0
0
0
2
1
1
0
1
1
2
0
2
2
2
1
1
1
0
1
2
2
1
1
2
1
1
2
1
1
1
2
0
0
1
2
2
1
1
0
1
2
1
0
1
1
2
1
1
1
1
1
1
1
1
2
1
0
1
1
2
2
0
1
1
2
2
2
1
0
1
1
1
1
3
1
2
2
0
1
1
1
0
1
1
0
0
1
2
1
2
1
1
1
1
1
0
0
0
1
1
2
2
0
2
2
1
1
1
0
1
1
1
2
1
0
1
1
1
1
2
0
1
1
0
2
2
1
1
1
1
0
0
1
1
2
0
1
1
0
1
1
1
0
1
2
1
1
2
1
0
2
0
0
1
1
1
1
1
2
0
1
2
0
0
1
0
0
1
2
0
1
1
0
0
1
0
2
0
1
2
1
2
1
0
4
0
0
0
2
0
1
0
1
1
1
1
1
2
1
2
1
0
0
2
1
0
2
2
0
2
1
0
1
1
1
0
0
2
0
1
1
1
0
1
0
0
1
0
2
1
2
1
1
1
1
0
1
0
1
0
1
1
0
1
1
0
0
1
0
0
1
1
0
1
0
1
0
2
1
1
0
2
0
1
2
1
1
0
1
1
0
0
1
1
0
1
0
1
1
1
0
2
2
1
1
1
2
1
1
1
1
1
0
1
2
1
1
1
1
1
2
2
1
2
1
0
1
1
2
2
1
0
1
1
0
1
1
1
0
1
2
0
1
1
0
1
0
1
2
2
1
1
1
0
1
2
1
1
0
0
1
1
1
0
0
0
2
2
2
2
1
1
2
1
0
1
2
0
1
1
0
0
1
2
1
0
0
1
1
1
0
1
2
2
1
0
0
0
1
1
1
1
1
0
1
0
2
1
1
1
0
1
1
2
0
2
2
1
1
0
1
1
1
0
1
1
1
0
0
3
1
1
2
1
1
1
2
1
1
2
1
1
1
2
1
1
0
2
0
1
0
1
2
1
1
1
1
0
1
0
1
1
1
0
2
0
2
1
1
2
0
1
1
1
1
1
1
1
2
1
1
2
1
0
0
0
5
0
1
1
1
1
2
1
0
0
2
2
2
0
0
0
0
1
0
2
0
1
1
1
1
1
0
1
0
0
0
1
1
1
1
0
2
2
1
1
0
1
1
0
1
1
0
2
1
1
1
1
1
1
1
2
0
1
1
1
1
1
1
1
0
1
2
2
2
1
0
1
1
2
2
0
2
0
0
1
1
2
3
0
1
1
1
0
0
1
0
2
1
0
1
2
0
1
1
1
0
1
2
0
0
2
1
1
2
1
0
0
1
2
2
1
2
0
1
1
1
2
1
0
1
0
0
0
0
1
0
2
2
1
2
3
1
0
1
0
1
2
1
2
2
0
1
0
1
1
2
0
1
0
4
0
0
1
1
1
0
2
1
0
1
2
1
2
2
0
2
2
1
0
1
2
1
1
0
0
1
1
1
0
1
2
0
1
2
1
1
0
0
1
1
2
0
2
1
2
0
1
1
0
1
1
0
2
2
0
2
1
0
1
2
1
1
1
0
1
0
0
1
1
2
0
1
1
0
2
1
1
2
1
2
0
2
0
0
1
2
0
1
1
2
1
0
0
2
2
1
1
0
1
0
1
1
1
0
2
1
1
1
1
1
1
1
0
2
1
1
0
1
2
1
0
2
0
1
1
0
0
1
1
0
1
0
1
0
2
1
1
0
2
1
0
1
1
0
1
0
1
1
1
1
1
1
1
2
2
1
1
2
1
0
0
1
2
1
1
0
1
2
1
1
1
1
0
0
1
1
2
0
1
1
2
1
1
0
0
2
0
1
2
0
1
0
0
1
1
1
1
0
0
0
1
1
1
0
0
0
2
2
1
1
0
1
1
0
1
1
1
2
0
2
1
0
0
2
1
1
1
0
1
1
1
1
1
0
0
1
1
2
1
0
1
1
1
0
0
1
0
1
0
2
1
2
1
1
1
1
1
1
1
0
0
0
1
1
1
1
0
0
0
0
1
1
0
1
1
0
0
1
0
2
2
2
1
0
0
1
2
1
1
1
2
1
1
1
1
1
2
3
1
1
2
1
0
1
1
2
1
1
2
1
1
1
2
0
1
1
1
1
1
2
1
1
1
1
1
0
1
1
2
2
2
3
1
0
2
0
2
1
2
1
2
0
1
1
1
1
1
1
2
2
3
1
1
1
1
1
0
2
2
1
0
0
1
0
1
2
0
1
1
1
1
1
1
1
1
1
1
1
2
0
0
2
0
1
2
3
1
1
3
1
1
1
2
2
1
1
0
1
1
0
0
0
1
2
0
1
0
1
2
0
1
1
0
1
2
1
2
0
0
1
3
2
1
1
2
0
1
0
1
2
3
0
2
0
2
0
2
1
1
0
0
1
2
1
1
1
1
1
2
1
1
2
0
1
0
1
1
0
2
1
2
1
0
1
1
2
1
1
1
0
1
1
0
1
1
1
0
2
1
1
0
1
1
1
0
0
0
0
2
1
2
2
1
2
1
1
0
1
1
0
1
0
1
2
2
1
2
1
1
0
0
1
1
0
1
0
1
0
1
0
1
1
1
0
1
2
1
1
2
1
0
0
1
2
1
1
2
0
1
1
1
1
1
1
0
0
0
1
1
0
1
2
1
2
1
1
1
1
1
2
2
1
2
2
1
0
0
2
0
1
1
1
2
1
0
1
1
2
0
1
0
1
0
1
0
0
1
1
1
2
1
1
0
1
1
1
0
1
2
2
0
0
1
1
1
0
0
1
1
0
1
2
2
0
1
1
0
2
1
1
1
1
1
0
2
2
2
2
2
1
6
1
0
0
1
0
2
2
1
1
1
0
1
0
1
1
1
0
1
0
0
1
1
1
0
0
1
0
1
0
1
1
1
3
0
1
2
1
4
0
2
0
0
1
0
2
1
0
1
1
0
0
2
1
1
1
2
1
1
1
0
1
1
0
3
0
1
1
0
1
2
2
0
1
1
1
1
2
1
1
2
2
1
1
2
0
1
2
2
2
0
1
1
1
1
0
0
1
1
0
1
3
0
1
0
1
1
1
1
2
1
0
0
0
1
1
1
0
1
1
1
1
0
2
0
1
0
1
1
1
2
1
1
2
0
1
1
1
0
1
0
0
0
0
1
1
1
1
1
1
1
1
0
0
0
1
2
0
1
1
0
1
1
1
1
0
1
0
1
0
0
1
2
1
0
1
1
1
0
1
1
0
1
0
0
2
0
1
2
1
1
0
2
1
0
0
1
2
1
0
1
2
0
0
2
1
1
0
1
1
0
1
2
0
0
1
2
0
1
2
1
1
0
0
1
0
1
2
0
1
0
2
0
0
2
1
0
3
1
1
0
1
1
0
0
0
1
1
0
1
1
2
1
0
2
0
1
1
0
1
1
2
2
1
1
0
1
1
0
0
1
0
1
1
1
2
0
0
2
1
1
0
1
1
1
1
1
1
0
1
2
1
1
1
1
1
2
2
0
1
0
2
2
1
1
0
0
0
1
2
1
0
1
1
0
1
1
1
2
0
0
1
2
2
0
1
0
2
2
2
2
1
0
0
1
1
2
1
2
2
1
1
0
1
0
2
1
0
1
1
1
0
1
0
1
0
0
0
0
1
0
1
1
1
0
1
1
1
0
0
0
1
1
2
1
0
2
2
1
1
1
0
0
0
1
0
0
0
1
2
1
2
2
0
0
1
0
1
1
1
1
0
1
0
1
2
1
1
0
2
0
1
1
2
0
1
2
1
1
2
0
1
1
1
0
1
0
0
1
1
1
1
1
1
0
1
1
2
1
1
1
0
2
2
1
1
0
1
1
0
1
0
0
1
1
1
0
2
1
1
2
0
1
1
0
1
2
5
2
1
0
1
1
1
1
0
0
2
1
2
2
0
1
1
1
1
0
1
1
1
0
2
2
0
1
0
2
1
0
0
2
1
0
1
3
1
0
0
1
0
1
0
2
0
0
1
2
0
1
2
1
0
1
0
1
1
1
0
1
0
0
1
0
1
1
0
2
1
0
1
0
1
1
2
1
1
1
1
0
0
1
3
1
1
2
1
1
0
1
1
1
2
1
1
2
2
1
1
1
0
2
0
0
2
2
1
2
1
1
3
1
1
2
1
1
0
1
2
1
1
1
1
1
1
2
1
1
0
1
2
0
0
2
1
2
1
1
1
1
0
2
2
0
1
1
1
1
1
1
2
1
1
1
0
2
1
1
1
1
1
0
1
1
0
1
0
0
1
0
0
1
2
1
0
1
0
1
1
0
2
1
0
1
0
0
2
1
1
2
1
2
0
0
1
0
1
1
1
2
1
2
1
1
0
2
1
1
0
1
0
1
1
2
1
1
2
1
2
1
2
1
2
2
1
1
0
1
0
0
2
1
1
0
0
0
0
2
1
2
1
1
1
1
2
1
2
0
1
2
1
1
2
2
0
1
2
1
0
1
1
1
2
1
2
1
1
1
1
1
1
0
0
1
1
0
2
1
2
0
2
1
1
1
1
0
0
1
1
2
1
1
0
1
1
1
0
2
0
0
1
0
0
1
2
1
1
1
0
0
1
2
0
1
0
1
1
1
2
1
0
0
1
0
1
2
1
2
2
1
1
2
2
0
2
0
0
0
2
1
3
2
3
2
0
1
2
0
0
2
1
1
2
1
2
1
1
2
0
1
1
0
0
1
2
1
1
0
2
1
2
1
1
1
0
2
2
0
1
0
1
1
1
0
1
1
1
0
0
0
1
0
0
1
0
1
1
0
2
0
0
2
3
2
1
1
1
1
1
0
1
1
1
1
0
1
1
2
3
0
3
0
1
1
2
0
0
0
1
1
2
1
1
0
1
2
0
0
1
0
1
2
1
0
0
1
1
1
1
1
1
1
2
1
1
1
2
2
0
2
1
1
1
0
0
0
1
1
0
2
1
1
1
3
0
2
1
1
1
2
1
1
1
2
0
1
1
2
2
1
0
1
1
2
2
1
1
1
1
0
1
2
0
0
1
1
7
1
2
0
1
0
2
1
1
1
1
2
2
1
1
0
1
1
1
0
0
2
5
1
3
1
0
0
1
0
1
1
2
0
2
1
1
0
0
2
2
1
0
2
1
1
2
0
2
3
0
2
0
1
1
1
2
1
1
1
1
1
0
1
1
0
2
1
2
2
0
1
1
1
1
2
1
1
0
0
1
1
1
1
1
1
2
1
0
0
3
1
0
1
0
1
0
1
1
1
1
2
0
2
1
1
1
2
1
0
1
1
4
2
1
2
1
1
1
0
1
1
0
1
2
1
1
1
2
2
2
1
2
0
1
2
3
1
0
1
1
2
0
0
1
1
1
2
0
1
2
0
1
1
0
2
1
1
2
1
1
0
2
0
1
1
0
1
2
2
2
1
1
2
2
0
1
1
0
1
1
1
0
3
0
1
0
2
1
0
1
0
1
2
1
1
1
1
0
1
1
1
0
1
0
1
2
2
1
1
1
0
1
1
1
1
0
1
1
2
1
0
1
1
1
1
1
1
2
2
1
1
1
1
0
1
1
1
1
0
1
1
2
0
1
1
1
2
1
2
1
0
1
0
2
0
1
1
1
1
1
1
0
1
1
1
0
1
0
1
1
0
0
0
1
1
0
1
1
0
1
2
2
0
1
1
2
1
0
1
1
1
0
2
2
0
2
0
1
1
1
1
1
0
2
0
0
0
2
0
0
0
2
1
2
0
1
1
0
2
1
1
2
0
0
0
1
1
0
1
0
0
1
0
1
1
1
1
2
1
1
1
1
1
1
2
3
1
0
2
1
2
0
0
1
1
1
1
1
0
1
0
1
0
2
1
1
1
1
1
1
0
2
1
1
0
2
1
0
0
1
1
2
1
0
2
1
0
2
1
0
2
1
2
0
0
1
1
1
1
2
0
1
1
1
0
1
1
0
0
1
1
0
1
1
1
1
2
1
2
1
2
1
1
2
1
2
1
1
1
0
1
0
1
2
1
1
0
1
1
1
1
1
1
1
0
1
0
0
1
0
0
2
1
1
2
0
2
1
2
1
0
2
1
1
1
2
0
1
0
0
1
1
1
1
1
1
1
1
0
2
1
1
1
1
2
1
2
1
1
1
0
0
2
1
2
0
1
0
1
1
0
3
2
1
1
1
1
1
1
0
0
2
0
0
1
1
1
4
1
1
1
2
0
0
1
1
1
2
0
1
2
2
1
1
1
0
0
0
1
1
1
0
1
1
2
2
2
2
1
0
2
0
1
1
2
1
2
0
1
0
1
2
1
0
2
1
3
2
1
1
1
1
1
0
2
0
1
2
2
0
1
2
2
0
0
1
0
1
2
0
1
0
1
1
2
3
0
2
2
1
1
1
1
1
1
1
0
1
6
1
8
1
1
1
1
0
0
1
1
2
2
1
2
0
0
0
0
2
4
2
1
0
1
2
2
0
0
1
0
1
1
1
1
1
1
2
1
1
0
1
2
1
0
0
2
1
0
1
1
1
1
1
0
1
0
1
0
0
1
0
0
0
2
1
1
0
1
0
1
0
1
0
1
1
2
0
0
1
1
1
2
1
0
2
1
2
0
1
1
0
2
1
1
1
1
0
2
1
2
1
2
1
1
1
0
0
1
2
2
1
1
1
1
1
1
2
2
1
2
1
2
1
1
0
2
1
0
1
2
1
2
1
0
1
2
3
2
1
1
0
0
1
1
2
1
1
2
1
2
1
1
0
1
2
1
1
3
1
0
1
0
0
0
1
0
1
0
1
0
2
0
1
1
2
1
2
0
0
2
1
1
0
1
1
1
2
1
0
2
1
0
1
1
3
1
1
0
1
2
1
1
1
1
1
2
0
2
1
2
1
1
1
0
1
1
2
0
0
1
2
0
1
1
1
1
1
0
0
0
2
1
1
1
1
0
2
0
0
1
1
1
3
1
2
0
3
1
2
2
2
0
1
2
1
1
0
1
1
2
2
1
1
1
0
1
1
1
2
0
2
0
0
0
0
1
2
2
4
2
2
1
0
2
1
1
1
1
1
1
2
1
0
1
1
1
0
1
1
1
2
1
2
2
1
0
1
0
0
0
2
2
1
0
1
1
0
2
1
1
0
2
0
2
1
1
1
3
0
1
1
2
1
2
0
1
1
0
1
1
2
2
1
1
1
2
2
1
0
2
1
0
1
0
1
1
1
1
0
1
0
1
1
0
0
0
1
1
0
1
2
1
5
1
2
1
1
1
0
1
1
1
0
1
0
0
1
2
1
1
0
0
0
1
1
1
1
2
2
1
1
1
3
1
1
1
0
1
1
0
1
1
0
1
1
1
1
0
1
0
1
2
1
1
2
0
2
1
0
1
1
1
0
0
1
2
2
2
0
1
2
1
2
1
2
1
1
0
0
2
0
0
0
0
1
0
1
1
1
1
1
2
2
1
0
0
2
2
1
0
0
0
0
1
3
1
1
1
1
1
1
2
1
1
0
0
1
1
2
2
3
1
1
0
1
0
2
1
1
1
2
1
1
1
2
1
0
0
1
1
1
0
0
2
0
2
1
1
1
1
1
1
1
1
1
2
0
1
1
1
2
1
1
1
2
0
1
2
2
1
1
1
2
2
0
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
0
0
1
1
1
2
1
1
0
1
0
2
1
1
2
0
1
0
1
0
2
0
0
0
1
0
1
0
1
1
2
1
1
1
2
1
1
2
1
1
1
1
0
0
0
0
1
2
2
1
2
2
1
0
1
2
1
1
1
1
2
2
1
2
1
0
1
1
2
0
1
1
1
0
2
0
0
2
0
1
2
1
1
2
1
1
0
2
1
1
0
2
1
1
0
0
0
0
1
1
0
1
0
1
1
2
1
1
2
2
2
0
2
2
1
1
1
1
1
0
1
1
0
1
1
3
0
0
1
1
0
1
1
0
2
0
2
0
2
0
0
0
0
1
0
1
1
1
1
0
1
0
0
1
1
1
0
0
0
2
2
0
1
2
2
1
2
0
0
0
1
1
1
1
1
2
0
1
1
0
1
1
0
2
1
0
0
1
2
2
2
0
1
1
1
1
2
0
0
1
0
1
2
1
1
0
0
1
1
2
1
0
1
1
0
1
1
0
1
0
1
1
2
1
0
2
0
1
1
1
1
0
0
0
1
0
2
0
0
2
1
0
1
1
0
0
1
1
1
0
2
1
1
1
2
0
2
1
0
2
1
1
1
2
1
0
2
2
1
1
1
0
1
2
1
0
2
1
1
1
1
0
0
1
1
2
1
1
0
1
1
0
1
0
1
1
0
0
2
2
0
1
0
3
2
1
1
1
1
2
1
1
0
1
0
1
1
2
1
1
0
1
1
1
3
2
2
0
3
2
2
1
2
1
0
1
2
1
1
1
1
1
0
0
0
1
1
2
0
2
1
1
1
1
2
1
1
2
1
0
0
1
1
0
0
1
3
2
2
1
0
1
1
1
2
1
1
2
1
0
1
1
2
2
1
1
1
0
1
1
1
1
0
0
0
2
1
1
0
1
2
0
1
1
2
2
1
0
2
0
1
1
1
0
2
1
2
1
1
1
1
1
1
1
0
2
0
1
1
1
1
2
0
2
0
0
1
1
0
1
2
0
0
1
1
2
1
2
2
1
1
0
1
1
2
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
0
2
2
0
0
2
2
1
0
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
0
0
1
1
1
1
1
2
0
1
1
0
1
1
0
2
0
0
1
2
2
1
0
1
1
1
1
0
2
1
1
0
2
2
1
1
1
1
1
0
2
1
1
1
2
1
2
2
1
1
1
1
0
1
0
1
2
2
1
2
1
1
0
1
0
0
1
1
0
1
2
1
1
0
2
1
1
2
0
1
2
1
1
0
0
2
0
1
1
1
1
0
0
2
2
2
2
0
0
0
1
2
3
1
1
2
1
0
2
1
1
1
1
0
2
0
1
0
1
2
0
1
0
1
1
1
2
2
0
1
1
2
0
2
0
1
1
1
0
1
3
1
2
2
1
2
1
2
0
1
0
0
0
0
0
1
1
1
0
1
2
1
1
1
1
1
2
1
0
2
1
2
1
1
1
1
2
1
1
1
1
1
1
0
1
0
1
1
1
0
1
2
1
1
2
1
1
1
1
2
0
0
0
2
1
1
0
1
0
1
1
1
1
1
0
2
1
1
0
0
0
2
0
0
1
1
1
0
2
0
2
2
2
0
2
0
1
0
0
1
1
1
2
2
0
1
0
2
2
1
1
2
1
1
0
1
0
1
1
0
0
1
0
0
1
0
1
0
2
2
1
0
0
1
2
0
2
1
1
1
1
1
1
1
2
0
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
1
1
0
0
2
1
1
0
1
0
1
2
1
2
0
0
1
1
0
1
2
1
1
1
1
0
0
1
2
0
1
1
2
0
2
0
2
1
1
1
1
1
2
0
2
0
1
2
1
2
0
2
2
1
1
1
1
0
1
1
1
0
2
0
1
1
0
1
1
1
2
1
1
2
0
1
0
1
0
2
1
2
1
2
2
0
1
1
1
1
1
2
1
1
0
1
1
1
1
1
2
0
0
1
0
1
2
1
1
0
0
1
1
0
1
0
0
1
1
2
1
2
0
1
0
1
1
1
0
1
1
2
2
2
2
2
1
2
1
3
1
2
1
2
2
0
0
1
0
0
0
0
0
1
0
1
1
0
2
0
1
1
1
0
1
1
1
0
1
0
1
0
1
0
0
1
0
1
2
1
1
1
2
1
1
0
1
2
0
1
1
1
0
1
1
0
0
1
1
1
2
2
0
1
1
1
2
1
2
0
1
0
1
1
1
0
2
1
2
0
1
0
1
2
2
2
1
0
2
2
0
1
1
1
1
1
0
1
1
1
1
0
2
2
1
1
0
1
0
2
0
1
1
0
2
0
2
2
1
1
0
1
2
0
3
3
2
1
0
4
4
1
1
1
1
1
0
2
1
0
2
3
0
2
0
0
1
0
2
1
1
0
0
2
0
1
2
1
1
1
1
1
1
2
1
1
1
1
0
0
1
1
2
1
2
1
1
1
1
1
1
3
2
1
1
2
1
2
2
1
1
1
1
0
0
1
2
1
1
0
1
0
1
1
1
1
0
1
0
0
2
0
1
2
2
1
1
0
1
1
1
2
2
0
1
0
1
1
2
1
1
1
0
1
1
1
2
1
0
1
1
0
1
1
1
1
0
2
2
1
1
0
2
1
1
2
1
2
0
0
1
3
1
1
1
2
0
0
1
1
2
1
1
1
1
0
1
0
2
1
1
1
1
1
1
1
0
2
1
1
0
1
0
0
0
1
1
0
1
1
1
2
1
1
1
0
2
0
2
1
1
0
1
2
0
1
1
1
0
0
0
0
1
1
1
0
0
1
2
0
1
0
0
2
0
2
1
2
1
2
2
1
1
1
1
2
2
0
0
1
1
2
2
0
0
1
2
2
2
1
1
0
1
1
2
1
0
1
1
0
0
1
1
1
0
1
0
2
0
0
0
1
1
1
0
2
0
0
1
1
1
0
2
0
0
0
2
1
1
2
2
1
2
3
2
0
1
0
2
0
1
2
1
3
1
2
2
1
1
1
2
0
1
3
0
1
0
0
1
1
0
2
1
2
1
1
1
2
1
0
2
2
0
2
0
0
0
0
1
1
1
0
1
3
1
1
1
2
1
1
0
2
2
1
1
0
2
0
1
1
2
1
2
0
1
1
1
1
1
0
1
0
2
1
2
1
0
1
2
1
2
2
1
1
1
1
1
1
1
3
0
1
0
1
1
1
1
2
2
0
1
0
3
2
2
0
1
1
0
1
1
1
0
1
0
1
1
2
0
1
1
1
0
1
1
0
1
2
0
1
0
1
0
2
0
2
1
0
0
1
0
1
0
1
1
0
0
1
2
4
1
2
2
1
1
1
5
0
0
1
1
1
1
0
1
1
0
0
1
2
0
0
2
0
2
1
1
2
0
1
0
0
1
1
2
2
2
1
1
0
2
0
1
1
0
2
1
0
1
1
2
2
0
1
1
1
1
2
0
1
2
1
1
2
1
4
1
1
1
0
1
1
1
2
0
1
1
1
0
1
1
1
1
0
0
1
1
2
1
1
3
1
0
1
0
1
0
1
1
1
2
1
1
0
1
1
1
0
2
2
0
0
1
1
1
2
0
0
1
1
1
2
1
1
0
0
1
1
1
1
1
2
1
1
1
1
0
0
1
2
0
2
1
1
0
2
1
2
1
1
1
2
1
1
1
1
0
2
2
1
1
1
3
2
1
0
1
1
0
1
1
1
1
1
0
1
2
2
2
1
1
0
1
0
1
0
1
1
2
0
1
1
1
1
1
1
0
0
1
2
0
1
1
0
0
0
0
2
1
1
1
0
1
0
0
2
2
1
1
2
1
0
0
0
1
2
0
0
1
2
0
2
2
1
0
0
0
1
1
1
2
0
2
1
1
1
2
1
1
1
1
0
1
1
1
3
0
1
1
0
1
2
2
1
0
1
0
3
1
1
1
2
1
0
1
1
1
2
0
0
2
2
1
1
1
1
0
0
2
0
0
2
1
1
2
1
1
2
0
2
0
1
0
1
2
1
1
1
4
1
1
0
1
1
0
1
1
1
0
0
2
0
1
1
1
1
1
0
1
0
2
0
1
1
1
1
1
0
0
1
1
2
0
0
0
1
2
0
1
1
1
1
0
2
2
1
1
1
2
0
2
1
1
2
0
1
2
1
1
1
1
1
0
0
1
1
2
2
2
1
1
1
0
2
0
1
0
1
2
1
2
0
1
2
1
0
1
1
2
3
0
1
2
0
1
1
1
0
0
1
2
0
1
1
1
0
2
1
1
2
1
1
0
0
1
1
0
0
0
1
0
1
0
1
1
1
1
3
1
1
0
1
1
2
1
2
0
1
0
1
2
1
2
2
2
1
0
1
1
1
1
1
1
1
1
0
1
2
0
1
1
2
2
1
0
1
2
0
3
1
1
2
1
0
0
1
1
0
0
0
1
1
1
1
2
1
1
1
1
0
0
0
2
1
1
1
2
2
1
1
0
0
2
1
2
0
1
2
1
1
0
2
1
0
2
2
1
0
0
1
1
1
2
2
2
1
2
2
0
0
1
1
2
0
1
0
1
1
0
2
1
1
1
1
2
1
3
2
0
1
2
1
0
2
1
1
1
1
0
1
1
0
0
1
1
1
1
0
1
1
1
1
0
0
1
1
2
1
1
1
1
2
1
1
0
1
1
1
1
2
0
4
0
1
1
2
1
1
0
1
0
0
1
1
0
1
1
1
1
2
1
1
0
0
1
2
1
0
2
0
2
2
0
2
2
1
2
1
2
1
1
1
1
0
0
1
1
1
0
0
2
1
0
1
1
0
2
0
2
1
1
1
1
1
1
1
1
0
1
1
1
2
1
2
0
1
1
0
1
1
1
0
1
1
1
1
1
1
2
2
1
1
2
0
1
1
2
0
1
1
1
0
2
0
1
1
1
1
1
0
0
1
1
1
1
1
0
1
2
2
2
2
0
0
1
1
0
1
0
1
1
2
0
1
1
1
2
1
1
1
0
0
0
1
0
7
2
0
0
1
5
1
0
0
2
1
0
0
2
0
1
2
1
0
1
1
1
0
2
1
1
1
1
1
0
1
1
1
1
2
1
1
1
1
1
1
1
2
2
2
2
1
1
0
1
1
1
2
1
1
1
1
0
0
1
3
2
1
1
0
1
1
2
1
0
1
0
1
0
1
1
1
1
1
2
1
0
0
0
1
1
2
1
0
2
1
0
3
1
2
1
2
1
1
1
1
1
2
0
2
0
0
1
2
2
2
1
2
2
3
1
1
1
0
1
2
1
1
0
2
0
1
1
0
1
2
2
2
2
0
0
1
1
0
1
1
1
1
0
3
0
0
1
2
1
1
1
2
0
1
0
0
2
1
0
2
1
1
1
1
2
1
1
0
1
1
2
2
2
2
1
1
2
1
0
2
1
0
0
1
0
0
2
1
1
1
0
2
2
0
1
1
1
2
0
2
0
2
2
0
1
1
0
2
2
0
2
0
1
0
1
2
2
2
1
1
1
1
1
0
1
0
2
1
1
0
1
1
0
1
1
1
1
2
0
1
1
1
2
1
1
1
0
1
2
6
0
0
0
1
0
1
3
1
1
3
2
1
1
0
0
2
0
2
0
1
0
1
1
1
1
2
1
0
2
1
1
0
1
0
1
1
0
1
0
1
1
1
1
1
1
2
1
0
2
1
2
2
1
0
0
2
0
1
2
1
0
0
1
1
0
0
1
2
2
0
0
2
2
1
1
1
1
2
1
2
2
1
1
1
0
1
1
1
1
1
0
1
2
2
0
1
0
0
1
0
0
0
0
2
1
2
1
1
0
1
1
2
0
1
1
0
0
1
0
1
0
0
0
1
2
1
2
1
0
0
0
3
2
1
0
2
1
2
0
1
1
1
1
1
0
1
2
0
1
1
0
1
2
2
1
1
0
1
1
2
1
2
1
0
2
1
4
0
2
0
0
1
1
1
2
1
2
2
1
0
1
1
2
2
1
0
1
1
1
1
0
1
1
1
0
2
1
1
1
1
1
2
1
1
2
0
0
1
1
0
1
0
1
2
1
1
1
1
1
1
0
1
1
1
1
3
2
1
1
0
1
1
1
2
1
0
1
0
0
0
3
0
1
1
0
0
2
1
0
1
1
2
2
0
0
1
1
1
1
2
2
1
1
2
1
0
2
1
1
1
0
1
2
1
2
1
1
1
1
0
2
1
2
1
1
2
2
1
1
1
0
2
1
0
1
0
0
1
1
1
1
0
0
2
1
2
1
1
1
2
1
0
2
1
1
1
2
0
2
1
2
1
1
1
0
1
2
0
1
2
2
0
1
1
0
0
1
1
2
1
0
1
1
1
2
1
1
2
1
1
2
2
1
0
0
2
1
1
1
2
0
0
1
1
1
1
1
2
1
1
1
1
2
2
1
1
1
2
2
1
1
1
0
1
1
2
2
1
1
1
0
2
0
1
1
2
1
0
1
0
1
1
2
2
1
1
1
1
0
1
1
0
0
0
0
2
1
1
0
0
2
1
0
2
1
1
1
1
1
1
1
2
1
2
0
0
1
1
2
0
0
1
0
0
2
0
1
2
2
1
0
0
0
2
1
2
0
0
1
1
1
1
1
1
0
0
1
2
2
1
1
1
0
1
1
0
1
2
1
1
1
0
1
1
1
1
1
1
3
0
1
1
0
2
1
1
2
1
1
2
2
2
2
1
1
1
1
0
1
1
2
0
2
1
1
1
0
1
2
1
2
2
0
0
2
1
2
0
1
2
1
1
1
1
0
1
1
1
2
2
2
1
1
1
1
2
2
1
0
1
1
1
0
1
0
1
1
0
1
2
1
1
1
1
0
1
1
1
1
1
2
1
1
0
1
1
2
1
0
1
2
1
0
1
0
2
1
0
1
0
1
1
5
1
1
0
0
4
1
1
2
0
2
1
1
2
1
0
0
1
1
1
1
2
1
1
1
0
1
1
0
1
0
1
1
2
3
0
0
1
0
1
0
2
1
1
1
0
1
2
1
1
2
2
0
1
0
0
1
0
0
0
0
1
0
1
1
2
1
1
1
0
1
1
1
0
1
1
1
3
0
1
2
0
2
1
2
0
1
1
0
1
1
1
1
0
1
1
1
1
1
2
1
1
0
1
0
1
2
0
0
0
1
0
1
2
2
1
2
1
2
1
1
1
2
1
1
2
1
1
0
0
2
1
1
0
1
1
0
1
0
1
0
0
1
1
1
2
1
0
0
0
2
1
1
2
0
2
0
2
2
2
0
2
2
2
2
0
0
1
1
0
1
0
0
1
1
1
2
1
1
2
1
2
2
0
1
0
1
2
2
0
1
0
1
1
1
2
0
1
1
1
1
1
1
0
0
1
1
1
1
1
2
1
1
1
1
2
1
1
0
1
0
1
0
1
2
0
2
1
1
1
2
1
0
1
2
1
0
1
0
1
1
2
0
1
1
1
2
2
1
1
1
0
0
1
2
1
1
1
1
0
1
1
2
1
2
0
1
1
1
0
1
1
0
1
1
1
1
2
0
0
2
0
0
2
2
2
2
1
2
1
1
2
1
0
2
1
0
0
0
1
4
0
1
2
1
0
1
1
0
2
0
2
1
0
2
1
0
2
2
1
1
0
2
0
1
1
1
0
1
0
1
1
1
2
0
1
1
2
1
3
2
2
0
1
2
3
1
1
2
1
1
0
1
1
1
2
1
1
1
2
1
2
2
1
1
1
2
2
1
0
1
1
1
2
1
0
0
0
2
2
0
1
2
0
1
1
1
1
1
1
1
0
1
0
2
1
2
0
2
0
1
1
1
1
0
2
1
0
1
1
0
1
2
1
1
1
1
2
1
1
0
0
1
1
2
1
0
1
0
1
2
1
1
1
1
0
1
0
1
2
3
0
0
1
0
1
2
1
2
1
0
1
1
2
1
1
2
0
0
1
1
1
1
0
1
1
1
1
2
0
0
1
0
2
2
0
2
0
1
1
1
0
0
0
1
1
1
2
1
0
0
2
1
1
1
1
1
0
0
1
1
1
0
1
1
0
1
1
1
1
2
1
1
0
0
1
1
2
1
0
1
0
1
1
1
1
1
0
1
1
1
1
0
0
2
0
0
0
3
1
1
2
2
2
1
2
0
1
1
0
1
0
0
1
1
2
0
0
1
1
1
0
1
1
0
1
1
2
1
0
0
1
0
1
1
1
2
2
1
2
1
0
1
2
1
1
0
1
0
1
0
1
1
1
0
1
2
2
0
2
0
1
1
1
0
2
2
0
2
1
1
0
0
0
2
2
0
1
2
0
0
1
2
2
1
2
0
1
2
1
1
1
1
0
1
1
2
0
1
1
0
2
0
4
0
1
2
1
1
1
1
0
0
2
2
1
1
1
1
0
1
1
1
1
1
1
1
1
0
0
0
0
2
1
1
2
0
0
1
1
1
2
0
0
1
2
1
1
2
0
0
1
1
1
1
2
1
2
0
1
0
1
1
0
1
1
0
1
1
0
2
1
1
2
2
0
1
1
1
2
1
1
1
1
0
0
0
1
1
1
0
1
2
1
1
1
2
1
1
0
0
1
0
2
1
1
2
0
2
2
0
1
2
4
1
0
1
0
1
0
1
1
2
2
1
2
1
1
0
0
1
2
0
0
0
1
0
0
1
0
2
2
1
1
0
2
1
2
1
1
1
0
1
2
1
0
1
0
1
1
2
2
0
1
1
0
1
1
1
0
1
2
1
1
1
1
1
1
1
0
2
1
0
1
1
2
1
1
1
3
1
2
0
2
1
1
0
2
2
0
1
2
1
1
1
1
0
1
1
2
1
2
2
0
0
0
1
0
0
1
1
1
0
0
1
1
1
0
1
1
0
1
2
1
2
1
2
1
0
2
1
1
1
1
0
1
1
0
1
1
0
0
1
0
2
1
0
1
0
0
1
0
1
1
0
1
1
0
2
1
0
1
1
1
1
1
1
0
0
1
1
1
0
1
1
1
1
1
1
0
1
1
0
1
0
1
0
2
1
0
1
1
0
0
1
1
1
0
1
2
2
1
1
1
1
0
2
0
1
1
1
1
0
2
0
1
1
2
1
0
1
1
0
0
2
0
1
1
2
2
1
1
2
1
1
2
1
2
1
0
0
1
0
2
0
0
1
0
0
1
2
1
0
1
1
2
1
1
1
0
1
2
1
1
1
1
1
1
1
0
0
1
1
1
0
1
2
1
0
0
2
0
1
2
1
1
1
2
2
2
1
0
1
2
2
1
0
1
2
0
1
0
0
0
1
1
1
1
0
0
1
1
1
0
1
0
2
2
1
1
0
0
0
0
1
1
0
1
1
1
1
1
0
2
1
1
2
0
0
1
1
1
1
1
2
2
0
2
0
1
0
1
0
2
1
1
0
1
1
2
1
1
2
1
1
0
1
1
1
1
0
2
1
1
2
1
2
0
2
2
0
1
2
1
1
0
0
0
1
0
1
0
0
0
1
1
1
2
1
1
1
2
0
1
1
2
1
1
2
2
2
1
2
0
1
0
2
0
1
0
1
1
2
1
1
1
0
1
1
1
1
1
1
1
2
2
1
1
2
0
1
1
1
2
2
1
0
1
2
2
0
1
0
1
1
1
1
1
0
1
0
0
1
2
1
0
1
2
0
1
1
1
1
2
2
0
1
2
1
1
0
1
1
1
1
0
1
1
0
0
2
0
0
1
1
1
0
1
1
0
0
1
1
1
1
0
1
1
2
0
1
2
1
1
0
1
1
1
1
0
2
1
1
2
1
1
2
1
1
1
1
1
1
1
0
1
1
0
1
2
1
1
2
0
1
2
1
2
0
0
1
0
1
1
2
1
0
2
0
1
0
1
1
1
1
0
1
0
0
1
2
1
1
0
0
0
1
2
1
1
1
0
0
1
1
2
1
1
1
0
0
1
1
3
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
0
1
0
1
2
2
1
1
0
0
1
0
0
1
1
2
1
1
2
1
2
1
1
0
1
1
0
0
0
1
0
1
1
0
1
1
0
2
2
0
2
1
0
1
0
2
0
1
2
0
1
0
1
1
1
1
1
2
1
0
3
1
1
2
2
0
1
2
1
2
1
1
2
2
1
2
0
1
1
2
1
1
1
1
0
1
0
1
1
2
1
1
2
1
1
0
0
2
2
0
1
1
3
1
0
2
1
1
1
1
0
0
1
2
1
1
1
2
1
1
1
1
0
1
1
2
2
1
1
1
2
3
1
1
0
2
1
1
1
2
1
2
1
1
1
1
2
1
1
1
0
1
2
1
2
1
2
1
0
1
1
2
0
0
1
1
2
1
1
2
0
1
1
1
1
1
2
1
2
2
2
1
1
1
3
1
2
0
0
1
1
1
1
1
1
0
0
2
1
1
0
0
0
0
0
2
1
1
2
1
0
1
1
0
0
1
1
0
1
2
1
1
0
0
1
0
1
1
2
1
1
2
1
1
2
1
1
2
1
0
1
2
1
0
1
2
1
2
2
0
1
2
0
1
0
0
2
1
1
1
0
0
2
1
2
1
2
0
2
1
2
1
1
0
2
1
1
0
1
2
1
1
0
1
1
1
1
1
1
0
0
2
1
1
2
1
0
1
2
1
0
1
1
1
1
2
1
1
0
2
0
0
1
1
0
2
1
1
1
2
1
0
0
1
1
2
1
1
1
1
1
1
2
1
2
1
0
1
0
1
1
1
0
1
1
2
1
0
1
0
1
1
2
1
1
1
1
1
2
0
1
0
1
1
0
0
2
1
0
0
2
2
0
0
0
2
2
0
2
2
1
0
0
1
1
1
2
2
3
2
2
1
2
0
2
2
1
1
1
1
2
1
1
1
0
2
2
0
1
1
1
0
1
0
2
1
1
1
0
1
1
1
1
1
2
1
2
0
1
0
1
1
0
1
2
1
1
0
2
1
1
1
1
1
0
2
2
1
2
0
0
0
1
1
0
0
0
1
0
1
1
0
2
1
2
2
4
0
1
0
2
0
1
0
0
1
1
0
0
2
0
1
1
1
1
1
1
1
2
2
2
1
1
1
1
0
1
2
1
0
2
1
0
1
1
1
2
1
2
0
2
0
2
1
2
0
1
0
1
2
2
1
2
1
1
2
2
1
0
1
1
1
3
1
1
2
1
1
1
2
2
1
0
1
2
0
1
1
0
2
1
0
1
5
1
2
1
0
1
1
2
1
1
1
1
0
2
1
4
2
1
1
0
1
1
1
1
0
1
0
1
1
1
1
0
2
0
1
1
1
0
1
1
1
1
2
0
1
0
1
2
1
0
1
0
0
2
1
1
0
0
1
2
1
1
2
1
1
0
0
2
1
1
0
1
1
2
2
2
0
1
1
0
1
1
0
0
0
0
1
0
0
0
2
1
1
2
1
3
0
1
1
1
1
0
0
1
0
0
1
1
1
0
0
1
2
1
1
0
1
2
0
0
1
0
1
2
2
2
1
1
1
2
0
1
2
1
1
1
2
1
1
1
0
2
0
0
2
1
1
2
2
1
1
0
1
2
1
1
1
0
2
1
1
0
0
1
1
1
0
1
1
1
0
0
1
1
0
1
1
0
1
0
1
2
1
2
1
1
0
1
0
0
1
0
1
2
1
1
1
1
0
1
1
2
0
1
0
1
0
2
1
2
1
1
1
3
0
0
2
0
1
0
1
0
1
0
0
1
1
1
1
2
1
1
0
0
2
2
2
1
1
2
2
0
2
2
0
0
2
1
1
1
1
2
1
2
1
0
1
1
1
1
0
1
1
1
2
0
0
1
1
1
4
0
0
0
0
2
2
1
1
2
1
1
0
2
1
0
1
1
1
2
1
0
2
1
1
2
0
0
2
0
2
2
1
2
1
1
2
1
2
0
0
1
2
2
0
2
0
0
1
1
1
2
1
1
0
0
2
1
0
1
2
1
1
1
1
1
0
1
1
1
0
2
1
2
1
1
1
1
2
1
1
1
1
1
2
1
0
1
0
0
1
1
1
0
1
0
0
0
1
2
1
0
0
1
0
2
1
1
0
0
0
2
0
2
0
1
1
0
1
1
2
0
1
0
1
1
1
1
1
1
1
0
0
1
2
0
1
1
0
1
1
1
0
1
1
1
1
1
0
1
2
1
0
0
2
0
2
2
1
0
2
1
1
2
0
1
1
1
1
1
1
1
1
1
2
1
0
1
1
1
1
2
1
1
1
1
1
1
2
2
0
2
1
0
0
3
2
1
1
0
1
1
2
1
1
0
1
0
1
2
2
2
1
1
0
1
1
1
1
0
1
1
0
1
2
1
1
0
0
1
1
1
1
1
1
2
1
1
2
1
1
1
0
1
0
0
2
2
0
1
1
2
1
1
1
1
0
1
0
0
0
0
2
0
2
2
1
1
2
1
0
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
0
1
1
1
1
1
2
0
2
0
0
1
2
1
1
0
0
1
1
1
1
1
0
1
2
1
2
2
1
0
2
1
1
1
0
1
3
0
1
1
1
2
1
0
1
1
0
1
2
1
0
1
1
2
0
1
1
1
2
0
2
0
0
1
2
1
1
2
2
1
1
0
1
1
1
0
1
2
1
0
1
1
1
0
2
0
2
1
0
1
2
0
1
2
0
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
2
2
1
1
1
2
1
1
1
0
1
1
1
1
1
1
1
0
0
0
0
1
0
1
1
1
1
2
0
1
1
2
0
0
1
0
3
1
1
0
0
2
0
1
1
1
1
1
2
1
1
1
1
0
1
2
1
0
0
2
0
1
0
0
2
1
0
1
1
0
1
2
2
1
1
1
1
1
2
1
2
1
1
1
1
2
1
0
1
2
0
2
0
0
1
2
0
1
1
1
1
1
2
1
0
2
1
2
0
1
1
1
1
0
0
1
1
1
0
2
2
0
2
2
2
1
2
1
1
3
1
3
2
1
1
1
1
1
1
0
0
0
0
2
1
0
2
2
1
1
0
2
1
1
1
0
0
2
1
1
1
1
0
1
1
0
1
1
1
0
1
1
1
4
3
3
1
1
2
1
1
1
1
1
2
1
0
1
1
3
0
1
2
1
1
2
2
0
1
2
2
2
0
1
1
2
0
1
2
3
1
1
1
1
1
2
2
1
0
1
0
2
1
1
0
1
0
1
2
1
2
2
1
1
2
1
1
2
1
1
1
0
0
1
2
2
1
1
0
2
2
1
1
0
1
1
1
2
1
0
0
2
1
1
2
1
0
0
2
1
0
0
2
1
1
0
1
1
1
2
1
2
2
2
1
2
1
1
1
2
1
0
2
1
0
1
1
1
1
1
1
0
0
2
1
2
1
1
1
2
1
1
2
2
2
2
0
2
0
1
1
1
2
2
1
1
1
1
0
1
1
1
0
0
0
1
2
2
1
1
1
2
2
0
1
1
1
1
1
1
0
1
1
2
3
3
0
1
2
1
0
0
1
1
2
1
2
0
2
1
1
0
1
1
2
0
1
0
2
1
1
1
0
2
2
3
1
1
1
1
1
1
1
2
0
1
2
1
2
1
0
1
1
1
1
0
0
1
1
1
2
2
1
1
1
1
1
2
1
2
1
0
2
0
1
1
1
2
2
0
2
0
1
0
0
0
1
0
1
0
1
1
1
0
0
1
1
2
3
1
1
1
1
1
1
0
0
3
1
1
1
1
1
1
0
2
0
2
2
1
0
0
0
1
1
1
0
0
0
1
3
2
1
1
2
1
2
2
2
0
0
1
1
0
1
1
1
2
2
1
2
1
0
1
0
2
1
1
1
1
2
1
1
1
2
1
0
0
2
1
1
1
1
0
0
2
1
0
0
0
1
1
0
1
2
1
1
0
1
0
0
0
1
2
1
2
1
1
0
1
1
1
2
1
1
1
0
2
1
2
2
1
1
2
2
1
1
1
1
1
0
0
1
1
0
1
2
0
1
0
1
2
2
1
2
0
1
1
2
0
0
0
2
1
0
2
1
1
1
0
1
1
1
0
0
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
0
1
0
1
2
1
1
1
1
2
0
0
1
2
2
0
2
0
1
0
0
0
0
1
0
1
1
2
1
1
0
1
1
1
2
0
0
0
1
0
1
0
0
2
2
1
2
2
2
2
2
2
2
1
0
0
0
2
1
1
0
2
1
0
1
1
2
2
1
2
1
1
0
1
0
2
0
2
2
2
2
0
1
1
2
2
2
1
1
0
1
0
1
1
2
1
2
0
2
3
2
1
2
0
1
1
1
0
1
2
0
2
0
1
0
2
2
1
0
2
2
1
2
1
1
1
1
1
2
2
1
0
2
0
0
1
2
0
1
1
2
2
1
1
1
1
2
1
0
0
1
0
1
1
0
0
1
2
1
1
2
1
1
2
0
1
1
1
2
2
2
1
1
0
1
1
1
1
2
0
2
1
1
0
0
2
1
2
0
0
1
1
1
2
0
1
2
1
1
0
1
1
1
2
0
1
1
1
0
1
1
0
2
2
2
1
1
2
1
2
0
1
1
0
2
1
1
1
1
1
1
1
0
0
1
0
1
0
0
0
1
0
1
1
1
1
1
2
1
2
2
1
0
0
1
2
1
1
0
2
2
0
0
2
0
1
1
1
0
1
2
1
3
1
2
0
2
0
1
1
1
0
2
0
0
0
1
0
1
1
0
1
1
1
0
2
1
0
0
1
1
1
1
1
0
1
1
1
1
0
0
1
1
0
1
2
1
1
2
2
1
0
1
2
1
2
2
0
0
1
2
1
2
1
1
2
2
1
2
1
1
0
1
1
1
1
1
0
1
1
1
0
1
0
2
1
1
1
2
0
0
0
0
1
2
0
1
0
0
0
1
0
0
0
1
1
1
3
1
1
1
0
1
2
0
2
1
2
2
2
2
2
0
1
1
0
1
2
1
2
1
1
2
2
1
1
2
1
1
1
1
0
1
2
1
0
1
1
2
1
0
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
0
2
2
1
1
2
1
2
1
1
0
0
1
1
1
0
2
0
0
0
0
1
1
0
1
2
1
0
1
1
2
0
1
0
0
2
2
1
1
1
0
2
1
0
0
1
0
1
1
1
0
0
1
1
1
1
1
0
0
1
0
2
2
1
0
1
2
1
1
1
1
1
1
0
0
1
1
0
0
0
1
0
1
0
1
1
0
0
0
1
1
0
1
2
2
2
1
1
0
0
1
2
1
0
0
2
2
0
2
0
1
1
2
1
1
0
1
1
1
2
0
1
2
1
1
1
2
1
2
2
0
0
1
1
2
1
1
1
0
0
1
2
3
0
0
2
1
2
1
1
1
1
2
1
2
2
0
1
0
2
2
2
0
1
1
0
0
1
1
1
1
1
0
1
1
0
1
0
1
0
2
1
0
1
2
1
1
1
3
2
0
1
1
1
1
1
1
1
0
1
2
1
4
1
0
1
1
1
1
2
1
1
2
1
1
2
2
1
1
1
2
1
2
1
2
2
2
1
0
1
1
4
2
1
1
1
1
2
1
0
2
1
0
2
1
1
1
1
1
1
2
0
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
2
0
0
1
2
2
0
1
1
1
0
1
2
0
0
2
1
2
1
0
1
0
1
1
1
0
0
1
1
1
0
1
1
2
1
1
1
0
1
1
1
1
1
2
1
1
1
1
0
1
1
0
1
1
1
2
1
1
1
0
2
0
1
0
1
1
1
1
0
0
2
1
0
1
1
1
1
2
1
0
1
1
1
2
1
0
2
1
1
2
1
1
2
1
0
1
1
2
1
1
2
1
0
2
0
0
2
1
2
0
0
1
0
1
0
2
2
0
0
2
1
1
0
1
3
0
0
1
2
0
0
1
2
1
2
0
2
2
0
1
1
0
2
1
1
2
0
1
1
2
1
1
1
1
0
0
1
1
0
2
2
1
1
1
2
1
2
0
0
0
1
2
1
0
1
2
0
0
0
1
0
1
0
0
0
1
3
1
1
1
3
1
0
1
1
0
1
1
1
2
1
2
1
1
0
0
0
2
2
2
1
2
1
1
0
0
0
1
1
1
2
0
1
0
1
1
2
0
1
0
2
1
2
1
2
1
1
1
1
0
1
1
3
2
2
1
1
2
1
0
1
1
1
1
1
1
0
2
1
0
2
1
0
1
1
2
2
0
1
2
1
1
1
2
1
0
2
1
1
2
1
2
0
2
1
1
1
1
1
2
1
3
1
1
1
1
2
1
1
0
1
1
0
2
1
1
1
1
2
2
2
1
2
0
1
1
2
2
1
1
2
2
2
1
1
1
1
0
1
1
2
2
0
1
2
1
1
1
0
2
1
0
1
0
1
0
1
2
2
1
2
2
1
0
1
1
1
1
1
0
0
2
1
3
1
1
0
5
2
2
1
2
1
0
0
1
0
4
1
1
1
1
1
1
1
0
0
1
0
3
1
1
0
0
0
2
1
1
3
1
0
0
2
0
2
2
1
1
0
2
0
0
1
1
1
1
2
0
1
0
1
1
2
1
2
1
1
0
1
1
1
3
1
0
0
2
1
1
0
1
2
1
2
1
1
1
0
1
1
1
1
0
1
1
0
1
1
2
1
2
1
1
2
1
1
0
1
1
0
1
1
1
1
1
0
1
2
2
1
0
2
1
1
2
1
2
1
0
1
1
1
0
0
1
1
2
1
2
0
0
1
1
0
1
2
2
0
0
0
0
4
0
2
1
1
2
1
1
1
1
1
2
1
1
1
1
4
1
2
2
1
1
0
2
0
2
1
1
2
0
2
1
2
2
1
2
1
1
0
1
0
2
0
1
1
1
0
0
1
1
1
1
2
1
1
0
0
1
0
2
1
1
2
1
1
2
1
1
1
0
0
1
1
0
1
2
1
1
0
0
1
1
1
2
2
1
0
1
1
0
1
2
1
1
2
2
0
0
0
1
1
1
0
1
1
1
0
1
1
2
1
1
1
0
1
1
1
0
1
0
2
1
1
2
1
1
0
1
2
0
0
0
1
1
0
1
1
1
0
1
1
1
0
1
2
1
2
0
1
1
2
1
2
1
1
2
1
2
1
0
1
1
2
2
0
0
1
1
2
1
1
1
1
2
0
1
1
0
0
0
2
1
1
2
1
0
0
1
2
0
1
1
2
1
0
1
0
2
1
0
1
0
1
0
2
1
1
1
1
2
1
1
2
0
1
1
1
1
0
2
1
1
2
1
1
0
2
1
2
1
1
1
0
1
0
1
1
1
1
0
0
1
2
0
1
0
2
0
0
0
0
1
0
1
2
2
1
0
0
1
0
0
1
2
1
1
0
1
2
1
1
1
1
1
1
0
1
0
1
0
1
0
2
1
2
1
1
2
0
1
0
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
2
1
2
1
0
1
1
0
1
0
1
2
0
0
1
1
1
1
1
0
1
1
0
1
3
2
1
0
1
1
1
1
1
1
0
0
2
1
2
1
2
1
0
0
1
0
1
0
0
0
0
0
2
1
1
4
2
1
1
1
2
1
1
3
1
0
1
2
2
2
2
1
0
1
1
1
2
2
1
1
0
1
1
0
0
0
1
1
0
1
1
1
1
0
1
0
2
0
1
1
1
1
0
0
1
2
1
2
1
2
1
1
2
0
2
1
2
1
0
1
1
1
0
1
1
0
0
2
0
1
1
1
0
1
1
1
1
1
1
2
0
2
2
1
1
1
1
2
1
1
2
0
0
1
0
0
1
2
1
1
1
0
1
1
2
0
2
2
0
2
0
1
2
2
0
1
1
1
1
0
0
1
1
1
1
0
0
0
1
2
2
1
1
1
1
1
1
1
1
0
1
2
0
0
2
1
0
0
0
2
1
0
0
1
1
1
2
0
2
1
2
0
2
1
1
1
0
1
2
1
1
1
1
0
1
2
0
1
0
2
0
1
1
1
1
1
0
2
1
0
1
1
1
1
1
1
0
2
1
0
1
1
1
3
0
0
1
0
1
0
1
1
1
2
0
2
1
1
1
2
2
0
2
1
1
2
0
1
1
0
0
1
2
1
1
0
1
1
1
1
1
1
2
0
0
2
1
1
1
0
1
1
1
1
1
1
2
1
2
2
0
1
0
1
2
0
0
0
1
0
2
2
1
3
2
1
1
2
1
0
2
2
1
2
2
1
2
1
1
0
1
3
2
1
1
2
1
0
1
0
0
0
0
0
1
2
0
1
1
2
0
1
1
1
1
1
1
0
0
2
1
1
0
1
2
2
1
1
1
1
1
2
2
2
1
1
1
1
0
3
1
1
0
0
2
2
1
1
0
1
1
2
1
1
2
1
1
1
0
1
2
1
1
0
1
1
0
1
1
1
1
1
0
1
0
1
0
2
1
2
1
1
1
2
3
1
4
1
0
0
1
2
1
2
1
2
0
1
2
1
1
1
0
1
1
0
0
1
1
1
2
0
1
1
0
0
1
2
1
1
2
1
1
2
0
0
0
0
2
1
2
1
1
0
1
2
1
0
2
1
1
0
1
1
1
1
1
0
1
1
1
0
1
0
1
1
1
2
1
0
0
2
2
1
2
0
0
1
1
1
0
0
1
1
2
0
1
1
1
1
1
0
2
2
1
0
0
1
1
0
2
1
1
2
2
0
1
0
2
0
2
1
0
0
1
2
2
1
0
2
1
0
1
0
0
1
0
1
0
2
1
1
2
1
1
2
1
0
2
1
1
1
1
1
1
2
2
2
0
0
0
0
1
1
1
1
1
1
1
2
0
0
1
0
1
1
1
2
0
2
2
1
0
0
1
1
1
0
4
2
0
0
1
2
1
0
1
1
2
1
1
1
2
2
1
1
1
2
1
0
2
0
1
2
2
1
1
1
1
2
2
1
0
1
1
1
1
2
1
2
1
1
2
2
1
1
1
0
0
1
0
0
1
1
2
1
1
0
1
1
1
0
0
1
1
1
0
1
1
1
1
1
0
0
0
2
2
0
1
1
2
1
0
1
2
2
1
2
1
1
0
0
2
2
0
2
1
2
1
2
1
2
2
1
0
2
1
1
1
0
1
1
1
0
2
0
1
1
1
2
2
1
2
1
0
1
2
2
0
1
2
2
0
0
0
1
1
1
1
2
0
1
1
1
1
0
2
0
0
0
0
0
1
1
0
1
2
0
2
1
1
2
2
0
0
1
2
1
2
1
2
1
2
1
2
2
0
2
1
1
1
1
0
0
1
1
2
1
2
1
0
1
2
1
0
0
1
1
2
1
0
0
0
0
1
0
1
0
0
0
1
0
2
1
1
2
1
0
1
1
1
0
1
2
1
1
1
1
1
1
2
1
0
3
1
1
0
0
2
0
2
0
2
1
1
1
1
1
1
1
1
1
2
1
0
1
1
0
1
2
1
1
2
2
2
1
1
0
1
2
2
0
2
1
0
1
1
0
1
1
2
0
1
1
1
1
1
0
2
2
1
1
1
0
1
1
2
1
0
1
0
0
0
1
1
2
1
1
1
0
2
1
1
0
1
2
1
1
1
0
1
1
1
0
2
1
2
1
2
1
0
1
1
2
2
0
1
2
1
1
0
0
1
1
1
1
1
0
0
1
2
0
2
1
2
1
2
1
1
2
1
1
0
0
1
1
4
0
1
1
1
1
0
1
0
0
1
1
1
1
0
2
1
0
2
1
0
2
3
1
2
0
0
1
1
1
0
0
2
2
0
1
1
0
2
2
1
0
1
1
1
1
0
0
1
1
1
3
0
2
0
2
1
0
2
1
0
1
1
0
0
2
1
1
0
0
2
1
0
0
2
1
1
1
2
0
2
2
2
0
0
2
4
0
2
0
0
0
2
0
1
2
1
2
0
1
1
0
0
2
0
1
1
1
2
1
2
1
2
2
1
1
2
0
0
0
2
1
1
2
1
1
1
1
1
2
2
0
0
1
2
0
1
1
2
2
2
1
2
1
1
1
1
1
1
1
1
1
3
1
2
1
1
0
0
1
2
0
1
2
0
1
2
1
1
0
0
0
0
1
0
1
2
1
2
1
0
1
1
0
0
0
2
1
1
0
1
1
2
1
0
1
1
2
0
1
1
2
2
0
0
1
1
2
2
1
0
0
1
1
1
1
1
1
1
0
1
2
0
1
1
1
1
1
0
1
0
1
0
1
1
0
2
1
1
1
2
4
1
1
0
0
1
1
1
0
0
0
1
1
0
1
3
0
1
1
2
1
2
2
0
1
1
1
1
1
2
0
0
0
2
1
2
1
1
1
0
1
0
2
0
1
3
0
1
1
1
0
1
1
1
1
1
2
2
0
1
0
2
0
1
1
1
0
0
1
1
0
1
2
0
1
1
1
2
1
1
1
2
1
1
1
2
2
0
0
0
1
0
1
1
1
0
0
0
0
1
2
0
0
1
2
2
1
2
1
0
1
1
1
0
2
2
2
0
1
1
1
1
1
2
2
1
1
0
2
0
1
0
2
0
2
1
1
2
3
1
1
1
0
1
1
2
2
0
0
1
1
0
2
2
2
1
1
2
0
1
0
1
1
2
1
1
2
1
1
1
1
2
1
1
0
0
2
1
0
1
1
0
1
1
2
2
1
0
1
0
1
0
1
1
1
1
1
1
2
1
0
0
1
2
2
2
1
1
1
0
0
0
0
1
2
1
1
0
1
0
1
0
0
1
0
1
2
0
1
1
2
1
2
1
0
2
0
1
2
2
1
2
1
1
0
0
2
1
1
0
2
1
2
1
2
2
1
2
2
2
0
1
2
0
1
2
2
1
1
1
2
0
0
2
2
2
2
1
0
1
1
1
1
1
1
1
1
1
0
2
2
2
1
1
0
1
2
0
1
0
1
1
1
0
1
1
1
0
1
1
1
1
1
2
2
1
1
0
0
0
2
0
0
0
0
1
2
1
0
1
0
1
1
0
1
2
0
1
0
1
1
1
0
1
2
1
1
1
0
2
2
1
2
1
2
2
1
0
0
1
1
2
1
1
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
0
1
1
1
1
1
1
1
1
1
0
1
1
1
2
1
1
0
1
2
0
0
1
0
0
0
1
0
2
1
1
1
1
1
0
1
2
1
1
2
1
2
2
1
1
2
3
1
1
2
0
0
1
1
1
1
1
1
1
1
1
1
2
1
1
0
2
0
1
3
2
1
2
1
1
0
0
1
0
1
0
0
1
2
2
2
0
2
0
1
1
0
1
1
2
1
0
0
2
1
1
1
1
1
1
3
2
2
2
1
0
2
1
1
1
2
1
1
2
0
1
1
1
0
0
1
1
2
1
1
1
1
0
2
1
2
1
1
0
1
0
1
2
2
1
2
1
1
2
1
2
1
2
0
2
2
1
0
1
1
0
0
1
1
0
0
0
0
1
0
2
2
2
1
2
2
1
1
2
1
2
2
0
0
1
1
1
1
1
2
1
1
1
1
1
0
1
2
0
0
1
1
2
1
2
2
1
1
1
1
0
1
1
0
1
1
2
2
0
1
2
1
1
2
1
1
2
1
2
1
0
0
2
1
1
0
2
1
1
1
0
1
2
1
1
0
2
2
1
1
1
0
1
1
2
1
2
1
0
2
1
1
2
1
0
1
2
1
1
1
2
1
1
0
0
0
0
1
1
1
1
2
1
1
2
1
0
0
1
1
1
2
2
2
1
0
1
0
2
1
1
1
2
1
1
0
0
1
2
0
0
1
1
1
1
2
2
1
1
2
1
0
0
1
1
1
1
1
1
1
1
2
1
1
2
1
0
1
1
3
1
1
1
0
1
2
2
0
2
2
0
0
1
0
1
1
1
1
1
0
0
1
2
1
1
0
0
0
0
1
1
1
1
1
2
2
1
1
0
2
0
0
1
2
2
2
2
2
1
2
1
0
1
2
2
0
1
1
1
1
1
2
2
0
1
1
0
1
1
1
2
1
0
1
0
1
1
1
1
1
2
1
0
1
1
2
1
0
0
1
0
2
1
1
1
1
0
1
1
1
1
2
1
0
1
2
2
0
0
1
1
1
0
0
1
1
0
1
1
1
0
1
2
1
1
1
2
1
1
1
1
1
1
2
1
0
1
2
1
1
2
0
1
1
1
2
1
0
2
0
2
0
2
2
1
2
1
1
1
1
0
1
0
1
1
0
0
2
2
0
1
2
1
2
0
1
1
1
2
0
1
1
0
1
2
2
0
2
2
1
1
0
1
1
2
1
1
1
0
1
0
1
2
2
1
1
0
1
1
1
1
2
1
1
0
1
1
0
0
2
2
0
0
0
1
1
0
2
1
0
1
2
1
2
1
2
2
2
2
0
1
0
0
1
1
1
1
1
0
2
0
0
1
1
0
0
1
1
0
2
0
0
1
0
1
0
1
1
1
2
1
2
1
2
1
2
2
2
0
1
1
0
0
1
1
1
1
0
0
2
0
1
2
2
0
0
1
0
2
0
2
0
1
1
2
2
0
2
2
0
0
1
2
0
1
1
0
1
1
0
0
0
1
2
2
0
1
2
1
1
2
1
0
1
1
0
3
1
1
1
1
1
1
2
1
0
2
0
1
1
1
0
1
0
2
2
2
1
1
1
2
2
1
1
1
1
1
1
1
1
0
1
2
2
1
0
1
1
2
0
0
0
1
1
1
1
0
2
3
1
1
2
1
1
2
0
0
3
1
0
2
0
0
2
0
1
1
1
1
1
2
2
1
0
1
2
0
0
1
0
0
1
0
0
1
0
1
1
2
1
0
1
0
1
0
0
0
1
0
1
0
1
1
2
1
2
2
1
1
0
1
0
1
1
1
0
0
1
1
1
1
1
0
0
1
0
1
2
1
0
1
0
2
2
1
1
2
2
2
2
1
2
1
1
1
2
0
1
1
0
1
1
0
0
2
2
1
1
1
1
1
1
0
0
1
1
0
1
0
0
1
1
0
1
0
1
0
2
1
0
0
0
1
1
1
1
0
1
0
2
1
1
2
2
0
2
1
1
1
1
1
1
0
1
3
1
1
1
0
1
2
0
1
1
1
2
2
1
1
1
1
2
1
2
1
1
0
1
0
1
1
1
1
0
1
1
0
2
1
1
2
2
2
0
2
2
1
0
2
2
2
1
0
1
2
0
1
1
2
1
1
1
1
0
2
1
0
1
1
1
1
1
1
1
1
3
1
1
1
0
2
2
1
2
0
0
1
0
1
1
1
0
2
0
0
1
1
2
1
1
1
1
1
2
2
0
1
1
1
0
0
2
2
1
1
0
0
1
0
1
0
1
1
0
1
2
2
0
2
1
2
1
2
1
0
1
0
0
2
0
2
0
2
0
1
2
0
2
1
0
0
0
1
2
0
1
1
6
1
3
1
1
1
0
1
1
0
0
1
1
1
0
1
0
2
1
2
1
2
0
0
1
0
1
1
1
1
0
1
2
2
2
2
1
1
1
1
1
2
1
0
1
1
1
2
1
1
1
3
2
1
1
2
0
1
2
1
1
2
0
2
2
1
0
0
3
1
1
2
1
0
0
1
0
1
1
1
1
1
2
1
2
2
0
1
2
1
2
0
1
0
2
1
1
2
1
1
1
1
1
1
0
1
2
1
0
0
1
1
1
2
1
0
1
2
1
1
1
1
0
1
1
0
1
1
1
2
0
1
2
1
0
1
0
0
1
1
0
1
0
1
1
2
1
2
1
2
1
0
0
0
0
1
1
0
1
2
0
1
0
1
2
1
1
1
2
2
1
1
1
0
1
0
0
1
0
0
1
1
0
1
0
1
1
2
2
0
2
1
2
0
1
0
2
2
1
1
2
1
0
1
2
0
1
1
1
1
1
1
2
0
2
1
1
1
1
0
1
2
1
1
1
0
1
1
1
0
1
1
1
0
2
0
0
0
2
1
1
0
1
1
1
1
1
0
0
1
0
1
0
1
2
0
1
0
2
2
0
1
0
2
1
1
1
0
1
1
2
2
1
1
1
0
1
0
2
3
1
2
1
1
0
0
0
0
1
1
1
1
0
0
2
1
0
1
1
2
1
1
0
2
2
1
3
0
0
1
1
1
0
1
1
2
1
2
0
1
0
1
1
0
1
1
1
2
1
0
0
1
1
2
1
0
0
0
1
1
1
2
0
2
1
0
1
2
1
0
1
0
1
1
2
1
1
2
0
2
1
1
1
1
1
2
0
0
0
2
1
1
1
0
1
1
0
1
0
2
0
0
0
2
0
0
0
1
1
1
1
1
1
2
2
2
1
0
2
1
0
1
1
0
1
1
2
1
1
0
1
1
1
1
0
0
0
0
1
0
1
3
1
1
2
0
2
1
1
2
1
2
0
0
0
1
1
2
2
1
1
0
1
1
0
1
2
0
0
1
0
2
2
1
0
1
1
0
1
1
1
1
0
1
1
1
1
2
1
0
1
1
2
1
1
0
0
1
1
0
1
2
1
1
2
2
0
0
0
0
2
0
1
2
2
1
1
1
1
1
1
1
0
1
1
1
1
1
1
0
0
2
1
2
1
0
0
0
1
0
1
1
1
1
1
1
0
1
0
1
1
1
2
1
0
1
0
1
0
1
0
1
0
1
0
0
2
2
1
0
2
2
0
0
1
1
1
0
0
1
2
1
1
1
1
1
1
2
0
1
1
2
1
2
1
1
0
1
0
1
3
0
0
2
0
1
0
1
0
2
2
0
1
1
1
2
0
1
2
1
1
2
1
2
1
2
0
1
2
1
0
0
1
2
1
2
0
1
1
0
0
0
1
2
0
2
0
0
0
2
1
1
1
0
1
1
1
1
2
1
0
1
1
1
2
1
1
1
1
1
1
2
1
1
0
0
1
1
1
1
1
0
1
2
2
1
1
0
0
2
2
0
1
1
2
1
0
1
2
0
1
0
0
0
1
0
0
0
0
0
2
0
0
1
1
1
1
2
0
0
1
2
1
0
1
0
0
0
2
2
1
0
0
3
0
1
0
1
1
2
1
1
1
0
1
1
2
0
2
1
2
2
0
1
2
1
2
2
0
1
2
1
0
3
0
1
0
1
1
1
1
1
0
2
1
1
0
1
1
2
1
1
0
1
2
1
1
1
1
0
2
0
2
1
1
1
1
2
0
1
2
1
0
1
2
1
1
2
0
1
1
1
1
1
1
0
2
2
1
1
1
2
2
1
2
2
0
1
0
2
0
2
1
0
1
1
1
4
2
1
1
0
1
0
2
1
1
1
0
0
2
0
1
1
1
1
1
1
1
0
0
0
0
1
0
0
1
1
1
1
0
2
1
2
1
0
1
1
0
0
0
2
1
2
2
1
1
1
0
1
2
0
2
2
2
0
1
2
1
1
1
1
1
0
1
0
0
1
1
2
1
1
1
1
0
0
1
1
2
1
0
1
0
0
1
1
1
1
1
0
0
1
1
0
0
2
1
1
1
0
0
0
1
2
1
1
1
0
2
2
1
1
2
1
0
0
0
1
1
0
2
2
1
0
1
1
1
1
2
0
1
1
0
1
0
1
0
0
0
1
1
1
2
0
1
1
0
1
1
0
0
0
0
1
1
1
1
1
0
1
1
2
1
1
2
0
1
1
1
1
1
1
2
0
1
1
0
2
1
0
2
0
1
2
1
2
2
1
2
0
1
0
1
2
1
1
2
1
2
1
1
2
3
0
3
0
2
2
2
1
2
1
1
1
2
2
2
1
1
1
1
1
1
1
0
2
1
1
0
1
2
0
1
0
1
0
1
1
2
0
1
1
1
0
3
1
0
1
1
1
3
2
2
0
3
0
2
1
0
1
0
1
1
0
0
2
2
1
3
0
1
0
2
1
1
1
2
1
1
0
1
1
1
0
2
1
0
0
0
2
1
1
0
1
1
1
0
1
0
2
1
2
1
0
0
0
1
0
1
0
3
1
2
1
1
2
1
0
1
0
0
0
1
1
0
0
1
1
0
2
2
0
1
1
0
1
2
1
0
1
1
2
1
1
0
1
2
1
1
3
0
0
1
2
1
1
2
1
0
1
2
0
1
2
1
0
1
1
2
2
1
1
1
0
0
0
1
1
2
1
1
1
3
1
1
1
2
1
1
1
1
1
1
2
1
2
2
1
0
0
0
0
0
0
1
0
1
1
1
0
1
1
1
2
1
2
1
1
0
2
1
1
2
1
1
2
1
3
1
2
2
2
1
1
1
2
1
0
1
0
2
0
1
1
1
0
1
1
2
1
0
0
0
1
2
1
2
0
0
0
1
1
0
1
2
2
1
0
0
1
0
1
0
0
0
0
1
0
0
1
2
2
1
0
1
2
1
2
1
1
1
2
0
0
1
1
0
2
1
1
2
1
2
1
2
1
0
2
2
2
1
1
2
0
1
0
0
0
0
1
1
0
1
0
2
1
0
2
0
2
1
1
1
1
1
1
1
2
1
0
5
1
2
1
0
0
2
1
1
1
0
1
2
1
2
1
1
1
2
0
0
1
1
1
2
1
0
1
2
0
1
1
0
0
1
1
0
1
1
0
0
2
1
2
2
1
1
1
1
0
1
1
1
1
1
2
1
1
1
0
1
1
0
1
1
1
0
0
1
3
1
2
1
1
1
0
2
1
2
1
1
1
0
1
2
1
1
1
2
2
1
1
1
1
0
2
1
1
1
1
0
2
2
2
1
0
2
1
2
1
3
2
0
0
0
2
1
1
1
1
0
1
1
1
1
2
1
1
0
1
2
2
1
0
1
2
2
1
0
2
2
1
1
2
0
0
1
1
1
0
1
1
0
1
1
2
3
2
0
1
1
1
1
2
2
1
0
0
1
2
1
2
2
0
0
1
0
1
1
0
2
1
1
1
0
1
1
1
2
1
1
0
2
1
1
1
0
2
1
1
1
0
0
1
0
0
1
0
0
1
1
1
1
1
0
0
1
1
1
0
2
0
1
1
0
1
0
2
0
1
1
2
0
1
2
1
2
0
2
1
0
1
0
1
0
3
2
1
1
2
1
2
0
0
1
2
1
3
0
0
1
1
2
0
1
1
2
0
2
1
1
0
1
1
1
0
1
1
1
1
1
2
0
1
1
0
1
0
1
1
1
2
0
0
0
1
2
1
1
0
1
2
1
0
1
0
1
1
1
1
1
2
0
1
1
1
1
1
2
1
0
0
1
1
0
1
0
0
1
1
0
1
2
1
1
1
2
1
0
1
1
0
0
2
1
1
2
1
1
2
1
1
2
1
1
1
2
1
0
1
1
0
0
1
1
0
1
1
1
0
2
0
1
1
1
0
0
2
0
0
1
1
1
2
1
0
1
1
1
2
0
1
1
1
0
1
1
1
1
0
0
1
3
1
1
1
1
1
2
2
1
1
1
1
2
0
2
1
0
2
2
1
2
1
0
1
0
1
0
0
1
0
2
2
1
1
1
1
2
0
0
2
0
2
0
2
1
1
0
1
1
0
0
1
1
1
3
1
1
2
2
1
2
0
2
1
1
0
1
2
1
0
0
2
3
2
1
2
1
0
1
1
2
0
2
2
1
1
2
2
1
1
1
1
2
1
2
2
0
1
2
0
1
1
1
1
1
1
2
3
1
0
1
2
0
3
0
0
1
0
1
1
2
1
0
1
0
1
1
0
0
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
0
1
1
1
0
2
2
0
1
1
1
0
0
1
1
1
1
1
1
1
1
1
1
0
0
1
1
0
1
2
1
0
2
2
2
1
0
1
1
1
1
1
1
1
1
1
0
0
2
0
0
0
2
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
0
0
1
0
0
1
2
2
0
1
1
1
2
1
1
0
1
2
1
1
1
1
1
1
2
0
1
0
1
2
0
1
1
2
0
0
1
2
1
1
1
1
1
0
1
1
0
1
2
1
1
1
1
2
0
1
0
1
1
2
2
1
1
1
2
1
0
1
0
1
1
1
1
0
1
0
1
0
1
1
1
1
1
0
1
2
2
2
2
1
2
1
1
1
0
1
2
2
2
1
1
0
1
0
1
1
0
1
1
0
2
1
1
1
1
3
0
1
3
2
1
2
1
1
1
1
2
1
0
1
0
1
3
0
2
3
2
2
1
2
1
2
1
1
1
0
0
1
1
0
1
0
2
1
1
1
1
1
1
0
0
2
1
0
1
1
3
2
0
1
0
2
1
1
1
0
1
1
1
2
0
2
0
2
0
1
1
1
0
1
2
1
0
2
1
2
0
1
1
1
1
2
2
1
0
2
1
1
0
1
1
1
0
0
0
0
1
0
0
0
2
1
2
2
1
1
2
1
2
0
0
1
0
1
1
1
1
0
1
1
1
0
0
1
0
1
2
0
1
0
1
2
2
2
2
1
2
1
1
0
1
1
1
1
1
1
1
1
0
0
0
1
2
1
2
1
2
1
0
1
1
0
0
0
1
2
1
2
2
2
1
2
1
2
2
1
1
1
1
2
1
1
1
1
1
2
2
1
1
0
2
1
1
2
2
0
2
0
1
2
0
1
0
2
1
2
1
2
0
1
1
1
1
1
1
0
0
1
1
0
0
0
2
1
1
0
0
0
2
2
1
2
1
1
1
1
0
1
0
1
0
0
1
0
0
1
2
1
1
0
1
0
1
0
1
1
1
0
2
1
1
1
1
0
0
1
2
0
1
0
2
0
1
3
1
2
0
1
0
1
2
2
0
0
2
1
1
2
2
2
2
1
1
1
2
1
1
2
1
2
2
1
1
1
0
0
1
1
1
1
1
1
0
2
0
1
1
1
1
1
0
2
2
2
1
1
1
1
1
1
4
0
1
0
1
3
2
1
2
0
0
0
1
0
1
0
0
0
0
2
0
1
2
2
1
1
1
0
1
1
1
1
1
2
2
0
2
2
1
0
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
0
1
1
1
0
1
1
1
0
1
1
0
1
2
0
0
1
1
1
1
2
1
1
1
1
0
1
1
2
1
0
1
0
1
1
1
0
1
1
2
1
2
1
0
1
2
2
0
1
0
1
0
0
1
1
1
1
0
1
0
1
1
0
1
0
0
1
2
0
1
1
1
1
1
1
1
1
1
0
0
2
1
2
1
1
2
0
1
1
1
2
1
5
0
2
2
0
1
2
0
0
1
2
1
0
2
1
1
2
2
1
1
1
0
2
0
1
1
1
0
1
0
1
2
2
2
2
1
1
1
2
0
1
1
1
1
1
1
1
1
0
2
2
2
0
2
2
1
1
1
0
0
1
1
1
1
1
1
1
0
1
1
1
0
1
1
1
1
1
3
1
1
1
0
1
1
1
0
1
2
0
1
0
1
1
1
0
2
1
1
1
0
1
1
1
1
0
0
1
1
1
1
1
2
2
1
2
0
2
1
0
2
1
2
1
1
1
1
1
0
1
1
1
1
2
1
1
1
1
1
0
2
1
2
1
0
0
1
1
1
2
2
1
0
1
1
2
2
2
1
1
2
0
1
1
1
1
1
1
2
0
0
1
1
2
0
0
0
0
2
1
1
1
1
2
1
2
3
1
0
2
0
1
1
0
1
1
2
2
2
0
1
1
0
1
0
0
1
2
1
0
2
1
2
1
1
2
1
1
1
1
3
0
1
1
2
1
1
0
0
2
1
1
1
1
0
2
0
1
2
2
2
1
1
2
0
2
1
2
1
0
1
1
0
0
1
2
0
2
1
4
2
1
0
1
1
0
1
0
1
1
0
1
2
0
1
1
0
1
2
2
1
0
2
0
1
1
1
1
2
1
1
0
1
1
1
2
1
2
1
2
0
1
1
0
0
1
0
1
0
1
0
1
9
2
2
0
1
2
2
1
1
1
2
1
1
2
2
1
1
2
1
1
2
1
1
1
1
2
1
2
2
1
1
1
2
1
2
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
2
1
1
1
0
1
0
0
1
1
1
1
1
0
0
1
0
1
3
1
2
2
1
1
0
1
1
1
1
1
2
2
1
2
1
0
0
1
1
1
0
1
0
0
2
1
3
1
1
0
2
1
1
0
1
1
1
0
1
0
1
0
1
0
1
1
0
1
0
0
3
2
2
1
1
2
2
1
1
0
1
1
1
1
1
0
1
1
1
1
1
1
1
1
0
0
1
0
0
1
3
2
1
1
2
0
2
0
0
0
1
1
1
1
0
1
1
0
2
0
2
1
1
1
0
1
2
1
1
2
0
0
1
1
1
0
1
1
2
0
1
1
3
0
1
1
0
1
1
1
1
0
1
1
1
1
1
1
1
0
0
1
1
1
1
1
1
1
2
1
0
1
1
2
1
1
1
0
0
0
1
0
2
1
0
2
1
0
0
2
0
4
1
0
2
1
1
1
0
1
1
1
2
1
1
1
1
0
1
3
1
1
3
2
1
1
1
1
1
0
0
1
0
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
0
1
1
2
0
1
0
2
1
0
0
1
1
0
1
1
2
0
2
1
2
1
1
1
2
1
2
1
1
2
1
1
2
1
2
1
1
1
2
1
1
0
0
0
1
2
0
1
2
0
2
2
2
1
2
0
2
2
2
1
2
1
0
4
1
0
1
0
0
1
1
0
1
0
0
1
2
0
3
1
1
2
2
0
0
1
1
1
1
1
1
1
2
1
1
1
1
2
0
0
1
1
1
0
2
1
0
0
0
1
1
1
1
2
0
2
1
0
0
1
1
0
2
3
0
0
2
0
2
1
1
2
1
1
0
1
1
0
0
1
1
2
2
0
0
0
1
0
2
1
0
1
0
2
1
1
3
2
2
1
0
2
1
1
2
1
0
1
0
0
2
2
1
1
2
1
1
0
1
2
0
1
2
1
0
1
0
0
1
1
2
1
2
1
0
1
1
1
2
0
2
0
0
2
1
1
1
1
2
1
1
2
1
2
1
0
0
1
1
0
1
1
0
0
0
1
2
0
0
1
1
1
3
0
1
0
2
0
1
1
2
1
2
1
2
2
1
1
0
2
0
0
0
1
2
1
1
0
0
1
1
0
0
1
1
1
1
1
1
1
1
0
0
1
1
2
1
0
0
0
0
0
2
1
0
2
0
1
1
1
1
2
1
2
0
1
2
2
1
1
2
2
0
1
0
1
1
1
1
1
2
3
1
0
1
1
1
0
1
1
1
2
1
2
1
1
1
1
1
0
0
2
1
1
2
1
0
1
1
1
2
1
0
1
1
1
0
1
0
1
1
1
2
0
0
2
1
0
1
2
1
0
1
1
2
2
0
1
1
1
0
1
1
1
1
0
1
1
2
0
1
0
1
0
0
0
0
1
1
1
1
1
0
1
0
1
1
1
1
2
1
1
1
0
0
1
1
2
2
1
2
0
1
0
1
1
2
1
1
1
1
1
0
0
2
1
0
1
1
0
0
2
1
1
1
1
1
2
1
2
0
2
0
1
1
1
2
1
1
0
1
1
0
0
0
2
2
1
0
0
2
2
2
1
0
1
2
0
0
0
0
1
1
0
1
2
2
1
1
2
2
2
0
0
0
1
2
1
1
0
2
1
0
0
2
0
2
1
1
0
2
0
1
1
3
1
1
1
1
0
1
1
0
1
1
0
0
0
1
1
0
1
1
0
2
0
2
1
1
1
1
0
1
1
1
0
0
1
1
1
1
0
0
1
1
1
1
2
1
0
1
1
0
0
0
1
2
1
1
1
0
1
1
0
0
1
0
1
1
2
2
1
0
0
1
0
0
1
2
1
1
1
1
1
0
1
2
1
0
2
1
1
0
1
0
1
2
0
1
0
0
1
1
1
1
2
1
2
1
1
2
1
2
2
2
0
0
0
2
1
1
1
1
0
1
0
0
2
1
0
2
0
1
3
1
2
1
0
1
2
1
1
0
1
0
1
2
1
2
1
0
1
2
2
1
1
3
1
1
2
2
0
2
0
0
1
1
1
1
1
2
3
1
0
1
2
0
1
2
2
0
1
2
1
0
1
1
0
1
1
1
0
1
2
1
2
1
2
1
1
2
1
2
1
2
0
1
3
1
1
2
2
2
2
1
1
1
1
2
1
0
0
0
2
1
1
1
1
0
1
1
1
1
2
1
2
1
2
1
1
2
0
1
2
2
0
1
0
0
1
1
1
1
1
0
0
1
1
1
0
0
0
1
0
2
2
2
1
1
1
1
1
2
3
1
1
1
1
2
1
0
0
1
2
0
1
1
1
1
2
0
0
0
1
1
1
1
0
0
1
0
1
2
2
1
0
1
1
0
1
0
0
1
4
2
2
0
2
1
2
2
2
1
1
1
1
0
1
2
1
0
1
0
2
0
1
1
0
0
1
1
0
0
0
1
1
1
0
1
2
0
0
1
0
1
0
1
2
1
1
0
0
1
1
0
0
1
2
1
1
1
2
1
1
1
1
0
1
0
1
1
1
1
0
1
0
1
2
2
0
2
1
1
1
1
1
1
0
2
1
2
2
1
1
1
2
0
2
1
3
1
0
1
1
1
2
1
2
1
1
0
1
1
1
0
0
0
2
0
0
0
0
1
1
1
0
0
2
1
0
1
0
1
1
2
0
2
0
0
1
1
0
1
0
2
2
2
2
1
0
2
3
1
1
0
2
0
0
1
0
0
1
1
1
1
0
2
1
0
1
0
0
1
2
0
0
1
1
1
0
0
1
2
2
1
1
1
1
2
2
1
2
0
1
2
0
0
1
1
0
1
1
2
0
2
1
1
2
0
1
0
1
1
1
1
1
1
1
0
1
1
2
1
1
0
1
1
1
1
2
0
0
0
0
1
0
0
5
1
1
1
0
1
0
1
1
0
1
2
1
0
1
0
2
2
2
1
2
2
1
1
0
0
1
1
1
0
1
1
0
1
0
1
0
2
1
2
1
1
0
1
1
1
0
2
1
2
1
0
0
0
1
1
2
1
1
2
1
2
1
2
2
1
1
1
1
1
1
1
1
4
1
1
0
0
0
1
1
1
1
1
1
0
2
2
0
1
2
2
1
2
2
2
0
1
1
0
0
1
0
1
2
0
0
2
2
1
0
1
0
0
2
0
1
1
0
1
1
1
0
2
0
1
5
1
0
1
1
1
0
0
1
1
2
0
1
0
0
2
1
1
2
1
0
1
2
1
1
0
1
0
1
2
0
0
1
1
1
0
1
0
1
1
2
0
2
2
1
1
1
2
1
1
0
0
2
2
1
1
0
0
2
1
0
1
0
1
0
1
2
1
2
0
2
2
1
1
0
0
1
1
0
1
1
2
1
1
2
1
2
1
2
1
0
1
2
0
1
1
1
1
2
0
1
0
4
1
1
1
1
1
0
1
1
1
1
2
2
1
2
1
0
1
1
1
1
1
1
0
2
1
1
2
2
2
1
1
0
1
1
0
1
1
1
0
2
1
1
0
0
0
2
1
1
1
2
1
1
1
1
1
0
1
1
1
0
0
1
1
2
2
1
4
1
0
1
1
1
0
1
0
2
1
1
1
0
0
1
3
1
1
1
1
1
1
1
0
1
1
1
1
2
0
1
0
1
1
1
1
2
1
2
0
1
0
0
1
2
1
1
2
1
0
1
1
0
0
1
0
0
0
2
0
1
2
1
2
1
1
2
1
1
1
1
2
2
0
1
1
1
3
1
1
1
1
1
0
1
1
1
2
1
0
2
2
0
1
2
0
1
1
2
0
0
2
1
2
1
1
1
1
1
2
0
1
1
0
2
1
0
1
1
1
1
1
2
1
1
1
1
1
1
2
0
0
0
1
0
1
1
1
1
2
2
0
1
1
1
2
1
2
1
1
1
2
0
1
2
2
1
0
1
2
2
2
1
0
1
1
1
1
2
1
0
1
1
1
1
0
1
1
2
1
2
0
1
1
0
1
1
1
1
1
1
0
0
1
1
2
0
1
1
1
1
0
1
2
1
2
2
0
0
1
2
0
1
2
1
0
0
1
1
2
2
1
1
1
0
1
1
1
1
1
1
2
1
0
1
2
2
1
2
0
0
2
0
1
0
1
0
0
1
2
0
0
0
0
0
0
1
0
2
1
0
1
2
1
0
2
0
1
2
0
0
2
2
0
1
2
1
2
0
1
1
0
2
1
0
1
2
1
0
2
1
1
2
0
2
0
1
1
2
1
2
0
1
0
0
1
1
0
2
2
0
1
0
1
0
1
1
2
2
1
1
3
0
1
2
0
2
1
1
4
1
1
2
1
1
1
2
1
1
1
1
2
1
2
2
1
2
1
2
0
1
1
7
1
1
0
1
1
2
1
1
0
0
1
1
1
1
1
1
1
2
2
0
1
1
2
0
1
1
1
1
2
1
1
1
1
2
1
1
0
1
0
1
0
1
1
0
2
1
0
0
2
2
1
1
1
0
1
1
0
2
1
1
1
0
1
2
0
2
0
2
1
1
1
0
0
1
0
1
0
3
1
1
1
0
1
1
1
0
1
1
1
2
1
2
1
0
1
1
1
0
2
2
1
2
1
1
2
2
0
1
1
1
1
1
1
0
1
0
1
2
2
0
1
1
0
3
2
3
1
1
1
1
0
1
1
0
2
0
1
1
1
2
2
1
0
0
1
0
2
0
2
1
0
1
1
0
1
0
1
1
1
2
0
0
0
1
1
2
0
2
1
1
1
2
2
1
0
0
1
1
0
1
0
1
1
0
1
2
1
0
1
1
2
1
0
1
1
2
1
1
1
0
1
1
1
1
1
1
1
0
1
1
0
0
1
1
2
1
1
2
1
1
1
1
1
1
0
1
1
0
0
0
1
2
0
1
2
1
1
2
1
1
1
1
1
0
1
1
1
1
1
1
1
0
2
2
1
1
0
2
0
1
0
1
1
2
1
0
0
1
1
2
1
0
1
0
1
1
0
1
0
0
1
2
1
0
0
1
1
0
2
1
0
3
1
1
0
1
0
1
0
1
0
0
1
1
2
1
2
0
1
0
0
0
1
1
2
2
1
1
1
2
0
2
2
2
2
1
1
0
1
2
1
1
1
1
0
1
1
0
0
3
1
1
2
1
2
0
0
0
2
2
2
1
1
0
0
0
0
1
2
1
2
1
0
1
1
1
1
2
2
1
2
0
1
1
2
0
1
1
2
1
0
1
1
0
1
0
0
1
1
1
0
0
1
1
2
0
1
0
0
1
0
1
1
0
0
2
0
0
0
0
0
1
2
1
1
2
0
0
1
1
1
1
2
0
1
2
1
2
1
1
1
0
2
1
1
2
2
1
1
1
1
0
0
1
0
1
2
1
1
0
1
1
1
0
1
1
0
0
1
3
2
1
0
1
2
1
0
1
1
3
2
1
1
3
2
2
2
2
0
1
2
0
1
1
1
2
1
1
1
1
1
0
1
1
1
1
1
1
2
2
2
2
0
1
1
1
1
1
1
2
2
1
1
0
2
1
2
1
1
1
2
2
1
1
2
0
1
0
1
1
0
2
2
0
1
1
0
2
2
1
0
1
1
2
2
1
2
2
1
1
0
0
2
0
1
0
1
2
1
1
2
2
0
1
1
1
1
1
1
1
0
1
1
1
1
2
1
0
0
1
1
2
2
1
0
0
2
1
1
2
0
1
1
2
0
1
1
2
1
1
1
1
1
0
3
1
1
2
0
0
0
0
1
1
1
1
2
1
2
1
0
0
1
1
2
0
0
1
0
2
1
1
2
2
0
1
1
1
1
2
2
2
1
0
2
1
0
2
1
1
1
1
2
1
1
0
2
1
0
1
0
1
2
2
2
2
2
1
1
1
0
1
0
1
1
1
1
0
1
1
2
0
0
1
0
2
1
1
1
0
1
2
1
0
2
1
2
1
1
3
1
1
1
1
2
1
1
0
1
2
1
0
1
2
2
2
1
0
0
0
1
0
1
2
0
1
1
0
2
1
1
0
1
0
1
1
1
1
0
1
0
2
1
0
2
0
1
1
2
0
1
0
1
1
1
0
1
2
1
0
1
1
1
1
0
1
1
0
0
1
1
1
1
1
1
2
1
0
1
0
1
0
1
1
1
1
2
2
1
1
2
0
0
1
1
2
3
0
0
0
0
1
2
1
1
2
0
2
2
1
2
1
0
0
2
1
1
0
2
1
1
1
1
1
0
2
1
0
0
1
0
1
1
1
0
1
1
0
1
1
1
1
1
1
1
2
1
1
2
1
1
1
0
1
2
1
2
2
2
0
1
1
1
1
1
2
2
0
2
2
1
1
1
1
0
1
1
2
0
1
0
1
2
2
1
0
1
0
0
3
0
2
1
1
2
0
0
1
0
0
1
0
0
0
1
1
0
2
1
1
1
1
1
1
0
1
1
0
1
1
2
1
1
0
0
0
0
1
1
1
2
0
2
1
1
0
1
1
1
0
0
1
2
1
0
0
0
1
1
1
1
2
1
1
0
1
2
2
0
0
1
2
1
1
1
0
1
2
1
1
1
0
0
0
2
0
2
0
1
0
2
1
2
2
1
0
2
0
1
0
1
0
2
1
1
2
1
2
2
2
1
1
0
0
0
1
1
1
0
1
1
1
0
0
1
1
1
1
0
0
0
1
1
1
1
1
1
1
0
1
2
0
2
1
1
2
1
2
1
1
0
1
1
0
2
2
2
1
1
1
0
1
0
0
2
1
1
1
1
2
1
1
1
3
1
2
2
1
1
1
1
1
2
1
1
0
2
2
1
1
1
1
0
5
2
2
0
0
2
1
0
1
1
0
1
2
1
0
0
0
0
2
1
3
2
0
1
2
1
0
1
1
0
1
1
2
2
1
1
0
2
0
1
0
3
2
1
0
2
1
0
0
0
1
2
0
1
0
1
1
1
0
1
1
0
1
2
2
1
1
0
2
2
0
2
2
2
1
1
1
1
1
0
0
0
1
0
2
1
0
0
0
1
1
0
0
1
2
3
0
1
2
0
1
0
2
1
1
1
1
0
1
0
1
1
1
1
2
2
1
2
1
1
2
2
1
1
0
1
2
0
1
1
0
0
1
0
1
0
1
0
1
1
1
1
1
1
0
1
3
1
1
2
3
1
1
1
1
1
0
1
1
1
1
2
1
1
1
1
1
1
1
0
2
0
1
2
1
0
1
0
1
0
0
2
1
1
2
0
0
2
1
1
1
0
1
1
1
1
2
2
0
1
0
1
1
2
1
2
2
0
1
1
0
1
1
1
0
1
2
1
1
0
0
0
1
1
0
2
2
2
0
1
0
1
1
2
2
1
1
0
0
0
1
2
1
1
1
0
2
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
2
1
2
1
0
1
1
1
1
1
0
0
1
1
0
2
2
1
1
2
1
0
1
2
0
1
2
2
2
0
1
2
0
2
1
0
1
1
0
1
2
2
1
2
0
0
1
1
1
1
2
2
0
2
2
2
1
2
0
2
1
2
1
1
1
1
1
2
1
1
1
1
1
2
2
1
0
1
0
1
1
1
1
2
1
0
1
2
1
1
2
0
1
1
1
2
1
1
0
1
2
0
2
1
1
1
0
2
0
1
1
0
0
2
1
1
1
1
1
0
0
0
1
2
1
2
1
1
2
0
1
1
1
1
1
0
1
1
2
2
2
1
1
1
0
0
0
1
0
1
0
2
1
1
2
2
1
1
1
1
0
2
0
0
1
3
2
0
1
2
1
1
1
0
0
1
0
2
2
1
2
3
3
1
0
1
2
0
0
0
0
2
5
1
1
3
1
2
2
1
0
1
1
1
1
1
1
0
1
1
1
2
0
1
1
2
1
1
2
1
1
2
1
0
0
2
0
0
0
1
2
0
2
0
1
1
2
1
3
2
2
1
0
1
2
1
1
1
2
0
1
0
7
1
1
0
3
2
1
0
2
3
1
1
1
1
1
2
2
1
0
1
1
1
1
0
1
1
2
1
1
1
1
1
2
1
2
1
1
2
2
1
1
1
1
0
1
1
1
2
2
2
1
0
0
2
1
2
2
0
1
1
2
1
1
3
2
2
1
1
1
1
2
1
1
2
2
1
0
0
1
0
1
1
2
0
2
0
0
2
0
0
2
0
1
1
0
2
1
0
1
0
1
0
1
1
1
1
2
1
0
1
1
1
1
2
1
0
0
0
2
2
2
1
0
0
1
1
1
1
3
1
2
1
0
2
1
1
0
2
1
0
1
0
1
1
2
0
1
1
1
1
1
2
1
0
1
0
1
0
0
1
2
0
2
0
1
1
1
1
1
1
2
1
1
1
0
0
2
2
1
2
2
1
1
1
1
0
1
2
1
1
2
1
0
1
2
1
2
1
1
0
1
2
0
0
2
0
0
1
1
1
2
1
2
1
1
2
1
2
1
3
0
0
0
2
1
0
2
2
1
1
0
1
1
1
0
0
0
1
1
1
0
0
1
1
1
0
0
1
1
1
1
1
0
0
3
1
0
1
0
1
0
1
0
2
2
1
0
0
2
0
2
1
0
1
4
0
3
1
2
1
1
3
2
0
0
2
2
1
2
0
1
1
2
0
2
0
1
1
1
0
1
1
1
0
0
0
2
2
1
0
1
1
2
0
2
0
1
1
2
2
2
0
1
2
1
0
1
1
1
1
1
1
0
0
1
0
0
1
1
1
1
1
0
2
1
0
2
1
1
2
0
0
1
2
1
0
0
1
1
0
1
1
1
0
1
2
1
1
1
1
1
1
2
1
1
0
2
0
0
1
1
1
0
0
0
0
0
1
2
2
1
1
0
3
1
0
1
0
1
1
2
1
0
0
1
2
0
0
0
1
2
0
2
1
1
1
3
1
0
2
0
0
1
2
1
0
2
1
0
1
1
0
2
2
0
1
0
0
0
1
1
4
1
1
2
1
0
2
2
2
1
2
0
0
1
2
0
1
2
1
1
0
1
1
1
2
1
2
2
0
2
0
1
1
2
2
0
1
0
1
1
1
1
1
1
1
1
0
0
0
0
1
1
0
1
1
2
1
1
1
1
1
2
0
1
1
0
6
1
1
1
1
1
2
1
2
1
0
2
1
1
2
1
2
0
0
0
1
1
2
1
1
0
0
2
1
1
1
0
0
0
1
2
2
0
1
1
3
1
1
0
1
1
1
1
1
1
0
1
0
1
0
1
0
0
2
1
1
2
0
0
1
1
0
1
0
1
1
0
1
1
1
1
1
1
2
1
1
2
0
1
0
2
1
1
2
0
1
1
2
1
1
1
1
1
1
1
1
0
1
1
1
1
1
0
1
2
2
1
0
2
0
1
2
0
2
1
1
1
1
2
2
1
2
1
1
0
1
2
2
1
2
0
1
1
2
1
2
1
1
1
2
1
1
1
1
0
0
1
1
0
1
2
1
1
1
1
0
1
1
0
2
1
0
1
0
0
1
2
1
2
2
1
1
2
1
1
0
2
1
1
0
1
1
2
0
3
1
1
2
1
1
2
1
2
2
1
1
1
1
2
1
0
2
1
2
1
0
1
0
2
1
2
1
2
2
2
1
0
0
2
1
1
1
0
0
2
2
1
1
0
2
0
1
0
1
1
1
1
1
1
0
1
2
1
2
1
2
1
0
1
0
1
1
2
1
1
0
1
0
1
1
1
0
1
0
0
1
3
1
2
2
1
1
0
0
1
1
0
3
1
0
0
0
2
2
1
2
0
5
0
0
0
1
0
1
1
1
1
1
0
1
1
1
1
0
2
0
1
1
1
1
1
2
1
2
1
1
0
1
0
1
1
2
1
2
1
2
0
1
2
0
1
2
2
1
0
1
1
1
1
1
0
0
0
0
1
2
1
0
1
0
0
0
2
1
1
1
2
0
0
1
1
1
2
0
1
1
0
0
1
2
0
1
1
1
0
1
1
1
2
0
3
1
1
2
0
0
1
1
0
2
0
1
1
0
0
1
2
2
1
1
0
1
0
2
2
2
1
2
1
2
2
2
0
0
1
2
0
2
0
1
1
0
0
1
1
0
1
2
1
2
2
1
1
0
0
2
1
2
2
1
1
1
1
1
1
1
0
1
1
2
1
1
0
2
1
0
0
1
1
1
2
0
1
2
1
1
2
1
3
2
0
1
2
1
1
2
2
1
1
0
1
1
1
2
0
1
2
2
1
2
1
0
0
0
1
2
1
2
0
1
1
0
1
1
1
1
1
0
0
0
1
0
1
2
1
0
1
2
0
1
0
0
0
1
0
1
2
1
0
2
1
1
1
1
2
1
0
1
2
1
2
1
1
1
1
0
0
0
0
0
0
1
1
1
1
1
0
1
1
0
0
0
1
2
1
1
2
2
2
1
1
0
0
1
2
0
1
0
0
2
1
0
0
0
0
0
2
0
2
0
1
1
1
2
0
1
0
1
0
2
1
2
2
0
0
1
0
2
1
1
0
1
1
1
2
1
2
1
1
1
1
1
1
0
2
0
1
1
0
1
1
1
1
0
2
0
2
1
0
1
1
2
2
2
1
0
2
0
0
2
1
1
1
0
2
0
1
2
1
1
2
1
1
2
1
1
0
1
1
2
1
1
1
1
1
1
2
2
0
2
0
1
1
0
1
0
2
0
0
1
1
2
2
1
1
1
1
1
0
1
1
1
1
2
0
1
1
2
0
1
1
2
0
0
1
1
1
0
1
2
1
2
0
1
1
0
1
0
0
2
0
1
1
1
1
0
0
1
0
1
2
1
2
2
1
1
0
0
2
1
1
1
1
2
1
1
2
2
1
1
0
0
2
2
4
1
2
1
3
1
1
1
0
0
0
1
1
1
1
2
0
1
1
1
1
1
0
0
2
0
1
2
1
2
0
1
2
0
1
2
1
1
0
0
1
1
0
1
1
0
1
0
1
0
1
1
1
2
1
2
2
2
3
0
1
1
1
0
2
0
3
2
0
1
0
0
2
1
1
2
1
2
2
0
0
1
3
2
0
2
2
0
0
1
2
1
1
1
2
2
1
0
1
1
2
0
1
2
0
0
2
1
0
1
2
1
1
0
2
2
1
1
1
0
0
1
1
1
2
1
1
1
0
0
0
1
3
1
1
1
1
1
1
1
1
0
1
1
0
1
0
1
0
1
1
1
1
0
0
2
2
1
0
0
1
0
2
0
1
1
0
1
0
2
1
0
1
0
1
1
0
2
0
0
1
1
2
1
1
1
0
1
0
1
2
0
1
1
2
2
2
1
0
1
1
1
1
1
2
1
0
2
0
2
1
1
1
0
1
1
1
0
1
2
0
1
1
0
0
0
2
1
1
1
0
1
1
0
0
3
1
0
1
1
0
1
1
2
0
1
0
1
1
2
1
1
0
0
1
1
0
1
1
1
1
2
1
2
1
2
1
1
1
1
1
0
1
0
1
0
2
1
1
0
0
2
0
2
1
2
1
1
1
1
1
2
1
1
2
1
0
2
2
1
2
1
1
1
1
1
1
2
0
1
1
0
0
2
1
0
0
1
1
2
1
0
1
2
0
0
2
2
1
2
2
0
2
1
2
0
2
0
1
2
2
1
0
1
1
2
1
1
1
0
1
2
1
1
2
1
0
2
1
2
0
2
2
1
0
0
1
0
3
0
2
0
1
0
1
3
2
0
0
1
1
0
2
1
2
2
1
2
1
1
1
1
1
1
1
1
1
1
0
2
2
1
1
0
1
1
0
1
1
2
1
0
1
1
2
1
0
0
0
2
0
0
1
0
0
0
1
1
0
1
0
0
1
1
2
1
1
2
0
2
1
0
0
2
0
1
1
0
0
2
1
1
1
1
2
2
1
1
0
2
0
3
2
2
1
1
1
2
2
2
0
1
2
1
0
0
1
1
1
0
0
2
2
0
1
1
1
1
1
1
0
1
0
1
1
0
2
1
1
1
1
0
2
1
0
1
2
2
0
2
1
2
0
2
0
2
2
1
1
2
1
1
1
0
1
1
1
1
2
1
1
2
2
1
1
1
1
0
1
1
2
0
1
0
0
2
1
1
2
0
1
0
1
1
3
2
1
1
1
0
1
0
1
3
1
1
1
0
1
2
0
3
2
1
0
2
2
2
1
1
2
2
0
2
0
2
1
1
0
1
1
1
1
1
1
1
0
2
1
2
4
0
1
1
2
2
2
1
2
0
2
2
1
1
1
0
0
0
1
2
2
1
1
1
2
1
1
1
2
1
0
1
1
1
2
1
1
2
0
1
1
2
1
0
1
2
1
1
0
1
2
1
1
1
1
1
1
1
1
2
1
0
2
1
0
1
1
0
1
1
2
2
2
1
1
1
2
2
1
1
1
1
2
1
1
3
1
1
1
1
1
1
1
2
1
1
2
2
1
1
1
2
2
1
2
2
0
1
1
1
0
0
1
2
1
1
0
1
1
1
1
1
2
1
0
0
2
1
1
1
2
1
2
1
1
1
0
0
0
1
1
0
2
1
1
0
1
1
1
1
2
1
0
2
0
2
1
1
1
0
1
1
0
0
2
1
4
1
1
2
1
0
1
2
0
2
0
1
1
1
0
1
2
2
0
0
1
1
1
2
0
1
1
1
2
2
0
2
1
3
1
0
2
1
0
2
1
0
0
1
2
2
0
0
1
0
1
1
0
1
3
2
0
1
1
0
0
0
1
1
0
1
2
1
0
1
1
1
0
1
0
0
2
0
1
1
1
1
0
0
0
1
1
2
0
2
0
1
1
0
1
1
1
2
1
2
0
1
2
1
0
1
4
0
2
1
1
1
1
2
0
2
1
0
1
1
0
0
2
0
0
0
1
2
1
0
1
2
1
0
2
0
1
2
1
2
2
1
3
1
2
1
2
0
1
0
1
0
2
0
1
0
2
1
1
1
1
1
2
1
1
1
1
0
2
2
2
0
1
1
2
1
0
1
1
1
1
1
0
0
1
1
2
2
0
2
2
0
0
1
0
1
0
1
1
1
1
2
0
1
0
1
2
2
0
0
1
1
1
0
1
1
1
1
1
1
2
1
1
0
1
2
1
1
1
2
2
0
1
1
1
0
0
1
2
1
0
0
1
1
1
1
1
0
1
0
1
0
0
1
0
0
2
1
0
1
2
2
0
0
1
2
1
1
0
2
1
2
0
1
1
0
2
1
1
0
0
1
1
1
0
0
2
0
0
1
1
1
1
1
1
1
1
1
2
1
0
1
1
1
1
1
0
1
0
0
1
0
0
2
0
0
0
2
1
1
2
2
2
1
2
1
0
1
2
0
2
0
1
1
1
1
2
1
1
1
1
1
1
0
0
0
1
1
2
1
2
0
1
0
0
2
2
0
1
1
1
1
0
1
0
1
1
3
2
0
1
0
2
0
1
3
1
0
0
1
1
0
0
2
2
1
2
1
1
1
0
1
0
0
0
1
1
1
0
1
2
2
1
1
2
0
2
1
1
2
0
2
2
0
0
1
1
1
1
0
2
1
1
2
1
1
1
0
1
0
1
1
1
0
2
1
2
1
0
2
1
2
1
1
2
2
1
1
0
0
1
2
0
1
1
1
1
1
1
2
1
0
0
1
1
0
1
1
1
2
1
2
2
1
1
1
2
1
1
0
0
1
1
1
0
0
1
2
1
0
2
1
0
2
0
2
0
2
2
1
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
2
2
0
1
0
0
0
1
0
0
1
1
1
0
0
1
2
1
0
1
1
1
2
1
1
1
1
2
1
1
0
2
0
2
0
1
0
1
2
1
1
0
1
2
2
0
1
1
1
0
1
1
1
1
1
2
1
2
1
2
0
0
0
0
0
1
1
0
0
1
1
0
2
1
1
0
2
1
1
0
0
1
1
1
1
1
1
1
1
0
1
1
1
1
0
0
2
3
1
0
0
2
0
1
1
1
1
1
1
0
1
0
0
0
1
1
0
1
0
0
2
2
1
0
1
2
0
0
1
1
0
1
1
0
0
1
1
1
0
2
0
1
1
1
1
0
1
4
1
2
1
2
1
1
1
1
2
0
2
1
2
0
1
0
2
1
1
0
1
1
1
1
0
2
0
0
0
0
1
0
2
1
0
2
1
1
1
0
2
2
0
0
1
0
0
2
2
1
0
1
0
0
1
0
1
2
0
0
0
1
1
1
2
1
1
0
2
1
2
1
1
0
0
0
1
1
1
1
1
2
1
1
1
2
2
1
0
0
0
1
1
2
2
2
1
0
1
1
0
1
2
2
1
1
0
1
1
1
1
1
1
2
1
2
1
2
1
0
2
1
0
0
0
2
1
0
1
0
1
2
0
1
1
1
2
0
1
1
1
0
1
1
1
0
0
0
2
2
2
2
1
0
0
1
0
1
1
1
2
1
3
1
2
1
2
1
1
1
2
1
0
1
0
1
2
0
1
0
2
1
2
0
1
2
1
1
1
1
2
1
0
1
1
2
0
0
1
2
2
1
0
1
0
2
3
2
0
2
2
0
1
2
2
2
1
1
1
1
0
2
2
1
0
1
1
2
2
1
1
1
0
1
1
1
2
1
0
0
1
1
1
1
1
0
3
2
1
1
1
2
0
2
0
1
1
1
1
2
1
0
1
1
1
0
1
2
0
0
1
2
1
2
1
1
2
0
1
2
1
1
1
1
0
1
0
1
1
1
0
1
1
1
1
1
1
0
1
0
1
1
0
1
1
1
1
2
0
0
0
1
1
0
2
1
1
1
1
2
0
2
1
0
0
1
1
0
0
0
0
1
0
2
1
1
1
1
0
1
0
2
0
0
2
1
1
1
1
0
2
0
1
1
1
2
1
1
1
0
1
1
1
2
1
1
2
2
0
0
0
2
0
0
2
2
1
0
1
1
4
1
2
2
2
2
2
2
1
2
2
1
2
0
0
1
1
0
0
1
2
0
0
0
2
0
1
1
1
0
1
1
1
0
1
1
2
0
0
0
1
1
2
2
0
1
1
1
1
2
1
1
2
1
1
2
1
1
2
1
0
0
0
0
1
0
1
2
0
1
0
0
1
1
7
1
2
1
1
0
1
1
1
1
1
0
0
1
0
1
2
2
0
2
0
1
2
1
2
0
1
1
1
1
1
3
2
2
0
2
1
0
1
1
2
1
0
1
0
0
1
1
1
1
1
2
0
2
0
1
0
0
0
1
0
1
2
0
2
1
2
1
0
2
1
1
2
1
2
1
2
1
1
4
1
2
0
0
0
1
1
2
1
0
1
0
1
1
1
1
1
2
1
0
1
3
1
1
1
2
1
0
2
3
1
0
1
0
1
2
2
2
0
1
1
0
1
1
2
1
0
1
1
1
1
1
1
1
0
0
0
1
1
0
1
0
1
1
0
3
1
2
1
0
1
0
1
0
1
1
1
0
3
1
1
1
0
0
1
2
0
1
0
2
1
1
1
1
1
2
1
0
0
0
1
2
1
1
1
1
1
2
1
1
1
2
1
1
0
2
2
1
0
1
3
2
0
0
1
2
0
1
1
1
0
2
0
1
0
1
1
2
1
1
0
1
1
1
0
0
2
2
1
1
2
1
0
1
1
1
1
0
0
2
0
2
2
3
1
1
2
0
2
2
0
1
0
0
2
2
0
2
1
3
1
2
1
0
1
1
2
0
0
0
2
2
1
1
2
1
2
2
0
0
0
0
2
1
2
1
0
2
1
1
1
0
2
1
1
1
1
1
1
1
0
0
1
0
0
1
1
3
0
1
0
3
2
0
2
1
1
0
1
1
1
1
1
0
1
1
1
1
1
1
1
2
1
2
1
0
2
1
1
0
2
2
2
1
1
2
0
1
0
2
1
3
1
2
1
1
0
2
2
1
1
1
2
1
1
1
1
2
2
1
0
0
2
2
0
1
1
2
2
1
0
1
1
0
1
3
0
1
1
0
1
1
0
1
2
1
1
0
0
1
2
1
2
1
0
2
2
0
2
1
1
1
1
0
1
1
3
2
1
1
0
1
2
3
1
0
2
1
2
0
1
2
0
0
2
1
1
2
1
2
0
0
1
1
1
0
0
2
1
1
0
1
1
1
1
1
0
1
1
2
1
1
1
2
2
0
0
1
1
0
1
0
2
2
1
0
0
1
1
1
2
0
1
1
2
0
2
2
2
1
0
1
0
2
0
2
0
1
1
1
1
1
1
0
0
2
2
0
1
0
1
1
1
1
1
1
0
2
1
1
2
1
1
2
1
0
1
1
1
1
0
1
1
1
1
0
4
0
1
1
1
2
2
2
1
0
1
0
1
1
1
2
1
2
0
2
1
1
2
0
2
0
1
2
1
0
0
1
1
1
1
0
2
1
1
0
1
1
1
0
1
1
1
0
1
1
1
1
2
0
0
1
0
1
0
1
0
1
2
1
1
1
1
3
1
0
0
0
1
1
1
1
1
0
1
2
1
2
2
1
1
1
2
2
1
0
2
2
0
1
1
0
2
1
0
0
1
3
2
0
0
0
1
1
1
1
1
0
0
0
0
1
2
1
1
1
1
2
0
0
0
2
1
2
2
1
1
1
0
1
0
1
1
2
2
0
2
2
2
1
1
1
0
1
1
1
2
1
1
1
1
0
1
1
2
2
1
1
1
1
2
0
2
2
2
3
3
1
2
0
1
1
1
1
1
1
1
1
2
0
1
1
1
1
2
1
1
1
0
2
0
0
1
0
0
1
2
1
2
2
1
0
0
1
0
0
1
1
1
1
2
2
1
2
1
0
1
1
0
1
1
0
2
2
0
1
0
1
2
1
1
2
2
0
1
1
1
1
1
0
2
0
1
0
1
0
1
1
2
1
2
1
5
1
1
1
2
0
3
2
0
2
0
2
2
1
2
1
0
0
0
1
2
1
0
2
2
3
1
2
1
1
1
0
2
1
0
0
2
1
1
1
2
1
1
0
1
1
0
1
2
1
1
2
0
1
2
1
0
0
2
0
0
2
2
2
0
1
0
1
0
2
0
1
2
1
1
0
1
2
0
1
1
2
0
2
1
2
0
2
2
2
1
3
0
0
1
2
1
1
0
1
0
1
0
2
1
1
1
2
0
2
1
1
0
1
1
2
1
1
2
2
1
2
0
0
1
1
1
1
2
0
0
0
2
0
1
1
2
2
0
2
1
0
2
2
2
1
0
1
0
1
0
1
0
2
2
2
0
1
1
5
0
0
1
1
0
2
1
1
0
2
1
1
2
2
1
1
2
2
1
2
2
1
1
2
1
1
0
2
1
0
0
1
0
2
0
1
2
2
1
0
1
1
1
2
2
1
2
1
1
0
0
0
1
1
1
1
1
0
1
2
1
0
1
1
1
0
1
1
0
1
2
0
2
1
0
0
1
1
1
1
3
0
0
0
1
2
0
0
0
2
1
1
1
0
1
2
1
2
5
1
1
2
1
1
1
2
1
2
2
1
2
0
1
1
1
0
1
1
1
0
4
1
2
1
1
0
0
1
1
0
2
0
1
2
2
2
2
1
1
0
3
0
2
1
1
2
1
1
0
0
1
0
1
0
0
0
1
1
1
1
2
1
1
1
0
0
1
1
0
1
0
0
1
0
1
1
1
1
0
1
1
1
1
1
1
0
4
1
2
2
0
1
1
1
2
1
0
0
2
1
2
0
0
1
1
1
0
1
1
0
2
0
0
1
0
2
1
0
1
1
1
1
0
0
0
0
0
2
1
1
1
1
1
0
2
0
0
0
1
2
0
2
0
0
0
0
1
0
2
1
2
2
1
2
1
1
1
1
0
2
2
0
2
2
1
0
1
1
1
1
1
2
0
0
1
1
1
1
2
0
1
1
1
0
1
1
3
3
1
2
1
0
1
0
1
1
1
1
0
1
1
1
0
0
2
0
2
0
0
0
2
0
1
0
1
2
2
0
3
1
0
1
2
0
2
1
0
0
1
2
1
0
0
0
0
0
1
1
2
0
0
1
1
1
0
2
0
0
1
2
2
1
1
1
2
0
1
1
0
1
2
1
1
2
1
0
1
1
0
1
1
0
0
1
1
2
1
1
1
1
1
1
1
1
2
0
1
2
1
1
0
1
2
1
0
1
0
0
1
2
2
0
0
1
0
1
2
1
2
1
2
0
1
0
1
0
1
1
1
2
0
1
1
0
0
2
1
1
0
1
0
1
1
0
1
0
2
1
0
0
2
0
1
1
2
1
1
1
0
1
1
1
0
1
0
2
1
1
0
2
1
0
0
0
2
0
0
1
0
1
1
1
1
2
1
0
5
2
0
0
2
0
0
0
2
0
2
2
0
1
1
2
1
1
1
0
1
0
0
0
0
0
1
0
1
1
1
0
0
1
1
0
1
2
1
1
1
0
1
2
1
1
2
0
3
0
2
0
1
0
0
2
1
2
1
1
1
0
2
1
0
1
0
0
1
0
1
1
1
1
1
1
1
2
2
1
1
0
0
1
1
2
0
0
1
2
0
2
2
0
2
1
0
2
1
2
1
1
0
0
1
1
0
1
0
0
1
1
0
0
1
1
1
1
1
1
1
2
0
1
0
1
1
2
1
0
1
1
1
1
2
2
0
1
2
1
1
6
0
0
0
1
1
2
2
1
1
1
1
1
1
1
2
0
2
1
2
0
0
1
1
0
1
2
1
0
0
0
1
0
2
1
2
0
1
2
1
1
1
0
6
2
0
2
1
1
1
1
2
1
0
2
0
2
1
2
0
2
0
2
0
1
1
1
1
0
1
2
0
0
1
1
1
1
1
0
1
2
1
1
1
2
2
2
2
1
1
2
0
1
1
2
1
1
1
1
1
1
2
1
0
1
2
1
1
0
1
1
0
0
0
1
0
2
1
3
2
2
2
0
1
1
2
1
1
1
0
1
1
1
1
2
2
1
1
1
1
2
0
1
1
0
1
1
0
1
0
2
0
1
0
1
0
1
0
1
2
1
1
1
0
0
0
1
1
1
1
0
1
2
0
1
1
1
2
1
1
1
1
0
0
1
1
2
1
1
1
1
1
2
2
1
2
2
2
1
2
1
1
0
1
0
1
0
2
1
1
2
1
1
1
2
0
1
1
1
0
0
0
1
2
0
1
0
2
0
1
1
1
1
0
1
0
0
1
1
1
1
2
0
1
2
1
2
0
0
1
0
2
1
1
0
1
1
0
2
0
1
2
1
0
0
0
1
0
1
1
1
2
2
1
2
1
1
2
1
0
0
0
0
2
1
1
1
0
1
1
1
0
0
0
2
1
1
2
3
2
1
0
1
2
1
1
2
2
0
0
1
1
1
0
1
1
0
2
1
1
1
2
1
2
2
0
2
1
1
1
2
1
0
0
2
1
2
0
1
1
2
0
1
1
1
0
2
1
1
1
1
0
1
1
1
2
2
0
2
1
1
2
1
2
1
1
0
1
1
3
1
2
2
1
0
1
1
1
0
1
1
0
1
1
2
0
2
0
1
2
1
2
2
2
0
1
1
0
0
2
1
1
1
2
1
1
2
0
0
1
1
1
0
0
0
0
1
2
1
2
2
2
2
0
2
0
0
1
0
0
0
0
1
1
1
1
0
1
0
1
1
1
0
0
1
1
0
1
1
2
0
2
2
0
0
1
0
1
2
1
1
1
0
1
1
2
1
1
1
1
1
1
0
0
0
1
1
0
2
3
0
2
0
0
1
1
2
0
2
1
1
2
1
1
1
1
0
1
1
1
1
1
1
1
0
2
2
1
0
2
2
1
2
2
0
0
0
0
2
1
2
2
2
0
1
0
1
0
2
2
1
1
0
1
1
1
1
1
1
0
2
0
1
1
0
0
0
2
0
1
3
4
0
0
0
0
0
1
1
1
2
1
1
1
2
1
2
0
1
1
1
2
1
1
0
1
1
1
2
1
1
0
1
0
1
1
2
1
1
0
0
1
1
1
0
1
1
1
2
0
0
2
0
2
1
1
1
1
1
0
1
0
2
1
0
1
1
0
2
2
1
0
1
0
0
2
1
2
0
0
1
0
2
2
1
1
2
1
0
0
1
1
2
1
2
1
2
0
3
1
3
0
1
0
2
1
2
1
0
1
0
1
1
1
0
0
2
1
2
0
1
1
0
0
1
0
1
1
0
1
1
2
1
0
0
1
0
0
1
1
1
2
1
0
2
1
2
1
0
1
1
1
0
0
1
1
1
1
1
2
1
1
0
1
1
1
0
1
0
1
1
1
0
0
1
2
1
1
0
1
1
1
1
1
0
0
2
1
1
1
2
2
0
0
1
1
2
2
3
1
1
1
0
1
1
0
2
2
0
2
1
0
1
1
2
0
1
1
0
1
0
0
2
1
2
0
0
1
0
1
0
0
0
1
0
3
1
0
0
1
1
1
1
1
0
0
1
2
2
1
1
0
1
1
1
2
1
0
1
2
0
1
1
0
1
1
2
2
0
1
0
1
1
1
0
1
0
2
2
1
2
0
1
2
0
1
1
1
0
1
1
0
2
2
1
1
1
0
0
1
1
1
1
0
2
0
1
1
1
1
2
1
0
1
1
0
1
1
1
1
0
0
1
0
0
1
1
0
0
0
1
2
1
1
0
3
1
1
1
1
2
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
2
0
1
3
2
3
1
2
1
0
4
0
0
0
2
1
2
2
0
0
1
1
0
0
2
1
1
0
2
0
1
1
1
0
1
1
0
1
1
2
1
0
2
1
0
0
0
2
0
0
1
1
0
2
0
1
1
0
0
0
0
0
0
1
2
2
1
1
2
0
0
0
2
1
1
1
2
0
1
1
1
0
0
0
0
1
0
1
1
2
1
2
0
1
2
1
2
1
2
1
0
1
2
3
2
0
2
1
2
0
1
1
1
0
1
2
2
1
1
2
2
2
2
1
0
2
1
0
1
1
1
1
2
1
2
1
1
2
0
1
0
1
1
2
1
1
1
1
2
1
1
1
0
0
0
1
0
1
0
2
2
1
1
1
2
0
1
1
0
0
1
2
1
1
0
2
2
1
1
2
0
1
1
1
1
0
0
1
0
5
1
0
0
0
1
1
2
0
0
0
0
0
1
1
1
0
2
0
2
0
0
2
1
1
0
0
0
0
1
2
1
1
0
1
2
1
1
1
1
1
1
2
0
0
0
1
1
1
1
1
1
1
1
0
1
1
0
1
0
1
2
1
1
2
2
1
0
1
1
1
2
0
1
1
1
2
1
2
2
2
0
1
3
0
1
0
3
0
1
0
1
1
2
3
1
2
2
1
1
1
0
0
1
1
1
1
2
1
0
0
1
2
2
0
2
0
2
2
1
1
2
1
2
1
1
1
1
0
1
0
2
2
1
1
1
1
1
0
0
0
1
2
2
1
2
1
1
1
1
0
1
1
1
2
2
1
1
1
1
1
0
1
2
2
0
1
0
1
1
1
0
1
0
1
0
1
2
0
1
2
1
0
2
1
2
1
1
0
1
1
1
1
0
1
0
0
2
2
1
1
1
0
1
2
2
1
1
0
2
1
0
1
1
0
1
2
1
0
1
2
1
0
1
1
2
1
1
0
0
1
1
1
1
0
0
0
1
2
1
1
2
3
1
0
0
0
0
2
2
1
1
1
1
2
1
0
2
1
0
1
1
1
0
1
0
0
1
0
1
1
1
1
0
1
2
1
2
2
2
1
2
1
1
0
2
1
1
2
1
1
1
0
0
1
0
1
2
1
0
1
1
0
1
0
1
1
0
0
1
2
1
0
0
2
1
0
1
2
1
1
1
1
2
1
1
2
1
0
0
1
0
1
1
0
2
1
1
1
0
1
0
5
1
0
1
0
1
0
2
1
1
2
1
0
1
2
0
2
1
0
1
1
1
1
1
2
2
1
1
1
2
0
0
0
0
1
2
0
2
0
1
0
1
0
1
1
0
1
1
1
2
1
0
0
0
0
1
0
0
2
1
1
1
1
2
1
1
1
0
0
2
1
0
2
1
1
2
1
0
2
0
1
1
1
1
1
1
2
0
0
2
1
1
1
2
1
1
1
1
2
3
3
2
2
1
1
1
0
1
2
1
2
1
2
1
0
4
2
2
1
0
1
0
0
2
1
1
1
2
1
1
0
1
1
0
1
2
0
0
2
1
0
1
1
1
0
1
2
2
1
0
1
1
1
1
1
0
1
1
0
1
1
0
0
1
2
1
0
1
1
2
2
0
0
1
0
1
2
1
2
1
1
2
0
2
2
3
1
1
1
2
1
1
0
1
1
1
0
1
3
1
2
1
1
0
1
1
1
0
0
1
1
1
1
2
0
0
1
2
1
1
2
1
1
1
2
2
2
1
1
1
1
1
1
2
0
0
1
2
1
1
2
1
1
0
0
1
1
2
0
2
0
1
2
1
1
0
1
1
1
1
0
1
1
1
0
1
1
2
0
2
1
1
1
0
1
0
0
2
2
1
0
1
0
1
0
1
0
0
1
2
1
1
2
0
1
2
2
1
1
1
1
1
1
1
3
2
2
1
2
1
0
1
0
1
1
2
0
1
2
0
1
2
1
1
0
1
1
0
1
1
1
1
0
2
2
1
1
2
2
1
1
2
2
1
1
1
1
2
0
2
0
0
1
2
0
1
2
1
0
2
0
1
1
1
1
0
2
0
2
2
4
0
2
0
1
1
1
1
0
2
0
2
1
0
1
0
2
1
1
0
1
1
1
1
1
1
2
1
0
1
1
0
1
0
2
2
1
1
0
0
1
2
0
1
1
1
2
0
2
1
0
0
1
0
0
1
0
1
0
0
1
1
1
1
0
1
0
1
2
1
1
2
2
0
0
0
0
1
1
0
2
1
1
1
2
1
1
0
2
1
1
1
0
1
2
0
1
1
0
0
0
0
0
0
2
1
1
0
0
1
1
1
1
2
2
1
0
2
1
2
0
1
1
1
1
0
1
2
2
2
1
0
1
1
3
0
1
0
1
0
2
0
0
0
1
1
1
1
0
2
1
0
0
1
1
1
2
1
2
1
1
1
1
1
1
2
2
1
1
1
2
2
2
0
1
0
2
1
1
2
2
2
1
1
1
1
1
2
0
1
0
1
0
0
1
2
1
1
1
1
1
1
1
1
1
1
1
0
0
1
0
5
1
1
0
1
1
0
1
1
1
3
0
2
4
0
0
1
1
2
1
1
1
1
2
1
2
0
1
1
2
0
2
2
1
2
0
2
1
0
0
1
1
1
1
1
1
1
1
2
1
1
1
0
0
2
1
1
2
2
1
0
2
1
1
0
1
1
2
1
1
1
1
0
2
1
0
2
1
2
0
2
1
1
0
1
3
2
1
1
2
1
1
1
1
1
2
1
0
2
1
1
3
1
2
1
0
0
0
2
1
1
1
1
2
2
1
0
1
5
0
0
1
2
1
3
0
1
3
0
1
1
1
1
1
0
2
1
1
1
2
1
1
1
0
0
1
0
0
0
0
1
1
2
0
1
0
1
1
2
0
2
1
1
1
1
1
2
0
1
0
2
0
1
1
2
2
1
2
1
1
2
1
2
1
0
1
2
2
1
0
1
0
1
1
0
1
2
2
0
1
0
1
1
0
2
0
0
1
2
0
2
0
0
1
1
2
0
1
2
0
0
1
2
0
1
1
1
2
2
0
2
1
1
2
1
1
1
1
1
1
1
0
2
2
0
0
1
1
0
0
0
1
1
2
2
1
1
2
1
1
2
1
0
1
2
0
2
1
1
1
1
2
0
1
1
2
0
2
1
1
1
1
3
1
1
2
1
1
1
1
1
1
2
0
2
2
1
0
0
0
0
1
0
1
1
1
2
3
1
1
2
0
0
0
1
1
2
1
1
2
1
1
1
0
0
2
0
1
3
1
1
1
2
1
1
1
1
1
2
2
2
2
1
1
1
0
0
1
1
2
1
1
1
1
1
0
0
1
1
1
1
0
0
1
2
1
1
1
2
2
0
1
1
0
1
1
0
2
1
1
0
1
2
0
0
2
1
1
2
0
1
0
1
2
0
1
0
2
2
1
2
1
1
1
1
0
2
1
1
0
0
2
0
2
1
1
1
1
2
1
0
2
1
0
1
1
1
1
1
3
1
2
1
1
0
1
1
2
1
1
0
0
1
1
1
1
0
0
1
2
1
1
1
1
2
2
1
1
1
2
0
0
0
0
1
2
0
0
1
1
0
1
1
2
2
1
0
1
2
0
1
0
1
2
0
2
2
1
2
1
1
0
1
2
0
0
1
1
1
2
0
0
0
1
1
1
0
1
1
2
0
1
2
0
0
2
1
1
1
1
1
1
0
1
2
1
1
2
0
0
1
1
2
1
1
1
1
1
3
2
0
0
0
1
1
1
1
1
1
1
2
1
0
1
1
2
0
1
0
1
2
0
1
2
0
2
2
1
0
0
1
1
1
1
0
1
0
1
2
2
3
0
1
2
2
1
0
1
1
0
1
1
1
0
1
2
1
2
1
1
0
1
1
1
0
1
0
0
0
0
0
2
0
2
0
0
1
0
2
1
1
1
1
1
2
1
1
0
0
1
1
1
2
1
2
1
1
1
2
0
1
0
0
0
0
2
1
0
1
1
1
1
0
2
1
1
2
1
1
1
0
2
0
1
1
1
2
3
2
1
0
1
1
0
1
1
2
0
1
1
0
2
1
2
1
1
1
1
0
2
1
0
0
2
1
1
0
1
2
0
1
1
1
2
0
1
1
1
0
0
1
1
0
1
3
0
1
0
1
0
1
0
1
2
0
2
1
2
1
0
1
1
1
1
0
1
2
0
1
1
1
2
2
2
1
1
1
1
1
2
1
1
2
1
0
1
0
0
1
1
1
1
1
0
1
1
1
1
2
0
0
1
1
0
1
1
1
2
1
1
0
1
1
1
0
0
1
0
1
2
2
0
1
2
2
1
1
1
1
0
0
2
1
1
1
0
0
1
2
1
1
2
1
1
2
2
2
0
2
1
1
1
2
1
0
0
0
0
2
2
1
1
1
0
1
2
1
0
1
2
3
1
1
1
2
1
1
1
0
1
1
2
1
1
0
1
0
0
1
1
1
1
0
1
0
1
1
1
2
0
1
1
0
1
0
0
1
1
2
1
3
2
2
1
0
0
0
2
1
1
0
0
2
1
0
1
0
1
1
1
1
1
0
1
2
1
1
2
2
2
1
0
1
0
0
1
2
1
2
0
2
2
1
1
0
1
1
1
0
0
0
1
0
2
0
1
1
1
1
0
0
1
1
1
0
0
2
2
0
1
2
2
0
1
1
1
1
2
2
1
0
1
2
0
2
1
1
1
2
1
0
1
1
2
2
2
1
0
0
0
2
1
0
2
1
0
2
1
2
0
0
0
1
2
1
1
1
2
1
1
2
0
1
0
1
1
1
1
1
1
2
1
2
1
1
1
1
2
0
1
0
1
2
2
1
0
1
1
1
0
2
1
1
1
1
1
1
2
1
2
1
2
1
1
1
6
0
2
1
1
1
1
3
0
2
2
1
0
1
1
0
1
1
1
1
1
2
0
2
1
1
1
2
1
1
1
1
1
0
1
1
2
1
2
1
1
1
0
1
2
2
2
2
1
1
0
0
0
2
0
0
1
1
2
1
1
1
1
1
1
1
1
1
1
0
1
1
2
0
0
1
1
1
0
1
1
1
2
1
0
1
1
2
0
0
1
3
2
0
1
1
1
0
1
0
0
1
1
1
2
0
0
1
1
1
1
1
2
1
1
1
1
0
0
1
0
1
1
0
1
0
1
1
1
0
2
0
1
0
0
1
1
1
0
1
1
1
0
0
3
2
2
1
0
1
1
1
1
2
2
1
0
1
2
1
1
2
0
1
0
1
1
1
1
1
0
1
2
1
0
0
1
1
1
1
2
1
0
2
2
0
1
0
1
0
1
2
4
1
0
1
1
1
0
1
1
0
1
0
0
1
1
1
2
0
2
1
3
0
1
3
0
1
1
1
1
1
1
2
2
0
1
2
1
1
1
2
2
1
1
0
2
0
2
0
2
1
0
1
1
1
0
0
0
1
1
1
2
1
2
1
0
1
2
0
0
1
1
1
1
1
0
1
0
1
0
2
1
0
0
1
2
1
0
1
0
1
0
0
2
1
0
2
0
1
2
0
1
1
1
2
0
1
0
1
1
1
1
0
1
1
6
1
1
0
0
0
0
1
1
1
0
0
0
1
1
2
2
1
2
1
1
1
2
1
1
1
0
2
1
1
0
1
1
0
1
0
1
2
1
2
1
0
1
2
0
1
1
1
2
0
1
2
1
1
2
1
0
2
2
0
2
2
0
0
0
1
1
1
0
0
2
1
1
1
2
0
1
0
2
2
1
1
2
0
1
2
1
1
1
1
1
2
2
1
2
2
0
1
1
1
1
0
1
1
0
0
0
1
1
2
2
1
0
1
1
3
1
0
0
1
0
0
1
1
1
1
0
1
1
2
2
1
1
0
2
1
1
2
2
0
0
1
1
1
0
0
1
1
1
1
1
0
2
0
1
1
1
1
2
0
0
1
0
1
1
1
1
1
1
1
1
0
0
1
1
2
1
1
0
0
0
0
1
2
1
2
0
1
2
1
1
0
2
0
1
2
1
1
1
0
1
0
1
0
0
2
2
2
0
1
1
1
1
2
1
1
1
0
1
2
2
2
0
1
1
0
0
2
0
1
1
2
0
1
0
2
1
1
0
1
1
0
2
1
0
0
1
0
0
0
0
1
1
0
1
2
1
1
0
1
1
2
2
1
1
1
3
1
2
1
1
2
1
0
1
1
1
1
2
1
0
0
1
1
1
1
1
1
0
1
1
1
1
2
0
1
1
1
0
0
1
0
1
0
0
1
0
1
0
2
1
1
1
1
0
1
0
0
1
2
0
0
2
0
2
1
1
2
1
0
1
1
2
1
1
1
3
0
1
1
0
0
1
1
0
1
1
2
2
0
1
2
1
0
0
2
0
2
1
1
0
0
0
2
1
0
1
0
1
1
2
1
1
1
2
0
1
1
0
1
1
2
0
1
1
2
1
1
1
2
2
0
0
1
0
0
3
1
2
2
3
0
1
2
1
0
2
0
0
2
2
2
0
1
1
1
0
2
0
1
0
0
2
1
1
2
0
0
0
1
0
0
1
1
2
0
0
1
1
0
0
1
0
2
1
0
2
1
1
0
1
1
2
1
0
1
0
0
1
1
0
1
0
1
3
2
1
2
1
0
2
1
0
1
1
1
2
1
1
1
1
1
1
1
0
0
2
1
1
1
1
1
2
2
1
2
1
2
0
0
1
1
1
1
1
1
1
0
0
1
1
2
1
1
3
3
1
2
1
0
1
2
1
0
0
0
0
2
1
0
1
2
1
1
1
2
2
1
0
2
1
0
1
1
1
1
2
1
1
1
0
1
2
1
0
2
0
0
1
0
1
2
1
1
0
0
1
2
1
1
1
1
1
1
1
1
0
2
2
1
0
0
1
1
2
1
2
2
2
1
1
1
1
1
0
1
1
3
2
2
1
2
1
2
1
2
1
1
0
0
2
0
2
4
2
0
2
2
0
1
1
1
1
0
1
6
2
0
1
2
1
1
1
0
0
0
2
1
2
1
0
1
2
1
0
0
0
1
3
1
0
0
0
2
1
1
1
1
1
2
2
0
3
0
1
0
1
1
1
1
0
1
2
1
0
1
0
1
1
1
1
1
1
1
2
2
1
0
1
0
1
1
0
1
0
0
2
2
0
0
2
1
1
2
0
0
1
1
1
1
1
0
1
2
2
1
1
1
0
2
0
1
1
1
1
1
2
1
2
1
0
1
1
1
1
2
2
1
1
0
1
0
0
1
2
1
1
3
1
0
0
0
2
2
1
2
1
0
4
0
1
0
0
0
1
0
0
1
0
0
1
1
2
1
2
2
1
0
1
2
1
2
1
1
0
1
1
1
0
0
0
1
0
2
1
2
1
1
0
1
0
0
2
2
2
0
1
1
2
0
2
1
1
1
1
2
1
2
2
1
1
1
1
1
1
2
2
1
0
0
1
1
0
1
1
1
1
0
1
1
0
1
0
1
1
1
1
0
1
1
1
1
1
2
1
1
0
0
1
1
1
1
0
1
1
1
2
0
2
0
1
1
1
1
0
0
0
1
0
0
2
0
1
2
1
2
1
0
1
1
0
1
0
1
0
0
1
2
1
2
1
1
1
1
1
1
2
1
0
1
1
0
2
0
0
1
1
2
1
1
0
2
1
1
1
0
1
1
0
1
1
0
0
0
2
1
1
2
1
0
1
0
0
0
2
2
1
1
0
0
2
1
1
1
2
1
1
1
0
0
1
0
2
1
0
1
2
1
0
2
1
2
2
2
1
2
2
1
1
0
2
1
1
1
0
0
1
1
1
0
2
2
0
0
0
0
0
2
2
1
1
1
2
1
1
1
2
3
1
0
0
1
1
0
2
1
1
2
2
0
1
1
1
1
2
1
1
1
2
2
1
0
1
0
0
1
2
1
0
0
2
0
1
1
0
1
2
0
1
1
1
1
2
2
2
1
1
2
2
0
1
2
1
1
1
2
1
2
1
2
1
2
0
0
2
1
0
2
1
2
1
1
1
1
1
1
1
1
1
1
1
0
1
2
1
1
1
1
1
1
1
0
0
2
2
2
0
2
1
1
0
1
1
2
1
1
1
1
2
0
1
1
1
2
1
3
0
2
3
1
2
0
1
1
1
0
2
1
1
0
1
2
2
2
0
1
0
1
0
0
1
1
0
1
1
2
1
1
1
2
1
1
1
0
1
1
0
2
2
0
2
2
2
1
2
1
1
1
0
1
0
0
0
1
0
1
0
1
1
2
1
1
2
2
2
2
2
1
1
1
0
1
1
1
0
1
1
0
0
1
1
1
1
1
1
0
0
0
1
0
0
1
1
1
1
2
1
1
1
1
1
1
1
0
1
0
0
1
2
1
1
0
1
1
1
1
2
1
0
0
1
1
1
1
0
1
0
1
1
1
0
1
2
2
1
0
0
1
2
0
1
0
1
1
1
0
0
0
1
2
2
1
2
1
1
2
2
0
1
1
1
1
1
1
2
0
0
1
0
0
1
0
1
1
2
0
1
2
1
0
0
0
0
2
1
1
1
0
2
1
2
2
1
1
1
2
1
1
0
1
1
0
1
1
2
0
3
1
0
1
1
1
1
2
1
2
1
2
0
1
1
1
1
0
0
1
2
1
2
2
0
0
1
2
1
1
1
1
0
2
1
2
1
2
0
2
1
0
1
1
1
0
1
1
1
1
0
1
1
2
0
2
1
0
1
1
1
2
2
1
2
2
2
1
1
1
0
1
2
0
1
2
1
0
3
1
1
0
0
1
1
2
0
1
1
2
1
0
1
0
2
0
1
2
1
0
1
1
1
0
0
2
1
2
1
2
1
3
2
0
0
0
1
0
2
1
0
1
3
3
1
1
2
1
1
1
1
3
1
1
0
1
2
1
2
2
1
0
1
2
0
1
2
1
1
1
1
2
2
0
0
1
2
2
2
1
1
2
1
2
1
0
0
1
1
1
1
2
0
0
2
1
1
1
0
0
1
2
0
1
1
1
1
2
2
2
1
2
1
2
1
1
2
1
1
1
2
2
1
2
0
1
1
1
0
2
2
1
1
2
0
1
1
1
0
1
0
1
2
0
1
1
0
0
1
1
1
0
1
0
2
1
2
1
2
1
1
0
2
0
0
0
1
1
1
1
2
0
1
1
1
0
1
2
1
2
2
2
1
1
2
1
1
0
1
0
1
1
1
0
2
0
0
0
1
2
0
0
2
2
0
0
2
0
1
0
2
0
1
0
0
0
1
1
0
1
0
1
2
1
1
1
1
1
1
1
0
0
1
1
0
0
0
1
1
1
1
1
2
2
0
1
0
1
1
1
1
1
1
0
1
1
2
2
0
0
0
1
0
1
0
1
1
0
3
1
2
0
1
1
0
1
1
1
1
1
0
1
1
0
1
2
1
0
0
1
0
1
1
1
2
1
1
0
0
1
2
0
1
3
1
1
2
2
1
1
0
1
1
1
1
1
0
2
1
1
1
0
3
2
1
0
1
1
1
1
1
0
1
1
0
2
1
2
1
1
1
1
0
1
1
1
1
2
1
2
1
2
1
0
1
1
0
0
2
1
2
2
0
2
2
1
0
0
1
1
1
1
0
1
2
1
2
1
0
1
1
0
1
1
0
1
2
0
2
1
1
0
2
3
2
1
1
1
0
0
0
1
0
1
4
0
2
0
3
1
1
0
0
1
1
0
0
1
1
2
1
0
1
1
0
1
2
0
2
1
1
1
2
1
0
0
1
1
0
2
1
0
1
1
1
0
2
1
1
2
2
2
1
0
0
0
1
1
2
0
0
0
1
1
1
1
2
1
1
1
0
2
2
1
2
1
0
1
2
1
2
0
2
1
1
2
1
1
0
1
2
1
1
2
2
1
2
2
2
1
1
1
1
1
1
1
1
0
1
2
2
2
2
0
0
1
2
0
1
1
1
1
2
0
1
2
1
1
1
1
2
1
0
1
1
2
1
1
1
1
1
0
1
1
1
0
1
1
1
0
1
1
1
1
1
1
3
1
1
2
1
0
0
1
1
1
1
0
1
0
0
1
1
1
1
0
0
0
1
1
1
0
2
2
1
1
1
1
3
1
1
0
1
0
2
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
2
1
1
1
1
2
2
1
0
1
0
1
1
0
0
1
0
1
2
1
1
2
1
2
1
1
1
1
0
1
1
1
1
1
1
1
2
0
2
1
1
1
1
2
1
0
1
1
2
0
2
2
2
0
1
0
1
0
1
0
1
1
0
0
0
1
1
0
1
0
2
0
1
1
1
0
1
1
1
2
1
1
0
1
1
1
0
1
1
2
2
0
0
1
1
1
0
0
2
1
1
2
1
1
1
0
1
0
1
1
2
2
2
1
1
1
0
0
1
1
3
0
1
2
1
0
3
1
1
0
1
1
2
2
2
0
1
0
0
0
0
1
1
1
0
2
1
1
1
1
1
1
2
1
0
1
0
2
1
0
0
1
0
1
2
1
1
0
1
0
1
1
1
0
0
2
1
0
1
0
1
0
1
1
1
2
1
0
1
1
0
1
1
2
0
1
1
2
1
1
1
0
2
0
0
0
1
0
1
1
0
1
2
1
1
2
2
1
2
2
0
1
0
1
2
1
1
2
0
1
0
1
1
1
0
0
1
2
1
1
1
0
0
1
0
1
0
0
2
3
1
1
0
0
2
1
2
1
1
1
4
1
2
0
1
1
1
1
0
1
1
1
0
0
2
1
1
1
2
1
2
2
1
2
0
2
0
1
1
1
2
1
2
1
2
0
2
2
1
1
0
1
0
1
1
0
0
1
0
2
1
1
1
2
0
0
1
1
1
0
0
1
1
1
0
0
2
2
1
2
3
0
1
1
0
2
0
0
0
0
2
2
1
1
1
1
1
1
1
1
1
1
0
0
1
2
1
1
1
0
1
1
0
0
0
1
1
1
2
2
1
2
1
0
2
0
1
0
1
1
1
1
0
1
1
1
1
0
2
1
0
2
1
1
1
0
1
1
1
0
1
0
2
0
1
1
2
1
1
1
0
0
2
0
0
2
1
0
0
2
1
1
0
0
1
1
2
0
1
1
0
2
1
1
0
1
0
0
0
1
1
0
1
1
0
1
1
0
1
3
2
1
2
0
2
0
0
0
1
0
4
2
0
1
1
0
0
1
1
2
1
0
1
1
0
1
1
2
1
3
0
1
1
1
1
0
1
2
1
1
0
2
1
1
0
2
0
1
1
1
1
1
1
1
2
1
0
1
0
0
1
2
0
0
1
1
2
2
1
1
1
1
1
1
0
1
0
1
0
2
2
1
1
1
1
2
2
1
0
0
1
1
1
2
1
1
1
1
1
0
1
1
0
1
1
1
2
2
1
1
0
1
2
1
1
0
2
1
1
2
1
1
1
1
1
1
1
2
0
0
1
0
1
1
1
1
1
1
0
1
1
0
1
1
1
2
0
1
2
1
2
2
0
0
2
2
2
1
0
2
1
2
1
1
1
2
1
2
1
1
1
2
0
1
1
1
1
1
1
0
1
2
1
1
0
0
0
3
2
0
0
1
0
0
0
2
0
0
0
1
1
1
0
1
2
1
1
0
2
0
1
1
2
0
1
1
1
1
2
2
0
1
2
1
1
0
2
1
1
2
1
2
1
1
1
0
0
2
1
1
2
1
1
1
1
2
0
1
1
2
2
6
2
1
2
2
1
1
1
1
1
2
2
0
1
2
1
1
1
1
2
1
1
1
2
2
1
0
1
2
2
1
1
2
2
1
1
1
3
1
1
1
2
0
0
0
1
1
1
0
2
1
0
1
1
1
2
0
1
2
1
2
0
2
0
1
2
1
1
2
1
1
0
2
2
0
2
1
1
0
1
0
2
1
1
1
0
2
0
0
1
1
1
1
1
1
0
1
0
2
1
1
2
2
1
0
2
1
2
2
1
1
1
2
1
2
0
0
1
0
0
0
2
0
0
2
2
0
0
1
1
0
1
1
1
1
1
0
0
1
1
1
1
1
0
1
2
2
0
1
2
1
1
1
1
3
0
1
1
0
1
2
1
2
0
1
1
2
1
1
0
1
1
1
1
0
0
1
1
1
0
1
0
1
0
0
0
1
2
1
2
1
0
1
0
1
0
1
2
6
1
1
0
1
1
0
1
3
2
2
1
1
1
2
1
0
1
1
1
0
0
0
0
1
1
0
2
2
0
1
1
1
1
1
1
1
0
1
0
1
1
1
2
2
1
2
0
0
1
2
2
0
1
1
1
1
2
1
2
1
2
1
1
2
1
1
1
0
2
1
1
1
1
2
1
2
1
2
0
2
1
0
0
1
0
1
0
1
0
0
1
1
1
1
1
0
0
1
2
1
1
2
0
0
1
0
0
1
1
1
2
1
1
0
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
0
2
0
0
0
1
0
1
1
1
0
1
0
1
1
0
1
0
0
1
1
2
1
2
2
1
2
1
0
1
2
2
2
1
1
0
1
0
1
1
1
0
0
3
1
0
1
0
1
1
0
1
1
1
0
0
1
0
0
0
1
1
2
1
2
1
1
1
1
1
3
0
1
1
2
1
1
1
2
1
1
1
1
0
0
2
1
2
0
1
0
0
1
0
1
1
1
0
1
0
2
0
1
2
1
0
1
1
2
0
2
1
0
0
1
2
0
1
0
1
1
2
1
1
1
1
1
1
0
1
0
1
1
1
1
2
2
2
1
0
1
0
1
0
0
0
2
1
0
1
1
3
1
1
1
0
0
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
2
1
1
0
3
2
1
1
0
2
2
0
0
1
0
1
2
1
2
1
2
1
0
1
0
1
1
1
1
0
1
1
0
2
1
1
3
1
1
1
1
0
2
0
0
0
0
1
0
2
1
0
0
1
1
1
1
1
1
1
1
1
0
0
0
1
1
0
2
1
0
2
2
0
0
1
1
1
0
1
1
2
2
1
1
1
1
0
1
0
1
2
2
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
0
3
0
1
1
2
1
1
0
1
0
2
2
0
0
1
2
0
1
2
1
2
1
1
0
1
0
2
1
1
2
1
2
1
0
1
3
2
1
1
2
1
1
0
1
2
0
0
0
0
1
2
0
1
2
0
1
1
0
1
1
1
0
1
1
2
2
1
2
1
1
1
1
1
0
2
0
2
1
2
0
2
1
0
1
0
0
1
0
0
1
1
1
1
1
1
1
1
0
2
2
1
1
2
1
0
1
1
1
1
0
2
2
3
1
1
0
1
1
0
1
1
1
0
2
0
1
0
3
0
1
1
1
2
1
1
0
2
1
1
2
2
1
2
2
0
1
1
0
1
2
0
1
1
1
0
2
1
0
1
0
1
1
1
1
1
1
2
1
2
1
0
1
0
0
1
1
0
1
1
2
1
1
1
1
0
1
1
0
1
1
0
1
1
1
0
2
1
2
0
1
0
1
1
2
1
0
1
2
1
2
1
1
2
0
1
2
1
1
0
1
2
0
1
2
2
2
1
0
0
1
0
1
1
0
2
1
0
1
1
2
1
1
0
2
1
1
1
1
2
1
1
0
2
1
1
2
1
1
1
0
2
2
2
0
1
1
2
1
0
1
0
0
1
0
1
0
0
0
1
1
1
1
1
0
1
1
1
2
1
1
5
2
0
2
0
1
1
2
1
0
0
2
1
0
0
0
0
0
1
2
0
1
1
0
1
2
0
0
0
1
0
0
0
0
2
1
0
0
1
1
1
1
2
1
2
1
0
0
1
1
2
2
1
0
1
1
0
0
1
1
1
1
0
0
1
0
0
1
2
0
1
1
0
6
1
1
4
1
2
0
1
2
1
2
0
0
1
1
1
2
1
1
1
1
0
1
1
1
2
0
3
1
0
2
0
2
1
0
1
2
2
0
1
1
0
1
1
2
1
3
1
1
1
1
1
0
1
2
1
2
2
0
0
2
1
2
2
1
0
0
2
1
1
0
1
1
1
1
1
0
0
1
1
1
1
1
0
1
0
0
1
1
1
1
1
0
1
2
1
2
2
0
1
1
1
1
2
1
2
1
1
1
1
2
1
1
2
2
1
1
0
1
2
2
0
0
2
1
1
2
2
0
1
0
0
1
1
1
1
1
1
1
1
0
1
2
1
0
1
0
2
1
2
1
1
0
2
1
0
2
2
1
0
0
2
1
1
0
1
0
2
2
1
0
1
2
0
2
2
1
1
0
1
1
1
0
2
1
2
0
0
1
1
0
1
1
1
0
0
1
0
1
2
2
1
2
0
1
1
1
1
1
1
1
1
1
1
1
1
0
0
2
0
1
1
2
0
0
0
1
1
2
1
1
1
1
1
2
1
0
1
1
2
0
1
1
1
1
2
2
1
1
0
1
2
1
0
1
1
0
1
1
1
1
2
2
0
1
0
0
0
2
1
1
1
1
1
1
2
1
1
2
2
1
1
0
1
2
2
1
1
1
1
2
2
2
1
0
0
0
1
0
1
2
1
1
1
2
2
2
2
2
2
0
2
1
2
1
1
1
1
2
3
1
0
0
0
1
0
2
1
1
1
0
1
0
1
0
0
2
1
1
1
1
0
1
1
0
0
2
0
1
2
0
1
1
1
2
2
0
1
1
1
1
0
2
0
1
0
0
2
0
2
0
2
1
0
0
2
1
0
1
1
0
1
2
1
1
1
0
0
0
1
1
2
1
2
1
1
1
2
0
1
1
0
1
0
2
0
0
2
2
0
0
2
1
1
1
1
0
2
1
2
2
1
1
1
1
1
1
1
0
2
2
1
0
0
0
0
2
0
0
0
1
2
2
2
1
4
1
0
0
2
1
1
2
1
1
1
1
1
2
2
0
0
2
2
1
0
2
2
0
1
2
2
1
0
0
1
0
2
0
1
2
0
1
2
1
1
1
1
1
1
1
0
0
1
1
1
0
0
2
0
1
1
1
1
0
1
0
1
1
0
2
1
1
2
0
2
1
0
2
1
2
2
0
1
0
0
2
1
1
1
1
2
0
1
1
1
0
1
1
1
1
1
2
0
2
1
0
1
0
0
3
1
2
1
1
0
0
1
2
1
0
1
2
0
1
1
1
0
2
2
1
2
0
2
2
3
1
1
0
1
2
3
1
1
2
1
0
1
15
2
1
1
6
1
1
1
2
0
1
2
1
0
2
1
1
2
2
2
2
1
0
1
2
0
0
1
1
1
1
1
1
1
1
1
3
0
0
1
2
0
2
0
1
0
0
0
0
1
1
1
0
0
2
1
1
2
0
2
1
1
1
0
1
1
1
1
0
0
2
2
1
1
1
2
2
2
0
1
0
2
2
1
1
1
1
0
1
2
1
1
1
0
1
1
0
1
1
1
1
2
0
2
1
0
1
1
2
1
1
0
1
1
2
1
2
1
1
0
2
1
2
1
1
1
0
1
1
1
1
1
3
0
1
0
2
1
1
1
3
0
0
0
0
0
1
0
1
1
2
1
1
0
0
2
1
2
2
1
0
1
2
1
1
1
1
2
1
1
2
0
1
1
1
1
2
1
1
1
2
2
1
1
0
0
1
1
0
0
0
4
1
1
1
0
1
0
1
1
2
1
2
2
0
0
1
0
1
2
1
1
1
2
1
0
2
0
2
1
0
1
2
1
1
2
0
0
1
1
1
2
1
0
1
1
1
2
1
1
0
1
0
1
1
1
2
2
2
1
2
1
0
2
0
0
1
2
2
1
0
1
1
1
0
3
1
0
1
0
2
1
1
1
0
1
1
0
1
0
1
1
1
1
1
0
0
0
1
1
1
1
1
1
0
1
2
1
0
1
1
1
1
1
2
0
2
1
0
1
1
1
0
0
2
1
0
1
1
1
1
3
0
1
2
1
0
0
2
1
2
0
1
1
1
1
1
0
2
2
1
0
1
1
1
2
0
1
1
2
0
1
1
0
0
1
1
1
2
0
2
1
1
0
1
0
1
1
1
0
0
1
0
1
2
1
1
1
1
2
2
2
1
0
0
2
1
1
1
0
0
1
1
0
1
1
1
1
1
2
0
2
1
1
1
1
2
0
1
1
1
2
1
1
0
0
1
0
2
0
2
1
0
2
1
0
1
2
0
0
0
0
1
2
1
1
2
1
0
0
1
1
2
1
1
0
0
0
2
2
1
2
0
0
1
1
0
1
1
1
1
1
1
0
0
1
0
2
1
1
1
0
1
1
0
1
1
1
1
0
0
2
2
1
0
0
1
1
1
1
1
1
0
1
1
1
2
0
0
0
0
1
1
1
0
2
0
1
0
0
2
1
1
1
2
1
0
0
2
2
0
0
2
0
1
0
1
1
1
0
0
0
1
1
1
1
0
0
1
1
1
1
3
1
0
1
2
1
3
2
2
2
2
1
0
1
2
1
2
1
1
0
1
1
1
2
1
1
1
0
2
0
1
0
1
2
0
2
0
0
0
1
1
1
1
1
1
0
0
1
2
0
2
0
0
1
1
1
1
1
1
1
2
2
0
2
2
1
1
0
1
0
1
1
1
1
2
0
1
0
0
1
1
1
0
2
2
2
0
2
1
1
2
2
0
2
0
2
1
2
0
1
0
0
0
2
0
0
1
1
2
1
2
2
1
2
0
0
1
1
1
0
2
1
2
0
1
0
0
2
1
1
1
1
1
1
2
2
1
2
2
1
0
1
0
0
1
2
0
0
2
0
3
2
2
1
2
1
1
1
1
1
2
1
1
2
0
2
0
1
1
0
0
1
1
1
2
2
2
2
0
0
0
1
1
2
1
0
1
0
1
1
1
1
1
1
1
2
1
1
1
1
1
0
1
3
1
0
1
0
1
1
0
1
1
2
1
0
1
2
1
1
1
1
1
0
1
1
0
2
0
1
2
1
0
2
1
1
1
0
1
1
1
0
2
0
0
0
1
0
1
1
1
1
0
0
1
0
1
1
1
1
0
0
1
2
2
1
1
1
1
1
1
2
2
0
1
2
1
0
1
1
0
1
1
0
1
0
1
1
1
1
1
2
1
0
2
1
1
1
2
0
2
1
2
1
0
2
0
2
0
1
0
0
1
1
1
1
1
1
0
0
0
1
1
1
0
2
0
1
1
1
1
1
1
1
2
2
1
0
1
0
1
1
0
1
0
1
1
1
1
1
0
1
1
2
0
1
2
1
1
0
1
2
1
0
0
1
2
1
0
0
1
1
2
1
2
1
0
3
2
1
2
1
1
2
0
1
1
1
0
1
1
2
1
1
2
1
2
1
1
1
1
0
1
2
1
1
2
1
2
2
1
0
0
1
0
1
1
2
1
1
1
1
1
1
1
1
0
1
1
1
2
2
0
4
1
0
1
2
0
1
0
0
2
2
1
1
1
0
1
1
1
1
1
1
4
0
1
1
1
2
2
0
0
1
0
0
0
0
2
0
0
2
1
2
1
1
2
2
1
1
2
0
1
1
1
2
1
0
1
2
1
1
2
2
1
2
1
2
1
1
0
1
0
1
0
0
2
0
1
2
1
1
0
0
2
1
2
0
3
0
0
1
2
3
1
2
1
2
0
0
1
0
1
2
1
1
1
1
0
0
1
1
1
1
1
0
1
2
1
1
1
2
0
1
1
0
2
1
1
0
1
1
1
1
2
1
1
2
0
1
0
1
0
1
0
1
0
2
0
1
1
2
1
0
1
1
0
3
1
2
1
3
0
0
2
1
0
0
2
1
2
1
1
2
1
4
1
0
1
1
2
0
0
0
0
0
1
1
0
1
1
0
1
0
1
2
1
0
0
1
0
2
0
0
2
1
1
1
1
1
0
1
1
2
1
0
0
2
1
0
1
1
0
0
1
0
0
1
0
1
1
0
2
1
3
2
1
1
1
0
1
1
2
0
2
1
1
2
2
1
1
0
0
1
2
0
2
2
2
2
1
0
1
1
2
2
1
1
1
0
1
1
1
1
1
0
2
2
1
1
1
1
2
1
0
1
1
2
1
1
1
1
1
2
2
2
0
1
1
1
0
1
1
1
2
0
2
1
0
1
1
1
2
2
1
2
1
1
1
1
0
1
1
0
1
0
1
1
0
0
1
1
2
0
0
0
1
1
0
0
0
2
0
1
1
1
0
0
1
0
1
1
1
1
1
0
1
1
1
1
0
1
2
0
2
0
1
0
0
0
1
1
2
1
1
2
1
1
2
2
1
1
0
1
1
2
1
1
2
1
1
0
1
2
0
0
0
1
2
1
1
0
1
2
1
1
1
2
0
0
1
1
2
0
1
1
1
1
1
1
2
1
0
0
0
2
2
1
1
1
1
1
0
0
3
0
1
0
0
1
1
0
2
0
1
1
2
1
0
0
2
1
1
1
2
0
2
1
1
1
0
1
1
2
1
0
1
3
0
0
2
2
1
3
2
1
1
2
1
1
2
2
1
2
1
2
0
0
2
1
1
0
1
1
2
1
2
0
1
0
1
0
0
2
0
1
2
1
1
1
1
1
0
1
1
2
1
0
1
1
1
2
1
0
1
1
1
1
1
1
2
2
1
2
1
1
1
1
1
2
0
2
1
1
0
0
2
1
0
2
1
1
0
1
1
1
1
2
2
2
1
1
2
2
2
0
0
2
1
2
1
1
2
1
2
1
1
1
1
0
0
0
0
2
1
0
1
2
1
1
0
0
0
1
0
0
2
1
1
2
1
1
2
2
1
2
1
1
2
2
0
0
2
1
2
1
1
2
1
1
1
2
0
1
1
1
1
0
0
1
1
1
0
1
0
2
1
2
1
2
0
1
1
3
1
1
0
0
0
1
0
2
0
1
0
0
0
1
1
1
0
0
0
1
1
1
1
0
1
0
0
0
1
0
1
0
1
0
1
1
3
2
1
2
0
0
1
1
2
2
0
0
0
2
2
0
1
1
1
1
1
1
1
2
0
2
1
1
0
1
3
0
1
1
1
1
1
0
0
1
0
1
1
1
2
0
2
1
1
1
1
1
1
0
0
2
1
1
1
2
2
0
2
0
2
2
2
1
1
0
1
1
1
2
0
1
0
1
0
1
1
1
1
1
1
2
2
0
0
1
1
2
0
1
1
2
1
2
2
1
1
1
1
1
1
1
0
1
1
0
1
0
1
0
0
0
0
1
1
0
1
0
1
1
0
1
1
1
1
1
2
1
1
1
0
1
1
0
1
1
2
2
1
0
1
0
0
0
2
1
1
1
1
1
1
1
1
1
1
2
1
1
0
2
1
0
0
0
1
0
0
1
1
0
1
2
1
0
0
1
2
1
1
1
0
0
0
0
1
1
2
1
1
2
0
1
1
0
0
0
0
2
2
1
0
1
1
1
0
2
0
0
1
1
1
1
1
0
1
2
1
0
1
1
1
1
1
0
1
1
2
2
2
2
0
1
1
1
2
0
2
0
1
1
1
1
1
2
0
1
2
1
2
1
0
0
1
1
1
0
1
2
1
1
1
1
1
1
1
2
1
0
2
2
0
2
0
1
1
0
2
2
1
1
1
2
1
0
1
1
1
1
1
0
2
1
1
1
2
0
1
2
2
2
2
0
0
1
1
1
1
0
1
0
0
0
1
2
2
0
0
0
1
1
0
0
2
2
1
1
2
0
1
3
1
0
1
2
1
1
1
1
1
1
0
1
3
1
1
0
1
1
1
0
1
1
2
1
1
0
1
1
0
0
0
2
0
1
2
0
2
1
1
2
1
1
0
2
1
2
1
2
1
0
1
2
1
1
1
1
2
1
1
0
0
2
0
1
1
0
1
1
1
1
1
1
1
0
2
1
1
2
2
1
2
2
1
2
0
2
1
1
2
1
1
1
1
1
0
1
1
1
2
1
0
1
1
2
1
0
0
2
2
0
1
0
0
2
1
1
1
2
0
0
2
1
0
0
1
0
1
1
1
0
0
1
1
1
1
2
0
1
1
0
1
1
1
1
1
1
0
0
1
2
1
1
0
1
0
1
2
1
0
2
1
1
0
2
0
1
1
2
1
2
1
1
0
1
1
1
2
1
1
2
1
2
1
1
2
1
1
1
0
1
2
1
2
1
0
1
1
0
2
1
0
1
1
2
0
2
1
2
1
1
2
2
2
0
2
2
1
0
2
1
2
1
1
0
1
2
0
1
1
2
2
2
1
1
1
1
0
0
2
0
1
1
1
1
0
1
1
3
1
2
0
2
0
1
0
1
1
1
0
0
1
2
1
0
1
1
2
1
1
2
0
2
1
0
1
0
2
2
1
2
1
1
1
0
0
1
0
1
1
0
1
2
1
1
1
0
0
1
2
2
0
1
1
0
0
0
1
1
1
1
1
2
3
2
1
0
0
0
0
1
2
0
1
2
1
0
2
1
1
2
1
1
0
1
0
1
1
2
2
2
1
1
1
2
0
0
0
1
2
0
1
0
2
0
1
1
1
2
1
0
0
0
2
1
1
1
1
1
1
0
1
0
2
0
0
2
1
0
0
1
1
2
1
1
1
1
1
0
1
2
1
2
1
3
1
1
2
1
1
1
2
1
1
1
2
0
1
2
1
0
0
2
1
1
0
1
2
1
1
2
2
1
0
1
2
0
2
1
1
0
1
2
0
1
2
3
0
0
0
2
1
0
0
2
0
1
1
2
1
2
1
1
1
1
0
0
1
1
1
0
2
1
0
1
0
3
3
0
1
2
1
1
2
1
2
1
1
2
2
0
0
0
1
1
1
0
0
2
2
1
2
0
0
1
1
1
1
2
1
1
2
0
1
0
1
1
1
1
2
2
1
1
0
2
1
1
1
0
1
1
0
2
1
1
1
1
1
2
3
2
1
1
0
1
2
0
2
0
1
2
2
2
1
0
1
0
2
0
2
1
0
1
1
2
2
1
1
1
2
1
1
0
1
0
1
0
1
2
0
1
1
1
1
2
0
0
0
1
1
0
1
1
0
0
0
1
1
3
0
1
1
1
0
1
1
2
1
2
2
0
2
0
2
2
1
1
2
0
2
1
0
2
1
1
2
0
1
0
1
0
0
0
1
1
0
1
2
1
1
2
1
0
2
1
1
1
0
1
2
1
0
0
0
1
1
1
0
1
0
1
1
1
0
0
0
0
0
2
2
0
2
1
0
0
1
1
0
1
1
1
1
1
1
0
0
1
1
0
0
0
1
1
1
3
1
1
0
2
0
1
2
2
1
0
1
2
1
1
1
2
1
1
2
2
0
1
1
2
1
1
2
0
2
0
0
0
1
1
2
0
1
2
0
5
1
0
2
1
0
1
8
0
1
2
0
2
1
1
1
1
2
1
0
1
2
1
0
0
0
1
0
0
0
0
1
0
2
0
2
1
0
1
1
1
2
1
1
1
1
1
1
2
1
1
0
0
0
0
2
1
1
1
2
1
1
1
2
2
0
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
1
2
1
1
0
1
1
1
1
1
1
0
2
2
1
2
1
1
1
1
2
2
1
2
3
1
2
0
1
2
1
0
2
1
1
2
1
2
2
2
1
1
1
0
0
1
0
1
0
1
1
1
1
1
0
1
1
1
0
1
0
1
0
2
1
1
1
1
0
0
1
2
0
2
1
0
1
1
0
1
0
1
2
2
1
1
1
2
1
0
1
1
0
1
2
2
2
1
2
0
0
0
1
2
1
1
0
1
1
1
1
1
2
0
2
0
0
0
1
1
2
1
1
1
1
1
1
0
0
1
0
2
1
1
2
1
0
1
1
1
1
0
1
1
0
2
1
1
0
2
0
1
2
2
1
2
2
1
0
1
0
0
1
1
1
2
0
1
1
0
1
1
1
1
2
1
0
1
1
1
2
1
1
1
1
2
1
0
0
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
0
4
1
0
2
1
2
1
0
2
1
2
0
1
2
2
1
1
1
2
1
1
1
1
0
1
1
1
2
1
0
0
1
0
1
0
1
2
1
0
2
2
1
1
0
1
3
1
0
1
2
1
2
1
1
0
0
1
1
1
0
0
1
1
0
1
2
1
2
2
1
1
1
1
0
1
0
1
2
1
1
2
1
0
2
0
1
1
1
1
1
1
1
0
1
1
1
1
1
1
0
2
2
2
1
1
1
1
2
0
1
0
1
1
0
1
4
2
2
6
2
1
1
1
0
0
1
0
2
0
1
0
1
1
1
1
1
1
1
1
1
1
0
1
1
2
0
1
1
2
1
0
1
2
1
0
1
1
1
2
1
0
1
2
1
2
0
0
0
1
2
1
1
2
1
1
2
1
1
3
4
0
2
1
0
1
1
2
0
0
1
1
1
0
1
1
1
2
2
1
0
1
1
1
1
1
1
1
1
1
1
0
1
2
1
0
0
1
2
0
1
1
1
0
1
1
1
1
0
1
1
1
0
1
2
1
1
0
1
1
1
1
1
0
1
1
1
1
1
2
0
1
1
0
0
2
1
1
1
1
0
1
2
1
1
2
2
2
1
0
0
1
0
1
1
2
1
1
0
1
1
1
1
0
1
3
0
0
0
2
2
1
1
0
2
2
1
1
2
1
2
2
0
1
1
2
1
0
0
2
1
0
0
1
2
2
0
1
1
2
2
2
2
1
2
2
0
2
0
1
2
0
1
0
0
0
0
1
0
1
2
1
0
1
1
2
1
1
0
0
0
1
1
0
1
2
1
0
1
2
2
0
2
0
2
1
1
1
1
1
1
1
0
2
0
0
2
1
2
1
0
1
0
1
1
1
1
2
1
0
1
0
1
2
2
1
1
0
2
1
2
1
2
3
0
1
1
0
1
0
0
0
1
2
2
1
1
1
1
2
2
2
1
0
1
2
1
0
2
1
2
0
0
1
1
2
0
1
1
0
0
1
2
2
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
2
2
1
0
2
1
1
1
0
1
0
1
1
1
1
2
1
1
1
0
0
1
1
1
1
0
0
1
0
1
0
1
1
0
1
0
1
1
2
0
1
1
0
2
1
0
1
1
1
1
1
1
3
1
1
2
2
0
1
1
2
1
1
1
1
0
0
1
1
2
0
1
1
2
0
2
0
0
1
1
2
0
0
0
2
1
1
1
1
1
1
0
1
0
2
0
1
1
0
1
1
1
1
1
1
0
1
0
1
1
0
1
2
0
1
0
1
1
2
0
1
1
1
1
0
0
1
1
0
1
1
1
1
2
1
0
2
1
1
3
1
1
1
1
1
0
2
1
0
2
2
2
1
1
1
1
0
0
1
1
1
1
3
2
0
1
1
2
0
0
2
1
0
1
1
2
1
2
1
1
1
1
1
1
2
0
1
1
2
1
1
0
0
1
0
2
1
1
2
1
1
1
1
0
0
2
1
2
2
1
1
2
2
2
1
0
1
2
0
1
1
1
1
1
0
3
2
1
0
0
1
2
1
1
1
1
2
1
0
0
1
1
1
0
0
1
1
2
1
2
2
1
0
1
1
1
2
1
2
0
1
0
1
2
0
1
1
1
0
1
1
1
1
0
1
1
2
1
2
2
0
1
1
1
1
0
1
2
1
1
2
1
1
1
1
1
0
2
1
1
1
0
1
2
1
1
1
1
1
1
0
0
1
0
1
2
1
1
1
0
2
0
2
2
1
1
1
2
2
0
2
0
2
1
0
1
1
1
1
0
0
2
1
1
2
0
1
1
1
1
1
1
1
1
0
1
1
2
2
1
1
1
1
0
0
1
2
0
0
1
1
0
1
1
1
0
1
1
1
0
1
0
1
1
1
2
2
1
1
2
1
1
1
1
1
3
0
2
1
0
1
1
1
1
1
1
0
1
1
1
1
0
3
1
1
2
2
1
2
2
1
0
0
1
0
3
1
0
0
2
1
1
0
2
1
1
2
1
0
0
2
1
0
1
0
1
1
0
0
1
1
1
0
0
0
1
2
2
1
0
1
2
1
1
1
0
1
1
0
0
2
1
1
0
1
1
0
0
1
2
0
0
0
2
0
2
0
0
0
0
1
0
1
1
1
2
0
0
2
0
1
1
2
1
1
1
1
1
0
0
1
1
3
2
1
1
0
1
0
2
1
1
1
2
1
0
0
1
3
0
0
2
2
0
1
1
2
1
0
0
0
1
1
0
1
2
0
1
1
1
1
1
1
2
1
1
1
2
2
1
1
2
2
0
1
1
1
0
0
0
1
2
2
0
1
1
0
0
0
1
2
1
1
1
1
1
2
1
2
0
0
2
2
1
1
2
1
0
1
0
1
2
1
1
1
1
0
1
0
1
1
0
2
2
1
1
2
1
2
1
1
2
3
1
1
1
0
1
1
0
1
2
0
1
1
1
0
2
1
0
1
1
1
2
1
1
0
1
0
1
0
2
1
1
0
1
1
1
1
1
1
1
1
1
2
0
1
1
1
2
0
2
1
1
1
0
1
1
2
0
1
1
1
0
2
1
1
2
0
1
1
0
1
1
1
1
2
0
2
1
1
1
1
3
1
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
0
1
2
1
1
1
0
1
1
2
0
2
1
1
1
0
0
1
2
1
3
1
0
0
0
1
3
0
0
3
2
1
1
2
1
1
2
2
2
1
0
1
2
0
0
0
1
4
4
0
0
1
2
1
0
1
1
0
2
0
2
1
1
1
2
1
1
2
1
0
2
1
1
1
1
1
2
2
1
1
0
1
2
1
1
1
0
0
0
1
0
0
1
1
0
0
2
1
1
2
3
1
1
1
1
0
1
2
0
2
1
1
1
1
1
0
2
1
2
1
2
1
2
1
1
2
1
1
1
1
0
2
2
2
1
1
1
1
1
1
1
0
0
1
0
0
0
1
1
0
1
1
0
1
0
1
2
1
1
1
0
0
0
2
1
0
2
1
1
1
0
2
2
2
1
1
0
1
1
3
1
1
1
0
1
0
1
0
1
1
1
1
1
2
1
2
1
1
1
0
1
1
0
1
1
2
1
2
3
2
2
1
2
1
1
1
2
2
0
0
0
1
1
0
1
2
1
1
1
2
1
1
1
1
2
6
1
0
1
1
1
0
0
1
0
2
1
1
3
1
1
1
0
0
2
1
2
0
1
1
2
0
0
1
2
1
2
1
1
1
1
1
0
2
1
2
1
1
1
0
1
1
1
1
1
1
1
1
1
2
2
1
0
1
1
0
2
2
0
2
1
1
2
0
1
0
1
1
2
2
0
1
2
1
1
2
1
2
1
1
2
1
0
1
1
1
3
1
1
1
0
2
0
1
1
0
3
1
0
2
1
1
2
1
2
2
1
0
1
0
1
2
1
1
2
1
1
1
0
1
2
1
2
2
0
0
1
1
1
1
0
0
1
1
0
0
2
1
1
0
2
1
1
2
0
2
0
0
1
2
0
1
1
1
1
1
0
0
1
0
0
1
1
1
1
2
1
2
1
0
0
1
2
1
1
1
2
1
0
1
1
2
1
1
0
1
1
1
2
1
0
4
0
2
1
1
1
2
1
2
1
1
0
0
2
1
0
1
1
0
1
2
1
1
2
0
1
2
1
1
2
2
0
1
1
1
2
1
1
1
1
0
1
1
1
0
1
2
2
0
1
0
2
1
1
2
1
1
2
1
1
2
0
2
1
1
2
2
1
0
0
1
1
0
0
0
1
1
2
1
0
1
0
1
2
1
1
0
2
2
1
1
0
1
1
2
1
1
2
1
1
1
0
0
1
1
1
1
0
0
1
1
1
2
2
1
2
1
2
1
1
1
1
0
0
0
1
2
2
0
1
1
1
1
4
0
1
0
1
1
1
1
3
2
2
1
0
2
2
0
1
1
1
0
5
2
0
2
2
1
2
1
0
2
1
0
0
2
2
2
1
1
1
0
1
2
0
1
2
0
2
1
1
2
2
1
0
1
0
1
1
0
1
1
2
1
1
1
1
2
1
3
1
1
1
1
1
0
1
2
0
1
0
1
1
2
1
1
1
1
0
1
1
1
1
1
1
2
2
0
1
1
2
1
2
0
0
2
2
1
1
2
0
1
1
1
1
0
0
2
0
0
2
2
2
0
1
0
0
2
1
1
0
2
1
0
1
1
1
0
0
0
1
1
1
2
2
0
1
1
1
1
2
0
1
2
1
0
0
0
2
1
0
3
1
2
0
1
1
2
2
1
1
1
2
0
0
0
1
1
1
0
2
2
1
2
0
0
1
2
1
3
1
0
0
2
1
1
0
1
2
2
2
1
0
1
1
0
2
2
1
1
2
0
2
1
0
1
1
1
1
2
2
2
1
0
0
1
0
1
1
1
0
1
0
1
2
1
0
2
0
2
1
1
1
1
0
2
2
2
0
1
0
1
1
1
3
0
1
1
1
0
0
1
0
1
2
1
1
2
1
2
1
1
1
0
2
1
1
1
0
1
0
0
0
1
0
1
1
2
1
2
2
1
1
1
1
1
1
2
2
1
2
1
1
2
0
2
1
2
1
1
2
1
0
0
0
2
1
2
0
1
1
0
0
0
2
0
0
1
1
1
2
1
1
1
1
1
2
1
1
1
1
0
2
1
0
2
1
0
0
2
0
1
0
1
1
1
0
0
1
0
1
2
2
1
1
2
1
0
1
0
2
1
2
2
1
1
1
0
0
1
1
1
0
1
2
2
1
1
1
2
1
1
1
1
1
1
1
0
0
0
2
1
1
1
0
2
0
1
1
1
0
1
1
1
2
0
1
1
3
2
1
0
1
0
2
2
1
2
1
1
2
1
1
1
0
1
1
2
1
0
1
0
1
1
2
2
0
0
2
1
1
1
1
0
1
0
1
0
1
1
1
1
0
1
2
1
2
1
1
0
0
2
1
0
2
1
1
2
1
0
0
1
0
1
0
0
2
2
1
0
0
1
1
1
1
1
2
0
2
2
1
2
2
2
0
1
1
0
1
1
2
1
0
1
1
1
1
1
1
1
2
2
1
1
0
1
1
2
0
1
1
1
2
3
2
2
0
0
1
2
0
1
1
0
1
2
3
1
1
3
1
1
1
0
1
1
1
1
2
2
2
2
1
1
2
1
1
2
2
2
1
0
1
1
1
1
1
0
1
1
1
0
1
0
1
2
1
1
2
1
1
0
0
2
2
2
1
2
0
2
1
2
1
1
1
1
2
1
2
0
3
0
1
0
1
1
1
1
0
2
1
1
0
2
0
1
2
1
2
1
0
2
1
1
2
1
1
1
1
1
1
2
1
1
2
0
1
0
1
2
3
1
2
1
1
1
0
2
1
1
0
1
1
1
2
1
2
2
0
1
2
1
1
1
2
0
0
2
0
1
2
1
2
2
1
0
4
1
1
0
2
0
1
0
1
1
2
0
0
1
1
0
0
1
1
1
0
1
2
2
1
2
0
1
0
1
1
0
0
1
1
0
0
1
1
2
0
1
0
1
1
2
1
3
2
2
1
1
0
1
1
1
0
1
1
0
1
1
0
2
2
1
2
1
1
2
1
1
1
2
1
1
1
1
0
1
1
2
2
1
1
2
2
1
2
0
2
1
1
0
2
1
0
2
1
2
1
0
0
1
1
0
2
0
2
1
1
1
0
1
1
1
1
0
1
0
2
0
2
2
2
0
1
1
2
1
0
1
0
1
0
2
1
0
2
1
2
1
1
2
1
1
2
0
0
0
1
0
1
1
0
2
0
1
1
1
2
1
1
1
0
1
3
2
1
1
1
1
1
2
0
1
1
0
0
2
1
0
1
2
0
1
1
2
2
2
1
2
1
1
0
1
1
1
0
1
1
2
2
1
0
0
1
2
0
1
1
0
1
1
1
1
0
3
1
1
1
1
1
1
0
1
1
1
1
0
0
1
1
2
0
1
0
0
1
0
0
0
1
2
1
1
1
2
2
2
1
2
1
0
1
0
1
0
1
1
1
1
2
2
0
2
2
3
0
2
0
1
1
2
1
2
0
2
2
0
0
0
2
1
1
2
2
0
1
0
0
1
1
0
0
0
0
1
0
1
2
1
1
1
1
3
0
1
0
1
1
2
1
1
0
1
1
2
0
0
1
1
3
1
0
0
1
1
1
0
1
2
1
1
1
2
2
1
1
1
2
0
2
1
0
1
1
1
1
1
1
2
1
1
1
4
1
1
0
1
0
1
1
2
2
1
1
0
0
1
2
1
0
2
1
1
0
1
0
0
0
0
0
2
0
1
0
1
0
1
1
2
2
2
0
1
1
0
1
1
2
0
1
0
1
1
1
2
2
1
0
2
1
1
0
1
0
1
1
2
1
0
1
0
1
1
0
2
2
1
0
1
1
1
1
1
1
2
2
2
0
2
1
2
1
0
2
2
1
2
1
0
0
1
0
0
2
2
1
1
1
0
1
1
0
1
1
1
0
1
2
1
0
2
0
0
2
1
0
3
0
0
1
1
0
1
1
1
1
3
2
1
1
2
1
2
0
1
1
1
1
1
0
1
2
1
1
1
0
1
1
1
2
1
1
1
0
0
1
2
1
1
1
1
1
1
1
1
0
1
2
0
1
1
1
1
0
1
2
0
2
1
0
1
1
1
1
1
1
0
0
1
2
0
0
1
2
1
0
1
2
0
0
1
1
1
0
2
1
1
2
2
1
1
1
1
0
0
1
0
2
2
1
0
0
2
0
2
1
2
0
1
2
1
1
2
2
1
1
1
1
1
0
1
2
1
2
1
2
2
1
1
1
1
1
0
0
2
0
0
1
2
1
1
1
1
1
0
2
1
1
2
1
1
0
1
0
1
1
2
2
1
1
2
0
1
0
2
0
1
1
1
0
1
0
2
2
1
1
1
0
1
0
1
0
0
0
2
2
0
1
0
1
1
2
1
2
1
1
2
1
1
1
0
1
2
1
1
1
1
1
1
1
1
1
2
4
2
2
1
2
1
2
1
1
2
1
2
2
2
1
1
0
2
1
2
0
1
2
2
0
0
1
1
0
2
1
0
0
1
0
1
2
0
2
1
1
1
1
2
1
2
1
2
0
0
1
0
2
1
1
1
0
1
1
0
0
1
0
0
0
1
3
1
2
1
1
1
1
1
1
0
2
0
0
1
2
2
1
0
1
2
1
1
1
1
2
0
1
2
1
1
1
1
2
1
1
1
2
0
2
0
2
2
1
1
2
1
0
1
2
1
1
1
0
1
0
1
1
0
0
0
2
1
0
2
2
1
1
0
2
1
1
0
0
1
1
1
0
1
2
0
2
1
0
1
2
0
3
2
1
1
0
0
1
1
0
1
1
1
0
1
2
2
0
0
2
1
1
0
1
1
1
2
1
0
1
1
1
0
0
1
0
1
1
1
1
0
0
1
2
1
1
2
1
2
2
1
0
1
2
1
0
2
1
1
3
1
2
2
0
1
0
0
2
1
2
0
2
0
2
2
1
0
2
0
0
0
1
1
1
2
1
1
2
1
1
2
1
0
0
1
2
2
1
1
1
0
1
0
2
0
2
1
1
1
1
2
0
2
1
1
1
2
1
1
1
1
2
1
1
1
0
1
0
0
0
0
1
2
0
3
2
0
1
1
2
1
0
2
1
1
1
1
1
2
0
1
0
1
2
2
0
2
2
0
0
2
0
3
1
0
1
1
1
1
1
1
0
1
1
1
2
1
1
0
1
0
1
1
0
1
1
1
0
1
0
1
1
1
0
0
1
0
2
2
0
1
1
2
2
1
1
1
2
1
0
1
1
0
0
1
1
2
0
2
0
0
1
1
0
1
1
1
1
1
1
1
1
0
1
1
0
2
1
1
0
1
1
2
1
2
0
2
1
1
0
0
0
1
3
0
0
1
4
0
0
1
2
0
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
0
1
0
1
1
1
2
2
1
1
2
2
2
2
1
2
1
2
1
0
1
0
1
1
1
1
0
0
1
2
0
0
0
1
2
1
0
2
1
0
1
0
1
1
2
0
1
0
1
1
1
2
2
1
0
2
1
4
1
1
2
1
1
1
2
0
1
1
1
2
1
2
1
1
1
1
1
1
7
0
0
1
1
0
2
1
2
2
2
2
3
1
0
1
1
0
1
1
2
1
2
1
1
2
1
0
0
2
2
2
0
2
1
1
0
2
1
1
1
1
2
0
1
0
0
0
2
1
1
0
0
0
2
3
0
1
1
1
0
2
1
1
0
3
2
2
1
0
1
1
0
1
2
0
0
1
2
2
2
2
1
0
1
2
0
1
2
2
1
1
0
1
1
3
2
2
1
2
1
1
1
1
1
2
2
2
2
0
1
0
0
0
0
1
1
1
1
1
1
2
2
1
2
1
1
1
2
1
2
0
1
0
1
1
0
2
0
1
0
1
1
2
1
0
1
1
1
2
1
2
1
1
1
1
1
0
0
1
1
2
2
0
1
1
2
0
1
1
1
1
1
1
1
0
1
1
1
1
0
1
1
1
0
2
1
1
0
2
1
1
0
1
1
1
0
2
0
1
2
1
1
1
0
1
0
0
1
1
2
0
1
0
2
1
1
0
1
1
1
1
0
1
1
1
2
1
2
0
2
1
2
2
0
0
1
0
0
0
2
1
2
1
1
2
0
1
1
0
1
2
2
1
1
1
1
1
1
2
1
0
0
1
2
2
0
0
0
1
1
1
1
0
1
1
2
1
0
1
2
0
1
1
1
1
0
1
0
1
1
1
2
1
2
0
1
1
0
1
2
2
2
1
2
2
0
0
2
0
1
0
1
0
2
1
0
0
0
2
1
0
2
1
0
1
0
0
1
1
1
2
1
1
0
0
1
2
1
1
1
1
1
0
1
1
1
0
1
1
0
1
2
1
1
2
1
0
2
1
2
2
1
1
1
1
1
1
1
1
0
0
2
1
2
2
0
1
0
1
1
0
0
1
2
1
2
2
1
1
1
1
2
1
1
1
1
1
2
0
3
0
2
1
1
2
1
2
0
0
0
1
1
2
1
0
1
1
0
1
2
0
0
1
2
1
1
1
2
1
0
1
1
1
2
1
2
0
2
1
1
2
0
1
1
1
0
1
0
2
1
1
1
1
0
1
2
2
1
0
0
0
0
1
0
1
1
1
2
1
2
0
0
1
0
1
1
0
1
0
1
2
2
1
1
0
1
1
1
2
2
1
1
1
1
0
1
2
1
1
1
0
0
1
1
2
0
0
2
2
1
1
1
0
0
0
1
1
2
1
2
2
1
1
1
1
2
0
1
1
1
1
0
1
1
1
0
1
1
2
0
2
0
1
2
1
0
1
1
2
2
2
1
2
0
1
1
1
1
1
1
0
2
2
1
1
1
1
1
1
0
1
0
1
1
1
1
0
0
0
1
0
1
1
1
0
1
1
1
2
2
1
1
2
2
1
0
1
1
1
0
3
1
2
1
2
1
1
1
0
1
1
2
1
0
1
0
0
2
0
1
1
1
1
1
2
2
2
2
1
0
1
1
1
1
0
2
0
1
0
0
1
2
1
1
2
0
1
2
1
1
1
1
2
0
0
2
3
0
2
1
1
1
2
1
0
0
2
1
0
1
2
2
2
1
2
2
0
0
2
2
1
1
1
2
1
0
2
1
1
2
0
1
0
1
1
1
2
0
1
1
1
1
0
1
1
2
1
2
0
1
2
2
1
0
0
3
2
0
2
0
1
1
0
0
2
1
0
1
2
1
2
2
0
1
1
0
1
1
1
0
0
3
2
0
1
2
2
1
0
1
2
0
0
1
2
1
1
1
0
2
1
0
2
2
1
0
2
2
2
1
0
1
2
2
1
2
1
1
0
1
1
0
2
0
2
0
2
1
2
1
1
1
1
2
0
0
0
1
2
1
2
1
2
1
2
1
1
0
1
0
2
0
0
2
0
0
1
0
1
2
2
1
2
1
2
1
2
0
1
0
1
2
0
1
1
0
2
0
0
2
1
2
1
1
1
1
0
0
2
2
1
1
0
2
0
1
1
1
0
2
1
1
1
1
0
2
0
1
0
1
1
2
2
1
1
1
1
1
2
1
0
2
1
2
0
1
2
1
1
1
0
1
2
1
1
2
1
1
1
1
0
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
0
2
1
1
1
1
0
1
1
2
0
0
0
1
0
1
1
1
1
1
1
1
1
1
1
0
1
2
2
1
1
1
0
0
0
1
1
2
1
1
1
1
0
1
1
1
1
2
0
2
1
2
2
0
1
1
2
1
0
0
1
1
1
1
1
1
2
0
3
0
0
1
1
0
0
2
0
1
0
1
2
2
1
1
1
0
1
2
1
1
1
1
2
1
1
0
0
1
1
1
2
2
0
0
1
0
1
2
1
0
1
1
0
2
0
0
1
2
1
2
0
1
1
3
2
0
1
1
1
0
1
0
0
1
0
1
0
1
1
1
0
0
0
2
0
0
0
1
1
0
0
0
1
2
3
2
2
0
0
1
0
0
1
0
1
2
1
0
1
1
1
0
0
0
0
1
1
2
1
1
0
1
0
1
1
0
1
3
1
2
1
0
0
2
1
1
2
0
1
1
1
1
1
1
1
2
1
1
2
1
2
2
2
1
0
1
1
1
1
1
1
0
2
2
2
0
1
1
1
0
1
2
0
1
1
1
0
0
0
0
1
0
1
1
0
0
1
1
2
1
1
1
2
1
0
1
1
1
1
0
1
2
0
2
0
1
1
2
1
1
1
1
1
0
0
0
1
0
2
1
0
2
0
2
1
0
1
1
0
0
1
1
0
4
0
1
1
3
1
2
0
0
2
0
1
1
1
3
1
2
1
1
1
2
2
1
1
0
1
2
2
1
1
1
2
2
1
1
1
1
2
1
0
2
0
0
1
1
0
0
2
0
1
1
2
2
1
2
0
0
0
1
1
0
1
0
0
2
1
1
1
1
1
0
0
2
1
1
1
0
0
1
1
2
0
0
3
2
1
1
1
0
1
2
1
1
1
1
0
1
1
1
2
0
3
1
2
1
1
0
1
1
0
2
2
2
1
0
1
2
1
1
2
1
1
1
1
0
0
0
0
1
0
2
1
1
2
1
0
1
0
1
1
1
0
2
1
1
2
1
2
0
1
0
0
0
0
1
1
0
2
2
2
1
0
1
1
1
0
1
1
2
0
1
2
1
1
1
0
2
1
1
1
1
1
0
1
1
1
2
1
1
0
2
1
0
1
1
1
1
1
1
0
1
2
0
1
2
0
2
2
1
1
2
1
2
1
0
2
0
1
0
2
1
1
1
2
1
1
2
2
1
2
0
0
1
1
1
1
1
0
1
2
0
1
1
0
0
0
0
1
0
2
1
1
1
2
1
0
1
2
0
1
2
2
0
1
3
1
0
1
1
0
0
0
1
1
1
0
1
1
2
2
1
1
0
1
2
1
0
1
1
1
2
1
1
1
0
0
1
1
1
2
0
0
1
0
2
0
1
0
2
1
2
2
0
0
1
1
1
0
0
2
0
1
0
1
1
2
2
1
0
1
1
1
0
0
1
3
1
1
0
1
0
0
2
1
0
1
0
1
0
1
1
0
1
0
2
1
1
0
1
0
2
0
1
0
0
1
1
0
1
1
1
0
0
2
1
2
2
1
0
1
0
1
1
2
0
1
1
1
0
1
0
1
2
0
1
1
1
1
2
2
1
3
1
0
0
0
0
2
1
1
0
0
1
1
2
1
0
2
0
0
1
1
1
1
1
1
2
1
1
0
1
0
2
1
1
2
1
1
2
2
1
0
1
2
1
1
0
1
3
0
0
2
2
2
1
2
2
0
0
1
0
1
1
1
1
1
1
1
1
2
1
0
0
0
1
1
1
0
0
1
1
1
1
0
0
1
0
2
1
0
1
2
1
1
2
2
1
1
1
2
2
0
0
1
2
1
1
0
1
1
2
0
2
1
0
1
1
1
1
1
0
0
1
2
1
0
2
1
2
1
1
2
0
2
1
1
2
0
1
0
1
1
0
1
0
2
0
1
2
2
1
1
1
0
2
0
2
0
0
1
1
2
2
0
0
1
3
1
1
1
1
1
0
1
1
1
1
1
2
1
1
1
1
1
0
0
1
1
1
1
1
1
0
2
2
1
1
1
2
1
1
1
1
1
1
0
1
2
1
0
0
1
1
0
0
2
1
0
1
1
1
1
2
0
2
0
1
0
1
3
1
0
1
1
1
1
1
0
0
0
1
2
2
1
1
0
1
1
2
1
2
2
1
0
0
1
1
0
0
2
1
0
2
1
0
2
2
2
1
0
1
0
1
0
0
1
2
2
1
0
1
1
0
1
0
0
0
1
1
1
1
0
1
2
1
0
0
2
1
2
1
1
1
0
2
0
1
0
2
1
1
1
0
1
2
0
0
0
1
0
2
1
1
2
0
2
1
1
1
2
2
0
0
0
1
0
1
1
1
1
1
3
5
0
0
1
0
2
0
1
1
1
1
2
2
1
1
1
0
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
0
1
1
1
0
1
2
0
1
2
1
0
2
0
0
1
2
2
0
1
1
2
1
1
2
1
0
1
1
0
3
0
1
0
0
0
1
1
2
1
1
0
1
0
0
1
2
1
1
0
3
0
0
1
2
2
1
1
2
0
1
2
1
1
1
2
1
0
0
0
1
1
0
0
1
0
1
1
1
1
1
2
2
1
0
2
1
1
2
1
1
1
0
1
1
0
7
0
1
0
1
1
0
1
1
1
1
0
1
1
2
2
2
1
0
0
1
1
1
1
0
1
1
1
1
0
1
0
0
0
1
0
1
1
1
1
0
1
3
0
1
1
1
1
1
0
1
1
0
0
2
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
0
2
1
0
2
1
2
2
0
1
2
1
1
1
1
0
1
1
1
1
0
1
0
1
1
1
1
1
0
1
0
1
1
2
2
0
2
1
0
1
0
1
0
2
1
2
2
1
1
1
2
2
1
0
2
0
0
0
2
0
1
1
1
0
1
2
1
1
1
1
3
1
0
2
1
0
1
0
1
2
1
2
0
0
1
0
1
2
0
1
1
1
0
2
1
1
1
1
2
1
2
0
1
1
1
1
1
1
2
1
1
2
2
0
1
0
2
2
1
1
0
2
1
1
2
2
0
1
1
0
1
1
2
2
0
1
2
0
1
0
0
0
1
2
0
1
0
1
1
0
1
1
0
1
1
1
1
1
1
1
1
1
2
3
0
2
1
2
1
1
1
0
0
0
1
1
1
1
1
0
1
1
1
2
0
1
1
1
0
1
1
0
2
1
2
1
2
0
0
0
1
2
2
2
0
1
1
2
2
2
3
2
0
1
1
1
3
0
1
1
2
1
0
2
1
1
0
1
0
0
2
1
1
0
2
1
2
1
2
1
2
0
1
1
1
2
2
1
0
0
2
2
0
0
1
1
1
1
1
0
2
1
2
1
1
1
1
1
0
1
1
1
1
3
2
1
2
0
1
1
2
1
2
1
0
1
1
2
1
1
1
1
1
1
0
0
2
1
1
1
1
0
0
2
0
2
1
1
1
1
1
0
1
2
0
0
2
0
1
1
1
1
1
2
1
1
0
0
1
1
1
2
2
0
1
2
1
1
2
2
2
1
2
1
1
1
0
1
1
1
0
0
1
1
2
1
0
0
1
1
1
1
1
2
2
1
1
1
1
2
2
1
0
1
1
0
1
1
0
1
1
1
2
1
1
1
0
1
1
0
0
1
0
1
1
1
2
1
0
1
1
2
3
1
1
1
1
2
0
0
2
2
1
2
1
0
1
1
1
2
2
1
2
0
0
1
1
1
0
1
0
2
1
0
1
1
1
0
0
1
1
1
2
1
1
2
0
1
2
0
0
1
1
2
1
0
1
1
1
1
2
0
2
2
1
0
1
1
1
0
1
2
0
0
1
0
1
2
0
1
1
4
2
1
0
2
2
1
1
1
0
1
1
0
2
1
2
1
0
1
1
1
0
1
1
1
1
0
1
1
1
3
0
2
0
2
0
1
0
1
1
0
1
2
1
2
2
1
1
1
1
1
1
0
1
1
1
0
1
2
2
0
1
1
2
0
1
1
0
0
5
1
2
0
2
1
1
1
2
1
0
0
1
1
0
1
0
3
2
0
0
0
1
2
1
0
1
1
1
1
1
2
0
2
0
1
0
2
1
1
1
1
1
1
1
2
1
2
1
0
2
2
1
2
2
1
1
2
1
1
0
1
1
2
0
1
1
1
1
0
1
0
1
0
2
1
1
2
1
2
1
1
1
1
1
1
1
1
2
0
1
1
1
1
1
1
1
2
1
2
0
0
1
1
1
0
0
1
0
2
1
2
0
0
0
1
1
1
0
0
0
1
1
0
0
1
1
1
2
0
1
1
2
1
1
0
1
0
0
1
1
0
1
1
2
1
2
1
0
1
2
0
2
2
1
0
1
2
2
0
1
1
2
0
0
0
1
0
0
1
3
1
0
1
1
0
0
0
1
0
3
1
0
1
1
1
1
2
1
1
2
2
1
2
1
0
2
1
2
1
1
1
1
0
1
1
1
1
2
0
0
0
1
2
0
1
1
1
1
0
1
0
0
1
2
2
1
1
2
0
1
2
1
0
1
1
1
1
2
1
0
2
0
0
0
0
1
0
1
2
1
1
0
1
1
1
1
3
1
1
1
1
1
1
1
1
1
3
0
0
0
0
2
0
1
1
2
0
2
0
0
0
2
0
0
1
0
2
0
1
1
1
1
1
1
1
2
2
1
1
1
0
2
2
2
2
2
0
1
2
2
0
1
2
2
1
1
1
1
1
0
1
1
2
0
1
1
1
2
2
0
1
1
2
1
1
2
1
0
0
0
1
2
1
1
1
1
1
1
0
1
2
1
0
1
0
0
2
2
1
0
2
0
1
2
2
1
1
2
0
1
1
2
1
1
1
1
0
0
1
3
0
1
1
1
2
2
2
1
1
2
1
1
1
0
0
1
0
0
1
2
1
1
2
1
1
0
1
2
1
2
1
1
1
1
0
0
0
0
1
0
0
1
0
1
1
1
0
1
1
2
2
1
1
1
1
1
1
2
2
1
2
1
1
2
1
2
2
0
1
1
1
1
1
1
1
1
1
0
2
3
1
1
1
1
1
2
1
0
2
1
1
1
2
0
2
2
1
0
1
2
1
0
1
0
2
1
2
0
2
0
0
1
2
1
0
0
0
1
1
0
1
1
2
2
0
1
1
2
1
0
1
1
2
0
1
1
0
1
0
1
0
1
1
0
0
1
2
0
1
1
1
0
2
2
0
1
1
2
1
0
1
1
2
1
1
2
1
0
2
1
1
1
1
1
0
1
1
0
0
1
2
0
1
1
2
0
2
1
1
1
1
1
0
2
2
1
0
1
1
1
1
2
0
1
1
1
1
1
1
0
2
0
2
0
1
1
2
1
2
0
1
1
2
0
1
0
1
1
0
2
2
1
1
0
0
1
1
1
2
2
2
0
0
1
0
1
1
1
1
0
1
1
2
1
0
4
0
1
2
2
1
1
1
0
2
1
1
1
2
2
1
1
1
2
1
0
0
1
1
1
0
2
1
1
2
1
2
0
0
1
2
1
1
1
1
1
1
2
2
1
1
0
2
2
2
2
1
1
1
1
1
1
2
0
1
0
1
1
1
0
1
1
2
2
2
1
2
0
1
2
0
1
1
1
1
1
2
1
1
2
2
0
0
2
1
1
1
1
2
0
1
1
0
0
1
1
0
0
2
1
0
2
1
0
0
1
1
1
0
1
0
0
0
1
0
2
1
1
0
2
0
2
1
2
0
0
0
2
1
0
1
0
0
1
2
0
1
2
1
1
1
0
1
0
0
1
1
0
1
1
0
0
1
2
0
0
0
1
1
1
1
0
0
2
1
0
1
0
1
2
1
0
1
1
1
1
0
1
1
0
1
0
2
1
0
2
1
0
1
0
0
1
0
1
2
1
0
1
0
1
1
2
1
1
2
0
1
2
1
2
0
1
1
1
1
0
1
1
1
1
2
1
2
2
1
2
2
0
2
4
1
2
1
1
1
1
0
1
0
0
2
1
1
0
1
1
0
1
1
1
1
0
0
1
1
2
0
2
0
1
0
1
1
0
1
0
0
0
2
2
1
2
1
3
2
0
2
0
1
2
1
1
2
0
0
1
1
0
1
0
0
1
1
0
1
0
2
1
0
1
1
0
1
1
0
1
0
1
1
1
1
2
0
1
1
1
0
1
2
1
1
0
1
0
1
2
0
1
2
1
2
2
1
2
1
0
1
0
1
1
1
1
0
1
1
1
0
0
0
0
1
1
1
1
1
1
0
0
0
1
3
1
1
1
2
2
2
1
1
0
1
0
2
2
2
2
1
0
1
0
2
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
0
1
0
1
1
0
1
2
1
1
1
1
0
1
1
2
1
2
2
1
1
1
0
1
1
1
1
2
3
1
0
1
1
2
0
3
2
2
1
2
1
1
1
2
0
2
2
2
1
1
1
1
1
0
1
1
1
1
1
0
2
0
1
0
1
1
1
2
0
2
1
0
1
1
1
1
2
2
1
2
2
0
1
1
1
1
1
1
1
2
2
1
0
2
0
1
0
1
2
2
1
1
1
1
1
0
3
1
0
2
1
2
1
1
1
2
1
0
0
1
1
1
1
0
2
0
2
2
1
1
1
2
1
1
1
0
1
1
0
1
1
2
1
0
1
0
0
0
1
1
0
2
2
2
3
1
2
0
2
1
0
1
2
1
1
2
2
1
0
1
1
0
0
1
1
2
1
1
1
2
2
2
1
2
2
1
0
2
0
0
0
1
1
1
1
1
1
0
0
0
1
0
1
1
1
2
1
0
1
1
2
2
1
0
0
1
0
0
0
2
1
0
1
1
1
1
1
0
1
1
0
0
0
1
1
0
1
2
2
1
2
1
1
1
2
2
1
0
1
1
1
0
0
0
1
3
2
3
0
2
1
1
1
1
0
0
1
1
2
1
1
1
1
1
1
1
0
1
0
2
1
1
0
2
0
1
2
0
1
1
0
1
0
0
1
2
4
1
0
0
1
0
1
0
2
1
1
0
1
1
2
0
1
1
0
1
2
0
0
1
1
0
0
1
2
1
2
3
2
2
0
1
0
1
2
0
1
2
2
1
1
0
1
1
2
1
2
1
1
2
2
1
3
1
1
2
1
0
1
0
0
0
1
0
1
1
0
1
0
1
0
1
0
2
1
0
1
2
1
0
1
2
1
1
2
1
2
4
0
0
3
2
0
0
1
2
1
1
0
0
1
1
1
1
1
0
2
2
2
0
1
1
0
2
0
2
1
1
0
0
2
1
1
1
1
2
1
1
1
1
2
0
1
1
0
1
0
0
0
4
1
0
0
1
2
1
2
2
0
1
1
0
1
1
1
1
2
1
1
0
2
2
0
0
1
0
1
1
1
1
0
1
2
0
0
0
1
1
1
2
2
0
2
1
2
1
1
2
0
1
2
0
1
2
1
2
1
1
0
2
1
2
1
1
1
0
2
2
2
1
1
1
2
0
1
0
1
1
2
1
0
2
1
0
3
1
1
1
1
2
1
0
0
0
1
0
1
1
1
0
2
1
1
1
0
2
0
0
0
0
2
0
1
2
1
1
1
2
0
1
1
2
1
1
2
1
0
0
0
0
1
1
1
1
2
0
2
1
2
1
3
1
2
1
1
1
2
1
0
1
1
0
1
1
1
1
1
1
1
1
1
2
1
0
0
0
1
1
0
0
1
1
2
0
0
2
1
1
1
1
2
0
2
0
1
0
1
2
1
1
1
0
1
0
0
2
1
1
1
1
0
1
0
0
1
1
1
1
1
0
1
0
2
0
1
2
1
0
0
2
1
0
1
0
0
0
1
0
2
1
0
1
1
1
1
2
0
1
1
1
2
2
0
0
1
1
1
1
2
1
1
1
1
1
0
0
0
2
2
2
1
0
0
1
2
2
0
1
1
1
0
0
1
1
0
1
1
1
1
1
1
0
0
1
1
1
0
2
1
0
2
1
2
2
1
1
0
1
1
1
1
0
2
1
0
1
1
1
1
2
1
1
0
0
1
1
1
0
0
1
2
2
1
2
0
2
0
0
1
0
2
0
0
1
1
1
1
0
1
2
1
1
1
0
1
4
0
1
0
2
1
2
1
2
1
1
0
2
1
0
1
1
0
0
1
1
0
1
0
1
1
0
1
2
1
0
1
1
2
2
1
1
1
0
0
1
1
1
1
1
2
1
1
1
0
2
1
1
0
1
0
1
2
1
1
1
0
0
0
0
1
1
1
1
2
1
1
1
1
1
2
1
3
1
1
0
2
1
1
2
1
2
1
1
0
1
0
1
2
1
0
2
1
1
1
1
2
1
1
2
1
0
0
0
1
0
1
1
1
2
0
0
2
0
1
1
1
1
1
1
2
1
0
1
1
1
2
0
1
0
2
1
1
1
2
3
2
1
1
2
1
0
0
1
0
0
1
0
1
1
1
1
1
0
1
1
1
0
2
2
1
1
1
2
1
1
1
1
2
1
1
0
0
1
0
1
0
2
2
0
0
0
1
1
0
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
0
1
1
0
1
2
1
2
2
1
2
2
1
1
1
1
2
1
0
0
1
1
0
1
0
0
0
1
2
0
1
2
1
2
1
1
0
0
1
2
1
1
2
0
1
1
1
2
1
2
1
0
0
0
1
2
1
0
1
0
1
1
0
0
1
2
1
1
1
2
2
0
2
1
1
1
0
0
1
0
1
1
2
0
0
0
0
2
1
1
1
1
1
2
0
0
2
1
2
0
1
1
0
1
0
0
1
1
1
0
2
1
1
1
0
2
1
0
1
0
1
0
1
2
1
4
2
2
0
1
2
1
1
3
0
2
1
2
1
1
1
0
0
1
0
1
0
0
2
1
2
0
1
3
1
0
0
1
0
2
1
1
1
0
1
0
0
1
1
1
1
2
2
1
2
0
1
0
1
1
1
1
2
1
1
2
1
2
2
1
1
1
1
2
1
0
0
0
0
1
2
0
2
0
1
1
1
0
3
1
1
2
1
1
1
1
1
0
1
2
2
1
0
0
2
2
1
0
1
1
1
1
2
2
0
2
1
0
0
0
1
0
1
1
1
1
1
2
0
1
1
2
1
0
1
1
1
2
2
0
1
0
1
1
0
1
2
1
1
2
0
1
0
0
1
0
2
1
0
0
1
1
0
1
1
2
0
1
1
1
1
1
0
2
1
1
2
1
1
2
1
2
1
2
2
2
2
1
1
2
1
0
0
1
1
2
2
1
1
1
0
1
1
1
1
0
1
0
0
2
1
2
1
2
0
2
1
1
1
1
1
1
0
0
1
1
1
1
0
2
3
0
2
0
0
0
1
1
1
4
1
1
1
1
2
1
1
1
1
1
1
1
1
1
0
0
2
1
1
1
0
1
1
2
0
1
0
1
1
0
1
0
1
0
1
0
1
2
2
1
0
1
0
1
1
1
1
1
0
0
1
1
1
0
1
0
1
2
0
0
0
2
0
1
2
1
0
1
1
1
0
0
0
1
2
0
0
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
0
1
2
1
0
0
0
1
1
0
1
0
1
1
1
1
1
0
1
2
1
1
2
0
1
1
2
1
0
2
1
0
1
1
2
1
1
1
2
2
2
0
1
0
1
2
0
1
1
1
0
1
0
1
1
1
0
1
0
1
1
0
1
0
0
1
2
0
1
1
0
2
2
1
1
1
2
0
0
1
0
1
0
1
2
0
1
2
1
1
0
1
1
1
2
2
1
0
1
1
0
2
2
0
0
1
1
1
0
2
1
1
2
0
2
2
0
1
0
1
2
2
1
0
0
1
1
1
2
2
1
0
2
0
1
2
3
2
1
2
1
1
3
0
1
2
0
0
1
1
3
1
0
1
1
0
1
1
1
1
2
0
2
1
1
2
1
2
2
1
0
1
0
3
1
0
2
1
3
2
2
1
2
2
1
0
1
1
0
2
1
1
1
1
1
1
2
1
0
1
1
1
1
2
0
1
2
0
1
2
0
2
1
1
2
0
1
1
0
1
1
2
1
0
1
0
0
1
1
1
1
1
1
1
2
0
1
1
0
2
0
0
1
1
1
1
0
1
1
1
2
2
2
1
0
1
0
0
0
2
1
0
1
1
2
1
1
1
2
0
1
2
1
1
2
1
2
0
0
1
0
1
1
1
1
3
0
1
2
1
1
4
1
0
1
1
1
1
1
0
0
1
2
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
0
0
0
0
1
2
1
1
2
1
1
0
1
0
2
2
1
1
2
0
0
1
0
1
1
1
1
2
3
2
1
0
0
1
1
1
1
2
1
1
1
0
1
1
0
0
0
1
1
0
1
1
1
1
2
1
0
0
0
0
0
1
0
2
0
2
1
2
1
1
1
1
1
1
2
1
1
2
2
0
1
0
0
0
1
0
2
1
1
1
0
1
1
0
2
1
1
0
1
2
1
2
1
1
1
1
1
1
1
0
0
1
2
0
2
2
1
1
2
1
1
1
0
0
0
0
1
1
0
0
2
0
1
2
2
0
1
2
1
2
1
1
0
1
0
1
2
1
0
0
1
1
1
0
1
1
0
1
0
2
1
3
1
1
1
1
1
1
2
1
1
0
0
1
1
1
1
1
1
2
1
0
1
1
0
2
1
0
2
1
1
2
1
1
2
1
2
1
1
1
1
1
0
1
2
1
1
2
1
1
0
0
1
1
2
0
0
2
1
1
1
1
1
3
2
1
0
0
1
2
1
1
0
1
1
2
1
1
1
1
0
1
1
2
0
1
1
2
1
1
1
0
2
2
1
2
0
0
1
0
0
0
1
2
2
0
1
1
1
0
2
1
0
0
0
1
1
0
1
1
0
0
1
0
0
1
1
1
2
1
1
0
0
1
0
1
2
1
1
1
2
2
0
1
0
1
2
1
0
0
2
1
1
1
0
1
1
2
2
1
1
1
1
1
2
1
1
0
1
1
1
0
0
4
1
1
0
1
1
1
0
2
1
2
1
0
1
2
1
1
0
2
1
0
1
1
1
1
1
1
0
0
1
0
2
2
0
1
1
0
0
1
1
2
1
0
1
2
1
1
2
0
2
2
0
0
1
0
1
1
2
3
1
2
1
1
0
1
1
2
1
1
2
1
0
1
1
1
1
2
0
0
0
2
1
1
0
0
1
1
1
2
0
2
2
1
1
2
1
0
0
2
2
2
1
0
2
0
1
2
1
0
2
1
0
2
0
0
1
0
0
1
1
1
1
0
1
1
0
2
1
1
2
0
2
2
1
1
2
1
1
1
0
1
2
2
0
1
2
2
0
0
1
2
1
2
2
2
0
2
2
1
2
1
1
1
1
1
0
1
8
2
1
0
0
0
0
1
1
3
1
1
1
1
0
1
1
0
1
0
2
2
1
2
1
0
1
1
1
1
1
0
1
2
0
0
1
0
1
2
1
2
0
1
2
2
1
2
2
2
2
1
1
1
1
1
1
1
2
0
1
1
1
0
2
1
1
2
2
1
2
2
0
0
2
1
1
0
1
1
1
1
1
2
1
1
1
1
1
1
1
1
0
0
1
1
1
1
1
2
2
2
1
1
1
0
1
2
1
0
1
0
0
1
1
1
2
1
2
1
0
1
1
2
1
1
1
0
1
1
0
0
2
2
1
1
1
1
1
0
2
1
2
1
1
1
1
3
1
1
1
2
2
2
1
0
1
1
1
1
1
0
1
1
1
0
1
3
0
1
0
0
1
2
2
1
1
1
1
1
1
2
1
1
0
1
1
1
1
0
0
1
0
2
1
0
1
1
2
1
1
0
1
2
1
2
1
1
1
0
1
1
1
1
1
0
1
2
0
1
2
1
1
1
1
1
1
2
2
1
1
1
1
0
2
1
1
0
1
0
1
1
1
0
1
0
2
0
0
2
2
2
1
0
1
1
1
1
1
1
2
1
1
2
1
2
0
2
0
1
1
1
1
1
1
0
1
1
1
0
1
1
0
2
1
2
1
2
1
1
0
1
0
1
2
2
0
2
2
0
0
0
0
0
1
1
2
2
0
2
0
1
0
1
0
0
2
2
1
0
0
1
1
2
2
1
1
2
1
1
1
2
0
2
0
3
1
1
0
1
2
0
2
1
2
1
1
2
2
1
2
0
0
1
1
1
2
1
1
1
1
1
1
2
0
2
1
2
1
1
1
1
0
0
1
0
0
1
0
1
2
2
0
2
1
1
1
0
1
0
2
2
0
1
1
1
1
2
1
1
1
0
1
1
0
1
1
0
0
1
0
1
0
1
1
1
1
2
1
0
2
0
0
1
0
0
0
1
1
0
1
1
1
2
0
0
2
1
2
1
2
2
0
1
1
1
0
1
1
0
2
1
0
2
0
1
0
0
1
1
0
1
1
1
1
0
1
0
0
1
2
1
1
1
1
0
1
1
0
1
0
1
0
1
1
0
1
0
1
0
1
0
1
0
0
2
1
1
2
0
0
0
1
1
1
2
1
1
1
2
1
1
1
0
1
1
1
0
1
0
0
2
1
1
3
0
0
1
1
0
2
1
2
1
0
0
1
2
0
0
0
1
2
2
1
1
0
1
0
2
1
1
2
0
1
5
2
0
1
1
2
0
1
1
1
0
1
1
0
1
2
0
0
0
1
0
1
1
2
1
1
1
2
1
2
2
2
1
2
1
1
1
0
1
0
0
1
1
2
1
0
1
0
0
1
1
0
1
1
2
1
1
0
0
1
2
1
0
0
0
0
1
1
1
1
1
2
0
2
0
1
0
1
1
1
1
0
1
1
0
1
2
1
0
0
1
1
2
2
1
0
1
0
1
1
1
2
0
1
1
0
0
0
1
2
3
2
1
1
0
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
3
1
0
1
2
1
1
0
2
1
1
0
1
1
3
1
1
0
3
0
1
1
0
1
2
0
2
1
0
1
0
1
2
0
2
1
1
0
0
0
1
1
2
2
0
1
1
2
0
1
1
1
1
0
1
1
1
0
0
0
2
1
1
0
1
2
0
0
2
0
1
1
1
2
0
2
2
0
1
0
1
2
1
1
1
2
1
1
1
1
1
2
2
1
0
0
1
2
1
1
0
2
0
1
0
0
0
1
1
1
2
1
2
2
2
1
1
2
0
0
1
1
0
2
1
1
2
1
0
1
0
1
1
2
2
1
0
2
2
1
0
1
0
2
0
2
2
1
0
1
0
1
0
1
2
2
0
1
0
1
2
1
1
0
2
0
2
2
1
1
1
1
1
1
1
2
0
1
2
1
1
1
1
2
1
2
1
1
2
0
1
1
0
0
2
0
2
1
1
2
0
0
0
1
2
1
2
0
0
1
0
2
0
1
1
2
1
1
2
2
1
2
0
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
1
0
2
1
0
0
2
1
2
0
0
2
2
2
1
1
1
2
2
0
1
2
1
0
2
1
1
3
0
1
2
1
1
1
2
1
1
1
1
1
2
1
0
0
1
1
1
1
0
1
1
1
2
2
2
1
0
1
1
1
2
0
1
2
2
2
0
1
2
1
1
1
0
1
0
0
1
2
0
1
1
0
1
2
1
1
3
1
2
1
0
1
1
1
2
1
1
1
1
2
1
2
0
1
0
0
0
1
1
1
0
1
1
2
2
1
1
0
2
1
0
1
1
2
2
1
0
0
1
1
0
1
0
1
1
0
2
2
0
1
2
2
1
0
1
1
2
0
0
0
2
1
1
0
1
0
2
2
1
1
1
1
0
0
0
1
1
1
1
1
2
2
0
0
0
1
1
0
2
1
1
1
0
1
1
1
2
1
1
1
1
0
1
1
0
1
1
2
0
0
0
1
2
0
1
0
1
3
1
0
2
1
1
2
0
2
1
1
1
1
0
2
2
1
0
1
1
1
1
2
0
0
1
1
1
2
1
1
1
1
0
0
1
2
1
1
3
1
2
1
0
0
2
0
1
1
1
1
1
2
2
2
1
1
2
0
0
1
0
1
2
1
1
1
2
1
2
2
1
2
1
0
0
1
0
1
1
1
2
0
2
2
2
1
0
0
0
2
1
1
1
0
1
0
2
1
0
1
1
0
0
1
1
0
0
0
0
1
2
1
0
2
2
2
0
1
0
1
1
2
0
0
1
2
2
0
1
0
2
0
0
1
1
1
1
0
1
1
0
1
0
2
2
1
1
1
2
2
1
1
1
1
1
2
0
2
2
1
0
1
1
0
1
1
1
2
1
1
0
1
0
1
0
1
0
1
1
1
1
2
1
1
2
0
0
1
1
2
1
0
1
0
0
0
0
0
1
1
2
1
1
1
1
1
1
1
1
2
2
1
0
1
2
0
1
0
1
1
0
1
0
0
2
2
0
0
0
2
2
0
1
0
1
1
1
0
2
1
0
0
0
1
2
0
2
1
1
0
2
2
0
2
2
1
1
1
1
1
0
1
1
0
1
1
2
1
1
1
1
0
1
1
2
1
1
1
2
1
1
1
0
0
2
2
1
0
1
1
1
1
1
0
0
2
1
2
2
0
2
0
0
1
1
2
1
1
2
4
0
1
0
2
1
0
1
0
0
1
0
1
0
1
0
2
1
3
0
2
0
1
2
1
2
1
1
1
0
0
1
0
0
2
1
1
0
1
1
1
1
1
2
1
1
1
0
2
1
1
0
0
2
0
2
2
2
1
1
1
1
1
1
3
0
1
0
1
0
2
2
1
2
1
0
2
1
2
1
0
0
1
1
1
0
2
1
1
1
1
1
1
1
0
0
1
1
0
0
1
2
2
2
4
1
0
0
1
0
1
2
1
2
1
1
2
1
1
0
0
0
1
2
1
1
1
0
1
1
1
1
1
0
2
1
1
1
0
1
0
0
1
2
1
1
1
0
1
0
0
1
1
0
1
0
0
1
0
1
1
2
2
0
1
2
0
1
1
0
1
1
2
1
1
0
1
2
1
1
0
0
2
0
2
2
0
1
1
2
1
0
1
1
2
1
1
0
2
1
0
2
2
0
1
1
3
1
2
0
1
1
2
1
0
0
1
2
0
2
0
1
0
0
2
2
1
1
1
2
0
1
2
1
1
1
2
2
1
0
0
1
0
1
2
1
1
1
0
2
1
1
1
1
0
1
1
2
1
1
1
2
0
1
2
1
1
1
1
1
0
2
1
0
0
1
2
0
1
1
1
1
2
2
0
2
1
1
1
3
2
1
0
0
0
1
2
1
1
1
0
1
1
1
1
2
0
1
2
2
0
0
2
2
2
1
1
1
0
1
1
1
1
1
1
0
0
1
0
1
0
1
1
1
1
2
2
2
0
1
1
1
0
1
2
0
1
1
3
1
1
1
1
0
1
0
0
1
1
0
0
1
1
2
0
2
2
0
1
0
1
2
2
2
0
1
1
1
2
1
1
1
2
0
1
0
1
2
0
1
1
2
2
4
1
2
2
1
1
2
1
1
1
1
1
2
1
2
0
1
1
0
1
0
1
1
2
1
1
2
3
1
1
1
0
1
1
1
2
1
0
1
0
2
0
1
0
0
2
1
1
1
0
1
0
1
1
3
1
0
2
3
1
1
1
1
1
0
1
1
1
3
1
1
2
1
1
0
0
1
2
1
0
2
0
1
2
1
0
3
1
1
1
1
1
0
1
1
2
1
1
1
2
0
1
1
1
2
2
0
1
1
1
0
1
0
0
0
0
1
1
1
1
0
2
1
1
1
1
2
1
0
1
1
1
1
0
0
0
2
1
1
0
0
2
2
1
1
1
0
0
1
1
1
1
1
1
1
1
0
1
2
1
0
2
0
0
2
1
1
1
1
1
2
0
0
1
1
2
2
0
2
1
0
1
2
1
2
1
2
1
1
0
1
1
1
5
1
1
0
1
1
0
1
1
0
2
1
1
1
1
0
1
0
1
1
0
1
0
1
0
1
1
2
0
1
0
1
0
1
1
1
1
0
1
1
1
1
2
1
2
0
1
1
1
1
0
1
1
0
1
1
2
1
1
1
2
1
2
1
2
0
3
0
2
1
1
1
2
0
1
1
3
0
2
1
1
1
1
1
0
0
1
0
1
1
1
1
0
1
1
1
1
2
1
0
0
1
2
0
1
0
1
0
0
2
1
1
1
2
2
2
2
0
1
1
0
1
2
2
1
2
1
0
2
1
0
1
1
0
1
1
2
0
0
1
0
1
1
1
1
1
1
0
2
1
2
1
1
1
0
1
1
1
0
1
0
2
1
1
1
2
0
1
1
1
0
1
0
0
1
1
1
1
1
1
1
2
1
1
2
0
0
2
2
1
2
1
1
1
0
1
1
2
1
1
3
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
3
1
2
2
0
1
1
1
1
0
3
1
1
1
0
1
0
1
1
4
0
2
1
1
2
1
1
2
2
1
1
1
1
0
2
0
0
1
0
0
1
1
1
2
0
0
1
0
0
1
1
0
0
1
2
1
1
3
2
1
0
2
2
1
1
1
1
0
1
1
0
1
0
2
1
1
1
1
1
1
2
0
1
0
0
0
0
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
0
1
0
0
1
1
1
1
0
2
2
1
2
0
1
1
1
2
1
1
0
1
1
1
1
1
2
1
0
0
1
1
0
1
0
1
0
2
2
1
0
1
2
2
1
1
0
1
2
2
2
0
1
0
0
1
0
1
1
0
1
1
2
3
1
2
2
1
1
0
2
2
0
1
1
1
2
1
1
1
1
0
1
1
1
2
1
1
1
2
1
0
0
2
2
2
0
1
2
1
1
2
1
1
1
1
2
0
1
1
2
1
0
2
1
0
2
1
1
3
0
2
1
1
1
0
0
2
2
3
0
1
1
1
1
0
1
1
1
0
1
1
1
0
1
0
0
2
1
1
2
0
1
2
1
1
1
2
2
3
0
1
1
0
2
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
0
2
1
2
2
2
1
0
1
2
1
2
1
0
3
2
0
0
2
1
1
1
1
1
1
1
1
0
1
0
1
1
0
1
0
2
1
1
1
1
1
1
0
1
1
1
2
1
1
1
2
2
1
1
2
1
1
2
0
0
1
1
1
0
0
1
1
1
1
1
2
0
1
1
2
1
0
1
1
2
1
1
1
0
1
1
0
2
1
1
0
2
1
0
2
0
1
1
2
2
0
1
0
2
0
0
0
1
0
0
1
1
2
2
0
0
1
1
0
1
1
2
0
1
1
2
1
0
1
2
2
0
0
1
1
0
1
2
0
1
2
0
0
0
1
2
1
1
1
0
0
1
0
1
1
1
0
1
2
1
1
2
0
0
1
1
1
0
0
1
2
1
1
1
3
1
1
0
0
2
0
1
1
1
2
0
0
1
1
0
1
1
0
2
1
2
1
0
0
1
1
0
0
1
1
1
1
1
4
1
1
1
1
0
1
0
1
1
0
1
1
0
1
1
1
0
1
2
1
1
1
2
2
1
2
0
1
3
0
1
0
1
1
1
1
1
0
0
1
1
0
2
2
2
2
0
2
1
1
1
2
2
1
0
0
2
2
0
1
2
2
1
1
1
2
0
1
1
1
0
1
2
0
1
1
2
1
0
1
0
1
2
1
2
1
1
0
1
1
1
1
2
0
0
2
0
2
1
1
1
1
0
1
1
1
1
2
0
1
2
1
1
2
2
0
2
0
2
2
0
1
0
2
0
0
2
1
1
1
1
1
0
0
2
1
1
2
2
1
1
0
0
0
2
1
2
2
0
1
1
2
0
3
2
1
1
0
0
2
1
1
1
1
2
1
0
1
0
1
1
2
2
2
2
1
1
2
1
0
0
2
2
0
0
1
2
2
0
1
1
4
0
0
1
0
0
0
2
1
0
2
1
1
1
1
2
0
2
1
1
2
1
1
1
1
1
1
2
1
1
2
1
2
2
1
1
1
1
0
1
1
1
2
2
2
0
1
1
0
0
1
0
0
1
0
1
1
2
1
1
0
1
0
1
1
2
1
0
3
0
1
1
0
1
0
3
2
2
2
2
1
1
1
1
2
2
1
1
0
2
2
0
1
0
2
1
2
0
1
1
0
1
1
0
1
1
1
1
1
0
1
2
2
1
2
2
1
1
0
1
1
0
1
0
2
1
0
0
0
1
1
0
1
1
0
2
1
1
1
0
1
0
1
1
2
1
2
1
1
0
1
1
2
1
1
0
2
1
2
1
2
1
1
1
2
1
0
2
0
1
2
1
2
2
1
1
1
1
2
1
1
1
0
2
1
1
2
0
2
1
0
1
0
1
0
0
1
1
2
0
2
0
1
2
1
0
1
1
1
2
0
2
2
1
2
1
0
0
1
1
1
0
0
2
2
0
1
1
1
1
1
0
1
1
1
2
1
2
1
0
1
0
0
0
0
0
2
2
1
2
1
1
3
1
0
2
0
1
1
2
2
2
2
1
2
1
0
0
1
1
1
3
1
1
1
2
1
1
2
1
2
2
0
2
1
0
0
1
1
1
1
1
2
2
1
1
1
0
0
0
2
0
0
1
0
2
1
1
1
2
1
0
1
0
1
1
1
2
2
4
2
0
0
2
0
1
1
0
1
0
1
1
2
1
1
0
1
1
2
1
1
2
0
0
1
0
2
2
1
1
0
2
2
1
1
2
1
2
2
2
2
2
0
1
1
1
1
0
0
0
1
1
0
1
0
1
1
1
0
1
1
0
1
1
1
1
0
1
1
2
0
1
1
2
1
0
1
0
1
1
1
1
1
2
1
2
2
1
0
0
1
2
0
0
1
1
1
2
0
1
0
2
0
0
1
1
0
1
2
2
1
1
2
0
0
4
1
0
1
1
0
1
1
2
2
1
1
2
1
1
2
1
0
1
2
2
1
2
0
1
1
2
1
1
2
2
1
0
1
2
1
0
1
1
2
2
1
2
1
0
1
1
1
2
0
2
1
0
2
1
0
1
1
1
1
1
1
1
1
0
0
2
1
2
1
1
2
1
2
0
0
1
2
1
0
1
1
1
1
2
2
0
0
0
1
1
2
1
0
1
2
2
0
2
2
2
1
1
0
1
1
0
0
2
2
2
2
0
1
2
0
0
2
1
1
0
1
1
1
0
0
1
1
2
2
1
1
0
1
0
0
2
1
1
1
2
3
0
1
1
1
2
1
1
2
2
1
1
0
1
3
2
1
2
1
0
0
2
2
1
2
1
0
1
0
1
0
1
1
2
0
2
1
1
2
1
0
2
0
1
1
1
0
2
1
1
1
1
0
1
2
1
0
2
1
0
0
0
2
2
0
0
1
2
1
1
1
0
1
0
0
1
0
1
2
1
1
2
2
0
1
1
1
2
2
2
0
1
1
2
1
0
1
1
2
0
2
1
1
1
1
0
2
1
2
0
1
1
1
1
3
0
1
1
2
0
2
1
2
0
1
1
1
1
1
0
0
2
1
0
2
2
2
1
1
1
1
1
1
0
0
1
0
2
0
1
2
0
1
1
1
1
1
2
2
1
0
2
1
2
0
2
1
0
3
1
0
1
2
1
1
0
2
0
0
2
1
0
1
2
1
1
0
0
2
1
1
2
2
1
1
1
2
2
2
0
1
1
1
2
1
2
0
0
2
0
0
0
2
1
1
1
0
0
1
2
1
0
1
0
2
4
2
0
1
0
1
0
1
2
0
1
1
1
3
1
0
3
1
2
0
1
3
0
2
1
1
2
2
1
1
1
2
1
2
0
0
1
1
2
2
1
1
2
1
1
2
2
0
0
1
0
1
1
0
2
3
1
1
2
1
1
1
1
1
1
0
1
1
0
1
0
1
0
0
0
2
1
0
1
2
0
1
2
2
0
0
0
1
0
0
1
0
2
1
1
1
2
1
1
1
1
1
1
1
1
0
2
1
0
1
0
3
2
2
0
0
0
2
2
0
2
0
2
2
1
1
1
1
1
1
0
2
2
0
2
1
1
0
1
0
0
0
1
1
2
1
1
0
0
1
1
0
2
1
2
0
1
1
2
1
1
0
1
1
1
1
0
2
1
1
2
1
0
1
2
2
2
1
1
1
0
1
1
1
0
2
1
0
1
0
2
0
1
1
0
0
1
0
1
0
2
0
0
1
0
2
0
1
1
2
1
1
1
1
1
1
0
0
1
1
0
1
1
2
2
1
0
1
1
1
1
0
0
1
1
1
1
0
0
2
0
2
1
0
1
1
3
1
0
0
0
1
2
3
1
2
2
1
0
1
1
2
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
0
0
1
2
1
1
1
1
0
1
0
1
2
1
0
0
0
1
1
0
1
0
0
0
1
0
1
1
1
1
0
0
1
1
0
0
1
0
4
1
1
0
3
0
0
1
1
0
1
1
1
0
2
0
2
1
2
1
0
1
1
1
1
1
2
1
1
2
3
1
1
2
1
2
5
1
1
1
0
2
1
1
2
3
1
0
1
2
0
1
1
1
1
2
2
2
0
0
0
0
1
0
2
1
1
2
1
2
1
1
2
0
2
0
1
2
1
1
0
1
1
2
2
1
0
1
2
2
2
0
2
1
1
1
1
1
0
0
0
1
0
2
1
1
1
0
0
1
1
0
0
1
1
0
1
1
1
1
2
1
1
1
0
2
2
2
2
0
0
0
0
1
1
1
0
1
0
2
0
2
1
2
0
1
0
1
1
1
2
2
1
0
1
0
2
1
1
2
1
1
1
0
1
1
0
1
2
1
0
2
1
1
2
3
2
1
0
2
2
2
1
1
2
0
0
1
1
2
0
2
0
1
0
1
2
1
1
3
1
0
2
0
1
1
1
2
1
0
1
2
2
1
2
2
0
2
1
0
1
1
0
2
0
1
1
2
1
0
0
0
0
1
1
1
1
1
0
1
0
0
1
1
1
2
1
1
2
1
1
1
0
1
1
2
0
1
1
1
0
0
1
2
1
2
1
0
1
1
1
0
1
1
0
1
0
2
1
0
1
0
1
1
2
0
1
1
2
0
2
2
2
1
1
1
2
1
0
2
2
1
1
0
1
0
0
0
2
1
2
1
3
0
0
2
1
2
1
2
2
1
1
0
1
1
0
0
0
1
1
1
1
2
0
0
1
1
2
0
0
2
1
1
0
2
0
2
0
0
0
1
0
2
0
2
2
2
3
2
2
2
0
1
0
1
0
1
1
0
1
1
1
0
1
0
2
1
2
0
1
2
1
1
2
2
0
2
1
1
2
1
1
0
1
2
1
0
1
1
1
1
2
1
1
1
2
2
2
0
1
1
1
0
0
0
2
1
1
0
0
1
0
1
1
0
0
1
0
2
1
1
1
0
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
0
1
1
1
2
2
2
3
0
1
0
0
0
1
1
2
2
2
1
1
0
1
0
1
1
1
1
1
1
0
0
0
0
1
1
0
1
2
1
0
2
0
1
2
1
1
2
0
0
1
1
0
2
1
1
2
1
0
1
0
0
2
2
1
1
1
1
2
0
2
1
1
4
1
2
1
3
0
1
1
1
0
1
1
1
1
0
1
1
0
2
2
0
1
0
1
1
1
1
2
2
2
1
1
2
1
1
2
2
0
2
2
1
2
2
2
0
1
0
0
1
1
0
1
1
0
1
0
1
1
1
1
0
0
1
1
1
1
1
1
2
1
1
1
1
1
1
0
0
1
2
0
2
1
1
3
0
2
0
0
1
1
1
0
0
1
0
2
1
2
1
0
1
0
1
2
0
2
1
1
0
0
0
1
1
1
1
0
0
1
0
1
1
2
2
2
0
1
1
2
2
1
2
0
0
1
0
1
1
0
1
0
1
0
2
2
1
2
0
2
2
1
1
1
2
2
2
2
2
1
1
1
1
1
1
1
1
0
2
1
1
2
1
0
2
2
1
0
0
0
1
1
0
2
1
2
1
2
1
2
2
0
2
1
1
1
1
1
2
2
0
1
1
1
1
1
0
2
0
1
1
1
1
0
1
0
0
0
1
2
1
1
1
1
1
1
1
2
1
1
0
0
0
1
2
1
2
1
1
2
1
1
1
2
0
0
1
1
0
1
2
1
0
2
0
0
2
1
1
0
2
1
1
0
1
0
1
1
1
0
1
0
0
0
0
0
2
1
1
1
0
1
2
0
0
3
2
2
0
1
0
1
0
1
2
1
1
1
1
2
1
2
0
0
2
1
1
0
1
1
1
0
0
2
0
1
0
1
2
0
0
2
0
1
0
0
0
1
0
1
2
1
1
0
0
2
1
1
1
1
2
1
0
2
1
1
0
1
2
2
0
0
1
2
0
1
1
0
0
0
0
1
1
0
2
1
2
1
0
2
1
1
1
1
0
0
4
0
2
2
3
0
0
1
2
4
1
0
1
1
0
2
0
1
0
1
1
1
0
1
1
1
2
0
0
1
1
1
2
0
2
1
1
0
1
1
1
2
1
0
0
1
1
1
2
1
3
1
0
1
1
1
1
1
3
1
1
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
3
0
1
2
1
1
2
1
2
1
1
0
2
2
2
0
0
1
2
2
1
1
2
1
2
1
1
0
2
0
2
1
1
0
0
0
2
1
1
2
1
1
2
2
1
1
2
1
1
0
1
0
1
2
2
0
1
2
1
2
1
0
0
0
1
0
0
1
1
0
0
2
1
2
0
1
0
1
2
2
0
1
2
1
0
1
1
1
1
1
1
0
2
2
2
0
2
1
1
1
1
1
1
1
1
2
1
1
0
2
2
1
2
0
2
1
0
2
1
1
0
1
1
2
1
1
1
0
0
1
0
1
1
1
1
1
1
1
0
0
1
1
1
2
1
1
1
0
1
1
1
2
1
0
1
1
1
2
0
0
1
0
6
1
2
1
0
1
1
1
2
0
1
0
1
1
2
0
2
3
2
1
2
1
1
0
2
1
1
1
1
0
0
1
1
1
0
0
1
1
0
1
1
1
1
1
1
1
0
2
1
1
1
0
0
0
0
1
0
1
0
1
1
1
0
0
1
4
1
1
0
0
2
2
1
1
0
2
2
1
0
2
0
1
1
2
2
1
1
0
3
1
2
0
0
1
0
0
2
0
1
0
2
2
0
1
0
1
1
1
2
1
1
2
1
2
1
1
1
3
1
2
1
1
1
1
0
1
0
1
1
0
0
1
1
1
2
1
2
1
1
1
0
2
1
0
2
0
1
1
1
0
1
1
1
0
0
1
1
0
1
0
2
1
1
2
0
1
1
2
1
1
0
1
1
3
1
0
1
1
1
0
1
1
1
0
2
0
2
1
1
1
2
2
2
2
0
1
0
1
0
1
1
1
2
2
1
0
2
1
0
1
1
1
2
0
2
0
1
1
1
1
1
2
0
3
0
1
1
1
2
1
1
1
0
1
1
1
0
1
1
1
1
0
1
0
0
1
0
2
2
1
1
1
0
1
0
0
1
0
0
1
2
1
1
0
1
2
1
2
1
0
1
0
1
1
1
0
0
0
1
0
0
1
2
1
0
2
2
1
1
0
0
0
2
1
0
0
0
0
1
1
1
0
1
0
1
0
1
1
2
1
1
0
0
1
1
0
1
0
1
0
2
2
0
0
2
1
1
2
2
1
0
0
2
3
2
1
0
0
1
1
2
2
2
1
2
2
1
0
0
2
1
2
0
2
1
0
1
1
1
1
1
0
1
0
0
1
1
1
1
1
1
1
1
3
0
1
0
0
2
0
0
2
1
0
2
2
1
0
1
0
0
1
1
0
2
1
2
0
0
0
2
2
1
2
0
1
1
1
2
1
1
0
1
1
2
1
0
2
2
1
0
0
1
1
1
0
0
0
1
1
0
1
1
1
0
1
0
2
2
1
2
0
1
0
1
2
1
2
1
2
2
0
2
0
1
0
2
0
1
1
1
1
1
1
0
1
1
1
2
0
1
0
0
2
1
2
1
0
0
0
0
2
0
2
0
0
1
2
1
0
0
1
2
2
1
2
1
1
2
1
2
2
0
1
1
1
2
1
0
0
1
1
1
1
0
0
0
0
0
1
0
1
1
1
1
0
0
1
1
0
1
0
2
1
1
1
1
1
2
1
1
0
1
1
0
1
1
0
2
0
1
1
1
1
1
1
0
1
2
1
0
0
2
1
1
1
1
2
0
0
0
2
0
1
1
1
0
0
0
1
0
1
1
1
1
0
0
1
0
0
1
1
1
0
1
1
0
2
0
1
1
1
1
0
1
2
2
1
1
1
1
1
0
0
2
0
1
2
0
1
0
0
1
0
0
0
1
2
1
1
0
1
1
1
1
0
1
2
1
1
0
2
0
1
1
0
2
1
2
2
1
0
1
1
0
0
0
2
2
1
1
1
1
1
2
0
0
1
2
1
1
2
1
1
2
1
0
1
0
2
0
1
1
1
2
0
1
2
1
1
2
2
1
2
0
1
1
2
1
1
1
2
5
2
0
0
1
0
0
2
1
0
1
1
1
2
0
1
0
0
2
1
2
1
1
1
1
2
1
0
0
1
2
1
0
2
1
1
1
2
1
1
0
0
2
1
1
2
0
2
1
1
0
1
1
2
2
1
1
2
0
2
2
1
1
1
1
1
1
1
1
1
1
1
1
0
1
2
2
2
0
0
2
1
0
1
1
2
0
1
2
1
0
1
1
2
0
6
1
1
0
1
0
1
0
1
1
1
0
2
1
1
1
1
1
1
1
0
1
2
1
0
0
0
0
1
2
0
1
2
1
2
1
1
2
1
0
1
2
1
1
0
0
1
3
2
0
0
2
0
1
2
0
1
1
1
1
2
0
1
1
1
1
0
2
2
1
0
2
1
2
1
1
1
2
2
1
1
2
0
1
0
1
1
1
2
2
0
1
2
2
1
0
2
1
1
2
2
0
0
2
2
1
1
0
1
2
1
1
2
0
1
0
4
1
2
1
1
1
0
0
1
5
1
1
1
2
0
1
1
2
1
2
0
1
0
1
2
1
1
0
1
0
1
0
1
1
2
1
1
1
2
1
1
2
2
2
2
2
1
0
0
1
0
1
0
1
1
0
1
0
2
0
0
1
1
1
1
1
0
1
1
1
1
2
1
0
1
0
2
2
0
1
0
0
2
1
1
1
2
1
2
1
2
1
0
1
1
0
1
0
2
1
2
2
1
1
1
0
2
0
1
2
1
1
2
1
2
1
1
2
1
2
1
0
4
1
1
0
0
1
1
2
1
1
2
1
0
0
0
2
1
2
1
2
1
0
2
0
0
1
0
0
0
1
0
1
2
1
1
1
2
0
0
1
1
2
1
1
0
0
0
1
1
1
2
1
0
0
0
1
1
2
0
1
1
0
2
1
0
1
1
1
1
2
1
0
1
7
1
1
2
1
1
1
2
1
2
1
0
1
1
1
1
1
2
0
1
1
1
2
2
2
1
1
0
1
1
1
1
1
1
1
1
1
1
2
1
1
0
0
0
1
0
1
0
0
1
1
0
1
1
0
0
1
1
1
2
2
1
1
1
0
1
2
0
1
2
1
0
1
1
1
2
0
1
1
0
3
0
1
1
1
2
0
0
1
0
1
1
0
1
1
0
1
1
2
1
2
1
1
1
1
2
1
1
2
0
2
1
2
1
0
0
1
1
0
1
0
1
2
1
2
0
2
2
0
1
1
2
1
2
1
0
1
0
1
1
2
0
1
2
1
2
1
1
2
2
2
1
2
0
3
0
1
1
0
1
2
1
1
0
1
1
1
1
1
0
0
0
0
1
1
1
1
0
0
1
2
0
2
1
0
2
2
1
0
2
1
2
1
1
2
1
1
1
1
1
0
1
0
0
1
2
1
0
1
2
2
2
1
0
1
2
1
1
2
2
1
0
0
0
1
2
2
0
0
2
1
0
2
1
1
2
2
2
0
0
1
1
0
1
0
2
0
1
0
1
1
0
1
1
1
1
1
0
0
0
0
1
1
0
1
1
1
2
1
1
0
1
1
2
1
1
2
2
0
1
2
1
1
1
2
1
2
1
1
0
2
2
0
0
1
1
1
1
1
1
3
1
1
0
2
2
2
1
1
1
0
0
1
1
1
1
0
1
1
1
0
0
2
0
0
1
0
2
2
1
2
2
1
2
1
0
1
2
2
1
0
0
0
0
2
1
1
0
2
2
2
2
1
1
2
2
0
0
1
1
1
1
1
1
0
1
0
0
0
0
1
2
1
2
1
1
2
1
1
1
1
0
1
0
1
2
0
1
0
1
0
2
2
2
1
2
0
1
2
1
1
1
1
1
0
2
1
2
0
1
1
1
2
1
1
1
0
0
0
2
2
2
0
2
0
0
1
1
2
1
2
2
3
1
1
1
2
2
0
1
2
1
1
1
1
1
1
0
1
1
1
1
1
1
1
2
2
0
2
1
0
0
2
1
0
0
1
2
1
1
1
2
2
1
1
2
0
1
0
0
1
2
1
1
1
0
1
2
0
0
2
0
1
1
0
1
1
1
0
2
1
1
1
0
2
0
1
1
1
1
0
1
1
2
1
2
1
2
1
1
0
0
2
0
2
0
1
2
1
1
1
0
0
1
0
1
0
1
0
2
1
1
2
1
0
1
2
2
1
1
1
0
1
1
1
0
2
1
1
1
1
1
1
1
1
0
0
0
0
1
1
1
0
4
2
2
1
1
0
1
1
1
3
1
2
0
2
1
0
1
1
0
2
1
1
0
2
0
0
0
0
2
1
1
1
0
1
0
1
1
1
1
0
0
0
2
1
1
0
1
1
0
2
2
1
1
2
1
1
3
1
1
1
1
1
2
1
1
1
0
2
1
0
1
1
0
2
1
0
2
1
0
2
1
1
1
2
1
1
0
1
1
2
0
1
1
0
1
1
0
1
1
0
1
1
1
1
1
1
0
1
2
1
1
2
1
2
0
2
1
1
0
2
1
0
2
1
2
3
1
2
1
0
0
0
1
2
1
2
0
0
1
1
1
1
2
1
0
4
2
1
1
2
2
1
0
1
1
2
0
0
0
2
1
1
0
2
2
1
1
1
2
1
1
2
1
2
1
1
1
2
2
1
2
1
1
0
0
2
1
1
2
0
2
1
1
1
0
0
1
0
0
1
0
2
0
0
0
2
1
2
1
0
1
3
2
1
1
2
2
1
2
1
2
1
1
1
1
2
0
2
0
2
0
0
2
1
1
0
1
0
1
1
0
1
1
0
2
2
0
1
0
2
1
1
1
1
1
0
1
1
1
0
1
0
0
1
1
1
0
1
1
0
1
1
0
0
1
0
1
1
0
2
2
0
1
2
1
1
1
2
0
0
0
0
1
2
1
0
0
1
1
1
1
2
2
1
1
2
0
1
1
1
1
1
1
1
1
1
2
0
0
1
0
2
1
1
0
1
1
0
1
0
1
1
1
2
1
1
0
2
1
0
1
1
1
0
1
1
1
0
0
1
1
1
2
1
1
0
1
2
2
1
2
1
2
1
0
1
2
0
0
0
2
1
0
0
0
1
2
0
1
2
1
1
2
1
1
1
0
0
1
1
0
0
0
1
0
2
1
1
1
1
1
1
1
1
1
0
1
1
0
1
1
1
1
2
1
0
1
1
0
0
1
0
1
2
1
1
2
1
2
1
1
1
1
0
2
1
1
1
0
0
0
1
0
1
1
1
2
0
0
1
1
1
1
1
1
2
1
2
1
0
5
1
1
2
2
1
1
1
1
1
1
2
1
0
2
1
1
2
0
1
2
2
0
0
1
1
2
0
1
1
1
0
1
1
1
2
1
2
2
1
0
1
1
2
0
1
1
2
2
2
0
1
2
1
2
2
1
1
1
1
1
0
2
0
0
1
1
2
1
0
1
0
1
0
1
0
1
1
0
1
1
2
0
2
1
1
0
0
1
1
2
1
1
1
2
0
2
2
1
2
2
1
0
1
1
1
2
0
1
0
1
1
2
1
1
2
0
1
1
2
1
0
1
1
1
0
1
1
2
1
0
2
0
0
0
0
0
2
1
0
1
1
0
2
2
1
1
1
0
2
0
1
2
1
2
1
0
1
0
1
0
1
2
1
2
0
0
0
0
1
2
0
2
0
0
1
1
0
2
0
0
2
2
2
2
1
2
2
2
1
2
1
2
0
2
2
0
1
0
1
1
0
0
0
1
1
1
2
1
0
1
1
1
2
2
0
2
1
1
1
1
0
2
1
1
2
2
2
0
1
1
2
1
1
1
1
2
1
2
2
0
1
1
1
0
1
1
2
1
1
1
2
0
0
1
1
0
1
0
0
0
2
1
2
2
0
1
1
2
1
0
1
1
1
1
2
0
0
1
0
0
0
2
1
1
1
0
1
1
2
0
2
1
1
1
1
0
1
1
2
1
2
0
1
2
1
1
1
0
1
0
1
0
0
0
0
2
1
1
1
2
0
1
1
1
0
1
1
1
1
1
1
0
1
0
0
1
1
1
0
2
1
2
0
1
2
0
1
0
1
0
0
1
1
1
2
0
1
1
0
0
1
2
1
0
2
0
1
1
0
0
1
1
2
0
1
0
2
1
1
0
1
1
1
0
1
1
1
1
1
0
1
1
2
2
0
2
1
1
1
0
1
1
0
0
1
0
2
0
1
2
1
1
0
1
1
0
1
1
2
1
0
1
1
0
1
1
1
0
2
1
2
0
0
1
0
1
1
2
1
1
1
1
1
1
2
1
1
2
1
2
2
1
0
2
2
1
1
1
1
2
1
1
0
2
1
0
1
1
0
1
0
2
0
0
0
1
1
1
1
0
1
0
1
0
1
0
1
2
1
0
0
3
0
1
1
2
1
2
1
0
1
1
1
1
1
1
2
0
0
1
1
0
2
1
1
0
5
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
0
0
0
0
1
2
2
0
0
0
0
1
1
0
1
1
0
1
2
1
1
0
1
2
2
0
0
1
0
1
2
2
1
1
1
1
1
2
0
0
1
0
0
1
1
1
1
1
3
2
0
0
0
0
1
1
0
1
0
0
0
2
3
2
1
2
2
1
1
0
1
1
1
1
0
1
2
1
2
1
2
1
1
1
0
2
0
1
1
1
1
1
1
2
0
1
1
1
1
0
2
0
0
0
2
1
0
0
2
0
0
1
0
0
1
1
1
1
0
1
1
1
0
0
1
0
2
2
1
1
1
2
0
2
0
1
1
1
1
1
2
1
2
0
1
1
1
1
1
2
1
2
1
2
0
0
0
1
1
1
1
0
2
1
1
1
2
2
0
1
1
1
1
2
1
1
0
1
2
1
1
2
1
2
1
2
2
1
0
0
1
0
2
2
2
1
0
1
1
1
2
2
0
1
1
0
0
1
0
1
1
1
2
0
2
1
1
0
2
2
1
2
0
2
0
2
2
0
2
0
1
0
1
1
2
1
0
1
2
2
0
0
2
1
0
1
0
1
0
0
0
2
1
1
0
2
2
0
1
1
2
0
0
1
0
1
0
0
2
2
0
1
0
1
2
2
0
1
0
0
1
1
1
2
0
0
1
0
2
0
1
2
1
1
1
1
0
1
1
2
2
1
1
2
0
1
0
1
1
0
0
2
1
0
2
2
1
1
1
1
1
1
1
2
2
1
1
2
0
1
2
0
6
0
1
1
0
0
1
1
0
1
2
2
0
1
1
1
1
2
1
1
1
1
0
0
2
2
0
1
2
0
1
1
0
1
2
3
1
1
1
0
0
1
1
1
0
2
1
0
1
2
1
2
0
1
0
1
1
0
2
1
1
3
1
1
0
1
0
2
1
0
2
3
0
1
2
1
0
1
1
1
1
2
0
2
2
1
1
2
1
1
0
0
1
1
1
5
1
2
1
2
0
2
1
1
0
0
1
1
1
3
1
2
1
1
1
1
0
1
1
1
2
2
2
2
1
0
1
0
1
1
1
0
1
1
2
0
0
1
1
2
1
1
0
1
1
0
1
2
0
0
1
1
0
1
1
1
0
1
2
1
1
0
1
0
0
0
1
1
1
1
1
1
2
2
1
1
0
1
1
1
1
1
1
0
2
0
2
2
1
2
0
0
2
1
0
2
1
1
1
2
0
1
1
1
3
1
1
2
0
2
1
1
1
2
2
1
1
1
0
1
2
1
0
1
0
1
0
1
1
0
0
2
1
1
1
1
0
2
1
0
1
1
0
1
1
1
0
0
1
1
1
1
1
0
2
1
1
2
1
1
0
0
2
0
1
1
1
1
0
0
0
2
0
1
0
1
1
1
1
1
1
1
1
1
1
0
3
1
0
2
1
1
1
1
0
1
1
0
1
0
1
1
1
0
1
0
2
2
0
1
2
1
0
1
1
1
1
0
1
0
1
1
2
1
0
1
1
1
1
2
1
2
0
1
1
1
1
1
2
2
0
0
1
2
1
2
1
1
2
0
1
1
0
0
1
0
1
0
0
0
0
1
1
2
2
2
2
1
1
1
1
2
1
1
1
2
2
0
1
0
2
1
2
1
0
1
2
0
0
1
1
1
1
1
0
1
1
1
1
1
1
1
0
1
1
1
2
0
0
1
1
1
0
1
1
1
0
1
0
0
1
0
1
1
1
1
1
0
1
0
2
0
0
1
1
2
0
4
1
1
1
1
1
1
1
0
2
0
2
1
0
2
1
0
1
2
2
1
0
0
2
1
1
0
0
2
1
1
2
1
0
1
1
1
1
1
2
2
0
1
0
1
0
0
0
2
1
2
1
2
0
1
2
0
1
1
1
3
1
0
0
1
1
0
1
1
0
1
1
2
1
1
2
0
1
1
1
1
2
1
1
0
1
0
1
2
2
1
2
1
2
1
0
1
0
2
1
1
0
1
2
1
3
1
3
1
0
0
0
0
1
0
1
1
1
1
1
1
1
0
0
3
1
1
2
0
1
0
1
2
1
0
2
1
1
0
1
1
2
1
1
2
1
1
1
1
1
0
2
1
1
0
1
1
1
1
1
1
2
2
0
1
1
2
1
1
0
1
2
1
0
0
1
1
2
1
0
1
1
2
1
1
2
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
0
0
2
1
0
1
0
2
1
1
3
1
0
1
0
0
1
1
2
1
2
0
1
1
1
1
1
1
1
0
0
1
2
0
1
0
0
1
2
1
1
0
1
1
2
1
2
0
1
0
1
0
2
1
1
1
1
1
1
1
1
1
0
1
1
2
1
1
1
1
0
2
1
1
2
2
1
0
2
0
0
1
1
2
0
2
1
1
0
0
0
1
2
1
0
1
0
0
0
0
1
1
1
3
1
1
1
1
1
1
1
0
1
2
0
1
0
1
0
1
0
1
2
0
1
0
0
1
1
1
1
2
1
2
1
0
0
2
0
0
0
1
1
1
0
1
2
1
1
1
1
0
2
2
2
1
1
1
0
1
1
1
1
2
1
2
1
1
2
1
1
2
0
0
0
0
1
0
1
1
2
2
1
0
0
0
0
1
2
2
2
1
2
1
1
1
0
1
0
1
0
1
2
1
0
1
1
1
1
1
1
0
2
1
4
0
1
0
1
1
1
1
1
1
1
0
0
2
1
1
0
1
0
0
1
1
1
2
0
1
1
1
1
1
0
2
1
2
1
1
1
2
1
0
0
1
0
0
0
5
1
1
1
1
1
0
1
1
0
2
1
2
2
2
1
0
0
1
1
1
1
1
1
2
2
1
1
1
0
2
1
1
2
1
2
2
1
1
0
0
2
0
0
1
0
1
1
1
1
0
2
2
1
2
1
1
1
1
1
1
1
2
1
2
2
1
1
0
1
2
1
1
1
1
2
0
0
1
0
1
1
1
1
2
2
1
1
1
1
1
1
1
1
0
1
1
1
0
0
2
1
0
1
1
0
0
1
1
2
1
0
1
2
2
2
0
1
10
1
2
0
0
1
0
0
1
1
2
1
1
1
2
1
1
1
1
0
1
1
2
1
1
2
0
1
1
1
1
0
1
1
0
0
1
0
0
1
1
1
1
1
1
1
2
0
0
1
0
2
1
2
1
1
2
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
0
1
0
1
2
1
1
1
1
0
1
1
1
0
1
1
0
1
0
0
0
1
0
1
1
1
1
1
1
1
2
0
2
1
2
1
0
1
0
0
2
2
1
1
0
2
1
2
1
2
0
1
0
1
4
2
1
1
1
2
1
0
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
0
1
1
0
0
1
0
1
0
0
2
1
2
2
1
0
1
1
1
0
1
0
1
2
1
2
0
2
1
0
2
2
1
1
0
2
0
1
1
2
0
1
1
0
1
1
0
1
2
1
1
2
2
0
1
1
0
1
2
1
1
2
2
2
1
0
1
0
2
0
1
1
0
1
1
2
0
1
1
1
1
1
0
0
2
1
1
1
1
1
2
0
1
1
1
1
0
0
1
2
1
2
3
1
1
0
1
1
1
1
0
1
1
0
0
1
2
0
0
0
2
1
1
2
1
0
2
2
0
1
2
1
0
0
1
1
0
1
0
1
1
0
2
1
1
0
0
1
2
1
2
0
0
2
2
1
0
2
1
1
2
1
1
2
2
0
1
0
1
0
1
1
2
0
1
1
1
4
2
0
1
1
0
1
1
2
0
1
2
0
1
1
1
0
1
2
1
0
1
1
1
1
2
3
2
2
0
1
1
1
2
1
1
1
1
1
0
1
2
0
2
1
2
0
2
2
1
2
1
2
2
1
2
1
1
2
1
0
0
1
2
2
2
0
1
1
1
1
0
2
1
1
2
2
0
1
1
1
0
1
1
2
3
1
2
1
1
2
1
1
2
2
1
1
1
2
2
1
2
1
2
1
2
1
0
0
0
2
0
1
0
1
0
1
2
1
1
0
3
2
1
1
2
0
1
2
1
0
1
1
1
1
0
0
2
1
2
3
1
0
1
0
1
1
0
1
0
1
1
0
1
1
0
1
2
1
0
0
0
1
1
2
0
0
7
0
1
2
1
1
1
2
3
0
2
1
1
3
2
0
1
2
1
1
0
2
1
0
0
1
0
2
1
1
0
1
1
2
1
1
2
1
1
2
1
2
2
1
0
2
0
2
2
0
1
2
1
2
1
1
1
2
1
1
2
1
1
0
2
2
1
1
2
0
1
1
0
0
0
2
2
1
1
0
1
2
1
1
1
1
1
0
1
2
0
0
1
1
1
2
1
0
0
1
0
1
1
1
2
0
0
1
0
1
1
0
2
1
1
2
2
1
0
1
0
1
1
1
0
1
3
1
0
0
0
1
0
2
0
1
0
1
1
2
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
2
2
1
1
2
1
2
1
1
2
1
2
1
0
1
2
1
0
1
0
2
2
1
2
0
0
1
1
1
2
1
1
2
1
0
1
2
1
2
2
1
2
1
1
1
0
1
1
2
1
2
1
1
2
1
1
1
1
0
1
0
0
2
2
1
0
1
0
0
0
1
2
0
1
1
2
2
2
2
3
1
1
2
1
2
1
2
0
1
1
0
1
1
1
1
0
1
1
1
1
2
2
0
1
0
1
2
1
0
1
1
1
0
0
3
1
0
1
0
0
0
0
1
1
1
2
0
1
1
0
0
0
1
1
0
3
1
1
0
1
0
1
2
2
1
2
1
1
2
2
1
1
2
1
1
0
0
1
1
2
0
1
1
0
2
1
0
0
0
1
1
1
1
0
0
1
1
1
2
1
1
1
1
0
1
2
1
2
1
1
2
1
2
2
1
1
1
1
2
1
2
1
1
0
1
0
1
1
1
2
2
1
1
0
1
0
2
2
0
1
1
1
1
1
1
2
0
0
3
2
0
1
1
1
1
2
0
1
0
0
0
1
1
2
1
1
1
1
1
1
1
1
0
1
1
2
2
1
1
1
1
1
1
0
0
1
0
0
0
2
2
0
1
1
2
1
2
2
1
1
0
1
1
0
2
2
0
1
2
3
0
1
1
1
2
1
1
2
2
2
1
2
0
0
2
2
1
2
1
1
1
1
1
2
2
0
1
1
1
2
1
1
3
2
1
2
0
1
0
0
2
1
2
1
1
0
4
1
1
0
1
0
2
1
0
1
2
1
1
1
1
1
1
0
1
1
1
1
0
2
2
1
1
1
0
1
2
0
1
0
2
1
0
2
0
0
1
1
2
1
3
1
1
1
1
1
2
1
1
3
0
2
0
2
1
1
1
0
1
1
0
2
1
1
1
0
0
1
1
1
1
1
1
3
1
1
2
1
1
1
1
1
1
1
0
1
2
0
1
2
0
0
1
2
2
0
4
0
0
1
1
0
1
1
1
0
1
1
1
1
1
1
0
1
2
0
0
0
1
1
1
1
1
2
0
1
0
0
1
1
2
1
1
1
2
1
1
1
1
2
2
1
1
1
1
1
1
0
1
1
0
1
1
2
2
0
1
0
1
0
1
0
0
0
2
1
2
0
1
1
1
1
0
2
2
1
2
0
0
2
0
1
1
1
1
2
2
0
1
2
0
1
2
1
1
0
1
1
7
1
0
0
2
2
1
1
1
3
2
1
2
0
0
1
1
2
1
2
1
1
0
2
1
1
0
0
3
2
0
1
1
1
0
1
0
0
1
0
0
1
1
0
1
1
1
2
1
1
0
2
2
2
0
1
0
1
1
1
2
2
0
1
1
2
0
1
1
2
1
1
1
0
2
1
0
2
1
1
2
1
1
2
2
1
1
1
0
0
1
0
1
1
2
1
2
1
1
0
2
1
1
1
0
1
1
0
1
3
0
1
2
2
1
1
0
0
1
1
1
1
2
2
1
1
0
0
0
1
1
1
0
0
0
0
2
2
1
1
0
2
1
1
0
0
2
1
1
2
1
1
1
2
1
1
1
1
0
1
0
0
0
1
1
0
0
2
0
2
2
1
0
1
1
1
0
2
0
2
0
0
1
2
1
1
1
1
2
1
1
1
2
1
1
2
3
0
1
2
0
2
0
1
1
1
1
0
1
0
1
1
0
1
1
1
0
1
0
1
1
1
2
1
1
1
0
1
0
0
0
2
0
1
2
1
2
2
0
1
1
2
1
1
1
1
2
1
1
1
0
0
1
1
2
1
2
1
0
1
2
0
2
1
0
1
1
1
0
1
2
2
1
2
0
0
0
1
1
0
1
0
2
2
1
0
0
1
1
2
2
1
2
1
1
0
1
1
1
1
1
1
0
2
1
1
2
1
1
1
2
2
1
1
1
1
2
1
1
0
2
1
0
2
1
0
1
0
2
1
1
0
0
2
0
1
3
0
2
1
1
1
2
1
1
1
2
0
3
2
2
1
1
0
1
1
1
1
1
1
0
0
1
1
0
4
2
1
1
1
1
0
1
1
1
2
1
1
0
2
2
1
1
2
0
1
1
0
0
1
2
0
2
1
1
2
1
1
1
0
1
1
1
2
4
2
1
0
1
2
1
2
1
1
1
2
0
1
1
2
1
1
1
0
1
1
2
0
1
0
1
1
1
0
1
2
1
2
0
1
1
1
1
0
0
0
1
2
0
2
0
0
1
1
1
1
2
2
1
0
1
0
2
0
1
0
1
0
0
1
0
2
1
2
1
0
1
0
2
2
1
1
1
0
1
1
2
0
2
1
1
0
1
1
1
0
1
1
0
1
1
1
1
2
1
4
1
0
1
1
0
1
1
1
0
1
1
0
2
2
2
2
0
1
2
4
0
1
0
1
2
0
2
4
2
1
1
0
1
1
1
2
1
1
0
1
1
2
1
1
2
1
2
1
2
2
0
2
1
1
0
0
0
1
2
0
1
1
1
1
2
1
1
1
1
1
2
0
1
0
1
0
2
2
1
1
0
1
0
1
1
0
1
1
1
1
0
1
2
1
1
1
0
0
1
1
1
0
1
1
2
1
3
1
2
1
0
0
0
1
2
1
1
2
1
0
1
0
0
2
1
1
1
1
1
1
1
1
0
0
1
1
0
0
1
2
2
2
0
2
0
2
0
1
0
1
1
1
2
1
0
2
1
1
1
2
2
1
1
1
2
0
1
2
1
2
0
2
1
1
1
1
1
1
2
1
0
0
1
1
1
1
2
1
2
1
1
2
1
1
1
1
0
1
2
0
1
2
1
1
1
0
0
0
1
1
1
1
2
1
2
1
2
1
1
2
2
0
2
0
1
2
1
0
2
0
1
0
1
0
2
0
2
1
1
0
0
0
1
0
2
1
1
0
2
0
1
1
0
0
1
1
1
1
1
1
1
1
0
7
2
4
0
1
1
0
1
2
1
1
1
2
2
1
1
1
1
1
0
0
0
1
0
1
1
1
1
0
1
2
0
1
1
1
2
1
1
1
0
1
0
0
0
1
2
0
1
0
2
1
5
0
1
0
1
0
2
1
1
1
2
0
2
0
1
2
0
2
1
0
1
1
2
0
1
1
1
1
0
2
0
1
1
1
1
0
1
1
1
4
0
1
2
2
0
1
0
0
1
2
1
1
2
0
1
1
0
0
2
2
1
1
1
2
3
0
2
0
2
1
1
0
1
0
4
1
2
2
0
2
0
0
1
0
2
2
0
1
1
0
0
0
0
1
1
2
1
1
1
1
2
0
2
1
2
1
3
1
2
0
1
1
1
2
1
2
2
1
0
1
1
1
0
1
1
0
1
1
1
1
1
2
0
0
0
2
1
1
1
0
1
1
1
1
0
1
2
1
1
2
1
0
2
1
2
1
1
1
1
1
1
1
2
1
0
1
1
2
1
2
2
1
2
0
1
2
1
0
2
0
3
0
1
1
1
1
1
1
0
1
0
2
1
0
2
1
1
1
1
2
1
1
1
1
0
1
1
0
2
1
1
2
1
1
1
1
0
2
0
1
2
2
0
1
2
1
1
2
0
0
1
2
1
1
0
1
0
0
0
1
1
1
2
0
1
2
3
1
0
4
1
1
2
1
1
0
1
0
1
2
1
1
2
1
2
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
0
1
1
1
2
1
1
1
0
0
2
0
2
2
0
0
2
0
0
2
2
0
2
1
1
0
1
1
0
1
2
0
0
1
1
1
2
1
1
1
1
1
1
1
2
1
0
2
1
0
0
2
1
1
1
1
1
1
0
1
1
0
0
2
2
2
0
0
1
0
2
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
0
0
0
1
2
1
2
2
1
1
0
1
0
2
0
1
2
2
0
2
1
1
0
1
2
2
1
0
1
2
1
1
0
2
1
1
1
1
0
1
1
0
2
0
1
1
1
1
1
0
0
0
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
0
2
0
1
1
2
2
2
0
2
1
0
1
1
1
0
0
1
0
1
1
1
1
0
1
0
0
1
1
2
3
1
0
0
0
0
2
1
1
1
2
0
2
1
0
1
0
2
1
1
5
0
2
1
1
0
1
2
1
2
1
1
0
1
2
1
0
0
2
0
0
1
1
2
1
2
1
2
2
0
1
2
0
2
1
1
0
0
2
2
0
1
1
1
0
1
2
2
1
0
2
0
1
0
1
1
1
2
0
1
1
2
2
1
2
1
2
1
0
1
1
1
0
0
1
1
1
1
2
1
0
1
3
2
2
1
1
1
0
1
1
2
0
1
1
1
1
2
1
1
1
0
1
1
2
2
2
1
0
0
3
1
1
0
1
2
1
1
2
1
0
2
1
1
2
1
0
1
0
1
2
2
0
1
0
1
0
2
3
1
0
1
1
1
0
1
1
1
2
1
2
1
2
1
0
1
1
0
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
0
1
1
0
0
0
2
2
1
2
1
1
1
1
1
1
2
0
2
2
1
0
0
1
1
1
0
1
0
0
3
0
1
1
2
1
0
0
1
1
2
1
1
1
1
1
2
1
0
2
1
3
2
1
2
1
1
3
2
1
0
1
1
1
2
1
1
1
1
1
1
0
1
1
2
1
0
2
2
2
2
2
2
1
2
1
1
0
1
1
0
0
1
2
0
1
2
1
1
1
0
1
1
2
1
1
1
1
1
1
1
0
1
0
1
2
1
1
2
1
1
0
2
1
2
0
2
2
1
0
1
1
2
1
4
2
1
1
0
1
1
0
2
0
2
0
1
1
1
0
0
1
0
0
1
1
2
1
1
2
1
1
2
2
1
1
2
0
1
1
2
0
0
1
2
1
1
2
0
2
1
2
1
1
1
0
1
0
1
1
2
1
2
2
0
1
1
3
1
1
1
1
1
1
1
2
0
2
2
0
0
2
0
0
1
2
2
1
1
1
2
0
1
0
1
0
1
2
1
1
1
1
1
0
2
1
0
2
1
2
1
1
2
1
1
2
1
1
1
1
1
0
1
1
0
2
1
1
1
2
0
0
1
1
2
1
1
1
0
1
2
1
2
1
1
2
2
1
0
0
1
1
1
1
0
1
2
0
0
1
1
1
0
1
0
0
1
0
1
0
0
0
1
0
1
2
1
1
0
0
1
1
1
1
1
0
1
2
1
2
2
1
1
1
1
1
0
0
1
2
1
1
1
1
1
1
1
1
3
1
1
1
0
1
0
1
0
2
2
2
2
0
1
2
1
0
1
1
0
1
1
2
2
1
1
0
0
0
0
0
2
0
2
1
1
1
1
1
1
0
1
0
0
0
1
0
1
2
1
0
2
0
2
1
0
1
2
2
1
1
1
1
1
1
0
1
0
1
0
2
1
0
1
1
0
1
1
1
1
1
0
1
0
1
0
1
0
1
1
1
2
1
1
2
1
0
1
1
0
1
0
1
1
0
1
1
2
0
1
0
0
1
2
0
1
1
0
0
0
1
0
1
2
0
0
1
0
1
0
0
1
1
2
2
2
1
0
0
2
1
1
0
1
0
1
1
0
2
1
1
2
0
0
3
2
1
1
3
1
1
2
1
0
0
2
0
1
1
0
0
1
2
0
1
0
1
0
2
0
1
1
2
0
1
1
2
1
0
1
1
1
0
2
2
0
0
0
1
2
1
0
2
1
1
0
2
1
1
2
2
2
2
2
0
1
2
2
1
0
1
0
2
1
1
1
2
1
0
1
1
0
0
2
0
1
0
0
1
1
0
1
0
2
1
1
1
1
2
0
2
2
1
2
0
0
0
1
0
0
2
1
1
2
1
1
2
1
1
0
2
1
1
2
1
0
1
1
2
2
1
1
0
1
1
2
2
1
1
0
0
1
4
1
1
1
1
2
1
2
1
2
1
5
3
0
2
0
1
1
1
1
0
0
2
1
1
0
1
0
0
1
1
1
2
0
2
2
1
1
1
2
1
1
1
0
2
2
0
1
2
2
1
1
1
2
1
1
0
1
1
1
0
0
0
0
2
1
0
1
1
1
1
0
1
0
1
1
0
0
1
2
1
1
1
1
2
2
2
2
1
1
0
0
1
1
2
1
1
1
1
0
1
0
1
0
0
2
0
0
2
2
0
1
2
1
2
1
1
0
0
0
1
1
1
0
0
1
1
1
2
1
0
1
0
0
1
0
1
0
1
0
1
1
1
0
1
0
0
1
2
1
0
0
0
0
0
0
1
1
0
1
1
0
1
1
2
1
0
1
1
1
1
1
1
0
1
1
1
1
0
1
0
2
1
0
1
2
1
1
1
3
1
1
0
1
0
1
1
0
1
0
1
0
1
1
0
1
1
0
1
0
0
1
2
1
0
1
0
1
0
0
0
0
1
1
1
1
1
1
0
1
1
2
1
2
0
1
0
1
1
0
2
0
2
0
1
0
1
1
0
1
1
0
0
1
1
1
1
0
2
1
2
1
2
1
2
1
2
2
2
1
1
0
2
0
0
1
0
2
2
1
2
1
0
2
2
1
1
1
1
3
1
2
1
0
0
1
1
0
1
2
1
1
1
2
0
1
1
1
1
1
0
1
0
2
2
1
0
1
1
1
1
2
0
1
0
2
1
1
1
0
0
1
1
1
2
1
1
0
0
1
1
1
0
1
2
1
1
1
0
2
0
1
2
1
0
2
1
0
1
0
1
1
1
1
1
1
1
0
2
1
1
0
1
0
0
1
2
1
2
2
0
1
2
1
1
0
0
2
2
1
1
1
0
0
1
2
1
2
1
1
0
1
1
1
0
1
1
0
1
1
1
1
1
0
0
1
2
1
1
1
2
1
2
2
2
0
1
1
0
1
1
1
3
0
0
0
0
0
1
0
1
1
0
1
1
2
1
0
1
1
2
1
2
1
2
0
1
1
0
2
2
1
1
0
0
0
0
1
1
0
0
1
1
0
1
1
0
0
1
1
1
1
1
1
1
1
1
2
0
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
2
1
2
2
0
1
1
1
1
0
1
0
1
0
2
0
1
1
2
0
1
2
1
0
0
0
1
2
1
0
1
1
1
1
1
1
1
0
2
2
2
0
1
2
1
1
1
1
1
2
1
1
0
0
1
1
1
0
1
1
1
1
0
0
1
0
1
2
1
2
2
2
1
1
1
0
0
2
1
0
2
2
2
1
1
1
1
1
1
1
2
0
1
1
0
1
1
1
2
1
1
1
1
1
0
0
1
1
1
2
2
0
2
1
1
2
2
1
1
0
3
1
0
1
0
1
2
2
0
1
1
2
0
1
1
1
3
1
2
1
1
1
1
1
0
1
2
0
1
1
0
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
0
1
2
2
1
2
2
0
2
1
0
0
0
1
1
2
1
2
0
2
1
1
1
1
1
1
1
1
1
1
1
1
2
0
2
0
1
0
2
0
2
1
2
2
2
1
1
1
1
1
0
0
1
2
1
1
2
1
1
2
1
2
1
2
2
1
1
1
2
1
1
1
2
2
0
2
2
0
1
1
1
1
2
1
1
3
1
2
1
0
1
1
1
0
1
0
0
0
1
2
1
1
0
2
2
1
2
1
1
1
1
0
1
0
2
0
0
2
2
1
1
0
1
0
1
1
2
2
0
0
0
1
0
1
1
2
2
1
1
0
0
1
1
1
1
1
0
1
1
0
2
0
0
1
1
1
1
1
0
1
1
0
1
1
1
1
0
1
0
1
2
0
0
1
2
1
1
2
1
2
1
1
1
0
0
0
1
2
1
1
0
1
1
2
0
1
1
3
0
1
1
1
2
1
1
1
0
1
1
0
1
1
0
1
0
0
1
0
1
1
1
1
1
0
1
1
1
0
0
1
1
1
0
2
0
1
2
3
0
1
2
1
2
0
2
1
0
1
2
1
3
1
1
1
1
1
1
1
1
1
2
0
1
2
2
0
1
1
2
1
2
1
1
2
3
1
0
1
0
1
1
1
1
1
1
1
1
0
1
1
1
2
0
1
0
0
2
2
2
2
0
2
0
0
1
1
1
2
2
0
1
1
2
2
1
2
1
1
1
1
0
2
0
2
1
1
2
0
0
1
1
0
1
1
1
2
2
1
1
2
0
1
1
1
0
0
0
1
1
1
1
0
0
1
0
1
2
0
1
1
0
1
1
1
1
1
1
2
0
1
1
1
1
1
1
0
1
2
0
2
2
1
1
1
1
0
0
2
1
0
2
1
1
1
1
2
0
0
1
1
1
1
1
1
1
1
2
1
1
2
0
1
1
0
1
1
1
2
0
1
1
1
2
1
1
0
1
0
1
2
0
1
1
0
1
0
1
0
2
2
1
0
1
1
2
1
0
2
1
1
0
1
2
1
1
0
0
2
0
1
2
1
1
0
2
1
1
1
0
0
1
1
0
1
1
2
0
2
2
0
2
1
2
0
1
1
2
0
0
1
1
2
0
0
1
1
0
1
1
2
1
1
1
0
1
1
0
2
2
1
1
0
1
1
1
1
1
1
1
1
2
0
2
1
1
1
1
1
1
1
1
0
2
0
1
1
0
0
1
0
2
0
2
1
0
2
1
1
0
1
2
1
0
0
0
1
0
0
1
0
0
1
1
1
2
2
0
0
2
1
2
0
1
1
2
2
0
0
0
2
2
2
0
0
1
0
0
1
1
1
2
1
0
1
1
2
1
3
1
1
1
2
2
1
1
1
1
2
0
0
1
1
2
1
2
1
1
0
1
1
2
0
1
0
1
1
1
1
2
0
0
2
2
1
1
0
1
1
0
1
1
1
1
1
1
1
0
1
0
2
2
1
1
1
0
2
1
2
1
1
1
0
1
0
0
2
2
0
0
2
1
0
1
1
0
2
1
1
0
0
0
0
2
1
1
2
1
1
2
0
0
0
2
1
1
0
1
1
1
2
1
1
0
1
2
2
0
1
1
1
1
1
0
1
1
0
1
1
1
0
1
0
4
1
2
1
1
2
0
2
1
2
1
2
0
1
0
1
1
1
1
1
0
0
0
1
1
0
2
2
1
1
1
2
0
0
1
1
2
0
2
2
1
0
1
0
2
1
1
0
1
1
1
0
1
0
2
1
2
2
0
1
1
1
0
0
0
2
0
2
1
0
0
1
1
0
1
0
1
1
1
2
1
1
1
2
0
1
1
0
2
1
0
2
1
1
2
0
0
1
1
1
0
2
2
0
1
1
0
1
1
2
1
0
1
2
1
2
2
1
0
0
1
1
1
1
0
2
2
1
1
1
0
2
1
1
1
3
0
2
1
1
2
1
2
0
1
1
1
2
0
1
1
0
1
1
1
1
1
1
2
0
0
2
1
0
2
0
2
0
0
1
1
1
1
0
1
1
1
1
1
0
1
0
0
1
1
1
2
0
0
0
0
1
2
2
1
1
1
1
1
0
1
1
2
1
0
0
1
2
0
1
0
1
1
3
0
1
0
0
2
1
1
2
1
0
1
1
2
1
1
1
2
1
1
0
0
2
2
2
0
0
1
2
3
1
1
0
1
1
1
0
2
1
0
0
1
0
0
1
1
1
1
0
0
0
1
2
1
2
0
1
1
1
1
2
1
1
1
1
2
0
1
1
0
1
0
2
0
1
2
0
0
2
1
1
1
1
2
1
1
2
1
1
1
0
2
2
2
2
2
1
1
0
1
1
0
2
1
0
0
0
1
1
0
1
1
1
1
1
2
0
0
0
1
1
1
1
1
1
1
1
3
1
1
1
1
2
1
0
1
1
2
0
1
0
1
2
0
2
1
1
1
0
1
1
1
1
0
2
2
0
1
1
0
1
1
0
0
1
1
0
2
2
0
3
2
1
1
1
1
2
1
0
1
2
2
0
1
1
1
2
0
0
0
1
2
1
0
0
0
1
1
0
1
2
0
0
1
2
1
3
1
0
1
0
2
1
1
1
0
1
1
1
0
2
2
1
1
2
0
1
0
2
0
1
1
0
2
2
1
1
1
1
0
2
0
0
0
0
1
2
0
1
1
3
0
0
0
0
2
0
0
1
1
1
1
2
0
0
2
2
2
0
1
1
0
1
2
1
1
1
1
2
2
2
2
2
1
1
0
0
2
0
1
0
2
2
2
2
1
1
0
1
1
0
1
1
1
2
1
1
2
0
0
0
2
2
1
2
0
1
0
0
1
1
1
2
0
1
1
2
1
1
1
1
0
1
1
1
2
1
1
0
1
2
2
1
2
1
0
1
0
3
2
1
1
1
2
1
0
1
1
1
1
1
0
1
1
0
0
1
0
0
1
1
1
2
1
0
1
0
2
0
1
2
1
2
0
2
1
1
2
0
1
1
0
0
1
1
0
1
1
0
1
1
0
1
1
1
0
0
1
1
1
1
1
0
1
1
1
2
1
2
1
0
0
2
1
1
3
1
1
0
1
1
1
2
1
1
1
2
0
1
1
0
0
1
2
1
2
2
1
1
1
1
2
2
1
0
1
3
1
2
0
1
1
1
1
1
0
1
2
1
0
1
0
0
1
1
1
0
2
0
2
1
1
0
0
0
1
1
0
1
1
0
1
0
1
0
2
0
1
0
1
1
1
1
1
1
3
1
0
1
0
0
0
1
2
1
0
1
0
1
1
0
0
1
0
0
1
1
1
1
1
1
1
0
2
1
0
1
2
2
2
1
0
1
0
2
0
1
0
1
2
1
0
0
2
5
1
2
1
1
1
2
2
1
1
2
1
1
1
2
1
0
1
0
1
0
1
1
1
1
1
1
0
1
0
2
1
2
1
3
1
1
2
0
2
1
0
0
2
1
1
1
1
0
0
1
0
2
1
2
1
0
1
1
0
2
2
1
2
2
1
1
2
1
2
1
1
2
2
2
1
1
0
2
1
1
2
1
1
1
1
1
0
1
0
1
1
0
1
1
2
2
2
0
1
0
2
1
1
0
1
1
1
1
1
1
2
2
0
0
0
0
1
2
1
2
0
0
1
0
2
0
1
1
2
1
1
0
1
0
1
0
0
0
0
1
0
1
0
0
0
1
2
1
0
1
0
2
2
0
0
0
1
2
1
1
1
2
2
2
1
0
2
1
2
0
0
1
1
0
1
0
1
0
1
0
2
1
4
1
2
2
2
0
1
0
2
1
1
1
0
1
1
2
2
1
1
0
0
2
2
1
2
0
2
1
2
0
1
1
1
0
1
2
1
1
0
1
1
1
0
1
1
2
1
1
1
0
0
2
0
0
1
0
1
2
1
0
1
1
1
1
0
1
2
1
1
1
0
0
1
5
1
1
1
0
1
0
1
0
1
2
1
1
2
0
0
2
2
0
2
1
1
0
1
0
1
1
1
0
0
1
1
1
1
1
1
0
1
1
1
2
0
1
1
2
0
1
0
1
1
1
0
1
1
0
0
1
1
0
1
0
1
0
2
1
2
1
1
2
0
1
2
0
0
0
1
0
0
2
1
1
1
0
1
2
0
0
0
0
1
0
2
0
0
2
0
0
1
2
1
2
1
1
2
1
1
0
1
1
1
1
0
1
0
1
1
1
1
2
1
1
1
1
1
0
1
1
1
0
1
1
1
1
0
0
2
1
2
0
2
0
1
0
0
2
1
0
0
2
0
0
2
0
1
1
1
1
0
0
0
1
0
1
0
1
1
0
2
1
1
3
0
1
0
1
1
1
1
1
1
0
2
1
1
2
1
1
2
0
1
1
1
1
1
1
1
2
2
1
1
2
0
1
1
2
0
2
2
0
1
1
1
1
0
1
0
0
3
2
2
0
1
2
1
1
1
2
0
0
1
0
1
1
0
1
1
1
1
1
1
1
2
2
1
2
2
1
0
1
1
1
1
2
0
0
1
1
0
1
1
2
2
2
1
0
1
1
1
1
2
0
1
1
1
0
1
0
1
4
2
3
0
1
2
2
1
4
0
1
0
4
0
2
1
1
1
1
0
2
1
1
1
1
1
2
1
0
1
1
2
1
1
1
0
1
2
1
1
2
0
1
1
0
2
2
1
0
1
0
2
1
1
1
1
1
1
1
2
2
1
0
1
2
1
1
0
1
0
2
1
2
0
1
2
0
1
1
0
1
1
1
0
1
2
0
1
0
1
1
0
0
1
0
1
0
2
0
1
1
1
0
1
1
0
0
2
2
1
2
0
1
0
1
0
1
1
0
1
1
2
1
1
1
2
0
1
2
1
0
2
1
1
1
2
1
1
2
1
0
1
0
1
0
2
1
2
1
3
0
1
2
0
2
0
0
0
1
0
0
1
2
0
1
0
0
1
0
1
2
2
2
0
1
0
0
0
1
1
1
1
2
1
2
1
2
1
1
2
1
0
0
1
2
2
0
1
0
1
1
1
1
2
1
1
2
2
0
1
2
1
4
0
1
3
1
1
0
1
1
0
1
0
1
2
2
1
2
0
0
2
2
1
1
1
2
1
2
2
2
1
1
1
1
2
0
0
2
1
1
1
1
1
0
1
1
2
1
1
1
1
1
1
0
1
1
1
1
0
2
0
0
1
2
2
1
1
1
1
1
2
1
1
1
1
1
1
1
0
1
1
2
2
1
0
1
0
1
0
1
1
0
2
1
0
0
0
0
1
2
0
1
2
1
0
1
1
1
2
1
1
0
1
1
0
0
2
1
2
1
1
2
2
1
1
1
1
2
0
1
0
1
0
1
1
0
2
1
2
1
1
0
0
0
1
2
1
1
0
0
0
1
1
1
1
1
0
1
1
2
0
0
2
1
1
1
1
1
1
2
2
1
0
2
2
2
1
2
2
1
1
0
2
1
1
1
0
1
2
2
1
0
1
1
1
5
1
0
1
1
1
1
2
1
1
0
1
2
0
2
0
2
2
1
1
1
1
1
0
1
1
1
2
2
0
1
1
2
2
1
1
1
1
1
0
0
1
1
1
1
2
1
1
0
1
1
1
1
0
2
0
2
0
0
1
1
2
0
2
1
1
0
2
2
2
2
1
2
1
1
1
1
0
2
2
0
0
2
1
1
0
2
2
1
1
1
1
2
2
1
0
0
1
0
1
2
2
1
0
0
0
1
1
0
0
2
2
1
1
1
0
1
1
1
1
1
2
2
0
2
1
2
2
2
1
1
1
1
1
2
2
0
1
2
1
3
2
1
0
1
0
2
0
1
1
0
1
0
1
1
1
1
1
1
1
1
0
1
0
1
1
1
0
1
1
1
1
2
0
1
0
1
1
2
1
1
1
1
1
1
0
0
0
1
2
1
1
4
2
1
1
0
0
2
1
0
1
1
1
1
1
2
2
1
0
1
0
1
0
2
0
1
1
1
0
2
1
2
0
1
1
1
1
1
3
1
2
1
0
2
1
1
1
0
1
1
0
1
1
1
0
1
1
2
1
0
1
1
1
1
1
1
1
1
0
2
2
0
0
1
1
1
0
1
1
1
0
0
1
0
0
0
1
1
1
1
0
1
1
0
1
1
2
1
2
1
1
0
0
1
2
1
1
2
0
1
0
0
1
1
1
2
1
1
1
1
1
1
1
0
0
1
0
1
0
2
0
1
2
1
2
0
1
1
1
1
0
1
0
2
2
1
0
0
0
1
1
1
2
0
1
1
0
1
1
2
1
1
0
1
0
0
2
2
2
1
1
1
1
2
1
2
1
2
1
0
1
1
2
1
1
1
1
1
0
2
0
1
2
1
2
2
2
1
1
1
1
1
0
2
0
1
1
1
0
1
0
1
1
0
1
1
1
0
1
0
1
1
1
0
1
2
1
0
1
1
1
1
1
3
1
1
0
0
0
2
0
1
1
2
1
1
2
1
2
0
1
1
1
0
0
1
0
0
1
0
1
1
2
0
1
1
0
1
1
2
2
1
2
0
0
1
1
0
0
2
0
0
1
0
1
2
0
0
2
1
0
0
2
0
1
2
1
2
1
0
2
0
0
1
1
1
2
1
1
0
0
2
1
0
1
1
1
1
2
1
0
1
1
1
1
0
1
1
1
1
1
0
0
1
0
1
0
1
1
2
1
1
1
1
2
0
1
0
0
2
0
2
2
1
2
0
0
2
0
0
0
1
1
0
2
1
2
1
0
1
2
0
0
1
1
1
1
1
2
2
2
2
1
2
1
2
0
1
0
2
1
0
1
1
1
0
0
1
0
2
1
1
1
0
2
1
1
0
1
0
0
1
2
1
2
1
2
0
0
1
1
1
0
2
1
1
1
1
0
0
0
2
2
1
2
1
2
0
1
1
2
1
2
0
0
2
1
1
1
2
1
0
2
0
1
0
1
2
1
3
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
0
2
2
1
1
1
2
1
2
0
1
1
1
0
1
1
1
2
1
1
1
2
1
0
0
1
2
1
1
1
2
0
1
0
1
0
0
0
2
0
2
1
1
2
2
1
1
2
2
0
2
1
0
1
0
1
1
1
1
1
0
2
0
2
0
2
1
1
1
0
2
0
0
1
2
1
2
1
2
0
1
1
1
1
1
1
1
1
0
1
1
2
1
1
0
0
1
1
1
0
1
1
1
2
1
1
1
0
1
1
2
1
1
1
1
1
1
2
1
1
2
0
1
1
0
0
0
1
1
1
3
1
1
1
1
1
2
1
0
1
2
0
1
0
0
1
1
1
1
0
0
2
1
2
0
1
1
0
2
1
2
0
0
1
0
0
1
1
1
2
2
1
0
0
1
1
1
0
2
1
0
2
1
0
1
1
0
2
0
1
0
1
1
1
1
0
1
0
1
2
1
0
1
0
0
1
2
1
2
2
2
2
1
1
1
1
1
1
1
1
0
2
0
2
1
0
0
1
2
0
1
1
1
0
1
7
1
2
0
1
2
0
0
2
1
0
1
1
0
0
2
0
0
1
1
1
2
1
1
1
1
2
0
1
1
1
2
2
2
1
2
1
2
1
1
0
1
1
1
1
1
0
0
0
2
1
0
2
1
1
0
2
1
1
1
2
1
2
1
1
1
1
1
1
1
2
2
2
1
1
2
1
1
0
2
1
0
2
1
0
1
1
0
3
0
1
0
2
1
0
1
1
1
1
1
1
1
1
1
1
0
2
1
1
1
0
2
1
1
0
0
0
1
0
1
2
0
1
1
2
1
1
0
0
2
0
1
1
0
1
0
0
1
2
0
0
2
0
1
1
2
2
1
1
2
0
0
1
2
0
0
1
0
0
2
0
2
2
2
1
1
2
1
1
0
1
1
1
2
0
1
0
2
1
1
0
2
1
0
0
1
1
1
0
0
1
1
1
0
1
1
0
1
1
0
1
1
2
1
2
1
1
1
1
0
1
2
1
2
0
1
0
0
1
1
1
1
1
1
1
2
0
1
1
3
1
2
1
1
0
1
2
0
0
1
0
0
1
2
2
0
0
2
1
0
1
1
1
2
1
1
2
1
2
1
1
1
1
1
3
1
0
1
0
0
1
0
1
1
3
1
2
1
1
0
2
1
0
1
0
2
1
1
1
0
0
1
0
2
0
1
2
1
1
1
1
1
0
1
1
1
2
1
2
1
1
0
1
0
1
1
2
1
2
1
0
0
0
2
0
1
0
1
1
0
2
1
1
1
0
1
1
1
2
2
2
2
1
1
1
1
0
2
1
2
0
1
1
1
0
1
0
1
1
2
1
1
0
1
1
3
2
1
0
2
1
1
1
0
2
0
2
2
1
2
2
1
0
1
1
1
2
1
2
0
1
1
0
1
1
2
1
1
2
1
1
1
2
2
1
1
0
2
1
1
2
1
2
1
1
2
2
1
0
1
1
1
0
1
0
1
0
0
1
2
0
1
1
1
0
0
2
1
2
0
2
0
9
1
1
2
1
1
0
0
0
1
0
0
1
1
1
1
1
1
1
2
0
1
0
1
1
0
1
2
1
2
2
1
1
1
0
0
1
2
0
0
1
2
1
1
1
1
0
2
1
1
2
2
1
1
1
1
2
1
1
1
2
3
1
1
1
0
2
0
1
0
1
1
1
1
2
1
2
1
2
1
1
1
1
2
0
2
1
3
2
0
1
1
2
1
1
2
2
1
0
1
1
0
1
0
1
1
1
1
1
1
0
1
1
1
1
2
2
2
0
0
2
2
1
2
1
0
2
1
0
0
1
1
2
1
1
2
1
0
1
0
1
1
1
1
0
2
1
2
3
0
1
1
1
2
1
1
1
1
1
1
1
0
0
2
1
2
1
2
1
1
2
1
2
0
2
2
1
0
0
0
1
2
1
3
1
0
1
1
1
1
1
0
1
1
0
1
1
2
2
1
0
1
1
1
1
1
1
3
1
1
1
0
1
1
0
0
0
1
0
2
1
2
0
2
1
2
0
2
2
2
0
1
0
1
0
2
1
0
2
0
0
1
1
0
1
1
0
2
2
1
1
1
1
1
0
2
1
2
0
1
1
0
0
2
0
0
1
1
2
2
2
0
1
0
2
2
1
0
1
0
0
0
1
1
1
0
1
2
0
1
1
1
3
0
0
2
1
1
1
1
1
0
0
1
0
0
2
1
2
2
0
1
0
1
1
2
1
1
0
2
2
2
1
1
0
1
1
1
1
1
1
1
0
1
2
2
1
1
1
2
0
0
2
2
2
0
2
1
1
2
0
2
0
1
1
1
1
1
0
2
0
0
1
2
1
3
2
3
2
2
1
1
1
0
1
1
0
0
0
1
2
1
1
2
1
2
1
1
1
4
1
0
2
2
1
0
1
1
2
1
2
2
2
2
0
2
1
0
2
3
0
0
1
1
0
0
1
1
0
1
0
2
2
1
1
3
2
2
1
1
1
0
1
1
0
1
1
1
1
0
2
0
0
1
0
2
1
2
0
0
3
1
1
1
1
1
1
0
1
0
1
2
1
1
2
0
1
2
0
2
1
1
1
2
2
1
1
1
1
3
2
1
0
1
1
1
1
2
0
1
1
1
2
0
1
0
2
0
0
0
0
1
0
1
0
1
1
0
0
1
0
1
1
1
0
1
1
0
1
1
1
0
2
1
1
0
0
2
2
1
0
2
1
1
0
2
0
0
1
0
1
1
1
1
0
1
1
0
0
2
2
2
0
1
2
1
0
1
1
1
1
0
1
1
0
2
2
1
2
1
1
2
1
0
0
1
3
1
1
2
1
2
1
1
1
1
1
1
1
0
1
1
1
0
0
2
1
0
1
0
0
0
1
1
1
0
0
2
1
1
1
0
1
1
0
1
2
1
1
0
1
2
2
1
1
1
2
1
0
1
1
3
0
0
2
2
1
1
1
1
0
1
1
1
1
1
1
2
0
0
0
2
1
1
1
2
2
1
1
1
2
0
1
1
0
2
1
0
1
2
1
2
1
2
0
1
1
1
1
1
1
2
1
1
1
1
2
2
1
1
2
0
0
2
1
2
0
1
2
2
2
1
1
1
1
1
1
1
1
1
2
2
1
2
2
1
1
0
0
1
0
1
1
1
2
1
1
1
1
1
1
0
0
0
0
2
1
1
1
2
1
0
1
0
0
1
2
1
2
1
2
1
0
1
1
0
1
2
0
1
1
2
1
1
1
2
2
0
0
0
2
1
1
3
1
1
1
1
1
1
2
1
1
1
1
0
1
0
1
2
1
1
0
1
1
1
0
1
2
2
1
4
1
1
1
1
1
2
1
1
1
1
1
1
0
0
1
0
1
2
1
0
0
1
1
2
1
1
2
2
0
0
1
1
1
1
1
2
1
0
2
2
1
5
0
0
1
0
1
2
2
1
0
0
1
1
2
1
2
1
1
0
1
0
2
1
0
1
2
1
0
0
0
0
1
2
1
1
2
1
0
0
1
0
1
0
1
0
0
1
0
1
2
1
2
2
1
0
0
1
2
0
0
1
1
1
1
0
1
1
1
0
0
0
2
3
0
1
1
1
1
1
2
0
1
1
2
1
0
1
2
0
1
1
0
2
1
1
2
1
2
1
2
0
1
0
2
1
2
1
1
0
1
1
2
1
1
2
3
1
1
1
0
1
0
1
1
0
2
1
1
0
1
1
2
0
0
1
3
1
1
1
0
2
2
1
1
1
1
1
0
1
1
1
2
1
0
1
1
1
1
1
2
1
0
2
1
1
0
1
0
2
0
0
0
1
2
1
1
0
0
1
2
3
1
1
0
2
1
0
0
2
1
1
1
0
1
2
0
0
1
0
1
1
1
3
0
1
1
2
1
0
2
2
1
0
1
1
0
2
2
0
0
2
1
1
1
0
0
1
0
1
2
2
1
0
1
1
1
0
2
1
1
1
2
0
2
2
1
0
0
0
1
2
1
2
2
1
1
1
0
0
1
2
1
2
0
1
1
1
0
0
1
1
1
1
1
2
1
2
1
1
1
2
1
1
1
1
1
0
1
1
0
1
1
2
0
1
0
1
0
1
1
2
0
1
1
1
1
1
0
2
0
0
1
1
1
1
0
0
0
2
0
1
1
1
1
1
1
1
0
1
1
2
1
1
2
2
0
2
1
1
0
1
1
1
1
2
1
2
1
2
0
0
0
1
1
0
0
2
1
1
0
1
0
0
2
1
1
0
4
2
1
1
0
1
1
1
0
2
3
0
3
0
0
0
1
2
0
1
0
1
2
1
0
1
1
1
1
4
0
2
1
1
1
1
0
0
1
0
0
1
0
0
0
1
1
0
1
1
2
2
0
1
2
2
1
1
2
0
1
1
1
1
0
2
0
2
1
1
1
0
1
0
0
0
2
1
1
1
0
1
2
1
1
1
2
1
1
0
2
0
1
2
1
1
2
0
1
0
2
1
1
2
1
0
1
1
0
1
0
4
2
2
1
1
0
0
1
1
1
1
0
2
0
2
0
1
1
1
0
1
1
2
0
1
2
0
0
0
0
1
1
1
1
0
0
1
1
1
1
1
1
0
1
0
1
1
2
0
0
0
1
1
1
1
1
2
0
1
0
1
0
1
1
0
2
0
2
1
1
2
1
0
1
2
2
1
1
1
0
2
2
2
0
1
0
0
1
1
1
1
1
1
1
1
1
0
1
2
1
1
2
1
0
1
1
0
2
0
0
2
1
2
2
1
8
2
0
1
2
2
0
2
0
1
1
0
1
1
1
4
1
0
0
1
0
2
0
1
1
1
0
2
1
2
0
0
1
1
1
2
1
0
0
1
2
1
0
1
1
1
1
1
1
0
0
1
1
2
1
1
2
2
0
2
2
0
2
1
1
0
2
1
0
1
1
1
0
1
1
1
2
2
0
1
2
2
1
0
2
1
1
0
0
2
1
1
1
0
1
5
2
0
1
2
2
1
1
2
0
1
0
0
2
1
0
1
2
0
1
2
3
2
1
1
2
0
1
1
1
0
1
0
1
2
1
2
1
2
1
1
0
0
1
1
2
1
1
1
1
1
2
1
2
2
1
1
1
1
1
0
1
1
0
1
0
0
2
0
2
0
1
0
1
1
1
1
2
1
1
0
1
2
1
1
0
2
1
0
1
0
2
2
2
1
1
0
3
1
1
2
1
1
0
0
1
1
2
1
1
2
2
3
4
0
1
2
1
0
1
2
2
1
0
1
0
1
2
1
1
0
1
1
0
1
1
1
1
1
1
1
2
0
1
2
1
2
1
1
1
2
1
1
1
0
1
1
1
2
1
2
0
2
1
1
0
1
1
0
0
2
1
1
0
0
2
1
1
0
1
1
2
1
0
2
0
2
1
0
2
1
0
2
1
0
0
2
1
1
0
1
2
1
0
1
0
0
1
1
1
1
1
0
0
1
1
2
1
0
1
1
1
0
1
1
1
1
1
0
0
1
0
1
1
0
2
1
2
0
1
1
1
1
1
0
2
1
0
0
1
2
4
2
1
0
1
0
0
1
1
2
0
1
1
0
1
1
2
1
2
0
1
1
2
1
2
1
2
0
1
2
2
1
2
1
1
3
1
2
1
0
1
2
2
1
0
2
2
2
0
2
1
1
2
4
1
2
1
0
1
1
1
0
0
2
1
1
2
1
1
1
2
1
2
1
1
1
2
1
0
1
0
2
1
0
1
0
1
1
0
1
1
2
1
1
2
2
2
3
1
1
1
1
1
1
1
1
0
7
1
2
0
0
1
0
1
1
0
2
2
2
1
1
1
1
1
6
1
1
1
2
1
0
0
1
0
2
2
1
2
1
2
1
1
1
1
1
0
1
0
2
2
2
0
0
2
0
1
2
0
2
2
1
1
0
0
1
2
0
2
2
1
1
1
2
2
1
0
2
0
0
0
1
1
1
1
0
2
1
1
0
2
2
1
0
0
0
1
1
1
0
0
1
1
2
1
1
0
1
0
0
1
0
0
0
1
2
1
1
1
1
1
2
1
1
1
0
0
1
1
0
2
2
1
0
0
4
1
0
1
0
1
2
0
0
1
1
1
1
1
1
2
1
2
1
0
0
1
2
1
0
1
1
0
0
0
1
1
2
0
0
2
1
1
2
1
1
1
1
0
1
1
0
1
2
1
1
2
1
0
1
3
1
2
1
0
1
3
1
1
2
2
1
0
1
0
1
0
0
0
1
0
2
2
1
2
1
0
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
0
1
0
1
1
2
0
1
0
0
3
1
1
0
0
1
1
1
2
2
0
1
1
1
2
1
0
1
2
1
0
3
2
1
1
1
0
0
1
2
0
2
2
1
0
1
1
0
1
1
1
2
0
0
1
2
1
1
1
2
0
2
1
0
1
1
1
1
0
2
1
1
1
0
0
1
0
0
2
1
0
1
1
1
0
1
1
1
0
1
1
1
1
2
1
1
1
0
0
1
1
1
2
2
1
1
1
0
2
2
0
0
1
1
2
1
0
1
2
1
1
0
1
0
1
1
0
1
1
0
1
1
1
1
2
1
2
1
1
1
2
0
0
0
1
2
1
2
2
2
0
0
1
2
3
0
2
1
0
1
2
1
0
0
3
0
1
0
0
1
1
2
1
1
0
0
1
1
1
0
1
1
0
1
1
2
0
1
2
0
1
1
1
2
1
1
2
1
0
0
1
1
1
1
1
1
1
2
1
1
0
2
0
0
1
1
1
1
0
1
1
1
0
1
2
1
0
2
1
0
1
1
1
1
0
0
2
1
2
1
1
1
2
1
5
1
0
1
0
2
1
2
0
0
0
1
1
1
1
0
1
1
1
2
1
2
1
1
1
1
1
2
1
1
0
0
1
1
2
0
1
0
2
1
1
1
1
1
1
2
1
1
1
1
1
1
1
0
1
1
2
1
1
1
0
1
2
0
2
0
0
2
1
2
2
1
2
0
0
1
0
0
1
1
2
0
1
2
0
1
0
2
2
1
0
0
1
1
0
1
1
1
1
0
1
1
0
0
1
0
1
1
1
2
1
0
1
1
1
3
1
2
0
0
0
1
0
0
0
1
0
1
1
0
2
1
1
1
2
0
0
2
1
0
1
1
2
2
2
1
1
0
1
1
1
0
1
1
2
1
1
2
1
1
1
0
0
3
0
1
1
0
1
1
0
1
1
1
1
1
1
2
0
1
2
0
1
0
0
1
2
1
1
1
1
1
1
1
0
1
1
1
2
1
2
1
1
1
1
2
1
1
1
1
2
1
1
0
1
2
1
1
1
1
1
2
1
1
0
0
0
0
1
1
2
1
1
1
2
1
0
2
2
1
0
2
1
1
1
0
2
0
0
0
1
1
1
1
2
2
2
1
0
0
0
0
1
2
0
1
2
2
1
1
1
2
1
0
1
1
1
0
2
1
2
1
2
1
1
1
1
1
2
1
1
0
0
1
3
0
2
2
2
1
1
1
1
0
2
2
0
1
1
0
0
1
1
1
0
0
1
1
0
1
1
0
0
1
0
0
2
1
1
0
1
1
2
1
0
1
1
1
2
0
1
1
0
1
1
0
2
0
2
1
1
0
2
1
2
0
1
1
2
0
2
1
1
1
2
0
1
0
0
1
2
0
0
1
0
1
1
1
1
2
1
1
2
0
1
0
2
1
1
1
0
0
1
1
1
0
2
2
2
1
1
0
1
1
1
0
1
2
1
2
2
1
1
2
0
0
2
0
1
1
1
0
1
1
1
0
1
0
1
1
1
2
0
0
1
1
1
0
0
1
1
1
1
1
2
2
2
1
1
0
2
2
1
0
1
1
0
1
2
1
0
2
1
1
2
1
2
1
0
1
2
1
0
1
0
2
0
2
2
1
0
1
0
1
0
1
0
1
1
1
1
1
0
1
2
1
0
1
0
0
5
1
3
2
1
0
0
1
0
1
1
0
2
0
1
2
0
1
1
1
1
0
1
1
1
1
1
1
0
0
0
1
1
0
1
1
0
1
1
1
1
0
2
1
2
1
2
0
0
0
1
1
1
1
1
1
2
2
0
0
2
1
2
1
0
1
0
2
0
1
0
1
1
0
1
1
1
2
1
1
2
2
2
0
2
0
0
2
1
2
1
0
2
0
1
2
1
1
2
1
1
0
0
0
0
0
1
1
1
1
3
0
1
2
1
2
0
1
1
0
1
1
1
0
1
2
2
0
0
1
0
1
1
0
1
0
1
1
2
3
1
2
0
1
1
1
0
1
0
0
0
1
1
1
2
1
0
1
1
1
0
0
1
1
0
2
0
0
0
2
2
2
0
0
2
1
1
1
1
0
3
0
2
1
1
1
1
1
1
0
1
1
2
1
0
0
0
0
2
2
2
0
1
1
1
0
0
0
1
2
0
1
0
0
0
2
1
2
0
0
2
0
1
1
1
0
2
0
0
1
0
1
0
0
1
1
1
1
0
0
2
1
0
2
0
1
1
0
1
1
4
1
1
1
1
1
2
1
1
0
1
4
2
2
0
1
0
1
1
1
1
2
1
2
1
1
0
1
2
0
1
1
1
0
2
0
2
0
2
0
0
1
1
1
2
1
1
3
1
2
1
2
0
2
1
2
1
1
1
0
0
0
2
0
1
2
1
2
0
0
1
1
1
1
2
1
0
1
1
0
1
1
2
1
1
2
1
0
0
0
2
0
0
0
1
2
0
1
0
0
2
2
2
1
1
1
1
1
1
1
0
0
1
0
1
0
2
1
1
1
2
1
1
4
0
2
0
0
0
1
0
2
2
1
0
1
0
0
1
0
1
1
0
1
2
2
1
1
1
2
0
1
1
0
1
2
0
1
0
1
1
1
1
2
1
1
0
1
2
0
1
0
0
0
1
0
1
1
1
1
1
1
1
1
1
1
0
2
1
0
1
0
1
1
2
1
1
0
0
1
1
2
0
0
0
1
0
1
1
0
1
1
1
0
1
0
1
1
1
2
1
0
0
1
2
0
2
0
1
0
1
1
0
2
3
0
2
0
1
0
1
0
0
1
0
2
1
1
2
1
0
2
0
2
2
1
1
1
2
1
0
1
0
2
0
1
0
0
1
2
1
2
0
1
2
0
0
1
0
1
0
0
1
2
0
0
2
1
1
1
1
0
0
2
2
1
1
1
2
0
1
1
2
1
0
1
0
1
1
2
3
0
2
0
2
1
2
1
1
1
1
2
0
1
1
1
4
0
1
1
0
1
0
2
1
2
3
2
1
1
0
2
0
0
0
1
1
1
1
2
0
1
1
1
2
1
1
1
2
0
2
1
1
1
2
2
1
0
0
1
1
1
2
2
1
1
2
1
1
1
0
1
1
2
1
1
1
0
1
1
2
0
1
1
0
0
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
0
0
1
2
1
1
1
1
1
0
1
0
1
0
0
0
2
1
0
1
1
2
2
1
1
1
0
1
0
0
1
2
3
1
2
2
0
1
1
2
1
0
1
1
1
1
1
0
1
2
2
0
1
2
0
1
2
1
1
1
0
1
0
1
0
0
1
2
0
1
0
2
1
1
2
0
1
2
0
4
0
0
1
1
1
1
0
2
0
1
1
1
1
0
0
2
1
3
3
0
2
2
0
2
1
1
2
0
1
0
0
1
2
0
1
2
1
1
0
1
1
0
1
1
1
2
1
1
1
1
1
1
1
1
1
3
1
2
1
1
1
1
0
1
0
1
2
0
1
1
1
0
0
3
1
2
2
2
1
1
0
1
2
1
1
1
1
1
2
1
1
1
0
1
0
1
1
1
1
2
1
2
1
1
0
2
1
1
2
1
0
1
0
1
0
1
1
1
1
0
2
1
1
2
0
0
1
1
1
2
1
1
2
1
2
1
0
1
2
1
2
0
0
1
1
0
2
0
1
1
0
0
0
1
1
0
2
0
1
1
0
2
2
0
1
1
0
2
2
2
0
1
1
0
0
0
1
0
1
1
0
2
1
2
2
2
0
1
2
1
0
1
0
1
1
1
2
0
1
1
2
1
1
1
1
2
1
1
0
1
1
0
1
1
1
1
0
2
2
1
1
0
0
1
1
2
1
0
0
1
1
2
0
2
1
1
1
2
2
1
2
2
1
1
0
1
0
0
1
1
1
0
1
1
0
2
1
1
0
2
1
1
0
1
0
1
2
1
1
1
1
1
2
0
1
1
0
0
2
1
2
2
1
2
2
1
2
1
2
2
1
0
2
1
1
1
1
1
0
0
1
1
0
1
2
1
1
1
1
1
2
1
0
1
1
0
1
0
0
1
1
0
0
1
1
1
1
0
1
1
1
1
2
1
2
1
2
0
0
1
1
2
1
1
1
1
2
1
1
2
0
1
0
1
1
0
2
2
1
2
2
2
1
1
1
2
1
0
0
1
1
1
1
1
0
0
1
1
2
2
1
0
0
1
0
2
1
1
1
1
2
1
1
1
1
0
2
0
1
1
1
0
0
1
1
1
1
1
2
1
0
1
2
1
1
0
1
1
2
1
2
1
2
2
1
1
0
1
1
1
1
2
3
1
0
0
0
1
0
1
1
2
0
1
2
1
2
0
2
1
0
1
1
1
1
1
1
1
1
1
1
2
4
2
1
0
1
1
2
1
0
0
1
0
1
3
1
0
2
0
1
1
1
1
1
1
2
2
2
1
1
0
2
0
1
0
0
0
1
2
2
2
0
1
1
1
1
1
1
1
1
1
1
1
1
1
2
3
2
1
0
1
0
0
2
1
1
1
1
1
2
1
1
1
3
1
0
0
1
1
0
1
2
1
1
0
0
2
1
2
2
0
1
1
0
2
2
1
1
1
0
1
0
0
1
2
0
2
1
0
0
0
1
1
0
0
1
2
0
2
1
1
1
0
0
2
1
1
0
1
2
0
1
0
1
1
1
1
1
1
1
1
2
2
1
0
2
2
0
2
1
1
2
2
2
2
0
1
1
2
1
1
0
2
0
1
1
2
0
1
0
1
2
1
0
2
1
1
1
0
0
0
2
2
2
1
2
1
0
2
1
1
0
2
1
0
0
1
1
0
1
2
1
1
2
1
0
1
2
2
1
0
0
1
0
0
1
0
0
1
1
0
2
2
1
0
1
2
2
1
1
1
1
1
1
1
0
2
1
1
2
2
1
0
1
1
1
2
5
1
1
2
2
1
1
3
1
1
2
0
1
1
1
2
2
1
0
1
4
1
2
1
1
1
2
3
0
1
1
1
0
1
1
1
0
2
1
1
1
3
3
1
3
1
1
1
0
1
2
1
1
0
1
2
1
0
2
2
2
1
0
2
1
1
1
1
2
0
1
1
1
1
1
1
2
1
2
1
2
1
2
1
2
0
0
1
1
1
1
1
1
1
0
1
2
1
1
3
1
1
1
0
2
2
1
2
1
1
1
1
1
1
0
2
0
1
1
2
0
1
1
3
2
1
0
1
0
1
1
0
2
0
2
1
0
0
1
1
2
2
0
2
0
1
0
1
2
0
0
0
0
1
0
2
2
0
0
0
2
1
1
2
0
3
2
1
2
2
1
1
1
2
1
0
2
0
2
1
2
2
1
1
1
1
2
2
0
1
2
1
1
0
0
2
2
0
1
1
0
2
1
1
1
1
1
3
2
1
2
3
1
1
2
1
1
0
1
1
1
2
1
0
1
3
1
0
1
1
0
1
2
0
1
0
1
0
2
1
0
2
1
0
1
2
2
1
0
1
2
2
1
2
0
0
1
2
1
0
0
2
1
1
0
1
2
0
1
2
1
2
1
1
1
2
0
1
1
1
1
2
1
1
0
1
0
2
0
1
0
0
0
1
2
2
0
0
1
1
2
1
1
1
1
0
0
2
1
1
1
0
1
1
1
2
0
1
1
1
2
1
1
1
2
1
1
0
0
0
1
1
2
0
0
1
1
2
2
0
0
2
1
0
2
2
2
1
1
1
1
0
0
1
1
2
1
1
2
1
1
1
1
0
1
1
1
0
0
1
0
1
1
1
2
0
1
2
1
1
2
2
0
1
2
1
1
2
4
1
0
2
1
1
1
1
1
1
1
1
2
2
2
0
1
0
2
1
0
1
1
1
1
0
0
1
2
2
0
0
1
2
0
2
0
0
2
2
1
0
1
1
1
1
1
0
1
1
1
0
1
1
1
1
2
1
2
0
1
1
0
1
2
2
1
1
2
1
1
1
0
1
1
2
1
0
2
1
0
2
1
1
2
0
1
0
2
1
0
0
0
1
1
2
0
0
0
1
1
1
1
2
0
1
2
2
1
1
2
1
2
1
1
0
1
0
2
1
1
1
0
1
0
2
1
2
1
1
0
1
1
1
1
1
0
0
0
1
1
0
1
1
0
1
2
0
2
1
1
1
1
1
1
1
2
2
1
1
2
1
2
2
2
2
1
2
1
2
1
0
2
0
0
2
2
0
1
1
3
1
0
1
1
2
1
0
2
0
1
2
1
1
2
0
0
0
1
1
1
1
0
0
2
1
0
2
1
1
1
1
1
0
1
0
0
1
2
2
2
2
1
1
0
1
2
0
2
1
2
1
1
1
1
1
1
2
1
1
0
1
1
0
1
0
0
2
0
2
2
1
2
1
1
1
2
1
0
0
1
2
1
2
0
2
0
2
1
1
1
3
2
1
1
1
0
0
1
0
1
1
2
2
1
0
1
2
1
1
2
1
0
1
1
0
1
2
0
1
1
0
0
2
1
3
1
1
1
1
1
1
1
2
1
0
2
0
0
1
2
0
1
2
2
1
2
1
1
1
1
1
0
1
2
1
1
1
1
1
2
0
1
2
1
1
2
0
1
1
2
1
2
1
0
2
1
2
1
2
1
0
0
1
1
3
2
2
1
1
1
2
1
1
1
0
1
1
2
1
1
1
1
2
1
1
0
0
1
0
2
1
1
0
0
0
1
1
1
2
2
1
1
0
0
0
1
1
0
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
0
2
1
1
1
1
1
1
1
1
1
1
2
2
2
1
0
0
2
0
0
1
1
2
3
1
1
1
1
1
1
0
1
1
0
1
1
1
1
1
1
1
2
1
0
2
1
1
0
2
0
0
1
2
0
0
0
0
2
1
1
1
2
1
2
2
1
0
0
1
1
2
1
1
1
1
1
2
1
1
1
0
2
1
1
1
1
1
1
0
2
1
1
1
1
2
1
1
2
0
0
1
2
2
1
0
1
1
1
1
0
1
1
2
0
1
1
2
1
0
2
0
0
0
1
0
2
0
0
0
1
1
1
1
1
1
0
1
2
1
2
0
1
1
0
1
0
1
1
2
1
1
1
1
0
1
1
1
1
2
0
1
0
1
0
1
1
3
1
2
1
2
1
1
0
1
0
1
1
1
0
1
1
0
1
1
2
2
0
1
0
1
0
2
0
0
2
1
3
1
2
1
2
1
1
1
1
1
1
0
1
1
1
2
0
1
1
0
1
2
1
1
2
1
0
1
0
1
1
1
1
0
1
1
2
1
0
2
2
1
2
0
1
0
1
2
2
1
0
1
0
1
1
0
1
0
3
1
2
1
1
1
1
0
1
1
1
0
1
2
1
1
1
1
0
1
1
2
1
1
1
1
1
1
1
0
0
0
2
1
1
0
0
1
0
1
1
1
1
1
1
1
1
1
2
0
0
3
2
1
1
0
0
1
1
0
1
0
0
4
0
1
3
1
1
1
2
2
1
1
1
0
1
0
1
0
1
1
1
2
0
1
1
2
1
0
0
1
0
1
1
0
2
0
2
2
1
2
0
1
0
1
0
1
1
0
1
1
0
2
0
0
2
0
3
1
0
2
1
1
2
1
1
1
1
1
0
1
2
2
1
1
0
0
0
1
1
2
2
1
1
2
1
2
2
0
1
1
1
1
1
1
0
1
1
0
2
1
2
1
1
1
0
1
1
1
0
1
1
1
1
0
0
1
1
0
2
1
1
0
1
0
0
0
1
1
1
1
1
1
1
1
2
0
0
1
1
0
1
0
2
2
2
0
0
2
0
2
0
1
0
1
2
1
1
0
1
2
0
1
0
0
2
0
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
3
1
1
2
1
1
1
0
1
2
0
1
2
2
2
1
0
1
0
1
1
1
2
0
1
0
0
2
1
1
2
2
1
0
1
1
2
0
1
1
2
1
1
1
2
1
1
1
1
1
0
0
2
1
1
1
2
1
1
1
0
1
2
2
0
0
0
0
1
0
2
1
1
2
1
0
0
1
1
1
1
0
2
0
2
0
1
0
2
1
3
5
1
1
2
1
0
1
2
1
0
1
2
1
0
1
0
1
0
1
1
1
2
1
1
0
1
2
0
1
2
1
1
1
1
0
1
1
0
1
1
1
1
2
1
1
1
1
1
1
1
1
1
0
0
2
2
0
0
2
0
1
0
1
0
1
1
2
0
1
1
1
2
2
0
1
1
2
2
0
5
1
2
1
1
0
1
0
2
1
1
2
1
0
2
2
1
1
0
0
1
2
1
1
1
1
1
1
2
1
0
2
1
1
1
1
2
2
1
0
0
1
1
1
0
1
2
0
0
2
1
1
1
2
1
1
1
1
0
1
2
1
2
1
1
2
1
2
3
1
1
2
1
1
1
0
1
1
1
0
1
0
0
0
1
1
2
0
1
2
1
1
1
0
1
1
1
0
2
1
2
1
0
2
1
0
2
2
0
2
1
0
1
0
1
1
0
1
2
2
2
0
1
0
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
0
2
1
1
0
0
0
2
2
2
0
0
1
0
1
1
1
2
1
2
2
0
2
1
0
1
1
0
1
1
0
1
3
1
0
1
1
2
1
0
1
2
2
0
1
1
0
1
1
1
2
1
0
2
1
1
0
0
1
0
1
1
0
1
0
2
0
0
1
2
0
2
0
1
1
1
0
2
0
0
1
2
2
1
1
1
1
1
2
2
1
0
1
1
1
0
0
2
0
2
1
2
1
1
0
1
2
1
0
1
1
1
1
1
0
0
2
1
1
1
1
2
0
1
2
1
1
0
0
1
1
1
0
0
1
2
2
0
0
1
0
0
0
0
0
0
1
1
0
1
2
0
2
0
1
0
2
2
0
0
1
0
1
0
1
1
0
2
1
0
1
1
1
1
2
0
1
0
0
1
1
1
0
2
1
2
0
0
1
1
0
1
1
0
1
1
3
1
0
1
2
1
0
1
1
1
1
2
1
1
0
2
1
1
1
2
0
2
1
1
0
2
0
1
2
0
1
0
1
1
2
1
1
1
1
0
2
2
0
2
1
1
0
0
1
1
2
2
1
1
0
0
0
0
1
0
0
1
1
0
1
2
2
0
0
1
1
1
1
0
1
1
3
0
1
1
0
1
0
2
1
0
1
0
2
1
2
2
1
1
1
2
0
0
1
1
1
0
0
2
1
1
1
1
2
0
1
0
1
0
1
0
2
0
1
2
0
2
0
1
1
1
1
1
1
2
2
0
2
1
0
2
0
1
2
1
1
1
0
1
1
0
1
2
1
0
0
1
1
0
1
1
0
0
0
1
0
1
1
0
1
0
1
1
0
0
1
1
0
1
1
0
0
0
1
0
2
2
1
1
1
0
0
2
2
2
1
0
0
0
1
1
2
1
1
1
1
1
1
1
1
1
1
0
0
2
2
1
1
1
3
1
1
1
0
1
1
1
2
1
1
1
1
0
0
2
1
0
0
1
1
1
2
2
2
1
1
0
2
1
2
2
1
0
0
0
0
1
1
0
1
1
2
0
1
1
0
1
1
1
1
1
1
1
2
2
1
0
1
1
0
1
1
2
1
1
1
0
1
1
2
1
2
2
0
0
1
2
0
1
0
1
1
1
1
0
2
0
1
1
3
1
0
2
1
1
2
1
2
1
1
0
0
0
2
1
1
2
1
0
1
2
1
2
1
2
1
2
2
2
1
1
0
0
1
1
1
2
2
1
1
1
2
1
1
2
2
0
2
1
1
2
2
1
0
2
0
2
2
0
2
1
1
2
1
2
2
1
0
1
0
0
2
1
2
1
0
2
2
1
2
1
2
1
0
2
1
2
0
0
1
1
1
1
1
0
0
1
1
0
1
1
1
0
1
2
0
1
0
1
0
0
1
1
1
1
2
0
1
1
1
0
1
1
2
0
1
2
0
1
2
1
2
0
0
0
2
1
2
1
2
0
1
0
2
1
1
1
2
0
1
0
1
0
1
0
2
2
1
1
2
0
1
1
1
0
1
0
1
2
0
1
1
1
1
1
0
2
2
1
1
2
0
1
2
1
0
1
0
1
0
1
0
1
0
2
2
2
0
2
0
0
1
2
1
1
0
1
1
1
2
0
0
1
1
0
2
1
2
1
1
2
1
1
2
0
1
1
1
2
1
1
0
0
1
2
2
1
1
0
1
1
1
0
0
2
1
1
0
1
0
1
1
2
2
1
0
1
0
0
1
1
2
0
1
2
1
0
1
1
0
1
1
0
1
3
1
2
0
2
1
2
0
0
2
2
0
2
1
1
0
2
2
1
1
1
0
2
2
1
1
1
1
1
2
2
2
1
0
1
1
1
0
0
1
1
2
0
2
0
1
0
0
0
1
1
2
2
2
2
1
1
1
0
1
0
0
1
2
2
1
2
0
0
0
4
0
1
0
2
4
1
0
2
0
1
1
2
2
1
1
2
1
1
2
0
0
0
0
1
1
2
0
2
1
1
1
1
0
1
2
2
2
2
0
1
2
1
2
1
2
1
1
1
1
0
2
1
0
3
0
2
1
2
2
1
1
0
1
1
1
0
2
1
1
0
0
1
0
1
1
2
2
2
0
1
2
1
0
1
1
1
1
1
1
1
1
2
1
1
1
1
0
1
0
1
0
1
2
2
1
1
2
0
2
0
0
1
1
0
0
1
0
0
1
0
1
2
0
1
0
2
1
1
1
1
1
0
0
0
1
1
1
1
2
1
1
1
1
2
3
1
0
1
1
0
1
0
1
1
1
2
0
1
1
1
0
2
1
0
1
2
0
1
2
0
2
2
1
0
1
1
0
2
1
1
0
1
0
1
2
1
1
0
1
1
1
1
2
2
1
1
1
0
1
1
2
1
1
1
1
1
0
1
2
1
2
2
0
1
0
1
2
2
0
0
2
1
2
1
1
0
1
1
2
2
1
1
0
2
2
0
1
1
1
0
1
1
2
0
0
2
0
2
2
1
0
1
1
2
1
1
1
1
1
1
2
1
0
1
0
2
0
1
0
1
2
1
1
0
1
2
2
0
0
0
1
1
0
0
2
1
1
1
0
0
1
1
1
1
2
1
2
0
1
0
0
0
1
4
1
2
1
1
3
0
1
2
2
2
1
1
2
2
2
1
0
1
2
1
1
1
1
0
0
1
0
1
0
2
1
1
0
0
0
0
0
1
1
1
0
0
0
1
2
1
0
1
1
0
0
2
2
2
0
1
1
2
0
2
1
1
2
1
1
1
0
1
1
0
0
2
2
2
2
1
1
1
0
2
2
2
1
3
2
1
2
2
2
1
1
1
0
1
1
2
1
2
0
2
1
0
1
1
0
1
2
0
0
1
1
1
1
1
1
3
1
0
0
2
2
0
1
1
1
1
2
1
2
2
1
1
1
0
1
1
0
1
1
2
2
0
2
1
0
0
2
0
0
0
1
0
1
1
0
1
0
1
2
1
1
1
1
1
0
1
2
2
0
1
2
0
0
2
0
1
1
0
1
0
1
1
2
1
1
1
1
1
1
0
1
1
1
0
1
2
2
0
1
1
1
2
1
1
0
1
1
1
1
5
0
0
1
2
1
2
1
1
2
1
1
0
1
1
0
0
0
1
0
1
0
0
1
2
1
1
1
2
1
2
1
2
1
1
0
1
1
0
1
0
1
1
2
1
1
0
1
1
1
1
1
0
1
0
0
2
1
0
1
1
1
1
1
1
0
2
1
1
0
0
1
1
0
1
1
1
2
2
2
1
1
1
0
1
1
2
1
0
1
3
2
2
0
1
1
0
1
1
0
1
0
1
0
1
1
1
1
1
0
0
1
0
1
0
2
2
2
2
2
2
2
0
0
1
1
1
0
0
1
0
1
1
1
1
1
0
1
2
0
1
1
0
1
1
1
1
2
2
1
0
2
1
1
1
2
0
1
1
2
2
2
1
1
0
1
1
0
2
1
1
2
1
0
0
0
0
0
2
1
1
0
0
1
2
2
1
1
1
1
1
2
2
1
0
0
2
1
1
1
11
2
1
2
1
0
1
0
0
2
1
2
1
1
1
1
2
1
1
1
0
1
0
1
0
0
1
0
2
2
2
1
0
1
0
1
2
1
0
3
1
0
1
0
2
2
0
3
1
1
1
1
1
1
2
0
2
2
1
0
1
2
0
1
0
1
2
1
0
0
2
0
1
0
0
1
0
0
1
1
1
1
2
1
1
0
1
2
0
1
2
0
1
1
1
2
1
1
2
1
1
1
1
0
1
2
2
2
1
1
2
1
0
2
1
1
2
1
2
1
1
0
1
0
2
1
1
1
1
2
1
2
0
1
0
2
1
1
1
0
3
0
2
1
0
1
1
0
1
1
2
1
1
1
0
1
2
0
1
0
1
1
0
1
0
0
1
0
1
1
2
1
1
1
1
0
0
0
1
2
0
0
0
2
1
1
0
1
1
1
0
2
1
1
1
1
2
1
0
2
1
2
1
0
0
1
2
0
0
0
1
1
0
3
1
2
0
1
1
1
1
2
0
2
1
1
1
0
1
0
2
0
1
2
3
1
1
1
1
1
0
1
1
1
2
0
0
2
1
0
2
3
1
1
1
2
1
0
1
2
0
0
1
2
1
1
2
1
1
0
2
0
0
1
1
1
2
2
2
1
1
1
0
1
2
2
1
0
1
2
1
1
1
2
1
2
1
0
1
1
0
1
0
1
1
0
1
1
1
2
2
0
2
1
0
0
4
0
1
1
1
2
2
1
1
1
0
1
1
2
1
2
1
1
1
0
1
1
1
2
1
0
1
0
1
1
1
0
2
2
0
1
2
2
2
2
0
1
0
0
0
1
1
1
0
1
1
1
2
2
2
1
1
1
0
1
1
1
2
0
2
1
2
1
1
0
1
1
1
2
0
1
1
0
0
0
1
2
0
2
1
0
1
1
1
1
1
0
1
0
2
0
0
2
1
1
2
1
0
0
1
0
0
1
0
1
1
1
2
0
1
0
1
1
2
0
1
1
3
0
2
1
0
0
2
1
0
0
2
1
1
5
2
1
2
1
0
1
0
1
1
1
0
1
0
0
2
1
1
1
1
1
1
1
2
2
1
1
1
2
0
2
1
0
1
1
1
2
1
0
1
2
3
1
2
1
0
1
0
1
1
0
2
1
2
1
1
0
2
0
1
2
0
1
0
1
5
2
1
2
1
1
1
0
1
1
1
1
1
1
1
1
1
1
0
1
2
0
1
2
0
2
0
0
2
1
2
2
1
0
1
1
1
1
0
1
1
1
1
1
0
1
0
0
1
0
0
1
1
4
1
0
1
2
2
0
1
1
1
2
0
0
2
2
1
1
0
1
1
2
1
0
1
1
2
1
0
2
1
1
0
1
2
0
2
1
0
2
1
2
1
1
0
0
2
1
1
1
2
1
1
0
1
1
1
0
2
1
2
1
1
2
1
1
1
0
0
1
1
1
0
1
1
2
1
1
2
1
1
1
0
1
0
1
0
1
0
0
1
1
0
0
1
1
2
2
1
1
1
1
2
0
1
0
1
2
1
1
1
1
0
0
1
2
0
1
1
2
1
0
2
1
0
1
2
1
2
1
2
0
1
1
2
0
1
1
1
2
1
0
1
0
1
1
1
3
1
0
1
1
1
1
1
1
0
0
1
1
2
1
1
1
2
2
1
1
0
1
2
0
1
1
2
1
2
1
1
0
0
1
2
1
0
1
0
2
1
1
1
2
1
0
2
1
1
0
1
0
0
1
2
0
2
1
1
3
1
0
1
0
1
0
1
0
2
2
1
1
1
1
2
2
2
2
1
2
1
1
2
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
0
1
1
1
2
2
0
0
1
2
1
2
0
0
1
1
1
1
1
2
0
1
1
2
0
1
2
2
0
0
1
1
2
1
2
0
1
0
1
3
1
2
2
2
2
0
1
1
1
0
1
1
0
1
0
0
1
1
0
1
0
0
1
0
0
2
1
0
1
1
1
1
1
0
2
0
0
2
1
1
2
0
2
1
2
1
1
1
1
0
0
1
1
0
2
1
2
2
1
1
1
0
1
1
1
0
1
1
0
1
1
0
0
1
3
1
1
2
1
0
1
1
2
0
1
1
2
2
0
0
0
1
0
1
0
1
0
1
1
1
2
0
1
2
1
1
1
1
0
0
1
1
0
1
0
1
1
2
2
3
0
0
0
1
1
1
1
0
1
1
1
1
1
0
0
0
1
0
1
1
1
2
2
1
1
2
3
1
1
0
0
0
1
2
2
0
1
1
1
2
1
1
1
0
1
1
2
1
1
1
1
0
1
1
1
1
0
1
2
1
1
0
0
1
1
1
1
1
1
2
1
1
0
0
1
0
2
2
1
0
1
0
1
0
1
1
0
2
1
0
1
0
1
1
1
1
2
0
2
2
2
1
0
1
2
2
1
0
0
1
1
0
2
1
1
1
1
1
0
0
1
1
1
0
0
1
0
1
1
1
0
1
2
1
1
0
1
0
2
1
1
1
1
0
1
2
0
0
0
2
1
2
2
0
1
2
1
2
1
1
2
1
0
1
2
1
1
0
0
1
1
1
1
2
1
1
1
1
1
2
0
2
1
1
1
0
0
1
2
2
1
1
2
1
0
2
0
1
0
1
1
0
1
1
1
0
0
14
2
2
2
1
1
0
0
1
1
0
0
1
2
1
1
2
0
1
0
2
1
0
0
1
1
1
0
1
1
2
0
1
1
1
1
2
0
2
2
1
2
1
2
1
1
2
2
0
0
1
0
0
1
0
1
2
1
0
0
0
1
1
1
2
0
2
0
0
0
0
1
0
1
1
0
0
1
0
0
1
1
1
1
1
1
2
1
1
2
2
1
0
2
1
0
2
1
1
0
1
0
1
1
1
1
0
1
2
1
2
1
2
0
1
1
0
1
0
2
1
1
0
1
1
1
2
1
0
1
1
1
0
2
1
1
1
0
2
0
1
1
2
0
1
1
1
2
2
0
1
1
0
2
1
1
2
0
1
0
1
1
1
1
2
2
0
0
1
0
0
0
2
1
2
0
3
1
1
2
0
0
2
2
0
1
0
1
2
1
1
1
0
1
1
2
1
0
2
0
0
1
2
1
1
0
1
1
0
0
1
2
1
2
1
1
1
3
2
1
1
1
0
2
1
0
1
1
1
0
1
1
1
2
0
1
0
1
1
2
2
1
1
1
1
0
0
1
2
1
1
1
2
2
1
1
1
1
0
0
0
2
0
0
0
0
1
1
0
0
0
2
1
1
0
0
0
0
1
1
1
4
1
1
0
2
1
0
1
1
1
1
1
1
1
1
0
1
0
0
1
2
0
1
1
1
1
2
1
0
2
1
0
0
1
1
1
1
1
1
0
0
0
0
1
1
1
2
0
1
1
1
1
2
1
2
1
0
0
1
2
1
1
0
0
2
2
2
1
0
0
1
1
1
0
1
2
2
1
1
1
1
2
1
1
1
1
1
1
0
0
0
0
1
0
1
2
0
1
0
2
1
1
1
0
1
2
2
2
0
2
0
0
1
1
1
2
2
1
2
0
1
1
2
0
2
2
2
2
2
0
1
1
0
2
1
1
0
2
1
1
1
1
2
0
0
1
0
1
0
1
1
0
1
1
2
1
2
0
1
1
1
0
1
1
1
1
0
0
2
1
1
1
1
1
1
0
2
1
1
1
1
1
1
1
0
0
1
1
1
2
1
0
1
0
1
1
1
2
1
1
1
1
2
2
0
2
1
1
1
0
0
0
1
1
1
0
1
0
2
1
1
2
1
0
1
1
0
0
1
1
1
1
1
1
1
1
1
1
2
0
1
2
1
1
1
1
1
1
2
2
1
1
0
2
2
1
2
1
2
0
1
2
1
0
2
1
1
1
1
1
1
0
1
1
0
2
1
0
1
1
1
0
1
1
0
0
1
0
0
1
0
1
0
1
0
1
1
1
1
1
2
1
0
1
1
0
1
0
2
1
0
0
1
1
0
0
1
3
2
2
1
1
3
1
2
1
1
1
1
0
1
2
1
0
1
0
1
2
1
1
1
1
0
0
1
1
1
0
1
0
1
1
1
2
1
1
1
1
2
2
1
1
1
2
1
5
0
0
0
1
0
1
0
1
1
0
1
2
1
2
1
0
0
1
2
0
0
0
0
1
2
0
0
1
1
2
2
1
1
1
2
1
0
1
2
1
1
2
0
0
1
1
2
2
1
1
1
1
1
2
0
0
1
2
1
1
2
2
1
1
0
1
1
0
0
3
0
2
1
1
0
1
1
1
1
0
1
0
1
1
1
0
0
0
2
1
1
2
0
2
1
2
1
1
1
0
2
0
0
0
2
0
1
0
0
2
1
0
1
0
2
1
1
1
0
1
1
1
2
0
1
0
1
1
1
1
2
1
2
0
0
1
2
0
2
1
2
0
0
0
0
2
0
0
0
0
1
1
2
0
1
2
0
0
1
1
0
2
0
0
0
1
2
2
1
1
2
0
1
1
2
1
1
1
0
0
1
2
1
0
2
0
1
1
1
1
0
1
1
0
1
0
1
0
0
2
1
1
1
0
0
1
1
0
1
1
1
1
1
2
2
1
0
1
0
0
1
1
1
1
0
0
1
1
0
0
1
2
1
1
1
2
0
1
1
0
1
1
0
2
1
0
2
1
1
0
2
2
1
2
0
1
0
0
1
1
0
2
1
2
0
0
1
0
2
1
1
0
1
2
2
2
1
2
1
2
1
0
1
1
0
1
0
0
1
0
1
1
2
0
0
0
1
1
1
2
0
2
1
2
1
2
2
1
1
1
1
1
0
0
1
2
0
0
1
0
2
1
2
1
1
0
1
0
1
1
1
0
1
1
2
1
2
1
2
0
1
2
0
0
2
1
1
1
1
1
1
1
0
2
1
2
0
1
3
1
1
1
0
1
1
1
2
0
1
0
0
0
2
0
2
1
0
0
2
2
1
1
1
2
0
1
1
1
1
1
0
1
1
2
1
2
0
0
0
1
0
1
0
1
2
1
1
0
1
1
1
0
1
1
1
1
1
2
1
1
3
2
1
1
2
2
1
1
2
1
1
0
0
2
1
1
2
1
1
1
2
1
0
1
2
0
0
2
2
2
1
1
1
0
1
0
2
1
2
1
1
0
1
0
2
0
0
1
0
2
2
1
2
2
1
2
1
1
3
1
3
0
0
2
1
0
2
1
1
1
0
2
2
2
1
1
1
0
2
1
1
2
2
2
1
1
1
2
1
1
1
1
0
1
0
1
1
2
1
1
1
0
0
1
1
1
0
1
1
1
1
0
2
1
0
0
0
1
0
0
0
0
1
2
1
0
1
1
1
1
2
0
1
0
1
0
1
2
0
0
1
1
2
0
2
1
0
1
2
0
2
2
0
1
1
1
2
1
2
1
0
0
0
2
1
1
0
0
1
0
1
1
0
2
0
1
1
2
1
1
2
1
0
0
0
1
2
1
1
0
0
0
0
2
0
1
2
1
1
1
1
2
0
1
1
1
1
2
1
0
1
0
1
2
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
2
0
2
0
2
1
2
0
5
2
2
0
1
1
1
0
0
1
2
2
1
1
1
2
1
0
1
2
2
1
1
1
0
2
1
1
2
2
0
1
1
2
2
1
1
2
2
1
2
2
0
1
1
2
1
0
1
0
0
2
1
1
1
1
2
1
1
0
2
1
1
0
1
1
1
0
1
0
2
2
0
2
1
0
1
1
1
2
1
1
1
1
1
0
1
2
1
1
0
1
3
1
1
0
1
0
1
1
1
2
0
1
2
1
0
1
0
1
4
2
0
1
0
1
0
0
0
0
1
0
1
1
0
1
1
0
1
1
1
1
1
2
1
0
0
1
2
0
1
0
0
0
0
3
1
1
2
0
1
1
2
0
2
1
0
2
1
0
2
0
1
1
0
2
0
1
1
2
0
1
1
0
1
1
2
1
1
0
1
0
1
1
1
0
1
1
3
1
1
1
1
2
1
2
0
1
0
1
0
0
0
1
0
1
2
1
1
0
1
1
1
1
1
1
1
1
1
0
1
1
0
2
1
2
2
1
2
0
1
1
2
1
2
1
0
1
2
0
0
1
1
0
1
1
0
1
2
1
0
0
2
1
1
1
0
1
1
0
1
1
0
0
1
0
2
1
1
2
1
2
1
0
1
1
1
1
1
2
1
2
0
2
0
1
1
0
0
1
2
2
1
1
1
2
0
1
0
1
1
0
1
1
1
2
2
0
0
2
0
0
1
2
1
2
0
1
1
1
0
1
1
1
1
1
1
1
0
0
1
1
1
1
0
0
2
2
1
1
1
0
1
2
2
0
0
2
2
1
2
2
1
2
1
2
1
2
1
0
2
1
0
2
3
0
1
2
1
2
0
0
2
1
2
0
2
2
1
1
0
1
1
1
0
1
3
0
2
2
1
0
1
1
1
1
0
1
1
0
1
0
2
1
1
1
0
1
1
1
0
1
0
1
2
0
1
1
1
1
1
1
2
1
1
1
0
2
1
2
0
1
1
0
2
2
1
1
2
1
0
1
1
0
0
1
1
0
1
0
1
2
0
0
2
1
1
1
0
2
1
1
2
1
1
1
1
0
1
0
0
2
1
0
0
1
0
1
1
3
1
1
1
2
1
2
2
1
2
2
1
1
1
0
2
0
0
1
0
0
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
0
1
1
1
1
0
0
0
1
0
1
0
1
1
1
0
0
1
2
1
1
1
0
1
1
0
1
0
2
1
2
0
1
1
1
1
0
0
1
1
1
0
1
1
2
1
2
1
1
2
2
1
3
1
3
1
1
1
1
0
2
0
2
0
1
2
2
1
2
0
0
1
1
1
2
1
1
1
0
0
0
1
1
1
2
1
0
1
1
0
1
1
2
1
1
1
0
1
1
0
1
1
2
2
1
0
1
0
1
0
0
1
1
2
2
1
0
0
2
0
2
2
1
2
1
1
2
1
0
1
0
1
2
0
1
1
1
2
2
1
1
1
1
2
1
1
1
2
1
1
2
1
1
0
2
0
2
1
0
0
1
2
0
0
0
1
0
0
0
2
1
0
1
2
0
2
1
2
0
0
1
1
2
1
0
1
0
2
1
0
1
1
2
0
2
2
2
0
0
2
2
2
1
1
2
0
1
1
2
0
1
0
0
0
1
1
1
1
1
0
1
1
1
0
2
2
2
1
2
1
0
5
1
1
0
1
2
1
0
1
1
0
0
0
1
1
2
2
1
1
1
1
0
1
1
0
0
1
1
0
0
1
1
2
1
0
1
1
1
0
3
0
2
1
2
1
2
1
1
1
1
1
1
1
0
0
0
2
1
1
2
0
1
1
0
1
1
2
0
1
1
2
1
2
1
1
1
0
2
1
0
0
1
1
2
2
0
2
1
2
1
2
0
0
1
1
1
0
0
0
2
1
1
0
0
2
0
1
1
0
1
1
1
1
1
1
1
1
1
0
1
1
1
0
1
1
1
1
1
2
1
0
2
0
1
0
0
1
2
1
0
2
0
1
1
2
0
1
0
1
1
0
2
2
0
0
2
0
1
0
0
2
0
1
1
2
2
1
0
1
2
1
1
1
0
1
0
0
1
3
1
1
2
1
1
1
1
2
0
0
1
1
2
1
1
0
0
0
2
0
2
2
1
1
1
1
1
1
0
0
0
1
2
1
1
2
1
1
1
2
1
1
0
0
1
1
2
2
2
1
0
2
0
1
1
1
0
2
1
1
1
1
1
1
1
1
1
1
0
2
1
0
1
0
0
2
1
2
0
2
0
1
0
0
0
1
1
0
1
1
0
1
0
1
0
2
1
1
1
1
0
2
2
2
1
1
0
2
2
1
2
2
1
0
1
2
1
2
2
1
1
0
0
0
1
0
2
2
2
1
1
1
2
0
1
0
1
0
0
1
1
1
1
2
1
2
0
2
1
1
1
2
0
1
1
0
1
1
1
1
1
0
0
2
2
1
0
0
3
1
1
0
1
1
1
0
1
2
1
1
1
1
0
0
3
1
1
1
0
1
2
1
1
2
0
0
1
1
1
2
0
1
1
0
1
1
2
2
1
1
1
2
0
0
2
0
1
1
0
1
1
1
2
1
0
1
1
1
1
1
1
1
1
1
0
1
2
0
1
1
1
1
2
1
0
1
1
2
0
0
0
0
1
0
2
0
1
2
0
0
0
1
0
0
2
1
0
0
1
0
0
1
1
1
2
1
1
1
2
0
1
1
2
1
1
1
0
2
2
1
1
1
1
1
0
1
1
0
2
1
0
0
1
2
0
2
2
1
0
1
1
2
1
1
1
0
1
2
1
1
1
2
1
1
1
0
2
1
1
2
0
2
2
1
2
0
1
1
1
1
1
2
2
1
1
0
0
2
0
0
0
2
0
3
0
1
1
1
1
1
0
1
2
0
1
0
0
0
0
1
1
1
1
2
0
2
2
1
0
1
1
1
1
1
1
0
2
1
0
0
1
1
1
2
0
1
1
1
0
0
1
1
0
1
0
1
1
0
3
1
2
1
0
2
1
1
1
1
0
1
1
2
2
2
0
1
0
0
1
2
1
1
0
1
0
0
0
0
1
1
0
1
1
1
1
2
0
2
0
1
2
1
0
1
2
1
2
1
0
1
4
0
1
2
2
3
2
0
1
2
2
2
0
1
2
1
2
0
2
1
0
0
0
1
1
1
0
1
1
0
2
1
0
1
0
1
0
1
0
2
0
1
0
1
1
1
2
1
1
0
1
2
1
1
1
2
1
1
1
0
1
0
2
1
1
1
2
1
2
2
1
2
0
0
1
1
1
1
1
1
0
2
2
1
1
0
1
1
1
1
1
1
0
1
1
0
1
1
1
0
2
1
1
3
2
0
1
1
0
2
1
0
1
2
1
1
1
0
1
1
1
1
0
0
0
2
0
1
0
1
0
0
1
2
2
0
1
0
1
2
1
2
1
3
1
0
2
1
1
2
1
0
1
0
1
2
0
2
2
1
0
2
1
1
0
0
2
2
2
1
1
1
1
1
0
0
1
2
2
1
2
2
2
1
2
1
1
0
0
1
0
0
0
0
1
1
2
1
2
0
0
2
1
1
0
0
1
1
0
1
1
0
1
0
2
1
0
2
1
1
1
0
1
2
0
0
0
1
0
2
0
0
1
2
2
0
0
0
2
3
3
1
2
0
0
1
2
1
0
0
2
1
1
0
1
1
1
0
1
1
1
1
0
1
2
1
0
2
1
2
1
0
1
0
2
2
0
1
1
2
1
0
1
0
1
1
2
1
1
0
1
2
1
1
1
2
1
1
0
2
0
1
2
1
2
1
1
2
1
1
0
0
2
1
1
1
2
0
1
1
0
1
1
1
1
0
1
1
1
1
2
1
0
1
2
2
3
1
2
1
2
1
1
1
1
2
1
1
0
1
0
1
2
1
1
0
1
1
2
0
0
1
2
2
1
1
1
0
2
0
1
1
1
2
0
0
0
1
1
1
0
2
1
4
3
2
0
1
1
1
1
1
0
2
0
1
0
1
1
0
1
1
0
1
1
2
1
1
1
2
1
1
1
0
1
2
0
1
2
2
0
2
1
1
0
1
1
1
1
1
0
2
1
2
0
2
2
1
1
1
2
14
0
0
2
1
1
1
0
1
1
1
1
2
2
1
2
1
1
2
1
2
0
1
1
1
1
1
0
2
1
2
1
1
2
1
1
1
2
1
0
2
2
2
1
2
1
1
1
1
1
1
1
2
1
1
0
1
2
1
1
1
1
0
1
1
1
0
1
2
2
1
0
0
1
1
0
1
1
1
1
1
1
1
1
2
2
2
1
0
0
1
2
1
0
1
1
1
1
2
2
2
2
2
0
1
1
1
1
1
1
0
1
1
0
1
2
1
1
1
0
1
1
1
1
1
1
1
0
0
1
1
1
2
1
1
0
1
2
0
2
0
0
2
2
1
2
1
0
2
0
1
1
1
1
0
0
2
1
1
0
2
1
1
1
1
1
2
0
2
0
2
0
0
0
1
1
2
0
1
2
1
1
1
1
0
1
0
0
1
2
2
2
2
1
1
1
3
1
2
2
0
1
0
1
0
2
1
1
2
1
2
1
1
1
0
1
1
1
1
0
0
1
1
1
1
0
1
2
0
2
1
0
1
0
1
0
1
0
0
2
1
0
1
2
1
1
1
1
2
1
2
0
1
1
1
1
1
2
2
2
3
0
1
1
2
2
2
2
0
2
1
1
1
2
1
1
1
0
1
0
2
1
2
1
1
1
1
1
1
1
1
1
0
2
0
2
2
1
2
0
0
0
1
1
0
1
1
2
1
0
0
0
2
2
0
0
1
1
1
1
1
0
1
0
1
1
0
0
1
0
0
1
1
0
2
1
0
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
2
1
1
0
0
0
1
2
2
0
0
1
2
2
2
3
1
1
1
1
0
1
0
1
1
1
0
2
1
0
0
0
2
2
0
0
0
2
1
1
0
2
1
1
0
1
2
3
1
0
0
1
1
0
0
1
1
2
0
1
0
1
0
2
2
1
1
1
1
2
2
1
1
1
1
0
0
1
0
1
1
2
2
1
2
2
2
0
1
1
1
1
2
0
1
0
2
1
2
1
1
1
1
0
1
2
0
2
2
0
0
1
1
2
1
2
1
2
1
2
1
1
0
1
0
1
2
1
1
1
0
1
0
1
1
1
1
0
1
0
0
2
0
1
0
1
1
2
2
1
1
2
1
1
1
0
1
1
0
0
1
2
0
1
1
2
1
1
1
1
1
1
1
1
1
1
2
0
2
1
0
2
0
0
1
1
1
0
0
1
1
1
1
0
1
1
0
1
1
0
0
0
0
2
2
1
1
1
1
2
1
1
1
1
1
2
0
2
1
1
1
2
0
0
1
0
1
1
0
1
1
1
1
0
1
2
0
1
0
1
2
1
1
1
1
2
0
2
1
1
0
1
1
2
1
2
0
2
1
1
1
1
2
1
2
2
1
0
1
1
1
1
1
2
2
1
1
1
2
0
2
0
0
1
2
0
2
1
0
1
0
0
2
1
1
2
2
1
1
1
1
1
1
2
2
1
0
1
2
2
1
1
1
2
0
0
1
0
1
1
2
0
0
0
0
1
1
1
2
1
1
1
0
3
1
1
2
1
0
1
1
1
1
1
1
2
1
1
0
0
2
0
1
0
1
2
1
1
1
1
1
2
1
1
0
2
0
2
0
0
0
1
0
1
1
0
1
2
0
0
1
1
0
0
0
2
1
1
0
1
1
1
1
0
1
2
1
1
1
0
2
1
1
2
1
1
0
1
1
0
0
0
1
1
0
1
0
1
1
1
2
0
1
1
1
1
2
2
0
2
1
2
2
1
1
1
0
1
0
2
1
2
1
1
1
1
1
0
1
0
0
0
1
1
2
2
1
1
1
0
0
2
2
1
1
1
1
1
1
1
1
1
1
2
2
0
1
0
0
1
0
1
2
1
0
2
2
0
0
1
1
0
1
2
1
1
2
2
1
1
0
2
1
2
0
2
1
0
1
1
1
0
0
2
1
0
2
2
1
1
1
2
0
2
2
2
1
1
0
1
1
0
1
1
1
1
0
1
1
0
0
0
2
1
1
1
1
1
1
0
0
0
0
0
0
2
0
0
2
1
1
1
1
1
1
1
0
0
0
1
0
2
1
1
1
0
0
1
2
1
1
1
1
1
1
1
2
2
2
1
0
0
2
2
0
1
2
0
1
1
0
0
2
1
0
1
1
1
1
1
1
0
1
1
2
0
1
0
1
1
2
0
2
0
1
2
3
1
1
1
0
2
3
0
2
1
2
1
0
0
1
1
1
2
1
2
0
2
3
2
2
1
0
2
1
1
1
1
1
1
1
2
2
0
2
1
2
1
1
1
0
1
2
1
1
0
2
2
0
0
1
0
1
2
1
1
2
1
2
1
1
2
1
1
2
1
1
1
1
2
2
1
2
3
2
2
1
1
1
1
1
2
1
1
2
1
1
1
0
1
1
1
0
0
1
0
1
2
1
1
0
2
0
1
0
0
1
1
1
0
1
1
0
0
0
1
1
2
1
2
2
1
1
1
2
2
2
1
2
0
0
2
2
2
2
1
1
1
0
2
1
1
1
0
1
2
3
2
0
1
1
1
0
0
1
1
2
0
1
2
1
1
1
1
1
2
2
0
2
1
2
1
1
0
4
1
1
0
1
1
0
1
0
1
1
2
1
1
2
0
2
1
0
2
0
2
0
0
1
0
1
2
1
2
5
0
2
0
2
1
1
1
0
1
1
2
1
1
1
1
1
2
1
1
2
0
0
1
0
2
0
1
1
1
2
1
2
0
0
1
1
0
2
1
0
0
0
1
2
2
2
1
2
0
2
1
1
2
0
1
1
3
1
1
1
0
0
0
1
0
1
1
0
0
1
1
0
1
2
1
1
1
2
1
2
0
0
0
2
1
1
1
1
0
2
1
0
1
0
3
1
1
1
0
1
0
1
1
0
0
0
1
2
2
1
1
0
1
0
1
1
1
0
2
2
0
0
4
0
1
1
1
2
1
1
1
1
1
0
1
1
1
2
1
1
1
1
1
2
0
1
1
2
1
1
1
1
0
0
0
1
1
2
1
1
0
1
1
2
1
0
2
0
0
1
0
0
2
1
1
1
1
0
0
0
2
2
1
1
0
0
1
2
0
0
1
1
2
2
0
2
1
1
2
2
1
2
0
1
1
1
1
1
1
2
2
0
2
1
1
2
2
0
0
1
2
2
1
1
1
0
1
1
1
1
0
0
2
1
1
0
3
1
2
0
0
1
1
0
2
1
0
1
2
2
1
2
0
1
0
1
0
0
1
1
2
1
0
2
1
1
2
1
0
1
1
0
1
0
0
2
2
3
0
1
1
1
2
0
0
0
2
1
1
1
1
2
1
0
2
1
1
1
3
1
2
0
2
0
0
1
1
1
2
1
0
0
1
1
0
1
0
0
0
0
1
0
2
1
1
0
1
2
0
0
1
2
0
1
1
1
1
1
1
1
2
1
1
1
1
0
2
1
0
1
0
2
0
2
1
1
0
0
0
1
0
1
1
0
1
0
1
3
1
1
0
1
2
1
0
0
1
2
2
0
0
1
1
0
1
0
1
0
1
2
1
3
2
0
1
1
1
1
1
0
1
2
1
0
0
1
0
0
1
1
2
1
1
2
1
0
1
1
1
1
0
2
2
1
1
1
2
2
0
1
0
1
0
0
2
0
1
0
1
2
2
1
2
2
1
0
1
1
1
1
1
1
2
1
1
2
1
1
0
0
1
2
1
1
0
1
1
1
2
2
0
1
1
1
2
1
1
1
2
0
2
1
2
1
1
0
1
2
0
1
1
1
1
1
1
1
1
1
0
2
1
1
2
0
1
1
0
1
2
1
1
2
0
1
1
1
2
0
1
2
0
3
1
2
2
0
2
2
0
2
1
0
1
0
1
0
0
1
1
1
0
2
1
0
2
0
1
0
1
1
0
1
1
2
2
1
2
1
2
2
1
1
1
2
1
1
1
1
0
1
0
1
2
1
0
0
2
1
0
0
1
2
1
2
1
2
1
2
0
0
1
3
1
1
1
0
1
2
2
0
0
1
1
1
1
0
1
2
1
1
2
1
2
1
0
2
1
1
1
1
1
1
1
1
1
0
1
1
2
2
0
2
0
2
2
1
2
1
1
1
0
1
1
1
1
1
0
2
0
1
1
0
1
1
2
0
1
2
2
0
1
1
1
1
1
3
0
0
1
2
1
2
0
0
1
2
1
2
0
2
0
1
2
0
1
1
1
1
1
1
1
0
1
1
4
2
1
0
0
1
0
1
1
2
1
1
0
1
0
0
2
0
1
1
1
0
0
1
1
2
2
1
1
0
1
1
1
1
0
1
2
0
2
1
0
2
1
0
2
2
1
1
1
2
2
1
1
2
1
2
2
0
2
2
0
1
1
1
0
1
1
2
0
0
1
2
0
1
1
2
0
2
1
1
1
0
1
0
1
0
0
1
1
1
0
1
1
1
2
1
2
2
0
1
0
0
1
0
1
2
2
1
0
2
2
2
3
1
1
0
1
1
1
2
1
1
0
2
1
1
2
1
0
1
0
1
0
1
0
1
0
0
1
1
0
1
1
2
1
1
2
1
1
1
1
1
1
1
0
1
1
1
1
3
1
2
2
1
1
1
0
1
1
1
1
2
1
2
0
1
1
0
0
1
1
1
0
0
0
1
1
2
1
2
2
0
1
0
2
0
2
0
1
1
2
1
2
0
1
2
1
1
1
1
2
1
2
2
0
1
2
2
1
1
1
1
0
2
0
2
1
1
2
1
2
1
0
1
1
2
1
1
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
3
1
2
0
0
0
1
0
2
2
1
1
1
2
1
1
2
1
3
1
1
1
0
0
0
0
2
1
2
2
0
0
1
1
1
0
2
2
0
1
1
2
2
0
2
1
1
0
1
2
1
1
1
1
1
2
1
1
1
1
0
2
1
0
2
1
0
2
0
1
1
2
1
1
1
1
2
2
1
0
1
1
1
2
1
1
0
0
0
0
1
1
1
1
0
1
2
2
2
1
1
0
1
0
0
0
2
3
0
1
1
1
0
2
1
0
2
1
0
0
1
0
1
2
0
2
1
1
2
1
2
0
0
0
1
2
1
0
0
0
1
0
0
1
2
0
2
1
1
1
2
0
1
0
1
0
2
0
2
1
0
1
0
1
1
0
0
1
1
0
1
0
1
2
1
1
0
2
1
1
0
2
1
1
2
1
1
2
1
1
2
2
1
2
0
0
1
1
1
0
2
2
2
0
2
1
2
2
2
0
2
1
1
2
1
1
1
0
0
1
0
1
2
2
0
0
2
1
1
1
2
2
0
1
1
2
6
1
0
1
0
1
1
1
0
0
2
1
0
0
2
1
0
1
1
1
0
1
1
0
0
0
0
1
2
0
1
2
1
1
2
1
0
0
1
1
0
1
1
1
1
0
1
1
1
1
1
0
0
1
1
0
2
0
0
1
1
2
0
0
0
0
0
0
1
0
1
2
1
1
0
2
1
0
2
1
2
1
1
1
0
0
0
1
1
0
0
2
0
2
1
1
1
3
1
2
2
0
2
2
0
1
2
0
1
1
0
1
1
0
0
2
1
1
0
2
1
0
1
0
0
0
2
1
2
2
1
2
1
1
2
2
0
2
1
1
2
0
0
0
0
2
0
2
1
4
1
0
2
0
1
2
0
0
2
0
1
0
0
1
1
2
0
0
1
2
0
0
1
0
1
1
1
2
2
0
2
2
1
0
2
2
0
0
1
1
1
0
1
0
1
1
2
0
1
1
0
0
1
0
1
2
1
1
2
1
1
1
0
1
0
0
1
2
1
1
1
1
0
2
0
0
0
1
1
2
1
0
2
2
2
1
2
1
1
1
1
1
2
1
2
3
0
1
2
2
2
0
1
1
2
1
1
0
2
2
1
2
0
1
1
2
0
2
1
0
1
1
1
1
2
1
1
2
2
0
1
0
2
1
3
1
1
0
1
0
1
1
1
1
1
4
0
1
2
2
1
2
1
1
1
0
1
1
0
1
2
1
1
2
2
1
2
1
0
0
0
2
0
1
1
1
0
1
1
2
2
1
0
2
0
1
0
1
1
2
1
0
1
0
2
0
2
1
0
1
0
0
0
0
2
2
1
0
1
0
1
2
1
1
2
0
1
2
1
1
2
0
0
2
0
1
1
2
2
2
2
0
2
1
1
1
1
1
0
1
1
0
0
0
0
1
2
0
2
1
1
1
1
1
1
1
0
1
1
1
2
0
2
1
0
1
2
1
1
1
1
2
0
1
1
2
1
1
2
1
1
2
1
1
0
1
1
2
0
1
0
2
1
1
1
0
1
1
1
0
2
2
2
1
1
2
1
1
1
2
2
2
4
0
0
1
1
1
1
2
1
0
0
1
0
1
1
1
2
0
0
1
1
1
2
1
1
1
0
1
0
1
0
0
0
1
1
2
0
1
0
2
2
0
1
1
1
1
0
0
0
0
0
2
1
2
1
1
1
0
1
1
0
0
1
0
1
0
0
0
4
1
2
1
1
1
0
1
0
0
2
0
1
1
0
1
0
0
1
2
1
0
0
2
0
1
1
2
1
1
0
1
1
2
1
1
2
1
2
2
1
1
2
1
1
1
1
1
2
0
1
1
0
1
1
1
1
1
0
0
0
2
1
1
1
1
0
1
1
1
1
1
2
0
1
1
1
1
0
2
2
2
1
1
1
1
0
0
1
0
1
0
1
1
3
2
1
1
1
1
2
2
2
0
0
2
2
0
1
0
0
1
1
0
2
1
0
1
1
1
1
1
1
1
2
0
2
2
0
2
1
2
1
1
1
0
1
0
2
1
1
1
1
1
1
0
2
1
1
2
2
2
1
2
2
2
0
2
1
1
1
3
1
2
0
1
0
2
1
1
1
1
1
2
1
2
1
2
1
0
1
0
0
1
1
1
1
0
0
1
1
1
1
2
1
0
0
1
2
0
0
1
0
0
1
0
1
1
0
1
1
0
1
1
1
1
1
3
1
1
1
1
0
0
0
2
0
0
0
2
0
2
0
0
0
1
2
2
1
2
0
1
2
0
0
2
0
0
0
1
0
1
1
0
1
2
1
1
1
1
1
1
1
1
1
1
1
4
0
0
1
2
0
1
1
1
0
1
1
1
2
2
1
0
1
2
2
2
0
0
1
0
1
2
1
2
1
0
1
1
1
2
2
1
1
2
0
1
0
1
0
0
1
1
1
1
1
2
2
1
0
2
0
2
0
1
2
1
1
0
0
2
2
1
2
1
2
1
1
2
2
2
1
1
1
1
2
2
2
0
1
1
1
1
2
0
1
2
1
1
1
1
2
1
1
2
2
0
2
1
0
1
0
0
1
0
2
1
2
1
2
0
2
0
0
1
2
1
1
2
0
1
1
1
0
1
1
1
1
1
0
2
2
2
1
1
0
1
0
0
1
0
0
0
1
0
1
1
1
2
1
0
3
0
1
1
1
0
1
1
1
1
2
0
1
1
1
2
1
1
1
1
2
0
1
0
0
1
0
0
0
2
1
1
1
0
1
1
1
1
1
2
1
2
1
2
0
1
2
1
0
0
1
1
2
1
1
1
2
1
1
3
1
1
1
1
0
1
1
1
2
4
1
1
1
1
1
0
2
1
2
1
1
0
0
0
2
1
1
0
1
1
1
0
1
2
0
0
2
1
2
1
1
1
2
2
0
1
2
1
1
1
0
2
1
2
4
1
2
0
1
2
1
1
1
2
1
0
1
1
1
2
1
0
0
1
1
1
2
1
1
1
0
1
1
0
0
0
0
2
2
1
2
1
1
2
1
1
0
2
1
2
1
2
1
1
1
2
1
1
0
0
0
1
1
0
0
1
0
1
2
0
1
2
0
3
1
2
0
0
1
0
0
2
2
2
2
1
2
2
2
2
1
1
0
1
1
1
1
1
0
0
1
1
0
1
1
1
0
1
0
1
1
2
0
0
0
1
1
0
1
1
2
1
0
1
1
1
2
0
1
2
1
2
1
1
0
2
0
1
0
0
0
2
2
2
1
1
1
0
1
2
0
1
1
1
2
1
2
1
1
0
2
1
1
1
3
1
1
0
1
0
2
2
0
1
2
2
0
1
0
1
0
1
1
1
2
2
1
1
2
2
0
0
0
1
0
2
1
1
1
0
0
1
2
1
1
0
1
0
1
1
0
1
1
0
2
2
0
1
0
1
0
0
0
0
0
1
1
2
1
2
2
1
1
0
1
1
1
1
1
0
1
4
0
0
0
2
0
1
1
1
0
1
1
1
2
2
2
0
1
2
2
1
0
1
1
0
2
1
1
0
0
0
1
1
1
0
1
1
0
2
2
1
2
2
1
1
1
0
1
0
1
0
1
0
0
0
1
0
0
0
1
1
1
1
1
1
2
1
1
1
1
1
2
1
2
1
2
1
0
1
1
1
1
0
1
1
2
1
1
1
1
1
1
0
1
1
1
1
1
1
1
0
1
0
0
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
2
0
1
1
1
0
2
1
2
1
0
0
0
0
1
1
1
1
1
2
1
1
2
1
0
2
2
1
0
1
1
0
2
1
1
1
2
3
2
1
1
1
1
1
1
1
1
1
2
2
0
1
1
0
2
1
1
1
2
0
1
1
1
1
1
0
1
1
0
0
1
1
1
0
3
1
1
1
1
1
2
1
1
1
3
1
1
1
0
0
1
2
1
0
1
0
0
1
2
3
1
0
2
1
1
0
1
0
2
0
0
1
1
1
1
2
1
2
2
1
1
0
0
1
1
1
1
0
0
0
1
2
1
1
2
3
1
1
1
2
1
0
2
2
0
0
1
2
1
1
1
2
1
1
0
3
0
2
1
1
0
3
2
1
0
1
1
1
0
0
1
1
0
1
1
1
2
2
1
0
1
1
1
1
0
2
0
0
1
2
2
1
1
1
1
4
2
0
1
2
2
1
1
2
0
1
1
1
2
0
1
1
2
1
1
1
0
1
0
1
0
2
2
1
0
0
1
1
1
2
0
2
2
2
1
1
1
1
1
1
2
1
1
4
2
1
0
1
0
2
1
1
0
1
2
0
1
3
1
1
0
1
0
0
1
2
1
1
1
2
1
2
0
0
0
0
0
0
1
2
1
2
2
0
0
2
1
0
1
1
2
2
2
1
0
1
2
1
1
0
2
2
0
1
1
1
0
1
1
1
1
0
2
0
1
1
1
1
1
1
1
0
0
1
1
2
1
1
0
1
0
1
1
1
1
2
0
0
2
1
1
0
1
1
1
0
1
1
0
2
1
0
1
1
1
0
1
1
1
1
2
1
1
1
2
2
1
1
1
1
2
1
0
1
1
1
1
0
1
2
0
1
1
2
0
2
1
1
1
2
0
1
1
0
1
1
1
1
1
1
1
0
0
0
1
1
2
1
1
0
1
0
1
2
1
0
2
2
1
0
0
0
0
1
2
0
1
1
0
1
1
0
0
2
1
1
1
1
1
1
2
0
1
1
1
1
1
2
0
0
0
0
1
1
0
1
1
2
1
1
0
0
0
0
0
1
0
0
2
1
2
1
1
0
2
1
0
1
1
1
2
1
1
0
1
1
3
1
0
2
1
0
1
2
1
1
0
0
1
2
0
1
1
1
0
1
0
1
0
1
2
0
1
1
1
1
2
0
1
2
0
0
0
1
2
1
0
1
1
2
0
0
0
0
1
2
1
0
1
3
2
1
0
1
0
0
1
1
1
1
1
2
2
0
1
2
0
1
0
2
1
2
1
1
1
1
1
1
0
2
2
0
1
2
1
2
0
0
2
1
0
0
1
1
0
0
2
3
1
1
1
0
2
1
2
1
1
1
1
2
1
2
0
1
2
1
1
2
1
2
1
1
0
3
2
2
1
1
1
2
0
0
0
1
1
0
1
0
1
2
1
2
1
2
1
1
1
1
1
1
2
1
1
1
3
1
1
2
0
1
0
0
2
2
0
1
2
1
1
1
0
2
1
1
0
0
1
2
2
1
1
0
2
1
1
0
2
2
0
1
1
2
2
1
1
1
1
2
1
1
2
0
1
0
1
0
0
1
0
0
1
0
1
0
0
1
2
1
2
1
0
1
0
2
1
3
2
0
1
2
1
1
0
2
0
0
0
0
1
0
1
0
0
1
0
1
1
1
2
2
1
2
0
0
1
1
1
1
0
1
0
0
2
1
1
0
1
2
0
1
1
2
2
1
1
1
0
2
2
1
2
2
2
1
1
5
1
1
1
2
1
1
0
1
1
2
0
1
1
0
1
2
0
1
0
1
1
1
2
1
1
1
1
2
2
1
1
1
1
1
1
1
2
0
0
1
0
1
2
2
0
1
0
2
2
1
1
0
0
1
3
1
1
0
2
0
2
1
2
0
0
1
1
1
2
1
0
1
1
1
0
1
0
1
2
1
1
0
0
1
1
1
1
0
1
2
1
1
2
1
1
1
1
1
1
1
0
1
1
0
1
1
0
0
2
2
0
0
1
1
1
0
1
1
0
2
1
2
1
1
1
1
1
1
0
1
1
1
1
1
0
1
1
0
0
2
1
1
2
1
0
1
0
1
0
1
1
1
1
2
0
1
1
2
1
1
1
1
2
0
2
1
0
1
1
0
2
2
2
1
0
0
0
0
1
1
0
2
10
1
1
2
0
1
1
0
1
1
2
1
0
1
1
1
1
2
2
1
1
0
1
1
1
1
1
0
1
2
1
0
0
1
1
0
1
1
1
1
1
0
1
0
0
0
1
2
1
2
0
1
1
2
2
0
0
1
2
0
0
1
0
2
1
2
1
1
1
1
1
0
1
2
2
1
0
1
2
2
3
1
1
2
1
0
2
1
0
1
1
1
0
0
2
1
1
1
2
1
1
1
2
1
1
1
1
0
0
1
1
0
2
1
0
1
1
2
1
2
0
0
2
1
0
1
0
0
2
2
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
0
2
2
1
1
1
1
1
2
1
1
1
1
1
1
1
0
1
1
0
1
2
1
1
1
0
1
2
0
1
1
0
0
0
1
2
2
2
0
1
2
1
1
0
0
2
2
1
0
1
0
1
1
2
2
1
1
1
2
1
2
2
0
0
0
0
2
1
1
0
1
1
0
1
1
1
0
0
1
1
1
1
0
2
2
0
0
1
0
1
1
2
2
0
1
1
1
0
0
2
0
1
0
1
1
1
1
2
1
1
0
2
2
1
1
0
1
0
1
3
1
1
0
1
2
1
1
1
0
0
2
0
0
0
0
1
1
0
0
1
2
2
0
1
0
1
0
0
0
0
1
1
2
0
1
1
2
1
1
2
2
0
2
1
2
0
2
1
1
0
0
1
0
1
0
2
1
0
2
1
1
2
0
2
0
0
2
1
2
1
1
0
0
1
2
0
1
2
2
1
0
0
2
0
1
1
0
0
0
1
1
1
1
2
1
0
1
2
1
2
2
1
1
1
0
1
2
1
3
1
0
1
0
1
2
0
1
1
0
1
1
0
1
1
2
0
0
2
2
2
1
1
1
1
0
2
0
1
1
2
1
2
2
2
1
0
2
2
1
0
1
2
1
0
2
1
1
1
0
1
1
1
1
2
0
1
1
0
0
1
1
0
0
2
1
0
1
0
1
1
0
1
0
1
2
1
0
1
0
2
1
2
2
1
3
1
2
1
1
1
2
1
0
0
1
0
2
0
1
1
0
1
2
2
1
2
2
2
0
1
2
1
2
1
2
1
1
0
1
2
0
1
2
1
2
1
0
1
1
2
1
1
2
1
2
1
0
1
1
2
1
1
1
0
2
0
1
1
1
2
0
3
0
1
2
0
1
2
2
0
2
1
1
0
1
1
1
0
2
1
1
1
0
1
0
2
2
2
2
0
1
1
0
1
0
1
2
1
0
3
0
2
1
1
1
1
2
0
1
1
2
0
0
1
1
0
0
1
1
0
1
2
2
2
0
2
0
2
1
1
2
1
1
1
1
2
1
2
1
1
1
2
1
0
1
1
1
1
2
0
1
1
0
2
0
1
1
0
0
0
4
2
1
1
2
0
2
2
2
2
1
0
1
0
1
1
1
1
1
0
2
2
0
1
0
2
2
1
1
0
1
2
0
1
1
0
2
2
2
1
1
1
1
1
1
1
1
2
0
2
1
0
1
1
0
0
1
0
1
3
2
1
1
1
1
1
2
1
1
1
1
3
1
1
1
2
2
1
2
0
0
1
0
0
1
1
1
0
1
2
1
1
1
0
0
1
0
2
1
2
1
1
1
1
1
0
2
1
0
0
1
1
1
0
2
1
1
1
0
0
0
2
1
1
1
2
1
1
1
1
1
0
1
0
1
1
0
2
1
1
2
0
0
1
1
1
1
0
1
1
2
1
1
2
0
0
1
1
2
1
1
1
1
1
1
1
0
0
1
2
3
0
1
2
1
0
1
1
0
1
1
2
1
1
1
0
2
1
1
0
1
1
1
0
0
0
0
1
1
2
1
2
0
1
2
0
1
1
1
0
1
0
1
1
3
1
1
1
0
0
1
0
1
1
1
2
0
0
1
1
1
1
0
0
1
2
0
0
1
1
2
1
0
2
2
1
1
0
0
1
1
0
1
1
0
1
1
0
2
1
1
1
1
0
2
1
0
1
1
1
1
1
0
1
1
1
1
0
0
1
6
1
1
0
2
0
2
1
0
1
0
1
2
1
1
1
0
1
1
0
1
0
0
0
1
1
2
2
1
0
0
1
0
0
0
1
1
1
1
1
2
0
1
2
2
1
2
0
1
1
2
1
2
1
2
2
1
1
2
3
1
1
1
2
2
2
1
2
2
1
1
0
1
1
1
0
1
2
0
1
0
1
1
2
4
2
0
1
3
1
1
1
1
1
1
0
1
2
1
0
2
1
1
1
1
0
1
2
1
1
1
0
0
2
2
2
2
0
1
1
0
1
1
1
1
2
1
1
0
2
0
2
1
1
1
1
1
1
0
2
0
1
1
0
1
1
1
2
1
1
1
1
1
1
0
1
1
1
0
1
0
2
0
1
0
0
0
2
2
0
2
1
1
2
1
0
1
1
1
2
1
1
1
1
0
1
0
0
3
0
2
1
0
0
0
0
2
2
1
0
1
1
0
1
0
2
1
0
1
2
1
2
1
1
0
1
2
1
0
2
2
4
1
1
1
1
2
1
2
1
8
1
1
1
0
2
1
0
2
0
2
1
0
1
1
0
1
0
1
2
1
2
1
2
1
2
1
0
1
0
1
0
2
1
5
1
1
2
0
2
1
1
2
1
1
0
1
2
1
1
1
2
1
2
1
0
1
2
1
0
1
2
1
0
1
0
1
1
1
1
1
1
1
0
0
0
0
1
1
1
0
2
0
1
2
3
2
1
1
1
1
2
2
2
1
2
0
1
0
0
1
1
0
1
0
1
1
2
2
2
1
1
2
0
1
0
0
0
1
1
2
1
2
1
0
0
1
1
1
0
2
1
1
0
0
0
1
1
0
1
1
1
0
1
0
1
2
2
0
2
1
0
1
1
0
1
1
0
1
0
2
1
0
1
1
3
1
1
0
2
1
1
1
2
1
2
1
1
1
1
0
1
1
1
1
0
1
1
1
0
0
2
0
1
0
1
1
2
1
2
0
1
1
1
1
0
1
1
2
1
2
1
0
3
1
0
1
1
1
2
1
3
1
1
1
0
0
0
1
2
0
0
1
1
0
0
0
1
0
2
2
4
1
3
1
0
0
1
1
1
2
1
2
2
2
1
2
1
1
0
1
2
0
2
2
0
0
1
1
1
2
3
2
2
2
1
0
1
0
0
1
1
1
1
2
2
0
1
1
0
2
2
1
1
0
2
1
1
2
1
1
1
0
1
0
1
2
2
1
2
1
1
1
1
1
2
0
0
0
1
1
1
0
2
0
1
1
2
0
1
0
0
2
0
1
0
1
0
0
1
1
1
1
1
4
1
1
2
2
1
0
1
0
2
0
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
0
0
1
1
1
0
1
1
0
1
1
0
1
1
1
0
1
0
2
1
1
1
2
1
0
1
1
1
1
1
1
2
0
1
1
0
1
1
1
3
1
1
1
1
1
0
1
2
1
1
0
0
1
1
1
1
1
1
1
0
2
1
0
2
2
2
1
2
2
1
0
1
2
2
2
1
1
2
1
1
0
1
1
1
0
2
0
1
1
0
2
2
1
0
0
2
2
1
0
2
0
2
1
1
0
0
0
2
1
1
1
0
1
1
0
2
2
1
2
0
0
1
0
0
1
1
0
0
1
1
1
2
2
1
1
0
0
1
2
1
0
2
2
2
2
1
1
1
2
1
1
0
1
0
0
0
1
1
1
0
1
1
1
0
2
1
0
0
1
1
2
1
2
1
0
2
2
0
0
1
1
0
2
2
0
0
1
1
0
1
1
0
0
1
1
0
1
1
4
2
1
1
0
0
1
0
1
1
2
1
1
2
1
1
1
0
0
2
0
0
1
0
1
1
0
0
1
0
1
1
0
1
0
2
0
1
0
2
0
1
1
1
0
1
1
1
0
0
0
0
1
1
1
1
1
2
0
0
1
1
1
1
2
0
1
1
1
1
0
1
0
1
0
1
0
2
1
1
2
0
2
1
2
1
0
0
2
1
1
2
0
1
1
0
1
1
1
2
1
1
1
0
2
0
1
1
1
2
2
0
1
1
1
1
2
2
2
0
2
1
1
1
1
0
1
3
0
0
1
1
1
1
1
1
1
0
3
1
1
0
1
2
0
0
2
1
1
0
1
0
1
0
2
1
3
1
1
1
1
1
0
1
1
0
0
1
2
1
2
1
1
3
1
0
0
2
1
1
1
1
1
1
2
1
2
2
1
2
2
0
2
0
0
1
0
0
1
1
0
2
2
1
0
1
1
0
1
1
0
0
1
0
2
1
1
2
0
1
2
1
0
1
1
1
2
2
2
1
1
0
2
0
1
1
1
1
0
1
0
1
1
2
0
1
1
1
1
2
1
0
1
1
2
0
0
3
2
2
2
2
1
1
1
2
1
1
0
1
1
0
1
0
1
2
3
2
0
1
1
1
1
0
1
0
1
0
1
0
1
1
2
1
1
1
1
2
1
1
2
1
1
0
0
2
1
0
0
0
1
0
2
1
1
0
0
2
1
2
1
1
2
2
1
1
2
0
2
0
0
2
1
0
1
2
1
2
2
2
0
2
0
1
1
0
2
1
1
2
0
1
1
0
1
1
1
1
1
0
1
1
1
1
1
2
0
2
1
0
2
1
2
1
1
0
1
1
0
2
2
1
1
2
0
1
0
1
3
1
1
1
1
1
1
2
1
2
1
1
1
2
0
3
1
1
1
1
1
1
2
2
0
2
2
0
1
0
0
1
1
0
2
1
1
0
1
1
2
1
2
1
1
0
1
0
2
2
1
2
1
0
0
1
0
1
1
1
0
1
1
2
1
2
0
1
1
2
0
1
1
1
1
1
1
2
0
2
0
1
1
0
1
0
0
2
1
0
1
1
2
1
1
1
1
1
2
0
1
1
0
1
0
1
1
0
2
1
5
5
2
2
1
1
1
0
0
1
2
1
2
0
1
0
2
1
1
0
2
1
0
2
1
0
0
0
2
0
2
0
2
1
1
0
0
1
2
0
1
1
1
1
1
1
1
2
1
1
4
0
2
1
2
2
1
2
2
2
0
1
0
0
1
1
2
1
1
1
1
1
0
2
1
1
1
1
0
0
2
0
1
2
1
1
1
1
1
0
1
2
2
1
1
1
0
1
0
2
1
2
1
2
2
0
0
1
0
1
1
0
1
2
1
1
1
0
0
2
3
0
2
1
2
1
1
2
1
0
1
0
0
1
2
1
2
0
1
2
1
0
2
1
0
0
1
5
2
0
2
1
0
1
0
0
1
2
1
1
0
2
2
1
1
2
1
0
1
1
0
0
1
1
0
2
2
0
1
2
1
1
1
0
1
1
1
1
1
1
0
1
2
1
0
1
2
1
2
2
0
0
0
1
1
0
0
2
0
0
0
1
2
1
0
0
1
1
0
0
1
1
1
1
2
1
1
1
1
0
1
2
1
2
1
1
1
1
0
1
0
0
2
0
0
0
2
4
2
1
0
1
1
3
0
1
1
0
1
2
1
1
2
1
1
0
1
0
1
1
1
1
1
2
0
2
0
0
0
2
1
1
1
1
2
1
1
1
0
0
2
2
0
0
1
1
0
2
0
0
1
1
1
0
1
1
2
0
0
2
0
2
1
1
2
1
1
2
2
4
1
0
2
1
1
0
1
1
0
0
1
2
2
3
2
2
2
1
0
1
1
1
2
1
1
2
0
2
1
1
0
1
0
1
1
2
1
2
2
0
0
0
1
0
1
0
0
1
2
2
2
1
0
1
1
1
1
1
1
2
0
2
1
2
0
1
1
1
1
1
0
1
2
0
1
2
1
1
4
1
1
0
2
1
2
0
1
1
2
0
2
0
2
2
1
1
0
0
2
1
0
2
1
3
1
1
1
1
1
2
0
2
0
1
1
0
1
1
1
0
1
2
1
2
2
2
0
0
1
2
1
1
1
0
0
1
1
2
1
2
2
2
2
1
1
1
2
1
1
0
0
1
1
1
0
1
1
0
1
1
2
1
0
0
0
1
1
0
1
2
2
1
1
1
3
1
0
1
1
1
0
0
1
1
1
1
0
2
1
2
1
0
0
1
2
1
1
2
2
0
1
0
0
1
1
0
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
3
2
1
2
1
1
1
1
1
2
2
1
0
1
2
2
1
1
1
0
0
0
2
0
1
0
0
1
2
2
3
1
1
2
2
1
1
1
1
1
1
2
2
1
0
2
1
1
1
2
2
2
1
1
1
0
1
0
1
0
1
0
2
1
0
0
0
2
1
0
2
0
1
1
2
1
1
0
1
1
1
1
0
0
0
1
3
1
3
1
2
0
1
2
0
1
1
2
1
2
1
2
1
0
1
0
2
0
1
1
0
2
0
2
2
0
1
1
0
0
0
2
0
0
1
1
1
1
1
2
0
2
2
1
1
2
0
0
2
0
1
2
1
1
2
1
0
0
0
1
1
1
1
1
1
0
2
1
1
0
1
1
0
2
1
0
0
1
2
0
0
1
2
1
0
1
0
0
1
1
1
1
1
0
2
1
0
1
1
1
0
1
0
1
0
1
1
0
1
1
1
2
0
1
3
0
0
2
0
2
1
1
4
0
0
1
1
1
2
1
2
2
1
1
1
1
2
2
1
2
2
1
1
1
1
0
2
1
1
1
0
3
0
2
0
2
2
1
1
2
1
0
2
0
1
2
0
2
1
1
0
0
1
0
1
1
0
1
2
2
2
2
0
0
2
1
2
0
2
2
2
2
0
0
1
1
7
0
1
3
2
1
1
1
1
1
1
0
2
1
1
1
1
0
2
1
1
2
1
1
1
1
0
2
1
3
0
2
1
1
1
2
1
1
1
1
1
2
0
2
2
1
1
2
1
1
2
2
2
1
0
1
1
2
0
1
1
1
1
0
1
1
2
3
1
2
2
1
2
2
1
1
1
1
2
1
1
2
1
1
1
2
2
0
1
2
1
1
2
1
2
0
1
2
0
1
1
1
1
0
2
1
0
2
1
0
0
2
2
0
1
1
1
0
1
1
2
2
0
3
0
2
0
0
1
1
0
1
1
1
1
2
1
2
1
1
1
1
0
2
1
2
2
2
2
1
0
1
1
1
0
1
0
2
1
0
0
1
0
1
2
1
1
2
0
0
1
1
1
1
1
1
2
0
1
1
2
0
1
1
0
1
0
1
1
1
1
1
1
0
1
1
1
1
0
2
0
0
2
1
0
1
1
1
1
1
0
1
0
1
0
1
0
0
1
1
1
0
0
1
1
1
1
0
1
1
2
2
1
0
1
1
1
1
1
1
2
1
0
0
0
1
1
2
0
1
1
2
1
2
1
1
1
0
2
2
0
1
2
1
1
1
2
1
2
1
3
1
1
2
1
0
1
3
1
1
1
2
1
1
1
2
1
0
2
1
2
1
2
1
2
1
0
0
2
1
2
0
1
2
1
1
1
0
1
0
4
2
1
2
2
1
0
2
1
0
2
1
0
1
2
1
0
2
0
1
1
0
0
1
2
0
1
2
1
1
1
1
1
1
1
0
1
2
2
1
1
1
2
1
0
0
1
0
1
3
1
1
1
2
1
1
2
1
1
1
1
0
1
1
0
1
1
2
1
1
2
0
1
1
3
0
1
1
1
1
1
1
1
0
1
2
1
1
1
1
1
2
1
1
1
2
2
1
1
2
1
0
1
2
1
0
0
0
2
1
1
1
2
0
1
1
1
1
0
1
1
1
1
0
2
1
0
0
0
0
0
1
1
2
0
1
1
1
2
1
1
2
0
0
1
0
0
0
1
1
1
3
0
1
1
1
0
1
2
1
3
0
1
1
1
1
0
1
1
2
0
0
1
1
1
1
0
2
1
1
1
2
2
0
1
1
1
1
1
1
0
1
2
0
1
0
1
0
0
0
1
1
1
1
2
2
0
0
1
1
0
0
1
0
2
2
1
1
1
2
0
1
1
1
1
1
1
0
1
3
0
0
1
1
1
1
1
1
2
0
1
1
1
1
1
1
1
1
1
1
0
1
2
1
1
0
1
2
0
1
1
1
0
1
5
1
2
1
0
2
2
0
1
2
1
0
1
1
1
1
1
0
0
0
1
2
1
1
0
0
0
0
1
1
1
1
0
1
1
3
1
2
0
1
1
1
1
0
0
2
1
1
1
2
1
1
4
2
0
1
0
1
1
0
0
0
1
1
2
0
0
0
1
1
0
1
0
2
2
2
2
2
0
0
2
0
1
1
1
1
1
0
1
2
1
0
0
0
1
1
1
0
1
0
1
1
0
0
2
1
1
1
0
1
2
0
1
0
3
0
2
0
0
1
0
2
0
1
0
0
1
2
0
0
1
1
1
1
0
1
1
2
0
1
1
0
1
1
2
1
1
0
0
2
1
1
1
4
1
1
0
2
0
0
1
1
1
0
1
1
1
1
1
0
1
1
1
2
1
0
1
1
1
0
2
2
1
0
1
2
1
0
1
1
1
3
2
1
1
0
1
0
0
0
2
1
0
1
1
0
0
1
1
0
2
0
0
1
0
1
0
1
2
0
0
1
1
2
1
1
3
1
1
1
1
2
0
2
1
0
1
1
2
0
1
2
2
1
0
1
0
1
2
0
1
1
2
1
0
1
1
1
1
0
1
2
1
1
1
0
2
1
2
2
1
0
0
2
1
1
2
1
1
1
1
1
1
1
1
1
1
0
2
1
1
0
2
1
1
0
2
1
1
1
1
2
0
0
2
0
1
0
1
2
1
1
2
1
1
1
2
1
2
0
0
0
1
1
1
1
2
1
0
0
1
0
2
1
1
2
1
0
2
0
0
1
1
0
1
1
0
1
1
2
0
1
0
0
1
1
0
1
2
1
1
1
2
0
1
0
0
2
0
0
1
2
0
0
1
1
1
1
1
2
0
0
0
0
0
1
1
1
1
0
2
0
1
4
2
1
2
1
0
2
1
0
0
1
0
2
1
1
1
0
1
2
1
0
1
0
1
2
1
3
1
2
1
1
2
0
1
1
1
1
1
0
1
1
2
1
0
0
1
1
1
2
2
2
1
1
1
1
1
0
1
1
2
1
1
1
1
0
1
0
0
1
2
0
1
2
1
2
1
1
1
1
1
0
2
1
2
1
1
5
1
1
2
2
1
2
0
1
0
0
1
0
1
0
1
2
1
1
1
0
1
1
2
2
1
0
0
1
1
1
0
2
2
0
1
1
2
1
1
0
0
2
1
1
0
2
2
0
2
1
1
2
0
2
0
0
1
1
1
0
1
1
0
2
1
1
1
1
1
0
1
1
2
1
1
1
0
1
2
2
1
1
0
2
1
0
1
1
1
1
2
1
0
0
1
0
1
0
0
1
1
1
2
1
1
1
0
0
1
1
1
1
1
1
0
1
1
1
1
1
2
1
1
0
0
0
1
1
0
0
1
1
2
2
0
0
1
1
2
1
2
0
0
1
0
2
1
0
0
1
1
2
1
1
1
2
1
2
2
1
2
1
1
1
1
2
0
2
1
1
2
0
2
0
1
1
0
0
0
1
1
0
1
1
1
0
0
1
0
0
3
1
0
1
1
1
1
1
1
1
1
0
1
1
1
1
1
2
2
1
1
0
0
0
1
1
1
1
0
1
1
0
0
0
0
0
0
2
1
1
1
2
1
1
0
0
0
2
1
0
2
1
1
1
1
1
1
1
1
1
1
0
1
0
1
0
1
1
0
1
1
1
1
1
1
0
1
0
1
1
0
1
0
0
2
2
0
2
1
0
1
0
0
1
1
0
0
1
0
0
0
1
1
0
0
1
0
2
1
1
2
1
2
0
0
2
2
1
2
1
1
0
2
1
1
1
1
1
1
0
2
1
1
2
2
1
1
2
4
0
0
0
1
1
0
2
0
2
1
0
2
0
1
2
2
0
1
1
0
0
0
1
2
2
1
1
1
1
1
2
1
1
1
0
1
0
1
0
1
1
2
1
1
2
0
1
1
1
2
2
1
1
2
2
0
1
1
1
1
0
1
0
2
2
1
1
1
0
0
0
1
2
0
2
2
0
1
1
0
1
0
0
0
0
1
1
1
1
0
1
2
0
2
2
2
1
0
1
2
0
1
1
3
1
1
2
1
2
1
2
1
1
1
1
0
2
2
2
0
0
0
1
0
0
0
0
2
1
1
0
1
1
1
1
1
1
1
0
1
1
1
2
0
1
1
0
2
0
1
0
1
1
1
1
1
1
2
2
2
1
0
1
1
1
0
1
1
1
1
1
0
0
0
0
1
1
0
2
2
1
1
1
1
1
1
2
0
0
0
0
1
2
1
1
3
1
2
1
0
1
1
0
1
1
2
1
2
1
2
2
1
1
0
1
2
1
2
2
2
1
0
0
2
2
0
0
2
0
1
0
2
1
1
1
0
1
1
1
1
0
2
0
2
1
1
1
1
1
1
1
1
1
1
0
1
2
1
0
1
0
1
0
2
0
1
1
2
0
1
0
1
1
1
0
1
1
0
1
1
2
0
1
2
1
0
0
2
1
0
1
2
2
0
0
2
0
1
1
2
1
1
0
0
0
0
1
1
1
0
1
2
1
0
1
1
1
0
1
3
2
2
2
1
0
0
1
1
0
1
1
1
1
0
2
0
1
1
1
2
2
0
0
1
1
1
3
1
0
2
0
0
1
3
0
2
0
1
1
0
1
1
1
1
1
1
0
1
0
1
1
1
2
1
1
0
2
2
1
1
0
1
0
2
2
1
3
0
1
1
2
1
2
1
1
2
0
0
1
1
3
0
1
2
1
1
2
1
1
2
0
1
0
1
1
1
2
1
1
0
2
1
0
1
1
1
1
1
1
2
1
1
1
0
1
2
1
0
2
1
1
2
0
0
1
1
0
1
3
2
2
1
1
1
2
1
1
0
1
0
1
1
0
2
1
1
2
0
1
2
1
1
1
0
2
1
1
2
1
0
0
1
1
1
0
2
2
1
0
1
1
1
0
3
2
1
1
0
2
3
0
0
2
2
2
1
1
1
1
1
1
1
2
0
0
2
1
1
1
0
1
0
2
1
0
1
0
2
0
0
1
2
2
0
0
1
2
1
1
2
1
0
2
1
1
0
1
1
1
0
2
2
0
1
0
0
1
0
2
2
0
2
1
2
2
1
2
3
1
0
0
1
1
0
0
1
1
1
1
2
1
1
0
1
2
1
2
2
1
1
2
1
0
1
0
1
1
0
2
2
0
2
0
1
1
1
0
2
1
0
1
1
1
1
2
1
2
2
1
1
0
0
2
0
2
1
1
1
1
0
1
2
1
1
1
1
1
0
2
2
0
1
3
1
1
1
0
2
0
0
1
1
1
1
1
0
0
1
0
0
1
1
1
1
2
1
3
1
2
1
1
1
0
0
1
1
0
2
1
1
2
0
1
2
1
0
1
1
2
1
0
2
1
2
0
0
1
1
3
2
2
1
0
1
0
1
1
0
2
1
2
1
0
0
1
1
1
2
2
1
1
2
0
1
1
1
1
1
0
2
1
1
1
1
0
2
1
1
3
3
2
3
2
0
1
1
0
1
2
1
2
0
2
0
2
1
0
2
0
1
2
0
1
1
1
0
2
2
1
1
0
2
0
2
1
1
0
0
1
1
1
2
2
2
0
1
1
1
2
1
2
2
1
2
0
0
1
1
0
2
1
2
2
0
0
1
0
1
2
0
1
0
1
1
1
1
1
2
0
0
1
1
2
0
1
1
2
1
0
0
1
2
1
1
1
2
0
1
2
1
1
2
1
1
1
1
0
2
1
2
1
2
1
0
1
1
0
1
0
2
2
1
1
1
1
1
0
1
0
2
3
0
0
2
1
1
1
1
2
2
0
0
2
0
1
0
1
1
1
1
1
2
1
0
1
1
2
1
1
1
0
1
1
1
0
1
2
1
1
2
1
0
0
1
0
2
0
1
1
0
1
0
0
1
1
0
1
1
2
0
1
3
2
1
2
2
1
0
2
0
1
1
0
1
2
1
0
1
0
0
0
1
1
1
0
2
2
0
2
1
1
2
1
2
2
0
0
0
1
1
1
2
1
1
2
1
1
1
2
1
0
0
2
1
1
1
1
1
2
1
2
0
0
1
1
2
1
1
1
1
1
1
1
0
2
1
2
0
0
1
2
1
1
1
1
2
1
2
2
2
1
2
1
0
0
2
0
1
1
3
2
0
2
2
1
1
1
0
2
0
1
2
1
1
0
1
1
2
0
1
1
1
1
1
1
1
0
1
2
1
1
1
0
2
1
1
1
0
1
1
2
0
1
1
1
0
2
1
0
1
1
0
0
1
1
1
0
1
0
2
0
0
0
1
0
1
1
1
1
1
0
0
0
0
0
4
1
1
1
1
2
1
2
1
1
1
1
2
0
0
2
2
2
2
1
2
2
2
0
1
2
2
0
1
1
0
0
0
1
1
2
1
0
1
1
0
2
1
1
1
1
1
2
0
1
0
1
0
1
1
1
2
0
1
2
0
1
1
1
1
1
0
1
0
2
1
1
1
1
1
0
1
2
1
1
1
1
0
1
2
1
0
1
1
2
0
1
2
1
0
1
1
0
1
1
2
0
2
1
1
1
1
0
1
1
1
1
1
1
1
1
0
1
0
1
0
1
2
0
1
0
0
1
2
0
0
1
3
1
1
1
0
1
1
2
1
0
1
1
2
1
0
1
1
1
0
0
2
2
1
0
2
1
1
0
1
2
2
1
1
2
0
1
1
1
0
1
1
1
1
1
1
1
1
0
1
2
1
2
0
1
1
2
1
1
0
1
0
2
2
1
0
1
1
2
1
1
1
0
1
1
1
0
0
0
0
2
0
1
0
1
2
1
1
2
1
2
2
1
1
2
1
0
2
0
0
3
1
0
0
1
1
1
1
3
1
2
1
0
0
1
1
1
0
0
0
1
2
1
2
1
1
2
1
0
1
0
2
1
0
1
0
2
1
0
0
1
0
2
0
2
0
1
2
0
2
1
1
1
2
0
0
0
2
2
1
0
1
0
2
1
2
1
1
1
2
1
2
0
1
2
1
2
1
1
1
1
1
1
2
2
1
1
0
1
1
1
1
2
0
1
1
0
2
1
0
1
2
0
1
1
0
1
2
2
1
1
0
1
1
3
0
2
1
1
0
0
0
2
1
2
1
0
1
1
1
2
0
1
0
0
1
0
1
2
0
0
1
2
1
1
1
0
1
2
1
1
1
1
1
1
1
0
1
0
0
1
0
0
1
2
1
2
1
0
1
1
1
1
0
1
1
0
0
1
1
1
1
1
1
1
2
1
1
1
1
0
1
1
2
2
0
0
0
0
1
2
0
0
1
1
2
1
1
1
2
1
0
1
0
2
1
0
0
1
1
2
1
1
1
0
0
1
1
1
1
2
1
1
1
2
1
1
0
2
0
2
1
1
1
0
0
1
0
2
2
1
1
0
1
1
1
0
0
2
0
0
1
1
1
1
0
0
0
1
1
1
2
0
1
1
0
1
2
1
2
1
0
2
1
1
1
0
1
0
2
1
0
1
0
1
1
0
1
2
1
1
2
2
0
1
1
1
0
0
1
5
2
1
0
2
2
1
1
0
2
2
1
0
1
2
1
1
2
0
2
2
2
2
0
1
1
1
0
1
1
2
2
2
1
2
0
1
0
2
1
2
2
2
1
1
1
0
2
1
1
0
2
0
0
0
2
0
2
1
0
1
1
2
0
1
1
1
1
1
2
1
2
1
1
1
1
1
0
0
1
1
1
1
1
1
2
1
1
1
0
1
2
2
0
1
3
2
1
1
0
0
1
1
1
1
2
2
1
1
2
1
1
0
2
1
1
1
0
0
1
1
1
0
1
2
1
1
2
1
1
0
2
1
1
1
0
0
2
2
2
1
1
2
0
0
0
1
0
0
0
2
1
1
0
1
2
1
2
1
2
0
1
1
1
0
1
1
1
2
1
2
0
1
1
1
1
1
2
0
1
2
1
1
1
1
1
1
1
1
1
1
1
0
0
2
0
0
1
1
1
1
0
0
0
1
0
2
1
0
1
1
1
1
2
2
0
1
2
2
1
1
1
1
1
0
1
1
1
1
1
0
0
0
0
2
1
1
2
1
2
0
1
1
0
1
1
1
3
2
2
0
0
0
2
0
0
3
1
0
1
1
0
1
2
0
1
1
1
2
1
3
2
0
2
2
2
1
1
1
1
2
1
2
1
1
1
1
1
1
2
1
0
1
0
1
1
0
2
2
0
1
0
1
1
1
0
1
0
0
2
2
1
1
2
1
1
1
1
1
2
1
0
1
1
2
1
1
3
2
1
1
2
2
2
1
1
1
2
0
1
0
0
1
2
1
0
2
1
0
2
1
2
2
2
2
0
1
1
0
0
0
0
1
1
0
0
1
2
1
2
0
0
2
1
1
0
2
2
1
2
2
1
1
0
0
1
0
1
2
2
1
1
1
1
0
2
1
1
1
1
0
1
2
2
2
1
1
0
2
2
1
0
1
3
1
1
0
1
3
1
0
1
1
1
1
1
0
1
1
1
1
2
0
2
1
2
1
1
1
0
1
1
2
1
1
2
1
1
0
1
0
2
2
1
1
2
0
1
1
2
0
0
1
1
1
1
2
3
2
0
0
1
0
1
0
3
1
1
1
1
1
0
1
0
1
2
1
1
1
2
1
1
2
1
1
0
0
1
0
0
1
2
1
2
0
2
3
1
1
1
0
2
1
0
0
1
2
1
1
1
1
1
1
1
0
1
1
2
4
1
0
1
1
1
1
0
1
1
0
2
0
0
3
1
3
1
2
1
1
1
1
0
1
1
1
1
2
1
1
1
0
1
1
1
2
2
0
1
0
1
1
1
1
0
1
1
1
1
0
2
1
1
0
2
1
1
1
2
1
1
0
2
1
0
0
1
2
0
1
0
1
2
1
2
1
1
2
1
1
1
1
2
2
0
1
0
1
2
0
0
1
1
2
1
1
2
1
1
1
1
0
1
2
1
1
3
1
2
1
1
0
1
0
1
0
1
1
2
2
2
2
0
1
2
2
1
1
2
1
1
0
2
1
1
1
1
2
2
1
2
1
0
0
0
1
1
1
1
2
0
1
1
2
2
1
0
1
0
1
0
0
1
2
2
1
0
0
1
1
1
0
1
0
2
1
0
1
2
0
0
1
1
2
1
0
2
1
1
1
1
1
1
1
1
1
1
2
0
3
1
0
1
1
0
2
1
1
1
1
0
1
1
2
1
1
1
1
0
1
1
1
2
1
1
1
1
1
2
1
2
1
1
1
0
0
2
1
0
2
1
1
1
1
1
0
1
2
2
0
1
1
0
1
1
1
1
2
1
1
1
2
0
1
1
1
0
1
0
2
0
1
0
0
0
2
1
1
1
2
0
1
0
1
2
2
1
0
0
1
2
1
1
1
1
1
2
1
0
1
2
1
2
1
1
1
0
2
2
1
1
1
1
1
2
0
1
1
1
0
2
1
1
0
1
0
1
2
1
0
2
1
0
1
2
0
1
2
2
0
0
1
1
0
1
1
2
1
0
2
0
2
1
2
2
1
1
1
1
1
2
2
0
1
2
2
2
0
0
0
2
2
2
2
1
0
0
1
2
2
0
1
0
0
2
0
1
1
0
1
1
1
1
2
0
0
1
4
0
2
0
1
1
0
1
0
1
2
1
1
0
1
0
0
2
1
3
1
0
0
1
2
1
1
1
0
1
1
0
1
2
0
2
2
2
2
1
1
1
1
2
1
2
2
0
0
0
2
1
2
1
2
1
2
1
1
2
2
2
1
0
1
2
1
1
2
1
2
1
1
1
2
2
1
1
1
1
0
1
1
1
1
1
1
2
1
1
2
2
1
2
2
2
0
1
1
2
1
0
0
1
1
1
0
1
2
1
1
2
2
0
0
1
0
1
0
0
2
1
2
1
0
1
0
0
1
1
1
2
1
1
3
1
1
1
0
1
0
2
0
0
0
1
0
2
0
1
3
1
0
0
1
1
2
0
1
1
1
0
1
2
1
3
1
2
1
2
2
1
1
0
2
1
2
0
0
2
2
1
1
5
1
1
1
1
0
1
1
0
1
0
0
1
1
2
2
3
1
2
1
1
2
0
0
1
1
1
1
1
2
2
1
1
0
7
1
1
0
1
1
1
2
0
2
0
1
1
2
0
0
0
1
0
1
1
1
0
1
1
1
0
0
1
1
0
2
0
1
0
0
1
2
0
1
2
2
1
1
0
2
1
1
1
0
1
0
2
0
0
1
2
1
1
0
0
1
1
2
2
1
1
0
1
0
0
1
2
1
0
1
1
1
2
2
1
0
1
0
1
2
1
2
1
0
1
2
1
0
0
1
1
2
1
2
1
0
0
0
0
1
1
1
2
1
0
0
1
1
1
1
1
1
1
2
1
0
1
1
2
0
0
2
1
1
0
1
1
1
2
0
0
2
1
2
1
1
1
0
0
2
1
0
1
1
1
0
1
2
2
1
2
0
1
1
1
0
2
0
1
1
0
0
1
0
1
1
1
1
1
1
1
0
0
1
1
1
1
2
1
1
1
0
3
0
0
1
1
1
0
1
2
2
2
2
0
0
1
0
0
1
1
0
0
1
3
0
0
1
1
1
1
3
1
2
1
2
1
0
1
2
1
1
0
1
1
1
2
1
0
1
1
1
2
0
1
1
1
1
2
0
0
2
1
0
2
1
0
1
0
1
1
2
0
0
1
0
1
1
0
2
1
0
0
1
0
0
0
0
1
1
1
1
1
1
2
2
1
1
1
0
0
1
1
0
1
1
1
0
0
1
1
1
1
1
0
1
1
0
1
0
0
1
0
0
0
2
2
3
1
2
2
1
0
1
0
1
2
1
1
1
1
2
1
2
1
0
1
0
0
0
0
2
1
0
3
2
1
2
1
0
0
3
0
2
1
2
2
0
2
0
2
2
2
1
1
0
1
2
1
0
1
2
1
1
4
1
2
0
2
0
1
1
1
1
1
2
1
1
2
0
1
1
3
1
1
1
1
0
1
1
2
2
0
1
1
1
2
2
1
0
0
1
1
1
1
1
1
1
1
1
1
0
1
2
1
1
1
1
1
1
2
2
2
1
2
2
1
2
3
0
1
2
3
0
2
1
1
1
0
2
1
1
2
1
1
1
0
2
2
0
0
1
1
1
1
1
1
1
2
0
1
3
1
1
2
2
0
1
0
1
2
0
0
2
1
1
0
1
1
1
0
0
0
1
1
1
2
1
1
1
0
1
2
1
2
1
0
0
1
0
1
0
2
2
0
1
1
1
0
2
2
1
1
1
0
0
0
1
1
1
1
1
1
0
1
2
1
2
0
1
1
1
1
1
1
0
0
2
0
1
1
1
1
1
1
2
1
2
2
0
2
1
1
0
1
2
2
2
2
1
2
1
0
1
0
1
2
2
1
2
1
0
2
1
1
0
0
1
1
2
2
2
0
2
2
0
0
0
1
1
0
0
1
1
1
1
0
1
0
2
2
0
1
1
1
2
1
1
0
0
0
0
1
1
1
0
1
1
0
1
2
0
1
1
1
0
2
1
0
2
1
2
2
0
1
1
1
2
0
0
0
1
3
2
0
0
2
1
1
0
1
1
2
2
1
3
1
1
0
1
2
1
1
1
2
0
1
0
0
1
1
1
1
0
1
2
2
2
1
2
1
1
4
1
1
1
1
0
0
1
1
0
2
1
2
2
0
1
1
1
0
2
1
3
0
1
0
1
1
1
2
1
2
0
0
0
1
2
1
1
1
2
2
1
0
3
0
1
2
0
0
1
1
1
1
0
0
1
0
1
2
1
2
0
0
0
1
0
1
1
1
0
2
1
2
2
2
0
1
1
0
1
2
1
1
1
2
2
0
1
1
2
1
2
2
1
2
1
1
1
1
1
2
1
0
2
1
0
0
0
0
1
2
2
1
2
1
0
1
1
1
2
1
0
2
2
2
0
1
1
2
1
0
1
1
1
2
2
2
2
1
2
1
1
1
1
1
1
1
0
0
3
1
3
1
2
1
1
0
1
0
1
1
0
1
0
2
2
0
1
0
1
0
0
0
1
1
0
1
0
1
0
2
0
1
2
2
2
0
1
0
2
1
0
0
1
1
1
2
1
1
1
1
0
1
0
2
1
0
0
2
1
3
1
1
1
1
2
0
1
1
0
2
2
0
1
2
1
1
0
2
2
1
0
1
2
1
0
2
1
0
0
0
2
1
2
1
1
1
1
1
2
0
0
0
1
0
1
0
1
1
1
0
1
1
0
1
2
2
1
3
1
1
2
0
1
2
2
0
0
0
1
1
0
1
0
1
1
0
1
1
1
1
3
1
1
2
2
2
1
1
4
1
2
2
1
2
1
0
1
1
1
1
2
0
1
0
2
1
2
0
2
1
0
1
1
1
2
2
1
2
2
0
0
1
2
1
1
1
1
1
1
2
0
0
2
1
2
0
0
1
1
0
1
0
1
1
1
1
1
1
1
0
2
0
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
2
1
1
1
0
0
1
0
1
1
1
1
1
2
0
0
0
0
1
0
2
0
1
1
2
1
0
0
0
1
1
1
0
1
2
2
2
1
1
0
2
1
1
1
2
0
1
1
1
1
0
1
1
0
1
1
0
1
2
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
0
0
1
0
0
1
1
0
1
1
2
0
0
0
0
2
0
2
0
1
1
1
1
2
1
2
2
0
1
1
0
1
2
1
0
0
6
1
1
1
1
2
0
0
0
1
2
1
1
0
1
2
1
3
0
1
0
0
1
1
0
2
1
1
2
0
2
1
2
1
0
2
1
2
1
2
3
1
0
1
1
0
1
1
1
2
2
1
1
0
1
1
1
1
0
3
1
1
0
0
0
2
1
0
0
2
1
1
2
1
1
1
0
1
1
0
1
2
1
1
1
1
0
0
2
0
1
2
2
1
2
2
2
1
2
1
2
1
1
0
0
0
0
1
1
0
1
2
1
0
0
2
2
2
1
2
3
0
1
1
1
1
2
0
0
2
1
2
0
0
2
2
1
0
1
0
1
1
2
1
1
2
0
0
0
2
1
0
1
2
2
0
0
0
2
2
2
0
0
2
0
0
2
1
1
1
1
0
5
3
2
1
0
2
2
0
1
1
2
1
1
1
1
0
0
2
1
2
2
0
1
2
2
0
1
1
1
1
1
1
2
1
0
1
1
1
1
1
2
1
1
1
2
1
2
2
0
0
1
2
2
1
2
2
1
1
0
1
2
2
1
1
1
0
1
0
1
1
1
0
1
0
0
1
0
1
1
1
0
2
1
1
0
2
2
2
1
2
1
1
0
1
2
0
2
1
1
0
1
2
1
2
1
0
0
0
1
1
1
1
1
0
0
1
1
1
0
1
1
2
0
1
0
0
2
1
3
1
0
1
0
1
2
0
0
0
0
1
0
0
1
1
1
0
1
0
0
2
1
1
1
1
2
1
1
1
2
1
0
1
1
1
1
1
1
1
1
1
1
0
1
2
2
1
0
1
0
0
1
2
1
2
1
2
1
2
1
2
1
1
1
0
1
0
1
1
3
1
0
2
0
2
1
1
1
0
0
1
1
0
1
0
1
0
1
1
0
0
1
1
0
0
0
2
2
1
1
3
0
1
1
2
2
2
1
1
0
1
2
2
1
1
1
1
0
1
1
1
1
1
0
1
1
0
2
2
1
0
1
2
2
1
0
1
1
1
0
0
1
1
2
1
1
1
1
1
1
2
1
0
1
1
1
0
2
0
0
2
2
1
1
0
0
2
1
0
2
1
2
1
1
1
0
1
2
0
0
1
2
2
0
0
0
2
1
2
0
1
1
0
3
1
0
1
0
0
1
2
1
1
1
1
1
1
2
1
1
0
1
0
1
1
0
0
2
1
1
0
1
2
0
1
1
1
0
2
1
1
1
1
0
2
1
1
2
1
1
0
0
1
0
1
1
2
1
1
1
1
1
1
2
0
1
2
1
1
1
0
1
1
2
1
0
2
1
2
2
1
2
2
1
1
0
1
1
0
1
1
1
0
0
2
0
0
1
1
2
1
0
2
1
5
1
2
1
1
2
0
2
0
2
2
2
2
1
1
2
0
0
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
0
1
2
2
0
1
1
1
1
0
1
1
1
0
0
0
1
1
1
1
1
6
1
0
2
1
1
0
1
0
1
0
0
2
0
2
0
2
1
1
1
0
1
0
0
0
0
2
1
1
2
2
1
0
2
1
2
1
2
1
2
4
1
0
1
0
0
1
0
2
1
0
2
1
1
1
2
1
2
2
1
1
1
1
1
1
2
1
0
1
1
2
1
1
1
0
1
2
0
1
1
1
1
0
0
1
0
0
2
1
1
1
1
2
1
2
0
1
1
4
1
1
1
1
1
1
2
2
1
1
0
1
1
1
2
0
0
0
1
1
2
1
2
0
0
2
2
1
2
0
2
0
0
2
1
1
0
1
2
2
1
1
1
1
1
0
1
1
1
1
0
1
2
1
2
2
2
0
1
2
1
0
0
1
1
3
1
0
1
0
1
0
2
0
1
1
1
2
0
1
2
1
2
1
2
1
0
2
1
2
0
1
1
1
0
2
0
0
2
1
0
1
1
2
2
1
1
0
2
1
2
1
2
1
1
1
2
0
0
0
1
2
2
1
1
1
1
1
1
1
2
2
0
0
0
1
1
2
0
1
1
1
1
0
1
2
1
1
1
1
0
1
0
1
1
1
1
0
2
1
0
2
2
2
1
0
0
1
0
0
1
2
0
1
2
2
2
1
0
2
2
2
0
1
2
1
1
1
1
1
2
2
2
0
2
1
1
2
2
0
1
1
1
2
2
2
1
1
0
1
1
0
0
1
1
1
0
0
0
1
1
2
1
1
2
1
1
1
0
1
2
2
1
0
0
1
1
1
0
1
1
2
2
1
1
1
1
1
1
0
1
1
2
0
0
1
1
1
1
1
1
3
2
0
0
0
0
0
0
0
0
1
1
1
0
1
1
0
0
1
2
1
0
1
1
2
4
0
1
0
6
1
0
2
1
1
1
0
0
2
1
0
1
1
1
1
1
1
1
2
1
3
1
1
2
3
0
1
0
1
0
2
1
2
1
0
1
1
1
1
0
0
1
1
2
1
1
1
2
0
0
1
1
1
1
2
1
1
1
1
0
0
1
1
1
1
2
2
0
1
0
1
0
1
1
0
0
1
1
0
0
0
1
2
1
2
1
1
0
0
0
1
0
1
1
2
2
1
1
2
1
0
0
1
1
1
0
1
1
1
1
1
1
0
1
1
0
0
0
1
1
1
1
0
0
2
0
0
2
1
2
1
1
0
1
0
0
2
1
1
2
0
1
1
1
4
1
2
1
2
1
2
0
1
2
2
0
1
2
0
0
0
0
2
0
2
1
1
2
2
2
0
2
2
0
1
1
1
1
1
1
1
0
1
0
1
2
2
1
2
1
0
2
0
1
1
1
0
1
2
1
1
1
0
1
1
1
0
1
1
2
1
1
0
2
1
2
1
2
2
1
1
0
1
0
1
2
1
2
2
0
2
1
3
1
0
1
0
2
0
0
0
1
1
1
2
1
0
1
1
1
0
1
1
1
0
2
0
0
0
2
2
0
1
2
1
1
1
0
1
1
1
1
1
1
1
2
1
1
1
1
1
1
0
1
1
0
2
1
1
0
1
1
1
2
1
2
1
1
1
2
2
1
1
1
1
1
1
2
1
1
0
1
1
1
1
0
1
0
1
1
1
1
0
2
0
1
0
0
2
1
0
2
0
1
1
1
1
1
0
2
1
1
1
0
1
0
1
2
0
0
1
1
1
0
0
2
1
1
0
1
1
1
1
2
2
0
0
2
1
1
1
1
1
1
1
1
0
1
2
1
1
1
1
1
1
1
0
0
0
1
0
0
2
1
1
0
0
1
1
0
2
2
0
1
2
1
1
0
1
2
2
1
0
2
1
0
2
2
1
0
1
0
1
1
0
1
1
0
0
1
1
1
1
2
1
1
1
1
2
1
1
2
1
2
1
1
0
1
0
1
1
2
1
2
1
0
0
2
2
1
0
1
0
2
1
1
3
2
1
0
1
2
1
1
1
0
0
0
1
0
0
0
0
1
1
1
2
1
2
1
0
2
1
0
0
1
0
2
1
1
1
1
2
2
1
3
0
1
1
1
0
1
2
0
1
1
0
1
1
1
1
0
2
2
1
0
1
1
0
2
0
0
3
0
1
1
1
0
1
0
0
1
1
1
1
1
2
0
1
1
2
1
1
2
0
1
1
2
0
2
0
2
1
1
1
0
1
0
1
1
1
0
0
2
1
2
0
2
2
2
2
1
2
0
2
1
0
2
0
2
2
1
0
0
1
1
0
0
1
1
1
1
1
1
1
1
1
1
1
0
2
1
1
1
1
0
1
1
1
0
1
2
1
1
1
0
1
2
1
0
1
0
1
0
1
1
1
2
0
2
1
2
0
0
1
1
2
1
0
0
1
1
0
0
0
1
0
1
2
2
0
1
1
1
2
1
2
1
2
0
1
2
2
1
1
1
1
2
0
0
0
0
1
0
0
1
0
1
1
1
1
1
1
1
1
1
2
1
1
2
0
0
1
1
1
0
0
1
1
0
2
2
1
1
2
0
2
0
2
1
0
1
1
0
0
0
1
0
1
1
0
1
1
1
0
1
1
2
0
1
2
0
2
1
1
1
2
1
1
1
1
0
1
1
1
0
0
2
0
1
0
1
2
0
1
1
2
1
2
1
2
1
1
1
1
1
0
2
1
1
1
0
1
1
0
2
2
1
1
2
1
1
1
2
1
2
0
1
1
1
0
3
1
1
0
0
0
2
1
1
0
2
0
1
1
0
1
1
1
1
0
1
1
0
1
0
1
1
1
0
1
1
0
2
1
1
0
1
2
0
0
1
0
0
0
1
1
2
2
1
0
0
1
1
0
0
0
1
1
1
3
0
2
2
0
1
0
1
1
1
0
0
2
2
1
1
2
1
2
1
2
0
1
2
0
0
0
1
1
2
1
0
1
0
1
0
1
0
0
0
0
0
1
1
2
2
2
1
0
0
2
2
0
0
2
1
2
1
1
1
1
2
0
0
0
1
0
0
2
0
1
1
1
0
1
2
1
1
0
1
1
1
1
2
1
1
1
0
1
1
0
2
0
1
0
1
1
1
1
1
0
0
1
1
1
0
1
1
1
1
1
0
2
0
1
2
2
1
1
2
0
2
1
2
1
1
2
1
0
1
3
1
1
0
2
2
1
1
2
2
0
2
1
3
3
2
1
2
1
1
1
2
0
2
1
1
1
1
2
1
0
1
0
0
2
0
1
0
2
2
2
1
2
1
1
1
1
0
2
1
1
1
1
0
1
1
1
1
1
1
1
1
2
1
0
0
2
1
1
0
0
0
2
1
3
2
0
2
0
0
2
2
1
2
2
2
1
2
1
1
2
0
1
2
1
2
2
0
1
1
2
1
1
1
2
1
0
1
0
1
1
2
1
1
0
2
1
1
1
0
0
2
1
1
1
4
1
1
2
1
0
0
0
2
1
2
1
0
2
1
1
0
1
1
0
1
2
2
1
0
1
1
1
1
1
0
1
0
1
2
1
1
2
2
1
0
2
1
1
1
1
1
1
0
0
1
1
1
2
1
1
2
2
1
0
1
0
0
1
0
1
1
1
0
1
2
1
1
1
2
0
0
1
1
1
1
1
2
1
1
1
1
1
0
1
1
0
0
0
2
3
1
4
1
1
1
1
1
1
1
1
2
1
2
0
2
1
1
1
1
1
0
1
1
0
0
0
2
0
1
0
1
0
0
2
2
1
1
0
0
2
1
0
1
1
1
2
1
0
2
1
1
1
1
1
1
2
1
2
2
0
0
1
1
0
1
1
0
0
1
1
1
0
1
1
0
2
0
1
1
1
0
2
1
1
0
2
0
0
2
2
1
0
2
1
1
0
0
0
2
2
1
1
2
0
2
2
1
2
1
1
1
1
1
1
1
0
1
0
1
0
1
2
1
0
1
1
1
2
1
1
0
1
2
0
0
1
1
2
0
0
1
2
2
2
1
0
0
0
1
0
0
4
0
1
1
1
0
1
1
2
0
2
0
1
1
2
1
1
0
1
0
2
1
2
1
1
3
0
2
1
2
1
4
0
3
1
2
0
0
1
2
2
1
2
4
0
1
1
1
0
1
2
1
1
3
1
1
0
1
1
1
0
2
0
1
0
1
0
0
1
2
1
0
3
2
3
1
1
2
0
2
0
0
2
1
1
0
0
1
1
0
0
2
1
2
1
0
1
1
2
0
0
1
1
2
0
1
1
0
0
1
0
1
1
1
0
1
1
0
2
2
1
2
1
1
2
1
1
2
1
1
2
1
1
1
2
1
0
1
2
2
1
1
2
1
0
0
1
0
1
2
1
0
1
1
1
2
1
1
0
1
1
2
1
0
1
0
2
1
1
1
0
0
1
1
1
1
2
0
1
0
0
1
1
1
0
0
1
2
1
2
1
1
0
0
1
0
2
1
0
0
2
1
2
0
1
0
0
0
1
1
0
1
1
1
0
1
2
1
0
0
1
5
0
2
1
1
0
2
1
1
1
2
1
0
1
2
1
1
2
2
3
2
2
1
1
0
1
2
0
2
2
1
1
0
1
2
0
2
1
2
1
0
1
0
0
1
1
1
1
1
0
2
1
0
1
0
1
1
2
2
0
0
3
1
1
1
2
1
1
1
0
2
1
1
0
0
1
0
1
1
0
1
1
1
1
1
1
1
1
2
0
1
1
1
1
1
1
1
0
0
2
0
1
0
1
2
1
1
1
0
1
2
1
1
0
2
1
2
2
1
1
2
1
1
0
2
0
2
1
1
0
0
0
1
2
1
0
1
1
0
1
1
2
1
0
1
1
1
1
1
2
0
0
1
0
0
1
2
1
1
1
0
0
1
0
0
1
0
0
0
1
1
0
1
0
1
1
1
2
1
0
0
1
2
1
1
1
1
2
2
1
2
2
1
1
1
1
2
0
0
0
1
2
1
2
2
0
1
1
1
1
1
1
1
1
2
2
1
2
1
2
1
1
1
1
1
1
1
2
2
1
0
2
1
2
1
1
1
2
0
1
0
0
2
1
2
1
0
0
1
1
2
0
0
1
1
2
2
1
2
0
1
2
0
3
0
2
1
1
0
0
0
1
0
0
1
1
1
1
2
2
2
2
2
1
0
2
1
1
1
1
1
1
1
1
1
1
1
1
0
0
2
2
2
0
2
2
0
2
1
2
2
1
1
2
2
1
0
4
0
2
2
2
0
0
0
1
1
1
0
1
1
1
2
0
0
1
1
1
0
1
1
1
1
0
0
1
1
1
0
2
0
1
0
1
0
2
0
1
2
1
3
1
0
2
0
0
0
1
1
1
0
0
0
1
0
1
1
0
0
0
2
1
2
2
1
1
2
3
2
0
1
1
0
0
1
1
12
1
2
0
0
2
1
2
0
3
0
2
1
1
1
1
0
1
0
1
2
2
0
1
0
1
0
0
0
1
2
0
1
0
0
1
1
2
2
2
1
1
2
2
2
0
2
0
0
1
1
1
2
2
0
2
2
0
2
0
1
1
1
2
1
1
1
0
0
1
0
0
2
1
2
1
1
1
0
1
2
1
2
3
1
3
1
1
3
2
1
1
0
1
0
0
0
1
2
1
2
1
1
0
2
1
2
1
1
2
2
1
1
0
2
0
1
0
1
1
0
0
1
1
1
2
0
2
1
0
0
1
1
0
0
1
2
2
1
1
1
2
1
2
0
1
0
1
1
2
1
1
2
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
2
0
1
1
2
2
0
0
1
1
0
1
1
1
0
2
1
2
1
2
1
2
1
2
2
1
1
0
0
1
1
0
2
0
0
4
2
1
0
0
2
0
1
1
0
0
1
2
0
1
0
1
0
1
1
1
1
2
2
1
3
1
1
1
2
1
0
0
2
2
1
1
1
1
1
1
1
0
1
0
2
1
0
1
1
1
1
3
2
2
1
0
0
1
0
2
1
3
1
0
1
1
2
1
2
1
1
2
1
0
1
2
0
0
2
2
1
2
1
1
1
1
2
0
1
0
2
2
1
0
2
1
1
1
1
1
2
1
1
0
0
2
1
1
0
1
1
1
0
1
1
2
1
3
2
0
0
0
1
1
0
1
2
0
0
1
1
0
2
1
1
2
0
0
0
1
0
1
1
0
2
1
1
1
2
2
1
1
1
0
1
2
1
1
1
1
1
0
1
2
1
0
3
1
1
1
1
2
1
0
2
1
1
1
1
0
1
1
2
1
0
2
1
2
1
0
1
0
2
0
2
2
1
1
2
2
0
1
2
3
0
1
1
0
1
1
1
1
0
1
1
1
1
2
0
1
0
1
1
1
2
1
1
1
0
1
0
1
1
0
1
0
0
0
0
0
0
2
1
0
0
2
2
1
1
0
1
1
1
1
1
1
0
1
0
2
2
2
0
2
2
1
2
0
3
0
1
0
2
1
1
1
2
1
2
0
1
1
2
1
1
1
1
0
0
0
0
0
0
2
1
0
1
1
0
1
0
1
2
0
0
1
2
1
1
2
1
1
1
0
2
0
1
0
1
1
2
1
2
0
1
1
2
1
0
2
0
1
0
0
1
1
1
1
1
0
0
3
2
1
1
0
1
1
1
1
1
0
2
2
2
0
2
1
1
2
0
1
1
2
2
1
0
1
2
0
1
2
0
2
1
2
1
2
2
1
0
1
1
1
0
1
2
0
1
2
1
1
1
1
2
1
1
1
1
0
1
2
2
0
0
1
2
1
1
1
1
0
1
0
1
1
2
0
2
1
1
1
0
1
2
1
0
1
1
1
1
0
2
1
1
1
1
1
1
1
0
0
1
1
0
1
0
0
1
1
2
0
0
1
1
0
0
1
0
1
1
1
1
1
1
1
0
1
2
1
2
1
0
0
1
1
1
2
2
1
1
1
2
1
2
1
2
1
2
2
2
1
0
1
1
1
0
1
1
2
0
1
1
1
1
0
2
2
2
0
3
0
2
0
1
1
1
1
0
0
1
0
0
1
0
1
1
1
1
1
1
2
0
0
0
0
1
0
1
2
2
1
0
1
0
1
1
0
1
1
0
1
2
0
1
0
2
0
0
1
3
0
1
0
1
0
0
0
1
1
1
0
1
0
0
2
2
0
1
2
1
1
1
0
2
1
0
1
2
1
1
1
0
1
2
0
0
0
2
0
1
2
2
1
2
1
1
1
1
1
2
1
1
0
1
1
0
1
1
1
2
0
1
1
1
1
1
0
1
1
1
2
1
1
0
0
0
1
2
1
1
1
1
1
0
1
2
1
1
3
0
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
1
0
1
0
1
1
0
1
1
1
0
1
0
0
1
2
1
1
2
1
1
0
2
1
0
0
1
1
1
2
2
0
1
2
1
0
2
0
1
1
1
1
1
1
2
1
0
1
0
1
1
1
2
1
1
1
1
1
2
0
1
1
1
0
0
1
1
1
1
0
1
1
0
2
0
2
1
1
0
2
1
1
0
1
1
1
1
2
0
2
0
0
0
1
1
2
0
1
1
1
0
2
1
0
0
1
1
3
1
1
1
2
1
1
2
2
2
0
2
1
1
1
1
2
2
1
1
1
1
2
2
1
1
1
2
1
1
1
1
1
1
1
1
1
0
0
2
1
1
1
0
1
1
1
2
1
0
0
2
1
1
2
2
1
1
1
1
1
2
1
2
1
0
1
2
3
2
1
1
2
0
2
2
1
2
2
3
2
1
2
0
0
1
1
1
0
2
2
1
1
2
2
2
1
1
1
1
1
0
1
0
1
2
1
2
0
0
1
0
0
2
1
1
1
1
1
0
1
1
1
0
1
1
1
1
0
0
1
1
1
1
1
0
1
0
2
1
1
2
1
1
1
0
1
1
1
2
1
2
0
1
2
1
2
0
1
1
2
1
1
1
1
2
0
1
3
1
0
0
1
0
1
1
2
1
1
0
0
1
1
2
1
0
1
0
0
0
1
1
2
1
1
0
2
1
1
1
1
2
2
1
1
1
1
2
0
1
1
1
1
0
0
1
1
1
2
2
0
1
2
1
0
0
1
0
0
1
1
0
1
0
3
0
1
1
1
2
2
2
2
2
0
0
1
0
0
1
1
1
1
1
1
0
1
2
1
1
1
1
1
0
0
1
2
1
0
0
1
1
0
2
0
0
1
0
2
0
1
1
1
1
1
1
0
0
1
1
2
1
1
0
1
0
2
1
1
0
0
1
1
1
0
1
2
1
1
1
1
1
0
2
1
0
1
1
1
2
0
2
2
2
2
2
1
0
0
1
1
1
1
0
1
1
1
0
0
1
1
0
1
4
1
0
1
1
2
0
1
1
0
1
1
2
0
0
1
1
1
0
2
0
1
1
0
0
1
1
0
0
0
1
0
0
2
1
1
3
1
1
0
1
2
2
1
1
2
1
0
1
4
1
1
1
1
0
2
1
0
0
1
1
1
2
1
0
0
0
1
0
1
0
2
0
1
1
0
2
1
1
0
2
1
1
1
1
1
0
2
1
0
0
1
1
2
1
0
1
1
0
1
1
2
2
0
0
1
0
1
0
1
1
1
1
1
2
0
0
2
1
1
1
0
1
0
0
0
1
0
1
1
1
2
1
1
0
1
0
1
2
1
1
1
1
1
2
2
0
2
2
1
0
0
0
0
2
0
1
1
1
1
0
1
0
1
1
1
1
0
0
2
2
1
0
1
0
3
2
0
2
1
2
1
1
1
1
1
0
1
0
1
0
2
1
1
0
0
0
0
2
0
1
0
0
2
2
2
1
2
1
1
0
3
2
1
2
0
1
1
4
1
2
0
0
0
2
0
1
2
0
2
7
1
2
1
2
0
1
0
2
2
1
1
0
1
1
1
1
1
2
1
2
2
1
1
2
2
0
0
1
1
1
2
0
2
1
1
1
1
2
2
1
1
1
0
2
1
1
0
1
2
0
1
2
1
3
1
1
1
1
2
1
2
1
1
1
0
1
2
1
1
1
2
1
2
1
1
0
1
1
1
0
0
2
2
1
1
1
2
1
2
1
0
0
0
1
1
0
1
0
1
0
2
2
0
2
1
0
0
1
1
1
2
1
1
1
1
1
2
0
1
2
1
1
0
2
0
2
1
0
0
0
2
1
2
1
0
1
1
1
2
1
0
2
0
2
1
1
0
1
0
0
1
0
0
1
1
2
1
0
0
1
2
2
0
2
0
2
1
0
1
1
1
0
1
1
1
1
2
1
0
1
0
0
2
1
1
1
2
2
1
0
2
0
0
0
0
1
1
2
1
2
2
2
2
0
0
1
1
0
0
0
0
1
1
1
1
0
0
1
1
1
1
0
2
2
0
1
1
1
0
1
1
1
0
0
0
2
1
1
1
0
0
0
0
2
2
2
1
1
0
2
2
1
1
2
2
1
1
2
0
0
0
1
0
0
1
0
0
2
0
1
1
0
0
1
0
1
1
1
1
1
1
1
1
0
0
0
1
1
1
1
2
1
1
1
1
0
2
0
0
2
1
0
0
0
2
0
1
0
1
1
1
0
1
0
1
2
1
1
0
1
0
0
2
1
1
1
1
0
0
1
0
1
1
1
0
0
2
0
1
1
1
3
0
0
0
0
2
1
1
1
3
1
2
1
1
2
0
0
0
1
1
1
1
1
0
0
1
1
0
1
0
0
0
0
1
1
1
1
1
1
0
1
1
2
0
1
1
0
1
2
1
1
1
2
1
1
0
1
1
2
1
1
0
0
1
1
2
1
0
0
1
1
1
1
1
0
2
0
2
1
2
0
1
0
1
1
2
2
2
1
1
1
1
1
2
0
1
0
1
0
0
1
0
1
1
1
1
1
1
1
1
1
0
1
3
0
1
1
1
1
1
0
2
0
3
1
1
2
1
2
1
1
1
1
0
0
1
1
1
0
1
1
1
1
2
1
1
3
0
2
2
2
0
0
2
2
2
1
0
1
0
0
1
0
0
0
1
0
2
0
1
1
1
1
0
1
1
0
2
2
1
2
0
1
1
0
1
1
0
0
2
2
3
0
1
0
1
1
1
2
1
0
0
1
2
2
1
1
0
1
0
2
1
1
1
1
2
2
0
2
1
1
0
2
1
0
0
0
1
0
1
2
0
1
1
0
1
0
1
2
0
0
1
1
1
1
2
1
1
1
1
0
3
2
1
0
2
0
1
1
1
0
0
1
1
2
1
2
1
2
1
1
2
0
0
1
1
2
1
1
0
1
2
1
1
1
1
1
1
1
2
0
1
1
0
1
1
1
2
1
1
0
0
2
1
2
1
0
1
1
1
1
2
2
1
1
1
3
1
2
1
0
2
0
1
0
1
1
2
0
0
1
1
1
1
0
2
1
1
1
2
2
0
1
1
2
0
2
2
2
1
1
3
1
2
1
1
0
1
1
1
0
1
2
2
0
2
0
3
1
2
2
2
1
1
1
0
1
1
1
1
1
0
3
1
0
0
1
1
1
1
0
0
1
1
1
1
0
2
0
1
1
1
1
0
0
1
2
0
1
2
1
1
1
1
1
0
1
2
0
1
1
1
0
2
0
1
1
1
1
1
1
2
1
1
2
2
2
0
1
1
1
0
0
0
2
1
2
1
2
1
2
1
0
1
2
2
0
1
0
0
1
1
1
1
0
1
0
2
2
1
0
1
0
0
1
1
2
2
0
0
2
0
2
1
4
1
0
1
2
0
0
1
1
0
2
1
0
2
2
0
0
1
1
1
0
2
1
1
0
1
1
0
2
1
0
1
1
1
2
1
1
1
0
2
1
0
2
2
2
0
1
1
1
0
1
2
1
1
1
0
1
2
2
2
1
1
1
1
2
2
2
1
1
0
0
1
2
1
1
1
1
2
0
1
2
3
1
2
1
1
1
2
1
0
1
2
1
1
1
1
1
3
0
1
1
0
1
1
1
2
0
1
0
1
1
1
1
1
1
1
1
1
0
0
1
1
1
1
1
1
0
1
1
1
1
1
1
3
5
2
0
1
0
0
1
1
0
0
1
1
0
0
1
1
0
1
2
0
2
0
1
0
0
1
0
0
2
2
0
1
1
1
1
1
0
1
2
1
1
1
1
2
1
0
0
1
2
1
1
0
2
1
1
1
2
1
2
1
0
1
1
1
1
1
1
0
2
1
2
2
1
0
0
0
1
2
0
1
0
1
0
0
2
1
3
2
2
0
1
1
1
2
0
1
1
2
0
0
1
1
1
0
2
1
1
0
1
2
0
1
0
1
0
1
0
1
1
1
1
0
0
2
1
1
1
0
2
2
2
1
1
1
1
1
1
1
1
1
0
1
1
1
2
2
1
1
1
1
0
1
1
0
1
0
1
0
1
1
0
1
1
0
1
1
2
1
1
0
2
1
1
1
2
0
2
1
0
1
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
1
0
1
2
0
1
0
1
2
2
1
1
1
1
0
2
1
1
2
0
1
1
0
1
1
1
2
3
0
1
0
1
1
1
2
1
0
0
0
1
0
1
1
3
1
0
1
0
1
0
2
2
1
1
1
1
0
1
2
0
1
2
1
1
1
1
0
1
1
1
0
1
2
2
1
1
1
1
1
2
2
1
1
1
2
1
1
0
0
1
0
2
2
2
1
1
0
1
1
1
0
1
1
2
2
0
2
1
1
2
2
1
1
1
0
1
0
1
2
1
1
1
1
2
1
0
3
2
0
1
1
2
1
0
1
1
1
1
0
2
1
1
0
2
1
2
0
1
1
1
1
2
2
1
2
1
1
0
1
1
1
1
2
0
1
0
1
0
2
2
2
2
0
2
1
0
1
0
1
0
1
1
2
2
0
1
1
0
0
0
1
1
1
1
2
1
1
0
1
3
1
1
1
1
2
2
3
1
1
0
0
2
1
2
1
1
1
0
2
0
0
0
2
2
0
1
3
1
0
1
1
2
1
0
2
1
2
0
1
1
1
0
1
2
3
2
1
1
0
0
1
1
1
0
0
0
1
0
1
1
4
1
1
2
2
0
1
0
1
2
1
1
2
0
2
0
2
1
1
0
1
1
0
2
1
2
1
1
2
0
1
3
2
1
2
1
1
2
2
0
1
0
1
0
1
0
2
1
0
2
0
1
2
1
1
0
1
1
1
1
1
1
1
2
1
2
0
2
1
1
0
2
2
2
1
0
2
1
1
2
0
1
0
2
1
2
2
1
2
2
2
1
1
0
0
1
1
1
1
2
1
0
1
2
1
0
1
1
1
1
1
1
1
0
1
0
1
1
1
1
1
0
1
2
0
1
1
0
1
1
0
2
1
2
2
1
1
1
1
2
0
0
0
1
1
2
1
0
0
2
2
1
2
1
2
1
1
1
1
1
0
1
1
1
1
0
1
0
1
2
0
2
1
0
1
2
1
0
1
0
0
0
1
1
2
1
1
2
1
1
0
0
0
0
2
1
0
2
2
1
0
0
0
0
2
1
1
1
2
1
0
1
0
0
1
2
1
1
2
1
2
0
2
0
2
2
0
1
0
1
3
0
1
0
1
1
1
1
1
1
0
1
0
0
2
0
1
2
1
1
0
1
1
0
1
1
1
2
1
2
1
2
1
1
0
2
2
1
1
1
1
1
0
0
2
0
0
1
0
3
1
1
1
1
1
1
0
0
0
1
1
2
0
0
1
1
1
2
1
2
2
2
0
0
2
1
0
0
1
2
1
2
1
1
0
2
1
1
1
1
1
1
0
1
1
2
2
1
0
2
0
3
1
1
1
0
1
2
2
1
1
1
1
1
1
1
1
2
1
1
0
3
2
1
0
1
2
1
0
1
1
1
1
1
2
1
2
1
2
2
2
1
0
1
1
1
0
0
2
1
2
0
0
1
1
0
1
2
0
0
1
1
1
1
0
1
0
0
1
1
1
1
0
0
1
0
0
2
1
1
1
0
1
0
1
1
2
0
0
2
0
1
1
1
2
1
0
2
1
1
1
1
0
2
1
2
2
0
1
0
1
2
1
1
1
1
0
2
2
1
1
1
1
1
1
0
0
0
1
1
2
1
2
1
2
0
2
2
1
0
1
1
2
0
0
1
1
0
2
0
0
1
1
2
0
2
1
1
0
1
0
2
0
2
1
0
0
1
2
0
1
1
1
0
1
1
1
2
3
1
1
1
0
2
1
0
0
2
1
1
0
3
1
2
2
1
1
0
1
2
1
2
0
1
0
0
1
1
1
1
0
1
1
1
0
1
1
1
1
2
1
1
1
1
0
2
0
2
1
0
1
1
0
1
0
0
0
2
2
1
0
2
1
0
1
2
1
1
0
1
0
1
1
2
2
1
1
2
0
1
2
2
1
1
2
1
0
2
0
1
0
0
2
0
2
2
1
1
1
1
2
1
1
1
0
1
2
2
0
1
1
1
1
1
0
0
1
1
1
1
2
0
0
1
3
4
2
1
0
1
1
0
1
1
2
1
1
0
1
2
1
1
0
2
0
1
1
0
1
2
1
1
0
2
1
1
3
0
1
0
1
2
0
2
1
0
1
1
2
0
1
1
2
1
1
0
3
1
1
2
1
0
1
2
1
0
0
1
2
0
2
2
1
1
1
1
1
0
1
1
2
1
0
1
0
1
2
1
1
2
0
1
1
2
1
1
1
0
1
2
1
1
2
0
2
2
1
0
0
2
1
1
1
1
5
1
1
0
0
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
0
1
1
2
0
1
0
2
2
1
1
2
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
0
0
2
0
1
2
2
2
1
1
1
1
1
1
0
0
2
2
1
1
2
0
1
0
0
1
0
0
1
1
1
2
1
1
1
1
1
1
1
1
0
2
1
1
0
1
1
1
1
0
2
0
3
1
1
2
1
2
0
1
0
1
2
3
0
1
1
1
1
2
0
2
1
1
2
0
0
0
2
1
2
0
1
0
0
1
1
1
1
2
2
1
2
0
1
1
0
2
1
0
0
1
0
1
1
2
1
1
0
0
0
2
0
2
1
1
1
0
1
0
1
0
2
2
0
1
1
1
0
1
0
0
0
1
2
1
1
0
1
1
0
0
0
1
1
0
0
1
0
1
1
0
2
1
1
2
1
1
2
1
1
1
1
1
1
0
1
1
0
1
1
1
1
2
1
2
2
1
2
1
0
2
1
0
1
2
2
1
0
0
0
0
2
1
0
1
1
1
1
1
2
2
1
0
0
2
2
1
0
0
2
0
1
1
1
2
1
2
2
1
0
1
1
1
1
1
1
0
1
0
2
1
1
4
1
0
2
1
0
1
2
1
1
1
2
0
1
1
0
2
1
0
1
0
0
0
1
0
3
1
1
1
2
0
1
1
1
0
1
0
1
2
1
0
1
2
0
2
0
1
0
1
4
1
2
0
1
1
1
2
1
1
2
1
1
0
2
1
1
0
2
1
1
0
1
1
0
2
1
0
0
1
0
1
0
1
0
0
0
1
1
1
1
2
3
0
1
1
0
0
2
0
1
1
2
1
0
1
1
1
1
0
2
1
2
1
2
1
1
1
2
1
0
1
1
0
0
2
1
1
1
1
1
1
2
1
1
2
0
1
0
1
0
0
2
0
1
2
1
1
2
2
0
1
0
2
2
0
1
2
2
0
1
2
1
3
1
1
0
2
0
1
0
0
1
1
1
2
2
1
2
1
0
1
0
1
1
1
1
1
1
1
1
0
1
2
2
1
2
0
2
1
0
0
2
2
1
0
1
1
0
2
1
2
2
3
1
1
1
1
2
1
1
0
1
2
1
1
2
0
0
1
2
1
0
2
1
2
1
0
0
0
1
0
2
2
1
2
1
1
2
1
0
1
1
1
0
0
2
1
2
0
1
1
1
1
1
1
0
1
0
0
1
1
0
0
1
0
1
0
2
2
1
1
2
3
1
1
0
2
0
1
1
1
1
2
1
1
0
1
0
1
0
0
0
1
1
0
2
1
3
1
1
1
0
1
0
2
2
1
2
1
1
1
2
0
0
0
0
1
1
2
0
1
0
0
0
1
1
2
1
2
1
1
2
1
2
1
1
0
0
1
0
1
2
1
2
0
1
1
1
1
1
1
2
0
3
2
1
0
1
0
1
1
1
1
1
2
1
1
1
1
0
2
0
0
2
1
1
1
1
1
0
1
1
1
1
0
1
0
1
2
2
2
0
0
1
4
1
1
1
1
1
1
1
2
2
2
2
1
2
0
2
1
0
1
1
1
2
1
3
1
1
1
1
1
1
1
1
1
1
0
1
0
1
1
1
1
0
0
1
2
0
0
1
2
1
1
2
1
2
1
1
2
1
1
0
1
2
0
0
1
2
1
0
2
1
2
1
1
1
2
1
1
0
1
2
1
2
1
1
1
0
1
1
1
1
1
1
1
2
1
1
1
0
1
1
2
2
0
0
1
1
2
0
2
1
2
1
1
1
0
1
1
2
2
2
2
1
1
1
2
1
0
2
2
1
0
1
1
1
2
1
0
0
0
2
1
2
1
1
1
2
1
1
1
2
1
0
0
1
1
3
1
2
1
2
1
1
1
0
0
0
0
1
1
1
0
2
0
1
1
0
2
1
2
1
1
1
2
1
0
1
1
1
0
1
1
1
1
1
1
0
0
1
0
0
2
1
0
2
1
2
1
1
2
1
1
1
1
1
1
0
0
0
2
1
1
1
2
1
1
1
0
0
0
2
0
1
1
0
1
0
1
1
2
0
1
1
0
1
0
0
1
1
2
1
1
2
1
1
2
2
2
2
0
1
1
0
1
2
1
0
0
1
0
0
0
1
1
0
2
1
1
0
0
0
0
3
1
0
1
0
1
1
0
0
1
0
0
1
1
1
0
0
0
1
0
2
2
0
0
1
1
1
0
1
1
2
1
1
1
2
5
0
1
0
2
2
1
1
1
2
2
1
2
1
0
1
2
0
0
0
0
2
1
1
1
8
1
1
0
0
1
1
0
0
1
1
1
1
1
1
2
1
0
1
0
2
0
0
0
0
1
2
1
0
0
2
1
2
2
1
2
0
2
1
1
1
0
2
0
2
2
0
3
1
1
1
0
2
0
0
0
1
0
1
0
1
0
0
0
1
2
2
1
0
1
1
0
0
1
1
2
0
1
0
1
1
2
0
0
2
0
1
1
3
1
2
1
1
2
0
1
2
0
2
2
0
0
0
0
1
2
1
1
0
0
1
0
0
2
0
1
1
1
1
0
1
1
1
1
2
0
1
0
1
1
2
1
1
1
2
1
1
2
2
0
2
1
1
0
0
1
1
0
2
1
1
2
1
2
0
2
1
2
2
1
0
0
1
0
0
2
0
2
1
1
1
1
1
1
1
0
1
1
0
1
1
1
1
1
1
1
1
0
0
1
2
1
0
2
1
1
2
1
1
1
1
2
1
0
0
1
1
1
1
1
0
0
2
0
2
0
1
0
1
1
1
0
0
1
2
2
1
0
1
1
1
1
0
0
0
0
0
0
2
0
1
1
1
0
0
0
2
1
1
2
0
0
1
1
2
1
1
0
0
0
3
0
5
0
1
2
1
2
1
0
0
2
1
1
0
1
1
1
1
1
1
1
1
2
1
1
1
2
1
0
1
1
1
1
0
1
0
1
2
1
0
1
0
0
1
1
0
0
1
0
1
1
0
0
0
1
0
2
2
0
0
0
1
0
2
1
1
1
1
1
1
0
1
1
2
1
0
0
1
2
2
2
2
1
1
2
3
1
2
2
1
0
1
1
0
0
1
1
0
2
0
1
2
1
1
2
1
2
2
2
0
0
0
0
2
1
0
1
1
2
2
0
2
0
1
1
1
2
0
0
0
1
1
0
0
1
0
2
1
1
2
2
1
1
1
0
2
0
0
0
2
0
1
1
1
1
1
1
1
0
0
2
1
0
0
1
2
0
1
1
1
0
1
1
2
0
1
1
1
2
0
0
1
1
2
2
1
2
0
2
1
0
0
1
1
1
1
0
2
0
2
1
0
0
2
1
0
0
1
1
1
2
0
0
0
2
1
1
1
1
2
1
1
2
1
1
1
1
1
1
0
1
2
1
1
0
0
2
1
0
1
1
1
0
1
0
1
0
2
0
1
0
1
1
1
1
2
1
2
1
2
1
1
2
0
0
0
1
0
1
2
0
1
1
0
3
1
0
1
1
1
0
1
1
2
2
0
0
1
2
2
1
2
2
1
1
1
1
1
1
0
1
0
1
0
0
1
0
1
1
1
1
1
2
0
1
1
2
1
2
1
1
0
2
0
0
0
2
1
2
2
2
2
1
1
1
1
1
1
1
1
0
1
1
1
2
0
1
1
1
0
1
1
2
1
1
0
1
0
2
1
2
0
1
1
0
1
1
1
0
1
0
1
1
0
1
0
1
1
1
2
0
1
0
2
1
2
2
1
0
1
1
0
2
5
2
2
1
2
2
1
1
1
0
0
1
2
1
1
1
1
1
2
1
2
1
1
1
1
1
2
2
1
1
2
1
0
1
1
0
0
1
1
1
2
2
0
1
1
0
1
1
1
1
1
2
0
1
0
0
1
1
1
2
1
0
1
2
2
1
0
1
1
1
2
0
2
0
1
2
0
1
0
1
1
2
1
1
0
0
2
1
2
1
2
1
2
2
1
1
0
1
2
2
1
1
1
1
0
1
0
2
1
1
2
1
2
1
2
1
1
1
1
2
1
0
2
1
0
2
0
0
0
0
1
2
1
1
1
2
2
2
0
2
1
2
0
2
0
1
2
2
2
2
0
1
1
2
0
2
2
0
1
0
0
1
1
1
2
1
1
2
1
0
1
2
1
0
0
1
1
1
2
2
2
1
1
0
1
1
1
2
1
1
0
1
1
1
1
2
1
1
1
0
0
0
2
2
1
1
1
2
1
1
0
1
2
2
1
1
1
0
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
0
2
0
1
1
1
1
0
0
0
0
2
1
1
1
1
1
2
0
2
2
1
1
1
3
1
1
0
1
1
1
1
1
2
1
0
1
0
2
0
1
1
1
0
0
1
1
0
1
0
1
1
1
0
2
0
1
0
1
1
1
1
0
2
0
0
1
0
0
1
1
1
1
1
1
0
0
2
1
1
1
2
0
2
0
0
1
1
2
1
0
1
1
0
0
0
3
0
0
2
2
2
0
2
1
2
0
1
0
2
2
2
1
1
0
0
0
2
0
1
1
1
1
0
1
1
2
1
1
1
1
1
0
1
1
2
1
0
2
2
1
0
0
0
1
1
1
1
1
1
1
1
0
0
1
0
2
0
2
1
1
1
1
0
2
2
1
2
1
0
1
1
0
0
1
1
0
1
0
2
2
2
0
1
2
0
1
0
1
1
2
2
1
1
1
1
1
0
1
0
3
1
1
2
2
0
1
2
2
1
1
2
2
1
1
1
1
1
0
1
1
0
1
2
0
2
2
1
1
0
1
3
2
2
1
1
1
0
0
0
1
2
1
1
2
1
0
1
1
1
0
2
1
1
1
1
0
0
2
2
2
0
2
1
1
1
0
1
2
1
1
1
1
1
1
1
1
1
0
0
1
0
1
2
1
0
0
1
0
1
1
1
1
2
1
1
1
1
1
2
0
1
2
1
0
2
2
1
1
1
0
1
2
0
1
0
1
1
1
2
2
1
1
2
1
1
2
2
1
1
1
0
2
2
1
1
1
1
1
1
0
0
1
2
1
1
1
1
0
1
1
0
1
2
1
2
1
2
1
2
1
2
0
1
0
1
1
1
0
0
2
3
0
1
0
0
1
0
1
1
0
2
1
0
1
1
0
1
2
0
0
0
2
0
1
0
0
2
2
0
1
2
0
1
2
1
1
1
1
1
0
0
1
1
1
0
0
0
1
1
1
1
1
1
0
1
1
1
0
0
1
1
0
1
1
2
1
0
1
2
1
1
1
2
0
1
1
0
2
1
1
1
1
1
1
0
2
0
0
1
1
1
1
1
0
1
0
0
1
2
1
1
1
0
1
2
2
0
2
2
1
1
3
2
1
0
1
1
1
0
0
2
2
1
1
0
1
0
0
3
1
2
3
1
1
0
0
0
1
0
0
1
0
1
1
1
2
1
1
1
2
1
0
2
1
0
2
1
1
1
0
2
1
0
1
1
0
1
0
2
0
0
0
2
0
1
1
1
1
1
0
1
1
1
0
1
1
2
3
1
1
1
0
1
0
1
2
1
0
2
1
2
1
1
1
1
2
0
0
0
1
1
1
2
2
1
2
0
1
0
1
0
1
0
1
0
2
1
1
1
1
0
1
1
1
1
0
2
0
2
1
1
0
1
1
1
1
0
1
0
1
1
2
1
1
2
1
0
0
1
1
2
1
1
2
1
2
1
2
2
0
2
1
0
1
0
1
0
0
1
1
0
0
1
2
1
1
1
1
1
2
2
1
1
2
2
1
0
1
2
0
1
1
1
1
0
1
0
1
0
1
0
2
1
1
0
0
0
2
2
0
0
0
1
0
2
0
1
2
2
1
2
1
1
1
2
0
1
1
1
1
1
1
0
0
1
1
0
1
0
0
1
0
1
1
0
2
0
0
1
2
0
2
0
0
1
2
0
1
2
1
1
1
2
0
1
2
1
0
2
1
0
1
0
2
0
0
1
2
1
2
1
0
0
2
0
1
2
1
1
3
1
0
1
0
0
2
1
2
0
0
0
1
2
1
0
1
1
0
1
1
0
1
2
1
2
4
0
1
0
1
1
2
3
0
0
1
2
1
0
2
2
1
1
0
0
2
1
0
1
1
1
1
1
1
1
2
0
2
0
1
1
1
0
1
0
1
1
1
2
2
1
1
2
2
0
0
2
1
0
2
0
0
1
0
2
0
1
1
0
1
1
0
0
0
1
1
1
2
0
2
0
1
2
2
0
0
2
1
1
2
1
2
1
0
1
3
1
2
1
2
0
2
0
2
0
1
1
0
2
2
3
0
0
1
1
1
0
1
0
1
1
2
1
0
2
1
0
0
0
1
1
1
1
1
0
2
0
2
0
1
0
1
2
1
1
1
0
1
1
1
2
0
0
1
1
1
1
2
1
2
1
1
2
0
1
1
1
1
2
1
1
1
1
0
2
0
1
1
1
2
1
2
1
2
1
0
2
1
1
1
2
1
1
1
1
1
2
2
1
1
0
1
1
1
2
1
1
0
1
1
1
0
2
1
1
1
2
0
2
2
2
1
1
0
1
2
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
2
2
1
0
2
1
2
1
2
1
1
1
1
2
1
1
2
0
2
2
1
0
0
1
1
1
1
1
1
0
2
1
1
1
0
1
1
0
0
0
1
1
2
1
1
1
2
0
0
0
0
1
0
1
2
0
1
2
0
0
1
1
1
1
1
1
1
2
2
1
2
1
1
0
2
0
2
1
1
2
1
2
3
1
1
2
2
0
1
0
1
1
0
2
2
1
0
2
1
1
2
1
1
1
1
1
0
1
1
1
1
1
1
1
0
1
1
0
1
1
2
2
1
2
0
2
1
1
1
1
2
0
1
1
2
2
1
1
1
1
2
0
1
2
1
2
1
1
1
2
2
1
1
1
2
0
1
2
2
1
0
2
1
3
0
3
0
1
1
1
2
0
1
0
0
1
1
0
1
1
0
1
0
0
0
1
0
2
1
2
1
1
0
1
1
0
1
2
1
1
1
2
0
0
1
1
0
0
1
2
1
1
1
1
1
1
1
1
2
1
0
1
2
2
0
0
1
0
1
2
1
0
0
0
1
0
1
1
1
0
0
2
1
1
0
1
2
2
1
1
0
1
1
1
1
1
1
1
2
1
0
0
0
0
1
2
1
1
1
1
1
0
0
0
0
1
1
1
0
0
1
0
2
1
0
1
1
1
1
2
0
1
1
0
1
0
1
1
1
1
0
2
2
0
1
2
1
2
1
1
1
2
2
1
1
0
1
1
0
0
0
0
1
1
2
1
0
1
2
1
2
1
2
0
0
1
1
1
2
1
0
2
2
1
1
0
1
0
1
1
0
1
1
2
1
2
1
0
0
2
1
1
0
0
0
1
0
0
2
2
1
2
0
1
1
1
2
0
1
0
1
0
1
1
0
2
0
2
1
1
1
0
1
1
2
1
1
1
1
2
1
3
1
2
2
1
1
1
1
2
0
0
0
1
2
2
1
1
1
1
0
1
1
1
2
1
0
1
1
1
0
0
1
1
1
2
1
2
0
1
2
2
1
0
0
2
1
0
1
1
1
1
1
0
0
1
1
1
0
1
1
2
0
1
2
1
1
1
0
0
0
2
0
1
0
1
0
0
2
0
2
1
2
1
2
2
0
2
1
1
1
0
1
1
1
2
1
1
2
1
1
1
1
0
0
1
0
2
1
0
1
0
1
2
1
1
1
1
2
2
0
1
2
1
1
2
2
2
1
1
0
1
1
2
0
1
0
1
2
0
1
0
0
2
1
1
1
2
0
0
2
1
1
1
1
1
2
0
1
1
0
1
1
0
2
0
1
1
1
1
1
0
0
0
1
1
3
2
1
2
1
1
1
2
0
0
0
0
1
1
1
0
1
0
1
0
0
0
0
1
1
1
1
1
1
1
0
1
0
0
2
1
0
1
1
0
0
1
0
1
1
0
4
1
4
1
0
0
1
0
0
1
2
2
2
1
1
0
0
1
2
0
0
2
1
0
2
0
2
1
2
0
1
1
0
0
0
1
0
1
1
1
2
1
2
2
1
2
1
1
1
0
1
1
0
1
0
1
2
0
0
1
1
1
1
1
0
1
1
1
1
0
1
1
1
0
2
2
0
2
0
1
1
1
0
0
4
2
1
1
0
1
1
2
0
0
0
1
1
1
1
2
1
1
1
1
2
1
1
1
0
1
1
1
1
2
0
0
1
2
2
1
1
0
1
2
2
2
0
0
1
0
1
0
1
1
1
1
1
1
2
1
0
2
0
1
3
1
2
0
0
2
2
1
2
1
1
1
1
1
1
0
1
0
2
2
1
2
0
2
1
1
1
0
0
1
0
1
1
0
1
1
1
0
0
1
1
1
2
1
1
0
1
1
2
0
1
0
1
2
0
2
1
0
1
1
2
2
1
0
2
0
0
1
1
1
1
1
2
0
1
2
0
1
1
1
1
1
2
1
2
0
1
1
0
0
1
1
0
0
1
0
1
2
2
0
2
0
0
2
1
1
1
2
0
1
1
1
1
2
2
1
2
1
0
1
1
1
0
1
0
1
1
1
4
0
0
0
1
0
1
1
1
1
1
3
0
1
1
2
0
1
1
1
1
1
1
1
1
0
1
1
1
0
2
0
2
2
2
1
1
2
2
2
1
0
1
2
1
2
0
1
2
1
1
2
1
2
0
1
1
1
1
1
2
1
2
2
1
2
0
2
1
2
0
2
0
1
2
1
0
2
0
0
1
1
1
1
0
2
1
0
0
2
1
0
0
1
2
1
1
1
0
2
0
1
1
0
1
2
1
2
1
1
0
1
1
1
1
0
1
1
0
1
1
1
1
1
1
1
2
1
0
2
0
1
1
0
0
2
1
1
1
1
0
1
1
0
2
1
2
0
1
1
1
1
0
0
0
1
0
2
2
1
2
0
2
1
2
0
1
2
0
2
1
1
0
2
0
1
1
2
1
1
0
2
2
2
1
1
2
1
2
1
0
0
2
1
1
0
1
0
2
1
1
0
0
0
0
1
0
1
1
1
1
1
2
1
2
1
0
1
1
1
3
2
1
0
0
2
1
0
0
1
0
2
1
1
2
2
1
2
2
1
2
0
2
1
0
0
2
2
2
1
1
1
2
1
0
2
0
0
0
2
0
2
2
0
0
0
1
1
2
1
1
0
1
2
0
2
3
1
1
1
1
1
1
1
1
1
1
2
2
1
1
0
1
1
0
1
1
1
2
2
2
1
2
0
1
1
1
1
1
0
0
1
1
0
1
1
1
1
0
2
0
1
1
1
0
0
2
0
2
2
1
0
1
1
0
1
0
1
3
0
1
1
1
1
0
1
1
2
1
0
1
2
1
1
1
0
1
2
1
2
1
2
0
0
1
1
1
2
1
1
1
1
2
2
0
2
0
2
0
1
0
1
1
1
1
0
1
1
2
1
1
1
1
0
2
0
1
0
2
3
3
0
1
3
0
2
0
1
1
2
1
2
0
1
2
0
1
0
0
1
2
0
1
0
1
1
1
0
0
1
0
2
2
2
1
1
3
1
2
2
1
1
1
0
1
1
1
1
0
1
1
0
1
1
1
1
0
0
1
1
2
1
1
1
1
0
0
1
0
1
1
0
1
0
2
1
2
0
1
1
1
0
1
2
1
2
1
1
1
1
2
0
0
2
0
1
1
2
1
1
0
2
2
1
1
1
1
0
0
1
0
0
2
1
0
1
0
2
0
0
1
1
0
1
0
0
1
1
2
2
0
1
2
0
0
2
1
0
0
0
2
1
0
2
0
1
0
1
1
1
1
1
2
1
1
1
1
1
3
1
1
0
2
2
2
1
1
1
1
0
1
1
1
1
1
3
1
0
0
1
2
2
1
1
1
1
1
2
0
1
0
0
1
0
3
0
2
1
2
0
1
2
1
1
1
1
2
1
2
1
0
1
0
2
0
0
0
2
1
1
2
1
1
1
2
1
1
1
2
1
2
1
1
1
0
2
2
2
0
1
1
0
2
1
2
1
1
1
1
2
0
2
0
1
1
0
0
2
0
0
2
0
1
0
1
1
1
1
2
1
0
2
0
2
1
1
1
0
3
2
2
1
0
1
1
1
1
0
1
1
2
0
1
1
1
0
1
2
2
1
2
2
0
1
2
1
1
1
0
2
2
1
0
0
1
1
1
1
1
0
0
0
1
0
1
2
1
2
0
1
2
1
1
2
0
1
1
2
1
2
0
1
1
1
2
0
0
1
0
0
1
1
0
1
0
1
0
0
2
0
1
0
1
1
2
2
2
1
0
1
1
2
1
2
2
1
1
1
1
2
1
1
1
1
0
0
1
1
2
1
0
1
1
1
0
1
0
2
2
1
1
1
0
1
1
0
0
1
0
1
1
1
1
1
0
1
0
2
1
0
1
0
0
2
1
0
0
0
1
2
0
0
2
1
1
2
1
1
1
1
1
0
2
1
1
1
1
0
1
1
1
0
0
1
1
0
2
2
1
1
1
2
0
10
2
1
1
1
2
0
1
1
0
1
1
1
1
1
1
0
1
1
1
2
2
0
2
0
2
2
1
0
2
1
1
2
1
1
1
2
2
0
0
1
0
2
1
0
1
1
0
1
0
1
1
1
2
1
4
1
1
2
1
0
0
1
1
2
2
1
2
0
2
2
1
0
1
1
0
1
0
0
1
1
2
0
1
2
1
0
1
0
1
2
1
1
0
1
1
2
1
1
0
2
1
0
2
0
1
0
1
1
0
1
2
0
2
0
1
0
1
0
1
0
1
0
1
1
1
1
0
1
1
1
1
2
1
1
1
1
1
0
1
2
1
1
1
2
2
1
3
1
2
0
1
0
1
0
1
1
1
1
0
0
1
0
2
0
1
2
1
1
1
0
0
3
1
0
0
2
1
1
0
2
0
0
2
0
1
0
1
1
1
1
0
2
2
0
1
2
1
2
2
1
1
1
0
1
3
1
1
2
1
1
1
0
1
1
0
0
0
2
2
1
1
1
0
1
2
2
0
1
1
2
0
0
0
1
1
1
2
1
2
1
2
0
1
2
1
1
1
1
0
1
0
1
2
1
0
0
0
0
1
2
1
1
2
1
1
2
1
0
1
2
1
1
2
1
2
1
3
1
3
2
3
0
1
2
1
1
1
0
0
1
0
1
1
1
1
1
1
1
0
0
1
1
1
1
1
1
2
2
2
2
1
2
0
1
2
0
1
2
1
1
0
1
0
2
0
1
1
0
2
0
0
0
0
2
1
2
0
2
0
0
2
2
1
2
2
1
1
1
2
1
0
1
0
2
1
1
0
0
0
1
1
1
1
2
0
2
1
1
1
2
1
1
2
1
1
2
1
2
0
1
1
2
1
2
1
1
1
0
2
1
0
1
1
1
1
0
2
0
1
0
0
1
2
0
1
0
3
0
2
1
1
2
1
2
1
0
2
1
3
1
2
2
2
2
2
1
1
2
1
0
1
2
1
2
1
0
1
2
1
1
2
0
1
2
1
0
1
1
1
0
1
1
1
1
1
1
1
0
1
1
1
1
1
1
2
1
0
0
3
1
1
3
1
1
0
1
1
1
2
1
1
0
1
1
1
1
2
0
1
1
0
0
0
2
1
0
2
0
1
1
1
1
2
1
0
1
1
1
0
1
0
0
1
1
1
0
1
2
1
2
1
1
1
1
1
1
2
1
1
0
2
1
0
2
2
1
0
2
2
0
0
2
1
0
1
2
2
2
2
0
2
2
1
0
1
0
1
0
1
1
1
1
0
0
2
2
1
1
0
1
0
1
2
2
0
0
1
0
1
1
0
1
1
1
1
1
1
1
2
2
2
1
2
1
1
1
0
1
1
2
1
2
1
0
0
2
1
2
1
1
0
0
1
2
1
2
1
1
0
0
1
1
1
1
0
0
0
1
2
2
2
3
1
1
2
1
1
1
0
2
1
1
1
2
1
1
1
1
1
1
1
1
1
0
1
0
0
1
1
1
2
0
0
1
2
0
1
1
1
0
2
1
1
2
0
1
0
1
0
1
1
0
1
1
1
1
1
2
2
3
3
1
1
1
1
1
1
1
0
2
1
2
2
1
1
0
1
2
2
1
0
0
1
1
2
1
1
1
1
2
1
2
1
0
1
1
0
1
0
1
0
2
2
0
2
1
2
1
0
0
1
1
2
2
1
0
0
2
1
1
0
1
1
2
0
0
0
0
2
0
1
2
2
1
0
0
1
1
1
1
2
1
4
2
2
2
0
1
1
0
1
2
0
1
1
0
0
1
1
2
0
1
0
1
1
1
1
1
1
1
0
1
0
0
1
1
1
0
1
1
1
1
0
3
1
2
1
0
1
1
1
2
1
0
1
0
1
1
2
2
0
1
1
2
0
1
1
1
0
0
1
1
1
0
3
1
2
0
0
1
0
0
0
0
0
2
0
0
1
1
1
2
2
1
1
1
1
1
0
0
1
1
2
0
2
1
0
1
3
2
0
3
4
1
0
2
0
2
1
1
1
1
1
1
1
2
0
2
2
1
1
0
1
2
1
2
2
0
1
1
1
1
2
2
1
0
1
1
0
0
2
2
0
1
1
1
0
1
2
1
0
0
3
2
1
1
0
0
1
0
0
0
0
1
0
1
2
2
1
1
0
1
0
0
2
1
1
0
1
0
0
2
1
1
1
1
0
2
1
2
1
0
1
1
1
1
1
1
2
1
1
1
1
1
0
1
1
1
2
1
1
0
2
2
6
1
1
0
0
1
1
0
1
0
0
2
0
2
1
2
1
0
0
0
1
2
2
1
1
1
0
0
2
1
0
2
1
1
5
1
2
2
2
0
1
1
1
1
1
1
2
0
1
2
1
1
1
1
2
1
2
1
0
0
0
1
1
1
1
1
2
2
1
0
2
2
1
0
1
0
1
2
1
1
1
1
0
0
1
2
2
2
1
0
1
1
1
2
1
0
1
1
0
0
1
1
1
1
1
1
1
2
0
1
0
1
2
1
2
1
0
1
1
2
1
1
1
2
0
1
1
0
1
0
0
0
0
0
2
0
2
1
1
0
0
1
1
0
0
0
1
0
1
1
0
0
0
0
0
1
0
1
0
0
2
1
1
0
1
1
1
1
0
1
1
1
1
2
1
0
0
1
2
0
1
0
1
1
1
0
2
1
0
0
2
0
0
1
0
1
1
1
1
2
0
1
0
1
2
2
0
1
1
1
0
1
1
0
0
1
0
1
1
2
1
0
2
0
2
1
2
1
1
1
0
0
2
1
1
1
0
0
1
1
1
1
1
1
1
2
1
1
2
2
2
2
1
1
1
2
1
1
0
1
2
3
2
1
1
0
1
1
2
0
1
2
0
1
1
1
2
1
2
0
1
1
1
0
2
1
1
0
1
1
1
2
1
0
1
1
1
2
1
0
0
2
1
2
1
1
2
1
0
2
1
1
0
1
1
0
0
0
0
2
1
1
1
1
1
2
0
1
1
1
0
1
2
1
2
1
1
0
1
0
1
2
1
0
3
1
1
1
1
1
0
2
0
0
1
1
1
0
1
1
0
1
2
0
1
1
1
0
1
2
1
1
2
1
1
1
0
1
0
2
0
1
0
1
0
1
1
0
1
1
1
2
1
0
1
0
2
2
0
3
1
1
1
0
0
1
2
1
2
1
1
0
2
2
0
2
1
2
0
0
2
1
1
0
1
0
1
2
2
2
1
0
0
2
1
2
1
1
1
1
0
0
2
1
0
1
1
1
2
1
0
2
1
1
0
2
1
1
1
1
0
0
2
3
1
1
0
1
0
0
0
1
3
1
2
0
0
0
0
0
1
3
0
1
0
1
0
1
2
0
2
0
1
2
1
1
0
0
2
2
0
0
0
2
1
0
2
1
1
1
1
0
0
2
1
0
1
1
2
1
0
1
1
1
1
2
1
1
1
1
1
1
0
1
0
0
1
1
0
1
1
1
1
1
1
0
1
2
1
0
0
1
1
1
2
2
1
2
0
5
1
0
0
1
0
1
1
0
2
1
2
0
1
2
2
0
2
2
0
0
2
0
1
1
0
1
2
0
0
1
1
1
0
0
1
1
2
1
1
0
1
1
2
1
2
1
0
0
0
1
0
1
0
1
1
0
1
1
2
1
1
1
1
1
1
0
0
1
2
1
0
2
0
0
0
1
0
1
1
2
0
1
2
1
1
1
2
0
2
1
2
1
1
1
1
1
1
0
1
1
1
0
1
1
1
0
1
1
0
1
1
2
0
1
1
1
1
1
3
1
2
1
3
2
2
0
0
1
1
1
2
2
0
0
1
2
1
0
3
0
1
0
1
1
0
1
2
1
1
1
2
0
1
0
1
2
2
0
0
1
2
0
0
0
0
1
0
1
1
1
1
1
2
1
2
2
1
1
1
1
1
3
0
1
2
1
0
1
1
1
2
1
1
1
1
2
0
0
1
2
2
1
1
1
1
0
1
2
1
2
2
1
1
1
1
0
0
1
2
2
1
2
1
1
0
2
1
2
1
2
1
0
1
1
1
0
1
2
2
1
1
0
0
0
1
1
0
1
0
1
1
0
0
1
1
1
2
2
1
1
1
0
1
1
0
1
2
0
3
1
1
1
1
1
0
0
2
0
0
2
1
0
0
0
0
0
1
1
1
3
0
0
1
1
1
0
1
0
1
1
0
0
2
1
1
2
1
1
1
0
1
1
2
1
2
1
1
2
1
0
1
1
0
1
0
2
2
1
1
1
1
1
1
3
0
2
1
1
0
0
1
1
2
1
1
1
2
1
2
1
1
1
0
2
0
2
2
0
1
1
2
1
1
1
1
0
2
0
0
1
2
1
2
2
2
0
1
1
0
2
0
1
0
0
1
1
0
1
0
0
0
1
0
2
0
1
1
1
0
0
0
0
0
1
1
1
0
1
0
1
1
0
1
1
1
2
1
1
1
0
1
2
1
1
0
1
0
1
1
1
2
1
0
0
0
1
1
0
2
0
0
0
0
0
2
2
1
0
1
1
2
1
0
0
1
1
2
1
2
1
1
0
0
2
1
2
1
0
1
0
2
0
0
2
1
2
0
0
2
2
2
2
1
0
1
2
1
1
1
1
2
1
1
0
0
1
1
0
0
1
0
2
0
1
1
0
1
0
1
1
2
1
1
1
1
1
0
1
1
1
2
0
3
1
2
2
1
2
1
1
2
0
1
2
1
0
1
2
2
1
0
0
1
1
1
0
1
2
1
1
0
1
0
1
2
1
1
1
0
0
0
1
1
1
0
0
1
2
2
0
1
2
1
0
1
1
2
1
1
1
1
2
2
2
0
1
0
1
1
1
1
1
1
2
3
1
1
1
2
1
0
1
1
1
1
0
0
2
0
1
1
0
0
0
0
1
1
1
0
1
0
0
1
2
1
0
0
0
1
1
1
0
1
2
0
1
0
1
1
2
1
1
1
0
1
2
0
1
1
1
2
0
2
0
1
2
2
1
2
2
2
2
1
1
0
1
0
1
0
1
2
1
1
1
2
0
1
0
1
0
1
1
1
1
0
0
2
2
0
0
1
1
1
2
1
1
2
1
3
1
1
1
4
0
0
0
2
1
1
0
1
0
1
1
1
0
1
1
2
0
0
0
1
1
2
1
1
1
1
1
0
1
1
1
1
2
2
2
1
1
1
1
1
2
2
0
1
1
1
2
0
1
1
0
1
2
1
1
2
1
1
2
2
1
0
1
2
1
0
1
2
1
1
0
1
1
1
2
0
1
1
2
0
1
2
2
1
1
1
2
1
1
2
1
2
0
1
1
1
0
1
2
0
0
2
1
1
1
0
2
0
1
1
0
1
1
2
3
1
1
2
1
0
1
1
0
1
1
0
1
1
2
0
1
2
2
1
1
0
1
1
1
0
1
0
1
0
2
1
2
2
2
1
1
1
0
1
3
0
0
1
1
1
0
2
0
0
0
2
0
1
1
0
1
0
0
2
1
1
1
2
2
1
1
2
1
0
1
1
0
1
1
1
0
0
0
2
1
0
1
2
0
0
10
0
0
0
0
2
0
1
0
1
1
0
1
0
1
1
2
1
2
1
0
1
1
1
1
0
1
0
1
0
1
0
2
1
2
1
0
1
1
1
1
0
0
1
0
1
0
1
1
0
2
0
1
1
2
2
1
1
1
0
1
1
1
1
0
1
0
1
0
0
0
2
1
2
2
2
1
2
1
2
0
0
0
1
0
2
1
1
1
0
1
1
0
2
0
0
1
2
1
1
1
1
1
2
0
1
1
2
0
1
1
1
1
1
2
0
2
1
0
1
0
2
1
2
1
1
2
0
1
1
1
0
0
0
1
0
0
1
1
1
1
1
0
2
1
1
0
0
2
2
1
1
0
1
1
2
1
1
1
0
1
2
0
1
0
1
2
0
1
1
2
1
1
0
1
0
2
2
0
1
2
1
1
2
1
1
2
1
1
0
0
0
1
2
1
0
0
1
0
0
0
2
1
1
1
2
1
0
1
0
0
0
0
1
0
1
1
2
1
1
1
0
1
1
0
1
2
0
2
1
1
1
2
2
3
0
0
1
1
0
1
2
2
0
1
0
1
0
1
1
1
1
1
2
0
1
0
0
1
3
1
2
1
1
2
0
2
1
1
0
2
0
0
1
1
1
1
2
2
1
2
0
0
0
1
1
0
1
3
1
0
0
1
0
1
1
2
2
2
2
0
1
2
1
0
1
2
1
1
1
1
0
1
0
0
1
2
1
1
1
1
2
1
1
2
1
2
0
2
1
1
1
1
0
1
0
1
1
1
0
1
0
0
1
2
1
0
1
0
1
2
1
1
0
3
1
0
0
1
0
1
0
1
0
1
2
1
2
1
1
1
1
1
1
2
2
0
1
1
1
1
1
2
1
1
2
2
1
1
2
1
0
1
2
1
1
1
0
1
2
1
1
1
0
1
1
0
0
1
1
2
0
2
1
1
1
0
1
0
0
1
2
0
0
2
1
0
0
1
1
1
0
1
2
1
1
1
0
1
2
1
1
1
1
0
2
1
1
0
0
2
0
2
1
1
2
1
1
1
1
1
0
1
2
2
0
1
0
0
2
1
0
1
0
0
2
2
0
1
2
1
1
2
1
2
1
1
0
0
0
1
0
1
2
1
2
1
2
1
1
1
2
1
1
1
1
1
0
1
1
1
1
1
0
1
0
0
1
1
0
0
1
0
2
1
1
0
0
1
1
1
2
2
0
2
1
0
2
3
1
0
1
1
2
0
1
1
1
0
0
1
1
1
0
1
0
2
1
1
1
1
1
1
1
1
1
0
1
0
1
2
2
2
1
2
0
2
1
1
1
2
0
2
2
1
1
0
0
1
0
1
0
3
0
1
2
2
1
2
1
2
1
1
1
0
0
0
0
1
0
1
2
1
1
0
1
1
1
0
1
1
2
1
0
1
1
0
1
0
1
1
2
1
1
0
1
1
2
0
2
1
1
2
2
1
1
1
2
1
0
0
3
1
1
1
1
2
0
1
0
2
3
1
1
0
2
1
1
2
1
0
0
2
0
1
1
0
2
1
1
1
2
2
1
1
1
1
1
1
2
2
2
2
1
0
0
0
0
0
0
2
1
1
1
0
0
1
1
2
1
1
0
0
1
2
1
0
2
1
1
1
0
1
0
0
1
1
0
1
1
1
1
0
2
0
1
2
0
0
1
1
1
2
0
0
1
1
1
1
1
0
0
0
1
0
0
2
0
1
0
1
1
1
1
1
0
0
0
0
1
1
1
1
1
1
2
0
2
1
1
1
1
1
1
0
1
1
1
0
0
1
2
0
0
1
0
0
0
0
1
0
2
2
1
0
0
1
0
0
2
0
2
1
2
0
1
1
1
1
1
0
3
1
0
0
0
0
1
1
0
1
0
1
1
1
2
1
2
1
2
0
1
0
0
1
1
1
0
1
0
2
2
0
1
0
1
0
1
2
1
1
1
1
1
1
2
1
1
0
2
0
2
2
0
1
1
0
1
0
1
0
1
1
1
1
2
1
1
1
1
0
0
2
2
2
0
1
0
2
1
1
1
0
1
0
1
0
1
1
1
1
1
1
1
1
1
2
1
1
2
1
0
0
0
2
1
0
2
0
0
1
1
3
2
2
0
2
2
1
1
0
1
1
0
2
1
0
1
0
1
1
1
1
1
0
0
1
0
1
1
2
1
1
2
0
1
1
1
0
0
0
2
0
1
1
0
1
1
2
2
0
1
2
2
0
0
0
1
2
2
1
1
0
2
1
0
1
2
2
1
1
1
1
2
1
0
0
1
0
0
2
1
0
1
1
0
1
1
1
2
0
1
1
0
0
0
1
1
1
0
2
1
1
0
1
2
2
1
0
2
0
1
1
1
1
1
2
1
1
0
2
0
1
0
1
1
2
1
1
1
2
1
0
1
1
2
2
0
0
0
1
0
1
1
2
1
1
2
1
3
1
2
1
0
1
2
1
1
1
0
1
1
1
2
2
1
1
1
2
2
1
0
1
0
1
0
1
1
1
0
1
2
1
0
1
1
3
0
1
1
1
2
1
1
0
0
1
1
1
1
2
1
0
1
2
1
1
0
0
1
1
1
1
1
6
0
1
1
1
1
1
1
0
1
1
1
0
1
1
1
0
0
0
1
0
1
1
1
1
0
1
0
0
2
0
1
1
1
1
1
0
0
1
2
1
1
2
1
0
0
0
1
1
2
2
1
0
2
0
0
2
2
1
1
1
2
2
1
2
1
1
1
1
0
0
0
2
0
0
1
0
0
1
1
1
1
1
0
1
0
2
2
0
0
1
2
1
2
0
1
2
1
1
2
0
1
1
2
1
1
1
2
1
1
0
0
1
2
0
1
3
2
2
0
2
1
1
1
2
1
2
0
2
1
1
1
1
1
1
2
0
1
1
2
1
1
0
0
0
0
2
1
1
1
0
2
1
1
1
1
0
1
0
2
1
0
1
2
0
0
1
0
0
1
2
0
1
0
1
0
1
1
1
0
1
1
2
0
0
0
1
0
2
1
1
0
2
2
1
1
1
0
4
2
0
1
1
0
1
2
1
0
1
2
1
1
0
1
0
1
1
0
0
0
1
1
1
1
2
2
2
0
1
1
1
0
0
0
1
0
1
2
1
0
2
2
0
2
0
1
0
2
1
1
1
2
2
0
0
0
1
0
0
0
0
1
1
0
0
1
1
1
2
1
2
2
2
0
2
1
1
1
0
1
1
2
1
1
1
1
1
1
2
1
1
1
1
0
2
1
2
0
2
0
2
2
1
1
1
0
2
1
1
0
1
0
0
1
1
1
1
1
2
0
1
2
1
0
1
2
2
1
0
0
0
2
1
0
2
2
1
0
1
0
1
0
2
2
1
1
1
1
2
0
1
0
1
1
1
1
2
0
1
2
2
0
0
0
2
2
2
1
0
0
0
1
1
1
1
1
1
1
1
2
1
1
2
1
1
2
2
0
0
1
1
1
0
1
0
1
0
0
1
1
1
2
0
1
2
1
1
2
0
0
1
0
1
1
1
2
1
1
1
0
0
0
0
1
1
0
4
2
2
2
2
2
0
1
1
0
2
1
0
0
1
1
1
0
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
1
2
1
2
1
1
1
1
0
0
0
0
2
2
0
2
1
0
1
2
1
1
2
2
2
1
1
0
2
1
1
0
1
1
0
1
1
2
0
1
0
0
0
0
1
1
1
1
1
2
0
1
1
1
2
2
1
1
0
2
1
0
2
1
3
0
2
1
0
1
0
1
1
1
1
1
0
0
2
1
1
0
1
1
2
1
0
0
0
0
1
1
4
1
1
0
2
1
0
0
1
0
1
2
0
1
0
2
1
1
2
0
2
1
1
2
2
0
1
1
2
0
0
2
2
1
1
0
1
0
0
1
0
0
0
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
0
1
1
2
0
0
0
1
2
1
2
1
1
2
3
3
1
1
0
4
1
0
0
1
2
0
0
1
2
0
0
0
2
0
2
0
1
1
1
0
1
1
1
1
0
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
1
1
0
2
1
1
1
1
0
0
0
1
2
4
1
0
0
1
1
2
2
1
1
1
2
0
2
0
1
2
0
2
4
0
0
2
1
1
1
0
2
0
2
0
0
1
1
1
0
0
1
1
1
1
1
1
1
2
1
0
0
0
1
0
1
2
1
0
1
1
0
1
2
1
1
1
1
2
0
0
2
1
2
1
2
2
0
1
1
0
2
0
2
0
1
2
1
1
2
1
2
2
0
2
1
2
1
2
1
0
1
1
2
0
0
3
0
1
0
1
1
2
1
0
1
0
0
1
2
1
1
1
1
2
2
2
1
0
3
1
1
1
0
2
1
0
2
1
1
1
2
1
2
2
1
0
1
0
1
2
1
1
0
2
1
0
1
3
2
1
2
1
0
1
1
1
1
1
1
1
3
1
1
1
1
0
0
1
0
0
1
1
2
1
1
0
1
1
1
2
1
2
2
1
0
2
1
1
1
0
1
0
1
0
0
1
1
1
2
1
1
0
0
0
2
1
1
0
0
2
0
1
0
1
1
1
1
1
1
1
1
0
1
1
1
1
2
1
1
1
1
0
0
2
1
1
1
1
0
1
1
0
1
2
0
2
1
2
1
1
1
1
1
0
1
1
0
1
1
2
2
0
1
1
1
2
1
2
0
0
1
1
1
1
2
0
1
1
2
1
1
1
1
0
1
0
0
1
1
0
0
2
1
0
1
2
1
1
2
0
1
1
1
1
1
1
1
2
2
0
1
0
1
1
1
0
0
0
1
1
1
1
0
1
2
1
1
1
1
1
1
1
1
0
2
1
1
1
2
2
1
0
1
2
2
1
1
0
2
1
2
0
1
1
1
1
1
1
1
1
0
2
1
0
1
1
0
2
1
2
1
1
1
1
0
1
1
1
2
1
0
0
1
1
1
1
2
1
2
2
2
0
0
0
0
1
1
0
1
1
1
1
2
0
2
1
1
0
2
2
1
0
1
1
2
0
2
0
1
1
2
0
1
0
1
2
0
1
1
0
1
0
1
1
1
1
0
2
1
2
1
0
2
0
2
1
1
1
1
2
1
0
0
2
2
1
2
1
1
0
1
1
2
1
2
1
1
0
1
1
1
1
0
1
2
2
1
1
0
1
1
1
4
1
1
2
1
0
0
1
2
3
0
0
2
2
1
0
1
2
0
1
0
2
3
1
0
1
2
1
1
1
4
1
1
1
2
1
1
1
3
1
1
1
0
1
1
0
1
1
0
0
1
0
1
1
1
1
2
2
0
2
1
1
2
1
1
1
1
0
1
0
0
0
1
1
1
2
1
0
2
2
1
0
1
1
1
1
1
1
2
2
1
0
2
0
1
2
1
1
2
2
0
1
1
0
2
1
3
1
1
0
0
0
0
1
1
1
1
1
1
1
1
0
1
0
0
1
1
0
0
0
1
2
2
2
1
1
2
2
2
0
0
0
1
2
2
0
1
0
0
2
2
1
2
1
0
1
2
2
2
1
3
1
3
1
1
1
1
0
1
0
0
0
1
1
1
1
1
0
1
2
2
1
1
2
0
1
1
0
0
1
2
1
2
0
1
1
0
0
1
1
0
1
1
2
2
2
1
0
1
0
2
1
1
1
1
1
0
1
0
1
2
1
2
2
0
2
2
1
2
1
0
2
2
0
1
1
1
0
0
1
0
2
0
1
0
1
1
2
1
0
1
2
2
1
1
1
1
2
1
0
0
0
1
1
0
0
1
1
2
1
1
1
2
1
2
2
1
0
1
1
1
1
1
1
1
0
0
0
1
1
0
0
1
1
2
1
1
2
1
1
2
2
1
1
1
1
1
0
1
1
2
2
0
1
1
1
2
2
1
2
0
1
2
1
1
1
1
1
2
1
1
0
2
2
2
2
1
2
1
1
0
0
0
0
0
1
1
2
2
1
2
1
1
1
1
1
2
1
1
0
1
1
1
0
1
1
3
1
1
0
1
1
0
2
0
1
1
2
0
1
0
0
1
1
1
2
0
0
1
1
0
0
0
0
0
2
1
2
2
2
1
1
2
0
2
0
7
1
1
2
0
2
1
1
1
1
2
0
2
0
1
2
2
0
1
1
1
1
0
1
1
1
2
2
1
1
2
0
1
1
2
0
0
1
1
0
1
1
1
0
0
1
2
0
1
2
1
0
2
1
0
0
2
0
2
1
1
1
2
1
0
2
4
2
1
0
0
1
2
0
1
1
1
1
2
1
1
2
1
0
1
1
1
1
0
1
0
0
1
1
0
2
1
1
1
1
2
1
0
1
2
0
0
0
0
0
1
1
1
1
1
0
1
1
1
1
2
1
1
0
0
1
1
2
0
0
2
0
0
2
1
1
1
0
0
2
2
2
0
1
2
0
0
1
0
2
1
1
1
0
1
1
0
2
1
2
1
1
1
1
2
0
1
0
1
1
2
1
0
1
1
1
2
0
1
0
0
2
2
1
3
1
1
2
2
1
2
0
3
0
0
1
1
1
1
1
1
2
0
2
1
1
0
1
1
1
1
1
1
0
1
2
1
0
1
1
1
1
0
1
1
0
1
1
3
2
0
1
1
1
0
0
0
0
2
1
0
1
1
2
1
1
1
0
1
1
1
2
1
0
1
2
1
1
1
1
1
1
4
2
0
1
1
0
2
1
1
2
1
2
2
2
0
1
1
1
1
1
1
2
1
1
0
2
0
1
1
1
1
1
2
0
1
1
1
1
1
1
1
1
1
1
2
1
1
1
0
0
0
1
1
0
1
1
0
2
0
0
2
1
1
1
1
2
1
1
2
1
0
1
0
1
0
1
1
0
1
1
0
1
0
1
1
0
1
0
0
1
1
4
0
1
1
1
1
0
2
1
3
0
0
1
2
1
1
1
0
3
0
0
2
1
1
2
2
0
2
1
0
1
0
1
1
1
2
0
2
0
0
1
1
1
0
2
0
1
1
0
3
1
2
1
2
2
1
1
2
1
1
1
1
0
1
1
1
1
1
2
1
0
1
0
1
1
0
1
1
2
0
0
1
0
0
1
1
2
0
1
1
0
1
1
1
2
0
2
2
1
3
1
1
2
2
1
1
1
1
0
1
1
1
0
0
1
1
2
4
2
2
1
0
1
2
2
1
0
0
1
1
0
1
1
2
1
0
0
1
2
2
2
3
1
0
2
0
0
1
0
2
0
2
2
1
0
1
1
1
1
1
1
0
1
0
0
2
2
1
2
1
1
1
1
1
1
2
1
0
1
2
1
1
0
1
1
1
1
0
1
1
0
1
1
1
1
1
1
0
2
0
2
1
1
0
1
1
1
1
1
2
3
2
1
1
1
1
1
1
1
1
2
0
1
2
1
2
1
1
1
1
1
1
0
1
1
1
0
0
0
1
0
2
0
3
1
2
0
0
2
0
2
2
0
1
1
1
0
0
1
1
0
2
1
2
0
0
2
2
1
0
1
1
1
0
1
1
1
2
1
0
0
0
1
1
2
1
1
0
1
1
1
0
1
1
2
1
1
2
1
1
1
2
1
0
2
2
1
1
1
2
1
0
2
1
1
1
0
1
1
0
1
2
2
0
2
1
1
0
1
2
1
1
1
1
1
0
0
2
1
2
2
1
2
0
1
2
1
0
1
1
1
1
0
1
1
1
0
2
1
0
1
0
1
1
0
1
0
1
1
2
0
1
0
2
2
1
0
2
1
1
0
2
0
1
0
1
0
2
1
3
1
0
1
1
2
1
2
2
1
2
1
1
3
1
1
1
1
1
0
0
0
2
3
1
1
2
0
2
0
2
1
1
1
1
2
0
1
1
1
1
1
0
0
1
0
1
1
0
1
2
4
1
1
2
1
0
1
1
1
1
2
0
1
1
1
0
1
0
1
0
1
0
2
2
2
0
1
2
1
2
0
1
1
1
1
2
3
0
1
1
0
1
1
0
1
2
2
2
2
1
0
2
0
1
1
1
1
1
1
2
1
1
1
1
1
1
3
1
0
0
1
2
2
0
1
0
1
1
1
1
0
1
1
1
1
1
2
0
1
1
1
1
2
2
1
0
0
0
1
1
2
1
0
1
0
0
2
1
0
1
2
0
1
1
1
1
0
1
1
1
1
2
1
2
1
1
1
0
2
0
0
1
2
2
0
2
0
2
1
1
1
0
2
1
2
1
2
2
0
0
1
2
0
1
1
1
1
1
0
2
0
2
2
1
1
2
1
1
0
1
0
2
2
0
1
1
1
1
2
2
1
1
0
2
1
1
1
1
1
1
1
0
0
0
1
2
0
1
0
1
2
1
0
2
2
2
2
2
1
0
1
1
2
1
0
0
1
1
1
1
1
1
0
1
0
1
2
0
0
1
2
0
2
2
1
1
1
1
0
2
2
1
1
1
1
2
2
0
4
0
1
2
1
2
2
1
4
1
0
0
1
0
2
1
1
0
0
1
1
1
1
1
0
1
0
1
1
1
1
1
2
1
1
1
3
1
1
0
0
1
2
1
1
1
0
2
2
0
1
1
1
1
1
1
1
1
0
2
0
1
0
1
1
2
0
0
0
1
1
2
2
0
1
0
1
1
0
1
2
1
0
1
1
0
1
1
1
0
0
1
1
0
0
1
1
0
1
1
2
1
1
1
0
1
1
2
1
1
0
2
0
0
1
0
0
1
1
0
0
0
1
1
1
2
1
0
1
0
2
0
1
0
2
1
1
1
0
1
1
1
1
3
1
1
1
3
3
2
0
1
1
1
0
0
1
2
2
0
1
1
2
1
1
2
1
2
0
1
1
0
0
1
0
1
1
2
1
1
1
2
1
1
1
0
1
0
1
1
1
2
1
2
1
0
0
2
0
1
0
2
0
1
2
1
2
1
1
3
1
2
1
0
1
0
1
0
1
1
1
0
0
2
1
2
0
1
1
1
0
1
2
1
1
1
1
1
1
0
1
3
2
2
2
0
1
1
1
2
1
1
1
2
2
1
1
1
0
1
1
1
1
1
0
1
1
0
1
1
2
2
0
1
1
1
1
2
0
1
1
1
1
0
2
1
1
1
1
0
1
1
0
0
0
2
0
1
0
2
2
2
1
2
1
1
2
1
0
0
1
2
4
2
1
1
0
2
1
1
1
1
1
1
1
1
1
0
1
2
0
1
1
0
1
1
1
1
1
1
1
0
2
0
2
2
2
1
1
0
2
2
1
0
1
3
0
1
1
1
1
1
0
1
1
2
1
2
0
2
0
2
0
0
2
1
1
1
1
1
0
1
0
1
2
1
1
0
1
2
2
0
0
1
0
0
0
1
0
1
2
0
1
1
2
0
0
1
1
0
0
2
2
1
1
0
1
0
1
0
0
2
2
1
1
0
2
0
2
0
1
1
1
1
0
1
2
0
1
0
1
0
1
1
1
1
1
1
0
0
0
1
1
1
1
2
1
2
1
1
1
2
0
0
1
2
1
1
1
2
1
0
1
0
0
1
1
0
0
0
1
2
1
1
2
2
0
1
1
2
2
1
1
0
1
0
1
2
2
0
1
3
0
2
1
0
2
1
1
0
1
1
0
1
1
2
1
0
0
0
1
1
1
1
1
1
1
2
1
1
1
1
1
1
0
2
1
1
1
0
1
2
2
1
0
0
1
1
1
0
0
2
1
0
2
1
2
1
2
1
2
1
0
0
0
0
0
1
1
2
0
1
0
2
1
1
0
0
2
1
0
0
2
1
0
0
2
1
1
2
1
1
1
0
2
0
1
1
0
0
2
1
1
1
2
2
3
0
1
1
1
1
2
1
1
1
0
1
1
0
1
1
0
0
0
1
1
1
0
0
1
1
0
2
0
4
1
1
1
1
1
2
2
0
0
2
1
2
0
1
0
1
0
0
1
1
1
2
1
0
1
0
2
2
1
0
1
1
1
1
0
1
1
1
1
1
1
2
1
0
1
2
0
1
0
1
0
0
0
2
0
0
0
1
1
0
2
1
0
0
1
1
0
1
1
0
2
2
1
2
0
1
1
1
2
0
1
1
0
2
1
0
1
1
1
1
2
1
1
1
1
0
1
0
2
1
1
1
1
1
2
1
1
1
1
2
1
2
2
3
1
2
3
1
2
2
1
0
0
1
0
1
2
0
0
1
0
1
1
2
1
3
2
1
1
0
0
2
1
1
1
1
0
1
0
1
1
1
1
1
0
4
1
0
0
1
1
2
1
0
2
1
0
1
1
1
2
1
3
2
0
1
1
1
2
1
1
2
2
1
3
2
3
2
0
0
1
1
1
1
1
2
1
2
0
0
1
0
0
2
1
2
1
1
1
2
1
2
1
0
1
2
2
2
1
1
1
0
0
0
1
2
1
0
1
0
0
4
1
0
0
0
1
2
2
1
0
1
0
1
2
0
2
1
2
2
0
0
1
1
1
1
0
1
1
0
1
2
2
1
2
1
1
1
1
2
1
1
1
1
0
2
1
2
1
1
2
1
0
1
1
2
0
1
1
0
1
2
1
1
2
1
1
1
2
1
0
1
1
0
1
2
1
2
0
1
2
0
1
1
0
1
0
1
0
1
0
0
1
1
1
0
0
1
1
2
2
0
0
0
2
1
0
2
0
1
1
1
1
1
2
1
1
0
2
1
1
1
1
0
2
0
0
0
0
1
2
0
0
1
1
1
2
0
0
1
0
0
1
0
1
1
2
2
1
1
0
0
1
2
0
0
1
2
1
1
1
0
2
1
1
1
0
1
2
1
1
1
0
0
2
1
1
1
2
0
1
2
2
2
2
2
1
0
1
2
1
2
1
1
1
1
0
2
2
0
1
1
0
0
2
0
0
2
1
0
1
0
0
2
1
1
0
0
2
1
1
1
2
1
2
0
0
1
2
1
1
2
2
1
1
1
0
1
2
1
2
1
0
0
0
2
2
2
0
1
1
1
2
0
1
1
2
1
0
0
1
0
0
1
1
1
0
1
0
2
1
1
1
1
0
2
1
2
1
0
2
1
1
1
2
0
2
1
0
1
1
2
0
1
0
2
1
0
2
1
2
0
2
1
1
0
0
1
1
1
2
1
2
1
0
1
1
1
1
2
2
2
2
0
1
1
1
1
1
1
2
0
3
0
1
2
1
2
0
1
1
2
1
0
1
1
2
2
0
1
1
1
1
1
1
0
0
1
2
2
1
1
1
1
2
2
2
0
0
2
0
1
0
0
1
2
1
1
1
1
2
0
0
2
1
1
0
1
1
1
1
2
2
0
0
1
2
1
0
3
0
0
1
2
0
0
2
1
0
1
1
0
1
1
1
1
0
1
2
1
2
1
0
2
1
2
2
0
1
1
1
0
2
0
1
0
1
1
0
2
0
0
2
1
1
1
0
1
0
0
1
1
0
1
1
0
1
1
2
0
1
2
0
2
0
1
1
1
1
0
1
1
1
2
1
0
1
0
2
1
1
2
0
0
2
1
2
3
2
1
1
0
1
0
0
2
0
1
1
0
0
0
1
1
1
1
1
1
2
2
1
3
1
1
1
1
1
0
1
1
0
1
1
2
0
0
0
1
2
2
1
1
1
1
1
1
0
0
0
1
0
2
2
0
1
1
1
2
0
2
2
1
2
1
1
2
1
2
2
1
1
0
1
1
0
1
1
1
1
0
1
0
1
1
1
0
1
3
1
1
0
0
1
2
1
0
1
0
1
0
0
0
1
1
1
1
2
1
1
1
1
2
2
0
2
1
1
2
0
1
0
2
1
1
2
0
2
2
0
1
1
2
1
1
1
3
0
0
1
1
2
1
2
0
1
1
1
1
1
2
2
1
1
1
1
0
1
0
0
1
1
0
0
2
0
1
0
1
1
1
2
1
1
2
2
0
2
1
1
0
2
2
1
1
1
1
1
2
1
0
0
2
1
1
2
0
1
1
1
4
1
0
0
0
1
0
1
1
1
2
1
0
1
1
2
2
2
0
1
1
1
1
2
0
1
2
1
2
0
0
1
1
1
0
1
0
2
1
1
1
1
1
0
1
0
0
1
0
2
1
2
1
1
1
1
1
1
1
0
1
2
0
2
1
0
1
1
1
1
2
0
2
0
1
2
2
0
0
2
1
2
2
0
2
4
0
1
2
1
0
1
1
0
1
2
1
2
3
2
1
1
1
1
1
0
0
1
1
1
0
2
0
2
2
1
2
2
1
1
2
0
1
2
1
1
1
0
3
1
0
2
0
0
2
1
0
1
0
1
1
0
1
1
0
0
1
0
1
1
1
1
1
2
2
2
1
2
2
1
1
1
1
0
2
1
2
2
2
1
1
2
1
1
0
0
1
0
1
1
1
1
1
0
2
0
1
2
1
1
0
2
0
2
2
1
0
2
2
0
1
1
1
0
0
1
2
0
2
1
0
1
1
0
1
0
1
0
1
1
1
1
1
0
2
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
1
1
1
0
0
3
2
1
0
1
1
1
1
1
0
1
0
2
2
1
1
1
2
1
1
1
1
2
2
2
0
2
2
1
2
0
1
1
0
2
1
1
2
0
2
1
1
2
1
0
1
0
0
0
1
2
0
0
0
1
2
1
0
2
1
2
0
1
0
0
1
0
2
1
1
0
1
0
2
0
2
2
1
2
1
0
0
0
0
2
0
1
1
1
1
1
1
0
1
1
2
2
1
1
1
1
2
0
2
2
0
1
0
1
0
2
0
1
2
0
2
1
1
2
0
1
2
1
1
2
1
2
1
1
2
1
1
1
2
2
2
0
1
1
1
1
1
1
0
0
2
0
0
2
1
2
0
1
2
0
2
1
1
0
1
0
1
1
0
2
1
0
1
1
1
1
1
2
0
1
0
1
1
2
3
2
1
1
0
1
1
1
0
0
0
0
0
1
1
2
1
2
2
1
1
2
1
1
0
1
2
0
3
3
2
0
2
1
1
1
2
1
1
1
1
0
1
2
0
1
0
2
2
2
1
2
0
2
2
0
0
1
0
1
0
0
1
1
1
2
0
1
0
1
1
1
1
0
1
1
2
0
0
1
1
0
1
1
2
1
1
1
1
1
0
1
2
1
0
0
1
2
1
0
1
1
2
1
0
0
1
1
1
1
1
1
2
1
1
0
1
0
1
0
1
1
1
0
1
1
0
4
1
2
0
0
2
1
1
1
0
1
0
1
1
2
1
2
2
0
1
1
1
2
1
2
1
0
1
1
2
1
1
0
1
2
2
0
1
1
1
1
1
1
1
0
0
1
0
0
1
0
1
1
1
2
1
1
1
1
0
0
0
0
3
1
2
1
0
1
1
0
2
2
1
1
1
0
1
3
1
1
1
2
1
0
0
2
1
1
1
2
2
0
0
0
1
2
1
1
1
0
1
1
2
1
1
2
2
2
1
1
1
1
1
2
1
1
1
1
1
1
0
1
1
1
1
2
2
2
1
1
1
2
1
1
0
0
0
1
2
0
1
0
1
0
2
2
2
1
1
0
0
1
1
0
0
0
1
2
1
1
0
0
2
1
1
1
1
0
1
2
2
0
0
0
0
0
1
0
0
1
1
0
2
1
1
0
1
0
2
2
1
0
1
1
1
2
1
0
1
2
2
0
1
1
1
1
1
2
1
0
1
1
1
1
2
1
2
0
0
1
0
2
1
1
1
1
1
1
0
0
2
1
0
1
1
1
0
0
1
0
1
1
0
1
2
2
1
2
1
2
0
1
1
2
1
0
2
1
2
0
2
2
1
0
0
2
2
1
1
1
1
0
2
1
1
0
0
0
1
0
0
1
1
2
1
2
1
2
1
0
1
2
2
1
1
2
1
0
1
2
1
0
1
2
2
0
1
0
1
0
1
1
1
1
2
1
1
1
2
0
0
1
1
1
1
1
1
0
1
1
1
0
0
1
0
0
2
1
1
2
0
2
1
2
2
1
1
1
0
1
1
2
2
1
1
2
2
0
0
2
0
2
0
2
2
1
1
0
0
0
0
1
2
2
1
1
2
1
0
0
2
1
2
1
4
2
0
1
0
1
0
1
2
1
1
2
0
1
0
2
2
1
1
1
1
1
2
1
1
2
1
1
1
1
1
2
1
2
0
1
1
0
1
1
1
1
0
0
0
2
1
1
0
1
1
1
2
1
1
1
1
2
2
1
0
2
0
0
0
1
0
1
3
0
1
1
0
1
3
1
1
2
1
1
2
0
0
0
1
3
1
2
1
0
1
2
1
1
1
2
1
1
0
1
1
1
2
1
1
1
1
1
1
1
2
0
1
0
1
1
2
1
1
0
3
2
0
0
0
0
1
2
1
1
0
0
1
0
1
0
1
1
2
0
2
1
2
1
1
1
2
0
1
1
2
2
1
1
0
0
2
0
1
1
0
0
0
0
2
0
1
0
2
1
2
1
1
1
1
2
1
1
0
1
1
1
1
2
1
1
1
1
1
1
0
1
1
1
0
1
1
1
0
1
0
1
2
0
0
1
0
2
2
0
1
1
0
0
1
3
1
2
0
2
1
2
0
1
2
1
1
0
2
0
0
0
2
0
1
0
1
2
0
0
2
1
2
0
1
0
2
1
0
1
1
2
0
1
1
0
1
1
2
1
1
1
0
1
1
0
1
1
1
1
0
1
1
2
1
0
2
1
0
0
2
1
0
1
1
2
1
1
1
0
1
0
1
1
1
1
0
1
1
1
1
1
1
2
2
0
1
1
0
1
1
1
0
1
1
1
1
0
1
2
1
0
1
1
1
0
1
2
0
0
1
0
1
2
2
2
1
1
2
1
2
2
1
0
1
0
1
1
1
2
1
1
1
1
0
1
1
1
1
0
1
1
1
1
0
2
1
0
2
0
2
0
2
0
0
1
0
2
1
0
1
2
1
0
1
1
2
1
0
0
1
1
1
1
1
1
1
1
1
1
0
1
1
2
1
1
1
0
2
1
1
1
1
1
0
0
0
0
0
1
2
1
1
1
1
2
1
1
2
2
2
0
2
1
0
1
1
2
1
0
2
1
1
1
1
2
2
1
1
0
2
0
1
2
1
1
0
1
0
1
1
1
0
0
1
1
0
1
1
1
0
2
1
1
1
2
2
0
1
1
1
0
1
2
2
2
1
0
1
1
0
0
1
0
1
2
1
0
0
2
2
2
1
2
1
1
1
1
0
1
0
1
2
2
2
0
1
2
1
1
1
2
1
1
1
1
1
1
2
2
1
1
2
1
2
2
0
1
1
0
2
1
1
1
2
2
0
2
0
2
1
1
1
0
1
0
0
0
1
0
1
1
0
1
1
0
0
2
1
1
0
2
1
1
2
0
1
1
1
2
1
0
1
0
2
0
3
1
0
1
1
0
1
0
1
0
1
1
1
1
2
1
0
0
1
1
2
1
0
0
1
1
1
0
1
0
0
1
2
1
1
1
1
1
1
1
2
1
0
0
1
2
1
2
2
1
0
0
2
1
1
2
0
1
1
1
1
1
0
0
2
1
0
0
1
2
1
2
1
1
2
1
0
0
0
0
1
1
2
2
0
1
1
2
0
1
2
1
2
1
2
1
1
1
1
0
0
2
0
0
1
1
0
2
1
1
1
1
2
2
0
2
1
1
1
0
1
1
1
1
1
1
1
2
0
1
1
1
1
1
0
0
1
2
1
0
2
2
0
1
2
2
0
1
2
2
1
2
1
1
1
1
1
0
1
1
2
0
0
1
1
0
0
1
0
1
1
2
1
1
2
1
1
1
2
0
0
2
1
1
1
0
0
1
0
2
1
2
2
0
2
0
1
3
1
0
1
0
0
2
0
1
1
2
0
1
1
1
2
0
0
1
1
2
2
1
1
0
2
0
2
1
1
1
0
2
1
2
1
1
1
0
1
1
1
1
0
1
2
1
1
1
2
0
1
1
0
1
0
0
1
2
0
2
0
2
2
2
1
2
1
1
1
1
1
1
0
1
1
2
1
2
1
1
1
1
0
1
2
0
1
2
2
1
2
2
0
1
1
0
1
1
2
2
1
1
1
0
1
2
1
2
1
0
1
0
1
1
0
0
1
0
2
0
0
2
1
1
0
1
1
0
1
1
1
2
0
0
1
1
0
1
1
1
0
1
0
0
1
1
2
0
0
0
0
0
1
1
1
0
2
1
1
0
0
1
1
1
1
1
1
1
1
0
0
1
0
2
1
3
2
1
2
3
2
1
1
0
1
1
2
1
1
0
1
2
0
2
2
1
1
2
1
1
3
2
0
0
2
1
0
2
1
0
1
1
1
1
1
1
1
0
1
0
2
2
1
2
1
1
1
1
1
0
1
0
1
1
1
2
1
1
2
2
1
1
1
1
0
1
0
0
0
1
0
2
0
1
1
1
2
6
1
0
0
1
3
1
1
1
1
1
0
2
1
1
1
0
2
2
0
0
1
1
1
2
0
1
1
0
2
0
0
0
2
1
1
1
2
2
0
1
0
0
2
1
2
1
2
0
0
0
1
2
1
2
1
1
1
2
1
2
0
1
0
1
1
0
1
1
1
1
1
1
2
0
2
1
1
2
2
0
1
0
1
1
1
2
0
1
1
1
2
0
1
1
1
0
0
1
2
1
1
1
2
0
1
1
1
0
1
1
1
2
1
1
1
1
0
1
1
1
1
2
0
1
1
2
2
1
0
1
2
1
1
2
0
3
3
1
2
1
0
1
2
1
0
1
1
0
1
1
1
2
2
1
1
0
1
1
1
1
2
4
2
1
2
0
1
2
1
1
0
1
1
0
1
0
0
2
1
1
2
0
2
1
1
1
2
1
1
0
1
1
0
2
0
1
1
2
3
2
0
1
1
1
2
2
2
2
1
2
0
1
2
1
1
1
2
1
0
0
1
1
0
1
0
2
2
1
0
1
1
0
0
1
0
2
2
0
2
1
2
1
1
2
1
1
1
1
1
1
0
1
1
0
3
0
1
0
1
1
2
0
1
0
2
0
4
1
1
1
2
0
1
1
0
1
0
1
1
1
1
1
2
1
1
1
0
1
2
0
1
1
2
3
1
1
2
2
2
1
1
0
2
2
1
1
1
1
0
1
0
2
1
1
1
2
1
2
1
1
0
0
1
2
2
0
0
2
1
1
2
0
2
1
2
2
0
1
0
1
0
1
2
1
2
2
3
1
1
1
1
0
1
0
1
1
0
0
0
0
2
2
1
1
1
1
1
1
1
1
2
0
2
1
1
0
2
1
1
0
1
2
1
0
2
1
0
2
0
0
0
1
1
1
1
2
0
1
0
1
1
1
1
2
1
2
2
1
2
2
1
2
1
2
1
1
2
0
1
0
2
1
1
2
1
1
1
1
1
0
2
0
2
2
2
1
1
1
0
0
1
3
2
2
1
2
1
2
1
2
1
0
0
1
1
1
0
1
1
0
2
1
1
1
1
2
1
0
1
0
0
0
2
1
1
2
2
0
1
1
2
2
2
1
1
0
1
1
0
1
0
1
0
1
2
1
2
1
2
2
1
8
2
0
2
0
2
0
0
2
2
1
1
1
1
1
1
0
1
1
1
1
2
2
1
1
1
1
1
1
2
0
0
1
1
1
0
2
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
0
1
1
0
0
1
1
1
0
1
1
1
0
2
1
1
1
1
2
2
2
0
0
1
0
1
1
1
1
1
0
0
2
1
0
2
1
1
1
2
1
1
5
3
1
1
0
0
1
1
1
1
0
3
0
2
1
1
0
1
1
1
2
1
1
0
1
1
2
2
0
1
2
1
0
0
2
1
0
1
1
0
1
0
1
1
1
2
1
1
0
1
1
1
9
0
1
2
1
1
0
1
2
2
1
0
2
1
1
2
1
2
0
0
1
1
1
1
2
0
1
1
1
1
0
0
0
0
0
2
1
1
1
1
1
1
1
0
0
1
1
0
1
1
1
0
1
0
1
1
2
0
2
2
4
2
1
0
1
0
1
1
0
0
2
2
1
2
2
1
1
1
1
0
1
1
2
2
1
2
1
2
1
1
2
0
0
0
1
2
1
0
1
0
1
1
1
1
0
1
0
1
2
2
1
1
1
1
1
1
0
1
1
1
0
1
1
0
1
1
0
2
0
0
3
0
0
2
0
0
1
2
1
2
2
1
0
2
2
3
1
2
1
1
1
0
1
1
2
1
0
2
0
2
0
1
2
0
2
0
1
0
0
1
0
2
0
2
2
1
1
0
2
2
2
2
1
2
1
1
1
1
0
3
0
0
0
2
2
0
4
0
1
2
1
1
1
1
2
1
1
1
0
2
1
1
1
1
1
0
0
1
1
1
0
1
1
2
1
1
1
2
1
1
2
2
1
0
0
0
1
0
1
1
2
0
1
4
1
0
2
1
1
1
2
1
1
1
0
1
1
0
2
0
1
1
0
0
1
1
0
2
1
2
1
2
2
0
1
0
1
0
1
0
2
1
1
1
1
0
1
0
1
2
1
1
0
2
1
1
2
1
0
1
1
2
1
1
1
0
2
3
0
0
1
0
0
1
1
0
2
1
1
2
1
1
2
0
2
0
1
1
1
1
6
2
1
1
1
2
1
1
2
1
2
1
1
1
2
0
0
1
2
2
1
1
1
0
0
1
1
2
1
1
2
1
1
2
2
2
1
0
0
2
2
1
2
1
0
2
2
2
2
1
1
1
0
0
2
1
2
1
2
1
2
2
1
1
1
0
1
0
1
0
1
1
2
1
0
0
1
1
3
1
1
1
0
0
0
1
1
0
0
1
1
0
0
2
1
2
1
2
1
1
2
1
0
0
1
1
0
0
3
1
0
1
2
2
1
1
0
1
2
1
1
0
1
0
1
1
0
1
1
0
2
0
1
0
1
1
1
2
2
0
1
1
1
1
1
0
0
2
0
1
3
0
2
1
1
1
1
1
1
1
2
0
1
0
1
1
0
1
0
1
2
1
2
0
0
0
2
1
1
2
2
3
1
2
0
1
2
0
2
1
0
1
1
1
0
1
1
1
2
1
1
2
0
0
1
0
1
2
2
2
2
0
0
1
1
1
1
1
2
0
1
1
1
0
0
2
2
2
1
2
2
0
0
0
0
1
1
1
1
2
2
0
2
1
1
1
1
2
1
1
2
1
1
1
0
1
0
1
2
1
1
2
1
2
2
0
0
2
2
1
2
1
1
1
1
1
1
1
2
0
2
1
1
0
0
1
2
1
1
1
1
2
1
2
1
0
0
2
2
0
2
1
2
1
0
1
1
1
1
1
2
0
0
1
2
1
0
2
2
2
1
1
1
2
1
2
1
0
0
1
1
2
2
2
1
2
1
1
0
1
1
1
0
1
2
1
2
1
1
0
1
0
0
1
0
1
1
0
1
1
1
1
1
1
2
0
0
0
1
1
0
2
1
1
1
2
2
0
1
1
1
1
0
1
1
2
1
1
2
2
2
0
1
2
1
2
1
0
2
1
1
2
1
2
2
1
0
1
1
1
1
1
2
1
0
1
1
1
2
2
2
0
1
1
1
0
0
1
2
1
1
0
1
0
0
1
1
1
2
1
1
1
1
0
2
1
2
1
1
0
1
1
1
1
1
2
2
1
1
1
2
1
1
2
1
0
1
0
0
0
3
2
2
1
1
0
0
2
1
0
1
1
1
2
1
2
1
3
2
2
2
0
0
0
1
1
2
1
1
1
0
2
1
2
0
0
0
0
1
1
0
1
3
2
0
1
1
2
1
2
1
0
0
1
3
1
0
0
0
1
1
1
2
2
2
2
1
1
1
0
0
1
2
2
0
0
1
1
1
1
1
1
2
1
1
2
2
0
0
0
2
0
0
0
1
2
1
2
2
2
1
1
1
1
1
0
1
2
2
1
1
1
0
1
0
0
2
2
0
0
2
1
2
0
0
1
0
1
1
2
1
1
1
1
1
2
1
1
1
1
0
2
2
2
0
1
1
2
1
0
0
2
1
2
1
1
0
2
1
1
1
1
1
1
0
1
1
1
0
0
0
2
2
1
0
1
0
1
2
0
1
0
1
2
0
2
1
0
1
2
0
1
2
2
1
2
0
1
1
1
3
1
1
1
0
1
0
0
1
0
1
1
0
1
1
2
2
0
2
2
1
1
0
2
3
1
1
1
1
0
2
2
0
1
2
1
1
0
1
0
1
1
1
0
1
1
1
0
1
1
1
1
1
1
4
2
1
0
1
1
0
1
1
1
1
0
2
2
0
0
1
1
0
1
2
0
1
0
1
1
1
0
1
1
1
2
0
1
2
0
1
1
2
0
0
0
1
0
2
1
0
2
0
0
0
1
2
0
1
2
1
1
1
1
0
0
1
0
1
1
0
0
0
1
2
1
1
0
0
2
1
2
1
1
1
1
1
1
1
1
0
1
1
0
0
1
3
1
1
0
0
0
1
1
2
1
0
1
2
0
2
2
2
1
1
1
1
1
1
1
0
2
1
1
0
0
1
0
0
1
1
1
1
1
2
0
1
2
2
1
2
0
1
2
2
2
2
0
0
1
2
1
0
0
0
1
1
1
2
1
2
1
2
1
1
2
1
0
1
1
1
2
1
1
0
2
0
1
1
2
0
2
2
1
2
0
0
1
0
2
2
1
0
0
0
1
0
0
0
1
0
0
1
2
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
0
1
0
2
0
2
0
1
2
1
1
4
1
2
0
1
1
2
0
0
2
1
1
0
0
0
1
1
1
1
2
1
1
1
0
1
0
1
0
1
2
2
1
0
0
1
1
2
0
0
0
0
0
1
2
1
2
0
2
1
1
0
0
2
1
1
0
2
1
1
1
1
2
0
1
2
1
0
1
0
0
2
1
0
1
1
1
0
1
0
0
1
1
5
0
2
0
2
0
2
2
2
0
2
1
1
0
2
0
1
1
1
2
2
2
1
1
1
1
1
2
1
2
1
1
2
1
2
0
2
1
1
1
0
0
2
1
2
1
1
1
1
0
2
1
1
1
1
1
1
1
0
2
1
0
1
0
2
0
2
1
1
0
1
1
2
1
2
1
0
0
1
2
1
2
1
1
0
2
1
1
0
0
2
1
2
1
2
1
2
0
0
1
1
0
0
2
1
1
1
1
0
0
2
2
1
1
1
1
1
2
2
0
1
1
1
1
0
1
2
0
1
1
0
2
1
1
2
0
1
3
1
1
2
2
0
0
2
1
1
1
1
2
1
0
1
1
0
1
1
0
1
0
2
0
1
3
1
1
1
1
1
1
2
2
2
0
0
0
2
0
0
1
0
1
1
0
2
2
1
2
1
0
0
1
1
1
1
2
1
1
0
1
2
1
1
1
2
2
1
2
0
0
1
2
1
0
2
0
1
0
0
1
1
1
1
1
0
2
1
1
0
1
1
2
1
2
2
0
1
0
0
2
1
1
0
2
0
2
1
1
2
2
2
2
1
0
0
0
2
1
0
1
1
1
1
1
1
0
2
1
1
2
0
1
2
1
1
0
0
0
0
1
2
1
0
0
1
0
0
1
1
0
1
1
0
0
2
1
1
1
1
0
1
0
2
1
0
0
2
0
0
1
1
1
0
2
2
0
1
1
2
1
1
1
2
0
0
1
2
1
1
2
1
0
2
2
1
2
2
1
0
0
1
2
0
1
1
1
1
1
1
0
1
1
1
2
2
0
2
1
2
1
0
1
1
1
1
1
1
1
2
1
1
0
1
0
0
1
0
1
0
1
0
1
1
0
2
1
1
1
0
0
1
1
1
0
1
1
2
3
1
1
1
1
1
1
1
2
0
1
2
1
2
2
0
0
2
1
2
0
2
0
0
0
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
2
1
1
0
0
1
1
1
1
1
0
0
1
0
0
1
1
0
2
0
1
1
2
1
0
1
1
2
2
1
2
0
2
0
2
1
1
1
0
2
1
1
2
0
0
1
0
1
1
0
0
1
2
0
1
1
1
1
1
2
1
0
1
2
2
2
0
1
1
1
1
1
1
1
0
1
1
2
1
1
0
1
1
2
1
0
0
2
1
1
1
0
0
1
0
2
1
1
1
0
1
1
0
1
2
1
1
1
1
1
1
0
2
2
0
0
1
1
2
2
2
3
1
1
1
1
0
1
3
1
1
1
2
1
1
1
0
0
0
1
1
0
0
2
0
2
2
1
0
2
1
2
1
1
0
1
0
2
0
1
1
1
0
0
1
2
1
1
1
0
0
2
1
2
0
1
1
1
1
1
0
0
0
0
1
1
0
1
0
0
0
0
2
1
0
2
1
0
0
1
1
1
0
0
1
1
1
0
0
2
1
1
0
1
1
1
1
1
2
1
2
2
1
1
0
0
2
1
1
2
0
2
2
1
0
1
1
2
0
2
0
1
0
1
2
0
1
1
1
0
1
2
1
2
1
2
2
2
0
0
0
0
1
2
1
0
0
1
0
1
0
1
1
0
1
2
2
2
0
0
1
1
1
1
0
2
0
1
1
1
0
1
1
0
0
0
1
0
1
0
1
1
0
1
0
1
0
2
1
1
1
2
1
0
0
1
2
2
2
1
0
1
1
1
1
1
0
1
1
2
1
1
0
1
0
1
0
0
0
2
1
1
1
0
1
1
0
2
1
2
0
0
0
1
1
2
2
0
1
1
0
0
1
1
0
0
1
1
1
0
0
0
1
1
2
0
1
1
0
1
2
0
1
0
2
1
1
1
0
0
0
2
1
1
3
0
0
1
1
0
1
2
0
2
2
2
1
2
2
2
2
2
1
1
0
0
0
2
1
0
2
2
1
1
2
1
1
1
1
1
2
2
2
1
1
1
2
1
1
1
2
0
1
2
0
0
1
1
2
1
3
2
0
1
0
1
2
1
1
0
1
1
1
2
0
1
1
1
1
0
1
0
1
0
1
1
2
1
1
1
1
0
0
3
2
1
3
0
1
1
2
2
0
0
0
0
1
2
2
1
2
1
2
0
1
1
2
1
1
1
1
0
1
1
1
2
1
1
0
1
1
2
1
0
1
1
1
2
2
0
0
1
2
1
0
1
0
0
1
1
2
1
0
2
1
2
0
0
2
0
1
1
1
2
1
1
1
1
0
1
2
1
0
1
0
0
0
0
1
2
1
1
0
1
0
1
1
0
1
6
0
1
1
0
2
2
0
1
0
0
1
0
2
1
0
0
1
0
1
0
0
2
0
1
1
0
1
1
1
1
2
2
0
1
1
1
2
1
1
2
0
1
0
1
2
2
1
1
1
0
0
2
1
2
1
1
1
0
0
0
1
0
2
0
1
1
2
0
0
0
1
1
0
2
1
1
1
1
0
1
1
1
0
2
1
1
1
0
1
2
1
0
0
0
1
2
1
1
0
0
2
1
2
1
0
1
2
0
1
0
0
1
1
2
1
0
1
2
1
0
0
2
0
1
1
0
1
1
0
2
1
0
1
1
2
2
1
1
1
2
0
1
2
1
2
1
1
0
1
0
2
1
1
0
1
0
1
2
0
0
1
1
0
1
0
2
0
1
0
0
2
2
1
0
1
0
0
1
1
1
1
1
1
2
1
2
2
3
0
2
2
1
3
1
0
1
1
0
2
4
1
0
1
1
1
1
1
1
0
1
2
0
1
2
1
1
1
1
1
1
0
2
0
1
1
1
0
0
0
1
1
0
0
2
0
2
1
1
1
1
1
2
1
1
2
1
1
0
1
0
2
1
1
2
2
1
1
1
1
1
2
2
4
2
0
0
0
0
2
1
1
0
1
2
1
2
2
1
1
1
1
1
2
1
2
1
1
1
0
1
1
2
1
1
1
2
1
1
1
2
1
1
0
1
1
1
1
0
1
0
1
0
2
2
2
1
0
0
2
1
2
1
1
2
2
2
2
1
0
1
1
0
1
0
0
2
1
2
1
1
0
1
1
2
1
2
0
2
3
0
2
1
1
1
2
2
0
2
0
0
1
0
1
1
1
1
0
0
1
1
1
0
0
2
1
1
1
2
0
1
1
1
1
3
0
0
2
1
2
1
0
1
1
1
1
2
1
2
1
1
0
0
0
1
0
1
1
2
2
1
1
2
1
0
2
1
1
0
1
1
0
1
1
3
1
0
1
1
0
1
1
1
1
2
1
1
1
1
3
0
1
1
1
0
1
0
1
0
1
2
1
1
2
0
0
3
2
0
0
2
2
1
1
1
1
0
0
2
1
0
2
2
1
0
2
1
1
1
1
1
1
1
1
0
1
1
1
1
2
0
1
4
1
2
2
0
0
1
1
0
1
1
1
1
0
0
0
1
1
1
1
1
2
1
0
1
1
0
2
1
0
2
1
2
1
2
0
1
2
1
1
0
0
0
1
1
1
1
2
0
0
0
0
0
2
1
1
0
2
1
1
2
1
1
2
1
1
0
1
1
1
1
0
1
2
1
2
0
1
1
1
1
1
2
2
0
1
1
0
1
1
1
1
1
1
0
1
1
2
1
2
0
0
3
1
2
1
1
1
2
1
2
1
1
1
1
2
1
1
2
1
2
0
2
2
1
2
0
2
0
0
0
1
1
2
0
1
1
0
1
0
2
1
1
0
0
1
0
1
0
1
1
1
2
3
2
2
0
1
1
0
1
1
1
0
1
1
0
1
0
1
1
1
2
1
1
2
1
1
0
0
1
3
2
2
0
1
2
0
0
2
1
0
0
0
1
2
1
0
0
0
0
1
3
1
1
1
2
1
1
0
1
0
0
2
2
2
1
2
1
2
0
0
0
2
1
1
1
0
0
0
1
1
1
1
1
0
1
0
2
1
2
2
1
1
2
1
1
1
2
2
0
1
0
0
1
2
0
0
1
0
2
2
1
1
0
1
0
1
1
0
0
1
2
1
1
0
0
0
1
0
1
0
1
2
3
1
1
1
1
1
1
2
1
0
2
2
1
1
0
1
1
2
1
1
1
1
1
1
0
1
0
1
1
1
0
0
2
1
1
1
1
1
2
2
2
1
0
1
2
2
0
1
0
0
0
1
1
1
0
2
2
1
1
0
0
2
0
1
0
0
1
1
1
0
0
0
0
2
1
1
1
1
0
1
1
1
1
1
0
2
0
1
2
1
1
2
1
1
2
0
1
0
1
0
0
1
1
1
1
0
2
2
1
1
0
2
0
1
1
0
1
1
0
0
2
1
2
1
2
1
2
0
1
0
2
2
0
1
1
2
1
1
0
1
0
1
2
1
1
1
1
0
1
2
1
1
2
2
0
2
1
2
0
1
0
0
2
2
0
3
2
1
0
1
1
0
2
0
0
1
1
2
2
1
2
1
1
2
0
1
1
1
0
2
0
0
2
0
2
1
1
0
1
1
1
2
1
0
1
2
1
2
0
0
0
1
0
1
2
2
0
2
2
1
2
0
2
2
1
1
1
1
2
0
3
0
1
2
1
2
0
2
3
0
1
1
2
0
0
1
0
1
2
2
1
2
1
2
1
1
2
1
1
0
1
0
1
1
1
0
2
0
1
0
1
1
2
1
0
1
0
2
0
2
1
0
1
1
1
1
1
0
2
1
2
1
2
1
1
2
1
1
1
2
0
1
1
1
1
1
0
1
0
1
1
2
0
1
1
1
0
0
0
2
1
1
1
0
1
1
1
2
1
1
2
2
0
1
2
1
1
0
0
2
2
0
1
2
2
1
1
1
1
0
0
1
1
1
2
0
4
1
1
2
1
1
0
0
1
1
1
1
0
1
1
0
2
2
2
2
2
1
1
0
0
1
1
1
2
1
0
0
0
1
1
1
1
1
1
0
1
1
0
1
1
1
1
1
2
1
1
1
2
2
0
1
1
1
2
3
2
0
2
1
2
0
2
0
1
1
1
0
1
2
1
2
0
0
1
1
0
0
0
2
1
0
2
1
0
0
1
0
1
2
2
1
0
1
0
1
1
1
1
1
1
0
2
1
1
1
0
1
0
1
1
7
1
2
2
0
1
1
2
0
2
1
1
1
2
1
0
0
3
14
1
1
2
1
0
2
0
1
0
0
1
1
1
0
2
2
2
1
0
1
1
2
2
0
2
1
2
0
0
1
1
2
1
1
2
1
0
1
2
2
2
1
1
0
1
1
0
1
1
1
2
1
2
2
1
1
2
1
1
2
1
1
0
1
0
1
0
1
1
2
1
1
1
1
1
2
1
1
1
0
0
0
0
2
0
0
0
2
0
1
1
1
1
1
2
1
1
0
2
1
2
1
2
1
1
2
2
1
1
1
1
1
2
0
1
0
2
2
2
0
1
1
1
0
0
2
2
1
1
0
0
0
1
0
0
1
0
1
2
1
1
0
1
0
1
1
1
0
0
0
1
3
1
2
1
2
2
1
2
0
1
1
1
0
0
1
0
1
2
1
0
2
1
1
0
0
0
2
1
2
1
2
0
2
0
3
1
1
1
0
1
2
2
1
0
1
0
1
1
0
0
2
3
2
0
1
1
2
0
1
1
1
1
2
1
2
0
1
1
0
2
1
0
4
0
0
1
1
1
2
1
1
2
2
1
1
1
1
1
2
1
1
1
1
1
0
1
2
1
1
1
1
1
1
1
1
1
0
1
1
0
1
2
1
0
1
0
2
2
0
1
1
1
0
2
0
0
2
1
1
0
0
2
1
2
0
0
0
1
0
2
0
0
1
1
1
1
1
0
1
2
1
1
1
1
1
0
1
2
2
0
2
2
0
1
1
1
0
0
2
1
1
1
0
2
1
0
2
1
0
1
2
1
0
0
1
0
1
0
2
2
1
3
1
0
2
1
0
2
2
2
3
1
1
1
1
0
1
0
1
0
0
2
1
1
1
2
0
1
3
1
1
1
1
1
1
0
2
2
3
1
1
0
0
0
0
1
2
1
0
0
2
1
2
2
1
0
2
2
1
0
2
0
3
2
1
1
1
1
1
1
1
2
2
1
1
0
1
0
0
0
0
2
2
0
1
0
1
2
1
0
1
1
1
1
1
1
2
0
2
1
2
0
1
1
1
1
0
1
1
3
1
2
0
1
2
1
1
1
2
2
0
0
0
1
1
2
2
0
1
0
2
1
1
1
0
1
1
0
1
0
1
1
1
2
0
1
1
1
1
1
2
0
2
1
2
2
2
1
1
1
0
1
2
0
1
0
1
1
1
1
2
1
0
2
1
0
1
1
0
1
0
2
1
2
1
1
0
2
2
1
0
1
0
0
1
0
2
1
0
1
0
2
1
1
0
2
0
1
3
1
0
1
0
1
1
1
1
0
0
1
0
0
2
1
1
2
1
1
1
1
0
2
2
0
0
0
2
1
1
1
2
1
0
1
0
1
1
1
0
2
0
2
0
2
0
0
1
1
2
2
1
0
1
0
0
0
2
0
1
0
1
3
0
0
1
1
0
1
0
1
2
2
1
1
1
2
1
2
2
1
1
1
1
0
2
1
0
1
2
2
2
2
0
2
1
2
1
0
1
1
0
1
1
1
1
1
1
3
1
1
1
0
1
0
1
1
0
1
2
1
2
0
0
1
1
1
1
0
0
1
2
2
1
0
1
1
1
2
1
0
2
1
0
0
1
1
1
1
0
1
2
1
1
3
1
1
1
1
1
1
1
1
0
0
2
1
2
1
2
1
2
1
0
1
2
0
1
1
1
1
2
1
1
0
1
1
1
1
1
1
3
0
1
0
0
1
1
1
0
2
1
0
1
0
1
1
1
1
1
1
1
0
1
0
1
1
0
2
1
0
1
1
1
2
0
0
1
1
0
1
1
2
0
1
3
1
1
1
1
0
2
3
1
2
1
1
1
0
0
1
2
1
0
0
1
1
1
0
1
1
1
1
2
0
2
1
1
2
1
1
2
2
0
1
2
2
1
1
1
2
0
1
1
1
2
1
1
4
1
1
0
1
1
2
1
2
2
0
2
0
0
1
0
1
2
1
1
1
1
0
2
1
1
1
2
1
2
1
0
0
2
1
0
1
1
1
0
0
0
1
1
1
2
2
1
2
1
2
0
2
0
1
1
1
0
0
1
2
1
0
1
1
0
1
2
1
1
1
0
2
0
0
2
1
1
1
1
2
1
0
2
0
2
1
2
2
0
0
1
2
1
2
1
1
1
1
0
1
0
1
1
0
1
1
1
2
1
0
2
0
2
1
0
0
0
0
0
3
2
1
2
0
1
1
1
0
1
0
1
1
1
0
2
1
1
1
1
1
0
1
1
1
1
1
0
1
1
1
2
1
2
0
0
1
0
2
1
1
1
1
1
1
1
0
2
1
0
1
0
2
0
1
0
1
2
1
2
1
2
2
2
1
2
2
1
1
0
1
1
1
0
2
2
1
0
2
0
1
0
2
1
2
1
2
2
0
1
0
1
1
1
1
1
2
0
0
1
2
0
1
0
1
0
0
1
2
1
2
1
3
2
1
1
1
2
1
0
1
2
1
2
1
1
0
1
0
0
1
0
2
0
1
1
2
1
3
0
0
2
0
1
1
1
0
0
2
1
2
1
2
2
1
1
1
1
2
1
0
2
0
1
1
1
0
1
1
1
2
1
2
0
1
1
2
1
1
1
2
2
1
2
0
1
2
1
0
2
0
0
1
1
0
2
1
0
1
1
2
1
2
2
0
2
0
2
1
2
2
1
1
1
0
0
1
1
1
2
2
1
2
1
0
2
1
2
2
0
2
1
1
2
1
2
1
1
1
0
0
2
0
1
1
1
1
0
1
1
1
1
1
1
3
1
0
1
2
0
0
1
1
1
1
1
0
0
1
1
1
0
1
1
0
1
1
2
1
0
0
2
1
1
1
1
1
1
2
1
2
2
0
1
3
0
1
1
2
1
1
2
0
0
0
1
1
0
2
0
2
0
2
1
0
2
1
1
0
1
1
1
0
0
1
2
2
1
0
0
1
0
2
2
0
0
1
1
2
1
1
2
1
1
1
0
2
2
1
1
2
1
0
1
0
2
0
1
0
2
1
1
1
0
0
1
2
2
2
3
2
1
1
1
2
2
2
0
1
1
0
1
2
1
1
2
1
1
2
0
0
2
2
0
0
1
1
2
0
0
0
1
2
1
2
3
0
0
2
1
0
0
0
2
1
1
2
0
1
1
1
1
1
1
1
1
1
0
0
1
1
0
2
0
0
0
1
1
1
1
1
1
1
1
2
1
0
2
2
0
1
0
1
0
2
1
2
1
2
1
1
0
2
0
1
0
1
0
2
0
1
1
2
0
1
1
1
1
2
1
0
0
1
2
1
1
1
0
2
1
2
1
0
1
1
2
0
0
0
2
1
1
0
0
1
0
1
0
2
2
1
0
1
0
1
1
1
2
0
1
2
1
1
1
2
2
2
1
1
2
0
1
0
0
2
2
1
1
1
0
2
1
1
1
0
1
1
0
1
1
1
1
1
1
1
1
0
0
2
1
2
0
2
2
1
1
2
1
0
0
1
1
1
2
1
1
1
2
0
1
1
1
1
1
1
3
2
1
2
0
2
1
1
1
0
0
2
1
0
1
1
1
1
1
1
1
2
1
1
1
2
0
2
2
0
1
0
1
0
1
2
2
2
1
0
2
0
1
2
0
1
2
1
0
1
1
0
2
1
0
1
1
2
0
0
2
1
1
2
0
2
0
1
2
1
0
2
1
1
0
2
1
1
2
1
1
0
1
0
1
0
1
2
0
2
5
0
2
1
0
0
1
0
1
1
1
2
0
0
0
0
0
1
1
2
1
1
1
1
1
1
1
0
1
2
2
1
0
0
0
0
2
0
1
1
2
1
0
2
2
2
4
1
1
2
1
0
2
0
1
2
0
1
1
1
0
1
1
2
1
1
0
1
1
1
2
1
0
0
1
1
1
0
2
1
1
1
1
0
1
1
2
0
1
0
1
2
1
1
1
1
1
0
0
0
2
0
0
1
1
0
0
1
0
0
1
1
1
1
1
1
1
2
2
1
1
2
1
2
1
2
1
0
1
0
2
0
1
1
1
1
0
0
1
0
0
2
2
1
1
1
0
1
2
1
2
3
0
2
0
1
1
0
1
0
0
2
1
2
2
1
0
2
1
0
0
1
0
0
0
1
1
1
1
0
1
1
2
2
1
0
1
1
1
0
4
0
1
1
0
1
2
0
1
2
2
2
1
1
1
1
2
0
1
1
1
0
2
1
1
0
1
0
2
1
1
0
1
1
1
2
1
3
2
2
2
0
1
0
0
3
2
0
1
0
1
2
1
1
0
1
0
0
2
1
1
0
0
2
0
0
1
1
1
2
2
1
1
2
1
1
1
1
1
0
1
2
1
2
1
1
1
1
1
1
1
1
1
0
2
1
2
2
1
2
1
2
1
1
1
1
0
1
0
1
2
0
2
2
1
1
1
1
0
1
1
1
2
2
0
1
1
2
1
1
0
1
1
1
1
1
2
0
1
0
0
1
5
0
0
0
2
1
1
1
1
0
1
0
1
1
2
6
1
2
2
1
1
1
1
0
0
0
1
0
2
1
0
1
1
0
1
1
0
1
0
1
1
2
0
1
2
1
1
1
0
2
1
1
2
0
0
1
0
1
2
2
0
0
0
2
0
1
1
1
0
1
2
1
0
1
2
0
2
0
1
1
1
1
3
0
1
0
1
1
1
1
0
0
3
3
2
2
0
1
1
1
0
2
1
0
0
1
1
0
1
0
1
2
1
1
0
1
1
1
1
1
2
1
1
2
1
1
2
2
1
2
1
1
0
1
1
1
2
0
0
1
0
2
0
2
2
0
1
2
0
1
1
1
1
0
1
2
1
0
0
1
0
2
0
1
0
1
2
0
1
0
1
1
0
1
0
1
0
1
2
1
1
1
1
1
0
1
0
1
1
2
1
1
1
1
0
1
2
1
1
2
1
1
1
0
1
1
0
2
1
1
1
0
0
1
2
1
0
1
1
1
0
0
2
2
0
0
2
0
1
1
0
2
1
1
1
0
1
1
1
1
1
1
2
1
0
1
0
1
2
2
2
2
1
1
1
1
0
1
2
1
2
0
1
2
1
1
1
2
2
1
1
1
1
0
1
2
1
0
0
1
2
1
0
0
2
0
1
1
1
2
0
1
0
0
0
1
1
1
1
1
2
0
1
4
1
1
2
0
2
1
2
0
1
0
1
0
1
2
1
0
1
1
0
1
0
0
0
0
1
1
1
2
1
0
1
1
0
1
1
1
1
1
1
1
0
2
1
2
0
1
1
1
0
0
1
2
2
0
1
1
1
1
1
1
2
1
0
3
0
0
1
2
0
1
0
2
1
1
1
2
2
2
0
0
0
1
1
1
1
0
1
1
1
1
0
1
2
1
2
2
1
1
2
0
1
2
1
2
0
1
0
0
1
1
1
2
1
1
1
1
1
0
2
0
0
2
1
1
1
1
1
1
1
1
2
0
1
0
1
0
1
0
1
1
1
2
0
2
1
0
1
1
1
1
0
1
0
0
1
3
0
0
1
1
1
1
2
1
0
1
2
2
2
0
0
1
1
1
0
1
1
4
0
1
1
1
1
1
1
1
1
1
0
1
0
1
2
0
1
2
1
0
0
1
0
1
1
1
0
0
2
0
1
0
1
1
0
1
2
1
1
1
0
2
0
1
1
2
0
1
2
1
1
1
2
0
1
2
0
0
0
0
0
0
1
1
1
1
1
0
1
1
0
1
1
0
0
2
1
1
0
0
1
2
1
3
0
0
3
1
0
0
2
1
1
2
2
0
2
0
1
2
1
0
1
0
0
0
2
1
2
2
1
1
0
1
2
1
2
1
1
1
1
1
0
2
2
0
0
1
1
0
1
2
2
2
0
1
2
0
2
1
2
2
0
2
2
2
1
0
0
1
0
2
1
1
1
2
1
0
2
1
1
1
1
1
1
1
1
0
2
2
1
1
0
2
1
0
1
1
1
0
0
1
0
2
1
1
0
2
0
2
0
0
1
1
0
3
2
0
1
1
1
0
1
2
2
1
1
0
0
1
1
1
2
1
1
1
1
1
2
0
1
1
1
0
2
1
1
2
0
2
0
1
1
1
1
0
1
0
1
1
2
2
2
0
0
1
0
1
1
0
1
2
1
0
1
0
1
2
2
1
0
1
0
1
0
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
0
0
2
0
2
1
1
0
1
1
2
0
0
1
2
0
1
1
1
1
2
0
0
0
1
2
1
1
1
1
2
1
0
0
0
1
2
2
1
0
1
1
0
0
1
2
1
1
0
0
1
0
0
1
0
1
1
1
2
1
1
2
2
2
1
0
1
1
0
2
1
0
1
2
2
0
1
1
1
2
2
1
2
0
2
1
1
1
2
1
1
1
1
1
1
1
1
0
0
0
1
2
1
1
1
2
1
1
0
1
1
1
1
0
1
0
0
0
2
0
1
1
0
1
2
1
1
0
1
1
1
0
2
1
1
1
3
0
1
0
2
0
1
1
0
1
1
0
2
0
3
1
1
2
1
3
1
0
2
2
1
1
2
0
2
0
1
1
2
0
1
0
3
1
2
0
1
0
1
0
1
1
1
2
1
1
1
1
1
0
1
1
1
0
2
0
1
2
1
3
0
1
1
1
1
0
0
0
1
1
1
0
2
2
1
1
1
1
1
0
0
1
0
2
2
1
1
1
1
0
0
0
1
1
1
2
0
1
1
1
0
1
0
1
1
2
1
0
1
1
1
3
2
1
0
0
2
0
1
1
1
0
0
0
1
0
1
2
1
1
1
2
1
0
1
2
0
1
0
0
2
2
1
0
1
1
1
1
2
1
0
1
2
1
1
1
0
2
0
0
0
0
2
1
1
1
2
1
2
0
0
0
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
0
1
1
1
0
1
1
1
2
1
1
2
2
0
0
1
1
0
1
1
1
1
1
1
1
0
2
0
1
2
1
2
0
2
0
1
0
0
1
1
2
1
1
0
0
1
1
1
0
1
2
0
1
0
1
2
1
1
1
0
0
1
1
1
2
1
0
1
1
0
1
1
0
0
0
1
0
0
2
2
1
1
1
2
1
1
1
1
0
2
1
0
2
2
1
1
1
0
0
1
0
2
1
0
1
0
2
1
1
0
1
2
1
2
1
0
0
1
0
1
1
0
1
0
2
2
1
0
0
0
0
1
3
0
1
0
1
2
0
1
0
2
1
0
2
2
0
0
2
0
1
1
1
2
1
1
1
1
2
2
0
0
1
0
1
1
2
0
2
1
0
0
1
2
1
2
1
1
3
0
1
0
1
0
1
1
0
2
1
0
1
1
1
2
1
0
1
1
1
1
1
1
1
2
0
1
0
1
0
1
2
1
0
0
2
1
1
0
3
1
1
0
1
1
0
1
1
1
2
0
1
0
2
1
1
2
1
1
2
0
2
2
1
1
2
1
0
1
2
2
1
1
1
1
1
0
1
0
1
1
1
2
1
1
0
0
1
0
0
0
0
0
1
1
1
2
0
0
1
1
1
1
1
1
0
2
1
1
1
1
1
2
0
1
1
1
0
1
2
1
2
2
2
1
1
1
1
1
2
0
0
0
0
0
2
1
2
1
1
1
0
2
1
2
1
1
2
2
2
1
1
1
1
1
0
1
0
2
1
0
1
1
1
2
2
2
1
0
1
1
0
0
0
1
0
2
1
0
1
2
1
1
1
2
2
1
2
2
0
0
2
0
0
1
0
0
2
1
1
0
2
2
2
1
0
0
2
1
0
2
1
0
1
1
1
1
0
1
1
2
1
0
1
1
0
1
1
2
0
1
1
2
1
0
2
1
1
1
1
1
2
0
2
2
1
1
2
0
1
2
2
0
1
0
1
2
0
2
2
1
0
1
2
0
1
1
1
1
2
1
1
1
2
1
2
0
1
1
3
1
1
1
1
2
1
1
1
1
0
1
0
2
0
0
0
1
0
3
0
1
1
2
0
0
0
2
0
1
1
2
2
2
1
0
1
1
2
1
0
1
2
0
0
2
1
1
0
1
0
2
0
2
1
2
1
2
1
0
1
1
0
1
1
1
1
1
0
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
0
2
1
2
0
0
2
1
1
1
1
1
1
1
1
0
1
2
0
0
1
1
1
1
1
2
0
1
2
0
1
1
1
0
1
1
2
2
1
0
1
2
1
0
0
1
1
1
0
1
0
1
1
1
0
1
1
1
2
2
1
2
1
1
2
2
1
1
1
0
0
0
1
0
1
1
0
1
2
0
1
1
2
2
1
1
2
1
1
1
0
2
2
1
1
1
2
0
1
0
1
2
0
1
2
0
0
1
1
1
0
2
0
1
2
1
0
1
2
1
1
0
0
0
1
0
2
0
1
1
1
2
0
1
1
1
0
2
2
2
1
2
1
1
1
0
1
2
0
1
0
1
1
2
0
1
1
1
1
1
1
1
1
0
2
1
2
2
0
0
0
1
1
0
0
1
1
1
1
1
1
1
2
1
2
1
1
1
1
2
0
0
0
1
2
0
0
2
0
0
0
0
0
2
0
2
0
2
0
2
0
2
1
0
1
0
0
1
1
0
2
0
1
1
1
1
1
1
1
1
1
1
2
2
1
0
0
1
1
1
2
0
1
1
1
1
1
1
1
0
1
0
0
1
2
0
1
2
0
0
1
1
1
2
2
0
1
0
1
1
1
1
2
1
1
2
1
1
0
0
0
1
0
1
0
1
1
2
0
1
1
1
1
0
1
0
1
2
1
2
1
2
2
1
1
0
1
1
0
0
1
1
2
2
2
1
2
0
2
2
0
1
0
1
2
0
1
0
2
0
0
2
1
0
2
1
1
1
1
1
2
0
1
0
0
1
1
1
2
0
1
2
2
1
1
1
0
1
1
2
0
1
1
1
0
2
0
1
1
0
1
1
1
0
0
0
2
1
0
1
0
0
1
1
2
1
1
0
2
1
1
1
0
1
0
1
1
1
1
0
0
1
2
1
1
1
1
0
0
1
1
1
2
0
1
2
1
1
1
0
2
2
1
0
1
1
2
1
2
2
0
0
2
2
2
0
2
1
1
1
2
1
0
1
1
0
1
1
0
2
2
1
1
0
2
0
1
1
1
1
1
1
1
2
1
1
1
0
1
1
0
1
1
0
1
1
1
0
0
2
1
0
2
0
1
0
1
1
0
1
2
0
1
2
1
0
1
2
0
1
0
1
0
1
2
1
0
2
1
0
1
1
0
1
1
0
2
1
0
1
1
0
1
1
1
1
0
1
2
1
0
2
2
2
1
0
2
0
0
1
0
1
0
0
2
3
1
0
1
1
1
1
1
0
0
0
0
1
1
0
2
2
1
0
1
1
1
1
1
1
2
0
2
2
1
1
1
0
0
2
0
1
1
1
2
1
1
1
1
1
1
2
0
1
2
1
2
1
1
1
0
0
0
1
1
0
0
1
1
1
1
1
2
1
1
0
1
2
1
3
0
1
1
0
2
2
2
1
0
0
0
1
0
2
2
0
1
2
1
1
1
1
1
0
2
0
2
0
0
1
1
0
1
1
2
0
1
2
1
1
1
1
2
2
0
0
1
0
1
1
1
1
1
2
1
1
0
0
0
2
1
1
1
1
0
0
0
1
2
2
1
0
0
0
1
2
1
0
2
1
1
0
1
1
1
1
1
1
2
1
1
2
2
1
0
1
0
2
0
1
2
1
1
1
2
1
0
1
2
0
0
1
0
2
1
1
0
1
1
1
1
2
1
2
1
0
0
2
0
0
1
2
1
1
0
0
2
2
6
1
1
2
1
0
1
0
2
1
2
1
0
1
1
0
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
0
2
1
1
2
0
2
0
2
1
1
1
1
1
2
2
1
1
1
2
0
1
1
1
0
1
0
1
0
1
1
1
2
3
1
1
1
1
0
1
1
1
0
2
2
1
0
1
1
0
0
2
2
2
1
2
0
1
2
1
1
1
0
2
1
2
2
2
2
2
3
1
1
1
1
0
2
0
1
1
1
1
0
0
1
1
2
2
0
0
1
1
0
2
1
0
0
1
0
1
1
2
1
1
1
2
0
2
1
0
0
1
2
0
1
1
1
0
1
0
2
0
0
2
0
0
1
1
1
1
2
2
1
1
1
0
2
1
0
0
1
1
1
2
0
2
0
0
2
1
1
0
1
1
1
0
0
1
1
1
1
1
2
0
1
1
1
2
2
0
1
2
0
2
0
1
0
0
1
2
2
0
0
2
2
1
0
1
2
0
2
1
0
0
1
0
1
2
2
1
0
1
0
1
1
2
2
0
0
1
1
3
0
1
1
1
1
0
1
0
1
0
0
0
0
1
1
0
1
1
1
0
1
1
1
1
2
2
1
0
0
1
0
1
2
1
0
1
1
0
2
0
2
1
1
1
2
1
1
1
2
1
1
0
1
1
1
2
1
2
0
1
0
0
2
1
1
2
1
0
1
2
2
0
0
2
1
3
1
0
0
1
1
2
1
1
2
0
1
0
1
2
1
3
2
1
0
0
1
0
1
1
1
2
0
3
1
2
1
1
1
1
2
1
2
4
1
2
0
0
2
2
0
2
1
1
1
1
2
2
1
0
1
1
1
1
0
2
0
3
2
2
1
1
1
2
1
1
2
1
0
1
2
0
0
0
1
0
1
0
1
3
0
1
2
1
1
1
0
0
0
2
2
1
2
1
2
0
0
1
1
0
1
1
2
1
2
2
2
1
0
1
1
1
0
1
1
2
1
0
1
1
0
2
0
2
1
2
1
2
0
1
0
1
1
0
1
0
2
0
2
0
1
1
1
1
1
0
1
1
1
2
0
0
0
0
1
1
1
1
2
1
1
1
1
1
0
1
0
1
0
0
1
1
1
2
1
1
1
2
2
1
0
1
1
1
0
2
1
1
0
2
0
1
0
0
2
1
1
1
1
1
1
1
0
1
2
2
1
2
1
0
2
1
2
1
0
1
2
0
0
0
2
1
1
0
2
0
1
0
0
0
2
0
2
1
2
0
1
1
1
0
0
1
1
1
0
1
0
1
1
3
1
1
0
1
0
0
1
0
1
0
2
1
1
1
1
4
2
2
1
2
1
2
2
2
2
1
2
1
0
2
1
1
1
1
1
0
1
1
0
0
0
1
2
2
0
0
2
2
0
2
0
0
1
1
1
1
0
2
1
2
1
1
1
2
2
1
1
2
1
1
2
0
0
1
0
2
0
2
1
0
1
2
2
2
0
0
2
1
0
0
1
2
0
1
2
0
1
0
0
1
1
1
1
2
1
2
1
1
1
1
2
0
1
1
1
1
1
1
2
1
2
0
0
2
2
1
1
0
1
1
1
1
1
2
1
2
2
1
1
2
0
0
1
2
0
0
1
1
1
1
1
1
0
1
2
1
1
2
1
1
1
2
1
0
0
0
0
1
2
1
1
2
2
1
2
1
1
2
2
0
0
2
0
1
1
1
1
0
2
1
3
1
1
1
1
1
2
1
1
0
1
2
0
1
1
1
0
0
2
2
0
0
0
0
1
0
1
1
1
1
1
2
0
1
2
1
2
1
0
0
1
0
1
1
0
1
0
0
0
1
1
2
1
1
0
1
0
1
2
2
0
1
1
0
0
0
0
1
2
0
1
1
2
2
0
1
2
1
1
1
1
0
0
2
1
1
1
0
1
1
1
1
0
1
1
2
0
1
2
0
0
1
0
0
1
2
2
1
0
2
0
1
1
0
0
2
2
0
1
2
2
2
1
1
1
1
1
1
1
0
1
0
1
0
0
1
1
1
1
2
2
1
1
2
0
1
1
2
1
0
0
1
1
2
2
0
1
1
0
1
2
2
1
0
0
2
1
2
1
1
1
2
0
0
0
0
0
0
1
1
2
1
1
2
1
0
0
1
1
0
1
1
0
0
1
1
1
1
1
2
1
1
1
2
2
0
1
0
2
1
0
1
0
0
0
2
2
1
2
1
0
1
2
1
1
1
1
0
1
0
1
0
1
0
1
2
0
0
0
1
1
1
1
2
2
1
0
1
0
1
1
2
1
0
1
0
2
1
1
1
1
0
1
0
1
1
0
1
1
1
2
0
0
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
2
0
1
1
0
1
0
1
1
1
2
1
0
2
2
2
0
1
2
2
0
0
3
1
1
0
1
0
1
1
1
1
0
2
0
1
1
1
1
1
1
0
0
0
2
1
0
1
1
1
0
1
0
1
0
2
2
2
1
0
1
1
2
1
0
2
2
1
2
2
1
1
1
2
1
1
2
0
1
2
1
1
2
2
1
1
0
0
2
1
1
1
2
1
1
1
0
0
2
1
1
0
1
1
0
1
1
0
1
2
1
0
1
1
1
2
1
1
1
0
0
0
2
1
2
3
0
1
1
1
1
1
1
1
1
1
1
0
0
2
0
2
1
0
1
1
3
1
0
0
1
1
2
3
1
1
1
0
1
1
0
2
2
1
0
1
2
1
1
2
1
1
1
1
0
0
1
1
0
1
1
1
1
1
0
0
0
1
1
1
1
1
1
1
1
1
0
0
1
0
1
1
0
1
1
0
1
2
0
1
1
1
0
1
0
1
2
2
1
0
2
2
1
2
1
1
2
1
1
1
0
0
2
1
1
2
0
2
4
2
0
1
1
1
1
1
0
1
1
1
1
1
2
0
0
1
2
1
1
1
0
1
1
1
2
1
2
0
1
2
0
1
1
2
2
1
1
1
0
1
2
1
1
1
1
1
0
2
0
1
2
2
0
0
2
0
1
2
2
1
0
2
2
1
1
2
2
0
1
1
0
1
1
1
2
2
2
1
1
1
2
1
1
0
1
0
0
2
1
0
1
1
0
1
1
1
2
2
0
1
0
1
0
0
2
2
1
1
0
1
2
1
0
2
1
2
2
0
2
0
0
1
1
1
0
1
1
1
0
1
2
0
0
1
2
0
1
1
2
1
1
0
2
2
0
3
0
1
2
0
0
2
1
0
2
1
1
1
1
1
1
0
1
1
2
1
2
1
2
1
0
0
2
1
2
2
1
1
1
0
1
2
1
1
2
2
0
0
2
2
1
2
1
1
1
2
1
1
2
0
1
1
2
1
1
2
0
2
1
2
1
1
0
1
0
0
0
1
2
1
0
2
1
1
2
0
1
1
0
1
2
1
0
0
1
1
2
2
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
2
1
2
1
2
1
2
1
0
1
0
1
2
2
0
1
1
1
0
1
2
0
0
2
0
0
1
0
1
1
1
0
1
1
0
0
1
2
2
2
2
1
1
0
1
0
0
2
1
0
2
0
2
1
2
0
1
2
0
0
2
2
0
0
2
2
1
0
1
0
1
1
1
0
2
0
0
0
1
2
0
1
1
1
1
2
1
1
0
1
3
0
1
0
1
1
0
1
0
2
1
1
1
1
1
2
0
1
1
1
1
1
1
1
1
1
1
1
0
2
0
1
2
0
0
2
0
1
0
1
1
0
0
1
1
2
1
4
0
0
0
1
1
2
1
2
2
1
1
1
0
1
1
1
0
2
1
1
0
2
2
1
1
1
1
1
0
2
1
1
1
0
1
0
1
1
0
0
0
1
0
2
0
2
1
1
2
1
0
0
0
1
1
2
0
1
1
1
2
1
1
1
1
2
1
1
0
1
0
2
0
0
1
1
0
1
0
1
1
0
2
0
1
1
2
1
2
0
1
1
1
1
1
1
1
0
0
0
0
0
2
2
1
0
2
1
1
0
0
1
0
1
1
1
1
1
2
1
2
0
2
1
1
1
2
1
0
0
0
0
1
0
1
1
2
2
2
0
0
1
1
0
0
0
1
0
0
1
2
2
2
0
2
1
1
1
0
1
0
1
1
0
1
1
1
1
0
1
0
1
1
1
1
1
1
1
0
0
1
0
1
2
0
0
1
2
0
0
1
1
1
1
0
1
1
1
2
1
1
1
0
1
0
2
1
0
0
1
1
1
1
1
1
0
1
2
0
0
0
1
0
0
0
0
0
2
1
0
1
1
1
3
0
1
0
1
1
1
2
2
1
2
0
1
1
0
1
1
2
0
2
1
2
1
0
0
0
1
1
2
2
1
1
1
1
1
0
2
0
1
2
1
0
0
2
1
2
1
0
2
1
1
1
2
1
2
3
1
0
1
1
1
1
1
1
1
2
2
1
1
1
0
1
1
1
1
1
1
0
1
2
1
0
1
0
2
0
2
1
0
0
3
0
0
1
0
1
2
1
1
1
1
0
1
1
2
1
0
0
1
1
1
1
0
0
0
1
2
2
1
3
2
0
1
1
1
2
1
1
1
0
1
0
2
0
1
1
2
1
1
1
2
1
1
0
1
0
1
2
1
1
1
0
0
2
0
2
2
1
1
1
1
1
1
1
1
1
0
0
1
1
0
1
2
0
1
1
1
1
1
1
1
0
0
2
1
0
1
0
2
1
1
1
0
1
1
2
0
1
1
0
2
1
0
0
0
1
2
1
0
1
2
1
0
1
1
1
1
0
0
1
1
1
2
1
2
0
1
0
2
2
2
0
1
1
1
2
0
1
0
0
1
1
0
3
1
2
0
1
1
1
0
2
0
1
2
1
1
1
2
1
0
2
1
1
0
1
1
2
1
1
1
1
0
0
0
2
1
1
0
0
0
2
1
2
1
1
0
1
2
1
1
1
1
1
1
1
1
0
1
0
1
0
1
0
0
2
1
2
0
2
1
0
1
1
2
2
1
1
1
0
0
1
0
1
1
2
2
1
0
1
0
0
2
1
1
1
0
0
2
0
1
1
1
1
1
0
1
2
0
1
0
0
2
1
1
3
2
1
0
1
4
1
0
2
1
0
1
1
0
0
1
1
1
0
1
2
2
1
0
2
1
1
2
1
2
1
0
1
2
0
1
2
1
1
1
2
0
0
0
1
1
2
1
1
2
0
0
2
2
2
2
1
0
2
0
2
2
1
2
2
2
0
2
0
2
1
1
0
2
1
1
0
0
0
1
0
0
2
2
2
1
1
0
1
2
2
1
1
1
0
1
0
1
1
1
1
0
1
1
0
0
1
1
1
0
1
2
1
1
1
1
1
1
2
1
1
1
1
1
0
2
1
0
2
2
2
0
2
0
0
1
1
0
1
1
2
1
2
0
4
1
2
0
1
1
1
1
0
1
1
0
1
2
2
1
1
2
1
1
1
0
0
0
1
1
1
1
1
1
2
3
1
1
1
1
1
0
2
1
0
2
1
0
1
1
0
0
1
1
3
2
1
1
1
2
2
1
2
1
1
1
1
0
0
1
2
2
0
2
1
3
2
1
2
0
0
1
1
2
1
1
2
0
1
2
1
2
1
1
2
2
2
1
0
0
0
1
2
0
1
5
1
1
1
1
0
1
1
1
0
1
1
1
1
2
1
0
0
1
0
1
1
0
0
2
1
1
2
0
1
1
0
2
2
0
1
0
1
3
0
2
1
1
1
1
1
1
1
0
2
1
1
2
2
2
2
0
0
0
2
1
1
2
1
0
2
0
0
0
1
1
1
1
0
1
1
0
0
1
0
2
2
2
1
1
1
2
0
2
1
1
1
0
1
0
0
1
2
0
2
1
0
1
1
0
0
2
3
1
1
1
2
1
1
1
2
0
1
1
0
2
2
1
2
1
2
1
0
2
0
1
2
1
1
0
1
1
0
0
0
1
1
1
1
0
0
2
1
1
1
1
1
1
1
1
1
1
0
1
1
0
0
1
0
1
0
0
2
0
1
2
0
1
2
1
2
0
0
1
1
1
2
2
0
1
1
0
0
0
2
1
3
1
2
1
1
1
1
1
0
0
0
0
2
1
1
1
2
1
0
1
2
1
2
0
0
1
1
0
1
1
1
0
1
2
1
0
1
2
1
0
0
0
1
1
1
0
1
1
0
1
1
2
0
1
1
2
1
1
1
0
1
0
1
2
1
2
0
2
0
1
1
0
2
2
1
0
1
1
1
1
1
1
1
1
0
0
1
1
0
1
0
0
2
1
2
1
0
0
1
0
1
2
1
2
1
1
1
1
2
2
1
2
2
2
0
2
0
1
1
0
1
0
2
2
1
0
2
2
1
1
1
2
1
0
1
0
0
1
1
1
1
2
1
1
0
2
0
1
1
1
0
0
1
2
1
2
2
2
1
2
0
1
1
0
1
1
0
1
2
2
1
1
1
2
0
0
0
1
2
1
1
2
1
1
2
1
0
1
1
1
0
1
0
1
1
1
1
1
1
2
1
0
0
0
1
0
0
1
1
2
1
0
1
0
1
1
1
1
2
1
1
2
0
1
2
1
2
1
0
1
0
3
2
2
1
1
0
0
1
1
2
2
1
1
1
2
2
1
1
2
1
1
0
1
1
0
0
0
0
1
0
1
1
1
1
2
2
0
0
1
0
0
0
2
2
2
1
0
1
1
0
1
0
1
1
1
0
1
2
2
1
0
3
1
1
1
2
1
1
1
1
1
0
1
1
1
0
1
0
1
0
1
2
1
1
2
0
1
1
1
3
1
3
1
1
1
1
1
0
1
1
0
0
0
0
1
2
3
0
2
1
0
0
1
1
0
1
0
2
1
0
2
2
0
2
0
2
2
2
2
1
1
2
2
1
1
1
1
1
1
1
1
0
1
1
1
0
0
2
1
1
1
2
0
2
1
2
1
1
1
1
1
0
1
2
1
1
2
2
1
2
0
0
0
1
0
0
1
2
2
2
1
2
1
0
1
2
1
1
2
1
1
0
1
2
2
0
0
1
1
1
1
1
0
1
1
2
1
1
1
0
0
0
0
1
1
2
0
1
1
1
1
1
1
1
1
0
1
0
1
2
1
1
2
2
2
1
1
1
0
2
2
1
1
0
2
1
0
2
1
1
2
0
1
1
2
1
1
1
1
0
0
1
1
0
1
1
1
4
2
2
1
1
1
0
0
1
1
2
2
2
1
2
2
1
1
1
0
1
0
2
2
2
0
1
1
2
1
1
0
2
1
1
2
2
0
1
1
2
1
0
1
2
0
0
1
2
1
1
1
0
2
2
1
2
1
0
0
2
2
1
0
1
1
1
2
0
2
1
1
1
1
0
1
1
1
1
2
2
1
1
2
2
1
1
0
2
1
1
0
0
2
0
0
1
1
1
2
1
0
1
0
1
2
2
1
1
1
0
2
0
1
1
0
1
1
2
2
2
2
2
0
2
2
1
2
2
1
1
1
0
2
2
2
2
0
0
0
1
0
2
1
1
2
0
1
0
2
0
0
1
1
2
2
0
1
2
0
0
0
2
1
1
0
2
0
1
1
0
1
1
1
3
1
1
1
0
1
1
0
2
1
1
2
0
1
1
1
1
1
1
1
0
2
1
1
0
2
1
0
2
0
1
1
0
2
3
1
1
1
1
1
1
1
1
0
1
2
0
2
1
2
2
2
0
1
1
0
2
2
0
2
1
1
2
2
1
2
1
0
2
0
2
0
1
1
2
1
0
1
1
1
1
0
1
1
0
2
0
0
1
1
2
0
1
1
0
0
1
1
0
1
1
1
0
0
1
1
1
1
0
1
2
1
1
1
1
0
2
1
0
0
0
1
2
2
0
1
2
1
0
1
1
1
0
0
0
0
0
0
1
2
2
1
1
1
1
1
0
1
1
1
0
1
2
2
1
0
1
1
1
1
2
0
2
0
0
0
2
1
2
0
0
0
2
0
0
1
0
0
1
2
2
2
0
2
0
1
1
2
2
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
0
2
0
1
0
0
0
1
1
3
1
0
1
1
0
0
0
2
1
1
1
2
1
1
2
1
1
0
0
1
0
0
0
1
1
2
2
1
0
1
1
0
0
0
1
0
1
1
1
0
2
0
0
1
0
0
1
1
1
1
1
2
0
2
2
1
1
1
1
1
1
1
1
2
1
0
2
2
2
0
1
0
0
0
1
1
1
2
0
1
0
1
0
1
2
2
1
1
1
1
1
1
2
0
1
1
1
2
1
1
2
0
1
0
1
1
1
0
2
1
1
1
1
1
0
1
0
1
0
1
2
1
1
1
1
2
1
0
2
1
0
1
1
2
0
1
2
1
0
2
1
2
0
0
1
1
1
1
0
1
1
1
0
3
0
0
1
2
2
1
1
0
0
2
1
0
0
1
1
1
0
1
0
0
0
1
0
2
1
1
0
1
1
1
1
1
0
1
1
1
1
1
1
1
0
0
2
0
1
0
2
2
0
1
1
0
1
2
2
0
0
0
0
0
1
0
2
1
1
1
2
1
0
0
1
0
2
0
1
1
0
2
1
1
2
2
1
2
2
1
0
1
0
1
1
1
1
1
2
1
1
1
1
1
1
0
1
0
2
2
2
1
0
1
1
0
0
0
1
0
1
1
1
0
1
2
0
0
0
1
2
0
1
2
0
0
1
0
3
0
1
1
1
1
1
2
1
0
0
2
2
1
0
1
1
1
0
1
2
1
0
1
2
1
1
0
2
1
3
1
0
2
1
1
1
2
1
1
0
2
2
1
1
1
2
1
1
0
1
1
0
2
0
1
1
2
2
0
1
1
1
1
0
0
0
1
2
2
1
1
1
0
1
1
1
2
3
1
1
0
1
2
1
1
0
1
0
1
2
1
1
2
1
1
1
1
1
1
2
0
0
2
1
2
1
1
0
1
0
1
2
1
0
2
1
2
1
1
1
1
2
1
1
0
0
2
1
1
1
2
1
1
0
1
0
0
0
2
0
0
0
2
2
1
1
1
1
2
1
1
1
0
2
1
2
0
2
1
1
1
0
1
0
1
1
1
1
2
0
1
2
2
2
2
0
0
1
1
2
2
1
1
0
1
1
0
0
0
0
1
1
1
1
0
1
1
1
1
1
0
0
2
1
3
1
1
1
0
0
1
1
3
2
1
1
1
0
1
1
0
1
0
1
1
2
1
1
1
2
2
1
1
2
1
1
2
1
0
1
0
1
0
1
1
1
1
1
2
1
0
1
1
2
1
1
1
2
1
0
0
1
1
1
1
0
0
1
1
1
1
2
1
2
1
1
1
2
0
0
0
1
1
1
1
1
0
1
1
0
1
0
1
1
0
1
2
0
0
1
0
2
1
0
1
0
0
2
1
1
0
1
1
1
1
1
2
0
1
1
1
1
2
2
0
0
1
1
2
0
1
1
1
0
1
1
1
1
1
2
1
2
1
0
2
0
1
1
1
1
1
1
1
1
2
0
2
1
2
1
2
1
2
1
1
0
2
2
1
2
0
1
2
2
0
2
1
1
0
2
1
2
1
2
1
1
2
1
1
1
2
1
1
1
1
1
2
2
1
1
0
1
1
1
0
1
1
1
2
1
1
1
0
0
1
1
1
1
3
1
1
1
2
2
0
1
0
1
2
0
1
2
0
0
1
0
1
0
0
1
1
1
0
1
1
1
2
0
0
0
1
0
0
2
1
1
1
2
2
1
0
0
1
0
2
0
1
2
1
1
2
1
1
1
2
2
1
2
0
1
2
1
1
1
2
0
2
2
2
1
1
1
0
2
0
1
2
3
2
2
1
2
0
1
2
1
1
1
2
1
1
1
0
1
2
1
1
2
1
1
1
1
0
0
2
1
0
0
1
2
1
1
1
2
0
1
1
0
1
1
0
2
1
0
1
0
1
2
1
0
2
1
1
1
2
1
2
1
1
2
0
2
0
2
1
1
1
1
1
0
1
2
1
1
1
1
1
0
0
1
4
2
1
1
1
1
1
1
0
1
1
1
2
0
2
2
1
2
1
0
2
0
1
1
1
0
1
0
1
0
1
0
2
0
2
1
2
1
0
1
2
2
1
0
1
1
1
1
0
0
1
2
1
2
2
1
0
0
2
2
2
1
2
2
0
1
1
0
1
0
1
1
0
2
1
1
1
1
2
0
1
1
1
0
1
1
0
2
2
1
2
1
1
1
1
0
2
0
1
0
2
1
2
1
2
2
1
2
0
1
1
1
1
2
0
1
2
2
1
1
2
2
0
3
1
0
2
2
1
2
0
0
0
2
1
1
0
1
1
1
1
2
1
0
0
0
1
1
1
2
0
2
0
2
0
2
0
1
1
1
1
2
2
0
1
1
1
0
0
0
0
1
0
0
2
2
1
1
1
1
1
2
1
1
1
0
1
0
2
0
0
1
1
1
1
1
1
0
0
0
1
0
1
0
2
1
1
1
0
1
1
1
1
1
1
0
1
2
2
0
1
1
2
2
0
1
1
0
2
2
2
2
0
1
1
2
1
1
1
1
1
0
1
1
1
1
2
1
0
1
1
2
1
2
2
1
1
2
4
2
1
1
2
1
0
1
1
1
2
1
1
1
0
0
1
1
1
1
0
0
1
1
1
1
2
2
0
1
1
1
2
1
1
0
1
1
1
1
1
1
2
1
1
1
1
0
1
0
0
2
1
1
2
0
0
1
1
0
2
1
2
0
1
1
1
2
2
1
2
2
1
1
1
2
2
0
2
1
2
0
1
2
2
0
1
2
1
1
0
0
1
0
3
2
1
1
0
0
0
1
1
0
0
2
2
1
1
0
1
1
2
2
1
2
2
1
1
2
2
1
1
0
1
0
1
0
1
1
1
1
1
2
2
1
2
0
2
1
0
1
1
0
0
0
0
1
1
1
1
1
1
0
0
1
1
1
1
1
1
1
2
1
1
1
0
1
2
2
1
0
1
1
1
1
1
1
1
0
0
0
1
1
1
0
2
2
0
2
0
1
1
1
2
1
1
0
1
1
2
0
2
1
2
1
0
0
1
1
1
1
1
1
1
0
1
0
0
0
0
1
1
1
2
1
2
1
2
2
0
0
1
1
1
1
1
2
1
2
0
2
1
1
0
1
0
0
1
0
1
1
2
0
1
0
1
1
2
1
2
1
2
0
1
1
1
1
3
2
1
1
2
1
1
1
1
2
0
0
1
0
1
2
2
0
1
1
1
2
2
0
1
2
2
1
1
2
4
0
1
1
1
2
1
1
1
1
0
0
0
1
0
0
1
0
0
1
1
1
0
0
1
1
2
1
2
0
1
2
1
2
1
1
1
2
0
1
2
1
1
1
2
1
1
1
1
0
2
2
0
1
1
1
2
1
0
3
1
0
1
2
1
0
0
0
0
2
1
0
2
0
2
2
1
1
1
1
1
2
1
0
1
1
0
1
2
1
1
0
1
0
1
0
1
2
1
2
2
1
0
1
0
1
0
2
0
1
0
1
1
1
0
1
0
1
0
2
1
1
1
2
1
1
1
2
1
0
0
2
1
2
0
0
0
1
1
1
2
1
0
1
0
2
2
0
1
1
0
2
1
1
2
0
0
1
1
0
2
1
0
1
1
1
2
1
1
0
1
1
1
2
0
1
1
2
1
1
0
0
1
1
1
0
1
2
1
2
0
2
1
1
1
1
2
0
0
1
0
1
1
1
1
0
1
1
2
2
0
0
2
1
0
0
0
1
0
1
1
1
0
1
1
0
0
1
2
0
1
0
1
1
4
2
2
2
0
0
1
2
1
2
1
1
0
2
1
1
1
2
1
0
2
1
0
1
1
0
2
2
1
1
1
2
1
0
1
2
2
2
2
0
1
2
0
1
1
1
2
1
1
0
0
0
1
1
1
2
1
0
2
0
0
1
0
0
1
2
1
1
1
2
2
3
1
0
2
1
1
1
0
1
2
0
1
1
1
1
2
0
1
1
0
1
1
1
1
0
0
0
1
2
2
1
0
1
1
1
3
0
1
1
2
2
1
0
1
0
2
1
1
2
3
2
0
1
0
2
1
1
1
0
1
1
1
1
3
0
2
1
0
0
2
1
2
1
0
2
1
0
1
2
2
2
0
2
0
0
0
1
2
1
0
0
1
2
2
2
1
1
2
2
1
1
0
0
1
1
1
1
2
2
2
2
0
1
0
1
1
1
2
1
0
0
2
2
1
0
0
0
2
2
1
1
1
0
1
2
1
0
0
0
1
3
2
1
2
1
0
1
2
1
1
0
0
0
1
1
2
0
0
1
0
1
2
1
1
1
1
1
2
2
2
2
1
1
1
1
1
1
1
0
0
0
0
2
2
1
2
1
0
1
0
1
1
1
1
2
2
2
1
1
1
2
0
0
0
1
1
1
0
0
2
2
0
1
0
1
0
0
1
1
1
0
1
1
1
1
2
1
0
0
0
0
2
0
2
1
1
2
2
2
2
1
2
3
1
2
0
1
1
0
0
2
1
1
1
2
2
0
2
1
2
1
1
0
1
2
0
1
1
1
1
1
1
0
1
2
1
0
0
1
1
1
2
2
0
1
0
2
1
2
1
0
1
1
1
0
0
0
0
2
1
2
1
1
2
0
1
0
2
1
1
1
0
0
2
1
2
0
1
1
1
0
2
3
1
1
2
2
2
1
0
2
2
0
0
1
0
0
1
1
2
2
1
2
1
2
1
2
1
1
0
2
1
2
0
1
0
1
0
2
1
1
1
1
0
2
1
0
1
4
1
2
1
1
0
1
2
1
1
0
0
0
1
1
0
2
2
2
1
1
1
2
3
1
2
1
2
1
1
1
2
2
1
1
2
1
0
2
0
1
0
1
0
0
1
1
3
0
1
2
1
0
1
1
0
1
0
1
2
1
0
0
1
1
2
2
0
1
1
1
0
2
1
1
1
1
2
1
0
1
0
0
1
1
1
0
0
0
1
1
1
1
1
1
1
1
2
0
0
1
1
1
0
2
0
1
1
2
0
0
1
0
0
1
4
1
2
0
1
2
1
1
1
2
0
2
1
1
2
0
0
2
2
0
1
1
0
1
1
0
1
1
1
0
0
0
2
1
2
1
0
1
1
1
1
1
2
2
1
0
2
0
2
2
0
1
1
1
1
2
1
0
0
0
1
0
1
1
1
1
2
1
0
0
0
1
0
1
1
1
1
2
2
2
2
1
0
0
0
1
2
0
3
2
1
1
1
1
1
0
2
1
2
2
3
1
1
0
1
1
1
1
1
0
2
0
1
2
1
1
0
2
2
2
1
0
3
1
1
1
1
1
2
1
1
2
2
1
0
0
1
0
1
2
1
1
1
1
2
2
1
2
2
2
0
0
1
1
0
1
2
1
1
1
2
2
1
0
0
2
1
0
1
1
2
2
1
2
1
0
1
2
2
0
0
1
1
0
1
0
0
1
1
1
0
0
1
1
2
0
1
1
2
2
1
1
0
1
1
0
1
1
2
0
2
1
2
1
2
1
0
2
1
0
1
1
1
1
0
1
1
0
2
2
1
1
1
2
1
0
2
1
2
1
0
0
1
2
1
1
1
1
1
0
3
1
1
1
1
2
1
2
0
0
0
1
2
1
2
2
1
1
1
1
0
1
0
1
1
1
1
1
2
0
0
1
2
1
2
1
1
2
1
2
0
1
3
1
0
2
0
3
1
1
1
0
1
0
2
2
0
2
2
1
2
2
1
1
1
0
1
0
0
2
2
1
1
0
0
2
1
1
0
0
1
0
2
2
1
2
1
2
0
1
1
0
0
1
1
1
1
1
1
1
0
2
2
1
2
1
1
1
1
1
0
1
0
0
1
1
2
0
2
1
1
2
1
1
1
1
0
1
1
1
3
0
1
2
0
0
1
1
1
2
1
1
1
0
1
1
1
0
2
2
0
1
1
0
1
0
0
0
0
1
2
1
1
1
1
0
1
1
1
2
1
2
1
2
0
0
0
0
1
1
0
3
2
1
2
0
1
2
0
1
0
0
1
0
0
1
1
0
0
0
1
0
2
1
1
1
0
1
2
1
0
1
0
0
1
2
1
0
1
1
1
0
1
1
1
1
0
1
1
1
1
1
2
2
0
1
1
0
0
0
1
1
1
0
1
1
1
0
1
1
0
0
1
1
3
0
0
2
2
1
1
0
1
1
0
2
0
0
0
2
1
1
2
1
1
0
0
1
1
1
0
1
1
0
0
2
0
2
1
2
0
2
1
2
0
1
2
1
0
1
2
1
1
2
2
1
0
1
1
1
0
1
0
0
1
1
0
0
1
1
1
2
1
1
2
1
1
1
0
1
1
2
1
1
0
1
1
1
0
2
1
1
1
2
1
1
1
1
3
0
1
1
1
1
2
1
0
2
1
2
0
1
1
1
0
1
0
1
1
0
1
1
1
1
1
2
1
0
1
0
0
1
0
2
2
1
2
1
2
2
0
2
1
1
1
0
0
2
2
2
1
0
2
1
1
0
2
1
1
1
0
1
0
0
1
0
0
2
2
1
0
0
0
1
1
1
1
1
1
0
0
1
2
0
0
0
1
1
0
1
1
1
2
1
0
1
1
1
1
0
0
2
1
0
0
2
1
0
1
2
0
0
1
1
1
0
1
1
1
2
1
1
0
1
2
2
1
0
2
1
1
1
1
1
1
1
1
1
2
2
0
1
1
0
0
1
0
1
2
1
0
2
0
1
1
0
2
0
2
0
2
3
0
0
1
2
2
0
1
2
0
1
1
1
2
1
1
1
0
1
1
1
1
1
2
1
1
0
0
1
1
1
0
1
2
1
2
2
1
0
1
1
2
2
1
0
2
1
1
1
1
1
2
2
1
1
0
2
1
2
2
1
2
1
1
2
0
1
1
1
0
1
0
1
0
2
0
2
1
1
2
0
2
0
1
1
1
1
1
2
0
0
2
0
2
1
0
0
0
2
1
1
0
1
1
2
2
2
1
2
1
2
0
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
0
1
1
2
1
1
2
1
1
2
0
2
2
0
1
2
1
2
2
0
0
1
1
0
0
0
1
0
1
2
0
2
1
2
0
1
1
0
1
0
2
2
2
1
0
1
0
2
0
2
0
1
1
0
0
1
1
1
1
2
0
0
1
1
2
0
1
1
1
1
0
0
1
0
1
0
1
2
1
0
0
0
1
1
1
1
0
0
2
2
1
2
1
1
0
2
1
1
1
0
0
1
1
1
2
1
1
1
0
1
2
0
1
1
0
2
0
2
0
1
2
2
0
0
0
0
1
0
2
0
1
2
2
1
1
1
1
1
1
2
0
1
1
2
1
1
0
0
1
1
1
1
0
1
1
2
1
0
2
1
1
0
1
1
1
1
2
1
0
2
2
2
1
0
2
0
2
1
1
1
1
0
1
0
1
1
1
1
2
0
2
0
1
7
1
2
0
1
1
1
1
1
2
2
0
0
0
0
0
2
0
1
0
0
1
2
0
1
0
0
0
1
0
1
1
0
1
1
1
0
0
2
2
0
1
1
1
0
0
1
2
1
0
1
2
0
0
1
1
0
1
2
0
1
1
0
2
1
1
1
0
1
1
2
0
2
1
1
2
0
0
2
0
0
2
0
0
0
0
0
1
0
2
0
3
1
2
1
1
2
0
1
1
1
1
1
0
1
1
0
1
2
0
0
1
0
2
1
0
1
1
1
2
0
1
1
2
2
2
2
1
2
1
1
1
0
0
1
2
2
2
1
1
1
1
0
2
0
0
2
2
3
2
1
0
0
1
2
1
1
1
1
2
0
1
1
1
2
1
2
1
1
1
0
0
2
1
2
1
1
0
0
3
1
0
2
2
1
2
1
1
1
1
1
0
0
1
2
1
1
1
2
0
2
1
1
1
1
2
2
2
1
1
2
1
1
1
0
1
1
1
1
1
0
1
2
2
1
1
1
1
1
0
1
1
0
1
1
0
0
2
0
1
1
0
1
0
1
1
1
0
1
1
1
1
0
1
0
0
1
2
1
2
1
1
1
0
1
0
0
1
1
1
0
1
2
1
1
2
1
1
1
2
2
1
1
1
2
1
1
1
0
1
1
2
3
1
1
0
1
2
1
1
1
2
1
1
1
1
2
1
0
2
1
1
1
1
1
1
1
2
0
1
1
0
1
1
1
1
1
0
2
0
2
1
1
2
0
1
0
1
1
1
2
1
1
1
1
1
2
1
0
0
1
0
0
1
2
0
1
1
1
0
0
1
1
1
1
2
0
2
0
1
1
2
1
0
2
1
1
1
0
2
1
2
1
2
1
1
3
1
1
1
0
1
2
2
1
1
2
1
0
2
1
0
1
2
2
0
2
2
3
1
0
1
1
2
0
1
1
0
1
0
1
0
1
0
0
1
1
1
0
2
2
1
0
2
1
0
3
2
1
1
2
0
2
0
2
1
2
1
1
2
1
1
0
1
1
1
2
1
2
1
0
2
1
1
2
1
1
2
2
1
2
1
0
0
2
0
0
2
1
0
1
1
2
1
2
1
1
0
0
1
2
1
1
1
1
0
2
0
1
1
0
2
1
1
0
0
0
1
1
2
1
1
3
1
0
1
0
0
1
0
1
1
3
1
2
1
0
1
2
2
1
0
0
1
1
1
2
2
0
1
1
1
1
1
0
1
1
2
1
0
1
1
2
0
1
2
1
1
1
1
1
1
1
1
1
0
1
2
2
0
0
0
1
1
1
1
2
2
0
2
1
1
1
2
2
1
0
1
1
1
1
0
1
0
2
1
1
0
1
1
1
0
1
1
0
1
2
2
0
0
2
1
0
0
1
1
1
1
0
1
1
1
0
2
1
0
1
0
0
1
0
1
1
2
0
1
1
0
2
2
1
1
1
1
2
1
0
0
1
0
0
1
1
1
1
1
1
0
1
1
1
1
1
1
0
1
2
1
2
1
2
2
0
1
0
0
1
0
1
2
1
0
1
1
1
0
0
2
1
2
2
2
0
0
0
1
1
2
1
1
1
1
1
0
2
2
1
1
1
1
0
1
1
1
1
2
1
1
0
1
1
1
1
2
2
1
1
1
2
0
0
0
0
1
0
0
0
1
1
0
1
2
1
0
1
2
1
1
1
1
0
1
2
0
0
1
0
1
1
1
1
1
1
1
1
1
1
1
2
2
0
2
0
1
1
1
0
0
0
1
2
1
1
0
1
0
1
2
1
0
1
0
1
0
1
1
1
2
2
1
2
2
1
1
1
1
1
1
0
2
2
0
1
0
2
1
1
0
2
0
1
1
1
1
1
1
1
2
2
1
1
1
1
1
0
1
2
0
2
1
1
2
3
0
1
2
2
1
1
4
1
1
1
0
0
1
0
1
0
1
1
1
1
1
0
1
0
1
2
2
0
0
1
1
1
2
0
1
1
2
0
1
2
0
1
0
0
2
2
0
0
2
1
1
1
2
1
2
1
1
2
0
2
1
0
1
2
0
1
0
0
0
0
1
1
1
1
1
1
2
2
2
2
0
1
1
1
0
2
0
0
0
1
0
1
2
1
0
2
2
0
0
0
5
0
2
1
1
2
0
2
0
1
2
1
2
0
2
1
1
0
0
0
1
0
2
2
2
0
1
2
1
1
1
1
0
0
2
2
0
0
0
1
1
2
1
2
2
1
1
1
0
1
2
1
1
0
0
2
2
1
2
1
1
0
0
1
1
1
1
0
2
1
1
1
0
1
1
0
0
1
0
0
1
3
0
1
0
0
0
2
1
2
0
1
0
1
1
1
1
1
1
2
2
3
1
0
1
1
2
2
0
1
0
1
1
2
2
0
0
1
1
1
2
1
1
1
1
0
1
0
2
1
1
1
1
0
1
1
2
1
2
0
1
2
2
1
2
0
1
0
1
1
1
1
0
1
2
1
1
1
2
1
1
0
1
0
2
0
1
2
0
0
1
1
1
1
1
1
2
0
0
0
2
1
1
1
0
3
0
0
3
2
1
1
1
0
2
1
0
1
1
1
1
0
1
1
1
2
0
1
1
2
0
0
2
1
1
1
2
0
0
1
0
1
2
2
0
0
2
1
1
1
1
1
1
0
0
1
0
1
1
0
0
3
1
0
2
2
1
2
1
0
0
1
0
2
0
1
1
0
1
1
1
6
1
1
1
1
1
1
0
2
1
0
1
1
0
1
1
0
1
1
1
2
1
0
2
2
2
0
1
0
1
2
2
2
2
1
1
2
1
1
0
0
1
0
1
1
1
1
0
1
0
1
1
0
1
2
2
0
0
2
1
1
1
1
1
1
1
11
1
2
1
0
2
0
1
2
0
2
0
0
1
2
1
0
1
1
0
1
1
1
0
1
0
1
1
1
0
2
3
2
0
0
1
1
1
1
1
0
2
2
1
2
1
0
0
1
1
1
1
1
1
1
1
1
2
1
0
1
1
2
0
1
1
1
0
0
1
1
0
1
1
1
1
1
1
2
1
2
0
0
2
2
1
1
2
1
2
1
2
1
0
1
0
2
1
2
1
1
1
2
1
0
2
0
1
1
1
1
2
0
0
1
1
1
2
2
1
1
2
1
0
1
1
1
1
1
1
1
0
0
0
2
0
1
1
0
0
1
1
2
0
1
1
2
0
1
1
1
1
1
1
1
1
1
0
1
1
0
1
1
2
0
3
0
2
0
1
0
2
0
1
1
1
1
1
1
1
1
2
2
2
2
1
1
1
2
0
1
1
1
2
1
1
0
1
1
1
0
1
1
2
1
0
2
1
1
0
1
0
0
1
0
1
0
0
1
1
1
2
1
0
2
0
2
0
1
2
1
1
1
0
1
1
1
1
1
0
1
2
2
1
2
1
1
1
0
0
1
0
1
0
1
0
2
1
1
1
1
2
1
2
1
0
0
0
0
1
1
1
1
1
0
1
2
1
1
0
1
0
1
0
2
1
0
1
1
2
0
1
1
1
2
0
0
0
1
0
1
2
1
0
2
0
2
0
1
2
2
1
1
1
1
1
0
1
0
1
1
2
2
1
2
1
1
0
1
1
1
1
0
2
2
0
1
1
1
0
2
0
2
1
0
0
2
1
1
1
2
1
2
1
2
1
1
0
0
2
1
1
2
1
0
2
1
2
2
1
0
1
0
1
1
1
0
1
1
1
1
2
1
1
2
0
0
1
4
1
1
1
1
0
0
2
1
1
0
0
1
1
0
2
0
2
1
2
0
0
1
1
1
2
0
1
1
0
1
2
1
1
2
0
0
1
2
1
1
0
1
1
1
2
1
1
1
1
1
1
2
1
1
0
0
0
2
2
1
1
2
2
0
1
1
1
2
2
1
1
1
0
1
0
1
2
2
1
1
1
1
0
2
0
1
1
0
1
0
1
0
1
0
1
1
2
1
1
1
0
0
2
1
0
2
1
1
2
1
3
1
1
1
2
1
0
0
0
1
2
1
1
1
1
2
1
0
0
0
1
0
0
0
1
2
1
0
2
0
0
1
1
0
0
0
0
2
0
1
1
1
1
1
2
0
1
1
1
1
2
0
1
1
2
1
2
1
2
1
2
1
1
1
0
3
2
2
0
2
0
2
1
1
1
2
1
0
1
0
0
5
0
1
1
0
2
0
1
0
0
0
1
0
1
1
0
2
1
0
1
2
1
0
0
1
1
2
0
0
0
0
1
0
2
2
2
0
2
2
0
2
0
1
0
0
1
0
1
1
1
2
2
1
1
1
1
1
9
0
0
1
0
1
1
1
1
1
4
0
0
1
1
2
0
2
1
2
0
1
1
2
2
1
1
2
1
0
2
0
1
2
1
1
1
1
1
1
0
2
2
0
1
0
1
2
0
1
2
1
2
1
0
1
1
2
1
1
2
0
0
0
0
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
0
2
1
2
2
2
1
2
0
1
1
2
1
2
1
1
0
1
0
0
0
1
1
0
1
1
1
1
1
1
1
0
1
1
1
2
1
1
0
2
0
1
2
0
1
1
1
1
0
1
0
0
0
1
1
2
0
1
0
0
0
2
2
2
2
4
1
1
1
0
0
2
1
0
0
0
0
2
1
2
1
0
0
0
1
0
2
1
0
1
1
1
0
1
2
1
0
0
1
1
1
2
2
1
1
0
1
0
2
0
0
1
1
1
1
1
0
0
1
1
1
1
1
0
2
2
1
1
2
2
1
1
1
0
0
1
0
0
0
1
0
1
1
1
2
2
2
2
1
1
0
1
1
1
1
2
1
0
1
2
0
2
1
0
1
1
1
1
1
1
0
1
1
1
0
2
0
1
1
1
1
1
2
2
1
1
1
0
1
2
2
0
1
0
1
0
0
0
1
1
1
0
0
2
1
2
0
1
2
2
1
0
1
1
0
0
1
2
1
0
1
1
1
1
2
1
1
1
2
0
2
2
0
1
1
1
1
1
1
1
0
1
2
2
1
1
0
1
1
2
1
2
0
2
1
2
1
1
1
2
0
0
0
2
1
0
1
0
2
1
1
1
1
0
1
0
1
0
1
0
2
1
0
0
1
0
2
1
1
1
0
0
1
2
1
0
0
1
0
0
0
1
2
0
0
1
1
0
1
1
0
2
1
1
1
0
1
1
1
0
0
1
1
1
1
2
1
2
1
1
1
2
0
2
1
2
2
2
2
2
0
2
0
2
1
0
1
1
1
2
1
1
3
1
2
2
0
2
2
1
1
1
0
1
0
1
1
2
2
2
1
1
2
1
1
1
0
1
1
1
1
0
1
0
0
0
0
0
2
1
1
1
3
1
1
0
1
0
1
1
1
1
2
1
0
1
1
1
1
0
1
1
2
2
1
1
1
0
2
1
2
2
0
1
0
1
2
1
0
1
0
1
1
1
1
2
1
2
0
1
1
1
0
0
0
1
1
1
3
0
0
1
2
0
1
2
2
2
0
0
1
1
1
2
1
1
2
0
0
1
1
1
1
1
1
1
1
0
1
1
0
2
1
0
3
2
1
1
0
1
1
2
1
2
1
1
1
0
1
1
2
0
2
2
1
0
0
1
2
2
1
0
1
0
0
1
0
2
0
1
1
1
1
1
0
1
0
1
1
1
1
2
1
1
0
2
0
0
1
0
1
1
1
2
0
1
1
1
1
1
0
3
1
0
1
2
1
1
1
1
1
0
1
1
0
2
2
0
2
0
1
1
1
1
1
2
1
0
0
0
2
2
0
0
1
2
1
2
0
0
1
1
2
2
0
2
2
1
2
1
2
0
1
1
0
2
2
1
0
0
0
1
2
1
1
2
0
0
2
0
2
1
1
1
1
1
0
0
2
0
2
1
1
0
0
2
1
1
1
0
1
0
1
1
2
1
1
0
0
2
0
1
0
0
1
0
0
1
1
1
0
1
1
0
2
1
0
1
2
0
0
0
1
1
0
1
0
2
1
1
1
1
1
2
1
0
0
0
1
1
1
1
0
1
1
1
1
0
1
0
2
1
1
1
2
1
0
1
4
1
1
1
1
1
1
2
2
2
1
2
2
1
2
1
0
0
2
1
1
1
1
1
0
0
0
1
1
2
2
0
1
1
0
2
2
1
1
0
0
0
0
1
0
1
1
0
1
1
1
2
1
1
2
2
1
0
0
1
2
2
0
0
0
0
2
1
1
1
2
2
1
1
1
2
0
2
1
1
0
1
0
1
0
0
1
1
1
2
0
0
1
2
3
1
1
1
1
0
0
0
0
2
1
2
0
2
2
0
1
1
2
1
1
0
1
1
2
1
0
2
1
1
1
0
2
1
0
1
1
0
1
1
0
1
1
1
1
1
1
0
1
1
1
0
0
0
2
0
1
1
1
1
2
1
1
2
1
1
2
0
2
1
1
1
1
2
1
0
2
0
2
2
2
2
1
0
0
0
1
1
0
0
0
1
1
1
0
0
2
0
1
1
2
2
2
2
1
1
3
0
2
1
1
2
1
0
0
0
1
1
0
1
1
1
0
2
1
1
0
0
1
0
2
1
4
0
1
1
1
1
1
1
2
1
1
2
1
2
1
0
2
1
2
0
0
1
0
1
1
1
1
2
1
1
1
1
0
0
0
1
2
1
1
1
1
1
2
2
1
0
1
2
1
0
0
1
0
1
1
0
1
1
1
2
1
2
0
0
0
1
2
1
2
1
2
2
2
2
1
1
1
1
3
2
1
2
1
1
2
0
2
1
1
1
1
0
1
0
2
1
2
0
0
1
1
1
1
1
1
1
1
1
1
0
1
0
1
1
2
2
2
2
0
0
1
2
1
1
1
2
0
0
0
1
2
1
2
1
0
2
1
1
1
0
0
2
1
1
0
1
2
1
1
1
1
1
1
1
1
2
0
2
2
2
0
2
1
2
1
0
2
1
2
2
2
2
2
1
1
2
1
0
1
1
1
1
1
0
2
1
1
0
0
1
2
0
2
0
1
2
1
0
1
1
0
1
0
0
1
2
1
0
1
1
1
1
1
1
2
1
1
1
1
2
2
2
2
1
1
1
1
1
2
1
1
1
1
1
0
2
0
2
2
1
0
0
2
1
2
1
1
1
1
1
0
2
1
0
2
2
0
1
2
0
1
1
1
2
2
0
2
2
1
1
1
0
0
1
1
2
0
0
1
0
2
2
0
1
1
2
1
0
1
1
3
1
2
2
0
1
2
1
0
1
0
1
1
1
2
1
0
1
1
1
0
2
0
0
1
1
0
1
1
2
0
1
1
0
0
1
0
0
1
1
1
1
0
1
2
1
1
1
1
2
1
0
2
0
3
0
1
1
1
1
3
0
2
1
1
0
1
0
2
1
0
2
0
1
0
1
0
1
2
0
0
2
1
1
0
0
2
1
1
0
2
2
1
2
0
1
0
2
2
1
0
0
1
2
1
0
1
0
1
1
2
1
0
1
1
1
1
1
0
1
1
0
0
5
1
1
1
1
2
0
1
1
1
0
1
0
1
1
0
1
0
2
0
0
2
1
1
1
0
1
2
1
0
2
2
0
1
2
1
2
2
1
1
0
1
1
1
1
0
1
1
1
2
1
0
1
0
1
2
0
0
0
1
2
0
0
0
0
0
0
2
0
2
0
1
1
2
1
1
0
1
0
3
1
1
1
1
0
2
3
1
1
0
2
1
0
0
1
1
1
1
2
0
1
1
2
2
1
0
0
1
0
1
0
0
1
1
1
1
1
2
2
1
0
1
2
1
2
1
1
2
0
0
2
1
2
1
2
2
1
1
2
1
2
2
2
2
1
0
1
1
1
0
1
1
1
0
2
1
2
1
1
1
1
1
0
1
1
1
0
3
1
0
2
2
1
0
1
2
1
1
2
1
2
0
3
0
1
0
0
0
1
1
0
1
1
0
1
0
1
2
1
2
0
0
0
1
1
2
3
1
1
1
0
1
1
0
2
0
1
1
2
0
0
2
1
1
0
0
1
1
0
1
1
1
0
1
0
1
1
0
1
1
1
0
0
1
1
0
0
0
1
1
2
0
2
0
1
1
0
1
0
1
1
0
2
2
2
1
1
1
2
0
0
1
2
1
1
1
1
2
0
2
0
1
0
1
0
0
2
2
0
0
1
2
1
2
1
1
1
0
2
0
1
2
1
1
2
1
0
0
1
0
1
1
2
0
1
2
1
1
0
0
1
1
1
1
2
1
1
1
2
1
0
2
0
0
0
2
0
2
1
0
0
2
0
1
0
1
1
2
1
1
1
1
1
2
1
2
0
2
1
2
2
0
1
1
0
0
1
2
0
2
1
1
1
0
0
1
2
1
1
0
2
3
2
1
2
1
0
1
0
2
0
1
1
2
1
1
2
0
2
0
0
1
1
2
0
1
1
1
0
1
1
0
0
1
1
1
0
1
0
2
2
0
2
0
4
1
2
0
2
0
1
0
0
1
1
1
2
2
1
1
1
2
0
2
0
0
2
0
1
2
1
0
1
1
1
1
0
2
1
0
1
1
2
2
0
1
2
1
0
1
0
0
0
0
0
1
1
1
2
2
1
1
1
1
0
0
1
1
1
0
1
2
1
1
2
1
1
2
2
2
2
1
0
1
1
1
0
1
1
1
2
0
1
1
1
0
1
1
2
1
2
1
1
0
0
2
2
0
2
1
1
1
1
2
1
2
1
2
1
1
1
1
0
1
1
0
1
0
0
1
1
1
2
1
2
1
0
1
1
2
0
1
1
3
0
2
0
1
2
2
2
0
1
1
1
1
0
2
1
2
1
2
1
2
0
1
2
1
1
1
0
0
1
1
2
1
2
1
1
1
1
0
1
0
1
0
1
1
0
2
1
0
2
0
2
1
3
1
1
2
0
2
0
1
2
1
0
1
2
0
1
2
1
1
1
0
1
1
1
1
1
0
2
1
2
0
0
1
1
1
1
1
0
2
0
0
1
1
0
0
0
1
0
2
1
1
1
1
2
1
0
0
1
0
0
1
0
0
2
1
1
2
0
1
1
2
0
1
0
2
0
0
2
0
1
2
4
2
0
1
1
1
1
2
2
2
1
1
0
2
1
1
1
1
1
2
1
0
0
1
2
0
1
0
0
1
1
1
1
0
2
1
1
2
0
2
1
1
0
2
2
1
1
1
2
2
1
2
0
1
1
1
0
1
2
0
0
1
1
1
0
0
0
1
1
0
1
1
1
0
0
0
1
2
1
1
0
3
0
1
1
1
1
2
2
1
2
2
2
0
0
0
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
1
1
1
5
2
0
1
1
1
1
2
1
1
1
1
1
1
1
1
0
1
2
2
0
1
1
2
1
0
2
0
0
0
2
1
1
1
1
1
2
2
0
2
2
0
2
1
1
2
1
1
0
0
1
1
2
1
1
1
0
1
1
2
2
1
1
1
1
0
0
0
0
1
1
2
0
3
1
2
1
1
1
6
1
0
1
2
3
1
1
1
1
1
0
2
0
1
2
0
2
1
1
1
1
0
1
1
0
1
1
1
2
1
1
2
0
0
1
1
1
0
1
2
1
0
1
1
2
1
2
0
1
0
1
1
1
1
1
1
0
1
2
0
2
0
1
2
1
1
0
1
1
2
2
2
0
0
1
0
2
0
1
1
3
0
4
1
1
0
1
0
0
2
2
1
1
3
2
1
2
1
1
1
0
0
1
2
1
2
1
0
1
1
0
0
1
0
1
0
2
1
1
0
0
1
0
2
1
2
0
1
0
1
2
1
0
1
0
0
1
1
0
1
0
0
1
1
1
1
1
1
1
0
2
1
2
1
1
1
0
1
2
2
1
0
2
2
0
0
0
1
1
3
0
1
2
0
1
1
2
1
1
2
1
1
1
0
1
1
1
0
1
0
0
0
1
0
2
0
2
0
2
0
0
0
1
2
1
1
1
0
0
1
0
2
1
1
1
2
2
2
1
3
2
1
2
1
2
1
1
0
1
1
1
0
1
0
2
0
2
1
0
0
0
1
2
1
0
0
1
1
1
2
0
1
2
1
1
2
3
1
2
0
1
2
1
1
0
0
1
1
0
0
1
1
1
1
1
1
2
0
2
2
2
2
1
2
1
1
0
1
2
1
2
0
1
1
0
1
0
0
1
1
0
0
1
1
0
0
0
2
2
0
0
1
0
0
1
2
1
1
0
0
0
0
2
1
1
0
1
1
0
1
1
0
1
1
0
1
1
1
1
1
2
1
2
2
2
0
0
1
2
0
1
1
2
1
0
1
1
1
1
0
1
1
2
1
2
2
1
0
0
0
3
1
1
2
1
0
2
2
0
0
2
1
2
1
1
0
2
5
0
2
2
1
0
1
1
1
1
3
1
1
0
1
2
0
0
1
0
1
1
1
0
2
1
1
1
2
2
0
0
2
0
1
1
2
1
0
1
1
0
1
0
2
1
0
1
0
1
1
1
1
1
1
1
1
1
0
1
2
1
1
0
0
0
1
1
2
0
2
0
0
0
1
0
2
0
1
0
0
1
2
1
2
1
1
1
2
0
1
2
1
0
0
0
1
1
0
2
1
2
1
1
1
2
0
2
2
2
0
0
3
0
2
1
1
1
1
2
0
0
1
1
1
1
1
0
1
1
0
1
2
0
2
2
2
0
1
0
0
1
1
0
1
1
1
0
1
1
0
2
0
2
0
0
1
0
0
1
0
2
2
2
1
0
1
1
1
0
2
1
0
2
1
1
1
2
0
1
1
2
1
1
2
1
0
1
1
2
0
1
1
2
1
1
1
0
2
2
1
1
1
0
1
1
1
1
1
1
0
1
1
0
1
1
1
2
2
1
1
3
1
1
0
1
1
0
1
1
0
1
1
2
2
0
1
0
0
2
0
0
1
1
0
3
0
1
1
2
0
1
0
1
1
1
0
1
1
1
2
1
2
2
1
1
2
1
0
1
1
1
0
1
1
1
1
1
0
0
0
1
1
0
3
1
0
2
2
1
0
2
1
0
1
1
0
0
1
1
0
2
1
1
2
0
2
1
1
0
2
1
0
1
2
1
1
2
1
2
1
1
4
1
1
1
2
0
1
0
2
0
1
1
0
2
0
1
0
0
1
0
1
1
1
0
1
2
0
1
1
1
0
1
1
0
1
0
2
1
1
1
2
0
0
1
1
2
1
1
1
1
0
0
2
1
1
0
1
2
1
1
1
0
1
0
1
0
1
1
1
0
1
0
2
2
1
1
1
1
2
0
1
0
0
1
1
0
2
2
1
2
1
1
1
1
1
2
0
0
0
0
0
2
1
0
0
0
0
1
0
1
1
1
1
1
2
1
1
1
3
1
0
0
1
2
1
1
2
2
1
1
0
3
2
2
0
1
1
1
2
0
1
1
1
1
0
1
2
1
2
1
0
0
0
0
1
2
1
2
2
2
0
2
2
1
2
1
2
0
1
1
1
2
1
3
1
0
2
2
1
1
1
1
2
1
1
2
1
0
0
1
1
0
2
1
1
2
0
1
1
1
2
2
1
0
1
1
0
1
0
1
1
1
1
1
0
2
0
1
1
1
1
1
0
2
2
0
0
1
1
0
0
2
1
2
1
1
2
1
0
1
1
2
1
1
2
2
1
0
2
0
0
2
2
0
1
1
0
4
2
1
0
1
0
1
1
1
1
1
0
1
2
1
1
1
2
0
2
1
0
2
0
1
0
2
0
1
2
1
1
1
1
2
1
1
0
2
0
0
0
1
1
2
0
1
2
0
2
2
1
0
2
1
1
2
1
2
0
0
2
1
0
0
1
1
2
0
1
1
0
2
1
1
1
1
1
1
0
2
1
1
1
1
1
1
2
1
1
1
1
1
2
2
1
2
0
1
0
0
0
1
1
2
1
1
1
0
1
0
1
1
2
1
1
1
1
1
1
1
0
3
1
2
2
0
1
0
0
1
2
1
1
1
0
0
1
2
2
1
1
2
0
0
1
0
2
0
1
1
1
1
1
3
2
1
2
1
0
0
3
1
0
2
1
0
1
1
1
0
1
0
2
1
1
0
1
1
1
1
2
0
0
0
1
0
1
1
1
0
1
1
0
0
1
2
1
1
1
1
0
0
0
0
0
1
1
1
2
1
1
1
1
1
2
0
1
1
2
2
2
0
1
1
1
0
0
1
0
3
1
1
1
0
0
2
1
1
2
1
0
0
0
2
1
2
2
2
1
1
2
0
0
1
1
1
0
2
1
0
1
1
1
0
1
1
0
2
1
1
1
1
0
1
1
0
0
2
0
1
1
2
1
0
0
2
1
0
1
1
2
1
1
1
1
1
2
1
0
1
1
1
0
0
2
1
2
0
2
1
1
2
0
0
1
2
0
0
3
0
2
0
0
1
1
0
2
1
1
2
2
0
1
0
1
1
2
1
1
0
2
2
1
1
0
0
1
2
0
0
0
1
0
2
0
1
0
0
2
0
1
0
1
1
1
2
1
2
1
1
1
1
0
1
1
1
0
1
1
2
1
2
1
1
1
1
3
1
1
2
1
1
2
1
6
2
2
1
1
1
1
0
0
1
1
1
0
1
1
1
1
0
1
0
2
1
1
1
1
1
1
2
1
1
1
1
0
0
0
2
1
1
1
0
0
0
2
1
0
2
1
1
0
0
2
1
1
0
1
1
2
1
1
1
1
1
0
2
1
1
1
1
0
1
1
2
1
1
2
1
0
0
1
1
1
1
1
1
1
0
1
1
2
2
0
0
2
1
0
2
0
1
2
0
1
0
6
1
0
2
0
0
0
1
0
1
0
2
1
1
1
0
0
1
1
0
2
1
1
2
1
1
1
1
1
0
0
1
0
0
2
2
1
2
2
1
1
2
1
1
1
2
1
1
1
1
1
0
1
1
2
2
2
1
1
2
1
2
1
1
3
2
1
1
0
1
1
1
1
2
1
1
1
2
0
0
0
1
1
0
1
2
0
2
1
1
0
2
2
1
1
1
2
0
2
0
0
1
0
1
1
0
0
0
0
2
1
1
2
0
1
1
2
0
2
1
1
1
0
1
1
1
1
1
1
0
1
1
0
2
1
1
2
0
1
0
1
1
1
1
0
2
1
1
1
2
0
1
0
3
1
1
2
0
2
1
2
1
1
3
1
1
1
0
1
1
0
1
0
2
2
1
1
2
1
0
1
0
2
1
2
1
0
2
0
2
1
2
1
1
1
1
1
1
0
1
1
1
2
1
1
0
1
1
0
2
0
2
0
1
0
2
1
1
1
1
0
1
2
1
1
1
1
0
1
2
1
1
2
0
1
1
0
1
2
1
2
2
0
2
1
1
1
0
2
1
2
1
0
1
1
1
1
1
2
0
1
1
1
2
0
0
1
2
0
2
1
1
1
1
0
1
1
0
1
1
1
0
0
1
0
2
2
0
0
0
1
0
2
1
0
1
0
0
1
2
1
2
2
2
1
1
1
1
0
2
0
0
1
1
0
1
1
0
0
0
2
2
1
1
2
0
1
2
1
1
2
1
2
0
2
1
1
1
2
1
1
1
1
1
0
0
2
0
1
1
0
1
1
2
1
1
0
1
3
0
0
0
0
1
2
2
1
1
1
0
2
2
0
2
2
1
1
0
2
0
1
2
0
1
0
1
1
1
1
2
2
0
0
1
0
2
2
1
0
0
1
2
1
1
2
1
2
2
0
0
0
1
2
2
1
1
0
1
4
1
1
1
1
1
1
1
1
1
0
1
0
2
0
0
1
2
0
2
1
0
0
0
0
0
1
1
1
1
1
1
1
0
1
0
0
0
1
1
1
0
0
1
2
2
1
1
1
0
0
2
1
1
1
1
0
0
1
2
0
2
1
2
0
1
1
2
0
1
1
1
0
1
2
0
0
1
1
2
2
0
1
1
0
2
1
1
0
0
0
1
0
0
0
1
1
0
0
1
2
1
2
4
1
1
1
0
0
2
0
1
1
0
1
1
0
1
2
1
1
0
0
0
1
2
1
0
1
2
2
1
2
1
1
0
1
1
2
1
0
1
1
0
1
1
2
1
0
1
2
2
1
1
0
0
1
1
2
1
1
0
1
0
1
2
1
1
1
2
0
1
2
2
2
0
1
1
1
2
0
2
0
1
1
1
1
1
0
1
2
1
1
1
1
1
2
1
0
1
1
2
1
0
1
0
0
1
0
0
1
1
0
0
1
1
2
0
1
1
1
2
2
1
0
0
1
2
0
0
0
1
1
1
0
2
1
1
2
2
2
0
2
2
2
0
1
0
0
1
1
0
1
0
2
2
1
1
1
0
1
0
1
1
2
1
2
0
1
0
1
2
1
0
2
2
0
0
2
2
1
0
1
2
1
2
0
1
0
1
1
1
3
0
1
1
1
1
1
1
0
1
1
1
0
0
0
1
2
1
1
1
1
1
1
2
0
0
1
1
1
0
1
3
0
0
2
1
1
1
1
0
1
0
0
2
0
2
2
1
0
1
1
0
1
2
1
1
0
0
0
1
2
1
1
1
0
1
1
0
1
1
1
0
2
2
1
1
1
1
1
2
1
0
1
2
2
1
0
1
2
1
1
2
2
2
2
1
1
1
1
0
1
1
0
1
0
0
0
0
1
1
2
1
2
0
0
5
0
0
2
2
1
1
0
1
1
0
1
0
1
1
0
2
1
1
2
2
1
1
1
1
0
1
1
2
1
1
1
1
2
1
2
1
1
0
0
0
1
1
1
0
2
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
0
1
0
0
0
1
1
1
1
2
1
3
2
1
1
1
2
2
1
2
0
0
1
0
1
0
0
0
1
1
1
1
1
1
2
0
0
2
2
1
1
1
0
1
2
0
1
1
1
0
1
1
2
0
2
1
0
1
1
1
1
0
1
2
1
1
1
1
0
0
1
1
1
0
2
0
1
2
1
1
2
1
2
2
2
1
2
0
2
0
0
0
1
0
1
1
1
1
1
1
1
1
0
1
0
0
1
1
0
1
0
1
0
1
5
0
0
0
1
1
1
1
1
1
1
1
2
1
1
0
1
1
0
0
1
1
1
2
1
0
1
1
1
2
0
1
1
2
0
1
0
1
1
1
1
1
2
1
1
0
3
2
2
1
2
1
2
1
1
1
0
1
1
1
0
0
1
2
1
1
1
2
0
0
0
1
0
1
1
1
2
1
0
2
0
2
1
0
0
1
0
1
1
1
1
2
0
1
1
1
0
1
1
0
2
1
1
2
1
0
2
0
2
1
1
1
1
1
0
1
1
2
1
0
1
0
2
0
1
1
1
1
0
2
1
2
1
0
0
0
1
0
1
1
2
1
2
0
1
0
2
0
2
1
2
0
1
2
1
1
2
1
0
1
1
2
1
0
1
1
2
1
1
0
1
1
2
1
2
0
0
1
2
0
1
1
2
1
1
1
0
1
0
2
2
1
2
1
1
0
1
1
1
1
2
0
1
1
0
1
2
0
2
0
2
0
0
1
1
1
1
0
1
1
0
1
1
1
0
1
2
2
2
0
1
1
0
2
1
2
1
1
1
1
2
0
1
1
2
0
1
1
0
0
1
0
1
1
1
2
2
1
0
1
1
0
1
1
1
2
1
1
2
0
1
1
2
1
1
0
0
0
1
2
0
1
2
2
0
0
1
0
1
0
2
1
2
1
0
1
2
1
1
0
1
1
1
0
0
0
1
1
2
1
1
0
2
1
1
1
0
1
1
0
1
0
1
1
1
1
0
1
2
0
0
0
0
2
0
1
0
1
1
1
0
1
0
2
1
1
2
2
0
0
1
2
1
1
2
1
2
1
1
1
1
1
1
1
0
0
0
2
2
1
0
1
2
1
1
1
0
0
1
1
1
0
2
1
1
1
1
1
0
2
2
2
1
1
0
1
1
2
1
0
1
1
0
0
1
2
1
0
0
2
1
1
1
1
0
1
0
2
2
0
0
1
0
0
1
2
2
1
0
1
2
0
2
1
1
1
2
1
1
2
1
1
2
0
1
1
1
1
1
1
0
0
0
2
1
1
1
2
0
1
1
2
1
0
1
0
0
1
2
1
0
0
4
1
1
2
0
1
1
2
2
1
2
1
1
0
1
1
2
1
2
1
1
1
1
0
1
0
2
1
1
1
1
2
0
1
2
1
1
2
0
0
0
2
5
2
1
2
2
0
1
1
1
1
0
1
2
1
1
1
0
1
1
1
0
2
1
0
1
2
2
1
1
0
2
1
0
0
2
2
0
1
0
1
0
1
2
1
0
1
2
0
1
1
2
1
0
1
0
1
0
2
1
1
1
0
2
1
1
0
0
1
1
1
2
2
0
1
1
1
2
1
2
1
1
1
0
0
0
2
2
1
1
0
1
2
1
1
2
2
0
2
1
1
2
1
1
2
1
1
1
0
0
2
2
2
1
2
0
1
1
2
0
0
0
0
1
1
1
2
1
2
1
1
2
2
1
2
0
2
1
1
1
2
0
1
3
2
2
1
2
1
0
1
0
2
2
1
0
1
2
2
1
0
1
2
2
1
1
2
2
2
0
2
1
2
2
1
0
1
0
0
1
0
0
0
2
1
1
1
1
1
1
1
1
0
0
1
1
1
1
1
0
1
4
0
1
1
0
1
2
1
1
1
0
2
0
0
1
1
0
2
0
1
0
0
1
1
0
1
1
0
2
1
2
1
0
1
1
2
1
1
1
1
1
1
2
1
2
0
2
1
1
1
0
1
1
1
1
1
0
1
1
0
2
1
1
1
0
2
1
0
0
0
2
2
0
1
2
2
1
1
2
1
1
0
1
1
1
2
0
2
1
1
1
1
2
1
0
1
2
1
1
2
1
1
0
3
2
2
1
2
2
1
2
1
1
0
0
0
1
1
1
2
1
1
1
1
2
2
2
1
0
1
0
1
1
1
0
1
2
1
1
2
1
1
1
0
1
0
1
1
2
1
1
0
2
1
1
1
1
1
0
2
1
2
2
2
1
0
1
1
2
0
0
2
1
2
1
2
1
1
1
0
2
1
2
2
0
1
1
1
1
1
1
0
0
1
2
0
0
0
2
1
1
1
0
1
1
2
2
0
0
1
2
1
1
1
0
0
1
2
0
1
2
0
0
0
2
1
0
1
1
2
2
1
1
1
2
2
2
2
1
0
1
1
1
1
0
1
1
2
0
1
0
0
0
2
2
1
0
2
1
1
1
1
0
0
1
1
1
0
0
2
1
2
0
1
1
0
0
1
0
0
1
0
1
1
1
0
2
0
1
0
1
0
1
0
1
1
4
0
0
2
1
1
0
1
2
1
2
1
1
1
2
2
1
0
2
2
2
1
1
0
1
2
2
1
1
1
1
0
1
1
2
2
0
1
0
0
1
2
0
2
1
1
1
1
0
1
0
1
1
1
1
1
0
1
1
0
1
2
0
2
1
1
1
2
0
0
1
2
0
2
0
0
0
0
0
2
3
1
1
0
0
0
1
1
0
0
0
0
0
0
1
1
2
0
0
1
1
2
1
2
0
1
2
2
2
2
1
0
1
2
0
2
0
1
1
1
1
2
1
1
2
1
1
0
1
2
2
2
2
1
0
1
2
1
1
0
2
1
1
1
1
2
0
0
0
2
1
1
1
1
0
0
0
0
1
1
2
1
2
2
1
1
1
0
2
1
2
2
2
1
1
2
0
2
2
3
1
2
0
1
1
0
1
1
1
1
1
1
2
0
1
2
2
0
2
16
1
2
2
0
0
1
1
1
1
0
1
1
2
0
1
1
1
2
0
0
1
0
0
1
1
1
2
2
0
0
0
1
0
1
2
1
0
1
1
1
1
0
1
0
1
2
1
0
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
0
0
1
3
1
2
1
3
2
1
2
1
1
0
0
1
2
1
1
0
1
1
1
0
1
1
1
1
1
1
2
1
3
1
1
1
1
1
1
1
2
0
1
0
1
1
0
1
0
1
1
2
0
1
1
0
2
1
0
1
0
1
0
2
2
1
1
0
0
1
1
0
1
2
1
0
0
0
0
0
0
1
1
0
1
2
0
2
1
0
2
2
2
0
1
1
2
1
1
1
1
1
1
1
3
1
1
0
1
1
0
3
1
1
2
1
0
2
1
1
0
1
1
2
1
1
0
0
0
2
1
2
2
1
0
0
2
2
1
0
1
1
1
1
0
1
1
0
1
0
1
1
1
0
1
2
1
1
2
2
1
0
2
1
1
2
3
0
3
0
1
0
1
0
1
1
1
1
0
1
1
1
0
1
1
2
1
1
1
2
1
1
1
0
1
2
2
2
1
2
0
2
0
1
1
1
1
1
0
1
1
1
1
1
1
0
0
1
1
1
1
0
1
1
1
2
1
1
1
0
1
0
1
1
1
1
1
0
0
1
1
1
2
1
1
2
0
1
0
2
1
0
2
1
0
2
4
0
1
2
1
0
1
1
2
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
0
0
2
1
1
1
1
1
1
1
2
1
2
1
1
0
1
2
3
0
1
1
2
0
1
1
1
2
2
1
0
0
1
1
0
1
2
3
1
1
1
2
1
0
1
3
2
1
1
1
2
1
1
2
1
1
1
1
2
1
0
1
0
1
0
0
0
2
1
1
1
0
0
1
1
1
1
0
1
1
2
1
0
1
0
2
1
1
1
2
0
1
1
2
0
0
1
0
1
1
1
1
0
1
2
1
2
1
1
1
0
2
1
1
0
0
1
0
0
0
0
0
1
1
0
0
2
1
1
2
1
2
1
0
2
1
1
1
0
0
0
1
0
1
1
0
0
0
2
0
1
1
2
0
1
2
0
0
2
2
2
1
1
0
1
1
1
0
1
0
1
0
1
0
0
1
1
1
1
1
2
1
1
1
2
0
2
2
1
0
1
0
2
2
1
0
1
2
0
2
1
1
0
2
1
2
1
1
2
1
1
1
1
0
0
1
0
2
0
1
1
1
1
1
1
1
2
1
1
1
0
1
2
0
0
1
2
0
2
0
0
1
2
2
1
2
1
1
2
2
2
2
2
0
2
0
2
1
0
0
0
1
1
0
2
1
2
1
1
1
0
1
1
1
2
0
1
2
1
0
1
1
0
0
1
1
1
0
1
1
1
1
3
1
0
1
2
1
2
0
1
2
1
1
0
1
1
0
0
1
2
0
1
2
1
1
1
0
0
2
2
2
2
2
1
0
1
1
1
1
0
2
2
2
0
1
1
1
0
2
2
1
1
1
0
2
1
1
1
1
0
0
1
1
0
2
1
0
0
0
2
1
1
1
0
2
1
0
1
0
0
2
1
3
2
1
1
1
1
1
2
1
1
1
1
2
1
0
2
0
1
0
1
1
2
2
1
0
0
1
0
1
2
1
1
0
1
0
2
2
0
0
0
1
1
1
1
0
0
2
0
1
0
2
2
1
1
1
0
1
0
2
1
2
1
0
2
1
2
0
1
1
2
2
1
1
1
1
0
1
1
1
2
1
1
0
0
1
0
3
0
2
1
1
1
0
1
1
0
1
1
0
1
1
1
0
1
1
1
0
2
1
0
0
1
0
1
2
2
1
1
1
1
2
2
1
1
1
2
1
0
1
1
1
0
3
1
1
0
1
1
2
1
0
1
0
1
1
0
0
2
1
1
0
0
0
0
1
1
1
2
2
1
1
1
1
1
0
0
1
1
0
1
1
1
4
2
2
3
1
0
2
1
1
1
1
0
0
0
0
2
1
3
1
1
1
0
1
1
1
1
2
0
1
2
1
2
1
2
0
2
1
0
1
1
1
1
1
0
0
1
2
1
1
0
2
2
1
1
0
0
2
0
0
1
2
1
3
2
0
2
0
1
1
1
1
0
1
0
1
1
1
0
0
0
1
1
2
0
1
2
0
1
0
1
1
1
0
1
1
0
1
1
0
0
2
0
0
1
1
2
1
1
0
0
2
2
0
1
1
0
0
1
1
1
1
1
1
0
2
1
1
0
1
1
2
1
1
2
2
0
2
2
1
1
1
1
0
0
0
0
0
1
0
1
2
1
2
0
1
1
1
1
1
1
0
2
1
1
0
0
0
2
1
0
0
1
0
2
0
0
0
1
1
3
0
1
1
1
1
1
2
2
1
2
1
1
1
0
1
0
1
0
1
0
1
1
1
1
1
2
1
0
2
2
0
2
0
0
2
1
1
1
1
0
0
1
1
2
2
2
1
0
2
1
2
2
1
2
1
2
1
1
2
2
1
0
0
2
1
0
1
1
2
1
0
1
1
1
2
1
0
1
1
0
1
1
1
1
1
1
2
2
0
0
0
1
1
1
1
0
1
1
2
1
1
1
0
0
1
2
2
1
2
2
1
1
0
2
1
0
0
1
2
0
1
1
1
0
2
0
1
2
2
2
1
0
0
0
0
1
0
1
0
0
0
1
1
2
0
1
1
3
1
1
1
1
2
1
0
1
1
1
1
1
0
2
2
1
1
0
1
1
1
0
2
1
1
2
1
1
0
0
1
0
1
2
0
0
1
0
1
0
2
0
0
0
0
1
3
1
0
1
0
1
1
0
1
1
1
1
0
1
0
1
0
2
1
0
1
1
1
0
1
1
1
0
0
1
1
0
2
1
2
1
2
1
0
0
1
0
1
2
1
0
0
0
0
0
1
1
1
1
1
1
1
0
0
1
0
1
1
1
0
1
1
2
0
1
1
2
1
1
1
3
0
2
0
0
0
0
0
1
1
2
1
2
2
2
2
0
1
2
0
0
2
1
0
1
1
1
0
1
2
1
1
0
1
1
2
0
1
1
1
1
1
1
1
1
2
1
0
2
0
1
1
2
1
1
1
1
1
1
1
1
1
1
0
2
1
2
2
1
2
1
1
0
2
1
0
1
2
2
0
3
1
1
2
2
2
1
2
0
1
1
0
2
0
0
1
1
1
2
0
2
0
0
2
0
0
0
1
1
1
0
1
1
2
0
1
0
1
0
3
1
0
1
2
1
0
0
1
0
1
1
1
0
1
1
1
0
2
0
0
1
1
1
1
0
1
1
2
1
2
1
2
0
1
3
3
1
0
1
1
1
1
1
0
1
1
1
1
0
1
0
1
0
0
0
0
1
2
0
1
1
1
0
0
2
1
1
1
0
1
0
2
1
2
1
0
1
0
2
0
2
1
0
0
1
2
0
1
1
1
0
2
1
1
2
1
1
0
1
1
2
1
2
0
1
2
2
0
1
0
0
2
1
0
2
1
2
1
1
0
1
1
2
2
1
1
0
2
2
2
2
1
3
1
1
1
2
2
1
0
0
1
0
1
2
1
0
3
1
0
2
2
2
1
1
0
0
1
2
1
1
1
2
1
1
0
0
0
1
2
2
1
1
1
0
1
2
0
1
1
2
0
0
0
2
0
1
2
1
1
2
1
2
1
1
1
2
0
1
1
0
0
0
1
2
1
1
0
2
0
1
0
1
1
1
1
1
0
1
1
2
0
2
1
0
1
2
0
1
1
0
0
2
1
2
2
2
1
1
1
1
1
1
2
1
1
2
2
1
2
0
1
1
0
0
1
0
1
0
1
1
2
2
1
0
1
0
1
1
1
0
0
1
1
1
2
2
1
1
1
1
1
1
0
2
1
2
1
0
1
2
1
0
2
1
1
1
1
0
2
0
0
1
2
3
1
1
0
1
1
1
2
1
2
1
2
1
2
0
0
1
1
2
0
1
1
1
2
1
2
0
1
1
0
1
1
1
0
0
0
0
1
1
2
1
1
0
2
0
0
1
1
1
0
1
1
1
2
1
2
1
1
0
0
1
0
1
1
0
1
1
0
0
1
3
0
1
1
0
0
2
1
1
1
0
0
1
1
0
1
0
0
1
1
1
2
1
1
2
1
1
1
1
1
1
0
1
1
1
2
2
1
0
1
1
1
2
2
1
2
1
2
1
1
1
1
2
1
2
0
1
1
1
0
1
0
1
1
0
1
2
1
1
1
1
0
2
2
1
0
0
2
1
1
2
2
0
1
1
1
2
0
2
0
0
0
1
1
2
1
0
1
1
1
0
1
0
1
0
1
2
2
2
0
2
1
1
2
2
3
2
0
1
2
1
2
0
2
1
0
0
0
2
0
0
1
1
1
1
2
0
1
0
1
2
1
1
2
1
0
2
1
0
1
2
1
1
1
0
1
1
2
1
2
1
0
0
1
0
2
1
1
1
1
1
2
0
2
1
2
0
1
1
2
1
0
1
0
2
1
2
0
0
0
0
2
1
0
0
0
1
1
1
2
1
0
1
0
0
0
2
1
1
1
2
1
1
1
1
1
1
1
0
0
1
1
1
1
1
0
1
1
0
2
1
0
2
1
2
2
1
0
2
2
1
1
1
0
0
0
1
1
0
1
0
1
1
1
0
1
0
2
1
0
2
0
1
1
1
2
1
2
2
0
0
2
0
1
1
0
1
3
1
1
0
1
4
0
0
0
2
0
0
0
1
2
2
1
2
0
1
1
1
1
1
1
1
2
1
1
1
0
1
1
0
1
0
2
1
1
2
2
0
2
1
1
1
0
3
1
3
0
0
2
0
0
1
1
1
1
1
1
1
0
1
0
2
2
0
0
1
1
3
2
1
1
0
2
0
2
1
1
0
0
2
1
1
1
1
0
1
1
1
1
2
0
2
2
1
0
2
1
1
1
1
1
0
0
2
1
1
3
0
1
0
2
0
1
0
1
2
1
1
2
2
2
1
1
1
2
1
1
0
2
1
1
1
1
0
1
0
2
1
1
1
0
1
1
1
1
1
1
0
0
0
2
1
1
1
2
1
0
2
2
1
1
1
1
0
0
0
1
1
2
0
1
1
0
1
1
1
3
1
0
1
1
1
3
1
1
1
2
0
3
1
1
2
1
1
1
1
1
1
0
1
1
1
1
2
1
1
1
1
2
0
2
1
2
1
1
1
0
1
2
2
2
1
0
1
0
1
2
3
1
0
2
0
0
2
1
0
1
2
1
1
1
0
1
2
1
2
0
1
1
2
0
1
0
1
2
2
0
2
2
1
1
1
1
0
1
0
2
0
1
1
0
0
0
2
1
1
2
1
1
0
1
1
2
1
1
1
2
1
1
0
1
1
1
1
1
1
1
1
1
0
0
1
1
0
0
2
1
1
1
1
2
1
1
0
1
0
1
0
1
0
0
1
0
1
0
0
1
1
0
2
0
2
0
1
1
2
1
1
1
2
2
1
1
1
0
1
0
1
1
0
1
1
2
1
1
1
1
2
1
0
1
2
0
4
1
0
1
0
0
0
1
1
1
0
0
1
1
1
2
2
0
1
1
2
1
1
3
0
1
1
2
0
1
1
1
2
1
2
1
1
2
1
1
2
1
0
1
1
1
2
1
1
1
1
1
1
0
1
2
1
0
2
2
1
0
1
3
0
1
1
1
0
1
1
0
2
0
1
1
2
2
0
1
2
0
1
1
1
0
0
1
0
1
2
0
0
2
1
1
1
2
2
1
0
1
1
1
1
1
2
1
0
1
0
1
1
0
2
1
0
0
1
1
1
0
2
1
0
2
1
2
1
1
0
0
2
1
2
1
0
0
0
1
1
1
0
1
1
2
2
1
1
1
2
0
0
1
0
2
1
1
0
2
1
0
2
1
0
1
1
1
0
0
1
1
1
1
0
1
2
1
1
3
0
2
2
1
1
0
1
0
1
0
0
2
1
3
1
0
0
2
1
2
0
1
2
2
2
1
0
1
1
0
1
1
0
0
2
1
1
1
0
1
2
1
1
1
1
0
1
1
1
2
2
0
0
1
1
0
1
0
1
1
1
0
1
1
1
1
1
1
1
1
2
1
1
1
0
0
1
2
0
2
1
2
1
2
2
2
1
0
0
2
1
1
1
0
0
0
1
1
2
1
1
1
2
1
2
1
3
0
2
1
2
0
1
0
1
2
2
2
0
2
1
2
2
0
1
1
1
0
1
0
1
0
2
0
0
0
1
1
1
2
1
0
1
2
0
0
2
0
0
2
2
1
1
1
0
1
0
1
0
2
1
1
1
1
1
1
0
0
1
1
2
0
0
2
1
1
0
2
1
1
1
0
1
1
0
1
0
1
0
2
0
1
0
3
1
1
1
1
1
0
1
1
1
1
2
1
2
2
1
1
2
0
1
1
1
0
1
2
1
0
0
2
1
1
1
0
1
0
1
1
2
1
1
1
0
1
2
1
0
1
1
1
1
1
2
1
0
1
1
0
2
1
1
1
0
0
2
0
1
2
1
1
0
1
0
0
1
0
1
0
1
2
1
1
0
0
0
2
2
2
2
1
1
1
1
1
1
1
0
4
0
1
1
1
0
1
1
1
0
1
1
1
1
0
0
1
1
2
1
1
1
2
0
0
1
1
0
1
0
1
1
1
0
0
1
1
0
1
1
3
2
1
2
1
2
1
0
1
0
2
1
1
1
1
2
0
1
0
1
0
0
1
2
2
1
0
2
1
1
1
1
1
3
1
1
1
1
0
1
1
2
3
0
1
2
0
1
0
1
3
1
1
0
2
0
0
0
1
1
0
0
1
1
0
2
1
2
1
1
1
3
0
1
1
2
1
2
2
1
0
1
0
1
1
1
0
1
0
1
1
0
1
0
1
1
2
1
1
0
1
1
1
0
0
1
0
1
1
1
0
2
2
1
4
0
0
2
2
1
2
1
1
1
0
1
0
1
2
1
0
2
0
1
1
2
3
2
2
2
1
0
1
0
2
0
1
2
1
0
0
0
2
2
1
0
1
0
1
2
1
0
0
0
0
0
1
2
0
1
1
1
1
1
1
0
1
3
2
1
1
1
0
0
1
1
2
1
2
1
1
1
1
2
0
1
0
0
1
3
1
1
1
1
1
2
2
1
0
1
1
1
1
0
0
1
2
1
1
1
1
2
1
1
1
1
0
1
2
2
1
1
2
1
2
1
1
1
0
2
1
1
1
0
1
2
1
2
1
1
2
2
2
0
0
1
1
1
1
1
0
2
0
1
0
1
0
1
1
1
0
0
1
1
1
0
1
1
2
0
1
0
1
0
0
0
1
0
1
1
2
2
2
1
1
1
0
0
1
1
1
1
1
0
2
1
1
0
1
2
0
1
2
0
2
2
0
0
0
0
2
2
0
1
1
2
1
0
0
2
2
1
0
2
2
1
1
2
1
1
2
2
0
2
1
1
1
2
1
1
0
1
2
1
1
0
2
1
0
1
2
0
3
1
2
0
1
0
2
4
1
1
2
2
1
0
0
1
0
0
3
0
1
6
1
0
0
1
2
0
2
0
1
2
0
1
0
1
0
0
0
2
2
0
1
1
1
1
2
2
1
1
1
1
1
0
0
1
2
0
1
1
0
1
0
1
2
1
0
1
2
1
1
2
1
0
2
0
1
1
1
1
1
0
1
1
2
0
2
2
0
1
0
2
0
0
2
2
0
1
2
2
1
0
2
0
2
1
0
4
0
2
1
1
1
0
0
2
1
0
1
1
1
1
0
2
2
2
3
1
2
2
2
1
1
0
1
2
1
1
0
1
1
1
2
1
1
0
1
1
1
1
1
0
1
2
0
1
2
2
0
1
2
1
0
0
0
0
0
1
0
1
1
1
1
0
1
0
0
1
1
1
1
0
0
0
0
1
1
0
1
1
2
2
0
1
2
0
0
0
2
1
2
1
2
1
2
0
0
1
1
2
0
1
1
1
1
1
2
0
1
1
1
1
1
0
1
1
2
1
2
2
2
1
1
1
0
1
1
0
1
1
2
0
1
2
0
1
2
0
1
3
2
1
0
1
2
1
1
0
0
1
1
1
1
2
2
1
1
1
1
1
1
2
1
2
0
1
0
1
1
1
0
0
1
1
0
0
1
1
1
1
0
0
0
1
0
2
1
1
0
1
1
1
1
0
0
1
1
2
1
1
0
0
0
1
1
1
1
1
1
0
1
1
1
3
0
1
0
0
2
3
1
4
2
1
1
0
2
0
1
2
0
1
0
2
1
1
1
0
2
1
0
1
1
0
1
1
1
1
1
0
0
1
2
1
1
0
0
2
2
0
1
1
1
1
1
0
0
1
1
2
1
2
1
2
0
2
1
0
2
1
1
1
1
1
1
1
1
0
0
0
2
1
0
0
0
2
2
2
1
1
0
0
1
1
1
2
2
0
0
0
1
0
0
0
1
1
1
1
3
1
2
3
1
0
2
0
1
0
2
1
0
2
2
0
1
1
0
1
0
2
2
0
1
1
2
2
0
1
0
0
0
0
0
2
0
2
0
0
1
0
0
1
2
0
1
3
1
0
2
0
1
3
1
0
0
1
1
0
3
1
2
1
2
1
2
1
1
1
1
1
2
1
1
0
1
1
1
0
0
2
2
0
1
0
0
0
2
1
0
0
1
2
2
2
1
0
0
0
2
0
1
0
2
1
0
1
0
1
2
1
1
1
2
0
1
0
0
0
1
1
0
2
2
0
1
1
1
1
2
1
0
2
1
2
2
0
1
1
1
1
0
1
1
0
2
1
1
2
1
1
1
1
1
0
1
0
0
1
2
3
1
1
0
0
2
1
1
1
1
0
0
1
1
0
1
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
0
0
1
1
0
1
0
1
1
1
1
1
1
2
0
1
1
1
2
1
2
1
1
1
4
2
0
1
0
2
0
1
2
1
1
0
1
0
1
0
0
2
1
0
1
1
1
1
1
1
1
0
1
1
0
2
1
1
0
1
1
2
0
0
0
1
1
0
1
0
1
2
1
1
1
2
1
1
1
1
0
1
1
2
1
0
0
0
1
0
2
0
0
1
2
1
1
1
0
1
1
2
1
1
1
1
2
1
0
0
1
1
1
2
1
1
0
1
1
2
2
1
0
1
1
0
0
1
0
0
2
0
1
3
0
2
2
1
2
2
1
1
1
1
1
2
1
0
2
0
0
0
0
0
1
2
1
1
1
1
2
1
0
2
1
1
1
0
1
0
1
0
1
0
1
2
0
2
2
1
2
1
2
1
1
0
2
0
2
2
1
1
1
1
1
1
0
1
2
0
0
2
1
0
1
0
1
1
1
0
0
2
2
2
2
0
0
1
1
1
2
1
1
1
1
2
2
1
1
0
2
3
1
2
1
0
2
1
1
0
1
0
0
1
1
0
1
1
1
0
1
1
0
2
0
1
2
2
2
1
1
1
0
2
1
2
0
1
1
1
1
0
1
1
2
1
1
0
2
1
1
1
2
1
1
0
2
1
0
1
2
1
1
2
1
1
0
0
1
0
1
1
0
0
0
2
2
2
1
2
0
1
0
0
1
1
0
1
0
1
1
0
0
0
1
2
1
1
0
2
2
1
0
2
1
0
1
2
2
2
1
2
1
1
1
0
1
1
2
0
1
1
2
1
1
1
1
2
0
1
1
0
2
1
0
1
1
0
1
1
2
1
0
1
1
2
1
1
2
0
1
0
0
1
3
1
0
1
1
1
0
2
2
0
1
2
1
1
1
1
1
2
0
1
1
2
0
0
1
0
1
0
1
1
1
0
1
2
0
0
1
1
1
1
2
1
1
2
2
0
2
0
1
2
1
2
2
1
1
2
1
0
1
2
1
1
2
1
1
1
1
1
1
0
0
1
1
0
2
2
2
0
0
2
1
2
0
2
1
2
0
1
0
1
1
1
1
2
1
1
1
0
1
1
1
0
1
1
1
2
1
1
2
1
1
1
2
2
0
1
1
2
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
2
2
2
1
0
0
1
1
1
1
1
2
2
1
0
2
2
1
1
1
1
1
2
0
1
0
1
1
1
2
1
0
2
1
2
1
0
1
0
2
2
0
1
0
0
1
1
0
1
1
0
1
0
0
0
0
0
1
0
2
0
0
1
1
1
1
1
0
0
2
0
1
1
1
1
1
0
1
0
1
1
2
0
1
0
1
0
1
1
1
0
0
1
1
1
1
2
1
2
2
0
2
1
0
1
1
2
1
1
1
2
1
0
2
1
2
0
1
1
0
0
4
2
0
1
1
2
0
2
2
1
1
1
1
1
2
2
1
0
1
1
1
1
0
1
1
0
2
2
1
0
1
1
0
1
1
1
1
2
1
1
1
1
1
0
1
0
2
0
1
0
2
2
2
1
3
2
2
0
1
1
1
0
1
0
1
2
2
1
2
2
1
1
1
2
0
1
1
0
1
1
1
3
0
3
1
3
0
1
2
1
1
1
1
1
1
1
2
1
2
0
0
2
1
2
1
1
1
0
2
1
1
1
3
0
2
0
0
1
1
1
1
1
2
2
0
2
1
0
2
1
0
0
1
2
2
1
1
1
0
0
1
2
2
1
2
1
0
0
2
2
2
1
0
1
3
3
0
0
1
2
0
1
2
2
0
2
0
1
1
1
1
2
1
1
1
3
1
2
2
1
0
2
2
2
0
1
1
1
0
1
0
0
1
1
2
0
1
1
1
1
1
0
1
1
1
2
1
1
1
1
1
0
1
0
1
1
1
1
2
0
1
0
2
0
1
0
2
1
1
1
1
1
1
2
1
1
1
1
0
1
1
1
2
1
1
1
2
2
1
3
1
2
0
1
0
1
1
1
1
1
1
0
0
1
2
2
1
2
2
0
2
2
1
1
1
0
0
1
0
0
1
0
1
0
0
1
1
1
2
1
1
1
2
1
0
0
1
1
1
1
1
1
1
1
2
1
1
1
2
1
0
2
1
0
1
1
1
0
1
1
1
0
1
1
1
0
0
1
1
0
0
1
1
1
2
0
2
2
0
2
2
1
1
0
2
0
0
0
1
0
1
1
0
2
2
0
1
0
0
0
1
1
1
0
1
1
0
1
0
2
2
0
0
2
2
1
1
1
1
1
1
1
0
2
0
0
1
0
2
1
2
1
1
1
2
2
1
0
1
0
1
0
1
0
0
1
1
1
2
1
2
1
2
0
2
1
2
2
2
1
1
0
0
1
0
1
0
1
0
2
0
1
1
0
1
3
0
2
2
1
1
1
2
1
1
1
1
1
1
2
0
0
1
1
1
2
2
1
1
0
2
1
1
1
3
2
1
2
0
0
0
0
1
1
2
2
1
0
1
2
1
1
1
2
1
1
1
1
1
0
0
2
2
2
2
0
1
0
1
1
2
1
1
0
1
0
2
1
1
0
0
1
1
1
1
0
1
2
1
1
1
1
1
2
0
1
1
2
1
1
1
2
0
0
2
1
1
1
2
1
1
0
1
2
0
2
1
1
1
1
1
1
2
1
1
2
0
1
0
2
0
1
0
1
2
1
1
1
0
0
0
2
1
0
0
1
0
0
1
0
2
1
1
2
1
0
1
1
1
1
0
0
1
1
2
0
1
1
0
1
2
1
0
1
1
1
2
1
2
1
2
1
0
2
0
2
0
0
0
1
0
2
0
2
0
0
1
0
1
1
0
1
2
0
2
1
0
2
0
0
2
2
1
1
1
0
1
1
2
1
1
1
1
0
2
1
1
1
1
0
1
1
1
1
2
1
2
0
1
2
1
1
1
1
2
1
0
1
1
0
0
1
0
1
1
1
1
1
2
0
0
0
0
1
0
1
1
1
2
1
0
1
0
1
2
1
0
2
1
2
1
1
0
2
1
0
2
1
2
1
1
1
0
0
2
0
2
1
2
2
1
2
0
0
1
0
1
0
1
1
1
1
2
0
0
1
1
2
0
2
2
0
0
1
1
1
1
1
0
1
2
0
2
0
0
1
0
2
2
1
1
1
0
2
0
1
2
1
1
2
2
0
1
1
1
1
2
1
0
1
0
1
1
2
2
2
1
1
2
0
1
1
1
1
1
1
1
3
0
1
2
1
1
0
2
1
2
1
1
0
0
0
1
0
0
1
1
0
0
1
2
2
2
0
1
2
0
1
1
2
1
1
1
1
1
0
1
1
1
4
3
1
1
1
1
1
1
2
2
1
2
1
1
0
1
1
1
1
0
1
0
0
1
2
0
0
1
2
2
1
1
2
1
1
1
0
0
0
1
1
1
0
1
0
0
0
1
1
2
0
1
0
1
1
2
1
1
0
1
2
1
0
0
1
1
1
1
0
0
1
2
1
1
2
1
1
1
1
1
1
0
1
1
2
1
0
0
1
2
2
1
0
2
1
2
1
0
0
1
0
1
0
0
1
0
2
1
1
1
1
1
1
0
0
0
1
1
0
1
2
1
1
1
0
2
1
1
1
2
0
1
1
1
2
1
2
2
1
1
1
2
0
0
0
1
1
1
1
0
0
0
2
0
1
1
1
0
0
2
1
1
0
2
1
0
0
2
2
1
2
0
2
3
0
1
1
1
0
0
2
2
1
2
2
2
2
1
2
2
3
0
0
0
0
1
0
0
1
2
2
0
2
0
1
2
0
0
1
1
1
2
0
2
0
1
1
1
0
1
0
1
1
0
1
1
0
1
1
1
1
1
0
0
1
1
1
1
0
2
0
1
0
1
1
1
1
0
1
3
2
1
1
2
1
1
1
4
1
0
0
4
1
1
1
0
1
1
1
1
1
2
1
3
1
1
1
1
1
2
2
2
0
1
2
1
2
2
1
1
2
1
2
1
2
0
1
0
2
2
1
0
2
1
1
2
1
2
2
2
1
2
1
1
1
0
0
0
1
1
0
2
2
1
2
1
0
1
0
0
2
0
2
1
1
0
2
0
1
1
0
0
0
1
1
2
2
0
2
1
1
2
1
0
1
1
2
0
1
1
0
1
2
0
2
1
2
1
0
1
1
1
1
1
1
1
0
1
2
1
2
4
0
1
0
2
1
1
0
1
1
1
0
2
1
1
1
2
1
2
1
1
1
1
2
2
1
1
0
2
0
0
1
2
0
2
1
0
1
2
1
0
0
1
1
0
0
1
0
1
0
1
1
0
1
0
1
1
1
2
2
2
1
1
1
1
1
1
2
1
2
1
0
1
1
1
1
3
1
1
1
0
1
0
0
2
0
1
1
1
1
1
1
2
3
1
2
2
1
1
1
1
1
1
1
2
0
1
1
1
1
1
2
0
0
1
2
0
0
1
0
1
2
1
1
0
2
1
2
2
0
2
1
1
1
1
2
2
1
0
2
0
0
1
1
1
0
1
1
0
1
0
2
1
2
0
2
1
2
1
1
1
0
0
0
1
0
1
0
1
2
1
0
0
0
1
2
1
0
1
0
1
1
1
2
0
1
1
2
1
1
1
2
0
2
0
0
1
1
0
1
0
2
1
0
1
1
1
2
1
1
2
1
2
0
2
2
1
0
1
1
0
2
1
0
0
2
2
1
1
2
1
1
2
0
0
0
1
2
0
1
0
0
1
0
1
2
1
0
1
1
1
2
2
1
0
1
3
0
2
2
1
0
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
2
0
1
1
1
0
3
2
4
0
1
0
1
2
1
0
0
0
1
1
1
1
1
1
0
0
1
1
0
0
2
1
0
1
0
0
1
1
1
0
1
1
1
0
1
0
0
1
0
0
1
0
2
2
1
0
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
1
1
2
1
1
1
0
0
1
0
0
1
2
1
1
1
0
1
2
2
1
1
1
1
0
2
1
2
0
1
0
1
2
1
1
0
0
2
1
1
2
1
0
0
1
1
0
1
2
0
0
1
1
2
2
1
2
0
1
0
2
1
1
1
2
1
1
1
1
1
1
1
0
1
1
2
0
1
1
2
1
2
0
0
2
0
1
2
1
0
1
1
1
3
1
1
2
2
1
2
1
1
1
0
0
2
1
0
1
1
0
0
1
1
0
1
1
2
1
2
0
1
3
0
3
0
1
0
1
1
2
0
1
1
2
0
1
1
0
1
0
2
1
0
2
1
2
2
2
1
2
0
1
1
0
1
1
1
1
2
1
3
2
2
0
1
0
1
1
0
0
1
0
0
0
0
0
1
1
2
2
1
1
3
0
1
1
1
2
0
1
2
0
0
0
5
1
1
1
1
2
2
0
0
1
0
0
0
1
0
0
1
2
0
1
2
1
2
1
2
2
2
1
0
1
1
0
1
1
1
7
1
2
2
2
1
0
1
2
1
1
1
1
0
0
2
1
1
1
0
1
1
1
0
0
1
2
0
0
0
0
2
1
2
1
0
1
2
1
2
0
2
0
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
1
0
0
1
2
0
0
0
1
1
1
2
0
1
1
0
0
0
1
1
2
1
1
1
1
1
1
1
2
0
2
1
1
1
1
2
2
2
3
1
2
2
0
1
0
0
2
0
1
1
1
2
1
1
1
1
0
1
1
2
0
1
1
1
1
1
0
1
1
0
2
4
1
1
0
1
1
2
1
1
1
1
1
1
2
0
0
1
1
0
0
0
1
0
1
0
0
1
2
2
0
2
2
1
0
1
2
0
1
1
1
0
2
1
1
1
1
1
2
1
1
0
2
0
1
0
2
1
1
1
1
1
0
0
2
1
1
1
2
0
0
1
1
1
0
0
2
1
1
2
2
1
1
1
1
1
1
1
1
0
1
1
3
0
1
1
1
0
1
2
1
0
0
2
1
1
1
1
0
1
2
0
1
0
0
0
2
0
1
1
1
2
0
1
1
1
1
0
0
3
1
0
2
0
1
1
0
1
0
0
2
1
2
0
2
0
1
0
2
0
1
1
0
1
1
1
0
2
2
2
1
1
1
2
1
1
0
1
1
1
0
0
3
1
2
0
2
1
2
1
1
2
1
2
1
1
0
1
1
0
1
0
1
0
1
1
1
1
0
1
1
2
1
1
0
0
2
2
1
0
1
1
0
1
2
1
0
1
0
0
0
1
2
1
2
1
1
2
1
1
1
0
0
1
1
0
2
0
1
0
1
2
1
1
1
1
0
3
1
1
0
1
1
1
1
0
1
2
1
1
2
0
0
1
1
1
1
1
1
1
2
1
1
0
1
2
2
0
0
2
1
2
1
2
0
1
1
1
1
2
0
2
2
0
0
1
2
1
1
2
1
1
1
1
1
0
1
1
3
0
0
2
1
1
2
0
1
0
0
2
0
1
1
1
1
3
0
1
2
1
1
1
2
2
0
1
0
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
0
1
1
0
1
1
0
1
1
0
0
2
1
1
1
1
1
1
2
0
1
0
0
1
0
0
0
1
1
1
1
0
1
0
0
1
0
1
1
1
0
2
0
2
1
1
1
1
0
1
0
0
1
0
2
1
2
1
1
0
1
2
0
1
1
1
1
1
1
0
0
1
0
1
2
1
1
1
1
1
1
1
0
1
2
2
2
2
3
0
0
0
1
0
1
0
0
1
0
1
1
1
2
1
1
1
3
1
1
1
2
1
1
1
1
1
1
1
0
1
1
1
1
2
0
1
1
1
2
0
1
1
1
2
0
1
1
2
2
2
2
2
1
1
1
2
0
1
2
2
1
2
1
0
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
0
0
1
1
1
2
1
1
1
0
2
0
3
0
1
0
1
2
2
1
1
1
1
2
1
1
2
1
0
1
1
0
1
2
2
0
0
0
1
1
1
1
0
1
0
1
1
1
1
1
1
0
2
2
2
1
1
2
0
1
1
1
1
1
1
1
2
1
1
1
0
1
2
2
2
1
0
2
0
2
0
1
1
0
0
1
1
1
1
2
1
1
1
1
1
1
0
2
0
2
1
1
1
0
2
1
0
1
1
2
0
0
2
2
2
0
1
5
1
0
2
1
0
0
0
1
0
0
1
0
1
0
1
2
2
1
1
1
2
1
1
2
1
1
0
2
1
0
1
1
1
1
2
1
1
1
2
0
1
1
1
1
1
0
0
1
0
0
2
1
1
1
1
1
2
2
2
1
2
2
1
0
0
1
2
1
1
2
0
2
0
1
2
1
1
2
1
0
1
0
1
0
1
2
1
2
1
0
2
1
1
1
2
1
2
2
0
1
2
0
1
2
1
1
1
0
1
0
0
2
1
1
1
1
0
0
1
0
2
2
1
2
1
1
0
1
2
1
0
1
0
0
1
2
0
1
1
1
1
1
1
1
2
2
1
0
1
0
0
2
1
0
1
1
1
1
1
0
2
1
0
0
1
0
1
1
0
0
1
2
1
1
0
1
1
1
2
1
1
1
0
0
1
2
0
1
1
1
1
2
1
1
1
1
1
2
0
2
2
1
1
1
1
0
2
1
1
2
1
2
1
1
0
0
1
2
1
1
1
1
1
3
2
0
1
1
1
1
2
1
0
0
1
0
0
0
1
2
0
0
0
0
0
1
0
1
1
1
1
0
0
1
1
0
0
1
1
1
0
1
2
0
0
1
1
0
2
1
0
0
1
1
1
0
2
2
1
0
2
1
1
2
1
0
2
0
2
2
1
2
1
2
0
2
0
1
1
0
1
2
0
0
1
1
1
2
1
0
2
1
1
1
0
0
0
1
1
0
2
1
0
1
0
1
2
0
0
2
1
2
0
1
0
1
1
0
0
1
0
1
0
0
2
0
2
1
0
1
0
2
1
2
1
0
1
2
1
0
2
2
1
0
0
1
1
1
1
1
1
2
1
0
2
1
1
1
1
1
1
1
2
1
0
1
2
1
1
1
2
2
1
1
1
1
1
1
1
0
0
0
1
2
2
0
2
0
1
1
2
1
0
0
1
0
0
2
2
2
1
1
0
0
0
1
0
1
0
0
2
1
0
1
2
1
2
0
1
0
1
0
1
1
2
1
0
1
1
1
1
0
0
2
1
2
1
0
1
1
1
1
2
2
1
1
0
1
1
2
0
1
2
0
1
1
2
1
1
0
1
1
0
1
0
1
1
1
0
1
1
0
0
1
1
1
0
0
2
1
1
1
2
1
0
0
2
2
1
0
1
2
1
0
2
2
1
2
1
2
2
2
0
1
1
2
2
1
0
1
2
1
1
1
1
1
1
1
1
1
0
0
2
2
0
2
1
1
2
0
1
1
0
1
1
0
0
1
2
1
1
1
0
1
1
1
1
0
1
1
1
2
1
1
0
1
2
2
1
1
0
0
1
0
2
1
0
0
1
0
1
1
2
1
2
0
3
0
3
0
1
0
1
1
1
2
1
1
1
1
1
2
2
1
2
1
1
2
0
2
1
0
1
1
1
1
0
1
0
1
0
0
1
1
1
1
2
0
0
1
2
1
0
0
1
1
1
2
1
1
1
0
1
2
1
3
1
0
1
2
1
1
1
1
1
0
1
1
2
1
1
1
1
1
2
2
1
1
1
2
2
1
1
0
1
0
2
1
0
1
1
0
2
1
1
0
2
1
1
1
2
1
0
1
1
1
1
2
0
2
1
2
2
0
0
0
0
0
1
2
1
0
1
2
1
1
2
2
1
1
2
1
1
1
1
2
1
1
2
1
2
0
1
1
2
1
0
1
1
1
1
0
1
0
0
0
1
1
1
1
0
2
1
0
1
1
2
1
1
0
2
1
1
2
1
0
1
1
1
0
0
1
2
1
2
1
2
1
0
0
1
2
0
0
2
1
0
1
1
1
1
2
0
1
1
1
1
1
1
1
1
1
1
2
2
0
2
1
0
2
2
0
0
1
0
2
0
1
1
0
2
1
1
0
0
2
2
0
2
1
2
0
1
1
0
2
1
1
1
0
2
2
1
1
0
0
1
1
1
0
1
0
1
0
1
1
0
0
2
1
0
0
1
0
1
1
1
2
1
2
1
1
2
1
2
1
1
2
2
2
2
1
0
1
0
1
0
1
1
0
0
1
2
1
1
1
0
0
0
1
0
2
0
1
1
1
0
1
0
2
1
0
1
1
0
0
0
2
1
0
0
0
0
1
2
1
2
2
2
2
0
2
3
1
1
1
1
2
1
1
0
2
2
1
0
0
1
1
1
0
1
2
1
0
2
1
2
1
2
1
1
0
1
1
1
1
2
2
1
0
1
0
1
1
2
0
1
1
1
0
0
1
2
2
1
0
1
0
1
2
1
1
2
1
1
2
1
1
2
0
2
1
0
0
2
1
0
1
1
0
0
1
1
0
0
1
0
1
1
1
1
1
1
0
1
0
0
1
0
2
1
1
1
0
1
0
1
2
2
2
1
1
1
0
0
1
1
0
2
1
2
0
1
2
1
0
3
1
1
1
1
1
1
1
1
2
2
2
2
1
1
0
1
1
0
0
0
0
2
0
1
1
1
1
1
1
0
1
0
2
1
1
0
0
1
1
1
1
1
1
1
1
1
0
1
2
1
1
0
1
1
1
2
0
1
1
0
1
1
2
0
0
2
0
0
0
1
0
1
2
0
0
2
2
1
2
1
1
2
1
2
0
1
0
1
1
1
0
2
2
1
1
1
0
1
2
0
0
1
1
0
1
1
0
2
1
1
1
0
1
1
1
1
0
0
0
1
2
2
2
1
0
1
0
1
1
1
1
1
0
0
1
1
1
1
0
1
1
1
2
1
0
0
1
1
1
0
2
0
1
2
1
0
1
0
1
1
1
0
1
0
2
1
2
2
2
1
1
1
2
2
1
1
0
2
1
3
0
0
1
1
1
1
1
0
2
0
0
2
0
2
1
2
1
0
0
0
1
1
1
1
2
0
3
1
1
1
1
1
1
1
2
0
1
1
1
0
2
0
0
2
2
1
2
2
1
1
1
0
2
1
0
1
1
1
2
1
0
0
2
0
3
2
0
4
1
1
2
0
0
1
1
2
0
1
2
0
1
1
0
1
0
1
1
1
1
1
0
1
1
1
2
1
0
1
2
1
2
2
2
0
2
2
2
2
2
1
1
0
2
1
1
1
1
0
0
2
2
2
1
1
1
1
1
2
1
2
4
1
2
1
0
2
1
1
1
2
0
0
0
0
0
1
1
1
1
1
1
1
1
1
2
1
2
1
2
0
2
1
0
1
1
2
0
1
1
1
1
0
0
0
2
2
2
1
1
2
1
1
0
1
2
0
2
1
1
1
1
0
0
0
3
1
0
0
1
1
1
0
1
1
0
1
1
2
1
0
0
1
2
1
3
2
1
1
0
0
0
0
1
2
2
0
1
1
2
1
1
1
0
0
0
0
0
2
1
1
0
0
1
1
1
0
2
1
0
1
0
1
2
1
1
2
1
2
1
0
0
2
1
0
1
0
2
0
1
2
1
1
0
0
1
1
0
1
0
1
2
1
2
1
1
1
0
1
2
1
0
1
1
2
1
0
1
2
0
0
0
1
1
1
1
1
1
3
2
0
0
1
2
3
1
1
0
2
0
1
0
2
1
1
0
1
0
1
1
1
1
1
1
2
1
0
1
2
0
1
0
1
0
0
0
1
0
1
0
1
0
2
1
0
1
2
1
1
1
2
0
1
0
0
2
1
1
1
2
0
0
1
1
1
1
0
0
0
2
0
1
0
1
2
1
1
0
2
1
2
0
5
1
2
0
1
1
0
0
1
1
2
0
1
0
1
2
1
2
2
0
2
0
1
2
2
2
1
0
1
0
0
1
1
1
2
2
1
1
2
1
0
0
1
2
1
0
0
0
4
1
1
2
1
0
2
0
1
1
1
2
0
1
1
1
0
1
2
1
1
2
0
1
1
1
1
2
0
2
1
1
0
0
3
0
1
2
0
1
0
1
1
2
1
1
2
0
1
1
1
2
2
0
2
1
1
1
1
2
1
1
1
2
2
0
2
1
1
0
1
1
0
2
2
2
2
1
1
1
1
2
0
2
1
0
2
2
2
0
1
2
1
2
1
2
2
0
1
1
1
1
0
0
0
1
1
3
0
2
1
1
0
1
0
1
2
0
0
0
0
0
0
2
1
1
1
2
1
2
1
1
0
1
2
1
0
2
0
1
0
1
2
0
1
2
0
2
0
0
2
2
2
1
1
0
2
1
2
2
1
1
1
0
1
1
0
1
1
2
1
1
1
1
2
0
1
1
1
0
0
0
1
2
1
1
0
1
0
1
3
0
1
1
1
0
0
0
0
2
1
0
2
1
2
0
0
1
1
0
1
2
0
1
0
2
1
1
1
2
1
1
1
2
1
1
1
2
2
1
1
0
1
1
1
1
1
1
1
2
2
2
1
1
0
1
2
1
1
1
0
0
0
4
1
1
0
0
2
1
1
1
2
1
0
0
0
2
1
1
1
1
2
1
0
1
2
0
1
0
0
1
1
1
0
1
0
0
1
1
0
1
0
0
1
2
2
0
2
2
1
1
1
0
1
1
1
2
1
1
1
1
1
0
3
2
1
1
1
1
1
0
1
1
1
1
2
0
0
1
1
2
0
1
1
1
0
2
2
0
1
2
0
2
1
1
2
0
0
1
1
0
2
0
2
1
0
1
2
1
0
1
1
0
1
1
1
0
0
1
0
0
0
2
1
1
2
2
1
1
1
0
1
2
2
2
1
0
0
0
1
0
0
1
2
1
1
0
1
2
0
0
1
1
1
2
1
0
1
1
2
0
0
2
2
0
1
1
1
0
1
2
1
0
1
0
0
1
1
1
1
0
2
1
1
2
1
1
0
1
2
1
1
1
1
0
2
0
0
2
0
1
0
2
2
1
2
2
1
1
2
1
1
1
0
1
1
0
1
0
1
1
1
2
0
2
1
0
1
1
1
0
2
1
1
2
1
1
1
1
0
0
2
0
0
0
1
0
1
0
1
2
2
1
2
1
0
1
1
1
0
0
1
1
0
0
2
1
1
2
0
0
2
0
0
2
0
2
2
2
0
0
0
0
1
1
2
1
0
1
1
1
0
0
1
1
1
2
1
1
0
1
1
1
1
1
0
1
0
1
1
1
0
1
1
2
0
2
1
0
1
0
1
1
0
1
2
1
2
2
1
1
1
0
1
2
2
0
1
1
2
1
0
2
1
1
1
1
2
1
2
0
1
0
2
1
2
1
4
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
0
0
1
0
1
2
0
1
1
1
1
2
0
1
1
0
1
1
1
1
1
1
0
1
1
1
0
1
0
1
1
0
2
0
1
2
1
1
2
1
0
1
0
1
0
2
2
1
2
1
1
1
0
1
0
0
2
0
0
2
1
2
1
1
0
1
0
1
0
2
1
1
0
2
0
1
0
1
0
0
1
1
1
1
0
1
2
1
1
1
1
1
0
1
1
0
0
2
2
2
2
1
2
2
1
3
1
1
0
1
0
2
0
1
0
1
1
1
2
1
0
0
1
0
0
0
1
1
1
0
0
2
1
1
2
2
1
2
1
0
0
2
0
1
0
2
2
1
0
0
1
2
1
0
0
1
1
1
0
3
1
1
0
2
2
1
0
1
1
1
1
1
2
1
1
1
1
2
1
0
2
1
0
3
0
0
2
2
2
0
1
1
1
1
2
1
2
3
1
2
0
0
0
1
0
0
2
1
2
0
1
1
1
0
0
1
1
0
2
2
1
1
2
1
1
0
0
1
0
1
0
1
0
1
1
0
0
1
1
1
0
2
1
0
1
2
1
0
2
0
2
0
2
0
1
1
1
0
2
1
0
1
0
0
0
0
0
2
2
1
1
1
2
1
2
0
1
0
0
1
2
2
1
1
1
2
1
0
0
0
0
2
1
1
1
2
2
0
1
1
1
1
1
2
0
1
1
0
0
0
0
2
1
1
0
1
1
1
0
1
0
1
0
1
2
0
0
1
2
2
2
1
2
0
1
1
0
2
1
1
0
1
1
1
0
0
0
1
1
1
2
1
2
1
1
1
2
2
2
2
1
1
1
2
1
0
2
1
0
2
0
1
1
1
1
1
1
1
1
0
2
1
1
1
1
1
1
0
0
0
1
1
2
1
5
1
2
0
1
0
0
0
2
2
0
0
0
1
1
0
2
1
2
1
0
1
1
0
0
1
0
1
2
2
0
1
1
2
1
0
2
0
1
0
1
1
1
1
1
1
0
0
1
1
1
2
0
2
2
1
0
0
2
0
1
2
1
1
2
1
1
1
0
1
1
1
2
1
1
0
0
1
1
2
1
1
0
0
1
0
3
2
1
1
1
1
0
0
1
1
1
1
0
0
0
1
2
1
1
0
0
1
0
0
1
1
1
1
1
0
1
1
1
1
1
1
0
2
0
2
1
2
3
1
1
1
0
1
1
1
2
2
0
0
1
2
0
2
2
2
2
0
0
0
2
2
2
1
1
0
2
1
1
1
0
1
2
0
1
2
0
1
1
1
1
2
1
0
0
0
1
2
2
1
2
0
0
0
1
0
1
2
2
1
0
1
1
0
1
1
1
1
1
0
1
0
1
1
1
0
1
1
1
2
2
1
1
0
1
0
0
1
0
0
0
0
1
1
0
1
0
0
1
1
0
0
2
1
1
1
1
1
2
0
1
1
0
1
0
0
1
1
1
1
1
1
0
2
1
1
0
1
1
1
1
1
2
1
1
2
1
1
2
2
0
1
1
0
0
1
1
1
1
0
1
2
1
1
1
2
2
1
0
2
1
1
0
3
1
0
0
1
2
0
1
1
1
2
1
0
0
1
2
1
1
0
0
2
0
0
2
0
0
0
1
1
2
1
1
1
0
1
1
1
0
1
2
1
1
2
1
0
1
1
1
2
1
2
1
0
2
1
0
1
1
1
1
1
2
2
0
2
1
3
1
1
1
1
0
1
2
2
2
1
1
0
1
1
2
1
1
2
1
2
1
1
1
0
1
0
1
2
0
1
0
1
0
0
1
1
0
0
1
2
1
0
1
1
0
1
1
2
2
1
1
2
1
2
1
1
2
1
3
1
1
2
1
2
2
1
0
1
1
1
0
1
0
1
0
1
1
1
0
1
0
2
0
3
0
1
1
0
0
0
0
1
1
0
1
1
1
0
2
2
0
1
1
0
1
0
1
1
1
1
0
1
2
1
1
1
1
1
1
1
1
1
1
0
2
2
2
0
0
1
0
1
2
1
1
2
2
1
1
0
1
1
2
1
0
1
2
0
2
1
1
2
1
1
1
1
0
1
2
1
0
2
0
1
2
2
3
0
1
1
0
1
1
1
2
1
0
0
2
0
2
4
1
0
2
2
1
2
1
1
1
2
1
1
1
0
1
1
2
0
0
1
0
2
1
2
0
1
0
0
1
0
1
2
0
1
3
1
1
1
0
0
2
0
1
1
0
0
1
1
0
0
1
1
1
0
2
0
2
1
0
1
1
1
1
2
1
2
0
1
1
2
0
1
0
1
2
1
2
1
1
1
1
0
0
0
0
1
2
1
1
1
1
3
1
1
1
2
0
1
0
0
1
2
0
1
0
2
1
1
0
2
2
0
1
1
1
0
2
0
1
2
1
2
1
1
1
0
1
1
0
2
2
0
1
2
1
0
0
1
0
2
1
0
0
0
0
2
1
1
1
0
1
0
0
2
0
0
2
1
2
0
1
1
2
0
1
1
1
1
1
2
0
2
0
1
2
1
3
1
2
0
1
0
1
1
1
0
2
1
1
0
0
1
1
0
1
2
1
1
0
2
1
1
1
1
0
1
1
0
0
2
1
0
1
0
1
1
0
3
1
1
0
0
0
1
1
1
0
2
1
0
1
1
1
1
0
1
0
1
1
1
0
1
3
1
0
1
0
2
1
1
1
1
0
0
1
0
0
1
2
1
1
1
0
0
0
1
1
1
2
1
1
1
2
1
2
1
0
1
1
0
0
0
1
2
1
2
2
1
2
1
2
0
1
1
1
1
0
0
1
1
1
0
1
2
1
3
1
1
0
2
0
2
1
1
0
1
0
2
1
1
1
0
1
1
2
1
0
2
0
0
2
2
0
0
0
0
3
1
3
2
1
0
1
1
2
2
0
0
2
1
1
1
2
0
0
0
1
1
1
1
2
1
1
0
3
2
0
1
1
0
1
2
1
0
1
1
2
1
0
1
2
1
2
1
1
0
1
2
2
0
0
1
0
1
1
1
1
0
0
2
2
1
0
1
1
1
0
1
2
0
1
1
2
1
1
1
1
1
0
2
1
1
1
1
0
0
1
1
1
1
1
1
0
1
1
1
2
0
0
1
1
2
1
0
1
1
1
2
1
1
2
0
1
1
2
1
1
1
1
0
0
3
1
1
2
1
2
1
2
3
0
1
0
2
2
1
2
2
1
0
2
1
1
2
0
1
0
2
0
1
0
1
0
2
0
2
0
1
2
1
0
0
0
0
1
1
1
0
1
1
2
2
0
1
2
0
1
2
2
0
0
0
1
0
0
2
0
3
0
0
1
2
0
1
3
1
0
1
0
2
1
1
1
0
1
2
0
1
0
2
2
1
1
1
1
1
1
0
1
1
1
0
2
1
1
1
0
1
0
0
0
1
1
0
2
0
2
0
1
0
0
1
1
1
2
1
0
0
0
0
2
0
0
1
1
2
0
1
2
0
1
0
1
0
1
1
1
0
2
1
1
0
2
0
1
1
0
1
2
2
0
1
1
1
2
2
1
1
1
1
2
2
1
2
1
1
1
2
0
2
0
1
2
1
2
2
1
1
0
0
0
2
1
1
1
1
1
1
2
3
1
1
0
1
2
0
1
1
1
1
2
0
0
1
0
1
1
0
1
0
0
1
2
1
2
1
0
2
1
0
2
0
1
1
1
1
1
1
0
1
1
1
0
1
1
0
0
1
1
1
1
1
0
0
1
0
2
1
2
1
1
0
1
1
2
1
1
1
1
0
1
0
1
2
0
3
1
2
0
1
2
1
1
1
2
1
2
0
1
1
0
1
2
0
1
1
1
2
0
1
2
0
1
2
0
1
1
2
1
0
1
1
1
2
1
1
2
2
1
1
1
1
1
1
0
1
2
1
0
1
1
1
1
0
2
3
1
2
0
2
2
1
0
0
0
1
0
0
0
2
2
1
1
1
1
0
1
1
0
2
2
2
2
2
0
0
1
0
0
2
0
1
0
1
1
0
1
1
1
2
0
0
2
1
1
1
1
0
0
0
1
1
2
0
0
2
1
1
1
2
0
0
1
1
1
1
2
1
0
1
0
0
2
1
1
2
1
2
3
0
2
0
0
1
1
1
1
1
1
1
0
1
1
2
1
0
2
0
1
1
0
2
2
1
0
0
2
0
1
1
1
5
1
1
0
1
2
0
2
0
1
1
1
1
2
1
0
2
1
2
2
2
0
2
1
1
1
0
0
1
2
1
0
2
1
1
0
2
1
2
0
1
1
1
1
1
1
1
0
1
0
2
2
1
2
2
0
0
0
2
1
1
1
1
0
2
0
2
1
0
1
0
1
1
0
1
0
2
1
1
1
1
0
1
1
2
1
2
1
2
0
1
1
1
0
0
1
0
1
2
0
0
0
1
1
0
0
1
1
2
1
1
1
2
1
1
0
0
0
0
0
2
0
0
0
1
1
1
1
1
1
0
2
1
1
1
1
1
0
0
2
1
0
2
1
1
0
2
2
1
4
1
1
1
2
0
1
1
0
2
0
0
1
1
0
1
3
2
1
2
1
2
1
2
0
1
1
2
0
1
1
2
1
0
0
1
0
1
0
1
1
3
2
1
0
2
1
0
0
1
1
1
0
1
2
2
3
0
1
1
1
2
1
0
1
1
0
0
1
1
1
2
1
1
1
1
2
1
0
0
2
1
1
1
1
0
0
1
0
1
2
1
1
0
0
0
1
0
0
1
0
2
2
1
1
2
1
0
2
2
2
1
1
1
2
1
1
2
2
1
0
0
0
0
2
2
0
0
0
0
2
1
0
1
0
0
1
1
6
1
2
0
2
0
1
2
2
1
1
0
1
0
0
1
3
0
0
1
0
1
1
0
1
1
1
2
0
1
2
0
1
0
0
0
0
1
1
1
1
1
0
0
0
1
0
1
1
0
1
2
2
2
1
1
1
2
1
2
0
0
2
1
1
1
1
1
0
1
2
0
0
1
1
0
0
1
1
2
1
2
2
1
2
1
1
1
0
2
1
1
1
2
1
1
1
1
2
0
1
1
2
2
2
1
2
1
1
2
0
0
0
2
2
1
1
2
2
0
3
0
1
2
2
1
1
1
0
2
1
1
1
0
0
1
1
1
1
1
1
1
1
1
0
0
2
2
2
2
1
1
1
2
1
1
1
0
1
1
2
0
0
1
1
1
2
1
1
2
0
1
0
2
0
0
1
2
0
1
1
0
1
0
0
1
1
1
0
1
2
2
1
2
1
0
0
0
2
1
1
1
2
0
0
0
2
1
1
2
2
1
1
0
0
1
0
1
0
0
0
0
1
0
2
0
1
1
1
1
1
0
1
1
0
1
1
1
1
0
0
0
2
1
2
1
2
0
0
1
0
1
1
2
1
1
1
0
1
1
0
1
1
0
1
0
0
1
2
1
3
1
2
1
2
2
2
3
1
2
2
0
1
0
1
1
1
0
1
2
0
0
0
1
1
1
1
2
0
0
1
1
1
1
0
0
1
1
2
1
0
1
1
2
1
2
1
1
0
1
0
1
2
1
2
1
1
0
2
0
2
0
2
1
0
2
0
2
2
0
1
1
1
1
1
1
1
1
1
3
0
1
1
0
0
0
1
1
1
2
2
2
0
1
1
0
1
2
2
1
2
1
1
1
2
0
1
0
1
1
0
1
0
1
1
1
0
1
1
1
0
1
1
3
1
2
0
2
1
1
0
0
1
2
0
1
2
0
0
0
2
0
2
2
1
0
0
0
1
2
1
2
3
0
1
0
1
0
2
2
2
1
1
0
0
2
1
1
1
2
0
1
0
1
1
1
0
0
1
0
0
2
2
0
0
1
2
1
2
2
1
0
1
1
2
1
1
0
3
2
1
0
0
1
2
2
2
1
1
0
1
1
0
1
1
0
1
2
2
0
1
1
2
2
1
1
0
0
0
0
0
1
1
2
2
0
2
1
1
0
1
1
2
0
3
1
2
1
1
1
1
1
2
1
1
1
2
1
2
2
3
1
1
2
2
0
1
1
0
0
2
2
1
0
2
0
2
1
2
0
1
1
1
1
1
2
1
1
3
0
1
1
1
1
1
0
0
1
1
0
0
1
2
0
1
1
1
2
2
2
1
1
1
0
0
1
1
1
2
2
0
1
1
2
1
1
0
2
2
4
1
2
1
2
1
0
1
1
2
2
1
1
0
0
2
2
3
1
0
2
1
1
1
1
0
0
1
1
2
0
1
0
0
0
1
1
1
1
0
0
1
0
1
1
1
1
1
1
0
2
1
0
0
0
1
1
1
1
2
1
2
1
1
2
1
2
1
1
0
0
7
1
3
2
2
1
1
0
0
1
1
0
1
2
0
2
2
1
0
0
0
1
1
2
2
2
2
0
1
2
0
2
0
1
1
0
0
1
0
1
1
1
0
2
0
1
1
0
1
2
1
0
2
1
1
1
0
0
1
1
2
0
3
0
1
2
0
2
0
0
1
1
1
1
2
1
0
1
0
1
1
1
0
1
1
2
2
0
0
2
1
1
0
2
0
3
1
0
0
0
1
1
1
1
1
0
1
1
1
1
2
0
0
2
1
2
2
0
1
0
1
0
1
1
0
1
0
1
1
1
2
2
1
0
2
1
1
0
2
2
1
1
1
1
2
2
0
1
1
1
0
1
0
2
1
2
0
2
1
0
0
2
1
1
1
2
1
1
0
0
0
0
2
0
2
2
4
0
1
1
1
0
2
0
1
0
2
1
1
0
1
0
1
2
1
0
2
1
0
0
1
1
0
2
1
1
2
2
1
1
0
0
2
1
1
0
1
2
1
0
0
1
2
0
1
2
1
2
3
1
2
1
0
1
2
0
1
0
1
2
2
2
2
1
2
0
1
1
1
1
1
1
1
2
1
1
0
1
1
0
2
0
1
1
1
0
1
2
1
0
2
1
2
1
1
2
1
1
2
1
1
1
0
1
1
1
1
0
1
1
1
0
1
1
0
1
1
1
0
0
2
1
1
0
2
1
0
2
1
1
2
1
2
1
1
1
0
1
2
1
1
1
1
1
1
1
1
2
1
1
1
0
1
1
0
0
2
1
1
1
2
2
2
1
0
1
0
1
1
0
2
2
0
0
1
3
0
1
1
2
1
2
2
1
2
1
1
1
1
1
1
3
0
2
1
0
0
1
0
2
1
2
0
1
1
1
1
1
1
1
1
2
1
1
0
1
1
2
1
2
1
1
1
0
0
0
2
1
2
1
1
1
1
2
1
1
0
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
0
0
2
1
2
0
1
1
2
0
1
1
2
2
2
2
0
2
1
1
2
0
0
1
1
2
2
2
0
1
0
2
0
0
0
1
1
0
1
0
1
0
2
2
1
1
2
2
1
1
0
2
2
2
1
0
2
1
1
1
1
1
0
0
1
1
1
2
1
2
1
1
1
1
0
1
2
2
2
1
1
0
1
1
1
0
2
1
1
0
1
1
1
1
0
0
0
1
2
1
1
5
1
2
1
1
2
1
1
2
4
1
2
0
1
1
1
2
0
0
1
0
2
0
2
1
1
1
1
1
0
0
1
0
2
0
1
1
2
0
1
0
0
1
2
1
1
1
1
1
1
1
2
1
0
2
3
1
1
1
1
2
1
0
2
2
0
1
1
1
1
2
2
1
2
0
1
1
0
1
2
1
0
1
0
0
1
1
1
0
2
1
1
0
1
2
1
0
0
1
0
0
1
1
1
2
1
1
2
0
2
1
2
0
0
1
1
1
2
0
2
1
0
0
1
1
1
0
2
0
0
0
1
0
2
0
0
1
1
1
2
2
1
1
1
1
1
0
2
1
1
0
1
2
0
1
2
0
1
1
1
1
1
1
1
1
1
1
1
0
1
5
0
1
0
0
1
1
1
2
0
2
1
1
1
0
1
1
0
0
1
1
1
1
1
1
2
1
1
2
2
1
1
1
1
2
2
1
1
0
1
1
2
2
0
0
0
0
2
2
2
2
1
0
1
2
0
1
1
1
2
1
2
1
2
2
1
2
1
1
1
1
2
0
1
1
3
2
1
0
2
1
1
0
0
1
0
1
1
1
2
0
2
1
1
0
0
0
0
2
1
0
2
0
1
1
2
1
2
2
1
0
0
1
2
1
0
2
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
0
1
0
2
0
1
2
2
1
1
1
0
0
2
1
1
1
0
1
1
0
1
1
1
2
0
0
1
2
1
2
0
0
2
1
1
2
0
0
1
1
1
0
1
2
2
0
1
2
0
1
1
1
1
0
2
0
1
0
2
2
1
0
2
2
1
1
1
2
1
0
1
1
1
1
0
1
1
1
1
1
0
0
1
1
1
1
0
0
1
2
2
1
0
0
1
2
0
0
3
1
1
1
1
2
2
1
0
0
1
2
0
2
1
0
0
1
2
1
1
1
0
0
2
2
1
0
1
0
1
0
0
1
2
1
0
1
1
1
2
2
2
1
0
3
0
2
1
1
1
0
0
1
1
1
0
1
2
2
0
1
0
0
0
0
2
0
0
2
1
1
0
0
0
0
0
0
0
2
1
1
1
1
1
1
1
1
0
1
1
1
0
1
0
1
2
2
1
0
1
1
2
0
1
2
0
2
1
2
1
0
1
0
1
2
0
1
0
2
1
1
1
0
2
0
2
0
1
2
1
1
0
2
1
1
0
2
2
0
2
0
3
2
1
1
1
1
1
2
2
1
1
2
1
1
2
1
1
1
1
2
1
0
1
0
2
0
0
0
0
1
0
1
1
0
1
0
1
1
1
2
2
0
2
2
0
1
1
1
2
1
0
1
1
0
2
1
0
1
1
2
0
2
0
1
1
1
0
1
1
1
0
1
0
1
1
0
1
1
2
2
1
1
6
0
0
0
1
0
1
1
0
1
2
1
1
0
1
1
1
1
1
1
2
0
1
2
1
1
1
2
1
1
2
2
2
0
2
1
1
1
2
2
2
0
2
0
1
1
0
0
0
2
0
2
1
1
1
1
2
1
2
0
1
2
1
0
0
1
1
1
1
1
0
0
2
1
1
0
1
0
2
2
1
2
1
1
0
1
1
1
0
2
2
1
1
0
1
2
1
1
0
1
1
1
0
2
1
0
1
1
0
1
0
1
0
1
2
1
1
0
1
1
2
1
0
0
1
0
1
0
1
0
1
4
1
1
1
1
1
1
0
1
1
1
1
1
1
2
1
1
0
0
1
0
1
0
1
1
1
2
1
1
1
0
2
0
0
2
0
1
1
1
3
2
0
1
1
1
1
0
1
1
1
1
1
2
0
0
2
2
0
1
0
1
2
2
1
2
1
0
1
1
1
1
0
1
0
2
1
1
0
1
0
1
2
0
2
1
1
1
1
2
2
1
0
1
1
0
2
1
0
1
2
1
2
0
0
0
0
1
2
2
1
1
1
1
1
1
1
1
0
2
2
3
0
1
1
1
1
2
0
1
1
0
1
1
1
1
1
1
1
2
1
2
1
1
1
2
1
1
1
1
0
1
1
2
2
0
1
0
1
1
1
1
1
2
1
0
1
1
1
2
2
5
2
1
1
0
1
1
2
2
2
0
2
1
1
2
0
1
2
1
1
0
0
1
2
2
2
1
1
2
2
1
2
1
0
1
1
1
1
1
0
0
0
0
1
0
0
1
0
0
1
2
1
2
0
1
0
0
1
2
1
1
0
0
1
3
0
1
1
0
2
1
1
0
2
2
2
2
1
2
1
1
1
1
0
0
1
1
1
1
0
1
1
1
1
1
0
0
1
0
0
1
0
2
1
1
2
0
0
0
0
0
1
1
1
1
0
1
1
1
0
2
0
2
1
0
1
2
1
0
2
1
1
0
1
2
1
1
2
1
0
2
1
2
1
1
1
1
1
2
0
1
1
1
3
0
1
0
1
1
3
2
1
1
1
1
1
1
1
1
2
1
2
0
2
1
1
1
1
0
1
0
0
1
1
2
2
1
1
1
1
0
2
2
0
0
0
1
0
1
1
1
2
0
1
0
1
2
0
0
1
2
1
1
1
0
1
2
0
1
1
2
1
1
1
1
1
1
1
1
1
1
11
0
0
1
2
1
2
1
0
0
2
0
0
1
1
2
1
0
1
1
1
1
3
1
0
1
1
1
1
1
1
1
1
0
1
1
1
2
0
1
0
0
0
0
2
0
1
2
2
2
1
2
1
2
1
1
0
2
0
1
1
0
1
2
2
0
0
1
0
0
1
2
1
2
1
1
2
1
2
0
0
1
1
1
0
1
1
2
1
0
1
1
2
1
0
1
2
0
1
1
1
2
2
1
2
1
1
0
1
2
1
1
1
1
1
0
1
1
1
0
1
0
1
1
0
1
0
2
0
1
0
0
1
1
2
1
1
1
0
0
0
1
2
0
1
0
2
1
0
1
2
1
1
0
1
1
0
1
0
2
1
4
0
1
1
1
0
2
1
1
1
1
1
1
2
1
1
1
0
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
0
2
1
1
0
0
0
1
2
0
2
1
2
0
1
1
2
2
0
1
1
1
1
0
1
0
1
0
2
0
1
1
0
1
1
1
2
1
2
1
0
0
1
0
0
0
1
0
0
2
2
0
1
1
1
2
3
1
0
1
1
1
0
1
0
2
0
1
1
2
0
1
0
1
1
1
0
1
2
1
1
0
1
1
1
1
1
1
0
0
1
0
0
1
0
1
0
0
1
1
1
1
2
1
1
0
1
1
0
0
1
1
1
1
2
2
1
1
2
1
2
0
0
0
0
1
1
1
0
1
0
1
1
2
1
1
0
1
1
0
1
1
0
2
0
2
3
1
2
2
2
1
1
1
1
1
1
2
1
2
1
1
1
1
0
1
3
2
1
1
1
0
1
2
1
1
1
2
0
0
1
2
1
1
1
2
2
1
0
2
2
1
1
0
1
1
0
1
0
1
1
2
1
1
0
0
2
1
1
1
1
0
2
0
1
1
1
0
1
2
2
0
0
2
0
0
0
1
1
0
2
2
2
0
1
1
1
1
0
2
1
2
0
0
0
0
1
1
2
2
2
0
1
1
0
1
1
1
0
1
4
1
1
1
2
1
3
2
1
0
1
1
0
2
1
0
1
1
1
1
2
2
1
1
2
2
1
0
1
2
2
0
2
1
1
2
0
0
0
0
2
0
2
2
0
1
0
1
0
2
1
2
1
1
1
1
1
1
1
2
0
0
1
0
1
4
0
1
1
1
0
0
0
1
1
2
1
0
1
1
2
0
2
1
0
2
1
0
1
1
0
1
2
1
1
1
1
0
1
2
1
0
1
1
1
1
2
1
0
2
0
0
2
1
1
0
1
1
1
1
2
1
1
1
1
0
2
1
0
1
1
0
1
0
0
1
1
1
1
1
1
1
1
0
4
1
0
1
2
1
1
0
0
2
0
1
0
1
0
1
0
0
2
2
1
1
1
2
2
1
0
0
1
0
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
0
2
0
2
1
2
1
1
1
2
0
2
1
1
2
1
2
1
0
2
2
1
1
0
2
1
0
2
0
1
1
0
1
2
1
0
0
1
0
1
1
0
2
2
1
1
2
0
0
0
1
1
0
3
0
1
0
0
0
2
1
2
0
1
2
1
1
2
1
1
0
2
1
1
1
1
1
0
2
1
0
1
1
1
1
1
0
1
3
0
1
0
1
0
0
0
2
1
1
3
1
1
1
1
2
1
0
1
2
1
1
1
1
1
2
1
0
1
1
1
1
0
2
2
2
2
1
2
1
1
0
1
1
2
2
0
1
0
1
1
0
1
1
1
0
1
0
2
1
0
1
0
0
0
2
1
1
1
3
4
0
2
1
2
1
1
2
0
1
2
0
1
1
2
2
0
2
1
2
0
1
1
1
2
1
0
2
0
1
2
1
1
2
0
1
1
2
1
0
1
1
0
0
2
1
1
0
2
1
1
0
1
1
0
0
1
1
1
1
1
1
2
1
2
2
1
1
1
1
2
2
1
3
1
2
1
0
2
2
2
1
1
2
2
0
2
1
2
0
0
2
0
2
1
4
0
0
1
1
1
1
2
1
0
1
1
1
0
2
2
1
1
2
1
1
0
1
0
1
0
2
2
2
2
0
1
2
0
1
1
1
1
0
1
1
1
2
1
1
1
2
1
0
1
1
1
2
0
1
1
0
1
0
2
9
1
1
0
2
0
1
0
0
2
1
1
1
1
1
1
1
0
0
1
2
1
2
1
1
0
1
1
1
1
1
1
1
2
0
1
1
0
0
2
3
1
1
2
0
1
1
1
0
1
1
2
1
1
1
2
2
1
2
1
0
1
2
1
1
1
1
1
1
1
1
0
1
1
2
3
0
2
2
0
0
2
2
1
1
0
1
1
1
0
0
0
2
1
0
1
2
1
0
1
0
2
1
1
1
0
0
1
1
2
1
1
2
1
1
0
1
2
1
2
1
2
1
1
1
1
2
1
2
1
1
1
1
2
1
1
0
0
2
1
2
1
1
2
1
0
2
1
1
2
2
1
1
1
0
1
1
0
1
1
1
1
1
1
2
0
0
2
1
1
2
2
0
2
1
2
1
2
1
2
2
2
1
1
1
1
1
2
2
1
0
1
0
1
1
0
2
0
0
2
2
2
1
2
0
1
1
1
0
1
1
1
1
0
2
0
1
0
1
2
1
2
0
1
0
0
0
1
1
1
0
2
1
1
0
1
1
2
2
0
1
1
0
1
2
1
0
4
0
0
1
1
0
2
1
1
2
0
2
2
1
2
2
1
1
1
1
1
1
0
0
1
0
0
1
0
1
2
1
2
1
1
1
0
0
1
0
1
1
1
0
2
1
1
1
2
1
0
0
1
1
1
1
2
1
1
1
0
1
0
0
1
1
1
1
0
0
0
1
1
0
1
1
0
1
0
1
0
1
1
1
2
1
0
1
2
2
1
0
1
1
1
2
2
3
2
0
1
2
1
0
1
1
2
1
0
0
2
1
1
0
0
1
1
1
0
1
0
2
2
1
2
0
1
1
1
2
0
2
1
1
2
1
2
1
1
2
1
1
1
1
1
1
2
0
0
2
1
2
1
0
1
0
1
0
0
1
1
1
1
0
1
0
2
1
1
1
1
1
0
1
1
1
1
2
1
2
2
1
2
1
0
0
2
2
1
1
1
1
1
1
1
1
2
1
0
2
1
0
2
0
1
1
1
1
1
1
1
1
2
1
0
2
1
1
2
1
1
2
1
2
2
1
1
1
1
0
1
2
0
1
1
2
0
1
1
0
1
2
1
1
1
2
0
1
2
0
1
0
1
1
3
0
3
2
0
1
1
1
1
2
0
1
0
0
2
1
0
1
1
1
1
1
2
2
1
1
2
1
1
1
1
1
1
0
1
1
0
2
1
0
2
0
0
1
2
1
1
2
1
0
2
0
2
1
2
1
1
1
1
1
1
1
0
2
0
0
1
2
0
1
0
1
1
0
0
1
0
0
2
1
2
0
0
1
2
0
0
2
0
0
0
1
1
0
1
0
0
1
2
0
2
1
1
1
1
1
2
2
0
2
0
1
1
1
1
1
2
0
1
1
0
1
1
1
1
2
0
1
1
0
1
1
1
0
2
1
1
2
1
1
2
0
1
1
2
2
0
2
2
1
1
1
0
2
0
0
2
1
0
2
1
2
1
2
1
1
1
1
0
2
1
2
1
1
3
1
1
1
1
0
0
1
1
1
1
1
1
1
1
2
1
0
1
1
2
1
2
1
0
0
1
1
2
1
2
2
0
3
1
2
0
1
0
0
0
1
1
2
1
0
2
4
0
1
3
1
0
1
0
2
1
1
1
1
2
4
1
1
2
0
0
2
1
2
1
0
1
0
1
1
2
1
2
1
2
0
1
1
2
1
1
0
3
2
1
1
2
2
0
0
2
1
2
1
2
2
1
0
0
0
1
1
1
1
1
0
1
0
0
2
2
2
2
1
1
1
1
1
1
1
1
1
1
1
0
2
0
1
0
2
1
1
1
1
2
1
1
4
1
1
1
1
0
0
1
2
2
1
1
2
0
0
1
0
0
2
1
1
0
1
0
0
0
1
1
0
0
1
1
1
1
2
0
1
2
1
0
0
1
1
1
2
1
1
1
1
1
2
2
3
0
1
0
1
0
0
1
2
2
2
2
1
1
1
1
0
1
1
2
1
2
1
0
1
2
1
1
1
1
0
1
0
1
0
2
0
4
1
1
1
0
2
2
1
1
1
1
1
1
2
2
0
1
1
1
2
1
1
1
0
0
0
2
0
4
1
2
2
0
1
1
0
1
0
6
1
1
1
1
1
0
1
1
1
1
2
0
1
1
1
1
0
2
1
1
0
0
1
1
1
0
0
0
0
1
2
3
0
1
0
0
2
2
1
1
0
2
1
1
1
0
1
1
2
0
0
3
1
1
2
1
1
2
2
2
1
0
0
1
2
0
1
1
0
1
1
1
2
0
2
0
2
1
2
0
1
1
0
1
1
1
0
2
0
2
0
1
2
0
14
0
1
1
2
1
1
1
1
2
1
1
0
1
1
2
1
1
2
1
1
2
1
1
1
0
1
1
1
1
1
2
0
1
2
2
1
1
2
0
0
1
0
3
0
4
1
1
1
1
1
1
1
1
1
1
2
0
2
0
2
2
0
1
1
0
1
0
2
1
0
2
1
0
1
1
1
1
1
1
1
1
1
0
1
2
0
0
1
0
1
1
0
0
3
1
1
2
1
1
1
1
2
1
1
2
1
0
0
0
1
1
2
0
0
1
0
1
1
0
1
0
2
0
1
2
1
2
3
1
1
1
2
1
0
1
2
0
0
0
0
1
0
0
0
1
1
0
0
1
1
2
2
1
1
0
0
1
0
0
0
2
3
2
1
4
1
0
2
0
1
1
0
2
0
1
0
0
1
1
3
0
0
0
0
0
2
1
1
1
1
0
1
0
2
2
1
2
2
0
0
0
0
1
0
1
1
0
2
1
1
1
1
3
1
1
2
2
0
2
0
1
0
1
0
0
0
3
2
0
1
1
2
1
0
1
2
0
1
1
0
1
0
1
2
0
0
1
1
1
1
0
0
1
0
0
1
0
0
0
0
1
1
0
1
1
2
0
1
1
2
0
2
1
0
0
1
0
1
1
2
2
2
3
2
1
1
0
2
1
1
1
1
1
1
1
1
1
1
1
2
1
0
1
0
1
1
1
1
0
0
1
2
1
0
1
0
1
2
0
1
2
0
0
1
1
1
1
1
1
0
0
0
1
1
1
0
1
2
0
1
2
1
1
1
2
0
2
0
1
0
1
2
0
0
2
1
0
1
1
2
1
1
1
1
2
1
1
1
0
2
0
1
1
1
1
0
1
2
1
2
0
0
1
1
1
1
0
2
2
2
1
0
2
2
2
2
2
2
1
1
0
1
1
1
2
0
1
1
0
0
1
1
1
2
1
1
1
0
2
2
1
1
0
0
0
1
3
1
1
1
1
3
0
1
0
1
1
0
1
1
1
0
0
2
1
1
2
0
0
1
2
0
0
1
0
1
2
1
2
0
1
1
1
0
1
2
2
0
1
0
0
1
1
1
2
1
1
1
1
1
1
0
0
1
2
0
2
1
1
2
2
0
0
2
2
2
1
0
0
2
1
1
1
1
1
1
1
0
1
1
0
0
0
2
1
0
2
0
0
0
1
1
0
0
1
0
1
1
1
1
0
1
0
0
2
0
2
1
1
2
2
0
1
0
2
2
1
2
2
0
1
1
1
0
2
1
0
1
1
0
0
2
0
0
1
1
1
1
2
1
2
0
1
1
2
0
2
1
1
2
0
1
1
2
1
1
0
0
2
1
1
2
2
1
0
2
1
1
1
1
2
1
1
1
1
0
1
0
1
0
1
1
0
0
0
1
0
0
1
1
0
1
0
1
2
1
0
2
1
1
2
1
1
0
1
2
0
2
1
0
1
1
1
2
1
1
2
1
1
1
3
0
0
0
2
1
0
1
0
1
2
1
2
0
2
0
2
1
0
1
1
1
0
2
2
2
1
1
0
0
0
0
0
0
2
1
1
1
1
1
2
1
1
2
2
1
1
3
2
0
1
1
1
2
1
1
4
0
0
0
1
2
0
1
1
0
1
0
1
1
1
1
0
2
1
1
2
2
1
0
1
3
0
1
1
3
1
2
0
1
1
1
1
1
2
1
0
2
0
1
2
0
2
0
1
0
2
0
1
2
0
2
2
0
1
1
1
3
0
0
1
2
2
0
1
0
1
1
0
0
1
1
0
1
1
0
1
1
1
2
1
2
0
1
1
1
1
0
0
2
1
1
1
2
0
1
3
0
1
1
1
2
2
0
1
0
0
1
1
0
2
1
1
1
0
1
1
1
0
1
1
0
2
0
0
2
0
0
0
1
1
2
0
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
2
1
0
1
1
2
0
1
1
0
1
1
0
1
0
0
2
1
2
0
1
1
1
1
2
1
1
1
1
0
2
1
1
2
2
1
1
0
1
1
0
0
2
1
0
0
1
2
1
1
1
3
0
2
1
1
1
1
0
1
0
0
2
1
1
1
2
0
1
0
1
2
2
1
0
0
1
1
1
1
0
1
2
1
1
1
1
1
1
1
1
1
1
1
0
2
1
1
0
0
0
1
1
0
1
1
1
0
0
1
1
1
2
0
0
1
2
2
1
0
2
2
1
1
2
0
0
2
1
1
0
0
0
1
1
0
0
1
1
1
2
1
1
2
0
2
2
0
1
0
2
1
0
1
1
0
1
2
0
0
1
2
1
2
2
1
0
0
0
1
2
2
1
0
0
2
0
2
0
1
0
1
1
0
1
1
2
0
0
1
2
0
1
1
1
1
1
1
1
0
1
1
2
2
1
1
1
2
1
0
2
0
0
1
1
0
1
1
1
0
0
1
1
1
1
2
0
1
2
0
1
0
2
1
2
1
0
1
2
1
1
0
1
1
2
2
1
0
0
1
1
2
0
1
0
1
0
1
2
1
0
2
2
1
0
0
1
2
0
0
0
1
1
1
0
1
0
1
1
1
1
2
1
2
0
0
3
0
2
1
1
1
1
1
2
0
0
2
0
1
1
1
0
0
2
0
2
0
1
1
1
1
2
1
2
1
0
1
0
1
1
2
1
1
0
2
1
1
1
1
0
1
1
2
0
0
2
1
2
1
1
0
0
2
2
2
1
1
2
0
1
2
2
1
1
1
2
1
1
1
1
1
2
2
1
0
1
1
0
0
0
0
2
1
1
0
1
1
0
1
5
1
1
0
1
1
0
1
1
2
2
0
1
1
1
1
1
1
2
0
1
1
1
1
0
1
2
1
1
2
1
1
2
1
0
2
1
0
1
1
2
1
0
1
1
0
1
1
1
1
1
2
2
2
0
0
1
0
1
2
1
2
2
1
2
2
2
1
2
2
0
1
2
1
1
2
2
1
1
1
1
1
1
1
2
1
0
1
2
0
0
1
1
2
1
0
1
1
0
1
1
1
1
0
1
1
1
2
1
0
1
0
1
0
0
1
1
1
2
0
2
2
1
0
1
1
2
0
2
0
1
1
1
1
2
0
0
1
1
0
0
1
1
2
0
1
1
0
0
1
1
2
1
2
0
1
2
0
5
1
2
2
1
1
1
1
1
1
0
0
0
1
1
1
1
2
2
2
1
1
1
2
2
0
2
2
1
1
0
1
1
2
1
1
3
0
2
0
0
1
0
1
1
2
0
1
1
2
1
1
2
2
0
1
0
0
0
1
1
2
2
0
1
1
1
1
1
1
0
1
1
1
2
2
1
1
0
1
2
2
2
1
1
0
1
2
0
0
1
1
2
1
1
1
2
1
0
0
2
0
0
1
0
1
1
0
2
1
1
1
2
0
0
2
1
0
1
1
0
1
0
1
1
1
1
1
2
1
1
0
1
1
1
2
1
1
2
2
0
1
2
0
1
0
2
0
2
1
1
2
1
1
1
1
1
1
1
1
0
1
1
2
2
1
0
0
1
1
2
1
2
1
1
1
2
2
1
2
1
2
2
2
1
0
2
1
2
1
1
1
1
1
1
1
2
1
2
1
1
0
2
0
0
1
2
1
0
0
1
0
2
2
1
1
2
1
0
1
0
2
0
1
0
1
1
2
1
1
2
1
1
1
1
0
2
0
2
2
1
0
2
0
1
1
2
0
0
1
1
1
0
1
1
1
2
0
0
0
3
2
2
1
1
1
0
2
1
1
1
1
0
1
1
2
0
0
1
1
0
1
1
1
1
0
2
0
0
0
1
1
0
1
2
0
1
1
2
0
2
2
2
1
1
1
2
3
1
0
2
0
1
0
0
1
1
2
1
1
1
1
0
2
0
2
1
0
0
1
1
1
2
1
2
2
1
2
0
1
2
2
1
2
1
1
2
1
1
1
2
2
1
0
1
0
1
1
0
2
0
2
2
1
1
1
0
1
2
0
0
1
1
1
1
1
1
1
1
0
1
1
1
0
1
2
0
1
1
2
0
1
2
1
1
0
2
1
0
0
0
1
1
2
1
1
0
1
0
1
1
1
1
2
1
1
1
1
2
2
0
1
0
0
1
1
1
2
0
0
0
1
2
2
2
1
1
0
1
3
2
1
2
1
1
0
1
1
2
1
2
1
1
2
1
2
0
2
2
2
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
2
0
0
1
2
1
1
1
2
1
0
1
1
0
1
1
1
1
1
2
1
1
1
2
1
1
2
0
1
1
0
1
2
0
1
1
4
1
1
1
2
1
2
1
1
0
0
1
1
1
0
1
2
1
3
1
1
1
1
0
1
0
1
0
1
1
2
2
1
1
2
1
0
0
1
0
1
1
2
1
1
2
1
1
1
0
0
2
1
1
1
0
0
2
2
2
1
0
2
1
0
1
1
1
1
2
1
1
0
1
2
1
1
0
1
1
2
2
1
1
2
1
0
1
0
1
1
1
0
0
1
1
1
0
1
1
1
1
0
1
1
1
1
1
1
0
1
0
1
1
1
0
1
2
0
1
1
1
1
0
2
1
0
1
1
1
1
1
0
0
2
0
1
1
0
2
1
1
4
2
1
0
0
0
3
0
1
1
0
1
1
1
0
0
1
2
0
1
1
0
1
1
1
1
0
2
0
1
1
0
1
0
2
1
0
2
2
1
0
1
1
1
1
0
1
0
1
1
1
1
2
1
0
1
2
1
2
1
2
1
2
1
1
1
1
1
1
2
1
1
1
0
2
2
2
1
1
2
1
1
2
1
1
1
1
1
1
0
2
1
0
2
0
2
2
1
1
1
0
0
1
2
1
1
1
1
0
1
2
1
0
0
1
0
1
1
1
0
0
0
1
0
1
2
1
1
1
1
1
1
1
1
1
0
1
1
1
5
1
0
1
1
1
2
1
0
1
2
1
1
1
1
2
1
1
1
1
2
0
2
1
1
2
2
0
1
1
2
1
1
0
2
2
2
1
2
2
1
0
0
1
1
1
4
1
1
1
1
0
1
1
2
0
1
0
2
3
1
0
2
2
0
2
2
1
1
0
1
2
1
1
1
1
2
0
1
1
1
1
2
0
1
0
1
0
2
0
1
2
1
1
1
1
1
2
2
1
0
0
1
1
1
0
1
1
3
1
0
1
1
1
1
2
1
1
2
1
1
0
1
1
1
1
1
1
2
1
0
1
1
1
1
1
0
1
1
1
0
1
0
2
1
1
2
1
0
1
1
1
2
0
1
0
1
1
1
2
1
2
1
1
1
1
0
1
1
1
1
2
1
2
1
1
0
1
1
1
2
1
1
0
0
0
1
0
0
1
1
1
0
1
1
0
0
2
1
1
0
1
2
1
2
1
1
0
1
0
0
0
1
1
2
1
0
0
2
1
1
2
0
1
0
0
1
2
1
0
1
1
1
1
0
0
1
0
0
0
0
0
0
1
0
1
1
1
1
1
2
2
1
2
1
1
2
1
1
2
0
0
1
0
0
2
1
1
1
1
0
1
1
0
1
1
0
1
1
1
1
2
1
0
0
1
2
1
2
1
1
0
0
1
1
0
1
1
1
1
1
1
0
2
2
0
2
1
1
1
1
1
1
2
1
1
0
1
2
2
1
1
1
0
0
1
0
0
0
0
1
1
1
0
1
1
0
2
2
0
2
1
1
1
1
1
2
1
0
0
0
1
2
0
2
1
1
2
1
1
1
0
1
1
2
0
2
1
4
2
2
1
1
2
0
1
1
1
0
0
2
2
0
2
1
1
1
1
1
1
1
2
2
1
1
2
0
1
1
1
0
1
0
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
2
2
0
2
1
1
1
0
1
1
2
1
0
1
1
1
0
2
1
2
1
0
0
0
1
1
0
2
1
0
1
1
0
1
1
0
0
2
1
1
0
1
1
2
0
1
1
2
1
2
6
1
0
2
1
1
3
2
1
1
2
1
0
1
2
2
1
1
2
1
1
1
1
1
2
1
2
1
1
0
0
1
2
1
2
1
0
1
1
2
1
3
2
1
2
1
1
0
2
2
1
0
1
0
1
0
0
0
1
1
1
2
0
2
2
1
2
1
1
1
1
2
0
0
1
1
0
2
1
2
1
2
1
1
0
2
1
1
2
1
1
1
1
0
2
1
1
1
2
2
0
1
0
1
2
1
1
1
1
0
1
0
0
2
1
1
2
1
1
1
1
0
1
1
1
1
1
0
2
0
1
2
0
1
1
2
1
1
1
2
1
2
1
1
1
1
1
0
1
0
1
1
1
1
1
1
0
1
0
1
0
1
1
1
1
0
1
0
0
1
2
0
2
2
1
1
0
1
1
1
1
0
1
0
1
1
1
0
1
2
1
0
0
2
2
1
1
2
2
0
2
0
1
1
1
1
0
1
2
1
1
1
0
3
1
1
0
1
0
0
1
1
0
1
1
2
1
1
1
1
0
1
2
1
0
2
0
1
2
2
1
2
1
2
1
1
1
1
1
1
2
0
1
0
2
1
0
2
1
3
1
0
1
0
2
1
0
1
1
0
1
2
0
2
2
0
1
0
2
1
1
0
0
1
0
0
2
2
0
2
0
1
0
0
1
1
0
1
1
0
1
1
0
2
2
1
2
2
2
0
2
1
1
1
1
1
0
1
0
1
2
0
2
3
2
1
1
1
0
0
0
0
0
0
2
1
1
1
1
2
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
1
2
0
1
1
0
0
1
2
0
1
0
1
1
0
2
1
1
1
1
2
0
1
1
0
0
2
1
3
1
1
1
2
1
0
1
1
2
1
2
1
2
1
1
1
2
2
2
1
0
1
2
1
1
1
0
0
1
1
0
0
1
0
2
2
0
2
0
0
2
1
0
0
2
1
0
0
2
1
1
1
0
0
1
0
0
0
0
1
1
1
1
2
0
2
0
2
1
1
0
1
3
2
1
1
1
2
1
1
0
1
0
1
0
1
1
2
1
1
1
3
1
0
1
2
1
2
0
2
1
3
2
1
1
2
0
2
2
1
2
0
1
0
1
0
0
1
1
0
0
1
1
1
0
1
1
2
0
0
2
1
2
1
0
1
1
0
2
0
1
1
0
1
0
2
1
1
1
2
0
2
1
1
1
1
1
0
0
0
2
0
1
1
2
1
1
0
2
3
2
1
1
1
2
1
3
2
1
1
1
1
0
1
0
2
0
2
1
2
2
2
1
1
2
0
1
1
1
1
2
1
1
1
2
0
1
0
0
0
2
0
2
0
0
2
1
2
0
2
1
1
3
2
1
1
1
0
1
2
1
0
1
1
1
1
1
1
0
1
0
2
1
1
0
2
1
2
1
2
1
1
2
2
1
1
2
2
0
1
1
2
0
2
1
2
1
0
2
1
0
1
3
0
0
2
0
1
1
1
1
1
1
1
1
0
2
1
1
1
1
1
1
0
2
1
1
2
1
2
2
1
1
2
0
1
2
1
0
0
1
1
0
2
2
2
0
2
1
1
1
2
1
1
2
2
0
1
1
2
1
0
1
1
0
1
0
0
0
1
0
2
0
1
1
0
0
1
1
2
0
2
1
1
0
0
1
0
0
1
1
0
2
1
1
2
2
0
1
1
1
1
0
1
1
1
1
1
1
1
2
1
2
1
0
1
1
0
2
1
1
1
2
1
0
0
0
1
0
0
0
1
1
0
1
0
1
1
1
1
1
0
1
0
1
1
1
0
1
0
1
1
1
1
2
1
1
0
1
2
1
1
1
0
1
1
2
0
1
0
1
2
1
1
2
1
1
1
2
1
1
0
1
0
1
0
1
0
1
0
1
1
0
0
0
1
0
0
2
2
0
0
1
1
1
1
0
0
1
1
1
1
2
0
1
1
0
0
0
1
0
1
1
2
0
1
1
0
1
1
0
1
2
1
1
2
0
1
0
1
1
1
1
0
0
2
2
2
1
2
0
2
2
0
1
0
0
1
2
1
0
0
1
2
0
1
0
2
0
2
0
2
1
0
0
1
2
0
2
2
1
1
1
1
0
1
0
1
0
0
1
0
0
1
1
1
0
1
1
1
2
2
2
1
1
1
1
1
2
0
1
1
1
1
2
1
1
1
0
2
1
1
0
3
1
0
0
2
0
1
2
3
2
1
2
2
1
1
2
2
1
0
2
1
1
0
0
2
1
1
1
1
1
2
1
1
0
1
2
1
2
0
1
1
0
0
1
0
0
2
0
0
0
0
1
2
1
0
1
2
2
1
1
0
1
1
1
1
1
1
1
1
1
2
1
1
0
2
1
1
0
1
2
2
1
1
2
2
1
1
1
2
2
0
2
1
1
1
1
1
2
0
2
1
2
0
0
1
2
1
2
1
1
2
1
1
0
0
1
3
2
1
1
1
2
0
0
1
2
2
1
0
1
1
0
2
1
1
1
1
1
1
1
0
0
2
1
2
1
1
1
0
1
0
0
0
2
1
2
1
1
1
2
0
1
1
0
1
1
1
1
2
1
0
1
4
0
0
1
1
1
1
0
2
1
1
2
0
1
1
1
1
2
1
4
0
3
1
1
1
3
1
2
2
0
2
1
1
2
1
0
1
2
1
1
1
0
1
0
2
1
1
1
0
2
1
1
2
0
3
2
1
0
1
1
2
0
0
0
1
1
1
1
1
0
2
0
1
1
1
1
2
1
0
1
0
1
1
1
1
0
1
2
1
3
1
2
0
0
1
1
1
2
1
1
0
1
1
2
1
1
2
0
1
1
0
1
1
1
0
2
1
0
1
0
1
2
2
1
1
1
0
1
1
1
0
0
1
2
2
2
0
2
1
0
0
1
1
1
1
1
0
1
0
1
0
2
2
1
1
1
1
1
1
2
1
0
1
0
1
1
2
0
1
1
2
0
0
1
1
0
1
2
2
2
1
1
1
1
1
1
1
0
2
3
1
0
1
1
1
1
1
2
2
1
1
1
0
0
2
2
2
2
1
1
1
0
2
2
1
1
2
1
1
0
1
0
0
2
2
2
1
1
1
1
2
1
0
1
1
0
2
1
1
0
1
0
1
2
2
1
1
0
1
1
2
2
2
1
1
2
2
2
2
1
0
1
1
2
2
1
1
1
0
1
2
0
1
1
1
0
1
1
1
1
0
1
1
0
1
1
3
0
0
1
1
1
1
2
1
1
2
0
1
1
2
2
1
0
2
1
2
2
1
1
2
0
0
0
1
1
1
2
2
0
2
2
0
1
1
1
2
0
0
0
0
1
1
1
0
2
0
1
2
2
0
1
1
0
3
1
2
0
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
2
0
1
0
1
0
0
1
0
1
1
2
0
2
1
1
1
2
2
3
1
2
0
1
1
1
2
2
0
2
2
2
0
1
0
2
2
0
2
1
1
1
0
2
0
2
2
0
2
1
0
2
2
2
2
1
0
1
0
2
1
0
0
2
0
0
1
2
2
1
0
1
1
1
1
1
0
1
1
1
0
2
0
0
2
0
1
1
1
0
0
0
0
0
0
1
3
1
2
0
2
1
0
3
0
1
1
1
0
2
0
1
1
1
0
3
1
2
1
0
0
0
1
1
1
0
1
1
0
2
1
0
2
0
0
2
0
1
0
1
1
2
1
2
0
2
2
2
2
2
2
1
0
2
2
1
1
1
0
2
1
0
1
1
0
2
2
0
2
2
1
1
0
2
1
0
1
1
0
1
2
2
1
1
1
1
2
2
1
2
0
1
1
0
1
1
1
1
0
0
1
0
0
1
0
0
1
1
1
1
2
1
0
0
0
1
1
2
1
1
0
1
1
2
1
2
0
1
1
1
1
0
2
1
2
2
1
0
0
1
2
2
0
0
1
1
1
0
2
1
1
1
1
2
2
1
1
1
0
0
1
0
0
0
1
2
0
1
1
1
1
1
0
1
1
2
1
1
1
0
0
1
2
1
1
0
1
1
2
2
1
2
1
1
1
1
1
2
1
1
2
1
1
1
1
1
2
2
1
0
0
2
1
1
1
1
0
0
1
1
1
1
0
0
1
2
0
0
1
1
1
1
2
0
1
0
2
2
1
0
1
0
1
0
1
1
1
0
1
0
1
1
2
1
1
0
1
0
1
0
0
2
2
0
1
1
0
2
1
2
1
1
0
1
2
2
1
1
1
1
2
1
0
1
1
0
2
0
2
1
1
0
1
1
2
1
2
1
1
0
2
1
1
2
2
1
2
1
1
0
0
0
1
2
0
1
0
1
1
1
2
1
1
1
1
1
1
1
0
1
0
2
0
2
0
2
0
1
1
0
1
0
0
0
0
1
1
2
0
1
4
0
1
1
0
2
0
1
2
1
1
0
1
0
0
2
2
2
1
0
1
1
1
2
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
1
1
0
2
1
0
1
1
1
0
1
0
1
0
1
0
1
1
1
1
0
1
0
0
0
2
0
1
1
1
2
1
1
0
2
2
1
1
0
1
2
2
1
1
0
1
1
1
1
2
1
0
2
1
2
1
1
1
2
1
2
2
0
1
1
1
1
1
2
1
1
2
0
1
1
1
0
2
1
0
0
2
2
1
0
0
0
1
0
1
1
1
2
2
0
1
1
2
2
1
1
0
1
2
1
1
1
0
1
1
0
2
2
0
1
1
0
1
0
1
1
2
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
1
0
0
2
0
0
1
0
2
1
1
2
2
0
1
1
1
1
2
2
1
1
0
0
0
2
1
1
1
0
1
1
1
1
1
1
1
2
1
2
0
0
1
1
0
1
2
1
2
1
10
1
2
0
1
0
1
2
1
0
1
2
2
1
0
0
0
1
0
1
0
1
0
1
1
2
0
2
1
0
0
2
0
2
2
1
0
1
1
0
2
2
1
3
1
3
1
1
1
1
2
1
0
1
1
1
1
1
1
1
2
2
0
1
1
2
1
1
0
1
1
2
1
1
1
0
1
1
1
1
0
1
2
2
0
0
1
1
2
1
1
0
0
0
1
2
0
0
1
2
2
2
0
1
1
2
2
1
0
2
2
0
2
2
0
1
2
1
1
0
0
1
1
1
1
1
1
0
1
2
0
1
2
1
1
0
0
0
0
1
0
0
1
0
1
2
1
3
0
2
2
1
0
1
2
0
0
0
1
0
1
1
2
1
1
1
1
0
1
0
1
1
1
0
0
1
2
0
2
1
0
2
1
3
1
1
0
1
1
1
1
0
1
1
1
2
1
0
2
1
2
4
0
4
0
1
1
2
2
1
1
1
1
4
1
2
0
2
1
2
3
2
0
0
0
1
0
1
1
1
0
1
1
0
0
1
3
0
0
1
0
0
1
0
1
1
1
0
0
0
1
2
0
2
0
1
1
2
3
3
2
2
0
1
1
0
0
2
0
1
1
1
1
1
1
1
1
0
1
1
1
0
1
1
0
2
2
1
1
0
2
2
2
1
2
1
0
1
1
2
1
0
0
1
1
1
1
2
2
0
1
1
2
0
2
1
1
0
2
1
1
1
1
1
1
1
2
0
0
0
1
2
2
1
2
0
1
0
1
1
2
1
2
1
2
1
1
2
0
1
1
2
1
1
1
2
2
0
1
2
2
1
0
1
1
1
1
2
1
1
1
1
0
1
2
1
0
0
1
1
2
1
1
1
1
0
0
1
0
0
1
1
1
0
1
1
0
2
1
1
2
2
2
1
0
1
1
0
0
1
1
1
0
1
1
1
1
2
1
1
2
1
1
1
2
0
0
1
1
0
1
2
0
0
1
1
1
1
0
0
1
0
1
2
1
1
2
2
1
1
2
0
0
1
0
1
0
0
1
0
2
2
1
1
1
0
1
2
2
2
0
1
1
2
1
1
2
1
0
2
1
1
2
2
1
1
1
1
0
1
0
1
2
1
1
0
0
1
2
1
2
1
0
1
2
2
0
1
1
1
1
1
0
2
1
2
1
1
0
1
0
1
1
2
2
0
1
0
0
1
1
1
1
1
1
1
1
2
1
1
1
1
0
2
2
2
1
0
1
1
1
1
0
1
2
1
1
1
1
1
0
1
2
1
2
1
1
1
0
0
1
0
1
2
1
0
1
1
1
1
2
1
1
0
1
1
1
1
1
0
1
1
1
0
2
2
1
1
1
1
1
2
0
2
0
1
1
0
2
0
2
1
1
2
1
0
1
0
1
1
1
0
0
1
1
0
0
1
1
2
1
2
0
1
1
2
0
2
2
0
1
2
2
0
2
1
0
0
1
1
1
0
2
1
0
1
1
0
0
1
2
0
1
1
1
1
2
1
1
1
0
1
1
0
1
0
1
0
2
2
0
1
1
0
1
1
1
1
1
2
1
0
0
1
1
1
1
0
2
1
0
1
1
0
2
1
1
1
2
1
0
0
0
2
0
0
1
0
0
2
1
1
1
1
2
1
1
1
1
2
0
1
2
1
1
2
1
0
1
2
0
1
1
1
0
1
2
0
2
1
1
1
1
2
2
1
2
0
2
0
1
1
1
0
2
1
2
1
1
1
1
1
2
1
0
1
1
2
0
1
0
2
0
0
2
2
2
3
1
0
1
0
1
1
0
1
1
1
0
1
1
1
0
1
2
1
0
0
1
0
3
1
0
1
1
0
2
1
2
1
1
1
2
0
2
2
1
1
1
1
3
2
2
1
1
1
1
1
0
1
1
0
1
1
1
1
1
1
0
2
0
0
1
1
0
0
2
2
0
1
1
1
1
2
0
2
0
2
1
2
1
1
0
1
0
1
1
1
1
2
0
1
1
1
0
1
1
0
1
1
0
1
0
1
1
1
0
1
1
1
2
2
1
1
1
0
1
0
1
2
2
0
1
1
1
1
1
1
2
1
2
0
1
1
1
2
0
1
1
1
0
1
1
2
0
1
0
1
1
1
1
1
0
1
0
0
1
1
2
0
2
0
1
0
1
1
0
1
2
0
2
1
1
1
1
0
2
1
1
1
1
2
1
2
2
2
2
1
1
0
1
1
1
1
1
1
1
1
0
1
1
2
0
0
1
2
1
1
2
1
0
2
1
0
1
1
0
1
1
1
0
2
1
0
1
2
2
0
3
0
0
0
0
1
1
2
2
0
1
0
0
0
1
1
0
1
1
1
1
2
1
0
2
0
2
1
0
0
2
0
1
1
1
1
1
0
0
1
1
1
1
1
0
0
0
1
2
0
2
0
1
1
0
1
1
1
2
2
1
1
0
1
0
2
3
1
2
1
0
3
2
1
1
1
1
2
1
1
0
2
2
0
0
1
1
2
1
1
0
2
1
0
1
1
2
1
0
0
0
0
0
2
1
1
1
0
1
1
1
1
1
1
1
2
1
0
1
0
1
1
0
0
0
1
0
0
1
2
2
1
0
1
1
1
2
0
1
1
0
2
1
2
1
1
1
1
0
0
1
0
1
1
1
1
2
2
1
0
0
1
1
1
1
2
0
1
1
2
0
1
0
1
1
2
1
1
2
2
1
1
1
1
0
1
1
1
2
0
1
1
2
0
1
2
1
0
0
1
2
1
2
3
1
0
2
0
1
0
2
0
2
1
2
0
0
1
1
4
1
1
1
1
1
1
2
0
2
1
0
0
1
2
1
2
1
1
3
1
1
0
1
3
1
0
3
1
2
1
1
2
0
1
1
1
0
0
1
1
2
1
1
1
0
0
2
0
1
1
1
1
1
0
1
1
1
2
1
1
1
0
1
2
1
0
2
0
2
0
2
0
1
1
2
0
0
2
0
1
0
1
0
1
2
1
1
1
2
1
1
2
2
0
2
0
1
1
1
1
1
1
1
1
1
1
1
0
0
0
1
1
0
1
1
1
1
2
1
1
0
1
1
1
1
0
1
1
1
1
0
0
0
1
2
2
0
1
1
0
1
1
1
0
0
1
1
2
0
1
1
1
1
1
2
2
0
2
2
0
2
1
2
2
0
1
2
1
1
1
0
0
1
0
1
2
1
1
0
0
0
1
2
1
0
2
0
2
1
0
1
0
1
1
2
1
1
1
1
0
0
0
2
1
1
1
0
1
0
1
1
2
0
1
2
0
2
1
0
0
1
1
2
0
1
0
1
2
1
1
1
2
1
1
0
2
1
1
1
2
2
1
0
1
0
2
1
1
2
1
1
2
2
0
1
1
1
2
2
2
1
1
0
1
1
2
1
1
0
1
2
1
1
1
1
2
2
0
1
1
0
1
0
1
2
0
0
1
2
1
2
0
1
0
2
0
1
1
1
1
1
1
2
1
0
1
2
0
1
1
0
1
1
1
2
1
1
2
1
2
2
1
1
2
0
1
0
0
1
1
1
1
0
1
1
0
2
1
1
1
0
1
1
1
1
1
1
2
1
0
2
0
0
1
2
0
1
1
1
1
1
2
0
2
1
0
2
0
0
1
0
1
2
1
2
2
2
1
4
1
1
1
2
1
1
1
2
2
1
1
0
2
3
0
1
0
1
1
1
1
0
1
1
1
1
1
1
1
1
1
2
1
0
1
2
1
2
2
1
0
1
1
2
1
1
1
1
1
0
1
0
0
1
2
1
1
1
1
1
2
1
0
2
0
0
1
0
2
0
1
2
1
1
1
1
0
1
2
0
1
0
2
1
1
1
1
1
1
0
1
2
2
0
1
1
2
2
2
2
2
2
0
0
1
1
2
2
1
1
0
1
1
1
2
1
1
1
1
1
1
1
0
1
0
1
1
1
1
2
1
0
1
2
1
4
1
2
1
1
2
2
1
2
1
2
1
1
1
0
1
2
0
2
2
1
1
1
0
1
2
0
0
3
1
0
1
1
1
1
0
2
0
0
1
1
2
1
2
0
1
1
2
1
1
1
2
0
0
1
1
0
1
6
1
2
0
2
0
2
0
0
1
0
1
0
1
0
2
1
1
1
1
1
0
0
1
2
0
1
1
0
0
1
2
1
2
0
2
1
1
0
1
1
0
0
1
1
1
1
2
1
2
0
1
1
2
1
2
1
2
1
0
1
2
1
1
2
1
1
1
0
1
1
1
2
1
0
0
1
2
1
0
0
0
1
1
0
1
1
0
1
2
0
0
1
0
1
1
0
1
0
2
1
1
0
1
0
1
1
1
1
1
1
0
1
1
1
0
0
0
1
1
2
1
1
1
2
1
1
0
1
1
1
2
1
2
1
0
0
2
1
2
0
0
1
2
0
1
2
1
1
1
2
0
3
0
1
1
1
0
0
1
0
1
1
2
1
1
1
1
1
0
2
1
1
2
2
2
1
0
1
1
0
1
2
1
0
2
1
1
0
1
1
1
1
1
0
1
2
1
0
1
1
1
2
1
0
1
1
1
0
0
1
1
2
1
0
1
1
0
0
2
1
2
1
2
0
1
1
0
0
1
2
3
1
1
1
1
0
0
1
1
1
1
2
1
1
2
1
1
2
0
2
1
2
1
1
1
3
3
2
1
1
1
0
1
1
0
1
0
0
3
2
0
1
1
0
0
1
1
1
1
0
1
1
0
1
1
2
1
2
1
0
2
0
2
2
1
0
1
1
1
1
0
1
2
1
1
1
2
1
1
2
1
0
0
2
0
1
1
0
1
1
1
0
2
1
2
1
1
1
1
0
1
0
1
2
0
0
2
1
2
1
1
1
2
0
2
2
1
1
0
0
0
1
0
0
1
1
2
1
2
2
1
1
0
1
0
1
1
0
2
1
1
1
0
0
1
0
1
1
1
1
1
1
0
1
2
2
0
1
0
0
1
0
1
1
1
2
0
1
2
3
2
2
3
1
1
1
2
0
1
0
0
2
0
2
1
0
0
1
2
2
2
2
1
0
1
2
1
0
1
1
0
1
2
1
2
1
0
1
0
1
1
1
1
2
2
1
1
1
2
1
1
0
0
1
0
0
0
1
1
0
1
1
0
0
1
1
1
0
1
0
1
0
2
0
2
2
0
1
1
1
0
2
0
0
1
0
1
0
2
1
2
2
1
2
2
0
1
1
2
0
0
1
1
1
2
0
2
1
0
2
1
0
0
1
1
1
1
1
1
0
1
1
2
1
2
1
2
2
1
1
2
1
1
2
1
2
2
0
1
1
2
0
0
1
1
1
0
1
3
1
1
1
0
1
1
1
2
1
1
2
0
1
1
2
1
1
1
0
2
1
1
1
2
1
1
2
2
2
1
1
0
0
0
1
1
0
0
1
0
2
1
1
1
0
1
1
0
0
0
1
2
2
2
1
1
0
1
0
1
1
2
2
1
0
1
2
1
0
0
1
1
1
1
0
1
1
2
1
2
1
1
1
1
1
1
1
1
0
0
1
1
1
0
0
1
1
1
1
4
2
1
1
3
2
1
1
2
0
2
2
2
0
0
0
0
1
0
2
0
1
0
1
0
1
0
2
0
2
1
0
1
2
1
0
0
0
1
2
2
1
0
0
1
0
2
1
2
0
1
0
2
1
1
2
0
1
1
1
2
0
2
2
1
1
1
2
0
0
1
1
1
2
1
3
0
1
1
1
0
1
2
1
0
0
1
0
2
1
1
1
1
2
0
2
1
1
1
0
2
1
1
0
2
0
0
2
1
1
2
2
1
1
1
0
1
1
1
2
0
0
0
0
1
1
2
1
0
2
1
1
2
0
0
1
2
1
1
0
0
0
1
2
0
0
1
1
0
2
2
0
1
2
1
1
0
2
0
1
1
1
1
1
0
1
0
0
0
0
0
1
1
0
1
2
0
1
1
1
0
1
1
1
1
1
1
1
0
2
2
1
1
1
0
2
1
0
2
1
2
1
1
1
1
1
2
1
1
1
1
1
1
0
0
0
2
0
1
2
0
2
1
1
1
1
2
1
2
0
1
0
1
1
1
1
0
2
2
1
1
1
1
0
0
0
1
1
1
1
0
2
1
1
2
1
1
0
1
1
0
1
1
2
2
1
1
1
2
2
0
2
1
1
1
1
0
1
1
1
2
0
1
1
2
1
1
0
0
0
0
1
2
0
2
0
0
0
0
0
1
1
2
1
1
1
2
1
2
1
2
1
2
1
2
1
1
1
0
2
2
1
1
1
0
2
0
1
1
1
0
0
1
1
0
1
0
1
1
1
1
1
1
1
1
1
2
2
0
1
0
1
1
2
2
0
1
2
1
1
1
1
0
1
0
1
1
1
0
0
1
2
1
0
1
2
1
0
1
0
0
1
1
2
3
2
1
1
1
0
1
0
0
1
2
1
1
1
0
0
1
1
0
0
1
2
1
1
0
1
2
1
1
0
1
1
0
1
0
0
1
0
1
1
1
1
0
1
1
0
0
1
2
2
1
1
0
1
1
2
0
1
0
0
0
1
1
0
1
2
2
2
0
1
1
0
1
2
1
2
0
1
0
0
1
1
2
1
1
0
1
1
1
0
2
2
2
0
2
1
1
1
0
1
1
2
1
1
2
2
1
1
1
0
0
1
0
1
1
1
0
1
0
2
0
3
0
0
1
1
2
1
2
1
2
1
0
2
2
1
1
1
2
0
2
0
1
2
1
0
2
3
1
2
2
2
1
0
1
1
1
1
0
1
2
2
1
1
1
2
1
0
1
2
1
0
1
0
1
0
1
1
2
0
1
1
1
0
2
2
1
0
2
1
1
1
2
0
1
2
1
0
1
0
1
2
2
2
1
0
1
0
1
1
2
2
0
1
1
0
2
0
1
1
2
2
1
1
1
0
1
1
1
1
1
2
0
1
1
2
1
1
0
2
1
0
2
3
1
0
0
1
1
0
1
2
1
1
1
0
1
1
1
1
1
0
1
0
1
0
1
1
1
0
2
0
1
1
1
2
0
2
0
2
1
1
1
0
0
0
0
1
1
1
0
1
0
0
1
1
0
1
1
1
3
2
2
0
1
1
1
1
1
0
0
1
1
2
1
0
1
0
1
0
1
2
1
1
0
3
1
1
1
2
1
0
1
2
1
2
2
0
0
1
0
2
1
2
1
1
1
0
0
3
0
2
0
1
2
2
2
2
1
0
1
1
1
1
1
0
1
1
1
1
0
0
2
0
1
2
2
0
2
0
1
1
0
2
2
1
0
0
0
1
2
1
1
2
1
2
2
1
1
0
0
2
0
1
0
2
0
0
2
1
1
1
1
2
0
1
1
1
1
1
0
0
1
1
0
2
1
1
1
1
1
2
1
0
1
2
0
1
1
1
0
0
1
1
1
3
1
1
1
2
1
1
0
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
0
1
1
2
0
2
2
0
1
3
1
1
2
0
1
2
0
1
1
1
1
1
2
2
1
2
1
2
1
0
2
1
0
0
1
1
0
0
0
1
0
1
1
2
2
1
1
0
1
2
1
2
1
0
1
0
1
1
1
2
0
1
2
1
1
1
1
0
0
1
1
2
2
2
1
1
1
1
2
1
0
0
0
1
1
1
1
2
1
1
0
0
1
0
1
1
1
2
0
1
0
1
2
0
2
1
0
1
1
1
0
1
0
1
2
4
3
0
2
1
0
1
0
2
1
3
0
1
0
1
0
1
2
1
0
0
2
1
0
1
3
0
0
2
2
1
1
2
1
0
1
1
0
0
0
0
2
0
0
0
2
1
1
0
1
0
3
1
1
0
1
0
1
0
0
1
2
0
0
1
0
3
2
1
0
0
2
1
1
1
0
1
2
0
2
1
2
1
0
1
0
0
1
2
2
1
1
1
1
0
1
1
1
0
1
0
1
1
2
2
2
1
0
2
1
1
1
0
1
1
2
1
2
0
1
0
1
0
1
2
1
1
2
1
2
1
0
0
0
0
1
1
1
2
0
1
0
0
1
1
0
0
2
0
1
0
0
2
2
0
1
1
3
0
1
2
1
0
2
1
1
1
0
1
1
0
0
2
2
1
1
1
1
1
2
2
1
0
0
0
1
1
1
1
1
0
2
1
1
1
1
1
1
1
1
0
0
1
2
2
1
1
1
2
1
1
1
1
1
0
1
1
2
1
1
1
1
1
2
1
0
0
0
1
1
1
0
2
0
1
2
1
0
2
2
2
0
2
0
2
1
1
2
0
1
1
0
3
0
0
0
2
0
1
1
1
1
0
1
2
1
1
1
1
0
2
0
1
1
1
0
0
2
1
0
2
1
2
0
0
1
0
1
2
2
0
1
1
0
1
0
0
1
2
1
2
0
1
0
2
1
1
1
1
2
0
0
1
2
1
0
1
1
1
0
2
0
1
1
1
1
1
0
1
1
1
1
0
2
1
0
1
0
1
0
1
2
1
1
2
1
2
1
1
2
0
0
2
3
3
1
0
0
1
1
2
1
1
0
1
1
1
1
1
1
1
0
1
1
1
1
1
0
1
2
0
1
1
1
1
2
1
0
2
1
1
2
0
1
0
1
0
1
1
1
1
1
1
1
0
2
0
1
0
1
1
0
0
1
0
2
1
0
2
0
1
1
0
1
1
1
1
2
2
1
2
5
2
2
0
0
0
2
1
0
0
1
1
0
1
0
1
1
1
0
0
2
1
0
1
2
1
1
2
0
0
1
1
1
2
1
2
0
1
1
1
2
0
0
1
1
1
1
1
0
0
1
2
2
1
1
1
0
1
2
1
1
2
1
2
1
1
0
1
0
1
0
2
0
2
1
1
0
1
0
1
4
2
1
2
1
0
2
1
1
1
2
2
1
1
1
0
1
0
0
2
1
1
2
1
1
2
1
1
1
1
0
1
0
2
0
1
1
2
0
1
0
1
0
4
1
3
1
1
0
2
2
1
1
1
1
1
1
1
1
0
1
2
0
2
0
1
1
2
2
2
1
2
1
2
0
2
0
1
1
2
1
0
2
0
1
1
0
1
1
2
2
1
1
0
1
1
0
0
1
3
3
2
1
0
0
2
1
2
2
1
5
2
1
1
0
2
3
1
2
0
1
1
0
1
0
1
0
1
1
0
1
1
1
2
1
1
2
0
1
2
2
1
2
2
0
1
1
2
1
0
0
0
0
2
2
1
0
2
0
1
1
1
0
0
2
2
1
0
2
0
1
1
1
2
2
2
1
1
1
2
0
0
1
2
2
0
3
1
1
3
0
1
0
1
1
0
0
1
1
2
0
1
0
0
0
0
1
0
1
1
1
0
0
0
0
1
2
2
2
0
1
0
0
0
0
1
0
2
0
0
1
1
2
1
2
1
1
0
1
1
2
1
1
0
0
0
2
0
0
1
1
1
2
0
1
1
1
0
0
2
2
2
0
2
1
1
1
1
1
0
1
1
0
2
0
1
2
1
1
2
0
1
2
2
1
1
1
0
1
2
2
0
1
0
0
1
2
1
2
0
0
1
2
1
1
1
0
2
0
1
1
1
1
2
2
2
0
0
2
2
0
2
1
1
1
1
2
1
0
2
1
0
0
0
2
0
2
1
1
1
1
1
2
1
1
0
1
2
1
2
1
2
0
1
1
0
1
2
1
1
0
0
1
1
2
0
1
0
1
0
1
0
2
1
1
0
2
0
2
1
1
1
0
1
2
1
1
0
0
0
1
0
1
0
1
1
1
1
1
0
1
1
0
1
1
1
1
1
2
2
1
1
1
1
1
2
0
1
0
1
1
1
1
0
1
0
1
1
2
0
1
2
0
1
1
1
2
1
0
1
2
0
1
1
3
0
2
0
2
2
2
0
2
1
1
2
0
1
2
2
0
1
1
1
0
1
2
1
1
1
0
2
2
2
1
0
1
1
0
2
2
0
0
1
2
1
0
0
1
2
1
1
1
1
1
2
2
1
1
2
1
1
0
0
2
2
1
2
2
1
0
1
1
1
1
1
1
1
1
1
2
1
2
1
1
0
2
1
2
1
1
2
1
0
0
0
0
1
1
1
0
2
1
2
1
0
1
2
1
1
1
1
2
2
1
1
1
0
2
1
2
1
1
1
1
0
1
2
1
0
2
1
2
2
0
2
1
1
1
1
2
1
3
0
0
1
2
1
0
0
2
1
0
2
2
2
3
1
2
0
2
0
1
1
0
1
1
0
1
1
0
1
1
2
0
2
1
1
2
1
1
1
2
0
0
0
1
1
1
2
2
2
1
1
1
1
2
1
1
0
0
1
0
2
1
1
2
2
0
0
2
2
1
1
1
1
2
2
1
1
0
1
2
1
0
1
1
1
2
0
0
1
0
0
0
2
1
2
0
1
1
1
1
0
2
1
1
1
1
2
1
0
0
1
2
0
1
0
2
1
2
1
1
1
0
1
1
1
1
0
0
1
0
1
1
1
1
1
0
1
1
1
1
1
0
1
1
1
0
1
0
2
1
1
1
1
2
0
1
1
1
1
1
1
0
1
0
2
1
1
0
2
1
0
1
1
0
0
1
1
2
0
1
1
1
2
1
1
1
1
2
0
1
2
0
1
0
1
1
1
1
0
2
1
1
1
1
0
1
2
0
1
0
1
0
0
0
0
1
1
0
2
2
1
0
1
1
0
2
1
0
0
0
1
1
2
2
2
1
1
1
1
1
0
0
1
1
1
1
1
1
0
2
1
0
1
1
1
1
0
1
2
1
1
1
2
1
1
1
1
1
1
1
0
1
0
1
1
2
0
0
2
0
0
2
0
1
0
1
0
1
1
0
2
1
0
0
1
2
1
1
2
1
1
2
0
1
0
2
1
2
2
2
1
1
2
1
0
1
1
2
0
1
2
1
1
1
1
1
2
2
1
1
2
1
2
1
1
0
2
1
2
1
1
0
3
2
1
2
1
1
2
2
1
0
1
1
0
1
1
1
1
2
1
0
2
1
2
1
1
3
1
0
1
2
2
2
1
0
1
1
0
1
2
0
2
2
0
2
1
2
2
0
1
2
1
2
0
1
1
0
2
0
2
0
1
1
1
0
0
0
2
0
1
1
2
0
2
1
0
0
1
0
1
2
0
1
0
2
0
0
0
1
1
1
2
1
1
0
0
0
2
1
2
1
0
0
0
1
1
2
0
1
1
1
0
1
0
1
1
1
2
1
0
1
1
0
1
1
0
2
1
0
2
0
2
1
1
1
2
1
2
2
0
0
1
1
1
0
0
1
1
3
1
1
0
0
0
1
1
0
1
0
0
0
3
1
0
0
1
1
1
1
0
1
0
0
1
2
0
2
1
1
1
1
1
1
2
0
2
0
1
0
1
2
1
1
0
0
0
0
1
0
1
1
1
1
0
1
1
0
1
1
2
1
1
2
1
1
2
1
0
0
0
0
1
1
0
1
1
1
1
1
0
2
1
1
2
2
2
1
1
0
2
1
1
1
0
1
1
1
1
1
0
1
2
0
1
1
2
1
1
0
3
2
0
1
2
1
1
1
2
1
0
0
2
0
1
1
0
0
1
1
1
1
1
1
1
1
2
0
0
1
1
1
0
2
0
1
0
2
1
0
0
0
0
1
0
1
2
2
2
1
1
0
2
2
1
1
1
0
0
1
0
1
0
2
0
1
0
0
0
1
1
1
1
2
1
0
0
1
1
1
1
2
0
1
1
2
1
1
1
1
2
2
2
0
1
1
1
1
1
1
1
2
0
1
3
0
0
0
2
0
1
2
2
0
0
0
2
2
1
2
0
2
1
0
1
2
2
0
0
0
2
1
0
1
0
0
1
1
1
1
0
2
1
2
1
2
1
1
1
1
0
1
1
0
1
2
0
1
1
2
1
2
1
2
2
1
1
1
1
0
1
1
2
1
1
3
1
1
0
2
2
1
1
1
1
1
0
0
2
0
0
2
0
1
0
1
0
0
0
0
0
2
0
0
0
1
2
2
1
0
2
0
2
1
0
0
2
1
1
1
0
2
2
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
2
0
2
2
0
1
2
1
0
0
1
0
0
0
0
1
1
2
2
1
1
2
2
1
3
1
2
1
0
1
1
1
1
1
0
1
1
0
1
1
1
1
1
0
1
1
1
1
2
2
1
2
2
2
2
1
1
3
0
2
1
0
0
1
2
1
1
1
4
2
1
0
0
1
1
1
0
1
2
2
0
0
1
1
1
1
2
0
1
3
0
1
1
0
0
1
2
2
0
0
1
1
1
1
0
0
1
0
0
2
1
1
1
1
1
1
1
2
1
1
1
0
0
1
1
2
1
0
0
0
1
1
1
2
2
1
2
0
1
1
1
0
1
2
2
1
1
0
1
2
0
0
0
2
1
1
2
1
1
0
1
0
1
2
2
2
1
0
3
0
1
1
1
1
0
1
1
2
2
1
1
2
0
0
0
2
2
1
1
1
2
1
1
0
2
1
1
1
2
1
2
1
0
0
2
1
1
0
1
1
1
1
1
1
1
1
1
1
1
0
2
2
2
1
0
0
0
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
2
0
1
1
1
0
1
1
2
0
1
1
2
1
2
2
2
1
1
0
1
1
0
1
0
0
0
1
0
0
0
3
1
0
1
0
1
2
0
2
0
2
1
2
1
1
1
2
2
0
0
1
1
0
2
1
0
1
0
0
2
3
1
1
1
2
1
0
2
2
2
2
1
1
1
2
0
1
1
1
1
1
2
1
2
1
1
2
1
1
1
0
2
1
1
2
0
1
1
0
1
1
1
0
0
1
1
1
1
0
0
2
2
2
1
3
2
1
2
0
2
1
2
1
1
1
0
1
2
1
1
0
1
1
0
0
2
0
0
1
1
0
2
2
1
3
3
1
2
1
1
1
0
0
0
1
3
0
2
1
0
1
1
0
1
1
2
1
0
1
1
1
1
1
1
1
0
0
1
1
0
2
1
1
0
1
0
1
1
1
1
2
2
1
2
1
0
0
2
2
1
2
1
0
1
0
0
1
0
0
1
0
1
1
1
1
1
1
2
2
1
1
2
0
2
1
0
1
1
0
1
1
0
1
0
0
1
0
1
1
0
0
0
1
1
1
1
1
0
1
0
2
0
0
0
0
1
1
0
2
0
3
0
2
2
2
0
1
0
3
2
0
0
1
1
2
1
0
1
2
1
2
1
0
0
0
2
2
1
1
0
2
1
1
1
2
0
1
1
1
0
0
2
1
1
2
1
1
1
1
1
1
2
1
0
2
1
0
0
0
2
0
1
1
0
1
0
0
1
2
1
0
1
2
0
1
1
1
2
2
1
1
0
1
0
1
1
1
2
0
1
0
0
0
1
2
1
2
0
0
2
1
2
0
1
2
1
0
1
0
1
1
0
1
1
1
0
0
1
1
1
0
0
1
0
0
0
2
2
1
1
1
0
1
1
1
1
2
1
2
1
2
1
1
1
1
0
0
0
0
1
0
1
0
1
0
1
0
0
2
1
1
0
1
0
1
2
1
1
1
1
1
1
1
2
1
1
1
0
0
2
1
2
0
0
2
1
0
1
1
1
1
2
1
1
0
1
1
1
1
2
0
2
0
2
0
2
0
1
1
1
1
1
2
2
2
1
2
1
0
1
2
1
0
1
1
1
1
1
0
2
1
0
1
0
1
1
1
1
1
0
0
1
2
1
1
0
2
2
2
1
1
1
1
1
1
2
1
0
2
0
2
2
2
1
1
1
0
0
1
2
1
1
2
1
2
1
2
1
1
1
0
0
2
1
1
1
0
2
1
0
1
0
1
1
1
1
1
0
1
0
1
1
2
0
1
1
1
1
1
0
1
0
1
0
2
0
0
1
1
1
1
0
1
0
1
2
0
1
2
1
1
1
1
1
1
0
1
1
0
4
0
2
0
3
1
2
2
2
0
1
0
2
2
0
1
1
1
1
1
1
1
1
1
0
1
2
0
1
1
2
2
1
1
0
2
1
1
1
1
1
2
1
0
0
2
1
1
0
1
1
2
1
1
0
1
2
1
2
1
0
2
0
2
1
1
2
1
2
1
1
1
0
1
1
3
1
1
1
1
0
2
1
0
2
1
0
2
1
2
2
1
1
1
0
2
1
1
1
2
1
2
1
2
0
0
1
1
1
1
0
1
1
0
1
1
0
1
2
1
2
1
0
0
0
0
1
2
2
0
0
1
2
0
0
1
2
0
1
1
2
1
0
1
0
2
1
1
0
1
2
2
1
0
1
1
0
1
0
1
2
1
1
0
2
0
2
1
1
0
1
1
2
0
1
0
3
1
1
1
0
0
0
1
1
2
1
1
0
0
2
2
2
1
0
2
0
1
1
1
0
1
0
0
1
0
1
3
2
0
0
0
2
1
1
1
0
0
0
1
1
1
2
1
1
1
2
1
1
1
7
1
1
1
2
1
1
2
2
0
1
1
1
1
1
1
0
2
2
1
1
1
1
1
1
3
1
1
2
0
0
0
2
0
0
1
1
1
1
1
1
2
1
1
0
1
2
1
3
0
6
0
2
2
1
1
2
0
1
0
1
2
1
0
2
1
1
0
2
1
1
1
1
0
0
0
2
1
2
0
2
1
1
1
0
1
1
2
1
1
1
2
0
1
2
1
3
1
1
2
2
1
2
3
1
1
0
0
0
0
0
1
0
1
1
1
1
1
0
2
2
2
2
2
1
0
1
0
1
1
0
0
1
2
1
1
0
2
0
0
2
2
1
1
2
1
0
0
2
0
1
1
0
0
0
1
2
1
0
2
1
1
1
0
0
1
2
1
1
3
2
1
2
0
2
2
0
1
2
0
0
0
1
1
1
0
1
3
0
1
0
2
1
0
2
1
1
0
0
0
2
1
1
0
1
1
1
1
1
2
2
1
1
1
0
0
0
2
1
1
2
1
1
1
2
0
1
1
0
2
1
0
1
0
2
1
0
0
1
1
2
0
1
0
1
2
0
2
2
1
0
1
0
0
1
0
1
0
1
0
1
1
1
1
1
1
0
1
2
3
1
1
2
1
0
1
1
0
1
1
1
2
1
0
1
2
0
1
2
1
2
1
1
0
0
1
1
0
2
0
2
1
2
2
0
1
3
1
1
1
2
1
1
2
2
1
2
0
1
1
0
0
1
0
1
1
2
1
0
1
0
1
1
0
1
1
0
1
1
3
0
0
1
1
1
1
2
1
0
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
0
0
2
2
0
2
0
1
1
2
1
1
1
2
1
1
1
1
0
1
0
2
2
1
0
0
1
1
1
0
1
1
2
0
2
2
2
1
0
0
0
0
1
2
1
2
2
1
1
2
0
1
2
0
2
0
2
1
1
1
0
1
2
1
2
0
1
2
1
0
2
0
2
1
1
2
2
0
1
1
2
1
1
1
1
0
0
1
2
1
2
1
1
2
1
1
0
0
1
2
1
2
1
1
1
1
1
1
0
1
0
1
2
1
1
0
0
1
1
1
1
0
0
2
1
2
0
0
2
1
2
0
0
2
1
2
2
2
1
0
1
1
1
1
1
0
0
1
0
1
1
2
1
0
0
2
1
1
1
1
0
1
0
1
1
0
1
1
0
1
1
2
1
2
2
0
2
1
0
0
2
2
1
1
1
1
2
1
2
1
2
0
2
2
0
1
1
1
0
2
1
1
2
1
1
1
2
0
1
1
0
2
0
1
0
0
0
1
2
0
1
1
1
1
1
1
1
0
1
0
1
1
2
0
1
1
1
1
2
1
1
2
0
1
0
1
0
1
0
0
1
0
0
1
2
2
1
2
0
0
1
0
2
1
1
2
0
2
2
2
2
2
1
1
1
1
1
0
1
0
1
0
1
1
1
0
1
0
2
1
1
0
1
1
1
1
0
1
0
1
1
1
2
1
0
2
1
2
1
2
2
0
0
0
3
1
1
1
0
1
2
2
2
1
1
2
0
1
0
0
2
1
1
1
1
0
1
2
1
1
0
0
1
2
1
2
0
1
1
2
2
1
1
0
2
2
0
1
1
0
0
1
1
1
2
0
1
1
1
0
1
0
2
1
0
1
2
0
1
1
2
2
1
1
1
2
1
1
2
0
2
1
2
0
1
2
0
0
1
1
1
2
2
1
2
2
2
1
0
1
2
1
0
2
1
2
1
2
0
0
0
2
1
1
1
2
0
1
0
1
1
0
0
0
1
1
0
1
0
0
1
1
2
0
2
1
1
0
1
0
2
2
2
2
1
0
1
2
0
2
1
2
0
0
0
0
0
2
0
0
0
1
1
2
0
1
2
1
1
0
1
0
1
2
0
1
2
0
1
1
0
1
1
0
2
1
1
0
2
1
1
1
1
0
1
2
1
1
0
0
1
2
1
2
3
1
0
2
2
1
1
1
0
1
2
0
0
2
0
0
0
1
1
1
1
1
0
0
2
2
0
1
1
0
2
2
0
1
1
1
2
1
1
1
1
2
2
0
0
1
1
2
1
1
1
3
0
2
1
1
0
0
0
1
0
0
0
1
1
0
2
1
1
0
0
0
0
1
2
2
0
1
1
2
0
0
0
2
0
0
1
2
1
0
0
1
1
1
1
1
2
1
0
2
1
1
1
2
1
1
0
2
1
2
1
0
0
0
1
1
0
1
0
1
0
1
0
1
1
1
0
0
2
1
1
1
1
1
1
2
1
1
2
2
0
0
1
1
1
0
2
2
1
1
2
2
2
1
0
1
1
0
1
0
1
2
1
1
0
1
1
1
1
0
1
1
1
1
2
0
1
0
2
2
2
1
1
0
0
1
1
1
0
1
0
2
2
0
1
1
1
1
2
0
1
1
1
1
0
1
1
2
2
2
2
2
1
1
1
1
1
1
0
1
1
0
1
0
0
2
0
1
1
0
1
1
2
1
0
1
1
0
1
0
3
0
1
2
1
1
1
0
1
1
1
2
2
1
0
1
1
0
0
1
2
1
1
0
0
0
1
0
2
0
2
0
2
1
1
1
0
2
0
0
1
1
1
0
1
3
0
3
0
1
1
2
1
1
1
0
1
2
3
2
1
1
0
1
2
2
1
1
2
1
2
2
1
2
0
0
1
0
0
1
1
1
2
1
2
1
1
2
1
1
0
1
1
2
0
1
1
1
2
1
1
1
1
0
0
1
2
0
0
2
1
0
0
1
0
1
3
0
1
1
1
0
1
2
1
1
0
0
2
1
1
1
1
2
0
1
1
0
0
0
1
1
1
2
2
2
1
1
1
2
1
0
0
1
1
0
1
0
0
2
0
2
2
0
2
0
2
1
0
0
0
2
2
1
2
0
1
1
2
1
0
1
0
0
2
0
2
1
2
1
1
0
1
1
0
1
1
3
1
1
1
0
0
0
1
4
0
0
0
1
2
1
1
2
1
0
1
1
1
1
1
1
0
0
1
1
0
2
2
1
1
0
0
0
0
0
1
1
0
0
1
1
0
2
1
2
0
1
1
1
2
1
0
0
0
1
3
0
1
2
0
2
0
0
1
0
0
1
0
2
2
1
2
1
0
0
3
1
2
1
0
0
1
1
1
1
0
2
0
1
1
1
1
0
1
1
1
0
1
1
1
1
0
0
0
1
1
1
0
0
1
2
1
2
2
2
1
2
1
1
0
0
0
1
1
1
2
1
1
1
0
0
1
0
1
0
2
0
1
1
1
2
1
2
2
1
0
2
0
2
1
1
0
0
2
1
1
0
1
1
2
1
1
1
1
1
1
1
0
1
0
2
2
1
2
0
0
1
0
2
1
1
1
1
1
1
2
1
1
2
1
2
0
1
1
1
0
1
2
0
1
3
1
2
2
0
1
0
0
2
0
0
0
1
2
2
1
1
0
0
1
1
0
2
1
1
1
0
1
0
1
1
0
0
0
1
2
2
0
1
1
1
0
1
1
1
2
2
0
2
0
0
1
2
1
0
1
1
1
1
3
1
1
0
1
1
0
1
1
2
0
2
2
2
1
1
1
2
1
2
0
1
0
0
0
0
0
1
2
0
1
0
1
2
1
1
1
1
0
1
1
2
1
1
1
0
1
0
2
1
2
1
2
0
1
2
2
0
2
0
1
0
2
1
1
1
1
0
1
1
1
0
2
1
1
1
1
0
1
2
1
0
1
2
2
1
0
0
1
1
0
1
0
2
1
0
3
1
2
1
1
1
1
3
1
1
1
2
2
1
1
1
2
1
0
1
0
1
2
1
2
3
1
2
1
1
1
3
1
1
1
2
1
0
1
0
3
1
2
2
1
0
2
0
2
1
1
1
2
2
2
2
2
0
1
0
1
1
1
1
0
1
2
1
0
0
1
0
0
0
0
2
1
0
1
0
1
2
1
1
0
1
1
0
0
0
2
1
1
0
1
2
1
2
0
1
2
0
2
1
1
2
1
0
1
0
1
0
1
1
1
0
1
1
1
1
1
1
0
0
1
1
1
1
0
2
2
2
1
0
1
0
1
1
1
2
0
1
1
1
1
1
2
0
1
1
1
2
2
1
1
1
1
1
1
2
1
1
0
0
1
0
1
1
0
0
1
1
2
2
0
1
2
0
1
1
1
1
0
2
1
1
2
2
2
0
0
1
1
1
0
0
1
1
1
0
0
3
1
3
1
2
1
1
1
0
0
0
2
0
2
0
2
0
2
1
1
1
1
3
1
2
2
1
0
2
1
2
1
1
1
1
2
1
0
2
0
0
2
2
1
1
1
0
1
0
2
0
2
0
0
1
0
1
1
0
1
1
1
1
1
0
1
1
2
1
1
0
1
2
1
1
1
0
0
0
1
1
1
1
1
1
1
0
0
2
0
1
1
0
2
1
0
0
1
1
2
1
1
1
2
2
0
0
0
1
2
0
1
2
1
0
1
0
1
1
1
0
2
1
1
2
1
2
1
2
0
2
1
0
2
1
1
1
2
0
0
1
2
1
1
1
2
2
1
0
0
1
1
0
1
1
1
0
1
0
1
1
3
1
3
2
1
1
1
2
1
1
1
1
3
1
2
0
1
1
2
1
1
2
1
2
1
0
1
2
1
2
4
1
2
0
2
1
1
2
1
1
0
0
1
1
1
2
0
1
0
0
2
0
1
1
1
1
1
1
0
2
0
1
1
2
1
0
0
1
1
1
1
1
1
1
2
1
1
1
2
2
1
2
1
0
0
1
2
1
0
1
2
1
1
1
2
0
0
1
1
2
1
1
2
1
1
1
0
0
0
2
2
1
2
0
0
0
1
2
1
0
2
1
1
1
1
1
1
0
1
2
1
1
1
1
2
0
3
1
1
0
1
1
2
0
2
2
0
2
1
0
1
1
1
1
1
0
1
0
2
1
2
0
1
2
2
0
0
1
1
1
2
1
1
2
0
1
0
0
1
0
0
1
2
2
1
1
1
0
0
1
0
0
1
0
0
1
1
1
2
1
2
1
1
0
0
1
1
1
1
1
0
0
0
2
1
2
0
1
0
1
2
1
1
1
1
1
1
1
1
1
0
2
1
0
2
1
0
2
2
1
0
0
0
0
0
0
0
2
0
1
1
1
1
2
0
0
1
0
0
0
1
2
2
1
1
2
1
1
2
1
1
0
0
0
0
1
1
0
1
0
1
0
0
2
0
0
1
1
1
2
1
1
0
2
1
0
2
1
1
1
2
1
1
2
1
2
1
2
1
0
1
1
1
0
0
2
1
0
1
1
1
2
0
0
2
0
1
1
0
1
0
2
1
1
2
1
1
1
1
0
1
0
1
2
1
1
0
1
0
1
0
1
2
0
1
1
1
1
0
1
1
1
2
3
0
2
0
1
1
2
1
1
2
1
1
1
1
1
1
2
2
2
1
0
0
0
0
1
2
0
2
0
0
1
1
2
0
2
2
0
0
1
1
0
1
2
1
1
2
1
1
2
2
1
2
1
0
0
2
1
2
0
0
1
1
0
1
2
0
1
3
0
1
2
2
0
1
2
1
0
1
0
0
1
0
1
1
1
0
0
0
2
0
0
0
1
1
1
1
1
2
2
1
1
1
2
2
0
1
1
1
0
1
1
0
2
2
1
1
1
0
1
0
1
1
0
0
1
1
2
0
1
0
0
1
1
0
1
1
0
1
1
1
0
0
0
1
1
2
1
1
2
1
0
0
2
2
1
1
2
1
2
0
1
1
1
1
1
1
3
0
1
1
1
0
1
1
2
1
2
2
1
1
1
1
0
1
1
2
1
0
1
1
0
2
1
1
1
1
2
1
1
0
1
1
0
1
1
0
2
1
1
0
1
1
1
2
0
1
1
2
0
2
1
1
1
2
1
1
1
1
0
1
1
2
2
2
2
0
0
1
2
0
1
2
1
2
1
1
1
0
0
1
1
2
1
2
1
1
1
0
0
1
2
0
0
1
0
1
2
0
1
0
0
1
1
1
0
0
0
0
1
1
0
0
1
1
1
0
1
1
2
0
0
1
1
1
1
0
1
1
1
0
1
1
0
1
2
1
2
2
1
2
2
0
1
2
0
1
2
0
1
2
1
1
1
1
2
1
1
0
1
0
1
1
0
2
1
1
1
1
1
0
1
1
1
1
0
2
1
2
2
1
1
1
2
1
1
1
0
1
1
0
1
1
1
2
1
1
2
2
0
2
0
1
0
0
0
2
2
1
2
2
1
0
1
2
2
0
0
1
0
1
1
1
1
0
0
0
0
1
2
0
0
1
1
1
1
2
0
0
0
1
1
2
1
1
1
2
0
2
0
2
1
0
2
2
1
0
1
1
2
2
1
1
2
1
1
2
1
0
1
1
1
1
2
1
1
1
1
1
2
2
1
1
0
0
1
0
2
0
1
2
0
1
2
1
1
1
1
1
1
1
1
1
0
1
1
2
1
1
1
2
0
1
2
1
0
1
1
1
1
1
0
0
1
0
0
0
0
1
1
1
1
2
0
1
1
2
0
1
1
0
0
1
2
1
1
1
0
2
0
1
1
1
0
2
0
1
1
1
0
0
1
0
1
2
0
2
1
0
1
1
0
1
0
2
1
2
0
1
2
1
0
1
0
0
1
2
1
1
0
1
2
1
0
0
2
2
2
3
0
1
1
2
2
0
0
0
1
0
0
0
1
0
1
0
1
1
0
1
1
2
2
0
2
2
1
1
1
1
1
2
0
2
2
1
1
1
1
0
2
2
1
1
0
1
2
1
0
1
1
0
1
0
1
1
1
0
1
0
2
1
0
1
1
1
0
1
1
2
1
1
2
1
1
1
1
0
1
0
0
0
1
1
1
2
1
2
1
1
2
1
1
2
1
2
2
2
1
1
1
1
2
1
0
1
1
0
2
0
1
1
1
1
1
1
1
2
0
1
1
1
1
2
0
2
1
1
1
1
0
0
0
1
1
1
0
1
0
2
1
1
1
3
1
1
2
1
0
2
1
0
1
1
0
1
0
1
2
0
1
2
1
1
1
1
1
1
2
1
2
0
2
0
0
1
1
1
1
0
1
0
1
2
1
1
0
0
1
1
2
2
0
2
0
1
0
1
2
1
1
1
3
2
0
1
1
2
1
1
0
0
0
0
2
0
1
1
1
1
1
0
0
1
0
0
1
1
0
1
1
1
1
0
1
2
1
1
2
1
2
2
1
2
1
0
0
1
1
0
1
2
0
1
1
0
1
1
1
1
2
1
1
1
1
1
0
0
2
0
1
2
0
1
2
1
0
1
0
1
0
1
0
1
1
0
1
1
2
2
0
1
0
1
1
2
0
2
1
1
1
1
1
1
2
1
1
0
1
0
2
2
0
1
1
0
1
3
2
0
1
0
2
2
0
1
1
1
1
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
2
2
2
0
0
2
1
1
2
1
0
0
0
1
1
2
1
2
0
2
1
1
1
1
0
1
1
2
0
1
1
1
2
1
0
1
1
2
0
1
1
0
1
0
1
1
1
1
1
0
0
1
2
1
1
1
1
0
0
1
0
0
3
1
1
1
0
1
2
1
3
0
0
1
2
1
1
1
1
0
1
1
2
1
0
1
0
0
1
0
1
1
1
0
0
1
1
1
0
1
1
1
0
2
1
1
0
1
1
2
1
1
2
1
0
2
1
2
1
1
0
1
1
1
2
1
0
0
0
1
1
1
1
0
1
1
1
2
2
1
2
0
3
1
2
1
0
2
1
0
1
0
0
2
1
0
1
0
0
0
2
1
1
0
2
1
0
1
2
1
1
1
0
0
1
0
1
1
1
1
0
1
0
1
3
0
0
1
1
1
2
1
1
0
1
1
1
1
1
1
1
1
1
2
1
0
1
2
0
1
0
2
0
2
2
1
1
1
2
1
1
1
2
1
1
1
2
2
1
0
2
1
2
3
1
1
2
1
2
3
1
0
1
2
1
1
2
0
2
0
2
2
3
1
1
1
0
2
0
0
0
0
1
0
2
0
2
2
1
1
0
2
0
2
0
1
1
1
3
0
0
1
1
2
1
1
2
1
0
1
1
1
0
2
0
1
0
2
0
0
0
0
1
1
1
1
2
2
1
0
2
1
1
1
0
0
2
2
1
0
1
1
1
1
1
0
1
1
1
2
1
0
1
1
1
0
0
2
1
0
2
1
0
2
2
1
2
1
0
2
0
1
1
1
2
1
2
0
2
1
1
2
1
1
0
0
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
0
1
1
2
1
2
1
1
1
1
2
1
2
0
0
1
1
0
0
1
1
1
2
0
1
1
1
1
3
0
0
2
1
1
1
1
1
1
2
0
1
1
1
2
1
2
3
0
0
0
1
0
1
2
0
1
1
1
1
1
0
1
1
1
2
2
2
1
0
1
2
1
3
1
0
0
0
1
1
0
0
1
1
3
0
2
0
0
0
2
2
1
0
1
0
1
1
0
1
1
1
0
2
2
0
1
1
1
0
2
0
1
0
2
0
2
1
2
1
2
1
0
1
1
1
1
2
1
2
1
0
1
0
0
1
1
0
1
2
2
1
1
0
0
1
1
1
2
1
2
1
2
1
0
0
2
1
1
5
1
1
2
0
2
0
1
2
2
0
1
0
1
2
0
0
1
1
1
2
1
1
0
1
0
0
1
1
1
0
1
0
1
0
1
0
0
1
1
2
1
2
0
2
0
2
0
0
6
2
1
0
2
1
1
1
2
1
2
2
0
1
1
2
1
1
0
0
1
0
2
2
0
0
1
0
1
0
0
2
2
1
0
1
2
1
0
2
0
0
1
2
1
0
1
2
1
1
1
1
1
2
1
0
2
0
1
0
1
1
1
1
2
1
1
1
1
0
1
1
2
1
3
1
0
1
1
1
1
0
1
1
1
0
1
0
2
1
1
1
2
0
1
0
0
1
2
1
0
1
1
1
1
0
1
1
1
1
2
1
0
1
1
3
1
1
1
1
2
1
1
1
0
1
1
1
2
0
2
1
0
0
1
1
0
2
2
0
1
1
1
1
2
1
2
2
1
1
1
1
2
0
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
0
1
0
1
2
1
1
2
2
1
0
1
0
2
0
1
0
2
1
1
1
1
2
2
2
0
2
2
2
2
2
0
1
0
0
0
0
1
0
0
0
0
1
1
2
2
1
0
2
0
2
0
0
2
1
0
0
0
1
0
2
1
1
0
2
0
2
0
2
0
0
2
0
1
2
1
2
1
0
0
2
0
2
1
0
1
2
1
0
2
1
2
1
1
1
2
1
2
1
1
2
1
1
1
1
1
1
0
0
1
1
1
0
2
0
0
1
0
2
1
0
1
1
1
1
4
1
1
2
1
2
0
1
3
1
1
0
0
2
1
2
0
0
0
1
0
1
1
0
1
1
1
1
1
1
0
2
2
2
1
1
2
1
2
1
1
1
1
2
0
1
2
1
0
2
2
1
2
0
2
1
1
1
0
2
1
2
0
0
1
1
1
1
2
1
2
1
2
1
1
1
0
0
2
1
1
1
1
1
1
0
1
0
1
0
2
0
1
0
0
1
1
0
1
1
1
1
1
1
2
0
1
0
1
2
1
1
0
2
1
2
1
1
1
2
2
1
0
1
1
1
1
1
2
0
0
1
0
0
1
1
1
1
1
2
2
1
1
1
1
1
2
1
0
2
0
0
2
1
1
0
2
0
2
0
2
1
2
1
0
0
1
2
1
0
2
0
1
1
1
0
1
1
2
2
1
1
1
2
0
1
1
2
2
2
2
1
0
1
1
1
0
1
1
1
1
1
1
0
1
1
0
2
1
0
2
0
0
0
0
2
1
0
1
2
2
1
1
0
1
0
1
1
0
2
1
0
2
1
2
2
1
2
0
2
2
0
2
2
1
1
0
1
1
2
2
0
0
1
0
2
0
0
1
2
0
0
1
1
0
1
1
0
1
1
0
1
1
1
2
0
0
1
1
2
2
2
1
1
1
2
1
1
1
2
1
1
2
1
1
1
1
1
2
0
0
1
0
1
0
1
2
0
1
1
1
2
0
1
1
0
2
1
1
1
1
1
1
0
1
1
2
0
2
0
0
1
0
1
0
2
0
1
0
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
2
0
0
1
0
1
1
1
1
0
0
1
1
1
1
2
1
1
1
1
1
1
2
1
0
1
0
1
1
1
1
2
1
1
1
0
2
1
2
2
2
0
0
1
1
1
1
0
2
1
1
4
2
1
1
2
0
0
1
2
1
1
0
0
0
2
2
1
0
2
1
2
0
0
0
1
0
0
0
0
1
2
0
0
0
0
1
1
1
0
1
0
0
1
0
0
2
1
1
1
2
1
0
1
0
2
1
2
0
1
1
1
1
3
2
1
1
2
0
1
0
0
1
2
1
2
0
1
1
1
1
1
1
2
1
0
2
0
1
1
1
0
0
1
2
2
0
2
1
1
0
0
1
1
0
1
1
1
1
1
1
1
1
1
1
0
0
1
2
1
1
1
2
1
0
1
0
0
1
1
1
0
0
2
1
0
0
1
1
1
0
1
3
0
0
0
1
1
2
1
0
1
1
1
0
2
0
2
2
0
0
0
2
2
0
2
0
2
1
0
0
2
0
2
1
1
0
1
1
2
1
1
0
0
1
0
1
0
2
0
1
2
0
1
1
2
1
0
1
2
1
1
2
1
0
0
2
4
1
1
1
2
0
0
0
1
1
1
2
1
1
2
2
1
2
1
1
0
0
2
1
1
2
1
1
2
0
1
2
1
2
2
1
0
1
2
0
1
1
0
0
1
1
1
0
2
1
1
1
1
1
0
1
1
2
0
0
1
1
0
3
1
0
0
0
1
0
1
0
1
1
2
1
1
1
1
1
1
0
0
1
0
1
0
1
2
0
0
1
1
1
2
2
2
1
0
1
0
0
1
1
2
0
0
1
0
1
1
1
0
1
0
0
1
0
2
0
0
1
2
2
2
3
1
0
1
1
1
0
1
1
1
1
0
1
1
0
1
1
1
2
2
0
1
1
0
1
1
2
1
0
1
2
0
2
2
1
1
2
2
2
0
0
1
1
1
2
1
0
0
1
0
0
2
0
2
0
1
0
2
1
0
1
2
1
1
0
1
2
0
0
0
2
1
1
1
2
1
0
1
0
1
1
1
0
1
1
1
1
0
1
2
1
2
1
1
1
1
1
2
2
0
0
0
2
2
1
2
1
1
0
1
1
0
2
1
1
1
1
1
0
1
2
0
2
1
0
1
1
1
0
0
0
0
1
1
1
1
1
1
0
0
1
0
2
1
1
1
0
0
2
0
2
0
1
0
0
1
0
1
1
2
1
1
1
0
2
0
2
0
2
1
1
0
1
2
1
2
1
1
1
0
0
2
1
1
1
1
1
1
1
0
1
1
1
0
1
1
1
1
1
1
2
1
1
1
1
0
2
2
1
2
0
0
1
0
0
2
2
0
1
0
1
1
1
1
1
0
0
1
1
1
1
0
1
1
1
2
1
0
0
1
1
2
2
1
0
1
0
2
1
1
1
2
0
1
1
0
1
0
1
1
1
1
1
1
0
0
0
0
1
1
0
1
1
0
0
2
1
1
1
1
0
1
1
1
1
0
1
1
1
2
1
2
0
1
2
1
2
1
1
0
1
2
1
0
1
1
0
0
2
1
0
2
1
1
2
2
1
2
1
1
1
0
2
2
1
1
2
0
0
0
1
0
1
1
1
2
1
0
0
1
2
1
2
1
0
1
2
0
0
1
2
2
0
0
1
1
1
1
0
0
1
0
1
2
0
1
2
0
0
1
0
1
0
1
1
0
2
0
2
0
2
2
0
1
1
0
1
1
1
0
3
3
2
1
0
5
1
0
1
2
0
2
1
2
2
1
2
1
1
1
2
0
1
2
1
2
0
1
1
2
0
2
2
0
0
1
1
1
1
1
1
1
1
1
0
0
1
1
1
1
0
1
1
2
0
2
0
2
1
1
1
0
0
2
0
0
0
0
2
1
2
2
2
2
1
0
0
0
2
2
0
1
1
1
1
2
1
1
1
1
0
1
2
1
1
1
1
1
2
1
0
1
0
3
1
1
1
2
0
2
1
1
1
0
0
1
0
0
1
3
2
1
2
0
1
2
1
1
2
2
0
1
0
2
0
2
1
2
1
1
0
2
2
2
2
1
2
0
2
1
2
1
1
0
1
1
0
2
1
0
1
2
0
1
2
0
1
1
2
1
1
1
2
0
2
1
2
2
2
0
2
0
0
0
0
0
1
1
1
1
0
1
1
1
0
1
0
1
0
1
1
1
0
0
1
1
1
2
1
1
0
1
1
1
1
0
1
0
0
1
1
2
0
1
1
1
0
0
0
1
0
1
0
2
2
0
2
0
1
1
1
1
0
1
1
1
1
0
1
1
1
1
0
2
0
1
1
0
1
1
1
0
2
3
2
2
1
1
0
1
0
1
0
1
0
0
1
2
1
0
1
0
1
2
0
1
2
0
1
1
1
1
1
1
1
2
0
1
2
0
1
2
1
0
1
2
1
1
1
1
2
1
1
0
1
1
0
0
1
0
0
1
1
0
0
1
2
1
2
2
2
0
1
0
0
1
0
1
1
0
0
1
1
1
0
2
2
1
2
1
2
2
0
2
0
0
1
1
0
1
1
2
0
1
1
0
0
1
2
2
1
1
1
0
0
1
1
1
0
0
1
1
0
2
2
1
0
0
1
1
1
2
2
2
1
1
0
1
0
1
1
1
1
0
0
2
2
1
2
1
2
1
1
0
2
1
0
0
2
0
2
0
2
2
1
2
2
2
1
0
1
1
0
3
1
1
0
1
1
1
1
1
2
2
1
2
1
0
0
1
1
1
1
1
0
1
0
1
0
1
1
1
0
2
0
2
0
1
0
1
2
1
2
0
1
0
2
1
1
1
0
0
1
1
0
1
0
1
0
1
1
1
2
1
0
2
1
1
1
0
1
2
2
1
1
0
0
0
0
1
1
1
0
1
1
0
1
2
0
3
4
1
2
0
0
1
2
1
1
2
2
1
2
1
2
1
1
0
0
1
1
1
2
0
1
1
1
2
2
1
1
1
1
0
0
0
0
2
2
0
0
1
2
1
0
1
1
1
2
2
2
1
0
1
1
1
2
1
1
2
1
2
0
1
0
0
2
0
2
1
1
0
1
1
1
1
0
1
1
0
1
0
0
0
2
2
2
2
2
1
1
1
1
1
0
0
1
1
1
0
1
1
0
1
1
1
0
1
1
2
1
2
2
1
0
0
1
0
1
1
1
0
2
1
1
1
0
1
1
1
1
1
1
1
0
1
2
1
1
1
1
0
0
1
0
1
1
1
0
1
1
2
1
2
1
2
0
1
0
0
1
0
2
2
1
1
3
0
1
1
0
1
1
1
1
1
1
0
1
1
0
1
1
1
1
1
0
1
1
2
1
2
0
0
1
1
0
1
1
0
2
1
1
1
2
1
1
0
0
0
0
1
1
0
0
1
1
2
2
1
1
0
0
1
1
1
0
0
2
1
0
1
2
0
0
1
2
1
2
1
1
1
1
2
2
1
0
1
0
1
0
0
1
2
1
0
1
1
0
1
1
0
1
1
1
1
0
2
1
0
1
0
1
0
0
2
1
0
1
1
2
3
4
2
1
0
0
1
0
0
1
0
0
1
1
2
1
0
2
0
2
1
1
0
0
1
2
0
1
0
2
2
0
2
1
1
0
1
0
1
2
0
2
1
0
1
1
2
1
1
0
1
1
2
2
0
0
1
2
1
1
1
1
2
0
0
1
2
2
1
1
2
0
1
0
1
1
1
1
2
1
1
0
1
1
1
1
0
1
1
0
1
1
2
0
1
1
1
1
0
1
1
0
3
2
0
2
1
1
0
0
0
2
1
1
1
1
0
2
2
2
1
0
3
1
0
1
1
0
0
2
2
0
2
0
1
1
2
0
2
0
0
1
0
1
1
1
2
2
2
1
1
0
1
1
0
2
2
1
1
1
1
1
0
1
0
1
0
0
0
0
1
1
1
1
2
1
1
0
1
2
2
0
1
2
1
2
1
1
1
1
1
0
1
0
0
1
1
2
1
1
1
1
0
1
1
1
0
2
1
1
0
1
1
1
1
0
0
2
2
2
1
2
1
1
1
1
1
1
0
1
2
1
2
1
1
1
0
3
1
1
0
0
1
1
1
0
0
0
2
2
1
2
1
1
0
4
0
0
0
0
1
2
0
2
2
0
1
2
1
1
0
2
1
1
2
0
2
1
2
2
0
0
0
1
0
1
1
2
0
1
1
1
2
2
1
0
1
0
1
2
1
2
1
2
1
2
2
1
1
0
2
1
1
1
0
2
1
1
1
0
0
1
2
2
2
0
1
1
2
1
1
1
1
2
1
1
2
1
1
1
2
2
1
1
1
1
1
2
2
0
0
1
1
1
1
1
0
4
1
0
1
1
1
0
0
0
1
1
0
1
1
1
1
1
0
0
0
1
0
1
1
0
0
1
2
1
0
0
1
1
1
1
2
2
0
2
0
2
1
1
1
2
1
1
0
1
3
0
1
1
2
1
1
2
1
2
1
1
1
2
0
1
1
1
1
2
1
0
0
2
2
2
1
1
1
0
1
2
1
1
2
1
1
0
2
0
1
0
2
0
1
0
2
1
1
2
0
1
2
0
0
0
1
1
0
1
2
2
0
2
2
1
1
0
1
1
1
1
3
0
0
1
1
0
1
0
1
2
2
2
2
2
1
1
0
1
1
0
0
1
1
2
1
1
1
0
1
1
2
1
0
2
1
2
1
0
2
2
0
2
1
2
2
1
1
0
2
0
0
2
0
2
0
1
2
2
1
1
2
1
1
1
2
0
2
1
1
2
0
0
2
0
0
2
0
3
2
1
1
0
0
2
1
2
2
2
2
1
0
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
2
1
1
1
0
2
1
0
0
1
1
3
1
1
2
2
2
2
1
1
0
2
3
2
1
1
1
1
2
1
1
2
1
2
0
0
1
1
0
1
1
1
1
1
1
1
1
2
0
0
1
0
1
0
3
1
1
1
0
2
1
1
1
1
0
0
1
1
1
2
2
2
0
0
0
2
2
1
0
1
2
2
1
1
1
1
0
3
1
2
0
2
1
1
2
3
0
1
0
1
1
1
1
2
0
1
1
1
1
0
1
1
1
0
1
0
1
1
2
2
0
0
1
1
1
2
1
1
1
0
1
0
1
0
0
1
1
0
1
1
1
1
1
0
1
1
2
0
1
2
0
2
0
1
1
2
0
0
1
0
0
1
1
0
1
1
1
1
1
1
2
2
2
1
1
1
2
1
1
2
0
1
1
0
2
0
3
1
0
1
1
1
0
2
1
2
1
0
1
2
0
2
1
1
0
0
1
0
2
2
0
1
1
1
1
1
2
1
1
1
0
1
2
2
0
1
1
2
1
1
1
0
1
1
1
1
1
1
1
2
1
0
1
1
0
1
2
0
1
2
0
2
2
0
2
0
1
0
2
1
1
0
0
2
0
0
1
2
0
1
0
0
1
1
1
1
1
0
1
1
1
1
3
0
1
1
1
1
0
2
1
0
1
0
1
2
2
0
2
1
2
1
0
0
1
1
1
0
0
1
2
0
2
2
1
1
1
2
2
2
0
0
1
1
2
0
1
2
1
2
0
1
1
1
0
0
1
2
1
1
0
1
1
2
1
2
1
1
2
2
2
1
0
0
1
2
1
0
1
1
2
1
1
1
2
0
1
2
0
0
0
1
1
1
0
0
1
1
0
0
0
1
1
1
0
1
0
1
1
1
2
1
2
0
1
0
1
1
2
0
1
1
0
0
2
1
2
1
1
2
1
1
1
4
0
1
2
1
1
0
1
0
2
1
1
0
1
2
1
2
2
2
2
1
1
0
0
2
0
0
0
2
2
2
0
2
1
2
1
1
2
1
0
0
0
1
0
1
1
1
0
2
1
1
2
1
1
1
2
1
2
1
2
0
0
2
2
1
0
0
0
2
2
2
1
3
1
2
1
0
2
2
2
1
1
0
0
2
1
1
1
1
2
0
1
1
1
1
0
1
1
2
2
1
0
0
0
1
1
2
2
1
0
1
1
0
1
2
0
4
0
1
2
2
2
1
0
1
1
1
0
1
1
0
2
1
1
2
2
1
1
0
1
1
1
1
1
0
5
1
1
1
0
0
1
1
1
2
1
1
0
1
2
0
0
1
1
3
0
1
0
0
1
0
2
1
0
2
0
1
2
1
0
1
1
1
0
2
2
0
0
1
1
1
1
1
0
1
1
0
2
0
1
0
1
2
0
1
1
1
2
0
0
1
2
2
1
0
1
1
0
1
2
1
1
0
2
0
1
1
2
0
1
2
1
1
1
1
1
2
1
0
1
0
2
1
3
0
1
2
1
1
1
1
1
2
1
1
1
1
0
1
1
2
1
0
1
1
0
4
0
1
2
0
1
3
2
0
2
0
0
0
0
1
3
1
1
2
1
1
1
0
1
1
2
0
1
1
0
1
0
0
2
0
1
1
2
1
2
1
2
1
1
1
2
2
0
0
1
1
1
0
0
2
0
1
1
1
1
0
1
1
2
1
1
2
1
1
1
0
1
1
2
1
0
0
1
0
1
0
0
2
0
1
0
1
0
2
1
0
1
1
0
1
1
1
2
0
1
1
2
1
1
1
1
2
0
0
1
2
1
0
2
0
0
0
1
1
1
0
2
2
1
0
1
2
0
0
2
1
0
1
1
1
0
0
1
0
0
1
1
0
1
1
1
1
0
0
1
1
1
0
0
1
1
1
1
1
1
0
0
1
0
1
0
1
1
0
0
2
1
2
0
1
0
2
2
0
1
1
1
0
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
0
2
0
1
2
2
1
1
2
2
1
1
0
1
0
0
1
2
1
1
1
0
0
2
2
2
1
2
1
2
1
1
0
1
1
0
1
4
1
2
0
1
1
2
1
1
2
1
0
0
2
2
0
0
0
3
1
0
1
1
2
0
1
1
2
1
0
0
2
1
0
1
0
1
1
1
1
1
1
0
1
0
1
1
0
0
0
1
2
0
1
1
1
1
0
1
0
1
2
1
2
0
1
1
2
0
1
2
1
1
1
2
2
1
0
1
1
0
0
2
1
1
1
2
1
1
0
1
1
1
1
1
0
1
2
0
1
1
0
1
0
4
2
2
1
0
2
1
0
2
1
0
1
0
2
2
1
2
1
1
1
1
3
2
1
0
1
1
1
1
1
0
0
2
1
1
1
1
2
1
1
2
1
1
1
0
1
1
1
1
1
1
0
1
2
2
1
0
0
0
2
2
1
2
1
2
1
1
1
0
2
1
1
1
0
0
1
2
1
1
1
1
1
2
2
1
1
0
2
1
2
2
1
1
0
1
1
3
1
1
2
1
0
1
2
1
0
1
1
0
2
0
1
0
1
1
1
0
1
2
1
1
1
1
0
1
0
2
1
0
2
1
1
0
0
1
0
0
1
1
1
2
1
2
2
1
1
2
2
1
0
1
2
1
0
1
1
1
2
2
0
0
1
0
1
1
0
2
1
1
1
2
0
1
0
1
2
0
1
1
1
0
0
0
0
1
1
1
0
0
1
1
1
2
1
1
1
1
1
1
0
0
1
1
0
1
0
1
1
1
1
0
0
1
0
0
2
1
1
2
2
3
2
1
2
2
0
1
0
0
0
0
1
1
1
2
1
2
2
0
0
2
1
1
2
0
0
2
0
1
0
1
1
1
1
1
0
1
2
1
1
0
1
1
2
1
0
1
1
1
1
1
1
0
1
1
1
1
0
1
1
1
0
1
2
2
1
1
0
1
0
1
1
1
2
1
0
0
0
1
1
0
2
1
0
1
1
0
0
0
1
1
1
1
1
1
0
1
1
1
1
1
0
1
1
2
0
2
2
0
1
0
0
1
2
2
1
0
1
2
0
2
0
1
1
1
1
2
1
0
0
0
0
0
2
1
2
0
0
0
2
2
1
1
1
0
1
1
0
2
1
1
1
2
2
0
1
1
0
1
1
0
2
2
1
1
0
2
3
2
0
1
1
1
1
1
0
1
0
1
0
1
2
1
2
2
0
1
0
0
0
1
2
1
1
1
0
2
1
0
0
0
2
1
1
1
2
1
0
2
1
1
2
0
2
1
2
1
1
1
1
0
2
0
0
3
2
0
1
1
2
1
0
1
1
0
0
0
0
1
1
2
0
1
0
1
1
1
1
1
0
2
2
2
1
3
0
1
0
1
1
0
1
1
2
1
0
2
1
1
1
1
0
2
1
1
1
0
1
1
1
1
1
1
1
1
2
0
1
2
0
0
1
1
1
1
2
1
1
1
1
0
1
1
1
1
1
0
2
0
0
1
1
1
2
1
1
2
0
2
0
1
1
2
0
1
2
2
2
1
0
2
1
0
1
1
2
2
1
0
0
0
2
2
1
1
2
0
1
1
1
2
0
1
1
2
1
1
1
0
2
1
2
0
2
2
1
1
2
1
1
0
1
0
1
1
2
1
0
1
2
1
2
1
0
2
1
1
1
1
1
0
2
2
2
2
1
1
0
1
0
0
1
0
2
1
1
1
1
2
2
1
2
1
2
1
1
3
1
2
3
0
3
2
1
2
1
2
0
2
6
2
2
1
1
1
2
1
1
2
1
0
0
1
1
1
1
0
1
1
0
1
2
0
2
0
0
1
1
1
5
0
2
2
2
1
1
1
2
2
1
1
1
0
2
1
1
0
1
2
1
1
2
1
1
2
0
1
1
1
1
1
0
1
2
0
0
0
0
2
2
2
1
1
1
1
1
1
1
1
1
1
0
1
1
0
1
0
1
1
1
0
1
0
1
1
1
1
1
1
1
1
2
2
2
0
1
0
0
1
1
1
1
1
2
0
2
0
1
2
0
1
0
1
2
1
1
1
2
1
1
1
0
2
2
1
1
0
1
1
1
1
0
2
1
0
0
2
0
1
2
1
0
1
1
2
2
0
1
0
1
1
1
2
1
1
0
0
0
0
1
2
0
0
1
1
1
2
0
1
1
1
1
1
0
1
1
0
1
0
1
1
1
0
2
2
1
1
1
2
1
1
2
2
1
0
0
0
2
0
0
0
1
0
1
1
1
2
0
2
0
1
2
1
1
1
1
2
2
1
1
1
1
0
2
1
0
2
2
3
2
1
0
1
0
1
0
0
1
1
1
1
0
2
0
1
0
0
1
1
2
1
1
1
2
2
0
1
0
1
0
1
1
1
1
0
0
1
1
1
1
1
0
0
1
2
2
1
1
0
0
0
1
2
1
2
1
1
2
1
1
1
1
0
1
0
0
0
1
1
1
0
1
2
2
0
0
2
2
0
1
1
1
0
1
1
0
1
2
1
2
1
0
1
1
0
2
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
1
0
0
2
1
1
0
0
1
0
1
1
1
1
1
2
0
0
2
0
2
1
2
1
0
2
2
0
1
2
2
2
2
1
1
0
0
2
2
0
1
1
1
2
1
1
0
1
2
0
0
2
1
0
1
2
1
2
0
1
1
0
2
1
1
1
1
1
0
2
0
1
1
2
0
1
1
1
0
1
1
1
1
1
2
0
1
2
0
2
0
0
2
1
1
2
2
0
1
0
1
1
1
1
1
0
1
0
1
1
1
0
1
0
1
0
1
1
0
2
1
1
0
1
1
2
0
2
2
1
2
1
1
1
2
2
1
2
0
0
2
0
2
2
2
0
1
1
1
2
0
1
1
3
1
0
1
1
1
1
1
0
2
2
0
1
0
1
0
0
1
0
1
1
1
1
1
0
0
1
0
1
1
1
1
1
0
1
2
1
2
1
1
2
1
2
1
1
2
1
1
1
1
1
2
1
1
0
1
0
1
1
2
2
4
2
2
0
2
1
1
0
0
1
1
1
0
1
1
2
1
1
2
1
2
1
2
2
1
2
1
0
2
1
2
1
2
1
1
1
1
2
1
0
2
2
0
1
2
0
1
0
1
0
0
1
2
0
1
2
2
1
1
1
1
1
0
0
4
2
1
2
1
2
1
2
0
1
1
2
2
2
1
1
1
1
0
0
2
2
1
2
1
2
0
2
1
1
2
1
0
1
1
1
1
1
1
1
2
1
1
2
1
0
2
2
1
1
2
1
2
2
0
1
2
1
1
1
1
2
0
2
1
1
1
1
1
2
0
2
2
2
2
0
1
1
0
2
2
0
0
1
0
1
0
0
1
1
1
1
1
0
2
0
1
0
2
0
2
2
1
1
1
1
0
0
2
1
1
1
0
0
2
1
1
1
2
0
1
1
2
0
1
1
0
1
2
1
1
1
1
2
0
1
0
1
0
2
1
0
1
0
1
0
2
1
0
2
1
0
1
1
2
1
0
0
1
2
0
2
1
2
0
2
0
1
1
2
2
1
1
1
1
1
2
1
0
2
1
2
2
0
1
0
1
1
1
1
1
1
0
0
1
1
1
2
0
0
1
0
1
1
1
2
1
1
1
2
0
1
0
0
2
1
0
1
2
0
2
2
2
1
1
2
2
1
2
1
0
2
2
1
1
1
1
2
1
1
0
1
2
1
1
1
0
1
1
0
1
2
0
0
0
1
1
1
1
1
1
1
1
1
1
2
1
0
2
1
1
2
2
1
1
1
1
1
1
0
2
1
1
1
1
2
2
0
2
1
1
0
0
2
2
1
1
1
1
0
0
2
2
2
1
1
0
0
0
0
2
1
0
1
0
1
2
1
0
1
0
3
1
0
2
1
1
1
0
1
1
1
1
1
1
2
1
2
2
0
0
1
1
1
1
2
0
1
0
2
2
1
0
0
0
0
1
1
2
1
2
1
1
1
2
1
2
2
1
0
4
1
2
1
0
0
2
0
0
2
1
1
0
2
2
0
1
1
2
1
1
1
1
1
1
1
2
1
2
0
2
1
1
1
0
0
1
1
2
3
1
1
2
2
2
0
1
0
2
0
1
2
1
1
1
1
0
1
0
1
4
1
0
1
1
1
1
1
1
0
1
1
0
1
0
1
1
0
2
1
0
1
1
1
1
1
3
1
2
2
0
2
1
1
1
2
0
0
1
1
4
2
2
2
1
0
1
0
0
0
1
1
2
1
2
0
0
2
2
0
1
1
1
1
2
1
0
1
2
1
1
1
1
1
1
0
2
0
2
1
2
0
0
1
1
2
1
0
1
1
1
0
1
2
1
0
1
0
1
0
1
0
1
0
2
1
1
0
1
1
0
0
1
1
1
1
1
0
0
1
1
0
1
0
1
0
1
0
1
1
2
0
1
1
2
2
0
3
1
2
1
2
0
1
1
1
1
1
1
1
1
0
0
2
1
1
1
0
2
1
1
0
2
0
1
1
1
1
1
0
0
1
0
0
0
1
2
1
2
2
1
2
2
0
2
1
0
2
1
1
0
2
1
1
2
0
0
0
1
1
1
1
1
3
2
1
1
0
1
0
1
0
2
0
1
0
0
2
2
0
0
2
1
1
1
1
0
2
1
0
1
2
1
1
0
1
1
1
0
0
1
1
3
1
2
0
1
1
0
0
0
2
2
5
1
0
1
0
2
0
2
2
1
1
1
1
1
2
1
0
1
0
1
2
0
1
1
1
2
1
0
0
0
0
1
2
1
0
0
0
2
1
1
1
2
0
2
1
1
1
1
2
0
0
0
0
1
1
1
2
1
2
1
1
1
1
1
2
1
1
2
0
2
1
1
0
1
1
1
1
2
2
0
2
1
1
0
2
2
1
1
1
1
0
1
1
1
0
2
1
1
2
1
1
2
0
1
1
0
1
1
1
0
1
0
0
1
2
2
0
1
1
2
1
0
1
2
3
1
1
1
0
1
1
1
2
0
0
1
1
2
1
0
1
1
0
1
0
2
1
0
1
0
2
0
0
2
1
1
0
0
0
1
0
0
2
2
0
0
1
1
1
2
1
0
2
0
1
0
1
0
1
2
2
2
1
0
1
1
1
0
2
0
0
0
1
0
1
1
1
1
1
2
2
0
1
0
1
1
0
0
1
2
1
7
1
1
1
1
0
1
1
2
2
0
1
0
1
1
0
0
1
2
1
1
1
1
0
0
0
0
1
3
1
1
1
1
2
0
0
1
2
0
1
1
1
2
1
1
1
1
2
1
1
2
2
2
1
1
0
1
0
0
2
0
2
0
0
2
1
1
1
0
0
1
0
1
1
1
2
1
1
0
0
1
1
1
2
1
2
3
2
1
0
1
1
1
1
2
2
2
1
0
1
1
0
2
1
1
1
1
1
1
2
0
0
0
0
2
1
0
1
2
2
0
2
2
2
1
1
1
2
2
2
0
0
1
0
0
2
1
0
0
2
2
2
2
0
1
1
1
1
1
1
1
1
2
1
2
1
1
1
2
1
2
0
1
1
0
0
1
0
1
1
0
1
2
0
2
0
0
0
0
0
1
2
1
2
1
1
1
2
2
2
1
2
0
1
0
2
1
1
0
0
2
1
1
1
1
1
2
2
2
1
1
1
1
2
1
1
1
2
1
2
1
2
2
1
1
0
1
2
1
1
2
1
1
1
1
1
1
1
2
1
0
0
1
0
0
1
2
1
0
1
1
1
1
1
1
0
1
0
0
2
2
1
2
1
1
2
0
2
0
1
0
1
1
2
1
1
0
2
1
0
1
2
0
2
0
1
1
0
2
2
1
1
1
1
2
1
1
2
2
2
2
2
0
2
0
2
1
1
1
0
1
5
1
1
1
1
0
0
2
0
1
0
0
1
2
1
1
2
1
0
1
1
0
2
1
1
0
2
2
0
1
1
2
2
0
2
0
2
1
1
1
1
1
1
1
2
0
1
0
1
1
1
1
1
0
1
1
2
0
2
0
1
2
1
1
1
1
0
1
2
2
1
1
0
1
1
1
2
2
2
1
1
1
1
1
0
0
1
1
2
0
0
1
0
1
1
2
1
1
1
0
0
0
2
2
1
1
0
1
1
2
2
1
0
2
1
1
2
0
0
1
1
2
1
1
1
1
0
1
1
2
2
0
0
0
2
0
2
1
0
1
0
0
1
3
2
1
1
2
1
2
1
1
2
0
0
0
1
3
0
0
1
1
1
1
2
1
1
2
1
1
1
1
1
0
1
2
1
0
1
3
0
2
1
2
0
1
1
1
0
1
2
1
1
1
2
1
2
0
0
2
1
1
1
1
2
1
1
0
2
1
1
1
1
1
0
1
1
1
0
1
1
1
2
0
1
1
2
1
1
0
1
2
1
1
2
1
1
1
2
2
2
0
1
2
1
1
1
2
1
1
1
1
0
0
0
2
2
1
1
2
1
1
1
1
1
0
1
1
2
4
0
1
1
1
1
1
2
1
2
0
0
1
1
0
0
1
1
1
1
0
1
1
1
1
0
2
0
0
2
1
1
0
2
0
1
1
1
1
1
1
2
2
1
0
2
0
0
0
0
0
0
1
0
1
2
2
1
1
1
1
1
1
0
1
2
0
1
1
0
1
1
2
0
1
2
2
1
0
2
1
0
1
1
0
0
1
0
2
1
1
2
1
1
2
0
1
2
1
1
1
0
1
1
2
1
1
1
1
1
0
1
0
1
2
2
2
1
1
3
1
0
0
2
1
1
0
0
1
1
0
0
2
1
1
1
1
2
1
0
1
1
0
1
1
1
1
0
1
1
1
2
5
1
0
1
0
2
0
1
0
1
2
1
1
2
1
1
1
2
0
1
2
0
1
0
1
1
2
1
1
0
1
0
0
1
0
1
1
1
2
1
2
1
0
0
1
1
1
1
0
1
0
1
0
0
1
1
1
1
1
0
2
2
2
1
1
2
0
1
0
2
2
3
2
1
1
1
0
2
2
1
1
1
0
2
1
0
1
0
1
1
3
0
1
1
1
1
0
2
0
0
1
1
1
1
0
1
1
2
1
0
2
1
2
0
0
0
2
1
1
0
1
0
0
1
1
2
1
1
1
1
2
2
2
1
0
1
1
2
0
1
1
2
0
0
1
0
1
0
2
1
0
2
0
0
1
0
2
1
3
2
0
1
2
1
0
2
2
2
0
1
1
1
1
2
2
1
0
0
2
1
2
1
1
2
0
2
0
0
1
0
1
1
1
2
1
1
1
2
3
0
2
2
1
0
2
2
1
1
1
1
1
1
1
1
0
1
1
2
0
2
1
1
1
2
1
1
1
1
1
2
1
4
1
0
0
2
2
2
2
0
1
1
0
0
1
1
0
1
1
2
1
1
0
1
0
1
0
0
2
0
1
0
1
1
1
1
1
2
1
0
1
1
1
1
0
1
0
1
1
0
2
0
1
0
0
1
0
2
1
1
0
1
2
1
1
1
1
1
0
0
1
1
2
1
2
2
0
1
1
2
0
0
1
1
1
1
0
1
0
2
1
1
2
0
1
2
1
1
0
1
1
1
1
1
4
2
1
1
0
1
0
0
1
1
1
1
1
2
1
1
1
1
1
0
1
2
2
0
2
1
1
1
0
1
2
1
0
1
2
2
2
1
2
0
0
1
0
2
1
1
0
2
1
1
1
1
0
1
2
0
1
1
1
1
1
2
1
1
0
0
0
1
1
2
1
1
0
1
0
1
0
1
1
1
1
1
0
0
1
1
1
2
1
1
1
0
1
1
2
0
1
2
0
2
2
1
1
1
0
1
1
1
1
0
1
2
1
1
2
1
1
1
1
1
0
0
0
0
2
0
1
1
1
0
1
0
0
1
1
1
1
1
1
1
0
1
0
0
1
1
3
2
1
1
1
1
0
2
2
1
2
0
0
1
1
2
2
2
2
1
2
2
1
1
2
0
0
1
0
0
1
0
0
0
2
1
2
1
2
0
0
0
1
1
0
0
1
1
0
2
1
1
1
1
2
1
1
1
1
0
0
1
4
0
1
2
2
1
2
0
1
0
1
1
1
1
1
0
0
0
1
2
0
1
0
1
1
0
0
0
1
1
1
0
1
1
0
2
1
1
1
1
2
0
1
1
1
1
1
0
0
2
1
2
2
1
1
0
1
0
1
0
2
2
0
1
1
0
2
2
1
1
0
1
2
1
1
1
1
1
1
0
2
1
2
1
2
0
2
0
0
0
1
0
1
2
1
0
1
2
0
1
0
1
0
0
0
1
0
0
0
0
1
0
2
0
0
2
1
0
1
0
0
2
2
1
2
1
1
2
2
1
2
0
2
3
0
1
1
1
1
1
0
1
0
1
0
1
0
2
1
1
2
0
1
0
2
1
0
0
0
1
0
1
1
0
2
2
0
1
2
2
1
1
1
1
1
1
1
1
0
2
1
3
1
1
2
1
2
1
0
1
3
2
2
1
2
3
1
1
2
0
1
2
0
0
2
0
1
1
1
1
1
2
0
1
1
2
1
1
2
1
1
0
1
1
1
1
0
1
1
1
0
1
1
1
1
0
1
2
1
0
0
1
0
1
1
0
0
1
1
0
1
1
1
1
0
0
1
2
1
1
1
1
1
2
1
2
1
1
0
1
0
0
1
2
1
0
0
0
1
3
2
1
1
1
1
0
1
1
0
1
1
0
2
1
2
2
0
0
1
1
2
1
1
0
1
1
2
2
1
1
0
0
1
2
1
1
0
0
0
0
1
0
1
1
5
1
1
2
0
0
1
0
0
1
0
1
1
1
1
1
1
1
1
1
2
1
1
2
0
1
2
0
0
1
0
1
1
0
1
0
0
1
1
1
0
1
1
1
2
2
1
0
0
1
0
1
1
0
0
0
1
1
0
0
2
2
1
1
0
1
1
0
1
1
2
1
2
2
2
1
1
0
1
0
1
1
1
0
0
1
1
2
1
0
1
2
0
1
2
0
1
0
1
2
1
0
0
1
1
0
1
1
0
1
1
1
0
0
1
1
1
2
2
2
2
1
1
1
0
1
1
1
1
1
1
2
0
1
0
2
0
1
1
1
1
1
1
0
1
1
0
0
0
2
1
1
1
1
0
2
0
2
0
0
1
1
1
1
1
1
1
1
2
2
0
0
0
0
0
1
1
0
1
1
1
0
2
0
0
2
2
1
0
1
2
0
2
1
0
0
1
1
1
0
0
0
0
1
2
0
1
0
0
2
1
1
1
1
1
1
1
1
0
0
0
1
2
0
1
0
1
1
1
1
1
1
1
2
1
1
0
0
1
1
1
2
1
0
1
1
1
0
2
0
1
2
0
2
1
1
1
2
1
2
0
1
1
2
1
1
1
0
1
2
1
2
1
2
2
1
1
1
0
2
0
1
0
1
2
0
1
2
0
1
2
1
1
1
1
2
2
0
2
1
2
1
1
1
0
2
1
0
0
1
1
0
0
2
1
0
2
3
2
1
0
1
0
1
1
1
0
0
0
1
0
1
1
1
0
1
1
1
1
1
2
3
0
3
8
1
1
0
1
2
1
1
0
1
0
0
2
1
0
1
0
1
1
2
0
1
1
0
0
0
2
1
1
1
0
2
2
0
2
1
1
0
1
1
2
0
1
1
1
0
1
1
1
1
0
2
0
0
0
0
0
0
1
1
2
1
2
1
0
0
1
2
1
0
1
1
2
1
1
0
1
0
1
2
1
1
1
1
1
1
0
1
1
0
2
1
1
1
2
1
1
1
0
2
1
1
0
0
1
1
1
0
0
2
2
0
1
1
1
1
0
2
0
2
1
1
1
0
1
2
2
1
1
2
0
2
0
2
1
1
2
0
0
1
2
1
0
2
2
0
2
4
1
0
0
0
2
0
1
1
1
0
0
1
1
1
2
2
2
2
0
2
1
0
1
3
1
0
1
1
0
0
1
1
1
2
1
0
0
3
3
0
2
0
0
1
1
1
2
0
1
1
0
0
2
2
1
1
0
0
1
1
1
1
1
1
1
1
1
1
0
1
1
2
0
1
1
0
0
2
2
1
1
1
2
1
0
0
1
0
1
1
1
0
2
0
1
0
2
1
2
1
0
0
1
0
0
2
1
1
2
2
1
1
0
1
3
1
2
0
1
1
2
0
1
1
2
1
1
2
1
2
0
0
2
0
1
2
1
2
0
2
2
1
2
1
1
0
0
0
1
2
1
1
1
1
1
2
1
1
2
0
0
1
0
2
0
1
0
1
0
0
1
0
1
2
0
1
0
1
1
1
0
0
0
1
1
1
3
0
0
0
3
2
1
1
1
0
0
1
2
1
0
0
1
1
1
2
2
1
1
1
0
1
1
1
2
1
1
1
1
0
1
0
1
1
1
0
1
1
2
0
1
1
1
0
2
2
1
0
0
0
0
2
2
1
1
2
1
0
0
2
2
2
1
0
1
0
1
0
2
1
1
1
1
2
1
2
0
0
1
0
1
0
2
0
2
0
0
0
1
1
1
1
1
1
0
0
1
1
0
2
1
2
1
0
2
2
0
2
0
2
0
1
1
0
1
1
2
0
0
2
0
1
1
1
0
2
0
1
1
1
1
3
3
1
1
0
0
1
1
1
1
1
2
1
0
1
1
1
1
1
1
1
1
2
1
1
1
1
0
1
2
1
2
0
1
1
0
2
0
2
0
1
0
1
0
1
2
1
1
2
1
0
0
2
0
1
1
1
2
1
0
1
2
2
2
2
2
1
1
0
1
2
2
0
1
1
1
1
1
0
1
1
1
0
2
2
1
1
0
1
1
1
1
0
1
0
1
1
0
1
1
0
0
0
1
2
1
1
2
0
1
2
1
1
2
0
2
1
1
0
0
1
1
0
1
2
1
1
2
1
2
3
2
2
0
2
1
1
1
1
0
0
1
3
0
2
1
1
0
1
1
2
1
2
0
1
0
2
1
0
0
0
0
1
1
2
0
0
1
2
2
0
1
1
0
0
0
2
2
0
2
1
1
2
1
0
0
2
1
1
2
1
2
2
1
1
1
0
1
0
1
2
0
0
1
1
2
0
0
1
0
1
0
1
2
0
0
1
2
1
1
0
0
1
1
0
0
0
1
1
0
1
0
0
2
0
0
2
1
1
1
1
1
1
2
3
1
1
1
0
0
2
1
2
1
1
0
1
2
1
2
0
0
1
2
0
1
0
1
1
2
1
1
1
1
0
1
0
2
1
1
1
0
1
1
1
0
1
1
1
0
1
0
1
0
2
1
2
1
0
0
1
2
1
2
1
1
0
2
1
0
1
0
1
0
3
2
2
1
1
2
1
1
2
1
2
0
1
0
1
1
0
0
1
1
2
2
1
1
2
1
1
1
2
1
2
1
2
2
1
2
2
2
0
3
1
0
1
0
0
0
1
1
1
0
1
0
0
0
1
0
1
0
0
0
0
1
1
1
2
1
0
1
1
0
0
1
1
1
0
1
1
1
1
0
0
2
1
2
1
0
1
0
1
1
2
0
1
1
0
2
0
0
1
2
1
2
1
0
2
1
0
2
2
0
1
2
1
1
0
0
1
0
2
1
2
1
0
0
3
2
1
1
1
1
1
1
0
0
0
0
1
0
0
1
1
2
0
1
1
1
1
1
1
1
1
2
0
1
1
1
2
1
2
1
2
1
1
1
1
2
0
0
1
0
0
1
0
1
1
2
1
1
1
1
1
0
1
1
1
2
0
1
2
2
1
1
1
1
0
1
1
1
2
2
1
0
0
1
2
1
0
1
1
1
2
1
1
1
0
2
0
0
1
1
1
1
1
1
1
0
1
1
1
2
0
1
1
1
2
1
0
1
1
2
0
0
0
1
0
2
0
1
2
2
1
1
0
0
1
0
1
1
1
1
0
2
0
2
2
1
1
1
0
1
2
1
1
1
1
1
2
0
2
0
2
1
1
2
1
0
0
2
2
2
1
1
1
2
1
0
2
2
1
1
2
2
1
1
2
0
1
2
2
1
2
0
1
1
0
2
2
0
1
0
0
1
2
2
0
1
1
2
1
0
1
2
1
1
1
2
2
2
1
2
1
1
1
1
1
1
0
1
1
2
1
2
1
0
0
1
2
0
1
0
1
0
0
0
0
2
1
1
0
3
1
2
0
2
1
1
1
1
2
2
1
1
1
2
1
0
2
2
0
1
1
0
0
0
1
1
1
1
0
2
2
2
3
2
0
2
2
1
1
2
1
1
1
0
0
3
1
0
2
1
2
1
1
0
2
2
1
1
2
2
1
0
2
0
1
1
0
1
1
1
1
1
1
1
0
0
2
0
1
1
1
1
2
1
1
1
0
0
1
2
2
0
1
1
2
2
0
2
1
1
1
0
1
1
1
1
1
1
0
0
0
3
1
1
1
1
1
1
0
1
1
2
1
2
1
1
0
2
1
0
1
0
0
1
1
2
2
1
0
1
1
0
2
3
2
1
1
0
0
1
0
2
1
1
2
0
1
0
2
1
0
2
1
0
1
2
0
1
0
1
0
1
2
2
0
1
2
1
2
1
0
1
1
0
0
2
2
2
1
2
1
1
1
0
1
1
1
1
1
2
1
0
1
0
0
1
0
1
1
0
1
0
1
1
0
0
2
1
1
2
2
2
1
0
2
0
2
2
2
1
1
0
0
0
1
2
0
1
3
1
1
1
1
1
2
2
1
1
1
1
1
0
1
0
1
0
1
0
1
1
2
1
0
2
0
1
2
0
0
1
1
1
2
1
2
1
0
1
1
1
0
2
0
1
1
1
0
1
1
1
0
0
1
2
1
1
0
2
1
2
0
1
1
0
0
1
2
0
1
2
2
1
2
0
1
3
1
1
1
1
1
0
1
1
1
1
1
1
1
0
1
0
1
0
3
1
1
0
1
0
1
1
1
2
0
0
1
2
1
1
2
0
1
1
1
0
0
0
0
1
0
1
1
1
1
0
2
0
1
1
0
1
0
1
1
1
0
2
2
1
0
3
0
0
2
2
0
1
1
0
1
2
0
1
2
2
1
1
1
1
2
1
1
1
1
0
0
0
0
1
1
1
2
1
1
1
1
1
0
2
0
1
2
0
1
1
0
1
0
0
1
1
0
0
2
1
2
1
0
0
2
1
0
1
1
2
1
0
0
0
1
0
2
0
0
0
0
0
1
2
0
2
0
1
1
2
2
1
0
1
2
1
1
1
2
2
1
1
2
0
1
0
0
1
1
1
0
2
1
1
1
3
2
2
1
0
1
1
1
1
0
0
0
1
1
0
1
2
1
1
1
0
1
1
1
0
1
1
1
2
2
1
1
1
2
1
2
1
1
2
1
2
0
1
0
1
2
1
1
1
1
1
0
1
2
0
1
2
2
1
0
2
1
0
1
2
0
1
2
1
0
1
0
1
0
1
2
1
1
2
0
2
2
1
2
1
2
1
2
1
2
1
1
1
1
1
2
1
1
1
2
2
2
1
2
1
2
1
0
1
1
2
1
1
2
0
2
2
1
1
0
1
2
1
1
0
0
1
2
2
1
2
1
2
1
1
1
1
0
0
3
1
1
0
0
0
0
1
1
1
2
1
0
0
1
0
1
0
1
2
0
2
1
1
2
1
1
0
2
1
1
1
1
2
1
2
0
1
0
1
1
1
2
2
1
0
0
1
1
0
1
2
1
0
1
0
1
2
0
2
1
1
0
1
0
0
2
2
1
1
0
1
0
1
0
2
1
0
0
1
1
1
1
1
1
2
1
1
1
2
1
1
0
2
2
1
2
1
1
2
2
0
0
1
0
1
1
0
1
2
2
1
1
1
1
1
1
0
1
1
0
2
2
1
0
2
0
0
0
0
1
1
0
1
0
1
1
2
1
0
1
1
0
2
1
1
0
0
0
2
1
1
1
1
1
1
2
1
1
1
1
1
2
2
2
1
1
0
2
1
0
0
0
1
0
1
1
1
2
1
2
1
1
0
2
2
2
1
2
1
1
1
1
1
2
1
1
2
0
0
0
1
1
0
2
1
1
1
1
2
1
1
1
1
1
1
2
0
2
2
0
0
2
2
1
1
1
0
1
2
1
1
2
1
1
1
0
0
2
1
1
1
1
2
1
1
1
0
1
1
1
0
1
0
1
0
2
1
1
1
0
1
2
2
2
2
1
2
1
2
2
0
1
1
1
0
0
1
1
0
1
1
0
1
2
2
1
2
2
2
0
0
2
1
0
1
0
1
1
1
2
1
1
1
2
2
0
2
0
1
1
0
2
1
1
0
2
1
1
1
1
1
1
2
1
0
2
1
2
1
1
1
0
0
1
1
1
2
0
2
1
1
1
0
0
1
2
0
1
0
1
0
2
1
1
1
1
1
3
1
2
1
1
0
2
0
1
1
0
0
0
0
2
0
1
0
1
1
1
2
1
1
1
0
0
1
0
0
0
2
1
1
2
2
2
0
1
0
0
0
3
1
1
2
2
0
0
1
1
2
0
0
0
1
2
0
0
0
1
1
1
2
1
2
0
0
0
2
2
0
1
0
1
0
1
2
1
0
1
1
1
1
2
1
0
1
1
2
1
1
1
2
0
1
1
2
0
2
2
2
1
0
0
1
1
1
1
2
1
0
2
1
0
1
0
1
2
0
2
1
1
1
1
1
2
1
0
2
1
2
2
1
1
1
2
1
3
0
0
1
1
2
1
1
2
2
1
1
2
0
0
0
1
1
0
1
1
1
2
0
1
1
1
2
1
1
0
1
2
1
2
0
0
1
2
1
1
0
1
0
1
1
2
1
0
0
0
1
2
1
0
2
1
0
0
2
1
0
1
0
1
1
2
2
2
0
0
1
2
1
3
2
2
2
1
1
1
1
2
1
1
1
1
2
0
1
1
1
0
0
2
1
0
2
0
2
2
1
2
1
1
2
0
1
1
1
2
1
1
0
0
2
2
1
1
2
0
0
1
1
2
1
2
2
2
1
0
0
2
1
2
1
1
1
1
2
1
2
2
0
1
1
1
2
0
1
0
1
0
0
2
1
1
1
1
0
2
0
2
1
3
0
1
2
0
1
2
1
1
2
1
1
2
1
1
1
1
1
0
2
1
1
1
2
1
1
2
2
2
1
0
1
0
0
1
1
1
0
1
1
1
0
2
2
1
2
0
0
1
1
0
1
2
1
2
0
2
1
2
1
0
1
1
1
2
1
1
0
0
1
2
1
1
1
1
2
1
0
0
0
1
0
0
1
2
1
1
0
1
2
0
1
0
1
1
2
2
1
1
1
2
0
1
1
2
0
1
0
2
2
0
1
1
2
2
1
1
1
1
1
2
1
2
2
0
0
0
3
1
1
1
0
2
1
0
1
2
0
2
1
0
0
2
0
1
1
2
2
1
1
0
1
2
0
0
0
1
2
1
1
0
1
1
2
1
1
1
1
0
1
1
1
2
0
1
1
1
1
1
0
0
1
0
1
1
1
2
1
0
1
1
1
1
1
0
0
1
0
0
1
1
1
2
2
2
0
1
1
1
1
0
1
0
1
0
1
1
2
2
0
1
1
2
1
0
0
2
2
2
1
1
2
1
1
0
1
0
1
1
0
2
1
1
3
2
1
1
0
0
1
2
1
0
1
1
1
0
2
1
1
1
1
0
1
2
2
1
2
1
1
0
1
1
1
0
1
1
0
2
0
2
1
1
2
1
0
0
0
1
3
1
1
0
1
1
1
1
1
0
0
1
1
2
0
1
1
1
0
1
1
1
0
2
1
1
1
1
1
1
1
2
1
0
1
1
1
1
0
1
1
1
1
1
1
2
1
0
1
0
0
2
1
1
2
0
2
1
0
2
0
1
0
0
1
1
1
1
0
1
0
0
1
1
1
1
2
1
0
1
0
2
1
0
1
1
2
1
2
2
1
1
2
0
1
0
1
1
0
2
0
0
2
2
0
1
2
1
1
1
1
1
1
2
2
0
2
0
1
2
0
2
0
0
0
2
0
1
1
2
0
2
0
0
2
1
0
0
2
0
0
2
0
1
1
1
2
1
1
2
1
1
0
1
1
0
1
1
2
0
1
0
2
0
2
1
1
2
1
1
2
2
2
2
1
0
0
1
1
1
2
0
1
0
0
1
0
1
0
2
1
1
1
1
1
0
0
0
1
1
0
2
0
0
1
1
0
2
0
1
1
1
1
1
1
2
1
1
0
1
2
1
0
2
0
0
0
0
1
1
1
1
0
2
1
2
1
1
1
2
1
2
0
2
2
1
1
1
1
1
1
1
0
1
0
1
1
1
1
1
1
2
2
2
2
0
1
1
3
0
1
2
1
1
1
1
1
2
2
2
0
1
1
1
1
0
1
1
1
1
1
1
0
1
2
0
1
1
2
2
1
1
1
1
1
1
1
1
2
1
0
1
2
2
2
1
1
0
2
0
0
1
1
0
3
1
1
1
1
0
3
1
1
1
2
0
0
0
1
1
1
0
1
1
1
1
1
2
0
1
0
1
2
1
1
1
1
1
0
1
1
0
1
0
1
1
1
2
2
1
0
0
2
1
1
1
0
0
2
1
1
1
1
1
0
2
1
1
0
0
1
0
1
0
0
1
0
0
2
1
1
2
1
1
1
1
1
1
0
1
2
1
2
0
1
2
1
1
1
1
1
1
1
1
0
0
2
1
1
1
1
0
2
2
1
2
1
1
0
0
1
0
1
1
1
0
1
1
1
2
0
1
0
2
1
2
1
0
1
1
2
1
1
1
1
2
1
2
2
1
1
2
0
7
2
2
1
0
0
0
2
1
1
0
1
1
2
0
1
2
2
1
1
1
0
1
1
1
1
0
1
2
1
1
0
2
1
0
1
0
1
1
1
0
1
2
1
1
1
5
1
0
1
2
2
0
1
0
1
0
1
2
1
0
2
1
0
1
1
1
0
0
1
0
1
2
1
1
2
2
1
2
1
1
1
1
1
0
1
1
1
0
1
2
1
0
2
1
1
1
0
0
1
1
1
2
2
0
1
2
0
0
0
0
1
0
1
1
0
0
0
1
1
0
1
1
1
1
1
0
1
0
1
0
2
0
2
0
1
0
1
2
1
2
2
2
1
2
1
1
2
0
0
1
0
2
1
1
0
0
3
2
2
1
3
0
1
1
1
1
1
1
2
0
2
2
1
1
1
0
0
2
0
1
1
1
1
0
0
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
1
3
1
2
1
0
1
1
0
2
1
1
0
2
1
1
1
2
0
1
1
1
0
1
0
1
2
2
1
1
1
5
2
1
0
1
1
1
1
1
0
2
2
1
1
1
0
1
1
1
2
0
1
0
2
0
2
0
0
2
0
2
1
0
1
1
0
1
1
3
0
1
1
1
0
1
1
1
0
1
1
1
2
2
0
1
1
0
1
2
1
0
2
0
1
0
2
0
1
1
1
1
1
0
0
1
0
2
0
0
1
0
0
1
1
1
1
2
1
1
1
2
1
0
0
1
0
0
0
2
1
0
2
0
0
0
1
0
0
0
0
2
0
1
1
2
1
1
0
1
1
2
0
2
1
0
0
2
2
1
2
0
0
1
0
1
1
1
2
2
1
1
1
2
0
1
0
1
1
2
0
0
0
1
1
2
1
1
1
1
2
1
1
0
1
1
2
1
1
0
0
0
0
1
1
1
2
1
1
1
0
1
2
1
0
0
0
1
1
0
1
2
1
1
0
1
1
1
1
1
2
1
2
1
1
1
1
0
2
1
1
1
1
0
2
0
1
1
2
2
1
1
2
2
0
1
2
1
2
2
2
0
1
0
1
2
1
0
1
0
0
1
1
2
1
1
2
1
1
0
0
1
0
2
1
1
1
0
0
0
0
2
1
2
1
1
0
1
0
1
1
1
0
0
2
2
4
0
0
0
1
2
2
2
2
1
0
2
1
1
1
2
1
2
2
1
0
2
1
2
1
1
1
0
1
1
2
1
2
1
1
0
1
1
2
0
0
1
0
2
2
0
0
1
0
2
1
0
2
1
0
0
1
2
0
0
1
1
2
1
2
1
1
2
1
1
1
1
0
0
0
0
1
0
0
1
2
0
1
0
1
0
0
2
0
1
2
1
1
0
1
2
1
1
0
1
0
1
1
1
1
1
0
1
1
2
1
0
0
0
1
2
2
1
0
1
1
1
2
0
2
0
0
0
1
0
1
1
0
2
1
0
0
1
0
1
1
0
1
2
1
1
1
1
1
2
0
1
1
1
1
1
2
1
1
0
0
0
0
1
0
0
0
0
0
1
0
1
1
2
2
1
1
1
1
1
0
1
1
1
0
1
2
1
0
2
2
2
2
0
1
1
2
1
0
0
1
1
1
0
2
1
0
1
1
0
1
1
1
1
0
2
1
1
1
2
1
1
1
1
2
1
1
9
1
1
0
0
2
1
1
1
0
1
1
1
1
0
1
1
2
1
1
1
2
1
1
1
2
2
2
2
0
1
1
0
1
1
1
0
2
1
1
0
0
0
1
1
0
1
0
1
0
1
1
1
1
2
1
2
2
1
1
0
1
1
0
1
1
2
1
1
2
1
2
1
1
0
0
1
2
2
0
1
1
1
1
2
1
2
1
2
0
1
0
2
2
0
1
1
0
1
2
0
1
0
1
2
2
0
2
0
1
1
2
0
1
1
0
2
2
1
2
2
1
2
1
1
1
2
1
2
1
1
1
5
0
1
1
0
0
1
2
2
2
1
1
1
1
2
0
2
0
2
1
0
0
3
1
0
1
1
1
1
0
1
0
1
2
0
0
3
1
0
2
1
1
1
2
0
1
0
2
2
1
1
1
2
0
1
1
0
8
1
1
2
0
0
1
0
1
0
0
1
1
0
0
1
0
1
1
2
0
1
1
1
1
1
1
0
2
0
1
1
1
0
0
3
0
1
1
1
1
0
1
0
2
2
1
1
1
3
0
1
3
2
0
0
1
2
0
1
1
3
2
1
1
1
1
1
2
0
2
1
1
1
1
1
1
0
2
2
1
1
1
0
0
0
1
1
0
1
2
2
0
0
1
0
0
2
1
2
0
2
0
1
2
1
2
2
0
0
2
1
1
0
1
1
1
2
1
0
2
1
3
0
2
0
1
1
1
2
1
1
1
1
1
0
0
2
1
1
1
0
2
0
0
1
1
1
1
0
0
1
1
1
1
2
2
1
2
1
1
2
1
0
2
2
1
0
1
1
1
1
0
0
0
1
2
1
2
1
0
2
0
1
1
1
2
1
0
2
1
1
0
2
2
2
1
1
0
1
0
1
1
1
1
1
2
1
1
0
1
2
2
0
1
1
2
1
1
1
1
0
1
0
0
0
1
0
2
0
1
2
1
2
2
0
1
1
0
1
2
0
1
0
0
1
1
1
1
3
1
2
1
1
1
0
2
1
1
1
2
1
1
1
1
1
0
1
0
1
0
1
1
1
1
1
1
1
1
1
1
1
0
1
1
0
0
1
0
0
1
2
1
0
1
0
0
2
2
1
1
0
1
0
1
2
2
1
2
2
1
0
0
0
0
1
1
0
1
0
0
1
2
0
1
1
1
0
0
0
2
0
2
2
1
1
0
0
1
0
2
1
0
2
1
0
1
0
0
0
1
1
1
1
0
2
1
2
0
0
2
2
2
1
2
2
1
2
3
1
1
0
1
2
1
1
2
1
1
1
0
1
1
1
2
0
1
1
1
1
0
1
0
2
2
0
2
2
0
0
1
0
1
1
2
0
0
0
2
1
0
2
1
0
1
2
1
0
2
11
1
1
2
2
2
0
1
1
2
0
2
2
0
0
3
1
1
0
1
1
1
2
2
1
0
0
1
1
0
1
1
1
0
1
0
2
0
1
1
1
0
1
1
0
1
1
1
1
0
1
1
1
0
1
0
2
0
1
1
1
2
1
1
1
1
1
0
1
0
1
0
1
0
0
1
1
2
1
0
0
1
1
0
0
2
1
3
0
1
1
1
1
1
1
0
1
2
0
0
1
1
2
1
1
1
2
1
1
1
0
2
1
1
0
1
0
1
2
1
1
1
3
1
1
1
0
1
1
2
0
1
1
2
0
2
0
1
2
2
1
1
1
0
1
2
1
0
1
2
1
1
1
1
1
1
0
1
1
2
1
1
1
1
1
1
1
1
0
0
2
1
0
2
0
2
0
1
0
2
1
0
2
0
0
0
1
0
2
2
1
1
3
0
1
1
1
2
1
0
0
1
1
1
1
0
1
1
1
0
1
0
1
2
1
1
2
1
3
0
2
2
1
0
2
2
1
0
1
1
1
1
1
1
1
1
2
2
1
2
1
2
1
1
1
0
0
0
1
1
1
1
2
1
1
1
2
0
1
1
1
1
1
1
2
0
1
2
1
1
1
2
1
1
1
2
2
1
2
0
2
2
0
1
1
0
2
2
1
1
1
1
2
1
2
2
1
0
1
0
0
0
0
2
1
1
2
1
2
0
1
2
1
1
1
2
0
2
0
1
1
0
1
1
1
1
1
0
2
1
0
1
0
0
2
0
1
1
1
0
1
1
1
2
1
0
0
0
0
2
1
0
0
0
1
1
0
0
0
2
1
1
0
1
0
2
1
1
2
2
0
3
2
0
0
0
0
1
2
0
1
0
1
1
1
0
2
1
0
1
1
0
2
0
1
0
1
2
0
1
2
1
0
0
0
5
1
1
0
2
1
1
0
1
1
0
1
0
1
1
2
1
2
2
0
0
0
0
0
2
2
0
0
0
1
2
1
2
0
1
2
2
0
1
1
1
2
3
1
1
1
0
2
1
0
1
0
1
1
0
1
2
2
0
0
1
2
6
1
0
1
0
0
1
1
3
2
0
2
2
1
4
0
1
0
0
2
0
1
0
1
1
1
1
0
2
1
2
2
0
1
1
2
1
1
2
1
1
1
1
1
1
0
0
2
0
2
1
0
1
1
2
1
1
1
2
1
1
1
2
1
0
1
1
0
2
1
1
0
2
1
1
0
2
0
1
1
1
0
3
1
2
2
2
0
1
0
1
0
1
1
2
1
1
0
1
0
1
1
1
1
3
2
2
1
1
2
0
0
1
1
1
1
1
0
3
2
2
0
0
1
0
1
1
1
1
1
1
1
1
1
0
1
1
0
0
1
0
0
0
3
2
2
0
0
2
3
0
0
2
0
0
1
1
2
0
1
1
0
3
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
0
1
1
1
2
2
0
1
0
0
4
0
1
1
0
2
2
1
2
1
2
1
0
2
0
2
0
3
0
0
1
0
1
1
0
1
1
1
1
0
1
2
1
1
0
2
0
1
1
2
2
1
1
1
1
0
1
1
1
0
2
0
1
2
2
1
1
1
3
2
1
0
1
2
3
1
2
2
1
1
2
2
1
1
1
0
2
1
0
1
2
0
1
0
0
2
1
0
1
1
1
1
2
1
1
2
0
0
1
1
1
1
2
1
1
1
1
0
0
0
1
1
1
1
0
0
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
2
1
1
0
1
0
1
0
1
1
0
2
2
0
2
1
0
2
2
2
2
0
1
1
0
2
2
2
1
1
0
1
2
1
1
1
0
2
1
2
1
0
2
1
1
2
0
2
1
2
1
1
0
0
0
2
0
2
0
0
2
0
0
1
2
1
1
0
1
1
1
1
0
1
0
1
1
0
0
2
1
1
1
0
2
1
1
0
1
1
2
0
0
1
1
1
2
1
2
0
1
1
1
0
1
2
1
0
0
0
1
2
1
0
1
0
1
2
0
2
2
2
2
0
1
0
2
1
1
1
2
0
2
0
0
2
1
1
1
2
1
0
2
1
0
2
0
0
1
0
1
0
1
1
0
1
0
0
2
1
1
0
1
1
2
2
0
1
1
1
0
0
1
0
1
1
1
1
0
0
1
1
2
2
2
0
1
1
0
1
2
1
0
1
1
1
1
0
2
2
3
0
1
1
1
1
1
1
1
1
0
1
1
1
2
1
1
0
1
2
1
0
0
0
1
1
0
1
1
1
1
2
1
0
1
1
1
1
0
1
0
1
0
0
1
2
2
1
1
0
0
2
0
1
2
2
1
2
2
2
0
1
1
2
1
0
0
2
2
2
1
1
0
0
1
1
1
2
1
0
0
1
2
2
1
0
1
0
1
1
0
1
0
2
3
0
1
1
2
1
0
1
1
1
2
1
1
0
1
1
1
2
1
0
1
0
0
0
2
1
0
0
2
3
0
0
1
1
2
2
2
1
0
1
1
1
1
2
2
0
1
2
1
1
2
2
2
2
1
1
1
1
2
1
1
1
0
1
2
2
1
0
0
2
2
2
1
0
2
1
0
0
1
0
2
2
1
2
0
1
2
0
1
0
0
2
1
2
0
1
1
1
0
1
0
1
0
2
0
1
2
0
1
2
1
1
1
2
1
1
1
0
1
2
1
2
0
1
2
1
0
1
2
1
1
2
1
2
1
1
2
1
1
0
0
1
0
1
2
1
1
1
1
0
1
2
1
1
2
2
2
1
2
1
1
2
2
1
1
1
1
2
0
1
1
1
1
1
1
1
0
2
2
0
0
0
1
1
0
1
1
1
2
1
2
1
2
0
1
1
2
0
1
2
1
0
1
0
0
2
2
0
2
0
2
1
2
1
1
1
0
0
1
1
1
2
2
1
0
1
1
0
1
0
1
1
1
0
0
0
1
1
5
1
2
2
2
1
1
1
1
0
0
0
2
2
2
2
2
1
1
1
1
1
1
2
1
2
0
1
1
2
1
0
2
0
1
1
0
1
0
1
1
0
1
3
1
0
2
1
2
2
0
1
0
1
1
2
2
1
1
1
1
2
1
1
2
1
1
2
2
1
1
1
1
1
1
2
1
1
0
0
1
0
1
1
0
1
1
1
1
3
1
1
1
1
1
0
1
1
1
1
1
0
2
2
0
1
2
1
0
1
1
1
2
1
2
2
2
1
0
0
0
1
2
0
1
2
2
1
1
0
1
2
1
1
1
1
2
2
1
1
1
1
1
0
2
1
1
2
1
2
1
2
1
2
0
2
1
0
1
0
1
0
1
1
1
1
1
1
1
0
2
0
1
1
1
0
1
0
1
2
1
1
2
1
1
1
0
0
1
1
1
1
1
1
1
1
1
1
2
0
0
2
2
0
2
2
2
0
0
2
0
0
0
1
0
1
1
2
0
1
1
1
1
2
0
3
0
1
1
1
1
1
0
1
2
2
1
0
2
0
1
1
0
2
1
0
0
2
0
2
1
1
2
2
0
1
1
1
1
2
0
0
0
0
2
2
1
1
1
0
0
0
0
1
0
1
1
1
1
1
1
2
1
2
1
1
1
2
1
1
0
1
0
0
2
1
0
1
1
1
1
2
1
2
0
0
1
1
0
0
1
2
0
1
1
1
1
1
0
2
0
0
2
0
2
1
0
0
1
2
1
1
1
0
0
1
1
0
0
0
1
0
1
2
2
2
1
1
1
2
2
1
2
0
1
1
1
1
1
1
1
1
1
1
2
1
0
0
1
2
1
1
0
0
1
1
2
1
1
1
1
1
1
1
2
1
1
0
1
2
1
1
0
0
1
0
0
0
0
1
0
2
2
1
0
2
1
1
0
2
1
1
1
2
1
1
0
1
2
1
0
1
0
1
1
1
0
0
1
0
1
1
1
2
0
1
0
0
1
2
2
2
2
2
0
1
1
1
1
1
1
1
1
0
0
0
1
1
0
2
0
0
0
1
0
1
1
1
1
0
1
1
2
1
1
0
0
1
2
1
0
0
0
0
0
0
0
2
0
1
0
1
1
2
1
1
2
2
1
0
1
2
0
2
2
0
0
0
1
2
1
0
1
1
1
1
2
1
1
1
0
3
0
0
1
1
1
1
0
2
1
1
0
0
1
0
0
0
2
1
0
1
2
1
2
2
1
2
6
1
1
1
3
1
1
1
2
0
1
0
1
1
1
1
0
2
0
1
1
1
0
2
2
1
1
2
0
2
2
2
1
0
0
0
1
0
1
0
1
1
1
2
2
1
1
2
0
1
2
0
1
2
1
1
1
1
2
1
0
2
1
1
1
0
2
1
2
2
0
0
1
2
1
0
1
1
0
1
1
1
1
1
1
1
1
1
2
0
0
0
2
0
3
1
0
1
2
0
1
1
1
1
1
1
1
2
1
1
2
1
1
2
1
1
0
4
1
0
2
1
0
4
1
2
1
1
1
0
0
1
1
1
1
1
1
2
1
0
2
1
2
0
2
1
2
2
1
1
0
1
1
1
1
3
0
0
1
1
1
1
2
2
1
1
1
2
1
1
1
1
1
0
1
3
0
1
2
2
2
0
1
1
2
1
2
1
1
1
1
1
2
2
1
2
0
1
1
1
2
1
1
0
0
0
3
0
0
1
0
2
2
2
1
1
1
2
0
1
0
1
1
2
0
0
1
2
1
1
0
0
0
2
1
2
1
1
0
1
1
1
0
1
1
0
1
1
1
1
0
1
1
1
1
1
0
3
0
2
0
2
0
1
1
0
1
1
2
2
1
0
0
2
1
1
0
2
1
2
2
0
1
0
2
0
1
2
1
2
1
1
1
3
1
1
0
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
0
1
1
2
1
1
1
2
2
1
0
0
1
1
1
0
1
1
0
1
1
2
0
2
1
2
2
0
1
1
0
1
2
2
2
1
2
0
0
0
2
1
0
1
1
0
1
2
0
2
1
1
1
1
1
2
0
1
1
0
1
1
1
2
1
1
0
1
0
0
2
1
2
1
1
2
2
0
1
2
1
1
1
1
1
0
2
0
1
2
1
0
2
1
2
1
1
0
1
2
1
1
0
0
0
1
0
1
1
0
1
2
1
1
1
1
1
1
0
2
1
1
1
2
1
1
2
0
0
2
0
0
1
1
2
1
1
0
1
1
1
1
1
0
0
1
2
1
0
1
1
1
0
0
1
1
1
1
2
0
1
0
1
1
1
1
2
2
1
0
1
2
1
1
0
0
1
2
0
0
0
1
0
0
0
0
3
1
1
1
2
1
0
1
0
2
1
1
2
2
0
0
1
2
0
1
1
1
2
1
1
2
1
2
1
1
0
1
2
1
0
2
1
0
0
2
0
0
0
0
1
0
1
2
0
1
2
1
1
1
2
0
1
1
1
0
0
2
2
1
2
1
1
0
2
0
1
1
1
1
1
1
0
0
1
1
0
1
0
0
2
4
1
0
1
2
0
0
0
1
0
2
1
0
1
1
1
1
1
1
1
1
2
0
1
1
0
0
1
1
2
1
0
2
0
2
1
0
1
0
1
1
2
1
0
2
0
2
0
2
1
0
2
1
1
2
1
0
1
1
1
2
1
1
1
2
1
0
1
1
0
0
2
1
2
0
0
0
0
0
2
2
1
0
1
1
0
1
1
1
1
0
1
1
1
0
1
2
0
0
0
1
1
1
1
0
1
1
1
0
2
2
2
2
1
1
1
1
1
2
0
1
0
1
1
1
2
1
1
0
1
0
1
1
1
2
1
1
0
1
3
2
0
1
1
1
1
1
2
0
0
1
1
2
1
2
1
1
2
1
2
2
1
1
1
0
2
0
0
1
1
0
2
1
2
0
2
1
0
1
1
2
1
1
1
2
2
2
3
1
1
1
1
1
0
1
1
1
0
2
1
1
2
0
1
1
0
0
2
1
1
2
2
1
1
1
0
1
1
1
0
0
1
1
2
0
0
1
0
0
1
1
0
0
2
0
0
1
1
2
1
2
0
1
2
2
1
1
1
1
1
0
2
0
0
3
1
0
1
1
0
1
0
1
0
2
1
1
1
0
1
1
0
0
1
1
1
2
1
0
0
1
0
1
1
1
1
2
1
0
0
1
1
1
1
1
0
1
1
0
2
1
1
1
1
1
1
3
0
1
2
1
1
2
0
2
1
0
0
0
1
0
1
0
2
1
1
2
0
1
0
1
2
1
0
1
1
0
0
1
1
1
1
0
1
1
2
0
0
1
1
1
1
0
0
3
1
1
1
2
0
1
1
0
2
1
2
1
1
0
1
1
2
0
2
2
2
1
0
0
1
0
0
1
2
0
2
1
0
0
1
1
0
1
0
1
2
1
1
1
1
2
1
1
1
1
2
2
1
0
2
0
2
0
0
0
0
0
0
0
1
1
1
0
1
1
1
1
1
0
0
2
0
1
1
2
0
1
0
1
1
1
0
1
2
1
0
1
2
0
0
1
1
1
0
0
3
0
0
1
1
1
1
0
0
1
2
0
1
1
2
4
1
2
1
2
0
2
2
2
1
1
1
1
1
2
2
1
1
1
2
3
0
1
0
1
1
0
2
1
1
2
1
1
2
1
2
1
0
1
0
2
1
0
1
0
1
1
2
0
1
1
1
1
2
1
1
2
1
0
0
1
2
0
1
1
1
2
1
2
1
0
0
2
2
2
1
1
0
2
0
2
1
1
1
1
1
0
2
0
1
0
1
3
2
1
1
1
1
2
2
0
0
1
1
1
1
0
1
2
1
1
0
1
1
1
1
2
2
2
0
2
1
1
0
1
1
0
2
2
2
1
0
3
1
0
1
1
2
2
2
1
1
0
1
0
2
1
1
0
1
1
0
1
0
1
1
0
1
2
0
3
1
2
2
2
1
1
0
2
2
1
1
0
0
2
0
1
1
1
1
2
2
0
0
1
1
1
2
0
1
1
2
1
3
0
0
1
1
2
0
2
1
2
1
1
2
2
0
2
0
1
2
0
1
0
1
2
0
0
1
1
2
0
0
1
1
1
1
1
0
0
1
2
1
2
1
1
0
0
1
0
0
2
1
1
1
1
1
1
1
2
2
0
1
1
1
1
2
0
0
1
0
1
0
1
0
0
1
1
0
0
1
1
1
1
2
0
1
1
0
0
1
0
1
1
1
2
1
1
0
0
1
2
1
1
1
1
0
2
0
1
1
0
1
1
2
1
1
2
1
1
0
1
0
1
1
2
2
1
0
1
2
0
0
2
1
1
1
0
1
0
1
2
1
1
1
1
2
1
2
1
1
1
1
0
1
1
0
2
0
1
1
1
1
2
1
1
1
0
1
1
2
1
1
0
0
1
1
2
2
0
1
0
1
1
0
1
1
1
2
2
0
0
0
1
1
1
2
2
3
2
1
0
1
2
2
2
2
0
1
1
1
1
5
1
0
1
2
1
0
0
2
1
1
2
0
1
1
1
1
1
1
1
1
1
1
0
1
0
1
1
0
1
0
1
2
1
0
0
1
1
1
0
1
1
0
1
1
1
0
2
1
0
1
1
2
1
1
1
0
1
1
2
0
1
1
1
1
0
1
0
1
1
3
1
1
1
2
2
2
1
0
0
1
1
1
2
1
1
0
0
0
2
2
1
1
0
0
2
0
0
0
2
1
1
0
1
1
0
0
0
3
1
0
2
1
1
2
1
1
0
2
1
0
0
2
2
2
0
1
1
1
2
0
0
1
1
1
0
0
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
0
1
0
2
0
0
1
1
1
0
0
1
1
0
0
1
1
0
1
2
0
1
2
2
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
0
0
1
1
1
0
2
1
2
1
0
2
1
1
0
2
2
1
1
0
1
1
1
1
2
1
1
1
1
1
1
2
0
2
1
1
0
1
2
1
2
2
1
1
1
2
1
2
1
2
0
1
0
1
1
2
1
1
1
1
0
0
0
0
2
2
1
1
2
2
1
1
1
1
2
1
1
1
2
0
2
0
1
0
1
0
1
1
1
0
1
1
1
1
1
1
2
1
0
2
1
1
1
1
1
1
2
0
1
0
1
0
2
2
0
0
0
1
2
1
0
0
1
1
1
0
1
1
1
1
0
1
0
0
2
2
2
2
1
1
1
1
2
1
2
2
2
1
1
0
1
0
2
1
1
1
2
0
2
1
1
0
2
1
0
1
0
0
1
2
0
1
1
1
0
1
0
2
0
1
1
1
0
0
0
2
0
0
0
1
1
1
1
1
1
3
0
1
1
0
0
0
3
0
1
2
0
1
0
1
0
1
1
2
0
1
1
0
2
1
1
2
1
1
1
1
1
1
2
2
1
2
1
2
1
1
1
0
0
1
1
1
1
2
0
0
1
0
1
2
1
1
2
0
0
1
0
2
1
0
1
1
1
0
1
1
2
1
1
1
1
1
0
0
1
1
1
1
1
1
0
0
2
0
0
1
2
0
1
0
0
1
1
0
1
2
1
2
2
0
1
1
1
1
1
0
1
2
2
0
2
1
1
1
1
2
0
2
2
0
1
0
1
1
1
0
1
1
0
2
0
2
1
1
0
1
0
1
1
1
2
0
0
0
0
1
1
1
0
2
0
0
2
2
1
1
1
1
0
1
2
1
1
1
2
2
1
1
1
0
1
1
0
1
1
1
2
0
0
0
1
1
1
1
0
1
2
1
1
1
2
1
1
2
1
1
1
0
2
1
1
1
1
1
1
1
1
1
2
2
0
1
0
0
1
2
1
1
0
1
2
2
0
1
1
0
1
1
1
2
1
1
2
1
2
1
0
1
1
0
1
1
0
1
1
1
0
1
0
1
1
1
1
1
1
0
0
0
1
0
0
1
1
1
2
0
0
1
1
2
1
1
0
3
0
0
0
1
0
1
1
1
1
1
2
1
0
1
1
1
1
1
1
1
1
0
0
0
1
1
1
2
2
0
2
1
1
1
1
1
0
0
1
1
0
0
2
1
2
0
0
2
1
2
1
2
0
1
1
0
0
0
1
1
1
1
1
3
1
1
0
2
0
0
1
0
2
0
2
2
0
1
2
1
0
1
2
1
2
1
1
1
1
0
1
0
0
0
0
1
0
0
1
1
1
0
1
1
1
2
2
1
1
0
0
2
2
2
0
2
1
2
0
0
2
0
2
1
1
1
1
2
1
1
0
1
0
1
1
1
1
1
0
1
0
1
2
0
1
1
1
1
2
1
1
2
2
2
1
0
2
0
1
1
1
2
0
0
1
0
1
2
0
0
1
1
2
2
1
1
1
1
1
0
0
2
0
1
1
1
2
0
1
1
0
2
1
1
2
1
0
1
1
0
2
0
3
1
0
2
0
1
1
1
0
2
2
0
2
1
0
1
0
1
1
1
1
3
1
0
1
1
0
1
1
1
1
0
1
1
1
2
2
2
1
1
1
0
0
1
0
1
1
1
1
1
1
1
1
1
0
2
0
0
0
1
2
1
1
1
0
0
1
2
0
1
2
0
0
2
0
2
0
1
0
1
1
1
0
1
1
2
2
1
1
0
2
0
0
1
1
1
1
2
1
1
0
1
1
0
1
2
1
1
1
2
1
2
2
1
1
2
1
5
2
1
1
1
2
0
2
1
1
2
1
1
1
0
2
2
0
2
0
1
0
0
1
1
0
0
2
1
1
0
0
1
0
1
1
1
2
2
1
1
1
1
1
1
0
0
1
1
1
1
0
0
1
1
1
1
0
1
1
1
2
1
3
1
0
1
1
2
1
1
1
2
1
1
1
1
2
1
2
0
1
1
1
1
1
1
1
1
2
2
2
0
2
1
1
1
1
0
0
1
3
2
1
1
1
0
2
2
1
1
2
0
0
0
2
2
1
1
1
0
1
1
1
0
0
0
0
1
0
2
0
1
1
2
2
0
0
1
0
0
0
1
2
2
1
1
1
4
2
0
1
1
2
1
1
1
0
2
2
1
0
0
2
1
1
0
0
1
1
0
1
1
0
1
1
0
2
0
1
2
1
1
1
0
1
0
1
2
1
1
1
1
1
1
2
2
1
1
0
1
1
0
0
2
1
1
1
1
1
0
0
0
0
0
1
1
1
0
2
0
2
1
0
1
0
0
1
1
2
1
2
2
2
0
0
1
1
1
1
1
1
0
1
1
1
1
0
1
2
2
1
1
0
2
1
1
1
1
1
1
1
1
2
1
1
1
0
1
2
1
0
2
2
1
1
1
2
1
0
2
1
1
0
1
2
1
1
1
0
1
1
1
1
2
1
0
1
0
2
2
1
1
1
1
0
1
1
1
1
1
1
0
1
2
1
0
2
0
2
0
1
1
2
2
1
2
0
1
3
1
1
0
1
0
1
1
2
3
1
1
1
1
1
0
0
2
0
1
0
1
1
0
1
1
1
1
1
4
1
1
2
1
2
1
1
3
0
1
0
1
1
0
2
1
1
1
1
2
1
0
0
1
2
1
0
2
1
1
1
1
0
2
1
0
1
2
1
2
2
0
1
1
1
1
1
0
1
1
2
2
1
3
1
0
2
1
0
2
0
1
1
1
1
1
1
1
1
0
1
2
2
1
1
1
1
0
2
3
0
2
1
1
2
0
2
0
1
4
1
2
1
2
1
0
0
0
2
0
1
1
1
0
1
1
0
2
1
1
2
1
1
1
1
0
0
0
1
0
0
1
1
2
0
2
0
1
0
1
2
1
0
1
1
0
2
0
1
1
2
1
1
1
2
1
0
0
1
2
2
1
0
1
1
1
0
2
0
1
1
1
1
0
1
1
1
2
0
1
1
2
1
0
0
0
0
1
1
3
1
1
0
0
1
1
0
1
0
1
0
0
1
2
1
2
2
1
2
0
0
2
1
0
1
2
2
1
1
2
1
1
0
2
1
2
1
1
0
1
1
1
1
1
1
2
1
1
2
0
1
1
1
1
2
1
1
1
1
1
1
2
0
1
1
1
0
1
0
2
1
1
0
2
2
0
2
2
2
1
0
1
0
2
0
0
1
1
0
2
1
1
1
0
1
2
0
0
1
1
1
1
0
1
1
1
0
1
0
1
0
1
1
0
2
2
0
1
2
2
1
0
1
0
0
1
1
1
2
1
2
1
0
0
1
2
2
1
0
2
2
2
2
1
0
2
0
1
1
0
0
1
1
1
1
1
0
0
0
1
1
1
1
1
2
0
0
1
0
1
1
2
2
2
0
0
1
1
1
1
0
1
2
0
0
0
2
1
0
1
1
0
0
1
1
2
1
0
4
2
1
2
1
1
1
1
1
1
0
1
1
2
1
0
1
2
1
1
1
1
0
1
1
0
1
1
2
1
1
0
2
2
1
0
1
0
0
0
0
0
0
1
0
2
0
2
0
1
0
2
2
1
1
2
1
1
0
1
1
2
0
1
1
1
2
1
1
2
1
0
1
0
1
1
1
1
0
2
1
1
0
1
1
0
1
0
0
1
1
1
2
0
1
0
1
2
0
0
1
0
2
1
0
1
1
2
2
2
1
1
1
1
0
2
1
0
2
1
2
0
1
1
0
1
0
2
0
0
0
1
2
1
1
2
0
1
1
1
2
1
0
0
0
2
1
1
1
1
2
2
0
0
2
1
1
1
1
0
1
1
2
1
1
0
1
2
0
1
1
1
2
0
2
1
2
3
1
1
0
1
1
2
1
1
2
1
2
2
0
2
1
0
2
1
1
1
0
1
0
0
3
2
2
0
2
1
2
0
1
1
2
2
1
0
1
2
2
1
0
1
1
2
0
1
1
2
1
1
2
0
2
0
0
2
1
1
1
0
0
0
1
1
1
0
1
1
0
1
1
0
1
2
3
0
0
0
0
0
1
2
1
2
2
0
0
0
2
1
1
1
1
0
1
1
0
1
2
2
1
2
2
1
0
1
1
1
2
2
0
2
1
0
0
1
2
1
1
2
2
2
1
1
2
2
1
1
1
1
2
2
2
2
1
2
1
2
2
0
0
1
1
2
3
1
4
1
1
1
1
1
1
0
1
0
0
1
2
1
2
1
1
1
2
0
1
0
0
2
1
0
1
2
2
1
0
2
1
0
0
1
1
2
0
1
0
0
1
1
1
1
1
2
0
0
2
1
0
1
1
2
1
1
1
0
1
1
1
1
1
0
0
2
1
0
1
1
1
1
1
2
2
2
1
0
1
0
2
0
1
1
2
2
1
2
1
2
4
2
1
1
1
0
2
1
1
1
1
2
1
0
5
1
0
1
1
1
0
1
1
0
0
0
1
0
1
1
2
1
2
0
1
0
1
1
1
1
0
1
1
2
0
1
2
0
2
2
1
1
1
1
1
1
0
1
2
2
1
1
1
2
1
1
1
0
0
1
0
1
1
1
2
1
2
1
1
1
1
0
0
1
2
1
0
1
1
2
1
1
0
1
1
1
1
0
1
0
0
2
2
0
0
1
0
1
1
2
2
1
1
2
1
0
1
2
0
1
1
0
0
0
2
2
1
1
1
2
1
2
1
2
0
1
1
1
1
0
1
1
2
2
1
1
1
0
1
1
1
0
2
1
1
0
1
1
1
1
1
0
0
1
2
1
1
1
2
1
2
0
1
1
1
0
0
1
1
1
0
0
2
0
1
1
0
1
0
0
1
1
1
2
2
1
2
1
1
0
1
1
1
1
1
1
1
1
1
0
1
1
3
2
1
0
1
1
1
1
1
1
1
1
0
1
1
0
1
1
1
1
0
1
2
2
2
1
1
0
0
1
1
0
0
1
1
1
1
0
1
0
1
2
0
2
0
1
2
2
1
1
1
1
1
1
1
1
0
1
0
0
1
1
1
1
2
0
1
2
1
1
0
0
1
0
2
1
0
1
1
0
1
1
0
1
1
0
2
1
2
1
2
1
1
0
1
0
2
1
1
0
1
1
1
1
0
1
1
0
1
1
0
1
4
0
2
0
0
0
0
0
1
1
0
1
2
0
1
2
1
2
2
2
0
1
1
1
2
2
0
0
2
0
0
1
1
2
1
0
1
1
0
2
2
1
0
1
3
1
1
3
2
3
1
0
1
1
2
2
1
0
1
0
1
1
2
0
2
1
1
1
1
1
1
1
0
1
1
1
1
2
1
1
0
2
0
2
0
1
1
1
1
1
1
1
1
0
2
2
1
0
1
2
1
0
0
2
2
0
1
1
1
1
1
0
0
2
2
2
1
0
2
2
2
0
2
1
1
1
1
1
1
2
1
0
0
0
0
1
1
0
0
1
1
0
0
0
1
1
1
0
1
1
1
0
0
2
1
1
1
0
3
2
1
2
0
1
2
1
2
2
2
1
0
1
0
1
1
2
1
0
1
0
2
1
0
0
1
2
1
0
0
0
0
1
1
0
3
2
1
1
3
2
2
2
1
1
1
1
2
0
2
0
1
1
0
1
1
2
1
1
1
1
1
1
0
1
1
1
1
0
1
0
1
1
2
2
1
1
1
0
1
0
0
1
0
0
1
2
0
0
1
0
2
0
0
1
0
2
1
2
1
1
2
1
2
2
1
1
1
1
1
2
1
1
1
1
0
2
2
2
1
0
1
1
1
0
2
1
2
1
1
1
2
0
1
0
1
2
1
0
1
1
1
0
2
0
1
0
1
2
1
0
1
0
1
2
1
0
2
1
1
1
1
1
0
1
1
1
1
0
2
0
1
1
0
1
0
0
1
1
0
1
0
1
1
1
2
1
2
0
0
1
0
1
1
0
1
1
0
1
0
1
1
1
2
1
1
2
0
0
0
1
2
1
1
0
2
0
2
0
0
0
1
2
2
1
1
1
2
1
2
0
0
0
0
2
1
0
1
0
1
2
1
1
1
1
1
0
1
0
1
0
2
1
2
0
0
2
1
0
1
1
1
1
0
1
2
1
0
1
1
1
1
0
2
1
2
2
0
1
1
0
2
1
1
3
0
1
1
0
1
1
1
1
2
0
1
1
1
1
1
0
1
1
1
1
0
0
1
1
1
1
2
0
1
1
1
2
1
1
1
1
0
0
1
0
0
3
0
1
0
1
1
1
1
1
2
0
1
2
1
1
1
2
0
1
1
0
2
1
0
1
1
1
2
0
1
1
0
0
1
1
2
1
1
2
1
1
1
1
2
0
2
1
2
1
1
0
1
2
0
1
2
2
5
2
0
1
1
0
3
1
2
0
1
1
0
2
1
0
0
1
1
0
2
0
1
0
1
1
1
0
1
2
2
0
1
1
1
0
1
1
1
1
1
0
2
0
2
1
1
2
0
1
0
1
1
1
2
2
1
1
0
2
1
1
0
1
0
1
0
1
1
0
0
2
0
0
1
0
1
1
0
0
1
2
1
0
1
1
1
2
0
0
1
1
2
1
0
2
0
0
1
0
1
1
2
1
2
0
1
1
1
1
0
2
0
2
2
0
0
1
2
2
1
2
1
0
1
1
2
0
2
1
0
1
1
3
1
1
1
3
2
0
2
1
0
1
1
1
2
0
0
2
2
0
1
1
0
2
2
0
1
2
2
0
0
1
0
1
1
1
0
0
2
0
2
1
1
1
1
1
1
1
1
0
1
1
2
1
0
0
1
0
0
1
1
1
1
2
1
2
0
0
1
1
3
2
2
2
0
1
1
1
2
1
1
1
1
0
0
1
1
0
2
2
0
1
1
3
2
0
2
2
1
0
0
1
5
2
1
0
1
0
0
1
1
0
1
1
1
1
2
2
1
0
1
1
0
1
1
1
2
3
0
0
1
0
1
0
2
1
0
1
0
1
1
2
0
1
1
2
1
1
0
0
1
1
2
2
0
0
0
1
0
1
0
0
2
1
0
1
1
1
2
1
1
0
1
0
1
0
0
0
1
1
1
0
2
0
1
1
1
0
1
1
0
1
2
1
1
2
0
2
1
2
1
1
1
0
1
1
2
1
1
2
2
0
0
2
1
0
1
1
1
0
2
1
2
2
2
2
1
1
1
1
1
1
1
1
2
0
2
1
1
2
0
0
1
0
0
0
1
1
1
0
1
1
2
0
1
1
2
0
1
0
0
1
1
2
1
0
2
0
1
0
1
1
1
0
0
1
0
0
2
1
0
1
1
2
1
0
1
0
2
1
1
2
1
0
1
2
0
0
2
1
1
2
1
1
1
3
1
0
1
2
0
0
0
0
0
0
2
0
0
1
1
0
1
1
0
0
2
4
1
2
1
1
2
2
2
1
1
2
1
1
1
0
1
0
1
2
1
1
0
1
1
1
0
0
1
1
0
1
1
1
2
0
1
2
1
1
0
1
1
1
1
0
1
1
1
0
0
1
1
1
0
1
1
0
0
1
1
0
0
0
0
1
2
2
2
1
1
1
1
1
0
1
0
1
0
0
2
1
0
0
1
2
2
1
0
0
1
0
0
1
2
0
0
1
2
1
0
0
1
1
0
2
0
1
1
1
0
2
1
1
1
1
0
1
2
2
0
0
0
1
0
1
1
1
1
2
2
0
0
0
1
1
1
0
0
1
1
0
2
1
0
0
0
1
0
0
0
1
1
0
1
0
1
0
0
0
1
0
2
0
0
1
0
0
1
1
1
2
1
2
1
2
0
2
1
1
1
1
2
1
0
2
2
1
1
1
2
1
1
1
3
2
2
0
2
2
1
1
1
1
0
1
2
2
0
1
1
1
1
1
0
1
1
1
1
1
0
1
1
0
0
2
0
0
0
0
0
2
2
2
0
2
1
10
0
0
2
2
0
1
1
1
2
0
1
1
1
0
2
2
0
0
1
1
2
0
0
0
1
1
1
1
1
1
2
0
2
0
0
1
1
2
0
2
1
1
0
2
0
1
1
1
1
1
2
1
2
0
0
1
0
2
1
1
1
1
2
2
1
2
0
1
1
1
2
1
1
0
0
1
1
1
1
2
0
0
1
2
2
0
0
2
1
1
3
0
0
0
2
2
3
0
2
0
2
0
1
0
1
0
2
2
1
2
0
1
1
1
4
2
1
1
1
2
2
1
1
0
1
1
1
0
1
2
1
1
1
3
1
1
1
1
1
0
2
2
2
1
1
2
1
1
1
1
2
1
0
1
2
1
1
1
1
1
2
0
0
2
0
2
2
2
0
0
1
0
1
1
0
2
0
0
1
1
1
1
1
1
1
1
2
1
1
0
1
1
2
1
1
2
0
1
1
2
1
3
1
0
1
2
2
1
2
1
1
1
1
1
1
0
1
0
1
0
1
1
1
2
1
1
0
0
0
1
1
1
0
1
2
2
0
0
2
0
0
0
2
2
1
1
1
0
1
1
1
1
0
0
2
2
1
2
2
1
0
0
1
0
2
2
2
1
0
2
2
1
2
0
1
2
1
1
1
0
2
1
0
1
1
0
1
0
0
1
2
2
0
1
1
1
0
0
1
1
1
2
2
0
1
1
1
0
1
0
2
0
1
2
2
1
1
2
1
0
0
1
1
0
1
1
1
0
1
1
0
1
0
1
1
0
1
0
0
0
1
1
1
2
1
0
0
0
0
1
1
1
2
2
0
1
1
1
0
1
0
1
1
1
0
1
1
1
1
2
1
1
1
2
0
2
1
1
1
0
1
1
0
1
1
1
2
1
1
1
1
2
0
2
2
0
1
2
2
0
0
1
0
0
2
0
2
0
1
1
1
3
2
1
2
1
2
1
2
1
1
1
1
1
0
0
1
1
1
1
0
2
1
2
1
0
1
0
1
1
2
1
2
0
2
1
2
1
0
0
1
1
0
0
2
1
0
0
2
0
0
1
1
1
1
0
2
1
1
0
0
2
0
0
0
1
1
1
1
1
1
1
1
1
2
1
1
1
0
1
1
1
1
1
1
1
0
2
1
1
0
1
0
2
2
1
2
1
1
1
2
1
1
2
1
1
0
1
1
0
1
3
1
2
4
2
1
1
1
1
2
1
1
0
2
0
1
0
0
0
1
2
2
1
0
2
1
1
2
1
2
0
1
1
0
1
0
1
0
0
0
2
2
2
4
0
1
1
1
2
1
2
0
1
1
0
2
1
1
0
1
1
1
1
2
1
1
0
0
2
2
3
0
2
2
0
2
1
1
4
1
2
0
1
2
1
0
3
1
1
1
1
2
1
1
1
1
1
1
2
0
0
0
2
0
1
1
1
0
2
1
1
0
1
0
1
1
1
1
1
0
2
2
2
2
1
2
0
2
2
2
1
0
2
2
2
1
1
1
1
2
1
0
2
1
2
1
1
0
2
1
2
0
1
1
1
1
0
0
1
1
1
1
1
2
1
2
1
1
0
0
0
0
0
0
0
0
1
2
0
2
1
1
1
1
4
1
1
2
0
1
2
1
1
1
1
0
1
1
0
2
1
2
0
1
1
3
2
0
2
1
2
2
1
1
0
2
1
0
1
1
1
2
1
1
0
2
0
1
1
1
1
0
1
2
1
0
1
3
0
1
0
0
2
1
1
2
0
1
0
1
1
0
2
0
3
0
2
2
2
0
2
0
0
1
1
1
0
1
1
0
1
1
2
1
2
0
1
1
0
1
1
0
1
3
0
1
2
1
1
1
1
0
1
2
1
1
1
1
2
1
1
0
0
1
1
1
2
2
0
1
2
2
0
1
1
1
1
0
1
1
2
0
2
0
2
2
1
1
1
2
1
1
1
0
1
0
1
1
1
1
2
0
2
2
2
1
1
1
1
1
0
1
0
0
0
1
1
1
1
1
1
1
2
1
0
0
1
1
1
1
1
0
1
1
1
0
1
0
1
0
2
2
1
1
1
1
1
0
1
0
1
2
1
1
1
1
2
0
0
0
2
1
1
0
1
1
1
0
1
0
1
1
1
1
1
0
0
1
1
1
2
2
1
2
1
1
2
1
1
1
0
2
1
0
1
1
2
0
1
1
1
1
1
1
1
1
2
1
0
2
1
2
2
2
1
2
0
0
1
0
0
0
0
1
0
1
2
0
1
1
1
2
0
1
1
2
1
0
0
1
2
2
1
0
1
0
0
2
1
1
1
1
1
2
0
1
0
0
2
2
1
0
0
1
1
1
1
0
1
0
1
2
1
0
0
1
1
1
0
0
1
2
2
2
2
0
2
1
0
1
0
1
0
2
1
1
1
1
1
1
1
0
2
1
1
1
0
1
1
1
1
1
1
2
2
1
0
1
1
1
0
2
0
1
0
1
0
2
2
0
0
0
1
1
2
2
2
2
2
2
2
1
1
1
0
0
2
1
0
1
1
2
2
1
0
0
0
1
2
0
1
1
0
1
2
2
2
1
2
1
2
1
1
1
0
1
1
1
0
1
2
0
1
1
2
0
2
1
1
2
2
1
1
2
0
0
0
1
1
1
1
1
0
1
1
2
0
0
7
1
0
0
0
2
2
0
0
1
0
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
2
0
1
2
1
0
1
1
0
2
2
1
1
2
1
1
1
2
1
2
2
2
0
1
0
2
0
1
0
1
2
2
2
1
2
2
2
2
1
1
1
1
1
1
5
0
2
2
1
1
2
1
1
0
1
1
0
1
2
1
1
1
0
1
2
1
2
1
0
1
1
2
1
2
3
1
1
0
1
0
0
0
1
0
2
2
1
2
1
1
1
1
1
1
1
1
0
0
2
1
0
0
0
1
0
0
1
1
1
0
0
2
1
0
1
1
2
3
2
1
1
1
1
2
1
1
1
0
0
1
0
2
1
1
1
0
5
1
1
2
2
0
0
1
0
2
1
0
1
2
1
1
0
1
1
0
2
0
2
2
1
1
1
2
1
2
1
1
0
1
1
0
1
0
2
0
0
2
0
0
1
1
1
1
0
0
1
0
1
1
1
1
1
1
2
1
0
0
1
2
0
1
1
0
0
2
1
1
0
0
3
2
0
2
5
2
1
0
1
0
1
1
0
1
0
0
1
0
2
0
1
1
0
0
1
1
2
1
2
1
1
1
1
0
1
0
3
1
0
2
2
2
2
1
0
2
1
2
1
1
2
1
0
1
1
1
0
0
0
0
1
1
1
1
1
0
0
0
2
2
0
1
1
1
1
0
1
0
1
0
1
3
1
1
1
2
1
0
1
1
2
0
1
1
0
1
0
1
1
0
2
2
0
0
1
1
2
0
1
1
1
2
1
0
2
1
2
1
0
2
1
2
0
1
1
1
1
1
1
1
2
1
2
1
1
1
1
2
0
0
1
1
1
2
2
1
0
2
1
2
0
1
2
0
1
1
0
1
0
1
1
1
1
1
0
0
1
1
1
1
1
1
2
0
0
1
1
0
0
1
2
1
2
0
1
1
1
1
1
1
1
2
2
1
1
2
2
1
2
1
1
0
1
1
2
0
1
1
0
1
1
0
2
2
0
1
1
2
0
1
1
1
0
1
0
0
2
2
2
1
0
1
0
1
1
0
0
2
0
3
2
2
1
1
0
1
2
2
2
4
1
0
0
1
0
1
1
2
1
1
1
2
0
2
1
0
1
1
1
2
3
2
0
0
0
0
2
1
0
1
0
2
1
1
0
1
0
2
1
2
0
1
1
0
1
1
1
2
1
1
2
0
1
0
1
1
1
2
2
2
0
2
1
2
1
0
2
2
1
2
0
0
0
0
1
2
1
0
1
2
2
1
0
0
1
0
2
2
1
1
0
0
0
1
0
1
1
2
1
1
1
1
2
1
1
1
1
0
1
1
1
2
0
0
0
1
1
0
2
0
2
0
1
2
2
2
0
1
1
1
1
2
0
1
2
1
1
1
2
0
2
1
1
0
3
1
1
1
1
3
2
2
2
2
1
1
1
1
1
0
1
1
2
1
2
1
1
2
1
2
0
1
2
0
0
2
1
1
1
1
1
1
0
2
0
0
2
1
1
0
1
1
1
1
2
0
1
1
1
1
2
2
0
0
1
1
1
0
0
0
0
2
0
0
0
0
2
1
0
0
2
1
2
2
0
1
0
1
0
1
0
2
1
1
1
2
1
2
1
1
1
1
0
2
1
1
1
2
1
1
1
1
1
1
2
2
0
0
1
0
0
4
1
1
1
0
0
2
1
1
1
1
2
1
0
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
0
0
0
1
1
0
0
1
1
0
0
1
1
1
0
0
2
0
0
2
3
1
0
0
2
0
1
0
1
2
2
1
1
1
0
2
0
0
2
1
1
2
1
0
0
1
2
1
1
2
1
0
1
3
2
0
0
1
1
1
1
2
2
0
1
0
2
0
1
0
1
1
1
0
1
1
1
1
0
1
0
1
1
1
2
1
0
1
1
2
0
2
1
2
2
1
0
0
1
1
0
1
2
0
0
2
1
1
2
2
2
1
0
1
1
2
0
2
1
1
1
1
0
0
0
2
1
1
1
0
0
1
2
0
1
1
0
0
1
0
1
0
1
1
2
0
1
1
1
2
1
1
2
0
1
2
0
2
1
0
1
0
0
0
1
2
0
0
1
1
1
0
1
1
1
0
0
0
1
0
1
2
1
1
0
2
0
1
1
2
2
0
0
1
1
1
1
0
1
1
1
2
0
1
1
0
2
2
2
1
0
1
1
1
1
0
2
2
3
1
1
1
0
1
0
1
2
1
0
1
0
1
1
1
2
0
1
0
0
0
1
0
1
2
1
2
2
1
1
2
1
1
0
0
0
0
1
2
1
1
1
1
2
1
1
2
0
1
0
1
0
1
1
1
1
0
2
2
2
2
0
1
1
1
2
1
1
1
1
2
0
0
0
2
0
2
0
1
1
1
2
0
1
1
1
2
1
1
1
2
2
0
2
2
0
2
1
1
2
1
1
0
0
2
2
0
1
2
2
1
0
1
1
1
2
1
2
1
1
1
2
0
0
3
1
1
7
1
0
2
1
0
0
1
2
0
1
2
2
1
0
0
0
0
1
1
1
1
0
0
1
2
1
1
0
1
1
1
1
1
1
0
2
1
0
2
1
0
2
1
1
0
1
0
1
1
3
0
1
1
1
1
1
1
1
1
0
1
2
2
2
1
1
0
1
1
0
1
0
1
2
1
1
1
0
2
2
2
0
2
1
1
1
2
1
2
1
1
2
0
0
0
0
0
1
0
0
1
2
1
1
1
0
1
0
0
2
0
2
0
1
1
2
0
2
0
1
1
0
0
0
0
1
1
1
2
1
1
1
0
2
1
1
1
0
2
1
1
0
1
2
2
0
1
0
2
0
1
1
2
2
0
1
0
1
1
0
2
1
0
2
1
1
0
1
0
1
1
0
0
0
1
1
1
0
1
2
2
1
1
1
1
1
1
2
3
2
0
0
1
2
2
2
1
1
0
1
0
0
2
0
0
1
1
1
1
2
0
0
2
1
0
2
1
2
1
2
0
2
1
0
1
0
1
0
2
1
2
1
1
1
0
1
2
0
2
1
1
0
0
2
1
0
1
1
1
0
0
0
1
1
1
0
1
1
1
0
0
2
0
2
2
1
2
2
1
1
2
2
4
1
0
0
0
2
1
1
2
1
2
2
0
1
0
2
1
2
1
2
1
0
0
1
1
0
0
1
0
2
1
1
0
1
1
1
2
0
1
1
0
1
2
1
0
2
3
1
0
2
1
1
1
2
0
3
1
1
2
1
1
1
0
1
1
0
1
0
1
1
3
2
0
0
0
1
1
1
1
2
1
1
1
1
2
1
2
2
4
0
1
1
1
1
0
1
2
0
2
2
2
0
1
1
0
2
1
2
1
0
2
1
1
1
0
1
0
1
2
1
1
1
1
0
1
1
1
1
0
0
1
2
1
0
1
1
1
0
1
1
1
1
1
2
2
1
2
0
1
1
1
1
1
1
0
1
1
1
1
1
0
0
3
1
0
0
0
1
2
0
1
1
1
1
1
1
1
1
1
0
2
0
1
1
0
1
0
0
1
0
1
1
1
2
0
1
1
0
1
2
0
2
0
2
1
2
0
1
2
1
2
1
0
2
1
2
2
1
1
2
1
0
2
1
1
1
1
1
2
1
2
0
0
1
0
2
1
0
0
1
1
2
0
1
0
2
3
1
1
1
0
1
1
0
0
1
1
1
3
1
1
0
1
1
0
1
1
1
1
0
0
1
1
1
2
0
0
1
1
0
0
2
1
0
1
1
2
1
1
1
1
1
1
1
0
3
1
0
1
1
0
0
0
3
2
0
2
2
2
0
1
0
1
2
0
0
0
1
1
0
0
1
1
1
1
0
0
0
0
2
1
1
0
1
1
1
0
1
1
1
1
1
1
2
2
2
0
0
1
2
2
1
1
0
0
1
1
1
1
1
1
1
1
2
1
0
1
1
0
1
1
3
1
1
1
0
1
0
2
0
2
2
0
1
1
0
1
1
0
0
1
1
0
1
0
0
0
1
1
1
0
0
1
1
0
1
1
1
0
0
0
0
1
1
2
0
2
2
4
2
0
2
0
1
2
1
1
1
2
1
1
1
0
1
1
3
1
0
0
2
1
0
1
1
0
1
0
2
1
1
1
2
2
0
0
0
1
1
2
1
1
0
2
0
1
1
1
0
0
1
0
1
0
1
1
0
1
0
2
0
1
1
0
2
0
2
2
2
0
1
1
1
1
2
0
1
1
1
1
1
0
1
0
1
0
0
0
0
2
0
1
1
0
1
1
1
0
1
0
1
2
1
1
2
0
1
1
1
0
1
1
2
2
1
1
2
1
0
1
1
1
2
2
0
0
0
2
0
0
3
2
1
1
1
2
2
0
0
1
1
1
1
1
1
0
0
1
2
2
1
1
1
2
1
1
2
0
2
2
0
1
1
1
1
1
2
1
1
1
2
1
0
0
3
2
1
1
1
1
2
1
0
1
1
1
1
2
0
0
1
1
2
0
1
1
1
1
2
0
1
1
2
1
0
0
1
0
1
0
2
1
1
1
1
1
1
1
0
1
2
1
1
1
0
1
1
1
1
2
1
2
1
0
2
2
0
0
1
1
2
0
2
1
0
1
0
1
2
0
1
1
0
1
1
0
2
1
1
1
1
1
1
1
0
2
2
1
0
1
0
2
1
0
1
1
3
2
0
0
2
0
1
0
2
0
0
0
0
0
1
1
2
1
1
2
2
0
1
1
2
1
1
0
0
1
2
1
1
1
1
1
1
0
1
2
2
1
0
0
0
2
0
0
1
1
1
0
1
1
1
1
1
2
0
2
1
1
1
0
1
1
2
1
1
0
2
1
0
0
0
1
0
1
1
2
2
1
0
0
1
2
1
0
0
0
2
0
0
1
1
1
0
0
0
1
1
0
2
1
0
1
1
1
2
0
1
1
2
1
1
2
0
1
0
1
1
1
2
1
1
1
1
1
1
0
0
1
3
1
1
2
1
1
0
1
1
1
1
0
0
0
0
1
2
1
1
0
1
2
1
2
1
1
1
2
0
2
1
1
1
0
0
2
1
2
2
1
1
0
0
0
1
2
2
1
0
2
1
1
1
1
1
1
0
1
0
1
0
0
1
1
1
1
1
1
3
1
1
1
0
2
1
1
1
1
0
2
1
0
1
0
1
1
2
0
2
0
2
2
1
0
1
2
1
1
0
1
2
0
0
1
1
0
1
1
2
1
2
3
1
1
2
1
0
0
1
0
1
1
0
1
0
1
1
0
2
2
1
0
1
1
1
0
2
1
2
0
0
1
1
1
1
1
0
1
1
2
2
0
2
2
1
2
2
0
1
0
1
0
1
0
1
1
1
1
1
2
1
2
0
0
1
0
0
1
1
1
1
1
2
1
1
1
1
1
1
2
2
2
1
1
0
1
2
1
2
1
1
1
0
2
0
1
2
0
1
0
1
0
0
1
1
1
2
0
0
1
1
1
0
0
0
2
1
1
1
3
1
1
0
1
2
2
1
1
2
0
0
2
1
1
1
2
2
1
0
2
0
0
1
1
1
1
2
1
1
2
1
1
1
1
1
1
0
2
3
0
1
1
0
1
2
0
1
1
0
1
1
1
1
1
0
2
2
2
1
0
2
1
0
2
0
0
1
2
1
1
1
2
1
1
1
0
1
1
1
1
0
1
2
1
1
0
1
1
0
2
1
1
2
1
1
1
0
2
1
2
1
0
0
1
0
1
2
2
0
2
2
0
1
2
1
1
1
0
1
0
1
0
1
1
0
1
0
1
1
1
0
1
0
0
1
2
1
1
1
1
1
1
0
1
2
1
2
0
1
0
1
1
2
1
0
2
1
1
1
1
1
2
2
1
1
1
1
1
1
2
2
1
2
0
1
1
1
1
1
0
1
1
1
2
1
2
0
2
1
2
1
1
0
0
1
1
0
1
2
1
1
1
2
0
1
0
2
2
1
1
2
1
2
2
0
1
1
0
1
1
0
1
1
0
1
0
2
2
2
1
1
1
1
1
0
1
0
1
1
0
1
0
1
1
0
0
1
1
1
1
2
0
1
1
1
1
1
0
1
2
1
1
0
1
2
2
1
0
0
1
1
0
1
1
0
1
0
0
1
0
2
0
1
0
0
1
1
1
1
2
0
1
1
1
1
2
1
2
2
2
1
1
1
2
0
2
1
0
2
1
1
0
1
1
1
1
1
5
1
0
1
0
1
1
1
1
0
1
1
1
0
1
2
1
2
1
1
1
1
2
0
2
1
1
1
2
1
1
1
0
1
1
0
1
0
3
1
0
1
2
1
1
0
0
1
0
2
1
0
1
1
1
2
1
2
1
1
2
2
0
1
1
1
1
1
2
1
0
2
1
2
2
1
1
1
0
1
0
1
2
1
1
0
1
0
0
1
1
2
1
1
2
2
1
0
0
1
0
1
1
0
2
0
1
0
2
1
0
0
0
2
1
1
2
2
0
1
2
0
2
2
0
1
1
1
1
2
2
1
1
1
2
0
1
1
2
0
1
1
0
1
0
2
0
1
2
1
1
1
0
0
2
1
1
1
1
1
1
1
0
2
2
0
2
0
2
1
0
1
2
0
0
1
2
1
1
2
1
2
0
1
1
0
1
3
1
1
0
2
1
2
1
1
1
1
2
1
0
1
2
1
2
2
2
0
1
0
1
3
1
2
1
3
2
2
0
0
0
1
1
0
1
0
1
2
2
1
1
2
1
1
2
1
1
2
1
1
0
2
1
0
2
1
0
0
2
1
1
1
2
0
1
0
1
1
1
1
2
1
2
0
1
1
0
1
2
2
0
1
2
1
1
0
1
0
2
1
1
1
2
1
0
1
2
1
0
0
2
1
1
1
0
0
1
1
1
1
1
1
0
0
1
0
3
2
1
2
1
2
3
1
4
1
0
2
0
0
1
1
0
0
1
1
1
2
0
1
2
1
1
2
2
1
1
1
1
1
0
1
1
1
0
0
2
1
1
1
1
0
1
2
2
2
1
0
1
2
1
0
1
1
1
1
0
0
1
1
1
0
0
0
1
1
1
1
2
0
0
2
2
1
1
1
1
1
2
2
1
1
1
0
1
0
2
2
0
2
1
2
1
0
1
0
0
0
1
0
1
1
0
1
0
1
1
2
1
1
2
1
1
1
1
1
0
1
1
1
1
1
1
1
1
0
1
0
0
1
1
2
1
1
1
0
0
1
1
2
2
0
1
1
2
1
1
1
2
1
1
1
6
1
0
1
1
0
0
2
0
1
1
0
1
0
1
1
0
1
0
2
1
2
2
2
0
1
1
0
2
0
1
0
1
1
0
1
0
3
0
1
0
0
2
2
1
1
1
2
1
0
0
0
1
2
2
2
2
0
1
2
2
1
1
1
1
1
1
1
0
1
0
1
2
2
0
0
1
1
2
1
1
1
2
3
1
0
1
1
3
0
0
1
2
2
1
2
1
1
1
1
1
1
1
0
1
1
0
0
1
0
3
0
0
1
2
1
2
0
0
0
1
1
2
0
1
2
0
1
1
0
1
0
0
1
0
1
0
0
1
1
1
0
1
1
1
2
0
0
1
2
1
1
1
0
1
2
1
0
2
1
0
1
1
2
2
1
0
0
2
2
1
1
0
0
0
1
2
1
1
0
1
0
1
0
1
2
2
1
1
1
2
2
1
1
1
0
0
0
2
1
2
2
2
0
2
2
0
1
1
2
1
2
1
1
1
1
2
0
2
1
2
1
2
2
0
0
0
2
1
2
2
1
1
1
1
0
1
2
1
1
0
0
1
2
0
2
1
1
1
1
1
2
2
1
1
0
1
0
2
1
1
1
1
0
1
2
1
0
0
1
1
4
1
1
1
1
2
1
0
2
0
1
1
0
1
1
1
1
1
1
1
0
0
2
0
1
0
2
0
1
1
1
2
0
1
2
2
2
2
1
1
1
0
1
2
0
1
2
2
0
1
1
0
0
1
1
0
2
0
0
0
1
2
1
2
1
1
1
1
1
0
2
2
3
1
1
2
1
1
1
0
1
1
1
1
0
0
0
0
1
1
1
1
2
0
1
1
2
0
1
1
0
1
1
1
1
2
1
0
2
1
2
1
2
2
0
0
2
2
2
2
1
1
1
2
1
1
1
1
1
2
0
1
1
1
2
1
1
2
1
2
1
0
0
2
0
2
2
0
1
1
1
0
0
0
2
1
1
0
0
1
1
0
2
0
1
2
0
1
1
1
1
0
0
1
1
1
1
1
0
0
1
1
0
0
1
2
2
2
0
1
0
1
1
0
2
1
0
2
0
2
1
0
1
2
1
2
1
0
0
1
2
0
0
0
0
1
1
0
1
0
1
0
0
1
0
0
1
2
2
0
1
0
1
1
1
1
2
0
0
1
2
2
0
3
1
1
2
1
1
0
2
0
0
1
2
1
1
1
2
1
0
0
2
1
2
1
2
0
1
2
1
0
1
2
1
2
1
1
1
1
1
1
0
1
0
1
1
2
2
1
0
1
1
3
1
1
0
1
1
2
1
1
0
0
0
1
1
1
1
0
1
2
2
0
1
2
1
0
1
1
0
1
1
0
2
1
2
1
2
0
0
1
3
2
1
1
2
2
1
1
1
1
1
2
1
1
2
0
1
1
2
1
1
1
1
2
1
0
1
1
1
2
1
1
0
1
1
1
2
1
0
0
1
0
2
1
1
1
1
1
2
2
1
1
2
0
1
1
0
1
0
0
1
0
0
2
3
0
1
0
2
2
1
1
0
1
2
1
1
1
1
0
1
1
2
1
1
1
1
1
2
0
2
2
0
4
1
1
2
3
1
1
0
0
2
1
1
1
0
1
1
1
0
2
0
2
2
0
1
0
1
1
0
1
1
2
1
0
2
1
1
1
2
1
1
1
2
2
1
1
2
0
1
1
1
3
1
0
0
1
0
1
1
2
1
1
2
0
1
1
1
0
0
2
2
2
1
0
0
1
2
1
1
2
1
0
1
1
0
1
0
0
2
1
1
0
1
1
0
0
1
0
1
0
1
1
0
2
2
0
2
2
1
0
1
1
1
2
2
2
1
2
1
1
1
2
2
1
2
1
1
2
0
0
1
1
0
1
1
2
1
0
2
0
0
0
1
0
0
1
2
0
1
1
1
0
2
1
1
1
1
2
2
1
1
1
2
1
1
1
1
1
1
1
1
0
1
2
1
2
1
1
1
0
0
1
0
1
1
2
0
1
1
1
1
1
2
0
2
0
1
1
1
1
0
0
2
1
2
1
1
1
1
1
1
0
0
1
1
1
1
1
0
1
1
0
1
0
1
0
1
1
1
0
1
1
1
2
1
2
1
1
1
0
0
2
2
0
2
0
2
1
1
0
1
1
1
2
2
1
2
2
2
1
1
1
1
1
0
1
1
1
1
2
0
0
1
1
0
2
2
1
0
1
0
1
2
0
1
2
0
1
1
2
1
1
1
1
2
1
1
0
0
0
2
1
1
0
1
1
0
1
1
2
1
2
0
2
1
1
0
1
1
0
0
1
1
2
0
1
1
1
1
2
1
1
1
0
1
2
0
1
1
0
1
1
2
2
1
1
1
0
1
1
1
0
1
1
0
0
1
1
1
1
0
1
1
3
1
1
1
0
0
2
0
2
1
0
1
0
1
1
2
1
1
1
2
1
2
1
1
2
0
2
1
2
0
2
1
0
1
0
1
2
1
2
1
1
1
1
1
1
1
2
1
2
1
1
0
2
1
0
2
2
2
2
1
1
0
3
1
0
1
1
1
0
0
1
0
1
0
1
2
0
1
2
1
0
1
1
1
1
0
1
1
1
2
0
2
2
1
1
0
0
1
0
2
0
1
2
1
0
1
1
2
2
0
1
2
1
2
2
0
2
1
2
1
1
1
1
1
0
0
1
0
3
1
1
1
0
1
1
1
0
1
1
1
1
2
0
2
1
1
5
0
0
1
1
2
0
2
1
0
1
1
1
0
2
2
1
2
1
1
1
1
2
2
0
1
0
2
1
1
1
1
2
0
1
0
1
0
0
1
1
1
1
1
2
1
1
0
1
1
1
2
1
2
1
0
0
2
1
1
2
1
0
0
0
2
1
0
2
1
1
0
1
2
2
1
0
1
2
2
2
2
0
0
1
0
2
0
1
1
1
1
1
1
1
1
1
1
1
0
0
2
2
1
1
1
2
2
2
0
1
0
0
0
1
2
1
1
2
0
1
1
1
0
1
1
0
1
0
0
1
0
0
1
0
1
2
1
0
1
1
1
0
1
1
0
1
2
0
0
1
1
1
1
0
1
1
1
1
1
1
2
0
1
1
1
2
1
0
1
0
2
2
1
2
2
1
0
0
2
1
0
0
0
0
2
1
1
0
1
0
2
0
0
1
0
2
1
0
0
1
1
1
1
1
1
2
2
2
0
0
1
1
1
1
1
0
1
0
2
2
1
1
1
0
2
2
0
1
1
2
1
0
1
1
1
1
0
0
0
1
1
0
2
2
0
0
2
0
0
1
1
2
1
2
0
0
2
0
2
1
2
1
2
1
0
0
0
0
1
0
1
0
1
0
2
2
1
1
2
1
1
2
2
0
1
1
1
1
1
1
1
1
1
1
1
1
2
0
2
2
0
1
1
0
0
2
1
2
1
1
2
1
2
1
1
2
2
1
0
1
2
1
0
1
1
1
1
1
1
2
2
0
1
2
1
0
0
2
1
1
1
1
0
1
1
0
2
1
2
0
2
0
1
1
0
2
0
2
2
1
1
0
0
1
0
0
0
0
0
0
1
3
1
2
2
1
0
1
2
1
4
0
1
2
2
1
2
2
1
1
2
2
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
2
1
0
1
2
0
0
1
2
1
0
0
1
1
2
1
1
1
1
1
1
1
1
0
1
2
1
2
1
2
1
1
2
1
0
2
2
0
2
1
1
0
2
1
0
2
2
1
1
2
2
2
0
1
2
1
1
2
1
3
0
2
1
0
1
1
0
2
0
1
2
1
1
2
1
2
1
1
1
1
1
2
2
1
1
1
2
2
0
1
0
1
1
1
0
1
2
3
0
1
0
1
1
2
0
2
1
2
1
1
2
0
2
2
1
1
2
1
0
1
0
1
0
0
1
1
0
1
1
1
0
1
2
0
2
1
1
1
0
2
2
1
2
2
1
0
0
0
1
2
1
1
1
1
1
1
1
1
1
0
1
2
1
1
1
0
1
0
2
1
1
0
1
1
1
0
2
0
1
1
1
1
2
1
2
1
2
2
1
0
1
0
1
1
0
1
0
0
1
0
0
1
3
0
0
2
1
1
1
0
2
1
1
2
1
1
1
1
0
1
1
0
0
0
1
1
1
1
2
0
2
0
1
1
2
0
1
0
1
0
0
0
2
0
1
1
0
2
2
1
1
1
0
1
0
0
2
1
1
0
1
1
0
0
0
1
1
1
0
0
0
1
4
1
2
2
2
1
1
1
2
1
2
1
0
1
2
1
0
2
2
0
1
2
0
0
1
1
1
2
2
1
1
1
1
2
2
1
0
1
1
1
1
1
1
0
1
1
1
1
0
1
2
1
1
1
2
0
2
0
1
0
0
0
1
0
1
1
1
0
0
2
1
0
1
0
1
1
2
2
0
1
1
1
1
2
1
1
1
1
2
0
0
1
2
1
1
1
1
1
1
0
1
0
1
1
2
0
2
1
1
1
1
1
2
1
0
2
2
0
0
0
1
1
2
2
1
1
1
2
1
1
0
1
1
1
0
1
1
2
0
0
1
0
1
1
1
0
1
2
0
0
1
2
1
1
0
0
1
1
2
1
1
1
2
1
1
1
1
1
1
1
0
1
1
2
1
0
2
2
1
1
1
1
1
1
1
0
1
1
0
1
1
2
2
3
1
0
1
1
1
2
1
1
1
0
2
1
1
1
1
1
1
0
2
2
1
1
1
3
2
1
1
1
1
0
1
1
0
1
1
1
1
1
2
0
2
2
0
2
0
1
0
1
1
1
1
1
0
0
2
1
0
1
1
2
0
1
0
0
0
1
2
2
2
1
0
1
0
0
2
1
1
1
1
1
0
2
2
2
1
1
1
1
1
0
1
1
1
1
1
0
0
0
2
2
2
1
1
0
2
1
1
2
2
2
0
0
2
1
1
1
1
0
0
1
1
1
2
1
1
0
1
0
2
1
3
1
1
0
1
1
0
1
1
1
1
0
1
0
2
0
1
1
1
1
1
1
0
0
1
1
2
1
0
0
1
1
1
1
1
1
0
1
1
0
2
0
2
1
1
0
1
0
0
0
1
1
2
1
1
1
1
2
1
1
1
2
1
1
2
0
2
1
2
2
1
1
0
0
0
2
2
0
0
1
1
2
0
2
2
0
1
0
1
1
1
0
2
1
2
1
2
2
2
0
0
1
2
1
0
2
1
1
0
0
1
1
2
1
1
2
2
0
0
0
3
1
2
2
1
2
2
1
2
1
1
1
2
0
0
1
1
1
0
0
1
1
1
1
1
1
1
0
1
2
1
1
0
2
1
1
0
2
0
1
1
1
1
0
0
1
0
2
2
0
1
3
2
1
1
2
1
1
0
2
2
0
1
1
0
1
1
2
1
3
1
1
1
1
0
1
1
3
1
1
1
1
0
1
0
1
1
0
2
2
1
1
1
1
1
1
0
2
0
0
1
1
2
1
1
1
1
2
0
1
0
0
1
0
0
1
0
2
2
0
0
1
0
0
1
1
1
2
1
1
2
1
0
0
0
2
2
1
0
2
0
1
2
1
1
0
1
0
1
1
2
1
1
1
1
0
2
2
0
1
0
1
1
1
2
2
1
0
1
1
1
1
1
2
2
1
0
0
1
2
1
1
0
1
0
2
0
0
0
1
1
2
2
1
1
1
0
1
2
1
0
1
1
1
2
0
0
1
0
0
0
1
1
1
2
1
0
0
0
1
0
1
2
0
1
0
1
0
1
0
1
1
1
0
1
0
1
0
0
2
0
1
1
0
1
0
1
0
1
0
1
0
1
1
1
2
1
0
1
1
2
1
0
0
2
1
1
1
1
1
1
0
2
0
0
0
1
2
1
1
1
1
0
1
2
1
1
1
0
0
0
1
2
1
1
3
2
2
1
1
1
0
0
0
3
1
1
1
2
2
2
0
0
1
1
2
1
1
0
0
2
1
2
0
0
2
0
0
1
1
1
1
1
0
0
0
1
1
2
0
0
0
2
1
1
1
1
0
0
2
1
2
0
1
1
0
1
2
1
1
1
1
1
0
1
0
1
1
1
1
1
2
0
1
1
2
1
0
1
0
2
0
2
1
2
1
1
0
0
1
2
1
2
2
3
1
1
0
2
1
1
1
0
1
1
0
1
1
1
1
0
0
1
1
1
1
1
1
0
1
2
2
1
0
0
2
0
0
0
1
1
1
1
1
0
0
0
1
1
1
2
1
1
0
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
0
1
2
1
0
0
2
0
0
1
2
2
0
1
2
1
0
2
2
1
1
1
0
0
0
1
1
1
1
0
2
0
1
1
2
1
1
1
0
1
1
1
2
1
0
1
1
1
1
1
1
1
1
6
1
2
0
3
1
0
1
1
0
1
2
2
1
0
1
0
2
1
2
1
1
1
0
1
0
2
1
2
0
0
2
1
1
1
2
0
1
0
1
0
1
1
0
2
1
1
2
0
2
0
1
2
0
2
0
2
1
1
2
1
1
1
1
0
1
0
1
0
2
1
2
1
1
0
2
2
2
0
0
1
2
1
2
1
2
2
1
0
1
2
2
1
2
1
1
2
1
1
1
1
1
1
1
1
2
1
0
1
0
1
1
2
3
0
1
2
1
1
2
2
2
0
2
2
1
2
0
1
2
0
0
1
0
1
1
2
2
0
0
0
0
0
1
1
0
0
2
0
0
0
0
1
1
1
1
1
1
0
0
2
0
2
1
2
0
2
0
0
2
0
0
1
2
2
1
2
1
1
0
2
2
0
2
2
0
0
0
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
2
0
2
1
2
0
1
1
0
0
0
1
2
2
2
1
0
1
2
0
0
2
1
2
2
0
2
1
2
0
0
0
1
1
2
0
0
0
2
3
2
2
1
0
2
2
1
1
1
0
0
0
0
2
1
0
2
2
1
3
2
0
0
1
0
0
0
2
0
2
1
0
1
1
0
2
2
0
1
0
1
3
1
1
2
2
2
2
2
0
2
1
1
1
1
1
1
1
2
0
2
0
1
1
2
1
0
1
1
1
0
1
1
1
0
2
0
1
1
1
1
1
2
0
0
1
5
1
1
2
2
2
1
0
1
2
1
1
2
1
1
1
1
0
1
1
2
2
0
1
2
1
1
1
0
1
0
2
1
1
2
3
1
1
2
1
1
1
1
0
0
0
2
2
0
1
2
1
0
0
1
0
2
0
0
1
2
1
0
2
0
1
1
0
0
2
1
2
0
0
2
1
0
0
1
1
0
0
2
2
0
1
1
0
1
0
0
1
0
1
1
2
0
1
0
1
1
2
1
1
1
1
1
2
3
2
0
0
2
0
1
2
1
1
1
1
2
1
0
2
1
1
2
1
1
1
2
1
1
1
1
2
1
2
1
1
1
0
1
0
2
1
0
0
2
0
1
1
0
2
1
1
0
0
2
1
1
1
1
0
1
2
1
0
0
2
0
4
2
0
1
1
1
1
1
2
1
2
5
0
1
0
1
2
1
0
1
3
0
1
1
2
2
1
0
0
1
1
0
0
1
1
0
0
2
1
1
0
0
2
1
2
1
1
2
0
0
2
1
2
1
2
1
1
1
0
1
0
1
1
2
1
1
2
2
2
1
0
0
0
0
1
1
0
1
1
2
1
1
1
0
1
1
1
0
0
2
1
0
1
0
1
1
1
1
0
1
2
1
0
1
1
1
1
1
1
0
1
0
1
1
1
1
1
1
2
2
1
1
1
1
2
2
2
1
0
1
2
1
1
1
1
2
0
1
1
0
1
1
0
1
1
1
1
2
1
1
0
1
2
2
1
0
2
2
1
2
2
1
1
1
1
0
2
1
0
0
0
1
2
2
0
2
0
1
1
2
1
2
0
1
0
2
0
0
1
0
0
1
1
1
0
1
1
1
2
1
1
1
1
2
1
0
0
1
2
2
1
1
0
1
1
0
1
0
0
1
1
1
2
1
2
2
1
0
1
2
1
1
0
2
1
0
1
0
1
0
1
1
0
2
2
1
0
0
1
1
1
2
1
1
2
2
1
1
1
1
2
1
1
0
0
1
1
2
1
0
1
0
1
1
0
1
2
1
0
0
0
1
2
2
1
1
1
0
1
2
0
2
0
1
0
2
0
0
1
1
2
1
1
2
0
2
1
0
0
0
1
1
1
1
0
1
1
1
0
2
0
3
0
4
1
1
1
1
1
0
2
2
1
1
1
2
0
1
2
0
1
0
1
2
1
0
1
1
1
2
0
1
2
1
0
0
1
1
0
1
0
0
1
0
2
1
1
1
2
1
0
0
2
1
0
0
0
0
2
1
2
2
0
1
1
0
2
0
1
2
1
2
1
1
0
0
0
2
0
0
2
0
2
2
0
0
1
1
1
2
2
0
1
1
2
1
1
1
0
1
1
1
1
1
1
1
2
0
1
0
1
1
0
0
1
1
0
1
1
1
1
0
0
1
1
1
1
0
1
1
1
2
1
1
1
1
2
1
1
1
1
1
1
2
0
1
1
5
1
0
1
2
1
0
2
2
1
1
1
1
2
1
1
1
1
0
2
1
1
1
1
1
0
1
1
1
0
2
1
2
0
1
1
1
0
1
1
2
2
1
1
0
1
1
0
0
0
1
0
0
1
1
1
3
0
1
1
1
2
1
2
0
1
0
1
0
1
2
1
1
1
1
1
1
1
3
1
2
0
1
2
2
1
1
1
1
0
1
0
1
1
0
2
1
2
0
1
2
1
1
2
0
0
1
0
1
1
1
0
2
0
1
0
0
1
1
0
0
2
1
0
1
2
1
0
0
1
1
0
2
0
2
1
2
0
1
2
1
2
1
0
1
2
2
0
1
1
1
5
1
0
1
0
1
1
0
0
1
0
1
1
0
0
1
1
0
1
0
1
1
1
0
0
1
2
2
2
1
2
2
0
1
0
1
1
1
1
2
0
1
1
1
1
1
2
0
1
0
0
0
1
2
1
1
1
0
0
0
1
2
0
0
2
0
2
1
1
1
1
1
2
0
0
1
2
0
2
1
0
1
1
1
1
1
1
1
0
0
1
1
1
0
1
0
1
1
2
1
2
1
1
1
1
2
1
0
0
2
2
0
1
0
0
1
1
1
0
2
1
0
1
1
2
1
0
1
1
0
1
1
0
2
0
1
1
1
1
2
1
1
1
1
0
0
2
2
0
2
2
1
1
0
2
2
2
1
0
0
1
1
0
1
2
1
1
0
1
0
1
1
0
2
1
1
1
0
1
1
3
0
1
2
1
2
0
1
0
1
1
2
1
1
0
1
1
0
1
1
1
0
1
0
0
2
0
0
1
0
0
0
2
0
1
0
1
1
2
0
2
1
1
1
1
2
1
0
1
1
1
1
1
2
1
0
1
0
1
0
0
2
1
2
1
2
1
2
1
1
2
1
1
1
2
2
1
1
1
1
2
1
0
1
0
0
1
2
1
0
1
1
1
1
1
1
2
1
1
2
1
2
1
1
1
1
0
1
1
1
0
1
1
0
1
0
1
1
1
1
1
0
1
1
1
0
11
0
2
0
2
1
1
2
2
1
0
0
1
0
2
1
1
1
0
0
1
2
0
1
1
0
2
1
0
2
1
1
1
2
1
0
1
2
0
2
0
2
0
1
2
2
1
0
1
0
0
0
1
1
1
1
1
0
1
0
2
2
1
2
2
3
0
1
1
1
0
1
2
1
0
0
0
1
1
1
2
4
1
1
2
0
0
1
2
0
1
0
2
2
0
0
1
1
0
1
1
2
1
1
1
0
2
1
1
1
1
3
0
2
0
1
1
0
2
0
1
2
2
0
1
1
2
1
1
0
1
2
2
1
2
0
1
0
3
0
2
0
2
1
1
0
1
1
1
2
1
1
1
1
1
1
1
0
1
1
1
1
0
0
2
2
1
0
2
1
1
2
0
0
1
1
1
2
2
1
1
2
0
1
1
2
2
0
1
0
1
1
1
0
1
1
0
1
0
2
0
2
1
1
2
2
0
0
1
0
1
2
1
1
0
2
0
1
1
1
1
1
1
1
1
1
1
0
1
1
2
2
1
0
2
0
1
1
1
2
2
0
1
1
2
2
2
2
1
1
1
1
0
2
1
1
1
1
0
1
2
2
1
1
1
1
1
0
2
1
1
2
0
0
1
0
2
0
1
2
1
1
1
0
1
0
0
1
1
0
1
2
2
0
1
1
1
0
1
1
2
1
0
1
1
2
1
0
1
1
2
1
0
0
2
1
1
1
1
2
2
0
1
2
1
1
2
2
0
0
1
1
0
1
1
1
1
1
2
0
2
0
1
1
1
1
1
2
0
2
0
1
2
2
0
1
0
1
0
1
0
3
1
0
1
0
0
1
0
2
1
1
0
0
2
0
0
1
2
1
1
2
2
1
1
1
2
1
1
2
1
2
1
2
2
0
1
2
0
1
1
1
0
0
0
2
1
1
0
2
1
2
0
1
2
0
1
2
1
1
2
1
1
1
2
2
1
1
1
3
1
2
1
1
2
0
0
2
0
1
0
1
1
1
1
1
0
1
2
1
1
0
1
2
1
1
0
1
1
1
1
2
1
0
1
1
0
1
2
1
0
0
1
1
0
2
2
1
1
0
1
1
1
0
1
1
1
1
0
1
1
2
1
2
3
2
0
1
0
1
2
1
0
1
1
2
0
1
2
0
0
0
2
0
1
0
1
2
0
1
0
2
0
1
1
2
1
1
2
1
1
1
1
1
1
1
0
0
1
1
2
1
2
0
1
1
2
1
1
2
2
0
1
1
1
2
2
1
0
1
0
1
2
1
2
1
0
1
0
0
1
1
0
1
1
1
1
1
1
0
2
1
0
1
2
1
1
1
1
0
1
1
1
0
1
2
1
1
1
0
1
2
1
1
2
0
1
0
1
2
2
3
1
1
1
1
2
1
1
1
2
1
1
0
1
1
1
2
2
1
2
1
1
1
1
1
0
1
1
0
2
2
1
2
2
0
0
1
1
1
1
1
1
1
1
0
0
1
1
1
0
1
1
0
1
0
2
1
2
1
1
1
2
2
0
1
0
2
1
1
0
1
2
1
1
1
3
1
1
3
1
1
2
1
2
0
2
1
0
2
2
2
1
1
0
0
0
0
2
1
0
1
1
1
2
1
1
0
0
0
0
1
1
1
2
1
2
0
0
0
0
1
1
0
1
2
1
1
0
1
0
0
1
1
0
2
1
1
0
1
2
2
0
0
2
1
1
1
1
1
0
2
0
2
1
1
1
0
0
1
1
0
1
1
1
0
1
2
2
2
1
1
2
0
1
1
1
1
1
2
0
1
1
1
1
2
2
0
2
0
1
2
1
2
3
0
1
0
2
0
1
0
0
1
1
1
2
1
1
1
2
2
1
2
0
0
0
0
2
0
1
1
1
1
0
1
1
0
0
1
0
0
1
2
1
1
1
2
1
1
0
2
1
1
1
2
1
0
1
3
1
0
2
0
2
0
2
2
2
1
1
1
1
2
2
1
1
1
1
1
1
0
2
2
1
1
1
1
0
1
0
1
1
0
1
0
0
1
1
1
1
0
1
1
0
1
1
1
1
0
1
0
0
2
1
1
2
1
1
2
0
2
0
0
1
1
2
2
1
1
2
0
2
1
0
2
2
1
0
1
1
0
0
1
1
2
1
1
1
1
4
1
0
0
2
0
1
1
1
0
0
1
1
0
2
0
0
0
1
0
2
1
1
1
1
1
1
0
1
1
1
2
1
0
0
0
1
0
0
1
0
1
2
1
1
1
2
1
2
0
1
1
2
1
1
0
1
1
1
2
0
2
2
2
1
1
2
2
1
1
1
0
1
2
2
0
1
1
1
1
1
3
1
1
0
1
2
0
1
0
1
2
2
2
1
0
2
0
0
0
2
1
1
1
1
1
0
1
0
0
1
0
0
1
0
2
1
0
2
1
0
0
0
1
1
1
1
1
1
1
1
0
1
2
0
1
2
2
0
0
1
1
1
1
1
1
1
0
0
2
2
1
2
1
2
1
0
2
0
1
0
1
2
1
1
1
2
0
1
0
1
2
1
1
1
1
1
1
1
1
1
1
0
1
1
0
0
1
1
0
1
1
1
0
1
1
3
0
1
1
1
1
3
1
1
1
2
1
1
1
0
1
1
1
0
2
1
0
1
1
1
1
0
0
1
1
2
1
2
0
1
0
1
2
2
2
1
0
2
2
0
1
1
0
1
1
1
1
0
1
3
4
1
1
0
1
1
1
0
1
0
0
1
1
0
0
2
0
1
0
1
1
1
0
1
1
1
4
1
1
0
3
0
1
0
0
2
2
1
2
0
1
2
1
0
0
2
2
0
0
1
2
1
2
1
1
2
1
1
2
0
1
1
1
2
1
0
0
2
2
2
0
1
1
1
3
2
2
1
2
2
3
1
1
1
1
0
1
0
0
2
1
0
2
2
2
2
1
0
1
2
0
0
0
1
2
1
0
0
0
1
1
0
0
1
7
1
0
2
1
2
2
0
0
1
1
0
1
2
1
1
1
2
2
1
0
1
0
0
0
0
1
2
0
2
1
1
0
0
1
1
1
2
1
2
1
2
1
2
1
0
0
1
0
1
2
2
1
2
2
1
1
2
1
0
0
1
2
1
1
1
1
1
2
1
1
0
1
0
0
1
1
1
1
2
0
0
2
1
3
0
1
0
0
2
1
1
1
1
1
0
0
2
0
1
0
2
1
1
0
2
0
1
0
0
1
1
2
0
1
2
1
0
2
1
1
1
0
2
0
1
0
1
1
1
0
1
0
1
1
1
1
0
1
2
1
0
0
0
0
0
1
2
1
0
1
1
1
0
2
2
1
2
1
1
1
2
2
0
1
1
1
2
3
0
1
0
2
1
1
2
0
1
1
1
1
0
2
2
1
2
1
1
1
1
2
1
0
1
1
0
1
2
1
2
1
0
0
2
0
1
2
1
1
0
1
1
2
0
0
1
2
1
2
1
0
0
1
1
0
1
2
1
1
2
0
0
0
1
0
1
0
2
2
0
3
2
0
2
0
0
1
1
1
1
0
0
0
2
1
0
1
0
2
2
1
1
2
1
1
0
2
2
2
2
1
2
2
2
2
1
1
1
1
1
1
0
0
0
0
0
1
1
1
2
2
2
1
1
0
2
1
2
0
1
1
2
2
3
0
1
1
1
0
2
0
2
1
1
1
1
1
0
0
1
2
2
2
2
0
2
1
1
1
2
1
1
2
3
1
1
0
2
0
1
1
1
2
0
0
1
1
1
0
0
0
0
0
1
0
1
0
0
1
1
1
2
1
1
1
0
0
2
2
2
1
1
0
1
0
1
1
1
1
1
0
0
0
1
1
0
2
1
1
0
1
0
2
0
1
2
2
2
0
0
1
0
1
1
0
2
2
2
0
1
1
2
1
0
0
2
1
2
0
0
1
1
1
0
1
1
1
1
1
1
1
1
1
1
2
1
2
2
2
1
1
1
1
1
0
1
0
0
0
1
2
1
1
1
2
2
0
0
0
0
2
0
1
0
0
1
2
1
1
0
1
1
2
1
0
1
0
2
0
2
2
2
0
0
1
0
1
1
1
1
0
2
1
1
2
0
0
0
2
1
1
1
0
0
2
2
2
1
0
1
1
1
0
0
0
1
1
0
1
1
1
1
1
0
1
0
1
0
1
1
0
0
2
1
2
0
1
2
1
2
0
0
1
0
1
1
1
0
1
1
1
1
2
0
1
0
0
0
2
2
2
1
0
2
2
1
1
0
2
2
0
0
1
1
1
1
2
1
1
1
1
0
0
1
0
1
1
1
1
1
1
0
1
1
2
0
1
0
2
1
1
0
0
0
0
1
0
0
2
2
1
5
0
1
1
0
1
1
1
2
0
2
2
0
1
1
1
1
0
2
0
0
1
1
0
1
1
0
1
1
1
0
2
1
1
1
0
1
2
2
1
1
2
1
2
2
0
1
1
1
1
2
0
1
2
1
0
1
0
1
1
1
1
1
2
0
2
1
1
2
1
1
1
0
0
0
1
0
2
1
1
0
1
0
2
0
2
2
1
1
1
1
0
2
2
1
1
2
1
0
1
0
0
1
0
2
1
1
2
1
1
1
3
0
0
0
2
1
0
1
1
1
1
0
0
1
0
1
2
2
1
2
0
1
1
1
1
1
2
1
0
1
2
1
1
2
2
0
2
1
1
2
1
2
1
2
2
0
1
2
0
1
2
2
1
1
1
2
1
1
2
2
1
1
2
1
1
1
2
2
1
1
1
0
0
1
1
1
2
0
1
1
1
1
1
1
0
2
2
0
0
0
2
1
1
1
2
1
1
0
0
1
2
0
1
2
1
2
2
1
1
2
0
0
0
0
1
1
1
1
1
1
1
2
0
2
1
0
2
1
3
1
0
1
1
2
1
0
0
0
2
1
1
2
1
0
1
1
1
1
2
1
2
1
1
1
1
1
3
0
1
1
1
1
2
0
2
0
1
1
2
0
1
1
1
1
1
1
1
1
1
0
1
2
0
0
2
1
2
1
1
1
0
1
1
0
0
1
1
2
2
2
1
1
1
2
1
3
1
1
2
1
1
2
2
2
0
1
1
1
0
2
1
1
1
0
1
1
0
1
1
1
0
1
1
2
1
1
0
0
1
1
0
1
0
0
2
0
1
1
1
2
1
1
1
1
2
2
1
1
2
0
2
0
1
2
1
0
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
2
3
0
2
2
1
1
1
1
1
0
1
2
1
1
1
2
1
1
1
2
0
0
2
1
2
1
2
1
1
1
1
2
1
1
0
1
1
0
1
1
1
1
2
1
1
1
2
1
2
1
1
2
2
1
2
1
0
0
2
0
1
0
1
1
0
1
1
1
2
1
0
1
0
2
1
0
0
0
1
1
1
2
0
1
2
0
2
1
1
0
0
0
1
1
1
2
1
1
0
1
0
1
1
0
1
1
1
1
0
1
0
1
2
2
2
1
0
0
1
1
1
0
1
2
0
1
1
1
1
1
1
1
1
1
1
0
1
1
1
0
0
1
1
0
0
1
1
0
0
1
1
1
1
2
2
1
1
1
2
1
2
1
1
2
1
1
1
1
1
1
2
2
1
1
2
1
1
1
1
0
1
1
2
1
1
0
1
1
2
1
1
2
2
2
2
0
2
0
2
1
2
1
1
2
0
1
2
2
0
0
1
2
1
0
1
2
1
1
2
1
1
1
2
1
1
1
1
2
0
2
1
2
1
1
0
0
1
1
1
1
1
1
1
1
1
1
2
1
1
0
1
0
1
2
0
2
2
1
1
0
0
1
0
1
0
2
2
2
0
1
2
2
0
1
2
1
2
1
2
2
1
0
0
2
1
0
2
1
1
1
1
1
1
1
1
0
0
1
2
2
1
1
2
0
2
1
1
1
1
0
0
0
0
0
1
0
1
1
0
1
2
0
0
1
1
1
1
1
0
1
1
0
1
1
0
1
1
0
0
1
2
1
1
1
1
1
2
1
2
0
0
1
1
1
2
1
2
1
2
1
1
1
1
1
2
1
0
1
1
0
2
0
2
1
1
1
1
0
1
1
2
2
1
0
0
1
1
2
0
0
1
1
2
1
2
0
1
1
1
1
1
2
0
1
1
2
1
1
1
1
2
1
2
2
2
0
0
1
0
2
2
1
1
1
0
2
1
1
1
0
1
2
0
1
1
1
0
0
1
0
1
1
2
1
2
0
0
0
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
0
2
1
1
1
2
1
1
1
0
0
1
2
0
1
1
1
1
2
1
0
2
2
3
1
2
0
0
1
4
1
0
0
0
1
1
1
1
2
0
1
1
1
1
0
1
0
1
1
0
1
0
1
2
2
1
1
0
1
2
0
1
2
1
0
1
1
1
1
0
0
0
1
1
2
2
1
2
1
1
2
1
1
0
1
1
2
0
0
0
1
1
2
1
2
2
0
1
1
1
1
1
1
1
2
1
2
1
2
1
0
0
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
0
2
1
1
1
1
1
1
1
0
2
0
1
1
0
1
1
0
1
0
1
1
0
1
2
0
0
3
0
0
1
2
2
1
2
1
1
1
1
0
0
1
2
1
2
0
1
2
0
1
1
1
2
1
1
2
1
0
1
1
2
2
1
0
2
1
2
1
1
1
0
0
2
0
0
1
1
1
0
0
2
0
2
1
2
0
0
0
1
1
1
2
1
1
2
0
2
1
1
0
1
2
2
0
1
1
0
1
1
1
2
1
2
0
0
1
2
2
1
0
1
0
2
1
1
0
1
2
1
0
1
1
2
2
0
1
0
0
2
2
0
0
0
2
2
1
2
1
1
1
2
1
1
1
0
2
0
0
0
0
1
1
1
2
1
1
1
1
0
1
1
1
1
2
0
1
1
2
1
0
0
1
0
1
1
1
0
1
1
1
2
1
2
2
1
0
1
1
2
1
1
1
0
0
0
1
1
2
0
0
0
1
0
0
1
1
1
0
1
1
1
1
1
0
0
0
2
2
3
1
1
1
1
0
1
1
1
2
0
1
0
1
0
1
1
0
1
2
0
1
0
0
2
1
2
0
1
1
1
0
2
1
1
2
2
2
1
1
1
1
0
0
0
1
0
5
0
2
2
1
1
1
1
1
0
1
0
2
1
2
0
2
1
1
2
0
2
0
1
1
1
2
2
2
3
2
0
2
2
0
2
2
0
0
2
1
1
2
1
1
2
2
2
1
2
1
2
2
1
1
0
0
0
1
0
2
1
1
1
0
1
1
1
1
1
0
3
0
1
1
0
0
1
1
1
1
2
1
0
1
1
0
0
1
1
0
1
1
0
1
0
3
2
2
1
1
1
1
1
1
0
1
1
1
1
1
0
1
1
1
1
0
1
0
0
1
0
2
1
1
2
0
2
0
2
1
0
0
1
0
0
2
1
0
2
0
1
2
0
1
0
1
2
1
1
1
2
2
1
1
2
1
0
0
6
2
0
0
0
1
1
1
2
0
0
2
0
0
1
0
1
1
1
1
0
1
1
2
1
1
1
1
0
1
2
0
1
0
0
2
1
0
1
0
2
1
0
1
1
2
1
1
1
0
0
0
1
1
1
1
1
2
1
0
1
2
1
0
2
0
2
2
2
1
1
1
2
1
0
1
1
0
1
2
2
1
0
2
1
1
0
2
0
2
1
2
0
1
1
1
0
0
0
1
0
1
1
1
1
2
2
1
1
1
1
2
0
1
2
0
0
0
2
1
1
2
1
1
0
1
2
1
2
1
0
1
1
1
1
2
2
1
2
1
0
1
1
1
0
1
1
1
1
0
0
2
1
1
2
2
1
0
1
0
1
2
2
1
1
1
1
1
3
1
1
1
0
1
1
1
1
1
2
1
2
1
0
0
1
1
0
2
0
1
1
0
0
0
1
0
1
0
1
2
1
1
2
2
2
1
2
1
1
2
1
0
2
2
1
2
0
2
0
0
2
1
1
1
1
0
0
1
1
0
1
2
1
2
1
0
1
2
0
1
1
1
0
1
2
3
0
1
1
1
1
1
2
0
1
1
2
1
2
1
1
2
1
0
1
0
1
4
1
0
0
1
1
1
1
1
1
0
2
2
2
0
0
1
1
0
1
2
1
2
1
1
0
1
1
0
1
1
2
2
1
1
1
2
0
2
1
1
0
0
1
0
1
1
0
1
2
0
1
2
0
1
2
2
1
0
0
1
0
1
1
1
2
2
0
1
1
1
1
0
1
1
1
2
0
0
1
1
1
2
1
0
1
1
1
1
1
1
1
0
1
1
2
0
1
0
1
0
1
2
1
1
1
1
1
2
1
0
0
2
1
0
1
1
0
1
0
2
2
2
2
1
1
1
1
1
0
0
1
1
1
1
0
0
1
0
1
0
0
0
1
1
1
0
1
3
2
0
1
1
0
1
0
2
2
0
0
0
1
1
2
1
2
1
1
0
2
0
0
2
0
1
0
1
0
2
1
1
1
1
1
0
1
1
1
1
2
2
2
0
0
1
1
0
3
1
1
1
2
2
0
0
1
0
1
1
0
2
0
1
2
1
0
2
0
2
1
0
1
0
0
2
1
0
1
0
1
1
2
1
1
3
2
1
1
1
1
1
1
1
1
2
0
2
0
0
2
2
1
3
1
2
1
0
2
1
0
0
1
0
2
1
1
1
2
2
1
0
0
1
2
1
2
0
1
0
2
0
2
1
0
0
2
0
0
0
0
1
2
1
0
2
1
1
2
2
2
0
1
1
1
1
2
0
1
1
2
1
1
2
1
3
2
2
1
1
0
1
1
0
1
0
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
1
0
0
0
1
2
1
2
2
0
1
1
2
5
1
1
1
2
0
0
3
0
1
1
1
0
0
1
2
1
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
0
0
1
1
1
1
1
2
2
0
0
2
0
1
0
1
2
1
1
1
1
2
1
1
1
1
3
1
1
2
0
0
1
1
1
2
1
1
2
0
0
1
0
1
0
1
2
0
2
0
0
0
0
2
0
1
1
0
0
2
1
0
1
1
0
2
1
0
1
2
0
1
0
1
1
1
2
1
1
1
2
0
1
0
1
0
0
0
2
1
0
2
1
1
2
1
0
1
1
1
1
0
0
1
1
1
1
1
0
1
2
2
1
1
1
2
1
1
1
1
2
2
1
0
1
2
1
1
1
0
0
0
2
2
3
1
1
2
1
0
2
0
1
2
0
1
2
0
0
0
1
0
1
0
0
1
0
1
1
1
1
2
1
0
0
1
0
1
1
1
2
0
1
2
2
0
0
1
1
1
1
1
0
1
1
0
0
2
0
0
1
0
1
1
2
0
1
1
0
2
2
0
1
2
0
1
2
0
1
2
1
1
2
1
1
1
2
2
0
1
1
1
0
1
1
0
1
1
1
1
0
0
1
1
2
1
0
1
0
1
2
0
1
0
1
0
3
1
1
1
0
2
0
1
2
0
1
2
1
0
1
2
1
2
0
2
0
1
0
1
1
0
0
2
1
1
2
0
2
0
2
0
0
2
0
1
1
1
0
2
0
0
1
2
2
0
0
3
2
1
1
1
1
0
0
0
1
2
0
1
1
0
0
1
1
0
1
1
0
2
2
1
1
1
2
0
1
0
1
1
2
1
1
1
0
2
2
2
2
1
2
2
1
2
0
2
2
1
1
1
0
1
3
1
1
1
1
1
1
3
3
0
1
0
1
1
2
1
2
2
1
2
1
1
1
0
2
1
2
2
1
0
2
0
1
1
1
1
3
0
1
1
0
1
1
0
1
1
1
1
1
1
1
1
1
1
2
2
1
1
0
1
1
1
1
0
0
1
1
1
2
2
1
1
1
0
0
1
0
1
1
1
1
1
1
1
0
0
1
2
0
0
1
0
4
1
1
1
0
1
0
0
1
2
2
0
0
2
2
1
1
2
1
1
0
0
1
0
0
0
0
0
1
1
1
0
2
2
1
1
1
0
1
1
1
1
2
0
0
1
1
1
2
2
2
1
1
0
1
1
0
0
2
0
0
3
1
2
1
1
1
1
0
0
0
2
2
2
2
1
0
0
1
1
1
1
2
2
2
1
1
1
1
2
1
1
0
0
0
1
0
1
0
1
1
0
2
1
0
1
2
1
1
1
2
1
1
2
1
0
1
1
0
0
0
0
1
1
2
1
2
1
2
2
2
2
2
1
0
0
1
0
0
0
1
2
0
0
0
1
1
1
2
2
1
2
1
1
2
1
0
0
0
2
1
0
0
1
1
2
2
0
0
1
1
0
1
1
1
0
1
1
2
0
1
1
1
1
1
0
0
1
0
1
2
0
0
0
0
2
0
1
1
1
0
2
0
1
1
2
2
2
1
1
1
0
2
1
1
1
2
1
2
1
1
0
0
1
2
0
1
2
1
2
0
1
0
0
0
1
0
1
2
0
1
1
1
2
1
2
0
1
1
0
0
1
2
0
1
0
2
1
1
0
0
0
0
1
1
0
1
1
1
0
2
1
1
1
0
1
1
2
1
0
1
1
1
1
2
1
1
0
0
0
1
1
1
0
1
0
1
1
2
0
2
2
1
1
2
2
2
1
1
1
2
0
1
2
1
1
1
0
0
1
0
1
2
0
1
2
1
0
1
2
1
1
0
1
1
0
1
0
1
0
1
2
0
1
1
1
1
2
0
2
2
1
0
0
1
1
2
1
0
1
0
0
0
2
0
1
1
1
1
0
0
1
0
1
0
2
0
1
0
3
0
2
0
1
0
1
0
1
0
2
0
1
0
0
1
2
0
1
2
1
1
2
2
1
1
0
1
0
0
2
1
1
1
1
0
2
0
1
1
2
1
1
1
2
1
1
2
1
1
1
0
1
3
1
2
2
1
1
1
0
1
0
0
2
0
1
0
1
0
1
1
0
1
0
1
2
1
1
0
1
0
0
2
2
1
0
1
0
1
1
0
0
0
2
1
0
0
1
1
0
1
0
1
2
2
2
1
1
1
1
2
0
1
0
0
0
1
1
1
0
2
1
2
1
0
2
2
0
2
2
2
1
2
0
1
1
0
1
2
1
0
1
1
1
1
1
1
1
0
2
2
1
1
2
1
1
2
1
2
1
2
0
1
2
1
1
1
2
1
1
1
2
0
1
1
2
1
0
0
2
0
1
1
1
0
0
1
2
0
1
1
1
0
1
1
0
0
2
1
1
2
0
1
1
2
1
2
1
2
1
1
0
1
1
2
1
0
1
1
1
1
1
1
1
1
1
1
1
2
1
3
2
1
1
0
1
2
1
0
0
2
2
1
1
1
0
0
1
1
0
1
2
1
1
1
2
1
1
0
1
0
0
1
2
1
0
1
2
2
2
0
1
1
1
0
0
1
0
1
1
1
2
2
1
1
1
1
0
1
1
1
1
1
1
0
1
2
1
1
1
1
0
2
2
1
1
1
0
2
1
2
1
2
1
2
0
1
1
1
0
1
0
1
1
1
1
2
1
2
1
1
2
0
1
0
2
0
1
0
2
1
1
1
0
1
0
1
2
1
0
0
2
1
1
2
2
1
1
1
2
0
0
1
1
1
2
2
0
1
0
1
1
1
2
0
1
1
1
0
2
1
1
0
0
1
0
0
0
1
0
1
1
0
1
1
2
0
2
2
0
1
2
2
1
1
1
1
2
1
2
0
0
1
2
0
1
0
1
1
0
0
1
2
1
0
0
1
0
2
0
1
2
2
2
0
0
1
0
1
0
0
1
3
0
0
2
0
1
2
1
2
2
0
0
1
2
0
2
1
1
1
0
1
2
1
0
1
0
1
2
2
0
1
2
0
1
1
1
1
1
2
1
2
1
1
1
0
2
2
2
2
0
1
1
1
0
1
2
1
0
1
0
1
0
2
2
0
1
0
1
0
1
0
1
0
0
1
1
0
0
1
2
1
1
0
0
1
2
0
0
0
0
2
0
0
0
2
1
1
1
0
2
2
1
1
2
1
0
2
1
0
1
1
1
0
1
0
0
1
1
1
1
0
1
0
2
1
0
1
1
2
1
1
0
2
0
0
1
1
1
2
3
2
1
1
1
0
2
0
1
0
0
2
1
2
1
2
0
1
1
1
1
1
2
1
2
2
0
2
2
1
1
0
2
1
2
1
0
0
2
2
1
1
1
1
1
1
2
1
1
1
0
1
0
0
2
1
0
0
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
0
2
0
1
0
1
1
1
0
0
1
0
2
0
2
2
1
2
1
1
2
1
0
1
3
1
1
2
1
1
1
1
2
1
1
1
0
1
2
0
0
1
1
0
1
1
1
2
1
1
1
1
2
0
2
2
1
0
1
1
1
1
0
1
1
1
2
2
1
1
0
0
2
0
0
0
1
0
1
1
1
1
0
2
2
1
1
0
1
2
1
1
2
1
1
1
1
1
1
0
1
2
0
2
0
0
1
0
1
0
2
0
1
0
0
0
0
0
1
1
1
1
0
1
0
1
1
0
2
1
1
1
0
1
1
0
1
2
1
2
2
1
1
1
0
2
1
1
1
0
0
1
1
2
2
1
1
1
1
1
0
1
1
0
1
1
1
1
1
0
0
2
0
0
0
1
1
0
2
2
0
1
0
2
2
1
1
0
2
2
2
1
0
1
1
0
1
2
1
1
1
0
0
1
0
2
2
1
1
1
2
1
2
0
2
1
1
0
1
0
1
1
2
1
1
1
2
1
0
1
1
1
1
6
1
1
2
1
1
0
1
1
1
2
1
0
2
1
2
0
2
0
1
1
0
1
1
1
1
1
1
0
1
1
2
0
1
2
1
2
1
0
1
2
2
2
2
0
1
2
2
2
0
1
2
0
0
2
1
1
0
0
0
1
1
2
0
2
0
2
0
0
1
1
2
0
1
0
2
1
2
1
3
1
2
1
0
2
1
0
1
2
0
0
0
1
2
1
1
0
0
1
0
2
1
2
1
1
1
2
0
1
2
1
2
1
1
2
1
0
1
0
1
1
1
1
0
0
1
1
1
2
0
0
1
2
1
0
2
1
1
0
1
1
1
0
0
2
1
1
1
2
1
2
2
1
1
1
2
1
2
1
2
1
0
1
1
1
0
0
1
1
1
1
1
1
1
0
0
0
1
2
0
1
2
2
1
1
1
2
2
0
1
1
2
1
2
0
0
2
0
0
0
1
2
3
1
1
0
2
1
1
0
2
2
0
1
1
2
1
1
2
2
0
1
1
1
1
3
2
1
1
2
1
2
2
1
1
1
1
0
1
1
0
0
2
2
2
2
2
1
0
1
1
2
0
1
0
0
1
1
0
1
1
1
0
1
1
1
2
2
0
2
1
3
1
2
1
1
1
0
1
0
0
1
1
1
1
0
1
0
1
2
2
0
1
1
1
1
0
1
0
0
0
1
2
1
1
0
1
0
1
2
1
1
1
0
0
2
1
1
1
1
1
1
1
1
2
0
1
1
0
1
0
1
2
1
1
1
2
1
1
2
2
1
1
0
0
0
0
2
1
2
1
1
0
2
0
3
2
2
1
1
1
1
2
1
1
1
0
1
1
1
1
1
1
0
1
1
1
0
0
1
1
1
1
1
1
2
1
1
1
0
1
2
1
1
1
1
2
1
1
1
0
0
1
0
0
0
0
1
1
2
1
1
0
2
2
1
2
1
0
0
0
1
1
1
0
1
0
1
1
1
1
1
2
0
1
1
0
2
0
1
0
1
0
1
1
1
1
2
1
1
1
0
1
1
1
1
0
1
1
1
1
2
1
1
1
1
1
1
1
1
0
2
2
1
0
2
1
0
1
1
1
1
1
1
1
1
1
2
2
1
2
0
0
1
2
1
1
1
0
0
2
1
0
2
1
1
1
0
0
1
1
0
0
0
0
1
0
2
1
0
0
2
2
0
1
1
0
1
1
1
0
1
0
1
1
1
0
1
2
0
2
1
1
1
1
1
0
2
0
0
2
2
0
0
0
1
0
1
1
2
2
1
1
1
1
1
2
0
2
0
2
0
0
1
1
2
1
2
1
2
1
0
1
1
2
0
0
2
1
1
2
1
0
0
1
1
1
2
2
1
1
2
1
2
2
2
1
1
1
2
2
1
2
0
0
1
2
1
0
0
1
0
0
1
3
2
2
2
1
0
0
1
1
1
1
1
2
1
0
0
0
0
1
2
1
0
2
1
1
2
1
1
0
1
2
2
1
1
2
0
0
1
2
1
1
1
1
2
2
1
2
0
0
1
2
2
1
1
0
0
1
2
0
0
0
2
1
1
0
2
2
1
1
1
0
1
2
2
1
0
1
0
1
1
1
2
1
1
0
1
2
1
1
1
2
0
1
0
1
1
1
1
1
1
1
1
0
0
1
1
0
2
1
1
1
2
1
1
1
2
0
0
0
1
2
1
4
1
1
2
1
1
1
0
1
2
1
1
1
1
0
0
0
1
1
0
0
1
1
0
1
1
1
1
0
1
0
0
0
2
2
2
0
3
2
2
2
0
1
0
0
1
1
2
1
2
2
1
1
1
1
1
2
1
2
2
0
1
1
3
3
1
1
2
1
1
1
1
1
0
0
0
0
2
1
1
1
1
0
1
2
0
2
1
1
1
1
1
1
0
1
1
0
0
1
1
0
1
2
1
1
2
1
2
1
2
2
1
2
1
1
0
1
0
0
0
0
1
2
0
1
1
2
1
1
2
0
1
1
0
0
1
1
0
0
0
1
2
1
2
1
1
1
0
0
2
1
0
1
0
0
0
1
2
1
1
1
1
1
1
1
1
2
0
1
2
1
1
1
1
0
0
1
0
2
2
1
1
1
1
2
1
1
0
1
0
1
2
1
0
1
0
1
1
2
0
2
1
2
1
0
1
1
0
0
0
1
1
1
1
1
0
1
1
1
0
1
0
1
0
1
0
1
2
1
2
1
2
1
1
2
1
2
1
1
0
1
0
0
2
1
1
0
1
1
0
2
2
2
2
2
0
0
0
1
0
1
2
1
0
1
1
1
2
1
2
2
1
0
0
1
2
1
0
2
0
1
1
1
2
2
1
0
1
0
2
1
1
1
1
0
1
0
1
1
1
1
0
0
0
0
0
1
1
1
1
2
1
2
1
1
2
1
0
1
0
0
1
1
2
0
0
1
0
1
1
1
1
1
2
2
0
2
2
0
0
2
2
1
2
1
1
3
1
2
0
1
1
0
1
1
1
1
1
0
1
1
2
1
0
1
1
2
0
1
2
1
9
0
1
0
1
1
0
1
0
1
1
1
1
3
1
2
1
1
1
2
1
0
1
0
1
1
0
0
2
2
1
1
2
2
2
1
1
1
1
1
0
1
0
0
1
0
0
2
2
0
1
2
2
0
1
0
2
1
2
2
0
1
2
1
2
1
2
1
0
0
1
0
0
0
1
1
0
1
1
0
1
2
1
1
0
1
2
1
0
0
1
1
1
0
0
1
2
2
1
2
0
1
1
1
1
0
2
1
1
2
1
0
1
1
0
1
1
1
1
2
0
0
1
1
2
2
0
2
1
2
2
3
1
2
0
0
2
2
1
2
3
1
0
1
1
2
1
1
1
2
1
1
0
2
0
0
0
0
2
2
1
2
1
1
1
0
2
1
1
1
0
1
1
2
1
0
1
2
1
1
1
0
1
1
0
1
1
2
0
1
1
0
1
1
2
1
1
3
2
1
1
2
1
1
1
1
1
1
1
1
1
3
1
0
2
0
0
2
1
2
1
1
1
2
0
2
0
0
1
1
1
2
1
2
2
1
1
1
0
1
0
0
2
0
0
1
0
0
0
0
1
1
0
0
2
2
0
2
1
0
3
2
1
0
2
2
0
0
1
1
1
2
0
1
1
0
0
2
0
1
0
2
1
2
1
1
2
1
0
1
1
1
1
1
1
1
0
2
1
2
2
1
3
0
2
2
1
0
0
1
1
3
0
1
1
7
2
1
1
1
1
1
2
0
2
2
1
1
0
1
2
0
1
1
1
1
1
0
1
2
1
0
1
2
1
0
1
1
0
0
1
0
1
0
1
1
2
2
1
2
1
1
0
0
1
1
0
0
0
1
2
2
0
1
0
1
1
3
0
1
1
1
1
2
1
2
1
1
1
1
0
1
1
1
1
1
1
0
2
2
1
2
2
0
1
1
0
1
1
1
0
0
1
1
1
1
1
0
1
0
2
1
1
0
4
1
0
2
2
2
0
1
2
0
0
1
1
1
0
1
2
0
1
1
2
1
2
0
1
0
1
1
0
1
1
0
2
1
1
1
2
1
1
1
2
0
0
0
2
1
1
0
2
2
1
0
1
2
1
2
2
1
0
2
0
1
2
1
2
1
1
0
0
1
0
0
0
0
1
1
1
0
2
1
2
2
1
0
1
1
1
1
2
1
1
0
1
1
0
1
0
1
2
1
0
1
0
1
2
0
2
1
0
2
0
0
0
0
1
0
0
0
1
2
0
1
2
1
2
1
2
2
0
1
1
1
1
2
1
1
0
1
0
0
1
1
1
1
1
1
1
1
2
1
0
1
1
1
1
1
1
1
2
1
1
1
1
2
0
1
1
0
1
2
2
1
1
2
0
0
0
2
2
1
1
2
1
1
2
1
2
1
4
1
0
1
1
2
2
0
1
1
1
1
2
1
0
1
1
1
1
1
1
1
1
1
1
1
2
0
1
2
1
2
1
0
1
2
0
1
0
2
0
2
0
1
1
0
1
1
2
1
1
2
1
0
1
2
1
1
1
0
1
0
2
2
0
2
1
2
1
2
1
0
0
0
3
1
1
2
0
1
1
1
1
0
1
1
0
1
0
2
1
1
1
0
1
2
2
1
0
0
1
0
2
4
0
0
1
0
0
2
1
0
2
2
1
2
1
2
2
0
1
1
0
1
1
1
2
2
0
1
1
1
2
1
2
0
1
1
1
0
0
1
2
1
1
1
1
0
1
2
1
0
0
1
1
2
1
1
0
0
1
2
1
1
1
2
1
0
0
2
1
1
1
1
1
0
0
0
2
0
1
1
0
2
1
1
1
1
1
0
1
1
0
2
1
0
1
1
1
1
0
1
0
1
2
1
2
0
2
2
1
1
0
2
1
0
1
1
0
1
2
2
2
1
0
2
2
1
0
1
1
1
2
2
1
1
2
0
1
1
1
2
2
2
1
1
1
1
1
1
0
1
2
2
1
0
2
2
1
0
1
0
1
1
0
1
2
1
1
0
1
1
1
1
0
2
0
2
0
0
0
2
2
1
2
2
0
2
0
1
1
1
0
2
1
1
0
0
1
1
0
0
2
0
1
1
0
0
2
1
2
1
0
1
1
0
1
0
1
1
0
1
1
1
0
1
2
2
0
1
0
1
1
1
0
0
0
1
1
1
1
2
1
0
1
1
1
0
1
1
0
1
5
1
2
1
1
1
0
0
1
2
0
0
1
0
1
2
0
1
1
2
1
1
2
2
1
0
0
2
0
0
0
1
1
2
0
2
1
1
1
1
1
1
0
2
2
1
1
2
1
1
2
1
1
0
0
2
1
0
0
1
3
2
1
0
1
1
1
1
2
1
2
2
1
1
2
2
0
1
0
1
3
2
1
2
2
1
0
1
1
2
1
0
0
1
1
1
1
2
1
2
2
2
0
0
2
0
1
1
1
1
1
0
1
1
0
1
1
1
0
1
0
1
1
2
1
0
2
2
0
2
1
1
1
0
1
0
1
2
2
0
1
1
3
0
1
1
1
0
0
1
3
0
1
2
2
1
0
2
1
2
0
1
2
1
1
1
1
0
0
1
1
0
1
0
0
2
1
1
2
2
1
1
1
1
1
2
1
1
0
0
0
2
1
1
0
1
2
1
2
1
1
1
0
0
1
1
0
0
0
1
2
0
1
1
1
2
0
0
0
0
2
2
1
0
1
1
1
0
1
1
0
2
1
1
1
1
1
1
0
1
0
1
0
1
1
1
1
4
2
1
0
0
0
1
1
0
0
1
1
0
1
1
1
0
2
0
0
1
1
0
2
0
1
2
2
0
1
1
2
2
2
1
2
0
1
0
1
1
1
1
2
0
1
1
1
2
2
1
1
2
1
1
1
1
1
2
1
0
1
2
0
2
3
0
2
0
1
0
1
1
1
0
1
2
1
0
2
1
1
1
0
1
1
1
0
2
0
2
1
0
1
1
2
0
2
1
1
1
0
0
2
0
1
1
0
1
2
1
1
1
1
0
1
1
1
2
1
2
0
1
2
0
1
1
1
1
1
2
0
1
2
2
1
0
0
1
2
2
2
1
1
1
2
1
1
2
1
1
1
0
1
2
3
2
1
1
0
0
0
2
2
2
2
1
1
1
0
3
1
2
1
0
0
1
1
1
0
1
0
1
2
2
2
0
2
2
1
1
1
1
2
1
0
1
2
0
1
1
1
2
1
1
0
1
2
1
0
1
2
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
1
1
2
1
0
1
1
1
1
0
0
2
1
0
0
1
2
0
0
0
0
3
0
1
2
0
1
1
1
0
1
2
2
0
1
0
2
1
1
1
1
1
1
2
0
2
1
1
0
2
1
1
1
0
2
2
2
0
2
1
0
0
2
0
0
1
1
1
1
1
1
2
2
0
2
1
1
1
0
0
0
1
1
0
1
0
0
0
2
1
1
2
1
1
1
0
1
0
2
1
0
2
2
2
0
1
0
0
1
0
0
0
2
1
0
2
1
2
2
1
1
1
1
1
1
1
1
1
0
1
0
2
0
0
0
2
0
0
1
2
1
1
1
2
2
0
2
1
1
1
1
1
0
0
0
1
0
1
1
0
1
1
2
0
1
2
1
0
1
0
1
0
0
2
1
2
0
3
2
0
0
0
0
1
0
0
1
2
1
1
0
1
1
1
2
1
1
2
1
1
1
1
0
1
1
1
1
1
0
1
2
2
1
1
0
0
0
1
0
1
0
0
1
2
1
0
2
1
1
1
2
0
0
1
1
2
1
2
1
1
1
0
0
1
2
0
1
1
1
1
2
2
1
1
2
2
1
2
2
1
0
1
1
1
1
2
1
1
2
1
2
2
2
0
1
2
0
2
1
1
2
1
2
1
2
0
0
1
1
0
0
0
0
1
1
1
1
1
2
0
0
0
0
2
1
1
1
0
0
2
0
1
2
0
0
2
7
1
0
0
0
1
2
2
0
0
1
2
1
0
1
1
1
0
1
0
0
0
1
1
1
1
1
1
1
0
1
1
2
1
1
2
0
0
1
0
1
1
1
1
1
1
0
1
1
1
0
0
2
1
0
0
1
1
1
1
0
1
1
1
2
2
1
1
0
2
2
0
0
1
1
0
0
2
0
0
1
2
1
0
0
0
1
1
0
0
1
1
0
1
1
0
1
0
0
0
0
0
1
0
1
4
2
2
0
1
3
0
1
1
2
2
2
1
2
1
2
0
1
1
2
1
0
2
2
1
0
0
1
1
0
1
2
2
1
1
0
1
1
1
1
2
2
2
1
2
2
1
1
0
0
2
1
0
1
1
2
2
1
1
0
1
0
1
0
1
0
0
2
0
0
2
1
2
0
2
1
1
1
1
1
1
0
2
1
1
1
2
1
1
2
1
2
2
1
1
1
1
1
0
0
0
1
0
1
2
0
2
1
0
0
0
0
1
3
1
1
1
0
1
1
0
1
1
1
2
2
2
2
0
2
2
2
1
2
1
1
1
2
1
1
0
0
1
0
2
0
0
1
0
2
1
1
1
0
2
1
2
2
1
0
2
1
2
2
1
0
0
2
2
1
1
1
2
1
1
2
1
0
0
1
2
1
1
0
2
0
0
1
2
1
2
2
1
0
0
0
2
0
1
1
1
1
1
0
1
2
2
1
1
0
1
1
1
1
2
2
1
1
2
1
1
1
1
0
1
1
0
2
0
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
2
0
1
1
1
2
1
1
1
0
0
0
2
0
1
2
1
2
2
1
2
0
2
0
1
1
1
0
1
1
1
0
2
1
1
0
1
0
1
1
0
1
1
2
1
2
1
2
1
1
0
1
1
0
1
1
3
1
1
1
1
1
1
3
0
2
1
0
1
2
0
1
1
0
1
1
1
2
1
2
1
1
0
1
1
0
2
1
1
2
1
0
1
0
1
1
1
2
1
2
1
0
0
1
0
0
1
1
2
1
0
1
1
1
1
1
1
0
1
0
1
1
1
0
1
1
1
2
2
0
1
0
1
0
1
1
1
0
0
0
2
0
2
0
1
2
1
1
1
1
1
1
0
1
1
1
1
1
1
0
0
1
1
1
1
1
1
1
1
0
1
1
2
1
2
0
1
2
2
1
1
1
1
1
2
1
1
0
2
0
0
0
1
1
0
1
1
0
2
1
0
1
1
0
0
1
2
0
0
0
1
0
1
1
0
2
1
1
2
1
1
0
2
2
0
2
1
1
1
1
0
0
0
0
1
1
1
1
1
2
2
0
1
1
1
10
2
2
0
0
0
0
2
2
0
2
1
2
2
1
1
1
1
0
0
0
0
2
0
1
1
1
2
0
1
2
1
1
1
2
0
0
1
0
1
2
0
1
1
4
0
0
1
1
2
1
0
1
1
0
2
2
1
1
0
0
0
1
2
0
0
2
2
1
2
0
1
0
1
1
0
2
0
2
2
1
2
1
0
1
2
1
2
0
2
2
1
0
0
0
0
0
2
2
2
1
1
1
1
0
1
1
2
2
2
1
1
1
1
0
0
0
1
1
1
2
2
1
2
1
1
1
0
2
1
2
0
1
2
1
1
1
1
0
0
1
1
1
2
1
1
2
0
1
2
1
0
2
0
2
2
1
1
0
2
1
2
1
0
1
0
1
0
1
2
2
2
2
1
1
0
0
0
1
0
1
1
1
0
1
1
1
2
1
1
0
1
1
1
1
1
1
0
1
2
1
1
0
0
1
1
2
2
1
1
1
0
0
2
1
0
1
0
0
1
1
0
1
1
0
3
0
0
2
0
0
1
1
2
1
1
2
0
2
1
0
1
5
2
0
1
0
0
1
0
0
2
1
1
2
2
1
1
0
0
0
2
1
1
2
1
0
1
1
0
1
0
1
1
1
1
2
1
2
2
1
1
0
2
0
2
2
1
1
2
0
1
1
1
0
2
0
1
0
1
1
1
2
1
2
2
1
0
2
0
1
2
2
0
2
1
1
1
1
2
2
0
0
0
1
1
1
1
1
2
1
1
1
2
1
0
2
2
1
1
1
1
2
2
0
0
1
0
0
0
2
2
2
0
1
2
1
1
1
1
1
2
2
2
1
1
2
1
1
1
1
0
1
0
1
0
0
0
1
2
2
1
1
2
1
1
0
0
1
1
0
0
0
1
2
1
1
0
0
1
0
1
2
1
1
1
0
0
1
1
0
0
1
1
1
2
0
0
0
1
1
2
1
1
1
0
0
1
0
1
1
2
2
1
0
2
1
2
1
1
1
0
1
1
0
1
2
0
2
2
1
2
1
0
0
1
2
1
1
1
1
1
0
1
0
1
1
1
1
0
1
2
1
1
2
0
1
1
1
1
0
0
0
1
2
1
2
0
2
2
1
1
0
0
1
2
1
1
0
0
1
1
2
1
0
1
2
1
0
1
2
0
1
0
0
2
1
0
1
2
2
1
1
0
0
1
2
1
3
1
1
2
1
2
1
1
0
2
2
1
1
1
1
1
1
0
1
1
0
1
0
0
1
2
0
1
0
1
1
1
2
2
1
1
1
1
2
1
2
0
1
0
0
0
2
1
1
1
1
1
0
1
1
0
2
1
2
0
1
1
2
2
2
2
1
0
1
0
2
2
0
1
1
2
1
1
1
1
1
0
2
2
1
1
2
1
1
0
2
2
0
0
1
0
1
2
1
1
0
1
3
2
1
1
1
1
2
2
0
1
3
1
1
1
0
1
2
2
2
1
0
1
1
1
0
0
2
0
0
0
1
2
0
1
1
0
2
1
1
1
0
2
1
2
2
2
1
0
2
1
1
1
0
1
3
0
1
1
1
0
1
0
0
0
1
1
1
1
0
1
1
0
0
0
0
0
1
0
1
2
2
1
1
1
1
2
1
1
1
0
1
2
3
2
2
1
0
0
1
0
2
1
1
1
1
0
1
2
2
0
0
1
1
2
1
1
2
0
2
2
1
1
2
1
1
0
0
1
1
1
1
2
1
1
1
1
2
2
0
1
2
1
0
1
1
1
2
1
2
1
1
2
1
1
1
1
1
1
1
2
0
0
1
1
1
1
1
2
1
1
1
1
1
0
1
1
1
2
1
0
0
0
1
0
0
1
1
0
1
2
1
1
0
1
1
0
2
2
1
0
0
0
0
1
1
2
1
1
2
0
0
1
2
2
1
1
1
1
1
1
1
1
0
1
2
1
1
1
2
0
0
1
1
1
3
0
1
1
0
0
0
1
0
2
0
1
1
1
2
2
1
0
0
2
1
1
1
1
1
2
1
0
1
1
1
0
2
0
1
1
1
1
1
1
1
2
0
0
1
1
1
1
0
1
2
0
0
1
1
2
1
1
1
2
1
2
1
1
1
0
1
2
0
2
1
1
0
0
0
0
0
1
0
1
2
1
0
1
0
1
1
1
0
0
1
2
1
2
1
0
1
0
2
1
1
4
0
1
0
0
1
0
1
0
1
1
2
0
2
2
1
0
1
2
1
2
1
0
1
1
2
0
2
1
1
1
1
1
2
0
1
1
1
1
0
2
0
1
0
1
1
1
1
1
2
2
1
0
1
2
1
1
1
1
1
1
0
1
0
1
1
1
1
1
0
0
0
1
2
1
0
2
4
0
3
1
2
2
1
0
0
1
1
2
0
0
3
1
1
0
1
0
1
1
2
1
1
1
0
1
1
0
1
1
0
2
0
0
1
1
1
0
1
2
1
0
2
2
1
0
2
1
2
2
1
2
1
1
2
2
1
1
3
2
0
1
1
0
0
1
1
0
0
2
0
1
1
1
1
1
1
1
1
0
2
0
1
2
2
1
0
0
0
1
1
1
1
0
0
1
0
1
1
2
2
0
0
1
1
2
0
0
1
1
0
0
3
1
1
1
1
2
1
0
1
1
2
0
0
1
2
1
0
1
1
2
2
2
1
0
1
1
2
0
2
0
0
0
1
2
0
1
0
0
1
2
2
0
2
0
0
0
1
0
1
0
2
2
1
0
2
1
0
1
2
1
1
1
0
0
1
1
1
1
0
1
2
0
1
1
1
1
1
1
0
1
2
0
0
1
1
1
1
0
2
2
1
1
1
3
1
1
1
0
1
1
0
1
1
1
1
1
1
0
1
2
1
0
2
2
0
0
2
1
1
0
0
1
2
1
0
2
2
2
0
2
1
1
1
1
1
2
0
1
2
0
2
2
0
0
0
0
1
0
2
1
1
1
0
0
1
2
1
0
1
2
0
2
2
0
1
1
0
0
1
0
1
2
1
2
2
0
0
0
1
2
2
1
2
0
0
0
0
2
0
1
1
0
2
1
2
1
1
0
1
1
1
2
1
0
1
2
0
1
1
0
1
2
1
1
1
1
1
0
0
1
1
2
2
0
1
2
2
1
2
0
0
1
0
1
0
0
1
1
1
1
1
1
0
1
0
0
0
1
1
1
1
2
2
1
0
0
1
0
2
1
1
1
1
0
2
0
2
2
1
1
2
2
0
0
0
0
0
1
0
1
1
1
1
0
0
1
0
1
2
2
2
2
2
0
0
1
2
2
1
0
2
0
0
1
1
1
1
0
1
0
0
0
1
1
1
1
0
1
1
1
0
1
0
1
1
0
1
0
1
1
1
1
1
0
1
2
0
0
0
1
2
0
1
2
0
0
1
2
1
1
1
1
1
1
0
1
2
2
0
1
2
1
1
0
1
1
1
0
0
1
0
1
1
1
0
2
1
0
2
2
2
2
0
0
0
2
0
2
2
0
0
2
1
1
1
1
2
2
0
1
1
1
1
0
1
1
1
0
1
1
1
0
1
0
1
1
0
1
1
2
1
0
1
1
1
2
0
0
1
0
2
1
1
0
2
1
2
2
1
0
1
0
0
2
0
1
1
2
1
2
1
1
2
2
1
0
1
0
1
2
2
1
1
2
0
2
2
2
0
1
1
0
1
2
2
1
2
0
1
3
2
1
0
0
2
2
2
3
3
1
1
1
2
1
2
1
1
2
0
2
2
1
1
1
0
2
1
1
0
1
0
1
1
2
1
0
2
1
1
1
1
1
1
2
0
1
1
0
1
1
1
0
1
0
3
0
0
0
1
1
1
1
1
0
4
0
1
1
2
1
1
0
2
0
1
2
2
2
1
1
1
1
0
0
2
1
1
2
2
0
2
0
2
2
2
1
0
1
1
2
2
2
2
2
2
1
0
2
1
1
2
1
2
2
1
1
0
1
2
0
1
1
1
1
0
1
1
2
2
1
2
2
1
1
1
1
1
1
0
1
0
1
2
0
0
1
1
2
2
1
1
3
1
1
2
2
2
2
0
1
2
1
1
0
1
0
1
1
0
1
0
1
0
0
2
2
1
0
1
1
0
0
0
1
2
1
1
1
0
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
0
2
2
1
1
2
1
1
1
0
1
0
0
1
1
1
1
2
1
1
1
1
1
0
1
1
1
1
2
0
1
0
1
2
1
1
1
0
1
2
1
0
1
1
0
0
0
0
1
1
0
2
1
1
1
2
1
2
1
0
0
0
1
2
1
1
1
1
0
0
1
1
1
0
2
0
1
0
1
1
2
1
1
1
0
1
2
1
0
1
1
0
2
0
2
1
0
1
0
0
2
1
0
1
2
1
0
2
2
0
1
2
1
0
1
0
1
0
0
0
1
1
1
1
2
2
1
2
1
1
0
0
2
2
1
2
1
0
1
2
2
1
0
2
0
1
1
4
0
1
0
2
3
1
0
1
1
3
1
0
0
0
1
2
1
1
1
1
0
1
1
2
2
0
1
2
2
2
1
1
0
0
1
1
1
0
2
0
2
2
2
0
2
1
1
2
1
2
0
0
1
1
1
1
2
0
1
2
1
2
2
1
1
2
1
2
2
2
1
0
0
1
1
2
2
0
0
3
3
1
1
1
2
1
1
0
0
0
2
2
1
2
1
0
0
2
1
0
0
2
0
0
1
2
1
1
2
2
1
1
2
1
0
2
1
1
2
1
1
2
1
0
1
1
0
1
0
2
1
2
1
0
0
1
0
2
1
1
1
1
2
0
1
0
1
1
0
2
0
1
1
1
2
1
1
0
0
2
0
2
1
1
2
2
2
1
2
1
1
2
1
2
0
1
2
1
2
2
1
2
2
1
1
0
2
0
2
0
2
2
1
2
1
1
2
1
1
2
1
2
0
2
1
0
1
1
1
1
2
3
1
1
1
0
1
1
1
1
0
1
2
0
1
1
1
2
1
1
1
1
0
1
0
0
1
0
1
0
1
1
1
0
1
1
1
1
5
2
1
0
1
0
0
0
1
2
1
2
2
1
1
0
0
0
1
2
2
1
0
0
2
1
2
1
1
0
1
1
0
0
1
1
1
2
1
0
1
0
2
2
1
1
1
1
1
2
1
0
1
2
2
1
1
2
0
2
0
2
2
0
1
1
0
3
2
2
0
2
1
0
0
1
1
0
1
1
0
1
0
2
0
1
1
0
1
0
0
1
1
2
1
0
2
1
3
1
2
1
0
0
2
2
2
1
1
0
0
0
0
2
0
1
1
2
1
1
1
1
1
0
0
1
0
1
3
0
1
1
1
0
0
1
0
1
0
0
2
1
0
1
1
0
1
1
1
3
1
0
0
1
0
1
0
2
1
1
1
0
1
2
1
0
0
0
1
0
0
1
1
1
1
1
0
2
1
1
0
1
1
1
1
1
0
0
0
1
2
1
0
0
2
2
1
1
0
1
0
0
1
0
1
1
1
3
2
1
0
0
1
0
1
1
0
3
1
1
1
2
0
1
1
0
1
0
0
0
1
1
1
0
1
1
0
0
2
2
1
1
2
1
1
1
0
2
0
1
0
1
0
3
1
0
0
3
2
2
0
1
0
1
2
2
1
1
0
0
2
0
1
1
1
1
1
1
1
1
2
0
1
1
0
2
0
1
1
1
1
1
1
2
1
2
0
0
2
1
2
2
1
2
1
0
2
0
1
0
2
0
0
0
1
1
1
1
1
1
2
1
0
0
1
0
1
3
0
1
2
2
0
2
1
2
1
0
1
2
1
0
1
1
0
2
1
1
2
0
0
1
1
4
1
2
1
0
1
1
0
1
0
2
2
1
0
0
1
0
1
1
1
1
1
0
1
2
1
1
1
0
1
1
2
1
1
1
1
3
1
2
1
1
0
1
1
1
1
0
1
2
1
1
0
2
0
3
1
0
0
1
0
1
0
0
1
1
1
0
0
1
1
1
0
1
1
1
1
0
0
2
0
0
1
2
1
0
1
0
1
1
0
1
0
1
0
1
1
1
1
1
1
1
1
0
2
0
2
1
1
0
1
2
1
2
1
0
2
1
2
1
1
1
1
1
1
0
1
0
0
4
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
0
0
0
1
1
1
1
1
2
1
1
2
1
1
1
0
1
1
2
2
1
1
0
2
1
1
1
2
1
1
0
1
1
1
2
1
0
1
1
0
1
2
1
1
0
1
2
2
1
2
1
1
0
1
1
0
0
1
0
1
1
1
1
1
0
2
0
0
1
1
2
1
0
1
0
1
0
2
0
2
2
0
0
2
0
1
1
0
0
2
0
2
1
1
2
0
1
0
1
1
2
2
2
1
0
0
1
2
2
2
0
2
0
1
0
1
1
1
1
1
1
2
3
1
1
2
1
1
0
0
1
0
0
0
1
0
1
0
1
1
0
0
2
0
2
1
0
0
2
1
1
2
1
2
1
2
0
0
1
1
1
0
0
0
1
0
2
2
0
0
1
0
0
0
1
1
0
0
1
1
0
0
0
0
0
1
2
0
0
0
2
1
1
1
2
1
0
1
0
1
0
1
0
1
2
2
2
1
1
1
0
1
2
1
1
1
2
2
0
1
2
2
2
0
2
1
1
1
2
2
2
1
1
0
1
1
2
0
1
0
1
2
1
2
1
2
0
1
2
0
2
1
1
1
0
1
1
0
1
2
1
1
1
1
2
1
1
2
1
1
0
2
0
1
2
1
1
2
1
2
0
1
0
1
2
1
1
1
1
1
1
1
1
1
1
0
0
1
0
1
1
1
1
2
2
0
2
1
0
1
1
1
1
1
2
1
1
0
2
1
0
0
0
2
2
1
0
2
0
2
1
1
1
0
1
1
1
2
1
1
2
1
0
0
0
0
1
1
1
0
1
1
2
2
2
1
0
1
1
0
2
1
2
1
0
1
2
1
1
1
1
1
1
0
1
0
0
1
0
1
0
1
0
2
1
2
0
1
2
1
1
1
1
3
1
1
1
1
1
2
0
0
1
1
2
1
0
0
1
1
1
0
1
1
2
1
0
1
2
0
1
1
1
1
1
1
1
0
2
1
1
1
0
0
0
0
1
1
1
2
1
2
2
0
0
1
1
0
1
0
1
2
0
2
1
2
0
1
1
1
2
4
2
1
1
0
1
2
0
1
1
1
0
1
0
1
1
1
1
1
2
0
1
1
1
0
2
1
1
0
1
1
1
0
0
2
1
1
1
1
1
1
2
2
3
0
1
0
0
0
1
1
2
1
0
1
2
0
0
0
1
1
1
2
0
2
0
1
1
0
1
1
0
1
2
2
1
1
1
1
0
0
1
2
0
1
1
2
2
0
0
1
2
0
0
0
2
0
0
2
2
1
0
0
0
1
0
2
0
0
2
2
1
1
1
1
1
2
2
1
2
2
1
1
2
1
0
1
1
1
0
0
1
2
2
2
1
0
1
0
1
2
2
0
1
1
2
2
1
1
2
1
0
2
1
0
3
0
2
1
1
1
1
1
1
0
0
2
2
3
1
2
1
1
1
0
1
0
1
1
2
0
0
1
1
1
1
1
0
1
1
0
0
1
2
1
1
1
0
0
1
1
0
1
0
1
0
1
1
1
2
1
0
2
2
0
0
1
1
1
2
0
2
2
1
0
1
1
1
1
2
2
0
0
1
1
2
1
1
0
2
0
0
1
1
1
1
0
3
2
2
1
2
0
2
1
0
2
1
1
1
2
0
1
1
2
0
2
2
0
2
2
0
1
2
1
2
1
1
1
1
2
0
1
1
2
1
1
1
1
1
1
0
2
1
0
0
0
0
0
1
0
1
0
0
0
0
2
0
2
1
1
0
2
2
2
0
0
1
1
0
0
1
1
1
1
1
1
1
2
3
2
1
2
0
1
2
2
2
0
2
1
1
2
1
1
1
1
0
1
1
1
0
1
2
1
1
1
1
0
1
0
2
2
1
0
0
0
1
0
0
0
1
1
1
3
0
2
1
1
2
1
2
1
0
1
0
2
2
1
2
0
1
1
0
2
0
2
1
2
1
0
1
1
0
1
0
2
0
0
0
0
1
1
0
1
2
2
2
1
0
1
1
0
0
1
2
2
2
1
0
0
1
0
1
0
1
1
0
1
0
0
1
2
1
1
0
0
1
1
1
1
1
2
0
3
4
1
1
0
0
1
0
2
1
0
2
3
1
2
1
2
2
5
0
1
0
1
0
1
1
2
0
2
2
1
2
0
2
1
0
0
0
0
0
0
0
2
1
1
1
2
0
2
2
1
0
1
0
2
1
1
0
0
0
0
1
1
1
1
2
0
0
1
0
1
2
2
1
2
1
1
1
1
1
0
1
1
1
2
0
0
1
2
1
2
2
0
1
0
1
2
1
0
1
0
0
2
0
1
1
0
1
2
1
1
1
1
1
0
2
0
2
2
1
1
1
1
0
1
2
1
0
0
0
0
0
2
2
1
2
0
1
2
1
2
0
1
0
1
1
2
1
1
2
2
1
0
2
0
0
1
1
2
1
1
1
1
3
1
1
0
1
1
1
1
0
1
0
1
1
1
1
0
1
2
1
0
1
0
1
1
1
1
1
2
2
2
1
0
1
1
1
1
1
1
0
0
0
1
0
0
0
1
1
0
0
1
1
1
2
1
0
1
2
0
0
1
1
1
1
2
1
1
2
1
0
1
1
1
1
2
1
1
1
2
2
2
0
1
1
1
1
1
1
0
0
2
1
2
0
0
0
1
0
1
0
1
1
1
2
0
0
0
1
1
1
0
1
0
1
1
2
1
1
1
1
0
0
1
0
1
2
2
2
2
0
1
0
1
1
0
0
1
1
1
1
0
1
1
0
2
1
1
1
0
2
1
1
1
2
0
0
1
1
2
0
1
1
1
3
1
0
1
1
1
1
2
1
1
2
2
0
1
1
2
0
2
1
0
1
1
0
1
2
1
0
0
1
2
2
1
0
2
1
2
0
1
2
1
1
2
0
2
1
0
0
1
0
1
1
0
0
0
0
1
1
1
0
1
0
0
1
1
2
1
2
1
1
1
1
1
2
1
0
2
1
0
2
0
0
1
1
2
1
1
2
0
1
1
0
1
0
2
1
1
1
0
1
1
0
1
1
0
0
1
1
0
1
1
1
1
1
1
2
0
1
1
2
1
0
1
1
1
3
1
1
1
0
0
1
0
1
5
1
0
1
2
1
0
1
1
2
3
1
1
1
0
1
2
1
0
1
1
2
1
0
0
1
0
1
0
0
1
1
2
2
2
2
1
2
0
0
0
0
1
0
1
0
1
1
1
1
2
1
0
1
0
0
1
1
1
0
1
2
1
1
0
1
0
1
2
0
1
0
0
0
0
2
1
0
1
2
1
2
2
2
2
2
2
1
1
2
1
2
0
0
0
0
2
1
0
2
2
2
1
0
0
2
2
2
2
2
1
1
1
1
1
0
1
0
0
1
2
2
0
0
1
2
1
1
0
0
1
1
1
1
1
1
1
2
1
1
1
1
0
2
1
2
1
2
0
1
1
0
1
1
0
0
2
0
1
1
1
1
1
1
1
0
2
2
1
1
2
1
2
1
0
1
0
0
1
1
0
1
0
2
2
1
2
1
2
1
0
2
1
0
1
0
1
1
1
0
2
0
1
1
1
1
1
1
1
1
0
1
0
1
0
0
1
1
1
2
1
0
2
3
1
2
1
1
1
1
2
2
2
0
0
2
1
1
1
1
0
1
1
0
0
2
0
1
1
1
1
0
1
1
0
1
1
0
0
1
1
1
1
1
1
0
1
1
1
1
0
0
1
1
2
0
1
1
0
3
1
2
1
1
2
1
1
0
1
1
2
1
1
2
1
1
1
0
1
0
0
1
2
2
2
0
2
1
1
2
1
2
1
1
0
1
0
0
0
1
0
2
1
0
0
0
1
1
0
2
1
0
0
1
1
1
1
1
2
1
1
2
1
2
1
2
1
0
1
2
1
0
2
1
2
2
0
2
1
1
0
1
2
1
0
2
1
1
1
1
2
1
2
1
1
2
2
1
2
0
2
1
2
2
0
1
2
1
2
1
1
1
1
0
1
0
1
1
1
1
1
1
0
1
1
2
2
1
2
2
2
0
2
1
0
0
1
1
0
2
1
1
0
1
1
1
1
1
1
1
1
2
0
2
2
2
2
0
0
0
0
0
1
1
2
0
0
1
0
1
1
1
1
0
0
1
0
1
0
0
1
1
0
1
1
2
1
1
0
2
1
3
1
1
2
2
0
0
2
1
1
1
2
1
2
1
1
1
2
1
1
1
0
0
1
1
2
2
2
0
3
1
1
2
0
1
0
1
0
0
0
0
2
0
0
2
2
0
2
1
1
1
2
0
0
0
1
1
1
2
2
2
0
1
1
2
1
1
2
0
0
0
0
0
2
0
1
1
2
0
1
0
1
2
2
2
1
1
1
0
1
1
1
0
1
1
1
2
1
1
0
1
0
1
1
1
1
0
1
1
1
1
1
0
1
1
1
1
0
0
1
0
1
1
0
0
1
1
1
0
0
2
2
1
1
1
0
2
1
0
0
1
2
1
1
1
1
2
0
0
1
0
2
0
1
0
2
0
1
0
1
1
1
1
2
2
1
1
1
0
2
1
1
0
1
1
0
1
4
1
1
0
2
1
1
1
1
0
1
1
1
1
0
0
1
0
0
1
2
1
2
1
1
1
0
1
1
2
2
1
0
1
1
0
1
0
0
0
1
0
1
2
1
1
0
1
1
1
0
0
1
2
1
0
1
2
2
2
2
2
2
2
1
1
2
2
0
1
1
2
1
2
0
2
1
2
0
0
0
1
1
1
1
1
0
1
0
1
2
1
2
1
1
1
0
2
1
1
1
2
2
1
0
1
2
0
1
2
1
2
1
1
1
1
2
1
0
2
1
2
0
0
1
0
1
1
0
1
1
0
2
1
1
1
0
0
1
1
2
2
1
1
1
1
1
0
0
1
0
1
1
1
2
1
1
0
1
2
1
1
2
1
1
0
1
0
0
2
2
1
1
0
1
1
0
3
0
0
0
1
2
1
2
2
1
1
1
1
2
0
2
1
0
1
1
2
0
0
1
1
1
2
2
2
2
0
1
1
0
0
2
1
0
2
2
0
2
0
3
2
1
1
0
0
2
2
0
2
1
6
0
1
2
1
1
1
1
1
2
1
0
2
1
1
1
0
0
2
2
0
4
2
1
1
0
1
0
1
0
1
2
1
2
2
1
1
1
2
1
2
1
1
2
1
1
0
2
1
2
0
0
2
1
2
1
1
0
1
0
2
0
1
1
1
1
0
0
1
1
2
1
0
0
1
1
0
1
0
1
0
1
1
1
2
0
1
1
2
1
0
2
1
1
1
2
1
0
0
0
1
0
1
1
1
1
2
1
1
1
1
1
2
0
2
0
1
0
2
0
1
2
1
2
0
3
2
2
1
0
1
1
1
0
1
1
1
1
1
1
1
0
0
1
0
2
2
1
0
2
1
0
1
0
2
3
2
0
1
1
0
2
0
2
0
1
0
0
1
0
1
1
1
0
2
2
1
0
0
0
2
1
2
1
1
0
1
2
1
0
2
2
1
2
1
1
2
0
1
1
1
0
0
1
1
1
0
2
0
0
1
1
1
1
1
1
0
1
1
1
0
1
0
2
1
2
1
0
0
1
0
1
2
1
0
1
1
1
1
1
2
0
0
0
1
2
1
0
1
1
1
1
0
0
0
1
0
1
2
0
0
1
0
1
1
1
1
1
0
0
0
2
0
1
0
2
0
1
1
1
1
0
2
2
2
2
0
1
1
2
0
0
1
1
2
1
0
1
1
2
0
1
1
0
1
2
2
2
2
1
1
0
1
2
1
0
1
1
0
0
0
1
1
2
0
2
1
1
1
1
1
2
2
1
1
0
0
2
1
0
2
1
1
0
1
1
1
2
0
1
1
1
0
1
8
1
0
3
1
1
0
0
1
2
0
0
0
2
1
1
0
2
1
2
2
0
0
2
2
1
0
1
1
1
1
2
1
1
0
1
1
1
1
1
1
1
0
2
0
1
0
3
0
1
0
0
2
1
0
1
2
1
1
1
2
1
1
0
1
0
2
1
1
1
0
0
2
2
1
1
1
1
3
1
1
0
0
2
1
2
1
2
1
0
2
2
1
1
2
0
2
0
0
0
2
2
2
2
1
0
0
1
1
1
1
1
2
0
1
2
2
1
1
0
1
0
1
0
2
3
1
2
1
2
2
0
0
1
1
0
3
1
2
2
1
1
0
0
1
1
2
1
1
1
1
0
1
1
0
1
1
1
1
2
1
2
1
2
2
0
1
2
0
2
0
1
1
0
0
0
0
1
2
1
1
0
1
1
0
1
1
1
0
1
0
1
3
1
0
1
1
2
0
1
1
1
1
1
0
1
0
1
1
1
1
1
0
0
2
0
1
1
1
2
1
1
2
0
0
2
0
1
1
0
1
1
1
0
2
1
0
2
2
2
1
2
1
1
2
0
1
1
2
1
2
0
0
1
0
2
1
1
0
1
2
0
0
0
0
0
1
1
1
2
0
2
0
3
0
1
1
0
1
1
2
1
1
2
1
0
0
2
2
1
1
2
1
0
1
2
0
1
1
0
0
2
2
0
0
1
1
1
2
1
1
0
2
0
1
1
2
1
1
2
2
1
2
1
0
2
1
1
0
1
1
0
1
0
1
1
1
1
1
2
1
0
1
1
0
0
1
2
1
2
1
1
1
2
0
2
1
1
2
1
0
1
1
1
2
0
1
0
2
2
1
0
1
2
2
0
1
1
1
0
2
1
0
0
0
1
0
2
0
2
0
1
0
0
0
1
2
2
1
0
1
2
2
0
1
1
0
1
0
0
2
0
1
0
0
0
2
1
2
1
0
0
1
1
2
0
1
1
0
1
0
1
0
2
2
2
1
1
1
0
2
1
0
1
1
2
2
1
1
1
1
1
0
1
1
2
1
1
1
1
1
1
0
1
0
1
0
1
2
1
0
1
1
4
0
1
1
2
1
3
3
0
1
0
2
4
0
2
2
2
1
1
1
1
1
2
1
2
1
0
1
1
1
2
0
0
1
1
0
1
1
0
1
0
2
0
1
1
1
2
1
1
2
2
1
0
2
0
2
0
0
1
0
1
2
1
2
2
1
1
1
0
1
2
1
1
0
1
1
0
1
0
1
2
2
2
1
1
2
1
1
1
0
2
1
1
3
2
1
1
1
0
0
0
1
1
1
1
1
1
2
1
0
1
0
1
0
2
2
1
0
1
2
2
2
2
1
2
2
2
2
2
1
1
2
1
1
2
1
1
2
2
1
2
0
1
1
1
1
1
1
0
1
0
0
1
1
2
1
1
2
1
1
1
2
1
1
1
0
0
1
1
1
1
2
1
0
2
2
1
1
0
0
2
0
1
0
1
1
2
0
1
1
1
2
0
1
1
0
1
1
1
1
0
1
1
2
1
2
1
0
0
1
1
2
1
1
0
2
0
1
0
2
0
1
0
2
1
2
0
1
0
1
1
1
2
0
1
0
1
1
0
0
1
1
0
1
0
1
1
1
2
1
2
2
0
0
1
2
2
1
1
0
2
0
0
1
1
1
0
4
1
0
1
0
1
0
0
3
1
0
1
1
0
0
2
1
1
0
0
0
1
1
1
1
3
0
1
2
1
2
1
1
1
1
0
3
0
2
1
1
1
1
2
1
1
2
1
2
2
1
1
0
1
1
1
0
1
1
0
1
1
1
1
1
0
1
1
1
1
0
2
1
1
1
1
1
1
0
2
1
2
0
0
1
0
1
1
1
1
0
2
0
1
0
1
2
1
1
1
1
0
1
1
1
1
1
1
1
2
0
1
0
2
1
0
1
0
0
1
0
1
2
1
0
0
2
1
1
1
1
2
1
1
1
7
1
2
1
1
2
2
1
0
0
3
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
2
0
1
0
1
2
2
1
0
2
0
0
0
1
0
1
2
1
2
1
1
0
3
1
1
1
1
1
0
2
0
2
1
2
1
1
0
1
0
1
1
1
0
0
1
1
0
3
0
1
2
2
1
1
0
0
1
2
1
1
0
1
1
1
2
2
0
1
1
1
2
1
2
0
2
1
1
0
1
1
0
1
1
0
1
2
2
2
1
1
1
1
2
2
0
1
1
1
1
1
0
1
0
2
1
2
0
1
1
1
2
0
0
1
1
2
1
0
0
2
0
0
1
2
0
2
2
1
1
1
1
0
1
1
1
3
0
0
1
1
0
1
1
0
0
1
2
0
1
2
0
1
1
1
2
1
1
1
2
1
2
1
1
1
0
0
2
2
3
1
0
1
1
2
2
3
1
1
2
2
2
1
0
0
1
1
1
1
1
1
1
1
0
1
1
1
1
1
2
0
1
2
1
0
0
1
1
1
0
0
0
1
1
1
1
1
1
1
2
1
1
0
2
1
1
1
3
0
1
0
3
0
0
1
1
4
0
0
1
1
1
1
1
1
2
1
2
1
0
1
1
1
1
1
0
0
1
0
1
1
1
2
2
1
1
1
0
1
2
2
2
2
1
1
2
1
1
1
2
1
2
0
1
0
3
1
1
2
2
2
1
1
1
0
1
1
0
0
1
0
1
1
0
0
1
1
2
1
1
2
1
0
2
0
0
1
2
1
1
0
1
0
1
2
1
0
1
1
0
0
3
2
2
0
1
0
1
0
2
0
2
1
0
4
0
1
1
0
1
0
0
0
0
2
0
1
1
1
1
0
0
2
1
1
1
0
2
1
1
1
0
2
2
2
1
2
2
1
2
1
0
1
0
2
1
1
0
2
1
1
0
2
2
3
2
0
0
0
1
0
0
0
0
1
1
2
1
0
2
1
0
1
0
0
2
2
1
2
1
1
1
0
1
1
2
1
1
0
0
2
1
1
2
0
1
1
1
2
1
2
1
1
1
1
2
1
2
0
2
1
1
1
0
2
1
0
1
0
0
0
3
0
2
3
1
0
3
1
1
1
1
1
2
2
0
2
1
0
2
1
0
1
0
2
1
1
1
1
0
1
1
0
1
1
1
0
1
2
0
0
1
1
1
1
1
2
2
1
0
1
1
0
1
0
0
1
2
0
1
1
0
2
1
1
2
1
0
1
1
2
2
1
1
0
1
1
0
1
1
2
0
1
1
0
0
1
2
1
2
0
0
1
1
1
1
2
0
1
0
2
1
2
1
1
1
1
0
1
0
1
0
0
2
1
1
0
2
0
1
0
2
0
2
1
2
1
2
1
1
2
1
0
0
1
0
1
2
1
0
2
1
2
2
2
1
1
2
1
2
0
1
1
0
2
1
2
1
0
1
2
0
1
0
2
1
2
0
1
1
1
0
1
1
1
0
1
1
0
1
2
0
2
3
2
2
2
0
1
0
2
1
0
1
1
1
1
1
1
1
2
0
2
0
2
0
1
2
1
1
1
0
1
2
2
0
1
1
1
1
2
1
1
0
1
1
1
1
2
1
1
2
0
1
1
0
0
0
2
2
1
0
1
2
1
2
1
1
0
0
0
1
1
1
1
0
0
2
0
1
2
1
1
1
1
1
0
0
0
0
1
1
1
2
2
1
1
1
2
1
1
2
1
1
1
1
0
2
1
0
0
1
2
1
1
2
1
0
0
2
1
1
1
1
1
1
1
1
1
1
0
1
2
0
0
0
0
1
1
1
1
0
0
1
2
2
1
0
1
1
1
2
0
1
1
1
0
2
0
1
2
0
1
1
1
1
2
0
1
2
1
0
1
2
1
2
2
1
1
2
1
1
0
2
0
2
0
0
2
2
0
2
1
1
0
1
0
1
1
1
1
1
2
2
1
1
2
2
1
1
0
1
0
1
0
2
1
2
1
2
2
0
1
2
0
2
0
1
1
1
0
1
0
1
2
0
1
2
1
2
2
1
2
2
1
1
2
2
1
2
0
1
1
1
1
2
1
1
1
1
1
1
1
2
0
1
1
0
0
2
0
1
0
1
1
1
1
1
1
0
2
1
2
2
2
1
0
1
1
1
0
1
0
2
1
1
0
3
2
1
1
1
1
0
1
1
1
1
1
1
1
1
1
0
2
1
0
1
0
0
2
1
1
1
1
2
1
0
0
0
2
2
1
2
1
1
0
0
0
1
0
2
1
0
2
0
1
1
0
0
0
1
1
0
2
1
2
1
1
2
1
2
0
0
1
1
1
1
1
2
1
1
2
2
0
1
2
0
1
1
1
1
1
1
1
2
0
1
1
1
1
2
2
1
0
0
0
1
1
1
1
1
1
0
1
1
2
1
1
2
1
1
1
1
0
0
2
1
2
0
1
0
1
0
0
1
1
1
2
1
0
2
1
1
2
1
1
3
1
0
3
2
0
0
1
1
2
3
1
1
2
1
1
1
0
1
2
1
2
1
2
1
0
0
1
1
1
1
1
2
1
1
0
2
2
1
2
1
1
2
2
2
1
1
1
0
3
1
0
0
1
1
1
2
2
1
1
0
1
2
1
0
1
1
0
1
1
1
4
1
0
0
1
1
2
0
1
2
1
1
0
1
1
1
0
1
1
1
0
2
1
2
1
1
1
0
0
1
2
2
2
0
1
1
2
0
3
1
0
0
2
2
0
1
1
0
1
1
2
1
1
2
0
0
2
2
0
1
1
1
1
1
1
1
1
0
1
1
0
1
1
2
1
1
1
1
1
0
1
0
2
1
1
0
0
1
2
1
2
1
0
1
0
0
2
1
1
1
1
0
2
0
1
2
1
1
1
1
1
7
0
1
1
2
0
0
0
2
1
0
0
2
2
0
1
0
0
0
1
1
0
1
2
2
1
1
1
1
1
2
1
0
1
2
1
1
1
0
2
1
1
4
1
0
0
2
2
2
2
0
1
2
1
1
0
0
2
2
1
3
1
0
0
0
1
1
3
1
0
1
1
1
2
1
1
1
1
2
1
0
1
1
1
2
1
0
1
2
1
0
1
0
1
1
1
2
2
2
2
1
1
2
3
1
0
0
1
0
0
0
2
1
1
0
1
0
0
1
0
2
1
1
2
2
2
1
1
2
2
1
1
1
1
0
1
1
2
1
1
0
0
0
1
1
0
1
0
0
1
1
2
1
2
1
2
1
1
1
1
1
0
1
1
1
1
1
1
0
2
2
2
1
1
1
1
1
1
1
2
1
1
1
0
1
1
1
0
1
2
1
0
0
1
2
1
1
2
0
1
1
1
2
2
1
1
1
1
2
2
2
0
1
1
2
2
0
3
2
1
0
2
1
2
0
0
2
1
1
0
0
1
2
0
1
1
2
1
2
1
1
0
1
1
1
1
0
1
2
1
1
0
1
4
0
1
0
1
0
0
1
0
2
1
1
2
0
1
1
0
2
0
1
2
0
1
1
0
1
1
2
2
0
1
1
2
1
0
1
1
0
1
1
1
0
1
0
1
0
1
1
1
1
0
0
1
1
1
1
0
2
1
1
1
2
1
1
2
1
0
1
2
2
2
1
2
0
1
1
2
1
2
0
0
0
1
1
2
1
0
1
1
1
1
1
2
1
0
1
1
1
1
3
1
0
1
1
0
1
1
0
0
2
0
1
1
1
0
0
1
1
2
2
0
2
0
0
2
0
1
1
1
1
1
1
0
1
1
1
2
1
1
2
2
1
0
1
0
1
1
1
3
1
0
1
1
2
0
1
1
1
1
0
1
0
1
0
0
2
0
1
1
1
2
1
1
0
1
2
1
2
0
0
1
1
0
0
2
1
1
1
1
2
0
0
1
1
1
2
1
0
0
2
0
2
1
1
2
2
1
2
0
0
2
1
1
1
0
0
0
0
1
1
0
0
1
1
1
1
0
2
1
0
0
1
1
1
2
2
0
1
1
1
2
0
2
1
1
2
2
1
1
0
1
1
2
2
1
2
1
1
1
2
1
1
0
0
1
2
2
2
0
0
1
0
0
0
0
2
1
2
3
1
1
2
1
0
1
2
1
1
2
0
1
2
1
1
1
0
0
2
1
1
1
2
1
0
1
1
2
2
1
1
0
1
1
1
1
0
2
0
0
1
1
1
1
0
0
2
2
1
0
2
2
1
1
1
0
0
0
1
1
0
1
1
2
1
0
1
1
1
0
1
0
1
1
1
3
1
1
0
1
0
1
0
0
1
0
0
1
2
1
1
1
1
2
2
2
1
1
1
1
1
0
1
0
2
1
1
1
2
0
1
1
0
1
2
1
2
1
1
1
0
2
2
1
0
0
2
0
2
2
0
1
1
1
0
0
2
1
2
1
1
0
0
1
0
1
2
1
1
2
1
0
0
1
1
2
1
1
2
2
2
2
1
1
2
1
1
1
2
1
1
1
1
2
0
1
1
2
1
1
2
1
1
1
1
0
0
1
0
2
1
1
1
2
0
0
1
1
1
2
1
0
1
0
2
1
2
0
1
1
1
1
0
1
5
1
1
0
1
2
0
2
0
0
1
1
1
2
1
0
1
1
0
0
2
1
0
1
1
1
0
0
1
1
0
0
1
0
0
0
0
0
0
1
1
0
1
1
1
1
2
0
1
0
1
1
0
2
0
0
1
1
2
1
1
2
1
2
1
1
0
0
1
0
1
1
1
2
1
1
0
1
1
0
1
1
0
2
0
2
1
2
2
3
2
2
1
0
1
1
1
2
1
1
1
0
1
1
1
2
0
0
1
2
1
1
1
0
1
0
1
0
0
2
0
0
0
1
2
1
2
1
0
2
2
1
1
1
2
1
1
0
0
1
2
2
2
1
1
0
1
1
1
1
1
0
0
2
1
2
0
0
2
1
1
1
1
1
0
0
1
1
2
0
1
1
0
1
1
1
1
1
0
0
1
1
1
0
0
0
2
0
1
1
2
1
1
1
1
1
1
2
0
2
0
1
2
1
1
1
0
1
1
1
1
1
0
1
1
0
1
2
1
1
2
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
0
2
0
1
1
0
1
1
1
1
1
2
2
1
2
0
1
1
2
2
1
2
1
1
1
1
0
0
1
1
1
1
0
0
1
0
1
0
1
1
0
1
1
0
1
2
0
0
1
1
0
1
2
1
0
0
0
2
0
2
1
2
1
2
1
1
2
1
1
1
0
1
0
0
2
2
0
2
2
1
2
1
0
0
2
1
1
2
2
1
1
1
2
1
0
3
1
0
2
2
1
2
1
1
1
1
1
2
1
1
2
1
1
1
3
2
0
1
1
1
1
0
2
0
0
2
1
2
1
1
0
1
1
1
1
2
1
0
2
2
0
1
1
1
0
1
1
1
0
2
0
0
1
1
1
2
0
2
0
1
1
0
0
1
1
1
0
1
2
0
1
0
0
0
2
1
0
1
1
2
2
0
0
0
2
0
2
1
2
0
2
1
1
2
1
0
1
1
0
0
0
2
1
1
1
1
1
0
1
2
0
1
0
1
1
1
0
0
0
2
1
0
0
1
1
1
1
1
2
2
2
0
0
0
1
0
2
1
2
0
3
0
0
2
1
0
2
2
1
2
2
1
1
1
2
1
2
2
1
0
1
0
2
2
1
1
1
2
0
2
1
1
1
1
0
1
1
0
1
0
0
0
0
1
1
1
0
1
2
2
1
2
1
2
1
2
1
1
1
0
2
1
0
2
1
2
3
1
0
1
0
4
1
2
1
1
0
1
0
0
2
0
1
0
0
2
1
2
1
0
1
2
2
1
0
1
0
1
1
1
1
1
0
1
0
2
0
1
0
0
2
1
0
0
0
1
1
1
0
1
1
0
2
1
1
0
3
2
0
0
1
0
0
1
1
2
1
1
1
0
0
1
0
3
1
2
1
1
0
1
2
1
1
2
1
3
0
1
1
0
1
0
1
2
2
2
1
1
2
2
2
1
2
2
2
1
1
2
1
1
2
1
1
1
1
2
0
2
0
2
1
1
1
0
1
1
1
1
0
0
0
1
2
1
1
0
0
2
0
1
0
1
2
1
1
0
1
2
0
0
1
0
0
2
0
1
1
7
1
1
1
2
2
1
1
0
0
1
1
0
1
1
1
1
2
2
1
1
0
0
1
0
1
1
5
1
2
2
1
2
0
1
0
2
2
1
0
1
1
0
2
2
1
1
1
1
2
1
0
0
2
2
2
1
1
1
1
1
0
1
0
1
0
1
0
0
0
1
1
1
1
1
1
1
1
2
2
2
1
2
1
1
0
2
1
0
2
0
2
0
2
1
1
1
0
1
1
1
0
0
1
1
0
1
0
0
1
1
1
3
0
1
2
1
1
1
1
0
0
1
2
0
1
2
2
1
1
1
0
1
1
2
1
1
2
1
0
1
1
0
2
1
1
1
1
1
1
1
2
2
0
1
0
1
0
0
1
0
1
1
1
2
0
1
0
0
0
1
1
1
0
0
2
1
1
1
2
0
2
0
2
1
1
1
0
2
1
0
1
2
1
1
2
2
1
1
0
2
1
1
1
0
1
2
0
0
1
0
0
0
2
1
1
0
1
2
2
1
1
0
1
1
0
1
0
1
1
0
0
1
1
1
2
0
1
1
0
0
1
1
1
2
2
0
1
2
0
2
1
0
1
0
1
1
0
1
1
1
1
1
0
1
0
0
0
1
2
1
2
3
0
1
1
1
2
2
2
0
1
0
2
1
1
2
1
2
2
0
2
1
0
1
1
1
1
1
0
0
1
1
0
1
0
2
2
1
2
2
0
1
0
1
1
0
1
1
0
1
1
2
1
0
0
1
0
1
1
0
2
1
2
1
1
0
2
1
1
2
1
1
1
2
0
1
1
0
1
1
0
0
0
0
2
1
2
0
0
1
2
2
2
1
0
1
2
1
2
1
0
2
0
1
0
1
0
1
0
1
1
2
1
2
1
0
2
0
1
1
1
0
0
1
3
1
1
2
0
1
0
1
2
1
2
2
1
2
1
0
1
1
1
1
1
2
1
1
2
2
1
2
0
1
1
1
1
1
2
1
1
1
0
2
1
1
1
0
0
2
1
2
1
1
2
1
1
1
1
1
0
1
1
2
0
1
1
1
1
1
0
0
1
0
2
0
1
0
2
1
2
2
0
2
0
1
1
1
0
1
1
2
1
1
1
1
0
1
1
2
2
0
1
1
1
1
1
1
1
1
1
1
0
1
1
1
2
1
1
2
1
1
2
1
3
0
0
1
2
1
0
0
1
1
1
1
1
0
1
1
1
1
0
1
1
2
2
1
1
0
2
1
1
1
0
1
1
1
1
2
0
2
1
0
1
0
1
1
0
1
1
2
2
0
1
1
1
1
1
0
1
1
1
0
1
1
0
0
1
0
2
0
1
1
2
1
2
1
0
2
2
0
1
2
0
1
3
1
0
1
1
1
0
0
1
0
0
2
1
1
0
0
2
1
2
0
0
2
0
2
1
0
2
0
1
1
1
1
1
1
0
2
0
2
2
2
1
3
1
1
0
2
0
1
1
1
2
0
0
0
1
0
1
2
1
0
0
2
2
1
1
2
1
2
1
1
0
1
1
2
1
0
2
0
1
2
1
0
2
2
1
0
0
1
1
2
1
2
1
0
2
1
1
2
1
3
2
0
0
0
0
1
0
2
1
2
1
0
2
1
0
1
2
1
0
2
2
0
2
2
0
1
0
0
2
1
2
0
2
1
0
0
2
1
1
1
0
1
1
1
2
0
1
0
1
1
0
1
1
0
1
2
1
2
0
1
1
0
2
2
1
1
1
0
2
1
1
0
1
1
1
1
2
1
1
0
1
1
0
1
0
1
2
0
0
1
1
0
1
1
1
0
1
1
1
0
0
1
2
1
1
1
1
0
1
2
1
1
2
0
0
1
2
1
1
2
0
2
2
0
2
1
1
0
1
1
0
1
2
2
1
1
2
0
1
1
1
1
1
0
1
0
0
0
0
1
0
3
2
1
0
1
1
1
2
1
1
1
2
0
0
0
1
2
1
1
3
1
2
0
2
0
0
1
0
1
1
0
0
1
0
0
1
0
0
1
0
0
1
1
0
2
1
1
1
2
0
1
2
2
1
1
1
1
3
2
0
2
2
1
1
1
1
0
1
1
1
2
1
0
1
2
0
1
1
2
0
2
0
0
1
0
2
2
0
1
0
1
2
2
1
1
0
1
0
0
1
3
1
1
2
0
1
1
0
0
0
0
1
2
0
1
1
0
0
1
0
0
1
2
1
1
2
2
1
0
1
2
1
2
2
0
1
2
1
1
0
0
2
1
1
1
1
2
1
0
1
1
1
2
2
1
1
1
0
1
1
2
2
1
1
1
2
0
1
1
1
0
1
1
0
1
3
1
1
0
2
1
1
0
1
1
1
1
2
1
1
2
1
1
1
2
2
0
1
1
1
1
2
1
0
0
2
1
0
1
1
1
1
0
2
1
2
1
2
0
2
1
1
1
1
0
1
1
1
0
1
1
1
2
0
1
2
0
2
1
1
0
1
0
1
1
1
2
2
0
0
1
1
2
2
1
0
2
2
0
1
2
2
2
0
1
2
0
1
1
1
1
1
2
1
0
1
1
1
1
1
2
2
0
1
1
2
0
2
2
0
0
0
1
1
0
1
1
2
0
1
1
1
0
2
0
2
1
0
1
1
1
1
1
0
1
1
1
2
1
0
2
1
1
1
1
2
1
0
1
3
0
1
0
1
1
1
1
1
2
0
0
0
1
1
1
0
2
1
1
1
2
2
2
1
2
0
0
2
0
1
2
1
0
1
1
0
2
0
1
2
0
1
1
1
1
1
2
0
1
1
0
1
1
2
0
0
3
2
2
0
0
2
0
0
1
1
1
0
0
1
2
1
1
2
1
0
0
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
2
3
0
1
1
1
2
0
0
1
2
2
0
1
2
2
2
1
0
1
1
1
0
2
2
0
2
2
1
0
1
1
1
2
2
1
1
1
0
1
0
2
2
1
0
1
2
2
1
2
0
1
1
0
1
1
1
1
2
1
2
1
1
0
1
0
1
1
1
0
0
1
1
1
1
1
1
0
1
1
0
1
1
1
1
1
1
1
2
0
0
1
2
0
2
1
1
1
2
1
1
0
0
1
0
1
1
1
1
2
1
0
2
1
0
1
0
2
0
1
2
1
0
1
2
1
1
0
0
0
1
1
1
1
1
2
1
0
1
1
0
1
3
1
3
0
0
1
1
0
2
1
2
0
1
1
1
0
0
1
0
1
0
2
0
1
2
2
1
1
2
1
1
1
1
2
0
0
1
2
0
2
0
1
1
1
1
1
1
0
1
0
1
1
0
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
0
1
1
1
1
1
0
1
2
0
2
2
1
0
0
0
0
2
2
1
0
0
1
1
0
1
0
1
1
1
0
1
2
1
3
0
0
0
2
1
2
1
1
1
1
2
1
1
2
0
1
1
0
0
0
1
1
1
2
0
0
1
1
2
0
0
0
0
2
0
1
4
1
1
1
2
1
1
1
2
0
1
2
0
0
0
2
1
0
0
1
0
2
0
0
0
2
2
2
1
1
0
1
1
0
1
1
2
1
1
0
1
0
2
1
2
0
1
1
1
0
2
0
1
0
1
1
1
0
2
2
1
2
0
2
2
2
3
0
1
1
0
0
1
0
0
1
1
1
1
2
2
0
1
0
1
0
1
1
0
1
1
1
1
1
0
1
2
1
2
0
2
2
0
0
0
0
1
1
0
2
0
2
1
2
1
0
0
0
1
0
1
1
1
2
2
2
1
2
0
2
0
2
1
2
1
1
2
1
2
1
0
1
1
0
0
1
1
2
0
1
2
0
2
3
1
2
0
0
2
0
1
1
1
1
1
1
0
0
2
1
0
0
0
0
0
0
1
1
2
1
1
1
0
1
1
1
0
0
2
0
4
0
1
1
0
1
2
0
1
0
1
1
2
1
2
1
0
0
1
2
2
1
0
1
2
1
1
1
1
2
0
1
1
1
0
0
2
1
2
0
1
0
1
1
1
1
1
0
1
0
2
2
1
2
1
0
1
2
1
2
1
1
2
1
1
1
1
2
1
0
0
0
1
1
0
2
1
1
1
1
1
0
1
1
0
1
0
1
2
0
1
0
1
1
1
1
1
2
2
0
0
1
1
1
0
1
0
0
0
1
1
2
0
1
1
2
1
2
0
2
2
2
1
0
0
1
1
1
2
0
1
0
1
0
1
0
0
1
0
1
1
0
0
1
1
1
1
1
1
2
2
1
1
0
1
0
1
0
0
1
0
0
1
2
1
2
0
1
1
0
1
1
2
1
1
2
1
1
1
1
0
0
0
1
2
1
2
1
2
1
1
2
1
1
0
0
1
0
1
0
1
1
1
2
2
1
1
1
1
1
0
2
2
2
1
0
1
1
0
1
0
1
1
1
3
2
1
1
1
0
2
0
1
0
2
0
1
0
2
1
1
0
1
0
1
1
9
1
2
3
1
0
1
2
0
1
1
1
1
0
1
3
1
1
0
0
1
1
0
1
2
1
2
0
1
0
1
1
1
1
2
1
1
2
1
0
1
1
1
2
2
1
0
0
1
1
1
1
1
0
0
1
1
1
1
1
0
0
2
0
2
1
1
0
2
2
1
2
0
1
0
0
1
1
0
2
2
1
1
1
0
0
1
0
0
0
1
0
0
2
1
1
0
1
0
2
0
1
0
1
1
0
0
0
1
0
0
0
1
2
1
1
0
0
0
1
2
1
2
1
2
1
1
1
1
2
0
0
2
0
1
1
1
2
2
0
1
1
0
2
1
1
1
1
1
1
2
0
0
2
1
2
1
0
0
2
1
1
1
1
1
1
1
2
1
2
1
1
0
1
1
1
0
1
2
1
2
0
1
1
0
2
2
1
0
2
0
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
3
0
2
2
1
1
0
2
2
2
1
1
1
1
0
0
0
2
2
1
2
2
1
0
2
0
1
0
0
2
0
0
0
1
0
0
1
1
1
2
1
1
2
1
2
2
2
2
2
2
1
1
2
1
1
0
1
0
1
1
1
0
1
1
1
1
1
1
1
0
1
1
1
2
0
2
2
1
0
0
1
2
2
0
1
1
1
0
1
1
0
2
0
0
1
0
0
1
1
1
1
1
0
2
1
0
1
1
1
1
1
3
0
2
1
1
1
0
1
1
2
1
1
0
1
0
1
1
1
1
1
0
1
1
0
1
2
0
1
2
1
0
0
2
0
2
0
0
2
2
2
2
1
1
0
1
1
3
0
1
1
1
0
1
1
1
1
1
1
0
1
1
2
2
1
1
0
2
1
2
2
1
2
2
1
2
1
1
0
1
0
0
0
2
0
1
2
1
1
2
2
1
2
1
1
1
0
2
1
0
0
1
1
1
2
1
1
2
2
0
2
2
1
1
2
2
0
1
1
1
1
0
0
0
2
1
0
0
0
1
0
1
2
2
0
0
1
0
3
2
2
1
0
0
1
0
0
2
0
1
1
1
2
1
0
0
1
1
1
0
2
2
1
1
0
0
2
2
1
1
1
0
0
1
1
3
0
1
0
0
0
0
2
0
1
1
1
1
1
1
1
2
0
2
0
0
2
0
1
1
1
1
1
0
2
2
0
1
0
0
1
1
2
2
2
1
1
0
0
0
0
0
0
0
1
1
1
1
0
0
2
1
2
1
2
1
0
0
2
0
0
1
1
1
1
1
1
0
1
2
2
1
0
2
1
1
1
0
1
1
1
0
2
0
1
0
0
1
1
1
1
1
1
2
2
1
1
0
1
0
1
2
1
2
0
1
2
1
2
0
1
2
0
1
1
0
1
1
1
0
2
1
2
1
0
0
1
1
1
2
0
1
1
1
0
1
0
2
1
0
0
2
1
1
1
1
0
0
1
2
1
1
1
0
1
1
0
1
0
2
1
1
0
2
1
4
2
0
1
1
1
0
1
0
2
1
2
1
1
1
1
1
1
1
2
1
2
2
2
2
1
1
1
2
1
1
1
2
1
0
1
1
2
0
0
1
1
0
4
0
1
2
0
3
0
2
1
1
1
2
1
2
2
1
1
1
1
2
0
1
1
1
1
1
2
0
0
0
0
2
2
1
1
2
0
0
0
1
1
1
1
2
0
1
2
2
0
0
0
4
1
2
2
1
0
1
1
2
1
0
2
2
1
0
1
1
1
1
1
2
3
1
1
1
1
0
1
2
0
0
0
1
0
1
2
1
2
2
1
1
0
1
1
2
0
1
0
1
2
0
1
0
2
1
1
2
2
1
1
1
0
1
2
1
2
1
1
0
1
1
0
2
1
1
1
2
2
0
0
0
2
1
2
0
1
1
0
2
1
1
1
0
1
2
1
3
2
2
0
1
3
2
1
0
3
1
0
1
1
1
0
0
2
0
2
0
1
1
0
1
0
0
2
1
0
0
2
1
0
1
2
1
0
1
1
2
1
1
2
0
1
0
1
0
0
2
0
1
1
1
1
2
1
1
2
0
2
1
1
1
0
1
0
1
1
1
2
0
1
2
1
1
2
2
0
1
1
1
1
1
2
2
1
1
2
1
1
1
2
1
3
3
2
1
1
0
0
1
0
1
1
1
1
0
1
0
2
2
2
1
1
1
1
0
0
0
1
0
0
2
1
0
1
1
1
1
1
0
2
0
1
1
0
1
2
0
2
1
1
2
2
0
2
1
1
1
0
0
1
1
2
0
3
1
0
1
1
1
2
1
1
1
0
1
0
2
0
0
1
0
1
1
1
1
0
2
1
0
1
1
1
1
1
0
0
0
2
1
1
1
0
2
1
1
1
2
1
1
1
0
1
2
2
0
0
1
1
2
0
0
1
0
1
1
1
0
2
0
1
2
2
0
0
2
1
0
0
1
1
1
2
1
1
0
0
2
1
1
1
2
1
1
2
1
1
1
1
0
0
2
1
1
1
0
1
2
0
1
1
1
2
1
1
2
2
1
1
1
1
1
0
2
2
1
1
2
0
0
1
1
1
1
1
1
1
1
1
2
0
2
2
2
1
0
1
3
0
1
1
2
1
1
2
1
1
0
1
0
2
0
1
0
2
1
2
1
0
2
1
1
1
1
0
1
0
2
2
0
1
1
0
1
0
2
1
0
0
0
1
1
0
0
0
1
0
1
2
1
0
1
1
1
0
2
1
1
0
1
2
1
1
1
1
2
1
2
1
1
3
1
2
1
0
0
0
1
1
0
2
0
1
2
0
3
1
1
1
0
1
0
0
1
0
0
0
1
3
2
1
0
1
0
2
1
1
1
0
2
2
2
0
1
0
0
0
1
0
1
0
0
0
2
2
0
1
0
0
2
2
2
1
1
1
0
1
1
1
2
1
1
2
0
2
0
0
1
1
1
0
1
2
2
1
0
1
0
0
0
1
1
0
0
1
1
1
1
2
0
1
1
1
0
0
1
1
1
1
0
1
1
1
1
1
1
0
2
1
2
1
2
2
1
1
0
0
1
0
1
0
0
0
1
1
0
1
1
1
0
1
1
0
0
0
1
2
2
1
2
1
1
1
0
1
2
2
1
1
2
0
0
1
0
1
2
2
1
1
1
2
1
2
2
1
1
1
2
0
1
1
0
1
0
1
1
1
1
1
1
0
1
1
1
1
2
1
0
1
0
1
1
1
0
1
0
0
2
1
2
2
1
1
1
0
1
1
3
0
2
1
0
0
2
1
1
2
1
1
2
0
0
0
1
1
1
1
1
1
1
0
2
2
2
1
0
3
0
0
0
1
1
0
1
0
0
1
2
0
1
1
1
1
1
1
2
2
1
1
2
0
1
1
2
2
2
1
1
1
3
1
1
0
1
2
1
0
1
2
1
1
0
2
0
1
1
0
1
0
0
2
2
1
0
1
1
2
2
1
0
1
1
0
1
0
0
0
1
2
0
2
1
2
0
1
0
1
0
0
0
1
2
2
0
0
1
1
1
0
1
3
1
2
1
1
2
1
1
1
1
2
0
0
1
1
0
0
0
1
3
1
1
2
2
1
0
2
3
1
0
2
1
1
0
1
1
1
0
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
0
1
1
1
1
2
1
1
0
1
1
1
1
1
1
1
1
0
1
1
2
1
1
0
1
1
2
2
0
1
2
1
2
0
0
0
1
1
0
1
1
0
0
0
1
2
0
0
1
1
1
0
0
1
1
0
0
1
1
2
1
1
1
1
1
1
1
3
0
2
1
1
1
1
1
0
1
1
2
0
1
2
0
0
0
0
1
2
0
1
0
1
1
1
1
1
1
1
0
1
1
0
0
2
0
1
1
0
1
1
1
1
0
0
0
3
0
1
1
1
2
0
1
2
0
2
1
1
2
2
2
1
0
0
1
1
1
1
0
1
0
2
1
1
1
1
1
1
1
1
0
1
1
0
1
1
0
1
0
1
0
0
1
0
1
2
1
0
1
1
1
1
1
0
2
2
1
1
1
0
2
1
1
1
0
2
2
2
0
1
3
0
1
1
2
1
1
1
0
1
1
1
2
0
2
1
1
0
1
1
0
0
2
2
0
1
1
2
1
1
1
1
0
2
1
1
3
1
1
0
2
1
1
0
0
1
0
2
1
0
2
0
2
0
1
0
1
3
1
1
1
1
2
1
0
1
1
2
1
1
0
1
1
1
1
0
0
1
0
0
2
0
2
0
1
1
1
2
0
1
2
1
2
1
2
2
1
2
1
1
2
2
0
1
2
1
1
0
0
1
0
0
0
1
2
0
1
1
1
1
0
1
1
1
0
1
1
1
2
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
0
2
1
1
1
3
1
1
0
0
1
1
1
0
2
2
2
0
0
1
1
1
0
2
1
1
0
0
0
0
0
2
1
2
1
2
1
2
1
0
1
1
1
1
1
1
0
0
1
1
2
1
1
2
0
1
2
0
1
0
2
0
2
2
0
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
0
2
1
1
2
1
0
1
2
2
0
2
1
1
0
1
0
1
0
0
0
2
0
0
1
0
1
1
1
2
2
1
1
1
0
2
1
1
1
0
1
1
1
1
1
0
1
0
0
3
2
2
1
0
1
1
2
1
1
1
1
1
3
2
2
0
1
4
1
0
1
0
1
1
0
0
1
1
2
0
1
2
1
1
1
0
1
2
1
2
2
1
1
0
1
1
1
1
1
1
1
1
1
2
2
0
1
1
0
1
3
0
1
1
0
1
2
1
3
2
0
1
0
2
0
2
0
2
1
1
0
1
1
0
0
3
1
0
1
1
3
1
0
1
0
1
1
1
2
1
0
1
0
1
1
1
1
1
1
2
0
0
0
0
1
1
1
1
1
2
0
1
1
2
1
1
2
0
0
0
2
1
1
0
1
2
1
0
0
1
1
1
1
1
1
0
2
1
0
2
1
2
1
1
0
0
1
1
0
2
1
2
1
1
1
1
1
2
0
0
1
0
0
0
2
1
0
1
1
0
0
1
1
0
1
2
1
1
1
1
2
1
1
2
2
1
2
1
1
0
1
0
1
0
1
1
0
2
1
1
1
0
1
2
1
0
1
0
0
1
0
1
1
2
1
1
1
1
1
0
1
0
2
1
0
1
0
1
1
1
2
1
1
1
1
1
1
0
0
1
1
2
1
0
1
1
1
0
1
3
1
0
1
1
1
1
1
2
1
1
0
1
1
1
1
1
1
0
1
2
0
0
1
0
1
1
2
4
1
2
0
1
1
0
2
0
1
1
0
1
1
1
0
0
2
1
1
1
2
0
0
1
0
1
1
2
2
0
1
1
2
0
0
0
1
1
0
1
2
1
0
0
1
1
1
1
1
2
2
0
1
0
0
1
1
1
2
2
0
2
1
2
1
2
2
0
1
1
1
1
0
2
0
0
1
0
1
0
0
0
0
2
1
1
2
2
1
1
1
1
1
2
2
2
1
1
1
0
1
1
1
0
1
0
2
1
1
2
1
1
1
1
1
1
1
0
1
0
2
2
0
1
1
1
5
0
1
1
2
1
1
1
1
1
1
1
1
2
1
2
1
0
0
1
1
1
2
0
1
0
1
0
1
2
0
1
0
2
0
2
2
1
2
1
0
1
1
2
0
0
0
2
1
0
1
0
0
1
2
1
0
1
0
0
1
0
2
2
0
1
2
1
0
1
1
3
0
0
0
2
2
0
0
0
2
0
2
2
1
0
1
0
1
1
2
1
1
0
1
2
1
1
1
1
2
0
1
0
0
1
1
0
2
2
0
0
2
2
1
1
1
1
1
2
1
0
1
0
0
3
0
2
0
1
1
1
1
1
0
2
1
1
1
2
0
2
1
1
2
0
1
0
1
2
1
2
1
1
1
0
2
1
2
1
1
0
1
1
1
2
0
1
1
0
2
1
0
1
2
1
1
0
1
1
1
2
1
1
2
2
1
1
0
1
2
0
1
0
2
1
1
2
2
1
0
1
2
1
1
0
1
2
2
1
0
0
1
2
1
1
0
1
1
1
0
2
1
1
2
0
1
1
0
1
0
1
1
2
1
1
1
0
0
1
1
2
1
1
1
1
0
0
0
2
1
0
2
2
1
2
2
2
2
1
2
3
2
1
0
2
0
1
2
1
0
2
0
1
2
0
0
0
0
1
1
1
1
1
0
1
0
0
1
2
0
2
2
1
0
1
0
0
0
1
0
1
2
1
1
2
1
0
1
2
2
1
1
1
2
2
1
2
0
0
0
0
0
1
1
0
1
0
1
0
2
0
1
2
1
2
0
1
1
1
1
1
0
1
2
2
0
0
2
1
2
1
0
0
1
1
0
2
1
0
1
1
0
1
2
1
2
1
0
0
0
2
1
0
1
2
1
1
1
2
1
0
0
1
1
1
1
1
0
0
1
1
1
2
2
1
1
2
2
1
1
1
1
0
0
1
2
0
1
1
0
1
1
1
1
0
2
2
2
1
0
1
2
0
0
0
1
3
3
2
0
1
1
2
1
1
2
2
1
0
2
2
1
1
1
1
2
0
1
1
1
2
0
1
1
1
0
1
1
0
0
0
0
0
1
0
0
0
1
0
3
1
0
2
1
1
2
0
1
1
1
1
0
1
1
0
2
0
0
0
1
0
2
1
3
2
0
2
2
1
1
1
1
1
0
3
1
0
1
1
2
1
1
1
1
0
0
0
1
1
1
2
2
0
1
1
0
0
0
1
2
0
1
0
1
2
1
2
1
1
0
0
2
1
0
2
0
2
2
1
1
0
1
0
1
1
2
1
1
1
1
2
1
1
0
0
1
1
1
0
2
1
1
1
1
1
1
1
1
1
1
2
1
1
0
0
1
1
0
1
1
1
1
2
1
2
2
0
1
2
2
0
1
0
0
2
1
2
0
0
2
1
1
2
1
1
1
2
2
2
2
0
2
1
1
1
1
2
1
1
2
0
2
1
1
0
1
1
1
0
0
0
0
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
2
2
0
0
2
1
1
0
1
1
0
0
0
0
0
1
1
0
2
1
2
1
2
1
0
1
2
1
0
0
1
0
1
1
0
2
0
1
1
2
1
2
1
1
0
0
1
1
0
1
0
2
1
2
0
2
1
1
0
1
1
1
1
2
0
1
1
0
1
2
0
1
1
1
2
2
1
0
0
2
1
1
0
0
1
2
1
1
0
1
1
2
2
0
1
2
1
1
0
2
2
0
2
0
1
1
1
2
0
0
1
2
1
0
1
0
1
0
0
0
1
0
1
1
1
1
1
0
0
1
0
0
1
2
0
1
1
2
1
1
1
0
1
0
1
1
1
0
0
0
1
0
1
0
0
2
0
1
0
1
1
2
2
0
2
0
1
0
2
1
2
2
1
2
1
2
0
1
0
2
0
0
1
0
1
1
1
0
1
1
2
2
1
1
1
2
1
1
1
1
2
1
2
1
2
1
0
1
1
0
1
2
1
1
1
0
1
0
1
0
2
1
1
1
1
0
1
0
1
0
0
1
2
1
1
2
1
0
2
1
1
2
2
1
0
2
1
1
0
0
2
0
2
1
2
1
1
2
0
1
1
2
2
1
0
1
0
0
2
2
2
1
2
0
1
0
1
2
0
1
2
1
2
1
0
0
0
0
0
1
0
0
0
1
0
1
1
1
1
2
1
1
2
2
1
1
2
2
0
1
0
1
2
1
0
2
1
0
2
2
0
2
0
0
1
1
1
0
3
1
2
2
1
1
2
1
0
1
1
1
2
1
1
1
2
1
1
0
1
1
0
1
1
0
0
0
1
1
1
1
0
1
1
1
0
1
1
1
2
1
0
2
1
0
0
1
0
1
1
1
1
1
1
2
2
1
0
0
3
1
2
0
3
1
0
0
1
1
0
0
1
1
2
1
1
2
0
1
2
1
2
0
1
0
0
0
2
0
1
1
1
0
0
1
0
1
1
1
1
1
0
1
0
0
0
1
1
0
0
1
1
0
2
2
1
1
1
1
1
2
1
0
1
1
1
1
1
2
2
0
1
1
0
1
1
1
2
2
0
1
0
0
1
0
0
0
1
2
1
1
1
1
1
1
1
1
1
0
1
0
1
0
1
1
2
0
0
1
1
2
2
0
1
2
0
0
0
1
1
1
2
2
0
0
1
1
0
1
0
2
1
0
0
1
0
1
1
2
1
1
0
1
1
1
0
2
1
2
1
1
1
1
1
1
1
1
0
1
1
1
1
0
1
0
1
1
1
1
1
0
1
2
0
1
1
2
0
1
1
1
1
1
3
0
1
1
1
1
1
1
1
2
2
1
1
1
0
1
2
1
1
0
0
1
2
1
0
1
0
1
1
2
1
0
1
1
1
1
2
2
0
2
1
1
0
0
0
0
2
1
0
2
1
2
2
0
0
1
0
2
1
1
2
1
2
1
2
1
0
1
2
0
2
1
1
0
1
0
1
1
0
0
0
1
1
0
3
1
1
2
2
1
1
0
2
1
0
1
0
1
1
2
2
1
1
1
0
1
1
1
1
3
2
0
0
0
0
0
1
2
0
1
1
3
1
0
0
1
1
1
1
1
1
0
3
1
2
1
2
0
1
1
1
1
0
1
0
0
0
1
0
0
2
0
0
0
1
1
1
1
1
0
2
1
2
2
2
1
1
1
0
1
2
1
2
1
0
1
1
0
2
1
0
2
0
1
1
1
2
3
2
2
0
3
0
3
0
1
3
0
0
2
1
1
1
1
2
1
2
0
1
2
0
0
2
2
0
1
1
1
2
1
2
1
1
1
1
2
2
0
1
2
1
2
0
2
1
0
0
2
2
1
1
1
1
1
1
2
1
1
1
1
0
1
1
2
0
1
1
1
1
1
2
1
1
2
2
0
0
1
0
0
1
0
1
2
1
1
1
1
1
1
1
2
0
1
0
0
0
1
0
1
1
2
1
1
1
1
1
0
1
1
0
2
1
1
1
2
1
1
1
1
0
2
0
1
2
0
1
1
1
0
1
1
2
0
1
1
1
2
1
0
1
1
1
1
1
1
0
1
2
2
1
0
0
2
2
2
0
1
1
2
0
1
2
2
2
1
1
1
1
2
2
1
2
2
1
1
0
1
1
1
1
1
1
1
2
1
2
0
1
2
2
2
1
1
1
0
1
1
1
2
0
2
0
2
2
0
0
0
0
2
2
2
1
2
2
1
0
1
1
0
0
2
1
1
1
0
0
0
2
1
1
0
1
2
2
1
1
2
0
0
0
1
0
2
1
0
0
1
1
2
1
0
1
2
1
2
2
2
1
1
0
0
1
1
1
2
0
0
0
1
0
1
1
2
1
2
2
1
2
1
1
0
1
2
2
0
1
2
2
1
0
1
2
0
1
1
0
1
2
1
0
1
0
1
0
0
1
1
1
1
1
2
1
1
1
1
2
0
1
0
0
0
1
0
0
1
1
1
2
0
1
1
2
1
1
1
1
0
0
1
0
1
1
0
3
1
2
0
1
1
1
1
4
1
1
0
0
1
0
1
1
0
0
2
2
0
0
0
2
2
1
0
1
0
1
0
2
0
2
1
1
1
1
2
0
0
1
1
1
1
0
0
1
1
1
2
2
1
2
2
1
1
0
2
1
0
0
1
1
0
0
1
2
1
2
1
1
0
1
2
1
0
0
1
0
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
1
1
0
1
2
1
2
1
1
1
1
1
1
1
1
2
2
1
0
2
1
1
1
2
1
2
1
1
1
1
1
1
2
1
0
1
2
1
0
1
2
3
1
2
1
0
1
2
2
1
1
1
2
1
2
0
0
1
0
1
2
1
2
0
1
2
1
1
0
0
0
0
2
1
0
0
0
2
2
0
0
1
1
2
2
2
2
2
1
1
1
1
2
1
1
0
1
1
0
0
2
0
1
2
0
1
1
1
0
0
0
0
2
1
2
1
0
0
1
1
0
2
1
1
0
2
1
0
2
0
1
1
1
1
1
1
0
1
1
1
1
0
1
1
2
1
2
2
2
2
1
2
0
2
0
0
1
1
1
0
1
1
1
0
1
0
1
1
3
2
1
0
1
0
1
0
0
1
1
1
0
1
0
1
1
1
0
2
1
0
1
1
2
1
1
0
0
2
0
1
2
2
1
5
1
1
0
2
2
1
0
1
1
1
2
1
1
1
1
0
2
2
1
1
4
0
1
1
0
2
0
2
2
2
1
1
1
0
0
1
2
2
1
1
1
1
1
0
1
2
0
2
0
1
1
1
0
0
0
1
2
3
1
1
1
0
2
0
1
1
1
1
1
1
0
1
0
1
1
2
0
0
1
2
1
0
1
2
0
0
0
1
0
1
1
1
0
2
0
1
2
1
0
1
2
0
0
1
4
1
2
1
1
1
1
0
0
1
1
1
1
2
0
1
0
0
1
0
1
1
1
1
1
1
0
1
0
2
1
1
0
0
0
1
0
1
1
1
1
1
0
1
0
1
2
2
2
2
1
1
1
0
1
0
0
1
1
1
2
1
2
2
0
0
1
1
1
2
0
2
1
0
0
1
2
1
2
2
1
1
2
3
0
1
0
0
0
1
0
0
1
1
1
1
1
1
1
0
1
1
3
1
0
2
0
1
1
1
1
1
1
1
0
0
1
1
1
1
1
0
2
2
1
1
0
0
1
0
1
1
2
1
2
2
1
0
0
1
1
1
0
1
0
1
2
1
1
0
2
2
0
1
2
1
2
2
1
1
1
0
1
1
3
2
0
0
1
0
0
1
0
0
2
1
2
1
1
1
1
1
0
0
1
0
1
1
1
2
1
1
1
2
1
1
1
1
0
1
1
2
2
1
1
2
1
1
0
1
1
1
1
0
1
0
1
0
0
1
0
1
1
1
1
1
2
0
1
1
1
1
0
1
0
2
1
2
1
1
1
2
1
0
0
1
0
1
1
2
0
1
1
0
0
0
1
2
1
0
1
0
2
2
2
1
0
2
1
1
0
2
1
1
1
1
0
0
1
1
1
2
2
0
0
1
0
1
0
0
1
1
0
0
0
0
1
1
1
1
1
1
0
1
1
1
2
2
0
1
2
1
1
0
1
3
2
2
1
0
0
1
3
1
1
2
1
1
1
1
0
0
0
0
1
1
1
2
1
1
1
1
1
1
0
0
0
2
1
1
1
1
1
1
1
0
0
1
2
1
1
1
2
2
0
1
1
2
2
0
2
2
1
1
0
0
1
2
1
1
1
0
0
1
1
1
0
2
0
0
2
1
1
2
1
1
1
2
1
1
1
0
1
1
0
0
1
1
2
0
2
1
1
1
1
1
1
0
0
0
2
1
2
0
1
2
1
0
1
1
0
1
1
0
1
1
3
0
0
3
1
0
2
1
2
1
0
0
0
1
0
1
0
2
2
1
0
1
1
1
1
0
1
2
2
1
1
1
2
2
0
2
1
0
1
0
0
1
2
1
1
0
1
0
1
1
1
1
1
1
0
1
2
0
2
0
1
2
1
1
2
2
1
1
2
1
1
0
1
0
1
1
0
2
1
0
2
0
2
0
1
2
0
1
0
1
2
1
1
5
1
0
1
0
1
0
0
0
1
2
1
0
1
1
0
2
0
1
0
1
0
1
1
1
0
1
1
1
2
0
1
2
0
1
1
1
1
0
1
2
0
0
0
3
1
1
1
1
2
1
1
1
1
0
1
2
2
2
2
1
1
1
1
0
0
0
1
0
0
2
1
1
1
2
1
1
1
2
2
2
2
0
1
2
3
1
2
1
0
1
1
0
2
1
1
1
1
1
0
1
1
1
1
1
1
0
1
0
1
2
1
0
1
1
1
1
3
1
0
0
0
1
0
2
0
0
1
1
1
0
1
1
0
0
0
1
0
1
1
0
1
2
1
1
0
2
1
1
0
1
1
0
1
1
1
1
0
2
1
1
1
0
2
1
0
0
0
1
1
1
1
2
1
2
0
1
0
1
2
2
0
1
2
1
2
1
1
0
1
2
1
2
1
2
1
1
1
1
1
1
0
0
1
0
2
1
1
2
1
0
2
1
1
1
0
2
2
0
1
1
1
1
1
1
1
1
2
1
0
2
0
3
1
1
1
1
0
1
1
1
2
1
1
0
2
1
2
0
1
0
1
0
1
1
2
2
2
1
2
1
0
0
1
0
2
1
0
1
2
0
0
0
0
0
1
1
2
1
1
0
1
1
0
0
1
2
1
1
1
0
1
0
0
2
2
2
0
0
0
0
2
1
1
0
1
1
1
1
1
1
0
2
0
1
1
0
1
0
1
0
0
1
3
1
1
0
2
1
2
1
1
0
2
1
2
0
1
1
2
1
1
1
2
3
2
2
1
1
1
3
2
2
2
0
2
2
0
1
1
0
0
3
1
1
1
1
3
2
0
2
1
2
1
2
1
1
1
1
2
1
1
1
0
0
1
1
0
0
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
0
1
2
2
3
0
1
0
2
2
3
2
2
1
1
2
0
1
1
1
2
1
1
1
1
1
0
2
1
1
0
0
1
2
1
1
1
0
0
0
1
1
1
0
1
1
1
0
2
2
1
2
1
2
0
1
0
2
2
1
1
1
0
0
1
2
1
1
1
1
0
1
1
0
1
0
0
1
0
1
1
0
1
0
0
2
1
1
2
0
0
1
0
0
1
0
2
0
2
1
2
1
0
2
0
1
1
2
0
0
2
1
2
1
2
2
2
1
0
1
1
1
0
2
1
2
1
1
0
1
1
1
2
1
2
1
1
2
1
2
1
2
2
1
0
0
1
1
1
0
1
1
1
0
2
1
3
1
0
1
0
0
1
1
1
2
0
2
1
1
1
1
1
2
1
1
1
0
1
1
1
1
1
2
1
1
2
2
1
1
1
1
0
0
2
2
0
0
2
2
1
1
2
1
1
0
1
0
0
2
0
1
1
1
2
0
0
1
0
1
1
2
1
0
1
1
1
1
1
2
0
2
1
2
0
2
1
1
1
2
1
0
1
2
2
1
0
1
0
1
1
1
2
1
0
1
0
1
1
1
1
1
0
1
1
1
1
2
1
1
0
1
1
2
1
1
2
0
1
2
1
1
0
2
2
0
2
1
1
1
1
1
0
0
1
1
1
1
0
2
1
2
0
1
1
0
0
0
0
1
1
1
2
1
0
0
3
1
1
3
0
1
1
1
2
0
2
1
0
1
1
1
1
1
0
1
0
1
1
2
1
2
0
3
2
2
1
2
1
0
1
2
0
1
1
1
0
1
1
2
1
1
2
0
1
1
1
1
1
2
1
1
1
1
0
1
2
0
0
2
2
0
2
1
1
1
1
1
1
1
0
0
1
0
1
1
1
1
0
1
1
1
1
1
0
0
0
2
0
1
1
1
1
1
2
1
1
1
0
1
2
0
1
1
0
1
1
2
0
2
1
0
2
1
1
0
1
1
1
2
2
0
1
1
0
2
1
2
1
2
0
0
0
0
2
2
0
2
0
1
1
1
1
2
0
1
0
1
0
0
2
1
2
1
1
0
2
1
2
1
1
1
1
0
2
2
3
0
2
0
0
1
1
1
1
0
2
1
0
1
1
1
0
1
1
0
0
1
0
1
1
1
0
2
1
1
1
1
2
2
1
1
2
1
1
2
2
1
1
0
1
2
2
0
1
2
1
1
1
3
1
1
2
1
0
0
0
0
1
0
1
1
0
1
0
2
1
2
1
0
1
0
1
1
0
1
0
0
0
1
1
2
1
2
1
1
1
1
1
3
1
2
1
1
2
2
1
0
2
1
1
1
1
1
3
1
2
1
2
1
0
2
0
0
1
0
1
1
1
1
1
1
0
1
1
1
1
1
0
0
2
2
2
1
1
1
0
1
1
1
1
0
2
1
0
2
2
0
1
1
2
1
2
1
0
2
2
2
2
1
1
2
0
1
1
0
2
1
1
0
1
0
1
3
1
1
0
2
0
0
1
3
1
1
1
0
1
0
2
1
1
0
1
2
1
1
0
0
1
1
1
0
0
0
1
1
2
2
1
0
1
0
2
0
0
1
1
1
1
2
2
2
1
0
1
2
1
1
0
1
1
2
2
0
2
1
2
0
0
2
1
2
1
1
2
0
2
1
2
1
1
1
0
2
0
2
1
1
0
1
1
1
1
1
1
1
1
1
2
1
0
1
2
0
1
1
1
0
1
1
1
0
1
2
1
1
1
1
2
0
1
1
1
1
2
1
1
1
1
1
0
1
1
1
1
0
1
2
2
0
0
1
1
1
1
1
2
1
1
1
2
0
1
0
2
1
2
2
2
1
1
1
1
1
1
1
1
1
1
1
2
1
0
1
0
0
1
1
2
1
0
0
2
1
1
1
1
0
2
1
0
1
0
1
2
1
1
0
1
2
1
1
1
2
1
0
2
0
1
1
1
1
2
0
0
0
3
1
2
1
0
3
1
2
1
1
2
1
2
1
0
2
1
0
1
2
1
2
2
1
1
2
1
0
2
1
1
2
1
2
0
1
0
0
1
1
1
2
2
1
1
0
1
2
0
1
2
2
1
1
1
1
1
1
1
1
0
1
1
1
0
1
0
1
0
1
1
2
1
1
1
1
1
1
0
2
0
2
2
1
0
1
1
2
0
1
1
0
2
1
2
1
1
0
2
2
0
0
1
0
3
2
0
1
0
1
1
0
1
2
2
1
2
1
2
0
1
2
1
1
1
0
0
0
0
2
2
1
1
2
1
0
2
1
0
1
0
0
2
1
1
3
0
1
1
1
1
1
1
2
0
1
2
1
2
0
2
0
1
0
2
0
2
0
0
0
2
0
2
1
1
1
1
2
1
0
1
1
1
0
0
0
0
1
2
0
1
0
1
1
1
1
1
0
1
1
1
2
1
2
2
1
1
1
0
1
1
1
0
2
0
1
0
1
0
1
2
1
1
1
2
0
0
1
1
1
0
0
1
0
2
1
1
2
0
1
1
1
1
0
2
1
2
1
1
1
1
1
2
1
2
1
2
1
0
1
1
1
1
1
1
1
0
1
2
0
4
1
2
0
1
2
0
2
0
1
0
1
1
0
2
2
1
1
2
1
1
1
1
0
0
0
1
0
1
2
1
2
3
0
2
1
0
1
2
1
2
0
0
0
1
1
0
1
0
2
2
0
0
2
1
0
1
0
1
1
1
1
1
0
1
2
2
1
1
1
1
1
2
1
1
1
1
1
0
0
2
1
1
1
3
2
0
2
1
1
1
1
1
2
1
1
0
1
2
0
1
1
1
1
1
1
1
0
2
2
1
2
1
1
1
0
0
2
1
2
1
0
1
1
1
2
2
2
1
1
1
0
1
0
2
3
1
0
0
1
1
2
0
0
2
2
1
0
2
1
1
1
1
1
0
1
1
1
1
0
1
1
1
0
1
1
1
1
1
1
2
0
0
1
1
0
0
0
1
2
0
0
1
1
1
1
1
0
0
1
2
0
1
0
1
1
1
0
1
1
1
1
0
1
0
2
1
1
1
1
1
2
1
2
3
1
1
1
1
2
1
0
1
1
2
0
0
1
1
1
1
1
2
0
2
1
5
1
0
0
1
1
2
1
0
1
2
2
1
1
1
1
0
1
1
0
2
1
1
2
2
0
1
0
0
2
0
1
1
2
2
1
1
2
1
1
1
2
0
1
0
3
0
1
2
1
0
1
0
0
1
3
1
1
0
1
2
0
1
1
1
0
2
1
1
1
2
2
1
1
1
2
1
1
2
1
2
1
1
2
1
0
0
0
0
0
1
0
1
1
0
1
1
1
1
2
1
1
2
1
1
0
1
2
2
2
2
1
1
1
0
1
2
1
1
0
1
1
1
0
1
2
2
2
2
1
1
1
1
1
1
1
1
0
1
0
2
0
1
1
2
1
0
1
0
1
1
1
1
2
0
0
2
0
1
0
2
2
1
0
2
0
2
1
3
2
1
1
2
0
0
1
0
1
1
0
0
1
1
1
0
2
1
0
2
1
1
1
1
2
2
1
1
1
1
0
2
2
2
1
2
1
1
1
2
1
1
1
1
0
0
0
1
2
1
0
1
0
1
0
0
0
1
0
2
1
2
2
1
1
1
1
2
1
1
1
3
0
2
0
2
1
1
1
1
1
3
0
2
1
1
1
0
2
2
0
1
2
2
1
2
1
0
1
2
1
1
1
0
1
1
1
0
1
0
3
1
1
1
1
3
7
1
2
2
1
0
0
1
1
0
1
1
1
2
0
2
2
1
1
2
0
1
2
2
2
2
1
0
1
0
1
0
1
1
2
0
2
1
2
1
0
1
2
0
0
0
0
2
1
0
2
0
0
2
2
1
1
1
1
2
2
1
1
1
2
1
2
0
3
0
1
0
1
1
2
1
3
1
1
1
1
2
2
0
2
1
1
1
1
1
2
2
1
1
2
0
0
1
0
1
1
0
2
0
1
0
2
1
1
1
1
2
0
1
1
0
1
2
1
1
0
2
1
2
1
1
1
1
2
2
2
1
1
2
1
2
1
0
2
1
1
0
1
1
1
1
1
1
0
2
1
2
0
1
0
2
2
1
1
2
1
1
2
1
0
1
1
2
0
0
2
1
1
0
2
0
1
2
2
0
1
2
3
0
1
1
0
0
1
2
2
0
1
0
0
2
0
1
0
1
0
2
2
1
0
1
1
1
1
0
0
1
1
2
1
1
1
0
1
2
2
1
1
0
1
2
1
1
2
1
1
0
0
1
0
1
2
1
0
0
1
1
0
1
1
1
0
1
3
2
2
1
2
1
1
2
1
1
1
2
1
0
1
0
1
2
0
2
1
1
2
1
1
0
0
1
1
1
1
1
2
1
0
2
1
0
0
1
2
0
2
2
1
0
1
2
2
2
1
0
1
2
1
2
1
0
1
0
0
0
1
2
0
2
1
1
1
0
2
1
2
1
1
0
1
1
1
0
1
1
2
3
1
1
1
0
0
1
0
1
0
0
1
1
1
1
0
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
0
2
1
0
0
1
1
0
2
0
2
2
1
0
1
2
2
0
1
1
0
0
0
0
2
1
1
1
0
0
2
1
1
0
1
1
1
1
0
1
1
1
1
3
1
1
2
1
0
1
2
0
1
0
1
1
2
1
2
0
0
1
1
2
0
0
1
2
1
0
0
1
2
1
1
2
0
0
2
2
1
1
2
1
0
1
1
0
0
0
1
1
2
2
1
3
3
1
2
1
0
2
1
0
0
2
2
0
1
1
0
1
2
0
0
2
2
1
1
0
1
0
1
1
1
2
1
1
0
0
0
1
0
1
1
1
0
1
1
1
0
0
1
1
1
1
2
1
1
1
2
2
2
1
1
0
1
1
0
1
0
1
1
2
2
2
1
1
1
2
0
1
1
0
2
1
1
2
1
1
0
0
0
1
1
1
1
0
2
1
1
1
0
1
0
0
1
1
0
1
0
1
0
0
1
1
2
0
1
1
0
0
2
2
1
1
2
2
1
0
1
2
1
0
2
1
1
1
0
1
0
1
0
1
2
2
0
0
1
1
0
1
2
0
1
0
0
2
1
2
1
0
1
0
1
0
1
2
1
1
1
0
1
1
1
0
0
1
1
1
1
2
1
0
2
1
2
0
1
2
1
1
1
1
0
2
1
1
0
0
1
2
1
1
0
0
0
2
1
2
1
0
1
1
0
2
1
0
0
2
0
1
0
1
3
1
0
1
2
1
1
1
1
1
1
2
0
2
1
1
2
1
1
1
1
0
0
1
0
1
0
1
2
1
2
2
1
1
2
2
1
0
0
0
0
1
0
1
1
2
1
1
1
0
1
0
2
0
0
2
1
2
1
0
1
2
2
0
2
0
1
2
1
2
2
0
0
0
1
0
4
2
1
2
0
2
1
0
1
1
0
1
2
0
1
1
0
1
2
2
1
3
1
2
0
1
2
1
0
1
1
2
1
1
1
2
0
1
1
2
1
1
1
0
1
2
1
1
1
0
1
1
1
2
0
2
1
2
1
1
0
2
2
1
1
1
1
2
1
0
0
0
1
1
1
2
0
0
1
1
0
0
2
1
2
0
1
1
1
1
0
0
3
0
1
1
2
1
2
1
1
2
1
0
1
1
0
1
1
5
1
0
0
0
1
2
0
2
0
1
1
0
0
1
0
1
1
1
0
1
0
0
1
0
0
0
2
0
1
0
1
0
1
3
1
1
3
2
1
1
1
1
0
1
2
1
1
1
1
1
2
1
2
2
1
1
1
1
3
1
1
2
0
1
1
1
1
1
1
0
1
0
2
1
0
1
2
0
1
1
2
2
2
2
2
2
1
0
1
1
1
2
0
2
1
1
3
2
1
2
1
2
0
0
1
1
3
0
0
1
1
1
0
1
1
1
1
1
2
1
1
2
2
2
2
0
2
1
1
0
3
0
1
2
1
0
1
0
1
0
0
1
0
0
2
2
1
2
1
0
1
1
2
1
2
0
1
2
1
1
2
1
1
0
0
2
2
1
1
0
1
2
1
1
0
1
2
1
2
1
0
5
2
0
1
1
1
2
1
2
0
1
1
0
1
2
2
1
1
1
1
2
1
1
1
2
1
2
1
0
0
1
2
0
1
0
1
1
1
2
1
2
1
2
2
0
2
3
1
1
1
0
1
0
0
2
1
2
2
1
1
2
0
2
2
1
1
1
1
1
1
2
1
1
1
1
0
1
1
1
1
2
2
1
1
1
0
3
0
2
2
0
0
1
1
1
1
1
2
1
0
0
1
2
1
1
1
1
2
2
2
1
0
1
0
5
1
1
1
1
1
2
1
2
0
0
1
1
1
1
1
1
1
1
2
2
1
0
1
1
0
1
0
1
0
1
1
2
2
1
2
1
1
1
0
0
1
0
2
2
0
1
0
2
4
2
0
1
0
1
2
0
1
2
1
1
1
4
0
0
1
1
1
0
3
2
0
1
0
1
1
0
0
1
2
0
0
0
0
2
0
1
1
1
2
0
0
2
0
2
0
1
2
1
1
1
1
1
0
0
1
0
1
1
0
1
0
0
3
1
1
2
2
0
1
2
1
2
0
0
0
1
2
1
1
1
1
1
0
1
1
0
2
1
0
1
2
2
2
1
1
2
1
2
0
1
1
1
1
1
1
1
1
1
0
0
0
2
1
2
0
1
1
1
1
1
1
0
0
2
0
1
0
1
1
1
0
0
2
1
1
1
2
2
8
1
1
1
1
1
0
1
2
0
2
1
1
2
1
1
0
0
0
0
2
1
1
1
1
0
1
0
1
1
0
0
1
0
1
1
1
2
1
1
2
2
0
0
0
1
0
1
0
2
1
1
1
0
0
0
1
1
1
2
1
1
0
4
2
1
1
0
2
1
1
1
1
1
2
1
1
0
1
0
1
1
1
1
0
2
1
0
0
1
0
1
1
1
0
2
1
0
1
0
1
2
1
1
2
1
2
0
2
2
0
1
2
0
0
0
1
2
1
1
2
1
2
1
2
0
1
0
1
0
0
1
1
1
1
1
0
2
2
1
1
1
0
2
1
1
2
2
2
1
1
2
2
0
2
2
1
2
1
0
2
2
0
1
1
2
2
0
1
1
2
1
2
0
0
1
1
1
1
0
1
1
2
0
1
3
0
1
0
1
0
0
0
0
1
0
0
1
2
2
1
2
3
1
0
1
1
0
1
2
1
0
2
0
2
2
0
1
1
2
1
1
2
1
0
0
1
1
0
2
1
0
0
4
1
1
1
2
1
0
1
1
2
1
1
1
0
1
1
0
1
0
2
2
1
3
2
0
1
0
1
2
1
2
0
1
2
2
1
2
1
1
0
1
1
1
0
1
0
0
0
1
1
1
0
2
0
1
0
2
1
2
1
1
0
1
1
0
2
1
2
2
2
2
1
2
1
1
0
1
0
2
0
0
0
1
1
1
1
1
0
2
1
2
1
1
1
1
1
1
1
1
0
1
1
0
1
1
2
2
1
1
0
0
1
2
1
2
1
0
2
1
0
1
1
1
1
0
1
1
1
0
1
1
1
1
2
2
1
1
0
1
1
1
2
0
0
1
1
1
0
1
0
0
1
1
2
1
1
0
2
1
2
1
0
2
2
0
1
1
1
2
2
0
1
1
0
2
0
0
2
0
1
1
2
1
1
2
0
1
1
2
1
1
1
1
1
1
1
1
0
1
1
0
0
2
1
1
1
0
2
1
1
1
1
2
1
0
1
1
0
2
0
0
1
1
1
2
2
0
1
2
0
0
0
1
1
0
0
0
2
1
2
2
1
2
1
1
2
0
1
2
0
0
2
2
4
1
1
0
2
3
1
1
0
0
1
1
1
0
2
0
0
0
1
2
2
2
1
1
1
2
0
1
1
0
0
1
1
0
2
0
0
1
1
1
2
1
1
1
0
1
0
2
2
1
1
0
0
1
1
1
1
0
1
2
0
2
1
0
2
1
2
0
2
1
1
1
1
1
1
2
0
2
2
1
0
1
1
1
0
2
2
1
1
1
2
1
1
1
2
2
3
0
1
2
2
1
1
1
1
0
1
1
2
1
2
1
1
0
2
1
2
1
1
1
2
0
2
0
1
1
0
2
1
0
1
0
0
1
1
1
1
0
1
1
1
2
1
2
2
1
1
2
1
1
2
2
2
2
0
4
2
1
0
1
1
0
1
0
1
2
0
1
1
0
0
0
1
0
3
1
1
0
0
2
2
0
1
2
1
2
0
0
1
0
1
1
0
1
1
0
1
1
1
2
1
2
0
1
1
0
1
1
1
1
2
0
1
1
2
0
1
1
1
0
0
2
1
1
0
1
0
1
0
2
1
2
3
1
1
1
2
2
1
2
2
1
0
1
1
0
0
2
2
0
1
1
1
2
1
0
2
1
2
2
1
0
0
1
1
0
1
1
1
0
3
2
1
1
0
2
0
1
2
1
1
0
1
2
2
1
0
2
0
1
1
2
1
1
2
0
2
1
1
0
1
0
1
2
1
0
0
1
1
1
1
0
0
3
1
0
1
1
0
1
0
2
0
2
1
2
1
1
2
0
2
0
1
0
0
0
1
0
0
1
0
0
2
1
3
1
1
0
1
1
1
1
1
0
1
0
0
2
0
0
0
1
0
2
2
2
1
1
1
2
1
2
2
0
1
3
1
2
1
2
2
1
1
0
1
2
1
2
1
1
1
0
1
0
2
1
0
1
1
0
0
1
2
1
0
0
0
1
2
0
0
0
2
0
0
1
0
0
0
2
1
2
0
0
2
0
2
1
1
1
0
0
2
1
2
1
0
1
1
1
0
1
0
0
1
0
0
1
1
1
1
1
1
0
2
0
2
2
0
1
1
1
2
1
2
1
1
1
1
1
1
1
0
0
0
1
1
2
0
1
1
0
2
0
1
1
2
1
2
0
2
2
1
2
2
1
1
1
1
1
1
0
0
1
0
1
2
1
1
0
2
1
2
1
1
1
2
1
0
0
2
0
1
2
1
0
1
1
2
1
2
0
0
2
1
1
1
1
1
1
2
1
1
1
0
2
0
2
0
1
1
0
1
0
1
1
1
1
1
1
0
1
2
0
1
2
1
2
2
1
0
1
2
1
2
2
1
1
1
0
0
1
1
1
1
1
2
2
1
0
0
1
1
1
2
1
1
0
0
1
1
1
0
1
1
1
0
1
2
0
1
0
1
1
1
0
2
0
1
1
1
0
1
0
2
1
0
1
1
1
1
2
2
1
0
1
1
0
0
2
1
2
1
1
4
0
1
0
0
1
2
1
0
0
1
0
0
1
0
1
0
1
2
1
0
1
1
1
0
0
2
2
2
1
1
1
1
1
0
1
1
0
2
0
1
1
2
1
0
0
1
1
1
1
1
0
1
0
1
0
1
1
2
2
2
1
1
2
0
0
2
1
2
2
1
1
2
1
0
1
1
1
1
1
2
1
0
1
2
1
1
1
0
0
1
2
0
1
1
2
1
1
2
0
0
0
1
0
2
1
1
0
1
0
2
2
1
2
0
0
0
2
2
2
1
0
1
2
0
0
1
0
0
1
1
1
1
0
2
0
1
1
1
1
2
0
1
3
2
0
3
1
0
0
1
2
2
0
2
1
1
1
1
1
0
1
0
0
0
2
0
2
0
0
0
1
0
1
1
0
1
1
2
0
0
1
0
0
0
2
0
1
2
1
0
1
1
2
2
0
1
0
0
0
1
2
1
1
1
1
1
0
1
2
1
1
0
1
1
2
1
1
1
0
1
1
2
1
2
1
1
1
1
1
2
2
1
1
1
0
0
0
1
0
0
2
1
1
1
2
1
0
0
0
1
2
0
0
1
0
1
2
2
1
1
0
1
0
0
2
0
2
2
0
2
2
1
1
0
0
2
1
1
0
1
1
0
0
2
1
1
0
0
1
1
0
0
1
2
1
1
0
1
1
0
1
0
0
1
1
0
0
0
1
0
1
1
1
1
2
1
1
0
0
2
1
1
0
1
1
2
1
0
2
1
1
0
0
2
2
1
2
1
2
1
1
0
2
1
1
0
0
0
1
0
0
2
0
2
0
3
1
1
1
2
1
2
0
0
1
1
1
2
0
2
0
1
0
2
1
2
1
1
2
0
1
1
2
1
2
2
1
2
2
1
0
2
0
2
1
1
1
1
0
2
0
0
2
1
0
1
2
1
3
1
0
2
0
1
1
3
1
0
1
1
0
1
3
0
2
1
0
0
0
1
0
0
0
1
1
1
1
0
2
1
1
1
3
2
1
0
2
1
2
0
0
1
1
1
1
0
1
0
1
0
2
2
1
1
1
0
0
1
1
2
2
2
0
1
2
2
2
2
2
2
1
0
0
2
0
1
0
1
2
1
0
1
1
0
1
2
1
1
1
1
2
1
1
2
1
2
1
1
1
1
0
0
2
2
1
1
1
0
0
1
0
0
0
1
0
0
2
2
2
0
0
0
0
1
0
0
2
0
1
2
1
2
0
1
0
1
2
2
4
2
0
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
0
2
2
0
1
0
2
2
1
2
2
2
1
1
1
0
0
1
1
0
1
1
2
1
0
2
1
0
1
1
1
0
1
1
1
1
1
2
2
2
0
2
0
2
1
0
1
2
1
0
0
1
0
2
1
0
1
1
1
0
1
1
1
1
0
2
0
1
1
1
1
1
2
1
2
0
1
2
1
0
1
0
1
1
1
1
1
1
0
0
1
0
2
0
2
1
1
1
0
1
2
0
1
0
1
0
1
1
1
2
1
1
0
0
1
0
2
2
2
1
1
1
0
1
1
0
0
1
0
2
0
1
0
0
1
2
0
0
0
1
1
2
0
2
0
1
2
1
1
0
0
2
1
1
2
1
1
2
1
1
0
1
2
1
0
0
2
0
2
0
1
3
1
1
1
1
0
2
1
1
0
1
2
1
0
1
1
1
1
1
0
0
1
1
0
1
1
1
0
1
2
2
1
1
0
1
1
0
1
2
1
1
1
1
0
2
1
1
1
1
0
1
1
1
1
0
1
0
0
1
1
1
1
0
0
1
2
1
1
0
0
1
1
0
1
0
0
0
0
2
2
0
0
1
1
0
0
1
2
1
1
0
1
1
2
1
0
1
3
1
1
0
1
0
1
1
1
1
1
0
1
0
1
2
0
3
2
1
2
0
1
1
1
2
1
0
3
3
1
0
1
2
1
1
1
2
1
0
2
1
2
1
0
0
2
1
0
1
1
1
1
1
0
1
2
1
0
1
1
1
1
2
0
0
0
0
1
2
2
1
1
0
2
0
1
1
2
1
1
1
1
0
1
2
2
1
0
0
1
1
2
3
1
0
0
2
2
1
1
1
0
2
1
0
1
1
2
1
0
0
1
1
1
2
0
1
0
1
2
1
0
1
2
1
1
1
0
2
1
1
1
0
1
3
2
3
1
0
0
1
1
0
1
2
0
0
1
0
0
0
1
0
1
1
0
2
2
1
0
0
0
1
1
0
1
1
1
1
1
1
1
1
0
0
1
1
1
0
1
0
0
2
1
1
1
2
1
1
0
2
0
1
0
1
1
2
1
0
1
0
2
2
2
2
1
1
0
1
1
2
0
0
2
0
1
0
1
1
2
0
0
1
0
1
0
2
1
0
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
2
0
0
0
1
1
2
2
2
1
0
0
1
2
1
1
1
1
1
1
1
0
0
1
1
2
1
1
2
0
0
1
0
1
1
1
1
1
1
1
0
1
2
3
2
0
1
1
1
1
0
0
0
0
1
1
1
0
1
1
0
0
0
2
1
2
0
1
0
2
1
2
1
0
1
0
1
0
1
0
1
2
0
2
1
2
1
1
0
0
0
1
1
1
1
0
2
2
1
1
2
2
0
1
0
1
1
0
0
1
1
1
1
0
2
2
2
1
2
1
0
2
0
1
1
1
2
1
1
1
1
1
1
0
1
0
1
0
1
2
1
1
0
2
0
1
2
1
0
1
1
1
4
1
0
0
1
0
1
1
1
1
1
1
0
1
2
0
1
1
2
1
0
1
1
2
1
0
0
1
1
0
2
2
2
1
0
2
1
1
1
0
1
1
0
1
0
2
0
1
0
1
1
1
2
2
2
0
4
0
2
1
0
0
2
2
2
1
1
1
1
0
2
1
0
1
1
1
0
1
1
0
2
0
0
1
2
2
0
2
2
0
1
0
0
1
2
2
1
1
0
2
0
1
2
1
0
1
2
1
2
2
1
0
0
0
2
1
0
1
1
1
2
2
0
1
1
1
2
1
2
0
0
0
1
0
2
2
0
1
1
0
1
1
1
1
1
2
1
1
1
1
0
1
1
2
1
2
2
2
1
1
0
1
0
1
1
1
0
0
1
0
2
0
2
1
0
1
0
1
1
1
2
2
1
1
0
1
1
1
2
1
2
1
1
1
1
0
1
0
0
1
0
0
1
1
1
1
1
1
1
1
1
1
2
2
2
2
1
1
1
1
0
2
2
1
0
1
1
1
1
2
0
0
1
2
0
0
0
3
1
2
2
0
2
0
0
1
0
2
1
0
0
1
1
0
2
1
1
2
1
1
1
0
1
1
0
1
1
1
1
0
1
1
1
1
0
1
1
1
2
0
3
0
1
1
1
1
1
0
0
1
2
1
0
1
2
0
3
1
1
2
0
0
3
0
0
0
1
0
1
1
0
0
1
0
1
0
1
2
0
1
1
0
0
1
1
1
2
0
1
2
1
0
1
2
1
1
1
0
1
0
1
1
2
1
0
1
1
0
1
0
2
1
2
1
2
0
1
0
0
2
1
2
1
1
2
1
1
2
1
2
1
0
1
0
1
1
3
1
0
2
0
2
2
0
1
1
2
0
0
1
1
1
0
0
1
1
0
2
1
2
0
2
0
1
1
1
1
2
1
1
0
0
1
1
1
1
1
0
1
1
1
0
0
2
0
2
1
1
2
1
1
2
0
1
2
1
0
0
0
2
1
0
1
0
1
2
2
0
1
2
2
0
1
0
1
2
1
1
1
1
1
1
1
1
1
1
1
1
0
0
1
0
2
1
2
0
0
2
1
1
1
1
0
1
0
0
1
1
0
1
1
1
1
1
2
2
0
1
1
0
1
1
1
2
2
0
1
1
0
0
1
1
1
0
2
1
0
2
1
2
0
1
0
1
1
1
1
2
1
2
0
2
0
1
1
1
1
1
1
0
0
2
1
1
1
1
1
2
1
1
1
1
1
1
2
0
2
1
2
1
1
2
2
2
0
0
0
1
1
1
0
2
1
1
2
2
0
0
1
1
0
0
1
1
0
0
1
1
2
0
1
0
1
2
0
1
1
1
1
0
1
1
1
2
0
1
1
1
1
1
1
1
2
1
0
2
0
0
2
0
1
0
2
1
2
0
0
2
2
1
1
2
0
1
2
2
2
0
0
1
1
1
1
3
1
0
0
0
0
1
0
2
2
1
0
0
0
0
1
1
0
1
1
0
1
0
0
2
1
1
1
2
2
0
2
0
1
0
0
1
2
0
1
1
1
1
1
2
1
0
2
1
1
1
0
2
1
2
0
0
0
1
1
1
1
2
2
1
2
2
3
1
1
2
1
2
0
1
0
0
1
2
2
0
1
0
1
2
1
1
1
1
2
1
1
2
13
1
2
2
0
0
2
1
0
1
1
0
0
0
0
1
1
0
1
1
2
1
1
1
1
1
1
1
1
2
1
1
0
1
2
0
1
1
1
1
2
1
1
2
1
0
2
1
0
2
1
2
0
2
1
1
1
1
2
2
1
1
0
0
1
1
0
2
0
1
1
0
1
0
3
0
1
1
1
1
2
0
0
0
1
1
1
1
0
1
2
1
2
0
1
2
2
0
1
1
1
1
1
0
1
1
1
1
2
2
0
0
1
1
2
2
2
1
1
1
0
1
0
1
0
0
0
2
1
1
0
1
2
1
1
2
2
1
2
1
2
1
1
0
1
1
1
1
0
0
0
1
0
1
1
1
1
4
0
3
1
1
1
1
1
1
0
1
1
1
1
1
0
0
1
1
1
1
1
1
2
2
2
0
1
2
1
2
1
2
1
2
0
0
1
2
0
2
2
1
1
1
1
0
2
1
2
0
0
0
0
2
1
2
2
0
4
1
0
2
1
1
2
1
1
1
2
1
2
0
1
0
1
1
0
0
1
1
2
1
0
1
1
0
2
0
2
0
1
0
1
1
2
2
0
2
0
3
1
3
0
0
1
1
2
0
0
2
2
0
3
1
2
0
1
1
6
1
0
0
1
1
1
1
2
0
0
1
0
0
1
1
2
2
0
1
0
1
2
2
0
0
1
2
1
1
0
1
1
0
0
1
2
1
1
1
2
1
0
0
2
2
2
2
0
1
1
1
2
0
1
0
1
1
1
1
2
2
1
2
0
0
0
0
1
1
1
1
1
1
2
0
2
2
1
0
0
1
1
1
2
1
1
1
0
0
1
2
2
2
0
1
2
0
0
2
1
0
0
1
1
1
2
0
2
2
2
0
1
0
0
1
1
1
1
1
0
1
1
2
1
2
1
1
1
0
0
0
1
2
2
1
2
1
1
0
1
1
1
0
1
1
1
1
1
0
0
0
0
2
1
8
0
1
1
0
1
0
2
2
0
0
1
1
1
1
2
0
1
1
2
1
0
2
0
0
1
1
0
2
0
1
0
0
0
0
0
0
0
1
1
1
0
2
2
0
1
0
0
1
1
1
2
1
2
1
1
2
1
1
2
1
1
2
1
0
1
2
1
2
2
1
1
0
1
3
1
2
0
1
0
1
1
0
1
0
1
1
0
0
1
1
1
1
1
1
1
1
1
1
1
0
0
1
0
1
0
2
1
1
0
0
1
1
1
1
1
0
2
0
2
2
0
2
0
2
2
1
1
0
2
2
1
2
0
1
1
2
2
1
1
2
1
2
0
1
1
2
0
0
1
0
1
1
1
1
1
1
1
1
0
1
3
1
0
0
0
1
1
2
0
1
2
1
1
1
2
1
2
0
0
1
1
1
0
1
0
0
0
0
2
1
1
1
2
1
2
1
0
2
1
2
1
1
2
0
1
1
1
2
2
2
2
2
2
0
1
1
1
0
2
1
2
2
0
0
2
1
0
0
1
1
0
1
0
0
2
1
0
1
1
2
1
1
2
1
1
0
1
1
1
0
1
2
2
0
0
0
2
0
2
1
1
0
0
2
1
2
0
1
1
1
1
1
3
0
0
1
1
2
1
2
2
2
0
2
2
1
1
0
1
1
1
0
1
1
1
2
2
2
1
1
1
1
1
1
2
2
1
0
2
2
2
1
1
0
0
1
2
1
1
1
1
1
1
2
0
1
1
1
1
1
0
1
2
0
2
1
0
0
1
0
0
0
2
1
1
1
1
0
0
1
2
0
3
0
1
2
0
0
0
0
1
1
1
1
2
0
0
1
0
1
1
1
1
1
1
2
2
1
1
1
1
1
1
0
0
0
2
0
0
1
1
1
1
0
2
1
1
1
0
1
1
1
0
1
2
0
1
2
2
0
0
0
0
1
0
2
1
1
0
1
2
2
0
2
0
0
1
1
0
1
1
1
1
1
1
1
0
1
1
1
1
0
1
1
1
1
0
2
1
1
2
2
1
1
0
1
0
1
0
0
2
1
0
0
1
5
2
0
2
1
1
2
0
0
2
1
2
1
2
1
0
1
1
1
2
1
1
1
1
1
1
1
2
1
0
2
1
1
1
0
1
0
1
1
0
1
0
0
1
1
1
2
1
3
1
0
2
1
1
1
2
1
0
0
0
1
2
2
1
2
1
1
0
1
2
1
3
2
1
1
1
0
1
2
2
1
1
2
0
0
2
0
0
0
1
1
0
1
2
0
0
0
1
1
2
1
0
2
3
1
0
1
2
1
0
1
1
0
2
1
7
1
1
2
0
2
1
1
1
1
0
1
0
0
0
1
1
2
1
1
0
1
1
2
0
1
1
1
1
2
1
0
1
1
1
0
2
1
0
2
1
0
3
1
2
0
2
1
1
1
1
1
1
1
0
1
1
1
2
2
1
1
1
1
2
0
0
0
0
1
0
2
1
1
2
0
1
1
0
2
1
1
1
0
1
1
0
1
1
0
0
1
2
0
0
1
1
1
2
0
0
2
1
2
1
0
0
1
1
0
2
1
0
2
0
0
2
0
1
1
1
2
1
1
1
0
0
1
1
1
0
2
1
2
2
0
1
0
1
0
0
1
2
2
2
1
2
1
0
2
1
0
2
0
1
1
1
0
2
1
2
2
1
0
2
1
0
1
0
1
2
3
1
0
2
2
1
0
1
1
1
1
1
0
1
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
2
1
2
1
1
4
2
1
1
1
2
1
2
1
0
2
1
1
1
0
2
2
1
1
2
2
1
1
1
0
1
1
1
2
1
1
1
1
2
1
2
1
0
2
2
0
1
2
1
1
1
1
0
2
1
1
0
0
0
1
2
1
1
1
0
1
1
1
1
0
0
0
1
2
0
0
0
0
0
3
0
0
1
1
0
1
0
1
0
0
1
1
0
1
1
1
1
1
0
2
1
0
0
1
2
0
1
3
2
1
1
1
1
1
2
0
2
1
0
1
1
1
1
0
1
0
1
0
0
1
2
1
1
1
0
1
1
2
1
1
1
2
0
1
2
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
0
1
2
1
2
1
2
0
2
0
1
1
1
1
0
1
1
0
1
1
4
2
0
1
0
0
1
0
1
1
0
1
2
3
1
1
1
1
1
2
1
0
0
1
1
2
1
2
0
2
1
1
1
2
2
1
1
1
0
1
0
1
0
0
2
1
0
1
1
0
0
1
1
2
1
0
1
0
1
0
0
1
1
1
0
1
1
1
0
1
1
1
1
1
2
1
0
1
0
0
1
2
2
0
1
1
2
1
2
4
1
1
1
1
1
0
1
1
1
0
0
1
1
1
0
1
2
1
1
1
0
2
0
1
1
1
0
2
1
2
2
0
1
2
1
1
0
1
1
1
1
1
0
2
2
1
2
1
4
2
1
1
1
1
1
1
2
2
1
2
0
2
1
2
0
1
1
2
1
0
1
1
1
0
1
0
2
1
0
1
0
0
1
0
1
2
1
1
0
1
0
0
1
1
2
2
0
1
1
1
1
1
1
1
2
1
0
1
1
0
1
1
1
0
1
2
0
2
0
1
0
0
1
1
2
1
1
1
1
1
0
1
1
1
1
1
0
1
0
1
2
1
0
0
1
1
1
1
1
2
2
0
1
0
1
1
1
1
0
1
0
0
2
1
0
1
0
1
0
2
1
1
0
0
1
1
2
2
1
2
1
1
1
0
0
1
2
2
1
0
1
1
0
2
0
2
1
2
1
0
0
2
1
2
0
1
0
2
0
2
1
2
1
0
1
0
0
1
1
1
1
0
1
0
1
1
2
1
1
2
0
0
2
1
0
1
1
1
0
1
1
2
2
1
0
2
1
2
1
0
1
1
1
0
1
1
1
0
2
0
0
2
0
1
0
1
1
1
2
1
1
1
1
1
0
1
1
1
1
1
1
0
1
0
1
1
1
1
0
1
0
0
0
1
1
1
0
0
1
1
1
2
1
1
2
1
0
0
1
2
1
1
3
1
1
1
0
2
0
0
2
1
2
1
0
1
1
1
1
2
2
0
0
0
1
1
2
2
2
1
0
1
2
1
2
2
1
1
0
2
1
0
1
0
2
1
1
2
2
1
2
0
1
1
1
1
4
2
0
0
1
0
1
0
1
0
1
1
2
1
1
0
0
1
2
2
1
1
0
0
2
1
2
0
1
0
1
0
0
2
0
1
2
2
1
1
1
0
0
3
0
0
1
1
2
0
0
0
0
2
0
2
2
2
1
0
0
0
2
2
1
0
2
2
1
1
3
1
2
1
0
1
1
0
1
2
0
2
1
0
1
1
1
2
2
1
0
1
1
1
1
1
1
0
2
1
1
1
0
1
1
2
1
1
1
2
0
0
1
0
1
1
2
0
1
2
1
2
1
0
1
2
1
2
2
0
2
0
0
0
2
1
1
1
1
1
0
1
1
0
2
2
1
0
1
0
2
0
1
1
0
0
1
1
2
2
1
1
1
0
0
1
3
0
1
1
1
2
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
2
0
2
1
1
1
1
1
0
1
1
1
1
1
2
1
2
1
1
1
0
1
1
1
0
0
2
3
0
2
1
0
1
2
1
0
0
1
4
2
2
0
1
2
2
1
1
2
1
0
0
1
0
1
0
1
2
1
0
2
0
1
2
0
2
0
0
1
1
1
1
1
2
1
2
0
1
0
1
1
1
1
1
1
2
2
0
1
0
1
0
2
1
1
1
0
1
1
2
0
2
2
0
2
2
1
1
2
1
0
1
1
1
1
2
1
1
1
1
2
1
1
1
2
2
0
1
1
1
2
2
1
2
1
2
0
2
1
1
0
1
0
1
1
0
0
1
1
1
1
1
0
1
1
0
1
1
1
2
2
1
2
1
2
1
1
1
0
2
1
1
1
1
2
0
1
0
1
0
0
1
0
1
3
2
1
1
1
1
0
2
2
1
1
1
2
1
2
1
0
1
1
1
1
0
2
1
2
2
0
0
1
1
0
1
2
0
1
1
2
0
1
1
1
1
1
1
1
0
2
1
0
1
0
0
1
2
1
0
1
1
2
2
2
1
1
0
1
1
1
1
1
2
1
1
3
1
2
1
1
0
1
2
0
0
2
1
2
2
1
2
1
1
1
0
1
2
1
1
1
2
2
0
1
0
1
1
1
1
1
2
0
0
1
2
2
2
2
1
3
1
1
1
0
1
1
0
2
0
1
1
2
0
2
3
2
3
1
2
1
0
3
1
2
1
1
1
1
2
2
0
1
1
1
0
1
1
0
1
1
1
0
1
4
2
0
0
1
1
1
1
1
1
1
1
4
1
1
0
2
2
1
1
1
1
0
1
1
0
2
1
1
1
2
1
2
1
2
2
2
0
2
2
0
1
1
2
0
0
1
1
0
0
0
1
0
2
1
2
1
1
1
2
2
0
2
2
0
0
0
1
1
1
0
1
0
1
2
2
2
2
2
2
1
1
0
2
2
3
2
0
1
0
1
1
0
2
1
1
2
2
2
2
0
0
1
1
1
1
0
0
1
2
1
1
1
1
0
1
1
2
0
1
2
1
1
2
0
1
2
2
2
1
0
1
1
1
1
0
1
1
1
0
0
1
0
2
1
1
0
2
0
0
1
1
1
1
1
0
1
1
1
0
2
1
1
2
1
1
1
1
2
2
0
1
1
1
1
1
1
1
1
1
3
1
1
1
1
0
2
2
1
1
2
0
0
2
0
2
1
1
1
2
0
1
1
1
0
1
0
1
2
1
0
1
1
1
1
0
1
1
1
0
1
2
2
0
1
1
0
1
2
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
0
2
1
0
1
1
1
1
2
2
1
1
2
1
2
0
0
1
1
0
0
0
0
1
0
2
0
0
1
2
1
2
2
0
0
1
1
2
1
0
1
2
1
2
1
0
0
0
1
0
1
1
0
1
1
2
2
2
1
1
1
1
1
3
0
0
1
0
0
1
0
0
1
0
1
1
1
0
1
2
1
1
0
0
0
0
1
1
1
1
1
2
1
0
1
0
1
1
1
2
0
1
1
0
1
1
0
2
2
1
0
1
0
0
1
0
1
1
2
2
1
1
1
1
2
1
1
0
1
1
1
1
1
0
1
0
0
1
1
3
0
2
1
1
1
0
1
1
0
1
2
1
0
1
1
1
2
1
0
0
1
0
1
0
0
2
1
1
1
1
0
0
1
0
2
2
1
0
2
1
1
1
1
3
1
2
0
0
1
1
1
1
0
0
2
2
1
1
1
0
0
1
2
1
1
0
0
2
2
1
4
1
1
2
2
1
1
0
1
0
0
1
0
0
1
0
1
1
2
2
1
1
1
2
1
1
0
0
1
2
2
1
1
1
1
0
1
2
0
0
0
0
1
1
1
2
2
0
1
0
1
0
0
1
1
0
1
0
1
1
0
1
1
1
1
1
1
1
1
1
0
1
1
1
5
1
0
1
1
2
1
2
0
0
2
1
0
1
3
0
0
1
0
0
1
1
2
0
2
1
0
0
0
2
1
1
1
1
0
1
1
0
0
1
1
1
1
1
1
2
2
1
0
1
2
1
0
1
1
2
2
1
2
1
1
1
1
10
0
1
1
0
0
0
1
0
1
0
1
2
0
1
1
1
1
1
1
1
3
1
1
2
0
0
0
1
0
1
1
1
1
1
2
1
1
1
2
2
0
2
0
0
1
0
3
1
0
1
1
2
1
3
1
3
1
1
1
1
1
0
3
1
0
1
2
2
1
1
0
1
2
2
0
1
1
1
1
0
1
1
1
1
1
1
0
1
2
0
2
1
0
1
0
2
2
1
1
0
1
1
1
1
1
1
2
0
1
2
1
1
3
2
1
2
1
2
1
0
2
1
2
0
1
2
0
2
1
2
1
1
0
1
1
1
1
2
1
1
1
2
2
0
1
0
0
1
0
1
0
1
0
0
0
1
2
1
0
2
1
1
1
1
0
2
1
1
2
1
0
1
1
1
2
2
2
1
1
2
1
2
1
0
0
0
2
2
2
1
0
1
0
1
1
0
2
0
1
2
1
1
1
0
1
1
1
0
1
0
0
0
1
1
0
1
1
0
1
1
1
1
1
1
0
0
0
1
0
1
2
1
1
1
1
1
1
0
1
0
1
1
0
2
1
1
1
1
0
2
1
1
0
1
0
1
0
1
0
2
1
1
0
0
0
1
1
1
0
1
1
1
1
1
2
1
1
1
0
2
0
0
2
0
0
2
0
0
2
1
0
2
3
2
1
1
1
2
0
0
1
2
0
0
2
2
2
0
1
1
0
1
1
1
1
1
1
0
0
1
2
2
2
2
0
0
2
1
2
1
1
0
2
1
1
0
0
1
1
0
1
1
0
2
1
2
2
1
2
1
1
1
1
2
2
0
1
0
0
0
0
0
2
1
1
1
2
1
1
2
1
0
1
2
1
2
3
1
1
0
2
1
0
1
1
1
2
0
1
2
0
0
0
2
1
1
0
2
2
1
1
0
1
2
1
1
1
0
2
2
1
1
0
1
0
2
1
1
0
1
2
1
0
2
1
0
0
2
0
1
1
1
0
1
2
1
0
2
0
2
1
1
1
6
1
2
1
0
1
1
1
0
1
3
1
1
1
1
1
1
1
1
0
1
1
1
1
0
0
2
1
1
1
0
2
2
2
1
1
1
2
1
0
1
0
1
0
2
2
1
2
1
0
0
1
1
1
2
1
1
2
2
0
0
1
2
0
2
2
1
2
0
1
0
0
2
1
1
1
1
0
2
2
1
0
0
0
1
2
0
2
1
1
1
1
1
1
1
2
1
1
2
2
1
2
4
0
0
0
1
1
1
0
1
2
1
2
1
0
1
1
1
1
3
0
1
0
0
1
2
1
1
0
1
2
1
1
2
0
1
1
1
1
0
0
0
3
1
2
1
0
0
1
2
1
1
0
0
1
2
1
2
1
0
0
1
1
0
1
0
0
1
1
2
1
1
2
2
2
2
1
2
1
0
3
0
1
0
0
0
0
1
0
1
1
1
1
2
0
0
1
0
1
1
1
2
0
1
2
2
1
0
2
2
1
3
2
1
1
1
1
0
1
2
1
0
2
1
0
1
0
2
1
2
2
3
0
1
1
1
2
1
2
2
2
0
1
2
1
1
0
1
2
1
2
1
0
1
0
2
0
1
2
1
2
1
0
2
1
1
0
0
0
0
2
1
1
0
1
1
0
2
1
1
1
2
0
0
1
1
1
1
1
1
1
0
1
1
0
2
0
1
2
0
1
2
2
2
1
1
1
2
0
1
1
1
2
1
2
1
3
1
0
1
1
2
2
1
2
1
1
0
0
2
0
0
1
1
2
1
1
2
1
1
2
1
1
1
1
1
1
2
2
1
1
0
1
1
0
1
1
1
0
1
0
1
1
2
2
1
1
0
1
1
1
0
0
0
2
2
1
0
0
0
2
1
1
1
1
2
1
3
1
0
2
1
1
1
0
1
1
0
1
1
2
0
1
1
0
0
0
0
2
1
0
0
0
2
1
1
2
1
0
2
0
2
1
0
1
0
0
1
2
1
1
0
1
1
1
0
1
1
1
1
1
0
2
1
0
0
1
1
1
2
1
0
2
2
2
1
1
1
0
1
2
2
1
2
0
2
0
1
2
1
1
1
1
1
1
0
1
1
0
2
2
0
1
0
2
1
1
1
1
0
1
0
1
1
1
1
0
2
0
0
0
1
0
1
1
2
0
0
1
0
0
0
2
2
1
2
1
1
0
1
0
0
1
4
2
0
1
1
0
1
1
1
3
1
0
0
0
1
2
2
1
0
1
1
0
1
1
1
0
1
1
1
0
0
2
2
2
2
1
0
2
1
1
1
1
2
0
1
1
1
1
1
2
0
0
0
1
2
2
1
1
1
3
1
1
1
1
0
1
1
1
1
0
0
0
0
1
1
1
1
2
1
2
0
2
1
1
2
2
0
0
2
1
0
0
0
1
1
1
1
1
0
0
0
1
2
1
2
1
0
1
1
1
2
2
1
1
0
0
1
1
1
2
0
1
0
0
0
0
1
1
2
1
0
2
1
2
0
1
2
0
1
2
1
0
0
2
1
2
2
2
1
1
0
2
2
0
0
1
1
1
0
1
2
1
1
0
2
1
2
1
2
2
0
2
2
0
1
1
1
1
1
1
2
1
1
0
2
1
0
0
1
1
3
1
1
0
2
1
1
2
1
0
1
3
2
0
0
1
2
1
1
1
2
1
2
1
0
0
1
0
1
0
2
1
1
0
2
0
1
1
0
2
2
1
1
1
1
0
2
0
1
0
0
1
0
1
1
0
0
1
0
1
1
0
0
1
1
1
1
1
2
1
0
0
0
0
0
1
0
1
0
2
1
1
0
0
1
0
1
0
0
1
1
2
1
2
0
1
1
1
1
0
1
0
2
1
1
1
2
0
1
2
1
1
0
1
2
1
1
1
0
1
1
1
6
0
1
1
2
2
0
1
2
3
1
3
2
0
0
1
1
1
1
0
1
1
1
1
2
0
0
2
1
1
1
0
0
1
1
1
0
1
1
2
1
1
1
1
0
1
1
1
1
0
2
2
4
0
1
2
0
1
1
3
2
0
1
1
1
0
0
0
2
2
2
1
0
2
1
0
1
1
1
2
0
1
1
1
2
1
2
1
2
2
1
2
0
1
1
0
1
0
1
1
0
0
1
1
2
2
2
1
3
0
1
0
1
1
0
1
1
0
0
1
1
0
2
0
0
1
2
1
1
1
2
3
1
2
1
1
2
1
1
2
0
2
2
2
0
2
1
1
1
2
0
1
1
2
1
0
2
0
1
1
1
2
1
1
2
0
1
1
2
1
1
0
1
1
2
1
1
1
2
1
0
1
1
1
0
0
0
0
0
1
1
1
0
2
1
2
1
2
1
1
1
1
0
1
0
0
1
1
2
1
1
1
0
2
1
2
1
3
1
1
1
1
1
1
0
1
1
0
2
0
2
2
2
1
1
2
2
1
0
0
1
0
1
1
1
1
0
1
2
2
1
1
0
0
0
1
1
1
1
2
1
2
0
0
1
1
0
2
1
1
0
2
1
0
0
1
1
1
1
2
1
1
0
1
2
1
1
2
1
1
0
2
1
3
2
1
1
1
0
2
2
1
0
0
1
2
1
1
0
1
2
1
1
1
2
0
0
1
0
1
0
1
0
2
1
0
1
1
1
1
0
0
1
0
2
1
1
1
2
0
0
2
1
1
1
0
1
0
0
1
1
0
1
1
1
1
0
0
2
0
0
1
1
1
1
1
1
0
0
1
1
1
1
2
1
1
1
0
2
2
2
0
1
0
1
2
0
1
2
1
1
1
0
1
3
1
1
2
2
1
0
1
0
0
1
2
2
1
2
0
1
0
2
1
0
2
2
1
2
2
1
0
1
0
0
1
1
0
3
1
1
1
1
1
1
0
2
1
1
0
1
1
1
2
2
2
0
1
0
1
3
2
0
0
1
0
2
0
0
1
2
0
1
1
0
0
2
1
1
1
0
1
1
5
2
1
1
0
1
0
0
1
1
1
0
2
0
1
1
0
1
1
2
2
1
0
1
1
1
1
2
2
2
1
0
1
2
1
6
1
2
2
0
2
2
1
1
1
1
1
0
0
1
0
0
2
0
0
0
0
0
1
1
2
1
2
0
1
1
2
1
2
1
0
1
2
1
1
0
2
0
1
1
1
2
1
2
2
1
1
1
1
1
0
0
2
1
1
0
1
0
2
0
1
1
0
1
1
1
3
1
1
0
1
1
1
2
3
1
1
2
0
1
1
2
2
1
2
1
1
2
1
1
0
0
0
0
1
0
1
0
2
1
2
1
0
1
0
0
0
1
1
0
2
1
2
1
2
0
0
1
1
1
1
2
0
1
0
0
0
1
0
2
1
2
1
1
1
2
1
1
1
2
0
0
1
0
1
0
1
1
2
1
0
1
1
0
1
1
2
0
0
0
0
1
0
2
1
1
0
2
2
1
2
2
0
1
2
0
2
1
2
1
1
1
0
1
1
2
0
0
1
2
1
0
0
1
0
1
1
2
0
1
1
2
2
1
2
1
0
2
2
0
1
0
2
1
0
2
1
2
1
1
0
1
0
0
0
1
1
2
1
1
1
1
1
2
1
1
1
1
2
2
1
1
0
1
0
2
1
1
1
2
1
1
1
2
2
2
1
0
2
0
0
2
2
1
0
1
1
0
2
3
2
2
1
0
1
1
1
1
1
0
1
0
1
1
1
1
1
1
1
0
0
1
2
1
2
1
1
1
0
1
0
1
0
1
2
0
1
1
1
1
1
1
1
1
0
0
1
1
1
0
1
1
0
1
2
2
1
1
2
1
1
0
1
1
1
1
1
1
1
1
0
1
1
2
0
2
1
2
0
1
1
1
0
0
0
2
1
0
2
1
1
1
2
0
1
1
1
2
0
1
2
1
2
1
1
1
0
2
0
2
1
1
1
1
2
2
1
1
1
0
1
2
0
1
2
0
1
1
0
2
2
1
2
2
2
1
1
1
0
1
2
1
0
0
1
2
0
1
1
0
1
0
0
1
1
1
1
0
1
1
1
2
1
1
1
1
2
1
0
0
1
0
0
0
0
0
1
1
2
2
1
1
2
1
1
1
2
1
1
0
2
0
2
1
0
2
1
1
1
0
1
0
0
1
1
1
0
1
0
1
1
1
0
1
0
0
2
0
1
0
0
0
2
0
6
0
2
2
0
1
0
0
0
1
1
1
1
0
2
2
1
1
1
1
1
1
1
2
0
0
1
3
2
2
2
1
1
1
2
2
1
1
1
1
2
2
2
1
1
0
1
0
0
0
1
1
1
0
1
1
1
0
0
2
2
1
0
1
0
1
1
1
1
2
1
1
1
0
0
1
3
0
1
2
2
2
1
1
2
2
0
1
1
1
1
1
0
0
0
1
1
1
1
0
1
2
1
1
3
0
1
1
0
1
0
1
1
2
1
1
2
2
1
0
1
2
1
1
1
1
1
1
2
2
1
0
1
1
1
2
0
1
1
2
0
2
0
1
2
2
1
1
0
1
2
0
1
0
2
2
0
1
1
2
0
2
1
0
1
0
1
0
1
1
1
0
0
2
1
0
1
2
4
0
2
1
0
0
1
1
1
1
2
0
1
1
2
1
1
1
2
1
1
1
1
0
0
0
1
1
0
2
1
2
0
1
1
0
1
1
0
1
2
1
1
1
2
2
2
1
1
1
2
0
2
2
0
1
2
2
1
1
0
0
1
0
1
0
0
0
1
1
2
0
0
1
1
2
1
0
2
2
0
0
0
1
1
0
1
3
0
0
2
1
1
2
2
2
1
1
1
1
1
2
1
1
1
1
1
2
1
0
1
1
1
0
1
0
0
2
2
2
1
1
0
1
1
1
0
1
0
1
1
0
0
0
0
2
0
1
0
2
0
3
2
1
2
2
0
1
1
2
0
1
1
2
2
1
0
1
2
1
1
1
2
0
1
1
1
1
0
1
1
4
1
0
1
0
2
0
0
1
1
0
1
1
1
1
1
1
2
2
1
2
0
1
2
1
0
2
1
0
0
2
1
2
0
1
1
0
2
1
0
0
1
0
0
2
1
2
1
1
0
1
2
1
3
0
2
1
1
1
1
3
0
1
0
0
0
1
2
1
1
1
1
0
0
1
1
2
1
0
1
1
1
1
1
2
1
0
0
1
0
1
1
0
0
1
1
1
1
0
1
1
1
3
1
1
2
2
0
2
2
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
0
1
1
0
2
0
1
0
2
0
1
0
1
1
0
1
0
0
1
1
0
2
2
0
1
0
2
1
0
2
2
1
2
1
1
2
1
1
1
2
1
0
1
0
2
0
2
1
0
1
1
0
0
2
1
2
0
0
1
2
0
1
2
1
1
1
1
0
1
2
0
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
0
1
0
0
1
1
2
1
2
2
2
1
0
1
1
1
1
0
2
1
2
1
2
0
2
1
0
0
2
1
1
2
0
1
2
2
1
1
0
1
2
1
2
2
2
0
2
1
1
2
1
1
1
1
1
2
0
1
2
2
1
1
1
0
1
2
0
2
2
2
2
0
1
2
0
1
2
1
1
1
0
2
1
1
1
1
1
1
0
1
0
1
1
1
1
0
0
1
0
1
1
1
1
0
1
1
0
1
0
2
1
2
0
1
1
2
1
1
1
0
2
1
1
2
1
1
1
1
0
0
0
0
1
1
1
2
1
1
1
2
1
0
2
2
2
2
1
0
1
0
1
1
0
1
1
1
2
2
1
0
1
1
0
0
1
1
0
0
1
1
2
0
2
1
1
2
0
1
1
1
0
1
1
2
1
0
1
1
2
1
2
1
1
1
0
1
0
0
1
1
0
1
2
2
0
1
1
0
2
1
1
1
1
2
0
1
0
1
1
2
0
2
0
1
1
0
1
1
1
0
0
1
2
0
1
1
1
1
0
2
0
1
1
0
1
1
0
1
0
2
3
1
0
2
0
3
1
0
1
0
3
0
0
1
2
1
2
2
2
0
2
1
0
0
0
0
1
0
1
0
2
1
1
1
0
1
1
0
1
1
1
0
0
1
0
2
0
0
0
1
1
0
3
1
0
2
0
2
0
0
1
2
1
0
2
1
0
2
1
1
1
0
2
1
2
1
1
1
0
1
1
1
1
0
1
1
0
1
1
2
0
1
0
0
2
2
0
1
0
1
1
0
1
1
0
0
0
2
1
1
1
0
2
1
2
0
1
1
1
0
0
1
0
1
2
2
1
1
2
1
0
0
0
1
0
0
1
1
1
0
4
1
0
2
1
1
2
1
2
1
1
1
1
3
1
2
0
0
1
0
1
1
2
0
0
2
0
1
0
2
1
1
2
2
0
1
1
0
2
2
2
1
1
0
2
1
1
0
0
2
2
1
1
1
1
0
0
1
4
0
1
1
1
0
1
0
2
0
2
1
1
1
0
0
1
0
1
0
2
0
2
0
1
0
1
0
2
0
0
0
0
1
1
1
2
2
1
0
1
1
1
1
1
0
2
1
1
1
0
0
1
3
2
2
2
1
2
2
0
1
2
1
0
0
1
0
0
1
1
0
1
1
0
1
2
0
0
1
2
2
2
1
1
0
0
2
1
2
0
2
0
1
1
1
1
1
2
1
1
0
2
0
1
2
0
2
1
0
1
2
1
1
1
0
1
1
1
0
1
1
0
1
0
1
0
1
2
2
0
1
1
2
3
2
1
0
1
1
1
0
2
2
1
1
1
0
0
1
1
0
1
1
1
2
2
2
1
0
0
1
1
2
0
1
0
1
2
1
1
1
2
1
2
2
1
1
1
1
0
1
1
0
1
2
0
1
1
1
1
1
1
1
0
2
1
0
2
1
1
0
0
1
1
1
1
1
1
3
1
2
2
1
0
1
0
1
1
1
2
2
1
0
0
1
0
1
1
1
0
0
0
1
1
2
2
1
0
1
1
1
2
2
2
0
1
1
1
2
1
2
1
2
2
2
0
1
1
2
1
0
1
0
1
2
2
0
2
0
0
1
1
1
0
1
1
0
2
1
1
0
1
1
0
0
1
2
2
1
2
0
0
2
1
1
2
0
0
1
2
1
1
3
2
0
1
1
1
1
1
1
0
1
1
2
1
1
1
2
2
0
1
1
1
0
1
1
1
1
2
0
1
0
1
2
1
2
0
2
0
0
0
1
1
0
2
1
1
1
1
2
1
2
1
2
0
2
2
2
0
2
1
2
1
2
0
2
2
1
1
1
1
1
1
3
1
1
1
1
2
0
0
1
0
0
1
0
1
0
2
2
0
0
0
1
1
2
2
1
0
1
1
0
1
1
1
2
2
1
1
0
0
0
1
1
1
2
1
1
2
1
3
1
2
0
1
0
0
1
0
0
2
1
0
1
1
2
0
1
2
1
2
1
2
0
2
0
2
1
1
1
1
0
1
1
1
2
2
0
1
2
1
2
1
0
1
0
1
2
0
1
1
1
2
1
1
2
0
1
1
0
2
1
1
0
1
0
1
1
2
1
1
3
1
0
2
2
1
1
1
2
0
1
1
0
0
1
1
2
1
2
0
2
2
2
0
1
0
1
1
0
1
0
1
0
0
1
2
0
0
1
1
1
0
1
1
1
2
0
0
1
1
1
1
2
1
0
0
1
2
0
1
0
1
1
1
0
1
0
2
1
0
0
1
0
1
0
0
1
0
0
1
1
1
2
0
2
1
1
1
0
1
2
2
2
0
0
1
1
1
1
1
2
1
0
2
1
0
1
0
2
0
2
1
1
2
1
0
1
2
0
1
2
2
0
0
1
1
1
1
1
1
2
2
1
2
1
2
1
1
2
1
1
1
1
1
1
0
2
2
1
1
1
1
2
1
0
0
2
2
2
1
0
1
1
0
2
0
0
1
1
1
1
1
1
1
1
0
1
1
2
0
2
0
0
0
0
1
1
1
2
1
1
2
3
1
0
1
0
0
1
1
0
1
1
1
3
1
0
0
1
0
1
1
1
0
1
0
0
2
1
0
1
3
1
1
2
1
0
1
1
1
0
2
2
0
2
1
1
2
2
3
1
1
1
0
2
2
0
1
1
4
2
0
0
2
0
0
1
2
1
0
1
0
1
1
3
2
1
1
1
1
2
1
1
0
2
0
1
0
0
0
0
1
1
0
0
2
2
0
1
1
1
1
2
0
2
1
1
2
2
1
1
0
2
1
0
1
1
2
0
0
2
2
1
0
0
1
2
1
0
2
1
1
0
1
1
0
2
0
1
1
0
1
1
2
0
1
0
0
1
1
2
1
1
0
2
1
1
0
1
1
0
1
1
1
2
0
0
0
1
0
1
2
1
0
1
1
2
1
1
1
1
1
1
0
1
1
1
1
1
3
1
3
0
1
1
0
0
2
1
2
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
2
0
1
1
0
1
0
1
2
1
2
0
0
2
1
1
2
1
1
1
1
0
1
0
1
1
2
1
1
1
1
0
2
1
2
1
0
1
2
2
0
1
0
1
1
2
0
2
2
0
1
0
2
1
2
0
1
2
1
1
1
2
0
1
2
1
1
1
0
0
1
1
1
3
0
1
1
1
1
1
2
1
1
2
2
1
1
2
1
0
0
2
1
0
1
1
0
2
1
1
1
1
0
0
0
0
2
0
1
0
2
2
2
1
0
0
2
0
1
1
1
1
1
1
0
0
0
1
2
1
2
1
1
2
3
1
3
1
2
2
1
2
1
1
0
2
1
1
1
0
0
0
0
0
3
0
1
2
0
0
0
0
1
2
1
1
1
0
1
2
1
1
1
0
1
1
1
2
1
0
1
2
0
1
1
0
1
1
1
0
2
1
1
2
1
1
1
0
2
2
0
2
1
2
1
1
1
0
1
0
1
0
0
0
2
0
1
0
2
0
2
1
2
1
2
2
1
0
1
1
0
2
2
1
1
0
0
1
0
1
1
2
0
2
1
0
1
0
0
1
2
2
1
1
1
0
1
0
0
1
0
1
1
1
1
0
1
1
1
3
0
6
1
0
1
2
0
1
1
1
1
2
1
1
1
1
0
0
0
1
1
1
1
1
1
1
2
0
0
1
1
1
1
1
0
0
0
1
1
1
1
0
0
1
1
1
0
1
1
1
1
1
0
1
1
0
1
0
1
2
2
2
1
1
0
2
1
1
2
0
0
0
1
2
0
1
1
1
2
0
1
1
1
2
1
2
1
0
1
0
0
2
1
1
1
1
1
2
0
1
2
1
1
2
0
1
1
0
1
0
1
1
1
0
1
1
0
1
0
1
1
0
1
0
2
0
2
1
0
1
1
2
0
1
1
0
1
1
1
0
0
0
1
1
1
1
2
0
1
2
2
0
1
0
1
0
2
1
2
1
0
1
3
1
1
1
2
0
1
1
1
1
1
1
1
1
1
1
0
0
1
1
1
1
0
1
1
1
1
11
0
2
0
0
1
2
1
0
1
0
0
2
1
2
0
0
4
1
1
2
1
1
2
2
2
0
1
0
1
3
1
1
0
0
1
1
2
1
2
1
2
1
0
2
2
1
1
2
1
2
2
2
2
1
0
1
2
2
1
1
2
1
1
2
2
0
0
0
1
1
1
0
2
1
1
1
1
0
1
0
1
1
1
1
2
0
0
2
1
2
2
1
2
2
1
0
1
1
1
0
1
0
2
1
1
1
1
1
1
1
0
2
1
1
0
0
2
1
1
1
0
3
1
2
1
1
0
1
2
0
2
1
1
2
1
2
1
1
1
2
1
0
1
0
0
1
2
1
0
1
0
2
2
1
1
1
1
1
2
0
0
1
3
1
1
2
1
0
1
1
1
1
0
1
0
1
0
1
1
1
1
1
1
1
1
1
0
1
2
1
0
0
1
1
2
1
1
1
1
1
0
1
1
1
1
1
1
2
1
2
0
2
1
0
0
1
1
1
0
1
1
1
1
4
1
2
0
0
0
1
0
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
0
0
1
0
2
0
0
1
1
2
2
2
1
2
1
0
1
0
1
0
1
0
1
0
1
0
2
1
0
1
1
2
2
1
1
1
1
2
3
2
1
2
1
1
2
1
2
1
2
0
0
2
2
2
2
1
1
1
1
1
0
2
2
2
1
1
1
1
0
1
0
1
0
1
0
0
0
1
1
1
1
0
3
0
1
1
2
1
1
1
1
2
1
2
1
1
0
1
1
2
1
2
0
1
0
0
1
1
0
1
1
0
1
1
1
0
0
1
1
0
1
0
0
2
2
1
1
2
1
1
0
2
0
1
0
1
0
1
2
2
1
1
2
2
0
1
0
2
2
2
2
1
1
2
0
0
1
0
1
1
2
2
2
2
1
0
1
1
1
0
1
1
0
1
1
1
1
0
1
1
1
1
0
2
2
2
1
0
0
1
0
0
0
0
0
1
2
0
0
2
1
1
0
1
1
1
1
0
1
1
1
2
1
2
1
1
1
1
1
0
0
2
1
0
1
2
1
0
1
1
1
2
0
0
2
1
1
1
0
2
2
0
2
2
1
1
0
1
0
1
1
1
0
0
1
0
2
4
0
2
2
0
1
2
1
1
1
1
1
1
1
0
1
1
1
0
1
0
1
2
1
1
1
1
1
1
0
1
1
2
2
1
0
0
1
2
1
1
2
1
2
2
2
0
0
0
0
1
1
0
3
0
1
1
1
1
1
1
1
0
2
1
1
4
2
1
1
1
1
0
2
0
1
1
1
0
1
2
0
0
2
1
0
1
0
0
2
1
1
1
0
1
1
1
1
2
1
0
1
2
0
0
1
1
2
1
2
1
1
0
0
1
1
0
1
0
2
1
1
1
0
0
0
0
0
1
1
2
1
1
0
1
1
2
0
1
1
2
1
0
0
1
1
1
0
0
0
1
0
1
2
1
1
2
1
1
1
1
1
2
1
0
0
1
0
1
0
2
0
1
2
2
2
1
2
2
1
1
2
1
0
3
2
1
1
1
0
1
0
1
1
0
1
0
1
0
2
1
0
1
1
1
1
1
1
2
0
1
0
1
0
1
2
0
1
0
1
0
2
0
2
2
0
1
0
0
1
1
1
1
2
2
0
1
1
1
2
0
1
2
2
2
1
1
2
1
0
2
2
0
0
2
1
1
0
1
1
1
1
1
1
1
0
1
1
1
6
1
1
0
1
2
1
2
1
1
2
2
1
0
1
1
0
2
1
1
1
1
1
1
0
0
1
2
0
2
2
1
1
1
1
2
1
2
2
1
0
1
2
3
1
1
2
2
1
1
0
2
1
2
1
2
1
2
1
0
1
1
1
2
1
2
0
1
0
1
1
1
2
0
2
0
2
1
0
0
1
1
2
1
1
2
0
1
2
2
0
0
2
1
0
2
0
1
0
1
1
0
0
1
1
0
1
2
2
1
0
2
0
1
1
1
1
1
0
1
1
1
1
1
1
3
1
1
1
0
0
0
1
0
1
0
0
1
1
0
2
2
1
0
1
1
0
1
0
0
1
0
2
2
0
0
0
1
0
1
0
1
2
1
0
0
0
1
1
0
2
1
0
2
2
2
2
2
2
1
1
2
2
0
2
2
1
0
2
1
1
0
1
1
0
0
1
1
0
1
1
1
1
1
1
0
1
1
1
1
1
1
0
1
0
0
2
1
1
0
2
0
1
1
2
2
1
1
2
0
0
1
1
0
1
1
0
0
0
1
2
2
0
0
0
0
1
2
1
0
0
1
0
1
2
1
1
0
1
0
1
2
2
1
1
2
1
0
1
1
1
1
0
0
1
0
0
1
1
2
1
0
2
2
1
1
0
2
1
0
0
1
1
1
0
2
1
0
1
0
1
2
1
0
2
2
1
0
2
2
2
0
2
0
0
1
0
0
0
0
1
0
1
0
0
0
0
2
0
1
2
2
2
0
0
1
0
1
0
1
1
0
1
1
1
1
0
2
0
0
3
1
2
0
1
0
1
2
1
1
0
0
1
1
1
1
1
3
1
1
1
1
4
1
1
1
2
1
1
2
0
1
0
1
1
0
0
1
1
2
2
2
1
1
0
1
1
0
0
1
1
2
2
0
2
1
1
2
1
0
2
2
1
0
1
1
0
1
0
1
2
0
1
0
1
1
2
1
1
6
1
2
0
1
0
1
2
0
1
0
0
0
0
1
2
0
1
1
1
2
1
1
0
1
3
1
1
1
1
1
2
0
0
0
1
2
0
2
0
0
1
1
2
1
1
1
0
2
2
1
1
2
2
1
0
2
1
1
1
0
2
1
1
1
1
2
0
0
1
1
2
0
1
2
1
1
1
0
0
0
0
2
1
1
2
0
1
0
1
1
1
1
2
1
0
2
2
1
1
2
1
2
2
2
2
1
1
2
1
1
1
1
1
1
1
1
2
0
2
1
1
1
1
0
0
0
2
0
0
1
2
1
0
0
0
1
2
0
3
1
0
2
1
0
2
0
1
1
0
2
2
2
0
2
0
2
0
1
1
1
0
0
0
0
1
2
1
1
2
1
1
1
2
2
0
1
0
0
1
1
1
1
0
2
0
0
1
1
1
1
2
0
2
1
1
0
1
0
2
0
0
0
0
1
0
1
3
1
0
2
0
1
1
2
1
2
0
1
1
0
0
2
1
1
1
1
0
0
2
1
0
0
0
1
1
1
1
1
1
0
1
1
1
1
1
1
1
2
1
0
0
1
1
1
1
1
1
1
1
2
2
2
1
1
0
1
0
1
3
1
0
0
0
1
0
1
3
1
1
1
3
1
1
1
1
1
2
3
1
1
1
2
1
0
0
2
1
0
2
2
1
0
0
0
1
1
0
1
2
7
0
0
1
2
1
0
2
0
1
1
0
0
1
0
1
1
1
1
2
1
1
1
1
3
2
0
2
0
1
1
1
1
0
0
2
0
1
1
2
2
1
0
1
1
1
2
1
2
2
1
2
0
0
1
2
2
2
1
1
1
0
1
1
2
1
1
2
1
1
0
0
0
1
1
0
0
0
1
0
1
2
1
1
1
2
1
0
1
1
1
0
0
1
1
1
1
0
0
1
1
0
1
0
2
1
1
1
1
1
2
0
2
1
1
1
1
2
0
1
1
1
1
1
1
0
1
1
1
1
1
0
1
1
2
0
2
1
0
1
1
1
1
2
2
2
0
2
3
0
0
1
1
0
1
2
3
1
1
2
1
0
1
0
2
1
0
1
2
1
2
0
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
2
1
0
0
2
2
0
2
0
1
4
2
2
2
0
0
1
3
0
1
1
0
1
1
1
1
1
1
1
1
2
2
1
1
0
0
2
3
2
0
2
2
1
0
0
1
1
2
1
1
0
1
2
2
0
1
0
1
2
1
0
1
2
1
2
1
2
0
2
1
1
1
1
0
0
1
1
1
1
0
0
1
2
1
1
0
0
2
0
0
2
0
3
2
1
3
2
1
0
0
2
2
2
1
1
1
2
1
2
1
2
2
1
0
0
1
0
1
1
0
1
0
1
1
1
1
1
0
0
2
1
0
1
2
0
0
1
0
2
0
2
1
0
0
0
1
0
2
2
1
0
0
2
1
1
1
2
1
2
0
1
1
1
1
0
0
1
2
1
1
1
1
0
2
0
2
1
0
1
1
1
0
1
0
0
0
0
0
1
2
3
0
1
2
1
1
1
1
2
1
1
1
1
0
1
2
1
1
1
2
0
1
0
2
1
1
0
0
0
1
1
2
1
1
1
2
2
1
1
0
0
1
0
1
1
1
2
1
0
2
1
2
0
1
1
0
1
2
0
1
2
1
2
0
1
1
0
1
1
2
1
2
2
1
1
1
1
0
0
2
1
2
1
1
1
1
1
1
1
1
1
0
1
0
1
2
2
1
1
1
2
1
0
1
0
1
0
0
0
0
1
1
1
2
1
0
2
2
1
0
0
0
1
2
1
0
0
2
2
0
1
2
1
0
0
1
2
1
1
1
1
1
1
1
1
1
2
1
1
3
0
2
1
1
1
2
1
2
1
0
2
2
1
1
1
2
1
1
0
1
0
1
1
2
0
2
0
1
1
2
2
0
0
0
0
0
1
2
1
1
1
0
2
0
1
0
3
2
2
1
1
0
0
1
1
1
1
0
1
0
1
1
4
2
1
2
1
0
0
0
1
1
0
1
1
1
0
2
1
1
0
2
2
0
1
1
1
1
1
0
0
1
2
0
2
1
0
2
1
1
1
0
1
0
0
0
2
1
0
1
0
0
1
0
2
1
2
1
2
1
1
0
0
0
1
1
1
2
1
1
1
0
1
1
2
1
0
2
2
2
0
0
2
1
0
1
1
0
1
1
2
2
2
1
1
1
1
1
1
1
1
0
2
0
2
1
2
2
1
0
2
1
2
0
1
1
0
1
0
1
1
1
1
0
1
0
1
0
2
1
1
2
1
2
1
1
1
0
0
2
0
1
1
0
1
1
3
0
1
1
1
1
1
2
0
0
0
1
0
1
0
0
0
0
2
0
2
1
3
0
1
0
1
1
0
1
1
0
1
1
1
1
1
0
0
1
2
1
1
2
0
1
1
2
1
2
2
2
1
1
0
1
1
1
0
1
1
2
1
2
1
2
1
2
1
2
1
1
0
0
1
1
2
1
2
2
1
1
0
0
2
0
1
0
2
0
1
1
2
0
0
1
0
1
1
1
3
1
2
0
2
1
1
0
2
1
1
1
2
1
0
0
2
1
1
2
0
1
2
1
1
0
0
3
2
0
2
1
1
1
3
1
1
0
2
1
1
0
2
0
1
0
2
1
1
1
3
1
2
2
1
1
1
0
1
0
0
2
1
1
2
2
1
0
1
0
1
1
1
0
1
1
1
2
1
1
1
1
0
2
0
0
1
2
1
1
0
1
0
1
1
2
2
1
2
0
0
1
1
1
1
2
2
1
1
1
1
2
1
1
0
1
1
0
1
0
1
1
2
0
1
2
1
0
1
0
1
0
1
1
1
1
0
1
0
0
1
1
1
1
0
2
0
0
0
1
1
1
2
0
2
0
2
1
1
1
0
1
1
0
1
1
1
1
0
0
0
1
0
1
1
0
1
2
2
0
2
0
1
1
0
0
2
0
1
1
0
1
0
2
1
1
0
1
2
0
2
0
3
1
0
3
1
1
0
0
2
0
2
1
0
1
1
1
1
2
0
1
0
1
1
0
1
1
2
1
2
1
0
1
3
0
1
2
0
2
1
1
1
2
1
2
1
2
2
1
2
2
1
0
1
1
1
2
1
0
1
0
1
2
1
1
2
2
1
2
1
0
1
0
1
1
1
0
1
0
0
2
0
1
1
1
1
1
0
1
1
1
2
0
1
1
2
1
1
1
1
0
1
1
0
1
0
1
0
0
0
3
2
1
0
0
1
1
1
1
1
1
1
0
2
1
0
2
0
0
0
2
1
1
0
1
1
1
1
1
1
1
0
1
0
0
0
1
0
2
2
1
2
1
1
2
1
1
1
1
1
0
1
0
1
1
0
1
1
1
2
1
0
2
2
0
1
0
1
1
0
1
1
1
1
2
1
1
0
2
0
2
1
0
2
2
2
2
2
1
1
2
2
1
1
2
0
0
2
1
1
2
2
0
1
0
1
1
1
2
1
1
2
2
1
2
0
0
2
0
1
1
0
2
1
1
0
0
2
1
1
2
0
1
1
0
0
0
1
2
2
1
2
1
1
1
1
1
2
2
2
1
2
0
0
1
1
1
1
2
2
1
1
1
2
2
1
1
2
0
1
2
2
1
0
0
1
1
1
1
1
0
0
0
0
1
2
3
1
1
0
2
0
1
1
1
1
1
1
1
0
0
1
1
2
2
1
0
0
1
1
0
1
2
2
2
1
1
0
1
1
1
1
1
2
1
1
1
2
1
0
1
3
2
2
0
1
0
2
1
0
1
1
1
1
2
0
0
1
0
1
1
4
1
0
0
1
0
0
1
1
1
1
0
1
1
1
0
2
1
1
1
0
2
2
0
1
0
0
2
0
1
1
1
0
0
1
2
0
2
1
2
2
1
0
0
0
1
1
2
1
0
1
1
2
1
1
2
1
1
1
0
1
1
2
2
2
1
2
1
1
1
0
2
0
1
1
1
1
0
0
2
2
2
1
0
2
2
2
1
2
1
1
1
1
0
1
1
1
0
1
1
1
1
1
1
1
0
1
0
1
1
0
1
1
1
6
1
1
1
0
1
2
0
2
2
2
0
1
3
0
1
2
1
1
1
1
2
1
0
1
1
0
2
1
1
1
0
2
1
1
1
2
0
1
1
2
2
1
3
1
1
1
2
1
1
2
1
2
2
1
0
0
1
2
0
0
1
1
1
0
0
2
3
3
0
1
1
0
2
1
0
1
2
1
0
0
0
1
1
2
3
2
0
0
1
1
2
0
1
1
2
0
2
0
1
1
1
1
1
1
0
1
0
1
1
1
2
2
0
1
2
0
2
2
1
2
2
1
1
1
1
1
3
0
1
1
1
0
1
2
0
1
0
0
0
1
1
2
1
0
0
1
1
1
2
1
1
2
0
1
0
3
1
1
1
1
2
1
1
1
1
1
1
1
1
0
1
2
0
1
2
2
0
1
0
1
1
1
1
1
1
3
2
1
1
1
1
0
1
1
1
2
1
1
2
1
1
1
2
0
0
0
1
1
1
1
1
2
1
1
1
2
2
0
1
1
1
1
0
0
1
2
0
1
0
1
1
2
1
1
2
1
0
1
1
0
1
1
2
1
2
1
0
1
1
1
1
0
1
0
1
2
1
1
0
1
2
1
0
1
1
0
1
2
0
1
0
0
0
1
1
1
0
2
2
1
2
2
1
1
2
2
1
1
1
2
1
0
1
1
1
0
2
0
1
0
1
0
1
2
2
2
1
0
2
1
2
0
1
1
2
1
1
2
2
0
1
1
2
2
1
1
0
1
1
0
1
1
1
2
0
2
1
0
2
0
1
1
1
2
1
1
2
1
1
1
1
2
1
1
0
2
1
1
2
1
1
1
1
0
1
1
0
1
2
1
1
1
2
1
1
1
2
2
0
1
1
2
1
2
1
1
1
1
5
1
0
0
1
2
1
1
2
1
2
0
0
1
0
0
0
0
0
1
1
1
0
1
1
1
1
1
0
1
2
2
1
0
1
2
2
0
1
0
2
1
0
0
1
1
2
1
1
1
2
0
2
1
1
0
1
0
1
2
1
1
0
0
1
2
0
2
1
1
1
0
2
2
1
0
2
1
2
1
2
0
2
1
2
2
0
0
1
1
1
2
0
0
0
1
2
0
2
2
2
0
2
0
1
0
2
2
0
2
2
1
0
2
1
1
0
1
1
0
1
2
1
0
1
1
1
0
2
1
1
2
2
2
1
1
0
2
0
0
1
0
1
0
2
1
0
0
1
0
0
2
2
1
1
1
1
0
1
1
0
2
1
1
1
1
0
1
2
0
1
2
1
0
2
0
2
0
2
0
1
1
0
0
2
1
0
1
1
0
0
2
1
1
0
2
2
1
0
1
0
3
1
0
0
0
1
0
1
1
1
0
1
2
1
1
0
0
0
0
1
1
1
1
1
2
2
1
1
1
1
0
0
1
0
0
1
0
0
0
0
0
0
2
1
2
1
2
2
2
2
1
1
1
1
0
3
2
1
1
1
2
1
0
1
1
3
1
0
0
1
1
1
1
2
0
1
1
1
1
2
1
1
0
0
1
2
0
0
2
1
1
2
1
1
1
1
0
2
1
0
1
1
1
2
0
0
1
2
1
1
1
1
2
1
2
2
2
2
2
1
0
0
1
0
1
2
1
1
0
0
1
0
0
2
0
1
2
1
2
0
1
0
1
1
1
1
3
0
1
2
1
1
1
1
1
0
2
1
2
1
1
1
1
1
0
2
0
0
1
1
1
1
2
1
2
2
2
1
1
1
0
3
1
1
0
1
1
2
2
1
2
0
1
1
1
1
1
2
1
0
2
1
1
1
2
1
1
2
1
0
1
0
2
0
1
2
1
1
1
1
1
0
2
1
1
0
2
2
1
2
2
2
1
1
2
1
1
1
0
1
0
1
1
1
1
1
1
1
1
0
2
1
1
2
1
1
0
2
0
1
3
2
1
1
1
2
1
1
1
0
2
1
0
2
1
1
0
0
0
2
1
3
2
1
2
0
2
1
1
1
1
1
2
1
0
1
0
0
1
1
3
1
0
2
1
1
1
0
2
0
0
1
2
2
0
0
0
0
1
0
2
1
2
2
1
2
1
1
0
0
1
1
0
0
2
2
2
0
1
1
0
1
0
1
1
1
1
0
1
1
1
1
0
1
1
1
0
0
1
1
1
1
1
0
2
0
1
1
1
0
2
1
0
1
2
0
1
1
2
1
0
0
0
1
2
1
1
1
0
2
1
1
1
1
3
0
0
1
1
2
1
1
0
2
2
1
0
1
1
0
0
0
0
0
1
1
0
1
1
0
1
0
2
2
2
1
1
2
1
0
2
2
1
0
0
1
1
1
1
0
0
0
0
1
1
0
1
0
4
1
2
2
1
1
0
0
1
1
1
1
0
0
2
1
1
2
2
1
1
1
1
0
1
1
1
0
1
1
0
2
1
2
1
0
1
0
0
1
1
0
0
2
1
0
1
3
2
2
2
1
1
1
1
4
0
1
1
0
1
1
1
1
0
1
2
1
1
2
0
1
1
1
1
1
2
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
0
1
0
2
1
2
1
1
1
1
0
1
0
0
1
1
0
2
1
1
0
4
1
1
0
1
0
0
0
1
1
2
1
1
1
0
2
2
1
2
0
0
0
1
1
1
0
2
1
0
1
1
2
1
0
0
0
1
0
2
1
1
0
1
0
1
1
1
1
2
1
0
1
2
1
2
2
1
1
1
1
1
1
1
1
1
2
0
1
2
1
2
0
1
1
0
1
0
1
2
1
1
1
0
0
1
2
1
1
2
0
1
2
1
0
0
0
2
1
1
1
0
0
0
1
1
1
1
2
1
2
1
2
1
1
1
1
1
1
2
1
2
1
0
1
0
1
1
0
1
1
1
2
0
0
2
2
2
1
1
1
3
0
0
0
0
1
1
2
0
0
1
0
1
0
1
0
1
1
1
1
2
1
0
1
1
1
0
0
2
2
1
1
1
0
0
1
1
0
1
0
1
2
1
0
1
1
1
2
1
0
1
1
0
0
0
1
2
1
0
1
1
1
1
2
1
2
1
2
1
1
1
1
2
2
1
2
1
0
1
2
1
1
2
0
1
1
1
0
0
1
0
1
1
1
2
0
1
2
0
0
1
0
2
1
1
2
0
0
1
1
0
1
2
2
1
2
0
1
1
1
0
1
2
0
0
2
1
0
1
1
1
1
0
2
1
1
0
0
0
0
1
2
2
2
1
1
2
1
0
1
0
0
1
1
1
0
1
0
2
1
2
0
1
1
1
2
2
0
1
1
2
0
1
2
0
2
2
1
1
1
2
0
2
2
0
1
0
0
0
1
0
2
2
1
0
2
2
0
1
1
1
1
1
2
1
0
1
2
2
1
2
2
1
1
0
2
1
1
0
0
2
1
1
0
1
0
1
0
1
1
1
0
2
2
0
1
1
1
1
1
1
0
1
1
0
2
1
2
2
2
1
0
1
1
1
1
1
0
2
2
1
1
1
1
1
1
2
1
1
1
0
1
1
1
1
0
1
1
0
0
0
1
1
1
1
1
1
1
0
1
2
1
1
2
1
0
2
2
1
1
1
1
1
1
2
0
2
1
3
1
1
1
1
1
1
1
0
1
0
2
1
1
1
1
1
1
2
1
1
0
1
1
0
1
1
1
0
1
1
0
1
1
0
0
1
0
1
0
1
1
1
1
1
1
1
1
0
1
1
1
2
0
0
1
0
1
2
2
0
1
0
2
2
0
2
0
2
2
2
0
1
1
1
1
1
1
2
0
1
4
0
0
0
0
1
1
0
1
1
1
2
1
1
2
2
2
1
1
1
1
1
2
1
0
1
0
2
2
1
1
1
1
0
1
1
1
0
1
2
0
0
1
2
1
1
1
1
2
1
1
2
0
1
1
0
1
0
0
1
0
1
1
1
2
1
1
1
1
1
0
0
0
1
1
1
1
1
2
0
1
1
1
2
2
0
1
1
0
1
0
1
1
2
1
0
1
0
1
1
1
0
1
0
0
1
1
0
1
1
1
0
1
1
1
1
2
0
1
2
1
1
1
3
1
1
0
2
0
1
0
1
1
2
0
1
1
1
0
1
0
2
0
0
0
1
0
1
1
2
0
1
1
1
1
2
2
1
2
1
2
0
1
0
2
2
1
3
2
1
1
1
2
2
1
1
0
0
2
1
0
0
0
2
1
2
1
2
0
1
1
1
2
1
1
1
1
1
3
2
1
1
2
1
2
1
2
0
1
1
1
1
0
0
0
1
0
1
1
2
1
0
2
0
1
2
1
1
1
1
2
1
0
0
2
0
1
1
1
1
1
0
0
0
0
2
2
0
0
2
0
0
1
1
1
0
2
0
1
2
2
2
0
2
1
2
1
2
2
1
2
0
1
1
1
1
1
2
0
1
1
1
0
0
1
1
0
1
0
1
1
1
2
1
0
2
2
0
2
1
1
0
0
1
1
1
0
1
1
1
1
1
1
1
1
2
2
0
1
1
1
1
2
2
0
0
1
0
0
1
1
2
0
1
1
0
0
1
2
2
1
2
1
0
1
0
2
1
1
0
1
0
1
1
1
1
0
0
0
1
2
0
1
1
2
0
1
1
2
2
1
0
1
2
1
1
3
0
1
0
1
0
1
1
1
1
1
2
1
1
2
1
2
1
2
0
1
1
1
0
2
1
0
1
1
1
2
1
2
2
1
1
2
1
1
1
1
1
1
1
2
2
0
1
1
1
1
0
1
1
0
2
1
1
1
1
2
2
1
1
1
1
0
1
2
1
1
0
0
1
0
2
1
1
1
1
2
0
1
0
1
0
0
0
1
1
1
0
1
0
2
1
2
1
1
0
1
0
0
0
1
1
2
1
0
1
1
1
2
1
1
1
1
1
0
1
1
0
1
1
1
1
2
1
1
1
0
1
1
1
0
1
0
0
2
1
1
1
0
1
0
4
2
0
0
1
1
1
0
2
1
1
1
0
1
2
1
0
1
1
1
1
2
2
0
1
2
0
1
0
0
1
1
0
1
1
1
1
1
2
1
1
1
1
0
1
1
1
1
2
1
0
2
1
2
1
0
1
1
1
0
1
1
1
0
1
1
0
1
1
1
2
1
1
1
2
0
0
1
1
1
1
2
2
2
2
2
1
2
0
1
0
2
1
0
2
2
0
2
0
1
2
1
2
1
0
0
1
1
0
2
1
0
0
1
1
1
2
1
1
1
0
0
1
2
1
0
0
0
1
1
1
0
2
1
1
0
1
0
2
0
1
1
0
1
1
0
0
1
1
1
0
0
2
1
1
2
2
1
0
0
0
0
2
1
2
0
0
1
1
1
1
1
0
0
1
1
1
1
2
1
1
0
1
1
2
0
0
0
2
1
0
1
2
2
2
0
1
1
0
1
1
1
1
1
2
0
1
1
0
1
2
1
1
0
1
2
2
0
0
0
2
1
1
2
1
1
1
1
0
1
0
2
1
0
0
2
1
1
0
1
1
1
2
0
1
1
1
0
1
1
1
1
0
2
0
1
1
0
0
1
1
2
2
1
0
2
2
0
2
1
0
2
2
0
0
1
1
1
1
0
0
1
0
0
0
1
1
2
0
0
0
1
1
1
1
0
0
2
1
2
1
1
1
1
2
1
0
2
0
1
1
0
2
1
2
2
1
3
0
0
1
1
0
2
0
0
2
1
1
1
2
2
1
0
1
0
1
2
1
0
1
1
1
1
0
0
2
1
1
1
2
1
1
1
0
1
1
2
0
1
1
0
1
1
1
1
1
0
0
0
1
1
0
1
1
2
0
2
2
1
1
2
1
1
2
0
2
2
0
2
1
2
2
2
1
0
2
1
1
1
2
1
1
1
0
2
1
2
0
0
2
1
0
0
1
2
1
1
2
1
1
0
1
1
2
2
1
1
2
1
0
1
1
2
1
3
0
0
1
1
0
1
1
1
2
0
0
0
0
0
1
1
1
0
0
1
0
1
0
2
1
1
1
1
1
0
1
1
1
0
0
1
1
1
1
2
2
1
1
1
0
0
1
0
1
0
1
1
0
1
0
2
2
0
2
2
1
1
0
1
1
0
1
2
0
1
2
1
1
1
0
0
1
2
1
1
0
0
0
1
1
0
2
0
0
2
0
0
1
2
0
0
1
0
2
2
1
1
1
1
0
1
2
1
0
2
1
1
1
0
2
1
0
0
0
0
1
1
1
2
1
1
2
0
1
2
2
2
1
1
2
1
1
0
2
1
2
1
2
1
0
1
0
2
1
1
0
1
1
0
1
0
1
2
2
0
1
0
1
2
2
0
1
2
1
2
2
1
1
0
0
2
0
1
2
0
0
1
2
1
0
1
1
0
1
0
3
0
0
1
0
1
1
1
0
2
0
1
1
0
0
0
2
2
2
0
0
0
1
1
1
1
2
0
2
1
2
2
0
1
1
1
2
1
1
1
1
1
1
1
2
2
2
0
2
1
2
0
1
2
1
0
0
0
2
1
1
2
1
1
1
0
2
1
2
1
1
0
1
0
0
0
0
1
1
0
2
1
1
1
1
0
2
2
1
1
1
1
1
1
2
0
1
1
1
0
1
0
1
2
1
0
2
2
1
1
1
1
1
1
0
1
2
0
1
1
2
1
1
0
2
0
1
1
1
1
2
0
1
0
0
1
1
2
1
2
1
0
1
2
2
1
1
1
1
1
2
1
1
0
2
2
2
1
0
0
2
0
1
2
1
1
2
1
0
2
2
1
2
4
2
1
1
1
1
0
2
1
2
2
2
0
1
0
1
2
0
2
1
0
1
1
1
1
1
1
0
0
2
2
2
1
1
1
2
2
2
0
2
1
1
2
1
1
0
1
2
1
1
1
0
1
1
1
1
1
2
0
2
0
2
1
1
0
1
1
0
0
0
1
0
1
0
2
0
1
0
0
1
1
0
1
2
0
1
0
1
1
1
1
1
0
2
1
1
0
2
0
1
1
1
1
2
1
2
0
1
2
2
1
1
0
2
0
0
1
1
1
0
0
1
0
2
3
1
0
1
1
1
1
1
0
2
1
1
1
1
1
1
0
0
1
0
0
2
2
1
2
2
2
1
2
1
1
2
2
1
1
0
0
1
2
0
1
1
1
1
0
1
0
1
1
1
1
2
1
1
0
2
0
2
1
0
2
1
1
1
2
1
0
2
1
1
1
0
1
1
1
1
1
1
1
2
2
2
0
1
1
1
2
1
0
2
2
2
3
1
0
1
1
2
1
2
2
1
1
0
1
1
0
1
0
0
1
1
1
0
2
1
1
1
1
0
1
1
2
0
1
0
0
1
1
0
2
1
0
1
0
1
2
0
1
2
0
3
0
1
1
1
0
2
1
1
0
1
1
1
0
2
0
0
1
0
0
0
2
2
1
1
1
1
1
1
2
1
1
0
4
1
0
1
1
1
1
0
1
1
1
0
1
0
1
1
1
2
1
0
1
1
1
3
1
1
0
1
1
1
0
0
1
1
1
1
1
2
1
2
2
0
1
0
1
2
1
1
0
0
1
1
0
1
1
1
1
1
1
1
0
2
0
0
2
2
1
0
1
1
1
0
1
2
1
1
1
1
2
2
1
1
2
1
1
0
2
1
2
1
0
1
1
1
0
0
1
2
1
1
3
0
1
1
1
1
1
0
2
0
1
1
0
1
1
1
1
0
3
1
1
0
2
0
2
1
1
0
0
2
1
0
1
2
1
2
2
1
1
2
0
0
0
2
1
1
0
0
1
0
0
1
1
1
2
1
0
2
1
1
2
2
1
0
1
1
0
0
1
0
1
0
2
1
1
0
1
0
1
1
0
0
1
1
0
0
0
0
0
0
1
1
1
2
1
1
1
1
1
2
0
0
1
1
1
0
0
0
2
1
1
0
3
0
0
0
1
1
0
0
0
1
0
0
2
2
2
1
0
1
1
1
2
1
2
0
0
2
1
0
1
1
2
0
1
1
0
1
0
1
0
1
2
1
2
1
1
1
0
1
2
2
0
1
2
2
1
1
1
0
1
1
2
1
1
1
2
0
1
2
2
1
1
1
0
0
0
1
2
1
2
2
1
1
1
0
2
1
1
1
0
2
1
1
2
1
1
1
0
0
0
2
0
1
0
2
1
1
1
0
0
1
1
1
1
1
2
1
1
0
1
0
0
0
2
1
0
1
1
0
0
1
1
0
2
1
0
1
0
0
1
1
1
0
1
0
1
0
0
0
1
1
2
2
2
0
1
1
2
2
1
1
0
2
1
0
0
1
2
0
4
1
1
2
1
1
1
0
1
1
1
2
2
0
0
2
0
2
0
1
2
1
0
0
2
2
1
0
2
1
1
0
1
1
2
0
0
2
0
0
1
1
2
0
0
2
1
1
0
0
0
2
1
1
0
0
1
9
1
2
2
1
1
2
2
2
2
1
3
1
0
1
0
0
2
1
1
2
1
1
1
2
1
1
0
0
1
0
1
4
2
0
1
2
1
1
2
2
0
2
1
1
0
0
1
1
2
0
1
0
1
2
1
1
0
0
1
0
1
1
0
0
2
1
2
1
2
0
1
0
3
1
1
1
2
1
1
1
1
1
0
1
2
1
0
0
1
1
0
0
1
0
2
1
0
0
2
0
1
1
3
0
2
0
2
1
1
1
1
1
0
2
1
1
1
1
1
2
1
0
0
1
2
1
0
2
1
0
2
0
1
1
1
1
2
2
1
3
2
0
0
1
0
1
1
0
0
2
0
1
1
1
1
2
1
2
0
0
1
1
2
2
0
1
1
0
2
0
2
1
1
1
0
1
1
1
0
1
1
1
0
1
1
2
2
2
1
0
1
1
0
2
2
1
0
1
1
2
1
1
1
1
0
1
1
0
0
0
1
0
1
0
2
1
0
2
0
1
2
1
2
2
0
1
1
0
2
2
0
2
2
1
1
2
0
1
2
1
2
1
2
1
2
0
2
1
2
1
1
2
0
1
1
1
0
1
0
1
1
1
0
0
0
1
1
0
1
2
1
2
1
0
0
1
1
2
1
2
0
1
2
1
1
2
1
2
0
0
1
0
2
1
1
2
1
2
1
2
0
1
1
2
1
1
1
2
0
1
1
1
2
0
0
1
1
1
2
1
1
0
2
2
1
0
0
1
2
1
2
1
1
1
2
0
1
1
2
1
1
1
1
1
0
1
1
1
1
1
1
0
1
0
1
1
0
2
1
0
2
2
1
2
1
0
1
2
0
2
1
1
0
1
0
1
1
2
1
1
1
1
1
1
1
0
2
1
1
0
0
2
2
0
0
0
0
2
0
1
2
1
0
0
0
1
1
0
0
1
0
0
2
1
1
1
2
1
0
1
1
1
1
1
2
2
1
0
0
1
1
1
1
2
2
2
0
0
0
1
1
1
1
2
1
2
0
2
1
1
2
0
1
2
0
1
1
0
2
1
2
2
2
1
1
3
2
0
1
2
0
2
0
0
0
2
2
0
2
0
2
1
2
1
0
2
2
1
2
0
0
1
1
0
0
1
2
0
0
1
0
0
0
1
1
2
0
1
2
0
2
0
1
2
0
1
0
1
2
0
1
1
2
1
0
1
1
2
0
0
2
2
1
1
1
0
1
2
1
1
2
1
0
0
0
0
0
1
2
0
1
1
1
0
2
1
0
0
0
1
4
1
2
1
1
1
1
2
1
0
1
1
1
1
1
1
2
1
2
0
1
1
2
0
1
1
1
1
1
0
1
1
1
2
1
2
2
1
2
1
1
2
1
0
0
1
0
2
1
1
2
1
1
2
2
1
1
1
1
1
1
0
0
4
1
2
2
2
1
0
0
0
1
0
0
0
2
0
0
1
1
1
1
0
1
0
1
1
0
1
2
1
1
0
1
0
0
1
1
0
1
2
2
1
0
1
0
2
2
0
1
1
1
2
2
1
2
1
0
1
2
0
1
1
1
1
1
1
1
0
1
0
1
0
2
0
0
0
0
1
1
1
1
1
1
2
0
1
1
1
0
0
1
1
0
0
2
1
0
2
2
1
1
0
0
0
0
0
1
1
1
3
1
2
1
1
1
1
0
1
0
1
1
1
1
1
0
1
1
2
2
2
2
0
1
0
0
1
1
1
4
1
0
1
1
0
0
0
1
0
1
0
1
0
1
1
1
1
1
1
0
2
0
0
0
1
0
2
0
1
2
1
0
1
0
0
0
1
1
1
1
1
2
0
1
1
1
1
0
1
1
1
1
1
2
0
2
0
2
2
1
0
1
0
2
1
2
0
1
2
1
0
0
2
1
1
0
1
2
2
0
0
2
1
0
1
0
1
2
1
0
1
2
2
1
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
1
0
2
0
1
2
1
0
1
2
0
1
1
0
1
0
0
1
1
0
0
2
1
2
1
2
0
1
2
3
1
1
1
0
0
1
1
1
0
1
2
1
1
0
1
0
2
0
2
1
2
1
2
2
1
2
1
1
2
1
2
1
0
1
1
1
0
1
2
1
1
1
2
2
1
1
0
0
2
0
1
1
0
1
1
0
1
1
0
2
1
1
0
1
2
0
1
1
2
2
1
1
1
1
0
2
2
1
1
1
1
0
0
1
1
1
1
0
1
2
2
0
1
0
0
1
0
0
1
0
0
1
0
0
2
3
1
2
0
1
1
0
0
2
2
2
1
2
0
1
1
0
0
0
1
4
1
0
2
2
1
1
1
0
1
1
1
1
1
0
1
0
0
1
1
2
1
0
2
0
1
1
1
2
2
0
1
1
1
1
1
1
0
1
1
1
1
1
2
1
2
0
0
0
1
1
1
1
1
1
1
2
2
1
1
1
1
2
0
1
0
0
0
0
1
0
1
0
1
0
1
2
1
1
2
1
2
0
2
2
0
2
1
1
1
0
1
1
2
1
2
1
0
1
1
1
1
1
0
2
1
0
1
2
1
1
2
0
1
1
2
1
1
1
1
0
0
1
2
1
2
0
2
0
1
1
1
1
1
0
0
1
0
1
1
1
1
1
1
1
1
1
2
1
1
0
1
1
0
0
1
0
1
1
1
1
1
2
1
1
1
1
0
2
1
1
1
0
1
1
2
1
1
1
0
1
1
2
2
0
2
1
1
1
1
1
1
1
1
1
1
1
2
0
2
0
0
0
2
2
1
1
2
1
1
1
1
3
1
0
1
3
1
2
1
1
1
0
2
5
2
1
0
0
2
1
2
1
0
0
1
2
1
2
1
1
1
0
0
2
1
1
1
1
1
2
2
0
2
0
1
1
1
1
2
1
0
1
1
2
0
2
3
2
1
0
1
1
1
0
2
0
2
1
0
1
2
2
3
1
1
0
1
2
1
2
0
1
1
2
1
1
1
2
1
1
0
1
0
2
2
1
0
1
1
1
2
2
2
1
0
1
1
0
1
1
2
2
2
1
0
2
0
1
2
0
2
0
3
1
1
1
0
1
1
0
2
1
1
2
1
2
1
0
2
2
2
1
1
0
0
0
1
2
1
2
1
1
0
0
0
2
1
2
0
1
0
2
1
0
0
2
2
0
2
0
1
1
1
2
0
1
2
1
1
1
1
1
2
1
2
0
4
1
0
1
1
0
0
2
1
1
1
1
0
2
0
2
1
2
1
2
2
1
2
0
0
1
0
1
2
1
1
0
0
1
2
1
0
1
1
0
1
1
2
1
2
1
2
0
0
1
1
0
1
0
1
1
2
3
1
2
1
2
2
2
0
1
0
1
1
2
0
1
1
2
1
0
0
1
2
2
1
0
2
1
2
1
1
1
2
2
1
0
2
0
0
2
2
2
0
2
1
0
0
2
0
1
1
1
2
0
0
2
1
0
1
0
0
1
0
1
1
1
0
1
1
2
1
2
2
1
1
0
3
1
0
2
1
3
2
1
2
2
0
1
0
1
1
1
1
0
1
1
2
1
1
2
2
0
2
1
1
1
1
1
0
2
1
1
0
0
0
2
1
1
1
1
2
0
1
0
0
2
2
0
2
0
0
2
1
1
1
1
1
0
1
2
1
0
0
1
2
0
2
1
1
2
1
1
0
2
1
0
1
1
2
2
0
1
1
1
2
0
2
2
1
1
1
1
0
2
2
1
0
1
1
0
0
2
0
0
1
1
0
1
2
2
1
0
0
1
1
1
1
0
1
0
2
2
1
0
0
2
1
1
2
0
0
1
0
1
0
0
2
0
0
1
2
2
0
2
1
2
2
1
0
1
1
1
0
1
1
1
0
1
2
2
1
1
1
2
2
0
2
2
0
0
1
0
0
1
1
1
2
1
0
1
1
1
2
2
1
1
0
1
1
1
0
1
1
1
0
0
1
1
0
2
1
1
1
2
0
1
1
1
1
2
0
1
1
1
2
1
0
0
2
1
0
1
2
1
0
2
1
1
1
0
1
0
1
1
2
1
1
1
0
2
1
0
0
2
2
1
2
3
1
0
1
1
2
2
0
1
1
0
2
1
1
2
0
0
1
2
0
1
0
2
1
1
1
1
0
2
0
0
1
1
0
0
2
1
1
2
2
0
1
1
1
1
1
2
0
3
0
1
0
1
1
1
1
2
1
1
3
1
2
1
3
1
1
0
2
0
1
4
1
1
0
2
1
1
0
0
1
1
0
1
0
1
0
2
0
1
0
0
0
0
0
2
2
2
1
1
2
1
2
0
2
1
2
2
1
2
2
1
1
0
0
2
1
1
2
1
2
1
1
0
2
1
2
1
0
2
1
0
2
0
2
1
0
2
0
1
2
1
2
1
0
2
1
1
0
2
2
0
2
1
0
0
1
1
0
0
0
0
1
1
2
1
2
1
1
1
1
0
2
2
1
2
1
2
0
1
2
1
0
1
1
2
0
0
1
1
1
2
2
3
0
1
0
1
1
0
2
2
0
2
1
0
1
1
1
1
0
1
1
1
0
1
0
1
1
0
1
2
2
2
2
0
0
1
1
1
0
2
1
1
0
2
0
1
1
2
0
1
1
1
1
1
1
1
0
0
1
1
0
0
1
1
1
1
0
0
2
1
2
0
1
1
1
1
1
0
0
0
1
1
1
0
0
1
0
2
1
2
2
1
1
1
1
1
0
0
0
1
0
2
1
0
2
0
0
2
2
1
2
0
1
1
2
1
0
1
0
2
2
1
0
2
1
2
0
1
1
4
1
0
1
2
1
0
2
2
2
1
2
1
0
2
1
1
0
2
1
1
0
1
1
2
1
1
0
3
0
0
1
0
1
1
1
2
0
2
0
0
2
0
3
1
1
1
2
2
1
1
1
0
1
1
0
2
0
1
0
1
0
1
1
2
1
1
1
1
1
0
0
2
1
1
1
1
0
2
1
0
2
2
5
0
0
1
1
1
1
1
1
1
1
1
1
2
0
0
1
0
1
2
2
1
2
0
0
1
1
2
2
1
0
0
0
0
1
0
1
1
1
0
1
1
1
2
0
1
2
1
0
1
1
1
1
0
0
2
1
1
0
1
2
0
1
1
1
1
2
2
1
3
2
2
1
1
2
1
2
1
1
2
2
1
2
1
2
2
0
1
2
1
2
0
1
0
1
2
2
1
1
2
0
2
0
1
2
2
1
2
1
0
1
1
0
1
1
0
1
1
0
1
0
2
1
1
2
1
0
1
1
2
1
0
0
1
1
0
1
1
1
0
2
1
1
2
1
1
2
0
1
0
1
1
1
1
2
0
2
0
0
1
2
1
1
1
2
2
2
2
0
1
1
2
1
1
2
0
1
1
1
2
1
2
0
2
1
2
1
1
1
1
1
2
0
1
2
1
2
1
3
1
0
1
1
2
1
1
1
1
1
1
2
1
1
1
0
1
0
0
1
1
2
2
1
1
0
0
2
2
1
0
0
0
1
0
1
0
1
0
0
1
1
0
0
2
1
1
1
1
1
1
3
1
1
0
2
2
1
1
2
1
1
1
1
1
1
0
1
2
1
1
4
0
0
0
1
2
2
0
1
1
3
1
2
0
0
2
1
2
1
1
2
2
1
1
1
2
2
1
1
1
1
0
0
0
1
1
2
2
0
2
2
1
1
2
1
1
0
1
0
0
1
2
1
1
1
1
0
1
0
2
1
1
1
1
1
2
1
0
2
1
1
0
1
1
1
2
1
1
0
1
0
1
2
1
1
0
1
0
1
2
1
1
0
1
0
1
1
0
1
2
2
1
1
1
0
1
1
1
2
2
1
0
2
0
1
1
0
2
0
1
1
0
1
1
1
2
1
1
1
1
1
1
1
1
2
0
0
0
1
2
0
0
1
1
1
2
0
2
2
1
1
2
2
2
0
0
0
2
0
1
2
0
1
0
1
1
0
2
0
1
2
2
0
2
2
0
2
1
0
1
1
0
1
1
1
0
0
1
0
1
2
1
1
1
1
0
1
1
2
2
0
2
2
2
1
1
3
1
1
1
2
1
0
0
2
1
2
0
1
1
1
1
1
2
1
1
2
1
1
0
0
2
3
1
2
1
2
2
1
1
0
3
2
2
1
1
1
0
0
1
2
2
0
0
2
2
1
1
1
2
1
1
1
0
2
1
1
1
2
1
1
0
1
2
0
1
0
1
0
0
6
2
1
1
2
1
0
1
2
1
2
0
2
1
2
0
1
1
1
2
1
2
1
0
1
1
0
1
1
1
0
1
1
0
1
0
0
0
0
1
2
1
1
2
1
2
0
0
2
1
2
1
0
1
1
1
1
2
1
1
2
1
1
0
0
1
0
2
0
2
1
1
2
2
0
1
0
1
1
2
1
1
1
0
1
2
1
1
2
1
0
0
1
2
2
0
2
1
0
1
5
0
1
2
1
1
1
2
1
2
0
0
1
1
1
3
1
1
2
0
0
1
1
0
2
2
2
1
0
2
0
1
1
0
1
1
3
1
2
1
1
2
0
1
1
2
1
2
1
1
2
1
1
1
2
0
0
1
1
1
0
0
2
0
1
1
0
1
1
1
1
0
1
0
1
1
0
0
2
2
1
1
1
2
1
0
0
1
1
0
0
1
0
2
4
1
1
0
1
1
1
2
0
1
2
1
0
1
1
1
1
1
0
1
0
0
1
0
1
1
1
0
0
1
0
1
1
2
1
0
2
1
1
2
0
0
1
1
2
1
1
1
1
1
2
1
2
1
1
1
0
0
2
1
2
1
3
2
1
0
0
2
1
2
1
0
0
1
2
1
0
2
0
0
2
2
0
1
2
3
0
0
2
1
2
0
1
0
1
2
0
0
1
1
0
2
2
0
2
3
0
0
0
0
1
1
2
2
1
1
0
1
0
1
0
1
1
4
2
1
1
1
1
0
1
1
1
1
2
2
0
2
2
1
1
1
0
1
0
1
1
1
2
1
2
1
1
2
2
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
0
1
1
2
0
2
0
1
1
1
0
0
1
1
1
2
1
0
2
0
0
0
0
1
1
1
0
1
1
2
1
1
1
0
1
0
0
0
1
1
2
0
1
1
1
1
0
1
0
2
1
1
1
1
1
2
1
3
1
2
1
1
3
1
1
0
1
0
2
3
1
2
1
0
0
0
1
0
0
2
1
3
1
0
1
1
2
2
1
0
2
0
2
0
0
0
2
1
2
1
2
0
1
2
1
2
0
2
0
0
1
0
0
0
1
0
1
1
1
0
1
1
1
0
0
0
1
1
0
2
1
2
2
1
1
1
1
1
2
2
0
1
2
0
1
2
1
1
2
0
0
0
1
2
2
0
0
1
0
2
1
1
1
0
0
2
1
1
1
1
1
0
2
1
2
1
2
1
1
1
2
0
0
0
0
1
0
2
2
1
1
1
2
2
2
1
1
0
0
1
0
1
0
2
1
1
2
0
0
0
0
0
0
1
1
1
0
2
0
0
2
2
0
1
0
1
2
2
3
1
0
2
1
0
2
1
1
1
0
0
2
1
1
2
1
1
1
0
0
1
3
2
0
1
1
1
1
1
0
4
1
0
1
3
1
0
2
2
2
2
0
1
1
1
1
0
1
0
0
1
0
1
0
0
1
1
2
0
0
2
1
1
1
0
2
0
0
1
2
1
2
1
1
0
1
1
1
2
1
1
4
2
0
1
2
1
1
2
1
2
1
0
1
1
2
3
2
2
2
1
0
2
2
1
1
2
3
0
1
1
0
1
1
0
1
0
0
0
1
1
1
0
1
1
2
2
1
1
1
1
2
1
0
0
1
1
0
1
1
0
1
1
2
0
0
1
1
1
1
0
0
1
1
1
0
1
1
1
0
0
1
2
0
2
1
1
1
1
1
1
2
1
0
0
1
1
1
1
2
1
1
1
0
3
0
1
1
1
0
2
2
0
0
0
1
1
2
0
1
2
2
1
1
0
1
1
1
2
1
1
1
1
2
1
1
1
0
1
1
0
1
2
2
0
1
1
1
1
1
1
1
1
1
0
1
2
0
1
0
0
1
0
1
1
1
1
0
0
0
0
1
0
1
2
0
2
1
1
2
1
2
2
1
1
1
1
0
1
0
2
1
1
2
1
1
2
2
1
1
0
1
0
1
2
1
1
1
1
1
2
2
0
0
1
2
1
1
2
0
1
0
1
0
2
1
1
1
0
0
1
2
1
1
2
1
1
1
1
1
0
2
1
0
1
1
2
0
1
0
1
0
1
1
1
1
1
1
1
2
1
1
0
2
0
1
0
0
1
2
0
1
1
1
0
1
1
1
2
1
1
0
0
1
1
0
0
0
1
1
2
0
2
0
1
3
1
1
2
2
2
0
2
2
0
1
0
1
0
2
1
1
1
1
0
2
1
2
1
1
1
0
0
1
2
1
2
1
1
1
0
0
0
1
1
2
0
1
2
1
0
0
0
0
0
0
0
0
1
2
1
0
0
0
1
0
2
0
0
0
1
0
1
1
1
1
2
0
1
2
1
1
2
2
1
1
1
1
0
1
1
1
0
2
1
0
2
0
2
1
0
0
1
1
2
1
0
1
1
2
0
1
1
3
1
1
0
1
0
2
0
1
1
0
1
2
1
1
3
0
1
1
1
1
1
2
2
1
1
2
1
0
2
1
2
1
1
1
2
1
2
1
0
1
2
0
1
2
1
0
1
0
2
1
1
1
1
0
3
0
0
2
2
0
1
1
2
1
0
1
0
2
1
1
1
1
1
1
0
2
1
1
1
1
1
1
1
0
1
1
1
0
1
2
0
1
1
0
1
1
1
0
0
0
1
1
1
3
1
0
1
2
1
1
1
1
1
1
1
1
0
0
0
2
1
1
0
0
1
0
1
1
1
2
1
1
1
1
1
1
1
2
1
1
2
2
1
0
1
2
1
1
1
0
1
1
0
1
2
0
1
0
0
2
2
0
0
1
1
1
0
1
1
2
0
1
0
1
2
1
0
1
1
2
1
1
1
0
0
0
2
1
1
2
1
2
0
1
1
0
1
2
1
1
2
1
1
1
1
1
1
1
2
0
1
1
0
0
1
1
0
0
1
2
0
2
0
1
0
0
0
0
0
2
2
1
0
1
1
1
1
1
2
1
0
0
0
2
1
1
1
2
2
0
1
2
1
1
0
1
1
1
0
2
1
2
2
1
1
1
0
1
1
1
0
2
1
0
2
1
1
1
1
0
0
2
1
1
0
0
1
2
0
1
1
1
2
0
2
1
1
1
1
1
0
0
2
1
0
1
0
1
2
0
2
1
2
1
1
2
1
2
0
1
0
1
1
2
1
2
0
0
1
0
1
0
1
1
1
1
2
1
2
1
0
0
2
1
1
1
1
1
1
1
1
1
1
1
2
1
0
3
2
2
0
2
1
2
2
1
2
1
0
0
1
1
1
0
0
0
1
0
1
1
1
2
1
0
0
3
2
2
1
2
2
1
1
0
1
2
0
2
1
1
1
0
0
1
0
2
1
1
0
1
0
1
0
1
2
0
0
1
1
2
2
1
1
1
0
0
0
2
1
2
2
1
1
0
2
0
1
1
1
1
1
1
2
1
1
2
0
0
2
1
1
0
1
0
1
0
1
1
1
0
0
1
1
1
2
1
0
1
1
2
2
2
1
0
1
0
1
1
2
0
3
2
1
0
1
0
1
2
2
2
1
2
1
1
1
1
2
1
2
1
0
0
1
1
0
2
0
2
0
2
1
1
2
2
0
1
1
0
2
0
0
0
1
1
1
0
1
1
1
3
0
2
2
1
1
1
2
1
1
1
1
1
1
1
1
1
0
2
1
1
2
0
2
1
1
0
1
0
2
2
2
0
1
0
1
1
1
3
1
1
0
1
0
1
1
1
1
0
2
1
1
3
3
1
1
1
1
1
0
1
2
0
0
2
1
1
0
1
1
1
0
1
0
1
2
0
1
0
1
0
1
1
0
1
0
1
1
1
3
2
1
3
0
1
1
0
0
1
0
1
0
1
1
1
1
0
1
1
2
1
1
0
0
2
1
2
2
1
2
2
1
1
1
1
2
0
0
1
1
0
0
1
1
2
0
1
0
1
0
2
0
1
1
2
1
0
1
1
2
1
1
2
0
0
2
0
2
2
1
0
3
1
1
2
2
1
1
2
1
1
0
2
1
0
1
0
1
1
2
0
1
1
1
1
1
2
1
1
1
0
1
2
1
2
2
1
1
2
1
1
0
1
0
1
2
0
2
2
0
2
0
1
1
1
0
2
1
0
1
1
2
1
5
1
0
0
1
0
2
1
2
2
1
2
2
0
0
1
0
1
0
1
0
1
0
1
1
3
0
2
1
0
1
1
1
0
2
0
2
1
2
0
0
0
2
0
0
2
1
1
1
0
0
0
1
1
1
1
1
2
0
1
0
1
0
1
1
2
1
1
0
1
0
2
1
0
1
2
1
0
1
1
0
1
1
1
1
1
0
1
1
1
2
1
2
0
1
0
1
2
1
1
2
1
2
1
1
1
0
1
1
0
2
0
2
1
0
0
2
1
2
0
1
0
1
1
1
1
0
1
1
1
1
0
1
1
0
0
1
1
0
2
0
1
0
0
0
1
1
1
0
2
1
0
1
1
1
2
1
1
1
1
1
1
0
0
0
1
1
1
1
1
2
0
1
1
0
1
2
1
1
1
1
2
1
0
1
0
2
1
0
0
0
1
2
1
1
2
0
2
2
1
0
0
2
1
0
2
0
0
4
0
1
1
1
0
1
1
1
2
0
1
1
0
1
2
1
1
0
1
1
1
0
1
2
1
2
1
2
1
0
0
1
1
1
1
0
2
1
1
1
0
1
1
1
0
1
1
1
0
0
0
0
1
1
0
2
2
1
1
1
1
0
1
1
0
2
1
1
2
2
1
2
1
2
1
1
0
1
1
1
1
2
1
0
1
0
1
1
1
1
1
2
0
1
1
1
0
0
0
1
0
0
1
1
0
2
2
1
0
1
1
1
2
1
2
2
0
1
1
2
1
1
0
1
1
1
1
1
0
1
2
1
2
1
1
2
1
2
0
0
1
0
1
1
1
0
1
2
1
2
0
0
2
1
0
1
1
1
2
0
1
2
1
0
1
1
1
0
2
1
2
1
1
1
1
2
0
0
1
1
0
1
1
1
1
0
0
2
1
2
1
2
0
1
0
1
0
1
0
1
1
2
1
1
2
1
1
1
2
0
1
2
1
1
2
1
2
2
1
2
0
1
1
0
2
1
1
0
0
1
1
0
1
1
2
1
0
2
0
2
2
0
0
0
1
1
0
2
1
0
0
2
1
0
0
2
0
2
1
2
0
0
0
0
0
0
1
2
0
0
1
0
1
1
1
0
1
2
2
1
2
1
1
1
1
1
1
2
2
2
1
0
2
0
1
0
2
1
1
1
1
1
1
2
0
0
2
1
2
1
2
1
0
1
1
1
0
1
1
1
2
0
2
2
2
0
0
2
1
0
1
2
1
1
0
0
2
1
0
0
2
1
1
1
0
2
1
1
2
3
1
1
1
1
1
2
0
1
1
1
1
0
1
1
0
1
0
1
1
0
2
1
0
1
1
1
0
1
1
1
0
1
0
1
3
2
3
1
1
1
2
1
1
2
1
1
2
1
1
0
1
1
0
3
0
1
1
1
1
1
2
1
2
2
0
1
1
1
2
1
0
1
0
2
0
0
0
1
1
2
0
2
0
0
2
1
0
1
1
1
1
1
2
1
1
0
1
2
1
1
0
0
1
0
1
2
1
0
1
1
2
0
0
1
2
2
1
0
0
0
1
1
2
2
1
1
0
1
1
0
0
1
1
1
0
1
1
1
1
1
2
0
1
2
2
1
1
2
1
1
1
0
1
2
0
1
1
1
0
1
2
1
0
1
1
2
1
1
1
1
2
1
3
1
1
3
2
2
1
0
1
1
2
0
1
1
1
2
1
1
0
1
1
1
2
0
0
2
1
1
1
1
1
2
0
1
0
1
0
1
1
1
0
0
2
0
1
2
1
1
1
1
0
1
1
1
2
0
1
0
1
0
1
1
2
1
1
2
1
0
0
1
1
1
0
1
2
0
1
2
2
0
1
2
0
1
1
1
0
1
2
0
2
2
1
1
1
1
2
1
1
0
1
2
1
2
0
2
0
0
1
1
1
1
2
1
0
0
1
2
2
1
1
1
1
1
1
2
0
1
1
1
1
1
1
2
2
1
1
1
2
1
1
0
1
0
1
1
0
2
1
0
2
2
1
1
1
0
1
0
1
2
1
1
1
0
0
1
0
2
0
1
1
1
1
1
2
0
2
1
2
2
2
1
0
1
1
0
2
1
1
1
0
1
1
2
1
0
0
0
1
0
1
1
1
1
1
1
0
0
0
1
0
1
0
0
1
1
1
0
2
1
1
1
2
1
2
1
0
2
1
0
1
1
1
0
3
2
0
1
2
2
2
2
0
1
0
1
2
1
1
1
1
2
2
1
1
2
3
1
2
2
0
2
8
1
0
1
0
1
2
1
1
1
0
1
2
1
0
1
0
0
2
1
0
1
2
0
2
0
1
3
0
1
0
2
0
0
2
1
1
1
1
1
0
1
1
1
0
1
1
1
0
1
1
2
2
0
0
2
1
1
1
2
2
0
0
1
1
1
1
0
1
1
0
1
2
0
0
1
0
1
2
0
1
1
2
0
1
0
1
2
0
1
1
2
0
1
0
2
0
0
2
2
1
0
1
1
0
0
2
1
0
1
0
0
0
1
0
2
2
1
1
1
1
1
0
1
1
1
2
1
0
0
1
2
1
2
1
2
0
1
2
2
2
1
2
2
1
1
0
0
1
1
2
0
0
1
2
1
0
1
0
2
0
2
1
1
1
0
1
1
1
0
1
2
0
0
1
2
2
1
1
0
0
1
1
0
1
0
1
2
2
2
1
1
1
1
2
0
1
1
0
0
0
1
1
0
2
2
1
0
1
0
3
1
2
2
2
0
2
1
2
1
1
1
2
2
1
0
0
2
2
2
0
0
0
1
0
1
1
1
1
2
2
0
0
0
1
2
0
0
1
2
2
2
1
2
1
1
1
1
1
0
1
1
2
2
1
0
0
2
1
1
0
0
1
0
1
2
2
1
1
1
1
0
2
1
1
2
2
2
0
2
1
1
0
1
1
1
1
2
1
1
0
1
1
2
1
2
1
1
0
2
2
1
2
1
1
1
2
0
0
1
1
0
1
0
1
1
1
0
1
0
0
1
1
1
1
0
0
1
2
1
2
2
1
0
1
3
1
1
1
2
1
1
1
2
1
1
1
0
0
0
0
0
1
0
1
0
1
0
0
2
1
1
0
2
2
1
2
0
0
0
0
4
0
2
1
0
0
1
2
2
0
1
1
1
1
1
1
0
1
1
1
2
2
1
1
0
1
2
0
1
0
1
2
0
1
1
2
1
0
1
1
2
2
0
0
2
1
0
1
1
1
1
1
0
1
1
3
0
1
0
1
1
1
2
0
1
2
1
1
1
0
0
1
2
1
1
1
0
0
2
1
2
2
1
1
2
0
0
1
1
2
1
1
1
0
1
2
1
0
0
0
1
2
0
0
2
1
1
2
1
1
0
0
2
0
0
2
1
0
1
1
0
0
2
1
1
0
2
1
2
2
0
2
1
1
1
2
1
1
1
1
1
0
1
6
1
0
2
0
1
1
1
1
2
1
1
0
2
1
1
1
2
0
1
1
2
1
0
1
1
0
2
1
0
0
1
0
1
1
1
1
1
0
2
0
0
0
1
0
2
1
1
2
2
0
1
1
1
0
0
1
2
0
1
2
1
0
1
1
1
0
1
1
0
0
0
1
0
1
1
2
1
0
2
1
1
1
1
2
1
1
0
0
1
1
0
1
2
1
2
1
0
2
2
1
0
1
2
2
1
1
2
2
1
0
1
1
1
1
1
0
1
1
2
1
2
2
1
0
1
1
1
2
1
0
2
1
1
2
1
1
2
0
1
1
0
1
1
1
0
2
3
1
1
0
2
1
0
1
2
1
2
2
1
0
1
1
2
1
2
0
0
0
0
1
0
1
2
0
1
0
0
1
1
2
0
0
0
0
2
0
0
2
1
2
1
0
1
1
1
2
0
1
1
0
1
1
0
1
1
1
1
0
1
1
1
1
0
1
3
0
1
0
0
1
1
0
0
0
0
0
2
0
1
0
0
1
2
2
1
1
2
1
1
0
0
0
1
0
0
0
0
1
0
1
1
1
0
1
0
1
1
0
0
0
0
1
1
0
1
2
0
1
1
0
0
1
2
2
1
0
1
1
0
1
0
1
0
1
0
1
1
1
2
2
1
2
0
0
1
1
2
2
1
0
1
1
1
0
2
2
1
0
0
0
1
2
2
0
1
1
2
0
1
1
1
1
1
2
1
1
0
2
2
1
1
1
2
0
0
2
2
1
2
1
0
1
2
2
2
2
1
1
1
0
1
2
1
1
3
1
1
2
1
3
0
1
1
2
1
1
1
0
0
0
1
1
1
1
1
1
2
0
1
0
1
1
3
0
1
1
1
1
2
0
1
0
1
1
2
1
2
1
2
0
2
2
1
0
1
1
2
1
1
1
2
0
2
1
1
1
1
1
1
1
1
2
0
2
1
0
1
2
3
1
1
0
2
1
1
1
1
1
2
0
0
2
1
0
3
0
0
0
2
1
0
2
0
2
2
1
1
2
1
0
1
2
0
0
0
2
2
1
2
0
1
1
2
1
1
2
1
1
1
3
0
0
1
2
1
0
1
2
2
0
1
1
1
0
0
1
1
1
1
1
1
3
0
1
1
0
0
2
1
0
1
0
1
1
1
1
0
2
1
2
1
0
2
1
1
0
0
1
1
0
0
1
2
1
0
1
1
0
3
2
0
1
1
0
0
0
1
1
0
1
2
2
1
1
0
1
1
2
0
1
2
2
1
0
0
0
1
0
1
1
2
1
1
1
1
0
2
1
0
0
0
1
0
1
2
0
2
2
2
1
1
1
1
0
0
2
1
1
0
2
1
2
0
1
1
1
1
1
1
1
1
2
0
0
0
1
0
1
1
1
1
1
2
2
0
2
0
1
2
0
0
0
1
1
2
1
1
1
1
1
0
0
1
1
1
2
1
0
1
0
2
1
2
1
2
1
3
0
0
1
0
1
1
0
2
3
1
2
1
1
1
2
1
1
0
0
2
1
1
1
1
1
1
2
0
0
1
2
1
1
2
0
0
1
2
0
0
0
2
1
0
1
2
1
1
0
1
1
2
2
1
1
0
1
1
1
0
1
0
2
0
1
1
1
1
0
1
1
0
0
1
2
2
1
1
1
2
1
0
1
2
1
0
0
1
1
3
1
2
0
0
0
2
1
2
0
1
0
1
1
1
1
0
3
1
0
2
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
0
1
1
1
1
0
2
1
2
0
0
2
1
1
0
1
2
1
1
1
1
1
1
0
0
2
1
1
2
2
0
1
0
1
2
0
1
1
0
1
1
1
0
0
0
2
1
1
0
1
1
1
1
0
3
1
1
0
0
1
1
1
2
2
0
1
2
0
1
1
1
1
0
1
0
0
1
1
1
0
2
2
0
1
2
0
0
0
0
0
2
1
0
1
1
1
0
1
0
1
1
0
1
2
1
1
2
1
2
1
0
1
2
0
1
1
1
0
2
0
0
1
1
0
0
1
2
0
0
1
1
0
2
0
1
1
1
0
0
1
0
1
1
1
0
1
1
1
1
1
1
0
1
1
1
0
2
1
1
2
0
0
1
1
1
1
1
1
2
0
1
2
2
1
2
0
2
0
0
1
1
0
2
0
1
0
0
0
2
0
2
2
1
1
0
0
2
5
1
1
1
1
1
2
0
1
2
0
2
1
1
0
1
0
1
1
0
1
1
0
1
1
2
1
1
1
0
2
1
0
0
0
0
1
1
0
2
1
2
1
0
2
0
2
1
2
2
0
1
0
1
1
0
1
1
2
1
1
1
1
2
1
1
1
0
1
0
2
2
1
2
1
1
2
2
1
2
2
1
0
1
2
0
1
0
1
1
1
0
3
1
2
2
1
2
1
0
1
0
1
1
2
0
0
1
1
0
1
0
2
2
1
2
1
1
1
0
1
2
1
0
1
1
2
0
0
1
1
2
0
1
1
0
1
2
1
0
2
1
2
2
2
1
1
2
1
2
1
1
1
2
2
1
0
3
1
1
1
1
1
1
0
0
1
1
1
0
2
1
1
2
1
2
2
1
0
0
1
2
2
1
1
1
2
2
1
2
1
0
0
1
2
0
0
0
0
1
1
1
1
2
0
0
1
2
1
2
0
1
1
0
1
0
1
1
1
0
1
0
1
1
1
2
1
2
1
0
1
0
2
1
1
1
0
1
0
2
3
1
0
2
1
1
1
1
1
2
2
0
1
1
0
0
1
0
1
0
1
2
0
2
2
0
1
1
0
2
2
0
1
1
2
1
1
1
1
1
0
1
0
1
2
1
1
0
0
2
1
2
1
1
1
4
1
0
1
0
0
1
0
0
0
2
1
0
2
1
1
0
1
1
0
0
0
0
1
0
1
2
1
1
1
2
1
1
1
0
1
1
1
1
2
1
1
2
1
0
2
1
1
0
1
0
0
1
1
2
1
0
2
1
0
0
1
0
1
0
0
1
0
1
0
2
1
1
1
0
2
1
1
1
1
2
1
1
1
1
2
1
0
1
1
2
1
0
2
1
3
1
2
1
1
2
1
2
1
2
0
1
1
0
1
1
2
1
1
2
1
2
1
0
0
0
0
1
0
1
0
1
1
1
1
1
0
1
1
2
1
0
1
1
1
1
2
1
3
0
0
1
1
1
2
2
2
2
1
1
0
1
1
0
1
1
0
2
0
1
2
1
1
1
1
2
0
1
2
2
1
1
1
1
2
2
1
2
1
1
0
0
0
1
1
1
1
1
1
0
1
2
2
1
0
2
3
1
2
2
4
0
1
1
1
2
1
2
1
3
2
1
1
0
1
1
2
1
0
2
0
0
0
1
0
1
0
0
1
1
1
0
0
0
1
1
0
0
1
1
1
2
2
1
1
1
1
1
2
1
1
0
1
0
1
1
2
0
1
0
1
1
0
0
0
1
1
0
0
2
0
1
1
1
0
1
0
1
0
1
0
1
2
1
1
1
2
2
0
4
2
2
0
1
2
1
1
1
1
1
0
1
1
1
1
2
0
1
1
0
1
0
1
0
1
1
1
0
1
0
0
2
1
1
1
2
0
1
0
1
1
2
1
1
0
2
2
0
2
1
1
1
0
2
1
2
2
0
1
1
1
2
2
2
0
2
0
0
2
2
0
4
0
0
1
0
2
1
2
1
2
1
0
2
1
1
2
1
2
0
1
2
2
0
2
1
0
1
0
1
1
1
1
2
2
1
0
1
1
1
1
0
2
0
0
2
1
0
0
2
1
0
1
1
1
1
1
1
2
1
1
1
1
1
1
0
1
1
2
1
0
0
1
0
0
2
1
1
1
2
0
2
1
1
0
1
2
1
0
1
1
1
1
2
0
1
1
1
2
0
1
2
1
1
1
1
1
1
2
1
1
1
1
1
0
1
0
1
1
1
1
0
0
0
1
4
0
0
1
1
0
1
1
2
1
2
1
2
0
1
0
0
1
2
1
1
0
1
1
1
1
1
2
0
0
0
1
1
2
1
2
2
0
1
2
1
2
1
1
0
1
2
1
2
0
2
1
0
1
0
1
1
0
1
1
0
1
1
1
1
2
0
1
0
0
0
2
2
2
1
1
4
0
1
2
1
0
2
2
1
0
1
1
2
1
2
1
1
0
0
2
2
1
1
1
1
0
1
2
1
0
0
1
2
1
1
1
1
1
2
0
0
1
1
1
2
2
2
1
0
1
1
1
0
0
1
1
1
1
1
2
1
1
0
0
1
0
2
1
0
2
1
1
1
2
1
1
0
2
1
0
1
1
2
2
1
0
0
0
1
1
2
2
0
1
0
1
1
1
1
0
3
0
1
0
1
0
0
1
0
2
1
0
1
1
1
0
2
0
0
2
1
2
1
0
1
1
0
1
2
1
2
2
1
2
1
0
1
0
1
2
1
0
1
0
1
1
2
1
2
1
1
2
1
2
1
0
1
0
1
0
2
1
2
2
1
0
1
0
0
1
1
0
0
0
2
1
1
1
2
1
1
1
1
0
1
1
0
2
1
1
3
1
2
1
0
0
1
1
2
2
2
1
0
1
1
1
1
1
0
1
0
1
2
1
1
1
2
1
1
1
1
1
1
2
1
2
1
0
1
1
0
1
2
2
1
2
1
1
0
1
4
1
1
0
0
0
0
2
1
1
0
0
1
2
0
1
0
1
1
1
2
1
1
1
2
2
1
1
1
1
1
0
1
1
0
1
0
0
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
2
0
1
0
2
0
2
1
1
2
1
2
1
0
1
2
1
2
1
1
1
3
1
1
2
1
1
1
0
1
1
0
1
2
0
2
0
1
0
1
0
0
1
1
1
2
0
2
1
2
0
1
2
1
2
0
0
1
0
1
0
0
0
1
1
1
2
1
0
1
1
1
1
1
1
0
1
1
0
2
0
2
0
1
0
1
0
0
0
0
1
0
0
0
1
1
0
0
2
1
2
0
1
2
2
1
2
1
0
2
1
0
1
0
1
2
1
0
1
2
1
1
2
1
0
2
2
1
1
2
1
1
2
2
2
0
0
1
0
1
1
1
1
0
0
1
0
1
1
1
2
0
0
1
1
1
1
1
0
1
2
1
2
1
1
2
2
1
0
2
1
0
1
0
1
1
0
2
1
2
1
1
0
1
2
0
0
1
1
2
1
0
2
2
1
1
1
1
1
0
0
1
2
1
1
2
0
1
2
2
0
2
1
2
1
1
0
0
2
0
0
1
0
0
2
1
2
1
1
2
1
2
0
1
0
1
0
2
1
0
0
2
1
0
2
2
1
2
1
2
1
1
0
1
1
1
1
1
0
1
2
1
1
1
1
2
1
1
0
1
1
1
1
0
0
1
1
1
1
0
1
1
0
2
1
1
2
1
0
1
1
1
2
2
0
2
2
1
2
1
1
0
1
1
2
0
1
1
1
0
1
1
0
0
1
0
1
1
2
0
1
1
1
0
1
2
0
2
1
2
1
2
1
1
2
0
1
1
1
1
1
1
2
1
1
2
1
0
0
1
1
1
1
0
0
1
1
1
0
1
0
2
0
0
0
1
0
2
2
1
1
1
0
2
1
2
1
1
0
2
0
0
1
0
1
1
2
1
1
1
0
1
1
0
2
1
1
1
0
1
0
0
2
1
2
2
2
0
1
1
1
1
0
2
1
0
0
0
1
2
0
1
1
1
1
1
1
0
1
0
0
0
2
0
1
2
2
1
1
0
2
2
1
2
2
1
2
1
1
1
0
0
1
1
1
3
1
1
0
1
2
1
1
1
1
2
2
2
1
1
0
3
1
3
0
1
1
2
0
0
1
1
1
1
2
1
1
2
0
1
1
1
2
0
2
1
0
0
1
1
0
1
0
0
0
1
2
0
3
1
1
1
1
1
1
14
1
1
0
1
2
1
1
1
2
1
2
0
0
2
0
2
1
1
1
1
0
1
1
0
1
0
0
0
2
1
1
1
1
0
0
1
2
1
1
2
2
1
2
1
1
2
2
0
1
1
1
2
0
1
0
2
1
1
1
2
2
0
0
1
0
1
0
0
0
2
1
0
2
1
0
0
1
2
0
1
1
0
2
2
0
6
1
1
0
2
1
0
0
2
0
0
1
2
1
0
1
1
0
1
1
0
0
1
0
1
0
2
1
2
0
1
1
1
1
2
0
1
1
1
2
1
1
1
0
2
1
0
0
0
2
1
1
1
1
2
0
1
0
2
0
1
0
0
1
1
0
1
1
1
1
0
1
1
0
0
2
0
2
3
1
1
2
0
0
0
1
0
0
2
2
1
1
1
2
0
1
0
1
2
1
2
1
2
1
1
2
1
1
1
1
1
0
2
1
2
0
0
0
1
1
1
1
2
1
0
1
0
1
2
2
2
1
1
1
2
0
1
0
1
1
1
2
1
1
1
0
1
1
0
1
1
0
1
2
2
1
0
1
1
1
1
2
2
2
2
1
1
2
1
1
0
2
2
2
2
1
2
1
1
0
2
0
1
0
1
1
1
1
1
1
1
1
1
1
2
0
0
0
1
1
2
1
2
0
1
1
0
0
2
2
1
2
0
2
0
1
0
2
2
2
0
2
0
1
0
1
2
2
0
1
1
1
1
0
1
1
2
1
0
1
1
2
0
0
1
0
0
0
0
1
0
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
1
0
1
1
0
0
1
0
1
1
2
2
1
2
0
1
0
1
2
2
0
6
1
2
0
0
2
1
4
1
0
1
0
1
1
1
2
0
2
1
2
0
1
0
2
2
2
1
3
1
1
2
1
1
0
2
2
1
0
1
2
0
1
1
2
3
2
1
0
2
0
1
1
2
1
0
1
2
0
1
1
1
2
1
1
0
0
1
1
1
2
1
1
0
2
1
1
2
1
1
1
1
1
1
0
1
0
1
1
1
2
1
1
1
1
2
1
0
1
0
2
2
0
0
0
1
0
1
0
1
0
0
1
2
0
0
1
1
1
1
1
1
0
0
1
1
1
1
1
1
1
1
1
3
1
1
1
0
1
1
1
0
0
0
1
1
0
1
1
1
1
0
1
3
0
1
1
2
0
1
1
1
0
0
1
0
0
1
0
1
1
0
0
2
4
1
1
2
1
1
1
0
1
1
1
1
1
1
1
1
0
0
1
1
0
0
2
2
1
2
1
1
2
2
2
2
1
1
1
1
1
0
1
1
1
0
0
2
2
1
1
0
0
1
1
2
1
1
2
2
1
2
0
1
0
0
0
2
1
0
1
0
1
0
0
2
0
0
0
0
2
0
1
2
0
1
2
1
0
0
2
2
0
1
1
2
0
1
0
0
1
1
1
0
1
1
3
1
0
1
1
2
2
1
0
0
1
2
1
1
2
0
1
0
0
2
1
1
1
2
0
2
1
2
0
2
0
1
0
0
0
2
2
1
2
2
1
1
1
1
1
1
1
2
0
1
1
1
2
0
1
0
0
1
0
1
1
0
1
0
2
1
1
2
2
0
1
1
2
1
1
1
1
0
1
0
1
3
1
0
0
1
1
1
0
0
1
0
1
0
1
2
2
1
0
1
2
1
1
1
1
0
0
0
1
1
1
0
2
1
1
1
2
1
1
0
1
1
0
1
0
1
2
1
0
2
0
1
2
1
1
1
1
0
1
0
2
0
0
2
1
2
1
2
0
0
1
1
1
1
0
1
2
0
2
2
1
1
1
2
2
2
0
0
2
2
1
1
1
1
2
1
0
0
2
0
1
1
1
1
0
1
2
1
2
0
1
1
1
1
1
1
1
0
1
1
2
1
1
1
1
0
2
2
1
0
0
0
1
2
2
1
1
1
0
1
2
0
1
1
0
0
1
0
2
2
1
2
0
0
1
0
0
1
1
1
0
2
1
1
1
2
0
2
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
0
0
2
1
0
1
2
1
1
1
1
2
1
1
0
0
2
0
2
2
1
1
0
0
1
1
1
0
1
1
1
2
1
1
0
1
2
1
0
1
0
0
1
1
1
1
1
0
1
1
1
2
0
1
2
0
1
0
2
1
2
1
1
1
1
1
1
1
0
3
0
0
0
0
1
3
0
0
1
1
2
1
1
1
1
2
1
1
0
1
1
1
0
2
2
0
1
1
1
0
1
0
0
1
1
0
0
2
2
2
1
1
0
1
0
0
1
2
1
1
1
0
1
1
2
0
1
1
1
1
2
1
1
0
2
1
1
1
2
1
1
1
0
1
0
1
1
1
1
1
1
0
1
1
1
2
2
1
2
1
1
0
1
1
0
2
1
1
1
1
0
2
2
1
1
0
2
2
0
0
1
2
0
1
2
1
3
2
2
1
3
2
1
2
0
1
0
1
1
1
3
1
1
1
2
0
1
1
0
1
0
0
1
0
0
1
1
1
1
2
1
1
0
1
0
2
0
0
1
2
0
2
1
2
2
1
1
2
2
0
1
2
1
1
1
2
2
1
2
1
1
1
1
1
2
0
0
0
2
1
1
1
1
1
1
2
2
0
2
0
2
2
1
1
1
1
2
0
2
1
1
1
1
0
1
2
1
2
1
1
1
1
1
2
2
2
2
2
2
1
1
1
1
1
1
2
0
2
2
1
1
2
2
0
1
1
1
1
2
0
1
1
0
0
0
1
2
1
2
1
1
0
0
1
2
0
1
1
1
2
0
2
1
0
1
0
1
2
1
1
1
1
1
0
1
1
1
1
1
2
1
0
1
2
0
0
0
1
1
0
2
1
0
2
0
1
1
2
0
1
1
2
0
0
1
0
1
0
1
1
1
1
1
1
1
2
1
2
2
1
0
0
2
1
0
1
0
2
2
1
0
0
1
0
2
2
1
1
1
2
0
0
1
1
0
1
0
1
1
1
0
0
0
0
1
1
1
1
2
1
1
1
2
1
0
1
2
1
0
2
0
1
1
0
1
1
1
0
2
1
0
1
1
0
1
2
0
0
1
1
1
1
1
1
1
0
2
1
1
0
2
1
1
0
1
0
1
1
0
2
1
2
3
1
0
2
1
2
1
1
2
1
2
0
0
1
1
1
2
1
0
2
1
2
1
1
0
0
2
1
2
1
0
2
3
1
2
1
0
0
1
0
1
0
2
0
2
2
2
1
1
2
1
0
1
0
0
2
2
1
2
0
0
2
1
2
1
1
3
1
1
0
2
1
0
0
0
1
1
0
1
0
1
1
1
0
1
1
0
1
2
2
0
0
1
2
1
0
0
2
2
0
1
1
0
1
1
1
1
1
1
1
1
0
1
1
1
1
0
0
0
0
0
1
1
1
1
0
1
1
2
1
2
1
0
2
2
1
0
1
1
1
1
1
2
0
2
2
0
0
1
1
0
0
2
2
1
2
1
1
1
1
1
2
2
1
0
1
3
2
1
2
3
1
1
2
1
0
1
0
1
1
1
4
2
0
1
1
2
0
2
2
0
1
1
1
0
2
1
0
1
2
0
1
1
0
0
0
1
1
2
1
1
1
0
0
1
0
0
0
1
0
1
1
1
1
1
0
2
1
1
0
0
0
1
1
0
1
1
1
1
1
5
2
0
0
1
2
0
1
0
0
1
0
1
1
1
1
1
0
1
0
2
1
1
1
2
1
1
1
1
1
0
2
2
0
0
1
1
0
1
0
0
1
1
1
0
0
2
0
0
1
0
0
1
1
1
0
3
1
0
0
1
1
0
1
1
0
1
2
1
1
1
0
1
1
2
1
1
2
1
1
1
1
2
0
1
2
2
0
1
9
1
0
0
1
0
0
2
1
1
1
2
0
1
1
1
0
0
1
2
1
0
1
1
1
1
1
0
2
1
2
0
0
2
0
1
0
1
1
0
1
1
1
2
1
2
3
0
1
0
1
1
1
1
1
0
0
0
0
1
1
1
2
2
2
0
1
2
1
2
1
1
1
2
2
1
0
2
1
1
0
1
1
1
1
0
6
1
1
1
2
1
2
1
1
1
1
0
3
2
2
1
1
1
2
1
0
0
2
0
2
2
0
2
1
1
1
1
1
0
1
1
1
1
2
1
2
1
0
1
2
3
0
1
1
2
1
1
0
1
2
0
1
2
0
1
1
1
1
0
1
0
2
1
1
0
1
1
0
1
2
2
1
0
2
1
2
1
1
0
0
0
2
2
2
2
0
0
2
1
1
2
1
0
1
1
0
1
1
0
1
0
0
1
0
1
1
1
3
1
1
1
0
2
1
5
1
2
1
0
0
2
2
0
0
2
2
2
2
0
1
0
1
1
1
2
1
2
2
1
1
1
0
1
0
0
1
3
1
1
1
1
1
1
2
0
0
1
0
1
1
1
0
1
1
1
2
2
0
2
0
0
1
1
0
1
0
2
1
1
2
2
0
0
2
1
1
2
1
1
1
1
0
0
1
0
1
1
0
1
1
1
0
1
2
0
4
1
1
1
0
0
1
1
1
0
1
0
0
2
0
2
0
1
2
2
0
2
2
0
0
1
1
1
0
2
1
0
1
1
0
1
1
1
0
2
3
1
1
1
1
0
1
1
2
4
1
1
1
2
2
1
2
2
1
2
0
2
1
2
2
2
1
2
1
1
0
1
0
1
1
1
1
1
1
1
1
0
1
0
2
2
0
1
1
0
2
0
0
0
1
1
0
1
1
1
2
1
0
0
2
0
0
2
0
1
0
0
2
2
0
1
1
1
0
1
0
0
0
2
1
1
1
1
1
2
1
1
0
0
1
0
1
0
1
2
1
2
0
0
1
1
1
2
1
1
0
2
1
1
1
1
1
1
2
2
1
0
2
1
0
1
2
0
0
1
1
0
1
0
2
1
1
1
1
2
1
1
1
1
2
1
0
0
1
0
1
0
0
1
0
0
1
0
2
0
0
2
0
1
0
1
1
1
1
2
1
1
1
0
2
1
1
1
1
2
1
1
0
1
0
2
2
1
2
0
2
0
0
0
0
1
1
2
1
1
0
0
1
1
1
1
2
0
1
1
2
0
1
1
1
2
1
1
1
1
0
0
1
1
0
1
2
1
2
2
2
0
1
2
2
2
1
1
1
0
2
1
0
1
0
2
2
1
0
1
1
0
1
1
2
1
3
2
2
1
1
2
1
1
0
5
0
1
2
1
1
0
1
1
1
1
1
1
1
1
2
1
1
1
1
0
1
0
2
1
0
1
1
1
1
1
0
1
0
0
2
2
1
1
0
1
2
1
0
0
1
0
1
2
0
1
2
2
0
1
0
0
1
1
0
1
2
2
0
0
2
1
1
1
0
1
0
2
0
2
1
1
0
1
1
0
1
1
2
0
1
1
2
0
1
0
0
0
1
1
1
1
1
2
1
1
2
2
2
0
1
1
1
1
1
2
1
1
2
0
1
1
0
0
0
0
1
1
0
0
1
1
0
2
1
1
1
1
1
1
2
0
2
1
4
1
1
1
0
1
2
2
0
0
2
0
0
0
2
1
1
1
2
0
1
1
2
1
1
2
1
1
0
1
0
0
3
1
1
1
2
1
1
2
2
1
0
1
1
1
1
1
1
2
1
0
0
0
1
1
0
2
1
0
2
2
1
1
0
0
0
1
1
1
0
1
1
2
2
2
2
1
1
1
2
1
2
0
1
1
0
0
1
0
0
1
1
1
0
1
1
0
0
1
1
1
2
1
1
1
2
3
1
1
0
0
2
0
1
2
2
1
1
0
2
2
1
0
0
1
1
1
1
2
1
0
1
1
0
0
0
0
0
0
1
1
1
1
1
0
0
2
1
0
0
0
1
2
0
1
1
1
0
1
1
1
0
1
2
1
1
1
1
1
1
0
0
0
0
2
1
1
2
1
1
1
0
2
1
0
1
1
1
0
0
1
0
2
1
1
0
1
0
2
1
1
0
1
1
1
2
0
0
1
1
2
1
1
0
0
1
1
0
1
0
3
1
1
1
2
1
2
1
1
2
2
0
1
2
0
0
0
1
1
0
2
1
1
2
1
0
1
3
0
0
1
2
1
0
1
1
1
2
0
2
2
2
1
3
0
0
0
2
1
1
2
1
0
1
1
1
0
0
2
1
2
1
1
2
0
1
2
1
1
2
1
2
0
0
1
1
2
2
1
0
1
1
1
2
0
0
1
0
1
1
0
0
1
2
1
1
1
1
1
1
0
1
1
1
0
0
0
0
1
1
1
1
0
0
1
0
1
0
0
1
1
0
0
2
0
0
1
1
2
2
1
2
1
2
0
1
0
0
2
1
1
0
1
1
2
2
1
3
2
2
1
0
1
2
2
1
1
0
0
1
0
1
1
1
0
0
1
1
1
2
0
1
0
2
1
2
1
0
3
1
2
0
1
0
1
0
1
0
1
1
0
0
1
0
1
0
1
1
1
2
1
0
0
1
0
0
2
2
1
0
2
1
0
0
0
0
1
2
1
2
1
1
2
2
1
2
1
1
1
1
2
1
2
0
2
1
2
2
0
1
1
1
0
1
0
0
1
1
2
0
1
1
2
0
2
1
2
0
1
1
2
1
1
1
1
1
0
2
1
3
0
1
1
0
1
0
0
2
1
1
0
1
0
2
0
1
2
0
2
2
1
2
0
1
0
0
1
1
1
2
0
1
0
0
0
1
2
0
2
2
1
1
2
1
2
0
2
1
1
0
1
0
1
1
2
2
1
2
1
0
0
0
0
0
1
2
0
0
1
0
2
1
2
1
1
0
2
2
0
1
1
0
1
1
3
1
0
1
1
1
1
1
1
2
1
1
1
0
0
1
1
1
1
2
1
1
1
0
1
2
1
0
1
0
1
1
2
1
0
1
0
0
1
1
0
1
1
1
1
0
2
1
1
0
0
0
2
1
1
0
1
0
1
0
1
0
1
0
1
1
1
1
1
1
1
1
0
1
2
1
1
2
0
0
0
2
2
2
1
2
2
1
2
2
1
2
1
0
1
0
0
1
2
1
0
1
0
2
2
1
2
3
1
1
0
0
0
0
2
2
1
1
0
2
1
1
1
0
0
1
1
1
0
2
0
2
2
3
1
0
0
0
0
0
1
0
0
2
0
2
1
0
1
0
1
0
1
1
1
0
1
1
1
1
1
2
1
1
0
0
1
1
1
0
0
1
2
0
2
2
1
2
1
1
1
0
2
0
1
1
0
2
1
0
1
0
0
2
3
1
2
1
0
1
1
0
0
1
1
2
2
1
0
1
0
1
1
1
1
1
2
1
1
1
1
1
0
2
0
2
1
1
1
3
1
2
1
1
1
2
0
1
1
2
1
2
2
1
2
1
1
2
1
1
0
0
0
0
0
2
0
0
0
0
2
2
0
1
0
0
2
0
1
0
1
1
0
1
1
1
1
1
2
0
3
1
1
1
1
1
2
2
0
1
0
2
0
1
0
1
0
1
1
1
0
1
2
0
1
1
2
1
1
0
1
1
1
0
0
2
2
2
0
0
1
0
0
1
1
1
0
0
1
1
2
0
1
1
2
2
0
1
1
1
1
1
1
1
1
2
1
0
1
1
2
1
1
1
3
0
0
1
2
0
2
0
0
1
2
0
1
0
1
1
1
2
0
0
1
1
1
0
1
2
1
1
0
0
2
1
1
2
1
1
1
0
2
2
0
1
1
2
1
1
0
1
1
1
1
1
1
1
2
0
2
0
0
1
2
1
0
2
0
1
2
1
0
1
1
1
0
1
1
2
1
0
2
1
0
1
1
1
1
0
1
2
1
0
0
1
0
1
1
1
2
1
2
2
0
2
1
1
1
1
1
1
1
1
1
0
0
1
0
1
0
2
2
2
1
2
1
1
2
2
1
0
1
1
1
2
0
2
1
0
1
1
0
1
0
0
2
0
1
2
1
3
1
0
1
2
1
0
2
0
0
1
2
0
1
1
0
0
1
2
1
1
1
1
0
0
1
3
1
1
1
2
2
1
1
0
1
1
2
0
2
0
1
1
1
4
1
2
2
2
2
2
0
2
2
0
2
1
2
0
0
2
1
2
2
0
1
0
1
1
2
0
1
1
0
1
0
1
0
1
1
2
1
2
0
2
1
2
1
0
2
2
1
1
1
1
1
0
2
1
1
1
2
1
1
1
0
0
1
2
1
1
0
1
1
1
1
0
1
1
0
1
1
1
1
1
0
2
1
2
1
2
1
2
2
1
1
0
0
1
2
1
2
2
1
0
0
1
1
0
1
1
2
2
1
1
1
1
0
2
2
1
1
1
1
1
1
0
2
2
0
1
0
1
1
0
1
3
1
2
1
1
0
2
0
1
1
0
0
0
1
1
1
1
0
0
1
0
0
1
1
1
1
2
1
0
2
1
1
1
0
0
1
1
2
2
0
2
2
1
2
0
0
2
2
1
1
1
1
2
0
1
1
1
1
0
0
0
1
1
1
1
1
1
1
0
0
2
1
0
1
2
2
1
1
0
1
1
1
1
0
1
1
0
1
1
17
1
0
1
1
1
1
2
1
1
2
1
0
1
2
2
2
2
2
0
1
0
2
1
1
1
2
1
0
0
1
1
1
1
2
0
1
1
1
2
0
1
1
0
0
2
1
2
1
1
2
0
2
1
1
2
0
2
1
1
0
1
0
0
1
0
2
2
1
2
2
0
1
3
0
1
0
2
1
0
1
1
1
1
1
0
0
2
1
2
1
2
0
1
1
1
2
1
0
0
0
1
1
2
1
2
1
0
1
2
2
0
0
2
1
1
2
1
0
2
1
0
2
0
2
1
1
2
1
1
1
2
1
1
1
0
0
2
2
1
1
1
2
0
0
2
1
0
1
2
1
0
1
1
2
2
0
2
1
2
1
0
1
1
2
1
2
1
1
2
1
1
0
0
1
1
1
1
0
1
2
0
0
1
2
2
2
2
1
1
1
2
2
1
0
0
2
0
1
1
0
1
1
2
1
0
1
1
0
0
2
1
2
2
0
1
1
1
1
1
1
1
2
0
1
2
1
0
1
2
1
0
0
0
0
1
0
0
0
2
0
1
1
0
1
1
1
1
0
0
2
0
0
2
1
1
0
1
1
1
2
1
1
1
1
1
2
1
10
2
1
0
0
0
1
1
1
2
2
3
1
2
0
1
2
1
1
0
1
0
0
2
1
0
0
1
1
1
0
1
1
1
2
1
0
1
0
2
0
0
2
1
1
0
1
1
0
1
1
1
1
1
2
0
2
1
1
1
1
0
2
1
1
1
2
1
1
1
2
1
1
1
2
1
0
1
0
2
2
1
1
2
0
1
1
1
0
0
1
1
1
2
1
1
1
1
1
0
1
0
2
1
1
1
1
0
1
0
1
0
0
1
1
0
2
2
1
1
1
1
1
2
1
2
2
1
1
0
2
2
1
2
1
2
1
2
1
1
1
0
1
1
0
1
0
1
0
1
1
2
0
0
1
1
1
1
1
2
0
1
1
2
2
0
0
0
1
1
2
2
1
2
1
1
1
1
0
0
0
0
1
1
2
0
1
1
1
0
1
2
1
0
1
2
2
1
1
1
1
1
1
1
0
2
1
1
1
2
1
1
1
1
1
1
0
0
0
1
1
2
2
1
0
0
2
1
1
1
2
0
0
0
1
2
1
0
3
0
1
2
2
0
1
1
1
2
1
0
1
1
1
0
1
1
1
2
2
0
1
2
2
1
1
1
2
0
1
1
0
0
0
1
1
1
0
0
1
1
1
0
2
2
1
1
2
1
4
1
1
1
2
2
1
2
2
0
2
1
1
1
1
2
0
1
1
0
1
2
1
3
0
2
0
3
1
1
1
0
2
1
1
1
1
1
1
0
1
1
1
0
1
1
1
2
0
2
0
1
0
2
2
0
0
0
1
2
2
1
2
1
0
1
2
1
1
1
2
0
1
2
0
2
2
1
0
1
0
0
2
2
1
1
0
2
2
1
1
1
1
2
0
1
0
1
0
1
1
0
0
2
2
2
1
3
1
0
1
0
1
1
2
0
2
0
0
0
1
0
2
2
1
0
1
2
1
1
1
0
0
0
1
1
0
2
2
1
0
1
1
1
2
1
1
1
0
0
0
0
1
1
0
0
0
2
0
0
1
1
1
1
0
2
1
2
0
1
2
1
1
1
0
1
1
0
1
0
1
1
0
1
1
1
0
1
1
2
1
0
2
0
2
0
1
1
1
0
0
1
0
0
3
2
1
0
1
0
0
0
0
0
2
1
1
1
1
1
1
1
1
1
1
0
1
2
2
0
1
1
0
0
0
0
1
1
1
1
0
1
1
1
1
0
1
0
1
1
2
0
1
2
4
1
1
1
1
2
0
1
1
0
1
1
1
1
0
1
2
2
0
0
1
0
2
0
1
1
1
1
1
0
1
1
1
1
1
0
0
0
0
0
0
0
1
1
1
0
1
1
0
0
1
0
1
1
2
1
1
2
1
0
2
0
1
0
2
0
0
1
1
1
1
2
1
1
0
1
1
0
2
0
0
0
1
0
1
2
0
1
1
1
0
1
1
2
1
1
1
0
0
1
1
1
0
1
1
1
1
1
0
1
2
0
1
1
2
1
1
1
2
0
1
2
1
1
1
1
1
2
2
0
0
0
1
2
0
0
1
2
1
0
1
1
1
1
0
1
1
1
2
1
0
2
1
0
1
0
2
1
1
2
1
2
2
1
0
1
0
0
0
2
0
1
4
1
1
1
0
1
2
1
1
1
2
2
1
1
1
1
3
0
1
2
2
1
0
1
0
2
1
1
1
0
2
0
2
0
1
1
1
1
0
2
1
1
1
1
0
1
0
1
1
2
1
1
2
1
1
2
3
1
0
2
1
1
1
0
1
2
1
1
0
2
0
1
3
1
0
2
2
0
0
3
2
1
2
1
0
2
1
1
0
1
2
3
1
2
1
2
1
1
1
0
1
1
2
1
1
1
1
0
2
1
2
1
2
1
0
1
1
1
0
1
1
1
0
1
2
0
1
2
2
2
1
1
1
1
2
2
2
1
2
1
0
0
2
1
1
2
1
1
0
2
0
2
2
1
2
2
2
1
1
2
1
1
1
1
1
2
0
2
2
2
2
0
1
1
2
2
2
0
0
1
0
1
1
0
1
1
1
2
1
2
1
1
2
1
2
1
1
1
1
0
2
2
2
2
2
1
0
0
1
1
1
0
1
1
0
0
0
1
0
0
0
1
1
1
2
2
1
1
0
0
1
0
1
1
1
1
2
1
1
0
1
0
1
2
1
1
1
0
1
1
1
1
0
1
2
0
2
2
1
2
2
0
0
1
1
0
0
0
4
1
2
2
1
0
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
2
1
0
2
1
2
0
2
1
1
1
2
1
0
0
1
0
1
1
1
1
1
1
2
1
2
1
0
1
1
1
2
1
1
1
1
0
1
0
1
2
2
1
1
2
0
1
0
0
1
0
1
1
2
0
0
2
1
2
2
0
0
0
2
0
1
0
1
0
1
2
0
1
1
1
1
0
1
0
2
2
2
1
1
2
0
0
1
0
2
2
1
0
3
1
3
1
2
0
1
2
1
1
1
2
0
0
3
0
0
0
0
0
1
0
1
1
0
1
2
2
0
2
1
1
2
1
2
1
3
1
0
1
1
1
2
1
1
1
0
0
1
1
0
0
1
0
1
1
1
1
2
1
0
2
2
1
2
1
1
0
0
0
0
1
0
0
0
0
0
0
1
1
1
2
0
1
1
1
1
1
0
1
1
1
1
1
1
1
1
0
2
0
1
15
1
2
2
1
2
0
1
0
1
2
1
1
0
1
0
1
2
1
0
2
0
0
1
1
1
0
1
1
1
0
1
1
0
0
2
2
0
1
1
2
0
1
2
0
1
1
1
1
0
3
0
2
2
0
1
1
1
1
2
1
2
1
1
2
0
0
2
1
1
2
1
0
2
0
1
1
1
0
1
2
2
0
0
1
2
1
0
1
0
1
1
2
0
1
1
3
1
2
2
1
1
1
1
2
0
1
1
1
1
0
1
0
1
2
0
1
2
1
0
0
2
1
2
1
0
0
1
1
1
1
4
1
0
2
1
1
1
0
0
0
0
1
2
3
1
0
0
0
1
0
1
1
0
0
1
0
0
0
2
1
1
1
0
1
0
1
0
2
0
1
0
2
0
2
0
0
1
1
0
1
1
1
0
1
0
2
2
2
0
1
2
1
0
1
0
1
1
1
1
1
2
2
0
2
0
1
0
0
1
2
0
0
2
1
0
2
0
0
2
2
0
0
1
1
0
1
2
0
2
0
1
1
2
0
0
1
0
0
2
1
1
0
0
1
1
1
1
0
0
1
1
2
0
0
0
2
2
1
1
1
1
0
0
1
1
1
1
1
0
0
1
1
0
1
0
1
1
0
1
1
1
1
1
1
3
1
1
0
0
1
0
0
2
1
1
0
0
0
1
0
1
0
2
3
2
1
0
1
0
1
0
2
0
0
1
0
0
2
1
2
1
2
1
1
1
0
0
1
0
1
1
0
0
2
2
3
1
0
1
1
1
1
1
0
0
1
0
2
1
1
0
1
2
1
2
2
0
0
2
0
2
1
0
1
0
2
0
1
0
1
1
2
0
0
2
2
2
1
0
0
1
0
0
0
1
1
2
1
2
0
1
1
0
1
2
1
0
1
2
2
1
0
1
0
0
1
2
1
2
1
1
1
1
2
1
1
1
2
3
1
1
0
0
1
1
1
0
1
1
0
1
1
0
1
0
0
1
3
0
1
0
1
0
0
1
0
1
0
1
1
1
0
0
1
1
1
1
2
1
0
1
1
0
0
1
2
1
2
1
0
1
2
1
2
0
1
1
2
1
2
0
1
1
0
2
1
1
1
1
1
2
1
0
1
1
1
1
0
0
0
1
3
0
1
0
0
1
2
1
1
1
1
0
0
1
2
1
0
1
1
2
2
1
0
1
0
1
1
1
2
1
2
1
0
2
1
1
0
0
1
1
2
2
1
0
1
1
2
0
1
1
1
1
1
0
2
1
0
0
2
1
2
1
1
1
2
0
0
2
1
1
0
0
1
0
2
0
1
0
1
1
2
0
1
2
1
3
1
0
0
1
1
0
0
1
0
2
1
1
0
1
0
2
0
1
1
0
2
1
0
1
0
2
2
1
1
1
0
1
1
2
1
0
1
2
1
1
1
1
2
1
1
0
1
1
0
0
2
1
2
1
1
0
2
1
2
0
0
1
0
2
0
0
0
2
0
1
1
0
0
2
0
1
1
1
2
1
2
1
1
2
2
1
0
1
1
1
0
2
1
1
1
0
1
2
0
1
1
2
0
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
0
0
0
1
1
1
0
1
1
0
1
1
1
0
2
1
1
0
1
0
1
1
1
0
0
2
1
0
0
2
1
0
1
2
2
0
1
2
2
0
1
2
1
1
0
1
0
0
1
0
1
1
1
0
1
2
1
1
0
0
1
0
0
0
2
1
1
0
0
0
2
1
1
2
0
1
1
0
0
2
1
1
1
2
1
0
1
2
0
2
1
0
2
1
1
1
0
1
1
1
0
0
0
1
2
2
2
1
2
1
2
0
1
1
1
1
1
3
4
2
0
1
1
2
1
0
0
1
0
1
2
2
0
1
1
2
1
2
2
2
1
1
1
0
0
1
1
1
0
1
3
2
2
1
0
1
0
0
2
0
0
0
2
1
1
1
1
1
1
2
1
0
1
1
1
0
0
3
0
1
2
0
2
1
0
0
1
2
2
0
1
2
1
0
1
0
1
1
2
0
1
0
1
1
2
1
2
1
1
1
1
3
1
1
2
0
1
0
2
2
0
1
2
1
2
0
1
0
1
0
2
3
0
1
2
5
1
1
1
2
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
0
0
1
1
2
1
1
1
0
1
2
1
2
1
1
2
0
1
0
1
0
2
1
0
2
1
1
2
0
1
1
1
1
0
0
0
1
2
2
2
2
0
0
0
1
0
1
1
2
0
1
0
1
1
0
1
2
0
1
0
1
2
2
1
1
2
1
1
2
0
1
1
0
0
1
2
1
1
2
0
0
1
2
1
1
1
0
2
2
1
0
2
1
1
2
1
0
1
1
1
3
1
1
1
1
0
1
1
0
0
0
2
1
1
2
1
0
1
2
0
0
1
1
2
2
0
0
1
1
1
1
0
2
0
1
1
1
1
1
1
1
3
1
0
0
1
0
1
1
2
1
0
0
0
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
0
1
1
0
0
2
1
0
1
2
0
1
1
1
1
1
2
1
2
1
0
1
0
1
1
0
0
1
1
1
0
2
0
1
0
2
1
1
0
0
3
0
0
2
1
2
1
0
1
1
0
1
1
1
1
1
2
1
1
0
0
1
1
1
1
1
1
1
2
1
2
2
1
0
1
1
1
1
0
1
2
0
1
0
1
0
1
1
2
1
1
1
2
1
1
0
0
2
0
1
1
0
0
2
2
1
1
0
2
2
2
1
2
1
0
2
0
2
0
1
1
1
0
1
0
2
1
1
2
1
3
1
2
0
0
1
1
1
1
1
1
0
0
0
0
1
1
2
0
1
0
0
1
1
0
1
0
0
1
0
1
2
1
1
0
2
1
1
3
2
0
2
1
2
0
1
1
1
1
0
0
0
1
2
2
1
0
1
0
2
1
1
1
1
0
1
2
1
2
1
2
2
1
2
1
1
1
0
1
1
2
1
0
0
1
1
1
2
1
0
0
0
0
1
2
1
2
1
0
0
1
2
2
1
2
0
0
1
2
2
1
2
0
0
1
1
4
1
1
3
1
1
1
0
1
0
1
1
1
2
1
2
2
2
2
0
1
0
1
1
2
0
2
1
2
0
1
1
2
1
0
2
1
0
0
1
0
1
1
1
2
1
2
0
2
1
1
1
0
1
1
2
1
1
0
1
0
2
0
1
1
1
2
1
1
1
1
1
2
2
1
2
1
1
0
0
1
1
0
1
1
2
0
0
2
0
2
2
1
5
1
0
0
1
2
1
1
1
2
0
1
2
1
1
1
0
1
1
1
2
1
0
1
0
2
2
1
0
1
2
2
1
1
2
0
1
2
2
1
1
1
2
0
0
0
1
1
2
1
1
2
0
1
1
1
0
2
0
1
0
1
2
2
1
2
0
2
1
0
1
1
0
0
1
1
2
0
1
1
1
0
0
0
0
0
2
0
0
1
1
1
0
1
0
0
0
2
1
1
0
1
2
1
1
2
2
2
1
2
1
0
1
1
1
2
1
2
0
2
1
0
2
0
1
0
1
1
1
1
0
1
1
2
1
1
0
1
2
0
2
2
2
1
1
1
1
2
2
1
1
1
1
0
2
1
0
1
0
1
1
2
1
0
0
2
0
0
1
1
1
1
0
1
2
0
0
1
0
1
0
0
0
1
2
2
1
2
2
1
1
0
0
2
1
0
3
0
1
1
0
0
2
1
1
1
1
2
1
1
0
0
2
0
1
0
1
1
1
1
2
2
0
1
1
1
2
1
0
0
0
1
2
0
0
1
0
0
1
1
0
1
0
0
1
1
2
1
1
1
1
1
1
1
2
1
0
0
2
2
1
1
1
2
1
2
2
2
1
0
1
1
1
1
0
1
1
1
0
1
1
1
1
1
1
1
0
0
1
2
1
0
0
1
2
2
2
2
2
0
1
0
0
1
1
1
1
0
1
0
0
1
0
1
2
2
1
1
0
0
0
2
1
1
1
1
2
1
1
2
2
0
2
0
1
1
1
1
0
0
1
0
1
2
1
1
1
0
2
0
0
0
0
1
1
2
1
2
1
2
1
1
0
1
1
1
2
2
3
1
0
0
2
1
1
1
1
1
0
1
1
1
2
1
0
2
1
1
1
0
0
1
1
2
1
0
1
1
1
2
2
2
1
0
2
2
1
1
1
0
2
1
1
1
1
1
1
1
1
0
2
1
1
2
1
0
1
0
1
0
0
2
0
2
2
0
1
0
1
1
2
1
1
2
0
2
0
2
1
2
2
1
0
1
0
1
0
1
3
1
2
0
2
1
2
1
2
0
1
1
1
2
0
1
1
1
0
0
1
0
0
1
1
1
1
0
0
2
2
0
1
1
1
0
1
0
1
2
0
0
1
1
1
1
1
1
0
1
1
1
0
1
2
1
0
1
1
0
1
1
0
1
0
0
1
1
2
1
1
3
1
3
1
1
1
2
1
1
1
1
1
1
0
1
0
2
1
1
0
2
1
0
0
1
0
0
0
0
2
2
2
0
1
1
0
1
1
2
1
2
1
1
1
1
1
2
1
0
0
1
1
0
0
0
2
1
1
1
0
1
0
0
1
1
1
0
0
0
2
1
0
1
1
2
1
1
2
1
0
2
1
1
1
1
0
1
0
1
0
1
0
1
1
1
0
1
0
2
0
2
1
1
2
2
0
1
1
1
1
1
1
1
0
2
0
1
0
0
1
2
0
1
1
0
0
1
0
0
2
0
0
1
1
1
2
0
1
0
2
1
0
0
2
0
1
0
0
0
0
2
1
0
1
0
1
2
1
1
1
1
0
2
0
1
1
2
1
1
1
0
1
2
0
1
0
0
1
3
1
2
2
2
1
1
0
1
0
1
1
1
0
1
1
2
0
2
1
1
1
4
2
0
0
0
2
1
2
1
1
1
1
1
1
0
1
0
1
1
1
1
1
1
1
1
1
0
1
0
0
0
0
2
1
0
1
2
1
1
0
0
0
2
0
0
0
1
1
1
0
1
1
1
1
2
0
1
1
1
1
0
0
0
0
2
2
0
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
0
1
0
3
2
1
1
1
0
0
1
2
0
1
1
1
1
2
1
2
1
1
1
0
1
0
2
0
0
1
1
0
1
0
1
0
1
0
2
1
0
0
1
3
3
0
0
1
2
0
0
0
3
1
1
0
2
0
1
0
1
0
0
1
0
0
1
2
0
1
1
1
3
0
2
1
1
0
0
2
0
2
0
2
0
1
0
0
1
1
1
0
2
1
0
0
1
0
0
1
1
2
0
0
0
2
1
2
0
0
1
1
3
2
1
1
1
1
0
2
2
1
0
1
1
0
0
1
0
0
0
2
1
1
0
2
2
1
2
1
2
1
0
1
1
1
1
1
1
2
1
1
1
1
2
1
2
1
1
1
2
1
0
1
1
1
2
1
0
1
2
2
2
0
2
1
0
0
2
0
2
0
1
1
1
0
2
1
0
0
0
1
2
2
1
1
1
1
2
2
1
0
1
1
0
0
1
1
0
0
0
2
1
1
1
2
1
0
0
0
0
1
1
1
1
1
1
2
1
1
0
0
2
1
1
1
1
2
2
0
0
1
2
1
1
0
2
1
1
1
1
1
2
1
0
1
0
0
0
2
1
0
1
1
0
1
1
1
1
0
1
2
1
1
0
1
0
2
1
0
1
3
1
2
1
1
2
1
2
2
0
1
1
0
1
0
1
1
0
1
1
0
1
2
1
1
1
0
1
1
1
0
1
2
1
1
0
0
2
0
1
0
1
2
2
1
2
1
1
1
0
0
2
2
1
2
2
1
2
1
1
0
1
0
1
1
1
0
1
2
0
0
1
1
2
3
1
1
0
1
0
0
1
0
1
1
0
0
1
1
1
0
0
1
1
1
0
2
2
0
1
0
0
0
1
2
1
0
1
2
1
1
1
2
2
0
2
1
2
2
1
1
0
2
2
1
0
1
1
0
1
2
1
1
2
0
2
0
2
0
0
2
1
2
1
1
1
2
2
2
0
1
1
2
0
1
2
1
0
0
2
0
0
0
1
0
0
1
0
1
0
2
2
2
1
0
1
2
0
2
4
2
2
2
0
1
2
1
2
1
2
1
1
2
0
1
1
2
1
0
1
2
0
1
0
2
1
1
1
0
2
2
0
0
0
1
0
0
1
2
0
1
1
1
0
1
1
0
2
1
1
1
0
1
2
0
0
0
0
1
2
1
1
1
0
1
1
0
2
1
1
1
2
1
1
1
1
0
2
1
0
0
1
2
2
1
0
0
0
2
0
1
1
0
0
2
2
0
1
1
0
1
0
0
0
2
0
0
1
0
1
0
1
0
1
1
0
1
1
1
1
1
1
0
0
2
1
0
1
1
2
1
0
0
0
0
1
1
1
1
1
1
2
1
1
0
1
2
1
0
1
2
2
1
1
1
1
0
0
1
1
1
0
0
1
1
1
0
1
0
1
1
2
1
0
2
2
0
1
2
3
1
1
0
1
0
1
1
1
2
1
1
2
1
1
1
1
2
1
1
0
1
2
0
0
3
1
1
1
1
1
2
1
1
0
1
1
1
0
1
1
1
1
1
1
3
0
1
1
1
1
0
1
2
0
1
1
2
0
1
2
2
1
1
2
2
1
0
1
0
1
1
1
1
1
0
1
2
0
2
1
1
0
2
1
1
2
1
0
2
1
1
1
1
2
1
0
0
1
1
2
1
0
2
1
2
0
0
2
2
2
1
1
1
2
2
0
0
2
0
1
1
1
0
1
0
1
1
0
1
2
1
1
0
2
1
1
2
1
1
1
0
0
2
0
1
0
0
1
0
3
2
2
0
0
1
1
2
1
2
1
1
1
1
2
1
2
1
1
1
1
3
1
0
0
1
2
1
1
1
1
2
2
1
1
0
0
0
1
1
1
0
1
0
1
2
1
1
2
1
2
0
1
1
1
0
0
1
1
2
1
2
1
0
1
1
0
0
0
1
1
1
2
1
1
2
0
2
0
1
2
0
2
0
2
1
0
0
1
1
1
1
1
0
0
1
0
2
1
0
0
2
1
1
2
2
1
0
0
1
1
0
1
0
1
0
2
1
1
0
2
3
1
0
0
1
0
1
0
1
2
0
0
2
2
1
0
0
2
1
2
0
0
0
1
2
1
1
0
2
1
2
2
1
2
1
1
2
0
0
1
2
1
0
2
0
1
2
1
0
1
2
0
1
0
1
1
2
2
1
1
2
2
2
0
1
1
0
2
2
1
0
1
2
1
1
2
1
0
0
1
1
0
1
1
1
2
2
1
2
0
0
2
2
2
1
2
1
2
0
1
2
1
1
1
2
0
2
1
2
1
1
1
1
1
1
2
0
0
0
1
0
0
2
0
0
1
2
2
0
1
2
3
2
2
1
2
2
1
0
3
2
2
1
2
1
0
1
1
1
2
1
2
1
2
0
0
1
1
1
1
2
2
2
1
1
1
1
1
0
0
1
0
1
1
0
0
2
0
1
2
2
2
0
1
1
0
1
0
2
2
1
1
0
1
2
0
0
1
2
1
2
1
0
1
1
1
1
2
0
2
2
2
1
1
0
2
2
1
1
0
0
1
0
0
1
0
0
1
1
1
0
0
2
0
2
1
2
1
1
1
1
1
1
2
1
1
0
1
1
2
0
1
2
2
0
0
1
1
1
2
0
0
0
2
1
1
0
1
0
1
0
1
2
2
2
1
1
1
0
1
1
1
0
1
2
0
1
2
1
1
2
1
1
0
1
1
1
1
2
0
2
2
2
1
1
0
1
0
1
2
0
2
1
1
0
0
1
1
1
1
1
0
0
1
0
1
1
1
1
0
2
0
1
1
1
1
2
0
0
1
2
1
0
0
0
2
1
1
1
0
2
2
1
2
1
0
0
0
1
0
1
1
2
1
1
1
1
0
1
2
2
1
1
1
1
1
2
0
0
0
2
1
2
1
2
1
0
1
0
0
0
1
0
1
2
1
1
1
1
1
0
1
1
1
1
1
0
1
1
2
1
1
0
0
0
2
1
0
0
1
2
2
1
1
2
0
1
1
1
1
1
2
1
0
0
1
1
2
0
2
2
2
1
2
1
1
2
2
1
1
1
0
0
0
1
0
1
0
2
1
1
2
1
0
0
2
0
1
1
0
2
1
1
1
1
1
1
2
1
0
2
1
3
1
1
1
1
1
1
2
0
1
1
0
2
1
1
1
1
0
1
1
1
2
1
2
1
1
1
2
0
0
1
0
2
1
1
2
1
1
0
1
2
2
1
1
1
1
1
0
2
2
1
1
2
1
1
2
1
0
2
2
1
0
1
0
1
1
1
1
2
0
1
2
2
1
1
0
2
1
1
0
2
0
1
1
2
1
0
2
2
0
1
1
2
2
1
2
2
1
2
0
2
0
2
2
2
1
0
1
1
0
0
2
1
0
0
1
0
1
2
0
0
2
2
1
0
1
1
1
1
1
2
1
1
0
2
1
0
1
2
1
1
2
2
0
2
2
0
1
1
1
1
1
1
1
0
0
0
0
1
1
2
1
0
1
1
1
0
1
1
1
3
1
1
2
0
0
0
2
1
0
2
1
2
1
2
1
1
2
2
2
0
2
2
1
1
0
2
1
0
2
0
1
0
1
0
3
2
2
1
1
1
4
2
1
0
2
0
2
2
0
0
1
2
2
1
2
1
1
0
1
1
2
3
1
1
2
1
0
1
1
1
2
2
0
0
2
2
0
2
1
0
0
1
0
3
1
1
0
1
1
1
0
0
2
1
1
2
1
0
2
1
1
1
2
0
2
1
2
2
0
2
1
0
0
2
1
0
1
2
4
1
1
1
1
0
0
1
0
2
1
1
1
1
0
1
0
1
1
1
1
0
1
3
2
1
3
0
0
1
2
1
0
0
1
1
0
0
1
2
1
0
2
1
0
2
1
0
1
0
1
1
1
1
1
2
0
2
0
1
1
1
0
2
1
2
0
2
2
0
2
2
0
2
1
1
1
1
0
1
0
0
2
0
2
1
1
1
5
2
0
0
0
1
0
1
1
0
1
0
1
1
1
1
2
2
0
2
0
1
1
1
0
1
1
1
1
1
0
1
2
3
2
2
1
0
1
1
1
2
1
0
0
1
1
3
1
1
2
0
2
2
2
1
1
1
0
2
0
1
0
1
1
1
1
1
0
1
2
2
0
1
0
1
1
1
2
1
2
1
0
1
0
0
1
1
1
0
1
1
1
0
1
0
1
1
1
1
1
1
0
1
1
0
0
1
1
0
1
1
0
0
2
0
1
1
2
1
0
1
0
0
1
1
1
2
1
1
0
1
2
1
2
1
1
0
1
1
2
1
0
1
0
2
6
0
1
0
1
1
1
1
1
1
0
2
2
1
0
1
2
1
0
0
0
2
1
1
0
1
1
0
2
1
0
2
2
2
2
0
2
0
0
1
1
2
2
0
1
1
1
1
0
1
1
1
1
1
0
1
0
1
1
2
0
2
0
0
1
2
1
0
0
2
2
1
1
1
1
1
0
1
1
0
0
0
2
0
1
1
1
0
0
1
1
1
2
1
1
2
1
2
1
0
1
2
1
1
0
2
3
1
1
0
1
1
0
1
1
1
0
2
0
1
2
1
2
1
1
1
2
1
0
1
1
1
2
0
1
1
1
0
0
0
1
1
1
1
1
1
1
1
0
0
1
0
0
1
2
1
0
4
1
0
1
2
1
1
1
0
1
1
1
0
1
1
0
1
1
2
1
0
1
1
0
0
1
0
1
1
0
2
0
1
0
1
1
2
1
2
1
1
1
2
0
1
0
2
0
0
0
2
0
0
3
2
2
1
1
2
1
1
2
1
0
1
3
1
0
0
1
2
0
2
1
1
1
0
1
1
0
1
2
1
1
2
0
1
2
0
0
0
1
1
0
2
1
0
1
1
0
2
1
2
1
1
2
2
0
1
1
1
0
1
1
1
2
1
1
1
1
2
2
1
2
1
1
2
1
1
1
1
1
0
0
2
0
0
1
1
2
0
0
1
2
1
1
1
2
2
1
1
0
1
1
2
0
1
0
1
1
1
0
1
2
0
0
1
1
1
2
1
0
2
0
1
3
1
0
1
0
2
3
0
1
1
1
0
0
0
0
1
2
1
1
0
1
1
1
1
0
2
0
1
1
0
2
2
1
1
1
1
1
2
1
1
0
1
1
1
2
1
0
2
0
2
1
0
0
2
1
0
0
1
1
1
1
1
2
1
1
1
1
0
1
2
2
1
1
0
2
1
0
1
1
1
0
1
1
0
1
1
1
1
2
1
2
1
0
0
2
1
0
0
1
1
1
2
1
1
2
1
0
0
0
0
0
2
0
1
2
0
1
0
0
1
2
1
1
1
0
1
2
2
2
2
1
2
1
0
1
2
1
2
1
0
1
1
1
2
0
0
1
1
0
1
1
1
1
1
0
2
1
1
1
0
2
1
0
1
2
1
1
2
1
1
0
0
0
2
2
1
0
1
1
1
1
1
1
0
0
1
1
1
1
0
2
0
0
1
1
1
0
0
2
1
0
1
1
2
0
0
1
1
2
2
1
1
1
0
2
2
0
1
2
0
1
0
0
1
2
1
2
1
1
1
2
2
1
2
1
1
2
1
1
1
0
0
2
1
0
1
2
1
1
2
2
0
1
0
2
2
1
1
1
3
1
0
2
2
1
1
2
1
0
1
2
1
0
1
1
0
0
0
1
1
1
2
0
1
1
1
1
2
1
2
1
1
2
1
1
0
0
0
1
1
2
1
0
1
1
1
0
0
1
1
1
2
1
1
2
1
1
1
1
1
1
0
0
1
2
1
1
1
0
1
1
1
0
1
0
2
0
0
1
1
1
1
0
1
1
2
2
1
0
1
0
1
1
2
1
0
0
2
0
1
1
0
1
0
0
2
1
0
1
2
2
1
1
1
2
1
2
0
1
1
1
1
1
1
2
1
1
1
1
0
1
1
2
0
1
2
2
1
0
1
2
2
2
0
2
1
2
1
0
1
1
2
0
1
2
1
2
1
2
2
1
3
1
1
1
2
1
0
1
2
1
2
1
1
2
1
1
1
0
0
1
0
1
0
0
0
1
1
3
1
0
2
0
1
1
1
0
1
0
0
2
1
0
1
1
1
0
1
2
0
1
1
0
1
1
0
2
2
1
1
0
1
1
2
1
0
2
2
0
1
1
0
0
0
0
2
1
2
2
0
0
0
1
2
1
0
1
0
1
1
0
1
1
1
4
0
0
0
0
1
1
1
1
1
2
1
0
1
1
2
0
0
0
1
0
1
1
1
1
2
1
1
1
2
2
1
1
1
2
2
1
0
0
1
0
1
0
0
0
1
2
0
0
0
0
1
1
1
2
0
0
0
2
1
2
2
0
1
1
1
1
1
1
1
1
2
0
1
1
2
2
2
2
1
2
1
1
1
1
1
0
1
1
0
1
1
1
0
0
1
1
0
1
0
1
1
1
1
1
1
0
1
1
0
1
1
1
0
1
1
1
1
0
0
2
2
1
1
2
0
2
0
1
1
0
1
1
2
1
0
1
0
1
0
1
2
0
0
2
0
2
0
8
1
0
1
2
0
1
1
1
1
1
2
1
1
0
1
1
0
1
2
1
3
0
1
1
2
1
1
1
1
0
2
0
1
1
2
1
1
2
1
0
1
1
0
1
1
0
1
1
1
2
0
1
0
1
2
0
1
2
0
1
1
2
1
4
0
2
0
1
1
1
0
0
1
1
1
1
2
2
0
1
0
1
1
1
0
0
2
2
0
1
2
1
1
0
2
1
1
1
0
1
0
2
2
1
3
0
0
1
3
1
1
1
1
2
1
1
1
0
0
1
1
1
2
1
2
1
1
1
0
1
0
0
0
1
0
0
2
2
1
1
1
1
2
1
1
0
1
0
1
2
1
1
1
1
2
1
0
2
0
0
1
2
2
2
2
1
2
2
1
1
0
1
0
1
1
1
1
2
1
1
1
1
0
1
1
2
2
0
1
1
2
0
0
1
2
1
1
1
0
0
0
2
1
1
0
2
1
1
1
1
1
0
1
1
1
1
0
0
1
1
0
1
2
2
2
0
1
0
1
0
1
1
2
2
0
0
1
1
2
0
0
2
0
1
0
2
2
0
1
1
1
1
1
1
1
1
2
1
1
0
0
1
1
0
2
2
2
0
0
0
1
0
0
0
1
1
2
1
2
1
1
1
0
1
2
1
0
1
0
1
1
1
2
1
2
1
2
0
1
1
0
0
1
2
1
0
1
0
1
0
0
1
0
1
1
1
1
2
1
2
2
2
2
1
2
0
1
0
0
0
0
1
1
0
1
1
1
0
0
1
1
1
0
0
1
0
0
1
1
1
1
1
2
1
0
2
1
0
2
1
1
2
1
3
0
0
2
1
0
0
1
1
1
2
1
0
2
1
1
1
2
2
1
2
2
2
2
1
0
2
1
2
2
2
1
1
2
0
1
0
0
0
0
1
1
2
1
0
1
0
2
2
0
1
1
1
1
0
1
1
2
0
2
2
0
0
1
1
1
1
1
1
2
2
0
2
0
0
1
1
1
0
1
0
1
2
0
1
1
3
0
0
0
1
0
0
1
0
1
0
1
2
1
1
2
2
2
2
0
1
0
2
1
0
1
1
1
2
0
2
1
1
1
1
1
2
0
1
1
2
1
0
0
1
2
1
0
1
0
1
1
1
1
1
1
1
1
1
2
1
2
1
0
1
1
1
1
0
1
0
1
0
1
0
0
2
1
0
1
0
1
0
0
2
0
2
0
0
1
1
1
2
1
0
1
1
1
0
1
2
1
1
0
2
1
1
1
1
1
2
0
1
1
1
1
1
2
0
2
1
1
1
1
0
2
0
0
1
0
1
1
1
0
0
2
1
0
1
0
1
0
1
0
1
0
1
1
0
0
0
1
1
0
0
1
1
2
1
1
2
0
1
2
1
0
1
1
1
1
0
1
0
1
1
1
0
0
1
0
2
0
1
1
3
0
1
1
0
0
1
0
0
0
1
1
2
1
1
0
1
0
1
3
1
2
2
1
1
1
2
1
2
2
0
1
1
1
1
2
1
1
1
2
1
2
1
1
1
0
2
1
1
0
2
2
2
0
0
1
1
1
0
2
1
1
1
2
2
1
2
1
2
1
1
1
1
1
2
1
0
1
1
1
1
2
2
1
1
2
2
1
1
1
0
0
1
2
0
1
2
0
1
0
1
2
1
1
1
0
2
1
1
0
1
2
1
1
2
2
3
2
1
0
1
2
1
2
0
1
2
1
1
0
2
1
2
1
1
1
2
0
1
1
1
2
0
0
0
0
0
1
1
0
0
1
1
0
0
1
2
1
0
1
0
0
1
2
2
2
1
1
1
2
0
1
1
2
1
0
1
2
0
2
1
0
0
1
0
0
2
1
0
2
0
1
1
1
1
1
1
2
2
0
2
1
1
2
0
2
0
0
0
1
2
1
2
1
1
0
1
2
1
1
2
1
1
1
1
1
0
1
0
1
0
1
1
2
1
0
1
1
2
0
1
2
1
1
2
0
1
1
1
1
0
0
0
0
0
1
1
0
0
0
2
0
1
2
1
0
0
0
1
1
1
0
0
1
1
0
1
0
1
0
2
1
1
2
0
1
1
0
0
1
1
0
2
1
1
2
1
2
1
1
1
0
1
1
1
1
1
0
0
2
1
1
0
0
1
1
2
0
0
1
2
1
1
2
1
2
1
2
1
0
1
1
0
1
1
2
2
0
0
0
1
2
1
2
1
2
2
1
0
1
2
1
0
1
0
1
1
0
1
1
1
1
1
1
0
2
0
0
2
4
1
0
2
1
1
1
1
0
0
2
1
1
1
0
2
1
1
2
1
0
0
1
1
2
0
1
1
1
1
0
0
1
0
1
1
1
1
2
0
0
1
1
0
1
2
0
0
0
0
2
1
0
1
1
2
2
0
3
3
0
0
1
0
1
2
1
1
1
1
0
1
2
2
1
1
0
1
0
1
1
1
1
0
2
2
0
1
0
0
1
1
1
1
2
1
1
1
1
3
1
1
0
0
2
1
2
1
0
0
1
2
0
1
1
2
1
2
0
1
1
1
1
2
1
0
1
1
0
1
1
1
1
1
2
0
0
0
1
0
2
2
1
0
0
0
2
1
0
1
1
0
0
2
1
1
2
0
1
0
2
1
2
2
1
2
2
0
1
1
1
0
1
1
1
2
2
1
0
0
1
1
1
0
2
2
1
1
1
2
1
1
2
1
1
1
1
1
1
0
0
0
0
1
0
2
2
1
0
1
0
2
2
2
0
1
0
2
2
1
0
2
1
0
1
1
1
2
1
2
1
1
0
1
1
1
1
1
1
0
1
1
2
1
1
0
1
0
1
1
2
0
0
2
0
2
2
1
1
0
2
1
1
1
0
2
0
1
1
0
1
1
1
0
1
1
0
2
0
0
2
0
1
0
0
1
0
0
1
1
1
1
1
0
2
1
2
1
0
2
1
0
0
1
2
1
1
1
0
0
2
1
1
1
2
1
1
1
1
1
2
1
0
1
1
0
1
0
2
2
1
0
2
1
2
1
0
2
0
0
2
1
0
1
1
2
0
0
2
2
1
1
0
2
1
1
0
0
1
1
1
1
2
1
1
0
1
1
0
1
1
2
1
1
1
1
0
0
0
1
2
0
1
2
1
2
1
2
2
0
1
1
1
1
1
0
3
1
1
2
1
2
1
2
1
0
0
0
1
1
1
1
1
1
1
2
0
0
0
3
2
1
1
0
0
0
0
0
2
0
2
1
1
0
1
0
0
2
0
2
1
2
1
1
1
1
2
1
1
0
1
1
1
0
2
2
2
0
0
1
1
0
0
0
2
1
0
0
2
1
0
1
3
1
1
0
1
1
1
2
1
0
2
0
2
0
1
0
1
0
1
1
0
1
0
0
0
1
0
0
1
0
2
1
0
3
0
1
1
2
2
2
0
0
1
1
3
1
2
2
1
1
1
1
2
0
1
0
1
1
0
2
1
1
1
1
1
1
2
1
1
0
1
2
1
1
0
1
1
0
1
1
2
1
1
1
0
0
2
0
1
1
1
1
2
1
3
1
1
1
0
1
1
1
1
2
2
2
1
1
2
1
0
2
2
1
0
1
2
0
1
2
0
0
1
0
2
1
0
1
2
1
2
2
0
2
1
2
2
2
0
0
0
0
0
1
1
1
2
1
1
1
0
0
1
0
1
1
0
1
1
1
0
0
0
1
1
1
1
0
1
0
0
0
1
2
2
0
2
1
1
1
1
1
0
1
1
2
0
3
0
0
1
1
2
2
1
2
0
2
3
1
1
1
1
0
1
1
2
1
1
1
2
0
1
4
2
2
0
2
0
2
0
2
2
0
1
2
1
2
2
0
0
2
1
1
1
1
1
0
1
2
2
1
2
1
1
2
1
0
1
0
1
1
2
0
1
1
2
0
1
1
1
1
1
1
0
1
1
0
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
0
1
1
1
0
1
1
1
0
2
0
2
1
2
2
2
0
1
1
2
2
1
0
2
0
0
1
2
1
0
1
2
2
0
1
2
1
1
0
1
0
1
1
0
0
2
0
0
0
1
0
1
1
1
0
1
2
1
0
1
1
1
1
1
0
1
1
2
0
1
1
1
2
0
0
2
1
0
2
1
1
1
2
1
2
1
1
0
1
1
2
1
1
1
1
2
0
1
2
0
0
1
0
1
1
0
1
1
1
2
0
1
0
0
2
1
1
1
1
3
1
0
2
3
2
1
2
1
1
2
1
2
1
1
2
1
1
2
0
2
1
1
1
1
1
1
2
2
0
1
1
1
0
5
0
2
0
2
0
1
0
0
1
1
1
2
1
0
2
2
1
1
0
2
1
1
2
2
0
2
0
1
2
2
2
0
1
2
2
0
1
1
1
1
1
0
2
1
1
1
1
2
4
0
2
1
1
1
2
1
0
1
1
2
1
2
1
0
1
1
2
2
1
1
1
2
0
1
1
0
2
1
1
2
1
1
1
3
1
2
0
1
0
0
2
0
0
0
0
0
0
1
1
1
2
2
1
0
2
0
0
1
1
0
2
2
1
4
0
0
1
1
2
2
0
1
1
0
0
2
0
1
1
1
1
1
0
1
1
1
1
0
1
1
1
1
1
1
1
2
0
2
1
0
2
2
1
1
1
1
1
2
1
0
0
1
1
2
2
1
2
1
1
1
0
0
0
1
1
2
1
1
2
1
0
0
1
1
0
0
0
2
1
2
1
2
1
0
1
0
1
2
2
1
2
2
0
1
2
0
1
2
0
3
1
0
1
9
1
2
1
2
0
1
0
0
0
1
1
1
0
1
3
2
0
2
1
2
0
0
2
1
1
1
0
1
2
1
0
0
0
2
0
1
1
1
1
2
2
1
0
1
1
1
1
0
0
0
0
1
1
1
2
1
2
2
1
2
1
2
0
1
1
1
1
1
1
1
1
1
2
1
3
0
0
2
1
1
1
0
0
0
0
0
2
0
0
0
1
2
1
0
1
1
2
1
2
0
2
1
2
0
1
0
1
1
1
0
2
1
2
2
2
0
3
0
1
1
1
0
2
2
0
2
0
0
1
0
2
2
1
1
2
2
0
1
1
0
1
1
0
2
1
2
0
2
0
1
0
1
2
2
2
2
1
1
1
1
0
0
1
0
1
3
2
1
1
0
1
1
1
1
2
2
2
1
1
2
0
1
1
1
2
0
1
1
0
2
1
2
0
1
0
0
0
4
0
1
2
0
1
1
0
1
1
0
0
1
1
0
1
1
0
2
1
1
0
0
1
2
1
0
0
2
1
1
0
1
9
1
8
1
0
1
1
1
1
2
2
2
1
1
1
2
1
1
0
0
2
0
0
0
2
1
1
1
3
0
0
0
0
1
1
0
2
1
1
2
1
0
1
1
2
1
1
1
1
1
1
0
1
1
0
1
0
0
1
1
0
1
1
1
2
1
1
0
2
1
0
1
2
2
2
2
0
0
1
1
1
2
1
0
1
1
0
1
1
1
1
0
1
1
1
0
1
2
1
2
3
1
3
1
1
3
1
0
0
1
1
0
1
0
2
0
1
0
1
9
2
1
0
2
1
3
1
1
0
1
2
1
1
0
0
1
1
1
1
2
1
1
0
2
2
1
1
0
0
2
2
1
2
0
1
2
1
1
0
0
2
1
1
1
2
2
0
1
0
1
2
2
0
1
0
1
0
1
0
1
1
1
0
1
1
0
1
2
2
1
1
0
0
0
1
1
1
2
1
0
0
0
0
1
1
2
1
2
0
0
1
0
1
1
0
1
1
1
0
2
1
0
1
0
1
2
1
1
1
1
1
0
2
0
1
0
1
0
1
1
0
1
1
0
1
2
1
2
1
0
1
0
1
0
2
1
1
1
2
1
0
1
1
1
1
1
2
3
0
1
2
2
1
2
2
0
1
1
1
0
2
1
2
2
0
1
1
1
0
0
1
1
1
1
1
0
1
1
1
1
0
1
1
1
1
0
1
1
1
0
1
0
1
0
0
1
1
1
2
0
1
2
1
0
0
2
2
0
0
0
0
1
1
2
2
0
2
1
2
2
0
0
2
1
1
2
1
1
0
0
0
1
1
0
1
2
0
0
1
2
1
2
0
1
1
1
1
1
1
0
1
1
2
1
0
1
2
2
0
0
1
1
1
0
1
0
2
2
1
2
1
0
1
1
2
1
1
0
1
1
0
1
0
1
1
2
2
1
1
2
2
1
0
1
2
2
2
1
0
0
1
2
1
1
1
2
1
0
1
2
1
1
0
1
1
2
0
2
1
0
1
2
0
1
0
1
2
1
1
1
0
2
1
1
1
0
1
0
1
2
1
1
2
2
0
1
0
2
1
1
1
1
0
1
0
2
1
0
1
2
1
1
1
1
0
2
2
1
0
1
2
0
1
1
1
1
0
0
2
1
2
2
1
0
1
0
2
1
1
2
2
2
1
2
0
1
0
0
1
1
2
1
2
1
1
1
1
2
1
1
2
1
0
1
1
1
1
1
1
1
1
1
1
0
1
2
0
2
1
2
0
1
1
1
1
1
0
2
1
1
1
1
1
1
0
2
0
2
2
1
0
1
2
1
1
1
1
1
1
1
1
1
2
2
0
1
1
1
1
0
1
1
0
0
0
2
0
1
1
2
2
0
2
0
2
1
1
1
0
0
1
2
0
0
1
0
0
1
0
1
2
1
1
0
0
0
1
3
1
0
1
0
1
0
0
2
2
0
1
1
0
0
1
0
2
2
0
2
0
1
1
2
1
2
1
1
0
2
1
1
1
0
2
0
2
2
1
1
1
1
2
0
0
0
1
0
1
1
1
1
1
1
0
2
1
2
2
1
2
1
1
1
0
1
0
0
2
1
1
1
1
1
2
2
1
1
1
0
1
2
2
1
1
0
1
1
2
1
2
1
2
0
1
0
0
0
0
1
1
1
1
2
1
2
2
1
1
2
0
0
0
1
1
1
0
1
0
1
1
1
1
1
1
1
2
0
0
2
0
2
0
1
2
1
2
0
0
1
1
1
0
1
1
0
0
1
1
1
1
1
1
0
1
0
1
0
0
1
3
0
0
1
0
1
1
0
0
1
2
2
1
0
1
2
0
2
1
1
1
0
2
2
1
1
0
0
0
2
2
0
2
3
1
1
1
2
2
1
0
0
2
2
0
2
0
1
0
1
2
1
1
1
1
1
3
2
1
1
1
1
0
2
0
1
1
1
0
1
1
0
0
0
1
0
1
0
0
0
2
1
1
1
1
1
2
2
0
1
2
1
0
2
0
2
0
0
1
3
0
0
1
2
2
1
2
1
1
0
0
0
2
0
2
0
1
1
2
0
2
2
1
1
2
4
1
2
0
4
1
2
0
1
1
1
1
1
1
1
0
1
0
1
1
1
0
2
0
2
2
0
2
1
0
1
1
1
1
1
1
2
2
1
2
1
0
1
1
0
1
2
1
0
1
1
2
1
1
0
0
1
1
1
0
2
2
1
2
2
1
1
1
1
1
2
1
1
1
2
0
0
1
0
0
0
1
1
0
0
2
0
0
1
1
0
2
2
1
1
1
0
1
0
1
1
0
3
2
1
1
0
1
2
2
1
2
2
1
1
1
1
2
1
1
2
0
1
1
1
0
0
0
2
0
1
2
1
1
2
1
0
1
2
1
1
1
1
0
2
1
0
1
1
0
2
0
0
1
1
1
0
1
1
1
1
1
1
2
1
0
1
2
2
2
1
2
1
1
1
1
1
2
0
0
1
2
0
2
1
2
1
2
1
2
1
0
1
2
1
1
1
2
1
1
0
1
1
0
2
0
1
1
2
1
1
1
0
1
0
0
1
1
1
0
0
0
1
1
1
1
1
0
0
0
1
0
2
4
0
1
1
2
1
0
1
2
2
1
1
1
1
1
1
0
1
1
1
1
1
2
2
1
1
1
1
1
1
1
0
0
1
1
0
1
2
0
1
1
1
1
0
1
1
1
1
1
0
0
0
0
2
1
1
1
0
2
1
1
1
1
2
2
2
1
1
1
1
0
1
0
1
1
1
0
1
1
1
0
1
2
1
1
1
1
1
1
0
0
1
1
6
0
1
1
1
2
1
0
1
1
1
0
1
1
1
1
1
0
2
1
1
2
1
2
0
1
0
1
1
1
0
1
1
1
1
1
1
1
2
0
0
0
2
2
2
0
0
1
1
2
1
2
2
0
1
0
1
3
1
1
0
1
2
1
2
1
2
2
1
1
2
1
1
2
3
2
1
1
1
0
1
0
1
1
2
1
1
0
1
0
0
2
1
0
2
2
2
0
0
0
2
1
2
0
0
1
2
1
1
1
0
0
0
1
1
1
1
0
2
1
0
2
1
1
0
2
2
2
1
1
1
1
1
2
1
1
2
0
0
1
2
1
2
0
2
2
1
0
1
2
0
1
1
0
0
1
1
1
0
0
1
2
1
1
1
1
0
1
1
0
1
1
1
1
0
2
0
1
0
0
1
1
0
1
2
1
1
1
2
0
1
0
2
0
2
2
3
0
2
0
1
1
1
2
3
1
0
0
0
1
0
1
0
1
1
1
1
0
2
2
0
0
0
0
1
0
1
1
1
1
2
1
1
0
1
2
0
1
0
1
0
1
2
1
1
1
0
1
2
0
1
0
0
1
2
1
1
2
2
1
1
0
1
1
2
1
1
1
0
0
1
1
1
2
0
1
1
2
1
1
2
0
1
1
0
2
1
0
1
1
1
1
1
1
0
2
0
1
1
2
1
2
2
0
1
1
1
1
1
0
2
1
0
1
1
0
1
1
1
1
0
0
1
2
0
1
0
2
1
0
1
1
1
1
1
2
0
1
1
2
2
1
2
1
1
2
1
2
0
1
2
3
0
1
1
2
2
1
1
2
0
2
1
1
1
1
1
2
1
1
2
0
2
1
1
1
1
1
1
1
0
1
2
1
0
1
1
2
1
2
0
0
1
1
1
2
0
3
1
1
0
2
2
0
0
1
0
1
1
1
0
2
0
0
1
0
2
2
1
0
1
1
1
1
0
0
0
1
1
2
0
1
1
1
1
2
2
0
2
0
0
2
1
0
1
1
1
1
1
0
2
1
1
1
0
0
1
0
1
3
1
0
1
1
2
1
2
0
2
2
1
2
1
2
2
1
1
2
1
0
1
1
1
1
1
2
0
1
1
0
0
1
0
0
0
2
0
1
1
0
1
1
1
1
2
2
1
0
1
1
1
4
0
1
1
1
1
0
1
2
1
0
1
1
0
2
0
0
1
1
2
0
0
1
1
3
2
2
2
0
1
0
2
2
1
4
0
3
1
1
1
1
1
1
1
1
1
0
1
2
0
1
1
2
0
1
2
1
2
1
2
2
2
2
1
1
1
1
1
1
1
1
0
1
1
1
1
0
1
2
0
1
0
1
1
1
1
1
1
1
1
0
1
0
3
1
1
1
0
1
1
1
1
2
0
0
1
1
2
2
0
2
2
0
1
0
2
0
1
2
2
1
1
1
1
2
2
1
0
2
2
0
0
0
0
1
1
0
0
2
0
1
1
2
1
1
1
1
0
1
1
0
0
0
1
1
1
2
2
1
1
0
1
1
1
1
1
1
1
0
2
0
1
0
0
1
0
1
1
1
2
1
0
1
1
1
0
1
2
2
1
1
1
2
1
1
1
0
0
0
0
2
0
2
0
0
1
1
0
0
2
0
1
0
0
0
0
0
2
0
0
1
1
1
2
2
1
2
1
2
1
1
1
1
2
0
1
0
1
1
0
0
1
0
1
0
1
1
1
0
1
1
1
1
1
2
2
1
2
0
1
0
2
0
0
1
2
1
1
0
1
2
1
1
0
0
2
1
2
1
0
1
1
1
2
0
1
1
1
0
1
1
0
0
2
0
2
2
1
0
0
1
1
1
1
2
0
1
0
0
2
1
1
1
2
1
1
0
0
2
0
0
2
1
0
0
1
1
1
1
1
1
2
1
2
0
0
0
2
4
2
0
0
0
1
1
0
1
1
1
1
3
0
0
0
1
1
2
0
1
0
1
0
1
0
2
5
1
1
1
0
2
2
1
2
2
1
0
1
2
1
1
2
3
1
0
1
0
1
1
1
1
0
1
1
1
2
0
1
2
2
0
1
1
1
1
0
2
1
2
0
2
1
1
1
1
0
2
1
1
2
1
0
0
1
2
2
0
0
2
1
2
2
0
0
2
0
1
2
2
1
1
1
1
1
2
1
0
0
1
0
2
1
0
2
1
2
1
2
1
2
2
0
2
1
1
0
1
1
0
0
0
1
1
2
1
1
1
2
2
2
3
1
1
1
1
0
1
1
0
1
2
2
2
0
0
2
1
1
0
0
2
1
0
2
1
0
2
1
0
0
1
3
1
1
1
0
2
0
1
0
2
2
0
0
0
1
1
0
0
2
0
2
1
1
0
2
1
1
0
0
1
0
1
1
1
0
2
1
2
0
2
1
1
1
0
1
1
1
0
1
1
1
1
1
1
1
1
0
1
1
0
0
1
1
2
3
1
0
2
1
1
2
1
2
1
2
1
1
1
1
1
1
0
0
1
1
1
0
2
3
1
0
0
0
0
0
0
1
1
1
1
0
2
1
1
2
2
2
0
0
0
1
1
2
1
0
0
1
0
0
0
0
0
1
0
1
2
1
1
2
1
1
1
2
0
0
1
0
0
1
1
2
1
2
0
1
0
1
1
1
1
1
0
0
1
1
0
0
2
1
0
0
1
1
1
2
1
0
1
0
1
0
1
0
1
1
1
2
1
1
1
2
2
1
0
1
1
2
0
0
0
0
2
1
1
0
1
0
0
0
1
1
1
1
1
1
0
1
0
1
2
1
1
2
1
1
0
0
2
0
1
2
1
1
0
2
2
2
2
0
0
1
1
1
2
2
0
2
0
2
1
1
2
1
0
0
2
1
0
0
1
1
1
1
1
1
0
2
1
1
1
0
0
0
1
1
1
3
2
0
1
1
1
0
1
0
1
1
0
0
0
2
1
0
1
0
1
0
0
0
1
0
2
0
2
1
0
2
2
2
1
1
1
2
2
0
0
1
0
0
2
2
0
0
0
1
1
1
1
3
1
1
1
0
1
0
1
1
2
0
0
0
2
2
1
0
1
1
1
1
1
0
1
0
2
0
1
2
0
1
0
2
1
1
1
2
1
2
0
1
1
1
0
1
0
0
1
1
2
0
1
0
1
1
1
1
1
1
1
1
0
0
1
0
1
1
1
1
1
0
1
1
1
1
1
1
2
1
1
0
1
0
1
2
0
0
2
0
0
1
0
1
0
2
1
1
1
2
2
1
1
0
1
1
1
1
1
2
0
2
2
2
0
0
1
0
2
0
1
0
1
0
1
1
1
1
1
2
1
1
1
0
1
0
0
1
1
0
0
0
1
2
1
0
0
1
1
1
1
1
0
1
2
2
1
2
0
1
1
0
1
2
1
2
0
2
0
0
1
0
0
0
0
0
1
1
1
1
0
1
2
1
0
1
2
1
1
0
0
0
1
1
1
2
2
2
1
1
1
1
2
1
1
2
1
0
1
2
1
2
0
0
0
0
1
0
0
2
0
1
1
2
0
1
1
2
1
1
1
0
0
2
2
1
1
0
1
1
1
2
2
0
1
2
1
1
1
1
0
1
1
0
1
1
1
0
2
0
0
0
1
1
2
1
1
0
1
1
2
2
1
0
2
1
1
1
0
1
2
1
0
2
2
2
1
0
2
1
1
1
1
0
1
1
1
1
0
1
0
1
0
2
0
0
2
0
0
2
1
0
2
1
2
1
0
1
0
0
2
0
1
1
0
1
0
0
1
0
1
1
0
2
0
2
1
2
2
2
1
2
0
2
1
0
1
0
1
1
1
2
2
0
1
1
0
1
0
2
0
1
1
1
0
0
1
1
1
1
0
2
1
1
1
1
2
2
0
1
2
0
1
2
1
0
0
1
2
0
2
0
1
2
2
0
1
0
1
0
0
0
1
2
2
1
0
1
0
1
2
1
2
1
1
2
0
2
1
0
2
1
2
1
0
2
1
1
2
0
2
2
1
2
0
1
1
0
2
1
1
1
1
0
0
1
1
0
1
0
1
1
0
1
2
1
2
1
0
1
2
1
1
0
2
2
1
1
2
1
0
0
0
0
2
1
1
1
1
1
1
0
1
0
2
1
1
3
2
0
0
1
0
0
2
2
1
0
1
2
0
0
0
1
2
2
1
0
0
1
2
1
1
0
1
0
1
0
1
1
2
1
1
1
1
1
0
1
1
1
1
0
0
2
1
1
0
2
1
0
1
2
0
0
2
0
2
1
0
1
1
1
1
0
0
3
2
0
1
2
2
1
1
0
1
0
1
1
0
0
2
1
1
0
0
1
1
1
1
1
1
2
1
2
0
0
0
0
1
0
0
2
1
1
1
1
2
0
0
1
0
1
0
2
0
1
0
2
1
1
2
1
2
1
1
1
2
2
1
1
0
2
2
1
1
1
0
1
1
1
2
2
0
1
1
2
1
0
2
0
1
0
1
1
1
2
1
2
1
2
1
1
1
2
1
0
1
1
0
3
0
2
1
1
0
0
1
2
2
1
2
0
2
0
2
2
2
2
2
0
1
0
0
0
2
1
2
0
0
1
1
0
1
1
1
2
1
1
0
1
2
2
0
0
0
2
1
1
1
1
2
0
2
1
2
1
0
1
1
0
1
1
0
0
2
2
1
1
0
0
0
1
1
1
1
2
1
0
0
1
0
1
1
2
0
1
1
2
1
1
1
2
1
0
1
2
1
1
0
1
0
0
1
1
0
0
1
1
2
0
0
1
1
1
0
0
0
1
2
1
2
1
2
1
1
2
1
2
0
0
2
2
1
0
2
1
0
0
2
0
2
2
0
0
1
0
1
1
0
0
1
1
2
2
1
0
0
2
1
1
0
1
2
1
1
1
2
0
2
1
2
1
1
0
1
1
1
1
2
1
2
1
0
0
1
1
1
0
0
2
2
1
1
2
0
1
2
1
1
0
0
1
0
1
2
1
1
0
2
1
1
1
1
1
0
0
1
2
0
0
1
1
0
1
1
1
2
0
2
1
1
2
1
0
0
1
0
1
1
1
2
1
1
0
1
0
1
1
1
1
1
1
2
1
0
0
1
1
0
1
1
0
0
0
2
1
1
0
2
1
1
0
1
0
0
1
1
1
0
0
2
0
1
0
2
1
1
0
1
1
0
1
0
2
0
1
1
0
1
1
2
1
0
1
0
1
1
2
0
2
1
0
1
1
2
2
0
0
3
1
1
0
1
3
0
0
1
1
0
0
0
1
1
1
1
0
0
1
1
1
1
1
1
1
1
2
0
1
1
1
2
0
0
1
1
0
2
1
1
2
1
0
1
2
1
0
1
0
2
2
1
2
1
1
2
1
0
0
1
0
2
0
0
2
0
2
0
2
0
0
0
1
0
1
0
3
2
0
1
0
1
2
0
1
1
2
1
1
1
1
1
0
1
0
2
1
0
1
0
2
1
4
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
2
2
1
1
1
1
1
1
1
1
0
0
1
2
1
2
1
1
1
1
1
0
1
2
0
1
1
2
2
1
1
2
2
1
1
1
2
1
1
1
0
2
1
1
1
1
1
1
0
0
1
0
1
1
0
1
1
1
1
1
1
0
0
1
1
0
0
1
0
0
1
1
1
2
2
1
1
2
2
0
1
1
0
1
1
1
1
0
2
0
1
1
2
1
0
0
1
1
1
2
1
2
1
0
0
2
1
0
1
1
1
0
1
1
1
0
1
1
1
1
0
2
1
2
0
0
1
1
2
0
1
1
0
2
1
1
0
2
0
2
0
1
2
1
0
0
0
2
2
2
1
0
1
1
1
0
1
2
0
0
0
0
1
1
1
0
1
2
2
1
1
1
1
1
0
1
1
0
1
1
1
0
0
2
0
1
0
1
2
2
2
0
1
1
1
0
0
1
2
2
2
2
0
0
2
1
1
2
1
1
8
4
1
2
0
1
1
0
2
1
1
1
1
0
1
1
1
0
1
0
1
2
1
0
1
1
1
1
1
1
1
0
1
2
1
0
1
1
2
1
1
2
1
1
0
2
1
1
0
1
0
0
0
1
1
1
1
1
0
2
1
0
2
0
1
1
1
1
0
0
0
1
2
1
2
2
1
2
0
1
1
0
2
1
2
1
0
2
1
2
1
0
1
0
0
1
0
2
2
2
2
2
1
1
1
0
0
1
2
2
2
0
0
1
1
2
2
1
2
1
2
0
0
2
2
2
2
1
2
1
0
1
0
1
1
1
0
1
2
0
1
2
1
1
0
1
0
2
0
1
2
2
0
1
0
1
0
1
2
2
3
1
0
1
1
2
0
1
2
0
1
0
2
1
0
0
2
1
0
1
1
1
0
2
2
2
1
1
0
1
1
0
2
1
2
2
1
1
0
0
2
0
0
0
0
1
2
0
1
2
0
2
1
1
1
1
1
0
0
1
1
1
2
1
1
1
1
1
2
4
1
1
2
0
2
1
0
0
1
1
2
0
1
1
0
0
1
2
0
1
0
1
1
0
1
2
0
0
1
2
1
0
1
1
2
1
1
2
2
1
1
1
1
1
0
2
1
1
0
1
1
1
1
1
0
1
0
1
2
2
1
1
2
1
2
0
1
1
1
1
0
1
0
1
1
1
1
0
1
1
1
0
0
1
1
1
2
1
1
0
1
0
1
2
2
1
1
1
0
0
2
0
1
1
0
1
2
1
1
1
0
1
2
1
0
1
1
2
0
1
1
2
2
0
1
1
1
2
2
1
1
2
2
0
1
2
1
2
1
1
1
1
2
1
0
0
2
1
2
0
0
2
2
1
0
2
1
1
0
0
0
2
2
1
1
1
1
0
1
1
2
1
1
2
0
1
1
2
1
1
1
0
1
1
2
1
1
1
0
1
0
0
2
1
0
0
1
1
0
3
1
0
0
1
1
1
1
0
0
2
1
2
1
1
1
1
1
0
1
1
1
1
1
0
1
1
1
1
2
2
1
1
0
0
1
2
1
0
1
0
0
1
0
1
2
2
0
1
0
0
0
1
1
0
2
1
1
0
0
1
0
0
0
2
1
1
1
1
1
0
1
2
1
1
1
1
0
1
1
2
1
1
0
1
0
2
0
3
0
2
1
1
1
1
2
1
1
1
0
0
2
0
0
0
2
0
2
2
0
1
0
1
1
1
1
2
1
2
2
1
1
0
0
0
2
1
1
1
0
0
1
0
1
1
1
1
1
0
1
2
0
1
0
1
1
1
1
0
1
1
1
2
1
0
0
1
1
2
1
1
1
1
0
2
1
0
1
2
1
1
2
0
2
0
1
1
1
1
2
1
0
1
1
1
1
1
3
1
1
1
1
1
0
0
1
0
1
1
1
0
1
0
1
1
1
2
0
2
0
0
1
1
0
2
2
0
0
0
2
0
2
1
0
1
3
1
2
0
0
1
1
1
1
3
2
0
1
1
0
1
0
1
1
0
1
2
2
1
2
1
1
0
2
1
2
1
1
0
0
0
1
0
1
0
1
0
1
1
1
1
2
1
0
0
0
1
0
1
1
0
1
1
0
0
2
2
0
2
0
0
2
2
1
4
1
1
2
0
0
1
0
0
1
1
1
2
1
0
0
0
1
0
2
0
2
2
2
1
1
1
2
1
2
1
0
2
0
1
0
1
0
1
0
1
2
1
0
1
2
1
1
1
1
4
1
1
2
1
1
0
1
0
0
1
1
1
0
1
1
1
0
1
1
2
1
1
0
2
1
1
2
1
1
0
0
2
2
1
1
0
2
0
1
0
0
0
1
0
1
2
0
0
1
0
0
1
1
1
0
1
1
0
4
1
1
2
1
2
1
1
1
1
1
2
1
1
1
2
3
0
1
1
1
1
0
2
0
2
1
2
2
0
1
2
1
0
1
1
1
2
1
1
1
1
1
1
1
0
2
2
1
2
0
1
1
1
1
1
1
0
0
2
1
0
2
2
1
1
2
1
1
1
0
1
0
1
1
1
0
0
0
1
1
0
0
0
1
2
1
0
0
1
2
0
1
1
2
0
2
1
1
2
1
3
1
0
1
1
0
2
2
2
2
2
0
1
1
0
1
0
1
0
1
0
0
0
1
1
0
0
1
0
2
2
1
0
0
1
1
1
0
2
1
1
0
1
0
1
2
2
0
1
1
1
1
1
2
1
1
1
1
2
0
1
1
1
0
0
0
0
1
2
1
1
2
1
1
1
1
2
1
1
1
2
2
1
2
2
0
1
2
0
0
0
1
0
1
0
2
2
0
1
1
0
0
0
0
1
0
1
0
0
2
1
2
1
1
1
1
0
1
0
2
0
3
1
1
2
2
1
1
1
1
1
2
1
0
0
1
1
1
0
0
1
0
1
2
1
0
2
2
2
0
0
1
2
1
1
2
0
0
1
2
1
1
1
1
1
1
0
1
0
1
1
0
3
1
1
0
0
1
2
1
2
2
2
1
0
0
1
0
1
1
0
0
1
1
2
1
1
0
1
2
0
1
2
2
1
0
0
1
1
0
0
1
1
2
0
0
1
0
1
1
2
2
1
0
1
1
1
0
2
0
0
2
1
2
1
1
1
0
1
1
1
2
2
0
0
1
1
2
1
1
0
1
1
0
0
1
1
0
1
0
1
0
1
1
1
1
1
1
2
1
1
2
0
1
1
1
2
2
1
0
1
1
2
1
1
1
0
2
1
1
1
0
2
1
1
0
0
2
1
0
1
1
1
1
0
2
1
2
1
1
1
2
2
2
0
1
0
2
1
1
2
2
1
1
1
2
2
2
1
1
0
2
1
0
2
0
1
2
1
2
3
0
0
2
0
0
1
0
1
1
1
1
2
0
1
0
0
2
2
2
1
2
1
0
0
1
0
2
0
1
2
0
0
2
1
1
1
1
1
2
0
1
2
1
1
1
1
0
1
1
1
2
2
1
2
3
1
1
1
1
0
1
0
1
0
0
0
0
1
1
1
1
1
1
1
1
1
1
1
0
2
2
1
0
1
1
0
1
2
1
0
2
2
1
1
0
0
1
0
2
1
1
2
1
1
1
1
0
2
0
1
0
1
2
1
1
0
1
1
1
0
0
1
1
0
0
1
1
1
1
0
1
0
1
2
1
0
1
2
1
1
0
0
0
2
1
1
1
1
0
1
2
1
1
1
2
1
1
2
0
1
1
0
2
0
2
1
1
0
2
0
2
1
0
1
2
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
2
0
0
1
1
1
2
0
0
1
1
1
0
1
2
2
1
1
1
0
1
0
1
1
1
0
0
0
1
1
1
0
1
1
1
2
1
0
1
1
1
1
1
1
2
0
0
1
1
2
2
1
0
2
2
0
1
1
1
1
1
1
0
0
2
2
1
1
1
1
0
1
2
1
1
2
1
2
1
0
2
1
0
1
1
2
1
1
0
1
2
2
1
1
1
1
1
2
1
1
0
1
1
1
1
0
3
2
2
1
0
1
1
0
0
2
1
1
0
0
1
1
2
1
0
1
2
0
1
1
2
1
0
0
1
1
2
1
1
3
1
1
1
1
0
0
0
0
1
2
1
2
0
0
2
1
1
1
0
1
0
0
1
1
1
0
2
0
1
2
1
1
1
2
1
1
2
1
1
0
0
0
2
2
0
3
1
2
1
0
2
1
0
1
1
0
1
0
1
1
1
0
0
0
1
1
2
1
1
1
1
0
1
1
3
0
1
0
2
2
0
1
1
2
1
0
2
1
2
1
1
2
1
1
1
1
0
0
1
0
2
2
2
1
0
0
1
1
2
1
0
3
2
2
1
1
2
2
1
1
1
1
0
2
2
0
1
2
1
2
1
2
2
0
1
1
0
1
2
0
0
1
1
1
0
1
0
1
2
0
0
0
0
1
1
1
1
1
0
1
1
1
2
2
0
1
0
2
1
2
0
1
1
0
1
1
1
2
0
1
1
1
0
2
0
1
0
1
1
0
0
2
2
0
1
3
1
1
1
1
1
1
1
2
1
1
2
1
2
2
1
0
0
1
1
1
1
0
0
2
1
1
2
1
0
0
2
0
0
1
2
0
2
0
1
0
1
2
0
2
2
1
0
2
0
1
0
1
1
1
2
2
1
0
1
0
1
1
3
0
2
0
1
1
1
0
1
1
1
0
0
1
1
2
1
0
1
1
1
2
2
0
2
0
0
3
1
1
2
0
0
1
1
0
1
2
3
1
1
1
0
0
1
2
0
2
2
0
2
0
1
1
1
0
1
2
1
0
2
2
1
1
0
1
0
1
0
1
2
1
1
0
2
1
0
1
1
1
1
0
0
1
0
1
1
0
1
1
2
1
0
0
2
0
1
2
2
0
1
1
0
1
0
1
0
1
1
1
0
1
2
2
0
1
1
0
0
2
1
1
0
1
1
1
1
1
2
2
1
0
0
0
1
0
1
2
1
1
0
2
1
0
1
1
1
2
2
1
1
0
0
2
0
1
1
1
1
1
1
2
0
1
0
0
2
2
0
0
1
1
2
2
1
2
0
0
2
1
1
1
1
2
0
2
1
0
0
0
1
2
2
2
2
1
1
1
1
2
1
1
0
0
1
1
1
0
0
0
1
1
0
0
0
2
1
2
0
2
0
0
1
1
1
1
1
1
0
0
2
0
0
2
2
1
0
1
1
1
0
1
2
1
1
1
1
1
0
0
0
0
1
0
0
1
1
1
1
1
1
2
1
0
0
2
0
0
1
1
1
1
2
0
1
0
1
1
1
1
0
1
0
1
2
1
3
1
0
1
2
1
2
1
2
2
0
0
1
1
1
1
1
1
1
2
1
0
1
1
1
1
0
1
2
2
0
1
1
1
1
1
0
3
0
0
1
1
0
1
2
1
0
0
2
0
0
2
1
2
0
2
0
0
1
0
1
2
1
0
0
1
0
1
3
1
0
0
1
2
0
1
2
0
0
0
1
1
1
0
2
1
1
1
2
1
0
0
0
2
1
2
2
1
2
2
2
0
2
1
1
0
1
0
1
1
2
1
1
1
0
1
1
1
2
1
2
0
2
0
1
2
1
1
1
0
2
0
1
2
1
0
1
1
1
0
2
2
0
0
2
0
1
1
0
1
0
1
2
0
1
1
1
1
0
0
2
1
2
2
2
0
1
1
1
0
1
1
1
0
2
2
0
1
0
2
1
2
1
0
0
1
4
1
1
1
1
2
0
0
0
0
0
1
0
2
1
2
1
0
0
1
1
1
1
0
0
1
0
1
1
1
1
0
2
2
1
1
0
2
0
2
2
1
1
1
1
2
2
2
2
2
2
1
2
0
1
2
2
0
1
0
0
0
0
1
2
0
1
2
2
2
1
2
1
0
2
1
2
0
1
1
1
1
1
0
1
1
1
1
0
2
0
1
2
3
2
0
0
1
0
0
2
1
2
0
1
0
1
2
1
3
1
1
0
0
2
1
1
1
0
2
0
1
1
2
0
0
1
0
2
1
0
1
0
2
2
1
1
1
1
1
1
0
0
1
2
1
0
1
1
1
1
2
0
2
1
0
0
1
2
2
2
1
0
2
1
1
0
1
0
1
0
1
1
1
0
2
1
1
2
1
1
1
1
1
1
1
0
0
1
1
1
0
1
0
1
1
0
0
1
1
1
2
1
1
2
0
1
1
0
2
1
1
1
1
1
1
2
1
1
1
1
2
0
3
1
1
0
1
2
2
1
1
1
2
1
0
0
0
1
1
0
0
2
2
0
0
1
0
0
1
2
0
0
1
1
1
0
2
1
2
1
0
0
1
0
2
1
2
2
0
1
1
0
2
2
1
0
2
1
1
1
0
1
2
2
0
0
0
2
1
1
1
1
1
1
1
2
0
0
1
2
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
1
2
1
1
0
1
2
2
1
3
0
1
1
1
1
2
1
1
1
0
0
0
2
0
1
2
1
1
4
1
1
1
1
1
1
1
0
1
0
0
1
0
1
0
1
1
1
0
1
2
1
1
2
2
0
0
1
2
1
0
1
1
2
1
1
0
1
1
1
1
2
1
0
1
0
1
0
2
0
1
1
1
2
2
1
1
0
2
1
2
0
1
1
2
2
1
1
0
1
1
1
2
0
1
1
2
1
2
1
2
1
2
5
1
1
1
2
2
1
1
1
1
1
2
0
2
0
2
0
0
0
0
1
0
0
2
0
1
1
0
0
2
2
1
0
2
1
1
0
0
0
2
1
1
1
1
0
0
0
0
1
2
2
1
1
2
0
1
1
1
2
0
1
0
1
1
1
1
2
1
1
1
1
0
0
0
0
2
0
0
1
2
2
1
1
2
1
1
0
1
1
0
2
2
1
1
2
2
2
1
1
1
0
0
1
2
1
0
2
1
2
0
0
0
0
0
2
1
2
2
0
1
0
1
1
1
1
0
0
1
0
0
0
1
0
0
2
1
1
1
1
1
2
1
1
1
2
1
0
1
1
1
1
1
2
0
1
2
3
0
1
1
1
0
2
2
1
1
0
0
2
1
1
1
2
1
0
0
0
1
1
0
2
2
1
1
1
0
1
0
2
1
1
1
0
2
1
2
1
0
0
2
1
1
1
1
0
2
0
1
2
1
2
1
1
1
2
2
1
1
0
0
2
1
1
0
0
0
1
1
1
2
1
1
2
0
1
1
2
1
0
2
1
1
0
2
0
2
1
1
0
1
1
0
0
1
1
2
2
1
1
1
0
1
1
0
1
1
0
1
1
0
1
1
1
1
1
0
1
1
2
1
0
1
0
2
1
0
1
1
0
1
2
1
2
1
0
0
1
2
0
2
0
1
0
1
2
1
2
2
1
0
2
0
0
1
2
1
2
1
1
1
1
2
1
0
0
2
1
1
1
1
3
0
0
0
1
1
1
2
0
0
1
1
1
1
0
0
1
1
2
1
1
2
2
0
1
2
0
0
1
1
1
1
2
0
1
2
1
0
2
2
0
2
0
2
0
0
1
0
1
2
1
0
1
2
0
0
1
2
0
1
1
1
1
1
3
1
1
1
1
1
1
1
1
2
0
0
1
0
1
7
1
1
0
2
1
1
1
1
2
2
1
1
1
1
1
1
0
1
2
1
2
1
1
0
0
1
0
1
2
2
1
1
1
0
0
0
1
0
1
1
0
1
2
2
1
0
1
0
2
1
1
1
1
3
0
0
2
1
0
2
0
0
1
1
1
1
2
1
1
2
1
0
1
1
1
0
2
2
2
1
2
1
1
1
2
1
1
0
1
0
0
1
0
2
2
1
0
1
1
3
1
2
0
0
1
0
0
1
1
0
1
0
0
0
2
1
1
1
1
3
2
1
0
1
1
0
0
2
1
1
1
1
1
2
0
2
1
1
1
2
0
1
1
1
2
1
1
2
0
2
1
2
1
1
0
2
1
0
0
0
1
0
1
1
1
0
2
2
2
1
2
1
1
1
1
0
2
2
1
1
0
1
0
2
0
1
1
1
1
0
0
1
0
1
0
2
1
2
0
0
2
1
1
2
1
2
0
0
0
1
0
2
1
0
1
2
1
2
1
0
1
0
0
1
1
1
2
1
2
1
1
1
1
2
2
1
0
1
2
0
1
1
1
1
0
1
2
1
1
1
1
2
0
0
1
1
2
0
2
1
1
0
1
1
1
0
2
1
0
1
0
1
2
0
1
1
1
0
1
0
1
2
1
1
1
2
0
1
0
1
1
1
0
1
3
0
2
0
1
2
0
2
1
0
0
1
2
1
1
0
0
2
0
1
2
2
1
2
1
2
1
1
2
0
0
0
0
1
1
1
2
1
1
1
3
2
0
3
1
2
1
0
2
0
0
1
2
0
1
0
2
0
1
0
0
1
0
1
0
1
2
1
1
1
1
1
1
1
0
2
1
2
1
2
1
3
1
0
0
3
0
0
2
1
0
2
1
1
1
3
0
0
0
1
2
1
0
1
0
2
0
0
1
1
0
1
2
1
0
0
0
1
1
1
2
1
2
1
1
1
0
1
2
0
2
1
0
2
1
0
1
1
0
1
0
1
4
0
1
2
1
1
0
1
1
1
0
1
1
1
1
2
2
0
1
0
1
4
1
0
0
2
2
0
0
0
1
2
1
0
1
2
2
2
1
0
0
0
2
1
1
1
1
1
0
2
1
1
1
2
1
1
1
1
2
1
1
0
1
1
2
1
2
1
1
1
1
0
1
0
0
0
0
0
0
2
0
1
0
1
0
2
0
1
2
0
0
1
1
1
2
1
0
1
0
1
1
2
1
0
1
1
1
1
0
1
2
2
1
1
2
1
2
0
1
0
1
1
0
1
1
1
1
1
0
0
0
0
0
1
2
1
1
0
0
1
1
0
0
1
0
1
0
1
1
2
1
1
1
0
1
1
0
0
1
0
2
1
0
2
0
2
1
0
1
0
2
1
1
1
1
0
1
0
1
1
0
0
0
2
0
0
0
0
1
0
0
2
1
1
2
1
1
1
1
1
0
1
0
0
1
1
0
1
2
1
0
0
1
1
1
1
1
1
1
0
0
1
0
0
2
1
2
1
1
1
1
1
1
1
1
3
1
2
0
1
2
1
1
2
2
0
2
1
0
1
1
1
1
2
2
1
1
2
1
0
0
2
1
2
1
1
1
2
1
1
1
0
2
1
1
0
1
1
1
1
0
0
2
1
0
1
1
2
1
1
1
1
1
0
1
1
0
0
1
2
1
1
1
2
1
0
1
1
0
1
1
2
1
1
1
1
1
2
0
2
2
0
2
2
0
1
1
2
1
0
4
2
0
0
1
1
1
0
1
1
2
0
2
1
1
0
1
0
1
0
2
3
1
2
1
2
1
1
2
0
0
1
0
1
1
0
2
2
2
1
1
1
1
2
2
1
0
1
1
2
1
0
0
0
0
0
1
1
0
0
2
0
2
0
2
0
1
1
0
2
0
2
1
1
1
1
2
0
3
1
1
1
1
0
2
1
1
0
1
1
1
1
1
0
1
0
0
0
0
1
2
1
1
0
1
0
1
2
1
1
1
1
2
2
0
0
1
2
1
0
1
1
2
2
1
0
2
1
2
1
0
2
1
1
2
1
0
1
0
2
2
1
0
1
1
2
1
1
1
0
1
1
2
0
1
2
0
2
1
2
2
0
1
2
1
1
2
0
0
1
0
0
1
2
1
0
0
0
0
0
0
6
1
2
2
2
2
1
2
2
0
0
1
1
1
1
1
1
1
1
2
1
0
0
1
1
0
1
2
1
2
0
2
0
1
2
1
1
1
2
0
1
1
1
0
2
0
1
1
3
0
1
1
1
0
2
1
0
0
1
1
0
1
1
0
0
1
1
1
0
2
1
1
1
2
1
2
0
2
1
1
0
1
1
0
1
0
3
1
0
0
0
0
0
1
2
1
1
1
1
1
0
1
1
0
1
1
1
1
0
2
1
1
2
1
1
0
1
0
1
0
1
1
0
0
1
1
0
0
1
1
1
1
1
1
0
0
2
2
2
1
1
0
2
0
1
2
0
2
1
1
1
0
1
1
1
0
1
0
0
1
2
1
2
1
1
1
0
1
1
1
1
0
1
1
1
0
0
1
2
1
2
1
1
0
2
1
1
0
0
3
2
0
2
1
1
1
1
1
1
0
1
0
0
2
1
0
1
2
1
1
1
1
0
1
1
1
1
0
0
1
1
2
2
1
1
1
1
0
2
1
1
2
2
2
0
1
2
2
2
2
1
0
1
1
0
1
2
0
1
1
1
1
1
2
1
1
0
1
0
1
0
1
2
1
0
1
0
1
1
2
2
2
0
1
0
0
1
1
0
0
1
0
1
1
1
2
0
0
1
1
2
2
0
1
1
0
2
2
1
0
0
1
0
0
1
0
1
1
1
1
1
1
1
0
0
0
1
1
0
1
0
1
0
1
2
1
0
0
1
0
1
1
2
1
1
1
2
1
2
2
2
2
1
1
1
1
1
0
0
2
0
2
1
1
1
0
1
0
1
1
1
1
1
1
0
1
0
0
2
1
1
2
1
2
2
1
2
1
0
0
2
0
0
1
0
2
1
1
2
1
1
2
1
0
1
1
0
2
1
1
0
2
1
2
1
2
1
0
1
1
0
0
2
1
2
2
0
2
1
2
1
1
1
2
0
1
0
1
1
1
1
1
1
1
2
0
1
2
0
0
1
0
1
1
1
1
1
1
0
0
1
1
1
0
1
1
2
1
1
2
2
1
2
2
1
2
1
1
1
1
0
1
1
1
1
2
1
0
3
0
0
0
2
0
1
0
1
0
0
0
0
0
1
0
2
1
0
0
2
2
1
1
1
0
1
0
1
0
0
2
1
2
2
1
0
0
2
2
1
0
1
1
1
1
0
1
0
1
1
1
2
2
1
0
1
0
0
1
1
0
2
0
1
1
1
2
2
1
1
1
1
0
0
0
0
1
1
1
1
2
0
1
1
1
1
0
0
2
0
2
1
1
1
0
3
0
1
0
0
1
2
0
0
1
1
2
0
2
1
0
1
1
2
2
0
0
1
1
1
1
0
1
0
1
0
2
1
2
1
2
2
1
2
0
1
2
0
2
2
2
1
2
1
1
1
0
0
0
0
1
2
1
0
0
1
1
2
0
1
2
1
2
0
1
1
1
1
1
0
2
2
2
1
3
1
2
1
1
1
1
0
2
1
1
0
1
0
1
0
1
1
1
1
1
1
1
0
1
1
0
1
1
0
1
2
2
0
1
1
2
4
0
1
1
1
0
0
2
1
0
0
1
0
2
0
0
0
2
1
0
2
0
2
1
0
2
1
4
1
0
2
0
2
0
2
1
1
0
1
1
0
3
2
1
1
1
0
1
1
1
1
0
1
1
1
2
0
1
0
2
1
2
0
0
1
0
2
2
2
2
1
1
1
0
1
1
1
0
1
1
2
0
1
0
1
1
1
0
1
0
0
1
1
1
1
2
1
0
2
1
0
1
0
1
0
1
1
0
4
2
0
1
0
1
0
1
1
1
0
0
1
0
1
1
0
0
2
2
2
2
0
2
2
1
1
1
1
2
0
2
1
2
2
2
0
2
1
1
2
2
0
1
2
1
1
0
0
2
1
1
1
0
1
1
0
1
1
1
1
1
3
1
2
2
1
1
1
2
0
0
0
0
0
1
1
1
0
1
0
1
1
0
1
0
1
2
1
1
1
1
2
2
1
1
1
2
3
1
2
0
1
2
1
0
0
2
0
1
1
2
1
2
0
0
0
0
2
0
1
1
2
0
1
1
1
2
2
0
0
0
2
3
0
0
0
2
1
1
1
2
2
1
0
2
1
2
0
2
0
1
1
2
0
0
1
0
1
0
2
1
0
2
1
1
2
2
0
1
1
0
2
0
1
0
1
1
1
1
2
2
2
1
1
0
1
1
2
0
0
2
0
0
1
1
1
0
1
2
2
2
2
1
2
1
1
1
1
1
1
1
1
1
1
0
1
2
1
2
3
2
2
0
2
2
0
2
1
2
1
1
1
2
1
1
2
1
0
1
1
3
1
1
1
2
0
1
1
0
1
1
1
0
1
2
3
1
1
1
0
1
0
1
1
0
1
0
0
1
2
1
1
0
1
2
0
1
1
1
2
2
1
0
2
2
1
0
2
0
0
0
2
1
1
0
1
1
0
1
1
0
0
0
1
0
1
0
0
1
2
0
2
2
1
2
2
1
1
0
0
1
1
0
2
1
2
2
2
1
0
1
1
1
1
0
1
2
1
2
1
1
1
1
0
0
1
0
1
1
2
1
1
1
0
1
1
0
0
2
1
0
1
1
1
2
1
1
2
0
1
0
0
1
0
1
1
1
1
1
2
1
0
2
1
1
1
1
0
0
0
1
0
1
0
1
2
1
1
0
0
2
2
1
2
1
0
0
1
0
2
0
0
0
0
1
1
1
2
2
1
1
1
1
0
2
1
1
2
1
0
1
0
1
1
0
1
1
2
1
0
1
0
0
1
0
1
1
1
0
2
1
3
0
0
1
1
2
2
1
0
1
1
0
0
1
3
2
2
1
1
0
0
2
0
0
1
1
0
0
1
0
1
1
1
0
1
1
1
1
2
2
1
2
2
2
2
1
2
1
2
2
1
1
1
1
1
0
1
1
0
1
1
2
1
1
0
1
0
1
0
1
1
1
1
0
2
0
1
0
2
1
0
2
1
2
2
1
1
2
0
1
2
1
1
1
2
1
2
0
2
0
1
1
1
1
2
1
1
1
1
0
1
2
1
0
2
1
1
2
2
1
1
1
1
2
0
1
3
1
2
1
1
1
2
0
1
1
1
1
1
2
1
2
1
1
0
1
0
1
0
2
3
0
1
0
1
1
0
0
0
1
1
1
1
0
0
2
1
1
0
1
2
1
2
1
0
1
1
2
1
1
0
1
1
2
0
1
2
1
2
1
2
1
1
1
2
0
1
1
1
2
1
1
0
1
0
1
1
0
1
2
2
0
2
1
1
1
2
2
1
1
0
2
2
2
0
2
0
1
0
1
1
1
2
0
1
0
1
1
1
2
1
1
0
2
2
0
2
0
2
2
2
1
2
0
1
1
0
2
1
0
1
2
1
0
0
0
2
0
0
1
1
0
0
1
1
0
0
0
1
1
0
2
1
1
0
2
0
1
1
0
1
1
1
1
1
2
0
2
2
2
0
2
1
0
1
0
1
0
1
0
1
1
1
1
1
0
1
0
1
1
1
1
0
2
2
1
2
1
0
1
2
1
2
4
0
0
1
1
2
0
0
2
1
1
1
0
2
2
0
1
1
2
1
1
2
1
3
1
0
1
1
0
1
1
0
2
1
0
1
1
1
0
0
1
0
2
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
0
1
2
0
2
1
1
1
2
2
2
1
2
1
1
1
0
0
0
2
1
0
1
3
2
0
1
0
0
0
2
1
1
1
1
0
2
1
0
2
1
0
1
1
5
2
0
2
1
1
1
0
2
2
0
0
0
1
1
0
0
1
1
1
1
1
1
2
1
2
0
2
2
1
1
0
0
2
1
0
0
0
0
0
1
0
1
0
2
1
1
1
1
0
2
0
1
1
1
2
2
0
2
1
1
0
0
1
2
0
1
1
0
0
1
0
1
1
1
0
2
0
0
2
1
0
1
0
1
2
2
1
1
2
0
2
1
1
1
3
1
1
2
2
0
0
1
2
0
1
3
1
2
2
1
0
1
0
1
1
1
1
1
2
0
1
1
0
1
0
2
0
0
0
2
1
1
1
1
0
0
1
1
0
2
1
1
2
2
0
0
1
1
0
1
1
1
1
1
0
1
1
2
2
1
1
2
1
0
0
0
2
0
1
1
1
1
1
1
0
2
1
1
0
2
2
2
1
3
2
3
1
1
2
1
1
0
2
1
0
0
1
2
0
0
1
1
1
1
1
2
1
1
1
1
1
1
2
1
2
0
1
2
0
0
1
1
1
0
0
0
1
1
0
1
2
2
0
1
1
2
1
1
1
2
0
1
2
0
0
2
0
1
3
1
2
1
1
1
1
1
0
2
1
2
2
1
2
0
2
2
0
1
2
0
0
1
1
1
1
1
1
1
1
2
2
2
1
1
2
0
0
1
1
0
0
1
1
0
1
0
1
0
0
1
2
0
0
1
0
0
0
1
0
2
1
1
1
2
2
2
2
1
0
1
2
1
1
0
2
0
0
1
1
0
0
1
1
1
1
2
1
1
2
1
0
1
2
0
1
0
1
0
2
0
1
0
2
1
2
1
1
2
0
1
1
2
2
0
2
1
1
3
2
2
0
3
1
1
0
2
2
0
1
0
0
1
1
2
1
2
1
0
1
2
0
0
0
0
1
0
0
0
2
0
0
1
0
0
1
1
0
1
1
1
1
1
0
1
1
1
1
1
0
0
2
0
1
1
1
2
0
1
1
0
1
1
0
1
1
3
2
1
3
1
0
1
0
0
0
0
0
1
1
1
0
2
0
1
0
1
1
1
0
0
1
2
1
1
1
2
1
0
2
1
0
1
0
1
1
0
1
2
2
1
0
1
0
1
2
1
1
1
1
1
2
1
2
2
1
2
3
2
1
1
0
2
3
1
2
0
0
1
2
1
0
1
1
1
2
2
1
2
1
1
2
2
0
0
0
1
1
4
1
0
1
2
1
3
2
0
0
2
1
1
1
0
2
1
2
2
1
0
1
0
2
1
1
0
1
1
1
2
2
0
1
0
0
2
1
1
1
2
0
2
0
2
1
2
0
2
0
0
1
0
1
2
2
1
2
2
2
1
2
1
1
1
1
1
0
0
2
0
1
1
2
1
0
1
2
1
1
0
1
1
0
1
1
2
1
1
0
1
1
2
1
0
2
1
1
0
1
1
1
1
2
2
0
1
0
1
1
1
1
1
1
1
2
1
1
0
1
1
1
0
1
1
0
0
1
1
2
2
0
2
1
2
0
1
0
0
1
2
1
1
0
0
0
2
2
1
1
1
1
1
1
2
1
1
2
0
0
1
1
1
0
1
3
2
0
0
1
1
1
0
1
2
1
0
0
0
1
1
1
1
1
2
1
2
2
1
1
1
1
1
2
1
0
1
0
0
0
1
0
1
2
0
3
1
1
1
1
0
3
1
2
0
1
2
1
1
3
1
1
0
1
2
1
2
1
0
0
1
1
1
2
0
1
1
2
1
1
1
2
1
1
1
1
1
0
1
2
1
2
0
2
1
1
1
0
1
0
2
2
2
1
1
2
1
2
1
2
2
1
1
2
1
0
0
2
1
0
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
2
0
2
2
2
1
1
3
1
1
1
0
2
0
1
1
0
0
1
1
1
1
0
3
1
0
0
3
1
0
2
1
1
1
1
1
0
1
3
0
1
1
0
2
1
1
0
2
0
0
1
1
0
1
2
0
1
0
1
0
1
0
0
1
2
0
0
1
1
0
0
2
0
2
2
0
2
1
0
0
1
2
0
1
1
1
2
1
3
2
0
1
2
0
1
2
0
1
0
1
0
1
0
0
2
1
0
1
0
2
0
0
2
1
1
1
2
0
0
1
0
0
1
1
1
1
0
1
0
1
1
1
0
2
0
1
1
0
1
3
1
2
0
0
1
1
1
1
0
1
2
0
0
0
0
1
1
1
2
1
0
1
2
1
1
2
1
1
2
1
0
0
1
0
1
1
1
2
0
1
1
2
4
2
1
2
1
1
1
1
1
1
2
1
0
2
1
1
2
1
1
1
1
0
1
2
0
1
2
1
1
0
1
0
1
1
0
1
1
1
1
1
1
1
1
1
1
0
0
2
1
2
1
1
3
1
1
0
1
0
2
0
0
1
1
2
2
1
1
1
1
2
0
2
2
0
1
0
1
2
1
1
1
2
0
0
1
1
0
1
2
1
1
0
1
0
1
2
1
0
1
1
0
2
1
1
1
1
1
0
2
1
1
2
2
1
1
1
1
0
2
1
0
1
0
2
0
1
0
1
2
1
1
1
0
2
1
2
1
2
1
2
1
0
1
2
1
0
2
2
1
0
1
3
0
0
2
1
1
1
0
2
0
2
0
1
1
0
1
2
1
2
1
1
1
1
1
1
1
0
0
0
0
1
0
1
2
1
2
0
1
0
0
0
2
1
0
1
2
2
1
1
1
0
1
2
0
0
3
1
1
2
1
0
1
2
2
1
1
2
3
0
0
0
0
1
0
1
2
2
0
1
1
1
0
1
0
1
2
1
1
1
1
1
1
2
0
1
1
1
0
1
0
0
1
1
1
1
1
1
2
1
2
2
0
0
1
0
2
1
1
1
1
1
2
1
1
0
1
1
2
1
0
2
0
0
1
1
1
0
1
0
1
1
1
1
1
0
0
2
2
1
1
1
2
0
1
1
0
1
1
1
0
1
2
1
1
2
1
1
0
0
1
1
1
1
0
0
0
0
0
1
1
0
2
2
1
0
2
1
0
1
1
2
0
2
0
1
1
0
1
1
1
1
0
1
2
2
1
1
0
0
1
1
0
2
0
0
1
2
1
1
1
2
1
1
1
0
0
1
0
0
0
1
1
1
1
0
0
1
1
1
3
0
1
1
1
0
0
1
3
2
3
1
0
2
0
1
1
0
1
2
1
2
0
0
1
2
0
1
1
1
1
3
2
1
1
1
0
1
2
0
1
1
1
0
0
2
0
2
1
0
1
1
1
1
2
0
0
3
0
1
2
2
2
0
1
1
2
0
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
1
1
0
1
0
2
1
0
0
1
0
1
1
1
1
0
0
2
2
0
1
1
1
0
1
2
2
2
1
1
2
1
1
1
1
0
2
1
1
2
2
0
2
1
1
0
1
0
1
1
1
2
0
1
0
0
1
1
1
1
0
1
1
1
0
0
1
1
0
1
1
0
1
1
0
1
2
2
1
1
2
2
0
0
1
1
1
1
1
0
1
1
2
0
0
1
1
0
0
1
1
1
1
2
0
1
3
2
0
1
1
2
0
2
2
1
0
2
1
2
0
2
0
1
1
0
1
1
1
1
2
1
2
0
2
2
0
1
1
0
0
1
1
1
0
0
0
0
2
1
2
0
2
2
1
1
1
2
0
1
1
1
1
1
0
1
2
1
1
2
0
2
1
1
0
2
2
0
0
1
2
2
1
1
1
1
1
1
0
1
2
2
2
1
1
0
0
1
2
0
3
1
1
0
1
2
1
1
1
1
2
2
2
1
1
1
1
1
0
2
2
1
2
2
1
0
1
0
1
1
2
2
1
1
2
0
1
0
1
1
2
1
0
2
1
2
2
1
1
2
0
1
1
1
1
1
1
2
0
0
1
1
1
0
0
1
1
0
1
1
2
1
1
1
1
1
2
1
2
1
2
2
1
1
1
2
2
0
1
1
2
0
1
0
0
1
2
0
0
1
1
1
1
1
2
2
4
1
0
1
2
1
0
1
1
2
1
1
1
1
1
1
2
2
0
1
1
1
0
0
2
1
1
1
2
1
1
2
0
0
2
1
1
1
2
1
0
1
2
1
0
1
2
1
0
2
1
2
2
1
0
1
0
1
2
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
3
0
0
0
1
2
0
1
0
0
2
1
2
1
1
1
2
2
3
0
0
1
1
1
1
1
1
1
0
1
1
1
1
0
1
1
0
2
1
1
1
1
1
2
0
1
2
1
1
0
1
1
1
1
1
1
0
2
3
1
0
1
1
1
1
2
1
2
2
0
2
0
1
0
1
2
1
0
1
2
1
0
0
2
1
0
1
0
1
1
2
1
0
2
1
2
0
2
1
1
0
0
1
0
1
2
2
1
1
1
0
1
1
2
0
0
0
1
1
0
2
1
0
1
2
1
0
1
0
1
0
0
0
1
1
0
1
1
2
1
2
0
0
1
2
0
1
1
0
1
1
0
0
1
2
1
2
1
2
2
2
0
0
0
1
2
1
0
0
5
0
0
2
2
1
1
2
2
0
1
1
0
1
0
0
2
1
1
0
0
0
2
1
1
1
0
0
1
1
1
1
0
0
2
0
1
2
3
0
1
0
1
0
2
2
1
0
1
1
0
1
0
2
1
1
0
0
1
1
2
2
1
1
0
0
2
0
0
1
1
0
2
1
1
1
1
1
1
2
0
1
2
1
0
1
1
2
2
1
0
2
2
0
1
1
0
1
2
1
2
0
1
2
1
1
1
1
1
1
1
3
1
1
2
1
0
1
1
1
2
2
2
0
0
1
2
0
1
0
3
0
2
0
1
2
0
2
2
1
1
2
2
1
1
1
0
1
0
0
0
1
2
0
2
2
1
1
0
1
1
2
0
2
1
0
1
1
1
1
2
2
1
2
1
0
0
1
2
2
1
0
1
1
1
1
2
2
1
1
0
1
2
1
0
1
3
1
2
1
2
1
0
1
1
0
1
1
0
1
0
0
2
1
1
0
1
0
1
2
0
1
1
2
1
1
1
2
0
1
1
0
1
0
1
1
1
0
1
2
0
1
2
1
1
2
1
2
2
0
1
1
2
3
1
2
2
1
0
2
2
1
0
2
1
1
0
0
0
1
1
1
2
1
1
0
2
0
1
1
0
0
2
1
1
1
1
0
1
1
1
0
2
1
1
1
0
1
1
0
2
1
0
1
0
2
1
0
2
0
1
1
1
0
1
2
2
1
1
0
1
1
0
2
4
1
0
1
2
0
0
0
1
0
0
2
1
2
1
0
2
2
2
0
0
1
0
2
1
2
2
0
1
2
1
1
0
0
1
2
0
1
1
0
1
0
1
0
1
1
1
1
1
1
1
2
1
2
1
0
0
1
1
0
0
1
2
2
0
2
0
0
1
1
1
0
1
0
0
1
3
0
0
1
1
0
1
0
1
1
0
2
1
1
2
2
1
2
0
2
0
1
1
1
1
1
1
1
0
0
0
2
1
1
1
1
0
1
0
1
1
1
2
2
1
0
1
1
1
2
2
2
1
0
0
0
1
0
2
1
1
1
0
1
2
1
0
1
2
2
2
1
1
1
2
1
2
0
1
1
0
0
2
1
0
1
1
1
0
1
2
1
1
1
1
2
1
0
1
2
2
0
2
1
1
1
1
2
0
1
1
0
1
2
1
0
1
1
1
0
1
1
2
1
1
2
1
1
1
1
1
0
0
2
2
0
0
1
2
1
1
0
0
1
3
1
1
1
0
0
2
1
2
0
1
1
0
0
1
1
0
0
0
0
2
1
1
0
1
0
0
0
2
1
1
2
1
1
2
1
1
0
0
1
1
0
2
2
0
0
2
0
1
1
1
2
0
1
1
4
2
2
1
1
1
1
0
1
2
1
0
1
1
1
1
0
0
0
1
0
1
1
0
1
0
1
1
0
0
1
1
1
1
1
1
1
1
0
0
1
3
2
1
1
1
0
2
0
0
0
0
2
0
2
0
1
2
0
3
2
2
1
0
1
0
2
2
1
2
1
0
0
2
2
1
2
0
2
2
0
0
1
1
1
2
1
0
0
0
1
3
1
1
0
1
1
1
0
1
2
1
1
1
2
1
0
1
2
1
0
1
1
2
0
0
1
1
1
1
1
0
1
0
0
1
1
0
0
1
2
1
1
2
0
1
0
1
0
1
1
1
0
1
1
1
0
1
1
0
0
2
0
0
1
2
2
2
0
0
0
0
1
0
2
1
0
0
0
0
1
2
2
1
1
0
1
0
1
1
0
1
1
1
1
0
1
2
2
1
1
0
0
2
0
1
1
1
0
1
0
2
2
0
0
0
0
0
0
2
0
1
0
0
1
1
1
2
1
1
0
2
2
1
2
0
0
0
1
1
1
0
2
0
3
1
1
2
0
1
1
1
1
0
1
2
0
1
0
2
1
1
1
1
1
0
1
1
1
1
1
0
0
2
0
1
0
2
1
0
0
2
1
2
1
1
1
2
2
0
0
1
2
2
1
0
1
1
1
1
1
2
3
2
0
0
1
2
2
1
1
1
2
1
1
2
0
0
0
2
1
1
2
0
1
1
0
1
2
1
1
1
1
0
1
2
1
1
0
1
1
0
1
2
0
1
2
0
2
0
0
1
0
1
1
1
1
1
1
0
0
2
2
1
1
1
2
1
0
0
1
0
1
1
1
1
1
2
0
2
1
1
1
1
1
1
1
1
1
1
0
1
1
1
2
2
1
2
1
2
0
0
1
1
0
2
1
1
0
1
0
0
1
1
1
0
2
1
0
1
1
0
1
0
2
1
0
0
1
1
0
0
1
1
1
1
2
1
0
1
1
1
2
1
1
2
0
1
0
2
1
1
1
1
0
2
1
1
1
1
1
1
1
1
1
1
0
1
1
2
1
1
1
0
0
1
1
0
1
0
0
2
0
0
0
0
2
2
1
1
1
0
0
2
2
1
1
1
1
0
2
0
0
2
1
2
1
1
1
1
2
1
1
1
2
1
1
0
1
1
1
0
1
1
2
2
0
1
1
0
1
1
2
1
0
1
1
2
2
4
0
2
1
0
0
1
2
1
1
1
1
1
1
1
0
2
1
0
0
1
1
0
2
0
2
1
1
1
0
1
2
0
1
1
0
1
2
0
1
2
1
1
1
2
2
0
0
0
1
0
0
1
1
2
1
1
2
1
0
2
0
1
0
0
0
0
1
1
0
0
0
2
1
2
0
1
0
1
0
0
2
0
1
2
1
1
2
0
1
1
0
0
1
1
2
1
1
1
1
1
0
1
2
2
2
1
0
0
2
1
1
1
1
3
1
0
1
1
1
1
1
1
2
2
1
1
0
2
1
0
1
1
1
0
2
1
1
1
1
0
0
1
0
1
2
1
1
2
3
1
0
0
0
0
0
2
0
0
2
2
1
1
1
0
1
2
1
1
1
3
1
0
1
2
0
1
1
1
0
1
1
1
1
1
0
1
2
0
0
1
1
2
1
1
1
2
0
2
1
1
0
1
1
1
0
1
0
1
0
0
1
1
1
2
1
1
0
1
1
0
1
2
1
1
0
1
1
0
1
2
0
2
1
1
1
2
1
1
0
1
1
1
0
0
0
1
1
1
2
1
2
1
2
0
0
0
1
1
1
2
0
2
0
1
0
1
1
1
0
1
2
2
2
0
1
1
1
1
0
0
1
0
1
2
0
1
1
1
0
0
2
0
2
0
2
1
1
2
1
1
1
2
1
1
2
2
0
0
0
1
2
1
0
1
0
2
1
0
1
1
1
2
1
1
0
1
0
1
0
1
1
1
1
2
1
0
1
1
2
2
1
1
1
0
0
2
1
1
0
1
2
3
0
2
1
0
2
1
0
2
2
0
0
1
2
1
0
5
2
2
2
1
2
1
1
0
3
1
1
1
0
1
1
1
1
2
1
1
2
0
0
0
0
0
1
0
2
2
1
0
0
2
1
1
1
1
2
1
2
0
1
0
0
1
2
1
1
2
1
0
2
1
1
0
2
0
0
1
4
0
1
1
1
0
2
2
2
0
1
2
2
1
2
1
2
1
0
1
1
0
1
1
1
2
2
2
2
1
0
0
1
0
2
1
2
1
2
0
1
2
2
1
1
1
1
2
0
2
0
2
1
1
0
0
0
0
1
0
0
1
2
1
1
1
1
2
1
0
1
1
1
1
1
2
1
2
0
0
0
2
0
1
2
0
1
0
1
0
0
1
1
0
2
1
1
1
2
2
1
2
1
1
2
1
2
0
0
1
1
1
1
0
1
2
0
0
1
1
1
2
1
2
1
0
2
0
1
1
0
1
1
0
0
1
1
2
0
1
1
0
1
1
1
1
1
2
1
0
0
2
0
0
0
2
0
1
1
1
2
2
2
0
1
2
1
1
1
0
1
2
1
1
0
1
1
0
0
0
2
0
1
2
2
1
0
1
2
2
1
0
1
1
1
1
2
1
1
1
0
0
0
0
2
1
1
1
1
0
2
1
0
1
1
0
2
1
1
0
0
1
1
2
0
0
2
1
1
1
2
0
0
0
1
1
0
1
0
1
2
1
1
1
1
2
1
0
4
2
2
0
1
2
1
1
2
0
1
1
1
1
0
2
0
0
1
2
0
1
1
1
1
1
1
1
2
0
1
1
1
1
1
3
0
0
1
1
1
0
1
0
1
1
2
1
0
0
1
0
1
0
0
1
2
2
1
0
1
2
0
1
1
1
1
1
0
0
1
1
1
0
1
1
1
2
1
0
3
0
0
1
0
0
1
1
2
0
2
2
2
1
1
1
0
1
1
1
0
0
0
2
0
0
1
2
1
2
0
2
0
1
0
0
0
0
2
0
1
0
1
1
2
0
2
1
1
2
1
1
0
1
0
1
1
2
1
0
2
1
1
2
2
2
1
0
2
1
1
1
2
1
1
1
0
2
2
0
2
2
0
2
0
1
1
1
1
1
1
0
0
0
2
0
2
1
1
1
1
1
1
1
2
2
3
2
1
2
1
1
2
0
1
0
1
1
2
1
1
1
0
1
0
2
0
2
1
1
0
1
2
1
1
0
1
0
1
2
1
0
1
0
0
1
1
0
0
1
1
0
0
1
2
1
0
1
2
0
1
1
0
0
2
1
1
2
1
2
1
1
0
1
1
1
0
1
0
1
0
1
2
1
1
1
0
1
1
2
0
1
2
0
1
0
1
2
1
1
0
1
0
1
1
0
0
2
0
2
2
3
1
1
1
1
2
2
2
0
2
0
0
1
0
1
1
1
2
2
2
1
2
1
1
2
0
0
0
4
1
1
2
1
0
2
0
0
2
1
0
1
0
1
0
1
2
3
0
1
4
2
2
2
0
1
1
0
0
0
0
0
1
1
1
1
1
2
0
1
0
0
2
1
1
1
1
1
1
1
1
0
0
1
0
1
2
0
1
1
2
2
0
0
1
0
1
1
2
1
1
1
0
1
2
1
1
1
1
0
0
1
1
1
0
1
0
2
0
1
1
0
1
1
1
1
0
2
2
1
2
1
0
0
1
1
0
1
1
1
0
0
0
0
0
1
1
2
2
1
2
1
1
0
2
2
1
1
1
1
1
2
2
2
2
0
1
1
1
2
2
1
0
0
1
1
2
1
1
1
1
1
2
0
1
1
0
2
2
1
0
1
1
0
2
2
1
0
0
2
1
2
1
1
1
0
2
0
0
0
2
1
1
0
2
0
0
2
1
0
2
0
2
2
1
1
1
1
1
1
1
2
2
1
2
1
0
1
1
1
0
1
2
1
2
1
0
1
1
1
0
1
0
1
1
0
1
1
0
1
1
1
0
0
1
0
1
1
0
1
1
1
1
1
1
1
0
0
1
2
1
0
0
0
1
0
0
1
2
1
2
1
1
1
0
0
0
1
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
0
1
1
1
1
1
1
1
1
0
1
1
1
0
1
0
1
0
0
1
2
2
0
1
0
0
0
2
2
0
0
1
2
1
2
1
1
1
0
0
1
1
1
2
1
0
0
1
1
0
1
1
2
2
2
1
0
0
1
1
1
1
1
1
1
1
1
1
3
0
2
0
1
0
1
1
0
0
1
0
0
0
1
1
1
2
2
2
2
0
0
1
1
2
1
1
1
0
0
2
1
1
0
1
0
0
2
0
2
1
1
1
1
1
1
1
2
3
1
2
1
0
1
3
0
1
0
0
0
2
2
2
1
1
2
2
1
2
1
2
1
2
1
1
1
1
1
0
2
0
2
1
1
1
1
0
2
1
1
0
1
2
1
1
1
1
1
1
1
0
1
2
1
2
1
1
1
1
0
0
1
2
0
0
0
2
0
1
2
0
1
1
1
0
1
0
0
1
0
0
1
2
1
2
0
1
2
1
0
0
1
2
0
0
1
1
1
1
1
2
0
2
1
1
2
2
0
1
2
0
0
1
2
1
0
1
1
1
1
0
0
1
1
0
1
1
1
0
1
0
2
1
0
1
2
1
1
1
0
1
0
1
1
1
0
2
0
1
2
1
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
0
0
1
1
1
2
1
1
0
0
2
1
1
0
2
1
0
0
1
0
0
1
1
1
1
2
2
2
1
2
1
1
0
1
1
0
1
2
2
2
1
1
2
1
0
2
0
0
1
2
0
0
1
1
1
0
1
2
2
2
2
0
1
0
1
1
0
0
1
1
2
0
2
0
1
1
1
1
0
1
1
0
1
1
1
2
2
0
2
1
1
0
2
0
1
2
1
1
1
0
1
1
1
1
1
1
1
1
1
1
0
0
3
0
2
0
0
2
0
1
1
2
0
0
0
1
1
1
1
0
0
0
1
1
2
1
1
0
1
1
0
0
1
0
0
1
1
0
2
1
2
1
0
1
1
0
1
0
1
1
0
1
2
0
1
1
0
2
1
1
1
0
1
0
1
1
1
1
2
1
0
1
1
2
1
0
1
1
0
1
1
1
1
2
1
0
1
1
2
1
1
0
0
0
2
2
1
2
2
2
1
2
3
0
2
0
0
1
3
1
1
0
1
1
2
2
1
0
1
1
1
1
0
1
1
2
2
0
0
0
1
1
2
0
2
2
2
0
2
0
1
1
1
0
0
2
1
1
2
1
0
1
0
2
0
1
2
1
0
2
1
2
0
0
1
1
0
1
1
0
1
0
1
1
1
1
1
0
1
2
1
1
1
1
1
1
1
2
1
2
0
1
1
1
2
1
1
0
2
2
1
0
2
2
1
0
0
2
1
0
1
0
1
1
2
2
1
1
2
1
0
1
0
2
1
2
2
1
1
2
1
2
1
2
1
2
2
0
1
1
0
0
3
0
1
0
1
1
2
0
1
1
1
2
2
1
2
1
0
1
0
1
2
0
2
1
1
2
0
0
1
2
2
0
2
0
2
1
1
0
1
0
1
1
0
1
2
0
2
1
2
1
0
1
1
0
0
1
2
1
0
0
1
0
2
1
1
0
1
0
0
2
2
1
2
1
0
0
1
1
2
0
1
1
0
2
1
0
0
0
1
0
0
1
2
3
1
1
0
2
1
0
2
0
0
1
2
1
1
1
1
1
2
1
0
1
0
1
0
0
1
2
1
2
1
2
1
0
1
1
0
2
0
1
2
1
2
2
2
2
0
1
1
2
2
1
1
1
1
0
3
1
0
1
0
1
1
0
1
1
1
1
2
1
0
0
0
1
1
1
1
1
1
1
0
2
0
1
0
1
1
1
1
0
1
0
0
0
1
1
1
1
0
1
1
1
2
0
2
0
0
1
1
1
0
0
3
1
0
2
1
2
1
1
1
1
2
1
2
2
1
2
1
1
1
1
0
1
2
1
0
0
0
2
2
1
2
1
0
0
2
0
0
2
0
0
1
0
1
0
1
2
1
2
0
1
2
0
1
2
1
0
0
1
0
1
0
2
0
1
1
0
0
1
1
0
0
0
1
1
1
1
1
1
1
0
2
1
2
1
0
2
1
0
2
2
1
1
1
0
3
1
0
2
1
0
0
0
0
0
0
1
1
2
1
1
1
1
0
1
2
2
2
1
1
0
0
1
1
1
1
2
0
0
3
1
2
1
0
0
1
1
1
1
0
1
1
1
1
1
1
1
1
1
0
0
0
2
1
0
0
1
2
1
1
2
1
1
1
1
0
2
0
1
1
0
1
1
1
0
2
1
1
1
1
1
1
1
1
0
1
1
1
1
0
1
2
2
1
1
3
2
0
0
1
1
2
1
1
1
0
1
2
1
1
2
2
2
1
2
0
1
0
1
1
1
1
0
1
2
2
1
0
3
1
1
0
0
1
1
1
0
0
1
2
1
1
2
1
1
1
1
2
2
1
1
1
1
0
0
1
0
1
1
2
1
1
1
1
1
1
1
0
2
0
0
1
2
1
1
2
1
1
1
1
2
0
2
1
1
0
1
0
1
1
1
1
2
0
0
0
1
2
1
1
1
0
0
1
2
2
0
1
1
1
1
0
1
0
1
1
2
1
1
1
1
0
1
1
0
1
0
2
1
0
0
1
1
1
0
1
1
1
0
1
1
2
2
1
0
1
0
2
1
1
2
1
0
1
1
1
0
1
2
2
0
0
1
2
1
1
1
1
1
0
2
0
0
1
1
0
0
1
1
0
1
0
1
1
1
1
0
2
1
1
3
1
0
0
1
3
1
0
1
2
1
1
0
1
0
1
0
1
0
3
1
1
0
0
1
2
1
1
1
1
1
1
1
1
0
1
1
2
1
2
1
2
0
1
2
1
2
0
1
2
2
0
2
1
0
1
1
2
1
2
0
1
1
1
0
1
2
0
1
2
1
1
1
1
1
1
1
2
1
1
0
2
1
0
1
0
1
1
2
1
1
2
0
1
1
1
0
1
2
2
1
1
1
0
0
1
1
2
0
2
0
1
1
1
1
0
0
1
1
1
0
1
2
0
1
0
1
0
0
1
1
1
1
0
2
1
0
0
1
1
1
2
1
1
2
0
0
2
1
1
0
1
1
0
2
0
0
2
1
1
2
0
1
2
0
2
1
1
0
1
1
0
1
1
1
0
1
0
1
1
0
0
1
0
1
1
1
0
2
1
1
1
1
1
2
1
0
0
3
1
2
0
0
2
2
1
1
0
1
2
2
0
2
2
1
1
1
3
0
2
1
1
2
0
1
2
1
0
0
1
1
0
2
2
1
0
0
1
0
1
2
0
1
1
2
1
0
0
1
1
0
0
2
0
5
1
1
2
0
1
1
1
2
1
2
2
1
0
1
2
2
0
2
1
1
1
1
1
1
2
1
1
1
1
1
2
0
2
1
2
1
2
2
0
2
1
2
0
0
2
2
1
1
1
2
1
2
1
0
0
1
2
2
0
2
1
0
0
0
2
0
1
2
0
0
1
1
1
1
1
2
1
0
1
1
1
1
1
0
2
2
1
1
2
0
0
0
0
0
1
2
1
2
1
0
0
0
2
1
1
2
0
2
2
1
2
1
2
2
0
1
0
2
1
2
1
1
0
1
0
1
1
1
1
1
1
0
0
1
1
2
2
1
0
1
2
0
1
2
2
0
1
0
1
2
0
1
1
2
2
0
2
1
1
2
1
1
2
1
0
0
2
2
1
1
1
2
0
1
0
1
1
2
1
1
1
0
1
1
1
2
0
0
1
2
1
0
4
1
1
2
1
2
1
2
1
1
2
1
1
1
1
0
0
2
1
2
0
0
1
1
0
2
0
0
2
0
1
1
1
2
0
2
2
0
2
1
1
1
1
2
2
0
1
1
1
2
2
1
1
0
2
1
1
1
1
2
2
2
1
0
1
1
2
1
2
1
0
0
1
2
2
1
0
1
1
2
0
0
0
2
1
2
2
1
1
1
2
0
0
0
0
2
1
1
1
2
1
0
2
0
0
1
1
1
1
1
3
2
0
0
1
2
0
1
2
3
1
2
1
0
0
1
2
2
2
1
0
1
1
0
1
1
2
1
1
1
1
0
1
1
0
0
0
2
2
0
1
1
1
0
2
0
1
2
1
1
6
2
1
0
1
1
0
2
2
0
2
1
2
2
1
2
2
1
0
1
2
0
1
2
1
0
0
1
1
1
1
1
2
2
1
1
1
1
0
1
4
1
0
1
1
1
0
1
1
2
1
2
2
0
3
1
1
0
1
1
0
1
1
1
0
1
0
0
1
2
2
0
1
1
2
0
0
2
0
0
0
1
1
0
1
1
1
0
1
2
0
1
2
2
1
2
0
1
1
2
1
2
1
2
0
1
1
0
0
1
1
0
2
2
2
2
1
2
2
0
0
1
0
0
1
0
1
1
2
1
2
1
2
1
2
1
1
1
1
1
1
0
1
4
1
7
0
0
0
1
0
1
0
1
0
0
0
2
1
2
0
1
1
1
1
0
1
4
0
1
1
0
1
2
0
1
0
1
1
0
1
0
2
1
1
1
2
0
2
1
2
1
0
1
1
1
2
1
1
0
2
0
1
1
1
0
0
0
1
1
0
1
0
0
0
2
0
0
1
1
0
1
2
1
1
1
1
1
2
1
1
1
0
1
0
1
0
1
1
1
1
0
1
2
0
2
2
1
1
0
1
2
1
1
1
0
1
3
0
1
1
1
1
1
1
1
1
0
2
0
1
1
1
0
1
2
1
0
1
1
1
1
2
0
0
1
2
1
1
3
1
1
0
3
2
0
0
2
1
0
1
1
1
1
2
2
0
1
0
0
1
0
1
1
2
2
1
1
1
1
1
0
1
0
2
0
0
2
1
1
1
1
1
1
0
1
1
0
1
0
1
0
1
2
1
0
0
1
1
0
0
1
1
1
1
1
0
0
1
0
1
1
1
2
2
0
1
1
0
1
0
2
0
2
2
1
1
0
1
2
1
2
2
0
1
1
1
2
1
1
1
2
1
0
0
0
0
1
2
0
1
2
0
1
1
0
1
1
0
0
0
1
0
1
3
1
1
1
2
0
2
2
0
0
0
2
0
1
2
1
0
1
2
1
1
1
1
1
2
0
0
2
0
2
1
0
1
1
0
2
1
2
1
0
1
1
2
1
1
0
1
0
0
0
1
1
2
1
1
1
1
0
1
1
0
0
1
1
2
1
1
0
1
0
1
1
1
1
1
1
2
2
0
0
1
2
0
1
1
1
0
2
0
2
2
1
1
3
1
0
0
1
1
0
1
0
0
0
0
0
1
0
1
0
1
1
1
1
1
2
1
2
1
1
1
2
2
0
0
0
2
1
2
1
1
1
1
1
2
1
1
1
0
2
1
0
2
3
2
2
1
0
2
0
2
0
0
1
2
2
2
1
1
0
1
1
1
0
1
0
1
1
1
0
1
0
1
2
1
1
0
0
0
2
2
1
0
1
1
1
0
2
1
2
1
0
2
2
1
2
1
1
2
1
2
0
0
0
2
1
1
1
1
1
1
1
1
0
7
1
1
0
1
0
1
0
2
1
1
1
0
1
2
1
0
0
1
1
1
1
0
0
1
1
1
1
1
2
1
1
0
2
0
0
2
2
2
0
0
1
1
1
1
1
0
2
0
2
2
1
1
2
1
1
1
1
2
2
1
1
1
1
1
1
1
1
2
2
1
1
1
0
0
2
2
1
0
1
1
1
1
1
1
1
1
2
0
1
2
1
1
2
1
0
1
0
0
0
0
2
1
1
0
2
2
3
4
2
1
1
1
1
0
2
1
0
2
1
1
2
1
2
0
1
2
2
1
1
2
1
2
0
0
0
0
2
0
2
0
1
0
1
0
1
1
1
1
1
0
1
2
1
0
1
1
1
1
0
1
2
1
1
0
0
0
1
1
2
1
0
0
0
1
1
0
1
0
1
0
0
0
1
0
1
0
1
2
0
1
1
1
0
1
0
1
0
1
0
1
1
1
0
1
1
0
2
1
1
1
1
1
1
0
1
1
1
1
1
0
0
1
0
1
1
1
1
1
0
1
1
1
2
1
1
1
1
1
1
2
1
1
0
1
2
1
1
1
1
2
1
1
0
1
1
1
2
0
2
1
1
0
2
1
0
0
0
1
2
0
1
2
2
0
1
1
0
2
1
0
2
1
2
0
3
1
1
2
1
2
0
2
2
0
1
1
0
2
1
1
0
1
1
1
1
0
0
0
1
1
1
1
1
1
1
0
0
1
0
2
1
1
1
1
0
1
2
1
0
0
0
0
0
1
0
0
1
2
2
1
2
1
2
2
0
1
1
1
0
0
2
1
0
1
1
2
0
0
1
2
1
0
1
0
0
1
2
0
1
1
0
1
1
1
1
1
1
1
1
0
0
1
0
1
1
1
1
1
1
2
1
2
1
1
0
1
1
1
0
2
0
1
1
1
0
0
0
2
0
2
0
1
1
0
2
0
1
1
1
1
0
1
2
0
1
0
2
0
2
2
1
1
1
1
2
2
1
1
1
0
1
1
1
1
1
1
1
1
1
0
1
1
2
1
2
0
0
2
1
2
2
1
1
1
1
1
0
2
2
0
0
2
1
0
1
1
0
2
0
0
1
1
1
2
0
2
1
1
0
1
1
2
2
0
0
1
1
1
1
1
0
2
1
2
0
0
0
1
0
0
1
1
1
1
1
1
1
0
0
0
1
2
1
0
1
0
1
1
2
0
2
1
0
1
2
0
1
0
0
1
2
1
1
1
0
1
1
1
1
0
2
1
0
0
1
0
1
0
1
0
1
1
1
1
0
2
0
1
1
2
1
1
2
1
1
1
0
1
2
1
2
0
1
1
1
0
2
2
1
1
1
1
1
0
3
0
2
2
2
1
1
1
1
0
1
1
2
3
1
1
2
1
1
1
1
1
0
0
1
0
2
1
0
2
1
2
0
1
2
0
1
1
1
1
1
1
1
2
0
0
1
1
1
1
0
0
1
1
0
1
1
1
1
1
0
1
1
1
0
1
1
0
1
0
1
2
1
2
1
1
1
1
1
1
1
0
1
1
2
1
2
1
2
2
0
0
1
1
2
1
1
1
1
0
1
2
2
1
1
0
1
1
1
0
2
1
0
0
1
2
1
1
0
1
1
2
1
2
1
2
1
0
0
0
1
0
1
2
2
2
1
1
0
0
2
1
1
0
1
1
1
0
1
1
1
2
1
2
1
1
1
0
0
0
1
0
1
1
0
2
2
2
1
1
1
0
0
1
2
1
2
1
1
1
2
2
0
2
1
1
1
2
2
0
1
1
1
2
1
1
0
0
0
0
1
1
0
1
1
0
1
2
1
0
1
1
1
2
0
1
2
1
2
1
2
0
0
1
0
2
0
1
2
0
0
0
1
1
2
1
1
2
0
1
0
0
1
0
1
1
0
0
0
1
2
0
1
0
1
2
1
1
0
1
1
1
1
1
0
1
2
2
1
0
1
1
1
2
0
2
1
1
1
0
1
0
1
1
1
1
0
2
0
2
2
0
3
1
1
1
1
1
1
0
1
1
0
1
1
0
1
3
0
1
2
0
0
1
1
1
1
1
1
1
1
0
1
4
1
1
1
3
0
1
2
1
1
2
0
1
3
2
2
1
2
0
2
2
0
1
1
2
1
1
2
0
2
1
1
1
1
1
0
2
0
1
1
1
1
1
1
2
0
0
1
1
0
1
1
0
0
1
2
1
2
2
1
1
0
3
0
2
1
1
1
2
1
0
1
2
0
1
0
0
2
2
1
1
1
0
0
0
0
1
1
1
1
0
1
1
0
2
0
0
1
2
1
1
1
1
2
0
1
3
1
0
0
0
0
1
1
1
2
1
1
2
0
0
0
1
1
1
1
0
2
0
0
0
0
1
1
3
2
1
2
2
0
0
2
1
1
1
2
2
2
2
1
0
1
0
1
1
0
1
0
1
0
1
0
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
0
0
0
1
1
1
0
2
1
1
0
0
1
1
1
0
0
0
1
0
0
2
1
1
1
0
0
1
0
2
1
1
1
1
1
1
1
0
4
2
0
0
1
0
2
1
2
1
1
1
1
1
0
2
1
0
0
1
0
2
1
2
1
1
1
2
1
1
0
1
1
1
2
0
1
2
1
0
0
1
1
1
2
1
1
1
0
1
1
2
1
2
1
2
1
1
1
2
2
1
1
0
2
2
0
1
1
1
1
1
2
1
1
0
0
0
2
0
1
0
1
1
2
0
1
3
2
1
1
1
0
1
0
2
0
2
1
1
1
1
2
1
1
1
1
2
0
1
1
1
1
1
1
1
0
3
1
1
2
1
1
1
0
0
0
0
1
2
1
2
2
0
2
1
1
0
0
0
2
1
2
1
1
1
2
2
1
0
0
0
1
0
1
1
2
0
0
2
1
0
1
1
1
0
1
0
2
1
1
1
0
1
1
0
1
0
1
1
0
0
2
1
0
1
2
1
2
2
1
0
1
2
0
1
0
1
2
2
1
0
1
1
0
0
0
0
2
1
0
1
0
1
1
1
0
0
2
0
0
0
0
1
1
2
0
2
1
2
3
0
1
0
2
1
1
2
0
1
1
0
1
0
0
2
0
2
2
0
0
0
0
2
1
1
1
2
1
0
3
0
1
0
2
0
1
0
1
0
0
1
0
1
0
1
1
0
0
0
0
0
1
1
2
2
1
2
1
2
0
1
1
2
1
1
0
1
1
0
0
0
1
1
1
2
1
4
0
0
2
1
1
1
2
1
2
1
1
0
2
1
1
1
1
2
1
1
1
0
1
1
0
0
1
0
1
0
1
2
2
0
1
0
0
1
1
2
1
1
2
1
1
2
2
0
2
0
1
1
2
0
0
0
0
1
1
0
2
0
2
1
0
2
2
2
1
1
1
0
1
1
2
1
0
2
1
1
1
1
1
2
2
1
0
2
0
1
2
2
0
1
2
1
2
1
0
0
3
1
0
1
1
1
1
1
1
0
1
2
0
1
1
1
1
0
2
1
0
1
2
1
0
1
0
1
1
2
1
0
1
1
1
1
1
0
3
0
1
1
1
1
1
2
2
1
2
0
0
1
0
1
2
2
0
0
1
0
1
2
2
0
0
0
0
0
2
1
0
2
2
1
2
1
1
0
0
1
2
1
2
0
1
2
0
2
2
0
1
2
1
1
0
0
1
2
0
1
1
0
1
2
0
1
1
0
1
1
4
2
1
2
1
1
1
2
0
0
1
1
2
1
1
2
2
1
0
2
6
2
0
1
0
3
1
1
2
0
0
1
0
1
1
2
2
2
1
0
1
2
2
0
2
2
0
2
0
0
2
2
1
1
1
1
1
2
2
1
0
0
1
5
1
0
2
0
0
1
2
1
2
0
1
0
0
1
0
1
1
0
1
1
1
0
0
2
0
1
2
1
1
2
0
1
0
2
1
1
1
0
1
2
1
2
1
2
1
1
0
1
1
0
1
0
1
0
2
1
1
1
0
2
0
2
0
1
0
0
1
1
1
1
0
2
1
2
0
1
1
0
1
2
1
1
1
2
1
0
1
1
2
1
0
1
1
2
2
1
0
1
2
0
1
0
2
2
1
1
1
2
1
1
1
0
1
3
0
2
1
2
1
1
1
1
2
0
1
1
2
1
1
1
0
1
2
0
1
1
1
1
1
2
1
0
1
0
1
1
0
1
1
3
1
1
0
2
2
2
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
0
1
1
0
1
1
2
1
1
2
1
1
2
0
0
0
1
1
1
1
2
1
0
0
0
0
0
1
1
1
1
1
1
1
2
0
0
2
2
0
0
1
1
1
1
1
0
0
2
1
1
0
1
0
0
0
2
0
1
0
1
2
1
0
2
0
1
2
2
0
1
1
1
1
2
1
0
1
0
1
0
0
1
2
1
1
1
2
1
0
1
1
0
2
3
1
1
1
0
1
1
0
1
1
2
2
0
0
2
0
2
0
2
0
2
1
0
0
2
2
1
1
1
1
0
0
1
1
1
1
1
2
1
1
0
2
0
1
0
1
2
2
1
3
0
0
2
2
0
1
1
1
2
1
1
1
0
2
2
1
0
0
0
1
0
0
2
1
2
0
1
0
1
0
0
1
1
1
2
1
0
0
1
1
1
0
1
2
1
1
1
1
1
2
0
1
2
1
0
0
0
1
1
1
1
1
2
1
1
1
0
1
2
0
1
2
2
1
2
1
2
0
1
0
0
0
1
1
1
0
1
1
1
0
2
1
0
0
1
1
1
1
2
2
1
0
1
2
2
2
3
0
1
0
1
0
0
1
1
1
0
1
1
0
2
2
2
1
1
1
2
1
0
2
1
1
1
1
1
1
0
1
1
1
1
0
1
2
0
2
1
0
1
0
0
0
1
0
1
1
1
1
1
1
0
2
1
1
2
0
0
2
1
1
4
2
0
2
1
1
1
2
0
2
1
3
2
1
2
0
0
0
1
1
2
3
0
1
2
2
2
0
0
2
1
2
1
0
0
1
2
1
1
1
1
1
0
1
2
0
1
1
1
1
1
2
1
1
2
0
2
2
0
1
1
1
2
1
1
2
1
0
1
1
0
0
2
2
2
2
1
1
2
0
0
0
2
2
0
2
0
0
1
0
1
2
1
0
1
2
1
2
0
1
1
1
1
0
0
2
1
1
2
1
1
1
1
0
0
1
0
0
0
1
1
1
1
0
1
0
0
0
1
2
0
1
1
0
2
1
1
2
1
1
1
2
2
0
0
2
2
0
0
1
2
2
0
2
2
1
2
1
1
1
0
2
2
0
1
2
1
1
2
1
0
0
1
2
0
0
0
2
1
0
0
0
0
1
0
1
1
1
2
2
1
1
2
0
0
0
1
0
1
1
0
1
1
0
0
1
0
2
2
2
0
1
2
0
0
0
2
1
0
2
2
0
2
1
1
2
1
0
0
1
0
1
2
0
3
0
0
1
1
1
2
1
2
1
0
1
1
1
0
0
1
2
0
2
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
1
0
4
2
2
0
1
0
1
1
0
1
1
2
0
1
1
0
2
2
1
0
1
0
0
1
2
1
1
2
1
0
1
2
1
1
2
1
2
0
1
1
0
1
2
1
1
1
2
1
1
1
2
1
2
0
1
1
1
1
2
1
0
1
1
2
2
1
1
2
0
1
2
1
1
1
0
1
1
2
2
2
2
1
2
1
1
1
0
1
1
1
3
2
2
1
1
3
1
0
1
1
1
1
0
0
1
0
1
2
1
1
0
1
1
1
0
0
1
1
2
0
0
0
0
1
3
1
1
1
1
1
1
0
0
0
1
1
1
1
1
1
1
1
2
1
1
0
1
1
1
2
1
1
0
1
1
2
1
1
0
1
0
0
1
1
0
0
0
2
1
0
1
1
0
0
0
0
2
2
0
1
2
1
2
2
1
1
2
2
0
2
1
1
1
1
1
1
1
1
1
0
0
2
2
1
0
1
1
0
1
0
2
1
1
0
0
0
2
0
1
1
2
1
0
1
0
1
1
0
1
1
1
1
0
1
1
1
1
1
2
0
1
0
2
0
1
0
2
1
1
1
2
0
2
1
1
1
1
0
1
2
2
0
1
0
1
0
1
1
0
2
1
1
0
0
1
1
0
1
1
1
0
1
1
1
1
1
1
1
2
1
2
2
0
2
1
1
0
1
0
2
1
1
2
0
0
1
0
1
0
1
1
1
1
1
0
0
1
0
1
0
1
2
1
1
0
1
2
1
1
1
0
1
1
3
2
0
2
0
1
0
0
1
2
1
0
0
1
1
2
0
1
2
2
1
1
0
0
2
2
0
0
1
2
1
2
0
0
1
1
0
2
1
1
1
1
0
0
1
3
1
5
1
1
0
1
1
1
1
2
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
0
0
2
3
1
1
2
1
1
2
1
1
1
1
0
2
2
1
0
1
1
7
1
2
0
1
2
0
0
1
0
1
1
1
0
0
2
2
1
0
1
2
1
0
1
1
0
0
1
2
2
1
1
1
0
1
0
1
0
2
1
1
2
1
2
1
2
1
1
1
0
1
1
0
1
1
2
0
1
0
1
0
1
1
0
1
1
1
1
1
1
1
1
0
1
2
1
0
1
1
1
1
1
1
0
1
1
2
1
1
0
0
0
1
2
0
0
2
1
2
2
0
1
0
1
0
1
1
1
0
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
0
1
0
2
0
1
1
2
1
0
1
0
1
0
2
1
0
1
2
2
1
1
1
2
2
1
1
0
2
1
1
0
2
1
2
0
1
1
1
1
2
1
2
2
1
1
1
1
1
2
1
0
1
1
0
2
0
0
1
0
1
2
1
0
1
0
0
2
1
1
1
0
1
1
1
1
1
2
1
1
1
1
1
1
0
1
1
2
1
1
0
2
2
0
0
1
2
0
0
0
2
1
1
1
2
2
1
1
1
1
1
0
0
0
2
0
1
2
1
2
1
1
0
1
0
0
1
2
1
0
0
2
1
1
1
1
4
1
0
0
0
1
1
1
0
2
0
2
1
1
1
1
1
1
0
1
2
1
1
0
0
1
1
2
1
0
0
0
1
1
1
2
1
1
1
0
1
1
1
0
1
2
1
2
0
2
0
0
2
0
2
1
2
1
1
4
2
2
1
2
1
1
1
0
1
2
0
0
1
2
1
1
1
1
0
2
1
1
2
1
1
0
1
2
2
1
0
1
1
1
1
0
1
1
1
0
1
0
1
1
1
2
4
2
0
1
2
0
1
2
0
2
0
1
1
2
0
0
1
1
0
0
1
1
0
2
2
2
2
0
0
1
1
2
1
1
0
2
1
1
0
2
0
1
1
1
2
2
1
2
1
0
1
0
0
1
2
1
0
0
0
2
0
2
0
1
0
2
1
1
3
1
2
2
1
1
0
0
1
2
1
1
1
0
2
1
2
1
1
2
1
2
1
1
0
0
0
1
0
0
2
1
1
0
2
1
0
2
0
2
0
2
1
0
0
2
1
0
0
1
1
0
2
6
0
1
1
0
1
1
1
0
2
1
1
0
1
1
2
1
0
0
1
0
1
1
1
2
0
1
0
2
1
0
1
0
2
2
1
1
1
0
1
0
1
1
2
1
1
1
2
1
0
1
2
1
1
0
0
0
1
0
1
0
1
2
0
1
2
0
0
0
1
0
1
2
2
1
2
1
0
0
1
1
1
0
2
0
1
2
1
1
2
1
2
2
2
2
0
2
1
2
1
1
1
2
0
0
0
2
0
0
1
1
1
1
0
2
2
1
0
1
1
1
1
2
1
0
0
1
1
1
1
2
0
2
2
0
0
2
1
1
1
0
1
1
1
0
0
1
2
2
2
0
1
1
2
1
2
1
1
0
3
2
1
2
1
0
0
0
2
2
1
2
0
1
2
1
1
1
0
2
1
2
1
0
1
1
1
2
1
2
0
1
2
1
1
2
1
0
0
1
1
1
0
0
0
2
0
1
1
1
1
0
0
0
0
0
0
1
2
0
1
2
1
0
0
1
0
1
1
2
1
1
0
1
1
1
2
2
1
0
0
0
1
1
0
0
1
0
0
1
2
2
1
0
1
2
0
1
3
1
0
0
1
2
1
2
0
1
2
1
0
1
0
0
2
1
0
0
0
0
1
0
1
1
0
2
1
1
1
1
1
0
1
1
1
1
1
0
1
0
1
1
0
1
2
1
1
1
0
1
1
0
0
2
2
1
2
2
1
1
2
0
0
1
2
2
1
2
2
0
1
1
2
0
0
0
2
0
0
1
0
1
2
1
1
1
0
1
0
1
1
0
0
0
0
1
1
1
1
2
1
2
0
1
1
1
0
1
1
0
0
2
1
1
0
2
1
0
1
1
0
2
1
1
0
1
1
0
0
1
1
1
1
1
2
0
2
1
0
0
0
1
1
0
2
0
1
0
1
1
1
1
0
2
2
0
1
1
2
1
1
2
1
1
1
2
2
1
1
1
0
2
1
2
0
1
2
1
1
0
0
0
0
2
2
2
1
0
1
1
1
1
2
0
1
1
1
0
1
0
1
1
1
1
2
0
1
0
0
1
1
1
1
2
0
1
1
3
2
1
1
1
2
1
2
1
0
2
0
0
1
1
1
0
1
0
1
1
0
2
0
1
0
1
0
2
1
1
1
1
1
1
2
0
1
0
1
1
1
0
1
2
1
1
0
2
1
1
0
2
1
1
1
1
2
1
0
1
1
1
3
0
2
1
0
2
2
0
1
1
1
0
2
1
1
1
2
1
0
1
1
1
1
0
2
1
1
1
1
1
0
1
0
2
0
1
1
0
1
1
0
2
1
2
1
0
1
0
2
0
1
1
1
1
1
1
2
0
0
0
2
0
1
1
0
0
0
1
2
1
2
0
1
1
2
1
1
1
1
0
2
1
1
1
1
1
1
2
1
1
1
1
0
1
2
0
1
0
0
2
0
0
0
1
1
1
2
0
1
2
0
0
1
1
2
0
0
2
1
0
1
0
1
1
0
1
0
2
0
0
2
0
1
3
1
1
1
0
1
1
1
1
2
1
1
1
1
2
1
1
0
1
1
1
0
1
1
0
2
1
0
0
0
1
2
1
1
1
1
1
1
1
1
2
0
0
0
3
0
1
1
1
1
0
1
1
1
1
2
0
2
1
1
2
1
2
0
0
1
2
2
1
0
1
0
1
0
2
1
0
2
0
2
1
1
1
0
2
1
0
1
1
2
0
2
1
1
1
0
1
0
2
1
1
1
0
2
2
1
1
1
0
1
0
0
1
2
1
3
0
0
1
1
0
0
2
0
0
0
2
0
1
4
1
0
3
2
1
2
1
2
1
0
1
1
1
3
1
0
0
2
0
1
0
1
1
1
1
1
0
0
0
2
1
0
0
1
0
1
1
1
1
2
3
1
1
1
0
1
2
1
2
2
2
1
1
1
1
0
0
2
1
1
0
2
1
2
0
2
0
1
0
1
1
0
1
1
1
1
2
0
1
1
0
1
1
0
2
1
1
0
2
1
0
2
0
0
1
1
0
1
1
1
1
1
1
0
0
0
1
1
0
0
1
1
1
0
0
1
1
1
1
2
0
2
1
1
1
2
0
0
1
1
2
0
0
1
2
1
0
1
2
3
0
1
0
2
1
0
1
0
0
1
1
1
1
1
2
2
1
1
1
0
0
2
0
2
2
2
1
1
1
1
0
0
1
1
2
1
1
0
2
1
1
1
2
2
1
0
1
1
2
1
1
0
2
1
0
1
1
1
1
1
2
2
2
1
1
1
0
1
1
2
2
0
1
1
1
0
1
1
1
0
0
1
0
1
1
0
1
1
1
1
1
1
1
2
1
1
0
2
1
1
4
1
0
0
1
1
1
1
1
0
1
1
1
0
0
1
0
3
1
0
1
0
2
0
1
2
1
2
0
1
0
2
1
1
0
0
1
0
1
1
1
1
2
2
1
2
2
1
1
2
1
1
0
2
1
1
0
2
2
0
1
1
0
1
0
0
0
1
1
0
2
1
0
1
1
0
1
2
1
0
0
0
1
0
2
2
1
1
2
1
0
0
1
0
1
1
1
1
2
1
1
1
1
2
2
2
1
0
2
1
3
1
0
1
1
1
0
1
2
0
2
0
1
0
0
2
0
1
1
0
1
1
2
2
1
2
2
1
2
1
1
2
1
1
0
2
2
1
0
1
1
1
1
2
0
1
0
2
1
2
2
1
0
1
0
1
0
2
1
2
1
1
3
2
1
0
1
0
1
1
0
0
1
1
0
1
1
0
1
2
1
1
0
1
0
0
1
2
1
0
1
1
1
2
2
2
2
1
1
2
0
1
2
2
1
2
1
1
0
0
1
1
2
0
2
2
0
1
0
0
1
0
1
1
2
1
1
0
1
1
0
0
0
1
1
1
1
0
2
0
2
1
1
1
1
2
1
4
0
0
2
1
0
0
1
1
1
1
1
2
0
1
0
2
2
2
1
1
1
2
0
0
1
2
0
0
1
1
0
1
0
3
2
1
2
2
1
2
0
1
2
0
1
1
1
0
1
1
0
2
2
0
1
0
0
1
1
1
0
1
1
0
1
1
2
2
2
0
0
0
0
1
1
1
1
1
0
2
2
2
0
0
0
1
1
2
0
2
1
2
0
2
1
2
0
1
1
0
0
1
2
1
1
1
0
0
2
1
2
1
1
2
2
1
1
1
1
1
0
1
1
1
2
0
0
0
0
0
1
2
1
1
1
2
2
1
1
0
1
0
2
3
1
1
0
1
1
1
2
1
1
1
0
1
2
2
0
1
1
1
2
1
1
2
2
2
1
2
1
1
1
0
1
1
1
0
0
2
1
1
2
1
0
1
2
1
2
0
1
2
0
0
2
1
0
2
2
1
0
2
1
1
0
0
1
2
1
1
1
1
0
2
0
1
1
0
0
1
0
0
1
1
0
0
1
0
1
0
1
0
1
0
1
2
2
1
0
2
1
0
0
1
1
2
2
0
1
1
1
2
1
2
1
2
0
1
2
1
1
0
1
2
1
1
1
0
0
1
0
1
2
2
1
2
2
0
0
1
1
1
1
2
0
0
2
1
1
1
1
1
1
0
1
1
1
1
1
1
2
0
2
2
0
2
1
2
1
2
0
1
2
2
0
0
1
1
2
1
1
0
0
0
1
1
0
0
2
0
0
1
0
1
1
1
1
1
1
1
1
1
1
0
1
2
0
0
1
2
1
2
0
1
0
1
0
0
0
0
0
1
1
0
2
1
1
2
1
1
1
1
1
0
2
0
1
1
2
1
0
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
0
1
2
2
1
1
1
0
0
0
2
1
1
1
1
0
0
0
1
0
1
1
0
1
2
1
0
1
1
1
1
0
1
1
1
1
2
1
0
1
1
2
0
0
1
0
1
1
2
2
2
1
1
1
1
1
0
0
1
1
1
1
1
1
1
1
0
1
1
1
1
2
1
1
2
2
2
1
0
0
2
2
0
1
0
1
1
1
1
1
1
0
1
0
1
2
2
1
2
1
0
0
2
1
0
1
1
0
1
1
1
0
0
1
0
1
2
1
1
1
2
2
0
2
1
2
1
1
1
1
2
2
0
1
1
0
2
0
0
0
1
0
1
1
1
1
1
2
1
0
0
3
0
1
1
1
1
1
0
2
0
1
2
2
0
1
1
1
1
1
2
2
1
1
1
1
1
2
1
0
0
1
1
2
1
1
2
1
0
0
1
1
1
2
2
1
1
0
1
1
1
2
1
1
0
1
0
1
2
2
2
1
0
1
1
0
1
1
0
2
2
1
1
2
1
1
2
2
1
1
1
0
0
1
1
1
2
1
2
1
3
2
0
1
2
0
0
1
0
1
1
0
1
0
0
1
1
0
1
1
1
1
1
1
2
0
1
2
1
1
1
2
1
1
1
2
1
0
0
0
1
1
1
1
0
2
0
0
1
1
1
1
1
1
0
0
1
1
2
0
0
0
1
1
0
0
0
0
0
2
0
2
1
1
2
1
0
2
1
1
0
1
0
0
2
1
2
0
0
1
1
1
2
1
1
1
1
1
3
1
0
1
1
0
0
2
1
2
0
1
1
0
1
2
1
1
1
1
2
1
0
0
1
1
0
0
1
1
1
2
1
0
0
2
1
2
1
1
1
1
0
1
1
0
1
1
2
1
1
0
0
1
0
1
1
2
1
1
1
0
2
1
0
0
0
1
0
1
0
1
0
2
0
0
1
0
0
1
0
0
0
0
1
1
1
0
0
1
1
2
2
1
1
0
0
1
0
1
3
1
1
0
2
0
1
0
0
1
1
2
1
1
2
2
0
2
1
1
0
2
2
0
1
0
1
2
0
2
1
1
2
1
0
0
1
2
1
1
2
1
1
1
0
1
1
0
2
2
2
1
1
1
0
0
2
2
2
0
2
1
0
0
0
1
0
0
1
1
1
2
0
1
0
1
1
0
1
0
1
0
0
1
1
2
1
0
1
1
1
2
1
1
1
0
1
1
1
2
1
2
1
4
2
1
1
2
0
1
1
1
1
2
0
1
1
1
0
1
2
1
2
1
1
0
0
1
2
2
1
1
1
2
2
1
2
1
1
1
1
3
0
1
1
1
0
1
2
2
1
0
0
1
1
0
0
0
1
1
1
2
0
1
2
1
0
0
2
1
1
0
2
0
0
0
1
2
0
1
1
0
1
0
0
0
1
2
1
1
1
2
0
0
0
2
1
2
0
1
1
1
1
1
0
2
3
1
2
1
1
1
0
0
2
0
1
1
3
1
0
0
0
1
1
1
0
2
0
2
1
0
1
0
0
1
2
1
2
2
0
1
2
1
2
0
2
2
2
0
2
0
1
1
1
1
0
0
1
0
2
0
1
0
1
1
1
0
1
1
2
0
0
2
1
0
1
2
1
1
0
0
0
1
1
0
0
0
1
2
0
1
1
1
1
0
1
1
0
0
2
0
0
0
1
1
0
1
1
0
0
0
0
1
1
1
1
1
2
1
2
0
0
1
1
2
1
0
1
1
1
0
0
1
2
2
1
1
1
1
2
2
1
1
0
2
2
0
0
1
0
1
1
1
2
0
0
0
1
1
1
0
1
2
1
0
0
1
0
2
1
2
1
1
2
1
2
0
2
0
0
3
0
0
1
1
0
0
1
1
2
2
3
3
0
1
0
1
2
1
2
0
0
0
0
1
1
1
2
1
1
1
1
1
1
0
2
1
1
1
0
0
2
1
1
2
1
1
1
1
0
1
0
0
1
0
0
1
1
2
2
2
2
0
0
1
1
2
1
0
2
1
2
2
1
1
1
0
0
1
1
1
2
1
0
1
0
2
1
1
0
1
2
1
2
0
1
0
2
2
1
0
1
0
1
1
1
1
1
0
0
0
1
2
0
1
0
1
2
1
1
1
2
0
1
1
1
1
0
1
1
2
1
0
1
1
1
1
1
0
0
1
1
1
0
0
1
3
2
2
0
1
0
1
1
2
0
1
1
1
1
0
0
1
1
1
1
1
1
0
1
1
1
2
3
2
0
2
0
1
1
0
0
2
2
0
1
1
1
0
1
0
1
2
0
1
0
1
0
0
1
1
1
0
0
1
2
0
1
3
5
1
0
2
2
1
1
1
1
0
0
0
1
1
0
1
0
1
1
2
1
1
1
1
1
1
1
2
1
1
0
0
0
1
2
2
1
1
1
2
0
2
0
0
0
1
2
2
0
1
2
2
0
1
1
1
0
0
2
0
0
0
2
0
1
1
2
2
1
0
1
0
1
0
2
1
0
2
1
1
1
1
1
1
1
2
1
1
1
1
0
1
0
2
0
1
2
1
1
2
0
1
1
0
1
1
2
2
1
1
1
1
1
1
2
0
0
1
1
0
1
1
1
0
1
2
0
1
0
1
0
2
1
1
2
0
1
2
1
2
1
1
1
0
1
2
1
0
0
1
1
1
1
2
1
1
2
1
1
0
1
1
1
2
1
2
0
1
0
2
2
1
2
0
0
2
2
2
1
1
1
1
1
0
0
1
1
1
1
1
1
1
2
2
1
1
1
2
1
2
1
0
1
1
1
0
1
1
2
1
1
1
1
1
0
1
0
2
2
0
0
0
0
1
1
0
1
0
1
2
0
1
1
2
2
1
1
2
1
1
1
0
1
1
2
1
2
0
1
0
1
2
1
1
0
1
1
2
0
0
1
2
1
2
1
2
1
1
1
1
0
1
2
2
1
1
1
1
2
2
1
0
1
2
1
3
1
1
0
3
1
2
0
1
1
1
1
1
2
2
0
1
0
1
1
1
1
1
1
2
0
0
1
0
1
1
2
1
0
2
0
2
0
0
1
1
2
1
0
1
2
1
0
0
2
1
2
2
3
3
1
1
2
1
0
1
0
0
1
0
2
0
0
1
1
1
1
1
1
2
0
1
2
1
1
1
0
0
1
0
2
0
1
2
2
1
0
1
2
2
2
0
0
1
1
1
0
1
1
0
2
1
2
0
1
2
2
1
1
1
0
2
1
1
1
1
0
0
0
2
1
1
3
1
0
1
1
1
2
1
1
0
1
1
1
1
0
2
2
0
0
2
1
1
1
0
1
2
2
0
1
1
1
1
0
2
0
0
1
1
0
2
0
0
1
0
2
2
2
0
2
1
0
1
1
1
2
1
3
1
0
2
2
1
2
0
2
0
0
1
1
1
0
2
1
0
1
1
0
1
2
1
0
0
0
1
2
2
2
1
1
0
2
0
1
1
2
2
1
1
1
1
1
0
0
1
0
0
0
1
0
2
2
0
1
0
2
2
2
1
1
1
2
0
1
0
1
2
2
2
4
0
0
1
0
0
1
2
0
0
1
1
2
0
2
0
1
0
1
1
1
1
1
0
0
1
1
0
2
2
2
2
0
2
1
1
1
2
1
1
2
1
1
2
0
2
2
1
1
2
2
1
1
1
1
1
1
2
0
2
0
1
2
2
1
1
0
1
2
2
0
0
1
1
0
0
1
1
2
1
2
1
1
2
2
2
0
0
1
1
3
0
1
2
0
0
0
1
0
1
0
1
1
1
0
0
2
0
0
1
1
1
2
2
2
1
0
0
1
0
0
0
0
1
0
0
1
0
2
0
0
1
1
2
2
0
3
0
0
0
1
1
1
0
2
1
0
0
1
2
1
1
1
2
0
1
0
1
2
0
0
1
0
2
1
1
1
0
2
1
0
1
1
0
2
1
1
1
1
0
0
1
1
1
2
1
1
1
1
1
0
1
1
2
1
1
1
1
0
1
0
1
2
1
1
0
0
2
0
1
1
0
1
1
0
1
1
0
0
0
0
1
1
0
1
1
2
0
1
1
2
1
1
1
2
1
0
0
0
1
0
1
2
1
2
1
0
2
2
1
2
1
1
2
1
0
1
1
1
1
2
0
1
1
2
1
0
1
1
1
1
0
1
1
0
0
0
1
1
1
1
0
2
1
1
1
1
1
0
0
1
1
0
0
1
1
1
2
1
2
1
0
0
2
0
1
2
1
1
1
1
1
0
2
2
2
2
0
1
2
0
1
1
1
0
1
1
0
1
1
2
0
1
1
0
1
2
2
0
2
0
1
0
2
1
1
1
0
1
3
1
0
1
1
0
1
0
1
1
2
0
0
1
2
2
0
0
1
1
1
2
1
0
1
0
0
2
0
2
1
1
2
0
2
0
0
0
1
1
1
1
2
1
1
0
0
1
1
1
1
1
1
1
2
0
1
0
0
1
2
1
1
1
1
1
1
0
1
1
1
2
0
0
0
0
2
2
1
2
1
0
1
1
2
1
1
1
2
0
1
2
0
1
1
2
1
1
1
1
1
1
1
1
0
2
1
0
0
1
1
0
0
2
2
0
1
1
2
1
0
1
0
1
1
0
1
2
1
0
2
1
0
2
1
1
1
0
1
1
2
1
1
0
0
1
2
2
2
2
1
1
1
1
0
1
0
2
2
2
1
0
0
0
0
0
0
0
2
0
2
2
0
0
2
1
0
1
1
1
0
2
1
2
0
0
0
1
2
1
0
2
1
1
1
1
1
2
0
1
1
1
1
1
1
1
1
0
0
1
1
0
1
1
1
2
1
2
1
1
0
1
1
1
0
1
1
1
2
0
1
2
2
1
1
1
0
0
2
2
1
1
1
1
1
0
0
1
1
0
1
1
0
1
0
1
1
1
0
1
1
0
1
1
1
1
1
1
1
1
2
1
2
0
2
2
2
1
1
2
1
1
1
2
2
2
2
0
2
3
1
2
1
2
1
1
2
1
1
1
0
0
0
1
2
1
0
0
2
1
0
0
2
1
2
0
2
1
2
0
1
0
1
2
2
1
0
0
0
1
1
1
1
2
1
1
1
2
1
1
0
2
1
0
1
1
1
2
1
1
1
2
1
0
2
2
1
1
1
0
2
0
2
2
2
0
3
3
1
0
2
1
1
1
0
0
0
1
0
1
1
0
1
1
2
1
2
1
0
2
1
0
1
0
1
1
1
1
1
2
0
1
0
0
1
0
0
1
0
1
1
0
0
1
1
0
0
2
2
2
2
2
2
1
0
1
1
2
1
1
2
1
1
0
1
0
1
1
1
1
1
1
0
1
0
1
1
1
1
0
1
1
0
1
1
1
1
1
2
1
2
0
2
0
1
2
1
1
0
2
0
1
2
1
0
0
0
1
2
2
1
0
0
1
0
0
2
1
1
0
2
2
1
0
1
0
2
0
1
2
2
1
0
1
2
2
1
1
0
1
1
1
1
2
1
2
1
1
1
0
0
1
1
1
1
2
0
2
1
0
0
0
1
0
2
1
0
2
3
3
2
1
2
2
1
0
2
1
1
1
1
1
5
1
2
0
1
1
0
1
0
0
0
0
0
0
0
1
1
4
0
2
2
1
0
2
1
2
0
1
1
3
1
1
1
2
0
0
1
1
1
1
1
1
2
1
0
1
1
1
2
1
1
1
1
2
2
2
0
1
2
0
2
2
2
1
1
0
0
0
2
0
1
2
2
1
0
1
0
1
1
1
1
0
0
0
0
0
1
1
0
0
1
1
1
0
1
0
0
1
0
1
1
0
1
2
1
1
1
2
1
2
0
1
1
0
0
1
1
1
1
1
1
1
1
1
0
1
1
2
0
1
0
1
0
0
0
1
2
1
1
0
1
1
1
2
0
0
0
0
2
2
2
1
0
1
1
2
0
1
0
1
0
2
1
2
0
0
0
1
1
2
2
1
0
2
1
0
2
1
1
0
1
0
0
1
0
1
1
2
2
1
0
1
0
2
1
1
1
1
0
2
0
0
1
2
1
0
1
2
1
1
2
2
2
2
1
2
1
1
1
1
2
3
2
2
0
1
2
2
1
1
1
0
1
2
2
2
2
1
0
1
0
0
1
0
1
2
0
2
2
1
1
1
1
2
0
0
1
1
2
1
1
2
1
1
1
0
1
1
1
1
2
1
0
1
1
0
0
1
1
0
0
2
1
1
1
0
1
1
0
0
1
0
2
1
0
1
0
1
1
0
2
0
2
2
1
0
2
2
1
1
1
0
1
1
0
0
1
1
1
2
1
0
1
1
1
2
0
1
2
1
1
1
1
0
1
1
2
1
0
1
1
2
0
2
1
1
0
1
1
0
0
2
2
3
2
1
2
1
1
1
1
1
1
1
0
0
1
1
0
1
1
0
4
0
0
2
1
1
2
1
2
1
2
1
2
1
0
1
1
2
3
2
1
1
1
1
0
2
1
1
0
0
1
0
0
2
1
1
0
0
0
1
2
4
1
1
1
0
2
0
0
1
0
1
1
2
0
1
0
0
3
1
2
1
0
1
0
0
1
2
2
1
0
1
0
0
2
0
1
1
1
0
0
1
2
0
1
1
0
2
0
1
0
1
0
1
0
0
1
0
1
1
1
0
2
0
2
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
0
0
2
0
2
0
0
2
2
3
1
0
1
0
0
1
2
1
1
2
1
0
3
1
0
1
0
0
2
2
0
0
1
1
1
1
0
3
2
1
0
1
2
1
1
1
1
2
1
1
2
0
0
1
1
2
1
2
2
2
0
4
1
0
0
1
1
1
0
0
2
0
1
1
2
0
1
1
1
1
0
1
2
2
0
1
0
2
1
0
0
2
1
2
1
1
1
2
1
1
0
1
0
2
0
2
1
0
2
1
1
2
0
1
2
1
1
2
1
1
1
1
0
1
2
0
2
1
0
0
0
1
1
2
1
2
0
1
0
0
0
0
1
1
0
1
2
2
2
2
2
0
1
1
0
0
1
1
0
1
0
1
0
1
1
0
1
1
0
0
3
1
1
2
1
1
1
2
1
1
1
0
0
1
1
2
1
0
1
0
0
1
1
2
1
0
0
0
1
0
1
1
1
1
1
1
1
1
2
1
1
0
2
0
2
1
1
0
1
0
1
1
1
1
2
2
1
0
0
0
0
0
1
2
0
1
1
0
2
0
2
1
1
1
1
1
1
1
1
0
0
1
1
1
2
1
1
2
1
2
1
1
2
1
2
1
0
1
2
1
0
1
0
2
0
0
0
2
1
0
0
1
0
1
2
1
2
0
1
1
2
1
1
1
1
1
1
0
1
0
1
2
1
0
0
2
1
1
1
2
0
1
1
1
0
0
1
1
1
1
0
2
1
0
2
4
0
2
0
2
1
0
0
1
0
1
2
1
1
0
1
2
0
1
2
0
0
0
1
1
1
1
0
1
1
1
0
2
1
0
1
2
0
0
0
0
1
1
0
0
2
2
1
0
2
0
0
2
0
2
0
2
0
2
1
1
2
1
1
0
0
1
2
2
0
0
1
0
0
0
1
2
0
1
1
1
2
1
0
1
3
1
1
2
2
0
1
0
1
2
1
1
1
2
0
1
0
0
2
0
0
1
2
1
1
0
0
0
1
0
0
0
2
2
1
2
0
1
1
0
1
2
1
1
2
1
1
1
1
2
2
2
1
2
1
0
1
0
1
0
2
0
1
2
0
2
1
0
1
0
2
1
1
1
1
0
1
0
2
2
2
0
0
0
1
0
0
3
2
0
0
1
2
1
0
2
0
1
2
0
1
2
1
0
1
1
1
3
0
0
1
1
1
1
1
1
1
1
1
0
0
2
1
1
1
1
2
1
0
2
2
2
1
2
0
0
2
1
1
2
1
1
1
0
1
0
1
2
1
1
2
1
1
2
0
2
1
1
1
1
1
1
1
1
2
1
1
0
1
2
1
2
1
2
1
1
0
0
1
1
1
2
2
0
2
1
2
1
1
1
1
1
2
1
1
1
2
2
1
2
1
0
0
2
1
1
1
0
1
0
1
1
0
0
0
1
2
1
1
1
1
2
1
1
1
2
1
1
1
1
0
2
1
1
0
0
0
1
2
2
0
1
1
2
1
1
1
2
1
2
1
3
1
2
1
1
2
1
0
1
1
1
1
0
0
1
1
1
0
1
1
1
1
0
0
2
1
0
0
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
2
0
2
0
0
2
2
0
1
0
1
1
1
0
1
2
3
1
0
2
0
2
1
1
1
2
1
2
1
1
0
0
1
0
1
0
2
0
0
1
1
1
0
1
2
1
1
1
0
3
0
1
1
0
0
1
1
0
1
0
0
1
1
2
1
1
1
1
2
2
0
1
1
1
2
1
1
1
2
1
1
1
2
0
1
1
1
2
1
4
1
0
1
2
2
0
1
1
0
1
1
2
2
1
0
2
2
1
1
1
1
1
1
1
0
0
1
2
1
2
2
1
1
1
1
0
2
1
1
1
1
1
1
0
2
1
0
1
0
1
2
1
2
1
1
1
2
1
2
1
1
1
2
1
2
0
0
0
1
1
0
0
0
0
0
1
1
0
1
1
1
1
2
1
0
0
0
0
0
1
2
2
1
1
2
0
1
1
0
0
0
2
1
0
0
1
1
1
0
2
1
0
1
1
0
1
0
2
1
0
1
2
2
2
2
1
0
0
1
2
1
2
1
1
2
1
2
0
1
2
1
1
0
2
0
2
1
2
1
1
0
1
2
1
2
1
2
1
1
2
0
1
2
1
0
1
1
0
0
2
1
1
2
1
0
1
1
0
1
1
1
1
1
1
1
2
1
1
1
0
2
1
1
0
1
1
0
2
2
1
0
2
0
2
3
0
1
1
2
2
0
0
1
0
2
1
0
1
0
1
1
1
8
2
0
0
1
2
1
0
1
1
2
2
2
0
1
0
0
1
1
0
1
1
2
0
1
1
1
1
0
1
1
1
1
2
2
2
2
2
0
2
1
1
1
1
0
2
0
1
1
3
2
1
2
1
1
1
1
0
1
0
1
2
1
1
0
1
2
0
1
1
1
1
1
0
1
0
2
1
1
0
0
1
1
0
1
0
2
1
1
2
1
1
1
0
1
1
2
1
2
2
2
1
1
1
1
0
1
0
1
1
1
1
1
0
1
1
0
1
1
1
1
1
2
2
1
1
0
1
1
0
1
2
1
1
1
0
2
1
0
2
1
1
1
1
1
0
1
0
0
0
2
2
1
1
1
1
1
1
1
2
1
1
1
0
1
0
2
0
2
1
2
0
1
0
1
2
0
2
2
1
2
1
1
1
2
2
0
1
1
1
1
2
0
1
0
1
0
1
1
0
0
2
0
0
1
1
1
0
0
1
1
2
1
0
1
0
1
2
1
1
1
1
0
1
2
0
0
0
1
2
2
2
2
1
1
2
1
2
1
1
1
1
2
1
2
0
1
1
1
1
0
1
1
0
0
1
1
1
1
1
1
1
1
0
0
2
0
0
1
1
1
0
1
1
0
1
0
2
2
2
0
2
2
2
1
1
1
1
1
0
2
1
1
2
2
1
1
1
2
1
1
1
2
0
2
0
2
0
2
1
1
2
2
1
2
1
0
1
1
1
1
1
1
1
0
1
0
1
2
1
1
1
0
0
1
1
1
1
1
2
0
0
1
2
2
2
0
2
1
1
1
1
1
0
2
0
0
2
1
0
1
2
1
1
1
1
1
1
1
2
1
1
2
2
2
1
1
1
1
0
2
1
1
1
0
1
1
1
1
1
2
1
0
0
0
0
1
1
2
1
0
2
1
2
2
1
1
3
0
1
1
0
1
1
0
2
2
1
1
0
1
1
1
0
2
2
0
0
2
0
1
1
0
1
1
1
1
1
1
0
5
1
1
1
0
1
1
0
0
1
1
0
2
1
1
1
1
1
2
1
2
1
0
1
1
1
1
1
1
2
1
1
1
1
0
1
0
1
2
1
1
1
0
1
2
1
0
3
2
1
0
2
0
1
1
1
0
1
1
1
0
1
1
1
1
1
2
1
1
1
1
2
3
1
1
1
1
1
2
1
0
1
2
0
1
1
0
1
0
2
2
1
0
1
1
0
0
1
1
0
0
1
1
1
0
0
2
0
2
1
0
1
1
2
1
1
1
0
1
1
0
0
1
1
3
1
0
2
1
2
0
1
2
2
0
2
1
2
1
1
1
1
1
2
0
1
0
0
1
1
1
1
1
0
2
1
1
1
1
1
2
2
0
1
2
2
0
0
1
1
2
0
2
0
2
1
1
1
0
1
1
0
2
1
2
1
0
1
2
2
0
1
1
0
1
2
0
2
1
1
1
1
1
2
1
0
1
2
0
1
1
1
1
2
1
2
2
0
1
1
1
2
1
1
0
1
2
2
1
2
1
1
2
0
0
2
0
2
1
2
0
1
1
1
0
0
1
0
0
1
1
2
0
2
0
1
1
1
2
0
0
2
2
1
1
1
2
2
1
1
1
1
1
2
0
0
1
0
1
1
1
0
1
1
1
1
1
1
1
1
0
1
0
2
0
1
0
2
1
2
1
1
1
2
2
0
0
0
1
2
4
0
0
1
1
3
0
1
1
1
1
1
2
2
0
1
1
1
1
1
1
1
2
1
2
1
2
1
1
0
1
1
0
2
0
0
1
1
2
2
1
1
0
2
2
0
0
0
0
0
1
2
1
1
2
1
2
1
2
0
0
1
1
1
0
2
1
1
1
1
1
1
0
0
0
1
0
3
1
2
1
1
0
2
1
2
1
0
1
0
0
0
1
0
1
1
0
2
2
0
2
1
1
1
0
0
1
1
0
0
1
0
1
1
0
0
2
1
0
1
2
0
1
1
1
1
1
2
1
1
0
0
1
1
0
1
0
1
0
1
2
1
1
1
1
2
2
1
0
2
1
1
1
0
1
0
2
0
1
1
1
2
0
0
1
2
0
0
1
0
1
1
2
2
0
0
1
2
1
0
1
0
2
2
0
1
1
2
2
0
1
1
0
1
0
2
1
0
2
1
1
0
1
1
0
2
1
1
1
2
1
2
1
1
2
1
1
1
1
1
2
0
0
1
1
1
2
2
1
2
0
2
1
1
0
0
2
2
1
2
1
1
1
0
1
2
1
2
2
1
1
1
1
1
2
1
1
1
0
2
1
1
0
1
0
1
2
0
1
0
1
2
1
0
1
3
1
0
2
1
2
2
4
0
1
4
1
1
1
2
1
1
0
1
2
1
1
1
1
1
1
1
1
1
1
2
1
2
0
1
1
1
0
1
0
2
2
1
0
2
3
1
0
2
1
1
1
0
2
1
1
1
0
1
0
1
1
1
2
1
0
2
2
1
2
0
2
1
2
1
2
1
1
1
1
0
0
1
1
1
1
0
1
2
2
2
1
0
0
1
1
0
1
1
0
3
0
1
2
2
1
0
2
0
2
2
1
1
1
0
1
2
1
0
1
2
2
0
1
1
2
2
1
0
1
2
1
1
2
0
1
1
2
2
1
0
2
0
1
1
1
0
1
0
1
1
0
0
1
0
1
1
2
1
2
0
1
0
1
0
1
0
0
1
2
1
1
2
1
0
2
2
1
2
0
2
0
1
2
1
0
1
2
1
0
2
0
1
0
2
1
0
2
0
1
1
1
1
1
2
0
0
0
1
1
1
1
1
1
1
0
2
1
2
1
0
2
0
1
1
1
0
2
1
0
1
3
2
1
2
1
2
0
2
1
0
1
1
0
1
2
1
1
2
2
0
1
1
2
0
2
2
0
1
0
2
1
1
0
2
2
1
2
2
2
0
1
2
1
1
0
0
1
2
0
2
2
1
1
1
2
2
0
1
1
0
1
0
1
2
0
0
1
1
1
0
1
1
1
2
2
1
1
0
1
3
1
1
1
2
2
2
0
1
1
1
1
0
0
1
1
1
0
2
1
1
2
1
0
0
1
0
0
1
1
1
1
1
1
1
1
0
2
0
1
1
1
1
1
1
0
0
0
1
1
2
0
2
0
1
1
1
2
1
1
2
1
2
0
4
0
2
1
0
1
1
0
1
0
1
0
1
2
2
0
2
1
0
1
1
2
1
1
0
0
0
0
2
1
2
1
1
1
1
2
1
1
1
0
1
2
1
2
2
1
1
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
1
2
1
2
2
1
1
0
1
1
1
2
0
1
3
1
0
1
0
0
1
1
2
1
0
1
1
2
1
1
1
2
0
1
0
0
1
2
1
2
1
1
1
1
1
0
1
2
1
2
2
2
2
2
1
1
0
2
1
2
2
0
0
1
1
0
0
1
0
1
1
0
3
0
0
1
1
1
2
1
1
0
2
1
1
1
1
1
2
1
1
0
0
0
0
0
1
0
1
1
2
2
1
2
2
1
1
1
2
1
2
1
1
2
0
1
1
1
0
0
1
2
1
1
0
1
2
2
1
1
1
1
1
1
1
2
0
1
2
2
1
0
1
1
0
1
3
2
1
1
2
1
2
1
1
2
0
0
1
1
1
1
2
1
1
1
1
0
2
1
0
1
1
1
1
1
0
1
1
1
2
1
1
1
2
0
1
1
1
1
1
0
0
2
1
1
3
0
2
0
1
1
0
2
0
1
3
1
0
2
2
1
0
1
2
2
3
0
0
1
1
2
1
2
1
2
2
0
2
2
0
1
1
1
3
1
2
1
0
0
0
2
1
2
1
1
1
2
2
1
0
1
1
2
1
2
2
2
1
1
3
1
0
1
0
1
1
1
1
2
1
0
1
1
1
0
1
1
1
1
1
1
1
1
2
1
2
1
0
0
1
3
1
0
0
2
0
1
1
0
0
2
0
1
1
1
2
1
0
1
0
1
1
1
0
2
0
1
2
2
1
2
0
1
2
2
2
0
1
0
0
2
2
3
1
2
2
0
1
0
0
1
2
1
1
1
0
2
2
1
0
0
2
2
1
1
1
1
1
2
1
1
1
2
0
1
0
1
1
0
0
2
1
1
0
2
1
0
1
2
1
0
2
1
1
1
1
2
1
1
1
2
1
1
2
1
1
2
1
1
0
0
2
2
1
1
0
1
2
1
1
1
0
1
0
0
1
2
2
1
1
1
1
1
1
2
1
2
1
2
1
0
1
1
1
0
1
2
1
1
2
0
0
1
0
2
1
1
1
0
0
1
2
1
1
1
1
1
1
0
1
2
2
2
0
1
0
2
1
0
1
1
0
2
2
1
2
2
0
1
0
0
2
1
2
0
2
0
0
1
2
1
1
2
0
0
1
1
1
0
2
0
1
1
1
1
2
0
2
2
1
1
1
1
1
1
1
1
0
1
1
2
1
1
1
2
2
2
2
1
1
0
0
0
0
1
1
1
1
0
0
2
1
1
0
1
0
0
1
1
1
1
0
0
1
2
0
1
2
1
0
2
1
1
2
2
0
2
1
1
1
2
1
0
0
0
3
1
1
2
2
1
1
1
1
1
2
0
2
1
1
2
2
3
0
1
3
0
0
1
1
1
2
1
1
2
2
1
0
1
2
2
1
0
1
1
1
1
1
0
2
2
0
0
2
0
3
0
1
1
1
2
1
1
1
1
1
1
2
0
1
1
0
1
0
2
2
0
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
0
0
1
1
0
1
1
1
1
2
1
1
2
0
2
0
1
0
2
1
2
2
1
0
1
2
1
1
1
1
2
1
0
1
0
1
1
1
1
0
1
0
1
1
1
1
1
1
1
0
0
0
1
1
1
1
0
0
1
1
1
1
1
2
1
2
1
2
1
1
2
0
2
1
1
2
0
1
0
1
1
1
0
1
1
1
2
1
2
1
2
1
0
0
0
2
0
0
1
2
1
0
1
0
0
1
2
1
0
1
0
2
0
2
1
0
1
1
0
1
0
0
1
1
1
1
1
1
2
1
1
1
0
1
0
2
1
1
2
1
2
1
0
1
2
0
2
0
2
1
1
1
2
2
0
1
0
1
1
1
0
1
1
1
0
2
1
1
0
1
0
3
2
0
0
1
2
2
1
0
1
0
2
0
1
0
2
0
1
1
2
1
1
1
0
1
1
2
1
1
2
0
1
0
0
1
1
2
0
1
1
1
1
0
0
0
1
1
1
1
1
2
1
0
2
0
1
0
1
1
1
1
1
0
2
0
1
2
1
1
0
0
1
1
0
1
1
0
2
2
1
1
0
1
1
0
0
2
1
1
2
1
2
1
0
1
1
1
2
1
1
1
2
0
1
1
1
0
1
1
1
2
2
1
2
1
1
1
0
0
1
1
1
1
0
1
1
1
1
1
2
1
0
1
0
2
1
1
1
1
0
0
1
3
0
1
1
1
1
2
0
1
1
1
0
2
1
2
1
0
2
1
1
0
1
2
1
1
2
1
1
1
2
1
0
0
1
0
1
1
0
2
0
3
0
0
1
0
1
1
1
1
1
2
1
1
1
1
1
1
1
0
0
2
1
1
0
1
1
1
2
3
2
0
1
0
3
2
1
0
1
1
0
1
2
1
1
1
1
0
1
2
0
1
1
1
1
1
2
1
0
2
1
1
2
1
0
1
2
1
1
0
1
0
0
2
1
2
1
1
2
2
1
3
0
1
1
1
1
1
1
1
1
1
1
1
3
1
1
1
0
0
1
2
1
1
1
0
0
0
0
1
0
1
2
1
2
0
2
0
1
2
1
1
1
1
0
2
1
2
1
1
2
3
0
1
0
2
1
2
0
0
2
2
1
1
1
1
0
1
1
2
1
1
0
2
2
1
0
2
1
3
2
2
1
1
1
1
0
1
0
0
1
1
0
2
2
1
1
1
1
1
1
1
1
2
1
2
1
2
1
0
2
1
2
1
1
2
1
0
2
0
1
0
1
7
1
1
1
2
0
1
0
1
2
1
1
1
1
1
2
1
1
0
0
1
0
0
0
1
1
1
2
1
1
0
0
2
1
1
2
0
0
2
0
2
1
1
1
2
0
1
1
1
2
2
1
1
1
0
0
0
0
2
0
2
0
1
1
0
1
0
1
1
0
1
0
1
2
2
0
3
0
2
1
1
1
1
0
0
2
2
0
1
1
2
0
2
2
2
1
2
1
0
2
2
1
0
1
1
1
0
0
0
1
1
1
2
2
1
1
2
2
2
0
0
2
0
1
0
1
1
2
1
0
2
0
1
0
1
2
2
2
1
2
1
0
1
2
0
1
1
0
2
1
1
2
1
0
1
0
1
2
0
2
1
0
1
1
2
1
2
0
1
2
1
1
0
0
1
1
0
2
2
1
0
0
1
1
0
1
3
1
0
1
0
0
0
2
0
1
2
0
0
1
1
2
1
0
1
1
1
0
1
1
0
1
2
4
1
0
2
1
1
1
2
0
1
1
2
1
0
2
1
2
0
0
1
2
1
0
0
0
1
1
0
1
1
1
1
1
1
1
0
2
1
1
0
1
0
2
1
1
1
1
3
2
0
1
1
1
1
0
0
0
1
0
1
2
1
2
1
2
2
2
0
2
1
0
0
1
1
0
1
1
1
1
1
2
1
1
1
2
1
0
2
1
1
2
1
1
0
1
1
0
0
2
3
2
0
2
0
2
0
0
1
1
1
1
1
2
0
0
1
2
1
1
0
1
0
0
2
1
2
1
1
1
1
1
2
1
1
0
0
2
2
4
1
1
1
0
1
0
0
1
1
1
1
1
1
0
1
2
1
2
1
1
2
2
1
2
0
0
1
3
0
0
1
2
1
1
1
0
1
2
2
1
0
2
1
1
1
0
1
0
0
1
2
1
0
0
1
0
2
1
0
2
1
1
1
0
2
1
1
0
1
2
1
2
0
1
1
0
0
2
1
2
0
0
1
0
1
2
0
1
3
0
0
1
0
0
2
0
0
1
2
0
2
2
0
1
1
2
0
2
1
0
1
1
1
1
0
2
1
2
1
0
2
1
3
0
1
2
1
1
0
0
1
2
1
1
1
0
1
0
0
1
1
0
0
2
0
1
1
0
2
0
2
1
1
0
1
2
1
1
1
1
1
1
0
1
1
2
0
1
1
1
1
0
1
1
0
1
0
1
2
0
0
1
1
2
0
2
1
1
0
0
0
0
2
1
2
1
3
0
1
2
1
2
1
1
0
0
2
1
0
0
1
1
0
0
1
1
1
0
2
1
1
0
1
1
2
0
1
2
1
0
1
1
1
1
0
0
1
0
2
1
2
2
0
1
0
1
2
1
1
1
0
2
0
1
2
1
2
1
0
1
1
2
1
0
0
2
0
0
2
1
1
2
1
0
1
1
1
0
0
0
0
0
2
1
1
0
0
1
2
0
2
2
1
1
1
2
2
2
2
1
1
1
0
0
0
2
1
2
1
1
1
0
1
1
2
1
0
2
1
1
2
1
1
0
1
1
0
0
0
0
1
0
2
2
1
2
2
1
1
1
1
0
0
1
2
1
0
0
1
0
2
1
0
1
1
1
1
2
0
1
0
1
1
1
2
2
1
1
2
0
0
1
0
1
1
1
1
1
0
1
0
1
1
1
0
1
1
1
2
1
0
1
0
1
1
1
0
1
0
2
2
1
1
1
0
0
2
2
0
0
2
0
0
1
0
1
1
2
0
0
1
1
1
2
1
1
1
2
1
1
1
1
1
1
0
0
1
0
1
0
1
1
0
1
2
2
1
1
0
0
1
2
1
0
1
2
1
1
1
2
2
1
0
0
1
1
0
1
0
1
0
1
0
2
2
1
2
1
1
1
1
2
0
1
1
1
2
2
0
2
1
2
2
1
0
0
2
2
1
0
1
0
1
2
0
2
0
0
0
0
0
1
0
0
1
0
1
1
1
2
0
0
1
1
2
1
1
1
0
2
0
1
1
2
1
1
1
1
1
1
1
2
1
2
2
1
1
0
1
1
0
1
0
1
0
0
1
1
0
0
1
2
1
2
0
2
0
2
1
0
0
1
1
1
1
1
0
2
0
1
1
1
2
0
0
1
1
2
2
0
0
1
1
1
1
1
2
1
1
0
0
0
1
2
2
1
0
0
0
0
0
2
1
1
0
0
1
1
1
0
2
0
0
1
1
0
0
1
1
1
1
1
2
1
0
1
2
0
1
1
1
1
2
0
1
2
1
0
0
1
2
0
1
0
3
1
1
1
1
1
1
0
1
1
0
1
0
2
0
1
2
2
0
0
2
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
0
0
0
0
0
1
1
1
1
2
1
2
1
0
2
0
0
1
0
0
1
1
0
1
1
1
2
1
1
1
0
1
0
0
0
2
1
2
0
1
0
2
1
2
1
0
0
1
1
0
0
1
1
0
1
1
0
2
1
0
2
2
0
2
2
0
1
1
1
2
1
0
2
1
2
1
2
2
2
0
0
1
0
0
1
0
0
0
0
2
2
0
0
2
0
0
1
0
0
1
1
1
1
2
1
1
1
1
1
0
1
1
1
0
0
1
2
1
3
0
1
1
0
1
1
0
0
1
3
1
1
0
0
2
0
0
1
1
2
1
1
1
1
1
0
2
1
0
2
2
1
0
2
0
1
2
1
1
3
1
1
2
1
1
1
2
1
1
1
2
1
1
2
1
2
1
1
1
1
2
1
1
1
1
0
1
0
1
3
2
2
1
0
1
1
0
0
1
0
0
1
2
1
0
1
1
1
2
2
1
0
0
2
2
1
1
1
0
1
1
0
0
1
0
1
1
0
1
0
1
0
2
1
1
1
1
1
0
2
2
1
0
1
1
0
1
1
0
1
0
0
1
0
1
2
1
0
2
1
1
2
0
1
0
2
1
0
2
1
2
3
1
1
1
1
2
1
1
1
1
2
0
2
1
1
2
0
1
3
1
1
2
1
0
1
1
1
2
4
0
1
2
1
2
2
1
1
2
1
1
0
1
1
0
2
1
0
1
0
2
1
1
1
1
1
1
0
2
0
1
2
2
2
2
1
1
2
3
2
0
1
2
1
1
1
2
1
1
1
1
1
2
1
2
2
0
2
2
0
1
1
2
0
2
1
0
1
0
0
1
0
1
2
2
0
0
2
0
1
1
2
1
1
0
0
2
1
0
1
2
1
1
0
0
1
1
2
0
1
1
1
2
1
2
2
1
2
2
2
1
1
2
1
1
1
1
1
1
0
3
2
0
3
0
2
2
0
0
1
0
2
0
0
0
1
1
1
2
1
1
2
0
1
1
1
2
1
0
0
1
5
0
0
1
2
1
0
1
1
0
1
0
0
2
2
2
1
0
1
1
1
1
1
1
1
1
1
1
1
2
0
0
1
1
0
0
1
1
0
2
0
0
1
1
1
2
2
1
1
1
0
1
1
1
1
0
3
1
0
2
1
0
1
1
1
1
1
1
1
0
0
1
1
0
1
1
0
1
0
1
4
2
1
1
0
0
1
2
2
2
2
0
2
0
2
0
3
0
1
2
0
1
1
0
1
0
1
3
1
0
0
2
0
0
0
2
1
1
1
0
1
1
2
1
1
2
1
1
1
0
0
1
2
0
1
1
1
0
0
2
0
1
1
1
1
1
2
2
2
1
2
2
1
2
1
1
2
0
1
0
1
0
2
1
0
0
2
0
0
2
1
1
1
1
1
1
1
2
1
1
0
2
0
1
1
1
1
1
2
2
1
1
0
0
1
0
2
0
2
1
2
1
1
1
1
1
0
1
2
0
0
2
0
1
1
2
0
1
2
1
2
2
0
1
1
2
1
1
1
2
1
1
2
1
2
2
1
0
1
1
2
0
0
1
1
1
0
1
1
1
1
2
1
2
1
1
0
0
1
2
1
2
1
1
0
1
1
0
2
0
1
2
0
1
0
0
0
0
1
2
1
0
1
1
0
1
1
1
0
2
2
1
1
2
0
1
1
2
2
2
0
2
1
2
1
1
0
0
2
1
1
1
1
0
1
0
1
0
0
1
1
1
1
1
1
2
1
2
1
0
0
2
2
1
1
0
1
2
0
1
0
1
0
0
1
0
2
1
2
0
0
1
0
0
1
1
2
2
1
0
0
1
0
1
0
1
1
1
1
2
1
1
0
0
1
0
1
2
0
1
1
1
1
1
0
1
1
0
1
1
0
1
1
1
0
1
1
1
1
0
1
0
2
1
0
2
2
0
1
0
2
0
2
2
1
2
1
1
1
2
1
2
0
1
1
1
2
2
0
0
2
2
0
0
1
1
2
1
0
0
1
3
1
1
0
2
0
1
2
0
1
2
1
1
2
2
2
1
0
0
0
1
1
1
1
1
1
0
0
1
0
2
2
0
1
2
2
1
0
2
1
0
2
2
1
0
1
0
1
1
1
0
0
0
0
1
1
1
2
0
1
2
2
1
2
1
1
0
2
0
1
1
2
0
2
1
0
0
0
2
2
1
1
1
1
1
0
0
1
1
0
0
1
1
2
1
1
1
1
1
2
1
0
0
1
2
1
0
0
1
1
1
0
1
2
1
0
1
2
1
1
2
1
0
1
0
1
0
1
2
1
1
0
1
1
2
2
1
2
0
1
1
3
1
1
1
0
0
1
1
1
0
1
2
2
2
2
1
1
1
1
1
2
2
2
1
2
1
1
1
1
1
0
1
1
2
0
1
1
1
1
1
4
1
1
1
2
1
1
1
0
1
1
1
1
1
1
2
1
2
3
1
0
1
0
0
1
0
1
2
1
1
0
1
1
2
0
2
0
1
2
1
2
1
1
0
1
1
0
1
1
0
1
2
0
2
2
0
1
1
0
1
1
1
2
1
1
0
0
0
2
1
1
0
1
1
1
0
0
0
0
0
1
1
1
0
2
0
2
1
1
1
1
0
1
1
0
3
2
2
0
2
1
1
0
1
1
1
1
1
2
0
0
1
2
2
2
1
1
1
1
2
2
0
1
2
1
1
0
1
1
2
1
0
1
1
0
1
1
2
1
2
1
1
0
1
2
1
0
2
1
2
1
2
0
1
1
2
1
2
0
0
1
1
0
1
1
0
0
1
3
1
0
1
0
1
1
1
0
1
1
1
1
1
0
1
0
1
0
2
1
0
0
0
0
1
2
2
0
1
1
1
0
1
0
2
0
2
1
2
1
0
1
2
0
2
2
1
1
1
2
0
2
2
1
2
1
2
1
1
1
2
1
3
0
4
2
0
0
1
0
1
2
1
1
0
0
0
1
1
0
2
2
1
1
1
2
1
1
0
1
1
1
0
1
0
2
0
1
2
2
0
0
1
2
0
0
1
0
2
0
1
2
1
2
1
2
2
1
0
1
1
2
1
0
1
0
0
1
2
2
0
0
0
1
1
1
1
0
2
0
0
0
0
1
2
4
1
2
0
1
1
1
0
2
1
1
1
1
0
1
1
1
0
1
0
2
2
2
0
1
0
0
0
2
1
1
1
1
4
2
1
2
1
1
1
1
0
1
0
1
1
2
2
1
0
1
1
1
0
1
2
0
0
0
0
0
1
2
1
0
1
1
0
2
0
1
1
1
1
1
1
0
2
0
1
1
1
1
2
0
0
1
2
1
3
0
2
0
1
2
1
0
0
0
0
1
1
2
0
0
1
1
2
0
1
1
1
0
1
1
1
1
0
1
1
1
0
2
1
1
2
2
0
1
0
0
1
1
1
2
3
2
1
1
0
1
2
1
1
0
1
1
0
1
0
1
0
1
3
0
1
1
0
1
2
0
1
2
0
1
1
1
0
1
0
1
1
2
1
1
2
0
1
2
0
1
1
2
2
0
1
1
0
0
1
2
0
3
2
1
0
0
2
0
1
1
0
1
1
2
1
0
1
0
0
0
0
0
2
2
1
2
0
2
1
1
1
0
2
1
1
1
1
2
2
1
0
0
0
1
1
0
0
1
0
1
1
0
1
1
0
2
2
1
0
1
1
1
2
1
1
1
0
0
0
0
1
0
2
2
0
0
2
1
2
0
1
0
0
1
0
1
1
1
2
0
0
0
0
1
1
1
2
0
1
1
1
1
2
1
1
2
1
1
1
1
0
0
1
2
1
2
1
2
2
0
1
0
1
2
0
1
2
0
0
1
1
1
0
1
0
1
0
0
2
1
1
1
0
1
0
1
1
0
0
0
1
1
0
2
2
0
1
1
1
1
1
0
1
1
0
1
0
2
0
2
1
0
1
0
0
0
2
1
1
2
1
1
1
1
1
1
1
1
0
0
1
0
0
2
2
2
1
0
1
0
0
1
1
2
1
0
0
2
1
0
1
1
1
1
2
1
1
0
0
1
0
1
1
2
0
1
2
1
1
2
2
1
0
1
1
0
0
2
1
1
0
1
1
1
1
1
1
1
1
2
2
1
0
1
0
2
1
1
1
1
1
1
2
2
0
0
2
0
0
1
0
1
1
0
2
2
1
0
2
2
1
1
0
2
0
1
2
0
1
2
1
0
0
1
4
2
1
1
1
2
1
2
1
0
1
2
2
0
1
0
0
0
2
0
1
0
2
2
1
2
0
1
1
1
1
2
1
1
1
2
1
1
0
1
4
1
2
1
0
0
2
0
0
1
1
0
1
2
0
1
0
1
0
1
2
3
2
1
1
2
1
1
0
0
1
2
1
2
1
1
2
0
1
0
2
1
1
1
0
1
2
0
1
1
1
0
1
0
1
1
1
1
0
2
1
0
2
0
1
0
1
0
2
0
1
1
2
1
1
1
0
1
2
1
1
1
0
1
1
0
2
0
2
2
0
2
0
2
0
4
0
2
1
0
1
1
0
1
1
2
2
1
2
2
0
2
1
1
1
1
1
1
1
0
2
2
1
1
1
2
1
0
2
2
1
2
2
1
2
1
1
1
0
2
2
2
2
1
2
0
0
1
3
1
2
1
2
1
1
1
0
2
0
0
2
0
1
2
1
2
1
1
0
0
1
0
0
1
1
1
2
1
1
1
2
2
1
2
0
3
2
1
2
1
1
1
2
2
2
2
1
3
0
1
0
1
1
2
1
0
1
1
1
0
1
0
1
0
2
2
2
1
1
1
1
0
2
2
1
0
0
2
1
0
0
1
0
1
1
2
1
1
1
0
2
2
2
1
1
0
2
0
2
1
1
2
1
0
1
0
1
0
1
1
2
1
2
1
1
1
1
1
1
0
0
2
2
1
0
1
1
1
1
0
2
1
2
1
1
1
2
1
0
1
0
1
1
1
0
1
3
1
1
1
0
1
1
1
1
1
1
1
1
1
1
0
0
2
1
2
2
1
1
1
1
0
1
2
0
1
2
2
1
1
1
0
1
0
1
2
0
1
1
0
1
2
1
0
1
1
0
1
0
2
2
1
1
1
0
1
1
1
1
2
1
2
2
0
1
0
0
1
1
1
0
0
2
0
1
1
0
1
1
2
1
0
1
2
1
1
1
1
2
2
1
2
0
2
1
2
1
1
0
1
0
0
2
1
0
0
2
1
1
1
0
2
2
1
1
0
2
2
0
2
1
1
2
0
1
1
1
1
0
1
0
2
0
1
1
0
2
1
1
1
2
1
1
1
1
2
1
0
1
1
1
1
1
0
1
0
1
0
1
0
1
0
1
0
0
1
0
0
0
1
0
1
2
0
2
0
0
0
2
1
1
1
0
1
2
0
1
0
1
2
1
0
0
2
1
1
0
0
1
0
1
0
0
1
0
1
1
0
0
1
0
0
2
2
1
1
0
0
0
2
0
2
1
1
0
0
0
1
0
4
1
1
1
0
1
0
1
1
2
2
1
1
1
1
1
1
0
1
1
1
1
1
1
1
0
0
1
1
2
1
2
1
1
0
1
0
0
1
1
1
1
0
1
0
1
2
1
2
0
1
1
1
2
3
2
3
0
2
1
2
1
0
1
0
0
0
1
0
1
1
1
1
1
1
0
2
2
2
0
1
0
0
2
2
1
0
2
1
1
0
1
0
1
1
1
0
1
2
2
0
1
1
2
0
1
3
2
1
1
1
1
1
1
0
0
1
2
1
1
0
2
2
1
1
0
2
1
1
0
0
0
1
0
1
3
1
1
1
0
1
1
1
2
0
1
0
1
0
0
0
1
1
1
1
2
2
1
1
1
1
1
2
0
0
0
0
3
1
0
0
1
0
1
0
1
0
0
0
2
1
1
1
0
0
0
1
0
2
0
0
0
2
2
0
2
1
1
1
0
1
1
0
1
1
2
0
0
1
1
1
0
0
2
1
1
0
1
1
2
1
1
2
2
1
1
2
2
0
1
0
2
2
2
2
2
2
1
2
1
2
1
2
1
1
1
1
1
1
1
2
1
0
1
1
1
2
1
2
0
0
2
0
2
1
1
2
0
1
1
2
1
1
1
1
0
0
1
1
1
1
1
2
1
0
2
1
0
1
0
1
1
1
1
2
1
2
0
1
2
2
1
0
1
1
1
2
1
0
1
0
2
1
1
1
0
2
1
2
1
0
1
2
2
1
1
1
1
1
0
0
1
1
1
0
1
0
1
1
0
2
1
1
2
2
1
2
0
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
0
1
1
0
3
1
1
1
0
1
0
1
1
1
1
2
0
0
2
0
1
1
0
1
1
0
0
1
2
1
2
1
0
1
0
1
0
1
0
1
2
1
1
1
2
1
1
1
1
1
2
0
0
2
0
0
1
1
0
0
2
1
2
2
1
2
2
0
2
1
1
2
0
1
2
1
2
1
1
1
0
2
1
1
1
1
2
1
3
0
2
1
0
2
1
1
1
1
2
0
1
1
1
0
1
0
2
2
0
2
0
1
0
1
1
0
1
2
2
1
1
2
2
2
2
0
1
0
0
2
1
2
1
0
1
0
1
2
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
2
0
1
2
2
1
1
1
1
2
1
2
4
1
1
1
0
2
3
1
1
1
2
2
0
1
2
2
1
1
0
2
2
0
1
1
1
0
4
2
0
1
1
1
1
3
1
0
1
1
0
2
2
1
1
0
0
0
2
2
1
2
3
1
2
1
0
1
0
0
1
2
0
0
0
1
1
1
0
1
2
1
1
2
1
1
6
2
1
1
1
2
1
0
2
1
0
1
2
2
2
1
1
1
3
1
0
2
0
2
1
1
1
2
0
0
1
1
1
0
0
2
0
0
0
2
2
1
2
2
0
0
0
1
0
1
1
1
1
2
0
1
1
2
0
1
1
1
0
1
1
0
1
0
1
1
0
2
2
1
3
2
0
1
0
2
0
0
1
0
2
0
1
1
0
3
1
1
2
0
0
0
0
0
1
2
2
0
1
1
1
0
1
1
1
0
1
1
0
1
0
2
1
1
3
1
0
1
1
0
2
0
0
1
1
1
1
0
0
2
1
0
1
1
2
1
0
0
2
1
1
1
0
1
1
1
1
0
0
1
0
1
1
2
6
0
0
0
2
2
2
0
1
0
1
0
0
1
1
1
0
0
1
0
2
0
2
0
1
1
1
0
2
0
1
2
2
2
2
1
0
1
1
1
1
2
1
1
0
1
1
1
2
1
1
1
1
1
1
2
0
1
1
1
1
2
1
1
1
1
2
1
0
0
1
1
0
2
2
0
1
2
0
0
1
1
1
1
1
0
1
1
1
2
0
1
2
0
2
1
2
1
1
0
2
1
1
3
1
0
1
1
0
0
1
1
0
2
0
0
1
2
2
1
0
0
1
1
1
1
1
1
0
0
0
0
2
0
1
1
1
1
2
0
0
2
1
2
1
1
1
1
0
0
2
0
1
1
2
1
1
1
0
2
1
0
0
1
1
1
1
2
0
0
1
1
0
0
0
2
1
2
0
1
1
1
0
1
0
2
1
1
2
1
1
1
2
3
1
1
2
1
1
1
1
1
1
0
0
2
1
0
2
1
1
1
1
1
0
3
2
0
1
1
2
0
0
2
1
2
0
1
1
1
2
1
1
2
0
1
0
0
2
0
2
0
2
1
1
2
1
0
2
1
0
1
1
1
1
0
1
0
2
2
1
1
0
1
1
1
1
1
1
1
2
2
1
0
1
1
1
2
1
1
1
2
2
2
0
2
2
2
2
2
2
1
2
0
0
1
1
0
2
1
0
1
1
2
0
1
1
2
0
0
1
0
1
2
1
3
2
1
2
2
1
0
1
2
1
1
1
2
0
1
1
1
1
1
1
1
0
0
0
1
2
1
1
2
0
0
1
4
0
2
1
2
2
1
2
0
0
1
0
0
1
0
2
1
1
1
0
1
1
1
0
2
1
1
2
1
2
1
1
1
0
1
1
1
2
0
4
0
0
2
1
4
1
0
0
0
0
2
0
2
1
2
0
1
2
1
1
1
1
1
0
0
1
2
2
0
1
1
0
2
1
1
1
1
1
0
1
0
1
2
1
2
1
2
3
1
1
2
1
2
1
1
1
0
1
1
1
2
2
1
1
0
1
0
0
2
2
1
0
0
1
2
1
1
1
1
1
1
0
1
1
0
2
1
1
1
1
2
1
2
0
0
1
2
1
1
0
1
1
2
1
1
0
2
1
1
0
2
2
1
1
0
1
1
1
2
1
1
0
1
2
1
1
0
1
1
1
1
2
0
1
0
2
1
2
0
2
2
0
1
1
1
1
1
0
1
1
0
1
2
2
1
1
1
2
0
1
0
1
1
0
2
0
0
1
0
1
0
2
0
1
1
1
0
2
1
0
1
1
2
1
1
0
1
1
0
1
1
0
2
1
0
2
1
1
0
1
0
1
1
2
1
2
1
1
1
1
0
1
1
2
0
3
0
0
2
0
0
2
1
0
1
2
0
1
1
1
0
0
1
2
0
2
1
1
1
0
2
2
2
1
1
2
2
2
1
0
0
0
0
0
0
1
1
1
2
2
0
2
1
2
1
0
2
1
0
0
0
0
0
0
0
2
2
1
1
0
0
0
1
1
0
1
2
1
1
1
1
1
2
0
0
1
1
0
1
0
2
2
1
1
1
1
2
0
3
1
0
1
1
1
0
1
1
1
2
2
1
2
1
0
0
0
2
0
1
1
0
2
0
2
2
1
1
2
0
0
2
1
1
1
1
1
0
2
1
1
2
0
1
1
2
0
2
2
1
2
1
1
2
1
0
0
1
0
1
1
0
1
1
2
1
1
2
1
2
0
1
0
0
1
1
1
1
1
1
0
1
1
0
1
1
0
1
3
1
1
1
0
0
1
1
0
1
0
0
1
0
1
0
2
1
0
2
0
2
2
2
0
0
1
1
1
1
1
1
1
2
1
1
1
0
0
2
1
2
0
1
2
0
1
1
2
2
2
1
0
0
0
0
1
0
0
1
1
0
2
1
1
0
1
0
0
1
1
0
1
2
3
1
1
1
1
1
0
0
1
0
1
1
1
0
1
0
2
0
0
1
2
2
1
1
1
1
2
1
1
2
1
1
0
0
0
0
2
1
0
1
0
2
2
2
1
1
1
1
0
2
1
0
2
0
0
2
1
2
1
0
1
1
1
2
1
2
0
1
2
1
0
1
1
1
2
1
0
2
0
1
1
1
1
2
2
1
1
1
1
0
1
2
0
1
2
0
1
0
2
1
0
2
1
0
1
1
0
2
2
1
1
1
1
2
2
1
0
1
1
1
1
0
1
1
1
1
1
2
1
0
2
1
2
1
2
1
1
1
1
0
0
1
0
0
1
0
0
1
2
2
0
0
0
1
1
1
2
2
2
2
1
1
0
0
0
0
0
0
0
1
1
1
2
1
0
0
0
0
0
0
1
1
2
1
0
2
0
2
0
1
1
2
0
2
0
2
1
2
0
1
2
1
1
1
0
1
1
1
0
1
0
1
2
1
2
0
0
0
1
0
3
1
0
0
2
1
0
0
1
1
1
1
1
1
1
1
1
1
1
1
2
0
1
2
0
2
0
1
0
2
0
1
0
2
2
0
2
1
1
1
2
0
1
2
2
2
1
1
2
2
1
2
0
2
2
1
0
0
1
1
0
1
1
1
2
0
2
1
1
0
0
2
2
1
0
0
2
1
1
1
0
2
1
0
3
1
2
2
1
2
0
1
1
0
0
0
1
1
2
1
1
1
2
0
1
2
1
1
1
2
0
2
2
1
0
1
1
2
0
0
1
1
1
0
0
1
1
0
1
1
0
0
1
2
1
1
2
1
2
1
0
0
1
1
2
0
2
1
2
2
1
1
1
1
1
1
2
1
1
1
0
1
2
0
0
0
1
0
1
2
1
1
1
2
1
1
0
1
1
1
2
1
2
1
0
0
2
2
1
1
2
1
2
2
0
2
1
0
2
1
0
1
0
2
0
0
0
2
1
0
2
2
1
1
2
1
1
0
1
1
0
0
0
0
1
0
2
2
1
1
1
1
2
1
0
2
1
1
0
1
1
1
2
2
0
2
0
1
1
1
0
1
2
0
1
1
1
2
1
0
1
2
1
2
0
2
1
0
1
0
0
1
1
1
1
2
0
1
2
3
2
2
1
1
1
1
2
0
1
1
2
2
0
0
0
1
2
0
0
2
1
1
2
1
3
1
0
0
1
1
1
1
1
1
0
2
2
2
2
1
1
1
2
2
1
1
2
1
1
0
0
0
2
0
2
1
2
2
2
0
0
2
1
1
1
0
0
1
1
0
0
0
2
0
1
1
2
2
2
2
0
2
1
0
0
0
1
1
1
1
1
1
1
0
0
1
1
0
1
2
1
0
1
0
1
1
1
0
1
1
2
2
2
1
2
1
1
0
2
0
1
1
0
3
1
1
2
1
2
1
2
1
4
1
1
1
0
0
0
0
0
1
0
1
2
1
1
0
1
1
2
1
0
1
1
1
0
0
1
0
1
0
1
0
1
1
1
0
2
1
1
0
0
0
1
1
0
1
0
1
1
0
0
2
0
0
2
1
1
0
2
0
2
0
1
2
1
2
1
2
1
1
1
0
1
0
1
2
1
0
1
0
1
1
0
1
0
0
2
1
1
2
0
1
1
2
1
1
0
0
0
2
2
0
1
1
1
1
2
1
0
0
2
0
2
2
1
1
0
0
0
1
1
1
0
0
1
3
1
2
1
2
1
1
2
2
0
0
1
1
2
0
1
2
1
1
2
2
1
0
0
1
0
1
1
1
2
1
0
0
0
1
1
2
1
0
1
1
0
1
2
1
0
1
2
0
1
0
1
1
1
0
1
2
1
1
0
1
2
1
1
2
0
1
1
1
1
1
2
1
0
2
0
1
1
0
1
1
1
1
1
2
1
1
1
0
1
1
1
1
1
1
2
2
1
2
0
2
1
1
0
0
0
1
1
1
0
2
1
1
1
2
0
0
2
1
2
1
1
1
2
1
1
1
1
0
0
2
1
0
2
0
1
1
0
0
2
0
0
1
0
2
2
0
1
1
0
0
0
1
1
1
1
2
2
2
2
2
1
2
1
1
1
1
1
0
1
1
1
2
1
0
1
1
1
1
1
0
2
2
1
0
1
1
0
0
1
1
1
1
1
1
2
0
1
2
1
1
2
1
0
2
1
0
0
1
1
1
2
1
1
2
0
1
1
1
1
0
2
1
1
1
1
1
0
1
2
1
1
1
1
2
0
2
2
1
2
1
1
1
1
2
1
1
0
1
1
1
0
1
0
1
1
1
1
1
0
0
1
2
1
2
1
0
2
0
0
1
1
0
1
1
2
1
1
1
1
1
1
0
1
1
0
1
0
1
1
2
2
2
1
1
2
1
0
1
2
1
1
2
0
2
0
1
1
0
1
1
1
1
1
1
0
2
1
1
0
1
1
1
0
1
1
1
1
2
1
1
0
1
1
0
1
1
1
1
1
1
0
1
1
0
2
1
0
2
1
1
2
1
0
1
0
0
1
1
0
1
0
0
2
1
1
1
0
1
1
0
0
0
0
1
1
1
0
3
1
1
1
1
2
1
1
1
1
0
1
1
0
0
1
2
0
2
2
0
2
2
1
0
0
0
1
2
1
2
2
2
2
2
1
1
1
0
1
1
3
0
2
0
0
2
2
0
0
1
0
1
1
0
2
0
0
2
1
2
1
0
2
2
1
2
1
2
2
2
1
1
0
1
1
0
1
1
2
0
1
1
2
1
1
1
0
0
2
0
2
1
1
0
1
0
0
1
2
2
0
1
1
1
0
1
1
0
2
1
2
1
1
0
1
2
1
1
2
2
1
1
1
0
2
0
1
1
1
0
2
1
2
2
0
0
0
2
1
1
2
0
0
0
1
1
0
1
0
2
0
2
2
1
1
2
0
1
2
1
0
2
1
0
1
1
0
0
1
2
1
1
0
0
2
0
0
1
1
2
1
1
1
1
1
1
0
0
3
1
2
0
1
1
1
0
1
1
0
2
0
1
1
1
1
1
0
1
2
0
0
1
1
0
1
0
2
2
0
0
1
8
1
1
1
1
2
1
1
1
1
1
0
1
2
1
1
1
1
1
1
1
0
2
1
0
2
1
0
0
0
0
1
0
1
1
2
2
0
1
0
0
2
1
0
1
0
1
1
0
1
1
1
0
2
1
1
2
1
1
1
1
2
1
1
1
1
2
0
1
1
1
1
1
0
1
1
2
0
1
1
0
1
1
1
1
1
1
1
1
1
2
1
0
1
0
1
1
1
1
1
2
1
1
1
0
0
0
1
1
1
1
0
0
0
1
1
0
1
1
0
0
0
1
1
1
2
1
1
0
1
0
1
1
2
0
0
1
2
2
1
0
2
0
1
2
0
0
1
0
1
1
0
1
1
0
2
1
2
0
2
1
0
1
1
1
1
1
1
1
2
0
0
3
2
1
1
1
2
0
2
1
0
1
2
2
2
1
0
0
1
1
1
1
2
1
1
1
0
1
0
3
1
2
0
0
1
1
2
1
1
1
1
1
1
2
1
0
0
1
0
1
1
1
1
1
2
2
2
1
2
0
0
1
2
1
1
2
1
1
1
1
1
2
1
1
0
2
0
2
1
1
1
1
1
2
0
0
0
2
1
1
1
0
0
2
2
2
1
1
2
1
1
1
0
1
1
2
3
1
2
1
2
2
1
0
1
1
0
1
1
2
1
3
1
1
1
1
1
0
1
0
1
0
0
0
1
1
0
2
2
1
2
2
2
2
1
1
1
1
1
3
1
0
0
1
0
1
2
0
1
0
2
1
0
1
1
2
1
2
1
1
1
2
1
2
2
2
0
1
1
1
1
3
1
1
1
0
0
1
0
1
0
1
0
1
0
0
2
1
0
1
1
0
0
0
0
2
0
2
1
1
1
1
0
1
1
2
1
0
2
0
1
1
1
2
0
1
1
1
2
2
0
0
0
0
0
1
2
0
0
1
1
2
0
2
1
2
2
2
1
1
1
2
1
2
0
0
1
0
2
2
0
1
2
1
1
2
1
1
1
0
1
0
1
1
1
0
1
1
0
1
1
0
1
0
1
2
1
0
2
0
2
1
1
0
1
0
1
0
1
1
1
1
1
0
1
1
1
1
2
1
1
1
1
0
1
2
1
3
1
1
0
1
1
1
0
1
1
0
0
0
1
0
1
2
1
1
1
2
1
1
1
0
4
1
0
0
1
2
0
1
2
1
0
0
2
1
2
1
1
0
0
1
2
1
1
1
0
1
1
2
1
0
1
0
0
0
2
1
1
0
2
1
6
0
0
1
1
2
1
1
2
2
1
1
0
1
0
1
1
1
1
2
1
0
1
3
0
2
0
0
1
1
1
1
0
1
0
1
2
2
0
1
1
1
0
1
1
1
0
0
1
2
1
1
2
3
0
1
1
2
0
1
1
1
0
1
1
1
1
1
1
2
0
2
1
1
1
0
0
1
1
1
2
1
0
0
1
2
2
2
2
0
0
1
2
1
1
1
1
1
2
1
1
3
0
0
1
2
0
0
2
1
2
0
1
0
0
0
0
0
0
1
2
2
1
1
2
1
0
1
0
1
0
1
1
1
0
1
1
1
1
1
1
1
0
0
2
1
0
1
1
2
1
1
1
1
0
1
1
1
0
1
2
1
2
2
1
1
1
2
1
2
1
1
1
1
1
0
0
1
2
1
2
1
2
1
1
0
2
2
2
1
0
1
1
1
1
1
2
1
0
2
0
0
0
0
1
1
0
2
0
1
1
1
1
1
2
2
1
2
2
0
1
2
1
0
0
0
0
1
2
1
1
2
2
2
0
1
1
1
2
1
2
1
1
1
1
0
2
1
1
1
2
2
1
1
1
1
0
1
1
1
0
0
1
0
1
2
1
1
1
1
1
1
1
0
0
1
1
0
0
2
2
0
0
1
1
1
1
1
1
2
1
1
1
1
2
0
2
0
0
0
2
1
0
0
0
1
0
1
0
2
2
1
0
0
2
0
0
1
1
0
1
0
2
1
2
1
0
2
0
0
2
1
1
2
1
1
0
0
1
0
0
1
0
0
1
1
0
1
0
1
3
1
1
0
1
2
0
2
2
1
1
0
0
0
1
1
0
2
1
3
0
0
0
0
1
0
0
1
1
1
1
2
1
1
1
1
1
1
0
1
1
1
2
2
0
0
1
2
2
2
0
1
1
1
1
1
1
2
0
2
1
0
0
0
1
1
1
0
1
3
1
1
0
1
1
1
0
2
1
2
1
1
2
0
2
1
0
1
1
1
1
1
1
0
1
1
1
2
3
2
1
1
0
1
1
2
2
0
2
1
0
1
1
2
1
1
2
1
2
0
0
1
1
0
1
0
1
1
1
0
2
0
1
1
1
1
1
1
0
1
0
1
1
0
0
1
2
1
1
1
1
0
1
0
2
1
1
0
0
1
2
1
1
1
1
1
1
0
2
1
0
2
1
0
1
0
1
0
2
1
2
2
1
0
1
1
0
1
1
1
1
1
0
1
1
1
1
2
2
0
0
1
0
0
0
2
2
1
1
1
0
0
0
0
0
1
1
0
0
2
1
2
1
2
0
1
0
2
0
1
1
1
0
1
1
1
2
2
1
0
2
1
1
0
2
2
0
1
1
1
2
1
0
1
1
2
0
2
1
1
0
1
0
1
1
0
0
1
2
2
1
1
1
0
2
1
1
2
1
1
0
2
1
1
2
2
1
1
1
4
3
0
1
0
0
1
1
0
1
2
0
0
2
0
1
0
0
1
0
1
1
1
0
1
0
2
1
0
6
2
1
0
1
1
1
2
2
1
0
1
0
2
1
1
0
2
1
1
0
1
2
1
1
0
2
1
1
1
0
1
1
2
1
2
1
3
1
1
2
0
0
2
1
1
1
0
0
0
1
1
1
2
0
1
1
2
0
2
1
2
0
2
1
1
0
1
1
1
0
1
1
1
2
2
0
1
1
1
1
1
1
0
1
0
0
1
1
1
1
1
1
2
1
2
0
1
1
1
1
2
1
1
1
1
1
2
2
0
0
1
2
2
1
1
0
1
2
0
1
1
1
0
0
1
0
0
1
1
3
0
1
2
1
1
1
0
1
1
2
0
2
1
1
2
0
0
0
1
2
1
1
2
1
0
1
1
1
1
1
1
0
1
1
1
2
1
1
0
1
2
2
1
2
1
1
1
2
2
3
0
1
0
1
1
1
1
2
0
1
1
1
0
0
0
1
2
1
2
1
2
2
1
0
0
1
0
2
1
2
1
1
2
1
1
0
1
0
1
1
0
1
0
1
2
0
0
1
1
0
1
1
1
1
0
1
2
1
1
1
1
0
2
1
2
0
2
2
1
1
0
0
2
2
0
1
1
1
0
1
1
0
0
2
1
1
1
1
0
1
1
3
0
1
1
1
0
0
1
1
1
0
1
2
1
2
0
1
1
1
1
2
1
2
1
1
1
1
2
1
2
1
1
2
1
2
2
2
0
2
2
0
0
0
2
1
1
1
2
0
1
1
1
0
0
0
1
1
0
0
2
0
0
1
1
1
0
1
2
1
2
0
1
1
4
1
1
1
1
1
0
1
1
1
1
2
0
0
1
0
1
0
0
1
0
1
1
1
1
1
0
2
2
2
0
1
1
1
1
0
1
1
0
0
2
1
1
1
0
1
1
1
1
2
0
1
1
1
1
0
0
1
0
0
1
1
0
0
2
1
0
0
1
0
0
1
0
1
0
1
2
0
1
0
0
1
0
0
1
1
0
1
1
0
2
1
1
0
0
0
0
1
1
2
3
1
1
2
2
0
2
0
1
0
1
1
0
2
0
2
0
1
1
2
1
3
1
0
0
2
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
0
1
1
2
1
1
1
0
0
1
0
2
0
0
2
1
2
0
2
2
1
1
2
0
1
0
1
1
1
0
0
1
0
1
0
0
0
1
1
1
1
0
0
1
1
1
1
1
3
2
1
1
0
2
2
1
0
1
0
0
2
0
1
1
1
0
1
1
0
1
1
0
1
0
2
1
0
1
0
1
0
0
2
1
0
1
2
2
0
2
0
0
1
1
1
1
1
1
0
1
0
0
1
1
1
2
0
2
2
2
2
1
0
1
1
1
1
1
1
1
1
0
1
1
0
2
0
1
1
1
1
4
2
1
1
1
0
1
0
1
1
2
1
0
0
1
1
1
1
3
1
2
1
1
0
0
0
1
0
1
1
1
1
1
1
0
1
2
0
0
0
1
0
2
1
1
0
0
1
1
1
0
1
1
1
0
0
0
1
1
1
0
1
1
3
1
1
1
1
0
1
1
1
1
0
0
1
0
0
0
1
2
2
1
0
1
2
0
1
0
0
2
0
0
1
1
1
2
1
2
1
2
1
1
2
1
1
3
1
0
1
2
1
2
1
1
0
2
1
1
0
0
2
1
2
2
0
0
1
2
1
1
1
1
0
2
0
0
1
0
1
1
0
2
1
2
1
0
1
1
0
0
2
1
1
2
1
2
1
1
1
1
0
1
1
1
2
0
2
1
1
1
1
1
2
1
1
2
2
1
0
2
2
1
1
0
1
1
1
1
1
0
0
0
0
1
1
1
1
1
1
1
1
0
0
1
0
1
0
0
1
1
1
0
1
1
0
0
2
2
1
1
0
0
0
2
1
0
2
0
1
2
2
0
0
1
1
1
4
1
1
0
1
2
1
1
1
2
1
0
2
1
1
1
0
0
1
2
1
1
2
2
1
0
0
2
1
1
1
0
1
2
0
0
0
1
2
0
1
0
2
1
0
2
1
0
2
2
0
0
1
0
1
2
2
1
1
1
2
2
1
2
1
1
2
0
1
1
2
2
1
2
0
1
0
1
1
0
1
1
0
1
1
1
0
1
1
0
1
1
1
1
0
1
1
1
0
2
0
1
1
1
2
1
2
1
1
1
1
0
1
2
1
2
1
1
1
0
1
2
1
1
2
1
0
0
1
1
3
1
2
1
1
2
1
1
0
1
1
0
1
2
0
0
2
2
0
1
1
0
2
0
2
1
1
1
1
1
0
1
1
1
0
9
0
1
2
2
2
1
2
2
0
0
0
1
0
1
0
1
0
0
5
0
0
0
0
2
1
2
2
2
2
2
1
0
1
1
1
1
0
1
1
0
2
1
2
1
1
0
1
2
0
0
0
1
1
1
2
1
1
1
1
1
1
2
2
0
0
0
1
0
2
1
1
1
0
1
0
1
1
1
1
0
2
1
1
1
1
2
1
1
1
2
0
0
2
1
0
1
0
1
1
0
2
1
1
0
2
1
0
1
1
2
2
1
2
0
1
1
0
0
1
0
1
2
0
0
1
0
0
1
1
2
1
1
2
1
1
2
1
0
1
1
0
0
0
0
1
0
1
0
0
2
1
1
2
1
1
1
1
0
1
1
1
1
2
0
2
1
0
1
0
1
1
0
1
1
0
0
3
0
1
0
0
1
2
1
2
1
1
1
1
2
0
0
0
0
1
1
2
2
0
0
1
1
0
2
1
0
1
0
0
1
1
0
1
1
0
0
1
1
1
2
0
1
1
0
0
0
1
1
1
1
1
0
0
1
1
1
1
1
1
2
1
2
2
0
1
2
2
2
1
1
0
0
1
0
0
1
2
2
1
1
1
0
1
1
1
0
1
0
2
2
1
1
2
1
2
2
1
1
1
0
1
2
1
0
0
2
2
1
1
1
1
2
2
1
1
1
1
1
0
2
1
1
2
1
1
0
1
1
1
1
1
2
1
3
2
0
2
0
1
1
1
0
2
2
2
1
0
1
0
1
1
1
1
1
2
1
1
0
0
0
2
2
1
0
1
1
2
1
1
1
2
2
1
0
1
2
0
1
2
1
1
1
0
1
1
1
0
0
1
0
1
1
0
1
1
0
0
1
0
2
0
0
1
2
2
0
0
4
0
0
0
0
1
1
0
0
0
0
1
1
1
1
2
1
0
1
0
1
0
0
2
0
0
1
0
1
2
1
1
2
1
0
1
1
1
2
0
1
1
0
0
1
1
0
2
1
2
1
0
1
3
1
1
1
1
2
1
1
0
1
2
1
1
0
1
1
1
0
2
1
0
4
0
0
2
0
0
1
1
1
0
2
2
0
1
1
1
2
2
2
2
1
1
1
0
1
0
1
2
0
0
1
0
0
1
2
1
0
1
1
0
2
2
1
1
1
1
0
2
2
1
1
2
0
0
1
1
1
1
1
1
0
1
2
1
1
1
1
1
0
1
2
1
1
1
1
2
1
2
0
1
1
2
2
1
0
2
1
1
1
1
0
0
1
1
1
1
0
1
1
1
0
2
0
1
2
0
1
0
1
1
0
0
1
2
1
1
1
1
1
2
1
0
0
1
1
0
2
1
1
0
1
2
1
1
1
0
1
1
1
1
1
1
0
1
2
1
1
1
1
2
1
2
1
1
1
1
0
0
1
0
0
0
0
1
1
1
1
0
2
1
0
2
0
1
0
3
2
2
0
1
0
0
2
1
2
1
1
1
1
1
0
1
1
0
1
2
0
1
1
0
0
1
0
1
1
0
1
0
1
1
1
1
1
2
0
1
1
0
1
1
0
1
1
2
1
1
1
1
2
1
1
2
0
2
1
0
2
2
1
1
1
0
1
2
0
2
2
1
2
0
1
1
1
0
1
0
2
2
0
0
2
1
1
1
1
2
0
0
1
2
2
2
2
0
0
0
1
1
1
1
1
1
1
0
1
0
1
2
1
2
1
1
1
1
0
0
0
0
0
2
2
0
1
1
1
1
1
0
4
0
1
1
2
2
1
1
0
2
0
2
0
0
1
1
1
1
1
2
0
2
0
0
0
1
1
0
2
1
1
1
1
1
1
2
1
2
0
1
1
2
1
0
1
2
1
1
2
2
1
1
0
0
1
0
2
1
1
2
1
0
1
1
0
0
2
1
1
1
1
1
1
0
2
1
0
1
1
1
2
0
2
1
2
2
1
0
2
0
1
1
2
0
1
0
0
0
1
2
0
1
1
2
1
0
2
1
0
1
0
2
1
1
0
1
1
0
2
2
0
1
0
0
2
0
0
2
1
3
0
1
3
0
0
0
0
2
1
1
0
1
1
0
1
1
2
0
2
0
1
1
1
1
0
0
1
1
1
0
1
0
0
1
2
1
2
0
1
2
1
1
1
0
2
1
2
0
1
1
2
0
1
0
0
0
1
1
1
0
0
1
1
1
1
1
1
0
1
0
1
0
0
0
0
1
0
2
1
0
1
2
1
2
2
2
0
1
1
0
2
1
0
0
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
0
0
0
1
1
1
1
1
2
0
0
1
1
0
2
2
2
1
1
1
1
1
2
1
1
0
0
2
0
0
1
2
1
1
1
2
1
0
1
1
3
0
1
1
1
2
1
2
1
4
2
2
1
1
1
0
2
1
1
0
1
2
1
0
3
2
1
1
1
0
0
1
1
1
2
1
1
0
0
0
2
1
2
1
2
1
0
1
1
2
0
2
1
2
0
1
1
0
0
1
1
2
1
1
0
1
2
1
1
1
0
1
0
1
2
2
1
1
1
1
0
1
2
1
0
1
1
2
1
1
1
1
1
1
0
1
1
2
0
2
0
1
1
2
0
0
1
0
2
2
1
1
1
0
0
1
2
1
0
0
1
0
0
2
1
1
0
0
1
1
1
1
0
1
1
1
1
0
1
1
1
1
1
2
0
2
1
1
1
1
1
1
2
1
1
1
1
0
1
2
2
0
2
2
1
0
0
1
2
3
0
0
0
1
1
1
0
1
0
1
1
2
1
1
0
0
1
1
2
0
4
1
1
1
1
1
1
0
2
0
2
2
1
1
0
1
1
1
2
2
1
1
1
1
1
0
1
2
1
1
1
0
2
2
0
1
0
1
2
0
1
1
2
2
0
0
0
1
0
0
1
1
2
1
0
2
1
0
1
0
1
2
1
0
1
0
1
0
1
1
0
2
0
2
1
2
0
0
2
2
1
0
0
1
1
1
0
1
1
1
1
0
1
1
1
1
1
1
0
1
1
1
1
1
1
1
0
1
1
2
0
1
1
1
1
2
1
1
1
1
0
2
0
0
1
1
2
1
1
1
1
0
0
0
1
2
0
1
2
2
2
1
1
2
1
1
0
2
1
0
1
1
1
2
0
0
1
2
0
1
1
0
2
1
1
1
2
0
0
1
0
2
1
1
0
1
1
2
2
0
1
1
2
1
0
1
1
1
2
0
0
2
1
1
2
0
1
0
0
1
0
2
1
0
1
1
2
0
1
2
1
4
2
1
1
1
2
0
2
1
1
2
0
2
0
0
2
1
0
2
1
1
2
0
1
0
1
3
1
1
0
1
1
1
2
1
1
1
1
0
2
2
0
0
0
3
0
1
1
2
0
0
1
0
0
2
0
1
2
0
1
0
1
1
0
2
0
1
2
0
1
1
1
1
0
0
0
1
2
0
2
1
2
2
1
1
1
1
1
0
1
1
2
2
0
2
0
2
1
0
1
1
2
1
1
2
0
1
2
1
0
1
1
0
2
2
1
1
2
1
1
1
0
1
1
0
0
0
2
2
1
2
1
1
1
1
1
1
1
0
1
0
1
0
1
1
1
2
2
2
1
1
0
2
1
1
1
1
0
0
2
1
1
0
1
0
1
0
0
1
1
0
2
0
2
1
1
1
2
0
2
1
2
1
0
1
0
1
1
0
1
1
2
2
1
1
0
0
1
3
1
0
1
1
1
0
1
0
1
1
1
0
0
1
2
2
2
1
1
1
0
1
1
0
1
0
1
3
0
1
0
1
2
0
1
1
0
2
1
2
1
1
0
2
0
1
0
1
1
2
2
0
2
1
1
2
0
0
1
0
0
1
0
0
1
1
1
1
1
1
1
1
1
0
1
0
0
0
1
1
2
2
2
1
3
1
0
0
1
2
0
0
1
0
1
0
0
2
1
1
0
1
1
0
1
1
1
2
1
1
1
0
1
2
1
0
0
1
0
1
1
2
1
1
1
2
1
2
1
2
1
2
0
0
0
0
2
0
0
1
1
1
1
1
1
0
2
1
1
2
1
0
0
0
1
1
1
1
1
1
0
2
1
0
1
1
1
1
1
1
2
1
0
2
2
2
1
2
3
0
0
0
1
1
1
1
1
2
2
1
2
0
1
1
0
1
2
0
1
1
0
0
1
1
2
2
1
1
0
0
2
1
1
1
2
0
1
2
2
1
2
0
1
0
0
0
2
1
1
1
1
0
1
0
2
1
2
1
1
2
0
1
2
2
0
1
1
1
1
1
3
1
2
1
0
1
2
0
0
1
1
0
0
3
2
1
1
0
2
1
1
1
1
2
1
1
2
1
0
1
2
2
0
1
0
1
2
2
1
1
0
1
0
1
0
1
1
2
1
1
0
1
0
0
1
2
0
0
2
0
2
2
1
2
0
1
2
1
1
2
0
0
2
1
1
0
1
0
0
0
2
2
1
0
1
2
1
1
0
1
0
1
0
0
2
0
1
2
0
1
1
1
0
0
0
1
1
0
0
1
1
0
2
2
1
1
1
0
0
1
1
2
0
2
1
1
0
0
2
2
2
1
2
2
1
1
1
0
0
1
0
1
2
1
1
1
2
2
0
1
1
1
0
1
1
0
1
2
2
0
2
1
1
1
0
1
1
1
1
1
1
0
1
1
1
2
2
0
1
0
1
1
1
1
0
0
1
0
0
2
1
1
1
0
0
1
1
1
1
0
1
1
0
0
0
1
1
2
0
1
0
0
1
2
1
1
1
0
1
1
0
1
2
2
1
1
1
1
2
1
1
2
1
0
0
2
1
2
2
3
1
1
2
0
1
2
2
2
1
0
1
1
1
1
0
3
0
1
1
1
2
2
0
2
2
0
0
2
2
0
0
0
0
0
1
1
1
1
1
1
1
1
0
0
1
1
1
0
1
0
1
1
0
1
1
1
1
0
0
0
1
1
1
1
0
0
1
1
2
1
0
2
3
1
1
0
0
1
0
0
1
0
1
1
1
3
0
2
1
1
0
1
1
1
1
0
2
1
2
1
0
1
2
2
2
1
1
2
1
1
0
1
2
1
1
0
1
2
0
1
1
1
1
1
1
0
2
0
0
0
0
0
1
0
1
1
1
0
1
1
1
0
0
1
0
1
2
0
0
1
0
2
0
2
0
2
1
1
1
1
1
1
0
2
0
1
1
2
1
1
2
1
1
1
1
2
1
0
2
3
1
1
1
0
1
1
2
0
1
1
1
1
1
1
1
1
1
0
1
1
1
1
2
1
1
2
1
0
0
1
3
0
1
1
0
1
2
2
2
1
0
2
1
0
1
1
1
0
0
0
1
2
0
1
1
2
2
1
1
1
0
0
1
0
0
1
2
1
0
1
0
1
1
0
1
2
1
0
1
1
1
0
2
1
2
1
1
1
1
2
1
2
1
1
1
1
0
1
0
1
1
0
1
1
1
1
1
1
1
1
0
1
1
1
0
0
0
1
1
0
0
0
1
2
1
0
1
1
0
0
0
2
1
1
1
1
1
0
0
2
1
2
0
2
1
0
2
1
1
2
1
1
2
1
0
2
1
1
1
2
1
0
2
0
1
0
1
0
2
0
1
0
0
1
1
0
0
1
2
1
0
2
1
1
1
2
2
1
1
2
1
0
1
1
2
0
1
0
1
1
2
2
0
0
2
0
0
1
2
0
2
1
1
0
2
2
0
1
2
2
1
1
1
1
1
2
2
1
1
1
1
0
0
3
1
1
0
2
1
3
1
2
0
2
2
0
1
1
1
0
1
2
1
1
0
0
1
2
1
1
2
0
0
1
1
0
0
2
1
0
1
2
1
1
0
0
2
1
2
1
1
1
0
1
1
0
2
1
2
1
1
1
1
1
1
1
2
1
0
2
1
0
0
1
2
0
1
1
1
2
1
1
1
2
2
2
1
1
1
1
1
1
0
2
0
0
1
1
1
1
1
0
1
1
1
1
1
2
1
0
0
2
1
0
0
3
2
2
2
2
1
1
0
1
1
0
1
1
0
1
1
1
2
0
2
0
1
1
1
1
2
2
1
0
0
0
2
1
1
1
0
2
1
2
1
1
1
1
1
1
1
0
2
1
0
2
1
1
1
1
0
2
2
0
1
1
1
2
1
2
1
1
1
2
1
2
1
0
0
2
2
0
1
1
1
1
1
1
2
1
1
0
1
1
1
2
0
0
0
1
1
1
1
0
2
1
0
0
0
1
2
0
1
2
0
1
1
1
0
1
1
1
0
0
1
1
0
2
0
1
0
3
1
1
2
1
1
3
0
0
1
0
1
2
1
1
1
0
1
0
1
2
2
1
1
2
1
1
1
1
1
1
1
1
1
1
0
1
1
1
2
1
1
2
1
2
0
1
3
2
1
0
1
1
1
2
1
1
0
1
2
1
2
1
2
1
1
1
0
0
1
2
2
1
0
1
0
1
1
1
1
1
2
2
0
1
1
1
1
2
1
0
0
1
1
1
1
1
2
2
1
1
0
2
1
0
1
2
1
1
2
0
0
1
1
1
1
2
2
1
1
0
0
1
0
1
1
2
1
2
2
1
1
1
0
1
1
1
2
1
2
2
1
1
0
1
1
1
0
0
1
2
1
1
0
1
1
0
2
1
1
2
1
0
1
0
2
1
0
1
0
0
2
1
1
0
2
1
2
0
2
0
1
1
1
1
1
1
2
0
0
0
1
2
2
1
1
2
3
0
3
1
1
0
2
0
0
0
1
1
1
0
1
1
1
0
2
1
2
1
0
0
2
2
1
1
1
1
2
2
1
1
1
1
0
1
1
1
2
1
1
2
2
1
1
0
1
1
0
0
2
0
0
0
1
1
2
2
1
1
0
0
1
1
1
1
2
1
1
0
0
1
0
1
1
2
0
1
2
2
0
1
1
2
1
0
0
0
1
1
1
2
1
2
1
1
1
1
0
1
0
1
2
0
2
0
1
2
1
2
0
0
0
0
0
1
0
1
1
1
1
2
1
1
1
1
1
2
1
2
1
1
2
2
0
1
1
1
1
1
2
1
1
1
1
1
0
1
2
2
0
1
1
1
0
2
1
0
1
2
1
1
0
2
2
0
0
2
1
1
0
2
1
1
2
1
1
1
2
0
0
1
0
0
0
0
1
1
1
0
1
0
1
1
2
2
1
2
1
1
0
1
2
0
0
0
0
1
0
0
0
0
1
2
1
1
1
0
1
2
1
1
1
1
2
1
2
3
1
1
2
0
1
2
1
1
1
2
2
1
0
1
1
0
0
2
0
1
0
2
0
1
2
1
2
2
1
1
1
0
1
2
1
1
0
0
1
0
0
0
2
1
1
0
1
0
1
1
1
0
1
2
1
1
1
1
1
1
2
0
0
1
0
2
2
0
0
1
1
2
2
0
1
1
1
0
1
2
2
0
1
2
1
0
2
0
0
1
0
0
0
0
1
0
0
1
1
0
2
1
2
1
1
0
2
1
2
2
0
1
1
1
0
1
0
2
1
0
1
1
0
1
1
2
0
3
1
0
1
1
1
1
2
1
1
2
0
1
0
0
2
2
1
1
2
1
1
0
1
1
1
0
1
2
1
0
1
0
0
2
0
1
0
1
1
0
0
0
0
0
1
0
2
1
1
1
0
1
1
0
0
1
1
1
0
1
1
0
2
3
0
1
1
1
1
1
0
1
0
2
0
0
0
1
1
0
1
1
1
2
1
3
2
0
1
1
2
0
1
1
0
1
2
0
0
1
1
0
1
0
1
0
0
4
0
0
0
1
1
1
1
1
1
1
0
1
1
3
1
2
2
2
3
1
1
1
0
0
2
1
0
1
1
1
1
1
1
1
1
1
1
0
1
2
1
1
0
1
0
1
0
1
1
1
0
1
1
1
2
1
2
1
1
1
2
0
2
0
1
1
1
1
2
0
1
0
1
1
1
2
0
2
0
2
0
2
2
0
2
1
1
2
1
0
0
2
1
0
2
1
2
0
1
0
2
1
1
0
3
1
1
2
1
0
0
1
1
1
1
1
1
1
0
0
1
1
0
2
0
1
0
1
1
1
2
0
1
0
1
1
0
0
0
0
0
1
0
2
1
1
0
2
1
1
1
1
2
1
1
0
1
1
2
1
1
1
0
0
1
2
0
1
2
2
2
1
1
1
1
1
1
0
2
1
1
0
2
1
1
1
1
0
1
1
1
1
1
1
1
2
1
1
1
2
1
1
0
0
0
1
1
1
2
2
0
2
1
1
1
1
1
1
2
1
2
0
1
2
2
1
1
1
1
1
1
2
2
2
2
2
1
1
0
1
1
0
2
1
2
1
3
0
1
0
1
1
1
1
3
1
1
1
0
2
2
1
1
1
1
0
1
1
2
0
2
2
1
2
1
0
0
1
2
1
1
0
2
2
0
1
1
1
0
2
2
2
1
0
2
1
2
0
0
0
1
1
2
1
0
2
0
1
1
1
2
2
1
2
1
1
0
0
2
1
2
1
1
0
0
0
1
2
0
2
1
1
1
0
1
0
0
0
0
2
1
0
1
2
1
1
3
1
2
0
0
0
0
2
1
0
1
1
0
1
1
1
0
0
0
1
1
0
1
2
0
1
1
0
0
1
1
1
2
1
0
1
1
2
2
0
2
0
0
2
0
0
1
2
2
0
0
2
1
1
0
0
1
0
0
1
1
1
1
1
0
1
1
2
0
1
1
0
0
2
1
2
2
0
0
1
0
1
2
0
1
1
1
0
2
1
1
0
1
1
1
2
2
2
2
1
0
1
1
2
5
1
2
2
1
1
0
1
0
1
0
0
2
2
3
0
2
1
1
2
0
1
1
2
0
1
1
1
0
0
1
0
1
0
0
1
0
1
0
2
1
2
1
0
0
1
0
1
1
1
1
0
0
1
1
1
1
1
0
2
1
1
2
0
1
2
1
1
1
1
1
1
1
1
1
1
0
0
1
1
0
0
1
0
0
1
1
1
1
1
2
2
0
2
1
1
1
0
1
1
0
0
1
1
0
2
1
1
1
0
1
1
2
1
1
1
1
2
1
0
2
1
1
2
1
0
2
0
2
1
0
1
0
0
1
0
1
2
1
1
0
1
1
0
2
1
1
1
2
2
0
0
2
1
0
2
3
2
2
1
1
1
1
0
3
1
1
1
1
1
1
1
1
3
1
1
2
0
0
1
0
0
1
1
2
0
1
2
1
1
0
0
1
1
1
0
0
2
2
0
0
1
2
1
1
2
1
3
0
1
1
1
1
1
1
2
2
1
0
4
1
0
1
1
2
1
1
0
0
0
1
2
0
0
0
1
1
2
2
1
1
1
1
0
1
1
2
1
0
0
0
1
1
2
1
1
0
0
1
2
1
1
1
1
1
0
0
2
2
1
1
1
2
1
1
2
1
1
4
0
1
1
1
1
1
0
2
1
1
1
1
1
0
0
1
2
1
2
0
2
1
3
0
0
1
2
1
2
2
0
1
1
1
2
1
1
2
1
1
0
0
0
1
2
0
1
0
1
1
0
0
0
1
1
2
2
2
1
0
1
1
1
1
1
2
0
2
0
1
0
0
1
1
0
1
1
1
1
1
2
0
0
1
1
1
0
1
0
2
0
1
0
1
0
3
1
0
1
0
0
1
3
1
1
1
1
0
1
2
1
1
2
0
2
0
1
1
1
1
1
1
0
1
0
1
1
3
1
0
1
0
2
2
0
1
0
1
0
2
1
1
1
2
0
0
0
1
1
1
1
1
1
1
2
1
2
0
0
2
1
1
2
1
1
1
0
2
1
2
0
1
2
1
1
0
1
0
1
1
1
0
1
0
1
0
0
1
1
2
1
1
1
1
2
1
1
0
1
1
1
0
1
1
1
1
1
0
1
1
2
2
1
0
2
1
0
1
0
1
1
2
1
1
0
1
1
1
0
2
0
0
1
1
1
0
1
0
1
1
0
0
0
1
1
2
1
1
2
0
2
0
1
0
1
0
2
0
1
1
0
2
1
0
1
2
0
1
1
0
0
1
1
0
0
2
1
0
3
0
1
0
2
0
0
0
0
0
1
0
1
1
1
0
1
2
1
1
1
1
1
0
2
0
1
0
1
0
2
1
0
2
1
0
2
2
1
1
1
1
1
1
1
1
1
1
1
0
2
1
0
1
0
1
2
1
0
1
1
1
2
1
0
0
1
2
1
1
1
2
1
2
1
2
1
1
0
1
0
2
1
0
1
1
0
1
1
1
2
0
0
0
1
1
0
1
1
0
0
1
1
1
1
1
1
1
0
0
1
0
0
1
0
1
1
0
1
0
1
0
1
1
2
1
0
2
2
1
2
2
1
1
0
1
1
1
0
0
2
1
1
2
1
1
0
1
2
2
0
0
0
1
0
4
1
1
0
1
2
2
0
1
0
2
1
1
1
0
1
2
1
1
0
1
1
1
1
1
2
1
1
1
2
0
0
1
2
1
0
1
1
2
0
1
0
2
0
1
2
1
1
1
2
1
0
2
2
1
2
1
1
1
0
0
0
1
2
0
0
1
1
1
1
0
0
2
1
1
1
2
1
0
0
1
0
2
0
1
0
0
0
1
0
1
0
2
2
2
1
1
1
1
2
2
0
2
1
0
1
1
0
1
0
0
2
1
0
2
1
0
0
2
1
1
1
2
0
0
2
0
0
2
2
1
2
2
1
0
0
1
1
0
0
0
1
0
1
1
1
0
0
0
4
2
1
0
1
2
1
1
0
0
0
0
1
1
1
1
2
1
2
1
0
0
2
1
0
1
2
0
4
1
1
1
0
1
1
1
2
0
1
1
0
0
0
0
1
2
1
1
2
2
1
1
1
1
1
0
0
0
1
0
1
4
1
1
1
2
2
2
1
1
1
1
1
1
1
0
1
2
1
0
2
1
2
1
0
0
1
1
2
2
0
1
2
2
1
2
1
1
2
1
1
0
0
1
1
1
2
1
1
1
1
2
1
0
1
1
1
2
0
2
0
0
0
0
2
1
1
0
0
1
1
2
1
0
0
1
0
1
1
1
1
0
2
1
1
2
1
1
2
0
2
2
0
1
1
1
1
1
1
0
1
1
1
0
2
2
1
3
1
2
0
2
0
0
0
1
1
1
1
1
0
3
1
1
0
0
2
1
0
1
1
1
1
2
1
0
1
1
1
0
2
0
1
2
1
1
1
1
2
2
1
1
1
2
1
2
0
1
1
0
0
2
1
2
1
0
1
1
1
2
1
1
2
1
1
0
1
0
0
0
1
1
1
2
1
1
1
1
2
1
1
1
2
2
1
1
0
2
1
1
1
1
1
1
1
0
0
0
1
1
0
1
1
1
1
0
0
2
1
1
1
1
1
1
1
0
1
1
1
1
1
2
1
0
1
0
1
1
2
0
1
2
1
1
3
2
1
1
2
2
1
2
0
2
2
0
0
0
0
2
0
0
1
2
1
1
1
0
0
0
1
0
0
0
2
1
0
1
2
0
1
1
1
1
1
1
0
1
1
0
1
0
2
0
2
0
2
1
1
1
1
2
1
0
1
2
0
2
0
1
2
1
0
1
1
0
0
1
1
2
2
0
1
1
1
1
1
2
1
1
0
1
0
1
0
0
1
1
2
2
0
1
0
2
1
0
1
0
0
0
2
1
0
2
1
1
0
1
1
1
1
1
1
1
1
1
1
0
1
2
0
1
1
0
1
1
2
0
1
1
1
1
0
0
1
1
1
1
0
1
1
1
3
1
0
2
1
1
0
2
2
1
0
1
1
1
1
0
1
1
2
0
0
0
1
2
1
2
1
0
1
2
1
2
1
1
1
1
0
2
2
0
0
1
0
1
1
3
1
2
1
1
0
1
0
1
1
1
0
0
1
1
1
1
2
0
1
0
1
1
1
1
0
1
1
0
0
0
0
0
1
3
0
0
0
0
2
1
1
0
2
1
1
1
1
0
1
0
1
1
2
2
0
2
1
1
2
2
0
1
1
2
1
1
1
1
1
2
0
2
1
1
1
2
0
0
0
1
0
0
2
2
0
1
3
1
0
1
1
1
1
0
1
0
7
0
1
1
1
0
1
2
1
0
1
1
1
2
2
1
1
2
1
0
0
1
2
0
1
2
0
1
0
0
2
1
1
1
1
1
1
0
0
2
1
1
0
1
2
1
2
1
1
1
0
1
2
0
2
0
1
0
1
2
1
1
2
1
1
1
3
2
1
1
0
1
1
0
0
0
2
1
1
2
1
1
0
0
1
1
1
1
2
0
2
0
3
3
1
1
1
1
1
0
1
1
0
1
1
1
1
2
0
1
1
2
1
0
1
2
1
2
0
0
1
2
0
1
2
0
1
0
1
0
1
0
1
0
0
0
0
1
0
0
1
1
0
0
2
2
0
0
0
1
2
0
1
1
2
1
2
1
1
0
2
0
1
0
0
1
0
1
1
2
1
1
1
0
2
1
1
1
1
0
1
0
1
2
2
2
0
1
0
1
2
1
2
2
1
0
1
1
0
1
1
2
0
1
1
1
1
1
0
2
0
3
2
2
0
2
1
1
2
0
1
0
0
1
0
1
1
1
1
1
1
1
1
0
1
1
2
1
1
1
1
3
1
1
0
1
0
0
1
0
0
0
2
1
0
0
0
1
1
1
1
1
0
1
0
1
0
1
0
1
1
1
1
1
0
1
1
1
1
2
1
0
1
2
1
2
1
2
1
1
2
0
1
0
0
1
1
1
2
1
1
0
2
1
1
2
1
0
0
1
0
1
1
2
2
0
1
1
1
1
1
0
1
0
1
0
1
0
1
2
0
0
3
2
2
3
1
0
1
1
2
0
0
2
1
2
0
0
0
0
2
1
0
1
0
2
1
0
1
0
1
0
0
1
0
2
0
0
1
0
0
1
2
0
0
1
0
1
1
2
1
2
0
0
1
2
0
1
1
1
1
1
1
0
0
1
1
2
0
2
1
1
0
0
1
0
0
1
2
0
1
2
1
1
0
1
0
0
0
2
1
1
1
2
1
1
0
1
1
1
2
0
2
0
1
1
1
1
1
1
1
2
0
2
2
1
2
0
1
1
1
1
0
1
0
0
1
1
2
1
2
2
0
1
0
0
1
1
1
1
0
2
1
0
1
2
1
2
1
1
1
2
0
0
0
0
2
2
1
1
2
1
1
1
1
0
1
1
1
1
2
0
2
1
1
2
1
1
0
1
3
1
0
2
0
0
0
0
2
0
1
0
0
1
2
0
1
1
2
1
0
1
2
1
1
0
2
0
2
2
2
2
0
1
1
2
2
2
1
1
1
0
1
1
0
1
0
0
0
0
1
2
1
1
2
1
1
1
2
2
1
1
0
0
1
1
2
1
0
1
2
1
2
1
1
1
2
0
1
2
2
1
1
1
0
1
1
1
1
1
1
1
1
2
1
1
1
1
0
1
1
1
0
0
1
0
1
1
1
2
1
0
1
2
1
1
0
1
0
1
0
1
2
0
2
1
0
1
0
0
0
1
0
2
0
1
1
0
0
0
1
0
1
1
1
1
1
2
1
1
0
1
1
2
3
0
1
0
1
2
1
0
1
0
1
3
1
1
0
2
1
1
1
0
0
2
1
2
0
2
1
0
0
1
0
0
0
0
1
1
2
2
0
1
1
1
1
2
1
2
0
0
0
1
2
1
2
0
1
0
0
1
2
1
1
0
2
2
0
0
1
2
2
1
1
0
2
1
1
2
2
1
1
1
1
0
0
0
0
2
2
1
2
0
2
0
0
1
1
0
0
2
0
0
0
1
2
0
2
1
0
1
1
1
0
1
2
2
1
0
1
1
1
1
2
1
1
0
0
1
1
1
1
1
0
2
0
1
1
1
2
1
1
1
2
1
1
1
1
0
1
2
1
1
0
1
2
0
2
1
1
2
0
1
1
0
1
2
0
1
1
0
0
1
0
1
1
1
0
0
0
0
1
0
1
1
1
1
0
0
2
0
0
1
1
1
0
1
1
1
1
0
0
0
1
1
2
0
1
1
2
0
0
1
1
1
2
1
2
2
1
2
2
2
0
1
1
1
2
2
1
1
0
2
0
1
1
1
1
1
2
0
1
1
1
0
1
2
0
1
1
1
1
1
0
0
1
2
1
1
0
1
0
0
1
0
1
1
0
2
2
1
1
1
0
1
2
0
1
0
1
1
1
1
0
1
1
1
1
0
1
2
1
0
0
1
0
2
1
0
1
2
1
1
0
1
1
2
0
1
1
0
2
2
1
1
1
1
1
0
1
1
1
0
1
1
1
0
2
0
1
2
0
0
1
1
2
0
1
1
2
0
1
2
1
0
0
0
1
1
1
0
2
2
1
1
1
2
1
1
1
0
1
1
0
2
1
1
1
0
1
0
0
1
0
0
1
0
1
1
1
1
1
1
1
0
1
0
1
2
1
0
0
2
0
1
2
0
0
1
0
0
1
2
1
0
2
1
1
1
1
0
2
2
0
0
0
0
1
0
1
1
1
1
0
1
1
2
0
0
2
1
2
2
1
1
0
1
2
1
1
0
0
1
1
0
1
1
0
1
1
0
2
2
1
2
1
1
1
1
0
1
0
1
0
1
1
1
0
2
2
1
1
1
1
3
1
0
1
1
0
2
1
2
1
1
0
0
4
2
1
0
0
1
1
1
1
1
2
2
2
1
0
1
1
2
0
1
0
1
0
0
0
1
1
0
0
1
1
1
1
2
0
1
1
1
1
2
1
1
0
0
1
1
1
2
1
1
0
0
1
1
1
1
0
2
1
1
1
2
0
1
1
2
2
2
1
1
1
0
0
2
1
1
1
1
2
1
3
0
1
1
0
1
2
1
2
2
1
1
1
1
1
1
0
1
0
2
0
2
1
1
2
2
2
0
1
2
1
0
0
0
1
1
0
2
2
1
0
1
1
1
1
2
1
0
0
0
2
0
2
0
0
0
0
0
2
1
1
1
1
0
2
0
2
1
0
1
2
2
2
1
2
0
2
1
3
1
2
0
2
1
1
1
0
0
1
2
0
2
0
0
1
1
1
0
1
1
1
1
1
2
1
2
1
0
1
0
1
1
0
1
1
1
1
0
1
1
1
3
2
0
1
1
2
0
1
0
2
1
2
1
0
0
0
2
2
2
1
1
2
2
2
0
0
0
2
0
2
0
1
1
1
1
1
1
1
0
2
2
2
0
1
1
2
1
1
1
0
0
0
0
0
1
0
2
1
2
2
0
0
1
0
0
2
1
2
1
1
1
0
1
1
1
0
2
0
2
0
2
1
0
2
1
1
0
2
1
1
0
1
1
2
2
0
2
1
1
1
1
2
1
1
1
0
1
1
0
2
1
0
1
2
2
1
2
1
1
1
1
0
1
0
0
1
0
3
0
2
1
0
0
0
0
1
1
2
2
0
1
1
1
1
1
0
0
1
0
0
0
0
0
2
1
1
2
1
1
1
1
2
1
0
2
0
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
2
0
0
1
1
1
1
2
0
1
2
1
1
1
1
1
2
1
2
1
0
0
2
1
2
1
1
0
0
1
1
0
2
1
1
0
2
1
0
0
1
0
2
0
0
2
2
1
0
0
0
2
2
2
0
1
0
0
1
0
1
1
1
4
0
1
1
1
1
2
2
2
1
0
0
1
1
0
1
1
2
1
1
0
1
1
2
1
1
1
0
1
0
2
2
1
0
2
1
0
2
0
0
1
0
2
0
1
1
1
1
2
0
1
1
1
1
0
1
0
1
2
0
2
0
1
2
1
2
2
0
2
0
0
1
1
0
1
1
1
1
1
1
1
2
0
0
0
1
1
0
1
1
1
2
0
1
2
2
1
1
1
1
0
2
1
2
0
2
1
1
1
1
2
1
1
0
1
1
0
2
0
2
2
2
2
1
2
0
1
1
0
1
1
1
2
1
1
1
1
0
0
2
2
1
1
2
0
1
1
1
2
0
0
0
1
0
1
1
1
1
1
0
0
1
1
1
2
1
1
1
1
1
1
1
1
1
0
2
1
2
1
1
2
0
1
1
1
1
2
6
1
0
0
2
0
0
1
0
1
1
1
1
0
1
1
1
0
1
0
1
1
1
1
2
1
0
1
1
1
1
0
1
1
2
2
1
0
2
0
0
1
0
2
0
1
2
1
0
1
2
1
1
0
1
0
0
0
2
0
0
1
0
0
1
1
1
3
1
1
1
2
1
2
0
0
1
1
1
1
2
0
1
0
1
1
1
1
2
2
5
2
1
1
2
0
1
1
1
1
1
0
1
2
1
2
1
1
0
2
0
0
2
1
0
2
0
1
1
1
0
1
1
1
1
1
0
0
1
1
1
0
1
1
1
1
0
1
2
1
0
0
1
0
0
1
0
1
1
1
0
2
1
0
1
1
1
1
0
1
1
1
2
3
1
0
0
1
0
2
0
0
0
1
1
0
1
2
1
1
1
0
0
2
0
0
0
1
1
1
1
2
0
1
1
1
1
0
0
2
2
1
2
1
0
1
1
0
2
2
0
0
2
2
0
1
2
0
1
0
2
1
2
1
1
1
0
1
0
0
1
2
0
1
1
2
1
2
0
1
1
1
1
2
1
1
1
1
1
0
2
1
0
0
1
2
1
3
0
2
0
1
0
1
0
1
3
0
1
1
2
0
2
0
1
1
1
0
1
0
1
1
1
1
2
0
2
1
0
1
2
0
1
1
2
1
0
1
1
1
2
2
0
1
2
0
2
2
1
0
2
3
2
2
0
1
1
1
1
2
1
1
0
1
1
1
2
2
1
1
1
1
2
1
1
0
1
1
2
1
1
1
1
1
1
2
0
1
1
1
1
1
1
0
1
1
1
1
0
1
0
1
1
2
0
1
2
1
1
1
1
0
0
1
1
0
2
0
2
1
2
0
1
1
0
1
1
1
0
1
1
1
0
2
0
1
2
0
1
1
2
0
1
0
0
1
1
0
1
1
0
1
1
2
0
1
0
2
2
1
0
1
1
1
1
1
1
1
1
0
2
1
1
2
2
2
2
1
1
3
2
1
1
1
1
4
2
1
1
1
0
0
1
1
0
2
2
1
0
0
1
1
1
1
0
1
1
1
2
2
1
0
1
1
1
1
1
0
0
1
2
2
2
2
3
1
1
0
1
1
1
1
0
0
0
1
1
1
1
0
0
1
1
0
1
1
0
2
1
1
1
2
1
1
1
0
1
2
0
2
2
0
1
1
1
0
1
2
0
2
1
1
1
2
2
2
1
0
1
1
1
2
1
1
1
1
2
2
1
1
0
1
1
2
0
1
0
1
0
1
0
1
0
1
1
1
0
1
1
1
1
2
0
2
2
2
2
0
0
2
1
1
1
1
0
1
0
0
2
2
2
2
1
1
1
2
0
1
1
2
1
1
0
1
1
1
1
2
1
2
0
0
2
0
2
1
1
2
2
1
2
1
1
0
0
1
0
1
0
0
1
1
1
1
0
1
2
0
3
2
2
0
0
1
2
0
1
2
2
2
0
1
1
0
0
0
1
1
0
0
1
1
0
1
2
2
2
1
1
1
1
0
0
0
1
1
1
1
0
1
1
1
0
2
2
1
2
1
1
1
0
1
1
0
1
0
0
1
2
1
1
1
2
0
1
0
1
1
1
2
1
0
2
1
1
0
1
0
1
1
2
0
1
1
2
0
1
2
0
1
0
1
0
1
1
2
1
1
1
0
1
0
2
2
1
0
0
0
1
1
0
0
1
1
2
0
1
1
0
0
0
1
1
1
1
1
2
1
1
2
0
1
1
1
0
0
1
2
1
0
2
2
0
0
1
0
1
1
1
2
1
2
0
2
7
1
0
0
0
1
2
1
0
1
0
2
0
1
1
1
0
0
1
0
1
1
0
1
1
2
0
2
1
1
0
1
2
0
1
1
0
1
1
1
1
0
0
0
2
1
2
0
0
1
1
1
0
1
1
0
0
0
1
1
2
1
1
1
1
0
1
0
0
1
0
0
1
0
1
0
1
2
1
2
0
2
1
2
0
0
2
2
1
2
0
1
1
0
0
1
0
1
0
1
1
2
0
0
1
1
2
1
1
0
1
1
0
1
0
1
1
0
1
1
2
0
1
1
1
1
0
1
1
1
0
2
2
1
1
1
1
0
1
1
1
1
1
1
0
1
2
1
1
0
1
1
0
1
1
0
0
1
0
1
0
1
1
1
2
1
1
0
1
0
3
0
0
1
0
1
1
0
0
2
0
0
0
0
2
1
2
2
0
2
1
0
1
1
0
1
1
0
1
2
1
2
0
0
1
0
1
1
1
1
0
2
0
0
1
2
1
2
0
1
0
2
2
2
0
0
2
1
2
1
2
2
1
0
3
1
1
0
0
2
1
1
2
2
1
1
0
1
1
0
0
3
1
1
1
2
2
1
2
0
2
0
1
1
2
1
1
0
1
1
2
2
1
0
1
1
2
2
1
2
0
1
1
1
0
1
1
0
2
2
1
0
2
1
2
1
0
1
1
2
1
2
0
1
1
1
1
2
0
2
3
0
1
1
2
2
0
2
1
0
2
2
1
2
2
0
1
2
1
1
1
1
1
1
2
1
1
1
1
3
1
2
0
1
2
2
0
1
1
1
0
2
1
1
0
1
2
2
1
1
0
1
1
1
2
1
1
2
2
2
1
0
0
2
0
2
2
0
1
1
1
1
1
1
0
1
2
1
1
3
1
2
2
1
0
2
1
1
2
2
0
1
1
1
2
1
1
2
0
1
0
0
1
0
1
1
0
1
2
1
1
2
1
0
1
1
1
1
2
2
0
2
1
1
1
1
1
2
1
1
5
0
0
0
1
1
2
2
1
0
2
2
1
1
1
1
1
2
0
0
1
2
2
2
0
0
1
2
1
2
0
2
1
0
1
0
1
1
2
2
0
1
2
2
0
0
2
3
2
1
1
1
1
0
2
0
1
2
2
0
1
1
0
0
0
1
0
1
1
1
1
0
1
2
2
0
1
2
1
2
0
1
1
0
2
0
0
0
1
1
0
1
1
2
2
2
1
0
1
1
1
0
1
1
2
1
1
2
0
1
0
2
2
1
1
1
2
0
1
1
1
0
2
1
2
0
0
0
1
1
0
0
2
1
1
2
2
0
2
1
2
2
1
1
1
0
1
1
0
0
3
0
2
1
0
1
1
1
1
2
2
1
1
0
1
0
1
1
0
0
1
1
1
1
1
0
1
1
1
1
0
1
2
2
0
0
2
2
2
0
1
1
0
1
1
0
2
1
1
0
2
2
0
2
1
1
1
0
1
0
0
2
1
2
1
1
1
1
0
1
1
1
2
2
1
1
4
1
1
1
2
0
1
0
1
1
0
1
1
2
1
0
0
0
1
1
0
1
0
1
2
2
0
1
0
0
2
1
0
1
0
2
1
1
1
1
2
1
1
0
1
0
2
1
1
2
1
2
1
0
2
0
1
0
2
1
0
1
1
1
0
1
0
0
0
1
1
1
0
0
1
1
1
2
1
1
0
2
1
1
2
2
0
2
1
2
1
1
0
3
0
1
1
0
1
1
0
1
1
2
0
1
0
1
2
0
1
2
0
1
1
2
2
2
1
1
1
2
2
1
0
2
1
1
2
1
1
0
1
1
1
1
0
1
1
0
1
1
0
0
1
0
0
1
0
0
0
1
2
1
2
0
1
1
2
1
1
1
1
2
2
1
1
2
0
1
0
2
1
1
2
1
0
1
0
0
1
1
1
1
0
1
1
1
0
1
1
1
1
1
1
1
0
2
3
2
0
0
0
2
1
0
0
1
3
2
0
1
1
0
1
1
0
1
1
2
1
2
1
0
0
0
2
1
0
2
2
1
1
0
0
1
2
2
1
1
1
0
0
0
1
1
2
1
0
0
0
1
1
1
3
2
2
2
0
0
0
2
3
2
0
1
2
0
0
1
1
1
1
1
1
1
2
0
2
1
2
2
1
0
0
2
1
1
1
2
1
1
1
2
0
1
1
1
0
1
2
0
2
2
2
1
1
1
2
2
1
1
1
0
0
2
1
1
1
1
1
2
0
1
1
0
1
2
0
1
1
1
2
1
1
0
2
1
0
1
1
2
1
2
0
1
2
0
1
1
1
1
2
2
1
1
2
0
1
1
1
0
2
1
2
1
3
1
1
0
0
0
2
2
0
0
2
1
0
1
0
1
1
2
0
1
1
1
0
2
0
1
1
0
1
0
1
2
0
1
0
1
0
1
1
0
0
1
1
1
0
1
2
1
0
2
1
1
0
0
0
0
1
1
1
1
1
1
2
0
2
1
3
3
1
3
1
0
0
1
1
2
0
0
1
0
1
1
0
1
1
2
2
1
1
1
1
1
0
0
0
0
2
1
0
1
0
0
2
0
2
1
2
1
1
1
1
1
2
0
1
2
2
0
2
1
1
1
1
3
0
0
1
1
1
2
1
1
0
0
0
2
1
1
0
1
1
1
2
2
2
1
0
1
1
0
2
0
1
1
2
1
0
0
1
0
2
0
2
0
1
1
1
1
1
1
0
2
0
1
0
2
2
2
1
1
1
0
3
2
2
0
1
2
1
1
2
0
0
1
0
2
1
2
1
0
1
0
1
2
0
1
1
2
3
0
0
0
1
1
1
1
2
0
2
0
2
1
2
2
1
0
1
1
1
2
0
1
1
0
1
0
1
1
1
1
1
0
2
0
1
2
0
2
1
2
1
1
1
0
1
2
0
1
1
0
0
1
1
4
0
2
0
0
1
0
0
2
1
0
0
2
2
0
1
3
2
2
1
1
1
2
2
0
2
2
0
1
1
2
1
1
0
1
2
0
3
1
2
1
6
1
1
0
1
1
2
0
0
1
2
1
1
1
1
0
1
0
1
1
0
2
1
1
1
0
1
1
1
2
0
1
0
1
0
0
1
0
0
1
0
1
1
2
2
1
0
0
1
1
1
1
1
1
1
1
0
0
2
3
1
0
1
1
2
1
1
2
0
2
1
1
1
1
1
0
1
2
1
2
2
1
1
0
1
1
2
1
2
2
2
0
1
0
0
0
2
1
1
0
0
2
1
0
0
1
1
0
0
1
2
1
2
2
0
1
1
0
1
0
0
1
2
1
1
1
1
0
1
0
0
0
1
1
2
1
2
1
1
1
0
1
1
2
1
1
1
1
1
1
2
0
2
2
0
2
2
1
2
1
1
1
0
1
2
1
0
1
2
1
2
1
2
2
0
1
0
1
1
0
0
2
2
2
0
1
1
1
1
0
1
1
0
0
1
2
0
0
1
1
2
1
1
2
0
0
2
1
2
2
2
0
0
1
1
1
1
0
0
0
2
1
0
0
1
3
2
1
0
0
0
1
1
0
1
1
0
1
1
0
0
2
2
0
0
2
1
1
2
0
1
1
1
2
1
2
2
1
2
1
1
1
2
0
2
1
1
1
1
2
0
1
0
1
0
0
2
0
1
2
2
1
1
2
0
2
2
0
1
0
0
1
2
0
1
0
1
0
1
2
1
1
2
1
1
1
1
1
2
2
4
1
1
0
2
0
1
1
1
1
0
1
1
1
0
1
1
1
2
0
1
1
2
0
1
1
1
1
1
2
0
2
2
1
0
1
2
1
1
2
3
1
1
0
1
2
1
0
1
1
0
2
0
1
1
2
1
1
1
1
1
1
1
0
0
1
0
1
0
2
1
0
2
2
1
1
1
1
3
0
0
1
1
0
1
2
2
1
2
1
2
0
1
1
1
0
1
1
1
1
2
1
0
2
0
2
0
1
0
0
1
1
0
1
2
1
2
0
1
2
0
1
2
1
1
0
2
2
1
1
1
2
1
1
0
1
1
2
1
1
1
2
0
2
1
1
1
2
2
1
2
0
1
1
0
1
1
0
1
1
3
1
0
2
2
0
0
1
3
1
0
2
2
2
2
1
1
1
1
2
1
0
1
0
2
1
0
1
2
1
0
0
0
1
1
1
1
0
2
1
2
1
0
1
2
2
1
1
1
1
0
1
1
0
0
1
1
1
1
1
1
0
1
0
0
1
1
3
2
1
1
1
0
2
1
2
1
1
1
1
0
1
1
1
1
0
1
0
0
1
2
3
0
0
2
2
1
2
1
1
1
1
2
1
2
1
1
0
0
1
0
0
1
1
1
2
1
2
0
2
0
1
1
0
0
0
1
2
1
1
1
0
1
0
2
0
0
3
1
0
1
0
1
0
0
3
2
2
0
0
2
1
0
2
0
0
1
1
0
3
0
1
1
2
1
1
2
1
0
2
0
0
1
1
1
2
1
1
1
2
0
0
2
2
2
1
1
0
2
1
1
1
1
2
1
2
0
3
2
0
1
1
0
1
0
1
2
1
1
2
2
3
1
0
1
1
1
1
1
1
0
1
1
1
1
2
1
1
1
0
1
1
1
1
0
1
1
1
1
1
1
1
0
2
0
2
1
1
1
2
1
1
1
0
1
0
1
1
1
0
0
1
0
1
0
0
1
1
0
0
1
2
0
1
1
1
1
0
0
1
1
1
0
1
2
1
2
1
2
1
1
2
2
0
2
1
1
0
1
3
1
2
1
1
2
1
1
1
0
0
2
2
1
0
1
1
2
1
2
0
0
0
2
2
0
0
0
3
0
0
0
1
1
1
2
1
2
0
1
0
0
0
0
0
2
0
1
0
2
1
1
1
1
2
1
1
2
0
2
0
1
1
1
1
1
0
1
1
0
1
1
1
2
0
0
0
0
1
0
2
0
1
2
2
0
1
0
1
1
0
1
2
1
1
1
1
0
1
1
0
1
1
0
1
1
0
2
0
0
1
1
1
1
0
0
1
0
1
0
1
1
2
1
2
1
1
0
1
2
1
1
1
0
2
1
0
0
1
0
0
1
3
1
1
1
0
2
0
1
1
1
0
1
2
2
0
0
1
2
1
1
1
1
0
0
2
2
1
0
2
1
1
0
0
1
0
1
2
1
1
0
1
0
1
1
1
1
0
0
0
0
0
0
1
1
0
0
1
1
1
1
1
0
1
0
2
1
1
2
3
1
2
0
1
1
1
1
1
2
0
1
2
1
1
2
0
0
1
1
1
1
1
1
1
2
0
1
1
1
1
0
1
0
1
1
0
2
0
2
1
1
2
2
0
1
1
1
1
0
2
1
0
1
1
1
1
0
3
1
0
1
0
0
2
2
0
0
1
2
1
0
0
2
1
1
2
0
1
1
1
0
0
0
4
1
1
1
0
1
1
1
0
2
1
2
1
1
1
1
0
1
1
1
0
0
0
1
1
2
0
1
0
1
2
1
0
1
0
2
2
1
1
0
1
2
0
2
1
0
0
1
1
2
0
1
2
2
2
0
2
0
2
1
1
3
2
1
1
1
1
1
1
0
2
1
1
3
0
1
0
1
0
2
0
1
2
1
1
0
0
2
0
1
1
1
2
1
1
1
2
2
1
1
1
2
2
1
0
1
2
1
0
1
0
0
2
0
0
1
1
0
1
1
0
0
1
1
0
1
1
0
1
2
1
1
1
0
1
1
0
2
1
0
2
0
0
0
0
0
0
2
1
2
2
0
1
2
1
1
1
5
0
2
0
1
2
0
1
2
0
1
0
1
1
1
0
1
2
1
1
2
0
2
0
0
1
2
1
0
0
1
0
0
0
2
0
1
1
2
0
2
1
2
2
2
2
1
1
0
2
2
2
0
0
1
1
2
2
1
1
1
2
2
1
1
0
1
1
0
0
2
1
0
0
2
2
0
1
1
1
2
2
0
1
1
2
2
1
0
1
1
2
0
1
2
1
2
1
1
0
2
1
2
2
0
2
1
0
1
0
0
1
1
0
1
1
2
1
0
2
2
1
1
1
1
1
2
1
1
1
0
1
0
1
1
1
1
0
2
0
1
0
2
1
2
1
1
0
0
2
1
0
1
0
1
1
1
1
0
0
2
2
0
1
1
0
1
1
1
1
1
2
1
1
1
2
0
1
2
0
1
1
0
2
0
0
2
0
0
2
1
1
2
0
0
1
2
0
1
0
2
4
1
0
3
2
1
1
1
1
1
1
1
0
1
2
2
1
2
0
1
1
1
1
1
1
1
2
1
0
1
1
0
0
1
2
1
1
2
3
0
1
0
0
1
1
1
0
1
0
1
1
1
1
0
2
0
0
0
1
1
1
0
0
0
1
2
1
2
3
1
0
2
0
1
1
1
0
0
2
0
1
5
1
0
2
1
0
1
2
1
2
1
2
0
0
2
1
0
1
0
1
1
2
1
1
1
1
0
1
1
1
1
2
0
0
2
1
0
0
2
0
1
1
0
0
1
1
2
0
0
2
2
1
0
1
1
1
1
0
2
1
3
1
1
0
0
2
0
0
1
1
1
0
2
1
0
2
1
0
1
1
0
0
1
1
1
1
1
1
1
2
0
2
1
1
1
0
1
1
0
1
2
0
1
1
1
1
0
1
2
1
1
1
1
1
0
0
1
0
2
1
0
0
0
1
1
1
0
0
1
1
1
1
0
1
1
1
1
1
0
1
1
0
2
1
1
1
0
0
1
2
1
1
2
2
2
1
1
0
1
1
0
0
1
2
1
0
1
1
0
1
0
1
1
1
1
0
2
1
0
1
1
1
1
1
1
2
1
0
2
1
1
1
0
0
1
1
1
1
0
1
1
1
1
0
1
2
1
2
1
1
1
0
1
2
2
2
0
1
0
1
1
1
3
1
0
2
1
0
0
1
1
1
1
1
2
0
1
1
2
1
2
0
1
2
0
1
1
2
0
0
2
1
2
0
2
0
0
1
1
1
1
0
1
0
0
1
1
1
1
1
1
2
1
0
1
1
0
1
2
1
1
1
0
0
1
0
0
1
0
0
0
1
2
1
1
2
1
1
0
1
1
0
1
3
1
1
2
2
1
0
0
1
0
0
2
0
0
2
1
2
0
1
1
2
1
0
1
1
1
0
0
1
1
1
1
1
0
0
1
1
1
2
0
1
0
1
1
2
1
1
1
1
0
1
0
1
2
1
1
2
2
2
0
1
1
1
1
1
1
1
0
2
2
0
1
0
1
1
1
1
0
0
1
1
1
0
1
1
0
2
1
1
1
0
0
1
2
1
0
0
1
0
2
0
1
1
1
0
2
1
0
1
1
1
2
1
1
1
1
1
0
2
1
1
2
1
2
1
1
1
1
0
2
2
2
1
1
2
2
0
0
2
0
2
1
1
0
1
1
1
0
0
1
0
2
1
1
2
0
1
0
1
1
1
2
0
0
0
1
1
1
0
1
2
2
1
1
2
0
1
1
2
0
0
0
1
0
1
1
1
1
2
1
1
0
1
1
2
2
0
1
1
0
2
1
0
2
0
1
1
0
2
1
0
1
0
1
0
0
1
1
1
1
1
0
0
0
1
1
0
1
0
1
2
2
1
0
1
1
0
1
1
1
0
1
2
2
0
2
0
0
1
0
2
1
1
2
1
2
2
0
1
1
1
1
1
2
0
1
1
1
0
1
1
2
1
1
1
1
1
2
0
1
1
1
1
2
1
2
2
1
0
1
0
1
0
1
0
2
1
1
1
0
1
0
1
1
0
1
1
1
2
2
1
1
1
1
1
1
0
2
1
1
0
1
1
1
1
1
0
1
1
1
0
0
2
2
2
2
1
2
1
1
1
1
1
1
0
1
1
0
1
2
1
0
1
1
1
1
1
0
1
1
1
0
2
1
0
0
2
1
2
0
0
1
1
1
1
0
1
1
0
2
1
1
1
0
1
2
2
1
2
0
0
1
3
1
2
1
0
0
2
1
1
0
2
0
1
2
2
0
1
0
2
1
1
2
2
0
0
1
1
2
2
1
0
0
0
3
2
1
1
1
1
1
0
1
1
1
0
2
2
2
1
0
1
2
1
0
0
1
1
1
1
1
2
2
1
1
1
1
1
0
1
0
2
0
1
1
0
1
2
1
1
0
1
1
0
1
2
1
1
1
1
2
1
1
1
1
1
1
1
2
3
1
2
1
1
0
0
2
0
0
1
0
2
1
1
2
2
1
2
0
2
1
0
0
0
1
1
0
1
0
2
1
0
0
2
0
1
1
0
1
2
2
1
0
2
0
1
2
1
1
1
2
2
2
0
1
2
1
1
1
2
1
1
0
0
2
2
2
1
1
1
0
1
1
1
1
0
1
0
1
0
1
1
1
0
1
2
0
2
0
0
0
0
1
1
0
1
2
2
0
0
2
1
0
1
1
1
1
1
1
1
2
1
1
2
1
0
0
0
0
2
1
1
0
0
2
2
2
1
1
1
1
1
0
0
1
0
2
0
1
0
1
0
1
2
0
1
2
1
1
0
1
2
1
1
1
0
2
0
1
2
1
1
1
1
1
1
2
2
1
1
1
1
0
2
1
1
1
2
0
2
1
2
2
0
0
1
1
0
0
1
1
0
2
1
2
3
1
1
1
0
1
2
1
4
2
0
1
1
1
2
1
2
0
1
1
2
1
2
1
1
0
1
1
1
0
1
0
0
2
1
1
2
1
1
2
2
1
1
1
0
0
1
0
3
1
1
1
7
0
0
1
1
1
2
1
0
0
1
1
2
3
0
1
2
2
0
2
1
1
1
1
1
3
1
2
0
1
0
1
0
1
2
1
0
1
1
0
0
2
1
0
2
1
0
0
1
1
1
0
0
1
1
0
2
0
2
2
0
2
1
0
0
0
1
1
2
0
1
1
0
1
1
0
0
1
1
0
1
0
1
2
1
2
1
1
2
2
1
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
0
1
1
2
2
0
2
1
0
0
1
1
1
1
0
1
0
1
0
1
2
2
1
2
0
1
1
1
2
1
1
0
1
1
1
2
2
0
2
2
1
1
0
2
2
2
2
2
1
0
2
2
1
2
1
1
0
1
1
0
1
0
1
1
1
1
0
2
0
2
1
0
1
1
1
1
0
1
1
1
2
0
2
2
2
1
1
2
2
1
2
2
1
2
1
3
1
1
2
1
1
2
0
1
1
2
2
2
0
1
1
1
1
2
1
0
2
0
2
0
0
0
1
2
1
1
2
1
1
2
1
1
1
0
1
2
2
2
2
0
0
2
3
1
1
1
9
0
1
1
1
0
1
1
2
1
1
0
2
0
1
1
2
1
0
0
0
2
1
0
1
1
1
1
0
1
1
1
2
1
1
2
2
1
1
0
2
0
0
0
1
0
0
0
1
2
0
2
2
1
1
2
1
1
1
1
0
1
1
1
1
0
0
2
1
1
1
2
0
2
1
0
0
1
0
0
0
1
1
0
1
0
1
2
1
1
0
1
1
1
0
1
0
2
0
0
1
1
1
1
0
2
1
2
2
0
0
1
2
0
0
0
1
2
0
1
0
1
1
0
0
1
2
2
1
1
1
0
1
0
1
1
2
1
0
2
2
1
1
1
0
2
0
0
0
1
1
1
1
0
2
1
2
2
1
3
1
1
2
2
0
2
0
1
0
1
2
0
1
1
1
1
1
2
1
1
1
0
1
0
2
1
0
1
2
0
1
1
2
1
2
1
2
1
2
0
1
1
2
0
0
0
0
3
2
1
3
1
1
2
2
1
1
2
1
1
1
2
0
0
1
0
2
1
3
2
2
0
2
1
0
0
1
1
0
0
2
0
2
1
0
0
2
2
1
1
1
2
2
1
1
1
1
2
1
1
1
1
1
1
0
1
2
1
1
0
0
2
0
1
0
2
1
2
1
1
0
8
1
1
3
1
1
1
1
1
2
1
1
1
1
2
0
1
2
2
1
1
2
1
2
2
0
0
2
1
0
1
1
1
1
1
1
0
0
1
0
0
1
1
1
1
2
0
0
1
1
1
1
2
1
0
0
1
1
1
0
2
0
2
1
1
0
1
1
1
2
0
1
2
1
0
1
2
1
0
1
1
1
2
1
1
1
1
1
1
1
1
1
1
0
0
0
2
1
0
0
1
2
0
1
0
1
0
0
1
1
1
1
0
2
0
1
0
2
1
2
0
0
1
1
2
0
1
0
2
1
1
0
1
1
1
0
1
2
1
2
1
0
0
0
1
0
0
1
1
1
1
1
2
2
0
0
0
2
0
1
0
0
1
0
1
0
1
0
0
2
0
0
1
2
1
1
1
1
2
0
1
2
1
2
1
0
2
0
1
2
0
1
1
2
2
0
1
0
2
0
0
2
2
1
2
0
2
1
1
0
0
0
1
3
1
1
1
1
1
1
1
1
1
2
0
2
0
1
1
0
1
1
2
1
1
1
1
0
1
2
1
3
2
2
1
1
1
2
1
0
2
1
1
2
1
0
1
1
2
1
1
0
2
0
2
0
1
3
1
0
2
2
1
0
1
1
1
1
0
2
1
2
1
0
2
0
2
1
0
0
2
2
1
1
1
0
1
0
1
2
0
1
1
1
1
0
2
0
0
0
1
1
1
3
1
1
1
2
1
0
0
1
1
0
0
1
1
1
1
3
1
1
0
0
0
1
1
1
0
2
2
1
2
1
1
2
1
1
1
1
1
1
2
1
2
0
1
0
1
2
0
1
0
1
1
1
2
1
0
2
3
2
1
0
2
0
1
2
0
2
0
1
0
1
0
1
2
0
1
1
1
1
1
1
1
1
0
1
1
1
0
0
1
1
1
2
2
0
1
1
1
2
1
1
2
2
2
1
1
2
2
0
2
1
0
2
0
2
0
1
3
2
1
1
2
2
1
1
1
1
1
1
1
0
2
3
0
1
0
0
1
1
2
0
2
1
1
2
2
0
1
2
0
1
2
1
1
2
2
0
2
1
2
1
1
1
1
1
0
1
1
0
1
2
0
1
1
0
2
1
1
1
1
1
0
0
1
1
0
1
1
1
1
1
0
1
0
2
1
2
1
0
0
0
0
1
2
1
1
2
2
2
1
2
1
1
0
0
2
0
2
1
1
0
2
1
0
2
1
1
1
0
1
2
2
2
0
1
0
1
1
0
1
2
1
1
0
2
2
2
1
1
2
1
1
2
2
1
2
1
2
1
1
0
2
2
2
1
1
0
0
2
1
1
2
2
0
2
0
0
1
0
1
1
2
0
1
0
0
0
1
1
1
2
0
1
1
0
0
0
2
2
1
2
1
1
2
1
1
2
1
0
0
2
0
1
1
1
1
0
2
2
0
1
0
0
2
1
0
1
0
0
1
1
2
1
0
0
2
0
1
1
2
1
0
0
1
1
0
1
0
2
1
1
1
2
1
0
0
1
1
0
1
1
1
2
1
1
0
1
0
1
2
1
2
0
1
1
2
1
1
1
1
2
1
2
1
2
2
0
0
0
1
0
2
1
1
1
2
0
2
1
1
2
0
0
1
1
2
0
2
1
1
1
0
1
1
0
1
1
0
2
1
2
0
1
1
0
1
1
1
2
1
1
1
0
1
2
2
2
1
0
2
1
1
2
2
1
0
1
0
0
0
3
1
0
0
2
1
0
1
1
0
0
1
0
2
2
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
2
1
1
2
1
1
2
2
1
2
1
1
0
0
1
2
1
1
1
1
0
0
1
1
2
2
2
3
2
0
0
2
1
2
1
1
1
0
0
2
1
1
0
2
1
1
3
2
1
1
1
1
1
4
2
0
0
1
1
1
1
1
1
1
0
1
1
1
1
2
1
2
0
2
0
0
1
1
2
2
1
1
0
1
0
1
1
1
2
2
1
1
1
0
1
1
1
0
4
1
1
2
0
1
1
0
0
2
1
1
0
0
0
2
2
1
1
2
1
2
2
1
1
1
1
0
1
3
1
2
1
1
2
1
1
1
1
0
0
1
1
1
1
0
0
1
2
1
1
0
1
0
0
0
1
1
2
0
1
2
2
0
0
1
1
1
1
1
0
2
0
1
0
0
2
2
1
0
0
2
0
0
1
0
1
1
0
0
0
1
0
1
1
0
1
1
0
0
2
1
2
2
1
0
1
1
1
2
0
1
0
2
1
1
1
1
0
1
2
1
1
0
0
1
1
0
1
1
1
0
1
2
1
2
2
2
1
1
1
1
1
0
0
2
1
0
1
1
0
1
2
2
1
1
1
1
1
1
0
1
2
1
1
0
1
1
0
1
1
0
1
1
1
0
0
1
1
1
1
0
1
2
0
1
2
0
1
2
1
1
1
0
0
0
1
1
1
0
0
2
1
3
0
1
0
1
2
1
2
0
1
0
2
0
0
1
1
2
1
1
1
1
0
1
2
0
1
2
0
1
2
1
2
0
1
0
2
1
0
0
1
2
1
0
3
1
0
2
0
0
1
1
2
1
0
1
2
1
1
2
0
1
1
1
0
3
4
2
1
1
1
1
1
2
0
1
1
1
0
0
1
1
1
1
1
0
1
1
1
0
2
2
0
1
1
0
1
1
1
1
0
1
1
1
0
2
0
2
1
2
1
0
2
1
1
2
1
1
1
2
0
0
1
1
1
1
1
1
0
0
2
0
1
2
2
1
4
1
2
1
2
1
0
1
1
0
1
0
2
3
2
2
1
1
2
1
1
0
2
2
1
0
0
1
2
0
2
1
1
0
0
1
1
3
2
3
2
1
0
1
0
1
1
0
1
2
1
1
1
1
0
2
1
2
1
1
0
1
0
1
0
1
1
2
2
1
2
0
1
2
2
0
1
1
0
1
2
1
2
0
0
2
0
0
1
1
1
0
1
2
0
1
0
1
1
1
1
1
2
0
1
1
0
1
2
2
0
1
0
1
0
1
1
2
1
1
1
1
1
2
1
1
0
1
1
2
1
1
2
0
1
0
2
2
2
1
2
1
1
2
0
1
1
0
0
1
2
1
1
2
1
0
1
2
1
1
1
1
1
1
1
1
0
1
2
2
0
1
0
1
1
1
1
1
1
1
0
2
1
1
1
0
0
1
0
0
2
1
2
0
2
0
0
1
0
1
1
1
1
1
2
1
2
1
2
0
0
3
0
2
1
2
1
0
0
1
1
1
6
1
1
1
1
2
1
1
1
3
1
2
1
0
1
0
1
0
2
1
1
2
2
2
0
0
1
1
2
0
0
0
1
1
0
1
1
1
0
1
2
1
2
0
1
2
1
1
1
1
1
1
2
1
1
1
0
1
0
1
0
2
0
1
1
1
0
0
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
2
2
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
0
0
2
1
0
2
1
2
0
1
1
2
0
1
1
2
1
0
2
0
1
1
1
0
2
1
2
1
1
1
1
1
0
0
1
0
1
2
1
1
2
0
0
0
2
1
1
0
1
2
1
0
1
1
2
1
0
0
1
1
1
0
1
1
1
2
2
1
1
1
0
0
2
3
1
2
1
1
0
1
0
1
1
1
1
1
2
2
1
1
1
1
0
0
0
2
0
0
1
0
0
1
1
2
2
0
2
1
1
1
0
1
0
2
0
2
1
1
2
1
1
1
0
1
1
2
2
1
1
0
1
1
0
0
2
1
0
0
1
0
0
1
0
1
1
0
0
1
1
1
0
2
1
2
1
1
0
2
1
1
1
0
1
2
2
1
0
0
1
0
1
0
2
1
1
0
1
2
1
1
0
1
1
3
4
2
1
1
3
1
1
2
0
2
1
2
0
2
1
0
1
1
0
5
0
0
1
0
1
0
0
1
1
2
2
0
0
1
0
1
1
1
1
1
2
1
1
0
1
2
1
1
0
1
0
0
0
1
1
0
2
0
2
0
1
1
1
2
1
1
0
2
1
1
2
0
1
1
1
1
1
0
1
2
1
0
0
1
1
1
1
1
1
0
2
1
1
2
1
1
1
2
1
2
1
2
1
2
0
1
1
2
2
2
1
1
2
1
0
1
2
1
1
1
0
1
2
1
0
0
1
0
0
2
0
0
1
2
0
1
0
0
1
2
0
1
1
1
1
2
0
1
0
2
2
1
1
2
2
1
1
2
0
1
2
2
1
2
0
1
2
1
1
0
1
0
0
1
1
1
1
2
3
0
2
0
1
0
2
0
0
1
0
1
1
1
2
2
0
1
2
2
1
0
0
1
1
2
1
1
0
1
2
1
1
1
1
2
0
1
1
2
0
1
1
1
0
1
0
0
2
1
0
1
1
1
1
1
0
1
1
1
2
3
0
1
0
0
1
2
0
0
0
2
1
2
2
0
2
1
1
1
1
1
1
1
2
2
2
2
1
2
0
1
2
1
1
1
1
2
2
1
0
1
1
0
2
1
2
2
0
3
1
2
1
0
0
1
0
0
2
2
2
0
1
1
0
1
2
0
1
2
0
2
0
0
0
2
1
1
0
0
0
0
1
0
0
1
1
0
2
1
1
1
1
2
1
1
1
1
1
0
1
1
1
2
1
2
1
1
2
1
0
1
1
1
2
0
0
0
1
2
2
2
1
0
1
2
2
0
2
0
1
2
0
1
2
1
1
0
2
1
1
1
2
2
2
2
1
2
1
0
1
2
2
2
2
1
0
1
2
1
1
1
1
0
1
0
1
1
2
1
1
1
1
0
2
2
1
1
1
2
1
2
0
0
3
0
2
1
1
0
1
1
1
0
1
1
1
1
1
0
0
0
1
0
1
2
1
0
0
0
1
1
1
2
1
0
1
1
1
1
1
2
0
2
2
0
0
2
0
1
2
1
0
1
1
3
1
1
0
1
0
0
2
0
1
1
1
1
1
2
2
1
2
1
1
2
0
1
0
0
1
0
2
2
2
1
1
1
0
2
1
2
1
2
0
2
1
0
1
0
3
0
1
0
2
1
2
1
1
2
1
1
2
2
2
1
1
1
0
0
0
1
0
2
1
1
0
0
3
0
0
1
0
1
0
0
0
2
1
1
0
0
1
1
1
2
2
1
0
0
0
2
2
1
1
1
1
2
1
1
1
1
1
0
1
0
2
0
1
1
0
1
0
1
1
2
1
1
0
0
1
1
1
1
2
1
0
1
1
0
2
2
0
1
1
1
0
1
0
0
2
1
1
0
1
1
1
1
2
1
0
0
2
2
2
1
1
1
0
1
0
0
2
1
1
2
1
0
0
2
1
0
0
2
1
1
2
0
2
2
1
0
0
2
2
1
1
1
1
0
1
1
1
0
1
1
2
0
1
1
2
1
2
2
1
1
1
2
1
0
1
3
2
1
1
2
0
1
1
1
1
3
1
1
0
0
1
2
1
0
0
1
1
1
0
0
2
1
1
1
2
2
2
2
1
1
0
1
1
2
2
1
1
0
1
0
0
0
1
1
2
2
1
2
1
1
1
1
1
0
0
1
1
0
1
1
0
2
1
1
1
1
0
1
1
3
0
2
0
2
1
1
0
0
2
2
0
1
0
0
2
0
1
0
1
2
0
0
0
2
0
2
0
2
0
0
1
1
1
1
1
1
1
2
1
1
2
2
2
1
1
1
1
1
2
1
2
1
2
1
0
1
1
0
1
1
1
2
2
1
1
0
2
1
3
0
1
0
1
2
2
1
1
0
1
1
1
2
2
0
0
1
2
0
0
1
1
1
0
2
1
1
0
1
0
1
0
1
2
2
0
1
0
1
1
1
3
1
0
0
0
1
3
0
0
0
0
1
2
0
0
0
0
1
1
1
1
1
1
0
1
0
1
0
2
0
2
1
1
1
0
1
1
1
2
1
1
0
1
1
1
1
1
1
2
1
0
1
0
0
0
0
1
1
1
1
0
1
1
1
0
0
1
2
2
2
2
1
0
0
1
1
1
2
0
1
2
0
2
1
1
2
0
2
1
2
1
1
1
1
2
0
1
2
1
1
1
2
0
0
0
1
0
1
0
2
0
1
1
2
1
1
2
1
1
1
1
2
1
1
0
2
2
1
1
0
1
2
1
1
1
1
1
2
2
0
2
1
1
0
0
1
2
1
1
0
0
2
0
0
0
1
0
1
1
1
2
2
1
1
1
1
1
1
0
1
2
2
1
0
2
1
1
1
1
1
2
1
2
1
0
1
0
0
1
2
2
2
2
0
2
1
2
1
0
1
1
0
2
1
2
0
2
0
1
1
1
2
1
0
1
0
1
0
1
0
1
1
2
1
2
1
0
1
1
1
1
2
1
1
0
2
2
0
0
2
1
0
1
0
2
2
1
1
1
2
1
2
1
2
3
2
2
1
1
1
1
1
1
0
2
0
2
1
1
1
1
0
2
0
1
0
0
1
2
0
1
0
1
1
1
0
0
0
0
1
2
0
2
0
1
1
3
1
2
1
0
1
1
1
3
0
1
1
0
2
2
1
0
2
1
1
1
0
1
2
2
1
1
0
2
2
1
3
2
0
2
2
1
1
1
2
0
1
1
1
2
0
2
1
0
0
0
2
0
1
1
2
1
2
2
1
1
0
1
0
1
0
2
1
1
1
1
0
2
2
2
1
1
1
0
2
0
0
2
0
1
0
1
2
1
2
1
0
1
1
1
1
2
2
2
1
0
1
2
1
1
1
1
0
2
1
1
0
0
0
2
1
2
0
2
2
1
1
1
2
1
1
0
1
1
2
1
1
2
1
0
1
2
2
1
2
0
1
1
1
2
1
1
0
2
0
1
1
1
1
2
1
1
1
0
1
1
1
2
2
0
1
0
1
1
2
1
2
1
1
2
2
0
1
1
2
1
2
1
1
2
1
1
2
1
1
0
0
2
1
1
1
1
1
1
2
0
1
0
0
2
0
0
1
1
0
1
2
0
1
0
1
0
1
0
0
2
0
1
0
0
0
0
1
1
1
0
2
0
0
0
1
1
1
1
0
1
0
1
1
2
0
2
1
0
0
1
1
0
0
0
1
0
1
1
1
1
1
0
1
1
0
0
1
1
0
1
1
1
2
1
0
1
2
1
0
1
1
0
0
0
0
1
0
0
2
1
0
1
2
0
0
0
2
1
1
1
0
1
0
0
0
1
2
2
2
1
1
2
0
1
2
1
0
0
1
2
2
0
2
1
0
1
0
1
1
1
1
1
1
0
1
2
2
3
0
1
0
0
2
0
2
1
0
2
2
1
1
1
1
0
1
1
1
0
1
1
2
0
1
1
1
1
1
0
0
0
1
2
2
2
1
1
0
1
1
0
1
0
3
1
1
0
1
1
0
1
0
1
1
0
0
1
1
1
2
0
0
0
2
1
0
1
1
1
1
1
1
1
1
0
2
1
0
1
1
1
2
1
1
0
1
1
0
2
0
2
0
0
1
1
1
2
1
1
1
1
1
0
1
0
2
2
0
2
2
1
2
0
1
2
1
2
1
1
2
0
0
1
1
2
1
0
0
1
1
0
1
1
0
1
1
0
0
1
1
1
0
2
0
1
2
0
1
0
2
1
1
0
2
0
0
3
1
0
1
1
1
0
0
2
1
0
1
2
1
0
0
1
1
0
1
1
1
1
1
0
1
3
1
1
1
1
2
0
3
0
2
2
2
1
1
1
1
1
1
2
0
1
1
1
2
1
1
1
2
1
1
0
2
1
1
1
1
1
1
1
0
1
0
1
1
1
1
1
1
2
1
0
1
1
1
2
2
1
1
0
1
1
1
1
1
2
1
2
1
1
2
1
1
1
2
1
1
1
1
0
1
1
0
1
1
2
2
1
0
1
2
0
1
0
1
2
1
2
0
1
2
1
2
1
2
1
2
0
1
4
1
1
1
2
0
2
1
1
1
2
0
0
2
1
1
0
1
2
1
1
1
2
1
2
1
1
1
2
1
1
1
2
1
1
1
1
0
1
2
0
2
2
1
4
2
2
1
1
0
1
2
2
0
0
1
2
1
1
1
2
1
0
0
1
0
0
0
2
1
0
1
2
1
1
1
1
1
0
1
0
0
1
1
1
1
2
1
0
1
0
1
1
0
1
1
1
0
2
0
0
2
1
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
2
1
0
0
2
3
0
0
0
1
2
1
1
1
0
2
1
1
0
1
2
2
1
1
0
1
2
0
2
0
1
1
1
1
1
1
1
0
1
1
1
1
1
1
2
2
0
0
0
1
0
0
0
1
1
1
0
2
1
0
1
1
1
2
1
2
1
1
1
2
2
2
1
1
1
1
2
1
1
0
1
1
0
1
1
0
0
2
2
2
0
1
1
1
1
1
1
0
1
1
2
1
1
0
1
1
1
0
0
1
1
1
1
1
0
1
1
1
2
2
2
1
2
0
2
2
1
0
1
0
1
1
1
1
2
0
1
0
1
1
2
0
1
0
0
0
0
0
1
3
1
1
1
0
1
1
2
0
1
0
1
1
1
2
0
1
0
0
1
0
0
1
2
0
2
1
0
2
2
0
0
1
1
2
0
2
2
2
2
0
1
1
0
1
0
1
0
1
2
2
1
1
2
0
1
1
0
1
1
1
0
1
1
1
0
1
2
2
1
1
3
1
1
1
2
1
1
1
1
1
1
1
3
1
1
0
0
1
2
0
0
2
1
1
2
1
1
1
1
1
1
0
0
0
1
2
1
2
1
2
1
1
1
0
1
1
1
2
1
1
1
1
1
1
2
2
1
0
1
2
1
0
1
0
0
2
1
1
0
1
2
2
1
2
0
1
1
2
1
2
0
0
1
1
1
1
1
0
1
1
0
1
0
1
0
1
1
0
0
1
1
0
1
0
1
0
3
1
0
2
1
3
1
1
2
1
1
1
0
1
2
0
1
0
0
0
2
2
1
1
2
0
2
0
2
1
1
1
0
1
1
1
1
2
1
1
1
0
1
1
2
1
2
1
1
0
2
1
0
1
0
2
0
2
1
0
1
1
1
1
2
0
1
1
1
1
1
2
0
2
2
0
1
0
1
1
0
2
2
1
2
0
1
1
3
1
0
0
0
2
1
0
1
2
1
0
2
1
3
1
0
2
1
0
1
1
2
0
1
0
0
0
1
1
2
1
1
1
2
1
1
1
3
1
1
0
1
1
2
0
1
1
1
1
0
1
0
1
1
0
1
1
0
2
0
1
1
0
0
1
2
2
1
1
1
0
0
1
0
0
1
2
0
1
1
2
1
1
1
2
1
2
1
2
0
3
1
2
0
1
1
1
1
2
0
1
1
0
1
0
1
0
2
0
1
1
0
0
1
0
0
2
0
0
2
1
1
2
1
0
0
1
1
1
1
1
2
0
1
2
1
2
0
2
2
1
0
2
1
1
3
2
1
2
4
0
1
0
2
1
2
0
0
0
1
1
1
0
2
1
1
1
0
0
1
1
1
2
1
0
1
2
1
1
1
0
0
1
1
0
0
1
2
1
1
1
1
1
0
0
0
2
0
0
0
0
1
2
1
2
0
1
0
2
0
1
0
1
1
0
1
0
0
1
2
0
1
0
1
0
0
1
1
0
1
0
1
0
1
0
1
1
1
1
2
0
0
1
0
2
1
2
0
2
1
0
1
2
1
0
1
0
0
1
1
1
0
1
2
0
0
1
2
1
1
2
1
1
1
0
0
0
2
0
1
0
1
0
2
0
2
0
1
0
1
0
1
2
1
1
2
0
2
0
2
2
0
0
1
1
2
0
1
1
2
1
1
1
1
1
1
0
1
2
1
1
1
1
0
1
1
1
1
0
1
1
1
2
0
0
0
1
2
1
1
1
1
0
0
1
2
2
1
1
0
0
0
1
2
1
1
1
1
1
1
1
1
1
1
2
2
1
2
2
2
1
0
0
0
2
2
1
1
1
1
1
1
1
0
0
1
1
0
2
1
1
0
1
1
0
1
0
1
2
1
1
1
1
1
0
2
1
0
2
1
2
0
0
0
1
1
2
1
0
1
2
1
1
0
1
1
0
1
1
1
0
0
1
0
3
2
1
0
1
1
0
0
1
2
1
1
0
1
2
1
0
2
1
1
0
0
2
2
0
1
1
0
2
0
1
1
1
1
0
1
1
1
0
1
0
1
1
2
1
1
1
1
1
0
1
2
2
0
2
0
0
1
1
1
0
2
6
1
0
2
1
1
1
1
1
1
1
0
1
1
0
0
2
0
0
0
1
1
1
1
1
1
1
1
0
1
0
1
1
2
1
1
0
0
1
2
0
1
0
2
0
1
2
0
0
1
0
1
2
0
0
1
2
1
0
0
0
1
0
2
1
2
1
2
2
2
2
1
1
1
1
0
1
0
1
0
1
0
1
0
2
1
2
2
1
1
1
1
1
0
2
0
0
1
2
1
0
2
2
1
1
0
0
1
1
1
0
1
1
1
2
2
1
1
0
2
1
1
1
1
2
0
0
1
1
0
1
0
1
0
1
0
1
0
0
1
1
2
1
1
1
2
1
2
1
2
2
1
1
1
1
0
2
1
1
1
1
1
4
1
0
2
2
0
2
2
2
0
1
0
2
1
2
2
1
0
1
1
1
1
3
1
3
1
1
2
2
1
1
0
1
0
0
0
1
0
2
0
2
1
0
2
1
1
1
1
1
0
0
1
2
2
2
0
0
0
2
1
1
1
1
1
0
0
1
0
0
1
2
1
1
0
0
0
0
1
1
2
1
1
1
1
0
1
1
0
0
0
1
0
1
0
1
0
0
1
2
1
1
0
0
1
2
4
2
0
2
1
1
1
1
1
0
1
2
2
1
0
1
0
0
1
1
1
0
0
0
0
1
1
0
1
1
0
0
0
1
1
2
2
0
2
1
1
2
2
0
1
1
2
1
1
0
0
1
1
1
1
1
1
0
1
1
2
1
1
1
0
2
0
2
0
0
1
2
1
2
1
1
1
1
1
1
2
0
0
0
0
0
1
2
1
0
2
0
0
0
1
1
2
2
0
0
1
2
1
0
1
2
0
1
1
2
0
1
0
1
0
1
0
1
0
2
2
1
2
1
1
1
2
0
1
1
2
1
2
1
0
0
1
2
0
1
0
2
1
2
0
1
1
0
1
0
0
0
1
2
1
1
1
2
0
2
2
0
1
1
2
1
0
1
2
1
2
1
0
1
1
2
0
2
1
1
1
1
2
3
2
1
1
1
1
2
0
1
0
1
1
0
0
1
0
1
0
1
1
1
0
1
0
3
2
2
1
0
1
1
2
1
1
0
0
1
2
1
2
2
2
0
0
2
0
0
1
2
0
1
0
1
1
2
1
1
0
0
1
1
0
1
0
0
2
0
1
1
1
1
0
0
0
1
1
2
0
1
1
2
2
2
0
1
1
1
1
0
2
0
1
1
0
1
1
0
1
0
1
0
2
2
0
2
1
2
1
0
1
1
2
1
2
0
1
1
0
2
1
1
1
0
0
1
1
0
1
0
0
1
1
1
1
1
2
1
0
1
0
1
2
2
2
2
1
1
0
2
1
1
1
1
0
1
0
1
0
1
1
0
1
0
1
1
2
1
1
0
0
0
1
2
1
1
1
1
1
1
0
0
1
1
1
0
1
1
0
0
0
0
0
0
0
1
0
1
1
0
1
1
0
1
2
1
0
1
0
2
1
2
2
0
2
1
2
0
0
1
0
1
1
0
1
1
2
1
0
0
1
2
1
0
2
0
0
0
1
1
0
1
1
1
2
0
0
1
0
1
1
0
1
0
2
0
0
1
1
0
1
1
1
1
1
1
2
1
0
1
1
1
0
1
0
1
2
2
0
1
0
0
2
1
1
2
1
1
1
1
2
1
1
1
1
0
1
0
0
1
0
1
1
0
2
1
2
1
0
1
2
3
2
2
1
1
1
1
2
1
1
2
3
2
1
0
0
2
1
2
1
0
1
1
0
2
1
1
1
1
1
1
1
2
1
1
1
0
0
1
1
1
2
0
0
0
1
1
0
1
1
1
1
1
2
1
0
0
1
1
0
0
1
1
1
1
2
2
2
1
1
0
2
1
1
1
1
2
1
1
0
0
0
1
0
0
1
1
0
1
2
0
1
0
0
0
2
0
2
2
1
1
1
0
0
1
1
1
0
1
1
1
1
7
0
1
1
1
0
1
0
1
3
0
0
2
2
1
0
1
2
1
3
2
2
2
1
1
2
1
0
1
1
1
0
1
2
2
1
2
1
1
1
2
2
1
2
1
1
0
3
0
0
0
1
1
0
2
2
1
2
2
1
1
1
0
1
1
1
2
1
0
0
2
0
1
0
2
0
1
1
1
0
2
1
1
2
1
1
0
2
1
1
1
1
3
1
0
2
2
2
2
0
2
1
0
1
1
0
0
1
2
1
2
2
1
1
3
2
1
0
1
2
2
0
2
2
1
0
2
0
2
1
1
0
1
1
1
1
2
1
1
2
0
0
1
1
0
2
1
1
0
2
2
0
0
1
2
1
1
2
2
1
1
1
1
1
0
1
1
2
1
1
1
1
0
0
1
0
0
1
0
1
3
1
1
1
1
2
1
0
1
1
1
0
2
1
0
1
1
1
1
1
0
1
1
0
1
1
1
1
1
1
1
0
2
0
1
2
2
2
0
2
0
1
1
0
1
0
2
1
1
1
2
1
1
0
1
0
0
0
1
0
0
0
1
1
2
1
0
2
0
0
1
1
0
0
2
0
0
2
1
1
1
1
2
0
3
1
1
1
1
1
0
2
0
0
1
1
1
0
1
1
0
1
5
1
2
2
0
2
0
1
1
0
1
1
2
1
0
0
1
1
1
1
1
1
1
0
1
0
1
2
2
2
1
2
1
1
0
4
0
0
2
2
1
1
1
0
1
2
1
2
2
1
1
1
1
1
2
1
0
0
0
0
0
1
1
1
1
1
1
1
1
1
1
0
1
2
0
0
0
2
1
2
2
1
1
1
1
1
1
0
2
0
0
0
2
1
1
1
2
0
1
2
0
0
0
1
2
2
0
0
1
1
1
1
1
1
1
1
0
1
0
1
1
2
2
1
3
1
1
3
2
1
1
2
2
1
0
0
0
0
1
2
2
1
1
1
2
0
0
2
0
0
1
0
0
2
1
1
1
1
0
1
1
0
1
2
1
0
1
1
2
1
2
1
3
1
1
1
1
1
0
2
2
1
2
1
1
1
0
2
2
2
1
0
1
1
2
1
1
1
0
1
1
2
1
0
1
2
1
2
1
2
0
1
0
0
1
1
1
0
1
1
0
1
1
0
2
2
3
2
0
1
0
1
2
0
1
0
1
0
2
1
0
1
1
1
1
2
1
1
0
1
0
1
0
1
0
0
1
0
1
2
2
0
1
0
1
1
0
0
1
1
0
1
0
0
1
0
2
0
2
2
1
0
1
0
2
2
0
0
1
1
0
2
2
2
1
2
1
0
0
0
1
1
2
1
1
2
1
2
2
1
2
1
0
1
0
1
0
1
1
2
1
2
1
0
0
0
1
1
2
0
0
2
2
1
2
2
2
1
1
0
0
2
3
2
1
0
1
0
0
2
0
0
2
1
1
2
2
1
1
2
5
1
1
1
1
1
0
1
1
1
1
1
0
1
1
1
1
1
1
1
3
1
1
2
0
1
2
0
2
2
2
0
0
0
4
0
1
1
2
0
1
1
1
1
1
0
1
1
0
0
1
0
1
0
1
1
0
1
3
2
1
0
2
0
1
1
1
1
0
0
1
1
1
2
1
0
2
0
1
1
0
0
2
1
1
1
2
2
2
1
2
1
2
1
0
1
2
0
1
0
1
0
2
0
1
1
1
2
0
1
1
1
0
2
1
0
2
1
0
0
1
1
1
1
1
0
1
1
2
0
1
1
2
2
2
0
0
1
2
0
2
1
2
1
1
1
1
1
1
1
0
0
2
0
1
1
0
1
2
1
0
1
2
1
1
0
1
2
2
0
0
1
0
1
0
1
0
1
1
0
0
2
0
2
0
1
0
1
1
1
1
1
1
2
1
2
1
1
0
2
0
1
1
1
1
1
2
2
2
2
1
3
1
1
0
1
1
0
1
2
0
2
1
1
2
1
2
1
1
1
0
0
2
0
2
0
0
0
2
0
2
2
0
2
1
0
0
1
1
1
1
0
1
2
1
1
0
2
1
1
1
0
1
2
1
1
1
0
1
0
1
1
0
1
2
2
2
1
0
1
0
1
3
1
1
1
0
2
2
1
1
1
2
1
1
2
1
1
0
0
1
2
1
1
3
1
1
0
0
1
0
1
0
2
0
2
1
2
0
1
0
1
2
1
0
1
1
2
1
0
1
0
1
1
1
0
1
2
0
1
0
0
2
1
1
1
2
1
1
0
0
1
2
2
0
1
1
2
1
0
0
2
1
1
0
0
1
1
1
2
1
0
0
1
0
2
1
1
0
1
1
2
1
1
1
1
1
1
1
1
2
0
1
0
1
0
0
0
0
1
1
1
2
0
1
1
0
3
1
1
1
1
2
1
2
1
0
1
0
1
1
2
2
0
0
1
1
1
1
0
1
1
1
2
1
1
0
1
2
1
2
1
2
1
1
1
1
0
2
0
2
0
1
1
0
2
2
1
0
1
2
1
0
0
0
0
1
0
2
2
1
0
0
0
1
2
1
0
1
1
1
1
0
1
2
1
1
1
1
1
1
1
2
1
0
2
1
1
0
1
1
1
1
1
0
0
1
3
1
0
1
1
1
2
0
2
2
0
1
0
2
1
0
1
1
1
2
1
1
0
1
0
1
2
1
0
1
1
2
1
0
1
1
2
0
0
1
1
0
1
0
2
2
0
1
0
0
0
2
0
2
0
0
2
2
2
2
1
1
2
0
2
0
0
2
0
1
0
1
1
1
0
1
1
2
1
1
0
0
1
0
2
2
1
1
0
0
2
2
1
1
0
2
0
0
1
1
0
1
1
0
2
2
0
1
0
1
2
1
1
1
1
2
1
1
0
1
1
1
2
2
2
1
2
0
2
2
0
2
0
1
1
1
3
2
0
1
1
0
1
1
0
1
1
2
2
1
1
1
2
1
1
1
2
2
1
1
0
2
0
1
1
2
0
1
1
0
0
0
1
3
1
1
2
2
2
1
2
1
2
0
1
0
0
0
0
2
0
1
1
0
1
2
1
0
1
1
1
1
2
1
0
2
0
0
1
2
0
0
1
0
1
2
1
0
2
1
2
1
2
2
1
1
0
0
1
1
0
0
2
1
0
1
1
1
2
2
1
2
0
0
1
3
1
1
2
0
1
1
0
1
1
2
1
0
1
2
1
2
2
0
2
0
0
1
1
1
1
1
2
1
2
1
1
1
1
3
0
0
1
1
2
0
2
1
2
0
1
2
0
1
1
0
1
2
0
1
0
2
2
0
1
1
0
1
1
1
1
2
1
1
1
2
0
1
1
1
1
1
1
1
1
1
0
1
1
0
0
0
0
2
1
2
2
1
1
1
1
0
1
4
0
2
1
0
0
1
1
1
2
2
2
0
1
1
0
0
1
0
0
1
0
0
0
2
1
1
2
1
1
1
0
0
0
2
2
1
1
1
1
0
1
1
0
2
1
0
0
1
1
1
1
2
2
0
2
0
2
2
1
0
0
0
1
2
1
2
2
2
1
2
1
0
0
1
0
2
1
1
1
1
1
1
2
0
1
0
1
2
2
1
2
0
1
2
1
2
0
1
1
1
1
1
0
1
1
1
2
2
1
1
1
1
1
2
0
1
1
1
0
0
1
0
1
1
0
0
2
0
0
2
2
2
1
0
1
1
2
2
1
1
0
1
1
1
0
2
1
1
1
0
1
1
1
0
1
0
2
1
1
0
1
1
1
1
0
1
0
1
1
1
1
1
0
1
1
1
1
1
1
1
0
1
1
0
0
0
0
1
2
1
2
3
0
1
1
2
0
2
2
1
2
1
1
0
0
1
1
1
2
2
2
0
1
1
1
0
3
1
2
0
1
1
2
1
0
0
0
1
2
2
0
1
1
1
0
1
1
1
0
1
1
0
0
1
1
0
1
0
0
0
0
0
2
0
0
1
1
0
1
0
1
2
1
2
0
0
0
1
1
1
0
0
2
2
0
0
1
1
1
2
0
1
0
0
1
1
0
1
0
0
1
1
0
0
1
0
0
0
0
1
0
0
2
1
1
2
1
1
3
0
1
1
1
2
1
1
1
0
0
1
0
1
1
2
2
3
1
0
0
1
2
1
0
0
1
0
0
1
1
1
2
1
0
1
0
1
2
2
2
2
2
2
0
0
1
1
1
1
2
1
2
0
0
0
2
1
0
2
0
0
2
0
2
0
0
1
0
1
2
0
2
0
1
1
2
1
1
0
2
1
1
1
1
1
2
1
1
1
0
2
1
2
1
1
2
1
1
1
1
1
1
1
0
2
1
1
2
1
1
1
1
1
1
2
0
1
1
1
0
2
0
1
1
0
2
1
0
1
0
0
0
0
2
0
1
2
1
1
2
2
2
1
1
0
1
1
0
1
1
2
2
0
1
2
1
2
1
1
1
1
1
0
0
0
1
1
1
1
1
1
1
0
2
1
2
1
1
1
0
1
0
1
2
3
0
2
1
2
0
1
1
0
2
1
0
1
1
1
1
1
1
2
2
1
0
2
1
2
1
2
2
1
0
1
0
1
0
0
1
0
1
2
2
1
0
1
1
1
0
1
0
1
2
1
1
1
0
0
1
1
1
1
2
1
0
1
2
2
1
1
2
0
0
1
0
1
0
1
1
1
1
1
0
1
0
2
2
0
1
0
4
1
2
0
1
0
0
0
0
1
1
1
1
0
1
1
1
2
2
2
0
1
1
1
1
2
2
1
1
0
1
0
1
2
1
0
1
1
1
0
0
2
0
2
2
0
1
1
0
1
1
2
1
1
1
0
0
0
0
1
1
2
1
2
1
0
0
2
2
0
1
1
0
2
0
1
1
1
0
1
1
2
0
1
2
1
1
1
1
1
2
1
1
1
0
1
1
2
1
1
2
0
2
0
0
1
0
0
2
1
1
1
0
1
1
0
2
0
2
2
2
1
1
1
2
1
1
1
1
2
1
0
0
1
1
2
1
2
1
2
0
1
0
1
1
2
1
2
2
0
0
2
2
1
0
2
0
2
1
0
2
2
2
2
1
0
0
1
0
0
0
1
0
0
2
2
2
0
0
2
1
0
1
3
1
2
2
0
1
2
0
1
1
3
1
1
2
0
1
0
0
1
1
1
2
1
0
1
2
1
2
1
1
1
0
1
1
1
1
1
1
0
1
0
1
1
0
1
1
1
1
0
1
1
1
1
1
1
1
0
1
0
1
2
2
0
0
1
2
1
1
2
1
2
0
0
2
2
0
1
1
2
2
1
2
1
2
1
1
0
1
1
1
2
0
2
1
1
1
0
2
1
1
1
0
2
1
2
0
1
0
1
0
1
1
1
1
0
3
1
0
1
1
1
1
2
1
2
1
0
0
1
1
1
1
0
2
0
1
1
0
1
1
0
0
1
2
1
1
2
2
1
1
2
0
2
1
1
2
1
2
1
1
2
1
1
1
1
1
2
1
1
0
1
1
1
0
1
4
1
1
1
1
1
0
1
1
2
0
2
1
2
0
0
2
1
1
1
0
2
2
2
1
1
1
2
2
0
2
2
1
1
1
1
0
0
2
3
1
1
1
1
1
0
1
1
1
2
2
0
1
0
0
2
0
4
0
1
1
1
1
2
0
1
2
2
0
2
2
2
1
1
1
0
0
1
2
2
0
0
1
0
0
2
1
0
1
1
2
2
1
1
0
0
0
1
0
0
1
1
0
2
2
1
1
1
2
1
2
1
0
1
1
1
0
0
1
2
0
0
1
2
2
1
0
1
0
2
1
0
0
1
0
2
1
1
1
0
1
1
2
1
0
1
0
0
1
1
1
0
1
2
1
1
1
1
1
0
1
1
1
1
0
1
1
1
2
1
0
1
1
0
0
1
1
0
2
1
1
0
2
3
0
0
2
0
0
1
0
1
2
0
1
1
0
2
1
1
1
0
0
2
2
2
0
1
1
0
3
0
1
1
2
2
0
4
2
1
1
1
2
1
1
2
1
1
1
1
0
0
1
0
5
1
0
0
0
1
1
2
2
1
2
0
0
0
2
1
1
2
1
1
1
2
1
1
1
1
2
0
1
1
0
1
1
0
0
1
0
1
0
1
1
2
2
0
0
1
0
1
2
0
0
0
0
1
1
0
1
2
2
0
0
0
1
2
1
1
1
1
1
0
1
2
0
1
1
1
0
1
1
1
1
1
1
0
1
0
1
0
2
1
0
0
1
1
1
1
2
2
1
0
1
1
0
0
2
1
2
0
1
1
1
0
1
0
1
1
2
0
0
1
2
0
1
2
1
2
0
1
2
0
1
1
0
1
1
1
1
0
1
2
2
1
0
2
1
2
2
0
1
1
1
1
1
2
0
1
2
2
0
2
1
2
1
1
0
0
1
2
1
1
1
1
0
2
1
1
1
1
1
0
1
2
1
1
0
0
2
0
1
0
2
1
0
2
2
0
1
0
1
2
2
1
0
1
1
1
1
2
0
2
2
1
2
1
2
0
1
3
0
0
0
2
2
1
2
1
1
1
1
0
1
1
1
1
1
2
1
1
1
1
0
1
0
0
2
2
0
1
1
2
1
1
1
1
2
1
2
2
0
2
2
0
0
1
1
1
2
1
1
1
2
0
1
1
2
1
1
2
1
1
1
2
2
1
0
2
2
0
1
1
1
1
1
1
1
2
0
1
1
1
0
0
0
0
0
2
0
1
1
0
1
1
1
1
2
1
2
0
0
1
3
0
1
0
1
0
1
0
1
0
2
1
2
2
0
2
1
0
1
1
1
0
0
1
2
1
1
0
0
2
1
0
1
1
1
1
0
0
1
0
1
2
0
1
2
0
0
1
1
1
2
0
1
1
0
1
0
1
1
1
0
1
2
0
1
1
1
1
1
1
2
1
2
1
3
1
0
0
1
1
0
0
1
2
1
1
1
2
1
1
2
2
0
1
1
1
0
1
0
0
1
1
2
2
1
0
1
0
1
1
1
0
1
1
2
2
0
1
0
0
0
1
0
2
2
1
0
1
1
1
1
1
1
0
0
1
2
2
1
2
1
1
2
2
1
2
1
0
1
1
2
2
0
1
0
2
0
0
1
1
1
2
1
1
0
0
2
2
0
0
0
0
1
2
1
0
2
1
1
1
0
0
0
0
2
0
1
0
1
2
0
2
1
1
0
1
1
1
2
1
1
1
1
2
1
1
0
1
1
1
1
0
0
1
0
0
1
0
0
1
1
1
1
1
0
2
1
0
1
2
0
1
0
1
0
0
1
0
2
1
1
1
0
2
0
1
1
2
1
1
1
2
0
1
1
0
0
0
1
2
1
2
0
0
0
1
2
2
1
1
2
1
1
0
2
0
1
1
1
1
1
0
0
1
1
0
1
2
1
1
2
0
1
0
0
2
0
2
3
1
0
1
0
1
2
0
2
1
1
1
1
2
1
0
0
1
0
1
0
2
1
0
3
0
1
0
1
1
0
1
1
7
0
0
0
2
1
1
1
1
0
1
1
2
2
1
1
2
0
2
1
1
1
1
1
1
1
1
1
3
1
1
0
1
2
1
0
1
0
0
2
1
2
1
1
1
1
1
0
1
1
0
1
2
2
1
0
1
1
0
0
0
0
1
1
1
1
1
1
1
0
0
2
1
1
1
2
0
1
2
0
2
1
2
0
0
0
1
0
1
1
2
1
2
3
0
0
1
0
1
1
1
2
1
1
1
0
1
1
2
1
1
1
2
1
2
2
0
1
1
1
1
1
1
1
1
1
0
2
1
1
1
1
2
0
2
0
2
1
0
0
2
1
0
0
1
1
1
2
1
1
0
2
2
1
0
1
1
1
2
2
1
1
1
1
0
2
0
1
1
2
0
1
0
2
1
1
1
2
2
0
2
1
1
0
1
1
0
2
1
1
1
2
1
0
1
1
1
1
0
1
2
1
0
1
0
1
2
1
1
2
1
1
0
1
1
1
1
0
1
1
1
2
2
1
0
1
2
0
0
1
1
0
1
1
1
2
1
1
1
1
0
1
2
1
1
1
2
1
1
0
1
2
1
2
2
2
0
1
1
1
1
2
1
2
1
1
1
1
0
1
1
1
1
0
0
1
1
1
0
2
0
2
0
0
1
0
2
2
1
2
0
0
1
2
2
2
1
1
2
0
1
1
1
1
1
0
1
1
4
1
0
1
1
0
2
1
1
2
1
2
1
0
0
0
2
0
0
0
0
2
1
2
1
2
1
0
2
1
0
0
1
1
2
1
2
2
2
2
0
1
2
0
1
1
0
1
0
1
1
1
1
0
0
1
1
1
2
1
0
0
0
0
0
1
2
1
1
1
2
0
0
0
2
1
0
0
1
0
1
1
2
1
2
1
2
0
0
1
1
1
1
1
0
1
1
5
2
2
0
2
2
2
0
0
2
1
0
1
3
2
0
1
1
1
1
1
2
0
1
2
1
2
1
1
1
1
1
0
1
2
2
1
0
1
2
0
0
2
1
1
1
1
1
0
1
2
1
1
1
0
0
1
1
1
1
2
0
1
0
0
0
0
1
2
2
2
1
1
1
3
0
1
2
2
0
2
0
0
1
1
0
0
1
2
2
1
1
1
1
2
5
1
2
1
1
0
2
0
1
2
0
1
1
1
0
0
0
1
0
1
1
0
1
1
1
1
0
1
0
0
1
1
1
1
1
2
0
2
2
0
1
1
1
2
0
0
1
1
2
1
1
1
1
0
1
1
1
1
1
2
0
1
2
1
2
1
0
1
1
2
2
1
1
1
0
2
0
1
3
1
0
2
1
1
2
1
0
0
1
0
1
0
2
1
0
1
0
1
2
0
1
1
2
1
2
0
1
1
1
2
1
0
0
1
1
2
2
0
0
0
1
1
2
1
1
0
1
1
2
1
0
1
0
1
1
1
1
2
1
1
0
2
1
1
1
0
0
1
1
2
1
1
1
2
1
2
1
1
1
1
0
2
2
1
1
1
0
0
1
1
1
1
1
0
0
2
2
2
1
1
2
1
0
2
1
0
1
1
1
1
1
1
2
1
2
0
1
1
1
2
0
1
1
1
0
1
1
2
1
2
1
1
0
1
1
2
1
0
2
1
2
1
2
1
1
2
2
2
2
1
2
0
3
2
0
2
1
2
1
1
1
0
1
2
2
0
1
2
0
1
0
1
1
1
0
1
1
0
0
0
1
1
1
1
1
0
2
3
1
1
1
2
0
1
1
1
1
2
0
2
1
2
1
1
2
2
1
1
0
2
1
2
1
0
1
1
1
2
2
1
0
0
1
1
1
1
1
1
1
1
1
1
2
1
2
1
0
1
2
1
0
0
1
0
0
1
1
0
1
1
1
1
0
2
0
1
0
1
1
2
1
1
2
0
2
1
0
0
2
0
1
4
2
1
1
2
0
0
2
2
2
2
0
1
2
2
0
1
1
0
1
0
1
1
2
2
0
1
1
0
2
2
0
1
1
1
1
1
1
4
0
1
0
0
1
2
0
2
2
1
1
0
0
1
1
1
1
1
0
2
1
0
0
0
2
0
1
2
0
0
1
1
2
2
0
1
1
0
1
2
2
2
0
2
1
1
1
1
0
2
0
1
1
1
1
1
0
1
1
1
0
1
2
0
1
1
0
1
1
2
0
1
0
2
1
1
0
2
1
1
1
2
1
1
1
2
2
0
0
1
0
0
1
0
1
2
1
2
0
0
1
0
0
2
0
1
3
0
1
2
1
1
2
1
1
1
1
1
1
0
1
1
1
1
1
0
0
1
1
1
1
1
2
0
0
0
0
1
1
0
1
0
1
1
1
0
2
1
0
2
1
2
2
1
0
0
0
2
1
3
1
1
1
1
0
1
0
0
2
0
1
1
0
1
0
1
0
1
1
1
1
0
1
1
1
1
1
1
0
1
0
1
1
0
2
0
2
1
1
0
1
0
0
2
1
2
1
0
0
0
0
0
1
1
2
1
1
2
1
0
1
0
2
2
0
3
1
1
1
1
1
1
1
2
1
1
1
1
0
1
2
1
1
0
1
1
1
1
2
0
1
0
0
0
0
2
0
2
2
1
1
1
0
1
0
1
1
2
1
0
1
2
1
1
0
1
1
1
0
1
1
1
1
1
1
1
2
1
2
1
0
0
1
2
0
0
1
1
0
2
2
2
1
2
1
1
2
0
0
2
0
1
0
2
1
0
1
1
1
1
2
1
2
1
0
1
0
2
0
0
2
1
2
0
1
0
1
1
1
1
0
0
2
0
0
1
1
1
1
0
1
2
1
0
0
1
1
0
0
1
1
1
0
1
2
1
1
0
1
1
1
2
0
2
1
1
0
0
1
1
0
1
2
2
1
1
1
1
2
2
1
1
1
0
1
1
1
0
0
1
2
2
1
1
1
2
3
1
1
1
2
1
1
2
1
1
0
1
1
1
1
1
1
2
2
1
1
1
0
0
2
1
1
2
0
1
1
0
2
1
2
1
0
1
2
1
0
2
1
0
2
0
2
0
2
1
1
2
1
0
1
0
0
0
1
1
1
2
0
1
2
2
1
2
0
2
2
1
1
0
1
1
3
0
0
0
0
1
2
1
1
2
2
1
0
1
0
0
1
2
0
1
1
0
1
0
2
1
1
0
1
1
1
1
0
2
1
1
1
1
1
1
1
1
1
2
1
2
2
0
0
2
1
0
2
1
1
2
2
2
1
1
0
1
0
0
1
1
1
1
2
2
1
0
3
3
0
1
1
2
1
0
0
0
1
2
1
0
0
1
0
1
1
1
2
1
1
2
2
2
1
1
1
2
2
2
1
2
1
2
0
2
2
1
1
1
2
1
1
1
0
2
1
1
2
2
0
2
1
0
1
1
0
1
0
2
1
0
1
1
1
3
1
0
2
1
1
0
1
0
2
0
1
0
1
1
2
0
1
1
1
2
2
1
2
1
1
1
0
0
2
0
0
1
0
1
1
0
0
2
2
1
0
1
1
1
0
0
0
2
1
2
1
0
1
0
1
1
1
1
1
1
1
0
0
1
0
0
1
0
1
1
1
1
1
1
1
1
1
1
1
0
2
1
1
1
2
1
1
1
1
0
1
2
1
1
1
0
2
1
2
2
2
0
2
0
0
2
1
0
1
1
0
1
1
1
2
0
4
1
1
1
1
1
0
0
0
0
1
2
0
1
1
1
0
2
0
2
1
1
1
2
1
0
1
1
0
0
1
1
1
0
0
1
1
0
2
1
1
1
1
1
0
1
2
2
3
1
0
0
0
0
2
1
1
1
1
1
0
1
1
1
0
1
1
0
1
0
0
3
1
0
1
2
0
1
2
1
1
1
1
2
1
1
0
1
0
2
2
2
1
1
1
2
1
1
1
3
1
1
0
1
0
2
0
1
0
1
1
2
1
1
1
0
1
1
1
0
1
1
1
2
1
1
2
2
0
0
1
1
0
1
2
2
1
1
1
2
2
2
2
1
0
1
1
2
2
0
1
2
1
2
0
2
1
2
1
0
0
0
0
0
0
2
1
1
0
1
1
1
1
0
1
1
1
0
1
0
2
1
1
1
0
0
0
2
1
1
2
1
3
1
0
0
0
1
4
2
0
1
0
1
1
2
1
1
0
2
0
0
3
2
0
0
2
1
0
1
1
1
1
1
2
1
0
1
2
0
2
1
1
1
0
1
1
0
2
1
2
1
2
1
0
2
1
1
1
2
2
0
0
1
1
1
1
1
2
2
1
1
1
2
2
4
0
0
2
1
2
0
2
2
0
0
0
0
1
0
0
0
1
0
1
1
1
2
1
1
1
2
0
1
0
2
1
0
2
1
0
0
2
1
0
0
1
0
2
1
1
1
1
0
0
1
2
1
1
2
1
2
0
1
2
2
2
2
1
0
2
1
1
1
1
1
3
1
0
0
1
1
2
0
2
2
1
1
0
2
0
0
1
1
1
1
0
0
1
0
1
1
1
1
1
3
1
0
0
1
1
2
1
0
1
1
2
1
0
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
0
1
2
1
0
1
4
1
1
0
0
1
1
1
2
2
1
0
1
2
1
1
1
2
1
2
0
0
1
1
0
1
1
1
2
1
1
2
0
2
2
1
1
0
0
1
1
1
1
0
1
0
0
3
1
2
1
1
1
1
2
2
1
2
1
0
0
0
1
0
1
0
1
0
0
0
0
1
1
0
1
0
0
1
1
1
0
0
2
2
1
0
1
1
2
1
2
1
2
1
1
0
1
2
1
1
0
1
2
0
1
3
1
2
1
1
1
2
2
0
1
1
0
0
2
1
1
2
0
2
1
1
2
1
1
0
1
2
1
1
2
0
1
0
2
1
0
1
2
2
2
1
0
1
0
1
1
0
1
2
1
1
2
2
2
0
0
1
0
1
0
1
2
1
1
0
2
1
1
0
2
2
1
0
1
1
0
2
1
2
1
1
0
1
1
1
0
1
1
1
3
2
1
1
1
1
3
0
1
2
1
1
1
1
1
0
2
0
0
1
1
0
1
1
2
2
0
1
2
1
0
1
1
0
0
2
1
0
0
1
0
1
0
0
2
1
0
1
0
0
1
0
0
2
1
1
1
0
1
1
1
1
2
2
0
1
0
0
1
1
0
0
0
2
0
2
1
2
1
1
1
1
1
0
2
1
2
1
2
1
1
1
2
1
0
0
1
1
2
1
1
0
0
1
2
0
1
1
1
0
2
1
1
0
1
1
1
1
1
1
1
1
1
0
1
0
2
0
0
0
1
1
0
1
0
0
1
1
2
1
1
0
2
1
1
2
0
1
1
1
0
2
2
0
1
1
0
2
1
1
0
2
1
1
2
0
1
2
1
1
1
1
1
0
1
1
2
1
2
3
1
0
1
0
0
2
0
2
2
1
1
1
0
2
1
1
1
1
0
2
0
0
1
0
0
0
2
2
1
2
1
1
1
1
1
0
0
2
1
0
2
3
0
1
2
0
2
1
1
0
1
1
1
1
0
1
0
2
1
1
0
0
1
1
1
1
0
2
2
2
1
1
0
2
0
1
0
1
1
1
0
1
1
0
1
1
0
0
1
2
2
1
1
0
1
2
1
1
2
2
1
1
2
1
1
1
0
0
2
0
0
0
1
0
1
0
1
2
1
2
2
2
1
1
0
1
2
2
1
1
1
2
1
0
2
0
0
1
1
0
1
1
2
1
1
0
2
0
1
1
0
1
1
1
1
1
0
2
2
0
1
0
1
2
0
1
0
1
1
1
1
1
2
0
1
1
1
2
2
1
2
1
1
1
1
0
1
2
0
1
1
2
1
1
2
1
0
1
1
0
0
1
0
1
1
1
2
0
2
1
1
0
0
0
2
2
0
1
1
3
0
0
2
1
1
1
1
0
2
0
1
2
1
1
0
0
1
1
1
2
1
1
2
1
2
2
1
1
2
1
1
0
1
1
1
1
0
1
0
2
1
0
0
0
1
2
1
1
1
1
1
2
0
1
1
2
0
0
1
0
2
1
1
2
2
1
2
1
0
0
2
1
1
0
0
1
1
2
2
0
0
1
2
0
1
0
1
1
2
2
1
0
1
1
0
0
0
1
1
0
0
1
2
0
1
1
0
1
1
2
0
0
0
1
2
1
1
1
1
2
0
2
1
0
0
1
1
1
0
1
1
1
0
1
2
1
0
0
0
2
2
2
1
0
1
2
0
0
0
0
1
1
0
1
0
0
1
1
2
0
1
0
0
0
0
0
0
0
4
0
2
0
2
1
1
1
1
1
0
1
2
1
1
0
2
1
0
2
0
0
1
2
1
2
1
1
1
2
0
0
0
1
3
1
0
0
2
0
0
0
0
1
2
0
1
1
1
0
1
0
1
0
0
0
1
2
1
1
2
2
1
1
2
1
2
0
1
2
1
1
2
1
1
1
2
0
2
1
0
1
2
0
1
1
0
2
1
1
1
1
1
0
1
3
0
1
0
0
0
1
0
1
2
0
1
0
1
0
0
1
1
0
1
1
2
1
1
1
0
0
1
0
0
0
1
0
1
1
0
1
0
2
1
1
1
0
1
1
1
2
1
0
1
0
0
1
2
0
2
1
0
1
1
1
1
0
1
1
1
2
1
0
1
0
2
0
1
2
0
1
1
0
0
1
2
1
1
1
2
2
0
1
2
1
1
0
0
1
0
1
2
2
1
1
1
2
1
1
1
0
2
0
2
3
1
0
1
0
2
2
1
1
1
1
1
2
1
0
2
1
4
1
3
2
2
2
0
1
1
2
1
2
2
0
1
1
1
2
2
1
2
0
1
1
1
2
0
2
1
1
1
1
1
1
1
2
0
1
2
2
1
0
1
2
2
0
1
1
1
0
1
1
1
2
2
1
1
1
1
1
1
1
0
1
0
2
1
1
2
1
1
1
0
1
0
2
0
2
1
2
0
1
2
0
0
1
2
2
0
2
1
2
0
1
2
4
1
2
1
1
1
2
1
1
1
2
1
1
2
1
1
2
1
0
1
2
2
1
1
1
1
0
1
1
2
0
1
0
1
2
0
1
0
1
1
0
0
0
1
1
1
1
0
1
1
2
0
1
2
1
2
2
0
0
2
0
0
2
1
1
2
2
1
2
2
0
1
1
1
1
2
1
1
2
0
2
2
1
1
1
1
0
1
2
0
0
0
1
2
2
1
1
1
1
1
1
0
1
2
1
3
0
1
2
1
2
0
1
2
3
2
0
1
1
1
2
0
0
1
0
0
0
2
0
1
1
1
1
2
0
1
1
1
1
0
0
1
0
1
0
0
1
1
0
1
1
1
1
1
1
0
1
1
2
1
0
2
1
0
1
1
0
1
1
2
2
1
0
1
0
0
1
2
1
2
1
1
1
1
1
0
1
0
2
0
1
1
1
1
1
0
1
1
0
2
1
0
0
1
0
0
1
0
0
2
0
1
1
1
1
2
1
2
1
1
1
1
2
0
1
0
2
0
1
1
0
1
1
1
2
2
1
1
1
1
1
1
1
1
1
2
1
1
1
2
0
1
0
0
1
0
1
1
2
2
1
1
1
1
1
0
1
2
1
0
0
2
1
1
2
1
1
2
2
1
0
1
0
1
1
2
0
1
1
1
1
0
0
1
0
1
0
2
1
1
0
1
2
0
1
2
0
2
0
0
1
1
1
1
0
1
1
1
1
1
0
3
1
0
0
1
1
2
1
1
1
0
2
2
0
0
1
0
0
0
1
1
0
0
1
0
1
0
0
1
2
1
1
1
1
0
0
0
2
1
0
0
1
2
0
0
1
1
0
1
1
1
1
0
2
1
2
0
1
0
1
2
0
1
3
1
1
1
2
1
1
1
0
0
0
1
1
2
1
0
0
0
1
0
1
2
1
1
1
0
2
2
0
0
0
2
0
0
2
0
1
0
1
2
1
1
1
2
2
0
0
0
1
2
0
0
2
0
2
1
0
0
0
2
1
0
1
1
0
1
1
4
0
0
1
2
1
1
2
1
1
0
1
0
2
0
1
1
0
2
1
0
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
0
2
1
1
1
0
1
1
1
1
1
0
0
1
1
1
2
0
0
1
0
0
0
1
1
1
2
1
2
2
1
1
1
0
0
1
0
1
0
1
0
1
2
0
1
2
2
0
1
1
1
0
0
1
1
1
2
0
1
2
2
1
1
1
2
1
2
1
0
2
1
1
2
0
0
2
0
1
1
1
0
2
1
2
2
0
2
2
1
0
1
1
0
2
1
0
2
1
0
2
2
1
0
1
2
0
0
1
1
2
1
2
0
2
2
1
1
0
1
1
0
1
0
0
0
1
2
2
2
0
1
2
2
0
0
1
1
0
0
1
2
0
1
2
1
1
1
1
0
0
2
2
1
0
1
2
0
1
1
1
1
0
0
2
0
1
2
1
2
0
2
0
1
0
1
2
0
1
1
1
1
1
1
0
1
1
1
0
2
1
0
1
1
1
2
2
0
1
1
2
1
0
0
1
2
3
0
0
1
1
1
1
1
1
0
2
1
0
0
1
0
1
0
2
1
0
1
1
1
1
4
0
0
2
1
1
2
1
1
0
1
0
3
2
1
0
0
0
1
1
1
0
1
2
1
0
2
1
1
1
1
1
0
1
1
1
0
2
0
2
2
0
1
0
1
4
1
1
0
1
0
1
1
2
3
2
1
1
2
1
1
0
2
0
0
1
1
0
2
2
2
2
1
1
1
2
2
2
1
0
1
1
0
2
0
2
1
2
1
1
0
2
1
0
1
2
1
0
2
1
1
0
0
1
1
1
1
2
1
0
2
2
1
1
0
2
2
2
2
2
1
0
1
1
1
0
2
2
1
1
1
1
1
0
2
1
1
2
1
0
1
1
0
0
0
3
2
3
1
1
1
0
1
1
1
0
3
2
0
0
1
1
0
2
0
1
1
1
2
1
2
1
0
0
1
3
1
0
0
0
1
0
1
0
2
1
1
2
2
2
0
1
1
1
0
1
1
1
1
0
2
1
1
2
0
0
2
2
0
1
0
0
2
1
2
2
1
2
1
1
1
1
1
3
0
1
2
0
1
2
2
1
1
1
0
2
1
2
3
0
1
1
2
0
0
0
0
1
2
1
1
2
0
0
0
0
2
1
1
0
2
1
1
0
1
1
2
0
0
0
0
2
1
1
1
1
0
0
0
0
1
0
1
1
1
1
2
1
1
2
2
0
0
1
1
1
2
1
1
1
1
1
2
0
1
1
1
2
1
1
1
2
1
0
3
2
1
1
0
1
0
1
1
2
1
2
0
2
0
2
0
0
1
1
0
1
0
1
2
0
1
1
1
1
2
1
0
1
2
1
0
2
1
1
0
2
0
2
2
0
0
1
1
1
0
0
1
1
0
2
1
2
2
1
1
1
2
1
0
1
0
0
0
0
1
1
1
1
2
0
2
1
1
0
2
1
0
2
1
0
1
1
1
1
0
2
0
0
1
1
1
1
1
1
2
1
1
1
0
1
1
1
1
2
0
1
2
0
0
1
2
1
1
0
0
1
1
0
0
1
1
1
0
1
0
1
0
1
1
0
1
1
1
2
1
1
2
0
1
2
2
1
1
1
2
2
2
1
1
1
1
1
1
2
1
1
1
1
0
2
0
1
1
1
1
1
0
1
0
2
2
2
0
1
1
1
1
0
1
2
1
0
1
1
1
1
1
1
0
1
1
1
1
1
1
2
1
1
0
2
1
0
0
0
1
0
0
1
1
2
1
2
0
1
1
1
1
0
1
1
0
2
2
0
2
1
1
0
0
1
2
0
2
1
1
1
0
1
0
1
0
1
2
2
1
0
2
1
0
2
0
2
0
1
1
0
0
1
1
1
1
0
1
2
2
1
1
1
0
1
0
2
2
1
1
1
1
1
1
1
2
0
2
2
2
2
0
2
1
2
1
1
1
0
2
1
1
2
2
1
0
2
0
1
1
0
1
1
0
1
1
1
1
2
1
2
0
2
1
0
0
1
0
0
1
0
1
0
1
0
2
0
1
1
0
1
2
2
1
2
1
0
1
4
2
1
1
1
1
1
2
2
0
0
0
1
1
1
1
1
0
1
0
2
2
1
2
1
1
0
2
0
1
0
0
1
1
1
2
1
1
0
1
1
1
2
2
1
1
0
1
2
2
2
2
1
1
0
2
1
0
1
1
0
0
2
0
0
2
2
1
1
1
1
1
1
2
1
1
2
1
0
0
0
1
1
1
1
4
0
1
1
2
0
1
1
0
0
1
0
1
0
1
2
1
1
2
1
1
0
1
0
1
1
1
2
1
1
0
0
2
1
1
1
2
1
4
1
1
1
0
2
0
2
0
0
2
1
2
1
1
2
0
0
1
2
1
0
0
0
1
1
1
1
2
3
2
1
2
2
1
0
2
1
2
0
2
1
1
0
0
1
1
0
1
2
1
1
0
2
0
2
0
2
0
1
0
1
2
0
1
1
0
2
0
2
2
1
1
2
1
0
0
1
1
3
1
1
3
0
0
2
2
1
2
1
1
0
1
1
0
0
2
0
1
0
1
0
1
0
1
0
1
1
0
2
1
0
0
0
1
2
0
0
1
0
1
1
2
0
2
2
0
1
1
0
1
2
2
0
0
1
0
1
2
0
1
0
1
1
0
2
1
1
1
0
1
1
2
1
2
2
2
1
0
1
1
2
1
1
1
1
0
1
1
0
0
0
2
0
0
2
2
1
0
1
1
1
0
1
1
0
2
0
1
2
2
1
1
0
0
1
0
0
2
1
1
1
1
2
2
1
2
2
0
1
1
1
1
1
2
1
1
2
1
1
2
1
0
1
0
1
1
1
1
1
1
2
1
0
1
1
1
1
1
3
2
2
0
1
0
1
1
0
2
2
1
2
0
0
2
1
1
2
1
2
1
0
0
1
2
2
2
1
1
1
1
1
2
2
1
0
0
1
1
1
1
1
1
1
1
1
1
2
1
2
1
0
0
1
1
1
0
0
2
3
1
0
2
0
1
0
1
2
0
1
5
2
0
1
1
0
0
0
0
0
1
0
2
0
0
1
1
0
1
2
0
1
2
1
1
0
2
1
0
0
0
0
0
1
0
0
0
2
1
1
0
1
0
1
2
0
0
1
1
1
0
1
1
1
1
1
1
1
1
2
0
1
2
1
0
0
1
1
3
1
2
1
0
1
1
2
3
1
1
0
0
1
1
1
1
1
2
1
1
0
0
0
1
1
2
1
2
1
1
1
1
2
1
2
1
0
0
1
1
2
1
3
1
0
1
0
1
0
2
1
0
2
2
1
0
1
2
1
1
3
1
2
1
1
1
1
1
1
3
0
0
1
1
0
1
2
1
1
2
1
2
2
0
1
0
1
2
1
0
2
1
0
1
1
0
1
1
1
2
2
1
1
1
0
1
2
1
1
1
1
2
1
1
4
1
1
2
0
3
2
0
0
1
2
1
2
2
0
2
1
1
2
1
1
0
1
2
1
1
2
2
1
2
1
0
0
1
2
1
1
1
1
1
2
0
1
1
1
1
1
2
1
2
2
0
2
0
1
2
1
1
0
0
2
1
1
0
0
1
1
1
1
0
1
1
1
1
1
0
1
2
1
2
1
1
2
1
0
0
0
1
1
0
2
1
0
1
2
1
2
1
1
2
1
0
2
2
1
1
2
1
1
1
0
2
1
1
0
1
1
0
1
0
1
0
2
0
0
1
0
0
1
1
1
1
1
2
1
1
2
1
0
1
1
1
0
1
1
1
2
0
0
2
1
1
0
2
0
2
1
1
1
1
1
2
1
1
0
1
1
1
2
2
0
0
0
1
1
1
0
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
0
0
1
1
1
1
0
2
1
1
1
1
0
1
1
2
0
1
1
1
2
0
1
2
1
1
2
1
0
2
1
2
0
1
1
0
1
0
1
1
0
1
1
0
1
0
2
1
1
0
1
0
1
1
1
1
1
2
1
0
2
1
2
0
1
1
1
1
0
1
1
1
1
1
2
1
1
2
0
1
1
1
1
2
2
2
0
2
2
1
1
0
1
2
2
1
1
0
1
3
0
2
1
1
1
1
1
0
1
1
1
0
0
0
0
1
0
0
1
0
0
0
1
0
2
1
2
0
1
1
2
1
1
0
2
0
1
1
0
2
1
1
1
1
1
1
1
1
2
1
1
1
0
1
1
1
2
2
1
1
0
1
1
2
1
0
1
2
1
1
2
1
0
0
1
1
1
1
2
0
1
2
1
3
2
2
1
0
5
0
1
1
1
0
1
0
0
3
1
0
1
1
2
0
1
1
0
0
1
1
1
2
1
0
1
1
1
1
2
2
0
1
1
1
1
2
1
1
1
0
1
0
2
1
1
0
2
2
0
2
1
1
1
1
1
1
0
2
0
0
1
0
2
0
0
1
1
1
1
0
0
1
1
1
1
1
1
0
2
1
1
1
1
0
2
2
1
1
2
1
0
1
0
2
2
2
1
1
1
2
2
1
0
0
0
2
2
1
0
1
1
1
1
1
1
1
1
0
1
2
0
2
2
1
1
1
0
0
1
0
0
1
2
1
1
1
0
0
1
0
1
1
0
1
2
1
0
1
2
1
2
1
1
1
0
1
2
0
0
0
1
1
1
1
0
1
1
0
1
2
2
0
1
0
0
1
0
1
2
1
2
1
1
0
2
1
1
1
1
1
0
0
1
0
1
4
2
1
1
1
2
0
1
1
0
2
2
1
2
1
0
1
1
0
1
2
1
1
0
0
1
0
2
0
0
1
1
0
0
1
0
0
1
1
0
0
1
1
1
1
2
1
1
0
1
1
1
0
0
3
1
0
1
2
1
1
0
0
2
2
2
1
0
1
0
1
2
1
2
0
0
2
2
1
0
2
1
1
1
0
1
2
0
1
2
1
0
0
1
1
0
0
1
1
1
2
2
2
2
1
0
1
1
1
3
1
1
1
1
1
1
0
0
0
0
0
2
1
1
2
0
1
0
1
1
1
2
2
0
1
2
1
2
1
1
1
1
0
2
2
0
1
2
1
2
2
2
2
2
2
2
1
1
0
1
1
0
1
1
1
2
0
2
1
1
0
2
1
1
1
2
2
1
1
1
2
0
1
1
1
1
2
2
1
2
2
2
1
0
1
0
0
1
0
0
2
1
0
0
1
1
0
1
1
2
1
2
1
0
0
0
0
1
1
0
0
1
0
1
1
0
0
1
0
0
1
1
1
0
0
1
1
2
1
0
0
2
2
1
0
1
1
0
1
1
1
0
2
1
1
1
1
2
1
2
0
2
0
1
1
1
2
0
2
1
1
0
1
2
1
2
1
1
1
0
0
1
1
0
2
0
1
1
1
1
1
0
1
1
0
2
3
1
0
0
2
1
2
2
1
1
1
2
3
1
0
2
2
0
1
2
1
0
0
1
0
1
1
1
0
1
0
2
1
1
0
0
1
1
1
0
1
1
1
0
1
0
1
1
0
1
1
1
0
2
1
0
3
1
1
1
3
2
0
1
0
0
0
1
1
1
1
1
1
2
1
1
1
0
0
0
1
2
0
0
0
2
1
1
0
2
2
1
0
1
1
0
1
0
1
2
1
1
1
1
0
2
2
1
0
1
1
0
1
2
2
2
0
1
1
2
1
1
1
2
1
2
1
1
0
1
0
0
1
2
2
0
1
1
1
1
1
3
0
0
0
1
0
0
1
1
2
1
2
0
1
0
1
0
2
2
1
1
3
1
0
0
2
0
0
0
0
1
0
1
2
1
0
1
1
2
0
1
1
2
2
1
1
1
2
0
0
1
2
2
2
2
2
0
1
1
0
1
2
2
0
0
0
1
1
1
0
2
2
1
1
0
1
2
1
0
1
2
2
0
1
0
1
0
1
0
0
1
1
2
3
1
1
0
1
0
1
0
1
1
0
1
0
2
0
0
0
1
2
1
1
1
1
2
0
0
1
2
2
0
1
2
1
1
1
1
2
1
2
0
0
1
0
1
1
1
1
2
1
1
1
1
1
0
1
1
6
0
1
1
1
1
1
0
2
2
0
1
1
1
0
1
1
0
1
0
0
0
0
2
2
0
0
1
0
1
1
2
1
1
1
2
1
0
0
0
1
2
2
2
0
1
1
1
0
0
2
0
1
1
1
0
3
2
2
0
1
1
0
1
2
1
1
1
0
1
2
0
2
1
1
1
1
1
0
1
1
0
1
0
1
0
1
0
0
0
0
1
1
0
1
1
0
1
1
0
1
1
0
2
1
1
2
1
3
2
1
1
1
1
0
1
0
0
1
1
1
0
0
1
0
2
1
1
1
2
1
0
0
1
1
0
0
0
0
0
2
1
0
1
2
1
1
3
1
1
1
1
1
1
3
0
0
1
0
1
2
2
0
1
3
1
1
1
0
1
2
1
1
0
1
1
0
1
1
1
1
1
1
2
0
2
0
0
1
0
2
2
1
2
1
0
2
2
1
2
0
0
2
1
2
2
1
0
2
2
0
1
2
2
2
1
1
1
1
0
1
1
0
0
0
1
0
2
0
2
1
2
1
1
2
0
2
1
1
1
2
1
2
1
1
0
2
1
0
1
1
2
0
1
1
1
0
1
1
1
3
1
0
2
1
2
0
1
1
0
0
1
1
1
0
1
1
1
0
1
1
0
1
0
0
1
0
0
1
0
1
0
1
1
1
0
2
0
0
0
1
1
1
2
1
0
1
1
1
2
1
1
1
0
1
2
0
1
1
1
1
0
1
1
0
0
1
0
0
0
1
1
0
1
0
0
1
0
1
1
1
0
1
2
0
0
1
0
2
2
2
1
1
1
0
1
0
1
1
0
0
1
1
2
0
1
0
2
1
1
1
1
2
0
3
2
2
1
1
0
1
0
1
1
1
1
0
2
0
2
2
0
1
2
1
1
1
1
1
1
1
2
2
1
1
2
0
0
0
1
0
1
2
1
0
0
1
1
1
2
2
0
1
2
1
1
0
0
0
1
2
0
1
1
2
2
2
1
2
0
0
0
2
1
1
0
1
1
1
1
1
0
1
0
0
0
1
1
0
1
1
1
0
0
0
2
0
1
2
1
1
0
2
2
2
0
1
1
0
1
1
1
0
0
0
1
1
2
0
2
1
2
2
0
0
2
1
0
1
1
1
1
2
2
1
1
1
1
0
2
2
0
2
1
1
0
0
2
0
2
2
2
2
1
0
1
0
2
0
2
1
2
1
1
0
1
0
0
1
2
1
2
1
0
1
1
1
1
1
1
2
0
1
0
1
1
1
0
1
2
2
1
1
1
1
2
1
1
1
0
1
2
1
1
0
0
2
2
0
2
1
0
0
1
1
1
1
2
2
2
0
1
1
1
1
1
0
1
1
1
1
0
2
2
0
0
1
1
1
0
2
0
0
1
1
0
0
2
2
1
1
0
1
2
1
1
1
1
1
0
1
1
2
1
0
2
1
1
1
2
0
1
1
1
1
0
0
1
2
2
1
2
0
0
1
2
1
1
1
0
1
0
1
2
1
1
1
1
0
1
1
2
1
1
0
1
1
1
1
2
1
0
1
3
1
2
2
2
0
1
2
0
1
1
0
2
1
1
1
2
2
1
1
2
0
0
2
2
1
1
0
0
1
1
1
1
1
1
1
1
0
1
1
2
1
0
1
1
0
2
1
0
2
2
1
2
1
3
1
0
1
1
2
1
1
1
1
2
1
1
1
1
1
0
1
1
1
2
1
0
1
0
0
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
0
1
0
1
0
0
1
1
2
1
1
2
0
1
1
1
2
0
0
1
0
2
2
1
1
0
1
1
2
0
1
1
1
2
1
1
1
1
1
0
2
0
1
1
1
2
1
1
2
2
0
2
1
0
1
1
1
0
0
2
2
1
1
1
0
1
2
1
2
1
1
1
0
1
2
1
1
1
0
1
1
2
1
1
2
1
1
0
1
1
1
0
2
2
1
2
1
2
0
1
1
1
1
2
2
1
1
0
1
1
0
2
1
1
0
2
1
1
1
2
2
0
2
0
2
0
1
0
1
1
0
1
1
0
1
1
1
1
2
1
1
1
1
1
0
0
2
2
1
1
0
1
1
0
1
0
2
0
2
1
2
2
1
1
2
0
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
0
2
1
1
0
0
1
2
3
1
1
2
1
1
1
2
1
1
2
0
0
0
0
1
1
0
1
0
1
2
1
1
1
0
1
0
1
1
1
1
2
0
1
1
3
0
2
3
0
1
1
1
2
2
1
1
0
0
0
2
0
1
0
5
1
2
2
1
2
2
2
1
0
2
0
2
2
1
0
1
1
0
0
1
1
1
0
1
1
6
1
2
1
1
0
2
0
0
1
1
1
2
1
0
1
0
1
1
1
0
1
1
0
1
0
1
2
1
0
1
1
2
1
1
1
1
1
0
0
1
0
0
2
1
1
1
2
1
1
0
1
1
2
1
1
0
0
1
0
0
1
2
1
1
1
1
0
1
1
2
3
1
1
1
1
1
2
1
0
0
2
2
1
1
1
0
1
0
1
0
1
0
2
1
2
0
1
0
1
0
0
1
0
1
1
2
0
1
1
1
1
0
1
2
0
1
2
1
1
0
1
1
2
2
1
1
2
1
0
0
1
0
1
1
0
1
2
0
2
1
2
1
1
0
1
2
2
1
0
1
3
0
1
0
1
1
1
0
0
1
1
0
0
2
1
2
1
1
1
0
1
0
1
1
0
1
0
0
0
0
2
0
2
2
0
2
0
0
1
0
0
0
0
0
0
0
1
1
1
1
1
2
1
1
1
1
0
0
1
1
1
1
2
1
2
1
1
0
0
1
1
1
2
2
2
2
2
1
0
2
2
1
0
0
1
1
2
0
2
2
1
2
2
0
2
1
1
0
1
1
0
2
1
1
0
1
2
1
3
1
0
1
0
1
2
2
1
0
1
1
2
1
1
1
1
1
1
1
1
1
2
1
0
1
0
0
2
1
1
2
1
0
2
1
1
2
2
1
1
2
1
1
0
2
1
1
0
0
0
1
2
2
2
0
0
2
0
1
1
1
1
1
1
2
1
0
0
0
1
2
0
1
1
2
1
2
1
2
0
2
2
0
1
0
0
1
1
1
0
1
2
1
2
1
2
1
2
0
1
2
2
0
1
1
1
0
1
1
2
4
2
0
1
1
2
1
1
3
1
1
0
0
1
1
1
0
2
1
1
2
2
3
1
2
2
1
0
2
1
3
0
1
0
0
1
1
1
2
1
0
1
0
1
2
1
1
2
1
0
0
2
0
1
2
1
1
1
1
0
2
1
0
2
1
2
1
1
2
0
1
1
2
0
1
0
1
0
1
1
2
2
0
2
1
1
2
1
0
0
1
1
1
2
1
1
1
0
2
1
1
0
0
1
0
1
2
1
1
1
0
2
1
2
0
2
2
1
1
1
2
0
2
0
0
1
1
1
1
1
1
1
0
1
0
1
1
1
0
0
1
1
1
2
0
1
2
1
2
1
0
1
1
1
1
1
0
0
1
1
1
2
1
1
0
1
1
1
0
1
1
0
0
1
2
1
2
1
0
1
1
2
1
0
3
1
1
0
0
2
1
1
1
1
2
1
1
1
0
1
1
0
1
0
1
1
2
2
0
2
1
0
1
2
0
1
0
1
1
1
1
0
1
1
0
2
0
1
0
2
1
1
0
1
0
1
2
2
2
1
1
0
2
2
0
1
1
1
0
0
2
0
0
2
1
1
1
2
0
1
2
0
0
2
1
1
0
1
2
0
1
0
2
2
0
0
0
0
1
2
1
1
1
1
1
2
0
1
2
1
0
1
1
2
1
2
0
0
2
2
1
1
0
2
1
1
1
2
1
0
0
2
1
2
2
1
1
0
1
2
3
2
1
1
1
1
1
0
0
1
0
0
0
1
1
1
0
1
0
0
1
0
1
2
0
1
1
0
1
1
0
2
1
2
1
2
1
0
2
1
1
1
0
2
1
1
1
0
1
1
2
0
2
2
1
1
0
1
1
2
2
1
0
2
1
1
1
1
0
1
0
0
2
1
2
1
2
1
0
0
1
1
0
0
0
1
1
1
2
2
1
1
1
1
1
2
1
0
1
1
1
1
0
2
1
0
1
1
1
0
0
1
2
1
1
1
1
1
1
1
0
1
1
1
1
1
0
0
2
2
0
0
2
0
1
0
2
2
1
1
2
1
2
0
2
1
2
1
0
2
1
1
1
0
2
0
1
1
1
1
1
0
1
0
2
1
0
1
2
1
1
2
1
0
1
2
1
0
0
1
1
1
0
0
2
1
1
1
0
2
0
0
2
1
1
1
0
1
0
0
1
1
1
2
0
0
3
1
1
2
2
0
1
2
0
2
1
1
2
1
1
2
0
1
1
0
1
0
2
1
1
0
1
0
1
2
1
0
1
0
0
1
1
1
0
0
2
1
1
1
2
1
2
0
1
1
1
0
1
0
1
1
1
2
2
0
1
2
2
2
1
2
1
2
0
0
1
1
2
0
2
0
0
1
0
1
0
2
2
0
0
2
2
1
2
0
3
0
0
0
0
2
0
2
2
1
0
2
1
1
1
3
1
1
2
1
2
1
3
1
1
1
3
1
1
2
0
1
1
0
0
2
0
0
0
2
0
0
2
2
1
2
0
0
2
1
1
2
2
2
0
1
2
1
0
2
1
2
0
0
1
1
1
1
0
0
1
1
1
1
1
0
2
2
1
1
1
0
1
0
0
1
1
2
1
2
2
0
0
0
1
0
1
0
1
0
1
2
1
2
0
1
0
1
0
1
1
1
1
0
3
1
0
1
0
1
2
0
1
2
0
1
1
0
1
0
2
1
1
1
0
2
0
0
1
2
1
0
1
1
0
2
1
1
0
1
0
2
2
1
1
0
1
1
2
2
0
1
0
2
0
0
0
0
0
1
1
1
0
0
2
1
1
1
1
1
1
1
0
1
2
2
2
1
2
2
2
1
1
1
0
1
0
0
0
1
1
1
1
0
1
1
0
2
1
4
2
0
0
2
1
0
1
2
1
2
0
1
1
1
2
1
1
1
1
1
0
1
2
1
0
1
1
0
1
2
0
2
1
1
2
1
1
1
1
0
1
1
1
2
1
1
2
2
1
0
0
1
0
2
1
0
1
1
0
0
1
2
1
1
1
1
1
1
1
0
1
1
0
1
1
1
2
1
0
1
1
1
0
1
0
2
1
2
0
1
1
0
0
2
1
1
2
2
0
2
0
1
1
0
1
2
1
1
0
0
1
2
0
1
1
1
1
1
1
1
1
2
0
1
1
2
0
2
1
1
1
1
0
1
1
1
2
1
2
1
0
2
1
1
1
1
0
1
3
0
1
0
1
1
1
1
2
1
1
1
1
2
1
4
2
2
1
1
2
0
0
1
2
1
0
0
0
1
0
2
0
1
2
0
0
0
2
0
1
0
0
1
1
2
1
1
2
2
1
2
1
2
1
2
2
2
1
1
0
0
2
1
0
1
1
1
1
1
0
0
1
1
2
1
0
0
1
0
1
1
2
1
0
1
2
1
1
1
1
0
0
1
0
1
0
1
1
1
1
0
2
0
0
0
2
2
1
2
0
2
1
2
1
0
1
1
0
0
1
1
0
1
1
0
1
1
1
1
2
0
1
4
1
1
0
1
1
2
1
1
0
0
2
1
2
0
1
1
0
0
1
2
1
1
2
1
1
0
2
0
0
1
2
1
0
1
1
0
0
1
2
0
0
1
1
2
1
1
2
1
1
1
1
1
2
4
0
0
2
0
1
1
0
1
0
0
1
1
1
1
1
2
2
0
1
2
0
1
2
1
0
1
1
2
1
1
1
1
0
1
0
0
2
2
1
1
1
0
1
1
0
0
0
2
1
0
2
1
2
0
0
1
1
0
2
1
1
0
1
1
1
1
2
0
1
2
2
1
0
1
2
0
0
0
2
2
2
2
3
1
2
1
1
1
1
1
0
0
1
1
1
0
0
0
0
1
0
0
2
2
0
1
1
1
2
0
0
2
0
0
1
1
1
0
1
1
2
0
0
1
1
2
1
0
1
1
2
1
1
1
1
1
1
1
0
2
2
1
1
1
2
1
1
0
2
1
0
1
0
1
1
1
0
1
1
0
0
1
0
0
1
2
2
1
1
2
2
1
0
2
1
0
2
0
1
1
0
1
2
1
1
1
0
1
0
2
1
0
1
1
0
1
2
2
1
2
1
0
1
2
0
0
0
2
1
0
0
2
1
1
2
1
2
0
2
2
2
2
2
1
0
1
2
0
1
2
1
1
1
0
2
1
0
2
1
1
1
0
0
2
0
1
2
0
1
1
1
1
1
1
0
1
2
1
1
2
1
1
0
1
3
2
1
0
1
1
1
0
1
0
1
0
1
1
0
0
1
1
2
0
0
0
1
2
1
1
1
2
2
1
0
1
1
1
1
2
2
1
2
1
2
1
0
2
2
1
1
1
2
1
2
1
1
0
2
1
1
1
0
1
1
1
2
2
1
1
1
1
1
1
0
0
2
0
1
2
2
1
0
0
1
1
1
0
1
1
2
1
1
2
2
1
2
1
1
6
0
1
2
2
1
1
2
0
1
2
1
0
1
1
1
1
2
2
1
1
1
1
0
1
1
0
0
0
1
2
0
1
0
1
2
2
0
1
1
0
0
1
1
1
1
1
2
1
1
1
1
1
1
1
1
0
1
2
1
1
1
2
0
1
2
1
0
1
1
1
1
1
2
1
3
1
0
0
1
3
1
1
2
2
1
1
2
1
1
1
2
0
1
2
1
1
0
3
0
1
2
2
1
2
1
2
1
0
1
0
1
2
2
2
2
0
0
1
0
2
1
3
1
1
1
1
1
2
1
0
0
1
1
0
1
1
1
1
1
0
1
2
1
0
1
1
1
0
0
2
0
2
2
1
2
1
1
1
1
1
1
1
1
0
2
0
0
2
1
1
1
1
0
1
1
1
0
0
2
1
2
1
1
0
2
0
2
0
1
1
1
1
0
1
1
0
1
1
1
0
0
1
1
0
1
0
1
2
0
1
2
1
2
0
1
1
1
1
3
1
1
1
1
1
1
1
0
0
1
2
0
1
0
3
2
1
0
1
1
0
1
0
3
0
2
1
1
1
2
1
1
0
1
2
0
1
2
1
1
2
0
1
0
0
1
0
1
1
2
0
1
0
1
1
1
1
1
0
2
0
1
0
2
1
1
0
0
1
0
1
0
1
1
0
0
1
0
0
0
1
2
0
2
1
0
2
1
2
2
0
2
1
2
2
2
1
1
0
1
2
0
2
0
1
1
2
1
1
1
2
2
0
1
0
0
1
1
2
1
0
0
2
0
0
2
3
1
1
1
1
1
1
0
1
1
0
1
0
2
1
1
1
0
1
1
1
0
1
3
1
0
1
1
2
2
2
2
1
0
2
1
1
2
1
1
0
1
1
1
2
3
1
0
1
1
1
1
2
1
0
1
1
0
2
0
2
1
1
1
2
0
1
3
1
1
2
1
1
1
1
1
1
2
1
1
0
1
1
0
1
2
0
1
0
1
1
2
1
2
0
1
0
1
1
0
2
1
2
0
1
3
0
2
1
1
1
1
0
1
2
1
0
2
2
1
2
1
2
1
1
1
1
0
1
1
0
2
0
1
1
1
2
0
1
0
1
0
1
1
1
1
2
1
0
2
1
2
1
1
0
0
1
2
0
1
2
0
2
1
1
2
1
2
1
1
0
2
2
1
1
0
1
0
0
2
0
0
1
1
1
0
2
1
2
1
0
1
0
0
2
0
2
1
1
0
0
1
0
0
1
1
1
0
2
0
1
0
2
2
1
3
1
2
1
0
1
1
0
1
0
0
0
0
1
2
1
0
1
1
2
1
2
2
2
0
0
1
1
1
1
0
1
0
1
1
2
0
1
1
1
1
0
0
2
1
1
1
0
1
0
1
1
0
0
1
2
2
0
0
1
2
0
1
2
2
2
0
1
1
2
1
1
0
1
1
1
2
0
2
0
1
1
2
0
2
0
1
1
0
2
0
1
1
1
1
1
2
1
2
0
0
1
1
2
0
1
0
1
2
0
0
0
2
1
2
0
0
1
0
1
1
1
0
1
1
2
0
1
0
2
1
0
1
1
2
0
1
1
0
0
0
1
2
2
3
1
2
0
0
0
1
1
2
1
1
2
1
0
1
1
1
1
1
1
0
1
1
2
0
2
1
1
1
2
1
1
1
2
1
0
1
2
1
1
1
0
3
0
2
2
3
0
1
1
2
1
1
2
0
0
0
1
0
3
0
1
0
1
0
0
0
1
0
1
1
1
0
1
0
2
1
2
1
1
1
1
1
1
1
0
1
1
0
0
0
1
1
1
0
1
0
0
0
1
1
0
2
2
2
2
1
0
1
1
1
1
1
0
2
2
2
1
1
1
1
0
1
1
0
1
0
1
2
1
0
2
2
0
2
2
0
0
0
1
0
2
1
2
2
1
1
2
1
0
0
1
2
1
1
0
2
1
0
0
1
2
2
2
2
1
1
0
2
1
2
2
0
2
0
1
1
1
1
1
2
0
2
1
0
1
1
0
0
1
0
0
1
1
2
1
0
1
1
1
0
0
0
1
1
2
0
0
1
1
0
1
0
2
1
0
0
1
0
0
1
2
0
2
1
1
1
1
1
1
1
0
2
2
2
0
0
1
2
0
1
3
2
1
0
2
2
0
0
1
1
1
1
2
1
1
1
0
1
0
1
0
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
0
0
1
2
1
1
1
1
1
2
0
1
2
1
1
0
2
0
1
0
1
0
1
1
0
1
1
1
0
1
2
2
1
1
1
1
2
0
1
2
1
1
1
0
0
1
0
2
1
1
0
0
2
1
1
1
1
1
1
0
4
1
1
1
1
3
1
0
1
1
2
1
1
1
1
1
0
2
1
1
1
2
0
0
2
1
0
1
2
2
1
0
0
0
1
2
1
1
0
1
2
1
0
0
1
0
0
1
2
1
0
1
1
0
1
1
0
1
0
1
1
1
1
1
0
2
1
0
1
2
0
2
0
1
1
0
1
1
1
1
1
2
0
0
2
1
2
0
2
1
1
1
0
0
2
0
0
0
1
1
1
0
0
2
1
1
1
2
0
0
1
0
1
0
1
1
0
5
0
1
1
1
0
2
2
3
1
1
3
1
1
0
2
0
1
0
0
0
0
0
0
1
1
1
2
1
1
2
0
1
0
1
0
0
0
1
1
1
2
1
5
2
1
1
2
0
2
1
0
2
0
1
1
1
2
1
2
1
2
2
1
1
1
1
1
1
1
0
0
1
1
1
1
1
0
1
1
0
2
1
0
0
1
1
2
2
1
1
2
2
1
0
1
0
1
2
2
1
3
0
0
1
1
1
1
0
1
1
1
1
1
0
1
2
2
1
1
2
0
1
1
0
2
2
1
0
0
1
2
1
2
1
1
1
0
0
0
2
1
1
0
0
0
1
1
1
2
1
0
1
1
1
0
1
1
1
1
1
0
1
1
0
1
0
0
1
0
1
1
1
1
2
2
1
1
1
1
0
1
0
1
2
1
2
1
2
0
1
1
0
2
2
2
1
2
1
0
1
1
1
2
1
0
2
1
1
2
1
2
1
0
1
3
0
1
1
1
0
0
2
1
0
1
2
1
1
2
1
0
2
1
2
1
0
1
1
0
0
0
1
2
1
1
1
2
1
1
0
2
2
0
1
2
2
1
1
0
1
1
0
1
1
1
1
0
2
2
2
2
0
2
1
1
2
1
0
0
1
1
0
0
0
1
2
1
0
0
0
1
2
2
1
1
2
0
2
0
3
1
3
0
0
1
0
1
1
1
1
1
1
2
0
0
1
1
0
2
2
2
1
1
0
0
1
0
0
1
1
1
2
1
2
1
1
2
1
0
2
1
1
0
0
0
1
1
0
0
0
2
1
1
1
2
1
0
0
1
1
1
2
1
1
1
0
1
0
0
0
0
0
0
2
1
2
2
1
0
1
1
2
1
1
1
2
0
0
1
2
1
1
0
0
0
1
1
0
2
1
0
0
2
1
1
2
1
1
0
1
1
0
2
0
0
2
0
0
2
2
0
1
0
1
0
2
2
3
1
1
2
1
1
1
0
1
1
1
2
2
1
2
1
1
0
1
1
1
0
2
1
1
0
0
0
0
0
0
1
3
1
1
2
1
0
1
2
0
1
1
1
0
2
2
1
1
2
0
3
1
0
1
1
1
0
2
1
0
1
2
0
1
2
1
0
0
0
0
0
2
1
1
0
1
0
1
1
1
1
1
0
1
1
1
1
2
1
1
0
2
2
1
1
0
1
1
1
2
1
1
1
0
1
0
1
0
1
1
0
1
2
1
1
2
1
0
1
1
2
1
1
1
1
0
0
0
1
1
1
2
0
1
2
1
2
0
2
1
1
2
1
0
2
1
1
0
1
0
2
2
0
0
2
0
1
2
1
2
1
1
3
1
1
1
1
1
0
0
1
2
1
2
1
1
1
2
1
0
2
2
1
0
1
1
0
2
1
2
2
1
0
0
1
1
1
1
0
0
1
1
1
0
2
1
2
1
1
1
1
1
0
1
1
2
1
2
1
1
1
0
1
0
1
1
1
2
1
2
1
0
1
1
0
0
2
0
0
1
0
1
2
1
1
1
0
1
0
1
0
0
2
0
1
1
2
1
1
2
0
2
0
1
1
0
1
1
1
1
2
1
1
1
1
1
0
1
1
0
2
1
2
2
1
0
1
0
0
0
2
1
1
0
0
1
2
2
1
0
2
1
1
1
2
1
2
1
1
0
1
1
1
1
1
1
1
2
1
1
0
1
0
1
1
1
1
0
1
1
2
1
4
0
2
1
1
2
1
0
2
1
0
2
0
2
1
1
1
0
1
1
1
0
1
2
1
2
0
1
1
0
0
1
1
1
2
0
0
0
1
1
1
0
2
1
2
1
1
1
1
2
1
1
0
1
0
1
1
1
1
2
2
2
1
0
0
2
1
0
0
1
1
2
0
1
0
2
1
2
1
0
0
0
1
1
2
1
0
1
1
1
0
1
0
2
2
2
2
0
0
0
1
1
1
1
0
1
3
0
1
2
0
0
0
0
1
0
1
1
1
1
0
2
1
2
1
1
2
1
1
1
2
0
1
0
1
0
1
0
0
1
1
1
1
2
1
1
1
1
2
1
5
1
1
1
1
2
0
1
1
1
1
0
0
0
0
3
0
1
1
1
2
1
1
1
1
2
1
2
1
1
0
1
1
0
1
1
1
0
0
0
0
1
1
0
0
1
0
0
0
1
2
1
1
2
2
1
0
2
1
1
1
1
3
0
1
2
1
1
0
2
0
0
1
0
0
1
1
1
1
1
0
1
1
1
0
1
1
1
1
0
1
1
0
1
1
2
0
1
1
0
0
1
1
1
2
1
1
1
0
0
2
2
1
1
2
2
0
1
1
0
2
1
1
0
1
1
2
2
0
2
0
1
1
1
1
1
5
0
0
1
1
1
1
1
0
1
1
2
1
2
2
1
2
0
3
0
0
0
2
1
2
0
2
0
0
2
1
0
1
0
1
2
1
1
0
1
0
1
1
1
1
2
1
0
1
1
1
1
1
2
1
0
1
2
1
1
1
1
1
1
2
2
1
0
1
0
0
1
0
2
0
0
0
1
0
1
0
1
0
2
2
4
1
0
1
1
1
0
0
0
1
2
2
0
2
1
1
1
1
2
0
2
2
0
0
1
1
1
0
2
1
1
1
0
0
2
0
1
2
2
1
1
1
1
1
1
0
1
0
0
1
1
1
2
0
1
1
2
1
2
0
1
2
1
1
0
2
2
0
1
0
1
2
3
0
1
0
2
1
2
1
0
0
1
2
1
1
2
0
1
0
2
0
0
1
0
1
1
1
0
1
1
0
1
2
0
1
2
1
2
1
1
1
0
1
1
1
1
0
1
1
1
2
1
1
0
0
2
0
2
0
1
1
0
0
1
1
0
0
1
1
0
2
2
1
1
2
0
2
1
0
0
1
1
1
1
1
1
0
2
2
1
1
1
1
0
1
1
2
0
0
1
1
1
0
1
0
1
1
0
1
1
2
0
1
2
1
2
1
1
0
2
1
1
0
1
1
2
0
1
0
2
2
1
1
1
1
2
0
0
0
2
1
2
0
0
1
0
0
2
1
2
0
1
0
2
2
2
1
0
2
0
1
1
2
2
1
1
1
2
1
1
0
1
1
1
0
2
0
0
0
0
1
1
1
1
1
0
1
2
1
1
1
1
0
1
1
0
1
0
1
2
2
0
1
1
0
1
0
1
0
1
0
1
1
2
1
0
1
1
1
0
1
2
1
0
2
2
1
1
1
1
0
1
0
1
1
0
1
2
1
1
2
2
1
0
1
0
0
0
1
2
2
0
1
1
1
1
2
1
1
2
0
0
0
2
2
0
2
2
1
1
1
2
0
1
1
1
1
1
0
3
0
1
2
1
1
1
1
1
1
1
1
0
0
0
0
1
0
1
1
2
0
0
1
0
2
2
1
2
1
1
0
1
1
0
1
0
1
2
1
2
1
2
1
3
0
1
2
1
0
0
0
1
2
0
1
1
1
0
1
0
1
2
1
1
2
1
1
1
1
2
0
1
0
1
1
1
1
2
2
0
1
1
3
0
2
1
1
1
1
1
0
1
1
1
1
0
1
0
0
1
0
1
0
0
1
1
2
1
0
0
1
1
1
0
2
2
1
1
0
1
2
0
2
1
1
1
0
0
2
0
0
1
0
2
0
1
2
2
1
1
1
2
1
1
0
0
1
2
0
1
1
1
1
1
0
4
1
2
2
1
0
0
3
1
1
0
0
2
1
1
1
0
0
1
0
2
1
1
2
0
1
2
0
1
1
2
1
0
0
1
1
1
2
1
0
2
1
0
0
0
0
0
2
1
2
1
1
3
0
2
1
2
2
2
1
0
0
0
0
0
1
0
2
2
1
1
1
1
2
1
0
1
1
1
0
1
1
1
2
2
1
1
1
2
2
1
1
1
1
1
0
2
1
1
0
1
2
0
0
1
1
2
1
1
0
2
1
1
1
1
0
0
0
2
2
1
0
1
1
2
1
0
2
1
0
1
1
1
2
2
1
1
0
1
2
2
0
1
1
0
2
0
1
1
1
1
0
2
0
2
1
1
0
2
1
1
0
2
0
0
4
1
1
0
2
2
0
0
1
2
1
2
2
1
0
3
1
0
2
0
1
2
1
2
1
1
1
1
2
2
1
1
1
1
2
1
0
1
2
2
1
0
1
0
1
0
1
1
1
0
0
1
1
1
1
0
1
1
1
1
1
1
0
1
1
1
0
1
1
0
1
1
1
1
0
1
2
1
1
2
2
0
0
2
1
1
2
0
1
2
1
2
0
0
1
2
0
1
1
1
1
1
1
1
0
1
2
1
1
2
0
0
3
1
1
2
0
0
2
0
2
3
0
2
2
2
1
0
0
1
1
1
2
1
2
1
1
1
0
2
1
2
1
0
2
0
1
2
0
1
2
1
2
2
1
0
1
1
1
1
1
1
1
0
0
1
2
2
3
2
1
2
1
3
1
1
1
0
0
1
1
1
2
1
3
2
0
1
0
2
0
1
1
2
0
0
2
1
2
1
0
1
2
1
1
1
0
0
1
1
2
1
2
2
1
1
1
1
0
0
1
1
0
1
1
2
0
0
0
0
3
0
1
1
1
0
1
0
0
1
1
0
1
1
0
1
1
1
2
2
0
2
2
1
0
1
2
1
2
2
1
1
1
2
1
1
1
1
1
1
2
0
1
2
2
0
2
1
0
1
2
1
0
2
1
1
0
1
0
1
1
0
0
1
0
1
1
1
1
1
1
2
2
0
1
2
0
0
0
1
1
1
0
2
1
1
1
1
1
0
2
1
0
1
2
1
1
2
2
2
0
1
0
1
1
1
1
2
0
0
1
3
1
1
2
1
0
2
1
2
1
2
1
0
0
1
1
2
1
0
1
1
2
0
1
2
1
2
2
1
1
2
0
0
1
1
0
1
1
1
1
1
1
0
1
0
1
2
3
0
2
1
1
1
1
1
0
0
2
0
2
1
1
2
0
1
1
2
2
1
1
1
1
1
0
1
1
0
1
0
1
1
1
1
2
1
0
1
2
1
1
0
0
0
1
1
1
1
1
2
1
0
3
1
0
2
0
0
0
0
1
1
2
2
2
1
0
1
1
1
1
2
0
2
1
2
1
0
0
1
0
1
2
0
0
1
0
2
1
1
2
1
2
1
1
0
1
0
0
1
2
1
1
0
1
0
1
1
1
0
2
1
1
1
2
1
1
0
0
0
2
0
0
1
0
1
2
0
1
1
1
1
1
2
2
1
1
2
0
1
1
1
2
1
1
1
0
1
0
0
1
0
1
1
2
2
2
0
2
1
0
0
1
0
0
2
1
0
2
1
1
1
0
0
3
2
0
2
1
1
0
1
1
0
1
1
0
2
0
3
0
2
1
0
0
1
1
0
1
1
1
2
0
1
0
1
0
0
1
0
1
0
0
1
0
1
0
1
1
1
1
1
0
0
3
1
1
0
2
0
2
1
2
1
1
0
1
2
1
1
0
1
2
2
0
0
2
0
0
1
1
3
0
1
1
0
0
1
1
1
1
1
2
1
2
1
0
2
1
0
0
2
0
1
1
0
0
1
1
1
1
1
1
2
0
1
2
2
0
0
2
0
2
0
0
1
0
2
0
0
0
2
1
2
2
2
2
2
2
1
2
0
0
1
1
1
1
2
1
1
0
0
1
1
1
1
0
0
1
2
2
1
0
0
0
1
1
0
0
2
0
1
2
0
0
1
1
1
1
2
1
1
1
1
1
2
2
1
1
1
2
0
0
2
0
1
1
1
0
0
2
1
1
1
1
3
1
2
1
1
1
0
1
2
1
3
0
1
0
3
1
2
0
2
1
1
0
1
1
1
2
0
2
1
0
1
1
1
0
2
2
1
2
0
1
0
1
2
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
0
1
2
1
0
2
1
2
0
0
1
1
1
2
1
0
2
1
1
1
1
0
1
3
1
2
1
1
1
1
1
1
1
1
0
0
1
0
2
1
2
0
0
1
2
2
0
0
0
0
2
2
1
1
0
0
0
2
1
1
1
1
2
1
2
1
1
1
2
0
0
1
1
2
1
1
1
1
1
2
2
2
0
1
0
1
2
0
2
2
1
0
3
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
1
2
0
0
2
1
2
2
1
1
2
0
1
1
2
1
2
1
2
0
1
1
1
2
1
4
2
1
0
0
2
1
0
1
2
0
1
1
0
1
1
1
1
2
2
0
1
1
0
1
1
1
3
2
1
2
0
2
1
1
1
0
2
1
1
0
1
1
0
1
1
1
0
1
1
1
2
0
0
1
1
1
1
1
6
2
1
2
1
0
2
2
1
2
0
2
1
0
0
1
1
0
1
1
1
1
2
0
0
0
2
1
0
0
1
2
2
1
2
1
1
0
1
1
1
0
1
2
0
1
1
2
1
0
1
1
2
1
0
0
2
1
2
1
2
1
1
3
1
0
0
0
0
2
0
0
1
1
1
0
1
2
1
0
0
1
1
2
0
2
0
0
1
1
2
1
2
0
1
2
0
0
2
1
1
1
1
0
0
0
1
2
2
1
2
0
2
2
1
1
0
1
1
2
1
1
1
1
1
1
1
0
2
1
2
1
1
2
0
2
2
1
1
2
0
2
2
2
1
1
1
2
2
0
2
1
0
0
2
0
2
0
1
2
1
1
0
1
0
1
0
2
0
1
1
1
1
1
2
1
1
1
1
1
2
0
0
1
2
1
2
0
0
2
1
1
1
2
1
1
2
4
0
0
0
1
0
0
2
1
1
1
0
0
0
0
1
1
0
0
1
2
0
1
1
0
2
1
1
1
1
2
2
1
1
1
1
2
0
2
2
2
0
2
0
0
1
1
1
1
1
1
1
1
1
0
1
0
1
2
2
2
1
1
1
0
2
1
1
1
1
1
1
1
0
2
0
2
1
2
2
0
1
2
0
2
1
0
0
2
0
1
2
1
2
1
2
1
1
0
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
2
0
0
1
4
0
1
1
1
1
2
1
0
1
2
1
1
1
0
0
1
2
2
2
2
1
0
1
1
0
1
2
1
0
2
1
1
1
0
2
0
1
0
1
1
1
0
1
1
0
2
2
0
2
1
1
2
1
0
1
1
0
1
1
1
0
1
1
1
2
1
1
1
1
1
1
2
1
1
0
0
2
2
0
1
1
3
1
1
1
1
0
2
0
1
0
0
0
0
1
1
2
0
1
2
0
1
0
0
1
1
1
2
0
1
0
1
0
2
2
0
1
0
3
1
2
1
1
1
0
0
2
3
1
1
0
0
1
2
2
0
1
1
2
1
1
2
1
0
0
1
2
1
0
2
2
1
1
0
0
1
1
1
0
1
0
2
1
2
1
2
0
1
0
1
1
2
0
2
0
1
0
2
0
1
0
1
0
0
2
1
2
0
0
1
0
1
1
1
1
2
1
5
1
0
1
1
1
1
1
2
1
0
1
2
3
0
1
0
1
2
0
3
1
2
0
1
2
0
2
0
0
1
1
1
1
1
0
1
0
0
1
1
1
1
1
0
1
1
2
1
1
0
1
1
0
0
1
1
1
1
1
1
1
2
1
1
3
1
1
1
1
1
1
2
0
1
2
2
2
1
1
1
2
1
1
0
1
0
1
1
2
5
0
1
1
0
2
2
2
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
1
7
1
1
2
1
0
1
1
1
2
1
0
1
2
2
0
1
1
0
2
1
1
0
2
0
2
0
0
1
1
0
1
0
0
2
1
2
1
1
1
0
1
2
1
2
0
0
2
1
1
1
1
1
2
1
1
1
0
2
1
0
1
1
1
0
0
0
2
0
0
0
2
3
2
0
1
1
2
1
1
2
1
1
0
1
1
2
0
4
1
2
1
2
0
1
1
0
0
1
1
1
1
2
0
1
2
1
1
2
0
0
1
1
1
0
1
2
1
2
0
0
1
0
0
1
2
1
1
2
2
1
3
1
1
1
1
1
1
1
0
0
1
0
0
2
0
0
0
2
1
0
1
0
1
1
1
0
1
0
2
1
2
1
0
1
0
1
0
1
1
0
2
1
0
1
1
2
0
0
1
1
1
1
2
1
1
1
1
1
0
2
1
1
1
0
0
1
0
1
0
0
2
2
2
2
1
0
1
0
1
0
1
1
1
1
2
1
1
2
0
2
2
2
1
2
2
0
0
0
1
5
0
1
1
2
1
0
0
1
2
0
1
1
1
1
2
1
2
2
0
1
1
1
0
0
1
0
1
0
0
1
0
1
0
0
2
4
2
2
3
0
2
0
1
1
0
2
1
1
0
0
1
1
1
2
1
1
1
2
0
1
0
1
1
0
2
1
0
0
1
1
1
1
2
1
2
2
1
1
2
0
1
1
1
0
0
0
1
1
0
2
1
1
0
1
2
1
2
1
1
1
2
1
1
2
3
1
0
2
2
0
0
1
1
0
1
2
1
1
2
1
2
1
1
1
2
1
1
1
1
0
0
1
1
1
1
0
2
0
0
2
1
1
2
1
0
0
0
2
2
1
3
1
1
1
0
2
2
2
1
1
1
1
1
2
1
1
2
0
2
1
0
0
0
1
2
1
0
0
1
0
1
2
0
1
1
2
1
0
1
0
2
1
1
2
2
1
1
1
1
2
2
0
2
1
2
1
1
1
2
2
1
2
1
1
2
0
4
0
1
2
2
0
1
2
1
0
2
0
1
0
1
1
1
2
1
2
0
0
1
2
1
1
0
1
1
0
0
2
1
0
2
1
0
1
1
1
0
2
1
1
0
2
0
1
0
1
0
0
1
0
1
2
0
0
2
1
0
0
1
1
1
0
1
1
1
2
2
2
1
1
2
1
2
0
0
0
1
1
1
1
1
0
1
1
1
1
0
1
1
0
1
1
0
0
0
1
1
1
2
0
1
1
0
0
2
1
0
0
0
1
2
2
1
1
5
1
0
2
2
2
2
1
1
0
0
2
0
1
1
2
1
1
1
1
0
1
1
1
1
1
0
1
0
1
0
2
1
1
1
0
1
2
1
0
1
1
0
7
2
2
0
1
1
0
1
1
0
2
1
1
1
1
0
2
0
1
1
1
1
1
1
2
1
2
0
0
1
0
1
2
1
1
2
0
1
0
1
2
1
1
1
0
1
3
0
2
1
1
1
1
1
1
1
2
2
1
1
2
1
1
2
0
1
0
1
0
0
1
1
0
2
0
1
1
1
0
1
1
1
1
0
0
1
1
1
1
0
1
1
1
0
2
1
0
1
1
1
1
0
1
2
2
1
2
2
2
0
1
2
1
1
0
0
1
1
0
2
1
1
1
1
2
0
1
1
0
0
1
0
0
1
2
1
0
1
1
0
2
0
1
1
0
1
0
0
1
1
0
0
2
1
1
0
1
2
1
0
0
1
1
1
1
1
1
0
1
1
1
1
1
0
2
1
2
0
2
1
2
0
1
0
1
0
1
1
0
2
1
0
0
0
1
2
0
1
2
1
0
1
0
1
2
1
2
2
2
2
0
2
1
1
0
0
0
0
0
1
1
0
0
1
0
1
1
2
1
1
1
1
0
1
0
2
1
1
1
2
0
0
2
0
1
0
0
0
1
0
2
1
1
2
1
1
0
1
2
1
0
1
0
1
2
1
0
1
1
1
2
1
0
2
1
1
2
1
2
1
2
0
1
0
1
2
0
0
0
3
1
2
0
2
1
1
2
1
0
2
1
1
1
0
0
0
1
0
1
1
1
0
1
1
2
1
2
1
1
1
0
0
1
0
1
0
0
0
1
1
1
1
1
1
2
2
1
2
2
0
2
2
1
2
2
0
1
0
1
1
1
0
3
2
1
1
1
0
1
0
0
1
0
3
0
2
0
1
2
0
2
0
1
2
2
2
0
2
1
1
1
1
0
0
2
1
0
0
0
1
1
0
1
0
0
0
0
2
1
1
0
0
0
0
2
1
1
0
0
0
2
1
2
0
1
0
0
0
0
1
2
0
1
1
0
1
0
2
2
0
1
1
2
0
2
3
1
2
1
0
1
1
2
0
2
0
1
1
1
1
0
1
2
1
1
0
1
1
0
0
1
0
1
0
0
2
1
0
2
1
1
1
0
1
2
0
1
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
0
1
2
1
2
1
0
0
1
1
1
2
0
0
0
0
1
1
1
4
0
2
1
0
2
2
2
1
0
2
0
2
1
0
0
2
1
2
0
1
0
1
1
1
1
1
1
2
0
0
1
2
1
3
0
0
0
2
1
0
1
1
2
0
1
2
1
1
0
0
2
2
1
3
0
1
1
0
0
0
0
2
1
0
0
10
2
0
0
0
1
2
1
0
1
1
1
1
2
1
2
1
2
2
1
2
1
0
1
1
1
1
1
0
1
0
1
0
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
0
1
0
1
1
0
1
1
0
2
0
2
1
1
0
0
1
1
2
2
1
1
1
1
1
2
2
2
1
0
2
1
1
0
0
2
0
0
1
1
1
1
1
1
1
2
1
1
2
1
1
0
0
0
0
0
2
1
1
0
0
0
0
1
0
1
2
0
1
1
2
2
2
2
0
0
0
1
1
0
1
1
1
0
1
1
0
1
0
0
1
2
0
2
1
1
1
0
2
1
1
2
0
0
2
1
0
0
0
1
2
1
1
1
1
1
1
1
1
2
1
1
1
2
1
3
0
0
1
0
2
1
1
1
0
2
1
1
1
2
0
2
0
1
1
0
0
1
0
1
2
0
0
1
1
2
0
1
2
1
1
2
0
0
2
0
0
2
1
2
1
2
2
0
0
2
1
0
1
1
1
1
3
2
1
2
2
2
1
1
1
1
2
1
0
1
0
0
1
0
0
2
1
0
1
1
2
1
0
0
1
2
1
2
1
0
0
2
2
2
2
2
0
1
1
1
1
1
2
1
0
0
1
1
2
2
1
0
0
1
1
0
1
1
1
2
1
2
1
0
1
1
0
2
2
0
1
1
0
0
2
1
0
2
0
1
1
0
1
2
2
1
1
1
0
1
1
1
1
1
1
1
0
1
1
1
0
1
0
1
2
1
1
0
2
1
0
0
2
0
1
0
2
1
0
2
2
2
2
0
3
1
2
0
2
2
1
1
1
1
0
1
0
0
0
0
1
1
1
2
1
2
1
1
1
0
1
2
1
0
0
0
0
2
0
1
0
1
1
1
1
1
1
0
1
1
1
1
1
2
0
0
1
0
0
0
2
0
0
2
1
0
0
1
0
0
1
2
1
0
2
2
0
1
1
1
2
2
1
1
2
1
1
1
2
1
0
1
1
0
0
1
1
0
0
1
1
1
4
1
0
1
1
1
0
0
0
0
0
2
1
1
1
1
1
0
1
1
0
1
1
1
1
1
1
1
0
2
0
1
0
0
1
0
1
0
0
2
0
2
2
1
2
0
1
2
1
2
0
2
1
1
1
2
0
1
1
0
1
0
1
1
0
1
0
1
0
2
1
1
1
0
0
1
1
1
1
1
1
1
1
1
0
2
1
1
2
0
2
0
1
0
1
2
0
0
1
0
2
0
2
0
0
1
1
1
0
1
2
0
2
0
2
2
2
1
1
2
1
1
1
0
2
0
1
1
3
1
2
1
4
0
2
0
0
1
1
1
1
1
0
1
2
1
1
0
1
1
1
0
1
1
2
1
0
0
0
0
0
1
1
2
0
1
2
1
1
0
1
2
2
1
1
2
1
2
1
1
0
1
2
1
0
2
1
1
0
1
1
1
1
1
1
1
0
1
1
2
1
0
1
2
0
1
1
2
2
0
1
1
0
1
2
1
1
2
0
2
0
1
0
1
1
0
0
0
1
1
2
0
0
0
1
2
1
1
1
1
1
0
1
2
1
0
1
0
1
2
1
1
2
1
1
2
1
2
2
2
0
1
1
1
1
0
1
1
1
2
1
0
1
2
2
1
1
1
2
0
1
3
0
1
0
1
0
1
0
2
1
2
1
0
0
0
0
0
0
1
1
0
1
0
1
2
1
0
1
1
0
0
1
1
1
1
2
0
1
2
2
1
0
2
0
1
0
0
2
2
0
1
0
1
1
0
1
0
1
2
0
1
1
2
2
3
1
0
0
1
0
2
0
1
0
1
0
2
0
0
0
0
2
1
0
0
1
2
2
1
1
2
2
1
0
1
2
0
1
1
1
2
1
1
0
1
1
1
2
1
1
0
1
1
0
2
1
1
1
1
2
1
0
1
2
1
1
2
0
1
1
1
1
1
0
0
4
1
1
1
1
2
2
1
1
2
2
1
1
2
2
1
0
0
2
1
0
1
1
1
1
0
1
1
1
0
2
0
0
0
1
1
2
1
2
1
2
2
0
1
1
1
1
1
2
1
0
2
2
0
2
1
1
2
1
2
1
1
0
1
0
1
1
2
1
1
1
1
1
1
0
2
1
2
0
1
1
2
0
0
1
2
2
2
1
1
1
0
2
0
1
0
0
1
2
1
0
1
1
1
1
2
1
1
1
1
0
1
1
1
1
0
0
0
1
1
2
1
0
0
1
2
0
2
2
2
0
1
0
2
1
1
0
1
0
1
0
0
2
0
1
1
1
1
1
0
1
1
2
1
1
1
2
0
0
2
1
1
4
0
0
0
2
0
2
0
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
0
1
1
3
1
0
1
1
0
1
0
2
1
1
1
0
1
1
0
0
1
1
2
1
1
1
1
1
1
1
1
0
1
1
3
2
1
1
2
2
1
2
0
0
1
2
1
2
0
1
1
2
2
0
2
0
1
1
1
0
1
1
1
2
1
0
2
1
1
0
0
0
1
1
0
1
0
1
0
0
0
2
1
0
2
1
1
0
0
2
0
0
1
0
0
1
2
2
1
0
0
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
0
2
1
1
1
2
1
1
0
2
0
1
2
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
2
0
0
1
1
1
1
1
1
0
2
1
1
0
2
0
1
2
2
0
1
1
1
1
1
1
0
1
0
0
0
0
1
0
1
2
1
1
1
1
2
2
0
0
1
0
1
1
0
1
0
0
1
1
0
1
1
1
0
0
1
1
0
0
1
0
2
2
2
1
0
2
1
1
2
1
0
1
0
1
1
2
1
0
0
2
1
0
1
1
2
1
1
2
1
2
1
2
1
0
1
0
1
1
0
1
0
1
0
1
1
1
2
1
1
2
1
2
6
2
1
1
0
1
2
2
1
0
0
0
1
0
0
2
2
1
2
1
1
2
4
0
1
1
2
2
0
1
3
1
1
1
1
1
0
1
0
1
2
1
0
2
0
1
1
2
1
1
2
1
2
1
1
1
0
1
0
1
1
2
1
1
2
2
0
1
0
2
1
1
1
0
2
1
1
1
1
0
2
1
0
2
1
0
1
0
2
1
1
0
1
1
1
0
1
2
1
1
1
2
0
0
1
1
1
1
1
0
0
2
3
2
0
2
2
1
0
2
0
1
1
2
0
1
0
1
1
0
0
1
1
0
1
0
1
1
0
1
1
2
1
0
1
0
0
0
2
0
0
2
1
2
0
0
2
1
1
2
0
1
0
2
1
2
1
1
0
4
0
1
1
2
0
1
7
0
3
1
0
1
1
1
1
0
1
1
0
0
4
0
0
2
0
2
0
2
1
1
0
2
1
0
1
0
3
1
2
1
2
2
1
1
0
1
0
1
1
2
1
1
2
2
1
3
1
1
1
0
1
1
0
1
2
2
0
2
3
1
1
0
0
2
1
0
1
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
2
1
1
1
0
2
1
2
2
1
1
2
1
1
0
1
1
1
1
2
2
1
1
1
2
2
1
1
0
1
0
2
1
1
2
0
1
2
0
1
0
1
0
2
0
1
2
0
1
0
0
1
1
1
2
1
0
0
2
4
1
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
1
1
1
0
1
1
2
1
1
1
1
1
2
1
1
1
0
2
0
1
1
1
0
0
2
2
1
1
2
0
1
1
1
0
0
1
1
1
0
1
1
1
0
2
1
1
1
0
1
1
1
1
0
1
0
2
1
1
1
1
1
2
1
1
1
1
1
1
1
0
0
0
0
2
2
2
0
2
2
2
2
0
0
1
0
2
0
1
1
2
1
0
2
2
0
0
1
0
1
0
0
0
1
2
2
1
2
1
0
1
1
1
1
2
1
0
2
1
0
1
0
1
2
2
1
1
1
0
1
1
1
0
2
1
0
1
1
1
0
1
1
1
2
2
1
2
2
1
2
0
1
0
2
1
0
2
1
1
1
1
0
0
1
1
0
1
1
2
1
0
1
0
1
2
0
0
2
1
0
1
2
1
0
0
1
1
2
1
1
1
0
2
2
1
1
2
1
2
2
1
1
0
2
1
1
1
1
2
1
1
0
1
2
0
2
2
1
2
1
0
1
2
2
1
2
1
0
1
2
0
1
1
0
2
1
2
1
1
1
1
1
2
1
1
3
1
0
0
1
0
0
1
0
2
1
2
2
0
0
2
1
2
2
0
2
2
2
0
2
1
0
1
2
2
1
0
0
2
0
0
1
1
0
1
1
2
1
2
0
2
1
1
2
1
1
1
1
2
1
2
1
1
0
0
0
1
1
0
0
2
0
2
2
2
0
1
0
0
1
1
0
1
2
1
0
1
1
1
1
1
1
0
0
1
2
1
0
1
1
2
0
1
2
1
0
2
0
2
2
1
0
0
3
0
2
0
0
1
1
1
1
0
0
2
1
0
2
2
1
1
1
2
1
0
0
2
1
1
1
2
2
1
2
0
2
2
0
0
1
0
1
1
1
1
1
0
2
0
1
0
0
1
1
1
2
1
0
2
2
1
1
1
1
1
2
0
2
0
0
1
2
1
0
1
2
1
1
2
0
2
0
0
0
2
2
2
1
0
0
1
1
1
0
1
1
1
2
2
2
0
2
1
0
1
1
1
2
0
1
1
0
1
1
1
1
0
1
0
0
2
1
1
0
1
1
1
0
1
1
1
2
1
2
1
0
1
1
1
3
0
1
2
1
0
3
0
0
1
0
0
1
0
1
1
0
1
2
2
1
1
1
0
2
0
0
1
1
1
0
0
1
0
1
0
1
0
1
2
1
1
2
1
1
2
1
2
2
2
1
1
1
1
0
1
1
0
2
2
2
2
2
0
2
0
0
1
1
2
0
1
0
2
1
0
1
3
2
1
1
0
1
0
1
2
1
1
0
1
2
0
1
1
0
2
1
2
0
1
1
2
1
1
1
0
1
1
0
1
1
1
0
1
0
0
2
1
1
1
1
0
1
1
1
2
0
0
2
1
1
1
1
0
0
1
0
1
2
0
2
0
0
1
2
0
0
2
2
1
0
1
2
0
1
2
0
1
0
2
1
1
1
2
1
1
0
0
0
0
1
0
1
1
2
1
0
0
0
0
1
0
1
1
1
1
0
0
0
1
0
1
1
1
0
1
1
0
1
1
1
1
2
2
1
0
1
2
1
1
2
0
0
0
1
2
2
1
1
1
1
1
1
1
1
1
1
2
1
2
0
1
1
1
1
1
0
2
1
0
0
2
0
0
1
0
1
0
0
0
1
1
1
4
0
1
1
1
1
3
2
1
1
2
1
2
2
1
2
1
1
1
0
1
0
1
2
1
1
1
1
3
1
0
0
1
1
2
1
2
0
2
2
1
2
0
1
1
1
1
0
1
0
1
0
2
1
2
1
1
0
1
1
1
1
1
1
1
0
1
0
1
0
1
1
1
0
1
1
0
0
2
2
2
0
1
0
2
1
0
1
0
2
1
2
1
1
2
2
1
2
2
2
1
2
1
1
1
1
1
2
1
1
1
1
2
1
1
1
0
3
0
2
1
1
1
0
0
1
1
1
1
2
1
1
2
1
1
1
2
1
1
1
1
1
1
3
2
1
2
1
0
0
2
1
1
0
0
1
0
2
1
1
0
1
1
1
1
2
1
1
2
0
0
1
1
2
0
1
1
1
0
0
1
1
1
1
0
1
2
1
1
0
0
1
0
1
0
2
0
0
1
1
2
1
1
0
0
2
0
0
1
0
1
0
0
1
1
1
1
1
2
2
1
1
0
1
0
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
0
1
0
0
1
1
1
2
1
1
2
0
1
0
1
0
1
2
0
1
2
0
0
0
2
1
2
0
3
2
1
0
2
0
1
2
2
2
0
2
1
1
2
1
1
1
0
2
2
0
1
0
1
1
3
1
1
1
2
1
1
1
1
0
2
0
1
1
1
1
2
0
1
2
1
2
1
0
0
1
1
1
0
1
0
1
1
0
1
2
0
1
1
0
1
0
2
0
1
1
1
1
0
2
1
1
1
0
0
0
2
2
0
1
1
1
2
1
0
1
0
2
1
3
2
0
1
2
1
0
1
2
2
1
1
1
0
2
2
1
0
2
0
1
2
1
1
1
0
1
0
1
0
1
2
1
2
1
1
1
1
0
1
1
3
1
2
1
1
1
2
0
1
1
1
2
1
0
1
1
2
1
1
0
3
0
1
0
1
1
1
0
2
1
2
1
1
0
1
1
1
1
0
1
3
1
1
1
1
1
1
0
4
2
0
2
0
1
1
0
1
1
1
2
0
1
1
0
1
1
0
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
0
2
0
1
1
0
2
1
0
1
1
2
0
2
1
0
0
2
1
1
3
1
1
0
0
2
1
0
2
0
2
0
1
2
1
0
2
2
2
0
2
0
2
0
1
3
1
1
2
0
1
1
2
1
0
0
3
1
1
0
0
0
1
1
0
1
1
3
1
1
0
1
0
1
1
1
1
0
0
0
0
2
2
1
1
0
0
2
2
0
0
1
1
0
1
0
0
0
0
1
1
2
2
1
1
1
2
1
1
1
1
2
0
1
0
1
1
1
1
1
1
0
1
1
1
1
1
2
1
1
1
2
1
0
1
0
2
2
1
0
1
1
0
0
0
1
0
0
1
2
0
1
1
1
1
2
1
2
1
2
1
0
0
1
2
1
0
0
1
0
2
0
1
1
1
0
1
0
0
1
0
0
1
1
1
2
1
0
2
1
1
1
2
1
0
1
1
1
0
1
1
0
1
1
0
1
0
0
1
0
1
3
2
1
0
1
1
0
1
1
0
1
2
1
1
2
1
1
0
0
1
2
1
1
1
1
2
2
2
1
1
1
0
1
0
1
0
1
1
1
2
1
2
1
1
1
1
0
0
1
2
2
0
2
1
0
2
2
1
1
1
1
1
0
0
0
1
0
0
2
1
0
1
0
1
1
1
0
1
1
1
1
1
0
1
2
0
1
0
2
0
0
1
1
1
2
1
2
1
1
2
0
2
0
2
1
1
2
1
1
0
0
1
1
0
1
1
2
1
2
1
1
1
2
0
2
1
2
2
1
0
1
1
2
0
1
1
2
0
2
1
0
2
1
0
1
0
1
0
1
1
0
2
1
1
1
2
0
1
1
1
1
2
1
2
1
1
2
0
2
1
2
1
2
2
0
1
2
0
1
1
2
1
0
0
1
0
0
2
0
1
0
1
5
1
0
2
2
1
2
0
1
0
1
1
0
0
2
2
0
1
0
0
1
1
1
2
2
0
1
1
0
1
2
1
0
0
1
1
1
1
0
1
0
1
0
1
2
0
1
0
1
1
1
0
1
1
2
1
2
1
2
0
0
1
2
1
0
1
1
0
0
0
0
0
2
1
1
1
1
1
2
0
0
1
1
0
2
0
2
1
1
2
0
1
0
0
1
2
1
1
0
3
1
0
2
0
1
0
0
0
2
0
1
1
2
1
2
1
1
2
1
0
0
2
2
0
2
0
2
1
0
0
0
2
1
0
1
0
0
0
0
2
1
2
0
1
1
0
0
1
1
0
1
1
2
0
1
1
0
1
0
1
0
0
1
1
0
2
1
1
0
1
1
1
1
1
0
2
1
1
1
2
0
1
1
0
1
1
2
2
1
0
1
1
2
0
0
0
0
0
2
2
1
1
2
0
0
1
1
1
1
0
1
2
2
2
2
1
1
1
1
2
1
0
0
2
0
1
2
1
2
0
2
1
2
1
1
0
0
1
0
1
1
2
1
2
1
3
1
2
2
1
0
0
2
1
1
2
1
1
1
0
0
0
1
0
1
2
2
1
1
2
1
2
2
1
2
1
1
1
1
2
2
2
1
1
1
0
1
2
0
1
1
1
2
1
1
1
2
0
4
0
0
1
1
0
0
0
1
1
2
1
0
1
1
1
2
2
1
2
0
1
0
0
1
2
1
2
0
1
0
1
1
1
1
1
1
2
2
1
0
1
1
4
1
0
0
1
0
2
1
1
1
1
2
1
2
1
1
2
1
3
0
2
1
0
2
1
0
2
0
1
2
0
1
1
1
2
2
1
1
1
1
2
0
0
1
1
1
1
0
1
1
0
1
0
1
2
1
0
1
1
0
1
1
1
2
1
1
1
1
0
1
0
1
1
1
0
1
1
2
1
0
2
0
0
0
1
0
0
0
2
1
1
1
1
1
0
2
1
1
3
2
1
0
1
1
0
1
1
1
0
0
1
1
3
2
1
1
0
1
0
0
1
0
1
1
1
1
1
0
2
1
6
1
2
1
1
1
1
1
1
0
2
1
1
1
1
1
2
1
1
0
1
1
1
2
2
1
2
2
1
1
1
0
1
0
2
2
0
2
1
2
1
1
1
0
2
1
2
2
1
2
1
1
0
1
0
1
1
1
1
1
0
1
0
0
0
0
0
1
2
0
1
1
0
2
1
1
1
1
1
1
0
2
1
1
1
1
1
1
2
1
0
4
0
1
1
0
1
1
0
0
1
2
1
2
2
2
0
0
1
1
2
0
1
1
0
2
1
2
1
0
0
2
0
0
0
0
2
1
1
0
0
0
1
1
1
0
2
0
1
0
1
1
1
0
0
1
1
1
0
1
2
2
2
0
1
0
3
0
0
1
1
2
0
1
2
1
1
0
1
1
2
0
3
0
0
0
1
2
1
0
1
2
0
0
1
1
0
0
0
0
1
1
0
0
1
4
0
1
2
1
2
2
0
1
1
2
1
1
1
0
2
0
2
2
1
1
0
2
1
1
1
0
0
0
1
1
2
2
1
1
1
1
1
2
0
2
0
0
1
1
0
0
1
1
1
0
1
0
1
0
0
1
2
0
2
2
0
1
2
0
2
1
1
1
0
1
1
2
1
0
0
1
1
1
0
0
0
1
0
0
1
0
1
0
1
2
0
1
0
0
0
1
1
1
1
0
1
2
1
1
0
2
1
1
0
1
1
0
0
0
0
3
1
1
1
2
1
2
1
1
1
1
3
0
0
1
0
0
1
2
1
2
1
2
0
1
1
1
2
2
0
2
1
1
1
0
1
0
0
0
0
1
0
2
1
2
1
1
1
0
0
0
2
2
1
2
2
0
1
0
2
1
0
1
0
1
0
1
1
0
3
1
0
1
2
1
1
1
1
1
2
1
1
2
2
2
2
0
2
1
1
1
2
1
1
1
1
1
2
0
1
0
1
0
2
1
1
1
1
3
0
2
0
1
2
5
1
1
2
3
0
0
0
1
2
3
1
0
1
2
0
0
1
1
1
1
1
0
1
2
1
2
3
1
2
0
1
2
1
3
1
0
0
1
1
1
1
0
1
1
1
0
2
0
0
2
0
1
1
1
0
1
1
2
1
1
0
1
0
0
2
1
0
1
1
1
1
1
1
1
1
1
1
2
0
0
0
1
0
1
0
2
0
1
0
2
0
1
0
1
0
1
0
3
1
1
1
0
2
1
0
0
2
1
1
1
2
1
2
1
1
1
1
2
0
1
2
0
1
1
2
1
0
1
1
0
2
0
0
0
1
1
0
2
0
1
1
1
0
1
1
0
2
1
2
1
2
0
0
1
1
2
1
0
2
3
1
0
0
1
1
1
1
1
0
2
2
2
0
1
0
1
2
2
1
1
1
1
1
0
1
2
0
0
0
1
1
2
1
2
0
0
0
1
2
2
0
0
0
2
0
0
0
2
2
2
1
1
1
2
2
1
0
0
2
1
1
0
2
0
1
2
1
1
1
2
0
0
2
1
1
0
1
1
2
2
1
0
2
0
1
2
0
2
0
1
3
2
1
0
2
0
1
1
2
1
0
1
1
1
2
1
2
0
1
0
2
1
0
0
0
2
1
1
1
2
1
1
1
2
1
1
3
2
2
0
1
1
0
1
0
1
1
1
0
0
0
2
1
1
1
1
1
2
1
0
1
1
1
1
0
1
2
1
1
1
0
0
0
0
1
0
2
2
1
0
0
1
1
2
2
1
1
1
1
1
1
0
1
2
1
1
2
1
2
1
0
1
1
1
0
1
2
0
0
0
1
1
1
1
0
1
2
1
1
2
1
2
0
2
1
1
1
0
2
2
1
1
2
0
1
0
2
1
1
0
0
2
0
0
2
1
0
0
2
0
1
1
0
1
1
2
2
0
1
0
1
2
0
2
0
0
1
1
1
1
0
0
1
3
1
1
2
1
1
1
1
1
1
1
1
2
2
2
1
1
2
1
1
0
1
2
0
2
1
2
0
0
2
0
2
2
1
2
2
1
1
0
1
1
1
1
1
2
1
0
1
0
1
1
1
1
0
1
2
2
0
2
1
0
1
1
0
1
1
2
2
2
0
0
1
2
1
0
0
0
0
1
0
0
2
1
1
1
0
0
0
1
0
1
0
1
1
1
1
0
1
1
3
0
1
1
1
2
1
2
0
1
1
2
1
1
1
0
2
1
0
1
1
1
1
2
1
1
1
1
1
0
0
0
1
2
2
0
1
1
0
1
0
0
1
2
1
1
0
2
1
1
0
1
2
1
1
3
1
0
1
1
1
1
1
2
3
1
1
2
0
0
1
1
0
1
2
1
2
2
1
1
1
1
0
1
1
1
1
0
2
0
0
2
0
0
1
1
2
2
1
1
1
2
0
1
2
2
1
3
1
2
1
1
1
2
1
2
0
1
0
2
1
1
1
1
2
1
2
2
0
0
0
1
0
1
1
1
1
2
2
0
2
2
1
0
1
0
1
2
0
0
0
2
2
1
3
1
0
1
1
1
2
1
0
1
0
0
0
2
1
1
2
0
0
2
2
1
2
1
0
1
2
1
0
2
1
1
1
0
2
1
2
2
1
2
1
1
0
0
1
3
0
1
2
1
1
2
0
2
1
0
1
2
2
1
1
2
0
0
1
0
1
2
2
1
1
1
1
1
1
1
0
1
1
1
2
1
2
1
1
0
1
0
0
1
1
2
1
0
0
0
2
1
1
1
3
1
1
2
2
1
0
2
1
3
1
2
2
0
0
1
1
0
0
1
2
0
0
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
1
2
1
1
1
4
0
0
2
1
1
0
1
2
1
1
1
1
0
0
1
2
1
1
0
0
2
2
1
2
2
1
1
2
0
1
0
0
1
0
1
0
2
2
0
0
0
1
0
2
1
2
2
1
2
0
1
1
1
1
1
1
0
1
1
0
1
0
0
1
1
1
1
2
0
2
1
0
1
0
1
1
1
1
0
1
2
0
1
2
1
1
0
1
1
0
0
1
1
2
1
1
2
1
0
0
2
2
1
1
1
1
1
1
3
1
1
1
1
0
2
1
2
1
1
1
1
0
2
0
1
2
4
0
1
1
1
1
0
2
1
2
2
1
0
1
1
1
1
2
1
2
0
1
1
1
2
0
1
2
0
0
1
1
1
1
2
1
0
2
0
0
0
1
1
0
0
1
1
0
0
0
2
0
1
2
2
2
1
1
0
1
2
1
0
0
1
2
0
1
2
0
2
1
1
0
1
1
0
2
1
1
2
1
6
0
2
0
1
1
2
1
1
0
1
1
2
1
1
1
1
0
1
1
0
0
1
1
1
1
1
1
3
0
1
2
0
2
1
2
2
0
1
1
1
1
2
1
1
1
1
0
1
2
1
0
0
0
0
0
0
1
1
1
0
0
0
0
2
1
2
2
1
1
1
0
0
1
1
2
1
1
1
1
1
1
0
1
0
0
0
2
1
2
0
3
2
0
1
1
2
1
2
1
0
2
2
0
1
2
1
2
1
1
2
2
0
0
1
1
1
2
1
1
0
1
0
0
1
1
2
0
1
1
1
2
1
1
0
1
0
2
1
0
0
2
1
1
1
1
2
2
1
0
0
0
0
1
2
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
0
0
2
1
2
2
1
1
1
0
1
0
2
1
0
1
0
0
1
1
1
0
1
2
1
0
1
1
2
1
1
1
0
1
1
2
1
1
0
2
0
2
1
0
1
1
2
0
2
1
2
1
1
0
1
1
0
2
0
0
2
1
0
1
2
1
1
0
0
1
2
0
1
1
2
1
2
2
2
1
0
1
2
1
1
1
2
1
0
1
1
0
1
1
2
2
1
2
2
1
1
1
1
2
0
1
1
1
1
1
1
0
2
2
1
1
1
0
1
0
1
2
1
1
1
2
1
1
1
1
0
0
0
2
1
1
0
1
1
1
2
1
1
2
0
1
0
0
0
2
1
2
0
0
1
0
0
1
0
2
2
1
2
0
0
2
0
1
2
2
1
0
1
0
2
0
0
0
0
0
1
1
1
1
1
1
0
1
2
0
1
1
1
1
1
1
1
0
2
1
1
2
1
2
1
3
3
1
1
1
0
1
0
1
1
2
0
0
1
1
2
1
0
1
2
0
1
1
0
0
1
1
0
1
2
0
0
1
1
0
0
1
1
1
1
0
2
0
1
1
1
1
3
0
2
0
1
2
0
1
1
1
1
2
2
1
1
0
2
1
1
0
2
0
1
2
1
2
1
1
0
1
2
1
1
2
0
0
2
2
1
0
1
1
0
2
1
1
2
1
0
1
1
0
1
1
2
1
1
1
1
0
0
1
0
2
1
1
0
2
1
2
2
1
0
2
1
1
0
1
1
0
2
1
1
1
3
2
1
1
0
0
0
1
1
2
1
2
1
1
1
2
1
0
0
1
1
1
1
1
0
1
1
0
1
1
0
1
2
1
0
1
3
2
0
1
1
1
1
1
2
2
0
1
0
0
0
0
1
0
1
2
1
1
0
2
1
2
1
2
2
2
1
0
3
2
1
2
0
1
2
0
1
1
2
0
0
1
1
2
2
0
1
1
0
1
1
0
2
2
1
1
2
0
1
1
1
1
2
2
1
1
2
1
1
1
0
0
1
1
1
2
1
2
1
2
1
2
0
1
0
0
0
2
0
0
1
0
2
0
0
0
2
2
1
1
1
1
1
1
1
1
0
1
0
1
2
2
1
1
1
1
2
1
1
1
0
2
1
1
2
1
1
2
2
1
2
1
0
1
1
1
1
1
0
0
0
4
2
1
0
1
1
0
2
1
2
2
1
1
2
1
0
1
1
1
2
1
0
1
1
1
0
1
1
3
1
1
0
2
1
1
1
1
0
0
1
0
1
0
0
1
1
1
2
2
1
3
0
1
1
1
1
0
1
1
2
1
2
2
1
0
0
0
1
1
0
1
0
1
1
0
1
2
1
2
1
0
0
0
2
0
1
0
0
1
2
1
0
0
0
0
1
1
1
1
1
2
1
1
1
3
1
2
2
0
1
2
1
0
1
1
1
0
1
1
1
1
0
1
0
0
0
2
0
0
0
1
0
1
1
1
2
1
2
0
1
6
2
1
1
0
0
0
2
0
0
1
0
1
1
0
1
1
0
1
2
0
0
1
1
2
0
0
1
0
0
0
1
1
1
1
1
1
1
2
0
1
1
1
0
1
2
1
1
2
1
2
1
2
1
1
1
0
2
0
2
0
1
0
2
1
0
1
0
0
1
1
0
0
1
1
1
1
0
1
0
1
1
2
1
0
2
0
1
0
0
0
0
1
0
2
0
2
0
2
2
1
2
2
1
1
0
2
1
2
1
1
1
2
2
1
0
3
1
1
1
0
0
1
1
2
0
1
0
0
0
1
1
1
2
2
1
2
1
2
0
1
0
1
0
0
0
1
1
1
1
2
2
0
1
1
1
1
1
0
3
0
2
0
1
1
1
1
1
1
1
2
2
0
2
1
0
1
1
2
0
1
1
1
1
1
1
1
0
0
0
2
2
0
1
1
2
1
0
2
2
1
2
0
0
0
0
2
1
2
1
1
0
1
1
2
1
1
1
1
1
2
0
1
1
1
1
1
1
0
2
1
0
2
2
1
1
0
1
1
1
0
2
2
0
2
1
2
1
1
0
0
0
2
2
0
1
1
1
0
1
2
1
1
1
1
1
0
1
1
0
0
1
0
2
2
3
0
2
1
2
1
2
2
2
0
1
2
2
0
0
2
1
1
2
1
0
2
1
1
0
1
2
2
1
0
2
2
0
2
1
0
2
1
1
0
0
1
0
1
1
0
1
1
1
0
1
1
1
1
0
2
1
1
1
2
1
2
1
1
1
1
1
0
1
0
1
1
1
0
1
1
1
1
0
1
1
2
1
0
1
2
1
1
1
0
1
0
1
0
0
2
2
0
2
0
1
0
1
1
2
1
0
0
1
0
0
0
0
0
2
1
2
2
0
2
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
0
1
1
1
1
0
1
0
0
1
2
1
0
0
5
0
0
1
1
2
0
1
0
2
0
1
2
1
0
0
1
1
0
0
1
2
1
0
2
1
1
0
1
1
2
3
0
0
1
2
1
2
1
1
1
0
1
2
1
1
1
0
0
0
0
0
1
0
1
1
1
0
1
2
0
2
1
2
2
1
1
0
1
2
3
1
1
2
2
2
0
1
3
1
2
0
0
1
1
0
1
1
2
0
0
1
1
1
1
2
3
0
2
1
1
1
1
2
0
2
1
1
1
1
1
0
2
0
1
1
0
1
1
0
1
2
1
2
2
2
2
0
1
1
0
0
1
0
1
0
1
0
0
1
0
2
2
1
0
1
1
1
1
0
2
1
1
2
2
1
2
2
0
0
2
0
1
1
1
1
0
1
2
3
1
2
2
1
2
1
1
1
1
0
1
1
1
1
2
2
1
0
1
2
1
1
1
2
1
1
1
1
0
1
2
1
1
0
2
0
1
1
0
1
0
1
1
1
1
1
0
1
2
1
1
0
1
2
1
0
1
1
0
1
1
0
2
1
1
1
0
1
1
1
0
0
2
1
2
2
1
0
1
0
1
0
1
1
0
1
1
1
2
2
1
1
1
0
1
1
1
0
0
2
0
1
1
1
1
1
1
1
0
1
1
2
1
1
0
2
1
0
0
1
1
2
2
1
1
1
1
1
0
2
2
2
1
4
1
0
0
1
1
1
1
1
4
0
4
0
1
0
2
0
2
1
1
0
2
2
0
0
1
0
2
0
0
1
1
1
1
1
2
2
3
1
2
2
1
1
1
0
0
1
2
1
0
2
1
0
1
0
0
1
0
1
0
2
1
2
0
1
1
2
0
1
1
0
1
1
1
1
1
1
4
1
0
1
0
1
1
1
1
1
1
3
1
0
1
3
1
1
2
1
0
0
0
1
0
0
1
2
0
2
1
1
0
2
1
1
1
1
0
1
1
1
0
0
1
1
0
2
1
1
2
1
1
0
2
1
1
1
2
0
1
1
0
1
0
2
1
1
0
1
1
1
1
1
0
2
1
0
0
1
1
2
0
0
0
0
1
0
1
3
1
2
2
2
1
0
0
1
1
1
1
1
1
1
0
1
0
1
0
2
0
0
2
0
2
2
0
1
2
1
2
1
2
1
0
0
0
2
1
1
1
2
1
0
1
1
0
1
0
1
0
1
0
2
0
2
0
0
0
1
1
1
0
1
0
1
1
2
1
1
2
1
1
4
0
1
0
1
1
0
1
0
0
1
1
1
0
2
1
2
0
1
1
1
2
1
1
1
1
1
0
1
2
2
1
2
0
0
1
0
1
1
1
0
1
1
1
0
1
1
1
1
2
1
0
1
1
2
0
0
0
1
0
1
0
2
1
0
1
1
0
2
1
2
0
0
1
1
1
0
1
1
3
1
1
1
0
0
0
1
3
1
0
1
1
0
1
0
1
0
1
1
1
0
1
1
0
0
0
1
1
0
0
1
1
0
0
0
0
0
1
1
0
2
1
2
0
1
1
1
1
1
1
1
1
1
1
0
2
1
0
1
2
1
1
2
2
1
0
1
0
1
0
1
1
1
1
0
1
1
1
1
0
1
0
1
7
2
1
0
1
0
1
2
1
0
2
2
0
2
1
0
1
1
2
0
1
0
0
1
0
0
1
0
1
1
0
2
0
0
1
0
1
1
2
3
1
0
2
1
1
2
0
0
1
1
0
0
2
2
1
1
1
2
1
2
0
1
2
1
0
2
2
0
1
2
1
1
1
2
0
0
2
0
2
0
1
0
1
0
2
1
1
0
1
2
2
1
1
1
0
1
0
3
1
1
0
0
3
2
0
1
1
0
1
1
1
2
0
2
1
1
3
2
2
0
2
0
1
0
2
1
1
0
1
1
1
1
1
0
0
1
1
1
1
1
1
3
1
1
1
1
1
2
1
2
1
0
0
1
1
0
0
2
0
1
0
1
1
1
0
1
1
1
0
1
1
0
0
2
2
2
1
0
1
1
1
1
2
0
2
0
1
0
0
1
2
0
0
2
2
0
1
1
3
1
2
2
1
1
0
1
1
1
2
1
2
2
0
2
2
1
1
1
1
1
0
2
1
1
0
0
0
0
0
2
0
0
1
0
1
2
2
1
1
1
1
1
1
0
2
0
1
1
2
0
1
1
1
0
1
1
0
1
2
1
0
1
0
0
1
0
1
1
2
1
2
2
0
1
2
0
1
0
0
2
1
1
0
0
1
0
1
1
1
1
1
1
1
2
1
0
1
1
1
1
2
2
1
1
0
1
0
1
0
2
0
2
0
1
2
1
0
1
2
1
1
0
1
0
2
1
1
1
1
2
2
2
2
0
1
0
1
1
0
0
1
1
0
1
0
2
1
0
2
0
0
0
0
2
0
1
0
3
1
1
1
0
1
3
2
0
1
0
1
1
1
1
1
0
1
0
1
1
1
0
1
0
2
2
1
2
1
1
1
1
1
0
1
1
1
2
2
0
0
1
1
1
1
2
0
1
1
0
0
1
0
0
1
2
1
0
2
1
1
1
0
0
0
1
1
1
2
2
1
1
0
0
1
1
0
1
1
2
0
0
0
1
1
2
2
0
0
2
1
2
1
0
1
1
2
0
0
1
1
0
1
1
2
2
1
2
0
0
0
0
1
0
0
0
2
1
1
1
0
1
2
1
1
4
0
1
0
0
0
2
0
2
2
2
1
1
1
1
2
0
1
0
1
2
0
1
1
1
1
2
1
1
0
1
1
2
1
1
2
2
1
1
1
2
1
1
0
1
0
1
1
0
0
3
3
1
1
1
1
1
2
0
1
1
0
1
1
2
0
0
0
2
1
1
0
2
0
0
1
0
0
1
1
1
0
1
1
1
1
1
2
2
0
1
0
0
1
0
2
1
1
2
1
2
1
0
1
0
1
0
1
0
0
2
0
1
1
1
1
0
1
1
2
2
2
1
2
1
2
2
1
1
1
0
0
2
2
1
1
0
0
0
1
2
1
1
0
2
0
1
0
0
0
3
0
2
1
1
1
2
0
2
1
2
0
1
1
3
2
1
1
1
0
2
0
1
1
1
0
1
2
2
2
2
0
1
0
2
0
0
1
1
0
1
0
1
0
0
1
1
0
0
1
0
0
0
0
1
2
1
1
1
0
0
0
0
1
1
1
0
1
1
1
1
1
1
2
2
1
0
2
2
0
6
1
1
3
1
1
1
0
1
1
0
0
0
2
0
0
1
1
1
4
0
0
0
0
1
2
0
2
1
1
2
2
1
1
2
1
1
2
1
1
0
2
1
2
0
2
1
1
1
0
2
0
0
2
1
2
1
4
2
1
1
1
1
1
1
2
4
1
2
1
2
2
1
1
1
1
1
2
1
2
1
1
1
2
1
0
1
0
1
0
1
1
1
1
0
1
1
1
1
0
0
1
0
1
0
1
0
1
1
2
1
0
1
0
2
1
1
0
0
0
2
0
0
0
1
1
1
1
2
1
0
1
0
0
1
4
0
0
0
2
1
2
2
0
1
1
0
2
1
0
0
0
1
0
0
0
2
2
1
4
0
2
0
0
1
2
0
2
1
1
2
0
1
0
1
2
2
2
0
1
2
1
2
1
1
1
1
1
2
2
1
1
1
0
0
0
0
1
1
2
1
1
1
0
0
1
1
2
1
1
0
0
2
1
0
2
1
1
1
0
1
2
0
1
1
0
0
1
2
0
1
2
2
1
1
2
0
1
1
1
1
0
1
2
1
2
1
0
1
1
1
1
1
2
1
0
2
0
0
0
2
1
1
2
1
1
2
2
2
1
1
1
0
1
1
2
0
4
0
2
1
1
1
0
1
0
2
1
0
1
2
0
0
1
1
0
0
3
1
1
0
2
2
2
0
2
2
1
1
1
1
2
2
1
1
1
0
0
3
2
1
1
1
2
1
2
0
2
1
1
2
1
2
2
1
0
1
0
1
1
1
0
1
1
1
1
0
0
1
1
0
1
2
2
2
0
1
1
2
1
2
0
2
1
0
1
2
0
1
2
1
1
1
1
1
1
1
1
1
2
1
1
0
0
1
0
2
0
1
2
2
0
2
2
0
1
2
1
0
1
1
0
1
1
1
2
0
0
1
2
1
2
2
1
1
0
0
1
0
1
1
1
0
1
2
0
1
0
2
3
1
0
1
0
1
0
1
0
2
1
0
0
2
1
2
1
1
2
1
1
1
1
3
0
1
1
0
0
2
1
1
2
2
0
0
1
1
1
2
2
1
1
0
1
0
0
1
2
1
1
0
2
1
1
2
2
1
0
1
1
1
1
1
1
0
2
0
0
0
2
2
0
1
2
2
1
1
2
1
0
2
0
2
2
2
2
1
2
1
0
1
1
1
2
1
3
1
1
0
0
1
2
2
2
1
1
1
1
1
1
0
2
1
1
2
2
0
2
3
1
1
2
1
1
0
2
0
0
0
1
2
1
1
2
1
1
1
0
1
1
0
0
1
1
1
0
1
1
1
1
1
1
1
2
1
0
1
1
1
2
1
0
0
1
2
1
1
1
0
1
1
1
1
1
0
1
0
0
2
2
4
1
4
2
1
1
1
2
1
2
1
2
1
2
1
0
1
2
1
2
2
1
1
0
1
1
2
2
1
0
0
0
1
2
1
1
1
0
1
2
1
0
1
1
1
0
0
1
0
0
1
0
1
1
2
1
2
2
1
0
1
0
2
1
1
1
1
1
1
1
0
2
0
0
1
0
1
1
1
1
2
1
1
1
0
1
0
1
2
1
1
1
2
2
1
1
0
1
1
1
1
2
0
1
1
2
1
1
2
1
2
1
0
1
1
1
2
1
0
1
1
1
2
0
2
1
1
0
1
1
1
1
2
1
1
1
1
1
0
1
1
1
1
0
1
0
1
0
1
0
2
1
2
0
1
0
0
2
1
1
1
1
1
0
1
3
0
0
0
1
2
2
0
1
2
2
1
0
0
2
1
2
1
1
1
1
2
1
1
2
0
1
1
2
0
1
1
2
1
0
1
1
1
1
1
2
2
2
1
1
1
2
1
0
2
1
1
1
0
0
2
1
0
1
0
1
2
2
0
1
1
1
2
1
0
1
1
0
1
1
2
1
1
0
0
0
1
1
1
1
0
2
0
1
1
0
1
0
2
0
1
1
0
0
0
1
2
1
2
0
0
1
1
1
1
1
2
1
1
1
0
1
1
1
1
1
1
1
2
0
1
1
1
1
1
2
0
1
1
1
2
1
1
1
1
2
0
1
0
1
1
2
0
1
1
2
2
1
0
1
2
2
1
1
1
1
1
0
0
2
1
2
2
2
2
1
0
1
1
1
1
1
1
2
1
1
0
0
2
0
0
1
2
0
0
0
2
2
1
0
1
2
1
2
0
1
1
1
1
1
1
2
1
1
2
2
2
1
1
0
1
2
1
1
2
1
1
1
1
0
1
3
0
0
1
1
0
1
0
1
1
1
1
1
0
1
0
0
1
2
0
0
1
2
2
0
2
1
1
1
0
1
0
1
2
1
1
1
0
1
1
0
0
1
1
0
0
1
1
0
2
1
1
0
2
1
2
0
1
1
1
0
2
1
0
1
0
1
2
2
1
2
2
1
1
2
2
0
1
1
1
2
1
1
1
0
1
1
1
0
1
1
1
1
3
0
0
0
1
0
2
1
0
1
1
1
1
3
1
1
2
2
0
1
1
0
0
2
1
2
1
2
0
1
2
1
1
0
1
2
1
0
0
1
2
1
2
2
2
2
0
1
0
1
1
1
1
0
0
1
3
1
0
1
1
0
0
1
1
1
0
1
1
1
1
1
2
2
0
2
1
1
1
1
2
1
2
1
2
1
1
2
0
0
2
2
0
0
2
1
0
0
2
2
2
1
0
2
1
1
1
1
1
2
1
1
2
2
2
2
0
2
1
1
0
1
1
1
2
0
1
1
1
1
0
0
1
0
1
1
0
2
1
1
2
2
0
1
0
0
1
1
1
1
1
1
1
1
1
0
1
0
1
1
1
0
0
1
2
0
0
1
1
0
0
2
1
2
1
0
1
1
0
1
1
1
1
0
2
2
1
1
1
1
0
1
2
1
1
1
1
1
2
0
1
1
0
2
0
1
1
1
1
0
1
1
1
2
1
1
0
2
2
1
1
1
2
0
1
0
1
1
1
1
1
1
1
2
1
0
0
3
1
1
1
0
1
1
0
2
1
1
0
2
1
0
2
1
2
1
2
1
1
2
1
1
0
1
0
1
2
0
1
2
2
1
1
2
2
1
0
0
2
0
1
2
1
1
1
1
1
0
1
1
1
1
0
1
1
2
1
2
2
0
1
1
0
1
0
0
1
1
1
0
1
1
2
2
1
2
1
2
1
1
1
0
0
0
2
2
2
0
1
0
1
1
1
1
0
0
2
0
1
0
1
1
1
0
0
1
1
1
1
2
1
1
1
0
1
2
2
1
1
2
0
1
0
1
2
1
0
2
2
0
2
1
3
0
1
0
1
2
1
2
1
0
1
1
2
1
0
0
2
2
2
0
1
0
1
2
2
0
2
0
1
0
1
0
1
0
1
0
0
1
0
1
0
0
0
2
2
1
2
0
0
0
1
1
0
0
1
2
2
2
1
2
1
2
2
0
1
1
1
3
1
2
1
1
0
1
1
1
1
1
0
1
1
2
2
1
0
1
1
2
0
2
2
1
3
2
0
3
1
2
0
2
0
2
1
1
1
0
0
0
0
3
2
3
1
1
1
0
1
2
1
2
1
0
0
2
0
1
2
0
1
1
1
1
2
0
1
1
2
2
1
0
1
1
1
0
3
1
1
2
1
1
0
0
1
0
2
0
1
0
2
0
1
1
1
2
0
1
0
1
3
1
1
1
1
0
2
2
1
0
2
0
0
1
2
1
2
0
1
0
3
3
1
0
1
0
1
1
0
0
1
1
1
2
2
1
1
1
2
2
2
1
1
1
1
1
1
2
1
0
0
2
2
0
1
0
0
0
2
2
0
2
1
1
2
1
2
2
1
0
1
0
1
0
1
0
1
1
1
1
1
1
1
0
0
2
1
1
1
1
2
1
2
1
1
1
2
1
1
1
2
1
2
1
0
1
0
0
2
2
0
1
0
2
2
1
1
1
1
2
1
1
1
2
1
0
0
1
2
0
0
0
1
1
0
1
0
0
1
1
0
1
1
1
0
0
0
1
0
1
0
1
1
2
3
1
1
0
5
0
0
1
1
0
1
0
1
1
1
0
0
1
0
1
0
2
2
2
1
1
0
1
2
1
1
1
1
1
0
1
0
1
1
1
0
2
1
1
1
0
1
2
1
1
2
1
1
0
1
1
1
1
0
1
3
1
1
0
0
0
0
1
2
1
0
1
1
2
1
1
1
1
0
2
1
1
1
0
0
0
0
0
1
1
0
1
1
1
1
0
2
1
2
1
1
2
1
1
1
0
1
1
1
0
1
0
1
2
1
1
0
1
0
1
2
1
1
0
1
1
2
0
0
1
0
2
1
1
1
1
0
1
1
2
1
2
1
1
1
1
1
2
2
0
1
2
1
3
2
1
1
1
1
2
1
2
1
3
0
0
2
1
1
1
2
1
0
0
0
0
1
0
0
0
2
1
1
0
2
1
2
1
0
0
0
1
2
0
1
1
2
1
1
1
1
1
1
2
2
2
2
1
0
2
2
2
2
0
2
1
1
1
1
2
0
0
4
1
1
1
2
1
1
2
1
1
0
1
1
1
0
2
1
2
1
1
1
0
1
1
0
2
2
1
1
2
2
1
2
0
2
0
2
1
1
0
1
0
0
2
2
1
2
1
1
2
1
1
1
0
0
1
1
2
1
1
2
0
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
0
5
2
1
0
1
0
1
2
1
2
1
1
1
1
0
0
1
0
1
2
0
1
2
1
0
1
1
2
0
2
1
2
0
0
2
1
0
1
1
0
1
1
1
0
2
1
3
1
2
0
1
2
0
1
2
2
0
0
1
2
2
1
1
1
1
0
2
0
1
1
1
0
2
1
1
2
0
2
2
1
2
2
3
1
1
1
2
0
0
1
0
4
2
0
0
2
2
1
0
1
0
0
1
0
1
2
1
0
1
1
0
1
1
1
1
1
1
1
1
1
2
2
2
1
1
0
1
0
1
1
2
0
1
1
0
1
1
1
1
0
1
1
1
2
2
0
0
0
1
0
2
1
1
1
2
1
1
1
1
2
0
2
0
0
1
0
0
1
0
1
3
2
1
2
1
2
2
1
1
1
0
0
2
1
0
1
2
1
1
0
1
1
0
2
1
0
0
0
0
1
2
0
2
1
1
1
0
0
2
0
2
1
1
0
1
1
2
2
1
0
1
0
2
1
1
2
1
1
1
0
2
0
2
0
2
2
1
2
1
2
0
0
0
1
2
1
1
0
1
1
1
2
2
2
1
2
1
2
0
0
1
2
0
3
1
0
1
0
2
0
2
2
2
2
0
1
0
3
1
2
1
1
1
0
2
0
1
1
1
0
2
0
1
2
0
0
0
1
1
0
1
2
2
2
2
1
1
1
0
2
0
0
0
3
1
1
1
0
1
1
1
1
1
1
0
0
0
1
1
0
0
0
1
1
1
0
2
1
2
1
0
0
1
2
1
0
2
1
1
1
1
1
1
1
2
0
2
0
1
1
1
1
1
1
0
1
2
2
1
0
0
1
0
1
2
0
1
0
2
1
1
0
2
1
1
1
1
0
1
1
2
2
1
1
1
0
2
1
1
0
1
1
1
0
2
0
0
2
1
0
1
0
1
0
1
1
1
1
1
1
0
1
1
0
0
1
1
0
1
0
1
1
1
1
1
1
3
1
0
0
1
2
1
2
2
2
1
2
1
1
1
1
1
1
0
1
1
1
1
0
0
2
1
2
1
2
1
0
2
0
1
1
0
1
1
1
1
2
1
2
0
0
2
0
2
2
0
1
2
1
0
2
1
1
1
0
2
2
1
2
1
0
2
0
1
1
1
1
1
1
1
1
1
0
0
0
1
1
1
1
0
1
1
1
1
1
2
2
0
2
3
0
1
1
1
0
1
1
1
2
0
1
0
2
1
2
1
1
1
1
1
1
0
1
2
2
0
0
1
4
2
2
1
2
1
2
3
2
0
2
1
1
0
1
1
1
0
2
2
1
1
0
1
1
1
1
2
1
0
2
1
2
2
0
2
2
2
0
0
1
2
1
2
1
1
1
1
1
0
1
2
0
1
0
1
0
0
1
2
1
0
2
0
1
1
2
0
0
1
1
3
0
1
1
2
2
1
0
0
1
0
0
0
3
0
0
2
1
2
0
1
1
2
0
0
1
2
0
0
0
0
1
2
1
1
0
2
0
0
1
1
0
1
1
0
1
3
1
0
1
0
2
0
1
1
0
0
2
0
0
1
1
1
1
0
0
0
2
0
2
1
0
0
1
1
2
2
2
2
1
1
2
1
1
0
0
1
2
1
1
1
1
1
0
0
1
2
1
1
1
1
1
1
1
1
1
0
1
1
3
0
2
2
1
1
1
0
1
0
1
2
2
1
2
0
0
0
1
0
0
0
1
1
0
0
1
1
0
0
1
1
1
1
0
0
1
2
2
1
0
2
0
1
1
0
1
1
1
0
1
0
1
1
1
1
2
2
0
2
1
1
0
0
1
0
1
2
4
0
2
0
1
1
0
1
2
0
1
1
1
2
0
2
1
2
1
1
1
0
2
1
1
0
1
1
1
0
0
0
0
1
1
1
1
1
2
1
1
0
0
1
1
0
0
1
0
2
2
0
1
0
2
0
1
0
1
2
1
2
1
0
1
0
1
1
2
1
0
1
0
0
1
2
2
1
0
1
2
1
1
1
1
0
1
0
1
2
1
1
0
0
1
0
2
1
1
1
0
1
1
1
1
1
0
2
1
1
2
2
1
2
0
0
1
2
1
0
2
3
0
2
2
2
1
1
1
1
2
1
1
2
1
1
1
2
1
1
0
1
2
2
0
2
0
1
1
1
0
1
1
1
1
0
1
1
2
1
1
0
1
0
0
2
1
1
2
1
0
1
2
2
1
0
2
2
0
1
0
2
1
1
2
2
0
1
0
1
0
0
0
0
2
0
2
1
1
0
0
1
1
2
0
0
0
2
0
0
1
1
1
0
0
0
1
1
0
1
1
0
1
0
1
1
1
1
0
0
2
2
2
1
0
1
1
0
1
0
1
0
2
0
1
0
1
2
2
3
2
0
1
1
1
2
1
0
1
0
4
0
1
1
1
1
1
1
0
1
0
1
1
1
0
0
1
0
0
1
1
0
1
2
1
0
1
2
0
1
1
2
3
1
2
0
0
0
0
1
0
1
1
1
0
1
0
2
1
1
0
0
2
2
1
1
2
0
2
2
0
1
0
1
1
1
1
1
0
2
2
2
1
0
1
1
0
0
0
2
1
1
1
1
2
1
1
0
1
2
0
1
1
0
1
0
1
1
0
1
1
1
1
1
1
0
1
0
1
2
1
1
0
0
1
1
0
0
0
2
0
1
1
1
1
1
0
2
0
2
1
1
1
1
1
1
1
0
0
0
2
0
1
0
1
0
0
2
1
0
2
0
1
1
1
2
1
1
1
1
1
0
2
2
1
2
1
2
1
0
2
0
0
0
0
0
1
2
1
0
2
0
1
2
2
1
2
1
0
1
2
1
1
0
2
1
0
3
3
1
1
0
0
1
1
1
0
0
1
0
1
0
1
0
2
1
1
0
2
1
1
1
0
0
0
1
1
0
1
2
2
0
1
1
1
1
2
0
1
1
1
0
0
2
2
1
3
1
0
1
2
0
1
1
2
0
1
2
0
2
0
1
1
2
0
1
0
0
1
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
2
1
1
0
0
1
2
1
1
1
2
1
2
0
1
2
2
2
1
1
2
1
0
1
0
0
1
0
2
1
2
1
0
2
1
1
3
0
1
1
2
1
1
0
1
1
1
1
2
1
1
1
0
1
1
0
1
0
0
0
2
2
2
0
1
1
0
1
2
0
0
1
2
1
0
1
0
1
0
1
2
1
1
1
1
1
1
0
0
0
0
0
0
0
0
2
2
2
1
1
1
2
0
1
1
2
1
2
0
0
0
1
1
2
1
1
0
1
0
0
0
1
0
2
1
0
1
0
1
1
0
0
0
1
1
1
0
1
2
2
0
0
1
0
1
2
2
2
2
1
1
1
1
2
1
0
0
1
2
1
1
1
0
1
1
2
1
0
2
1
1
1
2
1
1
1
3
1
2
1
1
2
2
1
1
1
1
1
1
1
0
2
1
1
2
0
0
1
1
1
3
1
0
1
1
0
1
1
2
0
1
1
5
2
1
1
1
1
0
0
1
2
2
0
1
0
1
1
2
2
0
2
0
0
1
2
1
1
1
0
1
0
2
2
1
1
1
0
1
1
1
2
1
1
2
1
0
1
0
2
2
2
2
2
0
0
0
0
0
1
1
1
2
0
0
1
1
0
2
1
2
0
0
1
0
2
1
2
1
2
1
2
0
0
4
0
1
0
1
2
2
1
1
1
1
1
1
2
0
0
1
0
1
1
0
1
1
1
2
2
0
1
1
1
0
0
0
1
0
1
1
2
2
0
1
1
1
2
1
0
2
1
1
1
0
6
1
1
0
1
1
2
1
2
1
1
1
0
1
2
1
1
0
0
2
0
1
1
1
1
1
1
2
1
1
0
1
1
1
1
1
1
2
1
1
1
0
0
0
1
1
2
1
2
3
1
0
1
1
1
1
2
1
1
2
0
1
1
1
2
3
1
0
2
1
0
0
2
1
1
2
2
1
1
1
2
3
1
0
1
1
1
1
0
2
1
0
0
1
1
1
1
2
0
0
0
1
1
2
2
1
1
2
1
1
4
1
1
2
1
1
2
0
2
2
1
0
1
0
0
0
1
0
0
2
1
2
2
1
1
2
0
0
2
1
1
1
3
2
1
1
0
1
1
1
2
2
1
1
1
0
1
1
1
1
1
1
0
1
0
0
1
2
0
1
2
0
0
2
0
2
1
1
2
1
0
1
2
1
1
2
0
1
1
0
2
1
0
1
0
2
0
0
1
1
1
1
2
0
2
0
0
1
0
1
0
1
1
0
0
2
2
1
1
1
0
0
0
1
0
0
1
0
1
1
0
2
1
0
1
0
1
1
0
1
1
2
0
2
2
0
1
1
2
0
0
0
1
1
1
0
0
0
0
0
1
1
0
0
2
0
1
1
0
2
1
2
1
0
1
0
0
1
1
0
0
0
0
1
2
1
1
1
0
1
1
0
1
1
0
2
0
0
1
0
2
1
0
1
0
2
1
0
0
1
1
1
1
1
1
0
1
1
1
1
0
1
1
1
2
2
0
2
1
1
1
1
1
0
0
2
2
0
1
1
1
0
2
0
1
0
1
1
5
2
1
0
1
0
1
0
1
1
0
0
1
0
2
0
2
2
1
1
1
2
1
2
0
2
1
2
2
1
2
1
0
1
0
1
1
2
2
0
1
1
0
1
2
2
1
1
0
2
1
1
2
1
0
1
1
0
1
1
1
1
1
1
1
1
0
2
1
2
1
1
2
1
0
0
0
1
0
1
1
0
1
1
2
2
1
1
2
0
1
2
1
0
1
0
1
2
1
1
2
2
1
1
1
1
1
1
0
0
0
1
0
0
0
1
0
0
1
1
0
2
1
2
0
2
1
2
1
0
1
0
1
0
0
1
1
1
0
1
2
1
1
1
2
1
2
0
0
2
1
0
2
0
2
1
2
0
1
0
2
1
1
0
0
1
2
2
0
0
1
2
0
1
1
0
1
1
2
2
0
1
1
2
0
1
2
1
1
2
1
0
2
1
3
2
2
2
1
1
0
1
0
0
1
1
1
1
1
1
1
0
0
2
1
2
2
0
0
1
1
1
0
1
0
2
0
1
1
2
1
1
2
2
0
0
2
0
2
2
1
0
2
0
0
2
1
1
1
1
2
2
1
1
1
1
1
0
0
0
1
2
1
0
1
2
0
2
1
1
2
1
1
2
0
1
1
2
2
1
1
1
0
1
0
0
0
0
2
3
1
0
2
0
0
1
0
1
0
0
0
1
1
1
6
1
1
1
1
2
1
1
1
2
0
1
1
1
0
1
0
1
1
1
2
1
0
0
2
2
2
0
0
2
1
2
1
2
1
0
3
1
0
1
1
1
1
2
1
2
0
1
2
1
1
1
1
1
1
2
0
1
0
1
0
2
2
2
1
0
0
1
1
1
1
1
0
1
0
1
3
2
0
1
1
1
1
0
1
0
2
2
1
1
2
0
1
1
0
0
2
1
0
2
0
1
0
1
0
1
1
1
0
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
3
1
1
1
2
2
1
0
0
1
1
1
0
0
4
0
1
1
1
0
0
1
1
0
1
2
1
2
1
1
1
1
2
2
1
1
1
0
0
2
0
0
1
1
1
0
0
1
0
2
1
0
0
0
1
1
0
0
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
0
1
1
1
0
2
1
2
0
1
1
2
0
1
2
0
1
2
1
1
1
2
0
0
0
1
0
0
1
1
1
1
0
0
1
2
1
0
0
1
1
2
1
2
0
0
0
0
2
1
1
1
1
1
2
0
1
0
1
2
1
1
1
1
2
2
1
3
2
1
2
0
0
2
1
0
1
1
1
1
0
1
1
1
1
0
0
2
0
0
0
1
0
1
2
1
2
2
2
0
0
2
1
2
1
0
1
2
1
1
2
1
1
0
1
0
0
0
2
1
1
2
0
0
1
2
1
2
1
1
1
1
2
1
2
1
0
1
1
1
2
0
0
0
2
0
1
2
1
0
2
1
1
1
0
1
0
0
2
0
0
1
3
0
0
1
0
0
1
2
2
0
2
2
1
2
0
1
0
1
1
1
1
0
0
1
0
1
0
0
0
2
2
1
2
0
1
1
2
0
1
1
1
0
0
2
2
1
1
1
0
1
0
0
0
1
2
1
1
2
2
1
1
2
0
1
0
1
1
0
1
1
1
1
2
2
1
2
2
1
2
1
0
1
0
0
1
0
0
0
2
2
1
0
1
2
0
0
0
0
2
1
2
0
0
1
1
0
1
1
0
1
1
0
1
0
2
1
2
2
2
1
2
0
0
1
1
0
0
0
1
1
0
1
0
1
1
0
1
0
1
1
1
1
2
0
2
1
1
0
2
1
2
1
1
1
1
0
0
2
1
0
1
0
1
2
0
0
2
1
0
2
1
0
1
1
1
2
0
1
1
1
1
2
1
1
1
0
1
0
2
2
1
1
1
2
1
2
2
1
0
0
0
2
2
1
0
1
1
1
2
1
1
0
2
2
2
1
1
1
1
0
1
0
1
1
0
1
2
1
2
0
1
2
1
2
1
1
1
0
1
2
1
2
1
0
1
1
2
1
0
2
2
1
1
1
2
0
0
1
2
1
0
1
1
0
1
1
1
2
1
3
2
1
1
2
0
2
2
1
1
0
1
1
0
1
0
1
1
0
0
1
1
2
0
1
1
0
2
0
0
0
0
2
1
0
1
1
1
0
0
1
1
1
1
1
1
0
6
0
1
1
0
2
1
1
0
1
1
2
1
0
1
1
1
1
1
2
0
1
2
0
1
0
1
0
1
2
1
2
1
1
1
1
2
0
1
0
0
1
1
2
1
0
0
1
1
0
2
1
1
0
0
0
2
1
1
1
1
2
1
1
2
2
0
1
0
2
1
2
1
1
1
0
2
1
0
1
1
1
2
0
0
2
1
1
1
1
1
1
0
1
0
2
1
1
1
1
0
1
0
1
2
0
1
2
1
1
1
1
0
1
2
1
0
2
0
1
2
0
1
0
2
2
2
2
2
2
1
0
2
1
2
2
0
1
2
2
2
1
2
1
1
0
0
2
0
0
0
1
1
3
0
2
0
2
1
0
0
1
0
1
1
0
2
1
2
1
0
0
1
0
1
2
1
2
2
1
1
2
3
1
1
0
1
1
1
0
1
2
2
1
2
1
2
0
1
2
1
2
1
1
2
1
1
0
1
2
2
2
0
0
2
1
1
1
1
0
1
0
1
1
2
1
1
2
2
0
2
0
1
0
2
1
1
1
2
0
0
2
1
2
0
0
2
0
0
1
2
1
1
0
1
1
1
2
1
2
0
1
1
1
1
1
0
2
1
3
1
0
1
1
2
0
1
2
3
2
0
0
2
1
1
0
2
0
0
2
1
1
1
2
2
1
1
1
0
1
2
0
0
0
2
1
0
1
1
0
1
1
0
2
2
1
0
2
1
0
1
1
1
1
0
1
2
1
2
0
0
0
2
1
0
1
0
0
1
1
2
6
0
1
1
1
1
1
1
1
1
1
1
2
1
2
0
2
1
0
0
2
0
0
1
1
0
0
1
1
1
0
0
1
1
1
2
2
1
1
1
2
2
1
1
1
1
2
2
2
0
0
1
1
1
0
2
0
2
0
0
0
1
0
1
1
1
1
2
1
2
0
1
3
0
1
1
0
2
1
0
0
1
1
2
0
1
0
1
0
1
0
2
1
1
1
0
1
1
0
1
1
0
1
0
1
1
2
1
2
2
1
1
2
2
2
2
2
1
2
1
1
1
1
2
0
2
0
1
0
0
0
1
1
1
2
2
1
1
1
2
1
0
0
0
1
0
1
1
0
0
3
5
1
2
1
1
1
0
0
0
2
2
0
1
1
2
0
1
0
1
0
2
2
0
2
1
1
0
1
2
1
1
1
1
2
0
1
1
1
1
2
1
2
0
2
0
0
1
2
1
2
2
0
0
1
1
0
0
1
2
0
1
0
4
1
1
1
1
1
2
1
2
0
0
0
1
1
1
1
1
0
1
1
2
1
1
1
0
1
2
1
1
2
0
1
1
2
1
1
2
0
1
0
1
2
1
0
2
1
0
0
1
0
2
2
1
1
1
1
0
3
0
1
2
0
1
2
0
1
2
0
1
1
1
1
2
2
0
2
2
2
1
1
1
1
0
0
1
1
0
1
1
2
2
0
0
1
2
0
1
1
1
1
1
2
0
1
1
1
2
1
2
2
1
1
0
2
1
2
2
1
1
1
1
0
0
1
0
0
2
1
1
1
2
2
1
0
1
1
1
0
1
1
2
1
1
2
1
2
0
1
2
0
1
1
1
0
0
1
1
1
1
4
0
0
0
1
2
1
1
0
1
0
1
1
1
0
1
1
2
2
0
2
1
2
1
0
1
1
1
1
1
1
1
2
0
1
2
2
0
3
0
3
1
2
1
1
1
1
1
1
1
1
1
1
0
1
0
0
2
1
1
2
1
0
0
0
2
1
0
0
1
1
2
2
1
1
1
0
0
1
2
1
1
0
2
2
0
1
3
1
1
2
1
1
0
0
0
1
2
1
1
0
0
1
1
0
0
1
1
1
1
1
0
2
0
1
1
2
1
0
1
2
1
2
0
1
2
2
0
1
0
0
1
1
1
2
1
0
1
0
1
0
1
2
1
2
2
0
1
0
0
0
0
1
2
0
1
0
2
0
1
0
1
0
1
0
1
0
0
2
2
0
1
0
3
2
0
0
1
1
1
1
0
2
1
0
1
2
1
0
1
0
2
0
1
0
1
1
1
0
2
0
2
1
2
0
2
2
2
2
1
1
1
1
1
1
1
0
1
0
1
1
1
1
1
0
0
1
0
1
2
1
0
1
0
0
1
0
0
1
1
0
2
0
1
0
1
2
0
2
0
0
1
2
1
1
1
0
1
1
2
1
1
0
1
1
1
0
1
1
1
1
2
2
2
2
1
8
1
0
1
1
1
1
0
1
1
1
0
1
1
0
0
1
0
2
0
2
0
1
0
2
1
1
0
2
2
0
1
1
1
0
1
1
1
1
2
1
0
1
0
0
0
1
0
1
1
1
1
0
0
1
2
1
0
0
1
0
0
0
2
1
0
2
0
2
1
1
0
1
2
1
2
1
1
2
2
1
1
1
0
1
1
1
2
1
1
1
2
1
0
0
2
2
1
0
1
0
1
1
1
0
1
0
0
2
0
1
1
0
1
3
1
2
4
0
0
1
1
4
0
0
0
1
0
1
2
0
2
2
0
1
1
1
1
2
2
1
0
2
2
1
1
1
3
1
0
2
0
0
2
1
1
1
0
1
1
2
0
1
1
0
1
2
1
2
2
1
1
0
2
2
0
1
1
2
1
2
1
1
0
1
0
6
0
2
1
0
1
1
1
1
6
1
0
2
2
1
1
1
2
0
1
0
2
1
0
0
0
2
2
2
1
1
0
2
1
0
0
1
1
1
1
1
1
1
0
1
1
0
1
0
1
1
0
1
0
0
0
1
0
0
0
1
1
2
1
1
0
0
1
0
2
1
0
1
1
1
0
2
1
0
1
2
0
3
1
0
1
1
1
0
0
1
1
2
1
0
1
1
1
0
1
0
1
1
1
2
2
1
0
2
0
1
1
0
1
0
0
2
1
0
0
1
2
0
0
1
1
2
1
0
1
1
1
2
1
2
1
1
2
2
0
1
1
0
1
0
0
1
2
1
1
1
0
1
1
1
0
2
2
2
0
1
2
1
0
1
2
1
0
0
1
1
1
0
0
1
2
2
1
1
0
1
1
1
1
0
1
0
1
2
0
2
1
1
2
2
1
2
2
1
2
1
1
2
1
2
1
1
1
1
0
2
1
2
2
0
1
0
0
1
1
0
2
1
0
1
1
0
2
1
0
0
1
2
1
1
0
2
0
1
2
2
0
1
2
1
1
0
1
2
1
2
0
0
1
1
3
2
1
0
1
1
1
0
0
1
2
2
2
1
2
1
1
1
1
0
0
1
1
0
1
2
0
1
2
1
1
1
1
2
0
0
1
1
2
1
2
1
1
1
1
0
1
1
1
1
1
1
2
2
1
1
1
1
0
1
0
0
1
1
2
1
1
1
0
1
0
0
2
1
1
1
2
3
2
0
2
2
1
2
1
0
2
0
1
0
1
2
1
2
1
0
1
1
1
0
1
1
2
1
2
1
1
1
1
2
1
1
0
1
0
1
1
2
1
1
1
1
1
0
0
0
1
1
1
1
2
0
1
1
2
1
1
1
2
1
1
0
0
1
1
1
0
1
1
0
2
0
2
0
0
1
0
1
1
1
1
1
1
0
1
2
1
1
4
0
1
1
0
1
1
2
0
1
1
0
1
2
1
0
2
1
1
3
1
2
1
2
2
2
0
1
2
1
1
2
1
2
2
0
1
1
2
0
0
3
2
1
2
1
1
1
1
0
0
2
1
2
1
1
2
5
2
1
2
2
2
1
1
0
0
2
1
1
1
1
1
2
1
0
0
2
2
2
1
1
1
2
0
1
1
1
1
2
0
0
2
1
1
2
1
2
1
1
1
1
0
1
0
2
1
0
0
1
1
1
0
1
0
2
1
2
0
0
0
1
1
1
0
2
2
0
0
1
1
0
0
2
0
1
0
1
0
1
0
0
0
2
2
0
0
0
1
1
1
1
2
2
2
0
1
2
1
0
0
1
1
0
1
3
1
2
1
2
1
2
1
0
1
0
2
1
1
1
0
2
1
0
0
1
1
0
1
1
2
1
1
0
2
1
2
1
2
2
1
0
1
1
2
1
1
2
1
1
2
2
1
0
1
2
1
0
0
2
1
1
1
1
0
0
1
0
1
1
1
0
2
0
0
0
2
2
2
0
2
0
2
1
1
1
0
0
2
2
0
0
0
2
3
1
1
1
2
1
0
1
0
2
0
2
2
1
2
0
0
1
1
0
1
1
1
1
0
1
2
1
2
1
1
1
0
0
1
1
0
2
1
1
2
1
0
1
1
2
1
1
1
0
1
1
1
1
1
1
1
0
1
2
1
0
2
1
1
2
1
0
2
2
2
2
1
2
0
1
1
1
0
0
2
1
1
1
0
1
1
2
1
0
0
1
0
0
2
1
0
0
0
1
1
1
2
1
1
0
1
1
0
1
0
1
0
0
3
0
1
1
1
1
2
0
1
1
1
0
0
0
1
2
0
2
0
0
2
0
1
2
1
2
1
1
2
1
2
0
1
2
1
0
1
1
0
1
1
0
1
2
2
1
1
1
1
1
0
0
1
1
1
0
1
1
1
2
1
1
0
0
0
4
2
0
1
0
1
1
2
0
1
1
1
0
1
1
0
0
2
2
0
0
1
1
1
0
1
1
0
1
1
2
1
1
0
1
1
1
1
2
0
1
1
1
1
2
0
1
1
0
1
2
0
2
2
1
1
1
2
0
1
1
1
1
1
2
0
1
1
1
2
0
2
1
2
0
0
0
2
1
0
1
1
0
0
1
0
2
3
1
2
0
2
2
0
1
2
2
2
2
0
2
1
0
0
1
1
1
1
1
2
1
2
7
0
0
1
1
0
2
1
2
1
2
2
2
2
1
0
1
1
2
2
1
1
0
2
2
1
1
1
2
0
0
1
0
1
2
1
0
2
1
1
1
2
1
1
2
2
1
1
1
3
1
2
0
1
1
1
1
0
2
1
0
1
1
1
0
0
0
1
1
1
1
0
2
2
1
2
2
2
1
1
1
1
1
0
2
1
1
1
1
1
0
1
2
0
1
0
1
0
3
1
1
1
2
3
2
2
1
2
1
2
1
1
2
1
0
1
1
0
1
0
0
0
1
1
0
2
2
2
0
1
0
1
2
0
3
2
1
0
2
1
0
2
1
1
0
1
1
1
0
1
0
1
0
1
1
1
2
0
1
2
2
0
0
1
2
2
2
0
1
1
1
0
2
2
1
1
1
0
1
1
2
1
0
0
0
0
1
0
1
2
1
2
2
2
1
1
0
0
0
1
0
1
0
1
0
0
1
2
2
2
1
1
2
1
1
1
1
0
1
2
2
2
1
0
2
1
2
1
2
1
0
2
0
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
0
2
2
1
2
1
0
1
1
0
1
1
2
1
1
1
1
0
1
0
1
2
2
1
0
0
2
0
1
2
1
1
1
0
0
1
1
1
0
0
1
1
0
2
2
0
2
2
2
1
2
2
2
2
1
1
1
0
0
1
1
0
1
2
2
1
0
1
2
0
1
0
2
1
0
1
1
0
2
2
0
0
0
2
1
0
1
1
2
1
2
1
2
1
0
2
1
1
1
2
2
1
1
2
1
1
2
0
1
0
0
0
2
2
1
1
0
3
1
0
1
0
0
1
1
1
2
1
2
0
0
0
1
1
1
0
2
1
0
1
1
2
4
2
1
2
2
2
2
0
0
1
1
1
1
0
1
1
1
2
2
1
1
1
0
2
1
1
1
2
0
0
1
1
1
0
2
1
1
1
1
2
1
1
1
0
1
1
1
1
1
1
0
1
1
1
0
0
0
0
1
1
0
1
1
1
0
0
1
4
2
1
0
2
0
0
3
1
2
2
1
0
1
1
1
1
1
1
0
0
2
0
1
2
1
2
1
0
1
2
1
2
1
2
3
1
1
1
0
1
1
0
1
2
0
1
1
2
0
1
1
1
1
1
1
1
1
4
2
1
1
0
1
1
2
0
0
1
2
2
1
0
0
0
1
1
2
2
0
2
0
2
0
1
2
2
2
2
1
1
3
1
1
1
0
1
1
1
1
2
1
1
2
1
2
2
1
1
1
1
1
1
0
1
2
0
1
2
1
0
1
1
1
0
1
0
0
1
0
0
1
1
1
1
2
0
0
2
1
1
2
1
1
0
1
0
0
1
1
0
1
2
1
1
1
1
1
2
1
0
1
0
1
0
1
1
2
2
0
3
1
0
2
1
1
11
0
2
1
1
1
1
1
1
1
1
1
1
0
1
1
0
1
0
1
0
0
1
1
1
1
1
2
2
2
1
0
1
1
1
2
0
1
1
2
1
0
2
2
1
0
1
2
0
2
1
0
0
1
0
2
0
1
1
0
1
2
1
1
0
1
2
2
1
2
0
1
1
3
2
0
2
1
1
2
1
1
1
0
1
0
0
1
2
2
1
1
2
1
1
1
2
1
1
2
0
1
1
0
1
1
1
2
0
1
2
1
2
0
1
0
0
2
1
0
1
3
1
2
0
1
2
1
0
1
0
1
1
2
1
1
1
1
1
0
2
0
1
1
1
0
1
1
1
2
1
0
1
0
1
2
1
0
0
2
1
1
0
0
0
1
2
1
1
1
0
1
1
0
0
1
0
1
0
1
1
1
1
0
1
0
0
2
1
0
1
1
0
2
2
1
1
1
1
1
1
1
0
1
3
0
1
1
0
1
1
1
0
1
1
2
1
1
1
1
0
0
0
1
2
2
1
2
0
0
1
1
0
1
2
1
2
1
1
0
0
2
1
1
1
0
0
0
0
0
0
1
2
0
0
2
2
1
1
2
0
0
1
0
1
2
2
1
1
1
1
4
1
1
1
1
1
1
0
1
1
1
0
2
1
2
1
1
1
2
1
1
0
1
2
1
0
1
1
0
0
1
1
1
0
1
0
1
1
2
2
0
0
1
0
1
0
0
2
1
2
1
0
2
1
1
1
1
1
0
1
2
1
2
1
2
1
2
2
2
1
0
0
1
1
0
1
1
2
1
1
2
1
2
0
1
1
1
2
1
1
1
0
2
2
1
2
0
2
0
1
0
2
1
0
0
2
1
0
2
0
0
1
2
1
0
1
2
1
1
1
2
1
0
1
1
2
1
1
0
0
0
1
2
1
1
2
2
2
0
1
0
2
2
1
1
1
0
1
1
1
2
2
2
1
1
1
2
1
2
2
1
1
1
2
1
0
1
0
1
1
2
1
0
1
0
1
1
0
1
1
2
0
2
1
2
1
0
0
0
1
0
0
0
1
1
2
1
1
1
2
0
1
1
0
1
0
0
0
0
1
1
1
1
2
0
0
1
2
1
0
1
1
1
1
1
2
2
2
1
2
2
1
2
1
0
0
2
0
0
1
1
2
2
1
0
1
0
1
1
1
1
1
2
0
2
1
0
0
1
0
0
1
1
2
3
0
1
2
2
1
0
0
1
0
0
2
1
2
2
2
2
2
1
0
1
1
1
1
2
0
1
1
1
1
1
1
1
1
0
1
1
0
0
1
0
1
0
1
0
0
0
1
2
1
1
0
0
2
1
1
1
0
1
1
2
1
0
2
0
2
1
2
0
1
2
2
2
1
2
0
1
1
1
7
1
2
0
1
1
1
1
1
1
2
0
1
2
1
1
2
1
1
0
1
0
2
1
0
0
1
2
0
1
1
1
1
0
1
1
1
1
0
1
0
1
1
1
1
1
0
2
2
1
1
2
1
0
1
1
1
1
1
0
0
1
2
1
2
1
1
1
0
1
1
1
1
0
0
1
0
1
2
1
1
1
2
0
1
1
1
1
1
1
0
1
0
1
0
1
2
1
1
0
1
2
0
0
3
0
2
0
1
1
1
1
1
1
2
1
2
0
1
0
0
0
1
0
1
1
1
0
0
1
1
1
0
1
0
2
1
1
1
1
0
0
1
2
0
2
2
1
1
2
2
3
1
0
2
2
2
1
2
0
1
2
2
1
2
1
0
1
0
0
2
2
0
0
1
0
2
1
2
1
1
1
2
1
1
1
0
1
1
1
0
1
0
2
1
0
2
2
1
0
1
1
1
2
0
1
1
1
1
2
3
1
1
1
1
1
2
1
2
0
2
1
0
0
1
1
0
2
1
0
1
3
0
0
1
0
2
1
1
0
0
0
1
0
0
1
1
0
1
1
1
0
1
1
0
1
0
1
0
0
1
1
1
0
2
2
1
3
0
0
1
0
0
1
1
0
1
1
0
1
0
1
1
0
1
0
0
0
1
0
0
1
2
1
0
0
0
1
2
1
1
1
1
2
0
0
1
1
1
0
0
0
2
1
1
0
0
1
1
1
1
1
1
1
0
1
3
0
0
1
1
0
2
1
1
0
1
1
2
2
1
1
2
2
1
1
1
1
1
1
2
2
1
0
1
2
1
2
0
1
2
1
2
0
0
1
1
2
0
0
0
1
1
1
0
1
1
0
1
1
2
0
1
0
1
1
1
0
1
1
2
2
0
0
1
1
1
3
2
1
1
1
1
1
0
0
1
1
0
2
0
2
1
1
2
1
0
0
0
1
1
2
1
0
1
1
2
1
1
0
1
1
2
2
2
2
1
1
0
0
2
0
2
1
0
1
1
0
1
0
0
1
1
1
1
1
1
1
2
2
0
1
1
0
1
0
1
0
1
1
0
0
1
1
2
0
2
2
1
0
0
0
0
1
2
1
2
0
0
1
2
1
1
1
2
2
0
2
1
1
1
0
1
1
2
0
1
2
1
1
0
1
0
1
1
1
2
0
1
0
0
1
1
1
1
1
0
2
1
1
0
0
1
2
1
2
0
3
0
2
1
1
2
0
2
2
0
0
1
1
0
2
0
0
1
1
0
1
1
1
0
1
0
1
0
1
1
1
2
1
1
2
0
1
0
0
0
3
2
1
1
2
1
1
2
0
0
1
1
1
0
2
0
3
0
1
2
1
0
1
1
1
2
0
2
4
1
0
1
2
1
1
0
2
1
1
1
2
2
1
2
0
1
1
1
1
1
1
1
2
0
0
2
1
0
1
0
1
1
0
1
0
1
0
1
1
1
2
0
0
2
2
1
1
1
1
1
1
2
0
1
1
0
0
2
0
0
1
2
1
0
0
2
0
2
1
1
2
1
1
0
2
2
0
2
2
1
2
2
2
1
1
1
0
1
1
2
0
0
2
1
1
0
2
2
0
2
0
1
0
0
1
0
2
1
2
1
1
2
2
1
1
1
1
1
1
1
1
2
0
1
2
1
1
1
1
2
1
1
1
0
1
2
1
1
1
0
0
1
1
1
0
1
1
0
2
2
1
0
2
0
2
1
2
1
2
1
1
0
1
0
2
2
0
1
1
2
0
1
1
2
1
1
1
1
3
1
1
0
1
1
0
1
1
1
2
1
1
0
1
1
0
1
0
0
1
0
2
1
2
0
1
1
1
1
2
1
0
1
1
1
1
0
1
0
0
0
0
0
2
1
1
1
0
1
1
1
0
2
2
1
1
1
0
1
2
0
1
0
2
2
1
2
2
2
2
2
1
0
0
0
1
1
1
2
0
0
1
2
2
1
0
1
1
0
1
0
1
0
2
0
1
1
0
0
0
1
3
1
1
2
1
1
1
2
6
1
2
0
1
1
1
2
1
1
2
1
0
2
1
1
1
1
1
1
2
1
2
1
2
1
1
1
1
1
1
0
0
2
2
2
0
2
1
1
1
0
0
2
1
1
1
0
1
1
0
1
0
0
1
1
2
1
0
2
1
1
2
1
1
1
2
2
0
2
1
2
0
2
1
1
1
2
0
2
0
0
2
1
1
1
0
2
1
0
1
1
2
1
0
2
1
1
1
2
0
2
2
1
0
0
3
1
0
2
1
2
1
1
2
1
2
2
2
0
0
2
1
2
0
2
0
0
0
1
1
0
0
1
1
2
1
2
1
0
0
0
1
1
0
1
1
1
2
0
3
2
1
1
1
1
2
0
1
1
1
1
1
1
1
3
2
0
2
1
2
0
0
0
2
1
1
1
2
1
2
1
1
1
1
0
0
2
1
2
1
1
1
1
2
0
0
1
2
1
1
0
0
1
1
1
0
1
0
1
0
0
0
1
0
1
1
1
1
0
1
2
1
1
1
0
1
1
0
1
2
1
1
1
1
1
1
2
0
1
0
1
1
1
1
0
1
3
0
2
2
2
0
0
1
1
1
2
1
1
1
2
1
1
0
2
2
1
2
0
2
2
2
4
3
1
2
0
0
1
1
1
1
1
0
1
0
1
1
1
0
0
0
1
2
0
0
0
2
2
2
1
0
1
2
0
1
0
1
1
1
0
1
0
0
2
1
1
1
1
2
1
1
0
0
1
2
1
1
1
0
0
1
1
3
1
2
1
2
1
0
0
2
2
2
1
1
2
1
0
0
0
1
1
1
0
0
1
1
1
2
2
2
2
0
1
0
1
2
0
1
0
2
1
1
0
1
1
0
1
2
0
1
2
0
1
1
0
2
1
4
2
1
0
2
0
2
1
0
1
1
1
0
1
2
2
1
1
1
1
1
0
0
0
5
1
1
1
0
0
0
1
1
2
1
1
2
1
2
2
1
0
1
1
1
1
0
0
1
1
0
2
2
1
1
0
0
0
1
1
1
0
0
1
1
0
2
1
1
1
1
2
0
1
1
0
1
1
2
0
1
2
2
0
2
0
0
1
1
2
2
1
2
1
1
1
1
1
1
0
0
1
0
1
2
0
1
1
0
0
1
1
1
0
0
0
0
1
1
1
2
1
1
1
1
1
1
2
0
0
0
1
1
1
2
1
1
0
2
1
1
1
0
1
2
2
1
0
0
0
1
2
0
1
1
2
1
2
0
0
1
2
0
1
2
1
0
0
2
1
0
0
1
0
1
0
1
1
3
0
0
0
1
1
0
1
0
2
1
1
2
0
0
0
1
0
0
1
0
1
3
0
1
1
2
1
1
1
1
2
2
1
2
0
1
2
2
2
1
1
1
1
1
1
2
2
1
0
0
1
0
2
2
1
1
1
1
0
0
1
0
1
1
2
1
0
2
1
0
0
1
1
1
2
1
1
2
0
2
0
1
1
0
0
1
0
0
0
0
3
0
1
0
1
1
2
1
0
0
1
1
1
3
1
0
1
1
2
1
2
0
2
0
0
0
2
0
2
2
2
1
2
1
2
0
1
2
1
1
2
1
0
0
0
0
2
1
1
1
1
1
1
1
0
1
0
0
1
2
0
1
2
1
1
1
0
0
1
1
1
1
2
1
1
2
1
0
0
1
1
0
0
0
1
1
0
1
1
1
2
1
0
1
0
1
0
2
1
2
1
0
1
1
1
3
0
0
0
1
2
1
1
1
0
0
1
1
2
2
2
1
1
0
0
2
1
0
1
2
1
1
1
1
4
1
2
0
1
2
1
2
0
1
1
0
1
1
0
2
1
0
1
0
3
0
1
1
2
1
1
2
0
1
1
0
1
1
0
1
1
0
1
1
2
0
2
0
1
2
1
0
1
1
0
1
2
0
2
0
1
2
2
0
1
0
1
1
1
2
0
1
1
2
1
2
0
1
1
1
0
1
0
0
0
3
1
1
0
2
1
1
2
2
1
0
1
0
0
1
0
1
1
0
2
2
0
1
1
1
0
1
1
1
1
1
2
0
0
0
1
1
0
2
1
1
1
2
0
1
1
0
2
2
1
0
0
2
0
1
1
0
1
2
0
2
1
0
2
1
3
1
1
0
0
1
1
0
0
0
0
1
2
0
0
1
1
1
1
1
0
1
2
0
0
1
1
1
0
2
0
1
2
0
1
1
1
1
1
1
1
1
0
1
0
1
1
2
0
3
0
1
1
1
1
1
2
1
0
1
2
1
0
2
1
1
0
0
1
1
1
0
0
2
1
1
2
1
2
2
0
1
1
0
3
2
1
1
2
0
0
0
2
1
0
1
1
1
2
0
1
1
1
0
1
2
2
1
0
2
1
3
1
0
1
0
1
1
1
0
0
2
1
2
2
0
2
1
0
1
1
4
1
1
2
0
1
1
0
1
2
0
1
0
0
1
0
2
1
1
2
1
1
1
1
0
0
1
1
1
0
1
2
1
1
2
1
0
0
2
1
1
0
1
1
0
1
1
1
0
0
0
2
2
2
1
1
0
0
1
1
1
1
2
2
2
0
1
2
1
1
0
2
1
0
1
2
1
2
1
0
1
1
0
1
0
0
2
0
2
2
2
0
0
2
2
3
0
0
1
2
1
0
1
1
1
2
2
1
1
1
0
0
2
1
1
1
0
1
1
1
0
2
2
1
2
1
1
2
1
0
1
0
1
1
1
2
0
1
1
1
1
0
1
2
0
1
1
3
0
1
1
0
2
1
2
0
0
3
2
0
0
2
0
1
0
1
1
0
2
0
2
2
1
1
2
1
2
0
1
1
1
1
1
2
0
1
1
1
1
2
0
2
0
2
2
2
0
1
2
1
0
1
1
1
0
2
1
1
1
0
1
1
2
2
0
1
0
1
1
0
1
0
2
2
0
1
1
1
1
1
0
0
1
0
0
0
2
0
2
1
7
1
1
1
1
0
2
0
2
1
1
0
0
1
0
1
2
2
0
1
2
2
1
2
2
0
1
1
1
0
1
1
1
0
1
0
0
1
1
1
1
1
1
2
1
0
0
2
1
2
1
0
1
1
1
0
0
0
1
1
1
1
0
2
1
1
1
1
1
2
0
1
0
1
2
1
0
0
1
1
1
0
0
0
2
1
1
0
0
1
3
1
1
1
1
2
0
1
0
0
1
0
0
1
1
0
1
0
2
0
1
0
2
1
0
1
2
1
1
0
1
1
1
0
0
0
1
1
1
0
1
1
2
1
1
1
0
0
1
1
0
1
0
1
2
0
0
2
1
2
1
1
1
1
0
2
0
2
0
1
1
2
1
1
0
0
1
1
2
1
1
2
2
2
0
2
1
0
1
1
1
2
1
1
1
2
0
1
2
2
1
1
0
0
2
0
1
1
1
1
0
1
1
1
2
1
0
1
1
1
2
2
0
1
3
2
1
0
0
1
1
1
1
1
0
1
2
1
0
0
0
2
0
1
0
1
0
1
1
1
1
0
1
0
1
1
2
1
2
1
0
1
0
1
2
0
0
0
1
0
0
0
1
2
1
0
1
1
0
0
0
1
2
0
1
1
1
1
1
2
1
1
0
0
1
1
2
0
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
2
1
2
0
1
1
1
1
2
2
1
1
1
2
0
1
1
0
1
1
1
0
1
1
1
1
1
1
2
5
1
0
1
2
2
0
1
1
0
0
1
0
1
0
0
1
0
0
2
2
1
1
0
1
1
0
2
1
1
2
0
1
2
0
2
1
1
0
1
2
1
2
1
1
0
0
0
2
1
1
0
1
0
1
0
1
1
1
2
1
1
0
2
1
3
2
1
1
1
2
0
2
0
4
0
2
2
1
0
1
0
1
1
0
1
1
2
1
2
0
0
0
2
1
0
1
1
0
1
1
2
2
0
1
0
0
1
1
1
2
1
0
1
0
1
0
1
1
1
1
0
1
2
1
2
1
0
1
0
0
1
0
1
1
1
2
1
1
1
1
1
0
1
2
2
1
1
0
2
1
1
2
0
2
1
0
1
0
2
2
1
1
1
1
0
1
0
1
2
2
0
1
2
1
0
1
0
1
1
1
1
0
2
1
0
1
2
0
2
1
1
2
2
1
1
2
1
2
0
1
0
0
2
2
1
0
0
2
1
1
1
0
0
2
2
1
0
1
1
1
2
0
0
1
1
2
2
1
2
2
0
1
1
0
1
1
1
2
1
2
0
1
2
1
0
1
1
1
0
1
0
3
0
0
1
1
1
1
0
2
1
2
2
0
0
0
0
2
0
1
0
2
0
2
0
1
1
0
1
0
1
1
2
1
1
2
0
2
0
1
1
1
0
1
2
2
0
1
1
0
0
1
2
1
2
2
1
1
0
1
1
0
1
2
1
0
1
2
0
0
0
1
2
0
2
1
1
0
2
1
1
0
0
2
0
1
1
0
1
1
0
1
0
1
0
0
0
2
0
1
1
1
1
2
0
1
1
1
1
2
1
1
1
1
1
2
1
1
1
0
1
2
0
0
1
2
1
1
2
2
1
1
0
1
1
1
1
0
1
1
1
1
1
2
1
0
1
1
1
1
0
1
1
2
1
0
2
1
1
1
1
0
0
0
1
1
2
0
0
1
2
1
2
2
1
0
1
0
1
1
0
1
1
2
1
1
2
1
1
1
0
1
0
0
1
1
1
2
1
2
2
0
1
1
2
1
1
1
0
1
1
1
1
2
1
1
0
1
1
0
0
1
1
0
1
0
1
0
2
2
2
1
2
1
1
1
1
1
5
2
0
1
0
1
1
1
0
1
1
1
1
0
1
2
2
2
1
3
1
1
1
1
0
0
1
2
2
1
2
0
1
1
0
1
2
2
1
1
1
2
2
1
1
1
0
1
0
0
0
1
2
1
0
1
0
0
1
0
0
1
2
1
0
1
1
1
1
1
1
0
2
1
0
1
2
2
0
1
1
2
1
0
1
2
2
1
1
1
2
2
1
0
0
0
0
3
1
1
1
0
0
1
1
1
2
0
1
1
1
0
0
1
1
0
2
1
1
1
2
2
1
0
3
0
1
2
2
1
0
0
2
1
0
2
1
0
2
1
2
0
1
1
2
1
2
2
2
1
0
1
1
1
2
2
2
1
1
2
1
1
1
0
2
1
1
2
1
0
1
1
1
1
1
1
0
1
0
0
0
1
1
2
1
0
1
1
1
1
1
1
0
2
1
2
0
0
1
0
2
1
0
1
0
1
1
1
0
1
2
0
2
0
0
2
0
1
1
1
1
3
1
1
1
1
1
0
1
1
1
2
0
0
2
1
1
2
1
1
1
0
2
1
1
0
0
1
1
2
1
0
1
1
1
1
1
0
2
1
0
2
1
0
0
0
1
1
0
1
0
0
1
1
2
1
2
3
0
1
2
1
2
1
2
2
1
0
1
2
1
1
1
1
1
1
1
2
0
0
2
0
0
1
1
0
2
0
1
2
2
2
0
0
1
0
2
1
0
0
0
1
0
0
1
0
1
2
1
0
1
2
1
2
2
0
1
1
1
2
1
1
0
1
1
1
1
2
1
1
1
1
0
2
0
2
0
1
1
0
1
0
1
1
0
1
1
2
0
0
1
0
0
0
1
2
1
1
2
0
1
2
1
1
1
0
1
2
1
1
1
2
1
1
1
2
2
1
0
0
2
1
1
0
2
0
2
1
2
1
0
2
1
0
2
1
1
2
0
0
0
2
2
2
1
2
0
0
0
0
0
0
0
0
1
0
0
1
0
2
3
1
0
0
0
2
1
1
0
2
3
1
1
2
1
1
0
2
2
0
2
1
1
0
1
2
0
0
2
0
3
0
0
0
2
0
1
2
1
1
0
2
2
1
0
1
1
1
1
1
3
1
0
0
0
2
1
1
3
0
2
0
0
2
5
3
1
2
2
2
1
0
1
1
1
1
0
1
0
2
2
0
0
0
1
1
1
0
2
1
0
1
1
1
0
1
0
1
1
1
0
1
2
1
1
2
1
1
1
2
0
0
0
1
1
4
1
0
0
1
2
0
1
2
0
0
1
1
2
2
1
1
1
1
2
1
1
0
1
0
1
3
1
0
0
1
2
2
0
0
1
1
0
1
1
2
0
0
1
2
1
1
0
2
1
2
1
1
0
1
2
2
2
0
3
2
0
2
3
1
0
2
0
0
0
3
0
1
2
1
2
1
2
1
1
0
1
0
1
1
0
0
1
0
1
0
1
2
1
1
1
2
0
0
0
1
0
1
1
1
1
1
1
2
1
0
2
2
2
2
1
0
1
1
1
1
1
1
1
1
1
0
0
2
1
0
2
0
0
1
1
1
1
1
2
1
1
1
1
1
0
1
2
2
2
1
2
1
1
2
2
0
1
0
2
2
0
2
1
1
2
1
0
0
0
2
0
1
1
1
1
0
0
2
1
1
0
1
0
2
0
1
2
1
1
0
0
0
2
1
0
1
1
1
1
1
0
0
2
2
1
0
1
1
1
1
2
0
1
2
1
1
1
2
2
2
1
0
1
0
0
1
1
0
1
1
0
0
0
1
1
2
1
1
1
0
0
2
2
1
1
0
0
2
1
1
0
3
0
1
1
2
0
2
2
1
4
1
1
1
0
3
1
1
2
1
1
1
0
1
1
1
1
1
1
1
2
1
2
0
1
2
2
2
1
0
0
2
2
2
1
1
1
1
0
0
0
1
1
0
0
0
1
1
1
2
2
0
0
1
1
1
1
0
0
0
0
1
2
1
2
0
0
2
0
2
1
1
1
2
2
1
1
0
2
0
1
1
1
0
1
0
1
1
0
1
0
2
1
0
1
1
1
0
1
1
0
1
1
1
1
1
1
2
1
0
1
0
1
0
0
1
1
1
1
1
0
1
0
1
1
0
2
1
1
0
1
1
1
0
1
1
0
1
1
0
1
1
0
1
0
1
1
2
1
1
1
2
0
1
1
1
2
1
1
0
2
0
1
0
1
2
2
1
2
2
2
1
1
1
2
1
0
1
2
0
0
1
0
2
1
2
1
2
0
2
2
3
1
2
1
1
1
1
0
2
1
1
0
1
2
0
2
2
1
2
2
2
0
1
1
0
1
2
1
0
0
1
0
1
0
1
2
0
0
1
1
1
0
1
0
0
2
0
0
2
0
2
1
1
2
2
2
2
1
1
0
1
2
0
1
0
2
1
0
1
1
0
0
1
2
1
1
2
1
1
1
0
1
0
2
0
0
1
3
0
1
1
1
2
2
0
1
2
1
2
1
0
1
1
0
2
1
1
1
0
1
0
1
1
1
1
1
1
1
0
1
0
0
1
0
1
1
1
2
1
1
1
2
1
2
1
0
1
2
0
1
0
0
0
1
1
0
2
1
1
2
1
2
1
2
1
0
0
1
1
1
0
1
1
2
2
1
2
1
1
1
2
2
1
2
1
0
1
1
1
0
1
1
1
0
0
1
1
1
1
0
1
1
1
2
2
1
0
0
1
1
2
2
0
1
1
0
2
3
1
1
0
0
1
0
0
2
2
1
1
1
0
1
1
1
0
1
1
2
1
0
1
2
0
2
1
2
0
2
2
2
1
0
1
2
0
2
1
1
2
2
2
2
2
2
2
1
0
1
1
1
2
1
2
1
0
0
1
0
0
0
1
0
1
2
1
2
2
1
1
0
1
0
0
1
1
1
1
1
1
1
1
0
2
1
2
1
1
1
1
3
2
0
2
1
1
0
4
0
2
2
1
2
1
0
1
2
1
0
1
1
0
2
1
1
1
2
1
0
2
2
1
1
0
1
2
0
2
1
2
1
0
1
2
0
1
1
0
1
0
1
0
2
0
1
1
2
3
1
0
2
0
1
0
0
1
2
1
0
2
0
1
1
0
0
1
2
2
0
0
0
3
2
0
0
2
0
1
1
1
0
1
0
0
1
2
1
2
1
2
1
1
1
0
1
0
2
7
0
0
2
0
0
2
0
1
1
2
0
0
0
1
1
2
0
0
1
1
0
1
2
1
2
1
0
1
1
0
1
2
2
2
2
1
2
2
1
0
2
2
2
1
1
2
1
0
1
2
1
0
2
1
1
1
0
0
1
0
0
2
1
1
2
2
1
1
0
1
2
0
2
0
1
0
1
0
1
2
1
1
0
0
2
1
1
1
1
0
0
1
0
1
0
1
0
1
0
1
1
0
1
1
2
2
1
1
0
2
1
1
1
2
1
1
0
2
1
1
2
2
1
0
0
1
0
1
1
1
1
1
1
2
0
0
1
1
1
0
1
2
1
2
1
1
0
1
0
0
2
0
0
0
2
0
2
2
1
0
1
1
0
0
1
2
2
1
1
0
0
1
1
1
0
0
2
2
2
1
0
1
0
1
2
1
0
0
1
0
2
2
1
2
0
1
0
0
0
0
2
1
0
0
1
0
2
0
0
1
1
1
1
1
0
0
1
1
1
2
2
2
1
0
2
0
0
1
0
0
1
1
1
1
0
0
0
1
1
1
1
1
1
1
2
1
0
1
1
1
1
1
1
1
0
0
1
0
1
1
1
0
1
0
0
1
3
0
2
0
0
1
5
2
2
1
0
1
2
1
2
1
1
1
2
1
0
1
2
2
0
2
2
0
1
0
2
2
0
0
1
1
1
2
2
2
1
1
1
1
3
2
1
0
2
2
1
1
2
1
1
0
2
1
2
0
1
3
1
1
1
1
1
2
2
1
1
1
1
1
2
1
0
1
1
2
0
1
0
1
2
0
0
2
0
2
1
1
1
2
1
2
2
0
1
1
2
2
1
1
2
0
1
0
1
1
0
0
0
1
0
2
2
2
1
0
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
0
2
1
1
2
1
0
0
2
1
0
1
1
2
2
1
1
1
1
2
2
1
1
1
0
0
0
1
2
1
1
1
1
0
1
0
0
2
2
2
0
1
0
2
2
1
2
0
1
0
0
0
0
0
1
1
1
0
1
1
3
2
1
1
1
1
1
1
1
0
1
1
0
0
2
0
0
1
1
2
0
2
1
0
0
1
1
1
2
1
1
0
0
2
1
1
1
1
1
1
2
2
1
2
2
1
1
0
1
0
1
1
1
1
1
1
0
0
1
1
1
0
0
1
1
0
1
1
0
2
1
1
2
2
0
1
1
0
0
1
2
0
2
1
0
1
1
0
0
1
1
1
1
2
0
0
2
0
0
1
3
1
0
0
0
0
1
1
1
1
2
1
0
0
0
0
2
0
0
0
1
1
1
1
2
2
1
2
0
1
1
1
1
1
0
15
1
1
1
1
0
1
2
1
1
0
0
0
1
1
2
2
2
0
2
1
1
2
1
0
2
2
2
0
1
1
2
2
2
2
1
2
1
0
1
0
0
2
0
1
0
2
5
0
1
2
1
0
2
1
1
1
0
2
1
0
0
2
1
1
1
1
1
0
0
2
0
0
2
2
0
2
1
1
2
1
2
1
0
1
2
0
2
0
0
0
1
1
1
2
1
1
0
2
1
0
1
1
1
2
1
0
1
1
1
1
0
2
1
0
2
1
2
0
2
2
1
1
0
1
0
2
0
1
2
1
1
1
1
0
1
0
5
2
2
1
2
1
1
1
2
1
1
0
1
1
1
1
2
2
0
2
0
1
2
1
1
1
1
2
1
2
1
2
1
1
3
1
1
1
2
1
1
0
1
2
0
1
1
0
1
0
0
2
1
2
0
1
0
1
0
1
1
0
1
1
1
0
0
1
1
1
1
2
2
1
1
1
1
1
0
1
1
0
2
2
1
0
0
1
1
1
1
1
1
1
3
1
1
1
1
0
1
1
1
1
0
2
0
1
1
1
0
0
0
2
0
1
0
1
1
0
0
1
1
1
1
0
1
2
1
2
0
2
1
2
1
0
1
3
0
1
2
1
1
2
2
1
0
2
0
1
3
2
1
1
1
2
1
2
1
0
1
0
0
1
2
1
0
1
3
1
0
2
0
0
0
0
2
1
1
2
0
2
1
2
1
1
1
0
1
1
1
2
1
1
1
1
1
1
0
1
1
0
1
1
1
1
1
2
2
1
1
1
1
3
0
0
1
2
0
0
0
2
1
1
1
0
1
1
2
1
1
0
1
2
1
0
2
0
0
1
2
0
1
1
0
0
1
1
1
1
0
1
0
1
0
0
2
0
1
2
2
1
1
0
0
0
0
2
0
2
1
0
2
2
0
2
1
1
0
2
0
0
1
2
0
1
1
1
0
0
1
1
1
0
2
0
1
1
1
1
3
2
1
0
1
2
1
2
1
1
1
1
0
1
1
0
1
1
1
1
1
0
0
1
1
0
0
1
2
1
0
2
2
1
0
1
0
1
1
2
1
1
0
1
2
1
1
1
1
0
1
0
3
1
1
2
1
1
2
1
0
0
1
1
3
2
1
1
0
2
2
1
1
1
0
1
1
2
2
0
0
0
1
0
0
1
2
1
1
0
2
0
0
1
2
1
1
2
1
0
2
2
0
1
2
2
1
1
0
1
1
0
1
0
1
1
1
1
0
1
0
1
0
1
0
1
0
0
0
1
0
2
1
0
0
0
2
0
1
0
2
2
1
1
0
0
1
1
2
1
0
0
1
1
0
3
0
2
2
2
2
2
2
0
2
2
1
2
2
0
1
0
2
0
1
1
2
0
1
1
1
1
1
2
1
1
0
1
0
2
0
0
0
2
0
2
0
1
2
2
1
0
0
2
2
1
2
2
1
0
1
1
0
0
0
1
2
1
0
1
1
1
3
0
0
0
1
1
0
1
1
0
2
1
0
1
1
1
2
2
0
2
1
1
2
1
1
1
1
1
0
1
1
2
2
0
1
2
1
1
0
0
2
2
1
0
0
1
1
0
2
0
2
2
1
2
1
0
1
1
2
0
0
0
1
0
1
2
0
1
1
0
1
1
0
1
0
1
1
1
0
0
0
1
0
0
0
2
2
1
0
1
2
1
0
2
2
0
1
1
2
0
0
2
2
0
2
0
1
2
2
0
1
2
2
0
0
0
1
2
0
0
1
1
0
0
0
0
2
2
1
2
0
1
1
4
2
1
1
1
1
2
1
1
2
0
1
1
1
0
2
2
1
1
1
1
1
0
0
1
2
1
2
1
1
1
1
0
0
1
1
1
1
1
1
1
1
0
1
1
0
1
1
2
2
1
2
1
1
1
1
0
2
1
2
1
0
1
1
0
0
0
2
1
0
1
2
1
2
1
1
0
1
2
1
1
1
1
1
1
2
2
1
1
1
2
1
1
1
0
1
1
1
2
0
1
1
1
0
1
0
1
1
1
0
0
1
1
1
0
1
0
2
1
1
1
1
2
1
1
1
1
1
1
2
2
0
1
1
1
1
1
1
2
1
1
2
0
1
2
1
1
1
1
1
1
2
2
2
0
0
1
2
1
1
0
1
1
2
1
1
1
0
1
2
1
2
1
2
0
1
2
1
1
1
1
2
0
1
0
0
0
1
1
0
1
2
0
2
1
2
1
1
1
1
0
1
1
1
1
0
1
2
0
0
1
1
1
1
1
1
1
1
2
0
1
1
2
0
0
1
1
1
1
1
1
0
2
0
1
1
0
2
0
1
2
1
0
1
2
2
0
2
1
2
1
1
1
2
1
0
1
1
0
0
0
1
1
2
2
2
2
2
1
1
1
1
1
2
1
1
0
1
0
2
1
0
0
2
2
0
0
0
0
1
0
1
1
0
2
0
0
1
1
1
2
0
2
1
2
1
0
1
1
0
1
1
1
0
0
0
1
0
1
1
0
1
2
2
0
0
1
1
2
1
0
0
0
1
1
2
0
0
1
1
1
0
2
2
1
0
2
1
1
0
0
1
0
1
0
3
2
0
1
2
1
1
1
1
1
0
1
1
0
1
1
0
4
2
1
1
1
0
2
1
1
0
1
1
1
1
1
0
2
2
0
2
1
0
1
2
1
0
1
1
2
0
1
0
2
2
2
0
1
0
1
1
2
1
0
1
2
0
1
1
1
2
1
0
1
2
1
0
1
2
1
0
0
0
2
0
2
0
2
1
1
0
1
0
1
1
2
1
2
1
0
1
1
1
1
1
1
0
0
1
1
1
2
1
1
0
1
2
2
1
1
1
1
1
0
1
1
1
0
2
0
1
0
1
1
1
1
1
1
0
1
2
0
0
1
1
0
1
0
2
1
1
1
0
2
1
2
1
1
0
1
2
1
0
0
1
0
0
1
2
1
0
0
1
2
1
1
1
0
0
2
1
2
1
1
2
1
1
0
1
1
1
2
1
1
2
0
0
1
1
0
0
1
1
1
1
2
0
2
0
2
1
0
1
0
2
1
1
1
2
1
0
1
2
1
0
1
0
1
2
2
0
0
0
0
1
0
0
2
0
2
2
0
2
1
0
1
1
1
1
1
2
1
1
1
2
0
1
1
0
0
1
1
2
1
2
0
2
1
0
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
2
1
0
0
1
1
1
2
2
1
1
0
2
1
1
0
2
1
2
1
1
1
1
1
0
1
2
2
0
0
1
1
1
1
1
2
1
1
2
1
0
1
1
1
1
1
0
1
2
1
1
1
1
1
1
1
0
1
1
0
2
1
1
1
0
2
2
1
0
1
1
2
2
2
1
1
0
1
1
2
0
1
1
2
3
5
2
1
0
1
0
1
0
1
2
0
1
1
1
2
1
2
2
1
1
0
1
2
1
0
1
1
1
1
1
2
0
1
0
2
0
2
2
1
1
0
1
1
0
0
0
2
0
1
0
1
4
1
1
2
0
0
2
1
2
2
0
1
1
0
0
2
1
0
0
0
0
0
1
1
0
3
1
0
0
0
1
1
0
1
1
3
0
2
1
1
1
2
1
0
2
0
2
0
0
1
1
0
1
1
0
0
0
1
0
0
2
0
1
2
1
0
1
1
0
1
0
0
0
0
0
1
2
1
0
1
2
1
1
1
1
1
0
0
0
1
0
1
1
1
0
1
1
1
1
0
1
1
2
3
2
0
1
0
2
0
1
1
2
1
0
0
1
1
1
2
1
2
1
1
1
2
1
1
1
1
1
1
1
2
2
0
1
1
1
0
1
1
1
0
1
1
1
1
1
1
0
0
0
0
1
1
1
1
1
1
1
0
1
1
2
1
0
2
1
0
2
0
0
1
1
1
1
1
0
1
1
2
0
1
1
2
0
0
1
0
1
0
0
0
1
0
1
2
1
1
2
0
1
3
1
0
2
0
1
2
2
2
0
1
1
0
1
2
1
1
2
0
2
2
0
0
1
0
2
2
1
0
1
2
2
2
0
0
2
1
1
1
2
1
1
1
0
1
1
1
2
1
1
0
0
1
0
0
2
0
1
1
1
2
1
0
1
1
1
0
2
1
0
1
1
0
1
1
1
1
1
1
2
2
1
0
1
0
1
1
2
0
1
1
2
0
0
0
1
1
1
1
0
1
0
1
0
1
1
1
1
2
1
1
0
1
1
0
1
2
1
1
2
1
1
1
1
1
0
0
0
1
1
1
1
1
2
2
1
0
1
1
1
2
0
1
2
2
0
2
1
0
1
2
0
2
0
0
1
1
1
1
1
2
1
1
2
0
1
1
1
1
1
2
1
1
2
2
1
1
1
0
1
0
2
1
1
1
1
1
0
1
1
0
3
2
1
5
1
0
2
2
2
1
1
1
2
0
1
1
1
0
1
1
2
0
1
1
1
1
1
1
1
2
1
2
1
1
0
2
0
2
0
2
1
0
1
2
0
0
1
1
1
0
1
1
0
1
0
2
1
0
0
1
1
0
1
0
0
1
3
2
1
0
1
0
0
1
1
0
1
1
2
1
1
0
1
1
1
1
1
1
1
1
1
0
1
1
1
0
2
1
2
1
2
1
1
1
0
1
2
0
1
1
1
1
2
1
0
0
0
1
2
1
1
2
1
2
0
1
0
1
0
1
2
0
2
2
1
1
2
2
1
1
1
0
2
0
2
1
1
1
0
1
2
1
1
1
2
2
1
1
1
1
2
1
2
1
0
0
0
1
1
1
1
1
1
0
0
1
2
2
1
2
0
0
0
1
1
0
1
0
2
0
2
0
2
0
0
0
1
0
1
2
0
0
1
1
1
2
1
0
1
0
1
0
1
0
2
1
1
2
2
1
0
0
1
1
0
1
2
0
1
1
1
0
0
0
0
2
1
0
1
1
2
0
2
1
2
1
0
1
1
1
1
1
2
1
1
2
2
1
1
0
0
0
1
2
1
1
0
1
0
0
1
1
2
1
1
1
0
1
1
0
0
1
1
1
0
2
1
1
2
1
2
1
1
1
2
1
0
0
1
1
1
4
1
1
1
1
1
2
2
1
1
6
2
0
0
2
1
1
1
1
2
0
1
1
0
1
2
2
0
0
2
1
2
0
0
2
1
1
1
1
0
1
0
1
2
0
2
0
1
0
0
0
0
1
2
1
1
0
2
2
1
2
2
1
2
1
1
0
2
0
2
1
1
2
1
1
1
0
1
0
2
1
1
2
2
0
1
1
1
1
1
1
1
1
1
1
2
2
1
1
0
1
0
1
2
0
0
1
3
1
0
1
0
2
1
0
2
1
0
1
1
1
1
0
0
0
0
0
1
1
0
1
1
1
0
2
0
0
1
0
0
0
2
1
1
1
1
1
1
0
1
1
1
0
0
1
0
1
1
0
0
0
1
0
1
0
1
1
0
1
0
2
0
0
1
2
1
1
1
1
1
2
1
3
1
1
0
0
0
0
0
1
0
1
1
1
1
1
1
2
0
1
1
1
0
2
1
2
1
0
0
1
1
1
1
1
1
1
2
1
1
0
2
2
1
1
2
0
0
0
1
1
1
1
0
1
2
2
1
1
0
1
1
2
1
0
0
0
0
1
1
1
1
0
0
1
1
0
2
2
1
1
2
1
4
1
2
1
0
1
0
1
1
1
0
1
2
0
1
1
1
1
1
0
0
2
1
1
0
1
1
2
1
1
1
1
1
1
1
1
1
0
0
1
1
1
0
2
2
1
2
1
0
1
2
1
1
1
1
1
0
1
0
1
1
2
2
2
0
0
1
0
1
2
1
2
1
0
1
1
1
0
1
1
1
1
1
1
0
1
1
2
2
0
1
0
0
1
1
0
1
0
2
2
1
2
1
0
1
1
0
2
1
1
1
1
2
1
0
2
1
1
1
2
1
1
1
0
0
1
2
0
1
0
0
1
0
0
1
2
1
1
1
1
2
3
0
1
1
1
3
2
1
0
1
0
0
1
0
2
2
2
0
2
1
1
1
0
0
2
1
1
1
2
1
1
1
1
2
1
1
1
0
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
0
1
0
1
2
1
0
0
1
1
0
1
0
0
1
1
1
0
1
2
0
2
0
1
1
1
0
0
1
2
1
1
2
1
0
1
1
1
1
1
2
2
2
0
1
1
0
2
1
1
0
2
1
1
1
1
1
5
1
1
2
2
1
1
1
1
1
1
0
1
1
0
0
1
1
1
2
0
2
0
0
2
1
1
2
1
0
1
2
1
1
1
1
2
2
0
0
2
1
0
0
1
0
1
4
1
1
1
2
2
0
1
2
2
1
0
1
1
1
1
1
1
1
1
2
1
1
2
2
1
0
2
0
1
0
1
2
0
1
2
0
1
2
1
2
0
1
1
0
0
1
2
1
1
0
1
2
1
1
1
1
0
2
1
2
1
0
1
2
1
0
4
1
0
1
0
2
2
1
1
2
0
1
1
1
1
1
2
1
1
1
0
0
2
1
0
2
1
1
2
2
0
2
0
0
0
1
2
0
1
1
0
1
2
1
1
0
0
1
1
0
2
1
0
0
0
0
2
1
1
1
1
1
2
2
0
0
1
1
0
0
0
1
1
1
2
1
2
1
1
1
1
1
2
1
1
0
0
1
0
1
0
0
1
2
1
2
1
1
1
0
1
0
1
1
1
0
0
1
1
2
2
0
1
0
2
1
1
1
0
2
1
1
1
4
1
0
1
0
1
0
0
1
1
1
1
0
2
0
1
1
0
2
2
0
1
1
0
0
2
0
1
1
1
1
1
0
1
2
0
2
2
0
2
1
1
1
1
1
1
0
1
2
1
0
2
2
0
1
1
1
1
1
1
0
1
0
1
1
0
0
0
2
2
0
1
1
1
1
1
1
0
1
0
0
2
2
1
0
0
2
1
1
1
1
2
2
0
1
1
1
1
0
2
2
1
0
2
0
1
0
1
1
1
0
0
2
1
0
1
1
1
0
0
2
1
0
0
1
1
0
2
0
0
2
0
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
0
1
1
1
1
1
0
1
1
1
2
1
0
1
1
1
2
1
1
2
0
1
0
2
1
1
2
1
2
1
0
1
0
0
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
0
0
0
1
2
2
0
2
0
2
4
1
2
1
1
0
0
1
1
0
0
1
1
1
2
1
1
2
0
1
1
2
2
2
1
1
0
1
1
0
2
1
2
2
0
1
1
1
1
1
1
2
0
0
2
0
3
1
1
0
0
0
0
2
0
0
2
1
0
2
1
0
0
1
1
0
1
1
1
1
0
1
2
0
2
1
1
1
2
1
2
1
0
0
0
0
1
0
1
1
0
1
1
1
0
1
1
1
1
1
1
1
0
0
1
0
1
1
2
1
2
1
1
1
1
0
1
0
1
1
2
2
1
2
0
2
1
1
1
2
2
2
1
1
1
0
1
1
2
1
1
1
2
0
1
1
1
0
0
1
1
1
1
1
1
0
1
0
1
0
0
0
1
1
1
1
1
2
2
1
0
1
0
0
0
2
0
1
3
0
1
1
1
2
0
1
0
1
1
3
1
2
1
1
0
0
1
0
0
1
2
0
1
0
0
1
2
1
0
1
2
1
1
1
1
0
2
2
2
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
2
0
1
1
1
2
2
1
1
1
1
1
1
2
1
1
1
0
1
1
2
2
0
2
1
1
2
1
0
0
1
1
0
1
2
1
2
1
1
0
0
0
2
2
2
1
2
1
0
1
2
2
0
1
0
0
1
1
0
0
0
1
1
0
1
1
1
2
1
1
2
2
0
2
1
1
0
0
1
0
0
1
1
0
2
0
0
0
1
2
0
1
1
1
0
1
0
0
0
0
2
2
1
1
1
0
0
0
1
2
1
2
1
1
1
0
2
0
1
1
3
2
1
2
0
1
0
0
1
0
2
1
0
2
1
1
0
0
1
1
1
1
0
0
1
1
3
0
1
0
1
0
0
0
2
1
1
1
2
1
2
1
1
2
0
2
1
0
2
1
1
1
2
0
1
1
1
0
0
0
1
0
0
1
0
1
1
1
1
1
1
1
1
1
2
1
1
1
1
3
1
0
1
2
2
1
1
1
0
0
1
2
0
1
0
0
0
1
1
1
1
1
0
0
1
3
2
1
1
2
1
2
1
1
1
1
0
1
2
1
1
1
1
0
1
1
1
0
1
0
1
1
1
2
0
3
1
2
1
0
3
0
0
1
3
1
1
1
1
1
0
1
2
1
1
2
1
0
1
0
1
2
0
1
1
1
1
1
1
1
1
1
2
1
1
0
1
0
1
1
2
2
0
1
2
2
1
0
0
2
2
2
1
0
1
1
2
0
0
0
0
0
1
2
0
2
1
1
0
1
2
1
0
1
0
2
2
0
2
1
0
0
1
1
1
0
1
2
1
0
2
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
2
2
0
0
2
1
0
2
1
1
0
0
1
2
1
2
0
1
0
1
2
2
2
1
0
2
1
1
0
2
0
1
1
1
1
1
1
0
1
1
2
1
2
2
2
1
0
1
0
0
2
2
1
0
0
1
0
1
1
1
1
2
1
2
2
1
1
1
1
2
1
0
1
1
1
0
1
2
2
1
0
0
0
0
1
0
1
2
1
1
3
2
0
1
1
1
1
0
1
1
1
1
1
1
0
0
2
1
1
1
0
1
2
2
1
1
0
1
2
1
1
2
0
1
1
2
1
2
0
1
1
0
0
1
1
1
0
1
0
0
2
1
0
2
2
0
0
0
0
2
1
1
1
1
0
0
1
0
1
0
0
1
1
0
1
2
0
2
1
0
2
2
2
3
1
2
1
0
1
0
1
0
2
0
1
1
0
0
1
1
2
1
1
2
0
1
1
0
0
0
1
2
2
1
2
1
1
1
1
2
0
1
2
1
0
1
1
0
1
1
0
0
2
1
1
1
1
4
0
1
0
0
1
0
2
1
1
1
2
1
0
0
0
1
1
0
1
2
0
1
1
0
0
2
2
1
0
0
2
1
0
2
0
1
4
2
1
1
0
1
2
0
1
0
0
1
0
1
0
0
2
1
1
2
1
1
1
1
1
1
0
2
2
2
2
0
2
0
2
1
2
0
1
1
1
0
1
3
1
1
0
2
0
1
1
0
1
1
1
0
2
1
2
1
2
2
0
1
0
2
0
0
1
1
1
1
0
0
1
1
1
1
1
2
0
0
0
1
1
1
1
1
1
1
0
2
1
1
1
1
0
1
2
1
1
0
2
1
2
0
0
1
1
1
0
1
0
1
2
2
1
2
1
2
0
2
1
2
1
1
2
0
1
1
2
1
1
0
1
0
2
2
1
0
1
1
0
1
1
0
2
2
0
2
0
1
1
1
1
0
1
1
2
0
0
1
3
1
1
2
1
0
2
0
1
2
2
0
1
1
0
2
0
2
2
1
1
1
1
1
0
1
2
1
1
3
2
0
1
1
1
2
0
0
2
0
2
1
1
1
1
2
1
1
0
0
1
1
2
1
2
1
1
0
1
1
1
2
2
1
2
0
1
1
1
0
1
0
0
0
2
1
2
0
1
1
2
1
2
1
0
1
1
1
2
2
0
1
1
1
0
0
2
0
1
0
1
1
1
1
1
0
1
0
0
2
1
2
0
1
2
1
0
1
2
1
0
1
1
0
0
0
1
0
1
2
0
1
1
2
1
1
2
1
1
1
1
1
1
2
1
0
2
1
0
1
2
1
1
1
1
0
1
0
0
0
1
3
0
1
1
1
1
0
1
1
2
1
0
1
0
2
1
1
1
0
0
0
0
0
1
1
0
0
2
0
1
1
0
2
1
1
1
2
0
1
0
0
1
1
1
1
1
0
0
0
1
1
1
1
0
1
1
1
2
1
1
1
2
2
0
1
1
1
0
2
1
0
1
1
1
1
2
1
0
3
2
1
2
2
1
0
3
1
1
2
0
1
2
1
1
2
1
2
2
1
1
1
1
2
1
1
1
0
0
1
2
1
2
0
0
1
0
2
1
1
0
1
2
1
0
1
2
0
1
0
0
2
1
0
2
0
1
2
0
0
1
1
1
2
2
2
2
0
1
2
1
0
1
2
2
1
2
1
1
0
1
0
0
1
2
0
0
1
2
2
1
1
1
2
1
2
1
0
1
1
0
1
1
1
0
1
1
2
1
1
1
1
2
1
0
3
0
1
0
1
1
1
1
1
2
1
2
1
0
1
1
5
2
2
2
0
1
0
1
1
0
0
0
0
1
1
2
0
1
0
1
2
2
1
1
2
0
1
2
1
3
2
1
0
0
2
1
1
0
1
1
1
0
0
0
1
2
0
2
1
1
1
1
1
1
1
1
0
0
0
1
1
3
2
0
1
1
2
2
1
1
1
0
1
1
3
0
1
1
2
0
1
0
1
1
1
0
0
1
0
1
0
1
0
0
2
1
1
0
0
1
0
1
2
1
1
0
0
2
2
2
1
1
2
1
0
0
2
1
2
1
2
1
0
1
1
0
1
2
1
1
1
1
0
1
1
1
1
2
0
0
0
0
1
2
1
1
1
0
2
1
1
2
2
0
1
0
1
1
2
1
1
1
1
1
2
1
0
0
0
1
1
2
0
1
1
2
1
0
1
0
0
0
2
0
0
1
1
0
1
2
0
2
0
2
1
2
0
1
3
1
1
1
1
1
2
1
1
1
1
0
2
0
1
1
0
0
1
0
2
1
1
1
2
1
1
2
1
1
0
1
1
0
1
1
1
1
2
2
1
2
1
1
2
1
1
1
1
1
1
0
1
1
1
0
2
1
1
1
1
1
1
0
1
0
1
1
1
1
2
0
0
0
1
1
1
1
1
1
2
1
1
1
2
1
2
1
1
2
1
0
1
1
2
1
1
1
0
1
1
1
1
1
1
0
1
1
0
2
2
0
1
1
2
0
1
1
1
0
1
2
0
2
1
2
1
0
0
1
2
1
1
1
2
1
2
1
0
1
1
2
1
1
0
2
0
1
2
1
1
1
1
1
1
1
2
2
0
2
1
0
1
0
2
1
2
0
2
1
1
0
1
0
0
0
1
1
1
0
1
1
0
1
3
0
1
1
1
0
1
1
0
1
1
1
1
0
0
1
0
0
1
2
0
1
1
2
1
1
1
0
1
1
2
1
2
1
2
1
1
1
1
1
0
1
0
1
1
1
1
1
1
1
1
2
0
1
1
0
1
1
1
1
1
0
0
1
1
1
1
2
0
1
0
1
2
1
0
1
0
1
1
1
1
1
2
1
0
1
1
0
1
1
0
1
2
1
1
0
0
2
2
2
1
0
1
1
1
2
2
1
1
0
1
1
1
1
1
1
1
1
2
0
2
2
2
3
1
0
2
2
0
0
1
1
0
1
0
2
1
1
0
2
0
0
1
2
1
1
2
1
1
1
1
0
1
2
0
0
0
0
0
1
0
1
1
2
1
0
2
0
1
0
2
0
2
3
1
1
1
1
0
0
1
1
0
2
2
0
1
3
0
1
1
1
1
0
1
1
2
1
1
0
0
1
0
1
2
2
0
2
2
1
0
1
2
1
2
0
1
2
0
1
2
1
1
2
1
0
1
0
1
1
1
1
0
0
0
1
1
1
1
0
2
2
1
0
1
0
1
0
2
2
0
1
1
1
1
1
0
2
1
0
0
2
1
0
0
0
0
1
0
0
2
2
1
1
3
1
0
1
2
1
0
0
2
0
1
0
1
0
1
2
1
1
0
0
2
0
0
6
1
1
1
0
0
1
1
2
2
2
1
1
1
3
1
2
1
0
0
0
1
0
1
1
1
2
2
1
1
0
2
1
2
0
1
1
1
0
0
1
2
0
0
0
1
1
1
1
1
1
0
0
0
2
1
1
1
1
2
0
0
1
1
1
0
2
1
1
1
1
0
1
1
0
1
1
2
0
0
0
0
0
1
1
1
0
0
1
1
1
0
1
2
2
1
1
1
1
1
1
0
2
2
1
2
0
1
1
0
2
0
0
2
1
2
0
1
0
0
2
1
2
0
2
1
1
1
0
1
0
0
1
1
1
1
1
1
1
0
1
2
1
1
2
2
2
1
0
2
1
1
0
1
1
2
1
0
1
0
0
2
0
1
0
1
1
1
1
1
1
1
2
1
1
1
2
1
0
1
0
1
0
0
2
0
0
1
1
0
1
0
1
1
0
2
2
1
2
0
1
2
1
1
0
1
0
2
2
2
1
1
0
1
2
1
1
1
2
1
1
1
1
2
0
1
2
2
1
1
1
1
1
1
0
2
0
0
1
2
0
2
0
2
0
1
0
1
0
1
2
1
1
0
2
1
1
1
2
1
0
2
2
1
1
1
2
1
1
0
1
0
1
0
1
2
0
1
1
1
1
1
0
1
1
1
0
1
2
2
0
1
1
2
2
0
1
2
0
0
0
4
0
1
2
1
1
1
0
1
1
1
1
0
1
0
1
1
2
0
0
2
1
2
0
0
1
2
0
1
0
3
1
0
2
2
1
2
1
0
1
3
1
1
2
1
2
2
0
1
2
1
0
1
1
0
2
1
2
0
1
2
0
1
0
2
1
1
0
1
2
1
2
2
1
1
1
1
1
2
0
1
1
1
1
1
1
1
0
0
0
1
1
1
1
0
1
0
2
0
1
1
1
1
2
1
1
1
1
0
1
2
1
0
2
1
0
1
1
1
2
1
1
0
1
1
1
2
1
1
1
2
2
1
2
2
2
2
2
0
1
2
0
0
0
2
0
0
2
0
1
0
0
2
2
1
0
0
1
1
1
0
1
1
1
0
0
2
1
1
2
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
0
2
0
1
0
2
0
1
1
0
0
1
1
0
0
0
0
1
2
1
1
0
1
2
2
1
1
0
2
2
1
0
2
0
0
2
2
0
1
0
0
1
1
0
1
0
0
2
1
1
0
0
1
1
1
2
1
1
2
2
0
1
1
1
0
1
1
1
1
0
0
1
0
1
0
1
1
0
1
1
1
0
2
0
2
2
1
0
0
0
1
1
2
1
0
1
0
1
0
0
1
1
2
1
1
2
2
1
1
0
1
1
2
2
1
0
1
1
2
0
2
2
1
1
1
1
1
2
1
1
1
1
1
1
0
2
0
0
0
1
1
1
1
1
2
1
0
2
2
1
1
1
1
1
1
1
0
2
1
0
0
1
3
0
1
2
3
1
0
0
0
1
1
1
1
0
1
1
1
1
2
0
2
0
1
2
0
2
1
1
1
1
2
1
1
0
0
1
0
1
0
2
1
1
2
1
0
2
0
0
3
0
0
1
2
1
2
1
1
0
2
2
0
1
1
2
1
0
1
2
1
0
1
2
1
0
2
1
1
0
1
1
0
1
1
2
2
1
1
0
2
1
1
0
1
0
1
2
0
1
1
1
2
0
1
2
0
0
0
1
2
0
2
1
1
2
2
1
1
0
2
2
1
1
1
0
0
0
1
0
0
1
2
0
1
1
0
0
0
2
2
2
1
2
1
0
1
0
0
1
1
1
1
1
0
2
1
1
0
1
2
1
1
0
2
1
1
1
0
2
1
1
1
1
2
0
2
1
1
1
2
2
0
1
0
1
2
1
1
1
0
1
2
1
0
1
1
1
0
2
1
1
1
1
0
0
0
1
1
1
1
2
1
2
2
2
0
2
2
0
1
0
0
1
2
0
1
1
1
1
1
0
1
1
2
1
1
1
0
0
1
1
1
0
1
2
2
0
1
0
0
2
1
0
0
2
1
1
2
0
0
2
1
1
1
2
2
2
1
1
2
1
1
2
0
1
1
1
2
0
1
1
2
0
1
0
1
1
2
1
1
2
1
1
1
2
0
1
2
2
1
1
2
1
0
1
2
2
1
2
0
2
0
2
2
1
1
0
0
1
1
0
0
2
1
1
2
1
2
0
1
0
0
2
1
2
1
1
2
4
0
2
2
1
0
0
1
2
0
1
1
1
0
1
1
1
0
1
0
2
2
1
1
2
1
0
1
2
0
2
2
0
1
1
0
1
2
0
1
1
0
0
1
1
1
1
2
1
1
0
1
2
1
1
1
0
1
0
0
1
1
0
3
2
0
0
2
2
0
2
1
2
1
2
3
2
2
1
1
1
0
1
2
0
1
0
0
2
1
0
1
3
2
1
2
1
1
0
3
0
2
1
1
1
0
1
3
2
2
1
1
1
0
0
0
1
0
1
0
2
1
1
1
3
0
1
0
0
2
1
1
2
0
1
3
2
1
1
0
0
1
1
1
0
1
1
1
1
1
2
0
1
0
0
0
1
2
2
1
0
1
0
1
1
2
0
1
2
0
0
1
2
1
2
0
1
1
1
1
1
2
1
1
1
2
0
0
1
1
1
1
1
1
0
0
1
2
0
1
2
2
1
1
2
1
2
0
0
1
1
1
1
2
1
0
0
1
0
1
0
1
1
0
2
4
2
2
1
1
2
2
0
1
2
2
2
3
0
1
0
1
2
1
1
2
1
2
2
1
2
2
1
1
1
1
2
1
1
1
0
1
0
1
3
1
1
2
2
1
2
0
2
1
1
1
1
1
1
1
1
3
3
0
2
1
2
2
1
0
2
1
0
1
0
1
2
1
1
1
4
1
2
1
0
2
0
1
1
1
1
1
2
1
1
1
0
2
2
1
1
1
0
1
1
1
1
2
1
0
0
1
0
3
1
1
1
2
1
0
1
1
2
2
2
1
2
1
2
1
0
2
2
1
1
2
1
0
0
0
0
0
1
1
0
1
2
2
1
0
1
1
2
0
2
1
2
0
0
2
0
2
1
0
1
2
2
1
2
0
0
1
1
2
0
1
2
1
0
1
0
2
3
2
0
1
0
0
0
1
1
0
2
1
0
1
0
1
0
1
0
0
1
0
0
1
1
0
0
0
2
1
0
0
1
1
2
1
2
1
1
2
1
2
2
1
0
2
1
1
2
1
1
1
1
1
1
1
2
2
2
0
1
1
2
1
2
1
1
1
0
0
1
1
1
2
0
2
1
1
0
1
0
1
0
2
0
1
1
0
0
2
1
1
1
1
0
1
2
0
2
1
0
2
0
0
2
1
1
2
0
1
1
1
1
1
2
1
2
1
1
1
1
1
1
0
0
1
0
1
2
0
1
0
1
1
1
0
2
0
1
2
1
0
0
2
1
1
2
0
2
2
1
2
2
1
1
1
1
2
1
2
0
1
1
0
1
1
1
0
1
0
1
3
0
1
1
1
0
1
1
1
1
0
1
1
1
1
1
1
0
1
1
1
0
1
0
2
1
0
1
1
1
0
0
1
1
1
2
2
1
1
1
0
1
1
2
1
1
0
1
0
1
1
2
1
2
1
0
1
1
2
1
1
1
2
1
1
1
1
1
1
0
1
1
1
0
1
1
0
0
2
0
0
2
0
0
0
1
1
1
2
0
0
1
1
1
1
1
0
1
0
1
1
1
1
0
0
1
2
1
1
1
2
1
0
2
0
0
0
1
0
2
1
1
0
1
1
3
0
1
0
1
1
0
1
1
2
1
1
0
0
1
1
0
2
1
0
0
1
1
1
0
1
1
1
2
1
2
2
2
2
0
0
1
1
1
0
1
1
1
2
2
2
1
2
1
2
1
0
1
1
0
0
1
2
1
0
1
1
0
1
1
0
1
1
2
0
0
1
1
1
0
0
1
1
1
1
1
1
0
1
2
2
3
1
0
1
1
2
1
1
1
1
2
2
0
1
2
1
2
1
1
0
1
2
1
1
1
0
2
0
2
1
1
2
0
1
0
1
2
1
1
1
2
2
1
2
1
0
1
0
1
0
0
1
0
0
1
2
1
1
2
0
2
2
1
0
1
0
0
0
1
1
1
2
1
0
1
1
1
1
0
1
2
1
0
1
2
0
1
1
1
0
2
2
1
0
1
1
0
1
0
1
0
1
1
2
1
1
1
0
1
1
2
1
2
1
1
1
1
0
1
1
1
1
0
1
0
2
0
1
1
2
1
2
2
1
1
0
0
1
0
2
0
1
0
1
1
1
1
0
2
0
1
1
1
1
1
1
1
2
0
0
1
2
1
2
1
1
0
2
1
2
1
2
4
3
1
2
1
2
2
1
1
0
0
2
2
2
2
0
1
1
2
1
1
0
0
1
0
2
1
1
0
0
0
0
1
2
2
0
1
1
0
1
1
1
1
1
2
0
1
1
1
2
1
1
1
0
2
1
1
0
2
1
1
1
1
0
1
2
1
1
0
1
1
0
1
1
0
2
2
2
0
1
0
2
0
2
1
4
1
2
1
1
2
1
1
2
0
1
1
0
1
1
1
0
0
1
1
2
2
0
0
2
1
1
1
0
2
1
0
1
0
0
1
2
0
1
0
0
1
1
1
1
0
0
1
2
1
0
2
3
1
1
1
2
0
0
1
1
0
2
2
0
0
0
2
1
1
0
1
0
0
0
1
0
1
1
0
1
0
1
2
0
0
1
1
0
0
1
0
1
1
1
1
1
2
1
2
1
1
1
1
2
0
2
1
1
0
0
1
1
1
1
1
0
0
0
2
1
1
1
0
2
1
0
1
1
3
0
1
1
0
1
2
2
2
0
1
1
1
0
2
1
1
2
1
0
2
2
1
2
1
2
1
2
2
1
0
0
1
1
0
1
0
1
1
1
2
2
1
0
2
1
0
1
0
0
2
0
1
0
2
1
0
1
1
2
0
2
0
0
1
0
1
1
1
0
2
2
2
1
0
2
1
0
1
1
1
2
0
1
0
1
0
1
1
2
2
0
2
0
1
0
1
0
1
0
1
2
1
1
1
2
0
1
1
2
1
2
0
2
1
1
2
1
1
2
2
2
1
2
1
1
1
1
2
2
1
2
1
1
1
0
1
1
1
2
1
0
2
0
0
1
1
1
2
0
1
0
1
1
1
0
0
1
1
1
1
1
2
1
0
1
1
0
2
1
0
1
0
1
0
2
0
1
0
1
1
1
1
1
2
1
1
1
1
0
1
2
2
0
1
1
1
1
0
2
1
0
1
0
2
2
1
2
1
0
2
2
1
4
1
0
1
1
0
2
0
1
1
0
2
1
1
1
2
2
1
1
1
1
5
1
0
1
2
1
1
1
1
0
1
1
1
1
1
1
0
1
2
1
0
1
0
1
1
1
2
1
1
1
0
3
1
0
0
1
1
0
1
1
1
1
1
1
0
0
1
0
2
1
0
1
2
2
1
2
2
0
1
1
2
0
1
1
0
2
1
0
0
1
1
1
1
1
1
2
0
1
0
0
2
2
2
1
1
1
1
1
1
1
1
2
1
2
0
2
1
0
0
0
1
1
1
2
0
1
1
1
2
1
2
2
0
0
0
1
2
1
0
1
2
1
0
1
1
0
1
0
0
2
1
0
1
1
1
2
1
1
1
1
0
1
1
2
1
2
1
3
0
2
1
1
2
0
0
1
0
0
1
0
1
2
1
0
0
1
1
1
0
0
2
0
2
2
1
3
1
1
1
1
0
0
1
1
1
2
2
0
1
0
1
0
1
0
0
2
0
0
0
1
0
1
1
1
0
1
2
0
1
0
0
0
2
2
2
1
0
2
1
2
1
0
1
1
1
0
2
2
0
0
1
1
2
2
0
1
0
1
1
1
1
2
0
0
1
1
1
0
0
1
2
2
0
0
2
0
1
0
1
0
2
2
0
1
1
1
1
0
1
0
1
2
2
1
2
0
0
1
0
1
0
1
1
2
2
1
1
1
1
0
0
2
0
2
0
0
1
0
0
2
2
0
0
2
1
1
1
2
1
0
1
1
2
1
0
2
0
1
0
1
0
1
2
1
0
0
0
1
1
1
0
2
2
0
1
0
1
1
0
0
1
1
0
0
2
2
2
1
2
1
2
1
2
1
2
0
0
2
1
1
0
2
1
2
1
1
1
1
1
0
2
1
1
2
1
2
0
1
0
1
1
1
0
0
1
1
0
2
0
1
1
2
0
0
1
1
0
1
0
1
2
3
1
0
2
0
2
1
1
2
1
1
1
1
2
1
0
1
1
1
1
2
1
2
0
1
1
1
1
2
0
2
1
2
2
1
0
1
1
1
0
1
1
1
1
1
1
2
1
1
1
0
1
0
1
2
2
0
0
1
0
1
2
1
1
2
2
1
1
0
1
1
1
0
1
1
1
1
0
2
1
1
2
1
0
2
2
2
0
1
0
1
1
1
2
2
1
1
0
1
1
1
0
1
0
1
0
1
1
2
2
0
3
0
0
2
0
0
1
1
1
2
1
1
1
0
1
1
0
0
2
1
1
1
0
0
0
0
1
1
2
2
2
1
1
0
1
0
1
0
1
0
1
2
2
0
2
1
2
1
0
2
0
2
0
1
1
1
0
2
2
2
1
1
0
2
1
1
0
2
1
1
0
1
1
0
0
2
2
1
1
1
1
0
2
0
1
1
1
0
1
1
1
0
3
2
1
1
0
0
1
2
1
0
0
1
1
1
1
2
0
1
2
0
0
1
3
0
2
1
2
1
1
2
2
1
1
1
0
0
1
1
0
1
0
0
1
1
0
1
0
2
1
2
1
0
1
1
1
1
2
0
2
1
1
1
1
0
0
1
2
2
1
2
2
2
1
0
0
2
1
1
1
1
1
2
0
0
1
0
1
0
1
2
0
1
1
0
1
1
8
1
2
1
0
1
1
0
1
2
0
1
2
1
1
2
0
1
1
2
1
1
1
1
2
1
2
1
1
2
1
0
2
2
0
0
0
1
0
0
0
1
1
0
1
1
2
1
1
2
2
3
0
0
2
1
0
0
1
1
2
0
2
0
1
1
2
1
1
1
1
2
0
2
0
1
1
1
1
2
1
1
1
1
1
1
1
0
2
1
2
2
0
1
1
1
0
0
2
0
0
2
2
1
0
0
1
1
0
1
1
1
1
1
2
1
1
2
2
1
0
1
0
0
2
0
1
1
1
1
3
1
1
1
1
0
1
1
3
2
1
1
1
2
1
1
0
1
1
0
2
1
0
1
1
2
1
2
1
1
1
0
0
0
1
1
1
0
1
1
3
0
0
0
1
3
1
0
0
2
1
2
1
2
1
1
1
2
1
1
0
2
0
1
1
2
1
1
2
1
0
2
0
1
1
1
0
0
2
1
2
0
1
2
1
1
2
1
1
1
1
1
1
1
1
2
2
0
0
2
0
2
2
2
0
0
0
0
1
0
2
1
1
0
1
1
1
0
2
0
1
0
2
1
1
1
1
0
2
0
1
1
2
0
1
1
1
1
2
1
2
0
1
2
2
2
1
1
2
2
1
0
0
1
2
2
1
0
2
1
1
0
1
1
2
0
1
1
0
0
3
0
1
2
1
1
1
1
2
1
2
1
1
1
1
2
0
1
3
0
1
2
1
1
1
2
2
1
1
0
1
1
0
0
2
0
1
1
1
1
1
2
2
0
1
0
1
0
1
1
1
0
2
1
1
2
3
0
1
1
0
1
0
2
1
1
0
1
1
1
1
2
5
1
1
1
0
1
0
0
1
1
0
1
1
1
1
1
2
1
1
1
1
1
1
2
0
1
1
1
1
0
1
1
1
0
0
1
5
1
1
1
1
2
1
2
1
1
2
1
0
1
1
1
1
1
1
1
2
1
2
1
2
1
1
0
0
0
1
0
2
0
1
0
2
0
0
1
2
2
0
1
2
1
0
0
1
0
0
1
2
1
2
0
2
1
0
1
1
1
1
0
2
0
1
1
0
0
1
2
0
1
1
1
1
1
1
1
0
8
2
1
2
1
2
1
1
2
1
0
1
0
1
1
1
1
1
2
1
0
0
1
0
0
1
1
1
0
2
2
1
2
1
0
2
2
0
1
2
0
1
0
1
0
1
0
1
1
1
1
2
0
1
0
2
1
4
1
0
0
0
0
0
0
1
1
1
2
2
2
1
0
1
1
0
0
0
2
0
1
1
1
1
0
1
1
0
1
0
1
1
1
1
2
2
0
1
2
1
1
1
2
1
0
2
0
2
1
1
1
0
0
0
1
1
2
1
1
0
1
0
1
1
1
0
1
1
1
0
0
1
0
1
0
0
1
0
2
2
1
0
1
0
1
1
0
0
1
1
1
0
0
1
1
1
1
0
1
2
1
1
2
2
2
1
2
1
1
0
1
0
1
1
1
0
1
0
1
0
0
0
1
1
1
3
1
2
2
0
1
0
0
2
1
0
1
2
1
0
0
0
1
1
1
0
1
2
0
2
1
2
1
1
0
1
2
1
1
0
0
2
0
1
0
0
1
2
2
0
1
0
0
1
0
0
2
2
1
0
0
1
2
2
1
1
0
2
0
1
0
3
2
1
2
0
0
1
1
2
1
0
2
1
1
0
0
1
0
0
0
1
1
1
1
0
2
1
2
1
1
2
0
0
1
1
1
2
1
0
1
1
1
2
1
4
0
1
1
1
0
1
0
1
2
1
2
1
0
0
2
2
1
1
1
2
1
1
0
2
1
1
0
1
2
1
0
1
1
1
0
1
2
2
2
1
1
0
2
1
0
0
1
2
2
0
2
1
1
1
1
1
2
2
1
0
0
1
0
1
1
2
0
2
0
1
0
1
1
1
1
0
1
0
2
2
1
2
2
0
1
0
0
2
2
2
2
2
0
0
0
2
2
0
1
1
1
0
2
0
0
2
0
0
2
1
1
2
2
0
0
0
1
0
1
1
2
0
2
1
1
2
1
2
1
1
1
1
1
0
2
1
1
1
1
0
1
1
1
0
1
2
1
2
1
1
1
2
0
2
1
1
1
0
2
1
2
1
0
0
1
2
0
0
0
2
1
0
0
1
1
0
2
0
1
1
0
1
0
1
2
1
0
2
1
0
0
1
0
0
1
1
0
2
1
0
0
1
1
0
2
2
2
1
0
1
1
1
1
1
2
2
0
1
1
2
1
0
1
2
2
2
1
2
1
1
1
0
0
2
0
2
2
1
1
0
1
2
0
1
0
1
2
2
1
2
1
1
1
1
1
2
0
2
0
1
1
1
1
0
2
0
1
1
1
1
1
0
0
1
0
1
0
2
1
1
1
2
1
2
0
1
1
2
0
1
1
2
1
1
1
1
1
1
1
0
0
1
0
1
0
0
2
1
2
2
1
1
1
1
2
1
2
0
0
1
1
0
0
1
1
0
0
1
0
1
0
1
1
1
1
1
4
2
1
1
1
0
1
1
0
2
1
0
1
1
1
2
1
1
0
0
1
1
2
1
1
2
1
0
0
2
1
9
1
1
0
1
0
2
1
1
1
0
1
0
1
0
1
1
0
1
1
2
1
2
2
2
1
0
1
2
1
1
1
1
2
0
2
1
1
2
0
0
2
2
1
2
0
1
1
1
2
0
0
0
0
1
0
0
2
0
2
0
0
1
1
2
0
1
1
1
2
1
1
0
1
2
0
1
1
1
0
2
1
1
0
1
0
1
2
1
1
1
0
0
1
2
1
2
1
2
1
1
1
0
2
2
0
0
1
2
1
1
2
1
2
1
1
0
0
2
0
1
2
0
1
1
0
1
2
0
2
0
1
1
0
1
0
0
0
0
0
1
0
0
2
1
2
1
2
2
0
1
0
1
1
1
1
1
2
1
1
2
2
0
2
0
0
0
2
2
2
1
0
2
1
2
1
0
2
2
2
2
1
0
1
1
2
0
0
1
1
2
2
0
0
0
1
0
1
2
2
2
2
0
0
2
0
1
1
0
1
1
3
2
2
0
2
1
0
0
2
1
1
2
0
0
1
1
0
1
2
1
2
0
1
1
1
1
1
0
1
2
0
0
2
2
1
2
0
1
2
1
0
1
1
1
0
0
0
2
1
0
0
2
0
2
0
1
0
0
2
1
0
0
2
2
2
2
2
0
0
2
1
0
2
1
0
1
2
3
1
1
1
1
1
1
1
1
0
0
0
1
1
0
0
1
1
1
2
0
1
1
1
2
1
0
0
1
1
1
1
1
1
2
2
0
2
2
0
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
2
0
1
1
1
0
0
2
1
2
2
0
1
1
0
1
1
1
1
2
1
1
2
0
1
2
1
2
0
1
1
1
0
2
2
0
1
1
0
2
0
1
1
1
1
0
0
1
2
0
1
0
2
2
1
1
1
1
1
2
1
3
1
1
1
1
1
1
0
2
0
1
1
2
1
1
1
0
0
0
2
2
1
2
1
0
2
1
1
2
0
0
1
1
0
1
1
0
0
2
2
1
1
1
0
0
2
1
0
0
1
1
1
0
1
1
2
2
0
1
2
0
2
1
1
2
2
1
1
1
1
0
1
1
0
1
0
1
2
1
2
2
1
0
2
0
2
0
2
0
0
1
1
1
1
0
2
1
0
2
1
0
1
2
2
0
1
1
0
0
2
2
1
1
2
1
0
1
0
1
1
0
2
0
1
0
1
1
0
0
1
1
1
0
2
0
0
1
0
0
0
0
0
0
1
2
2
0
0
1
1
2
1
1
0
2
2
0
1
1
1
3
1
1
0
1
1
0
1
2
0
1
0
1
1
1
1
1
1
2
0
2
2
1
1
1
3
1
1
0
2
2
0
1
0
2
2
0
0
1
2
2
2
1
2
0
2
2
1
1
0
0
2
2
1
1
1
1
0
2
0
0
2
2
1
0
1
3
0
0
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
2
1
0
1
1
1
1
1
2
1
2
2
1
1
2
1
1
1
1
2
2
2
1
2
1
0
1
1
1
1
1
0
2
1
1
0
0
1
2
1
1
1
1
1
1
1
1
2
1
0
1
1
1
0
2
3
2
0
2
0
0
0
0
1
1
1
1
1
1
0
0
0
1
2
1
1
3
2
1
1
1
0
0
0
2
1
1
1
0
1
1
1
2
2
2
1
2
1
1
0
1
2
2
0
1
1
2
0
2
1
2
1
1
2
1
1
1
0
0
1
0
1
1
0
2
2
1
2
1
1
2
1
2
1
1
0
0
0
0
0
1
1
1
1
1
1
1
0
1
1
0
0
0
1
1
0
0
0
2
1
0
0
0
2
2
1
1
1
2
1
1
1
1
1
0
1
3
2
1
1
0
2
2
2
0
1
0
0
1
1
1
1
0
0
0
0
1
2
1
0
2
2
1
3
0
0
1
0
0
0
1
1
3
5
1
2
1
2
2
1
1
1
0
0
2
1
1
0
1
2
0
1
1
1
1
2
1
0
2
1
1
0
1
0
2
0
2
0
1
1
1
1
1
1
0
2
0
1
0
0
1
1
0
1
1
2
2
2
1
1
2
2
0
2
2
0
2
0
1
1
1
2
1
0
1
1
0
0
1
2
1
1
0
2
1
2
2
2
0
0
1
1
2
1
2
2
1
0
1
1
1
2
1
1
1
1
1
2
1
1
0
1
2
1
1
1
1
1
1
2
0
0
2
2
1
0
2
0
3
0
0
1
0
0
1
0
1
1
1
0
1
1
1
0
0
1
1
1
1
1
0
1
0
2
0
2
1
1
1
1
1
1
0
1
1
2
0
0
1
1
0
2
1
1
5
1
2
0
2
0
1
0
1
1
0
0
1
0
1
2
1
0
0
1
2
1
2
1
0
0
1
1
0
0
2
0
1
0
1
0
1
1
1
1
0
2
1
1
0
1
1
0
2
1
2
1
0
0
2
2
1
3
0
0
0
0
1
2
1
2
1
2
0
1
1
1
2
1
1
1
1
0
2
0
1
1
1
0
0
2
0
1
1
0
1
1
1
2
1
0
2
0
2
0
0
1
1
1
1
1
0
0
0
2
0
1
1
0
1
1
1
2
2
2
0
0
1
1
1
1
0
1
1
1
1
1
1
0
0
1
1
2
1
1
1
1
2
0
2
1
3
1
0
1
0
0
1
1
1
1
1
1
0
1
1
1
2
1
0
1
1
2
2
1
0
0
1
1
0
1
0
0
1
2
0
1
1
1
1
0
2
2
2
1
1
1
2
2
1
0
2
1
1
0
2
2
1
1
0
1
2
1
1
1
1
0
0
1
0
1
0
1
0
1
2
1
0
1
2
1
0
1
2
2
1
2
0
1
1
0
1
2
1
0
1
1
1
2
1
0
2
2
0
1
1
2
1
1
0
1
2
1
1
0
1
2
2
2
2
0
1
2
2
1
0
2
0
2
1
1
0
1
0
0
2
1
1
0
1
1
1
0
1
2
1
0
1
1
0
1
0
1
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
0
0
0
1
1
1
0
2
1
2
2
1
1
1
2
1
1
2
1
1
1
1
1
2
1
1
0
1
0
0
0
1
2
0
2
1
1
2
0
2
2
2
1
0
2
1
1
0
2
2
2
0
1
2
2
1
2
1
1
1
1
1
2
1
1
2
0
1
1
2
0
1
1
0
1
2
1
2
1
1
1
0
0
1
1
1
1
2
0
1
1
0
0
1
0
1
1
2
0
1
1
1
1
2
2
2
0
1
1
0
1
0
0
2
1
0
1
0
1
0
1
1
2
0
0
0
1
1
1
0
0
3
2
2
1
2
1
2
2
1
0
1
1
2
0
1
2
1
1
2
1
0
0
0
0
2
0
1
0
1
2
1
2
1
1
0
1
1
0
0
0
2
1
0
1
1
0
2
1
1
1
0
1
0
1
2
0
0
2
3
0
0
2
1
0
1
1
1
2
2
1
1
0
2
2
1
0
2
1
1
1
0
1
1
0
1
0
2
0
1
2
1
1
0
1
0
1
2
1
0
0
1
1
1
0
1
0
2
0
1
0
0
1
1
0
0
1
2
1
0
1
1
0
1
1
1
0
1
1
0
1
1
1
1
0
0
2
1
0
2
1
0
2
0
2
2
1
1
0
0
0
2
0
1
2
2
0
1
0
2
0
1
0
0
1
1
1
2
1
0
1
0
2
1
1
2
1
0
0
7
1
1
0
1
1
1
1
2
1
0
1
1
2
0
1
1
1
1
1
0
2
2
1
2
0
0
2
0
0
1
0
0
1
1
1
1
1
1
2
0
1
0
1
1
2
0
0
2
3
1
2
1
2
1
2
1
0
2
1
1
0
1
2
1
0
0
0
1
1
0
2
1
0
1
0
0
1
0
1
7
1
1
1
2
1
1
1
1
0
0
0
0
1
1
0
2
2
0
2
2
2
1
1
1
2
0
2
0
2
2
1
1
1
1
0
1
2
0
1
1
2
1
2
1
1
1
0
1
1
0
0
1
1
0
2
1
0
2
0
1
1
1
1
1
2
0
1
1
2
1
1
0
1
1
1
2
1
1
0
0
0
1
2
1
1
2
0
0
0
2
1
0
1
1
1
1
0
1
0
1
2
0
1
0
1
1
2
1
1
1
1
1
3
1
2
0
0
1
2
0
2
0
2
1
2
1
2
1
1
1
2
0
1
0
1
1
1
0
1
1
0
1
1
1
1
2
3
1
1
1
2
2
1
2
2
1
1
1
0
2
1
1
0
2
0
1
1
2
0
0
0
0
1
2
0
1
1
0
0
0
1
1
1
1
0
2
1
1
2
0
1
2
0
2
1
0
1
0
0
2
0
2
1
1
0
1
0
1
0
1
2
0
0
2
0
1
2
0
2
1
1
1
1
2
2
0
1
1
0
1
1
1
1
1
2
1
0
1
1
2
1
1
2
0
2
2
1
1
1
2
1
0
0
1
1
1
0
2
0
1
1
2
1
0
1
1
2
0
1
0
2
0
0
1
2
3
0
3
1
0
1
1
1
0
2
2
0
1
0
2
0
0
0
1
1
2
1
0
1
2
0
1
2
2
1
1
0
1
1
0
1
2
0
1
1
1
2
2
1
1
0
0
1
1
1
1
1
1
1
0
1
1
2
0
1
1
1
1
1
1
1
0
0
1
2
1
2
0
2
1
1
1
1
1
2
0
1
2
0
0
1
0
1
1
1
1
2
0
2
1
0
1
1
1
0
1
3
2
1
2
1
0
2
0
0
3
1
1
2
0
0
2
2
0
1
1
0
1
1
0
0
2
1
1
2
1
1
1
0
0
1
1
1
1
2
1
1
1
2
1
2
2
2
0
1
2
2
2
1
0
0
2
1
2
0
1
2
4
2
5
1
2
0
2
2
1
1
2
0
1
0
1
0
0
1
0
1
0
0
0
2
0
1
0
0
0
2
0
1
1
0
1
1
2
2
1
0
1
1
1
1
1
3
0
1
0
2
0
2
2
1
1
1
1
1
1
0
1
1
2
2
0
2
0
0
1
1
1
1
2
0
0
0
2
0
1
1
0
0
0
2
1
2
0
0
0
2
0
1
1
1
1
1
4
2
2
1
2
1
1
1
0
0
1
0
1
2
0
1
0
0
0
0
1
1
1
1
0
2
1
1
2
2
0
1
1
1
1
2
0
1
0
0
2
0
0
1
1
1
0
1
1
1
1
3
2
2
1
0
1
0
2
0
0
2
0
1
0
0
0
2
0
1
1
1
2
0
2
2
0
1
1
0
1
1
1
0
0
0
0
1
1
1
3
1
1
0
2
1
1
1
0
1
0
2
2
1
1
2
0
1
3
0
1
0
2
1
0
2
1
1
1
1
2
1
1
2
1
2
1
0
1
1
1
1
0
0
1
0
1
1
1
2
1
0
0
1
1
1
1
2
0
2
0
2
1
2
1
2
1
0
0
1
1
1
2
0
0
0
1
0
1
1
2
1
0
0
0
1
0
0
1
0
0
1
1
1
1
1
2
1
1
0
2
2
0
1
0
1
1
1
0
0
0
1
1
1
1
2
1
0
1
1
0
1
1
1
1
1
2
0
1
2
0
1
1
1
1
1
2
2
2
1
1
1
1
2
1
1
2
1
0
0
2
2
0
1
0
1
2
2
2
1
1
0
2
1
0
0
1
2
1
2
0
1
0
1
1
1
1
0
1
0
0
1
1
1
2
1
2
1
1
1
2
1
1
1
2
2
2
2
0
1
1
1
2
1
0
0
0
4
0
0
0
1
2
2
1
2
2
2
0
1
1
2
2
2
2
0
0
2
1
1
0
0
1
0
1
2
1
1
2
0
2
0
1
0
1
2
1
2
1
1
2
2
1
1
1
0
1
2
1
1
2
0
0
2
1
1
0
1
0
2
1
1
2
0
0
1
2
1
1
1
1
1
0
1
1
2
0
1
1
0
2
1
1
1
2
1
1
1
1
3
2
1
1
0
0
1
1
0
1
1
2
1
0
2
0
2
2
2
1
2
1
1
2
1
2
1
1
1
0
1
2
0
1
1
1
2
1
1
2
2
1
0
1
1
1
1
0
1
1
1
2
1
1
1
0
1
2
1
1
2
2
1
1
2
0
0
0
1
1
3
1
1
2
1
0
2
2
3
0
1
1
1
2
1
1
1
1
1
1
2
0
0
1
1
0
1
1
1
0
1
0
1
0
0
1
1
0
1
1
1
1
1
0
1
0
1
1
0
0
0
0
1
1
2
1
1
1
0
0
2
2
1
1
2
1
2
2
2
2
2
0
2
1
2
1
1
0
1
1
1
1
2
1
0
1
1
1
0
0
1
1
1
1
1
1
2
1
1
2
0
1
0
1
1
2
2
0
0
0
1
1
2
0
2
2
1
1
1
0
1
0
1
1
1
0
0
0
1
2
2
1
1
1
1
2
1
1
1
2
1
1
1
1
0
0
2
2
2
1
0
1
1
1
0
1
0
0
1
0
1
1
2
1
2
2
2
2
1
1
0
2
2
2
2
0
0
1
1
0
2
1
0
2
0
2
2
0
0
0
1
0
3
2
1
1
1
1
0
1
0
2
1
1
0
1
2
1
1
2
1
1
2
2
1
1
1
1
2
1
1
2
1
1
0
1
2
1
1
2
1
2
2
2
0
0
0
0
0
2
1
1
2
0
1
2
2
1
2
1
0
1
1
2
1
1
0
1
1
1
2
1
1
0
0
1
1
1
0
1
2
0
1
0
2
0
1
0
1
0
1
1
1
0
0
1
0
2
1
0
1
2
0
1
0
1
1
1
1
0
1
0
1
1
0
1
2
2
1
1
0
1
0
2
1
1
0
1
1
1
2
0
2
2
2
0
2
1
2
0
1
0
1
1
1
0
0
2
1
1
2
1
1
0
1
2
0
0
0
1
0
0
1
2
1
0
2
0
1
0
1
0
0
1
2
1
1
1
1
1
0
0
2
0
1
1
1
0
2
0
1
1
2
1
2
1
0
2
1
1
1
1
1
1
1
1
1
1
1
1
3
0
1
1
2
0
1
0
0
1
2
0
3
1
1
2
1
1
0
1
1
2
2
1
1
0
1
1
0
1
0
1
1
2
2
1
1
1
2
2
1
0
0
1
2
2
1
1
0
0
1
2
3
2
1
0
1
1
2
3
0
0
2
0
0
0
1
2
0
0
0
1
1
0
1
1
1
0
1
0
1
2
0
0
0
0
0
0
2
0
3
1
1
1
1
2
1
0
1
1
0
1
2
0
1
2
0
2
0
1
1
0
0
1
0
1
1
0
0
1
1
1
0
1
2
0
2
1
2
0
1
1
0
0
1
1
1
0
1
1
0
0
2
1
1
1
1
0
3
2
1
0
1
1
2
0
1
1
1
0
1
1
1
0
1
1
1
1
1
0
0
3
2
2
1
1
1
2
1
2
2
1
2
0
2
1
0
1
3
1
1
0
0
0
2
1
1
1
2
1
1
0
0
2
2
0
1
1
0
1
1
1
0
2
1
1
0
1
0
1
0
1
1
1
2
2
1
1
1
1
1
1
1
1
2
1
1
0
1
1
0
0
2
1
1
1
1
0
2
0
1
2
1
1
1
0
1
2
1
0
1
0
0
0
2
2
1
1
2
2
2
0
3
1
2
1
1
1
2
2
2
1
1
1
1
1
1
1
0
2
0
2
1
0
1
1
1
1
2
1
0
2
1
1
1
0
2
0
0
1
1
2
1
1
0
1
0
1
0
1
1
1
2
1
0
1
1
1
2
2
0
1
2
0
1
0
1
0
0
1
0
1
2
1
1
1
0
2
0
1
1
1
2
0
1
1
0
1
0
0
1
1
2
1
0
0
2
0
1
1
1
0
2
0
1
1
1
3
1
2
2
0
0
1
0
0
1
0
3
0
2
0
2
1
0
1
0
2
2
2
1
2
0
2
1
2
1
1
2
0
3
1
1
1
1
2
2
2
2
2
1
1
1
2
5
1
2
1
1
1
0
1
0
1
1
1
2
0
1
2
0
1
2
1
0
0
1
1
0
2
1
1
1
1
1
2
2
1
2
1
1
1
0
1
0
2
2
1
0
1
0
1
2
1
1
3
0
0
0
1
2
0
1
1
2
0
0
0
1
1
0
1
2
0
2
2
1
1
1
3
1
1
1
1
0
0
1
0
0
2
1
1
1
1
0
0
2
0
0
1
0
0
0
0
0
1
1
2
4
1
1
1
1
1
2
1
2
2
1
1
0
2
0
0
0
0
2
1
1
1
1
1
2
3
0
0
2
1
0
0
1
0
2
1
1
1
2
2
1
1
2
1
0
2
1
1
1
1
2
2
1
1
0
0
1
1
1
1
0
1
1
0
1
0
0
1
1
1
1
1
0
0
1
1
1
1
1
1
2
2
1
1
1
0
0
2
2
1
1
2
2
2
0
1
2
1
0
0
0
0
1
1
1
1
0
2
1
0
1
2
1
1
1
0
2
0
1
1
2
1
1
1
1
1
0
3
2
2
0
1
0
1
1
3
0
0
1
1
1
0
0
2
2
2
0
1
0
0
1
1
1
1
1
1
1
0
1
3
1
1
0
1
2
0
0
0
1
2
0
2
1
0
1
0
0
1
1
1
1
0
1
1
1
1
1
0
1
1
2
1
1
1
2
2
0
0
0
0
0
1
1
1
1
0
0
1
2
1
1
1
1
2
1
2
1
1
0
1
0
1
1
0
2
2
1
2
2
2
0
1
0
0
1
1
1
0
2
1
0
2
0
1
1
3
1
1
1
1
0
1
2
1
2
1
2
1
2
0
0
2
2
2
1
1
1
0
1
0
1
0
1
3
1
1
2
2
2
1
2
3
0
0
1
1
0
1
2
0
1
1
0
0
0
1
1
1
1
0
1
1
0
2
3
1
1
1
1
2
1
0
2
1
0
0
0
1
2
1
1
2
2
2
1
1
0
1
0
0
1
0
1
0
1
2
1
1
2
1
0
0
2
1
2
0
1
0
0
0
1
1
2
2
0
0
4
0
1
2
2
0
1
0
0
1
0
2
1
1
2
1
1
1
1
0
2
1
1
1
1
1
1
1
1
1
2
2
0
0
1
1
2
0
1
1
1
1
2
2
1
1
1
1
1
4
0
0
2
0
2
0
1
1
1
1
0
1
0
1
1
3
0
1
3
1
1
1
2
1
2
1
1
1
1
1
0
1
1
1
0
1
1
0
1
1
2
1
1
0
1
0
1
2
2
0
2
2
1
0
2
2
2
0
0
1
2
1
1
0
1
0
2
0
2
0
1
1
0
1
1
0
1
1
1
1
0
1
1
1
1
1
1
2
1
2
0
2
2
1
1
1
2
1
1
0
1
2
2
0
0
0
0
0
2
0
1
0
1
0
0
0
2
1
1
0
1
1
2
1
1
0
0
1
2
1
1
1
0
1
1
1
1
0
0
0
1
1
1
0
2
1
3
2
1
1
1
1
1
1
1
0
1
2
1
0
2
2
0
0
1
1
1
0
2
0
1
1
1
1
1
1
2
0
4
1
1
1
0
2
1
1
1
0
1
2
2
1
1
0
2
1
2
0
1
1
1
1
1
2
1
2
0
1
2
2
1
1
0
1
0
1
2
1
1
1
1
2
0
1
1
1
2
1
1
0
2
2
2
2
1
1
1
1
1
2
0
1
0
2
1
0
1
7
2
0
1
2
2
0
2
0
0
0
1
0
1
0
1
1
1
2
1
0
1
0
1
1
0
1
1
1
2
0
0
0
1
1
2
2
1
0
1
1
1
1
1
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
1
1
2
0
1
0
1
1
1
1
0
1
1
1
0
1
1
2
0
1
0
1
1
1
0
0
1
0
2
1
0
1
2
1
1
2
0
0
0
2
0
0
2
0
1
1
1
1
0
0
2
0
0
0
0
1
1
2
0
1
0
2
2
1
1
0
1
1
0
1
0
2
1
2
1
1
0
1
0
1
1
1
0
2
2
0
1
2
1
1
1
1
0
1
0
1
2
2
0
0
1
2
0
2
0
1
1
1
0
2
2
1
1
1
1
1
2
2
1
1
2
0
2
1
2
1
1
1
1
0
1
1
0
1
1
1
2
0
1
2
0
0
2
2
2
1
1
1
1
1
1
1
0
0
1
1
1
2
1
2
1
0
1
0
1
2
1
0
1
0
1
0
0
1
0
2
1
0
1
1
1
2
1
1
1
0
0
0
1
1
0
1
2
1
0
0
1
2
0
1
1
1
2
0
1
2
0
0
2
1
1
2
1
0
0
1
0
1
0
0
3
0
0
1
1
2
1
0
1
1
1
1
1
0
1
2
2
1
1
1
2
2
0
1
0
1
1
0
0
1
0
0
2
2
1
1
0
1
1
2
0
1
2
1
0
0
1
2
0
0
2
2
1
2
0
1
2
0
0
0
2
1
0
0
1
2
0
0
2
1
0
2
1
1
1
0
0
0
2
1
0
1
2
1
2
4
1
0
1
1
1
1
0
2
0
1
1
2
1
0
2
1
2
2
1
1
0
2
0
1
1
1
1
1
1
1
0
2
0
1
3
0
1
2
0
2
0
1
1
1
2
2
0
1
2
1
2
1
2
1
0
1
0
1
1
1
1
1
1
2
2
1
1
1
1
1
0
2
1
0
2
1
1
1
3
0
1
2
0
1
1
2
1
1
2
2
1
0
1
0
0
2
2
0
1
1
0
1
1
1
1
1
1
2
1
0
0
0
0
0
1
1
1
1
2
0
1
1
0
0
1
1
1
2
0
1
1
1
1
0
1
0
2
2
0
0
1
1
1
1
2
2
0
2
2
0
2
0
0
1
1
0
1
1
0
0
1
1
2
2
2
2
1
0
1
2
1
0
2
2
2
1
1
1
1
1
0
1
2
2
1
2
2
1
0
1
1
2
0
2
1
2
1
2
2
1
1
1
2
1
0
0
2
1
3
2
1
1
0
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
0
1
1
0
1
2
2
2
1
1
1
0
1
0
2
0
1
0
2
1
1
0
1
0
0
0
1
0
2
1
1
1
1
0
0
0
1
0
1
1
2
2
0
1
0
0
1
0
1
0
0
0
1
1
2
2
1
1
1
1
2
0
1
1
2
1
1
2
1
1
2
3
1
0
0
0
2
1
3
1
1
0
1
0
0
0
1
0
2
0
1
0
0
2
1
0
0
1
2
0
1
1
1
2
2
0
2
1
2
1
1
0
0
1
2
2
0
2
1
2
1
0
1
2
1
1
1
1
2
1
1
2
2
2
2
1
1
0
2
1
0
1
0
2
2
0
2
0
1
1
2
0
0
0
1
1
1
2
1
0
1
1
2
2
1
1
1
1
1
1
1
0
2
0
2
1
1
0
1
2
2
0
0
0
0
1
1
1
1
1
1
2
1
1
1
1
2
2
1
1
0
1
0
1
1
1
1
0
2
2
1
0
2
1
1
0
0
2
1
1
1
0
1
0
2
1
0
1
1
0
1
1
1
2
2
1
1
1
1
2
0
0
1
1
1
1
1
1
0
0
1
0
1
1
0
1
0
2
1
0
1
1
0
1
1
2
2
0
0
1
1
1
2
0
2
1
2
0
0
1
1
1
0
2
1
2
1
0
1
1
1
0
2
0
1
0
2
2
2
0
1
0
2
2
1
1
0
1
2
1
1
0
0
1
1
2
0
0
0
0
0
2
0
0
0
1
1
1
1
0
1
2
2
1
3
1
0
2
0
1
1
0
1
1
2
0
1
0
0
2
0
0
0
2
1
0
1
2
1
1
1
2
1
2
1
2
1
1
0
0
0
1
1
1
0
0
2
1
1
1
1
1
1
0
2
1
1
0
0
1
2
2
1
2
1
1
0
0
2
1
0
1
0
0
1
1
0
1
1
1
0
2
0
2
0
1
1
1
1
1
1
1
0
1
1
1
0
1
1
1
0
0
1
2
0
1
1
1
2
1
1
0
0
0
0
2
0
1
1
2
2
1
1
1
1
2
0
1
2
0
2
2
1
1
1
0
1
0
1
1
1
1
0
1
0
2
1
0
2
2
1
2
1
1
1
0
2
1
1
0
1
1
1
1
1
1
1
1
0
1
0
1
1
1
0
1
2
0
1
1
1
0
0
2
2
2
0
1
0
2
1
2
1
1
1
1
0
1
0
2
0
0
0
1
0
2
1
1
0
2
2
0
1
1
1
2
2
0
1
1
2
1
1
0
0
1
1
1
0
0
1
1
1
1
1
1
0
0
1
0
1
1
1
0
2
1
2
0
1
1
2
1
1
1
2
0
1
0
1
0
1
0
0
2
0
0
1
0
1
1
2
0
1
0
0
0
2
1
1
2
1
0
1
1
0
1
2
0
2
0
2
1
1
0
0
1
0
1
1
3
1
2
0
1
1
0
1
0
2
0
1
0
2
2
1
2
2
2
1
1
1
1
1
0
1
2
1
1
1
0
1
2
0
1
1
1
0
0
0
1
1
1
0
2
0
0
1
0
0
1
1
0
0
0
0
2
1
0
0
0
1
0
0
1
1
0
2
0
1
2
2
1
1
1
0
1
0
0
1
2
0
1
1
1
7
4
1
1
1
1
2
2
1
1
1
1
1
1
2
0
2
1
1
1
0
0
1
2
2
0
1
1
1
1
2
1
0
0
0
1
2
0
1
2
0
0
1
0
0
2
1
1
1
2
1
1
1
0
1
2
0
1
2
1
3
1
1
0
2
0
1
1
2
1
1
0
1
1
2
0
1
2
0
2
1
2
1
0
1
1
0
1
1
1
2
1
1
1
1
1
2
1
2
0
1
0
1
0
1
0
2
1
1
1
0
0
1
2
1
2
2
2
0
1
0
0
2
0
1
1
0
0
0
2
1
0
1
2
2
1
1
2
1
1
1
1
0
0
2
2
0
1
0
1
1
1
1
0
1
2
1
1
0
0
0
1
0
0
2
2
0
0
1
1
1
1
0
1
2
0
1
2
0
2
1
0
2
1
1
1
1
1
2
2
2
0
1
1
1
2
1
0
1
1
2
2
0
1
2
0
1
1
1
1
0
1
1
1
0
0
2
1
2
0
2
0
2
2
2
1
1
2
1
2
2
0
2
0
1
0
0
0
1
1
1
1
1
0
1
2
1
1
1
1
1
2
3
0
1
2
2
0
1
1
1
0
1
1
2
0
0
1
0
0
2
1
1
1
1
1
1
1
0
1
2
1
1
0
1
1
1
1
0
1
1
1
1
2
0
0
1
1
0
1
1
0
1
2
1
1
1
1
2
0
0
1
0
1
1
1
1
0
1
0
0
1
1
0
2
2
1
0
0
2
2
0
1
1
1
0
1
0
1
2
1
1
2
2
1
0
2
1
1
0
2
1
0
0
0
0
0
1
1
1
1
2
1
1
1
1
2
0
2
1
1
0
1
0
0
1
2
1
1
2
0
1
2
2
2
1
1
1
0
0
1
2
0
1
1
1
2
1
2
0
1
1
2
0
1
1
1
0
0
1
0
0
1
2
1
0
0
1
0
1
0
1
0
0
1
0
0
0
1
2
0
1
1
2
0
1
1
0
1
0
1
0
1
0
1
1
0
2
1
1
1
2
0
1
1
1
0
2
0
1
0
0
0
2
1
1
1
2
1
1
1
1
1
2
1
1
1
2
2
2
0
1
2
1
1
2
1
0
1
1
1
1
0
0
1
1
1
1
1
0
0
0
0
1
2
1
2
1
1
1
1
1
1
0
1
0
1
1
0
1
0
2
1
2
1
1
0
2
2
1
1
0
1
0
1
1
1
2
1
1
1
0
2
2
1
2
2
1
1
1
2
0
1
0
1
1
0
1
1
2
1
2
0
0
1
1
2
2
2
1
1
1
1
2
1
1
0
1
1
1
2
0
1
2
0
1
2
0
1
2
1
2
0
1
1
0
1
0
1
2
2
2
0
0
1
1
1
0
1
2
0
2
0
3
2
1
2
2
2
2
1
1
1
1
0
7
2
2
1
2
1
4
0
0
1
2
2
0
1
2
1
0
2
0
0
1
0
0
1
2
0
1
2
0
1
1
1
1
2
2
2
1
0
1
1
0
1
1
1
0
1
1
2
1
1
1
0
1
1
1
1
1
1
1
2
0
1
1
1
1
1
2
0
2
1
0
1
2
2
2
1
1
1
1
0
1
0
1
1
2
2
1
1
2
1
0
2
1
1
1
1
2
0
0
0
1
0
1
1
0
0
1
1
1
2
1
2
1
1
2
1
1
0
0
0
1
0
1
1
2
0
1
2
3
5
0
2
1
2
1
0
0
1
0
0
0
1
3
0
0
1
2
1
0
1
1
1
0
1
1
1
1
2
0
1
2
0
1
1
1
0
1
0
2
2
0
1
1
1
2
0
2
2
0
0
1
0
1
2
1
2
1
0
2
2
1
0
1
2
1
1
1
1
1
1
1
0
1
0
1
1
1
0
2
0
2
1
0
2
1
2
2
1
2
0
1
2
1
2
1
1
1
1
0
1
1
1
1
0
2
1
0
1
1
0
0
1
1
1
1
2
0
1
0
2
1
0
1
1
0
0
1
2
2
0
2
0
1
1
1
2
2
0
1
1
1
0
1
1
0
1
1
1
1
1
0
1
2
0
0
0
2
1
0
0
0
2
2
2
1
1
2
1
1
1
1
0
0
0
1
1
3
3
0
1
1
1
1
1
0
1
0
0
0
2
0
0
1
0
2
2
1
1
1
0
0
0
1
0
2
1
2
2
2
1
1
0
2
2
1
0
2
1
1
0
1
2
2
1
0
1
2
1
1
1
1
1
1
1
0
1
2
0
1
1
1
1
1
2
1
2
1
0
1
2
0
2
1
1
1
1
1
1
0
1
0
2
2
0
0
1
1
1
0
1
1
1
1
1
2
0
1
2
0
0
3
1
0
0
1
0
2
1
1
1
0
0
1
1
2
2
0
2
2
0
0
2
2
1
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
1
0
1
2
2
1
2
1
0
0
0
1
1
1
1
1
1
0
1
1
2
1
0
0
0
0
1
1
0
1
0
1
1
1
1
1
0
1
2
0
1
0
2
1
0
1
0
0
1
0
0
1
2
2
1
1
0
1
1
1
0
1
0
1
1
0
2
0
0
1
0
1
1
1
1
1
0
2
1
0
1
1
2
0
1
1
1
1
1
0
1
2
1
0
1
2
0
1
1
0
2
2
0
2
2
2
1
1
0
0
0
0
1
1
2
1
1
1
2
1
2
3
0
1
0
1
0
1
0
7
0
1
1
1
0
2
2
0
2
1
0
2
2
1
0
2
1
0
2
1
1
0
1
0
0
1
2
1
1
2
1
0
1
3
1
1
1
1
2
2
2
1
2
1
0
1
2
2
1
1
0
1
2
1
0
1
1
2
1
1
1
0
1
1
1
0
1
1
1
0
0
1
1
1
0
2
0
1
2
1
0
2
1
0
2
1
4
2
0
1
1
2
1
1
1
1
1
2
1
2
1
1
2
2
0
2
2
1
2
1
0
1
1
4
0
1
1
1
1
1
2
1
1
0
0
2
0
0
1
1
1
1
0
1
2
1
2
2
1
0
2
1
0
1
2
1
0
1
1
1
1
0
2
0
1
1
1
2
1
1
1
1
1
0
1
0
1
1
2
1
1
1
2
1
1
0
1
2
1
2
2
0
1
0
1
2
1
1
2
1
1
2
0
1
0
3
0
1
0
3
0
1
1
2
1
1
1
0
1
1
2
2
1
2
1
1
2
0
0
2
0
1
1
2
1
1
0
2
0
1
1
1
0
0
1
0
1
1
2
2
1
1
0
1
0
2
1
0
1
2
2
1
0
1
0
1
0
0
0
0
0
2
1
2
2
1
0
2
1
2
1
1
1
2
1
2
0
1
2
1
1
1
1
1
3
0
1
0
1
1
0
1
1
0
1
1
0
0
1
1
1
1
1
1
1
3
1
2
2
1
2
0
2
1
1
1
1
1
1
2
1
0
0
1
0
2
1
1
0
0
0
1
1
1
1
0
0
0
1
0
1
2
2
0
1
2
0
0
0
0
0
2
1
1
1
1
1
1
0
1
0
1
0
1
0
0
1
1
1
2
0
0
1
2
0
1
1
0
1
1
2
1
2
2
0
0
2
0
1
2
2
1
0
2
1
1
0
1
1
1
0
0
0
2
1
2
2
0
2
1
0
3
2
0
2
2
0
0
2
0
1
0
2
1
2
2
1
3
0
1
2
1
0
2
0
1
1
1
1
1
0
0
0
1
3
1
1
1
0
1
1
0
1
1
1
1
2
0
1
1
2
0
2
1
2
0
1
1
1
0
1
2
1
1
0
0
1
1
0
1
0
1
1
3
2
0
1
2
1
2
1
0
1
0
0
1
1
1
3
2
1
1
1
2
2
1
1
2
1
2
2
1
2
1
0
1
1
1
1
0
2
1
1
1
1
1
0
1
0
2
1
0
1
1
0
0
0
1
3
2
0
1
1
2
0
3
2
1
1
1
0
1
0
1
1
1
0
1
0
1
1
2
1
1
1
1
2
2
1
1
2
1
1
3
1
1
1
2
1
0
1
1
0
1
1
1
1
2
2
2
1
1
2
3
0
0
0
1
0
1
1
2
1
1
0
1
1
2
0
0
0
1
2
2
2
0
1
1
0
0
1
2
1
2
1
1
1
1
1
1
1
0
2
2
1
2
1
2
1
1
0
3
1
1
0
2
1
1
1
2
1
2
0
2
0
2
2
1
0
1
0
2
2
1
1
1
2
3
1
0
1
2
5
1
2
0
2
2
1
0
1
1
1
0
1
1
1
1
0
1
1
0
0
2
1
0
1
1
0
1
1
0
0
1
0
1
1
1
0
0
2
1
0
2
1
1
2
1
1
0
1
0
1
1
1
1
1
0
2
1
1
2
1
2
2
0
1
2
1
1
1
2
0
1
2
3
1
1
1
1
2
1
0
1
2
1
2
2
2
1
1
0
2
1
1
1
1
1
0
1
4
1
1
0
1
2
0
2
1
1
0
2
0
1
0
0
2
1
1
1
1
2
1
1
3
0
2
1
1
2
2
2
2
1
2
2
2
1
1
0
0
1
1
2
1
2
2
0
1
1
0
1
2
2
1
1
0
1
1
2
0
2
1
1
1
1
2
1
2
0
0
0
1
2
0
0
0
1
2
0
1
1
1
1
1
1
0
2
1
1
1
0
1
1
0
1
1
1
1
2
1
1
0
2
0
0
2
0
2
1
1
0
0
1
1
0
1
0
2
1
0
1
2
1
1
0
0
0
0
1
1
1
1
1
2
2
1
2
1
1
1
0
1
1
0
0
2
1
1
2
1
1
0
2
0
1
1
1
1
1
1
1
2
1
2
0
1
0
2
0
1
2
3
1
1
0
2
1
1
0
1
1
1
2
1
1
1
0
0
2
1
1
0
2
1
1
0
2
1
0
2
1
0
1
1
1
1
1
0
1
1
0
0
2
1
1
0
2
2
1
1
1
1
0
1
3
1
0
1
1
1
1
0
2
2
1
0
1
0
1
1
0
1
1
2
0
1
2
1
2
1
1
1
1
1
0
0
1
1
1
1
1
2
0
2
2
0
1
1
2
1
1
0
2
1
1
2
0
1
0
2
1
1
2
0
1
0
1
1
1
1
1
1
1
1
0
1
0
0
1
0
1
1
1
2
1
0
1
0
1
1
1
1
1
1
1
1
1
2
0
2
2
0
1
1
2
2
2
2
2
1
0
0
2
1
1
1
1
1
2
1
1
1
2
1
0
1
1
2
2
1
1
2
0
1
1
1
1
1
2
2
1
0
0
2
1
1
2
1
1
1
2
1
1
0
1
2
0
1
0
1
1
1
2
2
1
1
1
1
2
1
1
3
1
0
2
2
0
2
0
0
0
1
0
0
2
2
0
0
2
1
1
0
1
0
1
1
1
2
1
1
0
0
2
2
0
2
0
1
1
1
2
0
1
2
1
0
2
1
2
1
1
2
2
2
1
1
3
1
0
0
1
1
2
1
2
1
2
1
1
0
2
1
1
1
2
1
2
0
1
2
2
1
2
1
1
0
1
0
1
2
1
1
1
1
1
2
1
0
1
1
1
0
1
1
1
1
2
1
0
1
2
1
2
2
1
1
1
1
1
1
0
1
0
2
0
2
2
1
0
2
1
0
1
2
2
0
0
1
1
2
1
1
1
0
1
3
1
2
3
0
0
1
2
0
0
1
1
0
1
0
1
1
1
0
1
1
0
1
0
1
1
2
1
2
0
1
0
0
1
2
2
1
2
2
1
0
1
1
2
1
1
1
0
0
1
2
0
0
2
0
1
1
0
1
2
0
1
1
2
2
0
1
1
1
0
0
1
2
2
1
1
0
1
2
2
1
1
1
1
2
0
1
0
2
1
1
1
1
1
1
1
1
1
1
0
0
1
0
1
2
1
0
1
1
0
0
0
0
1
0
1
2
1
1
1
1
0
0
1
0
1
1
1
0
1
1
0
2
2
1
1
1
2
0
2
1
1
2
1
1
1
2
1
0
1
1
0
1
0
1
2
2
1
1
1
0
1
0
2
1
1
0
1
0
2
0
2
1
1
1
1
2
1
1
1
0
1
1
0
0
2
1
1
0
1
1
1
1
1
0
1
2
0
1
1
2
0
0
1
2
0
0
1
2
1
1
3
1
2
0
1
1
1
0
2
0
2
1
2
1
1
1
1
1
1
0
1
1
0
1
1
1
0
1
2
1
1
2
2
0
3
1
0
1
2
3
2
0
1
1
1
1
0
1
0
1
2
2
2
0
2
1
0
1
2
1
0
0
2
0
0
1
0
2
0
2
1
0
2
2
2
1
1
2
1
0
1
1
2
0
1
1
1
0
1
1
1
1
2
1
4
2
1
0
1
0
2
0
0
1
1
0
1
1
2
0
2
1
1
1
1
1
2
1
1
2
1
0
1
0
1
0
2
1
1
1
1
1
1
0
1
1
0
0
1
4
1
0
1
1
0
0
1
0
1
2
2
1
0
2
0
0
1
1
1
1
0
0
2
2
0
1
1
1
1
1
3
1
2
1
1
0
1
1
2
0
0
1
1
1
2
0
1
1
2
0
1
0
1
2
1
2
1
2
1
0
1
1
1
1
0
2
1
1
2
1
0
0
1
1
2
2
1
0
0
0
1
1
1
0
1
0
0
1
2
0
0
0
1
1
1
1
1
0
1
0
2
1
2
0
1
2
1
2
0
1
1
1
0
1
1
1
1
0
2
2
1
2
1
1
1
2
1
1
0
1
1
2
1
2
0
1
0
2
0
1
0
2
1
1
2
0
0
0
1
0
0
2
2
0
2
1
1
3
1
1
1
1
1
0
2
0
2
1
0
2
0
1
2
1
1
2
0
1
1
0
1
2
1
1
0
2
0
1
0
0
2
1
2
2
1
0
1
1
0
1
2
0
2
0
1
0
0
1
1
0
1
0
2
1
1
0
2
0
0
2
1
0
0
0
0
1
0
0
1
1
1
2
1
1
2
0
0
2
0
1
1
0
1
3
1
1
2
1
0
0
1
2
1
2
0
1
1
2
1
0
2
0
1
2
1
0
1
1
1
0
2
0
2
1
2
0
0
2
0
0
0
0
1
0
0
1
1
1
1
2
1
2
0
1
2
0
0
1
0
1
2
0
1
1
2
1
0
1
1
1
1
0
2
2
1
2
1
1
0
0
1
0
1
4
0
0
1
1
0
0
1
1
1
1
0
1
0
1
1
1
1
1
2
2
1
0
1
1
0
1
0
1
1
0
0
0
1
0
1
1
2
0
2
1
2
2
0
0
1
0
1
2
0
0
0
0
1
2
0
2
0
1
1
0
0
1
1
0
2
2
1
0
1
1
1
1
2
2
1
1
2
2
0
0
1
1
1
1
1
0
0
4
2
1
2
2
2
1
2
1
0
1
0
1
1
2
1
1
1
1
0
0
1
1
0
1
1
2
1
0
0
1
0
2
1
1
0
2
0
1
1
1
1
0
1
1
1
2
0
2
1
0
3
2
1
0
2
0
1
1
0
1
1
2
1
0
2
2
1
0
0
1
0
1
2
1
0
1
2
2
2
1
1
1
0
0
0
1
0
1
2
0
2
1
2
2
1
0
0
1
1
1
2
1
1
2
0
0
1
1
1
1
1
1
1
2
0
1
0
1
1
0
0
1
1
1
1
1
1
1
0
3
0
1
1
1
1
0
0
2
0
2
1
0
1
1
1
2
0
2
0
1
2
1
1
1
1
0
1
1
0
0
2
0
1
2
1
0
2
2
0
2
1
1
2
1
1
2
1
1
1
2
2
0
1
1
3
1
0
1
1
2
2
1
1
2
1
1
1
2
1
1
1
0
1
1
1
0
1
2
0
1
0
1
0
2
1
1
0
0
2
0
1
1
1
1
2
1
2
0
1
1
0
1
2
0
0
2
1
0
2
0
0
1
2
1
2
0
3
1
0
0
2
1
1
0
0
0
0
1
1
2
2
1
1
2
0
0
1
0
1
0
1
1
2
2
2
0
0
0
2
1
1
1
1
0
1
1
0
1
2
1
1
2
1
1
1
0
0
1
1
2
1
1
2
2
3
2
1
0
2
0
1
1
1
2
1
3
0
1
1
2
1
1
1
1
2
0
0
0
1
2
0
1
1
1
0
0
0
1
2
0
1
1
0
1
2
1
2
0
1
0
0
0
0
0
0
1
2
0
1
0
0
2
1
2
1
2
1
1
1
0
1
1
0
1
2
1
0
1
1
1
3
2
0
0
1
1
0
2
0
2
2
0
1
1
0
1
0
1
1
2
0
0
0
2
0
2
0
0
1
0
1
0
1
0
0
1
0
2
1
1
0
1
1
2
0
1
2
1
1
1
2
1
1
1
2
1
1
0
2
2
2
1
1
2
1
3
2
0
1
2
0
1
0
1
2
1
0
1
2
0
2
2
1
1
0
1
1
1
0
1
1
0
0
1
0
0
1
0
1
0
0
2
1
1
2
1
1
0
1
2
1
0
1
0
0
0
0
0
1
0
2
1
1
1
0
1
0
1
2
1
1
1
1
0
0
0
0
1
2
2
1
1
0
1
0
1
0
1
0
2
0
0
2
1
2
2
0
1
0
2
1
1
0
2
1
1
1
2
2
1
1
4
1
1
0
0
1
0
1
2
2
1
0
2
1
1
1
1
2
0
0
0
0
2
2
0
0
0
1
0
1
1
1
0
1
2
1
2
2
1
0
1
2
0
0
1
0
2
2
2
1
1
1
0
2
0
1
1
2
2
1
0
2
2
1
3
1
1
0
1
1
2
0
1
1
1
1
0
2
2
0
1
2
0
2
0
1
1
0
0
2
0
0
1
0
1
0
0
2
1
1
2
0
1
1
0
0
1
2
1
0
2
1
1
2
1
0
2
1
1
1
1
1
1
1
0
0
1
1
2
0
2
1
2
1
1
0
1
2
0
2
1
0
1
0
5
0
1
0
3
1
1
0
0
0
0
1
1
2
0
0
0
2
1
1
2
0
1
1
1
1
0
1
1
0
1
1
1
2
0
1
1
2
0
2
1
0
2
0
1
1
0
1
0
2
1
2
1
1
2
1
2
1
1
1
2
0
0
3
1
2
1
0
0
0
1
1
2
1
1
0
0
2
0
0
1
0
1
1
0
1
2
1
2
1
1
1
2
1
1
1
1
1
2
1
1
0
1
0
1
2
0
1
0
0
1
1
0
1
0
0
0
0
1
0
1
1
1
1
2
0
2
1
0
1
2
2
1
1
0
1
0
0
0
1
1
1
1
0
1
1
3
0
1
1
1
1
1
2
2
1
0
1
2
0
2
4
1
0
1
2
1
2
3
1
1
1
2
1
0
1
2
1
0
2
1
0
1
1
2
1
1
2
1
1
2
0
1
1
2
1
0
2
1
0
2
2
2
0
1
0
0
1
0
2
1
1
1
2
1
1
1
2
2
2
0
1
1
0
1
1
0
0
2
2
1
2
2
1
1
2
0
1
0
2
1
1
1
1
0
0
1
1
1
2
1
0
0
1
1
1
0
1
1
0
0
2
0
0
2
1
1
2
0
0
0
2
0
0
1
2
0
1
1
0
2
0
0
0
1
1
0
0
0
2
2
0
1
1
0
0
2
0
0
1
1
1
1
1
1
1
1
2
0
2
1
2
1
1
2
2
1
0
0
1
0
2
0
1
0
2
1
2
0
2
0
1
0
1
1
0
1
2
2
1
2
0
1
2
0
1
1
1
1
0
1
1
1
1
1
1
0
1
1
0
0
1
2
3
1
1
0
1
1
0
1
1
1
1
1
1
0
0
1
0
0
1
2
1
1
3
1
2
0
1
0
1
1
0
0
1
2
1
1
1
2
0
1
1
0
1
1
1
0
0
1
0
2
1
3
1
1
2
2
2
1
0
1
1
0
1
0
1
2
1
0
2
2
2
2
0
1
1
1
1
1
2
1
0
1
1
1
0
0
1
0
1
1
1
1
2
1
1
2
0
0
2
0
2
0
3
1
0
0
0
2
0
2
1
0
1
1
0
0
0
1
2
2
1
1
1
2
1
1
0
1
0
0
1
0
2
2
0
1
1
2
1
0
2
1
1
1
1
2
1
1
1
0
1
1
1
0
1
2
0
0
1
1
0
1
2
1
1
1
1
2
2
1
2
1
2
2
1
0
0
1
1
1
2
0
1
1
1
0
1
2
0
1
0
1
1
0
0
1
0
2
0
0
2
0
2
0
1
0
2
0
1
2
1
1
2
2
1
0
1
1
1
1
0
1
0
1
1
1
0
2
2
0
2
1
1
2
1
1
0
2
0
2
1
1
0
0
1
1
0
0
0
0
1
2
0
2
0
2
1
0
0
0
1
1
0
1
0
1
1
1
2
0
1
0
0
1
0
1
0
1
0
1
1
2
1
0
1
1
1
1
0
0
1
1
1
0
2
0
1
2
1
1
0
1
1
1
1
2
1
1
1
0
0
2
1
1
0
0
1
0
1
2
0
1
1
1
2
0
0
1
0
2
2
1
0
2
1
2
0
1
1
1
2
1
1
1
1
2
0
0
1
0
0
1
1
1
2
0
0
1
1
1
2
3
0
1
0
2
1
0
0
1
1
0
1
0
0
1
0
2
0
0
1
1
1
0
0
3
2
1
2
0
0
0
0
1
0
1
1
1
1
0
1
0
0
2
0
2
1
1
1
1
0
0
1
0
1
1
0
2
2
0
1
0
0
0
1
2
2
1
1
1
1
1
2
0
1
0
1
1
0
1
2
1
1
2
0
1
3
2
2
1
1
0
1
0
1
1
1
2
2
2
1
1
2
0
0
1
2
1
1
0
0
1
1
0
1
1
1
2
0
0
1
1
1
0
1
1
1
2
1
1
0
3
1
0
1
0
2
1
1
1
0
0
1
2
1
1
2
0
0
1
0
2
1
1
1
1
2
1
0
1
1
0
1
0
1
1
2
0
1
1
1
1
2
2
2
1
1
2
1
0
1
1
2
3
0
1
0
1
0
2
1
1
1
0
1
2
0
1
1
1
2
1
2
1
1
0
1
1
1
2
0
1
2
1
1
0
1
2
2
1
2
1
1
1
1
0
2
2
1
1
0
1
2
0
0
0
2
1
1
1
2
1
1
0
1
0
1
1
1
2
0
1
2
1
0
0
2
4
1
0
0
2
1
2
1
0
1
0
2
1
0
1
1
1
0
0
1
2
1
1
2
1
1
0
1
2
0
2
1
0
1
0
0
0
2
1
0
1
1
1
1
1
1
0
0
1
1
1
1
1
2
0
1
2
1
1
1
1
2
0
0
1
1
2
1
1
1
1
0
1
0
2
1
2
1
1
0
1
0
0
1
2
2
2
1
1
1
1
1
1
2
1
2
0
0
1
0
2
0
1
1
1
1
1
1
1
2
1
0
2
1
1
1
1
2
1
1
2
2
1
1
0
2
0
1
1
1
1
1
0
1
0
2
1
4
1
0
1
1
2
0
1
1
2
1
0
1
1
1
0
0
0
0
1
1
2
1
1
2
2
0
2
0
2
0
1
1
1
0
1
0
0
1
2
0
0
1
1
0
1
1
2
0
1
0
1
1
2
1
1
0
0
1
2
1
1
0
1
1
1
0
2
1
1
1
0
0
1
1
2
1
2
1
1
0
1
1
2
1
3
0
1
1
0
0
1
0
1
0
0
2
2
3
0
2
0
0
1
1
1
1
1
1
1
0
0
1
2
2
2
2
1
1
2
1
1
2
0
2
2
1
1
1
1
2
1
1
1
0
0
1
1
1
1
1
1
0
1
2
0
1
0
0
1
1
2
0
1
1
1
0
1
2
1
2
0
1
0
1
0
2
0
2
0
2
0
1
0
0
0
1
0
0
1
3
1
1
0
1
1
1
1
0
0
2
1
1
1
1
0
0
1
2
0
0
0
1
1
0
0
0
0
2
0
1
1
1
1
0
1
1
0
1
1
0
0
2
1
0
2
1
5
0
0
1
1
1
0
1
2
0
1
1
1
0
2
1
0
1
1
1
0
0
2
1
1
1
0
0
1
1
1
0
0
1
2
1
2
1
2
0
1
2
2
2
0
2
1
0
2
1
0
2
0
1
1
2
1
1
1
0
0
1
1
1
1
1
2
1
2
1
0
1
2
0
1
0
2
1
1
0
2
0
1
2
2
0
1
0
1
1
1
2
0
1
1
1
0
1
1
0
1
2
0
2
2
1
1
1
1
2
1
1
2
1
0
0
1
1
0
0
1
0
1
2
2
1
1
1
0
1
2
1
1
0
1
1
1
0
1
1
0
2
0
1
0
2
0
0
0
1
0
0
0
2
1
0
2
0
2
0
1
1
0
2
2
0
1
1
1
1
1
0
0
0
2
0
1
1
1
0
1
0
0
1
0
1
0
1
2
1
1
0
0
1
1
1
0
1
1
1
1
1
0
2
2
1
0
2
1
1
0
0
2
2
2
1
1
2
2
1
0
0
1
0
1
1
1
2
0
1
1
1
2
1
2
2
1
1
1
1
2
2
1
2
0
1
1
2
1
1
1
1
0
2
0
2
1
0
0
0
1
1
1
1
2
1
1
1
1
2
1
1
1
4
1
0
0
1
2
1
1
0
1
0
1
1
2
1
0
1
2
2
1
1
1
1
0
1
2
1
1
0
1
1
1
2
0
1
0
0
1
1
1
2
0
1
0
0
1
0
1
0
1
2
1
2
1
2
2
0
2
1
0
1
1
0
1
0
2
1
1
2
0
1
1
1
1
0
1
1
1
1
2
2
1
0
0
0
1
0
2
2
0
0
0
1
0
2
1
1
0
1
1
0
1
2
1
2
2
1
0
0
0
0
1
0
1
2
2
1
1
1
1
1
1
1
1
2
2
1
2
2
0
1
0
1
1
1
1
0
1
1
2
1
0
1
1
1
3
0
1
1
2
1
2
1
0
3
1
0
2
0
1
1
1
1
1
2
2
2
1
2
0
0
2
1
1
0
1
0
1
0
1
1
1
2
1
2
1
1
0
1
0
1
2
1
1
1
1
0
0
1
0
2
0
0
0
1
1
2
2
1
1
2
1
0
0
2
0
2
0
0
2
1
0
1
1
1
0
1
1
1
2
1
1
0
4
0
1
1
0
1
0
1
1
0
2
1
1
2
0
1
0
1
2
1
0
0
0
0
1
1
1
1
0
0
0
1
1
2
0
0
0
2
0
1
1
1
1
1
1
0
0
2
2
0
0
0
0
1
2
0
1
1
0
1
1
0
1
0
2
0
0
0
0
1
0
1
0
0
0
1
1
0
0
2
0
2
2
2
0
0
1
0
1
1
1
0
2
1
2
2
2
0
1
1
1
1
1
1
1
1
1
1
0
0
2
0
1
0
1
1
1
2
1
1
1
0
1
1
0
1
1
2
2
1
0
1
2
1
1
1
1
1
0
0
0
1
1
1
1
1
1
0
1
0
1
1
1
0
1
0
1
0
2
0
1
1
1
1
1
1
0
1
2
0
0
1
0
1
1
1
0
1
0
1
0
1
0
0
1
2
1
1
0
1
1
1
0
0
1
1
2
1
1
2
0
0
0
0
1
1
0
1
2
1
1
2
0
1
2
0
1
1
1
1
1
1
1
0
2
0
0
1
0
1
2
1
1
2
2
1
2
2
2
0
1
0
2
0
1
2
0
1
1
1
1
0
1
3
0
1
2
0
0
1
1
0
1
1
1
2
0
1
0
1
2
2
1
1
1
0
2
1
0
0
2
2
0
1
0
1
2
0
2
2
2
1
1
1
1
1
0
0
2
1
1
1
1
1
1
0
0
1
1
1
0
2
1
1
2
1
0
2
1
0
1
0
0
1
1
0
1
1
0
3
1
0
1
1
1
1
1
2
2
0
1
1
1
1
2
1
0
0
1
2
1
1
2
1
1
1
1
0
0
1
1
1
2
0
1
1
2
1
0
2
2
1
1
1
1
1
2
1
1
0
1
1
0
1
1
1
1
0
1
1
0
0
0
1
1
0
1
1
1
1
0
2
2
1
1
0
0
0
0
2
1
0
1
1
1
1
2
1
1
2
1
1
1
0
0
0
0
1
0
2
1
2
0
0
1
1
0
1
0
1
0
0
1
0
0
0
1
0
1
1
0
0
0
1
0
2
1
0
1
2
1
1
1
1
1
1
2
2
0
1
0
1
1
1
1
1
2
0
0
0
2
1
1
1
1
0
1
1
1
2
2
1
0
0
1
0
0
0
0
0
1
2
0
1
0
0
2
0
2
0
2
0
0
1
0
1
1
1
2
1
1
0
2
1
1
1
1
2
2
0
1
1
2
1
0
1
0
1
0
0
2
1
1
0
1
3
1
1
1
1
1
1
0
1
1
1
0
1
1
2
0
0
2
1
1
2
1
1
0
0
1
1
1
1
1
0
2
0
1
1
1
1
1
1
0
2
1
2
1
1
0
1
0
1
1
1
2
2
1
1
0
1
1
0
2
2
1
1
1
0
2
1
1
0
0
1
0
2
1
1
1
1
1
1
2
0
1
2
1
1
0
2
0
1
0
0
1
1
1
1
1
1
0
2
2
0
1
2
1
1
2
1
1
1
2
2
1
1
1
2
1
0
1
1
0
0
0
0
3
1
0
1
0
1
2
2
2
0
0
0
1
2
2
1
0
1
0
1
2
1
2
0
1
2
1
1
1
1
1
2
1
1
2
1
1
1
1
0
0
0
2
0
0
2
2
1
1
1
1
1
1
1
0
1
0
1
1
1
0
1
0
0
0
0
2
1
2
1
1
1
0
1
1
2
0
1
1
1
0
1
1
1
2
0
0
1
1
1
1
1
1
0
1
1
3
0
1
1
0
2
1
1
1
1
2
0
0
1
1
0
2
2
1
0
0
1
1
1
1
1
1
0
1
1
1
1
0
0
0
1
1
2
2
1
0
0
1
0
2
2
0
1
1
1
0
0
0
1
1
1
2
2
0
0
2
0
2
1
1
0
0
0
1
1
0
2
1
1
1
0
2
1
1
1
0
0
1
3
1
0
2
0
2
0
0
0
2
1
1
0
2
1
2
1
2
2
2
1
1
2
0
0
1
1
0
1
1
2
1
2
0
1
0
0
1
2
1
1
0
2
2
1
1
1
0
1
1
1
1
1
1
1
1
1
2
2
0
1
0
1
1
0
0
1
0
2
1
0
1
1
2
1
1
1
1
1
2
1
0
0
0
2
1
0
1
1
2
2
1
2
2
0
0
1
1
1
0
0
2
0
0
2
1
1
0
1
0
1
1
0
0
2
1
0
1
1
1
2
1
1
1
0
1
1
3
0
2
2
1
1
1
1
1
0
1
2
1
1
0
1
0
1
0
2
0
1
0
1
2
2
0
1
1
2
1
1
1
0
0
1
0
1
1
2
2
0
0
1
0
1
0
1
0
1
2
2
1
1
1
0
1
0
0
1
1
1
0
0
1
1
1
2
1
2
0
1
1
0
0
1
1
0
2
1
1
0
1
1
3
1
1
1
0
1
1
1
1
1
2
1
0
1
1
0
1
2
2
0
2
0
0
0
1
2
2
2
1
2
2
0
0
1
1
2
0
2
1
2
0
0
0
0
2
2
0
2
2
2
1
0
1
1
1
1
1
1
2
0
1
1
1
1
2
1
1
1
1
1
2
1
1
2
2
0
0
0
2
2
3
0
0
1
1
2
1
0
2
1
1
1
1
2
1
1
0
1
1
1
0
1
0
0
1
1
1
1
0
2
1
2
0
2
0
1
0
1
1
0
2
0
1
1
0
0
1
0
2
0
0
1
1
1
2
1
2
1
1
1
2
1
1
0
2
2
2
1
1
1
0
2
1
1
0
1
1
1
1
2
0
2
1
0
1
2
3
1
1
1
0
1
1
1
2
0
2
2
2
0
0
1
0
1
0
1
0
0
0
0
0
1
4
0
0
1
1
0
0
1
1
1
0
2
0
0
1
0
0
1
1
1
1
1
2
3
1
1
1
1
1
1
1
1
2
0
1
0
2
0
1
1
1
2
1
1
1
1
1
0
1
1
1
1
1
1
2
0
0
1
0
0
0
2
1
0
1
0
0
0
1
0
2
0
1
0
0
1
0
1
0
2
1
3
0
1
0
1
2
0
0
2
1
0
1
1
2
0
0
0
0
2
2
1
1
1
1
0
2
0
0
1
2
0
1
1
0
1
1
1
2
0
0
1
2
1
1
1
0
1
1
0
2
1
1
0
2
1
0
1
1
0
1
2
1
0
1
0
1
1
1
0
1
1
1
1
1
1
1
0
1
1
0
2
0
2
0
2
0
1
2
1
0
1
1
0
1
1
1
0
0
1
1
0
2
0
0
2
1
1
1
1
2
0
1
0
2
1
1
1
0
1
1
0
0
1
0
0
0
0
1
1
1
1
1
1
1
1
2
1
2
0
2
1
3
1
1
1
0
0
2
2
1
2
1
2
2
2
0
2
1
0
1
1
2
2
0
1
1
0
0
1
2
0
1
2
1
1
1
1
0
1
1
1
0
1
2
1
1
1
0
1
0
1
0
1
1
2
2
1
2
1
1
2
2
1
1
2
2
1
1
1
2
1
1
0
1
1
2
1
1
0
1
2
0
2
1
1
2
1
1
1
1
0
1
0
1
0
0
1
1
2
2
2
2
1
2
2
1
1
1
2
1
1
2
1
0
1
1
1
1
1
1
0
1
2
2
0
1
1
3
0
1
1
0
2
1
2
2
0
1
2
1
1
1
2
1
1
0
1
0
1
0
2
2
0
1
0
1
0
2
0
3
1
0
2
0
0
1
2
2
1
1
1
1
1
2
1
1
1
2
2
1
1
0
2
2
2
1
1
0
4
1
0
0
2
1
2
1
0
1
0
1
2
0
0
2
1
2
1
2
2
1
2
0
0
1
2
1
1
0
1
1
1
0
1
1
0
2
1
1
2
1
2
1
2
1
2
2
0
0
1
2
1
0
1
2
1
1
1
2
2
1
0
1
1
1
1
0
1
1
0
2
0
2
1
2
2
2
1
1
1
2
1
1
1
1
1
0
1
2
2
2
0
1
1
1
1
0
1
1
1
1
2
1
1
1
1
1
0
1
0
1
1
1
1
0
1
0
1
1
0
2
1
1
2
1
1
0
0
0
1
1
1
0
1
0
1
1
1
1
1
2
0
2
1
2
2
0
0
1
0
1
0
0
0
0
1
2
1
2
1
2
1
1
2
1
0
1
1
1
0
1
1
0
1
2
1
1
2
0
1
2
0
1
0
1
1
3
2
1
2
1
0
1
1
1
1
0
0
1
0
1
2
2
1
1
0
0
1
1
1
0
0
0
1
0
1
1
0
1
1
1
1
0
1
1
1
2
2
1
1
0
3
1
1
1
1
2
1
2
0
1
0
1
0
1
1
0
2
2
1
1
1
2
1
1
1
1
1
0
1
1
1
2
2
0
0
1
2
0
2
3
1
1
1
1
1
1
2
2
1
1
0
2
1
2
1
1
0
1
1
0
2
1
0
2
1
1
0
1
1
1
1
0
1
1
1
0
0
2
1
1
0
1
1
0
1
0
0
1
1
0
2
1
1
1
1
0
0
0
0
2
1
2
1
1
1
0
1
1
0
1
0
0
1
0
1
1
0
1
2
0
2
1
1
0
1
1
1
1
2
3
2
2
2
1
2
2
0
1
2
1
0
1
2
0
2
2
1
0
1
1
0
2
1
0
1
2
0
0
2
1
1
1
0
0
2
0
1
2
0
2
1
1
0
2
0
1
1
2
1
0
0
2
1
0
1
2
1
0
1
2
1
1
1
1
3
1
1
0
0
2
2
1
2
1
0
2
0
1
0
2
1
0
0
0
1
1
0
1
0
1
0
1
1
1
2
0
1
0
1
0
1
0
2
1
1
1
1
1
1
0
1
0
1
0
1
1
1
0
1
0
0
1
2
1
1
1
2
0
1
2
0
0
1
0
2
2
2
1
0
0
1
0
0
1
1
1
1
4
1
1
1
2
1
2
2
1
1
2
0
1
1
2
2
0
1
2
1
2
1
1
2
3
1
0
1
1
0
1
1
2
1
1
2
1
1
1
0
1
1
2
1
2
1
1
2
1
1
0
1
3
1
1
1
1
1
2
1
0
1
2
1
1
2
1
0
2
0
1
0
1
0
1
0
0
1
2
0
1
1
1
1
0
1
0
1
1
0
2
1
1
0
1
1
0
1
0
2
1
0
1
2
2
2
0
0
1
0
1
1
0
1
2
1
0
0
2
1
1
1
2
0
2
1
1
0
1
1
2
2
1
1
0
0
1
1
0
1
0
1
0
1
0
2
1
0
1
2
0
1
2
0
0
1
3
0
1
2
1
2
2
2
0
1
1
1
1
1
2
1
1
1
2
1
0
2
2
2
1
2
1
1
1
0
1
1
0
0
1
2
1
0
1
2
1
1
1
1
2
0
1
0
0
1
0
1
1
0
2
0
0
0
2
2
1
1
1
2
2
2
2
1
0
1
2
2
0
1
1
2
0
1
0
0
0
1
0
1
1
2
1
0
2
0
2
1
2
1
0
1
1
1
1
0
1
2
1
2
0
1
0
1
2
1
0
2
0
1
0
1
1
1
1
0
2
0
1
0
2
2
0
2
1
0
1
2
0
0
2
1
1
0
2
1
1
1
2
1
1
1
2
1
0
0
2
1
2
1
1
1
1
2
1
0
2
2
0
2
2
0
0
0
1
0
2
1
0
1
0
1
0
2
0
1
1
1
1
2
1
2
2
0
1
1
2
0
1
1
0
2
0
1
1
1
0
1
1
0
2
2
1
0
1
1
1
1
1
0
2
1
1
1
1
1
1
2
2
1
1
0
0
1
0
0
0
1
0
1
1
2
1
2
0
2
1
2
1
1
2
0
1
1
1
1
0
0
0
1
0
1
3
1
2
0
2
2
0
1
1
1
2
1
1
0
2
1
1
0
1
1
2
1
3
0
1
1
0
0
1
1
2
0
1
2
1
1
2
1
0
4
2
1
1
1
2
1
1
0
2
0
2
1
0
0
2
1
0
1
0
1
2
1
1
1
1
2
0
1
1
1
1
0
1
1
1
0
0
0
4
0
1
1
0
2
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
0
2
1
2
0
2
2
1
0
0
0
0
0
1
1
0
1
2
0
1
0
2
1
1
1
1
1
2
2
1
1
1
1
1
2
0
1
2
0
1
1
2
2
2
2
1
0
0
0
0
1
2
1
0
1
1
1
0
1
1
1
1
2
6
0
1
1
1
1
0
0
1
1
2
0
0
1
0
1
1
1
1
1
2
0
2
1
1
0
1
1
0
0
2
2
1
0
2
4
1
2
1
1
2
0
1
1
2
1
1
2
1
0
1
0
1
1
1
1
0
2
2
2
1
1
0
0
0
1
0
1
1
2
2
2
0
1
0
1
1
2
0
2
1
0
0
1
3
0
0
0
0
1
1
2
1
0
0
0
1
0
2
2
2
1
1
1
1
0
0
0
1
0
1
1
1
0
0
1
0
2
1
1
2
2
0
1
0
1
0
1
0
1
0
1
0
2
1
1
1
1
2
0
0
1
1
1
0
2
2
1
1
2
0
2
1
1
0
0
1
2
1
2
1
1
1
0
1
0
0
1
3
1
1
2
0
1
1
2
2
2
1
0
2
2
1
2
0
1
1
0
1
2
0
0
0
2
2
1
1
0
0
0
2
1
0
2
1
1
2
0
0
1
1
0
2
0
2
1
2
0
1
0
0
0
1
1
1
1
0
2
1
2
0
1
0
3
1
0
0
1
1
1
2
1
0
2
1
2
2
2
3
1
0
2
2
0
1
1
2
2
2
2
1
0
1
1
1
2
1
2
2
0
2
2
2
0
2
1
0
1
2
2
2
0
0
0
1
1
1
0
2
2
1
1
2
0
1
1
0
2
2
1
2
1
1
0
0
0
1
1
1
0
1
1
1
1
3
2
1
1
0
0
1
1
1
0
0
2
2
1
1
1
0
0
0
1
1
0
0
0
1
2
2
1
0
2
1
1
1
2
0
0
0
0
1
2
1
1
0
0
2
1
2
2
1
2
1
1
0
0
0
2
1
1
1
1
0
1
2
0
0
2
1
1
1
1
1
1
1
2
0
1
0
0
0
1
0
2
1
1
1
1
1
0
0
2
0
1
1
2
1
1
1
1
1
1
0
1
2
1
0
1
1
1
0
1
0
1
2
0
0
0
1
2
2
2
0
2
1
2
2
0
0
1
0
2
1
1
2
1
1
0
1
0
1
2
2
1
0
2
1
1
0
1
1
0
1
1
1
1
1
2
1
0
0
1
0
1
1
1
2
0
2
1
1
1
0
1
1
2
3
1
1
2
2
0
0
1
1
1
2
1
0
0
0
2
0
0
0
1
0
1
1
1
2
2
1
1
1
2
1
2
2
1
0
1
0
0
1
0
1
1
1
0
1
0
2
1
1
2
1
2
1
0
0
2
0
0
1
0
1
1
1
1
0
0
1
2
2
0
2
1
0
1
1
1
1
0
1
0
1
1
0
1
0
1
1
0
0
1
1
1
1
1
1
2
1
1
0
1
0
1
1
1
2
1
0
1
0
1
0
2
1
2
1
2
1
1
0
0
0
0
1
0
1
2
1
1
1
2
1
1
1
1
2
0
3
1
1
1
1
2
1
1
1
1
2
0
2
1
1
1
2
0
3
1
1
0
0
1
1
2
0
0
1
0
1
0
1
2
1
0
0
2
1
0
2
1
1
0
1
1
2
1
1
0
2
1
1
1
2
1
1
0
1
1
2
1
1
1
0
0
2
0
0
1
0
1
1
2
0
1
1
1
1
1
1
1
2
2
1
0
2
2
1
0
0
0
1
1
1
2
1
0
1
1
2
0
0
1
1
2
2
2
0
3
0
1
0
1
0
0
1
1
0
1
1
1
1
1
1
1
1
1
1
0
1
0
0
2
2
0
1
1
0
2
1
0
0
1
1
0
2
1
0
0
0
1
1
2
1
2
1
0
1
2
0
0
0
2
0
0
1
2
0
1
1
1
0
0
0
0
1
1
0
1
3
2
0
0
1
2
3
1
2
2
1
2
0
1
1
1
1
1
0
2
0
1
2
1
0
2
2
0
0
1
1
1
1
1
1
2
0
2
1
0
1
0
1
1
1
2
1
1
0
0
1
1
0
1
0
0
1
0
1
1
1
0
1
2
1
3
1
1
1
1
1
0
0
2
1
1
2
1
2
0
2
1
0
1
1
1
0
2
0
2
1
1
1
1
0
0
0
0
0
1
2
1
0
1
0
0
1
1
0
2
0
1
1
2
1
1
1
1
2
1
0
1
0
1
0
0
1
1
2
2
0
1
1
3
1
0
1
2
1
1
0
0
0
1
0
1
1
0
3
1
1
0
0
0
0
2
0
1
2
0
0
1
1
2
2
1
3
1
1
0
0
1
1
2
2
1
1
0
2
0
1
2
0
1
1
1
1
0
2
0
2
0
2
1
2
2
0
1
2
0
1
1
1
0
1
0
1
1
0
1
1
1
0
1
1
1
0
1
1
2
2
1
1
3
2
1
1
0
0
1
0
0
2
0
1
1
1
1
0
0
1
1
0
1
0
1
1
1
2
1
0
1
0
1
1
1
0
1
0
1
0
1
2
1
0
0
1
0
0
0
0
1
1
2
1
1
1
0
2
1
2
1
0
2
2
1
1
1
2
1
2
0
0
1
0
1
1
1
0
1
2
0
2
1
2
1
1
0
2
1
0
1
1
1
1
2
2
0
1
0
2
0
2
1
2
1
0
2
1
1
1
1
2
1
0
0
2
0
2
1
2
1
1
1
1
1
0
2
2
0
1
0
0
1
1
0
1
0
2
1
1
2
1
1
1
0
0
0
1
1
1
0
2
1
1
1
1
0
2
0
0
1
2
1
1
0
1
2
0
1
1
0
0
1
1
1
2
3
2
1
1
0
1
4
0
0
0
1
1
2
1
2
1
0
1
2
0
0
1
1
0
1
1
0
1
0
0
0
1
2
0
0
1
1
1
1
2
2
0
2
1
0
0
0
0
2
1
1
2
0
1
1
1
0
0
0
0
2
1
1
0
1
1
1
1
1
0
2
1
0
1
0
1
2
0
2
1
1
2
1
2
0
3
1
2
0
2
1
2
2
1
1
1
0
1
0
1
1
1
2
4
0
2
1
0
0
1
1
1
1
0
2
0
0
0
1
1
1
1
2
1
1
0
0
0
2
1
1
0
2
2
2
0
1
1
1
1
2
2
1
1
2
0
1
1
0
1
0
1
0
0
0
1
0
0
2
1
2
2
0
1
1
1
1
0
0
1
0
1
2
1
2
0
1
2
1
0
1
1
0
0
0
1
1
1
2
1
0
2
2
2
2
2
2
0
0
2
2
0
1
2
1
1
1
0
2
1
1
1
2
2
0
2
1
1
1
2
2
1
3
2
2
1
0
0
1
0
2
1
0
1
0
1
0
5
2
1
2
0
2
1
1
2
2
1
0
2
0
2
1
1
2
0
0
0
0
7
1
2
1
2
0
1
1
2
2
5
0
0
1
0
1
1
0
3
1
1
1
1
1
1
1
1
0
1
1
1
0
0
1
2
0
1
2
0
2
0
0
0
1
1
0
2
2
0
0
2
0
2
0
2
1
1
0
0
2
1
1
1
0
0
0
0
1
0
1
0
1
1
1
0
0
1
1
1
1
1
0
0
1
0
1
0
0
2
0
2
1
1
0
1
2
0
1
1
4
0
1
1
2
2
2
0
0
2
1
2
1
2
2
0
0
0
2
2
1
2
1
3
1
1
2
2
1
1
1
2
1
2
1
3
1
2
0
1
1
2
2
1
1
1
1
0
1
2
0
1
0
0
1
0
1
1
0
2
2
0
2
2
1
0
1
3
1
0
2
3
2
1
2
2
2
0
1
0
0
1
0
0
1
1
0
1
2
4
2
0
1
1
1
0
2
1
1
1
1
1
1
2
2
0
1
1
1
0
2
0
0
1
1
1
1
1
1
0
1
2
0
0
2
0
1
1
1
0
0
1
1
0
1
0
2
1
1
1
1
1
0
2
1
0
0
2
1
0
1
1
1
0
1
1
1
2
1
1
0
0
0
2
1
1
0
1
1
1
0
1
1
0
1
0
2
2
1
2
0
0
1
1
1
1
1
2
2
2
0
1
2
2
2
0
0
0
1
0
1
0
1
1
0
2
2
2
0
1
2
0
2
1
1
1
0
1
1
0
1
1
1
1
0
2
0
1
1
1
2
1
1
1
2
1
1
1
0
0
1
1
1
1
2
1
1
1
0
1
1
1
1
0
0
0
1
0
0
1
2
1
1
2
1
2
1
1
2
1
1
3
2
2
2
0
1
2
0
1
0
0
1
1
0
1
2
1
0
0
1
1
1
1
2
1
1
1
1
1
1
1
0
0
1
2
0
2
1
1
2
0
0
1
0
3
1
0
2
0
1
1
2
1
0
1
2
1
1
2
1
1
1
1
1
2
0
0
1
1
0
1
1
0
1
2
1
1
1
1
1
1
1
1
1
0
1
1
0
0
1
2
3
1
2
1
0
1
2
0
0
2
2
1
1
2
0
1
2
2
0
0
1
1
1
0
2
1
1
1
0
2
2
0
1
1
0
1
1
1
1
1
2
1
0
3
0
1
3
1
1
0
0
1
1
1
0
1
2
2
0
1
0
0
0
0
1
1
1
0
1
0
1
1
0
1
0
1
2
1
2
2
0
2
1
1
2
2
1
2
1
0
1
3
0
1
1
1
0
1
1
0
0
1
0
0
1
1
0
1
1
2
1
1
2
0
0
1
0
2
1
1
0
1
1
1
0
1
1
1
1
2
1
1
1
2
2
1
2
1
0
1
0
1
1
0
0
2
1
1
1
2
1
1
2
2
1
1
0
0
1
2
0
2
0
0
0
1
1
2
1
2
1
1
0
2
0
1
1
1
1
2
1
1
0
0
0
2
1
1
0
2
0
0
0
0
1
1
0
0
0
2
1
2
1
0
1
0
1
1
2
1
1
1
0
1
1
1
1
1
1
1
1
0
1
0
1
1
0
1
1
1
0
0
0
1
1
0
1
1
1
1
0
1
0
2
1
2
1
2
0
0
0
0
0
0
1
0
0
2
0
1
0
1
1
1
0
2
1
1
1
2
2
1
0
0
0
1
1
1
0
0
1
0
0
1
2
1
0
1
1
1
0
1
1
0
1
2
10
2
1
0
1
0
2
1
2
2
0
2
1
0
0
1
0
1
2
1
2
2
0
0
1
2
1
1
1
0
0
0
1
1
0
1
0
1
1
1
0
2
0
1
3
1
1
0
1
0
1
0
1
0
1
0
1
4
2
1
0
0
2
0
0
2
1
1
1
0
1
1
2
0
1
1
1
1
1
1
2
1
2
1
1
0
1
2
1
1
0
1
3
1
1
1
1
3
1
1
1
2
2
0
0
1
0
0
1
0
1
1
1
0
0
2
1
1
0
2
1
1
2
0
1
2
1
1
0
2
2
1
0
0
0
1
2
1
1
3
2
0
1
1
1
1
2
2
1
2
0
2
2
2
1
0
0
2
0
2
2
2
1
0
1
0
0
1
1
1
2
0
1
1
1
2
0
2
1
0
1
2
0
2
1
1
1
0
0
1
1
0
0
2
0
2
1
1
0
0
1
0
0
1
1
2
0
2
0
1
0
1
1
0
0
1
2
0
0
0
1
0
1
0
0
1
0
1
2
1
1
0
0
0
1
1
1
2
2
1
2
2
1
2
1
1
1
2
0
1
1
1
1
2
1
1
1
1
4
0
1
1
1
1
2
1
0
1
1
1
2
0
2
2
1
0
1
2
1
0
1
2
1
1
0
1
0
1
1
1
1
1
1
0
4
0
1
1
0
0
1
0
1
1
0
0
0
1
1
1
0
1
1
3
2
0
1
1
1
0
0
1
0
1
2
0
1
0
0
1
1
1
1
1
0
0
1
0
0
2
1
0
2
0
0
1
0
0
2
2
1
1
1
1
9
1
1
1
1
0
0
2
0
0
1
1
1
1
1
0
1
1
2
0
0
2
1
1
0
1
1
1
1
1
0
2
1
1
1
1
2
2
1
2
1
0
1
2
2
0
1
0
1
0
2
1
0
1
0
3
1
1
1
2
2
2
0
1
1
1
2
1
1
1
1
2
1
0
2
0
2
1
1
1
0
1
0
2
1
2
2
0
1
0
1
0
1
2
1
1
0
2
1
0
2
0
1
0
2
1
0
1
0
2
1
0
1
1
1
1
1
1
1
0
0
0
2
0
0
1
1
1
0
1
0
0
1
1
2
1
1
1
1
0
1
1
0
1
1
0
2
2
1
1
1
2
2
2
0
1
1
1
0
2
0
0
1
1
1
2
1
0
1
2
1
2
2
1
0
2
0
1
1
0
1
1
0
1
1
1
2
2
1
1
2
2
0
1
4
1
1
0
0
1
1
0
1
0
1
1
0
1
1
1
1
1
2
0
2
0
1
2
0
1
2
2
1
2
0
0
1
1
1
1
1
0
1
1
0
0
2
1
2
0
1
1
1
1
2
0
0
0
1
1
1
1
2
0
1
1
2
1
1
3
2
0
1
1
1
1
1
1
1
0
1
0
1
1
2
0
0
1
1
1
2
1
1
2
2
0
0
2
2
1
1
1
1
1
1
0
1
2
1
1
0
1
1
0
2
3
0
1
1
0
2
2
1
1
1
1
0
1
1
1
0
1
1
2
1
0
1
1
1
1
1
1
1
1
0
1
1
1
1
2
1
2
1
2
2
1
0
2
0
0
1
0
1
0
1
2
1
0
0
1
1
2
1
0
1
0
0
1
1
0
0
0
2
1
1
0
1
1
2
0
1
0
2
2
2
1
1
1
1
1
1
1
1
2
2
1
2
2
1
3
0
2
1
0
0
2
1
2
0
1
2
0
1
1
2
0
1
1
0
2
1
1
0
1
2
1
1
2
1
0
1
2
2
1
1
1
1
0
1
0
0
1
1
0
1
2
2
2
1
2
1
1
2
2
1
1
2
1
0
1
1
1
1
2
0
0
1
2
1
1
1
0
1
0
2
1
0
1
0
2
1
1
1
3
2
0
1
1
0
1
2
0
1
1
1
2
2
1
1
2
1
4
1
1
0
1
0
1
1
1
0
1
2
1
1
0
1
0
1
2
1
2
2
1
0
0
0
1
0
0
3
1
2
1
1
1
3
1
0
1
1
2
1
1
2
1
1
0
1
1
2
1
2
1
3
1
1
0
0
0
3
0
1
2
1
0
0
1
2
0
1
1
1
1
2
1
2
0
1
0
1
2
1
2
1
1
0
2
1
3
1
0
0
0
0
1
0
0
0
2
0
2
2
0
2
0
1
2
1
2
3
2
1
2
1
0
1
1
1
2
0
1
2
2
2
0
1
1
1
1
0
1
1
0
0
0
2
1
1
1
1
3
0
0
1
1
2
2
0
0
1
2
0
1
2
1
0
1
2
1
0
2
2
1
1
1
2
1
0
0
0
2
1
1
0
0
2
1
0
0
1
1
2
1
1
1
1
1
0
2
2
1
2
1
2
0
1
1
2
1
0
1
0
1
1
1
2
1
1
1
3
1
1
1
0
1
0
0
1
0
0
1
2
2
1
1
1
2
1
1
0
1
2
0
0
0
0
1
0
2
2
2
0
1
1
1
2
2
2
0
0
0
0
1
0
2
2
2
0
1
1
0
0
2
1
1
1
1
0
0
1
1
0
2
0
0
2
1
0
0
2
1
2
1
0
1
0
1
2
2
2
0
1
1
0
1
1
1
1
1
2
1
1
1
1
2
1
0
1
0
2
0
2
2
1
1
1
1
1
1
0
1
0
1
1
1
2
1
2
2
1
1
2
1
1
1
2
1
0
1
2
1
2
0
0
0
0
2
1
1
1
1
1
2
1
2
1
1
2
0
2
1
2
1
1
1
0
1
2
1
1
0
1
0
1
1
1
1
1
1
2
1
0
0
1
0
2
1
1
1
0
0
0
0
2
0
1
2
1
1
1
1
1
1
2
1
0
1
1
1
1
0
0
0
0
2
0
1
1
1
2
1
2
0
1
1
1
1
2
2
0
2
2
0
2
1
0
1
2
1
0
0
1
0
2
2
1
0
0
0
1
2
0
0
1
1
3
1
1
1
2
1
1
1
0
1
0
2
0
0
1
0
0
1
0
1
1
0
1
1
0
2
2
0
2
0
0
4
0
1
1
1
1
2
0
1
1
0
1
2
2
1
0
0
1
1
1
2
2
1
2
0
2
1
0
1
1
0
0
1
3
1
1
1
2
1
1
2
1
0
2
1
1
1
0
2
0
0
1
0
1
2
1
2
1
0
0
1
2
0
1
2
1
1
2
1
1
0
2
0
1
1
0
1
0
1
0
1
0
1
2
2
0
1
1
0
1
1
0
0
1
2
1
1
0
0
0
1
3
1
0
1
1
1
1
1
0
3
2
1
1
0
1
1
0
2
0
1
1
2
1
2
1
2
3
1
1
0
0
2
1
1
1
0
1
2
2
1
1
2
0
0
0
1
1
1
0
0
10
0
0
1
1
2
0
0
2
1
1
1
1
2
0
2
1
2
1
0
0
1
1
2
1
1
1
1
1
1
1
2
1
0
2
1
5
1
0
1
0
1
0
0
0
2
1
1
0
1
0
2
2
1
0
1
0
1
1
1
1
4
0
1
2
2
1
1
1
1
1
1
0
1
1
1
0
1
0
2
0
0
1
1
1
2
2
0
1
2
0
0
1
0
2
1
2
1
1
2
0
1
0
0
1
0
1
1
1
1
2
1
0
1
1
2
1
4
0
1
2
0
1
1
2
0
0
2
0
0
1
1
1
2
1
0
1
0
2
0
1
0
0
1
1
0
1
0
0
1
0
3
0
1
2
0
0
2
2
1
1
1
2
1
0
1
1
1
0
1
2
0
2
1
1
0
0
2
2
3
0
0
1
1
0
1
1
1
1
0
1
1
0
0
1
1
0
2
0
1
2
0
2
0
0
1
1
1
1
1
1
1
2
0
1
0
1
1
1
1
1
0
0
0
0
1
0
0
2
2
1
1
0
2
0
2
2
2
1
0
2
1
1
0
1
1
1
1
1
2
1
2
1
2
1
0
0
1
1
1
1
1
0
1
0
2
1
1
1
1
0
1
0
2
0
1
0
1
2
2
1
0
1
0
4
1
2
0
0
2
1
1
1
1
2
2
1
1
2
2
1
5
1
0
0
0
0
2
2
1
1
1
2
1
1
1
1
2
1
0
1
1
1
1
1
0
0
1
1
1
1
1
0
1
2
2
2
1
1
1
1
1
1
0
0
1
2
1
1
1
1
1
1
1
0
2
0
1
0
1
2
1
2
0
0
2
1
1
0
1
1
0
1
0
0
2
1
1
1
0
2
1
2
1
1
2
2
2
1
2
1
1
1
0
0
1
1
1
2
1
0
0
1
2
1
0
0
2
1
1
2
0
0
2
1
0
2
1
0
2
1
0
2
0
1
1
1
1
2
0
1
2
1
0
0
2
0
2
0
1
1
1
2
0
2
1
0
1
1
1
0
1
2
0
1
1
1
0
0
2
1
0
1
0
0
2
2
2
2
1
1
1
1
4
2
0
1
1
1
1
1
1
1
2
1
1
1
1
3
1
1
0
1
1
1
1
0
1
1
1
2
1
1
1
0
2
0
2
1
2
1
1
2
0
0
0
1
2
1
1
1
2
1
1
0
0
0
0
1
1
0
0
0
1
1
2
1
0
2
2
0
1
0
1
1
0
2
1
1
0
1
0
0
1
0
1
5
0
1
1
3
1
1
0
1
2
2
1
0
1
1
1
2
1
0
1
2
3
2
0
0
2
1
2
0
2
0
1
0
2
2
0
0
0
1
1
2
1
1
1
1
1
0
1
1
0
2
1
1
1
1
1
2
2
2
1
0
2
1
0
0
2
0
1
1
0
0
1
0
0
1
1
2
2
1
2
2
1
0
1
1
0
1
1
1
0
2
1
1
0
1
0
2
0
1
1
0
2
0
1
1
1
0
2
2
1
2
1
2
2
1
1
0
2
1
1
1
1
1
0
1
1
1
1
1
1
2
2
1
1
2
2
1
1
1
1
0
0
0
0
0
0
0
1
0
1
0
2
1
1
2
0
1
1
2
1
1
1
1
2
1
1
0
0
1
5
1
1
1
2
0
1
1
1
1
2
1
1
0
1
1
4
1
1
2
1
1
2
0
1
2
0
0
0
0
0
2
0
2
1
1
0
1
2
1
2
1
2
2
1
0
1
1
0
2
1
0
0
2
1
2
2
2
1
2
2
1
1
1
1
1
0
1
1
0
1
1
0
0
0
1
1
1
1
2
0
1
2
1
1
1
1
2
0
1
2
3
1
1
1
1
1
1
0
1
0
1
0
2
0
1
2
0
0
1
2
1
2
2
2
1
1
1
2
1
1
1
0
0
1
1
1
0
3
1
0
1
0
1
1
0
1
0
1
2
0
0
0
1
2
1
0
2
1
1
1
1
0
0
1
2
1
1
0
1
1
1
2
1
0
1
1
1
0
1
1
0
2
1
1
1
2
2
1
3
0
1
0
1
0
2
1
1
2
2
1
1
2
0
1
2
2
1
2
2
0
0
1
0
1
2
1
1
1
2
0
1
1
1
2
1
1
1
0
1
1
1
2
2
1
2
1
0
1
0
1
1
0
2
1
1
0
1
2
1
1
0
2
0
4
0
2
2
1
1
0
0
1
1
2
1
0
1
1
1
0
2
2
1
1
1
1
0
1
2
0
1
1
1
1
2
2
0
2
1
0
1
2
2
1
1
2
1
2
1
1
1
3
0
2
1
1
2
1
0
2
1
0
0
1
2
0
2
0
1
0
2
0
1
0
0
2
1
1
2
2
2
1
1
1
1
0
1
1
2
0
1
0
1
1
1
0
1
1
1
1
1
2
2
0
0
0
1
0
2
2
0
1
0
0
0
2
1
1
1
1
2
1
1
2
1
1
1
1
0
1
1
1
1
0
1
2
1
0
1
1
0
1
0
1
0
0
2
2
1
1
1
0
1
2
3
1
1
2
1
0
2
1
1
2
1
1
0
0
1
2
0
1
0
2
2
1
3
0
1
1
0
2
0
2
0
2
1
0
1
1
2
1
0
2
0
1
0
2
1
0
1
0
2
1
1
1
0
2
1
1
2
1
1
2
1
2
1
1
0
1
1
1
2
1
1
0
1
0
0
1
1
2
1
1
2
0
1
0
1
1
1
2
1
2
1
1
2
1
0
2
1
1
0
1
0
0
1
2
0
1
0
1
1
0
1
2
2
1
1
1
2
0
1
1
1
1
0
2
0
1
0
0
1
0
2
1
1
0
1
1
1
1
2
1
1
2
2
1
0
2
0
0
0
1
2
1
1
1
0
0
1
0
0
1
2
1
1
2
0
1
1
1
1
0
0
1
0
1
0
1
0
1
1
1
0
1
1
1
2
1
1
1
2
1
1
0
0
0
1
1
0
2
0
0
1
1
1
0
1
1
2
1
0
1
1
1
2
1
1
2
0
1
1
1
0
0
1
1
1
1
1
1
0
1
1
2
2
0
2
1
0
1
1
2
1
2
0
0
2
0
0
0
0
1
1
0
1
1
1
1
3
0
0
1
3
2
1
1
0
2
2
1
2
0
1
0
1
1
2
1
1
0
1
2
2
0
1
1
2
1
0
1
0
1
1
1
1
1
2
1
1
2
1
0
0
0
1
1
0
1
0
1
1
1
1
1
2
2
2
2
2
2
1
0
1
2
1
1
2
1
1
0
0
0
2
1
1
1
1
0
0
2
1
2
1
1
1
1
1
1
2
1
1
0
0
2
2
0
2
0
0
1
0
1
2
1
1
2
1
2
1
0
1
0
1
0
2
0
2
1
1
1
1
0
1
1
0
0
0
1
2
2
2
1
1
0
2
1
1
1
1
2
0
1
1
1
1
2
1
0
0
1
2
2
1
1
1
2
1
2
2
1
1
1
2
1
3
1
1
1
0
0
0
0
0
1
1
0
1
1
1
2
1
1
1
1
0
1
0
1
1
2
0
1
1
0
2
0
1
0
0
0
2
0
2
0
1
1
1
0
2
6
1
1
1
0
1
1
2
2
1
0
1
0
2
0
1
2
1
0
0
1
1
1
1
2
1
2
1
3
2
1
2
1
1
1
2
0
2
1
0
1
1
1
1
0
0
1
0
1
2
1
1
1
0
1
1
0
1
1
0
1
1
2
0
1
0
0
2
1
0
0
1
1
1
0
1
1
1
1
0
2
2
0
1
1
1
0
0
2
1
1
1
2
0
1
0
2
0
2
0
2
2
2
1
1
0
1
1
2
1
1
0
2
1
2
2
0
2
1
2
2
1
2
2
1
1
2
0
0
0
1
2
1
1
1
0
1
2
0
2
0
0
2
2
2
1
1
0
0
1
1
1
1
1
1
2
2
0
1
0
0
0
1
0
0
1
0
0
0
0
1
2
1
1
2
2
2
1
1
2
0
1
1
1
0
2
1
2
1
1
2
0
0
1
1
2
2
1
0
2
0
1
0
0
1
1
1
0
1
2
0
1
1
0
2
2
0
1
1
2
1
1
1
1
1
1
1
0
1
0
2
1
2
1
1
2
2
2
1
2
1
2
1
2
0
1
2
1
1
3
0
1
1
1
1
1
0
1
1
0
1
0
1
1
0
1
1
0
1
0
2
0
1
0
0
1
1
3
1
2
2
0
1
2
0
2
1
1
1
1
1
1
1
1
1
1
1
1
0
1
2
1
0
1
1
0
1
1
0
1
1
1
2
2
1
1
1
0
1
2
1
2
1
1
0
2
1
1
2
0
1
2
1
0
1
0
1
1
0
0
1
2
0
1
1
0
1
2
1
1
1
1
1
1
1
0
2
1
0
2
1
0
2
1
2
2
1
0
1
2
0
1
1
1
1
0
0
1
1
2
0
4
0
1
0
1
1
2
1
0
0
1
1
1
2
1
1
1
2
1
0
1
1
0
0
1
2
2
1
1
1
1
0
0
1
0
0
0
1
1
1
2
0
1
0
0
0
1
0
0
1
1
2
2
1
2
1
1
0
0
2
2
1
1
0
1
0
1
2
1
1
1
1
2
1
1
1
0
1
1
1
0
0
1
1
0
2
1
1
1
1
0
0
1
1
0
1
0
1
0
2
2
1
1
0
0
0
1
2
1
2
1
0
1
1
1
1
2
2
1
2
1
0
0
0
1
1
1
2
1
0
2
0
2
0
1
1
2
2
0
1
1
0
2
0
2
0
1
2
0
0
2
1
1
0
0
1
2
1
1
1
1
0
0
2
0
2
1
0
0
1
1
1
1
1
1
1
1
2
1
2
0
2
0
1
1
1
0
2
2
2
1
1
0
1
0
1
1
1
1
1
0
0
0
2
2
0
1
0
0
0
0
2
1
2
0
2
1
1
0
1
0
2
2
1
0
1
1
1
1
0
1
1
1
1
2
0
1
1
2
2
1
2
1
1
1
1
1
0
1
1
1
0
1
2
0
1
0
0
1
0
0
1
2
1
0
1
1
2
1
1
1
0
2
1
2
1
0
1
1
1
0
2
0
0
2
1
2
0
1
1
0
1
0
1
0
1
1
2
2
2
1
2
1
0
1
2
1
1
1
1
1
1
1
1
1
2
2
1
0
0
0
0
2
0
1
1
0
1
0
2
2
2
1
1
0
0
1
2
0
1
2
2
2
1
0
1
1
1
0
1
0
1
1
1
2
1
1
1
0
2
1
1
1
1
0
1
0
0
1
1
1
2
0
0
0
1
1
1
1
1
2
2
3
2
1
1
2
2
1
1
1
0
1
2
1
0
1
0
0
0
1
0
2
0
1
1
1
1
1
1
2
1
0
1
0
0
0
0
1
1
1
1
1
1
1
2
1
2
1
2
1
1
1
1
1
0
1
1
1
0
1
0
0
1
2
1
1
1
1
1
0
2
0
1
0
1
2
1
1
0
1
2
2
0
2
1
1
1
1
1
2
2
1
0
1
2
1
2
0
1
0
1
1
0
0
1
0
0
1
0
0
2
1
1
1
1
0
0
1
1
1
1
2
1
1
0
1
1
1
0
1
0
1
0
1
1
1
1
0
2
2
1
1
0
1
0
1
0
1
0
1
1
1
0
1
1
1
1
0
1
1
2
2
1
2
2
0
1
0
2
0
1
1
1
2
1
2
2
0
1
0
1
0
1
1
0
0
2
1
1
0
0
1
0
0
1
1
1
0
0
1
0
1
0
1
3
1
2
1
2
0
0
1
2
0
1
1
2
1
1
1
1
2
0
1
0
2
1
1
0
0
1
1
0
1
1
1
2
2
3
1
1
1
1
1
1
2
2
1
0
0
2
1
1
1
2
2
0
1
1
0
1
0
1
1
0
1
0
2
1
0
1
1
0
1
2
1
0
1
1
0
0
1
2
1
1
1
0
2
1
0
1
1
2
2
2
0
1
1
2
1
1
1
1
1
1
1
1
1
2
0
1
1
1
2
0
0
1
2
1
1
0
0
0
1
1
1
2
1
2
1
1
0
1
1
2
1
1
0
1
1
1
1
1
0
0
1
0
1
2
1
1
0
0
1
0
0
1
0
0
0
4
2
2
2
1
0
2
1
1
4
0
0
0
1
1
1
2
2
1
1
0
0
0
2
0
1
1
1
2
1
1
0
2
1
1
1
0
1
2
2
1
2
1
1
1
1
2
0
2
1
2
1
2
1
1
1
1
1
2
1
2
1
2
1
2
2
1
2
1
0
1
0
0
2
1
0
0
2
0
1
1
1
0
2
0
1
0
1
1
1
1
1
1
2
1
0
0
0
1
1
2
2
0
1
0
2
1
1
0
1
0
1
2
0
1
0
1
1
0
0
1
1
1
1
0
1
2
0
0
1
1
0
0
0
2
0
0
1
1
1
0
2
1
1
0
2
0
1
0
0
0
1
1
0
0
0
0
1
2
2
1
0
1
1
0
2
0
2
1
1
1
0
1
2
1
0
0
2
1
0
1
1
1
0
0
1
2
0
1
1
0
0
1
2
0
1
0
1
1
0
0
2
0
1
0
1
1
0
2
2
2
2
0
0
2
1
1
1
1
1
1
0
2
3
1
1
1
0
0
0
1
2
2
1
2
2
0
0
1
1
0
1
2
0
1
1
1
1
1
1
0
2
2
1
0
0
1
1
0
1
2
2
1
2
1
1
0
1
1
0
0
1
1
1
1
0
1
1
0
2
1
2
0
2
2
0
2
1
2
1
1
1
0
1
1
1
1
0
1
1
2
1
2
0
2
0
1
1
1
1
0
1
1
1
2
1
0
1
2
1
1
1
2
1
0
2
1
1
1
0
1
1
2
2
1
2
0
1
1
0
0
0
1
2
1
0
0
0
0
0
0
0
2
1
1
1
0
2
2
1
1
1
0
1
0
0
2
1
1
1
1
2
0
3
1
1
0
2
1
1
0
1
1
0
0
2
0
2
2
1
2
1
0
1
0
1
1
1
1
0
1
0
0
2
0
0
0
2
1
1
1
0
0
0
1
1
2
0
2
2
0
2
0
0
1
1
3
1
1
1
1
1
0
2
2
0
0
0
1
1
0
1
1
2
0
1
1
1
0
0
0
1
0
1
0
1
1
1
2
1
0
1
1
2
1
1
0
1
2
1
2
0
0
1
2
0
1
1
1
2
1
0
1
1
0
1
1
1
1
2
0
1
2
2
1
1
0
0
1
2
1
0
0
1
0
0
1
1
2
2
0
1
1
2
0
2
0
0
1
1
0
1
0
0
0
1
0
1
1
1
1
0
0
1
1
1
1
1
1
0
2
0
1
0
1
0
2
0
1
1
1
1
1
0
0
2
0
1
1
1
1
1
2
0
1
0
0
2
1
1
1
0
1
1
1
1
0
2
1
1
2
2
1
0
1
2
0
1
0
2
0
1
1
0
0
1
0
1
1
0
1
2
0
2
1
0
0
1
2
1
1
1
0
1
1
1
1
0
0
1
1
2
1
3
1
0
1
2
0
1
1
1
1
0
2
0
2
1
2
1
0
1
1
1
1
1
2
2
1
2
1
1
1
2
0
0
2
1
1
2
2
0
0
0
1
1
0
0
1
1
1
4
1
3
0
2
1
2
3
1
0
1
1
1
2
0
1
1
1
2
1
1
1
2
2
0
2
1
0
0
1
1
1
1
1
0
0
2
1
2
2
1
1
0
1
0
1
2
2
1
1
0
0
1
1
1
1
0
1
0
1
2
1
0
1
1
0
1
1
2
1
0
1
1
2
1
1
0
1
1
1
0
1
1
1
1
1
1
0
1
1
2
1
1
1
1
1
1
1
0
0
0
1
0
2
0
1
1
2
1
1
0
0
0
0
0
0
0
2
0
1
1
1
1
1
1
0
1
1
0
1
2
1
1
2
0
0
2
0
0
1
2
1
0
1
1
1
1
1
2
0
1
0
2
0
2
0
2
1
0
0
1
1
2
1
1
0
1
1
1
1
0
1
1
1
2
0
0
0
2
1
1
2
1
2
0
0
2
1
1
2
0
0
1
2
0
1
0
1
1
1
1
0
0
1
1
1
2
2
1
2
0
1
2
1
1
1
0
1
2
1
0
0
0
1
0
1
1
0
2
1
1
1
1
0
1
1
1
0
1
2
0
1
2
1
2
2
2
0
2
1
0
0
2
0
2
1
2
0
1
0
0
0
2
1
0
1
1
0
0
0
1
0
0
2
1
2
2
1
0
0
1
2
1
1
2
1
2
2
1
0
2
1
1
1
1
1
0
1
1
0
0
2
2
1
2
1
0
2
1
1
0
2
1
2
1
1
1
2
1
1
1
2
0
0
0
1
1
1
1
1
0
0
0
1
1
2
1
0
0
3
2
2
0
2
0
1
0
2
0
1
1
1
2
2
1
2
1
0
1
1
0
0
0
1
2
1
1
1
1
1
2
1
2
2
2
2
2
1
0
1
1
1
0
0
2
1
1
0
6
0
1
1
2
1
2
2
1
2
0
1
1
1
1
2
1
2
2
1
2
0
0
0
1
0
0
2
0
1
1
0
2
1
2
0
2
1
1
2
0
2
1
0
2
1
2
1
2
0
1
1
0
1
0
1
1
0
1
0
0
0
1
1
1
1
1
1
2
1
1
0
1
0
1
0
2
1
1
1
0
2
1
1
1
0
1
1
1
1
1
0
1
1
2
0
1
1
2
2
1
0
1
2
1
2
0
1
1
1
0
0
0
1
0
2
1
2
0
1
1
1
0
1
0
0
1
2
0
1
2
1
1
2
1
1
2
1
1
0
1
1
1
2
1
1
1
1
0
0
1
2
2
1
1
0
0
1
1
0
0
1
1
0
2
0
1
1
1
2
1
1
1
1
1
2
0
2
2
0
1
1
0
1
0
1
1
1
1
1
0
1
1
1
1
1
0
1
1
1
1
1
1
0
1
0
2
1
1
0
1
2
3
1
2
0
2
2
1
1
2
1
6
2
0
1
2
1
1
1
2
2
1
0
2
1
1
1
1
0
1
0
1
2
1
0
0
3
2
1
0
1
1
1
0
1
0
0
0
2
0
0
0
1
1
1
1
1
0
2
0
0
2
0
1
1
0
0
1
1
0
1
0
1
1
2
0
0
0
1
0
2
2
1
2
0
1
1
1
1
1
2
1
1
1
1
1
0
1
1
1
2
0
3
1
2
2
0
0
1
1
0
2
1
2
0
0
1
0
0
0
1
2
1
1
1
0
1
1
1
0
0
1
1
1
1
0
1
2
1
1
1
0
1
0
0
1
1
0
1
0
0
1
2
1
0
1
1
2
0
1
1
1
1
1
1
2
0
1
0
0
1
2
2
1
2
1
0
1
2
0
1
1
0
1
0
1
2
1
1
2
1
0
2
1
0
2
0
1
2
1
1
1
1
2
0
0
2
0
0
1
1
1
2
0
1
2
1
1
1
1
1
0
1
0
1
1
1
0
1
1
2
2
2
1
0
0
0
1
2
0
1
0
3
1
0
0
1
0
1
1
0
1
2
0
1
1
1
1
1
1
0
0
1
1
0
1
0
0
0
0
1
0
2
1
1
1
1
0
2
2
2
2
2
1
3
1
1
1
1
2
1
1
0
2
0
2
3
1
1
0
0
1
2
0
1
1
1
1
1
2
3
2
1
0
2
0
1
1
1
0
1
0
1
2
2
1
0
1
1
0
0
0
1
0
2
2
2
2
0
1
1
2
2
1
0
0
0
2
1
1
0
2
1
0
2
1
1
1
1
1
2
2
2
2
1
1
0
1
2
1
1
1
1
1
0
2
1
1
1
3
1
0
1
0
1
0
1
2
1
0
0
1
2
2
0
1
1
1
1
1
1
1
1
0
1
0
2
1
0
1
0
2
2
1
1
2
1
2
1
2
2
2
1
1
0
1
1
2
2
1
0
1
0
1
1
0
1
1
1
2
0
3
2
0
1
1
1
0
3
1
1
2
2
1
0
0
0
2
5
0
1
1
0
1
1
2
0
1
1
1
1
1
3
2
2
1
0
1
3
2
1
0
0
0
2
2
1
0
2
1
0
0
1
0
1
1
0
3
0
0
2
1
2
1
2
1
0
2
1
1
1
0
2
0
1
1
0
1
2
2
1
3
0
0
0
0
0
1
1
2
1
1
0
2
1
0
1
1
2
2
0
1
2
1
1
1
2
1
1
1
1
2
1
0
1
1
0
1
1
2
0
1
2
1
0
1
0
1
1
1
1
0
1
2
1
1
1
1
0
0
1
1
1
1
0
1
1
1
1
2
2
1
2
1
1
0
1
0
1
2
2
0
0
1
1
0
2
0
1
2
1
2
0
1
2
1
1
1
0
1
0
2
1
1
2
1
1
0
1
0
1
2
1
1
1
0
2
2
2
2
0
1
2
0
1
1
0
1
1
0
1
2
1
0
0
1
1
0
0
0
1
1
1
2
2
0
0
0
0
1
1
0
1
1
1
0
0
1
0
0
2
2
1
0
1
2
1
1
2
2
1
2
2
1
1
0
1
1
1
2
1
1
1
0
2
0
0
2
1
1
1
1
1
2
1
0
0
2
0
1
1
1
0
1
0
1
2
1
1
1
1
1
1
1
1
1
1
1
2
0
2
1
1
1
2
2
0
0
1
1
1
2
1
1
0
1
1
1
0
1
1
1
1
1
1
0
1
0
1
1
0
1
0
1
0
0
2
5
0
1
1
0
1
1
2
0
2
1
1
1
0
0
2
2
1
0
1
2
1
0
0
3
0
1
2
1
2
1
1
2
0
2
0
1
2
2
2
1
1
1
1
0
0
1
1
1
0
2
1
2
2
1
1
1
0
1
0
0
1
2
1
1
0
2
1
1
2
1
1
2
0
0
0
0
0
1
1
1
0
1
1
2
1
2
0
0
2
1
0
6
1
1
1
1
2
1
1
2
1
0
1
1
1
2
0
1
0
2
1
0
1
0
0
1
1
1
1
1
2
0
2
1
2
1
1
1
2
1
1
1
0
1
2
1
1
0
1
0
2
0
1
1
1
2
2
1
1
0
1
0
2
0
0
0
1
2
2
1
2
1
2
1
0
0
1
0
1
2
1
1
1
1
0
0
0
1
1
1
0
1
0
1
0
1
0
2
1
1
1
0
2
4
1
0
1
1
1
0
1
1
1
0
0
1
0
1
0
0
2
1
1
1
1
0
2
1
2
1
0
1
1
0
2
0
0
0
2
0
2
0
2
3
2
0
1
1
1
0
0
2
2
0
2
2
1
0
2
2
1
0
1
2
1
2
2
0
1
1
1
1
0
0
1
1
1
1
0
2
0
2
1
2
1
2
1
1
2
1
1
1
1
1
1
0
2
0
1
1
2
0
2
2
1
2
1
1
1
1
0
1
1
0
0
1
1
2
1
1
2
1
1
0
1
0
0
1
0
0
1
1
2
1
2
1
1
1
1
0
2
0
0
1
0
2
1
1
1
0
0
2
0
0
1
0
1
1
1
2
1
0
0
1
1
2
0
2
0
2
1
1
2
1
1
2
1
1
1
1
1
1
0
2
1
1
2
2
1
1
0
2
1
0
1
2
2
1
1
2
0
2
1
1
2
0
1
1
2
0
2
0
0
1
1
2
1
1
2
2
2
1
0
2
0
1
1
1
3
1
0
2
2
0
1
1
2
1
1
0
1
1
1
1
0
1
0
1
1
1
2
2
0
0
2
0
1
1
2
1
0
1
0
0
2
1
2
1
1
0
1
1
1
0
0
1
0
1
1
0
1
1
1
2
2
2
2
2
1
1
0
2
1
2
0
2
0
1
0
0
2
2
1
1
1
2
1
1
1
2
1
2
1
2
1
0
0
0
1
3
2
0
1
1
2
1
0
1
0
1
1
1
2
1
1
1
0
1
1
0
1
1
1
1
2
1
1
1
1
0
2
0
0
2
1
1
1
2
2
2
3
0
2
0
1
1
2
0
2
1
1
0
1
0
1
1
1
2
1
0
2
2
0
1
2
0
0
1
2
0
1
1
1
1
0
0
2
2
0
0
1
0
1
1
1
1
1
2
1
1
2
2
1
0
1
1
1
0
0
1
0
1
1
1
1
1
2
0
1
1
1
0
1
1
2
0
1
1
1
0
0
0
1
0
2
0
2
1
1
1
0
0
2
0
1
1
1
0
1
0
2
1
0
1
1
1
1
1
1
0
1
2
3
0
2
1
1
1
0
2
0
1
1
1
0
2
0
1
2
1
1
0
1
2
1
0
1
0
0
0
1
0
2
1
1
2
1
4
0
1
1
2
1
1
1
0
1
2
0
1
1
0
1
0
1
2
1
0
2
1
2
3
1
1
0
1
1
1
1
1
2
2
0
0
1
0
2
0
1
1
1
1
1
1
2
1
2
1
0
0
1
1
1
1
2
1
1
1
2
1
1
2
0
0
1
4
1
1
1
1
1
2
1
1
1
0
1
0
0
1
1
1
3
1
1
0
1
2
0
1
1
1
0
0
1
1
0
0
2
0
1
1
1
1
1
1
1
2
1
2
1
0
0
1
1
0
1
0
2
2
0
1
0
1
1
1
0
1
2
1
0
1
1
1
0
2
0
0
1
1
1
1
2
0
1
1
0
0
1
2
1
1
0
1
1
1
0
1
1
1
1
1
2
1
2
0
2
0
1
0
0
1
1
1
0
1
1
1
0
1
2
2
1
2
0
1
2
1
1
3
1
1
1
0
1
2
3
1
2
0
1
0
1
1
1
2
0
0
2
2
1
1
2
2
1
0
0
2
2
2
1
1
1
1
1
1
0
0
1
1
2
2
1
2
0
1
2
2
0
0
0
2
1
0
1
2
2
2
0
2
1
1
1
1
1
1
0
1
2
0
2
0
1
1
0
1
1
1
0
0
1
1
1
1
1
2
2
1
1
0
1
0
1
1
1
1
1
2
2
1
1
0
1
2
0
0
1
0
2
0
1
0
1
0
0
2
1
1
2
2
1
2
1
0
0
3
0
0
0
1
1
0
2
1
2
1
2
1
2
1
1
1
1
2
2
2
2
0
0
1
1
2
2
0
0
1
2
0
0
0
1
1
1
1
2
1
0
0
2
1
1
1
0
1
0
1
2
2
2
1
2
0
0
0
1
2
2
2
1
1
0
1
0
1
2
1
2
0
2
1
2
0
1
0
1
1
0
2
3
0
1
1
0
0
1
1
0
1
1
1
0
1
1
2
2
1
6
1
2
2
1
2
1
2
2
1
0
0
1
0
0
0
2
1
1
2
1
0
0
1
2
1
0
0
0
1
2
0
1
1
1
1
2
1
0
0
1
0
0
1
0
1
2
1
1
1
1
1
2
1
0
2
2
0
1
2
1
0
0
0
1
1
0
1
2
2
0
0
1
2
2
1
2
1
2
0
1
2
0
2
2
0
1
0
0
3
2
1
0
1
3
1
1
2
1
1
0
1
3
1
1
0
0
0
0
2
0
2
1
1
1
2
0
0
0
1
1
1
1
3
2
1
2
2
0
1
1
1
1
1
0
0
1
1
1
0
1
2
1
2
1
1
2
1
0
0
3
2
0
0
1
1
1
0
1
1
0
1
1
1
3
2
0
1
0
1
1
1
0
1
0
2
2
0
1
1
0
1
2
1
1
1
1
2
0
1
1
0
1
0
0
1
1
0
1
1
0
1
0
1
0
0
1
0
1
0
0
0
0
1
1
2
2
0
1
0
0
2
1
0
1
1
1
0
1
1
1
1
1
1
1
0
1
1
1
0
0
1
2
1
0
1
1
1
1
2
1
1
0
2
0
0
1
1
2
1
0
1
0
1
2
0
1
1
1
3
0
1
2
1
1
1
1
0
1
1
0
0
2
1
0
0
1
1
2
1
0
1
2
1
1
0
2
0
1
1
1
1
2
0
0
1
1
4
0
1
1
0
1
1
1
1
1
2
1
1
0
1
0
2
1
1
1
1
1
3
1
1
1
0
1
1
2
1
1
1
0
2
0
1
3
1
1
1
1
4
1
1
0
2
1
1
1
2
2
1
0
0
0
1
2
2
0
1
1
1
1
1
1
0
0
0
0
0
0
1
2
2
1
2
1
1
2
0
1
1
1
1
1
1
0
1
0
0
1
0
1
1
1
1
2
2
1
1
0
1
0
0
1
0
1
1
1
1
1
2
2
1
2
0
1
1
0
1
2
0
2
0
0
1
1
0
1
1
1
2
1
1
2
0
0
1
1
1
1
1
1
1
1
0
0
1
0
2
0
2
3
2
1
1
1
0
1
2
2
1
2
1
1
0
2
1
1
1
1
0
0
1
1
1
0
1
1
1
0
1
1
2
2
1
2
1
1
1
2
1
0
1
3
0
0
2
2
1
1
2
0
0
0
2
1
1
2
1
2
0
1
2
0
1
1
1
0
1
0
1
1
1
0
0
2
0
0
2
1
1
0
1
0
0
0
1
1
1
0
0
1
1
1
0
1
1
2
2
2
1
2
0
1
0
2
1
1
2
0
2
1
0
0
1
1
2
1
1
1
1
1
1
0
1
0
1
0
1
1
2
0
2
1
0
1
2
1
2
0
2
1
1
0
1
1
1
0
2
1
2
2
2
0
1
1
1
2
2
0
0
0
1
1
1
0
1
2
1
2
0
1
1
0
2
0
0
1
2
1
0
2
1
1
1
0
4
2
2
1
2
1
1
1
0
1
0
1
0
0
0
0
1
1
0
0
0
1
1
2
2
2
0
1
1
0
2
2
1
1
1
1
2
2
2
0
2
0
1
0
1
1
1
0
0
0
0
2
0
1
1
1
0
0
2
1
2
1
1
1
0
2
1
1
3
2
1
1
1
2
2
0
1
1
1
1
2
0
1
1
2
3
1
1
1
1
0
2
1
1
2
2
1
1
1
1
0
0
1
1
0
1
1
1
1
0
1
2
0
1
2
1
1
1
0
1
2
2
0
0
2
1
0
0
2
1
0
0
0
1
1
0
2
0
2
2
0
0
1
0
0
1
2
1
2
0
1
1
2
2
2
0
1
1
0
1
2
1
0
0
0
0
2
1
1
2
1
0
1
1
1
2
1
0
1
1
1
1
2
1
1
3
0
1
1
1
2
1
1
0
1
0
0
0
1
1
2
2
1
1
0
1
0
2
2
2
1
1
1
1
2
0
1
1
2
0
1
1
1
1
1
1
1
1
1
0
0
2
0
1
1
2
0
1
1
1
2
0
1
2
2
1
2
0
1
2
1
1
3
0
1
1
2
1
0
2
1
1
1
2
1
0
1
1
1
0
1
2
0
0
1
2
0
1
1
2
2
1
0
1
1
2
0
1
2
2
1
0
2
0
2
0
7
2
1
1
1
1
0
1
1
2
1
1
2
1
1
1
2
1
0
1
0
1
0
3
2
1
1
1
1
0
2
2
1
2
2
1
1
2
1
2
0
1
2
2
1
1
1
0
1
2
1
0
0
1
0
2
0
0
1
1
1
1
0
1
2
1
1
1
1
0
2
1
0
1
1
1
0
1
1
2
1
1
2
1
0
0
1
1
1
0
0
2
2
1
1
2
1
2
0
1
2
2
2
1
0
2
0
1
0
1
0
1
1
1
1
1
1
1
1
1
1
0
1
2
0
1
1
2
1
1
1
0
1
2
1
2
1
1
1
0
0
0
2
1
1
0
2
1
0
2
2
2
2
1
0
1
1
1
2
1
1
1
1
1
0
3
1
0
1
2
1
0
0
1
1
1
0
0
1
0
2
1
1
1
1
1
1
1
0
2
1
1
1
1
0
1
0
1
1
2
0
1
1
3
0
1
0
1
2
2
1
1
0
1
1
0
0
1
2
1
2
0
2
0
0
1
0
0
1
1
2
1
1
2
1
0
1
2
0
0
1
2
1
1
2
1
2
2
2
0
1
0
2
1
1
1
1
0
2
1
2
2
1
1
2
0
1
1
1
1
2
1
1
0
1
0
2
0
1
1
0
0
2
0
0
1
2
1
1
1
0
1
0
0
2
2
0
1
1
1
1
2
0
0
2
1
1
2
1
1
1
1
1
1
0
3
1
1
0
1
1
2
2
1
2
0
0
2
1
0
0
1
1
1
1
2
0
1
1
1
1
1
2
0
1
1
0
1
1
1
0
0
0
1
1
1
0
0
1
1
1
1
1
1
1
1
0
1
1
0
1
0
1
2
2
1
0
0
2
1
1
1
0
2
0
2
0
0
1
0
0
0
1
1
0
1
1
1
1
2
2
1
0
0
2
0
1
1
2
1
1
1
1
2
1
1
0
0
1
2
0
1
1
1
0
1
1
3
2
0
1
0
0
1
1
0
0
2
1
2
0
2
0
1
1
2
0
1
2
1
0
1
1
1
1
2
1
0
0
1
2
1
2
2
1
2
1
1
1
2
1
1
0
1
0
0
1
2
2
2
0
0
1
1
0
1
0
2
0
1
1
2
0
1
1
1
1
1
0
1
1
0
0
0
2
0
2
2
1
1
0
1
1
1
0
1
1
1
1
0
1
1
0
0
2
2
0
2
0
0
1
2
1
0
1
1
1
1
0
1
0
0
2
0
5
0
0
0
0
0
1
0
0
1
1
2
1
2
1
2
1
2
1
1
1
3
2
2
1
0
2
2
2
0
1
2
0
0
2
0
1
2
2
2
2
1
0
1
1
1
1
0
0
0
0
0
0
0
1
2
0
0
0
1
2
1
1
0
1
1
1
1
2
2
0
2
1
1
0
1
1
0
0
0
0
1
1
0
1
1
0
0
0
1
1
2
1
1
2
1
2
1
2
1
3
0
1
1
2
0
2
0
2
0
2
1
0
1
1
2
1
0
2
1
2
0
1
0
1
2
1
0
1
1
1
1
1
0
1
2
0
1
1
2
1
1
1
1
2
0
1
2
1
0
1
1
1
1
2
2
1
2
2
2
1
1
0
1
1
0
2
0
1
0
0
1
1
1
2
1
2
2
1
1
2
1
1
1
0
1
1
2
1
1
2
2
0
1
2
1
1
2
1
3
1
1
0
1
1
1
0
1
2
0
1
1
1
1
1
1
2
0
1
1
1
2
2
1
2
1
1
2
1
1
2
1
1
0
0
2
0
2
1
1
2
1
0
1
2
1
0
0
1
2
1
2
1
1
1
1
2
1
1
2
0
1
2
0
1
0
1
0
0
2
1
1
2
2
0
2
2
1
1
1
1
2
1
2
2
2
1
1
1
0
0
0
1
1
1
2
1
1
1
0
2
2
1
2
0
1
1
1
1
2
0
0
1
1
1
2
1
1
0
2
1
0
0
1
1
1
0
0
2
2
0
2
1
1
2
1
2
2
0
1
1
2
0
1
2
0
2
1
0
1
2
1
1
0
1
2
0
0
1
2
1
1
1
1
0
0
1
1
3
1
0
1
1
1
1
1
0
0
1
1
2
2
0
1
1
2
1
0
1
1
1
0
2
1
1
1
1
0
2
1
1
2
0
1
2
1
1
0
1
0
2
1
1
2
1
1
1
1
1
1
2
2
2
1
1
1
2
0
2
1
1
1
1
2
1
0
2
1
1
0
2
0
2
1
0
2
0
1
0
0
2
2
0
0
1
1
0
2
0
1
0
0
1
1
1
2
1
3
0
2
2
1
0
2
0
0
1
1
2
1
0
1
1
0
0
0
1
0
0
1
1
1
2
0
0
1
2
2
0
1
1
0
1
1
2
2
0
1
0
1
1
1
0
0
1
1
1
2
0
0
1
1
1
1
2
1
1
1
1
1
1
0
0
0
0
2
0
1
1
2
1
1
2
1
1
2
1
2
1
1
1
1
0
1
1
1
0
0
2
1
1
1
0
1
1
1
1
0
2
1
1
1
1
1
1
0
0
2
1
1
0
0
1
1
1
1
2
0
0
0
2
1
1
0
2
1
2
1
1
0
0
0
1
0
1
1
0
1
1
1
1
1
1
2
2
1
1
1
0
1
1
1
0
0
1
1
1
0
0
2
1
1
1
2
0
0
0
1
1
1
1
1
1
2
2
1
1
1
1
1
2
2
2
1
2
1
0
1
1
1
1
1
2
1
1
1
1
0
1
1
2
0
1
0
0
0
1
1
1
1
0
0
0
0
1
0
1
1
2
1
1
1
2
1
1
0
2
1
1
1
1
1
0
2
0
1
2
1
2
1
0
1
1
0
0
1
0
1
0
2
2
2
2
1
1
1
2
2
1
1
1
1
0
0
0
0
1
1
1
1
0
0
1
2
0
1
1
0
1
1
1
1
0
0
0
1
1
0
0
0
0
1
0
1
1
2
1
2
0
0
1
2
1
0
1
1
1
1
2
2
1
0
2
1
1
1
2
1
0
0
1
1
1
1
2
0
0
1
0
0
1
2
0
0
1
2
1
1
1
1
2
1
0
0
1
2
0
1
1
1
1
1
1
1
0
1
1
1
1
1
1
2
2
1
1
2
2
1
2
0
1
1
1
3
1
0
1
1
0
1
1
2
2
1
1
0
1
0
1
1
0
1
2
2
1
2
1
1
1
0
1
0
0
2
2
1
0
9
1
0
1
1
2
0
2
1
0
2
1
0
0
1
1
1
1
1
1
1
1
0
0
0
2
0
1
1
1
1
1
0
1
0
0
0
1
0
1
1
1
2
1
0
1
0
1
0
1
1
1
2
0
1
1
1
0
0
1
0
1
1
0
1
2
1
2
1
1
0
1
3
1
0
2
1
1
1
0
1
1
2
1
1
1
1
1
0
1
2
1
1
2
1
1
1
1
1
1
1
1
0
0
2
0
0
2
2
1
1
1
1
0
0
1
0
1
0
1
1
1
2
1
0
1
1
1
1
2
0
1
0
1
1
3
1
1
0
1
1
1
2
1
1
2
2
1
2
2
1
1
1
2
1
1
2
1
2
1
0
0
0
0
2
2
1
0
0
1
0
1
0
1
1
0
0
1
1
1
1
2
0
0
1
0
2
1
2
1
0
0
2
2
2
1
2
1
1
0
1
2
1
0
1
0
2
4
0
0
2
1
2
1
1
1
1
0
1
0
1
2
1
1
1
1
2
1
2
2
1
0
2
1
0
2
0
1
2
1
1
1
1
2
1
1
0
0
2
1
2
2
1
3
2
1
0
0
2
2
0
2
0
0
0
0
1
1
1
2
1
1
1
1
2
1
2
1
2
0
3
0
1
0
1
1
2
1
0
1
1
0
0
1
2
1
2
1
1
0
0
1
1
1
2
1
0
1
0
2
1
1
2
1
1
1
2
2
2
1
1
1
2
2
2
2
1
0
1
0
2
2
0
1
1
1
2
1
0
1
2
3
0
1
2
2
0
1
2
1
1
1
1
1
1
2
1
1
0
1
1
1
0
2
0
1
2
1
2
0
2
0
0
1
1
1
0
1
2
0
1
1
1
1
1
1
1
0
1
0
0
1
1
0
1
2
0
1
1
0
1
2
0
3
1
0
2
1
1
1
0
0
0
1
1
1
1
1
1
0
1
1
0
0
1
1
2
0
0
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
0
1
1
0
2
1
2
2
2
1
2
2
2
2
2
1
1
1
1
1
1
0
2
2
0
1
2
2
0
1
0
1
1
2
1
2
1
0
2
0
1
2
2
0
1
2
1
2
2
0
1
0
1
1
0
0
0
2
0
0
0
1
1
0
1
1
2
1
2
0
0
0
0
1
1
2
1
0
1
1
0
1
1
1
2
0
1
1
2
1
2
1
1
1
0
1
1
0
0
0
1
0
0
1
1
0
2
0
2
3
0
0
0
1
1
1
1
1
1
2
2
2
1
0
1
0
1
1
0
0
1
0
1
1
2
0
1
2
0
1
1
2
0
2
2
1
1
1
0
1
1
2
0
1
1
2
0
0
1
1
1
1
1
1
0
0
2
1
1
0
0
1
1
0
0
1
2
0
0
0
1
2
0
2
1
0
1
0
1
1
1
2
1
2
2
0
2
2
1
1
1
1
2
1
1
2
2
0
2
1
1
2
1
1
1
0
1
2
1
0
4
0
2
2
1
1
2
0
2
1
1
2
1
0
1
2
1
0
0
1
0
2
1
0
1
2
1
1
2
0
1
0
4
0
1
0
1
1
0
0
1
2
2
1
0
1
1
0
2
1
1
1
1
0
1
0
2
0
0
0
1
1
1
1
1
0
1
2
0
2
1
1
2
0
0
0
1
1
1
1
2
2
2
0
1
1
0
0
1
1
0
0
0
2
1
0
2
0
1
2
2
1
1
1
2
1
1
3
0
1
1
2
1
2
2
1
1
0
1
1
1
2
2
1
2
1
1
1
1
1
1
1
0
1
2
0
0
0
2
2
1
1
0
0
2
1
0
0
1
1
2
2
1
1
1
1
2
1
2
1
0
1
1
0
1
0
0
0
0
1
0
1
2
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
2
2
1
0
2
0
1
0
1
0
0
1
1
1
0
3
0
2
2
1
0
0
0
1
0
1
1
1
1
0
1
0
0
1
3
2
1
1
1
0
0
3
0
1
2
0
1
0
1
1
1
2
0
0
2
1
1
2
1
2
1
3
2
1
1
1
1
1
2
1
1
1
1
0
1
1
1
2
0
1
1
0
1
2
2
1
1
1
0
2
2
2
1
1
1
1
2
0
0
2
3
0
1
2
1
1
2
0
0
1
1
2
1
1
0
1
1
2
2
1
1
1
0
2
0
1
3
2
2
1
1
0
1
0
0
2
2
1
0
2
1
0
0
2
2
1
2
0
1
2
1
0
0
2
1
0
1
0
2
2
0
1
2
1
2
1
0
2
1
0
6
2
2
1
1
1
0
1
2
0
0
3
1
1
1
1
2
1
0
2
0
0
1
0
0
1
1
1
1
2
2
0
1
2
1
1
1
2
2
0
1
1
0
0
1
2
1
0
1
2
2
1
1
2
1
1
0
0
1
1
1
1
1
1
0
1
0
0
1
1
0
2
0
0
2
2
1
1
0
0
1
0
2
1
1
1
1
1
0
0
1
1
1
0
0
1
2
2
0
1
1
0
1
1
1
2
1
1
1
1
0
1
1
1
0
2
1
1
1
1
1
0
0
0
1
0
0
0
1
1
0
1
2
2
1
1
1
1
1
1
1
1
2
0
0
0
1
1
1
0
2
1
0
2
1
1
1
0
2
2
0
1
1
1
1
2
0
1
2
0
0
3
2
2
2
2
0
1
0
0
0
1
2
0
1
1
2
1
1
1
1
1
0
1
0
0
1
1
1
1
1
1
1
2
0
2
0
0
2
0
2
2
2
1
1
2
2
0
0
1
2
0
1
0
1
0
1
1
1
2
1
1
0
1
1
1
2
0
1
1
1
0
2
0
1
1
2
1
2
2
0
1
1
0
0
1
0
2
0
0
2
0
0
0
2
0
0
0
1
0
1
0
1
0
1
0
0
1
1
2
0
1
2
1
1
0
1
1
0
2
0
0
2
0
1
2
2
2
0
1
1
1
2
1
2
1
2
1
2
2
1
0
2
1
1
1
1
1
0
0
1
1
1
2
0
0
0
0
2
1
1
0
1
1
2
1
1
1
0
1
0
1
1
1
0
1
2
2
1
2
2
2
2
0
0
0
2
1
0
1
2
2
0
0
0
2
0
1
2
1
0
1
1
2
0
2
0
2
1
0
1
1
1
1
1
0
1
0
0
2
0
0
1
1
0
0
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
2
1
1
0
0
1
2
4
0
0
2
2
0
1
1
1
1
1
1
1
0
2
3
1
2
2
2
1
2
2
1
0
1
1
1
1
0
1
0
1
1
1
0
1
1
1
1
1
2
1
0
1
0
0
2
0
2
1
0
2
1
0
2
0
0
1
1
0
0
2
1
1
0
0
0
1
0
0
0
0
3
0
1
2
2
0
1
1
1
2
1
2
2
2
0
0
2
0
0
1
0
0
3
1
1
0
1
1
1
0
1
0
2
1
1
1
1
0
0
1
1
1
1
1
2
1
2
1
2
1
0
0
0
0
0
1
1
2
1
1
1
1
1
0
0
2
2
2
0
0
1
0
1
0
0
1
1
0
2
1
0
0
1
1
0
1
1
2
1
1
1
1
2
0
1
2
1
1
0
0
2
1
2
1
0
2
1
4
1
1
1
2
0
1
1
0
0
0
1
1
1
2
2
1
2
0
1
2
0
0
1
1
1
0
1
0
0
1
0
2
2
0
1
1
0
0
2
0
1
0
1
1
0
0
1
1
1
0
2
0
1
2
0
1
1
1
2
1
1
0
0
1
0
2
1
1
1
2
0
1
2
0
0
2
2
2
2
1
2
2
1
1
0
1
0
0
0
0
1
1
2
1
1
0
1
0
1
2
1
1
1
2
2
2
1
1
2
1
1
2
2
1
2
0
1
1
2
1
0
0
0
0
2
0
1
1
0
1
0
0
1
1
0
1
2
0
0
0
2
1
0
1
0
1
1
2
1
0
0
3
1
1
1
2
1
1
1
1
1
1
2
2
0
1
1
2
2
0
0
2
2
1
0
1
1
2
1
1
2
2
1
1
2
1
0
0
1
0
0
2
2
0
1
1
3
3
1
1
1
2
1
0
1
1
1
1
1
2
1
1
1
1
1
2
0
0
1
1
2
0
0
1
2
1
1
0
0
1
1
1
1
1
0
0
2
1
1
1
2
1
0
1
1
1
1
1
0
1
0
1
1
3
1
2
1
1
1
2
0
1
1
1
1
0
0
1
1
1
2
1
1
2
1
0
1
0
1
2
2
1
1
1
1
2
1
0
0
2
1
0
1
1
0
0
1
0
1
0
0
0
0
1
1
1
1
1
1
2
0
0
1
1
2
3
1
1
1
1
1
1
1
2
1
2
1
2
1
1
0
0
1
0
1
2
1
1
0
0
1
3
0
1
2
1
1
1
1
1
0
0
1
2
0
1
0
1
0
1
1
0
1
0
1
1
0
0
0
1
2
1
1
1
1
0
1
2
1
0
0
0
0
2
2
0
2
1
1
4
0
0
1
1
1
1
1
0
2
1
2
1
1
1
1
2
0
1
0
1
1
1
1
2
2
1
0
1
1
1
2
2
9
1
0
0
2
1
0
2
2
1
1
0
0
1
0
1
0
0
1
1
2
1
1
1
2
1
2
0
2
1
2
1
0
0
0
1
0
1
0
1
0
2
0
0
2
0
1
1
1
1
1
2
1
0
1
0
1
1
1
2
0
2
2
0
1
0
2
0
1
1
2
2
2
1
1
1
0
1
1
0
1
2
0
1
2
2
0
1
1
1
0
1
1
0
0
1
0
1
1
1
0
1
1
1
0
1
0
2
1
1
1
2
0
0
1
1
0
2
0
0
0
0
0
1
1
1
2
2
1
2
2
1
2
1
2
0
0
1
0
0
2
2
1
2
1
0
0
1
1
1
2
2
1
1
1
0
0
1
1
1
1
1
1
1
1
1
1
1
1
0
0
1
2
2
1
1
1
0
1
0
1
1
0
1
1
0
0
0
1
1
1
2
2
1
1
0
0
1
0
0
1
0
1
1
2
2
1
0
0
1
1
0
0
2
1
1
0
2
1
1
1
0
1
2
2
2
2
0
2
1
0
2
0
1
1
1
1
0
2
2
2
2
1
1
1
2
0
1
1
0
1
0
1
2
1
2
1
1
1
1
0
0
0
1
2
0
0
1
1
0
2
0
0
0
0
0
1
1
3
1
2
1
1
0
0
2
1
2
1
1
2
2
1
2
2
1
1
0
1
1
1
1
2
2
1
0
0
2
2
2
1
0
1
3
2
1
2
0
0
0
1
1
1
2
1
1
0
0
0
1
0
2
2
1
1
0
2
1
0
1
1
1
2
1
1
1
2
2
1
1
1
1
2
1
0
1
0
1
3
1
1
1
2
0
1
0
1
0
0
1
2
0
1
2
2
1
3
0
2
0
1
0
0
1
0
2
0
0
1
1
0
1
1
2
0
1
2
1
1
0
0
1
1
0
1
1
0
0
0
1
1
1
0
2
1
0
2
0
0
1
1
2
1
1
1
1
0
0
1
0
1
0
2
1
0
2
1
3
0
0
2
1
1
1
2
1
2
0
0
2
2
3
1
1
1
1
0
1
1
0
1
0
0
2
0
2
1
1
1
1
1
1
1
2
0
1
2
1
1
1
0
0
0
0
1
2
0
0
1
2
1
0
0
1
1
1
1
1
3
2
1
1
0
1
0
1
0
2
0
0
0
0
1
1
0
1
1
1
1
2
1
0
2
0
0
2
1
0
1
2
0
1
1
2
1
0
0
1
1
1
2
1
0
1
1
2
1
1
1
1
0
1
0
0
2
0
1
1
2
1
1
1
1
1
1
1
1
1
0
2
1
0
0
0
1
1
2
2
1
1
0
0
1
1
1
1
1
2
1
1
1
1
0
1
0
2
2
1
2
2
0
0
2
0
1
1
2
2
1
2
2
1
1
1
2
1
2
2
1
1
1
1
0
1
0
0
2
1
2
1
1
2
1
1
0
2
2
1
1
1
2
0
2
0
2
1
2
0
0
0
1
1
1
1
1
1
1
1
2
1
2
0
1
0
1
0
2
0
2
0
1
1
1
1
1
1
1
0
2
2
0
0
1
0
1
2
1
0
3
0
1
0
0
1
1
2
2
0
1
1
1
0
0
2
2
1
0
0
2
1
1
0
1
0
0
1
1
1
0
1
1
1
0
1
1
1
1
2
1
1
0
1
1
2
2
0
6
1
1
2
0
1
0
2
1
1
0
1
0
0
1
1
2
0
1
1
0
1
1
0
1
1
0
1
2
1
0
1
1
0
2
1
1
1
2
1
2
2
1
0
1
1
1
2
2
1
1
0
2
1
2
0
1
0
0
1
2
1
1
1
1
1
1
0
0
0
2
2
1
1
2
1
2
2
1
1
1
1
0
1
1
2
0
0
1
1
0
1
1
1
1
1
2
1
1
1
1
2
0
1
1
1
1
1
1
1
1
0
1
1
1
1
1
2
1
0
2
1
2
1
1
2
0
0
1
2
1
0
1
1
1
0
3
0
1
1
2
1
1
2
2
1
2
0
1
1
2
2
1
1
0
0
1
0
0
0
1
0
1
0
0
0
0
2
1
0
1
1
1
2
1
1
0
2
0
0
1
2
2
1
1
0
0
1
0
1
2
0
1
2
2
1
2
7
0
2
1
0
1
2
1
1
0
1
2
0
1
0
1
0
1
0
0
1
1
1
1
0
0
1
2
2
1
0
2
7
2
0
0
1
2
2
1
1
1
2
0
0
0
2
2
1
0
1
1
3
0
1
0
1
1
0
1
1
1
1
0
0
1
0
1
2
0
2
1
1
2
1
2
2
2
2
1
1
1
1
1
0
0
1
2
1
0
1
1
2
1
1
1
1
1
2
1
1
2
1
1
0
1
1
2
2
2
1
0
0
1
2
1
2
1
1
0
1
1
1
1
0
0
1
0
0
1
2
2
1
0
3
1
0
1
0
1
1
2
0
1
1
0
1
2
1
1
1
2
1
2
1
1
1
2
0
1
2
2
2
2
2
0
2
1
0
2
1
1
1
1
2
1
1
1
1
0
1
0
1
0
0
2
1
1
2
0
1
1
0
0
1
1
0
0
2
1
1
1
0
1
1
3
1
2
0
1
0
1
0
0
1
1
1
1
1
1
1
1
1
2
0
0
1
1
1
1
0
2
1
0
3
1
1
1
2
1
1
1
0
1
2
2
0
2
2
2
1
1
1
1
1
0
0
0
1
0
2
0
0
1
2
1
0
2
0
1
0
1
0
1
1
0
2
0
1
0
2
1
2
1
0
1
0
2
1
0
1
2
1
1
1
1
1
0
1
1
0
2
2
0
0
1
0
2
1
0
2
1
1
1
2
2
1
0
1
1
1
1
0
1
1
1
1
0
1
1
2
0
1
2
2
1
1
1
1
1
1
0
0
2
1
2
1
0
1
0
0
0
0
0
2
2
3
1
1
1
0
1
1
1
1
1
1
1
0
2
1
2
2
2
2
2
2
0
1
2
1
1
0
0
1
0
1
1
0
0
1
0
1
1
0
1
0
1
1
0
1
0
0
0
0
1
2
1
1
1
0
1
1
2
0
1
1
1
1
1
1
1
1
1
2
1
1
0
1
1
2
1
1
1
1
0
0
1
1
2
2
1
1
0
2
0
1
1
0
0
0
0
0
0
0
1
0
1
2
1
0
1
1
3
1
0
1
1
1
3
1
0
2
2
1
1
0
2
2
0
1
0
2
0
1
1
1
1
2
1
0
1
2
1
1
1
0
0
1
2
1
0
0
1
2
1
1
1
2
1
2
2
3
2
0
0
1
2
0
1
0
1
1
1
2
1
2
1
2
1
2
1
0
1
1
1
1
0
1
0
1
0
1
2
1
0
0
0
2
1
0
1
0
0
1
2
1
0
1
0
0
2
0
2
1
1
1
1
2
0
2
1
2
1
0
0
0
1
1
0
0
1
1
1
1
1
2
2
0
2
1
0
1
2
0
1
0
0
0
0
1
1
0
0
1
1
2
0
1
4
1
0
1
2
0
0
1
1
1
1
1
0
0
1
0
2
2
1
1
1
0
0
0
2
1
2
1
0
0
1
0
2
0
1
1
1
0
0
1
2
1
1
1
0
1
0
1
1
0
2
2
2
1
1
1
2
1
0
0
1
2
2
1
0
1
1
1
1
2
0
2
0
0
0
2
1
1
0
1
2
1
1
1
0
1
1
0
2
0
0
0
1
0
1
1
2
0
2
1
1
0
1
1
1
0
1
0
1
1
1
1
0
0
0
1
2
0
1
2
3
0
1
1
0
1
2
1
1
2
3
1
0
2
2
0
2
1
1
1
1
0
1
1
1
0
1
0
2
1
1
1
2
1
1
0
1
2
1
1
1
1
2
1
1
1
2
2
1
1
1
2
1
1
0
1
1
0
0
1
3
1
2
1
0
1
1
1
0
0
0
2
1
2
0
1
2
0
2
2
1
0
0
1
1
0
3
1
1
0
0
0
0
2
1
0
1
1
1
0
1
0
1
2
2
1
1
1
0
2
2
2
0
1
2
1
0
1
1
1
0
2
0
0
0
1
2
2
1
0
1
1
0
2
2
1
2
2
0
1
1
0
1
1
0
1
0
1
0
1
1
1
0
1
2
0
2
2
0
1
0
0
0
0
1
1
0
2
2
1
0
2
2
1
0
1
0
1
1
2
0
0
1
1
1
0
0
1
1
1
0
2
2
1
0
1
1
1
0
0
1
1
1
1
2
1
0
1
0
0
2
0
1
1
1
1
1
2
0
1
1
1
1
1
0
2
0
1
1
1
1
1
1
0
3
2
1
1
1
1
1
1
0
0
1
2
1
0
1
1
2
1
1
1
4
1
0
1
2
0
1
0
1
2
2
1
1
0
2
0
2
2
0
0
1
1
1
2
1
0
1
2
1
2
0
2
1
1
2
1
0
1
0
1
1
2
2
0
0
1
1
2
0
2
2
1
2
0
1
2
1
1
1
0
2
0
1
1
1
1
1
2
0
2
1
1
1
2
0
0
1
1
2
1
0
1
2
1
1
0
1
1
1
0
1
1
1
1
0
1
0
0
2
2
2
1
0
1
0
2
2
0
2
1
0
1
1
2
2
0
1
1
1
1
0
1
1
2
1
1
1
1
1
0
1
2
1
2
0
0
0
2
0
1
1
1
1
0
1
2
1
2
0
2
1
2
1
1
1
1
0
1
2
0
2
2
0
1
0
0
1
0
2
0
1
0
1
2
2
2
1
1
1
1
1
1
1
1
0
1
0
1
2
0
1
1
1
0
2
0
0
1
2
2
2
2
1
1
1
1
3
0
1
1
0
1
2
0
0
1
2
0
1
1
0
1
0
1
1
2
1
0
0
2
0
2
1
0
2
1
1
0
2
2
2
1
1
1
2
1
1
1
1
1
0
1
0
0
1
1
1
3
1
1
2
0
0
0
0
0
0
1
1
1
1
2
2
1
1
1
0
1
1
1
2
0
1
0
0
1
0
1
1
4
1
1
0
0
2
1
1
1
1
0
1
3
1
2
0
1
2
1
2
0
1
1
0
2
2
1
1
1
0
1
0
0
1
2
1
2
0
1
0
0
1
2
1
1
3
0
1
2
0
1
2
1
0
0
4
2
1
3
1
1
1
0
1
1
0
2
1
1
2
0
1
1
0
2
0
2
1
1
1
1
0
0
0
1
0
0
1
3
1
1
2
1
2
0
1
0
0
2
1
1
1
1
2
1
1
5
0
2
1
2
0
1
1
0
3
1
1
1
0
0
2
1
1
1
2
0
2
1
1
0
2
1
1
1
1
1
1
1
1
1
0
2
2
2
1
0
2
0
1
1
0
0
1
3
1
0
1
1
2
0
1
1
2
3
0
0
1
1
2
0
1
2
1
2
1
0
1
2
0
0
1
0
0
0
1
1
2
2
1
2
0
1
1
2
0
0
0
0
2
2
0
0
0
1
2
1
1
0
2
1
1
1
0
1
2
1
1
0
2
0
2
0
1
1
1
1
1
1
1
1
2
2
1
1
0
1
2
1
1
2
0
0
1
1
1
1
1
1
1
1
2
2
1
1
1
1
0
0
2
1
0
1
1
2
0
1
1
2
0
0
1
1
2
1
1
1
0
1
1
1
0
1
1
1
2
1
2
0
0
0
1
2
2
2
1
1
0
0
3
2
1
2
2
0
2
0
2
1
1
0
1
0
0
1
2
3
1
0
2
0
1
1
1
3
1
1
1
0
0
1
1
0
1
2
0
2
0
1
0
1
2
0
2
0
2
1
0
2
2
1
2
3
2
0
1
1
0
1
1
0
0
2
1
2
1
0
0
0
1
1
1
2
1
0
1
0
0
0
2
0
0
0
2
1
1
1
1
3
1
0
1
1
1
1
1
2
3
0
2
0
1
2
1
1
2
1
1
1
2
2
1
1
2
1
0
0
0
1
1
0
1
0
0
1
2
2
2
0
0
2
1
1
2
0
1
1
2
1
2
2
1
0
1
2
2
0
1
0
3
1
0
1
1
0
2
1
2
1
2
1
1
1
0
0
1
0
1
1
1
1
2
1
1
1
0
2
2
1
0
2
1
0
2
0
1
2
2
1
1
1
1
1
1
1
2
0
1
0
1
0
2
1
1
1
1
1
0
1
0
0
2
1
0
2
1
0
1
1
2
0
1
1
1
1
2
0
1
0
1
1
2
0
1
0
0
0
1
0
1
0
0
0
0
1
1
0
1
0
0
1
1
1
0
1
0
2
0
1
2
0
1
0
1
0
1
0
0
1
0
0
1
1
2
2
1
1
0
1
1
1
0
1
1
0
1
1
2
0
0
0
2
0
1
0
1
2
2
0
2
0
1
1
1
1
1
2
2
0
0
1
1
2
0
1
1
0
1
1
0
1
0
2
1
1
0
0
1
0
1
3
0
1
0
0
1
2
1
1
1
1
2
1
0
0
0
1
0
0
0
1
0
1
1
2
2
0
1
0
1
0
2
2
1
1
2
2
0
1
1
2
1
2
2
2
1
2
1
1
1
2
2
0
1
0
0
1
2
2
0
1
1
1
0
0
0
0
2
1
0
1
1
2
1
1
2
2
1
2
0
1
1
0
1
1
1
1
0
0
0
2
1
1
1
2
2
1
0
0
0
0
1
1
0
0
0
1
1
0
1
1
2
1
1
2
1
0
1
1
1
1
0
0
0
1
2
0
1
1
1
0
0
1
0
1
1
1
1
0
1
1
2
1
1
2
2
1
0
0
1
0
2
1
1
2
1
2
1
1
2
1
1
1
0
1
2
1
1
0
0
0
0
2
0
1
1
2
1
0
1
1
1
0
1
0
1
0
0
3
1
1
2
1
1
1
1
1
1
0
0
1
1
1
1
2
0
1
1
1
1
1
0
2
1
1
2
0
1
0
1
2
1
1
1
1
0
0
2
1
0
0
2
2
1
0
1
0
2
0
0
1
1
1
2
1
2
0
0
5
1
2
1
1
2
1
1
0
2
2
1
1
0
2
1
1
1
1
1
1
1
0
0
1
1
2
2
0
2
0
1
1
1
1
1
0
1
0
1
2
2
1
1
1
1
2
1
0
1
1
1
1
1
2
0
1
1
1
2
0
0
1
1
1
1
1
0
1
1
1
0
0
0
0
1
2
1
2
1
1
1
0
0
1
2
1
1
0
0
1
1
1
0
2
1
0
2
1
1
1
0
1
1
2
0
0
1
1
0
0
1
0
1
0
2
1
1
1
1
1
2
0
1
1
1
1
1
1
0
1
2
0
0
2
1
0
1
2
1
2
0
0
1
1
1
1
1
1
1
1
2
1
1
1
0
1
1
1
1
2
2
2
1
1
1
1
3
1
1
1
2
1
1
2
2
0
4
1
2
1
2
1
1
1
5
1
0
1
1
0
2
1
2
0
0
0
1
0
0
1
0
2
1
1
0
1
1
1
2
2
0
0
1
1
1
1
1
1
0
1
0
0
6
1
1
2
0
1
1
1
1
0
0
1
0
1
4
0
0
0
1
2
2
1
2
2
1
1
2
1
1
1
0
1
2
1
1
1
0
0
1
2
0
1
0
1
1
0
1
1
0
1
1
0
1
0
0
0
1
1
0
1
2
1
1
1
2
1
4
0
1
0
1
2
1
1
0
0
1
0
1
1
0
1
3
2
1
1
1
0
1
0
1
2
2
0
0
2
1
1
0
1
1
1
1
2
1
0
2
1
0
1
2
1
1
0
1
2
1
2
2
1
1
0
2
1
0
2
1
1
0
1
1
1
1
1
1
2
1
2
1
1
2
1
0
0
0
1
2
0
3
0
0
2
1
0
2
1
2
0
2
1
1
1
1
0
1
1
1
0
1
1
1
0
1
0
2
1
0
2
0
0
1
1
1
2
1
1
1
2
2
1
1
0
1
0
1
1
1
1
2
3
0
1
1
1
0
1
2
1
1
6
1
0
1
2
2
0
2
1
0
0
1
0
1
0
1
2
2
0
2
0
1
0
1
0
2
1
1
1
0
1
1
1
0
1
1
1
1
1
2
2
2
0
0
0
0
2
0
1
1
1
0
1
3
1
1
1
1
0
2
1
1
0
1
2
1
0
1
1
2
0
1
0
2
1
0
1
0
1
1
2
2
0
2
0
0
2
2
1
0
0
0
2
1
2
1
1
2
1
1
1
1
2
1
0
1
1
1
1
2
1
0
1
0
0
0
0
1
1
2
2
1
2
0
1
0
1
1
0
0
0
1
0
1
0
0
1
1
1
0
1
1
2
0
1
1
3
1
1
1
0
1
1
0
1
3
1
0
2
0
1
1
1
0
0
1
1
1
0
1
0
4
1
1
2
0
1
1
0
4
1
1
1
1
0
1
3
1
1
1
0
1
1
0
1
1
0
1
0
1
0
0
0
2
1
0
1
0
2
0
2
1
0
0
0
1
2
2
1
1
2
1
1
2
1
0
0
2
1
2
2
0
1
1
2
1
1
2
1
1
0
2
0
3
0
1
0
1
0
1
0
0
1
0
1
0
1
0
1
1
0
2
1
1
1
0
2
1
1
2
2
0
0
2
0
2
1
0
0
0
1
2
1
0
2
0
2
2
0
0
0
1
1
1
0
1
2
0
4
1
0
1
2
1
0
1
1
0
1
1
2
1
1
2
1
2
1
0
3
0
1
1
1
1
1
1
1
1
0
1
1
0
1
1
0
1
1
0
1
0
1
0
0
1
1
2
1
1
2
2
0
1
2
1
0
3
1
2
0
2
1
0
0
2
0
2
0
1
0
0
1
1
0
1
1
0
1
2
0
1
1
2
0
2
0
0
2
0
1
2
1
1
0
0
1
3
2
2
1
1
1
0
2
1
0
0
2
0
0
1
1
1
1
1
2
0
2
1
1
0
0
1
2
2
2
1
0
0
1
1
0
2
0
1
0
1
1
2
1
1
1
0
0
1
2
1
2
1
0
2
1
1
2
2
1
2
2
1
2
0
1
1
1
0
1
2
1
0
1
0
1
0
1
2
0
0
1
1
1
1
2
1
1
2
2
0
1
1
3
1
0
5
0
1
1
2
1
2
1
1
1
0
2
1
1
1
2
0
1
0
0
2
2
1
1
2
1
1
0
0
1
1
1
1
0
1
0
1
0
2
2
2
1
1
0
2
2
0
0
2
1
1
1
1
2
0
0
0
0
1
0
0
2
1
1
1
0
0
0
0
1
0
2
1
2
2
1
1
0
0
2
0
2
1
1
1
1
2
0
0
2
1
1
0
2
1
2
0
0
1
1
0
2
1
2
0
1
1
0
1
2
2
1
2
0
1
1
1
1
0
2
1
1
0
0
0
0
0
0
1
1
0
1
2
1
1
0
0
0
1
1
2
0
2
1
1
1
2
0
1
1
1
2
0
1
0
2
1
0
1
1
2
1
2
1
1
1
3
2
1
0
0
2
1
0
1
2
0
1
0
1
1
2
0
1
1
1
1
2
0
1
1
2
0
1
2
1
1
0
1
1
0
2
1
2
2
2
0
0
1
0
1
2
1
1
1
0
1
2
2
1
1
1
1
2
1
2
0
0
1
0
1
1
0
0
1
0
1
1
1
0
1
1
1
2
1
2
0
1
1
4
1
0
1
1
1
0
2
0
0
2
2
1
2
0
1
1
1
1
2
0
2
0
1
1
1
1
3
1
2
2
1
0
2
1
1
2
1
1
1
1
2
2
1
1
2
0
1
2
0
2
1
0
1
0
2
0
0
2
0
1
2
0
0
1
1
1
1
0
1
1
1
1
1
1
1
2
1
1
1
1
1
2
0
0
2
0
2
2
1
2
2
0
1
2
1
2
0
0
1
2
0
1
1
0
1
1
1
1
0
1
1
1
2
2
2
0
1
1
0
1
1
1
1
1
0
0
0
0
1
1
1
1
0
1
1
1
1
2
1
1
1
0
1
0
1
3
1
2
1
2
0
1
0
0
0
0
2
1
0
1
0
1
1
1
2
2
2
2
1
2
1
1
2
1
0
0
0
1
1
1
0
0
2
0
2
0
1
1
0
1
1
3
2
1
1
1
0
2
1
1
1
1
1
1
1
2
1
1
1
1
2
2
0
5
0
1
1
1
1
1
0
0
0
1
1
1
1
1
1
2
0
1
1
0
1
1
1
0
1
1
1
1
0
2
1
0
1
0
1
1
1
1
1
1
0
2
1
1
1
1
2
2
1
2
2
1
0
1
0
1
1
0
0
1
0
1
1
0
0
1
1
1
0
1
1
1
1
1
1
1
1
2
1
1
0
1
0
2
1
1
1
2
1
0
1
2
1
0
0
2
0
1
0
0
0
2
1
1
1
1
1
0
1
1
0
0
0
1
1
0
1
0
1
0
0
2
2
3
2
2
1
2
1
1
1
1
1
1
2
1
0
1
1
2
0
1
1
1
2
1
1
4
0
1
1
1
0
1
2
1
1
1
1
0
1
0
1
0
1
2
2
2
0
0
3
2
1
2
0
0
0
1
2
2
1
2
2
1
0
2
0
1
0
0
1
1
0
1
2
1
0
0
1
1
1
1
1
0
1
1
0
3
1
0
2
1
2
3
2
0
0
1
0
0
2
1
0
1
2
1
2
1
1
1
0
1
1
0
2
1
0
0
0
0
0
2
1
2
1
1
1
0
1
1
1
0
2
1
1
2
0
1
1
0
2
0
1
0
0
2
1
1
1
1
2
2
1
0
0
2
1
0
2
2
1
2
1
1
1
1
0
1
0
1
0
1
0
2
1
1
1
0
0
0
0
2
0
1
1
1
1
1
0
1
2
1
1
0
1
1
1
2
1
0
0
0
2
1
1
1
1
1
3
1
1
0
0
1
1
1
1
2
0
2
0
0
1
0
1
1
1
1
1
1
1
0
1
0
1
2
0
1
1
1
1
0
0
2
1
1
0
2
1
0
0
2
2
1
1
0
1
1
1
1
2
0
0
1
0
1
0
2
0
0
1
1
1
1
1
1
1
2
2
1
0
2
3
1
0
0
0
1
3
1
1
1
2
1
1
2
2
2
2
1
0
1
1
0
0
0
2
1
1
0
1
0
0
0
1
1
1
1
1
1
1
0
0
1
1
2
0
2
0
1
0
1
1
1
0
1
1
1
1
1
1
1
1
0
0
0
1
1
2
0
1
0
1
0
1
2
0
1
0
1
1
2
0
1
1
1
1
1
1
2
0
2
1
1
0
1
1
0
0
2
1
0
1
0
0
1
1
0
1
0
2
0
1
0
1
1
1
2
0
0
0
0
1
0
1
1
1
2
1
2
0
1
1
0
1
0
0
1
0
1
2
2
0
2
2
0
0
1
1
1
1
1
2
1
0
0
1
1
1
0
1
1
2
0
1
0
1
2
2
1
0
2
1
1
0
1
1
1
1
0
2
2
2
1
0
0
1
0
0
2
1
1
1
1
1
1
1
0
2
3
2
1
1
1
1
2
1
2
0
0
1
1
0
2
1
1
0
1
2
1
1
0
1
1
1
1
1
2
1
1
1
1
0
2
1
3
1
1
1
1
2
1
1
1
1
0
1
0
0
1
0
1
1
1
1
0
0
1
1
1
2
2
2
1
1
1
0
1
1
1
1
2
2
0
0
1
1
0
0
2
0
0
1
2
2
2
1
1
1
0
0
2
0
0
1
0
1
1
1
1
0
1
1
2
2
1
1
1
2
1
6
0
0
2
1
1
1
0
2
3
0
1
1
0
2
0
2
1
1
1
2
2
0
0
0
0
1
1
0
0
0
1
1
0
1
1
2
1
2
1
1
2
0
2
1
0
0
1
2
1
2
1
3
0
1
1
1
1
1
0
0
0
1
0
1
0
1
1
1
2
1
1
1
2
0
1
1
1
1
1
1
0
1
0
1
2
0
1
0
1
1
2
0
0
2
0
1
0
1
1
1
1
0
2
1
1
1
0
1
2
0
2
2
1
0
1
1
0
1
0
2
1
4
1
1
1
0
0
0
0
1
2
2
1
1
1
0
2
1
1
2
1
1
2
0
0
1
1
2
1
1
0
1
0
1
1
0
1
1
1
0
2
1
0
1
0
0
2
1
0
1
0
1
1
2
2
0
1
1
1
0
2
1
2
1
1
1
1
1
1
1
1
0
0
1
1
1
0
1
0
1
1
1
2
0
1
0
1
1
1
2
1
0
3
1
0
1
1
1
0
2
0
1
0
0
2
0
1
1
1
2
1
1
0
1
2
1
0
1
2
2
1
0
2
1
0
1
1
0
1
1
2
1
1
1
1
0
1
1
1
0
0
0
0
1
1
0
0
1
0
2
0
1
2
1
0
1
0
0
1
0
2
1
1
0
1
0
0
1
2
2
1
1
0
2
1
6
0
0
1
1
1
1
0
2
2
1
1
0
1
1
2
1
2
2
0
2
1
0
2
0
2
1
0
1
2
1
1
2
2
1
1
2
1
0
1
1
1
2
0
1
1
1
1
0
3
1
1
1
0
1
1
1
1
1
1
2
1
0
1
1
1
1
2
0
1
2
1
1
1
1
2
0
1
0
0
0
1
0
2
1
2
1
1
1
2
1
1
1
0
1
1
1
0
3
2
1
1
2
2
1
0
1
1
1
1
2
1
1
1
0
1
1
1
0
1
0
1
2
1
2
2
1
0
2
1
2
0
0
1
1
1
1
0
0
0
2
1
1
0
1
0
0
1
2
2
1
0
3
1
0
2
1
1
1
0
1
1
1
1
0
2
2
1
0
1
1
2
1
2
1
2
1
2
2
1
1
0
0
1
1
1
1
1
0
1
1
1
1
1
3
2
0
1
1
2
2
2
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
0
1
2
1
1
1
1
1
0
0
0
0
1
0
1
1
0
0
1
1
0
2
0
1
1
2
0
1
0
1
0
1
2
0
1
1
0
1
0
1
2
2
1
1
2
0
1
1
2
0
2
2
1
0
1
2
1
2
0
1
2
0
2
1
2
2
1
0
1
1
0
0
2
1
2
1
2
1
2
1
1
1
1
1
0
2
1
0
1
0
1
1
0
1
1
1
1
3
1
1
1
1
1
1
2
0
1
1
0
1
0
0
1
1
1
1
2
1
2
2
1
1
2
2
1
2
1
1
1
0
1
1
2
1
0
2
1
1
0
2
0
1
1
1
1
0
2
1
0
1
2
1
0
0
1
1
0
2
2
0
1
1
3
1
0
0
1
1
1
2
1
2
1
0
0
2
1
1
1
1
1
2
1
1
2
1
1
2
0
1
1
2
0
2
1
1
1
1
1
0
0
1
1
1
1
0
2
0
0
1
0
1
1
0
0
1
2
1
4
1
0
0
2
1
1
0
2
2
1
1
1
0
1
2
2
2
2
1
1
1
2
2
2
1
1
1
1
2
2
1
3
1
2
1
1
1
1
2
1
1
1
0
1
1
0
0
2
2
1
0
1
1
0
1
2
1
1
1
1
1
2
1
0
0
1
0
2
1
0
2
0
2
0
0
1
4
1
1
0
2
0
1
1
2
1
0
1
0
1
4
1
1
0
0
0
1
1
1
0
0
1
0
2
0
1
2
2
2
0
3
1
1
1
1
1
1
0
2
1
0
2
1
0
1
2
2
2
0
0
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
0
0
1
1
1
1
1
0
1
1
1
0
0
2
2
1
1
0
0
1
0
2
1
1
1
2
1
0
0
0
2
1
1
1
2
2
1
0
1
1
3
0
1
1
0
1
1
0
1
2
1
1
1
1
0
1
2
1
0
0
0
2
1
2
1
0
2
0
1
1
1
1
1
2
0
1
0
1
0
2
1
0
1
2
2
1
0
0
1
2
0
1
1
1
1
1
2
0
1
0
0
0
1
0
2
1
1
1
0
1
1
2
2
0
1
2
2
1
1
1
1
1
2
1
1
1
1
1
1
1
0
1
0
2
0
2
0
0
1
1
1
2
2
0
1
2
1
0
0
2
1
1
2
1
0
1
0
2
1
1
1
1
1
0
1
1
1
0
0
1
1
1
2
0
2
1
2
0
1
0
3
0
0
0
0
1
1
0
0
0
1
1
1
2
1
1
1
1
1
1
1
2
1
1
0
1
0
0
1
1
2
2
2
2
1
0
1
0
1
2
0
3
0
0
1
1
1
0
1
2
0
0
1
1
1
0
0
0
1
2
0
0
2
1
0
1
1
0
0
0
0
0
1
1
2
1
1
1
1
0
1
1
0
2
0
1
1
1
0
2
2
0
0
1
0
0
0
1
1
3
0
1
1
0
2
1
0
0
1
1
2
1
0
1
2
0
2
0
2
1
1
0
2
0
0
0
0
1
1
1
2
0
0
1
0
0
1
1
1
1
2
2
2
2
2
0
2
1
1
2
1
1
2
2
1
1
1
1
0
1
0
2
1
1
1
2
1
0
1
1
1
1
2
2
2
1
2
2
0
0
1
1
0
2
0
1
0
2
0
1
1
0
1
2
1
1
1
0
1
1
2
1
1
1
1
1
0
1
2
0
1
0
1
2
2
1
1
0
2
1
2
2
1
0
1
2
0
0
0
1
1
2
0
2
2
1
1
1
2
1
1
0
1
1
1
2
2
1
1
0
1
0
1
1
2
1
0
1
1
2
1
1
1
0
1
0
1
2
1
1
1
2
0
0
2
0
1
1
2
0
3
0
0
2
0
0
3
2
0
1
1
1
1
0
2
2
1
1
0
1
2
1
2
1
0
1
1
1
1
1
0
1
2
1
0
2
1
1
1
2
1
1
1
1
3
1
0
0
1
1
2
0
1
1
1
0
0
1
1
2
1
1
1
2
1
1
0
1
1
1
0
2
2
0
0
1
0
0
1
1
1
0
1
1
1
2
1
1
1
2
0
2
2
0
1
0
1
2
3
2
1
1
0
0
0
1
1
0
2
0
1
0
0
0
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
2
0
1
1
1
0
0
1
1
1
2
1
2
2
0
1
1
0
1
1
1
0
1
1
0
1
1
2
1
1
1
2
1
1
1
1
2
2
1
1
1
1
2
1
0
4
0
0
2
0
1
0
0
2
1
1
0
0
1
1
2
2
1
1
0
1
1
0
0
2
0
0
1
1
1
0
0
0
0
1
0
2
0
0
1
0
2
1
0
1
0
0
1
2
1
1
1
0
0
2
1
1
2
2
0
1
2
2
0
0
0
1
0
1
2
2
1
1
1
0
1
1
1
1
1
1
0
1
1
1
1
1
1
1
0
1
0
2
0
1
0
1
1
0
1
1
2
1
2
2
2
1
2
2
0
0
1
0
1
2
1
1
0
0
0
2
2
2
0
0
1
1
0
0
1
1
0
1
0
1
0
1
2
1
0
1
1
0
2
1
1
0
2
1
1
1
0
2
1
1
1
2
0
0
0
3
1
1
1
1
0
1
2
2
1
0
1
1
0
1
0
0
2
2
0
1
4
1
1
1
2
0
1
1
1
1
1
0
0
1
0
2
1
1
1
2
0
0
0
2
1
1
1
2
2
1
1
1
1
0
1
1
1
0
1
1
2
0
3
0
2
0
1
0
1
2
0
1
1
0
2
2
1
0
1
0
0
0
1
2
1
0
2
2
1
1
1
2
0
1
1
0
0
2
2
3
1
0
2
2
0
1
0
2
1
1
1
1
1
1
0
1
2
1
1
2
1
2
2
0
1
0
2
2
1
0
1
1
1
1
2
2
2
2
2
0
0
1
0
1
0
1
2
1
1
0
0
4
0
1
1
0
0
1
1
0
2
1
0
1
1
0
2
2
1
0
0
2
0
1
1
1
2
1
1
2
2
2
1
1
2
2
1
1
2
1
0
1
0
1
2
1
1
2
2
0
1
2
1
2
0
2
1
2
0
0
3
1
1
2
1
1
0
1
1
1
1
1
0
0
1
1
1
1
2
2
0
1
1
0
0
1
1
0
1
2
1
1
2
1
0
1
2
0
1
1
2
2
1
1
1
0
1
0
0
0
1
0
0
0
1
1
1
1
1
2
2
2
0
1
2
1
1
0
1
0
0
0
1
0
0
0
1
2
1
1
1
2
2
0
0
2
1
1
0
1
0
0
1
0
1
0
2
1
0
0
1
2
1
1
2
1
2
0
0
3
1
1
1
2
1
2
1
1
2
0
0
1
1
2
1
2
1
1
2
2
1
0
0
1
0
1
1
0
0
1
0
1
1
1
1
2
1
0
1
1
2
0
1
0
0
2
2
0
2
1
1
2
1
2
1
2
1
0
1
0
1
1
0
2
0
2
1
1
1
0
2
1
2
2
1
0
1
1
1
0
0
1
1
0
2
2
1
1
2
1
1
0
1
1
0
1
0
2
0
1
0
1
1
0
1
1
1
1
1
1
0
2
1
1
0
0
2
1
1
1
1
2
2
2
2
2
1
1
0
1
2
2
1
2
0
2
0
1
2
1
1
1
1
2
2
0
1
1
0
0
0
1
1
1
1
2
2
1
0
1
1
0
1
0
1
0
2
1
2
0
1
2
1
0
1
0
1
1
1
0
0
1
0
1
2
1
0
1
1
0
0
1
1
1
2
0
1
1
1
1
2
1
0
1
0
2
2
1
3
1
2
1
0
1
0
1
2
2
0
2
1
1
2
2
0
1
1
1
1
0
1
3
0
0
0
2
0
0
0
1
0
2
0
1
2
1
2
1
1
2
1
0
0
1
2
0
0
2
0
2
2
0
2
1
0
0
1
2
0
1
1
1
1
0
1
0
0
1
2
1
1
1
2
0
1
1
2
0
1
0
2
1
1
0
1
2
1
3
1
1
1
2
1
0
0
0
1
1
1
1
1
0
0
1
1
1
0
2
1
2
1
2
0
2
1
0
2
1
1
2
1
1
0
0
1
2
1
1
1
2
0
0
2
0
2
1
1
1
1
2
1
1
1
0
1
0
0
0
1
1
2
0
1
1
1
1
1
0
1
2
1
0
2
0
0
2
1
2
1
1
2
0
1
0
0
2
0
1
1
1
2
0
0
2
0
2
1
2
0
0
0
0
1
1
1
0
1
0
1
3
0
1
0
1
2
0
2
1
1
1
0
0
0
0
1
1
2
1
0
0
0
1
0
1
2
0
2
1
0
2
0
1
1
0
0
0
1
1
1
1
2
2
1
1
1
1
0
1
0
2
1
2
1
2
1
0
2
1
3
2
2
3
1
1
1
1
2
2
1
0
0
2
1
2
2
2
2
0
0
2
1
0
0
1
0
2
1
1
1
1
0
2
0
5
0
1
2
1
1
0
2
1
1
1
0
1
1
2
1
1
2
1
0
0
0
1
2
0
0
0
0
1
1
1
2
1
1
1
2
1
3
1
2
0
1
0
1
0
1
2
0
1
1
0
2
0
4
1
0
1
1
2
1
1
1
0
1
1
1
0
2
0
1
0
0
1
2
0
1
1
2
2
2
1
0
0
1
1
0
1
1
1
1
0
1
1
2
1
2
1
1
1
2
2
0
2
1
0
2
1
1
2
0
2
1
1
1
0
0
2
0
2
1
1
2
0
0
1
1
0
1
0
1
1
1
0
0
0
0
1
1
1
0
0
0
1
1
0
0
2
0
2
0
1
0
1
0
1
0
1
3
1
1
1
0
0
1
2
0
1
1
1
2
0
1
1
1
1
1
1
2
1
1
2
0
1
1
0
1
1
1
1
0
0
1
0
1
2
2
0
0
1
0
2
0
2
1
2
1
1
2
2
1
1
1
0
0
1
0
1
1
0
0
1
1
0
2
2
2
2
1
0
2
1
0
1
1
1
1
2
1
1
1
1
3
1
0
0
2
2
0
1
0
0
0
1
1
0
1
1
1
1
1
2
1
0
2
1
2
0
1
0
2
0
1
1
1
1
2
1
2
0
1
1
1
1
1
2
1
2
0
1
0
0
0
2
1
1
0
1
1
0
1
1
1
0
2
1
2
1
0
1
0
0
0
0
2
0
0
1
1
0
1
0
1
2
0
2
2
0
0
2
0
0
1
2
0
2
1
1
1
1
0
0
2
2
3
0
0
1
0
1
1
0
0
1
1
0
2
0
1
1
1
0
1
1
1
1
2
1
0
1
0
0
0
1
0
2
1
1
1
2
1
1
1
0
3
0
1
1
2
0
1
0
0
2
1
1
1
0
2
0
0
1
1
1
1
1
2
1
0
3
2
1
1
0
1
2
0
2
1
1
1
2
1
1
0
1
0
1
0
2
0
0
1
2
0
2
3
0
2
0
2
0
2
2
1
2
0
2
0
0
1
1
1
2
1
1
1
1
1
0
1
1
1
1
1
2
2
0
0
0
1
0
2
2
1
1
2
1
1
0
1
1
1
2
2
1
0
1
1
1
1
1
0
1
1
1
1
1
1
0
1
1
1
2
0
2
0
1
0
0
0
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
0
2
2
2
1
1
2
0
1
0
2
1
0
0
2
1
0
2
0
0
1
2
0
2
2
0
1
2
0
1
1
1
0
2
0
0
0
0
0
0
0
2
1
0
0
0
1
2
1
1
1
3
0
0
0
2
0
1
1
1
1
0
1
2
1
2
2
1
0
1
0
1
2
2
0
1
1
0
1
1
0
2
1
0
1
2
2
1
1
0
2
1
1
1
1
1
1
1
0
1
2
1
1
0
1
0
1
2
0
1
2
2
1
1
0
1
1
1
0
1
2
1
1
1
2
1
1
1
0
1
1
0
1
1
1
0
1
0
0
2
1
2
1
1
1
1
1
2
1
0
0
0
3
1
3
2
1
1
1
0
2
2
0
1
1
1
1
0
2
0
2
2
2
2
1
1
1
0
1
2
2
1
0
0
0
2
0
0
2
2
1
1
2
0
0
0
2
0
1
1
1
1
1
1
0
1
1
0
1
1
1
1
1
1
0
0
1
1
0
1
1
1
0
1
0
1
1
1
1
0
2
2
2
1
1
2
1
1
0
0
1
1
2
1
2
2
1
1
1
1
1
2
1
0
0
1
2
1
2
2
0
1
0
1
1
0
0
1
0
0
2
2
0
1
2
1
1
1
3
0
1
1
1
2
1
0
2
1
1
0
0
0
1
1
0
0
0
2
1
0
1
1
0
1
1
2
0
1
1
1
2
2
0
1
2
0
0
2
1
1
1
2
1
1
1
2
2
1
2
1
2
1
1
2
1
0
2
1
1
1
0
1
2
0
1
1
0
1
1
0
0
0
1
2
1
1
1
0
2
0
2
2
2
1
2
0
0
0
1
3
1
1
1
1
1
2
1
4
1
1
1
1
2
0
1
1
1
0
1
1
1
1
1
2
2
1
1
2
0
0
0
1
1
1
0
1
2
0
1
1
1
2
1
1
0
1
0
1
0
1
2
2
1
0
1
1
1
2
1
1
1
2
1
1
2
1
2
0
2
1
1
1
1
0
1
2
0
1
2
2
0
2
1
2
1
1
1
1
1
2
1
2
1
2
1
2
1
1
2
1
3
0
0
0
2
1
1
1
2
1
1
2
1
0
0
2
2
1
0
1
2
2
0
0
1
0
0
1
1
0
2
2
0
0
0
0
1
1
1
2
1
1
0
1
0
1
1
0
0
2
0
1
0
1
2
0
1
2
0
1
1
1
1
1
2
2
1
1
2
1
0
2
0
0
1
2
0
1
2
1
2
2
1
0
0
1
1
1
2
0
1
2
1
1
1
1
0
1
1
2
2
0
2
2
0
1
1
1
1
1
1
5
0
1
1
0
1
2
0
2
0
1
0
1
1
0
1
1
0
0
0
1
1
0
1
1
0
2
0
0
1
1
0
1
1
2
2
1
0
1
0
0
0
1
1
2
0
2
1
1
1
1
1
1
2
0
1
0
1
0
1
1
1
0
1
1
1
1
1
1
1
0
1
1
2
0
0
0
1
0
1
0
1
1
1
1
1
1
2
1
0
1
1
2
2
0
0
1
1
1
1
0
1
2
1
0
2
1
2
2
1
0
0
1
1
2
0
2
1
0
0
1
1
1
1
1
1
2
1
1
1
1
3
0
1
1
1
1
1
2
1
0
0
1
2
1
2
1
2
1
1
2
2
1
1
0
2
2
5
1
1
1
1
1
1
0
0
2
1
1
1
1
1
1
0
0
1
2
0
0
2
2
2
1
1
2
1
1
1
1
1
1
2
1
2
1
2
1
0
2
0
2
2
0
1
1
2
2
0
0
1
1
1
1
0
1
1
0
0
2
5
2
1
0
1
1
0
1
1
0
1
0
0
1
0
1
0
2
1
2
1
2
2
1
1
2
1
1
1
2
0
1
1
1
2
1
1
1
1
0
0
1
2
1
0
1
0
1
1
0
1
1
1
2
1
0
2
1
1
0
0
0
1
2
0
0
1
0
0
1
1
1
1
1
1
0
1
0
0
0
0
1
0
2
0
1
0
1
0
1
1
0
1
0
0
1
2
0
0
1
0
2
1
1
0
1
1
1
0
1
0
1
1
2
0
1
1
1
1
0
0
1
1
1
1
1
1
0
1
0
2
0
1
1
2
1
2
0
1
0
1
0
1
2
0
1
1
1
0
1
0
2
1
0
0
2
1
1
0
0
0
1
1
0
1
1
2
0
1
0
1
0
2
0
0
1
1
1
1
0
5
2
2
2
0
1
0
1
1
0
2
1
1
1
0
1
1
2
1
1
0
1
1
1
1
1
2
0
0
1
2
0
0
0
1
1
1
1
0
0
0
0
1
2
1
1
1
1
1
1
1
1
2
0
1
1
2
1
1
1
1
1
1
1
0
2
2
2
1
2
0
2
1
0
1
2
0
1
1
1
0
0
1
2
2
1
2
1
2
2
1
1
0
0
1
1
1
1
2
1
0
1
2
0
0
1
0
1
1
0
2
1
1
1
0
0
2
1
0
0
1
2
2
0
1
2
1
0
1
0
0
0
0
1
1
0
1
2
1
2
0
3
0
1
1
1
1
1
1
1
1
3
0
1
1
0
2
1
0
1
1
1
1
2
0
2
1
2
1
0
1
0
1
0
0
2
2
1
2
0
1
1
0
2
1
2
1
2
1
0
2
1
1
0
1
1
0
1
2
2
0
2
1
1
1
2
0
1
1
1
2
0
1
1
1
2
1
0
0
0
1
1
2
1
1
1
0
1
0
1
1
1
1
1
1
0
0
0
1
0
0
0
0
1
0
1
1
1
0
1
1
1
0
1
1
2
1
1
0
3
1
0
1
2
0
1
1
1
0
1
1
1
0
0
1
1
2
1
1
1
2
1
1
2
0
1
0
0
1
0
2
0
1
2
0
1
1
2
1
1
1
2
0
0
0
3
2
1
0
1
2
0
2
1
1
2
1
0
2
0
1
2
0
1
0
1
0
1
2
1
0
1
2
1
1
0
2
1
1
0
2
0
0
1
1
1
1
0
1
0
0
3
0
0
0
0
2
1
1
2
0
1
1
2
1
2
0
0
1
0
0
1
1
1
1
1
0
1
1
2
0
2
2
0
2
1
1
2
0
1
1
1
0
1
1
2
0
1
0
1
0
2
0
1
2
2
2
2
2
1
2
2
1
1
1
1
1
2
1
1
1
0
2
1
1
1
2
1
2
1
2
1
0
1
1
1
1
0
0
0
0
2
1
1
1
1
0
0
2
0
0
1
0
1
1
0
1
0
1
0
2
0
1
1
2
2
1
2
0
0
0
2
1
1
2
3
0
1
1
1
1
0
2
2
1
1
0
2
1
1
1
2
0
1
0
1
1
0
2
1
1
1
2
0
0
0
1
4
1
1
0
0
0
0
1
1
1
0
1
2
2
0
1
1
1
1
0
1
0
2
1
2
2
1
0
1
0
1
2
1
1
0
1
3
1
2
1
1
2
0
1
0
0
1
2
2
1
1
1
2
2
1
2
0
1
0
1
1
2
1
1
1
1
1
0
0
1
2
1
2
2
2
0
0
1
1
0
2
2
0
0
1
1
1
0
0
1
2
1
1
1
1
1
2
1
1
1
1
2
1
0
0
1
2
0
0
0
1
2
2
2
0
1
1
0
1
2
0
1
2
1
0
2
1
2
0
2
3
0
2
2
0
1
1
0
0
0
1
2
2
2
2
2
0
2
2
1
1
1
1
0
0
0
1
1
1
1
1
1
0
1
0
1
0
1
1
1
2
0
2
1
1
2
1
1
1
0
1
0
1
1
1
2
1
1
1
2
0
1
0
1
1
1
0
1
0
0
1
1
1
1
0
2
0
0
1
1
0
0
0
2
2
2
0
1
1
2
1
1
2
0
2
2
0
1
3
2
1
1
2
2
1
2
1
2
0
0
1
0
1
2
0
0
0
2
1
0
1
1
0
1
3
0
1
1
0
1
0
0
1
1
1
1
0
1
1
0
1
0
2
1
1
2
0
1
1
1
2
1
0
1
0
1
2
1
1
1
0
0
1
1
2
2
1
0
0
2
1
1
0
1
1
0
1
2
1
1
0
1
1
1
1
1
1
0
1
1
0
1
0
0
1
1
1
1
2
1
1
2
1
1
2
1
0
1
2
0
1
0
1
5
1
0
0
1
1
1
2
1
1
4
2
2
2
0
1
1
0
1
1
0
1
2
1
1
1
0
2
1
1
1
0
3
0
2
2
1
0
1
1
1
0
0
1
0
0
3
0
1
0
1
2
1
1
1
2
2
2
0
2
2
3
0
1
1
1
0
2
1
0
1
2
0
1
1
2
1
0
0
2
1
3
1
2
1
0
1
0
1
0
1
1
2
1
1
1
1
1
1
2
1
2
1
1
2
1
0
2
1
2
2
1
0
1
0
0
1
0
1
0
1
1
0
0
0
1
1
1
1
0
2
1
1
0
1
1
1
1
1
1
1
1
1
1
1
0
2
0
0
0
1
1
0
2
2
1
1
0
2
1
2
0
1
2
1
2
1
0
0
0
1
1
0
1
1
2
1
1
0
1
2
0
2
1
1
0
0
1
2
1
1
0
1
1
2
1
1
3
1
0
0
2
2
2
0
0
2
4
0
1
0
1
1
0
0
0
0
0
2
1
1
1
0
2
2
1
2
2
1
0
0
1
2
0
2
2
1
1
1
1
2
2
0
2
2
0
2
1
0
2
0
0
1
0
1
2
2
0
1
1
0
0
1
1
0
1
4
1
1
1
2
0
1
2
2
1
1
2
0
0
1
1
1
2
0
1
1
1
1
0
1
1
2
1
1
1
1
1
1
0
1
0
2
1
1
1
1
2
1
1
2
0
0
2
1
1
0
1
2
1
0
2
1
2
1
0
0
0
0
0
1
2
2
1
1
1
0
0
2
0
1
2
3
1
2
0
2
0
1
1
0
1
1
1
1
0
1
2
2
0
2
0
1
0
0
2
2
1
0
2
0
0
1
0
2
1
1
1
2
1
2
1
0
1
2
1
1
0
1
0
1
1
1
0
1
1
1
1
1
2
1
0
0
1
1
2
2
2
1
1
1
0
1
0
1
1
0
1
0
1
1
1
5
1
1
0
1
0
1
0
0
2
2
1
2
1
1
0
2
1
1
0
0
0
0
1
1
2
0
1
1
1
0
0
2
2
1
1
1
0
1
1
1
0
2
1
1
1
0
1
2
1
1
1
0
0
2
0
1
1
0
1
0
1
2
1
1
1
2
1
2
1
2
1
1
1
1
2
2
1
2
1
1
1
2
1
1
1
1
1
1
2
1
0
1
1
0
0
0
1
1
2
0
0
1
2
0
1
1
1
0
1
0
1
1
0
1
1
0
0
1
0
2
1
1
1
2
2
1
3
1
1
1
0
1
2
1
1
1
0
2
1
1
3
1
1
0
0
1
1
2
1
1
0
1
0
1
1
1
1
1
1
1
2
0
1
2
1
2
0
0
1
1
1
1
1
2
1
1
0
0
1
1
1
1
0
1
2
0
2
0
0
1
0
0
0
1
0
1
0
1
2
0
1
2
2
1
1
0
0
0
0
1
2
1
2
2
3
0
0
0
1
2
1
1
0
0
1
1
2
2
2
1
1
0
0
1
2
2
1
2
2
1
2
0
2
2
0
0
0
0
2
1
1
1
0
1
0
2
1
2
2
2
0
1
0
2
0
0
1
0
1
1
0
1
1
1
2
0
1
0
0
1
1
1
0
1
0
1
1
1
1
1
1
0
2
0
2
2
2
1
2
0
1
1
0
1
1
1
1
0
2
1
0
2
0
1
1
0
1
1
1
2
1
2
0
0
1
1
0
1
2
1
0
1
1
0
1
0
0
2
2
1
1
1
2
2
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
1
1
1
1
1
1
1
2
2
1
2
1
2
0
0
0
2
2
0
1
0
1
1
1
1
1
2
0
1
0
2
2
1
2
1
1
1
0
1
0
3
1
0
2
0
1
1
0
0
1
1
2
0
1
0
1
0
2
2
0
1
1
0
1
2
2
0
0
0
0
0
2
0
2
1
0
2
0
1
0
0
2
0
1
0
2
0
1
2
0
0
2
1
2
0
1
1
1
1
0
1
1
1
0
0
2
2
1
1
0
2
2
1
1
1
2
1
1
1
1
1
2
0
0
1
1
0
1
0
1
1
2
1
1
1
0
1
0
1
0
0
2
1
5
1
2
0
3
0
1
2
2
2
0
2
0
0
1
1
0
1
0
2
2
1
0
2
1
2
2
1
2
1
0
1
2
1
1
2
1
1
1
1
2
1
0
1
2
2
1
1
2
2
2
0
1
0
1
0
1
0
1
0
1
1
1
0
1
1
1
2
2
1
2
3
1
1
3
1
1
5
0
1
1
1
2
1
1
1
1
0
1
2
2
1
0
1
1
0
0
0
2
1
1
2
1
1
1
2
1
1
1
0
1
2
1
2
1
1
2
2
1
1
1
0
1
1
1
2
1
2
0
0
2
2
2
1
2
1
1
1
1
1
1
2
0
1
0
1
1
2
2
0
1
1
0
1
1
1
2
1
0
0
0
0
1
0
1
1
0
1
1
1
2
1
0
0
1
2
2
1
2
1
1
0
0
1
2
2
1
2
2
1
0
0
1
1
1
1
0
0
1
1
1
1
1
2
1
0
0
2
0
1
1
1
1
1
2
4
1
1
1
0
1
1
2
0
1
0
1
0
1
1
1
0
1
0
2
1
1
1
0
1
1
0
0
1
0
0
0
1
2
1
1
2
1
0
0
2
2
0
1
2
1
2
2
4
0
2
0
0
1
2
1
2
1
1
1
1
1
1
1
0
0
0
1
0
0
2
1
2
1
1
0
2
0
1
2
1
1
1
0
1
2
0
2
2
0
1
1
1
1
1
0
1
0
1
1
1
1
1
1
2
0
1
1
2
1
1
2
1
0
1
0
1
1
0
0
0
1
1
1
2
2
1
1
1
0
0
0
2
0
1
2
1
2
1
1
1
0
0
1
2
1
0
0
1
1
1
1
1
3
2
2
0
0
1
2
1
1
2
1
0
2
1
2
1
1
1
1
1
1
2
1
2
1
1
1
0
1
0
0
1
1
2
1
1
1
1
1
0
2
0
0
0
1
2
0
0
0
0
2
1
2
2
1
1
2
1
0
1
1
1
1
2
1
0
1
2
1
1
2
0
1
1
1
1
0
0
1
1
0
1
1
1
2
1
4
1
0
1
1
0
0
0
0
1
1
1
2
0
0
1
2
1
1
2
2
1
1
0
1
1
0
1
1
2
0
0
0
1
0
0
1
1
0
1
1
1
1
0
1
1
0
1
1
0
2
2
0
2
0
0
1
0
1
1
2
0
1
1
0
1
1
1
1
0
1
2
0
0
1
0
1
0
1
1
0
0
1
1
2
0
0
0
2
1
2
1
1
1
1
1
0
2
2
1
0
1
1
1
0
1
0
1
0
0
0
1
2
2
1
1
1
2
1
1
1
2
0
0
1
1
2
1
1
1
1
1
1
2
1
0
2
0
1
1
2
0
0
1
1
1
1
0
1
1
2
0
1
0
1
1
1
1
0
0
0
1
2
0
1
1
0
1
0
1
0
1
1
1
1
1
1
0
1
1
0
2
1
0
2
1
0
2
1
2
0
1
1
0
1
1
0
0
0
1
0
1
1
1
1
1
2
1
0
1
1
2
2
1
1
0
0
0
1
1
1
1
1
0
1
1
1
1
0
2
2
1
2
1
1
0
1
1
2
2
1
2
0
0
1
2
1
2
0
2
2
0
0
0
3
2
1
1
0
1
1
1
0
1
1
2
0
2
1
0
0
1
1
2
1
0
1
2
0
1
0
2
0
1
0
1
1
0
0
0
1
0
0
1
2
1
2
1
1
0
1
2
0
2
1
0
1
2
1
0
0
2
1
0
0
0
1
1
1
2
2
4
2
0
1
1
3
2
1
1
1
1
0
0
1
1
1
2
1
0
1
2
2
0
1
1
0
1
1
0
1
0
1
1
0
1
0
2
2
1
2
1
1
2
1
0
0
0
1
2
1
1
1
1
1
2
0
1
1
0
0
2
0
0
0
1
0
2
1
2
1
2
0
1
1
1
2
1
3
0
1
1
2
1
1
1
2
0
1
1
2
2
0
2
1
0
1
2
1
0
1
2
0
1
1
0
1
2
2
2
2
1
1
1
0
1
1
1
2
1
0
1
0
1
1
1
1
1
1
1
0
0
0
2
2
1
0
2
2
1
1
0
1
1
0
1
0
1
0
1
0
1
0
0
1
2
2
0
1
0
1
1
1
0
1
2
0
0
2
1
1
2
0
1
0
1
0
0
1
0
0
1
1
0
0
1
1
2
2
2
0
2
0
0
0
0
1
1
0
1
1
0
0
0
1
0
0
1
0
2
0
1
1
0
0
1
1
1
1
1
1
0
1
0
1
0
1
0
2
2
1
1
0
1
1
0
1
1
0
1
1
0
0
1
1
0
1
1
0
0
0
1
0
2
2
6
2
2
1
2
0
0
1
1
1
1
3
1
2
1
1
1
1
0
2
1
1
2
3
2
0
2
2
1
1
1
1
2
1
2
0
0
0
1
1
2
1
2
2
2
1
0
2
1
2
1
0
2
1
0
2
2
1
2
2
1
1
2
0
0
0
1
1
0
0
1
1
2
0
0
0
0
1
1
1
1
1
1
2
0
1
1
1
1
2
1
1
0
0
0
1
1
1
1
1
2
2
0
2
1
0
1
0
2
2
1
1
1
1
1
0
1
0
0
0
1
1
1
1
1
0
1
0
0
0
1
1
2
1
0
2
2
1
2
1
0
0
1
0
2
2
1
1
2
1
2
0
1
2
2
1
0
4
0
2
2
1
1
0
0
0
0
1
2
3
2
1
1
0
1
1
0
0
1
1
0
0
1
1
0
1
0
2
0
1
1
0
2
1
0
1
0
1
0
1
0
0
1
1
1
2
2
1
0
0
1
0
1
1
0
1
0
1
2
2
1
2
0
1
1
1
1
0
1
1
2
0
1
0
0
0
1
1
1
0
1
1
1
2
1
1
1
0
1
2
1
2
0
2
1
1
2
1
2
0
2
1
2
2
0
0
2
1
1
2
1
2
1
1
1
0
0
2
0
2
2
1
0
0
2
1
1
2
3
3
0
2
0
1
0
0
0
1
1
1
0
0
1
1
0
1
2
0
1
5
1
1
1
1
1
2
1
0
1
1
2
0
1
1
2
4
0
1
1
1
1
0
1
2
0
0
0
0
0
1
2
1
1
1
1
1
1
1
2
1
1
2
1
3
1
1
2
0
2
0
1
1
2
1
1
1
0
1
2
2
1
0
1
1
0
0
1
0
0
1
0
0
1
0
2
2
1
1
2
2
2
1
1
0
0
1
0
1
1
1
1
2
1
0
0
1
1
0
1
1
2
1
0
1
1
0
1
1
2
1
2
0
2
2
3
0
2
0
1
1
0
2
1
1
1
1
2
2
0
1
0
0
1
0
0
0
1
0
1
2
4
0
2
2
1
0
0
0
0
2
2
0
0
0
2
1
1
0
1
0
1
1
1
0
0
0
1
0
1
0
1
1
1
1
1
2
1
0
1
1
1
2
2
1
0
0
1
1
1
2
1
0
0
0
2
1
0
2
1
0
0
0
2
1
0
1
0
2
0
2
1
1
1
3
1
1
1
0
1
0
2
0
1
1
2
1
1
1
1
2
1
1
1
0
2
2
2
1
2
1
1
1
0
0
2
1
1
0
1
3
2
0
1
0
2
1
0
0
2
0
1
0
0
0
1
1
2
1
0
1
0
2
1
2
0
1
0
1
0
2
0
0
1
3
2
2
2
1
0
1
2
0
1
1
2
1
1
2
1
1
0
1
2
1
1
1
2
0
0
0
2
0
1
1
0
2
2
1
0
2
2
1
1
1
2
0
1
1
1
1
1
2
0
2
1
1
2
1
2
1
1
1
1
1
1
1
0
1
0
0
1
1
2
0
2
0
2
0
0
2
0
1
0
0
1
1
1
1
0
2
0
2
2
2
0
1
2
1
0
2
2
1
0
1
2
1
0
1
1
0
1
0
0
2
1
2
1
1
1
1
2
1
1
0
2
0
1
0
1
1
1
0
1
4
1
1
1
1
1
0
2
0
1
1
1
0
0
0
2
2
1
1
1
0
0
0
0
2
1
2
1
1
2
0
0
2
2
0
2
1
1
0
1
1
0
2
1
0
1
0
1
0
0
1
1
2
1
1
1
2
2
0
1
1
1
0
2
0
0
0
1
1
1
1
2
1
2
0
1
1
1
1
1
1
1
0
2
1
1
1
2
2
1
0
1
0
0
1
1
2
1
1
1
0
1
1
0
2
1
2
1
0
1
2
0
1
1
2
2
1
1
1
1
2
3
2
0
0
2
0
0
1
1
0
0
2
1
0
1
1
1
0
2
0
1
0
1
1
0
1
2
1
1
1
1
1
2
0
0
1
0
1
2
1
0
1
2
0
0
2
1
0
1
1
1
2
1
1
1
1
0
1
1
1
0
1
2
0
1
1
0
2
0
1
0
1
1
2
1
1
1
1
1
1
1
0
0
1
2
1
0
1
2
2
1
1
2
0
0
2
0
0
1
0
0
1
1
1
2
2
1
1
1
0
1
0
2
0
2
2
2
2
1
1
1
0
1
2
1
1
2
0
2
1
1
2
1
1
1
0
0
1
2
1
1
2
1
1
1
0
1
1
0
0
1
1
1
1
1
2
2
3
1
1
1
0
1
0
1
0
1
1
0
0
1
1
1
1
1
2
1
2
1
2
1
1
0
1
2
1
2
1
0
1
1
0
2
1
1
1
0
1
1
1
1
0
0
0
0
0
1
1
2
1
1
0
1
9
2
1
0
1
1
0
0
1
2
1
3
1
1
1
1
1
1
2
1
1
2
1
1
0
1
2
1
0
2
2
1
2
2
1
2
2
2
1
1
2
0
1
1
1
1
0
1
2
0
1
1
0
2
1
2
0
1
1
0
1
0
1
1
0
0
1
1
0
1
0
1
1
1
2
1
1
1
0
0
0
1
0
1
0
2
1
2
2
0
1
2
0
0
0
1
0
2
0
1
2
1
1
2
1
0
0
1
1
2
2
1
2
1
0
1
1
1
0
2
0
1
1
0
0
1
1
1
1
1
1
1
0
1
2
0
0
1
1
1
0
1
0
0
1
3
2
1
1
0
0
1
2
1
2
0
0
2
3
2
0
1
1
0
1
1
1
1
2
2
2
2
0
1
2
2
0
1
2
0
0
1
1
2
0
0
0
1
0
1
1
1
1
1
2
2
0
0
0
1
2
1
0
1
2
2
1
0
0
1
0
0
1
1
0
2
0
0
0
2
0
0
1
0
0
0
1
1
3
1
0
1
0
1
1
2
0
0
0
1
1
1
1
1
0
1
1
2
2
0
1
2
1
2
1
1
2
1
1
1
1
0
0
0
0
0
1
1
0
2
2
2
1
1
1
1
1
2
2
1
1
1
1
0
1
1
1
0
1
1
2
1
1
1
1
1
0
0
2
1
1
0
2
1
1
0
1
1
2
0
2
1
2
1
2
1
1
0
1
2
2
2
0
1
0
1
1
1
0
0
1
0
1
1
0
2
2
1
1
1
1
1
1
1
2
2
2
1
1
1
0
2
1
2
0
0
0
0
1
1
1
0
1
0
2
1
3
1
0
1
1
1
2
1
1
2
1
1
0
1
2
1
0
3
1
0
0
0
1
0
2
1
0
1
0
1
1
1
2
0
2
2
1
2
0
0
1
1
0
0
1
1
0
2
2
0
1
1
1
1
1
1
1
0
1
2
1
1
2
2
1
0
0
1
2
1
0
2
1
1
1
1
1
1
0
2
1
2
1
1
2
2
0
1
1
1
1
1
1
0
1
1
0
2
2
0
1
1
1
1
2
1
0
1
0
0
1
2
1
1
1
0
1
2
2
0
1
0
1
2
2
1
0
1
1
1
2
0
2
0
2
0
0
0
1
0
0
0
1
0
1
0
1
0
1
1
0
2
2
1
1
1
0
3
1
1
1
1
0
1
0
0
1
2
1
2
1
0
1
3
0
1
2
0
1
2
1
2
0
0
0
1
1
1
2
2
0
0
1
2
0
1
1
1
2
1
1
2
1
1
1
1
1
2
0
1
1
0
1
1
1
2
0
0
1
2
0
1
1
1
1
1
1
1
1
1
1
0
1
2
1
1
2
1
0
1
1
1
0
1
2
1
0
0
2
1
1
2
0
2
1
1
1
2
1
1
2
0
1
4
0
2
1
1
1
2
0
1
0
1
1
0
1
0
2
1
1
0
1
0
1
0
1
1
0
0
2
0
2
2
1
1
0
0
2
2
0
2
1
1
1
1
1
2
1
2
1
0
1
2
2
0
0
0
2
2
2
1
1
1
0
1
0
1
1
0
0
1
2
1
1
2
1
1
0
2
0
1
0
0
1
1
0
1
0
1
1
1
2
0
1
2
1
2
3
2
2
1
1
1
1
1
0
2
1
1
2
3
1
0
1
1
1
1
0
2
1
1
1
0
1
0
2
0
2
1
1
1
2
1
2
2
1
0
0
1
1
0
0
0
2
0
1
2
1
1
1
0
0
2
1
1
0
1
1
1
0
0
1
0
1
1
2
1
1
0
0
2
1
1
0
1
0
1
0
2
0
1
0
2
1
5
0
1
1
0
1
2
1
0
1
2
1
1
0
1
0
2
4
2
1
1
0
1
2
2
0
2
0
1
2
2
2
2
0
1
1
0
0
2
1
1
0
2
1
0
0
0
1
0
1
1
1
0
1
0
0
1
0
0
0
2
2
1
1
0
1
1
3
1
2
1
0
0
0
0
1
1
0
1
0
13
1
1
0
1
1
1
0
1
0
0
1
3
1
1
1
0
1
1
3
1
1
1
1
0
1
1
1
0
1
0
1
2
1
0
1
2
1
1
0
2
1
0
0
1
1
0
2
1
2
1
1
0
0
2
2
1
0
0
2
3
1
2
0
0
2
0
1
1
0
1
2
1
1
1
1
1
0
0
1
1
1
2
2
1
2
0
1
1
2
1
1
0
1
1
0
1
2
1
0
1
2
0
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
1
1
2
0
1
0
0
2
0
1
1
0
0
0
1
1
1
1
1
1
1
2
0
1
0
1
1
1
0
1
1
1
1
0
2
1
1
1
1
1
1
1
1
1
2
0
2
2
0
1
1
1
0
2
1
0
1
1
1
2
0
1
1
2
0
1
0
0
1
0
1
0
1
0
1
0
1
2
2
3
1
1
2
1
1
1
1
1
0
2
2
2
2
1
0
1
0
1
2
2
0
0
2
0
0
2
2
0
1
1
3
0
0
1
1
2
1
0
1
1
1
0
1
1
1
0
1
2
2
1
1
1
1
2
2
1
1
0
0
1
1
0
1
2
1
1
0
1
1
1
1
1
2
2
1
2
1
1
0
1
1
0
2
1
0
2
1
1
1
2
1
2
0
0
1
1
1
2
2
2
1
0
1
1
2
1
1
1
1
0
0
0
1
0
2
1
1
0
0
1
0
0
1
0
0
2
0
1
1
0
1
0
0
1
0
1
1
0
2
0
1
0
2
1
1
0
1
1
0
1
0
1
1
2
2
1
2
1
2
1
1
1
2
1
1
1
0
2
1
0
0
1
2
2
1
2
0
0
1
1
0
1
0
1
1
1
0
1
1
2
1
0
1
2
0
1
2
1
1
1
2
1
1
2
0
1
2
0
2
0
1
0
2
1
1
0
3
2
2
0
1
0
2
1
0
1
2
0
2
1
1
0
0
1
0
0
0
1
2
0
0
0
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
1
1
0
0
0
1
1
1
1
2
1
0
1
0
2
0
0
2
0
1
0
1
1
2
1
0
1
1
2
0
2
1
1
5
1
2
0
1
0
2
1
0
2
1
1
0
2
1
0
1
1
0
0
0
1
1
0
0
1
2
2
1
0
1
2
1
1
1
2
0
1
2
2
0
1
1
2
1
1
1
0
0
2
1
1
1
1
1
1
0
0
0
1
1
1
1
0
2
0
0
2
0
1
0
0
1
0
0
1
1
1
1
2
1
2
1
1
0
0
0
1
1
2
0
1
2
0
0
1
2
2
2
2
0
2
1
1
1
2
2
1
0
0
1
0
2
2
1
1
1
1
1
2
1
1
1
0
1
1
1
0
0
1
1
2
2
0
3
1
3
2
2
1
0
0
0
1
0
2
0
1
2
1
1
1
1
2
2
1
2
0
2
2
0
1
0
1
2
2
1
2
0
1
1
0
1
0
0
2
1
1
0
1
1
1
0
2
1
0
1
2
0
1
1
1
2
1
1
1
2
0
0
0
1
2
1
1
0
0
1
1
0
0
1
1
2
0
1
1
1
2
1
1
1
0
2
1
1
1
2
1
2
0
1
1
1
0
1
1
1
2
0
1
1
0
1
0
1
0
2
2
1
1
2
0
0
1
1
1
0
1
0
2
1
2
1
0
0
1
2
1
1
0
1
1
0
0
2
0
0
4
1
0
2
2
2
1
1
1
0
2
1
0
1
1
0
0
1
1
1
1
1
1
0
0
1
1
0
1
2
0
2
2
1
1
1
0
1
1
1
1
0
0
1
2
0
1
1
1
1
0
0
0
0
0
1
2
0
0
0
1
1
1
1
1
0
1
1
2
2
1
2
0
2
2
1
1
0
1
0
1
2
1
0
1
1
0
0
1
0
2
1
1
1
1
1
1
2
1
0
1
1
1
1
1
1
0
1
1
2
1
1
1
0
2
0
1
0
1
0
1
1
2
0
1
1
2
1
1
2
0
0
1
0
1
1
1
2
1
0
1
0
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
3
1
1
2
1
2
1
1
2
2
1
1
1
2
0
0
1
1
1
0
1
1
1
0
1
1
1
2
1
1
0
1
1
1
1
1
1
1
1
0
2
1
1
2
0
0
2
0
2
2
1
1
1
1
2
1
0
1
1
2
2
0
1
2
1
1
1
1
0
2
1
1
1
0
0
2
0
0
0
0
1
1
2
1
1
1
1
2
0
1
2
0
0
0
1
1
0
2
1
3
1
1
1
1
0
0
1
2
1
0
0
1
1
0
1
2
1
2
1
1
1
0
2
2
2
1
0
1
0
2
1
2
2
1
0
1
0
2
0
1
1
0
1
1
0
1
0
2
2
2
1
2
0
0
2
1
2
2
1
2
2
1
2
1
1
1
0
1
0
1
1
1
1
0
2
1
0
1
0
0
1
0
0
0
1
1
2
1
0
0
1
0
2
0
2
2
2
1
1
2
1
1
1
0
2
0
0
1
1
0
1
0
1
1
0
0
0
2
2
0
1
0
1
1
0
2
0
1
0
0
0
2
1
1
0
2
2
2
0
1
0
0
1
2
1
2
0
1
2
0
2
1
1
0
1
1
0
2
0
2
1
2
1
0
0
1
1
2
1
1
0
2
1
1
0
1
1
2
1
2
1
1
1
1
0
1
0
1
1
0
1
1
0
0
1
1
0
2
0
0
1
1
1
1
1
0
1
0
0
1
2
1
2
2
1
2
0
1
2
0
0
2
1
1
1
2
1
1
1
0
1
1
1
1
1
0
0
1
1
0
1
1
1
2
1
2
1
1
1
1
1
1
0
0
1
0
1
0
1
0
1
0
2
2
1
1
2
2
1
2
1
1
2
1
1
1
1
2
2
0
1
2
0
2
2
0
1
2
0
1
1
1
1
2
1
2
1
0
2
2
1
1
0
1
2
0
1
1
1
1
1
0
1
1
1
0
1
1
2
2
2
2
1
1
1
0
2
1
0
2
0
1
0
1
2
0
0
0
1
1
0
0
1
1
1
1
1
1
2
2
0
1
1
1
0
2
2
2
1
2
1
0
1
1
0
1
1
2
2
1
1
0
1
0
1
0
0
1
1
2
1
0
1
1
1
1
0
1
2
1
1
1
0
1
1
2
1
1
1
2
1
1
2
0
0
2
2
2
2
2
1
1
1
1
2
0
1
0
1
2
1
1
0
0
0
2
0
1
1
1
1
1
0
1
0
1
1
1
2
0
1
1
0
1
1
1
0
1
1
1
1
1
1
1
0
1
0
1
0
1
0
1
2
0
0
1
2
1
2
2
0
1
2
1
2
2
2
1
1
1
0
1
1
3
1
2
0
2
0
1
1
1
1
1
1
0
0
2
1
0
1
2
1
0
1
0
1
1
1
1
1
2
1
0
1
1
1
1
0
1
2
1
0
1
2
2
1
0
2
2
2
1
1
0
2
1
2
0
2
2
0
2
2
0
1
0
1
0
0
0
0
1
1
0
1
0
1
1
1
2
1
2
1
2
0
1
1
0
0
1
1
1
0
3
1
0
0
1
3
1
2
2
0
0
1
1
2
1
2
1
0
3
0
1
1
1
0
1
2
2
1
0
1
1
1
1
0
0
1
2
1
1
1
1
1
0
1
1
0
1
1
2
1
1
0
1
1
2
1
1
0
1
0
1
0
0
1
1
1
1
1
1
1
1
1
1
1
0
0
2
1
1
1
2
1
1
0
1
2
0
1
2
0
1
2
2
1
1
2
1
0
1
2
2
1
1
1
1
1
2
1
1
0
1
1
0
2
1
1
1
2
0
0
2
1
2
2
1
0
2
2
2
1
1
1
2
0
2
1
1
2
0
1
2
1
2
2
0
1
0
2
1
2
1
1
2
2
0
2
1
0
1
1
1
2
2
1
1
2
1
1
1
2
0
0
0
1
1
2
0
1
0
1
1
2
1
2
0
0
2
0
1
1
2
1
1
1
1
0
0
0
1
2
2
1
2
0
2
0
0
1
1
2
0
1
2
0
1
1
0
0
1
1
0
0
1
2
0
0
0
1
2
0
1
1
0
0
1
1
1
1
1
2
2
2
0
1
1
1
1
1
1
1
1
1
1
1
1
0
1
0
2
2
1
0
2
0
0
1
0
1
1
0
1
2
1
1
1
0
1
2
1
2
1
0
1
1
1
2
1
2
0
0
1
1
0
1
1
0
1
1
0
1
1
1
0
1
2
2
0
1
0
0
0
1
1
2
0
0
2
2
1
2
0
1
0
2
1
1
1
1
2
1
0
2
0
1
2
1
1
0
0
1
0
2
1
1
1
2
2
2
2
2
0
0
1
1
1
2
0
2
1
2
0
1
1
1
1
0
1
1
0
2
2
0
1
1
1
1
1
0
1
1
0
0
2
0
0
1
0
1
2
1
1
1
1
0
1
1
2
1
1
2
0
1
1
1
1
1
1
1
1
0
1
1
0
0
0
2
2
0
2
2
2
2
2
1
1
1
2
2
1
0
0
1
1
1
1
1
1
1
0
1
0
0
1
1
0
0
2
0
1
1
0
1
1
2
1
1
1
1
2
2
2
0
1
0
2
2
0
2
1
0
1
1
1
2
1
1
1
1
1
1
2
0
1
0
0
0
1
1
2
0
1
0
1
0
2
0
1
0
0
1
1
1
1
1
2
1
1
2
1
0
1
1
1
1
1
1
1
0
0
0
0
0
1
2
1
2
1
0
0
1
1
0
0
0
2
0
1
2
1
1
2
2
0
1
2
0
0
0
2
0
1
0
0
2
0
1
1
1
2
0
2
2
1
2
1
1
1
2
0
2
1
0
1
0
2
1
2
1
1
2
0
0
1
1
0
2
1
0
1
1
0
1
0
2
1
0
1
2
1
1
0
1
0
1
1
1
1
2
2
2
3
1
1
0
3
1
1
1
1
2
2
0
1
0
0
0
0
1
1
2
1
1
2
1
0
0
1
0
2
1
0
1
1
2
0
1
2
1
1
1
0
0
0
1
1
0
0
2
1
1
0
1
1
2
1
2
0
2
1
2
1
1
2
0
1
0
1
0
2
1
0
0
0
0
2
1
2
2
1
1
1
1
0
2
1
1
2
1
1
1
1
2
1
0
0
2
0
0
0
0
1
2
2
2
1
1
0
2
1
1
2
0
1
1
1
1
1
1
2
1
1
1
1
1
2
0
1
2
2
0
1
1
0
0
2
0
0
0
2
1
1
1
1
0
1
0
0
1
0
2
0
2
2
2
1
0
1
1
0
0
1
1
0
2
0
0
1
0
1
1
0
2
2
2
1
1
1
0
0
0
0
1
0
1
0
1
2
0
2
2
0
0
1
2
1
1
1
1
1
1
2
1
0
1
2
2
0
1
0
0
1
1
1
1
1
0
1
0
1
0
1
2
0
2
0
0
2
2
1
2
0
2
1
0
2
1
2
1
2
1
2
2
1
0
0
2
2
1
0
3
0
0
2
0
1
2
0
2
2
1
2
1
1
0
0
0
1
1
1
0
2
2
1
2
1
1
0
0
2
0
2
2
2
0
1
1
0
2
0
2
0
1
0
0
1
1
2
1
0
0
1
1
2
1
1
1
0
0
0
2
0
1
3
0
1
1
2
0
1
1
1
2
1
1
2
0
1
2
1
0
1
0
0
1
0
0
0
1
1
0
0
2
0
1
1
1
2
1
1
1
1
1
2
0
2
1
1
4
1
1
0
1
0
1
0
1
1
0
1
2
2
1
0
1
1
1
1
2
2
1
1
0
1
1
1
0
1
0
0
0
2
0
2
1
1
0
0
1
1
1
2
2
0
0
2
1
0
2
0
1
2
2
1
0
0
1
2
1
0
1
1
1
2
1
2
0
0
1
0
2
0
0
1
1
2
1
1
1
1
1
1
2
1
1
1
1
0
0
1
0
0
0
0
2
1
1
0
1
2
1
2
1
0
1
1
1
0
1
1
0
1
0
1
1
2
1
0
0
2
1
0
0
1
2
1
0
1
0
0
1
2
1
0
0
0
2
1
2
1
2
1
0
1
1
2
1
2
0
1
1
2
0
1
2
2
2
1
2
2
2
2
1
1
3
0
1
1
1
1
0
1
1
1
1
0
1
1
0
2
1
1
1
1
1
3
1
1
1
0
1
1
2
1
1
1
0
2
1
1
1
1
1
1
0
1
1
2
0
1
1
1
2
0
1
0
1
1
0
1
0
1
0
1
1
2
0
2
1
0
1
1
3
3
1
1
0
1
0
0
2
1
0
0
2
2
0
0
2
1
2
0
1
1
1
1
0
0
1
1
0
1
1
0
1
0
2
2
1
1
1
1
1
1
0
0
0
2
0
2
2
1
1
1
2
0
2
2
2
0
0
1
1
1
1
1
0
0
0
1
1
2
1
1
0
0
0
1
2
1
1
0
1
2
1
2
1
0
2
1
1
3
3
1
2
0
1
0
2
0
1
1
1
1
0
1
1
0
1
0
1
1
0
0
0
0
0
1
2
1
1
2
1
2
4
0
1
1
1
1
1
0
1
0
1
0
0
2
1
1
1
0
1
0
1
1
1
1
0
0
1
0
1
0
2
1
0
0
0
2
0
0
1
1
1
1
0
0
0
1
1
1
1
3
0
2
1
1
2
1
2
0
1
2
1
1
1
0
1
0
1
1
1
0
0
3
2
2
1
0
1
2
1
2
0
1
2
0
1
0
1
2
1
2
1
2
1
1
0
0
1
2
1
0
2
1
2
0
2
1
0
1
0
1
1
0
0
2
1
1
1
3
2
2
1
2
1
1
1
0
2
1
1
2
1
1
0
1
1
0
1
2
0
1
1
0
1
0
1
2
0
0
0
2
0
2
0
1
1
1
2
2
1
1
0
2
1
1
0
0
1
0
2
1
1
1
0
2
2
0
1
1
0
2
1
2
1
2
1
2
1
2
1
2
2
1
0
1
2
1
1
2
1
1
1
2
1
1
1
0
1
0
1
0
0
1
1
0
1
2
5
1
1
2
2
1
0
1
1
1
1
0
1
1
1
0
2
1
1
2
0
1
0
1
2
1
2
1
2
0
1
2
1
2
1
1
0
1
1
1
0
1
1
1
0
2
1
1
0
2
0
1
2
2
0
1
0
1
1
2
0
3
0
1
0
0
0
2
0
1
1
1
0
0
1
2
1
0
1
1
0
1
0
2
0
0
1
0
2
2
1
1
0
1
2
2
2
1
5
1
2
1
1
1
1
2
0
1
2
0
0
2
0
2
2
1
0
1
1
1
1
1
2
1
0
2
1
0
0
1
1
0
0
0
2
1
0
1
1
1
2
1
2
2
1
0
1
1
0
2
1
0
1
1
2
0
0
2
2
1
0
1
1
1
0
1
1
1
1
0
1
0
2
1
1
1
1
1
1
0
0
1
3
2
1
0
1
1
0
0
1
1
1
1
2
1
1
1
0
1
2
1
0
1
1
0
2
0
1
2
1
1
1
2
0
1
2
1
0
1
1
1
1
0
2
1
2
2
1
0
1
1
1
1
0
1
1
0
1
1
1
3
1
1
2
2
0
1
0
0
0
1
0
2
2
2
1
0
0
2
1
1
1
1
1
1
1
1
1
0
0
1
1
1
3
2
1
1
2
2
0
1
1
1
2
2
0
1
1
0
0
1
2
1
1
1
1
2
1
0
0
1
1
1
0
2
1
0
2
1
0
1
1
0
1
1
1
1
1
1
2
1
1
0
1
1
2
0
0
0
2
1
1
2
3
1
1
1
2
2
1
1
1
0
0
1
1
2
2
1
1
2
0
1
0
2
1
0
1
1
1
2
0
2
0
2
1
1
0
3
0
2
1
1
0
1
0
1
0
0
1
0
1
0
0
1
1
1
1
0
0
1
3
0
1
1
0
0
0
1
0
1
1
0
1
0
1
2
2
1
0
0
1
0
1
0
0
2
2
1
1
1
1
1
0
1
1
1
1
0
1
1
1
0
2
1
1
0
2
1
1
0
2
1
1
1
1
1
2
1
2
2
1
0
1
1
0
1
0
1
0
0
0
0
1
0
2
1
0
1
1
1
1
1
2
1
2
0
2
0
1
2
2
0
2
1
0
1
1
0
1
1
1
0
2
0
1
1
1
1
1
1
0
2
2
1
0
1
1
1
1
1
0
0
0
1
2
2
1
1
1
1
1
0
0
1
0
2
1
0
1
2
2
0
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
2
1
0
1
2
0
0
0
0
1
1
1
0
0
1
0
1
2
2
1
2
1
1
0
1
0
1
2
2
1
1
0
1
2
1
1
2
0
0
1
2
1
0
1
2
1
1
2
1
2
0
0
2
1
0
3
1
2
2
2
1
1
2
1
1
1
0
2
1
0
1
1
0
0
2
0
0
1
2
0
0
0
1
1
1
0
1
1
1
1
2
1
0
2
1
1
1
0
0
0
0
1
0
1
1
1
2
1
1
1
0
1
2
1
1
0
1
2
0
1
1
2
1
1
1
1
0
1
0
0
2
1
1
2
0
0
0
1
1
1
1
0
2
0
3
1
1
1
1
1
1
1
1
0
2
0
3
0
1
1
0
1
1
1
1
0
1
1
1
1
1
2
0
1
0
1
1
2
0
0
1
1
1
0
0
2
0
2
1
2
0
0
1
0
1
0
1
0
0
2
0
1
1
1
1
3
2
2
1
1
2
1
1
1
0
2
1
0
0
1
2
1
1
0
0
1
2
0
2
1
1
0
2
2
0
1
1
2
1
1
3
1
0
2
0
0
1
1
1
1
0
0
1
1
0
0
0
1
0
0
1
0
2
1
1
2
0
1
0
1
1
1
1
1
2
2
2
0
1
1
2
2
1
1
2
1
1
2
1
2
1
4
1
4
1
2
1
1
2
1
1
1
1
1
1
0
1
1
1
2
0
0
1
2
1
0
0
1
1
1
2
1
1
1
1
1
0
0
1
1
1
1
1
2
2
1
1
0
1
0
1
1
0
1
2
2
0
2
0
1
1
1
1
2
2
0
2
0
0
2
1
1
2
1
1
1
2
1
0
0
1
1
1
1
2
1
2
1
0
1
1
0
2
0
1
1
1
0
0
0
1
0
1
1
0
6
1
1
1
1
0
2
1
1
2
1
2
2
1
0
2
1
1
2
2
1
1
1
1
1
1
2
0
1
0
1
0
0
1
0
1
1
1
0
1
1
2
1
0
0
0
1
2
1
1
1
1
1
1
2
1
1
2
0
0
2
2
0
1
1
1
1
0
1
2
1
3
1
1
0
0
2
1
2
2
1
0
1
2
1
1
1
2
1
1
1
1
0
0
2
1
1
0
2
1
0
0
0
1
1
2
2
1
2
0
3
1
0
2
1
1
1
2
1
2
0
0
2
1
2
0
2
0
2
2
1
1
1
1
1
1
0
1
0
2
1
0
1
2
0
4
2
1
1
1
0
0
2
2
2
0
1
0
0
1
0
0
1
0
1
2
1
3
0
1
0
2
1
1
2
0
1
0
1
0
1
0
1
1
1
0
1
2
0
0
1
0
0
1
1
1
0
0
0
1
2
0
2
1
0
1
1
0
2
2
1
2
0
1
1
1
1
1
1
0
2
0
1
0
1
1
0
0
1
1
2
0
1
1
0
2
1
0
1
1
2
1
1
0
1
0
2
2
2
1
2
1
1
1
1
0
0
1
2
0
1
3
1
1
1
2
1
2
1
0
0
0
1
1
1
0
1
1
1
1
0
2
1
1
2
2
0
1
0
1
2
2
0
1
1
1
0
0
1
0
0
1
1
0
2
1
0
4
1
1
1
2
1
1
2
1
1
1
1
2
0
1
2
1
0
1
1
2
1
1
1
1
2
1
3
1
2
0
0
1
2
2
1
0
1
1
1
0
2
1
0
0
1
1
2
2
1
0
1
0
1
0
2
1
1
2
0
1
1
0
1
0
0
1
0
0
1
2
1
0
1
1
1
0
0
0
2
2
2
1
1
0
1
1
2
1
1
1
1
0
0
1
3
2
1
1
0
1
1
1
1
2
1
1
0
0
2
0
2
0
2
0
1
0
1
1
0
0
1
2
0
1
1
1
0
2
1
1
0
2
0
2
1
0
0
0
0
2
0
1
1
1
1
1
2
0
0
0
1
1
1
0
1
2
0
1
0
2
1
1
1
2
1
1
0
0
1
2
0
1
2
0
1
1
2
1
0
2
2
1
2
1
1
1
2
2
0
1
1
1
1
1
2
1
3
1
0
2
0
1
1
2
0
0
0
0
1
0
1
1
2
0
1
1
0
1
1
0
1
1
1
1
1
0
0
2
1
2
1
1
1
0
1
0
1
1
0
1
2
2
1
1
2
2
0
0
1
0
1
2
1
1
0
0
1
0
1
1
2
2
2
1
1
1
0
2
1
0
1
1
1
1
1
1
1
0
1
1
1
0
0
0
2
1
2
2
2
0
1
0
2
0
0
0
2
2
0
1
2
0
1
2
0
0
0
0
0
1
1
1
2
2
2
0
0
2
1
0
1
0
0
1
1
3
1
1
1
0
0
1
2
1
2
1
2
0
0
1
1
2
2
1
1
2
1
2
1
1
1
1
1
1
0
1
1
0
1
0
1
1
1
2
1
1
1
1
1
2
0
1
1
1
2
1
0
2
0
0
1
1
2
0
1
1
1
1
2
1
1
1
1
2
1
2
1
0
0
1
1
1
1
2
0
0
0
1
2
1
1
1
0
0
2
2
0
0
1
1
1
1
1
1
1
2
1
0
0
0
0
0
2
2
2
0
1
2
0
0
0
0
2
1
2
3
0
0
0
1
5
0
1
2
0
2
2
2
0
0
1
0
0
1
1
0
2
3
1
0
1
0
0
0
1
1
1
1
1
0
0
1
0
2
1
1
1
0
2
1
1
1
1
1
0
2
2
0
1
1
0
1
1
0
0
1
0
2
2
1
1
1
1
2
0
0
2
1
0
1
1
0
1
0
1
0
1
0
1
1
1
1
1
1
0
1
1
1
1
2
0
0
0
1
2
2
0
1
0
2
1
1
1
1
1
1
1
0
2
1
0
1
0
1
2
0
1
0
1
1
1
2
1
0
1
2
0
1
1
0
0
2
1
0
0
1
1
2
2
2
0
2
1
1
2
1
0
0
2
0
1
0
1
0
1
1
0
0
0
1
1
1
0
1
1
0
1
1
0
1
2
1
0
0
0
0
0
0
1
0
1
2
1
0
1
1
1
0
3
1
1
1
0
0
2
0
1
2
2
2
0
0
0
0
2
1
0
1
1
0
0
1
3
2
1
0
0
0
1
1
1
1
0
1
1
0
1
1
2
1
2
2
1
2
1
0
2
0
2
2
1
2
1
0
1
2
0
2
0
1
2
0
2
1
1
0
1
1
2
1
0
0
1
2
0
1
1
0
1
0
2
1
2
0
1
1
0
1
2
1
1
2
1
0
2
0
1
0
0
2
0
0
1
2
0
4
0
2
1
1
3
0
1
1
2
2
1
1
1
2
1
1
0
1
2
1
1
0
2
0
1
2
1
0
0
1
2
1
1
1
1
1
1
0
2
2
0
1
1
2
1
1
1
0
1
1
1
1
1
2
0
0
0
0
2
0
1
1
1
2
1
0
0
0
1
2
1
1
0
12
0
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
0
1
2
0
0
0
1
2
1
1
1
1
1
1
1
0
1
1
1
0
1
2
1
1
1
1
2
0
1
0
1
1
0
0
1
2
1
1
0
0
1
0
1
0
0
2
1
2
1
1
2
2
1
0
2
0
1
1
1
1
2
1
1
0
0
1
2
1
0
1
1
1
0
0
0
1
1
1
2
1
1
1
1
1
1
1
1
0
0
2
1
1
0
2
1
0
1
0
2
2
1
1
0
1
1
1
2
1
2
0
1
1
2
1
0
1
1
1
2
0
1
2
2
1
1
1
1
1
2
1
0
1
1
1
2
0
2
0
2
1
0
2
1
1
0
0
0
0
0
1
1
1
2
1
1
1
2
2
0
2
0
5
0
0
0
0
2
1
1
2
0
2
1
1
2
1
1
0
2
0
0
0
1
1
0
2
1
1
1
1
2
2
1
0
0
0
1
1
2
2
0
0
1
1
1
0
1
2
1
0
0
3
2
0
1
1
1
0
1
2
0
0
0
0
1
2
0
1
0
1
0
1
1
1
1
0
1
3
2
1
1
2
1
2
0
2
0
1
1
0
1
2
0
0
1
1
1
1
2
0
1
0
1
1
1
1
0
2
0
2
0
2
1
1
2
0
1
1
1
1
1
1
1
2
2
2
0
1
0
1
2
1
1
1
0
1
1
2
2
1
0
1
0
1
1
0
1
0
2
2
1
2
1
1
2
2
2
2
2
1
0
2
0
0
0
1
1
2
0
0
1
2
0
1
0
0
1
1
2
1
2
2
2
1
0
2
1
1
2
1
1
2
0
1
1
1
1
1
0
0
2
2
1
0
0
1
2
0
0
1
1
2
1
1
0
1
1
1
2
1
1
0
1
1
2
2
1
0
1
0
1
0
2
0
0
1
0
2
1
1
2
0
1
9
0
0
0
2
1
1
1
0
1
1
0
2
1
0
0
1
2
0
1
2
0
2
1
0
0
3
2
1
0
2
2
1
0
1
0
2
2
1
2
1
1
2
1
2
0
1
2
2
2
0
0
0
1
1
1
2
2
0
0
1
0
0
0
0
1
1
2
0
1
2
1
2
0
2
1
1
2
0
0
1
2
2
1
1
1
0
2
0
1
2
1
0
1
1
0
1
1
2
2
2
1
1
1
2
1
1
1
0
0
0
0
1
0
2
0
1
2
1
1
1
0
1
1
1
1
1
0
1
0
2
2
2
1
1
0
1
1
3
0
1
1
1
1
1
0
0
0
1
1
2
1
1
0
1
1
2
2
0
1
2
1
0
0
2
1
0
1
1
1
1
1
1
0
1
1
3
2
1
0
1
0
0
1
2
1
0
1
0
1
0
2
0
1
1
2
2
0
2
0
2
0
1
1
1
0
1
2
1
0
0
0
2
0
2
2
2
1
1
2
1
0
0
1
2
1
2
1
1
1
0
0
1
1
0
2
0
1
0
1
1
1
1
0
0
1
1
0
0
1
1
1
2
0
1
1
1
1
1
1
1
1
1
1
0
2
2
1
1
2
0
1
1
1
1
2
1
2
1
1
2
0
2
0
0
2
1
2
1
1
1
1
1
0
2
1
1
1
0
2
1
0
1
1
1
2
2
1
1
2
1
0
0
1
1
0
0
0
0
1
1
2
0
0
1
1
2
0
1
3
2
0
1
0
0
3
1
0
1
1
1
2
0
1
1
1
1
0
2
1
1
0
1
1
1
2
1
1
1
1
1
2
1
0
2
0
2
1
2
2
1
1
1
2
2
0
1
1
1
1
0
0
0
1
2
0
1
0
1
0
2
1
2
1
2
1
1
1
1
1
2
2
1
2
1
1
2
0
1
2
2
1
0
0
1
1
0
1
0
1
1
0
2
0
1
1
1
1
0
1
0
1
2
0
0
2
0
2
1
0
1
0
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
2
1
1
2
1
1
2
1
1
2
1
1
0
0
2
0
0
0
1
2
2
2
1
2
2
1
2
2
1
0
0
0
1
0
1
1
2
1
1
0
2
1
1
1
1
2
0
0
2
1
0
1
2
1
0
0
2
0
2
0
2
2
1
1
0
0
1
2
1
1
0
1
0
1
1
1
1
2
0
1
2
2
0
1
0
1
1
1
1
0
0
2
1
0
1
1
1
0
1
1
1
2
2
2
1
1
0
1
1
0
1
1
2
1
1
1
2
1
2
1
1
0
0
2
1
1
0
1
1
1
2
1
0
4
1
2
3
1
1
1
1
0
2
2
1
1
2
0
1
1
2
2
1
1
2
1
0
2
0
0
1
0
1
1
0
0
2
1
2
1
2
1
2
0
0
1
1
1
1
1
0
1
0
0
1
0
1
0
0
2
1
1
1
1
1
1
0
0
0
1
1
2
1
5
2
1
2
0
1
1
1
0
1
1
0
2
2
1
1
1
0
1
2
2
2
0
0
2
0
1
1
1
1
1
1
1
1
1
1
0
2
0
1
2
1
2
0
0
0
0
3
0
1
0
1
0
2
1
2
1
1
1
1
0
2
0
0
1
2
2
2
2
0
1
0
0
0
0
1
1
0
0
1
0
0
1
0
1
1
0
1
0
2
1
1
1
0
0
0
1
0
1
1
0
0
0
1
1
1
0
1
1
2
0
1
2
1
1
1
2
0
2
1
1
2
1
3
0
1
1
0
1
1
0
1
1
1
1
0
2
1
0
1
1
2
0
1
1
1
0
1
2
2
1
1
2
1
0
0
0
0
2
0
1
1
1
2
0
0
0
2
0
0
1
1
0
2
0
1
0
0
2
2
0
1
0
2
0
1
2
0
0
1
2
1
1
1
2
0
1
1
1
0
2
1
0
0
1
2
1
2
1
1
1
0
0
0
0
1
1
0
1
1
0
1
1
2
1
1
0
0
2
1
0
2
1
1
0
0
0
1
1
2
1
0
2
0
1
1
1
2
1
1
0
2
1
0
1
0
1
1
2
0
1
0
0
0
1
1
2
1
0
1
2
2
0
0
0
1
2
1
1
1
0
0
1
1
2
1
1
0
1
1
1
1
2
1
2
0
1
1
0
1
2
0
0
2
2
2
0
1
0
1
1
1
2
2
0
1
1
1
1
2
2
2
0
0
0
1
2
2
1
1
1
1
2
1
1
2
0
0
0
0
1
0
1
2
1
0
0
1
1
2
0
2
1
1
0
1
0
3
1
0
0
1
1
0
0
0
0
1
0
1
0
2
0
1
0
2
1
3
1
3
1
1
1
1
2
1
1
1
0
0
2
2
1
1
1
1
1
1
0
1
2
1
0
1
0
1
1
0
1
0
2
1
1
1
0
2
0
0
1
1
1
2
2
2
1
0
0
1
1
0
0
0
1
1
1
0
3
1
1
0
2
1
0
0
1
2
1
1
1
0
0
0
1
1
0
1
2
1
0
1
0
1
1
1
0
0
0
1
1
2
2
1
0
1
1
2
2
1
1
1
1
1
1
0
0
0
1
0
1
1
2
1
1
1
1
2
0
1
0
1
0
1
1
1
0
1
0
1
2
0
1
1
1
2
1
1
2
3
1
1
0
2
1
1
1
0
2
2
1
2
1
1
2
0
1
1
1
2
2
1
1
1
0
2
3
1
1
0
0
1
2
0
1
0
1
0
1
1
1
2
1
0
0
0
1
2
2
1
0
0
1
1
0
0
0
1
1
1
1
1
1
1
1
2
0
0
1
1
0
1
1
1
0
1
1
0
1
1
2
1
1
0
0
1
1
0
0
0
0
1
2
2
1
1
1
2
1
0
1
1
1
1
0
2
2
1
2
1
1
0
0
1
1
0
0
1
2
1
2
2
0
0
1
0
2
2
2
1
1
2
0
2
0
2
0
1
1
1
1
0
1
0
2
0
1
1
1
1
2
0
0
1
0
1
1
0
2
1
2
1
1
1
1
1
1
1
1
1
0
1
1
3
2
1
2
1
1
2
1
1
1
0
2
2
1
0
1
0
2
2
2
2
0
1
0
1
1
0
1
1
0
1
0
0
0
2
1
1
0
1
0
0
0
1
1
1
1
1
0
1
1
1
0
2
1
1
0
0
1
2
1
0
2
1
1
1
1
0
1
2
0
1
1
1
1
2
0
1
1
1
1
1
1
0
0
1
1
0
1
0
1
2
0
2
2
2
0
0
2
0
1
1
1
0
0
0
1
2
4
1
2
0
2
2
2
1
1
1
2
1
1
1
1
0
0
1
2
1
1
0
0
1
0
1
1
2
0
0
0
0
2
0
1
2
0
2
1
1
1
2
1
2
1
1
2
1
5
1
0
2
1
1
1
2
2
1
0
2
2
1
1
0
1
1
1
0
1
2
2
1
1
1
0
2
1
2
0
2
0
0
0
1
1
1
0
1
1
1
1
1
0
0
1
1
1
1
1
0
1
1
1
1
0
1
2
1
1
0
1
0
0
1
1
2
0
1
1
0
1
1
1
2
0
2
1
1
1
0
1
1
0
0
1
1
2
1
0
1
1
0
2
2
2
0
1
0
2
2
1
2
2
2
1
1
1
1
2
2
1
2
0
2
0
1
1
2
1
2
2
2
1
1
1
1
1
1
1
2
0
1
1
1
2
1
1
1
1
1
1
1
0
2
0
0
1
1
1
0
0
1
1
1
0
1
0
1
1
2
2
1
0
0
2
0
1
0
0
1
1
1
2
1
0
1
1
1
1
1
2
0
1
2
1
0
2
0
0
2
2
1
1
1
1
2
1
1
0
4
0
1
2
1
0
3
1
2
1
0
1
1
2
1
1
1
1
0
0
0
1
1
0
1
0
2
1
2
0
1
1
2
0
0
1
1
1
0
1
1
1
1
0
1
1
0
2
1
1
2
2
0
0
1
2
1
0
1
0
2
1
1
1
1
1
0
1
0
1
1
1
1
2
1
2
1
1
1
1
1
1
2
1
2
1
0
1
1
0
1
1
1
1
1
0
1
2
0
0
1
0
2
0
2
0
0
2
1
0
1
1
1
1
2
1
1
0
1
0
1
1
1
1
1
0
1
1
0
1
1
1
2
0
2
1
1
1
1
1
1
2
1
1
0
1
0
1
0
1
1
0
0
1
1
1
1
1
2
2
0
2
0
3
0
2
3
1
1
1
0
1
1
1
0
0
0
0
0
0
1
1
1
2
1
1
1
1
0
1
0
2
2
2
1
2
1
1
2
0
1
3
0
1
0
1
1
0
2
0
2
1
1
0
2
1
1
1
1
1
1
0
2
2
1
0
0
1
2
0
1
3
0
1
2
1
2
2
1
1
1
0
1
2
1
1
1
0
2
1
3
0
2
0
0
2
0
0
1
0
1
1
3
2
0
1
3
1
1
1
1
1
1
0
0
1
2
1
0
1
0
0
2
0
1
1
1
2
1
1
1
1
0
0
2
0
0
2
3
1
1
0
1
0
2
1
0
1
1
1
1
1
1
2
1
0
1
0
0
0
1
2
0
0
1
2
0
0
2
1
0
0
2
1
3
1
1
1
1
0
1
2
2
1
1
1
2
1
1
0
2
2
2
0
1
0
2
2
1
1
1
1
1
2
1
1
0
0
2
1
0
0
0
1
1
2
1
2
2
2
0
0
1
1
1
1
1
2
1
0
1
2
0
1
1
1
1
1
1
0
2
1
2
0
1
1
1
0
1
1
1
1
0
1
0
1
0
0
1
0
0
1
1
2
1
1
0
2
2
0
0
1
1
1
1
2
1
1
0
2
1
2
0
2
0
1
0
0
1
0
0
0
0
1
1
1
0
2
0
1
0
2
0
1
1
1
0
1
0
0
1
2
1
2
0
1
0
0
1
2
2
1
1
2
0
1
2
0
2
3
1
0
1
1
0
2
2
1
1
1
0
1
1
1
1
3
0
0
0
1
0
1
1
0
1
1
2
0
1
1
1
2
1
1
1
1
2
1
1
1
2
1
2
1
3
1
5
0
2
1
1
1
0
1
1
1
1
1
1
0
0
1
1
1
0
0
1
2
2
1
1
0
2
0
0
1
1
1
1
2
1
1
1
1
0
0
0
1
0
1
1
1
0
0
1
1
0
2
1
2
1
1
2
1
1
1
2
2
0
2
1
0
2
1
2
0
0
2
2
2
1
1
2
2
1
1
1
1
2
1
2
1
1
2
0
1
0
1
2
1
0
0
1
1
1
0
1
0
0
1
0
1
2
2
1
1
0
1
0
1
0
1
1
2
1
1
1
2
1
2
1
1
2
2
2
1
0
2
1
2
1
1
1
0
1
0
2
1
1
1
1
2
0
0
1
0
1
1
2
0
1
1
2
0
2
4
2
1
2
0
2
1
1
0
1
0
1
1
0
1
1
1
2
2
1
5
2
1
0
2
0
0
0
0
1
2
1
1
3
1
1
1
0
0
1
1
1
1
1
0
2
3
2
0
1
1
1
0
2
2
1
1
2
1
0
1
2
1
1
2
0
2
0
0
0
1
1
1
0
0
0
1
1
2
1
1
0
2
1
2
1
1
2
1
0
1
2
1
1
2
1
0
2
1
1
0
0
1
1
1
0
1
1
1
1
2
1
2
0
2
0
1
1
1
1
2
1
0
1
1
1
1
1
1
1
2
0
1
1
1
1
0
0
0
1
0
2
0
0
0
1
2
1
0
0
2
2
1
1
0
2
0
1
1
0
1
2
1
1
2
1
1
2
1
0
1
1
2
1
1
2
1
1
1
1
1
0
1
0
1
1
1
0
0
0
1
1
1
0
0
1
1
2
0
1
1
1
2
1
1
2
1
0
1
1
1
0
0
1
0
2
1
0
1
1
2
1
0
0
1
0
2
1
1
1
1
0
0
2
1
0
0
0
2
1
1
2
0
1
1
1
2
1
0
1
1
1
1
0
0
1
1
1
2
2
0
0
1
0
2
1
1
2
1
0
2
0
0
0
0
2
0
1
1
2
1
1
1
1
0
1
1
1
1
2
1
0
1
4
1
2
0
1
2
0
0
1
2
0
2
0
1
1
1
1
0
2
3
1
1
2
1
1
2
1
1
1
0
0
3
3
2
0
0
1
0
0
0
1
2
0
1
0
1
1
2
0
0
0
1
1
0
1
1
0
1
1
1
1
2
1
1
1
2
0
0
1
1
1
1
2
1
1
0
0
1
1
0
1
2
1
2
2
1
1
0
2
2
1
1
1
1
2
2
1
1
1
2
0
0
1
0
2
2
0
2
0
2
2
0
0
0
2
1
0
1
0
1
1
0
0
1
0
1
0
2
1
0
1
1
1
1
1
1
1
1
1
1
2
0
0
1
2
0
0
0
0
1
1
1
2
0
1
1
2
1
2
0
2
1
1
4
1
1
1
1
1
0
1
1
1
1
2
1
2
0
2
1
2
0
1
0
3
0
1
1
1
2
1
1
2
1
1
2
1
1
0
1
0
0
2
1
1
2
2
0
1
3
2
0
1
0
1
0
1
1
0
0
3
0
2
0
0
1
1
0
0
2
0
1
2
1
1
2
0
1
0
0
0
1
1
1
1
2
1
0
0
1
0
1
1
1
0
1
0
0
1
2
1
0
1
0
1
0
0
2
1
0
0
0
0
0
0
0
0
2
1
0
0
1
2
1
1
1
2
1
2
2
1
2
1
2
0
0
1
0
1
2
0
1
0
1
1
1
1
1
1
0
1
1
0
2
1
1
2
1
1
0
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
0
0
2
1
2
1
1
1
0
1
0
0
0
0
1
0
2
0
1
1
2
1
0
2
3
0
0
1
1
0
1
1
1
1
1
2
0
1
1
2
1
0
0
2
1
1
0
1
0
1
1
2
2
2
0
0
2
2
1
1
2
1
2
2
0
0
1
1
1
0
1
2
1
2
1
3
0
0
1
0
1
1
1
2
1
2
0
2
1
0
0
1
1
2
1
0
1
0
2
0
0
0
1
1
1
1
1
1
1
1
0
1
1
1
1
1
0
4
1
1
1
1
0
1
1
1
2
1
1
2
1
1
1
1
0
0
1
0
0
0
1
2
0
1
0
0
0
0
0
2
1
0
0
1
2
1
1
1
1
2
0
1
2
2
1
2
1
2
1
0
1
1
0
1
1
0
1
0
1
1
0
1
0
1
1
2
1
1
0
2
0
0
1
1
1
0
1
1
2
0
2
1
2
0
2
1
1
0
0
1
1
2
2
2
2
2
1
0
1
2
0
0
1
0
2
1
1
2
0
0
1
2
1
2
1
1
1
0
2
1
0
1
1
0
0
1
1
1
1
2
0
1
1
2
0
1
1
0
1
1
1
1
1
1
0
1
1
2
1
1
2
0
0
0
0
1
0
0
2
0
1
0
1
2
2
1
1
0
1
0
2
2
0
2
1
1
0
0
2
0
2
1
1
1
1
2
0
0
0
1
2
1
1
2
0
1
2
1
1
1
0
2
1
1
0
2
2
1
1
1
1
1
1
1
2
1
1
2
1
0
0
0
1
0
1
1
1
1
0
1
1
2
1
1
0
0
0
1
0
0
0
0
1
1
2
1
0
0
2
0
2
1
1
2
2
1
1
0
1
2
0
1
0
1
0
1
1
0
2
2
0
1
1
1
2
1
1
0
2
1
2
1
1
1
1
1
0
0
1
1
1
0
1
0
1
0
1
1
1
1
1
1
1
1
1
2
0
1
0
0
2
0
2
0
1
1
0
1
1
2
0
2
0
1
1
1
2
2
2
1
0
0
1
1
0
2
0
1
1
6
1
1
1
1
0
1
0
1
1
1
1
2
0
1
1
1
1
1
0
1
1
1
1
1
0
1
1
0
2
0
0
0
0
2
0
2
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
3
1
1
1
2
1
1
0
1
0
2
1
0
0
1
1
0
2
1
1
1
1
1
1
0
1
0
1
1
1
1
1
1
1
1
0
1
1
3
2
0
2
0
2
2
0
1
0
1
0
1
0
2
0
1
1
2
2
2
1
1
2
1
0
1
0
2
1
0
1
0
1
2
1
1
1
1
1
0
2
2
2
1
1
1
1
0
1
1
1
2
1
0
2
0
0
1
2
1
1
1
1
1
0
1
2
1
0
2
1
0
1
2
0
1
1
0
1
1
1
1
0
2
2
2
0
1
1
2
1
0
0
2
1
1
1
1
0
3
1
1
0
0
1
0
0
1
1
0
1
1
1
2
1
2
0
2
0
3
2
1
1
1
2
1
1
1
5
1
1
0
1
0
0
1
1
1
0
2
1
1
1
1
1
1
0
1
0
1
2
1
2
1
1
1
0
1
1
1
2
2
1
0
1
0
1
2
2
1
0
1
1
1
1
2
2
1
1
2
1
0
2
1
1
1
0
1
0
1
1
1
2
1
0
1
2
3
1
0
0
1
0
1
1
1
2
0
1
1
0
1
0
0
1
1
1
1
0
0
0
1
1
0
0
0
1
1
1
1
2
1
1
1
1
1
3
1
1
1
0
2
1
1
1
1
0
1
0
0
2
1
2
1
1
0
2
1
2
1
1
1
1
0
1
1
2
0
0
1
0
1
1
1
0
2
1
0
1
1
1
1
1
1
2
1
3
0
1
2
1
1
0
1
0
0
0
1
1
1
2
1
0
1
2
1
0
1
3
1
0
1
1
1
2
1
2
1
2
1
1
2
1
1
3
0
2
1
2
0
1
0
0
1
0
0
1
1
1
1
1
1
0
0
2
0
2
1
0
1
0
1
1
1
0
1
1
1
0
3
0
0
1
1
3
2
1
2
1
1
1
1
0
1
1
1
0
2
1
0
2
1
2
1
1
1
1
0
2
0
1
2
0
1
1
1
1
0
1
2
2
1
1
1
2
1
1
1
1
0
0
1
2
0
1
2
2
1
0
2
3
2
0
0
0
3
1
0
0
1
1
1
2
0
1
1
1
2
1
1
1
0
1
2
2
0
1
1
0
0
0
4
0
1
1
0
1
1
2
0
0
1
1
1
1
1
2
0
1
1
1
1
1
1
1
2
0
1
1
0
1
1
2
2
0
2
1
1
1
0
0
2
2
1
2
1
1
2
1
0
0
0
2
0
1
0
1
1
1
1
2
1
1
2
2
0
1
2
1
1
1
2
1
0
0
1
2
1
2
1
0
1
1
0
0
1
1
2
2
1
2
1
1
1
1
2
1
1
1
1
1
2
2
2
2
1
2
2
1
0
1
0
1
0
3
0
1
2
0
1
1
0
1
1
1
0
1
0
1
0
1
1
1
1
0
2
1
0
2
1
0
0
1
0
0
1
1
0
1
0
1
1
2
1
2
1
1
2
2
0
0
0
2
1
0
0
0
0
1
0
2
1
0
1
1
0
0
0
1
2
2
1
2
1
1
0
1
0
0
1
2
0
1
0
1
2
0
0
1
3
0
0
0
2
1
2
1
0
1
2
1
2
1
0
1
0
2
2
1
1
1
1
1
1
1
0
0
2
1
2
2
0
2
2
3
1
1
0
1
0
0
1
0
1
0
1
1
0
1
0
1
0
1
1
1
0
0
1
2
3
1
1
0
0
1
2
0
1
1
1
1
0
2
1
0
2
0
0
1
1
0
0
1
1
1
0
0
0
2
0
2
1
1
2
1
0
1
1
2
0
0
1
1
1
0
0
1
1
2
1
1
2
2
1
1
1
2
0
0
0
1
1
2
0
0
1
0
0
2
2
1
1
2
0
0
1
1
0
0
1
1
1
2
0
0
0
1
1
2
0
2
2
0
2
1
0
0
0
1
0
2
1
1
2
0
1
1
0
1
1
2
2
0
0
2
2
1
0
2
0
0
0
1
1
1
1
2
2
1
2
0
1
0
1
1
0
0
2
2
1
1
2
1
0
2
1
1
2
0
1
1
1
1
1
2
0
0
1
2
0
3
0
1
1
1
2
1
1
1
0
1
0
1
1
1
2
0
1
0
0
1
1
0
2
2
1
0
0
2
1
0
1
2
0
2
0
1
1
1
1
1
1
0
0
2
0
1
2
0
1
1
1
0
0
2
2
0
1
0
0
0
3
1
2
2
1
2
2
1
0
2
1
0
1
1
2
1
3
2
2
1
1
1
1
1
1
2
2
0
0
0
2
1
0
0
1
2
1
0
1
0
0
2
1
2
2
1
0
2
0
0
2
0
2
2
1
3
0
1
1
0
1
0
0
2
0
1
2
1
1
0
0
1
1
1
0
1
1
0
1
1
2
0
1
0
3
0
2
0
0
1
1
2
1
2
1
1
0
1
2
2
0
2
1
1
0
1
2
0
2
1
1
0
0
1
1
1
1
1
1
2
1
1
1
0
1
2
0
1
1
2
1
2
1
1
1
1
1
1
1
3
0
2
2
1
1
1
1
0
1
1
1
1
1
0
0
1
1
1
2
2
2
2
0
1
2
3
0
1
2
1
2
1
0
1
0
0
2
0
1
2
0
0
2
2
0
1
0
0
0
1
0
1
0
0
1
1
0
0
2
2
0
0
1
0
1
0
0
1
0
0
2
0
2
2
0
0
1
1
1
2
1
1
2
0
1
2
1
2
0
2
2
0
3
0
2
3
0
1
0
0
0
1
1
1
2
0
0
0
1
2
1
1
1
1
0
0
1
2
1
2
1
1
2
0
1
0
0
1
2
2
1
1
2
1
2
2
0
1
3
1
1
1
1
1
0
2
0
0
2
0
1
1
1
2
1
0
2
1
0
0
2
0
1
0
1
2
1
2
2
1
1
2
1
1
1
0
1
1
0
0
1
2
2
1
1
2
1
2
0
1
3
1
2
0
2
3
0
1
1
2
0
1
2
2
2
1
2
1
1
1
2
1
2
1
1
0
2
2
1
0
0
1
1
0
2
1
0
1
0
0
2
0
1
1
1
2
0
2
1
0
1
2
0
0
0
1
1
1
1
1
1
1
0
1
1
1
1
0
1
2
0
1
0
2
2
2
1
1
1
1
1
1
2
1
1
2
0
1
0
1
2
1
1
0
0
1
1
0
1
0
0
2
0
1
1
1
1
0
0
1
2
1
0
1
2
1
0
1
1
1
1
0
0
0
1
1
0
1
2
0
0
1
1
2
0
1
2
1
1
2
1
1
1
2
0
0
0
0
1
0
1
0
0
0
0
1
1
1
1
1
0
1
2
1
1
2
2
2
0
0
2
2
0
0
0
1
2
0
1
0
0
1
1
1
0
2
0
2
1
1
1
1
1
0
2
2
2
2
0
3
1
2
0
1
0
0
1
1
1
1
1
0
2
1
2
1
2
1
2
1
1
2
1
1
0
2
1
1
2
1
4
0
1
2
1
2
0
0
1
1
1
1
1
0
3
2
0
2
2
0
2
0
0
1
1
1
2
2
1
1
2
1
0
2
0
0
2
1
0
1
0
1
1
0
2
1
1
2
3
1
1
1
0
2
0
0
2
2
0
1
1
1
1
1
1
1
1
0
1
1
1
2
2
0
1
0
0
1
1
2
1
1
1
0
2
2
5
1
1
1
0
1
0
1
0
0
1
2
0
1
0
1
2
2
0
1
1
2
0
2
0
2
0
0
1
2
0
2
1
1
2
0
0
1
1
1
1
0
2
1
1
0
1
2
2
1
1
1
0
0
1
0
2
0
0
1
1
0
0
0
1
0
1
1
0
1
1
1
1
2
2
0
2
0
1
0
0
0
1
1
1
1
0
0
0
0
0
0
3
1
1
0
2
0
0
1
1
1
2
2
1
2
0
1
1
1
0
0
0
1
1
1
0
2
1
1
2
2
1
0
1
1
0
1
0
1
2
1
0
1
1
1
0
0
0
2
1
1
1
2
0
1
1
1
1
0
1
1
1
2
1
0
2
0
1
0
0
0
0
1
2
0
0
2
1
2
1
2
0
2
2
0
0
0
2
0
1
2
2
1
1
1
0
2
1
1
2
2
0
1
1
0
1
1
1
0
1
0
2
1
2
1
2
0
1
2
2
1
2
0
1
0
1
0
2
2
1
0
2
2
1
2
1
1
1
2
0
1
1
0
1
1
1
2
0
1
0
0
1
1
1
0
1
0
2
1
0
1
1
2
1
0
1
1
0
2
3
4
1
1
1
2
0
0
1
1
1
0
2
0
1
0
0
0
2
1
2
0
1
1
1
0
2
2
2
1
0
1
0
0
1
1
0
1
2
0
1
0
1
2
1
0
0
1
2
1
0
0
1
0
2
2
1
1
2
1
0
2
2
1
1
1
0
0
2
1
0
0
1
2
2
1
2
2
1
1
2
0
1
1
1
2
1
1
1
0
1
0
1
1
0
1
2
1
0
1
1
0
2
1
0
1
1
2
1
1
0
0
1
1
2
2
0
2
1
1
0
1
2
0
0
7
1
0
2
2
1
1
0
0
0
0
0
0
0
1
0
2
0
0
1
0
1
0
1
1
0
1
2
2
0
0
1
1
2
1
1
1
0
2
2
2
1
0
1
1
2
0
2
2
1
0
1
1
2
1
1
1
1
2
1
1
0
2
0
1
2
1
1
1
0
0
2
3
0
1
1
1
0
0
1
0
1
1
2
0
2
1
1
2
1
1
0
2
1
1
1
1
2
0
1
0
2
1
0
0
0
0
0
0
1
1
0
1
3
0
1
1
1
1
1
2
0
2
1
1
0
1
2
0
0
1
1
1
1
1
1
1
1
1
1
2
2
1
1
0
1
2
1
0
1
1
0
0
0
2
0
0
0
2
1
1
1
0
1
1
1
0
1
1
2
0
1
2
2
1
1
2
0
0
2
2
2
2
1
1
0
1
0
0
0
0
2
2
1
1
1
2
2
3
1
1
1
0
1
2
2
0
0
1
1
0
0
1
0
1
2
2
1
0
2
1
2
1
1
2
0
1
1
1
1
1
1
0
3
2
2
0
0
1
0
1
1
1
1
2
1
2
0
1
1
1
3
1
1
1
1
1
2
1
0
0
1
1
1
4
1
2
2
3
1
2
1
0
2
0
1
0
1
1
0
1
0
1
1
1
1
1
1
1
1
1
1
1
1
2
0
1
2
1
0
2
1
1
0
1
1
1
1
0
1
0
1
1
1
1
2
0
2
0
0
1
1
2
0
0
0
1
2
1
1
1
0
1
1
1
1
1
0
1
0
2
1
1
1
1
1
1
2
2
0
0
2
0
0
2
1
0
2
2
0
1
0
3
1
0
1
1
1
1
0
2
2
0
1
2
4
0
1
1
1
2
2
0
1
0
3
2
1
1
1
1
0
2
1
2
1
1
1
0
1
0
1
2
0
2
0
1
1
0
0
1
2
1
1
2
1
1
1
1
1
0
1
0
0
1
0
1
0
2
2
1
1
2
1
1
1
1
0
0
2
1
1
1
1
0
1
2
1
0
1
0
0
0
1
0
2
1
0
0
1
0
1
1
1
0
2
0
1
0
1
1
0
1
1
1
1
1
3
1
0
1
0
1
1
1
1
1
0
0
1
0
1
1
1
1
1
1
2
1
0
1
1
1
1
2
0
0
2
1
2
1
0
0
1
0
1
1
2
0
0
1
1
0
0
0
1
0
1
1
2
0
0
1
0
0
1
1
1
0
2
0
1
1
2
0
0
1
0
2
2
0
1
2
0
2
0
0
1
1
2
1
1
1
1
0
0
0
1
2
0
2
0
0
2
1
0
1
0
1
1
1
1
1
1
1
1
1
2
1
0
1
1
2
0
0
1
1
1
2
2
1
2
0
1
1
0
1
1
2
1
2
2
1
0
1
0
0
4
2
1
1
0
1
1
0
1
1
0
2
1
2
2
0
1
1
2
1
2
1
1
1
1
2
0
2
1
1
1
0
1
1
0
0
2
1
1
2
0
1
0
0
1
1
1
1
0
1
1
0
1
0
1
0
1
2
1
1
0
0
1
0
1
3
1
2
1
1
1
1
1
2
1
0
2
1
3
1
2
0
1
1
1
1
1
1
1
2
3
0
0
0
0
1
0
1
0
0
1
0
2
0
1
0
1
0
1
3
1
1
0
1
1
1
1
2
0
3
2
1
2
2
2
1
1
1
1
2
0
0
0
4
0
1
1
2
1
1
0
0
3
1
0
1
0
1
2
2
1
1
2
2
1
1
2
1
1
1
0
0
2
3
1
2
1
0
1
0
2
0
2
1
1
1
1
1
2
1
1
0
1
1
1
1
1
2
2
1
1
1
1
1
0
1
1
2
2
0
0
2
1
1
1
1
1
2
1
3
0
0
2
0
0
1
1
2
2
0
1
0
1
2
1
1
2
1
0
1
0
0
1
1
0
1
2
1
0
0
0
2
1
1
1
2
2
0
1
1
1
0
0
1
2
0
2
0
0
2
0
0
1
1
2
0
2
0
0
1
1
1
0
0
2
0
1
1
1
1
2
1
1
1
0
2
1
1
1
2
0
0
0
0
0
1
2
1
0
2
1
0
0
1
1
0
0
0
0
2
0
2
1
1
0
1
2
1
1
1
1
1
1
1
2
1
1
1
0
1
1
1
1
1
0
2
2
0
0
1
1
0
1
2
1
1
1
1
3
2
0
0
1
1
1
1
1
2
0
1
1
1
0
2
0
2
1
2
1
0
0
1
2
0
1
2
0
1
0
1
1
0
0
1
0
0
1
1
1
0
0
2
2
2
1
0
1
1
1
1
1
2
1
1
1
5
1
1
1
1
1
1
0
0
2
1
1
1
0
1
1
0
1
0
0
1
0
0
2
1
3
1
1
0
1
0
1
0
1
1
1
3
1
0
0
1
1
0
1
0
2
0
1
1
0
1
2
1
1
1
0
0
1
2
1
1
0
2
2
1
2
1
0
1
2
1
1
1
1
0
0
1
1
2
1
0
1
0
1
1
1
0
2
1
1
0
0
1
1
2
0
0
1
0
0
0
5
1
1
1
1
2
2
1
1
1
0
1
2
2
1
0
0
0
1
1
1
1
1
1
1
0
1
0
1
0
1
0
1
0
0
2
1
1
1
1
0
2
1
0
2
0
1
1
1
1
0
1
0
1
2
1
1
0
1
1
0
1
0
1
1
2
2
1
0
1
1
1
1
1
3
0
1
2
1
1
1
1
1
2
2
2
1
2
1
0
0
1
1
2
0
1
1
1
1
0
2
1
1
0
1
2
2
0
0
1
1
0
0
2
0
2
1
1
1
0
0
1
1
1
0
0
1
1
0
2
0
2
1
1
0
2
2
1
1
2
1
1
1
2
2
0
1
0
1
0
1
1
0
2
0
2
2
2
0
0
1
1
1
0
1
2
1
0
1
1
1
1
0
2
1
0
2
0
1
1
2
1
1
1
0
1
2
0
3
1
0
0
0
1
1
0
0
1
1
0
2
3
0
1
0
0
0
0
2
1
0
1
1
2
1
2
0
2
0
1
0
0
1
0
0
1
1
1
0
0
1
1
1
2
1
1
0
2
1
0
2
1
1
1
1
1
1
2
1
1
2
1
1
0
0
1
0
0
1
1
2
1
0
1
1
1
2
2
1
1
1
1
0
1
1
1
2
0
1
0
1
1
1
1
1
1
0
2
0
1
0
1
1
0
1
1
0
2
2
1
1
0
2
2
2
2
1
2
0
0
1
1
1
0
0
1
0
1
1
2
1
1
1
2
1
0
1
0
0
2
1
1
2
0
0
1
0
0
0
2
1
2
1
1
2
1
1
1
2
0
2
0
2
1
1
1
1
2
0
1
0
1
1
1
2
1
1
2
0
2
0
0
0
1
0
1
1
0
2
1
1
0
1
1
2
1
2
2
1
1
1
1
2
1
1
1
0
2
2
2
0
2
0
2
2
0
1
0
1
1
1
2
2
0
0
1
1
2
1
1
2
0
0
2
0
2
0
1
0
1
1
1
1
1
0
1
1
0
0
1
2
1
1
1
0
1
1
2
0
2
1
1
1
1
1
2
1
2
1
3
1
1
2
1
1
1
2
0
0
0
1
1
1
0
2
1
2
1
0
1
2
2
0
2
1
2
2
3
1
2
0
0
1
0
0
2
1
1
1
1
1
0
2
1
0
2
1
0
1
2
2
0
1
1
1
0
0
2
1
0
2
1
0
1
2
2
0
1
1
0
1
1
1
1
1
1
1
1
1
0
1
2
2
2
0
0
2
2
0
1
1
2
2
1
1
2
0
2
2
2
0
1
2
0
2
2
2
1
2
1
1
0
0
1
2
1
1
1
1
1
1
0
2
0
1
1
2
1
2
0
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
1
2
0
1
0
0
0
1
1
0
0
1
1
2
2
1
1
1
1
1
1
1
2
0
0
1
0
1
0
0
1
1
1
1
1
1
1
2
3
0
2
0
1
1
1
2
1
1
0
1
0
0
1
0
0
0
1
1
0
1
0
1
1
2
2
1
2
1
0
2
1
1
2
1
1
1
1
1
1
1
0
2
1
1
2
1
2
1
0
1
1
2
1
0
1
1
0
0
1
0
2
0
2
2
0
1
1
0
0
1
1
1
0
0
0
1
1
2
0
1
1
2
0
1
0
1
0
1
1
0
0
0
2
1
2
1
0
1
1
1
0
1
1
1
2
0
1
0
2
2
1
2
1
0
1
0
1
0
1
1
2
1
1
0
1
0
1
1
1
1
1
2
1
0
1
1
1
1
1
1
1
1
1
1
0
1
2
0
1
2
0
0
2
2
1
1
2
1
2
0
2
0
1
0
0
1
1
1
0
2
6
0
1
0
1
1
1
0
1
1
1
0
0
1
1
1
2
1
1
1
1
2
0
1
0
0
0
1
2
1
0
1
0
0
1
1
0
0
1
0
2
2
1
2
1
2
0
0
1
1
0
1
1
2
1
1
0
1
1
0
2
1
0
2
1
1
1
1
2
0
2
1
0
1
1
1
0
0
2
0
1
1
2
2
1
0
0
1
1
1
1
1
2
1
0
2
2
1
0
2
4
0
2
1
0
1
1
1
1
0
0
0
1
1
1
0
1
1
0
1
1
1
1
0
1
1
2
0
4
1
1
1
2
1
2
0
1
2
0
1
2
1
0
1
1
1
1
1
1
1
1
1
1
0
2
1
1
0
1
1
1
1
0
1
2
0
1
0
1
1
2
0
1
0
0
1
1
1
1
1
1
1
0
1
1
1
2
1
1
1
1
0
0
2
2
0
2
1
1
2
0
0
1
2
1
1
0
0
1
2
0
1
0
1
2
2
0
1
1
2
2
0
0
1
1
0
0
0
1
0
1
0
1
0
0
2
1
2
2
0
0
3
1
0
1
0
0
1
1
2
2
2
1
1
1
2
2
0
3
1
2
1
0
2
2
1
0
1
1
1
2
1
1
1
1
1
0
1
1
2
1
1
1
1
0
2
0
2
0
1
1
0
1
1
1
1
0
1
1
1
1
1
1
1
1
0
1
1
1
2
0
0
1
1
0
1
1
2
1
1
0
2
2
1
0
2
0
1
1
0
2
1
1
2
2
1
1
2
1
1
1
1
1
1
1
1
0
2
1
0
2
1
1
0
0
0
2
0
2
2
1
2
2
1
0
2
1
1
1
1
1
0
0
0
0
1
1
1
1
1
0
2
1
2
0
1
1
0
1
0
1
1
1
0
2
0
2
1
0
2
1
1
1
1
1
0
1
0
2
0
0
1
0
2
2
2
1
1
2
1
1
1
1
0
1
1
1
2
1
1
1
0
2
0
1
1
0
1
1
2
1
1
1
1
0
1
1
2
2
1
0
2
1
0
0
2
2
0
1
1
2
2
1
1
1
1
2
0
1
1
0
2
1
2
1
2
1
0
1
1
2
1
0
1
0
1
2
1
0
2
1
0
0
2
1
0
1
2
1
2
1
0
1
0
1
1
2
2
1
0
2
1
1
0
3
0
1
1
1
1
0
1
1
1
1
0
1
0
2
1
1
1
1
0
1
1
1
0
2
1
1
0
2
2
1
1
1
1
1
2
0
1
2
1
1
2
0
2
1
1
1
0
0
0
1
1
0
0
1
2
1
2
0
1
1
1
1
0
2
1
0
1
0
2
1
2
1
1
0
1
3
0
0
1
0
1
1
1
1
1
1
2
1
1
0
0
1
1
2
1
0
1
1
1
1
0
1
2
0
0
1
1
1
1
2
2
1
1
0
0
0
0
0
2
1
2
2
2
1
1
2
1
2
1
1
0
0
0
2
1
0
2
2
1
1
1
0
0
2
0
2
3
1
1
1
2
0
2
2
2
2
1
1
1
2
1
0
0
1
1
0
1
0
1
1
0
0
1
1
1
0
1
1
2
0
0
2
0
1
2
0
1
1
1
1
0
1
0
1
1
2
1
1
1
2
1
2
1
1
0
0
2
0
1
0
3
1
1
2
1
0
1
1
1
0
2
1
0
0
1
2
0
1
0
1
2
0
2
2
0
0
1
0
0
0
0
2
1
1
0
1
0
2
2
1
2
0
3
2
2
0
1
0
1
1
2
1
1
1
1
1
1
2
1
2
0
1
2
1
0
2
0
2
1
1
0
1
2
1
1
2
1
1
1
2
1
1
2
1
1
1
1
0
0
2
0
2
1
1
1
1
1
2
1
2
1
2
1
2
2
1
2
2
0
0
1
2
2
1
0
1
0
2
0
1
0
2
1
2
1
1
1
1
2
0
1
1
1
2
2
1
2
0
0
0
2
1
2
0
0
1
1
1
0
0
2
1
2
2
1
0
2
1
1
0
2
1
2
1
2
0
1
1
1
1
1
2
1
0
0
1
1
0
1
2
1
2
1
2
2
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
0
2
1
1
2
0
0
1
2
1
1
1
0
0
0
2
0
1
1
0
0
1
1
1
1
1
2
0
0
1
2
2
1
2
2
0
1
2
2
1
0
0
1
1
1
0
0
2
1
2
2
2
0
1
0
1
1
1
0
0
1
0
2
2
2
1
2
1
0
1
1
0
2
2
0
1
1
0
0
0
1
0
0
0
0
3
1
5
0
2
1
1
1
1
1
1
1
0
0
1
1
0
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
0
1
0
1
2
0
1
0
0
0
2
1
0
2
1
1
1
0
0
1
2
1
2
1
0
2
2
0
0
2
0
2
0
1
1
1
1
1
2
1
0
1
1
0
1
0
0
1
2
0
1
1
1
1
2
1
2
1
1
1
1
0
2
1
2
0
0
1
2
1
1
2
1
2
0
0
0
1
1
0
2
1
2
0
0
1
0
0
1
1
0
0
1
1
1
2
2
2
1
2
1
0
1
0
0
2
2
0
0
0
0
1
1
2
1
1
0
1
0
1
1
1
0
2
0
2
1
0
0
0
1
1
2
1
1
1
1
1
1
0
0
1
1
2
2
2
0
1
1
0
1
1
2
1
1
1
2
1
1
1
2
2
0
1
1
0
0
0
0
1
2
1
1
0
1
0
1
2
0
2
1
1
2
2
0
1
1
0
1
2
1
2
0
1
2
0
1
0
1
1
1
0
1
1
0
1
1
0
1
1
1
1
1
1
1
2
1
0
1
1
1
1
2
1
2
1
1
0
1
1
1
2
2
1
1
0
1
0
2
0
1
0
1
0
2
1
0
1
1
1
0
0
1
0
1
0
2
2
0
0
1
2
2
1
2
1
1
2
0
1
1
1
2
1
2
1
1
2
2
1
1
1
3
1
1
1
1
1
0
2
1
0
0
2
1
0
1
2
1
0
1
1
1
2
1
1
1
0
1
0
0
1
2
1
1
2
0
1
0
2
0
1
0
2
0
1
1
1
0
1
1
2
0
1
1
0
1
1
1
2
1
1
1
1
0
1
4
1
1
2
1
1
0
0
1
0
2
2
1
1
1
0
1
1
0
1
1
3
0
1
0
1
2
0
2
2
2
2
0
2
3
0
1
1
0
1
1
1
0
1
0
1
1
1
1
1
1
1
1
1
1
1
2
2
1
0
1
0
1
1
1
1
1
1
2
0
1
0
1
1
0
1
1
2
2
1
5
1
1
1
1
1
1
1
1
0
1
0
2
0
2
1
0
1
2
1
1
0
2
1
1
0
1
3
2
2
1
0
1
0
0
0
1
0
1
1
2
0
1
0
3
0
1
1
1
1
0
2
0
2
0
0
2
1
0
0
2
1
1
1
1
0
2
1
0
0
2
1
0
0
2
1
0
0
0
2
0
0
2
2
0
1
1
2
1
1
0
1
0
2
1
1
1
0
2
2
0
1
1
2
1
2
0
1
1
1
0
1
1
0
1
1
0
1
1
1
1
0
0
1
2
0
2
1
2
2
0
1
1
2
1
0
1
2
1
2
1
0
1
0
2
1
1
1
2
1
1
1
2
1
0
1
1
1
1
1
2
1
0
2
0
0
0
1
2
2
0
1
2
2
1
0
2
0
1
2
0
2
1
1
1
2
1
1
1
1
1
0
1
2
0
2
0
1
0
1
2
1
0
2
1
1
0
1
1
1
0
2
0
0
2
0
0
2
2
3
1
1
1
1
1
2
1
0
1
1
1
1
0
1
0
1
1
2
3
1
0
2
0
1
0
2
1
1
0
1
1
1
2
1
1
0
1
2
1
1
2
0
1
2
1
1
1
2
2
2
1
0
2
0
0
1
0
1
1
1
0
0
2
1
1
1
1
0
1
2
1
1
1
2
1
0
0
1
1
2
2
2
1
1
1
2
1
0
1
1
1
1
1
0
1
1
3
2
2
1
0
2
2
2
1
1
0
2
1
1
1
0
0
1
1
1
1
1
2
0
2
2
1
0
1
1
1
2
1
0
1
1
1
2
2
4
1
1
1
1
0
1
0
2
0
0
2
1
2
0
1
0
0
1
0
0
0
0
1
1
1
1
2
1
0
0
0
0
2
2
1
1
1
1
0
0
1
0
0
0
1
0
1
0
1
1
1
2
1
0
1
1
1
1
2
1
2
2
1
1
2
0
1
2
0
2
1
0
0
1
0
0
2
2
0
1
2
1
3
1
1
0
0
1
1
1
0
1
1
1
1
1
2
1
0
1
1
0
1
0
1
1
1
1
1
2
2
0
1
1
2
0
1
0
0
0
1
1
0
2
2
1
1
0
0
0
3
2
0
0
2
0
0
1
2
1
1
1
1
1
0
1
1
0
0
1
0
2
1
0
0
0
1
1
2
0
0
1
0
1
1
1
0
0
0
1
0
0
1
1
1
0
1
0
1
0
2
0
2
2
1
1
2
1
1
1
2
0
1
1
2
1
0
1
2
0
0
1
1
1
0
0
0
2
2
1
1
1
1
1
0
1
0
1
0
0
0
0
1
1
0
2
1
0
1
2
1
1
2
0
1
1
2
1
1
1
1
1
0
2
1
0
2
1
0
0
0
0
0
0
2
2
1
1
1
2
1
1
1
0
0
0
0
1
0
1
1
1
1
1
2
1
2
1
0
1
1
0
1
2
2
1
0
1
1
0
2
1
2
2
0
1
0
0
2
1
0
1
2
2
0
2
0
1
1
0
1
1
2
1
1
1
2
2
0
0
3
1
1
1
0
1
1
0
2
1
1
0
1
1
1
0
0
1
1
0
2
1
0
1
1
2
0
1
0
0
2
1
2
1
0
1
1
2
1
1
1
0
2
1
1
1
1
1
0
0
1
1
1
2
0
1
0
2
0
0
0
1
0
2
0
0
2
0
1
1
2
1
1
1
1
2
1
1
0
1
0
2
0
0
1
0
1
0
0
1
1
0
0
1
2
1
1
2
1
2
0
1
1
1
2
1
0
2
1
1
0
0
2
1
2
1
1
2
0
1
1
1
2
2
1
0
2
1
0
1
1
1
1
2
2
0
1
2
1
1
1
2
2
1
1
0
2
1
1
1
0
0
0
1
0
2
0
1
1
1
2
1
0
2
0
1
1
1
2
3
1
3
2
1
1
2
2
1
1
2
1
2
2
0
0
1
1
1
1
1
0
0
2
0
1
1
0
2
1
1
1
1
0
0
0
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
0
0
1
0
1
0
1
2
2
1
0
2
2
1
1
1
0
3
2
1
2
1
0
0
1
1
1
1
1
1
1
2
1
0
1
0
2
1
1
0
1
0
1
0
2
1
1
2
0
0
1
0
2
0
1
1
1
1
2
1
1
1
1
1
1
0
2
1
1
0
1
1
0
0
0
0
2
0
0
0
0
1
1
3
1
0
1
1
1
1
0
0
0
2
2
2
2
1
1
1
0
2
1
2
0
0
1
1
0
1
0
1
1
0
1
1
0
2
0
1
1
1
2
1
0
1
0
0
1
1
1
1
0
1
0
1
1
0
2
1
2
1
2
0
0
0
0
0
2
2
0
1
1
1
1
2
0
1
1
0
1
2
0
1
1
1
2
2
1
0
2
0
1
1
2
0
0
2
0
0
1
0
0
2
1
1
1
1
1
1
2
0
0
0
0
1
2
2
1
0
1
1
2
1
1
0
1
1
1
0
1
0
0
2
2
1
2
1
1
0
0
2
1
0
1
2
2
2
1
0
0
1
1
2
2
1
1
0
1
1
2
2
2
2
1
0
1
1
2
2
0
0
0
1
1
0
0
1
0
1
3
1
1
1
2
2
0
1
1
0
3
0
2
0
1
0
1
1
2
2
2
1
1
1
0
0
0
1
0
1
1
1
2
1
2
1
0
0
2
1
1
0
2
1
2
1
2
0
1
0
0
2
1
0
1
0
1
2
0
1
1
0
1
1
2
2
3
1
3
2
0
1
1
1
0
0
2
1
1
0
1
1
2
0
0
1
2
3
1
0
3
2
2
0
1
1
1
1
1
1
2
1
0
1
1
1
0
2
0
1
0
0
2
1
0
0
0
0
0
0
0
1
0
1
1
1
1
1
2
1
0
0
1
1
0
1
0
2
1
0
1
2
1
3
1
2
0
1
2
0
0
1
2
1
1
2
0
2
1
0
2
0
2
1
0
0
1
2
1
0
0
0
1
0
2
2
1
0
2
1
2
1
0
1
1
0
1
1
0
0
0
1
1
0
1
1
0
2
1
0
0
1
0
1
1
1
0
2
2
0
2
0
0
1
2
0
1
0
2
0
1
2
1
2
2
2
1
1
1
1
0
0
2
0
1
1
1
1
1
1
1
2
2
2
0
1
0
1
1
1
1
0
1
1
1
1
2
1
1
1
2
2
1
1
0
1
2
1
1
0
1
0
2
2
2
0
2
1
3
2
0
1
1
1
1
0
1
0
1
0
2
2
1
0
2
1
1
1
0
1
0
0
4
0
1
2
0
1
1
1
1
0
0
2
0
0
2
1
1
2
1
1
1
2
1
1
2
2
1
1
1
2
1
0
2
0
2
1
0
0
0
0
2
1
1
1
1
1
1
1
0
1
2
1
0
1
1
1
2
0
2
0
1
0
1
1
0
1
1
2
0
1
1
0
0
0
0
1
0
2
0
1
1
2
1
1
3
2
1
0
1
1
0
1
1
1
1
1
1
0
0
1
1
0
1
0
1
0
0
1
1
1
2
2
0
1
2
1
0
1
0
0
2
2
1
1
0
2
1
1
0
1
1
2
2
0
0
1
1
1
1
1
2
0
2
1
1
0
2
1
0
0
0
1
1
2
0
1
2
0
0
1
1
0
3
1
1
1
1
1
0
1
0
0
2
1
2
0
0
0
1
1
2
1
0
1
2
1
1
0
1
1
1
2
1
1
0
1
1
0
1
1
1
1
0
0
1
2
1
2
2
1
0
3
1
1
2
0
1
0
1
1
1
0
1
0
0
1
2
0
1
3
0
0
0
1
0
2
1
2
1
1
1
2
2
2
1
1
1
1
2
2
1
1
0
0
0
1
2
0
1
0
1
2
1
1
0
1
1
2
1
0
0
1
0
0
2
0
2
1
2
0
0
1
0
1
1
1
1
0
2
1
2
1
1
1
0
1
1
1
1
1
0
0
1
0
2
1
1
1
1
2
0
1
0
1
0
0
1
0
1
1
1
0
1
0
0
0
1
1
2
1
2
0
1
2
2
1
0
1
2
0
1
0
2
1
1
2
1
0
0
0
1
2
2
1
2
1
0
2
0
1
0
0
1
1
1
1
1
0
2
2
0
1
1
1
2
0
3
1
0
2
0
1
2
1
1
1
1
0
0
1
0
2
0
1
0
1
3
1
1
2
3
2
1
1
1
2
2
1
1
1
2
1
1
2
0
1
1
1
0
0
1
1
1
2
1
2
0
0
1
2
1
1
0
1
1
1
0
0
1
1
1
2
1
2
0
0
1
2
2
0
1
0
1
1
2
0
2
3
1
1
1
0
2
2
1
2
2
2
1
0
2
1
0
1
0
1
0
2
1
1
0
1
1
1
0
1
1
1
1
1
0
1
1
1
0
2
1
1
1
2
1
0
1
1
1
1
1
0
0
2
1
0
1
4
1
0
0
0
1
1
1
0
2
1
1
0
2
1
1
1
0
1
0
0
1
1
1
1
2
1
0
0
2
1
1
2
2
0
1
1
1
1
0
1
1
1
0
1
2
2
1
1
1
0
0
1
2
0
0
1
1
1
0
1
1
0
2
1
0
0
1
1
0
1
1
0
1
1
2
1
2
1
2
0
2
0
0
1
1
1
1
1
4
2
1
1
1
1
1
2
2
1
1
1
0
1
1
2
0
0
2
0
0
1
1
2
2
0
2
1
1
2
0
0
1
1
1
1
0
0
1
1
2
2
2
2
1
0
1
1
0
0
1
0
1
2
1
1
2
0
0
1
1
2
1
2
1
1
1
0
2
2
1
1
1
1
0
1
1
1
1
2
0
0
1
0
1
2
1
1
0
3
1
0
0
1
2
0
1
1
0
2
2
0
1
0
1
1
1
1
1
1
0
2
1
1
0
1
2
1
1
1
1
0
0
1
1
0
1
2
2
1
1
2
0
2
2
0
0
2
1
0
0
2
1
1
2
1
1
1
0
1
0
0
1
0
2
0
2
2
1
1
1
0
1
2
1
1
2
0
0
0
1
1
0
0
0
2
2
0
1
2
0
1
0
1
0
2
1
0
2
1
2
1
1
2
0
2
1
0
2
1
1
1
0
2
1
2
1
1
0
0
1
1
1
0
2
0
0
0
2
0
2
1
3
1
0
2
1
2
0
0
1
0
0
1
0
0
2
3
1
1
2
1
1
1
2
2
1
2
1
1
1
1
1
1
0
0
0
1
1
0
1
1
2
0
0
2
1
1
2
2
2
0
0
1
1
0
0
1
2
2
2
0
0
1
0
0
1
1
0
0
2
2
1
1
2
2
1
1
2
1
2
1
1
2
0
1
1
2
0
1
0
1
1
1
0
0
1
1
0
2
1
1
1
1
1
1
2
1
0
0
1
2
0
2
1
0
2
0
1
1
1
1
1
0
1
2
0
0
0
2
1
1
1
1
1
0
1
0
0
0
1
1
1
1
1
1
1
1
2
0
1
1
1
0
1
0
1
1
1
2
1
1
1
0
2
0
1
1
2
1
1
2
1
0
1
0
3
2
0
0
1
0
0
0
2
0
1
0
1
1
0
1
0
0
2
2
0
2
1
2
0
2
1
0
1
0
1
0
0
1
0
1
0
1
1
1
0
1
0
0
1
0
2
0
1
1
0
0
2
1
1
1
1
2
0
1
1
1
1
2
0
2
0
2
1
2
1
2
2
0
0
0
0
0
2
2
1
1
1
2
2
1
1
1
1
1
1
0
0
2
0
1
2
1
2
1
1
1
0
1
1
2
1
0
2
1
2
1
0
2
2
0
0
1
0
1
0
1
1
1
0
1
1
2
1
0
2
1
0
0
2
1
1
2
2
1
0
1
1
2
0
1
1
0
0
0
0
1
0
2
1
1
0
2
0
1
2
1
1
1
1
0
0
1
1
0
0
2
1
2
1
1
1
1
0
0
1
2
1
0
0
1
1
2
2
0
2
0
0
1
2
0
0
0
1
1
1
1
2
0
0
0
1
0
1
0
1
0
1
2
2
2
1
1
2
1
1
4
1
0
0
0
0
1
2
1
0
1
2
1
1
0
2
1
2
3
2
1
2
0
2
1
1
1
0
0
1
1
1
0
1
1
1
0
2
2
0
1
1
1
2
0
0
1
1
2
0
0
2
0
0
1
1
1
1
1
1
0
1
0
0
0
1
1
2
0
0
1
1
0
1
1
1
1
1
2
0
1
0
1
4
2
0
1
1
1
0
1
2
1
1
1
0
1
1
0
0
2
1
0
1
2
0
2
1
0
2
1
1
1
1
2
1
1
1
1
1
1
1
1
0
1
1
2
0
1
1
0
1
2
1
1
2
2
1
1
2
2
0
0
0
1
0
2
1
0
1
1
0
1
1
1
1
1
1
0
0
0
2
0
2
1
1
1
0
1
2
1
1
2
1
0
1
1
0
0
1
2
2
2
2
1
2
1
2
3
1
1
1
1
0
0
0
1
1
1
1
1
2
1
0
0
1
0
2
1
0
1
1
2
1
1
1
0
1
2
0
0
1
2
2
0
0
0
1
1
1
1
2
2
1
1
2
1
0
1
1
1
1
1
1
1
2
1
1
1
0
1
2
3
1
2
1
1
0
1
1
1
1
2
1
1
0
2
2
1
1
0
1
0
0
0
1
1
3
0
1
3
1
2
3
0
1
0
1
1
1
1
0
2
2
2
2
0
3
1
2
1
0
1
2
1
1
2
0
1
0
1
1
1
1
2
0
2
1
0
0
1
2
0
2
2
1
1
3
0
1
2
2
2
1
1
1
1
1
1
1
0
2
2
2
2
1
2
0
0
0
0
1
2
2
0
0
2
2
1
1
0
2
2
1
0
2
0
2
0
0
1
1
1
2
1
1
1
1
1
1
1
1
2
0
1
2
1
1
0
0
0
0
0
1
0
0
0
0
1
1
1
0
1
1
0
1
0
1
1
1
1
2
0
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
2
2
1
2
2
0
1
2
2
0
1
2
0
2
1
1
1
0
1
0
2
2
1
0
0
1
0
2
1
1
2
2
1
2
0
1
1
0
0
2
2
0
0
1
2
0
1
2
1
1
1
1
2
1
0
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
0
1
2
1
1
2
1
2
1
2
1
0
2
2
2
0
2
2
0
1
1
1
0
1
2
0
0
1
2
0
1
2
0
0
1
1
0
1
0
1
0
1
0
0
1
0
1
1
2
1
1
1
1
0
1
0
1
2
0
1
0
0
1
1
2
1
0
1
2
1
1
2
1
1
0
0
2
1
0
2
2
1
2
0
1
1
0
1
2
1
0
1
1
0
1
1
1
1
0
0
1
1
0
1
1
1
2
1
2
1
1
1
0
4
1
0
1
1
1
0
1
0
1
1
2
0
0
0
2
0
2
1
2
3
0
1
1
1
0
2
0
1
2
1
0
2
1
1
1
1
1
0
1
1
1
1
0
2
1
0
2
1
1
0
1
1
2
0
1
1
1
0
1
1
2
2
0
1
1
1
2
0
1
2
0
1
2
0
2
1
1
1
0
2
1
4
1
0
1
0
0
1
2
1
1
0
1
0
0
2
1
0
0
2
2
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
2
3
0
0
1
0
2
0
1
0
0
2
1
3
2
2
1
1
0
1
2
1
0
0
0
2
0
1
1
1
3
1
1
0
2
0
2
0
0
1
0
2
1
1
1
0
0
0
1
1
1
0
1
1
1
0
1
2
2
2
1
0
1
2
1
1
0
1
1
1
1
2
1
2
0
1
1
2
2
0
2
0
1
1
1
0
1
1
1
1
1
1
2
1
1
0
0
0
1
1
1
1
1
2
2
1
0
1
2
0
0
1
2
1
1
1
1
1
1
2
1
2
1
0
0
0
2
1
0
1
1
2
2
1
1
2
0
1
1
1
0
0
1
0
0
1
0
0
0
1
0
0
2
2
1
2
0
0
0
1
1
2
1
1
1
2
0
1
1
0
2
0
0
1
1
1
0
1
1
0
1
1
1
1
2
0
1
1
1
0
1
1
1
2
1
1
1
1
3
0
0
0
0
0
0
0
1
0
1
1
1
1
1
1
1
1
1
1
0
1
1
0
2
0
0
1
1
1
0
0
1
0
2
1
1
0
3
1
2
2
3
0
3
1
0
1
2
1
1
0
0
0
1
1
0
2
0
1
1
0
2
0
2
2
1
1
0
0
2
0
0
0
0
2
1
1
2
1
1
2
0
1
1
0
0
3
1
1
1
0
1
1
2
1
2
0
1
2
0
1
2
0
0
2
2
1
1
1
2
2
0
1
1
1
0
1
1
1
1
1
0
1
1
0
1
1
1
3
2
0
1
2
0
0
1
0
1
0
0
2
0
2
0
1
2
1
0
0
1
0
1
1
0
0
1
1
2
0
1
1
2
1
0
0
0
2
1
2
1
1
1
1
0
1
1
1
1
1
2
2
2
2
0
1
2
1
2
1
1
1
0
2
2
0
1
0
0
0
1
1
0
1
0
0
3
0
0
2
2
1
2
1
1
0
1
1
0
0
1
1
2
2
1
0
2
0
1
0
1
0
1
1
1
1
0
2
1
1
2
0
1
2
1
2
2
1
0
0
0
2
1
2
0
1
2
1
1
1
0
0
2
1
1
1
0
1
0
2
2
1
1
0
1
1
0
1
2
2
1
1
1
1
1
0
1
1
1
2
2
1
2
1
2
0
1
2
2
0
2
1
1
2
2
1
2
1
1
0
1
0
1
2
0
1
1
1
1
0
0
1
1
0
1
0
0
1
2
1
1
0
2
1
1
1
1
2
1
1
2
1
2
1
1
1
1
0
1
2
0
1
1
1
0
2
0
2
3
1
0
0
1
1
1
1
2
0
1
3
0
0
1
1
1
1
0
1
1
1
1
2
0
2
1
0
0
1
1
1
1
1
2
1
0
0
0
0
2
1
1
1
2
2
0
0
2
1
0
1
0
1
1
0
0
1
1
1
2
2
0
1
2
2
1
0
1
0
1
1
0
1
1
1
2
0
1
0
0
0
1
1
1
2
0
0
1
1
2
1
0
1
2
2
2
0
2
1
3
4
2
1
1
1
0
3
1
1
2
2
2
2
1
0
0
2
0
1
0
0
0
2
10
2
0
0
1
1
1
2
1
0
1
1
1
1
0
1
1
3
0
1
0
0
1
0
1
1
1
0
0
1
0
1
1
1
1
0
1
0
2
1
1
2
0
0
0
1
1
1
1
1
1
1
1
1
2
0
2
2
0
0
1
1
1
0
0
2
2
1
2
1
2
1
2
0
0
1
1
2
0
1
1
2
0
1
2
1
1
2
1
1
2
1
1
0
3
0
0
1
1
1
0
1
1
1
0
0
2
0
0
0
1
1
2
0
1
0
1
1
1
1
1
0
0
2
1
0
0
2
1
0
0
0
1
1
1
2
1
0
1
2
1
2
2
1
1
1
3
1
1
1
2
1
1
1
1
1
2
0
1
2
0
0
0
1
1
1
1
2
1
0
2
1
1
1
2
2
1
1
0
0
2
1
1
1
1
0
2
0
0
2
2
0
1
1
2
0
2
1
2
0
0
0
1
1
2
0
1
1
2
2
2
1
1
1
1
2
1
2
1
0
0
0
7
2
2
1
1
2
0
2
2
1
1
0
2
2
1
2
1
0
0
2
0
2
1
1
1
1
2
1
1
1
1
1
2
1
0
1
1
1
0
1
1
1
1
0
2
2
1
1
0
0
2
0
0
1
2
1
1
2
0
1
1
0
1
2
2
2
0
1
1
1
0
1
1
2
2
2
1
1
2
1
0
0
1
1
2
2
0
2
1
2
0
1
0
1
1
1
0
1
1
0
0
0
0
2
2
2
0
0
1
2
2
1
1
1
0
2
1
2
1
1
1
2
2
0
1
0
1
0
1
1
1
1
1
2
0
1
2
1
1
1
1
0
2
0
1
4
1
1
2
1
1
1
2
1
0
1
1
1
1
2
0
0
0
1
1
1
2
1
2
0
1
1
1
2
1
1
1
2
1
2
2
1
2
0
1
1
1
0
2
2
1
0
1
1
2
1
2
0
1
1
1
1
1
1
1
1
1
2
2
1
2
0
0
1
2
2
0
1
1
1
2
3
0
2
2
1
0
1
2
2
2
0
0
0
0
1
2
1
0
1
0
1
1
1
0
1
2
2
0
2
2
1
2
1
1
1
1
1
1
0
1
2
1
2
0
0
2
1
0
0
1
0
1
2
1
0
0
1
1
1
0
1
2
1
0
1
0
1
0
0
1
1
1
1
2
1
0
0
1
0
1
1
1
1
2
3
1
2
1
2
1
0
2
1
1
1
1
1
1
0
2
2
1
2
1
0
1
2
0
2
2
1
1
1
1
2
1
3
1
0
1
1
0
0
1
0
1
1
2
2
1
2
1
1
1
1
2
2
2
0
1
1
1
0
2
1
1
0
2
0
2
1
0
1
1
2
1
2
0
2
2
1
1
0
0
0
2
1
1
2
2
1
1
1
2
0
2
1
1
1
0
1
2
2
1
3
0
1
1
1
0
1
2
0
0
1
1
2
0
2
0
2
1
1
1
1
2
2
2
0
1
2
1
0
0
1
0
1
1
0
0
0
1
0
1
2
0
1
0
0
1
1
1
2
2
0
0
2
1
1
1
1
1
2
2
2
2
0
2
2
1
2
1
1
1
1
2
1
1
1
1
3
0
2
0
2
1
1
1
2
1
2
1
1
2
0
1
1
0
1
0
2
1
2
1
0
1
0
1
1
1
1
2
1
2
0
1
0
0
0
2
1
1
2
0
1
1
0
2
1
2
1
1
0
1
1
1
1
2
0
0
2
1
0
2
1
1
2
1
1
1
0
0
1
2
1
2
0
2
1
0
1
0
1
2
1
0
2
1
1
1
2
1
0
2
1
1
1
0
0
1
0
0
0
0
0
1
1
1
1
2
1
2
2
1
1
2
1
0
2
0
1
1
1
0
0
2
1
2
0
1
0
1
1
1
0
0
2
1
0
2
1
2
1
1
1
2
2
1
1
1
1
1
0
1
1
1
1
2
1
2
0
1
1
3
1
2
1
0
2
0
0
1
2
1
0
0
1
0
0
2
2
2
1
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
0
1
1
2
0
1
1
1
1
0
1
0
0
1
1
0
0
1
1
2
1
0
0
2
1
1
1
2
1
1
0
1
1
0
1
1
1
1
3
1
0
2
3
1
1
0
1
0
1
1
2
1
1
2
0
1
0
0
1
2
1
1
1
2
1
2
0
1
2
2
2
0
0
2
0
2
0
0
1
1
1
0
0
2
1
0
2
0
2
0
0
0
1
1
0
1
0
1
0
0
1
1
2
1
0
1
1
0
1
2
0
0
2
1
1
1
2
1
1
2
2
1
1
1
2
1
1
1
1
0
1
3
1
0
1
1
2
2
2
1
1
2
2
0
1
0
0
1
1
0
1
1
2
0
1
0
0
1
2
2
0
1
0
0
2
1
2
1
2
0
2
2
1
1
1
0
0
1
1
1
1
2
1
2
1
1
1
1
0
1
0
1
1
1
0
0
1
1
0
1
0
0
0
1
0
1
2
0
1
0
1
1
2
1
0
0
1
0
1
0
2
1
1
2
0
2
2
0
1
2
2
0
1
0
0
0
1
0
0
0
0
1
1
0
1
1
1
2
2
2
0
0
1
1
2
1
1
1
1
1
1
0
0
0
0
0
1
0
1
1
2
1
1
1
2
0
2
0
2
1
2
0
0
1
0
1
1
2
2
1
0
1
1
1
2
0
1
1
2
1
2
0
1
3
0
1
1
2
0
0
1
2
1
0
0
0
2
0
1
0
1
2
1
1
0
1
1
2
1
0
1
2
0
0
0
1
1
1
1
2
1
1
3
0
1
0
2
2
0
2
0
0
1
1
1
2
0
1
1
1
1
0
2
0
0
1
1
2
1
2
1
0
1
1
1
1
1
0
0
1
1
1
1
0
1
0
1
2
1
1
1
1
1
1
1
1
0
1
1
5
1
1
1
0
1
2
1
2
1
2
1
2
1
2
2
0
0
1
0
1
1
1
0
0
0
1
2
1
2
0
2
1
1
1
2
0
2
1
2
1
0
0
0
2
1
1
2
1
1
0
1
2
1
1
1
1
0
0
2
1
0
0
0
1
0
1
2
2
0
1
4
1
1
1
1
2
2
0
0
1
2
1
1
0
1
1
1
2
1
1
1
0
1
2
1
1
0
1
1
1
1
2
0
0
2
1
1
1
2
0
2
0
1
0
1
1
1
2
1
1
1
1
1
2
2
0
2
1
1
1
0
1
1
0
1
0
0
1
2
2
1
1
1
1
2
0
1
2
2
1
2
3
1
1
1
2
1
1
1
1
1
1
1
1
0
1
2
1
1
2
1
1
0
1
0
1
0
1
2
0
1
1
2
0
0
1
0
1
1
1
1
0
0
2
1
0
2
1
1
1
1
1
1
1
2
1
0
2
1
2
1
0
1
2
1
0
0
2
0
1
0
0
1
2
2
2
1
1
1
2
0
2
1
0
2
1
1
1
0
2
1
2
1
0
1
0
0
3
1
0
2
0
1
0
1
1
3
1
1
1
0
1
1
2
1
0
1
0
1
0
1
1
1
0
0
1
2
0
0
1
2
1
1
1
1
1
1
0
1
0
0
0
1
1
0
0
1
2
1
1
0
1
1
0
1
0
2
1
3
1
1
1
1
1
1
2
1
0
1
0
2
2
1
0
2
2
0
1
2
0
1
2
0
0
0
2
2
1
0
1
1
1
2
1
2
1
1
2
1
1
0
0
0
2
0
2
1
2
0
1
1
2
0
2
0
1
0
0
0
2
0
1
0
1
1
1
0
0
1
1
2
0
0
1
1
1
1
1
0
1
0
1
1
1
2
2
1
1
1
1
1
1
1
1
1
0
0
0
1
1
1
0
1
0
2
2
1
2
1
0
2
0
0
2
2
0
1
2
2
2
1
1
2
2
1
2
0
0
0
0
1
2
1
1
0
1
1
1
0
1
2
0
2
2
2
0
1
1
1
0
1
2
2
1
3
1
0
1
1
0
1
1
1
1
0
2
0
1
1
0
0
0
1
1
2
2
1
1
2
0
2
1
0
1
1
5
1
1
2
1
2
0
1
2
1
1
1
0
1
0
0
2
0
2
0
1
1
1
0
0
1
1
3
1
1
0
1
1
1
1
1
0
0
0
1
1
1
0
2
1
0
1
1
1
1
1
1
0
0
1
1
1
1
1
2
1
1
1
0
1
3
1
1
2
2
2
2
0
0
1
2
1
1
1
1
0
1
1
1
1
1
2
1
1
2
2
1
1
0
0
1
0
1
2
0
2
0
0
1
0
1
1
1
1
1
1
3
1
1
1
1
1
2
0
2
0
0
1
1
1
1
2
0
0
1
1
1
1
1
1
2
1
0
1
0
1
0
2
0
0
1
1
1
0
1
2
1
1
0
0
1
1
1
1
1
1
0
1
1
2
2
2
1
0
1
0
1
1
0
1
1
1
0
0
0
0
1
1
2
2
0
0
0
1
1
2
0
0
0
2
0
0
2
2
1
0
1
1
0
1
3
1
0
2
1
1
0
1
1
0
1
2
1
1
1
2
1
1
0
1
0
1
2
2
0
1
4
0
1
0
0
0
2
2
1
1
1
1
1
1
1
2
2
0
2
0
1
0
3
1
1
1
1
2
1
1
1
1
2
0
1
2
2
1
0
1
1
1
2
0
0
1
1
2
1
1
0
0
1
1
0
0
1
0
2
2
0
0
0
1
0
2
1
1
1
2
1
1
1
0
1
2
1
1
1
1
2
1
1
1
1
0
2
2
1
1
1
0
2
1
0
1
1
0
0
0
0
1
0
1
0
1
0
1
1
1
0
2
1
1
2
0
0
0
1
1
0
2
1
1
1
1
1
2
1
1
0
0
2
1
0
2
2
0
2
2
0
0
1
2
1
1
0
0
1
1
1
0
1
0
1
0
1
1
1
1
2
0
0
0
2
1
0
2
1
2
0
1
1
0
2
0
0
2
2
1
1
1
1
0
0
0
2
1
2
1
1
2
0
1
1
1
0
0
1
0
1
1
1
0
2
1
1
2
1
2
2
1
0
1
1
0
1
1
1
1
2
1
1
1
1
1
0
0
1
1
2
1
1
1
2
1
1
0
0
2
0
1
1
2
0
2
0
1
2
2
0
1
1
1
2
0
0
1
2
1
0
1
1
2
0
0
1
1
0
1
0
2
1
1
2
1
1
2
1
2
0
2
2
2
1
1
1
0
2
0
1
0
1
2
1
1
1
2
1
2
4
2
0
2
1
2
1
3
1
2
0
1
1
1
1
0
0
0
1
1
0
1
2
1
0
2
0
0
1
1
1
1
1
1
1
1
1
1
2
1
2
0
2
0
2
1
1
1
1
1
0
1
1
1
2
1
2
1
1
1
1
1
1
0
2
0
1
2
1
1
1
2
1
1
1
0
1
1
1
1
1
0
2
1
1
1
0
1
2
1
1
2
2
0
0
2
1
1
0
0
4
1
2
1
1
1
1
1
0
1
2
0
2
0
2
0
1
1
1
1
1
1
1
2
1
1
2
1
1
0
1
0
1
0
0
0
0
1
1
2
1
1
1
1
1
2
0
1
1
0
2
0
1
2
1
1
1
1
0
2
2
1
1
1
1
1
0
1
2
1
2
1
0
1
2
2
1
2
0
1
2
0
1
0
1
2
0
1
0
1
2
1
1
0
1
1
1
1
2
1
1
2
1
0
2
0
1
0
1
1
2
2
1
0
2
1
1
1
2
0
0
0
1
2
1
1
1
1
1
1
1
1
1
1
0
1
1
1
0
1
2
0
1
1
0
0
0
1
2
1
1
0
2
1
0
1
1
1
0
1
1
1
1
1
2
1
1
1
1
1
1
0
1
0
1
1
1
1
1
0
2
2
1
0
0
1
2
1
1
1
0
1
0
5
2
1
1
1
0
2
1
0
1
0
2
0
0
1
1
0
1
2
1
1
2
1
1
0
0
0
1
1
0
2
1
2
2
1
1
0
0
2
0
0
1
9
0
1
1
2
1
0
0
1
0
1
1
1
0
1
2
1
0
2
1
0
1
2
1
2
0
0
0
2
0
0
0
1
5
0
1
1
1
2
0
1
4
1
2
2
1
0
0
0
1
1
1
2
2
0
1
1
1
1
1
0
0
2
2
1
1
0
0
0
0
1
1
3
1
1
1
2
1
0
1
0
0
1
2
1
0
0
2
1
1
2
1
0
0
1
1
2
1
0
2
2
1
1
0
0
1
0
0
1
0
2
0
1
1
2
0
0
1
0
2
1
0
1
1
1
1
0
1
1
2
1
2
0
1
0
1
2
1
1
1
2
1
1
1
1
0
1
1
0
1
2
0
2
0
1
1
1
0
1
1
1
3
2
1
0
1
1
0
2
2
0
0
1
1
1
0
2
1
1
2
1
1
2
1
0
1
2
1
0
0
1
1
2
1
0
0
0
2
0
2
1
2
1
0
1
2
1
2
1
1
2
2
0
0
1
2
1
0
2
1
0
1
1
1
0
1
1
1
1
1
1
0
0
1
1
1
0
0
1
1
1
1
1
2
2
1
1
0
1
1
1
0
1
1
0
1
1
1
0
1
0
1
1
0
2
1
0
0
1
0
1
1
2
0
2
1
0
2
0
3
0
0
1
1
1
0
1
1
1
2
1
1
2
1
0
0
0
1
1
1
1
0
1
0
1
0
0
0
1
1
1
2
1
1
0
0
2
0
2
1
1
0
0
0
0
1
1
1
2
0
0
1
1
1
2
1
2
2
0
1
2
1
0
1
0
2
0
0
1
1
1
1
0
1
1
0
2
1
0
1
0
0
1
2
0
2
0
2
2
1
2
1
0
0
1
1
1
2
0
1
1
1
2
2
0
0
2
2
0
1
0
2
1
1
1
0
1
1
1
1
2
1
0
1
0
1
1
1
0
1
2
9
2
0
1
1
1
0
1
1
1
1
1
1
1
2
1
1
1
2
1
0
1
1
0
1
0
1
1
0
1
2
2
1
0
0
0
1
0
2
2
0
1
1
1
1
0
1
0
1
1
0
1
1
2
2
2
1
0
2
1
1
1
0
1
0
2
1
0
1
1
0
1
1
2
0
0
0
1
1
1
3
1
2
1
1
1
0
1
1
1
2
2
1
2
1
1
1
1
2
1
0
1
2
1
1
1
0
1
2
0
2
2
0
1
0
1
2
1
0
2
1
0
2
1
0
0
0
1
0
0
1
1
1
1
0
1
0
1
1
1
1
0
2
0
1
2
0
1
2
1
0
2
0
0
1
1
2
2
0
1
0
1
0
1
2
1
0
0
1
1
1
1
1
1
1
2
0
1
1
1
1
1
0
2
0
0
1
1
1
0
0
0
1
1
1
1
0
0
0
1
2
0
1
2
1
1
1
1
1
2
1
1
2
1
2
1
1
1
0
1
1
1
1
1
1
2
2
1
1
2
2
2
3
1
1
1
1
0
1
2
1
1
1
0
1
1
2
1
2
1
1
1
1
2
0
0
0
0
1
2
1
0
1
1
1
1
1
1
1
1
1
1
0
1
1
1
0
1
1
1
1
1
0
2
1
1
1
1
2
1
1
2
1
0
1
0
2
1
1
1
2
1
0
2
0
0
0
4
2
2
0
1
1
0
0
1
2
0
2
1
0
1
0
0
1
0
1
1
2
1
1
1
1
0
2
1
1
2
1
2
0
2
1
1
1
1
1
0
1
2
2
0
2
0
2
1
2
1
0
1
2
2
1
0
0
2
1
0
1
0
1
2
1
1
0
0
1
1
1
0
0
1
0
2
2
0
1
1
1
0
2
1
2
1
0
0
0
0
1
2
2
1
1
0
0
1
1
2
1
2
1
0
1
0
1
2
0
1
1
1
0
0
1
0
0
0
1
0
2
1
0
1
1
1
1
0
1
1
0
0
2
0
2
1
0
2
0
2
0
1
0
1
2
3
1
1
1
2
0
1
1
1
1
0
0
2
1
0
1
0
1
1
0
1
1
1
2
0
0
2
2
0
2
1
1
1
0
1
1
0
2
2
0
0
0
2
1
2
1
1
2
1
1
1
3
0
1
1
1
1
1
0
0
1
0
1
0
1
2
1
2
1
2
0
1
1
1
0
2
1
2
0
1
0
2
1
1
2
0
0
1
1
1
1
2
1
2
0
1
0
1
1
1
1
0
1
0
0
1
1
0
2
0
0
1
2
2
1
1
1
0
1
1
1
2
0
1
1
0
1
0
0
1
1
2
1
2
1
1
0
1
0
1
2
1
0
1
1
2
2
1
0
1
1
1
0
1
0
1
2
1
2
0
2
1
2
0
0
1
1
1
0
0
1
0
2
1
0
1
1
1
2
1
2
1
2
1
1
1
0
1
1
1
0
2
1
2
1
1
1
1
0
1
1
2
2
2
2
0
1
1
1
0
0
2
0
2
0
2
2
2
0
1
2
0
0
2
0
2
2
2
0
1
1
0
1
2
0
0
1
0
2
0
2
1
1
1
0
1
2
0
1
2
0
1
1
1
1
2
1
1
3
3
1
1
1
1
1
1
0
1
1
1
0
1
1
0
2
2
0
1
2
1
1
0
0
1
2
1
2
2
0
0
1
1
2
2
1
0
2
1
0
1
2
2
1
0
0
2
1
1
2
1
2
1
1
1
0
0
1
2
0
2
1
1
1
1
1
1
0
0
1
1
0
1
1
2
0
1
2
1
0
1
2
1
1
1
2
4
2
1
0
1
0
2
1
1
0
1
1
1
0
1
2
2
0
0
0
0
1
4
0
2
0
0
1
2
1
0
3
2
0
1
0
1
2
2
1
2
0
0
2
2
1
2
0
1
1
1
3
0
1
2
1
0
0
0
1
1
3
1
0
1
1
1
3
1
0
1
1
0
1
1
0
1
2
0
2
2
1
1
2
1
2
2
0
1
0
2
2
1
1
0
2
0
2
2
1
2
2
0
0
1
0
2
2
0
1
1
1
1
1
1
2
2
1
0
0
1
1
1
0
2
2
2
1
1
2
0
0
1
1
1
1
2
1
0
0
0
0
1
1
2
2
1
1
2
1
0
1
0
1
2
2
0
1
0
2
1
1
1
1
2
4
1
2
0
0
0
2
0
1
1
0
2
1
1
2
2
1
1
1
0
0
2
1
1
0
0
1
1
1
2
1
1
2
1
2
0
2
0
1
1
1
0
1
1
1
1
0
1
1
1
2
1
0
1
1
1
1
1
1
0
2
1
2
2
0
1
0
1
1
1
1
1
1
1
0
3
2
1
0
2
0
2
2
1
1
2
1
0
0
2
1
1
2
2
0
1
1
0
1
2
1
0
1
1
0
0
1
1
2
0
0
0
1
2
0
2
1
0
2
2
1
0
2
2
1
2
2
0
2
2
1
2
2
1
2
0
2
1
2
0
1
2
1
1
4
1
2
1
0
1
2
1
2
2
1
1
1
2
1
2
1
3
1
0
1
2
0
1
1
1
0
1
1
2
0
2
2
1
2
1
1
2
2
0
1
0
1
1
1
1
1
1
0
2
1
1
0
2
2
0
1
1
1
1
0
0
1
0
0
2
1
1
0
1
1
1
2
0
1
1
0
0
1
2
0
0
1
1
1
2
1
0
1
2
1
2
1
1
0
0
0
1
1
2
2
2
2
2
1
1
1
2
1
1
1
0
1
0
2
2
0
2
1
0
0
0
0
1
1
1
0
1
2
0
2
1
0
1
2
0
1
1
1
2
1
2
0
1
0
2
1
1
0
2
3
1
0
1
2
0
1
0
0
1
1
2
2
1
2
0
1
1
1
1
2
1
1
1
2
0
1
2
1
1
1
1
0
2
1
2
0
2
1
0
0
1
2
1
3
1
1
0
1
1
0
0
0
0
0
1
1
1
0
2
1
1
1
2
1
2
1
0
1
1
1
1
0
0
2
1
1
2
1
1
1
1
1
1
2
1
0
0
2
3
2
0
1
1
2
2
1
1
1
1
2
2
1
2
0
2
1
2
0
2
0
1
2
1
0
1
1
1
1
0
1
0
1
1
2
1
2
0
1
1
1
1
1
0
0
1
0
1
1
1
2
1
0
1
1
1
0
0
0
2
1
1
2
0
1
2
1
2
2
1
1
1
2
1
0
0
0
0
0
0
1
1
1
2
1
1
0
2
0
2
1
1
1
1
1
1
1
1
0
0
0
1
0
1
0
1
1
1
2
1
1
1
2
0
1
1
2
0
0
1
1
1
1
1
1
1
1
1
0
0
0
2
1
1
2
2
1
1
1
2
4
0
0
0
1
0
0
1
0
0
2
1
1
1
0
2
0
1
0
0
2
1
1
0
0
0
1
1
0
2
1
2
2
2
1
1
0
3
0
0
0
0
2
1
1
0
0
0
0
1
1
0
1
0
0
2
2
0
2
2
2
0
0
0
1
1
2
1
1
0
1
0
2
0
0
1
1
2
0
0
0
0
0
1
1
1
1
1
1
1
1
2
1
2
1
2
1
0
1
0
1
1
1
1
0
1
1
1
0
2
1
2
1
1
1
1
1
1
0
1
1
1
1
1
0
1
0
0
0
2
1
1
0
2
0
1
2
1
0
1
2
0
3
0
1
1
2
1
2
1
2
2
1
1
1
0
0
1
2
0
0
0
1
0
1
2
1
1
1
2
0
1
2
4
2
0
0
1
1
1
1
0
1
2
1
1
1
1
1
0
1
0
1
1
1
2
0
1
1
1
2
2
1
1
1
1
2
0
1
1
2
1
0
1
0
1
1
0
1
1
0
2
1
1
1
1
0
1
2
1
1
1
0
1
2
1
0
1
0
0
0
2
1
0
2
0
1
1
2
2
0
1
0
1
0
1
1
0
1
0
2
3
0
1
0
2
1
0
1
2
1
0
1
0
2
2
1
1
1
1
0
1
0
1
0
0
1
0
1
2
0
1
0
1
0
1
1
2
1
1
1
1
4
1
0
0
1
1
0
1
0
0
0
1
1
0
1
1
2
1
1
1
0
1
2
0
0
1
1
0
1
0
0
2
1
1
1
1
2
1
1
1
2
1
2
2
0
0
2
0
0
2
2
1
1
0
0
0
0
1
0
1
2
1
1
0
4
1
1
1
2
1
0
1
0
1
0
1
0
1
1
1
1
1
2
2
0
0
0
2
1
2
0
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
0
2
2
0
1
0
1
1
3
2
1
0
1
1
0
1
1
0
2
1
1
0
0
0
1
1
1
1
2
2
1
0
0
1
2
0
1
0
1
1
2
2
1
1
1
1
2
1
2
2
1
0
0
2
1
1
0
1
1
1
1
1
1
2
1
1
2
2
1
1
0
4
1
0
1
2
1
0
0
2
2
2
0
1
2
0
2
0
1
1
1
1
1
1
0
2
1
1
1
1
1
2
2
2
0
2
1
1
1
1
2
0
0
1
1
2
1
2
3
0
1
0
0
2
1
1
0
2
1
0
1
1
1
1
1
0
0
1
2
1
2
0
1
0
1
2
0
1
2
2
0
0
0
1
1
1
3
2
2
1
0
0
1
0
1
2
1
1
1
1
0
1
2
1
0
0
1
1
1
0
1
2
1
1
0
1
1
0
1
1
1
2
1
1
1
2
1
1
2
2
0
0
1
1
0
1
1
0
2
2
1
0
1
2
2
0
1
1
1
0
1
0
2
1
1
1
0
1
1
0
1
2
1
1
0
2
0
1
1
0
0
0
1
1
1
1
2
2
1
1
0
1
1
2
0
1
0
2
0
0
1
1
0
1
0
1
0
0
1
2
1
1
0
1
1
1
2
2
0
0
3
1
1
0
1
1
0
0
0
1
0
1
0
1
0
0
0
1
1
1
1
0
2
2
1
1
2
1
2
1
1
1
0
2
1
2
0
0
0
2
0
2
1
0
1
1
1
1
1
1
0
0
1
1
1
2
1
1
1
0
2
0
2
1
0
1
2
0
1
2
0
1
0
1
1
0
0
0
1
1
1
1
1
2
1
1
1
1
1
0
1
0
2
0
2
0
0
1
0
2
1
1
2
0
0
0
1
1
1
2
1
1
1
0
2
2
2
2
1
0
1
0
2
0
0
6
1
0
1
1
1
1
2
1
1
1
0
1
1
0
2
2
2
1
0
0
1
1
2
1
1
1
1
1
0
1
0
2
1
1
1
1
0
0
1
0
0
0
1
1
1
1
2
2
1
1
1
0
0
0
2
1
1
1
2
1
2
2
2
2
2
2
1
1
1
0
1
0
1
1
1
1
1
2
1
1
0
1
1
1
1
1
1
1
0
2
0
2
1
1
2
1
2
0
1
1
1
0
2
1
1
0
1
0
1
0
1
1
2
1
1
0
1
1
0
1
2
1
1
2
1
0
2
2
1
2
2
2
0
1
1
1
1
2
1
1
1
1
0
1
1
1
2
1
1
3
1
0
1
1
0
0
1
1
2
0
2
0
1
2
1
0
0
0
2
0
0
0
1
0
0
1
1
1
2
2
1
2
1
0
2
0
1
0
2
0
0
1
1
2
2
1
0
0
1
1
0
2
1
0
1
1
0
2
0
1
1
1
0
0
1
0
1
2
1
0
1
1
1
2
1
1
1
1
2
1
2
1
2
1
1
1
2
1
2
3
0
1
1
1
1
2
1
1
2
1
1
1
1
2
0
0
1
2
0
1
1
1
2
0
2
0
2
0
1
0
2
2
1
1
1
1
0
1
1
1
1
1
2
1
2
2
2
1
0
2
0
1
1
0
0
1
0
0
2
1
1
1
2
1
1
2
1
0
0
0
2
1
1
0
1
0
1
2
1
1
3
1
2
1
1
2
0
2
1
1
1
0
2
1
2
0
1
1
1
1
0
0
1
2
0
1
1
2
1
2
0
2
2
1
1
0
1
1
1
0
2
2
2
3
1
1
0
1
2
0
2
1
0
0
1
1
1
1
1
1
2
0
1
1
0
2
1
2
1
1
0
0
2
1
1
2
0
2
0
0
0
0
2
0
0
1
1
1
1
1
2
0
1
1
1
2
2
0
0
1
1
0
1
0
1
2
1
2
1
1
1
1
2
1
1
1
1
1
2
2
1
0
1
0
2
2
1
1
1
1
0
1
1
1
1
0
2
0
1
0
1
1
2
2
2
0
2
0
1
1
0
2
0
0
0
1
2
0
1
1
2
0
2
1
2
1
1
1
0
1
1
0
2
2
2
1
1
1
2
1
1
4
1
2
0
0
1
2
0
0
0
0
1
4
2
0
1
0
1
1
5
2
0
1
1
1
2
1
2
0
2
1
1
0
1
1
0
0
0
1
0
1
0
0
1
0
2
1
0
1
0
1
1
2
1
2
0
1
1
0
0
1
2
1
3
1
0
1
1
2
0
1
1
0
1
1
1
1
2
0
0
1
1
1
1
0
0
1
0
1
1
1
0
0
1
1
0
2
1
1
1
1
0
1
0
1
0
0
0
1
1
4
1
1
0
1
1
2
1
1
0
2
0
1
1
2
0
2
0
2
0
2
2
1
0
0
1
0
0
1
1
1
0
3
0
0
2
2
1
1
1
1
2
0
1
1
1
0
1
4
1
1
1
1
0
1
1
0
1
0
1
0
0
2
0
2
0
2
0
0
1
2
1
2
1
2
1
0
0
0
2
1
1
1
1
1
0
1
0
1
1
0
1
0
1
0
1
1
0
1
1
1
1
1
2
2
1
1
2
1
1
2
2
1
1
1
1
0
1
1
0
0
0
1
0
0
1
2
1
0
1
1
2
1
1
0
2
1
1
2
1
1
1
0
1
1
1
1
0
2
0
1
1
2
0
0
2
1
0
1
0
1
2
2
1
1
0
1
1
1
0
1
0
0
0
0
2
0
1
2
2
2
0
2
1
1
1
1
1
1
1
1
0
1
1
2
2
2
2
1
1
1
0
1
0
1
1
1
0
2
1
0
0
0
1
0
2
1
1
1
1
0
0
0
1
1
0
0
2
0
2
1
1
2
0
3
0
0
1
2
0
0
0
1
2
1
1
2
0
0
1
1
1
1
1
1
2
1
2
2
1
0
1
1
1
1
1
1
2
0
0
0
0
0
1
1
2
1
2
1
0
0
1
0
0
1
1
1
0
1
2
1
2
2
1
0
1
0
2
1
1
0
1
1
1
1
1
0
0
2
1
0
1
0
2
1
1
1
1
1
1
1
1
2
0
0
0
1
0
1
1
2
0
1
1
1
2
1
2
2
2
0
1
1
0
1
0
1
1
2
1
1
1
1
0
1
1
0
0
0
2
1
2
0
1
1
2
1
1
2
0
0
1
0
1
1
1
1
1
1
2
1
2
2
1
1
2
2
1
1
1
0
1
1
1
1
0
1
1
1
0
1
2
1
0
1
1
2
1
1
2
2
1
0
1
0
1
1
1
1
1
1
1
2
1
1
1
2
1
1
0
1
1
0
1
2
1
1
1
1
2
1
1
1
1
1
1
0
1
1
1
0
2
1
2
0
1
0
1
2
2
1
0
1
1
1
1
1
1
0
1
0
0
2
2
0
2
1
1
2
1
1
1
0
1
2
2
2
1
1
0
0
2
0
1
1
0
1
1
0
0
0
2
2
2
1
2
0
1
2
2
1
1
2
1
1
0
2
1
2
0
0
2
0
1
1
0
1
1
1
1
1
1
1
1
2
0
1
0
0
0
2
2
1
1
0
0
0
1
0
1
0
1
2
1
0
1
1
1
1
0
1
1
0
1
2
1
1
0
1
2
0
1
1
2
0
2
2
0
2
1
2
1
2
1
2
1
1
0
0
1
0
2
1
2
1
1
0
0
1
1
0
2
1
1
1
2
1
0
1
0
1
1
0
1
0
1
2
1
2
2
1
0
0
0
2
1
1
1
2
0
0
1
1
1
0
1
0
0
2
1
1
1
1
2
0
1
0
1
0
1
0
1
0
1
1
1
1
0
1
1
1
0
1
2
1
0
1
0
1
0
1
1
2
2
2
1
1
3
0
1
1
1
1
0
1
1
0
1
0
0
1
2
2
0
0
1
1
0
0
1
1
1
1
2
1
1
2
1
2
5
0
1
0
2
0
2
1
1
0
2
1
0
0
2
1
1
1
0
0
2
0
1
1
2
2
2
1
0
1
2
2
0
0
1
2
1
0
1
0
0
0
1
1
2
2
0
1
0
1
1
1
0
0
1
1
1
1
1
1
1
0
1
1
1
2
0
2
0
1
1
1
1
0
2
2
1
1
1
0
1
2
1
1
1
1
2
1
1
1
2
1
0
2
0
1
0
2
2
1
2
1
1
1
0
2
0
2
2
1
1
2
1
0
1
1
1
1
1
2
1
1
0
1
1
1
0
1
1
2
0
1
2
1
0
0
0
1
1
1
2
2
1
0
1
1
1
1
1
2
1
0
1
2
0
1
2
1
2
2
1
0
0
1
1
0
0
2
2
0
1
1
2
1
1
1
0
0
1
1
1
1
0
1
0
1
1
1
1
0
1
0
0
0
1
1
2
0
1
2
0
2
2
0
1
0
1
2
0
1
1
0
0
0
0
0
2
1
2
0
0
2
1
0
2
1
0
1
2
3
1
2
1
1
1
2
0
1
1
0
1
1
0
2
0
0
1
0
1
1
0
2
1
0
1
3
1
0
1
2
0
0
1
2
0
2
1
1
0
1
1
1
2
1
1
2
0
1
2
0
1
0
1
1
1
1
1
1
0
0
1
1
2
1
1
1
1
0
0
0
2
0
1
1
1
1
1
1
0
1
2
2
1
2
3
0
0
2
1
1
1
1
1
2
2
2
1
0
1
1
1
1
1
1
1
1
0
0
1
1
0
2
0
1
1
1
2
1
1
1
1
1
1
0
1
2
0
0
0
2
0
2
2
1
1
2
1
2
0
1
0
2
1
1
2
1
0
1
0
1
0
0
1
0
0
1
0
5
0
1
1
1
0
1
2
0
1
2
0
0
2
1
1
2
1
1
3
0
1
2
0
0
0
0
0
1
2
1
2
1
2
2
0
1
2
1
1
1
1
1
0
1
2
1
1
0
1
1
2
0
1
1
1
1
2
2
0
2
1
2
0
1
1
3
2
0
1
1
1
1
0
1
0
1
6
1
1
1
1
1
0
0
2
1
1
3
2
2
0
1
1
1
1
2
2
2
0
0
1
2
2
2
1
1
1
1
1
0
0
0
0
0
2
0
1
1
3
0
1
1
1
0
1
2
1
0
1
1
0
0
1
1
0
2
0
1
1
2
1
1
2
1
1
1
1
0
2
0
1
2
1
2
1
0
0
0
2
1
0
1
2
1
1
1
1
0
2
0
0
0
1
0
1
1
1
1
1
0
1
0
0
1
0
2
1
2
1
2
1
0
1
5
0
1
0
2
0
1
2
2
1
2
1
0
2
1
1
0
1
0
1
1
1
1
1
1
1
2
0
2
0
0
1
0
0
0
1
2
1
2
1
1
1
1
1
2
0
1
1
0
1
2
2
0
4
1
1
1
1
1
0
1
0
2
4
0
1
1
2
1
1
0
4
0
1
2
0
1
1
2
0
1
2
2
0
2
1
1
0
0
1
0
1
1
1
1
2
0
1
1
3
2
0
1
0
1
0
2
0
0
1
0
1
0
1
0
2
1
2
1
0
0
1
2
1
2
1
0
2
0
1
0
1
1
1
1
1
1
2
2
0
2
1
1
2
1
1
0
1
1
1
1
2
2
2
1
1
1
2
2
1
2
2
0
2
0
1
1
2
2
1
1
1
1
1
1
1
1
2
1
1
0
1
1
1
1
1
1
2
1
0
2
2
2
1
1
0
1
0
1
1
2
0
0
0
1
1
1
1
2
1
0
0
1
0
1
1
0
2
2
0
1
1
2
0
2
2
1
1
1
0
1
0
1
1
1
1
3
0
1
1
1
3
3
1
1
1
1
1
1
0
1
1
1
1
0
2
0
2
0
2
1
0
1
0
1
2
0
1
1
1
1
1
0
1
1
0
0
1
0
0
0
2
0
2
1
1
1
1
0
0
0
0
2
1
0
3
0
2
1
1
2
1
1
0
1
1
0
1
0
0
1
1
1
1
0
0
0
1
1
1
1
1
1
0
1
0
1
2
1
1
2
0
1
1
1
1
1
0
1
1
1
1
0
2
0
2
1
3
0
2
2
1
1
2
0
1
1
0
2
1
1
1
1
1
1
2
1
3
0
1
0
2
2
0
0
1
2
1
2
2
1
0
0
1
1
0
0
3
1
1
2
1
0
2
2
0
2
1
1
1
0
2
0
3
1
1
2
2
1
2
0
1
1
2
0
2
1
0
1
2
0
1
1
2
1
1
0
1
1
0
2
0
1
2
0
1
0
2
2
1
2
1
1
0
1
1
1
1
2
1
1
0
2
1
0
1
0
1
1
0
0
2
1
2
2
1
0
0
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
1
2
1
1
1
0
1
1
2
1
2
1
1
2
0
1
2
1
1
0
2
1
1
0
1
0
2
1
0
2
1
0
1
1
2
0
1
1
1
0
1
1
0
2
2
2
1
1
0
1
1
1
0
2
0
1
1
1
1
1
1
1
1
1
0
1
0
2
0
2
0
1
1
1
1
2
2
0
1
1
1
2
1
1
2
1
1
2
1
0
2
1
0
2
0
1
0
0
2
1
1
1
0
1
0
0
1
1
2
1
0
0
1
2
1
1
1
1
1
2
1
1
1
1
1
1
0
0
1
1
0
0
0
2
1
0
1
1
0
1
1
2
2
2
2
1
2
0
1
0
1
1
0
2
2
1
1
1
0
1
0
1
1
1
0
0
1
1
0
2
2
0
2
0
1
1
0
0
0
1
2
0
0
1
0
1
0
2
2
0
2
2
1
2
1
1
2
1
0
1
1
1
1
3
2
2
0
2
0
0
1
1
0
0
2
1
1
1
1
0
1
1
2
1
1
1
0
1
1
2
0
1
0
0
0
2
1
0
1
1
1
2
0
2
1
1
1
0
0
0
0
1
1
0
3
0
0
2
2
2
0
4
0
0
1
1
2
1
0
2
1
1
0
0
1
0
1
1
0
0
1
0
2
1
1
1
0
2
2
1
0
1
0
1
1
2
1
1
1
1
2
1
1
0
1
0
1
2
0
1
2
2
1
1
1
2
1
1
1
1
2
2
1
1
2
2
1
0
1
0
1
1
1
2
1
1
0
1
1
1
2
1
1
1
1
0
1
2
0
2
1
2
0
1
1
1
0
1
0
0
2
1
0
0
1
2
2
2
1
0
0
2
0
0
2
1
1
1
0
0
1
2
1
1
2
1
0
2
0
1
1
1
2
0
0
0
1
1
2
1
0
0
1
1
0
0
2
0
1
1
1
0
1
2
1
0
1
0
1
1
1
0
0
1
2
1
1
1
2
0
2
0
1
0
1
1
1
1
0
2
1
0
2
0
1
2
2
0
0
1
1
1
0
1
0
1
0
0
0
2
1
0
2
2
1
1
0
1
1
1
1
2
1
1
2
1
1
0
1
2
2
0
1
1
1
1
1
1
2
0
1
1
0
0
0
0
1
0
1
0
1
1
0
1
1
2
0
0
1
1
1
0
1
0
1
0
3
1
0
2
1
0
2
0
0
2
2
1
1
1
1
1
2
2
0
1
0
0
0
1
1
0
1
2
1
2
1
2
2
1
2
0
0
2
0
1
1
1
0
1
0
0
2
1
1
1
2
0
2
1
1
1
2
2
2
1
0
2
1
0
2
4
2
0
2
0
1
1
0
1
2
1
0
1
1
1
0
1
0
1
1
0
0
2
1
2
1
1
1
0
0
2
0
1
2
1
1
2
0
0
1
0
1
0
1
1
0
1
0
0
2
2
0
1
0
0
0
1
2
0
0
1
1
0
2
0
1
0
1
1
0
2
0
2
2
0
2
2
1
1
2
0
1
1
1
2
2
0
2
1
0
0
0
1
1
0
2
2
0
2
1
3
0
1
0
0
2
1
1
2
2
0
1
1
1
1
2
1
1
1
1
2
0
2
1
2
1
1
1
1
1
2
1
1
2
0
1
1
2
1
1
1
1
1
1
0
1
1
2
1
1
1
1
0
2
2
1
1
1
0
1
1
1
1
2
2
0
0
1
0
1
2
1
1
2
0
1
1
2
2
2
2
1
1
0
1
0
0
1
0
2
1
0
1
2
1
0
2
0
2
1
2
1
1
2
2
0
1
0
1
0
0
1
1
0
2
1
1
1
0
1
1
2
3
1
0
1
2
0
1
1
1
1
0
2
1
2
2
1
1
1
1
0
1
1
0
2
1
0
2
1
1
2
1
1
0
0
2
1
0
0
1
1
1
1
0
1
0
0
1
0
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
2
0
1
1
1
1
2
0
0
1
0
0
0
1
2
1
0
0
1
1
0
0
0
0
1
1
1
0
0
1
1
0
1
1
1
1
0
2
1
1
2
3
2
0
2
2
0
1
1
1
1
2
2
0
1
1
0
2
1
0
2
2
2
1
1
0
1
2
1
1
2
2
0
0
2
0
1
1
1
0
0
1
1
0
2
1
0
1
1
2
2
1
2
1
0
1
2
1
1
1
0
1
1
2
2
1
1
1
0
2
1
0
1
2
3
1
0
2
0
0
1
1
1
2
1
1
1
1
1
1
2
2
2
1
1
1
2
1
0
2
1
2
1
0
2
2
1
1
1
0
1
2
0
0
0
2
1
1
0
0
1
2
2
1
0
1
1
0
1
0
1
1
2
2
0
1
1
0
1
1
1
2
1
1
2
2
1
1
0
1
1
1
0
1
1
1
1
2
0
1
3
2
2
2
1
3
0
1
1
1
1
0
1
1
0
0
3
1
2
1
1
0
1
2
1
0
0
0
0
1
0
1
1
1
0
0
2
1
1
2
1
0
1
1
1
0
2
2
0
2
0
1
2
1
2
1
2
0
0
1
1
2
0
0
2
1
1
1
1
0
2
2
1
0
0
1
2
1
1
1
1
1
1
1
1
1
1
0
2
1
1
1
2
1
1
1
2
0
2
1
0
1
2
1
2
1
0
1
0
0
2
1
1
1
2
1
0
1
1
0
1
2
0
1
1
1
2
1
1
1
2
1
0
1
2
1
1
1
2
1
1
1
1
1
1
1
1
0
1
1
1
2
1
1
0
1
0
2
1
0
2
2
1
0
0
1
1
1
1
0
1
2
0
0
1
0
2
1
1
2
2
1
1
0
2
0
0
0
2
2
1
1
1
0
1
1
1
1
2
1
0
1
1
0
0
0
0
1
1
1
1
1
0
1
0
2
1
1
0
1
1
2
1
2
2
0
1
2
1
1
1
1
1
1
1
1
1
0
0
1
0
2
0
2
0
0
1
0
0
1
1
1
0
0
2
1
2
1
1
0
1
0
1
1
2
1
1
1
1
1
0
2
0
1
1
1
2
1
1
1
0
0
1
1
1
2
1
1
0
2
2
2
1
2
1
1
1
1
1
1
1
1
2
2
1
1
1
1
2
0
0
0
0
0
1
0
2
1
0
1
0
0
2
3
0
1
1
0
2
2
0
1
1
0
1
2
1
0
3
2
3
1
1
0
1
1
0
5
1
1
2
1
1
1
1
0
1
1
1
2
1
2
2
1
1
0
2
2
1
0
0
1
2
0
0
1
2
2
1
1
1
1
1
2
1
0
1
2
1
1
1
1
2
2
1
2
2
2
1
0
1
1
2
1
2
2
1
0
2
0
1
2
2
1
1
0
1
0
0
1
0
1
2
1
1
1
1
2
1
2
0
1
1
1
2
1
2
0
2
0
0
2
0
0
0
1
0
1
3
0
1
0
1
1
0
2
1
0
0
1
2
0
1
2
1
2
0
0
1
1
2
0
1
2
1
1
1
1
1
0
1
0
1
1
1
2
0
1
1
2
1
2
1
2
0
2
2
0
2
1
0
1
1
0
1
2
1
1
1
1
1
1
1
0
0
1
1
1
2
1
0
2
1
0
0
1
1
1
1
1
1
1
0
1
1
0
0
0
2
1
2
1
0
0
1
0
2
2
2
1
1
0
1
1
0
1
1
2
0
1
1
1
1
1
1
2
1
1
1
0
1
1
2
2
2
1
1
1
0
1
0
2
2
1
1
1
1
2
2
1
0
1
0
1
1
2
0
0
2
2
1
0
1
0
2
1
0
1
0
1
0
0
2
2
3
0
1
1
1
0
0
1
0
1
2
1
2
2
2
1
0
2
2
2
1
1
1
1
1
2
2
1
1
2
1
1
0
1
2
2
1
1
1
1
1
2
0
1
1
1
2
1
0
2
2
1
1
3
1
0
1
1
1
1
2
1
1
1
2
2
1
2
1
1
1
2
0
0
0
2
1
2
0
2
0
1
1
0
1
1
2
2
0
1
1
0
1
1
0
2
0
2
1
0
3
1
1
1
1
1
0
1
1
0
1
1
0
1
1
0
0
1
1
1
0
0
3
0
1
0
1
0
1
1
1
1
1
1
1
1
1
1
2
0
2
0
0
1
2
0
2
1
1
2
2
2
2
0
1
1
0
0
1
1
3
1
1
1
1
1
0
1
2
1
1
1
0
1
1
0
1
2
0
1
0
1
1
1
2
1
1
1
1
0
1
1
0
2
2
1
1
0
2
0
0
1
1
0
1
2
1
0
1
1
1
1
1
1
0
0
2
2
0
1
1
2
2
1
0
0
1
0
1
1
1
0
2
0
1
1
1
5
1
1
1
1
0
1
0
2
0
0
1
1
2
0
1
1
2
0
1
1
1
1
0
1
1
2
1
1
1
0
0
0
2
1
1
1
0
2
1
1
1
0
0
1
1
1
1
0
1
0
0
1
3
0
1
1
0
0
1
0
1
1
1
1
1
1
2
0
1
0
0
1
0
1
0
0
0
1
1
1
2
1
0
1
2
1
2
0
1
0
1
0
1
1
1
3
1
0
1
0
2
1
1
1
0
0
0
1
1
1
2
1
0
1
0
2
1
2
1
1
2
0
0
1
1
1
1
1
1
1
1
4
0
2
0
1
1
0
0
2
2
0
1
1
3
1
0
2
0
1
1
1
1
1
0
1
2
1
2
0
2
1
2
1
1
1
2
1
0
0
2
2
1
2
1
0
0
1
1
1
1
2
2
2
0
1
0
1
2
1
1
2
0
1
1
0
1
2
1
1
2
1
2
0
1
0
1
2
0
1
0
1
1
0
1
1
1
0
2
1
1
2
1
1
1
2
0
1
1
1
1
1
0
1
1
0
0
1
1
1
0
2
1
0
0
1
0
1
0
0
2
1
0
1
0
1
1
1
1
1
1
1
1
1
1
2
0
1
2
1
0
1
1
2
1
1
2
1
1
2
1
1
0
2
1
0
1
0
1
2
1
1
1
1
0
2
0
2
1
2
1
0
0
1
1
1
1
1
1
0
0
1
2
2
2
2
1
0
0
1
0
2
1
0
0
0
1
1
0
0
0
1
1
0
0
0
2
0
0
1
1
0
2
0
2
1
0
1
0
1
1
1
1
0
2
1
1
1
0
1
0
1
1
2
0
1
1
2
1
1
0
0
1
1
1
0
2
2
0
2
2
1
0
1
0
1
1
2
0
0
1
1
1
1
0
0
0
0
1
2
2
1
2
2
0
2
2
1
1
1
2
2
0
0
1
1
0
1
1
0
1
1
1
2
1
1
1
1
1
1
2
1
2
1
1
1
2
1
1
2
1
1
1
1
1
1
0
1
1
1
1
1
2
1
0
0
2
0
2
2
2
2
1
1
0
2
0
1
0
0
2
1
2
0
1
1
1
1
1
0
0
2
2
1
1
1
0
2
0
1
2
1
1
0
0
0
0
3
2
1
0
2
1
1
1
1
2
1
1
3
2
2
2
0
2
0
1
0
0
1
1
0
1
1
0
0
0
0
1
1
2
0
0
1
2
1
1
1
0
1
0
1
1
0
1
1
0
1
2
2
1
3
0
2
2
1
0
3
1
0
0
1
0
1
2
1
1
0
1
1
1
0
0
1
1
0
1
1
1
1
0
4
0
1
1
1
0
1
0
1
1
0
0
0
0
2
1
2
1
1
0
1
1
1
1
1
0
0
1
2
0
1
0
1
1
0
1
2
2
0
1
0
1
2
1
3
1
0
1
0
0
1
1
1
0
1
1
1
0
0
1
0
1
0
1
1
0
0
0
1
1
0
1
0
2
2
2
0
1
1
1
2
1
0
1
0
1
1
0
1
0
1
0
2
0
2
0
1
1
0
1
2
1
1
1
0
0
1
0
1
1
2
1
2
2
1
2
2
1
2
0
0
2
1
2
1
0
0
1
1
1
1
2
2
1
2
1
1
0
1
1
2
1
1
0
2
1
1
1
0
0
0
2
1
2
2
2
0
0
1
0
2
1
1
0
0
3
2
0
2
0
2
1
1
0
1
1
1
1
0
0
1
1
2
1
1
1
1
2
0
2
2
2
1
0
2
2
0
1
0
2
0
2
2
1
1
1
0
1
0
0
2
0
1
1
1
1
1
0
1
1
2
0
1
0
1
0
1
1
1
2
1
0
0
0
1
1
1
1
0
0
0
2
3
1
0
1
2
0
1
2
0
1
1
0
1
0
2
0
2
0
2
0
1
4
0
0
1
1
1
1
0
2
1
1
1
1
2
1
1
1
1
1
0
2
2
1
1
1
1
1
2
1
0
1
2
1
2
0
2
1
2
1
0
1
1
0
2
1
2
1
2
2
1
2
1
1
1
2
1
1
2
0
0
1
0
1
0
1
0
2
0
1
0
1
1
1
1
2
1
1
2
1
1
0
0
0
2
1
1
1
0
1
1
0
2
2
3
0
0
1
1
2
1
0
1
2
1
1
1
2
0
0
0
0
0
1
0
1
0
1
2
1
1
0
0
0
1
2
0
1
0
0
1
2
1
1
2
0
0
1
0
1
0
0
0
1
0
0
2
2
1
1
1
1
1
1
1
2
2
1
0
1
1
2
1
0
1
1
0
1
1
1
1
2
1
1
0
1
0
1
0
1
2
1
1
1
1
1
1
1
1
1
1
0
0
0
1
1
1
0
2
1
1
0
1
1
2
1
0
0
0
1
0
2
0
2
1
1
0
1
1
0
2
2
1
1
0
0
0
1
0
1
1
0
1
1
1
1
1
1
2
1
1
0
0
0
0
0
2
0
0
2
0
1
1
1
1
1
1
1
0
1
2
1
1
0
2
1
1
0
2
2
0
0
1
1
0
0
0
1
0
1
1
0
1
0
1
0
1
0
1
1
1
0
1
0
0
1
2
1
1
0
0
1
1
2
1
2
1
1
1
0
0
1
2
2
0
0
2
0
2
1
0
1
2
1
2
1
1
1
0
0
0
1
0
1
0
0
1
1
0
1
2
1
1
1
1
1
0
1
1
1
0
0
3
1
0
1
1
1
1
1
1
1
0
1
0
0
0
0
1
2
1
1
1
1
2
4
1
0
1
1
1
1
0
2
0
1
1
2
1
2
1
0
0
1
2
1
1
1
1
2
1
1
1
1
1
2
0
1
0
2
2
2
1
2
1
2
1
1
0
0
1
0
0
1
0
2
1
2
2
1
1
0
3
1
0
1
2
2
2
0
1
2
0
0
0
1
1
1
1
3
0
0
1
0
0
1
0
0
1
2
0
0
1
0
2
1
0
1
2
1
1
0
1
0
0
1
0
1
1
1
2
1
1
0
1
0
0
2
1
0
0
0
1
2
1
0
0
0
0
1
1
0
2
1
2
2
1
0
1
1
1
1
0
1
0
2
2
1
0
1
2
1
1
1
1
0
0
2
2
1
0
1
2
1
1
1
2
1
1
1
1
1
1
2
0
0
2
3
1
0
0
1
2
1
0
1
2
0
0
1
1
1
0
0
1
1
0
0
1
1
1
1
1
0
1
1
1
1
0
1
0
0
1
1
2
2
1
1
0
2
0
2
1
1
1
0
0
1
1
2
1
1
1
0
2
1
1
0
1
1
1
1
1
0
1
0
0
1
1
1
1
1
2
0
1
2
1
0
0
1
0
1
1
0
1
2
1
1
1
1
2
0
2
0
0
2
1
1
1
2
1
1
2
0
1
0
2
2
1
2
1
1
0
1
0
1
1
2
0
1
2
1
1
0
1
1
0
2
0
1
1
2
1
2
1
2
1
1
1
1
1
1
0
1
0
0
1
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
0
0
1
2
0
2
0
2
1
1
1
0
1
1
0
0
2
0
2
2
0
1
2
1
2
1
1
1
2
1
2
1
2
0
1
2
1
2
0
0
0
2
0
0
1
1
2
0
1
1
2
1
2
0
1
2
0
1
1
1
1
2
0
0
1
0
1
0
1
0
1
1
0
2
1
2
0
2
1
1
2
0
1
2
2
1
1
2
0
0
1
1
0
3
1
1
1
2
1
1
0
2
2
1
1
0
2
0
2
0
1
2
1
0
1
1
0
1
2
1
2
0
1
0
2
1
0
1
1
0
0
2
0
1
0
0
1
1
0
1
0
1
1
2
1
2
1
1
1
1
1
1
2
0
1
1
2
1
0
0
0
1
1
1
1
1
1
1
0
1
0
1
2
0
0
1
1
1
1
0
2
0
2
0
2
1
1
1
2
0
0
0
0
1
1
1
1
0
1
2
1
1
1
1
0
1
1
1
2
2
0
0
0
2
1
1
2
2
2
0
0
1
2
0
1
2
1
2
0
0
1
0
1
0
2
2
2
2
0
0
1
1
1
1
1
0
1
1
0
1
2
0
1
0
0
1
2
0
1
0
1
1
0
0
2
0
1
1
1
1
1
0
1
1
1
0
0
0
1
0
0
1
2
2
1
1
0
2
1
2
0
0
2
1
0
1
0
0
1
1
1
0
2
1
0
2
1
1
2
0
2
2
0
2
2
1
1
5
2
1
0
0
0
1
1
0
1
1
1
0
1
1
1
0
2
3
0
1
1
2
2
0
1
2
0
1
1
1
2
1
1
1
1
1
0
0
2
1
0
0
1
1
1
1
2
1
1
0
0
1
1
1
1
2
1
1
0
2
1
2
1
2
0
2
1
1
2
1
1
0
0
1
2
1
1
0
1
0
1
2
1
1
0
1
2
0
1
1
0
0
0
0
1
1
0
1
0
1
0
1
1
0
1
1
0
1
0
1
0
1
0
1
0
0
1
1
1
2
1
2
0
1
1
1
1
1
1
2
1
0
0
0
0
1
1
3
0
1
2
2
1
1
2
1
1
2
0
0
0
2
1
0
0
0
0
1
2
1
1
1
2
0
1
2
0
1
1
1
1
2
1
1
0
1
2
0
1
1
1
2
0
1
1
1
0
0
0
1
0
1
1
1
1
1
1
1
0
0
2
3
0
0
2
1
1
2
2
0
2
1
0
1
1
1
0
0
0
1
0
0
2
1
1
0
1
1
0
0
1
1
1
1
2
1
2
0
0
0
0
0
0
1
1
2
2
0
1
1
0
2
1
1
1
0
1
1
1
2
0
1
0
0
0
1
0
0
1
1
2
2
2
1
1
1
2
1
0
0
1
0
1
1
1
2
2
0
1
0
1
1
1
2
2
1
1
1
2
1
0
0
2
1
1
1
1
2
1
2
1
1
1
1
1
0
0
1
1
1
1
1
0
1
1
1
0
2
1
1
0
0
1
0
1
1
1
2
1
1
0
1
2
2
4
1
0
1
1
0
1
0
0
1
1
1
1
0
1
0
1
1
2
2
2
1
1
2
1
1
0
0
1
2
0
0
1
1
0
1
1
0
2
1
1
1
1
2
1
1
1
0
0
1
2
2
0
2
1
1
1
1
1
1
1
1
1
1
0
0
1
0
0
0
1
1
1
1
1
0
1
1
2
2
0
1
1
1
1
2
1
1
1
1
1
0
1
1
2
0
0
1
1
0
2
2
0
1
0
1
0
2
0
1
1
0
1
0
0
0
0
2
1
1
2
1
1
1
1
0
1
3
2
1
2
1
0
1
1
2
1
1
0
1
1
0
1
2
1
0
1
1
0
1
1
1
0
1
1
1
2
1
1
0
2
2
0
0
0
1
1
2
0
1
2
1
1
0
0
0
1
1
1
1
1
1
2
0
0
0
1
2
1
0
1
1
1
1
1
0
1
1
0
0
0
2
2
1
1
2
1
0
1
2
1
1
1
0
2
1
0
1
2
1
2
0
2
2
0
0
0
0
2
0
0
2
0
1
1
1
1
1
1
0
1
0
0
2
1
2
1
2
1
2
1
1
2
0
0
3
1
1
0
1
1
1
2
1
0
2
2
2
2
2
1
0
2
1
1
0
2
0
1
0
0
1
2
0
1
1
0
0
1
1
2
2
1
1
1
0
1
1
2
0
1
0
2
1
1
0
1
1
2
0
1
1
1
2
2
0
1
1
0
1
2
0
0
0
0
0
2
0
1
2
1
1
1
1
0
0
1
1
1
2
1
1
1
1
1
2
2
1
1
1
9
1
0
2
1
1
1
0
2
2
2
1
1
1
0
1
1
1
1
1
1
1
0
2
1
1
1
1
0
1
1
1
2
1
1
1
1
2
1
2
3
2
1
1
0
0
1
1
2
2
1
2
1
1
0
2
1
0
2
2
0
1
1
0
0
1
2
1
1
0
1
1
2
0
1
1
1
0
2
0
0
2
0
0
0
2
1
1
1
1
1
2
2
2
1
1
1
2
1
2
3
0
1
2
0
1
1
2
1
0
0
0
1
0
0
2
0
1
0
1
2
1
1
0
0
1
0
1
2
1
1
0
0
0
0
2
1
2
0
1
1
2
0
1
1
1
1
1
1
1
1
1
2
1
0
1
1
1
2
1
1
2
0
2
0
0
1
1
0
0
2
2
1
0
0
1
1
1
0
2
1
1
1
2
0
2
0
0
1
1
1
1
2
0
1
1
1
0
1
2
2
2
0
1
2
1
1
0
1
1
0
1
1
1
1
0
0
0
3
1
0
2
2
2
1
1
2
0
0
1
1
1
1
1
1
1
0
2
1
1
0
0
0
0
2
1
2
0
0
2
1
1
2
1
0
1
0
1
1
0
0
0
0
2
2
1
2
2
1
1
0
1
1
1
2
0
2
1
0
1
2
0
1
0
1
1
0
1
1
1
1
1
1
1
1
1
0
2
2
1
0
1
1
1
1
2
0
1
1
0
1
1
1
0
0
1
2
1
1
2
1
2
2
1
2
0
0
1
0
2
0
1
0
1
1
1
2
1
1
1
1
2
0
1
1
1
1
0
1
1
2
1
1
2
0
2
1
2
0
0
0
2
1
0
1
1
1
0
2
0
0
2
2
2
0
1
2
1
0
1
2
1
1
0
0
1
1
1
1
0
0
2
1
1
1
0
1
3
2
0
1
0
1
0
0
1
2
1
2
1
1
1
1
0
1
2
1
2
2
1
1
0
2
2
1
1
0
0
0
2
2
1
1
2
1
2
1
2
1
2
1
1
1
0
2
2
1
1
1
1
2
1
1
2
1
2
1
2
1
0
2
0
1
1
1
0
1
2
2
0
0
0
0
1
1
1
0
1
1
0
1
1
0
1
2
2
0
1
0
1
1
0
1
1
0
2
0
1
1
0
0
1
1
2
1
1
0
1
1
0
2
2
0
2
2
2
0
1
1
2
1
1
0
2
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
0
1
1
0
0
0
3
0
1
1
0
1
2
1
0
1
2
4
0
2
1
0
0
0
1
0
0
1
0
2
1
1
0
0
1
1
1
2
1
1
2
1
2
1
1
2
0
1
0
2
1
0
0
1
2
0
1
2
0
1
1
2
1
1
1
2
1
1
1
1
2
0
1
2
1
2
1
0
2
1
0
2
1
0
1
0
2
1
2
1
1
1
1
0
0
1
1
1
1
0
0
1
1
0
2
1
1
0
0
1
2
2
0
1
2
2
1
2
1
1
0
0
2
0
1
0
0
2
0
2
1
1
2
0
1
2
1
1
1
2
1
2
2
2
1
2
1
0
1
2
0
1
1
1
1
0
1
2
1
1
1
1
2
0
0
1
0
1
1
1
0
1
0
1
0
1
1
1
1
2
0
1
0
1
2
2
1
0
1
0
0
1
1
1
1
2
0
2
0
1
1
1
1
0
1
0
1
0
1
2
1
1
1
0
0
1
0
1
2
0
2
1
0
1
1
1
1
1
3
2
1
0
1
1
0
1
0
1
0
0
1
2
0
0
0
1
1
1
2
1
1
1
1
1
2
0
1
2
1
0
2
1
1
2
1
1
1
2
2
2
2
1
1
1
1
0
0
2
1
1
0
1
2
2
0
2
3
2
2
2
1
1
1
1
1
1
0
0
1
1
0
1
0
1
1
0
1
1
2
1
1
2
2
1
1
1
1
1
0
1
2
1
0
0
0
0
1
1
0
2
2
1
1
2
2
1
2
1
1
3
1
1
0
1
1
2
0
0
1
1
2
0
1
1
1
0
0
0
0
1
2
1
1
2
2
0
3
1
1
0
1
1
2
1
1
2
1
0
2
1
0
1
1
0
1
1
2
0
0
1
2
3
1
1
0
1
2
1
1
1
0
1
2
0
1
0
2
1
0
1
1
2
0
1
2
0
1
0
0
0
0
2
1
1
0
0
2
0
2
1
1
1
0
2
1
2
2
2
2
0
1
0
2
1
0
1
0
0
1
1
0
0
0
2
2
1
2
0
2
2
2
1
0
2
2
0
1
0
0
2
1
1
0
2
0
1
0
1
2
1
1
1
1
0
0
2
1
0
1
0
1
0
1
1
2
2
1
2
1
2
1
0
2
1
1
1
1
0
2
2
2
0
1
0
1
1
2
1
0
0
2
1
1
1
3
1
1
1
1
1
2
0
1
2
1
1
1
1
1
2
1
1
0
1
2
0
0
1
0
2
0
1
1
2
2
2
6
1
0
2
1
0
0
1
1
1
1
0
1
2
1
0
1
1
1
0
1
1
0
1
0
1
2
0
1
1
0
0
1
0
1
0
1
0
1
0
1
0
0
1
0
1
1
1
2
2
0
2
3
0
2
1
3
0
0
1
2
0
2
1
1
2
2
1
0
2
1
0
1
0
1
2
1
0
1
2
2
0
1
1
1
1
1
1
1
0
2
1
1
3
1
2
0
1
2
0
1
1
0
0
1
0
2
1
1
1
0
0
0
2
2
1
1
0
1
0
1
1
1
2
2
0
1
1
2
1
0
1
1
1
1
2
2
2
2
0
2
1
1
0
2
1
1
1
0
1
2
2
2
1
2
2
1
0
2
1
0
0
1
1
1
1
0
1
2
0
2
2
1
1
1
0
1
2
0
2
1
1
1
3
2
0
1
2
2
1
2
0
0
0
1
2
2
1
0
1
1
0
2
2
0
1
2
1
1
0
1
2
0
1
0
1
0
0
1
1
2
4
1
1
1
1
1
1
1
1
2
2
1
1
0
1
1
0
1
2
1
0
1
1
0
1
1
2
0
2
0
1
1
9
1
1
2
0
1
1
0
2
2
1
2
0
0
1
1
1
2
0
0
1
1
0
1
1
0
1
1
1
1
0
0
1
2
2
0
1
0
1
1
1
1
1
1
1
1
1
2
2
1
1
0
0
2
0
0
1
1
1
1
1
2
0
2
0
2
0
1
1
1
0
1
1
1
0
1
1
1
2
2
1
1
2
1
1
1
0
1
1
0
0
2
2
2
3
0
2
1
0
2
0
1
1
1
0
1
1
1
0
2
1
0
1
1
0
1
1
2
2
1
2
1
2
0
1
1
2
0
1
1
1
0
1
2
1
0
0
2
1
2
0
0
1
1
2
0
0
2
1
1
0
2
1
2
1
0
1
1
2
1
1
1
0
6
1
1
2
2
1
2
2
1
1
0
0
2
1
2
1
1
0
1
1
1
0
2
2
0
0
0
0
0
2
2
2
1
2
2
2
3
2
2
0
1
2
2
1
1
0
0
1
0
1
0
0
0
0
0
2
2
1
3
0
0
0
1
2
1
2
0
4
2
1
2
1
2
1
1
1
0
0
1
1
1
4
0
0
0
0
1
2
1
1
1
1
0
0
1
0
2
0
4
0
2
2
0
1
1
2
0
1
1
0
2
0
1
0
2
0
0
0
1
0
1
1
0
1
0
2
2
0
1
1
1
0
1
1
1
0
0
0
1
2
1
0
0
2
1
1
1
0
2
2
2
0
2
0
2
1
1
0
0
2
1
1
1
1
2
2
2
2
0
2
1
1
0
1
0
0
0
2
1
1
2
1
2
2
0
2
0
0
1
1
1
1
0
2
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
2
2
2
1
1
1
3
2
1
2
1
1
2
0
1
2
1
1
1
0
1
1
0
0
1
2
2
0
0
0
1
1
1
0
0
1
0
1
1
1
2
2
1
1
1
0
0
2
1
0
1
0
0
2
1
0
0
1
0
2
1
1
0
2
0
1
1
0
0
1
1
1
1
0
1
0
1
1
0
1
0
2
0
2
1
1
1
1
2
2
0
0
2
0
2
0
1
0
1
2
2
1
1
0
0
0
2
2
0
2
2
1
2
1
1
1
0
0
2
1
1
1
1
1
1
0
1
0
2
2
1
2
1
0
1
2
0
0
0
1
1
1
2
2
2
1
0
2
1
1
1
1
0
0
1
1
2
1
1
1
1
1
1
0
1
1
1
1
0
0
2
0
1
2
0
1
1
0
1
1
2
0
1
2
1
1
1
2
1
1
1
0
0
2
0
1
1
1
1
1
1
0
2
2
2
1
1
1
2
1
2
1
2
2
0
2
0
0
2
1
2
0
0
0
0
1
2
0
0
1
1
1
1
2
2
0
1
1
0
0
1
1
2
0
1
2
2
1
0
2
2
1
1
1
0
0
2
2
1
0
1
1
1
2
1
1
1
1
4
1
1
1
2
1
1
0
2
0
0
1
1
0
1
0
2
1
2
1
2
1
1
2
0
0
1
2
2
0
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
0
0
1
2
1
2
0
1
1
2
1
1
0
1
2
1
0
2
1
1
1
0
0
0
0
1
1
0
0
0
1
1
0
1
2
2
2
1
1
0
0
0
1
1
1
1
0
1
1
0
2
1
0
1
1
0
2
1
2
0
1
0
1
2
1
0
0
0
1
0
2
2
1
1
1
1
2
1
1
0
1
2
0
0
1
0
1
1
3
0
1
1
0
1
1
0
0
1
0
2
1
1
1
1
2
2
0
1
2
1
1
0
2
1
0
2
0
2
1
1
2
2
1
0
2
1
4
2
1
2
1
1
2
1
0
1
1
0
2
0
2
1
1
2
2
1
2
1
0
0
1
1
1
1
1
1
1
0
0
0
2
1
1
0
1
1
1
1
1
1
1
2
3
2
1
1
0
2
0
1
0
1
0
2
1
2
0
0
0
0
0
1
1
1
0
0
1
2
0
0
2
1
1
2
1
2
1
1
1
0
1
1
2
1
1
2
1
2
1
1
1
0
1
1
1
1
0
2
1
1
0
1
0
1
1
1
1
1
1
0
0
0
0
1
1
1
0
1
1
1
1
1
1
2
1
0
1
0
2
1
2
1
1
1
2
2
2
1
1
0
3
1
2
1
1
1
2
0
1
2
0
1
1
2
0
1
2
2
1
0
0
2
1
0
2
0
1
1
1
1
1
1
2
2
0
1
2
1
1
0
1
2
2
1
1
1
0
1
1
2
1
0
0
1
0
2
0
0
1
1
1
0
0
2
2
1
0
1
2
1
1
1
1
1
1
1
1
1
0
2
0
0
1
1
2
1
0
1
0
0
2
2
1
1
2
1
0
1
2
0
1
0
1
1
0
2
1
1
1
0
2
1
1
1
1
0
1
2
0
1
1
0
0
2
2
1
0
1
1
1
0
1
0
1
0
2
1
1
0
1
2
2
1
1
1
1
1
1
1
0
1
0
2
1
1
3
1
1
1
1
1
1
1
1
2
0
0
1
4
0
0
1
0
2
1
2
2
1
1
2
0
0
0
1
0
1
1
1
1
1
2
1
1
3
0
0
0
1
1
2
0
1
1
1
0
0
2
0
2
2
2
0
1
0
0
1
0
2
2
2
0
1
1
1
2
1
1
0
0
1
1
0
0
0
1
1
2
0
1
1
1
0
0
1
2
0
2
2
0
1
1
1
1
1
2
1
1
0
1
1
0
2
1
0
0
0
1
1
2
1
2
0
2
1
1
0
0
0
1
0
1
0
0
0
2
1
0
2
3
1
1
2
0
2
0
0
1
2
2
0
1
2
1
0
0
1
2
1
1
2
1
0
1
1
1
1
0
1
0
1
2
0
1
1
0
1
1
1
2
0
2
1
1
2
1
2
1
1
1
2
1
1
0
2
2
0
1
1
2
0
2
1
1
1
1
1
1
0
0
0
0
2
1
4
0
1
2
1
1
1
1
2
1
1
1
1
2
1
0
2
0
1
0
2
1
1
2
1
2
0
1
2
1
1
1
1
1
2
1
1
0
2
2
1
0
2
0
0
1
2
0
1
0
2
0
1
1
1
1
1
2
1
1
0
0
2
1
2
1
0
2
2
1
2
1
1
2
1
0
1
1
2
1
1
0
0
0
2
0
1
0
0
1
0
1
1
0
1
1
0
2
0
0
0
1
0
1
0
0
1
0
1
2
1
2
1
1
1
2
1
2
0
0
1
2
1
1
1
2
1
1
1
1
0
1
2
2
1
0
2
1
2
1
1
1
1
0
2
2
2
0
1
0
2
1
0
1
1
1
0
2
1
2
2
0
1
1
0
1
1
1
1
1
2
2
1
0
2
0
0
0
1
1
1
1
0
1
1
1
0
2
1
1
1
0
2
1
1
0
1
1
1
1
2
2
1
1
1
2
1
2
1
0
1
2
2
2
1
1
2
1
2
1
1
1
0
2
2
1
1
2
1
0
2
1
1
1
0
1
0
2
1
1
1
1
0
0
2
0
2
1
0
1
2
1
1
0
0
1
1
1
1
1
1
1
1
2
1
2
2
1
0
0
1
1
0
0
4
2
0
0
1
2
1
0
1
1
0
1
1
1
1
2
1
1
1
2
0
1
1
1
1
0
1
2
1
2
2
1
1
3
1
0
1
1
0
1
2
1
0
1
2
0
1
1
2
2
2
0
0
0
1
1
1
0
1
0
0
1
0
1
1
1
1
0
2
1
2
2
1
0
0
0
1
0
1
3
1
1
0
0
1
2
2
1
0
1
1
0
2
0
0
2
1
1
0
0
1
0
0
2
0
2
1
1
4
0
1
1
2
1
0
2
1
1
2
1
0
0
1
1
1
1
1
1
2
2
1
1
1
1
2
1
0
0
0
1
2
2
1
1
1
1
1
1
0
2
1
2
0
1
1
1
1
0
1
1
1
1
1
1
1
2
1
1
1
1
0
0
1
1
1
0
0
1
0
1
1
1
1
1
1
2
1
2
1
0
0
0
0
0
1
2
0
0
0
1
0
2
1
1
1
1
1
0
0
1
0
2
1
1
1
0
0
2
1
0
1
0
1
1
1
1
1
1
2
2
1
1
1
0
1
0
1
2
0
3
1
1
1
2
1
2
1
2
1
2
2
1
0
1
0
0
2
2
0
0
2
2
1
2
1
0
0
1
1
0
1
1
1
0
1
2
2
1
1
1
1
1
2
1
2
1
0
1
0
0
1
0
2
1
0
2
1
1
1
0
0
2
0
1
2
2
1
2
1
2
2
0
2
1
1
1
0
1
2
1
0
1
0
0
1
1
1
2
1
0
0
2
1
1
2
0
2
0
1
2
1
1
2
0
1
1
1
2
1
2
1
0
0
1
1
0
2
2
1
3
1
3
0
2
2
1
0
2
0
2
0
2
0
0
1
0
0
1
1
1
0
2
1
1
2
1
1
2
1
3
2
1
2
1
1
0
1
0
0
1
1
0
1
1
1
1
0
1
0
0
1
2
0
0
0
2
2
1
0
1
1
2
1
1
0
0
2
2
0
1
1
0
2
1
1
1
1
0
1
2
1
2
1
2
1
1
1
2
0
2
2
1
0
1
1
1
2
0
0
1
1
1
0
1
1
1
1
1
2
0
1
1
1
1
1
1
2
2
1
1
2
0
1
2
0
1
1
0
0
0
1
1
1
1
2
4
1
1
1
0
1
2
1
2
1
1
0
1
1
1
2
1
1
0
2
2
0
1
0
2
1
1
1
1
1
2
1
1
2
2
1
1
2
0
1
2
1
1
2
2
1
2
2
1
1
1
1
1
2
1
0
2
0
1
0
1
1
0
1
1
1
1
2
1
0
0
1
1
0
1
0
2
1
1
0
2
1
1
0
1
1
1
0
0
1
1
0
1
2
1
1
2
1
2
1
2
0
1
1
1
0
0
1
3
0
1
1
2
1
1
2
0
2
1
2
1
1
0
1
1
1
1
1
0
1
0
1
1
2
1
1
0
2
0
1
1
1
0
1
0
2
3
1
0
1
2
1
1
0
1
2
0
0
0
1
2
1
1
1
1
0
0
1
1
2
2
0
1
0
1
1
2
1
2
1
0
1
1
1
1
0
0
2
1
1
0
1
0
2
1
0
1
0
0
0
0
1
1
1
2
0
1
1
1
0
1
1
0
2
0
0
0
1
0
2
1
0
1
2
2
1
1
2
0
1
1
1
2
1
1
1
1
1
0
1
0
1
2
1
0
1
1
2
0
2
2
1
0
2
2
2
1
0
1
2
1
1
1
1
0
2
0
2
2
3
1
2
2
1
0
0
1
0
1
1
1
1
1
1
2
0
0
1
0
2
2
2
2
0
1
1
1
1
0
0
1
0
0
1
2
0
1
1
0
2
0
1
1
1
1
1
1
0
0
2
0
0
1
1
1
2
1
0
0
1
1
0
1
1
2
1
1
1
1
1
2
1
1
1
1
1
0
1
1
1
1
1
0
1
0
0
2
1
1
0
0
0
2
0
0
0
2
2
1
0
1
0
2
1
1
2
1
2
1
1
9
2
0
1
0
0
1
1
1
1
2
1
1
0
1
1
0
0
2
1
2
1
0
1
1
1
1
0
0
1
0
1
1
2
0
2
0
1
1
1
1
0
1
0
1
1
1
1
2
1
1
0
0
1
0
0
1
1
2
1
0
1
1
0
2
2
1
1
1
1
1
1
1
0
0
2
0
1
2
0
0
1
1
2
1
0
0
3
1
0
0
2
1
0
0
0
1
0
0
1
1
1
0
2
1
1
2
1
2
2
1
0
1
2
1
0
2
1
1
1
1
2
1
1
0
2
2
1
1
1
1
2
1
2
1
2
0
1
1
2
0
2
0
2
0
0
2
0
0
1
1
1
1
0
1
2
0
2
1
1
2
1
1
0
1
1
2
1
2
2
1
1
0
1
1
0
1
1
1
0
1
1
1
1
1
2
0
2
1
1
0
2
0
1
1
0
1
1
1
0
0
1
2
1
0
2
1
0
1
0
1
1
0
0
2
1
2
1
2
0
1
0
1
1
0
2
2
1
0
0
0
0
1
0
2
1
2
0
1
1
0
1
1
1
0
1
1
1
1
1
0
1
1
0
1
0
2
0
1
0
0
1
2
2
0
0
0
2
0
0
0
1
1
2
1
0
1
0
1
2
2
1
2
1
1
1
1
0
2
0
1
1
0
1
0
1
1
1
1
1
1
2
0
0
2
2
0
2
0
2
0
0
1
3
0
1
2
1
1
1
1
0
0
0
1
0
0
0
2
1
2
1
1
1
0
1
0
2
1
2
2
1
2
2
0
1
0
0
1
1
2
2
1
1
2
0
1
0
2
1
0
0
0
1
0
2
0
1
1
1
1
0
1
1
0
1
0
2
1
2
0
1
1
1
2
2
2
1
1
2
0
0
0
0
0
0
0
1
2
0
1
1
0
2
1
0
1
1
1
2
1
0
0
1
2
1
0
0
1
1
0
1
0
2
1
2
2
0
1
0
1
0
1
1
0
1
0
0
2
1
2
0
0
1
0
1
0
2
1
1
1
2
1
1
1
0
1
2
1
2
2
2
0
0
2
1
1
1
2
1
0
2
2
1
1
2
1
2
0
0
1
0
1
3
2
2
1
1
0
0
0
1
1
2
1
2
1
2
0
0
1
0
1
1
0
2
0
2
0
2
1
1
1
1
0
1
1
1
0
2
0
0
1
0
0
0
1
1
1
1
0
2
1
1
0
2
1
2
1
0
0
2
2
1
1
1
1
1
2
0
1
0
1
0
1
1
0
1
0
1
0
0
0
1
1
2
0
1
2
0
2
2
0
0
1
1
0
1
1
1
1
0
1
1
2
1
2
0
1
1
2
0
1
2
1
0
0
1
1
1
2
1
1
2
0
2
0
1
2
1
0
0
1
0
1
1
1
0
1
2
1
1
0
1
2
1
2
1
0
0
1
1
1
1
0
1
0
0
1
0
2
1
1
2
2
2
1
2
1
1
1
2
1
1
0
7
2
1
2
0
1
1
0
2
1
1
1
0
1
1
1
2
0
0
1
1
2
1
1
0
3
2
1
2
0
1
1
1
2
1
1
1
1
0
0
0
2
0
2
1
1
1
1
0
0
1
1
0
2
0
1
0
0
0
1
1
1
1
1
1
1
0
1
2
1
1
1
2
2
1
1
1
1
0
2
0
1
1
1
2
2
1
1
2
1
0
1
2
0
1
2
2
2
2
0
2
1
1
1
1
0
0
1
0
1
0
1
2
0
1
0
2
1
1
2
0
0
1
1
0
0
1
0
0
0
1
1
1
2
0
1
1
1
1
1
2
1
0
0
0
1
2
2
0
1
2
1
0
2
0
1
0
1
1
1
1
2
2
1
2
1
0
1
1
1
1
1
3
1
2
1
1
0
2
2
1
0
2
0
1
0
0
0
0
2
1
0
1
0
2
1
2
1
0
1
0
0
1
0
0
0
0
1
1
0
0
1
0
1
1
1
2
1
2
1
2
1
1
1
2
2
1
1
2
1
1
0
0
1
0
1
1
0
2
0
1
1
1
1
1
0
0
0
2
1
0
1
1
1
0
0
2
1
2
1
1
1
0
1
2
1
2
1
1
1
0
1
0
0
1
2
2
2
0
0
0
0
1
0
1
0
1
0
1
1
1
0
0
2
1
2
0
1
2
2
2
0
0
0
0
2
0
2
1
0
1
2
0
1
2
1
1
1
1
2
1
2
1
0
2
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
0
1
1
1
1
0
1
1
1
0
1
2
0
1
1
1
2
1
2
2
0
2
1
1
1
2
2
2
3
0
0
0
1
1
1
0
0
1
2
0
1
2
0
3
2
2
1
2
0
1
3
0
1
0
1
1
1
1
1
0
0
1
0
1
1
0
1
0
0
1
1
0
1
2
1
1
0
0
1
2
1
1
0
1
2
1
1
1
1
1
0
1
1
1
1
1
1
2
0
0
2
1
1
1
2
1
2
2
1
1
1
1
2
1
2
0
0
1
1
2
1
1
0
2
0
2
0
2
1
0
1
2
1
1
0
0
3
0
0
0
1
0
1
1
1
1
1
1
1
0
2
0
1
2
1
1
1
2
1
0
1
2
0
1
1
1
1
1
1
1
1
1
2
3
0
1
1
0
1
2
1
0
0
1
1
1
1
0
0
1
1
2
2
0
0
0
0
0
2
1
0
2
1
1
0
1
2
1
2
2
2
1
2
0
0
1
1
1
3
2
1
1
2
1
0
1
0
1
2
1
2
0
1
4
1
2
1
2
1
1
0
2
1
0
1
0
3
0
0
0
1
0
1
1
1
1
1
0
0
0
2
1
0
0
0
2
0
1
0
0
1
1
1
1
1
0
1
1
0
2
2
2
1
1
1
1
0
2
1
1
1
1
2
1
1
1
0
0
2
3
2
1
0
1
0
0
2
1
1
1
1
1
0
2
1
1
2
1
1
1
1
2
2
1
0
0
1
2
0
0
1
1
1
1
1
0
0
1
1
2
1
1
2
1
1
2
2
0
1
0
1
1
1
1
0
1
1
0
0
1
1
1
0
2
1
1
1
1
1
2
1
0
3
1
1
1
1
2
0
2
0
0
2
2
1
0
0
2
0
1
1
1
1
1
2
0
1
0
1
1
1
1
1
1
1
0
0
0
2
0
1
0
1
1
1
1
1
1
0
1
0
2
0
0
0
1
1
2
1
0
2
0
1
0
2
0
1
0
2
0
0
0
1
0
0
1
0
1
1
1
1
2
1
1
0
0
0
1
2
0
1
0
1
1
0
1
1
2
2
1
0
1
0
1
1
1
0
0
2
1
1
1
2
1
1
2
1
0
0
1
1
5
1
1
1
1
2
0
0
1
2
1
0
1
0
0
0
2
0
1
1
0
1
0
1
2
1
0
1
1
1
0
2
1
2
2
1
0
2
1
0
0
2
1
0
0
1
2
0
2
2
1
1
0
1
0
1
1
0
0
1
1
0
2
1
1
1
0
1
1
2
0
0
1
1
1
2
0
0
3
1
1
0
2
0
1
1
1
0
1
0
0
0
2
1
1
1
1
2
2
0
2
0
1
0
1
1
0
1
0
1
0
0
0
1
2
1
1
2
1
1
0
1
1
1
2
1
0
2
1
2
0
1
1
1
1
1
2
1
1
2
0
1
2
1
0
1
1
1
1
0
1
2
1
1
1
0
1
1
1
0
0
1
1
2
1
1
1
0
1
2
2
0
0
2
0
1
2
2
1
2
0
2
1
1
1
2
0
2
1
2
1
0
2
1
1
2
2
1
1
1
2
2
1
1
1
1
2
1
1
1
2
0
0
1
1
0
2
1
2
1
2
1
1
1
0
1
0
0
1
1
0
0
1
1
0
2
1
2
0
1
2
2
2
2
2
2
2
1
1
2
0
1
1
0
1
3
1
1
1
1
1
2
0
2
1
1
1
1
2
1
0
1
1
0
2
2
0
0
1
1
1
1
0
1
0
1
1
2
0
1
2
0
0
1
0
1
0
1
2
1
2
2
0
0
1
1
1
1
2
0
1
1
1
1
1
2
2
3
2
1
0
1
1
1
0
2
1
1
1
1
0
1
0
2
1
0
1
1
2
2
0
0
1
2
1
0
1
2
1
4
1
1
1
1
0
1
1
0
1
2
1
1
1
1
0
0
1
0
2
1
2
0
0
0
1
1
2
1
0
0
0
0
0
1
2
1
1
0
1
1
1
1
2
1
1
2
1
1
1
1
0
2
4
0
1
2
0
2
1
1
1
1
2
1
1
1
1
1
1
4
2
0
1
2
1
1
2
1
1
0
1
1
1
0
0
0
0
0
0
2
1
0
1
1
0
0
0
2
1
2
0
1
0
1
2
3
2
2
2
1
2
0
1
0
1
1
1
0
1
0
2
2
1
0
1
1
0
1
1
1
2
2
1
2
2
1
2
0
1
0
1
1
0
0
0
0
2
1
0
0
1
2
1
0
0
1
2
1
0
2
1
1
2
1
1
1
1
0
2
1
0
1
2
1
1
0
0
1
1
1
1
0
0
0
0
1
1
1
0
1
1
1
1
2
1
2
2
2
0
2
0
1
0
1
0
1
0
0
1
0
1
0
1
0
1
2
1
0
1
2
2
0
2
1
2
1
1
0
1
1
1
5
0
1
1
1
1
0
0
1
1
2
1
2
2
1
0
1
1
1
0
1
2
0
1
2
0
1
1
1
1
1
0
1
1
1
0
0
0
1
1
1
1
0
1
2
1
1
2
2
1
1
1
2
0
1
1
2
2
1
1
1
2
1
2
1
0
1
1
1
1
2
1
2
1
0
1
1
0
2
0
0
0
1
1
1
1
0
0
0
1
2
2
1
1
2
2
1
2
1
1
0
1
2
1
3
1
0
0
0
1
0
1
0
0
2
2
1
0
1
1
0
1
1
0
0
1
2
1
2
0
1
2
0
1
1
1
1
1
1
1
0
1
2
0
0
2
1
1
1
2
2
0
2
1
1
2
2
1
0
1
0
1
1
3
1
1
1
0
1
0
0
1
1
1
1
0
2
2
1
0
2
1
1
0
0
0
2
0
1
1
1
0
1
1
1
0
2
0
1
2
1
1
2
2
0
2
1
1
0
1
0
2
2
2
1
1
2
2
1
1
1
1
1
0
2
1
2
2
0
1
1
2
2
2
1
0
1
5
0
2
2
0
1
1
1
0
2
1
1
1
1
1
1
0
0
0
0
0
0
1
0
1
1
0
1
0
1
1
3
1
2
0
1
1
2
0
0
0
0
1
1
1
1
2
1
0
2
2
1
1
2
2
2
2
0
2
1
2
2
1
0
1
1
1
0
2
1
1
1
0
0
0
2
1
1
2
1
1
1
0
1
1
2
2
1
1
1
1
1
1
0
1
2
0
2
1
1
1
1
0
2
1
1
1
1
0
1
1
1
2
0
2
1
0
1
1
1
1
2
0
0
2
2
3
2
1
1
1
2
1
2
0
0
1
1
0
0
1
1
0
0
1
1
1
2
1
2
0
1
2
2
1
2
1
2
0
0
0
1
1
2
1
2
0
1
2
1
1
0
0
1
1
1
0
1
1
1
0
2
1
0
0
1
1
1
1
1
1
0
2
1
1
0
1
1
7
0
0
2
1
0
1
0
0
1
2
2
1
2
1
0
1
2
1
1
0
2
1
0
1
2
1
1
0
0
1
2
1
2
1
0
2
0
0
0
1
0
0
1
1
1
1
4
2
1
1
1
1
1
1
1
2
2
0
2
0
1
2
0
0
1
1
3
0
1
0
1
1
2
2
1
1
2
1
2
0
1
1
1
2
1
1
1
2
1
0
2
2
0
0
0
0
0
0
1
2
2
0
1
0
1
2
2
1
1
0
0
1
3
0
1
0
0
0
1
1
0
1
0
3
2
0
0
0
1
2
1
1
2
0
1
1
2
2
0
1
1
0
1
1
1
2
1
0
1
2
1
0
2
1
2
0
1
0
0
4
1
2
1
2
2
1
2
3
0
1
1
0
1
1
1
1
1
0
0
1
1
1
1
2
1
0
1
1
1
0
0
1
1
1
2
1
2
1
1
1
1
0
1
0
3
2
1
1
0
2
1
1
0
1
2
0
1
1
2
1
2
2
0
2
1
1
2
2
1
0
1
0
1
1
1
2
0
2
2
1
0
2
0
2
0
2
2
1
0
1
1
2
0
2
1
2
2
2
0
1
1
2
1
2
0
0
1
0
2
1
1
0
1
1
0
2
1
1
0
0
2
1
1
1
1
1
1
1
1
1
1
1
0
1
0
1
0
1
1
0
1
2
0
2
1
0
0
0
1
1
2
1
2
0
0
2
0
1
1
1
1
1
2
2
0
1
1
1
2
2
1
1
1
0
2
0
1
0
1
2
1
1
0
1
1
2
0
2
1
0
0
2
0
1
1
1
2
0
1
0
1
1
0
1
1
1
0
1
1
1
0
1
2
0
1
1
1
1
0
0
0
2
0
1
1
1
0
0
0
2
1
1
1
0
1
1
2
0
1
2
0
0
0
1
1
0
1
2
1
0
1
1
1
2
0
1
1
0
1
3
2
1
3
1
1
0
1
1
0
0
2
0
2
1
2
1
1
0
0
1
1
1
1
0
1
1
1
0
1
0
2
2
1
0
1
1
2
0
3
0
0
4
3
1
2
0
1
0
2
0
0
0
2
1
1
1
2
2
1
1
0
2
0
1
2
2
0
0
2
2
4
1
0
1
1
1
1
1
1
1
0
1
1
0
0
2
0
2
0
2
0
2
1
1
0
2
1
2
0
0
3
2
2
0
1
2
1
1
1
0
1
2
1
1
0
0
1
1
1
1
1
0
2
1
1
2
0
1
2
2
1
0
2
0
2
1
1
0
0
1
1
0
0
6
2
0
2
1
2
2
0
2
1
2
1
0
1
1
0
0
0
0
1
1
2
0
0
2
2
2
1
1
1
2
0
1
2
2
2
0
2
1
0
2
2
2
0
1
1
0
2
1
1
0
0
0
1
2
2
0
1
0
1
0
0
1
1
1
1
0
0
0
1
0
1
2
0
1
2
0
0
1
0
1
1
1
1
1
1
0
1
2
1
1
1
0
1
0
0
2
1
1
0
1
1
1
1
1
1
1
1
1
2
2
2
0
2
1
0
0
1
0
1
2
0
0
0
2
0
1
2
0
2
0
0
1
0
0
2
0
1
1
1
1
1
0
1
2
1
1
1
0
1
0
0
0
1
1
1
1
1
0
1
0
0
2
1
2
0
2
1
0
1
1
1
1
0
1
1
0
0
1
1
0
0
1
1
0
1
2
1
2
0
0
2
1
1
4
1
1
0
2
1
1
2
0
1
1
0
1
1
2
1
3
2
2
1
1
2
1
2
0
1
2
2
2
2
1
0
1
2
2
0
1
2
2
1
0
1
0
0
1
2
1
1
0
0
0
0
0
2
1
1
1
1
1
1
0
2
0
1
1
2
1
1
1
1
1
0
0
0
2
1
0
0
1
1
1
2
1
1
0
0
1
0
2
1
0
1
0
2
3
2
0
2
0
1
0
1
0
1
1
0
1
1
1
2
1
1
2
1
1
1
0
1
1
1
1
1
2
2
2
1
0
2
2
1
1
2
1
2
0
0
0
1
1
2
0
0
3
0
0
0
1
0
0
1
0
2
0
2
0
1
1
1
1
0
1
0
1
1
2
2
1
1
2
1
0
2
0
2
0
0
2
0
1
1
0
1
2
1
2
1
1
1
1
1
0
1
1
0
2
1
0
2
2
2
0
0
0
0
2
0
0
2
1
0
2
1
1
0
2
1
1
0
0
1
0
0
1
3
0
0
2
3
1
0
2
1
1
1
1
1
2
0
0
1
1
0
3
1
1
1
1
1
0
2
0
2
0
0
1
2
2
0
1
0
2
1
4
1
2
1
0
0
1
0
0
1
1
1
2
1
0
0
0
2
1
0
1
1
1
1
2
0
1
1
1
1
0
1
0
1
1
1
0
1
1
0
0
0
0
1
1
1
1
0
1
2
1
1
0
0
1
1
1
1
0
1
1
1
1
1
3
0
0
1
2
2
1
1
0
1
0
2
2
0
1
1
0
1
2
2
2
1
2
0
0
2
0
0
0
1
2
0
1
1
1
1
1
1
2
1
1
1
1
0
1
0
0
0
1
1
2
1
2
1
0
1
0
0
0
1
0
1
1
0
0
1
2
1
0
0
2
1
1
1
1
0
2
0
1
0
1
2
0
2
1
0
1
2
1
0
1
0
1
1
0
0
0
0
3
1
1
2
1
0
1
0
1
1
0
2
1
0
1
1
1
2
1
0
2
2
0
1
0
1
1
1
0
1
1
1
0
1
3
1
2
0
1
2
1
1
2
1
2
2
2
2
0
1
2
1
1
3
1
0
1
1
1
2
0
1
1
1
1
1
1
0
0
1
1
0
1
1
0
2
1
2
0
3
1
1
0
1
1
1
2
1
0
1
0
1
1
1
0
1
0
2
2
1
1
1
1
0
1
1
2
1
1
2
1
1
0
1
1
0
2
2
1
1
1
0
0
1
2
0
1
2
1
1
1
1
1
0
0
1
2
1
0
0
1
2
1
0
0
0
2
1
1
2
1
0
0
0
2
0
0
0
1
1
1
0
1
0
0
1
2
0
2
2
1
0
3
1
0
1
1
0
0
0
0
1
2
1
0
0
2
1
0
1
1
1
4
3
2
1
1
1
1
2
2
0
0
2
1
1
1
1
2
0
0
1
1
1
1
1
1
1
1
2
2
1
0
1
1
0
1
0
0
2
1
0
2
2
2
0
0
1
1
1
0
2
1
1
1
2
2
1
2
1
2
1
1
0
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
2
1
0
3
0
1
1
2
1
1
1
0
1
2
0
0
1
1
1
1
2
1
1
1
0
1
2
1
1
1
1
1
0
1
1
2
0
1
1
1
1
0
1
1
0
1
1
2
1
0
1
0
0
2
0
1
2
1
2
1
1
0
1
1
0
1
0
1
0
2
1
1
0
1
1
2
2
1
2
0
2
2
2
2
1
1
2
1
0
0
2
1
1
2
1
1
2
1
1
0
0
1
1
0
1
1
1
0
0
1
1
2
1
1
2
1
0
1
2
0
0
2
0
1
0
0
1
1
1
2
1
0
1
3
1
2
0
0
1
2
1
1
1
1
1
1
0
1
2
1
1
2
1
0
1
2
0
0
1
0
1
1
0
0
1
1
1
0
1
0
1
2
1
2
0
3
2
1
2
0
2
2
1
1
0
1
0
1
1
0
2
0
1
0
1
0
0
1
3
1
1
1
1
1
2
1
0
1
2
1
0
1
1
1
2
1
1
0
0
0
1
1
0
2
1
1
0
2
2
1
1
0
1
0
0
0
1
0
0
1
0
2
1
1
2
0
1
0
0
1
1
1
0
1
1
2
3
2
1
0
1
1
3
2
1
1
1
1
2
1
0
2
2
1
1
2
0
0
1
1
0
1
1
1
0
2
3
1
0
2
2
0
2
3
1
1
1
1
1
2
0
1
2
1
1
1
1
2
1
0
1
0
1
0
1
2
1
2
1
1
1
2
2
2
1
1
0
0
0
0
0
2
1
1
1
2
1
1
2
1
1
2
1
2
1
1
0
1
1
0
2
1
0
0
1
1
2
1
0
0
2
1
1
1
2
0
1
2
3
1
1
1
1
1
1
0
1
1
1
2
1
1
0
1
0
1
2
1
2
2
2
0
0
1
1
1
0
2
1
1
1
0
1
0
2
1
1
1
1
0
2
1
1
1
1
1
1
1
1
1
0
1
1
0
0
0
1
3
1
2
0
0
0
1
1
0
1
1
0
1
0
0
1
2
2
0
1
2
2
0
2
3
1
1
1
0
1
2
1
1
1
1
1
2
2
2
0
1
0
1
1
1
1
0
1
1
0
0
0
1
2
0
1
2
2
0
2
1
1
1
0
0
0
0
1
0
1
0
1
1
1
1
1
0
1
0
2
0
1
0
1
0
1
0
1
1
1
1
1
1
1
0
1
1
0
2
0
2
1
0
0
1
0
1
1
2
0
2
2
2
0
1
3
1
0
2
0
1
2
1
3
0
1
0
0
0
2
2
1
2
1
2
0
2
1
2
1
0
1
2
1
1
2
1
1
0
0
2
1
1
0
1
1
0
2
1
0
1
2
1
1
1
0
2
2
1
1
3
0
1
1
1
1
2
1
1
1
0
1
0
1
1
0
2
1
1
0
0
1
1
0
1
0
1
2
0
1
0
1
1
1
1
0
1
1
1
1
0
1
2
0
1
1
1
0
2
2
1
1
1
1
0
0
1
1
0
2
1
2
1
1
1
1
1
0
1
1
2
2
0
1
0
0
1
0
1
1
2
1
0
1
1
2
1
0
0
1
2
0
1
0
0
1
0
1
2
1
1
1
0
1
2
2
2
1
3
1
1
1
2
1
0
1
1
3
0
1
1
2
1
0
0
1
1
1
2
0
2
0
1
1
1
0
1
1
2
2
1
1
0
0
0
0
1
1
0
1
1
0
1
1
2
0
1
0
1
0
0
1
1
1
1
1
2
2
1
2
2
1
2
1
0
0
0
0
1
1
1
0
0
0
1
1
0
1
2
1
1
1
1
0
1
2
1
1
0
1
1
1
1
2
0
0
1
1
0
0
1
0
0
1
1
0
1
1
1
3
2
1
0
0
0
1
3
1
2
2
0
1
0
1
1
1
2
1
0
1
1
2
1
2
1
2
0
1
1
2
2
1
1
1
0
1
1
0
0
1
1
2
1
0
1
0
3
0
2
1
1
1
0
1
1
1
1
0
1
0
2
0
0
0
0
1
1
0
2
2
1
1
1
2
1
1
1
0
1
1
0
0
1
1
1
1
0
0
1
1
2
1
0
0
1
2
1
1
2
0
0
0
1
2
2
1
1
1
0
1
2
2
1
1
2
2
0
1
1
1
0
1
2
0
1
2
1
0
1
0
1
2
1
2
2
2
1
0
0
1
1
1
1
1
0
1
1
1
0
0
1
1
1
1
0
1
1
1
1
0
0
1
2
1
1
1
1
1
2
0
2
1
1
2
0
1
2
2
0
1
2
2
1
0
2
1
0
1
2
2
0
1
0
0
1
2
1
2
0
0
0
1
1
1
1
1
1
0
1
1
1
2
1
2
1
0
0
2
1
0
2
1
0
1
2
0
1
1
1
0
0
0
2
0
1
0
2
0
1
1
1
1
1
1
3
2
0
0
1
1
2
1
0
0
0
0
2
2
0
0
1
1
2
0
1
0
1
1
0
1
1
0
0
0
1
2
0
0
1
1
1
0
0
0
2
1
1
1
1
1
1
1
0
0
1
1
1
1
1
1
2
2
0
1
1
0
2
2
1
1
2
1
2
1
1
1
1
1
0
1
0
1
1
0
0
1
3
1
2
1
0
1
1
1
1
0
1
1
1
0
2
1
1
0
0
1
0
0
1
2
1
2
2
1
0
1
0
2
0
1
1
0
0
2
0
1
2
2
1
1
0
1
2
0
1
1
2
0
0
0
2
0
1
1
1
0
1
1
0
1
1
1
1
3
1
0
1
1
2
1
1
0
1
1
2
2
2
2
1
0
0
1
1
1
2
1
1
1
0
1
2
2
1
1
1
0
1
2
1
0
2
1
2
1
3
0
0
1
2
2
1
1
0
1
2
1
1
0
1
1
2
1
2
1
0
1
0
1
2
1
1
0
1
1
1
1
2
1
2
1
1
1
0
0
2
2
2
2
0
1
1
2
0
1
1
2
1
2
1
1
2
1
0
0
0
2
1
1
2
0
0
1
1
1
2
1
1
1
1
2
1
0
1
0
2
0
1
1
0
1
0
2
1
1
1
1
1
2
0
2
0
1
1
2
1
1
1
0
0
0
2
1
1
0
0
0
1
2
2
1
1
0
0
1
2
0
1
1
2
1
1
2
1
1
1
0
2
1
0
1
1
2
1
2
1
0
0
0
1
1
0
1
2
2
0
1
1
1
1
2
0
1
1
1
2
1
1
0
1
1
1
2
2
1
0
2
1
1
1
1
1
2
1
2
1
1
2
1
2
0
1
2
1
1
2
1
0
0
1
1
1
1
1
1
1
2
2
0
1
2
1
2
1
1
1
1
0
0
2
2
0
1
0
2
0
1
1
2
1
0
2
2
1
2
1
1
1
1
1
0
1
1
0
0
1
2
1
1
1
2
0
0
0
1
1
1
1
2
0
1
0
1
2
1
1
1
1
1
1
0
1
1
1
1
1
1
0
0
1
1
1
1
0
1
1
1
0
2
1
2
1
0
0
0
0
1
1
2
2
1
2
1
2
3
1
1
0
2
1
1
1
0
2
2
0
1
0
0
1
1
1
0
2
0
1
2
1
0
1
1
1
0
0
0
3
1
2
1
0
1
1
0
2
2
1
0
1
0
0
1
2
2
2
0
0
1
0
1
0
0
1
1
0
2
1
0
0
0
2
1
1
1
0
0
0
1
2
0
1
0
1
1
0
2
0
1
2
1
0
2
0
1
2
1
2
0
2
0
1
2
0
0
0
0
0
1
2
0
2
2
1
1
1
1
3
1
0
2
1
2
1
1
0
1
2
0
0
0
0
1
2
1
1
0
1
2
2
0
2
2
2
1
1
0
1
1
1
1
1
0
1
3
0
1
0
0
1
2
2
2
1
0
1
2
1
1
2
1
1
1
0
0
2
2
2
1
1
0
0
2
1
2
1
2
0
0
1
2
2
0
0
3
1
2
0
1
0
0
1
0
0
0
3
1
0
1
0
1
2
0
0
0
1
1
1
1
0
2
0
0
0
0
1
0
0
1
1
2
1
0
0
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
0
1
1
0
1
0
0
0
1
2
0
1
2
0
2
1
0
1
1
2
0
1
0
3
0
1
1
2
0
0
0
1
1
2
5
1
0
0
0
3
0
1
1
2
1
1
1
1
0
1
3
2
2
2
1
1
1
1
0
2
1
1
0
1
2
0
0
1
0
1
0
0
2
0
1
0
3
0
1
2
0
1
0
1
1
2
1
2
2
0
0
1
2
2
1
1
0
0
2
1
3
2
0
1
1
2
0
1
2
1
1
2
0
3
0
0
1
2
0
1
1
1
1
1
1
0
1
0
2
2
2
2
1
1
2
2
0
2
1
1
0
0
0
2
0
2
1
2
1
2
1
1
0
0
1
1
1
1
0
1
1
1
2
1
3
1
1
2
0
0
1
1
1
0
2
0
1
2
0
1
1
0
0
1
1
0
0
2
0
1
0
1
1
1
2
2
1
0
1
0
1
2
1
2
1
0
2
1
1
0
1
0
0
1
2
2
0
0
1
1
0
0
1
1
0
1
1
1
1
0
2
1
0
1
2
1
2
0
0
1
0
0
1
0
1
1
0
0
0
0
0
1
1
1
2
0
1
0
0
2
1
1
2
2
0
1
2
0
1
1
2
2
1
1
0
0
0
2
2
0
1
1
0
2
0
1
0
1
0
1
0
1
0
0
1
0
1
2
0
1
2
1
2
1
0
0
1
1
2
2
1
1
1
2
2
1
1
2
0
0
1
2
1
1
2
0
2
0
0
0
0
0
1
1
0
0
1
1
1
1
1
2
1
1
1
1
0
0
1
1
0
1
1
1
2
0
1
1
0
1
0
1
1
0
0
1
1
0
1
1
0
0
2
0
1
1
2
0
0
1
2
2
0
2
1
1
2
0
1
0
1
0
2
1
2
1
1
2
1
3
0
0
1
0
0
0
0
0
1
1
1
2
1
4
1
1
2
1
2
0
1
0
2
0
1
0
1
0
0
0
2
1
2
1
1
1
1
1
2
1
1
0
2
0
1
1
1
1
2
1
0
0
0
0
0
1
1
1
1
1
0
2
1
2
1
2
0
2
1
3
1
0
2
1
2
2
1
1
1
1
1
1
0
1
2
1
1
0
0
0
1
2
1
0
0
2
1
0
1
1
2
1
2
2
1
1
1
0
3
2
1
1
2
2
0
3
2
0
1
1
1
2
0
1
2
1
0
2
2
1
1
1
2
0
1
1
0
0
1
1
1
0
1
1
0
0
1
1
1
0
0
3
2
2
2
2
1
0
1
0
0
0
2
1
0
0
0
1
2
1
1
0
1
0
1
1
1
2
1
1
3
2
0
0
1
0
2
2
1
1
0
0
1
1
2
0
1
2
1
1
2
2
0
1
0
1
0
0
1
3
0
1
1
0
1
1
0
1
2
2
1
2
1
1
1
0
1
1
0
0
0
2
1
1
0
1
2
2
1
2
1
1
0
0
1
1
2
1
1
0
0
2
1
2
1
1
1
0
0
0
1
1
1
2
2
1
1
0
2
0
1
1
1
1
1
1
1
0
1
2
1
1
0
0
2
0
0
1
1
2
2
1
2
1
0
2
0
0
0
0
1
2
1
0
0
0
0
1
0
0
2
1
1
0
1
1
1
1
1
1
1
1
2
1
2
0
0
2
1
1
0
1
1
2
1
0
1
1
1
2
1
1
1
1
2
1
1
2
1
0
2
1
2
0
1
0
1
1
2
1
1
1
2
4
1
2
0
0
1
0
1
1
0
1
2
1
2
0
1
1
2
0
1
0
1
0
0
0
1
0
2
1
1
1
0
1
0
0
0
1
2
1
0
0
1
1
1
1
0
2
2
0
1
0
1
1
1
1
2
2
1
0
2
0
1
1
1
0
2
1
1
0
2
2
0
0
1
1
1
2
0
1
2
0
1
1
0
1
2
1
1
0
0
2
2
2
0
0
1
2
0
2
1
0
1
1
1
1
1
1
0
2
1
2
1
1
1
0
1
1
1
0
0
1
2
0
1
1
1
2
0
1
0
1
1
0
2
2
2
0
0
0
1
0
1
4
0
0
1
1
1
2
1
1
0
0
1
1
1
1
1
1
3
0
1
1
0
1
1
3
1
1
1
2
0
1
0
1
1
1
0
1
1
0
2
2
2
2
0
0
1
0
2
1
1
1
2
1
1
1
1
3
2
1
1
0
0
1
0
0
1
1
0
1
1
2
1
0
2
1
1
1
2
0
1
1
1
1
0
2
1
1
1
1
0
0
0
0
1
0
0
0
2
0
0
1
1
0
2
1
1
1
1
0
2
2
0
1
1
2
1
0
1
0
2
0
1
1
2
1
1
1
2
1
1
1
1
1
0
0
1
1
1
1
1
1
0
1
2
2
0
1
1
0
1
2
1
0
1
0
1
1
0
1
1
1
1
0
2
2
0
2
1
1
1
1
0
1
0
1
1
1
0
2
1
1
2
2
0
2
1
0
2
2
0
2
0
1
0
2
2
2
2
1
0
2
1
2
1
1
2
2
2
1
2
1
1
1
0
1
0
0
1
0
2
1
1
1
0
2
2
1
1
1
2
1
1
2
2
1
2
0
0
1
0
1
2
1
0
0
0
0
1
0
1
1
2
1
1
2
1
1
2
2
1
1
0
0
2
2
2
1
2
2
0
1
1
2
1
2
1
1
1
2
0
1
0
1
1
0
0
1
0
1
1
1
0
2
2
1
1
1
1
2
1
5
1
2
1
1
0
1
0
2
3
0
0
1
1
1
1
1
0
1
0
0
2
2
1
0
0
2
2
1
1
1
1
1
1
0
2
0
2
0
1
0
1
1
0
0
0
1
0
1
2
0
0
0
1
2
1
1
1
0
1
1
2
1
2
1
0
2
0
2
2
1
2
1
0
1
1
1
1
0
1
0
1
1
0
2
1
0
1
1
1
0
1
0
1
1
0
0
2
2
0
0
0
0
1
1
1
1
2
1
1
0
1
1
1
1
2
1
0
0
1
1
1
1
1
1
1
1
1
0
1
2
0
1
0
0
0
1
1
1
1
1
0
0
2
1
0
1
1
0
2
1
1
0
0
0
1
1
2
0
1
0
2
1
1
1
1
1
1
0
2
1
2
1
2
1
1
0
1
0
1
0
3
1
1
1
1
1
1
0
2
0
1
0
0
0
1
2
0
0
0
1
0
2
0
1
1
1
2
0
1
0
1
1
1
1
1
2
1
0
0
0
1
1
1
1
0
2
0
2
0
1
2
0
1
2
1
0
1
1
1
1
1
0
1
1
2
1
2
0
1
1
2
1
0
2
1
1
0
1
0
0
1
0
0
1
1
1
1
1
0
0
1
0
0
1
0
1
1
1
2
1
1
1
1
1
0
1
2
0
1
1
0
1
1
0
0
1
0
1
2
2
1
2
2
1
0
1
1
2
1
0
2
0
1
0
1
2
0
1
1
2
2
1
1
0
0
2
1
1
2
1
2
1
1
2
1
0
0
0
1
1
0
2
2
1
2
0
3
1
1
1
1
3
1
3
0
1
0
1
1
0
1
0
1
1
1
2
1
1
1
1
1
0
1
1
2
1
1
1
1
2
1
0
2
2
1
0
0
1
0
7
2
1
1
2
2
1
0
1
0
1
1
0
0
2
2
1
0
1
1
2
1
0
0
1
2
1
2
2
2
1
2
2
1
2
0
1
1
0
1
0
2
1
2
0
0
0
0
2
2
2
0
1
1
0
0
1
2
1
1
1
0
2
1
0
0
1
1
0
1
0
0
1
1
1
1
1
0
0
2
1
0
1
5
0
1
2
2
1
0
0
0
1
1
0
1
0
1
0
2
1
0
0
1
2
2
1
1
1
0
0
1
1
1
0
1
2
1
0
0
1
1
0
1
2
2
1
1
1
0
0
1
2
0
0
1
1
0
0
2
1
0
1
0
2
0
1
1
0
2
0
1
0
1
2
2
0
2
2
1
1
1
1
1
1
0
1
0
1
0
1
1
0
0
2
1
1
0
1
2
0
1
1
0
1
0
0
0
1
1
0
1
1
2
0
1
2
2
1
0
0
0
1
0
0
0
1
1
0
0
0
1
1
1
0
2
2
1
0
0
0
1
1
1
0
0
2
1
2
1
1
1
0
1
2
0
0
0
1
0
0
2
0
0
1
1
0
0
1
1
0
2
0
1
1
1
0
0
0
1
1
0
1
1
0
1
1
0
1
0
1
0
2
1
1
1
1
1
1
2
2
0
1
2
0
1
1
2
0
0
0
0
1
1
0
2
1
0
1
1
1
0
2
0
1
0
1
0
1
1
1
1
1
0
1
1
1
0
1
1
0
1
0
0
0
1
1
0
0
1
2
1
2
1
2
1
1
1
0
1
2
0
0
0
1
1
1
0
1
1
1
1
1
1
1
1
2
1
1
0
0
2
1
0
0
1
1
2
0
0
2
1
1
0
1
1
1
0
1
1
0
1
1
2
0
0
1
1
2
1
2
3
1
2
0
0
0
2
0
1
1
0
0
2
0
1
1
0
1
0
1
1
0
0
1
0
1
0
1
0
1
1
1
0
0
1
0
1
1
2
1
0
0
1
2
1
2
0
1
1
2
2
1
2
1
0
1
0
0
2
0
0
2
0
2
0
0
2
1
2
1
1
1
2
3
1
1
0
1
1
1
1
4
0
0
0
2
0
1
1
1
2
1
2
1
1
1
0
1
0
0
1
2
2
1
1
1
2
1
1
0
1
1
2
1
0
2
2
1
1
1
0
1
2
0
2
2
1
1
0
1
1
0
1
0
1
1
2
0
2
3
1
1
1
1
1
2
1
0
0
0
0
1
0
1
1
0
1
1
0
1
0
1
1
0
1
1
1
0
1
0
1
3
1
0
3
1
1
0
0
1
0
0
0
2
1
2
0
0
0
1
1
1
0
1
2
0
1
2
1
0
1
2
2
1
1
1
2
2
0
0
2
1
0
0
0
1
2
1
0
2
1
0
0
1
0
1
1
2
0
0
1
0
1
0
0
0
2
1
0
2
0
1
0
1
1
3
1
2
1
1
0
0
1
0
3
0
2
1
0
1
2
2
0
0
2
1
2
1
2
0
1
1
1
1
2
1
1
1
1
1
0
1
2
1
1
0
1
2
1
2
2
1
0
2
1
1
1
0
1
1
1
0
1
0
1
2
0
1
1
1
2
1
2
1
1
0
1
2
2
2
1
0
0
2
1
1
1
1
2
1
0
1
1
1
2
1
0
2
1
2
0
1
1
1
1
2
1
1
1
1
2
3
0
2
0
1
2
2
0
2
1
1
2
0
1
0
1
1
0
0
1
2
2
0
0
0
1
0
1
3
0
1
0
1
0
2
0
1
2
3
1
1
2
0
1
2
1
1
2
1
1
2
0
2
1
0
0
2
0
1
1
0
0
0
0
1
1
1
1
0
2
1
1
0
0
1
0
2
1
1
2
1
1
0
0
1
1
2
0
1
1
1
2
0
1
0
1
1
1
1
2
1
1
1
1
1
0
2
0
2
0
2
1
1
0
1
1
1
0
0
2
1
2
0
0
0
1
1
0
1
1
1
1
1
2
0
3
0
0
1
0
1
0
1
2
1
2
0
0
2
1
0
1
2
1
2
0
0
0
0
1
0
1
0
2
3
1
2
1
2
0
2
0
1
1
1
1
0
1
0
1
1
2
2
2
0
1
1
2
1
1
1
0
1
2
1
1
2
1
3
1
2
2
2
2
3
0
1
1
1
1
1
2
2
1
2
1
0
1
0
1
0
1
1
1
1
1
0
0
1
1
0
1
3
1
1
2
0
1
1
1
1
0
1
1
1
2
0
1
2
0
0
0
1
1
1
0
1
1
1
1
1
2
1
1
1
2
1
1
1
0
1
1
0
0
1
2
1
1
1
1
1
1
1
1
2
2
0
0
1
2
1
1
6
1
0
1
2
1
2
0
2
2
1
1
0
0
2
1
2
0
1
0
0
1
2
1
1
2
2
0
0
0
1
1
1
1
0
1
0
1
4
0
1
0
2
1
0
1
0
1
1
0
0
1
2
1
1
3
0
0
1
0
1
2
2
0
1
0
0
3
1
0
2
2
1
2
0
1
2
0
2
1
2
1
2
0
2
0
0
0
1
2
1
0
1
1
1
0
2
1
2
1
1
0
1
1
0
1
0
2
1
1
1
1
3
1
2
1
1
2
2
2
1
1
2
1
1
1
2
1
0
1
1
2
2
0
0
2
2
1
2
2
0
1
1
1
1
1
2
0
2
1
2
1
1
1
1
0
1
1
0
0
0
2
1
1
1
3
2
1
1
2
1
0
0
0
1
1
1
2
0
1
1
0
2
1
1
2
1
1
0
1
2
1
1
1
0
0
0
1
0
0
1
2
2
0
1
2
2
2
0
2
0
1
2
0
2
0
1
1
1
0
2
2
1
1
1
1
2
1
0
0
0
2
0
1
2
2
0
0
0
0
0
2
1
1
1
1
2
1
0
1
1
0
1
0
1
1
1
2
2
2
2
0
0
1
1
2
1
2
1
0
0
1
0
1
0
1
1
0
0
0
2
0
2
0
1
1
2
0
2
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
0
1
0
0
2
1
3
1
0
1
0
0
1
0
1
3
0
1
0
0
0
1
2
0
1
1
1
2
1
2
2
2
0
0
1
1
2
1
1
1
2
2
1
0
0
1
0
1
1
1
1
1
0
2
1
0
1
1
0
0
1
1
1
0
1
1
1
1
2
0
0
0
0
1
0
0
2
1
2
1
1
2
1
0
2
0
2
1
1
1
1
2
1
0
1
1
1
1
1
1
0
0
1
1
1
1
1
2
2
1
1
1
2
2
1
1
0
3
1
0
1
1
0
1
2
0
2
0
2
0
1
2
2
1
0
1
1
2
2
1
2
2
1
0
0
0
2
1
2
1
0
1
2
0
2
1
1
1
0
0
0
2
0
2
1
0
0
0
1
0
0
1
1
1
2
2
1
0
1
1
1
1
1
0
1
1
1
1
2
1
1
1
0
2
2
3
1
0
0
0
0
5
1
0
1
1
2
2
1
2
0
2
2
1
1
2
0
0
0
2
1
2
0
0
1
1
0
1
0
1
1
2
0
1
0
1
2
2
1
1
1
0
1
1
1
0
2
0
0
2
0
2
2
0
2
2
1
0
0
1
1
2
1
1
1
0
0
0
0
1
0
1
0
1
2
1
1
1
1
0
1
1
1
2
1
2
1
1
2
1
1
0
1
1
1
0
1
1
0
1
0
1
0
1
2
1
3
1
1
0
2
2
2
2
0
2
2
2
1
1
0
1
1
1
2
1
1
1
0
1
1
1
2
0
0
2
1
1
2
1
2
1
1
1
0
1
0
1
1
0
1
1
1
0
1
1
1
0
1
1
2
0
1
1
0
1
2
0
2
1
0
0
1
2
1
1
0
0
0
0
0
0
1
2
2
0
1
1
0
1
0
2
1
2
1
1
1
0
2
1
2
0
1
1
1
1
2
1
1
1
2
1
0
1
0
1
2
1
0
1
2
1
1
2
0
1
1
1
1
0
1
2
1
1
2
2
1
0
0
1
1
1
1
1
2
1
1
1
0
2
0
1
1
1
1
1
2
1
2
1
0
2
2
0
1
1
0
2
1
0
1
0
1
0
1
0
2
1
2
1
0
1
2
0
0
1
0
1
1
1
0
1
2
0
2
0
1
1
0
0
0
1
1
0
1
1
2
0
1
2
2
2
0
1
1
1
1
1
1
0
1
1
0
0
1
0
0
1
1
0
2
1
1
2
1
2
1
0
1
0
2
0
1
1
2
1
1
0
1
0
1
1
3
2
1
0
2
2
1
1
0
1
0
2
1
1
0
2
1
4
1
1
1
0
0
1
1
1
0
0
2
0
0
1
1
1
1
1
0
1
1
1
1
0
1
2
0
1
1
0
0
1
2
0
2
1
0
1
1
0
1
1
2
2
1
2
0
1
1
1
1
1
0
0
2
1
1
0
0
1
1
1
0
0
1
1
0
5
1
0
0
1
1
0
0
1
2
0
2
1
1
1
0
1
1
2
1
1
0
1
2
1
0
1
1
1
1
0
2
0
1
0
1
1
0
2
1
2
0
1
1
1
0
1
1
0
0
2
2
0
0
2
1
0
2
2
1
2
2
1
1
1
0
1
0
1
2
1
2
0
0
1
2
2
0
1
0
1
1
1
1
1
1
2
1
2
1
1
2
0
1
1
1
0
0
1
2
1
1
1
1
0
1
1
0
1
0
1
0
0
1
1
1
1
2
1
1
1
0
1
0
1
1
1
2
0
1
1
1
1
2
2
1
1
1
1
1
1
0
1
1
2
0
1
0
1
0
0
1
0
1
0
2
1
0
0
0
0
1
0
0
2
1
2
1
1
2
1
1
2
2
1
1
2
0
1
2
1
1
0
2
1
1
1
1
1
1
1
1
0
0
2
0
1
1
1
0
0
1
2
0
0
2
1
1
2
0
0
1
0
1
2
1
1
1
1
2
1
2
2
1
2
2
1
1
2
1
0
1
1
0
1
1
1
1
1
1
2
1
1
0
1
1
1
1
0
2
0
0
0
0
1
2
0
1
1
0
0
0
1
0
1
0
0
0
1
1
1
1
1
0
1
1
1
2
2
0
1
1
1
0
0
1
2
2
2
0
1
3
1
2
2
0
0
0
1
1
2
0
0
0
0
1
1
1
1
1
2
3
2
0
1
0
1
1
1
0
0
0
1
0
1
1
1
1
1
0
2
3
1
1
0
0
1
1
3
1
1
1
2
1
2
0
1
2
2
0
1
1
1
1
2
1
1
0
1
1
1
1
1
2
0
1
2
1
0
1
1
0
2
2
2
0
0
1
2
1
1
0
1
0
2
1
1
1
1
1
2
1
1
2
1
1
1
0
0
0
1
2
0
0
0
1
1
1
1
0
1
0
1
1
1
1
2
1
1
1
0
0
2
0
1
2
0
1
1
2
0
1
0
1
1
3
1
1
1
2
0
1
1
1
1
2
2
1
1
1
0
1
1
3
1
1
1
1
0
1
0
1
0
0
0
2
1
0
2
2
1
0
1
0
0
0
2
1
1
2
1
1
2
2
1
1
1
0
0
1
2
2
1
1
0
0
1
1
1
0
1
1
0
0
0
2
3
0
0
0
1
1
1
2
0
1
1
1
2
1
0
1
1
2
1
0
1
1
1
2
0
1
0
2
0
1
2
1
0
1
1
0
2
1
0
0
0
0
1
1
1
3
2
0
1
0
1
2
2
1
2
1
3
1
2
2
0
0
1
1
2
1
0
0
2
0
0
1
0
1
0
0
0
1
0
0
1
0
1
0
1
1
1
2
1
1
0
2
1
1
1
1
0
2
0
1
1
2
0
1
2
0
1
0
2
1
1
2
2
1
0
0
1
0
1
0
1
1
2
1
1
1
1
2
2
0
1
0
0
2
2
1
2
0
1
1
1
1
1
2
2
1
0
1
0
1
2
1
1
0
1
1
0
0
1
0
0
1
1
0
1
1
0
1
0
1
1
1
1
0
0
1
1
1
1
1
4
0
1
2
0
2
1
2
0
2
1
0
0
2
0
1
0
0
0
2
1
2
1
2
1
0
2
0
1
1
1
0
0
1
2
2
2
1
1
1
1
1
0
1
2
1
2
1
2
1
1
0
2
2
1
1
0
0
1
2
0
0
0
1
1
1
1
1
1
3
1
1
0
1
2
1
2
1
1
2
1
1
1
1
1
0
2
0
1
0
0
0
1
0
0
1
1
2
0
2
0
0
1
0
2
1
1
0
0
2
1
1
1
0
1
1
0
1
2
1
1
2
1
1
2
0
0
2
1
2
1
1
0
1
1
0
1
1
0
0
0
2
1
1
1
2
1
2
1
1
1
1
2
1
2
1
4
1
0
1
1
0
0
2
1
0
2
1
1
0
1
0
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
0
0
0
2
0
1
1
2
1
1
1
0
1
1
2
1
1
0
1
1
0
2
0
1
0
1
0
1
2
0
1
2
1
1
1
2
1
1
1
0
0
1
0
1
1
0
0
1
1
1
0
2
1
2
0
1
0
2
1
1
1
0
1
1
0
0
1
2
1
1
0
1
1
2
2
1
1
2
0
1
1
1
1
3
1
1
1
2
1
2
1
0
0
1
2
2
2
1
1
0
1
2
2
1
0
1
2
1
1
0
0
3
0
0
1
2
2
1
1
2
1
1
2
0
1
2
1
0
0
1
1
1
2
1
1
1
2
2
0
0
1
1
0
1
1
1
2
1
1
2
0
1
1
0
1
1
1
2
0
2
1
1
0
2
2
2
0
2
1
1
1
1
0
1
0
2
1
0
0
1
0
1
1
1
1
1
1
0
1
0
1
0
1
1
1
2
2
1
1
1
2
1
0
1
0
1
1
1
0
1
2
2
1
0
0
1
1
0
2
0
1
1
1
0
0
0
1
0
1
1
1
1
0
0
1
0
1
0
0
1
0
1
1
0
1
1
1
0
0
1
2
1
1
1
2
1
1
0
1
1
0
0
2
2
0
0
1
2
1
2
0
0
0
1
1
1
2
1
1
2
1
1
1
2
0
0
1
0
1
1
1
0
1
2
1
0
1
1
1
0
1
2
0
0
1
2
0
1
0
0
2
2
0
0
2
2
0
1
1
2
2
1
2
0
8
2
1
0
1
1
2
1
1
1
0
1
2
1
1
1
2
1
0
1
1
0
1
1
0
0
0
0
2
2
1
2
2
0
2
2
0
1
1
2
2
1
2
2
0
2
1
2
0
1
0
1
0
2
1
0
0
1
1
0
1
2
1
2
1
1
1
0
2
0
1
1
0
1
0
1
1
2
0
1
0
1
1
2
1
1
0
1
1
2
1
2
0
2
0
0
1
1
1
1
1
0
1
2
1
1
1
1
2
1
2
1
1
1
2
1
1
2
2
1
2
0
2
1
2
1
1
1
2
1
3
0
1
0
1
0
1
1
1
1
0
1
1
1
0
0
1
1
2
0
1
1
0
2
1
2
2
1
1
1
0
0
0
2
1
0
0
1
0
0
1
0
1
0
2
1
0
0
0
1
0
0
1
1
0
2
0
0
0
1
2
0
3
1
2
0
1
1
1
1
0
1
1
1
2
2
0
1
2
0
1
1
2
0
0
0
2
0
1
1
1
0
1
2
1
1
1
1
1
0
1
1
1
1
1
0
1
1
1
0
0
0
0
2
2
2
1
1
2
1
1
2
0
2
1
1
1
0
1
1
1
0
1
0
1
2
1
2
0
1
0
1
1
1
2
2
0
1
1
2
1
1
1
1
0
0
1
1
0
2
0
0
1
1
0
1
1
1
0
2
0
2
1
1
1
0
1
0
1
0
0
1
0
1
1
1
1
0
1
2
1
0
1
1
1
1
1
0
3
1
2
1
1
1
1
2
2
1
0
2
0
1
0
2
1
0
0
2
0
1
1
0
0
1
2
1
2
0
2
0
5
0
2
1
1
1
0
1
1
1
1
1
1
0
1
1
0
0
0
1
1
2
2
2
1
0
2
0
2
1
1
2
1
1
1
0
1
0
1
0
2
0
1
2
1
2
0
1
0
1
1
2
1
2
1
0
0
1
0
1
1
2
1
0
1
1
1
0
2
0
1
1
1
1
0
0
0
1
2
0
0
1
1
0
3
1
0
1
0
0
0
0
2
2
2
0
1
0
1
1
1
1
0
0
1
0
0
1
1
0
1
1
0
0
1
1
1
2
1
2
1
1
0
0
0
2
1
1
1
0
1
1
0
3
1
1
1
1
1
2
1
0
1
1
2
1
2
1
1
2
1
2
0
0
1
0
0
3
0
2
0
1
1
1
1
1
0
3
1
1
0
1
1
1
1
2
0
0
2
1
1
1
1
2
2
1
1
0
1
0
1
2
0
2
0
2
0
2
0
1
0
1
2
1
0
1
0
1
0
1
1
0
2
1
1
1
0
1
0
0
2
1
2
0
0
0
0
2
2
1
0
2
1
1
1
0
1
2
0
2
1
1
0
2
1
1
1
1
1
1
1
0
1
0
0
0
1
0
1
2
2
1
2
1
0
1
0
1
2
2
1
2
1
1
1
2
2
0
0
1
1
1
0
0
1
1
1
1
2
1
0
0
0
1
2
2
2
1
2
2
2
0
1
0
1
2
2
1
1
2
0
0
0
0
1
3
2
1
1
2
1
0
1
2
0
0
1
1
1
1
2
2
2
0
0
0
0
1
0
0
0
1
2
2
1
1
0
0
2
0
0
0
2
2
2
0
1
1
1
2
2
2
1
1
2
1
0
1
2
1
2
0
1
1
1
1
2
1
2
0
1
1
1
1
0
2
1
1
1
1
2
1
2
1
2
1
0
1
1
1
0
0
1
1
2
1
1
0
2
1
1
1
1
0
0
1
1
0
0
0
0
1
0
1
0
1
3
2
1
0
1
1
0
2
1
1
0
2
0
1
0
1
1
1
1
0
2
1
0
1
1
0
2
1
0
0
1
1
0
0
1
1
3
2
0
1
1
1
1
1
1
1
2
1
1
0
1
1
2
1
1
2
1
2
2
2
2
1
2
1
2
1
1
1
0
2
1
1
1
2
0
1
0
1
1
0
1
0
2
1
1
0
0
1
1
1
0
2
1
2
1
0
1
1
1
0
0
1
2
0
2
1
2
0
0
0
2
0
1
1
2
1
1
0
1
2
2
1
2
2
0
1
1
2
1
0
1
1
1
1
0
2
2
1
1
0
0
1
1
1
0
0
2
0
1
0
2
1
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
2
2
0
1
0
1
1
1
0
1
1
2
1
2
2
2
0
1
1
1
1
1
1
2
1
2
1
0
2
2
0
0
0
0
1
1
1
2
1
2
2
1
0
2
2
1
1
1
1
1
2
0
0
1
1
1
2
2
1
1
3
1
1
0
1
1
2
1
2
1
1
0
2
2
0
3
1
1
0
0
1
1
1
0
2
1
0
1
1
0
1
1
0
2
2
0
0
0
0
0
2
1
0
0
0
1
1
1
1
2
1
1
1
1
1
1
1
1
0
2
1
1
1
0
1
2
1
1
1
1
0
2
1
0
1
1
1
0
1
1
2
1
1
1
2
2
1
1
1
1
1
0
0
1
2
0
1
1
0
1
1
1
1
0
0
1
2
2
0
1
2
0
0
0
1
1
1
1
0
0
2
1
1
1
2
2
2
2
1
0
0
1
0
0
1
1
0
1
2
1
1
0
0
1
0
1
2
1
2
1
1
1
1
1
1
1
2
0
2
2
0
0
0
1
0
1
2
0
0
2
1
1
1
1
1
0
0
1
1
1
1
1
0
0
1
0
1
1
0
1
1
1
1
1
1
1
1
1
1
2
2
0
1
1
2
0
2
1
1
2
2
1
1
0
0
2
1
1
0
0
1
1
2
1
1
2
1
4
1
1
1
1
1
2
0
2
0
1
2
0
0
2
2
2
1
0
0
2
0
1
1
2
2
3
0
2
2
1
1
1
1
0
2
2
0
1
1
2
1
1
2
1
1
1
1
0
1
1
0
1
1
1
1
1
1
0
1
1
0
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
1
1
0
1
0
1
2
1
2
1
1
0
1
1
1
0
0
1
0
1
0
0
2
1
0
2
0
0
1
2
2
2
1
2
1
2
1
2
0
0
1
1
1
0
2
1
2
0
1
0
1
1
1
0
1
0
1
0
0
1
0
2
2
1
1
2
2
0
2
1
0
1
0
1
0
1
1
2
3
1
0
1
1
1
0
1
1
1
0
1
1
1
0
2
1
1
0
2
1
2
0
2
1
0
2
2
2
2
1
1
0
0
1
2
0
0
1
1
0
1
0
1
2
0
0
2
0
1
0
1
1
1
1
0
1
0
0
1
2
0
2
0
1
1
2
1
1
1
2
1
1
0
0
1
0
1
1
2
0
0
2
2
1
0
1
2
0
1
3
2
0
1
1
1
0
0
0
2
1
1
1
1
1
1
0
2
0
0
1
1
1
0
1
0
1
1
1
1
2
1
0
0
1
1
0
2
1
1
1
1
1
1
0
2
0
1
1
1
1
0
1
1
1
0
1
0
1
0
2
1
1
2
0
0
1
1
1
1
0
1
2
0
1
1
1
2
1
0
0
1
2
0
1
0
0
2
2
1
1
1
1
2
0
1
2
0
1
2
1
1
2
2
1
2
1
1
1
1
1
0
0
2
0
0
1
2
1
2
2
2
1
1
1
0
2
2
2
2
1
2
1
0
2
2
1
1
2
2
2
0
2
2
1
1
1
2
2
1
1
1
2
0
0
2
2
1
1
1
0
0
1
1
3
2
0
1
2
1
2
1
2
0
0
3
2
1
2
1
1
0
1
2
0
2
1
1
1
1
0
0
1
0
2
1
0
1
1
2
1
1
0
0
0
1
1
2
2
2
1
3
0
2
1
3
3
1
2
3
1
1
1
1
1
2
1
1
2
1
1
1
1
2
1
3
1
0
1
2
1
1
0
0
2
0
2
1
1
1
1
0
2
1
0
0
0
1
1
2
1
1
0
0
1
0
0
0
2
1
1
0
2
2
1
0
1
1
1
0
2
2
1
0
2
2
1
0
2
1
1
0
1
1
2
2
0
0
0
2
1
1
2
1
2
0
0
1
0
2
2
1
1
2
1
0
2
1
1
1
1
0
1
1
1
1
1
2
1
1
2
1
2
1
2
0
2
1
0
1
0
1
1
1
2
1
2
2
0
1
2
1
0
0
1
0
1
2
1
1
1
1
0
0
2
2
1
0
2
0
1
0
1
1
1
2
2
1
1
0
1
1
1
2
1
1
0
1
0
1
1
0
1
1
2
0
1
1
0
1
2
1
0
0
1
0
1
1
0
0
0
1
0
2
1
1
1
0
2
1
0
0
2
2
1
2
2
1
1
0
1
0
2
0
0
0
2
0
2
1
1
1
0
0
1
1
1
1
1
1
2
1
0
0
0
1
1
1
0
2
1
1
1
0
0
2
1
1
1
1
0
1
0
2
2
1
1
1
0
0
1
1
1
1
2
1
2
1
0
0
2
2
0
1
1
1
1
0
1
0
1
2
0
1
0
1
0
0
1
0
0
0
1
2
1
1
2
1
1
2
0
1
0
2
2
2
1
1
0
0
0
0
2
0
1
1
0
2
1
1
0
2
2
0
0
2
0
1
1
1
2
2
0
0
0
1
2
0
2
2
0
1
1
1
1
1
2
1
0
1
0
0
1
0
1
0
0
1
1
2
1
0
2
1
1
1
0
1
2
1
2
2
1
0
2
1
1
1
0
1
1
0
1
3
1
1
0
0
1
2
1
1
0
1
1
1
1
0
1
1
2
1
2
1
1
1
0
1
1
1
2
1
0
1
1
1
0
2
2
1
2
2
2
1
0
1
2
1
1
1
0
0
1
1
1
1
1
0
1
0
1
0
1
1
1
2
1
0
0
0
1
2
1
1
1
1
1
1
1
0
0
2
0
1
0
2
2
2
0
0
2
0
1
2
1
0
2
0
1
0
1
1
0
1
1
1
1
0
1
0
1
2
1
2
1
1
1
1
2
1
1
2
1
0
1
0
2
2
1
0
1
1
1
1
1
1
1
1
0
1
1
1
0
1
2
0
2
1
1
0
2
1
1
0
1
1
1
1
0
1
1
2
1
1
1
1
1
1
1
0
1
1
0
1
1
1
2
1
1
1
1
1
0
2
1
1
2
0
0
1
1
1
0
3
1
1
0
1
0
1
1
1
1
2
1
2
1
0
1
1
0
0
2
1
1
0
2
0
1
0
0
2
1
2
1
0
2
1
1
1
0
2
1
1
1
0
1
1
2
2
1
1
0
2
1
1
0
1
2
1
2
0
1
2
1
1
1
1
2
2
1
1
0
1
0
2
0
2
1
1
1
2
0
1
1
1
2
2
0
0
0
0
1
0
1
0
1
2
0
1
1
2
1
0
1
1
1
0
2
1
1
1
0
1
1
0
0
1
0
1
0
1
1
2
0
1
1
0
2
1
1
2
0
2
0
1
0
1
1
1
1
1
1
1
0
0
2
1
1
1
1
1
1
1
0
2
0
1
0
0
1
1
1
0
1
1
0
2
0
0
2
1
2
2
1
0
1
0
1
2
2
4
0
0
0
1
1
2
1
1
0
1
0
2
1
1
1
2
1
1
2
1
0
0
1
1
0
1
1
1
1
0
1
1
2
1
2
0
1
2
0
1
1
0
0
1
1
1
1
1
1
1
2
0
0
0
0
1
1
1
2
1
3
2
2
1
1
1
2
0
0
1
1
1
1
1
2
2
1
2
2
1
1
1
1
1
1
1
1
0
0
1
1
1
2
2
1
2
1
1
2
1
1
2
2
1
2
2
1
1
0
1
2
0
1
2
2
0
2
1
0
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
0
1
1
2
1
2
1
1
1
0
1
1
1
1
0
2
2
0
2
2
1
1
1
0
1
3
0
2
1
1
2
0
2
0
1
2
2
2
1
0
0
0
1
1
0
0
1
0
1
1
0
1
0
0
1
0
1
1
1
1
0
1
0
4
2
1
1
2
1
1
0
0
2
1
0
2
0
0
2
0
0
1
0
0
1
1
0
0
0
0
2
2
1
1
1
2
2
0
1
1
0
2
2
1
0
0
3
2
1
2
2
1
2
1
1
1
1
2
2
0
2
1
1
1
2
1
0
2
1
1
0
1
1
1
2
1
0
1
1
2
2
1
2
1
0
1
1
1
2
1
1
1
1
0
0
1
1
2
1
0
1
1
1
1
0
1
2
0
1
1
0
1
1
1
1
1
2
0
0
0
0
1
1
2
0
2
1
1
1
1
1
0
0
1
1
1
1
1
2
0
1
1
0
2
2
1
1
1
0
0
1
1
1
1
1
2
2
2
2
1
1
1
0
1
1
0
2
1
0
2
0
1
2
2
0
2
1
1
4
1
1
2
1
1
0
1
1
1
1
0
1
0
1
1
1
2
1
1
1
1
1
1
2
0
0
1
1
1
0
2
0
1
1
2
1
0
2
2
1
2
0
1
1
1
2
1
1
2
2
2
1
0
1
0
2
0
0
0
1
1
1
0
2
1
1
0
1
2
1
2
0
1
1
0
0
0
1
1
3
0
1
1
1
1
3
1
0
1
1
1
2
2
0
1
1
1
1
0
0
0
2
1
0
1
1
2
2
0
1
1
1
0
1
1
1
1
1
1
0
0
0
1
0
1
0
2
1
1
1
2
0
0
2
1
1
1
0
2
1
0
1
1
0
2
1
1
0
2
0
0
0
2
2
2
1
1
1
1
2
1
1
2
1
2
1
1
2
0
0
0
0
1
1
1
0
1
0
2
1
0
0
1
0
2
2
0
1
1
1
2
1
2
1
1
2
2
1
0
1
1
0
1
0
2
1
1
1
2
1
1
2
1
2
0
2
2
2
2
2
2
1
0
1
2
0
1
2
2
1
1
1
1
2
1
0
1
0
0
2
2
1
1
2
2
1
1
2
1
1
0
1
1
1
1
0
1
2
1
2
0
1
0
0
1
1
1
2
0
0
0
2
1
1
2
0
2
1
2
1
0
1
0
2
1
1
1
1
1
0
0
1
1
1
1
0
0
1
1
0
1
2
1
2
0
0
2
2
1
1
1
1
1
0
0
1
0
1
1
2
2
1
1
1
0
1
1
2
1
1
1
1
2
1
1
1
2
0
0
2
2
1
0
0
2
1
2
2
2
1
0
0
0
1
1
0
0
1
1
1
0
0
1
0
1
2
1
1
2
0
1
1
0
1
2
1
1
2
0
1
1
1
0
1
1
1
1
1
1
1
0
0
0
2
0
1
1
1
2
2
2
1
1
1
1
1
1
3
1
1
1
1
1
1
0
0
0
0
1
0
0
1
1
0
1
1
1
2
2
1
1
1
2
1
1
0
0
0
1
2
0
1
1
1
2
0
0
1
1
0
2
1
3
0
2
1
1
2
1
1
1
0
1
1
1
2
1
2
2
1
1
1
1
1
0
2
1
1
0
2
0
1
2
2
1
1
1
1
2
0
1
1
2
1
0
1
1
1
0
0
1
2
1
1
1
2
3
1
1
2
2
1
0
2
1
0
1
1
2
0
1
2
0
2
1
2
0
1
0
2
0
1
0
1
1
1
1
0
2
1
0
1
1
1
0
1
1
1
1
0
2
1
0
0
1
1
2
2
1
0
0
0
2
1
1
1
2
0
1
0
1
1
0
0
0
1
0
2
2
0
2
1
2
0
2
2
2
2
1
1
1
1
1
2
1
1
2
1
2
2
0
1
1
1
0
1
1
0
1
0
0
1
2
0
1
1
1
0
1
2
0
0
1
2
0
1
2
1
2
1
0
0
0
1
0
0
1
1
2
2
0
1
2
3
1
1
1
0
1
1
1
0
0
0
1
1
1
1
0
0
2
1
0
0
2
1
1
0
1
3
0
0
2
2
3
1
1
1
1
2
1
2
3
0
2
1
1
1
1
1
0
1
2
1
1
1
1
2
0
0
1
1
0
2
2
1
2
0
0
2
1
1
0
1
0
1
0
1
0
1
0
2
1
1
0
0
1
0
0
1
2
2
2
1
1
1
2
3
1
1
1
0
0
2
2
2
1
1
2
1
2
1
1
0
1
1
0
1
1
1
2
1
0
1
2
1
0
0
1
1
1
0
0
0
2
1
2
1
2
1
1
2
0
2
2
1
0
1
0
3
2
0
1
2
0
1
1
1
2
0
1
1
2
0
1
1
1
2
0
0
1
1
0
0
1
0
1
1
1
1
1
0
0
2
2
2
0
1
1
0
0
0
2
1
1
1
2
2
1
1
1
1
1
0
0
0
1
2
6
0
1
0
1
1
1
0
1
1
0
2
0
2
0
1
3
1
1
0
1
1
1
1
0
0
1
2
1
0
1
1
0
1
0
2
0
0
1
1
1
1
1
1
1
1
1
1
1
1
0
0
0
0
1
2
1
2
2
0
0
0
1
1
0
1
0
0
1
0
2
0
1
1
2
0
1
1
0
2
1
1
1
1
2
1
2
1
1
1
2
1
2
1
1
0
0
1
2
1
2
1
0
2
1
1
2
1
2
1
0
0
1
2
0
1
0
0
1
1
1
1
0
0
2
0
1
1
0
1
1
1
0
1
1
2
1
0
1
2
0
0
2
2
0
1
2
0
2
0
2
1
0
1
0
2
2
0
0
1
0
0
1
1
1
0
1
1
2
1
1
1
1
0
1
1
0
2
2
2
0
1
1
1
0
1
0
1
0
1
0
1
0
0
3
0
2
2
2
0
2
1
2
1
1
1
1
1
1
1
1
1
3
1
1
1
1
0
2
1
2
1
1
1
1
2
1
2
2
1
2
1
1
2
1
1
0
1
1
2
0
1
0
1
1
1
1
1
0
0
1
1
1
0
2
0
1
1
1
0
0
0
1
1
0
3
1
2
1
0
2
1
1
1
1
1
1
1
0
0
1
3
1
1
0
0
3
1
1
1
1
0
0
1
0
2
1
0
0
0
1
1
0
2
0
2
2
0
0
0
0
2
1
1
2
1
1
0
1
1
1
0
1
1
1
0
1
0
0
0
0
1
1
1
0
1
1
1
1
0
1
2
0
2
1
1
1
2
0
2
1
2
1
2
0
1
2
2
2
2
2
1
2
1
1
1
2
1
1
1
0
1
1
0
1
1
0
0
0
2
1
1
1
1
2
2
0
0
1
1
0
0
2
1
2
1
0
2
0
1
1
1
2
0
1
2
1
2
1
2
2
2
1
1
2
2
0
0
1
0
0
0
1
1
1
1
1
1
2
2
0
1
0
1
1
1
1
1
0
2
1
0
1
5
0
1
2
1
1
2
1
1
0
2
1
0
0
2
1
1
1
0
1
0
1
1
1
2
1
1
2
2
2
1
1
2
2
1
0
1
1
0
2
1
1
1
0
1
0
0
0
0
1
0
0
0
1
2
2
0
1
0
1
0
1
2
2
0
1
1
0
2
1
2
1
1
2
1
1
2
1
1
1
0
1
0
1
1
2
1
1
2
0
0
1
1
2
1
1
2
1
2
0
1
2
1
1
1
0
1
0
1
0
1
1
0
1
0
1
1
1
2
1
0
0
1
1
1
2
2
0
1
1
0
1
0
1
2
1
1
1
0
2
2
5
2
2
0
0
1
2
1
1
1
1
1
2
1
1
1
1
1
0
1
1
1
0
1
0
1
0
2
0
1
2
2
2
2
1
2
2
1
1
1
1
1
0
0
0
0
1
2
1
0
1
2
2
0
1
0
1
1
1
1
0
1
2
1
1
1
2
1
1
1
2
0
1
2
1
0
1
0
2
0
0
0
2
1
2
0
0
0
1
1
0
1
0
2
1
0
1
1
0
0
1
0
1
1
2
1
1
1
1
2
1
1
0
0
0
1
1
2
2
1
1
1
1
1
0
0
1
1
2
2
2
0
1
0
0
2
0
0
1
2
1
2
1
0
2
0
1
0
1
1
1
1
3
1
0
2
1
2
1
0
0
1
2
2
0
1
2
0
2
1
2
1
1
1
1
1
0
1
0
1
1
2
0
0
1
1
1
1
0
0
2
2
2
0
1
2
1
1
0
1
1
0
2
1
0
1
0
1
0
0
1
1
1
1
1
0
1
1
1
1
1
1
0
1
2
1
1
1
1
0
0
2
2
2
1
0
1
1
1
2
1
1
0
1
1
0
0
0
1
2
1
1
0
0
1
1
0
2
1
1
0
1
1
1
1
2
1
2
0
1
0
1
1
1
1
1
0
0
1
1
0
2
1
0
1
1
2
2
2
0
1
0
1
1
2
0
3
0
1
1
2
2
0
1
1
2
0
1
0
2
1
4
1
1
3
2
0
2
1
0
1
0
1
2
2
1
1
1
1
1
0
0
1
2
0
2
2
1
0
2
2
1
2
0
1
1
0
0
0
1
1
2
0
0
0
1
1
2
0
2
1
0
2
1
1
3
1
2
1
1
0
0
0
1
0
1
0
0
0
0
2
1
1
0
1
1
2
2
0
1
0
1
0
1
1
1
1
1
0
1
1
1
2
3
2
1
2
1
1
2
2
1
1
1
1
2
0
2
0
2
0
1
0
2
2
2
1
1
1
1
2
2
0
1
2
1
2
2
1
0
1
1
2
0
0
2
0
1
1
1
1
1
2
3
1
2
1
1
0
0
2
1
2
0
2
1
0
0
1
1
1
2
1
0
1
0
1
1
0
1
1
1
1
1
1
2
1
3
0
1
0
1
2
2
1
0
0
1
1
0
1
0
1
2
1
1
1
0
2
1
0
1
1
1
1
2
1
0
1
1
1
1
1
1
1
1
2
1
1
0
2
1
1
2
0
1
0
0
2
2
2
0
0
0
0
2
0
1
2
1
1
1
1
0
0
0
0
2
0
2
1
0
2
0
1
1
1
1
1
0
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
0
1
0
1
0
1
1
0
1
2
2
0
2
0
0
1
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
2
1
2
1
1
1
0
1
0
2
2
0
1
2
1
2
0
0
1
1
1
0
2
1
2
0
1
2
1
0
0
0
2
2
2
0
0
1
2
2
0
2
2
1
0
1
1
1
1
0
1
0
1
1
1
1
1
1
1
1
1
1
1
0
1
2
1
0
1
1
1
0
2
2
0
1
0
0
0
2
1
0
2
0
0
2
1
0
1
1
1
1
1
0
2
2
2
1
2
1
0
2
1
1
0
1
1
1
0
1
2
2
1
2
0
1
1
2
1
0
1
1
1
1
1
1
1
2
1
1
1
1
1
0
1
2
0
0
2
2
2
2
1
1
2
0
2
1
0
2
0
1
2
0
1
0
1
3
1
1
1
0
1
1
0
1
1
1
1
2
0
1
0
2
2
1
1
1
2
0
1
1
1
2
1
0
1
1
1
1
2
1
2
0
1
1
2
0
1
0
2
0
2
1
1
2
2
2
1
2
1
1
1
1
0
1
1
2
1
1
0
1
2
2
2
1
1
0
1
0
1
1
0
1
1
2
0
1
2
0
1
1
0
0
0
1
0
1
1
0
2
0
1
1
1
1
0
0
1
1
1
1
1
2
2
1
1
0
0
1
2
2
1
1
1
1
1
1
3
1
1
0
0
0
0
1
0
2
1
1
0
1
1
0
1
0
1
2
1
1
1
1
2
1
1
1
1
2
2
2
1
0
0
1
1
1
1
0
1
2
1
2
0
0
1
0
2
0
2
2
2
1
1
1
1
0
1
2
1
0
2
0
1
2
1
1
1
1
1
1
1
2
2
3
2
0
2
2
1
1
0
1
2
0
0
1
0
1
1
1
2
1
1
1
2
1
0
2
1
1
1
1
0
2
0
2
1
1
2
0
2
2
1
1
0
2
1
2
0
0
1
0
1
2
1
1
1
2
1
1
0
0
1
0
2
1
1
2
1
2
0
2
4
2
1
1
0
2
1
1
0
2
1
1
1
1
1
2
1
1
1
0
2
1
0
0
0
1
2
2
2
1
1
1
1
1
2
0
1
1
1
0
2
1
0
1
2
0
1
0
0
0
0
1
0
2
0
0
2
0
1
0
1
1
2
3
1
0
2
1
1
1
0
1
1
0
2
1
2
1
2
1
2
2
1
0
2
0
1
2
2
0
0
1
1
1
2
2
0
0
2
2
0
1
1
1
0
1
0
1
1
0
1
1
1
2
2
1
0
0
0
2
1
2
1
2
2
2
1
0
0
0
2
2
2
0
0
0
1
1
2
2
1
2
1
1
1
1
0
0
1
1
1
1
0
0
3
1
2
0
1
2
1
1
2
1
1
1
2
1
1
1
2
3
1
0
1
1
0
1
1
1
0
0
0
2
1
1
1
0
1
0
0
2
0
1
1
3
0
1
0
1
1
0
1
1
1
1
1
1
2
1
2
1
2
0
0
2
1
0
1
2
0
2
0
0
3
1
1
1
0
0
2
0
1
1
1
2
2
0
1
1
3
1
1
1
0
0
1
2
2
0
1
1
0
1
1
1
1
2
1
3
1
0
0
1
1
0
0
1
2
0
1
1
1
1
1
1
1
1
1
0
1
1
1
2
1
0
2
2
1
1
2
2
0
1
1
1
2
1
2
1
1
1
0
1
1
1
1
0
2
1
1
1
2
0
1
0
2
1
2
1
1
1
1
1
0
1
0
1
0
2
2
2
1
0
1
0
0
0
0
1
0
1
1
1
0
1
0
1
1
1
2
1
1
1
1
0
2
2
1
1
1
2
1
0
2
1
1
1
1
1
1
1
1
1
0
0
2
1
1
1
1
1
1
0
2
2
2
0
1
2
0
2
1
0
2
0
2
1
0
0
1
1
2
1
2
0
0
0
0
1
1
1
1
1
0
2
0
1
1
2
1
1
2
0
2
0
0
2
1
1
0
0
0
1
1
1
1
1
1
1
0
0
0
1
1
0
1
1
1
1
2
1
1
0
1
1
1
1
1
0
1
1
1
0
2
1
1
0
2
0
1
0
1
0
2
0
2
0
2
1
0
2
4
2
1
0
1
0
0
0
0
1
0
1
1
1
2
2
1
0
1
0
1
1
1
2
2
1
1
1
6
0
1
1
0
0
0
1
1
1
2
1
1
3
0
0
2
0
1
1
0
1
1
1
1
0
1
2
1
0
0
2
0
0
2
1
2
1
0
1
0
0
0
1
0
2
2
0
2
1
0
1
2
0
1
0
2
2
0
0
1
0
1
1
0
2
2
0
1
3
1
0
1
1
1
1
0
1
1
1
0
2
0
2
2
0
1
2
1
1
1
0
1
2
1
1
1
1
0
0
2
0
2
1
0
1
1
0
1
1
1
0
0
2
1
2
0
1
0
1
1
0
1
1
0
1
0
2
0
1
3
1
2
2
0
2
1
1
1
0
1
1
2
2
0
1
1
1
2
1
1
1
1
2
0
1
2
0
1
1
2
0
0
0
1
2
1
0
1
0
2
2
0
1
2
1
0
1
0
0
2
1
0
0
0
1
0
1
0
1
0
1
2
1
0
1
1
1
0
0
0
1
0
1
1
0
1
1
1
1
1
2
1
1
1
1
1
0
2
2
1
2
0
1
1
2
1
2
0
2
1
2
1
2
1
1
0
1
1
0
1
2
2
1
1
1
0
0
1
0
1
0
0
1
0
1
1
1
1
1
1
1
0
1
1
1
1
0
0
2
1
1
1
1
0
0
0
1
1
0
2
1
0
1
1
4
1
2
1
1
0
1
2
1
1
1
1
0
1
2
2
2
0
0
2
2
0
0
2
2
0
1
1
0
1
0
1
1
0
1
2
0
1
1
1
1
0
1
2
0
0
1
1
5
0
0
1
1
1
0
0
0
1
2
0
1
2
0
2
1
1
2
2
1
1
1
0
1
1
2
1
0
1
1
0
2
1
1
2
0
0
1
2
1
1
3
1
2
1
0
0
1
0
1
2
1
1
1
2
2
2
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
0
1
0
0
1
0
1
1
0
1
1
1
2
2
0
1
0
1
0
1
0
1
0
0
2
1
2
0
0
1
0
0
1
2
1
2
1
1
0
2
1
1
1
0
1
1
0
0
1
2
1
2
2
2
1
1
1
2
1
0
1
2
1
1
3
0
0
1
1
0
1
3
0
1
0
1
1
1
0
0
1
1
0
0
2
0
1
2
1
2
0
1
0
1
0
1
2
1
1
0
2
1
2
1
1
0
0
0
1
1
0
0
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
0
0
2
2
1
2
0
1
1
1
0
1
0
0
1
0
0
1
2
1
0
2
0
1
2
1
1
0
0
0
1
2
0
0
1
1
1
1
2
2
1
0
0
2
1
1
1
2
0
1
1
0
1
2
1
0
0
0
0
1
1
0
1
1
0
1
1
0
1
0
0
1
0
2
1
1
2
0
2
1
0
1
3
0
2
1
1
2
1
0
2
0
2
1
2
0
0
0
1
2
0
2
0
0
1
1
1
2
2
0
1
2
1
2
0
2
0
1
0
1
0
1
0
1
0
1
1
2
1
2
2
1
1
1
0
0
1
1
1
2
0
0
0
2
0
0
2
0
2
1
1
1
0
1
0
1
1
0
1
1
1
0
2
0
0
0
0
1
1
2
1
1
1
1
1
0
1
1
0
0
1
1
1
1
1
2
0
1
1
0
0
2
1
2
2
2
1
2
1
0
1
1
1
0
7
0
0
1
2
2
2
0
2
1
1
1
2
2
1
0
0
0
1
1
2
0
1
0
1
1
2
1
1
1
0
2
1
0
1
1
2
0
2
2
1
2
1
2
2
1
0
1
1
1
2
0
0
2
3
1
1
1
1
1
0
1
1
1
2
0
0
1
2
1
1
1
1
0
3
1
0
0
1
0
0
2
2
1
2
2
1
2
1
1
3
2
1
0
0
0
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
0
0
0
0
1
1
1
1
2
0
2
1
2
0
1
0
1
2
1
1
1
1
1
0
1
0
0
1
2
2
2
2
0
1
2
1
1
1
2
1
1
2
2
0
2
2
1
1
0
0
1
2
0
1
2
1
1
0
1
0
1
1
3
1
2
1
2
0
2
0
1
0
1
2
0
1
0
0
1
2
2
1
0
1
1
1
1
1
0
1
2
3
1
1
0
1
2
1
1
1
2
1
1
0
1
4
1
1
1
2
2
1
1
2
0
2
0
2
0
1
2
1
1
1
2
0
2
2
2
1
0
2
1
1
1
0
0
0
1
1
0
1
1
2
1
1
1
1
1
1
1
1
0
2
1
1
1
2
0
1
0
1
1
1
1
0
0
2
1
1
0
0
0
1
1
2
1
2
1
2
2
1
0
1
1
0
0
1
0
1
0
1
1
2
0
1
1
1
0
1
1
1
1
0
1
2
1
1
1
1
2
2
2
1
0
0
1
0
1
1
2
2
0
0
1
2
0
1
2
1
0
1
0
1
1
0
1
2
2
2
1
0
2
2
0
2
0
1
2
1
0
0
1
0
1
1
0
0
2
1
1
1
2
1
0
2
0
2
0
1
2
1
1
1
0
1
2
1
2
1
0
2
1
1
2
0
0
0
2
0
0
2
1
2
0
1
2
0
0
2
1
1
1
2
1
1
1
1
2
2
0
2
1
0
1
2
2
1
1
1
0
2
1
0
0
0
0
1
1
1
1
2
0
3
1
2
1
1
1
1
0
2
2
1
0
1
8
1
1
0
0
1
1
0
0
1
1
1
1
0
1
2
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
0
1
1
1
0
1
1
1
1
0
2
1
0
1
0
1
0
0
1
0
1
1
1
0
0
1
0
1
1
2
2
1
1
2
1
1
1
1
1
2
2
2
2
1
1
0
1
0
1
0
1
1
0
1
1
0
1
1
0
1
1
1
2
1
0
0
1
1
1
0
0
2
2
1
0
2
1
0
1
2
0
1
1
1
1
1
0
2
0
0
2
0
2
1
1
0
0
1
2
1
2
1
3
0
1
2
2
1
1
0
0
1
0
1
1
1
1
1
1
0
2
1
1
1
0
1
2
2
1
1
2
1
0
1
0
1
2
1
0
1
0
1
0
0
2
2
1
1
2
1
0
0
1
1
1
2
1
1
1
2
2
0
2
1
1
0
1
1
1
0
1
2
2
0
1
1
0
1
1
0
0
2
1
2
0
1
1
0
1
2
0
2
1
0
3
1
1
2
1
3
1
2
2
1
2
0
0
1
0
0
0
0
1
1
0
2
0
2
2
1
1
1
1
0
2
1
1
0
2
1
0
1
2
1
0
0
1
2
0
4
0
1
1
1
2
2
1
0
0
1
1
1
1
1
1
2
1
0
1
1
1
2
2
0
0
1
2
0
1
0
2
0
2
2
1
0
0
0
2
1
0
0
0
1
1
1
1
0
1
0
1
0
1
0
2
2
1
1
0
2
1
1
0
2
1
0
2
1
1
0
0
2
0
1
2
0
0
2
0
1
7
2
2
1
0
2
1
2
2
1
1
0
1
1
2
1
0
1
0
1
1
1
2
1
1
1
1
1
2
3
0
1
1
0
1
0
0
1
0
1
1
1
1
3
2
0
0
1
0
2
2
2
0
1
0
0
1
0
0
2
2
2
1
1
2
1
2
2
1
0
0
0
0
1
1
2
1
0
1
1
1
1
1
1
1
0
0
0
3
1
2
1
2
2
1
0
0
1
0
1
1
2
1
1
1
2
0
1
1
1
2
0
1
1
1
2
1
2
1
1
2
2
1
1
0
1
2
0
1
0
0
1
1
1
1
2
1
0
1
1
0
1
1
0
1
2
1
1
2
0
1
1
0
1
2
1
1
1
1
2
1
0
0
0
2
1
0
1
2
2
2
1
1
0
2
2
1
2
1
0
2
1
1
1
2
1
0
1
0
1
1
2
1
1
0
0
1
2
0
2
0
1
1
0
2
1
0
2
2
1
3
2
1
1
1
0
2
1
1
2
1
0
1
0
1
1
1
0
1
0
0
1
1
1
1
1
1
0
0
0
0
0
1
0
1
2
2
0
1
1
1
2
1
2
2
2
1
1
1
1
1
0
1
0
0
1
1
0
1
2
1
1
1
1
0
1
2
0
0
1
0
1
1
1
1
0
0
2
2
0
1
1
1
2
1
0
1
2
2
1
1
2
0
2
1
0
1
0
1
2
1
1
1
1
0
1
1
1
0
0
1
2
1
2
2
1
1
1
2
0
1
0
0
2
1
0
1
2
1
1
1
1
1
2
0
0
1
1
1
2
0
0
2
2
0
1
0
0
1
1
1
0
0
0
1
1
1
1
2
2
0
0
0
1
0
1
0
1
0
2
0
1
1
2
0
0
1
0
1
1
1
1
0
0
0
0
1
1
0
1
0
1
0
0
1
1
1
1
0
1
2
2
2
1
0
0
1
1
2
1
1
2
0
1
0
1
2
0
1
1
1
1
0
1
2
0
1
1
0
1
2
0
1
0
0
2
1
3
2
1
2
1
1
2
1
1
0
1
0
1
1
0
1
1
1
0
1
0
1
2
0
0
2
2
2
2
1
1
2
2
1
0
2
2
1
2
2
1
0
0
1
0
2
0
1
2
2
2
1
0
2
1
2
0
2
1
1
0
0
1
1
1
0
2
0
0
1
1
1
1
0
0
2
1
1
0
1
0
0
1
1
1
1
2
1
1
2
1
1
0
2
0
2
1
1
0
3
2
1
0
1
1
2
1
1
1
1
0
0
1
1
1
1
2
2
1
0
2
2
1
2
1
2
1
2
1
1
2
2
0
1
1
1
0
0
2
2
1
0
1
1
2
0
0
0
0
0
1
2
2
1
2
1
1
0
0
1
2
0
0
2
1
0
0
1
0
0
0
1
1
0
1
1
1
1
0
0
1
0
0
2
1
2
1
1
1
1
3
2
1
1
1
1
1
1
0
2
0
1
1
2
0
1
1
2
2
2
2
0
1
1
1
1
0
0
1
0
0
1
0
1
0
1
1
1
3
0
4
2
1
1
1
0
0
1
0
0
3
1
1
1
1
0
0
1
1
2
1
1
1
1
0
2
2
1
1
0
2
0
2
1
0
1
1
0
0
2
1
0
2
2
1
1
0
1
1
0
1
2
1
2
0
0
2
1
0
0
0
1
0
1
2
0
1
1
1
0
1
0
1
1
1
0
2
1
3
0
0
2
1
2
1
0
1
1
2
1
0
1
0
1
2
1
1
2
1
1
0
2
0
0
1
0
2
1
0
2
2
2
1
2
0
0
1
1
2
1
2
0
2
1
1
2
2
2
0
1
0
0
0
1
0
1
1
2
1
1
0
1
2
0
0
1
2
0
1
1
1
2
1
2
2
2
1
2
1
2
1
0
0
2
0
1
1
1
1
0
1
0
2
1
1
1
1
1
1
1
0
2
0
0
0
1
1
2
1
1
1
0
2
2
1
1
1
2
0
1
1
2
2
0
1
0
1
3
1
1
0
1
1
0
0
1
0
2
1
2
2
1
0
1
1
0
1
1
2
0
2
2
0
0
2
1
0
2
1
1
3
0
1
2
0
2
2
0
0
1
1
1
1
1
1
1
0
0
2
2
1
1
2
2
2
1
0
1
1
0
0
0
1
1
0
1
0
1
1
1
0
0
1
0
1
1
1
0
0
0
2
1
1
1
2
2
0
2
1
1
2
1
2
0
0
1
0
2
1
0
1
0
1
1
0
1
1
1
1
2
0
0
1
0
1
0
0
2
1
1
2
1
1
2
1
2
1
1
2
0
0
1
2
1
1
1
0
1
2
1
1
0
0
0
1
1
1
1
1
1
0
0
0
2
1
1
0
0
0
1
0
2
0
1
1
2
2
1
0
1
1
2
2
2
1
1
1
0
1
1
1
1
0
1
0
0
1
1
0
1
1
0
1
0
2
0
1
2
0
0
1
1
2
1
0
0
2
1
0
1
1
2
0
0
1
1
1
1
1
1
2
1
0
1
1
1
0
2
1
1
1
0
0
1
1
1
0
1
0
1
1
2
1
0
0
2
1
0
0
1
1
3
1
2
1
2
2
0
1
1
1
1
1
1
0
0
0
0
0
1
2
0
1
1
2
1
1
1
0
1
0
1
0
4
0
0
1
3
2
1
1
1
1
1
1
2
1
2
0
2
1
1
1
1
0
1
1
0
1
1
0
2
1
0
1
0
1
0
1
1
0
1
1
1
0
1
1
1
1
1
1
1
0
0
0
1
1
0
1
7
2
0
2
2
1
1
0
1
2
1
1
0
1
0
1
2
2
0
1
0
0
2
0
0
0
1
2
0
1
0
1
2
2
2
1
1
2
0
1
1
1
1
3
0
0
2
1
0
2
0
1
0
0
1
2
0
2
2
0
0
1
1
1
0
2
2
0
1
1
0
1
0
1
1
1
2
0
0
0
1
1
2
1
1
1
1
0
1
2
0
0
0
1
2
2
1
1
2
3
2
1
0
2
0
1
2
1
0
0
0
0
0
1
1
1
1
0
1
0
0
1
1
2
2
2
2
2
0
2
1
1
0
1
2
2
1
1
0
1
1
1
1
1
1
1
2
0
1
0
1
1
1
1
0
1
1
2
1
1
0
1
0
1
1
2
2
1
1
1
0
2
1
0
1
0
1
1
1
1
1
1
0
1
1
1
0
1
1
0
0
0
0
1
1
0
1
2
0
2
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
0
1
1
1
2
1
0
1
1
1
1
1
1
0
1
2
0
0
1
0
1
0
0
1
0
1
0
1
2
1
0
1
2
0
1
0
1
1
1
1
2
0
2
0
0
0
1
2
1
1
1
0
1
1
1
1
1
1
1
1
2
1
1
1
0
2
2
1
2
1
0
1
1
1
2
0
1
2
0
2
1
0
1
0
1
1
1
1
1
1
0
1
0
0
2
2
0
2
2
0
2
1
1
1
1
0
2
0
0
1
0
0
0
1
1
1
0
0
0
1
2
1
0
0
1
1
0
1
1
0
0
1
1
1
1
2
1
0
1
0
2
1
1
0
1
1
0
1
1
1
1
2
1
1
0
0
0
1
0
1
1
3
0
1
1
2
1
0
2
0
1
1
1
2
2
1
0
1
0
1
1
1
0
1
2
1
0
1
0
1
1
1
0
0
1
1
2
0
1
0
1
0
1
1
2
1
1
2
1
1
1
2
2
2
1
2
1
0
1
2
1
1
0
2
0
1
0
2
1
2
0
2
1
2
0
0
2
1
2
2
1
1
1
2
0
1
0
2
2
2
2
2
0
0
2
0
0
1
4
1
1
1
0
3
1
3
2
1
2
0
1
0
0
0
2
2
0
1
3
1
2
1
0
0
0
0
1
2
1
2
1
1
1
0
1
2
1
0
0
0
1
0
1
2
0
1
2
1
1
1
2
2
1
1
0
1
1
0
1
1
0
2
2
1
2
2
2
2
2
1
2
2
1
1
1
2
1
1
0
1
1
2
1
1
1
1
1
2
2
1
1
1
2
1
1
0
0
1
1
1
1
1
2
0
3
0
3
2
1
1
1
1
1
0
0
2
0
1
0
0
1
2
0
0
2
1
2
1
1
2
0
1
1
1
1
1
0
1
2
0
0
1
0
1
2
1
1
1
1
0
0
0
2
0
1
0
1
3
1
0
1
1
1
0
1
3
0
1
1
1
2
1
1
2
0
1
0
0
0
2
1
2
0
0
0
0
0
1
0
0
2
1
1
2
1
1
1
0
0
1
1
1
3
1
1
2
1
2
3
2
0
1
1
1
1
1
1
0
1
2
1
1
1
0
0
0
0
2
1
2
2
1
4
0
1
1
1
2
1
0
2
1
0
1
1
1
0
1
1
1
0
1
1
1
3
0
1
3
1
2
1
1
2
1
0
3
1
1
2
2
1
0
2
1
1
0
2
1
2
3
0
1
1
1
2
1
1
0
1
1
1
0
1
2
2
1
1
2
1
1
2
2
1
1
1
0
2
1
2
2
2
0
1
2
1
2
2
2
1
1
1
2
2
1
2
1
1
0
0
0
2
2
0
2
2
1
1
1
0
1
1
1
2
0
1
2
2
2
0
0
2
2
1
1
0
0
0
2
2
1
1
2
1
1
0
1
1
0
1
0
2
1
2
1
1
2
1
2
2
0
2
0
1
1
1
2
0
1
1
1
1
0
0
1
1
1
1
2
2
1
1
0
0
0
1
2
0
2
1
1
2
1
0
2
0
1
1
1
2
1
1
1
0
1
1
0
1
2
0
1
1
1
2
2
1
2
2
2
1
1
1
1
1
1
1
1
2
1
1
1
1
0
1
1
2
1
1
2
0
0
1
1
2
2
2
0
2
0
0
2
2
1
1
0
1
0
1
1
1
0
1
0
0
1
0
2
2
1
0
0
2
1
0
2
0
0
1
0
1
2
1
1
1
0
2
1
1
1
1
1
1
2
0
1
1
0
0
1
0
0
1
1
1
1
0
1
1
1
1
1
0
1
2
1
2
0
1
2
1
0
1
1
1
2
2
1
1
2
2
2
1
1
1
2
2
2
1
0
1
2
1
2
3
1
0
0
0
2
1
1
0
2
1
0
0
1
1
2
2
1
0
1
1
0
1
2
0
0
1
0
1
1
0
0
0
2
0
2
0
0
2
1
2
1
1
1
0
2
1
1
1
2
2
0
1
4
1
1
1
1
1
0
0
2
2
1
0
1
1
0
2
1
1
1
2
0
1
0
2
2
1
0
2
1
0
0
3
1
1
1
2
0
1
2
1
1
1
2
1
1
1
0
1
0
1
1
1
2
0
0
1
1
0
1
1
1
1
0
0
1
2
2
1
1
0
1
1
2
2
2
3
1
1
2
1
0
1
1
1
1
1
1
1
0
1
0
2
0
2
1
1
1
0
0
0
2
2
2
2
0
1
0
1
2
0
2
1
2
0
1
1
0
2
1
1
2
0
2
0
2
0
0
0
1
1
1
1
1
1
1
2
1
0
0
1
2
2
0
0
1
2
1
1
2
1
1
1
1
1
1
0
0
1
1
0
0
2
0
1
1
0
1
2
0
1
1
2
1
1
1
1
2
0
1
1
1
1
1
2
1
2
1
1
0
1
1
1
0
2
0
1
2
0
2
0
0
2
1
2
1
1
0
1
1
0
1
0
1
1
2
2
1
0
0
2
1
2
2
0
0
1
1
0
1
2
2
1
1
1
1
0
2
1
1
2
0
2
1
1
2
1
1
1
2
0
1
1
1
1
0
1
0
1
0
1
2
1
1
1
1
1
1
1
2
2
0
0
0
1
0
0
0
0
1
1
1
0
1
0
1
1
0
1
2
1
0
1
0
1
1
2
1
1
0
0
0
2
2
1
1
0
0
1
0
1
0
0
1
1
0
1
2
2
2
2
1
0
0
2
1
2
1
1
1
2
1
0
1
1
1
2
1
1
1
1
0
1
1
1
0
0
1
1
0
1
1
0
1
2
1
1
0
1
0
1
1
0
1
1
2
1
0
1
1
1
2
2
1
1
1
0
1
2
0
0
1
2
1
1
1
1
0
1
1
1
1
1
1
1
0
1
0
2
1
0
2
3
2
2
1
1
1
0
0
1
0
2
0
1
2
1
1
2
2
0
2
2
0
0
1
1
1
2
1
1
2
1
0
1
0
2
1
0
0
1
1
0
4
1
2
0
1
1
0
1
1
2
1
2
2
1
0
0
0
0
0
2
1
1
1
1
1
1
2
1
1
1
0
0
0
2
2
1
1
1
1
1
1
0
2
1
1
1
1
0
2
1
0
1
0
1
1
0
2
0
1
0
1
2
2
0
1
1
2
2
0
0
2
1
1
0
0
1
2
2
0
1
2
0
0
1
2
0
1
0
1
1
1
0
1
0
1
0
1
1
0
0
1
0
1
1
0
1
0
0
1
1
0
1
0
1
0
1
0
1
0
2
2
1
1
0
2
1
0
0
1
1
1
1
4
2
1
1
2
1
1
1
1
1
0
1
1
0
0
2
0
1
1
1
1
1
0
2
1
2
2
2
2
1
0
1
0
1
1
0
1
1
1
1
1
1
0
1
2
2
1
2
0
1
2
0
2
2
2
1
2
0
1
2
2
2
2
1
2
1
1
0
2
0
1
0
1
0
2
2
2
0
1
0
1
1
1
1
1
0
0
2
0
1
1
2
1
1
0
2
0
1
0
0
1
0
0
0
1
2
1
2
1
0
1
1
2
1
1
1
1
1
2
0
1
1
1
1
0
0
0
2
1
0
2
1
2
2
1
1
1
2
1
1
1
0
2
1
0
0
1
1
1
0
1
1
2
1
0
2
0
1
1
4
0
2
1
2
0
1
0
1
1
0
1
0
2
0
1
0
1
2
2
1
0
0
2
2
3
1
1
2
1
1
1
0
1
1
2
0
2
1
0
2
0
1
0
1
1
1
2
2
0
1
1
1
1
1
1
1
1
1
1
2
2
0
2
1
2
1
1
1
1
1
1
1
0
3
1
2
0
0
1
0
1
0
0
2
0
1
1
1
0
1
2
0
2
4
0
1
2
2
1
2
2
1
1
1
0
1
1
1
1
1
2
2
1
2
2
1
1
0
1
0
2
1
1
0
1
2
0
1
0
0
1
1
0
1
2
1
2
1
0
1
1
4
1
0
0
0
0
1
1
1
1
2
1
1
2
1
1
2
1
0
0
0
0
1
1
1
0
0
2
0
1
1
2
1
0
1
1
1
2
0
1
0
1
2
4
0
1
0
0
0
1
1
2
2
1
1
0
1
1
2
2
2
2
1
1
1
2
1
1
0
1
1
0
0
0
2
0
2
1
1
0
2
1
0
0
1
0
2
2
2
2
0
1
0
0
1
1
1
0
2
1
2
1
1
0
1
1
5
0
1
1
1
1
1
0
0
2
2
1
1
1
0
0
1
2
2
1
0
1
2
0
1
2
1
2
1
1
1
1
0
1
1
2
1
1
2
0
2
1
1
1
2
2
0
0
2
0
2
0
0
1
1
1
0
1
0
1
0
1
2
0
0
1
1
1
2
1
2
2
0
0
0
1
1
0
1
0
1
2
1
1
1
2
1
1
2
1
1
1
1
0
1
0
1
0
2
1
1
1
1
1
1
1
2
1
0
1
1
4
1
1
1
0
1
2
2
0
0
0
1
0
1
2
2
1
1
1
0
2
0
1
1
2
1
2
1
1
1
2
0
3
2
1
1
3
1
1
2
2
3
1
0
1
0
0
2
1
2
1
1
1
1
1
1
0
2
0
0
2
1
1
0
1
0
0
0
0
1
2
1
1
1
1
0
1
0
0
1
0
1
1
1
1
1
0
1
1
3
0
0
1
1
1
1
2
2
0
1
1
0
1
2
0
1
0
1
1
1
1
0
0
1
1
1
0
1
2
1
2
0
2
0
1
1
1
0
1
0
1
1
1
1
0
0
1
2
0
1
0
1
0
1
1
2
0
2
2
1
2
3
0
2
0
1
0
0
1
2
1
0
0
1
1
1
1
2
1
1
1
2
1
2
1
0
1
2
0
1
0
1
1
0
1
1
1
0
2
1
1
1
1
1
1
1
2
2
1
1
1
1
2
2
2
0
1
0
1
1
1
1
1
0
1
1
1
0
1
1
3
1
1
1
1
2
2
1
1
2
2
1
1
0
1
3
1
0
0
0
2
1
0
0
1
2
1
0
0
0
2
1
2
1
0
1
1
1
0
2
1
0
2
1
1
2
1
1
2
0
0
0
2
2
2
0
0
2
2
0
1
1
0
2
1
1
1
1
1
3
2
1
2
1
2
1
1
1
1
0
2
0
1
1
1
2
1
1
2
1
1
0
1
1
2
1
2
1
1
3
0
1
2
1
1
0
0
1
2
0
2
2
0
0
2
2
0
2
1
1
0
2
1
2
0
2
1
1
1
1
0
1
1
1
0
0
1
0
0
1
0
2
2
1
1
1
2
1
1
1
0
2
1
3
1
1
1
2
0
2
0
1
1
2
1
0
1
0
0
1
1
0
0
1
0
2
0
1
1
2
0
0
1
1
2
1
2
2
1
1
1
1
2
0
1
1
0
2
1
2
0
2
1
0
1
2
0
0
1
1
2
1
0
0
1
1
2
1
2
1
1
2
0
0
1
1
2
1
0
1
1
0
1
0
0
0
0
1
0
0
1
0
1
1
0
0
1
1
1
1
0
0
1
0
2
1
2
1
1
1
0
0
1
1
0
1
1
1
2
0
2
1
1
0
2
1
1
2
1
0
0
1
0
2
0
1
1
1
1
1
2
2
1
0
2
1
0
1
2
0
0
0
1
1
0
1
0
0
2
1
1
1
1
0
0
0
1
2
2
1
1
2
1
1
0
3
0
1
1
2
2
1
2
2
2
0
1
1
1
1
2
1
1
0
2
0
1
1
0
1
2
1
0
1
0
0
0
1
1
1
0
2
2
2
2
1
0
1
1
0
1
0
1
0
1
0
0
1
1
1
0
1
2
1
1
2
1
0
2
1
1
1
1
0
1
2
1
0
1
1
1
1
1
0
0
1
1
1
0
1
1
1
2
1
2
0
1
1
2
5
1
2
2
0
1
2
0
2
0
5
0
2
1
0
1
0
0
1
1
0
0
2
1
0
1
1
1
0
4
2
2
2
0
1
1
0
1
1
1
1
1
0
1
2
2
2
1
1
2
2
1
1
1
2
1
1
2
1
2
1
0
0
0
0
2
1
2
1
1
0
1
4
1
0
1
1
0
2
1
2
0
1
1
1
1
1
2
0
1
1
1
1
2
1
1
0
0
2
2
2
1
0
1
0
1
2
0
2
2
0
2
0
1
2
0
2
0
0
0
1
1
0
1
2
1
1
1
1
0
1
2
1
0
2
1
1
2
1
0
2
5
5
1
0
0
1
0
1
0
1
2
2
0
1
2
0
1
1
2
1
0
1
2
1
0
0
2
0
2
2
2
0
1
2
1
2
0
0
1
1
0
2
1
2
1
1
1
1
0
2
1
1
0
0
2
2
0
1
1
2
0
0
0
0
1
2
1
1
0
2
1
2
1
1
1
1
0
0
0
0
1
1
1
2
1
1
1
2
2
2
1
1
1
0
1
1
0
1
2
1
2
1
0
1
0
2
1
1
1
2
2
2
1
1
1
1
1
2
0
1
0
2
1
0
0
1
2
2
2
1
2
1
0
1
1
1
1
0
1
2
2
0
1
0
1
0
0
2
0
0
0
2
2
0
1
1
1
2
1
2
1
2
1
0
2
2
1
1
1
2
1
1
0
1
1
1
1
1
1
1
1
0
1
0
2
1
1
0
2
2
3
2
0
0
1
0
2
1
1
1
1
0
1
3
0
1
4
0
2
1
2
1
2
2
0
2
1
1
0
1
0
2
0
1
1
1
2
0
1
2
2
1
1
2
1
1
0
0
1
1
1
1
2
1
1
2
0
1
0
1
2
0
2
0
1
0
1
1
0
0
0
2
1
1
1
0
0
1
0
2
0
1
1
0
1
1
0
0
1
0
1
2
1
0
0
2
2
0
0
0
1
0
0
1
0
2
2
0
1
2
1
2
1
1
1
1
2
1
0
0
0
0
1
0
1
2
1
1
1
1
1
2
1
1
1
0
1
2
0
1
0
1
1
1
1
0
2
1
1
3
2
1
1
1
2
1
2
1
0
1
0
0
1
1
1
1
0
1
2
2
1
1
1
1
1
0
1
1
1
1
1
0
1
2
1
2
2
0
1
1
0
1
1
0
2
1
2
2
1
0
1
0
1
1
1
1
2
1
1
1
1
1
0
0
1
0
1
1
1
1
1
1
1
2
1
1
1
0
0
1
2
0
1
1
0
0
1
1
0
0
0
0
1
1
1
2
2
2
2
1
1
0
0
0
0
2
2
2
1
0
1
0
0
1
0
1
2
1
1
0
0
0
1
2
1
1
1
0
1
2
1
1
1
2
0
1
1
1
2
2
1
1
2
1
0
1
1
1
2
1
2
0
2
1
2
2
1
1
2
1
1
1
0
1
1
1
1
2
2
0
2
0
0
0
0
1
2
0
2
1
1
1
1
2
0
1
1
0
2
1
0
2
2
0
2
1
1
1
1
0
1
0
2
2
0
2
0
0
2
1
1
1
1
0
0
2
0
1
1
1
1
1
2
2
1
0
1
1
2
1
0
1
0
1
1
1
2
2
1
0
0
1
1
1
1
1
2
1
1
2
1
1
1
2
0
2
2
1
0
1
2
1
2
2
1
2
0
2
1
1
0
0
0
0
2
1
2
1
2
2
2
0
1
1
2
1
1
0
1
0
1
1
1
1
1
1
1
1
1
2
0
1
2
1
0
1
1
1
0
1
0
1
1
1
1
2
1
1
0
1
1
1
1
0
1
0
2
0
0
0
2
1
1
0
2
1
1
1
2
1
2
0
1
1
1
0
1
0
1
0
2
1
1
0
1
1
0
0
1
1
2
1
1
0
1
1
1
1
0
0
1
0
2
1
1
1
1
0
2
0
0
1
0
0
1
1
0
1
1
0
2
0
1
0
1
1
0
1
1
0
1
2
1
1
1
0
1
0
2
1
1
0
2
1
1
0
0
1
1
2
0
0
0
0
1
2
0
0
1
2
2
2
0
1
1
0
1
1
1
2
0
0
1
1
0
1
1
0
1
1
0
1
1
0
0
0
1
0
1
0
0
1
0
0
0
1
3
1
1
1
2
1
0
0
1
0
2
1
1
1
1
0
2
1
0
1
1
2
2
2
0
1
2
2
2
1
0
1
0
1
1
1
0
1
1
1
0
0
1
0
1
0
0
1
0
0
1
0
1
2
0
1
0
1
1
1
1
2
2
0
1
1
2
1
1
1
1
3
1
2
1
1
0
1
1
2
1
1
0
2
1
3
1
1
1
1
2
1
0
1
0
0
2
1
1
2
0
1
1
1
1
1
0
1
1
1
1
1
2
1
0
0
1
1
1
1
2
1
2
2
1
1
0
0
1
1
1
1
0
1
2
1
1
2
2
0
2
1
2
0
1
1
1
1
2
1
2
1
1
2
1
1
1
0
1
2
1
1
1
0
2
1
1
1
2
2
1
0
1
2
0
1
1
0
1
1
1
1
1
2
1
1
1
1
1
1
0
2
2
2
2
1
3
1
0
0
1
1
1
1
0
0
1
0
1
2
1
2
1
0
1
1
1
0
1
1
2
0
0
2
2
1
1
0
0
1
0
1
2
1
1
2
1
0
1
2
1
0
2
1
2
1
1
0
1
2
1
2
0
1
1
2
0
1
0
1
0
0
2
1
2
1
1
0
2
2
1
1
1
1
0
2
1
0
1
1
1
1
1
2
2
1
1
0
0
2
1
0
1
2
1
2
1
0
0
1
1
2
1
2
0
2
2
2
1
1
1
2
0
2
1
1
2
1
1
1
1
2
2
1
0
2
0
2
1
2
2
2
1
2
1
2
0
0
1
1
1
0
0
0
1
1
2
1
2
0
0
1
3
2
1
0
2
1
0
1
0
1
1
2
2
0
2
0
2
2
2
2
1
1
0
1
2
1
2
0
0
2
1
0
0
1
1
1
0
2
1
3
1
2
1
0
1
0
0
1
0
2
2
2
1
1
1
1
2
1
0
2
1
1
1
2
1
0
1
1
2
0
2
1
0
2
0
0
2
1
1
0
1
1
1
0
2
0
1
2
1
1
0
1
2
0
2
1
2
1
2
1
0
2
1
0
0
0
3
2
2
0
1
2
2
1
0
0
1
2
2
0
0
1
0
0
1
1
1
0
1
0
2
1
1
0
2
3
2
1
2
0
1
0
0
1
2
0
2
1
1
2
2
1
1
1
2
1
1
2
2
0
0
1
1
0
1
2
1
0
1
2
1
0
0
1
1
2
1
0
1
0
1
1
1
0
2
1
2
0
2
0
1
1
0
1
0
1
1
2
1
1
1
1
1
1
1
0
2
1
0
0
1
1
1
0
0
0
0
0
1
0
0
0
2
1
0
0
1
2
1
2
0
1
0
1
1
2
1
1
1
1
0
2
1
1
2
1
2
0
1
0
0
1
2
2
2
0
1
0
1
1
2
1
2
0
1
1
1
1
1
0
0
2
1
1
1
0
2
1
1
2
1
4
0
2
1
0
2
1
1
0
1
1
1
0
1
1
2
0
1
0
1
1
2
2
0
1
0
1
0
1
0
0
1
1
0
1
0
1
1
0
0
1
1
1
1
2
2
2
1
1
1
0
0
0
1
1
1
2
2
0
1
0
1
0
0
2
1
1
1
2
1
0
2
0
1
1
1
1
1
1
0
1
0
1
1
1
0
1
1
1
1
0
1
0
1
1
0
0
0
0
2
0
2
2
1
2
1
1
2
1
2
1
1
0
0
2
0
1
1
1
0
1
1
0
2
1
2
1
3
2
1
1
1
0
1
1
1
2
1
0
1
1
1
1
3
0
1
2
1
1
0
1
0
1
2
1
1
0
1
0
0
1
1
1
3
0
1
1
0
1
0
2
0
1
1
1
2
1
1
1
0
0
2
0
1
1
1
0
0
1
2
0
1
2
2
0
2
2
1
1
2
1
0
1
0
1
1
2
2
1
1
0
1
2
0
1
1
1
1
0
2
1
1
0
1
2
2
1
1
2
0
1
1
0
1
1
1
0
2
1
0
1
1
2
1
2
0
1
0
1
0
0
0
1
0
1
1
3
1
1
1
2
2
0
0
2
2
1
1
0
0
0
1
2
2
1
1
1
1
2
0
0
2
0
0
1
1
1
1
0
2
1
1
0
1
1
0
1
0
2
1
1
1
1
2
0
1
1
1
0
0
2
0
1
2
1
0
2
0
1
0
1
1
2
2
2
1
0
2
0
1
1
1
1
0
0
0
2
0
1
0
1
0
1
1
1
1
1
1
2
2
0
1
2
1
1
0
1
0
1
1
1
2
0
1
2
2
0
2
1
0
1
2
1
1
1
1
0
1
0
1
0
2
1
0
0
0
2
1
1
0
0
1
1
0
2
0
1
0
2
1
1
1
0
1
1
1
0
1
2
1
1
2
0
0
0
1
1
1
1
1
0
1
1
1
0
2
1
2
2
1
1
1
1
1
0
1
0
0
1
0
2
1
0
1
1
1
1
2
0
1
0
0
1
2
1
1
1
1
0
2
2
0
2
0
1
1
2
1
1
1
0
1
0
1
1
2
1
1
1
0
1
0
1
2
0
1
1
1
1
1
1
3
1
0
2
0
0
0
1
1
1
1
2
2
1
1
2
0
1
0
1
2
0
0
1
3
0
1
0
1
1
4
1
1
1
0
1
1
1
1
1
0
0
1
1
0
3
0
1
1
1
1
0
2
1
0
0
1
1
0
1
1
0
2
1
2
2
0
1
0
0
2
1
1
0
1
1
1
1
1
1
2
1
1
2
1
1
1
0
1
0
1
1
0
0
1
2
0
2
0
1
1
0
1
1
2
2
1
1
0
0
1
2
1
0
0
1
1
1
0
2
2
0
1
0
1
0
2
0
1
2
1
1
1
0
1
1
0
1
1
0
1
0
0
1
0
1
2
0
0
3
1
1
0
1
1
0
1
1
1
2
0
2
1
1
1
0
1
1
2
2
1
0
2
2
1
0
1
1
0
0
1
0
1
1
1
0
0
1
0
0
2
1
1
0
0
1
0
1
1
1
1
1
1
0
0
2
1
1
2
2
1
1
0
1
1
0
0
0
1
0
1
1
1
1
1
1
0
2
1
1
0
1
0
1
1
1
0
1
1
0
1
1
2
0
1
0
0
2
0
0
0
1
1
1
0
2
2
0
1
1
2
0
2
1
2
0
1
1
1
0
1
0
1
1
1
1
0
1
1
1
0
2
1
0
1
0
1
1
1
1
0
2
1
1
1
2
1
2
1
0
0
1
2
1
0
1
0
1
0
1
1
0
2
1
2
2
1
2
1
1
2
2
1
0
1
1
2
1
1
1
1
2
2
1
2
0
0
0
1
1
2
0
1
1
2
2
0
2
1
2
1
1
1
2
1
0
0
1
1
1
0
1
1
3
2
1
1
1
0
2
2
1
1
0
1
1
1
0
0
0
0
1
0
1
0
0
3
1
1
1
0
2
2
0
0
0
1
1
0
1
2
1
1
2
1
1
1
0
2
2
2
2
0
2
1
0
2
2
1
1
1
0
2
2
0
1
2
1
1
0
1
0
3
2
0
0
1
3
1
1
1
1
1
1
2
0
1
1
2
0
2
1
1
1
1
1
0
1
2
1
1
0
1
1
2
1
0
2
0
2
0
2
0
1
2
1
1
1
2
1
1
1
1
0
2
2
1
3
1
1
0
1
1
2
1
2
0
2
1
0
0
1
1
0
1
1
1
0
1
2
1
1
2
2
0
1
1
2
0
1
1
0
1
2
1
0
1
0
2
0
1
2
1
0
1
1
0
0
1
2
1
0
2
2
0
0
0
0
0
1
1
2
1
0
1
1
1
1
1
0
1
1
1
3
2
1
1
1
1
0
1
0
1
0
2
0
0
1
1
1
0
2
1
0
1
2
2
0
1
1
1
1
0
1
1
0
1
2
1
1
1
1
1
2
2
1
2
1
1
0
0
1
2
1
0
1
2
0
0
0
3
1
1
2
1
1
1
2
0
0
0
2
0
0
1
1
1
1
1
2
0
2
0
1
1
0
2
0
1
1
1
1
0
1
1
0
1
1
1
1
1
0
1
0
0
2
0
1
1
1
2
1
1
0
2
1
0
1
1
1
1
1
2
1
1
2
1
0
1
1
1
1
1
0
1
0
1
1
1
1
1
0
1
2
1
1
2
2
1
1
2
1
0
0
2
1
1
1
1
1
1
0
0
2
0
0
0
0
1
1
1
1
1
1
2
0
0
1
1
1
0
1
0
0
2
1
0
0
1
2
0
1
1
2
0
1
1
2
0
1
1
1
1
1
0
1
1
1
1
3
0
0
1
2
1
1
1
1
1
2
1
1
2
2
0
0
0
2
1
1
2
1
0
1
1
2
1
1
0
2
2
1
1
0
0
1
1
2
1
1
0
1
0
0
0
1
0
0
0
1
2
1
1
0
1
3
0
2
3
1
0
2
1
1
1
0
1
5
0
1
1
0
0
1
0
1
4
0
1
0
1
2
1
1
0
0
1
1
1
1
1
1
1
2
1
0
1
1
1
1
2
1
0
1
2
2
1
1
1
0
1
0
2
1
0
1
0
0
0
2
1
1
1
0
0
2
1
2
2
2
1
0
0
1
1
1
2
1
1
1
1
0
0
1
1
1
1
0
2
0
1
2
1
0
1
0
1
0
0
0
2
1
1
1
1
2
1
1
1
2
1
1
0
0
1
2
0
1
1
1
1
1
0
1
2
1
1
1
2
1
0
1
1
0
2
1
0
3
0
1
0
0
2
1
1
0
2
1
2
0
0
2
1
0
2
2
1
1
1
1
1
1
0
1
3
0
1
1
1
0
2
2
0
1
1
0
1
2
1
1
0
1
1
1
2
1
1
1
1
2
2
1
2
0
1
1
2
1
1
2
2
2
1
1
0
1
2
1
2
1
2
1
1
2
1
1
1
1
2
1
2
1
1
1
2
1
2
1
0
1
1
1
1
1
1
1
2
1
0
1
2
1
1
0
1
0
1
1
2
0
0
2
2
1
0
0
1
0
0
0
0
0
1
1
0
1
1
1
1
2
2
1
2
1
1
0
0
2
0
1
0
2
1
2
2
2
1
1
0
3
2
1
1
1
2
1
2
0
0
2
1
3
1
1
1
0
1
1
1
1
2
1
0
2
1
1
1
1
1
0
0
1
2
1
2
1
1
1
1
1
2
1
0
0
0
1
0
1
1
2
1
1
2
1
0
1
1
0
2
1
1
1
1
2
1
1
0
1
2
1
1
2
0
2
2
0
1
0
2
1
2
0
1
1
0
1
1
1
1
2
1
1
1
0
1
1
0
1
1
0
1
0
1
1
1
1
0
1
1
0
2
0
0
2
1
1
2
2
1
1
0
1
1
2
0
1
0
2
1
0
1
1
0
2
0
1
1
2
1
2
1
0
1
1
1
2
1
0
1
1
1
1
2
1
0
1
2
2
2
1
1
0
1
1
0
1
1
2
0
0
1
2
1
1
0
1
2
2
2
1
0
2
1
0
2
0
2
1
2
1
1
1
0
0
1
0
0
2
1
0
2
0
1
0
0
0
1
0
1
0
1
1
0
2
0
1
1
1
1
1
1
1
1
1
3
1
2
1
3
1
1
2
1
0
1
2
1
0
1
1
1
0
1
2
1
0
0
2
0
2
2
0
2
1
1
1
1
2
1
0
1
1
0
1
1
1
0
1
1
0
0
1
2
1
2
0
2
2
1
0
2
2
2
0
1
0
1
3
1
3
1
1
1
0
1
1
0
0
1
1
0
1
2
0
2
1
1
0
1
1
1
0
2
2
1
1
2
1
0
2
2
2
1
1
1
2
1
1
1
1
2
2
2
2
1
2
1
1
2
0
1
1
2
2
1
2
1
1
1
2
0
1
1
1
0
1
0
0
1
1
1
1
1
0
0
1
1
2
1
0
0
2
1
1
1
0
0
0
0
1
0
0
1
0
1
1
1
1
1
0
0
0
1
1
2
1
0
2
0
1
1
1
2
1
1
0
1
1
0
1
0
1
3
1
1
2
0
2
0
1
1
0
0
0
2
1
1
1
1
2
0
1
0
1
1
2
1
0
2
1
0
0
1
0
0
0
1
1
1
1
1
5
1
1
3
0
2
2
2
2
1
0
1
1
0
1
2
1
0
1
1
0
0
0
1
3
2
1
2
0
1
1
1
1
1
1
2
0
2
2
0
2
1
0
2
1
0
0
0
1
0
0
1
2
1
1
0
0
2
1
0
0
1
1
1
2
2
0
1
2
1
2
1
1
1
1
1
2
0
1
0
1
2
0
2
1
1
0
1
1
0
2
0
1
1
1
1
0
2
1
1
0
0
2
2
0
2
2
1
0
1
0
0
1
1
1
0
0
1
2
2
0
0
2
1
1
1
2
2
1
1
1
1
0
1
2
1
0
1
0
0
1
1
1
1
0
1
0
2
2
1
1
1
1
2
1
1
0
0
0
2
2
2
0
2
1
0
1
0
2
0
1
1
2
1
0
0
1
0
2
0
2
0
0
1
0
2
0
0
1
0
2
1
1
1
1
1
2
1
1
2
1
1
2
1
0
3
2
1
2
1
1
1
1
0
3
0
1
1
2
1
1
0
2
1
0
0
2
1
0
2
1
1
1
0
1
1
1
0
1
0
0
2
1
0
0
1
0
0
1
1
1
1
1
1
1
2
0
2
1
2
2
2
1
1
1
1
1
0
1
0
0
1
1
2
1
2
0
0
2
1
1
0
2
2
1
1
0
1
0
2
0
0
1
1
2
0
1
1
0
2
1
1
4
1
0
0
0
1
1
1
1
2
0
0
2
1
0
1
3
1
2
1
1
1
0
2
1
1
0
2
0
1
2
1
1
1
0
1
1
0
1
2
0
1
1
2
2
1
2
0
0
1
1
1
1
2
1
1
0
0
1
1
0
0
0
1
2
1
2
1
0
1
2
1
2
1
1
1
1
1
0
2
2
1
1
1
2
1
2
1
1
2
0
2
2
1
0
1
0
0
0
1
2
0
1
2
0
1
0
1
2
0
0
0
1
1
0
1
0
1
1
1
1
0
2
1
0
1
1
2
0
0
1
2
1
0
1
0
1
2
2
2
1
2
0
1
0
2
0
1
1
1
0
1
1
1
2
2
0
1
1
2
1
1
2
1
1
2
0
1
1
1
1
0
2
0
0
2
0
0
1
2
1
0
2
2
2
1
1
1
0
1
1
1
2
1
2
2
1
1
0
2
1
1
2
0
1
1
1
2
3
0
2
1
0
2
2
0
1
0
1
2
2
1
0
1
1
2
0
0
2
1
1
1
1
0
2
2
1
1
2
1
0
0
2
1
1
1
1
1
1
1
0
1
1
1
0
1
0
0
0
1
2
1
1
1
1
1
1
1
1
0
2
2
1
1
1
1
0
2
0
1
2
1
0
2
2
2
0
0
1
1
0
0
1
0
1
0
1
2
2
2
1
0
0
2
1
0
1
1
1
0
0
0
1
1
0
1
1
1
1
0
1
1
1
0
1
0
0
1
3
2
2
1
1
0
0
1
2
2
1
1
1
1
1
4
2
0
1
2
0
1
1
2
0
0
1
1
2
1
1
1
1
0
1
2
1
1
1
3
1
2
2
0
0
1
1
2
2
1
1
1
0
2
1
2
1
1
0
3
0
1
0
0
0
2
1
1
1
1
1
1
2
2
0
1
1
1
1
1
1
2
2
1
1
2
1
1
1
0
2
0
0
1
0
1
0
1
0
0
0
2
0
0
0
0
0
1
0
2
1
1
1
0
4
0
0
1
1
0
2
1
0
1
2
2
2
2
1
0
2
1
0
1
0
2
0
0
0
0
1
2
1
1
2
2
2
1
0
0
1
2
0
1
1
0
0
0
1
2
2
2
0
1
0
1
0
0
1
2
1
1
1
1
0
0
2
1
1
3
2
1
0
0
0
0
1
1
1
1
1
1
1
1
0
1
0
1
1
0
1
1
1
0
1
1
0
0
2
1
1
0
1
1
0
1
0
2
1
0
1
1
0
1
1
2
1
0
2
0
1
0
1
1
0
1
2
2
1
0
1
0
1
1
0
0
2
1
2
0
1
1
2
2
2
1
1
2
2
1
1
0
0
2
1
1
1
2
1
0
1
1
0
0
1
1
2
0
1
1
0
1
0
0
1
0
2
0
1
1
0
1
2
1
1
1
1
1
1
0
1
1
1
0
1
1
0
1
1
0
1
0
1
0
1
2
2
2
1
2
1
2
2
0
1
1
2
1
4
2
1
0
0
2
1
0
1
0
1
0
1
1
1
0
2
1
0
1
0
1
1
1
1
1
1
0
0
1
0
0
1
2
2
2
1
0
0
0
1
1
1
2
1
0
2
2
2
0
5
0
1
0
0
1
2
1
2
1
0
1
0
0
2
1
0
1
0
1
2
1
2
2
0
0
0
2
1
0
1
2
1
1
1
1
1
1
1
2
1
1
1
1
0
2
1
0
1
0
2
0
1
0
1
2
1
2
1
1
2
0
1
2
1
2
1
2
1
1
4
2
1
1
1
1
0
0
1
2
2
0
2
2
1
2
1
1
2
0
1
2
0
2
1
0
0
1
1
0
1
1
1
1
2
1
0
2
0
1
1
1
2
1
0
1
2
1
0
0
1
1
1
1
2
1
0
1
2
0
1
0
1
0
1
1
0
2
0
2
1
1
1
0
1
1
0
1
1
1
0
1
1
0
1
1
0
1
1
2
2
1
2
2
1
1
1
2
1
1
2
2
1
2
1
1
2
0
1
2
2
0
1
1
0
0
2
1
3
1
1
1
2
2
1
0
0
0
0
1
1
1
0
2
0
0
1
1
0
1
1
1
1
1
0
1
0
1
1
1
2
0
0
2
1
0
1
0
2
2
0
2
1
3
2
1
1
1
1
1
2
1
1
1
1
2
2
1
1
1
2
2
1
1
1
0
0
0
2
2
0
0
2
0
0
1
1
1
1
2
2
2
1
0
1
1
2
2
2
1
0
0
2
1
2
1
1
1
0
1
0
0
1
1
2
1
5
1
1
1
1
1
1
1
3
1
0
2
1
1
1
1
2
0
2
2
0
1
0
2
2
2
0
1
2
1
3
1
1
1
0
1
1
1
1
1
0
2
2
1
1
2
1
2
0
0
1
1
2
0
0
0
1
1
0
1
0
1
1
1
0
1
1
1
0
2
1
1
0
2
0
1
1
2
2
2
0
2
0
2
1
1
1
1
1
1
2
0
2
0
1
0
1
0
3
0
2
2
2
3
0
1
0
2
1
0
1
1
1
1
0
2
1
1
1
0
1
0
1
0
1
1
1
1
2
1
2
2
2
1
2
1
5
1
1
1
0
1
1
0
1
2
2
1
2
0
1
2
1
1
1
0
0
1
2
0
1
2
0
1
2
1
0
1
1
1
0
2
0
1
1
2
0
1
1
0
1
1
0
1
2
2
1
1
1
1
2
0
1
2
0
1
1
0
0
2
1
1
1
0
1
1
1
0
1
1
1
0
2
1
0
0
0
1
1
0
3
1
0
2
1
1
3
1
1
2
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
2
1
1
2
2
1
1
1
1
1
1
1
1
2
1
0
1
0
2
2
0
1
1
2
1
1
0
2
1
0
0
2
2
0
2
1
0
2
2
2
2
2
2
1
1
2
2
1
1
0
2
0
0
1
1
1
0
0
0
0
1
2
1
2
0
0
0
2
1
1
1
0
1
1
1
1
1
2
1
0
0
2
1
0
1
1
1
1
0
2
2
1
0
1
2
1
2
1
1
2
2
1
2
1
0
0
1
2
1
2
1
1
1
1
0
1
0
0
2
0
1
1
1
0
1
2
1
0
1
0
2
0
0
2
2
0
1
1
2
2
0
1
1
1
2
1
1
2
0
2
1
1
1
2
0
1
2
2
1
2
0
0
2
1
0
0
0
1
0
2
2
0
0
1
0
1
1
1
0
1
3
1
1
1
2
1
1
2
0
1
1
1
1
2
2
0
1
1
0
0
1
1
0
0
1
1
1
0
1
1
0
1
1
1
2
1
1
3
0
1
1
0
1
1
1
1
1
1
0
1
1
0
1
2
0
2
2
1
1
1
2
2
2
1
0
1
1
0
0
1
1
0
1
0
1
0
1
1
0
1
1
2
1
2
1
1
0
1
2
1
0
1
2
2
2
0
1
1
1
3
1
1
0
2
1
2
0
1
1
2
0
1
0
1
0
1
1
1
2
1
1
1
2
1
1
1
1
1
1
0
1
1
1
2
1
2
1
0
1
2
1
0
2
2
1
0
1
1
2
0
1
1
0
1
1
1
1
2
1
0
1
1
2
2
0
1
1
1
0
1
2
2
1
1
1
0
1
1
1
2
1
2
2
1
1
2
0
0
1
0
0
3
2
2
1
1
1
0
2
0
1
2
1
0
4
1
1
1
0
2
0
1
0
2
2
0
0
2
2
0
2
1
1
0
2
0
0
2
1
0
1
1
1
2
2
2
0
2
2
2
3
1
0
0
1
1
1
2
0
1
0
2
1
2
2
1
0
1
1
0
1
1
1
1
3
0
1
1
0
2
2
0
0
2
1
0
1
1
1
0
0
1
1
1
0
0
0
1
1
1
0
1
1
0
1
2
0
2
0
0
1
0
2
3
0
1
2
2
1
1
2
2
1
0
1
0
1
1
2
4
1
1
1
0
3
0
3
1
1
5
2
1
2
1
2
0
1
1
0
0
1
1
2
1
1
0
1
2
0
1
2
1
1
0
2
2
2
1
1
2
1
1
2
2
0
1
1
0
1
1
1
2
0
0
2
2
2
2
0
1
0
0
1
0
0
2
1
1
1
1
1
1
1
1
1
2
1
0
1
1
2
2
1
1
2
0
2
1
1
0
1
2
0
1
1
1
1
0
1
0
2
0
0
0
0
1
1
1
0
2
2
1
1
1
0
1
2
0
2
2
0
0
0
0
1
0
0
1
0
1
0
2
1
1
1
1
0
1
2
0
0
1
1
2
1
0
3
2
1
1
1
1
1
1
1
2
2
1
2
2
2
2
0
1
1
1
1
0
1
1
0
2
2
2
2
2
2
1
2
2
1
1
0
0
1
1
1
2
2
1
1
0
1
0
2
1
0
1
1
0
0
1
1
1
1
1
1
0
2
0
1
0
1
2
2
1
0
0
2
1
1
0
1
1
1
1
0
0
1
1
2
0
2
0
1
0
1
1
1
2
1
1
1
2
0
1
1
0
0
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
0
1
2
1
0
2
1
0
1
2
2
1
1
1
1
1
0
1
1
1
1
2
0
1
0
1
0
0
0
2
1
0
1
1
2
2
0
1
1
1
1
1
1
1
1
1
0
1
1
0
2
2
1
2
1
2
2
0
0
1
1
1
0
1
1
2
1
0
1
1
2
1
1
1
4
2
1
0
0
1
1
2
0
1
2
1
0
0
1
1
0
0
1
1
1
1
1
1
0
0
0
1
1
1
0
2
0
1
2
2
1
1
1
1
1
0
1
1
1
1
1
1
1
2
2
1
1
1
2
0
1
1
0
2
0
0
1
1
1
1
1
1
0
1
1
1
2
2
2
0
1
0
1
1
2
3
0
0
0
2
1
1
1
0
1
1
2
1
3
0
2
0
1
0
1
2
1
1
0
0
0
0
1
0
1
1
2
0
1
1
1
2
0
1
1
1
1
2
1
1
1
0
1
2
1
2
2
0
0
1
1
0
1
1
1
0
2
0
1
2
0
1
2
1
1
2
2
1
1
1
2
0
1
0
1
1
1
1
0
1
0
2
1
1
1
1
2
0
2
2
2
2
1
1
0
1
1
0
1
0
0
1
3
2
1
2
0
0
2
1
1
1
0
1
1
0
1
0
1
0
2
1
2
1
2
0
0
0
0
1
1
0
1
1
1
1
1
1
2
0
2
1
1
2
1
1
1
1
0
0
2
0
1
0
1
1
2
1
1
1
1
1
2
0
1
1
0
1
0
1
1
2
1
1
1
2
1
1
0
2
2
1
2
1
1
0
2
1
1
1
0
1
2
1
1
1
1
1
1
1
1
1
2
0
0
1
1
1
1
1
1
1
0
0
1
1
1
0
0
0
2
1
1
1
1
2
1
1
2
1
1
1
0
1
1
2
1
1
1
0
0
1
0
2
2
0
1
2
1
1
1
0
0
1
2
1
0
1
1
0
2
0
0
1
1
0
1
1
2
0
1
2
1
0
2
1
2
1
1
0
1
2
1
2
1
1
0
0
1
0
1
2
0
1
0
1
1
0
1
1
0
0
0
0
1
1
0
1
0
1
1
1
1
2
3
2
2
0
1
0
4
1
2
2
1
2
1
1
0
1
0
0
1
1
2
1
2
0
4
2
0
1
0
0
1
0
1
0
1
1
1
0
1
1
0
0
2
0
2
1
1
1
0
0
2
2
2
2
1
1
2
0
1
1
1
2
1
1
1
2
1
1
0
1
2
0
0
1
1
0
1
0
1
1
2
1
1
2
1
1
1
1
1
0
1
0
3
1
1
1
2
1
1
1
1
1
2
0
2
1
2
0
1
1
4
1
2
1
2
1
0
3
1
2
0
1
0
2
2
0
0
1
1
0
0
1
2
1
1
1
0
0
3
0
1
1
1
0
0
1
0
0
2
2
1
1
0
1
0
0
1
2
2
0
0
0
1
1
0
1
0
0
1
0
2
2
1
0
0
3
1
2
1
0
1
1
1
2
2
0
0
1
1
2
2
1
0
1
1
1
0
0
2
1
0
2
1
1
1
1
1
1
1
1
1
0
1
1
1
3
2
2
1
1
2
2
1
0
1
0
2
1
1
1
1
0
2
0
0
2
1
1
1
1
1
0
1
0
2
2
1
1
1
2
1
2
1
1
1
0
1
0
1
0
1
0
0
1
2
0
1
2
1
0
0
3
1
2
0
1
1
2
2
2
0
1
1
0
1
0
1
1
1
2
1
0
2
1
1
2
1
2
1
0
2
0
1
1
2
1
0
2
0
0
1
1
0
1
1
1
0
1
1
2
0
0
2
2
2
0
2
1
1
2
2
2
0
2
2
1
2
1
2
2
0
2
2
0
1
2
1
1
4
2
1
0
1
0
1
1
2
1
1
0
1
2
2
1
1
1
2
1
2
1
0
1
2
0
2
0
2
1
1
1
0
1
1
0
1
0
2
1
2
1
1
1
0
1
0
1
1
0
1
2
2
2
0
0
1
2
0
0
3
0
1
2
2
2
0
1
1
1
2
0
1
1
0
1
1
0
0
1
1
1
1
1
1
0
2
2
1
1
1
1
1
1
1
2
1
1
0
1
2
1
0
1
1
0
2
0
0
1
1
1
1
0
2
2
1
0
1
1
0
0
1
0
0
1
1
0
1
0
1
2
0
1
2
2
1
0
1
1
1
0
0
1
0
0
2
0
3
1
0
1
1
1
0
1
1
1
1
1
1
1
0
0
1
0
0
0
2
1
2
1
2
1
2
1
1
0
1
0
1
2
0
1
0
0
0
1
2
2
1
1
1
0
0
1
2
0
1
1
1
1
1
0
0
0
1
1
0
2
1
2
0
1
1
2
0
0
0
1
2
2
1
1
0
1
1
1
1
1
0
0
1
2
0
1
1
2
1
1
1
1
3
0
0
1
1
1
1
1
0
2
1
1
2
1
1
0
2
2
2
0
1
0
1
1
1
1
2
0
0
1
2
1
1
1
2
1
2
1
0
1
0
0
1
1
2
0
1
1
1
1
2
1
1
2
2
0
2
0
2
1
0
0
0
2
0
1
1
0
2
1
1
0
2
1
1
0
1
2
0
0
1
2
1
0
0
2
1
1
1
0
1
0
1
2
2
2
0
0
2
1
2
0
1
1
1
1
1
1
1
0
1
2
0
1
1
1
2
1
1
1
1
1
0
1
0
0
0
2
0
1
1
2
0
0
2
1
1
1
2
0
0
0
0
4
1
2
2
1
0
1
1
0
0
0
2
1
1
2
1
0
0
0
2
1
0
1
0
2
1
1
0
1
0
1
1
2
1
1
1
1
1
0
1
1
1
1
2
0
1
1
2
0
0
2
0
1
0
1
2
0
1
1
2
0
0
0
0
1
1
0
1
0
1
1
0
0
1
0
1
1
0
1
0
0
1
1
0
0
0
2
1
1
0
1
1
0
0
2
1
1
0
2
0
1
2
0
0
0
1
0
0
2
2
2
2
0
1
0
1
0
2
3
1
2
0
1
2
0
0
0
0
0
0
1
1
1
2
1
2
1
1
0
2
1
0
1
2
1
0
1
2
1
2
1
1
1
0
1
1
0
1
2
2
1
1
2
2
2
1
1
1
1
1
1
1
0
1
1
1
1
0
5
1
2
1
2
1
2
0
0
1
2
1
1
1
2
0
0
2
1
1
0
1
1
1
1
0
2
2
1
1
1
0
1
1
0
2
1
1
2
1
1
1
0
2
1
0
0
0
1
0
1
0
0
1
1
1
0
0
0
2
3
1
1
2
0
1
1
1
0
1
1
2
1
1
1
2
1
0
1
1
0
1
1
1
1
0
1
2
1
1
0
1
1
1
0
4
1
0
2
2
1
2
1
0
1
1
1
2
2
2
2
1
1
1
0
1
1
0
0
1
1
2
1
0
1
1
0
0
2
0
1
1
1
2
1
2
2
1
0
2
0
0
0
1
2
1
0
0
2
1
1
0
0
2
0
1
1
1
1
1
0
2
0
1
1
1
1
1
1
2
1
1
0
0
2
1
2
1
1
0
1
1
0
1
2
0
1
2
2
1
2
2
0
1
2
1
0
2
0
2
1
0
0
0
1
1
1
0
1
1
2
1
1
0
1
2
1
0
1
2
0
0
1
1
1
2
0
0
1
2
1
2
1
1
2
2
0
1
0
1
1
1
2
1
1
1
0
2
2
0
1
1
1
1
2
0
2
2
0
1
1
1
0
0
1
0
1
0
2
1
1
1
0
1
1
1
0
0
2
1
1
1
0
2
1
0
1
0
1
1
1
2
2
0
1
0
2
1
1
1
0
2
1
0
2
0
2
1
1
1
1
2
1
2
1
0
2
1
1
0
1
0
0
0
1
2
2
0
2
1
3
0
1
2
1
0
1
1
0
1
0
2
0
1
2
0
0
1
1
1
0
2
1
2
0
0
2
1
1
2
0
2
3
1
1
0
1
1
0
2
2
0
1
2
1
2
0
1
1
2
1
1
0
2
0
1
1
1
1
1
1
1
1
1
2
1
2
2
1
1
1
0
1
2
2
1
0
1
0
2
0
1
1
1
1
1
0
1
1
0
1
0
1
0
1
2
1
2
1
1
1
1
1
0
0
2
1
2
2
1
0
1
1
1
0
1
0
2
1
1
0
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
0
1
1
1
0
1
1
0
2
0
1
0
1
0
1
1
1
1
1
0
0
2
1
1
0
0
1
1
1
0
2
0
2
2
1
1
1
2
1
1
0
2
0
1
0
2
1
2
0
1
1
1
1
1
0
1
2
0
0
0
2
2
0
1
1
0
2
2
0
1
3
0
3
1
2
2
1
1
3
2
0
0
1
0
1
2
2
1
2
1
1
1
2
1
1
1
1
1
1
0
2
1
0
1
1
1
2
1
1
1
1
2
1
2
1
1
2
1
1
1
0
1
1
2
1
2
0
0
0
1
1
1
1
0
1
1
2
1
1
0
2
1
3
1
0
2
1
0
1
1
2
0
0
1
0
2
1
4
0
0
1
1
1
1
1
0
1
1
1
1
1
2
1
2
1
2
1
2
1
1
1
1
1
1
0
2
2
1
0
0
1
0
0
1
1
2
1
1
0
0
1
1
2
0
0
2
0
1
0
5
1
0
1
0
1
0
0
2
0
1
1
1
1
1
2
0
0
0
3
0
1
1
2
1
0
0
0
1
2
1
0
1
1
1
0
0
1
1
0
1
1
1
1
1
2
1
0
1
0
2
1
1
1
0
2
1
1
1
1
1
1
1
1
0
2
0
1
1
1
1
1
1
2
1
0
1
1
0
0
0
2
2
2
1
2
0
1
1
1
1
1
1
1
1
1
1
1
2
0
1
1
1
2
1
1
1
1
1
1
1
1
0
1
2
0
0
0
1
2
1
1
1
1
0
2
0
1
2
1
0
0
1
1
1
1
1
1
1
1
1
1
0
0
1
1
2
1
0
1
1
1
0
1
0
2
1
1
1
1
1
2
1
0
1
1
1
0
2
1
1
0
1
0
2
2
1
0
0
0
1
2
1
1
0
1
2
1
0
1
1
0
1
0
2
1
0
0
1
0
1
0
0
1
1
1
0
2
1
2
0
0
1
1
1
1
1
1
1
1
0
1
0
0
1
2
0
1
1
0
0
1
0
1
2
2
1
1
1
0
1
2
1
1
0
1
1
0
1
0
1
2
1
0
2
1
0
1
0
2
0
2
1
0
1
2
1
1
1
1
1
1
1
1
0
1
1
1
2
1
1
1
1
1
2
1
1
2
1
1
1
1
0
1
0
1
2
0
2
1
0
1
1
1
0
1
2
0
1
1
1
0
0
0
1
1
1
2
0
0
1
0
1
1
1
1
1
1
1
1
2
1
1
1
1
0
2
0
0
1
1
1
1
0
1
1
1
2
1
2
1
1
1
1
0
2
1
1
0
2
1
1
2
1
2
2
1
2
1
1
2
0
1
0
1
1
2
1
1
1
0
1
1
1
2
1
1
0
1
2
1
2
1
1
0
2
1
1
1
1
0
1
0
1
2
2
1
0
1
2
2
1
1
0
2
1
0
2
1
0
0
1
1
2
0
1
1
1
1
2
2
1
1
2
0
1
1
0
1
2
1
1
2
0
2
0
1
0
0
1
1
1
2
1
1
1
1
1
1
0
0
2
1
1
1
1
0
0
1
0
0
2
1
1
2
1
1
1
1
0
1
1
2
1
2
1
1
1
0
2
1
2
0
0
0
4
2
1
1
1
0
1
1
2
3
1
1
2
1
2
0
1
1
0
0
1
0
1
0
2
1
1
1
1
1
1
0
0
2
0
1
0
1
1
1
1
1
0
1
1
0
1
0
0
1
1
2
0
1
1
1
2
2
0
0
1
1
3
0
1
1
1
0
1
0
0
1
1
1
2
2
3
1
1
0
1
0
1
2
1
2
1
1
1
0
1
0
0
1
1
0
1
1
0
2
1
0
1
0
0
1
1
1
2
0
3
0
1
0
1
0
2
2
0
2
0
1
1
0
0
1
2
1
1
1
1
0
0
1
0
1
2
1
0
1
0
1
1
1
0
0
2
1
0
1
2
1
0
1
0
1
1
2
1
2
1
1
1
2
2
0
2
2
1
0
2
1
1
0
2
0
0
1
1
2
2
1
1
2
0
2
0
1
1
1
0
0
1
2
1
2
0
0
2
1
0
0
1
1
1
0
1
1
1
1
2
1
1
1
0
0
2
0
2
2
1
2
2
1
0
2
1
0
1
2
1
0
1
0
0
1
1
1
1
1
2
2
2
2
2
1
1
2
0
0
1
1
0
2
1
0
0
6
1
1
2
0
0
1
0
1
1
1
0
2
0
1
3
0
1
0
1
0
1
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
0
2
1
0
0
0
0
0
2
2
1
1
1
2
0
1
1
0
0
1
0
0
0
1
1
0
0
1
1
1
0
2
0
1
0
1
2
1
1
1
0
1
0
1
1
1
1
0
1
0
1
2
1
1
1
2
0
0
0
1
1
1
1
0
1
2
1
0
1
0
0
3
1
1
2
2
1
1
1
1
1
1
1
1
0
2
1
1
1
0
0
0
1
2
0
1
2
0
1
1
0
2
1
1
1
2
0
2
0
0
1
2
1
0
1
1
1
1
0
0
1
1
2
1
2
2
1
2
0
1
2
1
1
2
4
0
1
1
1
0
1
0
1
1
1
2
2
2
1
1
1
0
0
1
0
0
1
1
0
1
1
2
2
1
1
2
2
1
1
1
1
1
0
1
2
0
0
0
1
1
1
1
1
1
1
1
2
1
2
1
1
0
1
1
1
0
1
2
2
0
1
1
2
1
1
1
1
0
2
0
1
2
0
2
1
1
1
2
0
2
1
1
1
1
2
3
0
0
1
1
2
1
0
0
1
0
1
2
1
1
1
1
2
3
1
2
1
0
0
0
1
1
0
1
1
1
0
1
0
1
1
1
1
1
1
1
1
2
2
1
2
1
1
1
0
1
0
2
1
1
2
2
0
1
0
1
1
0
2
1
1
1
2
1
1
1
0
2
1
0
1
1
2
0
1
1
0
1
0
1
4
1
1
0
1
3
2
0
1
1
1
1
2
1
1
2
2
0
0
2
0
0
2
0
1
1
0
0
2
2
1
2
2
0
2
1
0
0
1
0
0
0
1
0
1
1
1
1
1
1
2
1
2
2
1
1
2
3
2
1
2
2
0
1
2
2
2
1
1
0
0
1
1
1
1
2
0
5
2
0
1
0
1
2
0
1
1
2
1
1
3
2
2
2
2
1
1
2
2
2
1
1
1
1
1
1
4
1
1
0
1
2
1
1
0
0
2
0
1
2
1
2
0
2
1
0
0
1
0
2
1
2
1
1
0
1
2
2
1
2
1
0
1
0
2
0
2
1
1
1
2
1
0
0
1
1
1
1
1
1
1
1
0
1
1
2
0
1
1
1
2
2
2
0
0
1
1
1
1
0
2
0
1
3
2
1
2
0
1
0
1
2
1
1
0
2
1
1
2
0
0
0
2
1
0
1
1
1
0
1
1
1
0
2
0
1
1
0
2
1
0
1
0
2
0
0
1
1
1
1
1
1
1
0
0
0
0
1
0
2
1
1
1
1
0
0
1
1
0
2
0
1
1
1
1
0
1
2
1
0
1
1
2
1
1
2
0
0
2
1
0
2
0
1
0
2
4
0
1
0
0
0
0
1
0
0
2
1
1
2
0
0
1
1
1
2
0
1
1
1
1
1
1
2
0
0
2
0
3
2
0
0
2
0
0
1
2
2
0
0
1
0
0
1
1
1
1
0
1
0
1
1
0
0
2
0
1
1
1
1
1
0
0
1
2
1
1
0
1
2
1
0
0
0
1
1
2
2
2
1
2
1
0
1
1
1
1
2
2
1
1
1
1
1
1
1
1
0
1
2
1
0
1
0
2
1
1
0
2
1
1
2
0
0
2
2
1
1
2
0
1
1
2
0
1
1
1
1
1
2
2
1
0
0
0
1
1
1
2
1
1
0
0
2
1
2
1
1
2
1
1
1
1
0
2
1
0
1
1
1
1
0
1
2
1
0
1
0
0
2
1
1
2
2
2
2
1
0
1
0
1
1
1
0
2
2
1
1
1
0
1
2
1
1
1
0
1
1
1
0
1
1
1
2
2
0
1
0
1
1
2
1
0
2
1
2
1
2
2
1
1
2
1
2
0
0
2
1
0
2
1
1
1
0
0
1
1
1
1
1
3
0
1
1
1
1
1
1
0
1
1
1
1
1
1
2
0
1
1
2
1
1
1
2
1
2
1
0
1
0
1
0
0
1
1
1
0
2
1
1
1
1
1
0
2
1
2
0
0
2
0
1
0
2
3
0
0
1
3
1
1
1
0
2
1
2
1
0
1
2
1
0
1
1
2
1
1
0
1
1
2
0
0
1
0
1
2
1
1
1
0
0
1
2
1
1
0
1
1
1
1
2
1
1
1
1
1
1
2
0
0
2
2
0
1
1
1
0
1
1
1
0
1
2
1
0
0
1
1
0
1
2
2
0
1
2
2
1
1
1
1
1
1
1
1
1
1
0
2
1
0
1
1
0
0
1
0
2
1
1
2
0
1
1
2
0
0
0
1
1
0
2
1
1
1
1
1
1
1
0
1
0
1
2
1
2
1
1
1
2
3
1
1
0
0
1
0
1
1
1
0
0
1
2
1
1
2
1
2
1
0
1
2
2
1
2
1
1
1
0
1
0
0
1
0
1
1
1
0
2
2
1
1
1
1
1
2
2
1
1
1
0
1
1
1
0
1
2
1
0
2
2
2
1
1
0
1
1
1
0
2
1
1
0
2
1
2
1
0
1
2
1
1
1
2
1
1
0
2
0
0
0
0
2
0
1
1
1
1
1
5
0
4
0
1
1
1
0
1
1
1
0
1
1
0
1
2
0
2
2
2
0
1
1
0
1
0
1
0
1
2
1
3
1
0
2
1
0
0
0
1
2
1
1
1
2
1
1
0
2
0
1
1
2
1
1
1
0
0
2
2
0
0
0
1
2
2
1
1
1
1
1
1
2
1
1
1
0
0
0
1
1
2
1
2
1
2
0
0
2
0
1
1
0
2
1
2
1
1
2
1
0
2
1
1
1
1
0
1
2
2
2
1
0
0
0
1
0
1
1
1
1
1
2
2
0
1
1
1
1
0
1
0
0
1
2
1
0
1
1
0
0
1
2
0
2
0
2
1
2
0
1
0
0
1
0
2
0
0
0
0
2
1
2
0
1
2
0
1
0
0
0
0
1
2
1
1
0
1
1
1
0
0
1
0
1
0
0
1
1
0
2
1
1
1
1
1
0
0
1
1
0
1
1
2
2
1
0
2
0
0
1
2
1
0
0
0
0
1
1
1
2
1
1
0
0
1
1
0
1
0
0
1
0
2
2
1
1
2
1
1
0
1
0
1
2
1
0
2
1
1
0
2
0
1
0
0
1
1
2
1
1
0
2
2
0
1
1
1
1
1
0
1
1
2
0
1
1
2
2
0
1
0
1
1
1
1
1
0
2
0
1
1
1
1
0
2
2
2
1
1
0
1
1
1
1
2
1
2
0
1
1
2
1
0
2
2
1
2
1
1
0
1
4
1
1
0
0
2
1
1
1
2
1
1
1
2
1
0
0
1
1
0
0
1
1
2
2
1
1
0
0
1
2
1
0
2
2
0
1
1
1
1
1
2
0
1
1
1
1
0
1
0
1
1
1
2
0
0
1
2
0
1
1
1
0
1
1
1
1
2
0
0
0
0
1
1
2
1
1
1
1
1
0
1
2
1
1
2
0
0
1
0
1
1
1
2
1
1
1
1
0
4
0
2
1
2
0
2
1
0
1
0
1
1
2
0
2
2
0
1
1
2
0
2
2
1
0
0
1
1
2
1
0
0
2
1
1
1
1
2
1
1
0
1
0
0
1
1
2
1
0
1
2
1
2
1
0
2
1
2
0
0
0
1
1
2
0
0
0
2
1
1
0
0
1
0
2
1
0
1
1
2
0
1
0
1
0
1
0
1
1
1
0
1
1
2
1
1
1
1
0
0
2
2
1
0
1
0
1
0
1
1
0
1
1
1
0
3
1
0
1
1
1
1
0
1
2
2
1
2
2
1
2
1
0
1
1
1
2
1
0
1
1
1
0
1
0
1
2
1
0
1
1
2
1
1
2
0
0
1
0
1
2
2
0
0
2
1
0
4
1
1
0
0
2
0
1
2
1
1
1
0
1
1
1
1
1
0
1
1
0
1
0
0
1
1
1
2
1
1
0
1
0
1
1
1
0
0
0
0
2
0
1
2
1
0
0
0
1
2
1
2
1
0
1
2
1
2
1
1
2
1
2
0
1
0
1
1
2
0
1
0
0
1
1
0
0
1
0
0
1
1
0
2
1
0
1
0
2
0
2
1
1
0
1
1
2
0
0
2
2
1
1
0
1
0
1
1
2
0
0
1
1
1
1
1
1
0
1
1
1
2
0
0
2
2
1
1
1
1
2
1
2
2
1
1
1
1
1
2
0
1
1
2
0
1
2
1
0
1
0
2
2
1
1
1
2
1
2
1
0
1
0
2
1
0
1
2
1
2
2
1
0
3
1
2
1
0
1
1
2
2
1
0
1
0
1
1
0
0
0
1
1
1
1
2
1
1
1
2
0
1
0
1
1
1
0
1
2
1
1
1
0
1
1
2
1
2
1
0
1
1
0
1
2
2
1
0
2
1
1
1
1
2
1
2
1
0
0
0
0
0
0
1
2
0
1
2
2
2
0
1
0
2
0
1
1
1
2
0
0
1
2
0
1
0
2
1
1
0
2
1
0
0
0
1
1
1
1
1
2
1
1
1
0
1
0
0
1
2
1
1
0
1
2
0
1
0
1
0
0
1
1
3
1
1
0
1
1
1
0
1
1
1
1
2
0
0
3
0
3
1
1
1
1
0
1
1
1
1
2
1
1
0
1
0
0
1
2
1
1
1
3
0
1
2
1
1
0
1
0
0
1
1
0
2
1
2
0
1
1
1
1
2
2
1
0
2
2
0
1
0
2
1
0
1
4
1
1
0
2
2
0
1
0
1
2
2
1
2
2
0
1
1
0
1
1
0
0
0
2
1
0
0
2
1
1
1
1
2
0
0
0
1
0
1
2
2
0
1
0
1
1
0
0
1
2
2
0
1
1
0
2
0
0
1
1
1
1
0
1
2
1
1
1
2
2
2
1
2
2
2
0
0
1
1
1
1
2
0
2
1
1
2
1
1
1
0
1
1
1
1
0
1
1
1
2
1
0
0
0
0
2
6
1
1
1
0
0
2
1
0
1
2
1
1
1
2
0
0
1
0
1
1
1
1
0
1
2
1
0
0
1
0
0
2
1
1
0
1
2
1
2
2
2
0
1
1
1
1
1
1
1
1
1
2
1
2
0
1
1
1
2
0
1
1
1
1
1
1
2
2
1
1
1
1
1
2
2
0
1
0
1
1
2
2
1
0
1
0
2
1
1
0
1
0
1
2
1
0
0
1
2
2
0
0
1
1
1
2
0
2
1
0
0
1
1
1
1
0
1
0
1
1
1
1
0
0
0
0
2
1
1
0
1
2
1
4
2
1
1
1
1
1
1
1
1
1
1
1
1
0
0
1
1
2
1
1
2
0
2
0
0
0
1
0
1
2
1
1
1
0
1
1
0
0
1
2
0
0
0
1
2
1
0
1
1
1
1
2
1
0
0
1
1
1
0
2
2
0
1
2
0
1
1
0
1
0
0
1
0
2
0
2
1
1
0
3
1
1
2
0
2
0
1
1
1
1
0
2
0
0
0
0
0
1
1
1
1
1
1
0
1
0
3
1
1
1
0
2
1
1
0
1
1
1
0
1
1
0
1
1
2
0
1
1
1
1
1
1
2
1
1
1
1
1
2
2
0
2
1
0
0
0
0
0
1
1
0
0
0
0
2
2
0
0
0
1
0
1
1
2
1
1
0
1
0
1
0
1
1
2
1
1
1
0
4
2
2
2
0
2
1
0
1
1
1
0
0
1
0
1
1
1
2
0
1
1
0
0
0
0
2
0
2
1
2
2
2
1
0
0
1
1
1
1
0
0
2
1
2
2
1
2
1
1
1
1
0
0
0
0
1
0
1
1
0
1
1
0
1
1
0
1
1
1
2
0
2
0
1
1
1
1
1
1
0
2
2
1
2
2
1
0
1
0
0
1
0
0
1
1
1
0
0
0
2
1
1
1
1
0
1
2
1
0
1
0
0
1
1
2
1
1
1
1
0
1
1
1
1
1
0
0
0
0
1
1
1
0
1
2
0
0
1
0
1
1
0
1
2
1
1
1
1
1
2
1
1
1
0
0
0
0
1
1
1
1
1
0
2
0
1
2
1
2
2
0
0
0
1
2
1
2
2
1
1
2
1
0
0
2
0
1
0
1
1
0
0
0
1
0
1
2
2
0
1
1
0
1
1
1
0
2
0
1
0
0
0
0
1
1
0
1
0
0
1
1
0
0
0
2
1
1
1
1
0
2
2
2
1
1
1
1
0
0
2
1
3
1
0
2
1
0
0
0
0
0
2
1
0
0
2
0
1
1
1
1
1
2
1
1
1
2
2
1
1
2
1
1
1
0
2
1
1
1
1
1
2
2
0
0
2
0
2
2
0
0
0
1
1
1
0
1
0
2
1
1
2
0
0
1
1
2
0
1
0
2
2
0
1
1
1
1
1
0
2
1
1
1
1
2
1
1
1
1
0
0
1
1
0
1
1
1
1
0
0
1
2
1
2
1
1
0
1
1
1
0
1
0
2
1
2
0
1
0
0
1
0
2
2
1
1
2
2
2
2
0
1
0
1
0
1
1
0
1
1
1
0
1
2
1
0
2
1
1
0
0
0
1
0
2
1
1
1
0
0
0
1
1
1
0
2
0
2
1
1
1
0
1
1
1
0
0
1
2
2
2
1
2
2
0
1
1
1
0
1
2
2
0
0
1
2
1
2
1
0
1
1
1
1
1
0
1
1
1
0
0
0
1
0
1
1
2
0
1
1
0
0
0
3
0
2
2
2
2
0
0
0
1
1
4
2
2
1
3
1
1
0
2
2
0
1
0
1
1
1
0
2
1
1
0
1
0
2
0
2
0
1
0
1
1
0
1
1
0
2
1
0
2
1
3
1
2
0
0
0
2
1
1
1
3
0
2
0
1
1
2
0
2
2
0
1
1
0
0
1
1
1
1
1
1
1
1
0
1
0
1
1
2
0
1
2
0
1
0
2
1
2
1
1
0
1
2
0
0
1
1
1
2
0
2
1
1
0
1
0
0
2
0
2
0
0
1
0
0
0
0
1
2
2
1
1
1
1
3
0
3
2
2
1
1
1
1
1
1
0
1
2
0
0
0
1
1
2
2
2
1
1
2
2
2
0
2
1
1
2
0
2
2
2
2
1
1
0
1
1
1
1
1
2
2
0
1
1
1
0
1
0
1
2
0
1
1
1
2
0
1
2
2
1
3
0
2
1
1
1
1
2
0
0
1
1
1
1
0
0
2
1
1
0
0
0
2
1
5
1
1
0
1
0
0
1
0
0
1
1
2
1
2
1
1
0
0
1
1
2
1
0
1
2
1
1
1
1
2
0
1
1
0
2
1
3
1
0
0
2
1
2
1
1
1
0
0
1
1
0
0
1
1
1
0
0
4
2
0
1
1
1
0
0
0
0
1
1
1
2
1
0
0
3
2
1
1
1
1
0
2
1
2
1
1
0
2
0
0
1
0
0
0
2
1
1
1
1
2
1
2
1
1
1
1
2
1
0
1
0
2
2
0
0
0
1
1
1
0
0
2
0
2
2
1
1
1
0
1
1
2
1
0
1
1
1
0
1
1
1
2
1
1
2
0
2
2
1
1
0
1
2
2
1
2
0
0
1
1
1
0
0
1
1
1
1
1
1
0
0
1
1
1
1
0
2
0
1
1
0
1
2
3
1
1
2
1
1
1
0
2
2
2
1
1
0
1
1
2
2
1
2
1
2
2
1
2
1
2
1
1
0
0
0
0
1
1
1
3
2
1
0
0
2
2
2
1
1
1
2
1
0
1
1
1
0
0
1
1
0
0
0
0
0
1
3
1
1
0
0
0
1
0
1
1
0
1
0
0
1
1
2
1
2
1
1
1
1
0
1
1
1
0
2
2
1
1
2
3
1
1
2
1
2
0
2
1
2
1
0
1
1
0
1
1
2
1
0
2
0
1
2
1
3
0
1
1
1
2
1
1
1
1
0
1
1
1
2
1
1
0
1
1
1
1
2
0
1
1
1
2
0
0
2
1
2
2
2
2
1
1
2
1
1
1
1
0
1
0
1
1
1
1
1
0
1
2
1
1
2
2
0
0
1
1
1
2
2
2
3
2
2
1
0
2
2
1
1
1
1
2
1
0
2
0
2
1
1
0
0
1
2
0
1
1
0
0
0
0
1
1
1
2
2
1
1
0
0
1
1
1
1
1
0
1
0
1
1
1
2
1
2
1
1
1
1
2
1
2
1
1
2
2
1
1
2
0
1
0
1
0
1
1
1
2
1
1
0
2
1
1
0
2
1
1
0
0
1
0
1
1
0
0
1
0
1
2
1
0
1
1
0
0
2
1
1
1
0
2
0
2
2
1
3
1
2
2
1
0
1
0
3
0
1
0
1
2
1
0
1
2
0
1
1
2
1
1
2
1
1
2
2
1
2
1
2
1
0
1
1
1
1
1
1
0
3
2
2
0
2
0
2
2
1
1
1
2
1
1
0
1
1
0
2
0
1
1
0
1
0
1
1
0
1
0
1
1
1
1
0
2
1
2
1
2
0
0
0
1
1
1
2
1
2
1
1
0
3
1
0
1
0
2
1
0
1
1
2
0
1
0
1
3
0
1
1
2
4
1
3
0
1
1
0
1
1
1
2
1
3
1
1
1
1
1
1
0
0
1
0
0
1
1
2
0
1
2
1
0
1
1
2
1
1
1
0
1
0
2
1
1
1
1
2
1
1
1
1
2
0
2
0
1
0
2
2
0
0
0
2
1
2
2
0
1
2
0
1
2
0
0
2
0
2
1
1
2
2
1
1
1
1
1
1
1
1
0
0
1
1
1
0
1
0
2
0
0
1
0
2
1
2
0
0
1
2
0
0
1
0
0
1
0
0
2
1
2
1
0
0
2
2
2
1
2
1
1
1
2
1
0
1
0
1
0
1
1
0
2
1
1
1
1
2
1
0
1
0
2
1
0
1
1
1
1
0
1
1
2
0
1
1
1
2
0
1
0
1
0
1
0
0
1
2
1
2
0
1
1
2
2
1
1
0
1
0
3
0
0
2
2
0
2
1
1
0
0
1
1
2
1
0
0
1
1
1
1
2
2
1
1
1
0
1
0
2
0
1
1
1
0
0
0
1
1
1
0
1
0
1
2
1
1
1
0
1
1
2
1
1
0
1
1
1
0
1
0
0
0
1
1
1
0
2
2
0
2
0
3
1
2
2
1
2
1
2
0
1
0
1
1
0
1
1
1
2
2
1
0
2
0
2
2
1
0
2
1
0
1
0
2
0
1
1
1
2
0
1
1
1
1
1
1
0
1
1
1
1
1
1
1
2
0
0
1
0
0
0
0
3
1
1
0
1
1
2
0
1
0
1
1
1
1
2
0
1
1
0
0
1
0
2
0
0
0
1
0
0
1
2
1
2
1
1
0
2
2
0
1
1
1
1
2
2
2
0
0
0
1
1
0
0
2
0
1
1
0
1
1
0
1
0
0
2
1
2
1
0
1
0
0
1
0
2
1
1
0
1
1
2
0
2
1
0
0
1
0
2
0
1
1
0
0
0
2
0
2
1
1
0
1
1
0
2
2
0
2
1
1
0
1
2
2
0
1
2
0
1
0
2
0
1
0
2
0
1
1
1
1
2
0
1
1
0
0
1
2
2
1
2
1
0
1
2
0
1
1
2
0
1
0
1
1
0
1
0
0
1
1
1
0
1
2
1
1
2
0
0
0
1
2
1
2
1
1
2
0
0
1
2
1
1
1
1
1
2
1
1
0
1
2
0
1
1
0
1
1
1
1
1
1
1
2
1
1
0
1
0
2
1
0
1
2
0
1
1
1
2
1
2
2
0
1
0
2
2
1
2
1
1
0
2
1
0
1
1
0
1
1
0
2
0
2
1
2
1
0
1
1
2
1
1
1
1
1
1
0
1
1
1
1
0
0
1
2
1
1
1
1
1
0
0
1
1
0
1
2
1
2
2
0
1
2
1
2
0
2
0
2
1
2
1
0
1
0
0
0
0
1
0
1
1
1
0
1
1
2
0
0
0
1
1
1
0
1
2
0
1
1
1
0
2
2
1
1
1
1
1
0
1
0
0
0
2
0
0
0
1
1
2
1
1
3
1
0
1
0
0
2
1
1
1
1
2
1
2
0
0
0
2
1
7
2
2
1
2
0
2
1
0
0
0
0
1
2
1
0
0
2
1
2
1
0
1
2
1
2
2
1
1
0
1
0
1
0
0
0
1
1
1
2
0
1
0
1
1
2
2
0
1
0
2
1
2
0
1
3
2
1
1
1
0
1
0
1
0
0
0
3
0
0
0
1
2
1
0
2
0
1
1
0
2
1
2
2
2
1
0
1
2
2
2
1
1
1
1
1
0
1
0
2
0
0
1
1
1
2
2
0
1
1
1
0
1
0
1
1
1
0
1
2
0
1
0
1
2
0
0
1
1
0
0
1
1
0
1
1
1
1
1
0
2
0
0
1
1
2
0
1
2
1
0
1
2
2
1
1
1
0
1
2
1
1
1
0
2
0
1
1
0
0
1
1
0
1
1
1
0
1
2
1
1
1
2
1
2
0
2
1
1
2
1
0
1
1
1
1
0
2
1
2
2
1
1
1
0
2
5
1
1
1
1
1
1
0
1
2
1
2
1
0
1
1
1
2
2
1
1
0
0
1
2
1
1
0
1
2
1
0
1
1
0
0
0
1
1
2
0
2
2
1
1
1
0
1
0
1
1
0
1
1
1
1
2
1
1
1
1
1
1
1
1
1
0
1
0
2
2
1
1
1
1
1
1
1
1
1
1
1
1
0
0
1
1
1
2
1
1
0
4
1
1
1
0
1
2
2
1
1
1
2
2
0
2
0
0
1
1
1
1
0
2
0
1
1
0
1
1
2
2
0
2
1
2
0
1
1
1
1
0
1
2
0
0
1
2
1
1
2
1
1
1
1
0
1
1
1
1
0
1
2
1
1
3
0
1
1
1
1
1
0
1
1
1
1
1
3
2
1
0
2
0
2
0
0
1
1
2
1
1
1
0
0
0
2
0
1
1
1
0
0
1
0
0
1
1
1
1
1
0
1
1
2
0
0
1
1
2
2
2
1
1
1
3
0
0
3
2
2
1
1
0
0
1
0
0
1
3
2
2
1
0
0
0
0
0
0
1
1
1
1
1
0
1
2
0
1
1
0
2
2
0
2
1
2
1
2
1
1
1
2
0
1
0
2
0
2
1
2
0
0
1
2
0
1
1
2
2
2
0
0
2
2
2
2
0
2
1
0
0
2
2
0
1
2
0
1
0
2
1
2
1
1
1
2
1
1
1
1
1
2
0
0
0
1
2
1
0
0
2
1
1
1
0
0
2
0
2
0
0
0
0
1
0
2
1
2
2
1
1
1
0
0
0
1
2
1
1
1
1
3
1
0
1
1
0
1
2
0
1
1
0
1
0
1
1
0
2
0
2
1
0
1
0
2
1
2
0
0
0
2
1
0
0
0
0
1
1
0
1
2
2
0
1
0
2
0
0
2
1
2
0
1
2
2
0
0
1
1
1
1
0
1
2
3
1
1
1
0
0
0
2
1
1
2
0
0
1
1
1
3
1
1
2
1
0
2
0
1
1
2
1
0
1
2
0
1
0
0
0
1
1
1
1
0
2
0
1
0
2
0
0
2
0
1
0
1
1
1
0
0
0
2
0
1
2
1
1
1
1
0
1
0
0
2
2
0
1
1
0
1
1
0
2
1
0
1
1
1
1
0
2
0
2
1
1
1
1
0
1
1
0
1
0
1
1
1
2
2
1
1
0
1
0
2
1
1
1
1
0
1
1
1
1
1
0
1
1
1
0
1
1
2
2
1
0
2
2
1
1
1
1
0
1
0
2
0
0
0
0
2
2
1
2
0
2
2
2
0
0
0
1
2
1
1
1
2
2
1
2
1
1
1
2
1
2
0
1
0
0
1
2
0
1
1
2
2
0
2
1
0
0
1
1
1
1
1
2
1
2
1
1
1
1
2
1
0
0
1
0
1
0
1
2
0
2
1
2
1
1
1
1
1
1
0
0
0
0
0
1
1
2
0
1
1
1
2
1
2
1
2
2
1
1
1
1
0
1
0
0
2
1
0
1
2
1
2
0
1
1
1
0
3
2
2
1
1
0
1
2
1
1
3
1
1
0
0
2
1
0
2
2
2
1
0
1
1
1
1
1
1
1
1
1
0
0
0
1
1
0
1
0
0
2
2
1
1
1
2
1
0
0
1
1
1
2
0
1
0
0
0
0
2
1
2
1
0
4
0
0
2
2
2
0
2
1
1
2
2
3
1
2
2
1
1
1
1
0
1
0
2
0
1
0
1
1
1
1
1
0
1
2
0
0
1
2
1
0
1
0
0
1
2
2
1
2
1
1
2
0
2
1
1
1
1
0
0
1
1
0
0
0
0
0
1
1
1
1
0
1
0
2
0
1
1
1
1
1
1
2
2
0
1
1
2
1
2
1
1
1
1
2
2
0
2
2
1
1
1
1
1
2
2
1
1
2
0
1
1
1
1
0
0
2
0
1
0
1
1
0
2
0
2
2
1
1
1
1
1
0
0
3
2
1
0
1
1
1
1
0
0
0
2
2
0
1
2
1
1
1
0
1
1
2
2
0
1
0
1
0
1
0
1
1
2
2
0
0
1
1
1
0
1
1
1
1
3
1
0
0
1
1
1
0
2
0
2
1
0
1
1
0
2
0
2
0
1
1
1
1
0
0
2
2
0
1
2
0
0
0
1
1
2
1
2
1
1
2
0
1
2
1
1
1
1
3
1
2
0
2
1
0
1
1
0
0
0
1
1
0
2
0
2
2
1
0
1
2
2
1
4
2
0
2
2
2
2
0
0
0
2
0
0
1
1
2
1
1
2
1
1
2
0
1
1
1
1
2
0
2
1
2
2
1
0
1
0
0
0
0
1
1
3
1
0
1
2
0
1
1
2
0
0
2
1
0
1
1
2
1
0
0
2
0
1
1
1
0
1
2
0
2
2
0
0
1
0
1
1
1
2
0
1
1
1
0
1
0
1
1
2
1
1
0
1
0
2
1
1
2
1
0
1
1
2
1
1
0
1
0
0
1
0
0
2
0
0
2
1
1
1
1
0
0
2
1
2
1
2
2
0
2
1
0
1
2
1
2
0
1
2
1
2
1
1
0
1
1
2
1
0
2
1
1
1
1
1
0
1
2
2
1
1
1
2
1
1
2
0
1
1
0
1
0
0
0
0
0
2
1
0
0
2
0
1
1
2
1
0
3
0
1
1
1
1
1
2
1
0
2
0
1
1
2
2
0
2
1
1
1
1
0
0
0
1
2
1
2
2
0
1
0
0
1
0
0
1
1
3
1
2
1
1
1
0
2
1
1
1
1
0
2
1
1
2
1
0
0
1
1
1
0
0
1
1
1
0
2
1
2
2
0
1
2
1
1
1
2
1
1
0
0
0
1
1
1
0
0
0
2
0
1
0
1
2
2
0
1
1
1
0
0
2
2
2
1
1
1
2
1
0
0
0
1
0
1
1
0
1
0
1
1
1
1
4
1
0
1
2
1
1
2
1
0
1
1
0
1
2
1
0
0
1
1
2
0
1
2
2
2
0
1
2
1
1
1
2
1
2
0
0
2
1
0
0
1
1
1
0
1
0
1
0
0
2
0
0
2
1
2
2
1
2
0
1
2
1
1
1
0
0
1
0
2
0
0
2
2
0
2
0
1
2
2
1
4
2
3
2
0
1
1
2
1
1
1
0
2
0
1
1
2
2
0
1
1
0
1
1
0
1
2
2
1
1
1
2
1
1
1
1
2
0
2
0
1
1
0
0
2
2
0
1
1
2
1
0
2
1
1
0
1
2
1
1
1
1
1
1
1
2
1
0
1
1
1
0
1
1
1
1
1
1
1
0
2
1
2
1
1
1
0
0
1
1
2
1
1
2
1
1
2
0
2
1
1
1
2
0
2
0
1
2
2
2
2
2
2
0
1
0
0
1
1
2
1
1
0
2
3
1
2
1
1
1
2
1
0
1
1
1
0
0
0
0
1
1
0
1
0
2
1
0
2
0
2
1
2
1
0
0
2
1
1
0
2
1
1
0
1
0
1
2
1
2
1
0
1
2
0
1
1
0
1
2
1
1
0
0
2
2
1
1
1
1
1
2
0
0
0
2
2
1
0
0
1
2
0
2
1
2
1
2
2
1
0
0
1
0
1
2
0
2
0
1
1
0
0
0
1
1
2
2
0
0
1
0
1
2
1
1
1
1
0
1
1
1
1
1
0
0
1
1
1
0
2
1
2
2
0
0
2
1
0
2
2
1
2
0
2
1
1
1
1
1
0
0
2
1
1
1
2
1
1
0
2
1
1
1
0
1
2
1
1
0
1
1
0
1
3
1
0
0
1
0
0
2
1
2
0
0
2
0
1
1
1
0
0
0
0
0
2
1
1
0
1
0
1
1
1
1
2
2
1
2
1
0
1
2
0
0
1
0
0
0
0
2
1
2
4
1
0
1
1
1
0
1
0
2
1
2
1
1
2
1
0
1
1
2
0
2
0
0
1
0
2
2
1
0
2
1
1
2
3
2
0
1
2
1
1
0
1
0
1
1
1
0
1
0
1
1
1
2
0
1
0
1
1
1
2
1
0
0
1
1
2
1
1
2
1
0
2
2
0
1
1
2
2
0
0
1
0
2
2
1
2
1
1
2
3
1
0
0
2
1
0
2
1
1
0
2
1
1
1
0
1
2
1
0
1
0
0
2
2
1
1
0
2
0
0
1
1
0
2
1
1
1
0
1
1
1
0
1
1
0
1
1
1
1
1
1
0
1
1
1
1
2
2
0
1
1
2
2
0
0
2
0
0
1
0
1
0
1
1
2
0
1
1
1
0
2
1
0
2
0
1
1
0
2
3
2
1
1
0
0
0
1
0
3
0
1
0
1
0
0
1
2
1
2
0
2
0
1
1
0
2
2
0
1
1
1
1
2
2
0
1
2
1
0
1
1
1
1
1
2
1
1
0
1
1
1
2
0
0
1
1
2
0
1
5
1
1
2
3
1
2
1
0
1
1
2
0
0
1
0
2
0
1
0
1
1
0
1
0
1
0
2
0
2
2
2
2
1
1
0
0
0
1
1
1
0
0
0
0
1
3
2
0
0
1
2
2
1
1
1
1
1
0
2
1
1
1
2
0
1
1
2
1
2
0
1
0
1
1
1
1
1
2
1
1
0
1
4
1
1
0
1
1
1
2
1
1
0
1
1
2
1
2
1
2
0
2
1
1
1
0
2
1
0
1
1
2
0
1
1
1
1
0
0
1
2
1
1
1
2
1
1
1
1
1
1
0
1
1
1
1
0
1
2
1
0
1
1
1
1
0
0
0
1
0
1
1
2
1
2
1
2
1
1
2
2
2
1
2
1
0
1
2
0
0
0
1
0
1
2
0
1
1
2
0
0
0
1
1
1
0
2
1
0
0
2
0
1
1
1
2
0
1
2
0
2
2
0
0
1
1
1
1
0
0
2
1
0
0
1
2
1
2
2
0
2
2
0
0
1
0
0
3
2
3
1
0
1
0
2
2
3
1
2
0
2
1
1
1
2
1
0
1
1
0
2
0
1
0
1
2
2
0
1
1
0
2
1
1
1
1
2
0
1
3
2
2
0
1
1
0
1
1
0
0
0
0
1
2
0
0
1
1
1
1
2
1
2
0
1
1
1
2
2
1
0
0
0
0
2
1
2
1
0
0
2
2
1
1
0
0
0
0
1
1
1
0
1
1
1
2
0
1
1
1
1
1
0
1
1
0
1
0
2
1
1
1
1
1
0
0
1
2
1
0
2
0
0
1
2
0
0
1
0
1
1
0
1
1
1
1
1
1
1
1
0
1
2
0
0
0
1
1
0
2
1
1
2
0
1
2
1
0
2
0
1
2
1
2
0
1
1
1
0
0
1
1
1
0
2
1
1
1
2
1
0
2
1
2
2
1
1
0
3
0
0
2
2
1
1
0
0
0
0
2
0
2
1
0
1
0
2
1
1
2
0
0
1
1
2
1
0
0
1
0
0
0
2
1
0
1
0
2
0
1
1
1
2
1
1
0
1
1
1
1
1
0
1
0
2
2
0
1
0
1
1
1
2
0
2
1
1
1
1
0
0
1
1
0
1
1
0
1
1
1
2
1
1
0
1
2
0
1
2
1
1
0
0
1
0
2
0
0
2
0
0
0
1
2
0
1
1
1
1
1
0
0
0
0
1
0
0
0
1
2
0
0
0
2
1
0
1
1
2
1
1
2
0
0
0
2
0
1
1
1
2
0
1
2
1
1
1
2
0
2
1
1
1
1
2
1
2
1
1
1
1
1
1
1
0
1
2
1
2
0
2
1
0
0
1
0
1
0
0
1
1
1
1
1
0
2
1
1
2
1
0
1
2
0
1
0
1
2
1
1
1
0
1
1
2
2
0
1
1
0
1
0
1
0
1
1
0
0
0
1
0
1
2
2
0
0
1
1
0
1
2
0
1
0
1
1
1
1
0
2
1
2
1
2
1
0
0
0
1
2
1
0
0
1
2
1
2
2
1
1
1
2
2
1
1
1
2
0
1
1
1
0
1
1
1
1
0
1
1
2
2
1
2
1
1
0
1
1
1
0
1
0
2
1
2
2
1
0
1
2
0
1
0
1
2
1
1
2
2
1
2
1
0
1
1
1
1
2
0
1
0
0
1
1
1
1
1
1
1
1
1
0
2
2
1
1
1
1
0
0
1
1
1
0
2
1
2
1
1
0
0
0
1
1
0
0
1
2
0
0
0
2
0
0
1
2
0
1
1
1
0
2
2
0
1
1
0
0
1
0
1
1
1
0
2
0
0
2
1
1
2
0
2
1
0
1
0
1
1
1
1
0
1
2
1
2
0
1
0
0
1
0
1
1
2
0
1
2
2
1
1
2
1
1
0
1
2
0
2
1
0
1
1
1
4
1
4
0
2
0
0
1
0
1
2
0
0
0
0
2
1
2
3
1
0
1
1
2
1
2
1
0
2
1
1
1
0
2
1
0
1
0
1
1
1
1
0
1
1
0
1
1
2
2
1
1
1
1
2
2
0
1
0
2
2
0
1
1
1
1
2
1
1
0
0
2
1
1
1
1
1
0
0
0
1
2
0
1
2
2
1
2
0
2
1
2
2
3
2
0
0
2
1
2
2
1
2
0
2
1
1
0
1
1
1
2
1
1
1
1
2
2
2
1
1
2
1
0
2
2
0
0
1
0
0
0
0
0
2
1
0
0
1
0
2
2
1
0
1
2
0
0
1
2
1
0
2
2
2
1
2
1
1
0
1
0
0
0
1
1
1
1
1
1
0
0
0
1
1
1
1
2
2
1
1
1
1
1
0
0
2
2
1
0
1
0
1
0
0
1
1
1
1
2
1
1
1
0
0
1
1
1
0
1
1
2
0
2
1
0
2
2
0
0
0
2
2
1
0
1
2
1
1
1
2
1
1
2
1
0
2
1
0
1
0
1
1
2
2
1
1
0
0
1
0
0
2
0
2
0
2
0
0
1
2
2
1
2
0
2
2
2
0
1
1
1
0
0
1
1
2
2
0
1
2
2
0
1
2
1
0
2
0
2
2
2
2
1
0
1
2
1
0
1
1
1
1
0
0
1
1
1
1
0
0
1
2
1
2
1
1
1
1
0
1
0
1
2
0
0
1
1
1
1
1
1
0
1
2
0
1
0
0
1
1
0
0
2
1
0
1
1
1
0
1
2
2
0
1
2
0
0
2
2
1
0
1
1
1
2
1
1
0
1
0
1
1
1
1
2
1
1
1
0
0
1
0
0
1
1
0
1
1
1
0
0
1
0
0
0
1
1
1
0
2
1
2
1
0
0
1
0
1
1
1
2
0
0
1
1
0
1
1
1
1
0
0
1
1
1
1
2
2
2
1
1
1
2
0
1
0
1
2
1
2
2
0
1
0
1
0
1
1
1
2
1
0
1
0
1
1
1
1
1
1
1
1
0
1
0
2
0
0
0
1
0
1
0
2
0
1
2
0
2
1
0
0
1
1
2
1
2
1
3
1
0
0
1
1
1
2
1
0
2
0
0
1
0
0
1
0
1
1
0
0
1
0
2
1
1
1
1
2
0
1
0
1
1
0
2
0
1
1
1
0
2
2
2
0
1
0
0
1
1
2
2
0
2
1
0
2
0
1
1
1
1
2
0
2
1
1
1
0
3
1
0
0
1
1
1
0
1
1
1
2
1
2
2
1
0
0
1
1
0
2
2
0
1
1
1
0
3
1
1
1
2
1
2
1
2
0
0
0
0
1
2
1
0
1
0
0
2
0
0
0
1
1
1
1
0
1
1
0
0
0
1
1
2
2
1
1
1
0
2
1
1
2
2
2
1
1
0
1
0
0
1
1
1
1
2
0
0
0
0
1
1
0
1
1
1
1
2
1
0
2
1
1
0
0
2
1
1
0
0
2
1
1
2
1
1
0
0
1
2
2
1
0
1
1
1
0
0
1
1
1
2
1
0
0
0
0
1
0
1
1
1
1
2
2
0
2
0
1
0
1
0
3
1
2
2
1
1
0
2
0
1
1
1
1
1
0
1
1
2
2
1
1
1
1
1
1
2
0
2
1
2
0
2
2
0
0
0
1
1
0
1
0
2
0
1
0
1
1
1
0
1
0
0
1
2
1
0
2
1
0
0
1
2
1
1
3
2
1
1
2
1
0
2
1
1
1
2
0
1
1
1
0
1
1
1
1
1
0
0
1
2
1
0
2
1
1
0
1
0
2
1
1
1
1
2
1
0
0
2
1
1
1
0
1
2
1
1
0
2
1
1
1
1
2
1
1
0
1
1
1
2
0
1
1
2
1
1
1
2
1
3
1
1
0
2
1
2
3
0
0
0
2
0
0
0
1
1
1
0
1
2
0
1
1
3
2
1
1
1
1
1
0
0
4
1
2
1
1
3
1
0
1
0
1
0
2
0
0
1
0
1
0
1
0
2
1
2
2
2
0
1
0
3
0
1
0
0
0
0
1
2
1
2
2
2
2
2
2
1
0
2
4
0
2
1
1
1
1
2
2
2
2
1
2
1
2
1
0
1
0
1
2
0
1
1
3
2
2
1
1
1
2
2
0
1
1
0
0
2
0
2
0
2
2
0
1
1
1
1
1
1
1
0
1
0
3
2
1
1
1
1
1
0
2
0
0
1
2
0
1
1
2
1
1
1
1
2
1
1
1
2
1
1
1
1
2
1
0
1
1
2
1
0
1
0
2
1
2
2
0
1
1
0
0
0
1
1
2
2
2
1
1
0
0
0
1
2
2
2
2
1
1
1
0
0
0
1
1
2
0
0
1
2
2
1
0
1
2
0
1
2
2
2
0
1
1
0
1
2
1
1
0
1
1
1
0
0
0
2
1
0
1
2
1
1
2
1
2
0
1
2
0
0
2
0
2
0
0
2
2
1
1
1
0
2
2
0
1
1
1
1
0
1
2
0
1
0
1
0
1
1
1
0
2
2
1
0
2
1
1
2
1
2
1
2
1
2
1
1
2
0
2
1
1
0
2
1
0
1
0
1
0
2
1
2
1
2
0
0
1
1
2
2
2
1
0
0
2
1
2
0
0
1
1
2
0
1
1
2
1
2
0
1
1
0
1
1
1
0
0
0
1
1
2
1
1
2
0
0
1
3
1
1
1
0
0
1
1
1
1
1
2
1
0
2
1
0
1
0
0
1
1
2
2
1
1
0
1
1
2
0
0
2
1
1
0
2
1
1
0
1
0
0
1
1
2
2
1
0
1
1
1
1
1
2
2
0
2
1
1
1
1
1
2
1
2
1
0
1
1
1
2
1
1
0
0
0
1
1
1
2
0
0
2
2
2
1
0
2
1
2
0
1
1
1
0
0
2
1
0
0
0
1
1
1
2
0
0
1
1
1
1
0
1
1
1
0
0
2
1
0
1
1
1
0
0
1
2
1
1
1
2
1
0
1
1
1
0
1
0
2
1
1
2
1
1
1
1
1
0
1
0
0
1
0
0
2
0
1
0
1
0
1
1
2
1
0
2
1
1
0
2
1
2
1
2
0
1
1
1
1
1
1
2
2
2
1
0
1
2
1
0
1
0
1
1
1
2
1
1
0
0
1
1
1
2
1
0
1
2
2
0
1
1
1
1
1
2
2
1
0
1
0
1
1
2
0
3
0
0
2
2
2
2
0
1
0
0
0
1
1
2
1
1
2
1
1
1
0
2
1
0
0
2
0
2
1
0
2
1
2
0
0
1
0
1
1
1
0
2
1
2
1
2
0
2
2
1
1
2
1
1
1
2
1
1
2
1
0
1
1
2
2
1
1
2
1
2
3
2
1
1
1
1
0
0
1
0
1
0
0
0
3
1
1
0
1
1
2
0
1
2
3
0
1
0
0
1
1
2
1
3
1
1
1
0
0
2
1
1
1
4
1
1
1
0
1
3
1
1
2
1
1
1
1
1
1
1
0
1
2
0
1
1
0
3
1
3
1
1
1
1
0
2
1
2
1
1
1
1
0
2
1
1
2
1
1
0
1
0
2
0
1
2
0
0
1
0
1
1
1
0
1
0
1
1
0
0
1
2
1
1
0
1
1
1
2
1
1
1
0
1
1
2
0
1
1
0
3
0
0
1
2
0
1
1
0
0
2
1
1
0
0
1
1
1
1
0
1
1
1
1
2
0
0
0
1
0
0
1
2
1
0
1
0
1
0
0
1
0
1
3
2
1
0
1
4
2
1
1
1
1
0
0
1
1
1
1
0
1
1
0
1
1
1
2
2
2
3
1
3
1
1
0
1
0
1
1
1
2
0
1
1
1
1
0
0
0
0
0
1
1
1
1
1
0
1
1
1
2
2
1
1
1
2
1
1
1
0
1
1
1
0
2
2
1
0
2
1
2
3
1
1
2
2
0
0
1
1
0
1
1
0
1
0
1
1
1
2
1
1
1
0
2
1
1
1
1
1
1
1
0
1
0
1
1
1
2
0
3
2
0
1
1
0
0
0
2
1
0
0
1
1
1
0
1
0
1
1
2
0
0
1
0
0
1
2
1
2
2
0
1
2
2
0
2
1
1
2
1
1
1
1
0
0
1
1
1
1
2
2
1
1
0
1
2
0
2
0
2
0
2
0
1
1
1
1
0
0
0
1
0
1
1
2
2
1
2
0
2
1
1
1
1
0
1
0
1
2
2
2
0
2
2
0
1
1
1
2
2
1
1
0
1
2
1
0
1
1
1
1
1
1
1
1
1
0
2
1
1
2
1
1
0
2
1
1
2
1
0
1
1
1
0
2
1
2
1
0
2
1
2
1
0
1
2
2
1
2
0
1
2
0
0
2
0
1
1
0
1
0
2
2
1
2
2
1
1
0
1
0
0
2
0
2
3
2
2
1
0
0
0
0
2
0
2
2
1
0
1
1
1
0
2
7
1
1
2
1
0
0
2
1
1
0
1
2
0
1
1
1
1
1
2
0
1
1
0
1
1
2
1
0
1
2
0
1
2
0
1
2
0
2
1
1
1
1
1
1
1
2
2
1
2
1
0
0
3
1
1
1
1
2
1
2
0
1
2
2
1
1
3
0
1
3
1
2
1
1
2
2
0
0
2
1
0
2
1
1
1
1
0
0
0
2
2
1
1
1
0
1
0
0
2
1
0
0
1
2
0
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
0
2
0
1
1
2
0
2
1
0
1
1
0
1
0
1
1
1
2
1
1
0
1
1
1
1
0
1
0
1
0
2
1
1
0
2
2
1
1
1
1
0
1
1
0
1
1
0
0
5
0
0
2
2
2
2
0
1
2
1
1
1
1
1
1
1
1
1
0
0
1
1
0
1
1
1
0
0
1
2
1
2
1
0
0
0
1
1
1
2
1
1
1
2
0
0
2
1
2
1
1
0
1
1
1
0
2
0
1
1
1
0
1
1
1
1
1
1
2
2
0
0
0
1
0
0
1
0
1
1
1
0
3
2
0
1
1
2
1
0
0
0
1
1
1
1
1
1
1
1
2
1
1
2
2
2
0
1
0
1
0
1
0
0
5
1
2
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
0
0
1
1
2
1
1
1
0
1
0
1
1
1
1
1
1
1
1
0
2
0
1
1
1
2
1
0
0
2
2
0
2
0
2
1
4
0
0
1
1
2
1
1
1
1
2
2
1
2
1
0
1
3
0
1
1
0
1
1
0
0
0
2
2
2
2
1
2
1
1
0
1
0
1
4
0
0
0
0
2
0
1
2
1
1
0
1
0
2
1
0
2
0
2
0
2
1
1
0
1
1
1
2
1
1
1
1
1
2
1
1
0
0
0
1
1
1
0
1
2
0
0
0
1
1
2
0
0
1
0
1
1
1
1
1
0
0
0
1
1
1
2
1
1
1
2
0
2
0
1
0
1
1
1
2
1
0
2
2
2
0
0
1
0
0
0
0
1
0
0
0
1
1
1
2
2
1
1
0
1
1
1
2
0
1
0
1
1
4
0
0
1
0
1
2
1
0
0
1
1
1
1
2
0
1
0
1
1
0
0
1
2
0
1
1
1
2
1
0
2
2
0
1
1
0
2
1
0
1
0
2
1
1
1
1
0
3
1
1
0
0
1
2
0
1
4
0
0
1
2
2
2
2
0
0
0
0
1
0
2
2
2
2
0
0
0
1
1
2
1
2
1
1
0
0
2
2
2
2
1
3
0
1
1
2
2
1
0
1
0
1
2
3
1
0
1
0
0
0
1
2
0
1
0
1
0
6
0
0
2
0
1
0
1
0
0
1
0
2
0
1
0
2
1
1
2
2
0
1
0
1
1
1
0
0
1
2
1
1
0
2
1
0
1
1
0
0
1
1
0
0
0
2
0
1
1
1
2
1
0
2
1
1
1
1
0
1
1
1
0
1
1
1
1
1
2
1
1
0
1
2
1
0
1
1
1
0
1
1
2
0
0
0
1
0
0
0
1
1
0
2
1
1
1
2
0
1
1
2
1
1
1
1
1
1
0
0
1
1
2
2
1
2
0
1
2
1
1
1
1
0
2
1
1
2
1
1
0
0
2
0
2
2
1
0
1
1
2
0
0
1
1
1
2
0
0
2
0
0
0
1
1
1
1
1
0
0
1
2
2
1
2
0
0
2
0
0
1
0
0
1
0
2
0
1
0
2
0
0
0
1
1
1
2
3
0
2
0
1
1
0
1
1
1
2
0
0
1
1
1
1
0
0
0
1
0
1
0
1
2
1
0
1
1
1
0
1
0
1
0
0
1
1
2
1
1
0
1
2
1
1
1
0
2
1
0
1
1
2
2
2
2
1
1
2
0
0
1
2
1
0
2
0
0
1
1
0
1
0
1
2
1
1
0
0
1
1
1
2
1
0
1
2
1
1
2
1
2
0
1
2
2
1
0
1
1
1
1
0
1
0
1
0
1
0
0
0
0
0
0
1
0
2
2
0
0
1
1
0
0
0
2
1
0
0
0
1
1
0
2
0
1
1
2
0
1
0
0
2
1
1
0
1
1
0
1
0
1
2
1
2
1
1
1
2
1
1
1
0
0
2
1
1
0
1
1
2
0
2
1
2
0
2
2
0
2
0
0
2
2
1
0
1
1
2
1
0
1
1
0
2
2
2
0
1
0
1
1
0
1
1
0
2
2
1
1
1
3
1
1
1
0
2
1
1
1
2
1
0
0
2
1
1
1
0
3
1
1
0
1
0
2
1
2
0
1
0
1
0
0
1
0
0
2
0
1
1
0
2
1
0
1
1
2
2
1
2
0
0
0
1
1
2
0
1
0
0
1
1
1
1
1
2
1
2
1
0
1
1
1
1
0
2
1
1
1
1
0
0
0
0
0
1
0
2
1
0
2
0
0
2
1
0
1
1
0
1
1
2
1
0
1
2
0
3
1
0
0
1
0
1
0
1
1
1
1
2
1
1
0
2
1
0
0
2
2
2
2
1
1
1
1
1
1
1
0
1
1
1
0
1
0
0
1
1
1
0
1
1
1
1
2
0
1
1
0
1
2
1
0
1
0
1
1
1
1
1
2
2
2
3
1
2
1
2
1
2
0
1
1
2
0
1
1
0
1
0
0
1
1
2
3
0
0
2
1
1
1
1
1
0
2
0
2
1
0
2
1
2
0
0
3
1
1
0
2
1
2
2
1
1
0
1
0
0
0
0
1
2
1
1
2
1
2
2
1
0
2
0
1
0
1
2
2
0
1
2
1
1
1
1
3
3
1
2
1
1
2
0
0
2
1
1
1
1
0
1
0
2
1
1
1
1
1
1
0
1
2
1
0
1
2
2
1
3
2
0
1
1
1
1
0
2
1
0
1
2
0
1
0
0
2
0
1
0
1
1
1
1
1
0
1
0
1
2
2
1
0
1
1
0
2
0
1
2
2
1
2
2
1
0
0
2
1
1
0
1
0
1
1
1
0
1
1
1
1
1
0
1
2
0
2
0
1
2
1
0
1
1
1
1
1
0
1
2
1
2
1
0
1
1
0
1
1
2
1
3
2
1
1
0
1
1
2
2
0
2
1
0
1
0
0
2
2
0
2
1
0
2
0
1
1
1
2
2
1
1
2
0
1
1
0
1
1
1
2
0
1
2
2
2
1
1
0
1
0
2
0
1
1
1
3
0
1
2
1
0
0
1
0
2
0
0
1
0
0
1
1
0
0
2
1
2
1
0
2
2
0
0
1
0
0
1
1
1
1
2
1
1
0
0
1
1
0
1
3
1
2
0
1
1
1
0
2
0
2
1
2
1
1
0
1
0
0
1
1
1
2
2
1
1
1
1
1
1
1
1
0
2
2
0
1
0
0
1
1
0
1
0
1
0
1
1
1
1
1
1
0
1
1
2
0
0
2
1
0
1
1
2
1
1
0
1
0
1
1
1
1
1
1
2
0
1
0
1
0
1
1
0
1
0
1
1
2
2
0
1
0
2
2
1
1
10
1
0
0
1
2
2
1
0
0
1
1
1
0
1
1
2
1
1
1
1
0
0
2
1
1
1
0
0
1
1
1
1
0
1
1
0
0
2
1
1
1
2
1
1
1
1
1
1
0
0
0
4
0
0
0
1
0
0
1
2
2
2
2
1
1
1
2
1
0
1
1
3
2
0
1
0
0
1
2
2
1
0
2
1
1
1
0
1
1
1
0
2
0
1
2
1
0
1
0
2
0
1
2
2
0
1
1
0
0
1
1
2
1
0
1
1
0
1
0
0
2
1
1
2
1
1
1
0
2
2
0
2
1
0
1
0
1
2
1
0
1
0
1
3
2
1
0
3
2
1
1
1
2
1
0
2
1
2
0
1
1
2
0
1
0
0
0
1
1
2
1
1
1
1
1
0
0
1
2
1
1
0
0
2
1
2
1
0
2
1
0
1
1
1
2
2
0
1
2
1
0
0
1
2
1
1
0
1
0
1
2
0
1
2
1
2
1
1
1
1
2
2
1
1
1
2
2
1
0
0
2
0
0
1
2
2
1
1
0
3
0
1
3
1
1
0
1
1
0
0
1
2
1
1
1
1
1
1
2
1
0
0
0
0
1
0
1
0
2
1
1
0
0
1
0
1
0
0
0
1
2
0
0
0
1
1
2
2
2
1
0
1
2
0
0
1
0
0
1
1
2
0
0
1
1
1
2
1
0
0
1
1
0
1
1
1
1
1
2
1
1
0
1
1
1
0
1
1
0
1
0
1
2
1
2
0
1
2
1
2
0
1
1
1
1
1
0
1
2
1
1
1
1
2
1
0
0
1
0
1
2
2
1
1
2
2
0
0
0
2
1
1
1
2
1
0
1
1
0
2
0
0
1
2
1
1
0
1
1
0
2
1
1
0
2
1
2
0
1
0
1
1
1
0
1
1
0
0
1
2
0
1
1
1
1
1
1
1
2
0
1
0
0
1
2
1
1
1
0
1
0
1
1
1
1
1
1
1
0
1
1
1
0
0
2
0
0
1
0
2
1
2
1
0
0
2
1
2
1
1
2
2
1
1
1
4
0
0
0
1
1
0
1
1
1
1
0
2
2
1
2
1
2
1
1
2
0
0
0
2
1
1
1
1
1
1
1
1
1
0
2
1
0
1
2
1
0
1
1
0
1
0
1
1
1
1
0
0
0
1
1
0
0
1
1
1
1
1
0
0
0
0
1
2
0
1
1
2
0
2
1
1
1
1
0
1
1
2
0
1
1
1
0
0
0
0
1
0
2
1
0
2
1
2
2
1
1
1
2
0
1
1
0
2
1
2
3
1
2
2
1
0
1
1
1
1
0
1
1
0
1
1
0
1
1
0
1
1
1
0
1
1
1
0
1
0
0
1
2
2
0
0
0
0
0
0
1
1
0
1
2
0
1
1
2
1
1
0
1
2
1
1
0
2
1
1
2
1
2
2
0
1
2
0
0
1
1
1
1
1
1
1
1
1
0
1
0
1
2
1
1
1
1
1
0
0
1
1
1
1
1
1
2
1
1
1
2
1
2
0
0
2
1
1
2
0
1
2
2
1
0
2
2
1
0
1
1
0
0
0
0
0
1
1
0
0
1
1
1
1
1
4
1
1
0
2
0
1
2
2
0
1
1
1
0
1
1
0
0
2
0
0
0
1
1
1
1
1
1
2
1
1
2
0
0
2
0
1
1
2
2
2
1
0
1
1
1
1
0
0
1
2
1
0
2
2
1
3
1
1
1
0
1
0
1
1
3
1
0
0
1
1
2
1
1
1
1
0
0
1
0
1
2
2
1
1
0
1
1
1
2
2
1
0
2
1
1
2
2
2
0
1
3
1
1
1
1
1
0
1
1
2
1
1
1
1
1
1
0
1
1
1
1
0
2
1
1
1
1
1
0
1
0
2
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
0
4
1
0
2
1
1
1
2
0
0
0
1
0
2
0
0
0
0
0
1
1
1
1
1
1
0
1
1
2
2
2
2
1
2
2
2
0
2
0
1
1
0
2
2
0
2
0
3
1
0
2
0
0
2
1
2
1
3
1
2
1
1
1
1
1
1
1
0
2
1
0
1
0
0
5
2
0
1
2
0
0
2
2
1
0
1
1
1
1
1
3
0
1
2
1
0
1
1
1
1
1
1
2
0
1
1
0
0
2
0
0
1
2
1
1
0
0
2
0
2
2
0
1
0
0
1
1
1
1
1
0
0
1
1
1
1
1
2
2
1
0
0
0
1
1
0
1
2
1
2
0
1
1
1
1
1
1
1
0
1
2
1
1
1
0
1
0
1
1
1
1
0
0
1
1
1
1
2
1
0
2
0
1
0
2
1
0
1
2
2
1
2
0
1
2
1
1
1
0
1
0
0
1
1
1
1
2
2
1
1
1
0
0
5
1
1
1
1
1
0
1
1
0
2
2
2
1
5
2
0
0
1
2
0
1
1
1
2
2
2
0
1
0
1
2
0
2
1
1
2
2
1
0
1
2
1
0
1
1
1
0
1
1
0
2
1
2
2
0
1
0
2
1
1
1
0
1
1
0
2
3
1
1
1
0
0
0
0
1
1
0
1
2
1
0
0
0
1
0
0
2
0
1
0
1
1
1
0
1
2
0
1
2
0
0
1
2
3
2
1
1
1
1
1
3
2
0
2
1
1
0
2
2
0
2
2
0
1
0
1
2
0
1
0
0
1
1
1
1
2
1
1
2
2
0
1
1
1
2
1
0
1
2
1
0
1
1
0
1
1
2
0
1
0
2
1
2
1
1
0
1
1
1
0
1
2
1
2
1
1
2
1
1
2
1
1
1
2
0
1
0
0
1
1
0
0
0
2
2
1
0
0
0
0
1
1
0
0
2
1
1
1
2
0
1
0
1
0
0
2
1
2
3
1
0
0
1
1
0
1
1
2
0
2
1
1
2
1
3
0
0
1
2
0
1
1
1
1
1
1
1
2
1
2
0
1
2
1
1
1
0
0
1
1
2
1
1
2
1
0
1
1
1
1
1
1
1
0
2
2
1
1
0
2
1
1
1
1
1
1
0
1
3
2
1
1
1
0
1
1
1
2
0
2
1
2
1
1
2
1
1
1
1
1
1
1
0
2
2
1
0
1
0
1
3
0
1
0
0
1
2
1
0
2
2
0
1
1
2
1
0
2
1
1
1
1
0
0
1
0
1
2
1
1
1
2
0
0
2
0
1
1
0
1
1
2
1
1
0
1
2
1
2
1
1
0
2
1
1
1
2
1
2
0
1
0
0
0
1
0
1
0
0
2
1
1
1
1
2
1
0
1
1
2
2
1
1
3
0
1
1
0
0
0
1
2
2
1
0
0
0
1
1
1
2
0
1
1
1
2
1
0
0
1
1
2
1
1
1
0
0
2
0
1
2
1
1
0
1
1
1
0
1
0
0
0
0
0
1
1
0
1
2
2
1
2
0
1
0
3
0
0
0
1
1
1
1
1
1
1
1
0
2
0
1
1
2
1
0
0
0
1
2
0
1
0
0
1
1
1
0
2
2
1
0
0
1
1
1
2
0
1
0
0
1
1
0
1
1
1
0
2
2
1
2
1
0
2
1
1
1
0
1
1
1
0
2
1
1
2
1
2
0
0
0
0
2
2
0
1
1
2
1
0
1
2
1
1
2
1
0
2
2
0
2
1
0
1
0
0
1
0
1
0
1
2
1
0
1
1
0
0
1
1
0
2
1
0
0
1
1
1
0
1
2
2
1
0
4
1
1
0
2
1
1
1
0
1
0
0
0
1
1
2
1
2
2
1
2
0
2
1
1
1
2
2
1
1
1
0
1
0
1
0
2
1
2
1
1
2
0
1
3
0
0
1
0
1
0
0
2
1
1
0
1
1
0
1
1
1
1
2
0
1
1
2
0
1
1
1
1
0
1
2
0
2
1
1
1
1
2
1
0
2
7
0
1
1
1
1
1
1
0
1
0
0
1
1
0
2
1
1
1
2
1
1
3
2
1
1
0
0
0
2
1
1
0
1
0
0
0
1
1
0
0
0
1
1
0
2
1
0
1
1
1
3
0
0
1
0
0
1
1
1
2
1
2
1
1
0
1
0
1
0
1
1
2
1
0
0
1
0
1
1
0
2
0
1
0
3
1
2
2
2
0
1
2
1
2
1
1
0
2
2
1
1
2
2
0
1
1
1
0
0
2
1
0
2
0
0
1
2
1
1
0
1
1
1
0
1
2
0
1
1
0
1
0
1
1
1
1
1
1
1
0
2
2
1
1
1
0
2
1
2
1
1
1
2
1
1
1
1
1
1
0
2
1
0
1
0
2
1
0
0
2
4
1
0
1
1
1
0
0
0
2
1
0
0
0
1
1
1
2
2
0
0
2
1
1
1
1
1
0
2
2
2
0
0
0
1
1
1
0
2
2
0
1
2
0
2
2
0
2
1
0
1
1
1
1
1
0
2
1
1
2
2
1
1
1
0
1
1
0
2
1
1
2
1
1
1
1
1
1
2
2
0
1
0
0
0
1
2
1
1
2
2
0
1
0
1
0
2
1
1
1
0
1
0
1
0
1
1
1
2
0
1
1
1
0
1
1
1
0
0
0
1
1
0
1
0
1
0
1
0
1
0
1
1
1
1
0
0
1
2
1
1
2
1
2
0
0
1
2
0
2
0
1
0
0
1
1
0
0
2
1
1
0
2
0
1
1
1
1
0
1
1
1
0
0
1
0
2
1
1
0
0
0
1
1
1
1
1
1
1
1
0
1
4
3
1
0
1
0
0
0
1
1
2
1
2
0
1
1
2
2
1
1
2
2
2
0
1
1
1
1
0
1
1
1
0
1
0
1
2
0
1
1
1
1
2
0
1
1
0
0
2
1
2
0
0
0
1
0
1
0
1
1
1
1
1
1
1
1
1
1
1
1
0
0
2
1
1
0
1
2
1
2
2
1
1
0
1
2
2
1
1
2
2
1
1
1
1
1
1
1
1
2
1
2
1
2
1
1
0
2
2
0
0
1
1
0
2
1
1
1
1
0
1
2
2
0
1
0
1
2
1
2
0
0
2
0
2
1
1
1
0
0
0
2
1
2
0
2
0
2
1
2
0
1
1
0
1
1
0
0
1
2
1
1
0
1
1
0
2
2
2
0
1
0
1
1
0
0
2
0
2
2
2
2
1
1
1
1
1
0
0
2
1
1
0
2
1
0
1
2
0
1
0
2
0
0
0
1
2
0
1
1
1
1
1
1
2
1
2
0
1
1
1
1
1
0
1
1
2
1
2
1
0
1
0
1
2
0
1
2
0
0
0
0
2
1
1
1
1
0
1
1
0
1
2
2
0
1
2
1
1
1
1
1
0
1
1
2
0
0
2
0
2
1
1
2
2
1
0
1
2
1
0
2
1
0
1
0
1
1
1
1
1
1
1
1
0
1
1
1
3
1
2
0
1
1
0
1
0
0
1
3
2
1
1
2
1
2
2
2
0
1
0
0
0
1
1
2
0
1
0
0
1
2
1
0
1
1
2
0
1
2
1
0
1
1
2
0
5
1
1
1
0
2
1
1
0
0
1
1
2
2
1
1
1
1
0
1
1
2
1
1
0
2
0
0
1
1
1
0
1
1
0
1
1
1
1
2
0
1
2
0
1
0
1
1
4
1
1
2
0
2
1
1
2
2
1
2
1
0
0
1
2
1
0
1
1
1
1
1
0
1
2
1
1
1
2
1
1
1
2
0
0
1
1
1
2
0
1
0
0
1
1
1
1
2
1
0
1
1
0
1
0
1
1
1
2
2
2
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
0
2
2
1
1
1
1
1
1
1
1
1
0
2
0
1
0
0
1
0
1
0
1
1
0
0
1
1
1
1
1
1
1
0
1
1
1
1
2
1
1
1
3
0
1
1
1
1
0
2
1
1
1
1
1
0
0
1
0
0
0
2
0
1
1
0
0
0
1
2
0
2
1
2
0
1
1
1
0
1
1
2
1
1
1
1
1
2
1
1
4
0
0
1
2
0
1
2
1
1
1
1
0
0
1
2
0
2
0
1
0
1
0
1
1
2
0
1
0
0
0
0
2
0
2
2
1
2
2
0
2
1
2
0
2
1
1
0
1
0
2
1
2
2
2
1
0
0
1
0
0
0
0
0
1
2
0
1
0
1
0
1
2
1
0
1
0
0
0
1
0
0
1
0
1
0
1
0
1
1
0
2
2
1
1
1
0
1
0
0
1
0
1
2
2
1
1
1
2
1
3
0
2
1
1
1
2
1
3
2
0
0
1
0
1
1
0
0
1
0
2
0
1
2
2
0
2
2
1
1
0
2
1
1
2
1
0
2
1
3
0
1
1
1
1
2
1
1
2
1
1
1
1
0
0
0
1
0
2
1
0
1
0
1
1
1
1
2
1
1
2
0
2
0
0
2
2
1
0
1
0
0
1
0
2
2
0
2
1
1
1
2
0
1
2
1
0
0
1
0
0
1
0
1
0
2
2
0
1
1
1
1
2
0
2
0
2
1
1
0
1
1
1
0
0
1
3
0
1
0
1
0
2
0
1
1
1
2
1
0
2
1
1
0
0
2
2
2
2
1
2
1
1
1
1
0
1
1
0
2
0
0
0
1
1
0
2
1
1
1
0
2
1
1
1
0
2
2
1
1
2
1
1
1
2
0
1
0
3
1
1
2
0
2
1
4
0
1
1
1
1
0
0
2
1
1
0
5
1
5
2
0
0
1
1
2
1
2
0
0
1
1
1
1
0
1
1
1
1
2
1
1
0
1
1
0
0
1
2
0
1
1
1
0
1
0
1
1
1
0
1
1
2
3
1
2
2
0
0
1
1
2
1
1
0
0
1
1
1
1
2
2
1
1
2
0
1
2
1
1
1
0
0
0
0
0
1
1
0
1
1
0
1
0
1
1
0
1
0
0
1
1
1
2
1
1
0
1
1
0
1
1
0
2
1
1
2
0
0
0
1
0
0
1
1
1
1
1
1
1
0
2
1
1
2
1
1
1
0
1
1
2
2
1
1
0
0
0
1
2
1
1
2
2
2
0
1
0
0
1
2
1
0
1
1
1
1
0
0
2
1
1
0
2
0
1
1
1
2
0
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
0
0
1
0
1
2
0
1
1
0
1
1
1
1
2
2
0
2
1
0
0
1
1
1
0
2
0
1
2
4
2
0
0
1
1
2
0
0
1
0
1
0
0
1
1
2
0
1
0
1
0
1
0
1
2
2
2
1
1
0
1
2
1
1
1
1
0
2
0
1
1
1
1
1
1
1
2
0
0
1
0
1
0
0
2
2
0
1
0
1
0
2
1
0
0
0
1
0
0
1
1
0
2
1
1
1
0
0
2
0
2
2
0
1
0
0
1
1
1
0
2
0
1
0
0
0
1
0
2
0
1
1
1
2
0
1
1
1
1
2
1
1
1
1
1
0
2
2
1
1
1
1
2
1
1
0
2
1
1
1
0
0
2
1
1
0
2
2
1
2
0
1
0
0
0
1
1
1
2
1
1
1
0
0
1
1
1
0
1
0
1
1
2
0
1
0
0
1
2
0
3
2
1
1
2
1
1
2
1
1
4
2
1
1
1
1
1
2
1
1
2
1
0
2
1
1
2
0
2
1
1
2
2
1
2
1
1
1
0
1
2
2
1
1
1
1
1
1
1
1
0
0
0
1
1
1
0
2
1
1
1
1
1
1
0
0
2
0
1
3
1
1
1
2
1
0
0
2
1
0
1
1
0
0
2
1
2
0
1
0
2
0
1
2
1
0
2
0
1
2
1
1
1
0
1
0
2
1
0
1
2
0
1
1
1
1
1
2
1
1
1
2
0
1
0
2
1
2
1
1
0
1
1
0
1
0
0
0
1
1
1
1
1
0
0
2
2
1
0
2
1
1
1
1
1
2
1
0
2
2
1
0
1
2
1
0
1
0
1
1
1
0
1
1
0
1
2
2
1
2
2
1
1
1
2
1
1
0
1
1
1
1
1
1
1
2
1
2
0
0
2
2
1
1
1
1
1
2
1
1
1
2
1
1
2
2
0
1
1
1
2
0
2
0
1
1
0
1
2
1
2
1
2
0
2
1
1
1
0
2
1
1
1
1
1
2
2
0
1
2
0
1
1
1
2
0
1
2
1
1
2
0
0
0
1
0
1
0
1
0
1
0
2
0
2
1
3
0
1
2
2
2
1
2
0
1
2
1
1
2
0
1
1
2
0
0
1
0
1
1
1
1
0
1
0
0
1
0
1
1
2
1
1
0
1
0
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
2
1
1
1
1
2
1
2
2
0
0
0
1
0
0
0
2
1
0
0
1
1
0
2
1
2
3
1
0
1
1
1
0
1
1
1
1
1
2
1
1
1
2
1
2
2
1
0
1
1
1
1
2
1
1
2
1
2
1
1
1
1
0
1
1
2
1
2
2
2
2
0
1
1
0
1
0
2
1
0
2
0
1
0
1
1
1
2
1
1
1
2
2
1
0
0
2
2
2
0
1
1
1
0
0
1
0
0
0
2
1
2
0
0
1
1
2
1
2
0
2
1
2
0
0
1
1
0
1
0
1
2
1
2
1
0
1
1
1
2
1
1
1
1
1
0
1
1
1
2
1
0
0
0
1
1
1
1
2
1
1
2
1
2
1
1
2
2
1
1
1
2
0
1
1
1
1
1
1
0
0
1
2
2
1
2
1
0
0
2
1
1
1
2
1
1
1
0
0
0
0
1
1
0
1
1
0
1
1
0
1
0
0
0
2
0
1
2
2
2
0
2
0
1
1
0
1
0
1
0
2
0
1
0
0
2
2
1
2
1
1
2
1
0
1
2
2
0
0
1
2
1
1
2
1
0
0
1
1
0
1
2
0
2
0
1
1
0
0
2
0
0
2
1
1
0
0
3
1
1
1
1
2
1
2
1
1
0
0
0
1
1
0
1
0
1
2
0
1
1
1
1
1
1
0
1
2
0
1
1
2
2
1
1
0
2
0
0
1
0
2
2
1
0
1
2
0
1
2
1
1
0
1
1
2
1
1
1
0
1
2
1
1
0
1
0
1
1
0
1
0
0
0
1
2
1
0
1
2
2
0
1
1
1
1
1
2
1
2
0
1
3
0
0
1
1
2
1
0
0
2
2
1
2
2
2
2
2
3
0
1
1
0
1
0
1
1
0
2
1
2
1
1
1
1
1
1
1
0
1
1
1
1
0
0
1
1
1
0
1
1
0
2
1
1
0
2
1
2
1
1
0
0
1
1
1
1
2
1
2
2
0
1
1
0
1
1
0
2
0
1
2
0
1
1
0
0
1
1
1
1
1
0
1
1
1
1
1
2
1
0
1
2
1
2
0
1
1
1
1
0
0
1
0
1
1
0
0
1
1
1
1
1
1
2
1
1
0
2
1
0
0
1
2
1
0
3
0
1
1
2
2
1
1
2
0
1
0
1
2
1
1
0
1
0
0
1
1
0
0
1
1
0
2
1
0
2
0
0
1
1
1
2
0
2
0
1
1
2
0
1
1
0
0
1
2
1
1
1
1
2
1
1
1
0
1
2
1
1
1
1
1
1
2
1
0
1
1
2
0
1
0
1
1
0
2
1
1
2
2
1
1
0
1
1
2
0
1
1
1
1
1
0
1
0
2
0
0
2
2
0
1
1
1
1
1
0
1
1
2
0
2
1
1
1
2
1
1
2
1
1
0
0
1
1
0
2
2
1
1
2
0
0
0
1
0
2
1
2
1
0
0
0
2
1
1
2
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
1
2
0
1
1
0
1
1
1
0
2
0
0
2
1
1
1
1
1
1
1
0
2
0
0
0
1
2
1
1
1
1
0
2
1
1
2
1
2
0
1
1
1
1
2
1
0
2
2
2
1
1
2
2
2
0
1
0
2
1
1
1
2
2
1
0
1
4
1
1
1
0
2
1
1
2
0
2
1
0
1
1
1
0
0
0
0
1
2
1
2
1
1
1
1
0
0
1
0
0
1
2
1
1
2
1
1
3
0
2
0
0
0
1
2
0
0
1
1
1
0
0
1
1
1
0
1
0
0
0
1
0
0
3
1
1
1
1
1
2
2
1
1
2
0
0
1
0
2
1
0
1
1
0
0
0
2
1
1
0
1
1
2
2
0
1
0
1
0
0
0
1
0
2
1
1
1
0
0
0
0
1
1
1
1
1
0
2
2
1
1
2
2
0
1
2
1
2
0
1
1
1
0
2
0
0
1
2
1
1
0
2
1
0
1
0
1
0
0
2
2
2
1
1
1
0
0
2
1
1
2
1
0
1
2
1
0
0
0
2
1
1
1
1
0
1
0
1
2
1
2
2
1
1
1
1
2
1
1
1
2
1
1
1
2
1
0
1
1
2
2
0
0
2
1
0
1
2
0
1
1
0
2
1
1
0
0
1
0
1
1
1
2
0
1
1
1
1
2
1
1
0
1
0
1
0
1
2
1
3
1
2
0
1
0
2
1
0
1
2
1
1
2
1
2
2
1
2
1
2
2
2
1
1
1
1
2
3
0
0
1
1
0
0
2
0
2
0
0
1
1
0
1
1
1
1
1
1
1
1
1
0
1
0
1
1
0
1
2
2
1
0
1
0
0
0
1
1
1
0
2
1
2
0
2
0
0
0
1
0
2
1
2
1
1
1
0
1
1
1
2
1
1
1
0
1
1
1
1
0
0
2
1
1
1
0
2
0
1
1
1
1
2
2
0
1
1
1
0
2
1
1
1
1
2
1
1
2
1
0
1
2
2
2
0
1
0
2
2
1
1
0
1
1
0
1
1
2
1
2
1
0
1
1
1
2
1
1
2
1
1
1
2
1
1
1
1
2
1
0
0
1
1
2
1
3
1
2
0
0
1
0
0
1
0
2
1
1
1
1
1
0
2
1
1
0
1
0
1
1
2
0
1
1
1
0
1
1
1
1
2
1
2
0
2
3
2
0
2
2
0
0
0
2
1
1
1
2
2
2
2
0
1
2
1
1
1
0
0
1
1
1
0
2
1
1
2
0
1
0
1
0
0
0
1
1
2
1
1
2
1
0
2
0
2
2
0
2
1
1
0
2
0
2
2
0
1
0
2
2
1
2
0
1
2
1
0
2
1
0
2
1
0
1
1
1
0
1
1
2
1
0
0
1
0
2
2
1
0
2
1
2
1
1
2
0
2
1
1
0
1
0
2
1
0
1
0
0
1
1
0
2
0
0
0
2
1
0
1
0
1
1
2
1
1
0
0
1
1
1
1
1
1
0
0
0
1
2
1
0
0
0
1
1
1
1
0
1
1
1
1
1
3
1
1
1
0
2
1
0
2
1
1
0
0
0
0
1
1
0
1
2
1
1
1
0
1
1
0
1
1
1
2
1
0
0
1
2
2
1
1
1
0
2
2
1
1
0
1
1
1
1
1
0
0
1
1
1
0
0
1
0
0
1
2
1
0
0
0
1
2
1
1
2
0
0
0
2
2
0
1
2
2
1
1
1
1
0
1
2
0
2
1
1
1
1
0
0
1
2
1
2
0
2
1
1
0
1
1
2
1
0
0
0
1
1
1
1
2
1
0
0
3
1
1
1
0
0
1
1
0
1
1
1
0
0
0
1
1
1
1
1
1
1
0
1
1
1
2
0
1
1
0
1
2
1
2
0
2
0
1
1
0
1
0
1
1
1
2
1
1
1
2
2
1
1
2
1
1
0
0
0
1
0
3
0
1
2
1
1
0
2
1
1
1
1
0
2
2
1
1
1
0
1
1
1
1
1
1
0
0
2
1
0
1
1
3
1
0
3
0
0
0
0
1
0
1
1
2
0
0
2
1
1
1
1
1
1
0
0
0
1
2
2
0
0
2
0
0
1
0
1
0
2
2
2
2
0
1
1
2
0
2
1
2
1
2
1
0
0
1
2
0
2
1
1
1
0
2
0
2
7
2
0
0
2
1
1
1
1
1
1
1
2
0
2
2
0
0
1
1
1
1
0
2
2
2
1
0
0
2
1
0
1
0
0
1
1
0
2
0
1
0
2
1
0
2
0
0
2
0
1
0
0
1
0
0
1
1
0
2
2
1
2
1
0
1
2
1
1
0
1
1
2
1
1
1
1
0
1
0
0
0
1
0
0
0
2
1
2
1
1
1
1
1
0
1
1
1
1
1
1
0
2
1
1
1
1
1
2
0
1
2
2
2
2
0
1
0
2
1
0
1
1
0
3
0
1
1
1
0
2
0
1
1
1
1
1
2
1
0
1
2
0
0
0
2
1
2
2
2
1
1
0
1
1
0
0
1
6
1
0
0
1
1
2
1
0
2
1
0
0
1
0
0
0
0
2
1
1
2
2
1
1
2
2
2
0
0
0
0
1
1
1
0
1
2
1
2
1
1
1
0
2
1
0
0
1
1
0
0
1
2
0
2
0
0
2
2
0
1
1
0
1
1
1
2
1
1
2
2
0
2
0
0
1
2
0
1
1
2
1
1
1
0
0
0
1
0
2
1
0
0
0
0
2
1
0
2
0
1
0
3
1
1
0
0
1
0
0
0
1
1
1
0
0
2
2
1
2
0
2
1
1
1
0
1
1
0
1
1
0
2
1
1
1
0
2
2
0
2
1
2
1
0
1
1
1
1
2
0
2
0
2
0
1
0
1
2
0
1
1
2
1
1
1
0
2
2
0
1
0
1
0
1
1
1
1
2
1
2
1
2
1
1
1
2
0
3
0
2
1
1
1
0
0
2
3
1
2
2
2
0
0
1
1
1
2
1
2
1
1
0
2
1
2
0
0
1
1
1
0
0
0
2
2
0
1
1
2
2
0
0
2
1
0
1
1
1
1
1
1
0
2
0
0
3
1
1
2
0
0
1
2
1
0
0
0
1
2
2
1
0
1
0
2
0
0
1
1
1
2
0
0
0
0
1
2
1
1
1
1
0
0
1
0
2
1
1
0
1
0
1
0
1
1
2
1
3
1
3
1
1
1
2
1
1
0
2
0
2
0
2
1
0
1
1
1
1
0
0
2
2
0
0
0
1
1
0
2
1
0
1
0
1
1
1
0
0
1
1
1
1
2
0
1
2
1
1
2
1
1
1
2
1
0
0
0
0
0
0
1
1
0
1
1
0
0
1
0
1
1
1
1
1
0
1
1
0
1
1
0
0
2
2
0
2
0
1
1
0
0
1
2
2
0
0
0
0
0
1
1
1
1
1
0
2
0
1
0
1
0
2
0
1
1
0
0
2
1
1
1
1
0
0
2
1
1
2
1
1
0
0
2
0
0
0
0
2
0
1
1
1
0
2
2
1
2
3
1
1
1
0
0
1
0
2
2
0
1
2
1
1
2
0
0
1
0
1
1
1
0
1
0
1
1
1
1
1
1
0
0
0
2
1
1
0
1
1
1
2
1
0
2
1
0
1
1
1
1
1
0
0
0
0
2
1
1
2
1
1
2
1
2
2
1
0
2
1
1
2
1
1
0
2
0
1
1
1
1
1
1
2
1
0
1
1
2
0
1
0
0
0
0
1
0
1
0
1
0
2
1
0
0
1
2
1
1
1
0
1
1
1
0
1
1
1
1
1
1
1
2
2
0
0
0
0
1
1
1
2
1
1
1
0
1
1
0
0
0
0
0
2
1
1
2
1
2
1
1
1
0
2
2
4
0
1
1
0
2
2
0
0
2
1
1
1
0
1
0
2
0
2
1
1
1
2
1
2
1
1
1
1
1
1
2
0
1
2
1
2
2
1
2
1
2
1
1
2
1
0
1
0
1
2
1
1
1
1
1
1
0
0
1
1
0
0
2
1
2
1
1
1
1
2
2
1
1
0
0
1
0
1
0
3
0
2
1
0
1
2
2
2
0
1
1
0
1
0
0
0
1
1
0
2
1
1
1
1
0
2
1
1
1
1
1
1
0
0
1
2
1
1
1
1
0
1
1
1
1
1
1
1
1
2
0
1
1
1
1
0
1
2
1
1
0
1
1
0
0
1
2
1
0
1
0
1
1
1
0
1
0
1
0
1
1
0
0
1
1
1
1
0
1
0
1
2
1
2
1
1
1
1
0
1
1
1
1
2
3
1
1
1
2
1
0
1
0
0
1
0
1
1
1
1
1
0
2
1
1
0
0
1
1
3
0
0
1
0
0
2
0
0
1
0
2
1
1
0
1
2
1
0
2
0
1
0
1
1
1
0
2
0
0
0
1
1
1
1
2
0
1
1
2
2
0
1
1
0
1
1
0
1
2
1
2
2
2
1
0
0
1
1
1
0
2
1
1
1
0
1
2
2
2
2
0
2
0
0
0
0
1
2
1
2
0
2
0
1
0
1
1
0
0
1
1
3
2
0
1
3
1
1
2
2
2
1
0
0
2
2
1
1
1
1
0
2
0
1
1
0
1
2
1
0
2
1
0
1
1
1
2
1
2
0
1
0
0
2
1
0
1
0
1
1
0
0
1
1
0
1
1
0
1
1
1
2
0
1
1
1
1
0
1
1
1
0
0
1
1
0
0
1
2
1
1
2
2
1
2
1
0
1
0
1
1
2
2
1
1
1
1
1
1
1
1
2
2
1
0
1
1
1
0
1
2
1
1
2
1
2
1
1
0
1
1
1
1
1
0
2
2
0
1
1
1
1
0
0
2
2
0
0
1
1
0
0
1
0
1
2
1
2
2
0
1
1
1
3
0
1
1
2
3
0
0
1
0
2
1
2
1
0
1
2
1
1
1
1
0
0
0
0
2
1
2
0
0
1
2
1
1
1
2
1
2
2
1
1
2
0
1
1
1
1
1
0
1
0
1
1
0
2
2
1
0
2
1
0
1
2
2
0
2
0
0
1
2
1
0
1
0
2
0
0
2
1
3
1
1
0
2
0
1
1
1
2
1
2
1
2
1
2
2
0
0
2
1
1
1
1
1
2
2
1
1
1
0
1
1
0
1
1
1
2
0
1
0
1
1
1
3
0
2
1
0
1
0
0
1
1
0
0
2
1
1
0
0
2
2
1
0
1
0
0
2
1
1
1
0
0
1
1
0
2
1
1
2
1
1
2
1
1
2
1
2
1
2
2
0
1
1
1
1
2
0
1
1
2
0
0
2
0
0
1
1
1
2
1
0
2
2
1
1
0
1
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
0
1
1
1
0
1
1
2
2
1
0
0
4
1
1
0
0
1
1
3
1
2
0
0
1
1
0
1
2
0
2
1
1
1
1
0
2
2
2
0
0
2
2
1
1
1
2
2
0
0
2
1
0
1
1
2
0
1
2
1
0
1
2
1
1
2
1
1
0
1
2
0
1
0
0
1
1
2
1
1
1
0
0
1
0
0
0
1
1
0
0
0
2
1
1
2
1
0
0
1
1
1
0
1
1
2
1
1
1
0
2
2
1
0
1
1
1
2
1
1
2
1
0
0
2
1
1
1
0
0
1
1
1
0
1
1
3
0
1
0
0
1
1
3
1
1
2
1
1
1
1
1
0
1
1
0
2
2
2
1
1
1
2
1
1
2
0
1
1
0
2
2
0
2
2
0
0
0
7
1
1
0
2
1
1
0
0
0
0
1
3
1
0
3
1
1
2
0
0
0
1
2
2
2
1
1
0
4
0
0
2
1
2
0
1
1
0
2
1
1
1
2
1
0
1
2
2
1
0
1
2
1
0
1
1
0
0
1
1
1
1
1
1
1
2
0
0
1
0
1
1
0
1
1
1
1
1
0
1
0
1
1
2
2
1
1
1
1
2
0
1
1
3
0
1
1
0
1
0
0
1
2
0
2
0
1
2
3
1
1
0
2
2
1
2
0
0
0
2
1
0
2
1
1
1
1
0
2
1
1
0
2
2
2
1
1
1
1
0
1
1
0
2
1
0
1
2
1
1
1
1
2
2
2
1
0
3
1
0
2
5
1
1
1
1
1
0
1
1
1
1
0
0
1
0
1
1
1
3
0
0
2
2
2
2
2
2
0
4
1
2
2
2
0
0
1
1
0
2
1
2
2
2
1
1
1
2
0
0
1
1
2
1
1
1
0
1
1
2
0
2
0
0
1
1
2
0
2
0
1
1
1
0
2
1
1
1
2
1
2
1
1
1
1
1
1
0
0
1
1
1
2
0
0
0
0
0
0
1
0
0
0
1
3
1
0
0
1
0
0
1
1
0
1
0
1
1
0
0
0
2
0
2
1
1
0
2
2
0
1
1
2
1
1
0
0
1
2
0
1
1
1
1
0
2
0
2
2
1
2
1
1
1
1
1
2
1
1
1
0
1
0
1
1
1
1
0
1
0
2
1
2
1
1
0
1
0
0
1
0
0
1
2
0
2
1
0
1
0
2
1
2
1
2
0
0
2
1
1
1
0
0
0
1
1
0
1
1
0
2
1
1
1
0
1
2
1
1
1
1
0
0
1
2
2
1
1
2
0
0
0
0
1
2
0
0
1
2
0
0
0
0
0
1
0
1
1
1
0
2
1
1
1
1
0
2
0
0
1
2
1
1
3
2
0
2
1
0
1
0
1
2
2
1
1
0
2
0
1
1
0
1
0
2
1
1
2
1
2
2
2
0
1
1
1
1
0
2
2
2
0
1
1
1
0
1
1
0
1
1
0
2
2
3
0
1
0
2
1
0
2
3
1
2
2
0
0
2
0
1
0
1
2
1
1
2
1
1
1
0
0
1
0
1
2
1
2
1
1
1
1
2
0
1
0
0
0
0
1
2
2
1
1
2
2
1
2
2
1
0
1
1
1
2
0
2
2
1
2
0
2
1
0
1
1
2
1
2
1
0
1
1
0
2
2
0
1
2
0
1
1
0
0
2
0
2
2
2
0
0
1
2
1
1
1
0
0
0
1
2
1
0
0
2
1
1
1
1
0
0
0
1
1
0
1
1
2
0
2
1
0
2
0
0
0
1
0
0
1
4
2
1
5
0
0
0
2
2
2
1
0
2
3
0
0
2
1
0
1
1
1
0
2
1
1
1
2
1
0
2
1
1
0
2
0
2
0
1
2
1
0
0
2
0
1
1
2
1
0
0
1
0
1
1
1
1
2
3
1
1
1
0
2
1
2
1
2
1
2
2
0
0
1
0
0
2
1
0
1
2
1
1
0
1
0
2
0
1
0
2
1
2
1
0
0
1
1
1
0
1
1
1
1
0
0
0
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
0
0
2
2
0
2
1
0
0
1
0
1
0
1
1
0
2
2
0
1
1
1
1
1
2
1
1
2
0
0
0
1
1
2
2
0
1
1
0
0
1
0
1
0
1
0
0
1
1
1
2
1
1
0
2
3
0
1
2
2
1
2
1
0
1
0
1
1
1
1
2
1
2
1
1
1
2
0
3
1
0
2
0
1
0
1
1
0
1
2
1
4
1
0
1
0
1
1
1
0
1
1
1
1
1
1
0
0
2
2
2
1
1
1
0
0
1
0
0
1
1
1
1
1
1
0
2
2
3
0
2
1
2
2
1
2
1
0
1
1
2
1
2
1
1
1
0
2
2
2
1
2
1
1
1
1
1
2
1
0
1
1
1
0
0
2
0
0
2
2
0
1
1
1
2
0
1
3
2
2
1
0
0
1
1
1
2
0
1
0
0
1
1
0
3
2
1
0
2
2
2
1
2
1
2
0
2
1
2
0
2
1
0
2
1
1
3
1
1
0
1
1
1
1
1
1
1
1
2
1
1
2
2
0
1
2
0
2
1
2
1
0
0
2
2
0
2
0
1
1
0
0
2
0
0
1
0
0
2
1
0
1
0
1
1
0
2
0
0
0
0
2
0
0
0
0
1
2
2
2
1
1
1
1
2
0
1
1
2
1
0
2
1
1
1
1
1
0
0
2
0
1
1
0
1
2
1
1
1
2
1
1
1
0
2
1
1
1
0
1
2
2
1
2
2
0
1
0
1
1
2
1
2
0
1
0
1
1
1
2
1
0
1
1
0
2
2
2
1
1
1
2
2
1
0
2
2
1
1
0
1
0
1
0
1
0
1
9
0
2
1
0
0
1
0
1
2
1
1
0
1
1
0
1
0
0
1
1
0
1
1
1
1
1
2
1
1
0
2
2
1
2
1
1
1
1
2
2
0
2
1
0
0
1
1
1
1
2
1
0
2
2
1
1
1
1
1
0
1
1
2
2
2
1
0
1
2
2
3
0
0
2
1
0
0
0
0
1
1
1
2
2
1
0
1
1
1
1
1
2
0
2
1
1
1
1
0
1
1
1
3
1
1
2
1
2
0
1
1
1
0
1
1
0
2
1
1
1
1
1
1
1
1
2
2
0
1
2
1
2
0
0
2
2
0
0
1
0
1
2
1
2
0
2
1
0
1
1
2
0
1
0
2
1
0
1
0
0
0
0
2
0
1
1
1
1
0
0
2
0
2
0
1
1
2
0
0
0
1
2
2
1
0
1
1
1
2
1
0
2
2
1
2
1
1
1
1
1
1
2
1
0
1
2
1
2
0
1
0
2
0
2
1
1
2
1
2
1
2
2
1
1
2
1
1
1
1
1
0
3
0
2
0
1
1
0
0
0
1
1
1
0
2
0
2
0
1
1
2
0
1
1
0
2
1
2
2
2
1
1
1
1
1
0
1
2
1
2
1
0
0
0
2
0
1
1
1
2
1
1
0
1
1
1
2
1
0
2
1
0
1
0
2
1
1
1
2
1
2
1
0
2
0
1
1
0
0
1
0
0
1
2
2
0
0
0
0
0
1
2
1
1
0
0
0
0
0
0
2
1
1
1
0
2
0
1
0
6
1
2
1
1
0
2
0
1
1
1
0
2
2
0
1
0
3
2
0
1
1
1
1
1
1
1
1
1
0
2
0
0
1
1
1
1
2
1
0
0
0
1
2
1
1
1
2
0
1
1
0
0
1
0
1
1
1
1
1
0
0
1
1
2
0
0
2
0
1
0
1
0
1
0
1
0
1
2
0
1
0
1
0
1
1
1
2
2
1
1
0
0
0
1
1
1
0
2
2
1
0
1
1
1
0
0
2
1
0
2
1
1
1
2
1
1
1
0
2
2
1
1
0
0
2
2
0
3
1
0
1
1
2
1
0
0
1
1
2
0
2
1
2
1
0
1
2
1
0
1
0
2
0
0
2
2
0
1
2
2
1
1
0
1
2
1
1
0
0
0
1
0
1
1
2
1
1
1
2
1
1
1
3
1
2
1
0
0
1
0
0
0
1
0
1
0
0
2
1
1
1
0
1
1
1
1
1
0
0
1
1
2
2
0
1
1
1
2
1
2
1
1
0
1
1
2
3
1
0
1
2
1
2
0
1
1
0
2
1
1
2
1
1
1
2
1
2
1
2
0
2
0
0
1
2
1
0
2
1
0
2
0
0
1
0
2
1
0
0
1
1
0
2
1
0
2
1
1
2
1
1
1
1
0
2
1
2
1
1
1
0
0
1
0
1
1
1
0
0
0
0
2
1
2
2
1
1
1
1
0
2
1
0
1
1
2
2
0
2
0
0
1
1
2
0
0
2
1
0
1
2
1
2
1
1
1
1
1
0
1
1
1
2
1
3
0
0
1
2
1
1
0
0
2
0
1
1
1
1
1
0
1
1
1
0
1
0
1
1
0
2
1
0
0
1
0
1
0
1
0
2
1
0
1
0
1
1
1
1
0
1
1
1
1
1
1
1
2
1
2
2
2
2
2
1
1
1
1
1
2
1
0
2
1
1
1
0
1
0
3
1
2
2
2
1
0
1
0
2
1
0
3
0
1
0
1
1
0
1
1
0
0
2
1
2
1
0
1
1
1
1
1
0
1
2
2
1
0
2
1
2
1
0
0
2
1
1
1
0
1
2
1
1
0
0
2
1
1
2
1
0
2
2
1
1
0
1
1
1
2
1
0
2
1
1
0
2
1
1
0
2
0
1
0
0
1
2
1
1
1
1
0
0
0
1
2
0
2
1
1
2
2
2
2
0
0
1
0
0
2
2
1
1
2
0
1
1
2
1
2
1
0
1
1
2
0
0
2
2
1
1
2
1
1
1
1
2
0
0
0
0
2
1
0
2
0
1
0
0
2
2
0
1
2
0
1
1
0
2
1
0
2
1
1
2
0
0
0
1
1
1
1
1
1
1
1
0
0
1
0
0
0
1
0
0
1
0
1
0
1
2
1
1
0
1
0
0
2
1
1
1
1
0
1
2
1
1
1
2
1
2
1
0
1
1
2
0
2
0
0
1
0
1
1
0
1
1
2
1
0
1
0
0
1
0
1
0
0
2
1
2
1
1
1
1
1
1
1
1
1
2
2
0
1
1
1
2
0
0
0
1
1
0
1
0
1
2
1
2
1
1
0
1
1
1
0
1
2
1
1
2
1
0
0
1
1
2
0
2
0
1
0
1
1
0
0
1
1
2
2
1
0
0
1
1
0
2
0
1
2
2
1
2
3
1
1
1
1
1
1
0
1
1
0
1
2
1
2
1
0
2
2
1
0
1
1
0
1
2
2
1
2
0
1
0
2
2
1
1
1
2
1
2
0
1
0
1
1
0
3
0
2
1
1
2
1
0
1
1
1
1
0
2
1
1
0
0
3
1
2
0
3
1
2
0
1
0
1
1
2
1
2
1
1
2
0
1
0
0
0
0
0
0
1
2
1
2
1
1
2
2
0
0
1
1
1
2
1
2
2
2
2
0
1
1
1
0
2
1
1
1
1
2
1
1
2
1
1
2
1
1
1
0
0
0
0
2
1
1
2
1
1
1
1
0
0
0
1
1
1
1
1
1
1
1
0
0
1
1
2
0
0
1
1
2
2
1
1
2
0
2
1
1
2
2
0
1
1
2
1
2
0
2
1
0
0
0
0
0
1
1
1
1
0
0
1
2
0
1
1
1
1
1
0
1
0
1
1
0
0
2
0
0
1
2
1
1
0
2
3
1
1
2
1
2
0
1
2
3
0
2
1
1
1
0
0
0
1
0
2
0
1
1
1
0
1
1
2
1
0
0
0
0
1
2
1
1
2
0
0
1
1
1
2
1
2
2
0
1
2
2
0
0
1
0
2
1
1
1
1
2
2
2
2
2
0
2
2
0
3
2
2
1
1
2
0
2
0
1
0
1
0
1
1
1
1
2
2
1
1
0
1
1
1
2
0
0
0
0
1
1
1
1
1
1
1
1
1
2
2
1
0
2
1
0
2
1
1
2
0
1
0
0
1
0
2
0
2
1
1
0
2
2
0
0
1
1
0
2
2
2
2
2
1
0
1
2
1
0
1
0
1
0
1
1
0
0
1
1
1
1
1
0
2
1
1
2
0
2
1
1
2
2
1
0
1
0
1
2
1
0
2
0
0
2
1
0
1
0
0
1
0
1
1
0
2
1
1
1
0
1
2
1
2
1
0
2
1
1
1
2
1
2
1
2
2
0
1
1
1
0
0
2
3
2
1
1
2
0
0
0
1
1
1
2
0
1
0
0
0
2
0
0
2
1
1
1
0
1
1
1
2
0
1
0
1
1
0
1
0
1
2
2
1
2
1
0
2
2
0
1
1
1
1
0
2
1
5
1
1
0
1
2
0
1
2
2
1
0
3
0
2
0
0
1
1
1
0
0
0
1
0
1
2
2
0
0
3
1
1
0
0
1
1
1
1
2
1
1
2
0
1
2
0
1
2
1
1
1
0
1
2
1
1
2
1
1
0
1
2
1
2
1
2
2
2
1
1
0
0
1
0
2
1
1
2
2
2
0
2
1
2
1
0
0
1
1
2
1
1
0
1
0
0
1
2
1
0
0
1
1
1
0
2
0
1
1
3
1
2
1
0
1
2
2
1
0
1
1
1
1
1
1
2
0
2
2
1
0
2
0
1
1
1
1
2
2
2
0
1
1
1
0
1
0
0
1
2
0
1
2
0
1
0
1
0
1
2
0
1
1
1
2
1
1
2
0
1
1
0
2
1
0
1
1
1
1
1
1
1
1
1
1
0
0
0
1
3
1
1
1
1
1
1
0
0
0
0
1
0
1
0
2
1
1
0
1
1
1
0
0
0
1
2
0
2
0
1
2
1
0
2
2
1
1
1
1
0
1
0
0
1
1
0
1
1
1
1
1
1
0
1
1
1
3
1
1
2
1
1
0
1
1
1
0
1
0
2
2
2
1
1
2
1
1
0
1
1
1
1
1
1
1
1
2
1
1
2
2
1
2
0
1
1
1
0
1
1
1
1
1
1
0
2
0
1
0
2
2
1
0
1
2
0
1
1
1
0
1
0
1
2
2
0
1
0
1
0
0
2
1
0
2
1
2
0
1
3
1
0
0
1
2
0
1
0
1
1
0
1
1
1
0
1
1
1
0
0
1
0
0
1
1
1
1
0
1
0
0
2
2
2
1
0
2
1
2
2
1
1
2
2
0
0
0
1
1
1
0
0
0
0
0
2
0
1
0
1
0
1
0
0
1
1
2
1
2
1
1
1
0
2
0
0
2
1
0
0
0
1
2
1
2
1
1
0
0
1
0
1
0
1
0
2
0
1
1
2
1
1
1
1
0
1
1
0
1
1
2
0
1
1
2
1
1
0
1
1
2
1
1
2
0
1
1
2
2
0
2
1
0
1
1
2
1
1
1
1
1
1
2
1
0
1
2
1
1
2
1
1
1
1
0
2
1
1
0
1
1
2
2
1
2
2
1
1
1
0
2
2
1
0
1
2
0
1
1
1
0
0
1
1
1
1
1
1
0
0
0
1
1
1
0
1
2
1
1
0
1
1
1
0
0
1
1
0
0
2
0
1
0
0
1
1
1
2
1
1
0
2
2
1
1
0
1
1
1
2
0
2
0
2
0
0
1
1
1
1
1
1
1
0
1
0
1
0
1
1
0
2
1
1
2
1
1
0
1
1
1
2
0
1
2
2
1
0
0
1
2
1
1
2
2
0
1
2
2
2
1
1
0
2
1
2
0
2
0
2
1
0
1
2
1
0
1
2
1
1
0
0
2
2
1
0
1
0
0
1
1
1
1
0
0
1
2
2
1
0
1
0
1
1
1
1
1
0
1
0
2
1
1
2
0
1
1
1
1
1
0
0
2
5
1
1
0
0
0
1
2
1
0
1
2
1
2
1
1
0
1
1
1
1
1
0
1
1
2
0
0
0
1
0
1
1
3
2
0
1
0
1
2
1
0
1
1
1
0
2
1
1
1
1
1
2
1
1
1
0
1
1
2
0
2
0
1
1
0
2
0
0
0
1
0
1
1
0
2
1
0
1
0
0
2
2
0
0
2
1
2
2
1
0
0
1
1
1
0
2
1
2
0
1
1
1
0
0
0
1
1
1
2
1
0
1
1
2
1
1
1
1
1
2
0
1
1
2
1
2
2
2
1
0
0
0
0
0
1
1
1
2
0
1
0
1
0
0
1
1
0
1
1
1
2
1
1
2
1
2
1
0
1
2
0
1
2
1
0
2
0
2
2
1
2
0
0
1
1
1
1
2
0
1
0
1
0
1
1
2
1
0
0
0
2
1
1
0
1
1
1
0
0
0
1
1
2
1
1
0
1
1
3
2
2
1
2
0
0
1
1
0
0
1
1
1
1
1
1
0
1
1
0
2
1
2
2
1
1
1
1
1
0
2
1
1
1
1
2
1
1
0
2
2
1
1
2
2
5
1
2
1
1
0
1
1
2
2
2
0
1
0
1
1
0
1
1
1
1
0
1
0
0
1
1
1
0
1
1
1
1
1
1
1
5
1
2
1
0
1
2
1
2
2
0
1
1
1
2
2
0
0
0
1
1
0
1
1
1
0
2
2
2
1
0
1
1
0
0
2
0
0
1
2
0
1
1
0
1
1
1
1
1
1
1
0
2
1
0
1
1
0
1
2
1
0
2
4
1
0
2
1
0
2
1
1
2
1
0
0
0
1
2
0
0
1
1
1
0
1
0
2
1
1
1
0
1
0
1
2
1
3
0
0
1
0
0
0
0
0
1
1
1
0
1
2
1
0
2
1
1
0
0
0
1
1
2
1
1
3
0
1
1
0
1
1
2
2
1
1
1
2
0
0
1
1
0
0
2
1
1
2
1
4
2
1
3
1
1
2
2
1
1
1
1
0
0
1
1
2
1
0
2
1
0
0
0
1
1
1
1
1
1
1
1
1
2
1
1
3
2
0
1
1
2
3
1
1
0
1
1
0
0
0
2
1
0
0
2
1
0
0
1
1
2
1
1
4
1
1
2
1
0
1
0
1
2
1
1
1
0
0
2
1
1
1
2
1
0
1
2
1
3
1
1
0
0
0
1
3
2
1
1
0
0
1
1
1
1
0
0
2
1
1
2
1
2
0
1
1
1
1
2
1
1
1
0
1
0
0
1
0
0
2
0
2
0
1
1
2
2
1
0
2
1
0
1
2
2
2
1
1
1
2
2
1
0
0
1
1
1
2
2
0
1
1
1
0
0
0
1
3
1
1
0
2
2
1
1
1
2
1
2
0
0
0
0
0
1
1
0
2
1
0
1
2
0
2
1
1
1
2
2
1
1
1
1
1
0
2
1
0
0
0
1
0
2
1
1
0
1
0
0
0
1
0
1
0
0
1
1
1
1
0
1
1
0
2
1
1
1
2
2
2
1
1
0
1
1
1
1
0
1
1
2
0
1
1
1
2
1
1
1
1
1
1
1
0
2
2
1
0
1
1
2
0
0
1
2
2
1
1
1
2
1
2
0
0
0
1
2
0
1
2
1
0
0
2
0
1
2
0
2
0
2
0
0
0
2
4
0
1
1
1
2
1
1
0
1
2
2
1
2
2
1
1
1
0
2
1
1
0
1
0
1
1
1
1
2
1
1
2
2
1
1
3
1
0
1
0
0
2
1
2
0
2
1
0
2
0
1
0
0
2
1
2
2
1
3
1
2
1
1
2
2
1
1
0
1
0
0
1
1
1
2
1
0
1
0
1
0
1
2
1
0
1
2
0
1
2
1
0
1
1
1
0
1
1
1
0
0
1
1
1
1
0
1
1
2
1
0
9
1
1
1
1
1
0
1
1
1
1
1
1
0
1
0
1
2
0
0
0
1
1
1
1
1
1
2
1
1
1
1
1
0
1
0
0
0
1
1
1
2
1
1
1
0
0
0
4
2
1
2
0
1
1
0
1
1
2
0
1
2
2
0
3
1
2
0
2
1
2
1
1
1
2
1
0
0
1
2
0
2
2
0
0
1
1
1
1
2
0
0
2
1
2
0
2
1
1
1
1
1
1
0
0
1
0
1
1
1
1
2
2
2
1
1
1
0
1
1
0
1
1
1
0
2
2
1
2
1
1
1
0
2
2
1
2
2
1
0
1
0
2
2
1
1
1
0
2
1
1
1
0
1
1
1
1
2
2
0
1
1
1
1
1
1
2
2
1
0
0
1
2
0
1
1
0
1
1
1
1
1
1
1
1
0
1
1
1
4
1
0
3
0
1
1
2
0
1
1
1
1
1
0
2
0
1
2
0
2
2
1
1
2
2
2
1
0
2
0
0
0
1
0
0
0
1
2
0
1
0
1
2
0
1
0
0
1
2
1
1
1
1
1
2
0
2
2
1
0
1
1
2
2
1
0
0
0
1
1
0
1
1
2
0
0
0
1
0
1
1
3
0
1
1
2
2
1
1
0
1
1
0
2
0
1
1
1
1
1
2
1
0
0
2
1
2
1
2
1
0
2
0
0
1
1
2
0
2
0
1
0
2
2
1
2
1
1
2
1
1
1
1
1
2
2
0
2
0
1
2
0
1
2
2
1
1
1
1
1
1
3
2
1
0
0
1
1
0
1
3
0
0
2
2
1
1
1
1
1
1
2
0
0
0
3
0
0
1
0
1
1
2
0
1
2
2
2
1
1
0
1
2
0
1
0
1
1
0
0
1
1
1
0
0
0
2
1
1
1
0
0
1
1
1
1
0
0
2
3
1
2
1
1
0
1
1
1
2
1
1
1
0
1
1
1
2
0
0
2
2
0
1
2
2
1
1
2
1
2
1
2
1
1
1
1
0
1
1
0
1
1
3
1
2
1
1
0
0
1
2
2
0
1
1
1
0
1
2
1
1
2
3
3
1
0
1
0
2
1
2
1
1
1
1
1
2
1
1
1
2
0
1
2
1
0
2
1
1
2
1
0
1
1
0
1
1
1
2
2
0
0
2
1
2
1
0
0
1
2
0
2
1
1
1
2
1
2
0
1
1
2
1
0
0
0
0
3
1
1
2
1
0
0
2
2
0
1
2
1
0
0
2
0
1
0
1
2
0
0
1
1
0
0
1
1
1
0
0
0
1
0
1
0
1
1
2
1
1
1
0
2
1
1
0
0
1
1
0
1
0
1
0
1
1
1
1
0
1
0
3
1
1
1
2
1
1
0
2
0
1
1
2
2
1
1
0
1
0
1
3
2
1
2
0
0
1
1
2
1
2
1
0
0
0
1
0
1
0
1
1
1
0
0
2
0
1
2
1
2
0
1
0
0
1
0
1
1
2
1
0
1
2
1
1
1
1
0
1
2
1
1
1
1
0
1
1
1
2
1
1
1
1
2
1
0
0
0
2
0
0
1
1
0
1
2
1
1
1
2
1
0
0
1
1
1
1
2
1
0
2
1
2
1
2
0
0
1
2
1
1
0
2
1
0
1
1
1
1
0
2
2
0
3
1
1
1
1
0
1
1
2
1
2
1
2
1
3
1
2
0
0
1
1
1
0
2
1
1
0
1
1
1
0
2
1
2
2
1
2
2
1
1
1
1
2
0
0
1
1
0
1
1
2
1
0
0
1
0
1
0
1
0
0
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
1
0
0
1
1
1
0
0
1
4
0
1
0
1
0
1
1
2
0
0
0
1
1
0
1
0
1
1
1
0
1
1
2
2
1
1
1
0
0
0
1
1
1
2
1
1
1
0
0
2
1
2
1
1
1
1
1
1
2
1
1
2
0
1
1
0
1
0
1
1
0
2
1
0
0
1
1
2
1
0
0
1
2
1
2
1
1
1
1
2
1
1
1
0
1
2
1
1
1
2
1
0
0
0
2
0
1
0
2
2
1
1
2
1
2
1
1
1
0
0
0
1
1
2
0
9
1
2
0
0
1
1
0
2
0
1
1
2
1
1
0
2
0
1
2
0
1
1
1
1
2
0
0
0
1
2
1
2
1
0
0
1
1
1
1
0
1
1
1
0
2
2
1
1
2
1
4
0
0
3
0
2
2
1
0
1
0
1
0
2
4
1
0
1
1
2
1
0
2
1
1
0
0
1
1
1
0
2
0
1
1
1
2
1
0
0
0
1
2
1
0
1
1
1
1
1
1
1
1
1
1
1
0
1
2
1
0
2
0
1
1
0
2
1
0
2
0
1
0
2
0
1
1
0
0
2
1
1
0
1
0
1
5
0
1
1
1
1
2
1
0
0
0
2
1
1
1
1
1
1
0
1
1
2
0
2
2
1
1
2
1
1
1
2
0
0
0
1
0
0
2
2
1
0
1
1
0
2
1
1
1
0
1
2
1
1
0
2
2
1
1
1
2
0
1
0
2
1
2
1
4
0
1
1
1
1
0
2
0
1
0
1
0
2
0
1
1
1
2
0
1
0
0
1
1
0
0
0
1
2
1
2
1
0
1
0
0
0
2
1
2
0
0
2
0
2
2
1
0
1
0
1
1
4
1
0
2
2
1
0
1
1
1
0
1
1
1
0
0
0
1
2
1
1
0
1
1
0
1
2
1
1
1
2
0
1
1
1
0
0
2
1
1
2
1
2
1
2
0
1
2
0
0
1
2
1
1
1
1
1
1
3
0
1
1
1
0
2
1
1
0
2
0
1
1
2
2
1
2
1
1
0
1
2
1
0
1
3
2
0
1
0
1
1
2
1
1
0
1
1
0
1
0
1
1
1
1
0
2
0
1
0
0
1
2
0
1
1
1
1
1
1
0
1
0
0
0
0
2
1
1
2
0
1
1
2
1
1
1
0
2
1
1
1
1
1
0
0
2
3
1
0
1
2
1
2
1
0
2
2
2
1
1
2
0
1
1
5
0
2
2
1
0
1
0
4
0
0
0
1
0
1
1
0
0
1
1
0
2
0
1
1
0
1
0
1
1
1
2
1
1
0
0
2
2
1
1
1
1
1
1
0
1
1
1
2
0
1
2
1
1
1
1
0
1
0
0
2
2
0
0
2
2
1
1
1
0
2
0
1
1
1
1
2
0
0
2
0
1
2
1
2
1
2
2
1
2
1
1
1
2
1
1
0
1
1
2
0
0
1
1
2
2
2
0
1
1
1
1
1
2
1
0
1
0
1
3
1
1
1
0
0
1
2
0
1
0
0
1
0
1
0
2
0
2
1
1
1
2
1
0
2
2
0
1
0
1
2
0
1
0
1
2
2
1
0
1
1
0
2
1
1
0
2
0
1
2
1
1
1
0
1
1
1
0
1
0
1
0
0
2
2
0
1
1
1
0
1
1
1
1
0
1
2
1
1
1
2
1
1
2
2
1
0
0
1
0
1
1
0
1
1
1
0
0
0
1
0
0
0
2
2
0
1
0
0
1
1
1
0
2
1
1
1
1
2
1
1
1
1
1
1
2
2
2
1
2
1
2
0
2
1
2
1
0
0
2
1
2
0
2
1
1
0
1
1
2
2
0
1
1
1
2
1
1
1
0
1
1
0
1
1
1
1
1
1
1
1
0
1
1
0
0
1
2
1
2
1
2
1
1
1
1
0
0
1
0
1
1
1
1
0
4
3
1
1
1
0
0
1
1
1
2
1
0
1
2
0
1
1
2
0
1
0
1
0
0
1
0
0
1
1
0
1
1
1
1
1
2
1
1
0
0
1
0
2
2
0
3
1
0
2
1
1
1
0
1
1
2
1
0
1
1
0
1
1
1
2
0
2
2
1
0
1
1
0
0
1
1
1
1
0
1
2
2
1
1
1
1
0
0
1
1
0
0
0
5
1
1
2
0
1
2
2
0
1
1
2
0
1
0
1
1
1
0
2
0
2
1
0
2
1
0
1
1
1
2
0
0
2
1
1
1
2
1
1
1
0
1
1
0
1
1
1
0
1
2
0
2
1
1
3
1
0
1
2
0
0
1
2
2
1
0
1
0
2
1
1
1
1
1
0
2
0
2
0
0
0
1
0
1
0
1
1
2
1
0
0
0
1
1
1
0
2
1
0
1
1
1
1
0
2
2
0
1
0
2
2
1
1
0
2
1
0
0
1
1
0
0
1
0
1
2
1
3
0
0
2
0
0
1
1
2
1
2
2
1
0
0
0
1
2
2
0
2
1
0
0
1
2
0
0
1
1
1
1
2
2
1
1
0
1
1
1
2
1
1
1
2
1
2
0
1
0
1
0
0
1
1
0
1
1
0
0
1
0
0
1
0
0
1
1
1
2
1
0
1
1
2
2
2
2
1
1
0
0
0
0
2
0
0
1
1
1
1
1
1
1
0
0
1
1
1
1
1
1
1
1
2
1
3
0
3
1
1
0
2
0
0
2
1
2
2
2
0
1
1
0
1
0
1
2
2
1
3
1
1
1
1
2
1
1
1
0
0
1
0
1
1
1
0
0
0
1
1
1
1
0
1
1
2
1
2
1
0
2
0
2
1
1
1
1
1
1
1
1
1
0
1
1
1
1
0
2
1
0
1
1
1
1
0
1
1
1
0
1
0
0
2
2
2
2
3
0
0
1
1
1
0
2
1
1
0
1
1
1
2
1
1
1
1
0
1
0
0
0
1
1
1
0
2
2
1
2
0
0
3
0
2
1
2
2
2
1
2
0
0
0
2
1
1
0
0
2
1
1
0
0
1
1
0
3
1
1
1
0
0
1
1
0
2
1
1
1
0
0
0
3
2
2
1
0
1
1
1
1
2
0
1
2
2
0
0
1
2
1
0
1
2
1
2
1
1
2
0
1
0
2
1
1
1
1
2
1
1
1
2
1
2
0
1
0
1
2
0
0
2
1
2
2
1
1
1
1
1
0
0
1
0
0
2
1
1
0
2
1
0
0
2
0
1
2
0
0
1
1
1
1
2
1
1
1
1
0
0
1
2
1
1
2
2
0
2
1
1
1
4
2
1
1
0
1
1
1
1
1
0
1
1
1
1
2
2
1
0
2
2
0
1
0
1
1
2
0
0
1
3
0
2
1
2
1
2
1
1
1
1
2
1
1
2
2
0
0
0
1
1
1
1
0
0
2
1
0
0
1
1
0
1
1
0
2
2
1
2
1
1
1
2
0
0
1
1
1
0
0
0
1
1
0
0
1
2
1
1
2
1
2
1
1
0
1
1
1
0
1
2
0
1
1
1
2
1
0
1
0
1
0
0
1
2
1
1
2
1
0
2
1
2
1
1
1
1
0
0
0
2
0
0
1
1
1
1
2
1
0
1
0
1
0
1
0
1
1
0
2
2
0
1
2
1
1
1
0
1
1
1
1
1
0
1
0
1
1
2
0
1
2
2
2
1
1
3
1
0
1
2
0
0
0
1
1
1
1
0
1
2
2
2
1
1
1
1
0
0
2
1
0
1
1
3
0
1
1
1
1
1
5
0
2
1
1
1
0
1
1
1
1
1
1
2
2
1
2
2
0
0
0
1
2
0
1
1
1
1
1
0
0
0
0
0
1
0
1
2
2
2
2
1
2
0
0
1
2
0
1
0
1
2
1
1
0
1
2
1
0
1
2
0
2
1
1
0
0
1
0
2
1
1
0
0
1
1
0
1
1
2
0
1
2
2
1
2
0
1
1
2
1
1
1
0
0
1
0
1
0
2
1
1
1
0
1
2
1
2
1
0
2
1
2
1
0
0
1
1
1
2
2
2
1
1
1
2
1
1
0
1
0
1
1
2
2
0
1
2
0
1
1
1
2
1
1
0
3
1
1
0
1
0
0
1
0
0
2
0
1
0
0
0
1
1
2
0
1
0
2
2
1
1
1
2
2
0
2
0
2
1
0
0
1
1
1
0
0
1
2
2
0
1
1
0
1
2
0
1
1
1
2
2
0
1
2
0
1
0
1
0
2
1
0
0
0
0
1
0
2
1
0
1
1
1
1
0
0
1
0
0
1
0
0
1
1
1
1
1
2
2
2
1
0
0
3
1
1
1
0
2
2
1
2
0
1
2
1
1
1
0
0
2
1
0
1
1
0
1
2
2
0
1
0
2
0
2
1
0
2
0
2
1
2
2
1
2
1
1
1
1
1
1
1
2
1
1
0
2
0
0
2
0
1
2
0
0
2
0
1
2
1
1
1
2
1
2
1
0
1
1
2
0
0
0
2
2
2
2
2
1
0
2
0
0
0
0
1
1
1
0
2
1
1
1
1
2
0
1
2
0
2
3
0
2
2
1
0
1
1
1
1
1
1
2
1
0
1
0
0
1
0
1
1
0
0
2
2
0
1
0
1
2
2
0
1
1
1
2
1
2
0
0
1
1
0
2
0
1
1
1
1
0
0
1
1
1
1
2
0
1
1
1
2
1
2
1
1
1
2
1
1
1
2
1
1
1
0
1
1
1
1
0
1
1
1
1
0
1
0
1
2
1
0
0
1
0
1
1
0
1
2
1
1
1
2
0
0
0
0
0
0
0
0
1
1
1
2
2
0
2
1
0
0
1
2
2
1
0
0
1
2
0
2
0
1
1
0
1
2
2
2
0
0
0
1
1
2
1
0
1
1
1
2
0
1
1
2
0
2
1
1
1
1
0
1
1
0
1
2
1
1
1
1
1
1
1
2
0
1
1
1
2
0
2
1
0
1
1
1
0
2
1
0
2
0
2
1
1
2
1
0
0
2
0
2
1
0
0
1
1
0
0
1
1
0
1
1
0
0
0
2
1
0
0
1
3
1
1
1
2
3
1
1
2
2
2
1
0
0
0
1
1
1
0
3
2
1
0
1
0
2
2
1
1
2
1
2
0
0
0
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
0
1
1
1
1
0
0
2
2
2
0
0
0
1
0
0
2
0
2
0
1
0
0
0
2
1
0
2
1
1
1
0
2
1
3
0
1
1
0
2
0
2
0
1
2
1
0
2
1
2
1
1
1
0
3
0
2
1
0
0
1
0
0
1
1
1
0
1
2
1
1
1
0
1
1
0
1
1
0
1
1
1
1
1
2
0
1
2
1
2
0
1
1
2
2
2
2
2
0
1
1
1
0
1
1
1
1
0
1
2
1
2
1
0
0
1
1
2
0
2
1
0
1
1
2
2
0
1
2
1
0
1
1
1
2
0
0
1
1
2
1
1
1
0
1
0
1
0
0
2
0
0
1
1
1
2
2
1
1
2
2
1
0
1
2
0
0
0
3
1
1
1
2
2
2
2
2
1
2
2
1
0
2
1
1
2
0
1
0
0
1
2
1
0
0
2
1
0
1
1
0
1
1
1
1
2
1
1
1
0
0
0
1
1
1
1
1
1
0
0
0
0
1
1
1
1
0
0
1
1
0
0
1
1
0
0
2
1
2
1
1
1
1
1
1
1
1
0
1
1
0
1
2
1
2
1
2
1
0
2
1
1
0
1
0
2
0
1
2
1
1
1
1
1
0
0
2
1
0
2
2
0
1
0
1
1
2
0
0
2
2
1
1
0
0
1
1
1
0
1
1
1
1
1
1
1
1
1
0
1
1
1
0
2
1
2
1
1
1
1
0
1
1
1
2
0
0
1
1
0
0
2
1
2
1
1
2
1
2
1
0
2
1
0
0
2
0
1
1
1
4
2
0
0
1
1
2
0
1
1
0
2
1
1
2
1
0
1
0
0
0
1
2
0
2
0
0
1
1
0
2
1
1
1
1
0
0
2
0
1
1
1
1
2
1
1
0
0
0
3
0
1
0
1
2
2
2
1
1
2
1
1
2
0
2
0
1
1
0
1
0
2
4
1
2
1
1
2
1
2
1
1
1
2
0
1
0
1
1
1
0
0
2
1
2
0
1
0
2
0
0
0
2
0
1
1
1
2
2
1
1
1
1
2
0
1
2
1
0
1
0
0
0
2
1
1
0
1
1
2
0
2
1
1
0
1
1
2
2
1
0
1
1
1
0
1
1
2
0
1
1
0
1
0
2
1
1
2
0
2
1
1
2
2
3
2
0
1
2
0
2
1
0
0
0
6
2
2
1
1
5
1
2
0
0
1
1
1
0
1
2
0
1
1
1
2
1
2
0
1
1
1
1
2
1
1
1
1
0
1
1
0
0
1
1
1
1
2
1
2
2
2
1
0
1
1
2
0
2
0
0
0
0
0
0
0
1
0
1
1
2
1
1
0
1
0
2
0
2
1
1
1
1
0
2
1
1
0
0
2
2
2
1
1
1
1
1
3
0
1
2
0
1
1
1
1
2
1
2
1
2
2
1
2
3
1
1
1
1
1
1
0
1
3
1
0
2
1
1
2
0
1
1
1
1
1
1
1
0
2
1
0
2
1
2
0
1
0
2
0
1
0
2
0
2
1
1
0
2
0
0
1
1
1
1
2
2
2
0
1
2
1
0
1
0
1
2
2
1
2
1
0
1
1
2
1
0
1
0
1
2
1
0
1
1
0
1
1
0
1
0
1
1
1
1
0
1
2
1
1
0
1
1
1
1
1
2
1
1
1
0
1
0
1
0
1
0
2
1
1
2
1
1
2
0
1
1
2
2
1
0
0
1
1
1
1
1
0
0
1
1
0
2
0
2
0
1
1
0
2
2
0
2
2
2
2
1
1
0
1
0
2
1
0
1
0
0
0
1
0
1
0
1
0
0
2
0
2
0
1
0
0
6
2
1
0
1
0
0
0
1
1
1
1
1
1
2
1
2
0
0
0
1
1
1
1
1
1
1
1
0
1
1
2
2
0
1
0
0
2
1
1
1
1
0
0
0
2
2
1
1
1
2
1
2
2
1
0
2
1
1
1
2
1
1
1
1
2
0
1
2
1
0
2
1
1
0
4
2
1
0
0
2
1
2
0
1
1
1
1
0
1
1
2
1
2
2
1
2
0
2
2
2
0
0
1
1
0
2
1
1
1
1
1
1
2
1
1
1
0
0
0
2
2
1
1
0
0
2
1
1
1
0
0
0
1
1
0
0
1
2
1
1
2
1
0
1
3
0
0
2
1
0
1
1
1
2
1
1
0
0
1
2
2
2
0
0
1
1
1
0
1
0
2
3
1
1
1
0
1
3
2
1
1
1
0
1
1
2
1
0
1
2
1
0
1
1
0
1
0
0
1
1
1
1
0
0
2
1
1
1
1
1
0
2
0
2
0
0
0
2
1
2
2
0
1
1
1
1
2
1
0
2
0
2
2
0
0
1
0
0
0
1
2
1
0
1
1
0
0
1
1
2
1
1
3
0
2
1
2
0
1
1
1
0
1
1
2
2
2
1
1
1
1
0
0
0
1
2
1
1
2
2
1
2
2
0
1
1
0
2
0
3
0
0
0
2
1
1
1
1
1
1
1
1
0
0
0
0
2
3
1
2
0
2
0
1
0
0
1
2
0
1
0
1
2
0
0
0
1
0
0
1
0
0
1
2
1
2
1
0
1
1
0
2
2
0
2
3
1
2
1
0
0
1
1
1
0
1
0
2
1
0
0
0
1
0
1
1
1
0
1
0
0
0
0
1
1
1
0
1
0
2
0
1
2
1
2
1
1
2
1
2
1
1
1
0
2
0
0
2
1
0
2
1
0
0
1
2
1
2
1
1
1
0
1
1
1
2
1
1
1
2
0
3
1
2
1
1
2
0
0
0
2
2
0
2
1
1
1
1
1
0
2
0
1
0
1
1
1
1
1
1
0
2
1
1
1
0
0
1
1
1
0
1
1
1
2
2
2
1
2
1
0
2
1
1
1
2
0
0
0
2
2
2
1
1
2
2
1
1
1
2
0
2
2
1
0
1
0
0
1
1
0
2
1
0
1
1
1
0
1
2
0
2
1
2
1
0
1
0
1
2
1
1
1
2
1
1
0
0
1
0
0
1
1
2
1
1
1
0
1
1
1
1
1
0
1
1
2
1
0
2
1
1
0
0
0
0
2
0
2
2
1
0
1
2
1
2
1
1
0
1
1
2
2
1
1
1
1
1
2
1
2
1
1
1
2
2
1
0
1
0
1
0
1
1
0
0
0
1
0
0
1
0
1
1
0
2
1
0
0
1
2
2
1
1
2
1
2
0
2
2
0
1
1
0
1
2
0
2
2
1
0
0
1
0
1
1
1
1
1
2
2
0
1
1
0
2
1
2
0
0
0
2
2
1
1
2
1
1
2
2
1
1
2
1
2
2
0
1
0
1
1
0
0
1
1
3
2
1
2
2
1
1
1
0
0
0
0
1
2
2
1
0
1
2
2
2
2
0
2
1
1
1
1
0
1
2
0
0
0
2
1
1
0
1
2
1
1
1
0
0
0
1
0
1
0
1
4
0
1
1
1
0
1
1
1
3
1
1
1
1
0
1
1
1
0
1
0
1
1
1
2
1
0
1
1
1
1
1
1
0
1
1
1
2
1
1
1
1
0
1
1
1
2
1
0
1
3
1
1
1
0
2
1
2
1
1
1
1
1
1
1
1
0
1
2
1
0
2
0
1
0
0
1
2
2
2
2
1
0
1
1
1
2
0
1
1
1
0
2
1
1
2
0
2
2
1
2
0
1
1
0
0
0
0
0
0
0
0
2
1
0
1
0
2
1
1
1
1
2
1
1
1
0
1
1
1
0
1
1
0
2
2
0
2
0
0
1
1
0
0
1
0
1
1
0
2
1
2
2
1
1
2
0
1
1
1
0
2
1
0
0
0
2
2
1
1
0
1
1
1
1
0
0
1
0
0
1
1
1
0
0
2
1
1
0
2
1
1
0
1
0
3
1
1
1
0
1
2
2
1
0
0
1
1
0
1
1
1
1
1
0
2
1
1
1
0
1
1
0
1
0
1
1
3
0
2
2
2
0
2
1
1
0
2
1
1
1
1
1
2
1
2
0
0
1
0
5
0
1
1
2
1
0
0
2
1
1
1
1
2
2
0
2
1
0
1
0
2
1
1
2
2
1
1
1
0
0
2
1
1
2
2
1
1
0
1
1
2
1
1
0
2
2
0
0
1
1
1
0
1
2
1
2
1
1
0
2
2
2
2
3
0
0
0
3
1
1
1
0
0
2
0
1
2
1
1
2
1
0
1
1
0
1
1
0
1
2
2
1
0
2
2
1
0
2
1
2
1
1
2
1
1
3
0
0
2
0
0
1
0
1
1
1
0
1
1
2
2
1
0
1
0
4
1
1
2
0
2
2
0
0
0
1
2
2
1
1
0
1
2
0
1
2
0
2
2
3
1
0
1
0
1
0
1
0
0
1
1
0
1
0
1
2
1
0
0
1
0
1
7
1
0
1
2
1
2
1
1
2
1
2
1
0
1
1
0
1
2
1
1
1
0
1
1
1
2
1
1
2
2
1
2
1
2
0
1
0
1
2
1
1
2
1
2
1
1
2
1
0
0
1
2
0
0
0
2
2
2
2
2
4
0
0
0
1
0
1
1
2
2
1
1
1
1
1
1
1
0
0
0
1
0
1
2
2
2
1
0
0
1
1
0
2
2
0
1
0
0
1
1
1
2
1
2
2
1
1
1
0
1
2
0
0
2
0
0
1
1
0
2
2
1
0
1
2
1
2
1
2
0
2
1
0
2
1
0
0
2
0
2
1
1
0
2
0
1
0
0
2
1
1
0
0
1
0
1
1
1
0
1
1
0
1
2
2
1
0
1
1
2
1
1
2
2
1
0
1
1
1
0
1
1
0
2
1
1
1
1
0
0
0
2
1
1
1
2
1
0
0
2
0
1
0
0
0
1
0
1
2
1
2
0
2
1
1
0
2
2
1
2
0
0
1
1
0
0
2
6
0
0
0
1
1
1
0
1
2
1
0
1
0
0
2
1
2
1
1
0
2
0
0
0
0
1
0
1
2
0
2
1
1
1
2
1
1
0
0
0
1
0
0
1
0
1
1
0
1
1
2
1
2
1
1
2
0
1
1
1
2
1
0
2
1
2
0
0
1
1
1
0
2
1
1
0
2
2
0
1
1
1
0
2
0
2
1
1
1
2
2
1
1
0
2
0
0
1
0
1
1
1
1
0
1
2
0
1
1
0
0
1
2
1
1
2
2
0
1
0
1
0
2
0
0
0
2
1
1
0
1
1
1
0
1
0
2
0
2
0
1
0
1
2
1
0
0
0
2
2
0
2
1
1
0
1
1
1
1
1
2
2
1
2
2
2
1
1
2
1
1
1
1
2
1
2
0
0
1
2
1
2
1
0
2
2
1
1
0
1
0
0
0
1
1
1
1
0
1
1
2
1
2
1
2
2
2
1
1
1
1
1
2
2
0
0
1
1
0
0
1
1
1
0
1
1
1
2
2
0
2
1
1
1
1
1
0
1
0
1
1
1
1
0
2
1
0
1
1
1
1
0
1
1
0
0
1
1
1
1
0
2
1
1
1
1
1
1
1
0
2
0
1
1
1
1
0
1
0
2
1
1
2
1
1
0
0
1
0
1
0
2
2
2
1
2
0
0
1
1
1
1
0
1
1
0
1
1
1
1
0
1
0
1
2
1
2
0
2
1
1
1
1
1
1
1
0
0
1
1
2
0
2
1
0
1
1
1
0
0
1
0
2
1
1
0
0
1
0
1
1
1
3
2
2
1
1
0
1
1
1
0
1
1
0
1
0
0
1
0
0
1
1
1
0
0
1
1
2
0
0
1
1
1
2
1
2
2
1
0
0
1
0
0
3
2
2
1
2
2
1
1
0
0
4
0
2
2
1
1
2
0
0
2
0
0
1
2
1
0
2
2
1
1
1
2
0
0
1
1
0
1
2
1
1
1
1
1
1
1
0
1
0
1
2
2
1
2
1
1
1
1
2
1
1
0
1
1
1
1
0
0
1
1
0
1
1
1
1
1
2
1
1
2
2
2
3
1
1
0
1
1
1
1
0
2
1
2
0
2
1
1
1
1
1
0
1
1
1
2
0
1
0
1
1
0
0
1
1
0
1
1
1
1
1
2
1
1
1
0
0
1
1
1
0
1
0
1
0
1
0
1
2
1
1
1
1
0
1
1
0
1
1
2
1
1
2
2
1
1
1
1
1
0
1
1
0
1
1
2
2
1
1
1
1
1
2
1
1
0
1
1
1
1
1
0
1
1
1
2
1
2
1
2
1
1
0
1
1
0
1
0
0
0
1
2
2
1
1
0
1
1
0
1
1
0
2
1
0
0
0
2
2
0
0
0
1
0
3
0
1
1
1
2
2
1
0
1
1
0
2
1
2
1
2
1
2
1
1
0
1
0
2
0
1
1
1
2
2
2
2
1
1
0
2
1
2
0
1
0
2
1
1
0
2
1
0
1
1
2
1
0
2
1
1
2
1
1
2
1
0
1
1
0
1
1
1
0
0
2
1
1
1
2
1
0
0
1
2
2
1
10
2
1
1
1
1
0
1
1
1
2
1
0
0
1
0
2
1
1
1
1
1
1
0
1
0
0
1
0
1
0
1
1
1
0
0
1
0
1
0
2
1
1
0
0
2
1
2
1
1
1
1
1
0
1
2
0
1
1
0
2
2
0
2
1
1
0
1
1
2
0
1
1
1
0
0
0
1
1
2
1
0
1
2
1
0
0
0
1
1
0
1
0
0
0
0
1
0
1
2
2
0
0
0
2
2
1
1
0
1
1
1
1
3
2
1
1
0
2
0
0
0
0
0
0
2
0
1
2
1
3
0
2
1
0
0
1
0
2
2
2
2
1
0
0
2
2
0
0
1
0
0
1
1
2
0
2
1
2
1
2
2
1
0
0
0
2
1
1
2
1
0
2
1
2
1
0
2
0
1
1
0
2
0
1
1
1
1
1
2
0
0
1
0
0
2
1
1
1
2
1
0
1
0
0
1
1
0
1
1
1
1
1
0
1
2
0
2
1
2
1
1
2
3
0
1
1
0
0
1
1
0
2
1
2
1
1
0
1
1
2
0
1
1
0
0
0
2
1
1
2
0
0
1
2
1
2
2
1
1
0
1
2
1
0
1
2
1
0
2
2
2
2
0
0
1
0
2
0
1
0
2
0
1
1
0
1
1
1
1
2
1
1
0
2
2
2
1
0
0
2
0
1
0
2
1
2
1
0
2
2
1
1
2
0
2
1
1
1
2
0
0
1
0
2
1
1
0
2
1
0
1
2
1
1
1
1
1
1
2
2
1
0
1
1
1
0
0
2
1
1
1
0
2
0
0
2
1
2
1
1
1
2
1
0
2
0
1
0
1
1
0
0
0
0
2
1
2
0
2
2
2
2
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
0
1
0
0
1
2
0
0
1
1
0
1
0
0
1
1
1
0
1
1
1
2
1
1
1
1
2
0
0
2
1
1
0
0
0
0
0
1
1
1
1
1
2
1
0
1
1
1
0
1
1
0
0
2
1
1
1
1
2
0
1
1
1
1
2
1
1
0
1
0
1
1
1
1
2
0
1
0
1
2
0
1
0
1
1
0
0
1
0
0
1
0
2
1
1
1
0
1
1
2
1
1
1
1
1
0
1
0
0
1
1
0
1
2
1
1
0
2
2
1
0
0
1
1
0
1
1
0
1
1
1
0
1
1
0
0
1
1
1
0
0
1
4
1
2
1
1
1
1
1
0
1
2
1
1
0
1
0
0
2
1
2
1
1
0
0
1
1
1
4
0
1
0
1
1
0
2
0
2
1
1
1
2
1
1
1
0
1
2
2
2
2
1
1
0
1
1
1
2
1
2
1
1
0
0
0
1
1
0
2
1
0
1
2
2
0
1
0
1
1
1
3
2
1
1
1
2
1
1
1
1
0
1
0
2
2
1
0
0
1
1
0
1
2
2
0
1
1
0
1
2
1
0
0
1
0
2
2
1
1
2
1
2
1
0
1
0
1
1
1
0
0
0
0
1
1
0
2
2
1
2
2
0
2
1
2
1
2
1
1
1
0
2
2
2
1
1
1
0
1
2
1
2
1
1
2
0
1
1
1
1
0
0
1
2
2
2
1
1
1
1
0
1
0
1
1
1
1
0
2
0
1
0
0
1
2
0
1
0
3
0
0
1
1
0
0
1
2
2
0
0
2
0
0
2
3
1
1
1
1
2
2
1
0
1
0
0
2
0
0
2
0
1
1
1
1
1
0
0
1
1
1
0
0
1
1
0
1
1
1
2
1
1
2
1
5
0
1
1
0
1
1
1
2
1
1
1
1
0
1
0
0
0
0
0
1
2
2
0
2
2
1
1
2
2
0
1
1
1
0
0
2
1
0
1
1
2
1
2
2
1
0
0
0
1
1
1
0
1
0
1
1
0
1
2
0
2
0
1
1
1
1
2
2
1
0
1
0
1
1
1
2
1
0
1
0
1
0
2
1
1
0
1
2
2
1
1
1
0
1
0
0
3
2
1
2
0
0
1
1
1
0
1
1
1
0
1
3
1
2
2
2
1
0
0
1
0
0
2
1
0
0
1
1
0
1
1
1
2
2
1
4
1
0
1
2
0
0
0
3
0
1
2
2
1
1
3
2
1
2
1
1
2
0
0
1
1
1
1
2
2
0
2
1
2
1
2
1
1
1
0
1
1
1
0
1
2
2
0
1
1
1
2
2
2
0
1
2
1
1
0
2
1
0
1
1
1
0
1
0
1
1
1
0
0
2
0
0
1
1
2
2
2
1
1
1
1
0
1
2
2
2
2
2
1
1
1
2
1
0
0
1
1
1
1
1
1
0
2
0
0
1
1
1
0
2
2
0
0
2
1
0
1
0
1
2
1
1
0
0
0
1
1
1
1
1
2
0
1
0
1
0
1
1
0
0
1
2
2
0
1
0
3
1
1
1
0
1
1
1
1
1
1
2
0
2
1
1
1
0
1
0
0
0
0
1
0
2
1
1
0
1
2
2
1
1
1
0
1
1
1
1
2
2
0
0
0
1
0
1
2
0
0
0
2
1
1
0
1
1
1
0
1
1
1
2
1
2
0
0
1
0
1
1
0
1
0
1
0
1
2
1
1
1
1
2
1
1
0
1
2
1
0
1
0
1
2
1
1
0
1
1
1
1
1
0
0
1
2
2
2
1
1
1
2
2
1
0
0
1
0
2
0
1
2
1
0
0
0
1
1
0
0
1
0
2
1
1
0
1
1
1
1
1
0
2
0
2
0
0
0
2
1
1
2
1
1
1
1
1
1
1
1
2
2
1
1
0
1
1
1
2
0
0
1
2
2
1
1
1
2
1
1
2
2
1
2
0
0
2
2
2
3
0
1
2
2
0
2
1
1
3
2
1
0
2
2
2
1
1
1
1
0
1
1
0
2
2
6
1
0
1
1
2
2
2
1
0
1
0
1
2
2
1
1
1
0
2
1
1
2
1
0
1
1
1
0
2
2
1
0
1
1
1
0
1
1
0
2
2
1
1
1
1
1
2
2
0
2
1
1
1
1
1
0
1
2
1
0
0
2
0
0
1
1
2
0
0
1
1
1
1
0
1
1
0
2
0
2
1
1
1
1
1
1
2
0
0
1
1
1
1
1
0
1
1
0
1
1
0
0
0
0
1
0
2
1
1
1
1
1
2
0
1
1
2
0
2
0
0
1
2
2
0
1
1
2
2
1
0
0
2
1
1
0
2
1
1
1
0
2
0
1
5
1
0
0
2
0
2
0
1
2
2
1
1
4
0
0
0
0
2
2
2
2
1
2
1
0
1
1
2
2
0
0
1
0
1
0
1
0
1
1
1
1
0
0
1
0
1
0
0
1
1
0
1
1
1
2
1
0
1
1
0
1
2
1
1
1
1
0
2
2
2
0
2
1
1
1
2
2
2
1
1
1
0
4
1
1
0
2
1
1
1
0
0
0
0
2
1
1
1
1
1
1
1
2
2
2
1
0
1
1
1
1
1
1
1
0
1
1
1
1
2
0
1
2
0
1
1
2
1
1
2
1
2
1
1
3
1
0
1
1
0
2
1
0
2
0
0
1
2
2
1
1
1
1
1
0
2
2
0
1
0
1
2
0
0
1
2
1
1
1
0
2
1
1
1
0
0
0
0
1
0
1
1
1
0
0
2
0
0
1
1
2
0
2
2
0
0
2
1
1
1
0
0
1
1
1
2
2
2
2
1
0
0
2
1
1
1
0
1
2
0
1
1
0
1
1
1
1
2
0
1
2
0
1
0
1
1
2
1
0
2
1
3
1
0
2
0
1
2
0
0
2
1
0
0
0
1
1
2
1
1
1
1
0
1
1
1
1
1
1
0
1
0
1
2
1
1
1
1
1
1
1
0
1
1
2
4
1
1
1
2
2
1
2
0
0
2
0
1
2
2
0
1
0
1
0
1
1
1
1
3
0
1
1
1
1
0
1
1
1
0
1
0
1
2
1
2
1
0
0
1
0
2
1
0
0
0
0
0
1
0
1
0
0
2
0
0
1
0
1
0
1
1
2
1
0
0
2
0
1
1
1
1
2
0
1
1
1
2
1
2
1
1
0
1
2
2
0
2
0
1
1
2
2
1
2
0
1
0
0
1
2
0
2
1
1
1
1
2
1
1
1
1
1
1
2
0
1
1
1
1
1
1
0
0
1
1
1
0
2
1
2
0
0
0
1
1
1
1
1
1
2
3
2
0
0
1
1
1
2
0
1
0
2
3
1
2
1
0
1
0
0
1
0
2
0
2
1
2
2
1
2
2
1
1
1
1
0
1
1
1
1
1
0
0
1
2
3
1
0
1
1
1
1
0
0
0
1
1
0
1
1
0
0
1
2
1
2
1
1
0
1
2
2
0
2
1
2
2
0
1
1
0
1
2
0
2
0
0
1
3
1
0
1
2
2
1
0
1
0
2
0
1
2
0
1
0
1
3
0
0
2
0
2
0
2
1
2
1
2
0
0
2
1
1
1
2
1
0
1
2
0
1
1
2
2
0
1
0
1
0
0
1
1
1
1
0
1
1
0
2
0
1
0
1
2
1
1
1
0
2
1
1
2
2
0
1
1
0
1
1
1
1
0
2
0
1
0
2
2
1
0
1
0
3
2
1
2
0
1
0
1
1
2
0
0
1
1
0
1
3
2
1
1
0
0
2
1
1
1
0
1
2
2
1
2
2
0
0
1
0
0
1
2
0
0
1
1
1
0
1
1
0
1
1
1
2
1
2
3
0
0
1
0
2
1
0
1
1
0
1
1
2
1
1
0
1
0
1
1
2
0
1
1
0
1
2
1
2
1
1
0
1
2
1
1
1
1
1
2
0
0
1
0
1
0
1
2
2
1
0
0
1
2
2
0
0
0
1
0
1
0
1
2
1
1
1
2
1
1
1
0
2
1
0
1
2
0
2
1
1
2
1
0
1
2
0
1
0
0
1
1
1
1
0
1
2
1
0
2
1
0
2
2
1
0
1
2
1
0
1
2
1
2
0
1
1
2
2
2
1
0
1
1
0
1
1
2
1
0
0
2
1
0
0
0
0
1
0
1
1
0
1
0
1
1
0
0
2
1
0
1
2
1
1
1
2
1
0
1
1
0
2
1
0
0
1
0
0
1
2
0
0
1
1
1
1
0
2
0
2
2
1
1
0
0
0
1
1
1
2
0
0
0
0
3
1
2
1
2
1
1
2
0
1
1
0
1
1
2
1
0
0
1
2
1
2
1
1
0
1
0
0
1
2
1
2
1
0
2
1
1
1
3
1
1
1
2
1
0
0
0
0
0
0
2
2
1
2
0
2
3
1
0
2
1
0
0
1
2
1
0
1
1
2
2
1
1
1
0
2
0
3
0
1
2
1
1
0
2
0
1
0
0
1
1
1
1
0
2
1
1
0
1
1
1
0
1
1
1
1
2
0
0
1
1
1
2
1
1
4
0
1
1
1
1
0
1
0
1
0
1
1
0
2
0
2
2
1
0
0
1
0
1
2
2
0
1
1
0
0
2
1
1
1
1
2
0
1
2
1
1
1
2
2
0
1
1
0
0
0
1
1
0
1
1
0
1
1
0
1
1
1
1
0
2
1
0
0
1
2
3
2
1
0
2
1
1
0
0
0
1
1
4
1
1
1
1
3
2
0
1
2
0
3
1
2
0
2
2
0
2
1
1
0
1
0
0
1
0
0
1
1
0
2
2
1
1
1
1
3
1
1
0
1
1
1
0
0
1
1
0
0
1
1
1
2
0
0
0
2
2
0
0
2
1
1
0
3
1
0
0
1
2
0
1
2
1
2
2
1
1
0
0
1
4
0
2
1
2
2
1
0
1
1
2
1
1
0
1
0
0
2
0
2
1
1
1
0
1
2
2
0
0
1
1
1
1
1
1
1
1
0
0
1
1
1
1
0
1
0
0
0
0
1
0
1
1
1
0
0
2
1
1
2
0
1
1
2
1
0
2
1
2
1
2
0
1
1
1
2
0
1
1
0
0
1
0
0
1
1
1
0
2
2
0
1
1
1
1
1
1
1
1
1
0
1
0
1
1
1
1
2
1
1
2
1
2
1
1
1
1
0
1
0
1
1
1
3
0
0
1
0
1
2
2
1
1
0
1
1
0
2
1
0
2
2
1
0
1
1
1
2
0
1
1
1
1
1
2
0
0
0
2
2
2
3
1
2
2
1
1
0
1
0
1
0
1
1
2
1
0
2
1
2
3
1
1
1
1
0
1
2
1
0
1
1
0
2
1
1
2
1
2
0
0
0
1
1
0
1
0
1
1
2
3
1
1
0
1
1
1
1
0
0
2
0
1
0
2
1
0
1
1
2
1
2
0
2
1
4
0
1
2
0
1
1
1
0
1
2
1
0
1
0
0
1
2
0
2
1
0
0
0
1
2
0
1
2
1
0
2
2
1
2
0
2
1
0
2
2
2
0
0
0
1
1
0
2
2
0
2
4
2
1
1
1
2
1
0
2
2
1
1
2
0
2
1
1
0
2
0
1
1
0
0
1
2
1
1
2
0
0
1
1
1
1
1
2
1
0
2
2
3
2
1
0
1
0
2
2
1
0
0
1
2
1
0
0
1
1
1
2
1
0
1
0
1
1
2
0
2
1
1
0
1
1
1
1
0
1
0
0
1
2
0
2
0
2
2
1
0
3
2
1
0
1
0
1
0
1
2
0
2
1
1
2
1
1
1
0
0
1
1
1
0
3
1
0
0
1
0
1
1
1
2
2
1
1
1
0
3
1
1
1
2
2
0
0
1
0
3
2
1
0
2
0
0
1
0
1
2
1
0
2
1
1
1
2
1
1
0
0
1
1
1
0
1
2
1
2
1
1
2
2
0
2
0
2
1
1
1
2
0
0
3
1
1
3
1
0
0
1
1
1
1
0
1
0
1
1
2
1
1
1
2
2
2
2
0
1
2
3
1
1
1
0
0
1
1
2
2
1
1
1
1
1
0
0
1
2
0
1
1
1
1
0
1
2
1
1
1
1
1
2
1
1
1
0
1
0
1
0
2
1
0
1
0
1
0
1
1
1
1
0
0
1
1
1
0
1
1
1
1
1
1
2
0
0
0
2
1
1
1
0
1
1
2
1
1
1
2
0
1
1
1
0
2
0
1
1
0
2
0
1
0
1
1
1
2
1
1
1
1
2
1
0
0
2
2
1
0
1
1
1
2
0
1
0
1
2
2
1
0
0
0
1
1
2
1
1
1
2
2
1
0
2
2
1
1
0
1
1
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
1
2
0
1
1
1
2
1
1
1
1
2
1
0
1
0
1
1
1
1
1
1
1
1
2
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
2
2
1
2
1
0
1
0
1
0
0
1
0
1
2
1
2
2
1
3
1
0
1
0
2
2
0
2
1
1
2
2
1
2
0
1
2
0
0
1
0
2
1
1
1
2
1
0
0
0
1
1
1
0
1
0
1
0
1
1
1
1
0
2
1
1
1
0
0
0
0
0
1
1
1
1
1
2
1
0
1
0
1
1
1
2
0
1
1
2
0
1
1
1
0
0
1
1
0
0
1
1
1
1
1
1
0
1
2
1
0
2
0
2
1
1
0
2
2
1
0
0
0
0
1
1
0
1
1
0
2
1
1
0
2
1
1
1
1
1
1
0
0
2
0
2
1
1
0
1
0
1
1
2
2
2
1
1
0
1
0
1
1
2
1
1
0
1
0
0
0
3
2
1
1
1
2
1
1
1
2
1
0
1
0
1
2
2
1
2
0
1
0
1
2
1
2
0
1
2
2
1
1
2
1
1
2
1
0
1
1
1
1
1
1
2
0
2
1
1
0
1
1
1
1
2
0
1
1
1
1
2
2
1
1
2
0
1
1
1
1
1
1
0
0
1
0
1
0
1
2
2
1
1
2
2
1
2
0
1
2
1
2
1
0
2
1
1
0
1
2
0
2
0
0
3
1
1
1
1
0
1
1
2
1
1
0
0
0
0
1
2
2
0
1
0
1
0
0
1
1
0
1
0
1
0
1
1
0
0
1
1
1
1
1
2
1
1
2
2
2
1
1
0
1
0
1
0
0
1
2
2
2
1
0
1
1
0
1
1
0
1
1
1
1
2
0
1
1
0
3
1
2
0
2
1
1
2
1
1
0
1
1
1
2
2
2
0
0
2
1
1
1
2
0
0
1
2
1
0
1
1
1
2
2
1
2
1
0
1
0
1
1
0
0
0
2
0
0
0
1
1
0
2
1
0
1
0
1
0
0
2
1
1
1
1
1
2
1
0
2
1
1
2
2
2
1
1
2
2
0
0
1
1
2
1
1
1
1
0
2
0
2
0
0
1
1
0
2
1
0
0
1
2
0
0
0
2
1
1
1
1
1
0
0
2
2
0
1
0
2
2
0
2
1
2
1
0
0
1
1
2
0
0
1
2
0
0
0
0
2
1
1
2
0
1
1
2
0
0
0
1
0
0
1
0
1
2
1
1
0
0
0
2
1
1
0
2
1
1
1
1
2
1
0
2
1
2
0
0
1
2
1
0
2
0
2
1
1
2
0
1
0
1
2
2
1
2
2
0
2
1
1
0
1
1
0
1
1
2
1
0
2
0
0
1
0
1
2
0
1
0
2
1
1
2
2
1
1
1
0
1
1
0
0
0
2
0
1
0
3
0
1
0
0
1
1
2
1
1
1
2
1
1
1
0
0
0
0
1
1
0
2
1
2
1
1
1
0
0
1
0
0
1
0
1
0
1
1
1
0
1
1
2
1
0
0
0
1
1
2
1
1
2
0
1
1
2
0
2
2
1
3
1
1
2
0
0
1
0
2
3
1
0
2
1
1
2
0
3
0
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
0
1
1
0
1
1
1
0
1
1
1
0
1
0
1
0
1
1
0
1
2
1
2
0
0
2
2
3
0
2
0
0
1
0
1
1
1
1
1
2
3
1
1
2
1
2
1
2
2
0
1
1
2
1
0
0
1
0
3
0
1
1
1
1
0
2
0
1
1
1
1
0
2
0
1
0
0
1
1
1
1
0
1
1
1
2
2
3
1
0
1
1
1
1
0
1
2
1
1
1
0
2
2
1
0
1
0
0
0
1
1
1
2
1
1
2
1
0
2
2
1
1
0
2
0
2
1
0
1
0
0
1
2
0
1
0
0
0
1
1
0
1
2
1
2
0
1
0
1
2
0
0
0
2
1
2
2
2
2
1
2
1
1
0
0
2
0
2
0
2
1
1
1
2
0
0
1
0
1
1
0
0
1
0
0
2
1
2
0
1
2
1
1
1
0
1
0
1
0
1
0
1
2
0
0
1
0
0
1
0
1
1
1
1
0
1
2
1
2
0
1
1
2
0
0
1
2
2
0
1
0
1
1
1
0
0
1
1
1
0
1
0
1
1
2
1
0
1
3
2
0
0
3
0
1
0
0
2
1
1
1
1
0
0
2
2
2
1
1
0
1
1
0
1
0
1
0
1
0
1
1
1
1
1
1
1
0
1
0
2
1
2
1
0
0
2
0
0
2
0
0
2
0
2
1
2
1
0
0
1
0
1
0
1
1
1
1
0
2
1
2
0
2
1
0
0
0
2
0
2
1
1
1
0
1
1
0
0
1
1
0
1
1
2
1
1
1
0
1
1
1
1
0
0
0
1
1
1
1
0
1
1
1
1
1
1
0
0
2
0
1
0
1
1
1
1
0
1
1
0
1
0
2
1
1
1
0
1
1
1
0
2
1
2
1
0
1
2
0
2
1
0
0
1
0
2
0
1
1
0
0
1
2
1
0
1
1
1
1
1
2
1
1
2
2
1
2
0
1
2
0
2
2
1
1
0
1
1
2
1
1
1
1
1
1
1
0
2
1
1
2
0
2
2
0
1
1
0
2
0
0
0
1
1
0
1
2
2
1
1
0
0
0
2
1
1
0
1
2
1
0
0
0
2
1
2
0
3
2
1
2
2
2
0
0
0
0
2
1
1
0
0
0
1
2
1
2
1
2
1
2
2
1
1
1
0
0
0
2
1
1
0
1
0
0
1
2
0
1
1
0
1
2
1
1
1
1
2
1
2
1
1
2
1
2
0
1
1
1
1
1
3
1
0
2
1
1
1
1
0
2
1
2
1
2
2
2
1
1
1
0
0
1
2
1
1
0
1
2
1
0
1
0
1
1
0
0
1
1
2
0
1
1
2
1
1
1
1
1
2
1
0
2
0
1
0
1
0
1
1
1
2
1
1
1
0
1
2
1
2
2
1
1
2
2
1
1
2
1
4
0
1
0
1
1
2
2
1
1
1
1
0
0
1
2
1
2
2
2
1
1
2
2
1
1
1
1
0
0
1
1
1
0
0
1
0
0
1
0
0
0
2
0
1
1
2
2
1
1
0
2
2
2
2
2
1
0
0
1
1
2
2
1
0
1
0
1
2
0
0
2
1
1
1
1
1
0
2
1
1
0
1
1
0
1
2
0
2
2
1
1
1
1
0
0
1
1
0
0
1
1
2
1
1
2
1
1
1
2
0
2
0
2
2
1
2
0
1
2
0
0
0
1
2
1
0
2
0
2
2
1
0
2
1
1
1
2
0
0
0
0
0
0
0
0
1
2
0
1
0
0
2
1
2
0
1
2
2
1
1
0
1
0
8
1
2
2
1
0
1
1
1
0
0
0
0
2
0
1
1
2
0
0
1
1
2
0
1
0
1
1
0
1
0
1
2
0
2
2
0
1
1
1
1
1
1
0
1
0
1
4
0
2
0
1
1
2
2
1
2
0
1
1
0
0
0
1
1
1
2
2
0
1
2
0
2
0
1
2
1
1
0
2
2
1
1
1
1
1
1
2
1
2
1
1
1
2
1
0
2
1
0
1
1
1
0
0
1
0
1
2
0
1
1
0
0
1
2
0
1
1
1
1
0
2
2
1
1
2
0
1
1
1
1
0
0
1
0
1
2
1
0
1
0
1
2
2
1
0
0
1
2
1
1
1
2
1
1
1
2
2
3
1
0
0
1
1
0
2
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
2
0
2
0
0
0
2
1
0
1
1
1
2
2
1
0
2
1
0
1
2
0
1
2
2
1
0
1
2
1
2
0
2
1
2
0
1
2
2
1
1
0
2
2
0
1
1
1
1
1
0
2
1
1
0
1
0
0
0
1
0
1
1
1
0
1
1
0
0
2
1
0
2
1
2
0
2
0
1
2
0
1
2
1
0
1
0
0
1
0
0
0
1
1
1
0
2
1
1
1
1
2
0
1
0
1
2
1
1
1
0
0
0
2
1
1
1
1
0
0
1
1
0
1
1
2
0
2
0
1
1
1
0
0
0
1
2
2
2
2
1
1
2
2
1
0
1
2
2
2
0
1
1
1
1
0
2
1
1
1
1
1
1
1
1
0
1
1
2
0
1
1
1
0
0
2
0
3
1
2
1
2
2
0
0
0
1
1
1
1
0
1
1
1
0
2
1
0
1
1
1
1
1
0
0
0
1
1
1
1
0
1
0
0
0
1
1
1
1
2
0
1
2
3
1
0
1
1
2
2
0
2
2
0
0
0
1
1
2
1
1
1
1
1
1
0
0
1
2
1
0
1
1
1
2
1
2
1
1
1
0
2
1
0
1
0
1
1
2
0
1
1
1
1
1
1
0
2
1
2
0
2
0
0
2
1
2
1
2
1
0
1
1
0
2
1
0
2
1
1
0
0
2
2
1
0
1
2
2
2
1
1
2
2
1
1
0
0
1
1
1
1
1
3
1
1
1
1
1
1
2
1
2
0
1
1
1
2
2
2
1
0
1
1
1
0
0
1
1
1
1
1
1
0
1
0
2
0
0
1
0
1
2
1
1
1
1
0
1
1
0
0
0
2
2
1
1
1
0
2
2
1
1
2
0
1
1
2
1
2
0
0
1
0
1
1
1
1
0
1
2
2
0
0
2
2
1
2
0
1
1
2
0
0
1
2
0
1
0
0
1
1
2
1
2
2
0
1
1
0
1
0
2
2
0
1
1
0
1
1
0
0
0
1
0
1
1
2
0
1
0
0
0
1
4
0
0
1
1
1
2
1
1
1
1
0
2
2
2
1
0
2
0
0
1
2
1
1
1
1
1
2
1
1
1
0
1
2
2
1
1
1
0
0
1
2
1
1
2
0
0
0
0
0
0
0
0
1
1
2
2
0
1
0
1
0
1
0
0
1
1
2
1
1
1
1
1
1
0
1
2
2
0
1
1
1
2
1
0
2
2
1
1
1
2
2
0
2
1
1
1
1
1
2
1
1
1
1
1
1
1
0
2
0
0
2
1
1
1
0
1
0
1
1
2
0
1
2
1
2
1
1
1
1
1
1
1
1
0
1
1
1
1
1
2
1
1
1
1
1
1
1
1
0
1
1
2
1
0
1
1
2
0
1
1
0
2
1
2
0
2
1
0
1
1
1
1
1
1
1
1
1
1
2
0
1
1
2
0
1
1
1
0
1
1
0
0
1
0
2
0
2
1
2
1
0
2
1
1
1
0
1
2
2
1
1
1
2
1
0
0
0
2
0
0
2
1
1
1
1
1
0
1
2
1
2
3
1
0
1
1
1
1
2
1
1
4
0
0
1
1
1
2
1
1
2
0
4
0
1
2
1
2
0
1
0
1
2
2
1
0
2
2
1
1
0
3
1
1
1
1
1
1
0
2
0
2
0
1
2
1
0
0
2
3
0
2
2
1
0
2
2
1
1
1
0
1
2
0
1
1
1
2
1
2
1
1
0
1
0
1
1
0
0
2
1
2
2
2
1
0
1
1
1
1
2
0
2
1
1
1
2
2
0
0
0
1
1
2
1
1
1
1
2
1
1
0
1
1
1
0
2
1
1
1
0
0
2
1
0
0
1
2
1
2
0
1
1
0
2
3
2
2
2
1
1
1
0
0
0
1
1
4
1
0
0
2
1
0
1
1
1
0
2
1
1
1
1
1
1
1
1
0
1
2
1
1
0
1
1
0
1
0
0
0
1
1
1
2
0
1
0
2
0
0
0
0
0
1
1
1
2
0
1
0
0
1
1
1
2
2
2
1
1
0
1
0
0
1
2
0
1
1
0
1
0
0
2
1
1
1
2
2
1
0
0
0
1
1
2
2
1
0
2
1
2
1
1
0
0
0
0
0
2
2
1
1
1
0
2
1
0
1
1
0
2
0
1
2
0
2
1
1
0
2
0
1
3
0
1
1
1
0
1
1
0
1
1
1
1
0
1
1
2
1
0
2
0
0
0
0
1
2
1
1
1
1
1
0
2
1
0
2
1
1
1
1
1
1
2
2
1
1
0
1
1
2
1
0
1
0
1
0
0
1
1
1
0
0
1
2
2
2
0
2
2
0
1
1
0
1
2
1
1
2
1
1
1
1
0
1
1
0
1
0
1
1
1
1
1
1
0
1
0
1
0
0
1
2
2
0
1
1
2
0
1
1
0
1
0
2
1
1
1
1
0
1
1
0
1
2
1
1
1
2
1
0
1
1
1
1
2
0
2
0
1
1
0
2
1
2
1
0
2
2
2
1
2
1
2
0
0
0
2
0
2
1
1
1
1
1
1
2
1
1
0
0
1
2
1
0
0
1
0
0
1
0
1
0
1
1
1
2
0
2
2
2
0
1
0
2
1
1
1
1
1
2
2
1
4
1
0
0
2
1
1
0
0
2
2
0
2
1
1
2
2
1
1
0
2
1
1
1
1
2
1
1
0
1
0
0
1
1
0
0
1
0
0
1
1
1
1
1
2
1
1
1
1
0
2
1
0
1
0
1
0
1
1
0
1
0
1
0
2
1
2
2
1
2
1
2
2
1
1
1
1
2
0
2
2
2
1
2
0
0
1
2
0
2
1
2
1
0
2
0
1
2
1
1
2
0
2
1
2
1
1
1
1
1
1
2
1
2
2
2
2
1
2
0
0
1
3
0
1
1
1
1
1
0
2
0
0
1
0
0
2
1
1
0
1
1
0
1
0
0
1
0
1
1
0
1
0
1
1
1
1
1
1
2
0
1
0
1
0
0
0
1
0
0
1
2
1
2
1
2
0
3
1
1
0
1
0
1
1
1
0
1
2
1
2
1
0
2
3
1
0
1
1
0
0
1
1
1
1
0
2
1
2
2
2
2
3
1
1
1
0
0
0
2
1
1
2
1
1
0
0
1
2
1
0
0
1
0
2
1
0
1
0
1
5
1
1
1
2
0
2
2
1
2
0
1
2
1
1
2
0
1
1
1
1
1
0
1
1
1
1
1
1
0
1
1
1
0
0
0
1
2
0
1
1
1
1
1
2
1
1
2
1
1
1
1
2
1
0
0
0
2
0
0
0
2
0
0
1
1
0
1
0
1
2
0
1
1
1
1
2
1
2
1
0
2
0
1
1
2
0
0
1
0
1
3
0
1
1
0
0
1
0
1
1
2
2
0
0
1
2
2
0
0
1
1
1
0
1
2
2
1
1
1
0
1
2
2
1
1
2
2
1
0
0
0
1
0
1
2
2
1
2
0
2
1
1
1
2
2
0
0
0
0
1
0
0
1
1
1
2
1
0
1
0
1
3
2
1
2
1
0
1
2
2
1
1
1
1
1
0
0
1
2
1
2
0
0
1
2
0
1
1
1
0
2
1
1
2
3
1
1
0
1
1
0
2
1
1
2
0
2
1
1
0
3
1
1
0
1
1
1
2
0
3
1
2
1
1
2
1
1
1
1
1
2
0
2
1
1
1
0
0
2
3
0
1
2
1
1
0
1
1
2
2
0
1
1
3
2
1
1
0
1
2
0
0
2
1
2
0
2
3
0
2
1
0
0
2
1
0
1
2
2
1
2
2
1
1
1
1
2
1
1
2
1
0
1
0
0
0
0
2
0
0
0
2
1
0
2
1
0
0
1
0
1
0
0
2
1
1
0
1
1
1
0
1
0
1
1
1
1
2
0
1
0
1
0
1
1
0
1
2
1
0
1
0
0
1
1
2
2
1
2
2
1
1
1
0
0
2
1
2
0
0
0
1
2
2
0
0
1
1
1
1
1
1
2
2
0
1
1
2
1
0
0
1
0
2
1
2
2
0
0
1
2
2
1
2
0
1
1
2
1
0
1
0
2
1
1
2
0
1
1
0
2
2
0
0
0
2
0
1
2
2
0
0
0
1
1
1
1
1
1
0
0
1
1
0
0
1
2
1
2
1
2
2
0
1
1
1
1
1
1
1
0
1
0
0
0
2
1
0
2
1
0
1
1
1
1
1
0
0
1
0
1
2
1
2
1
2
1
0
1
0
1
2
1
1
0
1
1
1
0
0
0
1
1
0
2
0
0
1
3
2
2
0
0
2
0
1
0
0
1
2
0
0
1
1
1
0
0
1
2
1
1
1
1
0
1
2
0
1
1
1
0
1
0
2
2
0
0
1
2
1
1
2
1
0
2
0
0
0
1
1
1
0
3
1
2
0
2
0
0
1
2
2
1
2
0
1
1
1
1
0
0
1
1
2
1
1
3
1
1
1
2
0
1
2
1
1
2
1
0
0
1
1
1
3
0
1
0
2
0
2
1
2
1
1
1
0
1
1
1
2
1
0
0
1
0
2
1
0
1
2
0
1
1
2
0
1
1
1
0
2
2
0
2
0
2
1
0
2
1
1
1
1
1
1
2
0
1
1
1
0
1
1
0
0
1
1
1
2
0
2
2
1
1
0
0
1
2
1
2
2
0
1
4
0
0
1
1
1
2
1
1
1
1
0
0
0
1
1
1
0
1
0
1
2
0
1
0
1
1
1
1
0
2
2
2
1
1
2
1
2
1
1
2
1
2
2
1
2
1
0
0
4
0
1
1
1
1
2
2
0
1
1
1
0
1
2
1
2
1
2
1
1
2
0
1
0
2
0
1
1
2
0
2
2
1
2
0
2
1
0
1
2
0
1
0
1
1
0
0
1
1
1
2
1
1
2
1
0
1
2
1
1
0
1
0
1
0
2
1
2
2
1
0
1
1
2
1
1
2
1
1
1
1
2
0
0
0
2
2
1
1
1
0
2
0
1
2
0
1
1
1
1
2
1
1
1
0
1
1
0
2
0
1
1
2
0
0
1
1
2
1
2
1
0
1
0
2
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
2
2
1
0
1
2
2
1
2
2
0
2
0
0
0
2
1
1
0
2
1
3
1
1
1
1
1
1
1
0
0
0
0
1
0
3
0
1
0
0
0
0
1
2
0
2
2
0
0
1
1
2
1
1
1
0
0
2
1
1
3
0
0
0
2
2
1
1
2
1
1
1
1
1
3
1
2
1
1
1
1
0
0
0
2
1
3
1
1
0
2
1
0
2
2
0
1
1
1
1
0
1
1
0
1
0
1
2
0
0
0
1
1
1
1
2
0
0
1
0
1
0
0
1
2
0
2
1
0
0
0
1
1
2
1
0
0
0
1
1
1
0
2
2
1
2
1
1
1
1
2
1
0
1
0
0
2
2
1
1
2
1
1
0
2
0
1
0
1
1
0
2
0
1
1
2
0
2
1
1
1
0
1
1
2
1
2
0
2
2
2
1
0
0
1
2
1
2
2
2
0
1
1
0
2
0
1
1
2
4
0
1
1
0
1
2
1
0
2
0
1
1
1
2
1
1
1
2
1
2
0
1
1
4
1
0
1
2
1
0
0
0
0
0
1
1
0
1
1
1
2
1
2
1
2
0
1
0
2
2
0
1
1
1
0
2
1
1
0
0
0
1
1
2
2
2
3
1
0
0
1
0
1
1
2
1
1
2
1
1
1
2
1
1
2
2
1
1
2
1
2
1
1
0
1
0
0
1
1
1
2
0
1
0
1
1
1
2
0
1
1
0
2
0
1
2
2
1
1
0
0
1
1
1
0
1
1
0
2
1
2
0
0
2
1
1
1
0
0
2
0
2
0
0
2
2
1
0
2
2
1
2
1
1
1
0
1
2
2
2
0
0
2
1
1
0
0
3
1
0
0
1
0
0
0
1
0
1
2
1
2
0
1
2
2
0
2
0
1
1
2
1
0
2
1
0
0
0
2
2
1
1
0
1
0
1
1
1
1
0
3
1
0
0
2
1
0
0
1
2
2
1
1
1
2
1
0
1
1
0
1
0
0
1
1
1
0
1
0
1
2
0
1
1
1
1
1
1
3
2
2
2
0
2
0
2
2
1
1
3
1
0
1
1
1
1
1
0
1
2
1
1
0
1
2
2
1
2
1
1
1
1
0
1
1
1
2
2
2
1
1
4
0
1
1
2
1
0
2
1
1
0
4
0
0
1
1
0
1
1
1
0
0
2
0
0
2
0
1
1
1
1
0
1
1
2
1
1
1
1
1
1
0
1
0
1
0
2
1
1
1
0
1
1
1
0
1
3
2
1
0
1
0
1
1
0
1
0
0
1
0
1
2
2
0
1
1
2
1
0
1
1
1
0
1
2
2
2
1
0
1
1
0
0
2
1
1
1
2
2
1
0
2
0
0
2
0
1
1
1
1
0
2
1
0
1
1
2
1
2
1
0
1
1
1
1
0
2
0
1
0
0
1
1
0
1
1
0
0
0
0
2
1
1
1
0
2
1
1
1
0
0
0
2
2
1
1
1
1
2
0
2
1
2
2
1
2
1
1
1
2
2
1
0
1
0
1
0
2
0
0
3
1
1
2
0
1
0
1
1
1
0
2
2
0
1
1
1
3
1
2
2
0
1
2
2
2
2
0
1
1
0
0
1
1
0
1
0
1
1
0
0
1
1
2
1
1
1
1
2
1
1
1
2
2
3
1
1
2
2
1
2
3
1
1
0
0
1
1
2
0
1
0
2
1
0
2
0
1
0
1
1
1
1
1
1
0
2
1
0
1
1
0
0
1
1
1
1
0
1
1
1
1
0
1
1
2
1
1
2
0
1
1
2
1
0
0
0
0
1
2
1
1
1
1
1
2
1
2
0
1
1
1
1
0
1
1
1
1
1
0
0
2
1
1
0
1
5
1
1
1
1
1
1
1
1
2
0
1
0
2
1
1
0
1
2
0
1
1
0
1
1
1
2
0
1
2
0
0
0
0
2
2
1
2
1
1
2
1
0
0
1
2
0
1
0
1
0
2
1
1
1
1
1
1
1
0
1
2
0
0
2
1
1
2
3
0
0
1
0
2
0
0
2
1
1
1
1
1
0
1
2
2
1
1
0
1
1
1
2
1
2
1
1
2
1
0
0
0
1
0
2
1
2
0
1
2
0
1
1
0
0
2
2
1
0
2
2
0
1
1
0
0
0
0
1
1
1
0
0
0
2
1
1
2
1
1
1
0
1
1
0
0
1
0
1
1
0
0
2
2
1
1
1
1
0
1
0
1
1
2
2
1
1
0
1
1
1
2
2
1
1
0
0
1
2
1
1
1
0
1
1
1
1
0
1
1
1
0
1
0
0
2
2
1
1
1
1
1
2
1
0
0
1
1
0
1
1
0
1
1
1
0
2
0
0
1
2
1
2
0
1
4
1
1
2
0
1
1
2
1
1
1
1
0
1
1
1
1
0
2
1
2
0
1
2
0
1
0
0
0
1
1
1
0
0
0
1
2
2
1
1
1
1
1
1
1
1
0
0
1
0
1
1
0
1
1
0
2
0
2
1
1
1
0
0
1
1
0
1
1
1
1
0
0
0
0
1
0
2
0
3
0
0
1
2
1
2
1
1
3
1
1
1
1
0
1
0
0
1
0
0
1
0
2
2
1
2
2
2
2
1
1
1
1
0
1
1
1
0
2
1
1
2
2
0
0
1
0
2
0
1
1
1
2
1
1
1
1
0
1
1
0
1
2
0
0
2
0
1
0
1
0
1
1
1
0
2
1
1
0
1
1
0
2
2
1
0
0
2
2
2
0
2
2
1
2
1
1
0
1
0
1
1
1
1
2
1
1
1
1
2
0
0
0
2
0
1
1
0
2
0
1
1
1
2
1
0
1
1
1
0
2
1
1
2
1
0
1
1
1
1
1
1
1
0
0
0
0
0
0
0
1
1
2
1
0
2
2
1
0
1
1
1
1
0
1
2
0
2
1
0
0
1
2
0
0
2
2
0
1
0
1
1
1
1
2
2
0
1
0
1
1
1
0
0
1
1
1
2
0
0
1
0
1
0
1
1
2
1
0
1
1
1
2
0
1
1
2
0
1
0
0
0
1
0
1
0
2
2
0
2
0
0
1
2
1
2
1
0
0
0
1
0
1
0
1
1
0
0
0
1
1
1
0
1
1
0
1
0
0
0
1
1
0
1
2
1
2
0
1
0
1
1
2
1
1
1
0
2
2
0
3
0
1
3
2
0
0
0
2
1
0
2
0
2
1
1
1
1
0
1
1
0
0
0
2
1
0
0
1
0
1
2
2
2
1
0
0
2
0
1
3
1
0
1
1
1
0
1
2
1
1
1
0
0
0
4
0
1
1
1
2
2
1
1
1
2
0
0
1
0
1
1
1
2
0
1
0
0
1
1
0
1
1
1
0
1
0
1
0
2
0
1
1
0
1
1
0
0
1
0
1
0
0
1
1
1
0
1
1
1
3
0
0
1
2
2
0
1
1
1
2
2
2
0
1
1
1
3
0
1
1
2
0
1
2
2
1
0
1
1
2
2
2
0
1
1
0
1
1
2
1
1
0
1
1
2
2
1
1
1
1
0
1
1
1
0
1
1
0
1
1
0
0
3
1
0
2
0
1
1
0
1
1
0
0
2
1
0
1
1
1
0
0
1
1
1
2
1
1
1
1
0
1
1
1
1
2
1
0
1
0
0
1
2
0
0
0
1
1
2
4
0
0
1
1
0
1
0
0
1
1
3
4
1
1
1
2
0
2
0
1
2
1
3
2
2
0
1
2
0
0
1
2
1
1
1
1
0
2
2
1
1
1
1
0
1
1
1
2
1
1
0
0
2
1
2
1
2
1
0
0
0
0
0
0
1
2
1
0
0
0
0
2
1
1
0
0
1
0
2
1
2
1
2
0
2
2
0
0
1
1
0
0
0
0
1
0
1
0
1
0
1
1
1
1
0
0
1
0
1
1
0
2
1
1
1
0
0
1
1
1
1
0
0
0
1
2
0
1
1
1
2
1
1
1
2
0
1
1
1
1
0
1
2
1
0
2
1
1
1
1
1
0
1
1
1
0
1
1
1
0
1
0
0
1
1
0
1
0
1
0
1
1
0
0
0
2
1
0
2
2
1
1
1
1
1
1
2
0
0
0
2
1
0
2
2
1
1
2
1
1
0
1
1
2
2
1
1
1
0
0
0
0
1
1
2
0
2
0
0
1
0
1
0
1
1
1
1
2
2
0
0
1
0
1
2
2
1
1
1
2
2
0
1
1
0
1
1
1
1
1
0
1
1
2
1
1
0
1
1
0
0
1
0
1
0
1
2
0
2
1
1
0
0
0
1
0
1
0
0
1
1
2
1
1
0
0
2
1
1
1
1
1
0
0
2
0
0
1
1
2
1
1
1
1
2
2
2
2
2
1
2
1
2
1
2
1
1
1
0
1
3
0
1
2
0
1
1
2
2
1
1
1
0
2
0
2
1
1
1
1
0
0
2
1
1
1
1
1
2
1
2
0
0
0
2
2
1
2
1
1
1
0
0
2
2
0
1
1
2
0
2
1
2
0
0
0
1
0
1
2
1
1
1
1
0
0
4
2
1
2
1
0
2
0
1
0
2
1
1
1
3
1
1
2
2
0
1
2
1
1
1
1
0
1
1
1
1
0
1
1
1
1
0
1
1
1
1
1
0
1
1
2
1
0
1
1
2
1
0
1
0
2
1
1
1
1
0
0
3
0
1
2
2
1
0
1
0
0
0
1
0
0
0
2
1
0
0
1
2
0
1
0
1
0
1
1
1
1
0
0
1
1
1
0
1
0
1
1
1
1
1
0
1
0
0
0
2
1
0
2
2
0
2
1
0
0
1
0
0
1
0
0
0
0
1
1
1
0
0
0
0
1
0
2
0
1
0
1
0
1
1
0
1
0
1
1
1
1
1
0
0
2
2
1
2
2
0
2
0
0
0
2
2
2
0
1
2
0
0
0
1
3
0
0
1
1
1
0
0
2
1
1
0
1
1
1
3
2
1
1
1
2
0
1
2
1
0
1
1
2
1
2
1
1
1
0
1
0
0
1
2
2
2
2
2
1
1
1
1
0
0
0
1
1
2
0
1
1
0
2
0
2
1
1
0
1
2
1
0
1
2
1
1
3
2
0
1
1
1
1
0
1
1
1
1
2
2
1
1
1
1
0
1
1
0
0
1
0
1
0
1
2
1
0
2
0
1
1
2
1
0
1
1
1
1
0
0
0
2
1
1
2
2
2
1
1
3
1
0
0
0
0
0
0
3
1
1
2
2
0
2
0
1
1
1
2
1
0
1
1
0
1
1
0
2
1
1
2
0
2
0
0
1
0
2
1
1
2
2
1
1
1
1
1
0
1
0
1
1
1
1
1
1
1
2
2
0
0
1
1
1
1
1
1
1
2
2
1
0
1
0
1
0
1
2
0
0
0
1
2
0
1
0
0
1
0
1
2
0
0
0
1
0
2
0
1
1
1
1
1
2
2
1
0
1
1
1
1
0
1
0
1
0
1
1
0
1
1
1
1
2
2
1
0
1
1
1
2
1
0
1
0
1
1
1
1
0
1
1
0
0
2
1
1
2
2
0
1
1
1
2
2
0
1
0
0
1
0
1
1
1
1
1
1
1
0
1
2
1
0
0
1
1
0
1
0
3
0
1
1
0
1
1
2
1
1
1
0
2
0
2
0
0
1
0
1
0
1
0
0
0
1
1
0
1
2
0
1
1
0
0
1
0
0
1
1
0
1
1
1
1
0
1
0
1
2
1
3
2
0
1
1
2
0
0
1
0
1
1
1
0
1
0
1
2
0
1
1
1
1
2
1
2
3
2
1
2
0
1
0
0
1
2
1
2
1
1
1
0
1
0
0
0
1
0
1
2
2
1
2
2
0
2
1
1
0
2
1
1
0
0
2
1
2
1
1
1
1
2
1
2
0
0
0
1
1
1
1
0
0
1
1
1
1
1
1
2
1
2
2
1
1
1
1
2
0
1
0
2
1
2
0
1
2
0
2
1
2
1
0
2
0
2
1
0
1
1
1
1
1
1
0
2
2
1
1
0
2
1
1
2
1
1
1
1
2
1
2
1
0
2
1
2
1
1
0
1
1
0
1
0
0
2
2
2
0
0
2
1
0
1
1
2
0
1
2
1
0
1
0
0
1
1
1
0
1
1
0
1
2
1
1
0
1
2
2
1
1
1
0
1
2
1
1
1
1
2
0
0
0
1
2
0
2
0
0
2
1
1
2
1
1
0
2
0
1
1
1
0
0
1
0
0
0
2
0
1
2
1
1
0
0
0
0
1
2
1
1
1
1
1
0
2
1
1
0
2
0
1
2
1
1
2
2
0
2
1
0
1
0
0
0
0
1
1
0
2
1
1
1
1
1
1
1
2
2
1
1
1
1
1
2
1
1
2
1
1
1
0
0
1
0
1
1
2
0
2
0
2
1
2
2
1
1
1
1
1
1
1
1
0
2
1
1
2
1
1
2
2
1
1
1
1
0
2
0
2
1
1
1
1
1
2
0
1
1
1
1
2
1
1
2
1
0
1
1
1
0
0
1
0
0
2
1
1
2
1
1
0
1
1
1
2
0
1
0
2
2
2
1
1
0
1
1
0
1
1
1
0
2
1
0
0
0
1
0
0
0
1
0
2
1
1
0
1
1
1
0
0
1
2
0
1
1
1
2
1
1
0
0
2
1
2
0
2
1
1
2
0
1
0
1
1
1
2
0
2
1
3
1
0
1
2
0
1
1
0
0
1
1
0
1
1
1
2
0
1
0
1
1
1
0
0
1
1
1
2
0
0
1
2
1
0
1
1
0
1
2
1
1
0
2
1
1
2
2
1
1
1
2
2
0
0
1
1
2
1
1
1
2
1
1
2
0
0
1
0
0
1
1
3
2
1
2
1
1
2
0
2
1
1
2
1
1
2
1
0
0
2
0
0
1
2
1
0
1
2
0
2
1
0
1
1
2
0
2
0
1
1
2
1
0
2
1
2
2
1
1
0
0
0
1
0
1
2
2
2
0
1
2
0
1
1
1
1
2
1
0
1
1
0
0
0
0
0
0
1
2
0
0
1
2
1
1
1
1
0
2
1
1
2
1
2
1
1
0
1
1
2
2
1
1
0
0
1
0
2
1
1
0
1
1
0
1
1
1
0
0
2
1
2
2
2
0
1
0
0
2
2
1
0
1
0
0
2
2
0
2
0
0
1
1
1
2
2
0
2
1
0
0
1
1
0
0
0
1
2
1
0
2
0
1
0
2
1
2
2
0
2
2
1
1
1
1
1
1
1
2
1
0
1
1
1
1
1
2
0
1
0
1
6
0
1
2
2
0
2
0
0
0
1
1
0
0
2
1
0
0
1
2
0
0
2
0
3
1
1
1
0
0
0
0
1
1
1
1
7
1
1
0
0
0
2
0
2
1
2
1
2
0
0
1
1
0
1
1
1
0
1
1
1
1
1
2
1
1
2
1
1
2
1
2
1
2
0
0
0
2
1
1
1
0
1
0
1
2
2
1
0
0
0
0
2
2
0
0
1
1
0
1
2
0
2
1
1
1
0
1
2
0
0
1
1
2
1
0
1
2
2
1
1
0
1
0
2
1
1
2
2
0
1
1
0
1
2
1
1
0
1
0
0
0
1
1
1
0
1
1
1
2
1
1
1
1
0
2
1
1
1
2
0
1
1
0
3
1
1
2
1
0
2
0
0
1
1
1
2
2
0
0
2
2
0
1
1
2
0
1
1
1
2
0
1
0
4
2
1
1
0
1
0
1
1
0
0
0
1
1
1
2
0
1
1
0
0
1
0
1
1
1
1
0
1
2
1
2
3
1
1
1
0
1
1
1
1
0
1
1
1
2
1
2
2
2
0
0
1
2
0
2
1
1
0
2
2
1
2
1
1
0
1
0
1
2
2
1
1
0
1
1
0
0
3
1
0
1
0
1
0
1
1
0
0
0
0
1
2
1
1
0
1
1
0
0
1
1
2
1
2
0
2
2
0
0
1
1
2
0
1
1
1
2
0
1
1
1
1
0
0
0
1
1
2
1
1
1
1
2
0
1
1
1
0
0
1
1
1
1
1
1
1
1
1
0
2
1
2
2
2
1
0
1
1
1
2
1
0
0
2
1
1
1
2
0
0
1
2
0
1
1
2
0
1
0
1
2
1
1
1
1
2
0
1
1
0
1
1
1
2
1
1
1
0
1
0
1
2
1
1
1
0
0
1
3
1
2
3
2
0
0
1
1
1
0
0
1
1
1
0
1
1
2
0
2
1
0
1
2
0
1
0
1
1
1
0
3
1
1
1
1
1
0
1
2
0
2
1
0
0
0
1
1
0
0
1
0
0
1
0
0
1
1
2
3
1
1
1
1
0
2
1
0
1
1
1
1
1
0
2
0
0
0
0
0
2
1
1
0
2
2
1
2
2
0
2
1
1
2
2
1
1
0
1
0
1
1
1
0
0
1
0
0
1
1
1
0
1
0
0
1
0
1
0
1
1
3
2
1
1
1
1
1
1
0
2
1
0
0
1
1
0
0
2
1
0
0
0
1
1
0
0
2
1
1
0
1
3
2
2
1
1
0
0
1
2
0
1
2
1
2
0
1
1
1
2
2
0
0
2
0
3
1
1
1
2
1
1
1
2
1
1
0
0
0
1
2
1
1
1
1
1
1
0
2
0
1
2
0
0
1
0
1
0
0
1
1
0
0
2
0
1
1
1
2
0
1
2
0
0
1
1
0
1
1
2
2
1
1
1
0
2
2
0
1
1
1
1
1
4
0
1
1
0
1
1
2
0
1
1
0
1
1
0
2
1
0
0
0
1
2
0
0
1
0
0
1
1
0
2
0
2
1
1
0
1
2
1
1
1
0
0
1
1
0
0
1
1
1
1
1
1
2
1
0
0
1
0
1
0
1
2
1
1
2
1
1
0
2
2
1
0
1
0
0
1
2
1
1
2
2
2
2
1
0
1
1
1
1
1
0
2
0
1
0
0
1
0
0
2
1
1
1
0
2
1
1
2
1
1
0
1
1
3
2
1
1
1
2
1
0
1
1
2
1
1
1
2
0
2
1
1
1
1
1
0
1
1
1
2
0
1
0
1
1
2
2
0
0
4
0
0
1
1
2
1
1
0
1
0
2
1
1
0
0
0
2
2
0
1
1
1
2
0
1
0
1
0
1
0
1
0
1
2
1
2
1
2
1
1
1
2
0
1
1
1
1
1
0
1
2
1
2
0
2
2
0
0
1
1
0
1
1
0
1
1
1
1
1
1
1
0
1
0
0
1
1
2
1
1
1
0
0
2
1
2
0
0
0
0
1
1
0
0
0
2
1
3
1
1
0
2
1
1
1
0
1
1
1
0
0
1
0
0
2
0
0
1
0
0
0
1
0
0
1
2
2
0
1
1
0
1
2
2
1
0
1
2
0
1
2
1
1
0
0
1
1
1
1
1
1
2
1
2
1
0
1
2
1
1
1
1
2
1
1
1
0
1
2
0
0
1
0
1
1
0
1
2
1
0
2
1
0
1
0
1
0
2
1
2
2
2
0
0
1
1
1
1
1
0
1
1
2
2
0
1
1
1
1
2
5
2
0
0
1
1
1
1
0
1
2
0
1
1
2
1
1
1
0
1
0
1
2
2
1
0
3
1
2
1
1
1
1
1
1
2
2
2
0
3
1
1
0
2
1
2
0
0
1
2
1
1
0
1
1
2
1
0
2
1
0
1
1
1
0
1
1
0
1
1
0
2
0
1
1
1
1
1
1
2
0
1
0
2
1
2
2
1
0
1
0
1
1
1
1
0
0
2
1
2
1
1
1
2
0
2
1
1
1
1
1
1
1
0
1
1
0
1
0
1
1
1
1
0
1
2
1
1
2
2
0
1
1
1
2
1
1
1
2
1
1
1
2
0
2
0
1
1
0
1
0
1
1
1
0
1
0
0
0
1
2
1
2
1
2
0
1
1
0
2
1
0
1
1
1
1
1
1
0
2
0
2
2
0
0
1
1
0
1
1
1
0
1
2
2
0
1
0
0
0
2
1
1
0
1
1
1
0
0
0
1
2
1
1
2
1
1
2
2
2
1
1
0
1
0
1
0
0
1
1
2
1
1
0
0
2
1
0
1
1
2
0
0
1
0
0
1
0
0
2
1
1
1
2
2
1
2
1
1
1
0
0
0
1
1
1
0
2
1
0
1
1
2
1
0
1
2
0
1
1
1
1
0
1
1
2
0
1
0
1
1
0
1
2
1
0
1
2
1
1
2
1
1
1
2
1
1
1
1
1
2
1
0
1
2
2
2
0
0
1
1
0
0
1
0
1
0
2
1
2
1
2
0
1
0
1
1
1
0
2
1
2
1
2
1
2
2
1
1
1
2
2
1
0
1
1
2
1
0
2
0
2
0
1
1
1
1
0
2
1
1
1
1
1
1
1
0
2
2
0
0
1
0
1
1
0
0
1
0
1
0
2
0
0
2
2
1
1
2
1
1
1
1
0
1
0
0
1
1
1
0
1
0
1
0
2
1
1
1
0
2
1
1
0
1
1
1
0
2
2
1
2
2
0
1
2
1
1
0
1
1
0
0
2
0
0
2
0
2
1
1
2
1
1
0
0
1
0
1
1
0
1
1
0
0
2
1
0
0
1
2
1
2
1
1
2
1
0
1
1
1
2
0
2
1
2
1
1
0
1
1
2
1
2
1
0
2
2
0
0
0
2
0
3
1
1
1
1
1
0
2
0
0
2
3
1
0
1
1
1
1
0
1
2
0
1
1
2
0
1
1
1
1
4
1
2
0
1
0
2
1
0
1
1
2
2
2
1
0
0
0
0
0
2
1
1
2
0
0
1
1
2
1
0
1
1
1
0
2
1
1
1
1
0
1
2
2
1
1
1
1
1
0
1
1
1
1
2
1
1
0
0
0
1
1
2
2
0
1
2
1
0
1
1
1
0
1
1
1
0
2
2
1
2
2
0
1
1
2
2
2
0
2
0
1
1
1
2
1
1
2
1
1
2
2
1
1
3
1
0
0
1
0
0
1
1
1
1
0
1
1
1
2
0
1
0
1
1
2
0
2
0
2
2
2
2
2
1
1
1
2
0
1
2
2
0
0
0
1
1
1
0
0
3
1
1
1
1
2
2
1
0
1
1
1
1
1
2
1
1
2
1
2
0
2
1
1
2
0
0
2
1
2
2
1
1
0
2
1
2
1
0
1
1
1
0
1
4
1
1
1
0
1
2
1
2
1
0
0
1
1
1
1
2
2
0
2
1
0
0
2
1
1
2
0
1
1
0
1
2
0
1
1
0
0
1
1
1
0
2
3
2
1
1
2
2
1
2
1
0
2
1
2
1
1
0
2
1
1
0
1
2
1
1
1
2
1
0
3
1
1
3
1
1
1
0
2
1
2
2
2
2
0
0
1
0
2
1
0
0
2
1
0
1
2
0
2
1
0
0
1
1
1
2
2
2
0
1
0
2
2
2
0
1
1
0
1
1
1
0
1
1
2
1
0
1
0
1
2
1
0
1
2
0
1
1
1
1
0
1
0
0
1
0
1
1
1
0
1
1
0
1
0
1
1
1
1
1
0
2
0
1
1
0
2
2
2
1
1
0
1
3
1
1
2
2
1
1
1
1
0
0
0
0
1
0
5
1
1
0
1
1
1
2
1
1
0
1
0
0
1
0
2
0
1
0
1
2
2
1
1
1
2
4
1
0
0
0
2
2
0
1
1
1
0
1
1
0
0
0
2
0
0
1
1
1
1
2
0
2
2
0
1
2
2
0
1
0
2
1
1
2
2
0
1
0
0
1
0
0
1
1
1
1
0
2
2
0
1
2
0
1
1
1
1
2
0
1
2
0
1
1
1
0
1
0
1
2
0
1
2
2
2
0
2
2
2
2
1
1
2
0
1
1
1
1
1
1
1
0
0
1
0
0
2
0
2
1
1
2
1
0
0
1
0
1
2
0
0
0
1
2
1
1
2
0
0
1
1
2
1
0
2
1
1
1
1
0
1
1
1
2
1
1
0
1
0
0
2
2
2
1
1
1
1
1
1
1
1
2
1
2
2
0
2
0
1
0
2
1
1
2
0
2
1
1
1
2
2
1
1
1
0
1
1
1
0
1
0
0
1
1
0
2
0
2
1
1
1
0
1
1
1
0
2
0
0
1
2
1
0
0
0
1
1
0
1
0
0
1
2
0
2
0
0
1
0
0
1
1
2
1
0
1
1
2
1
0
1
1
0
2
2
1
3
1
1
1
0
1
2
0
1
1
1
2
0
1
1
1
1
1
1
0
0
2
1
2
1
0
1
1
1
0
0
0
1
2
2
3
2
1
2
2
2
0
1
2
0
0
2
1
1
0
1
0
2
1
0
1
1
1
1
2
2
2
0
1
1
1
1
2
0
2
2
1
0
1
1
1
2
1
2
1
0
0
0
0
1
0
0
2
1
0
2
1
2
2
1
0
2
1
0
1
1
1
1
1
1
2
2
1
1
1
2
0
1
0
0
2
0
1
2
4
0
1
1
2
1
1
1
1
0
1
1
2
2
1
0
1
1
2
0
1
1
1
1
2
1
0
1
0
2
1
1
0
1
0
1
2
1
0
1
1
2
1
0
2
2
1
1
1
1
2
0
1
2
1
1
0
0
1
1
1
0
0
2
2
0
0
1
0
0
1
2
1
0
0
1
1
2
2
2
0
0
1
0
1
1
1
1
0
1
1
2
2
2
1
0
4
0
1
1
2
1
1
0
1
1
1
2
1
0
1
1
1
1
1
1
2
0
2
1
1
1
2
1
0
1
0
1
0
1
2
0
1
2
1
0
1
1
1
1
2
1
0
1
0
2
2
2
2
2
1
0
2
0
2
1
0
2
0
1
0
0
0
1
1
1
1
0
2
1
0
2
2
2
1
1
0
0
2
0
1
0
1
0
4
2
0
1
1
1
2
0
0
1
2
0
2
0
0
0
0
0
1
1
1
0
1
0
0
1
1
1
1
1
1
1
2
0
1
1
0
1
0
1
2
1
1
0
2
1
1
1
1
0
0
1
2
2
1
2
0
2
1
0
1
2
2
0
1
1
2
1
2
1
1
0
2
1
0
1
1
1
1
0
1
0
1
1
0
0
1
0
2
0
1
1
0
2
1
2
0
1
1
0
1
2
1
0
1
1
1
1
1
2
0
1
1
3
2
2
0
2
1
1
0
1
0
0
2
3
1
3
0
1
1
0
0
1
1
1
2
2
0
0
1
2
0
0
0
2
2
0
1
0
2
1
2
1
0
1
0
0
1
1
1
0
2
0
0
1
0
1
0
2
0
1
0
0
1
1
0
1
1
0
2
0
2
0
1
1
0
2
1
2
0
1
1
0
0
0
2
0
0
1
1
1
1
1
2
0
0
2
2
1
1
0
0
1
0
1
1
0
3
1
1
0
1
0
1
3
0
1
0
0
1
1
1
0
1
0
0
0
1
1
1
2
1
0
0
0
1
1
1
0
1
3
1
1
1
2
2
0
1
0
1
1
1
1
0
2
1
1
0
1
2
1
0
0
0
0
2
1
1
1
1
1
1
1
0
0
1
1
2
1
1
0
0
0
2
1
2
1
1
0
2
0
1
1
2
1
1
1
1
1
0
1
1
0
1
0
1
1
1
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
0
1
0
1
2
1
1
2
0
1
2
0
2
0
3
1
1
0
1
1
2
0
2
1
0
1
1
0
1
1
2
1
1
2
1
2
2
1
1
1
1
2
2
1
0
1
2
0
1
0
1
1
2
1
2
1
0
2
1
1
0
0
0
1
0
1
1
0
2
1
1
0
1
3
2
2
2
0
2
0
2
2
1
1
0
2
1
1
0
1
1
0
2
1
1
2
2
2
1
1
0
0
1
0
1
0
1
0
0
2
2
2
0
2
2
1
1
0
2
2
2
0
1
1
2
1
1
3
0
1
1
2
0
1
1
1
1
0
1
2
1
2
1
2
0
2
2
0
1
0
0
1
1
2
1
1
0
2
1
2
1
2
2
1
3
1
0
1
1
1
0
1
1
1
1
2
1
2
1
0
0
1
1
1
2
1
1
1
1
0
1
0
1
2
1
0
1
1
1
1
1
0
1
1
2
0
2
1
1
1
1
2
1
1
0
2
0
2
2
2
2
0
2
0
1
0
0
0
0
0
0
2
0
2
1
1
0
2
1
2
2
0
1
2
0
1
1
1
0
2
2
0
1
1
1
1
1
1
0
1
0
1
0
2
1
2
0
2
3
1
1
0
1
0
1
1
1
1
2
1
1
0
0
1
1
1
1
1
1
1
2
1
1
1
2
0
0
1
0
0
0
0
0
1
1
0
1
0
0
2
0
1
1
2
1
2
1
0
0
1
0
2
2
0
2
2
1
0
0
0
1
1
0
1
1
0
1
2
1
1
0
1
1
1
0
1
0
2
1
0
1
0
0
1
0
0
2
1
1
1
2
2
1
0
0
1
0
1
0
0
2
2
1
0
1
1
1
2
1
2
1
1
0
2
3
1
0
0
1
2
1
1
0
1
2
1
0
2
2
0
1
1
1
1
2
1
1
2
2
2
0
0
1
0
0
1
0
2
0
1
1
0
1
1
1
1
0
0
1
2
2
0
0
1
1
0
2
0
2
1
0
2
2
2
1
0
0
0
1
1
1
1
1
0
0
0
0
0
1
2
2
0
2
0
0
2
0
1
1
1
0
2
1
2
1
1
1
1
2
1
0
2
1
1
1
0
1
2
2
1
2
1
2
1
0
0
1
2
1
1
0
1
1
2
1
2
0
1
1
0
1
0
0
1
1
0
2
0
0
1
1
0
0
0
0
0
0
2
0
1
1
0
0
2
2
0
1
2
0
2
2
1
1
1
1
0
1
2
2
1
0
2
1
2
1
0
1
1
3
1
1
1
1
2
1
0
1
2
0
0
0
2
0
1
0
1
2
1
1
0
1
1
1
2
1
0
1
1
1
1
0
1
1
1
2
2
2
1
0
1
1
1
1
1
2
2
2
1
1
0
2
1
2
0
1
1
0
0
2
0
0
1
3
0
0
1
1
1
2
0
0
1
1
1
2
1
2
0
1
2
1
1
0
0
6
1
2
0
2
0
0
1
1
1
1
1
0
1
0
1
1
0
0
0
1
1
1
2
1
1
2
1
2
0
1
2
0
1
1
2
1
1
0
2
0
0
1
0
1
2
0
1
1
1
1
1
1
1
1
0
1
2
1
0
2
1
1
1
0
0
0
1
1
0
1
0
0
0
0
0
0
1
2
0
1
2
0
0
1
1
1
1
0
1
1
1
1
2
2
1
1
1
1
1
0
0
1
1
2
1
1
0
0
1
1
1
1
2
1
1
1
2
0
1
0
0
0
0
0
1
1
2
2
1
0
2
0
0
1
2
2
0
1
1
1
0
1
1
1
0
1
0
0
2
1
0
2
2
0
1
0
0
0
1
1
2
0
1
0
0
0
0
1
1
0
2
1
2
1
2
0
1
0
0
0
2
1
1
1
1
1
0
1
2
0
0
0
1
1
1
0
1
1
1
3
1
1
1
2
1
0
1
1
1
2
2
0
4
2
1
0
1
0
2
1
0
1
1
2
1
0
1
1
0
1
2
0
2
1
1
0
1
2
0
2
1
1
0
2
0
1
0
1
1
1
0
1
2
1
0
1
1
1
1
1
2
0
0
0
2
2
2
2
0
1
1
2
0
2
1
3
0
2
2
2
2
0
1
1
0
1
2
1
1
1
1
1
1
0
1
1
0
2
1
2
1
1
0
1
1
1
0
2
2
1
2
0
0
2
0
0
0
1
2
2
0
2
0
1
2
1
0
1
0
3
0
0
1
0
2
1
1
1
1
2
1
2
1
2
0
0
1
2
1
0
0
1
2
2
1
0
1
3
0
2
1
1
0
1
1
1
0
0
1
1
0
1
2
2
2
2
1
1
0
1
1
1
0
0
0
0
0
1
2
2
1
2
0
1
1
1
2
0
2
2
2
0
1
1
2
1
0
2
1
2
1
0
1
1
0
1
1
1
1
0
1
1
1
0
0
0
0
1
0
0
2
1
1
0
1
1
2
1
0
1
1
0
1
0
1
1
2
0
1
0
1
1
1
2
1
1
2
1
1
1
1
2
1
1
0
2
1
1
0
1
1
1
2
1
1
1
1
0
1
1
0
1
1
1
1
0
1
1
2
1
0
2
1
3
0
0
0
1
0
2
1
0
1
0
1
0
1
1
0
0
2
1
0
2
1
0
0
2
2
2
0
1
2
0
0
1
1
0
0
1
0
0
1
0
2
1
0
2
1
1
1
2
1
0
2
0
2
0
2
2
0
0
1
0
0
1
0
1
2
1
0
1
1
0
1
1
2
1
1
1
1
1
1
2
1
1
0
1
1
3
1
2
1
1
1
2
1
0
2
1
0
0
1
1
2
1
1
1
1
1
3
1
2
0
0
1
1
2
0
0
1
0
0
1
0
1
1
0
2
2
0
1
0
1
1
1
1
0
1
1
2
2
0
0
1
1
0
0
0
0
2
0
1
2
1
1
2
2
0
1
2
1
0
1
1
1
0
0
1
2
1
2
1
0
2
1
0
1
1
1
1
1
0
1
1
1
1
1
1
0
2
0
0
1
0
1
0
2
0
1
1
1
0
0
1
1
0
0
1
2
1
1
1
0
1
1
0
0
1
0
1
1
1
0
2
0
0
2
1
0
0
1
1
1
1
0
2
1
1
1
1
1
2
2
2
0
2
1
1
1
1
1
1
1
1
0
0
1
0
1
1
1
5
1
1
2
2
0
1
0
0
1
0
0
0
2
2
1
0
2
0
2
0
1
0
0
1
1
0
1
2
0
1
2
1
1
0
1
1
0
0
2
1
1
1
0
0
2
0
2
2
0
0
1
1
1
0
1
1
3
1
2
1
4
2
1
2
1
1
0
0
0
1
0
1
0
2
0
0
0
0
2
2
1
1
1
1
0
0
0
2
2
2
0
1
1
1
1
2
1
1
0
1
1
2
1
1
2
1
1
0
2
2
0
1
0
2
2
2
1
1
0
1
0
2
0
1
0
1
0
1
1
1
1
1
1
1
1
1
0
2
1
0
0
1
0
0
2
1
2
1
0
2
1
1
1
1
1
0
1
1
0
1
2
2
1
1
0
2
0
1
0
1
1
0
1
0
2
1
0
2
1
2
1
1
1
0
0
2
1
0
2
1
2
1
0
0
1
1
1
0
2
1
1
1
0
2
2
0
2
1
1
1
1
2
0
1
2
1
2
1
2
1
1
0
1
1
1
2
0
0
0
0
1
1
1
1
1
1
0
1
0
1
1
1
2
1
1
1
2
0
0
1
0
1
1
0
1
2
1
2
0
2
2
2
0
0
1
2
1
0
0
1
2
1
2
0
0
2
1
1
1
2
1
2
1
1
0
1
1
2
0
1
0
2
0
1
1
2
2
1
1
1
0
0
2
0
1
1
0
1
1
0
2
2
4
1
1
1
2
0
2
2
3
1
1
0
0
1
0
1
0
0
0
2
1
0
2
0
2
2
0
1
0
0
1
0
2
0
0
0
2
1
0
2
1
3
1
1
1
1
1
2
1
0
2
0
2
0
1
1
2
2
1
1
0
1
1
1
1
2
1
0
0
2
0
0
2
0
0
0
1
0
1
1
0
1
1
0
1
0
0
0
0
1
1
2
0
1
2
1
1
0
1
1
1
1
1
0
1
2
0
0
1
2
0
1
2
2
1
0
0
2
1
2
1
1
1
4
1
1
2
1
2
0
1
2
2
2
0
1
4
1
1
2
1
0
2
2
1
1
3
1
2
1
2
0
1
0
1
1
2
1
1
1
0
2
2
0
1
1
1
3
1
0
1
2
0
3
1
0
1
0
2
2
1
1
0
2
1
2
0
2
0
0
0
0
0
1
0
0
0
1
0
1
1
2
2
2
1
2
1
2
0
2
1
1
1
0
1
1
2
1
2
0
0
0
1
0
2
1
0
1
1
1
2
0
2
1
1
2
1
1
1
1
1
2
0
2
1
1
1
1
2
0
1
0
2
1
0
0
1
2
1
1
1
0
0
0
0
1
0
1
1
2
1
0
2
0
1
2
1
1
0
2
1
1
1
1
1
1
1
1
0
2
2
1
1
1
1
1
2
0
0
0
2
1
2
0
1
1
1
1
0
1
0
1
0
0
0
1
1
0
1
1
0
1
0
0
0
1
1
1
1
2
1
2
1
1
0
1
1
0
2
2
1
1
1
1
1
0
0
1
1
0
1
2
0
2
0
2
0
1
2
0
2
0
3
1
1
0
0
1
1
1
0
1
0
1
0
0
0
1
2
0
2
1
0
1
0
1
1
0
1
1
3
0
1
0
3
1
2
1
0
1
0
1
1
1
0
1
1
1
1
1
2
1
4
0
1
1
2
1
0
0
1
1
1
0
2
1
1
0
1
0
1
0
2
1
2
2
1
1
1
0
0
1
2
1
1
2
1
1
1
1
0
1
1
0
1
0
2
0
2
1
1
1
0
0
2
0
0
1
1
2
1
0
1
1
1
1
1
1
1
1
2
1
2
1
3
1
1
0
1
2
1
1
1
1
1
2
1
1
2
2
1
1
0
2
1
1
2
0
0
1
1
1
1
1
1
1
1
0
1
0
1
1
0
0
0
0
1
4
2
2
2
2
1
2
1
0
1
1
1
0
0
0
0
1
1
2
1
0
2
1
1
0
1
1
0
1
1
0
0
0
0
1
1
2
1
2
0
1
1
1
2
0
0
1
1
1
1
1
0
1
1
0
0
1
2
2
2
1
1
1
0
1
2
2
0
1
0
2
1
2
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
0
1
0
2
2
0
2
0
2
1
1
1
2
1
1
0
1
1
0
0
0
1
1
0
4
0
2
0
1
2
1
2
1
1
1
2
0
1
0
0
1
2
1
1
1
2
1
0
2
2
1
1
0
1
1
0
1
0
0
2
1
0
1
1
2
1
2
1
1
1
0
1
1
1
1
1
1
0
1
1
1
1
1
1
0
1
1
2
1
2
1
1
0
1
2
0
1
2
0
0
2
0
2
0
0
0
0
0
1
2
2
2
1
2
2
1
0
0
0
0
1
1
0
1
0
1
0
0
1
1
2
2
2
0
0
2
0
1
1
2
1
1
1
0
1
0
1
0
0
2
0
1
0
0
1
2
1
1
1
1
1
1
0
1
1
2
4
0
2
1
1
1
2
1
1
0
0
1
1
0
1
1
0
2
2
0
4
1
2
2
2
0
3
1
1
1
2
1
1
0
1
1
1
0
2
1
1
1
1
0
2
1
1
1
1
0
1
1
0
1
1
0
0
1
0
0
2
2
0
1
0
0
2
0
2
1
2
2
2
0
0
1
2
1
0
2
2
1
0
1
1
1
0
2
1
2
3
2
2
1
3
0
1
1
1
2
1
0
0
1
2
0
0
0
2
2
1
1
1
0
3
3
1
2
1
2
1
0
1
1
0
1
0
1
0
1
1
2
1
1
1
0
1
0
2
0
0
1
2
1
1
0
0
1
1
0
0
2
2
0
1
0
1
0
0
0
1
0
1
0
1
2
2
0
1
0
2
0
1
1
1
1
2
2
1
1
1
2
2
2
1
0
1
1
0
2
2
1
0
1
1
1
0
1
1
1
1
2
0
2
0
2
2
1
0
2
1
0
0
2
1
1
2
1
1
1
1
2
0
0
2
2
0
2
0
1
1
0
1
2
1
1
1
1
1
1
1
1
0
0
1
1
3
1
0
1
2
1
1
0
1
2
1
1
0
2
1
0
1
1
0
0
1
2
1
1
2
0
1
1
0
0
2
1
2
0
1
0
2
2
1
1
2
0
2
1
1
1
2
0
0
1
1
1
0
0
2
0
1
1
0
1
0
0
2
1
1
1
2
0
2
2
0
2
1
2
1
3
2
1
5
0
2
1
2
0
0
0
1
1
2
1
1
0
0
1
1
1
2
1
1
1
1
1
0
2
0
1
1
1
1
1
0
0
0
2
0
1
0
1
1
1
0
1
2
1
1
2
0
1
2
0
0
0
1
1
0
0
1
0
0
2
2
1
2
1
1
1
1
1
1
0
2
0
0
1
0
2
1
2
1
1
2
1
1
1
2
2
0
1
2
1
2
0
1
1
1
1
2
1
0
2
2
0
2
1
2
0
2
1
0
2
1
0
2
1
1
1
1
1
2
1
2
1
1
0
1
1
0
1
0
0
1
0
0
0
1
1
0
0
0
1
0
1
1
0
0
0
0
1
1
1
1
1
1
0
0
2
0
0
1
1
0
2
1
1
0
1
2
0
2
1
0
1
0
0
1
2
0
1
2
1
0
1
0
2
2
1
0
1
0
2
1
2
1
1
0
1
1
2
2
1
1
0
2
1
2
2
0
1
1
2
1
1
2
0
0
1
1
1
1
0
2
1
1
2
2
1
0
0
1
1
1
1
1
1
1
1
0
1
1
0
1
1
1
1
2
1
2
1
0
1
1
1
0
0
0
1
1
0
0
2
0
1
1
1
2
1
2
1
2
1
1
1
1
0
2
1
1
2
2
1
0
2
2
1
1
1
0
0
1
1
1
0
1
1
1
2
1
1
0
1
0
2
2
0
1
1
0
2
1
0
0
3
2
1
1
2
1
0
1
1
0
0
1
1
1
2
1
1
0
2
0
0
2
1
0
1
0
0
1
1
1
0
1
0
0
2
1
2
1
0
1
2
1
2
1
1
1
0
0
1
1
1
1
0
1
1
1
0
0
1
2
0
0
2
1
1
1
1
0
1
0
2
1
2
1
2
0
1
2
1
0
2
1
0
1
1
2
1
1
2
0
0
1
2
1
1
1
0
1
2
0
1
0
0
0
2
2
1
1
1
0
2
1
1
2
1
1
0
1
2
0
1
0
0
1
2
1
0
2
0
0
1
1
0
0
2
2
2
1
1
1
1
1
3
1
2
1
0
3
2
1
0
1
1
2
0
1
2
0
0
1
1
1
1
1
1
1
0
1
1
2
1
2
0
1
1
1
2
1
1
1
2
1
1
1
1
1
0
3
0
1
1
1
2
2
2
2
0
1
2
1
1
2
0
1
1
0
1
0
1
2
1
0
1
1
1
3
2
3
0
1
1
1
1
1
1
1
1
2
2
0
1
0
1
3
0
1
1
1
2
1
0
0
1
2
1
1
1
1
2
2
2
1
2
0
0
1
2
1
1
1
2
1
1
0
2
0
0
1
0
0
1
0
0
1
1
1
1
1
1
1
1
1
2
0
1
2
2
1
1
0
1
2
2
1
0
1
1
1
1
2
1
0
2
0
0
1
1
1
1
1
0
0
0
0
1
2
2
0
0
2
1
2
1
0
1
1
1
2
2
0
1
1
1
0
0
1
1
1
0
0
0
0
0
0
1
1
0
1
1
1
2
1
1
1
2
1
1
2
1
1
3
2
1
0
0
1
1
0
1
1
2
1
2
0
0
0
0
1
1
1
2
1
0
0
0
1
0
2
2
1
0
1
0
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
3
0
1
0
2
1
1
1
1
1
1
1
1
0
1
0
1
1
2
1
1
1
1
1
1
1
2
2
1
2
0
1
1
1
0
1
1
0
1
1
1
1
1
0
1
1
1
2
1
0
1
1
0
1
1
1
1
1
2
1
0
1
2
1
1
1
2
1
1
1
0
1
1
2
0
2
2
1
2
1
2
0
1
0
1
0
1
4
0
1
0
0
1
0
1
1
1
1
1
1
1
0
1
2
1
1
1
1
0
0
0
1
0
1
1
0
0
1
1
0
1
1
1
2
2
0
0
1
2
0
1
1
1
1
0
2
1
1
1
0
2
0
2
2
2
1
1
1
2
2
2
1
2
1
0
2
2
1
0
1
1
2
1
2
2
2
0
2
1
0
0
1
0
1
0
2
1
2
0
1
0
1
0
1
2
2
0
2
2
2
1
0
0
1
1
1
1
1
0
2
0
0
2
1
1
1
1
1
1
2
0
0
0
0
1
1
0
1
2
0
0
1
2
1
1
2
1
0
1
1
1
1
1
1
1
0
2
1
0
1
1
1
2
1
0
0
0
1
1
0
1
0
0
1
0
2
1
1
0
1
0
0
1
1
1
1
1
2
0
2
0
0
0
2
0
0
0
1
1
1
2
1
1
1
0
1
1
1
1
2
2
0
1
1
0
2
0
1
0
2
2
0
1
0
1
1
0
0
1
1
0
0
0
1
0
0
1
3
1
2
1
0
1
1
1
0
1
0
1
1
0
1
0
2
2
1
0
0
1
0
1
1
0
1
0
0
1
0
1
1
2
0
2
1
1
1
0
1
1
2
0
1
0
0
2
1
1
2
0
0
0
0
0
1
1
1
1
1
1
1
1
0
0
1
2
0
0
2
1
0
1
0
2
2
0
1
1
1
2
2
0
1
2
0
1
1
0
1
1
1
1
4
2
0
1
1
1
1
0
0
0
1
1
2
1
0
1
1
1
2
1
0
1
0
1
0
0
1
0
0
1
2
0
1
2
0
1
0
2
0
0
0
0
1
0
0
0
1
1
1
2
0
1
1
0
2
0
1
1
0
1
0
0
2
1
0
1
1
4
2
0
0
2
2
1
1
1
2
0
0
1
2
1
2
1
1
2
0
1
2
2
0
2
1
2
1
1
1
2
0
0
1
1
0
0
0
1
2
0
1
1
1
1
1
0
0
1
0
2
0
0
2
0
0
0
1
0
1
2
0
1
0
1
1
1
0
2
1
1
1
2
0
1
1
2
1
1
1
1
2
0
1
1
0
1
2
0
1
2
0
1
1
1
0
0
2
0
0
0
1
1
2
1
0
2
0
1
1
2
0
0
1
0
1
2
1
1
2
1
2
1
1
1
2
1
0
0
1
1
0
2
1
1
1
1
1
0
2
2
0
0
2
1
0
0
1
2
0
3
1
0
3
1
1
1
2
2
1
2
1
1
0
0
1
1
1
1
0
2
0
0
1
1
1
1
1
1
1
0
1
0
0
2
1
1
3
2
1
1
0
1
0
2
1
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
0
1
1
1
1
0
2
2
1
1
1
1
3
1
0
0
3
1
2
1
2
2
0
0
1
2
0
2
0
1
1
1
1
0
1
1
2
1
0
1
1
1
2
2
1
1
2
0
2
0
1
1
1
1
2
1
0
1
1
2
0
0
1
0
1
1
1
1
0
1
1
1
0
1
2
0
0
1
1
1
1
1
1
0
1
1
0
1
0
0
1
1
1
2
0
1
1
0
1
1
1
0
2
1
3
1
1
2
0
0
2
3
1
0
1
0
0
0
1
0
1
1
2
1
1
1
0
1
1
0
1
1
1
2
1
0
1
1
0
2
2
1
1
1
1
1
1
1
1
1
0
0
1
1
1
0
0
1
1
1
1
1
2
1
1
0
1
4
1
2
1
1
1
0
2
0
1
1
1
1
0
2
3
1
1
0
0
0
1
1
2
1
0
3
0
2
2
1
0
0
1
1
0
1
2
1
1
0
0
0
3
1
1
4
0
2
2
0
4
0
2
3
1
1
1
0
1
0
2
0
0
1
1
2
1
1
1
1
0
0
2
1
1
2
1
2
0
1
2
0
0
1
2
2
0
2
0
1
1
0
1
1
0
0
1
1
2
0
2
2
1
1
1
1
1
1
1
1
1
0
0
1
1
0
0
1
1
1
1
2
0
1
1
2
1
1
0
0
0
1
1
1
0
1
1
0
1
0
1
1
0
1
2
1
2
1
0
0
1
2
0
0
1
0
0
0
1
2
1
2
0
1
0
0
2
2
0
1
1
1
2
2
1
2
1
2
1
0
1
2
1
0
0
1
2
1
0
0
2
1
0
1
1
1
2
0
2
2
0
1
1
2
0
2
1
0
1
2
0
0
1
1
0
0
1
2
1
0
1
2
0
2
0
2
0
0
1
2
0
2
1
0
1
1
2
1
3
2
2
0
0
1
1
1
2
1
1
2
0
2
1
0
1
2
1
2
0
1
1
1
1
3
1
1
0
2
1
2
2
1
1
1
0
2
1
1
1
0
2
1
1
1
1
1
0
2
1
1
1
1
1
1
0
2
1
0
3
0
0
0
1
1
2
2
1
2
2
2
1
1
1
2
1
1
1
1
2
2
1
2
1
1
2
1
2
1
1
2
1
2
1
0
0
0
2
0
0
1
1
2
1
1
1
2
2
1
0
1
0
2
1
2
0
0
1
0
1
1
0
1
1
1
2
0
1
1
1
1
1
1
2
2
1
0
0
1
1
0
1
1
0
0
1
1
1
1
2
1
1
1
1
0
1
1
0
0
2
2
2
0
0
1
0
1
0
4
1
1
0
0
2
2
1
0
0
0
1
0
1
2
2
1
2
0
2
1
1
1
1
1
0
1
0
2
1
0
1
0
1
2
3
1
1
0
2
1
2
2
0
0
1
0
1
1
2
0
2
0
1
0
1
0
2
0
1
0
2
1
1
1
1
0
2
3
0
0
0
1
1
0
1
0
1
0
1
0
2
0
0
2
1
1
0
1
1
1
1
0
1
1
1
1
1
2
1
2
2
2
1
1
0
0
1
1
1
1
2
0
2
1
3
0
0
0
1
1
1
1
0
1
1
1
1
1
1
0
1
2
0
1
0
0
1
1
0
0
1
0
0
1
0
0
1
1
1
2
0
1
0
0
1
0
1
1
1
1
1
2
1
2
1
1
1
2
2
1
0
2
1
2
3
1
1
0
0
0
1
1
0
0
2
1
1
2
0
1
2
1
0
1
0
0
0
0
0
1
1
0
0
1
1
2
1
2
0
1
1
1
1
0
0
1
1
0
2
2
0
1
0
0
1
1
1
1
1
0
0
2
1
1
0
1
2
2
2
1
0
2
0
2
0
2
1
0
1
1
0
1
0
1
0
1
2
1
2
1
1
0
1
1
2
0
1
1
1
1
1
1
1
2
0
2
0
2
0
1
0
2
2
0
1
2
1
2
0
1
1
0
2
2
0
1
1
0
1
1
1
1
1
2
0
0
0
1
1
1
0
0
0
0
1
0
1
0
1
1
1
0
0
2
1
0
1
3
2
1
1
2
1
0
1
1
1
2
1
1
1
1
1
2
1
0
2
7
0
0
0
1
0
0
2
0
0
1
2
1
1
0
1
1
1
0
0
0
1
1
1
0
1
1
1
3
0
2
1
0
2
0
0
1
1
2
1
0
3
1
1
1
1
0
0
1
1
1
1
0
2
2
1
0
2
1
1
0
0
1
1
0
0
1
1
1
1
3
0
2
2
1
0
1
1
0
1
0
1
2
0
0
0
1
1
0
1
1
0
2
1
2
1
1
0
0
0
1
1
2
2
0
1
1
1
1
2
2
0
0
2
2
2
0
1
1
0
2
1
1
1
0
0
0
0
1
2
2
1
1
2
0
1
1
2
1
0
0
0
0
1
2
0
2
2
0
1
2
2
2
1
2
2
1
1
1
1
0
1
0
1
1
1
0
1
1
1
0
2
1
2
1
1
1
1
1
1
1
1
1
0
2
0
0
0
1
0
1
1
1
1
0
0
1
1
1
1
1
2
2
1
2
1
1
2
0
1
0
1
1
1
0
1
2
1
1
0
0
1
0
1
1
0
1
1
1
2
1
2
3
2
0
1
0
0
0
1
2
2
2
1
1
1
2
0
1
2
1
2
2
1
1
2
1
1
2
0
2
1
1
1
1
1
1
0
1
2
0
0
1
1
0
1
0
1
2
1
0
1
1
0
3
1
1
1
2
2
0
1
1
0
2
1
1
1
1
1
2
2
1
2
1
0
1
0
1
2
0
0
0
2
2
2
1
1
2
0
0
1
0
0
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
2
0
0
0
0
1
1
0
0
1
1
0
1
1
2
2
2
2
0
1
2
2
1
1
2
2
1
0
0
1
2
1
1
1
1
1
0
0
0
1
1
0
0
2
0
1
0
1
1
1
1
1
2
1
1
1
4
1
1
2
1
1
1
2
1
1
1
0
0
0
1
0
1
0
0
1
1
1
0
1
2
2
0
1
1
1
1
1
1
1
1
1
0
0
0
0
1
1
2
1
2
1
1
1
2
1
0
1
1
0
1
1
1
1
1
1
1
2
1
0
2
1
1
1
1
2
1
2
1
1
1
2
0
1
1
0
1
2
2
1
1
1
1
2
1
0
0
1
1
1
0
1
0
0
0
1
0
2
1
0
0
0
1
0
0
0
0
1
1
1
1
1
1
0
0
1
2
1
1
0
2
0
0
1
1
1
1
2
2
1
1
1
0
0
2
1
2
1
0
1
0
1
1
1
2
1
1
0
1
0
2
0
1
0
0
0
1
1
2
0
2
0
1
0
2
0
1
1
0
2
0
2
2
0
2
2
0
1
1
0
1
2
0
1
1
1
0
0
1
2
3
0
1
1
0
1
3
1
0
1
2
1
0
2
0
2
0
0
0
2
2
2
0
1
1
0
1
1
1
0
1
1
0
1
1
1
2
0
0
0
2
0
2
0
0
0
1
1
0
0
0
0
1
2
1
2
0
1
2
0
2
1
1
1
1
3
1
2
2
0
1
0
1
1
0
1
1
1
0
1
1
2
0
2
1
1
1
1
1
2
1
0
1
0
1
1
1
2
1
0
0
1
1
0
1
2
2
0
1
0
1
2
0
1
1
2
2
1
1
0
1
1
0
1
1
1
1
2
1
3
0
0
1
1
1
0
2
1
1
2
2
1
3
1
3
2
1
1
1
2
0
2
0
1
1
0
0
0
1
1
1
0
0
1
2
2
2
2
1
1
1
0
0
0
0
0
1
1
3
2
2
1
1
1
2
1
0
1
2
2
1
1
0
1
2
3
0
1
1
1
1
0
2
0
0
0
0
0
0
1
1
0
1
2
1
1
2
0
2
2
1
0
1
2
1
1
0
2
0
2
0
1
0
0
0
1
2
2
0
0
1
1
2
2
2
2
1
0
2
1
2
2
1
1
1
1
2
1
1
2
2
1
1
1
1
1
0
1
1
2
0
1
0
1
1
1
1
1
1
0
1
0
1
2
2
1
1
2
1
1
2
1
0
1
2
2
1
1
1
1
0
1
1
1
0
0
0
0
1
2
0
2
0
0
4
0
0
0
0
1
2
0
1
1
0
1
0
2
1
2
1
0
1
1
0
1
2
1
1
0
1
0
3
1
1
1
2
1
1
1
1
2
2
0
1
1
2
0
2
0
1
1
3
1
1
1
0
1
2
2
0
1
2
0
0
1
1
0
2
2
0
2
1
2
2
1
0
1
2
2
2
2
2
1
1
1
1
0
0
1
0
1
0
0
0
2
0
1
0
1
2
1
1
2
1
1
2
0
2
1
0
1
1
1
0
1
0
1
2
1
1
1
0
0
0
1
1
1
0
0
0
1
1
0
1
1
1
0
1
2
1
2
2
2
1
1
1
0
1
1
2
2
1
1
0
2
1
1
2
2
0
2
1
1
1
1
1
2
2
0
0
1
1
0
2
1
0
0
2
0
2
1
2
0
1
1
1
1
1
2
1
1
1
2
1
1
1
2
1
1
1
0
0
1
1
2
1
0
2
2
1
2
0
0
2
1
1
0
1
0
0
1
1
1
0
2
0
1
1
2
1
0
1
0
0
0
1
2
1
0
1
2
1
1
1
1
2
0
0
1
1
1
2
1
0
1
2
1
1
1
1
1
1
1
1
0
1
0
0
1
2
0
2
1
0
0
0
2
0
2
0
1
0
1
2
2
1
1
1
0
2
1
1
0
0
2
1
1
1
0
0
1
1
1
1
1
1
0
1
1
0
2
1
1
2
2
2
1
3
1
1
0
1
2
1
1
1
1
1
1
1
1
0
1
0
0
0
1
1
2
1
0
0
1
2
2
1
2
0
1
1
2
1
2
0
2
0
1
1
0
1
1
1
0
2
1
0
1
1
1
2
1
1
2
1
1
2
1
1
1
1
0
1
0
1
1
1
2
0
2
2
1
0
0
1
0
0
1
1
1
0
0
0
0
1
2
0
0
1
2
1
1
1
0
1
2
1
0
2
0
1
1
0
1
0
0
1
1
0
1
1
0
1
1
1
1
1
1
2
0
1
1
0
1
1
2
1
0
1
1
0
1
2
2
1
1
1
1
1
2
1
3
1
2
0
1
1
1
0
2
1
2
1
0
1
0
0
1
0
2
1
0
0
2
2
1
0
0
1
2
2
1
1
0
2
0
0
1
1
0
1
0
1
1
1
0
0
0
2
0
0
0
1
1
0
0
2
1
0
0
0
3
1
2
1
0
2
1
0
1
2
1
1
1
1
1
1
0
1
0
1
0
0
1
0
0
2
1
1
0
1
2
1
0
1
1
1
1
1
0
0
1
1
1
1
2
0
0
1
0
0
1
2
0
0
0
2
2
0
1
1
0
2
1
1
0
1
1
2
1
1
2
1
1
1
0
1
2
0
0
2
1
2
1
2
1
1
1
0
2
1
1
0
2
0
0
2
0
1
1
1
1
2
2
1
2
1
1
1
0
0
3
1
1
2
0
1
2
1
1
1
1
1
2
0
1
2
1
1
1
0
0
2
0
0
0
2
1
1
1
1
1
2
0
1
0
0
2
0
1
1
1
1
1
2
1
1
1
2
0
1
0
1
1
2
2
2
1
1
1
0
1
0
1
0
2
2
1
2
1
2
0
0
1
0
1
0
2
0
1
0
2
1
2
2
0
2
1
0
0
1
1
0
0
0
1
0
2
2
0
2
1
1
1
1
2
0
1
1
1
1
0
1
0
0
0
3
0
2
1
2
1
1
0
1
1
1
1
1
0
0
0
1
1
0
1
1
1
1
1
1
2
1
2
0
2
1
0
1
1
2
0
0
0
1
0
2
1
2
2
1
1
0
1
0
3
0
0
1
0
1
0
0
1
1
1
0
0
1
0
1
0
2
0
1
1
1
1
1
0
2
1
0
1
1
1
1
2
1
2
1
1
1
1
0
1
0
0
0
1
1
1
0
3
1
0
1
2
1
0
0
0
0
0
1
2
1
0
1
2
0
3
1
1
2
2
1
2
2
1
0
0
1
1
0
0
0
0
1
1
1
1
2
0
2
0
1
0
2
1
1
0
0
1
0
1
1
1
2
1
1
1
2
1
1
1
1
1
1
2
1
0
2
2
2
1
2
2
1
1
2
0
0
2
0
1
1
0
2
1
1
1
0
0
0
1
1
0
2
1
0
1
2
1
0
0
0
0
2
0
1
1
0
1
1
1
0
0
0
0
2
1
0
2
1
2
1
1
1
1
1
1
1
0
1
1
1
2
2
1
2
2
0
1
1
2
2
2
1
1
0
2
1
1
0
1
0
1
1
2
1
0
2
1
2
1
1
2
1
2
2
1
1
0
0
1
1
0
1
2
1
0
1
2
2
1
1
2
1
0
0
1
1
1
2
1
0
0
2
1
1
1
1
1
2
2
0
1
1
1
1
0
0
2
1
2
0
1
1
0
0
1
1
0
1
0
2
0
1
2
1
5
1
1
0
2
1
1
1
0
1
1
0
1
1
1
2
0
1
2
2
1
1
1
0
1
1
1
0
0
2
1
1
1
1
2
2
0
1
1
1
1
2
0
0
1
1
1
1
1
0
0
1
1
1
0
0
0
2
2
0
0
1
0
0
1
1
2
0
0
1
0
2
1
2
2
0
1
1
1
1
0
1
0
0
1
2
2
2
2
0
1
0
0
1
1
1
0
1
1
1
1
1
2
1
1
1
0
1
2
8
1
1
1
0
1
2
1
1
2
1
0
0
2
2
0
0
2
0
1
1
0
2
1
1
1
1
1
1
1
1
0
1
2
1
0
0
0
1
1
0
1
1
1
1
1
1
1
0
1
1
0
0
1
2
2
0
0
1
3
1
1
2
1
0
2
1
1
1
0
1
2
0
2
1
2
1
0
0
1
0
1
2
0
0
1
2
2
1
0
1
1
0
2
0
1
0
0
1
0
2
0
0
1
1
2
1
0
0
0
0
1
1
1
1
1
0
0
0
0
1
2
2
1
1
2
1
1
0
2
0
2
1
1
1
2
1
0
0
0
0
1
2
2
2
0
2
0
2
0
1
2
1
1
1
1
1
0
0
1
1
1
1
1
1
1
1
1
0
0
2
1
1
2
2
2
2
1
2
2
1
1
0
2
1
1
2
0
0
2
1
1
1
1
1
1
0
2
0
1
2
0
0
1
1
1
2
1
0
1
2
0
0
1
1
1
2
0
1
0
1
0
0
2
0
1
1
1
0
2
0
0
0
1
0
1
1
1
1
0
2
1
1
2
0
1
1
0
0
2
2
2
1
1
0
1
2
0
2
1
0
1
0
1
0
0
1
0
1
2
2
2
1
1
0
1
2
2
1
0
2
2
1
1
1
1
2
1
1
1
0
2
1
1
0
0
0
0
1
2
1
0
0
1
1
0
1
2
0
1
0
2
0
1
0
1
1
0
1
1
0
1
1
0
1
2
1
2
0
1
1
1
1
1
1
1
2
1
2
0
2
1
3
1
1
2
1
0
1
0
0
1
1
1
1
1
0
1
1
2
0
1
0
0
0
1
1
2
2
1
1
3
1
1
1
0
0
0
2
2
1
1
2
1
1
0
1
2
1
0
1
1
1
1
1
2
1
1
1
0
1
2
0
1
0
0
2
0
0
0
1
1
1
1
1
1
1
1
1
0
0
1
2
0
0
1
0
0
1
2
0
2
2
0
1
1
2
0
0
2
1
0
0
2
0
1
1
0
2
0
1
1
0
2
0
1
2
1
1
0
1
2
0
1
1
1
0
2
1
1
1
0
2
0
1
1
1
1
1
2
2
1
1
1
0
1
0
1
1
1
1
2
1
2
1
0
1
2
1
2
1
2
1
1
1
2
0
0
1
0
1
1
1
0
1
1
1
2
2
2
1
2
0
0
2
1
1
2
2
1
0
0
1
0
1
2
0
2
0
0
1
2
1
2
1
1
0
0
1
0
1
0
2
2
0
0
0
1
1
1
0
0
1
0
1
1
1
1
1
1
1
2
1
0
2
0
1
1
1
0
0
1
0
1
1
2
2
1
1
2
1
1
2
0
2
0
2
0
1
1
0
1
0
1
0
1
1
2
0
2
1
1
1
1
3
2
1
1
2
0
2
0
1
1
1
0
1
1
1
0
1
1
1
2
0
1
3
1
2
0
0
1
1
1
1
2
1
1
9
2
1
0
1
1
1
1
1
0
1
0
2
1
0
2
0
0
1
0
1
0
1
1
0
2
1
0
1
0
0
1
1
0
1
2
1
0
1
0
8
0
1
1
2
1
0
2
0
1
0
0
0
1
1
2
2
1
0
3
2
0
0
0
0
1
1
1
1
1
0
0
1
0
1
2
1
1
2
1
1
0
1
1
1
1
1
0
0
1
0
1
2
2
0
0
2
0
1
0
2
1
1
0
0
1
1
0
1
0
1
0
1
1
0
1
1
0
1
1
1
1
2
1
1
1
2
1
0
1
0
2
0
0
1
1
1
0
0
0
1
1
1
2
1
2
0
2
1
1
1
1
1
1
0
1
1
1
1
2
1
2
1
1
0
0
2
0
2
2
2
1
2
0
1
2
0
0
1
2
1
2
1
0
0
0
0
2
1
0
1
1
2
1
1
1
1
1
0
0
1
2
2
1
2
1
1
2
1
2
2
1
0
1
1
1
0
0
1
0
2
2
1
0
1
1
1
0
1
1
2
1
1
1
2
2
1
2
2
1
2
0
1
1
1
1
0
0
1
0
0
2
2
0
1
1
1
1
0
2
0
2
1
1
0
2
1
2
2
0
1
1
2
0
1
1
0
1
1
1
0
1
0
1
2
1
1
0
2
1
2
1
0
1
1
2
2
0
0
1
1
1
2
1
2
1
1
0
0
2
1
2
1
1
0
1
0
0
2
0
2
0
0
2
0
1
1
0
0
2
0
1
2
0
0
1
0
0
0
1
1
1
0
1
1
1
1
0
2
2
1
1
1
0
1
1
1
1
0
1
0
2
0
1
0
2
1
1
2
1
0
1
2
2
1
1
2
0
0
1
0
1
0
1
1
1
2
0
2
1
0
0
0
2
2
2
0
0
1
0
1
1
1
3
1
1
2
2
0
0
2
1
0
1
0
2
1
1
0
1
0
1
0
1
0
1
2
1
1
0
0
1
1
1
2
2
0
2
1
0
2
0
0
1
1
0
0
2
1
2
0
2
1
2
1
1
1
0
1
1
1
1
1
2
2
2
1
1
0
2
1
0
2
1
2
0
0
1
2
2
0
2
0
1
1
0
0
1
1
1
1
1
1
1
0
0
0
1
2
0
1
2
1
1
1
1
1
0
2
0
0
0
0
0
2
0
0
2
1
3
1
1
1
2
1
1
1
1
1
0
0
1
1
1
2
0
1
1
1
1
2
0
2
2
0
2
0
2
1
0
1
0
1
1
1
1
1
1
1
0
1
1
0
0
0
1
1
1
0
1
0
1
2
0
0
1
0
1
1
1
1
1
1
2
0
1
2
0
1
0
2
2
0
0
0
1
1
1
2
1
2
1
2
2
2
1
1
0
1
1
0
1
2
1
1
0
1
2
0
1
0
1
0
2
1
0
1
1
0
0
2
1
0
1
1
1
1
1
1
0
0
1
1
1
1
1
1
1
1
2
1
2
0
1
1
2
0
1
1
1
0
1
0
1
0
2
0
1
2
1
2
1
2
2
0
1
2
1
1
1
1
1
0
1
1
1
2
0
1
2
2
2
1
1
1
2
2
0
0
2
1
0
1
3
0
1
1
1
1
3
2
2
1
2
1
2
2
1
1
1
1
1
0
1
1
2
1
0
1
0
0
0
1
0
1
1
1
1
1
1
1
2
0
0
1
0
1
2
2
1
2
1
0
1
1
1
1
0
0
1
0
0
1
2
2
1
0
1
0
1
0
1
0
0
0
1
0
0
1
1
1
1
1
0
1
1
0
2
1
1
2
2
2
1
1
2
1
1
2
1
1
2
0
1
0
2
0
1
0
1
1
0
1
1
1
1
0
0
0
0
1
1
1
1
1
0
2
0
0
1
1
2
2
2
1
1
2
2
1
2
1
0
0
0
1
0
1
2
2
1
1
1
1
2
0
2
0
1
2
1
1
1
1
1
0
1
1
2
1
2
0
2
0
0
1
1
1
1
2
0
2
2
0
2
2
0
2
2
0
1
1
2
1
2
0
2
0
1
2
1
0
0
2
1
0
1
1
1
0
2
1
3
0
0
1
0
1
1
1
2
1
2
0
1
3
1
2
1
1
0
1
2
1
2
0
1
1
2
0
1
2
0
1
1
0
2
0
0
0
2
1
1
1
1
0
3
1
2
0
1
1
1
0
1
1
0
0
1
0
2
2
0
1
0
1
0
1
1
2
2
1
2
1
1
1
2
0
0
1
2
1
2
0
1
1
1
0
0
1
1
2
0
1
2
1
1
1
1
1
1
3
2
1
1
0
0
1
0
1
2
0
1
1
2
1
1
1
0
2
3
0
1
1
0
2
1
1
1
1
0
2
1
2
1
2
1
1
0
2
0
1
1
1
1
0
1
2
2
1
2
1
2
2
0
1
1
1
0
1
0
1
0
0
0
0
1
1
1
0
1
0
1
1
1
2
0
1
1
2
2
2
0
1
0
0
1
0
1
1
2
1
2
1
1
2
1
1
0
0
1
2
1
1
1
1
1
0
0
1
2
0
2
1
2
1
0
0
0
2
2
2
1
2
1
1
0
0
1
1
1
1
1
1
1
1
1
2
1
0
0
1
1
1
2
2
1
1
1
1
1
1
2
0
0
1
1
1
0
1
0
1
1
1
1
1
0
0
1
0
1
0
2
2
1
1
1
1
1
0
2
2
1
1
1
2
1
0
0
1
1
0
0
1
1
2
1
0
1
1
1
1
1
0
0
1
0
1
1
1
1
2
2
2
1
1
1
0
1
0
1
2
0
0
1
1
0
2
2
1
0
0
1
2
2
0
1
1
1
2
0
0
1
1
0
2
3
1
1
0
2
1
1
1
1
0
2
2
1
0
1
2
2
1
1
2
2
1
0
1
0
0
1
1
1
1
2
2
2
0
1
0
0
1
1
1
1
2
1
1
1
1
1
1
1
2
1
0
0
1
0
1
0
2
1
2
0
1
2
1
0
1
1
0
1
1
1
2
1
2
1
1
0
1
1
2
0
1
1
1
1
0
0
1
0
1
2
1
0
0
2
0
0
2
0
2
1
2
2
1
0
0
0
2
2
2
0
2
1
1
0
2
0
0
0
0
1
0
0
1
1
0
2
0
1
2
1
2
1
3
1
2
0
1
0
1
0
1
1
0
0
1
1
0
0
1
0
2
1
1
0
0
1
2
1
2
1
0
3
1
0
1
0
1
1
0
2
1
2
1
2
1
0
2
1
1
1
0
0
0
1
1
0
0
0
1
1
1
1
0
0
1
0
1
0
0
1
1
0
1
0
1
1
1
0
1
0
2
2
1
1
1
0
2
0
1
1
2
2
2
0
1
1
2
1
2
1
2
0
0
1
2
1
1
1
2
2
1
0
2
1
2
1
1
1
1
0
2
1
2
2
2
1
1
0
1
1
1
2
2
0
0
0
0
2
1
1
2
0
0
1
1
2
3
0
1
1
0
1
0
1
1
1
1
1
1
0
0
4
1
2
0
1
1
1
2
1
0
1
0
2
0
1
2
1
0
1
3
0
1
1
0
0
0
2
1
2
1
2
0
2
1
1
0
1
2
2
2
0
2
1
1
2
1
1
2
1
1
2
1
2
1
1
0
0
0
0
0
0
1
1
2
0
1
1
1
2
1
0
2
0
1
1
0
1
1
1
0
0
1
2
1
3
1
1
0
0
1
2
2
0
2
2
0
1
1
1
2
1
2
1
1
0
2
1
3
1
1
0
1
1
2
2
0
2
0
1
1
2
2
1
1
1
0
1
0
0
0
0
1
1
0
1
2
1
1
1
0
0
1
2
2
0
0
1
1
1
2
1
2
1
2
4
2
2
1
0
0
1
1
0
0
2
1
1
1
1
1
0
2
0
1
1
2
3
1
4
0
1
1
2
0
0
1
2
2
0
1
0
0
2
0
3
1
0
0
0
2
2
2
1
1
1
2
3
1
1
1
1
1
2
0
1
1
2
0
1
2
0
1
1
0
1
0
2
2
1
1
1
1
0
1
1
0
1
1
1
0
0
0
2
0
2
0
0
1
1
1
2
1
1
1
2
1
0
1
1
0
2
1
2
0
1
2
1
1
1
1
1
3
1
1
1
1
2
1
0
0
1
1
2
1
0
1
2
3
2
1
2
2
0
1
1
0
3
1
1
1
1
0
1
2
0
1
2
1
1
1
2
2
2
0
2
1
1
0
1
1
1
1
2
1
1
0
2
0
1
0
0
0
1
2
1
1
2
1
1
0
1
0
1
1
2
1
1
2
2
0
2
1
1
0
1
1
1
0
0
2
0
1
1
5
0
1
0
1
2
0
1
0
0
3
0
1
1
1
2
0
1
1
2
2
2
1
1
1
0
1
0
0
2
0
1
0
0
0
2
0
1
1
1
2
0
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
0
1
2
1
1
1
2
0
1
1
1
0
0
0
1
0
12
1
1
1
1
2
1
1
0
1
0
1
1
0
2
0
1
2
2
1
0
1
1
0
1
1
1
1
1
2
2
1
1
1
1
1
1
0
0
1
0
0
1
1
1
0
1
2
1
0
0
4
1
0
1
2
1
1
1
1
1
2
2
1
1
0
1
2
0
1
2
1
1
1
2
1
2
1
0
1
0
1
0
1
1
2
0
0
1
1
1
0
1
0
0
1
1
1
0
0
2
1
0
1
0
1
1
1
0
1
2
0
1
1
2
1
0
0
1
1
0
1
2
0
2
2
1
1
0
1
1
0
1
1
2
1
0
0
4
1
1
1
0
0
1
1
2
2
2
2
1
2
1
0
2
1
1
1
1
0
0
0
2
1
2
0
2
2
1
1
0
1
0
0
0
2
1
0
1
0
0
1
0
1
0
1
0
1
2
1
1
1
1
2
1
1
2
0
2
1
1
1
0
1
0
2
2
2
1
0
1
0
0
0
1
1
0
2
2
1
0
0
1
1
1
1
1
2
1
2
1
2
1
2
1
1
1
1
0
1
0
0
2
0
0
1
0
1
1
0
1
0
1
1
2
0
2
1
1
1
1
3
1
0
2
0
2
1
1
1
0
1
1
1
0
2
1
1
1
1
0
0
0
1
1
1
0
1
1
1
1
1
1
1
0
1
0
0
1
1
2
2
1
0
1
2
2
1
1
1
1
0
1
1
1
3
0
2
0
2
0
0
0
1
0
2
0
2
1
1
2
0
1
1
1
0
0
2
0
2
1
2
2
1
0
1
1
0
1
1
1
1
2
2
1
0
1
2
2
2
0
0
1
1
4
1
2
1
1
0
0
1
1
1
2
0
0
0
2
2
1
1
0
1
1
1
2
1
2
0
1
2
0
0
1
1
2
2
2
0
0
1
2
1
2
0
1
2
0
1
0
1
0
2
1
2
1
1
0
1
2
1
2
2
1
0
0
0
1
1
1
1
2
2
1
1
0
2
2
1
0
2
0
0
2
1
0
2
1
1
2
2
2
1
0
2
1
0
0
0
1
3
1
1
0
0
0
2
0
1
2
0
1
0
2
1
2
1
0
2
2
0
2
0
2
1
1
2
1
1
2
1
0
1
1
1
0
1
1
0
0
1
1
1
2
1
2
0
0
1
1
1
2
0
3
1
1
1
0
0
0
0
1
2
1
2
1
0
1
0
0
0
1
2
0
1
0
1
0
0
1
1
1
1
0
1
0
1
3
1
2
1
1
3
2
1
1
0
2
1
1
1
1
1
0
1
0
1
0
1
2
7
1
1
2
1
2
1
0
1
1
1
1
1
0
2
2
1
1
1
1
0
1
0
1
1
1
2
0
0
0
0
0
0
1
2
2
0
0
2
0
1
2
2
1
1
2
0
1
1
3
1
1
1
1
0
1
0
2
1
2
0
2
0
0
0
1
0
1
0
0
2
1
2
2
1
2
1
1
0
2
1
2
0
0
0
1
1
0
1
1
1
2
2
1
1
0
1
1
1
2
0
0
1
0
2
1
1
1
2
0
2
1
1
1
1
3
2
1
0
1
2
1
2
1
1
0
0
2
0
1
0
1
1
1
0
2
0
0
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
0
1
1
1
1
2
2
1
0
1
1
1
0
1
0
0
0
1
1
1
1
0
1
1
0
0
1
1
2
2
0
2
2
1
1
1
2
0
1
2
1
2
1
0
1
2
0
1
2
1
1
1
1
0
1
2
3
1
2
1
1
0
1
0
1
2
1
2
0
2
2
0
3
0
2
0
1
1
2
1
1
0
1
2
1
1
0
1
2
1
0
1
1
1
1
0
1
2
2
1
2
1
0
1
3
1
1
1
1
1
0
0
2
2
0
0
4
0
1
2
2
0
1
0
0
0
0
1
1
0
1
0
2
1
2
1
1
0
1
1
1
0
2
1
1
1
0
0
1
1
0
0
1
0
0
1
1
0
1
2
0
0
1
0
1
1
0
1
1
1
2
2
1
1
1
1
2
0
2
1
0
1
1
1
1
1
1
0
0
1
0
1
1
1
2
0
2
1
2
2
1
0
1
2
1
1
2
1
1
1
0
1
1
2
1
1
2
0
1
2
1
2
1
0
1
2
1
2
2
0
0
0
0
1
1
3
0
2
2
2
1
2
1
1
1
1
0
1
1
2
1
2
1
1
0
2
1
0
0
1
1
0
0
1
1
1
0
1
1
1
1
1
1
1
1
0
2
2
0
1
1
2
0
2
0
2
0
0
2
1
0
2
2
0
1
2
2
2
0
1
0
1
1
0
2
1
1
2
0
1
1
1
0
2
1
0
1
2
1
0
1
0
1
2
0
1
2
1
4
2
0
1
1
1
2
1
2
1
1
1
1
0
1
1
1
1
0
0
1
1
1
1
1
0
1
0
0
2
0
0
1
1
2
1
0
1
1
1
2
1
0
2
1
0
1
0
1
0
1
1
1
0
1
1
1
0
1
0
0
2
2
2
0
1
1
0
1
1
0
1
1
1
1
0
2
2
1
1
1
2
0
1
1
2
0
1
1
2
1
0
0
1
0
1
2
1
2
3
0
2
0
0
1
1
1
1
1
0
0
0
0
1
1
1
1
1
1
0
1
2
2
1
2
1
1
1
1
2
1
0
0
0
1
1
0
1
0
1
1
1
0
1
1
1
1
2
1
1
1
1
0
2
2
2
1
1
2
2
0
2
0
1
1
2
1
0
0
2
0
1
1
3
0
0
0
0
1
1
1
1
1
0
0
2
1
1
2
1
1
0
0
0
1
2
1
1
1
1
1
2
1
1
1
2
2
1
0
0
0
1
1
0
1
1
2
0
1
0
1
0
0
0
1
2
1
1
1
1
0
1
2
1
3
2
2
2
0
1
2
1
1
1
1
2
1
0
1
1
1
1
0
0
2
1
1
0
1
1
1
1
1
1
0
1
1
2
2
2
0
1
0
0
1
0
0
1
1
0
0
1
1
0
2
0
0
2
1
0
1
1
1
2
1
1
2
0
1
1
0
1
0
2
0
2
1
1
0
1
1
6
2
0
1
0
1
0
0
2
1
2
1
2
2
0
2
0
1
0
1
1
0
1
2
2
1
1
2
0
2
1
1
2
1
1
1
1
0
0
0
1
0
1
1
3
1
2
0
1
1
1
0
1
1
1
2
0
1
1
1
1
0
2
1
1
2
0
3
2
2
1
2
1
1
1
0
0
1
1
1
2
1
0
1
1
2
1
1
1
3
1
1
1
1
1
0
2
0
0
1
0
1
2
0
1
0
0
1
0
2
1
1
1
2
1
1
2
0
1
2
2
2
1
3
1
2
0
0
0
2
2
0
1
1
0
1
2
0
1
0
0
0
0
0
1
1
0
2
1
0
1
0
2
1
1
0
0
0
1
1
1
0
1
2
1
1
2
1
2
1
1
1
2
0
1
1
0
0
2
1
1
1
1
2
2
1
1
2
1
1
0
2
2
0
1
2
1
1
0
1
0
2
1
1
1
1
0
1
0
0
0
0
1
2
0
0
2
1
0
1
2
2
1
1
1
0
1
2
2
1
1
1
2
2
2
1
2
1
2
0
1
0
1
0
1
1
0
0
2
1
1
0
1
1
1
0
1
0
2
0
0
0
0
1
1
2
1
2
2
1
1
2
0
1
0
0
2
1
0
1
1
0
1
1
2
1
1
0
1
0
1
2
1
1
0
1
2
0
2
1
2
1
1
3
2
2
0
2
0
1
1
0
0
0
1
2
0
1
2
1
2
1
1
2
2
2
1
2
1
0
0
1
1
0
1
0
1
2
0
0
0
2
3
2
1
1
0
0
1
1
1
0
1
0
3
2
2
2
2
1
0
2
1
0
1
1
1
1
1
1
0
2
1
0
1
2
1
0
1
1
1
1
0
0
1
1
0
1
0
1
0
1
1
0
1
1
1
1
0
2
1
0
1
1
1
0
0
1
0
2
0
1
2
0
1
2
1
1
2
1
0
0
1
1
0
2
1
0
0
2
1
2
0
0
1
0
2
0
1
0
1
1
2
0
1
1
1
1
1
2
0
2
1
1
2
0
1
0
0
1
0
1
0
1
1
0
1
1
0
2
1
1
2
1
1
2
1
0
0
0
1
3
0
1
2
0
1
1
1
1
1
1
1
1
2
2
0
0
0
0
1
2
2
1
0
0
0
0
1
0
1
2
1
1
0
0
1
1
1
1
0
1
2
1
1
1
2
0
1
1
1
1
1
1
0
0
0
1
0
1
0
1
1
0
0
1
0
1
2
0
1
1
0
2
2
0
1
1
2
0
3
1
0
0
1
2
1
2
0
0
1
0
0
1
1
1
1
1
0
2
1
1
1
1
0
0
0
2
1
1
0
1
2
1
1
0
1
0
2
1
2
1
2
1
1
1
0
1
1
1
2
1
1
2
1
0
1
1
0
1
0
0
1
2
0
0
1
1
0
2
2
2
1
1
1
0
0
1
1
3
0
2
1
1
2
0
2
0
1
1
0
2
0
0
2
2
0
0
0
1
1
0
1
0
1
1
0
1
1
1
1
2
0
1
2
0
2
1
1
2
1
1
1
1
0
1
2
2
1
1
1
2
0
0
1
1
1
1
1
0
1
2
2
1
2
1
2
0
1
0
1
0
1
0
2
0
2
2
1
0
1
1
1
1
2
1
0
1
2
1
1
0
0
2
0
2
0
0
0
1
1
1
0
2
0
1
2
1
2
1
0
1
0
1
2
3
0
1
1
1
2
1
1
1
1
1
1
1
1
0
0
2
1
0
1
1
1
0
1
2
1
1
1
1
1
0
1
1
1
0
0
1
0
1
1
0
1
1
0
1
0
0
2
1
1
1
1
0
0
0
1
1
1
1
0
1
2
1
1
0
2
0
1
0
1
1
1
1
1
1
0
2
2
1
1
2
2
2
1
0
1
1
1
0
1
1
0
0
2
1
0
1
1
3
2
0
0
1
0
1
1
2
2
1
0
1
1
1
2
0
0
1
1
1
1
1
1
2
0
1
1
1
3
0
2
0
1
1
0
2
2
1
0
1
2
1
2
1
0
1
1
1
1
0
0
0
2
1
0
1
0
0
1
2
1
1
2
2
1
0
1
0
2
0
1
1
1
1
2
1
2
3
0
1
1
0
0
2
1
2
2
1
0
1
2
0
0
0
1
1
0
2
0
1
2
0
0
1
2
0
0
1
0
2
0
2
1
1
1
1
3
1
1
2
0
1
0
2
1
2
1
0
1
1
0
1
0
0
0
1
0
2
1
1
1
1
2
1
2
1
1
1
0
4
2
2
0
0
1
0
0
1
1
1
1
1
0
0
1
1
1
1
1
1
1
1
1
0
1
1
1
0
1
1
0
2
1
2
1
0
1
1
1
1
0
1
1
1
1
1
0
2
1
1
0
0
2
1
2
2
2
2
0
2
0
2
0
1
1
0
2
0
1
2
1
3
1
2
0
0
2
3
1
1
1
1
2
0
1
0
1
1
1
1
1
0
2
2
1
1
2
0
0
1
1
1
2
2
1
1
1
2
1
1
0
1
1
0
1
0
1
1
1
1
2
2
1
0
2
3
1
2
0
1
2
1
1
1
1
2
1
1
2
0
1
1
1
1
1
2
0
2
1
2
1
1
1
1
1
0
1
1
2
0
2
0
1
5
1
1
2
2
1
1
2
1
2
1
1
2
1
1
2
0
0
0
1
0
0
2
1
2
2
1
1
2
1
2
1
1
2
1
1
0
1
0
1
2
0
0
2
0
1
1
1
1
0
1
2
0
1
0
0
0
0
1
1
0
1
2
2
0
2
1
1
1
2
2
1
0
1
0
1
0
1
2
1
1
1
0
2
1
2
2
2
0
0
2
0
0
2
0
4
1
1
0
1
0
0
0
0
2
2
1
2
0
1
1
1
2
1
1
1
0
1
1
1
1
1
1
1
2
2
1
1
1
0
0
1
1
2
1
2
0
1
1
2
0
0
0
1
2
1
1
1
1
1
1
2
0
2
1
2
1
1
0
1
2
1
1
1
0
1
0
0
1
1
0
1
0
1
0
4
0
2
1
0
0
1
1
1
2
0
0
1
1
1
0
1
0
0
0
0
0
1
1
0
0
1
1
1
2
1
2
2
1
1
2
0
1
1
0
0
0
1
2
2
1
1
1
1
1
1
2
1
3
0
2
1
1
1
1
1
1
3
1
2
1
0
1
1
1
1
0
0
1
2
1
1
2
0
2
1
0
0
1
1
0
0
0
1
1
2
0
2
0
2
1
0
0
0
0
0
0
1
1
1
0
1
0
1
1
0
1
2
1
2
0
1
2
2
1
1
0
1
1
0
0
2
1
1
0
0
0
1
1
1
1
1
0
1
0
1
1
0
1
1
1
1
1
0
1
0
1
1
0
2
0
1
2
1
0
0
0
0
2
0
2
0
1
0
1
1
2
1
0
1
1
0
1
2
1
2
0
0
1
0
2
2
0
1
2
1
1
0
1
2
0
1
0
2
2
1
0
0
0
0
0
1
1
1
0
1
1
0
1
8
1
0
2
0
0
2
2
1
1
1
1
1
2
0
0
1
1
2
0
1
2
1
2
0
2
1
1
1
1
2
0
1
1
1
1
0
1
1
1
0
1
2
1
2
2
1
1
1
1
0
0
1
0
0
0
1
1
2
0
1
1
2
1
0
0
3
1
2
2
0
2
1
1
1
1
1
1
1
0
0
1
2
1
0
1
2
1
1
1
1
0
3
0
1
0
1
0
1
1
1
2
0
1
1
1
3
0
2
2
0
0
1
1
1
0
1
1
1
2
0
1
0
1
1
1
0
0
1
2
2
1
0
1
1
0
0
1
0
1
0
2
1
2
0
1
1
1
2
2
2
2
1
0
1
1
1
0
0
0
1
0
0
0
1
1
0
2
1
2
2
1
1
0
2
0
1
2
0
0
1
1
0
1
1
1
1
1
1
2
2
2
2
1
1
0
1
0
1
0
0
1
1
1
0
0
1
0
1
1
0
2
2
1
2
2
1
0
1
1
0
1
0
0
1
0
2
1
1
1
0
0
1
0
0
1
0
1
1
1
2
1
8
0
1
1
0
1
1
1
2
1
2
0
1
1
2
0
1
0
2
1
2
2
2
0
1
1
1
1
0
2
1
1
0
1
1
0
0
1
1
1
0
1
0
1
1
0
0
2
1
1
0
1
2
1
2
0
1
2
1
0
1
0
2
1
0
1
1
1
0
0
1
0
0
0
1
0
0
0
1
2
1
0
1
0
1
2
0
1
1
1
1
1
1
2
2
0
2
2
1
2
2
1
1
2
2
2
0
1
1
0
1
2
0
1
0
0
1
0
0
1
0
1
2
2
2
3
1
0
0
2
0
1
1
2
1
1
1
1
1
1
1
0
1
1
0
0
0
3
0
1
1
0
0
1
0
0
0
1
1
1
1
1
0
1
0
1
1
0
1
0
1
2
0
1
0
1
1
0
0
1
2
1
0
1
1
0
0
0
1
0
1
1
0
1
1
2
0
2
0
1
2
2
0
0
2
1
2
1
1
1
0
1
0
0
1
0
0
1
0
1
2
1
1
0
1
1
1
1
1
0
1
1
0
0
1
0
0
0
1
1
2
1
1
2
1
1
1
1
2
2
0
1
0
1
0
2
1
1
1
1
2
0
2
1
1
0
0
1
1
1
0
1
0
2
1
2
0
0
0
0
1
0
0
1
1
2
1
0
1
0
2
0
1
2
0
0
2
1
0
1
0
2
1
1
1
0
2
1
2
2
0
1
1
2
1
2
0
1
1
0
1
1
1
1
1
2
0
2
0
1
1
0
1
1
2
1
1
0
0
1
2
1
2
1
2
1
2
0
1
1
1
1
2
1
0
1
0
0
1
0
0
1
2
0
1
0
2
1
2
2
1
1
1
0
2
1
2
0
2
0
0
1
0
0
1
1
1
2
0
1
1
1
2
2
2
1
0
5
1
0
0
1
1
1
0
0
1
0
0
1
0
2
0
1
2
1
0
1
1
1
1
0
0
2
0
1
1
1
1
0
0
1
1
1
1
1
2
1
1
2
0
2
1
0
0
1
1
2
2
3
1
0
1
1
0
0
1
1
1
1
1
0
1
0
0
2
0
1
2
1
2
0
2
0
1
1
0
0
0
2
0
2
0
1
1
0
1
0
1
1
1
1
1
0
0
1
1
0
1
0
1
0
1
2
1
1
0
1
1
2
1
1
2
0
0
1
1
2
1
1
0
1
1
0
1
0
0
0
1
1
2
3
0
1
1
1
2
1
2
0
1
1
0
2
1
2
0
3
1
1
1
2
1
1
1
1
0
0
2
0
2
1
1
1
1
2
2
0
0
1
1
1
1
2
1
2
0
2
2
2
0
0
0
2
2
1
0
2
2
1
1
0
1
1
2
2
1
1
0
2
0
1
1
0
2
1
0
1
0
0
1
1
1
0
1
1
1
0
2
2
0
1
1
1
1
0
0
2
0
0
0
1
2
0
0
1
1
2
1
1
1
0
1
0
0
0
2
2
1
2
1
1
2
2
1
1
2
1
1
1
3
1
0
1
1
1
0
1
1
1
0
0
1
1
1
1
2
1
1
1
1
1
1
2
0
1
0
1
0
3
0
1
0
1
0
0
1
0
0
1
1
1
3
2
1
2
2
1
2
0
2
2
1
1
1
1
3
2
1
1
1
0
2
2
1
1
1
0
0
2
0
0
1
1
1
1
3
1
1
1
2
1
2
1
1
2
0
1
0
1
0
2
0
1
1
1
0
2
1
1
2
2
1
0
1
1
0
2
0
2
1
0
1
2
0
0
1
1
2
1
1
0
0
1
1
0
1
2
1
1
1
0
1
0
5
1
0
1
2
2
0
1
2
1
0
1
0
0
2
0
0
2
1
1
0
1
0
0
2
2
0
0
2
2
0
2
1
2
1
1
1
0
1
2
1
0
2
0
1
1
1
2
2
2
1
2
1
1
1
1
1
1
2
2
1
0
1
0
1
2
0
2
0
2
0
1
2
1
2
0
0
1
0
1
0
0
1
0
0
0
0
1
1
1
1
2
2
1
1
1
2
2
0
1
0
0
0
0
1
2
1
2
1
0
1
2
1
1
1
1
0
1
1
0
2
1
1
2
1
0
2
1
2
0
1
1
1
1
2
1
0
1
1
0
1
1
0
2
10
1
0
1
1
2
2
0
0
0
0
2
0
0
0
0
2
0
1
2
2
0
1
1
1
2
1
0
0
1
0
0
1
2
0
2
0
1
1
1
1
1
1
1
1
0
0
1
0
0
1
2
1
3
1
1
1
1
1
1
2
0
0
1
2
0
1
0
1
1
1
2
0
1
0
2
0
1
0
1
2
1
0
2
1
2
1
2
0
1
2
0
2
2
1
0
1
2
0
3
1
1
0
2
1
1
2
1
1
1
1
1
0
1
0
0
2
1
1
2
1
1
2
1
0
1
1
1
1
0
0
1
1
0
2
0
0
1
2
1
1
0
1
1
0
1
1
1
0
0
1
1
1
0
1
0
1
1
1
0
0
0
1
1
1
1
1
0
1
1
1
1
2
1
0
1
1
1
1
2
0
0
1
1
1
0
0
1
1
1
1
1
3
0
0
1
0
2
0
2
0
0
2
0
2
1
0
0
0
0
2
1
1
1
0
1
0
1
1
2
1
1
1
2
2
2
2
2
1
0
0
1
2
1
1
2
0
0
1
1
1
0
0
1
1
1
0
1
1
2
0
0
1
3
2
2
1
0
1
0
2
3
1
2
1
1
0
1
0
1
1
1
0
1
1
2
1
0
1
0
0
0
2
2
2
1
1
2
1
2
1
1
0
0
2
1
2
0
1
2
1
1
0
1
2
1
2
1
1
0
1
0
1
1
1
1
1
1
0
0
1
1
1
2
0
0
1
1
1
0
0
0
2
1
0
1
2
0
0
2
0
2
2
1
2
2
1
3
1
1
1
1
0
2
0
2
2
3
0
1
0
0
1
1
1
2
0
0
2
2
2
2
1
1
1
0
1
1
1
1
1
0
2
1
1
1
2
1
2
0
2
1
0
1
0
1
2
1
1
1
2
2
2
1
2
1
1
0
1
2
1
2
1
2
1
1
0
1
3
2
0
1
1
2
0
0
0
1
1
0
1
1
1
0
1
2
2
0
1
1
2
2
0
1
1
1
1
0
1
0
2
1
2
0
2
1
1
5
1
0
2
0
2
0
0
1
0
0
1
1
1
1
0
0
1
0
0
1
1
1
1
1
2
1
1
1
2
0
1
0
2
0
1
1
1
1
2
1
1
1
1
2
1
2
1
1
0
1
1
1
1
0
2
2
0
1
2
2
0
0
2
1
2
2
1
0
2
0
0
2
1
1
1
2
1
2
0
1
0
1
0
1
2
2
1
0
1
1
1
0
1
2
1
2
2
1
2
1
1
0
1
1
2
2
2
1
1
2
0
1
2
2
1
2
0
1
1
1
2
2
1
0
0
2
1
1
1
0
2
1
1
1
1
1
2
1
0
1
1
2
1
2
1
0
1
2
0
2
0
0
2
1
2
0
2
4
0
1
0
2
2
1
1
1
1
1
0
1
1
2
1
0
1
1
0
1
1
1
1
0
0
1
1
1
1
2
1
1
0
1
1
1
1
1
0
2
2
0
0
0
0
0
1
0
1
1
1
0
1
1
2
1
1
1
0
0
1
1
1
1
1
0
1
1
1
1
1
0
0
1
1
1
2
6
2
1
1
1
3
1
0
1
1
0
0
0
2
2
1
0
1
1
2
1
1
2
0
2
1
0
1
1
1
2
1
1
1
1
1
1
1
1
4
0
1
1
0
2
1
1
1
1
1
1
1
2
1
1
0
1
1
2
0
1
1
0
2
1
0
1
1
0
1
2
0
1
2
1
1
2
2
1
2
0
0
2
1
1
2
1
1
2
0
1
0
2
0
0
0
2
2
1
1
1
0
2
1
1
1
0
2
1
1
0
0
1
0
1
1
1
3
0
1
0
0
1
0
0
1
2
2
1
1
1
2
2
2
2
2
1
1
3
1
1
2
1
2
0
1
0
1
0
1
1
1
1
1
1
1
1
1
1
1
1
2
0
1
0
2
1
1
0
1
1
1
0
2
1
0
1
2
1
1
1
2
1
0
1
1
1
2
1
0
2
2
1
1
1
1
0
0
2
0
2
0
1
1
1
1
2
2
1
2
1
1
0
1
1
0
0
0
1
1
1
1
1
0
1
1
0
2
1
0
1
1
1
2
1
1
0
1
1
1
1
1
2
2
0
0
1
1
0
1
1
1
4
0
2
1
1
0
1
2
1
2
0
3
2
1
0
1
1
1
1
2
2
1
1
1
0
2
2
1
1
1
2
2
1
1
1
1
2
2
0
1
1
2
1
0
0
1
2
1
0
1
1
0
1
0
0
1
0
2
2
0
1
2
1
0
2
0
2
2
1
1
2
0
1
1
1
1
2
3
1
0
1
2
1
2
2
1
1
0
0
0
2
2
0
1
0
1
0
0
1
0
1
1
1
1
1
1
1
1
0
1
2
2
1
0
2
0
1
2
0
1
0
2
0
2
1
1
2
0
2
1
1
1
1
2
1
0
2
1
2
1
1
1
0
2
1
1
0
1
0
2
2
2
0
0
1
1
1
1
0
1
1
2
0
1
1
1
2
1
1
1
0
0
1
1
1
1
1
0
1
0
1
1
0
0
1
0
2
0
1
1
0
1
2
1
1
1
0
1
1
2
0
1
1
1
1
0
1
1
1
0
1
2
0
1
0
0
1
0
1
1
1
1
1
1
0
0
2
3
1
1
2
1
1
1
0
2
1
1
0
0
0
2
2
1
1
2
1
1
1
1
1
0
2
1
0
1
1
2
1
0
0
0
2
1
1
0
2
2
0
1
2
3
1
1
1
0
2
1
2
0
2
1
1
1
1
0
2
1
1
1
2
1
1
0
0
0
2
1
1
0
1
1
1
1
3
1
1
0
1
2
0
2
1
0
1
1
3
1
1
0
1
1
1
1
2
1
1
1
0
0
2
0
1
0
1
1
1
0
1
1
1
0
1
1
1
1
2
1
0
0
2
1
2
1
1
1
0
1
1
1
2
0
1
0
2
1
1
1
2
0
0
0
2
1
1
0
0
1
1
0
1
1
2
1
0
2
1
1
1
2
1
0
1
0
2
1
2
0
0
1
1
1
2
1
1
1
0
1
2
2
2
0
2
1
0
0
1
1
1
2
1
0
1
1
0
1
0
0
1
1
0
2
1
2
1
2
2
1
1
2
1
1
2
1
1
0
1
1
0
2
1
1
2
1
2
2
0
2
0
1
2
1
1
0
0
2
1
1
1
0
1
1
1
2
2
1
1
2
1
0
1
2
1
1
1
1
2
1
3
1
0
0
1
1
1
1
1
1
1
0
1
3
0
1
1
2
0
1
2
0
1
1
2
1
0
1
1
1
1
1
1
0
1
0
1
2
0
1
0
0
1
1
2
1
2
1
1
1
0
0
1
1
2
0
2
1
2
0
1
0
1
0
1
1
2
0
1
3
0
0
1
2
1
0
0
1
1
1
1
1
2
2
1
0
2
2
2
0
2
1
2
1
1
2
1
1
2
1
2
0
1
1
0
1
2
1
1
0
1
0
1
2
1
0
0
2
3
0
1
1
2
1
2
0
1
2
2
2
1
1
0
1
1
2
1
1
0
1
0
0
0
2
1
0
2
1
0
0
1
1
0
0
1
0
1
1
1
2
1
2
2
2
0
1
2
1
2
0
1
1
1
1
1
2
1
1
1
2
3
2
1
0
0
1
2
1
1
1
2
1
3
2
0
1
1
1
1
1
1
1
0
2
1
0
1
0
1
1
1
2
0
1
1
1
1
1
2
0
0
1
1
0
0
2
1
1
4
0
1
1
1
2
0
0
0
2
0
2
0
1
1
1
0
1
1
0
1
2
0
1
0
0
2
1
2
1
0
1
1
1
1
2
1
1
0
1
0
1
1
1
1
0
1
1
0
0
0
0
1
2
1
1
1
0
0
0
0
0
2
0
0
0
0
0
3
0
1
1
2
2
1
0
1
1
0
1
1
0
1
1
0
1
1
2
1
0
0
1
0
2
2
0
1
1
1
1
0
2
0
1
0
1
0
1
0
0
2
0
1
0
1
1
1
2
2
1
1
1
2
0
1
2
2
0
0
2
2
0
2
0
1
2
2
2
1
0
1
0
1
1
1
0
0
0
1
1
1
0
1
2
1
1
1
1
0
1
2
1
1
1
0
1
1
1
0
1
1
1
1
1
1
1
0
0
0
0
1
1
2
1
1
0
0
0
1
0
0
2
1
0
0
0
1
1
1
1
3
1
1
1
0
1
0
0
1
1
0
1
0
1
1
1
0
2
2
0
0
0
1
2
0
0
0
0
1
0
2
1
1
2
2
2
1
2
1
1
2
1
1
2
1
2
1
0
1
0
1
2
1
0
1
1
2
2
0
1
1
1
1
1
1
0
1
0
1
0
1
2
0
0
0
2
1
0
2
1
1
2
1
2
1
1
1
1
0
1
1
0
0
1
0
2
0
1
2
0
1
1
1
1
2
1
2
0
1
0
3
1
1
1
1
0
0
1
1
0
2
1
2
0
1
1
1
1
0
1
2
2
1
2
0
2
0
1
1
2
1
2
1
1
0
1
2
1
1
0
2
0
1
1
0
2
1
2
1
0
1
0
1
1
0
0
1
1
1
2
2
1
2
1
0
1
1
1
0
2
1
1
2
1
2
1
0
1
2
1
1
2
0
2
1
1
1
1
1
0
0
3
1
1
2
1
0
1
1
1
0
1
1
1
1
0
1
0
1
1
0
1
0
1
1
0
2
1
0
1
1
0
0
1
3
1
0
3
1
3
1
2
1
2
2
2
0
1
0
1
1
0
1
2
0
1
1
1
1
1
2
1
0
1
1
1
0
0
1
0
1
2
0
1
1
2
1
0
0
2
1
0
0
0
1
1
2
0
0
2
1
1
2
0
1
0
1
1
0
2
1
1
0
1
1
1
0
2
2
0
0
1
1
1
1
1
1
2
1
0
1
0
0
1
1
0
0
0
2
1
1
1
0
1
0
1
0
1
2
2
2
2
1
1
1
0
1
0
2
0
1
2
1
0
1
3
0
1
0
1
0
1
1
0
1
1
1
1
0
0
1
0
2
1
1
1
1
1
2
2
0
0
1
1
1
1
1
2
1
1
1
2
2
0
1
1
1
0
0
1
1
1
0
0
0
0
1
1
2
0
1
0
0
1
2
1
2
1
1
1
1
0
1
2
1
0
2
1
1
2
1
2
1
0
1
2
1
2
1
1
1
0
0
1
1
2
0
2
1
1
1
1
2
1
1
0
1
2
1
0
0
1
2
0
1
0
1
0
0
2
0
0
2
1
1
1
0
1
0
1
1
0
0
2
2
1
2
0
0
1
1
0
1
1
1
0
2
0
1
2
1
0
0
0
1
1
1
1
1
1
2
0
1
1
2
0
0
0
0
2
2
1
0
1
0
0
1
1
0
1
0
0
0
1
1
1
2
1
1
0
2
2
1
1
0
1
0
3
2
1
1
1
1
1
1
1
0
2
0
1
0
1
1
1
1
0
0
1
0
1
2
1
1
5
0
0
1
1
0
1
1
2
1
0
2
1
1
0
2
1
1
1
0
1
2
0
0
0
2
0
1
2
0
2
2
1
0
1
1
1
1
0
1
2
1
2
1
2
0
1
1
1
2
1
0
2
0
2
1
1
3
1
0
0
0
0
3
2
1
1
0
0
2
3
0
2
2
0
1
2
2
0
2
1
2
1
2
1
0
2
1
1
1
2
1
1
1
1
1
0
1
0
2
1
1
0
1
0
0
1
2
2
0
0
0
0
2
1
1
2
1
0
2
2
2
1
1
2
1
1
1
2
2
1
1
2
1
2
1
1
1
2
0
1
1
1
0
2
0
2
1
1
2
2
1
0
0
0
1
1
1
2
0
1
0
0
1
1
2
0
1
0
1
1
2
1
1
0
0
1
1
0
1
2
0
1
2
2
2
1
0
0
0
1
1
3
2
0
0
1
1
2
2
1
1
0
0
0
1
1
0
0
0
2
0
2
1
1
1
1
1
1
3
1
1
2
1
1
1
2
1
1
0
1
0
1
2
1
1
2
0
0
2
0
2
1
1
1
0
0
0
0
0
3
2
2
1
2
1
1
0
2
2
2
1
1
1
1
1
0
1
0
1
1
0
0
2
0
0
1
1
1
1
1
1
4
1
2
1
2
1
1
0
2
2
1
1
0
2
0
0
0
0
1
0
1
1
0
2
1
2
0
0
1
0
1
1
1
2
0
1
1
1
1
2
1
0
0
1
0
2
1
1
0
1
0
2
1
2
1
1
1
1
0
1
4
2
1
1
1
1
0
1
1
2
1
1
1
1
2
2
1
1
0
2
1
2
2
0
1
0
1
0
2
1
0
0
2
0
1
1
1
2
2
1
0
2
2
2
0
1
0
2
1
1
1
1
0
0
0
1
1
1
1
2
1
1
2
0
0
2
1
2
1
2
1
0
2
2
1
2
4
2
0
1
3
1
0
1
2
1
1
0
0
1
1
2
0
0
0
1
2
1
1
1
1
2
2
0
2
1
0
2
1
1
1
0
1
1
2
0
0
0
0
0
2
0
0
1
1
0
1
1
0
2
2
1
1
2
1
1
1
2
1
0
1
2
0
1
1
1
1
0
1
1
3
7
3
1
1
0
0
0
0
1
0
2
1
0
0
1
1
1
0
1
0
1
1
0
0
0
0
0
3
2
1
1
0
0
1
3
2
2
2
1
1
0
1
1
1
2
1
0
0
2
2
1
2
0
0
3
0
1
2
0
2
2
0
0
2
0
0
0
1
0
1
1
2
2
2
2
1
0
1
1
2
0
1
2
0
2
0
0
1
0
2
1
1
2
1
1
0
1
1
0
2
1
2
0
5
1
0
1
1
1
2
1
2
1
0
1
1
1
2
1
0
0
2
2
1
0
2
1
1
0
1
2
2
1
1
1
2
2
1
1
2
0
2
1
1
1
2
1
0
1
0
1
2
0
1
1
1
2
0
1
1
0
1
0
2
2
1
2
1
0
0
2
1
1
1
1
2
1
1
1
1
1
0
0
1
1
1
1
2
1
1
1
1
1
1
0
1
0
1
1
1
1
0
2
0
2
1
0
1
2
0
0
0
2
1
0
0
0
1
1
1
1
0
1
0
1
0
0
1
1
1
1
1
1
0
2
1
0
0
1
2
1
0
0
0
0
2
1
0
0
1
1
0
1
1
1
2
1
1
0
0
0
2
1
1
0
2
2
1
0
2
0
0
0
1
1
1
0
1
0
1
1
1
2
1
1
1
2
1
1
0
2
1
2
1
1
1
1
1
0
2
6
2
1
1
0
0
2
2
2
0
1
2
1
1
1
0
3
1
2
1
2
2
0
0
1
1
1
0
0
1
1
2
1
0
0
2
0
1
1
0
2
1
1
0
0
1
1
0
2
0
0
1
1
2
2
1
1
1
0
0
1
1
1
1
1
2
1
2
1
1
0
0
2
2
1
1
1
0
2
1
2
1
0
0
0
0
0
1
2
2
2
0
2
1
1
0
1
0
0
0
0
2
2
1
0
1
0
1
1
1
2
0
0
1
1
2
2
2
1
2
0
2
1
1
0
1
2
2
1
1
1
1
0
0
1
0
0
0
2
1
0
1
1
1
0
2
0
1
1
0
1
1
1
1
1
1
2
1
1
0
1
2
1
1
1
2
1
1
1
0
1
1
1
1
0
1
0
2
1
1
1
1
1
0
0
1
0
1
0
1
1
0
0
1
1
2
2
2
1
2
1
3
1
1
1
1
0
1
1
2
1
1
1
2
1
0
0
1
1
1
0
1
2
1
1
1
1
0
0
0
2
1
0
2
0
1
0
1
1
1
1
2
0
0
1
3
1
1
2
0
1
1
0
1
0
2
0
0
1
0
2
0
1
2
3
1
0
1
1
0
1
0
1
1
1
1
1
1
1
0
0
1
2
1
1
0
2
1
0
2
1
1
1
2
1
2
0
1
1
1
1
0
0
2
2
0
1
0
1
0
1
1
3
0
1
1
1
1
0
1
0
1
1
0
1
2
1
1
2
3
1
0
1
0
1
0
1
0
0
0
2
2
1
0
1
0
0
0
0
0
0
1
0
0
0
2
1
1
1
1
2
1
2
0
2
1
2
2
2
0
1
1
1
0
1
0
1
0
0
2
1
2
0
2
2
1
1
1
2
1
0
0
2
1
2
0
1
0
1
1
0
0
2
2
1
2
0
0
0
1
1
1
0
1
1
1
1
1
2
1
1
2
2
0
1
1
0
1
2
2
1
1
1
1
1
1
0
1
1
1
1
1
1
1
2
1
1
0
2
1
1
0
0
1
1
1
0
0
2
1
1
2
2
2
1
0
2
1
0
1
1
0
1
1
1
0
0
1
2
1
1
1
1
1
0
1
2
1
1
1
2
1
0
0
0
0
2
0
0
2
1
0
2
1
0
1
0
1
0
1
0
0
1
2
2
1
0
1
1
1
1
1
0
2
0
1
2
0
0
0
0
1
1
1
2
1
2
1
1
0
1
1
2
1
0
2
2
1
1
1
2
2
2
2
0
1
1
1
1
1
0
1
0
1
2
2
1
1
1
1
1
0
2
0
1
0
0
1
1
0
0
2
1
0
0
1
0
1
1
1
0
0
1
1
0
0
2
1
1
1
2
0
0
0
1
1
2
0
1
0
1
1
2
0
2
1
1
2
2
1
1
2
0
1
2
1
1
1
0
2
4
0
1
1
1
1
1
0
0
1
1
1
2
1
1
1
2
2
1
2
0
1
1
1
0
1
1
1
1
1
2
1
0
1
2
0
0
1
1
1
1
2
1
0
0
1
2
1
1
0
2
3
1
0
0
1
1
2
0
0
1
0
0
0
1
1
0
0
1
0
2
1
1
2
2
0
2
1
0
1
0
0
2
1
1
1
3
1
0
0
2
1
1
1
1
2
0
0
1
1
2
3
2
0
1
2
1
0
1
1
1
0
1
2
1
2
1
0
1
1
0
1
0
1
1
0
2
1
1
2
0
1
0
0
2
0
1
2
2
2
2
0
2
0
1
1
0
0
5
2
1
1
0
0
1
2
1
1
1
2
1
1
0
2
1
2
0
1
1
1
1
2
1
0
1
1
1
1
1
1
2
0
0
0
2
1
1
1
0
3
0
1
0
0
1
1
1
1
0
1
0
0
1
0
1
1
1
1
1
0
1
1
1
0
0
1
2
0
1
2
2
0
1
2
1
0
0
1
0
1
0
0
1
2
0
2
0
1
1
0
0
3
2
1
2
1
1
1
1
0
1
1
1
1
1
1
1
1
2
1
0
1
2
2
0
1
0
0
2
1
1
1
0
0
1
0
2
0
2
1
1
0
0
0
1
1
2
2
0
0
0
1
1
0
0
2
2
0
1
2
0
2
1
1
1
1
1
0
2
3
0
2
0
1
1
1
1
1
2
0
2
1
0
1
1
2
0
0
2
1
0
0
0
2
2
2
1
1
0
1
0
1
1
1
2
1
1
1
1
0
1
1
0
1
1
0
0
1
1
1
1
1
2
1
1
1
2
0
0
2
0
1
1
1
1
2
1
2
0
1
0
1
0
2
1
2
1
1
1
1
1
1
0
1
1
1
1
1
1
2
1
1
1
2
1
1
2
0
2
0
2
0
1
1
1
0
1
2
1
2
1
2
2
1
2
0
1
1
2
1
2
2
0
0
1
0
0
2
0
1
0
1
0
2
1
0
1
0
1
1
2
1
1
1
0
0
2
1
0
0
1
1
1
2
1
0
0
1
5
2
0
0
1
0
1
2
1
4
1
0
1
1
1
1
0
1
0
0
0
0
0
0
2
2
2
2
1
1
1
1
0
0
1
1
2
0
3
1
1
1
2
1
2
2
0
2
1
0
1
2
1
2
1
2
2
1
1
0
1
2
2
1
0
2
2
0
1
0
0
1
0
2
2
1
1
2
1
1
0
0
1
2
0
0
2
1
0
0
1
1
1
0
1
0
1
0
1
1
1
1
1
0
2
1
2
1
0
2
1
2
0
0
1
1
1
1
0
1
1
1
1
1
2
0
0
3
1
0
0
0
0
1
2
0
0
1
0
1
0
0
1
1
1
2
0
2
1
1
2
1
1
2
1
1
2
2
2
2
0
0
1
1
0
2
1
1
0
2
1
1
3
0
1
1
2
0
1
0
2
0
1
0
0
1
1
0
1
1
0
2
2
0
1
1
0
0
1
1
0
1
1
1
0
1
0
0
1
0
1
0
1
1
1
2
0
0
2
2
2
0
0
1
1
0
2
2
0
0
2
0
2
1
0
2
0
0
1
0
1
3
1
0
1
1
1
1
1
1
1
1
1
2
1
2
1
2
1
1
0
2
1
2
2
0
1
2
0
1
0
2
0
2
1
0
2
2
0
1
0
1
1
0
1
2
2
1
0
0
0
1
0
1
2
0
1
2
0
1
1
3
1
0
2
2
1
1
1
0
1
2
0
0
0
0
0
0
0
1
0
2
1
2
2
0
0
1
1
3
1
1
1
1
0
1
1
1
2
1
1
0
0
2
0
0
2
2
2
1
1
0
2
0
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
0
0
0
1
0
0
0
2
1
1
1
0
1
2
2
1
0
1
1
1
1
1
1
0
0
1
1
0
0
2
0
0
0
0
1
0
2
2
1
0
1
1
0
2
1
2
1
1
0
1
1
0
2
1
2
1
2
0
2
1
1
1
1
1
0
1
0
1
2
1
1
1
0
0
1
1
0
1
2
0
1
2
2
0
1
2
1
0
0
1
0
2
2
2
1
1
2
0
0
1
2
2
1
1
0
1
0
1
1
0
2
1
2
3
2
2
1
2
2
0
1
2
2
0
0
2
0
0
0
1
0
2
1
0
0
0
0
0
1
3
1
2
0
1
0
4
2
0
1
0
0
2
1
1
1
1
1
2
2
1
0
1
0
1
0
0
1
2
0
2
2
1
1
1
1
1
0
1
2
1
2
1
1
1
1
1
2
2
1
0
0
2
3
1
1
1
1
0
2
1
1
1
1
1
2
1
1
1
0
1
1
0
0
2
1
1
1
1
0
2
1
1
1
0
0
0
1
1
2
1
2
0
2
1
1
1
0
1
0
1
1
2
2
1
1
2
1
1
2
2
1
2
1
0
0
1
1
0
2
1
0
2
1
2
1
1
1
0
1
1
1
1
1
1
0
2
1
0
2
1
2
1
1
3
2
0
1
1
1
1
0
2
1
0
0
1
2
0
1
2
1
1
1
0
0
1
1
1
2
1
1
1
0
0
1
2
0
2
0
2
2
2
1
1
2
0
1
1
1
0
1
1
1
0
0
1
2
0
1
0
2
0
1
2
0
2
1
1
2
3
1
2
1
0
1
2
0
2
1
1
2
0
1
1
1
1
1
0
3
1
0
1
1
1
1
1
1
1
1
0
0
2
1
0
0
2
0
2
1
2
1
1
2
2
0
1
1
2
1
0
2
0
1
2
2
1
1
1
1
2
1
1
0
1
0
1
1
2
2
1
2
1
0
0
1
1
7
0
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
1
2
2
0
2
1
1
0
1
1
0
4
0
1
1
2
1
1
1
1
0
1
1
1
1
0
1
1
0
1
2
1
0
0
0
1
1
0
0
1
0
1
1
0
1
0
1
0
0
1
2
0
0
0
2
1
2
1
0
1
1
1
1
0
2
1
0
3
1
1
0
3
1
1
0
0
2
1
2
2
2
1
1
1
1
1
0
0
1
1
2
1
2
0
0
2
1
1
1
0
0
0
0
1
0
0
2
0
1
2
0
1
0
0
0
1
1
2
1
1
0
1
1
1
2
2
2
0
1
1
1
1
1
0
1
0
1
1
0
1
1
0
1
1
2
1
1
0
1
0
1
0
1
1
0
0
3
1
0
1
0
1
3
1
1
2
2
1
0
1
1
1
2
0
3
1
1
1
1
0
0
1
1
1
0
1
0
2
1
2
1
2
1
0
1
1
1
1
0
1
2
1
2
1
0
1
2
2
0
1
0
0
1
1
2
0
1
2
0
2
1
1
0
1
1
2
2
0
1
0
0
2
0
0
2
1
1
1
1
0
2
1
0
0
2
1
0
0
0
2
0
2
1
1
1
1
2
1
1
0
0
2
1
2
0
2
2
1
2
1
0
1
1
0
1
0
1
1
2
2
0
0
0
2
0
1
2
1
2
2
0
1
2
0
2
2
0
2
2
2
1
1
2
1
0
2
0
2
1
0
0
1
1
1
1
2
1
2
2
1
0
0
1
1
1
1
1
0
1
1
1
1
2
2
0
0
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
2
0
0
2
0
0
1
2
2
1
2
1
0
1
2
0
0
1
0
0
0
0
1
0
0
0
4
0
1
1
2
1
0
0
1
1
2
0
1
1
0
2
0
1
0
1
2
1
1
0
0
1
0
1
2
1
0
0
0
2
2
2
0
1
0
1
2
1
0
1
1
1
1
0
1
1
1
0
1
0
1
2
0
1
2
1
1
1
1
0
2
1
0
0
0
1
2
2
1
0
0
1
1
1
1
2
2
1
0
1
0
0
1
1
1
0
1
1
1
2
1
0
0
1
0
1
1
0
2
2
0
2
0
1
0
0
0
1
1
1
2
1
2
2
1
1
2
2
1
0
1
0
1
1
1
1
0
0
1
2
1
1
1
0
1
2
0
1
2
2
1
2
0
1
1
1
2
1
1
0
1
1
2
0
0
1
2
1
2
1
2
1
1
1
0
0
2
1
1
1
1
0
1
0
2
2
1
1
1
1
1
0
2
1
0
1
0
1
1
2
2
1
0
1
1
0
1
0
1
1
1
0
1
1
2
1
1
0
1
2
1
1
2
0
1
1
0
0
2
1
1
1
0
0
2
1
1
1
2
0
0
2
1
1
1
2
2
1
1
2
2
1
1
2
1
1
0
1
0
3
1
1
0
2
1
1
0
1
0
2
0
1
1
0
1
0
2
1
1
1
0
0
0
2
1
2
1
1
1
0
1
1
1
1
0
1
1
1
2
1
2
1
1
2
2
0
1
0
2
1
1
2
1
1
2
2
1
2
0
0
2
0
0
2
0
1
0
0
1
1
1
1
1
2
0
0
1
3
1
1
0
0
2
2
2
0
1
0
0
1
0
0
2
1
1
1
0
1
1
1
1
0
1
1
0
1
1
3
2
2
2
0
0
0
1
1
1
1
1
1
2
1
0
1
1
1
1
0
0
1
0
2
1
2
3
1
2
1
1
2
0
0
0
2
2
1
2
0
2
1
1
0
1
2
1
2
2
1
1
1
0
2
1
0
0
0
2
2
0
1
0
1
2
2
1
1
0
0
1
1
0
2
0
2
1
2
0
2
0
1
2
0
0
0
0
0
0
1
1
1
1
0
1
0
0
2
1
0
1
0
2
1
2
2
0
1
1
0
1
2
2
0
2
2
1
2
1
1
0
0
2
2
1
0
0
0
1
1
1
1
0
0
2
0
1
1
1
1
0
1
2
0
1
1
1
0
0
1
0
2
0
1
1
3
2
2
1
1
0
2
1
0
0
1
0
0
1
2
1
1
1
1
0
1
1
1
0
1
1
2
1
1
1
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
2
1
1
1
0
0
0
1
0
1
0
1
1
2
1
1
1
1
0
1
1
1
0
1
0
0
1
2
0
1
1
1
1
1
0
2
1
1
2
0
1
1
1
2
1
1
1
0
2
0
1
0
1
0
1
1
1
1
1
1
0
0
0
0
2
1
2
1
0
1
1
0
2
2
0
1
1
2
2
2
2
1
0
1
1
1
0
2
2
2
1
1
3
0
0
4
2
1
1
0
2
2
0
2
1
0
1
0
1
1
0
1
1
0
1
1
0
1
2
1
1
1
0
1
1
0
1
1
2
1
3
2
0
1
1
2
0
1
0
1
1
1
0
1
0
2
1
1
1
0
2
2
0
0
1
0
0
1
1
0
1
2
0
1
0
1
0
1
2
6
1
0
0
1
0
1
1
2
0
2
0
0
1
1
0
1
0
1
1
1
1
1
1
1
0
1
2
1
1
1
2
0
1
1
1
0
0
2
1
2
1
1
1
1
1
2
1
2
1
0
0
1
1
0
1
1
2
1
1
0
2
0
1
1
0
1
0
1
0
1
1
1
0
2
1
1
0
1
0
1
1
1
0
2
0
2
1
1
2
2
1
0
0
1
0
0
2
1
1
0
1
2
1
2
2
1
1
0
0
2
1
1
0
2
0
0
1
1
1
0
0
0
1
1
1
1
1
2
1
2
0
0
0
1
1
1
2
0
0
0
0
2
2
1
0
1
0
0
1
0
1
1
1
0
1
1
0
2
0
2
1
0
0
1
1
1
1
0
0
1
1
1
2
1
0
0
1
0
0
2
2
0
0
0
1
1
0
0
1
1
2
1
1
1
0
1
5
1
0
1
1
0
1
0
1
1
1
1
2
0
1
1
0
1
0
1
1
1
0
1
2
0
1
1
0
1
0
1
1
1
2
2
0
3
1
1
0
1
0
0
2
1
0
1
1
0
1
2
1
0
1
1
0
0
0
1
0
2
2
0
1
0
1
1
2
2
1
0
1
1
2
0
1
1
0
1
0
1
1
2
1
0
1
1
1
0
1
1
2
1
0
1
1
3
0
0
1
1
0
2
1
0
2
1
1
1
1
2
1
2
1
1
1
1
1
3
1
2
2
0
2
0
1
2
1
2
1
1
0
1
1
1
2
1
1
0
1
1
1
1
0
1
2
0
1
2
0
1
1
1
0
1
0
2
2
1
1
1
2
1
1
2
1
1
1
0
0
0
2
0
0
1
2
2
2
1
1
2
0
1
1
2
0
1
0
1
3
1
1
1
1
0
0
1
1
2
2
1
2
2
0
1
2
1
2
1
1
0
0
1
0
1
0
1
1
1
1
1
1
2
1
1
1
1
1
1
1
0
2
1
2
1
2
1
2
1
0
0
0
2
0
1
2
1
1
0
1
1
0
1
0
2
2
1
0
1
3
0
1
0
0
0
2
1
1
1
0
1
1
2
1
1
2
1
2
1
1
1
2
1
1
0
1
1
1
2
2
0
2
0
0
1
1
1
0
1
1
1
1
2
2
2
1
0
1
1
1
1
1
0
2
0
1
2
1
1
1
1
0
1
0
1
1
0
0
1
1
2
2
0
1
0
2
2
1
2
1
1
2
1
0
1
1
1
2
1
0
1
1
0
1
0
1
1
1
1
0
1
1
2
1
2
1
0
1
0
0
1
1
2
0
3
1
0
1
1
1
1
1
2
1
2
1
1
1
2
1
1
0
0
0
1
2
2
2
2
1
2
1
1
1
1
1
1
0
1
1
0
1
0
1
1
2
0
1
0
1
1
0
1
1
1
2
2
1
0
1
1
1
3
1
1
1
1
1
1
2
0
0
1
2
1
0
0
0
1
2
0
1
0
2
1
2
1
1
1
0
0
1
1
2
1
2
1
1
1
0
1
1
1
1
1
1
1
2
0
1
2
0
0
3
2
0
0
0
2
1
1
2
2
1
1
0
0
2
1
0
0
0
1
1
1
0
0
2
2
2
0
1
2
0
0
1
1
1
2
1
0
0
0
0
0
2
2
1
0
1
2
1
1
1
2
1
2
1
1
1
0
2
0
1
2
1
0
1
1
0
2
0
0
1
1
1
1
2
1
1
0
1
3
2
0
2
0
0
0
1
1
1
0
0
2
2
2
1
0
0
1
2
1
2
1
0
2
1
2
1
1
1
2
1
1
0
0
4
2
0
0
1
0
1
2
0
1
1
1
1
0
3
1
1
2
0
1
0
1
1
1
1
2
2
1
0
0
1
2
0
2
1
2
1
2
1
0
0
2
2
1
0
1
0
3
0
1
2
4
2
1
0
0
2
0
2
1
1
2
0
2
2
1
2
1
1
1
1
1
1
0
1
1
1
1
1
1
0
1
0
1
0
1
2
7
1
1
0
0
1
0
0
0
1
2
0
1
0
0
1
1
1
2
2
2
2
0
2
2
0
1
2
2
1
1
0
0
0
1
1
1
1
2
0
0
1
1
1
1
2
0
0
1
1
1
1
0
0
0
1
1
1
1
0
2
2
0
2
0
2
0
3
0
1
0
1
1
1
1
1
2
2
1
2
2
3
0
1
0
2
1
1
1
1
1
0
0
1
2
1
1
0
1
1
1
2
0
0
1
2
2
1
0
0
0
0
1
1
1
0
0
0
2
1
2
0
2
1
1
0
1
2
1
1
1
2
1
1
4
1
2
1
1
1
0
2
1
2
1
0
1
0
0
1
0
2
1
1
1
0
3
0
0
1
1
0
1
0
0
1
1
1
2
1
1
0
1
1
0
1
1
0
1
2
0
1
1
0
2
1
0
0
0
0
1
0
0
0
1
1
0
0
1
1
1
1
0
2
1
1
1
2
1
2
1
1
1
1
0
1
1
1
2
2
2
0
3
1
2
2
0
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
3
1
1
1
1
1
1
2
0
1
2
1
0
1
1
1
0
1
1
0
1
1
3
1
1
1
0
1
1
1
1
1
1
1
1
0
1
0
1
1
2
1
1
0
1
2
0
0
1
0
0
1
1
1
0
1
1
0
1
1
0
0
1
2
0
2
1
1
0
1
1
2
2
0
1
3
4
0
2
2
1
1
0
2
1
1
1
0
2
1
1
0
2
1
2
0
2
1
1
2
0
0
0
0
1
1
2
1
2
0
1
1
2
0
2
2
1
2
1
1
1
1
0
1
2
1
1
1
0
0
1
2
2
1
0
1
1
1
0
0
1
1
3
0
0
0
2
0
1
0
1
1
1
0
1
1
1
1
1
1
0
2
1
1
0
1
1
1
1
0
2
1
2
0
1
1
1
0
1
1
0
1
1
3
0
1
2
1
1
1
1
1
1
0
1
0
0
0
2
1
2
2
2
1
1
2
1
2
1
1
1
1
1
1
2
1
2
2
1
1
1
2
0
0
0
2
1
1
0
0
1
1
0
1
0
0
0
1
2
0
0
1
0
1
1
2
0
2
1
0
0
2
0
2
1
1
0
0
0
0
2
0
2
2
1
1
1
0
0
1
1
0
1
0
2
1
0
3
1
1
1
2
1
2
1
1
1
0
1
0
0
2
1
2
2
1
0
1
1
0
1
1
2
0
1
0
0
1
1
2
1
1
0
0
2
1
1
1
2
2
1
2
1
1
1
0
1
0
2
0
2
1
0
0
1
1
2
1
0
1
2
2
0
1
1
1
1
1
1
0
1
2
2
1
0
2
1
0
0
1
2
0
2
1
0
1
0
1
0
0
0
1
1
1
1
1
1
1
1
0
1
1
1
1
0
1
2
1
1
2
1
1
1
2
0
1
2
1
0
1
1
2
0
0
1
0
1
0
0
2
0
2
1
1
1
1
2
1
2
1
0
0
1
1
1
1
1
2
1
1
1
2
1
0
1
0
2
1
1
1
0
2
2
1
1
0
1
0
0
2
0
2
1
0
1
2
0
0
2
1
2
2
2
1
0
2
1
1
2
0
0
1
0
1
0
0
2
0
1
0
0
0
2
1
0
1
1
1
2
0
0
0
2
1
1
2
2
0
2
1
0
2
1
1
0
1
1
1
0
0
2
0
1
1
1
1
1
2
2
1
0
1
0
2
0
1
1
0
2
1
1
0
1
2
2
1
1
2
1
0
1
1
2
1
1
0
2
0
0
1
1
2
1
0
1
1
0
1
2
0
0
0
1
2
0
1
0
2
0
2
0
0
1
0
0
2
0
1
1
1
1
1
1
0
2
1
0
2
2
0
0
1
2
1
1
1
0
2
0
1
2
1
1
2
1
0
1
2
2
1
1
1
0
0
1
1
2
0
2
2
0
2
2
2
1
1
2
0
1
0
0
0
2
2
1
0
0
1
0
1
1
2
1
1
0
1
0
0
1
2
0
1
2
0
2
1
0
1
2
1
1
1
1
1
2
3
0
0
1
0
1
1
0
0
0
1
1
0
0
1
2
1
2
2
1
0
1
0
2
3
2
0
1
2
0
1
1
1
1
0
0
1
1
1
0
0
2
1
0
2
2
1
1
2
0
1
2
1
0
0
0
0
1
0
1
1
1
1
0
2
0
0
0
1
2
2
2
0
0
1
1
1
2
1
1
0
2
1
2
1
2
1
1
0
2
0
0
0
3
1
1
1
2
1
1
1
1
0
1
2
0
1
2
2
3
1
1
2
0
1
0
2
1
1
2
1
1
0
1
4
0
2
2
2
0
1
1
0
0
0
2
4
2
2
1
2
1
1
0
1
1
2
0
1
1
1
1
1
2
5
3
0
0
1
2
1
0
0
2
1
1
1
2
0
1
0
2
1
1
1
1
2
1
0
0
1
1
0
1
2
0
1
1
2
1
1
0
3
1
2
2
1
1
0
0
1
0
1
1
0
1
1
0
0
0
1
1
0
0
1
1
0
0
2
1
1
1
2
0
1
2
1
1
1
1
0
1
2
1
1
1
1
2
2
1
1
0
2
1
2
0
2
0
1
2
1
1
1
0
1
1
2
2
0
0
1
1
1
1
2
1
1
0
0
1
1
2
0
1
2
0
1
1
1
1
1
1
1
2
0
1
1
1
0
1
1
0
2
0
1
2
2
1
1
1
1
2
1
0
1
3
2
0
1
1
1
0
1
2
0
2
1
0
1
1
0
1
1
1
2
1
1
0
1
0
1
2
2
1
1
1
1
0
1
1
1
0
2
1
0
0
1
2
0
2
1
2
2
1
2
1
1
1
0
1
1
2
0
1
2
1
0
1
0
1
0
1
1
2
1
2
1
2
2
0
0
4
1
1
0
0
0
2
1
1
2
1
1
1
0
1
2
2
0
1
2
1
0
1
2
1
1
1
1
1
0
1
0
2
2
2
1
2
2
2
2
2
1
1
0
1
1
0
2
0
2
1
1
0
1
0
1
1
2
1
1
2
2
1
2
1
0
1
2
0
1
1
1
1
0
1
2
2
2
1
2
1
1
1
0
1
0
2
1
2
1
0
1
2
0
0
2
1
0
2
0
1
1
1
2
0
0
2
0
1
2
1
1
2
3
0
1
1
0
0
0
1
0
0
0
1
1
1
0
1
0
0
1
1
1
2
1
0
2
1
1
0
0
2
1
1
0
2
1
0
1
2
0
1
0
1
0
0
1
1
2
1
1
1
2
0
1
2
1
1
0
1
3
0
1
0
0
1
0
0
1
0
1
2
1
0
1
0
0
0
1
3
0
1
0
1
1
1
2
2
0
0
0
1
1
0
1
0
1
2
0
1
2
2
1
1
1
0
0
2
0
0
0
0
0
0
0
2
1
1
1
1
2
1
0
0
0
2
0
1
1
1
1
2
0
0
2
1
3
0
1
2
1
1
0
0
2
1
1
0
1
1
2
1
1
2
1
1
1
1
1
1
1
0
2
1
1
2
1
2
1
2
0
2
1
2
0
3
0
2
1
1
1
1
2
0
2
0
0
1
1
0
1
1
1
2
1
0
2
3
0
0
1
0
1
1
1
1
1
2
1
1
1
1
2
1
1
0
0
1
0
1
0
1
1
1
2
0
0
1
0
1
1
2
1
1
1
1
0
1
1
1
1
1
1
2
0
0
1
1
1
0
1
0
0
1
0
1
0
0
2
0
2
0
1
0
1
2
2
1
2
0
1
2
1
1
1
0
1
1
1
1
0
1
1
1
2
2
1
1
1
1
1
2
0
1
0
2
0
1
2
1
2
0
0
1
0
0
1
2
1
2
3
2
1
1
0
1
1
1
1
2
1
0
1
0
1
0
1
0
1
1
0
0
1
1
1
2
1
1
1
2
1
0
1
1
0
1
2
1
1
1
1
1
1
0
1
1
1
1
1
2
1
1
0
1
2
2
1
1
2
1
1
0
1
2
2
1
0
1
1
2
1
1
0
1
2
1
1
0
1
0
0
1
1
0
2
2
1
0
2
1
0
1
0
0
2
1
5
2
1
1
0
0
1
0
3
1
2
1
0
1
0
1
0
2
1
1
2
2
0
1
0
1
1
1
0
0
1
1
4
2
0
2
0
0
1
1
2
2
2
2
2
2
1
2
0
1
0
0
0
1
2
2
0
0
2
1
2
1
1
2
1
1
1
1
2
0
1
1
0
2
0
1
1
1
0
0
0
1
0
0
0
3
0
0
1
1
0
1
1
1
1
1
2
1
0
1
1
1
0
1
1
1
2
1
0
2
1
2
2
0
1
2
0
2
1
1
0
1
0
2
2
1
1
1
1
2
0
0
2
0
1
1
2
0
0
1
0
0
1
0
1
0
1
2
0
2
2
0
1
2
1
2
1
0
0
0
1
0
1
0
1
1
1
0
0
2
0
2
1
2
1
0
1
2
1
1
2
1
1
3
1
1
1
1
0
2
0
0
1
1
0
2
1
1
1
1
1
2
1
1
2
2
1
1
1
1
2
2
2
1
2
1
0
1
1
0
1
0
1
0
1
1
1
2
1
0
0
2
1
1
0
1
1
1
1
0
0
0
2
0
1
0
1
1
1
1
1
2
1
1
1
1
2
2
1
0
1
2
1
1
0
0
2
1
2
2
3
2
0
1
2
2
0
0
1
1
2
1
2
1
0
0
2
1
0
2
1
0
2
2
2
0
2
1
1
1
0
1
0
1
0
1
1
2
1
0
0
1
1
1
0
2
0
2
1
0
2
2
2
0
0
2
1
2
0
1
2
0
1
2
1
2
2
2
2
2
2
1
1
1
0
1
0
0
2
2
0
0
0
2
2
0
1
0
1
2
1
0
1
1
0
0
1
2
1
1
0
2
1
1
1
2
0
1
2
1
0
1
1
1
0
1
1
2
2
1
1
1
1
2
1
1
1
2
1
0
1
1
1
0
0
0
1
2
1
1
0
0
2
2
2
1
0
0
2
0
0
1
1
0
1
1
0
1
1
0
0
2
1
2
1
0
1
0
1
1
1
1
0
0
1
1
1
1
1
2
0
1
0
1
1
1
2
0
2
1
1
1
0
1
0
1
0
0
1
1
0
1
1
0
0
1
1
2
1
0
1
1
0
1
2
2
0
1
2
1
1
0
0
1
1
0
0
1
1
0
2
0
0
1
2
1
0
1
2
0
0
1
2
2
0
0
1
0
1
0
0
1
1
1
1
1
0
1
1
1
1
1
1
2
0
0
1
1
0
0
0
2
1
0
0
1
1
0
0
0
2
1
0
1
1
2
1
1
0
1
1
2
2
1
1
2
0
1
3
0
1
1
0
1
0
1
1
1
2
1
0
1
1
2
1
1
1
1
1
2
0
1
1
0
0
1
1
2
1
2
1
1
1
1
2
1
0
1
1
0
1
0
1
1
1
1
2
1
1
0
0
3
1
1
2
1
0
1
2
0
0
1
0
0
2
0
1
1
0
1
2
2
2
2
0
0
1
0
0
2
1
2
1
1
1
1
2
1
0
1
1
0
1
1
1
1
1
2
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
2
1
2
2
1
0
1
2
2
1
1
1
2
1
1
0
0
0
0
0
2
1
2
3
2
1
1
1
1
2
0
1
2
0
0
2
1
1
1
0
2
1
0
2
0
0
0
1
1
1
1
0
0
1
0
1
1
0
2
1
0
2
0
1
1
1
0
2
1
1
1
1
1
0
2
2
0
1
2
2
2
1
1
1
1
1
1
1
1
2
1
1
1
0
0
1
2
1
1
0
2
1
1
0
1
2
2
1
2
0
0
0
2
1
0
0
3
1
1
0
2
0
0
0
2
1
1
0
0
1
3
0
1
1
3
1
1
0
1
0
0
1
1
2
1
1
0
0
1
2
1
1
0
0
1
1
2
1
2
2
0
1
2
0
1
0
1
2
1
0
1
0
1
0
0
1
2
1
3
1
1
1
1
1
2
1
1
0
0
0
1
2
1
0
0
1
1
1
1
2
1
1
2
1
1
0
2
2
1
1
2
0
0
1
1
1
1
0
1
1
0
2
1
0
1
2
1
0
2
2
0
1
0
1
1
2
0
0
1
1
2
2
1
0
1
0
0
1
0
0
0
1
2
0
1
0
2
1
2
2
1
0
1
1
1
1
1
2
1
1
1
2
1
1
1
0
2
3
2
2
1
1
1
0
0
0
0
1
0
1
0
1
2
1
2
1
2
2
1
1
2
2
1
0
0
1
1
1
0
0
0
0
0
2
1
2
1
0
1
1
0
0
1
0
0
0
3
1
2
0
2
1
1
1
0
1
0
1
1
2
1
1
2
1
2
1
1
1
1
1
4
2
0
0
0
4
0
2
2
1
1
2
0
1
2
1
1
2
0
0
1
1
1
2
1
3
0
1
1
1
1
0
1
1
0
1
1
1
0
1
1
1
0
0
1
0
1
0
0
1
0
3
0
1
0
1
2
1
1
1
1
2
1
1
1
1
1
2
1
1
2
1
1
1
1
1
0
0
1
2
2
0
1
1
1
1
1
0
0
1
1
0
1
0
1
1
1
0
0
1
1
0
1
1
1
1
0
1
1
1
1
1
2
1
2
2
1
1
1
0
4
2
1
0
0
1
1
2
1
2
1
0
0
0
0
2
2
0
0
1
1
0
2
1
1
1
1
1
0
1
0
1
1
1
0
2
0
0
1
1
1
1
2
0
1
2
1
1
0
0
1
0
0
1
2
0
2
1
2
2
0
2
2
0
1
0
1
1
1
2
0
1
1
1
0
0
1
0
1
1
2
1
0
1
1
0
3
2
0
0
1
0
1
0
1
2
2
1
0
2
1
1
1
0
1
0
0
2
1
2
1
1
0
1
3
2
0
3
0
2
0
1
1
1
2
1
0
1
1
1
0
0
1
1
1
1
0
1
1
2
2
1
2
1
1
0
0
1
0
0
1
1
2
0
1
0
1
1
2
1
1
1
2
1
2
1
0
0
1
1
1
0
0
1
0
2
1
1
1
2
2
0
1
1
1
4
1
3
1
0
1
0
1
0
2
1
0
2
0
1
0
1
1
1
2
1
0
1
0
0
2
1
2
1
0
2
0
0
0
1
1
0
1
1
1
1
2
1
1
2
1
1
1
3
1
1
1
2
0
0
2
0
2
1
0
2
2
1
2
0
2
2
2
2
1
0
2
2
1
1
0
2
0
1
2
0
2
0
1
0
1
1
1
0
2
1
0
1
0
2
0
2
0
1
1
0
1
0
0
2
2
1
1
1
1
1
0
1
0
1
2
1
1
1
1
1
0
1
1
2
1
0
1
1
2
0
1
2
0
0
0
0
1
2
2
2
1
1
0
2
1
1
2
0
2
1
2
0
1
1
2
1
1
1
1
2
1
0
0
1
2
0
1
0
2
1
1
0
0
1
2
1
1
2
1
1
0
0
2
1
3
1
1
1
1
0
1
1
2
1
1
2
1
2
0
1
2
2
1
2
1
0
1
1
0
0
1
1
0
0
0
0
1
2
0
1
1
2
1
1
0
0
1
2
2
1
1
0
0
1
1
0
1
1
1
1
1
2
0
1
1
1
2
1
1
0
0
1
2
1
0
1
1
2
1
0
1
1
0
2
0
0
1
1
1
3
2
0
0
2
1
2
1
2
2
1
1
0
0
1
1
2
1
0
1
2
0
1
1
1
2
1
2
2
0
1
1
1
1
1
2
3
1
1
1
1
2
1
0
1
0
1
0
1
1
1
1
2
0
2
1
1
2
2
0
2
1
1
2
2
1
0
0
1
2
2
0
0
1
2
1
1
1
2
2
0
1
2
0
0
1
1
2
2
0
0
1
1
1
2
2
1
0
2
0
2
2
1
1
1
0
0
2
1
0
1
1
1
0
1
1
0
1
1
0
0
1
0
0
1
2
2
1
2
2
0
2
2
2
2
1
1
2
1
1
1
2
0
1
2
1
2
0
1
1
1
1
1
0
2
1
1
1
0
2
0
1
0
1
0
1
1
2
1
1
1
2
1
0
2
0
0
3
1
1
3
0
3
1
0
1
2
1
1
1
2
1
0
1
1
1
1
0
2
1
1
0
3
1
1
2
1
1
2
0
0
2
0
1
1
0
1
0
0
1
1
2
1
0
1
1
0
0
0
0
1
1
1
1
2
1
0
0
1
1
1
1
1
0
2
2
0
1
1
1
1
2
0
0
1
0
1
1
2
2
0
1
1
1
0
1
1
0
0
2
0
0
2
3
0
1
0
1
0
1
1
0
3
1
1
2
1
0
1
0
1
1
2
1
1
1
0
1
1
1
1
1
0
2
2
2
1
1
0
1
1
0
0
0
1
0
2
1
1
1
1
0
1
2
2
1
0
0
0
1
0
1
3
1
1
1
0
0
2
1
1
0
1
0
2
1
1
1
1
0
1
0
1
1
1
0
0
2
1
0
0
2
1
0
2
1
1
1
0
0
2
1
2
1
0
2
1
1
1
1
2
2
0
1
1
1
0
1
2
0
2
0
2
0
1
1
2
0
2
0
1
0
0
1
0
1
1
0
0
0
0
1
0
1
1
1
1
1
0
2
1
1
0
1
2
1
2
0
0
0
2
2
1
1
1
0
2
0
0
1
0
1
1
1
2
1
1
1
1
0
1
1
0
0
1
0
0
2
1
1
1
2
0
0
0
2
0
1
2
1
2
0
1
1
1
2
1
0
2
2
2
2
1
1
1
1
0
2
0
2
2
1
1
1
2
1
1
1
0
0
1
1
1
1
1
1
1
0
1
1
1
2
1
0
0
1
0
1
0
1
1
0
0
1
0
1
1
1
2
2
1
1
1
1
1
2
2
1
0
1
1
2
0
0
0
2
0
1
1
1
0
1
0
1
1
2
0
2
0
0
1
0
1
1
0
1
1
1
0
1
1
2
1
1
0
1
1
0
1
2
1
0
1
0
1
0
2
1
2
1
1
2
1
0
2
0
0
1
1
1
0
1
1
1
1
1
1
2
2
1
2
2
2
0
2
2
1
1
0
2
1
0
1
0
1
0
0
2
1
0
2
4
0
1
1
0
1
3
2
1
2
0
0
1
0
1
1
0
0
0
0
2
3
1
2
0
2
0
1
0
1
1
1
0
2
1
2
1
1
1
1
1
2
1
1
0
0
2
0
2
1
3
0
1
2
1
0
0
1
2
1
1
1
0
1
1
0
0
0
0
1
1
2
1
0
1
1
0
1
1
1
0
0
1
0
1
1
0
0
1
2
1
2
2
0
0
0
0
1
1
2
0
0
2
1
1
0
0
2
0
1
1
1
0
0
0
0
1
2
0
3
0
1
2
0
1
1
0
1
0
0
2
1
1
2
0
0
2
0
0
1
1
0
1
2
1
1
0
0
2
0
1
1
1
1
1
0
1
2
1
1
1
2
1
1
0
0
1
0
1
2
1
1
2
2
2
1
2
0
0
0
1
1
0
2
0
0
1
0
1
0
0
1
2
1
0
1
1
0
0
1
2
1
0
2
0
2
2
2
2
2
1
0
1
1
1
2
0
0
1
2
1
1
2
2
0
2
1
0
1
0
1
1
1
3
1
2
1
0
1
2
0
1
1
1
1
1
2
0
0
0
0
1
0
1
2
1
1
0
1
1
0
0
0
1
2
1
0
0
2
1
1
0
1
1
1
0
2
2
1
1
0
1
1
1
2
1
1
2
1
2
1
0
0
1
2
1
1
0
1
2
2
1
1
1
1
1
1
0
1
1
1
2
1
2
1
1
1
1
0
2
0
1
1
0
2
0
2
1
1
2
0
1
2
0
1
2
1
2
0
1
1
1
0
2
1
1
1
0
1
2
2
1
0
1
0
0
1
0
1
2
1
1
1
2
1
1
2
0
1
1
0
1
1
1
0
2
0
1
0
1
1
1
1
1
1
2
2
2
0
0
2
1
1
1
2
1
0
2
0
3
0
1
1
0
2
0
1
1
0
2
1
2
2
3
1
1
3
0
0
2
1
1
1
0
2
1
2
1
2
1
1
0
2
0
1
1
2
2
1
1
1
0
0
1
1
0
2
1
1
0
1
0
1
0
2
1
2
3
0
0
2
0
2
1
1
1
2
0
1
1
1
1
2
2
0
0
0
0
1
1
1
2
1
2
2
1
1
1
0
0
1
0
0
1
1
2
0
1
2
1
2
2
2
1
0
0
2
1
1
1
0
1
2
1
2
1
1
2
1
0
1
1
0
0
2
2
0
2
1
1
0
2
1
0
0
0
1
0
2
0
2
2
1
1
0
1
1
1
0
1
2
1
1
1
1
0
2
1
1
1
1
0
1
0
0
1
1
2
0
1
1
1
1
2
0
0
0
1
0
0
0
1
0
2
1
0
1
1
0
0
2
0
1
0
1
1
0
2
2
2
0
0
2
1
1
2
2
1
1
0
0
1
1
2
2
1
2
0
2
2
1
2
1
1
1
0
2
0
0
1
1
1
1
0
1
2
2
1
1
1
0
1
0
2
0
1
1
1
1
1
1
1
0
2
1
1
2
1
1
0
0
1
0
1
2
2
1
0
1
1
1
0
2
1
0
1
0
1
2
2
2
1
1
0
0
1
0
1
1
2
2
1
1
0
2
2
0
1
1
2
1
1
0
2
0
0
1
2
0
0
2
1
1
0
1
1
1
1
0
0
1
0
1
1
1
1
1
1
1
1
1
0
2
1
0
1
0
1
2
0
0
0
1
1
1
1
2
1
1
0
0
1
1
1
1
1
0
1
1
2
1
1
1
1
1
0
1
1
0
2
1
0
0
2
1
0
0
0
1
1
2
0
2
0
0
1
1
0
1
1
2
2
2
2
1
0
0
1
1
1
1
1
0
0
1
1
1
0
1
2
1
1
1
0
2
1
0
1
1
1
1
0
2
1
1
0
1
1
1
1
0
2
2
1
1
2
1
1
0
2
0
2
0
0
2
0
1
0
1
1
2
1
1
2
0
2
0
2
0
1
1
1
0
1
1
0
2
1
1
2
1
0
1
1
1
0
1
1
0
1
0
2
0
0
2
1
0
1
1
2
0
0
1
1
1
1
2
1
2
1
2
1
1
1
1
1
2
1
1
2
0
0
2
1
0
2
0
1
0
0
1
1
0
1
1
1
1
2
1
1
2
0
1
1
1
2
1
1
2
0
0
1
1
2
1
2
1
1
1
1
1
1
0
1
1
0
0
1
0
0
3
0
0
0
1
0
1
1
2
1
0
2
1
1
0
1
0
1
1
1
1
0
1
0
1
0
0
3
1
1
0
1
3
2
0
0
1
1
2
0
1
1
1
1
0
0
0
2
0
1
0
0
1
1
0
1
2
1
2
2
0
1
0
1
1
1
1
1
2
1
1
1
2
2
1
2
1
0
1
1
1
1
0
0
1
2
0
2
1
2
0
0
1
0
0
1
1
0
2
0
1
1
1
2
2
1
0
1
0
1
2
1
1
0
1
0
1
0
1
2
0
1
1
1
0
2
2
1
2
1
1
1
0
1
2
1
1
2
1
1
0
2
1
2
2
2
0
1
1
2
0
2
1
2
0
2
1
1
1
0
1
1
1
0
0
1
1
0
1
2
1
0
2
1
1
1
1
1
1
1
0
1
1
0
1
2
2
1
2
2
1
0
2
0
0
0
1
1
1
1
1
0
1
1
1
1
1
0
1
2
1
0
1
1
2
2
1
1
1
0
3
2
0
0
0
1
0
0
0
2
1
0
1
2
0
0
2
2
1
0
1
2
1
0
1
2
2
0
2
1
2
0
1
0
1
1
1
1
0
1
0
0
0
1
2
1
0
1
1
1
3
1
0
1
1
2
1
1
1
1
1
0
0
0
1
2
1
3
1
1
2
0
1
1
2
0
1
2
1
0
2
2
0
1
1
2
1
2
1
2
1
2
0
2
1
2
0
0
1
2
0
0
2
1
1
0
0
0
1
2
1
1
2
2
0
2
0
1
1
1
1
1
0
1
0
1
0
2
0
2
3
1
1
1
0
1
2
3
2
0
0
0
0
1
1
1
0
0
2
1
1
1
1
2
2
1
0
2
2
2
1
0
2
2
1
1
0
2
1
0
1
1
1
0
1
2
1
2
1
2
1
1
0
0
0
0
2
0
1
0
2
0
1
0
0
0
1
1
1
2
0
2
2
1
1
1
1
2
1
0
0
2
0
0
0
1
1
0
1
1
1
1
1
0
1
0
2
2
1
1
0
0
1
3
1
0
0
0
2
2
0
2
0
0
0
2
0
6
0
2
0
0
1
1
2
1
0
0
1
2
1
1
1
2
0
2
1
1
1
0
1
1
1
1
0
2
2
1
0
3
1
0
2
2
0
1
0
2
1
1
1
0
1
1
0
1
2
0
0
0
1
0
1
1
0
1
1
1
0
2
0
1
1
1
1
3
1
0
0
2
2
2
0
0
1
0
1
2
0
2
1
1
1
1
0
0
1
1
2
0
0
2
1
0
1
1
0
1
0
0
1
2
2
1
1
0
1
1
2
1
0
0
0
0
1
1
0
0
1
2
1
2
1
1
2
1
1
1
1
0
0
1
0
1
1
1
1
0
2
1
1
1
2
2
2
0
0
1
1
0
1
0
2
1
1
1
0
1
2
1
1
2
1
0
1
1
2
3
2
1
0
2
0
6
1
1
1
0
1
2
2
1
2
0
1
0
0
1
1
2
0
1
2
0
1
1
1
0
1
1
0
2
0
1
1
1
1
1
1
0
0
0
1
0
0
3
4
0
0
1
1
0
2
0
0
1
2
1
1
0
1
1
1
0
1
0
1
1
1
1
1
1
1
1
2
0
0
1
1
1
3
1
2
1
2
1
0
0
1
0
0
1
0
0
2
1
1
0
1
2
0
2
0
1
2
2
0
1
0
0
1
1
1
1
1
1
2
1
0
1
0
1
2
0
2
2
1
2
2
0
0
0
0
1
0
1
1
0
1
1
2
0
1
1
2
2
1
1
1
0
1
1
2
2
1
0
2
0
0
0
1
2
0
1
2
1
2
2
0
1
1
0
0
0
1
1
1
2
1
1
0
1
1
1
1
2
0
1
1
0
2
0
1
0
2
1
0
0
0
1
1
2
2
0
0
2
0
1
1
1
1
1
1
0
2
2
1
1
1
1
1
0
0
0
0
1
2
0
1
0
2
1
1
1
1
1
2
1
1
0
0
1
0
1
1
1
1
0
1
0
1
1
0
0
0
1
0
2
0
2
1
2
0
0
1
1
0
2
1
2
0
2
0
1
1
1
1
1
0
1
1
2
0
0
0
1
0
1
1
1
2
2
1
1
0
1
1
0
1
1
0
1
1
1
0
0
0
1
0
1
2
1
0
1
0
1
1
0
1
1
2
0
1
2
0
1
1
2
0
0
1
2
1
0
0
0
0
2
0
0
1
1
1
1
0
1
0
1
1
1
1
1
0
0
0
1
0
1
1
1
1
1
0
1
2
2
1
2
1
0
2
2
1
2
1
1
2
1
2
1
1
1
1
1
1
1
2
1
0
0
0
1
1
1
2
0
1
0
0
1
1
1
0
1
1
2
0
1
0
1
1
1
2
1
1
1
4
1
4
0
2
2
2
0
1
1
2
1
2
2
2
1
0
1
2
0
2
1
1
1
1
1
1
1
2
1
2
1
1
1
1
0
1
0
2
1
1
1
1
1
1
0
0
2
2
1
1
2
0
2
2
1
1
1
0
2
1
2
2
1
2
2
1
2
0
3
2
2
1
1
1
1
1
3
1
1
2
2
1
1
0
1
1
2
0
0
2
1
1
0
1
1
2
1
2
0
2
2
2
0
0
1
2
0
2
0
1
0
2
1
1
2
0
2
0
1
1
2
1
0
1
2
1
2
0
1
1
1
0
2
0
1
2
1
1
1
0
2
0
0
1
1
1
2
1
0
2
1
0
2
1
2
1
1
2
0
1
1
0
1
2
0
1
2
1
1
1
1
0
1
0
2
0
2
1
1
1
0
0
0
1
1
0
1
1
0
1
0
0
1
1
1
0
1
1
1
2
0
1
2
1
1
1
1
1
1
2
1
1
2
0
0
1
2
2
0
0
1
1
2
1
0
0
1
3
0
2
1
1
1
0
1
1
1
2
1
1
1
0
0
2
1
0
0
1
2
1
2
0
1
0
0
1
0
2
1
1
1
1
2
1
1
1
2
1
1
0
0
0
0
1
1
1
1
2
1
0
1
1
0
1
1
1
1
1
0
1
0
2
2
0
1
2
1
2
0
0
1
2
0
1
2
0
2
1
2
1
2
0
0
0
2
1
1
2
0
1
2
0
4
0
1
1
0
0
2
0
2
1
2
2
1
0
0
1
0
0
1
2
1
1
2
1
1
0
0
2
1
0
2
1
2
1
1
0
1
0
0
1
2
2
2
2
0
2
2
0
1
2
2
2
1
1
0
1
1
0
1
0
2
0
1
1
2
1
0
2
1
2
1
1
1
0
1
0
1
1
0
1
0
1
0
0
2
0
1
2
2
1
2
2
1
0
1
1
1
0
1
1
1
1
2
2
1
0
1
2
1
1
1
0
1
0
1
2
2
1
1
0
2
1
0
1
1
1
0
1
0
2
1
2
1
0
0
0
1
1
1
1
2
1
2
1
1
0
0
1
2
0
2
2
2
2
1
0
0
0
1
1
2
0
1
1
1
2
0
1
0
0
1
0
0
1
0
1
2
0
1
2
2
0
1
1
1
0
1
1
2
1
0
0
0
1
1
2
1
0
1
1
0
0
2
1
1
0
0
0
1
1
1
0
2
2
1
0
2
2
2
2
1
0
1
1
1
2
1
2
2
2
1
0
1
1
2
1
1
1
2
0
3
1
0
1
0
2
1
0
1
1
1
1
0
1
1
0
1
1
2
1
1
1
2
0
2
2
0
0
1
1
0
2
0
2
0
2
1
1
1
1
2
0
1
0
2
0
2
1
1
0
2
2
2
0
0
1
1
0
2
1
0
0
2
2
1
1
1
1
1
2
1
1
1
1
2
0
2
1
1
1
1
2
0
2
0
2
1
1
1
0
2
1
1
1
1
2
0
1
1
1
1
1
1
1
2
1
1
2
0
0
1
1
0
1
1
1
0
1
1
0
1
0
0
1
1
2
0
0
1
1
1
2
0
0
1
1
2
1
0
2
1
0
0
2
2
0
1
2
1
0
0
1
0
1
1
1
2
0
1
1
0
1
2
1
1
1
0
1
0
1
1
0
1
1
0
1
2
1
1
0
0
1
2
1
1
2
0
0
2
0
1
0
2
0
2
1
1
1
1
2
1
1
2
1
1
2
0
0
0
1
2
1
1
0
2
1
1
1
1
1
0
0
1
0
0
1
0
1
2
0
0
1
1
0
1
2
1
2
1
0
2
1
1
1
1
1
0
0
1
1
0
2
0
1
1
1
1
1
1
0
1
0
0
1
0
2
0
0
1
0
1
1
1
2
1
2
1
1
1
2
1
2
0
1
1
1
1
2
0
1
0
1
1
1
2
0
1
1
1
2
1
2
1
1
0
2
1
1
1
1
1
2
1
0
2
1
1
0
1
0
0
0
1
0
0
0
1
0
1
1
2
0
1
2
2
1
1
1
0
3
1
1
1
0
1
1
1
2
1
2
0
1
2
1
0
2
2
0
1
1
1
0
1
2
1
2
1
1
1
1
1
1
2
2
0
1
0
2
1
0
1
1
1
0
1
1
1
0
2
2
2
0
2
1
1
1
2
3
1
2
2
0
1
1
0
0
1
0
1
2
1
0
0
2
1
1
2
0
2
2
0
0
1
3
0
1
1
1
1
1
1
1
0
0
2
0
2
2
0
2
1
1
1
2
1
0
0
2
1
1
0
0
1
1
2
1
2
1
2
0
3
1
1
1
1
0
1
0
0
1
1
1
2
1
1
1
1
0
0
2
1
1
0
1
1
2
0
2
1
0
1
0
1
0
2
2
2
0
2
2
1
2
1
1
1
1
0
0
0
2
1
3
1
1
2
3
0
2
0
0
1
1
1
1
1
1
1
0
0
1
0
2
0
2
1
1
2
0
0
0
0
0
2
1
1
1
2
0
0
1
2
1
2
2
1
1
0
0
1
1
1
0
0
1
2
2
0
1
1
1
0
0
0
2
1
1
1
1
1
1
1
1
1
1
0
2
0
0
0
1
0
0
0
1
0
1
1
0
1
1
1
1
1
1
1
0
1
2
0
1
0
0
1
0
1
2
1
1
0
1
1
1
2
2
2
0
1
1
3
0
1
0
0
1
1
0
0
0
1
0
1
0
0
1
0
2
1
0
0
1
1
0
0
0
0
1
1
1
0
1
1
0
0
2
1
0
0
1
2
1
1
1
1
2
2
0
1
0
0
1
1
2
2
2
1
1
1
0
1
0
0
1
2
2
1
0
2
2
0
1
0
2
0
2
1
1
0
2
1
1
0
1
2
0
2
0
2
0
0
1
2
0
1
1
2
1
2
2
0
1
0
0
2
0
0
1
1
0
2
2
2
1
2
2
0
0
3
0
1
0
1
2
2
2
1
1
1
1
0
1
0
1
1
0
0
1
0
0
2
1
3
0
0
2
1
1
1
2
0
1
1
1
0
0
2
0
1
2
2
2
0
0
1
1
2
2
1
2
0
1
2
0
1
1
0
0
1
1
0
0
1
1
0
0
1
2
1
0
0
2
2
1
0
2
1
0
2
2
2
0
1
1
1
0
1
1
0
1
0
1
2
2
2
1
1
0
1
1
1
2
1
1
0
0
1
1
1
1
1
2
0
1
0
1
1
1
1
1
2
0
0
1
3
2
0
0
0
1
1
2
2
0
2
2
0
1
1
1
1
1
0
0
0
0
0
1
2
1
0
0
1
0
0
0
1
1
0
0
1
2
1
2
2
2
1
1
1
1
2
1
0
0
1
1
0
0
1
1
2
0
2
0
0
1
1
1
1
2
2
1
0
1
0
0
1
0
1
1
2
2
2
2
1
1
2
1
2
1
0
0
0
2
1
0
0
2
1
2
0
1
2
2
1
1
1
1
1
1
1
0
1
0
2
1
0
1
1
1
2
0
1
10
1
2
2
0
0
0
0
0
2
1
2
0
1
0
1
1
0
1
1
0
0
1
2
1
1
2
1
0
2
1
1
1
2
1
1
1
2
1
1
1
0
1
2
0
2
1
1
0
1
2
0
1
1
2
1
0
1
1
1
0
0
0
2
2
2
1
0
0
1
1
0
0
1
1
1
2
1
1
0
1
2
1
0
2
0
1
1
2
0
2
1
0
0
0
0
0
1
0
1
0
0
2
1
1
3
1
2
1
0
1
1
1
0
0
1
1
0
0
1
1
0
1
1
2
1
1
1
1
0
1
2
1
1
0
1
0
2
0
0
2
2
2
0
1
0
2
1
0
1
1
2
1
1
2
3
1
0
1
1
1
0
1
0
0
2
1
1
2
1
1
0
0
0
1
1
1
0
0
2
3
1
2
0
1
2
1
0
1
1
2
1
1
1
2
0
1
2
0
2
0
1
2
1
1
2
1
1
1
0
1
1
2
0
2
0
0
1
2
2
1
1
0
1
1
1
0
1
1
0
1
0
2
1
0
1
1
1
1
0
0
0
2
1
1
1
1
2
1
2
2
2
1
2
2
1
0
2
0
1
1
0
1
1
2
1
1
0
0
1
2
2
1
0
1
1
2
0
1
1
2
1
1
1
1
0
0
0
2
1
1
2
1
0
1
2
2
1
2
1
1
0
2
2
0
1
2
1
1
1
2
1
1
1
0
1
1
0
1
1
1
1
0
1
1
1
0
1
0
0
1
0
0
2
1
2
1
2
2
1
0
1
0
2
0
1
1
2
1
1
0
1
1
0
0
1
1
0
1
1
0
2
1
0
2
2
1
0
1
1
2
2
2
0
1
2
0
1
1
2
2
0
1
1
0
2
1
1
1
2
1
2
1
0
1
0
0
2
0
1
2
0
2
0
1
2
1
0
1
0
1
0
0
1
1
0
1
0
1
2
1
1
1
1
2
1
0
0
0
0
0
2
1
1
1
1
1
1
1
1
1
4
1
1
0
0
1
0
0
1
1
2
1
0
0
1
0
1
0
1
1
2
1
2
1
0
0
1
0
1
2
0
1
1
1
0
1
1
1
0
0
1
0
1
0
1
0
1
0
2
1
2
1
1
1
1
0
1
2
1
2
1
1
2
1
1
2
2
1
1
1
1
1
1
1
1
1
2
1
1
0
1
2
1
1
0
1
0
1
0
0
0
0
3
2
1
1
1
2
1
1
0
0
2
0
1
1
1
0
2
2
1
1
0
1
2
0
3
0
0
0
0
0
1
1
1
0
2
1
2
1
1
1
0
1
0
0
0
3
2
2
2
1
1
1
2
1
0
0
1
0
2
0
1
2
0
1
1
1
1
1
2
1
1
1
0
1
2
1
1
1
1
1
2
0
1
1
1
2
0
1
0
1
2
0
2
1
1
0
0
1
0
1
0
1
2
2
1
1
0
0
1
2
1
2
1
1
1
2
1
2
1
3
0
1
0
1
1
1
0
0
0
1
2
0
1
0
2
1
2
1
2
1
1
0
0
1
1
1
2
1
1
1
1
1
1
0
2
1
0
1
0
2
1
1
2
1
1
2
2
1
2
0
1
1
2
1
1
1
1
1
0
2
1
0
2
0
1
1
1
2
2
1
2
0
1
0
2
1
1
1
2
1
1
1
0
1
1
0
0
0
0
2
1
1
1
0
0
1
1
1
3
0
1
2
1
2
1
1
2
1
0
0
0
2
1
1
1
2
1
2
1
3
1
1
2
2
1
0
1
2
2
1
1
1
1
2
2
2
1
0
1
1
3
2
1
1
1
1
2
2
1
1
1
1
0
2
1
1
1
1
0
1
0
2
1
1
1
2
2
1
1
0
0
2
0
1
1
0
1
1
1
2
2
1
0
1
2
2
0
2
1
2
0
1
2
2
0
2
1
1
1
0
2
1
1
0
1
1
1
0
1
1
1
2
2
1
1
2
1
1
1
0
0
2
0
1
1
1
1
0
0
0
1
1
1
1
0
1
2
0
0
0
1
2
3
1
0
2
1
0
1
2
1
3
2
0
1
2
1
0
1
0
1
1
1
1
1
1
1
0
1
0
1
2
0
0
1
2
1
2
2
2
1
1
2
2
1
1
1
1
1
2
0
2
1
0
2
0
0
2
1
1
2
1
1
0
1
0
1
0
1
1
2
1
1
1
1
2
0
1
1
1
0
1
1
2
1
0
2
2
0
0
2
1
1
2
1
1
0
2
0
0
0
1
0
0
1
0
0
1
0
0
0
1
2
1
0
0
1
1
0
0
1
1
2
0
1
2
1
1
1
0
0
1
1
1
0
0
0
1
0
0
1
1
1
0
1
1
1
1
1
1
3
1
2
0
1
2
2
1
0
0
2
1
1
1
0
1
1
0
2
2
2
1
1
1
1
1
2
0
0
0
1
1
0
1
0
1
2
0
1
1
1
1
1
2
2
2
1
0
0
1
1
2
0
1
0
0
1
0
1
0
1
0
3
2
1
1
1
1
0
0
1
1
1
2
2
0
0
2
2
1
1
1
1
0
2
0
2
1
1
1
0
4
1
1
1
1
0
1
1
1
1
1
0
0
1
0
1
1
0
0
0
0
0
1
1
0
1
1
1
2
2
2
0
2
1
1
1
1
0
2
2
0
0
1
0
1
1
2
0
0
1
1
0
1
1
1
1
2
2
1
1
2
1
1
2
0
1
1
1
0
0
1
1
1
1
0
0
1
2
2
1
0
1
1
2
1
1
0
2
2
4
0
1
1
0
2
2
2
0
2
1
0
0
0
1
1
1
1
2
0
1
0
1
0
2
1
1
1
1
0
0
1
2
1
1
0
2
0
1
1
2
2
1
2
0
1
2
0
1
2
1
1
0
1
2
0
0
1
1
1
1
2
0
1
1
1
1
2
1
1
2
1
1
2
2
2
1
0
0
1
1
1
1
0
1
1
1
1
1
2
1
1
1
1
1
1
0
1
1
1
3
1
0
1
4
0
1
2
0
2
0
1
2
2
1
0
0
2
2
0
0
1
1
0
1
2
1
0
1
1
2
0
1
2
1
1
2
2
0
1
1
0
1
0
2
3
2
0
1
1
0
0
0
1
1
2
0
1
1
0
1
0
0
0
1
0
1
0
0
0
1
1
2
1
2
0
0
1
1
2
1
0
0
0
3
0
1
0
2
1
0
1
1
1
1
1
1
0
1
1
1
0
0
2
1
1
0
1
1
3
0
1
0
2
1
1
2
2
2
1
1
1
1
1
0
2
1
0
1
1
1
1
1
2
1
1
1
2
1
0
0
1
2
0
1
0
1
0
1
0
0
2
0
1
1
2
1
1
1
1
0
2
1
1
2
1
0
0
2
2
0
0
1
1
1
1
4
1
1
1
1
0
1
0
2
1
2
2
1
1
2
1
1
0
0
1
0
1
2
0
0
0
1
1
1
1
0
0
2
1
1
0
2
1
2
1
1
1
0
1
2
0
0
2
1
1
1
1
0
1
0
0
0
1
1
1
1
1
1
1
2
1
1
1
2
1
3
0
1
1
1
1
0
1
2
1
0
2
1
2
1
2
2
1
1
0
1
2
2
0
1
0
0
1
2
2
0
1
1
2
1
1
0
1
1
0
2
1
0
1
1
1
0
0
2
4
1
2
0
1
1
1
1
2
0
0
1
2
1
1
1
1
1
0
0
0
0
1
2
0
0
1
0
0
0
2
0
1
0
1
0
2
0
2
1
1
1
1
1
0
2
0
1
1
1
1
1
0
2
4
0
2
2
1
1
1
1
1
1
1
1
1
2
0
1
3
1
1
0
0
2
1
2
1
2
1
1
2
0
0
1
1
0
3
1
1
2
2
1
1
1
1
1
1
3
0
0
0
1
0
1
0
0
0
1
0
2
2
0
0
2
1
0
1
1
1
1
0
1
0
0
1
1
1
1
0
0
1
1
1
2
1
1
1
2
0
0
2
0
1
1
1
1
1
1
1
1
1
1
2
0
0
1
3
0
2
1
0
0
0
1
1
0
2
0
2
0
1
2
0
1
0
1
0
0
1
1
1
1
0
1
1
1
2
0
0
1
1
1
2
1
1
2
1
0
1
0
0
1
2
2
1
4
2
2
2
1
2
0
1
1
1
1
0
0
0
1
2
2
2
1
1
1
1
0
2
1
3
0
1
1
1
2
1
1
0
0
1
1
1
0
0
0
0
1
1
1
1
1
2
2
2
0
2
1
0
1
1
1
1
0
0
3
1
0
1
1
1
2
1
0
0
2
2
2
0
1
1
0
2
0
3
1
1
2
1
2
2
1
0
0
1
1
1
1
2
0
1
1
0
1
0
2
2
2
1
2
0
0
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
0
0
0
0
1
2
0
2
1
1
1
2
1
1
0
1
0
1
1
0
1
0
1
0
1
1
1
1
1
1
2
1
2
0
1
1
2
2
1
1
1
2
1
2
0
0
1
1
1
1
1
1
0
2
1
1
0
0
2
1
0
1
2
2
1
1
1
1
2
1
0
1
1
2
1
1
1
2
0
0
2
0
0
0
2
0
1
1
0
0
2
1
1
1
1
1
1
1
0
0
0
2
1
0
0
0
0
0
1
2
3
1
2
1
1
2
2
1
1
1
1
0
2
2
0
0
2
0
0
2
1
1
2
0
0
0
0
1
0
2
2
2
0
0
2
1
2
1
2
0
0
0
0
1
1
0
3
2
2
1
1
2
1
3
2
2
2
2
1
1
1
1
1
1
1
0
0
1
1
0
1
3
0
2
0
2
0
0
0
1
1
1
1
1
0
0
0
1
0
2
2
1
1
0
2
2
2
0
2
1
0
2
0
0
2
3
0
1
0
0
1
0
0
0
2
1
1
1
1
1
1
1
1
1
0
1
1
0
0
1
0
2
0
1
1
1
2
0
0
0
2
0
2
1
0
1
1
1
0
2
1
0
0
2
1
2
1
0
1
1
1
1
1
1
0
0
0
1
2
1
1
1
1
0
1
0
0
1
1
1
0
1
1
1
1
1
2
1
1
2
1
0
1
1
0
1
1
2
1
2
1
1
0
1
1
0
2
1
2
1
1
1
1
0
1
0
2
1
1
2
0
0
0
0
1
1
1
2
1
2
1
1
1
0
0
1
1
1
1
0
2
1
2
0
0
1
0
2
1
2
1
1
2
2
1
0
1
1
1
2
1
2
1
2
1
1
2
1
1
2
0
1
0
1
0
2
1
2
1
2
1
1
0
0
2
1
2
0
2
1
1
0
0
0
1
1
2
1
1
1
0
2
2
0
0
1
1
0
0
0
1
0
0
2
2
1
1
1
0
1
1
1
0
0
1
1
1
1
1
1
0
1
2
1
2
1
1
1
0
1
1
1
2
0
1
2
4
0
0
1
2
1
1
2
1
1
0
0
0
0
2
1
2
1
1
0
1
1
2
1
2
0
2
2
1
0
0
2
0
1
1
2
3
0
1
1
0
1
1
0
1
0
1
0
0
1
1
1
1
1
2
0
1
2
1
1
1
0
1
2
2
1
0
0
2
0
2
2
1
0
2
1
2
1
1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
2
0
1
1
1
1
1
0
0
2
1
0
2
1
0
2
2
1
1
1
1
0
1
1
0
0
0
2
1
3
0
0
0
0
1
1
1
0
2
1
1
1
1
2
1
2
0
1
0
1
0
1
1
1
2
1
1
2
1
0
0
2
1
1
1
1
1
0
1
1
1
1
1
1
2
2
0
1
1
0
2
2
1
2
1
1
0
1
2
0
2
1
0
0
0
1
1
0
1
0
1
0
1
1
1
0
1
1
2
0
1
0
1
3
1
2
1
0
1
0
1
0
1
1
1
0
1
2
1
0
0
0
0
1
1
1
1
2
2
2
2
0
0
2
1
1
2
1
1
0
0
2
1
1
1
1
1
1
0
1
1
0
2
1
2
1
0
1
1
1
1
1
0
1
1
0
1
0
2
0
0
0
1
3
1
0
0
1
2
0
0
0
1
2
1
2
2
1
0
1
1
1
0
0
2
0
1
0
0
1
1
1
1
0
1
2
0
2
1
0
1
0
2
1
1
1
1
2
0
4
1
1
1
3
1
1
2
1
1
0
1
1
0
1
0
1
2
2
1
0
0
2
2
1
0
0
1
1
1
2
1
1
2
2
1
1
2
1
0
1
0
3
0
1
1
0
0
0
1
1
1
1
1
3
1
1
1
0
0
2
1
2
0
1
2
0
1
1
1
1
0
2
1
1
4
1
1
1
2
1
4
2
2
0
0
2
1
1
1
0
1
1
1
0
1
0
0
0
1
2
0
0
0
0
0
1
1
1
2
1
1
0
1
1
1
2
1
1
2
2
1
0
0
1
0
0
0
0
2
1
2
0
1
1
1
2
1
1
2
1
1
2
3
0
0
1
2
0
2
0
1
1
0
2
0
0
1
1
2
1
0
1
2
1
2
0
1
1
0
0
2
0
2
0
2
0
1
2
2
0
1
0
2
1
2
1
0
2
1
1
2
2
1
1
0
1
0
2
1
1
2
1
1
1
1
3
1
2
1
0
1
2
1
2
0
1
0
2
1
1
1
2
1
2
1
1
2
1
1
0
2
1
1
2
1
2
0
2
0
0
1
2
1
1
1
0
2
2
1
1
2
1
0
0
1
1
1
1
1
1
1
1
2
1
1
1
1
0
2
0
0
1
0
2
1
0
3
0
1
1
0
0
2
1
2
1
1
2
2
0
0
1
0
1
2
1
1
0
1
1
1
0
1
1
0
2
2
0
2
0
0
2
1
1
1
0
1
1
1
1
1
2
0
2
2
0
0
1
1
1
1
1
0
0
0
0
0
1
2
1
1
0
1
2
0
0
1
2
2
2
2
1
2
1
0
1
0
0
1
1
2
1
0
0
1
1
0
0
1
2
2
1
2
1
3
0
0
0
2
1
1
0
2
0
1
1
0
2
1
1
2
0
1
0
0
1
1
1
1
1
0
1
0
2
1
1
1
0
1
2
1
1
0
0
2
0
2
1
0
1
1
1
1
0
1
1
1
2
0
1
0
1
2
0
1
2
1
0
1
0
2
2
1
1
0
2
1
1
2
1
0
2
1
1
1
0
2
1
1
1
1
0
2
1
2
1
0
0
1
2
1
1
1
0
1
0
0
0
2
1
1
0
1
1
0
0
2
1
1
1
0
1
0
1
0
1
2
1
0
0
0
2
2
1
1
3
0
0
0
0
1
1
1
0
0
1
2
0
1
0
0
1
1
1
1
0
2
1
1
1
0
2
1
2
0
1
1
1
1
1
0
2
2
0
1
2
2
1
1
0
0
1
1
1
1
2
1
0
1
0
0
2
2
0
0
1
1
2
2
1
0
2
2
1
2
1
2
1
1
1
2
0
1
0
2
0
1
1
1
1
1
1
0
1
1
0
1
1
1
1
0
1
1
0
2
1
1
1
1
2
0
0
2
0
1
0
2
1
1
3
0
1
1
1
0
1
2
2
1
2
0
1
1
1
0
1
1
0
1
1
2
0
2
1
1
1
1
1
1
0
1
0
1
5
0
2
2
1
1
1
1
2
2
0
0
2
1
1
0
2
0
2
1
2
0
1
2
0
1
2
1
0
2
1
0
2
1
1
0
1
0
2
0
2
0
1
0
1
1
1
2
2
1
1
0
1
2
1
2
1
1
2
0
1
2
1
1
0
1
1
0
0
0
1
1
2
0
1
0
1
1
1
0
0
0
2
1
0
1
1
2
0
1
1
2
1
2
0
0
2
1
1
2
1
1
2
1
1
1
0
1
2
0
2
1
1
1
1
1
1
1
0
0
2
0
1
1
1
0
1
0
1
1
1
2
0
0
1
2
1
0
1
1
0
1
1
2
1
1
0
1
0
1
1
1
2
1
2
1
1
1
1
2
4
1
1
1
1
0
0
1
1
1
1
2
1
0
1
1
1
1
2
0
1
2
1
1
0
2
1
0
0
1
1
0
1
0
1
2
1
1
2
1
0
0
0
1
0
1
1
0
1
1
1
1
2
1
1
1
2
1
1
1
1
0
2
1
1
1
0
1
2
0
1
1
1
2
1
1
0
0
1
2
0
0
0
4
0
0
1
1
1
0
2
2
1
2
0
0
2
1
2
1
0
1
1
2
0
1
0
1
1
2
1
1
2
0
3
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
2
1
1
1
3
0
1
1
0
1
0
1
2
0
3
1
1
1
1
0
1
0
2
2
2
1
2
0
0
0
0
1
2
0
1
0
1
0
2
0
1
2
2
0
1
1
1
0
1
2
2
1
1
1
0
1
0
1
1
0
1
0
2
1
3
0
0
1
1
2
1
2
2
1
1
0
1
2
2
1
2
1
1
1
0
2
1
0
0
1
1
1
0
1
1
3
1
0
0
2
1
1
1
1
0
1
1
0
2
1
1
1
2
2
1
1
2
1
1
1
2
0
1
3
1
1
1
1
0
0
2
0
0
1
3
1
1
1
0
0
0
0
1
1
2
0
1
1
1
1
2
1
0
1
2
1
1
0
2
2
2
0
1
1
2
0
2
0
1
2
0
1
0
0
1
1
0
1
2
2
1
0
1
1
0
1
2
1
1
0
0
1
1
0
1
1
2
0
1
0
0
0
1
2
2
1
2
2
1
2
1
1
0
0
0
0
0
1
2
3
1
0
2
1
0
2
1
1
0
1
0
1
0
2
4
1
1
0
1
2
1
1
0
1
2
0
0
1
1
2
1
2
1
1
2
1
1
1
1
1
1
1
0
0
1
2
3
2
1
0
0
0
1
2
0
1
1
0
2
2
1
1
0
0
1
0
1
2
2
0
1
2
1
1
2
1
0
2
1
3
2
2
0
1
1
1
2
2
2
1
0
1
1
0
0
0
1
1
0
0
1
0
0
1
2
0
2
1
1
0
2
2
1
2
0
1
0
1
1
2
1
1
1
1
0
0
2
0
1
0
0
2
1
0
1
0
1
1
2
1
2
1
2
2
0
2
1
0
0
2
0
1
2
0
0
2
0
2
1
1
2
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
0
1
2
2
0
1
1
1
2
0
0
0
1
1
2
1
0
2
2
0
1
0
2
0
0
1
0
1
1
2
1
1
2
0
0
1
0
0
1
1
1
0
2
0
2
1
0
1
1
2
1
2
1
2
0
0
0
1
0
1
2
2
1
0
2
1
0
0
0
1
2
2
0
1
1
2
2
0
1
1
1
0
1
2
1
0
1
2
0
0
1
2
2
0
0
1
0
1
1
2
2
2
2
0
1
1
1
1
1
1
0
0
2
1
2
1
2
0
2
2
0
0
1
2
1
0
0
2
1
0
1
1
2
1
2
2
0
0
2
1
1
0
2
2
0
2
0
1
2
1
1
0
1
2
1
1
1
0
0
1
1
1
1
1
1
0
0
2
1
2
1
1
2
1
0
1
1
1
1
1
1
1
2
1
0
1
0
0
0
1
1
2
1
2
1
1
2
0
2
1
1
2
2
2
0
2
2
1
1
1
1
1
1
3
0
1
0
2
0
1
2
0
1
2
2
1
2
1
2
1
0
2
1
0
1
3
0
2
2
1
1
1
2
1
1
1
1
1
1
1
2
2
0
1
1
1
0
0
1
1
2
1
0
0
2
0
2
0
1
0
1
1
2
1
2
0
2
2
1
1
0
1
1
0
1
1
1
1
1
0
0
2
1
0
1
0
2
1
1
1
1
1
0
1
1
1
2
1
1
2
1
2
2
1
2
0
1
2
1
2
0
1
0
1
0
2
0
1
1
0
0
2
1
2
1
0
2
2
0
1
2
0
1
1
0
0
2
0
2
0
1
1
1
1
1
2
1
1
2
1
1
1
1
2
1
2
1
0
2
0
1
1
2
1
0
1
1
1
1
1
1
2
1
2
1
2
0
0
1
1
0
2
1
2
2
2
2
1
0
1
1
0
2
1
0
1
0
0
0
1
2
2
1
0
1
1
1
1
2
2
1
0
1
1
2
2
2
0
0
1
1
1
1
2
1
0
1
0
1
0
1
0
2
1
1
1
2
1
1
2
0
0
1
0
0
0
0
3
2
0
1
1
0
1
1
0
2
2
1
1
0
0
0
1
1
1
0
0
1
2
3
1
0
3
2
1
1
1
0
1
0
1
0
1
1
1
1
1
1
0
1
2
1
1
1
1
1
0
1
2
2
1
0
0
1
2
1
0
0
0
1
0
1
1
2
1
0
1
1
1
0
1
0
0
0
1
1
0
1
1
1
2
1
0
1
2
1
1
0
1
2
1
2
0
0
2
1
0
0
1
0
2
1
0
0
2
2
0
0
1
2
1
1
1
1
1
3
1
1
0
1
1
1
1
2
1
2
0
1
1
2
2
2
1
1
1
1
0
1
1
1
1
1
1
1
1
1
2
1
2
1
0
1
0
1
1
1
1
1
0
1
1
2
0
1
2
0
1
1
1
1
3
2
0
1
0
1
2
2
0
0
1
2
2
1
0
0
0
1
0
2
0
0
1
0
1
1
1
0
1
2
2
2
1
1
1
0
1
0
0
1
0
2
0
1
2
0
0
0
2
2
2
2
0
0
1
1
1
0
2
0
0
1
1
1
1
1
1
1
1
1
1
2
1
1
0
1
2
0
1
1
2
1
2
1
1
0
1
1
0
1
2
1
0
1
1
0
2
1
0
1
0
0
0
1
1
0
0
1
1
2
2
3
1
0
1
4
1
0
1
1
2
1
0
1
0
2
0
0
0
1
2
0
0
0
1
0
2
1
2
0
1
1
0
0
2
2
0
1
1
1
0
2
1
0
2
1
0
0
0
1
2
0
1
1
1
0
0
1
1
1
0
1
0
2
2
1
1
2
0
2
2
1
1
1
2
1
1
0
0
2
1
1
1
0
1
1
2
1
1
1
2
2
1
1
1
1
2
3
1
0
0
0
2
1
2
0
1
1
1
0
4
2
1
1
1
0
2
1
1
1
0
0
1
0
1
0
1
1
1
2
0
1
2
1
3
1
1
0
1
0
2
0
1
1
1
0
2
0
1
1
2
1
0
1
0
2
2
0
1
2
1
0
1
1
1
1
2
2
0
2
0
1
0
0
1
1
1
1
0
2
2
4
1
2
0
0
1
1
1
2
1
2
2
0
0
1
1
1
0
4
1
0
2
1
0
1
2
2
1
0
2
1
2
1
0
0
1
1
0
3
1
1
0
0
1
0
1
1
1
1
0
1
0
1
2
1
1
2
1
1
0
2
0
0
2
2
1
2
1
1
1
1
1
1
2
1
1
1
1
0
1
1
1
0
2
2
2
2
1
2
1
0
0
1
1
0
0
1
0
2
0
1
1
1
2
0
1
1
0
3
3
1
2
1
0
0
2
0
2
1
1
0
1
1
2
1
1
1
3
0
1
2
1
1
0
1
0
1
0
1
1
0
1
2
0
1
2
1
0
0
2
0
1
0
1
1
0
1
0
2
0
2
2
1
0
1
0
1
1
2
1
2
0
1
1
2
2
0
2
1
1
1
1
1
1
2
1
0
0
1
1
0
0
1
1
0
2
2
1
1
0
2
2
2
0
1
1
4
1
0
1
2
1
2
0
0
0
0
2
1
1
1
0
1
1
0
0
1
1
1
1
1
1
1
2
1
1
1
0
1
2
2
1
1
1
1
0
1
1
1
0
2
1
2
0
1
1
1
3
0
0
1
0
2
1
2
1
2
1
1
1
0
0
1
1
1
2
1
1
1
1
1
0
0
0
1
0
1
2
0
0
2
1
0
1
0
1
1
0
1
1
0
0
0
1
1
1
0
1
0
0
0
0
2
0
2
0
0
2
1
2
2
0
1
2
3
1
1
1
0
0
0
2
2
2
2
0
1
1
2
1
1
1
0
1
0
0
1
1
0
0
0
1
2
1
1
1
1
0
0
1
1
1
1
2
1
1
1
3
2
0
0
1
1
1
1
0
2
1
0
1
2
2
0
1
0
1
0
2
0
1
0
2
1
2
1
1
0
1
2
1
0
0
1
1
2
1
1
0
1
1
0
2
0
0
2
0
2
0
2
0
2
1
1
1
3
1
2
0
0
1
0
2
2
1
2
2
1
1
1
1
1
0
1
1
1
1
0
2
0
2
1
2
0
1
0
0
2
0
0
1
0
0
0
1
2
1
1
0
0
0
2
0
2
3
1
0
1
1
0
2
1
0
2
1
0
1
1
2
1
1
0
1
0
1
2
2
2
0
0
0
1
1
1
1
0
2
1
2
0
1
2
2
1
0
0
1
2
1
0
0
2
0
1
1
1
1
1
3
1
1
1
1
2
1
1
1
2
0
0
1
0
1
0
1
2
2
1
1
2
2
1
1
3
1
1
2
1
1
1
0
2
1
1
1
2
2
2
1
2
2
2
1
2
1
1
0
2
2
0
1
1
2
2
1
1
1
2
0
1
1
0
1
1
2
2
1
1
1
0
2
1
1
1
1
2
1
1
1
1
1
1
0
2
1
0
1
2
2
1
0
1
2
1
2
2
2
0
1
1
1
1
1
0
2
2
1
1
2
0
0
0
1
1
2
1
1
0
2
1
1
0
2
0
2
2
2
0
0
1
0
0
1
1
2
1
2
2
1
2
1
1
1
1
0
1
1
1
2
1
1
1
0
0
1
2
0
1
1
1
1
1
0
0
1
1
2
0
1
1
1
1
0
1
1
2
2
1
1
2
1
0
1
1
0
1
1
1
1
0
1
0
3
1
4
1
0
0
1
1
3
1
1
0
1
2
1
0
1
1
1
1
0
0
0
2
0
2
2
1
0
1
0
1
1
1
0
0
1
0
0
2
1
0
1
1
2
0
1
0
0
1
1
1
2
2
2
0
2
1
0
0
0
1
2
1
0
1
1
2
1
1
1
1
2
0
1
0
0
1
0
1
1
0
0
0
1
0
0
1
1
0
2
1
0
0
1
1
2
1
1
1
1
0
1
1
2
1
1
0
1
0
1
0
1
1
2
0
2
0
0
1
0
1
1
1
2
2
0
2
0
0
1
1
1
2
1
1
1
1
1
0
1
2
2
0
2
2
1
1
2
2
2
0
1
1
0
1
2
1
2
1
2
1
0
0
1
0
2
2
1
0
2
1
3
1
1
2
0
2
2
2
0
2
2
0
2
1
0
1
0
0
1
1
1
0
0
1
1
1
0
1
1
2
0
2
1
2
0
0
2
2
2
0
1
1
1
3
1
1
1
1
0
2
0
1
0
1
0
1
0
1
0
0
1
1
1
1
0
0
1
3
0
0
0
1
1
2
0
2
1
1
0
1
1
0
2
1
1
1
2
0
2
2
1
1
0
1
1
1
2
1
1
0
1
1
2
1
2
2
0
2
1
1
2
1
1
3
0
1
1
1
1
1
1
6
1
1
0
3
1
0
1
0
1
1
1
0
0
2
1
2
0
1
0
1
2
2
0
0
1
0
2
1
1
2
2
1
0
1
1
1
0
0
0
1
1
0
1
1
1
2
1
2
0
1
1
1
2
1
1
2
1
1
2
0
1
0
2
2
0
1
2
1
1
1
0
1
2
1
1
1
2
1
1
1
1
1
0
0
1
1
0
2
2
1
2
1
1
0
0
2
1
1
1
2
1
1
1
1
2
1
2
2
1
1
0
2
0
1
1
1
1
0
1
0
0
0
2
2
2
0
1
1
2
2
0
2
0
0
1
1
0
1
0
2
1
2
1
1
0
2
2
1
2
2
1
1
0
0
0
0
2
0
0
1
2
1
2
1
0
0
2
1
1
2
1
1
0
1
0
0
0
2
1
1
1
0
0
0
1
2
1
0
2
1
1
2
2
1
0
0
1
2
1
0
0
1
1
1
2
1
2
1
2
0
0
1
2
1
2
2
0
1
0
2
0
1
1
1
1
0
0
0
2
1
1
1
1
2
0
2
1
1
1
2
1
2
1
1
1
1
2
0
1
2
0
1
1
0
1
2
1
0
1
1
0
1
0
1
2
1
0
2
3
1
2
0
1
1
0
1
0
1
1
0
1
1
1
0
0
2
0
1
2
1
0
0
0
2
0
1
0
0
2
1
0
0
2
0
0
0
1
1
0
0
1
1
0
1
0
2
2
1
1
0
1
0
0
1
1
1
0
1
0
2
0
1
2
1
1
1
0
1
1
0
1
1
2
0
2
1
2
0
1
1
0
0
1
1
2
1
1
0
2
1
2
2
1
2
1
1
2
1
2
1
1
0
1
1
1
1
0
1
0
2
3
1
0
2
2
0
0
1
2
1
0
2
0
2
2
1
5
2
1
0
1
1
0
0
1
1
2
1
3
1
0
2
1
1
1
1
0
2
1
0
0
2
0
1
1
1
0
1
0
1
1
0
1
0
0
0
1
1
2
0
0
2
1
1
1
1
1
0
1
0
0
0
2
1
2
1
0
1
1
1
0
1
0
0
1
1
0
1
1
1
2
0
1
2
1
0
1
0
1
0
0
1
1
0
2
1
2
1
0
2
2
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
1
1
2
2
1
0
1
1
0
1
2
1
0
3
1
0
2
0
1
6
1
0
1
0
2
1
0
1
2
1
1
2
0
1
1
0
0
0
0
0
0
2
1
1
0
1
1
1
0
0
2
1
1
1
1
0
1
2
0
2
1
1
2
2
2
1
1
1
1
0
0
0
2
0
2
0
2
0
0
1
2
1
0
1
1
1
1
1
1
1
1
0
1
2
2
2
2
1
1
1
1
1
1
1
1
3
1
2
0
0
0
0
2
1
2
0
1
1
0
0
1
1
1
1
1
2
0
0
0
1
1
0
1
0
0
1
2
1
2
1
2
1
0
1
1
2
1
1
1
0
2
1
2
1
1
2
2
0
1
1
1
1
1
1
0
0
2
1
0
0
0
1
1
1
1
1
2
1
2
2
1
0
1
2
0
1
2
1
0
2
1
0
0
1
1
0
2
0
2
1
2
1
1
0
3
0
0
2
1
0
0
2
1
2
2
3
0
1
1
0
1
0
0
1
0
1
3
0
1
1
1
1
1
1
1
2
0
0
1
2
1
1
1
1
1
1
0
1
1
2
2
1
1
1
1
2
1
1
2
1
3
0
1
1
3
2
1
1
1
1
1
0
2
1
3
4
1
1
2
1
1
1
1
2
2
3
0
0
0
1
0
2
1
1
0
1
0
2
0
0
0
0
0
0
1
2
1
0
1
1
1
1
0
1
1
1
1
1
1
2
2
1
0
0
1
0
1
1
1
0
0
1
1
1
1
1
2
1
0
1
2
2
2
2
0
1
1
0
2
1
2
1
1
0
0
1
1
1
1
0
1
1
4
0
0
2
0
1
1
2
2
0
1
1
1
1
0
2
1
1
0
1
1
2
0
0
1
1
2
1
2
1
1
1
1
1
3
1
0
1
2
2
1
2
1
1
0
2
0
1
0
2
1
0
3
2
0
1
2
0
1
1
0
1
1
2
1
0
1
1
0
0
2
2
0
2
2
1
1
1
1
0
1
0
1
1
1
0
2
0
0
1
1
1
2
0
0
2
2
1
1
1
1
1
2
2
1
2
2
0
0
2
0
0
2
1
2
1
0
2
2
0
1
2
1
1
2
0
1
1
2
1
1
1
0
1
1
2
2
2
2
0
1
2
0
0
1
2
1
1
2
0
1
0
1
0
1
0
1
0
1
0
1
1
2
3
2
1
1
1
1
1
1
0
2
0
1
2
1
1
1
2
2
0
1
1
1
1
1
0
2
1
0
1
1
1
0
1
1
2
0
0
2
1
0
0
2
1
0
1
0
1
1
1
3
1
1
0
0
1
1
1
2
0
0
1
2
0
1
0
0
1
1
1
1
1
1
0
2
0
0
0
1
0
0
2
0
0
1
2
2
0
0
1
1
1
0
1
0
1
1
1
1
0
1
1
2
0
0
2
1
0
2
1
2
2
1
2
1
0
1
1
1
1
2
1
3
1
2
2
2
1
2
1
0
1
1
0
1
1
1
0
2
0
1
1
1
0
1
0
1
0
1
0
1
0
2
2
0
1
1
0
2
0
0
2
1
0
1
1
1
0
1
1
0
1
0
1
1
0
1
2
1
2
1
1
2
2
0
1
1
2
1
2
1
1
0
3
1
0
2
2
0
0
1
1
0
0
2
1
1
1
1
0
1
1
0
1
1
1
3
2
1
1
1
1
1
1
1
2
0
2
0
1
0
1
1
1
1
1
0
2
4
1
1
1
0
2
1
1
1
1
1
0
1
2
0
0
1
1
1
1
0
1
1
1
1
0
1
1
2
1
1
1
1
1
1
1
0
1
1
1
1
1
0
0
1
2
0
1
1
2
1
2
1
2
2
0
1
1
0
0
1
1
1
0
0
2
1
0
0
0
0
1
0
2
1
1
1
2
1
0
1
1
1
1
1
1
1
0
2
1
1
1
2
1
2
1
0
1
2
1
1
0
1
1
2
1
1
2
1
1
2
1
1
0
2
0
1
1
0
1
1
2
0
0
1
1
1
1
1
1
2
2
1
2
1
1
1
1
2
1
1
0
0
0
2
0
0
1
2
0
0
3
0
0
0
0
1
1
1
1
2
1
1
1
1
0
1
2
0
2
1
2
1
2
0
2
1
1
1
1
1
1
0
1
0
1
1
0
0
1
1
2
1
0
1
2
1
1
0
1
1
2
0
1
2
1
1
1
1
1
2
1
1
1
1
1
2
0
1
1
1
2
1
2
0
1
0
0
1
1
2
1
1
1
2
3
2
1
1
0
1
4
1
0
1
0
2
1
1
0
1
1
0
1
2
1
0
0
0
0
1
1
0
1
1
0
1
1
0
1
1
1
2
2
0
2
2
0
1
1
2
1
2
1
1
1
1
2
2
1
0
1
2
1
1
1
1
0
0
1
1
1
1
2
2
2
2
0
1
1
1
1
2
1
0
1
3
2
1
2
1
1
2
1
0
0
0
0
0
0
1
0
1
1
1
1
1
0
2
2
0
0
2
0
1
0
1
1
1
1
0
0
1
1
0
1
1
0
1
2
1
2
1
0
1
1
1
0
2
0
2
0
1
1
0
2
0
1
1
2
1
0
2
1
2
2
0
2
0
2
1
2
0
1
1
2
0
1
1
0
0
1
2
2
1
0
2
2
0
1
2
1
2
0
1
1
1
2
0
0
1
1
0
2
1
2
1
1
1
0
0
1
5
1
0
1
2
1
2
0
1
1
1
1
1
0
0
1
1
1
0
1
1
0
1
1
1
1
0
1
0
1
2
0
1
0
0
1
2
1
0
1
0
0
2
0
0
2
1
0
1
1
0
1
3
2
1
1
1
1
1
2
1
1
1
1
1
0
1
1
1
1
1
0
0
1
1
1
1
2
1
2
1
1
1
1
2
2
0
0
2
2
1
1
1
0
2
1
0
1
2
2
2
2
1
1
1
1
0
0
1
0
1
1
1
1
0
1
0
1
0
1
0
1
1
1
0
1
2
2
1
1
0
1
2
0
2
0
1
1
2
2
0
1
0
1
1
2
2
1
1
2
3
1
1
0
0
2
0
0
1
1
2
1
1
1
1
0
1
1
0
0
1
0
1
1
1
0
2
1
0
0
1
0
0
0
1
1
1
1
1
1
2
0
1
1
1
0
0
2
1
1
1
1
0
2
1
1
0
1
1
1
0
0
1
1
1
1
1
1
1
1
0
2
1
1
1
2
1
0
2
1
1
2
0
0
0
1
0
2
2
1
4
0
1
1
1
1
1
2
1
2
0
2
1
2
1
1
1
1
1
0
1
2
0
1
0
2
1
0
1
0
1
0
0
1
1
1
0
2
1
1
2
1
2
1
2
1
1
1
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
1
0
2
1
0
0
0
2
0
0
1
0
1
1
2
1
0
2
1
2
0
1
1
0
1
0
1
2
0
1
1
1
0
2
0
0
1
0
2
1
0
0
0
2
1
1
2
2
1
0
1
0
0
1
1
2
2
1
1
0
0
1
1
0
1
1
2
2
2
1
1
0
0
2
2
1
1
1
1
1
2
2
1
0
0
2
1
1
0
1
1
2
0
1
0
0
2
0
2
1
1
2
0
2
1
1
1
1
1
1
1
0
1
0
1
1
1
2
1
1
1
0
1
1
0
2
1
0
1
0
1
0
1
1
2
0
1
1
1
0
0
0
1
1
0
1
1
1
0
2
0
2
0
0
3
1
3
1
0
2
1
2
2
0
0
2
1
1
0
1
1
2
1
2
1
1
1
1
0
2
1
0
1
1
1
1
1
0
1
1
0
2
1
0
3
1
1
0
0
0
1
2
0
1
0
1
2
3
0
1
2
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
2
1
2
1
1
2
0
1
0
1
0
0
1
1
0
2
0
1
2
0
0
1
1
1
0
0
1
1
1
1
1
2
2
1
3
2
1
1
2
0
2
0
0
1
0
1
0
0
1
0
2
2
1
0
1
1
1
1
1
1
1
1
2
1
2
1
2
0
0
2
1
2
2
0
2
1
0
2
1
1
0
1
0
1
2
0
1
1
2
1
2
1
1
0
0
2
1
0
0
0
0
0
3
0
1
1
1
2
0
2
2
1
1
1
1
1
0
1
1
2
2
1
1
2
2
1
1
0
0
0
0
1
1
1
1
0
0
1
1
2
5
2
2
0
1
1
2
0
1
2
1
2
1
2
0
1
1
1
0
0
1
0
0
1
1
0
0
2
1
2
0
0
2
1
0
1
1
0
0
1
2
1
1
0
1
0
0
1
1
0
1
1
1
1
0
2
1
0
1
1
0
1
0
0
1
1
0
2
1
0
2
1
1
1
1
0
1
1
0
1
1
1
0
0
2
2
1
1
0
2
1
0
2
1
0
2
0
1
0
2
1
2
1
1
2
1
2
1
2
1
0
0
1
1
0
1
2
0
1
0
0
0
1
1
1
0
1
1
0
1
1
0
1
0
0
0
0
2
2
0
1
1
0
0
0
0
2
1
1
1
1
1
1
0
1
2
2
1
0
3
1
2
0
1
2
0
0
1
1
2
1
0
0
0
2
0
1
1
1
0
0
0
0
1
1
1
2
2
1
0
1
4
1
0
1
0
0
1
0
1
1
0
0
1
0
1
0
0
1
1
2
1
2
0
2
1
1
1
0
1
1
1
1
0
1
1
1
1
0
1
1
1
2
1
0
0
1
1
1
1
0
1
2
0
1
0
1
1
1
0
0
1
2
0
1
2
1
0
1
0
2
1
1
1
1
0
1
0
0
0
1
1
1
1
0
0
1
2
0
2
1
1
1
0
2
1
0
0
2
1
0
2
1
1
0
1
0
0
0
2
1
1
1
2
1
0
1
1
0
2
1
2
2
0
2
2
0
2
2
0
1
2
2
1
1
1
1
1
1
2
1
1
2
1
1
2
1
0
2
0
1
2
0
0
1
2
1
0
1
1
1
0
2
2
1
1
2
1
0
1
1
1
2
1
2
2
0
1
0
2
2
0
0
1
1
2
2
0
1
1
1
1
0
0
1
1
1
2
2
1
0
1
1
1
1
1
0
1
1
1
0
1
1
1
0
2
0
1
1
1
2
1
0
1
1
1
2
2
2
1
2
1
1
1
1
1
1
0
0
1
1
1
2
0
0
0
0
0
2
1
1
1
1
1
1
2
0
3
1
1
0
1
0
0
0
1
0
1
1
1
1
0
1
0
3
1
0
1
1
0
2
0
1
1
1
2
1
1
0
1
1
1
0
1
1
0
2
0
1
1
1
1
1
2
1
2
0
0
0
2
0
1
1
0
2
0
1
2
1
1
0
1
1
2
1
0
1
0
0
0
1
2
1
1
0
0
0
2
1
1
1
0
0
1
1
2
2
0
1
0
1
0
1
0
1
0
2
1
1
1
1
0
0
0
2
2
1
1
1
1
1
1
1
0
0
0
1
2
1
0
0
1
1
1
2
0
0
0
1
0
0
1
1
0
1
1
0
1
2
1
0
0
1
1
1
1
1
1
0
1
1
0
1
1
1
1
2
2
1
0
0
0
2
0
1
1
0
0
1
2
0
1
0
2
2
1
1
1
1
1
1
1
1
1
0
1
1
2
0
1
2
2
0
1
1
1
0
1
2
1
0
1
1
1
1
0
2
0
1
1
1
2
1
0
0
1
1
1
1
1
1
1
0
2
1
1
1
1
0
1
1
2
1
1
0
0
3
1
1
1
1
2
2
1
0
1
0
2
2
1
0
0
1
2
2
1
1
1
1
2
1
1
0
0
0
1
1
1
2
0
1
1
1
2
1
1
0
1
1
2
1
1
2
0
0
0
1
1
1
1
0
1
2
3
3
1
0
0
2
2
0
1
1
0
0
1
1
0
0
0
1
1
1
1
0
0
1
1
1
1
2
1
1
0
2
0
1
2
1
1
1
1
0
1
1
1
0
1
0
1
2
1
2
1
0
1
1
2
0
2
1
2
1
0
0
2
0
2
0
0
1
2
1
1
1
1
1
2
2
1
2
1
1
2
1
0
0
2
0
1
1
0
1
1
1
1
1
1
2
1
1
0
2
1
1
1
0
1
1
1
0
0
0
0
1
1
1
0
2
0
0
0
0
0
0
1
2
0
1
1
1
1
0
0
2
1
0
0
0
2
1
1
2
0
1
1
0
1
2
0
0
4
1
0
1
0
0
1
1
3
1
1
1
0
0
1
0
0
3
0
0
1
2
1
0
1
0
1
1
0
1
1
1
0
1
1
1
1
1
0
2
0
1
1
1
1
1
1
0
2
0
0
1
0
0
2
1
1
1
2
2
0
1
2
2
0
1
1
1
1
1
1
2
1
2
2
2
0
2
1
1
1
2
1
1
3
0
1
1
0
1
1
1
0
0
1
0
1
1
0
1
2
1
2
4
1
2
1
3
1
2
1
1
2
2
2
1
2
2
1
1
2
2
1
1
2
2
0
1
2
0
0
1
1
1
2
0
1
0
1
2
1
1
0
2
1
2
0
0
1
2
0
1
1
0
2
0
0
2
2
0
1
2
2
1
0
1
0
1
1
0
2
0
1
1
1
0
1
0
1
0
0
1
0
1
1
0
1
1
1
0
0
1
1
1
1
0
0
2
2
1
1
1
0
0
1
1
1
1
0
2
1
0
0
0
1
1
0
1
1
1
1
0
1
1
1
1
3
1
1
1
2
1
0
1
0
1
1
1
2
1
1
2
1
1
2
2
1
2
1
1
2
1
1
1
2
2
1
2
1
1
1
1
0
1
1
0
2
1
1
0
0
1
2
1
2
0
1
2
1
1
2
2
2
0
1
0
0
1
3
0
1
2
2
2
1
1
0
1
0
1
1
1
0
2
2
1
2
0
0
0
1
0
0
0
2
2
1
1
0
1
2
1
1
0
0
2
0
1
0
0
2
1
1
1
1
0
1
0
1
0
2
1
1
1
0
1
2
1
0
1
0
0
2
0
1
1
1
4
1
1
1
1
1
1
2
1
0
0
2
1
0
1
0
2
0
1
2
1
2
0
1
1
1
2
0
1
0
0
0
1
0
1
1
1
1
1
1
1
1
2
2
2
0
1
1
1
1
0
0
1
1
0
2
0
1
1
0
0
0
1
1
0
0
2
1
0
1
2
1
1
0
1
1
1
2
0
1
0
1
1
1
1
1
0
1
1
1
1
3
1
1
2
1
1
2
0
1
1
0
1
2
1
1
1
1
1
1
1
2
1
1
1
0
1
1
1
2
2
0
1
1
1
1
1
2
2
2
1
1
0
1
1
0
0
0
0
0
1
2
0
1
1
1
1
2
0
1
1
2
1
0
1
2
2
1
0
1
0
2
1
1
2
0
1
0
0
1
0
1
1
0
0
1
1
1
0
1
0
0
2
1
0
1
1
1
1
0
0
1
0
2
1
0
0
1
0
0
0
1
1
1
1
2
0
1
1
0
2
2
2
2
1
0
2
0
1
1
1
0
0
1
2
2
2
1
0
1
2
1
1
2
1
1
0
2
2
2
0
1
2
1
2
1
1
1
0
2
1
2
1
2
2
1
0
0
1
1
1
0
1
1
2
2
2
1
5
0
0
1
1
1
0
0
0
1
2
2
2
1
0
1
2
2
2
0
1
1
1
2
1
1
1
0
2
0
0
2
2
1
0
1
0
0
0
2
1
0
2
1
1
1
0
1
1
1
0
2
0
0
1
1
0
1
0
0
1
1
0
2
2
1
1
1
2
2
1
2
0
1
0
0
1
1
0
1
1
2
1
0
0
1
1
0
1
0
2
0
0
1
2
1
1
1
0
2
2
0
1
0
1
2
0
2
1
1
0
2
2
0
2
1
1
1
1
1
1
2
1
2
1
1
2
2
1
0
1
2
0
4
1
0
1
2
2
1
0
0
0
0
1
0
0
1
2
2
1
2
1
0
2
0
1
1
1
0
1
0
1
2
2
0
0
1
1
0
1
0
1
0
2
1
1
0
0
0
0
1
1
0
1
1
0
1
1
1
1
1
1
0
1
0
2
1
1
1
2
0
1
0
0
2
1
0
2
2
1
1
0
0
0
1
0
2
1
0
0
1
1
2
1
0
0
1
1
1
1
1
1
1
0
0
2
1
1
0
2
2
1
1
0
1
0
1
1
1
0
3
1
2
1
2
1
1
1
1
1
1
0
2
0
2
1
1
0
2
1
0
0
1
1
1
1
0
0
1
1
0
1
0
1
0
2
1
2
0
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
0
1
0
1
1
1
1
1
1
2
2
1
1
0
1
0
1
2
1
1
1
2
1
2
1
0
1
2
1
1
1
0
2
2
1
1
1
1
2
0
1
1
1
0
2
2
0
0
2
1
1
1
1
0
1
3
1
2
0
1
2
1
0
1
2
1
1
1
1
0
0
0
0
0
1
2
2
0
1
0
2
2
1
1
1
1
2
2
0
1
1
1
2
1
1
0
0
2
2
0
0
1
1
1
1
1
0
0
1
1
2
0
1
0
1
2
1
0
1
1
0
1
1
1
1
3
3
3
0
1
2
1
2
2
1
1
0
2
3
1
1
2
1
0
0
2
2
1
1
1
2
0
2
2
0
1
1
1
2
1
0
0
0
1
1
2
1
0
0
1
1
0
1
2
1
1
1
0
1
1
1
1
0
0
1
1
1
0
0
8
2
1
0
2
2
0
2
2
1
1
0
2
2
1
0
0
0
1
0
1
1
1
2
1
2
1
1
0
1
3
1
1
2
1
2
2
1
2
2
0
1
2
0
1
0
1
1
2
3
2
1
1
1
1
2
1
1
1
2
1
1
0
1
2
0
1
0
1
0
2
1
1
2
0
1
0
0
1
0
0
1
0
1
0
1
1
0
2
1
0
2
1
2
0
2
1
0
1
1
2
1
1
1
0
2
1
1
0
2
2
1
1
2
1
1
0
0
1
2
1
1
2
1
2
1
3
1
1
2
1
1
0
0
0
2
2
1
1
1
1
1
2
1
1
0
1
0
0
2
1
0
0
2
2
1
1
1
0
1
0
3
1
1
0
1
2
2
2
1
1
1
0
1
2
0
0
2
1
1
2
1
2
2
1
1
0
0
1
0
1
1
2
2
1
1
2
1
0
1
0
1
1
1
1
2
1
2
3
1
1
1
2
0
1
2
2
2
0
1
1
0
1
1
1
1
0
0
7
1
0
0
1
2
1
0
1
1
0
0
0
0
2
2
1
0
0
1
1
1
1
0
0
1
2
1
0
2
1
1
0
0
1
0
1
0
1
2
1
0
2
1
0
1
1
1
1
1
0
1
1
1
1
1
2
1
1
0
1
0
2
0
1
0
2
1
1
2
2
1
2
2
1
2
2
1
1
1
0
2
1
1
0
2
0
1
2
0
2
2
0
2
1
1
1
0
1
0
2
1
0
2
1
0
1
2
1
0
2
0
1
0
1
1
1
0
0
1
1
1
3
2
2
1
1
0
1
1
1
1
0
1
0
1
2
2
0
1
0
0
2
3
2
0
0
0
1
1
0
1
0
1
0
2
1
1
0
0
1
1
1
0
0
0
2
1
1
0
0
1
2
1
2
0
1
0
1
0
0
1
1
2
0
2
2
1
1
2
0
0
1
2
1
1
1
1
1
0
0
2
1
0
1
1
1
1
0
1
1
1
2
0
1
2
0
1
2
2
0
1
0
0
0
1
1
0
1
0
0
1
1
1
1
2
1
2
1
0
0
1
1
1
1
1
0
0
1
0
1
1
0
0
1
0
1
1
1
1
1
0
1
1
0
2
1
2
0
2
0
2
1
1
1
1
1
1
1
1
1
1
0
2
1
1
1
1
1
0
1
2
1
0
1
2
2
1
0
1
0
1
1
1
1
2
1
1
0
1
1
2
0
2
0
1
1
2
0
0
2
1
1
0
2
2
1
1
1
0
1
2
2
1
1
2
1
1
1
3
2
3
1
1
1
1
3
0
0
1
1
1
0
0
1
1
0
1
2
1
1
1
1
1
1
1
0
0
2
1
1
1
1
2
1
2
2
2
1
1
0
1
1
1
2
0
2
0
2
2
1
1
1
1
0
0
1
0
2
2
1
1
0
1
2
1
2
1
0
1
2
1
0
1
1
1
1
2
1
2
0
2
1
2
2
1
1
0
1
2
1
1
0
1
0
1
1
0
1
1
1
2
1
0
2
0
1
1
1
0
2
2
0
0
2
2
1
1
1
2
1
0
1
2
2
2
0
1
4
0
1
0
0
2
2
1
0
1
0
2
2
0
1
0
2
0
1
0
4
1
1
1
1
2
1
0
0
1
2
1
1
0
0
1
0
1
0
1
1
1
1
1
2
0
1
2
1
2
1
1
1
1
1
1
2
1
0
1
2
1
0
2
0
2
1
0
2
0
2
0
1
1
0
1
0
2
1
1
0
0
1
2
1
0
0
2
1
1
0
2
2
1
1
2
1
2
0
1
2
0
2
0
2
2
2
1
1
1
0
2
1
2
1
0
0
1
1
2
0
1
0
1
2
0
1
0
1
2
1
1
2
2
1
0
0
2
1
1
1
1
0
0
1
1
2
1
1
1
1
2
1
0
2
2
0
2
1
0
1
0
1
2
2
1
2
1
1
1
1
1
1
1
1
0
0
0
1
2
1
1
0
1
0
1
1
1
1
0
1
0
2
1
1
0
1
1
1
2
2
1
1
2
1
0
1
0
2
1
1
1
1
1
0
2
2
3
0
0
1
1
1
1
1
1
1
0
1
1
1
0
0
2
1
1
1
1
1
0
1
2
0
0
2
2
1
0
2
1
2
0
0
0
1
1
1
2
1
2
1
0
1
0
1
1
2
1
2
1
0
1
4
1
2
0
2
1
0
1
1
1
2
2
0
1
1
0
2
2
1
1
0
1
1
0
0
1
2
1
0
2
0
1
0
0
1
1
1
0
1
1
1
1
1
1
0
1
2
0
0
1
1
1
1
2
1
0
2
2
1
2
2
2
1
1
0
2
1
0
0
1
2
1
1
0
1
0
1
0
0
1
1
1
0
2
0
0
1
0
0
0
1
1
3
0
1
2
0
1
0
0
0
0
1
1
0
1
2
2
1
1
1
0
2
1
0
1
1
1
1
1
1
1
1
1
1
2
0
1
0
0
1
1
1
1
1
1
0
1
1
1
2
1
1
0
1
1
2
0
1
1
1
1
0
0
1
1
2
1
1
1
1
1
1
1
0
2
1
1
0
2
2
1
0
1
1
1
1
1
0
2
2
1
0
1
2
1
1
2
1
1
0
2
0
1
1
1
0
1
2
1
2
0
0
1
1
5
0
2
0
2
0
1
2
1
0
1
0
2
2
0
0
1
1
1
0
2
1
0
1
1
1
2
1
1
0
2
1
0
1
1
0
1
0
1
1
1
0
0
2
0
0
1
0
1
2
0
2
1
2
1
2
0
0
2
0
1
2
1
1
0
1
0
1
1
0
1
2
0
0
1
1
1
1
1
1
2
0
1
0
0
1
1
1
0
1
1
1
2
1
1
0
1
1
0
1
0
1
0
1
1
2
1
1
0
2
3
1
1
0
2
1
2
1
0
1
2
0
1
1
1
0
2
1
0
2
2
1
1
1
1
1
1
0
0
2
1
2
2
2
1
0
0
2
2
1
1
5
1
0
1
1
0
0
2
2
0
1
1
2
1
2
2
1
2
1
1
2
1
2
0
0
2
1
1
2
2
2
1
2
1
1
1
1
2
1
2
1
2
1
1
0
2
1
0
1
0
1
1
0
2
0
0
2
0
1
0
2
0
0
1
1
0
1
1
2
1
1
2
1
2
1
2
1
1
0
2
0
1
2
0
1
1
0
1
2
2
1
0
1
1
2
2
0
2
0
0
2
0
1
1
1
0
0
1
2
2
1
2
1
1
0
2
0
1
0
1
0
1
1
0
1
2
2
0
1
0
1
2
1
0
1
1
0
1
2
1
0
3
1
0
0
1
1
0
2
1
0
1
1
4
0
1
0
2
1
1
0
1
0
1
1
0
0
2
1
0
0
1
2
0
0
2
1
0
2
1
1
2
1
0
1
0
0
1
2
1
0
0
2
0
2
1
2
2
0
1
1
2
2
0
1
2
2
2
1
0
2
0
0
1
1
2
1
1
1
2
0
0
2
2
0
1
1
2
2
1
1
1
1
2
0
1
1
2
0
0
0
1
2
1
0
1
0
1
2
1
0
2
1
0
2
1
1
2
1
0
1
1
1
0
1
0
0
1
1
1
1
0
0
2
2
1
1
0
1
2
1
1
1
0
1
2
1
0
2
1
0
3
1
2
1
2
0
0
1
1
2
0
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
0
1
2
3
3
2
1
2
1
1
0
0
1
2
1
1
2
2
0
1
0
1
1
1
0
1
1
2
1
2
1
1
1
1
0
1
0
1
1
1
3
1
1
2
1
0
2
0
1
1
1
1
0
1
0
2
0
1
2
0
0
1
2
0
1
1
2
1
2
2
1
2
1
0
2
0
0
1
2
0
2
0
1
1
2
2
1
1
1
1
2
1
2
1
0
1
1
1
0
0
1
6
1
1
1
1
2
0
1
1
2
1
0
2
1
1
1
0
0
2
1
2
0
1
2
2
0
0
1
1
1
0
0
1
1
0
0
1
1
1
0
1
1
2
1
2
0
2
0
2
2
2
2
1
1
1
2
0
1
0
0
2
0
2
1
0
1
1
0
1
1
1
2
1
1
0
0
2
3
1
0
1
1
7
1
1
1
1
0
2
1
1
1
1
0
1
1
1
1
0
3
1
1
1
1
0
2
1
1
2
2
1
0
1
1
1
1
1
2
0
2
1
0
1
2
1
2
0
2
1
2
0
1
2
2
1
2
0
0
1
1
1
1
0
1
2
0
0
0
0
2
0
2
0
1
1
0
2
0
1
0
1
1
1
1
1
1
0
0
0
1
0
1
1
1
1
2
2
2
0
2
1
0
1
1
1
1
1
0
0
1
2
1
1
0
0
1
2
1
2
0
0
2
1
2
1
1
2
1
1
2
1
0
0
0
1
1
2
1
1
1
0
1
0
1
0
2
1
2
0
1
1
2
1
1
1
0
2
1
0
2
1
1
0
0
1
2
1
1
2
1
2
2
1
0
1
1
1
0
0
0
1
0
0
1
1
1
0
0
0
2
2
1
0
1
0
1
1
0
2
0
1
1
2
2
2
2
2
2
0
1
2
1
2
2
2
1
2
1
1
0
2
0
2
1
1
1
0
1
1
2
1
1
0
1
1
1
2
0
1
1
0
2
2
2
2
0
1
0
0
0
0
1
1
0
0
2
1
1
1
0
1
0
2
2
1
2
0
0
1
1
1
1
1
1
2
0
1
1
0
0
2
1
2
1
1
1
2
1
0
2
1
0
1
1
0
1
0
2
1
2
1
0
1
1
0
2
0
1
0
0
2
2
1
1
1
0
0
0
1
0
0
0
1
2
1
0
1
0
2
1
2
1
0
1
0
1
2
1
0
1
0
0
2
0
1
1
1
1
1
0
2
3
1
1
0
2
2
1
1
2
1
2
1
0
1
2
1
1
2
1
2
1
0
2
1
1
1
0
0
1
2
2
2
0
2
1
2
1
2
1
1
0
1
2
1
2
2
2
1
1
0
0
2
1
0
1
0
1
1
0
2
1
1
2
2
1
1
1
1
0
0
0
1
0
1
2
5
0
0
2
0
2
2
1
0
0
2
1
0
2
1
1
1
0
0
1
1
1
1
1
1
1
0
1
2
1
1
2
2
1
2
0
1
2
2
1
1
2
0
0
2
1
2
1
1
1
0
1
1
2
0
1
1
0
1
0
1
1
0
0
2
0
1
0
2
2
1
1
0
0
1
0
0
2
3
0
1
1
0
1
1
2
2
1
1
0
1
1
1
1
1
1
1
1
0
0
1
1
1
1
2
1
1
2
0
1
1
1
2
1
2
0
2
1
1
0
2
1
1
2
0
0
1
1
1
0
2
2
2
0
0
2
1
0
1
2
0
1
1
0
1
0
0
2
2
1
1
1
1
2
1
0
1
0
1
0
2
0
0
1
1
1
1
1
1
1
2
0
0
1
1
2
1
2
1
2
1
0
0
1
1
2
1
1
0
1
2
1
2
1
0
0
1
1
1
2
0
1
2
2
1
0
0
0
1
0
0
1
1
1
0
2
2
1
0
1
1
0
2
0
2
1
2
0
2
1
1
1
2
0
1
1
1
0
2
1
1
1
2
2
1
1
0
1
2
2
1
2
1
0
0
1
2
1
1
0
1
1
0
0
2
1
2
2
0
0
0
1
1
1
0
2
1
1
0
1
1
0
1
0
1
1
1
0
0
1
0
1
0
0
2
2
1
2
0
2
1
2
2
2
1
0
0
1
1
1
0
0
1
1
0
0
1
2
0
1
0
0
2
1
1
1
0
3
2
2
2
1
2
0
1
1
1
2
1
1
0
0
0
0
1
1
1
1
2
2
1
1
1
2
0
1
0
1
1
1
1
2
2
1
1
1
1
0
0
0
1
1
0
1
0
2
1
0
2
0
1
1
0
0
0
1
1
2
1
0
0
1
0
1
0
2
1
0
0
2
1
1
1
1
1
1
2
1
1
0
0
1
1
0
1
0
0
3
1
2
2
1
1
0
1
1
1
2
1
1
2
2
0
0
1
2
1
1
2
1
1
1
0
1
1
2
1
1
0
0
0
2
0
1
1
1
2
1
0
1
0
2
2
2
1
0
2
2
0
0
1
1
2
1
1
0
0
1
2
1
0
0
0
0
2
2
0
1
2
1
0
1
0
1
2
1
1
2
0
1
0
1
0
2
1
1
2
1
1
0
2
0
3
0
0
1
1
2
1
0
1
0
1
2
3
2
2
1
1
2
0
1
1
2
1
1
3
2
0
1
0
1
1
0
1
1
4
2
0
2
1
2
1
1
2
0
1
1
1
1
1
1
1
0
0
1
2
1
1
0
2
1
1
1
1
1
0
1
0
0
0
0
1
0
0
0
2
2
1
0
0
1
1
1
1
2
1
1
1
0
0
17
1
1
1
1
0
2
0
1
1
1
1
1
2
2
0
0
1
0
1
1
1
1
2
1
1
1
2
1
1
2
1
2
1
0
1
0
0
0
1
2
1
1
2
1
2
0
1
0
0
1
0
1
0
1
2
1
1
1
1
0
1
1
1
2
1
0
1
0
1
1
0
0
1
2
1
2
0
2
2
0
2
1
2
1
0
1
1
0
0
1
0
1
0
1
0
1
0
0
0
1
0
1
0
1
0
0
0
1
1
1
1
0
1
1
2
1
2
2
2
1
1
2
0
0
1
0
0
0
0
2
2
1
2
1
1
2
0
2
1
2
2
1
1
2
1
1
1
0
2
0
2
0
2
2
1
2
0
2
2
0
1
2
1
2
1
0
0
0
1
1
1
2
1
0
1
1
1
0
1
1
1
1
2
0
0
2
0
1
2
2
1
2
1
0
1
0
1
1
0
1
1
0
1
0
2
1
1
2
0
0
2
0
1
2
1
2
1
0
2
0
1
0
0
2
1
0
2
2
0
1
2
1
0
0
1
1
1
1
1
0
1
1
1
1
1
0
1
2
0
1
1
0
0
0
0
0
0
1
1
1
0
2
2
1
0
0
3
0
0
0
1
0
2
1
2
1
0
0
1
2
2
1
0
2
0
1
1
1
0
0
2
1
1
0
5
1
0
0
1
1
1
1
0
2
0
1
0
1
1
1
2
1
0
2
2
1
1
0
0
0
0
0
1
1
1
1
1
0
1
3
1
0
0
1
2
1
0
1
1
1
1
2
1
1
1
1
1
1
1
0
1
1
1
0
2
0
0
1
0
0
0
0
2
1
1
1
2
1
1
2
1
1
0
1
2
0
0
1
1
2
0
2
1
2
0
1
1
1
1
2
1
1
0
1
1
0
1
0
0
1
0
0
2
1
2
1
1
0
1
4
1
0
1
0
1
1
1
0
1
1
1
1
2
0
2
1
1
1
0
2
1
2
1
2
0
1
1
2
0
0
1
2
2
0
1
1
1
1
1
2
0
1
1
1
1
1
0
1
0
3
1
2
0
0
0
0
1
2
2
1
1
2
1
1
1
2
0
1
2
1
1
0
1
1
2
0
0
1
0
1
2
1
1
0
1
1
1
1
2
1
2
1
0
0
1
1
2
0
0
1
1
1
0
2
2
0
0
2
1
0
1
1
1
0
0
1
0
1
0
1
2
1
0
1
2
2
1
0
0
0
1
0
1
2
0
2
2
2
2
0
0
0
0
1
1
1
1
0
0
2
0
1
1
0
2
2
1
1
2
1
2
1
1
2
0
1
1
1
0
1
0
3
1
1
0
1
0
1
2
0
1
1
2
0
2
1
2
0
1
1
1
1
0
2
1
0
2
2
0
0
0
1
2
1
1
0
2
0
2
2
1
2
1
0
1
1
1
0
2
2
2
0
1
1
2
1
0
0
0
0
1
2
2
0
2
1
1
0
0
0
2
1
0
2
1
0
2
1
2
1
2
1
1
0
1
1
2
1
1
2
1
2
2
0
0
0
0
1
2
1
1
0
1
1
0
1
2
1
1
1
2
0
0
2
2
1
1
1
0
1
2
1
0
0
1
2
2
0
1
1
2
1
1
0
1
1
2
3
1
1
2
1
1
2
0
1
1
1
1
0
1
2
2
2
1
2
2
1
0
0
1
2
2
2
1
1
1
0
2
2
2
0
1
1
0
1
1
1
0
0
0
2
1
1
1
0
1
2
1
1
1
1
1
3
2
0
1
0
0
1
2
0
0
2
1
1
1
1
1
0
1
1
2
1
0
1
1
1
1
1
1
2
1
1
0
0
2
2
0
1
2
0
1
1
1
1
2
2
2
1
1
1
1
1
1
2
1
1
1
1
1
1
0
1
1
0
1
0
1
2
1
1
0
0
2
1
1
1
2
1
1
1
1
2
0
1
1
1
0
0
0
1
0
0
0
0
1
1
1
1
1
0
1
0
0
2
2
2
1
0
2
1
0
0
1
1
0
2
0
0
0
1
1
1
0
0
1
0
1
0
1
0
0
0
2
1
3
2
1
0
1
1
1
0
2
0
2
2
1
1
0
1
0
2
0
1
0
0
2
0
0
1
0
1
1
1
1
0
1
2
1
1
0
1
0
0
2
2
1
2
1
0
1
0
1
0
0
1
1
0
0
0
1
2
2
2
0
0
1
0
1
1
0
2
2
1
2
0
2
1
2
1
1
0
1
0
1
0
2
1
0
1
1
1
0
0
0
0
1
1
2
0
1
1
1
0
2
1
0
2
0
1
3
1
1
1
0
1
0
2
1
0
2
2
1
0
0
1
2
2
1
2
0
1
1
1
2
1
1
0
0
0
3
0
1
1
1
1
2
1
1
2
0
1
1
2
0
1
2
1
2
1
0
1
1
2
0
2
0
2
2
1
0
1
2
2
2
4
0
1
1
1
1
1
2
0
1
0
1
1
2
0
2
1
1
2
0
1
1
2
1
1
1
1
0
2
1
0
1
2
2
2
0
2
1
2
2
2
1
2
1
1
1
1
1
0
2
1
0
1
1
2
2
1
0
1
0
1
2
0
1
0
0
1
1
1
2
2
0
1
1
0
2
0
2
1
0
0
0
0
2
2
1
1
1
2
2
1
0
0
0
1
0
2
1
1
2
1
1
2
2
1
1
1
1
1
2
1
1
2
1
2
2
1
0
0
1
0
3
1
2
1
2
1
1
1
2
1
1
1
0
2
0
0
1
2
1
2
0
0
0
1
0
2
1
0
1
0
1
2
1
2
1
0
0
2
1
0
0
1
1
1
1
1
1
1
1
2
0
2
2
1
1
1
1
0
1
1
2
0
2
1
2
1
1
0
2
1
1
0
1
1
1
1
0
1
1
0
0
1
2
1
0
1
2
0
0
0
1
1
1
0
1
2
1
1
2
1
1
0
0
1
1
2
2
1
2
0
1
2
1
0
1
1
2
1
0
0
2
0
1
1
0
0
1
1
1
0
3
1
1
2
0
1
0
1
0
0
0
1
1
1
0
1
0
1
0
2
1
1
0
1
1
2
0
0
1
0
0
1
1
0
1
2
1
0
1
0
2
2
1
2
0
1
1
2
1
1
1
1
0
1
0
2
1
0
0
2
1
0
2
1
0
1
2
1
1
2
2
2
1
0
1
0
0
2
2
2
2
1
0
2
1
1
0
2
0
0
1
0
0
2
0
1
1
1
1
3
4
0
1
0
3
1
0
1
1
0
1
1
1
1
1
0
1
1
0
2
2
0
0
1
2
0
2
1
1
1
2
1
0
1
1
1
1
0
0
1
1
2
0
0
0
1
1
1
2
2
1
1
1
0
2
1
0
1
2
1
1
0
0
2
1
0
1
1
1
2
0
1
0
0
2
1
1
1
2
1
1
2
2
3
1
0
1
1
2
0
2
1
2
1
1
2
1
0
2
1
1
1
0
1
0
1
2
0
1
0
1
0
2
1
1
1
2
0
0
2
0
1
1
0
1
1
1
2
0
2
0
2
1
1
1
0
2
1
2
0
0
2
1
2
1
1
3
2
2
0
1
0
0
1
1
2
0
0
1
1
1
1
1
0
1
0
1
2
1
1
2
0
0
0
0
1
2
1
0
0
2
0
0
1
1
1
1
0
2
1
0
2
0
2
1
2
0
0
1
0
1
2
1
1
0
0
1
1
2
2
1
1
0
1
1
1
0
1
1
0
1
2
1
2
1
2
2
1
1
2
1
1
1
0
0
1
1
1
1
0
0
1
1
1
1
2
2
1
0
0
1
1
1
1
1
2
0
2
2
1
1
1
1
2
1
0
1
2
2
3
1
5
1
1
1
2
1
0
2
2
1
1
1
0
2
0
0
0
1
0
1
1
1
0
0
0
0
1
1
0
1
0
0
1
0
1
1
1
2
1
1
1
1
2
0
2
1
2
1
2
1
0
2
1
1
2
1
1
0
1
1
2
0
3
0
1
0
1
1
1
0
0
1
0
1
2
1
1
2
1
0
1
0
0
1
1
2
1
0
0
0
2
1
2
1
1
1
1
2
0
0
1
0
2
1
0
3
0
0
1
1
1
0
1
0
0
0
3
0
1
0
1
1
2
1
1
2
0
1
1
2
1
2
0
2
2
0
1
0
2
0
1
0
1
0
2
1
0
1
1
1
3
1
1
0
1
3
2
1
2
0
0
1
1
2
1
2
0
2
0
1
2
0
2
1
0
2
0
1
2
2
1
1
0
1
1
1
2
0
1
1
2
0
1
1
0
2
1
2
2
2
1
0
1
0
1
1
1
2
1
2
0
1
1
0
1
2
0
1
0
1
1
0
2
2
0
0
1
1
0
1
1
1
1
1
2
0
1
1
2
1
2
0
0
0
2
0
1
1
0
1
2
0
2
0
1
1
2
0
0
1
1
1
2
0
1
0
0
0
2
0
1
2
0
1
1
0
0
1
1
1
2
1
1
1
1
1
1
4
1
1
1
1
2
1
0
1
1
0
1
1
2
0
1
1
1
3
1
1
1
0
1
1
2
1
1
2
1
1
2
1
0
2
2
0
1
1
2
2
1
0
1
1
0
1
1
0
1
1
1
0
1
1
1
1
1
1
2
0
2
1
2
2
2
1
2
0
0
2
0
1
0
0
1
1
0
1
2
1
0
1
2
1
0
0
1
1
1
2
0
2
2
1
0
1
0
0
2
1
0
2
2
1
2
1
0
1
0
2
0
0
1
1
1
1
2
0
0
0
2
1
1
0
0
0
1
1
2
3
1
1
1
2
1
1
1
2
2
1
1
1
1
1
0
1
1
1
0
0
0
1
1
1
0
1
1
2
0
0
2
0
2
2
1
1
1
1
2
1
2
1
1
1
0
1
2
1
1
0
0
0
0
0
2
1
1
1
0
0
3
0
0
1
0
1
2
1
0
1
1
0
1
1
1
2
1
1
2
1
2
0
1
1
2
1
1
1
1
2
1
1
2
2
1
1
0
1
1
1
0
0
1
1
2
0
2
1
0
2
1
1
0
2
0
2
1
1
1
2
2
1
1
0
1
0
0
2
1
1
2
0
1
0
1
1
1
0
1
1
0
1
2
1
2
1
1
1
0
1
1
1
2
1
2
2
2
1
1
1
1
0
1
1
1
1
2
2
0
0
3
1
1
1
1
0
1
1
0
1
1
0
1
0
0
1
2
0
2
1
1
2
1
0
1
1
2
2
0
0
1
2
1
1
1
1
1
1
1
1
0
1
1
2
0
2
2
1
2
1
1
1
0
0
1
6
2
2
1
2
2
0
1
2
1
1
1
0
1
1
1
1
0
0
1
1
2
1
1
2
2
1
2
0
1
0
2
1
1
0
2
2
1
0
0
2
1
2
1
1
2
0
1
1
1
1
2
1
0
0
2
1
0
0
1
2
1
2
1
1
2
1
0
2
1
1
1
1
1
1
1
1
2
0
0
1
0
1
0
0
2
1
1
0
1
1
0
4
0
1
2
1
1
3
1
0
2
1
1
1
0
1
1
0
2
1
2
2
1
2
1
1
0
1
1
2
4
2
1
2
0
1
0
2
0
1
2
1
2
1
3
1
0
2
0
2
1
2
1
0
1
1
1
2
2
1
2
1
2
1
1
1
0
1
1
0
0
0
1
1
0
1
1
0
3
0
1
1
1
0
2
4
0
1
1
1
1
1
1
1
1
1
1
1
0
1
0
2
0
0
2
2
1
0
0
2
1
1
1
1
3
2
0
1
0
0
0
1
1
0
0
1
0
1
1
0
2
1
2
0
1
2
0
2
1
0
1
1
0
0
1
1
2
0
0
2
1
0
0
2
0
1
1
1
1
2
1
1
0
2
2
2
2
3
1
1
0
1
0
0
1
1
2
0
1
1
1
1
1
0
1
1
2
0
1
0
2
1
1
0
0
2
0
0
1
0
0
1
0
2
0
1
1
1
1
1
0
1
0
0
0
2
1
1
1
1
1
0
2
0
1
0
0
0
1
2
1
0
1
1
1
1
2
2
2
0
1
1
1
0
1
1
0
1
0
2
0
0
0
1
1
0
1
2
0
1
1
1
1
0
1
1
2
0
2
2
2
0
1
0
1
2
1
2
2
0
2
2
2
1
0
2
1
1
0
2
0
0
0
0
0
0
1
0
0
0
0
2
2
1
0
0
0
2
0
2
1
2
1
2
2
2
0
1
2
0
0
1
1
1
1
2
2
0
1
1
0
0
1
0
1
0
1
1
0
1
1
0
1
1
2
0
1
0
0
1
0
3
2
0
1
1
1
1
0
1
1
0
1
1
1
0
0
1
2
2
1
1
1
1
1
2
0
1
1
2
1
1
0
0
1
1
1
0
0
0
0
2
1
1
0
2
1
1
2
0
1
1
0
1
2
1
1
0
2
2
0
0
1
0
2
0
2
0
1
2
1
1
0
0
0
2
2
2
1
2
1
1
0
0
1
0
1
1
1
2
1
0
1
2
0
1
1
0
2
1
2
1
0
3
0
0
0
2
1
1
1
1
0
2
1
0
0
3
0
0
0
1
2
1
0
1
0
0
1
1
0
2
2
1
2
0
1
0
0
1
2
1
1
0
1
1
1
1
0
1
1
1
2
0
1
1
1
1
0
1
1
1
0
2
1
0
1
1
2
3
0
2
0
1
1
1
2
0
1
2
1
1
0
1
0
1
2
0
2
3
1
1
0
0
0
0
0
1
1
0
1
1
1
1
1
2
1
1
2
0
0
0
2
0
0
1
2
0
1
3
0
1
0
1
1
1
2
1
2
0
2
1
0
1
1
1
1
1
1
1
1
1
2
2
1
1
0
1
0
2
0
2
0
1
3
2
0
0
0
1
1
1
2
3
0
1
0
1
2
1
1
1
0
2
2
1
0
1
1
0
0
1
1
1
2
2
1
1
1
2
0
1
2
1
0
1
1
1
2
2
1
2
0
2
0
0
1
2
0
1
2
0
1
2
1
1
1
1
1
1
1
1
0
2
0
0
2
1
1
1
0
0
0
1
3
1
2
1
1
2
2
1
0
1
0
1
0
0
1
1
1
2
2
1
1
1
1
2
0
1
0
1
2
0
1
0
1
1
1
0
0
1
2
0
2
1
1
0
2
1
1
0
3
0
2
0
1
0
0
1
1
1
1
0
2
0
1
0
1
2
0
1
1
1
1
1
1
1
1
1
1
1
0
1
0
1
1
0
2
1
1
1
1
2
0
1
0
1
0
0
0
2
1
1
1
1
1
1
1
0
1
0
1
2
0
2
1
1
1
1
2
2
2
2
1
0
2
1
1
1
1
2
1
0
0
1
2
0
1
2
1
1
2
0
1
1
1
0
3
1
1
1
1
1
0
0
1
0
2
2
1
1
1
1
2
0
2
1
1
0
1
1
1
0
1
2
1
1
0
2
1
1
1
1
0
2
1
1
8
0
2
1
0
2
1
1
0
1
2
2
1
1
2
0
1
1
2
1
2
0
1
0
1
1
1
1
2
1
0
1
1
2
0
0
1
0
0
1
1
1
2
2
2
1
1
1
0
2
2
1
0
0
1
0
1
0
0
1
1
1
1
0
2
2
1
1
0
0
1
2
2
2
1
0
2
0
1
1
0
1
1
0
1
0
0
1
1
1
1
1
0
1
0
1
1
0
0
0
2
1
2
1
1
2
1
1
2
1
2
2
0
2
0
0
1
2
2
0
0
0
1
2
2
0
0
0
2
0
2
0
2
0
2
2
0
1
2
1
0
1
1
2
2
1
1
1
0
2
1
0
1
1
1
2
1
1
1
0
0
2
0
0
1
1
1
0
1
3
0
2
0
2
1
9
1
1
2
2
0
2
2
1
0
2
1
1
1
1
1
1
0
1
1
0
2
1
0
2
1
1
0
1
1
1
1
1
1
0
0
3
2
0
1
1
0
2
3
1
0
0
0
1
1
1
2
0
2
1
2
0
0
0
1
2
1
1
1
1
0
1
2
0
0
1
2
1
1
1
1
1
0
1
0
1
1
1
1
2
1
2
1
0
1
1
1
0
2
2
0
1
3
1
0
0
0
0
1
1
0
2
1
0
1
0
1
0
2
2
2
2
0
1
1
1
0
1
0
1
1
2
1
0
0
1
1
1
1
1
1
1
0
2
0
0
0
0
0
1
1
1
0
0
0
1
0
1
1
1
0
0
1
2
1
2
1
1
0
0
0
1
0
0
0
1
1
0
1
1
1
0
2
1
1
2
1
1
0
0
2
1
1
0
0
1
1
1
0
1
2
1
0
1
0
0
0
2
0
1
1
2
1
1
1
1
1
3
1
1
2
1
2
2
0
1
1
2
1
2
1
1
0
1
1
1
2
1
2
1
1
1
0
2
0
1
0
1
0
2
1
1
2
1
1
0
0
0
1
1
1
0
1
0
2
0
0
1
1
1
1
1
0
2
1
2
0
1
1
0
2
1
2
1
0
0
1
2
1
2
1
0
1
2
0
1
1
2
4
1
0
0
1
1
1
2
2
0
1
1
1
1
2
0
1
1
1
1
0
1
1
1
1
0
1
1
2
2
1
0
2
1
0
2
0
2
0
0
1
1
0
0
1
0
1
1
1
2
1
0
1
1
2
1
1
2
1
1
1
2
1
1
1
2
1
1
0
1
0
1
0
2
1
0
2
1
1
0
1
0
1
0
0
0
2
1
1
0
2
0
2
1
1
1
0
0
1
0
1
1
2
2
1
0
2
0
2
2
1
2
1
0
0
1
1
0
0
2
1
2
0
1
1
2
0
1
0
0
2
0
0
0
1
1
2
1
0
1
1
2
1
2
1
1
3
1
2
1
0
1
1
2
1
0
1
1
1
1
1
2
1
1
0
1
1
1
0
2
2
1
0
1
1
1
1
0
1
2
1
1
2
2
1
1
1
1
1
0
0
1
2
0
1
1
2
0
3
1
2
1
1
2
1
1
2
0
1
1
1
1
1
2
1
2
1
2
1
1
1
1
2
1
1
1
2
0
1
1
1
0
1
2
2
0
2
0
1
1
3
1
1
0
0
1
1
1
1
1
1
1
1
0
0
0
1
1
2
1
0
1
1
1
0
2
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
0
1
1
1
2
1
1
2
1
0
0
1
1
1
0
1
3
1
0
0
1
1
0
3
0
0
0
0
1
1
0
1
3
2
1
1
0
1
1
1
2
2
1
1
1
1
2
0
0
1
0
1
2
0
0
3
2
0
0
0
1
1
1
1
2
1
1
1
1
2
0
1
1
0
1
2
0
0
1
1
1
1
0
1
1
1
1
1
0
2
0
1
0
0
0
0
1
1
0
0
3
1
1
1
1
0
1
2
2
0
2
0
0
0
0
3
1
1
1
1
2
3
1
0
1
1
0
0
2
1
1
0
1
0
2
0
1
2
2
2
1
1
2
1
2
2
0
1
1
1
1
2
1
1
0
2
2
2
0
3
0
1
0
1
1
2
1
1
1
0
1
0
0
0
1
1
1
0
1
2
2
1
1
0
1
1
2
0
2
0
0
1
2
2
1
2
2
2
0
1
1
1
0
0
2
0
0
0
0
0
0
2
1
1
0
1
2
0
1
0
1
2
1
1
1
2
0
0
0
2
1
2
1
1
2
1
0
1
0
2
1
0
0
1
0
1
0
2
2
1
1
1
0
0
1
0
1
2
1
1
1
2
1
1
2
1
1
0
0
0
1
0
1
0
1
0
0
1
1
1
0
2
1
2
2
1
2
0
1
0
1
1
0
0
0
1
0
1
1
0
0
2
2
1
0
1
2
1
2
2
0
1
0
0
1
0
1
1
1
0
1
0
2
1
1
1
1
1
2
1
0
0
2
0
1
1
1
0
2
1
1
1
1
2
0
2
0
0
1
0
1
1
1
0
1
0
3
0
1
0
1
1
0
2
1
0
0
1
1
1
2
1
0
0
1
0
2
1
1
0
2
2
1
1
0
1
2
1
2
0
1
1
0
1
0
0
1
2
1
1
0
0
1
0
2
1
0
1
1
1
1
0
2
0
1
1
1
0
0
0
1
0
1
1
2
1
1
2
1
0
1
1
0
1
0
1
2
0
0
0
1
2
1
1
0
2
2
1
1
0
1
1
1
1
0
2
0
1
1
2
1
0
1
1
2
0
0
2
2
0
3
1
2
1
1
0
1
1
2
1
0
0
0
1
1
1
1
0
1
1
1
1
1
2
0
0
1
0
1
2
0
0
1
1
2
2
0
1
0
1
1
1
1
0
1
2
1
0
2
2
1
1
0
2
1
1
0
0
1
1
1
2
1
1
2
1
2
1
0
0
1
1
1
1
1
1
2
1
1
1
1
0
2
2
0
2
1
2
0
2
0
0
0
2
1
0
1
0
2
0
1
1
1
1
1
2
0
2
1
2
0
2
2
2
0
1
1
1
0
1
0
1
1
1
1
0
1
1
1
1
2
1
1
1
0
2
0
0
1
3
1
1
2
1
2
0
1
0
4
1
0
1
0
1
2
0
0
1
2
0
1
1
1
1
2
1
1
2
0
1
1
1
2
1
0
0
2
1
0
1
2
0
1
1
1
1
1
1
1
1
2
3
0
2
0
0
1
2
0
2
1
1
0
0
0
1
0
2
0
2
2
0
0
0
0
2
0
2
1
0
1
1
1
0
0
0
1
1
0
0
1
1
2
2
0
1
0
2
1
1
2
1
0
1
1
3
0
1
1
1
0
1
2
2
0
2
1
1
1
1
0
0
1
1
1
1
1
0
1
1
0
1
0
1
1
1
1
1
0
2
0
0
0
1
1
0
1
1
1
1
5
1
1
2
1
1
1
0
0
2
0
2
1
2
1
1
0
1
2
2
2
1
1
1
0
0
2
2
1
1
1
1
2
0
1
0
1
1
2
1
2
0
0
1
1
0
2
1
1
1
2
2
0
2
1
0
1
1
0
2
2
1
0
1
1
2
1
1
1
1
1
1
0
0
1
0
1
1
1
2
0
0
1
2
2
0
2
1
0
0
1
0
1
2
0
1
1
0
1
0
1
1
1
0
0
0
0
1
0
0
2
1
2
0
1
1
0
0
2
1
0
1
0
0
0
1
1
1
0
0
2
0
2
0
1
0
2
0
2
2
1
4
0
1
0
1
1
0
0
1
2
1
0
1
0
1
1
2
1
1
0
1
1
1
1
1
1
1
3
2
1
1
3
1
2
2
2
1
2
1
0
1
0
1
0
1
0
1
1
1
1
1
1
2
2
1
2
2
1
0
1
1
1
0
2
1
2
1
1
1
0
1
1
1
1
1
2
2
2
1
1
2
1
1
2
1
0
0
1
2
1
1
2
2
2
2
1
1
2
0
2
2
2
0
1
2
2
2
1
0
2
0
0
2
1
0
2
1
1
1
0
0
2
0
0
1
1
1
1
0
1
0
0
0
1
1
1
1
0
1
0
1
2
1
2
1
2
1
1
2
1
2
0
2
3
0
1
1
0
1
2
0
1
0
1
0
1
1
1
1
1
2
1
2
2
0
0
2
1
1
1
1
0
0
2
2
1
2
1
0
1
1
0
1
0
0
0
1
0
1
2
0
0
0
2
1
1
2
0
5
1
1
1
2
1
0
1
0
1
0
1
1
1
1
2
2
1
1
0
0
1
2
2
1
1
1
2
1
2
1
0
0
0
0
0
1
2
1
1
0
1
0
0
1
1
1
0
2
1
1
0
1
0
0
1
1
1
2
1
1
1
1
0
0
0
1
2
2
0
1
2
0
0
2
2
1
0
1
2
0
0
2
2
2
1
1
1
2
0
1
0
1
2
1
0
2
1
1
1
2
1
0
1
1
0
0
0
0
0
1
1
0
0
2
0
1
2
0
2
1
0
1
0
2
1
1
2
1
2
2
1
1
1
2
2
3
1
2
1
0
2
1
2
0
2
1
1
0
2
1
0
1
1
2
2
2
1
0
1
1
1
2
0
1
1
0
1
1
0
1
1
2
0
1
1
0
2
1
2
1
0
0
1
0
0
1
0
1
1
1
1
0
0
2
1
2
1
2
1
1
4
2
1
1
0
1
1
1
1
2
1
2
2
1
1
0
0
2
1
0
1
1
0
1
2
0
2
0
1
2
2
1
0
2
1
1
0
2
1
2
2
0
2
0
2
0
1
1
1
0
1
0
0
0
0
0
1
0
1
1
1
1
2
2
1
1
1
0
1
1
0
2
2
0
2
1
1
1
0
1
1
2
0
1
0
0
0
2
1
0
2
1
0
2
1
1
1
1
1
2
1
1
0
0
1
1
1
1
0
1
1
1
2
1
1
1
1
3
1
1
1
2
0
2
1
0
1
1
2
1
0
1
2
1
1
2
2
0
2
0
1
1
2
0
0
1
0
1
2
1
0
1
0
0
2
0
2
1
0
1
0
0
1
0
1
2
0
1
1
1
0
1
1
0
2
2
0
1
1
1
0
1
1
1
2
0
1
2
1
2
1
0
1
0
1
2
0
1
1
1
2
1
0
1
0
2
0
2
1
1
1
1
1
2
1
1
0
1
0
2
2
1
0
2
0
2
0
1
3
1
0
2
1
0
0
1
0
0
1
0
2
1
1
1
0
1
0
0
2
1
2
1
0
1
1
0
0
1
2
1
1
2
1
2
1
1
1
3
1
1
0
0
2
2
2
2
0
2
0
1
1
0
1
1
0
0
1
1
1
1
1
1
0
1
1
2
0
2
2
1
1
0
0
2
0
1
0
2
1
0
0
0
1
1
1
0
0
2
1
1
0
0
1
1
1
0
0
2
0
1
2
1
0
1
1
0
0
1
2
1
0
0
2
0
0
2
0
2
1
1
1
0
1
2
0
0
2
0
0
1
1
1
1
2
1
2
2
2
1
1
0
1
0
1
2
0
1
0
0
2
1
1
2
1
0
0
1
2
0
0
1
2
1
1
0
0
1
0
1
1
1
2
1
1
0
0
0
2
0
1
0
1
2
0
0
0
2
1
0
1
1
1
1
1
0
1
1
1
0
0
2
0
2
1
2
1
0
0
2
2
1
3
0
0
2
1
1
1
1
2
0
1
2
2
1
1
1
0
1
1
0
0
0
1
0
0
1
0
1
0
1
1
2
1
1
1
1
0
0
2
0
1
0
2
2
1
0
1
2
1
1
1
1
0
0
1
2
2
0
0
1
1
1
0
2
1
0
0
1
1
0
0
0
2
1
2
1
0
1
1
0
1
2
2
1
2
1
0
1
0
1
2
1
1
2
1
1
1
2
0
1
1
1
0
1
0
1
1
1
1
1
0
2
2
2
0
2
0
1
0
1
0
1
2
2
3
1
2
1
0
1
2
1
0
2
2
1
2
1
1
1
1
1
0
2
2
1
1
0
1
0
1
0
1
2
2
1
1
1
2
1
2
1
1
0
3
1
1
1
1
0
1
2
1
0
1
0
0
1
1
0
2
2
0
1
2
0
0
0
1
2
0
1
1
2
1
1
0
1
1
1
2
0
2
1
0
1
0
1
2
1
1
1
1
1
0
1
0
1
1
0
0
1
1
2
1
1
0
1
2
0
1
2
1
1
2
1
0
0
1
0
0
0
1
1
1
2
2
2
1
0
1
0
2
1
1
1
0
1
2
0
1
1
1
1
1
0
1
0
1
1
0
1
2
1
1
0
1
2
1
1
1
2
1
1
2
1
1
3
1
2
0
1
1
1
1
2
1
0
1
0
1
0
1
0
0
0
1
0
0
1
0
0
2
2
1
2
2
1
1
0
0
1
1
2
0
2
0
0
4
1
1
0
2
1
1
1
0
1
1
0
0
1
1
1
1
1
1
1
0
0
1
0
1
1
0
1
2
2
1
2
0
1
1
2
1
2
1
0
1
2
0
1
1
1
2
0
1
0
1
2
0
0
0
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
0
2
2
1
2
0
1
0
0
0
1
1
1
1
1
3
0
1
0
1
2
0
0
0
1
2
2
1
1
1
1
2
2
1
1
0
0
2
0
2
0
0
1
0
0
0
1
0
0
1
0
1
0
1
0
6
0
2
1
2
1
1
0
0
2
1
1
1
1
1
2
2
0
2
0
2
1
1
1
2
2
0
1
1
0
1
0
0
1
0
0
1
0
1
1
2
1
1
1
1
2
1
1
2
2
2
0
2
1
0
0
1
1
0
0
1
1
0
2
1
3
1
2
1
1
0
1
0
0
1
1
2
1
0
2
0
1
1
1
2
0
1
1
0
2
2
2
1
0
2
0
1
0
2
1
1
0
1
0
1
0
2
2
0
1
1
1
1
1
2
0
0
1
2
1
2
2
1
0
2
0
1
0
0
1
1
0
0
1
1
0
1
1
1
1
1
0
2
1
1
2
2
1
0
1
1
0
1
1
1
2
0
1
1
1
0
0
0
1
1
0
1
1
1
1
1
1
0
2
1
1
0
1
1
0
1
1
0
2
1
0
1
2
0
1
2
1
2
1
0
1
0
0
0
0
0
2
1
0
0
2
0
0
0
1
0
3
0
2
1
1
0
1
0
1
2
1
1
1
1
1
1
0
1
1
1
0
0
2
1
0
2
1
0
1
0
1
0
0
2
0
1
1
0
1
0
0
0
2
1
1
1
0
0
1
1
2
1
1
1
2
0
1
0
0
2
1
1
1
1
1
0
0
1
1
0
0
1
1
1
0
2
0
1
2
1
0
2
1
2
1
1
0
1
0
1
1
2
1
2
1
2
0
1
1
0
0
2
0
2
1
2
1
1
1
2
0
1
0
1
3
2
1
1
1
1
0
1
1
0
1
2
1
0
2
1
1
1
1
2
1
1
2
1
2
1
2
0
1
2
0
1
0
1
2
0
1
2
1
2
0
1
1
2
1
0
2
1
2
1
1
0
0
2
0
1
0
0
1
1
1
0
2
0
1
1
1
0
0
2
0
1
0
0
2
2
1
1
0
1
1
2
1
0
0
0
0
1
1
2
1
1
1
0
2
1
1
0
2
0
2
1
1
2
1
1
1
0
2
0
1
1
2
1
1
3
1
2
1
1
3
2
3
2
0
1
1
0
1
1
0
0
1
2
1
0
1
0
1
0
1
2
0
0
0
1
1
2
2
1
1
2
1
1
1
0
1
0
0
2
0
1
0
1
1
1
1
2
2
1
0
1
0
0
1
1
1
0
1
0
5
1
2
2
1
1
1
0
1
1
1
1
0
1
1
2
0
1
1
0
0
2
0
2
1
1
1
2
1
1
0
0
2
2
1
1
2
0
1
0
1
1
2
0
0
1
0
1
0
2
0
0
2
2
1
1
0
1
1
0
2
1
1
2
2
1
1
1
1
1
1
2
1
1
1
1
0
1
2
0
2
0
1
1
1
0
0
2
0
1
1
1
1
0
0
2
1
1
1
1
0
0
1
1
1
0
2
0
1
0
0
2
2
1
1
4
0
2
2
1
2
0
0
1
1
0
1
2
1
2
1
1
1
1
0
0
1
1
1
1
1
0
0
2
0
2
1
1
1
1
0
1
2
1
2
2
2
1
1
0
1
2
1
1
0
2
1
1
1
1
1
1
1
2
0
0
2
1
1
1
2
1
1
8
3
1
1
1
1
1
0
2
1
0
0
1
0
2
0
0
0
1
2
2
1
1
1
1
1
1
1
2
0
1
1
1
1
1
1
1
1
0
0
1
0
0
1
1
1
2
1
3
0
1
1
2
0
2
1
1
1
1
1
2
2
1
0
1
2
0
1
1
1
1
1
2
1
2
2
2
2
1
2
1
1
1
1
1
0
1
2
1
0
0
0
1
1
0
1
0
2
0
0
2
1
2
1
0
0
2
1
1
1
1
0
1
0
1
1
1
2
2
1
1
1
0
1
0
1
2
4
0
1
1
1
0
0
1
2
1
1
1
1
1
2
2
1
1
2
1
1
1
0
2
1
0
1
2
1
0
1
1
2
1
2
1
2
1
0
1
1
2
0
3
0
1
2
1
1
2
1
1
3
0
0
2
1
1
1
2
1
1
2
1
0
0
1
1
2
0
1
1
0
1
1
0
1
0
0
2
1
1
1
0
1
1
1
2
0
0
2
0
0
1
1
1
2
1
0
1
2
2
1
1
1
1
2
1
1
1
1
0
1
0
2
0
1
1
1
0
0
1
2
1
0
1
1
1
1
2
0
0
0
0
2
0
1
2
1
1
0
1
1
1
2
1
2
2
1
1
2
0
0
0
1
0
2
2
2
1
2
0
2
0
0
0
0
1
1
0
1
1
0
0
1
1
0
0
1
0
1
2
0
0
0
0
2
0
2
1
1
1
0
2
1
1
1
0
0
2
1
2
0
1
1
1
0
0
1
2
1
1
2
0
0
2
1
2
2
1
1
1
0
1
1
0
0
0
2
0
1
1
1
2
1
2
0
3
0
2
0
1
0
2
0
1
1
0
1
1
0
1
1
1
1
0
0
1
1
2
1
1
1
0
1
1
2
1
1
2
1
1
1
1
2
1
2
0
1
1
0
3
1
1
2
0
1
1
1
2
2
1
1
1
1
1
0
2
1
0
2
1
0
1
1
0
1
0
1
1
1
1
2
2
1
2
1
1
1
2
0
1
2
1
0
1
1
1
2
2
1
1
0
1
1
1
1
2
2
0
0
3
1
2
1
1
0
2
0
2
2
1
0
1
0
1
0
1
0
2
1
1
1
2
0
0
1
0
0
0
2
1
2
0
0
1
1
1
1
0
0
1
1
1
1
1
1
1
0
2
2
2
0
1
0
1
0
1
1
0
1
2
0
0
0
2
0
2
0
1
1
0
1
1
1
0
2
1
2
1
1
1
2
2
0
1
0
1
1
0
0
0
1
1
1
1
0
0
0
2
2
1
0
1
1
2
1
0
0
0
1
2
1
0
0
1
0
1
1
1
1
1
0
1
2
1
1
1
0
2
0
0
1
1
1
0
1
2
1
1
1
1
0
2
1
1
0
0
0
0
1
1
1
0
1
1
1
2
0
0
1
1
0
0
3
0
1
1
0
1
2
2
1
0
1
1
1
1
1
1
1
1
0
2
0
0
3
2
2
1
2
1
1
0
1
1
1
0
1
2
1
0
1
1
1
0
1
1
1
1
1
0
0
1
0
3
2
1
2
1
2
1
1
2
1
0
2
1
2
0
2
1
1
2
1
1
0
2
1
2
0
0
2
1
0
2
1
2
2
0
1
0
2
0
1
1
0
0
1
0
1
1
1
0
1
2
1
1
1
0
1
0
2
0
1
1
1
0
2
1
2
1
2
0
1
0
0
0
1
1
1
1
2
1
1
2
0
3
1
2
1
1
1
1
1
0
1
1
0
0
2
0
1
2
0
1
2
2
1
0
2
1
1
2
2
0
1
2
1
1
1
0
1
1
1
0
1
0
1
1
2
1
2
1
1
2
2
1
0
0
2
2
1
2
0
0
1
2
1
1
1
1
0
2
1
2
1
0
1
0
0
2
0
0
1
1
1
0
2
0
2
0
0
1
1
2
2
0
0
0
0
0
2
0
1
0
0
1
1
0
1
1
1
1
1
1
1
1
1
0
1
1
0
1
0
1
1
0
0
1
2
3
1
1
1
0
2
1
1
2
2
2
0
2
0
0
1
1
2
0
2
2
0
1
0
2
1
1
2
0
1
1
0
1
0
1
1
1
2
7
1
0
1
1
1
2
0
3
0
1
1
0
1
0
1
1
2
1
2
2
1
1
2
0
1
0
2
1
1
2
1
2
0
1
0
0
1
0
0
1
2
0
2
1
0
0
0
1
1
1
1
0
1
0
1
1
2
2
2
1
2
0
1
1
1
1
1
0
1
1
1
1
0
2
1
2
1
2
2
1
1
1
1
1
2
0
2
2
1
1
1
0
0
2
0
1
0
1
0
1
2
2
0
1
1
1
0
0
0
4
0
1
1
0
0
0
0
0
0
1
2
2
1
0
2
2
0
0
1
2
2
1
0
1
0
0
1
1
2
1
1
2
0
1
0
1
0
1
1
1
4
1
2
0
0
0
1
1
1
1
1
2
0
2
2
0
1
1
1
0
2
2
0
1
2
0
1
0
1
1
1
0
2
0
0
1
1
1
2
1
1
2
1
1
1
0
1
0
0
0
1
1
1
0
1
1
2
1
2
0
0
0
2
0
1
0
0
1
2
2
0
2
1
0
0
1
1
0
2
0
0
0
1
0
0
2
1
1
1
1
2
1
1
1
0
1
1
2
0
0
1
0
2
1
1
0
0
0
2
2
1
1
1
0
1
1
1
1
1
1
0
2
2
2
1
1
2
2
1
1
0
1
0
1
1
2
1
1
1
0
1
1
1
1
0
1
1
2
0
0
2
2
1
1
1
2
0
1
2
2
2
2
2
1
0
1
2
1
0
1
1
1
0
0
2
1
1
1
0
1
2
1
0
1
0
1
0
1
1
2
2
1
1
1
1
2
0
1
1
1
1
0
0
0
0
2
1
1
0
3
0
2
1
2
2
0
2
2
1
1
2
1
1
0
0
0
1
1
1
1
1
2
1
1
2
1
2
2
1
0
1
0
0
1
1
1
1
2
0
0
0
2
1
0
1
0
1
2
1
0
1
1
1
0
1
0
1
1
2
0
0
2
0
2
1
2
0
1
1
0
2
1
0
1
2
2
1
2
2
1
1
2
1
2
1
0
1
1
1
1
0
1
0
1
1
2
2
1
1
0
0
0
0
2
2
2
2
1
0
0
2
1
0
1
1
0
1
1
1
1
2
1
2
1
2
2
0
1
0
1
0
1
1
0
3
0
1
0
1
1
0
0
1
1
1
1
0
0
0
1
0
1
0
0
1
1
0
0
1
2
0
0
1
1
1
0
0
2
2
0
1
0
1
0
1
0
1
0
1
2
0
1
2
2
1
1
0
0
0
1
1
0
1
1
2
0
1
0
1
0
1
2
2
0
2
0
0
1
0
0
0
0
0
3
0
0
1
2
1
1
2
1
0
1
4
1
1
0
1
1
1
1
0
0
1
0
0
2
2
0
2
1
1
1
2
1
1
0
2
2
1
1
0
2
1
2
0
1
0
1
1
1
1
0
1
0
1
1
1
1
0
1
1
2
2
1
2
1
0
0
1
0
2
2
0
0
1
1
1
2
0
2
1
1
1
0
1
0
3
1
1
0
1
1
2
1
1
2
1
2
1
1
2
1
0
1
2
2
2
1
2
1
1
1
1
2
0
2
1
0
1
1
1
2
1
0
2
1
0
2
0
2
1
0
0
1
1
2
0
1
0
0
1
1
0
0
0
1
0
0
1
2
2
0
2
0
0
1
1
1
2
0
0
1
0
1
1
0
1
1
1
0
2
0
1
2
1
1
1
0
2
1
1
2
0
1
0
2
1
1
0
1
1
1
2
2
0
2
0
1
1
0
2
1
1
0
1
2
0
0
1
1
0
1
2
0
1
1
0
1
1
3
1
1
1
0
1
1
1
1
0
1
0
1
1
1
0
1
0
1
0
1
0
0
1
1
1
0
2
1
1
2
1
1
1
2
1
1
0
0
1
0
2
2
1
1
1
1
1
1
2
0
1
0
2
1
1
1
1
1
1
0
1
2
1
0
0
1
1
0
1
1
0
0
1
2
0
0
1
2
1
3
1
0
1
1
1
0
1
1
0
1
1
1
1
1
1
1
2
0
2
2
1
0
1
1
0
1
1
0
1
1
2
2
1
1
0
0
2
0
0
0
1
1
1
1
1
1
1
2
1
0
1
1
1
2
3
0
2
2
2
0
1
2
0
0
1
2
1
3
0
2
0
1
3
1
1
2
2
2
1
2
1
1
1
1
1
1
2
1
1
1
1
2
1
2
0
1
1
2
0
1
0
0
0
0
2
1
1
1
1
1
1
1
1
0
2
2
1
1
2
1
1
0
2
1
0
1
0
0
0
1
0
4
0
1
0
0
1
1
1
3
2
2
2
0
0
1
1
1
1
1
1
0
2
0
0
0
1
1
1
0
2
2
0
0
1
2
1
0
0
2
1
0
1
0
1
1
1
1
1
2
0
2
2
0
1
2
1
2
2
2
1
1
1
0
1
1
0
1
1
0
1
1
0
0
1
0
0
0
0
1
1
1
1
0
1
2
0
0
0
1
2
2
0
2
1
1
1
1
0
2
0
0
0
0
0
1
1
1
0
1
0
1
0
1
1
1
1
1
1
2
3
0
1
1
1
1
1
1
2
1
4
1
2
1
0
1
1
1
1
0
2
1
1
2
1
1
1
0
1
0
0
0
1
0
0
0
1
0
0
1
2
1
0
1
0
0
2
2
0
0
0
1
1
1
2
1
0
1
2
1
1
0
1
1
1
1
0
0
0
2
1
1
1
1
0
0
0
4
2
1
2
1
0
1
0
1
1
1
1
2
1
1
0
1
2
0
2
2
0
1
1
0
1
1
1
0
1
0
1
1
1
0
1
1
1
1
1
0
1
2
1
2
0
0
0
1
1
1
1
0
0
1
1
1
1
1
0
0
0
1
1
1
0
1
2
0
2
1
1
1
1
1
1
1
1
1
0
1
2
1
1
2
0
0
0
0
1
2
1
0
1
2
1
2
1
2
1
1
1
0
2
1
1
1
1
1
2
1
0
1
2
2
2
1
2
0
2
2
0
1
2
1
1
2
1
1
1
1
1
2
1
1
1
0
1
0
1
1
0
2
0
0
2
0
0
2
1
1
1
0
2
0
0
2
1
1
1
2
0
1
1
2
2
0
0
3
0
1
0
0
0
2
1
1
2
0
0
1
1
2
1
1
1
1
0
1
1
1
0
2
1
1
2
2
0
2
0
1
1
1
1
2
0
0
1
1
0
1
2
0
2
1
3
1
1
1
1
1
1
0
2
1
1
0
0
1
0
2
0
1
1
2
2
2
2
1
1
2
1
2
0
2
1
2
1
1
2
1
0
1
1
1
0
1
1
0
1
2
0
0
0
1
1
1
1
1
0
2
2
1
2
0
0
2
1
0
0
1
0
0
1
0
2
0
1
1
2
1
1
0
2
0
2
1
0
2
0
1
1
0
0
1
0
1
1
4
1
1
0
1
2
2
1
1
1
0
2
1
2
0
1
1
0
1
1
2
1
1
2
0
0
2
0
2
0
1
1
1
1
0
1
1
0
0
1
0
2
2
2
2
1
0
0
1
0
1
1
1
2
1
2
0
1
2
7
1
1
0
1
0
0
1
0
2
1
2
1
2
0
1
0
1
0
2
0
1
1
2
1
2
1
1
1
1
0
0
1
0
1
0
1
0
1
1
2
0
0
0
1
1
1
1
1
0
0
1
1
0
3
0
1
1
2
1
0
1
2
0
0
1
1
1
1
1
1
1
1
1
2
1
1
0
0
0
0
1
2
0
1
1
0
1
1
0
1
2
1
0
1
0
1
1
0
1
0
2
1
1
2
2
0
1
2
2
3
2
2
0
1
0
1
2
0
1
1
0
0
0
0
1
1
1
0
1
0
0
2
1
1
1
1
0
0
2
2
0
1
1
0
0
0
1
2
1
0
2
1
1
2
0
0
2
2
0
2
0
1
1
0
0
1
2
1
0
2
0
1
1
2
0
0
2
1
2
1
2
1
1
0
0
0
1
0
2
1
0
2
1
0
2
1
2
1
1
2
1
1
1
0
2
2
2
1
2
1
0
0
1
1
0
1
1
1
1
0
0
1
0
1
1
1
2
1
1
0
1
1
1
1
1
1
0
0
1
2
1
1
2
1
1
1
1
1
0
1
2
0
1
2
1
0
0
2
1
0
2
1
1
1
1
0
1
1
0
1
1
1
0
0
0
0
0
0
0
1
1
1
4
0
0
1
1
1
0
0
1
0
1
1
2
1
1
2
1
1
1
2
1
2
2
1
1
1
1
1
0
1
2
2
0
1
2
1
1
1
1
2
2
2
1
0
0
1
1
2
0
1
0
0
2
1
2
0
0
1
2
0
1
1
2
1
1
0
0
1
1
1
2
1
1
1
1
1
1
1
1
0
0
2
1
0
1
2
1
1
0
0
0
0
1
2
1
0
1
1
2
0
1
1
1
1
1
0
0
1
1
2
0
2
1
2
1
0
1
2
0
2
0
2
0
1
2
1
1
0
1
1
1
1
1
1
1
1
0
1
0
2
0
1
1
1
0
1
0
2
0
1
1
2
1
1
0
0
1
0
1
0
0
2
3
2
2
1
1
1
0
3
2
0
1
0
0
1
1
1
0
2
0
0
1
1
1
0
0
1
0
1
0
1
1
1
0
3
1
0
0
1
1
1
1
0
1
0
1
1
2
1
1
2
0
1
1
1
1
1
0
0
0
0
1
2
0
0
1
2
0
0
2
1
1
1
1
0
1
2
1
2
1
0
2
0
2
1
2
1
1
1
1
1
1
0
1
2
2
0
1
1
2
2
1
3
1
1
0
2
1
2
1
2
0
1
1
1
1
1
1
0
1
1
1
1
2
1
2
1
2
1
1
0
1
1
1
1
1
1
1
1
1
2
0
1
2
0
1
0
0
1
0
0
2
1
2
0
5
2
2
1
1
0
0
2
1
1
1
0
0
1
0
2
1
0
0
1
2
2
0
2
1
1
0
1
0
0
2
0
2
1
0
1
1
1
1
1
2
1
1
0
1
1
2
1
1
0
0
0
2
0
1
2
1
1
1
1
0
1
0
1
1
1
1
2
0
0
1
2
2
2
1
0
1
1
2
1
1
2
1
1
1
1
2
0
1
1
1
1
1
1
1
0
0
2
0
1
0
1
2
1
2
2
0
1
0
1
2
2
2
1
1
1
1
1
1
2
1
2
1
0
0
0
0
1
1
2
1
1
0
2
5
2
1
2
2
2
0
1
1
1
2
1
1
3
0
1
1
1
1
1
1
1
1
1
1
0
2
1
1
3
1
1
0
1
1
1
0
1
0
0
1
1
1
1
2
1
0
0
2
0
0
1
1
0
0
2
1
1
1
1
2
1
0
1
1
1
0
0
1
0
1
0
1
1
0
2
1
1
0
1
1
0
1
0
2
0
1
0
2
0
1
1
1
1
1
2
1
1
2
0
1
1
1
1
2
2
0
2
0
0
2
1
1
1
1
1
0
0
0
1
0
2
2
1
0
0
1
1
1
1
0
2
2
1
1
1
2
1
1
1
1
1
0
1
0
1
0
2
1
1
0
0
1
1
2
2
1
1
2
1
2
1
1
2
1
1
0
0
1
1
1
0
0
1
1
0
0
1
1
1
2
0
1
0
1
1
0
0
1
1
0
1
0
0
0
2
2
2
1
2
1
1
1
0
1
3
0
1
1
1
1
2
3
1
0
1
0
1
2
1
1
2
1
1
1
0
0
1
1
1
2
1
1
2
1
2
1
1
1
0
1
0
0
2
2
0
2
2
1
0
1
1
1
1
0
0
1
1
1
2
1
0
1
0
2
1
1
1
2
1
1
0
0
0
1
1
1
0
0
1
1
1
1
2
1
0
0
1
1
1
2
1
1
1
1
0
1
0
0
1
1
2
1
1
2
0
0
0
1
0
1
0
1
0
1
0
2
0
1
0
0
0
2
2
1
1
2
1
0
2
2
1
2
1
0
0
2
2
1
1
3
0
0
2
1
0
1
2
2
0
1
1
1
1
0
1
1
0
1
2
2
1
1
1
1
1
2
2
1
1
1
1
1
2
0
1
1
1
0
1
1
1
1
0
2
2
0
0
1
1
0
0
0
2
2
0
2
0
1
1
0
1
1
0
0
1
0
1
1
0
1
0
0
0
2
0
2
2
1
0
1
1
2
2
1
2
2
2
1
1
2
1
1
1
2
2
1
1
2
2
1
0
1
0
0
0
1
1
2
0
1
1
1
1
1
2
0
0
1
0
1
1
1
1
1
1
2
1
2
1
1
1
2
2
1
1
1
2
0
1
0
2
0
1
1
3
2
1
1
1
2
1
1
2
1
1
2
0
0
0
1
0
2
2
0
0
1
1
2
0
1
2
1
1
1
0
2
1
1
1
1
1
1
0
0
2
1
1
1
14
0
1
1
1
1
0
1
1
2
1
0
1
0
1
0
0
1
0
0
0
1
1
1
1
0
0
1
1
1
1
0
1
1
1
1
1
0
1
0
1
1
0
1
2
2
2
2
1
1
1
0
2
1
2
1
0
2
1
1
1
0
1
0
1
1
1
2
2
1
0
2
2
1
1
0
0
0
0
2
2
1
2
1
2
1
1
1
2
0
2
1
2
0
1
2
1
3
1
2
0
1
1
2
0
1
0
0
1
1
1
1
2
1
2
1
0
2
2
1
2
2
1
2
1
1
1
1
2
1
0
1
1
2
2
1
1
2
0
1
1
1
2
0
1
2
2
0
1
1
1
0
1
1
1
2
2
1
1
0
1
0
0
0
2
1
1
1
0
0
1
2
0
0
1
0
1
2
0
1
1
0
2
1
1
1
1
1
1
1
2
1
2
1
1
0
0
1
0
1
1
1
0
0
1
1
1
0
1
0
1
0
2
2
2
1
2
1
1
1
1
0
2
0
1
0
0
0
0
1
1
2
0
0
0
2
1
0
0
0
1
1
1
1
1
2
2
2
1
1
2
1
1
0
1
1
0
1
2
1
1
0
0
2
1
1
0
1
1
2
0
0
0
2
0
0
1
2
1
1
2
1
0
0
2
0
1
9
1
0
0
1
0
1
1
1
1
2
2
1
1
0
0
1
1
7
2
1
1
0
1
2
0
0
1
1
2
2
0
2
1
1
2
0
1
1
0
1
0
1
1
1
2
1
1
2
1
1
0
1
0
1
1
1
1
0
1
1
1
2
2
0
2
1
1
2
1
0
2
0
1
0
1
0
0
1
2
0
0
1
2
2
0
0
1
2
2
2
0
2
0
2
0
2
1
3
0
1
0
2
1
1
1
1
2
0
1
1
2
2
0
2
1
2
0
0
0
1
1
1
0
1
0
1
1
1
1
0
1
2
1
1
1
1
1
0
1
1
2
1
1
0
1
0
1
0
0
2
1
1
0
2
2
1
1
0
1
0
1
0
1
0
1
1
1
0
0
0
1
1
2
2
2
0
1
0
1
1
0
0
1
1
0
1
1
3
1
1
0
2
1
1
0
0
2
2
1
0
0
0
0
2
0
1
1
0
1
1
2
1
1
0
1
0
1
1
2
0
1
2
1
0
1
1
1
0
2
1
1
1
2
2
2
2
1
0
1
1
2
1
1
1
0
0
1
1
1
1
0
1
2
0
0
1
2
1
1
0
2
1
0
1
1
0
1
1
1
2
1
0
0
2
0
1
0
1
1
1
0
1
0
1
2
0
2
1
0
1
1
0
0
0
1
1
2
1
1
1
0
1
1
0
0
1
2
0
1
0
0
1
1
1
0
0
2
2
0
1
2
1
2
2
2
0
0
2
2
1
0
1
1
1
0
2
2
1
2
2
1
1
1
1
0
2
1
0
0
2
1
1
1
0
1
1
1
0
1
0
0
0
0
1
1
0
2
1
1
1
2
1
0
1
2
2
3
0
2
1
0
0
0
1
1
1
0
0
0
1
1
2
3
1
1
0
2
1
1
0
1
1
0
1
1
1
0
2
2
1
2
1
1
2
1
0
2
0
1
1
1
2
0
0
0
1
1
1
1
1
1
1
1
1
1
2
1
2
1
2
1
2
0
0
1
0
1
0
0
0
1
1
0
0
0
2
0
0
2
1
4
2
1
0
0
0
1
2
1
0
1
1
2
0
2
1
4
1
1
2
1
2
2
1
2
1
1
2
1
1
0
2
0
0
1
1
1
0
0
1
2
1
1
1
0
1
0
1
1
1
1
2
0
1
2
0
0
2
2
1
0
1
0
0
3
1
2
1
1
1
2
3
0
1
1
0
0
0
0
1
2
0
0
1
0
1
2
1
2
0
1
0
2
2
1
2
1
1
0
3
2
2
1
0
1
1
1
1
1
2
1
0
2
1
1
1
1
1
1
1
1
1
1
0
2
0
0
1
1
2
1
2
1
0
2
2
2
1
1
0
0
0
1
1
1
0
1
0
1
1
1
1
1
0
0
0
0
1
1
2
1
1
0
0
0
0
1
0
0
2
1
1
1
1
1
2
1
0
2
0
0
0
2
2
1
1
0
0
1
2
1
0
0
1
1
0
1
2
0
1
0
0
0
0
0
2
1
1
0
2
2
2
0
1
1
1
1
1
0
0
1
2
1
2
1
2
2
1
0
1
0
0
1
1
0
1
1
0
2
1
1
1
0
1
0
0
1
1
0
2
1
1
1
1
1
2
0
1
2
0
1
1
0
2
0
0
2
1
1
0
1
0
1
2
2
1
0
2
1
1
1
1
0
2
1
1
2
2
1
0
3
1
0
1
0
2
1
0
2
1
2
1
1
1
1
1
0
0
0
1
1
2
0
1
1
1
0
1
0
1
2
2
1
3
1
0
1
0
0
1
3
2
1
0
2
0
1
0
1
0
0
0
1
1
2
1
1
0
1
0
1
1
1
2
2
0
2
1
0
1
1
2
1
1
0
0
1
1
1
1
0
0
1
1
1
2
0
1
0
1
1
1
0
1
2
1
2
1
1
1
2
0
2
1
1
1
1
1
2
2
0
1
2
1
2
1
1
1
2
0
2
0
2
2
1
1
2
1
1
0
0
1
1
0
2
1
0
2
1
1
1
1
1
1
1
0
2
1
1
0
2
1
1
1
0
0
0
2
2
0
1
0
0
1
2
1
0
1
1
0
1
2
1
2
1
0
1
1
1
0
1
0
1
2
0
1
2
1
1
2
1
0
0
2
1
2
1
1
1
0
1
1
2
1
1
1
0
2
2
1
1
1
1
1
1
1
0
0
2
0
1
0
2
1
1
1
1
2
2
2
0
0
2
1
0
0
1
1
0
0
1
0
0
1
1
1
1
2
1
2
2
2
1
2
2
1
1
2
0
1
2
0
1
2
1
3
0
2
1
1
0
1
1
0
0
2
1
1
0
0
0
0
2
2
1
2
2
1
2
1
2
0
1
1
2
1
0
0
2
0
1
1
1
0
0
0
0
2
2
0
2
1
1
2
1
2
1
0
1
1
1
2
1
1
0
1
1
1
1
1
1
0
2
1
2
1
1
2
1
1
0
1
2
2
1
1
0
1
2
1
0
1
1
0
0
0
2
0
2
1
1
2
1
1
2
0
1
1
1
2
1
2
1
1
2
1
1
0
0
0
2
2
2
0
1
1
1
0
0
2
1
0
0
1
1
1
1
3
1
1
1
1
1
1
0
1
1
0
1
2
2
0
1
1
1
0
0
2
0
0
1
2
2
1
2
2
1
2
0
0
0
1
0
0
1
1
3
0
1
1
2
0
2
1
1
2
1
0
1
0
2
0
2
0
0
0
2
1
1
1
2
0
1
1
2
1
1
0
3
1
1
0
0
1
2
0
1
2
2
2
2
1
1
2
0
1
1
1
0
1
1
1
0
1
2
1
0
1
1
1
2
0
4
0
0
0
2
1
2
0
2
1
1
1
1
1
2
1
0
2
1
2
0
0
2
1
0
0
0
0
2
2
1
1
1
1
0
2
1
0
1
2
2
0
2
1
1
1
0
0
2
1
1
0
0
0
0
0
1
1
1
2
2
1
1
1
0
1
1
1
0
1
1
0
1
1
0
1
2
1
1
1
0
0
0
1
1
0
1
1
0
0
1
1
0
0
1
1
1
0
0
2
1
1
1
1
1
2
1
1
1
2
0
2
1
1
0
0
1
0
1
1
0
2
2
1
1
1
1
0
0
1
0
1
1
1
2
1
3
1
1
0
1
1
1
1
0
0
2
2
0
1
2
1
1
1
0
0
1
0
0
1
1
0
0
0
0
1
1
2
2
1
0
0
0
1
2
1
1
1
0
1
1
1
1
1
2
2
0
1
0
1
1
1
1
1
1
1
1
1
2
0
0
1
0
2
1
1
2
1
1
1
1
0
1
0
0
2
1
2
0
1
0
0
1
1
0
1
0
1
1
0
1
1
1
1
0
2
1
1
0
1
0
0
1
2
0
0
2
1
1
1
2
1
1
2
1
2
2
1
1
1
1
1
2
0
2
1
1
1
1
1
1
0
1
2
2
1
2
0
2
2
0
2
0
0
1
1
0
1
1
0
1
2
1
1
1
2
1
1
0
1
1
2
1
1
0
1
1
0
2
0
1
0
0
2
0
1
0
2
5
1
0
2
0
0
0
2
1
0
1
1
1
0
1
0
2
0
3
0
1
0
2
1
0
1
2
1
1
1
0
1
2
1
0
1
0
1
1
1
0
1
2
1
2
1
0
2
0
1
2
0
0
1
1
1
2
2
2
1
0
2
1
1
1
1
1
1
0
1
1
0
3
2
1
0
2
2
1
1
2
2
2
1
2
1
1
2
0
0
1
1
2
2
0
1
1
2
2
1
0
0
1
1
2
0
0
2
1
1
1
1
1
1
2
1
2
0
0
0
1
1
0
1
0
2
1
0
1
1
0
1
1
1
0
0
1
0
2
0
0
1
2
0
1
0
0
0
0
1
0
2
2
1
2
2
1
0
1
1
1
0
1
1
1
1
2
0
1
1
1
2
1
2
0
0
1
2
1
0
0
1
0
1
1
2
1
2
0
0
0
1
0
2
1
2
1
0
0
2
1
0
1
1
1
1
0
1
2
1
1
1
2
0
0
0
1
2
0
1
1
1
0
0
2
1
0
2
1
1
1
1
2
1
2
0
0
1
1
0
0
1
1
1
1
0
0
2
0
1
2
2
1
1
1
1
1
1
2
0
0
0
1
3
2
0
2
1
1
1
1
0
0
1
0
1
1
0
1
1
2
1
3
0
1
1
0
0
0
1
2
0
1
1
2
2
0
0
2
2
1
0
1
0
1
1
0
0
2
1
2
1
1
1
2
1
2
0
0
2
2
1
0
0
2
1
1
0
0
1
1
2
0
2
0
1
0
1
0
2
1
1
1
2
1
2
1
1
1
3
1
1
2
0
2
0
1
0
3
0
1
1
0
1
1
1
1
0
2
1
2
1
0
1
1
1
2
0
1
1
0
1
0
1
1
1
0
1
1
2
1
0
2
1
1
1
2
1
0
1
2
1
2
1
1
0
0
1
0
0
0
0
1
1
1
1
1
2
1
0
1
0
0
2
1
2
1
2
0
2
0
1
2
0
1
1
2
0
1
2
2
1
2
0
1
0
0
2
2
2
2
0
2
1
1
0
1
0
0
1
1
1
1
1
0
0
2
1
2
0
0
1
1
0
0
0
1
1
1
2
2
1
1
0
1
1
0
3
2
0
2
2
2
0
0
1
2
0
2
1
1
2
1
1
1
1
2
1
2
2
1
2
0
1
0
2
1
1
0
1
1
0
1
0
1
1
1
1
2
0
1
1
0
2
1
1
0
2
1
0
2
1
2
1
1
2
1
1
1
0
1
2
1
1
0
1
2
1
2
2
1
0
2
1
1
1
2
1
1
1
2
0
1
0
1
1
1
1
0
3
1
2
0
1
1
0
2
1
0
1
0
1
2
1
1
1
2
2
2
2
1
0
1
0
1
1
1
2
0
1
2
0
0
2
1
1
0
1
0
1
2
2
0
1
2
0
1
2
0
0
1
1
1
1
2
1
2
0
1
0
1
2
3
1
1
1
2
2
1
1
1
1
1
2
1
1
1
1
0
2
1
1
1
2
1
0
1
0
2
2
1
1
0
0
2
2
1
2
1
1
1
1
2
0
2
2
1
1
1
1
1
1
1
2
1
0
0
0
1
1
2
2
2
1
1
0
2
1
1
1
1
2
1
2
2
0
0
2
1
2
2
0
1
0
2
1
2
2
1
1
1
0
1
1
2
1
1
1
0
0
1
1
2
1
1
1
1
0
1
1
1
0
2
0
0
1
0
2
2
1
2
0
0
0
1
1
4
2
0
0
2
0
1
1
1
1
2
0
0
1
2
0
1
1
1
0
0
1
2
0
1
2
1
1
0
1
0
1
1
2
0
1
1
1
1
0
1
0
1
1
1
1
1
1
1
0
1
2
1
0
1
1
2
1
0
0
0
0
2
1
1
1
1
2
2
2
1
1
2
1
0
1
3
0
1
2
1
1
0
0
1
0
2
1
1
1
0
0
0
1
1
1
1
1
1
1
1
0
1
1
1
0
0
2
1
1
0
1
0
0
1
1
2
2
1
0
2
0
1
2
1
0
1
0
1
0
0
2
2
0
1
1
1
1
1
0
1
1
1
1
0
1
1
1
0
1
1
1
1
1
1
0
0
0
1
1
2
0
2
0
1
1
0
2
1
0
1
1
1
0
1
2
2
2
1
0
0
2
2
1
1
1
1
1
1
2
1
0
1
1
1
0
1
0
0
0
1
1
1
0
2
0
2
0
1
2
1
2
1
2
1
2
0
2
1
0
0
2
1
2
1
0
1
1
1
2
0
0
3
1
2
1
0
0
2
1
1
0
1
2
0
0
0
1
0
2
0
1
1
1
0
0
0
0
0
1
1
0
2
0
2
1
1
1
1
1
0
1
2
0
0
0
1
1
1
0
1
1
0
1
2
2
0
1
1
2
1
2
2
1
0
2
1
2
1
1
1
0
0
1
1
2
2
1
1
1
0
2
2
1
1
0
1
2
3
1
0
2
0
1
0
0
1
1
1
1
1
1
4
1
0
0
1
0
2
6
1
1
0
0
2
1
1
2
0
1
0
0
1
1
1
2
1
0
1
0
1
1
1
1
1
2
1
0
2
0
2
1
0
2
1
0
1
1
1
0
1
0
7
0
2
0
1
1
0
0
1
2
0
1
2
0
1
0
0
1
1
1
1
0
1
3
1
0
0
2
0
1
0
1
1
2
1
1
0
2
0
1
1
0
1
1
1
1
0
2
2
1
0
1
0
2
2
0
1
1
0
3
0
1
2
1
0
1
2
2
0
2
2
0
1
0
2
0
1
1
1
2
1
1
1
2
0
2
2
0
0
2
1
0
2
2
1
0
2
1
1
0
1
1
1
0
2
0
1
1
1
0
1
0
1
0
1
1
0
1
1
1
2
0
0
1
2
0
1
2
0
1
1
0
0
1
0
1
1
1
1
2
2
1
0
0
1
0
1
0
1
2
1
1
2
1
1
1
1
2
1
2
1
1
1
1
2
2
0
0
0
0
0
1
2
1
1
1
0
1
2
1
1
1
0
1
1
0
0
1
1
2
0
2
1
0
0
2
1
1
1
0
1
1
2
0
2
2
2
0
1
0
1
1
0
2
1
1
0
0
0
1
0
1
1
1
0
1
1
2
1
1
2
1
1
2
1
0
1
0
1
1
1
2
1
1
0
2
1
1
0
0
2
1
0
0
1
0
1
0
1
2
1
2
2
1
2
2
0
1
1
0
0
0
2
2
1
0
0
1
1
0
1
1
1
0
1
2
2
1
1
0
2
1
1
2
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
2
2
0
0
1
1
9
2
1
1
0
2
2
0
1
0
2
2
1
1
0
1
0
1
1
1
1
2
1
0
0
1
1
1
0
0
2
0
0
2
2
1
0
1
0
1
1
1
2
1
0
0
2
0
1
2
0
1
2
1
0
1
0
1
1
2
1
1
0
1
1
0
0
1
0
2
0
1
2
2
1
2
0
1
1
1
1
0
0
1
2
1
1
1
0
0
1
1
1
2
0
0
0
1
1
1
1
1
1
2
1
1
2
1
0
0
1
1
0
1
1
1
2
0
0
2
1
2
1
1
2
1
0
1
2
1
2
1
2
1
1
2
1
1
0
2
2
1
2
1
1
0
0
1
3
0
1
1
1
2
1
2
0
0
1
1
2
1
1
1
2
0
3
1
0
0
0
1
1
0
0
1
2
1
1
0
2
3
0
1
2
1
1
1
1
0
0
1
3
1
1
2
0
1
1
1
1
1
0
2
0
0
2
2
1
2
1
2
2
1
1
0
0
0
1
2
1
1
1
1
1
1
0
1
0
0
1
0
2
1
1
0
0
2
2
2
0
0
2
1
0
1
1
0
1
2
0
1
3
0
0
1
0
1
1
1
1
0
1
0
1
0
1
0
1
2
0
0
2
1
1
0
1
1
2
1
1
0
1
0
0
1
1
2
1
2
0
2
1
1
1
2
0
0
0
0
0
1
1
1
1
1
1
2
0
0
1
1
0
2
1
1
1
2
1
0
1
1
1
1
0
0
2
1
0
1
1
0
2
2
2
1
1
2
1
2
1
2
0
0
0
1
2
0
1
2
1
2
1
2
1
2
1
1
0
1
0
0
1
0
2
1
1
2
1
1
2
0
2
1
2
2
1
2
1
2
2
2
1
1
2
1
1
1
2
1
1
0
0
2
2
2
1
1
0
0
1
4
1
2
1
0
1
0
1
0
1
2
1
0
1
1
1
2
0
0
0
0
1
0
0
0
0
1
1
2
1
2
1
0
0
2
2
1
1
1
0
0
2
0
2
1
0
0
1
1
2
2
1
0
0
1
2
1
1
4
2
2
1
0
2
1
1
2
1
3
0
0
0
0
0
2
0
0
2
2
1
1
1
1
1
2
0
2
1
1
1
2
2
0
0
2
2
0
0
1
1
2
0
1
2
1
1
2
0
1
1
1
0
2
1
0
2
1
2
0
1
1
1
2
1
1
0
1
0
1
1
1
0
0
1
0
0
1
1
1
2
2
0
2
1
3
0
1
0
0
1
2
3
0
1
0
1
1
1
1
1
1
1
0
1
2
0
2
0
1
1
1
3
1
1
2
0
0
0
1
0
0
0
1
0
0
1
3
1
1
3
1
0
1
2
1
0
1
0
2
1
3
2
2
1
1
1
2
2
0
1
1
1
0
1
0
1
0
2
0
1
1
2
1
0
1
2
2
2
0
1
1
0
0
0
1
2
1
1
0
0
1
1
1
0
1
1
0
1
1
1
1
2
1
0
2
1
1
2
1
1
1
1
0
1
1
0
0
0
1
0
0
1
1
0
1
1
2
2
1
2
1
1
2
0
1
2
2
0
0
2
2
0
1
0
1
1
2
0
1
1
2
0
2
0
1
1
0
0
1
1
1
1
0
1
0
1
2
3
2
0
0
2
0
0
1
1
0
1
1
1
1
1
2
1
1
2
1
1
1
1
0
1
2
2
1
1
1
1
2
1
1
2
2
0
1
0
0
0
2
1
1
1
1
1
1
0
1
1
1
1
0
1
2
1
0
2
1
0
1
0
1
1
1
2
0
1
2
1
0
1
0
1
2
1
1
0
1
1
1
1
1
0
1
2
1
2
2
2
2
2
0
0
1
2
2
0
1
1
2
1
0
1
2
0
1
2
0
0
1
2
0
1
1
2
1
1
1
1
1
1
2
0
1
1
0
0
2
0
1
2
2
1
1
1
0
1
2
1
2
1
0
1
0
2
1
2
1
2
1
1
2
1
2
1
2
2
2
1
0
1
1
1
1
0
1
2
2
2
0
2
1
2
1
1
1
0
1
1
2
1
0
1
0
0
1
1
1
2
1
2
2
2
2
0
1
0
0
1
1
1
1
1
1
1
1
2
2
1
1
1
1
0
3
1
2
1
1
0
1
0
1
1
1
2
1
1
0
1
1
1
1
0
1
2
0
0
0
1
2
2
1
0
1
1
0
2
0
1
1
1
1
0
1
1
1
1
1
1
1
0
2
0
0
2
1
0
1
1
1
0
2
0
1
1
1
1
1
1
1
2
1
1
2
0
0
1
1
1
1
1
0
1
1
2
1
1
1
1
2
1
2
2
1
1
1
0
1
1
0
1
2
2
2
2
1
8
1
1
0
1
0
2
0
1
2
1
2
2
0
2
1
1
1
0
1
2
1
0
2
1
0
1
1
0
0
1
1
0
1
1
0
1
1
1
0
1
2
0
1
0
1
1
2
1
1
1
1
0
1
2
0
1
0
1
1
2
1
1
2
2
1
1
1
0
0
0
2
2
1
1
0
0
2
1
1
2
1
0
0
2
1
2
1
1
0
1
0
0
1
1
1
0
0
2
0
0
1
1
1
2
2
2
2
2
1
0
2
1
2
1
1
0
1
0
1
0
0
1
2
1
0
0
1
0
2
1
1
1
1
0
1
1
0
0
0
0
2
0
1
2
1
1
1
1
1
2
1
0
2
0
1
1
1
1
1
1
1
1
0
0
1
0
1
2
2
1
2
2
0
0
2
2
1
0
2
0
0
1
0
0
0
1
1
2
0
1
1
1
1
1
0
1
2
0
0
1
0
1
2
2
1
1
0
1
2
1
1
1
1
0
1
0
2
2
1
1
0
0
0
0
0
0
1
1
2
1
0
0
1
2
1
0
1
1
0
2
0
1
0
0
1
2
1
2
2
1
1
1
1
0
0
1
0
1
2
1
1
1
2
0
1
0
0
0
1
1
0
1
1
1
5
0
0
2
1
0
1
1
0
0
2
0
1
1
2
1
1
0
1
1
1
0
2
1
2
1
1
2
2
1
0
0
0
0
1
0
1
1
1
1
0
1
1
1
2
0
2
0
1
1
2
1
2
2
0
1
0
2
0
1
1
2
1
2
0
1
1
0
2
2
0
0
1
2
2
0
1
1
1
2
0
1
1
0
1
0
0
0
2
2
0
2
1
1
2
0
2
1
1
2
1
2
1
2
1
1
0
2
1
2
0
0
1
0
0
0
2
1
1
1
0
1
0
2
2
2
0
1
1
1
1
1
2
1
1
1
2
1
1
1
0
1
1
1
1
1
1
1
1
1
2
2
1
0
1
2
0
1
1
2
1
1
2
0
2
1
0
1
0
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
1
2
1
1
1
1
1
0
1
1
2
1
0
0
1
1
1
2
2
0
0
1
1
0
1
2
0
1
1
3
0
2
0
1
2
1
2
1
1
1
0
2
1
0
1
1
1
1
0
1
0
1
1
1
1
0
1
1
1
1
0
1
0
1
0
0
1
2
0
3
2
1
1
1
1
0
1
2
2
1
1
0
1
1
0
1
0
1
1
1
1
2
1
0
1
1
1
1
1
0
0
0
0
2
1
1
1
1
1
1
1
0
1
0
0
0
0
1
0
0
1
0
2
1
1
1
0
2
1
1
0
2
0
2
1
2
4
1
1
1
2
2
2
1
0
1
2
0
1
1
2
2
1
0
1
1
0
2
1
1
1
0
0
1
1
0
0
0
3
0
0
0
0
0
1
1
3
0
1
1
1
1
1
1
2
1
1
2
0
1
0
0
0
2
1
0
1
0
0
1
0
0
2
0
0
0
2
1
2
2
0
1
2
2
2
2
2
1
0
0
1
0
2
1
0
0
1
1
0
1
1
0
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
0
1
3
2
2
2
2
1
1
1
0
0
1
0
2
1
1
1
2
0
1
1
0
2
1
0
2
1
0
2
0
1
1
1
2
0
2
1
2
2
0
1
0
1
1
2
2
1
1
1
0
1
1
2
1
1
1
1
0
0
2
2
2
0
0
2
2
0
1
2
0
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
1
0
0
1
1
1
1
1
0
2
0
0
2
1
0
0
1
1
1
0
1
0
1
1
2
0
0
0
2
0
1
1
0
0
1
1
1
0
1
1
0
2
1
1
1
0
1
1
1
1
0
1
0
2
1
0
2
1
1
0
2
2
0
2
1
1
0
1
0
1
1
1
1
1
0
1
0
0
2
1
0
0
1
1
1
1
1
1
2
0
0
0
2
2
3
1
1
1
2
2
0
2
1
2
0
1
2
1
1
1
1
1
1
0
1
1
0
0
1
0
1
0
0
0
1
1
2
2
0
1
0
1
0
1
2
6
1
0
0
0
2
2
1
0
0
1
3
1
0
2
1
1
3
0
2
1
1
0
1
1
1
0
1
2
1
0
1
0
0
2
1
0
1
2
1
2
0
1
1
1
2
1
1
1
2
1
1
0
1
1
0
1
0
2
1
0
2
0
1
0
1
1
0
3
1
1
0
1
2
0
0
1
0
0
1
1
2
0
1
1
0
0
0
1
0
0
2
1
1
1
0
2
1
1
1
0
1
1
1
1
0
2
2
0
1
1
0
2
1
1
2
2
1
0
2
1
1
1
2
2
1
1
2
0
2
1
0
0
1
0
0
0
0
0
1
1
1
0
0
2
1
2
1
1
2
1
0
1
2
1
1
1
2
1
2
0
1
1
0
1
2
2
1
1
1
2
0
0
0
1
3
1
1
1
2
1
2
1
2
0
0
0
2
0
2
2
1
0
0
0
1
1
1
0
1
1
0
1
0
1
1
0
0
1
1
1
0
0
1
0
2
0
0
1
1
1
1
1
0
1
1
2
2
2
1
2
0
2
1
1
2
1
0
2
1
0
2
1
1
1
2
1
1
1
1
0
2
2
1
0
1
1
0
0
1
1
1
2
0
2
0
2
1
2
1
1
0
0
0
0
0
1
1
0
0
1
2
1
1
0
1
1
1
0
2
0
0
3
2
0
1
1
2
0
1
0
1
1
2
2
1
0
0
0
1
1
2
0
0
0
1
0
1
2
0
0
0
0
2
0
0
0
1
0
1
1
1
1
0
0
2
2
0
0
1
1
1
1
1
2
0
1
2
1
1
2
0
0
0
1
0
1
2
1
1
2
3
1
0
2
2
0
1
1
0
0
1
1
1
1
1
1
1
1
1
1
0
0
1
1
0
1
2
1
1
0
1
1
2
2
0
0
0
0
2
1
1
2
0
1
1
1
2
1
1
1
1
0
0
0
1
1
1
1
1
1
2
0
1
0
1
1
1
1
1
1
0
0
0
2
1
2
0
0
1
0
0
0
1
1
1
2
1
1
2
2
1
2
0
1
1
0
1
1
0
1
1
0
0
1
1
1
1
1
1
0
1
0
0
2
1
1
1
0
1
1
2
1
2
0
2
2
0
0
2
1
1
1
1
2
1
1
1
0
0
2
0
2
1
1
0
2
2
1
2
0
0
1
1
0
2
2
0
1
1
1
1
1
1
1
1
2
0
0
0
0
0
2
0
0
2
0
1
1
1
1
0
0
1
0
0
3
0
2
2
1
1
1
0
0
0
1
1
0
1
1
1
1
0
1
1
0
1
1
2
0
2
0
3
1
2
1
1
2
2
2
1
2
1
0
1
1
1
1
1
3
1
0
1
2
2
1
0
1
1
0
1
2
1
1
0
1
1
0
1
1
0
1
1
2
1
1
1
2
2
0
2
1
1
2
1
1
1
0
0
1
2
2
1
0
0
2
0
2
1
3
0
0
0
0
1
1
0
0
0
3
1
1
1
2
0
1
0
1
1
1
1
2
0
0
3
2
2
2
0
1
1
2
2
1
1
2
0
1
1
1
1
0
2
2
0
0
0
2
1
0
0
0
1
2
0
0
2
0
2
0
2
0
1
0
2
0
1
1
1
2
0
2
0
1
2
0
0
2
0
1
1
2
0
1
1
0
2
1
0
0
1
1
1
1
2
0
0
1
1
2
1
1
1
0
1
0
2
2
2
1
0
2
1
2
1
2
2
1
1
1
0
1
1
2
1
1
1
2
1
2
1
2
1
1
1
0
1
0
1
0
0
0
4
0
0
0
1
0
1
0
1
1
1
1
1
1
1
0
1
1
3
0
1
1
0
2
1
0
1
2
1
0
1
1
1
1
1
1
1
0
2
2
1
0
1
1
0
1
0
2
1
0
1
1
1
2
0
1
2
1
0
0
1
1
2
1
1
2
0
1
0
0
1
0
0
0
1
1
1
1
2
1
1
0
0
1
2
0
2
1
0
1
0
0
0
1
1
2
1
2
1
1
1
1
1
1
2
2
2
2
2
0
2
2
2
2
0
2
1
1
2
1
2
1
0
2
1
2
0
0
0
1
1
0
1
0
2
0
0
0
0
3
1
2
2
2
2
0
2
1
2
1
2
2
1
2
2
1
2
1
2
0
1
2
1
2
1
2
2
2
2
1
0
1
1
1
1
1
0
1
1
2
0
1
1
1
1
1
1
0
0
1
0
2
0
0
0
1
4
0
1
1
1
1
0
0
0
1
0
2
1
2
0
2
0
1
2
1
4
1
2
1
1
2
1
3
2
1
0
2
1
1
2
1
1
1
2
1
1
2
1
1
2
1
1
0
0
1
2
1
1
0
1
1
2
0
1
1
1
0
0
1
1
0
1
1
2
0
0
1
2
1
2
2
1
1
2
1
1
0
0
1
2
1
2
1
1
0
0
1
1
2
2
0
1
1
0
4
2
2
2
1
1
0
1
1
0
2
1
1
0
2
2
1
1
2
1
2
1
2
2
2
1
2
2
1
0
0
2
0
1
0
0
1
2
1
1
2
1
1
1
1
0
0
1
2
0
2
3
1
0
1
1
1
2
1
1
1
1
1
1
0
1
1
0
2
2
0
1
1
0
0
0
0
1
0
1
1
1
0
2
2
1
1
0
0
0
0
2
1
0
1
0
0
0
1
2
1
1
1
1
2
1
2
2
0
1
0
0
0
0
0
0
1
1
0
0
1
0
1
2
1
0
0
5
1
1
1
2
2
2
0
1
1
0
1
1
0
1
2
0
0
1
1
2
1
0
0
0
2
2
1
1
1
8
0
0
0
0
0
1
2
1
2
0
0
1
1
2
1
0
0
1
0
1
1
2
1
0
0
2
0
1
0
1
1
1
2
1
2
1
0
1
0
0
1
0
1
1
0
0
1
2
2
1
0
0
1
0
1
2
0
2
1
1
1
0
2
0
0
1
1
0
0
2
1
1
2
0
1
1
1
0
1
0
2
1
1
2
2
1
0
1
2
1
0
1
1
1
0
2
10
0
0
0
0
1
0
1
2
1
1
1
0
1
1
1
2
1
2
1
1
3
2
1
2
2
0
2
2
1
0
2
1
2
1
1
1
1
1
0
1
2
1
1
2
1
1
1
1
0
0
3
0
1
1
1
2
2
2
1
0
0
1
1
2
0
1
0
0
0
2
0
1
1
2
2
1
2
1
2
0
0
2
0
2
0
1
1
1
2
1
2
2
2
1
2
1
0
1
0
2
0
1
1
0
1
1
0
1
0
1
1
0
2
0
5
1
1
1
1
1
2
0
1
1
1
3
0
2
1
0
1
1
1
0
0
1
2
1
1
2
0
1
1
0
0
0
0
0
1
1
0
1
1
0
1
1
1
2
0
2
0
1
0
0
2
2
1
2
1
0
2
0
0
2
1
4
2
0
2
2
1
0
1
2
0
2
0
1
1
0
1
0
1
1
1
0
0
0
1
1
2
1
1
1
2
0
1
0
1
0
2
1
0
0
0
1
0
0
2
2
1
1
2
1
0
2
1
1
1
0
1
1
1
1
1
1
1
2
2
1
1
0
1
0
1
1
0
1
0
0
1
1
2
2
1
1
2
0
1
1
1
0
1
1
1
2
1
1
1
1
1
0
1
1
1
0
1
1
1
1
1
2
1
0
1
1
1
0
1
1
2
1
1
1
1
2
1
1
1
3
0
1
1
1
0
1
1
2
1
0
2
1
1
1
2
1
0
2
1
1
0
1
1
1
1
1
2
2
2
1
1
0
3
1
0
1
0
2
1
1
0
1
1
1
0
1
0
1
0
0
2
1
2
0
1
1
2
1
2
1
1
1
2
0
1
1
0
1
0
1
1
1
1
2
0
0
1
1
3
1
2
0
2
1
0
1
1
1
1
2
2
1
0
0
0
0
1
0
0
0
0
1
1
1
1
0
0
0
1
1
2
0
1
0
1
2
1
0
1
2
1
2
2
3
1
2
0
1
0
0
1
1
0
2
2
0
1
0
1
1
0
2
1
0
0
1
2
1
1
1
1
2
1
1
0
1
2
0
1
1
2
1
0
2
0
2
1
2
0
2
1
2
2
1
1
2
0
1
1
1
0
0
0
0
0
2
2
2
0
1
0
1
1
1
2
1
1
0
1
1
1
0
2
0
0
0
2
0
0
1
1
0
2
1
0
0
1
1
1
1
0
2
0
2
2
2
1
0
1
1
2
1
1
0
0
0
2
1
1
1
0
1
0
0
0
2
2
2
0
2
2
0
1
0
2
1
0
0
1
1
0
1
1
1
2
0
0
1
0
1
2
1
1
1
0
2
2
0
1
1
1
0
2
1
1
1
1
2
1
1
2
1
1
1
1
1
1
0
0
2
0
2
0
1
1
0
2
0
1
0
2
1
0
1
2
1
2
0
2
1
2
1
0
1
0
0
1
1
1
1
2
1
0
2
2
2
1
0
1
0
2
0
1
1
1
2
0
1
0
0
1
2
0
1
1
1
0
0
1
1
2
2
1
1
2
0
1
0
1
0
1
1
0
2
0
1
2
2
2
1
1
1
1
1
1
0
1
1
1
1
1
1
1
2
0
0
1
2
0
1
2
2
1
0
0
0
1
1
1
2
1
1
0
1
1
2
1
2
1
0
2
0
3
1
2
1
0
1
1
1
0
0
0
1
0
1
1
1
2
0
1
1
0
0
0
1
1
1
1
0
1
1
0
1
0
0
0
0
1
1
1
1
1
1
2
1
2
1
0
2
1
1
2
1
1
0
1
1
0
2
0
0
1
1
2
1
1
1
1
1
2
2
2
0
1
0
1
0
1
1
1
1
2
1
1
0
2
0
1
1
1
1
2
0
1
1
0
0
0
0
0
2
1
2
1
2
1
0
2
0
0
2
2
1
0
1
1
3
1
1
2
2
2
0
1
1
0
0
1
1
1
1
1
0
2
2
0
0
2
1
1
1
1
0
1
1
0
0
1
1
1
0
0
0
0
1
1
1
2
0
1
1
1
1
1
1
2
2
1
2
0
2
2
2
1
1
1
1
0
1
2
0
2
0
1
1
1
2
1
0
0
0
2
1
1
1
2
0
1
1
1
0
1
1
2
1
0
1
0
1
0
1
0
1
2
2
1
1
1
2
1
1
0
1
1
0
0
2
0
1
2
1
2
1
2
2
1
0
0
1
0
0
1
1
2
2
1
2
1
2
1
1
0
1
0
1
1
1
0
0
2
2
0
1
2
1
1
1
0
1
1
1
1
2
1
2
0
0
0
0
2
0
2
0
2
2
1
1
0
2
0
1
0
3
0
0
0
0
0
0
1
1
1
1
0
0
2
2
2
1
1
1
1
0
2
0
1
0
0
0
1
1
1
1
0
1
1
1
1
0
0
1
1
2
1
2
0
1
0
1
1
0
2
1
1
1
1
0
0
2
0
0
1
2
1
1
1
0
1
1
2
0
2
0
1
1
1
0
2
1
0
0
0
2
1
0
1
1
1
1
1
0
1
1
1
1
0
1
0
1
3
1
1
2
2
1
1
1
0
1
2
0
2
0
1
1
1
1
1
0
1
2
2
1
1
1
2
1
1
2
1
1
1
1
0
0
1
1
0
0
1
2
0
1
1
2
1
1
2
1
1
2
1
0
1
0
1
0
0
2
2
1
2
0
0
0
0
1
1
1
0
1
1
0
0
1
2
0
1
0
1
1
2
1
2
0
2
0
2
1
0
1
1
0
2
2
2
1
2
2
1
0
1
1
1
1
1
1
2
1
2
0
1
1
1
1
1
2
2
1
1
1
0
1
0
0
0
1
1
0
0
0
0
1
1
1
0
0
0
0
1
0
1
2
1
0
1
0
0
0
1
1
0
1
1
2
1
0
0
0
0
0
2
2
0
1
0
1
0
0
0
1
1
1
1
1
1
2
2
1
0
1
1
2
0
0
0
0
0
1
1
2
2
2
1
2
2
1
2
0
1
0
0
0
1
1
1
1
2
1
2
3
2
0
0
1
3
1
1
2
1
1
1
1
2
1
0
1
0
2
0
2
0
2
2
1
1
2
2
2
2
1
0
0
2
1
2
1
1
1
2
0
0
1
2
1
1
0
2
1
1
1
0
0
1
0
1
1
2
1
1
1
0
0
1
1
1
0
1
0
1
1
0
1
1
1
1
1
0
1
1
1
0
1
1
0
1
1
0
1
2
1
1
1
0
0
1
0
0
2
2
0
1
1
1
2
0
2
0
2
0
0
1
1
0
2
0
1
0
1
0
2
1
0
1
0
2
0
2
0
0
1
1
2
0
1
2
1
0
1
0
0
1
1
1
1
2
0
2
1
1
1
2
1
2
0
1
1
2
2
2
1
1
1
1
0
1
1
1
2
2
0
1
1
1
1
1
1
1
2
1
1
1
1
0
2
0
1
2
0
0
2
0
2
2
1
2
1
2
2
1
1
0
1
0
2
2
1
2
1
1
1
0
1
1
0
1
1
1
0
1
1
0
1
1
1
2
2
1
1
1
1
1
2
1
0
0
1
0
1
1
0
1
1
1
0
0
1
1
1
1
1
1
1
1
1
0
0
1
1
2
2
1
1
0
2
1
1
1
0
2
0
0
0
0
1
0
2
1
2
1
1
2
0
2
2
1
1
1
1
0
1
1
2
0
1
0
1
1
1
0
0
1
1
1
0
0
0
1
1
1
2
2
2
0
1
0
1
2
0
1
1
0
1
1
1
1
2
0
1
2
1
1
1
0
1
1
0
0
1
1
0
1
0
1
1
0
2
0
0
2
1
1
2
1
1
0
0
2
2
1
1
1
2
1
2
2
2
1
1
0
2
1
1
2
1
1
2
1
1
3
1
1
1
1
0
2
1
0
2
1
2
0
2
0
1
0
1
1
1
0
1
0
0
1
0
0
2
1
1
2
0
2
2
0
1
2
1
1
1
1
2
2
1
1
1
1
0
2
0
1
0
1
2
0
0
2
2
2
1
1
0
1
0
0
2
0
1
1
0
0
1
0
0
1
1
1
1
0
1
1
1
1
1
2
1
3
0
1
0
2
1
2
1
2
1
1
1
1
1
0
1
0
0
2
1
2
2
0
2
0
1
0
2
0
0
0
2
0
0
0
2
2
2
2
2
1
2
0
0
1
1
1
1
2
2
1
1
1
1
1
1
2
0
2
0
3
2
0
0
1
1
1
1
1
2
0
1
1
1
0
0
1
2
1
1
1
1
0
0
1
2
1
2
1
1
1
1
2
2
2
1
2
2
1
1
1
2
0
1
1
1
2
1
2
1
1
0
2
1
1
2
1
2
1
1
0
2
0
0
1
1
1
1
1
1
1
2
1
1
0
1
2
1
0
2
1
1
2
1
1
1
1
1
1
0
0
2
0
0
2
0
2
1
1
0
0
1
1
0
1
1
1
1
0
1
1
0
0
1
3
1
0
0
0
2
0
1
0
0
2
2
1
2
1
0
0
0
1
1
0
1
1
1
1
1
1
1
1
2
1
1
0
2
2
1
0
1
1
1
1
0
2
1
1
0
1
2
1
1
2
1
2
1
0
0
2
1
0
1
1
0
2
0
0
2
1
0
0
0
1
1
0
1
2
2
0
0
0
0
1
1
2
1
1
1
0
0
0
0
1
1
0
0
1
2
1
1
1
1
1
2
1
1
1
2
0
1
1
2
0
1
1
1
1
2
0
2
1
1
0
2
0
1
1
1
3
0
2
1
0
1
4
0
0
1
1
2
0
0
3
0
2
1
2
0
0
1
1
1
2
1
2
1
0
2
0
0
1
0
1
2
1
2
1
1
0
0
1
1
2
1
0
1
0
1
1
0
2
0
0
1
0
2
1
2
1
0
1
1
0
0
1
1
1
2
1
1
0
0
2
2
1
2
0
2
1
1
0
0
2
1
1
1
1
0
0
1
1
1
1
1
2
0
0
2
0
0
0
0
2
0
1
1
1
1
0
1
0
2
1
0
2
0
1
0
1
1
0
2
1
0
1
0
1
1
1
0
0
2
1
2
2
0
2
1
1
1
1
0
1
1
0
2
1
1
3
0
2
1
1
2
1
0
2
0
0
2
2
1
2
1
2
2
0
1
0
1
2
2
1
1
1
0
2
0
0
2
1
2
2
1
1
0
1
2
1
1
1
0
0
5
0
1
1
1
1
0
0
1
1
1
2
1
1
1
0
2
0
2
1
1
1
3
1
1
1
0
1
2
1
1
1
1
2
0
2
1
1
2
0
1
0
2
1
0
1
2
2
2
1
1
1
1
0
1
2
1
2
1
0
1
1
0
1
1
2
1
1
0
1
2
2
1
1
0
1
1
1
1
1
2
0
1
1
0
0
1
0
0
1
2
0
1
1
0
0
1
1
1
0
1
1
1
1
0
2
0
2
1
1
1
0
2
1
1
0
1
1
0
1
1
0
1
1
2
0
1
2
2
1
2
1
1
1
2
1
1
1
1
1
0
1
1
2
1
1
1
1
2
0
1
0
0
1
2
2
1
0
0
1
1
1
0
0
2
0
1
1
1
1
0
0
0
0
1
1
1
0
1
0
1
2
0
0
1
2
1
2
2
1
0
1
1
2
1
2
1
1
1
0
1
1
1
2
0
1
1
2
1
2
2
2
1
1
1
0
1
1
1
1
1
1
0
2
1
1
1
0
0
1
2
2
0
1
0
0
1
0
0
1
2
2
0
1
0
1
1
0
1
0
0
2
1
0
1
0
3
2
0
2
2
0
2
1
1
0
0
1
1
1
1
2
0
1
2
1
0
1
1
1
1
2
2
1
1
2
2
2
2
0
2
0
1
1
1
1
1
2
2
1
0
1
1
1
1
1
1
1
1
0
1
1
1
0
2
2
0
0
0
2
1
2
1
1
0
1
0
1
1
2
2
2
2
0
1
1
2
1
1
1
1
1
1
0
1
2
1
1
2
1
4
1
0
0
0
1
2
1
0
1
0
0
1
1
1
2
0
1
0
0
2
0
1
0
1
2
1
2
1
0
2
0
0
1
0
1
0
1
1
0
0
1
0
1
0
0
1
0
2
0
1
0
0
1
2
0
0
0
2
1
1
1
1
2
1
2
1
1
0
1
0
1
0
1
2
2
0
1
2
1
3
2
1
1
2
0
2
3
2
1
0
1
2
1
0
1
2
0
0
0
0
1
1
1
1
0
1
2
1
1
1
1
0
1
1
3
2
1
1
0
2
1
0
1
1
1
0
2
1
0
2
0
1
2
2
1
1
0
1
1
0
2
2
2
2
1
1
2
0
1
1
0
1
1
1
1
3
0
1
1
0
0
0
2
0
1
1
0
2
1
2
1
0
2
1
2
1
1
1
2
1
1
1
0
0
1
1
2
1
2
1
0
0
1
1
1
1
1
1
0
1
0
2
1
1
2
2
0
0
1
1
1
1
1
1
0
2
1
1
0
1
2
1
2
2
1
1
1
0
1
0
0
2
1
1
0
1
1
0
0
0
1
1
1
1
0
1
0
1
0
1
1
0
1
0
1
1
1
0
2
1
1
1
1
1
2
1
2
0
1
0
0
1
0
0
1
1
1
2
2
1
0
2
2
1
1
2
2
0
1
1
1
1
1
1
1
0
0
1
1
2
2
2
1
2
0
0
2
0
1
1
1
1
1
1
0
0
1
1
1
0
1
1
1
1
1
2
1
1
0
0
1
1
0
0
1
2
1
1
1
1
1
2
1
1
1
1
2
1
2
1
1
1
3
0
1
2
0
1
2
2
1
1
0
1
1
0
0
1
1
0
0
1
1
1
1
0
0
2
1
2
1
3
1
0
0
1
0
1
1
1
1
1
1
2
0
2
0
0
0
0
1
1
0
0
0
1
1
1
2
2
0
0
0
1
1
2
1
0
1
1
1
0
1
0
2
0
1
1
1
1
1
0
1
1
2
2
1
0
1
1
2
0
0
0
0
1
0
1
0
1
1
1
1
0
1
1
2
1
1
0
1
0
2
1
1
1
1
1
0
0
2
1
0
0
2
0
7
2
2
2
2
1
1
0
1
1
1
2
2
2
1
1
0
0
2
2
1
0
1
1
2
1
1
1
2
1
0
2
0
0
0
1
1
1
1
1
1
1
1
2
1
1
2
0
1
0
1
1
2
1
2
2
1
0
0
1
1
1
1
1
2
1
2
2
2
2
0
0
1
2
2
0
1
1
1
1
0
1
1
1
1
0
1
0
1
2
0
1
2
1
1
0
0
1
2
1
1
1
1
2
1
1
1
0
2
1
0
1
0
0
1
2
1
1
0
0
1
0
0
0
1
1
0
1
1
0
1
0
1
0
2
1
1
2
0
2
1
2
1
1
0
1
0
0
0
1
1
2
1
1
1
1
1
1
2
1
0
0
2
2
1
1
1
0
1
0
0
1
2
1
2
1
2
3
0
2
0
2
2
0
1
2
0
1
0
2
2
0
2
1
1
1
2
0
1
0
2
2
1
1
1
0
1
2
2
1
2
1
2
0
0
1
0
0
1
2
1
2
0
2
0
2
1
0
1
0
1
1
0
0
0
1
3
2
2
0
1
0
1
0
0
1
1
1
1
1
2
2
1
0
2
0
0
2
0
0
0
1
2
2
1
1
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
2
0
1
2
0
1
2
1
1
1
2
2
1
0
0
1
1
0
0
1
2
1
0
1
1
1
2
0
2
0
0
1
1
1
1
1
3
0
1
2
0
1
1
1
1
1
0
2
1
0
1
1
1
1
2
1
1
2
2
1
0
1
1
1
1
1
2
1
1
1
1
1
2
1
0
1
0
2
0
1
1
0
1
2
0
1
1
0
0
1
1
0
1
1
1
1
1
1
0
2
3
1
1
0
3
1
1
0
1
2
0
2
1
1
1
1
1
2
2
1
1
0
1
0
1
2
0
1
2
0
2
0
0
2
1
0
3
2
2
1
1
1
1
2
1
1
1
0
1
2
2
2
2
2
0
1
0
0
0
2
1
1
1
2
0
0
0
0
0
0
2
1
0
1
2
1
0
0
1
2
1
4
1
1
0
1
1
1
0
2
1
1
1
0
1
2
1
1
1
2
0
1
2
1
0
1
2
1
1
1
0
1
1
0
1
1
1
0
1
0
0
1
1
0
1
1
1
0
0
1
1
0
1
0
2
0
1
1
1
1
0
2
1
0
1
1
0
1
0
1
0
0
2
1
1
0
1
0
1
0
2
2
2
1
1
1
2
2
0
2
1
0
2
1
1
2
2
0
0
1
2
2
1
2
0
0
0
1
1
1
1
0
0
0
2
1
2
1
2
2
0
2
1
1
1
0
0
0
0
1
1
0
2
1
1
1
1
0
2
0
1
1
0
0
1
0
2
2
1
1
1
1
0
2
2
3
1
0
2
1
1
1
1
1
1
1
2
1
1
2
2
2
1
2
0
0
0
1
1
2
0
1
1
2
0
0
1
2
0
2
1
2
2
0
1
1
0
0
1
1
2
1
0
0
1
0
1
1
0
0
0
1
3
2
1
0
0
0
2
2
1
0
2
0
1
1
1
1
0
1
2
1
0
2
0
0
1
1
1
1
1
0
1
1
0
2
1
0
0
0
2
1
2
1
2
0
2
1
1
1
3
1
2
2
0
2
0
0
1
0
1
2
1
0
1
1
0
0
1
0
0
1
2
1
1
0
2
0
0
1
1
1
0
0
1
0
1
2
4
1
0
2
0
1
0
1
1
1
2
1
2
1
2
0
2
0
1
2
1
1
1
1
1
0
1
1
3
1
1
2
1
0
0
2
1
2
1
0
2
1
0
0
2
1
2
0
0
2
8
1
2
1
2
2
0
0
1
1
0
1
1
1
1
2
0
1
1
1
0
0
2
0
0
0
1
1
0
1
0
2
1
2
1
2
2
1
2
1
0
0
0
1
0
2
1
1
2
2
1
0
1
1
1
0
1
1
2
2
0
2
1
1
1
2
2
2
0
1
1
2
2
0
0
2
0
2
1
2
0
1
1
1
2
2
2
1
0
1
1
1
2
1
1
2
1
1
1
2
1
1
1
0
1
0
2
0
1
1
1
2
1
1
0
0
1
1
1
1
1
2
1
0
1
1
3
0
1
2
1
1
1
0
1
2
1
0
1
1
1
0
1
1
1
1
2
2
0
0
1
1
2
2
1
0
0
0
2
0
1
1
0
2
1
0
1
1
0
5
2
1
1
1
1
1
0
1
0
1
0
2
1
1
0
2
1
0
0
2
0
0
1
1
0
1
2
0
1
2
1
0
1
1
1
1
1
1
0
1
0
0
2
1
0
1
1
0
2
1
1
0
1
1
2
2
2
2
0
1
1
1
1
0
2
1
0
2
0
1
7
1
1
1
1
2
1
2
1
2
0
1
0
1
0
2
2
1
0
2
1
2
0
1
1
1
1
0
0
0
2
1
1
1
1
1
2
1
1
1
1
0
0
1
0
2
1
1
1
1
2
2
1
1
1
1
1
1
0
0
0
1
1
1
2
0
2
1
0
1
0
0
0
1
2
0
1
1
2
1
2
1
1
1
1
0
1
0
0
1
2
0
1
1
0
1
1
0
1
1
1
1
1
0
2
1
1
1
2
0
1
2
0
1
1
1
1
1
0
2
1
1
0
0
1
1
1
1
1
1
1
1
2
1
1
1
0
1
1
1
0
0
1
1
0
1
2
1
1
2
0
1
1
0
2
1
1
0
0
2
2
1
1
0
1
1
2
1
2
1
1
1
2
1
1
2
1
0
1
1
2
1
1
1
0
1
0
2
1
1
0
2
0
1
2
0
2
2
1
1
0
2
1
2
2
1
3
1
0
1
1
2
2
1
1
2
1
2
0
1
2
1
2
1
1
1
0
1
1
2
1
2
2
2
1
2
1
2
0
0
1
1
1
1
2
0
0
1
2
0
1
1
1
1
1
1
1
2
1
2
1
0
2
2
1
1
1
2
1
0
2
1
0
1
2
1
0
2
1
0
1
0
0
1
0
1
0
1
1
0
0
2
0
2
0
1
0
1
0
2
0
1
1
1
1
0
2
1
3
1
0
1
2
1
1
1
0
0
1
0
2
2
2
0
1
0
1
2
1
1
2
2
1
1
0
2
0
2
1
1
1
1
1
0
0
0
1
3
1
1
1
1
0
0
1
0
1
4
1
2
0
2
0
0
1
1
2
1
1
0
2
0
0
0
0
0
1
0
1
1
2
2
1
0
0
1
1
3
1
3
2
2
2
1
2
1
2
1
2
1
1
2
2
1
1
1
2
1
1
2
0
1
1
1
3
1
1
0
1
1
0
1
0
0
0
0
1
2
1
0
0
2
0
0
0
1
3
0
2
1
1
0
2
1
1
1
1
1
1
2
1
0
0
1
2
1
0
2
2
1
0
1
1
1
1
0
0
1
0
0
0
1
2
0
1
1
1
1
0
0
1
1
1
0
0
2
0
1
1
2
0
1
1
1
0
1
0
1
0
0
2
2
1
1
1
1
0
2
1
0
2
1
1
1
1
0
0
0
1
1
0
1
0
2
0
1
1
1
1
2
1
1
0
1
1
2
2
1
0
0
1
0
0
2
0
1
0
2
1
0
0
0
1
0
0
0
1
2
2
1
0
1
1
1
1
0
2
1
1
1
1
0
1
1
0
1
2
0
1
2
1
1
1
1
0
1
1
3
2
1
2
0
1
0
2
2
1
0
0
1
0
0
2
1
0
1
3
1
0
0
2
0
1
1
1
0
2
0
1
0
0
1
0
0
1
1
1
1
0
2
2
1
0
1
1
0
2
1
1
0
2
1
2
1
0
0
1
1
1
0
1
1
0
2
1
0
1
1
0
1
2
1
1
1
1
0
0
0
0
3
1
2
2
0
1
0
0
1
2
1
0
0
1
0
2
1
0
1
2
2
2
1
2
0
2
0
0
1
0
1
1
0
2
0
1
1
3
1
2
2
1
1
4
1
0
1
0
1
0
0
1
1
2
0
1
1
2
1
2
1
1
1
2
1
1
1
2
1
1
1
0
0
1
1
1
1
1
1
1
1
1
0
2
3
1
2
1
1
2
0
2
1
1
2
1
2
2
0
0
1
0
5
2
1
0
2
1
1
0
1
0
0
0
0
0
2
0
0
0
0
3
4
0
1
0
2
5
0
0
0
1
2
1
1
0
1
2
2
2
0
0
0
0
1
2
1
1
0
2
2
2
1
2
0
2
1
0
0
0
1
1
0
1
0
3
1
1
2
0
2
2
2
1
1
0
1
0
1
1
1
0
2
1
1
1
2
1
1
1
0
0
2
2
0
2
0
2
0
0
0
2
1
2
0
1
1
1
1
1
1
2
1
0
1
1
1
1
0
1
0
3
1
2
0
1
1
1
1
0
1
2
1
1
2
1
1
1
1
1
2
0
2
0
1
1
0
1
2
0
2
2
1
1
0
2
1
0
2
1
2
2
1
2
1
2
0
1
0
2
1
0
1
1
1
2
1
1
2
0
1
2
1
1
1
1
2
1
0
1
1
1
1
2
2
0
1
1
0
2
1
2
0
1
1
1
2
1
1
1
1
2
0
2
0
1
1
1
0
2
0
1
2
0
2
0
1
0
0
2
0
1
0
0
1
1
0
0
2
2
2
2
0
0
2
0
0
2
2
2
2
1
1
1
0
2
0
2
0
0
1
1
2
1
2
2
0
1
2
0
1
1
1
0
2
1
0
0
1
1
0
0
0
0
2
1
1
2
1
1
0
2
2
2
1
2
1
1
1
0
0
1
2
2
0
2
1
1
2
2
1
1
0
1
2
1
1
3
0
2
1
1
1
1
1
2
1
0
1
2
2
2
1
1
1
0
1
3
1
1
2
2
0
1
0
1
0
2
0
0
1
0
1
2
0
2
1
1
1
0
1
1
1
0
0
0
2
1
1
1
1
0
1
1
0
1
0
0
2
2
1
1
2
1
2
0
2
2
2
0
0
2
0
1
1
1
0
1
1
1
1
2
0
2
1
2
1
3
1
2
0
1
1
1
0
2
2
0
0
2
0
1
1
1
1
1
1
1
2
1
2
0
2
1
1
1
3
2
1
0
1
2
1
2
0
0
1
2
2
1
1
1
2
1
0
0
0
1
0
1
1
2
1
1
1
1
2
0
1
2
1
0
1
0
2
1
1
0
2
0
0
1
2
2
2
0
0
1
1
0
2
0
0
0
1
0
0
1
2
1
1
0
1
2
1
0
2
1
0
1
0
1
0
0
1
1
1
1
0
1
1
0
1
1
2
0
1
1
0
0
1
2
1
0
1
2
0
1
0
2
1
1
2
1
1
2
2
2
2
2
2
1
2
1
2
1
0
1
0
2
0
1
0
2
0
0
2
2
1
1
1
0
1
1
1
1
1
2
1
2
1
0
0
0
2
1
0
1
1
1
1
1
1
0
2
0
0
1
1
1
1
0
0
1
1
0
2
1
0
2
1
0
2
1
1
0
1
1
1
0
2
1
2
1
0
1
2
1
1
1
1
0
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
0
2
0
0
1
2
0
1
0
1
1
1
1
1
0
1
1
2
1
0
0
1
2
0
2
0
1
0
1
0
2
2
1
1
2
0
0
1
1
0
1
0
1
0
0
0
2
0
1
0
0
2
2
2
0
1
1
0
1
1
2
1
2
2
2
0
2
2
0
1
0
1
1
1
0
2
1
1
0
1
1
1
0
1
2
1
1
1
1
2
2
1
0
0
0
0
0
1
0
1
2
1
1
0
2
2
1
1
0
1
0
1
2
1
0
1
1
1
2
1
0
1
1
0
1
2
1
1
1
1
2
1
2
0
1
1
0
2
0
1
1
2
1
0
2
1
0
1
2
0
0
1
1
0
2
2
2
0
0
2
2
0
1
1
2
0
1
1
2
1
2
2
1
2
0
1
1
1
1
0
1
1
1
1
1
1
1
1
1
0
1
1
2
0
1
1
0
1
2
2
0
1
0
0
2
0
0
2
0
1
1
2
1
1
1
2
1
1
0
0
2
0
1
1
0
2
1
0
1
1
1
2
2
1
0
0
2
1
1
0
0
1
0
1
1
1
0
3
0
1
1
1
2
0
0
1
1
1
0
0
0
1
1
1
2
1
0
2
1
1
1
1
1
1
1
2
4
2
1
0
1
1
1
1
0
1
2
1
1
1
0
0
1
0
0
1
0
1
0
0
2
0
2
0
0
0
2
1
1
0
1
0
2
1
0
0
0
1
2
0
1
1
1
0
0
2
1
2
1
0
0
2
1
1
2
1
1
0
1
1
1
1
1
2
2
2
2
1
1
2
1
2
0
2
2
1
0
0
1
1
1
2
1
1
1
0
0
0
1
1
2
0
1
1
1
1
2
1
2
0
0
0
1
0
1
0
1
2
1
0
1
2
1
0
1
1
1
0
1
2
0
2
1
2
0
1
0
2
0
0
0
1
2
1
0
0
1
1
1
0
2
2
1
2
0
1
2
0
1
0
1
1
1
0
1
1
2
0
0
0
2
0
2
1
1
0
2
1
0
0
0
0
1
0
2
1
2
0
1
1
1
0
0
1
1
1
1
0
1
1
1
1
2
0
1
0
2
2
1
2
0
1
0
2
0
0
1
1
1
1
1
0
0
1
1
0
2
1
1
1
0
2
1
1
0
2
0
0
0
0
0
2
2
1
0
2
0
2
1
2
2
1
0
2
1
2
0
2
1
2
0
2
2
1
1
0
2
1
1
1
1
2
1
1
1
1
2
1
1
1
0
1
2
0
1
2
2
1
2
1
1
1
0
2
2
1
1
0
1
1
1
1
2
2
0
1
0
1
0
1
2
1
2
1
1
1
1
1
0
0
1
0
1
1
1
2
1
0
1
0
1
2
0
0
1
1
1
1
0
2
1
0
1
0
1
0
1
0
0
1
1
2
1
2
1
2
1
0
1
0
2
3
1
2
0
1
1
1
1
2
0
1
1
2
0
1
0
0
2
1
2
1
2
1
1
1
0
0
1
1
2
0
1
0
1
1
1
1
2
0
2
0
1
1
1
1
0
0
1
2
1
0
2
0
1
0
0
1
1
0
1
1
1
1
1
1
1
1
3
1
1
1
1
0
2
1
2
0
0
1
0
1
1
1
1
1
1
2
1
1
1
0
1
0
1
0
0
1
1
0
0
1
1
0
2
0
0
1
0
2
1
2
3
1
1
2
1
2
1
1
0
1
0
2
1
0
1
1
1
1
1
0
0
2
1
1
0
0
1
2
0
1
2
1
1
0
1
1
1
1
2
0
2
0
1
4
2
1
1
1
0
0
1
1
1
0
2
2
1
2
1
1
1
0
1
0
2
1
2
0
1
1
1
1
2
1
2
0
2
1
2
2
0
1
1
1
1
2
1
0
0
1
1
2
0
0
0
1
1
1
2
2
1
1
0
1
0
0
1
0
0
0
2
0
1
0
1
1
1
1
1
0
1
0
1
1
0
1
1
4
2
2
1
0
1
3
0
0
2
0
1
0
0
1
2
0
2
1
0
1
2
4
0
1
1
2
0
0
1
1
2
1
0
2
2
1
1
2
0
1
0
1
1
1
1
0
2
0
2
1
1
0
2
0
0
4
2
0
0
1
1
0
1
2
0
1
0
1
1
2
1
2
0
1
0
0
1
1
1
1
0
1
0
1
1
0
2
2
0
0
1
2
0
1
1
0
2
0
1
1
2
1
1
1
0
1
1
1
1
2
0
1
2
0
1
1
2
0
2
1
0
1
0
1
1
0
1
1
1
1
0
0
1
0
1
1
1
1
1
1
0
0
0
2
0
2
1
2
0
2
1
2
1
2
1
1
1
1
1
0
3
1
0
4
2
2
1
3
2
1
1
1
2
1
0
0
1
2
2
1
0
2
0
1
1
1
1
1
1
0
2
1
0
1
1
0
1
0
0
0
3
2
1
1
0
0
1
2
1
0
1
1
1
0
0
2
1
2
2
1
2
1
1
1
1
1
1
1
1
1
1
2
0
2
1
0
1
2
0
1
1
0
1
1
2
0
0
1
2
0
1
1
0
1
2
1
1
2
2
1
2
1
2
1
0
1
1
1
1
2
0
0
2
1
1
2
1
1
1
1
1
2
1
2
1
0
1
1
2
1
2
1
0
1
0
1
1
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
1
0
1
1
1
0
2
1
0
2
1
0
0
1
1
1
2
1
1
0
1
0
1
0
1
1
1
1
2
0
0
1
0
1
0
2
2
1
1
1
1
0
1
0
2
1
1
1
1
1
0
1
1
0
1
2
1
0
1
0
2
0
1
1
1
1
0
2
0
1
1
2
1
1
0
0
1
1
2
1
1
1
2
2
1
0
0
0
1
1
2
0
1
1
1
1
2
1
1
1
2
1
0
1
1
0
2
1
0
1
1
2
0
0
1
1
1
2
2
1
2
3
0
2
2
1
1
1
1
0
2
0
1
1
1
0
2
0
1
0
1
1
0
0
1
1
1
2
1
1
1
1
0
0
1
1
0
1
1
2
1
1
0
1
0
1
2
2
1
2
1
1
0
1
1
1
1
0
2
0
2
2
1
1
1
0
1
1
2
0
1
0
2
2
1
2
1
0
1
1
2
1
2
2
1
1
1
0
1
0
0
2
1
2
2
0
0
1
0
1
1
1
1
1
0
2
2
1
1
2
0
1
1
0
1
2
2
0
1
0
0
1
1
1
2
4
1
0
0
0
0
1
1
2
1
1
0
1
0
2
1
1
1
1
1
1
1
2
0
0
1
4
1
1
0
1
0
1
1
0
0
1
2
1
0
1
0
0
2
1
0
2
1
1
1
1
0
0
0
1
2
1
1
1
0
2
1
1
2
0
0
1
1
1
1
1
1
0
0
1
0
1
1
1
1
1
0
0
1
2
1
0
0
2
1
1
1
1
1
1
1
0
2
0
1
1
0
1
0
1
0
1
0
0
0
1
0
0
1
2
1
1
1
1
1
1
1
0
2
2
1
2
2
1
1
1
1
1
2
1
2
2
0
1
1
1
1
1
2
1
0
0
0
2
2
1
0
1
0
1
1
1
1
1
2
1
0
0
1
1
2
0
0
0
1
0
2
1
0
1
1
1
1
1
2
0
1
1
0
0
1
2
0
2
1
1
0
2
3
1
1
2
0
2
0
0
1
2
0
2
1
2
1
2
2
1
1
0
2
0
1
1
1
0
1
2
1
0
0
2
0
1
1
2
1
0
1
2
0
0
0
2
1
0
2
2
0
2
0
2
1
1
0
0
1
2
1
1
1
1
1
1
1
2
2
1
1
0
1
0
1
1
0
2
1
1
1
0
0
1
0
1
0
1
2
0
0
1
1
1
1
2
2
2
1
2
1
1
1
1
0
1
1
1
1
1
0
1
1
1
0
1
0
1
1
0
1
2
1
2
1
1
3
1
2
0
1
1
1
1
0
1
0
0
1
1
0
1
1
1
0
1
0
1
1
1
1
1
2
0
0
1
2
2
0
1
2
1
0
1
1
1
2
0
1
0
0
1
0
2
0
0
1
1
2
0
2
1
0
2
1
1
2
0
1
0
0
1
1
1
0
1
1
1
1
0
0
2
0
2
2
1
1
0
2
0
2
0
0
1
3
1
0
1
0
2
1
0
1
0
1
0
2
2
1
1
1
0
1
0
1
0
2
1
2
1
0
0
1
1
1
0
1
1
1
2
0
0
0
1
1
0
0
0
0
0
1
1
0
1
1
0
1
1
1
2
2
2
1
3
1
1
1
1
1
0
1
1
0
2
1
1
0
1
0
1
0
2
0
2
0
0
1
0
3
2
2
2
0
0
1
0
1
1
2
0
0
2
1
2
1
0
2
1
4
0
2
2
0
2
2
0
1
1
1
1
1
2
0
2
2
0
1
0
0
1
2
1
1
1
1
2
1
1
0
0
1
1
2
2
1
1
1
1
1
1
1
1
2
1
1
2
2
1
2
1
0
1
0
1
1
0
2
0
2
1
1
2
1
1
1
0
1
0
1
1
1
1
1
2
0
1
1
0
2
1
1
1
1
2
2
2
2
0
2
1
1
1
0
0
0
0
2
2
0
1
1
0
0
1
1
0
1
1
1
1
2
0
1
1
2
2
1
0
1
0
1
0
0
1
1
0
0
1
0
0
1
0
1
1
2
1
0
0
1
3
1
1
0
1
1
2
1
1
1
1
0
0
2
0
0
0
1
1
0
2
1
0
2
2
0
1
0
0
0
2
1
1
1
0
0
0
1
0
1
0
0
0
1
2
0
1
2
1
1
1
1
1
1
2
1
1
1
1
1
0
1
0
1
0
1
2
1
1
0
0
3
1
2
2
2
0
0
2
1
1
2
1
1
1
0
0
1
2
1
2
2
1
2
1
2
1
1
2
1
1
2
1
1
1
1
1
1
1
2
0
0
2
3
0
1
1
2
1
2
2
2
1
0
2
1
2
2
1
1
0
2
1
1
1
1
1
1
1
4
2
1
2
1
2
2
2
1
1
0
1
1
1
0
0
2
1
1
0
0
0
1
0
1
1
2
1
3
0
1
2
1
0
0
0
1
1
0
0
1
0
0
0
0
2
1
1
0
2
1
0
2
0
1
0
1
1
0
0
2
0
1
1
1
1
1
1
1
0
2
0
0
0
1
1
0
2
1
2
1
0
2
1
1
1
0
1
1
0
1
1
1
0
1
1
2
2
0
1
0
0
0
2
1
1
1
0
1
0
1
1
1
0
0
2
0
0
1
0
0
1
2
1
1
1
0
0
0
0
1
2
0
0
0
1
1
0
1
1
1
0
1
1
0
1
1
0
1
0
1
0
1
0
0
2
1
2
2
2
1
1
3
2
2
2
1
1
1
0
1
0
0
1
2
0
2
0
1
1
1
2
0
1
1
0
0
0
2
1
1
1
0
2
1
0
2
2
1
2
1
2
1
1
2
3
1
1
2
1
1
2
1
2
1
1
0
1
1
1
1
2
2
1
2
1
1
0
0
2
0
1
0
1
0
1
0
1
0
0
1
0
1
2
1
0
1
1
1
0
0
1
1
1
2
1
1
0
1
2
1
1
1
0
1
1
1
1
1
0
1
0
1
1
1
2
0
0
1
3
0
1
1
1
0
2
1
2
0
1
1
1
1
2
0
1
0
1
2
1
1
1
1
1
2
1
1
1
1
0
1
1
1
2
1
1
2
1
1
1
1
0
0
2
2
0
1
1
2
0
0
1
2
1
0
0
2
0
0
1
0
1
2
1
2
1
0
3
1
1
1
1
2
1
1
2
2
1
1
1
1
0
1
2
0
1
1
2
1
0
2
1
1
3
1
1
1
1
1
1
2
1
1
2
1
1
0
0
2
2
1
2
2
0
1
1
1
1
2
1
1
1
1
1
1
1
1
0
0
1
0
1
1
1
1
0
0
1
1
1
0
1
2
2
1
1
1
0
2
1
2
0
0
2
1
2
1
0
2
1
0
2
1
1
1
0
0
2
0
1
1
1
1
2
1
0
0
0
1
2
1
2
1
1
0
0
1
1
1
1
1
0
2
1
0
1
0
1
0
0
2
0
1
2
2
1
1
0
0
0
2
1
1
2
1
1
1
2
0
1
0
2
0
1
2
0
2
1
2
1
0
1
2
1
1
1
2
0
2
1
1
1
1
0
2
1
1
2
0
2
0
1
0
0
1
1
0
0
1
1
2
2
1
0
1
1
1
0
2
2
0
0
1
1
2
1
0
0
1
1
1
0
1
1
0
2
2
0
1
1
0
1
1
1
1
1
1
2
1
2
2
0
1
2
0
1
1
1
3
1
0
1
2
0
1
0
1
0
1
2
0
1
2
1
0
0
1
2
1
2
1
1
0
2
0
1
0
2
0
2
2
0
2
2
1
1
2
1
2
1
2
1
1
1
2
1
2
1
2
1
2
2
2
0
1
1
1
1
1
0
0
0
1
1
0
1
0
1
0
1
0
0
2
2
1
0
3
1
1
2
0
4
2
0
1
2
1
1
2
2
1
0
1
1
3
1
1
1
1
1
1
1
1
0
2
1
1
0
1
1
1
2
1
0
1
1
1
3
1
1
1
0
0
0
0
2
1
2
2
0
1
1
1
0
1
1
0
1
1
2
0
1
1
1
2
0
0
1
0
2
1
1
1
1
1
1
2
1
1
0
1
1
2
0
0
1
2
1
1
0
4
2
1
1
1
2
1
1
1
0
1
0
0
2
1
2
1
1
2
1
0
2
1
1
2
2
0
1
1
2
1
0
0
1
2
1
1
1
0
1
1
0
0
2
2
1
0
1
1
1
2
2
2
1
2
1
1
1
1
1
1
0
0
1
1
1
2
2
0
1
0
2
1
1
2
1
1
1
0
1
2
2
1
0
0
0
0
2
1
1
0
1
1
1
0
0
0
1
1
2
2
0
1
1
1
0
2
0
1
0
2
0
0
1
2
2
2
0
0
2
0
1
1
0
2
1
1
1
0
2
0
1
1
0
1
1
1
1
0
0
1
0
0
0
1
1
1
2
0
2
0
1
1
2
2
0
1
1
0
1
1
1
1
1
2
2
1
2
1
1
0
0
1
1
1
0
0
1
1
1
1
2
1
1
1
2
1
0
1
1
1
2
1
2
1
1
2
1
1
2
1
3
1
0
0
1
1
1
2
1
1
2
1
2
1
0
2
1
0
1
2
2
2
1
0
1
1
1
0
1
1
2
1
0
2
1
0
0
1
2
1
2
1
0
2
0
0
1
1
2
1
1
1
1
0
2
0
0
1
1
1
0
1
2
0
1
2
1
1
0
0
1
0
2
1
1
1
1
0
1
1
1
0
1
8
1
1
0
1
1
2
1
0
0
0
0
1
2
1
0
0
1
2
0
1
1
2
2
0
2
2
1
1
1
1
6
1
0
1
1
1
1
1
3
1
0
1
0
1
1
0
2
2
2
1
1
1
1
2
2
2
1
2
1
0
0
0
0
2
1
1
0
1
2
2
1
1
2
1
1
0
1
1
0
0
1
0
0
1
1
0
1
1
0
2
1
0
1
2
1
0
1
1
1
1
0
0
1
1
1
2
1
2
1
0
1
1
1
2
1
2
0
0
1
2
0
0
3
1
0
0
1
1
2
1
0
0
0
2
1
1
2
0
1
0
1
1
1
1
2
1
1
1
1
1
1
1
1
0
1
2
0
1
1
2
0
2
1
1
1
2
0
0
0
1
0
2
1
0
1
0
0
1
1
2
1
2
2
2
1
0
2
2
2
0
0
2
0
1
1
0
1
0
2
0
2
1
2
0
0
1
0
2
2
2
1
0
1
1
2
0
0
0
1
0
0
0
1
1
2
1
0
0
1
1
2
1
2
0
1
0
1
1
2
0
1
1
2
0
1
1
0
2
0
2
1
0
2
1
1
1
1
1
0
2
2
1
0
1
1
1
0
0
2
0
0
0
1
1
1
0
2
1
1
1
1
1
1
1
0
1
1
1
2
1
0
1
0
1
1
2
2
0
2
2
1
1
1
0
1
1
1
1
1
1
0
1
1
1
2
1
1
0
0
0
2
1
1
1
1
1
2
1
0
1
1
1
0
0
0
2
1
1
0
2
2
0
1
4
0
0
0
1
1
0
0
1
0
0
0
1
1
1
2
1
0
1
0
2
0
0
0
0
0
1
1
1
0
2
0
1
1
0
1
2
1
2
1
0
1
1
2
0
2
1
1
2
1
0
1
2
1
1
3
0
1
1
1
1
2
0
0
2
1
1
1
1
1
1
0
0
1
1
1
1
1
2
3
1
1
1
1
1
1
1
1
1
1
0
0
1
1
0
1
1
1
1
0
2
1
1
2
1
1
1
1
2
1
4
1
2
1
2
0
1
1
1
1
1
1
2
2
1
1
0
1
0
0
1
0
1
0
1
2
1
1
1
1
1
1
0
2
1
1
1
0
1
0
1
0
0
0
1
0
1
2
1
0
0
2
0
0
1
0
0
0
0
2
1
1
0
2
2
0
2
0
1
0
0
0
2
0
3
1
1
2
1
0
0
1
2
0
2
2
0
1
0
2
0
1
1
2
1
1
2
1
1
0
1
2
0
2
0
1
2
1
0
0
1
0
2
1
2
2
1
1
0
1
0
0
2
2
0
1
2
2
0
2
1
2
1
0
1
1
0
0
0
0
1
2
0
0
2
0
1
1
1
2
2
2
1
2
2
1
1
0
0
1
0
0
1
1
1
0
0
1
1
1
0
1
2
0
1
2
0
1
1
1
1
0
1
0
1
0
1
1
1
0
1
2
0
1
2
0
2
1
1
2
1
1
1
2
1
2
1
1
1
1
2
0
2
1
0
1
0
2
1
2
2
1
0
2
2
1
1
0
0
0
1
2
2
1
1
1
1
1
1
3
0
0
1
1
1
1
1
0
2
2
1
0
0
0
2
1
2
1
1
1
1
1
1
1
1
1
2
1
0
2
1
1
2
1
1
1
0
0
0
1
1
0
1
2
0
0
1
0
0
1
0
0
2
1
2
0
2
0
1
1
2
0
1
0
0
2
2
1
1
0
1
2
0
0
1
1
0
2
1
0
2
0
1
0
1
1
0
1
2
0
2
1
2
1
1
1
3
2
2
1
2
1
0
0
0
3
0
0
1
1
1
0
1
1
1
1
0
2
0
1
1
1
0
1
2
0
2
1
0
0
0
1
0
2
0
1
1
0
0
1
2
1
2
1
0
0
2
1
1
1
1
1
1
1
1
1
0
0
0
1
0
1
0
1
1
1
1
2
1
1
1
1
0
0
1
0
1
1
0
1
2
0
2
0
0
1
1
1
1
1
1
1
0
1
2
0
0
2
2
1
2
1
1
2
1
0
1
1
1
2
1
1
1
2
0
1
0
1
1
1
1
1
2
1
1
1
2
1
2
1
2
1
1
1
0
0
0
2
2
0
2
1
1
1
1
1
1
0
2
3
1
2
1
1
1
0
1
2
1
1
0
1
1
1
0
0
1
0
1
0
1
2
0
0
1
2
1
2
1
0
1
1
1
1
0
0
0
2
1
0
0
1
2
1
1
1
2
2
1
1
0
0
2
2
1
0
2
2
2
1
0
2
0
3
2
1
1
1
1
1
1
2
0
1
2
1
1
1
1
2
2
1
1
2
2
2
1
0
2
1
2
1
1
1
2
2
1
1
3
1
2
4
1
1
1
1
1
1
2
2
0
5
2
1
0
2
0
0
0
0
0
0
0
1
2
1
1
1
2
2
1
1
1
0
1
2
1
1
0
0
0
0
0
1
1
1
1
0
0
1
1
1
1
2
1
0
1
0
2
2
1
2
1
5
1
1
0
2
1
0
1
1
0
1
1
1
2
0
1
1
2
1
1
1
3
1
2
2
1
1
0
0
2
1
2
2
1
2
0
0
0
2
1
0
2
1
0
2
2
1
4
1
1
1
1
2
0
1
1
0
2
1
2
1
1
1
0
1
0
1
0
2
1
1
1
1
1
1
1
1
0
0
2
2
1
1
2
1
1
1
1
0
0
1
0
0
0
0
1
2
1
0
0
1
0
2
2
1
2
0
0
1
0
0
2
2
1
0
1
1
1
2
0
1
0
1
0
1
1
1
2
2
1
0
0
2
0
1
1
1
0
2
0
0
2
1
1
1
0
1
0
0
1
2
1
3
2
1
0
1
1
1
2
1
1
0
0
0
0
0
0
2
1
1
0
1
1
1
1
0
1
0
2
0
1
0
0
1
0
1
0
1
1
0
2
1
1
2
2
1
2
0
1
0
0
2
1
2
1
1
0
2
1
0
2
2
2
1
2
1
2
1
1
1
1
0
1
0
1
2
1
2
1
1
0
2
2
0
1
1
0
0
0
1
1
1
1
1
1
1
0
0
0
1
0
1
0
1
1
0
0
1
0
1
1
0
0
1
1
1
3
1
0
1
2
2
2
2
1
0
1
1
1
1
0
1
1
2
2
0
1
2
1
1
1
0
2
3
0
1
1
1
1
2
1
0
1
1
1
0
0
2
1
1
1
2
0
1
1
2
0
0
1
1
2
1
1
2
1
2
1
0
0
1
1
1
1
0
1
1
1
1
1
1
0
0
1
2
1
1
0
1
1
0
0
1
0
1
2
1
2
1
1
0
1
0
0
1
1
1
1
2
0
2
0
1
2
1
2
1
1
1
1
1
2
2
1
0
1
0
1
1
1
0
0
0
3
1
2
0
0
1
2
2
1
0
1
1
1
1
0
2
0
4
0
1
1
1
0
1
3
1
1
1
2
1
1
1
1
1
0
0
1
2
1
1
2
0
1
0
0
1
1
0
2
1
1
2
0
1
1
0
1
1
3
1
1
1
0
1
0
1
0
1
0
0
2
0
2
0
2
2
1
0
2
0
2
1
0
1
1
1
1
1
0
1
0
1
1
2
2
0
1
1
1
1
2
1
0
1
1
1
1
1
2
1
1
1
1
0
2
2
0
4
1
0
0
1
1
1
1
2
0
1
2
0
0
1
0
1
1
1
2
1
1
1
1
0
1
1
0
2
1
1
1
1
1
1
0
1
0
0
1
1
0
1
1
0
0
1
1
1
1
1
2
2
0
1
0
1
0
1
1
1
0
0
1
0
0
1
0
2
1
1
1
1
0
1
1
1
1
0
1
0
1
0
1
2
1
3
1
0
0
1
1
1
2
0
1
2
1
2
1
2
0
1
2
2
1
1
0
1
0
0
1
1
0
1
1
1
1
1
1
0
0
1
1
0
0
1
1
0
2
0
1
1
0
1
0
0
1
0
0
0
2
0
1
1
0
1
0
1
1
1
2
1
0
0
0
1
1
0
1
1
0
3
1
3
1
0
0
0
1
0
1
0
1
1
0
1
1
2
2
1
0
2
0
1
0
0
1
1
1
2
2
1
1
1
2
1
1
2
1
1
1
0
0
2
0
0
2
0
1
1
1
0
0
0
2
1
2
2
2
1
2
0
0
2
2
0
0
0
0
0
1
2
3
1
1
0
1
1
2
1
0
2
1
0
1
0
0
1
0
1
2
1
0
1
1
2
1
2
1
2
0
2
1
1
0
0
1
1
0
1
1
1
1
1
0
1
2
0
2
2
1
1
1
1
2
0
0
0
0
2
2
0
1
2
1
1
0
0
0
1
2
2
1
2
1
2
0
2
0
1
0
3
1
2
1
1
1
1
0
1
0
0
1
1
0
0
1
2
0
3
1
0
1
2
2
0
0
2
1
2
0
2
1
2
0
0
2
0
2
1
1
1
1
1
1
1
0
1
1
0
0
0
1
1
1
1
0
2
0
2
2
1
2
0
0
1
0
1
0
1
1
1
1
0
2
0
0
0
0
1
0
2
2
0
1
0
1
0
1
0
1
1
1
1
1
1
1
1
2
0
1
0
1
0
1
0
0
1
1
0
0
1
0
1
1
1
1
1
1
1
1
2
2
1
0
0
0
0
1
1
0
2
2
0
1
2
2
1
1
2
1
0
1
0
0
1
0
0
0
0
2
1
2
1
1
2
0
2
0
1
1
1
1
1
2
0
1
0
1
2
2
0
1
1
1
1
0
1
0
1
0
2
1
2
0
2
0
1
2
1
0
2
1
2
1
0
1
0
1
2
1
3
0
2
3
1
1
2
0
1
0
1
1
0
0
1
1
0
1
0
2
1
1
1
1
1
0
1
2
2
1
1
1
1
2
2
0
1
1
1
0
1
1
1
2
1
0
1
1
1
1
2
0
1
2
1
0
2
1
1
1
2
4
0
2
2
1
2
2
0
1
2
0
1
2
2
2
0
1
1
0
0
1
1
0
2
0
0
2
1
1
1
1
2
3
0
2
0
1
1
1
1
2
2
1
0
1
1
0
1
0
1
1
0
1
1
0
2
1
2
0
0
0
1
1
1
1
1
1
0
1
0
0
1
2
1
0
2
1
1
2
1
1
0
1
1
0
2
1
1
0
1
0
1
1
0
2
1
0
5
1
2
0
0
0
1
1
1
1
0
2
0
2
0
1
1
1
0
2
1
1
0
1
1
1
1
2
0
2
2
0
0
1
1
1
0
0
0
0
1
2
1
0
0
2
2
0
0
1
2
1
1
0
0
1
1
1
2
1
2
1
1
0
0
1
1
1
1
0
1
1
1
1
2
1
2
0
2
1
1
1
1
1
1
1
2
1
1
1
0
2
1
1
1
1
1
1
0
1
1
1
0
0
1
1
2
1
0
0
0
1
0
1
2
0
0
1
2
1
1
1
0
0
2
1
2
1
1
1
2
2
2
2
1
1
1
2
2
2
1
1
2
1
3
1
0
1
1
1
0
1
2
0
1
3
0
1
1
3
1
1
0
0
1
1
1
1
1
0
1
0
1
1
1
1
0
1
1
1
0
1
1
1
2
1
1
0
1
0
1
0
1
1
2
1
0
3
0
0
2
0
1
0
1
1
0
3
1
0
2
0
2
1
0
2
2
1
1
0
2
1
0
1
2
0
0
1
0
1
3
0
0
1
0
0
1
0
1
1
1
1
1
2
0
1
0
0
1
0
2
1
0
1
2
0
2
1
0
0
1
1
0
1
1
1
1
2
2
0
1
1
1
2
1
1
2
0
1
0
1
0
1
0
2
0
1
0
2
1
1
1
1
1
1
0
0
0
0
1
1
2
0
0
0
2
2
2
1
1
0
1
0
2
1
2
2
1
1
3
0
1
1
0
2
2
2
1
0
1
1
2
0
1
1
1
1
1
1
1
0
2
0
1
0
1
0
1
1
0
1
3
2
2
2
0
1
0
1
1
0
0
0
2
1
1
2
0
1
0
2
1
0
1
1
2
2
2
1
0
1
1
1
1
1
2
1
1
1
1
0
2
1
2
1
0
2
0
0
0
0
0
0
2
1
1
1
2
1
2
2
1
0
1
2
0
0
1
2
2
1
2
0
1
2
1
2
2
1
1
0
1
1
1
1
2
1
1
1
1
2
1
3
1
0
2
1
0
1
0
1
1
1
1
1
0
0
1
1
1
0
1
2
1
1
1
1
0
1
0
0
1
2
2
2
1
0
0
1
0
0
0
1
1
1
2
1
1
2
1
0
1
2
1
2
1
1
0
1
3
1
0
0
2
2
0
1
2
2
1
1
0
1
1
1
1
2
0
0
1
1
2
0
1
1
0
2
0
0
2
0
0
2
1
2
1
1
1
2
0
1
2
0
2
2
1
0
1
1
1
3
1
1
1
2
1
1
1
0
0
1
0
0
0
1
2
1
2
1
1
1
1
2
3
1
2
1
2
1
0
1
0
1
0
1
1
0
0
1
1
1
1
2
0
1
1
2
2
0
2
1
0
1
0
1
1
0
2
2
2
1
0
1
2
1
2
0
1
2
1
1
0
1
0
2
0
0
0
0
1
1
1
0
1
2
1
2
1
1
0
1
0
1
1
1
0
0
0
0
1
0
2
2
1
0
1
1
0
0
0
1
1
0
1
2
1
1
1
2
1
2
10
2
2
0
0
0
1
0
0
1
2
1
1
1
1
1
0
0
1
1
1
2
0
1
0
0
1
2
0
1
0
1
0
2
0
1
0
1
1
0
1
0
0
0
1
1
1
1
2
0
1
0
0
2
1
1
2
2
1
1
2
1
2
1
2
1
2
2
0
0
0
1
0
1
3
4
0
0
2
0
0
1
1
1
0
1
1
1
1
1
0
0
2
0
2
1
0
2
1
0
1
1
0
1
1
1
1
1
1
1
0
0
0
1
1
2
1
2
1
0
1
1
0
1
1
1
0
1
1
1
0
0
1
1
0
2
2
2
1
0
1
1
1
2
2
0
3
1
0
1
2
0
2
3
1
0
1
1
1
0
1
1
2
0
2
1
0
0
0
1
1
1
1
1
0
0
1
2
0
2
0
2
0
2
1
2
2
2
0
0
1
1
0
1
1
0
1
2
2
0
1
1
0
1
0
2
0
2
2
1
1
0
0
2
0
0
0
1
0
1
0
1
1
0
1
0
0
2
4
3
0
1
0
1
2
0
1
2
0
0
1
1
0
1
1
0
1
0
2
1
3
2
1
0
2
2
0
0
1
0
0
2
2
0
0
0
0
1
1
0
0
1
1
2
0
1
2
0
0
1
0
1
1
1
1
0
1
1
1
1
1
2
0
2
0
0
1
0
1
1
1
1
0
1
1
2
1
2
1
0
1
1
0
0
1
1
0
1
1
0
2
1
1
0
2
0
1
0
2
1
0
2
1
1
2
1
0
1
0
1
0
2
0
0
1
2
0
0
1
2
2
0
0
2
1
2
0
0
0
1
1
4
2
2
0
0
2
0
1
1
0
1
1
1
1
0
1
1
0
2
0
0
1
1
0
1
0
1
1
0
0
1
1
1
2
0
1
0
1
1
1
1
1
0
1
2
0
0
2
1
1
0
2
0
2
0
1
2
1
0
0
2
1
0
2
1
0
2
1
1
0
0
2
0
2
0
1
1
1
1
1
1
1
0
1
0
1
2
2
0
0
1
2
0
1
0
2
1
1
0
1
0
2
1
1
2
1
1
1
0
1
1
1
1
1
0
1
0
0
0
2
1
1
1
1
0
1
1
0
0
0
1
1
0
1
0
0
2
0
0
1
2
1
1
0
1
1
2
0
1
1
0
1
0
1
1
1
1
2
0
0
1
1
3
2
2
0
0
1
1
0
1
0
1
0
2
1
0
0
1
0
0
1
0
2
2
1
1
2
1
1
1
2
1
0
2
0
1
0
0
1
1
2
1
2
2
1
2
2
1
1
0
0
0
0
2
2
0
2
0
1
1
1
0
1
2
0
0
0
2
1
1
0
2
0
1
0
1
1
0
2
0
2
1
2
1
2
0
2
1
1
0
1
1
1
1
2
0
0
2
0
2
1
1
1
1
1
2
1
1
1
1
1
1
2
0
2
1
2
0
1
1
1
1
0
2
1
1
1
1
2
0
1
0
1
0
0
0
0
1
0
1
1
2
0
0
1
1
0
1
1
2
2
0
1
1
1
1
2
2
1
1
1
1
1
1
0
0
1
1
2
2
0
1
0
2
4
0
0
0
2
0
1
2
1
0
1
1
2
0
2
0
1
2
1
0
2
0
0
2
2
1
6
0
1
2
1
1
1
2
1
2
1
0
2
2
1
2
1
1
0
1
2
1
1
0
2
0
1
1
1
1
1
0
1
0
3
1
1
1
1
2
2
0
0
0
1
1
0
0
2
1
1
0
2
1
2
0
1
1
0
1
0
2
2
0
0
0
3
2
1
1
0
1
0
1
2
2
0
0
1
1
1
1
2
1
2
0
0
0
1
2
1
0
2
0
2
2
1
1
3
1
1
1
1
0
1
2
1
0
0
2
2
0
1
1
1
0
2
0
2
2
0
0
1
2
1
0
0
1
1
0
2
0
1
2
2
1
0
1
2
1
1
2
0
1
1
1
1
1
1
1
1
0
2
1
1
1
0
1
1
2
0
1
1
1
2
0
2
0
1
1
1
1
1
0
1
0
0
0
0
1
2
0
1
1
0
1
1
1
1
1
1
0
0
1
1
1
1
1
0
1
0
1
1
1
1
0
1
0
1
1
1
0
1
1
0
0
3
1
2
2
1
1
1
1
1
1
0
0
0
1
0
0
0
1
1
1
0
0
1
1
1
1
2
0
3
1
0
1
1
2
2
1
1
1
0
2
2
0
2
0
1
1
2
0
0
1
1
2
1
2
0
2
2
0
0
1
1
1
0
2
1
3
2
0
1
1
1
0
1
1
1
1
0
2
1
1
0
0
1
0
2
1
1
1
1
0
1
1
2
1
0
0
0
1
1
1
2
1
0
0
1
1
2
0
2
2
0
0
1
1
1
1
1
1
1
2
0
1
0
2
1
1
2
0
1
1
1
1
0
1
0
0
4
0
0
1
1
1
1
1
0
0
1
0
0
1
1
1
1
2
1
1
0
0
2
0
1
2
1
1
2
2
0
1
2
1
2
0
1
0
2
1
2
0
1
0
2
1
1
0
1
1
2
0
1
0
1
1
1
1
2
2
1
1
1
1
0
3
1
0
1
2
0
2
2
2
1
1
1
1
1
1
0
1
2
2
0
0
0
1
1
1
2
1
1
1
0
2
0
0
0
1
1
1
2
2
1
1
1
1
1
1
3
1
1
0
1
1
0
0
0
1
2
1
0
1
1
2
2
1
2
0
1
1
1
1
1
1
2
0
1
0
1
1
1
2
0
1
1
0
0
1
0
1
1
0
2
0
0
0
1
1
1
1
0
0
1
1
2
0
2
2
2
0
2
1
0
0
1
1
2
0
2
0
2
1
1
1
0
1
2
1
0
2
1
1
1
0
1
1
1
1
1
0
2
1
0
2
1
0
0
1
2
1
1
1
2
3
2
2
0
0
1
1
2
0
0
4
2
1
1
1
1
0
0
1
0
2
1
1
0
1
1
1
0
1
0
0
0
1
1
0
4
1
1
0
1
1
1
2
1
1
2
1
1
1
0
0
1
2
0
1
0
0
2
1
1
2
1
1
1
0
1
1
0
1
1
1
0
3
1
1
1
2
1
1
1
1
1
0
2
1
1
1
1
0
1
1
1
2
2
2
2
1
0
1
0
2
1
1
1
1
1
1
0
1
2
1
0
0
1
1
1
1
2
1
0
0
1
1
0
0
1
1
1
0
1
2
2
0
0
1
0
0
2
1
2
1
0
0
0
2
0
1
2
1
1
1
2
2
1
2
3
0
2
1
0
1
1
0
1
2
1
0
1
0
1
0
0
1
0
1
1
1
1
1
1
0
0
0
2
2
0
0
2
1
1
1
1
1
2
0
1
1
2
1
0
0
1
0
2
2
1
1
1
1
1
1
0
2
0
0
1
2
0
0
1
1
1
2
0
0
1
1
2
1
3
1
1
1
0
0
0
1
1
2
2
2
1
0
1
1
0
2
1
1
1
1
0
0
1
1
0
1
0
1
1
1
0
2
0
1
1
2
1
1
1
1
0
3
2
1
1
0
0
1
1
2
0
2
1
1
0
2
1
0
2
1
1
2
2
1
2
0
1
0
1
1
1
1
0
0
2
2
1
0
0
1
2
1
1
1
1
1
1
1
2
0
2
0
2
1
1
1
0
0
2
2
1
1
1
1
2
1
0
1
0
1
0
1
2
1
1
1
1
1
1
1
2
1
1
1
1
2
2
0
1
1
0
1
1
1
1
1
0
0
1
1
0
1
0
0
2
2
0
2
1
0
1
2
0
2
1
2
0
0
2
0
2
1
1
0
1
0
1
1
2
1
1
2
2
0
2
2
0
2
1
2
1
0
1
0
2
1
2
1
1
1
1
2
1
2
1
1
1
2
1
1
0
1
1
1
1
1
2
2
0
0
2
0
2
2
1
2
3
1
0
1
0
0
2
1
0
2
1
1
0
0
1
0
1
0
2
1
0
0
0
0
1
0
2
2
2
1
1
0
0
1
2
0
1
2
1
1
0
1
1
0
1
1
2
1
1
0
1
2
1
1
2
1
2
1
1
1
1
1
2
2
1
2
1
1
0
0
0
1
2
1
1
2
1
0
2
1
0
1
2
1
1
1
1
1
1
0
0
1
0
1
0
0
0
2
1
1
0
0
0
0
1
0
1
0
0
2
1
1
2
1
2
1
1
1
1
0
1
1
0
0
2
1
1
1
0
2
0
1
1
1
2
1
2
0
1
1
1
2
2
0
1
1
1
1
1
1
1
1
0
1
2
3
0
0
1
1
1
1
0
1
2
1
1
0
1
2
1
0
2
2
1
0
1
1
2
1
1
1
1
1
1
2
2
1
2
1
1
1
1
0
1
0
1
1
2
1
0
1
1
1
1
1
2
1
0
0
1
0
0
4
0
0
1
1
0
0
0
0
2
0
1
1
0
1
2
0
1
2
1
1
1
0
0
0
1
2
0
1
1
0
1
1
1
0
0
0
2
1
0
1
1
0
1
1
1
0
1
1
1
1
2
2
2
0
1
1
1
1
1
0
1
1
2
2
0
1
1
0
2
0
1
1
1
1
2
1
0
2
0
1
1
3
0
5
1
1
0
2
0
1
2
1
1
2
1
0
1
1
0
1
1
1
2
0
0
1
1
2
3
0
1
0
2
1
2
1
1
2
2
2
0
0
1
0
2
1
2
2
0
0
0
1
1
0
1
2
1
1
1
2
1
1
1
2
0
0
0
2
1
1
0
2
1
1
1
2
1
2
1
1
2
1
2
0
1
0
2
2
0
2
1
2
0
2
1
1
1
2
1
0
1
0
0
1
1
0
0
1
0
1
0
1
0
1
1
1
0
2
0
0
1
1
0
1
0
0
1
1
2
0
1
1
1
0
1
2
1
1
1
0
2
0
1
1
1
0
0
0
1
2
2
2
0
0
0
1
1
1
0
1
1
1
1
1
0
1
0
1
1
1
1
1
0
1
0
0
1
0
1
1
1
0
0
2
0
2
2
1
1
1
0
0
0
0
2
1
2
1
1
1
1
2
2
0
2
1
0
2
0
2
0
0
0
1
0
2
2
2
0
1
2
0
2
0
1
1
0
1
0
0
0
2
1
0
2
0
0
1
2
1
0
1
0
0
0
1
0
2
2
0
1
3
1
1
1
2
1
0
0
2
2
0
0
1
1
1
0
0
0
1
1
0
1
1
1
0
2
1
0
1
0
1
2
0
0
0
1
0
2
1
0
0
1
1
2
0
1
1
1
1
1
0
0
2
1
1
0
1
1
1
1
0
0
2
1
2
1
2
2
0
1
2
1
1
0
1
2
2
1
1
0
2
0
1
1
0
1
1
2
0
2
2
1
2
0
1
1
1
2
1
1
1
0
0
1
0
0
1
1
0
0
2
1
1
1
1
0
0
0
0
1
1
1
0
1
1
0
0
2
1
1
2
1
1
1
0
0
4
0
0
1
1
0
2
1
2
3
0
2
0
1
1
2
1
2
2
0
1
1
2
1
1
1
2
2
0
2
1
0
2
0
1
1
2
1
2
1
1
1
1
0
1
1
1
0
1
2
1
2
1
1
0
0
2
0
0
1
1
2
2
0
0
1
1
1
0
0
3
1
0
0
1
1
1
2
2
2
0
1
1
1
2
1
3
0
2
1
0
0
2
1
1
1
1
1
2
1
2
2
0
1
0
0
0
1
1
2
1
0
2
1
1
3
0
1
1
2
2
1
1
0
1
2
0
2
2
1
0
0
1
2
2
1
1
0
1
2
0
1
1
1
2
0
2
0
1
1
0
0
0
0
1
2
2
1
1
1
0
1
2
2
1
0
2
0
2
0
1
1
1
0
1
1
2
2
1
0
2
2
1
2
1
1
0
0
0
3
1
1
0
0
2
0
0
0
1
0
2
1
0
2
2
2
1
0
1
1
1
1
0
2
1
0
0
0
0
0
2
1
1
2
1
1
1
0
1
0
1
1
0
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
0
1
1
0
2
1
1
0
1
0
2
1
1
1
0
2
1
1
1
0
2
1
2
1
0
1
1
0
0
0
1
1
1
0
2
0
1
0
1
1
1
1
1
0
1
1
0
1
0
1
2
1
2
0
1
2
2
1
0
1
1
1
1
1
1
1
0
1
0
2
1
0
1
1
1
1
0
1
1
1
0
1
2
2
0
0
2
0
2
0
2
0
1
1
2
2
0
1
1
0
0
1
0
1
1
2
1
1
2
1
0
1
1
0
1
1
1
0
1
5
1
1
0
1
1
2
0
1
2
0
0
0
1
1
1
1
1
2
0
1
0
1
0
1
1
1
2
1
2
1
0
0
1
1
1
2
2
1
1
2
0
1
1
1
1
2
1
0
3
0
1
1
2
1
1
1
1
1
0
0
0
0
2
0
1
0
1
1
2
2
1
0
1
0
2
1
0
1
1
1
1
1
1
1
1
2
0
1
2
1
1
1
0
2
0
2
1
1
0
1
1
1
1
1
1
1
1
0
1
0
1
0
2
1
1
0
1
1
2
2
1
1
1
2
1
1
0
2
0
1
1
2
0
2
1
0
1
2
4
1
0
2
1
1
2
0
1
1
0
0
1
0
0
2
1
1
0
0
1
1
0
1
1
2
0
0
1
2
0
0
2
2
0
1
1
0
0
2
0
0
2
0
0
1
1
0
0
0
1
2
0
0
2
1
0
0
2
1
0
0
1
2
0
2
0
1
1
1
0
1
0
1
1
2
0
1
2
0
0
3
2
1
0
1
0
2
1
1
0
0
0
0
1
1
1
0
2
1
0
1
0
1
1
1
2
1
2
2
1
2
0
1
2
1
1
3
0
1
2
0
1
0
2
1
1
1
0
0
1
2
1
0
1
0
2
0
1
0
2
1
1
0
1
0
2
2
2
0
1
1
2
0
1
0
2
1
1
1
0
1
1
1
2
0
2
2
2
0
0
1
1
0
2
4
0
2
2
1
1
1
1
0
1
1
0
1
1
1
1
2
0
2
0
2
1
0
1
0
1
0
1
2
0
1
0
0
0
0
0
1
2
0
2
1
0
1
2
0
1
1
1
1
1
2
0
1
0
1
0
1
1
2
0
0
0
2
2
1
1
1
1
1
2
1
1
1
1
1
1
0
0
1
1
1
0
0
2
0
2
1
3
0
0
1
1
2
0
2
1
2
2
2
0
1
0
2
1
1
0
0
1
1
1
0
1
1
0
1
0
1
1
1
1
1
2
1
0
1
0
2
1
1
2
2
0
2
1
1
1
2
0
1
1
1
1
2
1
2
2
2
0
1
1
0
1
1
2
0
1
1
1
2
1
1
1
2
3
1
1
1
2
2
2
2
1
1
1
1
0
0
0
2
0
2
0
0
1
2
0
1
2
1
0
0
1
0
1
1
0
1
1
1
1
1
0
2
1
2
2
2
0
1
1
1
1
1
1
1
2
1
0
1
2
1
1
0
1
1
0
0
1
0
2
2
2
1
2
0
1
2
2
1
0
1
2
1
2
1
1
2
1
0
1
1
2
2
1
1
0
0
0
1
0
0
2
2
2
1
2
1
1
0
1
1
2
1
0
0
1
1
0
0
0
0
2
0
2
2
1
2
0
1
0
0
1
1
0
1
2
0
0
2
0
2
1
2
1
1
0
1
1
0
0
1
0
2
1
2
2
0
1
0
1
0
0
2
0
2
1
2
1
1
1
0
1
2
0
2
1
1
1
1
0
1
0
1
1
1
1
1
1
1
1
1
2
0
2
1
0
0
1
2
1
1
0
1
2
0
0
0
1
1
0
0
2
1
0
0
1
0
3
1
1
1
1
1
1
0
1
0
2
1
1
0
1
0
0
2
1
1
0
2
1
1
0
1
2
1
1
2
1
2
2
0
1
0
0
1
0
0
1
1
0
0
0
2
1
0
1
0
1
1
0
1
2
2
1
1
1
1
0
0
1
1
1
2
0
1
1
1
2
2
2
0
1
1
0
1
2
1
1
0
1
1
0
0
2
0
1
2
2
1
0
1
1
2
2
1
2
1
1
1
1
1
0
2
1
0
0
0
1
2
0
0
0
2
2
5
0
0
2
2
0
1
1
0
0
1
2
1
0
1
0
0
1
1
0
0
0
1
2
1
1
1
1
1
1
1
1
0
2
1
0
1
0
1
1
0
0
1
1
1
0
0
1
1
0
2
1
1
2
0
0
1
1
1
1
1
1
1
1
0
1
0
2
2
1
0
1
3
0
1
2
1
2
2
2
3
1
2
2
2
1
0
0
0
2
1
1
1
1
0
1
1
0
0
0
1
0
1
1
1
1
1
0
0
0
1
2
1
1
0
0
2
0
1
1
1
1
0
2
0
0
1
1
1
1
1
0
1
0
1
0
1
1
1
2
0
2
1
0
1
1
0
1
2
2
0
0
0
1
1
1
2
0
1
2
1
2
0
1
1
1
0
1
1
2
0
2
1
1
0
1
1
1
1
2
1
1
1
1
1
0
1
1
2
1
2
0
2
1
1
1
1
2
1
1
2
2
1
0
2
0
3
0
2
0
1
1
0
1
1
1
1
3
1
1
1
1
1
3
1
1
2
0
2
2
1
0
0
1
1
0
2
0
1
2
1
0
0
2
0
1
0
1
2
2
0
0
2
0
1
0
1
1
1
1
0
1
1
1
2
1
0
1
1
2
0
1
2
1
1
2
0
2
0
0
2
0
3
1
1
2
1
1
1
1
1
1
1
1
2
1
1
0
1
0
1
0
1
0
0
0
0
2
1
0
0
1
1
0
0
2
1
1
0
1
2
2
0
1
0
1
0
0
1
1
2
1
1
1
2
0
1
3
0
2
1
1
0
0
0
2
0
1
2
1
0
1
0
0
2
1
1
1
2
2
1
3
0
1
2
1
2
2
0
1
1
1
0
1
0
0
2
1
1
2
0
1
1
0
1
2
2
1
1
1
2
0
1
2
1
0
1
1
0
1
0
1
0
3
0
2
2
2
1
0
0
1
1
0
1
0
2
1
0
2
0
0
0
2
2
2
2
1
1
1
1
2
1
1
1
1
0
0
2
0
1
2
0
1
2
1
0
2
2
1
0
0
2
2
1
1
0
1
0
0
1
2
1
1
2
0
1
2
2
0
1
1
0
2
1
1
1
0
0
0
1
1
2
1
1
0
0
1
1
1
1
0
0
0
1
2
6
1
1
1
2
0
1
1
0
2
0
1
0
1
1
1
1
1
1
2
1
1
1
2
0
1
0
0
1
1
1
1
1
0
1
1
2
1
0
1
2
0
1
2
1
1
0
1
0
1
2
1
2
2
2
2
3
1
1
2
1
1
1
1
1
1
1
1
0
1
2
0
1
2
0
1
1
0
2
1
2
1
1
0
1
2
1
0
0
0
2
2
0
0
0
0
0
1
1
1
1
1
2
1
1
1
1
2
2
0
1
1
0
1
1
1
0
2
0
1
1
1
1
0
1
1
1
0
2
3
1
0
1
1
0
0
1
3
1
0
0
1
0
2
1
1
1
0
2
1
2
1
1
1
2
2
0
0
0
1
0
0
0
3
1
2
1
0
1
2
1
1
2
0
1
1
0
1
1
0
1
1
1
1
0
2
0
1
0
0
1
1
1
0
0
2
2
0
1
0
0
0
2
1
1
0
0
1
0
0
1
0
1
1
1
1
2
1
0
2
1
1
2
2
1
1
2
1
0
1
0
1
2
1
1
0
1
1
1
1
0
1
1
2
0
0
0
2
0
1
0
1
1
1
0
2
1
0
1
0
1
0
1
0
0
1
0
1
1
1
0
1
5
2
1
0
1
1
3
0
1
1
1
0
2
0
0
0
0
1
2
1
0
2
1
0
3
1
1
1
0
0
1
0
1
1
1
1
2
2
2
0
0
2
1
2
2
0
2
1
1
1
1
0
1
2
1
1
1
1
1
0
1
1
1
2
1
0
0
1
0
1
1
1
0
1
1
0
0
1
2
1
1
0
1
0
1
0
1
0
0
1
2
2
1
1
0
0
1
2
1
0
1
0
2
0
0
1
0
1
1
2
0
2
0
2
2
2
1
2
1
1
2
1
1
2
1
2
1
0
1
0
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
0
1
1
1
1
1
2
2
1
0
1
1
0
1
0
2
1
3
0
0
1
1
2
1
1
1
1
2
0
0
0
1
2
2
1
1
1
0
2
0
1
1
2
1
1
1
0
1
1
1
1
1
0
2
0
1
0
1
2
0
0
1
1
1
2
1
2
2
2
2
0
1
0
0
2
0
1
1
0
1
0
1
2
1
2
0
1
0
1
1
1
1
0
1
1
2
1
0
0
0
1
1
0
1
0
2
2
0
2
1
0
2
0
1
0
2
0
1
0
0
1
1
2
1
1
1
1
2
2
0
1
1
0
0
2
0
0
1
1
0
2
0
1
0
1
1
1
2
2
2
1
1
1
1
1
0
1
0
2
0
0
1
2
0
2
0
2
1
1
0
0
0
1
1
2
0
2
2
1
0
1
4
1
3
1
2
2
0
1
2
2
1
1
0
0
2
1
2
1
1
0
0
0
2
1
1
1
2
1
1
1
1
2
1
1
0
0
1
2
1
2
1
0
2
2
2
0
0
1
1
1
1
2
2
3
1
0
1
0
4
2
2
0
0
2
1
1
2
3
2
0
2
1
2
0
0
2
0
2
2
2
0
1
1
2
0
1
1
0
1
0
1
1
1
2
1
0
0
0
1
0
2
0
2
0
1
0
1
1
0
1
1
1
1
1
1
0
1
3
0
1
2
0
1
1
3
0
2
1
1
2
0
1
1
0
1
2
1
2
1
2
1
0
2
1
1
1
0
1
1
0
1
0
0
1
2
0
2
0
1
1
1
0
0
1
0
1
0
0
1
0
1
1
1
1
2
0
1
1
1
0
0
1
2
0
1
0
2
0
0
1
2
0
1
0
2
1
0
2
1
0
1
1
0
0
2
2
1
1
1
1
1
1
2
2
1
1
1
0
1
1
1
2
1
0
2
1
1
1
0
0
1
0
2
1
1
1
0
1
1
1
0
1
1
0
2
1
0
2
1
1
1
1
0
0
2
1
1
1
1
0
1
1
0
1
2
0
2
2
0
2
2
1
1
0
1
1
1
1
1
2
0
1
1
2
0
2
2
1
2
1
0
2
2
1
0
1
1
0
2
0
2
0
2
0
0
1
1
1
0
1
1
1
1
1
0
1
1
1
1
2
0
0
0
2
0
2
1
0
3
2
2
2
0
0
1
2
1
0
0
1
2
1
0
0
1
2
2
0
0
0
1
0
1
1
0
0
0
1
1
1
1
1
1
1
1
1
2
1
0
0
0
0
0
0
1
1
2
2
0
0
1
1
0
0
1
1
2
0
0
1
1
1
0
0
0
1
0
2
1
1
0
2
1
1
1
1
1
1
0
2
1
0
1
1
1
1
0
2
2
2
0
1
1
1
0
1
1
0
1
2
1
2
1
1
1
1
0
1
2
1
0
0
0
0
2
1
2
1
1
1
2
0
0
1
1
1
0
1
1
1
2
0
1
0
1
1
0
2
0
0
1
1
2
0
2
2
1
0
1
1
2
1
2
0
1
1
1
0
1
1
1
0
0
2
1
4
1
0
1
1
0
0
2
1
1
0
0
0
2
0
2
1
1
1
1
1
1
0
0
0
2
1
3
0
2
1
1
1
0
1
1
1
1
0
1
0
0
2
2
0
1
0
1
0
0
1
1
0
1
2
1
1
0
1
0
1
2
2
2
0
1
0
0
0
2
1
1
0
2
1
3
1
2
2
0
1
0
1
1
2
2
0
0
1
2
1
1
1
1
1
0
1
2
1
1
1
0
0
0
0
1
2
2
2
1
0
1
1
1
1
1
1
1
0
0
2
0
2
1
0
0
1
2
1
2
1
0
1
1
1
1
2
2
0
1
0
1
0
1
1
0
2
0
2
1
2
1
0
1
2
1
1
3
0
1
1
2
1
1
2
1
1
1
1
0
1
1
1
0
2
2
1
1
1
2
1
1
0
0
2
0
2
1
2
1
2
1
1
1
1
1
1
1
1
1
1
0
3
1
1
2
0
0
1
0
1
0
2
1
1
1
1
0
1
2
1
1
0
2
0
1
0
1
1
2
1
2
1
0
1
1
1
1
2
0
0
0
1
1
1
1
1
1
1
1
1
1
1
0
1
0
2
2
0
1
1
0
2
1
1
1
1
1
1
1
2
2
2
1
1
2
2
2
2
2
1
1
1
1
5
0
2
0
1
2
0
1
1
1
1
0
1
0
0
2
1
2
1
1
2
0
1
1
2
2
0
3
1
0
0
1
1
2
1
0
1
0
0
2
2
1
2
2
0
1
0
0
2
1
2
1
1
2
1
0
1
2
1
2
0
1
2
1
3
1
0
1
1
0
1
2
1
0
0
1
1
1
2
1
1
0
3
1
1
1
1
0
1
2
0
1
1
0
1
1
1
1
0
0
1
1
1
1
1
1
0
1
2
0
1
0
1
0
1
1
1
1
1
1
1
0
0
1
0
2
0
1
1
0
1
1
0
1
0
0
1
3
1
0
0
1
1
2
1
2
0
2
0
2
0
0
1
2
1
1
2
1
2
1
0
0
0
0
0
2
1
0
1
1
2
1
1
0
0
1
2
4
0
1
2
0
1
2
1
2
1
2
0
1
3
2
1
1
0
1
2
1
1
3
0
1
1
0
0
0
1
1
2
0
1
0
0
1
1
1
1
1
1
1
2
0
0
0
2
1
3
1
0
2
0
2
2
0
0
0
2
1
0
0
1
1
0
0
2
1
2
2
1
2
0
1
1
1
0
1
0
0
2
0
1
0
2
1
0
2
2
1
2
2
2
2
2
1
2
1
2
1
2
3
1
1
0
1
1
0
1
1
1
0
2
0
1
2
0
1
1
0
2
2
0
0
1
2
1
1
0
0
1
1
0
1
1
2
0
0
1
1
0
0
1
0
1
1
2
0
0
0
0
2
0
1
1
1
2
0
1
1
1
2
0
3
1
1
2
1
2
1
2
1
1
1
2
1
2
0
1
0
0
0
1
1
1
0
0
1
0
1
0
2
1
1
0
0
0
2
1
0
2
2
2
1
0
0
0
0
2
1
1
1
0
1
0
2
1
1
4
1
1
2
0
2
0
2
1
2
0
0
1
1
9
1
1
0
2
2
1
2
1
0
1
2
1
1
0
2
0
2
2
2
0
2
2
2
1
1
1
0
1
2
2
0
0
1
1
1
1
2
0
1
0
1
1
1
0
1
0
1
0
2
1
2
1
1
2
1
0
1
0
1
0
0
1
2
0
2
0
1
1
2
1
1
1
1
2
3
0
0
2
1
0
0
1
2
0
1
0
0
0
1
1
1
0
0
0
1
1
1
1
0
1
1
2
1
1
1
1
1
1
2
2
2
1
2
1
0
1
2
1
1
2
1
1
0
2
2
1
0
0
0
0
0
1
0
2
1
2
0
1
2
1
0
1
0
0
0
0
1
1
2
1
0
1
1
2
1
0
1
1
1
1
2
1
1
1
2
1
1
2
1
1
1
2
1
1
1
0
1
2
0
2
0
1
1
1
0
0
2
1
1
2
1
1
0
2
1
1
3
0
2
0
0
0
2
0
1
1
1
1
0
1
1
2
1
1
1
1
0
1
1
1
1
2
1
1
1
1
1
1
1
0
2
2
2
1
1
2
2
1
1
1
3
2
0
0
1
1
1
1
1
1
0
2
0
0
1
1
1
2
1
1
1
1
0
0
1
0
0
0
0
1
1
0
1
1
1
0
1
1
2
0
2
0
1
0
0
1
0
1
1
0
0
1
1
3
1
3
0
2
1
6
4
0
1
1
1
0
0
2
2
1
0
1
0
0
2
0
3
1
2
1
1
0
1
1
1
1
0
0
1
1
1
0
1
1
0
0
0
0
1
1
0
1
1
0
2
1
1
0
1
1
0
0
0
0
0
1
1
0
2
1
1
1
1
1
1
1
2
0
0
1
2
0
1
1
0
2
1
2
0
1
0
0
0
1
0
0
2
1
1
0
1
0
2
0
1
2
2
2
2
1
2
1
2
1
3
1
2
1
2
1
1
1
1
0
1
2
2
1
1
1
1
1
1
0
0
2
2
0
1
0
1
0
0
1
2
1
1
1
1
0
0
0
1
1
0
2
1
1
2
0
1
0
1
2
1
0
1
0
0
1
0
0
0
0
1
1
0
1
1
2
0
1
1
0
0
1
1
2
0
1
0
1
2
0
1
1
1
0
1
2
1
2
2
1
2
1
0
1
1
1
1
1
1
1
0
2
1
1
1
2
2
2
2
0
1
2
0
0
1
1
1
0
2
2
1
2
1
2
1
1
0
0
0
0
0
0
2
1
1
0
1
1
0
1
1
1
1
1
2
0
2
0
2
1
1
0
1
1
1
2
1
1
3
0
1
1
2
1
2
1
1
1
2
0
1
0
1
0
1
1
1
1
1
1
1
0
1
0
1
0
1
1
1
0
1
3
1
1
1
0
1
1
2
1
2
0
0
2
0
1
1
1
1
0
2
0
2
1
1
0
2
1
1
0
2
1
2
1
2
0
2
1
3
1
0
0
2
1
1
1
1
1
0
1
1
0
0
1
2
1
0
2
2
1
0
0
2
2
2
2
1
0
0
2
2
1
0
2
1
2
1
2
1
2
1
1
0
0
2
2
0
1
1
1
1
1
0
1
1
1
0
0
2
2
0
2
1
1
0
0
0
0
0
6
1
1
0
0
0
0
0
2
1
0
2
1
1
0
1
1
1
1
0
2
1
2
0
1
2
2
0
0
0
1
2
0
0
1
0
0
2
1
1
1
2
3
0
1
1
0
1
2
1
0
0
1
1
3
0
2
1
1
2
1
0
2
2
1
0
2
1
1
1
2
1
1
0
1
1
1
0
1
1
0
0
1
2
0
1
2
1
0
1
0
1
1
0
2
0
1
1
1
1
1
2
2
1
0
0
0
2
1
0
1
0
0
1
2
1
1
1
0
0
0
2
1
0
1
0
0
1
1
0
1
1
2
3
1
1
0
1
0
0
1
1
1
1
1
1
2
2
2
0
1
1
1
1
1
2
0
1
2
1
2
0
3
1
1
1
0
1
0
1
2
1
1
0
2
1
0
1
1
1
1
1
1
0
1
1
0
1
2
1
0
1
0
0
1
1
0
1
2
1
1
1
2
1
2
0
1
2
1
0
1
2
1
1
1
1
1
1
1
1
2
1
2
1
1
0
1
1
0
0
1
1
2
1
1
2
1
1
1
0
0
2
1
1
0
0
0
1
1
0
1
0
1
0
1
1
0
1
1
1
1
2
1
1
0
0
0
0
2
1
2
1
2
1
1
2
1
1
2
0
1
1
3
1
1
0
1
1
1
0
2
0
2
2
0
2
2
1
1
2
1
2
0
0
1
0
1
2
2
1
1
1
1
1
3
0
0
1
0
0
0
1
1
1
1
0
2
0
0
1
2
0
1
0
0
1
0
2
1
1
2
1
0
1
1
1
0
1
0
2
2
0
0
1
0
2
1
0
1
2
0
0
2
1
1
2
3
1
2
1
2
1
1
0
1
1
2
2
2
1
2
2
1
0
1
0
0
1
0
1
1
1
1
1
1
2
2
3
1
2
1
1
1
1
1
0
1
1
0
0
2
1
1
2
2
1
1
0
1
1
1
0
1
1
2
4
1
1
0
0
0
0
0
2
1
1
1
1
0
2
0
0
1
1
2
1
1
1
1
1
0
1
1
1
1
0
1
1
0
1
0
0
1
2
0
2
2
1
1
1
1
1
1
0
1
0
2
1
1
2
3
1
1
1
1
2
1
2
2
0
1
1
1
2
0
0
1
0
1
0
2
1
2
1
0
2
2
1
0
1
1
0
2
2
2
1
1
1
1
1
3
0
1
2
1
0
1
1
2
2
2
0
2
1
2
0
2
1
2
2
1
1
0
2
2
1
0
2
2
0
0
2
2
1
0
1
1
1
1
0
2
1
1
0
1
1
1
1
0
0
1
0
1
1
1
1
1
1
0
0
1
1
1
1
1
1
0
1
1
1
1
1
2
1
0
1
2
1
0
0
0
0
0
2
1
1
2
1
1
1
1
1
1
2
0
2
1
1
1
2
2
2
1
2
0
1
1
0
1
0
1
0
2
1
2
1
0
1
2
1
1
1
1
0
2
2
1
2
2
1
0
0
1
1
2
1
0
1
0
0
2
0
1
1
1
1
1
0
2
2
2
1
0
0
1
2
0
1
1
1
1
0
1
1
1
1
0
1
0
2
1
1
0
0
1
2
0
0
0
0
1
1
0
0
1
0
3
0
1
1
2
1
0
1
0
2
0
1
1
0
2
1
2
1
1
1
0
0
1
2
0
0
1
2
1
2
0
2
0
0
1
0
2
1
2
0
0
1
1
0
1
1
1
2
0
1
1
2
1
1
1
0
0
0
2
1
0
1
2
0
0
1
1
0
1
1
1
1
1
2
2
6
1
1
2
1
1
2
1
1
1
1
1
1
0
1
1
0
1
1
2
1
1
1
0
1
2
0
1
0
0
1
2
0
1
0
0
0
2
1
0
2
2
1
1
1
1
1
0
0
1
2
0
1
2
1
1
1
1
1
2
0
1
1
1
1
2
1
1
1
2
0
1
1
1
2
0
1
1
1
1
2
1
0
2
0
0
1
1
1
0
0
0
1
0
0
1
1
1
3
2
2
1
1
0
0
2
0
1
0
3
1
1
0
1
1
2
1
1
1
0
1
1
1
1
2
1
0
1
0
0
1
0
2
2
0
0
3
2
1
1
2
0
2
1
0
0
1
1
0
2
0
1
0
1
1
2
1
1
1
2
0
0
1
2
1
1
0
1
2
1
2
1
1
1
1
1
2
1
2
1
0
0
0
1
1
0
1
1
1
0
0
1
0
0
2
3
1
1
0
1
1
0
1
1
1
1
2
2
1
1
1
0
2
2
1
1
1
1
0
2
1
1
1
1
0
1
1
0
1
1
1
1
1
2
0
1
0
2
2
2
1
0
1
0
0
1
2
1
0
1
0
1
1
1
1
2
1
1
2
1
1
1
1
3
0
1
0
1
0
2
0
2
1
1
1
2
2
2
0
2
1
1
1
1
0
1
2
1
1
1
1
0
2
2
2
0
0
2
1
0
2
1
2
0
1
1
2
1
1
2
1
1
1
1
1
0
1
2
1
1
0
2
2
0
1
1
0
0
1
0
1
1
2
1
0
0
1
1
0
0
1
2
1
1
1
0
2
1
2
1
0
1
0
1
0
2
1
1
1
0
0
0
2
1
2
1
1
1
1
0
1
2
1
1
0
0
1
0
0
1
1
2
1
1
1
2
0
1
0
0
0
1
1
2
1
1
2
1
1
1
1
2
1
1
0
1
2
1
1
1
1
0
0
1
2
1
1
1
1
2
1
1
2
0
0
1
1
0
1
0
1
1
0
3
2
2
0
0
1
1
2
0
1
1
1
0
0
0
0
1
0
0
1
1
1
0
0
0
2
0
3
1
1
1
2
0
0
0
1
1
2
0
1
2
1
1
2
0
2
1
0
2
1
5
0
1
1
1
2
0
0
1
1
2
2
1
1
0
1
1
2
1
0
0
0
1
1
0
2
1
0
0
1
0
0
2
1
3
1
2
0
1
1
1
2
2
1
0
1
1
1
3
1
0
0
0
2
0
0
2
1
1
2
1
3
0
1
1
0
2
1
3
1
0
2
2
1
1
0
1
2
0
0
0
0
0
1
0
1
1
0
1
1
2
0
2
1
2
3
1
1
0
1
1
1
1
1
0
1
2
0
0
1
0
1
0
0
0
1
1
1
2
0
1
0
1
1
0
1
2
1
1
1
1
1
2
0
2
1
1
1
1
0
1
2
1
0
1
0
1
1
1
0
3
2
0
2
1
0
1
1
1
0
0
1
2
0
2
0
1
2
0
0
1
2
2
1
0
2
0
1
0
1
0
2
2
1
2
2
0
1
1
0
0
1
1
1
0
1
0
0
1
1
1
1
1
1
1
2
1
0
1
2
2
0
1
0
0
0
2
0
1
1
2
1
2
1
1
1
2
1
0
1
1
1
0
3
0
1
1
1
1
0
1
1
1
0
1
1
1
0
2
1
0
1
0
1
0
0
1
1
0
0
0
0
1
1
2
1
1
0
0
1
0
1
2
0
0
1
1
0
1
1
0
1
1
1
2
1
0
1
2
1
0
0
0
4
1
2
2
1
0
0
0
1
0
1
2
1
1
1
0
0
1
0
1
1
2
1
0
1
2
1
2
0
0
1
1
2
1
2
2
0
0
0
0
0
0
1
0
0
0
2
2
1
0
0
1
1
1
0
0
0
1
0
1
2
0
1
0
1
1
1
0
0
1
1
0
2
0
1
0
0
1
1
2
1
1
0
3
0
2
0
0
1
0
1
0
1
1
1
2
3
0
1
0
2
1
1
2
1
1
0
1
0
1
0
1
1
0
1
0
2
0
1
1
0
1
0
2
1
1
1
0
2
2
0
0
0
1
1
1
2
1
0
0
0
0
1
1
0
1
1
1
2
2
1
0
1
2
1
2
1
1
0
1
0
2
2
0
0
0
2
1
2
2
1
1
1
0
1
2
2
1
1
1
1
1
1
1
0
2
0
2
0
2
0
1
1
1
0
2
1
2
1
2
1
1
1
1
1
2
0
0
1
2
2
1
1
0
1
2
1
1
1
2
1
1
0
1
1
1
2
2
0
2
2
1
1
1
0
1
0
1
0
2
1
2
1
1
0
1
1
3
1
2
1
1
1
2
2
1
1
1
1
0
2
0
1
1
1
2
1
1
1
0
0
0
2
1
1
1
2
2
1
1
0
0
2
0
1
1
1
2
1
0
1
0
1
0
1
0
1
1
1
0
2
0
0
1
1
1
1
0
1
2
1
1
1
0
0
2
2
1
1
1
2
0
2
0
1
0
1
2
0
1
1
2
1
0
1
1
2
1
1
0
1
1
0
2
2
2
2
1
0
2
1
1
2
2
0
2
1
0
1
0
2
0
1
2
0
1
2
2
2
2
1
0
1
1
1
1
1
0
1
0
2
1
1
1
1
1
1
2
2
2
1
1
1
1
1
0
0
3
2
1
0
1
1
0
1
1
1
0
2
1
2
0
0
2
1
1
1
1
2
0
0
0
1
2
1
1
2
1
1
1
1
0
2
1
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
3
4
2
1
0
2
1
1
1
0
0
0
0
0
1
1
1
2
2
1
2
1
0
1
0
0
0
1
2
2
0
1
1
0
0
2
1
1
2
1
0
1
2
2
1
1
1
2
0
2
1
1
0
0
0
1
1
0
0
0
1
1
1
1
1
1
1
2
2
0
0
1
1
0
1
1
0
1
1
2
1
1
1
2
0
0
1
0
0
1
0
2
1
0
0
1
2
0
1
2
1
1
1
2
1
2
1
1
1
2
1
0
1
1
0
0
1
1
1
1
1
2
1
1
1
1
2
0
1
2
2
1
0
1
1
1
2
1
2
1
0
2
0
0
1
1
1
0
1
1
1
0
1
2
0
2
1
1
2
1
1
0
1
2
0
0
0
2
1
1
0
1
1
1
0
1
1
3
1
0
2
1
2
0
2
1
1
1
0
0
0
1
0
1
2
1
1
2
1
1
2
0
2
1
1
2
1
0
1
2
2
0
1
1
0
1
1
0
1
1
1
0
1
0
2
1
2
2
0
2
0
0
1
1
0
1
0
1
1
1
0
2
0
1
0
2
2
2
1
1
0
1
1
0
0
1
1
2
1
1
1
1
1
1
1
1
2
1
2
2
0
2
0
1
0
0
1
0
0
1
1
0
1
2
2
0
1
1
1
0
2
0
1
0
0
1
0
1
1
2
1
1
2
1
0
1
0
0
1
1
0
0
1
0
1
0
0
0
1
1
1
0
0
1
1
0
1
1
0
2
1
0
1
2
0
1
1
0
5
1
2
0
2
2
0
1
1
2
1
1
0
0
0
0
0
2
0
0
2
2
1
1
3
1
2
1
2
1
0
1
1
1
1
1
1
0
1
0
1
1
1
1
1
1
0
1
0
2
2
1
2
1
2
0
1
0
0
0
1
1
1
0
1
0
0
2
1
0
1
2
0
2
2
1
0
1
1
0
2
2
2
0
1
1
1
0
1
0
1
1
1
1
1
1
0
1
1
1
1
2
1
1
0
1
2
1
1
0
1
2
1
1
1
1
0
0
1
1
0
0
1
0
0
0
0
1
1
2
2
1
0
0
1
1
1
1
1
1
0
3
0
2
2
0
1
1
0
1
0
0
2
1
1
2
2
2
2
1
1
0
1
1
1
0
2
1
0
1
1
1
0
1
1
2
1
1
1
0
1
0
0
1
1
0
1
1
2
3
2
1
0
3
2
0
1
2
1
1
2
1
0
1
2
1
1
0
1
1
1
1
1
1
1
0
0
1
2
1
2
1
0
2
1
0
1
1
0
1
1
1
0
0
1
0
3
0
2
0
1
0
1
1
1
2
1
1
0
0
1
0
1
0
1
1
0
1
0
0
1
2
1
1
1
1
1
1
0
1
1
2
1
1
2
1
0
1
1
2
1
1
1
1
2
1
0
1
2
0
1
0
2
1
2
1
0
1
0
1
2
2
0
1
1
0
2
0
1
0
1
2
2
0
2
2
1
0
1
1
1
1
1
1
1
0
0
1
0
1
1
1
1
1
2
1
0
1
1
1
0
1
1
1
1
0
0
1
1
0
2
1
0
1
3
1
1
2
1
3
0
1
1
0
0
1
0
2
1
1
1
1
1
2
1
1
1
2
1
1
2
0
2
0
1
3
1
1
1
0
0
0
2
2
2
0
2
1
2
0
2
1
1
1
1
0
1
0
0
1
0
0
0
0
0
1
1
1
0
0
2
1
0
1
2
2
1
0
2
1
2
0
2
2
1
0
1
0
1
0
1
1
1
0
1
1
2
1
1
0
1
2
0
1
0
0
3
2
0
1
1
2
1
2
0
0
1
1
0
1
3
0
0
1
1
1
2
2
0
1
0
1
1
1
1
1
2
2
1
0
1
2
3
0
2
1
1
2
2
1
1
0
3
0
0
0
0
2
1
1
0
0
0
1
1
2
1
1
1
0
0
0
0
1
0
0
0
1
1
0
0
2
1
2
1
0
1
0
0
1
1
3
2
1
0
0
1
1
2
1
1
0
1
1
0
0
1
2
2
1
1
1
2
1
0
1
1
1
1
0
2
0
1
1
0
1
2
2
0
0
1
1
1
0
2
1
1
0
3
0
2
1
2
1
1
2
2
1
0
1
1
0
1
0
0
1
0
2
0
1
0
1
1
0
2
1
0
1
1
2
1
1
2
1
0
1
1
1
1
1
2
1
1
1
1
0
0
1
2
0
1
1
2
1
2
0
1
1
2
0
1
1
1
1
0
1
1
2
1
0
0
0
0
1
2
0
1
0
0
1
2
0
1
0
0
0
1
0
2
2
1
1
2
1
1
1
2
1
0
1
1
0
1
1
1
0
0
3
1
1
1
1
1
2
0
0
1
1
2
1
1
2
1
0
1
1
0
1
1
0
1
1
1
1
2
1
2
1
1
2
1
1
1
1
1
1
1
0
1
0
1
1
0
1
1
1
1
1
2
0
2
1
2
1
0
1
2
1
0
1
2
2
2
1
1
1
1
2
2
0
0
1
1
1
2
0
0
1
1
1
1
0
2
2
2
0
0
1
1
1
0
1
1
1
1
1
2
0
1
0
2
2
0
1
0
1
1
1
2
1
0
1
1
1
0
2
0
2
1
0
0
1
1
1
1
0
1
1
1
1
0
0
0
0
0
2
2
0
0
1
1
1
0
0
2
1
0
1
0
2
2
2
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
1
1
0
0
1
2
1
1
2
1
1
0
1
0
0
1
1
0
2
1
1
1
2
0
0
1
0
3
1
1
1
0
0
2
2
0
1
0
1
2
0
2
1
1
1
2
1
0
1
1
2
2
0
3
1
1
0
0
0
2
1
1
1
1
0
2
2
2
0
0
1
1
0
1
0
2
1
0
2
1
2
0
1
1
1
2
1
0
1
2
1
1
1
0
0
1
1
2
0
2
1
1
1
1
1
1
0
0
1
1
1
1
0
1
0
1
2
0
1
1
1
1
0
1
0
1
1
1
1
1
1
1
1
1
1
1
1
0
1
0
1
1
1
1
2
1
1
1
1
1
1
1
0
0
1
0
0
0
1
2
1
1
2
1
1
1
0
0
1
3
1
1
2
2
1
0
1
2
2
2
0
2
2
1
2
0
1
1
0
0
0
0
1
0
1
0
1
1
1
2
1
2
1
1
1
1
1
0
1
1
0
1
2
1
1
0
2
1
2
2
1
2
1
1
1
1
0
0
2
0
1
1
2
1
0
1
0
1
2
2
1
1
1
2
2
0
0
0
1
1
1
1
1
0
2
2
1
2
1
1
0
0
1
0
0
1
2
0
0
1
1
1
1
1
1
2
1
1
2
2
0
2
1
1
0
2
1
1
1
2
0
0
2
2
1
1
2
0
0
2
2
2
1
1
1
0
0
1
2
0
0
1
0
0
0
1
0
2
1
1
0
1
2
1
1
0
2
0
2
1
0
1
1
2
1
1
1
2
0
1
0
0
1
0
1
1
3
0
2
1
2
1
2
1
2
2
2
1
1
1
0
1
1
1
1
0
1
0
1
1
0
1
0
1
0
2
1
1
1
2
2
0
1
1
3
0
1
1
0
1
2
1
0
1
1
1
1
1
2
1
2
1
2
1
1
1
1
0
0
2
1
1
1
1
1
2
2
2
1
0
0
0
1
1
0
0
2
1
1
0
2
1
1
2
1
0
1
1
1
0
1
1
1
1
2
1
1
1
2
1
2
1
1
1
1
1
0
5
0
1
0
1
1
2
0
0
1
1
2
1
2
0
1
1
0
0
2
0
1
0
2
0
2
0
1
0
0
2
1
2
1
2
2
0
0
2
0
1
0
1
1
0
0
2
0
1
0
1
0
2
0
0
2
1
0
0
0
0
1
1
1
0
1
2
1
2
0
1
0
1
1
0
1
1
0
2
2
1
2
0
2
0
0
1
1
1
1
1
1
1
1
2
1
1
1
0
0
0
2
1
2
4
2
1
1
0
0
1
2
1
2
2
1
1
2
0
0
0
1
0
1
1
0
1
1
2
0
0
1
2
2
1
1
2
0
0
1
2
2
2
1
1
0
1
2
2
1
1
1
2
0
1
0
2
2
0
1
2
1
1
1
0
2
2
1
2
1
0
1
1
0
1
0
2
1
0
1
2
0
2
0
2
1
2
1
1
0
1
2
1
1
1
0
1
1
0
0
1
1
0
0
0
2
1
2
1
1
2
2
2
1
2
1
0
1
1
2
2
1
1
0
0
1
1
1
2
0
1
1
1
2
2
0
2
1
0
2
1
0
2
2
2
1
1
0
0
1
1
1
0
0
0
1
1
1
1
0
2
1
1
0
1
1
1
2
1
0
0
1
0
1
1
1
1
2
0
1
0
0
1
2
1
2
1
0
1
3
0
2
1
0
1
1
1
1
1
1
1
0
0
2
1
1
2
1
0
1
1
0
1
1
0
2
1
2
1
0
0
1
0
1
2
0
1
0
1
1
2
1
0
1
1
1
0
0
1
1
1
1
2
0
2
1
1
1
2
1
2
0
0
1
1
1
0
1
0
1
1
0
1
1
2
1
2
0
0
0
0
2
0
1
0
0
0
2
2
0
0
1
1
1
1
1
2
2
0
1
2
0
0
1
1
1
2
1
1
3
1
1
2
2
2
0
2
2
2
4
1
2
1
1
1
1
0
1
1
1
1
1
1
0
0
0
1
2
1
0
2
1
0
0
2
0
0
1
0
2
2
0
2
0
1
0
1
2
0
0
1
1
1
0
2
0
2
2
0
0
1
1
0
0
0
2
0
1
0
0
1
1
2
2
1
0
1
1
0
1
1
1
1
1
0
0
1
1
1
0
1
1
1
2
2
1
1
0
1
2
1
2
2
0
1
0
1
0
0
0
0
1
0
1
1
1
0
0
0
1
0
0
0
0
2
0
1
0
1
2
1
2
0
1
1
0
1
1
1
1
2
0
1
0
1
2
0
0
2
1
1
0
4
2
0
0
4
1
0
1
1
1
1
0
0
1
1
2
1
1
0
0
0
1
1
2
2
2
2
2
1
1
2
1
2
1
1
1
1
1
0
1
1
0
1
1
0
2
0
1
0
1
1
1
0
0
1
1
0
0
1
2
2
1
0
1
1
2
1
1
0
0
2
1
0
2
0
1
0
0
1
0
2
1
2
0
1
0
1
1
2
1
1
1
0
2
2
1
1
1
1
1
1
1
0
2
1
2
1
1
2
0
1
0
1
1
1
0
1
2
0
1
1
2
1
1
0
0
1
0
0
0
1
0
1
2
2
0
2
0
3
2
2
0
1
2
1
0
0
1
1
2
1
2
0
2
1
1
1
1
1
0
3
0
0
0
1
1
0
1
3
1
1
1
0
0
2
0
2
0
2
2
0
1
0
1
1
1
4
0
1
1
1
1
1
1
2
2
0
1
1
1
1
1
0
0
0
1
0
1
1
0
1
2
0
1
0
2
0
2
1
1
1
1
2
2
1
0
1
1
1
1
0
1
1
0
2
2
1
2
2
0
0
1
1
0
1
1
0
1
0
1
1
0
1
2
1
1
0
1
0
0
2
2
2
0
0
2
2
0
1
1
0
1
1
0
2
2
1
0
2
1
1
0
1
0
0
0
0
0
2
1
0
2
2
0
1
1
1
2
1
0
1
1
0
2
1
1
1
0
0
2
1
1
1
2
2
1
1
0
0
3
2
0
1
1
2
0
1
2
1
2
3
1
0
2
1
2
1
3
2
1
0
0
1
2
1
1
0
2
1
0
0
1
2
2
1
1
2
1
1
1
1
0
1
0
2
1
1
2
1
1
0
0
1
1
2
1
1
1
1
1
2
0
1
0
0
1
2
1
1
1
1
2
1
0
1
1
1
2
1
2
0
1
1
0
1
1
0
0
2
2
0
3
1
1
0
0
0
0
0
2
1
1
2
1
2
2
1
1
0
0
1
2
0
1
2
1
1
1
0
3
0
2
0
0
2
1
1
1
0
1
1
1
1
1
0
0
0
1
1
1
2
1
2
1
1
0
2
2
1
2
1
1
1
1
1
1
0
1
1
1
1
0
1
0
1
1
1
2
1
1
2
0
0
0
0
0
4
1
0
0
1
1
0
2
1
3
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
1
1
1
1
0
1
1
1
2
0
2
0
2
3
1
0
1
0
0
2
1
1
0
2
1
1
1
1
2
2
0
1
1
0
0
0
1
1
1
1
1
1
0
0
1
2
1
0
1
2
2
2
1
0
0
0
0
0
1
1
1
1
1
0
0
1
0
0
1
1
1
2
0
0
1
0
0
1
2
0
0
2
0
1
1
0
1
1
1
0
0
0
1
0
1
0
1
0
2
0
1
1
0
1
0
1
2
2
1
2
1
1
1
0
1
1
1
1
0
0
1
2
0
1
1
1
2
1
1
2
0
0
1
2
1
2
2
0
0
0
2
1
1
1
1
0
2
2
1
0
1
1
1
1
1
1
0
2
0
1
2
2
1
1
1
1
0
1
1
0
1
2
0
1
1
0
2
0
0
1
0
2
0
2
1
1
2
1
0
1
1
1
1
1
0
2
1
2
1
0
2
1
2
1
1
0
0
0
1
0
0
0
1
2
1
0
1
0
1
1
1
1
0
1
2
1
1
3
2
0
0
2
1
1
0
0
1
1
0
1
1
2
0
2
1
1
2
1
0
2
1
1
0
2
1
1
2
0
3
0
0
2
2
1
0
2
1
1
1
2
0
2
2
1
0
2
0
1
1
2
1
0
1
0
1
1
2
1
2
2
1
1
1
1
1
1
2
2
1
0
1
1
1
0
0
1
1
2
1
0
0
1
2
1
1
0
0
1
2
1
0
2
2
2
0
1
0
2
0
1
1
2
0
2
1
1
0
0
1
1
1
2
0
2
1
0
1
1
0
1
0
2
1
0
0
1
0
1
1
0
0
2
0
1
0
1
1
0
1
2
0
1
0
1
1
2
1
1
1
1
0
1
1
1
0
0
2
2
1
0
1
1
2
1
0
0
1
0
1
0
0
0
1
1
1
0
0
1
2
2
2
1
3
1
1
1
2
1
2
0
0
1
2
0
0
1
2
1
1
1
1
1
0
0
1
1
0
0
0
1
2
2
1
1
2
1
3
2
1
1
0
1
1
1
0
0
1
2
0
1
1
0
1
1
1
2
1
0
1
0
1
2
1
1
2
2
1
1
2
0
0
1
1
1
1
0
0
1
2
2
0
1
0
1
2
2
1
0
1
1
1
3
2
1
2
0
1
1
1
1
2
0
2
1
0
0
2
2
2
1
1
0
1
1
1
1
0
1
0
0
1
0
0
0
1
2
0
0
0
1
0
3
0
1
2
2
1
2
1
0
0
0
1
1
1
4
2
1
1
0
1
1
0
0
1
0
0
1
0
0
1
0
0
0
0
2
1
0
1
2
0
2
1
2
2
2
0
1
0
0
1
0
0
1
2
1
1
1
1
2
0
0
2
1
0
1
0
1
1
0
0
1
1
0
1
1
1
0
1
2
1
1
2
2
2
2
1
0
2
2
2
2
1
1
0
1
3
1
0
2
0
0
0
1
1
2
0
1
2
1
2
0
1
1
1
1
1
0
0
1
1
1
0
1
1
2
0
2
1
1
0
1
0
1
1
0
2
1
0
1
1
2
0
3
1
1
1
1
1
2
1
1
0
0
1
1
1
2
2
0
2
2
1
2
1
1
0
1
2
0
0
2
1
1
1
1
1
2
1
0
2
0
2
1
0
0
2
0
0
0
0
2
1
0
1
0
1
1
2
1
2
1
4
0
0
1
1
1
3
1
2
1
0
1
1
0
0
1
0
2
0
2
1
0
1
0
0
2
0
2
1
2
0
2
1
2
2
0
2
1
1
1
1
0
0
1
1
0
1
1
0
1
2
2
0
2
0
0
0
1
1
0
2
1
1
1
2
1
0
4
1
1
2
0
1
0
2
2
1
0
1
0
1
2
0
1
1
2
1
1
1
1
1
1
1
2
1
2
2
2
0
1
0
1
1
1
2
0
0
1
1
1
2
1
2
2
1
2
0
1
1
2
2
1
2
1
1
0
1
1
1
0
2
1
1
1
0
1
0
1
1
0
1
1
1
1
1
2
0
1
2
2
1
0
0
1
2
2
0
0
0
2
1
2
0
1
1
1
0
1
1
0
1
0
0
0
1
0
1
2
1
1
1
0
1
0
1
1
0
1
1
1
0
1
0
1
1
1
1
1
1
0
0
2
1
0
0
0
0
1
0
1
1
1
1
2
2
2
2
1
1
1
0
0
0
1
2
1
1
1
0
2
1
1
1
0
0
1
0
1
0
2
1
1
1
1
0
1
0
1
2
0
0
0
2
1
1
0
1
0
2
2
1
1
2
0
1
1
1
0
2
1
0
1
1
2
1
0
2
1
1
0
2
2
1
1
1
1
0
2
2
1
1
1
1
0
1
2
1
1
1
1
0
0
0
2
1
1
1
0
1
1
1
1
0
1
2
1
2
1
2
2
1
2
0
1
2
2
0
1
0
1
0
1
0
1
0
0
0
1
1
1
0
1
2
1
1
0
1
1
1
1
0
1
1
2
1
0
0
1
2
1
1
0
1
0
1
0
2
1
1
1
1
1
0
2
1
1
1
0
0
1
2
2
1
2
1
1
1
2
1
2
0
1
1
1
2
2
1
2
0
0
0
2
1
2
2
1
0
2
1
1
0
1
0
1
0
2
0
0
0
2
1
0
1
1
1
1
2
1
2
0
0
1
0
1
1
2
1
1
0
1
4
1
1
1
0
1
2
0
1
1
1
1
1
1
2
1
1
1
0
2
1
1
0
1
2
2
0
1
1
0
2
0
2
0
0
1
1
1
0
1
1
1
1
1
1
2
1
2
2
1
1
2
2
1
1
1
1
2
1
0
1
2
2
0
1
1
2
0
1
1
2
2
2
0
0
1
0
2
2
0
2
1
1
1
1
1
1
0
2
1
1
0
1
1
2
2
1
1
1
0
1
1
2
1
0
1
1
0
1
2
1
1
0
1
0
2
1
1
1
1
0
1
2
2
0
2
1
1
1
1
0
2
0
0
0
1
0
1
2
1
1
0
0
1
0
2
0
3
0
0
2
1
1
2
2
1
2
1
1
0
1
1
0
0
0
2
1
1
2
1
1
2
1
1
1
0
1
0
1
1
1
0
1
0
2
2
0
1
1
2
2
0
0
0
1
2
2
2
1
2
0
1
1
2
0
0
0
0
1
1
1
1
1
0
2
1
0
1
0
0
3
0
2
3
2
1
2
2
1
0
1
2
1
1
0
0
1
2
0
1
1
2
1
1
3
0
1
0
1
1
1
0
0
1
1
0
2
1
1
2
1
1
0
0
1
0
0
1
1
0
0
1
1
1
0
0
2
0
0
1
1
2
1
1
1
0
3
1
1
0
0
1
0
1
1
2
2
0
0
2
1
1
1
1
0
1
2
2
2
0
1
1
2
0
0
0
1
1
1
2
1
1
0
2
1
1
1
1
0
1
2
1
1
1
2
1
1
0
0
2
1
1
0
1
2
2
1
0
1
0
2
2
0
1
0
1
1
1
1
2
1
1
1
1
1
1
1
1
0
1
0
1
1
1
1
1
0
0
1
1
0
2
0
2
1
2
2
0
0
1
1
1
0
0
1
1
1
0
1
1
1
2
1
1
0
0
1
1
1
0
0
2
0
0
0
0
1
2
2
1
0
2
2
2
1
1
1
1
1
1
0
1
5
1
1
0
1
1
1
1
0
2
1
1
2
0
0
2
0
0
1
1
1
1
1
1
0
2
0
0
2
0
2
2
1
0
1
2
0
0
1
1
2
0
1
0
0
2
1
1
2
1
0
1
1
1
0
1
1
1
2
0
0
1
1
1
0
0
0
1
1
0
0
1
1
0
0
0
1
1
0
1
0
2
1
0
1
0
2
1
0
1
1
1
2
0
1
1
1
0
1
1
1
0
0
1
0
0
1
1
2
2
0
1
0
1
1
0
1
0
1
2
2
1
1
1
0
1
1
0
0
1
1
1
1
1
1
1
2
0
1
1
1
2
1
1
2
2
1
1
2
0
1
1
1
2
0
1
2
2
1
1
0
0
2
1
1
0
0
1
1
0
3
1
1
1
2
0
1
0
1
0
1
1
0
2
1
2
1
1
1
0
1
2
1
1
0
1
2
1
2
1
0
0
2
1
2
4
1
0
1
0
0
1
1
1
1
0
0
1
2
0
2
1
0
0
0
0
0
2
0
0
2
1
1
2
1
3
2
0
0
2
1
0
0
2
1
1
0
2
2
1
2
1
0
1
0
1
1
0
0
1
1
2
1
0
0
1
2
0
0
0
1
2
1
1
2
2
3
1
1
1
2
0
0
0
1
2
1
1
2
1
1
1
2
2
0
1
1
0
4
2
0
1
2
0
1
0
1
2
1
0
0
3
1
1
4
0
1
0
0
2
1
1
0
0
1
1
2
1
1
0
1
1
0
2
1
0
0
2
1
2
1
2
1
1
1
1
1
0
1
1
1
0
2
1
1
1
1
1
1
1
0
0
3
0
1
0
1
0
0
0
0
1
1
0
0
1
1
3
0
0
1
1
2
1
0
2
1
1
0
1
1
1
0
0
1
1
0
1
0
0
1
0
0
1
1
0
1
0
0
1
0
0
1
1
2
0
1
0
0
1
1
1
1
2
1
2
2
1
1
0
2
2
1
2
2
1
1
1
1
0
0
1
0
2
1
0
0
0
2
0
2
1
1
2
0
0
2
1
2
2
0
1
0
1
1
1
2
1
0
1
0
2
0
0
0
1
2
0
1
1
2
2
0
0
1
0
1
2
0
0
2
0
2
1
1
0
1
3
1
1
0
1
0
0
0
1
1
1
1
1
0
0
1
1
1
0
1
1
2
2
1
1
1
1
0
1
2
1
1
1
2
2
1
2
1
0
1
1
2
2
2
2
1
1
1
1
0
0
1
2
2
1
1
0
0
1
1
1
1
2
1
1
1
1
0
2
1
0
1
1
2
1
2
0
0
0
2
1
2
1
1
1
1
2
2
2
1
1
1
2
1
0
1
0
0
2
0
1
1
1
0
1
1
1
1
2
1
2
0
3
0
1
1
1
0
1
1
2
1
1
0
2
1
1
0
1
1
1
0
1
0
1
3
0
0
0
0
0
0
1
1
0
2
0
2
0
0
0
1
1
1
1
1
1
1
2
0
1
2
2
1
0
1
1
2
2
1
0
2
0
0
1
2
0
3
1
0
1
0
0
1
0
1
1
1
2
2
1
2
0
1
0
0
2
0
1
1
0
1
0
1
1
2
3
1
2
1
0
1
2
2
1
1
1
1
0
2
1
2
1
2
2
1
0
1
0
1
0
1
0
2
0
1
1
0
1
0
2
2
1
0
1
1
0
2
2
1
0
1
1
2
1
0
1
1
2
2
0
1
1
1
2
1
1
2
1
0
2
0
1
1
1
0
0
2
2
2
0
1
1
0
1
0
0
0
2
2
1
2
0
0
1
1
2
1
0
1
0
2
1
1
0
2
1
1
1
0
0
1
2
0
1
1
1
2
0
1
0
1
2
1
2
1
1
0
1
0
2
0
1
1
0
0
2
1
3
0
0
4
0
1
2
1
1
2
0
1
0
1
1
1
2
0
2
2
1
1
2
0
1
1
3
2
1
2
1
1
0
1
0
0
2
1
0
0
1
2
2
1
2
1
0
0
1
0
3
1
1
0
1
1
2
0
2
1
0
1
1
0
1
0
0
1
1
1
0
1
0
1
0
1
0
0
2
1
0
1
1
1
2
0
1
1
1
1
0
1
2
2
0
0
1
1
0
0
1
1
1
0
2
0
1
0
2
1
2
1
1
1
1
1
2
0
1
2
0
2
1
2
1
2
2
1
0
1
0
0
1
1
0
1
0
0
1
0
1
0
1
1
2
0
1
1
1
1
1
1
1
0
0
1
2
2
2
1
2
0
1
1
1
2
0
2
1
0
0
0
1
0
1
0
2
1
1
1
2
1
1
0
0
0
1
0
0
1
0
1
1
1
0
2
2
2
0
1
0
2
0
1
2
1
2
0
0
0
1
0
1
2
1
0
0
2
1
1
2
1
0
0
2
0
0
0
0
0
0
1
0
1
1
1
1
2
1
1
2
1
1
1
2
0
2
1
0
1
0
1
1
1
1
2
2
1
2
1
1
1
1
0
1
2
0
0
0
2
0
0
1
2
1
2
0
0
1
1
1
1
1
0
2
1
0
0
1
1
1
1
1
2
0
1
1
2
2
0
0
1
0
2
1
2
0
1
0
1
0
1
2
2
1
0
0
1
1
2
0
1
1
0
1
3
1
2
1
1
0
2
2
2
0
2
0
2
0
1
2
3
2
0
1
1
2
1
0
0
1
1
1
0
1
2
1
1
1
1
1
0
0
2
1
1
2
1
1
1
2
2
2
2
1
1
0
4
1
2
0
1
1
0
2
1
1
1
0
1
1
1
1
0
0
1
0
2
2
0
0
0
2
0
2
1
1
1
1
1
2
0
0
1
0
0
1
0
0
2
0
0
1
1
1
2
1
2
0
1
0
2
0
0
2
0
2
1
2
2
1
0
0
1
1
2
1
1
1
0
0
2
1
2
2
1
1
2
1
0
2
1
1
2
2
0
0
1
0
0
1
1
0
1
1
1
2
2
0
2
1
0
1
0
2
1
0
1
0
1
1
1
1
1
1
2
0
1
1
2
2
0
2
1
1
0
2
0
2
2
0
0
2
2
0
0
0
1
0
1
2
1
0
2
1
2
2
2
2
1
1
1
0
1
1
1
2
0
1
1
1
1
1
2
1
0
1
1
0
0
0
1
1
0
0
2
0
2
0
0
2
2
0
2
0
1
1
1
1
1
1
2
1
1
1
2
1
4
2
0
0
2
1
2
1
2
1
1
1
0
1
1
0
1
0
2
1
2
1
1
2
0
0
1
1
2
2
0
1
0
1
1
1
2
0
1
0
3
2
0
1
1
1
0
1
2
1
1
1
2
1
1
1
1
1
0
2
1
0
3
1
0
1
0
0
2
2
0
2
2
2
2
0
1
2
0
1
0
1
0
1
2
2
0
1
1
1
0
1
2
1
1
2
2
2
1
1
1
0
0
0
0
1
1
2
0
0
0
1
0
0
1
1
2
1
2
1
0
1
0
0
1
1
1
0
3
1
1
2
1
1
1
1
2
0
0
2
0
0
0
2
0
1
2
2
2
0
1
0
1
3
0
1
1
2
0
1
1
1
0
2
0
1
1
0
1
1
1
1
2
1
1
1
0
1
2
1
2
1
0
2
2
2
1
1
0
2
1
0
0
0
2
2
1
1
1
1
0
1
1
2
2
1
1
0
1
1
2
2
1
2
0
2
1
0
2
1
2
1
1
0
2
1
0
1
2
1
2
1
2
1
2
1
1
1
2
2
1
1
0
1
0
1
2
2
1
1
1
1
1
0
2
1
0
1
0
1
1
2
1
2
2
1
0
1
2
0
1
2
1
0
1
0
2
0
0
2
2
1
1
0
1
2
1
1
0
1
1
0
0
1
0
0
2
0
0
2
1
1
1
2
1
1
1
1
1
2
1
2
1
0
2
0
1
1
2
0
1
0
1
1
2
1
2
0
0
1
2
1
0
1
0
0
1
2
2
2
0
1
1
1
2
2
1
0
1
1
1
0
2
1
0
0
0
0
0
1
0
2
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
2
1
1
1
2
2
2
0
1
1
0
1
0
1
0
1
1
1
2
2
2
2
1
2
1
0
3
0
1
2
1
2
0
1
0
1
0
1
0
1
0
0
1
2
1
2
2
2
0
2
1
0
1
1
1
0
1
4
2
0
2
1
1
1
2
0
0
2
1
2
1
0
1
1
1
1
1
2
0
1
2
0
2
0
0
0
1
1
2
0
1
0
1
1
2
2
1
1
1
1
1
1
1
1
2
1
1
2
2
0
0
0
1
1
1
2
2
1
1
1
1
1
1
1
0
2
2
1
2
1
3
2
1
1
2
1
1
1
1
1
1
1
2
2
1
0
1
1
1
1
0
1
1
1
1
1
1
2
1
1
1
0
1
0
1
2
1
1
0
1
0
2
0
1
0
0
0
1
1
1
0
1
1
0
1
1
1
0
0
0
0
3
1
1
2
2
2
1
2
1
2
0
2
2
0
2
1
0
2
2
2
0
1
1
1
1
0
0
0
1
1
0
1
2
2
1
1
1
0
0
1
2
1
2
2
1
2
1
2
1
1
1
1
2
1
1
2
2
0
2
1
0
0
1
1
1
1
1
1
0
0
0
1
0
1
1
0
2
1
1
2
2
0
1
1
0
2
1
1
0
1
0
2
0
1
1
0
2
1
0
1
1
0
0
2
0
0
2
1
1
0
0
1
0
1
1
1
1
0
0
0
2
1
1
2
1
1
2
2
1
2
0
1
1
1
0
2
2
2
2
1
1
0
1
1
2
0
0
1
3
0
2
1
1
1
1
1
0
1
1
1
0
1
0
0
1
0
2
1
1
1
2
0
0
2
1
1
1
1
1
1
0
1
1
1
0
0
0
2
1
1
0
1
1
1
0
1
0
3
1
1
1
1
1
1
0
2
1
3
0
1
0
2
1
1
0
1
1
2
2
0
0
0
0
0
0
1
1
1
2
0
1
1
1
0
1
0
1
1
1
0
1
1
1
1
2
1
2
0
1
0
2
1
1
2
2
2
6
1
2
2
2
1
0
1
1
1
0
1
1
1
1
2
2
2
0
0
1
1
1
2
1
1
1
0
1
1
0
1
1
1
1
2
1
1
1
1
1
1
1
0
2
2
1
1
0
1
1
0
1
2
0
1
1
1
2
1
0
1
1
1
1
1
2
0
2
1
0
2
0
1
0
1
1
2
0
1
1
1
2
0
0
0
2
2
1
0
1
2
0
0
1
1
2
2
0
0
1
0
0
1
1
0
1
0
2
0
2
0
1
1
2
2
1
1
0
1
0
2
1
1
1
1
0
0
1
1
2
2
1
0
0
1
1
1
2
2
1
1
1
2
1
0
0
0
1
1
1
1
1
1
0
0
1
1
1
2
1
1
1
0
1
1
1
1
1
1
0
3
0
1
1
1
2
2
1
2
0
0
1
0
0
0
2
2
1
1
1
2
2
1
1
1
0
1
1
2
1
1
1
3
1
1
1
1
1
0
1
0
0
0
0
2
0
1
2
2
1
1
1
1
1
1
2
2
2
1
1
0
1
1
1
1
0
1
1
0
0
0
2
1
2
1
0
0
0
2
1
1
2
0
1
0
0
2
0
2
1
2
0
1
2
0
1
1
1
1
1
2
2
1
1
1
1
2
0
0
0
0
1
0
1
0
2
1
0
1
0
1
1
2
4
1
0
1
1
1
0
1
1
1
1
0
0
1
0
1
1
0
2
2
1
1
1
0
2
1
1
1
1
2
1
1
1
1
2
0
1
1
0
2
1
0
1
1
0
2
1
2
2
2
1
0
2
0
1
0
1
1
0
1
1
0
1
0
0
1
1
2
0
2
1
1
0
0
0
1
0
0
0
1
0
1
1
2
0
2
1
1
1
1
0
0
1
0
1
1
0
1
3
1
2
1
1
0
3
1
1
0
2
1
2
2
1
0
2
0
2
1
0
0
1
2
0
2
1
1
1
1
2
2
1
2
2
2
0
1
1
0
3
0
2
1
1
2
1
1
0
1
0
1
1
0
0
0
1
1
1
1
1
3
1
0
1
2
1
2
1
0
2
1
1
1
0
2
2
0
0
0
1
1
1
0
1
1
2
2
1
1
2
2
2
3
1
1
0
0
0
0
0
1
1
2
0
2
2
2
1
1
0
2
1
2
1
1
1
0
1
1
1
2
1
1
0
1
2
0
0
1
1
0
1
2
1
1
0
2
1
1
1
2
0
0
1
2
2
1
0
1
0
1
0
1
1
1
1
1
1
2
1
0
1
1
1
1
1
1
0
1
1
0
0
0
2
0
1
2
1
0
0
1
1
1
0
0
1
0
0
1
2
2
1
1
0
0
1
2
1
1
1
1
1
2
0
1
0
1
1
1
0
1
1
0
1
1
2
1
2
1
1
0
2
0
0
2
0
2
2
0
1
1
0
2
1
2
0
2
0
1
1
1
1
0
1
0
0
1
1
1
1
0
0
1
2
1
1
1
0
1
1
2
0
2
2
1
1
1
1
1
2
0
2
0
1
1
1
1
1
1
0
0
2
0
2
0
0
1
1
0
0
2
1
1
1
1
1
0
0
1
2
0
1
1
2
1
2
1
1
2
1
1
1
1
1
1
2
1
2
2
0
1
1
2
1
1
1
2
1
0
1
0
2
0
1
0
0
0
2
2
2
0
1
2
1
1
1
0
0
1
0
2
1
2
0
0
0
0
0
2
1
2
1
1
2
0
1
1
2
1
1
1
2
0
1
1
0
1
1
2
1
1
2
1
1
2
1
2
2
2
1
2
1
2
4
1
2
1
2
0
0
0
1
2
1
2
1
1
2
2
0
2
2
1
1
0
0
1
0
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
0
1
1
0
2
1
1
1
3
0
2
2
0
0
1
1
1
2
2
1
2
2
2
1
1
0
1
0
1
1
1
0
1
3
1
0
1
0
1
0
0
1
1
2
1
0
1
0
1
1
1
1
0
2
1
1
0
1
1
1
1
1
2
2
0
0
0
1
0
1
0
1
2
0
1
2
1
1
1
1
0
1
1
1
1
2
2
0
1
1
0
1
0
2
0
1
2
1
2
2
2
1
1
1
0
0
1
1
0
1
0
1
0
1
1
0
1
1
0
0
1
0
1
1
1
2
2
0
0
1
0
2
2
2
0
0
1
2
0
1
1
1
0
2
1
1
2
0
0
1
0
1
0
1
3
1
1
0
0
2
1
0
1
2
1
1
2
1
0
0
2
1
2
2
1
1
2
0
2
1
1
1
1
0
1
1
1
0
1
0
2
0
1
1
1
2
1
1
2
1
1
3
1
1
1
1
1
2
0
0
0
2
0
1
1
1
0
0
2
2
1
2
0
2
2
1
1
1
1
2
2
2
1
1
0
2
2
1
1
1
0
1
2
1
0
1
1
1
2
1
1
1
0
2
2
4
0
2
0
1
0
0
2
1
1
1
2
0
1
1
1
2
0
0
2
0
2
0
1
1
0
1
1
0
2
2
1
1
0
1
1
0
2
1
2
1
2
0
0
0
1
1
2
0
1
2
1
0
1
1
0
1
1
1
0
0
0
1
0
1
1
0
1
1
2
2
1
2
1
1
1
1
0
1
1
1
1
1
1
1
2
2
0
2
3
1
1
0
1
1
1
2
1
0
2
1
1
1
0
2
0
0
0
0
0
2
0
1
1
2
0
1
0
2
1
2
1
1
0
1
4
1
2
1
2
1
2
1
0
1
0
1
2
1
0
0
0
1
1
1
0
2
1
0
1
1
1
1
2
1
2
2
0
0
2
1
0
0
1
1
1
1
1
0
0
1
2
0
0
1
0
0
1
0
1
2
1
0
1
1
2
1
1
1
1
2
1
2
1
0
1
2
1
1
0
1
1
1
1
1
1
2
1
0
0
1
1
0
2
1
0
1
0
1
0
0
1
0
2
1
1
0
1
1
0
1
0
0
0
0
1
1
2
0
0
2
2
1
0
1
2
1
0
1
0
1
1
2
1
0
2
1
1
0
1
0
1
0
1
1
1
0
1
1
1
0
3
2
1
1
1
0
2
2
1
2
0
0
3
1
1
2
2
2
2
2
2
2
1
1
1
1
0
1
0
1
0
3
1
1
1
0
1
1
0
1
1
0
0
1
1
2
1
1
1
1
1
0
2
0
1
2
2
0
1
1
0
0
1
0
1
1
0
0
1
1
1
0
0
0
2
1
2
1
1
0
2
3
2
0
0
1
1
1
1
2
0
2
1
1
2
2
0
1
0
0
2
0
0
1
0
0
1
2
1
0
0
0
2
0
1
0
0
0
1
1
1
1
2
0
0
2
0
1
1
1
2
1
1
0
3
1
1
2
1
1
1
1
1
1
0
1
0
2
0
2
1
1
1
2
2
1
1
1
1
1
0
1
0
1
1
0
0
1
0
0
2
2
2
1
0
0
1
1
1
1
2
0
1
1
2
2
1
0
1
1
0
0
0
1
1
1
1
1
2
0
1
1
4
0
2
1
0
0
1
1
0
1
1
1
1
2
1
1
1
1
0
1
2
1
1
2
1
0
0
0
2
2
0
2
3
0
1
0
2
1
1
0
1
0
0
2
2
1
2
0
1
2
1
0
1
2
2
1
0
0
0
2
1
2
1
1
1
0
2
1
1
0
1
0
0
1
1
0
1
1
2
2
1
2
1
1
1
1
1
2
0
1
0
0
1
2
2
0
1
1
1
1
0
1
1
2
1
1
2
2
0
0
1
1
1
1
0
0
2
0
1
1
3
0
1
0
1
1
0
1
0
2
1
1
0
2
0
1
1
1
2
0
0
1
1
0
2
2
0
1
1
2
0
1
2
1
1
1
2
2
1
1
0
1
2
2
1
2
2
2
1
1
1
1
2
2
2
1
0
1
0
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
0
1
0
1
1
1
1
0
1
1
0
0
1
2
1
1
1
0
1
0
1
1
1
2
2
2
2
1
1
2
1
1
0
2
1
1
1
0
0
0
1
1
1
0
1
1
1
0
1
1
0
1
1
0
1
2
1
0
1
0
1
1
1
2
2
0
2
2
1
2
1
0
0
0
1
2
0
0
1
1
0
2
1
2
1
1
1
1
2
1
2
0
2
1
1
1
1
0
0
2
0
0
2
1
0
1
0
2
2
1
0
1
2
1
1
1
2
1
1
1
2
2
2
0
1
2
2
1
1
1
0
1
2
0
0
1
1
1
0
1
1
2
1
1
1
0
1
2
0
0
0
1
2
0
1
1
1
2
1
2
2
1
0
0
0
0
1
2
0
1
1
2
1
1
2
2
1
0
2
1
1
1
2
2
1
0
0
0
0
2
0
2
2
1
1
1
1
1
2
0
0
0
0
0
1
1
0
2
2
1
1
0
0
1
1
0
0
0
1
0
0
1
1
1
0
1
1
0
2
2
2
1
1
0
1
0
1
1
0
1
1
2
1
1
1
1
1
0
0
2
0
0
1
2
1
1
1
1
2
1
0
0
2
0
1
1
1
1
1
2
0
2
0
1
1
1
0
0
1
0
1
1
1
1
2
1
1
1
0
2
1
1
1
1
1
2
1
1
0
1
1
1
1
1
1
1
2
1
1
1
0
1
2
1
2
2
0
0
2
1
1
0
0
1
1
1
1
0
1
1
1
2
1
0
1
0
0
0
2
1
0
2
0
0
1
0
0
1
0
2
0
2
2
2
0
1
1
1
1
2
0
0
1
2
1
1
1
0
1
0
2
0
0
0
0
0
2
0
0
1
2
1
1
2
2
1
1
0
1
1
4
1
1
1
1
1
0
1
1
1
0
1
0
0
1
1
0
2
1
1
1
0
1
1
1
0
1
1
0
1
2
1
2
1
0
1
1
2
1
1
1
1
1
1
0
1
1
1
2
1
1
1
1
0
0
1
1
2
1
1
0
1
1
1
1
2
2
1
1
2
0
2
0
0
1
1
0
1
1
1
1
3
1
1
1
1
0
1
0
2
1
1
2
0
2
2
0
2
0
1
0
0
1
0
2
1
1
0
1
1
0
0
0
2
0
0
1
1
1
1
1
2
0
2
1
0
1
2
1
3
1
1
1
1
0
1
1
0
2
1
1
0
1
0
0
1
1
0
2
2
1
1
2
1
1
1
1
1
1
0
1
1
0
1
1
1
0
1
1
0
2
1
1
1
0
2
2
0
1
0
0
0
2
0
0
0
0
1
1
1
1
1
2
1
0
2
0
1
0
1
0
1
1
0
0
0
1
1
1
0
1
1
1
1
2
1
2
2
3
0
2
0
2
2
0
1
1
1
1
2
2
1
0
1
1
1
0
0
1
0
1
2
0
1
2
1
1
2
1
1
1
1
2
1
1
2
2
2
1
2
0
0
1
1
1
0
1
1
1
2
2
1
1
2
0
1
0
1
0
0
2
0
0
1
1
1
1
0
2
1
2
1
0
1
1
0
1
0
1
1
0
2
1
1
0
1
1
1
0
0
1
1
1
2
0
1
0
0
0
1
1
1
2
2
1
1
0
0
1
0
1
0
2
2
0
1
1
2
1
0
1
0
2
4
1
2
1
1
0
0
2
0
1
0
2
1
0
2
1
1
0
0
1
0
2
0
0
1
1
0
2
2
1
2
1
0
0
0
1
1
0
2
1
2
2
1
2
1
0
2
2
1
1
3
1
1
1
1
0
1
1
0
2
2
1
2
1
1
1
2
0
1
1
0
2
1
2
1
1
2
1
0
0
1
1
1
2
2
1
1
2
1
2
0
1
1
1
1
0
1
1
0
1
1
2
2
1
0
1
1
1
1
1
2
0
0
2
2
0
1
1
0
0
0
0
2
1
0
0
1
0
1
2
1
2
0
1
2
1
0
0
1
1
1
1
1
2
1
1
1
1
2
1
2
1
2
0
0
1
2
1
0
0
0
2
1
1
0
1
1
2
1
2
1
1
1
0
2
1
0
2
1
1
1
2
1
1
1
0
1
0
1
1
2
0
1
2
1
1
0
0
1
0
1
1
0
1
1
2
0
0
2
2
2
1
0
1
0
2
1
0
1
1
2
1
1
1
1
1
2
2
2
1
1
0
0
0
1
1
0
2
1
1
0
2
2
2
0
0
0
0
1
1
1
2
2
1
1
2
2
1
1
2
1
0
0
1
1
1
0
1
0
2
1
2
2
0
3
0
0
0
0
0
0
0
1
0
1
0
1
2
0
1
2
1
1
1
1
0
1
0
2
2
1
1
0
0
1
2
2
0
2
0
1
1
1
0
2
1
2
1
0
2
0
1
1
0
1
2
2
1
1
1
2
1
1
2
1
1
2
0
2
1
1
1
1
1
1
1
2
1
0
1
1
2
1
0
1
0
1
1
0
0
0
2
1
1
1
1
0
0
0
1
0
0
0
1
0
1
0
2
1
0
1
1
1
1
0
0
0
2
2
0
1
0
1
1
2
1
0
2
1
1
1
1
2
1
2
2
2
1
0
2
1
2
0
1
0
2
0
0
1
3
1
1
3
1
1
1
0
0
0
1
2
0
2
1
1
0
0
2
1
0
1
0
1
1
2
1
1
1
2
2
0
0
1
2
2
2
2
0
0
1
0
1
1
2
1
0
1
2
2
0
0
1
0
1
1
1
1
1
1
2
1
0
1
0
1
1
1
1
2
0
2
2
1
1
1
1
2
1
1
0
0
2
1
0
2
1
1
1
0
1
0
1
0
1
1
2
0
1
2
2
0
2
0
1
1
1
2
1
0
1
2
1
1
0
1
0
1
0
0
1
0
1
1
0
1
1
0
1
2
2
0
0
1
1
2
0
0
0
0
0
1
1
2
0
2
0
2
1
2
2
1
0
2
1
2
0
0
0
1
1
0
1
1
2
2
1
1
0
1
0
2
2
0
2
1
2
1
1
2
1
2
2
1
0
2
0
1
0
2
1
0
2
0
1
2
1
1
0
0
1
0
1
1
2
1
1
0
1
2
1
0
1
1
2
1
0
1
0
2
1
1
1
1
1
0
1
0
1
0
2
1
0
2
2
1
2
2
1
1
2
2
1
1
1
1
1
1
1
0
1
0
0
1
1
1
2
0
1
1
1
2
0
1
2
0
0
2
1
1
2
1
1
1
2
1
1
0
2
1
1
1
0
1
1
4
2
1
2
1
0
1
2
0
2
1
1
2
1
1
2
1
2
0
0
1
1
0
2
0
2
1
0
0
1
0
1
0
0
2
1
3
0
0
0
0
1
1
0
1
2
1
1
1
0
0
0
1
2
0
1
0
1
1
2
1
1
1
0
0
2
0
1
0
1
0
1
0
0
1
1
3
0
0
1
0
2
0
1
1
0
1
1
1
0
2
0
0
1
1
1
0
0
1
1
2
1
1
0
0
1
0
0
0
1
1
2
1
1
1
0
0
1
2
1
1
0
1
0
2
2
1
1
1
1
0
1
2
1
0
0
1
1
2
0
0
1
1
1
0
1
0
0
1
0
2
1
1
1
0
0
0
1
0
1
1
0
2
0
0
2
1
1
0
1
0
3
2
1
1
1
3
0
0
1
2
1
0
2
1
1
2
1
0
0
1
1
1
1
0
1
0
0
0
2
2
1
0
0
0
1
2
1
1
1
0
2
2
0
1
0
1
1
1
1
2
0
3
0
2
2
0
0
1
2
2
1
0
1
1
0
0
2
0
0
0
2
1
0
1
2
1
1
1
1
2
1
0
1
0
1
1
1
2
0
1
2
1
1
0
1
2
0
2
1
1
1
2
2
2
0
0
1
1
1
1
1
1
2
2
0
0
1
0
0
0
0
1
1
1
1
2
1
0
1
1
1
1
0
2
0
1
1
2
0
2
1
2
0
0
2
3
1
2
1
1
2
1
0
1
1
2
1
1
3
1
1
0
2
1
1
0
2
1
1
1
1
0
1
2
1
2
1
2
1
1
1
0
2
2
2
1
0
1
0
3
1
1
0
1
1
0
1
1
0
1
0
0
1
0
1
1
3
2
2
0
1
1
1
1
0
2
0
1
2
1
1
1
2
0
0
1
1
0
1
0
0
2
1
1
1
0
1
1
1
1
1
1
1
2
0
2
4
1
1
0
1
1
0
1
2
1
1
0
2
1
1
0
2
1
0
2
1
2
1
1
1
2
1
1
2
2
2
2
1
0
3
2
0
2
0
1
0
1
1
1
1
2
1
2
1
2
0
0
0
1
1
1
1
0
0
1
0
1
0
1
0
2
0
0
1
0
2
1
0
1
1
1
0
0
1
1
1
1
1
1
0
0
0
0
1
0
2
2
2
1
1
0
0
0
0
1
2
2
1
1
0
2
0
1
1
0
0
0
1
1
2
1
1
0
1
1
1
0
2
0
1
1
1
0
1
1
1
1
0
0
1
1
2
0
0
2
0
1
2
1
1
1
1
2
1
0
1
1
1
0
2
0
0
1
1
0
1
1
0
1
0
2
1
1
0
1
1
1
0
1
2
0
0
1
1
0
2
1
1
2
2
1
0
2
1
1
2
0
0
0
2
0
1
1
1
0
2
2
1
0
1
1
1
0
0
1
2
0
0
0
1
2
0
1
2
1
2
0
0
2
1
2
0
1
1
2
0
0
1
2
1
1
1
1
2
1
0
1
1
2
1
0
1
1
2
1
0
1
1
1
0
2
0
0
1
3
1
1
1
1
0
1
1
0
0
2
2
1
1
1
2
0
0
2
1
1
0
1
1
1
1
1
1
1
0
0
1
1
1
2
0
2
1
1
1
2
2
1
0
1
1
2
0
2
1
1
1
0
1
1
1
0
0
1
1
1
0
0
1
1
0
2
1
1
0
1
0
1
0
2
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
1
0
1
2
2
1
2
0
2
2
1
0
0
2
0
1
0
1
0
0
0
1
2
2
1
1
0
1
1
0
0
1
1
1
1
1
0
2
1
1
1
0
0
0
1
0
2
1
1
1
1
1
1
1
0
0
1
1
0
1
1
0
0
1
4
1
1
1
2
2
0
0
0
0
2
2
1
2
2
1
1
2
0
1
1
1
1
1
2
1
2
1
1
1
0
0
1
2
2
1
0
0
3
0
0
1
2
1
0
2
1
1
1
0
2
0
1
0
1
2
1
1
0
0
0
1
1
2
2
0
3
2
1
1
1
1
0
0
0
1
1
1
0
0
1
0
1
2
1
2
1
0
0
1
1
1
1
1
8
1
2
3
1
2
2
0
2
0
2
1
2
1
2
2
1
1
0
0
2
2
1
0
1
2
2
0
0
1
0
1
0
0
0
2
1
1
2
2
1
1
1
2
0
0
1
1
1
1
1
2
0
1
1
1
1
0
1
1
0
2
1
0
1
0
1
1
2
1
1
2
0
1
2
3
0
1
3
1
2
1
0
1
2
1
2
1
1
1
0
2
1
1
0
1
1
1
1
1
0
0
1
2
1
1
1
2
1
1
0
1
0
0
2
0
1
2
1
2
0
1
1
0
0
1
0
0
1
1
0
2
1
1
1
0
1
0
1
2
1
1
0
1
0
1
2
1
0
0
0
2
1
0
0
1
0
0
1
1
2
0
1
0
1
0
2
2
1
0
2
0
1
0
1
1
1
0
1
1
1
2
1
1
1
0
1
1
0
0
1
1
0
1
1
1
2
1
0
2
1
1
1
2
1
1
1
0
3
2
0
1
2
3
1
1
0
2
0
1
0
1
1
1
1
0
1
0
1
0
0
0
2
1
2
2
2
1
1
0
1
1
2
2
2
2
1
1
1
1
1
1
1
2
0
1
1
1
2
2
1
0
0
0
1
1
0
1
1
1
2
1
1
1
1
0
2
0
1
1
1
2
2
0
1
1
0
0
2
0
1
0
1
0
2
2
1
2
0
1
0
1
2
1
1
1
2
1
1
1
1
0
0
1
1
1
0
0
1
1
2
1
1
0
1
1
2
1
1
1
1
0
0
1
1
0
2
2
0
1
0
0
0
0
1
2
2
1
0
1
1
1
1
0
2
1
0
0
0
1
0
2
1
1
0
2
2
2
2
0
2
1
2
0
1
1
1
0
0
1
1
2
2
1
0
2
0
1
1
1
0
0
1
2
0
2
1
2
0
1
2
1
1
0
0
0
2
2
1
1
0
2
1
2
1
0
2
0
0
2
1
1
2
1
2
1
0
0
1
1
2
2
1
1
1
1
0
1
0
2
1
1
0
0
0
1
0
0
1
2
1
2
0
1
0
0
0
1
1
1
0
1
2
2
1
1
1
0
0
1
0
1
1
1
1
0
2
1
0
0
0
1
2
1
2
1
1
2
1
2
1
1
1
2
1
1
1
1
0
0
1
0
1
2
2
0
0
1
0
3
1
1
2
1
0
1
1
2
1
0
1
0
1
1
1
1
1
2
1
1
1
2
1
1
1
1
0
1
2
0
0
1
1
1
2
2
2
1
2
1
2
1
1
0
0
2
1
2
3
1
1
1
0
1
1
3
2
2
2
0
0
1
1
1
2
0
1
1
1
0
0
1
2
1
2
2
0
1
3
2
1
1
0
2
2
2
1
1
0
0
1
2
1
1
0
0
2
1
1
0
2
1
1
1
0
1
2
2
2
0
0
2
1
1
1
0
3
0
1
1
2
0
2
1
0
1
2
0
1
1
1
0
0
1
1
1
2
0
1
1
0
1
0
2
0
1
1
0
2
0
0
1
2
2
0
0
1
2
1
2
1
0
2
2
1
1
1
0
0
2
2
0
1
2
1
1
0
1
1
1
2
1
1
2
1
2
1
0
0
2
1
1
1
1
2
1
1
1
1
1
1
0
0
1
2
0
1
2
1
1
2
1
0
0
1
1
1
1
1
0
0
1
0
1
1
1
0
1
0
2
1
2
0
1
2
1
1
1
1
1
1
1
1
1
2
2
2
2
1
3
0
1
0
1
2
2
2
1
2
1
0
0
0
1
1
1
0
1
0
1
0
1
1
2
1
1
1
2
0
2
1
1
1
0
0
1
0
1
2
1
2
2
1
1
1
2
1
0
1
0
1
1
0
2
0
1
0
1
1
2
0
2
2
1
2
2
0
1
2
0
1
0
1
2
1
2
1
0
1
2
1
2
1
1
1
1
1
0
1
1
1
1
2
0
0
1
0
2
1
1
0
0
1
0
1
0
0
0
1
1
0
1
1
2
1
1
2
1
1
1
1
2
1
1
1
1
2
1
0
4
2
0
2
1
1
0
0
2
1
0
1
1
0
1
1
2
2
2
2
1
0
2
1
0
1
1
2
1
2
1
1
2
2
0
1
1
1
1
2
0
1
1
1
1
1
0
1
1
1
1
1
4
2
1
0
2
1
1
1
1
0
1
1
2
1
2
1
2
1
1
0
1
0
0
1
0
1
0
1
1
2
0
0
1
1
0
2
0
1
2
0
0
2
2
1
1
2
0
1
1
2
0
1
1
0
1
0
2
1
2
1
1
0
2
1
0
2
1
1
0
2
2
1
1
0
0
0
0
2
1
0
1
0
1
1
2
1
1
1
1
2
0
1
2
1
1
0
1
1
0
1
0
1
0
1
1
0
1
1
0
0
1
1
2
1
2
1
2
1
0
2
3
1
2
0
3
0
1
1
0
0
1
2
0
1
0
2
2
2
0
0
2
1
1
1
1
0
1
1
1
2
1
2
2
1
1
1
0
1
1
0
1
2
2
0
2
0
1
0
0
1
0
2
1
1
0
1
1
2
0
0
0
1
1
1
1
0
0
1
1
2
0
2
0
1
2
1
1
1
2
2
2
2
1
1
0
2
1
2
1
0
0
0
2
1
1
0
0
1
2
0
1
1
1
0
0
0
1
1
0
0
0
1
1
0
1
2
0
0
0
2
2
2
0
1
1
0
2
1
0
0
1
2
1
1
1
2
1
1
2
0
1
1
1
1
0
1
1
1
1
2
0
2
1
1
0
2
0
1
0
0
2
2
2
2
1
1
0
2
0
2
1
0
1
2
0
4
1
1
1
1
2
1
2
0
0
1
1
0
2
1
0
0
2
1
0
2
1
1
1
2
0
2
1
2
1
0
1
1
1
1
1
1
1
1
2
1
1
1
0
1
0
1
0
1
1
1
2
0
2
1
2
1
1
2
0
1
1
1
1
0
1
0
2
1
0
0
0
0
2
1
2
1
2
0
2
2
1
1
1
0
1
1
0
0
1
1
2
2
1
2
1
1
0
0
1
0
1
1
1
1
0
1
0
2
2
1
1
1
1
1
2
1
0
1
0
2
1
0
1
0
0
0
1
1
0
2
1
2
2
1
1
1
0
1
1
0
2
0
2
1
1
0
1
1
0
0
1
1
1
1
1
2
2
1
0
1
0
0
0
2
2
0
2
1
0
0
1
1
2
1
1
0
0
2
1
1
0
2
1
2
1
1
2
1
2
1
1
0
1
1
2
2
2
1
1
1
3
0
1
1
1
2
0
0
0
1
1
1
1
2
1
1
1
0
1
1
1
1
2
1
0
1
0
0
3
1
0
1
1
1
1
1
1
1
1
1
1
1
1
2
1
0
2
1
0
1
2
2
0
1
1
1
0
0
0
2
0
1
2
0
2
1
1
2
0
1
1
1
0
2
2
2
0
2
0
2
0
0
1
0
0
0
1
1
2
0
2
0
2
2
1
0
2
2
1
16
1
3
0
1
1
1
0
1
2
1
1
1
0
1
1
0
1
3
1
2
1
2
0
0
1
0
2
1
1
2
1
1
0
1
1
1
1
1
1
0
2
1
2
1
2
2
1
0
1
0
2
0
0
0
0
1
1
1
2
2
3
2
0
0
1
2
1
1
0
2
0
1
1
1
0
1
2
0
0
1
1
2
0
1
1
1
1
2
1
0
1
0
0
1
1
2
0
1
1
0
0
2
1
0
1
0
0
0
1
0
1
1
1
0
1
2
1
1
2
1
1
1
0
2
1
2
1
2
0
2
1
2
1
3
2
2
1
2
0
0
1
1
1
0
1
1
1
1
1
0
0
2
3
1
0
2
1
1
0
2
2
0
2
1
0
2
1
0
1
2
1
2
2
1
1
2
0
0
0
1
0
1
1
2
2
1
2
1
2
2
1
2
1
0
0
0
2
0
1
1
0
1
1
0
2
0
3
1
0
1
1
0
1
1
0
0
0
0
0
1
0
1
1
0
1
1
1
0
1
2
0
1
0
0
2
1
0
2
2
1
2
1
1
1
0
1
1
1
0
0
0
0
0
1
0
1
0
1
1
0
2
0
0
2
2
4
1
1
1
1
1
2
0
2
2
2
1
1
0
0
1
2
4
0
0
1
1
1
1
2
1
2
0
0
0
1
1
1
1
1
2
1
1
1
1
0
1
1
0
0
2
2
0
0
2
0
2
1
0
1
0
1
1
1
1
1
0
1
2
1
0
1
2
1
1
1
1
1
0
1
1
0
0
0
1
1
1
0
0
1
2
1
1
0
0
2
0
2
1
0
2
2
1
1
1
1
0
0
1
2
1
0
1
0
2
1
1
0
2
0
0
0
1
1
1
1
1
0
1
1
0
0
0
1
1
0
1
0
0
1
1
1
0
0
1
1
2
3
1
0
1
0
1
2
0
1
2
0
1
0
1
2
0
1
2
1
0
2
2
2
1
1
1
2
2
1
2
1
1
2
1
0
0
0
1
0
1
1
1
1
4
2
1
1
2
1
0
1
2
1
1
1
3
1
0
2
1
0
2
2
0
0
0
1
1
0
1
1
2
2
0
0
1
0
2
2
1
0
2
1
1
0
1
0
1
1
1
0
2
1
2
0
2
1
1
1
1
1
1
1
1
2
2
0
0
2
1
0
0
2
1
2
2
2
1
0
1
2
2
1
0
1
2
1
1
1
1
1
1
2
0
0
1
1
0
0
1
0
2
1
1
0
1
1
0
2
1
0
0
2
0
1
0
6
1
1
2
1
0
2
0
1
2
0
1
1
2
1
1
0
1
1
0
0
1
0
1
0
2
1
1
0
1
1
2
0
1
1
0
1
1
0
1
0
0
1
1
2
2
1
2
2
0
0
2
1
2
1
0
1
2
0
1
2
0
2
1
2
0
1
1
0
2
1
0
0
1
0
1
2
0
2
2
1
0
1
0
1
1
1
2
1
1
1
1
0
0
2
1
1
2
2
1
2
0
2
0
2
1
0
0
0
1
2
1
0
1
1
2
1
1
1
1
1
2
0
1
3
0
2
2
0
2
2
1
1
1
1
0
0
1
0
1
0
1
2
0
1
2
0
1
1
1
1
0
1
1
1
0
2
0
0
1
0
2
0
1
1
1
1
1
2
0
1
0
0
1
1
0
0
2
1
1
2
1
0
1
1
1
1
1
2
1
1
1
2
0
2
0
1
0
2
0
1
2
0
0
2
0
1
1
1
1
1
0
2
2
1
2
1
3
0
0
1
1
2
0
0
1
1
1
1
0
1
2
1
1
0
1
1
0
0
1
0
1
0
1
0
1
1
1
1
0
1
2
2
0
0
2
1
1
1
1
0
1
1
0
0
1
1
1
1
1
1
1
0
0
2
0
1
1
0
2
0
2
1
0
0
1
1
1
1
0
2
1
1
1
2
2
0
1
0
2
2
1
1
1
0
0
1
2
2
1
1
2
0
0
1
0
1
1
1
0
1
1
0
2
2
1
2
2
2
2
1
2
0
0
2
1
1
2
1
2
1
0
0
1
1
0
1
1
1
0
2
2
1
2
1
1
1
0
1
0
0
2
0
1
1
0
0
2
0
1
1
0
1
0
0
0
2
1
1
1
1
0
1
0
1
1
0
1
2
1
0
1
2
0
2
0
2
1
1
8
1
0
1
0
1
0
0
3
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
0
1
1
1
1
1
0
0
0
2
1
0
0
1
0
1
0
0
1
3
1
1
0
2
2
1
0
0
1
1
0
1
1
2
3
2
1
1
1
0
2
1
1
0
0
1
0
2
0
2
0
2
2
1
1
1
1
1
1
0
1
1
1
0
1
0
1
2
1
1
1
2
1
0
1
1
0
1
2
2
1
1
2
1
1
2
1
1
1
1
1
1
0
1
1
0
0
1
3
0
2
0
1
1
2
0
1
1
0
2
2
1
2
3
0
1
2
1
1
1
2
1
0
2
1
2
1
2
0
1
2
1
0
2
2
1
1
1
1
1
1
1
2
0
1
0
1
2
0
1
0
1
2
0
2
1
0
1
1
2
0
0
1
2
0
1
0
2
1
1
1
1
1
0
0
2
0
0
3
1
0
0
0
0
2
1
2
0
2
2
1
1
1
0
2
0
2
1
1
2
1
0
0
1
1
1
1
1
0
2
1
2
0
1
0
0
0
2
1
0
0
0
1
1
2
1
0
1
0
1
1
2
1
2
0
0
0
0
1
2
1
0
1
0
1
2
0
1
1
0
0
1
0
1
1
1
1
0
1
2
1
1
0
1
0
1
2
1
0
1
1
0
1
0
2
1
0
0
1
1
1
1
0
1
0
1
2
0
1
1
3
0
2
2
0
1
1
2
1
2
1
1
2
1
1
2
1
0
2
3
2
1
1
0
1
1
2
0
2
0
0
0
1
1
1
2
0
3
1
1
1
1
1
0
0
1
0
1
0
2
1
2
2
1
1
2
0
1
2
1
0
0
1
0
0
1
1
1
1
1
2
1
2
0
2
1
1
0
0
1
1
1
0
1
1
0
0
2
0
1
1
1
1
1
3
1
1
1
1
1
1
0
2
2
2
1
2
0
0
1
1
0
0
2
0
1
0
2
1
1
1
1
2
1
1
0
0
2
1
1
1
2
1
1
1
1
0
1
1
0
2
1
1
0
1
0
2
1
1
2
0
1
2
0
1
1
1
2
1
1
2
0
1
0
1
1
0
1
1
1
1
1
2
0
0
0
0
0
0
1
1
2
0
0
0
1
0
1
2
2
0
1
2
1
1
2
1
0
1
1
3
1
0
2
1
1
2
2
1
1
1
0
1
2
0
2
1
1
0
1
0
2
1
0
0
1
0
0
2
1
1
2
0
2
1
1
2
1
1
0
1
0
1
0
2
2
2
0
1
0
1
2
1
2
1
1
1
0
0
1
0
2
2
1
0
1
2
1
2
0
2
2
2
1
0
1
0
0
0
2
2
1
1
1
2
1
1
0
1
1
2
1
0
1
2
0
1
0
1
0
1
2
1
0
1
1
0
0
1
2
1
1
1
0
1
1
0
2
0
0
2
2
1
2
1
1
1
1
0
1
2
1
0
1
0
2
2
1
1
0
2
1
0
1
1
1
2
2
2
1
0
1
2
1
1
1
2
1
1
0
2
0
2
1
1
2
1
0
1
1
1
1
1
2
1
0
1
1
0
2
1
2
1
0
1
1
2
0
1
1
1
1
1
1
1
1
0
0
2
0
1
2
0
0
0
0
0
1
1
0
2
1
1
0
1
1
0
0
1
0
1
0
1
0
2
2
1
0
0
1
0
0
1
0
1
0
2
0
0
1
1
1
1
1
1
1
2
1
1
0
1
0
1
1
2
0
0
0
1
1
1
1
0
1
1
0
2
0
1
0
2
1
1
0
1
1
0
0
1
0
2
1
0
0
1
1
0
0
1
1
3
1
2
1
0
1
2
0
1
2
1
0
1
1
1
2
1
2
1
1
1
0
1
0
1
1
2
1
0
1
1
0
1
1
2
1
1
2
0
3
1
0
1
0
1
1
0
2
1
1
0
1
0
1
1
0
0
1
0
0
0
0
2
1
2
3
0
1
1
1
0
0
1
2
2
1
2
2
1
0
1
0
0
1
2
0
0
1
1
1
0
2
2
0
2
1
1
0
2
2
1
1
1
1
1
0
0
0
0
0
0
1
0
2
3
1
1
1
2
1
0
2
1
1
0
1
2
1
1
2
2
0
0
2
0
2
2
1
0
0
1
0
0
2
1
1
2
1
2
2
0
1
0
1
1
0
1
1
2
1
2
1
2
1
1
1
2
1
1
1
1
1
0
0
0
1
1
1
0
1
2
1
0
0
2
2
1
1
0
0
1
1
2
1
1
0
2
2
2
0
2
1
1
2
1
0
1
1
1
1
1
0
2
0
0
0
1
1
1
1
1
1
1
0
0
2
1
2
1
1
1
1
1
1
1
1
1
1
0
1
2
0
0
1
0
2
0
0
1
1
2
1
1
2
1
1
1
1
1
1
1
1
2
2
1
1
1
0
0
1
0
1
1
1
0
1
2
2
1
0
2
1
1
1
0
0
1
1
1
1
0
1
0
1
1
1
1
1
1
0
1
0
0
3
1
1
2
1
0
2
2
2
1
1
1
0
1
1
1
1
0
2
1
1
0
1
0
2
1
1
2
1
0
1
0
2
2
0
0
1
1
1
1
1
1
2
2
2
1
1
1
0
0
1
2
1
1
0
1
1
1
1
1
0
2
2
1
0
0
2
1
1
0
0
1
2
0
0
1
1
1
0
0
0
1
1
1
1
1
1
1
0
0
2
1
2
1
1
1
1
1
2
1
1
0
1
1
1
1
0
0
1
1
0
1
0
1
3
2
1
1
0
1
1
1
0
2
0
0
2
1
0
1
1
0
0
1
1
0
1
3
1
1
1
1
0
1
0
2
0
2
0
2
2
0
0
1
1
0
2
1
2
1
1
1
1
1
1
1
0
1
1
1
1
1
1
2
0
1
1
1
0
0
1
2
1
1
2
2
0
2
2
0
1
2
1
0
1
1
1
1
1
1
0
1
1
0
0
0
0
1
1
1
1
2
1
1
1
1
0
1
1
0
2
1
1
0
0
1
3
1
0
1
2
0
0
0
1
1
1
1
1
1
2
0
0
3
1
2
2
2
1
2
1
1
1
0
0
0
1
1
1
1
1
1
1
1
2
1
0
1
0
0
4
1
0
0
2
1
2
2
1
1
0
1
1
1
1
1
0
1
0
1
0
1
2
1
2
2
0
1
0
1
1
2
0
1
2
0
0
1
1
2
2
0
1
1
1
2
2
0
2
1
1
1
2
1
1
1
0
1
0
1
1
1
0
2
1
2
1
2
1
2
1
1
0
2
1
0
1
1
1
1
1
2
1
1
0
2
1
2
2
1
1
0
2
0
0
2
0
2
1
1
1
0
1
1
3
2
1
1
0
1
1
1
1
2
0
1
1
1
2
1
2
2
1
0
1
1
1
0
1
1
1
0
1
0
1
1
0
0
2
2
0
2
0
0
1
0
0
1
0
1
0
2
0
2
0
1
1
0
0
1
2
2
1
0
1
0
1
0
0
2
0
2
0
1
1
0
1
1
2
1
0
1
0
1
0
0
1
2
3
0
0
0
1
1
1
0
1
0
0
2
2
2
2
0
1
1
2
1
1
2
0
1
1
2
2
2
0
4
1
1
2
1
1
1
1
1
2
2
1
1
2
2
1
1
0
1
0
1
2
1
0
1
1
1
0
0
2
1
2
0
2
0
1
1
0
1
2
1
1
2
0
1
1
0
0
1
1
1
0
1
1
0
1
1
1
1
1
0
0
2
0
1
2
1
1
0
1
0
1
1
1
1
2
1
1
1
0
0
2
1
0
2
1
1
0
0
2
0
2
1
1
1
1
3
2
0
1
1
2
0
0
0
1
1
1
0
1
2
2
2
1
1
1
1
2
1
1
0
0
1
2
1
1
0
0
1
1
0
1
0
0
1
0
2
0
0
0
1
0
2
0
2
2
2
1
1
1
2
1
0
1
0
2
0
1
0
0
1
1
2
3
1
0
1
1
0
1
1
0
2
1
1
0
2
1
1
0
0
1
1
2
1
1
2
1
0
1
1
0
1
2
0
1
1
1
0
0
1
1
2
2
2
2
0
1
1
0
0
1
0
1
2
1
1
0
1
1
1
1
0
1
1
0
0
0
0
1
1
1
2
1
1
1
2
2
1
1
1
2
1
2
0
2
0
1
1
1
1
2
1
2
1
0
2
1
1
1
1
0
1
2
1
1
0
0
0
1
1
0
1
1
2
2
0
0
2
1
1
1
2
2
2
0
0
1
1
1
0
1
1
1
1
1
1
1
1
0
0
1
0
1
3
1
3
1
2
1
1
1
1
0
0
1
0
1
1
0
2
0
0
1
2
0
2
1
2
2
0
1
1
2
2
1
2
0
0
1
1
0
1
0
0
1
1
1
1
1
1
1
1
0
0
1
0
0
0
0
1
2
0
0
1
2
1
1
0
0
1
1
1
0
0
2
1
0
1
2
1
1
0
1
1
0
1
0
0
1
2
2
2
0
0
0
2
2
2
1
2
0
0
2
1
2
1
0
2
1
1
1
1
0
1
1
1
1
0
1
0
1
1
0
1
2
0
1
1
1
1
1
2
0
2
1
1
2
0
1
1
1
1
0
2
1
2
0
0
0
1
0
1
1
0
2
2
2
2
0
2
1
2
1
0
2
1
1
1
2
2
2
2
1
2
1
0
1
1
1
2
2
1
1
1
1
0
2
1
1
0
1
1
1
0
1
1
0
2
1
1
1
0
0
1
1
1
1
1
1
2
1
2
2
1
1
1
1
1
1
0
1
1
1
0
2
1
1
2
1
2
1
0
0
2
0
1
1
2
1
1
2
1
0
2
1
0
1
1
3
0
1
2
1
0
0
2
1
0
2
1
0
1
3
1
0
1
1
0
2
0
1
0
2
0
0
1
1
0
1
1
0
2
1
2
0
1
0
1
2
2
0
2
1
0
1
1
0
1
0
1
1
0
0
2
1
1
2
1
1
2
2
0
2
2
1
1
1
2
1
2
0
1
1
1
1
0
1
1
2
1
1
0
0
1
1
1
1
1
0
2
1
2
1
2
4
1
0
2
2
1
0
1
0
1
2
0
0
2
1
2
1
0
1
1
1
1
1
1
1
2
1
5
1
2
2
2
0
0
0
1
1
1
3
1
2
1
1
2
1
1
1
0
2
1
1
0
0
1
1
2
1
0
2
1
2
0
1
1
0
0
1
0
0
1
1
0
0
0
1
2
1
1
1
1
0
1
1
1
1
1
2
1
2
1
0
0
1
1
1
0
0
1
0
2
1
1
1
1
1
0
1
1
2
1
0
0
0
1
2
1
0
2
1
2
0
1
2
1
1
0
2
0
2
1
1
0
2
0
0
0
2
2
0
1
0
0
1
2
3
1
1
1
1
1
2
1
1
2
1
1
0
1
0
1
2
0
1
1
0
0
1
0
1
0
1
1
0
0
0
1
1
2
0
1
2
1
1
1
1
1
2
0
1
1
0
0
2
0
1
2
0
1
0
0
2
0
0
1
2
0
0
1
2
1
0
2
1
0
1
0
0
2
1
1
0
2
0
2
0
1
0
1
0
2
0
0
1
0
2
0
0
0
1
0
0
0
1
1
0
1
2
1
0
1
2
2
0
0
1
1
0
0
1
1
2
1
1
2
2
1
1
1
1
0
0
1
1
0
0
0
0
1
0
0
2
1
1
2
0
0
0
0
1
0
1
0
2
2
1
1
2
3
1
2
1
2
3
0
0
0
0
1
1
0
0
2
1
1
1
0
1
1
1
1
2
0
1
0
1
1
1
0
0
2
2
1
1
2
1
0
1
1
1
1
1
2
0
2
1
2
1
2
0
1
1
2
0
0
0
1
1
0
1
0
0
1
0
1
0
2
1
0
0
1
2
1
0
0
2
0
0
1
2
0
1
1
2
1
1
0
1
1
0
1
1
1
1
1
0
1
1
1
2
1
0
0
1
1
1
2
0
0
1
0
0
0
1
1
2
1
1
1
0
1
1
1
1
0
0
1
1
1
2
1
1
0
2
0
0
2
0
0
0
0
2
1
2
1
2
1
0
1
2
1
1
0
1
1
1
1
1
1
1
1
4
2
0
2
2
1
1
0
0
1
0
1
1
0
1
1
2
1
0
0
2
2
0
1
0
1
1
2
0
1
0
0
4
0
1
0
1
1
0
2
0
1
1
1
2
2
2
2
2
0
1
0
0
1
0
1
1
2
1
1
0
2
0
2
2
1
1
0
0
1
2
1
2
1
1
0
0
0
1
2
0
1
0
1
0
0
0
1
2
2
0
0
1
0
3
0
1
0
1
1
2
0
1
2
2
1
1
2
2
0
1
1
0
1
2
1
0
1
0
1
0
1
0
1
1
2
1
1
0
1
1
1
2
0
0
1
1
1
0
1
1
0
1
1
1
2
2
1
1
0
1
2
0
2
0
1
2
1
0
2
2
2
1
0
2
1
0
1
2
2
1
1
2
1
2
0
0
0
1
1
1
1
2
0
1
0
0
0
0
1
2
0
2
1
0
2
1
0
1
0
3
1
2
1
1
1
2
0
2
0
0
1
0
0
1
1
1
0
1
1
1
0
2
0
1
0
1
0
0
1
2
1
1
1
1
1
1
1
1
2
0
1
1
2
0
0
1
1
1
1
1
1
0
0
1
0
2
1
2
1
1
0
1
0
1
1
2
1
2
1
2
1
1
1
0
2
1
2
0
2
2
1
1
1
1
0
2
2
1
2
1
0
0
2
1
0
6
0
0
1
3
1
0
2
1
1
1
2
1
0
0
0
1
1
1
0
0
1
2
2
0
0
1
1
0
1
1
1
1
0
1
0
2
0
2
1
0
1
0
1
1
2
0
2
2
1
2
0
0
1
2
0
1
1
0
1
0
1
0
1
2
2
1
1
1
1
0
0
0
2
3
1
2
1
0
1
2
1
0
0
2
1
1
1
2
1
2
2
0
0
1
1
1
2
0
1
1
1
2
0
0
1
0
1
2
0
1
0
1
2
1
1
0
1
2
0
1
2
0
1
0
1
0
0
2
0
0
1
1
1
2
2
1
1
1
1
1
2
2
2
1
1
1
0
2
2
1
0
0
1
1
0
0
2
0
1
0
2
2
1
1
2
2
1
2
1
2
1
1
1
2
0
0
0
2
0
3
1
2
1
0
2
1
2
0
1
2
1
1
2
1
1
1
1
1
0
2
0
2
0
0
1
2
1
0
1
0
2
2
1
1
0
1
1
0
1
1
1
1
6
1
1
1
2
2
1
1
1
1
0
1
2
0
1
2
1
0
1
3
1
2
1
1
1
0
2
2
0
1
1
0
1
0
2
2
1
0
2
2
1
0
1
0
1
1
0
1
1
1
2
2
2
1
2
0
1
0
0
2
0
0
0
2
0
1
1
0
2
2
1
0
2
2
0
1
1
0
0
0
0
2
0
1
0
2
1
2
1
0
2
1
1
2
0
1
2
1
1
0
1
2
1
1
0
1
1
1
1
1
2
2
2
2
1
0
1
0
1
1
1
1
1
1
1
1
1
1
1
2
1
0
1
0
0
0
2
0
0
1
2
1
1
1
2
0
1
1
1
2
0
1
2
1
1
1
0
1
2
0
1
0
1
2
1
1
1
1
1
0
1
1
1
0
0
1
1
0
1
1
1
0
1
0
0
1
1
0
1
1
0
2
2
1
1
1
1
2
0
1
2
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
0
1
2
0
0
0
1
1
1
1
2
1
0
1
1
2
0
1
1
1
1
2
1
0
1
1
1
2
1
1
0
2
0
0
1
1
0
2
1
0
2
2
1
0
0
2
2
0
0
2
1
1
0
0
0
0
2
9
1
0
2
1
0
1
2
1
1
2
2
0
1
2
0
1
0
1
2
3
2
1
1
1
1
1
2
2
1
0
0
2
1
1
1
1
1
1
0
0
1
1
1
0
1
4
2
0
1
2
1
1
0
3
1
1
2
0
2
2
0
0
1
1
1
0
1
2
1
1
0
2
2
1
0
1
1
2
2
0
1
1
1
2
0
1
0
1
1
1
1
0
1
0
0
0
1
1
1
1
0
0
0
1
1
2
0
2
2
1
1
2
3
1
0
1
2
0
1
1
1
2
1
0
2
0
0
2
1
1
0
2
1
1
1
2
0
1
1
1
1
0
0
1
2
2
1
0
1
2
1
1
0
1
0
1
1
1
1
0
1
1
1
2
1
2
0
0
1
1
0
1
0
4
1
2
2
0
1
1
1
0
1
1
0
1
1
0
2
2
2
0
1
1
1
0
0
1
0
0
2
1
1
1
3
1
0
1
0
1
0
0
1
1
1
2
1
1
1
1
1
1
0
0
0
1
2
1
0
2
1
1
1
1
2
2
1
2
1
1
1
0
1
2
2
1
1
0
2
2
1
0
2
0
1
1
0
1
0
1
0
1
1
0
2
2
0
1
1
2
1
1
1
1
0
2
1
1
1
2
0
1
1
1
2
1
1
1
0
1
0
1
1
3
1
2
1
2
0
1
0
0
1
2
2
1
1
0
1
1
1
1
1
1
0
1
0
0
1
1
2
1
1
0
1
1
2
1
1
1
2
0
0
0
1
0
1
0
1
0
1
1
1
0
1
1
1
1
1
1
2
1
1
2
2
1
0
1
0
1
1
1
2
1
1
1
2
1
1
2
2
1
1
1
1
0
1
1
0
2
1
1
0
1
2
2
2
1
0
0
2
1
0
1
2
0
2
1
2
0
0
1
0
2
0
0
1
0
0
1
0
1
1
0
1
1
0
0
1
2
1
2
2
1
1
0
1
3
0
1
1
1
1
0
2
1
1
1
1
1
0
2
0
1
0
2
0
1
1
2
1
0
0
0
1
2
1
2
1
2
0
1
0
0
0
1
1
1
1
0
0
0
2
2
0
0
1
1
1
1
2
1
0
1
1
1
1
1
0
1
0
1
0
2
2
1
2
0
1
0
0
0
1
1
1
1
1
1
1
0
1
1
0
2
3
1
1
2
0
1
1
0
1
0
1
1
1
0
0
1
1
0
2
1
2
2
2
0
0
0
0
1
2
0
1
0
1
0
0
0
0
0
1
0
1
2
0
0
1
1
0
0
1
0
3
1
2
1
1
0
2
1
2
2
0
0
0
1
1
2
1
1
0
0
0
0
0
0
1
1
0
1
0
2
0
0
0
0
1
2
2
1
1
0
2
1
1
1
1
2
0
2
0
2
1
0
2
0
1
1
2
0
0
0
2
0
2
1
2
2
0
1
1
0
2
1
1
0
1
0
1
2
2
1
0
2
0
3
2
1
1
1
1
2
1
2
2
0
1
0
0
1
0
2
2
0
1
1
1
2
1
0
1
0
2
1
1
1
0
1
0
1
2
0
0
2
2
0
1
0
1
0
2
1
1
3
0
0
0
1
1
0
0
1
0
2
1
4
0
1
0
1
0
1
1
2
1
0
1
1
0
1
0
2
0
1
2
1
0
0
1
2
1
2
1
2
1
1
0
1
1
2
2
1
2
0
2
1
1
1
1
0
1
1
2
2
1
1
1
0
1
1
0
1
1
1
1
1
1
2
0
1
1
1
0
1
1
1
1
0
2
0
1
1
2
1
0
1
1
1
2
1
1
1
2
1
2
2
0
0
1
1
0
1
2
1
0
0
0
2
0
1
0
1
1
0
0
1
0
2
0
0
0
1
0
0
1
2
1
2
0
0
2
0
1
1
1
0
0
1
0
1
1
1
1
1
2
1
1
1
1
0
0
0
1
0
0
0
1
0
0
1
2
2
1
1
1
1
1
0
1
0
0
0
1
0
2
1
0
1
1
1
2
1
1
1
0
0
1
1
2
0
2
1
1
0
0
1
0
0
2
1
2
1
0
1
3
1
1
1
1
0
1
1
2
0
1
2
0
1
3
3
1
2
1
3
2
2
1
1
0
1
1
1
2
1
2
1
0
2
1
2
0
1
0
0
1
0
1
0
1
2
0
1
1
3
1
1
1
0
0
0
1
1
0
0
0
0
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
2
2
0
1
2
2
1
0
1
2
1
2
1
0
0
2
2
2
0
0
0
1
0
2
0
0
0
3
1
0
1
1
1
1
2
1
2
0
0
1
1
1
1
2
1
1
2
0
1
1
1
1
1
0
0
2
1
1
1
1
0
0
0
0
1
0
2
0
2
0
1
2
2
1
1
1
1
4
0
1
1
0
1
1
2
1
0
2
2
0
1
2
1
0
2
0
1
1
1
1
1
1
1
1
1
0
0
1
0
2
2
1
2
1
1
0
2
1
0
0
1
0
1
2
1
1
2
1
1
0
1
0
1
3
2
0
0
1
1
2
2
1
1
2
1
1
1
1
0
1
0
1
1
0
0
4
1
1
0
1
0
1
1
1
0
2
0
0
0
0
2
1
0
2
1
0
1
1
1
1
1
1
1
1
1
0
1
1
3
1
2
1
1
2
1
1
0
0
1
1
0
2
2
1
1
1
1
2
1
1
1
2
1
0
1
1
2
0
1
1
0
1
2
1
1
2
1
1
0
0
2
1
1
1
1
0
1
1
1
2
0
1
0
0
1
1
0
0
1
0
2
1
1
2
2
1
2
1
0
2
2
1
1
1
1
0
0
1
0
1
1
1
0
2
0
0
0
2
2
0
1
2
1
1
2
2
0
1
0
1
0
1
2
1
1
0
2
1
2
1
3
0
0
2
2
1
2
1
0
2
2
1
1
1
1
0
0
0
0
2
1
1
1
1
0
3
1
2
2
1
1
1
1
0
0
1
1
0
1
1
2
1
1
1
0
2
1
2
1
1
1
2
1
0
0
3
1
1
1
0
1
2
1
1
1
1
1
0
1
1
2
1
1
0
0
2
0
2
1
1
2
2
1
3
1
1
2
1
2
2
1
1
1
0
5
1
0
2
2
2
2
1
1
1
1
1
2
1
2
1
0
2
1
0
0
1
0
1
1
1
1
3
0
0
2
1
1
1
1
1
0
1
3
1
1
0
1
1
1
2
2
1
1
1
1
2
0
1
0
1
1
1
0
0
2
0
2
0
0
0
0
1
2
1
1
1
1
0
1
1
1
1
0
0
1
1
2
1
0
0
2
1
2
0
0
0
0
0
1
1
0
0
2
1
0
2
1
1
1
0
2
1
1
0
2
1
0
2
1
2
0
0
1
0
2
1
0
1
2
1
1
2
0
1
1
1
1
0
1
0
1
0
2
1
2
1
0
1
2
3
0
1
1
2
2
1
0
2
1
1
1
0
1
0
1
0
0
1
0
0
1
1
0
1
0
1
1
0
1
0
0
3
1
0
0
0
1
0
0
1
1
0
0
1
2
1
0
1
1
0
1
2
1
1
2
0
2
1
0
1
1
1
1
0
1
0
1
1
1
1
2
1
2
1
2
1
1
0
0
1
0
0
2
2
2
2
1
0
1
2
1
1
1
0
1
2
0
0
1
0
2
1
1
1
2
1
1
0
1
0
1
1
0
1
1
1
0
0
0
2
1
2
1
0
2
0
2
1
1
0
1
1
0
0
1
2
2
1
1
0
1
1
0
1
1
4
1
0
0
1
1
1
1
1
1
1
1
1
2
1
1
1
1
0
0
1
1
0
1
2
1
1
1
1
0
0
1
1
1
1
1
2
0
0
2
0
1
0
0
1
0
1
0
0
0
0
2
0
2
0
0
1
0
0
0
1
2
2
2
0
1
0
0
0
1
0
1
2
0
1
0
1
1
1
3
1
1
1
0
0
2
2
2
3
0
2
0
1
2
2
0
0
0
0
1
0
0
1
1
2
1
1
0
1
3
1
1
1
0
1
0
1
1
1
1
2
1
1
2
2
0
1
1
1
2
1
0
1
1
1
1
2
1
0
0
0
0
0
1
1
1
2
0
0
0
0
0
1
0
2
0
1
1
2
0
1
1
2
0
1
0
1
0
1
1
0
2
0
0
2
1
1
1
1
1
0
2
1
1
1
1
0
1
1
3
1
1
0
0
1
0
1
1
2
1
2
2
1
2
2
1
0
1
2
0
1
2
0
1
1
1
1
1
0
2
2
2
1
2
1
1
0
2
2
1
1
1
2
2
1
2
2
1
0
0
1
3
1
0
1
2
2
0
0
1
1
0
0
1
1
0
0
0
0
2
1
0
0
0
1
1
1
0
1
1
2
2
0
1
1
2
1
2
1
1
0
2
2
1
0
2
0
1
1
0
10
0
0
2
2
2
0
2
0
2
2
1
1
2
1
1
2
0
1
1
0
0
1
1
2
1
0
1
1
0
0
2
1
0
0
1
2
2
0
1
0
3
2
1
1
2
2
0
1
2
0
1
1
1
1
2
1
1
0
0
1
0
1
0
0
2
1
0
2
1
1
0
1
0
1
1
2
1
1
0
3
2
1
0
1
1
1
1
1
1
0
0
0
1
0
2
0
1
1
2
1
1
4
1
0
1
0
0
2
0
0
1
1
0
1
1
2
1
1
1
1
1
0
1
2
1
1
1
1
1
1
1
0
3
1
1
0
2
2
1
1
2
2
1
1
2
2
0
2
0
2
2
0
2
1
0
1
2
2
0
0
2
0
2
2
0
1
1
0
2
0
2
1
1
1
2
2
0
1
1
0
1
1
2
2
1
1
0
1
2
1
2
1
0
0
0
1
0
0
0
0
0
1
2
0
1
0
1
0
0
0
4
3
1
0
1
1
1
1
0
1
0
0
2
0
2
0
0
2
1
1
1
0
1
0
1
1
2
1
1
2
1
1
0
0
0
1
1
1
0
1
1
2
0
1
2
0
0
1
1
1
0
1
1
1
0
0
1
0
1
0
1
2
1
0
2
0
1
1
0
0
0
2
1
1
4
0
1
1
1
0
1
1
1
0
1
2
2
0
1
1
0
1
1
1
0
2
1
2
0
2
1
1
1
1
0
2
1
0
1
1
0
0
0
0
1
1
2
1
2
2
0
1
1
1
2
2
0
2
1
2
2
1
1
2
1
0
0
1
0
1
2
0
2
1
1
2
0
1
2
1
0
1
2
1
1
1
2
0
1
0
0
0
1
0
1
0
0
1
0
1
0
1
2
2
0
0
0
0
1
1
0
2
2
0
1
0
1
1
2
0
1
2
1
1
1
1
0
1
1
0
1
0
2
2
1
1
1
1
0
2
0
0
1
0
0
1
0
0
0
0
0
0
1
0
2
2
0
1
1
0
0
1
4
1
1
1
0
1
0
2
0
0
1
2
1
1
0
0
2
1
2
1
0
1
0
1
2
1
2
1
0
0
2
0
2
1
3
1
1
0
0
1
2
2
0
1
0
0
0
1
2
2
1
1
0
0
0
0
1
2
1
1
2
1
0
1
1
1
0
1
1
2
1
2
2
0
1
2
2
2
0
1
1
1
0
0
2
1
1
0
0
1
0
0
1
0
0
1
1
1
1
2
0
2
0
0
2
1
1
1
1
0
1
1
1
2
1
2
0
1
0
1
1
1
1
0
2
1
0
0
2
1
1
3
2
0
1
2
1
1
0
1
1
1
2
1
1
1
2
2
1
0
2
2
1
0
1
0
2
0
2
2
0
2
1
1
1
1
2
2
1
1
1
1
1
1
1
0
0
2
0
1
1
2
0
1
1
2
1
2
0
1
1
0
0
2
1
1
1
1
2
2
2
2
0
2
0
1
1
0
2
0
1
1
0
1
2
3
1
0
0
1
1
1
1
1
0
1
1
1
1
0
0
1
1
0
0
1
2
0
3
0
1
1
2
0
0
0
1
0
1
1
3
2
0
2
2
0
1
1
1
1
1
1
0
1
2
1
1
1
1
1
4
0
0
0
2
2
2
1
0
1
2
1
2
0
1
2
2
1
2
2
1
2
1
1
1
1
0
0
2
0
1
1
1
0
0
1
0
0
2
0
2
1
1
0
1
1
1
0
1
0
1
0
1
0
2
1
1
1
1
0
0
0
1
1
2
0
0
1
2
0
1
1
1
0
1
2
1
0
1
1
1
0
0
0
0
0
1
0
0
0
1
1
1
1
2
1
1
1
1
1
0
0
1
1
1
1
4
1
1
0
1
0
2
0
2
1
1
0
1
0
1
2
2
0
0
1
0
1
0
0
1
2
1
0
1
0
2
1
1
1
1
2
1
1
1
2
1
2
1
1
1
2
1
1
1
2
0
1
1
0
1
1
1
0
2
2
0
1
2
1
0
1
1
1
2
1
1
1
0
1
1
0
1
2
1
0
3
2
2
0
1
1
1
0
0
2
2
1
1
1
0
2
0
2
1
1
1
0
0
0
2
1
0
1
2
1
1
0
1
0
0
1
2
1
2
2
0
1
0
1
1
1
0
2
1
0
2
0
1
2
1
2
1
0
1
1
0
1
1
2
1
1
0
0
1
2
1
4
1
1
0
0
2
2
0
0
1
3
0
0
1
1
1
2
0
0
2
1
2
0
1
1
1
1
1
2
2
2
1
0
1
0
1
2
0
1
0
0
1
0
1
0
1
1
1
1
2
1
2
1
2
5
2
1
0
0
1
1
0
0
1
1
1
1
2
0
1
2
0
0
0
1
1
2
1
1
1
1
2
1
1
0
2
1
1
2
1
1
2
1
1
2
1
2
0
1
0
1
1
1
2
1
2
1
1
1
1
1
2
0
1
1
1
2
0
1
1
1
2
5
1
1
1
0
1
2
1
1
1
2
2
0
1
2
2
1
2
2
1
1
1
0
0
0
1
3
1
1
1
0
1
1
1
2
1
0
2
1
2
1
1
1
1
1
0
2
2
2
1
2
1
2
2
2
2
2
2
0
1
0
1
0
0
1
1
2
2
1
0
1
0
1
1
1
1
1
2
1
1
0
1
1
0
0
1
1
2
1
0
0
0
2
1
0
2
1
2
1
1
0
0
0
1
0
3
1
2
2
1
0
1
2
1
0
1
1
1
1
1
1
0
2
1
1
0
0
0
2
0
0
1
2
1
1
0
2
0
1
0
0
1
1
0
2
2
2
1
1
2
1
1
2
0
2
0
1
1
0
0
1
1
1
0
0
0
0
2
2
2
1
0
0
2
0
0
1
0
1
2
1
0
1
2
0
1
0
1
0
2
1
1
1
1
3
1
1
1
1
1
1
0
1
2
0
1
0
2
0
2
1
1
1
1
0
1
0
1
0
2
0
0
1
1
1
2
0
1
1
2
2
0
1
0
1
1
1
1
1
1
1
0
0
2
1
2
2
1
2
0
1
3
2
2
1
2
1
1
1
0
1
1
1
0
2
1
2
1
2
2
0
0
1
2
1
1
1
1
2
1
0
1
2
1
1
1
1
0
0
2
1
1
1
0
1
1
1
0
1
3
1
2
1
0
1
1
1
2
2
1
0
0
0
1
0
0
2
0
0
1
0
1
0
1
1
1
2
0
0
1
1
2
0
1
0
1
1
1
2
1
1
1
1
1
2
2
1
0
1
2
0
0
2
0
1
1
0
0
0
4
2
0
2
2
1
1
1
1
1
0
0
1
2
1
1
1
0
1
0
0
2
1
0
1
2
1
2
1
2
0
2
0
0
1
1
1
1
1
0
0
1
0
2
0
1
0
0
1
0
1
1
0
2
1
1
0
1
0
2
1
0
1
1
2
1
2
0
1
2
1
0
0
1
0
2
1
1
2
0
2
0
1
0
0
0
3
1
2
0
1
0
1
1
1
0
2
1
1
1
2
1
0
0
0
1
2
0
2
0
1
1
1
2
0
1
0
2
1
0
1
0
2
2
1
1
1
1
1
0
2
0
1
2
2
0
2
2
1
2
1
0
0
2
1
1
1
0
2
1
1
2
1
1
2
2
1
2
1
2
1
1
0
0
1
2
1
0
0
1
0
1
0
1
2
1
0
0
0
2
1
0
2
0
0
1
1
0
1
0
1
0
0
1
1
2
0
0
0
0
0
0
2
0
1
1
1
0
0
1
1
2
1
1
1
1
2
0
2
1
1
2
1
1
1
1
1
2
1
1
0
0
2
0
5
2
1
1
1
0
1
1
1
1
0
1
1
0
0
0
0
2
0
1
1
1
2
1
3
0
2
2
1
1
1
1
2
0
1
0
1
1
1
0
2
1
0
1
1
0
1
1
1
0
1
1
2
1
1
2
1
1
3
0
0
1
2
0
1
0
2
0
0
1
0
1
0
1
2
1
1
1
0
0
1
1
1
0
0
1
1
1
1
2
2
2
1
0
2
1
2
0
0
0
2
1
0
1
0
2
0
2
1
2
2
1
3
0
1
0
2
0
1
1
1
2
0
0
1
1
1
1
1
0
1
0
1
0
1
1
1
0
2
1
1
1
0
0
0
2
2
1
2
1
2
2
1
0
1
1
1
1
0
0
1
2
1
1
0
0
0
0
1
2
0
2
1
1
0
1
2
0
1
1
2
1
2
1
1
1
1
1
2
1
0
0
2
1
2
2
1
1
2
1
1
1
2
1
1
1
1
0
0
2
1
1
2
1
2
1
1
1
2
1
2
1
0
1
1
2
0
1
1
2
0
1
2
1
1
0
1
2
1
1
0
2
2
1
0
1
0
2
2
1
1
1
1
0
0
0
0
1
1
0
1
0
2
1
1
1
0
1
0
1
2
1
1
0
2
1
1
1
2
0
0
2
1
1
1
0
0
1
1
1
1
0
2
1
1
1
0
0
1
1
0
2
0
0
1
1
1
1
1
0
0
0
1
0
2
0
0
2
0
0
2
0
2
1
2
1
1
0
0
1
0
0
0
1
0
0
2
0
1
0
0
1
2
0
1
0
1
1
1
2
1
1
1
0
0
1
1
1
1
0
2
1
1
1
1
0
2
0
1
1
2
2
1
0
1
0
0
0
0
1
1
0
1
0
2
1
1
0
1
1
0
0
1
1
1
0
3
1
1
0
1
2
1
0
1
0
1
0
1
1
0
0
2
0
0
1
1
0
2
1
1
2
2
1
1
0
1
2
2
0
1
1
2
1
0
2
2
1
1
0
0
1
1
0
0
2
3
1
0
1
2
2
1
2
0
0
1
0
1
1
2
1
1
1
0
1
1
2
1
1
0
1
4
1
1
0
1
1
0
2
2
2
1
1
1
1
2
3
1
2
1
1
0
1
1
1
0
1
1
0
1
0
1
1
2
0
0
1
2
2
0
2
0
2
2
0
2
0
1
0
1
2
0
0
0
1
1
1
0
0
0
2
2
1
1
1
1
0
0
0
1
2
0
2
1
1
0
1
1
2
1
1
1
0
0
2
0
0
2
0
1
2
1
2
1
0
0
1
1
1
1
1
1
2
1
2
2
1
0
0
0
0
2
1
2
1
2
0
0
1
0
2
0
1
0
1
0
0
0
1
0
2
1
0
0
1
1
1
1
1
1
1
1
1
1
1
13
1
2
0
1
2
0
0
2
2
1
1
1
1
2
0
0
2
2
0
1
1
0
2
2
0
1
0
2
1
1
1
1
2
1
1
1
0
1
1
0
1
1
1
0
0
2
2
1
2
2
0
0
0
2
1
0
0
0
0
1
1
0
0
1
1
2
1
0
1
0
1
1
1
0
1
0
1
1
1
1
1
0
1
0
1
1
2
0
1
1
1
1
1
1
1
1
0
2
0
0
1
1
1
1
1
0
0
0
2
1
2
1
0
2
0
1
2
0
0
1
1
1
0
2
2
1
0
0
1
2
1
1
1
1
1
1
2
0
1
1
0
1
2
2
0
2
1
1
1
0
0
0
1
0
0
1
0
1
1
0
1
1
1
0
1
1
2
0
2
0
0
1
0
2
0
1
1
0
1
1
1
1
0
1
1
1
1
2
0
0
1
1
1
1
2
1
2
1
1
0
1
0
1
1
1
2
0
1
0
1
1
1
2
1
1
0
2
1
1
2
0
0
1
1
0
1
0
0
2
2
2
1
0
1
0
1
2
0
1
1
1
2
0
0
1
1
2
1
1
1
2
1
1
1
1
1
2
2
0
2
1
1
2
0
1
1
0
0
1
2
0
2
2
0
0
0
1
2
2
1
1
0
2
1
1
1
1
1
2
2
0
1
0
1
2
0
0
1
2
0
1
1
1
1
2
1
1
1
0
2
0
1
3
1
2
0
1
1
2
0
1
1
1
1
2
1
1
0
0
2
3
1
1
1
2
2
1
1
1
2
1
1
1
0
1
0
2
2
1
0
1
1
0
0
0
2
2
1
3
1
0
0
1
1
2
2
1
1
0
2
1
1
0
0
1
0
1
0
1
2
1
1
2
0
1
2
0
0
1
1
1
1
1
2
2
1
2
2
1
1
0
2
1
3
0
1
2
1
1
1
2
1
2
0
0
0
1
1
1
1
2
0
1
1
1
0
0
0
1
1
2
0
2
0
1
0
1
1
2
2
1
0
1
0
2
0
1
1
2
1
1
1
0
2
1
1
1
1
2
0
0
0
1
2
1
0
1
0
1
1
2
1
0
2
2
0
2
2
2
1
1
1
1
1
2
1
1
0
0
0
0
2
1
0
1
1
1
2
1
1
1
6
2
1
1
2
1
0
1
1
0
1
3
2
1
1
1
1
1
1
1
0
0
1
1
1
0
2
1
1
0
2
0
1
1
1
1
1
1
1
1
2
0
2
0
1
2
0
0
1
1
0
1
0
1
0
0
1
1
0
1
1
2
1
1
0
0
0
1
2
2
0
2
2
2
1
1
0
0
0
1
1
1
0
1
1
1
0
1
1
0
0
0
1
1
0
0
2
1
1
0
1
0
0
0
1
1
1
0
1
0
0
2
1
1
0
1
1
0
0
0
2
0
2
0
0
1
1
2
0
2
1
1
2
1
1
2
0
0
0
1
1
1
1
1
0
0
0
2
1
1
1
0
1
0
1
2
1
0
1
0
2
1
1
2
1
0
0
0
1
1
1
0
0
0
1
1
3
1
0
1
0
1
1
0
1
0
1
0
1
1
1
0
1
1
0
1
1
0
1
0
1
2
1
1
1
0
0
1
2
2
1
2
2
1
1
1
0
1
1
2
1
0
1
0
1
2
0
2
0
0
1
1
0
2
2
1
2
2
1
0
0
1
0
1
1
5
1
2
2
1
0
1
2
1
1
1
0
1
2
2
1
1
0
1
2
1
2
0
1
0
0
0
1
2
0
1
1
0
0
1
2
2
0
1
1
0
0
1
1
1
0
0
1
0
0
1
1
1
1
1
1
1
1
3
1
1
1
3
0
1
1
1
1
2
1
0
0
0
1
0
0
1
1
0
2
1
0
0
1
1
1
1
2
2
0
2
1
1
0
2
1
1
1
2
2
0
0
2
0
1
2
1
1
2
1
2
0
1
2
0
2
1
1
2
2
1
1
1
0
2
1
0
1
2
1
1
0
1
1
1
2
1
1
0
0
1
1
0
0
2
1
1
1
0
1
0
2
1
1
1
0
1
2
1
0
2
1
1
1
0
1
1
1
1
0
0
2
2
2
1
1
1
2
1
0
0
1
1
0
0
1
1
1
0
3
1
1
1
0
1
1
1
2
1
1
1
1
0
1
0
0
0
2
1
0
1
2
0
0
1
2
1
2
1
1
1
0
0
0
2
0
1
7
1
2
2
0
1
1
0
0
2
1
3
1
1
1
0
2
0
2
1
2
1
0
1
1
1
0
2
2
1
0
2
2
0
1
0
1
2
0
0
1
1
1
1
2
0
2
1
1
1
0
1
1
0
0
1
1
5
2
1
0
1
1
1
0
1
2
1
2
1
2
2
1
1
1
0
1
0
1
1
0
1
1
0
1
0
0
1
2
1
1
1
1
2
1
0
1
2
1
0
0
1
2
0
2
1
1
2
2
0
0
0
0
2
2
1
0
2
1
1
3
0
2
1
0
1
2
1
1
1
2
1
1
1
1
2
0
0
0
2
1
0
1
1
1
1
1
0
1
0
0
0
2
5
2
0
1
1
2
0
0
1
1
1
1
1
2
0
1
2
1
1
1
1
2
1
0
2
2
1
0
0
1
1
1
1
0
0
0
1
0
0
1
0
1
1
0
1
1
2
1
2
1
0
1
0
3
2
0
2
0
1
1
2
2
2
1
1
1
0
0
1
0
1
1
2
1
1
1
1
2
2
1
0
0
0
2
1
1
0
0
1
0
0
1
2
1
1
0
0
0
1
1
0
2
1
2
1
2
2
0
1
1
1
0
2
1
2
1
0
1
3
0
1
2
0
1
1
1
0
1
1
0
1
1
2
0
0
0
1
0
0
0
0
1
1
1
1
1
2
2
2
0
0
2
2
1
1
1
0
0
1
1
1
1
1
0
0
1
1
2
1
1
2
1
2
1
2
1
0
0
1
2
2
0
1
0
2
1
1
1
0
1
0
0
2
1
0
1
0
2
0
1
0
1
1
1
1
2
1
1
1
2
2
0
0
0
1
0
2
1
2
0
2
1
1
0
1
1
3
0
1
1
3
1
2
1
1
1
2
1
1
2
0
2
1
0
1
1
1
1
2
2
0
0
0
0
1
0
0
0
1
1
1
0
0
0
1
2
1
1
0
1
1
0
1
1
2
1
2
0
0
1
1
0
1
2
1
1
1
0
1
0
1
2
1
1
0
0
2
2
0
1
1
1
1
1
1
1
1
2
1
1
2
0
1
1
1
1
1
1
1
1
2
2
0
0
1
1
0
1
0
1
1
1
0
0
1
1
1
1
2
2
0
1
1
1
2
0
2
1
2
1
1
2
0
1
1
2
0
0
1
1
0
1
0
1
2
0
1
0
1
1
1
1
2
0
2
2
2
0
1
1
1
0
1
0
2
2
2
1
0
2
0
1
1
1
2
1
0
2
1
2
1
2
2
0
1
1
2
0
1
1
1
3
0
1
1
1
1
1
0
1
2
0
1
0
2
1
0
1
3
0
0
0
1
2
2
1
0
0
1
2
2
0
1
0
1
0
1
1
2
1
1
1
0
0
1
0
1
1
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
1
1
1
1
2
0
1
1
1
1
1
0
2
1
0
1
1
1
0
2
0
2
0
2
1
0
1
1
2
1
1
1
0
0
0
0
1
2
1
1
1
1
2
1
1
1
1
1
0
1
0
1
1
2
2
2
1
0
2
1
1
2
0
1
1
1
1
0
1
1
0
0
0
2
1
1
1
2
0
1
1
1
1
0
0
1
1
1
1
1
1
0
1
2
0
1
1
1
0
2
1
2
1
0
1
6
2
2
1
1
0
1
0
1
1
1
1
2
2
1
1
2
0
1
1
0
0
1
0
0
1
2
1
1
0
1
2
1
1
1
1
1
1
1
2
0
0
1
1
1
3
1
1
1
2
2
1
0
2
1
2
1
1
1
2
1
0
0
2
1
0
2
1
1
0
0
2
0
1
1
1
2
2
1
0
1
0
0
1
1
1
1
2
1
1
2
0
1
1
0
0
1
1
0
0
1
2
0
1
2
1
1
1
1
1
1
2
0
1
0
1
2
1
0
1
1
1
1
1
0
1
1
0
1
0
2
1
0
1
0
2
2
0
1
2
1
1
1
1
2
1
2
2
2
0
0
1
0
0
1
1
1
1
0
1
1
1
0
0
0
1
2
1
1
2
0
2
2
1
2
2
1
2
2
2
2
1
1
1
1
1
2
0
2
1
0
1
0
0
1
1
1
0
1
1
3
1
0
0
1
1
0
2
1
2
1
1
0
0
2
2
0
1
1
1
1
2
1
1
0
1
1
1
1
1
1
2
0
2
1
1
3
1
2
0
1
1
1
0
2
1
1
0
0
0
1
1
1
1
1
0
0
1
1
1
0
0
2
1
1
0
2
1
0
2
1
2
0
1
1
1
2
1
1
0
1
1
0
1
2
2
1
0
0
0
1
1
2
2
0
0
0
1
0
0
2
2
2
1
0
0
0
1
2
1
2
1
1
0
2
2
1
2
2
0
0
1
2
1
1
2
1
1
0
1
2
1
1
1
0
2
1
1
1
0
1
1
0
0
1
1
0
1
0
2
2
0
1
1
0
2
0
0
1
1
0
2
0
2
1
1
1
2
0
2
2
0
1
0
0
1
0
0
1
2
2
1
2
1
2
1
1
1
0
0
2
2
1
1
1
0
2
2
1
0
1
0
1
1
1
3
1
1
2
1
1
0
1
1
2
2
2
0
2
2
0
0
1
1
1
0
3
1
1
1
0
1
2
0
0
1
1
0
0
2
0
1
1
1
1
0
1
1
1
1
2
0
1
2
1
1
1
1
2
1
2
0
1
1
0
1
4
2
0
1
0
5
0
2
1
1
2
2
1
1
2
2
0
0
0
2
0
2
0
0
0
0
1
2
1
1
1
0
1
1
0
0
0
0
2
2
1
1
2
2
0
2
0
0
1
1
2
1
0
1
0
1
2
1
1
1
1
1
0
0
0
1
0
0
2
1
1
0
0
0
2
1
1
1
0
2
1
0
0
1
0
1
0
2
1
0
2
0
1
2
2
2
1
0
1
1
1
1
1
3
3
0
1
1
1
0
1
1
1
1
3
2
1
1
1
2
0
3
1
1
1
1
1
1
1
1
1
0
2
1
1
2
1
1
2
1
2
1
1
1
1
0
0
1
1
2
0
1
1
1
1
1
0
2
0
0
2
0
0
0
1
1
0
1
1
0
2
3
2
1
1
1
2
2
0
1
0
2
1
2
0
0
1
1
2
1
0
0
2
1
0
1
0
1
2
1
0
0
3
1
0
1
1
0
1
1
1
0
0
1
1
0
1
2
1
1
0
0
1
1
0
0
1
1
0
1
1
0
1
1
2
1
1
1
1
1
1
1
0
3
1
0
1
1
0
2
1
2
1
1
0
1
0
1
1
1
0
2
1
1
0
1
4
2
1
0
1
1
1
2
1
0
0
0
1
1
1
0
2
2
2
0
2
1
1
1
1
0
2
0
1
1
1
1
1
2
1
0
0
1
1
1
2
1
1
1
2
1
0
2
1
1
2
0
1
2
1
0
0
1
0
0
1
0
2
2
1
1
1
1
1
2
0
2
0
1
1
1
0
2
1
1
1
1
1
2
1
1
1
2
1
2
1
0
1
0
0
1
0
0
0
2
1
1
0
2
0
1
1
1
2
1
0
0
1
2
0
0
1
2
0
0
2
0
0
1
1
1
0
0
1
2
2
1
1
0
1
0
0
1
1
1
2
1
1
1
0
1
1
0
0
0
1
2
2
1
0
1
0
2
0
2
0
0
1
2
2
1
0
0
0
0
1
0
0
1
1
0
2
2
1
0
1
0
1
2
0
1
1
1
2
3
1
0
2
1
1
1
1
1
0
1
1
1
1
1
0
1
0
1
1
1
1
0
1
1
3
0
0
1
1
1
1
1
1
2
0
0
0
1
2
1
0
0
2
2
1
1
1
1
1
0
2
2
1
2
1
1
0
1
0
1
0
1
0
0
1
1
1
0
0
1
2
1
2
2
1
0
2
2
0
1
0
1
0
1
2
0
0
1
2
0
2
1
1
1
0
1
1
1
1
1
2
2
1
2
1
1
0
0
2
0
1
1
0
1
0
0
1
0
1
1
2
2
2
1
2
1
1
1
1
1
1
1
2
1
1
2
1
1
1
2
2
0
1
1
1
1
1
1
0
1
1
0
2
1
1
2
1
1
0
2
0
1
2
0
1
0
2
0
1
0
1
2
1
1
0
1
0
2
1
2
1
1
1
1
2
0
1
2
1
1
2
1
0
1
0
0
0
0
1
1
1
1
0
0
2
0
1
0
2
1
1
1
0
2
1
2
2
0
2
1
2
1
0
1
2
1
1
0
1
0
0
1
0
1
0
2
1
0
0
0
1
1
0
2
1
1
0
1
1
0
0
1
1
1
0
1
1
4
2
1
1
1
1
1
1
0
1
0
1
1
1
1
2
0
1
1
1
2
1
0
0
1
1
1
1
1
1
1
2
0
1
1
2
2
0
0
2
1
2
1
1
2
0
1
0
0
0
1
1
1
1
0
1
2
1
0
0
0
1
1
2
0
1
2
1
2
1
1
1
1
0
0
1
2
1
1
0
0
1
0
1
2
2
1
1
1
2
1
2
0
0
0
1
0
1
2
0
1
0
1
0
2
1
1
1
2
0
2
1
0
0
0
1
2
2
1
2
1
0
2
1
0
3
0
1
2
0
0
0
2
1
1
2
2
0
2
0
1
0
0
1
0
1
0
1
1
1
0
1
2
2
0
2
1
0
1
2
0
1
1
0
1
1
2
0
2
1
0
1
1
1
1
2
2
2
1
1
1
1
1
1
0
1
2
0
1
2
0
0
1
1
2
1
0
1
1
1
0
0
1
1
2
2
1
1
1
1
2
2
1
1
1
0
1
2
1
1
0
1
1
0
1
2
1
2
1
1
2
1
1
1
2
1
1
1
1
2
2
1
0
1
0
1
1
0
1
2
0
1
1
1
2
1
0
1
1
0
2
1
2
1
1
1
1
0
0
1
0
1
1
0
2
2
1
0
0
1
1
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
2
1
1
0
1
2
1
1
0
0
0
1
2
1
0
2
0
1
0
1
4
0
1
1
1
1
0
2
1
1
2
1
1
0
0
1
2
0
0
2
1
2
1
2
1
1
1
1
0
1
2
1
1
0
2
1
2
2
3
0
0
2
0
1
0
1
1
0
1
2
1
1
1
1
1
1
0
0
1
1
0
0
1
1
1
1
1
0
2
1
0
0
0
2
0
2
0
1
1
1
2
2
1
0
1
1
0
0
0
1
1
2
1
0
0
0
1
1
2
1
1
0
0
1
0
3
2
1
0
1
2
2
1
0
1
1
0
2
0
2
1
1
0
1
1
1
2
2
1
1
1
1
1
0
1
1
1
1
1
0
0
1
0
0
1
0
0
1
1
1
1
1
1
1
0
1
2
1
0
1
1
0
0
1
1
1
2
1
0
1
2
1
1
0
0
2
1
1
0
1
1
1
0
1
2
0
1
2
0
1
2
2
2
2
0
2
0
1
2
2
2
0
2
0
1
1
0
0
1
1
2
0
0
0
1
2
3
0
1
1
1
1
2
0
2
1
1
1
2
1
1
1
1
1
0
0
0
0
0
0
1
1
2
1
1
1
1
0
1
2
2
1
2
1
0
1
1
3
1
1
1
1
2
1
1
1
2
0
1
0
0
0
2
0
1
2
1
1
0
2
2
1
1
0
2
2
2
1
0
1
0
1
1
1
1
2
1
1
1
0
1
0
2
1
1
1
1
1
0
0
0
1
0
1
2
1
3
2
2
1
1
1
2
1
0
1
0
1
1
2
0
1
0
2
2
1
1
1
2
0
0
2
0
0
1
2
1
1
2
2
2
0
1
0
1
1
2
1
2
1
1
1
2
0
1
0
2
0
1
1
0
1
0
1
0
0
0
0
1
1
0
1
2
0
2
1
0
1
0
2
2
1
1
2
1
2
1
0
1
0
0
2
1
1
1
1
1
2
1
1
0
1
0
1
1
0
2
1
1
1
1
1
0
2
0
1
1
0
1
2
1
1
1
0
1
1
2
2
2
1
1
0
1
1
3
0
0
0
2
1
4
1
1
0
0
0
1
0
1
1
2
1
1
1
0
1
1
1
0
1
0
1
1
1
1
1
2
0
1
0
1
1
0
1
0
0
1
1
0
1
1
0
1
0
1
1
1
1
3
1
2
1
0
1
1
1
1
2
0
1
0
1
1
2
1
2
0
0
1
0
1
1
0
0
1
0
2
1
0
0
2
1
1
0
2
2
0
1
1
2
1
1
2
2
0
0
1
0
1
1
2
0
2
0
0
1
1
1
1
0
2
1
1
1
2
3
1
0
1
1
1
0
1
2
2
2
1
2
1
1
2
0
1
0
0
0
2
2
1
0
2
2
0
1
2
2
2
2
0
1
2
0
0
0
1
0
1
1
1
2
1
0
0
1
2
3
0
1
1
0
2
1
1
0
2
0
1
0
2
2
1
0
1
1
0
0
2
1
1
2
1
2
1
1
1
1
0
1
1
1
0
1
2
2
1
0
1
1
1
1
0
1
2
1
1
1
0
1
1
1
2
2
1
0
1
1
0
1
0
1
4
1
2
0
1
0
1
0
0
0
0
0
2
1
0
1
3
0
1
1
0
0
1
2
1
0
2
2
1
1
0
1
1
1
1
2
0
2
0
2
1
1
1
2
2
1
1
2
0
2
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
0
1
1
1
1
0
1
0
1
1
0
2
0
2
0
1
0
1
0
0
1
0
0
2
2
2
1
1
1
1
1
0
2
0
0
0
0
0
0
1
1
1
1
13
0
1
1
0
1
1
0
2
1
1
1
1
1
1
1
0
1
1
1
1
2
1
0
1
1
1
0
1
1
1
0
2
2
1
0
1
0
1
1
1
0
1
1
1
1
0
0
1
0
2
1
1
1
1
2
2
1
2
1
1
1
0
1
1
4
0
0
1
0
1
2
0
2
0
2
1
1
1
0
0
1
2
1
0
1
0
1
1
1
2
0
0
0
2
3
1
0
0
2
2
2
0
2
1
0
0
0
0
0
0
1
0
2
1
2
0
0
1
1
2
2
3
2
1
1
0
0
2
1
2
2
0
1
1
1
1
0
0
1
1
1
1
1
2
0
0
2
2
0
0
0
1
1
1
1
2
0
1
0
1
0
0
1
1
1
1
0
2
0
0
0
0
2
1
1
0
0
1
2
1
1
1
0
0
2
1
2
0
2
1
1
1
1
1
2
1
2
2
1
0
1
1
1
1
2
0
1
0
1
1
0
1
0
0
0
2
0
2
1
1
1
1
1
1
2
0
1
6
2
1
2
1
1
0
1
2
1
1
0
0
1
0
2
1
0
0
1
0
1
2
2
2
1
0
1
1
0
2
1
1
2
1
1
1
1
0
1
1
0
1
2
2
1
1
1
2
2
2
0
1
1
1
1
0
0
1
0
0
1
0
1
0
1
1
1
0
1
2
2
1
1
0
0
2
2
0
0
2
0
2
1
0
0
1
1
1
1
1
1
1
1
0
0
1
1
1
2
1
1
2
0
1
1
1
2
0
2
1
2
2
1
2
0
1
1
1
0
0
0
1
2
0
0
1
1
1
1
2
1
1
0
1
0
1
0
1
1
1
1
0
1
1
0
2
1
1
1
1
0
1
2
1
1
2
0
1
1
0
2
1
2
0
0
1
0
1
0
2
2
1
1
0
2
0
2
1
1
0
1
2
2
0
1
1
1
1
1
2
0
2
0
0
1
0
0
1
1
1
1
1
1
0
2
0
2
1
1
1
0
1
1
2
1
2
1
0
1
2
1
0
1
1
0
0
1
1
1
1
1
1
1
3
2
1
0
1
0
1
1
0
0
2
1
2
1
1
0
0
2
1
0
1
2
0
2
1
0
0
1
1
0
1
2
1
0
1
1
2
1
1
2
1
0
1
2
1
0
2
1
2
0
0
1
1
1
0
2
2
1
0
1
1
2
0
0
1
1
1
2
0
0
0
2
1
1
1
2
1
1
1
1
0
1
0
1
1
1
2
0
0
0
0
0
0
0
1
0
1
1
1
1
2
0
0
1
1
1
1
1
1
1
0
1
2
0
1
1
2
0
0
0
1
2
0
1
1
1
1
2
1
0
0
0
2
2
1
3
1
2
2
2
2
0
3
1
1
0
0
0
1
0
2
1
1
0
2
2
0
1
1
0
1
0
0
1
1
0
1
0
1
0
0
0
0
1
2
1
1
0
1
0
0
1
1
1
1
3
0
2
0
0
1
1
0
0
0
1
0
1
3
1
1
0
0
1
1
1
1
0
1
1
0
2
2
1
0
1
2
0
0
1
1
1
1
2
1
1
3
2
0
1
1
0
1
0
0
1
0
0
0
1
1
1
0
1
1
2
1
0
0
1
1
2
1
1
1
2
2
0
1
0
2
2
2
2
1
1
2
1
0
0
0
1
1
1
2
1
0
1
2
1
1
0
1
1
1
1
1
1
0
0
2
1
2
1
2
1
1
0
0
1
1
0
2
2
0
2
2
2
2
1
1
1
1
1
2
1
1
1
0
1
0
0
1
1
1
6
1
2
0
1
1
1
1
0
2
0
0
1
1
1
0
0
2
1
0
1
1
0
1
0
1
1
1
2
0
0
1
1
0
3
1
0
0
2
1
1
2
0
1
1
2
1
1
1
1
0
1
0
1
1
0
0
2
0
2
2
1
1
1
0
2
3
1
1
2
2
2
0
2
0
2
1
0
0
1
0
0
1
1
1
1
1
1
2
1
2
0
1
4
1
2
0
2
1
0
2
2
0
1
0
1
1
0
1
1
0
1
1
1
1
2
1
0
1
1
1
1
1
2
1
2
1
1
2
1
0
1
1
1
0
1
0
2
3
1
2
1
0
2
1
1
0
1
0
1
1
1
1
1
0
1
0
2
0
2
0
1
0
1
2
2
2
0
1
2
1
0
1
2
0
1
3
0
1
1
0
2
0
1
1
0
0
2
0
2
1
2
0
1
2
0
1
0
1
3
2
1
0
2
2
0
2
1
1
1
1
1
1
2
2
1
0
1
1
0
2
2
4
1
0
1
2
1
0
1
1
1
0
1
1
1
0
2
1
1
2
0
1
1
2
1
2
1
2
0
1
1
1
0
0
2
1
0
2
3
1
0
1
1
2
1
2
1
2
1
0
0
1
6
0
1
2
0
2
0
1
1
0
1
1
0
1
2
0
2
1
1
1
0
0
2
1
1
3
1
2
1
1
1
1
0
0
1
1
2
0
1
0
2
2
2
1
2
1
2
1
0
2
0
2
2
1
0
2
1
2
0
1
2
1
1
1
2
1
1
1
2
2
4
2
1
1
1
1
0
1
1
1
2
0
1
1
0
0
1
2
1
1
1
2
1
1
1
0
1
1
0
0
1
0
1
1
0
1
0
0
0
1
1
1
0
0
1
1
2
1
0
1
1
1
1
1
3
1
2
0
1
1
1
2
1
1
0
0
2
1
1
1
1
1
1
1
1
0
2
1
2
1
1
0
1
0
2
1
1
0
1
1
1
0
2
1
1
1
1
2
1
1
1
1
0
1
2
0
2
3
1
1
1
0
1
1
0
2
1
2
0
1
1
1
0
1
1
1
0
1
0
0
2
2
2
0
0
1
1
0
2
2
1
1
1
1
1
2
1
1
1
2
1
1
0
0
0
2
1
2
1
0
1
0
0
0
1
0
1
0
1
2
1
1
0
2
2
1
1
0
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
0
2
1
2
0
2
0
0
1
3
1
1
1
3
0
1
0
1
1
1
1
2
0
1
2
1
1
1
1
0
2
2
0
1
2
2
1
0
1
2
1
2
2
1
3
2
0
1
1
0
0
0
0
0
1
1
2
1
0
0
0
0
0
2
1
1
0
1
0
3
1
0
2
2
0
1
1
1
1
0
1
2
1
2
1
0
0
0
1
0
0
1
0
1
1
0
2
0
1
1
1
0
1
1
1
2
0
1
1
1
1
1
1
0
1
1
2
1
0
1
1
1
2
2
1
0
0
2
1
2
2
1
1
1
1
2
1
0
1
2
1
1
1
0
1
1
1
1
1
2
1
2
1
0
2
0
2
1
0
1
0
1
2
1
1
2
2
2
1
1
1
2
0
1
0
1
1
1
2
0
1
1
1
2
1
1
2
1
2
0
0
1
0
0
0
1
2
1
4
0
2
1
2
1
0
1
1
1
2
0
0
2
1
1
1
2
0
0
1
1
0
0
0
2
1
2
1
1
1
1
1
2
1
1
1
0
1
1
0
1
0
1
1
1
2
1
0
1
1
2
1
1
2
1
1
0
2
1
0
0
1
1
1
0
2
1
1
0
1
1
1
0
2
0
2
2
2
1
1
0
2
1
2
0
2
1
1
1
1
0
0
0
1
1
2
0
1
0
1
1
1
1
2
0
1
0
2
2
1
0
1
0
1
1
2
0
1
0
1
0
0
0
1
1
2
1
1
1
0
1
0
1
1
1
1
1
1
1
1
1
2
0
0
0
1
2
0
2
1
1
1
1
1
1
2
1
1
1
1
2
1
1
0
0
2
1
2
2
1
2
0
1
0
1
2
1
0
1
2
2
1
1
1
1
1
1
2
1
2
2
0
1
1
1
2
0
1
2
0
2
1
2
0
2
2
1
1
1
1
2
1
0
2
1
1
0
0
1
1
0
1
0
2
0
1
2
1
1
2
0
1
1
2
2
1
1
1
2
1
0
0
2
1
0
1
2
0
1
1
0
0
0
1
1
2
1
1
1
1
1
1
0
1
1
2
0
1
2
1
0
1
2
1
2
1
0
0
1
2
1
1
0
0
0
2
1
1
1
1
2
2
2
1
1
2
1
1
1
2
2
2
2
0
0
1
1
0
1
0
2
0
1
0
1
2
1
1
1
1
1
0
0
0
0
1
1
1
1
1
2
2
3
1
2
0
0
1
1
2
2
2
1
2
0
1
0
1
0
0
1
2
1
3
2
0
0
0
1
2
1
1
0
0
2
2
0
1
1
0
0
0
1
1
2
1
1
1
1
0
1
1
2
1
1
2
1
2
2
0
0
1
2
0
0
1
2
1
0
1
0
1
2
0
1
0
1
1
1
1
0
2
1
0
1
2
1
1
1
2
1
0
1
2
0
1
1
1
1
1
2
0
2
1
0
1
2
0
1
1
0
2
2
0
3
0
2
1
1
1
1
0
0
1
1
2
1
2
0
1
2
2
0
1
0
2
1
2
1
0
1
1
1
1
1
0
0
0
1
2
1
0
0
2
0
0
2
0
3
0
2
1
1
2
1
1
0
0
2
0
0
2
1
1
1
0
1
2
1
0
0
1
0
1
0
0
0
0
0
1
1
1
1
2
1
0
1
0
1
1
2
1
1
0
0
2
3
1
1
1
2
0
0
2
1
1
0
2
0
1
0
2
2
2
2
1
1
1
1
2
2
2
1
1
2
0
1
0
1
0
2
3
2
2
4
1
1
0
0
2
0
1
0
1
3
1
1
0
2
0
1
0
1
0
0
1
0
1
1
1
0
1
0
2
1
1
0
1
1
1
1
2
1
2
1
1
1
1
1
2
0
1
0
1
0
1
1
1
3
0
0
2
1
1
3
0
2
0
2
0
1
0
1
0
1
1
6
0
1
0
0
1
2
0
0
0
0
5
1
1
0
2
0
1
0
0
1
1
2
1
1
1
3
1
1
1
1
2
2
1
1
0
2
1
2
1
1
1
0
0
2
0
1
1
1
0
0
0
0
1
2
2
1
1
1
0
2
2
2
1
0
0
2
1
0
2
1
1
0
0
2
1
1
2
0
1
1
1
2
1
1
1
1
1
0
2
1
1
2
1
0
1
1
2
1
2
1
1
1
0
0
1
2
1
1
2
1
1
1
1
1
0
0
2
2
0
2
1
1
1
1
1
1
1
1
2
2
2
1
1
0
1
1
2
1
1
1
1
1
1
1
1
1
0
0
1
1
2
2
1
1
1
1
1
0
1
0
1
0
2
0
1
0
0
1
1
1
0
2
2
1
1
0
1
1
1
2
1
0
0
1
0
1
1
0
1
2
1
1
2
1
1
1
1
1
1
0
2
5
0
0
1
1
2
0
0
0
2
0
0
1
2
0
2
1
0
1
0
0
0
1
2
1
2
0
1
2
1
1
1
2
1
2
1
1
0
0
0
1
2
1
1
0
1
1
0
0
1
0
1
0
0
0
1
1
0
1
0
2
1
0
1
0
0
1
0
0
1
2
2
0
2
2
4
1
1
1
2
2
0
0
0
1
0
2
0
1
0
2
2
1
1
2
1
2
1
2
0
1
1
2
2
2
0
2
0
1
1
0
1
1
0
0
1
1
1
1
0
0
1
1
0
1
1
2
1
1
2
1
1
2
1
1
0
1
0
0
0
1
1
1
1
0
1
1
1
1
1
0
1
5
2
1
1
1
0
1
2
2
1
1
1
1
2
2
1
1
0
0
1
1
0
1
1
0
1
1
1
1
1
1
0
1
0
1
1
0
1
1
1
1
0
1
1
1
2
0
1
1
2
1
1
1
1
2
6
2
2
1
1
1
1
2
1
2
2
1
0
1
1
2
1
2
2
1
1
0
0
2
1
1
1
2
0
2
1
0
1
0
1
2
1
2
0
0
1
1
1
0
1
0
2
0
1
1
1
2
1
0
0
1
1
1
0
2
2
1
2
1
1
1
2
1
1
2
0
2
1
1
1
0
1
1
2
2
1
2
2
1
2
2
1
1
0
1
1
1
0
0
1
2
1
1
2
1
1
1
0
4
2
1
2
1
0
1
2
1
1
1
1
0
0
0
1
1
2
0
1
1
1
0
2
0
0
0
1
2
1
1
0
0
3
2
1
1
1
1
2
0
2
0
1
0
1
1
0
2
0
1
2
1
0
2
0
2
1
0
2
2
2
0
2
2
2
1
1
1
1
2
0
1
1
2
2
1
1
1
0
1
0
0
2
1
2
1
1
1
0
1
1
1
2
0
1
0
1
1
1
1
0
1
0
1
0
2
0
0
1
0
2
2
1
2
0
1
1
1
1
2
2
2
0
0
2
2
0
2
0
1
1
1
2
1
0
1
0
1
1
1
1
1
0
1
0
0
1
1
0
1
1
2
2
1
0
2
0
1
1
0
1
0
1
0
0
1
1
0
2
1
0
0
1
1
1
0
0
1
2
0
0
1
1
1
1
2
1
0
1
4
1
2
1
2
2
2
1
1
1
2
1
1
0
1
1
0
0
1
0
2
1
1
0
1
1
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
2
0
1
0
1
0
1
1
1
1
0
2
1
0
0
2
0
1
1
1
0
0
0
0
1
0
2
1
2
0
2
1
2
2
1
1
0
1
0
2
2
1
0
2
1
1
1
0
1
0
3
2
2
1
0
1
0
1
1
1
1
1
0
1
2
2
2
2
0
1
4
0
1
1
0
1
0
2
0
0
1
2
1
1
2
1
2
0
1
1
0
1
1
1
0
1
0
1
0
2
0
2
1
2
2
0
0
0
1
2
1
0
2
1
2
0
1
2
0
0
0
1
1
2
2
3
0
0
0
1
1
3
1
0
2
0
0
2
0
0
2
4
1
0
0
0
1
1
1
1
1
1
1
1
0
2
0
2
0
1
2
2
1
0
1
1
1
0
1
2
1
2
1
0
1
1
1
0
1
2
0
1
0
1
2
1
0
2
1
1
0
0
1
1
2
0
1
2
1
1
1
1
0
2
1
2
2
1
1
1
2
1
0
2
0
2
1
2
1
2
0
3
2
4
1
1
0
1
1
0
1
1
0
0
1
0
1
2
1
1
2
1
1
2
0
2
2
1
1
0
0
1
1
2
0
0
1
1
1
2
1
1
2
1
1
1
1
1
1
0
0
0
1
0
2
1
0
0
1
0
1
1
0
2
1
0
1
1
1
1
0
1
1
2
1
2
0
1
0
1
1
0
0
1
1
1
1
0
1
1
0
0
0
2
0
0
1
1
1
1
1
2
2
1
1
0
1
0
1
1
1
0
1
1
1
0
0
1
0
0
1
1
0
1
1
3
0
1
1
0
1
1
1
0
1
2
1
1
0
1
2
2
0
2
1
1
2
2
1
1
1
1
1
1
1
0
1
1
0
2
1
1
1
1
1
0
1
1
2
1
1
1
1
1
0
0
0
1
0
1
0
1
0
0
1
1
2
2
1
1
1
0
0
0
0
1
2
0
2
0
1
0
2
1
2
2
1
1
2
2
1
2
1
2
0
1
1
1
1
1
2
2
1
2
0
2
2
2
2
1
2
1
0
1
0
2
2
1
1
0
1
0
1
2
3
2
1
1
2
0
0
0
1
2
1
1
1
1
0
0
0
2
1
1
0
1
0
1
2
1
1
2
1
0
1
2
1
1
2
1
1
0
1
1
1
1
0
1
1
1
1
0
2
1
1
1
1
2
1
1
1
1
1
0
1
1
1
1
0
2
1
1
1
0
0
0
1
0
0
1
1
0
1
1
0
2
0
1
0
2
1
1
0
0
1
0
2
1
1
0
0
0
1
1
1
0
1
0
0
1
0
1
0
0
1
1
1
1
1
1
1
1
1
0
2
1
1
1
1
1
2
0
1
1
1
0
0
0
1
1
1
1
0
1
0
0
1
1
0
0
1
2
0
0
1
2
0
2
1
2
2
1
2
0
1
0
1
1
2
1
1
1
2
0
1
2
1
1
1
2
0
0
1
1
2
1
0
1
2
1
2
0
1
1
1
2
0
0
0
2
1
2
0
1
1
1
0
1
1
1
0
1
0
1
2
1
2
0
1
1
1
0
1
1
0
2
1
1
1
2
0
1
2
1
0
0
1
1
1
1
1
0
0
2
0
1
2
2
1
2
2
2
0
2
1
2
2
2
2
0
0
2
1
1
2
1
1
1
0
0
0
1
2
1
0
0
1
2
0
1
1
1
0
1
0
1
1
0
2
2
0
2
1
2
0
0
0
1
1
0
2
0
3
1
0
1
1
1
1
3
0
2
3
1
2
1
0
1
2
2
1
0
0
2
2
0
0
0
2
0
1
2
2
0
2
0
1
1
1
3
2
1
0
0
1
0
0
1
1
2
2
0
1
0
0
1
1
1
1
1
1
0
1
1
1
1
1
2
2
1
1
0
1
1
1
1
0
1
1
0
2
1
0
0
1
1
0
1
2
2
1
0
0
1
1
2
0
0
0
2
0
0
2
1
0
0
1
0
1
1
2
0
2
1
2
0
2
1
2
2
1
2
0
0
1
0
0
0
0
1
1
0
0
1
2
2
1
1
0
1
2
0
1
0
1
1
1
0
1
1
2
2
1
1
1
0
2
1
2
1
1
1
2
2
2
1
0
1
1
0
1
1
2
1
1
2
1
1
0
1
2
2
2
1
1
0
1
2
0
1
1
2
2
1
1
0
1
1
1
2
1
1
2
0
3
1
1
1
0
2
2
2
2
2
1
0
2
1
3
0
0
2
0
0
0
1
1
2
2
1
0
1
0
1
1
1
1
1
0
1
2
1
1
1
0
0
1
2
1
1
2
1
0
1
1
2
1
0
0
0
0
2
2
1
0
1
2
2
0
1
2
0
1
2
1
1
0
1
1
1
2
2
1
1
1
4
2
0
1
0
2
0
1
0
1
2
1
2
1
1
1
1
1
0
0
1
1
0
0
0
1
1
1
0
0
2
0
2
0
0
0
1
1
0
0
2
1
2
1
2
2
2
0
2
1
1
0
1
0
1
0
2
0
0
3
0
1
1
0
0
0
1
0
0
1
0
0
1
0
2
1
1
1
0
0
0
0
4
1
1
1
1
0
1
0
1
1
0
1
2
0
0
0
0
1
1
0
1
1
1
2
1
1
1
1
0
0
0
0
1
1
1
0
1
0
0
1
1
0
2
1
1
0
0
2
1
0
1
2
0
0
0
2
0
2
1
1
1
0
1
1
1
2
2
1
2
0
2
0
1
1
2
0
1
1
1
1
2
1
0
3
2
3
1
1
0
1
2
1
2
1
1
0
1
2
0
1
2
1
2
1
0
1
1
2
1
0
2
1
0
1
2
1
0
3
1
0
1
2
1
2
1
0
1
1
3
1
1
1
1
1
1
0
1
1
2
1
1
1
1
0
1
1
1
1
1
1
1
1
0
2
0
1
0
1
2
0
0
1
2
2
0
1
0
2
1
2
0
1
1
3
2
0
0
0
1
1
1
1
1
1
1
1
1
0
2
0
2
1
0
1
1
1
2
2
0
1
2
1
0
1
1
1
1
1
0
0
1
1
2
1
0
0
1
2
2
2
2
0
2
1
0
4
2
1
2
1
1
1
1
1
1
0
1
2
1
0
0
1
0
1
1
1
1
1
0
0
1
1
1
1
1
2
1
2
1
1
1
1
1
1
0
0
0
2
0
0
0
2
2
1
1
2
1
1
1
1
2
1
0
3
1
1
1
1
0
1
0
2
1
0
1
0
0
2
1
2
0
1
1
0
1
0
0
2
2
1
1
2
2
1
1
1
1
1
1
1
0
2
2
0
0
1
0
1
1
3
1
2
2
3
0
0
0
1
2
1
1
1
1
0
2
1
2
1
1
0
2
0
1
0
3
2
1
1
0
1
2
1
0
1
0
0
0
0
1
1
1
0
0
1
1
2
1
1
1
0
2
2
2
0
1
2
0
1
1
0
1
2
0
1
0
0
0
0
2
0
2
1
2
2
1
1
0
2
1
2
4
0
2
1
1
0
0
1
0
0
0
2
2
1
0
0
1
2
1
0
2
1
1
0
2
2
3
1
0
2
2
1
0
1
0
0
0
1
2
1
0
0
2
1
1
1
0
0
0
0
2
1
1
1
2
1
3
1
1
1
1
1
1
2
0
2
2
2
1
0
1
1
1
1
0
2
1
2
0
2
1
2
1
0
0
1
1
1
2
2
1
1
0
1
1
1
2
2
1
0
1
0
1
0
0
1
0
0
2
1
1
1
1
0
1
0
1
0
0
1
2
2
1
0
0
1
2
1
0
0
1
1
2
1
1
0
1
2
2
1
0
1
1
1
3
2
0
0
1
1
1
1
0
1
0
2
0
0
1
1
1
1
0
0
2
1
2
1
1
0
2
2
2
1
1
2
2
2
2
1
1
1
1
2
2
2
1
1
0
0
2
0
1
0
1
1
1
1
3
2
4
1
2
1
1
2
1
1
1
0
0
1
2
2
1
2
1
0
0
1
2
1
2
2
0
2
1
1
1
0
1
1
0
2
1
1
1
0
2
0
2
2
1
1
0
0
2
3
1
1
0
0
0
0
0
1
2
2
0
2
0
1
1
1
0
1
1
2
0
0
2
1
1
0
0
1
0
1
1
0
0
0
0
1
1
0
3
0
2
1
2
0
1
2
2
0
1
0
1
2
0
1
2
1
0
2
1
2
1
2
1
1
1
1
1
1
0
2
0
0
2
0
0
2
2
2
2
0
1
2
1
2
2
1
0
1
0
0
1
0
0
0
0
1
1
2
1
1
0
0
0
0
0
1
2
1
2
2
2
1
0
2
1
1
2
0
0
1
1
0
2
1
0
1
1
2
1
0
1
2
0
2
1
1
2
0
0
1
2
1
0
1
1
1
1
1
0
1
2
0
1
1
1
2
2
2
3
0
2
1
0
1
0
1
0
1
1
3
1
0
1
0
0
0
0
3
1
1
1
0
2
2
2
2
1
2
1
0
0
2
2
1
0
1
1
1
0
2
1
1
0
1
0
0
0
0
1
0
2
1
2
1
3
0
1
1
1
1
1
1
1
1
2
1
1
1
2
1
0
0
1
1
1
1
1
0
1
2
0
1
2
0
1
1
1
2
0
2
1
0
1
1
0
1
1
1
1
1
0
1
2
1
0
2
2
0
0
1
1
1
1
0
2
2
1
1
1
2
3
1
0
1
0
2
1
2
1
1
1
0
0
1
1
0
2
0
1
0
1
0
2
1
0
2
1
0
1
2
0
0
1
1
1
0
1
1
0
0
0
0
2
1
2
1
1
1
0
0
1
0
1
1
0
2
1
2
1
0
1
1
1
1
0
0
0
1
0
2
1
2
0
1
1
1
1
1
2
0
1
2
1
1
1
0
1
0
2
2
1
2
0
0
0
3
1
2
0
0
0
1
1
2
2
1
2
0
2
2
0
1
0
0
1
1
2
1
0
0
1
1
1
1
1
0
1
0
1
1
1
2
2
0
2
1
0
1
0
2
2
1
1
1
1
2
2
0
0
1
2
1
1
2
0
1
1
0
1
0
1
2
1
2
2
1
1
0
0
2
1
0
1
1
1
2
1
0
2
0
2
2
2
1
1
1
0
0
1
1
1
1
2
1
1
0
0
2
1
1
1
2
2
1
1
0
0
1
1
1
0
1
0
1
0
1
1
0
2
2
1
1
1
2
0
2
2
0
0
0
0
2
0
1
0
1
0
0
1
0
2
2
2
1
1
0
0
0
2
1
0
1
1
2
0
1
2
1
0
0
1
2
1
0
0
2
2
1
2
1
1
1
2
1
1
1
0
1
0
1
1
2
1
2
1
2
2
2
1
1
1
1
2
1
1
0
1
0
0
0
0
1
0
1
1
1
2
1
2
1
1
1
1
0
3
2
1
0
0
1
1
1
1
0
1
2
2
0
1
1
1
0
1
1
1
1
0
1
2
1
2
1
0
0
1
1
1
1
1
2
1
1
2
2
1
1
0
2
1
0
1
0
0
1
0
0
1
0
1
1
0
2
2
1
1
0
2
1
0
2
1
1
1
1
1
1
0
0
0
1
2
2
0
2
0
0
0
2
2
1
1
1
2
1
1
2
2
1
1
0
1
2
1
1
2
1
1
1
0
2
1
1
0
2
0
0
1
1
1
2
1
1
0
1
0
1
2
1
1
2
1
1
1
1
0
0
1
1
2
0
1
1
1
1
0
0
1
0
1
1
2
0
1
1
1
2
0
0
1
1
2
1
0
2
1
2
0
1
0
1
1
1
0
1
0
1
1
1
0
0
1
1
2
2
2
0
1
0
0
1
0
1
0
1
1
0
2
2
1
2
1
1
2
0
3
0
2
2
2
0
1
0
0
2
1
0
1
1
1
1
0
0
1
1
1
0
0
0
2
2
1
1
2
1
0
1
2
1
2
1
0
0
1
0
0
2
3
1
2
1
0
0
1
1
1
1
1
1
1
1
1
2
2
0
1
0
1
0
1
0
0
0
2
2
2
1
2
1
0
1
0
3
1
0
0
1
2
0
1
0
1
2
2
2
1
1
0
0
2
1
1
2
0
1
2
1
1
0
1
2
1
2
1
2
1
2
0
1
2
0
1
0
0
2
1
0
2
0
0
2
2
0
1
2
2
0
0
2
2
1
0
0
1
0
2
1
2
2
1
0
1
1
1
3
1
2
0
2
2
0
2
2
0
1
1
0
1
2
2
1
2
2
2
2
0
0
2
0
1
0
2
1
1
1
0
2
2
1
2
0
0
0
2
1
1
1
0
0
0
1
1
1
1
0
1
1
0
1
0
0
1
0
2
1
2
0
2
0
2
0
0
1
1
1
1
2
1
0
2
2
0
0
1
0
1
2
1
2
0
0
1
2
0
2
2
2
1
0
2
1
1
0
0
1
2
1
1
2
2
1
1
0
1
1
0
2
1
1
1
0
1
2
1
0
0
2
0
2
2
0
2
1
0
1
1
0
1
1
1
1
0
0
1
0
1
1
0
2
2
2
1
1
0
1
1
2
0
1
2
1
0
2
2
1
0
1
0
0
2
1
0
1
0
1
1
1
1
2
1
0
2
0
1
1
0
2
1
0
1
0
2
0
1
3
1
1
2
1
0
1
1
1
0
2
1
1
0
0
1
1
2
1
2
1
2
1
1
0
2
0
1
0
0
0
0
0
1
1
2
1
1
2
1
0
0
2
0
1
0
1
1
1
0
2
0
1
0
1
2
1
1
2
2
2
0
0
0
1
0
1
1
1
0
1
1
1
1
1
0
2
0
0
1
1
0
0
4
3
1
1
1
1
1
1
1
0
2
1
2
2
1
1
1
2
0
2
1
2
2
0
2
1
1
0
1
1
0
0
1
1
0
1
2
2
1
1
1
1
1
0
0
0
2
1
0
2
2
1
1
0
0
0
2
0
2
0
1
1
0
0
0
1
1
0
0
0
1
2
3
3
1
0
0
1
1
1
1
2
1
0
0
0
0
0
1
0
0
1
0
0
2
1
2
2
2
1
1
1
1
1
1
0
2
1
1
0
1
0
0
1
0
2
0
0
2
1
0
1
2
0
1
2
0
1
2
2
0
0
0
0
0
0
1
0
1
1
0
0
1
0
1
1
2
1
1
2
1
1
1
2
1
2
1
2
0
0
2
0
1
0
0
0
0
2
2
0
1
1
1
0
1
0
1
1
1
2
0
0
1
4
0
0
2
1
2
0
0
0
1
0
1
1
0
1
0
2
1
1
1
1
0
2
1
1
0
1
0
2
1
2
1
2
3
0
1
1
0
2
1
0
1
2
0
2
0
0
1
0
1
0
1
1
1
0
0
1
0
1
1
1
0
2
0
2
1
0
0
1
1
1
1
2
1
1
2
2
1
3
1
2
1
1
1
1
1
0
1
2
0
1
0
1
1
3
0
0
0
2
0
0
2
1
1
1
0
1
1
0
1
2
0
1
1
0
2
1
1
1
1
0
2
1
0
0
0
1
2
0
1
1
2
2
1
1
2
1
2
1
1
0
2
0
1
1
1
1
1
0
1
2
0
2
0
2
2
0
1
1
1
0
1
0
1
2
2
1
0
1
2
1
0
0
2
0
0
1
0
1
0
1
1
1
1
1
0
1
0
2
1
1
2
1
2
1
1
2
0
1
0
1
2
0
0
1
3
1
0
2
2
1
0
0
2
0
1
0
2
0
1
0
1
2
1
0
1
0
0
2
1
1
0
1
1
1
0
0
0
2
0
1
2
1
2
1
2
1
1
1
2
1
0
1
1
1
2
0
0
0
0
1
1
2
1
1
0
0
1
0
1
1
0
2
0
0
0
1
1
0
0
0
1
2
0
0
2
1
1
1
1
1
1
2
0
2
1
0
1
1
1
2
0
1
2
0
1
2
0
1
2
2
2
1
1
0
0
1
1
1
0
0
1
0
1
0
1
2
0
1
0
2
1
0
2
1
0
3
0
2
2
2
1
1
0
1
3
1
0
1
0
1
0
0
1
1
1
0
1
0
1
1
1
1
0
1
1
2
0
0
0
2
0
1
1
2
1
1
0
2
2
2
1
1
0
1
0
0
2
1
1
2
1
1
0
1
2
2
0
1
1
0
1
2
1
0
1
2
0
1
1
0
1
2
2
2
1
1
0
0
0
4
0
0
1
1
1
1
1
0
0
1
0
0
2
0
0
1
0
0
0
3
1
0
2
1
0
1
1
2
1
1
0
2
1
2
2
0
2
0
2
1
1
1
0
1
1
2
0
0
1
0
0
1
2
1
1
1
0
0
2
1
0
0
2
1
0
0
1
2
2
1
1
2
0
1
1
1
1
1
1
0
0
1
0
0
2
2
1
2
1
1
0
0
0
1
2
1
2
2
0
1
1
1
1
0
1
1
2
2
2
0
0
2
2
1
0
1
1
0
1
2
1
2
2
1
0
2
1
0
1
0
0
0
2
0
1
2
1
1
1
0
0
0
0
2
0
1
2
1
2
1
0
1
1
1
0
6
1
1
0
2
1
1
1
1
0
1
1
1
1
1
1
0
1
0
1
2
1
3
1
0
2
2
2
0
2
1
1
0
0
2
1
0
2
2
0
1
0
1
0
2
0
1
2
1
0
2
1
1
2
1
0
0
0
0
2
2
2
1
0
0
1
1
2
0
2
1
1
1
1
0
2
1
2
1
1
1
1
0
1
2
1
1
0
1
2
1
1
1
1
1
0
0
2
0
0
2
2
2
2
2
0
1
1
0
1
0
2
1
0
2
2
0
0
1
1
2
1
0
2
2
1
1
2
0
0
1
1
1
1
1
1
1
1
1
1
0
0
1
0
2
3
0
0
1
2
1
1
2
1
1
0
1
1
1
1
0
1
0
2
1
0
1
1
1
2
2
1
0
1
1
0
1
1
0
1
1
0
1
0
0
0
1
1
0
1
0
3
2
0
1
1
0
0
1
2
1
1
2
1
0
1
1
1
1
0
4
1
1
1
1
1
1
1
1
1
2
0
2
1
2
0
1
0
1
0
1
1
2
1
1
0
1
1
2
0
0
0
2
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
1
0
2
2
3
0
1
0
0
0
1
1
1
0
1
2
1
1
1
1
2
1
0
2
1
1
2
0
1
1
2
0
0
2
1
2
1
1
0
2
2
1
2
1
1
0
2
1
1
1
1
2
0
0
2
1
1
2
1
1
1
2
1
0
0
2
2
0
1
1
2
1
0
0
1
1
2
2
1
0
1
2
2
2
1
2
0
0
2
1
2
1
0
1
0
1
2
1
0
0
0
1
2
1
1
1
1
1
1
1
0
1
1
1
0
1
2
2
0
2
2
1
1
0
0
2
1
1
1
2
1
1
1
1
1
0
1
0
1
2
1
0
1
2
0
0
2
1
1
1
1
1
1
1
1
2
1
0
2
2
1
1
0
2
2
1
2
2
0
1
1
1
0
1
1
1
0
1
2
0
0
0
1
1
0
1
0
2
0
2
1
1
0
1
0
1
1
2
0
0
1
0
1
0
1
1
1
1
2
2
2
0
2
1
2
0
2
1
0
1
1
0
2
0
0
2
2
0
1
0
2
1
0
0
1
0
2
1
0
0
1
2
1
2
0
1
1
1
0
0
2
2
2
1
0
1
0
0
2
1
1
1
2
1
1
0
3
1
0
1
1
1
2
1
1
1
2
0
0
0
0
1
1
2
1
0
0
1
1
1
1
1
2
0
1
2
0
0
1
1
2
0
0
1
1
2
2
2
0
1
1
1
1
2
1
0
1
0
1
1
1
0
0
1
0
1
2
2
0
0
2
2
1
1
1
2
1
1
2
1
1
1
1
1
2
2
0
0
0
0
1
1
1
1
1
1
1
0
2
2
0
0
1
0
2
2
4
1
1
1
1
1
1
2
2
1
1
1
1
2
0
1
0
1
2
1
0
1
1
0
1
4
2
2
1
1
0
1
0
0
1
1
1
0
0
2
2
2
0
1
1
1
1
2
1
1
0
0
0
1
1
1
1
1
1
2
0
2
2
1
0
1
0
1
1
2
2
0
0
0
1
1
0
2
1
0
1
0
1
1
0
1
2
2
2
1
1
1
2
1
2
1
0
1
1
0
2
1
1
1
0
1
2
1
1
0
1
1
2
0
0
2
1
1
1
1
2
1
0
1
1
0
1
1
0
2
2
0
2
0
0
2
1
1
2
1
1
1
1
1
1
1
0
2
1
0
1
2
1
1
1
0
1
1
1
2
2
1
1
2
1
1
1
1
1
0
1
0
1
0
0
1
1
1
1
0
0
1
1
0
2
2
1
1
1
2
1
2
0
1
0
1
1
1
0
2
0
1
0
0
2
0
0
2
1
3
2
2
2
1
1
1
2
1
2
1
0
1
2
1
1
1
0
0
1
0
0
0
0
1
1
2
0
1
0
1
0
0
1
1
1
0
1
2
1
1
1
1
1
1
1
2
0
0
0
0
1
0
0
1
1
2
1
2
1
0
0
1
1
1
1
0
1
1
1
1
1
2
2
1
0
1
1
0
0
2
1
2
1
1
2
2
2
1
0
0
2
1
1
1
2
1
2
2
1
0
1
1
0
1
1
0
1
2
0
2
0
1
1
2
1
1
1
2
1
2
2
2
1
0
0
2
1
0
0
0
2
1
1
0
1
1
1
0
1
2
0
1
2
2
2
2
0
2
2
0
0
2
1
1
1
0
0
0
0
0
0
1
1
1
2
2
0
1
0
2
0
1
0
0
0
2
0
2
1
0
0
0
1
4
2
1
1
2
1
1
0
1
1
2
0
0
1
0
1
1
1
0
2
1
1
2
0
1
2
0
2
1
0
1
2
0
1
1
2
1
1
1
0
0
1
2
1
1
0
0
0
1
1
1
1
0
2
2
1
0
1
1
1
2
1
0
1
2
0
0
1
0
0
1
1
3
1
1
1
0
2
0
1
0
1
1
1
2
2
1
1
1
1
1
2
2
0
1
0
1
1
0
2
1
1
2
1
1
1
2
0
1
0
0
1
3
1
1
2
0
0
2
1
1
2
2
0
2
2
1
1
0
1
1
0
1
0
2
1
1
1
1
2
1
2
2
0
2
0
1
1
1
1
1
0
1
1
1
1
1
0
0
2
1
0
0
2
1
0
1
1
0
0
2
1
2
0
1
1
3
2
1
2
0
1
1
2
0
0
0
2
1
1
1
3
0
4
1
1
2
1
2
2
1
1
1
1
0
0
0
1
0
2
2
0
1
1
1
0
0
1
0
1
1
1
0
1
0
1
2
1
1
1
1
2
1
1
2
2
2
3
2
1
1
1
1
1
2
0
2
2
3
2
2
1
0
2
0
1
0
0
0
0
1
0
2
2
2
2
0
1
0
1
1
0
2
1
1
0
2
2
1
0
2
0
2
1
0
0
1
1
0
2
2
0
1
1
1
1
2
0
2
1
1
0
1
1
0
0
1
2
1
3
1
2
1
0
1
0
1
1
0
1
1
1
2
1
1
0
0
1
0
1
0
0
0
2
0
0
1
2
1
0
1
1
2
2
0
0
1
1
2
0
1
0
2
1
1
2
1
1
2
1
0
0
0
1
2
2
2
1
1
2
1
0
1
2
1
1
0
1
2
0
1
1
2
1
1
0
1
1
0
1
0
0
0
2
1
1
1
1
2
0
3
0
2
0
0
0
1
2
0
2
1
0
1
3
0
0
2
1
2
0
6
2
2
0
1
1
1
1
0
1
1
2
0
0
1
1
1
0
1
1
2
2
0
0
2
1
0
1
0
1
2
1
2
1
0
2
2
0
1
2
2
1
2
2
1
1
0
1
1
1
0
1
1
1
0
2
0
1
1
2
1
1
0
1
1
1
0
0
0
0
0
1
1
0
2
1
2
0
1
0
1
1
0
2
1
1
1
2
0
2
0
2
2
1
0
0
1
0
0
2
1
1
1
0
1
2
0
0
1
0
1
2
2
0
1
2
2
1
1
2
1
2
1
0
0
2
1
2
1
1
1
2
1
0
0
1
1
2
0
1
1
1
2
0
1
0
1
0
2
1
1
1
0
0
1
1
1
3
0
1
0
0
2
2
1
2
1
0
1
1
2
1
1
2
0
0
2
0
2
2
1
0
1
2
1
1
2
2
0
2
1
1
1
1
1
1
1
0
1
1
1
1
0
0
1
2
0
1
2
1
1
1
1
0
1
0
1
1
2
1
0
1
1
0
1
2
1
1
1
2
0
1
2
1
1
1
0
1
0
1
2
1
1
0
0
1
0
1
0
1
1
1
0
0
0
1
0
2
1
1
1
2
2
2
1
1
0
1
1
0
1
1
0
1
2
3
2
1
1
1
2
1
0
0
1
1
1
0
2
1
1
1
2
1
1
1
0
2
2
1
0
0
1
1
0
0
0
0
1
0
0
3
2
2
3
0
1
0
2
0
1
1
1
1
1
1
1
1
2
0
1
1
1
2
2
1
1
0
1
1
1
1
1
0
1
0
0
0
0
2
2
1
1
3
0
1
2
1
2
1
2
1
0
2
0
1
2
1
3
0
1
1
1
1
1
0
2
0
1
1
1
1
2
1
0
1
2
0
1
1
3
1
0
3
1
2
1
1
0
2
0
1
0
1
1
0
1
1
0
0
1
1
1
1
0
0
1
2
1
1
1
0
1
1
1
0
5
2
1
2
0
1
0
1
1
1
1
0
0
0
2
1
1
0
2
2
2
0
1
0
0
1
1
2
2
1
0
1
0
1
1
2
1
0
0
1
1
1
2
0
1
1
2
2
1
1
1
1
1
2
1
1
0
2
2
0
0
0
1
0
1
1
1
1
2
2
2
1
1
0
1
0
1
0
0
0
0
1
2
1
2
0
1
1
0
0
1
1
1
2
1
0
0
1
2
1
1
0
1
2
0
2
1
2
2
0
1
1
0
2
0
0
2
1
2
1
1
1
0
2
1
2
1
1
1
0
1
1
1
1
2
1
1
1
0
0
1
1
2
0
0
2
1
0
0
1
0
1
1
2
1
0
1
0
1
0
0
1
1
1
2
1
1
1
1
1
1
1
1
0
1
0
2
0
0
1
0
1
1
1
0
1
4
1
0
3
2
1
0
0
2
0
1
0
0
1
1
1
1
1
0
1
2
0
0
1
1
2
2
1
0
1
0
1
0
0
1
1
2
1
0
1
1
3
0
2
0
2
1
1
1
1
1
1
0
1
1
1
1
1
1
0
2
0
2
1
1
0
1
0
1
1
0
2
1
1
1
2
2
2
1
2
1
1
1
1
0
1
2
0
0
2
1
2
0
2
0
0
1
1
2
1
2
1
1
0
1
0
1
0
0
1
1
2
0
2
0
1
1
1
1
1
2
1
1
1
2
1
1
1
0
0
1
2
2
1
0
1
2
0
1
0
1
0
1
2
0
1
1
1
1
2
1
2
1
1
1
1
1
1
1
0
2
0
1
1
2
2
0
0
1
0
1
1
1
1
2
2
0
0
2
1
2
1
1
2
1
2
1
1
1
1
1
2
1
2
1
1
0
0
1
2
0
0
1
1
1
0
2
1
1
0
0
2
1
2
0
1
1
1
1
2
1
1
1
2
1
0
1
1
4
0
0
1
1
0
1
0
1
0
1
1
1
1
0
1
1
1
1
1
0
0
1
1
1
0
0
1
0
1
1
0
2
0
0
0
1
1
0
1
1
2
2
1
2
0
0
1
2
1
0
1
1
0
1
1
0
0
1
1
0
0
1
1
0
1
0
2
2
0
2
1
1
2
2
2
1
2
1
1
2
0
1
1
0
1
1
0
0
2
0
2
1
1
1
2
2
0
0
0
0
2
2
1
2
3
1
2
0
2
1
2
1
0
2
1
1
1
3
2
2
2
2
1
1
0
0
0
1
2
0
0
0
0
2
1
1
0
2
1
1
0
1
1
1
1
1
1
1
3
1
0
1
1
0
1
1
2
1
2
3
1
2
1
2
1
0
1
1
1
0
0
1
1
1
0
0
1
1
1
3
2
1
1
1
1
2
0
0
0
0
0
1
1
0
1
2
2
0
1
2
0
2
1
0
0
2
1
1
1
1
0
2
1
2
1
1
1
0
2
2
0
1
0
1
2
1
1
1
0
1
0
1
0
0
2
0
2
1
0
0
1
1
0
0
0
4
1
1
1
0
2
1
0
1
2
1
1
2
1
1
1
1
1
0
2
0
2
1
4
0
0
1
2
2
0
1
1
1
1
2
1
1
1
2
2
2
2
1
0
1
1
0
0
1
1
0
1
2
2
0
2
0
1
2
0
2
1
0
2
0
0
1
2
1
1
1
2
0
0
1
0
1
2
0
1
1
2
1
0
1
0
5
1
1
0
0
1
0
1
1
2
1
1
1
0
2
0
1
2
0
0
1
1
1
1
1
2
1
2
2
2
1
2
0
0
0
1
2
0
2
2
1
0
1
0
0
0
2
0
5
0
2
0
1
1
0
2
1
2
1
1
1
0
0
2
1
0
1
1
1
1
1
2
1
1
0
1
1
1
1
2
0
0
0
0
0
1
2
0
1
0
1
2
0
0
2
2
1
1
1
1
2
0
0
1
2
1
0
1
1
1
1
1
1
2
2
0
0
1
0
1
1
2
2
1
0
1
2
1
1
2
1
2
0
0
1
2
1
1
1
1
1
1
2
0
0
1
1
1
2
0
2
0
0
1
0
1
0
0
0
2
2
0
2
2
0
2
2
2
0
1
0
1
0
1
1
0
0
2
0
3
2
0
2
2
0
2
2
0
1
2
1
2
1
0
1
2
1
1
1
2
0
1
0
2
0
0
0
0
2
0
1
1
1
1
1
0
1
1
1
2
1
1
2
1
1
1
1
1
0
1
1
2
0
0
1
0
2
0
1
0
1
0
0
1
1
1
2
2
2
0
0
0
0
1
0
1
2
1
2
1
0
1
0
0
2
1
1
1
0
0
0
1
1
1
1
2
0
0
1
1
1
0
0
1
2
0
2
2
2
1
2
1
1
0
0
0
2
0
1
1
0
0
1
0
1
0
1
1
0
1
1
0
1
0
1
1
2
2
2
1
0
1
1
2
1
2
1
2
0
1
1
1
1
0
0
2
2
1
1
0
0
2
1
1
1
0
1
1
1
1
2
1
1
1
2
0
1
0
2
1
1
1
2
0
0
1
2
2
0
1
1
0
2
0
2
0
1
1
2
1
2
0
0
1
1
0
1
1
0
2
1
1
0
0
0
1
0
1
1
1
1
1
2
1
0
0
0
0
1
1
0
2
1
0
0
1
0
2
0
2
1
0
0
0
0
3
0
1
0
1
2
0
0
1
2
1
3
0
1
1
1
2
2
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
2
0
1
2
2
1
0
2
1
0
2
1
1
2
1
2
0
1
1
0
0
1
1
0
0
2
1
0
2
0
2
0
1
1
1
1
0
0
1
1
2
2
1
0
1
1
1
2
0
1
2
0
0
0
1
0
1
0
0
0
1
1
1
0
2
2
1
2
2
0
1
0
1
0
2
1
2
1
1
2
1
1
1
2
1
1
1
2
2
2
1
1
1
0
1
2
1
0
0
0
0
1
2
1
0
1
0
2
1
1
1
2
2
2
1
1
1
2
0
0
0
0
2
0
1
1
1
1
1
2
1
2
1
1
0
0
2
1
1
0
1
2
1
1
0
2
0
1
0
0
0
2
0
1
2
1
2
2
1
0
1
0
1
1
2
0
1
0
1
1
1
2
0
0
2
1
2
0
2
1
1
1
2
3
1
0
1
1
1
2
2
0
0
3
1
0
0
1
0
2
0
1
1
1
2
1
1
0
0
1
1
0
0
1
1
0
0
1
2
1
2
0
1
1
0
2
2
2
1
0
1
0
2
0
1
0
2
1
1
0
0
0
2
0
0
2
1
1
1
2
2
1
0
1
2
1
1
0
1
1
2
1
2
0
1
1
0
0
0
1
2
0
1
0
2
1
1
1
0
1
0
1
0
1
1
0
1
1
1
2
1
1
2
0
2
1
0
2
1
1
1
1
0
1
1
0
1
1
2
1
1
0
2
2
0
0
0
0
0
0
0
1
1
2
0
2
0
2
1
1
2
1
2
3
2
0
2
1
1
0
2
1
0
2
1
1
0
0
0
0
0
1
0
1
1
0
1
2
0
0
1
1
0
1
2
1
0
0
1
2
2
1
2
1
1
1
1
1
0
1
1
2
2
1
1
1
0
0
0
2
1
1
2
2
0
1
1
0
0
0
0
0
1
1
1
1
1
1
0
0
1
2
2
1
2
1
2
1
0
0
0
1
4
1
1
2
1
1
1
0
0
1
2
2
2
2
1
1
1
1
1
2
1
2
1
2
2
0
1
0
0
2
0
0
1
1
0
2
0
0
0
1
2
1
0
0
1
0
2
2
1
2
1
1
1
0
0
0
1
2
1
1
2
1
0
0
2
2
2
1
1
1
0
1
1
1
2
2
1
0
1
1
2
0
0
0
2
1
1
1
1
1
2
1
1
0
0
2
2
1
0
1
1
2
0
1
1
1
0
0
0
0
1
1
1
1
1
0
1
1
3
1
0
1
1
2
0
1
0
1
1
1
1
2
1
2
1
1
0
0
0
0
0
1
1
0
2
1
1
1
2
0
0
0
0
1
0
1
1
1
1
1
0
1
1
2
2
1
0
2
2
0
1
0
2
1
1
2
0
1
1
1
2
3
1
2
2
2
1
2
0
1
2
2
1
1
0
1
1
1
2
2
0
1
1
1
2
1
1
0
3
0
2
0
0
1
2
1
0
1
1
1
1
0
1
1
0
0
1
2
0
1
1
0
1
0
0
0
1
0
1
1
1
1
0
1
2
0
1
2
0
1
1
1
0
2
1
1
2
0
1
1
0
1
1
1
1
0
0
1
3
1
0
1
2
1
1
2
1
0
0
2
1
2
0
2
2
0
2
2
2
1
2
0
2
1
0
2
1
0
1
1
2
1
1
0
1
1
1
0
1
0
1
0
2
1
2
1
0
0
2
1
2
2
1
1
0
1
0
1
0
1
1
0
1
1
2
1
0
1
1
1
1
0
2
1
2
1
1
0
1
2
2
0
1
0
1
1
1
0
1
0
2
1
2
0
0
2
1
1
0
2
1
0
2
0
1
1
0
2
0
0
1
1
1
1
1
2
1
1
1
0
2
1
1
0
2
1
1
2
1
1
0
1
0
1
1
0
2
2
1
1
1
0
1
0
1
1
1
1
2
1
2
1
1
1
2
1
0
0
1
0
1
1
0
1
1
2
1
2
2
0
1
0
0
0
1
1
2
2
1
1
1
2
1
2
1
0
0
2
0
0
1
0
1
1
1
0
2
1
0
0
1
2
1
2
0
1
0
0
2
0
1
2
0
1
1
2
1
0
1
1
1
0
0
1
1
1
0
1
0
0
0
2
1
0
1
2
0
1
0
2
1
0
1
2
1
1
2
0
0
1
1
2
1
1
1
1
1
2
1
2
1
2
2
0
1
1
1
1
1
0
0
1
0
1
0
2
0
0
0
0
0
1
1
1
2
3
1
1
1
0
1
2
2
0
0
1
1
2
2
1
0
2
1
1
1
0
1
1
1
0
1
1
0
0
0
0
0
2
0
1
0
2
1
1
1
0
2
1
0
1
1
0
1
0
1
1
0
1
0
2
0
0
1
1
0
1
0
1
1
2
2
1
0
2
1
1
0
2
2
1
1
1
2
1
1
1
0
0
2
1
1
2
1
1
1
0
1
1
2
0
1
2
5
2
1
0
1
1
0
1
0
1
1
1
1
1
0
1
1
1
2
1
0
1
1
2
0
0
1
1
0
0
1
1
2
0
0
0
2
0
2
1
1
1
0
2
2
1
0
1
2
1
1
2
1
2
1
0
2
1
1
1
1
1
1
0
2
1
1
1
2
1
0
0
2
1
1
1
1
2
2
1
1
1
0
0
1
0
1
0
1
1
1
0
0
1
0
1
1
1
2
0
1
0
1
0
2
2
1
1
0
2
1
1
1
1
1
1
1
2
2
0
1
1
0
0
0
1
0
0
2
2
2
1
2
1
1
2
1
1
1
1
1
2
0
0
1
0
1
0
1
1
1
1
2
2
2
1
1
2
1
1
1
1
1
2
1
0
1
2
0
2
1
0
0
1
1
0
1
1
0
0
0
1
0
1
0
1
2
2
1
2
1
0
1
0
2
2
1
1
1
0
0
1
2
2
1
1
1
1
0
2
0
1
1
0
1
2
0
1
1
1
1
1
0
1
2
1
1
1
1
0
1
1
1
0
0
2
1
1
3
0
1
1
0
0
1
1
2
0
0
2
2
0
1
0
2
2
2
2
0
2
2
0
0
1
1
0
1
0
1
1
1
0
1
2
1
0
2
2
1
1
0
1
0
1
0
0
1
1
2
1
2
1
1
1
0
2
0
1
1
1
1
1
1
1
0
2
0
1
0
1
1
1
1
1
0
2
2
0
1
0
0
1
1
1
2
0
1
1
0
1
1
1
0
2
2
1
0
0
2
0
2
2
0
2
1
0
2
1
1
1
0
0
1
2
2
1
2
1
0
0
1
0
0
1
1
1
1
0
0
2
0
0
1
0
1
0
1
0
0
2
1
1
4
0
1
2
2
1
0
1
2
1
1
0
0
1
1
1
0
1
0
1
1
0
0
1
1
0
0
0
1
1
1
2
0
1
1
0
1
1
0
1
1
2
0
1
1
0
0
0
1
0
1
1
0
1
2
1
2
0
1
1
1
2
1
0
2
1
1
1
2
1
1
0
2
1
0
0
1
2
0
2
1
1
1
1
1
0
2
1
2
1
0
0
1
1
1
2
1
1
0
1
2
0
2
0
0
1
0
1
3
2
1
0
1
1
0
1
1
0
0
2
1
1
2
1
2
2
1
0
1
8
1
1
0
0
2
1
0
1
2
0
0
1
2
1
2
2
1
1
2
2
0
1
1
2
1
2
1
1
0
1
1
1
0
1
1
2
1
1
1
1
2
1
1
2
0
1
0
1
1
1
0
0
1
3
1
0
0
1
2
2
1
1
2
1
1
1
1
2
1
0
0
0
1
1
2
1
1
1
0
1
1
1
0
2
1
2
0
1
0
2
1
0
1
1
1
1
1
1
1
2
0
1
0
2
2
0
2
0
0
1
1
1
1
0
1
1
2
1
0
1
1
0
1
2
1
0
2
1
1
2
2
2
1
1
2
2
0
0
0
2
1
0
1
1
1
1
1
0
1
0
1
2
1
2
3
1
0
0
1
1
1
0
0
2
0
1
1
1
0
1
2
1
0
1
1
0
0
0
1
1
0
2
1
1
2
1
1
1
1
0
0
1
1
2
1
1
2
1
0
1
0
1
1
0
1
0
1
1
1
1
1
0
0
0
1
1
0
0
2
1
1
1
1
1
1
1
1
1
0
2
0
1
2
3
1
1
1
1
0
1
1
1
0
1
1
0
3
1
0
1
0
1
1
1
1
0
2
1
1
1
1
0
1
1
1
0
1
1
1
1
0
1
0
1
0
0
2
1
1
1
1
2
1
2
1
2
1
2
1
1
0
0
1
1
1
1
1
1
0
1
2
2
1
2
2
1
0
2
1
1
1
1
0
0
2
1
2
2
0
1
0
1
2
0
1
2
1
1
2
1
0
0
1
1
0
0
0
1
0
1
1
1
0
0
0
0
4
1
2
1
2
2
2
0
2
1
2
1
1
1
1
1
1
0
1
1
1
1
1
1
2
2
2
1
2
1
2
0
0
1
0
2
2
1
2
1
1
1
1
2
1
3
1
1
1
0
3
1
2
0
1
2
1
1
1
1
1
1
0
2
2
1
1
1
1
1
1
0
1
2
1
0
2
2
1
2
0
1
2
0
0
2
1
0
1
2
2
1
2
1
2
2
1
1
1
0
0
1
1
1
2
1
0
2
0
0
1
1
2
0
2
1
2
0
1
2
1
2
0
1
1
1
1
1
1
1
1
1
2
0
2
1
0
0
0
2
1
0
1
0
2
1
1
1
2
0
0
1
2
1
0
2
0
1
0
0
2
1
0
1
0
1
0
2
0
1
0
1
0
0
2
1
1
0
0
2
2
0
0
0
3
1
1
1
1
1
1
1
0
1
1
0
1
0
0
2
1
1
1
0
1
2
1
1
2
2
0
1
1
2
3
0
0
2
1
1
1
1
2
1
2
2
0
1
2
1
1
1
1
2
0
1
0
1
1
0
1
1
1
1
0
2
1
1
2
1
1
0
0
2
0
0
0
2
1
2
0
2
1
2
1
1
0
0
0
2
0
2
0
2
1
1
1
2
0
0
1
0
0
1
1
1
1
1
1
1
2
0
0
1
2
2
2
2
1
2
0
0
1
2
5
0
2
2
1
1
1
1
0
0
0
1
0
1
0
1
0
0
0
0
2
1
2
1
1
0
1
1
0
1
1
0
1
0
1
2
0
0
0
1
1
0
2
2
2
1
1
0
2
1
2
1
2
1
1
0
1
0
2
2
1
0
1
1
0
0
0
1
1
0
4
0
1
3
1
0
1
1
1
1
2
1
2
2
1
2
1
0
0
0
1
2
0
1
1
1
2
1
1
2
1
2
1
1
1
2
0
1
1
2
0
0
1
0
1
1
2
1
0
1
1
0
1
1
1
1
0
1
0
2
0
2
1
1
2
1
0
1
1
1
1
3
1
0
0
1
0
2
0
1
0
0
1
1
1
0
2
1
1
0
1
2
1
0
0
0
0
2
1
1
2
2
2
1
0
2
1
1
1
1
1
1
1
0
1
1
2
2
1
0
1
2
0
1
0
0
1
1
1
0
0
1
1
1
1
1
2
2
1
1
0
1
2
1
2
2
1
0
2
0
1
1
1
1
0
2
0
0
1
1
2
2
1
1
0
1
1
2
1
1
1
1
1
0
1
1
0
2
1
2
2
2
1
0
2
2
0
2
0
0
1
1
1
0
0
0
2
0
2
0
1
2
2
1
0
0
0
2
1
1
1
2
2
1
0
1
0
0
1
0
0
2
2
2
1
0
0
0
0
0
0
0
0
1
0
1
2
1
1
0
0
1
1
0
1
0
1
2
1
1
0
0
1
0
0
1
2
0
1
2
1
1
0
1
2
0
1
1
2
0
0
2
1
2
2
1
2
1
1
1
0
3
0
1
0
2
1
2
1
2
1
1
2
1
0
2
0
1
1
0
1
1
1
1
0
0
0
1
1
1
1
1
1
0
1
2
0
2
1
1
2
1
1
0
2
2
1
0
0
2
0
1
0
1
1
2
1
1
1
2
1
1
1
1
0
2
2
1
1
2
2
1
2
0
2
1
1
2
0
0
2
0
2
1
1
0
0
2
0
1
1
1
1
2
2
1
0
2
1
1
2
0
1
0
1
1
2
2
1
2
1
0
0
1
1
0
0
1
2
0
0
2
0
2
2
1
1
1
0
0
1
0
0
0
1
0
1
0
1
0
0
0
1
0
1
1
1
1
0
1
1
0
0
1
1
0
0
1
0
2
0
1
0
0
1
1
0
2
0
2
1
1
0
1
0
0
1
1
1
2
0
1
2
1
3
1
1
0
1
1
0
1
2
1
1
2
2
0
1
0
0
1
0
1
1
1
2
0
2
2
0
0
1
2
1
1
0
0
1
2
1
1
2
0
1
1
0
1
0
1
1
1
1
0
2
0
0
1
0
0
2
1
1
1
0
0
0
0
1
11
0
1
0
1
0
1
1
2
2
1
0
2
0
1
1
1
0
0
1
1
1
1
0
1
1
1
2
2
1
1
2
1
0
2
0
1
0
1
1
1
2
1
1
2
0
0
1
1
1
0
1
2
0
1
0
1
1
0
0
1
1
1
2
0
2
0
1
1
0
2
2
0
1
2
0
1
1
1
1
1
2
1
0
0
1
0
2
1
1
1
1
3
1
2
1
1
1
1
0
0
0
1
1
0
2
1
1
0
3
1
1
1
2
0
1
1
1
2
2
1
2
1
1
1
0
0
1
1
2
2
1
1
0
1
1
1
1
0
1
0
2
0
1
0
2
1
2
1
2
1
0
1
2
1
2
1
1
0
1
2
2
0
2
2
1
2
2
1
0
1
0
3
0
0
2
0
1
2
2
2
1
2
3
1
1
0
2
0
0
0
1
2
1
1
0
0
1
1
1
1
1
0
0
2
2
0
0
0
1
2
1
2
2
1
0
0
2
3
1
0
0
1
1
1
1
1
0
0
0
2
2
0
1
0
2
1
2
0
1
1
0
2
0
1
1
2
1
1
0
1
0
0
1
1
2
0
1
1
0
1
0
0
0
1
0
1
0
2
2
2
1
0
1
1
1
1
1
1
1
1
0
2
2
2
1
0
1
1
1
1
2
1
0
2
0
1
1
1
0
2
1
1
1
0
2
1
0
1
0
1
1
2
0
2
1
0
0
1
1
1
2
1
1
0
0
1
1
1
1
2
1
1
0
2
1
1
2
0
1
2
0
1
1
3
2
1
1
1
1
1
1
2
3
2
1
2
1
1
1
1
1
1
2
2
1
1
1
2
2
0
1
1
0
1
1
2
1
1
0
2
1
1
0
1
0
1
0
0
2
0
0
0
2
0
0
0
0
1
2
1
1
0
2
0
1
1
0
1
1
1
1
0
0
1
1
2
1
1
2
1
1
2
0
0
1
1
1
1
1
0
1
1
1
0
2
2
0
0
0
0
1
1
0
1
2
1
2
1
2
1
1
1
0
0
1
1
1
0
0
0
1
1
0
1
0
1
1
2
2
1
2
2
1
0
1
1
1
0
0
1
0
0
0
3
1
0
1
1
2
1
1
0
2
2
1
1
2
1
0
1
0
1
0
0
0
1
2
1
2
1
1
1
1
1
0
1
2
2
0
1
1
1
0
1
1
1
1
1
1
1
1
1
0
1
0
0
1
0
1
1
1
0
1
0
1
2
0
1
4
0
0
0
0
2
1
2
2
1
1
2
1
1
1
0
2
1
0
0
1
0
2
1
0
1
2
2
1
1
1
4
0
1
0
2
1
1
0
1
0
2
0
2
0
0
0
0
2
1
0
1
1
0
2
1
1
2
2
1
1
0
0
1
0
0
0
0
1
1
2
1
0
2
1
0
1
0
1
1
0
1
2
2
0
0
0
1
2
2
1
1
0
0
1
0
0
1
1
3
1
1
1
0
1
1
0
0
1
1
1
1
0
3
0
0
1
0
1
2
0
0
0
1
0
0
1
2
0
1
0
2
1
0
1
0
2
1
2
1
1
3
1
1
2
1
1
1
1
0
2
1
2
1
2
0
1
1
1
2
0
0
0
2
0
1
2
0
1
1
2
1
1
2
0
1
0
2
2
1
0
1
1
1
1
2
1
0
1
2
0
2
2
2
0
2
0
2
1
1
1
0
0
0
0
1
0
1
1
0
1
0
1
0
1
0
2
2
1
1
2
3
0
0
0
2
1
1
2
2
1
2
0
0
1
0
0
0
2
2
0
2
1
0
1
2
1
0
1
0
1
2
1
1
1
2
2
2
1
2
1
1
1
1
1
2
2
1
0
0
1
2
1
0
2
1
1
2
0
0
2
1
2
2
1
0
1
1
1
1
0
0
1
0
0
1
0
2
1
1
1
1
1
2
1
1
0
0
2
0
0
1
1
1
0
0
0
0
2
2
2
1
2
2
2
1
1
0
1
0
2
0
1
2
0
1
0
2
0
1
1
0
0
1
0
2
0
1
2
1
0
1
0
0
1
2
2
1
1
0
2
1
1
1
0
1
1
2
0
1
0
2
1
0
2
1
0
1
1
2
2
1
1
1
0
1
0
1
0
2
1
0
0
1
0
0
1
0
2
0
2
1
1
1
1
1
2
1
0
0
1
0
1
0
1
1
1
1
1
0
1
2
0
1
1
0
0
1
1
1
0
1
0
0
0
2
2
0
1
1
0
2
1
1
1
1
2
1
0
2
2
0
0
0
1
1
1
1
3
1
2
2
0
1
2
1
1
1
1
2
0
0
1
1
0
0
1
1
0
1
2
0
1
0
1
2
0
1
1
2
1
0
0
1
1
1
1
1
1
1
1
0
1
1
1
2
1
1
2
1
2
1
1
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
2
2
0
0
0
2
0
0
1
2
1
0
1
1
0
1
2
1
2
1
1
0
2
1
0
2
1
0
1
1
2
1
1
1
1
1
0
1
1
1
1
1
2
0
1
1
0
1
1
0
2
0
1
2
2
1
1
1
2
2
1
1
0
1
1
0
1
1
1
2
0
1
1
1
0
0
1
1
2
0
0
0
1
1
1
1
1
1
1
2
0
1
1
1
1
1
1
1
1
0
1
1
1
1
1
0
1
1
0
0
0
1
2
1
0
1
2
1
0
0
0
1
1
1
0
2
2
0
0
0
0
0
2
1
1
2
1
0
1
2
2
1
2
0
0
1
2
0
1
2
0
0
0
2
1
0
2
0
1
2
2
1
0
1
0
0
1
1
0
1
0
0
1
0
0
0
2
2
1
1
1
2
1
2
1
2
0
2
1
1
1
0
0
1
0
0
2
1
1
1
0
1
1
2
1
2
1
0
0
1
1
0
0
1
1
0
2
0
1
1
2
1
0
2
1
2
1
2
0
0
0
1
1
1
0
2
1
0
0
1
0
1
2
1
1
2
1
1
1
2
2
0
1
1
0
0
1
2
0
2
0
1
2
0
1
2
1
0
1
1
0
1
1
2
1
2
0
0
2
0
2
1
1
2
0
2
1
2
0
2
1
0
1
2
0
0
1
1
1
1
1
1
1
1
6
1
1
1
0
2
0
0
2
0
2
0
0
2
0
0
0
2
1
1
0
1
2
0
2
2
1
2
0
1
1
1
1
1
1
0
1
2
1
1
2
1
1
1
1
0
1
2
1
0
0
1
1
2
1
2
1
0
1
0
0
1
1
1
0
2
2
1
0
0
1
1
1
2
0
2
0
1
3
1
0
0
2
0
1
0
1
0
2
0
1
1
2
1
2
0
1
2
0
0
2
0
0
2
1
1
1
0
1
0
1
1
1
1
1
0
0
1
1
0
0
1
0
1
0
1
0
2
2
1
1
0
1
1
1
0
2
0
0
0
1
2
0
0
1
0
0
2
1
0
0
1
0
1
2
1
1
1
1
1
2
0
2
0
1
0
0
1
1
0
1
0
1
1
2
1
2
1
2
0
2
2
3
2
2
0
0
1
0
2
2
1
2
1
2
0
2
2
2
1
1
0
0
1
1
2
1
0
1
0
1
1
1
1
0
2
4
1
0
2
0
1
2
0
1
2
1
1
1
1
0
2
1
0
2
1
0
2
0
2
1
2
0
0
1
2
2
2
0
2
0
1
0
1
1
2
1
0
1
1
2
1
2
1
1
1
0
0
1
1
1
1
0
2
0
0
1
0
0
1
1
1
0
1
1
0
0
1
1
1
1
2
1
1
1
1
0
1
1
0
2
0
1
2
0
1
2
2
0
0
2
1
1
0
1
0
1
1
1
1
1
2
1
1
1
1
0
2
0
1
1
1
1
2
0
0
0
0
1
1
2
0
0
1
0
1
1
1
0
1
1
1
1
1
0
3
2
1
1
1
0
0
1
1
1
2
1
2
2
0
0
0
0
1
1
0
0
2
1
0
1
2
1
0
1
1
1
2
2
1
0
0
0
1
1
2
2
0
1
2
0
1
1
2
0
1
1
2
2
2
1
0
2
1
0
2
1
1
1
2
2
1
1
1
1
0
2
2
2
2
1
2
1
1
1
0
2
0
1
1
0
1
2
1
0
1
2
1
1
0
1
2
0
0
1
2
0
1
2
2
1
1
1
0
1
0
2
1
1
1
2
1
2
1
0
0
1
2
1
0
1
0
0
1
0
0
1
0
1
0
0
0
0
1
0
1
0
1
1
1
1
2
1
1
0
1
1
1
2
1
0
0
0
2
2
2
1
2
0
0
2
0
1
1
1
1
1
2
0
1
1
0
1
0
0
2
1
2
0
1
1
0
2
1
1
0
2
0
1
1
0
0
0
1
2
0
0
1
0
0
1
0
2
1
2
1
1
0
5
1
1
1
1
0
0
0
1
1
2
2
1
1
1
2
0
1
0
1
1
1
2
1
0
0
1
0
1
2
2
0
0
1
1
0
0
1
1
1
1
0
1
1
2
1
1
1
0
1
1
2
0
1
1
0
1
1
1
1
0
0
0
2
1
2
2
1
1
0
1
2
1
1
1
1
1
2
1
0
1
0
1
1
1
0
1
0
2
1
1
1
0
0
0
0
2
1
1
2
2
0
1
0
1
2
2
0
1
1
0
0
2
2
2
1
0
2
3
1
2
1
3
1
2
0
0
1
1
0
0
2
1
1
1
0
0
2
0
2
1
2
1
0
2
0
1
0
0
1
0
1
1
1
1
2
1
2
1
1
1
1
1
2
0
2
1
2
2
1
1
1
1
1
2
0
1
2
1
1
1
2
0
2
0
0
1
0
2
0
1
3
1
0
0
1
0
1
1
2
1
0
1
1
1
1
2
0
2
0
0
1
1
0
1
1
0
0
1
0
1
1
0
0
1
2
0
0
1
1
1
1
0
1
0
0
1
1
2
0
1
0
2
3
1
1
1
1
1
0
1
2
2
1
0
2
1
0
1
1
1
1
1
1
0
1
1
1
1
2
1
0
0
1
1
1
1
2
1
1
0
2
1
2
1
2
1
2
0
0
0
0
1
1
1
1
1
1
2
0
0
1
2
1
0
1
2
1
1
1
0
2
1
0
1
1
1
0
1
1
2
0
1
0
1
1
2
2
1
0
0
1
2
3
1
1
1
1
0
1
2
2
1
1
2
1
1
2
2
1
1
0
2
2
2
1
1
0
1
2
0
1
1
0
1
1
2
0
0
1
1
0
0
0
0
2
1
1
0
1
1
1
1
0
1
0
1
0
0
1
2
1
1
2
0
0
1
1
1
1
2
1
2
0
0
1
0
2
0
0
0
1
1
2
1
1
2
1
0
2
1
1
0
1
1
1
1
0
1
1
0
1
2
1
1
1
0
2
1
1
1
2
2
1
1
0
0
0
1
2
1
0
2
1
0
0
2
1
1
1
2
2
1
2
2
2
0
1
0
0
1
2
1
1
1
0
0
1
1
0
0
0
0
0
2
0
1
1
0
1
0
1
0
2
2
2
1
1
0
0
1
0
0
1
0
1
0
1
1
1
1
1
2
1
1
1
0
0
0
1
2
1
1
1
1
1
1
1
1
1
0
2
2
0
1
1
0
1
2
1
0
0
1
4
0
0
2
0
2
1
0
1
0
1
1
1
1
0
1
0
0
1
1
1
1
2
2
0
1
0
1
0
0
1
0
1
2
3
1
0
1
0
0
1
0
0
1
1
0
0
1
1
2
2
0
1
0
0
1
1
2
0
1
1
0
1
2
0
1
2
0
1
1
1
1
1
2
1
0
0
0
2
0
2
2
1
0
1
1
1
1
0
2
2
2
2
0
1
2
1
1
2
1
1
0
1
1
1
0
1
2
1
0
2
2
2
0
2
1
0
2
0
1
0
0
0
0
1
1
0
1
0
2
1
0
1
1
1
2
1
2
1
1
2
1
2
2
2
2
1
0
1
1
1
1
0
1
1
1
1
1
1
2
1
0
0
1
1
1
1
0
1
0
0
1
1
2
1
0
0
1
0
1
5
1
1
2
0
0
1
1
1
1
1
0
0
2
2
1
2
0
0
1
2
1
2
0
1
0
1
1
2
1
1
0
1
0
0
1
1
0
1
1
1
3
0
0
0
1
0
2
2
2
1
0
1
2
1
3
2
1
1
1
1
0
0
1
1
0
1
1
1
1
1
1
1
0
2
1
2
0
0
1
1
2
0
0
0
2
5
1
0
1
0
1
0
0
2
0
1
1
1
0
1
1
0
1
0
2
1
1
1
1
0
0
2
1
0
1
1
2
0
1
1
0
0
1
1
1
1
2
1
1
1
0
0
0
1
1
1
2
3
1
1
1
1
0
1
1
2
1
1
0
1
0
1
1
1
0
2
1
0
0
1
0
1
2
2
1
1
2
1
1
1
1
1
1
1
2
1
2
1
0
2
2
1
2
0
1
1
1
1
1
1
0
2
1
1
1
0
2
1
1
2
0
1
1
2
1
1
2
0
0
0
1
0
1
1
1
1
2
2
1
0
1
1
2
1
1
0
1
4
1
1
0
0
2
1
1
2
1
2
1
2
1
1
1
0
1
0
0
0
2
1
2
1
1
1
1
1
0
1
1
2
2
1
0
1
0
0
0
1
1
2
1
2
2
0
1
2
2
1
2
1
0
1
1
1
2
1
1
1
1
0
2
1
0
1
2
1
1
0
1
1
0
1
1
1
1
0
1
1
1
0
0
0
0
0
0
1
1
0
0
2
2
0
0
2
0
2
2
2
0
2
1
1
1
1
0
0
0
1
1
0
0
0
1
1
0
12
1
1
2
1
0
0
2
2
0
3
0
1
2
0
0
0
0
2
1
2
0
1
0
0
0
1
0
1
2
0
1
2
1
0
1
1
1
1
1
1
0
2
1
0
2
0
1
0
0
1
1
0
1
1
2
0
0
1
2
2
1
2
1
2
1
1
1
1
0
1
2
1
0
2
0
1
2
2
2
2
1
1
1
1
0
2
1
0
1
0
2
3
1
1
2
1
1
1
2
2
1
1
1
1
1
2
1
1
0
0
2
1
1
0
1
2
1
1
1
0
2
0
0
1
4
1
0
2
0
1
1
0
1
2
2
1
0
1
1
0
1
1
1
0
1
1
2
1
0
2
1
1
2
0
2
1
0
0
2
1
2
1
0
1
1
0
0
1
1
1
1
2
1
1
1
1
2
1
2
0
0
0
1
1
1
1
1
1
1
2
1
2
0
0
0
0
0
1
1
2
1
1
2
0
2
0
2
0
1
1
0
1
1
2
1
0
2
0
1
1
2
1
2
2
0
0
2
1
1
2
1
1
2
0
1
0
2
1
2
1
1
0
1
0
2
0
1
0
1
1
0
0
1
0
1
0
0
1
1
1
0
0
1
2
2
1
1
1
0
1
1
1
1
0
1
1
2
1
0
2
2
1
1
1
1
2
1
0
2
2
1
2
0
1
1
1
2
1
0
2
2
1
2
1
2
1
1
0
1
2
0
1
2
1
1
0
2
1
1
2
1
2
1
1
2
0
1
1
2
2
0
0
1
1
2
2
1
0
2
2
0
2
0
2
2
0
1
2
0
1
0
1
0
1
0
1
1
1
1
0
1
1
1
1
1
1
1
2
1
1
1
2
0
2
0
0
0
0
1
1
0
1
0
2
1
0
1
2
2
2
2
2
0
1
1
1
0
0
1
0
2
1
2
1
2
2
1
0
1
0
0
0
2
1
1
0
0
0
1
1
1
1
2
1
1
0
1
2
0
0
2
1
1
0
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
1
1
1
0
1
1
0
0
1
0
2
1
1
0
1
3
0
1
1
0
1
1
0
1
1
1
1
0
2
0
2
0
2
1
0
1
2
0
1
0
1
0
2
2
0
1
0
2
2
0
1
0
1
1
0
0
2
1
1
2
1
0
2
1
1
2
2
2
2
1
1
0
0
1
1
1
1
1
1
1
1
1
1
2
1
2
2
0
1
0
1
1
0
0
1
1
2
2
0
1
1
0
1
2
2
1
0
2
0
1
0
1
1
2
0
1
2
0
1
1
1
1
2
2
1
1
2
0
1
1
2
1
1
0
1
1
1
1
2
1
0
2
1
1
2
0
1
2
1
1
0
2
1
1
1
1
1
0
1
0
0
1
0
2
1
1
2
1
1
1
0
1
0
4
1
1
0
1
1
2
3
1
1
1
1
3
0
1
0
1
0
2
1
1
0
1
1
0
1
0
1
1
0
2
0
0
0
1
1
1
0
0
1
0
1
1
2
2
0
2
1
1
1
2
3
2
0
2
0
1
0
2
0
1
1
1
0
0
0
2
0
1
2
0
1
0
2
0
0
2
1
0
1
1
1
2
1
2
1
2
1
2
0
1
2
1
1
3
1
0
2
1
2
1
1
3
1
1
1
1
1
0
0
0
2
2
2
1
1
2
0
1
1
1
2
2
2
1
1
2
2
1
1
1
2
1
1
3
2
0
2
1
0
1
1
1
2
2
0
1
2
0
0
2
1
2
0
1
1
0
1
2
1
1
2
1
1
2
0
0
1
0
1
0
2
0
1
1
1
1
1
2
2
0
0
1
1
1
1
1
1
1
1
0
1
2
0
1
0
1
1
2
2
2
1
1
0
1
0
0
1
0
1
0
1
1
2
1
1
0
2
1
3
1
1
1
2
0
0
1
1
3
0
1
1
0
0
0
0
2
3
0
2
1
0
1
0
1
1
0
0
2
0
0
1
1
0
2
2
0
0
0
1
6
1
2
1
0
1
0
1
0
0
2
1
1
1
1
2
0
2
0
1
0
0
0
1
2
0
0
1
1
1
0
1
2
0
1
2
1
0
0
0
2
2
2
1
1
1
1
1
2
2
0
0
0
0
0
1
0
1
1
2
1
2
1
2
1
2
0
0
1
2
1
1
0
1
0
1
1
1
2
0
1
0
1
1
0
1
1
1
0
0
0
2
0
0
0
1
0
1
1
0
1
0
1
0
0
2
1
1
2
0
0
0
2
1
2
1
0
1
2
0
2
2
1
0
1
0
0
2
3
1
1
2
1
2
1
1
2
2
1
0
2
0
1
1
1
1
0
2
4
0
0
0
0
4
0
0
0
0
0
0
1
2
2
2
1
1
0
0
2
1
1
2
1
2
1
1
0
0
0
1
0
0
2
2
1
2
1
0
1
0
0
1
2
2
1
1
0
1
1
1
0
0
1
2
2
0
1
1
0
1
0
1
1
1
0
0
1
1
2
2
2
1
0
1
2
0
2
1
1
1
1
1
0
1
1
1
0
0
0
1
1
0
1
1
1
2
0
0
0
1
1
0
1
0
2
2
1
2
1
0
0
1
1
1
0
1
1
0
1
2
1
3
1
1
2
1
1
1
1
2
2
1
0
0
0
0
2
0
0
0
1
1
2
0
0
1
0
2
0
2
1
1
0
1
0
1
2
1
2
2
1
0
0
0
0
0
0
2
0
1
1
1
1
1
0
1
1
1
1
0
1
1
2
2
2
1
0
0
2
1
0
1
1
2
1
1
2
2
2
1
1
1
1
1
1
0
1
0
1
1
1
0
1
0
0
1
2
1
0
2
1
1
1
1
0
2
2
1
2
1
0
2
0
1
0
1
1
3
1
2
1
2
1
4
1
1
0
0
2
1
0
1
2
0
2
0
2
2
2
1
1
0
0
0
1
2
0
2
1
0
0
3
0
0
1
0
1
1
0
0
2
0
1
1
0
1
0
1
1
0
0
2
1
1
1
2
0
2
1
0
1
0
1
2
0
1
1
1
1
1
1
0
1
0
0
2
2
1
1
1
2
1
1
0
0
0
2
0
2
1
1
1
0
0
2
2
1
0
1
1
1
1
1
0
2
0
0
1
1
2
0
2
2
0
2
1
0
0
1
4
1
1
1
2
2
1
0
0
2
0
1
1
1
2
2
1
2
1
1
0
1
1
1
1
1
1
1
0
2
2
2
1
2
1
1
0
2
1
2
1
1
0
1
0
1
2
2
1
1
0
2
2
1
0
0
0
1
1
2
1
1
2
1
2
1
1
2
0
1
1
1
1
1
1
1
0
1
0
0
1
2
0
4
0
1
0
1
0
1
0
0
1
0
1
1
0
0
1
1
0
1
1
1
1
2
1
1
1
2
0
1
0
1
1
0
0
2
0
0
0
1
1
1
1
1
1
0
0
1
1
0
2
0
0
2
2
0
2
0
1
1
1
1
1
1
0
0
1
2
0
1
0
1
2
1
1
2
1
0
0
1
1
2
0
2
1
1
0
1
1
2
0
2
1
1
0
1
2
1
1
1
1
2
2
0
1
1
1
2
2
0
0
1
2
0
2
1
3
0
2
0
1
2
1
1
1
1
1
2
0
1
1
0
2
1
0
2
1
1
2
0
2
1
1
1
0
1
1
1
2
0
1
2
0
1
1
1
0
1
1
2
2
1
1
0
2
0
2
1
1
0
2
0
1
2
1
1
1
0
1
1
3
0
0
2
1
1
0
1
1
1
2
3
0
1
0
2
0
0
1
0
1
1
0
1
0
1
4
1
1
1
1
2
1
1
1
0
1
0
1
1
1
3
0
0
2
1
1
2
0
3
2
1
0
0
2
8
2
0
1
2
1
0
1
2
2
2
1
0
0
1
0
1
1
1
0
1
2
0
0
2
1
1
1
0
1
1
0
1
3
1
1
1
1
1
0
1
0
0
0
2
0
0
1
1
0
0
1
0
0
0
2
0
1
1
0
1
0
1
1
1
2
0
0
1
1
0
1
1
2
1
1
1
0
0
0
1
0
2
2
1
1
1
1
1
1
2
2
1
0
2
1
0
0
0
1
1
1
1
1
2
1
2
1
0
2
1
1
2
0
0
1
1
0
1
1
0
0
0
1
0
1
1
0
0
0
0
1
0
1
1
0
2
1
0
0
0
1
1
2
2
2
1
0
1
0
2
2
0
1
0
1
0
1
0
1
1
0
0
1
1
1
1
0
0
1
2
1
1
1
0
2
0
1
1
1
1
1
1
1
2
0
0
1
2
0
1
0
1
0
0
0
2
2
2
0
1
1
1
1
1
2
1
1
0
2
0
0
1
0
0
0
1
1
1
0
1
1
2
1
0
0
2
0
2
1
1
1
0
1
1
0
0
1
1
0
1
1
0
2
1
2
2
1
2
1
3
1
1
1
3
2
1
0
1
2
1
0
1
1
2
1
1
0
2
1
2
0
0
0
2
0
1
1
2
2
1
1
0
2
1
0
2
0
0
2
2
1
1
0
1
1
1
0
0
2
1
0
2
1
1
0
1
0
2
2
1
1
0
0
0
1
0
0
0
0
0
0
0
2
2
0
2
1
1
1
0
0
1
1
1
2
0
0
0
0
3
1
0
2
0
2
0
1
1
1
0
1
1
2
1
0
0
1
2
1
0
1
0
1
1
1
1
1
0
1
1
1
0
1
0
0
1
1
1
1
1
0
1
2
1
2
2
1
2
1
0
2
1
1
0
2
0
1
2
0
0
0
2
1
0
1
1
1
1
1
2
1
0
1
1
1
1
1
1
1
1
0
2
0
1
1
0
0
1
1
1
0
1
1
1
1
2
1
2
2
1
1
0
0
2
1
1
2
2
3
1
1
2
1
2
2
1
1
2
1
0
1
3
1
2
0
1
1
2
1
2
2
1
1
1
1
0
1
1
1
0
2
1
2
1
2
1
1
1
0
0
1
0
0
0
0
2
1
2
1
1
0
1
2
1
1
0
0
2
2
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
0
2
1
1
0
1
2
1
0
0
1
1
1
0
1
2
0
0
2
1
1
1
0
1
1
2
2
0
1
1
0
1
2
4
2
1
1
2
1
0
1
2
1
2
0
2
0
0
0
1
2
1
0
0
1
1
2
1
2
1
1
1
1
1
1
0
1
1
1
2
1
3
1
1
0
1
2
1
2
1
0
0
1
2
1
1
1
2
1
1
2
2
2
1
1
2
2
0
1
2
0
0
0
2
1
2
1
1
0
2
0
1
2
0
0
1
1
2
1
2
1
2
2
1
2
1
1
1
0
0
1
1
2
1
0
1
0
1
3
1
0
1
3
2
1
1
1
0
0
2
1
1
1
2
1
2
1
2
1
1
1
1
1
2
1
0
1
2
0
1
2
0
2
1
1
1
0
1
2
0
1
2
0
1
0
1
0
0
1
0
3
2
1
1
0
0
0
2
1
1
1
0
1
1
0
3
2
2
0
1
0
2
1
1
0
1
0
1
0
0
3
1
0
2
1
0
1
0
2
0
1
0
0
1
1
0
1
1
0
1
1
2
1
2
1
1
1
0
0
2
0
2
1
2
0
0
2
2
1
1
1
1
2
0
2
1
0
1
2
0
2
2
3
0
1
2
2
0
1
1
2
1
1
2
1
1
1
1
0
1
2
1
0
1
1
1
2
2
2
0
1
1
0
1
2
1
2
1
1
1
1
0
1
1
2
1
1
0
2
1
1
2
2
0
1
1
1
1
1
2
1
2
1
1
0
2
0
1
1
1
2
0
1
0
1
0
2
1
2
1
1
1
1
1
2
2
1
0
2
1
1
2
1
1
0
2
1
0
1
0
0
0
1
1
1
0
1
1
1
0
0
2
1
1
1
1
2
1
0
1
3
2
2
2
0
2
1
1
2
1
0
1
2
2
1
1
0
1
2
1
1
0
1
1
1
2
1
1
2
2
1
2
0
1
1
1
1
0
1
0
1
0
2
1
1
1
2
0
1
1
2
1
0
0
1
1
1
1
1
1
2
1
0
0
0
1
0
1
1
1
0
1
0
0
2
2
0
2
1
0
2
1
1
1
0
1
1
0
2
2
1
0
1
2
2
1
1
2
0
0
0
0
2
2
1
2
1
2
0
2
1
1
2
2
0
0
1
1
0
2
0
0
1
1
3
2
1
1
2
2
2
0
0
1
1
2
0
1
1
0
0
2
0
1
1
0
1
2
2
0
0
1
2
1
1
1
0
0
0
2
1
0
0
0
1
1
1
1
0
1
0
4
2
1
2
1
2
1
0
2
1
1
2
0
0
0
1
2
1
0
2
1
1
0
0
1
0
0
1
1
2
1
1
2
0
1
1
2
1
1
1
1
2
1
0
2
1
1
0
2
0
1
1
1
4
1
2
0
1
1
1
1
1
1
0
0
1
1
1
2
2
0
0
0
0
0
1
1
2
2
1
1
1
2
2
1
1
1
1
1
2
1
1
0
1
1
0
2
2
0
2
1
0
0
1
1
1
0
1
2
1
0
0
1
1
0
0
1
2
1
3
0
1
1
1
3
1
1
1
1
2
2
2
0
0
0
2
1
2
2
0
0
1
2
0
1
2
0
2
1
2
1
1
2
1
0
1
1
0
0
0
1
2
0
2
2
1
1
0
1
3
1
1
1
1
1
1
1
0
2
0
0
1
1
1
1
0
1
0
2
2
0
0
2
0
1
0
2
2
2
0
2
1
1
1
0
0
2
1
2
1
1
2
2
1
0
0
4
1
3
2
1
0
2
2
1
1
1
1
1
1
2
2
1
1
2
2
2
2
1
1
2
0
2
2
0
1
1
1
1
0
0
2
2
0
1
1
0
2
2
2
1
1
2
1
1
0
0
0
1
1
1
1
1
0
1
1
0
1
2
0
0
2
2
2
1
2
1
2
1
1
1
1
2
0
1
1
0
0
1
1
0
0
0
2
1
2
1
1
1
2
2
0
0
2
1
1
1
1
1
1
1
1
1
2
0
0
2
1
2
0
1
1
1
1
1
1
1
0
1
2
1
1
1
1
0
1
1
2
2
1
2
1
1
2
0
1
1
1
2
0
0
1
1
1
2
1
1
0
1
2
1
1
2
1
0
2
2
1
1
0
0
1
1
1
0
1
2
1
2
1
2
1
1
0
1
2
2
0
0
1
1
0
0
1
0
1
1
1
0
2
1
1
0
1
1
1
1
0
1
1
0
0
2
0
1
1
2
2
2
1
0
2
1
0
2
0
1
1
2
1
1
1
3
2
1
1
0
1
1
0
0
1
0
1
2
1
1
0
1
0
0
0
1
0
1
1
1
1
1
0
1
0
2
0
0
1
0
1
0
1
1
1
0
1
1
1
1
0
1
0
1
0
1
0
0
0
2
1
1
1
1
0
0
0
1
1
2
1
0
1
2
1
1
1
1
2
1
1
0
2
0
1
1
1
1
2
1
1
1
0
0
1
2
0
0
0
2
1
2
0
1
1
1
1
2
0
0
0
1
0
0
0
0
2
0
1
1
1
2
0
0
0
0
0
1
1
1
2
1
2
1
1
0
1
0
1
0
1
1
1
0
1
0
0
1
2
3
1
0
0
1
0
0
2
2
1
0
0
1
0
2
1
4
1
0
0
1
0
0
1
2
1
1
1
2
0
2
1
2
1
1
0
1
1
0
0
0
2
1
2
1
1
1
0
0
1
1
0
2
4
0
2
1
1
0
1
0
1
1
0
0
2
1
1
1
0
1
1
2
0
0
2
2
1
1
0
1
1
0
1
2
2
1
1
1
1
1
1
2
2
1
2
0
2
1
1
1
1
1
0
2
0
1
0
2
1
2
0
2
1
0
2
1
2
2
2
1
1
0
1
0
2
1
0
1
0
1
2
1
0
1
0
2
0
1
0
1
2
2
1
2
1
2
1
1
0
1
1
1
1
1
0
1
1
1
2
2
2
1
1
1
1
1
0
1
1
0
2
2
1
1
1
0
2
1
1
2
0
2
2
1
0
2
0
0
0
2
0
1
0
1
1
0
2
1
2
2
1
2
1
1
0
1
1
2
0
0
3
1
1
0
1
1
2
1
1
1
0
1
0
1
1
1
1
0
2
1
1
1
1
2
2
1
0
2
1
0
0
1
1
1
0
1
0
2
1
1
1
1
1
0
2
0
1
2
0
2
1
0
1
2
1
0
1
1
1
1
2
1
1
0
2
0
1
1
2
1
0
0
0
1
0
1
0
2
1
1
1
1
2
1
0
2
1
1
0
1
1
0
0
1
1
0
2
1
1
0
1
1
1
1
1
0
1
1
1
0
0
1
1
2
1
1
1
2
2
1
1
0
1
1
1
1
2
0
0
1
1
0
1
2
1
0
1
0
2
0
1
1
2
2
1
1
1
0
2
1
0
0
0
1
0
0
1
2
1
1
2
1
0
1
0
2
2
0
1
1
2
1
0
0
1
2
1
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
2
1
1
1
1
2
2
1
2
1
2
1
1
0
1
1
1
0
3
0
2
1
0
0
1
0
2
1
1
1
1
1
1
1
0
0
1
1
1
1
1
1
1
1
0
1
1
1
2
1
2
0
1
2
0
1
1
1
2
1
0
2
2
0
1
0
1
1
0
2
2
0
2
0
1
1
0
0
0
1
2
0
3
1
1
1
1
0
2
1
0
0
1
0
2
1
1
2
1
1
2
1
2
1
0
2
1
0
1
0
1
1
0
1
0
0
1
2
0
2
1
1
1
0
1
1
1
1
0
2
1
1
2
1
3
0
1
1
1
3
2
0
2
0
1
1
1
2
1
1
1
2
1
1
1
1
0
1
0
1
1
0
0
0
1
1
2
2
1
2
0
1
2
1
1
0
2
0
0
1
1
0
1
2
1
1
1
1
2
0
1
1
2
2
0
1
1
1
1
1
0
1
2
1
2
1
2
0
2
0
0
0
0
0
2
2
0
1
1
0
3
1
0
1
2
2
3
1
0
1
2
1
1
1
1
1
1
3
1
0
1
0
1
2
0
1
0
1
1
1
1
2
0
0
1
2
2
1
1
2
1
2
1
2
0
2
2
1
0
0
1
2
0
1
1
1
1
1
0
0
1
1
1
2
0
1
2
1
1
3
1
2
1
1
0
0
0
1
1
1
2
2
2
0
0
1
1
2
2
1
1
0
0
2
2
0
1
1
2
1
0
1
0
2
1
0
2
2
0
1
1
2
1
1
1
1
1
0
0
0
2
1
1
1
1
1
1
0
3
0
1
1
2
1
1
0
1
1
0
1
0
1
1
0
1
1
1
1
0
0
1
1
0
0
2
1
1
2
2
0
0
4
1
0
1
2
2
1
1
1
0
3
1
0
1
1
2
1
2
1
1
1
0
1
0
0
2
0
1
1
2
0
0
0
1
0
0
2
1
2
0
1
2
2
2
1
0
2
0
1
0
1
1
0
1
0
1
0
2
1
0
1
1
1
0
2
0
1
0
2
1
1
0
0
1
1
0
0
2
1
2
1
1
2
1
1
1
2
2
2
1
0
1
2
1
1
0
1
2
1
0
1
0
0
1
1
1
0
1
1
2
2
1
0
1
2
1
1
1
1
1
2
1
2
0
1
0
2
0
0
0
1
1
1
0
1
0
2
1
0
0
2
1
0
1
1
0
0
2
2
0
1
1
1
0
0
2
1
0
2
2
0
2
0
1
2
1
0
1
1
2
1
0
0
0
3
1
1
2
0
0
2
1
1
1
1
1
0
1
0
0
0
2
1
2
0
1
2
0
1
1
1
1
1
2
1
1
2
2
1
2
0
1
0
1
2
1
1
0
2
2
2
0
1
1
1
2
1
1
1
2
1
1
2
1
1
2
1
0
1
2
1
0
0
1
2
2
0
2
0
0
0
1
0
1
1
1
1
1
0
0
2
2
1
2
1
1
2
1
1
0
0
0
0
0
1
0
1
2
1
0
1
0
2
1
2
0
0
0
1
2
0
1
1
2
1
1
1
1
1
1
2
0
0
1
1
2
0
1
1
0
1
0
1
1
2
0
0
1
1
1
1
1
1
0
2
1
0
0
1
1
1
1
1
0
0
2
1
1
0
1
2
1
0
1
2
1
2
1
0
0
2
3
1
0
1
0
2
0
2
0
2
1
1
1
2
2
1
1
1
2
0
1
1
0
1
1
1
0
2
1
1
1
1
1
2
0
1
2
2
1
1
2
3
1
0
1
1
1
2
3
1
1
2
1
0
0
1
0
0
1
0
1
1
3
0
2
1
1
0
1
1
2
0
0
1
1
0
0
0
0
1
1
0
0
1
1
0
1
1
1
0
2
1
2
1
0
1
1
2
1
2
0
1
1
0
1
2
1
1
1
2
1
2
1
1
1
1
0
1
1
1
1
2
0
2
0
1
0
1
0
1
1
0
1
0
0
2
1
0
1
2
1
1
1
1
0
1
0
2
2
2
2
2
1
2
1
1
1
2
1
1
2
0
0
0
1
0
2
0
2
0
0
1
1
2
0
1
1
1
1
1
1
0
2
6
2
2
0
1
3
0
1
1
2
1
1
2
1
0
0
2
0
2
0
0
1
1
0
1
1
0
2
2
0
0
1
1
2
1
0
1
2
2
2
3
2
0
0
1
0
1
1
2
0
1
0
2
1
0
0
0
1
1
1
1
0
0
2
2
2
1
1
0
1
0
1
1
2
1
1
2
1
1
1
2
1
2
1
1
2
3
2
2
1
0
1
1
1
1
1
2
4
1
1
1
1
2
1
1
0
1
1
0
3
0
2
1
1
0
2
1
1
1
1
0
0
1
2
1
2
1
1
2
1
2
1
0
0
0
2
2
0
2
1
0
0
1
2
0
3
0
2
1
0
2
1
2
1
1
2
0
0
1
1
1
1
0
2
0
0
0
1
1
0
1
2
1
1
1
0
0
0
0
1
1
0
1
1
0
2
1
1
1
1
1
1
0
0
0
0
0
1
0
0
0
2
1
1
2
1
1
0
0
1
1
0
1
0
1
1
1
2
1
2
1
2
1
2
1
0
0
1
1
2
0
1
2
1
2
1
1
1
1
1
2
1
0
1
1
0
2
1
1
1
1
2
1
0
0
0
1
1
0
1
1
2
1
0
3
0
1
1
1
3
1
2
1
1
0
1
0
0
1
0
1
0
1
0
1
1
1
1
0
1
2
1
2
0
0
2
0
1
2
6
2
1
1
1
1
0
1
2
1
1
1
2
0
1
0
1
1
0
2
1
0
0
1
1
1
1
2
0
1
0
8
0
3
1
0
1
1
1
1
1
0
1
1
2
2
0
0
1
0
1
0
1
0
1
2
0
2
2
0
2
1
1
3
0
1
1
0
0
2
1
2
0
1
1
0
2
1
2
1
0
1
0
0
0
2
1
2
1
2
2
2
0
1
1
1
1
2
0
0
2
1
1
0
1
1
2
0
1
1
1
1
1
0
1
2
2
1
1
1
1
0
0
2
2
2
2
1
0
3
1
1
2
2
0
1
2
1
0
0
1
1
1
1
1
0
1
1
1
2
2
1
0
2
0
0
1
0
1
2
1
2
0
1
2
2
2
1
0
1
0
2
2
1
0
2
1
1
1
1
1
1
2
1
2
0
0
1
1
1
1
1
1
1
2
0
1
1
0
2
1
2
1
2
0
1
1
1
0
1
0
1
1
0
0
2
1
1
2
1
1
1
1
0
1
2
0
1
3
1
0
1
1
1
2
1
1
2
0
1
1
2
1
1
1
0
1
2
1
0
0
0
1
0
0
0
1
0
2
1
1
1
2
0
2
2
2
0
0
1
2
0
0
1
0
0
1
0
0
0
2
1
0
0
1
2
2
2
1
0
0
3
2
0
0
1
2
1
0
0
0
0
0
1
1
1
0
1
2
1
1
1
2
2
1
0
0
2
1
1
2
1
1
2
2
0
1
1
1
1
1
0
2
1
0
1
2
2
1
0
1
1
1
1
0
1
1
0
2
0
2
1
0
1
1
2
0
0
0
0
0
1
0
1
0
2
0
0
1
1
1
2
1
0
0
1
0
2
1
1
0
0
1
1
0
2
1
1
2
0
0
1
1
1
1
1
0
2
2
1
1
2
0
1
2
1
1
1
0
1
1
2
1
0
0
0
1
2
0
1
0
1
2
1
1
1
0
2
1
2
1
1
0
1
0
0
0
2
1
1
1
2
1
0
1
0
1
1
0
0
1
1
1
1
0
1
1
1
1
0
2
2
1
1
0
0
1
0
1
2
0
1
0
1
0
0
1
0
1
1
1
1
0
1
0
0
0
1
0
1
0
1
1
1
1
0
1
2
1
1
1
0
1
2
1
1
2
0
1
2
0
1
1
0
1
0
1
1
3
1
1
3
0
2
0
1
1
3
1
1
3
0
2
0
1
1
0
0
1
1
0
0
0
2
1
1
0
1
1
1
1
0
1
1
2
1
0
1
0
1
2
1
1
0
0
0
0
0
1
2
1
1
1
4
0
1
0
0
0
1
2
1
0
0
0
0
0
0
0
0
1
0
1
2
0
1
1
3
0
1
0
1
2
2
0
1
2
1
0
2
0
0
2
0
3
0
0
2
0
1
0
1
1
1
1
2
0
0
1
1
1
0
0
1
1
1
1
0
0
0
2
0
1
2
2
1
1
0
0
1
1
1
0
1
1
0
0
1
1
0
2
1
2
0
1
0
1
1
0
1
1
2
2
2
1
2
1
2
2
1
1
0
2
0
2
1
1
1
1
0
1
0
1
0
1
2
2
0
0
0
0
2
0
0
2
1
1
0
1
1
1
1
0
1
1
0
1
0
0
0
0
1
1
0
1
0
1
2
1
1
1
0
1
2
1
1
0
1
1
1
1
0
1
1
0
0
1
1
1
1
1
1
0
1
1
0
1
2
1
1
2
2
0
1
2
0
0
1
1
1
1
0
2
1
0
0
0
0
0
2
1
1
0
1
2
1
1
0
2
0
0
1
0
2
0
1
2
0
2
2
2
0
0
1
1
0
1
1
2
1
1
1
1
0
0
1
1
1
0
1
2
0
1
2
2
2
1
2
1
1
1
1
2
2
1
0
2
0
0
0
1
1
1
1
0
1
1
1
1
0
0
1
0
0
1
2
1
2
2
1
2
1
1
1
2
2
1
1
1
1
1
2
1
1
1
0
1
1
1
0
0
1
2
2
1
0
1
2
2
1
2
0
0
1
1
1
2
0
1
2
1
2
1
0
0
1
1
0
1
1
0
0
0
0
2
1
1
1
0
1
2
0
1
0
2
1
0
1
1
1
1
1
2
2
0
0
2
0
1
0
0
2
0
0
2
0
1
2
2
2
1
1
0
1
0
2
2
0
1
2
2
1
0
1
2
1
2
0
1
1
0
2
1
1
2
1
2
1
0
0
0
2
1
2
1
1
0
2
0
0
2
2
1
2
1
1
1
1
0
1
1
1
0
2
1
0
0
1
1
1
1
1
1
0
0
0
2
2
0
0
1
1
1
1
1
0
1
1
0
0
1
0
1
0
1
2
1
1
1
3
2
2
1
1
0
2
2
1
1
1
2
1
0
1
1
1
1
0
2
1
1
1
0
2
1
1
0
1
2
2
2
2
1
1
1
2
0
2
2
0
1
0
1
2
1
0
1
1
0
0
2
1
0
1
2
1
1
0
2
0
0
0
0
0
2
2
1
0
1
2
1
2
0
0
2
2
1
1
0
2
0
1
1
0
1
1
0
0
0
0
1
0
0
2
0
0
2
1
1
1
1
2
0
1
1
0
0
2
2
1
0
3
1
0
1
2
2
0
2
1
1
2
1
0
1
0
1
2
1
1
1
0
0
1
2
1
0
1
1
0
2
0
2
2
0
1
1
2
2
1
1
2
0
1
0
1
1
0
1
1
1
1
0
1
0
1
1
1
2
1
0
1
1
2
1
0
1
0
1
2
0
2
1
1
0
1
1
1
2
2
1
1
1
2
2
1
1
2
0
0
1
1
1
2
1
0
1
1
1
0
0
0
2
2
1
2
1
1
2
0
1
2
1
1
1
2
3
0
1
1
0
1
0
1
0
1
0
0
1
1
1
1
0
0
0
0
1
0
1
1
2
0
1
1
2
0
2
0
0
0
1
2
1
1
0
1
0
0
0
1
1
1
0
1
1
1
2
1
0
1
0
0
2
1
1
0
1
1
0
2
0
1
1
0
0
2
0
0
2
1
1
1
1
1
2
1
1
0
0
1
0
1
2
1
1
1
1
2
2
0
1
1
1
1
1
1
2
1
2
1
2
1
3
0
0
2
2
1
1
1
1
1
1
1
1
2
0
1
2
2
1
1
1
2
0
1
2
2
0
1
2
0
1
1
1
0
0
1
1
1
0
2
2
2
0
0
2
1
1
0
0
2
1
2
0
1
2
2
1
0
1
0
1
0
1
0
0
2
1
1
2
1
0
0
0
2
2
1
2
1
1
2
1
0
1
2
0
1
2
1
1
0
1
0
1
2
0
3
1
1
1
2
2
0
2
2
2
1
1
1
1
1
0
1
0
0
2
1
0
0
1
3
1
0
1
1
1
1
1
1
0
0
1
2
3
1
0
1
0
1
1
0
1
1
0
1
1
2
2
1
0
1
1
0
3
1
1
2
0
1
0
0
3
1
1
1
0
2
1
0
1
1
1
1
1
0
2
0
2
2
1
2
1
1
0
1
0
1
2
1
0
1
0
1
1
1
1
2
1
1
0
0
2
0
1
1
1
2
1
1
3
1
2
1
1
1
1
2
1
2
2
1
1
0
0
1
0
2
0
1
1
1
0
0
0
2
1
1
2
1
1
0
2
0
0
0
2
1
1
1
0
1
0
0
0
2
0
1
1
1
1
0
1
0
1
2
0
1
3
1
2
0
1
0
2
1
1
1
1
0
2
3
0
0
1
2
0
2
0
0
0
1
1
0
1
0
2
1
1
1
1
0
1
0
2
1
0
1
1
0
1
1
2
0
1
1
1
2
0
1
2
2
2
2
0
1
1
1
1
1
0
0
2
1
0
1
0
2
2
1
2
2
1
0
2
0
0
2
1
1
1
0
0
0
1
0
1
2
1
1
1
1
0
2
1
2
0
1
0
1
1
0
1
1
2
2
1
0
0
2
2
1
1
1
1
1
0
1
5
1
0
2
1
2
2
0
0
2
0
2
0
1
1
0
2
2
0
1
2
2
2
1
1
0
1
1
2
1
0
1
2
1
2
0
2
1
1
1
1
0
2
1
1
1
1
1
2
2
2
1
1
0
1
2
1
2
3
1
0
0
1
0
2
1
1
2
0
0
1
0
1
1
0
1
1
1
1
1
0
1
1
1
2
1
1
1
1
1
1
0
1
0
2
1
2
0
2
0
2
1
2
2
0
1
2
5
0
1
0
2
1
1
1
2
0
2
0
2
1
0
0
1
0
1
2
0
1
1
1
2
1
1
0
2
0
1
1
1
2
1
2
0
1
1
1
1
1
1
1
0
2
1
1
1
0
0
1
0
2
1
1
0
0
2
0
0
2
0
0
0
1
1
2
1
2
1
0
0
2
0
0
1
1
1
0
1
1
2
0
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
0
0
1
1
1
1
1
0
0
0
0
0
0
2
0
0
1
1
2
0
0
2
1
1
2
1
1
0
1
1
1
0
2
0
2
0
1
0
2
1
1
0
0
3
1
2
1
1
2
0
1
1
2
0
1
1
0
2
1
1
2
1
1
1
0
2
0
1
1
1
0
0
2
1
1
2
1
0
0
0
2
0
2
1
2
0
1
1
0
2
1
1
0
0
0
1
0
1
1
1
1
1
1
1
1
1
2
0
1
1
0
1
0
1
0
1
1
4
0
1
1
1
1
1
1
2
2
2
0
1
0
1
1
2
1
1
1
0
1
1
1
1
1
1
2
0
1
0
2
2
0
1
2
1
1
0
0
1
2
1
2
1
0
4
0
0
2
0
0
1
2
2
1
0
0
2
0
2
0
2
1
2
5
1
0
1
2
2
2
0
1
1
1
0
1
1
0
1
0
0
2
2
2
0
1
1
0
1
1
0
0
0
0
1
1
0
0
1
0
0
1
2
2
1
1
1
0
1
0
1
1
0
1
1
2
1
1
1
0
0
2
1
0
0
1
1
1
1
1
1
1
0
1
2
1
1
2
1
1
0
1
1
2
2
1
1
1
1
1
0
1
1
2
1
2
1
1
2
1
1
0
0
0
0
1
1
1
2
2
2
0
1
1
1
1
2
1
1
0
1
0
1
2
1
1
1
1
1
1
1
0
2
1
2
0
0
2
1
1
0
0
1
1
1
2
1
0
1
1
0
1
2
0
0
0
0
1
1
1
0
0
2
1
1
1
0
1
1
1
2
1
1
1
1
1
0
2
0
1
1
0
2
1
2
1
1
1
0
0
0
0
1
1
0
1
1
1
0
2
1
0
0
0
1
1
1
2
1
0
0
1
0
2
2
0
2
1
1
1
0
0
2
1
2
2
1
0
2
2
1
1
1
0
1
0
1
2
2
1
0
0
2
1
1
2
0
0
1
1
1
1
1
1
1
1
0
0
2
1
1
2
0
2
1
1
2
2
1
0
2
1
0
2
1
0
1
1
0
0
1
1
1
1
1
0
1
1
1
1
0
0
1
0
2
0
2
1
1
1
1
2
0
1
2
1
1
0
2
0
0
1
1
2
0
1
2
2
1
0
1
1
1
1
1
1
1
0
0
1
1
1
1
1
1
2
1
0
0
1
2
1
1
2
1
0
2
1
1
0
0
1
2
1
1
1
1
1
2
1
0
2
0
1
1
2
1
0
2
0
1
1
1
0
1
0
2
1
0
2
1
0
1
2
2
2
0
2
1
2
2
0
2
1
1
1
1
2
2
0
2
0
1
0
1
1
2
1
2
0
1
2
1
0
1
0
1
1
1
2
0
1
2
2
0
0
0
1
1
1
2
0
0
0
1
1
0
1
2
0
1
2
1
3
0
2
2
1
2
1
2
0
0
0
0
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
2
0
1
2
1
1
1
2
1
1
2
0
1
1
1
0
0
2
0
2
0
0
0
1
1
0
1
0
0
2
1
1
1
1
1
1
1
1
2
2
1
0
0
2
0
0
0
1
1
0
1
0
1
0
0
1
1
0
0
1
2
2
0
1
1
1
1
0
1
1
2
1
0
0
2
0
1
1
0
1
0
1
0
0
0
1
0
1
1
1
1
0
0
2
0
0
1
1
1
1
2
0
1
1
1
1
1
0
1
2
0
1
2
0
1
1
2
2
0
0
1
1
1
2
0
1
1
1
1
1
0
0
1
1
1
1
1
1
1
1
0
1
1
1
0
1
1
2
1
1
1
2
2
1
1
2
0
2
1
0
1
1
2
0
1
2
1
0
0
1
2
1
1
0
0
1
1
0
0
0
0
1
1
0
1
0
1
1
2
0
1
1
2
1
1
2
1
1
1
1
0
0
1
1
1
2
1
0
1
0
1
1
0
0
2
1
1
3
2
1
0
1
0
0
1
1
2
2
1
1
0
0
1
2
2
2
0
1
3
0
2
2
2
1
1
1
1
0
1
1
0
0
1
2
1
1
0
2
1
0
0
0
0
0
1
1
1
1
0
0
2
0
1
1
1
0
1
1
1
0
1
1
1
0
1
1
0
0
1
0
2
1
1
0
0
1
1
0
1
0
1
0
0
0
0
1
2
1
1
1
1
2
0
1
2
0
2
1
0
1
1
1
2
1
1
1
1
1
0
1
2
0
1
1
1
1
1
1
1
1
0
1
0
2
2
2
0
0
1
0
1
3
1
3
1
1
1
2
1
1
0
1
2
2
1
1
2
1
0
1
1
1
2
0
2
2
2
0
0
0
2
1
2
1
1
1
0
1
0
0
1
1
1
2
2
2
1
1
1
1
2
1
2
1
2
1
0
2
0
2
1
1
1
1
0
1
2
1
1
2
1
1
1
1
2
1
0
1
0
1
0
0
0
1
0
0
1
2
2
1
1
0
1
0
1
2
1
1
1
0
2
1
1
1
1
1
1
0
1
0
0
1
0
2
2
1
2
2
1
1
0
2
1
1
2
1
0
2
2
1
1
0
1
0
0
2
1
1
2
1
1
2
1
3
0
2
1
1
2
1
1
1
0
1
2
0
0
1
1
1
1
2
0
1
2
0
2
0
1
2
1
1
1
1
2
1
1
5
1
1
0
1
2
1
1
0
0
0
2
0
1
2
1
1
1
1
0
1
1
2
2
2
2
2
4
0
0
2
1
0
3
2
0
1
0
1
0
0
2
1
1
0
2
0
1
1
1
1
2
0
1
1
1
2
1
1
1
1
1
0
1
0
0
1
0
1
1
0
1
0
2
1
0
1
1
1
1
1
0
0
0
1
1
1
0
0
2
1
1
2
1
0
2
1
1
2
2
2
0
0
2
1
1
0
0
2
0
1
1
3
2
1
2
1
1
1
0
1
1
2
1
1
1
1
0
1
1
0
0
1
1
0
0
0
2
1
1
0
1
0
2
1
1
1
1
1
0
0
0
0
1
1
1
0
0
1
1
1
0
1
1
0
1
0
2
1
0
0
2
0
0
1
2
0
1
0
1
2
0
1
0
1
2
2
1
2
0
1
1
0
0
2
0
2
0
0
1
1
2
1
2
1
1
1
1
0
0
1
0
1
1
1
1
2
1
1
0
2
0
1
1
2
1
1
2
2
0
1
1
1
0
1
2
2
1
2
1
0
0
6
0
1
0
1
1
1
1
1
1
0
1
0
2
2
2
1
0
1
2
1
2
1
2
1
1
2
0
0
1
2
1
0
2
1
2
1
1
0
1
1
1
0
0
1
1
1
2
2
2
1
1
1
1
1
2
0
0
1
2
1
2
1
2
0
2
0
0
2
2
0
0
1
1
0
2
2
1
0
1
1
1
1
1
1
2
0
0
2
1
0
0
1
0
1
2
2
0
1
0
1
1
1
0
1
1
0
1
0
0
1
2
0
1
1
0
0
1
0
2
1
1
2
1
0
1
2
1
0
1
0
1
0
1
1
0
2
0
1
0
2
1
0
1
1
2
2
1
0
2
0
1
1
0
0
1
0
3
1
1
0
2
1
0
1
0
0
0
1
1
2
1
0
1
0
0
1
1
0
1
1
1
1
0
1
1
0
2
2
1
1
1
1
0
0
0
1
0
0
2
0
1
1
0
2
0
1
0
4
1
1
0
1
1
1
1
1
0
1
2
1
0
2
0
0
1
1
1
0
1
1
1
1
2
0
0
2
1
1
0
1
2
1
0
4
0
1
3
1
0
2
0
1
1
1
1
1
0
1
2
1
0
0
0
0
0
1
1
1
1
0
1
1
2
1
2
1
1
1
0
1
1
2
1
1
1
1
0
0
1
1
0
1
0
2
1
1
0
1
1
1
2
1
0
0
0
2
1
0
2
0
1
0
0
1
1
1
0
0
0
0
1
0
2
0
2
0
0
1
2
1
0
2
1
1
0
2
1
1
1
1
0
2
1
2
3
0
1
0
0
1
0
0
2
0
0
1
0
0
2
1
2
0
1
1
1
1
2
1
2
2
2
1
1
0
0
0
0
1
3
1
0
1
1
1
1
0
2
2
1
2
1
1
2
2
1
1
0
1
1
1
1
2
1
1
1
1
2
0
2
1
1
0
1
1
1
0
1
0
1
2
0
1
1
2
1
0
1
0
1
2
2
2
2
1
1
1
1
1
0
1
0
2
0
2
1
2
1
2
1
1
1
1
0
0
1
2
0
1
0
2
2
2
1
1
1
0
0
0
0
1
2
0
1
1
1
1
1
2
2
0
1
1
1
1
1
1
0
1
1
1
0
0
0
0
2
2
0
2
0
2
1
1
1
1
1
0
0
1
0
2
0
1
0
1
0
1
0
1
0
1
2
0
0
1
1
0
2
1
0
1
2
0
1
1
0
0
1
1
1
1
0
0
1
2
1
2
1
1
2
0
1
0
2
1
2
1
0
0
2
0
1
2
2
0
0
2
0
1
2
1
0
1
2
1
0
2
2
1
1
1
0
1
0
1
2
0
0
1
1
2
2
4
0
0
0
2
0
1
0
1
1
1
2
2
1
1
1
1
2
2
1
2
2
1
1
2
2
2
2
0
0
2
0
0
0
2
1
1
2
0
1
0
1
1
0
1
1
2
1
1
0
1
2
0
0
0
1
0
0
0
2
1
1
1
0
0
1
1
2
2
1
0
2
1
1
2
0
2
1
1
2
2
0
2
1
3
1
1
0
2
2
1
1
0
2
2
0
1
0
1
1
1
1
0
2
2
1
0
2
0
2
2
1
0
1
0
1
2
1
1
1
1
1
2
0
2
2
1
1
1
1
1
0
1
1
1
1
1
2
2
0
2
0
0
1
0
1
1
1
1
1
1
2
1
1
0
0
1
1
0
1
0
1
0
3
1
1
1
2
1
1
1
1
2
2
1
1
1
1
0
0
3
0
1
0
1
1
1
1
0
0
2
1
1
1
1
0
0
1
2
2
0
1
2
1
1
1
1
1
2
1
1
0
0
1
0
0
1
0
1
0
0
1
1
0
2
0
1
0
0
0
1
1
2
0
1
0
1
2
1
2
0
1
2
1
0
1
2
1
1
1
0
1
1
0
1
0
1
1
0
1
1
1
2
1
1
0
2
1
1
1
1
0
0
2
2
0
3
0
1
1
0
1
0
1
0
1
0
1
0
2
0
0
1
2
1
1
1
2
1
1
1
2
1
1
0
1
1
1
2
1
0
0
1
1
0
1
1
1
0
1
1
1
0
0
1
1
1
2
0
1
0
1
0
0
1
1
1
1
2
1
1
1
1
0
0
1
2
2
1
0
1
2
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
2
1
1
1
0
1
1
3
2
1
0
0
0
1
2
2
1
1
0
1
1
1
0
2
2
2
1
1
0
0
2
1
0
0
0
2
1
0
2
1
0
1
2
0
1
2
0
0
1
2
1
0
1
1
2
1
1
0
1
0
1
1
1
0
1
1
1
0
1
1
2
0
1
1
0
0
1
2
0
2
2
0
0
1
1
0
1
1
0
2
1
1
1
2
1
2
1
1
0
0
2
1
1
0
1
1
1
0
1
1
2
0
0
2
0
2
0
1
0
1
2
1
1
1
2
1
1
2
0
2
1
1
2
2
1
1
2
0
2
1
1
0
0
0
0
1
0
1
0
0
0
1
1
0
1
2
2
1
1
1
0
2
1
2
1
2
2
2
1
2
0
1
1
1
2
1
1
1
1
1
1
1
2
0
0
1
2
1
1
1
0
1
0
0
2
1
1
0
0
1
2
1
2
0
1
1
0
0
0
0
1
0
1
1
1
0
1
0
1
0
1
1
1
1
0
0
1
1
0
1
2
0
1
1
1
1
1
0
0
0
1
2
1
0
0
1
0
1
2
0
2
1
1
2
1
0
0
0
1
1
0
1
1
0
1
1
1
0
1
1
0
0
0
1
2
1
2
1
1
1
1
2
1
1
0
1
0
1
0
2
0
2
0
1
1
0
0
0
1
0
0
1
2
1
0
1
2
2
2
3
2
0
0
1
1
2
2
0
0
1
0
1
0
0
1
0
1
1
2
1
1
1
1
1
2
1
1
1
2
2
1
1
0
2
0
2
1
1
1
1
1
2
0
1
0
2
1
2
1
1
0
0
0
0
2
1
1
2
1
1
0
1
1
1
0
1
1
1
1
0
0
1
0
1
1
2
0
2
1
0
1
1
0
2
0
2
2
1
2
0
0
0
1
1
0
0
1
2
2
1
1
1
1
0
0
0
0
2
1
1
1
1
2
0
0
1
2
1
2
1
1
0
1
1
2
0
1
1
2
1
1
0
1
0
2
1
1
1
1
0
1
2
2
2
2
1
2
2
0
1
0
1
1
1
1
1
0
1
1
1
0
0
1
0
1
2
0
2
1
1
2
0
1
2
2
1
2
1
2
1
0
1
1
0
0
0
0
2
0
2
0
1
0
1
2
1
0
1
0
0
1
0
0
1
1
0
1
0
1
0
1
1
1
0
1
1
1
1
0
1
0
1
1
1
1
1
1
1
1
1
1
0
0
1
0
0
2
2
0
2
0
0
1
0
1
2
1
0
0
1
0
1
1
0
1
1
1
1
1
2
2
2
0
0
1
0
0
1
1
2
0
1
1
1
2
1
2
1
2
1
0
1
0
2
1
2
0
0
0
1
1
0
1
1
2
1
1
1
0
2
1
0
1
1
1
0
0
0
1
1
2
1
1
0
0
2
1
1
0
0
1
1
1
0
0
0
0
0
3
2
0
1
1
1
2
1
1
2
1
1
0
0
2
1
0
1
1
0
1
1
1
1
1
0
0
2
1
2
1
1
0
1
1
1
1
0
1
1
0
1
1
1
2
1
1
1
0
1
2
0
2
1
0
0
2
0
2
1
1
1
0
0
2
2
0
2
2
0
0
1
1
2
0
1
1
1
0
2
1
1
0
2
2
0
1
3
0
1
0
4
0
0
1
0
5
1
2
1
1
2
1
1
1
2
2
1
2
0
0
1
1
1
2
1
2
3
1
1
1
0
0
1
1
1
1
1
0
1
0
1
1
1
0
2
1
0
2
0
1
0
1
1
0
2
1
0
0
1
1
1
1
1
1
0
0
1
2
1
0
2
1
1
1
0
1
1
2
0
1
0
1
1
1
1
1
0
0
1
2
1
2
0
1
1
1
0
1
4
0
2
2
1
1
1
1
1
2
1
1
1
0
0
0
2
1
1
1
1
0
0
2
0
2
2
1
2
1
0
1
2
0
2
1
1
1
0
1
1
2
2
2
1
0
2
1
1
1
2
0
0
2
1
0
0
1
1
1
2
2
2
0
2
1
0
0
1
1
1
2
0
1
1
1
1
2
1
2
0
1
0
1
0
2
0
1
1
0
1
2
0
3
1
0
1
0
0
0
0
1
1
1
1
2
2
2
1
2
2
0
2
1
1
0
1
1
0
1
1
2
1
1
2
2
1
0
1
1
2
1
1
2
1
0
2
1
0
1
1
0
2
1
1
3
1
1
0
0
2
0
1
0
1
1
0
2
2
1
1
2
0
2
2
0
1
1
0
1
1
1
0
0
1
1
2
0
2
1
1
0
0
1
0
2
1
1
2
1
1
1
1
1
0
1
1
0
0
0
1
0
1
1
0
0
1
1
1
3
1
0
1
0
1
1
2
1
1
1
1
1
2
0
1
0
1
0
1
1
0
1
1
1
1
0
3
0
1
0
2
1
2
1
0
2
0
2
1
1
1
1
1
2
0
0
0
1
1
1
1
1
1
2
0
1
0
1
0
0
0
0
2
2
1
1
1
1
0
2
1
0
0
1
1
1
0
0
1
2
1
2
2
1
0
1
1
0
0
1
1
1
1
0
1
1
2
1
2
1
0
0
1
1
1
1
0
0
1
0
0
1
2
2
1
2
1
0
0
1
2
0
2
2
0
1
0
1
0
0
0
1
2
2
1
1
2
2
1
1
0
1
0
1
1
2
1
0
1
1
2
2
1
0
1
0
1
0
1
1
0
0
0
1
2
1
1
0
0
0
2
1
0
2
1
1
1
0
0
1
1
2
1
0
1
1
2
1
1
0
1
0
2
2
1
0
0
1
2
0
2
1
1
1
0
2
1
1
1
1
2
1
2
1
2
0
0
0
0
0
2
0
1
0
1
1
0
1
2
2
1
0
0
1
1
1
0
1
1
0
1
1
1
0
0
1
1
2
0
0
1
0
0
1
1
1
1
2
0
0
0
1
2
1
1
2
1
3
0
1
2
1
1
3
1
0
4
3
0
1
1
1
1
1
1
1
3
2
0
1
1
2
1
0
1
1
2
0
1
0
1
1
1
2
1
1
2
0
0
1
0
1
1
1
1
0
0
1
0
0
3
2
0
1
0
1
2
2
2
2
2
1
2
1
2
1
1
1
0
0
0
2
1
0
1
0
0
1
1
1
2
1
1
2
1
1
1
0
0
0
0
0
1
0
1
2
1
1
1
1
1
1
0
1
0
1
0
0
1
1
1
0
1
2
1
1
0
1
0
2
2
2
2
2
1
1
1
1
0
0
1
0
1
2
1
0
2
1
0
1
1
2
1
2
1
0
1
1
0
0
2
0
1
1
1
0
1
1
2
1
1
2
1
1
2
0
0
0
1
1
2
0
0
2
2
1
1
0
0
0
1
1
2
1
1
2
0
2
1
0
0
0
0
1
0
1
0
1
1
1
1
2
1
1
2
0
0
1
0
2
1
0
1
2
1
0
4
0
2
2
2
1
0
1
1
1
1
1
0
1
1
1
1
1
1
2
0
1
1
1
1
0
0
1
1
1
2
1
1
2
2
1
0
0
1
1
1
2
0
2
0
2
0
1
1
1
1
1
1
1
2
1
1
1
0
1
1
2
2
0
2
0
1
1
1
0
2
1
1
1
1
1
0
2
3
1
0
0
0
0
0
1
1
0
2
1
2
2
1
1
1
1
1
0
0
0
1
0
0
1
0
0
0
2
1
1
1
2
2
0
0
1
2
0
2
1
1
1
2
2
1
1
2
2
0
0
1
0
1
1
1
1
2
2
5
2
1
1
1
0
1
0
0
0
1
2
0
3
0
1
2
1
4
1
2
0
0
0
2
0
0
1
1
0
1
1
1
2
1
0
1
1
0
2
2
1
1
1
0
1
0
1
1
1
2
1
1
0
1
1
0
2
2
1
1
1
3
3
1
1
0
4
1
1
0
0
1
0
0
1
1
1
0
2
0
1
1
2
1
1
2
1
1
0
0
0
0
0
2
1
0
1
2
2
1
1
0
0
1
1
1
0
2
1
1
2
0
0
0
1
0
2
0
1
2
1
1
0
0
1
1
2
0
1
2
0
1
1
2
0
0
1
1
2
0
2
0
1
1
1
1
2
1
1
2
2
2
0
0
1
2
1
1
1
1
2
1
0
2
0
1
1
2
0
1
1
1
0
1
1
2
3
1
0
2
0
0
0
0
0
0
1
1
1
1
1
0
1
0
1
2
0
1
1
2
0
1
1
0
1
2
0
1
1
1
2
1
2
2
1
2
0
2
0
2
2
0
0
1
1
1
1
2
1
1
1
2
1
1
1
1
0
2
1
2
1
2
1
0
1
2
2
0
0
2
0
1
0
0
1
1
1
1
1
2
1
0
1
2
1
2
1
2
2
2
0
0
0
0
2
1
0
0
1
1
0
1
0
1
0
2
0
1
1
0
0
1
1
2
2
1
0
0
1
1
1
2
1
1
1
0
1
0
1
1
1
0
2
1
0
1
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
0
1
0
1
1
2
1
2
1
0
2
1
1
1
1
0
0
1
1
0
1
1
0
2
4
2
1
2
1
1
0
2
0
1
1
0
0
0
0
3
2
1
0
0
1
2
2
0
1
1
1
1
1
0
2
0
2
1
2
1
0
1
0
2
0
2
1
2
2
1
0
2
2
2
1
2
2
0
0
1
1
0
1
2
1
1
0
1
0
0
0
1
0
1
2
0
1
1
1
1
2
0
2
1
1
0
0
0
1
1
2
2
0
2
1
0
1
0
1
0
0
1
1
1
1
1
1
1
1
1
1
1
2
0
0
1
1
1
0
2
2
1
0
1
2
0
0
1
1
2
0
1
1
1
0
0
1
0
2
1
1
1
0
1
1
0
1
0
2
2
0
0
1
0
1
2
1
0
2
1
0
3
3
2
2
1
0
1
1
2
2
1
2
0
2
1
1
1
1
2
0
2
0
1
2
1
1
2
5
2
1
1
1
2
2
1
1
1
1
1
2
1
0
0
0
1
0
1
1
0
0
0
0
0
1
1
1
1
2
2
1
0
0
2
0
2
0
2
1
0
2
1
0
1
1
1
1
1
0
0
0
0
1
1
1
1
0
2
1
1
0
1
0
2
0
1
0
1
2
2
0
0
1
2
0
3
1
1
2
0
2
1
1
0
1
1
0
2
2
2
1
1
0
1
0
2
1
1
1
0
0
2
1
0
1
1
2
1
1
2
1
2
1
0
1
0
0
0
1
2
1
0
1
1
1
0
1
0
0
1
0
2
0
0
0
1
1
1
0
1
3
1
1
2
1
1
1
1
1
1
2
1
1
0
3
1
1
1
3
2
1
1
2
1
1
1
1
1
1
2
2
0
1
1
1
1
0
2
1
2
1
1
2
0
0
1
1
1
1
1
1
2
2
1
0
1
2
0
2
0
2
1
1
1
1
1
2
1
1
2
1
1
2
2
1
1
0
0
2
1
1
1
1
0
0
0
1
2
1
0
1
2
1
1
0
0
1
1
1
0
1
0
0
2
2
0
0
0
1
2
1
1
0
1
2
0
1
2
1
1
1
1
1
2
1
1
1
2
1
0
0
0
2
1
2
2
1
0
0
0
1
1
0
2
1
2
0
1
1
0
0
0
2
0
2
2
1
1
1
2
2
0
1
2
0
1
1
1
0
2
1
1
0
1
1
1
1
0
1
1
2
0
2
1
1
0
0
2
1
0
1
1
1
1
2
0
1
0
1
0
1
0
1
1
2
2
1
1
0
2
0
0
0
2
1
0
1
1
2
0
1
1
1
2
1
2
1
1
1
2
3
2
1
0
2
1
1
1
0
1
2
2
1
0
1
1
2
0
2
1
1
1
1
1
1
1
0
0
1
1
0
1
0
1
1
0
1
1
0
0
0
1
2
2
1
1
1
1
1
1
0
1
0
1
1
0
2
1
1
0
1
2
0
1
4
1
1
1
1
1
0
1
0
1
1
2
0
2
2
0
0
2
0
1
1
1
0
1
1
1
1
0
1
2
1
1
1
1
1
0
0
1
1
1
0
1
1
0
2
1
2
1
1
2
1
0
1
1
0
1
0
1
1
0
2
1
2
1
2
0
0
1
1
1
2
0
0
1
0
1
0
1
1
2
2
1
0
1
2
1
2
0
1
1
0
1
0
1
1
1
1
2
1
0
2
2
1
1
0
1
1
0
2
1
1
1
2
2
2
2
0
1
1
1
0
1
1
1
2
1
0
1
1
0
2
1
1
0
2
1
0
1
0
2
2
1
1
1
1
1
0
0
1
0
1
5
1
1
0
2
0
2
0
1
0
1
1
0
0
1
1
1
1
1
0
0
0
0
1
2
1
0
1
0
1
1
0
0
1
1
1
1
2
2
0
1
0
0
0
1
0
1
1
2
2
2
1
2
1
0
1
2
1
1
1
1
1
1
2
2
2
1
0
1
2
0
0
2
2
1
0
1
1
0
2
0
0
1
1
1
0
2
1
0
2
0
0
2
2
2
0
1
1
1
2
1
1
1
0
2
1
1
1
1
1
1
0
0
0
0
1
2
1
1
1
0
0
1
1
2
1
2
2
1
1
1
1
0
1
1
1
1
0
1
0
1
1
2
0
2
1
1
1
2
1
2
1
2
1
1
0
2
1
2
0
1
1
1
1
1
1
0
1
1
0
2
2
1
1
1
2
2
1
1
1
1
1
1
2
1
0
2
1
1
1
1
2
2
1
2
1
1
1
2
1
0
1
0
1
1
2
0
1
0
2
1
1
2
1
3
1
2
1
0
1
1
1
0
1
2
2
2
0
1
1
0
0
2
2
1
1
1
1
2
0
0
0
0
1
0
1
4
1
2
5
0
1
2
1
0
2
1
1
0
1
0
2
2
1
2
1
1
1
0
0
0
2
1
0
1
0
2
1
1
0
1
0
0
2
1
0
2
1
1
1
1
0
2
1
0
1
1
3
1
2
0
2
0
1
1
3
1
1
2
1
1
0
0
0
2
2
0
2
0
0
1
1
1
2
0
1
1
1
1
1
1
2
1
1
1
0
1
1
1
1
2
1
1
1
1
1
1
0
1
1
2
2
0
0
1
1
1
2
1
1
2
0
1
0
2
0
0
0
0
1
1
2
1
1
1
1
2
1
2
1
2
0
1
0
1
2
2
0
0
1
2
1
0
0
0
2
2
2
2
0
0
2
1
1
2
2
1
2
1
1
1
1
2
2
0
1
2
1
1
2
1
2
2
1
2
2
0
1
0
1
0
0
1
1
0
0
1
1
2
1
1
0
1
1
1
1
2
1
1
1
1
1
1
1
0
2
2
0
1
1
1
1
0
1
1
1
1
1
1
2
1
2
1
0
1
1
0
0
2
1
1
1
2
1
0
1
1
2
2
1
1
1
0
1
0
1
2
1
2
2
0
3
0
1
1
1
0
2
1
1
2
2
1
1
0
1
2
1
1
1
2
0
0
1
1
1
1
0
0
0
0
2
1
1
1
0
1
0
0
0
1
1
1
1
0
1
1
0
0
1
1
1
1
2
1
1
2
0
1
1
1
0
1
0
1
1
2
1
2
1
1
0
0
1
0
1
0
0
2
0
2
2
1
1
2
0
1
1
1
0
1
2
1
1
1
0
1
1
0
0
2
0
2
2
1
1
1
1
0
0
0
2
1
0
0
2
0
1
0
1
0
0
1
0
2
2
2
0
0
1
0
2
2
0
2
2
0
1
0
1
2
0
1
0
1
0
0
1
1
2
1
1
2
0
0
0
0
0
0
1
1
1
0
2
1
1
1
0
0
1
0
2
2
0
0
0
1
0
1
4
2
0
2
1
1
2
1
1
1
0
1
2
1
2
1
2
1
1
2
1
0
1
1
4
1
0
1
1
0
1
0
1
0
0
1
1
2
0
2
2
0
1
1
2
2
1
0
1
1
1
2
1
1
2
1
0
1
0
1
1
0
2
1
1
1
2
1
1
1
1
0
1
0
1
1
2
1
2
2
1
1
2
2
0
1
2
2
2
0
1
1
1
1
0
0
0
1
1
1
0
1
1
1
1
1
2
2
0
1
1
1
2
1
1
1
0
2
1
0
1
1
0
1
1
2
1
2
1
0
0
1
1
0
1
1
0
1
2
2
1
0
1
1
2
1
1
2
1
0
1
2
0
1
1
1
1
0
2
2
0
1
1
0
1
1
2
1
2
1
0
0
0
2
0
1
2
0
0
0
0
0
0
2
1
1
0
1
2
1
2
1
2
2
1
1
1
1
0
2
1
0
0
1
0
3
0
1
0
2
0
0
0
1
1
2
1
0
1
0
1
0
1
2
1
2
0
1
2
1
1
1
2
1
0
1
2
2
1
0
0
2
0
0
1
1
1
1
2
2
1
0
1
1
1
1
2
2
2
1
2
1
2
1
1
0
2
2
2
2
0
0
2
0
1
1
1
1
1
2
1
1
1
1
0
1
2
1
1
1
1
1
2
1
0
0
3
1
0
2
1
1
0
1
0
2
1
1
2
1
1
1
2
2
1
1
0
2
0
1
0
1
1
1
1
1
0
1
0
1
0
1
0
0
1
1
1
1
1
2
0
1
1
1
1
1
1
1
1
1
2
1
1
2
0
0
1
1
1
1
0
1
2
2
1
1
1
1
4
1
2
1
1
0
0
1
0
0
1
0
2
1
1
2
1
1
1
1
0
0
2
1
2
1
2
0
1
1
0
0
1
2
2
0
1
0
1
0
2
2
0
1
1
2
0
0
1
1
1
0
1
1
1
2
0
2
0
1
1
1
1
0
1
1
1
3
1
1
0
1
0
1
1
1
1
1
2
0
0
0
0
0
0
0
0
1
1
0
2
0
0
1
1
1
1
1
2
0
0
1
1
2
2
1
1
1
2
1
1
2
0
1
1
0
0
2
0
2
0
1
0
1
0
0
1
1
1
2
0
1
1
0
0
1
1
0
1
1
2
1
1
1
2
1
1
0
1
1
1
2
0
1
2
1
1
1
1
2
1
1
0
5
0
1
0
1
0
1
0
2
0
0
0
0
0
1
1
1
0
2
0
0
1
1
1
1
1
0
1
0
1
1
1
0
1
1
1
2
1
0
1
0
0
1
2
0
2
0
1
0
1
0
1
1
1
1
1
0
2
0
0
0
0
2
2
1
0
3
2
2
1
0
2
1
1
2
1
0
1
1
0
1
0
1
0
0
2
1
1
1
0
1
1
1
1
1
1
0
1
2
0
0
0
2
1
1
0
0
2
1
2
1
2
1
1
0
0
1
0
2
1
0
0
1
0
2
1
1
0
3
0
1
1
0
1
0
0
1
1
1
1
1
1
2
1
1
0
1
2
0
0
2
0
1
0
1
1
0
1
1
1
2
1
1
1
0
0
2
1
0
1
1
0
0
0
0
1
0
2
1
0
0
0
1
1
1
1
0
2
1
1
1
0
2
1
1
2
0
2
0
0
1
1
0
2
1
1
0
1
0
2
0
0
2
1
1
2
1
1
2
0
1
0
2
0
1
1
1
2
2
0
0
2
2
2
1
1
1
1
1
1
2
1
1
1
3
2
1
0
1
0
2
1
1
1
6
0
1
0
1
1
0
1
2
0
1
1
2
1
1
1
0
0
3
0
1
0
1
1
1
3
1
0
0
1
1
1
0
2
2
0
0
1
1
1
2
0
1
1
1
1
0
0
1
2
1
2
1
1
2
1
0
1
1
1
0
2
1
2
1
1
2
1
1
0
0
2
2
1
1
1
1
2
1
0
1
1
2
1
1
2
0
1
0
0
1
1
1
1
1
1
1
2
2
1
0
1
2
0
1
1
0
2
0
2
0
1
1
1
2
2
1
1
1
1
1
1
2
1
2
1
1
0
1
1
2
1
0
2
0
2
2
1
2
0
1
3
1
0
1
1
0
0
0
2
0
0
2
1
3
1
0
1
1
1
0
2
2
0
1
1
2
1
1
1
1
0
1
1
2
1
0
0
0
2
1
0
1
2
0
2
2
2
2
0
0
1
2
1
1
2
2
0
1
0
1
1
0
1
1
1
2
0
0
1
1
0
0
1
1
1
1
0
1
2
1
1
1
0
1
0
1
1
2
0
1
2
0
1
1
1
2
2
2
1
0
2
0
2
0
1
2
2
0
0
0
2
1
2
0
0
2
1
0
2
0
1
1
1
3
1
2
0
1
1
0
1
0
1
0
0
0
2
1
1
1
1
1
2
1
2
0
2
2
0
0
1
1
0
0
2
1
1
3
1
2
0
2
0
1
1
0
1
1
1
1
0
2
1
1
1
2
1
0
2
1
1
0
0
2
1
1
1
1
0
2
2
1
1
1
0
1
1
2
0
1
1
2
2
0
1
2
1
0
0
0
0
2
2
1
0
2
1
1
2
0
0
0
1
0
0
1
1
2
1
1
1
0
1
0
0
0
2
1
1
1
0
1
2
2
4
1
0
1
1
2
1
1
1
2
1
0
1
2
1
1
1
0
2
0
1
2
0
2
1
2
1
1
1
0
1
1
0
2
1
1
1
2
1
1
2
1
0
1
2
1
0
0
1
2
2
0
0
1
2
1
2
3
0
2
1
1
1
1
1
0
1
1
1
2
1
0
1
1
2
0
1
1
2
1
0
0
1
1
1
1
1
0
1
1
0
0
1
0
0
1
1
0
1
0
0
1
0
2
1
1
2
1
1
0
0
2
1
1
2
1
0
1
0
0
1
0
1
2
1
1
1
2
1
1
2
2
0
3
1
2
1
2
1
1
0
2
0
1
0
0
2
1
1
1
2
2
2
1
1
1
2
0
2
2
2
0
2
0
1
0
0
2
2
2
0
2
1
0
0
1
0
0
2
1
1
0
1
2
1
0
0
0
1
1
1
1
2
2
0
1
1
1
1
2
2
1
1
2
1
2
1
2
0
1
1
0
2
0
1
1
2
1
1
1
1
2
0
1
1
1
2
1
2
0
1
1
1
1
0
0
1
1
1
0
1
1
2
1
2
0
2
0
1
1
2
1
2
0
1
0
1
1
0
0
1
0
0
1
0
0
1
2
2
0
1
0
0
1
1
1
0
1
0
1
2
0
0
0
0
1
1
1
1
1
1
0
1
0
0
0
1
0
1
1
2
1
2
1
1
1
2
0
1
2
0
1
1
1
2
1
1
1
0
0
1
2
3
1
1
1
0
1
1
1
1
0
0
0
1
2
1
0
2
2
1
0
1
0
0
1
1
0
0
1
0
1
1
0
1
3
2
1
0
1
1
0
2
2
2
0
0
1
1
1
1
2
2
0
0
0
1
0
1
1
2
0
2
1
0
1
1
1
2
1
2
0
1
1
0
1
2
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
2
2
2
2
1
0
1
0
1
0
0
0
2
1
2
2
1
0
0
1
1
2
2
2
1
2
1
0
1
0
1
1
2
1
2
2
0
1
0
1
2
2
1
2
1
1
1
1
0
1
1
1
4
1
1
0
2
0
2
1
0
0
1
2
1
0
0
1
0
1
1
0
0
1
1
1
0
2
2
1
2
2
1
0
0
2
2
1
2
0
0
1
1
0
0
0
1
1
0
2
2
0
2
1
0
1
0
1
2
0
0
0
1
1
2
1
1
1
0
1
0
1
1
0
1
1
0
2
2
1
1
2
0
0
0
1
2
2
0
0
0
1
0
1
0
2
2
2
0
1
2
1
1
1
0
0
1
0
1
1
1
1
1
0
0
1
1
1
1
0
1
1
1
1
1
0
0
0
1
2
1
2
2
1
2
0
0
1
1
1
2
1
2
1
1
2
1
2
1
0
1
0
0
2
2
2
1
1
1
1
2
1
1
1
0
0
1
0
0
1
1
1
0
1
1
1
4
0
1
1
1
1
0
1
1
1
1
2
0
1
1
0
1
1
1
0
0
1
0
1
1
1
2
1
1
1
2
0
0
2
2
0
0
1
1
1
0
0
1
1
1
2
0
2
1
1
1
0
0
0
1
2
2
1
1
0
1
0
2
0
0
1
1
1
2
1
1
0
2
1
1
1
1
1
2
1
2
2
0
0
1
2
1
1
1
1
1
1
2
1
2
1
1
0
0
0
1
1
0
0
1
4
0
1
2
2
2
0
1
1
1
0
0
0
2
1
0
0
2
1
1
2
2
0
2
1
1
1
0
1
2
1
0
1
0
1
1
2
2
0
1
1
1
1
1
0
1
1
2
3
1
1
0
0
1
0
0
1
1
1
1
2
1
1
1
1
1
1
0
2
1
1
0
2
1
2
2
2
2
1
1
0
1
4
0
1
1
1
1
0
2
1
0
2
1
1
1
0
2
1
1
2
2
1
0
0
0
0
0
1
2
1
2
2
2
1
0
2
1
0
1
0
2
1
2
1
1
1
1
0
0
1
1
1
1
0
0
1
1
0
3
0
2
1
2
1
1
1
2
1
1
1
2
0
1
0
1
1
1
2
1
1
1
1
2
0
1
2
2
2
0
0
1
2
2
1
1
0
1
0
1
1
2
1
1
1
1
2
1
1
1
2
1
1
1
1
0
0
1
0
1
0
1
1
0
1
2
1
1
0
2
1
1
1
1
1
2
0
2
1
2
0
1
0
0
1
1
0
1
3
1
1
1
0
0
2
1
1
0
1
1
1
0
2
1
1
1
0
2
1
2
1
1
0
2
1
1
2
1
1
1
2
1
1
0
1
0
2
1
1
2
1
2
1
1
1
1
1
1
1
1
0
1
1
1
1
1
0
1
0
1
0
1
2
3
0
2
2
1
2
2
0
1
0
1
1
3
1
1
0
2
0
0
0
1
1
1
0
1
0
1
1
1
0
1
0
2
0
0
1
1
2
1
2
1
1
2
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
0
1
1
2
0
2
0
2
0
0
1
2
2
2
1
1
0
1
0
1
1
2
2
2
0
0
0
0
1
1
2
0
1
1
2
0
1
1
1
1
2
1
1
1
0
1
0
0
1
2
1
1
1
0
1
0
2
2
0
2
0
1
0
0
2
2
0
0
3
2
1
2
2
1
1
1
0
0
1
0
0
1
1
1
1
0
1
1
1
0
0
2
1
1
1
2
1
2
2
1
1
0
0
0
2
1
2
1
0
1
1
0
2
3
0
1
2
0
1
1
1
1
1
1
1
2
1
0
1
1
1
1
1
0
1
2
2
1
1
1
2
1
0
1
0
2
0
1
0
1
1
1
1
1
0
2
0
0
1
2
1
2
2
1
2
2
2
1
0
1
1
0
1
1
2
1
1
2
1
1
1
1
2
0
1
0
1
0
2
1
1
2
0
0
2
2
1
1
1
1
2
2
1
1
2
0
1
0
0
1
1
0
2
0
2
0
0
1
0
1
0
2
1
0
0
2
1
0
0
0
1
2
2
0
1
1
1
1
0
2
2
1
1
1
1
1
2
0
1
0
1
1
2
1
0
2
0
0
0
2
0
0
1
2
1
1
1
0
0
1
1
0
1
1
1
2
1
0
1
2
2
1
1
1
2
2
0
0
2
1
2
1
1
1
1
1
1
1
0
1
1
1
1
0
0
0
1
2
1
2
2
3
0
1
1
2
0
1
1
1
1
2
1
1
2
1
2
1
0
0
1
1
1
1
1
1
0
1
0
2
1
0
2
2
1
2
0
1
0
1
1
0
2
0
2
0
2
1
0
1
2
1
1
1
1
0
0
1
1
0
0
1
1
1
0
0
1
0
2
0
1
1
2
1
0
2
2
1
1
1
1
0
0
1
1
0
1
0
1
1
0
0
1
1
0
0
0
0
1
0
2
1
1
0
1
2
1
0
0
0
1
2
1
1
2
0
2
2
1
1
1
1
1
0
1
1
4
1
2
2
1
0
0
2
1
0
1
1
1
1
0
0
1
0
1
2
2
1
1
1
0
1
0
1
3
0
1
1
0
1
2
1
0
1
0
4
1
0
1
1
1
0
0
0
1
1
0
1
0
2
0
2
1
1
0
0
1
0
1
0
0
1
2
1
1
1
0
1
2
0
1
2
0
1
1
0
0
1
1
2
1
1
1
2
1
0
1
0
0
1
1
0
0
1
1
1
1
1
2
0
1
1
2
1
0
1
1
0
2
2
0
2
0
0
1
1
1
0
1
2
1
1
1
0
1
0
0
1
1
2
0
2
1
1
2
1
1
2
1
0
1
1
0
1
1
1
1
1
0
0
1
1
1
1
1
1
1
1
0
0
0
0
1
2
2
1
2
0
1
0
1
1
1
2
1
1
2
0
1
0
1
1
1
1
2
1
0
1
1
0
0
2
1
0
1
2
2
1
1
2
1
1
0
2
1
1
1
2
2
0
2
0
1
0
0
0
2
2
2
2
2
2
2
1
0
1
2
1
1
0
1
0
0
1
0
0
1
0
0
0
1
2
1
0
1
2
0
0
2
1
0
1
0
0
1
1
1
0
1
1
1
2
1
2
1
1
0
0
1
2
0
2
2
1
2
3
0
2
1
1
2
2
1
0
1
1
2
1
0
2
0
3
1
1
1
0
1
0
0
0
0
1
0
1
1
1
2
2
0
1
1
2
0
1
0
1
1
1
1
1
0
1
1
2
1
0
0
1
0
1
2
1
2
0
1
1
0
2
0
1
2
1
1
1
1
1
0
0
1
1
1
0
0
2
1
1
2
1
0
1
0
0
1
1
1
0
2
0
2
0
0
1
1
1
0
2
1
0
1
1
1
1
2
1
2
0
0
5
2
0
0
0
0
1
1
2
1
1
1
2
1
1
2
0
2
1
1
1
1
1
0
1
1
0
2
0
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
0
1
1
2
1
2
1
0
1
1
1
1
2
1
3
1
1
1
1
2
0
1
0
0
1
1
1
0
0
1
5
1
1
0
0
0
0
1
1
0
1
0
2
1
1
1
4
2
0
1
1
2
3
0
0
1
0
1
2
1
0
2
1
4
1
0
0
1
0
2
0
0
0
2
0
1
5
1
1
1
1
0
1
1
2
1
0
1
1
1
1
1
1
0
0
0
0
1
0
1
1
2
1
1
0
1
0
1
0
0
0
2
1
0
0
1
0
2
2
2
2
1
1
1
0
1
0
1
0
1
1
1
1
3
2
2
0
0
2
2
1
1
0
1
0
1
1
2
0
0
1
1
0
1
1
2
1
1
1
1
2
2
0
2
1
0
0
1
1
1
1
1
0
1
1
1
4
1
2
2
2
0
1
1
0
1
2
0
1
1
1
0
1
0
1
1
0
0
1
2
0
2
1
1
1
2
0
1
1
0
0
3
1
1
0
1
1
2
1
0
1
0
1
1
1
2
2
0
1
0
1
2
0
2
1
2
2
1
1
2
1
4
1
0
2
2
2
1
0
0
1
0
1
1
1
0
3
1
1
1
1
1
0
2
2
3
1
2
1
1
1
2
2
1
1
2
0
1
1
1
1
0
2
1
1
2
2
1
1
1
2
1
1
0
1
1
0
1
2
0
2
1
1
1
2
1
1
2
1
1
1
2
2
0
0
0
1
0
2
1
1
1
1
0
2
2
1
1
0
0
1
0
0
2
1
1
0
1
0
1
1
1
2
1
2
1
1
1
2
2
1
1
1
2
1
0
0
2
2
1
0
1
0
2
1
2
1
1
0
1
1
1
0
1
2
1
1
1
1
0
1
1
0
0
1
2
1
1
1
1
1
1
0
1
0
1
1
0
1
0
2
2
2
1
3
2
0
1
1
1
1
0
1
2
2
0
4
5
0
0
1
1
2
2
1
2
1
0
1
0
0
0
1
0
1
1
1
2
0
0
1
0
0
0
0
0
1
1
1
1
1
1
1
2
1
0
1
0
2
1
2
0
0
2
1
0
1
2
2
2
0
1
1
1
0
0
1
0
2
0
1
2
1
1
1
0
0
0
0
1
1
1
0
0
1
2
1
1
2
1
2
0
2
2
2
2
0
2
0
1
0
0
1
2
0
3
1
0
3
2
1
1
0
0
0
1
0
0
2
1
0
1
1
1
0
1
0
1
3
1
0
0
2
0
2
2
1
0
0
0
1
1
1
1
2
2
2
2
2
1
2
0
1
1
1
0
0
2
0
1
2
1
2
2
1
0
1
1
1
0
2
1
2
0
1
1
1
1
1
0
1
0
1
2
0
1
0
0
0
1
0
0
0
2
1
0
2
2
1
1
1
0
1
1
0
1
0
2
1
1
1
0
0
1
1
1
1
0
2
0
2
1
2
1
0
2
1
1
2
3
1
1
0
0
2
1
0
1
0
0
0
2
2
1
0
0
2
1
1
1
2
1
1
1
0
2
0
2
1
1
1
1
1
1
2
0
0
2
1
0
1
1
1
1
1
2
0
1
0
0
2
2
0
2
2
0
2
0
1
2
1
1
1
1
2
1
2
1
1
0
1
0
1
2
1
1
0
0
1
1
0
0
1
1
1
2
1
1
1
0
0
0
1
0
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
0
1
2
1
1
1
0
1
0
1
1
1
1
0
0
1
0
0
1
0
1
2
0
2
1
0
1
1
0
0
1
0
0
1
1
1
2
1
1
1
1
0
0
0
0
2
0
1
0
1
1
2
0
1
0
2
1
2
2
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
6
0
1
2
2
2
2
1
0
1
0
0
1
0
1
0
1
1
1
2
0
1
1
1
2
0
1
1
1
1
2
0
2
1
0
0
1
1
1
0
1
0
1
2
2
1
0
0
1
2
1
1
1
0
1
0
0
1
0
1
1
1
0
0
1
1
1
1
2
2
1
1
1
0
1
1
1
0
1
0
0
1
1
0
1
1
0
1
2
1
0
2
0
0
2
1
1
2
1
1
1
0
2
2
1
2
2
0
2
0
0
0
1
0
0
1
1
1
1
1
0
1
1
1
2
0
1
2
1
1
1
1
2
2
1
1
1
0
2
1
1
1
1
0
1
1
1
2
0
2
2
1
0
0
0
1
2
1
1
1
2
1
1
0
0
1
2
0
1
0
0
1
1
1
1
2
1
1
1
0
1
1
1
0
0
0
0
0
1
0
1
1
1
1
1
1
0
2
0
0
0
0
2
2
0
0
0
1
0
0
1
0
2
0
1
1
1
0
2
1
1
2
1
1
2
2
2
0
1
1
2
2
2
0
2
2
1
1
2
2
1
1
2
1
0
0
0
0
2
2
1
1
1
0
0
1
0
2
1
1
0
0
0
0
1
0
1
2
1
2
0
0
0
0
1
2
2
1
2
1
1
1
1
0
1
1
0
1
0
1
1
1
1
1
2
2
1
0
0
1
1
2
1
1
2
0
0
1
1
0
1
1
2
1
0
2
1
2
1
1
2
0
1
1
1
1
2
0
2
2
0
2
1
1
0
0
0
0
1
1
1
1
1
1
1
1
0
0
0
1
1
1
1
0
1
0
1
0
0
1
1
1
1
2
1
0
2
1
0
0
1
1
2
1
0
1
1
1
2
1
1
0
1
1
1
1
1
1
2
0
1
0
0
1
2
0
0
0
1
2
1
1
1
1
2
0
0
2
1
0
2
1
2
1
1
1
2
2
1
0
2
2
2
2
1
1
1
0
2
2
1
1
1
1
1
2
1
0
1
0
1
1
1
2
1
2
1
1
2
2
3
1
0
1
3
0
0
0
0
2
2
1
0
2
1
1
2
1
1
0
2
0
0
0
1
1
1
1
0
2
0
2
1
1
1
2
1
1
0
1
1
1
1
1
0
0
1
0
1
1
2
1
1
1
1
0
1
1
0
1
0
1
2
1
1
2
1
2
1
0
1
2
2
1
1
2
1
1
2
0
0
2
0
1
2
1
0
0
1
1
1
2
1
1
1
0
1
2
1
2
1
1
2
2
1
1
2
1
2
1
1
2
0
0
2
2
1
1
0
0
0
0
2
0
1
0
2
2
1
1
2
2
1
2
0
2
0
1
2
1
1
2
2
1
0
1
0
2
1
1
1
0
0
1
1
0
2
0
2
0
0
1
0
0
1
0
1
0
0
1
1
0
1
1
0
2
0
0
2
0
1
1
2
0
1
2
1
0
2
0
1
0
1
1
1
1
0
0
2
0
0
0
0
2
1
1
0
2
2
1
1
3
1
1
2
1
1
1
1
2
1
1
1
1
1
6
1
0
1
1
2
0
1
1
1
0
0
1
0
0
0
0
1
1
1
2
0
2
0
2
0
1
0
1
2
1
2
2
1
0
1
0
1
1
0
0
0
1
1
2
1
0
1
0
1
1
1
1
0
2
0
0
1
1
0
2
0
1
2
0
2
1
1
0
2
1
2
0
2
0
0
2
0
1
1
1
1
0
0
1
1
0
1
0
0
0
0
1
2
0
2
0
1
1
1
1
1
1
2
1
2
1
1
2
1
1
0
1
1
2
0
1
2
0
0
1
1
1
2
2
1
1
0
0
1
2
2
1
1
0
0
0
1
1
2
0
0
1
0
1
1
1
1
1
2
1
1
1
1
0
1
1
1
0
0
2
0
1
2
0
2
0
0
1
1
2
2
2
2
1
1
0
0
2
0
0
1
2
1
0
0
2
1
1
0
1
1
0
1
0
1
1
1
1
1
0
0
2
0
2
1
0
2
0
2
1
2
0
2
1
0
0
1
1
1
0
2
0
2
2
2
0
2
2
1
0
0
1
1
0
1
0
2
1
2
2
2
2
0
2
1
2
1
1
2
1
0
1
2
1
0
1
1
2
0
2
0
1
2
2
1
0
1
1
0
1
1
0
1
2
0
0
1
3
1
1
2
1
2
1
1
1
0
2
1
2
0
1
1
2
2
2
1
0
0
1
1
1
1
1
2
1
1
0
0
1
2
1
2
1
0
1
1
2
0
2
1
1
1
1
0
1
0
1
5
1
2
1
1
0
1
1
2
0
2
1
1
1
1
1
2
1
0
1
1
2
1
1
2
1
2
2
2
0
0
0
1
0
0
1
1
1
2
0
0
0
2
2
1
0
1
0
0
1
1
0
1
1
2
1
0
2
0
1
1
0
2
0
0
1
1
2
1
0
2
2
2
1
1
2
1
1
0
1
0
0
0
0
2
0
2
1
2
1
3
2
1
0
2
2
0
1
1
1
0
2
1
0
0
1
2
0
2
1
1
3
2
1
1
1
1
1
2
0
0
1
1
2
1
1
0
1
1
0
1
1
0
1
2
0
2
1
2
1
0
0
1
1
2
2
0
1
1
1
1
0
0
2
0
0
1
1
1
0
1
1
0
2
0
0
0
2
0
1
3
0
0
2
0
2
0
1
0
0
1
2
1
0
2
1
1
2
0
2
1
2
1
0
1
1
1
0
2
1
1
1
0
0
2
1
2
0
0
2
1
1
1
1
2
2
1
1
1
3
2
1
1
0
1
2
1
1
1
2
1
1
0
0
2
0
1
0
0
1
0
0
0
2
2
0
1
1
0
0
0
1
1
1
0
1
3
0
1
2
0
0
0
1
0
2
0
2
1
1
0
1
1
1
2
1
1
1
0
0
1
1
0
2
0
3
1
2
1
2
0
1
2
0
2
3
2
1
0
1
1
2
1
0
0
1
2
2
1
1
2
1
0
2
1
1
0
2
1
2
2
1
2
0
0
1
0
0
2
1
0
0
1
1
1
1
1
2
1
1
1
1
2
0
2
2
1
2
0
1
0
2
0
0
1
0
0
0
0
0
0
0
2
0
2
0
1
1
0
0
1
1
0
1
1
1
0
1
2
1
2
1
1
0
2
2
2
2
1
0
0
0
1
1
0
1
1
0
0
2
0
0
1
0
0
1
1
1
1
0
1
0
1
2
1
1
1
0
2
2
0
0
0
1
0
1
0
1
0
1
0
1
2
2
0
1
1
0
0
2
5
0
1
1
2
1
1
2
2
2
0
2
1
1
2
2
1
0
2
2
1
0
2
0
2
1
0
1
0
0
2
1
1
1
0
1
0
1
1
1
0
0
1
1
1
2
2
2
1
2
0
1
0
1
0
0
2
2
2
2
0
2
0
0
0
1
2
1
2
1
1
0
1
1
1
1
2
0
0
2
0
1
1
1
1
0
0
2
2
0
0
0
1
2
0
1
0
0
2
1
1
0
1
0
1
1
0
0
2
2
1
2
0
1
1
1
2
0
0
1
2
1
1
1
1
2
2
1
0
0
1
0
1
2
0
1
1
2
0
1
1
0
0
1
1
2
1
1
2
2
2
1
0
2
1
1
1
1
1
1
0
0
1
1
0
2
0
2
2
0
1
0
1
0
1
0
0
0
1
0
1
1
2
0
1
1
1
1
0
0
1
1
1
2
1
0
0
1
1
1
0
1
1
0
0
0
1
1
1
1
1
0
0
1
1
0
1
2
0
0
1
1
0
1
2
0
0
1
0
0
1
2
1
0
1
2
0
2
1
1
2
0
1
0
2
1
1
1
0
1
1
1
1
1
0
5
1
1
1
0
1
1
1
1
0
0
2
0
2
0
1
0
2
1
2
1
1
1
1
2
1
1
1
1
1
1
2
0
2
2
1
1
1
1
2
1
0
0
1
2
2
1
1
0
0
1
2
1
1
1
1
0
2
0
1
1
2
1
1
1
1
1
1
2
0
1
1
1
0
2
1
1
1
2
0
2
1
1
0
1
1
1
1
0
0
2
1
1
0
1
1
0
1
2
1
1
1
1
0
0
1
2
1
0
1
1
1
0
0
1
0
1
2
1
0
1
0
2
2
1
0
1
2
0
0
1
1
1
0
1
0
0
1
2
1
1
1
1
0
1
0
2
0
2
1
1
1
0
1
0
0
0
1
2
0
1
2
0
0
1
1
1
2
1
2
2
2
1
2
0
0
2
1
1
3
0
0
0
2
0
0
1
1
1
1
0
1
0
1
2
1
1
1
2
0
1
2
1
1
1
1
0
2
1
2
1
0
1
2
1
1
3
0
1
1
0
1
1
1
1
3
0
0
0
1
1
2
2
0
0
1
1
2
1
1
0
0
1
3
0
0
2
0
0
2
0
2
1
1
2
1
0
1
0
1
2
1
1
2
3
1
2
0
1
1
1
1
4
0
1
0
1
1
0
0
2
2
0
1
1
2
1
1
0
0
1
2
0
2
1
2
1
1
1
2
0
1
2
0
1
1
0
0
1
2
1
3
0
0
1
1
2
1
0
0
0
0
2
1
2
1
1
1
0
1
0
0
0
0
1
1
1
0
0
0
2
0
1
1
1
2
2
2
1
1
0
0
2
0
1
2
0
0
1
1
1
2
2
1
2
2
0
1
0
1
1
0
2
2
1
2
0
2
0
2
0
1
2
0
0
1
1
0
1
2
2
1
0
0
2
1
0
0
3
1
1
2
0
1
0
0
2
0
0
1
1
0
1
1
1
0
0
0
2
1
1
1
1
2
1
2
0
0
2
0
0
2
0
0
4
1
2
1
0
1
0
2
1
1
1
1
0
0
1
0
2
1
1
0
1
1
2
0
0
0
1
1
2
0
1
1
1
1
1
0
2
1
1
1
2
0
0
1
2
0
2
1
0
1
0
2
0
0
0
1
0
0
1
1
1
1
0
0
1
2
1
2
1
0
0
0
1
1
1
1
0
1
0
3
0
0
1
1
1
1
1
1
1
1
1
1
1
0
0
4
1
2
1
0
0
2
1
1
1
1
1
2
1
0
1
0
1
0
0
0
1
1
0
1
0
1
2
1
0
1
1
2
2
2
1
1
0
1
0
0
2
0
2
1
0
0
2
1
1
1
1
1
1
1
3
2
1
1
1
2
0
0
2
2
1
2
0
0
1
1
1
1
1
2
1
1
1
1
0
0
1
2
1
1
0
0
1
1
1
1
0
1
0
0
1
1
1
1
1
2
1
1
1
0
1
0
0
0
1
2
1
0
1
1
1
0
0
1
0
1
1
0
0
1
0
1
0
1
2
0
1
2
0
0
1
1
1
1
0
1
0
0
0
1
1
1
2
1
0
0
0
0
0
2
1
1
2
2
2
1
0
1
1
2
1
0
1
0
0
1
1
1
1
0
1
1
0
0
2
1
1
1
0
0
2
2
1
1
2
1
2
2
1
0
2
0
1
1
1
0
3
1
0
4
1
1
2
1
1
0
2
0
1
0
1
1
1
1
2
1
1
1
1
1
2
1
0
1
1
2
2
1
0
0
0
2
0
1
1
0
1
1
1
1
3
2
0
1
1
0
2
2
1
2
6
1
0
2
0
0
0
1
1
1
1
1
0
0
2
2
1
0
2
1
1
1
1
3
0
1
1
1
1
0
2
1
2
1
0
2
1
1
1
2
1
1
2
2
2
1
0
1
2
1
0
0
1
1
0
1
1
1
2
1
3
2
0
1
2
0
1
1
2
1
2
1
2
2
1
2
2
1
1
0
1
1
1
1
1
1
0
2
2
2
2
2
0
3
2
1
3
1
2
1
1
5
0
0
2
1
1
2
2
1
0
1
0
1
0
1
2
1
1
1
1
1
1
1
0
1
1
0
2
1
2
1
0
1
2
0
2
1
1
1
1
0
0
2
1
0
1
0
1
1
1
2
1
1
2
1
1
0
1
2
1
1
2
1
1
1
3
1
2
1
1
0
1
1
0
1
2
1
2
1
1
1
2
1
2
1
1
0
3
2
0
1
0
0
1
1
0
1
0
0
2
1
1
1
2
2
0
0
1
1
1
0
1
0
1
2
1
0
0
2
1
2
0
2
1
1
0
2
1
1
0
0
0
1
1
2
1
1
2
1
1
0
0
1
1
1
1
1
1
2
1
2
1
0
0
1
1
0
1
2
0
2
2
0
2
1
0
0
2
1
1
2
2
1
2
2
0
1
2
2
3
1
1
2
1
2
1
0
2
1
1
2
1
1
2
1
1
0
0
1
0
1
1
2
0
1
1
1
2
1
1
0
0
2
4
2
1
1
0
0
2
0
1
2
1
2
0
1
1
2
1
1
0
2
2
1
0
0
1
0
2
0
1
1
1
0
1
2
2
2
1
1
2
0
1
2
2
0
1
3
1
0
0
0
2
1
1
2
2
1
1
1
2
0
2
0
0
1
2
2
0
1
0
0
1
1
1
1
1
0
2
2
2
1
0
0
1
1
1
0
1
1
1
1
0
1
2
2
1
1
0
0
0
1
1
2
0
0
2
1
1
2
1
0
1
1
0
2
2
0
1
1
1
2
2
2
0
2
0
1
2
2
1
0
1
1
1
1
0
1
0
1
2
1
0
0
1
0
1
1
1
1
0
0
1
1
0
1
1
2
0
1
2
1
0
1
1
1
1
1
2
2
1
0
0
1
1
2
1
1
0
1
2
0
2
2
0
2
1
1
1
2
2
0
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
1
0
1
1
1
0
0
1
0
2
0
1
1
2
1
1
2
1
0
0
1
1
0
2
1
1
2
1
2
1
1
2
1
0
1
0
1
2
1
3
1
1
1
1
1
1
2
1
1
1
2
1
1
3
0
1
1
1
1
0
0
1
1
2
2
2
1
1
1
0
0
1
2
1
0
1
1
2
2
1
0
0
2
1
1
1
1
0
2
0
1
2
1
1
2
1
3
0
1
2
2
2
0
0
1
2
1
2
1
1
1
1
1
2
1
1
1
1
0
2
0
0
1
1
0
1
0
0
1
0
1
1
0
2
0
2
0
0
2
1
1
1
0
1
0
1
1
1
0
1
1
0
0
1
1
2
2
0
1
1
0
1
1
2
1
0
0
1
2
2
2
1
0
0
3
0
1
1
1
1
1
0
1
0
1
2
1
5
1
0
2
0
0
0
0
1
1
0
1
0
1
0
1
1
2
2
1
0
0
1
1
0
1
0
1
1
2
1
1
3
1
1
1
1
2
0
1
0
1
1
1
0
1
2
1
0
1
2
1
2
0
1
0
1
0
0
2
1
1
0
1
1
1
2
0
1
1
0
0
2
2
3
0
1
1
1
2
0
0
1
0
1
4
2
0
1
1
0
1
0
1
0
2
1
3
1
1
0
0
1
1
0
2
1
1
1
2
3
1
1
0
0
1
0
1
0
1
0
1
0
1
1
0
0
0
1
0
1
1
2
0
1
0
1
0
1
2
0
0
1
0
1
0
0
1
1
0
2
0
0
3
0
2
1
1
2
2
1
1
2
1
0
2
1
1
0
1
1
2
2
2
1
0
1
1
0
0
2
0
1
1
1
1
0
0
0
2
1
2
1
2
1
2
1
1
2
1
1
1
2
0
2
2
1
1
2
1
1
1
2
1
1
1
2
1
2
0
1
1
1
1
2
1
1
2
0
2
0
1
0
2
1
1
1
2
0
1
2
0
2
1
1
1
1
0
1
1
2
2
0
1
2
0
2
1
1
1
2
0
0
0
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
2
1
0
0
1
0
1
3
0
0
2
1
0
2
1
2
2
1
1
0
0
1
3
0
1
2
1
1
0
2
2
1
0
1
0
1
1
0
1
0
1
2
1
0
2
0
2
0
1
1
1
0
0
1
1
0
1
0
2
1
0
3
1
1
2
1
0
0
1
1
1
2
2
1
1
1
1
0
1
0
1
1
1
2
2
0
0
1
1
2
2
1
0
2
2
1
0
1
1
1
1
1
0
2
1
0
1
1
2
0
1
0
1
2
1
0
1
1
0
0
1
2
1
0
1
1
1
2
1
0
1
2
2
2
0
1
2
0
0
0
1
1
0
1
1
1
1
0
1
1
0
4
2
0
1
2
1
1
1
0
1
1
0
2
0
0
2
0
1
1
1
2
2
2
2
1
2
1
1
0
0
1
1
1
1
1
0
1
1
2
1
2
1
2
1
2
1
2
2
1
1
0
1
1
1
1
0
1
1
1
1
1
0
1
1
0
2
2
0
0
0
0
0
2
1
2
1
0
1
1
0
1
0
1
0
2
1
0
2
0
2
0
0
1
2
1
2
1
1
1
2
1
2
0
1
2
0
2
2
0
1
1
1
1
1
2
2
1
1
0
1
2
0
1
2
2
0
0
1
1
1
0
1
1
1
1
0
1
2
0
2
1
2
2
0
1
1
1
0
0
2
1
1
1
2
1
0
1
1
1
0
1
1
1
2
1
6
1
14
1
2
1
1
0
1
1
1
1
2
2
1
2
1
3
1
0
2
1
2
0
2
2
1
1
0
0
2
1
1
0
1
2
0
0
1
1
1
0
2
1
1
1
1
1
1
0
1
1
1
1
1
3
1
2
2
0
0
1
0
1
1
1
0
1
2
1
0
2
0
1
0
0
2
1
1
1
1
1
1
1
0
1
0
0
0
0
2
0
1
0
2
1
2
0
1
1
0
0
1
1
1
1
0
0
2
0
0
0
1
0
1
2
1
1
1
1
2
0
1
1
1
1
0
0
1
0
0
1
0
1
1
2
0
1
2
1
0
2
1
2
2
1
2
2
0
1
0
0
0
1
1
0
0
0
2
2
2
0
1
1
1
1
1
1
1
2
1
0
0
0
5
2
1
1
1
0
1
1
1
1
2
0
3
1
1
1
1
1
1
1
1
0
0
1
0
1
0
1
2
0
0
1
2
1
2
0
1
1
1
0
1
0
1
0
1
1
0
2
1
0
1
1
1
4
1
1
2
0
1
6
1
1
2
2
2
0
1
0
1
1
0
0
1
1
2
0
2
2
3
1
2
2
0
0
2
0
1
2
0
0
1
1
0
2
0
1
2
1
1
1
0
3
1
2
1
1
1
2
0
2
2
1
1
1
0
1
0
0
0
1
1
1
1
2
0
1
0
2
2
0
1
2
2
0
1
0
0
2
2
0
1
1
0
1
1
2
1
2
1
0
1
1
1
1
0
0
2
2
0
1
2
2
1
1
1
0
1
1
2
1
2
1
0
0
1
0
2
1
0
0
0
1
1
0
1
1
1
1
1
2
2
0
2
1
1
2
0
1
2
1
1
1
2
1
0
1
1
1
0
1
1
2
2
1
0
1
0
1
1
1
2
0
0
0
1
0
0
2
2
1
1
0
1
1
0
1
0
1
1
0
2
1
0
0
1
1
0
1
1
0
1
1
2
2
0
0
1
2
1
1
0
1
0
0
0
2
0
0
1
2
0
0
1
2
2
2
0
0
1
1
1
0
1
0
0
2
1
1
0
0
1
1
0
0
0
2
1
1
1
1
0
1
0
0
1
0
1
2
1
1
1
1
2
2
1
2
0
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
2
1
2
0
2
1
0
1
1
1
1
1
3
1
2
0
1
0
1
0
0
0
1
1
2
1
0
1
1
1
1
0
1
1
1
1
1
1
1
1
1
0
1
1
1
1
2
0
1
1
0
1
3
0
1
1
1
0
1
2
1
1
0
1
1
2
1
2
3
1
2
1
1
2
1
1
0
1
1
2
2
0
0
2
0
2
2
2
0
1
2
0
1
1
3
1
1
2
1
1
2
1
2
1
1
1
2
0
0
0
0
1
0
1
0
0
2
0
0
1
3
0
1
0
1
2
1
1
1
3
1
1
1
0
1
1
0
8
1
2
1
1
0
1
1
1
2
0
1
0
1
1
2
0
1
0
1
1
1
0
0
2
1
1
3
0
2
0
1
2
2
2
0
2
1
1
1
2
1
1
3
1
2
1
1
1
2
1
2
1
0
2
1
0
1
1
1
2
1
2
0
1
3
2
1
1
0
1
1
1
0
1
1
2
1
2
1
0
2
0
1
1
0
0
0
1
0
2
2
1
2
1
2
1
0
2
1
1
1
1
1
1
0
2
1
1
2
0
1
0
1
1
0
1
1
1
1
1
2
2
2
2
0
1
1
0
0
2
2
0
1
0
0
1
1
1
0
0
0
1
0
2
0
2
1
0
1
0
0
1
1
0
1
1
0
1
1
2
0
2
1
1
1
1
0
1
1
2
0
2
1
3
1
1
1
1
2
2
3
1
1
1
2
0
0
2
0
0
0
1
0
1
1
0
0
1
1
1
0
1
0
0
2
2
1
1
1
2
2
2
0
1
1
1
1
2
1
2
0
2
0
0
2
1
1
0
1
2
1
1
1
1
2
0
1
0
2
0
1
0
0
1
1
1
2
2
1
2
1
1
0
1
2
1
1
2
1
2
1
1
2
0
1
1
0
3
0
1
1
1
0
1
1
0
1
0
2
2
7
1
1
1
0
1
1
0
1
0
1
1
1
0
2
1
2
0
2
1
0
1
0
1
1
1
2
1
1
2
0
2
1
1
0
1
1
1
1
1
2
1
1
2
2
2
2
0
1
0
2
0
2
1
1
0
1
1
2
1
0
3
2
2
0
1
0
1
1
2
1
2
2
1
0
0
2
1
1
1
1
0
1
1
1
0
1
0
1
1
2
0
0
1
1
1
2
0
1
2
0
1
0
0
1
1
1
0
1
1
1
1
1
0
0
2
0
2
1
0
0
1
2
0
0
0
1
1
1
1
1
1
1
0
1
1
1
3
1
1
0
2
0
1
1
3
1
0
1
0
1
1
2
1
0
1
2
2
1
1
0
1
1
0
2
1
1
1
1
1
1
1
1
0
1
1
0
1
2
0
3
1
0
1
1
1
1
0
1
1
1
2
0
1
1
2
1
1
1
1
1
0
2
1
1
4
1
2
0
2
1
2
2
0
1
1
0
1
0
2
1
2
1
2
1
1
2
2
1
0
0
0
2
2
0
1
0
0
2
1
1
1
1
1
0
0
2
2
1
2
2
2
2
1
1
1
0
1
1
1
1
2
0
2
2
0
0
0
1
1
2
1
0
0
0
1
2
0
0
1
1
0
1
0
2
1
1
1
1
3
1
2
0
1
0
0
1
2
0
0
1
1
1
0
2
0
1
1
1
0
2
1
1
2
2
1
2
1
1
0
1
1
2
0
2
0
1
3
2
1
1
1
1
1
1
0
2
1
1
2
2
2
2
2
1
2
1
1
0
2
0
2
0
0
0
1
0
2
1
0
1
0
1
1
2
1
2
1
1
3
2
1
1
1
0
1
1
0
1
0
1
1
1
0
1
0
0
1
2
1
1
1
1
2
2
1
0
2
1
1
1
1
2
1
1
1
0
0
0
1
0
0
1
2
0
0
1
1
1
1
0
0
1
1
1
2
2
2
1
2
1
1
2
0
0
0
1
2
1
2
1
0
1
1
0
0
0
1
1
0
1
0
0
2
2
1
1
1
1
1
1
0
1
1
0
1
1
1
2
1
2
1
2
2
2
0
1
1
2
1
0
1
1
1
1
2
0
1
2
1
2
2
2
1
0
1
1
0
1
2
0
0
2
2
1
0
1
1
1
2
1
1
0
1
2
1
0
0
0
1
1
2
2
1
1
2
2
1
1
0
2
2
0
0
1
1
1
0
0
2
1
1
2
1
1
1
1
1
1
1
2
2
1
0
1
1
1
2
1
1
2
1
1
0
0
1
2
2
0
1
3
0
1
1
0
1
0
1
1
2
2
1
1
0
1
1
1
1
2
1
0
1
1
2
0
1
1
0
1
0
0
1
0
0
2
1
1
1
1
0
2
1
1
0
1
0
2
1
1
1
0
2
2
1
1
1
1
1
1
1
3
1
0
0
0
1
2
0
0
0
0
0
0
3
0
0
1
1
0
0
1
1
1
4
1
1
0
0
1
1
2
0
0
0
2
1
0
1
2
1
2
2
1
1
2
0
3
2
1
0
1
1
1
0
2
1
1
1
1
0
2
1
2
1
0
1
0
1
1
1
2
0
2
1
1
1
0
0
2
2
0
2
3
2
1
0
0
0
1
1
1
0
1
0
2
1
2
1
1
0
1
0
0
3
0
1
0
1
1
1
2
2
1
0
2
2
0
1
1
0
2
2
1
2
1
4
0
1
1
2
0
1
1
1
1
1
1
1
0
0
2
1
0
2
0
1
1
1
2
1
0
1
2
1
0
0
1
1
1
0
2
0
1
1
1
1
1
1
0
1
1
1
2
0
1
1
1
1
0
2
0
1
1
2
1
1
0
0
1
1
0
0
1
2
1
2
0
1
1
0
1
1
0
1
1
1
1
0
1
1
1
1
0
0
0
0
2
0
1
1
2
1
2
1
1
0
1
2
0
1
2
2
1
2
0
1
0
1
0
1
2
1
1
0
1
2
1
0
1
1
1
2
0
0
0
2
1
1
0
1
1
0
1
0
1
0
1
1
0
1
2
1
1
1
1
1
1
0
1
0
2
1
1
1
0
1
1
0
1
0
0
1
0
0
1
1
2
1
1
3
3
2
1
0
2
2
0
1
0
1
3
1
1
2
0
0
2
2
1
2
0
1
0
1
1
2
2
2
1
1
2
1
0
0
1
1
2
0
0
2
1
0
1
1
0
0
1
1
2
0
1
2
1
1
2
0
1
0
1
1
1
0
1
1
1
1
1
1
1
2
1
0
1
2
1
1
0
2
0
1
1
1
1
1
1
0
1
1
0
0
0
1
1
1
1
0
2
0
1
1
1
2
1
0
0
0
1
1
2
2
1
0
1
2
1
2
0
2
0
0
2
1
0
2
3
2
1
1
1
2
2
2
0
2
1
0
1
0
1
1
1
0
0
0
0
0
1
1
2
0
2
2
1
1
1
2
1
1
1
1
0
0
1
0
1
1
1
2
0
2
0
1
1
0
2
0
2
1
1
1
0
0
0
2
0
1
2
1
2
0
1
1
1
1
0
0
2
1
1
2
1
1
2
2
1
0
0
1
1
0
1
0
0
1
0
0
1
0
1
1
1
0
1
0
0
0
1
1
1
0
1
0
0
1
1
1
1
0
2
0
1
0
0
0
2
2
0
2
2
0
1
1
2
1
1
1
2
1
2
1
1
3
1
0
1
1
2
1
1
1
1
0
1
1
1
1
2
0
1
2
3
2
1
0
1
1
2
1
2
0
0
0
0
0
1
1
2
1
1
3
1
0
0
0
2
1
1
0
0
1
1
2
1
2
1
0
0
2
0
0
1
1
0
0
2
2
1
1
1
2
1
1
0
1
1
0
1
1
1
1
0
1
1
1
2
1
1
1
1
1
1
0
2
1
1
0
1
1
1
1
2
1
2
1
1
1
2
0
0
1
0
0
2
1
0
2
1
0
0
0
1
2
1
1
1
0
1
1
3
2
1
1
2
0
1
0
1
2
1
2
0
0
2
2
0
1
1
2
0
2
1
1
1
0
2
1
0
1
0
1
0
0
0
1
0
2
1
0
2
2
2
1
0
0
1
1
1
1
1
0
0
1
1
0
0
1
0
1
0
3
1
2
2
1
0
0
2
1
1
2
0
1
1
0
2
0
1
0
3
0
1
2
1
0
1
2
0
1
0
1
1
0
1
2
2
1
2
1
0
1
0
1
0
1
2
2
1
1
0
1
1
1
0
2
2
1
0
2
1
0
0
1
1
1
2
1
1
0
2
1
0
0
1
0
2
1
1
1
2
2
0
0
1
1
1
0
0
2
0
1
2
2
2
1
0
0
1
1
2
1
1
2
0
2
2
1
2
2
0
1
1
1
1
2
0
1
2
1
1
1
2
1
2
1
2
0
1
1
0
0
0
1
1
2
0
0
1
2
0
1
2
1
1
0
1
1
1
2
0
2
1
1
1
1
0
1
1
1
0
0
0
0
1
1
0
1
2
1
0
1
2
0
2
1
2
1
0
2
1
1
1
0
1
1
2
2
1
0
0
2
0
1
0
1
1
1
2
2
1
1
1
1
0
3
2
1
1
1
1
0
0
1
1
0
2
1
1
2
0
1
2
1
2
0
1
0
2
0
1
1
1
1
0
0
0
1
2
2
0
0
2
2
0
0
0
1
2
0
1
0
0
2
2
1
1
1
0
0
0
1
1
2
0
1
1
2
2
0
2
2
1
2
2
1
2
2
2
0
2
0
0
0
1
1
0
1
0
1
0
1
0
2
3
3
1
0
1
1
0
1
1
1
2
0
2
2
1
1
1
1
1
0
1
2
1
0
1
0
2
1
1
0
1
1
1
2
0
1
1
1
1
1
1
1
2
0
1
0
0
1
1
2
0
2
1
2
0
1
0
0
0
2
2
0
2
1
1
2
0
2
0
0
0
0
2
0
1
0
0
1
2
1
1
1
1
0
2
1
1
1
2
1
1
1
2
0
1
1
1
1
1
2
1
1
2
2
0
2
2
1
0
1
0
1
2
1
2
1
1
0
2
1
2
0
1
0
1
1
2
1
1
2
1
0
1
1
0
1
0
1
2
0
1
0
0
2
1
0
0
0
0
2
1
1
1
1
0
1
0
2
1
1
0
1
1
0
1
1
1
1
1
1
1
1
0
0
0
1
1
1
0
1
1
0
0
1
0
1
0
0
2
1
0
1
1
2
0
0
0
2
2
1
1
1
1
0
1
2
0
1
1
1
0
2
1
1
1
0
2
2
1
1
0
1
0
1
1
0
0
2
0
1
1
0
2
1
0
0
0
1
2
1
2
0
1
1
2
1
2
1
2
0
1
1
1
1
0
1
2
0
2
1
1
1
1
0
1
2
1
1
3
2
1
0
2
0
0
0
1
1
1
2
0
1
1
0
1
2
2
2
1
2
1
1
1
2
2
1
1
1
2
1
2
2
1
1
1
2
0
1
0
1
1
1
1
1
0
1
1
1
0
0
2
1
0
0
2
0
2
1
0
2
1
1
0
2
1
1
2
1
1
0
0
1
1
1
2
0
1
0
2
1
0
1
1
0
1
1
1
1
1
2
0
1
1
0
1
1
2
1
0
1
0
1
2
1
2
0
1
2
0
1
1
2
1
2
2
0
1
2
0
2
1
1
0
1
2
1
1
1
3
2
2
0
0
0
1
0
1
0
0
1
1
0
0
1
1
2
0
0
1
0
0
2
2
2
2
1
2
1
0
1
1
1
2
2
2
2
1
2
0
0
2
0
1
0
2
0
1
2
1
1
1
0
1
2
2
1
2
2
1
0
2
3
1
2
1
0
1
1
1
2
0
1
2
0
0
2
1
1
1
2
2
1
0
0
1
2
0
0
1
0
0
0
1
1
0
0
0
0
2
1
1
1
1
0
0
1
1
0
1
0
1
0
1
1
2
1
0
2
1
0
0
0
0
2
1
1
1
1
0
2
2
2
2
1
2
0
0
0
1
2
1
1
1
2
2
1
2
0
0
0
0
0
2
0
0
1
0
1
1
1
1
1
1
1
1
1
1
1
2
0
1
0
2
1
2
3
1
2
1
1
1
1
2
1
1
1
2
1
1
1
1
2
2
0
1
1
1
2
3
1
1
1
1
2
1
2
1
2
1
1
2
1
0
0
1
0
1
1
1
1
1
2
0
1
1
2
1
2
0
2
0
1
2
0
1
1
0
1
1
0
1
0
1
0
2
0
2
2
2
0
1
1
0
3
2
1
1
2
1
0
2
1
0
0
1
1
2
0
0
2
1
1
1
1
1
2
1
0
1
1
1
1
2
1
0
1
4
0
1
0
2
1
1
1
2
0
0
1
1
1
2
0
0
1
1
0
0
1
0
0
1
1
1
1
1
0
1
1
1
1
0
2
0
2
2
1
0
1
2
0
1
1
0
1
1
1
2
1
1
1
2
1
0
2
2
0
0
2
2
1
2
1
2
1
2
2
1
1
1
0
2
0
1
2
1
0
1
1
2
1
1
1
2
2
2
0
0
1
0
1
1
2
1
2
1
0
0
2
3
2
2
0
2
1
1
0
0
2
1
2
1
0
1
1
0
0
2
1
1
2
0
1
1
0
0
1
1
1
2
1
2
1
2
1
2
1
0
1
1
3
0
2
2
1
1
0
1
1
1
1
2
0
0
1
1
2
1
1
1
0
1
2
1
1
1
2
1
1
1
1
2
1
1
1
2
1
1
2
1
2
0
3
0
1
1
2
1
0
1
2
2
1
2
1
0
1
1
2
0
1
2
2
0
1
1
2
1
1
1
2
2
1
0
1
0
0
2
1
1
0
1
1
0
0
1
1
1
1
2
1
0
1
1
0
1
2
1
0
1
2
0
0
1
1
1
1
0
0
1
0
2
0
1
2
0
2
1
2
0
1
1
2
2
0
2
2
0
2
2
2
1
1
0
0
0
1
2
2
2
1
0
2
0
0
0
2
2
1
1
1
1
0
0
2
0
1
1
1
0
1
1
1
0
5
1
1
1
0
0
1
1
1
0
2
1
1
2
1
1
1
1
2
1
0
1
1
1
1
0
1
1
0
0
0
1
1
1
1
0
1
2
1
2
1
0
0
1
1
2
2
0
1
1
0
0
2
0
1
1
1
1
0
0
0
1
1
0
1
1
0
1
1
2
0
1
2
1
0
0
2
1
0
1
1
2
3
2
1
0
0
0
2
1
1
1
1
1
0
0
1
2
0
1
0
1
1
0
0
0
0
1
2
1
1
2
2
2
0
2
1
1
1
0
0
0
0
2
1
0
0
0
1
1
1
1
1
1
2
1
0
1
1
1
0
0
0
2
1
0
1
2
0
2
1
2
0
1
1
0
0
0
1
1
1
2
2
1
0
1
1
1
1
1
0
1
0
1
3
2
1
0
1
1
0
2
1
0
1
0
0
2
1
2
1
2
3
1
1
2
1
1
1
1
0
0
0
0
0
1
1
1
2
1
1
1
0
0
2
2
1
0
2
1
1
0
0
0
1
1
2
2
1
1
1
1
1
1
0
0
1
2
1
2
1
2
2
1
1
1
1
1
0
2
2
1
1
0
1
0
2
3
0
2
2
2
2
0
0
0
1
1
1
0
0
1
1
2
2
1
0
0
1
1
2
2
1
1
0
1
1
0
0
0
0
0
0
0
1
1
1
1
2
1
2
1
1
0
0
1
1
1
0
2
2
1
1
0
0
0
0
2
2
2
0
1
0
2
2
0
1
0
0
0
1
0
2
1
1
0
0
2
1
0
0
1
1
1
1
1
0
1
0
1
0
2
2
0
1
1
0
1
0
1
1
0
0
1
1
1
0
1
3
1
1
2
1
2
1
0
1
2
1
2
0
1
1
1
1
0
0
1
0
2
0
1
1
2
1
0
2
0
2
0
1
0
0
0
2
2
2
1
0
0
1
1
1
3
0
1
1
2
1
2
0
0
1
0
1
0
1
1
1
0
0
0
1
1
1
1
0
1
1
1
1
1
2
0
1
2
0
1
1
1
1
0
2
1
0
1
2
1
1
2
1
2
1
1
1
1
0
1
0
2
0
1
1
0
0
2
2
2
2
1
1
0
2
2
0
2
0
1
1
0
0
0
1
1
1
1
0
1
1
2
0
0
0
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
0
0
0
0
2
0
1
0
2
1
2
1
2
1
1
1
2
0
2
0
2
1
0
2
1
0
0
1
0
2
1
1
1
0
1
1
0
1
1
1
0
1
0
2
1
1
2
3
1
1
1
1
0
1
1
2
2
2
1
2
1
1
1
0
0
1
1
1
1
1
0
0
1
0
0
2
2
0
1
1
0
1
2
0
0
3
0
0
0
1
2
1
2
1
1
1
0
0
2
1
1
2
1
1
2
0
1
4
0
1
1
1
2
1
2
2
0
1
0
1
2
1
1
1
1
0
0
2
0
1
0
1
0
0
2
1
2
0
0
1
1
2
1
1
1
0
0
0
1
1
1
0
1
1
0
1
2
1
1
1
2
1
0
1
0
1
1
1
0
0
0
1
2
0
2
0
0
1
2
1
0
2
2
2
2
1
1
0
1
2
1
0
1
1
1
1
1
1
0
2
0
0
0
1
2
1
0
2
1
0
0
1
1
1
0
2
0
1
1
1
1
1
2
0
1
1
2
0
0
0
0
1
2
1
1
1
1
1
1
2
1
1
0
1
0
1
2
1
0
2
0
1
1
0
0
1
2
1
1
1
0
0
0
2
1
1
1
2
1
0
0
0
1
1
0
2
2
1
2
2
2
0
1
1
1
1
2
0
1
0
1
0
1
2
2
2
0
0
1
0
1
1
0
1
1
1
1
2
2
1
1
0
1
0
1
0
1
1
1
0
2
0
1
1
1
1
0
1
2
1
0
1
1
1
0
0
2
1
1
0
0
2
1
1
1
2
1
0
1
2
0
0
1
0
1
1
0
0
1
1
1
1
1
2
1
0
2
0
2
0
1
0
1
0
1
1
1
1
1
1
0
1
2
1
1
1
0
2
2
2
0
1
0
1
0
0
0
2
2
1
0
2
2
1
2
0
0
1
1
1
2
1
2
1
2
1
1
2
0
2
0
1
0
0
1
1
1
2
1
2
1
1
1
2
0
1
2
0
2
0
1
0
1
0
2
2
0
1
0
2
1
1
1
0
1
0
0
2
1
1
1
1
1
1
1
3
0
0
1
1
1
0
0
1
0
0
0
1
2
2
2
0
1
0
1
1
1
2
0
0
1
2
1
0
0
1
2
1
1
0
0
1
2
0
2
3
2
1
2
0
3
0
1
1
2
1
1
0
1
1
0
1
2
1
2
1
1
2
1
1
1
0
1
2
1
1
2
1
1
1
1
1
1
2
1
2
2
1
1
0
2
1
0
0
1
0
1
2
2
1
2
0
2
0
1
1
1
0
0
0
1
1
1
0
2
1
1
1
2
2
1
1
0
1
1
0
1
1
2
0
0
2
1
0
0
1
1
1
2
2
0
2
0
1
1
1
1
2
2
1
1
0
1
0
2
1
0
1
1
1
0
1
0
3
0
1
1
0
0
2
1
0
1
2
3
1
2
1
0
1
1
1
1
1
1
1
1
0
1
1
1
0
0
1
2
2
1
2
1
2
2
1
0
0
1
1
2
1
2
1
1
1
1
2
1
2
1
1
1
2
1
2
2
2
0
1
2
1
0
1
2
0
1
0
2
1
2
2
2
1
1
1
1
0
0
1
0
2
1
1
1
1
1
1
0
1
1
2
1
1
1
0
1
1
0
1
0
0
2
0
1
1
0
1
1
0
1
0
1
1
1
2
0
1
1
0
0
0
1
1
2
0
1
0
1
1
1
1
1
0
2
1
0
1
0
0
1
0
0
2
0
0
1
0
0
1
0
1
1
1
0
0
1
1
2
2
1
1
0
1
1
1
1
1
1
1
2
0
1
1
2
1
0
1
0
1
1
2
1
0
0
0
1
2
2
0
1
0
2
1
1
0
1
2
1
2
2
1
1
1
1
0
1
0
1
0
1
1
0
2
2
2
1
2
0
0
0
3
0
1
1
0
1
1
2
0
1
1
2
1
0
2
2
2
0
1
2
1
2
1
0
1
1
2
2
1
2
1
0
0
0
2
2
1
1
1
2
1
0
1
1
1
1
1
0
1
1
2
2
2
0
1
1
2
0
1
1
0
0
1
1
1
2
1
0
1
2
1
1
0
1
1
1
0
2
1
1
1
1
2
1
0
0
0
1
1
2
0
0
1
0
0
0
0
1
0
1
1
0
1
0
0
3
1
1
1
1
0
1
1
2
0
1
2
0
0
1
1
0
1
1
0
0
1
1
1
1
1
1
1
1
1
0
2
0
1
0
2
1
0
2
1
1
0
0
1
2
0
2
0
1
0
1
0
2
0
1
0
0
1
1
0
2
2
1
2
0
2
1
0
0
1
1
2
2
0
0
1
1
1
1
2
2
0
1
2
1
1
1
1
1
1
1
2
1
2
2
0
1
0
1
0
0
0
0
1
2
2
1
1
1
1
0
2
1
1
2
0
1
0
2
2
0
1
1
1
0
1
3
1
1
0
1
1
1
1
1
0
1
1
1
0
2
1
1
0
0
2
1
2
1
1
1
1
1
1
2
1
1
0
1
0
2
2
1
1
2
0
0
1
0
2
0
0
1
2
1
2
1
0
1
1
2
1
1
2
1
1
2
1
0
1
2
1
1
1
1
3
1
1
1
0
1
2
1
1
0
1
2
1
1
2
0
1
1
1
1
0
2
1
1
1
0
0
0
0
1
1
0
1
0
0
1
2
2
1
2
1
1
1
0
1
2
2
1
1
0
1
2
2
0
2
1
0
1
1
1
1
2
0
1
2
0
1
1
0
1
1
0
1
1
2
0
1
1
1
2
0
0
1
1
0
1
0
0
1
1
0
0
0
0
1
0
1
1
1
0
1
1
1
0
0
0
1
0
1
0
1
0
1
1
2
1
2
1
1
1
0
2
2
0
0
1
2
1
2
1
2
0
2
0
1
0
2
0
3
1
2
2
1
1
1
0
0
2
0
0
1
2
0
0
2
1
2
0
3
1
1
2
1
2
2
1
1
2
1
1
1
1
0
0
1
1
2
1
1
1
1
1
1
1
1
1
1
0
0
2
1
1
2
1
1
2
2
1
2
0
2
2
0
1
1
1
0
1
4
0
1
2
0
0
2
1
0
1
1
0
2
0
3
2
1
2
1
0
1
1
1
2
0
0
2
1
2
2
1
1
1
0
1
1
2
0
0
2
2
1
0
0
1
0
3
2
1
1
1
1
2
2
0
2
2
0
1
1
2
2
0
2
1
0
0
2
2
0
0
1
0
1
0
1
0
1
1
0
2
1
2
0
0
0
2
1
2
1
1
1
1
2
1
0
1
1
1
0
0
1
2
0
0
0
0
1
1
1
1
1
0
0
1
1
2
1
0
1
0
0
1
1
0
1
1
0
2
1
2
1
1
1
2
1
0
0
0
2
2
2
1
3
2
2
1
1
1
1
1
1
2
2
1
0
1
2
1
0
1
1
0
1
0
1
1
2
1
0
0
2
2
1
2
1
0
1
1
1
0
0
0
2
0
3
1
2
1
5
1
2
0
1
1
1
1
1
1
0
1
2
1
3
0
0
1
1
1
2
1
1
1
1
0
0
0
1
1
1
1
1
1
1
1
1
0
1
0
0
1
1
1
1
2
1
2
0
0
1
0
1
1
0
0
3
0
1
1
2
1
2
0
2
0
2
1
1
1
0
2
0
1
1
0
0
1
0
2
2
1
1
2
2
2
1
0
2
2
0
2
2
0
1
0
1
1
1
2
1
1
2
1
2
1
1
0
1
1
0
2
1
1
1
1
2
1
1
1
1
1
2
1
1
1
0
0
1
1
1
1
0
1
1
1
1
0
1
1
0
1
1
2
0
0
1
0
1
1
1
0
1
1
1
1
2
1
0
2
1
0
1
0
1
1
1
0
0
2
1
1
0
1
1
0
1
1
1
1
2
2
2
1
1
2
1
1
2
0
2
1
0
0
1
1
0
0
2
0
1
1
1
1
1
1
1
0
0
1
1
0
0
0
1
1
0
1
1
2
1
0
0
0
1
1
0
2
1
0
1
0
2
0
0
1
2
0
1
0
2
2
8
1
1
1
0
1
0
2
1
0
1
1
0
2
1
1
0
1
0
1
0
1
2
1
1
0
0
0
0
2
2
1
0
1
0
0
0
1
0
0
1
2
0
0
1
2
0
0
1
0
1
1
0
2
1
0
1
1
1
1
2
2
2
1
0
0
2
1
0
0
2
2
0
0
1
1
0
2
0
0
1
1
1
1
0
0
1
1
4
0
1
0
1
1
0
1
1
1
1
1
0
0
0
1
0
0
1
0
0
1
2
0
2
2
2
0
1
1
2
0
1
2
2
0
1
1
2
0
0
0
0
2
1
2
0
0
0
0
1
0
1
0
0
1
2
1
0
1
1
0
1
2
1
1
1
1
1
1
3
1
1
1
2
1
0
2
1
1
0
1
2
1
2
3
1
1
0
1
2
1
1
2
1
1
1
1
2
1
1
1
1
1
0
0
1
1
0
1
0
0
1
0
0
2
1
2
2
0
1
1
0
1
1
1
0
1
1
1
1
2
2
0
0
1
0
1
2
2
1
0
1
0
2
1
0
1
0
2
1
0
1
3
1
1
1
1
0
1
1
0
2
1
1
2
1
1
0
2
0
1
2
2
0
1
2
1
0
2
1
1
0
2
0
1
0
0
1
1
1
0
2
2
1
2
1
2
1
0
1
0
1
2
1
1
1
1
1
1
1
1
0
0
0
6
3
0
2
0
1
2
2
1
0
0
0
1
0
1
2
0
2
0
0
1
1
2
1
1
0
1
1
1
1
1
1
0
2
1
1
0
2
1
0
1
0
2
0
0
1
1
1
1
1
1
0
2
1
1
2
0
1
1
1
1
1
0
1
1
2
0
0
1
0
0
1
1
0
2
1
1
2
0
0
1
0
2
0
1
0
2
0
1
1
1
1
2
0
0
1
1
0
1
1
1
0
1
1
2
1
1
1
2
0
2
0
2
1
0
1
2
1
0
1
1
1
1
1
1
0
0
1
1
0
2
1
0
1
0
1
0
1
1
2
0
0
1
1
1
0
1
1
1
1
0
0
1
0
0
1
1
0
0
1
0
0
2
1
0
2
1
1
1
0
1
1
1
1
1
2
1
2
1
2
1
2
1
2
2
0
0
2
1
1
1
1
1
0
1
2
1
0
0
1
1
2
1
0
1
1
1
0
0
0
1
1
2
1
0
0
0
1
1
2
1
1
0
0
0
1
1
1
0
0
1
1
0
0
0
1
1
2
1
0
1
2
1
2
1
1
1
1
2
1
3
1
1
1
0
1
3
0
0
2
2
0
0
1
1
2
1
2
1
2
1
2
0
1
1
1
1
1
1
2
0
2
2
1
1
0
1
1
2
1
1
1
0
0
2
1
2
1
1
1
1
0
1
1
0
1
0
1
1
1
1
1
1
1
1
0
0
1
1
1
0
2
0
1
1
1
1
1
1
1
1
1
0
1
1
1
3
0
1
0
2
0
1
1
1
0
0
0
0
1
0
1
1
0
2
0
1
2
1
0
1
2
1
0
1
2
0
1
1
1
1
0
2
0
0
2
1
2
1
1
0
2
1
0
0
2
2
1
2
2
1
1
2
0
0
1
2
1
1
1
0
1
1
1
1
1
0
1
2
1
0
0
1
0
0
0
0
2
2
1
1
1
0
2
1
0
0
2
2
0
2
1
0
0
1
1
0
0
0
0
1
0
1
1
0
0
1
0
0
0
1
1
1
0
1
2
2
1
2
0
1
2
1
2
2
0
1
2
1
1
0
0
1
1
1
0
2
0
1
0
0
0
2
1
1
1
0
2
1
1
1
1
1
2
1
0
0
2
1
2
1
1
0
0
1
1
1
0
2
0
1
1
0
0
1
1
0
0
1
0
2
0
1
2
2
1
1
2
1
1
1
3
0
3
0
1
2
1
0
0
1
1
1
3
0
1
1
0
1
1
1
0
1
0
1
0
2
0
2
2
1
0
3
0
0
0
1
1
0
1
1
2
2
2
1
1
1
1
1
1
1
0
0
0
1
0
1
0
1
1
1
0
0
0
2
0
1
1
2
0
2
1
0
1
1
1
0
1
1
1
2
1
0
1
1
2
1
1
2
0
1
0
1
0
1
0
2
2
0
1
2
2
0
2
2
2
1
0
0
2
0
2
1
0
2
0
2
0
0
1
2
1
0
1
0
0
0
1
2
1
1
0
0
1
0
2
1
2
2
2
2
1
1
2
1
1
2
1
0
1
1
2
0
0
1
2
2
0
1
0
1
1
1
0
1
2
0
2
0
0
1
1
2
1
0
2
1
0
1
1
0
0
0
1
1
1
2
0
2
0
1
1
1
1
0
2
1
1
0
2
1
1
0
1
1
1
1
1
1
1
1
2
2
0
0
1
1
1
1
1
2
2
1
0
1
2
0
1
1
1
0
1
1
1
0
0
1
2
2
1
1
1
1
1
1
1
1
2
1
1
0
1
3
1
0
1
1
0
1
0
1
2
1
1
1
1
2
0
1
1
0
0
1
2
1
0
0
2
1
1
1
2
1
0
0
0
1
1
1
1
2
1
1
2
1
2
1
0
1
0
0
0
1
2
2
2
0
1
0
1
2
1
0
2
0
1
2
1
0
2
2
0
1
1
0
0
2
1
0
0
1
2
0
2
1
1
1
1
1
1
1
1
0
0
0
0
1
1
1
1
1
0
2
0
1
1
1
2
1
1
2
1
0
1
1
1
1
1
3
1
0
1
0
1
0
2
1
0
1
0
1
2
0
1
2
1
1
0
1
2
0
1
0
1
0
1
3
0
0
1
1
1
0
1
2
0
1
1
0
1
2
3
2
0
1
1
2
0
0
1
1
1
1
1
1
0
2
0
2
1
0
1
2
0
0
1
0
0
0
2
2
0
0
2
2
1
1
0
2
1
2
2
1
1
2
1
1
2
1
1
2
1
0
1
1
0
0
1
0
1
1
2
0
1
1
2
0
1
1
2
0
1
1
1
0
1
0
2
2
1
1
1
0
2
0
0
1
2
1
1
1
0
2
1
2
2
1
1
0
0
0
0
1
1
1
1
0
1
0
0
1
2
1
2
1
0
0
1
2
0
0
1
1
0
0
2
2
1
1
2
2
1
1
2
1
0
1
1
0
0
2
2
1
1
1
0
0
0
4
1
0
0
2
0
1
0
0
0
1
0
2
1
1
1
1
1
0
2
0
1
1
2
2
1
1
2
1
1
1
2
1
0
2
2
1
1
0
1
1
1
2
2
0
0
1
1
3
1
0
2
1
0
0
2
0
0
1
1
1
0
1
2
1
1
2
1
1
0
2
0
1
0
1
1
0
0
1
0
0
1
1
1
0
2
0
2
1
1
0
0
0
1
1
1
1
1
1
2
3
0
2
0
0
1
0
0
1
2
0
0
1
2
0
1
2
2
1
0
1
0
0
1
0
0
2
1
2
0
2
0
1
0
1
1
3
1
0
2
2
1
1
0
1
1
0
2
2
1
1
0
1
2
0
0
1
1
0
1
0
1
1
1
0
0
2
1
1
0
2
1
2
0
0
1
0
2
1
1
3
1
0
0
0
1
1
1
1
1
0
0
2
2
0
1
2
0
1
2
2
1
1
1
1
2
1
1
2
1
1
2
1
2
1
2
1
0
1
1
0
0
2
1
1
1
1
0
1
1
2
1
1
2
1
2
2
2
1
1
1
0
1
1
1
0
2
0
1
2
2
0
2
0
1
1
0
1
1
1
2
0
0
0
2
1
1
1
0
1
1
1
0
2
0
2
1
1
1
1
2
3
1
1
2
1
0
1
0
2
0
1
2
1
2
0
0
1
2
0
2
0
0
1
1
0
0
0
2
0
2
1
2
1
2
0
1
2
1
0
0
1
1
0
1
1
1
1
1
1
1
1
0
1
1
1
0
0
0
0
2
1
0
0
1
0
0
1
1
1
0
0
1
1
1
2
2
1
2
0
1
1
0
1
0
2
0
0
1
2
1
2
0
2
2
1
1
0
0
0
2
1
1
1
1
1
0
1
1
1
1
2
0
1
0
0
1
0
1
1
0
0
0
1
0
1
0
0
1
1
1
0
2
0
0
1
1
1
1
3
1
1
0
1
2
2
1
0
0
1
1
1
1
1
1
1
1
2
1
0
0
2
1
0
0
2
1
1
1
0
0
1
0
0
1
1
1
2
2
0
2
2
2
0
1
1
2
1
1
1
0
0
1
2
0
1
0
0
1
1
0
2
0
1
1
2
0
0
1
0
0
1
2
0
1
2
0
2
1
0
0
1
1
1
2
0
1
0
2
0
1
2
3
0
1
0
1
0
1
0
1
1
1
0
1
1
1
1
2
0
0
0
1
0
0
1
1
2
1
0
1
2
0
1
1
0
1
1
1
0
2
1
1
2
0
2
2
0
1
0
1
0
2
1
2
0
1
0
0
0
0
0
0
1
0
0
1
1
2
1
1
0
1
1
1
1
2
2
0
1
1
2
1
1
0
2
1
0
2
1
1
0
0
1
2
2
2
1
1
1
0
1
0
1
0
1
1
2
0
0
0
1
0
2
1
2
0
0
0
2
1
2
0
0
1
1
1
1
1
1
2
0
2
2
0
0
1
0
0
0
0
2
2
1
1
0
0
0
1
1
0
1
1
1
2
1
0
1
1
1
1
1
0
1
1
0
0
0
1
0
4
1
1
1
1
0
2
0
0
2
1
1
2
1
1
2
0
1
1
0
1
2
1
0
1
2
1
0
0
0
0
2
1
1
1
0
1
1
1
1
0
2
1
1
2
2
1
1
1
4
1
2
1
1
1
1
2
2
2
1
1
0
0
0
3
0
0
1
0
1
1
2
2
0
1
2
0
0
1
4
2
0
2
2
1
0
1
5
1
2
1
0
0
1
1
0
1
2
0
0
2
2
1
1
1
1
0
1
0
1
0
1
0
0
1
0
2
2
2
1
0
1
1
1
1
1
0
0
0
1
1
2
1
0
1
0
1
2
1
0
1
1
0
1
2
0
1
0
2
1
0
0
2
0
1
1
1
1
0
1
0
1
1
2
1
1
1
0
1
2
0
0
0
1
2
0
2
0
1
0
2
0
0
0
2
1
2
1
0
1
2
1
1
1
1
3
1
1
2
1
0
0
1
1
0
0
1
0
1
0
0
1
2
1
1
1
0
2
2
1
1
1
1
0
0
2
1
2
1
2
2
2
1
0
1
0
1
1
2
2
1
1
0
1
2
2
1
0
2
1
1
2
1
1
1
1
1
2
1
1
0
1
0
0
0
1
2
1
1
0
0
1
2
1
1
2
1
2
0
0
1
2
2
1
1
0
1
1
2
2
0
1
1
0
2
1
1
0
1
0
1
1
1
0
1
2
1
1
1
0
2
1
1
0
3
2
1
1
3
2
2
1
2
2
1
0
1
1
2
1
1
0
1
0
1
0
1
3
1
0
0
1
0
1
0
0
1
1
1
2
2
1
0
0
0
2
1
1
0
1
2
0
2
0
1
1
1
1
1
2
0
1
1
1
0
2
2
1
1
1
1
1
1
0
0
0
2
1
1
2
1
2
0
0
2
1
0
2
1
2
0
1
2
2
1
0
1
1
1
1
1
0
1
2
2
0
1
0
1
1
2
1
3
1
0
0
1
1
0
0
1
2
2
1
1
2
0
2
0
2
0
0
2
0
1
2
0
1
0
0
1
1
1
1
0
1
2
0
0
2
1
0
1
0
2
1
0
3
0
3
2
1
2
2
1
1
1
2
2
2
1
1
0
1
1
0
0
2
1
1
1
2
2
0
1
2
1
2
1
0
2
1
0
1
1
1
0
1
1
0
1
2
2
2
0
1
1
1
2
0
1
0
1
1
0
1
1
0
1
1
2
0
2
1
1
0
1
1
2
1
0
1
1
0
0
2
2
1
0
0
2
1
2
1
1
1
1
1
1
1
1
0
1
2
0
0
1
1
0
2
0
0
2
1
2
1
1
1
2
1
2
1
2
1
1
2
0
0
1
1
1
1
1
1
0
1
0
1
1
1
0
1
1
0
1
1
2
1
0
1
0
1
0
1
1
0
0
2
0
2
3
2
0
1
0
3
1
1
0
0
2
2
1
1
1
0
0
1
0
1
2
0
0
1
1
0
1
0
0
1
1
2
0
1
1
1
1
1
0
2
2
0
0
1
2
2
2
0
1
1
1
1
1
1
1
1
1
2
0
1
0
4
2
1
0
0
1
0
1
0
2
0
1
0
3
1
0
0
0
1
0
1
0
0
0
0
4
1
1
0
1
0
1
2
1
0
0
0
1
0
1
0
0
1
1
1
0
1
1
1
1
0
1
2
0
0
2
0
1
0
1
2
1
0
0
0
1
0
1
1
0
1
1
1
1
0
0
1
0
1
1
0
2
2
1
0
2
2
1
0
2
1
2
0
0
0
1
1
0
1
1
1
2
2
1
0
2
1
1
2
1
0
1
1
0
1
1
2
3
1
0
0
1
2
0
0
1
1
1
2
1
1
0
1
1
0
1
0
0
1
2
0
1
1
1
2
0
2
1
1
2
1
0
1
0
0
0
0
1
0
0
1
2
4
0
0
2
0
0
3
2
0
1
2
1
2
2
1
1
0
1
0
0
1
2
2
1
1
1
1
1
1
1
1
1
2
2
1
1
0
0
0
0
1
1
0
1
0
0
2
0
0
1
1
0
2
1
0
0
2
2
1
1
1
2
0
0
2
1
1
2
0
0
0
1
1
0
2
0
0
1
0
0
1
0
1
0
2
0
1
0
1
2
0
1
2
1
1
1
1
1
1
1
0
1
1
1
0
0
0
2
1
1
1
1
1
0
2
2
0
1
1
1
0
0
2
1
1
1
1
1
1
1
1
0
0
2
1
1
0
1
1
0
0
1
3
1
0
1
1
3
1
2
2
2
0
0
2
0
0
0
0
2
2
1
1
1
0
1
2
2
0
0
1
2
2
1
0
1
0
2
1
0
1
0
1
1
1
1
2
1
1
2
0
1
1
2
1
0
1
2
1
1
1
2
0
1
0
2
1
1
1
2
0
1
2
0
1
0
0
0
2
0
1
0
1
0
2
1
1
0
0
2
2
1
0
1
1
1
3
1
1
0
0
0
2
1
2
0
1
1
1
1
1
2
1
1
0
0
0
0
0
0
1
0
1
3
1
2
0
0
0
0
1
0
1
2
2
1
0
1
0
1
1
0
0
2
2
2
1
1
0
0
1
1
1
2
0
0
2
0
1
1
0
2
1
0
1
0
0
0
1
0
0
1
1
1
0
1
0
0
2
0
1
2
1
1
1
2
1
1
0
1
1
2
1
1
0
2
0
1
1
1
2
0
1
2
1
1
0
1
4
0
2
1
0
2
0
1
1
1
0
3
0
1
1
1
0
1
0
2
0
1
1
2
2
1
1
1
2
1
0
1
0
2
1
0
3
1
1
0
1
0
0
2
2
1
2
1
0
2
0
1
2
3
1
2
0
0
2
0
1
1
1
1
1
2
0
1
1
1
0
1
2
1
1
0
1
0
1
1
0
0
1
1
0
0
2
2
3
2
0
0
1
2
1
1
2
1
1
2
1
0
1
1
1
1
1
1
1
1
1
2
2
0
0
2
1
0
2
1
1
2
1
0
2
2
1
0
2
1
1
2
0
1
2
1
0
2
1
0
0
1
1
2
1
3
1
2
1
1
3
1
0
1
0
2
1
1
1
0
2
0
0
1
0
2
2
1
1
0
1
1
1
2
0
1
1
1
1
2
1
2
2
2
2
1
0
1
1
0
1
2
1
1
2
2
1
0
1
0
2
2
1
2
0
0
2
0
2
0
0
1
0
2
0
2
1
1
1
0
0
1
1
2
1
2
2
1
1
1
2
1
1
2
0
2
0
1
1
1
2
0
1
2
2
0
1
1
0
2
1
0
1
1
0
1
1
1
1
1
1
1
1
0
1
1
0
1
1
2
1
2
2
0
1
2
1
0
1
1
0
1
1
0
0
2
0
1
1
0
0
0
0
2
0
0
0
1
1
2
1
2
1
2
2
1
0
1
0
1
1
0
0
1
1
2
2
2
0
0
1
1
1
2
1
2
2
1
0
0
1
1
1
0
1
0
0
1
2
1
0
1
0
2
0
0
1
1
1
1
0
0
2
1
2
0
0
2
1
2
0
1
1
0
1
1
0
0
0
0
1
2
0
0
2
0
1
1
1
2
2
2
1
1
1
1
2
1
0
1
1
0
1
0
1
1
0
2
1
2
2
1
0
0
1
2
0
1
1
1
1
1
0
0
0
1
1
1
1
0
1
1
0
2
2
0
1
1
1
5
0
0
2
1
0
2
2
0
1
1
1
1
1
2
1
2
0
2
1
1
2
1
1
2
0
2
2
0
1
0
4
0
1
3
1
2
2
2
1
2
5
1
2
1
2
2
1
1
0
0
2
1
1
1
1
1
0
1
2
0
1
1
1
0
0
1
1
0
1
0
1
2
2
1
1
0
0
1
2
0
0
0
1
1
2
0
1
1
2
1
1
0
1
1
1
1
2
1
0
1
2
1
1
1
3
0
0
0
0
0
1
2
1
1
1
0
1
3
0
5
1
2
1
1
1
0
2
0
1
2
0
0
2
0
1
1
0
2
1
1
0
2
2
1
1
2
1
1
1
1
2
0
1
1
1
1
1
0
1
1
0
1
0
1
0
1
1
0
0
1
1
2
0
2
0
1
0
0
1
0
2
1
1
1
1
0
1
2
1
3
2
2
1
1
0
1
0
1
1
1
1
2
2
1
1
0
2
1
2
2
1
2
0
0
0
1
1
2
1
1
0
1
3
1
1
0
1
1
1
0
2
1
1
1
1
0
1
2
0
0
1
0
1
1
1
0
2
1
1
1
1
0
1
0
3
0
1
0
0
1
1
1
1
0
1
1
1
0
0
2
1
0
0
0
1
0
1
1
1
3
0
1
1
1
0
1
0
1
1
0
0
2
1
0
1
2
2
1
1
0
2
1
1
0
0
1
2
0
1
0
1
1
1
0
0
1
2
1
2
2
1
0
1
1
1
2
1
0
1
0
1
0
1
1
1
2
1
0
2
2
0
1
0
2
0
1
1
1
2
1
2
2
2
0
1
2
0
0
2
1
2
2
0
1
0
1
0
0
3
1
2
0
0
2
1
0
1
0
1
1
0
2
1
2
2
1
1
1
0
0
1
1
1
1
1
1
1
2
0
0
1
1
0
2
2
0
1
1
1
2
1
2
1
1
1
1
2
2
1
1
1
2
1
0
0
2
1
2
1
2
0
2
0
0
1
0
2
1
1
0
2
0
0
1
0
1
0
2
1
1
2
0
1
2
1
2
2
1
1
0
1
0
0
2
1
1
0
3
2
1
2
0
1
1
2
2
1
1
1
1
1
1
2
0
2
1
1
2
1
1
0
0
1
2
2
0
0
2
1
2
1
0
1
0
1
2
1
2
0
1
1
2
1
1
0
2
1
1
1
1
0
0
2
1
0
0
1
2
0
1
2
1
1
0
1
1
0
0
1
0
1
4
0
1
1
1
0
1
2
1
1
2
1
0
1
1
2
2
2
2
1
1
0
1
2
1
2
0
2
1
1
1
0
0
0
0
1
1
0
2
2
0
1
1
2
0
1
0
1
0
1
0
0
1
0
1
2
1
2
0
1
0
0
1
0
1
1
2
1
0
1
1
2
0
1
0
0
0
0
1
1
0
1
1
0
1
2
2
1
2
1
1
1
0
0
0
2
1
2
2
1
1
3
1
0
1
0
1
1
0
1
1
1
2
2
3
2
1
0
1
2
1
1
0
1
0
1
0
0
0
1
1
1
2
2
1
0
0
1
0
1
1
2
1
1
0
0
0
1
2
1
1
0
0
1
2
0
2
1
2
1
0
1
1
0
2
0
2
0
1
0
1
1
0
1
0
2
1
0
0
1
1
1
0
0
2
1
1
0
2
2
0
0
1
1
0
1
0
2
2
0
3
1
0
2
0
0
0
2
4
2
1
1
2
1
1
0
1
2
2
0
2
0
1
0
0
1
1
1
0
1
1
0
1
1
1
1
1
1
1
2
0
1
1
0
0
0
1
2
1
0
0
1
1
1
2
0
1
0
1
1
1
0
1
2
2
0
2
2
0
0
0
1
1
2
1
0
2
2
1
1
1
0
1
1
1
0
0
0
1
2
1
1
0
1
1
0
0
1
1
0
2
1
0
2
0
0
1
1
1
2
0
1
0
1
0
1
1
1
2
1
0
1
2
2
0
2
2
2
0
2
1
1
1
0
0
0
1
2
0
1
2
1
0
1
1
2
1
1
0
0
0
2
2
0
2
2
3
1
0
0
1
0
0
1
0
1
1
1
0
1
1
1
0
0
0
0
2
0
2
1
1
1
2
1
1
2
2
2
1
1
2
4
0
2
0
0
0
1
2
1
0
0
1
1
0
2
0
1
0
0
2
2
1
1
1
2
2
1
1
1
1
0
2
2
1
2
0
2
1
1
2
2
0
0
0
1
1
1
0
1
2
0
0
0
0
1
1
2
2
1
0
1
2
2
1
1
1
1
2
0
0
1
0
1
2
2
1
0
2
1
1
1
1
4
0
1
2
1
1
2
1
1
0
1
1
0
2
1
1
2
3
1
1
1
1
1
0
0
2
1
1
2
0
1
1
0
2
1
1
0
1
1
1
1
2
2
2
1
1
1
3
1
1
1
0
1
1
1
2
1
1
2
2
1
1
0
2
2
1
1
1
1
1
2
2
1
0
1
2
1
2
1
2
1
1
1
1
1
1
0
0
2
1
1
1
0
2
1
0
2
2
1
0
0
2
0
2
1
1
2
1
1
2
1
2
0
0
0
0
2
2
1
1
1
1
0
1
1
1
0
1
2
0
2
2
1
2
1
1
1
2
1
1
1
1
0
2
0
1
1
0
1
1
0
2
1
0
0
0
1
1
2
1
1
0
4
0
1
0
1
0
1
2
1
1
0
1
0
1
1
1
2
1
1
0
0
1
1
1
1
0
1
1
3
1
0
1
0
1
1
1
1
4
2
1
1
0
2
1
0
1
0
1
2
1
1
1
0
0
2
1
2
1
1
3
2
2
1
1
1
1
0
1
1
0
1
2
1
2
1
2
0
0
0
2
1
0
1
0
1
1
1
1
0
0
2
1
0
1
1
2
1
1
1
1
1
1
2
2
1
1
0
0
1
1
2
1
3
2
0
0
1
0
1
3
2
1
1
0
0
0
2
2
0
1
1
2
2
1
1
0
0
1
1
1
2
0
1
2
0
2
0
1
0
1
0
1
1
2
2
1
0
1
0
1
1
2
0
2
0
1
1
1
1
0
0
1
2
1
0
1
1
1
1
2
0
2
0
0
1
1
2
1
2
1
1
1
0
0
1
1
1
3
1
1
1
1
1
1
1
2
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
2
1
0
2
1
0
0
1
2
2
1
1
1
0
1
1
1
1
1
1
0
1
0
2
1
1
2
0
0
0
1
2
2
2
2
0
1
1
2
1
1
0
0
1
0
4
2
1
1
1
2
1
2
1
2
0
0
1
1
2
1
2
1
0
1
2
1
1
2
0
1
2
0
2
1
1
1
1
0
1
1
1
1
1
2
2
1
0
2
2
1
1
0
2
1
0
1
1
0
2
2
0
1
1
2
0
1
0
0
0
0
2
0
0
2
3
2
2
2
0
1
1
0
1
3
0
1
1
0
4
0
0
1
1
1
1
1
1
2
1
0
0
1
1
0
0
1
2
0
1
0
1
1
1
0
0
1
2
0
0
1
1
0
1
0
0
2
0
1
0
1
0
0
2
0
0
0
0
1
1
1
1
1
1
0
1
0
0
0
0
1
1
1
2
2
0
1
1
1
0
2
1
0
1
1
2
0
2
0
1
1
0
1
0
0
2
0
2
0
2
1
1
1
0
1
0
1
0
1
0
1
2
1
2
1
0
1
0
0
1
3
2
0
0
0
1
0
1
2
1
0
1
2
1
2
1
2
0
2
2
1
1
1
0
0
2
1
1
3
0
1
1
0
1
0
0
2
1
0
1
2
1
1
1
2
0
1
1
1
1
1
2
0
1
1
0
1
1
1
0
0
2
1
0
0
2
1
1
2
1
0
0
1
0
1
0
1
0
2
0
2
1
2
0
1
1
1
1
1
2
1
1
1
1
1
1
0
1
1
0
1
0
1
2
2
0
0
2
2
0
1
1
1
2
1
1
0
1
0
0
0
1
1
1
2
1
1
0
1
0
1
0
1
1
1
2
2
0
1
0
1
1
3
2
2
1
0
0
0
1
1
2
0
1
2
1
2
0
1
1
1
0
0
0
1
1
2
0
1
0
1
1
0
1
2
1
2
0
1
0
1
1
0
1
2
1
0
1
1
2
1
0
2
0
2
2
0
0
0
2
1
2
0
2
3
1
2
2
1
0
1
1
1
1
2
0
0
1
1
1
2
1
0
1
1
1
1
0
0
0
0
0
0
0
1
0
1
2
2
1
2
1
0
1
1
1
1
1
0
0
1
0
1
2
0
0
2
1
2
1
1
1
1
0
1
2
1
1
0
1
1
1
1
1
1
0
0
1
1
1
0
2
2
2
2
0
0
0
1
1
1
1
2
0
1
0
0
2
2
1
0
1
0
0
1
0
1
1
1
0
1
0
0
1
1
1
1
1
2
0
0
2
1
0
0
1
1
1
0
1
1
1
1
1
1
2
1
2
0
1
2
0
0
1
1
1
1
1
1
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
1
0
0
1
2
2
1
1
1
1
0
0
2
1
1
1
1
1
2
2
1
2
1
1
1
1
2
0
0
2
2
0
0
1
1
1
1
1
1
1
2
1
1
1
1
0
2
2
0
2
0
1
2
1
0
0
1
0
1
1
0
1
1
2
1
1
0
0
1
0
1
2
1
1
2
0
1
2
0
1
1
1
1
2
0
1
2
1
0
2
1
1
2
1
1
0
1
0
0
0
1
1
0
1
2
2
2
2
2
2
1
1
0
2
0
1
2
2
1
1
1
1
1
2
1
1
0
0
0
1
2
0
2
1
2
0
0
1
1
1
0
0
1
2
0
2
2
0
0
1
2
1
2
1
1
0
0
0
1
1
1
0
0
2
1
1
1
2
0
1
0
1
1
0
1
0
2
1
3
1
1
0
0
1
0
1
1
1
1
1
1
2
2
2
1
2
0
0
2
1
1
1
1
0
1
0
1
2
0
1
2
1
1
3
2
1
1
1
0
1
1
2
1
1
0
0
1
2
1
1
1
2
1
0
1
0
1
0
2
1
0
1
2
1
1
0
2
1
4
1
0
0
2
2
0
2
1
0
2
2
1
2
0
1
0
5
2
1
2
0
1
1
1
0
0
2
1
0
1
1
1
1
1
1
2
0
1
1
2
1
1
1
1
1
1
2
1
0
1
0
1
1
2
2
2
1
1
2
0
2
1
0
1
1
1
2
2
2
2
2
1
1
1
0
1
2
1
0
2
2
0
0
1
0
0
0
0
0
1
1
1
1
0
1
1
2
1
0
2
1
2
1
0
1
2
1
1
0
1
2
1
1
1
2
1
1
2
1
0
1
2
0
2
0
1
1
0
1
0
1
1
1
0
0
0
1
1
0
1
1
1
0
2
2
0
1
0
1
0
0
2
1
0
1
1
2
2
1
2
2
0
1
3
1
0
0
1
1
1
2
2
1
0
1
1
1
3
1
2
0
1
1
1
1
0
0
1
1
0
1
1
0
2
1
2
0
1
1
2
1
0
1
1
5
1
0
2
1
0
1
3
0
1
1
2
1
0
2
0
1
1
1
1
1
1
2
1
2
1
2
0
0
2
1
2
1
1
1
0
1
0
1
0
0
0
0
2
1
0
0
2
1
0
0
1
1
2
1
1
2
1
1
0
2
0
2
1
1
0
2
0
0
1
1
2
1
0
2
2
1
1
1
1
1
0
0
1
1
1
1
2
1
0
0
1
1
0
1
0
2
1
0
2
0
1
1
1
0
2
1
0
2
1
0
2
1
1
1
2
1
1
1
1
1
2
1
0
2
0
2
1
1
1
1
1
2
1
1
1
3
1
1
0
1
0
0
1
1
1
1
1
1
1
1
1
1
0
2
1
0
0
1
0
2
1
1
0
1
1
3
2
1
1
1
1
2
1
0
0
1
2
0
0
0
1
1
0
2
2
1
0
2
0
1
1
2
1
0
0
0
0
2
2
1
0
2
1
2
1
0
1
2
0
1
1
0
0
2
1
2
1
1
0
1
0
1
2
1
1
0
3
1
4
1
1
1
1
0
0
0
2
1
0
0
2
1
1
1
0
2
1
0
1
0
1
1
1
1
0
0
0
2
2
2
1
2
1
1
2
0
2
1
1
1
2
1
1
2
1
0
0
0
2
2
3
1
1
1
0
0
0
2
0
0
1
0
2
0
1
1
2
3
1
1
1
1
1
0
0
0
1
0
0
1
1
0
2
0
1
2
0
1
2
1
2
2
1
2
2
1
2
1
0
0
1
1
0
2
1
0
1
2
1
0
1
1
1
0
2
2
1
0
2
0
0
0
2
0
2
2
3
1
0
0
0
3
1
1
2
1
0
1
1
0
2
0
1
0
2
1
2
1
0
1
0
1
1
2
1
1
1
0
1
0
2
4
0
2
0
0
1
1
0
1
1
2
2
1
1
1
0
1
2
2
2
1
1
2
1
1
2
3
2
1
0
0
0
0
3
1
1
0
2
2
1
2
1
2
1
3
1
2
1
1
2
0
2
1
0
1
1
1
2
1
0
1
2
0
2
1
0
1
0
2
0
1
1
1
0
2
3
2
2
1
0
0
1
1
1
2
0
1
1
2
1
0
1
1
2
0
0
2
1
1
0
2
0
0
1
1
1
1
0
2
1
2
1
1
0
1
1
2
1
1
1
2
0
0
3
0
0
1
2
0
2
0
2
1
0
1
2
0
2
0
1
0
2
1
1
1
1
2
1
1
2
0
1
2
0
0
0
1
0
1
1
1
0
1
1
2
0
1
0
2
0
2
1
1
2
0
1
1
1
0
0
2
1
1
0
3
1
2
0
1
0
1
2
1
1
2
1
3
0
1
0
2
2
2
0
3
1
1
1
1
0
1
1
1
0
2
2
0
1
0
2
0
0
0
0
0
1
1
2
1
0
0
3
0
1
2
2
1
1
1
1
0
1
1
1
1
3
0
1
2
1
0
2
1
1
1
2
1
0
0
2
1
1
0
0
2
1
3
1
0
0
0
0
1
0
1
1
0
0
1
2
2
1
0
2
0
1
0
2
1
2
1
2
3
1
2
0
2
0
1
1
1
1
2
0
1
0
2
1
1
1
0
2
2
0
1
1
1
1
0
1
1
0
1
0
1
0
0
0
2
1
2
0
1
0
1
2
1
0
2
1
1
0
1
0
1
1
0
1
1
2
2
1
0
0
0
1
1
1
1
0
1
1
1
1
0
0
1
1
1
1
0
2
0
1
0
0
2
1
0
2
1
0
1
0
2
0
0
1
0
1
2
0
2
1
0
0
1
0
1
0
1
2
1
1
2
1
1
1
2
0
0
1
1
1
0
0
2
0
1
2
1
1
1
2
2
0
0
3
0
1
1
0
1
1
0
0
0
1
1
2
1
1
2
0
0
1
1
1
1
0
1
1
1
1
2
1
1
1
0
2
1
1
1
0
1
1
1
1
3
2
1
1
0
0
2
1
1
1
0
0
2
0
1
0
2
2
2
1
1
1
1
1
1
1
2
1
1
0
0
1
2
0
1
0
2
0
1
0
0
2
1
1
2
1
0
1
1
2
1
0
1
0
2
1
1
1
1
1
1
1
2
1
0
1
0
3
1
2
2
1
0
1
0
0
2
2
1
1
0
2
1
0
1
1
2
0
1
1
0
1
0
0
0
1
3
1
1
0
1
1
0
0
1
0
2
0
6
2
2
1
0
0
2
1
0
1
1
2
1
1
2
1
3
0
2
1
2
1
1
2
0
0
0
1
1
1
1
2
3
1
0
1
0
2
2
1
2
1
0
2
2
1
1
0
0
1
0
1
0
0
1
0
2
1
2
1
1
1
0
0
2
1
1
0
0
1
1
1
1
2
2
0
1
1
1
1
0
1
1
1
2
1
1
1
2
1
2
1
1
2
1
0
1
1
1
1
1
1
2
0
1
0
0
2
1
1
1
1
0
1
1
2
0
2
1
0
0
0
1
1
1
0
0
1
2
0
1
0
0
1
0
0
2
1
0
1
2
2
1
0
0
1
1
1
2
1
0
0
2
0
0
2
0
2
2
2
1
0
1
0
0
1
0
1
1
1
0
1
1
1
1
0
2
2
0
1
1
1
2
1
1
1
2
1
1
1
1
1
0
0
1
1
1
1
0
2
1
2
1
1
1
0
1
0
1
2
0
1
2
1
1
0
1
1
1
0
0
0
2
1
1
1
1
1
1
0
2
1
0
1
2
1
0
0
2
1
2
1
1
2
0
1
2
1
0
0
1
1
1
1
1
2
0
1
0
2
1
2
3
1
1
2
1
2
1
1
0
1
2
1
0
0
2
0
1
0
2
2
1
0
0
0
2
1
1
3
1
0
2
0
2
1
2
1
1
0
1
0
1
1
2
0
1
1
1
2
0
2
1
1
0
2
2
1
1
1
1
1
0
0
1
1
1
1
0
0
2
0
1
0
1
1
1
0
1
0
2
0
1
0
0
0
1
1
0
2
1
0
0
1
1
1
1
1
1
1
1
0
1
1
1
0
1
1
1
1
2
2
0
2
1
1
0
2
1
2
1
0
0
2
1
1
1
2
0
0
0
3
1
1
1
2
0
2
0
0
1
1
1
1
2
1
1
1
1
0
1
1
0
2
1
1
1
1
1
0
1
1
1
1
0
0
2
0
0
1
1
1
1
1
1
2
1
1
1
1
2
1
0
0
1
2
0
1
1
0
2
2
2
1
1
1
2
1
1
0
2
0
1
2
1
1
1
1
0
1
2
2
2
2
0
1
1
0
1
0
1
2
1
0
3
1
1
1
0
2
2
2
1
1
2
1
1
0
2
0
1
1
0
1
2
0
2
1
0
1
1
1
0
1
2
1
0
1
1
1
1
1
0
0
1
0
0
0
1
2
2
1
2
1
1
1
2
1
1
2
2
1
1
0
1
1
0
4
2
2
0
0
2
0
0
0
1
1
1
1
1
1
1
1
0
0
1
0
1
1
2
1
0
0
1
0
2
1
1
1
0
2
0
1
0
2
1
0
0
2
0
1
0
0
1
2
0
0
2
0
2
0
2
1
1
1
1
2
1
1
1
1
0
0
2
2
2
1
1
0
0
0
0
1
0
2
0
1
1
1
0
2
0
1
1
0
1
1
0
1
0
1
1
1
0
1
2
1
2
1
2
1
1
1
0
2
1
2
0
0
0
0
1
0
0
1
1
0
0
1
0
1
1
0
1
1
0
0
2
0
2
0
1
1
2
2
2
1
2
1
1
0
2
0
1
1
0
0
1
1
1
0
1
1
1
1
1
2
1
1
1
2
1
3
1
1
3
2
2
1
0
0
1
1
2
0
2
1
2
0
1
1
0
1
1
2
1
0
0
1
1
0
1
0
0
1
0
1
1
0
0
3
1
0
2
1
1
0
0
1
1
1
0
0
0
0
1
1
1
1
3
2
1
1
0
0
2
2
1
1
2
1
0
1
0
0
1
2
3
3
1
1
0
1
1
0
2
1
1
1
0
1
1
2
0
0
2
0
0
0
1
2
1
1
2
1
0
0
3
0
0
0
1
1
0
2
1
1
1
0
1
1
1
1
2
1
1
2
1
0
1
1
1
0
1
1
0
1
1
1
0
0
1
1
1
1
1
1
0
1
1
1
1
1
1
2
1
1
1
0
1
0
2
1
0
0
1
0
0
1
1
1
1
1
2
1
2
2
2
1
1
0
1
0
1
2
0
0
0
0
0
1
1
1
0
1
0
0
0
1
1
0
1
0
2
1
2
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
2
2
2
1
1
1
1
0
1
0
1
1
1
1
1
1
1
0
2
0
2
2
2
1
0
1
1
1
0
1
1
1
2
0
1
2
1
0
0
1
1
0
1
3
2
2
0
2
0
2
0
1
0
1
2
0
1
0
1
0
2
2
2
1
2
0
1
1
2
0
0
1
1
2
1
0
1
2
1
1
0
0
0
2
1
1
2
0
5
0
1
0
0
0
2
0
1
2
1
1
1
1
1
2
1
2
1
1
0
1
0
2
0
1
1
0
1
0
0
2
0
2
3
1
3
0
0
1
2
0
2
1
2
1
0
1
0
0
1
1
2
1
0
2
0
2
1
0
1
1
1
2
1
1
1
2
0
1
0
2
2
0
0
0
2
1
1
1
0
2
1
4
0
0
4
0
1
2
1
1
2
0
1
1
1
1
0
2
0
1
0
1
0
1
0
2
0
0
1
0
0
1
1
1
1
0
0
1
2
1
0
2
1
2
0
0
1
3
2
2
0
3
0
2
2
1
1
1
1
1
1
1
0
2
2
1
1
1
2
2
1
1
2
0
2
0
0
1
0
1
0
0
0
0
2
3
0
0
0
1
1
2
1
2
0
1
0
2
1
1
1
1
1
0
1
0
1
2
0
2
1
2
1
2
0
2
0
1
2
1
2
1
1
2
1
0
0
1
0
2
1
0
1
1
1
1
1
1
0
0
1
1
0
2
0
2
1
1
0
0
0
1
0
1
2
0
1
1
2
1
2
2
1
2
1
3
1
1
1
1
1
2
1
0
0
1
0
1
2
0
0
1
0
1
0
0
1
1
2
0
1
3
2
0
0
1
1
0
1
2
1
2
1
0
0
1
1
0
1
1
0
1
1
0
2
0
1
0
3
0
1
0
1
0
0
0
0
1
1
0
1
1
1
2
1
1
2
1
0
2
1
1
1
0
0
1
1
1
1
1
1
0
0
1
2
1
1
1
1
2
1
1
2
2
0
1
1
0
0
2
1
1
2
0
1
0
0
1
1
0
1
1
1
1
1
1
1
1
1
0
1
1
2
1
1
2
2
0
1
0
1
1
1
2
1
2
1
1
2
0
1
2
1
2
0
0
1
0
0
1
2
2
2
0
1
0
2
1
2
0
0
0
1
1
1
1
0
1
0
2
0
1
1
2
0
2
2
0
0
1
2
2
1
1
1
1
1
1
1
2
0
0
0
1
0
2
1
1
1
0
0
1
1
1
1
0
1
1
1
1
0
0
1
1
2
1
1
1
1
0
1
0
1
0
0
1
0
1
1
2
0
1
2
1
4
2
0
1
1
2
2
1
1
0
1
1
0
1
2
1
1
1
1
3
1
4
0
1
1
1
0
2
1
0
0
0
2
2
1
1
0
1
2
1
0
1
0
1
0
1
1
0
1
1
1
0
2
0
1
1
1
0
1
1
0
0
2
0
1
0
0
2
0
1
1
0
1
2
1
0
1
0
1
2
1
2
2
1
0
2
1
2
1
0
1
1
0
1
1
2
1
1
1
1
0
0
2
0
2
1
1
0
1
2
1
0
1
2
0
0
1
0
1
0
2
1
1
2
0
0
1
0
2
0
1
2
1
1
1
1
1
1
1
0
0
2
1
1
0
0
1
1
2
1
2
1
1
0
2
0
1
0
2
2
1
0
0
2
1
2
1
1
0
2
2
1
0
1
1
0
1
1
1
1
0
0
0
1
1
0
0
1
0
2
0
0
1
0
0
0
2
2
0
0
2
2
0
1
0
0
0
0
1
2
1
1
1
2
1
0
1
1
1
0
1
0
1
1
1
2
0
0
2
2
2
2
1
1
1
1
1
1
0
0
1
2
1
1
0
2
0
1
1
2
1
1
0
1
2
2
2
1
0
1
1
0
0
1
1
0
2
0
1
2
1
2
0
1
1
1
2
0
1
2
3
0
1
2
0
1
2
2
0
0
2
2
1
0
0
2
1
1
0
2
1
0
0
0
1
2
1
1
1
0
1
0
2
1
0
1
0
2
0
0
0
1
2
2
0
1
2
2
0
2
0
1
1
1
1
0
2
1
1
1
1
1
0
1
2
1
1
1
0
0
1
1
2
0
1
0
0
1
1
0
1
2
2
1
1
1
0
2
1
2
0
1
0
1
1
1
1
0
1
0
1
0
1
0
1
0
1
1
1
2
1
0
5
0
1
1
1
2
2
0
1
1
3
1
1
1
1
1
1
1
1
0
2
1
1
1
1
3
1
1
1
1
2
2
0
2
2
2
1
0
2
1
2
1
3
0
1
2
1
0
1
1
1
2
1
0
1
1
0
0
2
0
2
0
1
1
1
2
1
0
1
1
0
1
2
1
2
0
0
1
2
2
1
1
1
1
1
1
1
2
1
1
1
0
0
0
1
2
1
0
2
0
0
1
1
1
1
2
0
2
0
0
0
0
2
0
1
2
2
0
0
2
1
1
1
1
3
1
2
0
0
1
1
1
1
1
1
1
0
1
1
1
0
1
1
0
0
0
2
1
0
1
1
2
2
0
1
1
0
0
1
2
2
1
1
0
2
1
2
0
0
1
0
2
1
2
0
2
1
1
1
1
2
1
1
0
0
1
1
0
1
0
1
0
0
0
1
1
1
0
1
1
2
2
1
2
1
1
1
1
1
0
1
1
1
0
0
1
2
1
0
0
2
1
1
1
2
2
1
0
0
1
0
1
1
2
1
0
1
4
1
2
2
1
1
3
2
0
1
0
0
0
0
1
0
2
1
1
0
1
1
1
0
1
1
1
0
1
1
0
1
0
1
1
1
1
1
1
0
1
1
1
1
1
0
2
1
0
1
2
1
1
2
0
1
1
0
3
0
0
1
0
0
1
0
1
0
0
1
0
2
0
1
1
0
2
1
0
1
1
1
2
2
2
1
0
1
1
1
2
2
1
1
1
0
1
2
1
1
2
1
0
1
1
0
1
2
1
3
2
0
2
1
1
1
1
1
0
2
0
0
1
2
2
1
1
2
0
0
0
2
1
2
1
2
1
1
2
1
0
1
0
0
0
0
2
0
2
0
1
0
0
1
1
0
1
0
1
1
1
0
0
2
2
1
1
1
0
2
0
1
0
0
1
0
1
2
1
1
1
2
1
0
1
1
0
1
1
2
0
1
1
1
0
0
1
0
2
1
0
1
0
2
1
0
1
1
2
1
1
1
1
0
1
0
1
1
1
0
1
1
0
2
2
1
2
1
0
0
0
2
2
0
1
0
1
1
0
0
1
2
2
3
2
1
1
2
1
1
0
2
1
1
2
0
1
0
2
2
0
0
1
1
0
2
1
1
1
0
0
1
1
2
1
0
1
1
0
1
1
2
2
1
1
0
1
1
1
0
1
0
1
0
0
1
1
2
1
1
1
2
1
3
1
0
0
1
1
1
0
0
1
1
2
1
0
0
2
1
1
1
1
1
1
2
0
1
0
2
1
0
1
1
1
1
0
3
2
1
1
1
2
2
2
1
1
0
1
0
1
0
1
1
1
0
1
0
2
2
1
1
1
1
0
0
1
2
1
1
0
0
0
0
0
1
0
2
2
1
2
1
2
1
1
2
1
0
2
1
0
1
1
0
1
2
0
2
0
0
1
1
2
2
0
2
2
2
1
0
0
1
0
1
2
1
0
0
1
2
2
1
0
0
2
1
0
1
0
2
1
0
1
1
0
1
0
1
2
0
2
1
2
1
2
1
2
0
1
2
0
0
2
2
0
1
0
2
0
1
1
1
1
0
1
1
2
1
2
1
0
2
0
1
2
1
1
0
1
0
1
1
1
1
0
1
2
2
0
1
0
0
1
2
2
0
1
1
1
2
0
0
1
1
2
2
1
2
2
0
1
1
0
2
0
0
1
2
0
1
0
1
1
2
1
1
1
1
1
1
0
1
2
2
2
2
0
2
2
1
1
1
2
0
1
1
1
1
1
1
0
2
1
0
1
0
0
1
2
1
0
1
2
0
1
0
0
1
1
1
0
2
2
1
2
1
0
0
3
0
1
0
0
2
1
0
0
2
3
1
0
2
1
1
2
0
0
0
0
2
1
1
2
1
1
1
0
1
0
1
0
2
1
1
0
2
1
0
1
0
0
1
0
1
1
1
1
0
1
2
1
0
1
1
0
1
0
2
2
1
1
0
0
0
1
1
0
0
2
1
1
0
1
2
2
0
1
1
1
2
3
1
1
0
1
1
2
0
0
1
1
1
1
2
1
1
1
2
1
1
2
1
1
1
2
0
0
0
1
2
1
1
0
2
0
2
3
1
2
1
1
1
1
2
2
1
1
0
2
2
1
0
0
1
1
1
0
1
1
1
0
1
2
1
2
0
1
2
2
1
1
1
2
1
0
1
2
1
1
0
2
0
1
1
0
0
1
0
1
1
1
0
4
1
0
0
1
0
1
2
0
1
1
0
1
1
1
0
0
0
1
0
2
0
1
1
2
1
1
1
3
0
2
1
0
1
1
0
1
1
0
1
1
2
0
0
2
1
0
1
1
0
1
0
0
1
2
1
2
2
1
1
1
1
1
2
0
1
1
1
0
2
1
0
0
1
1
1
2
1
1
1
1
1
2
3
1
0
1
1
2
0
1
0
1
1
1
0
0
1
1
1
2
2
2
0
2
1
0
0
1
0
2
2
0
0
1
1
1
1
2
0
1
2
3
1
1
0
1
2
1
1
2
0
1
0
1
0
1
0
0
0
0
1
0
0
2
1
0
1
0
2
1
1
0
1
2
2
1
0
2
2
0
0
1
1
1
1
1
1
2
1
0
0
1
1
1
1
1
1
2
2
0
0
0
1
1
1
2
2
0
0
0
1
1
2
2
1
0
1
1
0
1
1
1
2
1
1
1
1
1
1
1
1
0
1
1
0
1
1
1
0
1
2
0
0
1
1
2
1
1
2
1
2
0
1
1
1
0
2
1
1
2
0
1
0
1
2
1
1
1
1
0
1
1
2
0
2
2
0
1
0
1
1
1
1
1
0
1
1
1
1
1
0
0
1
1
1
1
1
2
1
0
0
2
1
1
0
1
1
0
0
1
2
0
2
0
2
1
2
1
1
0
2
1
0
1
1
1
1
1
0
1
2
1
2
2
0
0
0
0
0
1
2
2
2
0
0
1
0
0
0
3
1
2
2
0
0
0
1
0
0
2
1
1
0
1
2
1
2
1
5
0
2
0
2
2
1
1
1
1
1
1
0
0
0
2
1
0
0
1
1
3
0
0
2
1
0
2
0
0
1
1
1
1
2
0
1
1
1
0
0
2
1
0
1
2
0
0
1
1
1
0
0
2
1
2
0
0
1
0
1
0
2
2
1
2
1
0
1
0
0
0
0
0
1
1
0
1
3
0
1
3
1
1
1
1
0
0
1
1
1
1
2
0
0
0
0
1
1
0
0
0
1
2
0
2
2
2
0
2
1
0
2
0
0
0
2
5
0
1
1
1
2
1
1
0
1
2
2
1
1
1
0
0
1
2
1
1
1
1
2
2
2
1
1
1
0
1
0
1
1
1
1
0
0
1
0
1
1
0
1
2
1
1
0
0
1
1
1
2
2
2
4
1
1
2
1
1
1
0
2
1
2
0
1
0
0
0
2
0
1
0
0
0
0
1
1
0
1
1
2
0
0
0
1
2
1
1
2
1
0
0
1
1
1
1
1
0
1
2
0
2
2
0
2
1
1
1
0
0
3
1
1
2
0
1
1
1
2
2
0
1
0
2
1
2
1
1
1
1
1
1
2
1
1
1
2
2
0
1
1
2
1
1
0
2
0
1
1
1
1
1
0
1
1
1
2
1
1
0
1
1
0
0
2
1
1
1
1
0
1
1
0
1
1
1
1
0
1
1
1
3
0
1
0
1
1
1
1
0
1
1
0
0
2
2
0
1
2
1
2
0
0
2
0
1
1
1
1
1
0
2
0
2
1
2
1
1
1
1
1
0
2
1
0
2
0
0
1
1
1
2
1
2
1
1
1
2
0
2
2
1
2
0
0
1
0
0
0
1
2
2
0
1
1
1
2
0
1
1
1
0
2
2
2
0
0
0
1
2
1
0
2
0
1
1
1
0
1
2
1
1
2
1
1
0
2
1
0
1
1
0
0
0
1
2
2
1
0
0
1
0
1
1
2
1
1
1
1
0
1
1
2
1
0
1
2
1
3
1
0
0
1
0
2
1
2
1
0
2
0
0
2
2
2
2
0
2
2
1
0
2
1
2
1
2
1
0
2
0
1
1
2
0
0
2
1
3
1
1
1
0
0
0
2
1
1
3
1
2
1
1
1
1
1
0
1
1
0
1
1
0
0
0
1
2
1
1
5
1
0
0
1
2
2
1
0
1
0
2
0
1
1
2
1
1
1
1
1
1
1
0
1
3
1
1
1
2
1
0
1
0
0
1
1
1
1
1
1
1
2
1
0
0
2
0
1
0
1
0
2
2
1
1
1
0
1
2
0
0
0
0
1
1
0
0
0
1
2
0
2
0
1
1
1
2
1
2
0
1
2
2
1
0
1
2
0
1
0
1
0
0
1
2
1
2
1
1
1
0
1
2
1
0
1
2
1
2
1
1
1
0
0
0
0
0
1
1
2
2
2
0
0
1
1
1
1
1
0
2
0
1
1
0
1
1
1
0
1
1
1
1
1
2
0
1
1
2
0
2
2
2
1
2
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
1
0
2
0
2
1
0
2
2
2
1
1
1
1
2
1
1
2
1
0
0
1
1
0
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
0
1
2
2
1
1
1
1
2
1
0
0
1
1
0
0
1
1
0
0
1
0
1
2
1
2
1
0
1
1
2
2
2
1
2
0
3
1
1
2
0
1
2
1
0
2
1
2
2
0
0
1
2
2
0
0
1
0
1
1
0
1
0
0
0
0
1
1
1
2
2
3
1
0
2
1
0
1
0
1
0
0
1
1
1
0
0
1
0
1
0
0
2
0
1
1
1
1
2
0
2
2
1
1
1
0
0
2
2
1
2
1
1
1
4
2
2
1
1
1
1
0
2
2
0
1
3
2
1
2
0
1
0
1
0
1
1
1
0
0
0
1
1
1
0
1
1
1
2
2
1
0
2
1
1
0
1
0
1
1
0
1
2
1
2
0
1
1
1
0
1
2
0
2
1
0
2
1
1
2
1
1
1
0
0
0
1
1
1
2
0
1
0
2
2
1
1
1
0
1
0
0
2
2
1
2
1
0
1
1
0
0
1
0
1
0
2
0
1
1
1
0
2
1
1
1
2
0
1
0
1
1
1
1
2
1
1
0
1
1
1
1
1
0
0
1
0
0
0
1
3
0
2
0
3
1
1
2
1
1
1
2
0
0
2
2
0
1
1
1
1
1
1
0
2
1
1
1
0
1
1
0
1
2
1
0
2
2
2
0
0
1
1
1
0
2
0
0
1
0
0
2
2
0
0
2
1
0
1
1
1
2
0
1
1
1
0
0
1
1
1
5
2
1
0
1
1
1
1
1
1
0
0
1
1
2
1
1
2
2
1
1
1
1
0
4
2
1
0
0
2
1
1
0
1
1
0
1
1
0
1
1
0
1
1
0
1
2
1
1
0
0
1
0
1
1
2
1
2
1
0
1
2
1
0
2
1
2
2
2
0
1
2
1
0
1
1
1
1
1
0
1
2
2
2
1
1
1
1
1
1
2
2
2
1
0
1
1
0
1
1
0
1
0
1
1
0
2
1
0
1
1
0
0
0
0
2
1
2
0
1
0
2
1
1
1
1
2
0
2
2
1
0
1
1
1
0
2
0
1
0
2
1
1
1
1
0
0
0
1
1
1
1
2
2
0
1
0
0
0
1
1
0
1
1
1
0
0
2
0
1
1
2
1
0
2
2
1
1
2
1
2
2
0
1
0
0
0
0
0
2
1
0
2
0
1
2
0
1
1
2
1
2
0
1
2
1
0
1
1
2
2
1
0
0
1
0
0
1
2
2
1
1
0
3
1
2
1
1
0
2
1
1
2
1
1
2
0
1
1
2
0
1
1
1
2
1
0
1
1
1
1
0
0
1
1
0
2
1
1
0
0
1
2
0
1
1
1
2
0
1
1
0
1
1
2
1
0
2
2
1
0
1
1
2
1
1
1
0
2
2
2
0
1
1
0
1
0
0
2
2
1
1
2
1
1
1
0
0
1
2
0
1
0
2
1
1
0
1
1
0
1
1
1
0
1
1
1
0
1
0
1
2
1
0
1
0
1
1
1
0
1
1
1
1
0
0
2
1
0
1
1
1
0
2
1
1
2
2
0
0
1
1
2
2
0
0
0
2
1
0
0
1
0
2
1
0
2
0
2
1
2
2
0
0
0
1
1
1
0
0
0
0
1
2
1
0
1
4
2
0
5
2
1
0
1
2
0
1
2
0
2
0
1
2
1
0
0
1
1
1
1
1
2
0
2
2
0
2
1
2
2
1
0
2
0
1
1
0
0
0
2
0
1
2
0
2
1
2
0
0
1
1
2
1
2
1
1
0
0
0
0
1
0
1
1
2
2
1
1
1
2
0
0
1
2
0
2
2
0
2
1
1
2
3
2
1
1
2
2
1
1
0
4
0
2
0
0
2
2
1
2
2
1
1
0
0
0
2
0
1
0
2
1
0
0
2
1
0
1
1
1
0
2
2
1
0
1
0
1
1
1
0
1
2
2
1
1
1
1
0
0
1
2
2
1
1
2
1
1
0
0
0
0
2
1
2
1
1
0
1
2
1
0
1
0
1
0
0
0
2
2
2
1
0
0
2
1
1
1
1
2
2
1
2
2
2
1
1
1
0
1
0
0
1
1
2
2
0
1
1
2
1
1
1
2
0
0
2
0
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
0
0
1
0
1
0
1
2
1
2
1
2
1
1
2
0
2
2
2
1
0
0
2
1
1
0
2
1
2
1
0
2
1
0
1
2
0
2
0
1
1
2
0
1
1
2
2
1
0
1
2
0
1
1
0
1
2
1
1
0
2
2
0
1
1
0
2
0
0
1
1
1
2
0
2
0
1
1
0
2
2
2
2
1
1
0
1
2
1
1
2
1
0
1
2
1
1
0
2
2
2
1
0
2
1
1
2
1
1
1
2
1
1
0
0
0
0
1
1
0
2
1
2
1
1
1
1
1
1
2
1
0
1
0
1
0
2
0
1
0
1
2
1
0
1
0
1
1
1
1
2
1
2
3
1
0
2
0
1
2
2
0
1
1
2
1
1
0
0
0
0
1
1
2
1
2
0
0
1
1
1
1
1
1
2
0
2
2
1
0
0
0
2
0
1
1
2
1
1
1
2
2
1
0
2
1
2
1
2
0
0
1
0
1
1
2
1
1
0
0
1
0
1
2
0
0
1
0
1
1
2
1
1
1
1
0
1
0
2
0
1
1
1
1
1
0
1
1
0
0
0
1
2
3
4
0
0
2
1
0
1
1
2
1
0
2
1
0
1
1
1
3
0
1
1
1
1
0
2
2
1
1
1
0
1
1
1
1
2
2
1
1
1
1
0
1
1
0
2
1
1
0
1
0
2
1
1
1
2
0
0
1
2
1
1
2
0
1
0
1
2
1
2
2
0
0
1
1
0
1
1
1
1
1
1
0
0
1
1
1
0
2
0
1
0
2
0
0
1
0
2
2
0
0
1
1
1
2
2
1
0
0
0
1
0
1
2
2
1
1
0
1
1
0
1
0
0
1
2
1
0
2
1
1
2
1
0
2
1
1
1
1
2
2
1
2
1
1
1
0
1
0
1
0
1
1
1
0
2
0
2
2
1
1
1
1
1
1
0
1
1
0
2
0
0
1
1
1
0
2
0
1
1
0
1
0
1
0
2
2
0
2
1
0
1
0
2
1
1
1
0
0
2
0
2
0
2
0
1
2
0
0
1
0
0
0
1
1
0
2
1
1
0
1
1
0
0
0
1
1
2
2
1
0
1
0
2
2
0
2
0
0
0
1
1
2
1
1
0
0
1
1
1
3
1
1
1
0
0
2
1
1
2
2
2
2
0
2
1
1
1
1
1
1
2
0
0
1
1
0
2
1
3
1
0
0
1
1
0
1
1
1
1
1
2
1
1
0
1
0
0
1
2
2
1
1
0
1
0
1
0
0
1
1
1
2
1
0
2
2
0
1
2
1
2
2
1
0
2
1
1
1
1
1
0
0
0
3
2
1
0
1
1
1
2
2
0
1
0
2
1
2
1
1
0
2
1
1
0
0
1
1
1
3
1
1
1
2
1
1
1
0
2
1
1
2
1
1
2
2
0
2
0
1
1
2
1
0
2
1
1
1
0
2
1
1
1
1
0
2
1
1
0
0
1
2
1
1
0
1
2
1
1
1
1
1
0
1
0
0
1
0
0
1
2
1
1
0
2
1
0
0
2
1
0
1
1
0
0
2
2
1
0
2
1
1
0
1
2
0
1
1
2
1
1
3
0
1
2
0
2
1
0
1
1
0
1
1
0
1
1
0
1
2
1
0
0
0
2
1
0
2
2
1
2
0
1
2
1
2
1
2
0
2
1
1
0
1
3
0
1
1
1
0
1
1
1
1
0
1
1
1
0
1
1
0
0
0
1
2
2
2
1
0
0
1
2
2
2
2
1
1
0
0
1
1
1
1
2
0
2
2
1
1
1
1
2
0
0
1
1
1
1
0
2
1
2
1
0
0
2
0
1
1
2
0
1
1
1
0
0
1
1
2
1
1
1
1
0
0
1
1
0
1
1
1
1
2
1
1
2
1
0
0
2
0
1
0
0
1
1
1
1
0
1
1
0
1
2
2
0
0
1
1
1
0
1
2
0
1
1
1
0
1
0
0
2
1
2
1
0
1
0
2
2
1
0
1
1
1
2
0
1
1
1
1
1
1
1
1
0
1
1
1
1
2
0
1
1
2
2
2
2
0
2
1
1
0
1
2
2
0
1
0
1
2
1
2
2
1
0
0
0
1
0
1
1
1
1
5
1
2
1
0
0
3
1
1
0
2
1
2
1
1
1
2
1
0
1
1
2
1
1
1
1
1
0
0
2
1
2
0
1
1
0
1
1
0
1
2
1
1
0
1
2
1
1
0
0
1
0
1
0
2
2
1
1
1
1
1
1
2
2
4
2
0
0
0
1
0
1
1
1
0
0
1
0
0
1
0
2
0
2
1
0
1
1
1
0
2
1
1
2
2
1
2
1
0
1
1
0
2
1
1
1
0
1
0
0
1
1
2
2
0
1
0
0
1
2
1
2
1
1
1
1
2
2
0
1
1
1
1
0
1
2
1
1
0
1
0
1
0
2
1
1
1
2
1
4
0
2
1
1
1
0
2
1
1
1
2
2
0
1
1
1
1
2
2
0
0
0
1
2
0
2
0
0
0
0
0
0
0
1
2
2
0
1
1
1
0
1
1
1
1
1
2
1
2
0
2
1
1
1
1
2
2
1
1
1
0
1
0
2
1
0
1
1
0
1
0
2
1
1
1
2
0
1
1
0
1
1
1
0
1
1
1
1
1
0
0
1
2
1
1
1
0
0
2
1
0
1
2
2
1
0
1
1
1
2
2
0
1
2
1
1
1
2
1
0
1
2
1
0
2
1
1
1
3
1
0
2
0
1
1
0
1
3
0
1
1
0
1
0
2
2
1
2
1
0
2
2
0
1
1
1
2
2
1
1
2
2
0
2
2
1
0
1
1
0
1
0
0
1
1
2
0
0
1
0
1
1
1
1
1
0
0
2
1
2
1
0
1
0
0
1
0
1
2
1
1
1
0
0
0
0
0
1
1
2
1
1
1
1
1
2
2
0
2
0
1
1
1
1
2
0
1
1
1
2
1
1
2
1
1
1
1
1
0
1
1
0
1
0
2
1
0
2
1
1
0
1
1
2
1
1
1
0
1
0
0
2
2
1
1
3
2
1
2
1
1
1
2
1
0
2
2
0
1
0
0
2
2
1
2
1
1
0
1
1
1
1
6
0
2
1
0
0
2
0
1
1
0
0
0
1
1
0
0
2
1
0
2
0
0
0
1
0
0
1
1
3
1
0
1
1
1
2
0
1
1
1
1
0
0
1
1
0
2
1
0
1
0
0
0
0
1
2
1
2
1
2
0
1
2
1
2
0
1
0
1
1
2
1
2
2
1
2
1
2
1
0
2
1
1
1
0
1
1
1
1
1
2
1
2
2
0
1
1
1
2
1
1
1
1
2
0
1
1
0
1
1
1
1
2
1
0
2
1
2
1
2
1
2
1
0
1
1
1
1
2
1
0
2
1
1
1
1
2
1
1
2
0
1
0
1
1
0
1
2
0
0
1
2
1
1
0
0
2
1
2
1
0
1
0
1
0
1
1
0
1
1
1
2
0
2
1
2
0
1
1
2
2
1
1
5
1
2
0
0
2
1
2
1
2
0
1
1
1
1
0
1
1
1
1
0
2
0
1
1
1
1
0
1
2
2
0
0
1
1
1
2
1
0
1
0
1
0
1
2
1
1
4
0
2
1
2
0
1
1
2
1
1
0
1
1
1
1
0
1
1
1
0
1
1
1
1
0
2
1
1
0
0
1
1
1
1
0
2
0
0
0
1
1
2
1
1
0
0
0
1
1
0
2
2
0
2
1
1
1
0
0
1
1
1
1
1
1
1
3
0
1
2
0
2
1
0
1
1
0
2
0
2
2
2
1
0
2
2
1
2
1
2
0
0
0
0
2
2
0
0
1
1
1
1
3
1
2
0
1
2
1
2
1
1
0
2
2
0
1
0
2
1
0
2
0
1
1
1
1
0
1
2
1
2
1
1
0
1
0
2
1
0
0
0
1
1
1
2
2
1
2
0
0
1
2
0
1
1
1
1
1
0
0
1
1
0
1
1
2
0
2
1
3
0
0
1
1
1
0
1
1
1
0
1
1
2
1
1
1
1
1
1
1
1
0
1
1
2
0
1
2
0
1
2
0
0
0
2
2
1
0
0
2
1
0
3
0
0
2
1
1
0
2
0
0
0
0
2
1
1
1
0
1
2
1
1
1
1
0
1
0
0
2
1
0
1
0
0
1
1
0
1
2
0
1
2
1
1
1
1
1
0
1
1
1
1
1
1
1
2
1
3
2
1
2
1
2
1
1
0
0
2
0
2
1
1
1
1
1
2
1
0
0
1
2
3
1
0
0
1
1
0
1
1
1
0
1
1
1
1
1
1
1
0
1
2
1
0
0
2
0
0
0
0
2
1
2
2
2
2
0
1
0
1
0
0
1
2
2
0
1
0
0
0
0
2
0
1
0
2
2
1
2
0
1
1
1
0
0
2
1
1
0
1
1
1
1
1
0
1
1
1
1
0
2
1
3
1
0
0
1
0
1
1
0
1
1
2
1
1
2
2
0
2
1
1
1
0
3
1
0
1
0
0
1
1
0
2
1
0
1
1
2
1
1
2
1
0
2
1
2
0
1
1
0
0
2
2
2
0
1
1
1
2
1
1
1
2
1
1
1
0
2
2
0
1
1
0
2
0
1
1
1
1
1
1
3
2
1
2
1
2
1
0
1
3
2
0
1
0
0
0
1
2
2
2
1
1
1
2
1
1
0
1
2
1
0
0
1
0
0
1
1
5
1
3
0
1
1
1
0
0
1
1
1
0
1
1
0
1
2
1
0
0
1
1
1
2
2
1
0
1
1
1
1
1
1
2
0
0
2
1
1
1
0
1
1
0
2
1
2
2
1
1
2
1
0
2
0
1
1
0
1
0
1
2
2
0
2
0
1
2
3
1
0
1
1
2
2
3
1
0
0
1
1
1
1
1
0
2
2
1
0
2
0
0
2
0
1
2
1
0
2
0
1
1
1
1
1
2
2
0
1
2
1
0
2
2
0
0
1
1
1
2
0
0
1
1
1
1
0
0
1
1
0
1
1
1
1
1
0
1
1
3
0
1
2
1
1
2
1
1
1
0
1
0
2
1
0
0
0
1
2
0
1
1
1
2
2
0
0
1
1
2
1
0
1
2
1
1
1
1
1
2
1
0
2
2
3
0
0
0
1
0
2
1
1
2
0
1
1
2
1
0
2
1
1
0
1
0
0
2
0
1
2
1
1
1
1
0
0
2
1
1
1
0
2
1
0
1
0
0
2
0
1
0
1
0
2
0
1
0
1
2
0
1
1
0
1
0
0
2
0
1
1
2
1
1
2
1
2
1
1
1
1
0
0
1
0
0
1
1
1
1
1
2
2
1
0
0
0
0
1
1
1
1
1
0
2
0
1
2
2
1
1
1
2
0
2
1
1
2
1
2
2
0
1
0
1
2
0
1
0
1
1
2
1
2
1
2
1
0
1
1
1
1
1
1
0
2
1
2
0
1
1
1
1
1
2
1
0
1
1
1
0
0
0
1
1
0
0
1
0
0
0
1
0
2
1
2
1
1
1
1
2
1
0
1
2
2
0
2
2
2
1
0
2
0
1
2
0
1
0
0
1
1
1
0
0
2
2
1
1
1
1
1
0
1
2
1
1
1
0
2
1
1
0
0
2
2
1
1
0
1
2
2
1
2
2
2
0
0
1
0
2
1
0
2
0
1
1
2
0
1
0
0
0
1
0
0
1
0
2
0
1
2
1
2
2
0
1
0
2
1
0
2
0
1
4
0
1
1
0
1
0
1
0
2
2
2
1
2
0
1
2
2
1
2
1
0
0
3
1
0
1
0
1
1
1
0
1
1
0
1
1
1
0
0
2
0
0
2
2
0
1
1
2
1
2
1
1
0
0
0
2
1
2
0
0
0
2
2
2
1
1
2
1
0
2
2
1
1
1
1
1
1
2
1
0
0
1
1
0
1
1
0
1
0
1
0
0
1
0
1
0
1
1
2
0
0
1
1
0
1
0
2
1
1
2
0
1
2
1
1
1
1
1
1
2
1
1
2
1
0
2
2
1
1
0
1
1
1
1
0
0
1
1
1
1
1
0
0
1
0
1
1
1
0
2
0
2
1
3
0
1
1
1
0
1
0
0
2
1
1
0
0
1
1
0
0
2
1
0
0
2
0
1
1
0
0
1
1
1
0
2
2
1
0
1
1
1
2
0
1
2
1
0
1
0
0
0
2
0
0
1
1
0
0
1
2
0
1
0
1
1
1
1
1
2
0
0
1
1
2
1
1
0
2
1
0
1
1
2
2
0
2
0
1
2
0
0
0
1
0
1
1
0
2
1
0
1
1
1
0
0
1
1
1
2
1
1
2
1
1
1
0
0
0
2
2
1
0
1
1
1
1
2
1
2
1
1
2
1
1
1
2
1
0
2
0
0
1
1
2
1
2
1
1
0
0
2
0
1
1
1
1
2
1
1
2
2
1
2
1
0
1
1
0
0
1
1
1
2
1
1
1
1
2
0
1
1
0
2
1
0
2
2
1
0
2
1
1
1
1
2
1
0
1
5
0
1
1
1
1
1
0
0
0
5
0
1
1
1
1
1
2
1
0
1
1
1
1
2
1
2
0
1
1
1
2
1
1
1
0
2
1
0
0
1
0
0
0
0
1
2
1
2
1
1
1
1
2
0
1
0
1
1
1
1
2
0
0
2
2
0
2
1
0
1
1
0
1
1
1
1
1
0
0
1
1
1
2
0
1
0
2
0
0
2
1
1
2
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
1
2
1
0
1
0
1
1
0
1
1
1
2
0
0
1
1
0
1
0
2
0
1
0
1
2
0
2
0
2
2
3
0
1
2
1
1
1
0
1
0
1
0
0
1
1
1
0
2
1
1
1
1
2
1
1
2
1
2
2
1
2
1
0
1
1
2
0
2
0
5
0
1
1
2
2
1
1
1
1
0
0
1
1
1
1
0
1
0
2
1
1
2
2
1
2
1
1
0
1
0
2
1
2
1
0
0
2
2
0
1
1
1
1
0
1
1
1
2
1
1
2
0
1
0
0
0
2
1
1
0
1
2
1
2
1
1
1
2
1
1
1
2
2
1
1
1
2
1
0
2
1
0
1
1
2
1
1
2
0
2
1
1
1
1
0
1
1
0
0
2
1
0
0
0
2
0
1
2
1
1
8
1
0
1
1
1
0
0
2
0
1
1
0
0
0
0
1
1
2
0
1
0
2
1
3
1
2
1
0
1
1
1
3
1
0
1
2
1
1
0
2
0
1
0
1
0
0
1
0
1
2
1
2
4
2
1
0
4
2
1
0
0
1
1
1
2
1
2
0
1
2
0
2
0
1
1
1
2
1
1
1
2
1
1
1
1
1
1
0
1
0
1
0
2
1
2
2
2
0
2
2
1
2
0
2
2
1
1
1
2
0
1
1
1
1
0
2
0
2
0
2
0
1
0
1
0
1
1
1
1
2
1
1
1
1
0
2
1
1
1
1
0
0
2
2
4
1
2
1
1
2
0
1
2
2
1
1
1
2
2
0
1
1
2
2
0
2
0
2
2
1
1
0
1
1
0
1
1
1
1
2
2
2
1
1
2
1
0
1
1
1
0
0
0
0
0
1
1
2
0
0
2
1
1
2
2
1
0
1
2
0
0
2
2
0
1
1
1
1
1
0
1
1
1
1
1
2
0
1
1
2
1
2
1
0
2
0
2
1
1
1
1
1
1
1
1
2
2
2
1
1
0
2
2
2
1
0
0
0
1
2
1
1
1
1
2
1
2
1
1
0
1
1
2
1
1
0
1
2
0
2
2
0
0
2
2
1
2
1
0
1
0
0
1
1
1
1
0
1
1
1
1
1
0
1
0
1
1
2
1
1
1
2
1
2
1
3
1
2
1
0
1
1
1
2
0
2
0
0
0
0
0
1
2
0
2
2
0
1
0
1
1
1
0
0
1
0
0
0
2
1
0
1
0
2
0
2
1
1
2
2
0
0
2
1
1
1
1
1
1
2
1
2
1
1
2
2
0
1
1
0
1
1
1
1
2
1
0
2
0
1
2
2
2
0
1
2
1
4
1
0
0
0
0
2
0
2
0
1
1
1
1
1
0
1
0
1
1
1
1
0
2
1
2
0
0
2
1
1
1
2
0
2
1
0
0
1
1
1
2
2
1
1
2
1
0
1
1
1
1
2
2
2
1
0
1
2
0
1
0
2
1
0
0
2
2
0
2
2
1
1
2
1
1
1
3
2
1
2
0
2
2
2
0
1
1
1
1
1
0
1
1
1
0
1
1
1
0
2
0
0
0
0
1
1
0
2
2
0
2
1
0
1
1
1
2
2
1
2
2
0
1
1
1
1
1
2
1
1
0
1
1
1
1
2
2
0
0
1
1
0
0
0
1
1
2
1
1
1
2
0
1
1
0
0
2
1
1
2
0
0
1
1
1
2
2
1
1
2
1
0
1
2
1
1
3
1
1
1
2
0
1
1
1
1
0
1
1
0
0
1
2
1
1
1
0
1
1
1
0
1
1
1
2
2
2
1
0
0
1
1
2
2
1
0
0
0
0
1
0
1
0
1
1
1
2
1
1
0
2
1
0
1
1
0
0
1
1
1
0
0
1
0
0
1
1
2
0
0
2
1
2
0
1
0
1
1
0
1
1
0
0
1
2
0
2
0
1
1
2
2
0
1
1
1
2
1
1
1
2
1
1
2
0
2
0
1
0
0
2
1
0
2
1
1
0
2
2
0
1
1
0
0
0
0
2
0
1
2
0
1
1
1
1
1
1
1
1
3
1
1
0
1
1
1
1
1
2
2
1
1
1
0
2
1
2
2
0
0
1
1
1
0
0
0
1
2
1
0
1
2
1
0
0
2
1
1
2
0
0
1
1
1
1
1
0
2
3
0
2
0
2
2
1
0
0
1
0
1
0
0
2
0
0
1
3
1
2
1
1
1
1
0
1
2
1
0
1
1
2
2
1
1
0
1
0
1
1
0
1
1
1
1
1
0
1
1
0
0
1
2
1
3
0
0
1
1
1
1
0
0
0
2
1
1
1
2
0
2
0
0
2
0
0
1
1
1
0
1
0
1
1
1
1
0
2
1
2
2
2
1
0
2
0
2
1
0
1
2
1
2
1
1
2
1
1
0
2
0
0
0
0
1
1
1
1
1
1
1
2
0
1
1
2
1
1
2
1
1
2
1
1
1
0
2
1
1
0
2
1
1
2
1
2
0
0
0
1
2
0
0
1
0
1
2
0
1
1
0
1
1
4
2
3
0
2
1
0
1
1
1
0
1
1
1
0
2
1
2
1
1
0
2
2
1
1
2
2
0
1
1
2
1
1
0
0
1
0
1
1
2
1
0
1
2
2
1
1
1
0
0
1
1
2
0
1
1
2
1
0
1
1
1
1
0
1
0
0
0
1
1
2
1
1
1
1
0
0
0
2
0
1
1
1
2
1
2
2
0
1
1
0
1
5
1
1
1
0
0
1
0
2
0
0
0
0
2
1
0
2
1
2
1
2
2
2
1
3
1
1
0
0
1
1
1
1
1
1
0
2
2
1
1
0
1
1
2
0
0
0
2
1
1
2
1
1
1
0
1
1
1
1
1
0
0
1
0
1
1
2
0
1
2
1
1
1
1
0
1
0
1
2
3
1
1
2
0
1
2
1
1
1
1
1
0
1
1
1
1
0
0
0
0
0
1
0
0
2
2
1
1
1
2
1
0
0
1
2
0
1
1
2
0
1
1
1
0
1
2
1
3
1
2
2
1
0
1
1
2
0
1
1
2
1
1
0
2
1
1
1
0
0
1
1
0
1
2
2
1
1
0
2
1
0
1
1
1
0
1
1
0
1
0
0
0
0
1
1
1
2
1
2
3
0
1
1
2
1
1
1
1
0
0
0
1
1
0
0
2
2
0
0
1
0
0
2
0
0
0
0
2
1
0
2
0
1
2
0
2
2
0
0
1
0
0
0
0
2
1
2
2
1
0
0
0
0
0
1
1
1
0
1
2
0
1
1
0
2
1
1
1
2
1
2
2
3
1
1
0
1
1
0
0
0
1
0
0
1
2
2
0
2
1
1
1
1
1
1
1
0
0
1
1
1
1
0
1
0
1
0
0
3
1
0
1
1
0
1
1
2
0
0
1
1
1
0
2
0
1
1
1
1
1
0
1
0
0
0
2
2
0
1
0
1
1
0
1
0
1
2
1
1
0
2
1
0
1
0
1
0
0
1
1
2
1
1
0
1
0
2
2
0
1
1
1
1
1
0
1
1
2
1
2
2
0
2
1
1
0
0
1
0
2
2
1
0
0
0
2
1
1
1
1
1
2
0
0
1
0
2
1
2
2
0
1
1
1
1
1
2
1
2
1
1
0
1
0
0
1
0
1
1
0
1
1
0
1
2
1
2
2
1
1
1
2
2
1
0
1
1
1
0
1
0
2
1
2
0
1
2
1
2
1
1
1
0
2
1
1
0
0
2
2
0
1
2
1
1
0
0
1
0
3
1
0
0
1
1
2
1
1
2
0
2
1
0
0
0
0
0
3
0
0
1
1
1
1
1
0
1
0
0
0
1
1
2
1
0
2
1
1
2
1
0
0
2
1
1
2
0
1
2
1
2
1
1
1
2
1
0
0
1
1
1
1
2
2
1
1
1
1
0
1
1
1
2
2
2
1
1
1
0
2
0
2
1
1
1
1
1
0
1
1
1
2
0
0
0
0
1
0
1
1
0
0
2
1
1
5
0
1
2
1
1
1
1
1
2
1
1
0
2
1
1
0
1
1
1
1
2
0
2
1
1
3
0
1
1
1
0
2
0
0
2
0
1
0
1
1
0
1
1
0
1
0
1
2
0
1
2
0
2
1
0
1
0
0
0
1
2
1
1
0
1
1
0
2
0
2
0
1
1
1
1
0
1
0
3
0
0
1
2
1
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
0
0
0
2
0
1
1
0
0
0
1
2
2
1
2
0
3
1
0
1
1
0
1
1
1
2
1
1
0
1
0
1
0
1
1
1
2
2
1
0
1
0
3
1
0
1
0
1
1
1
2
2
1
1
1
1
1
1
1
2
1
1
0
1
0
0
2
1
1
0
0
1
1
0
1
1
2
1
0
1
1
1
2
1
1
1
2
0
1
2
1
1
1
0
2
0
1
2
1
3
3
0
1
5
1
0
2
2
2
0
0
1
1
1
0
1
0
0
2
1
1
0
2
2
2
1
1
1
1
2
1
0
1
1
2
3
0
2
1
1
1
2
1
0
1
2
0
2
0
1
1
0
1
1
1
1
1
0
0
1
1
0
3
1
1
1
1
2
1
0
0
2
2
1
0
2
1
2
0
0
1
1
2
2
1
2
2
1
1
0
1
3
1
0
1
1
0
0
1
2
0
0
1
2
0
1
0
0
0
0
2
2
2
1
1
2
1
0
2
0
1
1
0
1
1
0
0
1
2
1
1
0
1
1
2
1
2
1
2
2
1
3
0
1
1
0
0
2
0
1
0
0
1
1
1
2
1
1
1
1
1
2
1
1
2
1
0
2
0
1
0
1
2
0
0
1
1
0
0
1
0
1
1
2
1
2
1
1
0
1
1
0
1
0
1
0
0
1
1
1
2
0
0
1
2
2
2
0
0
0
1
2
1
1
2
2
1
1
0
0
1
0
0
2
1
2
1
0
1
1
1
0
1
1
1
1
1
1
0
2
0
0
1
0
0
0
2
0
2
2
2
1
1
0
0
0
2
0
1
1
1
2
0
2
0
1
0
1
1
0
1
0
2
1
1
1
0
1
1
1
1
2
1
1
2
2
0
0
0
0
2
1
1
0
1
2
2
1
1
0
2
0
1
0
0
1
1
0
2
0
1
0
2
1
0
0
0
2
1
2
1
1
0
0
0
1
1
1
1
3
1
1
1
1
1
2
1
2
0
0
2
1
1
2
1
2
0
1
0
2
1
1
1
2
0
2
0
0
1
0
2
0
1
1
1
2
0
1
1
1
2
2
1
0
0
1
1
1
1
0
1
0
1
1
1
1
2
1
0
0
1
1
0
0
1
1
0
0
3
1
1
1
2
1
0
2
3
1
2
1
1
0
2
0
0
1
0
1
1
0
1
1
2
0
2
0
1
1
1
1
1
0
1
1
2
1
0
1
0
0
0
1
1
2
2
2
0
1
2
2
0
1
0
0
2
1
1
1
0
0
0
1
1
3
1
2
0
0
1
1
1
2
1
2
1
1
1
0
2
1
2
1
1
2
1
1
1
0
2
1
2
0
1
1
0
2
0
0
0
1
1
0
1
1
1
2
1
1
1
1
0
1
2
1
1
0
0
1
0
1
0
2
1
2
2
0
2
1
1
1
2
1
0
1
1
2
1
2
1
2
1
1
2
0
1
0
0
1
1
1
1
2
2
1
1
0
1
1
1
1
0
2
1
1
2
1
1
0
1
1
1
2
1
1
2
1
1
0
2
0
0
0
2
1
1
2
0
1
4
1
1
0
2
0
1
2
1
1
1
0
3
2
2
1
2
0
0
2
1
2
1
0
1
1
0
1
1
0
1
2
0
1
2
2
1
1
1
1
0
1
2
2
1
0
1
2
2
2
1
0
0
0
2
1
1
1
1
1
1
0
0
1
1
0
2
0
0
1
0
1
2
1
2
1
0
0
1
0
2
1
1
0
0
0
0
2
2
2
0
1
2
1
2
0
1
2
0
1
1
1
1
0
2
1
0
1
3
1
2
2
0
1
2
2
2
0
1
0
1
2
5
1
0
0
1
1
1
1
0
2
1
0
1
0
1
1
0
1
1
1
1
1
1
0
2
1
0
1
1
1
1
1
2
1
2
0
0
2
1
1
0
1
0
2
2
1
4
1
2
1
1
2
1
1
0
2
1
2
1
1
1
1
1
2
0
0
0
0
0
1
0
2
2
1
2
1
1
1
1
1
0
1
2
1
0
0
0
1
1
0
0
0
0
0
1
0
2
1
1
1
1
1
0
2
1
1
1
1
1
0
2
1
0
1
0
1
0
1
1
1
1
0
1
1
2
0
1
1
2
0
0
1
2
1
1
1
0
1
2
1
2
3
0
1
1
1
2
1
1
1
1
0
1
2
2
1
1
1
2
4
1
1
1
1
0
1
1
1
2
1
1
2
2
1
1
1
1
1
2
0
1
0
2
0
1
1
0
1
1
0
0
1
2
1
1
1
2
1
2
0
1
1
2
2
1
2
0
2
1
1
1
2
2
1
0
2
0
0
2
2
1
0
3
1
1
1
1
1
0
2
2
1
0
0
1
0
1
1
1
1
0
1
2
0
2
1
0
0
1
2
1
1
1
1
0
4
1
0
1
1
1
0
2
0
0
0
1
2
0
1
3
1
1
0
1
0
0
1
2
2
0
0
1
1
1
3
0
1
2
2
1
1
0
2
1
0
1
1
2
1
1
2
1
1
2
1
1
2
1
1
1
2
0
0
2
2
0
1
1
1
3
0
2
0
1
1
1
1
1
0
0
0
2
2
1
0
1
1
0
0
1
1
1
0
2
2
1
2
1
2
0
1
3
2
1
2
1
1
1
1
0
1
1
1
1
0
1
1
2
2
1
1
0
2
1
0
1
3
1
0
1
2
0
2
0
1
0
1
3
3
2
1
1
1
0
1
0
0
2
2
1
1
2
1
1
2
2
1
1
1
3
1
0
0
0
0
0
0
0
0
0
1
2
1
1
1
0
2
2
1
0
0
1
1
0
0
1
0
0
1
2
0
1
2
0
0
1
1
2
2
0
2
0
1
0
2
1
2
2
2
2
1
1
2
1
2
1
1
1
1
2
2
1
1
2
1
1
0
0
0
1
0
1
1
1
1
0
1
1
1
0
0
0
1
0
1
0
2
0
1
0
2
1
1
1
1
2
2
0
2
1
0
2
0
0
2
1
0
0
0
2
0
1
0
1
2
0
0
0
2
0
2
1
1
0
0
0
1
2
2
1
0
1
1
2
1
1
1
1
2
0
0
1
1
2
2
2
0
0
2
0
1
1
1
0
1
0
2
2
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
0
0
1
1
0
1
1
0
1
0
2
1
1
1
2
1
0
1
1
0
1
0
1
1
0
0
1
0
2
1
2
0
1
1
1
0
1
0
0
1
1
1
1
2
1
0
2
0
0
1
0
0
2
0
0
0
1
2
0
1
1
1
2
1
2
1
1
1
1
0
0
1
0
1
1
2
2
1
1
1
2
2
1
2
0
0
2
1
2
0
2
2
0
2
2
2
1
1
2
2
1
2
2
1
1
1
0
1
1
1
0
0
0
1
1
1
0
1
1
1
1
1
1
1
0
2
2
0
1
0
0
0
2
0
0
0
1
1
1
1
0
3
0
0
1
1
2
0
1
1
0
1
0
1
1
1
0
1
1
1
0
0
1
0
2
0
0
0
0
0
0
0
0
1
2
1
2
1
0
0
0
1
1
1
0
0
1
2
0
1
1
2
1
1
0
1
3
1
0
0
1
1
2
2
1
0
0
2
0
0
0
1
1
1
2
0
1
3
1
1
7
1
0
1
0
2
1
1
1
1
1
0
1
1
1
1
2
2
0
1
2
1
2
0
0
1
2
2
0
0
1
2
1
0
0
0
1
1
1
3
0
1
1
1
0
1
1
2
0
0
2
2
2
1
0
0
1
0
1
1
2
2
1
0
1
1
2
1
2
2
0
1
1
0
0
1
1
1
2
0
1
2
0
1
2
0
0
1
0
0
2
0
1
1
1
1
1
2
1
2
0
0
0
2
1
1
1
0
2
0
2
2
0
0
0
1
1
2
1
1
2
1
1
1
1
1
1
3
0
0
1
2
1
1
1
2
1
1
1
1
2
1
1
1
2
1
1
0
0
1
2
1
0
1
1
0
1
1
0
1
2
4
2
1
1
1
1
2
0
1
1
0
1
1
2
0
0
2
1
0
0
0
0
2
1
1
1
6
1
1
0
0
1
0
1
2
1
1
1
1
2
0
0
2
1
2
1
0
1
0
0
1
0
2
0
2
2
2
3
1
0
1
2
2
2
1
0
1
0
2
0
0
1
2
1
0
2
0
0
1
1
1
1
1
1
1
0
1
1
0
1
0
1
1
1
1
1
1
0
0
1
2
1
0
0
1
0
1
1
0
0
2
1
1
0
1
1
1
0
0
1
1
1
1
0
0
0
0
0
0
1
2
2
2
0
1
2
0
1
1
1
2
0
1
1
1
0
1
1
0
1
1
1
2
1
0
1
0
1
0
1
1
1
2
1
1
1
1
0
1
1
1
1
1
0
1
1
0
1
2
1
0
1
1
0
1
2
2
2
0
1
1
1
1
2
1
0
0
0
1
1
0
1
1
0
1
0
0
0
0
2
0
2
2
1
0
1
0
1
0
1
1
0
1
1
2
0
0
1
1
0
1
1
1
1
1
1
0
1
2
0
1
1
0
2
1
0
0
0
0
1
0
1
1
1
3
1
0
1
1
1
2
2
2
1
1
2
0
1
2
0
0
0
1
2
1
2
3
1
1
2
0
1
3
1
0
0
3
2
1
1
0
0
0
1
2
0
1
0
1
0
0
1
2
1
0
0
1
0
0
1
2
2
1
4
0
2
1
2
1
0
1
0
1
1
2
1
0
1
2
0
2
0
1
1
1
0
0
0
2
1
1
0
0
0
1
1
1
1
2
0
1
1
0
1
2
1
1
1
1
0
0
1
2
1
1
0
0
2
1
0
1
1
2
1
0
1
0
1
1
0
2
0
0
0
3
2
1
0
1
1
1
2
2
0
1
1
0
1
0
1
0
1
1
2
1
1
2
0
1
1
0
0
2
0
1
1
1
1
2
0
0
0
1
0
1
0
1
0
0
1
0
2
2
1
1
1
1
0
0
2
0
0
0
2
1
0
1
2
2
1
2
1
2
0
1
1
1
1
0
2
0
1
2
1
1
0
2
1
2
0
1
0
0
1
2
0
0
2
1
0
1
2
1
0
1
0
2
1
1
2
2
0
1
2
1
1
0
1
1
0
0
0
1
0
0
2
2
0
1
1
2
0
0
1
1
0
1
2
1
2
1
1
1
1
1
1
1
0
0
2
1
1
1
0
1
0
0
1
0
0
1
1
2
1
1
0
1
1
1
1
0
0
1
1
0
0
3
1
1
0
1
0
2
0
0
2
2
0
2
1
2
0
2
1
0
1
1
1
0
1
0
0
2
3
1
1
1
1
0
2
1
2
1
1
1
0
2
0
1
2
2
0
2
1
1
0
2
0
1
1
2
2
0
3
0
2
1
1
1
0
1
0
1
1
0
0
0
1
0
1
2
1
0
1
2
0
1
1
1
1
0
0
1
2
0
1
0
1
1
1
1
0
0
2
2
2
2
1
0
0
2
1
0
2
0
1
1
0
2
0
1
1
0
2
2
1
1
2
1
0
1
0
1
1
2
2
1
2
0
2
0
1
0
2
3
1
0
1
1
0
0
2
1
1
1
2
1
1
1
0
1
0
1
2
0
2
1
1
1
0
0
1
0
1
1
2
0
2
1
0
1
2
0
2
0
0
1
2
0
2
1
0
0
2
1
2
1
1
1
1
0
2
1
1
0
0
2
2
2
2
1
0
1
0
0
1
1
0
1
1
1
1
1
2
2
2
1
0
2
1
2
0
0
1
1
1
2
1
2
1
1
1
1
1
1
0
1
1
1
2
1
2
0
1
2
1
2
0
0
2
0
1
0
1
1
2
1
0
1
1
1
2
2
0
0
0
0
1
1
1
1
1
1
0
1
0
2
1
0
1
1
0
0
0
2
2
0
0
1
1
1
3
1
2
2
1
0
1
2
2
0
1
0
1
0
0
2
2
1
1
2
0
0
0
1
2
1
1
0
1
0
1
1
0
0
2
1
1
0
1
0
1
1
1
1
1
2
1
1
0
1
1
1
2
2
1
1
2
1
1
0
0
0
1
2
0
0
2
1
0
0
1
1
1
1
2
1
1
1
0
0
1
2
0
2
1
0
2
1
1
0
0
0
1
1
1
1
0
0
1
1
1
0
0
0
1
2
1
0
2
0
1
1
1
1
1
1
1
1
2
1
0
2
1
0
0
1
0
0
1
2
0
2
1
1
0
1
0
0
2
0
1
0
1
1
1
0
2
0
0
0
0
0
2
1
1
2
0
2
2
2
1
1
1
1
1
2
1
1
1
0
1
0
1
1
1
2
1
2
0
0
1
0
1
1
1
0
1
0
1
2
0
1
1
2
1
1
1
1
1
2
0
0
2
1
0
0
2
1
1
0
1
0
1
0
0
0
1
0
1
1
0
0
1
2
2
2
0
0
2
0
0
2
2
0
1
2
2
2
0
1
0
0
2
2
0
1
1
1
1
2
0
2
0
1
2
1
0
1
1
2
1
0
1
1
1
3
0
1
1
1
0
0
1
1
1
0
2
2
0
2
1
3
1
0
2
2
0
0
1
1
2
1
1
1
0
1
0
1
0
0
2
0
0
0
1
1
2
1
1
0
0
0
1
0
0
2
1
1
2
1
1
1
2
0
2
1
2
0
0
0
2
1
1
2
1
2
1
1
2
1
1
2
1
0
0
2
2
0
1
2
1
1
1
1
2
2
0
0
1
0
1
1
2
1
2
1
1
2
3
1
0
2
1
2
0
2
1
1
1
1
2
1
2
0
1
0
2
0
1
1
1
2
2
2
1
0
0
1
1
1
0
1
2
1
0
1
2
1
1
1
2
1
0
1
1
0
0
1
2
1
0
2
2
0
8
2
0
0
2
1
2
1
2
0
1
0
0
2
0
1
3
1
2
1
1
1
0
2
1
1
2
1
1
1
2
1
2
1
2
0
1
1
2
1
1
0
1
0
1
0
1
1
1
2
2
0
0
2
2
0
1
1
1
0
0
2
1
0
0
0
0
1
1
2
1
2
2
0
1
1
1
0
0
2
1
1
2
3
1
1
1
0
0
0
1
1
3
1
1
1
1
0
2
1
1
1
2
0
1
2
1
2
1
2
1
1
0
2
1
0
0
1
2
1
1
2
1
1
1
0
1
1
0
0
0
0
1
1
0
1
1
0
0
2
0
2
2
0
2
1
1
0
0
1
0
1
1
0
0
1
0
1
1
1
1
0
1
1
2
1
1
0
0
1
1
1
2
2
2
1
2
2
1
1
1
0
1
1
2
0
2
0
1
0
0
0
0
1
2
1
1
1
1
0
0
0
0
0
0
2
1
1
1
1
1
1
2
1
2
1
0
1
2
2
1
1
1
0
1
1
1
0
1
1
1
1
1
1
0
2
0
0
0
2
1
1
1
1
1
0
0
1
1
1
0
2
1
2
0
1
1
0
1
0
2
2
1
1
1
2
1
1
1
2
1
1
2
1
2
2
2
0
1
1
2
1
0
1
0
0
0
0
1
1
0
1
1
0
2
1
1
2
0
2
1
2
1
1
1
0
1
1
2
1
2
0
0
1
2
0
0
2
1
2
1
1
1
1
0
1
1
2
1
2
1
1
1
1
1
0
1
0
1
1
0
2
1
1
2
1
2
2
1
2
1
0
1
1
1
1
1
0
1
0
2
1
2
0
1
1
1
1
1
0
1
0
0
2
0
1
2
1
1
1
1
0
1
0
0
1
0
0
1
2
1
1
0
1
0
0
0
0
0
1
0
0
2
1
1
0
0
1
0
0
2
1
1
0
2
1
2
1
0
2
0
1
1
2
1
0
0
0
1
1
2
1
0
1
0
1
0
2
0
1
0
1
1
1
1
1
1
1
2
2
1
0
1
1
1
0
1
1
1
1
1
0
0
2
2
0
1
1
1
0
1
1
1
2
2
1
1
1
1
0
1
1
1
2
1
1
1
1
1
0
1
0
2
0
0
1
0
0
2
0
1
1
1
1
1
2
1
1
1
1
0
0
1
1
2
1
1
1
2
0
1
2
1
2
0
1
1
2
0
1
1
0
1
0
0
0
1
6
1
0
1
1
1
0
0
0
1
1
1
1
1
0
1
2
1
1
0
0
1
1
1
1
0
0
1
2
1
2
2
0
0
0
1
2
2
1
1
0
0
1
2
0
1
1
0
1
1
2
2
2
1
2
1
0
1
1
0
2
1
1
0
1
0
2
2
1
1
2
1
1
2
1
1
0
2
1
2
0
0
0
1
2
0
0
1
1
0
2
2
0
1
2
1
1
0
2
1
0
0
0
1
1
2
2
2
1
0
1
1
0
1
1
1
2
1
0
1
1
0
1
0
1
0
0
0
1
2
0
1
2
1
1
2
0
2
1
0
2
0
1
0
2
0
2
1
1
0
2
1
1
2
1
1
0
0
2
2
1
1
1
1
1
1
0
2
2
1
0
1
0
0
3
2
0
1
1
0
2
2
2
2
1
1
0
0
0
1
0
1
1
1
1
2
2
1
1
0
0
0
1
0
1
1
1
0
2
2
2
1
0
2
1
1
1
2
1
0
1
1
1
1
0
1
0
2
1
4
1
2
0
0
0
1
1
1
1
2
1
0
0
1
0
0
1
1
1
2
0
1
3
1
1
0
0
0
1
2
2
0
2
0
1
1
1
2
1
2
2
1
1
2
1
1
2
0
1
1
0
1
0
1
1
2
1
0
1
1
3
1
1
0
0
1
2
1
1
0
2
1
1
2
0
0
1
1
1
1
2
1
1
2
0
0
1
1
2
0
1
1
1
2
1
2
1
0
0
2
1
0
2
2
1
1
1
0
0
0
2
0
2
1
0
1
1
1
1
2
1
1
1
1
2
1
1
1
0
1
1
3
2
1
1
1
2
0
2
2
1
2
0
2
0
2
1
0
1
0
1
0
1
1
1
1
1
1
1
1
1
1
2
0
1
1
1
0
0
2
0
1
0
1
1
1
2
1
2
1
1
2
1
1
1
1
1
0
2
1
0
0
3
1
1
1
1
2
0
0
0
1
1
1
1
2
0
2
3
0
1
0
0
1
0
2
2
3
2
0
2
1
0
2
0
2
2
0
0
0
0
1
0
1
2
0
2
0
2
1
1
1
1
0
0
1
1
1
1
1
1
0
2
1
0
1
1
1
1
1
1
2
3
0
1
2
1
2
1
0
1
1
1
1
0
0
1
0
1
0
0
1
0
1
0
1
2
0
0
1
1
1
1
1
1
0
0
1
0
2
1
1
2
1
1
1
1
1
0
0
1
0
1
2
1
1
2
1
0
2
2
1
2
1
0
0
0
3
0
0
2
2
3
0
1
2
2
3
1
1
1
1
1
1
0
4
0
0
1
1
1
1
0
1
1
0
0
1
2
1
1
0
3
0
1
0
1
1
1
1
0
0
2
1
1
1
2
1
0
1
1
1
0
0
1
2
1
1
0
1
0
1
0
0
2
0
1
1
1
1
1
1
0
2
2
1
1
1
0
1
0
2
0
0
1
1
0
1
0
1
0
0
2
1
1
1
2
2
0
1
1
1
2
0
1
0
1
0
1
1
1
3
2
2
0
1
1
2
1
2
2
1
0
1
1
2
2
1
0
1
0
1
1
1
1
1
1
1
0
2
1
1
0
0
1
2
1
1
1
2
1
1
2
2
0
0
0
2
1
1
0
1
1
0
2
2
2
0
1
1
1
0
0
2
1
2
0
2
0
1
1
2
1
1
0
1
2
2
1
1
2
0
2
0
0
0
1
1
0
1
0
0
0
2
1
2
1
1
1
0
1
1
0
1
1
1
0
1
2
0
0
2
1
0
1
0
2
1
1
2
1
2
1
0
0
0
1
2
1
1
1
1
1
1
1
1
0
1
1
2
0
0
1
1
1
1
1
0
1
1
0
2
0
2
1
1
2
1
0
2
0
2
1
1
0
0
2
1
0
0
1
1
0
2
1
0
1
1
1
1
2
1
1
1
0
3
0
1
0
1
0
2
1
1
0
1
1
0
1
0
0
1
1
1
1
1
1
0
1
0
1
0
0
2
0
1
2
2
1
1
0
1
1
1
1
0
1
1
1
1
1
0
1
0
2
1
2
1
0
1
0
0
1
0
2
2
1
0
0
0
0
1
2
0
0
2
1
0
2
1
1
1
0
0
2
1
2
1
0
2
0
0
2
1
1
2
0
0
1
2
1
2
2
0
2
2
0
1
1
1
1
0
0
1
2
2
1
0
0
0
1
2
1
2
1
0
0
1
2
1
0
2
2
1
0
1
1
1
2
1
0
0
0
1
2
1
0
1
1
0
1
1
1
1
1
2
2
1
1
0
1
2
0
1
0
2
1
1
1
1
2
1
1
1
2
2
1
0
2
0
2
1
0
0
0
2
0
1
1
0
1
0
1
0
2
1
1
1
1
0
2
2
1
2
1
1
1
1
3
2
0
1
1
1
1
1
0
1
2
2
1
1
0
1
1
0
2
1
0
1
2
0
0
0
1
0
0
1
2
0
0
1
1
0
2
2
1
2
1
0
1
1
0
2
0
2
1
2
1
1
1
0
1
1
0
1
0
1
1
0
1
1
2
1
1
1
2
1
1
1
1
0
0
1
1
3
1
1
0
1
0
2
2
0
0
0
1
1
2
1
1
1
0
1
1
0
1
1
1
1
1
1
1
3
1
2
0
1
2
0
1
1
2
2
0
0
2
1
2
2
2
1
1
1
1
1
1
0
1
1
2
1
0
1
1
1
2
4
0
2
0
1
1
1
0
1
2
1
1
1
0
2
1
2
1
0
1
1
1
2
0
0
1
1
1
1
2
1
1
1
1
0
1
4
1
0
2
1
0
2
1
0
1
1
1
0
1
0
1
0
1
2
0
1
2
0
0
1
0
1
1
1
0
0
1
1
1
0
1
2
1
1
1
1
0
1
0
2
1
1
0
1
2
2
1
0
0
2
2
0
0
1
1
1
1
1
2
1
1
0
0
2
1
0
1
1
0
0
2
1
1
0
2
1
1
1
1
0
1
2
0
1
0
2
1
0
2
2
1
0
2
1
1
2
1
1
2
0
1
0
0
2
1
2
0
0
0
2
1
0
0
1
1
1
0
0
1
1
0
0
1
0
1
0
1
1
1
0
2
2
1
1
0
1
1
0
1
0
1
1
1
1
0
1
0
1
1
0
1
0
0
0
1
0
1
0
1
3
0
1
1
0
2
2
1
0
1
1
0
2
0
1
2
1
0
1
1
0
2
2
1
2
0
0
1
2
0
0
1
0
0
2
0
2
2
1
0
1
2
2
1
1
0
1
2
1
1
1
0
1
2
2
0
1
0
1
2
1
1
1
2
1
1
1
1
1
2
0
1
1
1
2
2
1
1
0
0
3
0
1
1
2
3
1
1
2
1
0
1
0
1
1
4
0
0
2
0
1
0
1
3
2
1
1
1
1
0
0
1
0
2
2
2
1
0
2
1
1
1
0
1
2
1
0
1
2
2
1
0
1
0
1
1
1
1
1
0
1
1
1
1
1
1
2
2
0
1
0
1
1
1
1
2
0
0
1
1
1
2
2
1
1
2
0
1
2
1
1
1
1
2
1
1
2
1
1
1
0
0
2
0
1
0
2
1
0
2
1
1
0
2
1
2
1
1
0
1
1
0
0
0
0
1
1
0
0
2
0
0
0
0
1
2
0
1
2
1
2
1
1
1
2
0
1
0
1
1
2
1
0
0
1
2
1
1
1
1
2
2
2
0
0
0
1
0
1
0
1
0
1
2
2
0
2
2
2
1
1
2
1
2
0
2
1
2
2
1
0
2
0
0
2
0
1
1
1
0
1
3
1
2
1
1
1
0
0
1
2
0
0
1
1
1
1
1
0
0
1
1
2
1
0
0
5
0
1
1
1
1
2
1
2
1
0
0
1
0
0
1
2
1
2
0
1
2
1
0
1
0
1
1
1
0
2
1
1
0
0
0
0
1
1
1
2
1
1
0
0
2
2
1
2
1
1
1
0
0
0
1
1
1
0
0
0
2
0
0
1
1
1
0
0
0
1
0
0
1
1
1
0
1
0
2
1
0
0
0
1
2
2
1
0
1
0
2
1
1
0
0
1
1
1
1
0
0
1
0
0
2
1
1
1
2
1
1
1
0
0
2
1
1
1
0
1
1
1
2
0
2
1
1
1
1
3
1
1
0
0
1
2
1
1
0
1
0
0
1
1
2
1
2
0
0
0
1
0
2
1
2
0
0
2
1
1
1
2
0
0
2
1
1
1
0
0
0
2
0
0
1
1
0
0
0
1
3
1
3
1
1
0
0
1
1
0
1
1
2
2
1
0
1
1
0
1
0
2
0
2
1
0
0
1
0
1
1
1
0
1
1
0
1
0
2
1
1
0
1
0
1
2
0
1
1
0
1
1
1
1
0
1
2
1
2
0
1
1
1
1
1
1
0
0
0
2
0
2
1
0
2
0
2
0
0
0
1
1
1
2
1
2
1
1
1
0
1
1
1
1
2
0
1
1
1
1
0
1
1
0
2
1
0
0
2
2
0
0
0
1
1
0
2
1
1
1
2
2
0
2
0
1
1
1
1
2
0
2
1
2
1
0
1
0
2
0
1
1
0
1
1
0
0
2
2
1
1
1
2
0
1
2
1
1
1
0
0
0
1
2
2
1
0
2
0
1
2
1
0
0
0
0
1
1
0
1
2
2
2
1
1
0
1
1
2
0
2
1
1
1
1
0
1
0
0
1
3
0
1
1
2
1
1
1
1
0
1
1
0
2
2
1
0
1
1
0
0
2
1
1
1
0
2
2
1
1
2
0
0
1
1
0
1
1
1
1
1
1
2
1
1
2
1
0
1
0
1
1
0
1
2
2
0
1
1
1
0
1
1
0
0
0
1
1
1
1
1
2
2
1
2
1
1
0
1
1
1
0
1
0
2
1
2
2
2
1
2
1
2
2
1
0
0
0
1
0
1
3
2
1
0
1
0
1
0
0
0
1
0
2
0
1
1
1
1
0
1
2
1
1
2
2
1
2
1
0
1
1
0
0
0
0
0
0
1
1
1
1
2
1
1
1
1
1
1
0
3
2
0
0
1
1
1
0
1
0
1
2
2
1
1
2
2
1
1
1
1
1
1
1
0
0
2
1
0
0
1
0
0
0
1
1
2
2
2
2
1
1
1
0
1
1
1
1
0
0
1
0
1
1
1
1
1
2
0
1
2
1
1
1
1
0
2
2
1
1
2
2
2
2
2
1
1
1
0
2
0
1
0
0
2
1
0
0
0
1
1
1
2
1
0
1
1
2
0
0
2
2
2
1
0
0
1
0
0
2
3
1
1
0
2
1
2
0
2
2
1
1
1
0
0
1
1
2
1
1
1
1
2
1
0
1
1
0
1
1
1
2
2
0
1
1
1
0
0
2
0
0
0
1
0
1
0
3
0
2
1
1
1
2
0
1
0
2
0
0
1
2
1
1
2
0
1
1
2
1
0
1
1
1
2
1
2
1
1
0
2
1
1
2
0
0
0
1
1
1
2
1
2
0
2
1
0
1
0
0
1
1
2
0
1
1
1
2
0
0
2
2
1
1
1
0
1
2
1
1
2
0
0
1
0
1
0
0
1
0
1
0
0
0
1
1
1
0
1
2
0
2
1
2
1
1
2
1
1
1
1
2
1
0
1
1
2
0
0
1
2
0
0
0
1
1
1
1
1
1
0
0
0
1
1
0
1
0
0
2
1
1
1
1
1
1
1
1
2
2
1
0
1
1
1
0
1
1
0
0
0
1
0
2
1
0
0
2
1
1
1
1
1
2
1
1
1
2
0
2
2
0
1
1
1
2
0
0
0
2
1
0
1
1
1
3
0
1
1
1
1
2
1
2
0
1
1
3
1
1
1
1
1
0
1
0
0
4
1
0
2
0
3
0
0
1
2
1
0
0
0
0
0
1
1
2
1
1
2
1
1
2
1
2
0
1
2
0
2
1
0
0
1
2
1
0
0
2
3
1
1
1
1
0
1
0
0
1
1
0
2
0
1
1
1
1
1
0
2
0
1
1
0
2
1
0
1
1
1
1
1
2
1
2
1
1
1
1
2
1
1
2
2
2
1
1
0
2
0
1
1
1
1
1
2
1
1
2
0
1
0
1
0
1
1
0
2
1
1
2
1
1
1
1
1
0
0
0
1
2
5
0
1
1
1
2
0
1
2
1
0
1
0
0
2
1
2
1
0
1
1
1
2
2
0
0
2
1
1
1
1
2
1
2
2
1
1
1
0
1
2
1
0
0
1
1
0
1
1
1
2
1
1
0
2
0
1
2
1
2
1
0
1
2
0
1
2
2
0
0
1
1
1
1
0
1
1
1
0
1
0
1
0
2
1
2
2
1
1
2
1
2
1
4
0
1
2
1
1
2
0
1
1
1
1
1
0
1
1
1
1
0
1
0
0
1
2
1
2
2
0
1
0
5
2
1
2
1
0
2
2
2
1
2
2
2
1
2
2
0
1
1
0
1
0
1
2
0
2
1
0
2
0
2
2
1
0
1
2
1
2
1
2
1
1
2
2
1
1
0
1
0
1
1
1
1
2
0
1
0
3
1
1
1
2
1
1
0
0
1
1
1
0
0
0
2
1
2
1
1
1
1
1
1
1
0
0
0
1
1
2
1
1
0
1
0
0
1
1
1
0
1
1
2
1
0
0
1
1
1
0
1
2
1
0
1
0
0
2
1
2
1
2
2
0
0
1
2
1
1
2
0
1
0
2
1
1
2
2
1
1
0
1
1
0
1
2
1
1
0
1
1
0
0
1
1
2
2
1
1
0
1
0
2
1
1
1
0
1
2
2
0
0
1
1
1
0
1
1
1
0
1
1
1
1
0
1
1
1
2
1
5
1
1
1
0
1
1
1
1
0
1
2
1
1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
0
1
0
1
1
1
0
1
0
1
0
1
0
1
1
0
1
2
1
0
1
0
2
2
2
0
2
2
1
1
1
1
2
2
2
1
1
1
1
0
1
1
1
0
0
1
0
1
0
1
0
0
1
2
2
2
1
1
1
0
0
1
1
1
0
1
0
0
2
2
2
2
0
0
1
1
0
1
1
0
1
0
1
0
0
1
1
0
1
1
1
2
0
1
1
1
1
0
0
1
1
1
1
1
1
1
1
2
1
1
2
1
1
0
0
2
3
1
1
0
1
0
0
0
0
0
0
0
0
0
1
1
2
1
1
2
1
1
1
0
1
1
1
1
1
1
1
2
2
2
1
2
0
0
1
0
0
2
2
1
0
0
0
0
1
1
1
1
1
0
1
1
0
0
0
1
2
1
0
0
1
1
1
0
1
1
1
0
0
0
1
1
2
0
1
2
1
1
2
1
0
0
1
1
1
2
2
0
0
0
1
1
0
2
1
1
2
1
3
1
1
0
0
1
0
0
1
1
1
0
3
2
2
1
0
1
1
1
1
1
1
2
1
0
1
1
1
0
1
1
1
0
0
1
1
0
0
0
2
1
1
2
2
0
1
0
2
1
2
1
1
2
1
1
1
0
1
0
0
2
1
2
0
1
2
1
2
1
0
0
1
2
1
2
1
2
2
0
0
1
1
1
1
2
1
0
2
0
0
2
0
0
1
0
1
1
0
0
0
3
0
0
1
1
0
1
1
0
1
1
2
0
1
1
1
2
0
0
0
0
1
2
0
1
0
2
0
2
1
1
1
2
0
1
0
2
1
2
1
1
2
2
2
1
1
2
0
1
1
2
2
0
0
1
0
0
0
1
0
1
2
0
1
1
1
1
0
0
1
2
1
3
0
1
1
1
1
1
0
1
1
1
2
1
0
1
0
1
1
2
1
1
0
1
1
2
0
0
0
0
1
0
1
1
1
1
1
2
1
1
2
0
1
1
0
0
0
1
1
1
1
1
1
2
2
1
1
0
1
1
1
1
1
0
1
0
2
0
2
2
0
1
0
0
0
1
0
1
0
1
2
1
0
1
1
1
0
1
0
2
0
1
2
0
1
1
0
0
2
1
0
0
1
1
1
0
1
1
1
0
3
1
1
2
2
1
0
1
1
2
1
1
0
1
1
0
1
1
1
2
1
1
1
1
1
0
1
1
1
1
0
2
1
1
2
1
0
0
0
1
1
1
1
2
2
0
0
3
0
1
2
1
1
0
1
1
1
1
2
1
1
0
2
0
0
1
1
2
1
0
1
0
1
1
2
1
0
0
0
2
1
1
1
2
2
0
1
0
1
0
0
1
2
0
0
1
2
2
1
1
1
1
1
0
0
1
1
1
2
2
1
0
1
0
1
1
0
2
1
3
1
0
1
0
2
1
2
2
1
1
0
1
0
1
1
2
1
2
1
1
1
2
1
1
1
2
2
2
0
1
2
1
3
2
2
1
2
2
2
2
2
1
1
1
2
2
2
1
2
1
1
0
0
0
1
1
0
0
1
0
0
1
0
1
0
1
1
1
2
1
1
0
0
1
0
1
2
0
1
1
0
1
2
1
0
2
1
0
0
0
2
0
0
2
2
1
0
2
1
1
1
2
0
2
1
0
2
0
1
1
1
1
2
1
0
1
1
1
0
2
1
1
1
0
1
1
1
2
1
0
1
2
0
2
2
2
0
1
0
1
0
1
1
0
2
1
1
1
0
0
1
0
1
1
2
2
1
1
0
1
0
1
2
1
0
1
0
2
0
1
1
2
1
0
1
1
0
2
2
0
1
0
0
0
1
0
0
1
1
2
1
2
2
1
4
1
0
2
1
2
1
1
1
1
1
0
1
2
1
0
4
2
1
1
0
0
1
1
1
0
1
2
1
1
2
1
1
1
3
1
0
1
1
1
0
1
0
0
1
1
1
0
1
2
1
1
1
1
1
0
1
0
0
1
1
0
2
0
2
1
2
2
1
1
2
1
1
1
3
0
1
0
0
0
0
0
1
1
1
1
1
1
1
1
0
2
1
0
2
0
3
1
1
0
1
1
0
0
1
0
2
1
0
1
0
0
0
1
1
2
0
3
0
1
1
2
2
1
0
2
1
2
0
2
1
1
2
1
1
1
1
2
1
1
1
0
1
2
1
2
0
0
1
0
1
4
1
1
0
0
1
2
2
1
1
0
0
1
1
1
1
2
2
1
1
1
2
1
0
1
1
1
1
0
1
0
1
1
0
1
2
1
1
0
2
0
0
3
1
0
1
2
1
1
2
0
0
0
2
3
0
1
2
2
0
1
2
1
0
1
1
1
2
2
0
1
1
2
0
1
2
1
2
1
1
1
2
2
0
1
1
3
1
1
0
2
0
0
2
0
1
2
1
2
1
0
0
1
1
0
1
1
0
0
1
2
1
1
0
1
0
1
1
0
1
1
2
2
1
0
1
1
2
0
0
2
2
0
2
0
1
1
0
1
0
2
0
0
1
0
0
2
2
1
2
1
1
0
3
1
0
2
1
2
2
2
1
2
0
0
1
0
0
1
1
0
1
1
1
0
1
0
1
1
1
2
0
1
1
1
1
2
1
0
0
1
1
1
2
1
1
0
1
2
1
1
2
2
2
2
0
1
1
1
1
2
0
1
0
1
1
0
1
1
2
1
1
1
1
2
0
1
1
2
1
1
1
1
0
1
1
0
1
1
1
1
1
1
2
2
1
0
0
1
1
1
1
1
0
2
0
1
1
2
2
1
1
1
0
2
0
0
1
1
0
1
1
2
0
1
1
2
1
1
2
0
1
0
2
0
2
1
1
1
0
0
1
2
2
0
1
1
0
1
0
1
0
1
2
1
2
1
1
1
1
2
0
1
4
1
2
0
1
1
1
1
1
1
1
2
1
1
0
1
2
2
1
1
2
0
0
1
0
1
0
0
2
2
2
0
1
1
2
1
0
1
0
2
1
1
0
1
1
1
1
1
2
1
2
2
1
1
0
1
1
2
1
0
2
1
2
2
2
1
2
2
1
0
1
1
2
1
0
0
0
0
2
1
0
1
1
0
1
1
0
2
2
1
0
0
1
0
1
1
1
2
0
1
4
1
1
1
0
1
1
2
0
0
0
1
2
2
1
0
1
2
0
0
2
1
2
0
0
1
1
0
0
1
1
1
2
1
0
0
1
0
0
0
1
0
2
2
0
1
0
0
0
1
1
1
0
1
0
1
0
1
1
0
2
0
1
0
0
1
1
0
0
0
1
1
1
2
0
1
1
0
1
1
1
2
1
1
1
1
0
1
0
0
0
3
1
1
1
1
0
1
2
1
0
2
1
2
0
0
1
1
0
2
1
1
0
1
0
1
0
1
1
1
0
0
1
2
3
2
2
1
2
1
1
2
0
1
0
0
2
2
4
1
0
1
2
1
0
0
1
1
1
0
0
1
1
1
2
0
1
1
0
1
0
0
1
1
0
2
1
1
1
2
1
1
1
1
1
1
1
1
1
0
1
2
2
1
1
0
2
1
0
1
1
1
1
0
0
2
0
2
2
2
0
2
1
3
2
1
1
0
1
2
1
1
1
0
1
0
1
1
1
1
1
0
1
1
1
2
1
0
1
0
1
2
1
1
0
2
0
2
1
1
0
1
0
2
1
1
1
0
1
1
2
0
0
0
1
1
0
0
1
0
0
2
0
1
1
0
2
2
1
1
0
1
1
0
2
0
1
1
1
2
2
2
0
0
1
1
1
2
0
2
1
2
1
0
1
0
1
0
1
1
0
1
2
2
0
1
0
0
0
0
0
1
3
1
1
0
0
2
0
1
1
0
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
0
1
1
2
0
1
1
0
0
0
1
1
2
1
1
2
1
1
2
1
0
0
1
0
2
2
1
1
1
1
1
1
1
1
2
1
1
0
2
1
0
0
1
0
1
1
1
1
0
0
1
1
0
0
0
2
1
2
0
2
1
0
0
2
2
2
1
1
0
1
0
2
2
0
0
1
0
1
1
0
1
1
0
0
2
1
1
0
2
1
1
2
1
1
0
2
5
1
0
2
2
1
2
0
2
1
2
1
0
1
1
2
1
1
1
1
2
1
1
1
1
0
1
1
2
0
1
2
1
1
0
0
0
0
1
1
0
0
2
1
1
2
1
0
1
1
1
1
0
1
2
0
1
1
0
1
2
2
2
0
1
0
0
2
0
2
1
2
2
0
0
1
0
1
2
1
1
1
2
1
1
1
1
2
0
2
1
1
2
1
0
0
1
1
4
0
0
1
2
2
0
1
1
1
2
1
1
2
1
2
2
1
0
0
1
0
1
1
0
0
0
0
1
1
0
0
1
2
1
1
0
1
1
0
2
2
2
2
2
1
2
2
0
2
1
1
0
1
1
0
2
1
1
1
1
1
1
0
1
1
0
2
0
2
2
0
1
1
1
1
1
0
0
1
1
1
1
1
0
0
2
1
0
2
1
0
2
1
2
1
0
0
2
1
0
0
0
1
2
1
2
0
0
1
0
1
1
0
1
2
1
3
2
2
0
1
0
0
2
1
2
2
2
0
2
1
1
1
3
1
1
1
0
0
1
0
0
0
2
2
0
1
0
1
0
1
1
2
2
0
0
1
1
2
0
2
1
1
0
1
1
2
0
1
1
2
0
1
2
1
1
1
2
1
1
1
0
0
1
1
1
1
0
1
1
0
2
1
2
1
1
1
1
0
2
3
1
1
0
1
2
1
1
0
1
1
0
1
0
1
1
0
2
0
1
0
2
1
0
1
1
0
1
2
0
2
0
1
0
2
1
2
1
1
0
1
2
0
0
1
1
1
0
2
1
1
2
2
2
2
0
1
0
0
0
1
1
0
1
1
2
1
0
0
0
2
1
1
1
0
1
0
2
1
2
2
2
1
0
1
0
1
1
1
1
0
1
1
0
2
1
0
0
1
2
0
2
1
1
1
2
0
1
2
1
1
0
0
2
2
2
2
2
0
0
0
2
1
0
2
0
1
0
2
0
1
1
2
0
0
2
1
1
2
1
1
0
1
1
0
1
1
1
2
2
1
2
0
1
0
0
0
0
0
1
2
0
1
1
1
1
1
0
2
1
0
0
0
0
1
1
1
1
1
1
2
1
0
0
1
1
1
2
0
1
0
1
1
2
0
0
2
1
0
2
1
2
0
1
0
1
2
0
1
2
2
0
1
1
1
1
0
1
2
0
0
0
0
1
1
0
1
2
0
1
3
0
0
2
2
0
0
0
2
1
2
1
0
0
1
2
1
2
2
2
0
1
1
0
1
1
0
2
1
1
2
0
1
0
0
1
1
1
1
1
0
1
1
1
1
0
0
1
0
0
0
0
1
1
1
1
1
0
0
6
0
0
1
2
1
0
2
2
0
2
1
0
2
1
2
1
1
1
2
2
0
1
1
0
0
2
0
1
1
1
0
2
2
2
0
1
1
2
0
1
1
0
0
2
1
0
1
0
0
0
2
1
1
1
1
1
1
3
1
2
1
1
0
0
2
0
0
0
1
0
1
1
1
0
0
2
1
0
0
1
1
2
1
0
1
0
2
0
1
1
1
0
1
1
1
1
1
1
1
2
1
1
2
1
1
0
1
2
1
1
0
1
1
0
2
1
1
1
0
0
1
0
1
1
2
1
1
1
0
2
2
0
0
1
1
1
2
0
1
2
1
2
0
0
1
1
1
0
1
2
1
0
0
0
2
0
1
0
0
1
2
1
0
1
1
2
1
2
1
0
1
1
3
0
2
2
1
1
1
1
0
1
2
0
2
0
1
1
0
0
1
1
0
1
0
2
1
0
0
1
1
0
1
0
1
1
1
1
2
1
0
2
1
0
2
0
0
1
0
0
1
1
3
0
1
2
0
0
1
1
0
2
0
1
1
1
0
2
1
1
1
1
0
2
1
1
0
1
1
1
1
1
2
1
1
2
1
2
0
2
2
2
1
2
1
0
2
1
1
1
2
1
2
0
0
1
1
2
1
1
2
1
0
2
1
1
2
2
4
1
3
1
0
1
0
2
0
0
1
1
0
1
1
0
0
2
1
0
0
0
1
0
1
2
1
1
1
1
1
1
2
2
1
2
2
1
1
1
1
1
0
0
0
0
0
0
2
1
1
1
1
1
1
0
1
2
1
0
0
0
1
1
0
1
1
1
0
0
1
0
2
1
0
1
1
1
0
1
1
1
1
2
1
0
1
0
0
2
1
1
2
1
0
1
1
0
2
1
0
1
1
0
1
0
1
1
1
1
0
1
1
1
1
2
2
1
1
2
1
1
1
1
2
0
0
2
3
1
1
1
2
2
2
1
1
1
1
1
2
1
0
1
0
1
0
3
0
1
1
1
0
2
2
1
0
1
2
1
1
1
1
1
0
1
1
1
1
1
1
0
2
1
1
1
1
1
0
1
1
0
2
1
1
2
1
0
1
0
0
0
0
0
1
2
1
1
1
0
1
1
0
1
1
0
2
0
2
1
1
1
1
2
1
0
2
1
0
0
0
0
1
0
0
1
0
1
1
2
2
1
1
2
0
1
0
2
0
1
0
1
1
1
1
2
1
0
2
1
1
1
1
0
1
0
1
1
0
2
1
2
1
1
0
0
0
1
0
1
0
1
0
0
1
2
0
1
0
0
0
0
1
2
0
0
0
0
2
1
1
1
1
1
1
0
0
2
1
1
1
1
1
2
1
1
0
0
0
0
1
2
0
2
0
0
1
1
2
1
1
1
1
1
1
2
1
0
1
1
1
0
0
1
1
1
0
1
1
2
0
1
2
1
0
1
1
1
2
0
1
0
1
0
2
1
0
0
0
0
0
0
1
1
1
0
2
1
1
0
1
0
1
1
1
1
1
1
1
3
1
2
2
1
1
2
2
0
2
1
1
0
0
1
2
1
1
0
1
1
2
1
0
0
0
2
1
2
1
1
2
0
2
0
1
2
1
1
1
0
1
0
0
1
0
0
0
0
1
2
0
1
0
1
1
1
2
2
0
0
0
0
0
1
1
0
1
0
1
2
1
1
2
1
2
0
1
1
1
0
0
0
1
0
2
1
2
1
1
1
2
0
2
0
1
0
2
1
0
1
1
2
1
1
1
0
1
1
0
0
1
0
0
1
0
2
0
1
2
2
0
1
2
0
0
2
1
1
1
2
1
1
0
2
2
0
1
1
0
1
2
4
1
2
0
0
1
1
0
1
1
1
0
1
0
2
0
2
1
2
1
0
1
1
1
1
0
1
0
0
1
0
0
1
1
1
1
1
0
1
1
1
0
0
1
1
1
2
0
1
1
0
1
2
3
2
2
1
1
1
1
0
2
0
2
0
2
0
1
0
1
2
1
3
1
1
2
0
1
1
1
2
2
1
2
1
2
2
1
0
1
1
2
0
1
0
0
1
2
0
1
1
0
0
0
1
2
2
1
0
1
2
0
0
1
2
1
1
2
0
0
0
2
2
1
1
1
2
0
1
0
1
1
2
1
0
1
1
1
1
0
2
1
1
1
2
1
0
0
0
1
0
1
2
2
1
1
1
2
0
1
1
1
1
3
0
0
1
0
2
0
1
1
0
0
1
1
0
1
2
0
2
2
0
1
2
2
1
1
0
1
1
2
2
2
2
2
1
1
1
1
1
0
0
1
1
1
1
0
2
0
1
1
1
1
2
0
0
1
1
0
1
1
1
1
1
2
1
1
0
2
0
0
0
1
0
1
0
2
1
2
2
1
0
0
0
0
1
0
0
1
0
2
0
1
1
1
2
2
1
1
0
1
1
1
1
1
2
1
1
1
0
1
1
0
2
2
1
0
1
0
2
2
1
2
1
2
1
1
1
1
0
1
1
0
1
1
1
2
1
1
2
1
0
1
0
1
2
0
0
1
1
1
0
0
1
1
2
0
0
0
2
1
1
1
1
1
1
1
2
2
2
1
1
1
1
0
1
0
0
2
0
0
1
1
2
2
0
1
1
1
0
0
3
0
1
1
2
1
1
2
1
1
1
1
1
0
0
1
1
2
1
0
0
1
0
2
1
0
0
0
2
1
0
1
1
1
2
1
1
1
0
2
0
1
1
2
0
1
0
1
1
1
2
0
2
1
2
1
1
0
1
1
2
0
0
0
0
2
0
1
1
0
1
0
1
2
1
1
0
1
1
0
2
0
1
1
1
2
0
0
1
0
0
1
4
0
1
1
2
1
1
1
2
0
1
1
1
0
1
1
1
0
1
1
2
0
0
2
1
0
2
1
2
1
1
1
1
0
1
1
1
1
0
2
2
1
1
1
0
1
0
1
0
1
0
0
0
2
0
0
1
0
1
1
2
0
1
1
0
1
2
2
2
1
1
1
0
0
2
1
0
1
0
1
1
1
1
0
2
1
1
1
1
0
1
0
0
1
0
2
1
1
0
2
1
1
1
4
1
1
0
1
2
1
0
1
1
0
1
1
2
2
0
1
2
0
0
1
2
1
1
2
1
2
1
1
1
0
2
2
0
0
2
2
1
1
0
0
1
1
0
2
0
1
2
2
2
1
1
2
1
0
3
0
1
0
1
1
1
0
2
1
1
1
2
0
2
1
1
1
0
2
0
1
1
0
1
3
2
0
1
1
2
0
2
0
1
0
1
0
2
0
1
1
1
2
0
0
0
0
1
1
1
1
0
1
2
1
1
3
1
1
0
1
0
1
1
0
0
0
0
0
1
0
1
1
1
1
0
0
2
1
1
1
1
1
1
2
0
2
0
0
1
2
1
0
2
1
2
0
1
1
0
0
0
1
1
2
0
1
1
2
1
1
0
0
0
1
2
0
1
0
1
0
1
1
1
0
0
2
1
0
3
1
0
3
1
0
0
1
0
0
0
1
1
0
2
1
0
1
1
1
1
1
1
2
1
1
0
1
1
0
0
1
1
0
0
0
2
2
2
1
1
0
1
0
1
0
1
1
0
0
2
1
1
0
0
0
0
1
0
1
1
0
1
0
1
1
1
2
0
0
1
2
0
1
3
1
1
2
1
1
1
2
0
0
0
0
1
1
2
1
1
1
2
1
0
0
1
1
1
2
1
2
0
0
0
1
1
2
0
2
0
2
0
2
0
1
0
0
1
1
0
2
2
0
1
0
0
2
1
1
2
1
1
1
1
0
0
2
0
0
1
1
2
0
2
2
1
0
1
0
0
1
1
2
1
1
0
0
0
1
0
1
2
2
1
1
2
1
1
1
1
0
1
0
1
1
2
3
0
1
1
2
0
2
1
2
1
2
0
0
0
1
2
1
1
2
0
2
1
2
0
1
1
1
1
1
2
1
1
2
1
0
0
0
1
1
1
1
2
1
1
1
1
2
2
1
1
1
1
2
0
0
2
1
1
0
0
1
2
1
1
1
2
2
1
1
0
2
1
0
1
1
2
0
1
1
1
1
1
1
1
1
0
1
2
0
1
1
2
1
2
0
1
1
2
1
1
0
2
1
2
0
1
1
0
2
0
0
1
0
0
1
1
0
1
0
0
0
0
2
1
0
1
1
1
2
0
2
1
1
1
2
1
2
2
0
1
1
1
2
1
1
3
0
1
0
0
1
1
2
1
1
1
0
3
0
0
2
2
1
1
0
1
2
0
0
0
1
0
1
0
1
1
2
0
2
1
2
1
1
3
0
1
0
2
1
0
1
0
2
1
1
1
1
1
1
0
0
2
1
2
2
1
0
0
1
1
1
1
0
1
2
0
0
0
1
0
2
1
1
1
1
2
1
1
0
3
0
0
1
1
1
1
1
0
1
2
0
1
2
1
1
2
0
1
2
1
1
2
1
3
0
1
0
2
1
2
2
2
1
2
0
1
0
1
1
1
0
0
0
2
1
1
2
1
1
1
1
0
0
1
1
0
2
0
1
1
0
2
0
1
1
1
1
0
2
1
1
2
1
2
2
2
0
1
1
2
1
4
1
1
1
1
2
0
1
0
2
1
1
2
1
1
0
2
2
1
0
1
1
1
1
1
1
1
0
0
1
1
2
1
1
0
0
1
1
1
0
1
1
1
2
1
2
0
1
0
0
0
0
2
1
0
0
1
0
1
0
0
0
0
2
3
1
1
1
1
0
0
1
2
1
2
1
2
1
1
3
1
1
2
1
2
1
1
0
2
1
2
1
1
0
1
0
2
1
1
1
0
0
1
2
1
1
2
2
1
1
1
2
0
1
1
1
0
1
1
4
1
0
1
1
1
1
2
0
1
0
1
1
2
0
0
1
0
0
1
1
2
0
1
1
1
0
0
1
1
2
1
1
1
1
1
2
1
1
2
0
0
1
0
1
0
1
2
1
1
0
1
7
1
0
1
2
1
2
2
2
0
1
0
2
0
1
1
1
2
0
0
1
1
3
3
2
1
2
1
1
0
1
0
1
1
2
0
0
1
0
1
2
0
1
2
1
1
2
0
1
1
1
0
2
1
2
1
2
2
1
0
1
1
1
0
1
1
2
1
0
2
2
1
1
1
1
1
1
1
2
1
1
0
2
1
2
2
0
1
1
1
1
2
1
1
1
1
1
1
0
1
0
0
1
1
1
0
1
0
1
2
0
0
2
0
1
0
0
1
1
1
1
0
2
1
0
0
1
0
1
0
1
1
0
1
1
0
1
4
1
2
1
1
0
0
0
1
1
2
2
0
1
1
1
1
2
1
2
1
1
0
1
2
1
1
1
1
1
0
0
1
0
1
2
2
1
1
0
1
2
1
2
1
1
1
1
2
2
1
0
1
1
0
1
2
2
2
2
1
1
1
1
0
2
1
1
2
1
2
0
0
1
1
1
0
2
1
0
2
2
0
1
1
2
0
0
2
1
1
1
0
1
0
1
2
1
0
1
1
2
1
1
2
2
1
2
1
0
1
0
0
0
1
0
1
1
0
0
1
2
1
1
1
1
0
2
0
1
1
1
1
1
2
0
0
2
0
1
0
2
1
0
0
1
1
0
0
4
1
1
1
2
0
0
1
1
1
2
2
0
2
2
0
1
0
1
1
1
1
1
1
2
1
1
1
0
1
2
2
0
1
1
1
0
0
1
0
2
2
1
3
1
2
1
1
1
1
1
2
0
1
0
2
1
1
0
2
0
0
1
1
2
0
1
2
1
1
0
1
1
0
1
1
1
2
1
0
0
0
1
2
1
1
2
1
0
0
1
1
1
0
1
1
2
0
2
1
2
0
2
0
2
1
1
1
1
2
1
0
0
2
0
0
1
0
1
1
0
1
1
1
0
2
2
1
0
1
0
0
2
0
0
1
0
1
0
1
0
1
0
0
1
1
2
0
1
2
0
0
2
2
2
2
0
1
1
0
1
0
1
1
0
2
0
0
1
1
2
1
0
2
1
0
0
0
0
2
1
0
1
1
1
2
0
1
1
2
2
1
2
2
2
0
1
0
1
2
2
1
1
1
2
2
0
0
1
2
1
1
3
1
0
0
1
0
1
1
1
1
0
1
1
2
1
0
1
0
1
2
0
1
2
2
1
0
0
1
1
1
0
1
0
0
1
0
1
2
1
1
1
1
0
2
0
1
0
1
2
0
0
1
1
1
2
1
2
0
1
1
1
1
1
2
0
2
2
1
2
1
2
1
3
0
1
0
1
0
1
2
0
1
1
1
2
0
1
1
1
1
2
1
1
2
3
1
1
1
0
1
1
0
1
0
0
0
2
2
1
1
2
1
0
0
3
1
0
2
1
0
0
1
1
1
1
1
0
2
1
2
0
1
2
2
1
1
1
2
0
1
2
1
2
2
1
2
1
0
3
0
1
1
2
1
0
0
1
0
1
1
0
0
0
0
1
1
1
2
2
2
0
1
0
1
1
0
1
2
1
1
2
1
0
1
1
1
1
1
1
1
0
0
3
3
0
1
1
1
1
0
1
1
1
0
0
1
1
1
1
2
0
0
3
1
2
1
0
0
2
1
2
1
0
1
0
0
1
2
0
0
1
1
1
1
1
2
1
1
1
2
0
1
2
1
0
0
3
1
2
1
0
3
0
2
1
0
1
1
2
1
1
1
1
0
1
0
2
0
2
1
1
0
1
0
1
2
1
1
0
1
0
1
1
1
1
2
1
1
2
1
0
0
1
1
0
0
1
1
1
0
1
1
1
3
1
0
1
2
1
1
0
0
1
1
1
2
0
1
0
1
1
0
1
0
1
2
0
2
2
1
2
2
1
0
1
1
0
0
0
3
1
3
0
0
2
1
0
1
3
0
0
1
0
1
0
1
0
2
1
0
0
1
0
2
0
1
2
0
2
0
1
1
1
0
1
2
2
0
1
1
2
0
1
2
2
0
0
0
1
1
1
0
1
1
0
2
2
0
1
1
1
0
2
1
1
1
0
1
2
0
1
1
0
1
1
3
2
0
1
1
1
2
2
1
1
1
1
0
0
1
1
2
1
0
0
1
0
0
1
1
0
0
1
1
1
2
0
2
1
0
1
0
1
1
2
2
2
1
0
2
2
1
1
0
1
2
0
1
2
0
0
1
1
2
1
1
1
1
2
1
0
0
2
0
1
1
1
1
2
1
0
1
1
0
1
2
0
1
1
1
2
0
0
2
0
1
2
2
3
2
1
0
0
0
0
0
0
1
2
1
1
1
1
2
1
1
2
1
1
1
2
0
1
1
0
1
0
0
1
1
2
1
1
1
1
1
0
0
1
1
1
2
1
0
1
1
0
1
1
0
1
1
1
0
0
1
1
1
0
2
1
1
1
2
1
1
1
1
1
0
0
2
2
1
1
0
1
2
1
1
2
0
1
1
0
1
2
1
1
2
0
1
1
1
2
1
1
2
2
0
1
0
1
0
1
2
1
1
1
2
0
1
1
2
1
2
1
1
0
0
1
2
0
2
2
1
1
2
1
2
0
1
0
1
1
0
2
1
2
1
1
1
1
0
1
2
1
1
1
1
1
0
0
0
2
0
6
0
2
1
1
0
1
1
2
0
1
0
1
1
2
0
1
1
1
0
0
0
0
1
0
0
1
2
1
0
2
0
1
1
1
0
0
2
2
1
2
2
2
1
1
0
2
1
1
2
1
1
1
1
1
1
2
2
1
1
2
0
1
1
1
1
1
2
1
1
1
1
0
1
0
2
0
1
2
2
1
0
1
0
1
1
0
1
0
1
0
0
1
1
1
2
1
1
0
0
2
0
0
1
0
1
1
1
0
3
0
1
2
2
1
1
1
1
1
1
1
1
0
1
0
1
1
1
1
2
2
1
1
2
0
1
1
1
1
1
1
2
0
2
1
0
2
2
2
1
1
0
0
1
1
0
2
0
0
1
1
0
1
1
2
1
1
1
0
1
1
1
0
1
1
1
0
1
2
0
0
1
1
1
1
1
0
1
0
0
2
1
0
1
1
1
1
2
1
0
0
0
1
0
1
1
1
1
0
2
1
0
1
2
2
1
1
1
0
1
0
2
1
1
1
1
2
2
2
1
1
0
1
2
2
0
0
1
0
1
0
2
0
0
2
1
1
1
2
2
3
1
0
2
1
1
1
1
2
2
1
0
2
0
2
1
1
1
1
0
0
1
0
2
1
1
1
1
1
0
1
1
0
1
0
1
1
1
1
2
2
1
1
2
1
2
4
0
1
2
2
1
1
2
1
1
0
0
1
0
0
1
2
0
0
1
0
0
3
2
1
1
0
2
1
0
2
1
1
0
0
2
2
1
0
0
2
1
2
0
1
0
1
2
1
1
1
1
0
1
2
1
0
0
0
2
2
0
0
1
1
0
1
1
1
2
1
1
2
0
0
0
1
1
2
1
1
2
0
1
0
1
1
1
2
1
0
1
0
0
2
1
2
1
1
0
0
1
1
1
1
2
0
1
2
1
0
1
2
1
1
0
1
1
1
1
1
2
1
0
1
0
1
1
1
2
2
0
0
2
2
0
1
1
2
2
1
2
1
1
0
1
1
1
0
0
2
1
1
0
1
1
1
0
1
2
0
1
0
0
1
0
0
1
0
1
1
2
1
1
2
1
0
2
1
2
1
2
0
1
2
1
1
2
0
1
1
0
1
0
0
1
1
1
0
0
2
1
0
2
1
1
1
1
1
0
1
1
1
1
2
1
0
2
1
0
0
1
2
1
0
1
0
2
1
1
1
2
2
0
0
1
2
1
1
1
1
2
2
1
0
0
0
0
2
0
1
1
1
2
1
1
0
0
0
1
1
2
2
2
2
2
1
0
1
1
1
1
0
0
1
1
1
0
0
1
1
2
1
1
1
0
0
1
2
1
1
1
0
0
1
0
1
0
2
0
0
1
1
1
1
1
0
0
1
4
2
1
1
0
1
2
1
1
1
0
2
1
0
0
1
1
2
1
0
2
1
0
0
1
0
0
1
1
1
1
0
1
1
0
0
1
1
1
2
2
0
0
1
1
1
1
1
0
1
2
1
2
2
1
1
1
0
1
1
0
1
1
2
2
0
0
1
1
0
0
2
1
2
1
1
1
1
2
1
1
1
1
1
1
0
0
0
1
0
1
1
1
0
0
1
1
1
1
1
2
1
0
1
1
2
0
1
1
1
1
1
0
2
1
1
0
1
1
0
0
1
2
2
1
1
2
1
1
1
2
1
2
1
0
2
1
2
0
1
1
0
2
0
1
1
2
1
1
1
1
1
0
0
0
0
2
1
0
2
1
2
2
1
1
0
1
0
1
0
1
1
0
2
1
0
3
1
1
2
2
1
0
1
1
1
0
1
1
1
1
2
1
1
0
0
1
0
0
1
2
1
0
1
0
1
1
2
0
2
2
0
1
5
1
2
1
1
0
1
0
2
2
0
1
1
1
0
2
0
0
0
0
0
1
1
1
0
1
1
1
1
1
2
0
1
2
1
0
2
2
2
1
1
1
1
0
1
0
0
1
0
0
1
2
2
0
2
1
2
1
1
0
1
1
2
0
1
0
1
0
1
1
0
1
1
1
2
0
1
1
0
1
1
1
1
2
1
0
0
2
1
2
2
1
1
1
1
0
0
1
2
0
0
0
2
1
0
1
2
0
2
0
1
1
2
1
0
1
2
2
0
0
1
1
2
1
1
0
2
2
1
2
0
2
1
0
0
1
1
0
0
0
0
1
1
1
1
0
2
1
1
1
0
1
1
0
2
0
1
1
1
1
2
1
1
1
0
0
1
0
2
2
1
1
0
2
2
1
1
0
1
0
0
1
1
1
1
1
1
0
1
2
1
1
1
1
2
1
1
0
1
1
1
0
0
1
1
2
0
1
2
0
1
0
1
0
0
0
1
1
0
1
0
2
1
1
2
1
0
1
1
1
1
1
1
0
1
1
0
1
1
2
1
0
2
1
2
1
1
1
1
0
1
2
2
2
1
0
1
1
2
1
2
1
2
0
2
0
0
1
1
0
0
1
1
2
1
1
1
2
1
1
0
2
2
1
1
0
1
2
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
2
1
0
2
2
1
0
0
0
0
0
0
2
1
0
0
1
2
1
2
0
2
1
1
0
2
0
0
2
1
1
1
0
2
2
0
0
1
0
0
1
0
0
1
2
0
1
1
0
1
2
0
1
1
1
1
1
0
0
1
0
0
1
1
0
1
1
0
2
0
2
1
1
1
0
1
2
2
1
2
0
1
2
0
0
1
3
0
0
1
2
1
1
0
0
1
0
1
0
1
1
1
0
0
1
1
1
0
1
2
1
1
1
1
1
1
0
0
1
1
0
0
2
0
1
1
0
0
0
1
1
1
1
0
1
1
1
0
0
1
1
2
1
0
0
1
0
0
0
2
0
2
1
1
0
3
1
1
2
0
0
1
2
0
1
1
0
0
1
2
2
1
1
1
1
1
0
1
0
1
2
0
0
1
0
1
0
0
1
2
1
2
1
0
0
2
0
1
2
1
1
0
0
1
0
1
0
1
1
0
1
0
2
1
2
0
2
1
1
1
0
1
2
1
1
0
0
2
0
1
2
0
0
0
0
1
2
1
0
0
0
1
1
0
1
0
0
1
1
0
0
0
1
0
0
2
0
2
1
0
1
1
3
1
0
1
0
1
2
2
2
2
1
0
0
2
1
2
1
0
0
0
0
0
1
2
1
1
1
0
1
2
0
0
0
1
0
0
1
1
1
1
1
1
0
2
1
3
2
2
1
0
1
0
1
2
1
1
0
1
1
1
2
2
1
2
0
1
1
1
1
3
2
2
1
1
1
1
1
2
0
1
0
1
2
1
0
0
1
1
1
2
0
1
1
0
2
1
1
1
0
2
1
1
2
1
1
0
1
1
0
2
1
2
2
0
2
1
1
1
3
0
1
1
0
0
1
1
0
2
0
2
1
2
0
1
0
0
1
1
2
1
2
1
1
0
1
1
2
1
1
0
1
1
1
0
0
1
0
1
1
1
1
0
0
1
0
2
1
1
3
1
2
2
0
2
1
0
0
1
2
0
1
2
0
1
1
2
1
2
1
2
1
1
2
0
2
1
1
0
1
1
2
1
2
1
2
1
2
1
1
2
1
1
1
1
1
2
1
2
1
2
1
3
1
0
1
2
0
1
2
0
1
0
0
2
2
2
1
0
2
1
2
1
1
1
0
0
2
2
0
0
1
1
1
0
2
1
2
2
0
1
0
2
0
1
0
1
2
0
0
0
0
2
2
0
1
3
0
1
0
0
1
0
0
1
1
0
1
1
2
1
1
0
0
0
1
4
0
1
1
0
0
1
2
1
0
1
0
1
2
0
0
2
0
0
1
1
2
0
1
1
0
1
1
1
1
1
1
0
0
2
2
1
1
1
2
1
1
0
2
2
1
1
0
1
1
2
2
0
1
0
0
1
1
1
1
1
2
1
1
2
0
0
2
1
2
0
0
0
0
2
0
2
1
1
2
1
2
0
0
0
0
0
1
2
1
1
0
1
2
0
1
1
1
1
1
1
0
0
0
0
2
0
2
2
0
2
0
1
0
0
2
1
1
0
2
2
2
1
1
0
2
1
1
0
3
2
1
5
1
1
0
2
0
1
1
0
1
0
2
1
0
0
1
1
2
0
0
1
1
2
0
0
2
2
1
0
1
0
0
0
0
2
2
1
2
1
1
1
1
1
1
2
1
2
1
0
1
0
1
2
2
0
0
1
1
3
1
1
1
0
1
0
1
0
1
1
2
1
2
2
2
0
0
1
2
0
1
0
2
1
0
0
0
2
1
1
1
1
2
0
2
1
2
1
2
1
0
2
1
1
1
1
2
0
2
1
2
0
1
0
0
0
1
0
1
1
1
0
1
0
0
1
1
1
1
1
1
1
2
1
0
2
1
1
0
0
1
0
1
0
0
2
2
0
0
1
0
1
1
0
1
1
2
1
1
0
0
2
2
2
1
1
0
0
2
0
1
0
1
1
1
1
2
0
1
1
1
2
1
1
1
0
2
2
0
1
2
2
1
2
1
1
2
0
1
1
1
0
2
2
2
1
0
2
1
1
1
0
1
0
1
0
1
0
0
2
2
2
1
1
0
1
1
1
1
1
2
1
1
1
1
1
0
1
2
1
2
1
0
2
1
1
1
0
0
0
0
0
1
2
1
0
1
1
1
1
0
1
1
2
1
2
0
1
1
2
0
0
1
1
1
1
2
2
1
2
1
1
2
1
2
1
1
1
0
1
1
1
2
2
1
0
1
0
1
1
0
1
0
1
1
1
1
1
0
1
0
1
1
0
0
3
0
0
1
1
0
1
1
0
2
1
2
3
1
1
1
2
1
2
0
0
0
2
1
1
1
1
0
0
1
0
1
2
1
1
1
1
1
1
0
0
1
1
2
3
1
0
0
2
1
1
1
1
2
2
0
1
1
2
0
1
0
0
1
0
0
1
1
2
0
1
0
0
1
0
0
2
0
1
0
1
1
1
2
1
1
0
0
1
0
2
1
2
0
0
2
0
1
0
1
1
1
1
1
2
0
3
1
1
2
1
1
1
2
2
1
1
3
2
1
1
1
1
0
2
0
1
0
0
0
1
1
2
1
0
1
2
1
1
2
0
1
0
1
1
1
0
1
0
0
0
1
1
2
1
1
1
0
1
2
1
1
2
2
3
2
2
1
1
1
2
1
2
1
2
1
0
1
1
2
1
0
0
2
0
1
1
2
0
0
2
0
2
0
0
2
0
0
1
2
0
0
2
1
1
0
1
0
1
1
0
0
1
1
1
1
2
2
2
1
2
1
0
0
0
2
0
1
0
1
1
2
2
1
1
0
1
1
2
2
1
0
1
1
0
1
0
2
0
1
1
0
2
1
1
1
0
1
2
1
1
1
0
0
2
1
1
0
0
1
0
0
1
1
0
0
1
0
0
3
1
1
1
1
1
0
1
1
0
2
1
2
1
0
1
2
0
1
1
0
2
1
2
1
0
1
0
0
1
0
1
0
1
0
1
1
0
1
2
2
1
0
0
1
0
0
2
1
0
1
1
1
0
1
2
1
0
0
2
2
0
0
1
0
2
0
1
2
0
1
1
1
2
0
0
2
2
0
1
0
0
1
2
2
1
1
2
2
1
2
0
0
3
2
0
1
0
0
1
0
1
0
2
2
2
1
0
1
2
0
1
0
1
0
1
1
1
0
1
0
1
2
1
1
0
1
2
0
1
1
2
1
0
0
2
1
0
0
1
1
0
2
0
2
1
1
0
1
2
1
1
0
0
0
0
1
1
2
1
0
1
0
0
1
1
2
1
0
0
1
2
0
1
1
1
1
1
1
1
1
1
1
1
0
1
0
2
1
0
1
1
1
0
0
1
1
0
1
2
0
1
2
0
1
1
1
1
2
0
3
1
1
0
1
1
1
0
1
1
2
1
1
0
1
0
1
1
2
2
2
0
2
1
0
1
2
2
2
2
1
0
1
2
0
0
0
1
2
1
1
2
1
0
0
1
0
0
1
1
1
0
0
0
2
2
1
1
2
1
2
2
0
2
0
0
0
1
0
0
1
1
1
1
0
1
1
0
1
0
2
3
1
0
1
1
0
0
0
0
1
1
2
1
0
1
2
1
0
0
0
1
1
0
1
1
2
0
2
2
0
1
0
1
0
1
2
1
2
2
2
0
1
2
2
1
1
2
0
2
2
0
0
1
0
0
1
1
0
2
1
1
2
1
1
2
3
1
1
2
0
0
1
2
2
1
1
0
0
0
1
0
0
1
1
1
1
1
2
0
1
1
1
1
1
0
2
2
2
1
2
2
1
0
2
1
1
1
1
1
1
0
1
1
1
0
0
1
1
1
1
2
2
0
1
1
1
1
0
2
1
0
0
2
1
0
0
1
1
0
1
1
2
1
1
0
2
2
2
1
1
0
2
1
0
1
2
1
0
1
0
1
1
2
1
0
1
1
1
1
1
1
0
1
1
0
0
0
1
1
1
2
0
0
1
0
1
1
0
1
1
1
0
0
1
0
1
1
1
0
1
0
1
1
0
0
1
1
0
1
1
1
1
1
1
0
1
2
0
0
2
0
2
0
1
1
1
2
1
1
1
0
0
0
0
2
1
1
1
2
0
1
1
2
0
1
0
1
2
0
0
2
1
0
1
0
1
1
0
2
1
2
1
3
1
0
0
0
1
2
0
1
1
2
2
0
2
0
1
2
0
2
1
1
1
0
2
1
1
1
2
0
2
1
0
1
2
1
2
0
2
0
3
2
1
1
1
1
4
1
0
0
2
2
0
0
1
0
0
1
1
1
2
1
3
1
1
1
1
0
1
0
1
1
1
0
1
2
0
1
0
1
2
1
1
1
0
0
1
2
1
2
0
1
1
0
2
0
2
0
1
1
1
1
1
1
5
0
0
0
2
2
1
0
1
1
0
2
1
0
0
0
0
1
1
2
0
1
1
1
1
0
1
0
0
1
1
2
2
1
0
1
2
2
0
1
1
1
0
3
0
2
2
1
0
1
1
1
2
1
0
0
1
1
0
2
1
0
1
0
0
1
2
1
0
0
1
1
0
1
0
2
1
1
1
1
1
1
0
1
0
1
0
1
0
0
0
1
0
1
1
2
1
0
0
2
1
0
1
0
1
2
3
0
1
1
0
1
0
1
0
1
2
0
2
3
2
3
1
0
1
0
0
2
0
1
0
1
0
0
1
2
1
2
0
1
0
1
2
0
1
2
1
2
1
2
0
1
0
1
1
0
2
1
1
0
1
0
1
1
0
2
1
2
2
1
1
1
0
1
2
1
0
0
2
0
0
0
1
1
1
1
1
0
1
1
0
1
1
0
1
1
1
0
1
0
0
1
1
1
0
1
0
0
0
1
1
1
1
2
0
1
2
1
1
2
1
1
2
0
1
1
2
1
2
0
2
1
0
3
2
0
1
2
0
1
0
2
2
0
2
1
3
2
0
1
0
0
1
1
0
1
2
2
0
1
7
0
0
1
0
1
0
1
2
1
1
0
1
1
0
1
1
2
0
0
1
1
2
0
2
0
1
1
1
1
2
1
1
2
0
2
1
0
1
1
1
1
1
0
0
1
2
2
1
1
1
1
1
1
0
1
0
1
0
1
2
0
1
1
1
4
1
1
0
1
0
0
2
0
1
0
0
1
3
1
1
0
1
2
1
2
0
0
0
0
1
2
2
1
1
0
1
1
2
2
2
0
1
1
2
0
1
2
1
1
0
0
1
0
1
1
1
1
1
0
1
1
0
1
0
1
0
1
0
1
1
0
1
0
1
0
1
1
1
0
1
0
2
1
0
1
0
0
1
1
1
2
0
1
1
1
1
1
1
0
0
1
1
0
0
1
0
1
0
1
1
0
1
1
0
0
1
0
1
0
1
2
0
0
2
0
0
1
2
1
1
1
1
2
1
1
1
0
2
0
1
1
2
2
1
1
1
0
0
1
1
1
3
0
0
1
0
2
0
2
2
0
0
1
2
1
1
1
1
2
1
1
1
0
0
1
2
0
1
1
1
1
0
1
1
1
1
1
2
0
1
0
0
1
1
0
0
1
1
1
0
1
1
1
0
1
0
1
2
2
0
1
2
0
0
0
1
1
1
0
1
1
1
1
2
1
1
0
0
1
2
0
0
1
1
0
2
1
0
0
3
0
0
1
2
1
1
2
0
2
0
0
0
1
0
2
1
0
1
1
1
2
0
0
1
2
1
0
2
1
1
1
1
1
1
2
0
0
1
2
2
1
1
2
2
0
1
0
0
0
1
0
0
0
2
1
2
2
2
1
2
1
1
0
2
1
1
1
2
0
2
1
1
1
1
0
1
0
1
1
2
1
0
0
0
1
0
2
1
2
1
2
1
0
1
0
0
1
1
1
0
0
1
1
1
0
1
0
1
0
1
0
1
2
2
1
0
0
2
1
2
1
1
1
1
1
1
0
1
2
2
1
0
0
0
2
1
1
1
1
2
0
1
0
0
1
0
1
0
1
1
1
0
0
1
1
0
0
0
1
3
1
0
1
0
0
1
0
0
1
0
0
3
2
1
1
2
0
2
0
2
1
2
4
2
1
0
0
2
1
2
1
1
1
1
2
1
0
0
1
0
1
0
1
0
1
2
1
1
0
1
2
0
1
1
0
1
1
0
1
1
1
0
1
1
1
1
1
1
0
1
2
1
0
0
0
0
1
1
1
0
1
1
1
2
1
1
3
1
0
0
2
0
1
1
0
0
0
1
1
0
0
0
2
1
1
1
1
0
2
0
0
2
2
2
1
1
2
2
0
1
3
1
0
2
1
1
0
1
1
1
0
1
0
2
2
0
2
0
0
0
1
0
2
1
1
1
0
1
2
0
0
2
1
1
0
1
1
2
0
0
2
2
0
0
1
0
1
0
2
1
2
1
2
2
0
1
0
1
2
0
0
0
2
0
0
1
1
2
2
2
1
0
0
1
1
1
2
0
2
2
0
0
1
0
1
2
0
1
2
2
1
1
0
2
1
0
1
0
1
0
1
2
1
1
2
1
2
2
1
2
1
2
0
1
2
2
1
1
1
0
1
0
1
1
0
2
0
0
1
1
0
3
1
1
0
1
1
2
1
1
0
0
1
2
0
2
2
0
0
0
1
1
1
0
1
1
0
1
3
5
2
2
1
0
1
1
0
1
1
1
0
2
1
1
0
1
1
0
2
1
2
0
0
2
0
1
0
1
1
1
1
1
1
0
2
0
2
1
1
0
0
1
2
1
0
1
1
1
0
1
0
1
1
0
1
1
1
1
2
0
1
2
0
1
1
3
1
1
1
0
2
1
1
0
0
1
1
0
1
0
1
1
2
2
2
2
1
2
1
0
2
2
0
0
1
0
0
1
0
2
0
1
1
0
0
1
1
0
3
2
0
1
2
0
0
2
2
1
2
0
2
1
0
1
1
1
0
0
1
2
1
0
1
1
0
1
0
0
1
1
2
1
0
1
1
2
0
0
2
1
1
1
0
0
0
0
2
1
2
1
0
3
1
2
1
0
1
2
0
1
2
2
1
1
1
0
0
0
2
1
1
0
1
1
0
1
1
1
0
2
0
0
1
2
0
1
0
1
1
0
1
0
0
0
1
1
2
1
0
1
2
2
1
1
0
0
1
0
1
3
0
0
0
0
2
1
1
1
1
0
1
2
1
1
1
0
0
0
1
0
0
1
2
2
1
1
2
1
1
1
0
1
1
1
1
1
0
1
2
0
0
1
2
0
1
1
1
1
2
0
1
0
0
2
0
0
0
0
0
1
1
1
1
1
1
2
0
1
1
1
2
0
2
2
1
1
1
1
2
2
1
1
1
1
0
1
0
1
1
1
1
2
1
1
0
1
0
2
1
1
0
1
0
2
1
1
1
0
2
1
1
1
0
2
1
2
2
1
2
1
1
1
0
0
1
2
2
1
0
3
2
2
0
1
1
1
2
1
1
0
1
1
0
1
1
1
2
1
1
1
0
0
0
0
1
3
1
2
0
1
1
1
2
1
1
0
3
1
1
1
1
2
1
3
0
0
2
0
1
0
0
1
2
2
0
1
1
0
0
1
4
0
1
1
1
1
2
1
1
0
2
2
1
2
2
2
1
1
1
1
1
0
2
1
0
2
0
0
1
1
0
0
0
1
0
1
1
2
0
0
1
0
0
2
1
1
2
1
1
1
1
0
0
2
1
0
1
1
1
2
1
0
1
0
1
3
1
1
1
1
1
1
1
1
1
0
1
0
0
1
3
1
0
0
1
1
1
1
1
1
1
2
1
0
1
0
1
0
0
1
1
1
1
1
2
2
0
1
1
0
0
0
2
1
2
1
0
0
1
1
1
0
1
1
1
2
2
0
1
1
2
1
2
2
1
1
0
3
2
2
1
0
1
2
0
1
2
1
0
2
2
1
1
0
1
1
0
0
2
1
2
0
0
1
2
2
1
0
2
1
1
2
1
1
1
1
0
1
1
1
1
2
1
1
0
0
1
2
1
1
0
1
0
2
0
0
0
3
1
2
1
0
2
1
1
1
0
1
2
0
1
1
1
1
1
1
0
1
1
1
1
2
0
1
2
2
2
0
1
1
1
1
1
2
0
1
1
0
0
1
1
2
1
1
1
1
2
1
0
2
2
1
1
0
1
1
1
1
2
0
0
1
1
0
2
0
1
1
1
1
0
1
2
1
1
1
2
1
2
3
0
0
2
0
0
2
0
1
0
1
2
2
2
2
1
3
1
0
2
2
1
2
2
1
0
0
1
0
2
1
0
0
1
3
1
0
0
2
1
0
0
1
0
2
0
0
1
0
0
0
0
1
1
2
0
2
2
1
1
1
0
1
2
1
0
0
1
1
0
1
0
1
0
1
1
2
1
1
0
1
0
1
2
1
0
0
2
0
1
1
0
1
0
1
1
1
0
0
1
1
1
2
1
1
1
2
1
2
0
0
1
1
1
0
1
1
1
1
1
3
0
1
1
2
1
1
1
1
2
2
0
0
1
0
0
1
1
2
1
2
0
2
2
1
1
2
1
1
1
1
1
1
1
0
2
1
1
0
0
0
1
0
1
2
1
1
1
0
0
1
2
1
1
1
0
2
0
2
0
0
1
0
0
1
1
1
1
2
0
0
1
1
1
1
1
0
0
0
2
1
2
1
1
1
1
1
1
0
0
1
0
1
1
2
0
0
0
0
0
0
1
1
1
2
1
0
1
2
1
2
1
0
1
1
1
1
1
1
1
1
0
1
2
1
0
0
1
1
0
0
2
1
0
1
0
0
0
1
0
0
0
0
0
1
2
4
0
1
1
1
2
1
0
1
1
1
0
0
1
1
0
1
2
0
1
1
2
2
1
0
1
1
0
1
1
0
0
1
2
2
1
2
0
1
0
1
1
0
0
1
1
0
1
1
1
0
0
2
1
1
1
1
0
0
0
1
0
0
2
2
3
0
1
2
1
0
1
1
0
1
1
0
1
0
1
2
2
2
2
1
1
0
1
0
1
0
1
0
1
0
2
1
2
1
2
1
0
1
0
1
2
1
0
0
0
0
2
1
0
2
1
0
0
1
2
0
1
1
1
2
0
0
1
1
0
1
0
0
0
0
0
0
1
2
2
1
1
1
0
1
1
1
2
1
0
1
1
1
1
6
1
2
0
0
1
2
1
2
1
0
0
2
2
1
0
1
1
1
1
0
0
1
0
0
2
0
2
1
0
0
1
1
1
0
1
1
1
1
3
2
2
2
1
0
1
2
1
1
0
1
0
1
0
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
1
0
2
1
1
2
1
0
1
1
1
1
1
0
0
0
0
2
1
1
0
0
0
2
1
1
1
2
1
1
2
2
2
1
1
2
1
2
1
1
1
1
0
1
2
0
2
0
1
1
1
1
0
0
2
2
1
0
0
1
2
2
3
0
1
2
0
1
1
0
1
1
0
1
1
0
1
2
0
0
1
1
2
1
0
1
0
0
1
0
1
2
1
1
1
1
0
2
0
1
0
1
0
1
1
0
1
1
2
2
1
1
2
2
1
0
1
0
1
0
1
1
1
1
0
1
2
0
1
2
1
1
2
1
1
1
0
1
1
1
0
2
0
2
1
2
2
1
1
1
1
1
2
1
0
2
0
1
2
0
0
1
1
0
1
2
2
0
1
1
2
1
1
0
1
1
0
1
1
2
1
1
0
1
0
1
1
3
0
2
1
1
2
2
1
2
0
1
0
0
1
1
0
0
1
1
1
1
1
2
1
2
0
1
0
2
2
1
1
0
0
2
1
1
1
0
1
1
0
0
1
0
1
1
0
0
2
0
0
1
1
2
2
0
0
1
0
2
2
3
0
2
1
1
2
2
1
1
1
2
0
1
2
1
0
1
1
1
1
1
2
1
0
0
2
2
0
0
2
0
1
0
1
0
2
2
1
1
0
1
1
0
1
2
1
2
1
2
2
2
1
1
2
3
2
1
0
1
2
2
0
1
0
1
3
1
1
0
1
1
2
2
1
0
0
1
1
0
0
1
1
0
0
2
2
1
1
2
2
2
1
1
1
0
0
1
1
1
1
1
0
1
1
1
0
2
2
1
2
1
0
1
0
2
1
2
0
2
1
0
0
0
0
1
1
0
2
1
0
1
2
2
2
2
0
2
0
2
1
1
1
1
1
3
1
2
0
0
0
0
0
0
0
1
1
0
3
0
0
1
2
1
2
1
2
1
1
0
0
1
0
1
1
1
1
1
1
2
1
1
1
0
1
0
1
0
1
2
0
0
1
0
1
0
0
1
1
2
1
2
0
2
0
2
1
2
2
0
1
2
2
2
1
0
1
1
2
2
0
0
2
1
1
1
1
1
3
2
0
1
1
1
0
2
1
1
2
1
1
1
1
0
1
0
0
1
1
2
1
1
4
1
0
1
3
1
1
3
0
2
1
2
0
0
2
0
1
2
1
1
0
1
4
1
3
1
0
1
1
0
0
2
0
1
2
0
1
1
0
2
1
1
0
0
1
0
1
1
4
2
1
0
1
1
0
1
0
1
2
1
2
1
0
1
0
0
1
1
1
0
1
1
0
0
1
1
1
1
0
0
1
1
1
1
0
2
1
0
1
1
0
1
0
1
1
0
1
0
1
0
1
1
2
2
1
0
2
0
1
1
0
2
1
0
0
2
2
1
1
1
0
1
0
1
1
1
0
0
1
0
0
3
1
1
2
2
2
1
1
1
2
1
1
1
2
1
0
1
0
0
1
1
1
0
4
0
0
1
1
2
1
1
1
2
1
1
2
1
2
1
0
1
1
2
0
1
1
0
2
0
2
1
1
1
1
1
2
2
0
1
1
0
0
0
0
1
0
1
1
1
3
1
1
3
2
0
1
1
0
1
0
1
1
0
1
1
1
1
0
0
1
1
0
2
0
1
2
0
2
1
1
0
2
1
0
0
1
1
1
1
0
1
1
0
1
1
2
1
2
2
0
1
2
1
1
1
1
0
2
1
1
1
2
1
2
1
1
2
0
1
0
2
1
1
1
1
0
2
1
0
1
1
1
1
0
0
1
0
0
1
1
0
2
0
0
2
2
1
1
1
1
0
1
1
2
1
0
1
1
0
2
2
1
1
0
0
1
1
0
0
1
0
2
2
1
0
1
1
1
1
1
2
2
1
1
1
1
2
0
0
0
1
1
1
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
2
0
1
2
1
1
1
1
2
1
3
2
2
2
1
1
1
1
1
0
2
0
1
0
1
1
1
1
1
0
1
1
0
1
1
1
2
1
1
0
2
0
1
1
0
1
1
1
0
1
0
1
1
1
0
1
1
0
1
2
2
0
0
1
2
0
1
0
0
1
1
2
0
2
0
0
2
2
2
2
0
1
1
2
1
1
1
2
1
0
2
0
0
1
2
2
1
1
2
0
2
0
1
1
1
1
0
0
1
1
0
1
1
1
0
0
1
0
2
1
0
3
0
1
1
0
0
1
1
2
0
2
2
1
1
1
1
1
2
1
0
1
0
2
1
2
0
2
0
2
1
1
2
2
1
1
0
2
1
2
1
2
0
1
1
1
1
2
2
0
2
2
2
1
1
1
1
1
1
1
1
2
0
1
0
0
1
1
2
1
2
1
0
0
2
1
2
1
1
1
2
2
2
1
1
1
2
2
1
2
1
1
0
1
1
1
1
2
2
1
0
1
2
1
0
1
2
1
1
0
0
1
2
2
1
2
0
0
2
1
0
0
0
1
1
1
1
1
1
1
1
1
1
1
0
0
0
0
2
1
0
0
0
1
1
2
1
1
2
1
0
1
0
2
1
1
1
1
1
0
1
1
1
1
1
1
2
0
0
2
1
1
1
0
1
0
1
1
2
1
1
0
2
1
2
2
1
0
0
0
1
2
1
4
3
1
2
1
1
1
1
1
0
2
1
0
1
1
3
2
1
2
1
1
0
1
0
2
2
0
1
0
0
0
2
2
1
1
0
0
2
1
0
1
1
1
0
1
1
2
1
0
0
1
2
1
2
0
0
1
0
0
1
2
1
0
1
1
0
0
0
2
1
0
2
0
1
1
1
1
1
0
2
2
1
1
0
2
0
1
2
1
1
1
1
1
2
1
2
1
0
1
1
0
1
0
1
1
1
1
0
1
0
0
1
2
2
0
2
0
2
1
1
1
3
0
0
0
2
1
1
0
1
0
1
1
2
1
3
2
1
0
2
4
0
0
0
2
1
2
0
1
0
1
1
0
1
0
1
1
1
0
0
1
0
1
0
1
1
0
2
1
1
2
1
2
0
1
0
0
2
0
0
0
2
1
1
3
1
1
1
2
0
0
0
1
6
0
1
2
1
1
2
1
2
2
0
1
0
1
1
2
0
2
0
0
1
1
1
0
2
1
1
1
1
1
2
2
1
0
0
1
1
1
1
0
1
0
1
0
2
1
1
1
1
0
0
1
2
0
2
1
0
1
1
1
0
1
1
1
0
1
2
1
1
1
1
1
1
0
1
0
1
0
0
1
1
2
1
0
0
0
0
0
2
1
1
0
0
0
0
1
0
1
1
3
1
1
2
2
0
1
1
1
1
0
0
0
2
2
1
1
1
1
1
1
0
1
1
0
1
1
0
1
1
1
1
1
0
1
2
1
2
2
0
1
1
1
0
2
1
0
1
1
0
1
1
1
1
1
2
1
1
2
1
0
0
1
1
0
8
2
0
1
1
0
1
1
0
1
3
1
1
1
1
1
0
3
2
1
5
2
0
0
2
1
0
1
2
1
2
1
1
1
1
2
2
1
0
1
1
1
0
2
0
1
2
1
3
2
2
2
1
2
1
1
0
1
1
1
2
1
1
1
1
0
1
1
2
1
1
1
2
1
1
2
2
0
0
1
2
2
2
1
1
1
2
1
0
0
2
0
0
1
2
1
2
0
1
1
1
0
0
2
2
1
0
1
1
1
1
0
2
0
1
2
1
0
2
1
0
0
1
1
2
1
1
1
0
2
1
1
1
1
0
1
0
1
1
1
0
1
1
1
1
2
1
2
0
2
0
2
1
1
2
1
2
1
1
0
2
1
2
4
1
1
0
2
1
1
0
0
1
2
1
0
0
1
1
0
1
1
1
0
1
0
0
2
0
2
1
0
1
1
0
1
1
1
1
0
1
0
1
2
0
0
0
0
0
1
2
2
0
0
2
1
1
0
1
0
2
1
1
1
1
0
2
2
1
2
1
0
2
0
1
1
1
1
1
0
1
1
0
2
0
1
2
1
0
2
0
0
1
1
0
2
1
1
0
1
1
1
1
2
2
1
0
2
1
1
2
1
2
0
0
1
2
2
2
2
1
1
0
0
0
1
0
0
1
1
1
0
2
0
0
2
1
2
1
1
1
0
1
1
0
1
1
0
0
2
1
1
1
1
1
1
2
1
2
0
0
0
2
2
1
0
0
2
1
1
1
1
2
2
1
0
1
0
1
0
1
2
0
1
0
0
1
1
0
0
1
2
1
1
1
2
2
1
1
1
1
0
0
1
2
1
1
2
1
1
1
2
0
1
0
0
1
0
1
0
1
1
1
1
2
1
2
2
1
1
1
0
1
2
0
1
1
0
2
0
1
0
0
1
0
2
1
1
1
1
2
1
2
1
2
1
2
1
1
1
2
1
0
0
2
0
2
0
0
2
0
2
1
0
1
1
1
1
2
1
2
1
0
1
2
0
2
0
2
2
1
1
1
0
1
1
2
2
0
1
0
0
1
1
1
0
2
1
1
1
0
1
1
0
0
0
2
2
0
1
2
1
0
1
2
1
0
1
1
2
2
0
0
0
1
2
0
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
0
1
1
1
0
1
0
0
2
0
1
0
1
1
2
2
1
2
1
0
0
2
1
1
1
0
2
2
2
2
1
1
2
1
2
1
1
0
2
1
1
2
1
2
1
0
0
1
0
1
2
2
1
2
1
2
0
2
2
2
0
1
0
0
1
0
1
1
1
1
1
0
1
2
1
1
2
0
0
2
0
1
1
1
1
0
2
0
0
1
0
1
0
0
1
2
1
2
1
3
1
1
1
1
0
1
0
0
1
0
0
1
2
1
0
2
0
0
1
3
1
0
2
0
0
0
1
1
0
1
0
1
1
0
1
1
1
1
0
0
1
1
2
1
2
2
0
0
2
1
0
2
1
1
0
0
4
1
3
1
0
1
1
0
0
2
2
1
1
2
0
2
1
1
1
2
2
1
1
0
0
0
1
0
0
0
1
0
1
1
0
2
3
0
1
0
0
1
2
2
2
2
1
2
2
1
1
0
0
2
1
2
2
1
0
2
2
1
2
2
0
1
0
1
1
3
1
0
2
1
1
1
2
1
1
0
2
1
1
2
1
1
1
1
1
0
0
2
0
1
1
1
0
0
1
0
2
2
1
0
0
0
2
2
1
1
1
1
0
0
1
2
1
2
0
0
1
1
1
0
0
1
2
0
0
3
2
1
1
0
2
0
1
1
2
1
2
2
2
2
1
1
0
2
1
2
2
1
1
2
2
2
1
1
0
1
1
2
1
0
1
2
1
1
1
1
0
1
1
2
0
2
0
2
0
2
1
2
2
0
1
1
2
1
2
1
0
1
2
1
1
2
0
1
1
2
2
0
1
1
1
1
1
2
2
2
1
1
1
1
1
2
2
0
0
1
0
1
2
1
2
3
2
0
0
1
1
2
1
1
2
1
1
1
1
0
1
1
0
1
1
1
1
0
0
0
1
2
1
1
0
0
2
1
0
0
1
2
0
2
5
0
0
1
0
2
2
0
2
2
1
1
1
1
0
2
0
0
2
1
1
0
0
2
1
2
1
2
1
0
2
0
0
2
0
0
0
1
0
0
0
1
2
2
0
0
0
0
1
2
2
1
1
1
1
2
2
0
0
2
1
2
1
1
0
2
2
1
2
1
1
1
1
1
1
1
0
0
0
1
1
0
0
0
0
1
0
2
1
0
1
2
0
2
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
3
1
1
1
1
1
2
1
0
0
1
1
1
1
1
1
1
1
0
2
2
2
1
2
1
1
1
1
1
1
1
1
0
1
0
1
0
2
2
1
0
1
1
2
2
1
0
1
1
0
0
0
1
1
0
1
1
1
0
1
1
1
1
0
1
0
1
1
1
1
1
2
1
0
1
2
1
0
0
1
1
0
1
1
0
0
0
3
0
2
1
1
0
0
1
0
0
2
0
1
1
0
1
0
1
1
1
1
0
2
0
1
2
0
1
2
1
0
1
2
2
1
1
0
0
2
0
2
2
1
1
0
0
1
2
0
1
1
2
1
1
0
1
0
1
1
2
0
1
2
1
0
0
1
1
0
2
0
1
0
1
1
0
1
1
1
1
1
1
2
1
0
2
2
1
0
0
0
0
0
1
1
2
1
1
2
0
0
0
0
0
1
2
0
0
2
1
0
0
2
1
1
1
1
1
1
5
2
1
1
1
1
1
0
0
0
1
2
1
1
1
2
1
1
1
1
0
1
2
0
1
0
0
3
0
2
1
0
0
1
1
2
1
1
2
0
0
0
0
2
0
0
2
0
1
1
0
0
2
1
1
2
1
2
2
0
1
1
0
1
1
1
0
1
0
0
2
0
2
1
2
1
0
0
2
0
2
1
0
1
1
3
0
3
1
0
0
0
1
1
0
1
1
1
1
0
0
0
1
1
1
0
2
1
16
0
0
0
1
2
1
1
1
1
0
0
2
0
1
1
2
2
2
1
1
1
2
1
1
1
0
0
2
1
0
0
1
1
0
2
1
2
1
1
0
1
0
1
1
0
1
2
2
0
1
1
1
2
0
1
1
0
0
1
0
1
0
2
0
1
1
2
2
0
0
1
1
3
1
1
1
2
2
2
1
3
2
2
1
0
1
2
1
0
0
1
1
1
0
1
1
2
1
1
1
1
2
0
2
0
2
0
1
0
0
2
0
0
2
1
0
2
1
1
1
2
1
1
1
2
1
0
1
1
1
2
0
1
1
1
1
1
1
1
0
0
2
1
2
0
2
2
1
1
0
2
0
1
1
2
1
1
1
0
2
3
0
2
1
2
1
2
0
1
3
2
1
1
0
1
0
1
1
0
1
0
0
1
1
1
0
0
0
0
1
0
2
1
1
1
2
1
1
1
1
0
2
0
0
1
1
0
2
0
0
0
1
0
0
0
0
1
2
1
1
1
0
1
1
0
0
2
1
0
2
0
1
0
0
1
4
1
1
1
0
1
2
1
1
1
1
0
2
1
0
0
1
1
1
1
2
1
1
1
1
2
0
0
1
1
1
1
1
2
2
0
1
1
0
0
2
0
2
2
1
2
0
1
1
0
0
1
0
2
2
0
1
0
2
0
0
1
1
1
2
1
2
0
1
1
1
2
1
2
1
2
2
1
0
1
0
2
2
0
0
0
0
0
1
1
1
1
1
0
1
0
1
2
2
1
1
2
1
1
0
1
1
0
2
1
1
1
1
1
0
2
2
2
1
1
0
1
1
0
0
0
0
1
1
1
1
1
3
1
2
2
0
1
1
0
0
1
1
1
0
1
1
2
0
2
2
0
0
1
0
1
1
2
1
1
1
1
1
1
2
1
1
1
0
2
3
2
0
1
0
2
0
0
1
0
1
0
0
0
2
1
0
1
1
1
1
1
1
0
1
0
1
0
0
2
0
1
2
0
1
2
4
0
0
0
0
0
2
1
1
0
2
3
2
1
1
2
1
1
1
1
0
2
1
2
1
0
1
1
1
1
1
2
0
0
0
1
2
1
1
1
0
2
2
0
1
1
1
2
1
2
1
1
2
1
0
1
1
1
1
0
0
1
1
1
1
0
1
2
0
1
0
0
1
1
1
0
0
1
0
1
1
1
1
1
1
3
1
2
2
1
1
3
1
1
1
1
1
1
2
1
1
2
1
2
2
0
0
2
1
1
1
0
1
1
2
1
1
1
1
1
0
0
1
1
0
1
1
1
0
2
2
1
0
1
1
1
2
1
1
1
2
1
0
1
1
0
1
2
1
2
0
2
1
0
1
1
2
2
1
2
2
0
1
0
0
1
2
1
1
2
0
1
2
0
0
1
2
1
1
1
1
1
0
2
0
2
1
2
1
1
0
1
2
0
1
1
1
1
2
0
1
1
2
1
2
1
2
1
2
0
2
1
2
1
0
1
0
1
1
0
0
1
2
0
1
1
2
0
2
1
2
1
1
2
2
0
1
1
1
1
1
0
1
2
1
0
0
0
2
2
2
0
0
2
0
2
0
1
2
1
2
0
0
0
0
0
1
0
1
1
2
0
0
0
0
2
2
2
2
1
0
0
1
1
1
1
1
2
1
2
2
1
1
2
1
0
3
1
2
1
1
2
1
1
2
1
2
2
1
1
2
1
2
0
0
2
0
0
1
0
0
1
0
2
1
1
0
1
1
0
0
0
2
1
1
2
2
2
2
1
1
0
1
1
0
2
2
1
1
1
1
1
0
2
2
1
0
1
0
1
0
1
1
0
1
1
1
1
1
2
0
2
2
2
2
1
0
2
2
1
1
1
1
1
1
0
1
2
2
2
1
0
1
1
0
0
2
0
1
1
1
1
0
1
1
2
1
1
0
1
1
1
0
1
1
1
0
2
2
1
1
1
1
0
1
1
1
1
0
1
1
1
0
1
1
1
0
2
1
1
1
1
2
1
0
0
1
1
1
0
0
1
2
1
2
1
1
2
1
1
2
1
2
0
0
2
1
2
1
1
1
1
1
0
0
1
0
1
2
2
1
1
0
1
1
1
1
0
1
1
0
0
0
1
1
0
2
1
0
2
0
2
2
1
1
1
1
1
2
1
2
2
2
1
1
1
1
1
1
1
0
1
1
0
2
0
0
1
1
2
2
2
2
0
2
0
1
1
1
0
1
0
1
0
1
1
1
1
1
0
1
2
2
1
1
2
0
3
0
0
0
0
2
1
0
1
1
1
1
1
0
1
0
0
4
1
1
1
0
0
1
1
0
6
1
0
2
2
0
0
2
1
2
0
1
1
1
0
1
0
1
1
0
1
1
2
1
1
0
1
1
0
0
1
1
0
1
0
1
0
0
0
0
2
0
2
2
0
1
0
1
0
0
1
1
1
1
0
2
0
0
0
1
1
2
0
1
0
0
1
1
1
0
2
2
0
1
0
1
1
0
2
1
2
0
2
0
1
0
0
0
0
2
0
2
0
1
1
2
1
1
0
0
0
0
1
1
1
1
0
1
1
2
2
0
1
1
1
1
1
1
1
2
1
2
1
2
0
0
2
1
0
0
1
1
1
0
1
1
1
1
1
2
0
0
0
1
2
1
1
0
0
1
1
1
1
0
0
2
1
0
1
1
3
1
1
2
1
1
2
1
1
3
1
1
1
0
0
1
2
2
1
1
1
2
1
2
2
1
1
1
1
0
1
1
1
1
2
1
0
1
1
0
1
2
2
0
1
2
2
1
2
1
1
2
1
3
1
0
0
0
0
1
3
1
1
2
1
0
2
1
0
1
1
0
2
1
2
0
2
0
2
1
1
2
1
1
0
1
1
2
2
2
0
0
1
0
0
1
2
0
1
0
1
1
1
0
0
1
0
1
2
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
0
2
0
0
0
1
0
1
1
2
1
2
1
2
1
2
1
0
1
0
1
1
1
1
1
0
1
1
2
1
0
0
2
0
0
2
2
1
2
1
1
1
2
1
0
0
0
1
1
2
0
0
0
0
1
0
2
3
1
2
1
1
1
1
0
2
1
0
0
2
2
2
0
1
2
2
0
1
1
1
0
1
0
0
1
0
1
2
1
0
0
1
1
1
0
2
1
0
1
3
1
1
0
2
0
1
2
0
1
1
1
2
0
2
1
0
3
1
2
0
1
0
1
1
1
0
1
0
1
1
2
1
1
2
1
1
1
0
0
1
2
0
0
0
1
0
0
1
0
0
0
2
0
1
0
1
1
1
1
1
1
0
0
1
0
1
1
0
1
1
1
2
0
1
1
1
1
2
2
1
1
0
0
2
0
1
1
1
1
0
1
0
1
0
2
0
1
2
0
1
2
1
2
0
0
0
0
0
0
1
2
2
2
0
2
1
0
0
1
0
1
0
1
1
2
0
2
0
1
1
1
0
0
2
0
1
0
2
1
2
0
2
1
1
1
1
0
1
0
1
0
0
1
2
2
1
1
2
0
0
0
1
0
1
0
1
1
1
0
1
0
0
2
1
1
1
2
0
1
1
0
1
0
0
0
2
0
0
0
0
0
1
2
0
2
1
2
1
1
0
1
1
1
1
0
1
0
0
2
2
1
0
0
0
1
2
0
2
1
0
2
1
0
0
1
0
2
0
2
0
1
1
0
2
1
1
2
1
0
0
1
2
0
1
0
2
1
1
1
0
2
0
1
1
1
2
1
2
2
2
1
2
1
2
1
0
2
1
1
2
2
1
1
1
0
1
0
1
1
1
1
1
0
2
2
2
0
2
1
0
1
0
1
2
2
2
1
1
1
0
1
1
0
1
0
1
1
1
2
2
0
1
0
1
2
0
1
1
1
0
1
2
1
1
0
2
0
1
1
2
1
1
0
2
0
1
2
1
0
2
1
1
1
0
1
1
1
0
1
1
0
0
0
0
1
1
2
1
0
1
1
2
0
0
1
0
1
1
0
1
1
0
2
1
0
1
2
0
1
1
1
0
0
1
1
0
1
1
1
0
2
0
0
1
0
0
0
0
1
1
0
0
1
0
2
0
1
0
1
1
1
1
1
2
2
1
2
1
0
0
1
2
1
1
1
0
0
0
1
0
1
0
1
0
1
2
1
0
2
1
1
1
0
0
1
0
1
1
1
1
0
1
2
1
1
2
1
2
1
1
0
1
1
1
1
1
1
0
1
2
2
2
1
1
0
1
1
1
1
2
0
0
0
1
1
1
2
2
1
0
0
0
1
1
1
2
1
2
1
0
0
1
2
1
1
1
2
0
1
1
2
1
1
1
1
0
1
0
2
1
2
2
0
1
1
0
1
0
1
1
2
1
1
0
0
0
1
0
0
1
1
1
1
0
1
1
1
1
1
1
1
0
2
2
2
2
1
1
1
0
1
2
0
0
0
0
0
2
0
0
2
1
2
1
1
1
1
0
0
1
0
0
1
0
2
1
2
0
0
0
0
1
1
1
2
0
2
2
1
0
1
2
1
2
2
1
0
2
2
1
1
1
0
0
1
1
2
0
3
0
2
1
1
1
0
1
1
2
2
0
0
4
2
0
1
2
1
1
3
1
0
1
2
2
0
2
0
1
1
1
1
0
1
0
2
1
1
0
1
2
1
1
2
1
1
2
2
1
0
1
1
0
0
1
0
1
1
0
1
0
1
1
1
1
2
1
0
1
0
1
1
2
0
1
1
2
1
2
2
1
0
0
2
0
0
1
1
2
1
1
0
0
1
0
0
0
1
1
1
0
1
0
2
3
0
1
1
2
0
0
0
2
1
1
1
0
2
1
2
1
1
1
0
1
2
0
1
2
4
1
1
2
2
1
0
1
1
2
0
1
1
2
0
1
2
2
2
1
0
1
1
1
1
1
1
0
0
2
0
1
1
0
1
1
2
1
2
1
1
0
1
1
1
0
2
0
1
2
1
2
2
1
1
1
2
1
2
1
1
1
3
2
1
0
1
1
1
3
1
0
2
0
0
2
0
0
2
1
2
2
2
0
0
1
1
0
0
1
0
1
0
0
1
0
2
1
0
0
0
1
2
0
1
1
1
0
2
1
1
1
1
0
0
2
1
2
2
1
1
0
0
2
2
1
1
1
0
2
0
1
1
1
1
1
0
1
1
2
1
0
0
2
1
1
1
1
0
1
1
0
1
0
0
2
1
2
1
1
0
1
2
1
1
0
1
1
0
0
0
2
0
1
0
0
1
2
2
1
1
0
0
2
0
0
2
0
0
1
2
0
1
2
1
0
3
0
2
1
1
1
1
1
1
2
0
0
1
0
1
1
1
0
2
1
0
0
0
1
1
1
0
2
0
1
1
0
1
1
2
1
0
1
2
0
1
1
2
2
1
1
2
2
1
2
0
2
1
2
2
0
3
1
2
1
2
0
0
1
1
1
1
1
1
2
1
1
0
1
1
1
2
1
0
2
2
2
0
1
1
1
0
0
3
1
2
2
0
1
1
1
0
2
0
0
0
0
0
1
0
2
1
2
1
0
1
2
0
0
1
1
2
1
1
2
0
1
2
1
1
2
0
0
1
0
1
1
2
1
0
0
2
2
0
1
1
1
1
0
1
2
1
2
0
0
1
0
0
2
0
3
1
0
1
1
0
0
1
0
1
1
1
2
2
1
2
0
1
1
1
1
0
0
2
2
1
0
1
0
2
1
1
1
1
2
2
1
1
2
2
1
1
0
0
1
1
2
1
2
1
0
1
1
1
0
0
1
1
1
0
0
1
0
2
0
1
1
1
2
1
0
1
2
1
1
0
2
2
0
1
0
1
1
1
1
1
3
1
0
0
1
1
1
1
0
0
2
0
2
2
3
0
1
0
4
0
0
3
1
1
1
0
2
1
2
0
1
0
2
1
1
2
1
1
1
0
0
0
1
0
1
1
1
1
2
0
1
1
2
1
1
0
0
0
0
1
0
0
1
1
1
1
2
0
0
1
1
2
0
1
0
2
0
1
1
2
1
0
1
0
2
0
2
0
1
0
1
2
1
1
1
2
1
2
1
0
1
2
0
0
2
1
0
1
0
1
2
1
0
2
2
1
2
1
2
1
0
1
1
1
2
2
0
1
0
0
0
0
0
1
0
1
2
0
3
1
1
1
0
1
0
2
1
1
1
1
1
1
2
1
2
1
0
1
2
1
0
1
1
1
1
0
2
1
3
0
0
1
2
1
2
0
2
0
2
2
0
0
0
1
1
2
0
0
2
0
0
0
0
1
1
1
0
1
0
1
1
2
1
0
1
0
2
1
2
1
1
1
2
2
0
1
1
1
1
1
0
1
1
2
0
2
2
0
1
1
0
2
1
1
0
1
0
1
2
1
1
1
1
2
0
0
0
2
2
0
1
1
0
2
0
1
1
0
2
2
1
0
0
1
0
1
0
2
0
1
0
0
0
0
1
1
0
1
0
2
1
1
1
1
0
2
1
1
1
0
1
1
1
1
2
2
2
0
1
2
2
1
0
1
1
2
1
0
1
0
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
0
1
0
0
1
1
2
0
0
1
2
0
1
1
2
2
1
2
1
2
1
1
2
1
0
0
2
0
2
1
2
1
1
1
1
1
2
2
0
1
2
1
2
1
2
1
0
0
1
1
1
2
1
0
2
2
1
2
0
0
0
1
0
0
1
0
0
1
2
1
2
0
0
0
1
0
1
2
1
1
1
1
2
1
0
1
2
1
0
2
1
3
3
1
1
0
2
0
1
1
1
2
1
1
2
1
0
0
1
1
1
1
0
1
0
1
1
0
2
1
1
2
2
0
0
1
1
1
1
2
0
1
1
1
0
1
1
1
2
0
1
1
1
1
1
1
2
1
4
0
2
2
0
1
1
1
1
0
1
2
1
1
0
1
1
0
1
0
2
2
1
1
1
2
0
1
2
1
0
1
0
1
1
2
1
1
1
0
1
0
2
0
2
1
1
1
3
1
2
1
2
1
0
1
2
0
1
1
1
2
2
1
1
1
1
1
0
0
2
0
1
1
2
0
1
0
1
2
0
1
1
2
2
0
2
1
1
1
1
1
1
0
0
1
2
0
1
1
1
0
0
1
1
0
0
1
1
0
1
1
2
1
1
1
1
1
2
1
2
1
1
0
1
1
0
0
1
1
1
1
1
0
0
1
1
0
2
1
1
1
1
1
2
0
1
1
1
1
1
1
1
1
1
0
1
1
1
1
0
1
1
0
0
1
1
2
1
1
1
1
1
1
0
2
1
0
1
2
0
0
0
0
2
1
1
1
2
1
0
0
2
1
1
2
1
0
1
0
0
2
2
1
1
1
0
1
3
1
0
1
1
0
1
2
1
2
1
2
1
2
1
0
0
1
1
1
1
0
3
0
2
0
1
1
1
0
0
1
0
0
0
1
2
2
0
1
1
2
1
1
1
1
0
1
2
2
2
1
1
2
1
1
1
1
2
0
0
1
2
1
1
1
3
1
1
0
0
0
1
2
1
1
0
0
2
1
3
0
0
0
1
2
1
3
1
0
0
0
2
0
1
1
2
0
2
1
1
1
1
2
1
2
1
0
1
1
1
1
2
1
0
2
2
1
2
0
2
0
1
0
2
0
2
2
0
1
1
0
0
1
2
0
1
1
1
0
2
2
2
1
1
0
1
3
0
1
1
3
2
1
2
1
0
1
1
0
1
2
1
1
1
0
1
1
0
1
1
1
1
1
0
1
0
0
0
0
0
2
0
0
1
1
0
1
0
1
1
1
2
0
0
1
0
1
0
0
1
2
2
1
0
2
2
1
0
1
2
2
2
0
1
0
1
1
1
1
1
2
0
2
1
2
1
2
1
0
2
1
0
1
2
1
1
1
0
1
0
2
1
0
0
1
1
1
1
1
1
2
2
0
1
1
2
2
0
0
1
1
0
0
1
0
1
0
1
0
0
0
0
0
0
2
0
1
1
0
2
2
1
2
2
0
3
0
0
1
1
2
2
1
1
1
0
0
2
1
2
0
1
2
1
1
2
1
0
0
1
1
0
1
2
1
1
4
0
0
2
2
0
1
0
3
0
2
0
2
1
0
1
2
2
1
1
1
1
1
2
0
0
0
0
1
1
1
0
0
1
0
0
1
2
1
1
0
0
1
2
1
0
1
0
0
1
0
0
2
0
0
1
1
0
2
0
1
1
2
2
0
0
0
1
2
0
0
0
0
0
0
2
1
1
1
1
1
0
1
2
0
0
0
1
1
1
2
1
1
1
1
0
2
1
2
0
0
0
0
1
1
1
0
1
1
0
1
1
0
2
0
2
0
1
2
1
2
3
2
0
2
1
1
1
2
1
2
1
2
1
2
1
0
1
2
1
1
0
1
2
1
2
0
1
0
1
2
1
1
1
1
1
0
2
1
1
1
2
1
1
1
2
1
1
0
2
1
0
0
0
1
1
0
0
0
0
1
0
2
0
1
1
1
1
1
1
2
1
1
1
1
1
1
1
0
1
1
1
2
1
1
0
1
0
1
0
2
2
2
1
3
1
0
2
2
0
0
1
0
1
1
0
0
0
1
1
1
0
1
0
0
1
0
0
1
0
2
0
2
1
1
0
2
0
1
0
1
1
1
2
0
0
0
1
1
1
0
2
1
0
1
1
1
1
1
0
1
0
0
0
2
1
2
0
3
0
1
0
2
1
2
1
0
0
1
2
0
1
1
0
0
1
0
2
1
0
2
0
0
1
3
1
1
2
1
2
1
1
1
1
2
0
1
1
1
2
1
1
0
1
1
0
1
1
0
0
1
0
1
0
0
1
2
0
0
0
2
1
0
0
0
2
2
0
0
0
2
1
1
0
1
2
1
1
1
0
0
2
1
2
1
0
1
1
1
0
0
2
1
1
1
2
1
1
2
0
1
0
2
0
2
2
1
2
1
1
1
1
1
2
0
0
0
1
0
0
0
1
2
1
1
1
2
1
0
1
2
0
0
1
0
0
0
3
0
0
1
1
0
0
0
1
2
1
1
0
0
1
0
1
0
0
1
1
1
1
1
1
1
2
1
0
1
0
2
0
2
0
2
0
1
1
2
1
1
2
0
1
0
1
1
0
1
0
1
0
0
2
2
2
1
1
0
1
1
2
0
1
0
2
1
1
2
1
1
0
1
0
2
0
0
2
0
2
1
1
1
1
0
2
1
1
0
0
2
1
2
1
0
0
1
1
0
1
1
0
1
0
0
0
2
2
1
1
0
1
1
0
1
2
0
1
0
0
1
2
0
1
1
2
0
0
0
2
1
1
2
1
0
2
0
1
2
0
1
1
1
0
1
0
1
0
0
0
0
1
1
1
0
0
1
1
1
2
1
0
2
0
1
0
2
1
2
1
1
2
1
0
1
1
1
2
0
2
1
1
0
1
2
1
0
2
1
2
2
1
0
1
1
1
1
0
1
0
1
1
2
1
1
1
1
0
0
1
1
1
0
1
2
2
1
0
2
2
0
1
1
1
0
0
0
1
2
2
1
0
0
2
2
0
1
0
0
1
2
1
2
0
0
0
1
2
0
0
1
1
1
2
2
0
2
1
0
0
1
1
2
0
1
2
1
1
1
1
1
2
2
1
1
1
1
0
0
2
0
2
1
0
0
1
1
0
1
1
0
1
2
1
1
0
1
0
1
2
0
1
0
0
2
2
1
1
1
1
2
2
0
2
2
1
1
0
1
1
0
1
1
1
0
1
0
1
2
2
1
1
0
1
1
2
1
3
1
2
2
1
2
0
0
2
1
2
1
2
1
1
1
0
0
1
1
0
1
1
2
2
1
0
1
0
1
1
1
0
2
1
1
1
0
0
0
1
1
0
2
1
0
3
1
0
2
0
1
0
2
1
1
0
2
1
2
0
1
0
1
0
0
0
1
1
0
1
1
1
2
0
1
1
2
0
1
0
3
1
1
0
1
1
1
0
2
0
2
0
0
0
1
0
0
0
1
0
2
1
1
0
1
0
0
1
2
2
0
0
1
2
1
1
1
0
1
2
2
0
1
0
1
2
0
1
2
2
2
0
2
2
2
1
2
2
0
1
0
0
0
2
0
2
2
0
1
1
2
1
0
1
0
1
0
1
1
0
0
0
0
2
1
2
0
0
1
2
2
0
0
0
1
2
0
2
0
2
1
2
0
0
2
1
1
2
0
1
0
0
2
1
1
2
1
1
2
1
1
1
0
1
1
4
0
1
2
0
0
0
0
2
1
2
1
1
2
1
1
1
0
1
0
1
1
1
0
1
0
0
1
1
0
1
1
2
0
0
0
2
1
1
0
1
4
1
2
2
0
1
1
0
0
0
0
1
2
1
1
1
1
1
1
0
0
1
0
1
1
0
2
1
2
2
1
2
0
1
0
0
0
1
0
2
0
2
1
1
2
2
1
0
1
0
0
2
0
0
0
0
0
0
0
1
2
0
0
1
0
2
1
1
0
2
1
0
1
1
1
1
1
2
1
1
1
2
0
2
1
1
2
0
1
0
1
2
2
0
2
0
1
1
0
0
0
0
0
1
1
1
1
1
2
0
1
1
1
1
1
0
1
0
1
0
1
1
1
0
1
1
0
0
1
2
1
2
1
0
0
1
1
1
0
2
1
0
0
0
0
1
0
0
1
1
1
1
2
1
1
0
1
0
1
0
2
1
2
1
1
1
1
1
0
2
1
1
1
1
1
1
0
1
2
1
2
0
1
1
2
1
1
1
0
0
1
1
1
0
0
0
1
0
1
0
1
0
1
1
0
0
0
1
2
1
2
1
2
0
1
3
0
1
1
1
1
2
2
0
1
0
1
1
1
2
1
1
1
2
2
1
2
2
0
1
0
1
2
4
1
1
1
0
1
1
2
0
1
2
1
1
2
1
0
2
1
1
1
2
1
0
0
1
0
2
1
1
0
1
0
3
1
1
0
1
0
1
0
1
2
1
2
1
0
0
0
0
1
0
0
1
2
0
1
1
0
1
2
1
1
2
1
1
1
2
1
0
2
1
1
1
1
1
1
2
1
0
1
2
1
0
0
0
1
2
0
2
2
1
0
2
2
1
0
1
2
1
1
1
2
2
0
0
1
0
0
1
0
1
0
0
0
0
1
2
1
0
1
2
0
1
0
0
1
1
0
2
1
2
1
1
2
1
2
0
0
1
0
0
1
1
1
1
1
0
0
1
0
2
2
1
1
0
1
0
0
1
1
2
2
1
1
0
1
1
1
0
1
0
1
1
1
0
0
1
1
0
1
2
1
0
1
1
2
1
0
1
1
1
2
2
0
0
2
2
1
1
1
0
2
1
0
2
0
1
0
1
1
1
0
0
0
1
2
1
1
1
2
2
2
1
1
2
3
1
1
0
2
0
1
1
1
0
2
0
1
0
0
2
1
0
2
1
2
1
1
1
2
1
1
1
0
1
0
2
2
0
0
1
0
2
0
1
2
1
1
1
2
1
1
1
1
0
1
2
0
1
1
1
3
0
1
1
2
1
0
0
1
1
1
2
0
0
1
1
1
2
0
2
1
1
2
1
0
1
1
0
1
2
2
1
2
1
1
1
0
1
2
0
1
2
1
1
2
0
2
1
0
2
1
1
1
1
1
1
1
1
1
1
1
0
1
1
0
0
1
1
1
1
1
1
2
1
0
1
0
1
2
2
1
1
1
1
1
1
0
1
1
2
1
1
2
0
2
0
1
2
2
2
0
8
3
0
1
1
1
1
2
1
0
1
1
1
0
1
0
1
1
0
3
1
1
2
1
1
1
1
1
3
1
2
0
0
0
2
2
1
1
0
1
0
0
2
1
0
1
1
1
0
2
0
1
0
1
1
2
2
0
1
0
0
1
1
2
1
2
2
0
0
0
0
1
6
0
1
2
1
0
0
1
1
2
3
1
1
1
2
1
1
0
2
1
0
1
0
1
2
1
2
0
0
2
1
2
1
1
0
1
1
0
2
1
0
0
2
0
2
0
0
0
1
0
0
1
2
1
1
1
2
1
0
1
2
1
0
1
1
0
1
1
0
0
0
0
1
1
2
1
1
1
1
1
2
1
1
0
0
1
1
0
2
2
1
2
1
1
0
2
2
1
2
0
1
1
0
1
2
1
1
2
0
1
1
2
2
1
0
0
1
2
1
2
0
2
0
3
2
1
0
2
0
1
0
1
2
1
2
1
2
1
1
0
2
2
1
0
0
1
2
1
0
1
0
1
1
1
1
0
1
0
2
1
2
2
1
1
5
2
1
0
0
2
0
2
1
1
1
0
2
2
0
1
0
0
1
2
1
1
1
1
1
0
1
0
1
0
0
2
1
0
0
2
1
0
0
1
1
1
1
1
2
1
1
0
0
1
1
1
0
1
2
0
2
0
0
0
0
1
1
5
1
1
1
0
1
1
2
0
0
0
2
0
1
1
0
1
1
1
2
1
2
2
1
2
2
1
1
2
1
0
0
1
2
2
0
0
1
0
2
0
0
1
1
2
1
0
0
2
0
2
1
0
1
1
1
0
2
1
0
1
0
2
2
1
0
2
0
1
0
1
1
0
2
1
0
1
0
1
2
1
1
1
1
1
1
0
1
2
2
2
2
0
1
0
0
2
1
1
0
0
1
1
0
2
0
1
1
1
2
1
1
0
2
1
1
2
1
0
1
1
2
0
2
1
2
1
0
1
0
1
1
1
1
2
1
0
2
1
0
2
0
0
2
1
1
2
1
1
1
1
2
2
1
1
0
1
1
2
0
0
0
2
1
2
0
1
1
2
1
0
1
2
1
2
1
2
1
0
0
1
2
0
1
0
0
1
1
1
2
0
1
1
1
1
2
1
0
1
2
0
1
0
0
0
1
1
1
1
1
0
0
1
0
0
1
0
1
0
2
1
2
0
0
2
1
1
1
1
0
1
1
1
1
2
0
2
0
1
1
3
0
0
1
1
0
1
0
0
1
0
2
1
1
2
0
1
3
1
3
1
1
1
0
1
1
1
1
1
0
1
1
1
0
1
1
1
0
0
0
1
0
2
1
1
1
1
1
2
1
1
0
0
3
1
1
2
0
1
1
1
1
2
0
1
2
1
0
0
1
1
2
2
2
2
0
1
2
1
1
1
2
1
0
0
1
2
1
2
1
2
0
2
1
0
0
0
1
1
0
2
1
1
1
0
0
2
3
2
0
0
0
1
1
1
0
2
0
1
1
2
1
1
0
2
0
0
3
1
1
1
0
1
1
2
1
2
1
0
1
2
2
2
1
1
1
2
0
2
0
0
1
8
2
1
1
0
0
1
1
1
0
1
2
1
1
1
1
0
2
1
0
1
1
0
1
1
0
0
0
0
0
1
0
0
1
0
1
0
1
1
1
1
2
1
2
1
1
1
2
1
2
1
2
1
1
1
2
1
1
2
1
2
1
1
1
2
0
0
0
1
2
2
1
2
2
0
1
0
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
2
0
1
1
1
1
1
0
1
0
0
0
1
0
1
0
0
0
1
1
0
2
1
2
2
0
2
2
1
2
2
0
2
0
2
1
2
1
0
1
1
1
1
0
1
0
0
1
0
2
0
0
1
1
1
1
2
1
0
2
1
1
2
1
1
2
1
2
0
0
1
1
2
0
2
2
1
2
0
0
0
1
2
1
1
0
0
1
2
0
1
0
1
0
1
0
0
0
1
0
1
0
1
2
0
1
0
1
1
1
2
1
2
1
2
2
1
1
2
1
0
2
1
0
1
0
1
2
2
1
1
1
1
0
1
1
2
1
2
0
1
1
0
1
0
0
0
0
1
2
1
1
0
1
2
1
1
1
2
1
2
1
1
1
2
2
1
2
0
1
2
2
1
1
0
2
0
1
2
1
1
1
2
2
2
2
1
1
1
0
2
1
3
2
0
1
1
1
2
2
0
0
2
2
1
1
2
0
1
1
2
0
1
0
1
0
0
0
1
1
1
0
1
0
2
1
1
1
1
1
0
1
0
2
0
1
2
0
2
1
1
1
0
0
0
1
1
1
1
1
1
2
0
2
0
0
0
1
1
2
2
0
0
2
1
2
1
0
1
2
2
1
1
0
3
0
2
0
0
2
1
1
2
1
0
2
2
1
1
1
2
1
0
1
1
1
2
0
2
1
1
1
2
1
1
2
1
2
2
2
1
0
1
1
0
1
0
0
1
2
2
1
1
1
2
0
1
1
1
1
2
2
2
0
2
2
0
1
1
1
1
0
0
0
1
1
0
1
1
1
0
1
1
1
2
1
0
1
1
0
2
1
1
2
1
0
1
1
2
1
2
0
2
2
0
1
2
0
1
1
1
0
1
2
1
2
1
1
0
1
1
0
2
1
1
2
1
2
1
0
2
2
1
1
0
2
0
0
1
1
1
2
0
0
1
1
1
1
1
2
1
0
0
2
1
2
2
2
0
0
1
1
1
1
0
2
2
0
1
1
1
1
1
1
1
1
0
1
1
0
2
0
0
2
0
1
1
1
0
0
1
1
1
0
1
1
1
0
3
1
2
0
0
2
1
1
1
2
2
0
1
1
1
1
1
1
2
0
0
1
1
1
0
0
1
0
0
1
0
1
1
0
2
1
0
1
0
1
1
0
0
0
1
2
2
0
0
1
1
0
2
1
2
2
1
1
0
0
1
2
0
0
0
1
2
1
0
2
1
1
0
0
1
0
0
1
1
0
2
1
1
1
2
2
2
2
1
2
2
1
1
1
1
1
2
1
2
2
1
2
1
2
0
0
1
1
0
1
1
0
2
1
0
2
2
1
1
1
2
0
1
0
0
2
0
1
0
1
1
1
0
0
1
1
0
0
7
0
1
2
2
1
1
0
2
2
0
1
2
1
1
0
1
2
1
2
1
2
1
1
0
1
1
1
1
0
1
0
0
1
0
1
1
1
1
1
1
1
1
4
2
1
1
0
1
1
1
1
1
1
1
1
1
0
2
1
0
2
0
2
1
1
1
0
1
2
2
0
1
0
2
0
1
0
1
2
1
1
1
1
0
1
1
1
0
2
3
0
1
3
0
0
1
1
1
0
1
1
1
1
0
1
0
1
0
1
1
1
0
0
2
1
2
1
1
0
1
0
0
2
0
2
0
1
2
0
1
1
1
0
1
1
0
1
1
0
1
2
2
1
0
2
2
0
1
0
0
1
1
2
2
2
1
1
1
0
1
2
1
2
1
1
1
0
0
0
0
2
1
2
2
1
0
1
1
0
1
0
0
1
0
1
2
1
2
1
1
0
0
0
1
0
2
1
2
1
0
0
1
1
1
1
1
1
2
0
1
1
1
1
0
0
0
0
1
1
2
1
0
1
0
2
1
1
2
1
1
0
1
1
1
1
1
1
0
0
1
1
2
1
0
0
1
2
0
1
1
1
2
1
2
1
1
1
1
1
2
1
2
0
0
1
3
1
1
0
2
1
2
2
0
1
2
1
1
1
0
0
2
1
0
0
1
1
2
0
1
2
1
1
1
1
0
0
0
1
2
2
0
1
1
1
0
1
0
2
2
2
0
1
1
1
2
0
1
2
1
1
1
0
2
1
1
1
0
1
0
1
0
2
0
0
2
0
2
2
1
2
1
0
2
0
0
1
0
0
0
2
2
1
1
0
0
3
2
0
2
1
0
1
0
1
1
1
1
0
1
1
0
0
0
1
2
3
0
1
2
2
0
1
1
2
0
2
2
1
1
1
2
0
1
1
1
0
1
1
1
0
0
1
2
2
2
1
0
0
2
0
1
1
2
1
1
1
0
2
1
0
1
2
0
0
1
0
2
1
1
2
0
1
0
0
1
1
0
0
2
0
1
2
1
1
1
2
2
1
0
1
2
1
1
1
0
1
1
1
1
1
0
1
1
2
0
2
2
1
1
2
0
2
1
2
2
1
1
1
2
0
1
0
0
1
0
1
1
0
1
2
0
0
0
2
1
1
0
3
1
0
1
1
1
1
0
0
1
1
1
1
2
2
0
1
2
2
1
1
2
1
1
0
2
2
0
2
1
1
1
1
2
2
1
1
0
1
0
2
2
1
0
1
0
1
0
1
1
0
2
1
2
1
1
2
1
0
2
1
0
1
0
0
0
1
1
0
2
1
1
2
1
1
2
0
1
2
0
2
0
0
1
2
2
1
1
0
1
0
1
0
1
2
0
0
0
2
0
1
0
0
1
1
0
0
2
2
1
0
1
0
1
1
2
0
1
1
1
2
1
0
4
1
2
1
1
1
0
2
1
0
0
0
2
1
2
0
1
1
0
2
1
0
0
0
1
1
2
1
1
0
1
0
1
0
2
2
2
1
1
2
0
0
1
1
1
1
2
2
1
2
2
1
2
2
0
1
0
0
1
1
0
0
2
0
1
2
1
1
0
1
0
2
1
1
0
1
1
2
0
1
1
1
0
2
1
1
1
1
2
2
7
1
0
1
1
2
2
2
1
1
1
1
0
2
3
1
2
1
1
0
1
0
1
1
2
0
1
1
1
2
0
1
1
0
3
1
1
1
0
1
2
0
0
1
0
1
0
0
1
2
1
1
2
1
0
0
1
1
1
1
0
0
2
1
0
2
2
1
2
1
2
1
0
0
1
1
2
1
1
1
0
1
0
2
1
1
1
1
0
1
0
0
1
1
1
0
2
1
0
0
1
1
1
1
2
0
2
2
0
1
0
0
2
1
1
1
1
1
1
1
1
1
2
0
0
1
1
1
1
2
1
1
1
2
1
2
0
1
3
0
2
2
2
2
1
1
1
0
1
0
1
0
1
1
0
1
1
1
0
1
1
2
1
1
1
2
1
0
2
1
2
0
0
1
1
1
2
1
1
2
0
1
0
2
1
0
2
1
0
1
1
0
2
1
0
0
0
0
1
1
2
1
2
0
0
1
1
1
1
0
2
0
0
1
0
0
2
0
1
0
0
1
1
1
0
1
0
1
1
1
1
1
1
0
1
0
1
0
1
0
1
1
0
2
1
0
0
0
1
0
0
1
1
0
2
0
2
1
1
0
2
1
0
2
1
1
1
0
1
1
1
1
0
0
0
0
1
0
1
1
0
1
1
2
1
1
1
2
2
0
1
1
1
1
0
0
1
2
0
0
2
1
0
1
0
1
1
1
1
2
0
1
0
2
0
1
1
1
2
0
2
1
2
2
1
1
2
2
1
1
2
0
0
2
0
1
2
0
1
1
2
1
0
0
0
1
1
0
2
1
1
1
1
1
0
2
0
2
3
0
1
1
1
1
2
1
0
2
1
2
0
1
0
1
1
2
1
2
1
1
1
0
1
2
1
1
0
1
1
1
1
2
2
1
1
1
1
0
1
2
0
0
1
0
1
1
1
2
1
1
0
3
0
1
0
1
2
2
0
1
1
0
1
2
1
1
1
0
2
1
1
1
1
3
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
2
3
0
1
1
1
1
1
1
1
1
0
1
0
0
2
1
1
1
2
1
1
2
0
1
1
1
2
0
1
2
2
0
0
1
0
1
2
1
0
1
2
1
2
1
1
1
2
1
0
1
2
1
0
2
0
1
2
1
1
2
1
2
0
0
1
0
0
0
1
2
1
0
0
1
0
2
2
0
1
0
1
1
2
1
0
1
2
1
2
2
0
2
0
0
1
0
2
1
1
0
1
2
2
1
1
2
1
0
0
2
2
2
0
0
1
1
1
2
1
1
2
0
0
1
1
1
1
1
0
1
1
1
1
0
1
1
0
1
1
1
1
0
1
0
0
2
0
1
0
0
1
0
1
1
2
2
2
0
2
1
2
0
1
1
1
1
0
2
1
1
2
2
2
6
1
1
3
0
1
1
0
0
1
0
2
1
1
0
2
0
2
1
1
2
0
1
1
1
1
1
0
0
0
2
0
2
2
1
1
1
1
2
1
2
0
1
0
0
1
0
3
1
1
1
1
1
3
1
0
0
1
0
2
1
0
0
2
0
2
0
1
1
2
1
2
0
1
1
1
3
0
1
1
0
1
0
3
0
2
0
2
2
2
1
0
2
0
2
2
0
1
1
2
1
1
2
1
1
0
1
0
2
1
1
1
1
0
2
1
1
1
2
0
1
1
0
2
1
2
2
2
0
0
2
0
1
0
1
2
1
1
1
3
0
0
0
0
0
2
1
0
1
1
1
2
1
2
1
0
2
1
1
0
1
0
1
1
2
1
2
0
0
2
0
2
1
1
1
2
2
1
1
1
0
0
1
1
1
0
2
2
1
1
1
2
2
1
1
1
0
1
1
1
2
2
0
1
1
1
2
1
4
0
1
1
1
1
0
1
2
0
0
1
1
2
0
0
0
2
0
2
2
1
1
1
0
1
1
2
1
0
0
0
1
0
1
0
1
2
1
2
1
0
1
0
1
1
1
1
2
0
2
1
0
1
2
0
0
2
0
1
0
2
2
2
1
1
0
0
1
1
1
2
1
1
2
0
2
0
1
2
2
0
2
1
1
1
0
0
2
0
2
0
2
2
1
2
1
1
2
1
1
0
0
0
0
0
0
1
2
1
0
0
0
1
2
1
0
1
1
2
0
1
1
0
1
2
2
2
0
0
0
1
2
2
1
0
1
2
2
1
2
0
0
1
0
0
1
0
1
4
1
0
1
4
2
2
0
1
0
2
0
0
1
0
1
0
2
1
0
2
0
0
1
0
1
1
1
0
0
2
2
2
1
0
2
0
1
1
1
1
1
2
1
2
1
1
1
1
0
1
0
2
0
0
1
0
0
1
0
0
2
0
1
1
1
1
0
1
0
0
1
0
0
0
1
1
0
1
1
1
1
2
1
1
0
2
0
0
2
2
2
1
2
1
1
1
0
2
2
2
0
1
0
1
2
1
2
2
0
0
1
1
1
1
3
0
1
1
2
2
1
0
0
1
1
1
2
2
0
2
2
0
1
1
0
0
2
1
0
0
1
1
1
1
0
0
1
2
1
1
1
1
2
0
1
1
1
2
1
1
0
0
1
0
0
1
1
2
0
2
0
0
1
2
0
2
1
1
2
2
1
1
1
1
0
0
2
1
1
2
1
1
0
1
1
0
1
2
1
1
1
1
0
1
1
1
0
2
0
1
1
2
1
1
1
0
1
2
0
0
1
1
0
2
1
1
1
2
1
1
1
1
1
0
0
1
1
1
0
0
0
2
1
2
1
2
1
0
3
2
2
1
0
1
2
1
0
2
0
2
0
0
1
1
0
1
1
1
0
2
1
1
2
2
1
1
0
4
0
0
1
1
0
2
0
1
0
1
0
1
1
2
1
1
1
1
1
0
1
1
1
1
1
1
2
0
1
0
1
0
1
1
2
2
0
1
1
0
1
2
0
1
1
0
2
2
0
1
1
1
0
0
2
0
0
0
0
0
1
0
1
1
1
2
1
1
2
1
1
1
1
0
1
2
1
2
1
1
1
1
1
1
0
2
2
1
0
1
0
1
3
1
1
1
1
0
1
1
3
0
1
0
2
1
1
2
1
1
1
1
0
0
2
0
2
1
1
1
0
1
2
1
1
1
0
0
1
1
2
2
1
1
2
0
2
0
2
2
2
1
2
0
0
1
0
1
1
2
2
2
1
1
1
0
0
1
1
0
1
1
1
2
1
0
1
2
0
2
2
1
1
1
1
2
1
2
0
1
0
0
1
1
0
1
2
2
1
2
0
1
1
1
0
1
0
2
2
0
0
1
0
0
2
1
2
2
2
1
2
2
2
1
0
1
1
1
1
1
0
0
0
1
0
1
0
1
1
2
2
1
1
1
0
2
1
1
1
1
0
0
1
2
0
1
2
0
0
2
0
1
0
2
2
0
2
2
2
1
1
0
2
0
0
1
0
1
2
1
0
2
1
0
2
1
1
1
1
0
2
2
1
0
1
1
2
1
0
1
4
0
0
1
2
0
1
0
1
1
1
1
1
2
1
1
1
2
1
0
1
1
0
1
1
1
0
2
0
0
1
0
1
0
1
0
1
2
0
1
2
1
0
0
2
2
1
2
1
1
2
1
2
1
2
1
1
1
1
1
1
2
0
1
1
2
1
2
0
1
0
2
1
1
2
1
0
0
0
0
1
1
0
0
1
0
1
2
1
1
0
0
0
4
1
2
1
0
1
0
1
1
2
0
2
2
1
2
2
0
2
0
2
1
1
1
1
1
1
1
0
1
1
0
2
1
0
1
2
2
0
1
1
1
0
0
0
2
2
1
0
1
1
2
0
2
1
2
1
1
2
0
5
2
3
2
1
0
1
1
1
0
2
2
1
0
1
0
1
1
2
1
2
0
2
1
0
2
1
1
1
0
0
1
3
0
0
2
2
1
5
1
2
1
1
0
2
2
0
1
0
1
1
0
1
1
1
1
1
2
1
1
0
0
1
0
0
1
1
1
1
0
1
1
2
1
0
1
0
1
0
1
4
0
2
0
2
2
1
1
0
1
2
0
0
1
1
1
2
0
0
1
0
1
1
1
1
0
1
1
2
0
1
1
1
0
2
1
0
0
1
0
1
0
1
1
1
1
1
1
2
1
2
1
2
1
2
1
0
1
0
0
1
2
1
1
0
0
2
1
0
1
2
1
1
1
0
1
2
2
1
0
1
0
1
2
1
1
1
0
1
0
2
2
0
0
1
1
1
0
1
0
0
2
0
1
0
1
1
1
2
1
1
0
0
2
1
1
1
1
2
0
2
0
0
1
1
2
2
0
1
0
1
2
1
0
4
0
0
2
1
1
1
0
1
2
1
0
2
0
2
1
1
2
0
2
1
2
0
1
0
1
1
1
0
4
2
0
1
1
2
1
2
1
2
2
2
0
2
0
1
2
2
0
1
1
0
0
2
1
1
1
1
1
1
1
0
1
0
1
0
2
1
0
1
1
0
1
2
0
1
3
1
1
0
0
0
1
1
1
1
2
0
0
2
1
1
2
1
0
1
0
1
1
0
1
1
0
1
1
1
2
1
1
1
2
1
1
2
1
0
1
0
0
0
1
1
0
0
1
0
0
2
1
0
1
0
0
1
0
1
0
0
0
1
1
0
1
1
1
0
2
1
2
3
2
0
2
1
1
2
0
0
2
0
2
3
1
0
0
5
2
0
2
0
1
1
1
2
1
1
1
1
0
0
0
1
0
0
0
0
1
2
0
0
2
0
1
2
2
2
1
2
1
1
1
1
2
1
0
0
0
0
1
0
0
1
1
1
0
1
1
1
1
1
1
0
1
2
1
0
1
1
2
0
1
0
2
1
1
1
1
2
1
1
1
1
0
0
1
2
1
2
0
0
1
0
3
1
1
1
1
0
2
2
1
1
1
0
2
0
0
0
2
1
0
0
1
1
0
1
2
1
1
1
0
1
3
1
2
2
0
1
1
0
2
1
1
1
0
1
1
0
2
1
0
2
1
1
0
1
1
2
1
1
2
0
1
4
0
2
2
1
0
1
1
2
0
0
1
2
1
1
2
2
1
0
2
1
0
0
0
1
0
1
1
6
2
0
0
1
1
1
1
1
1
1
1
2
1
1
1
2
2
1
0
0
2
0
2
0
0
3
0
0
0
2
2
1
1
0
0
2
0
2
0
0
1
2
2
1
1
0
2
2
1
0
1
1
1
1
0
1
2
0
2
1
0
1
1
2
2
0
1
2
1
1
1
1
1
1
2
1
1
2
1
2
1
1
0
2
1
1
0
2
2
1
1
1
0
0
1
2
2
1
1
0
1
1
1
1
0
0
2
1
1
1
2
1
1
1
1
0
2
1
2
0
1
1
2
1
0
1
1
0
0
0
1
1
2
1
0
0
0
1
1
0
1
1
2
3
3
1
2
0
2
1
2
1
2
0
2
1
2
0
1
2
4
2
0
0
2
0
0
1
1
1
2
1
1
2
0
0
1
0
1
1
2
1
1
2
1
1
2
0
0
0
1
2
1
1
2
1
2
2
1
1
1
5
2
2
2
2
1
1
2
2
1
0
2
2
0
3
2
1
2
0
1
2
0
1
2
2
0
2
0
2
1
0
2
1
0
0
2
0
2
1
1
0
0
1
1
1
1
1
1
1
1
2
1
1
1
0
0
1
1
1
1
2
0
1
1
1
1
1
2
1
1
1
1
1
1
1
3
0
0
0
1
1
1
2
2
0
1
0
0
0
1
2
1
2
1
1
1
1
1
2
2
1
0
0
0
2
2
1
2
1
1
1
2
2
0
0
0
2
1
0
2
1
2
1
2
1
1
0
1
1
0
1
1
1
0
1
2
0
0
0
1
2
2
0
1
0
2
2
0
0
1
2
1
1
2
2
2
1
1
0
1
0
2
1
0
1
2
0
0
0
1
1
1
1
1
0
0
1
2
1
1
0
0
2
0
1
2
1
1
0
1
1
0
1
0
2
2
2
1
2
2
2
1
2
1
2
1
1
1
1
0
2
1
2
1
0
1
1
1
0
0
1
1
2
1
1
1
0
1
0
0
1
0
0
1
1
1
1
1
1
1
1
0
1
1
0
0
1
0
2
1
1
2
1
1
1
0
1
0
0
2
1
2
0
0
1
1
2
0
1
1
0
0
0
2
2
0
2
1
1
1
0
1
1
1
1
0
2
1
1
0
1
0
0
2
1
0
0
3
1
1
1
1
2
1
2
2
1
1
1
2
0
2
1
1
1
2
2
1
1
0
1
1
2
2
0
1
0
0
1
0
0
1
1
0
2
2
0
0
1
1
0
1
1
1
0
1
0
2
1
2
0
1
1
1
1
0
0
1
2
0
3
1
0
2
1
1
1
1
2
2
3
0
2
0
1
0
0
0
2
1
2
0
1
1
0
2
2
1
2
0
1
1
0
0
1
2
0
1
2
0
1
2
2
0
1
2
1
2
1
0
1
1
2
1
0
2
0
2
1
2
1
1
0
1
2
0
1
2
0
1
0
2
0
1
0
2
0
1
1
1
0
0
2
1
1
1
1
2
0
1
1
0
1
2
0
1
0
0
1
1
1
2
1
2
1
0
0
2
1
1
1
1
0
1
1
2
0
1
0
1
1
0
2
2
0
1
1
1
2
1
2
1
0
1
1
0
2
0
0
0
2
1
0
2
2
1
1
0
0
1
1
2
0
0
1
1
2
0
1
0
1
0
0
0
2
1
0
0
1
1
0
1
0
1
1
2
2
0
0
1
0
1
1
1
1
1
1
1
2
0
1
1
1
0
1
0
2
0
1
1
1
1
2
2
1
0
2
0
1
1
0
2
1
1
1
1
0
2
2
1
2
1
0
1
1
2
0
1
0
0
1
1
2
1
2
0
1
1
0
0
1
2
1
0
0
1
0
1
0
1
2
1
0
1
1
0
1
0
1
1
2
2
0
0
2
1
0
1
1
1
0
1
1
2
2
2
2
0
0
1
0
2
0
3
1
1
1
2
0
1
1
2
2
0
0
1
0
1
1
1
0
0
0
1
1
0
0
2
1
1
3
0
1
0
0
1
1
0
2
1
1
0
1
0
0
1
2
2
1
1
2
1
1
2
0
0
0
0
1
1
1
0
1
1
1
1
2
0
0
0
0
2
0
1
5
2
2
1
0
1
1
2
0
1
1
1
2
1
1
1
0
1
2
1
1
1
1
2
2
1
2
1
1
1
1
1
0
1
2
1
1
1
1
0
1
1
1
1
0
0
2
0
0
1
0
0
1
2
0
2
1
1
1
0
0
1
0
1
0
1
1
1
1
2
2
1
0
0
1
0
0
0
1
1
1
1
1
0
2
1
2
1
2
1
1
1
0
1
0
0
1
2
2
1
1
2
2
1
1
1
1
0
2
0
1
0
1
1
2
1
1
2
1
2
1
1
1
2
1
0
0
1
2
0
0
1
2
0
2
1
1
0
1
1
2
1
1
1
2
1
1
0
1
1
1
0
1
1
1
0
2
1
0
0
1
3
2
1
1
1
1
0
0
0
0
1
0
0
0
2
1
1
1
0
0
1
0
1
1
1
1
1
1
1
1
2
2
0
0
1
1
0
1
2
0
0
0
2
1
1
2
1
1
0
1
0
1
0
2
2
2
1
1
1
0
1
1
1
0
0
2
1
1
1
2
2
1
2
2
2
1
0
1
1
1
1
3
2
0
1
0
0
1
1
1
0
1
0
1
0
1
1
0
2
2
1
1
1
0
1
1
2
1
1
1
2
0
1
1
0
1
0
1
0
1
1
2
0
1
0
2
2
0
1
1
0
2
1
1
0
1
1
4
1
1
1
1
3
1
1
2
0
3
2
2
1
1
1
0
0
0
0
1
1
2
1
2
0
0
1
1
0
1
1
1
0
2
1
0
2
2
0
1
1
1
1
1
1
2
0
0
1
1
0
0
2
2
0
2
2
1
3
2
0
1
0
0
0
1
1
0
1
2
2
1
0
1
2
3
0
0
1
1
1
1
1
1
1
1
1
0
1
2
0
0
1
1
1
1
0
1
0
1
1
2
0
1
1
1
0
1
0
2
1
0
2
1
1
1
2
1
0
2
2
1
0
1
1
0
0
0
1
1
0
2
0
1
0
0
1
0
0
1
1
1
1
0
1
1
1
0
1
1
1
2
2
0
0
2
1
1
2
1
1
2
2
1
1
0
1
1
0
2
2
1
1
1
1
1
1
1
2
2
2
0
1
1
2
1
0
0
0
0
1
2
1
1
2
2
2
1
1
1
0
1
2
1
0
1
1
1
1
0
1
1
1
1
0
2
1
1
0
0
0
1
2
0
0
0
2
0
1
1
0
1
0
0
2
1
3
1
1
2
1
1
1
1
2
0
0
0
0
1
1
0
1
2
1
0
1
0
1
6
1
2
1
1
0
3
1
0
2
2
0
2
1
0
2
1
2
1
1
1
0
0
1
1
1
1
3
2
1
1
0
1
2
0
0
0
0
1
1
0
1
2
1
1
2
1
2
1
2
1
0
1
0
1
1
0
1
1
1
1
2
1
0
1
1
1
0
2
1
2
0
1
1
2
2
0
0
0
2
2
0
1
1
1
1
1
1
1
2
1
3
1
1
1
1
0
2
2
1
2
1
0
1
2
1
1
1
2
0
2
1
2
0
2
0
2
2
2
0
1
1
2
0
2
1
0
1
2
2
0
2
0
2
0
0
1
2
2
0
1
0
0
0
1
1
1
1
2
0
1
1
2
0
1
1
1
0
1
0
0
0
1
0
1
1
1
1
1
0
1
1
0
2
1
2
1
1
2
1
2
1
2
0
1
0
1
1
1
2
0
1
2
4
0
1
1
2
1
1
1
2
1
1
1
0
2
0
1
0
1
1
1
1
1
1
1
0
0
2
1
0
2
0
1
1
1
1
0
1
1
1
0
1
1
0
2
1
0
1
1
1
1
1
1
1
2
1
3
2
0
2
0
0
1
2
1
1
2
1
0
1
0
1
0
1
0
1
0
2
1
1
2
1
1
0
2
1
0
2
3
0
1
1
2
1
1
0
1
0
0
0
0
1
2
2
2
0
0
0
1
1
2
0
1
1
2
2
1
1
0
1
1
1
1
1
0
1
0
1
0
2
2
1
1
3
1
1
1
2
2
2
2
0
0
1
1
0
2
1
1
2
0
2
0
1
0
0
0
2
0
2
0
0
1
1
0
1
2
1
1
1
1
1
1
1
2
1
0
1
1
1
1
1
2
1
2
0
0
2
1
2
0
0
1
1
1
1
5
0
1
0
1
2
2
0
1
1
1
2
1
1
1
1
0
2
1
0
2
1
1
1
1
0
0
2
1
2
2
0
1
1
1
1
1
0
0
0
2
1
1
1
0
1
1
0
0
1
0
1
1
1
2
1
0
1
2
2
2
1
3
2
1
1
0
0
1
1
0
1
0
2
0
1
1
1
1
0
1
2
2
2
0
0
3
1
0
0
1
1
2
0
1
2
1
1
0
1
2
2
2
2
2
1
1
0
1
1
0
1
1
1
0
1
1
2
1
2
0
2
0
1
1
1
2
1
4
1
0
1
0
1
2
1
0
2
0
1
0
0
1
0
1
0
1
1
0
2
1
1
0
4
2
2
1
1
1
0
0
1
1
1
0
2
2
2
0
0
2
1
2
0
2
0
0
0
1
0
1
0
1
4
1
0
1
1
0
1
1
1
1
2
1
1
1
0
0
1
0
1
2
2
1
1
0
1
2
1
6
1
1
0
1
1
1
2
0
2
1
1
2
1
0
1
1
1
1
2
0
2
1
2
0
0
2
1
1
1
0
1
0
1
1
1
2
1
1
0
2
2
1
1
1
1
1
1
1
0
1
1
1
0
0
0
2
1
0
0
1
0
2
2
1
1
0
2
2
0
2
2
1
1
1
2
1
1
1
1
1
1
2
2
1
1
1
2
1
0
1
0
1
1
0
1
2
0
1
1
0
2
1
2
1
0
0
1
2
1
2
0
0
2
1
0
1
1
0
1
1
2
1
0
0
0
2
1
2
0
1
1
0
1
1
1
1
1
1
1
1
1
1
2
1
0
1
1
0
0
2
1
1
1
0
1
2
1
1
0
2
0
1
2
1
2
0
1
1
1
0
1
2
0
1
2
1
1
0
1
1
1
2
1
2
1
2
2
1
0
0
0
2
0
0
1
2
1
1
0
0
2
1
0
2
1
1
3
2
1
1
0
0
1
2
0
1
2
1
1
1
1
1
1
1
1
2
2
1
1
2
1
1
0
1
3
1
1
0
0
0
0
0
1
1
2
1
1
0
0
0
0
1
1
0
1
2
1
1
0
3
1
0
1
1
0
1
1
2
0
1
0
0
1
1
0
3
2
2
1
1
0
0
0
0
0
0
1
1
2
0
1
0
0
1
2
2
0
1
1
0
0
1
0
1
1
0
1
1
1
1
1
1
2
1
3
1
1
1
1
1
1
1
1
1
2
4
0
1
1
0
2
1
0
0
1
2
1
1
0
0
2
2
1
1
1
2
0
2
1
0
1
0
0
2
2
1
1
0
3
0
1
1
1
2
2
1
0
2
2
0
1
2
2
0
1
1
1
1
0
0
1
1
0
0
1
1
1
1
0
1
1
0
4
2
0
2
1
2
1
1
0
0
0
2
2
1
1
2
0
1
1
1
1
2
0
0
1
0
1
0
1
1
1
1
1
0
2
0
1
1
1
1
0
0
1
1
1
1
0
1
0
1
1
0
1
0
0
2
0
2
2
2
1
1
1
0
1
0
1
1
2
1
0
0
1
1
0
0
2
0
0
1
0
1
1
0
1
0
2
0
1
2
0
0
0
1
1
1
0
0
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
0
1
1
0
1
1
1
2
0
1
1
1
1
1
1
2
1
1
0
0
1
0
1
1
0
2
2
1
4
2
1
1
1
1
0
0
1
1
1
0
2
1
0
1
0
2
1
1
0
1
1
1
1
2
2
0
2
1
0
1
1
0
1
1
2
0
3
0
2
0
0
2
2
1
2
1
2
2
0
0
1
0
0
2
0
0
1
1
0
3
1
0
1
2
0
2
0
1
0
0
1
0
1
1
2
0
1
2
1
0
1
0
0
1
2
1
0
1
2
0
1
2
1
1
0
0
1
1
0
1
0
0
3
1
2
1
1
1
2
1
1
0
2
1
0
2
1
1
1
1
0
1
2
2
2
0
0
0
1
2
1
2
1
1
1
5
1
0
0
1
1
0
1
1
2
0
0
1
1
1
1
0
2
0
2
0
0
3
1
2
0
1
1
0
1
1
0
0
2
0
0
0
2
2
1
2
0
1
1
0
0
1
0
1
1
2
0
2
1
2
1
1
0
0
0
2
1
1
1
1
0
2
1
1
2
2
2
0
2
0
0
0
0
1
1
1
2
0
1
0
1
2
1
1
0
0
1
1
0
1
1
0
1
0
0
1
0
2
1
2
2
1
0
1
1
1
1
0
1
1
1
0
1
1
1
3
1
2
0
1
1
0
1
0
1
1
1
2
2
1
1
1
0
1
1
1
0
0
1
1
1
0
1
1
0
1
1
2
1
1
1
0
1
1
2
0
1
1
0
1
2
1
2
0
2
1
1
0
1
0
0
1
2
0
0
1
2
0
2
1
0
1
0
2
0
1
0
1
1
2
1
1
2
0
1
2
1
1
1
1
1
1
2
1
0
1
1
2
2
1
2
2
2
1
0
0
0
0
0
0
1
1
1
2
1
0
1
0
1
1
0
0
1
1
1
1
1
1
1
2
1
1
2
2
2
1
0
2
1
1
2
1
2
1
2
0
0
1
0
1
1
1
1
1
0
0
1
1
2
1
1
2
1
0
3
1
1
0
1
2
0
0
1
0
0
1
0
0
1
1
1
1
0
1
0
1
1
2
1
1
0
1
1
2
0
1
0
1
1
2
2
0
0
2
1
1
1
1
0
2
2
1
2
0
0
1
2
1
0
1
0
1
1
1
0
2
1
0
0
1
0
1
2
1
2
0
0
1
1
0
0
0
1
0
2
1
1
1
1
1
1
0
1
2
1
1
0
1
2
1
1
2
2
1
0
0
1
1
2
0
2
2
1
1
0
1
0
1
0
1
1
1
2
0
0
1
2
2
2
0
0
0
0
2
2
1
1
1
2
0
0
1
1
2
0
1
1
0
0
1
1
1
1
1
2
2
1
1
0
2
0
1
1
2
2
0
0
1
1
3
0
1
1
1
0
1
0
2
1
0
0
2
0
0
1
0
2
1
3
0
1
0
1
1
0
0
1
1
2
1
1
0
2
1
0
2
2
0
1
0
1
1
0
1
1
0
2
1
2
1
1
2
1
1
0
0
1
0
2
0
0
1
1
1
2
0
1
2
0
1
0
1
1
1
2
1
1
1
1
1
1
1
1
0
0
1
1
1
0
2
1
2
1
0
1
0
0
1
1
1
0
2
0
1
1
0
1
2
1
0
1
1
0
0
1
2
1
1
0
1
0
2
0
1
1
1
1
1
2
1
1
2
13
1
0
2
1
4
2
0
0
0
1
0
2
1
0
1
2
1
0
1
0
1
1
1
2
1
0
1
0
1
2
1
2
0
2
1
0
2
0
2
0
2
2
1
1
1
1
1
1
1
1
1
0
0
0
1
2
1
1
0
2
2
2
1
1
0
0
1
1
2
2
1
1
1
1
2
1
1
1
0
2
0
0
0
1
0
0
0
1
1
1
2
2
1
0
1
2
2
1
1
2
0
0
1
1
0
1
0
1
0
1
2
1
1
1
2
0
2
1
2
0
1
2
0
2
2
0
1
1
1
1
1
1
0
2
2
0
2
1
2
2
1
2
1
1
1
0
1
2
0
0
2
2
2
1
0
1
1
1
0
2
0
0
0
1
0
2
1
0
0
0
1
2
1
1
2
1
1
1
1
0
1
1
1
1
2
0
1
1
0
2
2
1
1
1
1
1
2
2
2
0
0
0
0
0
1
0
0
0
1
2
1
1
1
1
1
1
1
1
1
1
0
2
2
0
1
0
2
0
1
0
0
1
1
2
1
2
1
2
0
1
1
1
1
1
0
0
1
1
0
0
2
1
1
1
1
0
2
1
0
0
0
2
2
2
1
2
2
1
2
0
1
0
1
0
0
0
1
1
2
0
2
2
0
1
0
0
0
2
0
1
1
0
3
1
1
2
0
0
1
0
1
1
0
2
0
0
1
1
1
2
0
1
2
1
0
1
1
1
1
1
0
0
1
1
0
1
0
1
1
1
1
0
1
2
2
2
1
2
0
2
1
0
1
1
1
0
1
1
1
1
0
1
2
0
1
0
1
1
1
2
0
1
1
1
2
2
1
0
0
2
1
0
2
2
0
1
2
1
0
2
1
0
1
2
0
1
1
0
2
0
1
1
0
0
1
1
2
0
0
4
1
2
0
1
0
1
0
0
0
1
1
0
0
0
1
0
0
0
1
1
1
0
1
1
0
0
0
1
0
0
1
0
0
0
1
1
0
0
2
1
1
2
1
1
2
1
1
0
1
0
2
2
1
1
0
1
0
0
1
2
2
1
1
0
1
2
1
0
0
2
1
1
1
1
0
1
0
1
1
0
0
1
2
3
0
4
2
2
0
0
2
1
1
0
1
0
0
0
2
2
2
1
0
0
1
0
0
0
1
1
1
1
1
1
1
2
1
1
1
0
1
1
2
0
0
2
2
1
1
0
0
1
0
0
0
2
1
1
1
0
2
2
1
2
1
0
2
1
2
1
1
0
0
1
0
0
1
0
2
2
1
1
1
1
1
2
0
2
2
1
1
1
0
2
1
0
3
2
2
0
2
2
2
1
1
1
0
0
1
1
1
1
2
1
0
1
1
0
0
2
1
0
1
1
0
1
1
1
1
0
2
0
3
0
1
1
1
2
1
3
0
1
0
1
1
2
0
1
1
0
1
1
0
1
1
0
0
0
0
0
0
2
0
1
2
1
2
2
0
0
1
0
1
0
1
1
1
0
1
0
1
2
1
1
0
2
0
0
0
1
1
2
1
2
1
1
0
1
1
1
0
1
0
1
0
1
2
0
1
1
3
3
1
0
1
1
1
0
2
3
1
1
0
1
1
1
1
0
2
0
0
1
1
1
1
3
2
2
2
0
1
2
1
1
1
2
1
0
1
1
0
0
0
1
1
1
1
0
0
1
0
0
1
0
2
0
1
1
1
2
1
1
1
0
1
1
1
1
1
1
0
1
1
1
0
0
2
3
1
0
1
1
0
1
0
0
2
2
1
2
1
1
0
1
1
0
1
1
1
1
1
0
1
1
0
0
1
2
0
1
0
0
2
1
1
1
1
2
1
1
1
2
1
0
1
2
1
1
1
1
1
0
0
2
0
1
1
0
1
0
1
0
1
1
1
1
2
1
1
0
1
1
1
0
2
2
2
1
1
1
1
0
1
1
1
1
0
0
1
1
2
1
1
1
1
0
1
3
2
2
1
1
1
1
0
1
1
0
1
1
0
1
2
2
1
0
1
1
0
2
2
1
1
0
1
1
0
0
1
1
2
1
2
0
1
1
1
1
2
0
1
0
1
1
1
1
2
1
2
2
0
2
1
0
1
0
1
1
0
1
0
1
1
1
0
0
1
1
1
1
1
1
0
0
0
1
0
1
1
1
2
0
2
1
2
1
1
0
1
1
1
2
1
1
2
0
1
1
2
2
1
1
1
0
2
1
0
1
2
1
2
0
1
0
1
1
1
0
2
2
4
1
1
1
1
1
1
1
2
0
0
1
0
1
0
2
2
2
1
0
2
1
0
1
2
1
3
0
2
1
1
0
2
1
1
2
1
1
0
0
0
1
2
1
0
0
2
1
0
0
2
1
0
1
1
1
1
1
0
0
0
0
1
1
1
2
1
0
0
2
0
1
1
1
0
0
1
1
1
1
2
0
0
1
1
2
1
1
1
0
2
0
1
1
1
0
0
1
1
0
1
1
1
3
2
1
0
1
0
1
0
2
0
2
1
0
2
1
2
2
1
0
1
2
2
0
1
1
1
1
0
0
2
2
1
2
2
1
2
1
1
0
1
0
0
1
1
0
0
2
0
0
2
0
0
0
1
1
0
1
0
1
1
0
0
0
0
2
1
0
2
0
2
1
1
2
2
1
1
1
0
2
0
0
3
1
0
2
1
1
1
1
1
0
0
0
0
0
1
2
0
0
2
1
0
2
0
2
1
0
0
0
0
1
1
1
0
1
0
0
1
0
1
1
1
2
0
0
0
0
0
0
1
2
0
2
2
0
1
0
2
1
2
2
1
0
1
1
0
1
0
2
1
1
0
0
0
1
2
2
0
0
1
1
1
1
1
1
1
1
0
1
0
1
2
2
0
0
2
1
1
1
1
1
0
1
0
1
0
0
1
0
1
2
1
2
2
0
1
0
0
1
0
0
1
1
0
0
0
1
0
1
0
1
0
1
2
1
1
1
2
1
0
1
1
0
1
0
1
2
1
1
1
1
2
2
1
0
1
0
2
0
0
0
1
0
1
1
2
0
1
1
2
1
1
1
2
1
1
1
2
1
1
0
1
0
1
1
2
1
1
1
1
2
1
0
1
2
1
1
2
2
0
4
0
1
2
1
0
1
1
1
0
1
0
0
2
1
1
1
1
1
1
1
1
0
1
1
2
0
3
2
1
1
0
1
1
0
0
1
2
2
1
0
1
1
1
1
1
0
1
0
1
2
0
1
1
2
2
1
1
1
0
0
2
2
2
2
0
0
1
2
1
1
1
2
1
3
2
2
1
2
1
2
1
0
1
1
2
0
2
1
1
1
0
2
0
1
2
0
1
1
2
1
1
1
1
0
0
0
1
1
0
0
1
0
0
0
0
0
1
1
1
2
1
0
0
1
0
3
2
2
0
1
1
0
0
0
2
1
0
2
0
2
1
0
1
0
0
1
1
1
2
1
0
0
2
0
1
0
3
1
1
1
0
1
0
1
1
1
1
0
2
1
1
1
2
1
0
1
2
1
1
1
1
0
0
2
1
1
2
0
2
3
0
0
1
1
1
0
0
0
0
2
1
1
1
1
0
1
0
0
2
1
0
2
1
1
0
0
1
2
0
1
4
1
1
1
0
1
1
1
0
0
1
2
1
0
0
1
1
1
1
2
1
0
1
0
1
2
0
1
0
1
1
2
2
2
1
0
1
1
1
1
1
0
1
0
1
0
2
2
0
1
1
1
1
1
1
0
1
0
1
1
1
0
1
1
1
1
0
1
0
3
1
1
1
0
0
2
2
1
1
1
1
0
1
1
2
1
1
1
1
1
1
1
1
1
2
2
2
1
2
2
1
1
1
0
0
2
2
2
0
1
1
2
0
1
1
2
0
1
1
0
1
2
2
1
0
1
0
1
2
0
1
2
1
0
0
1
0
0
1
0
3
1
0
1
1
1
0
2
2
0
1
2
2
0
1
1
1
1
1
2
2
2
1
1
1
2
0
0
1
2
2
1
1
3
1
2
1
2
1
2
0
1
1
1
1
2
0
1
1
2
1
1
0
1
1
1
3
0
1
1
1
1
0
1
0
0
1
2
1
1
3
0
0
0
1
1
1
1
1
1
1
0
1
2
2
1
2
1
1
0
2
1
1
1
1
1
0
1
1
1
0
1
0
2
1
1
1
1
1
0
2
2
0
1
1
1
1
1
0
1
1
0
3
0
1
0
1
2
1
0
1
1
1
2
2
2
1
0
2
1
2
0
1
1
1
1
0
2
2
0
2
1
2
2
1
0
1
2
2
2
0
1
1
2
1
1
1
1
1
2
1
2
1
0
2
0
2
1
1
0
1
1
0
1
2
0
1
0
0
1
2
2
1
2
1
1
2
1
0
1
1
2
1
0
1
1
0
1
1
2
0
2
1
2
0
1
1
1
1
0
6
0
1
1
1
2
0
1
1
2
2
2
0
2
0
1
1
1
2
1
0
0
1
1
1
0
1
2
0
1
2
0
1
1
1
0
0
1
1
1
0
1
1
0
1
1
1
1
1
1
1
1
0
2
1
0
1
0
1
1
3
1
1
1
2
0
0
1
0
1
1
2
0
0
1
2
0
1
1
1
1
0
0
0
1
0
1
1
0
0
1
1
2
2
1
0
2
2
0
0
2
0
0
1
0
0
2
2
1
1
0
1
0
1
0
0
0
0
1
2
1
0
2
1
2
2
1
1
2
1
1
1
0
1
1
2
0
1
2
0
0
0
0
1
0
0
2
1
1
2
1
2
1
0
0
1
0
1
1
0
3
1
0
0
1
2
0
2
1
1
1
0
1
2
0
1
1
2
2
1
0
1
0
1
1
0
2
2
0
1
1
1
1
1
2
0
1
1
2
2
0
1
1
1
1
0
2
1
2
3
1
2
2
1
1
2
1
1
0
0
2
1
1
1
1
2
1
0
1
2
1
0
2
0
0
0
1
2
1
2
2
2
1
0
0
1
0
0
1
1
1
0
2
1
1
0
2
1
2
1
0
1
0
0
1
0
0
1
2
1
1
0
0
1
2
0
1
1
1
0
1
1
1
0
0
2
1
1
1
1
2
1
0
2
2
3
0
1
1
0
2
1
1
2
1
3
1
1
0
1
1
2
0
1
2
1
1
0
0
0
1
1
1
0
1
2
0
1
1
0
1
1
1
0
0
2
1
1
0
0
1
0
1
0
0
0
2
0
1
0
2
2
1
1
0
1
2
2
1
2
2
1
2
1
2
1
2
0
1
2
1
1
1
1
1
1
1
0
1
0
1
1
1
0
2
1
1
1
2
2
0
0
1
0
2
2
2
0
1
2
1
2
2
2
0
1
1
0
2
1
2
1
0
0
1
1
0
1
1
1
0
1
2
2
1
1
2
1
0
1
0
2
1
0
1
2
1
1
2
2
0
2
2
2
1
2
2
3
0
2
1
1
1
1
1
1
2
1
0
1
1
1
2
2
1
1
0
0
2
1
2
1
0
1
1
2
1
0
1
1
0
2
0
0
0
2
0
2
1
2
1
0
0
1
1
2
0
0
3
0
0
0
0
1
0
1
2
1
1
0
1
2
2
1
1
1
1
2
0
0
1
0
1
0
0
1
2
2
1
2
2
1
2
1
0
1
0
2
0
2
2
0
1
1
2
0
0
1
2
2
0
2
2
1
2
1
0
1
1
1
1
2
0
1
2
1
0
0
1
1
0
0
2
1
1
0
1
1
10
0
1
0
0
0
0
0
2
1
2
1
2
1
2
2
3
1
0
3
2
0
0
1
0
1
0
1
1
1
2
2
2
0
1
1
2
1
2
0
0
0
1
1
1
1
0
0
0
2
1
2
0
1
0
1
0
1
1
0
1
2
1
1
0
0
1
1
1
1
3
1
2
2
1
2
0
1
0
1
1
0
0
1
1
1
1
1
1
0
2
0
1
1
3
0
1
1
1
1
1
2
2
1
0
1
1
2
2
3
0
1
2
0
1
1
1
1
0
1
2
0
0
1
2
0
1
1
1
0
1
2
1
1
1
1
1
1
2
2
1
0
0
2
0
1
0
1
1
0
2
2
1
1
1
1
2
1
0
2
0
1
1
1
2
0
2
0
1
1
0
1
2
1
1
1
0
1
1
1
1
1
1
1
0
2
0
2
1
1
2
0
2
0
0
1
0
1
1
2
2
0
0
2
1
0
0
0
1
1
1
0
1
2
1
1
2
2
1
1
0
0
1
1
1
1
1
1
1
0
0
2
0
1
2
1
2
1
0
0
1
1
1
1
2
1
1
0
0
0
0
0
0
1
1
0
1
1
2
1
2
1
1
1
2
2
0
1
0
1
1
1
0
1
0
2
1
1
2
1
1
0
0
0
2
1
1
2
1
1
2
2
1
1
0
2
0
1
0
2
0
3
2
0
0
2
0
0
4
0
2
2
2
1
1
2
1
1
1
1
1
1
0
0
2
1
1
1
1
0
1
1
1
0
0
1
1
1
2
2
0
0
0
0
1
0
2
0
2
0
0
1
0
0
0
1
1
1
2
1
1
1
2
1
0
1
0
2
1
1
2
2
1
1
1
0
1
1
1
0
1
1
0
1
1
0
2
1
2
2
1
1
1
1
1
1
1
0
1
2
0
1
1
1
0
0
2
0
0
2
0
0
1
1
0
1
1
0
1
2
2
1
1
2
0
0
1
0
0
1
1
1
0
1
1
2
1
2
2
0
2
1
1
2
1
0
2
0
1
0
2
1
0
1
1
0
0
2
0
0
1
1
0
1
0
1
1
1
0
2
0
0
1
0
0
1
2
1
0
1
1
0
1
1
2
1
1
1
1
0
1
2
1
0
1
2
1
1
1
1
1
2
2
2
2
1
2
0
0
1
2
0
1
2
0
1
2
1
1
2
0
1
0
1
0
2
1
0
0
1
0
1
0
1
0
0
1
0
1
1
1
0
2
1
2
1
0
1
0
1
1
1
1
2
2
0
0
0
1
1
0
1
0
1
2
0
0
1
2
1
0
1
1
2
1
1
0
0
1
1
0
0
1
1
0
0
1
1
0
0
2
2
1
0
1
0
1
2
1
1
1
1
0
0
0
1
1
0
0
0
2
1
1
1
0
0
1
1
1
1
1
2
0
1
1
0
1
1
1
2
1
1
0
1
0
2
1
0
1
1
0
2
1
1
1
0
0
2
1
0
0
1
0
1
1
2
0
1
2
1
1
1
0
1
0
0
1
0
2
0
0
1
2
0
1
2
1
0
2
0
0
0
2
0
1
2
1
1
1
2
0
1
1
2
2
2
1
2
3
1
1
0
0
2
1
0
2
2
1
0
1
1
1
2
2
1
1
2
1
1
0
2
2
0
1
0
1
0
0
0
1
0
0
1
0
2
1
1
0
1
2
1
0
0
0
2
2
0
1
2
0
2
1
1
1
2
0
1
1
1
1
2
1
1
1
1
1
1
1
0
1
2
0
1
1
1
2
0
5
1
2
1
2
1
2
0
1
2
1
1
1
0
1
1
1
1
1
2
1
1
1
1
0
1
1
2
1
1
0
1
2
2
1
0
1
1
1
1
0
0
2
1
0
0
0
0
2
1
0
3
2
1
0
1
1
0
1
1
1
6
1
1
0
1
1
2
0
0
1
0
0
1
3
1
2
1
0
1
1
2
2
0
1
0
0
1
2
1
2
1
1
1
1
3
0
1
0
0
1
0
2
0
1
1
1
1
0
1
1
1
1
1
1
2
1
0
2
0
0
0
0
0
0
0
0
1
1
0
2
0
1
1
1
0
1
1
2
0
2
2
0
0
1
1
0
0
1
1
0
1
1
1
1
1
2
2
2
2
2
0
1
0
1
0
0
1
0
1
2
3
1
0
1
1
0
1
2
0
1
1
1
0
2
2
2
1
1
3
1
0
2
1
0
1
1
1
2
1
1
1
1
1
2
2
2
1
1
1
0
1
1
0
1
0
0
0
1
1
1
1
2
0
1
0
1
2
2
0
1
1
2
1
2
1
1
0
1
1
1
1
1
1
0
1
2
1
1
1
2
2
1
0
0
1
1
1
2
0
1
1
0
1
1
1
1
2
2
2
1
3
2
2
2
0
2
0
1
2
1
0
1
2
1
1
1
0
2
1
1
1
1
2
2
0
1
2
1
1
0
1
1
2
0
1
1
2
0
2
0
0
2
1
1
1
1
0
0
1
1
1
1
0
0
2
1
0
1
2
1
1
1
0
0
0
2
0
1
1
1
2
0
2
1
2
0
1
2
1
3
1
1
0
2
1
2
0
0
0
0
0
2
1
0
0
1
1
4
0
1
1
0
0
1
0
1
1
0
1
2
1
0
2
0
0
1
1
1
2
1
2
2
1
1
1
1
1
2
1
0
1
1
1
1
2
0
0
2
0
0
1
1
1
1
1
0
0
1
0
1
1
1
2
2
1
1
1
1
1
0
0
1
0
1
1
2
2
0
0
1
1
2
1
2
1
0
0
1
2
1
1
1
2
0
1
2
1
1
2
0
1
0
0
0
0
2
0
1
1
1
0
0
2
2
1
2
1
1
1
2
0
1
1
2
1
1
1
2
1
0
1
0
2
2
1
1
0
0
2
1
0
2
1
1
2
2
1
1
1
0
2
2
1
1
1
2
2
0
2
0
1
2
2
2
1
0
0
1
1
1
1
1
0
0
1
0
0
0
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
2
2
1
0
0
1
0
1
2
1
1
0
1
0
1
0
1
3
1
2
1
0
1
0
0
2
1
0
0
1
0
1
1
2
1
1
2
3
2
2
1
1
1
2
4
0
1
0
0
0
2
2
1
1
0
1
2
1
0
0
1
2
1
1
0
0
0
1
0
1
1
1
1
1
1
1
0
2
1
1
1
0
2
2
0
2
1
1
1
2
0
0
2
0
1
1
2
1
0
1
0
0
0
1
2
2
1
0
1
1
1
0
2
0
0
1
1
1
1
1
1
1
0
1
0
0
2
1
1
0
1
0
1
1
1
1
1
1
1
1
1
1
2
2
2
1
1
2
1
1
1
1
0
0
0
1
0
2
2
1
2
1
1
1
2
1
2
1
2
1
1
2
1
2
0
2
0
0
2
0
2
0
2
1
1
1
0
1
0
0
1
1
0
1
1
2
0
2
1
1
1
0
2
1
3
0
1
2
0
1
2
0
1
0
0
0
1
1
1
2
0
0
2
1
1
2
1
0
1
0
1
1
0
2
0
0
1
0
0
3
1
0
1
1
0
2
1
1
1
1
0
1
1
1
1
2
1
1
1
1
1
2
1
2
2
1
0
0
1
1
1
0
1
0
1
0
1
1
1
0
0
1
1
0
2
2
1
0
3
1
1
1
3
1
0
1
0
2
0
1
2
0
1
2
0
2
0
1
1
2
0
0
2
2
2
0
1
2
1
1
1
1
1
2
1
1
1
0
0
1
2
0
2
1
1
2
1
1
0
0
1
1
1
1
1
0
1
0
0
2
1
1
0
1
2
2
1
2
1
1
1
1
2
0
1
1
0
2
0
1
1
1
0
2
0
1
1
1
2
0
1
1
2
1
1
2
1
1
0
0
1
1
1
1
1
1
0
1
2
0
2
1
0
0
1
1
0
0
1
1
0
0
2
2
1
1
0
0
0
0
0
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
0
0
1
1
1
0
0
2
1
2
0
1
2
1
0
1
1
1
0
0
2
2
2
1
1
1
0
2
1
0
2
1
1
0
1
1
0
2
1
1
1
1
2
1
2
1
1
1
1
2
1
1
1
0
0
3
1
1
1
2
1
2
1
2
2
0
1
1
1
0
0
1
1
1
1
2
2
2
1
1
0
1
2
0
1
0
1
2
3
2
1
1
2
1
0
4
1
1
0
0
4
1
0
1
2
1
2
1
1
2
0
1
1
1
1
2
0
1
0
1
0
1
2
1
0
1
1
0
0
1
0
0
1
0
1
1
1
2
0
1
0
0
1
1
1
0
1
1
2
0
2
1
2
0
1
1
0
1
0
0
1
1
1
1
1
1
1
0
0
1
1
2
1
0
2
1
1
2
0
1
1
0
1
2
0
0
1
1
0
0
1
2
2
1
2
0
2
1
1
2
2
0
0
1
0
2
2
2
2
0
0
0
0
2
1
2
1
2
1
2
1
0
0
1
2
2
2
0
1
1
1
2
3
0
1
1
2
1
1
1
1
0
2
1
1
0
0
1
1
1
2
1
1
0
1
1
0
1
2
0
0
3
2
1
1
1
1
1
0
0
1
0
1
3
1
0
0
1
1
1
0
3
1
2
1
0
2
0
1
0
0
0
2
0
1
1
2
2
0
0
1
1
1
1
1
0
1
1
2
2
1
1
0
0
1
1
0
2
1
2
1
0
1
1
0
2
1
1
0
0
0
0
1
2
0
1
1
1
1
1
0
0
1
1
1
0
1
2
0
2
1
0
0
1
0
1
0
0
1
1
1
0
1
1
2
1
1
0
2
1
0
2
2
2
1
0
0
1
2
2
0
0
1
1
2
1
1
2
0
1
3
2
2
0
0
1
2
1
1
0
1
3
2
0
0
1
1
0
2
1
0
1
1
2
0
1
1
0
0
2
0
1
2
0
1
1
1
0
1
0
1
1
1
0
1
1
0
0
1
1
1
1
0
1
2
1
1
1
0
0
0
1
1
0
0
1
1
1
2
1
2
1
1
0
0
0
1
0
2
1
2
0
2
0
1
1
1
1
1
0
2
0
1
2
1
0
2
1
0
1
2
2
1
1
2
2
1
2
2
1
0
1
1
0
0
0
1
1
1
0
0
1
1
0
1
1
0
0
0
1
0
2
0
0
0
1
2
1
1
1
0
1
0
2
0
2
1
1
0
1
1
1
1
2
0
0
3
0
0
0
0
2
1
0
1
0
1
1
0
0
1
1
1
0
0
2
0
1
3
1
1
0
1
2
1
2
0
2
1
1
2
0
2
2
0
0
1
1
0
2
2
0
0
1
2
2
2
2
1
2
0
2
0
0
1
1
0
1
0
0
1
0
1
1
0
2
0
2
0
1
2
1
1
1
0
0
0
2
0
0
1
1
0
2
0
1
0
1
1
0
1
0
1
1
0
0
1
1
1
0
1
1
0
3
1
1
1
0
0
1
0
2
0
1
2
2
2
0
0
1
1
1
1
0
2
2
1
2
1
1
0
2
0
1
1
0
1
0
2
0
1
0
1
1
1
1
0
2
2
1
2
1
0
2
0
2
2
0
1
1
2
0
1
1
1
0
1
1
0
0
0
0
1
0
1
2
2
0
1
1
2
1
0
1
1
0
0
1
0
2
1
0
2
0
1
2
0
1
0
1
2
1
2
1
1
0
1
0
1
1
1
1
1
0
1
1
2
0
2
2
2
2
1
2
1
2
2
1
0
1
0
0
3
1
0
0
0
1
2
1
1
1
0
1
1
1
1
1
0
0
2
0
2
0
0
2
0
1
2
2
1
2
3
1
0
3
2
1
0
0
0
2
0
2
1
0
0
0
0
1
1
1
2
0
0
1
1
1
1
0
1
2
1
1
2
1
2
1
2
2
1
1
0
0
2
0
1
1
1
1
1
2
0
1
1
0
2
1
1
1
0
2
0
0
1
0
2
0
0
0
0
0
0
1
1
0
1
1
2
0
1
0
1
1
0
1
0
1
1
1
0
1
0
1
0
2
0
1
0
1
1
0
2
1
1
0
0
3
1
1
1
1
0
0
0
0
2
0
1
2
1
1
0
0
1
0
0
2
1
1
1
1
0
2
1
0
0
0
0
0
0
1
1
2
0
1
5
0
0
0
1
0
0
0
0
1
1
0
0
2
0
1
1
2
1
1
2
1
0
2
1
2
2
1
2
1
0
1
1
2
0
1
2
0
1
1
2
2
2
1
0
1
1
0
0
0
2
1
2
0
2
0
0
3
1
1
2
1
0
0
0
2
1
1
2
2
2
1
1
1
0
1
1
2
1
1
0
2
0
2
0
0
0
1
1
4
1
1
1
1
1
0
1
1
1
0
1
2
0
0
0
1
0
1
0
1
1
2
1
1
0
1
0
1
0
2
0
1
2
1
2
1
1
0
1
2
0
1
2
1
1
0
2
1
0
1
0
1
2
2
1
1
1
0
2
2
1
1
1
2
2
1
3
1
2
0
1
1
1
0
0
1
0
1
1
2
1
1
0
1
1
2
0
2
0
2
0
1
1
1
1
2
1
1
2
1
2
1
1
0
1
3
1
1
1
1
1
2
0
1
1
0
0
1
2
1
1
0
0
2
2
1
1
2
2
0
1
2
1
0
2
2
1
1
1
1
1
1
0
1
3
2
0
1
0
1
0
0
2
0
2
1
0
1
2
1
0
1
0
1
2
1
0
0
2
1
1
1
0
0
1
5
0
0
1
2
0
2
0
1
2
0
2
1
1
1
2
1
1
0
1
2
0
0
2
3
1
2
0
2
1
1
1
1
1
0
2
0
0
0
1
1
1
2
1
0
1
0
0
1
2
0
1
2
3
0
0
1
1
0
1
1
2
1
0
2
0
2
0
1
1
0
0
2
1
1
1
1
0
0
0
2
1
0
1
1
1
2
2
1
1
0
0
1
0
1
1
1
2
1
0
1
2
1
1
2
0
0
2
2
1
1
0
0
1
1
1
0
2
2
0
2
0
1
1
1
1
2
2
0
2
0
0
0
1
0
0
1
0
2
1
1
0
1
1
0
1
0
1
2
1
4
1
0
2
0
1
1
2
1
1
0
1
0
1
1
1
0
2
1
1
1
1
0
1
2
1
0
4
4
0
1
1
1
1
2
2
1
1
1
1
1
1
0
1
0
1
1
1
1
1
2
2
0
0
1
0
0
1
1
1
2
0
2
1
1
0
0
1
1
1
1
0
0
1
1
1
0
0
1
0
1
2
1
1
0
1
1
2
0
0
1
1
1
0
1
2
0
2
1
1
0
0
1
1
1
2
1
1
2
1
0
1
1
1
1
2
1
1
1
1
0
1
1
1
1
2
2
1
1
0
1
1
1
1
1
0
1
0
2
1
1
2
1
0
0
1
1
1
1
1
1
0
0
0
1
0
2
2
0
1
0
2
1
1
0
0
0
1
1
0
0
2
0
0
1
1
1
1
1
0
1
1
1
0
0
1
1
1
2
0
2
0
1
2
1
0
0
0
1
0
1
2
1
1
1
0
0
0
0
0
1
1
1
0
1
2
1
1
0
1
0
1
1
1
1
1
0
0
0
1
1
1
1
2
0
3
1
1
0
1
0
0
1
1
1
1
2
1
0
1
1
2
2
2
0
1
1
1
1
2
1
2
1
1
0
2
1
0
1
1
2
1
1
1
2
1
1
3
0
1
2
3
0
1
1
2
0
0
2
0
1
1
1
2
1
1
2
0
0
1
2
0
1
1
1
2
0
1
3
0
1
1
1
0
0
3
2
1
1
1
2
1
1
1
2
1
1
1
1
2
1
1
1
2
1
0
2
2
1
2
2
0
2
1
1
0
1
1
1
1
2
1
0
0
0
1
2
2
0
1
0
1
2
0
0
0
0
1
0
2
1
2
2
1
0
0
0
0
0
2
1
1
1
0
2
0
1
0
0
2
2
1
1
0
1
0
0
0
2
0
1
0
0
2
1
1
3
1
1
1
0
1
1
2
1
0
2
2
1
1
0
1
1
2
0
0
1
0
2
0
2
0
0
0
1
2
0
2
1
0
0
1
2
1
0
2
2
0
2
2
0
0
1
1
0
2
0
0
2
2
2
1
1
2
1
0
1
0
1
0
1
1
0
2
1
0
1
1
1
1
0
1
2
2
1
1
1
0
0
0
0
1
0
2
1
2
2
0
0
2
1
0
0
2
1
1
2
1
0
1
1
1
3
0
1
1
0
1
2
0
1
2
0
2
2
0
1
1
1
1
1
0
2
0
1
0
2
1
2
2
1
0
0
1
1
1
1
1
0
1
1
1
0
0
1
2
1
1
0
1
2
2
0
1
1
1
2
1
2
2
1
0
0
0
0
1
1
1
2
0
1
1
1
2
1
0
0
2
0
1
1
0
0
1
1
1
1
1
0
0
0
1
0
0
1
1
1
0
1
1
0
1
2
0
0
0
1
1
1
2
2
1
1
0
0
2
1
1
0
1
1
1
2
1
1
2
0
1
1
1
0
0
1
0
0
2
2
1
1
0
1
1
0
2
0
2
0
1
2
1
1
1
0
1
1
1
0
1
2
0
2
0
2
2
1
1
2
0
1
1
0
1
1
1
2
0
0
0
0
2
0
1
1
1
1
2
2
1
0
1
0
1
2
1
1
2
2
1
2
1
1
2
1
0
0
1
1
1
2
0
2
1
1
1
1
1
2
2
2
1
2
0
0
2
2
1
0
1
0
1
1
1
1
0
1
1
2
1
1
1
0
1
1
1
1
1
2
1
0
1
2
1
1
5
1
1
0
1
2
1
1
0
0
1
0
0
0
1
0
1
1
1
0
1
0
1
2
1
1
0
2
1
0
0
1
1
1
0
2
0
1
0
0
0
0
0
0
2
0
2
1
1
1
2
3
1
1
1
1
1
1
1
2
2
0
1
2
1
1
0
0
1
1
2
0
1
1
0
1
0
2
0
1
2
1
1
1
1
0
0
0
0
0
1
2
2
1
1
1
2
2
0
1
2
1
2
1
0
1
1
1
2
1
1
1
0
0
1
1
0
0
1
2
1
1
0
1
1
0
3
2
1
0
1
1
3
1
0
0
1
1
0
2
1
1
2
2
2
1
1
0
0
1
2
1
1
1
0
1
2
1
1
0
2
1
2
0
0
2
2
0
1
1
1
1
1
1
1
0
1
1
0
0
0
0
0
0
2
1
1
2
1
0
1
1
1
1
0
0
0
2
1
1
0
2
1
1
0
1
1
0
0
0
0
2
0
0
0
2
1
0
2
2
0
0
1
0
0
1
1
1
0
1
1
1
2
0
0
1
0
2
0
0
1
0
0
2
1
1
2
1
3
1
1
2
1
0
0
1
1
1
0
1
0
1
1
0
0
2
1
0
1
0
1
2
2
1
0
1
0
2
1
0
0
1
0
1
2
0
1
2
0
1
0
1
0
0
1
0
0
1
2
0
1
0
2
1
1
1
0
1
1
1
1
1
2
0
1
1
2
1
1
3
0
1
0
1
2
0
0
1
0
2
1
1
1
2
1
1
0
1
1
1
1
0
0
1
3
2
3
0
0
2
1
0
0
1
0
1
0
1
1
1
2
1
0
0
1
1
1
0
2
0
1
1
2
1
1
3
2
1
2
0
0
2
1
0
1
0
0
1
0
1
1
1
2
0
1
3
1
1
1
1
1
2
2
1
1
0
0
1
1
1
1
1
1
1
0
0
1
0
1
2
1
1
2
1
1
1
0
3
1
1
1
2
1
0
1
1
1
1
0
2
1
0
1
1
2
1
1
1
1
0
0
1
0
2
0
1
1
2
2
0
1
1
0
1
2
1
2
0
2
3
1
0
0
1
0
0
1
1
0
1
1
0
1
2
0
2
1
0
2
0
2
1
1
0
1
1
2
1
1
2
1
0
1
1
0
0
2
0
1
2
0
1
1
1
2
4
1
0
0
1
1
1
2
1
1
1
1
2
0
2
1
0
1
1
2
0
0
1
0
0
1
0
0
1
1
2
0
0
0
1
1
1
0
0
2
2
1
1
1
1
0
1
2
1
1
1
0
1
1
2
1
1
2
1
1
0
2
1
0
1
1
1
1
0
2
0
0
1
1
1
0
2
0
2
1
1
1
1
2
0
1
1
0
2
2
1
0
2
0
1
0
0
0
1
0
0
2
0
1
1
1
1
2
0
0
1
2
1
0
0
1
1
2
2
2
2
2
2
0
0
1
1
0
0
1
2
1
0
0
2
0
1
0
2
0
1
2
1
2
2
1
1
2
2
2
1
0
1
0
1
0
1
1
1
2
2
1
0
1
2
2
1
2
0
0
0
1
2
2
2
1
1
1
0
1
1
1
1
1
1
2
1
0
2
2
2
1
1
1
2
1
1
0
1
1
0
2
0
2
1
0
0
1
1
0
0
1
1
1
1
1
1
0
1
0
1
1
0
1
1
2
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
0
0
1
1
1
2
0
2
1
0
1
1
2
0
1
2
1
0
0
1
0
1
2
4
2
2
1
1
0
0
2
1
2
0
0
1
2
1
0
1
1
2
2
3
2
0
1
2
0
2
0
0
0
0
2
2
1
2
2
1
1
1
1
2
1
0
2
0
1
2
1
1
0
1
2
1
0
1
0
0
1
0
2
0
1
2
0
4
1
0
0
0
2
1
1
1
0
2
1
0
1
1
1
0
2
0
2
1
2
2
1
0
1
2
0
0
0
1
1
0
1
1
2
2
1
0
1
1
0
1
3
2
1
1
1
2
1
1
1
1
1
1
0
2
0
2
1
1
1
1
0
0
1
2
1
2
0
1
2
1
0
0
1
1
0
2
2
1
1
1
1
1
1
1
1
1
1
1
0
1
1
2
0
0
1
2
1
1
0
2
0
0
1
2
0
1
2
2
2
1
2
0
2
1
1
2
0
1
1
1
0
1
1
1
2
2
2
1
1
4
1
0
0
1
1
1
0
2
1
1
1
2
1
2
2
1
0
1
1
0
1
0
0
1
0
1
1
1
0
2
1
2
2
0
1
2
1
1
1
3
1
1
1
0
1
1
0
1
0
2
0
2
1
1
1
0
1
0
0
1
1
1
0
1
1
1
2
1
0
1
1
2
1
0
0
1
2
1
0
0
0
1
1
2
2
1
1
2
2
1
1
1
1
2
1
2
1
0
1
0
1
2
0
0
1
2
1
0
2
1
0
0
1
1
1
1
0
2
0
2
1
0
1
1
1
1
0
0
2
1
1
1
1
0
0
0
1
0
1
3
1
2
1
2
1
1
0
0
1
2
0
1
0
1
0
0
1
2
1
0
1
0
0
2
1
2
1
1
0
1
2
0
2
0
0
1
2
2
0
1
1
1
2
1
1
1
2
2
1
1
2
1
0
1
1
0
2
1
2
0
1
1
1
1
2
1
2
1
1
0
3
0
0
1
0
2
1
2
2
1
0
1
1
1
2
1
0
1
2
2
1
0
1
0
2
2
0
0
0
0
2
2
1
1
1
1
0
1
0
1
1
1
0
2
1
2
1
0
1
1
1
1
0
1
0
0
1
1
1
1
2
1
0
1
1
2
2
2
2
1
1
0
1
0
1
2
1
0
1
2
0
0
1
2
1
0
2
1
1
0
1
1
2
0
0
0
2
1
1
1
0
0
0
2
2
1
1
1
1
0
0
1
0
1
1
1
1
3
0
2
2
1
2
0
2
0
0
1
0
0
0
1
2
0
0
1
0
0
1
1
1
1
1
1
0
0
1
0
0
1
1
2
0
1
0
1
1
1
2
0
0
1
1
1
0
1
1
1
2
1
1
1
2
2
1
0
2
2
1
2
1
1
1
2
1
1
2
1
1
2
0
0
1
2
0
1
0
2
1
2
1
2
0
1
1
1
2
1
1
0
1
1
1
2
2
1
1
0
0
0
2
2
1
2
1
0
1
1
0
1
2
0
2
1
0
0
1
1
1
0
1
1
0
0
1
1
1
1
0
0
1
1
0
0
1
1
2
2
1
1
0
2
2
1
0
1
1
1
1
1
0
0
1
1
0
1
0
0
1
1
2
1
0
0
2
1
1
0
0
0
0
0
1
1
1
0
1
1
1
1
1
0
2
0
1
1
1
2
1
0
2
1
1
2
1
1
0
1
1
1
2
1
2
0
1
0
2
1
2
1
1
0
0
0
0
0
3
0
1
2
1
2
1
0
0
1
1
0
2
2
1
1
1
0
2
1
1
1
2
1
0
1
1
1
0
0
0
1
1
1
1
1
1
0
2
0
1
1
1
0
0
1
1
1
2
1
0
0
0
1
0
0
3
1
3
2
1
1
1
1
1
2
1
0
0
0
1
0
2
1
1
0
1
0
0
0
1
1
0
2
0
2
1
0
2
2
0
0
1
1
1
2
1
1
1
1
1
1
2
0
0
1
0
1
0
1
0
0
1
1
1
1
0
1
1
2
1
0
2
1
1
1
0
0
2
0
0
1
1
1
0
1
1
0
1
1
1
0
0
0
2
1
2
2
0
1
0
0
1
2
1
2
3
1
0
1
0
0
0
0
1
0
1
2
1
2
1
2
0
0
1
1
0
2
0
1
0
2
0
1
0
1
1
2
1
2
2
1
1
1
2
1
1
1
1
1
1
1
2
0
1
1
1
1
1
0
2
1
1
0
1
0
1
1
1
0
1
2
1
1
2
2
1
1
0
2
1
2
0
0
1
1
2
0
1
1
2
1
1
1
2
0
0
0
0
0
0
0
2
0
2
1
0
1
2
2
1
0
0
1
0
1
1
1
1
2
1
0
0
0
2
2
0
1
2
2
1
0
0
0
2
1
0
0
2
1
1
0
0
1
0
0
2
1
1
0
1
1
0
0
0
2
2
0
1
3
1
1
0
2
1
0
2
0
1
0
1
1
2
1
0
1
1
0
1
2
2
1
0
0
1
1
1
1
0
1
0
0
0
0
1
0
0
1
2
2
1
1
2
1
1
2
2
1
1
0
1
1
1
1
0
1
2
2
1
1
1
1
1
2
1
2
2
0
0
0
1
1
1
1
1
1
1
1
0
0
2
0
1
0
1
2
1
1
2
2
1
1
0
1
1
1
1
1
2
1
1
1
1
1
0
2
1
1
0
0
1
2
0
1
1
0
3
1
0
1
2
1
0
0
1
0
0
1
2
2
1
0
2
1
1
0
1
2
1
2
1
1
0
1
0
0
0
1
1
1
0
2
0
1
1
2
1
1
2
2
0
1
2
2
0
1
1
1
0
2
1
0
2
0
2
2
2
3
2
1
0
0
1
2
1
0
1
1
2
0
0
1
1
1
1
1
1
1
0
1
2
1
1
1
1
2
2
2
0
1
1
0
1
0
0
4
1
1
1
2
1
1
0
0
0
2
2
1
1
1
0
1
1
1
1
2
0
0
0
1
1
1
1
2
1
2
2
2
0
1
0
0
0
2
1
1
0
1
1
0
0
0
0
2
2
0
1
1
2
0
0
0
1
2
1
1
0
2
1
0
0
1
0
0
1
1
1
1
1
2
0
3
7
1
0
1
1
1
1
2
0
2
0
0
1
1
2
2
2
3
0
1
0
1
1
2
1
0
0
0
0
2
0
0
2
1
2
1
0
0
1
2
1
1
1
2
0
2
2
2
1
1
0
0
0
2
1
2
2
1
1
1
0
2
1
1
0
0
0
1
1
0
1
1
1
1
1
1
1
1
1
2
0
2
2
1
0
2
0
2
1
0
2
1
1
0
1
0
1
1
0
1
1
1
0
1
2
1
1
2
1
1
1
1
1
1
1
0
1
2
2
1
1
1
0
1
2
1
1
1
1
2
1
0
1
1
1
1
1
1
0
1
1
0
0
0
2
1
0
2
0
0
1
0
1
1
2
1
2
2
2
1
1
0
1
0
0
2
1
1
1
2
1
1
2
1
2
1
2
1
0
1
1
1
2
2
1
1
1
1
2
1
2
0
1
1
0
0
2
1
1
0
0
1
1
0
0
1
0
2
1
1
0
0
1
1
1
1
1
1
2
0
1
1
1
1
1
0
0
1
1
0
2
2
0
0
0
1
1
2
0
0
1
1
0
2
0
1
1
1
0
1
1
1
2
4
1
1
1
2
0
1
0
2
0
0
0
1
1
2
1
0
2
0
1
1
1
1
1
2
0
1
2
1
1
0
1
1
1
1
0
0
3
1
1
2
2
1
4
2
1
2
0
0
2
1
1
0
1
3
0
1
0
1
1
1
0
2
2
0
0
0
0
0
2
0
1
1
1
0
2
0
0
0
1
1
1
0
2
2
1
2
0
0
1
2
2
1
1
1
0
1
1
2
1
1
0
2
2
0
1
2
3
1
0
0
2
1
1
2
1
1
1
0
0
1
2
2
1
1
1
2
2
2
1
0
0
1
0
1
1
2
1
2
2
1
0
2
2
2
1
2
1
0
0
2
3
0
1
1
1
0
0
1
1
2
2
0
1
0
1
1
2
1
0
2
1
2
1
2
2
1
1
0
1
1
2
1
2
1
2
1
3
0
1
0
1
0
2
0
0
0
1
1
2
0
1
1
0
1
0
0
1
0
1
1
2
1
1
0
2
0
2
1
1
0
1
0
0
0
0
0
2
2
0
2
1
0
2
1
1
3
2
1
0
1
0
0
0
0
1
1
1
1
3
1
0
1
2
2
1
0
1
0
2
1
1
2
1
1
1
3
2
0
0
1
2
1
2
0
2
1
2
1
2
1
2
1
1
1
4
1
1
0
1
2
1
1
0
0
2
1
0
0
0
1
2
0
2
1
0
0
2
1
0
1
1
0
1
0
2
0
0
0
2
2
0
0
1
0
1
1
1
0
1
1
1
0
0
1
0
0
1
1
0
1
0
1
2
1
0
1
2
0
1
1
2
1
2
1
1
2
1
1
1
1
1
0
1
1
2
1
1
1
1
1
1
0
0
1
1
1
0
1
1
1
0
0
0
1
0
1
1
0
1
2
1
2
2
0
0
1
2
2
1
2
2
0
0
0
0
2
1
0
0
1
1
1
0
1
2
0
0
0
2
3
0
2
1
2
2
0
0
1
1
0
1
3
1
1
1
2
1
1
2
4
0
0
1
0
2
1
0
1
2
0
0
1
0
1
2
1
2
1
2
1
1
2
1
2
0
2
1
1
1
0
0
1
1
2
2
0
1
2
1
1
1
0
1
1
0
2
0
1
0
1
0
0
0
0
1
0
0
1
2
0
0
1
0
1
0
1
0
1
1
1
0
1
1
1
1
1
2
1
0
0
2
0
1
0
1
1
1
2
1
1
2
1
2
0
0
0
2
1
2
1
1
0
1
1
1
1
0
0
1
2
2
0
2
0
1
0
0
0
1
1
2
1
2
2
1
0
1
2
1
1
0
1
1
1
1
0
1
2
0
2
1
1
0
2
0
1
1
1
0
2
2
0
1
2
0
1
1
2
1
2
0
1
0
0
0
1
0
2
2
1
0
1
2
1
1
1
1
2
1
2
1
1
2
1
1
2
2
1
1
0
1
1
2
2
0
0
1
2
0
2
1
0
0
1
0
2
0
4
1
1
1
2
1
1
0
2
1
1
1
0
0
1
1
1
0
0
0
1
1
1
0
0
0
2
1
0
2
1
1
1
2
1
1
1
1
0
1
1
1
1
1
2
0
1
1
1
1
1
0
0
0
1
1
2
2
0
1
0
2
1
1
2
2
1
1
0
2
1
2
0
0
2
1
0
3
1
1
2
0
2
1
2
1
1
0
0
1
2
0
1
1
1
1
3
0
1
1
2
2
2
0
1
2
1
2
2
1
1
0
1
1
3
1
2
1
0
1
0
0
0
1
0
1
1
2
2
2
1
2
2
1
2
2
1
1
2
1
2
1
2
0
1
1
1
1
1
2
2
1
0
0
2
1
0
1
0
2
1
1
2
2
2
1
0
0
1
1
2
0
1
1
1
0
0
2
2
1
1
0
1
1
2
1
0
1
1
1
1
1
1
2
1
2
0
0
1
1
1
1
1
2
1
1
1
1
1
2
1
2
2
1
1
0
2
1
1
2
1
1
2
0
3
0
1
0
0
2
1
1
1
2
1
2
0
1
0
1
1
0
1
1
3
1
2
0
1
0
1
1
0
0
1
1
2
2
1
1
0
1
1
0
1
1
2
0
2
1
2
1
0
0
0
4
0
1
2
1
2
2
1
0
0
0
0
2
1
0
1
2
1
0
2
1
1
2
1
1
0
1
1
1
0
1
1
2
2
1
1
3
2
2
0
2
0
1
0
2
0
1
2
1
1
0
2
0
0
1
1
1
1
1
1
0
1
1
1
2
0
1
1
2
2
0
0
2
1
1
0
1
1
1
0
1
2
1
1
1
1
2
2
2
0
1
1
1
1
1
0
1
1
0
0
1
1
1
2
1
1
0
0
1
2
1
1
0
1
1
0
1
0
1
0
1
0
2
0
2
1
0
1
1
2
2
0
0
0
1
0
1
2
1
1
1
2
1
0
2
2
1
0
0
0
1
1
1
0
1
0
0
1
2
1
0
3
3
1
1
0
1
1
0
1
1
2
0
1
0
3
1
1
0
0
0
0
1
0
0
3
2
1
0
0
2
1
1
0
0
0
0
0
0
2
1
0
1
1
0
0
1
1
2
2
3
0
0
1
1
0
1
2
1
2
1
1
0
1
1
1
0
1
0
1
1
0
0
1
0
0
1
2
0
0
2
2
2
2
0
1
1
1
1
2
1
1
1
0
1
0
1
1
1
1
1
0
1
1
2
1
1
1
1
1
1
1
1
1
0
1
1
0
0
1
1
2
1
1
1
2
0
1
1
0
0
1
1
5
1
2
0
2
2
2
1
2
0
2
2
1
2
2
0
0
1
2
0
2
1
0
1
1
1
1
2
1
0
1
1
1
1
0
0
1
2
1
2
2
0
1
1
0
1
1
1
0
1
2
1
2
0
0
2
0
1
2
1
0
2
1
1
0
1
1
0
0
1
1
0
2
2
0
1
2
1
0
1
0
0
2
1
1
2
1
1
1
3
2
0
1
2
1
0
0
1
1
1
2
0
3
0
0
1
2
1
1
0
0
0
2
0
1
0
0
1
0
1
2
1
0
1
1
0
1
1
0
2
0
1
2
1
1
0
2
2
2
0
2
2
1
1
0
0
0
0
1
0
1
2
1
3
0
1
0
2
2
0
1
2
0
0
0
1
2
3
1
2
1
1
1
1
2
1
1
0
2
1
0
2
1
1
1
1
1
1
2
0
1
2
1
0
0
2
2
1
2
2
0
0
0
0
0
1
0
1
1
1
1
1
2
1
2
1
1
3
0
0
1
0
1
0
0
1
1
2
0
0
2
1
1
1
1
0
0
2
0
0
1
2
0
2
0
1
2
1
1
1
1
1
1
1
1
0
1
0
1
0
3
1
0
1
1
2
2
1
1
1
0
1
1
1
1
2
1
0
1
0
0
2
2
0
0
1
2
0
1
1
1
1
2
1
2
1
1
0
1
0
2
0
2
1
1
0
0
1
2
1
0
1
0
0
0
0
0
1
0
1
1
0
1
1
2
0
0
1
1
0
1
0
0
0
1
2
0
2
0
0
2
0
0
1
2
3
1
1
1
0
1
2
1
1
1
1
0
0
0
1
0
2
2
1
0
0
0
0
0
1
1
1
1
1
0
2
1
1
1
1
0
1
2
1
0
2
1
1
0
2
2
0
1
2
1
0
0
1
0
2
2
2
1
1
2
1
2
1
0
1
1
0
2
1
2
1
2
0
0
0
2
2
0
1
2
1
1
0
1
0
0
2
0
1
2
1
0
1
1
0
0
1
1
2
0
0
1
2
1
1
0
0
1
2
0
2
0
2
0
1
0
1
2
1
1
2
1
1
1
1
2
2
0
0
2
2
1
1
1
2
0
1
1
1
2
1
1
2
1
1
2
2
1
2
1
1
2
0
2
1
2
1
1
1
0
2
1
0
0
2
0
2
0
2
2
2
0
1
0
0
0
0
0
1
1
1
0
1
1
1
2
0
1
1
0
0
1
0
0
2
1
1
0
0
1
1
2
0
1
1
1
1
2
1
1
0
0
2
1
2
1
2
0
1
1
1
1
1
1
1
2
0
1
0
0
1
1
0
1
0
0
0
1
2
2
2
1
2
1
1
1
1
1
1
1
1
1
0
2
0
1
2
1
0
0
1
2
0
0
2
1
2
2
1
1
0
2
0
0
1
2
1
0
1
0
1
1
2
2
1
1
1
0
1
0
0
0
1
1
1
1
1
1
0
0
1
1
1
0
0
1
1
2
0
2
1
2
1
2
1
0
2
1
1
0
0
1
0
0
1
0
1
1
2
1
2
1
1
0
1
1
0
1
2
1
1
1
1
0
2
1
0
2
2
1
1
1
1
0
1
0
0
0
1
2
0
0
2
1
2
1
1
2
1
1
2
1
1
0
1
1
2
0
2
0
0
2
2
0
1
1
0
1
0
1
0
0
2
1
1
1
1
2
0
2
0
2
0
1
1
0
1
0
0
2
2
1
0
0
1
1
1
0
1
1
2
1
0
1
2
0
2
0
1
1
1
0
2
0
1
1
1
0
1
1
1
2
0
2
1
0
1
2
1
1
2
0
1
1
1
1
1
1
1
2
0
2
2
2
0
1
1
1
1
1
1
1
2
1
3
0
1
1
1
0
1
1
1
1
2
0
2
1
1
1
2
1
2
0
1
0
1
2
2
1
0
0
0
0
0
0
0
1
2
1
0
1
0
0
1
0
2
0
1
2
1
1
0
0
1
0
0
2
0
1
0
0
2
1
0
1
0
2
1
1
1
0
1
1
1
2
1
0
0
2
1
2
2
1
0
0
0
1
0
1
1
0
1
1
1
0
1
0
1
1
1
1
1
2
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
2
0
2
0
1
1
1
0
1
2
1
0
1
1
0
1
0
2
1
2
1
2
1
1
1
0
0
0
0
1
0
0
0
1
1
2
1
0
0
0
1
2
0
1
0
2
2
0
0
2
0
1
1
0
1
1
2
1
2
1
0
0
2
1
2
0
0
2
2
1
1
2
0
1
1
1
2
1
0
2
1
1
2
0
1
1
0
0
0
1
1
1
1
1
0
1
2
1
0
1
1
2
2
2
2
2
2
1
2
1
0
0
2
1
0
0
1
0
0
0
0
1
1
2
2
1
1
1
0
1
2
2
1
1
0
0
1
1
0
1
1
2
1
0
1
2
3
1
1
0
2
1
0
1
1
1
2
0
3
2
1
1
0
0
2
0
0
2
0
0
1
0
2
1
2
2
1
0
1
1
0
1
0
1
2
0
1
2
1
1
2
0
1
1
1
1
1
2
1
2
1
2
1
1
1
1
0
1
1
2
1
1
2
2
0
2
2
2
2
1
1
1
2
1
1
1
1
2
0
2
0
0
1
1
1
0
2
2
0
1
0
1
2
1
3
1
0
1
2
0
1
2
2
1
0
1
2
1
0
2
0
0
1
0
2
2
1
0
0
0
1
2
1
0
2
2
2
1
2
2
0
1
1
0
1
1
2
1
1
0
0
2
1
2
2
2
2
1
2
0
0
1
1
6
2
1
2
1
1
1
0
0
2
1
1
1
0
2
1
1
0
2
2
1
1
1
1
0
1
1
1
1
0
2
2
1
1
1
0
2
1
0
1
2
1
1
2
1
2
1
1
1
1
0
0
1
0
1
1
0
1
0
0
2
0
1
0
2
2
1
1
0
3
1
1
3
1
2
1
1
1
1
1
1
1
0
0
1
2
1
1
1
1
0
0
2
1
1
0
1
1
0
2
1
0
1
1
1
0
1
1
0
0
3
0
1
2
0
0
1
2
1
2
0
1
2
0
0
0
0
1
3
1
1
1
2
2
1
0
0
0
1
2
2
0
0
1
0
0
0
0
0
1
0
2
1
1
0
2
2
1
1
1
0
1
2
1
1
1
1
1
1
0
1
1
1
1
1
1
3
1
1
2
1
0
1
0
1
0
1
0
1
2
2
0
1
0
1
0
1
1
1
0
0
1
2
2
0
2
2
0
1
1
1
1
1
0
1
1
0
1
1
1
0
3
0
0
1
2
1
0
2
0
1
2
1
1
1
2
0
1
0
2
0
2
0
1
1
0
2
0
1
0
1
1
1
0
0
1
0
1
1
2
1
2
3
0
1
0
0
0
1
1
0
2
1
0
1
1
1
1
0
2
1
1
0
2
0
2
0
2
0
1
0
1
1
2
1
1
1
1
0
1
1
0
0
1
2
1
5
1
2
2
1
0
1
1
1
0
0
0
0
1
0
1
1
1
0
3
1
1
1
1
1
1
2
3
0
0
0
0
1
1
0
2
0
1
1
2
2
1
1
1
0
0
1
1
1
2
1
1
1
0
2
2
1
1
1
0
1
0
2
0
0
0
0
1
1
1
1
1
2
0
0
1
1
1
1
0
2
1
2
2
2
1
0
1
1
2
1
1
0
0
0
1
0
2
2
1
2
0
2
0
2
0
1
2
0
1
0
1
0
1
2
1
1
2
0
0
2
1
0
2
1
2
1
1
1
0
1
0
2
0
0
0
1
0
2
1
1
1
1
2
2
1
1
1
1
0
1
1
1
1
0
2
1
1
0
1
1
0
1
1
0
0
1
0
1
0
1
1
1
2
2
1
0
0
1
1
1
0
0
1
2
1
1
1
0
1
0
0
0
0
1
2
1
1
0
1
0
0
1
1
1
1
2
1
1
1
0
1
1
2
0
3
1
1
2
1
1
2
1
0
1
3
1
0
1
1
1
2
1
2
2
0
0
0
1
1
2
2
2
2
0
0
1
0
1
2
1
1
2
1
1
1
1
1
1
0
1
1
1
1
0
0
2
0
1
1
0
0
0
1
1
1
1
1
0
1
1
0
2
1
1
2
2
1
2
2
7
1
2
1
1
0
0
0
0
1
0
1
2
1
2
1
0
2
0
0
0
2
1
1
1
1
5
0
0
0
1
2
1
0
1
1
1
1
2
1
2
0
0
0
1
0
0
0
1
1
0
0
1
0
2
1
1
1
0
0
0
1
2
1
0
1
0
2
1
1
1
1
1
1
1
0
2
1
1
2
0
2
2
1
1
0
0
1
1
2
1
1
2
2
1
0
0
2
0
1
1
2
2
0
0
1
2
0
1
3
0
1
1
1
1
2
2
1
1
1
0
1
1
0
1
3
1
2
1
2
1
1
1
0
1
0
0
1
1
1
1
1
1
0
0
0
1
0
1
0
0
0
1
0
2
1
1
0
1
0
2
1
1
1
0
0
1
2
1
1
3
1
1
1
1
1
0
3
0
1
2
1
0
1
1
1
0
1
1
2
2
1
0
0
0
0
0
0
2
2
0
1
2
0
0
2
1
0
0
2
1
1
1
0
0
1
1
1
0
2
0
1
1
1
1
1
0
0
1
1
3
1
1
1
1
1
0
1
1
1
2
0
0
1
0
1
0
2
2
1
2
0
2
1
0
1
0
1
1
0
0
2
0
0
2
1
2
1
1
1
0
0
2
1
1
0
1
2
0
2
1
1
0
1
1
1
1
2
1
1
2
2
1
2
1
1
0
0
1
0
1
1
3
1
0
1
2
1
1
0
2
1
0
0
0
0
0
0
1
0
1
1
0
1
1
1
0
2
1
0
3
0
1
1
1
0
0
1
0
0
1
1
1
0
1
1
2
2
1
2
0
1
2
2
0
1
0
2
1
0
0
2
1
1
1
0
0
3
3
0
2
1
0
1
2
0
1
1
0
2
2
1
1
1
1
1
2
0
1
0
1
2
1
1
0
0
1
1
1
1
0
1
2
1
0
0
0
2
0
0
2
0
1
1
0
1
0
1
2
1
0
2
0
2
0
1
1
2
2
1
1
1
1
1
2
2
1
0
2
1
1
2
1
1
0
0
0
1
3
0
2
0
1
0
1
2
1
2
2
1
2
0
1
1
1
1
2
1
2
1
1
0
0
1
1
1
2
0
1
1
1
0
0
3
1
2
1
2
0
1
1
1
0
1
2
0
1
2
1
1
1
0
1
1
1
2
1
2
2
2
1
2
1
0
2
0
0
0
1
0
1
1
1
0
4
0
2
1
0
1
2
0
0
1
2
1
0
1
2
2
1
0
2
2
1
1
1
2
1
1
1
1
0
1
1
0
1
1
0
0
0
1
0
2
0
1
1
1
1
0
2
1
1
2
0
1
2
0
1
1
2
0
1
1
1
2
0
0
1
0
1
1
2
2
2
1
1
1
0
1
2
0
1
0
0
0
1
1
1
2
2
0
0
2
1
0
2
1
1
1
1
1
1
0
1
1
3
2
1
0
1
2
0
1
0
0
1
0
2
1
2
1
0
1
1
2
1
0
0
2
1
1
0
1
0
2
2
0
1
1
1
0
0
2
0
2
1
1
0
3
1
0
0
1
0
1
1
1
1
0
0
2
1
0
1
1
1
1
0
2
0
1
1
2
0
0
0
1
0
2
2
1
0
0
2
1
1
0
2
0
1
1
2
1
0
0
2
2
0
1
0
1
2
2
0
1
2
1
1
1
2
0
1
1
2
1
1
2
2
2
0
1
1
0
2
1
2
1
0
1
0
0
1
0
2
0
1
1
1
2
1
0
2
2
1
1
0
0
0
1
2
0
2
1
0
2
2
1
1
0
0
2
2
0
1
0
2
1
1
2
1
2
1
2
0
1
1
0
1
3
0
2
0
0
1
2
1
1
1
0
0
1
0
0
1
1
1
1
2
1
0
0
1
0
1
1
2
1
0
1
0
1
1
2
0
1
1
0
1
2
2
0
1
2
0
1
1
2
1
0
1
0
2
1
1
0
0
1
1
0
2
1
0
1
0
2
1
2
0
1
1
1
2
1
2
2
1
1
1
1
1
0
1
2
2
0
2
0
0
1
1
2
0
1
1
1
1
1
1
1
1
0
0
1
1
1
2
1
1
1
2
2
2
2
0
1
1
1
1
0
1
1
0
2
1
1
1
1
2
1
1
2
2
1
2
2
1
1
1
1
2
0
2
1
1
1
1
2
1
1
1
1
1
1
2
2
1
1
2
1
1
0
2
2
2
0
1
2
1
3
0
1
1
0
1
0
2
0
2
1
0
1
0
0
1
2
0
1
0
1
0
0
0
2
1
1
1
1
1
0
1
0
0
0
0
0
0
1
1
2
1
2
1
3
1
0
1
1
2
1
1
1
1
1
0
1
1
2
0
1
1
1
0
1
1
1
0
1
2
1
0
1
0
2
1
2
0
1
1
0
0
1
0
1
0
2
2
0
0
0
1
2
1
1
1
1
2
1
2
1
2
1
1
2
0
1
1
2
1
1
1
0
0
0
2
2
0
2
1
2
0
1
1
2
1
0
1
1
1
0
0
0
1
0
0
0
1
1
0
1
1
0
0
2
2
1
1
2
0
1
1
1
1
2
1
1
0
0
2
0
1
1
1
2
0
1
2
2
1
1
1
0
0
1
1
1
2
2
0
0
2
0
1
1
1
1
1
0
1
1
1
2
2
1
2
1
1
1
0
1
0
1
0
0
0
0
1
2
1
1
1
2
0
1
2
2
1
0
1
1
1
2
1
1
2
0
2
1
0
2
0
1
1
2
1
1
0
2
1
1
1
0
1
1
2
1
0
1
3
1
2
1
2
1
0
0
1
0
1
1
1
4
1
0
1
1
2
0
0
2
0
1
0
1
0
0
0
2
1
0
0
0
0
1
0
2
1
0
3
1
0
1
1
0
1
2
0
2
2
2
1
2
2
4
2
1
0
2
2
1
1
1
1
2
1
2
2
0
2
1
0
1
0
1
1
1
0
1
1
0
0
2
0
0
2
0
0
1
2
0
1
4
0
2
2
2
1
0
1
1
1
0
2
3
1
1
1
1
1
1
1
0
2
1
0
1
0
1
1
1
2
1
0
0
2
0
0
1
1
1
1
2
1
2
1
0
3
1
1
1
0
0
0
0
0
1
1
0
1
2
1
2
1
1
1
0
0
3
3
2
0
3
2
1
0
0
1
1
1
1
1
1
2
0
1
2
1
2
1
1
0
2
2
1
1
1
1
2
0
1
1
0
0
0
1
1
0
1
1
1
0
1
0
0
1
0
2
2
1
1
1
1
0
1
2
2
3
0
0
1
1
0
1
1
1
0
1
1
1
0
1
0
1
1
3
1
0
2
1
0
3
1
0
1
0
1
0
1
1
1
2
2
1
1
0
2
2
0
1
1
2
0
0
2
3
1
1
1
1
2
0
2
1
2
1
2
1
1
1
1
0
2
2
2
1
1
0
1
1
0
1
1
2
0
1
1
1
0
1
2
1
2
1
2
2
0
1
2
1
1
1
1
1
0
1
2
0
1
1
2
0
1
1
2
1
1
1
2
1
1
0
1
1
0
0
2
2
3
1
0
0
1
2
0
1
1
1
0
0
1
0
0
2
0
1
2
2
1
0
1
1
1
0
1
1
0
1
1
1
2
4
1
1
1
1
0
0
2
2
1
0
0
0
2
2
2
1
0
2
1
0
1
0
1
0
1
1
2
1
1
1
1
0
1
1
1
0
1
1
1
2
1
1
2
1
1
0
1
1
1
2
1
6
1
1
0
0
0
0
0
0
1
2
1
2
1
1
2
0
1
1
1
1
0
2
3
1
1
0
0
2
0
2
1
1
1
0
1
1
2
1
1
1
2
2
0
1
2
2
0
1
2
1
0
0
1
0
0
0
1
0
1
1
1
0
1
1
0
1
2
1
0
3
1
1
1
2
1
2
2
1
0
2
1
0
2
1
1
0
1
0
0
0
1
1
0
0
2
0
1
0
1
1
1
1
0
1
1
0
1
0
1
0
2
0
1
2
1
1
0
2
0
2
0
1
1
2
0
0
1
1
0
2
2
2
1
1
2
1
2
1
0
1
1
1
1
1
0
0
2
2
1
0
0
0
1
0
0
1
2
2
1
0
1
2
2
1
3
1
0
1
1
0
1
2
2
1
0
1
0
2
1
1
0
2
1
1
2
0
2
1
1
2
1
0
1
2
1
0
1
2
1
1
1
0
1
2
1
2
2
2
1
1
2
2
1
1
2
0
1
1
2
1
1
2
2
2
0
1
0
1
0
2
2
0
1
0
0
1
1
1
1
2
1
1
1
0
1
1
0
1
1
2
1
0
0
2
0
1
1
2
0
3
2
1
2
1
1
1
0
1
1
1
0
0
1
0
2
1
0
0
1
2
1
0
0
1
2
0
1
0
2
0
0
1
1
2
0
2
2
2
0
1
1
1
1
2
2
1
0
2
2
0
1
1
1
0
2
0
0
0
2
1
1
0
2
1
1
0
2
0
1
1
2
0
1
2
1
1
0
1
2
1
2
0
2
1
1
1
2
2
2
0
2
1
2
1
2
0
0
0
6
1
0
2
1
0
0
0
1
2
1
1
1
2
4
1
2
0
1
2
2
1
1
1
2
1
1
1
0
0
2
2
2
1
1
0
0
0
2
1
1
2
0
0
0
1
0
2
0
0
1
1
1
1
1
1
2
2
2
0
0
0
1
0
1
0
0
2
1
0
0
2
1
2
2
0
1
0
2
1
2
1
1
2
1
0
0
2
0
2
3
2
1
1
1
2
2
1
0
4
0
1
2
1
0
0
0
1
1
0
0
0
1
1
0
2
0
1
0
3
1
1
0
2
2
1
0
1
2
2
0
0
0
1
1
2
0
0
1
2
1
1
1
1
1
0
1
1
1
0
0
0
1
2
0
1
0
1
0
3
0
1
1
1
1
0
1
1
1
0
1
1
0
1
0
2
2
1
0
1
1
0
1
2
1
1
1
1
0
1
2
1
1
0
0
1
2
1
1
2
0
0
1
2
0
0
1
0
1
1
1
1
0
0
1
1
0
0
1
2
1
2
0
1
2
1
1
0
1
1
0
0
0
0
2
1
0
1
1
1
1
0
1
2
0
1
1
1
1
0
1
0
1
0
1
1
1
0
2
0
1
1
1
2
1
1
2
2
1
1
1
1
2
1
1
1
0
0
2
0
1
1
0
2
0
0
1
1
0
2
0
2
1
1
2
2
0
1
1
1
1
0
0
1
0
1
1
1
1
0
1
1
0
0
1
1
0
2
0
1
1
2
1
0
2
1
1
1
0
0
1
2
2
1
0
0
1
0
1
0
1
1
1
0
1
2
0
1
1
1
1
1
1
2
0
1
2
1
1
1
0
1
0
1
0
2
0
0
1
2
1
1
1
1
2
1
1
1
1
0
2
1
1
1
1
1
2
0
1
0
1
1
2
0
1
1
0
1
0
1
1
2
2
2
1
2
0
1
1
0
0
1
1
1
2
1
0
1
1
1
0
0
0
1
2
1
1
1
0
0
1
0
1
0
1
0
1
1
1
1
2
2
0
1
1
0
0
2
0
1
2
2
0
2
1
0
0
0
1
2
0
2
1
1
0
0
1
1
1
3
1
0
1
0
1
2
2
1
1
1
2
2
2
2
0
1
2
0
0
2
2
0
1
0
2
0
1
1
1
0
1
0
2
1
0
1
0
1
2
0
0
2
2
5
1
1
1
0
0
1
1
0
1
1
0
0
2
1
0
1
1
0
0
1
1
1
0
0
1
2
1
1
2
1
0
0
0
1
1
2
1
0
0
0
1
0
0
1
0
1
1
0
0
1
0
1
1
0
2
0
1
0
1
1
1
1
1
0
2
2
1
1
1
0
2
2
0
1
1
0
1
1
2
0
2
1
2
2
1
2
0
1
2
0
1
1
1
2
1
2
1
1
1
1
2
3
2
0
0
1
1
1
1
1
1
0
0
3
1
1
1
0
2
1
1
0
2
1
1
1
1
0
0
2
0
0
1
1
2
1
2
0
1
1
0
2
0
1
1
2
2
0
1
0
1
1
0
2
1
2
0
0
1
0
1
1
0
0
1
1
2
0
1
2
1
3
1
2
2
1
0
0
3
1
2
1
1
1
0
1
0
1
2
1
0
0
0
1
0
1
1
1
1
2
2
1
1
0
2
1
1
1
0
2
3
2
1
1
0
1
3
2
2
2
1
1
0
0
0
0
1
0
0
1
0
1
1
2
1
0
1
1
1
1
1
1
1
2
1
0
0
2
1
1
0
1
1
0
1
1
2
2
2
2
0
2
2
0
1
0
0
1
2
0
1
0
2
1
3
2
0
0
2
0
1
1
1
0
2
1
0
0
0
1
0
0
1
2
2
1
2
1
0
2
1
2
2
1
1
0
1
2
1
1
0
0
1
1
0
0
1
0
1
1
1
0
0
0
1
0
1
2
1
1
1
0
2
2
0
1
0
0
1
0
1
2
1
1
1
1
2
1
1
0
1
0
0
2
1
2
1
1
1
0
1
0
1
1
1
1
3
1
2
1
0
1
2
0
2
1
1
0
0
0
1
1
0
2
1
0
1
0
0
0
0
1
2
0
1
1
1
1
0
1
1
1
0
1
1
0
1
1
2
0
0
2
0
1
0
1
0
13
0
1
2
0
1
0
1
3
3
1
1
1
2
1
1
1
2
2
1
3
0
2
1
1
0
1
1
2
1
0
1
1
1
1
2
0
1
0
1
1
0
0
0
1
2
0
2
1
0
2
1
1
1
2
0
1
2
2
0
2
0
1
0
1
1
0
0
2
0
1
0
0
1
0
0
1
0
2
2
2
0
2
2
2
0
1
1
3
0
2
1
0
0
2
2
2
2
1
0
1
1
2
0
1
1
1
0
1
1
2
0
1
0
0
0
1
1
1
1
0
1
0
0
1
2
2
0
0
1
0
1
1
1
0
1
1
1
1
0
1
2
0
1
2
1
0
1
2
2
1
1
1
0
2
1
0
1
1
1
0
0
1
2
0
0
1
1
1
1
1
0
2
1
0
1
0
1
2
1
3
1
2
2
1
0
0
0
1
1
1
1
2
1
1
1
2
2
1
2
2
0
1
0
0
0
2
2
2
1
0
1
0
2
0
1
0
1
0
2
0
1
1
1
0
0
1
0
0
1
0
1
1
0
2
2
0
2
2
1
2
1
1
2
0
2
0
0
1
0
0
2
1
3
1
0
1
2
1
0
0
0
0
1
1
2
0
1
0
1
2
2
1
1
1
0
2
0
1
2
1
1
0
0
1
1
0
1
2
1
1
0
1
1
1
1
0
0
1
0
1
0
1
1
1
1
0
0
2
1
1
1
1
1
1
1
1
1
1
0
0
1
0
0
2
2
1
2
2
1
2
1
0
0
0
1
1
0
1
1
0
2
1
1
1
1
2
1
1
1
1
1
0
2
1
1
1
1
0
1
0
1
1
3
1
0
2
1
1
0
1
1
1
0
1
0
0
0
0
3
1
1
2
0
1
1
0
0
1
1
1
0
1
2
1
1
2
2
0
1
2
0
1
1
2
0
1
1
0
2
0
1
0
0
0
1
1
2
1
1
2
0
2
1
1
1
1
2
1
1
1
0
1
0
1
0
1
1
2
1
3
0
1
0
1
0
2
1
1
0
0
1
0
0
0
2
1
1
0
2
0
1
0
1
0
1
1
0
0
2
1
0
0
2
2
2
1
2
1
0
1
1
2
1
1
1
1
1
2
2
1
2
2
2
1
1
2
1
1
1
2
2
5
1
1
2
0
1
0
0
1
0
1
2
0
1
0
0
1
1
1
2
1
1
0
1
1
1
0
0
1
0
0
1
0
1
1
1
1
0
2
1
1
1
0
1
0
1
1
1
0
1
1
1
1
2
1
1
1
2
1
1
0
1
1
2
0
1
2
5
1
0
1
1
1
0
2
1
2
2
1
0
1
0
2
2
1
0
1
0
1
1
1
0
0
1
1
1
1
2
1
1
1
1
0
1
2
0
1
2
2
1
1
1
0
3
1
2
1
2
0
1
0
1
0
1
1
1
1
1
1
1
0
2
0
0
1
1
1
2
1
0
1
1
2
0
0
2
2
1
1
1
0
1
1
0
2
1
1
2
1
1
1
1
1
1
0
0
1
1
1
0
2
1
0
0
1
1
2
1
1
0
1
2
2
0
0
0
1
2
1
1
1
2
1
2
1
0
2
0
1
1
1
0
0
1
1
1
1
0
1
0
1
0
0
0
0
0
1
1
2
1
0
0
0
1
1
0
0
1
2
0
2
1
1
1
2
2
0
1
2
0
1
2
2
1
1
1
2
1
1
1
0
1
1
0
0
0
0
2
1
1
3
2
1
1
2
1
1
1
1
0
1
1
1
2
0
0
1
1
0
1
1
1
1
2
2
0
1
2
2
0
2
2
1
1
1
1
0
2
0
2
2
1
0
1
0
0
1
1
0
0
0
1
0
1
0
1
0
1
1
1
2
0
0
1
1
0
2
1
1
0
2
0
1
0
1
0
0
2
1
1
0
1
0
1
1
1
1
0
1
0
2
0
1
0
1
2
0
0
0
1
1
0
0
2
0
2
1
2
1
1
1
1
3
0
1
2
1
1
2
0
1
1
0
2
1
2
1
1
1
1
0
1
0
1
2
1
2
2
1
1
1
0
0
2
0
2
1
0
1
0
1
1
1
5
2
1
1
1
0
0
0
2
1
1
0
1
0
1
0
1
2
2
2
0
1
1
2
2
1
2
2
0
2
1
1
1
0
0
0
0
2
0
1
1
0
0
1
0
2
0
0
2
1
1
1
1
0
2
1
2
1
0
0
1
2
2
1
1
1
1
0
0
0
1
1
0
1
1
0
1
0
1
0
1
2
0
1
0
1
3
0
1
0
0
1
0
1
2
0
1
0
1
1
2
0
1
1
0
1
0
1
1
1
1
2
0
0
0
0
2
0
1
2
0
1
1
0
2
1
2
1
1
0
2
0
0
1
1
2
0
1
1
0
2
2
1
2
0
1
1
0
1
1
1
1
1
1
1
1
1
0
2
1
1
2
0
2
1
0
0
1
1
1
0
1
1
1
2
0
2
2
1
1
1
2
2
2
1
1
2
2
2
1
2
1
2
1
1
2
0
0
1
1
0
1
1
2
1
1
1
0
2
2
0
1
0
2
1
0
1
1
0
1
1
0
0
0
1
2
0
0
2
0
2
1
0
1
2
1
2
0
2
0
1
0
1
2
2
1
1
2
0
1
1
1
2
0
2
1
0
1
1
1
1
1
0
2
1
1
1
2
1
2
0
2
0
0
0
1
0
0
0
2
1
1
1
0
0
1
1
0
2
1
0
0
0
2
1
1
0
0
1
1
1
1
2
2
1
1
1
2
0
0
1
2
1
1
2
2
0
0
2
1
2
1
2
0
0
2
1
1
0
1
1
2
2
0
0
1
0
1
1
1
1
0
1
0
1
2
3
2
2
0
1
0
1
0
2
1
1
3
1
0
0
1
0
1
0
1
1
2
0
2
2
0
1
1
0
1
1
0
2
1
0
2
1
0
0
0
1
1
1
2
0
1
0
1
1
0
2
2
1
1
2
2
0
2
0
2
1
2
1
2
1
0
1
1
0
0
0
1
0
0
1
1
0
1
1
1
2
0
2
2
1
0
1
1
0
0
0
3
1
0
0
2
1
1
0
1
1
2
1
0
2
0
0
0
0
1
1
0
0
1
0
2
1
2
0
2
0
1
2
0
0
1
1
1
1
1
0
1
1
0
1
2
0
1
0
1
1
1
1
0
2
1
1
0
2
0
0
1
2
1
1
2
1
0
1
1
0
1
0
0
2
0
2
1
1
2
1
1
0
1
1
0
1
1
0
2
2
2
1
2
2
0
0
1
1
0
1
0
1
1
0
1
1
1
0
1
1
1
0
1
0
1
1
1
0
0
1
1
1
2
0
0
2
0
1
1
1
0
1
0
2
0
1
1
0
2
1
1
1
1
1
2
1
1
2
0
1
1
0
1
0
1
2
0
0
1
1
0
2
2
0
2
1
1
0
1
1
1
2
0
1
0
1
0
1
2
2
1
1
0
2
2
2
1
0
1
2
1
1
2
2
1
1
1
1
1
1
1
0
2
1
1
0
2
1
1
0
1
2
0
1
0
0
1
1
2
2
1
1
2
1
1
0
1
0
2
1
0
1
0
1
1
2
2
1
0
0
0
1
2
0
0
1
1
0
1
1
0
1
2
0
2
2
2
1
1
1
1
2
1
2
1
2
0
0
1
1
0
1
2
1
0
2
2
2
1
2
0
0
1
0
2
2
1
0
1
2
0
2
1
1
1
0
1
2
1
0
2
2
0
2
0
1
2
1
2
2
0
0
0
2
1
1
0
0
1
1
0
0
0
2
0
0
1
1
1
2
0
2
0
1
1
0
1
0
0
1
2
2
1
1
1
1
0
1
0
0
2
1
1
1
1
2
1
1
1
0
1
0
0
1
0
2
1
0
0
0
1
1
2
1
1
1
1
0
2
2
1
0
1
1
2
1
0
1
1
0
1
1
1
1
2
0
2
1
1
2
2
1
1
0
1
1
1
0
2
0
0
0
2
1
1
1
1
1
1
2
2
1
1
0
1
0
1
1
0
2
1
1
0
0
0
2
1
0
1
0
1
3
1
1
4
0
2
1
0
0
0
2
0
1
1
1
1
1
1
0
1
1
1
0
0
2
1
2
0
0
1
0
0
2
1
1
2
1
0
0
1
2
0
1
1
2
1
1
1
0
0
0
2
0
1
2
2
1
2
1
0
1
1
0
1
1
0
1
1
1
0
1
1
1
1
1
1
1
0
1
1
0
1
1
2
1
0
1
2
0
1
0
0
2
0
1
0
1
0
1
0
1
1
2
1
1
2
0
2
0
0
0
1
0
2
0
0
2
0
2
0
1
1
1
1
0
1
1
0
0
2
1
1
0
1
2
2
1
1
0
0
1
0
2
1
0
1
2
0
1
2
0
2
2
0
2
1
2
2
1
2
0
0
0
0
1
1
1
1
0
1
1
0
1
0
3
2
0
1
1
0
0
2
1
1
1
2
1
1
1
2
0
1
0
0
0
2
1
2
0
1
1
1
0
1
1
0
1
1
2
0
2
1
2
1
1
2
1
2
2
0
0
1
2
0
0
2
1
0
1
1
1
1
0
1
1
1
1
1
0
0
1
0
0
0
0
0
0
0
0
1
2
1
1
2
1
0
0
0
1
1
2
1
0
0
1
2
1
1
0
0
1
0
2
0
0
2
0
2
1
1
2
1
2
1
2
0
2
0
1
1
2
2
1
1
0
0
2
0
0
1
0
1
0
0
2
1
1
2
1
0
0
0
1
0
1
1
2
1
1
2
2
1
1
2
2
0
0
1
1
1
0
1
1
1
1
0
1
0
0
1
0
1
0
1
1
2
1
1
0
1
0
1
3
0
0
1
2
1
1
2
1
0
0
2
0
1
2
0
2
1
1
1
0
0
2
0
2
1
1
1
0
0
1
2
0
1
0
0
1
0
2
1
0
1
1
1
1
0
1
1
0
2
2
2
1
1
1
2
1
0
1
1
0
1
1
3
1
2
1
1
1
2
1
2
1
0
2
0
1
1
1
2
1
0
0
0
2
1
2
2
1
1
0
1
0
1
1
1
2
1
1
2
1
1
0
2
1
1
0
0
2
1
3
1
1
1
0
1
1
0
1
1
1
2
1
0
1
0
1
0
1
1
2
2
0
0
1
1
0
2
1
0
0
0
1
1
1
1
1
0
1
2
2
1
2
0
1
0
2
0
2
2
1
1
0
0
2
1
1
0
0
0
0
1
0
1
1
1
1
1
2
2
0
0
1
1
0
0
0
2
1
1
0
1
0
1
1
1
2
1
3
4
1
2
1
0
1
0
0
1
0
1
0
1
1
0
0
0
1
1
1
1
0
1
2
0
0
1
0
2
0
2
1
2
0
3
1
1
0
2
1
2
1
2
2
0
1
2
2
0
0
1
0
1
0
0
2
2
1
0
1
0
1
1
0
1
2
2
1
1
1
1
1
1
0
1
2
1
2
0
1
1
2
1
1
2
2
0
2
0
1
2
1
4
1
3
0
1
0
1
1
0
0
0
1
1
2
1
0
0
0
2
1
1
0
1
0
1
1
2
1
1
1
2
1
0
1
2
2
0
1
1
0
1
2
0
0
0
0
0
0
0
0
3
0
2
0
2
0
0
1
0
2
1
2
0
1
2
1
1
0
1
0
1
0
0
1
0
2
0
0
1
0
2
1
1
0
0
1
1
1
0
0
0
2
0
1
0
1
0
0
2
6
0
0
0
1
2
0
0
2
1
1
2
1
1
1
0
0
1
1
1
2
1
1
1
2
0
0
0
0
1
1
0
1
1
2
1
2
1
1
2
1
2
1
1
1
1
0
0
0
0
1
1
2
1
1
0
1
2
1
1
1
1
1
1
1
2
1
0
1
0
1
2
1
0
0
1
0
0
1
3
0
1
0
1
1
0
0
0
1
2
0
0
1
0
1
0
4
0
1
1
1
0
1
1
1
1
2
0
1
0
1
2
1
1
0
2
1
0
1
0
1
0
2
1
0
1
1
2
1
1
0
0
0
2
2
0
1
1
1
2
0
1
0
1
2
2
1
1
1
1
0
0
2
0
0
2
1
1
1
1
0
1
3
1
1
2
0
0
1
13
1
0
1
1
1
1
2
1
0
1
0
1
1
2
1
1
1
1
1
0
1
2
0
1
2
0
2
2
0
0
1
1
2
0
1
1
0
0
0
2
2
0
1
1
1
1
0
1
0
0
1
1
0
0
1
1
1
1
2
0
0
2
1
2
0
0
1
0
0
1
1
0
0
0
1
1
1
1
0
0
1
1
2
1
2
2
0
1
2
1
1
0
1
2
2
1
2
0
1
1
0
1
0
1
2
0
1
1
0
1
0
0
0
0
1
0
2
0
2
2
1
2
0
1
1
1
0
0
2
2
0
1
0
2
2
1
2
0
1
1
1
1
0
1
1
2
2
0
1
1
2
0
1
1
1
1
1
1
0
1
1
1
1
2
1
2
0
2
1
1
0
1
1
1
2
2
1
1
1
1
0
1
1
1
1
1
0
0
0
2
4
1
2
1
2
0
2
1
0
1
0
1
1
2
0
1
0
1
0
1
1
2
1
1
0
1
3
0
2
0
1
0
0
2
0
1
1
2
0
0
2
1
1
0
2
2
1
2
0
1
2
1
1
2
1
1
3
2
0
2
1
2
1
2
1
1
2
2
1
2
1
1
1
1
1
2
2
2
1
1
0
1
1
0
3
1
2
1
0
1
0
0
0
1
2
0
0
2
1
1
0
1
0
1
0
2
3
1
0
0
0
2
0
1
1
2
1
1
1
2
2
2
0
2
2
0
0
1
2
1
1
1
0
0
1
1
1
0
0
1
0
1
1
1
0
2
1
2
0
1
1
1
0
2
2
0
1
1
8
1
1
0
1
1
1
2
0
1
0
0
2
1
2
0
0
1
0
0
2
1
0
1
1
0
1
1
1
1
2
0
2
2
2
1
0
2
1
1
0
1
0
0
1
4
1
1
0
1
2
1
2
0
1
0
1
1
0
1
1
1
0
1
0
2
2
0
1
2
1
2
1
0
0
1
2
0
0
0
0
1
1
2
1
1
1
1
0
0
0
0
1
1
2
0
1
1
0
0
1
2
0
2
1
0
1
1
1
3
0
0
0
1
1
0
0
0
2
2
0
2
1
0
1
2
1
0
0
1
0
2
2
0
0
0
3
1
1
1
0
1
1
2
0
0
1
1
1
0
1
1
1
2
0
0
0
0
1
1
1
0
2
1
1
1
2
1
2
0
1
1
1
2
1
1
2
0
1
1
2
1
0
1
0
1
1
2
1
0
1
1
2
1
1
0
0
0
2
1
1
0
2
2
0
0
1
1
0
0
1
1
1
1
1
2
0
2
1
0
1
2
1
0
2
0
1
0
1
0
1
1
1
2
2
0
1
2
0
0
0
0
0
1
1
2
2
1
1
1
0
1
0
1
0
1
2
2
0
1
1
1
2
1
0
2
2
1
1
1
1
1
1
1
0
0
1
1
2
1
2
1
1
0
0
0
0
1
1
0
2
2
0
0
1
0
0
1
1
1
1
1
3
0
1
1
1
1
0
0
2
3
2
0
0
2
1
1
2
0
0
2
0
0
2
2
1
2
0
0
1
0
1
2
0
2
1
0
1
2
1
1
2
2
0
1
0
0
1
2
2
1
2
0
1
1
0
1
1
0
1
0
1
0
1
0
1
0
2
1
0
1
2
1
0
1
1
1
1
2
0
2
1
1
1
1
1
0
0
1
1
2
1
1
0
2
0
1
1
1
1
1
0
2
1
2
1
0
2
1
2
0
1
2
1
0
2
1
1
0
2
1
1
1
1
2
0
0
1
0
1
0
2
1
0
0
0
0
0
1
1
1
1
1
1
1
1
1
0
0
1
3
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
2
1
0
0
0
1
2
1
1
2
1
1
1
1
1
1
1
1
2
0
2
2
1
0
0
0
0
1
0
0
0
1
1
2
0
1
1
0
1
1
1
1
1
1
2
1
1
0
0
1
1
1
0
1
2
0
1
1
1
1
1
2
2
2
0
2
1
1
1
1
1
0
1
1
1
1
0
2
0
1
1
1
0
2
1
1
1
0
2
1
0
1
0
1
0
0
1
0
1
1
0
2
0
2
0
2
1
2
0
1
1
2
1
1
0
2
0
0
2
1
2
1
0
1
2
0
2
2
2
0
1
1
2
0
1
2
1
2
1
2
1
1
1
2
1
2
0
2
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
0
0
2
0
1
2
1
2
0
1
2
1
1
0
1
1
0
1
0
1
0
1
1
2
1
1
1
1
1
0
2
0
2
2
0
0
1
1
1
2
0
1
2
2
0
2
2
0
1
0
1
2
1
0
0
1
0
1
0
0
1
0
1
1
1
1
0
1
2
0
1
1
1
0
3
2
1
0
2
2
0
2
1
1
0
0
0
2
0
0
1
0
1
2
2
1
2
1
2
0
1
1
1
1
1
2
0
1
2
0
1
1
0
1
0
2
2
1
2
0
1
0
1
0
1
0
0
1
2
2
1
1
2
2
1
2
2
0
1
2
2
1
1
0
0
2
2
1
1
1
0
2
0
1
2
0
1
0
0
1
0
0
1
0
2
2
1
1
2
0
1
0
0
1
1
0
0
1
0
1
0
1
1
0
1
0
0
0
2
2
2
1
0
2
2
1
1
2
1
0
0
2
1
1
1
1
1
1
1
1
0
1
2
0
1
0
2
0
0
1
1
0
1
2
1
1
0
1
0
1
0
2
1
1
1
1
1
2
0
1
1
1
1
0
1
1
2
1
0
1
1
1
0
1
1
0
1
0
1
0
2
2
0
0
2
1
2
3
0
0
1
1
1
1
0
0
2
1
1
0
1
1
1
2
0
0
2
1
1
0
1
0
0
2
0
2
0
0
0
0
2
0
1
1
1
0
1
1
0
2
0
0
0
1
0
0
2
0
0
0
2
2
0
0
1
1
2
1
0
1
0
1
1
0
0
2
0
1
1
0
0
1
1
1
1
2
1
0
2
1
1
1
1
2
1
1
0
0
1
2
0
0
0
1
1
1
2
1
2
1
1
1
1
1
0
0
1
1
2
0
1
2
0
3
1
2
1
2
2
1
2
0
1
1
1
0
0
1
1
1
0
1
0
1
0
1
2
1
1
2
2
0
1
1
2
1
1
0
0
1
1
2
2
2
1
2
0
2
1
2
0
1
1
3
1
1
0
1
1
1
1
1
1
1
0
1
0
0
2
1
1
1
1
4
1
0
1
2
0
1
2
0
1
0
1
1
0
2
0
0
1
1
2
1
1
1
1
1
2
1
1
1
1
0
0
1
0
0
1
1
0
2
1
1
0
1
0
2
1
1
2
0
1
1
0
2
0
1
0
0
1
1
2
1
1
0
0
1
1
1
1
1
1
1
1
1
2
2
0
2
2
1
1
2
1
2
0
2
1
1
1
1
0
2
0
0
0
1
2
1
2
0
2
1
0
1
0
0
1
1
1
1
1
2
1
1
0
0
1
3
1
2
1
2
0
1
1
2
1
2
2
0
1
1
1
0
1
1
2
1
2
1
1
1
1
0
0
0
1
2
1
0
2
0
2
1
6
1
0
1
0
0
1
2
2
0
1
2
2
1
1
0
1
1
1
2
1
0
0
1
1
1
1
0
1
0
2
2
1
1
2
0
2
0
1
1
1
0
1
2
0
2
1
1
1
1
1
0
2
1
3
1
2
1
0
2
0
0
1
1
0
0
0
1
2
1
2
2
1
0
1
0
1
1
1
1
0
2
1
0
0
1
1
0
0
0
0
0
1
2
0
2
0
1
1
1
0
1
1
1
0
1
0
1
1
0
1
1
1
1
0
0
2
0
0
1
2
0
0
0
1
2
1
1
0
0
0
0
2
1
1
0
0
1
1
1
1
2
3
2
0
2
1
1
1
2
1
2
2
2
1
1
0
1
0
1
1
0
2
0
1
0
1
1
1
1
1
1
0
0
0
2
2
1
1
1
2
0
1
2
1
1
1
1
1
1
0
2
1
1
2
2
2
0
1
1
1
0
2
3
1
1
1
1
1
2
1
1
2
2
1
1
1
2
2
2
1
1
0
2
1
1
4
0
1
1
1
1
1
2
1
0
2
0
1
1
1
0
1
2
0
1
1
2
0
0
0
1
0
0
1
2
1
2
4
1
0
0
2
1
1
0
0
1
2
0
1
2
0
1
1
2
2
2
0
2
2
2
1
2
1
1
0
2
1
0
1
0
1
1
0
0
1
2
2
1
1
2
1
0
0
1
1
1
1
0
2
0
1
1
1
2
2
1
0
1
1
2
2
0
0
1
1
1
2
0
0
1
0
1
1
0
0
0
1
2
0
3
0
0
1
1
0
1
0
0
2
1
1
0
1
0
1
0
2
0
1
2
2
1
0
1
1
0
0
1
2
1
1
1
1
1
2
1
0
1
2
0
0
2
2
1
2
1
3
1
1
1
1
0
1
0
1
0
0
0
1
1
0
0
2
0
1
1
1
0
1
1
2
1
0
1
0
0
0
1
1
0
2
2
1
1
1
1
1
0
2
2
0
1
1
0
0
2
0
1
1
1
0
0
0
1
1
0
0
0
0
1
2
1
1
0
1
1
1
2
2
0
1
2
0
0
1
1
1
1
1
1
3
0
1
1
1
0
0
0
1
1
2
1
2
2
1
1
0
2
0
0
1
0
2
1
1
0
1
0
2
2
3
1
0
1
1
0
1
1
0
1
2
1
1
1
0
1
1
0
1
0
0
0
1
1
1
2
0
1
1
2
1
1
0
0
2
1
1
1
2
1
0
1
0
0
0
2
2
1
1
1
1
1
1
0
0
0
1
1
2
1
1
1
1
3
1
1
0
0
1
2
1
0
2
0
1
2
1
0
0
1
1
1
1
1
0
1
1
1
2
1
1
1
0
2
1
2
0
0
1
2
0
2
1
2
0
1
0
1
2
1
1
0
2
1
1
1
1
1
0
1
1
2
1
1
1
0
1
1
1
1
2
0
3
1
0
1
0
2
1
1
0
0
1
1
1
0
2
1
0
1
1
0
0
0
1
2
1
0
1
0
1
0
2
0
0
2
1
2
1
1
1
0
2
0
2
2
0
1
0
1
0
0
1
1
2
1
0
2
2
0
1
0
0
0
1
1
1
0
0
2
2
1
1
1
2
1
2
0
1
1
1
1
1
0
1
0
2
0
2
2
1
1
1
1
1
0
0
1
1
1
1
1
1
0
0
1
0
2
2
1
2
0
1
1
1
1
2
1
1
0
2
1
2
1
1
1
1
1
1
1
1
2
0
2
1
1
1
1
2
0
0
2
1
2
1
0
0
1
0
1
1
0
1
0
1
0
1
1
2
1
2
2
1
3
0
1
0
2
0
0
1
0
0
1
0
1
1
1
0
1
1
1
2
1
1
1
1
2
0
1
0
2
2
2
0
0
1
1
1
1
1
1
0
2
2
1
1
0
1
2
1
0
0
2
1
1
0
1
0
0
2
2
0
2
1
0
1
1
0
2
3
1
2
0
1
0
0
1
1
1
1
1
0
1
1
2
0
0
0
1
0
1
1
0
1
0
2
0
2
1
0
3
1
0
1
0
2
1
1
1
1
1
2
2
1
0
2
0
1
1
1
1
0
0
1
1
2
1
1
1
0
2
1
1
0
1
1
1
1
1
1
0
1
1
0
2
1
1
1
2
2
1
2
1
2
1
2
2
0
1
2
1
2
1
0
0
0
1
2
1
0
1
2
2
2
1
0
2
2
2
1
2
0
2
0
0
1
1
1
0
0
1
2
0
1
1
1
0
2
1
2
1
0
2
0
0
2
1
0
2
2
1
1
0
0
1
2
0
1
1
1
1
2
1
0
0
0
0
2
0
1
2
2
2
1
2
0
1
0
2
0
0
2
0
1
0
1
1
3
0
0
0
2
0
1
1
2
1
2
1
1
0
2
0
0
2
1
1
0
1
1
2
0
2
1
2
1
0
0
2
2
0
1
1
1
2
2
0
1
1
1
2
1
1
0
0
2
0
0
0
0
1
0
1
0
0
0
1
1
0
1
0
2
1
2
0
2
2
0
1
1
0
1
2
2
0
0
0
1
1
3
1
1
1
1
1
1
1
0
2
0
0
0
1
0
2
1
1
0
1
2
0
2
1
1
2
1
1
1
1
1
0
0
0
1
1
1
0
0
1
0
2
0
1
1
0
0
0
1
1
1
1
2
1
0
2
2
1
1
0
1
2
1
1
0
1
0
2
1
1
0
2
0
1
2
1
2
0
2
0
0
1
2
1
1
1
1
1
0
1
0
1
2
0
1
0
0
0
1
0
0
1
0
0
2
0
0
1
1
1
1
1
0
1
1
0
1
2
0
1
1
0
2
1
1
0
1
1
1
0
1
0
0
0
1
0
1
2
1
1
0
1
1
1
1
0
0
0
0
1
1
0
0
1
2
1
1
0
0
0
1
1
1
1
1
2
1
1
0
1
1
1
1
0
0
3
1
1
0
2
1
1
2
1
3
0
1
0
2
2
1
2
1
1
1
0
1
2
0
1
1
1
2
0
0
2
1
1
2
0
1
1
0
0
0
3
0
2
1
2
2
1
0
0
1
0
2
0
1
0
2
1
0
2
1
0
1
1
1
2
1
1
0
1
1
1
1
0
1
1
2
1
0
2
0
2
0
0
1
0
0
1
2
0
1
1
1
0
0
1
1
1
0
1
1
0
2
1
1
1
1
1
1
1
0
0
2
1
2
2
0
1
0
1
1
2
1
1
0
0
1
1
1
1
1
2
1
3
1
1
1
0
1
1
0
0
2
1
0
0
0
1
2
2
0
0
1
2
1
2
1
0
1
1
2
1
1
0
1
1
2
0
0
0
1
1
2
1
1
0
0
0
2
0
1
1
1
1
0
1
2
2
2
1
1
0
1
1
1
1
1
1
1
0
1
0
1
1
1
1
1
1
1
0
1
0
1
1
0
1
2
1
2
2
2
1
2
1
1
0
2
0
1
2
1
0
1
1
1
1
2
2
0
1
1
2
1
1
2
0
1
1
0
2
1
1
1
0
1
1
1
0
2
2
2
0
1
0
0
0
1
1
0
1
2
0
1
1
1
0
0
0
1
1
2
1
1
1
0
0
0
1
0
1
1
0
1
1
0
1
0
2
2
1
1
0
1
0
1
1
0
1
1
2
1
7
1
1
1
2
0
0
1
1
1
0
0
1
2
2
2
0
1
1
1
0
2
2
2
2
1
1
0
0
2
1
1
0
0
1
1
0
1
1
2
2
1
2
2
1
0
1
0
0
1
2
0
1
0
0
2
0
2
1
1
2
1
1
0
2
2
1
0
2
2
0
1
1
0
0
1
1
2
1
2
0
2
0
1
0
0
1
1
0
0
0
0
0
1
1
2
1
0
0
0
1
0
1
0
2
2
0
0
0
2
1
1
0
2
1
1
1
1
1
1
1
0
1
1
1
0
2
0
1
1
1
2
0
1
1
2
0
2
0
1
1
1
0
2
1
2
0
0
1
2
0
0
1
0
2
1
2
1
0
0
2
1
0
0
1
3
0
0
2
0
2
1
0
0
2
0
0
1
1
1
1
2
1
1
0
1
2
1
1
1
0
2
2
1
1
1
0
2
1
3
0
0
0
1
1
1
1
1
0
0
1
1
1
0
1
1
2
1
0
1
0
1
1
1
1
0
1
2
2
1
2
0
1
1
1
1
1
2
2
0
1
1
0
0
1
1
1
2
2
1
3
2
2
0
2
0
0
1
2
1
1
1
1
0
2
2
0
2
2
0
0
0
0
1
2
0
1
1
2
1
0
2
1
0
1
1
1
1
0
1
0
1
1
4
1
1
1
2
0
0
2
1
2
2
0
2
0
0
0
2
0
1
1
1
1
0
2
1
0
1
2
1
1
1
2
1
1
1
0
1
1
2
0
0
1
2
0
1
1
1
1
0
1
1
1
1
0
1
1
2
1
2
1
1
2
0
2
1
2
0
1
1
1
2
1
0
1
0
0
0
1
1
1
1
1
1
1
1
1
1
0
1
2
0
1
0
0
0
0
1
2
1
0
1
0
1
1
0
2
1
2
1
3
2
0
0
0
1
2
1
2
0
2
0
1
1
1
2
1
1
0
2
2
2
2
3
0
0
2
1
1
0
0
0
0
0
0
0
2
2
0
0
1
0
1
0
1
2
1
0
0
1
0
1
1
1
1
1
0
1
1
1
0
2
1
1
0
0
1
1
1
1
2
0
1
0
1
0
0
0
2
1
1
2
0
1
0
2
0
2
0
0
1
2
0
0
0
1
2
0
2
2
0
1
1
0
2
0
1
2
0
1
1
1
0
1
2
1
1
2
1
0
2
0
0
0
1
2
0
0
0
0
1
1
0
2
0
1
2
0
1
2
1
1
1
1
1
1
0
1
2
1
1
0
2
0
1
2
0
2
1
1
0
2
1
0
1
2
2
2
0
1
0
1
0
1
2
1
1
0
1
2
1
1
2
0
2
2
1
2
0
2
1
1
0
0
1
2
1
1
1
0
1
0
1
1
0
1
2
0
0
0
0
0
2
2
1
2
2
1
1
0
1
0
2
1
1
5
1
0
1
2
1
1
1
0
0
1
2
5
2
1
1
0
0
0
0
1
0
1
2
0
1
1
0
1
1
1
0
1
0
1
5
1
1
0
1
1
1
0
2
2
0
1
0
1
0
1
0
0
0
0
0
0
1
1
1
0
2
1
0
2
3
1
0
1
2
0
1
1
1
2
0
1
0
2
1
0
0
1
2
0
2
1
2
1
1
1
1
0
1
0
1
0
0
2
0
1
1
1
2
2
0
1
1
1
2
1
1
2
0
1
1
0
1
0
0
0
2
1
1
0
0
0
1
0
0
4
1
0
1
1
1
0
1
1
1
0
1
1
1
0
1
1
0
1
0
0
1
1
2
1
2
1
1
1
1
1
0
1
1
0
1
1
2
0
1
1
0
2
1
0
1
0
1
1
2
1
2
1
1
2
2
1
1
1
1
1
1
0
1
1
1
2
2
1
0
0
0
0
2
0
1
2
1
2
1
1
0
2
0
1
1
2
0
2
1
2
1
1
0
2
1
2
1
0
1
2
1
0
1
1
2
1
1
2
1
2
1
1
2
2
1
1
0
1
1
0
0
1
0
0
0
0
1
3
0
1
3
0
1
1
1
1
1
1
1
2
2
1
0
1
1
1
2
1
1
2
0
1
2
2
0
2
0
0
0
0
1
2
1
0
0
1
1
0
0
0
1
0
0
0
2
1
2
1
1
1
0
1
1
1
1
0
0
0
1
0
1
2
0
2
2
1
1
1
2
1
1
1
0
1
0
2
2
0
1
1
1
0
2
1
0
2
1
1
0
1
1
1
0
2
1
1
2
1
0
0
2
2
1
1
1
0
2
1
0
0
2
1
2
0
2
1
1
0
1
1
2
2
1
0
2
0
1
1
1
2
0
2
2
2
0
2
3
0
1
1
0
2
1
0
3
1
0
0
0
1
1
2
1
1
1
1
2
2
3
2
2
2
1
0
1
0
0
1
0
2
2
0
1
1
0
2
0
1
0
2
1
1
1
0
2
1
0
0
0
1
2
2
0
2
2
0
2
2
2
1
2
1
1
2
2
0
1
0
0
2
2
1
0
1
0
1
2
3
1
1
1
0
2
1
0
2
1
2
1
2
1
0
2
1
1
1
2
1
0
2
2
2
0
0
1
1
2
1
1
0
1
1
0
2
0
1
1
0
1
0
1
2
1
1
0
1
0
1
1
1
1
0
2
1
6
0
0
0
2
1
1
2
1
1
0
1
1
1
1
0
1
1
0
0
0
1
2
0
1
0
1
0
1
1
4
0
1
1
0
0
1
1
2
0
1
1
0
1
1
0
1
1
2
0
1
1
1
0
1
2
2
1
1
1
0
0
1
2
1
1
1
1
0
0
1
0
1
2
2
1
0
1
2
0
1
1
2
0
1
0
1
1
1
0
0
2
1
1
1
0
1
1
0
0
1
1
0
1
1
1
2
1
1
0
0
0
2
2
1
1
1
0
1
1
2
4
0
2
1
1
0
2
1
0
0
2
0
1
0
0
0
1
1
1
1
1
1
0
0
1
2
1
0
2
2
0
2
1
2
2
2
1
0
1
1
1
2
0
1
0
1
2
1
0
2
0
2
3
2
0
1
2
1
1
1
1
1
2
0
2
0
1
1
2
1
1
1
1
1
1
0
0
0
1
1
1
1
2
0
1
0
1
1
0
3
1
0
2
1
1
1
1
0
1
1
0
0
1
1
1
0
1
2
1
1
1
0
1
1
0
0
1
0
2
1
1
0
2
0
1
1
0
1
1
1
1
2
2
0
1
2
1
2
1
0
1
1
1
1
2
1
2
1
2
0
1
1
0
2
1
1
1
1
0
1
2
1
1
1
1
2
1
1
1
1
1
0
1
2
2
1
0
0
2
1
1
0
0
3
1
2
2
1
1
0
1
0
0
2
1
1
1
0
1
1
0
2
1
2
0
1
2
1
1
0
1
1
2
0
0
1
2
0
1
1
2
1
2
2
0
1
2
1
0
0
1
0
1
1
1
1
1
1
1
2
1
1
0
0
0
1
3
1
1
1
1
5
1
1
1
1
0
2
2
0
1
1
2
2
1
2
1
1
2
0
2
1
1
1
0
1
1
1
2
1
0
2
0
2
0
2
1
0
0
2
1
0
2
1
2
0
1
0
1
0
1
2
1
2
0
1
2
0
1
0
2
1
1
0
0
0
1
0
1
1
1
1
2
0
2
1
0
1
1
1
0
2
0
0
1
2
1
1
1
1
1
0
1
2
0
2
1
1
1
1
1
1
2
1
0
1
1
1
0
0
2
2
0
1
0
2
1
0
0
1
1
0
2
1
0
0
1
0
2
2
0
1
0
1
0
2
2
1
1
0
1
1
1
1
0
0
1
2
1
1
1
2
0
1
1
1
1
0
2
0
2
0
0
0
1
2
0
1
0
0
0
0
0
2
2
0
2
1
1
0
0
0
1
1
1
2
1
0
0
0
1
0
2
1
5
0
0
1
2
0
2
0
1
1
0
1
2
0
1
0
0
0
1
0
0
1
0
0
1
1
2
0
1
1
2
1
1
1
2
1
0
0
1
1
0
1
1
1
1
1
1
3
1
1
1
1
0
1
1
1
0
1
0
0
0
1
0
1
1
1
2
1
1
0
0
0
1
0
2
1
0
1
0
1
1
0
1
1
2
1
2
0
1
1
0
1
0
1
1
0
0
0
0
0
1
0
0
0
1
1
1
2
1
0
1
0
1
1
2
1
1
2
1
1
2
0
1
0
0
1
1
2
1
1
1
1
1
0
1
0
2
1
0
2
1
1
1
1
1
1
2
0
2
1
0
1
2
2
0
1
2
1
0
0
1
1
1
1
1
2
0
2
1
1
1
1
0
0
1
1
1
0
1
2
2
0
2
1
1
1
1
1
1
0
2
1
0
1
0
0
1
0
1
1
1
2
1
2
1
1
2
0
0
2
1
1
2
1
0
1
1
1
1
1
0
0
1
1
0
1
2
1
2
0
2
0
1
1
2
1
1
1
1
1
0
2
1
2
1
0
0
2
0
2
2
1
1
1
1
0
2
0
1
1
2
0
0
0
1
0
1
0
0
2
1
2
1
1
2
1
0
1
0
1
0
0
0
1
1
0
0
1
2
1
1
1
1
3
1
1
1
0
1
1
1
0
0
1
0
1
0
1
0
2
1
0
0
0
0
2
1
1
2
2
1
0
1
1
1
1
1
2
1
0
1
2
1
1
1
0
0
0
1
1
0
0
1
1
1
0
1
0
1
2
1
0
1
1
1
1
1
1
1
0
2
1
1
0
0
1
1
2
1
0
1
1
1
0
0
0
0
1
0
1
0
1
1
1
1
1
1
1
2
1
1
1
2
1
1
1
1
2
1
2
2
1
1
1
0
1
2
2
1
2
3
0
2
1
1
1
0
1
2
1
1
2
0
0
1
0
1
1
0
1
2
2
1
1
1
0
1
1
1
1
0
1
1
0
1
1
1
2
2
1
1
0
0
1
1
1
1
1
5
2
2
1
2
1
1
1
2
0
1
2
1
1
2
2
1
0
0
1
0
0
1
0
0
2
0
0
0
0
1
0
1
1
2
0
0
0
0
1
1
1
0
1
0
0
1
0
0
1
1
1
1
2
1
1
1
1
0
0
0
2
1
2
1
0
2
1
1
0
0
1
2
2
3
1
2
1
1
1
1
1
1
0
0
2
1
2
2
1
1
1
1
1
1
0
0
1
0
1
1
2
1
1
0
2
2
1
1
0
1
0
0
1
2
2
1
1
1
0
0
0
2
0
0
2
1
0
1
1
1
1
0
1
2
1
2
1
2
1
1
0
2
0
1
1
1
0
1
1
1
2
2
1
2
0
1
0
1
0
1
0
2
2
0
1
0
2
3
0
1
0
1
1
2
1
0
1
0
2
1
0
1
1
0
1
1
1
0
1
1
1
0
0
1
3
2
1
1
1
1
0
0
2
1
1
2
1
1
1
1
1
2
2
1
1
1
1
0
0
1
2
0
0
0
0
0
0
1
1
1
1
1
1
2
1
0
1
1
2
0
1
2
2
2
4
1
0
1
1
2
1
0
0
1
1
1
0
0
1
0
2
2
2
1
0
2
1
1
2
1
1
1
1
0
0
0
1
2
0
0
0
0
2
1
1
1
1
1
5
2
0
0
3
1
0
3
2
2
1
2
2
0
2
2
1
0
0
2
2
1
1
0
1
0
2
0
1
1
1
2
0
1
0
0
1
2
2
2
2
1
1
0
1
1
0
0
1
1
1
1
0
2
0
1
1
2
1
2
2
0
1
0
1
1
0
1
1
0
1
1
2
1
2
0
1
1
0
0
0
2
1
2
2
1
1
0
0
0
1
2
1
1
1
2
0
1
3
0
0
2
1
0
0
1
0
2
0
1
2
2
1
1
1
0
1
1
1
1
1
0
1
2
2
1
0
1
1
1
1
1
1
1
0
1
0
1
1
1
0
1
0
1
1
0
1
0
1
2
2
0
1
0
0
1
2
0
1
1
0
0
1
1
1
1
0
2
0
1
1
2
2
1
1
0
0
0
0
0
0
2
2
1
1
0
0
0
0
0
1
1
2
2
1
0
2
1
0
3
2
1
1
1
1
1
1
0
0
1
1
1
0
1
0
1
1
2
1
0
2
1
1
1
0
1
1
1
0
1
0
1
1
1
0
1
1
2
0
2
0
1
1
0
0
1
1
1
0
0
2
1
0
0
1
0
1
0
0
2
1
1
0
2
2
2
2
1
1
1
0
0
1
1
2
0
0
1
2
1
0
1
2
1
1
0
1
0
0
1
1
2
1
0
1
1
2
2
2
1
1
1
2
0
1
0
1
1
2
2
0
1
0
1
0
1
1
0
2
1
2
1
0
0
1
1
1
0
0
1
2
2
0
1
2
1
1
1
0
0
0
1
1
2
2
0
0
2
1
1
1
2
0
1
1
1
1
1
0
1
1
1
1
1
1
1
2
0
2
1
1
2
0
0
0
1
0
2
1
1
0
0
1
0
0
2
0
1
0
1
0
1
3
2
2
1
2
0
0
0
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
2
0
1
2
2
0
2
1
0
0
2
1
2
1
1
1
1
1
2
1
1
0
1
0
2
2
2
1
1
1
1
0
0
1
0
0
2
1
1
1
0
1
1
1
0
1
1
2
1
1
1
2
2
2
1
1
1
1
0
0
2
2
1
0
1
1
0
0
1
0
2
2
1
1
0
0
0
1
1
2
0
2
1
1
0
1
1
0
1
1
1
1
2
0
1
1
0
1
0
0
1
0
0
0
0
0
1
2
0
1
0
2
4
0
1
1
2
2
1
2
1
0
2
1
2
0
1
1
1
2
1
1
0
1
1
2
1
2
1
1
2
1
1
2
0
1
0
1
2
2
0
2
2
1
0
1
1
0
0
0
1
0
0
1
1
1
1
1
0
2
2
2
0
2
1
3
1
0
1
1
5
1
0
0
1
0
2
2
0
2
1
0
0
1
1
1
4
1
1
0
2
1
1
0
1
1
1
2
0
2
0
1
1
0
0
0
1
1
2
0
0
1
0
0
1
1
0
3
1
1
1
2
0
2
1
1
1
1
1
2
2
1
1
0
1
2
2
0
1
1
1
1
2
1
1
2
0
2
2
1
0
1
2
4
1
1
1
2
0
1
1
0
1
0
0
1
0
1
1
2
2
0
1
0
0
2
1
2
1
1
0
1
0
0
1
1
0
1
0
0
0
1
1
2
2
2
0
0
1
1
2
0
0
2
0
2
2
0
2
1
0
0
0
1
2
1
1
1
1
1
0
1
0
1
1
0
0
0
0
1
1
1
1
1
2
2
2
0
2
2
1
0
2
1
0
0
0
0
0
1
1
0
0
0
1
0
2
0
1
1
1
0
2
1
2
0
1
1
4
1
1
1
0
1
2
1
0
1
1
1
1
1
2
1
0
2
3
1
1
1
1
2
2
2
1
1
1
1
0
0
0
1
1
2
1
1
1
1
1
2
3
0
1
1
2
2
1
1
0
1
1
2
0
2
2
1
1
1
1
2
2
1
1
1
1
0
0
1
0
0
0
1
5
1
1
1
0
3
1
0
1
1
0
1
1
1
2
1
1
1
0
2
2
0
2
1
0
2
1
0
2
1
1
1
1
1
0
1
1
2
2
0
0
1
0
0
2
1
1
0
1
1
1
0
1
2
0
0
0
2
0
0
1
0
1
2
1
1
0
1
1
1
2
0
2
1
2
1
1
1
0
0
1
1
1
2
2
1
0
0
2
1
2
0
0
1
1
2
1
0
1
1
2
2
2
1
1
1
0
1
1
0
1
2
1
1
0
0
2
1
0
1
1
2
2
0
1
0
0
2
0
0
2
1
0
0
0
1
0
2
2
0
0
2
2
0
1
2
1
1
1
0
1
1
0
2
0
0
1
0
1
1
1
3
1
1
1
0
1
2
2
0
0
0
1
1
1
1
1
1
0
0
0
1
2
2
1
0
1
1
0
2
2
0
1
1
0
1
2
0
1
0
0
1
1
0
1
2
0
2
2
0
3
1
2
1
1
1
1
1
1
1
1
1
1
1
1
0
0
0
0
2
0
1
1
0
1
1
2
1
0
0
1
1
2
1
0
0
0
2
1
0
2
1
2
0
1
1
0
0
0
2
2
1
1
1
1
2
2
0
2
0
1
1
1
0
0
2
0
0
2
1
1
1
1
2
1
0
0
1
2
0
1
1
0
2
0
1
1
1
0
1
0
2
2
2
1
1
1
1
1
0
2
2
0
1
0
0
2
2
0
1
1
0
1
1
1
1
1
1
1
1
1
1
2
1
2
0
2
0
1
2
1
1
0
1
2
2
0
1
2
2
2
1
0
1
1
0
1
2
0
0
1
1
1
1
0
2
1
1
0
1
0
0
2
2
1
0
1
1
0
0
2
1
2
1
2
0
1
0
2
1
1
1
0
0
1
1
0
3
2
1
1
2
1
1
1
1
0
0
0
0
2
1
1
0
0
0
0
1
1
1
1
1
1
0
2
0
1
1
1
0
0
1
1
1
1
1
1
1
2
0
1
2
0
1
2
0
2
1
2
2
0
0
1
0
0
2
0
3
1
1
1
1
1
2
2
1
2
1
1
0
1
2
1
1
2
1
1
0
1
1
1
2
1
1
1
2
1
1
1
1
0
1
2
1
1
1
1
0
0
1
1
0
2
0
2
3
1
2
0
1
1
2
1
1
2
2
1
1
1
1
2
1
2
0
1
2
1
0
1
1
2
1
1
1
0
2
0
1
1
0
0
1
0
1
2
1
0
0
0
2
1
2
1
2
2
3
1
1
0
1
1
1
0
1
0
1
0
0
0
2
1
1
1
1
1
1
1
2
1
0
2
1
0
2
0
1
2
0
1
1
0
0
0
0
2
1
1
0
0
1
2
1
3
1
1
0
0
1
0
1
2
2
0
0
2
1
0
2
2
2
0
1
0
2
0
2
1
1
1
1
2
1
1
1
1
1
1
2
1
1
2
1
1
0
3
1
2
4
0
1
1
1
2
1
1
2
0
1
0
2
0
0
0
2
0
0
1
0
1
2
1
1
0
1
1
0
0
1
2
1
0
1
0
1
1
0
1
1
1
0
2
1
1
0
0
2
1
0
2
2
0
0
0
2
2
0
2
1
1
1
1
1
3
0
0
1
0
0
2
0
1
1
1
2
2
0
1
1
0
0
2
0
1
1
2
1
2
0
2
0
1
1
1
1
1
0
1
1
0
0
0
0
1
0
0
2
0
2
2
2
1
0
0
0
1
1
1
1
0
1
0
1
1
2
0
1
2
1
1
1
1
1
1
1
1
3
0
0
0
1
1
0
2
2
1
2
1
2
1
1
0
2
2
2
1
0
1
2
2
2
4
0
2
0
0
0
2
0
2
0
1
1
3
1
1
1
1
0
0
2
1
1
1
1
1
0
1
0
1
0
1
1
0
1
0
0
1
0
0
2
1
2
4
0
1
1
2
1
2
1
1
0
2
1
0
1
2
1
1
0
1
1
2
3
2
1
0
0
2
0
2
1
2
1
1
1
1
2
1
0
0
0
0
2
2
2
1
1
1
0
1
0
1
1
1
1
1
2
2
1
1
1
2
1
0
1
1
0
0
1
1
2
2
0
2
1
1
2
2
1
1
2
1
0
1
1
0
0
1
0
0
0
2
1
2
0
1
0
1
2
0
0
1
1
0
1
1
1
0
1
1
1
1
1
3
0
1
1
1
2
0
1
0
1
1
2
2
0
1
0
1
1
0
1
0
1
0
1
2
1
1
0
0
0
1
1
1
1
2
2
1
1
1
1
2
2
0
1
1
0
0
1
1
1
1
1
1
1
2
3
0
2
1
2
3
0
0
0
1
0
0
0
2
0
1
2
0
1
1
2
1
2
2
1
2
0
0
2
1
1
1
0
2
0
2
2
1
2
1
1
1
1
0
0
0
0
0
0
2
2
0
0
1
0
1
1
1
2
1
1
1
2
2
2
0
0
1
0
1
0
2
1
0
1
0
1
1
0
1
1
0
2
0
2
1
1
2
0
2
0
1
1
1
2
1
1
0
2
0
3
0
2
1
2
2
0
2
0
2
1
0
1
1
2
1
1
0
1
0
0
2
1
1
2
2
0
1
0
1
0
0
0
0
0
1
0
0
1
1
1
1
1
1
0
1
1
1
0
0
2
1
1
3
0
2
3
1
1
1
1
1
1
1
2
1
1
1
0
0
1
1
0
1
1
0
1
2
1
1
1
0
0
2
0
0
0
2
2
1
0
1
1
0
1
2
0
0
1
0
1
2
1
0
2
1
0
0
0
0
0
2
1
1
1
2
1
2
1
1
2
0
2
0
2
1
1
0
1
1
0
1
1
1
1
1
1
0
2
0
0
1
1
1
0
1
0
1
1
2
2
1
2
2
2
1
2
2
0
0
1
2
1
2
1
1
1
0
1
0
2
1
1
0
0
1
0
2
2
1
1
1
1
1
0
1
0
1
1
0
1
1
1
2
1
0
0
1
1
1
1
1
2
1
1
1
1
0
1
0
3
1
1
0
1
2
0
1
2
2
0
0
2
1
1
1
0
1
1
1
1
1
0
0
1
0
0
1
1
0
0
0
0
1
2
0
0
1
1
2
1
1
0
1
0
2
1
2
3
2
1
0
1
0
1
1
1
2
2
0
1
2
1
1
0
1
0
1
0
1
2
1
1
0
1
1
2
1
0
1
0
1
0
1
2
0
2
0
3
0
0
2
1
0
1
0
0
1
0
1
0
2
1
2
1
1
2
1
1
1
2
0
1
2
1
2
1
0
0
2
2
2
0
2
0
0
4
0
1
2
1
1
1
2
0
0
2
1
0
1
0
1
1
1
2
0
2
2
0
1
2
1
2
1
1
1
1
2
2
1
1
1
0
0
1
1
2
0
2
0
0
1
2
0
0
1
0
1
2
1
1
1
1
1
0
0
1
1
1
0
1
0
0
2
0
2
1
1
2
0
1
1
1
2
0
2
1
2
2
2
2
1
0
2
2
1
1
0
0
1
0
1
2
0
1
1
2
1
2
1
2
1
0
2
1
1
1
0
1
2
2
2
1
1
0
1
1
1
2
2
0
1
1
1
1
1
1
1
0
0
0
1
0
0
0
0
1
0
0
1
1
2
0
0
2
0
2
1
2
1
2
1
0
0
2
1
0
0
0
1
1
1
1
0
1
0
1
2
1
0
2
2
2
1
2
2
3
1
0
0
1
0
1
1
2
1
1
0
1
0
0
0
2
1
0
2
1
2
1
1
2
2
1
0
1
1
1
1
1
2
1
0
1
0
1
1
1
1
0
0
1
1
2
2
2
0
1
0
1
1
1
0
2
2
1
1
1
0
1
1
0
0
2
0
2
1
0
0
2
1
0
0
1
1
1
1
0
2
0
2
0
2
1
1
1
2
2
2
2
1
1
2
2
1
1
2
1
1
0
2
2
2
1
0
2
0
1
1
2
1
0
4
1
1
0
1
1
2
1
1
1
2
2
1
1
1
0
1
1
1
2
2
1
0
0
1
0
0
1
1
1
1
0
1
1
1
0
2
1
1
0
1
1
1
1
2
1
0
0
1
1
1
2
1
0
0
0
0
1
1
0
1
1
2
0
0
2
3
0
1
2
1
1
1
0
1
1
1
1
1
1
1
1
0
1
1
1
1
1
0
1
1
2
1
0
1
0
1
1
1
0
0
1
1
0
1
0
1
1
0
0
2
0
1
1
1
1
0
0
1
1
1
1
1
1
1
1
1
1
1
0
0
1
1
0
2
1
1
2
0
1
1
0
1
2
1
1
0
1
2
2
1
1
1
0
2
1
1
0
1
1
2
1
0
1
0
0
1
2
2
0
1
1
0
0
1
0
1
2
0
0
1
2
1
1
0
1
1
1
0
2
1
2
1
0
1
0
1
1
1
1
1
1
1
1
0
1
3
0
1
1
1
0
2
2
1
1
0
1
1
2
1
1
1
1
1
1
1
2
0
1
1
1
1
2
0
2
1
0
1
0
1
1
0
0
0
2
0
3
2
1
1
1
0
0
1
1
2
1
0
2
1
1
0
2
0
1
1
1
0
0
0
0
1
0
1
1
1
1
1
2
0
0
1
0
2
0
0
0
1
1
2
1
2
1
2
1
2
2
2
2
2
0
1
0
1
1
1
1
2
0
0
2
2
2
1
2
0
1
0
0
1
2
1
1
0
1
0
2
1
2
2
2
0
1
1
0
0
2
2
1
0
1
1
1
2
1
0
2
1
1
1
1
1
0
1
1
0
1
1
1
1
1
0
0
0
3
0
2
2
1
1
2
2
1
1
2
2
1
0
1
1
1
2
1
1
1
0
1
1
1
1
0
1
0
0
0
2
1
2
1
1
1
2
1
2
0
0
1
1
2
0
1
2
1
2
2
1
0
1
1
0
0
2
0
0
2
0
0
1
1
0
1
1
0
1
1
1
1
1
1
1
0
0
1
1
0
0
2
1
2
1
1
1
0
1
1
0
1
2
1
2
0
2
0
0
1
0
2
1
1
1
1
0
1
2
0
2
0
1
2
0
2
1
0
1
0
1
1
0
2
1
2
1
1
0
0
0
2
1
0
0
0
2
0
0
0
0
1
3
3
0
1
1
0
0
1
1
1
1
1
1
2
0
1
0
1
1
1
1
2
1
7
0
0
0
0
1
1
0
2
1
0
2
1
1
1
1
0
1
1
2
1
1
0
1
2
1
0
0
0
1
1
1
1
1
1
2
0
3
0
0
1
1
1
1
1
1
0
1
1
0
1
1
0
1
1
2
0
1
0
2
1
1
0
1
2
2
1
1
0
0
2
1
0
1
1
2
2
0
1
1
1
2
0
1
0
1
2
1
1
2
1
1
0
1
4
0
0
1
0
1
0
2
0
1
0
0
1
1
1
4
1
1
2
2
1
0
1
2
1
1
0
3
1
0
0
1
0
1
1
1
0
1
2
0
1
0
2
1
0
1
0
1
1
1
1
2
0
1
2
2
2
2
2
1
0
0
0
1
1
0
0
1
2
0
1
2
0
2
1
1
1
0
2
1
2
1
1
2
0
1
2
0
2
2
2
1
1
1
1
0
0
1
0
1
0
1
1
1
2
1
0
1
2
0
1
0
0
2
2
1
0
1
1
0
1
0
2
1
2
1
1
0
1
1
0
2
2
1
1
0
2
2
1
1
1
1
0
2
1
0
0
0
1
0
2
1
2
2
2
0
1
0
1
1
2
0
2
0
0
1
1
0
1
1
2
0
1
0
1
1
1
1
3
1
1
1
0
1
0
1
1
0
1
1
1
1
1
0
0
1
1
2
1
1
1
0
1
1
0
1
2
2
2
0
2
0
2
1
2
1
0
1
1
1
1
0
1
0
1
2
2
1
1
1
0
1
1
1
0
1
1
2
0
1
1
1
1
0
1
1
0
1
1
0
2
0
0
1
1
0
1
1
0
2
2
1
1
0
0
0
2
1
0
1
1
0
2
1
1
1
0
0
1
1
2
1
1
2
2
1
3
1
1
1
1
1
1
1
0
1
1
0
1
0
1
2
2
2
1
0
1
1
2
1
1
1
2
1
0
1
1
2
2
2
0
1
0
1
1
2
0
1
0
0
2
1
1
1
0
1
1
1
0
1
0
1
2
1
0
0
0
2
1
2
1
1
1
1
1
1
1
1
0
1
1
1
1
0
2
1
1
1
0
0
1
1
2
0
0
1
1
1
0
0
1
1
1
2
1
0
1
2
2
1
1
2
2
1
0
2
1
0
1
1
1
0
0
0
0
1
1
2
2
1
0
2
2
1
0
1
1
1
1
0
1
0
1
1
1
1
1
2
2
0
1
1
1
0
2
1
1
2
0
3
1
1
1
1
1
0
1
0
1
0
0
2
2
0
1
2
1
0
0
1
0
0
1
1
0
0
1
1
1
1
2
1
1
1
1
1
2
1
2
2
1
0
1
1
1
1
1
1
2
1
0
0
2
1
1
2
1
0
0
2
2
1
0
2
1
1
2
1
2
2
1
0
0
1
1
1
1
0
0
1
2
1
1
2
0
0
1
1
1
0
1
0
2
1
0
2
1
1
1
0
1
1
0
2
1
1
1
0
3
0
0
1
1
0
0
2
0
1
2
0
0
3
1
0
2
1
0
0
0
2
2
1
0
2
1
1
0
2
0
0
0
1
1
1
1
0
1
2
1
2
1
1
1
1
1
1
1
1
1
0
2
0
1
1
1
1
1
1
0
2
1
1
0
1
1
2
0
1
0
1
1
2
0
1
0
1
1
1
0
0
2
1
0
1
2
0
0
1
2
2
1
1
1
1
1
1
1
1
0
1
2
0
1
0
1
0
0
0
0
1
0
2
2
1
2
0
2
1
2
2
2
1
0
1
1
0
2
1
1
2
0
1
2
2
1
1
1
1
1
0
1
1
0
1
0
0
2
1
1
0
2
1
2
1
2
0
0
2
1
2
1
1
2
1
1
0
0
1
0
0
2
2
2
2
1
1
1
0
2
1
1
0
2
1
2
1
0
1
0
0
0
2
1
1
0
0
0
1
2
2
1
0
1
1
0
0
0
1
0
2
1
1
0
0
1
1
1
1
1
2
2
2
0
0
0
1
1
0
0
2
1
0
1
2
0
0
0
1
1
1
3
2
3
1
1
0
0
2
1
0
0
3
2
2
1
2
0
1
0
1
0
0
0
0
1
0
2
1
0
1
1
2
1
0
2
1
0
4
1
2
1
1
1
2
1
2
1
1
0
1
2
2
1
1
0
0
2
0
0
2
1
0
1
1
3
0
0
2
0
1
0
0
1
2
0
0
1
1
0
1
2
2
1
1
2
2
2
0
1
2
0
0
0
2
0
1
1
0
0
0
1
2
1
2
2
0
1
1
0
1
1
2
1
1
1
1
1
1
1
0
1
0
0
0
0
0
1
1
1
2
0
1
2
0
1
1
0
3
0
1
2
0
0
4
0
0
2
1
2
1
1
0
1
0
2
1
2
1
2
2
1
1
0
0
0
3
3
1
0
0
0
1
1
1
1
1
2
1
0
1
1
0
1
1
1
1
2
1
1
1
1
0
2
1
0
1
1
0
0
1
2
2
0
0
1
1
0
1
1
0
0
1
1
2
1
0
0
1
0
1
1
1
0
2
1
2
0
0
0
2
1
2
0
0
1
1
1
1
1
1
2
0
0
0
1
1
1
1
1
0
0
0
1
2
2
0
0
2
0
1
1
2
1
1
1
2
1
1
0
2
4
1
2
1
0
0
1
0
1
0
2
0
0
2
0
1
1
1
2
1
1
0
1
1
0
2
1
2
1
2
0
1
1
2
2
0
1
1
2
3
2
0
1
1
0
2
1
2
1
0
0
0
1
0
0
0
1
0
1
1
0
1
0
1
2
1
2
0
2
2
0
1
0
2
1
1
0
2
0
1
1
1
2
2
1
0
0
1
0
2
1
1
1
1
0
3
1
1
1
2
1
1
1
0
0
0
0
0
1
2
0
3
1
0
1
2
1
1
2
2
2
1
1
0
1
2
0
2
1
1
2
1
1
0
0
1
2
0
1
1
0
1
1
1
2
1
1
2
0
0
0
2
0
0
2
0
0
1
0
1
0
0
1
1
0
0
1
1
0
1
2
2
0
1
1
2
1
0
0
0
1
1
0
2
1
0
2
0
1
2
2
0
1
1
2
1
2
1
0
2
2
2
1
1
1
0
2
0
0
1
1
1
1
1
0
1
1
0
0
1
0
1
1
2
1
0
0
2
1
0
1
1
1
1
2
1
1
2
1
2
1
0
1
2
1
1
2
0
1
2
1
2
0
1
1
0
0
0
0
2
1
0
1
1
2
0
1
2
1
0
1
1
2
2
1
0
0
1
1
0
1
2
1
1
1
1
0
1
0
1
1
0
1
1
0
1
1
1
0
0
0
1
0
1
2
1
0
1
2
1
1
2
1
1
2
2
0
2
4
1
1
1
1
2
2
1
2
1
1
0
1
1
1
1
1
1
1
1
0
0
2
0
1
0
0
1
2
0
0
2
0
1
2
1
1
1
1
0
0
0
2
0
2
1
2
0
1
1
1
0
0
2
0
0
1
2
2
1
0
2
0
0
1
1
0
0
1
0
1
0
1
1
2
0
2
2
0
0
1
0
1
0
0
1
2
0
2
1
2
2
1
1
2
1
1
0
1
1
1
1
0
0
1
1
0
1
1
0
1
0
2
1
1
1
1
1
1
0
1
1
2
0
1
2
1
2
1
2
2
2
0
0
2
0
1
2
2
2
0
1
1
1
1
1
1
0
0
1
0
0
2
2
1
4
0
1
1
1
0
1
0
1
0
2
1
0
2
2
1
1
1
1
2
1
0
2
0
1
2
2
2
2
0
0
1
1
1
1
2
0
1
0
0
2
1
2
2
2
2
1
1
2
1
1
2
1
1
1
2
1
2
1
2
0
2
0
1
1
0
0
1
2
0
0
0
1
2
3
2
2
1
1
1
1
0
0
1
1
0
1
0
0
0
1
0
0
0
1
2
0
1
2
1
3
2
1
1
2
0
1
2
1
0
1
2
1
1
0
1
2
0
2
0
1
0
1
2
1
1
1
0
1
1
0
2
2
1
0
2
3
1
1
3
1
0
0
0
1
2
1
0
0
0
2
0
2
0
0
1
0
0
0
1
0
2
2
1
0
0
0
1
0
1
1
0
1
2
0
1
0
1
2
1
0
1
0
1
2
1
0
1
0
1
1
0
0
1
0
1
0
2
2
0
2
2
0
1
2
0
1
1
1
2
0
1
1
0
1
1
0
2
0
1
1
1
1
0
1
0
1
1
1
0
1
1
2
0
2
1
1
1
0
0
1
1
1
1
0
2
1
0
0
1
0
1
2
1
0
2
0
0
1
0
0
0
0
0
1
1
0
0
2
2
0
1
0
1
0
2
0
1
1
0
1
0
0
0
0
1
1
1
2
1
1
1
0
0
2
2
1
0
2
0
2
0
1
1
1
1
1
0
0
1
1
0
0
1
0
1
1
2
1
1
2
1
2
1
1
1
0
2
2
0
2
1
1
2
1
1
1
0
0
1
0
1
0
2
2
0
0
1
0
1
1
0
2
0
2
1
1
1
1
1
0
0
1
1
1
2
2
0
3
2
2
1
1
1
2
2
0
1
0
1
1
2
0
1
1
1
0
1
1
0
0
0
0
2
0
1
1
1
2
1
1
2
0
0
0
2
2
1
0
1
1
0
0
1
1
1
0
1
0
2
1
0
2
1
1
1
2
1
0
1
2
1
1
2
2
0
1
1
1
0
1
1
1
1
1
2
0
0
2
1
1
0
1
1
0
1
1
0
0
1
0
1
2
0
3
2
1
2
2
0
1
1
1
0
1
1
1
1
0
2
0
0
0
2
1
1
1
1
1
0
0
1
1
2
1
1
2
0
0
2
1
1
0
0
0
1
1
0
0
0
1
1
1
0
1
0
1
1
1
2
1
0
2
1
1
2
2
1
2
2
0
0
2
1
2
1
1
1
2
1
1
2
1
0
0
1
0
0
0
1
2
0
1
2
0
2
0
0
1
0
1
1
0
0
2
0
0
2
2
1
1
0
1
2
0
1
0
1
2
2
0
2
1
1
0
2
1
1
0
2
2
1
1
3
1
1
1
1
2
2
0
0
2
0
1
1
0
1
0
0
1
0
1
1
2
2
2
1
0
1
1
1
1
1
1
1
1
0
1
0
1
2
2
0
1
1
2
1
1
1
0
1
2
1
0
1
1
0
2
1
1
1
1
0
2
3
2
1
1
1
1
1
0
0
2
1
2
0
1
1
1
0
0
1
0
1
1
1
0
0
2
0
1
0
0
2
0
0
1
1
2
0
2
2
0
2
0
1
2
1
0
1
1
1
0
1
1
1
1
0
2
1
1
1
1
1
1
1
1
0
1
1
2
2
1
0
1
0
2
1
1
1
1
1
1
0
1
1
0
2
1
1
1
2
2
2
1
1
1
1
0
1
1
1
1
1
2
1
1
1
1
0
0
2
0
1
2
1
2
1
2
0
0
2
2
1
1
2
1
1
0
1
1
1
1
1
2
1
0
1
2
0
0
1
1
2
0
0
2
1
1
1
2
0
1
1
0
2
1
1
0
0
0
2
0
1
1
0
2
0
2
1
1
1
0
1
1
1
1
0
0
0
1
1
0
0
0
0
1
0
0
1
2
0
1
1
1
1
0
1
1
1
1
2
0
1
0
1
1
1
1
0
0
0
1
0
1
1
1
1
1
1
1
1
2
1
1
0
1
1
1
1
1
0
1
1
1
1
2
1
1
3
1
2
1
0
2
0
0
0
1
2
1
2
1
1
0
1
1
1
0
1
0
2
2
1
1
1
1
1
2
4
1
1
1
1
1
0
2
1
1
1
0
2
1
1
1
2
0
0
0
1
1
1
0
2
1
1
1
0
1
1
1
1
2
0
1
1
1
1
1
1
0
1
1
0
1
1
1
0
2
1
1
1
1
1
2
0
1
0
0
2
1
2
1
0
1
1
1
1
2
2
1
1
2
1
0
1
1
1
1
1
1
1
1
1
0
1
1
1
1
2
1
0
0
0
1
1
2
1
2
1
1
1
3
1
0
1
0
1
0
2
1
2
0
1
0
2
0
2
0
1
1
1
1
0
2
0
0
0
1
3
1
0
0
3
0
2
0
0
0
0
1
1
1
1
0
0
1
0
0
0
1
0
0
2
1
2
1
0
0
1
1
1
2
1
1
1
1
1
1
1
0
3
1
1
0
0
1
2
2
1
0
1
1
0
1
2
2
2
1
0
1
1
0
1
0
2
1
2
0
0
1
1
0
1
0
0
0
0
0
2
1
0
0
1
1
1
1
0
1
0
0
0
0
2
1
1
1
1
1
0
0
0
0
1
1
0
2
1
0
0
0
0
0
1
0
1
0
0
0
1
1
2
2
2
2
1
1
1
1
2
1
0
0
2
1
1
2
2
1
1
2
0
0
1
1
0
1
1
1
1
2
0
0
0
1
0
0
1
1
1
0
2
1
2
1
0
0
0
0
1
0
2
2
1
1
1
0
2
1
0
0
0
2
0
1
0
0
0
0
0
1
2
2
0
0
1
2
0
2
2
1
2
2
0
0
2
1
1
1
1
0
1
1
1
2
2
0
2
2
1
2
1
1
0
0
1
1
0
1
1
1
0
0
2
2
0
0
1
0
2
2
0
2
1
1
0
0
1
0
3
1
1
1
0
1
0
0
0
2
0
2
0
1
2
1
1
2
1
2
2
1
0
1
0
0
0
1
0
0
0
1
1
1
1
2
1
2
0
0
0
1
0
1
1
1
1
1
1
2
0
1
0
1
2
1
1
1
1
2
1
0
3
2
0
1
1
2
1
1
2
0
1
1
2
2
1
2
2
1
2
2
1
1
1
2
1
0
0
1
2
0
0
1
1
1
0
1
0
0
1
2
1
4
1
1
1
1
1
1
1
3
0
1
2
1
1
0
0
1
1
1
0
1
1
1
2
2
1
1
1
1
2
1
2
1
0
1
0
1
0
1
0
2
1
0
1
1
0
2
2
0
0
0
0
0
2
0
1
2
1
1
2
2
1
2
0
2
2
2
1
1
0
1
0
1
0
1
0
1
1
1
2
0
0
1
1
1
0
2
0
1
1
0
1
1
1
1
1
1
2
2
1
2
1
1
0
4
2
1
1
2
2
1
0
1
1
0
1
0
2
1
0
1
2
1
1
2
1
1
2
2
1
0
1
1
1
2
1
2
1
2
1
1
2
1
2
1
1
1
0
1
0
1
0
1
0
1
0
2
1
1
0
0
0
1
1
1
0
0
2
0
1
2
1
1
2
2
2
1
1
1
1
1
1
1
0
0
2
4
1
1
2
2
0
0
1
1
0
1
1
2
0
2
0
1
2
0
1
1
1
1
2
1
0
2
1
1
1
0
1
2
1
1
2
1
0
1
0
0
2
0
0
1
1
1
1
2
0
2
0
0
0
0
1
0
1
2
1
1
0
0
1
2
0
1
1
2
2
1
2
1
1
0
0
0
1
2
3
1
1
2
0
0
2
1
1
2
1
1
1
0
2
2
1
0
1
2
1
1
0
1
1
0
1
1
1
2
0
0
0
0
1
1
3
1
1
0
0
1
0
1
0
1
1
2
1
0
1
2
2
0
1
0
3
0
0
1
1
1
2
2
1
0
0
2
1
1
2
0
0
1
1
1
1
0
1
2
0
1
0
1
0
1
0
0
0
0
1
0
0
1
1
1
0
1
1
2
1
1
2
1
1
1
0
0
1
1
1
0
0
1
2
0
0
2
0
3
1
1
1
1
0
1
0
1
1
0
2
1
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
0
1
2
1
0
1
1
2
0
0
0
1
0
0
2
0
0
1
1
0
0
0
1
1
1
1
0
1
0
1
2
0
1
1
0
2
1
1
0
1
1
2
0
0
5
0
1
1
2
2
1
1
2
0
0
0
0
1
2
1
2
1
3
1
1
0
1
1
1
1
0
1
1
1
2
0
1
1
1
1
1
1
0
1
2
0
2
2
2
2
0
1
1
1
1
1
0
1
0
0
2
1
1
1
1
0
1
2
2
1
1
1
0
0
2
0
1
1
1
2
1
1
4
1
1
2
1
1
1
3
1
2
1
0
1
2
1
1
1
0
1
1
1
1
0
1
1
0
1
2
0
1
1
3
0
1
1
2
0
1
3
2
1
1
4
1
2
1
0
2
2
1
0
0
0
1
1
1
1
2
0
0
0
0
1
0
1
2
2
1
0
2
0
1
0
1
1
1
0
1
2
0
0
1
1
1
1
1
0
0
1
2
0
0
1
1
1
1
1
1
1
1
1
1
2
0
2
0
1
0
0
2
1
1
2
1
1
3
0
2
0
0
1
1
0
0
0
2
0
1
0
0
2
0
2
1
2
0
2
2
1
2
1
0
1
1
1
2
1
1
1
0
1
0
1
1
0
1
0
1
0
1
1
1
1
1
0
1
1
0
1
0
0
1
1
1
1
1
1
1
0
1
1
1
1
2
0
1
1
0
1
0
1
2
2
1
1
0
2
1
2
1
1
1
1
0
1
0
0
0
0
0
0
2
0
1
1
1
1
1
0
2
2
2
0
1
0
1
0
1
1
1
1
1
2
1
1
1
2
2
1
1
2
1
1
1
1
2
1
0
1
2
1
1
1
1
0
1
1
2
1
0
1
2
0
1
2
2
1
0
1
0
0
1
2
2
1
0
0
1
1
1
2
0
1
0
0
0
0
0
1
1
1
0
1
1
0
1
0
0
0
2
1
0
0
0
0
2
0
1
1
1
1
0
2
1
1
2
2
0
1
0
0
2
2
2
0
1
2
1
0
1
1
1
1
1
2
1
2
0
1
0
0
0
1
1
1
0
1
0
0
1
0
0
1
1
2
1
0
0
1
2
1
1
2
0
2
1
1
0
1
1
2
1
0
1
2
1
0
1
1
1
0
1
0
2
1
0
1
1
2
1
2
1
2
0
0
0
1
0
0
1
1
1
0
2
1
0
1
2
1
1
1
1
1
0
0
2
1
1
0
0
0
0
2
1
1
1
2
0
0
1
1
0
0
0
1
2
1
0
2
2
1
2
1
2
1
0
0
1
2
1
1
2
2
2
1
0
2
1
0
1
1
1
0
1
0
0
1
2
1
1
1
0
0
0
0
0
0
0
1
2
0
0
1
1
0
2
1
2
1
1
1
2
1
1
0
1
1
1
0
0
0
0
1
0
2
1
1
0
0
1
1
2
1
1
2
1
1
0
0
2
2
2
1
0
0
2
1
1
1
0
0
1
1
1
0
1
1
0
2
1
0
1
1
2
1
1
3
1
1
0
0
1
2
0
1
1
0
1
3
1
1
0
0
1
2
4
1
0
0
2
2
1
0
1
1
1
0
2
2
2
1
0
0
2
1
2
1
1
1
1
2
2
1
0
2
2
0
1
2
2
1
2
1
2
1
1
1
1
0
2
1
0
1
1
0
1
2
2
0
1
2
2
0
0
1
1
0
1
0
1
2
2
4
2
1
0
1
2
1
2
1
0
1
1
0
1
1
2
1
0
1
0
0
0
2
2
0
0
1
1
1
1
2
1
2
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
2
1
0
0
0
1
1
1
1
1
2
1
1
0
2
1
2
1
2
1
1
1
1
1
0
1
0
0
2
1
0
0
0
0
1
1
0
2
1
0
0
1
0
0
1
2
0
1
3
2
0
1
2
1
1
0
0
0
1
3
1
1
0
1
0
0
2
0
2
1
0
0
1
1
0
2
0
1
2
1
1
1
0
0
2
1
1
1
1
0
0
1
1
0
1
1
1
1
1
0
0
1
0
2
1
1
1
1
0
0
0
0
1
0
2
0
1
2
2
1
1
1
2
1
2
2
1
0
1
0
0
1
1
1
0
1
2
1
0
1
1
1
1
1
0
0
1
0
0
2
0
2
1
1
2
2
0
0
0
1
0
0
1
2
0
1
2
2
1
1
1
2
0
1
1
2
1
1
2
0
1
2
1
2
1
0
0
0
1
1
1
1
2
0
2
2
0
1
1
0
1
1
2
0
2
1
1
2
1
2
0
0
1
0
1
0
0
1
2
1
0
0
0
2
0
0
1
1
0
1
1
0
2
0
1
1
1
1
3
2
2
2
1
1
2
0
1
1
1
1
1
0
2
1
0
2
1
1
2
1
0
2
2
0
1
0
2
2
0
2
1
2
0
0
1
1
0
0
1
1
1
2
2
1
1
0
1
0
2
1
1
2
1
1
1
0
0
0
1
0
1
1
0
2
0
1
1
1
1
0
1
1
2
2
0
1
1
3
1
1
1
2
0
0
1
2
2
2
1
2
0
0
1
1
0
0
2
0
0
1
1
1
0
1
0
1
1
1
2
1
2
0
1
1
2
1
0
1
4
2
0
0
0
0
0
2
0
2
2
1
1
1
2
0
0
1
1
0
0
0
1
1
0
2
2
1
0
0
0
1
1
1
2
1
1
1
2
0
1
0
2
0
1
0
0
1
1
1
1
1
1
2
1
0
1
1
1
1
1
0
2
0
1
1
0
1
2
2
1
0
1
1
0
1
0
0
1
1
0
1
0
1
1
0
0
1
1
1
0
1
0
0
0
0
0
1
2
1
1
1
2
1
0
1
1
1
0
0
2
1
2
0
1
1
0
0
0
0
2
1
1
1
1
1
1
2
1
0
1
0
2
0
2
0
2
1
1
1
1
0
1
1
1
1
1
1
0
0
2
0
1
1
0
1
2
1
0
2
2
2
0
0
2
1
0
2
0
1
1
1
0
2
0
3
0
0
0
1
0
1
2
0
0
1
1
1
1
1
1
1
1
0
0
1
1
0
2
1
1
1
0
0
1
0
2
0
0
2
0
1
2
1
1
2
1
2
0
0
1
1
0
2
1
1
0
0
0
0
0
1
0
1
1
2
1
0
0
1
1
1
2
0
2
1
0
0
1
1
1
2
0
2
2
1
1
1
1
1
1
2
2
1
1
0
2
3
0
0
0
1
0
0
2
0
1
2
2
1
2
1
2
0
0
0
2
3
1
2
1
2
1
0
0
1
1
0
0
1
0
1
2
0
0
2
1
1
1
1
2
1
0
2
0
1
0
1
2
1
0
1
2
1
1
1
1
1
1
1
1
2
2
1
1
0
2
1
2
0
1
1
0
2
1
1
2
1
1
0
2
2
1
1
0
1
1
2
1
1
0
1
0
0
2
1
0
1
0
0
2
1
2
0
2
0
0
0
0
1
0
0
2
1
1
0
0
2
0
2
2
2
2
0
1
1
1
0
1
0
1
1
2
4
1
0
1
1
0
1
1
1
0
2
1
1
1
1
1
2
0
2
1
1
2
3
1
2
0
1
1
2
0
1
2
2
0
1
0
2
2
1
0
0
1
0
1
1
1
0
1
1
1
1
0
1
1
1
1
1
1
1
1
2
2
0
1
0
0
1
1
0
0
0
2
0
1
1
2
1
1
1
0
2
2
1
1
0
0
0
1
1
2
2
0
0
1
1
1
0
1
0
0
1
1
1
1
0
2
2
2
0
0
1
3
1
1
1
2
2
1
1
1
0
1
1
2
1
1
1
0
0
2
1
1
3
1
1
0
1
2
2
2
1
1
3
1
0
1
1
1
0
0
0
0
1
1
0
1
2
2
1
2
1
2
1
1
0
1
0
0
1
1
1
1
1
1
2
0
1
1
1
1
0
2
1
1
0
2
2
1
1
1
2
1
2
1
2
1
1
2
1
2
1
0
1
2
0
0
0
1
1
0
0
2
1
1
2
1
0
2
2
2
1
1
0
0
2
1
1
2
1
2
0
2
0
1
1
3
1
2
0
0
0
1
2
0
0
2
2
1
3
2
1
0
1
1
0
0
2
2
0
1
1
0
2
0
1
1
0
0
0
0
1
0
1
2
2
1
1
1
0
1
2
0
2
2
1
2
1
1
1
1
1
1
2
1
1
1
1
0
2
2
1
1
1
0
2
0
2
2
2
0
0
1
2
1
1
2
1
0
1
2
2
2
1
0
0
0
1
2
4
1
0
0
0
1
1
1
1
2
1
1
1
1
0
2
1
0
1
1
0
0
1
0
2
1
0
1
1
0
1
1
0
1
0
1
0
1
1
1
1
2
2
1
0
1
2
0
2
0
1
0
1
3
1
1
1
0
2
0
0
2
1
2
1
1
0
1
1
0
1
1
2
1
1
2
0
1
1
1
1
1
2
2
2
1
1
1
1
0
0
1
1
0
2
1
0
0
0
1
1
1
0
1
2
0
2
1
1
2
0
1
1
0
2
1
2
3
0
0
2
2
2
2
0
1
1
0
1
2
0
0
1
0
1
1
2
2
1
1
1
0
0
1
2
1
2
1
0
1
1
1
0
1
2
1
0
2
1
1
2
1
1
0
0
2
1
1
1
0
1
1
2
1
1
1
1
1
1
1
0
1
1
1
1
0
1
3
1
1
0
2
2
0
1
2
1
2
1
2
1
1
1
0
1
2
2
0
2
1
1
1
0
0
1
1
1
2
2
1
1
0
0
1
0
0
0
0
0
2
2
1
0
2
0
1
2
1
0
1
1
1
0
1
1
0
1
0
1
1
1
0
1
2
1
1
1
1
1
1
2
0
2
0
1
0
1
0
0
1
0
0
0
0
1
1
1
0
0
1
1
1
0
1
1
0
1
2
1
2
1
1
0
1
2
0
1
1
1
1
1
1
2
0
0
1
1
0
1
1
0
1
1
2
1
2
1
2
1
0
1
1
1
1
2
0
3
2
1
1
0
1
0
2
0
1
0
1
2
1
3
1
1
1
0
0
1
2
2
2
1
1
1
0
2
1
1
0
2
1
0
1
1
1
2
0
1
1
0
2
0
2
1
2
2
1
0
1
0
0
0
1
2
1
0
0
0
2
1
1
0
1
0
1
0
4
0
0
1
1
4
1
0
1
1
2
0
0
1
1
2
1
0
1
1
1
0
2
2
0
1
1
0
0
1
1
1
2
0
2
1
1
2
1
0
0
1
2
1
0
1
1
2
2
0
0
1
2
2
2
1
1
0
0
0
1
0
4
2
0
1
2
1
2
1
2
1
1
1
1
0
1
1
0
1
2
2
9
2
2
1
1
2
0
1
0
1
0
0
1
0
1
1
1
1
1
1
0
0
0
0
0
1
0
0
1
1
1
3
0
1
0
2
2
2
2
1
2
1
2
1
2
2
1
1
0
2
0
0
0
2
1
1
1
3
2
0
1
0
1
1
1
1
1
0
0
0
2
0
0
0
1
2
1
1
0
0
0
0
0
2
1
2
1
1
2
2
0
1
1
1
1
1
1
0
1
0
1
2
0
2
0
1
1
0
0
0
1
1
0
1
1
1
0
1
1
0
2
1
2
2
1
1
2
0
1
1
3
1
1
1
2
1
1
1
1
1
0
1
2
1
2
1
1
1
0
1
1
0
1
0
2
1
0
1
1
1
2
1
0
0
0
2
1
0
0
1
0
1
2
1
1
0
1
1
0
1
1
0
1
1
2
1
0
2
1
1
0
1
1
2
1
2
1
0
0
1
0
1
0
0
1
2
2
0
1
1
1
0
0
0
1
0
1
1
1
0
1
2
2
1
1
0
0
0
0
0
0
0
2
1
1
1
1
1
2
1
0
1
1
0
0
2
1
0
0
1
1
2
0
0
1
1
0
2
1
1
2
0
1
1
0
1
1
1
0
0
1
0
0
1
1
1
1
1
1
2
1
0
1
1
0
0
1
0
0
1
1
2
1
0
2
1
1
1
0
0
1
2
1
0
1
0
1
2
1
0
1
1
1
1
0
0
0
0
1
1
1
0
1
1
0
1
0
1
0
1
1
1
1
1
1
0
1
1
2
2
1
0
0
1
0
0
1
1
1
2
0
1
0
0
1
0
1
1
2
1
1
0
1
2
1
2
1
1
0
1
3
1
0
1
1
1
2
1
2
1
2
1
1
0
1
1
1
1
0
0
0
0
1
2
1
0
1
1
1
0
2
0
0
0
0
1
1
1
1
1
1
2
0
2
1
0
1
2
1
0
0
2
0
2
1
1
2
0
0
2
0
1
2
0
2
2
2
0
2
1
1
1
2
0
1
1
1
2
2
2
2
1
2
1
2
1
1
3
2
1
1
3
1
1
1
5
2
0
0
0
1
0
1
0
1
2
2
1
1
2
1
1
2
1
2
0
0
0
1
1
1
1
0
1
1
1
1
0
1
0
2
2
0
1
2
1
1
0
1
0
1
1
4
2
0
0
2
0
0
0
1
0
0
1
2
0
1
1
3
0
1
0
1
2
1
1
0
2
1
1
1
1
0
1
1
1
0
1
1
1
1
2
2
1
2
1
1
1
0
1
0
1
0
1
1
2
2
1
1
0
1
1
2
0
1
0
1
0
1
1
2
1
2
0
0
1
0
0
1
0
1
0
1
1
7
1
1
0
0
1
1
2
1
1
0
2
2
2
1
0
0
2
1
1
1
2
0
2
1
0
2
1
1
0
1
0
1
1
1
0
1
1
1
2
1
2
1
2
1
1
2
2
1
1
2
1
1
2
0
0
1
1
1
1
2
1
2
1
0
0
2
1
1
2
1
1
1
0
1
1
2
1
2
1
2
1
0
1
1
1
1
0
1
2
0
2
0
1
2
1
2
0
0
1
1
1
0
1
0
1
1
1
3
0
1
1
2
1
0
2
1
1
2
0
2
0
1
1
1
1
0
2
1
1
1
0
0
0
0
1
1
1
2
1
0
0
2
1
0
0
1
1
2
1
1
2
1
1
1
1
0
0
2
1
0
0
0
1
1
0
1
1
0
1
0
1
1
0
1
2
1
1
1
2
1
2
2
0
10
1
2
1
1
1
3
1
1
1
2
0
1
3
1
1
1
0
2
2
2
1
2
1
1
2
1
2
2
2
0
1
0
2
1
0
1
0
0
0
1
0
1
2
0
1
1
2
0
0
0
0
1
0
0
2
1
1
1
1
3
1
0
0
2
1
0
1
1
2
0
2
1
2
0
0
1
1
1
0
2
2
1
0
1
2
1
0
0
1
1
2
2
1
0
1
1
2
1
1
0
1
2
2
3
1
1
4
1
2
0
2
1
0
2
0
1
1
1
0
0
0
0
1
0
1
1
0
0
1
0
1
0
1
1
2
0
1
2
0
1
1
1
3
0
1
2
1
1
1
0
0
0
2
2
0
2
0
1
2
1
3
0
1
2
0
0
2
0
0
0
1
1
0
1
1
2
1
1
1
0
2
1
0
2
2
0
2
2
1
2
0
1
1
2
1
0
2
2
0
2
0
0
2
2
1
0
1
2
1
1
1
2
1
1
0
1
1
1
2
1
3
2
2
1
1
1
1
1
0
1
0
2
1
2
0
2
0
0
0
1
2
0
1
2
1
0
2
1
0
5
2
0
1
1
1
1
0
1
0
1
2
0
1
1
1
0
1
0
0
0
1
1
2
1
0
1
1
1
3
0
0
1
0
2
0
1
2
0
1
1
2
2
1
1
1
0
1
0
1
0
1
2
1
0
1
1
1
1
1
1
0
2
0
1
1
2
2
0
0
0
2
0
0
0
2
1
1
0
1
1
0
0
0
2
2
1
1
0
1
1
0
3
2
0
1
1
1
1
1
1
0
2
1
0
2
1
2
1
0
2
0
0
2
1
0
2
1
0
2
2
0
1
1
2
0
1
0
1
1
1
1
0
2
2
0
1
0
1
2
1
0
0
0
0
1
0
0
2
0
1
1
1
0
0
0
1
1
0
1
1
2
2
0
1
1
1
1
2
1
2
0
1
0
1
2
1
1
1
1
0
1
1
2
0
1
1
2
1
0
1
0
0
1
1
0
0
1
0
1
1
1
0
0
1
0
0
1
2
0
0
1
1
0
2
1
2
1
1
1
0
1
1
0
0
1
1
0
0
0
1
0
0
0
0
2
2
1
0
2
2
1
1
2
0
0
1
0
2
0
0
2
0
0
1
1
1
2
1
1
0
1
1
2
0
1
1
2
1
0
2
1
2
1
0
0
2
1
2
1
2
1
1
2
2
0
8
1
1
0
1
2
1
1
0
0
0
1
0
1
0
1
2
1
2
1
1
1
0
1
1
1
0
1
0
1
0
1
1
1
2
2
0
2
1
1
1
1
0
1
0
0
1
2
1
1
1
1
1
1
2
0
0
1
2
1
0
1
1
1
2
2
1
0
1
2
1
0
0
1
2
1
0
0
1
0
0
2
2
2
0
1
1
1
0
0
2
0
2
1
1
4
1
0
0
2
0
0
1
1
2
1
1
2
1
1
0
0
1
0
2
2
2
4
2
0
2
1
2
1
2
2
1
0
2
1
1
2
2
0
0
1
1
1
1
0
1
0
2
1
1
1
1
1
2
2
3
2
0
1
2
1
0
1
1
1
1
0
1
2
1
0
2
0
1
1
0
1
1
1
1
1
1
1
1
0
2
1
1
1
1
0
0
1
1
0
1
2
1
1
0
1
2
2
0
2
1
1
2
1
1
1
1
1
0
1
0
2
0
1
0
2
0
0
0
1
1
1
0
2
0
1
1
2
1
1
0
1
1
2
1
0
2
1
1
2
1
1
0
1
2
2
0
1
0
2
1
1
2
1
0
0
1
2
2
2
1
1
0
1
3
1
1
1
0
1
1
1
2
1
0
2
1
1
0
0
1
1
2
0
1
2
2
0
0
0
1
1
1
2
1
1
2
1
2
1
0
1
0
0
0
2
1
1
1
2
1
2
1
0
0
1
0
1
1
1
1
1
0
1
1
1
0
0
0
1
1
0
0
2
2
1
1
1
0
0
1
0
1
1
1
3
1
1
0
0
1
2
1
1
2
2
1
1
2
0
1
2
1
1
0
2
2
1
0
0
0
0
0
1
2
2
2
1
0
1
0
0
1
1
1
0
0
0
0
2
1
2
0
1
1
2
1
0
1
1
1
0
0
1
1
1
2
0
1
2
1
1
1
1
1
1
1
2
0
0
2
0
1
0
1
1
0
2
1
0
4
2
1
1
1
2
2
1
1
1
2
2
1
0
0
1
1
0
1
1
0
2
1
0
1
1
1
1
1
0
1
0
1
1
1
1
1
1
0
1
1
2
2
0
1
1
2
1
1
0
1
2
1
1
0
0
1
2
1
2
2
1
1
2
1
2
1
1
2
1
1
1
2
2
1
1
0
1
1
2
1
1
1
0
2
0
1
2
0
1
0
1
3
1
0
2
0
1
2
2
0
0
1
3
0
0
2
1
1
1
0
2
0
1
1
2
0
0
4
0
1
1
1
1
1
0
1
2
0
2
0
1
0
0
2
1
1
2
2
0
1
2
0
1
1
1
0
2
1
1
1
0
2
0
0
0
1
1
0
3
1
2
1
1
1
1
0
1
1
0
1
2
3
1
1
1
2
0
1
0
1
0
0
2
1
0
1
1
1
2
2
0
0
1
1
2
1
2
0
1
0
0
1
0
3
1
1
1
0
0
1
0
1
1
2
1
1
2
1
1
2
1
1
1
1
1
2
1
2
0
1
2
1
1
2
0
1
2
2
2
1
0
1
0
1
1
1
1
0
1
2
1
2
2
2
1
0
1
1
2
2
1
0
1
0
0
1
1
1
2
1
1
2
2
1
1
2
1
0
0
1
1
0
2
1
0
2
1
2
0
0
2
2
2
2
0
1
1
1
1
1
1
1
0
1
1
1
0
1
1
1
2
1
2
0
1
1
2
1
0
0
1
1
1
0
1
2
1
2
1
1
2
4
1
0
3
1
1
1
2
1
1
1
1
0
1
1
2
1
0
0
1
0
1
1
2
3
2
1
2
0
0
2
2
1
2
1
1
1
2
0
0
1
2
1
1
1
1
1
0
0
2
1
1
0
1
1
1
1
0
1
0
1
2
1
0
1
0
1
1
0
2
1
1
1
1
0
1
2
0
1
1
0
1
0
1
1
1
1
0
1
1
2
2
1
2
2
2
1
1
1
1
0
2
1
0
3
1
1
2
0
1
0
0
0
0
2
0
2
1
0
2
1
1
0
0
1
0
1
2
1
0
0
1
1
2
1
1
0
1
1
1
1
1
1
1
2
0
1
1
1
1
5
2
1
1
0
1
1
2
2
0
0
1
0
2
4
2
0
1
2
0
2
1
1
0
2
1
0
1
2
1
2
1
1
1
1
2
2
1
2
1
0
2
1
1
1
1
1
1
2
1
2
0
2
1
2
0
1
1
0
2
1
0
1
0
1
0
0
0
0
0
2
1
0
1
2
2
1
1
1
1
0
1
1
0
1
1
0
1
1
0
0
0
1
1
0
1
1
2
0
2
0
1
0
3
0
1
2
0
1
2
1
1
0
1
0
0
0
2
2
2
0
1
0
1
0
2
0
1
1
2
1
1
1
1
2
1
1
0
1
2
2
1
1
1
1
1
0
1
1
2
1
1
0
0
2
2
2
0
1
2
0
1
2
0
1
1
0
2
0
2
2
1
1
1
2
1
1
0
1
0
2
1
1
2
2
1
2
2
0
0
2
2
2
2
1
2
1
2
0
0
2
0
1
0
1
0
1
2
0
0
0
0
0
1
2
1
1
1
1
0
1
1
1
2
1
2
1
1
0
2
0
1
1
0
1
1
0
2
1
0
1
2
2
1
3
2
0
0
1
3
2
0
1
0
0
1
2
1
0
0
2
2
2
1
1
0
1
1
2
2
2
2
1
1
1
1
1
2
0
1
2
1
1
0
1
0
1
1
2
0
1
2
1
2
1
0
2
2
2
2
2
0
1
2
0
0
1
0
0
2
1
2
0
2
2
1
0
1
1
1
0
1
1
0
1
1
1
1
1
1
2
1
0
0
0
1
1
0
0
1
0
5
1
3
1
0
2
2
0
0
0
0
1
1
1
0
0
1
0
1
2
12
1
0
1
2
0
1
0
2
0
1
1
0
1
2
0
2
1
1
1
2
1
0
0
1
0
1
0
1
1
1
1
1
1
2
0
0
2
0
1
1
1
1
1
0
2
2
0
1
1
0
0
1
1
1
1
0
0
1
2
1
1
2
1
1
2
1
1
1
1
2
3
1
0
0
0
1
1
1
0
1
1
2
1
1
1
1
1
1
1
2
2
1
2
1
1
2
1
2
2
2
0
0
1
1
2
0
4
2
1
1
0
2
1
2
0
2
1
1
0
1
0
1
1
1
1
0
1
0
1
1
1
1
1
1
1
1
2
1
1
1
1
1
0
0
2
0
1
1
0
1
1
2
1
2
2
1
0
1
1
0
1
1
1
0
1
2
1
1
0
0
1
0
1
2
1
0
1
2
1
1
1
1
1
2
1
0
1
1
2
1
1
2
1
1
1
0
0
0
2
1
0
2
1
1
2
1
2
1
0
2
1
0
1
2
0
1
0
0
0
0
1
1
3
2
1
1
0
0
0
0
1
2
1
0
2
1
1
2
1
1
2
1
1
1
0
1
2
2
4
1
1
1
0
1
2
1
0
2
0
1
2
1
1
1
0
1
2
2
0
1
0
2
1
1
1
1
1
1
1
2
1
1
2
0
0
0
0
1
0
1
1
1
1
1
0
1
1
1
1
0
0
0
2
1
1
1
2
1
1
1
0
0
1
2
1
1
0
1
1
1
1
0
2
1
1
0
0
1
2
1
1
2
0
2
2
0
2
0
0
1
2
1
1
0
0
2
1
1
2
1
1
2
0
0
0
1
1
2
1
1
1
2
1
2
1
1
0
0
1
1
1
2
2
2
0
1
0
0
0
1
1
0
1
1
2
0
1
0
2
1
1
1
1
2
0
0
0
1
0
2
0
2
1
0
2
0
1
0
1
2
0
0
1
1
0
1
1
1
0
2
1
0
3
0
0
0
1
1
1
2
1
1
1
1
1
1
1
2
1
1
2
2
1
0
0
1
1
1
1
2
1
2
2
1
1
1
1
2
1
0
1
0
2
1
2
0
0
1
0
2
1
1
1
0
0
0
1
2
1
1
0
2
2
1
0
1
1
0
0
0
2
2
2
1
1
0
1
0
2
1
0
0
1
2
1
0
2
0
2
1
1
0
1
0
1
2
1
2
2
1
0
1
2
2
0
2
1
0
1
2
0
2
0
1
1
1
2
1
2
2
1
1
1
2
1
2
0
1
1
0
2
2
1
2
1
1
2
0
0
0
1
1
1
1
0
1
2
2
6
2
1
2
2
1
1
0
0
2
1
0
1
0
1
0
0
1
0
1
2
2
1
2
2
1
0
0
1
2
2
2
3
1
0
1
1
2
1
0
2
1
1
2
1
0
1
1
0
1
1
1
0
0
1
1
3
1
2
1
0
0
0
1
0
1
0
1
6
0
1
2
1
1
2
1
1
1
2
1
2
0
1
0
0
1
1
1
0
0
1
0
0
0
0
1
1
0
0
1
2
2
2
1
1
2
2
0
1
1
1
0
1
1
1
1
1
1
1
0
2
1
0
0
1
1
0
1
0
1
0
3
1
0
1
0
1
2
1
0
1
1
2
2
1
1
1
3
1
1
1
2
2
1
2
0
0
0
1
1
1
2
0
0
1
1
1
0
1
0
1
1
1
1
1
1
0
0
1
2
0
1
1
0
1
1
1
1
1
2
1
1
1
1
2
2
1
1
0
2
1
1
1
0
2
0
1
2
4
1
1
2
1
0
0
1
2
1
1
0
1
0
1
0
1
2
1
2
0
1
1
0
1
2
1
0
0
2
2
2
0
1
0
2
1
0
0
1
1
1
1
1
0
0
2
2
0
1
1
1
0
1
2
1
1
0
1
0
2
1
0
1
1
2
0
2
0
2
1
1
2
0
1
0
1
0
0
1
1
2
0
0
1
1
2
1
2
2
2
1
0
0
1
1
0
1
0
0
0
1
0
1
1
0
2
0
1
2
2
1
0
1
1
1
1
0
1
2
2
1
2
1
1
0
2
1
0
0
0
1
1
2
0
2
2
1
1
1
0
1
2
0
0
1
1
1
2
2
1
1
0
1
2
1
2
2
0
0
2
1
0
2
0
1
1
0
1
1
1
0
2
1
2
1
1
1
1
2
1
1
0
0
0
2
1
1
1
1
2
1
2
1
1
1
1
1
0
1
0
1
0
1
0
0
1
0
1
2
0
0
2
2
2
0
0
0
1
2
1
1
0
0
1
1
0
1
2
1
0
1
1
2
1
1
0
0
0
1
1
0
0
1
2
2
1
0
0
2
0
2
0
2
1
2
0
1
1
1
0
0
0
1
2
1
0
1
1
2
1
2
1
0
0
0
2
1
3
2
0
1
2
1
2
0
0
1
0
0
1
1
1
0
1
0
0
2
1
1
1
2
1
1
1
2
1
0
0
1
1
1
0
1
1
1
0
1
2
1
1
2
1
0
0
0
2
2
1
1
1
1
2
2
1
2
2
3
1
0
2
1
1
0
1
1
0
0
1
2
1
1
2
0
1
2
0
0
2
0
0
0
2
1
1
0
1
1
0
1
0
0
1
3
1
2
1
0
0
1
1
2
1
2
0
1
1
1
0
1
1
1
2
1
0
1
1
0
0
3
2
0
0
1
1
2
1
0
0
2
1
0
1
0
1
1
1
1
1
0
1
1
2
1
1
0
1
1
1
1
0
1
0
1
0
2
1
0
1
2
1
1
2
1
1
2
1
2
0
2
2
2
2
1
6
1
1
1
0
1
1
0
1
1
1
1
2
1
1
1
1
2
0
1
2
0
1
0
0
1
1
1
1
2
1
1
2
2
1
2
2
2
0
0
1
0
1
1
1
1
0
0
1
1
0
2
1
2
1
1
0
1
1
1
1
1
1
1
1
1
1
0
1
1
1
2
1
1
0
2
0
1
2
0
0
2
2
1
0
2
0
0
2
1
1
0
1
0
0
2
0
1
1
1
1
0
0
1
1
1
2
1
1
1
1
2
1
0
1
2
1
0
0
0
0
1
1
0
0
2
0
1
1
0
1
1
2
1
1
1
2
2
0
1
0
0
0
1
1
1
2
2
1
0
0
2
1
1
1
1
0
1
1
1
0
0
1
2
0
1
1
1
1
2
0
1
1
2
1
2
0
1
0
0
3
1
1
0
0
1
1
2
0
0
2
2
1
0
1
1
2
2
1
1
0
1
1
2
1
0
1
0
1
1
2
1
0
4
1
0
1
1
0
1
2
0
1
1
1
2
2
0
1
2
1
1
1
0
0
2
0
0
0
1
0
1
1
1
0
1
1
2
2
1
0
2
1
1
2
2
2
4
0
1
2
1
1
2
1
1
1
2
0
0
0
1
2
1
0
1
0
2
1
1
0
1
1
0
2
1
2
1
1
1
1
1
2
0
1
2
0
0
1
1
1
1
2
2
0
0
2
1
0
2
1
0
1
1
1
1
0
0
3
1
2
0
1
0
1
1
2
0
1
1
1
3
1
1
2
1
1
2
1
0
2
2
1
1
1
2
1
1
1
0
0
0
0
0
1
1
1
0
0
1
2
0
1
0
2
1
1
2
1
0
2
2
2
0
1
1
1
2
0
1
2
0
0
1
1
1
1
2
1
1
1
0
1
1
2
0
1
1
1
2
0
2
1
2
0
0
2
0
1
2
0
2
1
1
1
1
2
1
1
1
1
2
1
0
1
1
0
0
1
1
0
1
0
0
1
1
1
0
0
0
1
0
1
2
1
1
1
2
1
1
1
2
0
1
0
1
1
1
2
2
0
1
0
2
0
1
1
0
1
1
2
1
2
1
0
1
1
1
1
1
0
3
1
0
0
1
1
1
1
1
1
2
2
0
0
1
2
1
0
0
0
0
1
0
1
2
1
1
1
0
2
2
1
1
2
0
2
1
0
2
0
1
1
2
0
1
2
1
1
1
1
1
0
1
2
1
0
2
1
0
1
0
1
2
2
1
1
2
0
1
1
1
0
2
1
2
0
0
0
1
0
1
2
2
1
1
2
1
1
0
1
1
0
0
1
0
1
1
0
1
1
0
2
0
1
3
0
0
0
1
1
0
1
0
1
3
0
0
1
1
0
0
2
1
0
1
1
0
0
1
1
2
1
0
2
0
0
2
2
2
1
0
1
1
0
2
1
1
1
1
1
1
1
0
1
0
2
1
0
0
0
1
1
2
1
0
2
2
1
1
2
2
2
1
0
2
1
0
1
1
0
0
2
1
1
2
0
1
1
0
0
0
0
8
0
0
1
0
2
0
0
1
0
0
1
1
1
1
2
1
1
1
1
1
1
1
0
2
1
1
0
1
2
1
0
2
1
2
1
1
1
2
0
1
1
1
2
1
1
1
2
1
1
1
2
0
1
1
1
1
0
1
1
2
2
0
2
1
0
0
1
0
0
1
2
1
1
1
0
0
1
1
1
1
2
2
1
1
1
1
1
1
1
2
0
0
2
1
10
1
2
2
1
1
0
2
1
1
0
2
0
0
0
1
1
2
2
1
1
1
2
0
2
2
0
2
0
2
1
1
1
1
2
2
2
2
1
0
1
1
2
1
2
1
0
1
0
0
0
1
1
1
0
0
1
0
0
2
0
1
1
0
1
1
0
1
1
1
2
1
0
1
2
1
1
0
1
1
0
2
0
1
1
1
0
1
1
0
3
0
2
0
0
1
1
2
0
1
0
1
0
0
1
3
0
0
1
1
2
1
0
1
2
1
2
0
1
0
0
0
1
2
1
1
2
1
1
0
0
5
2
0
2
1
1
1
1
1
1
2
1
2
2
1
1
0
1
1
1
2
1
1
1
0
0
1
2
1
2
1
1
0
0
0
1
1
1
2
1
1
1
1
1
1
1
1
1
1
2
2
0
2
1
1
1
0
1
2
2
2
2
0
2
1
1
0
2
1
1
1
2
0
0
0
1
3
1
0
0
0
0
0
0
0
1
2
1
0
0
1
1
1
2
1
1
0
1
1
2
0
1
1
1
1
0
1
2
1
1
0
0
2
0
0
0
1
2
1
2
0
1
1
1
0
1
1
2
1
0
1
1
1
2
1
1
1
1
0
4
0
2
0
1
3
0
0
0
1
1
0
1
1
1
1
0
1
2
1
3
1
2
0
2
0
2
2
0
0
1
0
0
1
0
2
1
2
1
0
2
2
2
2
1
0
2
0
1
1
2
0
0
2
2
0
1
0
1
1
1
2
1
2
2
2
1
1
1
1
1
2
0
1
2
0
2
2
2
1
0
1
1
1
1
1
1
0
2
2
1
1
1
0
0
0
1
0
0
2
0
1
2
0
1
1
2
2
0
0
1
1
0
2
1
0
2
1
2
1
1
1
0
2
1
2
0
0
1
2
1
0
0
1
0
0
1
1
1
1
0
1
1
2
1
1
1
0
1
0
1
0
1
2
1
0
1
1
1
0
1
1
1
2
1
1
0
1
1
0
1
1
1
0
1
1
1
1
1
0
0
0
2
1
1
1
2
0
0
2
2
1
0
2
1
1
1
1
2
0
2
1
1
1
1
4
1
1
2
1
1
2
2
0
0
0
1
1
1
1
0
0
1
0
0
0
1
1
1
2
0
2
1
1
0
0
3
1
0
1
1
1
2
0
0
0
0
3
3
0
1
0
0
1
2
1
2
2
1
0
0
1
0
1
1
0
0
2
1
0
1
2
1
0
0
1
1
0
2
2
1
1
0
2
1
1
1
1
0
2
0
1
1
1
0
0
1
2
1
5
2
0
1
2
0
0
0
1
0
0
1
2
2
0
1
0
0
1
1
1
0
0
1
1
0
2
0
2
0
2
1
2
0
0
0
1
3
1
1
1
0
1
0
1
0
0
1
2
1
1
1
0
1
1
1
1
0
2
0
1
2
2
1
1
0
1
1
1
2
1
1
2
1
1
1
1
1
0
2
1
2
1
1
2
10
1
2
1
2
1
2
2
1
1
1
2
1
2
1
1
0
0
1
1
0
1
2
0
2
1
1
0
1
1
1
1
1
1
0
1
1
1
1
0
0
0
1
2
1
2
1
1
1
0
1
0
1
0
2
0
2
0
1
0
1
0
1
1
0
0
1
2
1
0
2
1
2
1
0
1
0
2
0
1
1
1
1
2
1
1
0
1
2
3
1
3
2
1
2
1
1
0
1
1
0
1
2
1
0
1
0
2
0
2
0
2
1
1
2
0
1
0
5
0
1
0
0
1
2
0
1
2
1
0
0
1
1
2
0
0
0
1
1
2
0
1
1
1
1
1
7
1
1
1
0
1
1
1
1
1
0
1
3
1
2
1
0
1
1
2
1
0
1
2
1
2
2
0
1
1
1
1
1
1
1
2
1
1
2
1
2
0
1
0
1
2
1
0
1
0
1
1
0
1
1
1
1
1
1
2
0
1
1
1
2
1
2
3
2
0
1
1
1
1
1
0
0
1
1
1
1
0
1
0
0
0
2
1
2
1
2
0
0
1
1
0
1
0
1
1
2
1
0
0
1
1
0
1
2
1
2
0
1
2
2
2
1
0
2
1
0
1
1
0
1
1
0
2
2
5
0
1
1
0
1
0
1
2
1
1
2
1
0
1
0
2
0
1
2
1
1
1
2
1
2
0
2
1
0
1
1
1
1
2
1
1
2
2
0
2
2
0
1
0
0
2
1
0
1
0
1
0
1
0
0
1
2
0
1
1
1
3
1
1
0
1
1
1
2
1
0
0
1
1
1
0
1
1
1
1
0
1
0
0
1
1
0
0
2
1
2
0
2
1
2
0
1
1
0
0
1
1
1
1
1
1
0
1
0
1
0
2
2
0
1
0
2
1
2
1
1
1
1
1
1
1
1
2
0
2
2
0
1
0
1
1
0
1
1
0
0
1
0
1
1
1
1
1
0
2
2
1
0
1
2
0
2
0
1
2
2
1
2
0
1
0
1
1
1
2
1
1
1
2
0
0
1
1
3
0
1
1
1
2
0
1
1
1
2
1
0
1
0
2
1
1
0
1
2
0
1
0
2
1
1
1
2
1
0
1
1
0
0
0
1
0
0
2
0
1
0
1
1
1
0
0
1
1
1
1
1
1
1
1
0
1
0
0
1
1
0
0
1
2
0
2
1
0
0
1
0
0
0
0
1
0
2
1
0
0
2
2
1
0
1
0
0
0
1
1
1
1
1
0
0
2
1
1
0
2
1
2
0
1
0
2
0
0
1
1
2
1
0
0
1
0
1
1
0
2
1
1
0
0
0
0
1
2
2
1
1
0
2
2
1
1
1
0
1
1
1
0
2
1
0
1
1
2
2
1
1
1
0
1
1
2
0
0
1
3
0
2
0
0
1
0
1
0
0
1
1
0
0
2
0
1
1
1
1
2
2
1
2
2
0
1
1
1
1
1
1
1
1
0
2
1
1
1
1
1
2
0
1
2
2
1
2
1
0
1
1
2
2
1
1
1
1
0
1
2
1
1
1
0
1
1
1
0
1
1
0
0
0
1
0
1
0
2
1
0
2
0
0
1
3
2
1
1
3
1
3
0
0
2
2
1
0
0
1
2
2
0
0
0
1
0
1
0
0
0
2
1
1
1
0
1
1
0
0
0
0
2
1
2
0
1
0
1
0
1
2
1
1
1
0
1
1
0
1
1
0
0
0
2
0
0
0
0
1
1
2
2
1
0
1
1
1
2
2
1
1
0
1
2
1
1
0
1
2
0
1
1
2
2
1
0
1
0
0
2
0
1
1
1
0
1
2
2
0
1
1
0
1
0
1
0
1
2
1
2
5
0
0
1
0
2
2
1
0
2
1
2
2
2
1
1
0
2
0
0
2
1
2
2
0
1
1
0
0
0
0
1
1
2
0
1
1
1
1
2
1
2
0
0
1
0
1
1
0
1
2
2
2
1
2
1
0
0
3
2
1
1
0
0
0
0
2
1
1
0
0
3
2
0
2
0
0
2
0
1
2
2
0
1
2
0
0
0
1
2
5
1
0
1
2
1
2
1
0
1
1
1
1
2
1
2
1
2
0
0
2
1
1
0
1
2
0
1
1
0
1
0
1
1
1
2
0
2
1
1
1
1
0
2
1
2
2
1
0
0
1
1
1
2
1
2
1
1
2
1
1
1
1
1
0
2
0
1
1
1
1
0
2
1
2
0
1
1
1
1
1
2
0
0
2
0
0
0
1
2
0
0
0
1
0
1
1
0
1
0
2
0
1
0
1
1
0
0
1
1
2
0
1
2
1
0
3
1
0
1
1
1
1
1
2
2
0
1
0
2
1
1
2
1
1
1
0
2
1
1
1
0
1
0
0
1
0
1
1
0
2
2
2
1
1
0
2
1
1
1
1
1
1
2
2
0
0
2
2
1
2
0
1
2
1
1
1
2
1
1
1
0
2
0
1
0
1
1
1
0
0
1
1
2
0
0
1
0
1
0
0
1
0
1
2
1
1
1
1
1
0
2
1
1
1
1
1
0
2
1
2
1
1
0
3
3
0
1
1
1
0
1
1
1
2
2
1
2
2
1
0
1
2
0
1
2
2
1
0
1
1
0
2
1
1
0
1
0
1
1
0
2
1
1
0
1
1
1
2
0
2
2
0
1
2
0
2
2
1
0
1
0
1
0
0
0
1
2
2
1
1
1
1
2
1
0
1
2
1
0
0
2
0
1
0
1
0
0
1
2
1
1
1
0
2
0
2
1
1
1
1
2
0
1
0
0
0
1
0
1
1
0
0
4
1
3
2
1
0
1
0
0
1
2
0
1
1
1
2
0
1
0
2
2
0
1
1
1
1
0
1
0
2
2
0
1
0
0
1
1
2
2
0
2
0
1
1
1
2
1
0
1
0
1
1
1
0
1
0
0
2
0
1
1
1
1
0
2
1
1
1
2
2
0
1
1
0
1
1
0
0
0
2
2
2
1
0
0
1
0
0
0
0
1
0
2
1
0
1
1
1
0
1
1
2
1
1
2
1
2
1
0
2
0
1
2
1
2
0
1
1
0
1
2
2
0
2
1
0
1
1
1
0
1
2
2
0
0
1
0
2
0
1
1
0
2
1
1
0
1
0
1
2
0
2
0
1
1
1
1
1
0
2
1
0
0
2
1
1
1
0
1
0
1
3
2
0
2
1
1
0
1
2
1
1
1
2
0
0
1
1
1
1
0
1
1
1
0
1
1
0
1
1
1
1
0
0
1
1
1
1
3
1
2
1
0
0
1
0
1
2
0
1
2
2
1
0
1
1
1
0
1
2
1
0
0
1
1
0
0
0
3
2
0
1
1
2
2
1
2
0
0
0
0
1
2
1
1
1
1
2
1
0
2
1
0
1
2
1
2
1
2
0
0
2
2
1
1
0
2
0
1
0
2
2
0
0
1
0
1
1
1
9
2
0
0
0
1
1
0
2
1
0
2
1
0
2
2
2
0
1
1
1
2
1
1
1
1
2
2
2
1
2
1
1
1
2
1
2
1
2
0
1
1
0
4
0
2
2
1
0
1
0
1
1
1
0
2
0
2
1
0
0
1
0
0
1
1
1
0
1
1
0
1
0
0
2
0
2
2
1
0
0
2
0
0
1
1
1
2
1
0
2
1
0
1
0
2
1
1
1
0
1
0
0
2
1
1
1
1
1
1
0
0
1
2
1
1
1
1
0
0
1
1
1
0
0
0
2
1
0
0
1
0
1
2
1
1
2
2
3
0
0
1
2
0
1
3
1
1
0
0
0
1
1
1
0
0
0
2
0
1
1
1
0
1
1
2
1
1
2
2
1
0
0
1
2
1
0
0
1
1
0
0
1
2
1
0
0
1
1
1
1
1
1
0
1
2
2
1
0
1
0
2
2
1
2
1
1
0
1
0
0
0
0
1
0
2
1
1
2
2
0
0
0
2
0
3
1
2
1
1
1
0
1
0
3
2
1
0
1
0
0
0
0
1
2
1
1
0
1
0
1
1
1
0
1
2
1
0
2
2
2
0
2
1
1
2
1
1
0
1
0
1
0
2
0
1
2
2
0
1
1
1
0
0
0
2
0
1
1
0
1
1
1
0
1
1
1
1
1
2
0
1
1
0
2
1
1
3
0
0
0
2
0
0
2
2
2
2
1
3
2
1
1
5
0
1
0
2
2
2
2
1
0
1
1
1
2
1
1
2
2
1
1
1
1
0
0
3
0
1
2
0
0
1
1
2
0
1
2
1
1
1
1
1
0
0
1
1
0
1
2
2
0
1
0
0
1
2
0
2
2
0
1
1
1
1
1
0
1
2
1
1
1
1
1
2
1
1
0
2
2
2
0
0
0
1
1
0
0
1
0
0
2
0
1
0
0
1
1
1
0
2
2
1
3
1
0
2
1
1
0
0
2
0
0
1
2
0
1
1
1
2
0
2
0
0
2
0
1
1
2
1
2
0
1
0
0
2
0
1
1
0
0
0
2
1
2
1
0
1
1
2
0
0
1
0
0
2
2
1
2
2
1
2
0
2
2
2
1
1
2
1
1
1
1
0
1
2
1
1
2
0
2
1
2
0
1
1
2
2
1
0
0
0
0
2
2
1
1
1
2
0
1
0
2
0
1
0
2
0
0
2
1
1
2
0
4
2
1
1
1
1
2
0
0
0
0
1
1
1
0
1
1
2
0
2
1
1
1
1
0
1
2
2
1
0
1
1
1
0
2
1
1
0
1
1
2
1
1
2
1
1
1
1
1
1
0
1
0
2
2
0
1
1
1
2
1
0
1
0
1
1
1
2
1
1
1
3
0
0
4
1
0
1
1
0
0
0
1
1
0
0
1
0
1
1
1
1
0
1
0
2
1
2
1
2
2
0
1
0
2
1
1
2
1
0
0
0
1
0
1
1
2
1
2
1
1
2
2
2
1
0
1
2
0
1
1
1
2
7
0
2
1
1
1
1
0
1
1
0
1
0
0
2
2
0
0
1
1
0
0
2
2
1
1
2
1
1
0
1
0
1
0
0
0
4
2
1
1
2
1
0
0
1
0
0
1
1
1
2
1
1
2
0
0
1
0
2
0
1
0
0
1
1
0
1
1
2
2
2
0
1
0
0
4
2
0
0
2
0
1
1
1
1
0
2
0
0
1
0
2
1
0
2
2
2
2
1
1
1
0
2
1
1
0
1
1
2
2
0
1
0
1
0
1
3
0
1
1
0
1
0
1
1
1
1
1
1
1
2
0
0
1
0
2
2
0
2
1
1
0
1
1
0
1
0
1
1
2
0
1
0
1
3
0
0
1
2
0
0
0
1
2
1
0
0
1
1
2
1
1
2
2
1
1
1
3
0
1
0
1
1
0
1
1
1
1
2
1
2
0
1
1
0
0
0
0
1
2
1
1
0
1
2
1
1
0
0
1
1
0
2
0
0
1
1
0
0
1
0
1
1
0
1
0
1
2
1
0
2
1
1
1
2
1
1
1
1
0
0
0
1
1
1
3
0
0
1
1
0
0
0
1
1
1
2
1
1
1
1
2
0
1
0
1
1
1
1
1
2
0
1
2
1
2
1
1
1
1
2
2
1
2
1
0
2
0
2
0
2
1
1
1
2
1
1
1
2
1
1
0
1
0
1
0
0
1
1
1
2
1
1
2
2
0
2
1
0
1
0
1
0
1
1
1
0
0
1
1
2
2
0
1
1
2
1
1
2
1
1
2
1
0
1
1
0
1
1
2
1
1
0
2
1
0
0
0
0
2
1
0
1
2
2
0
0
0
1
1
2
0
0
2
0
3
1
1
0
1
0
2
0
1
0
2
1
2
1
1
1
1
1
2
1
3
0
1
0
0
0
1
0
1
1
1
1
0
1
2
1
1
0
1
0
0
2
1
0
0
0
1
2
0
0
0
0
0
1
0
2
2
2
2
1
2
0
1
1
1
0
0
1
0
1
1
1
1
0
0
2
0
1
1
1
1
2
1
0
0
0
0
0
1
2
0
1
1
0
1
0
1
1
3
1
2
2
1
2
0
0
1
2
1
0
2
2
2
3
1
2
0
2
0
1
0
1
2
1
1
1
0
1
0
1
0
0
0
2
1
1
0
2
1
1
1
1
1
2
1
1
1
0
0
2
2
1
0
2
1
0
1
1
0
2
1
0
2
1
1
0
0
2
2
0
1
1
0
1
0
1
1
0
0
2
2
1
1
1
1
1
0
1
0
0
1
2
2
0
0
2
1
1
0
1
1
0
2
1
1
2
0
1
1
1
1
0
1
3
2
1
0
2
0
1
2
1
1
0
0
1
2
1
0
0
2
1
2
0
2
0
2
0
1
0
2
1
1
0
0
1
2
0
0
0
3
0
1
1
0
1
1
0
0
1
0
0
2
0
1
0
1
1
1
0
2
0
0
2
1
0
1
2
2
0
1
1
1
2
0
2
2
2
1
1
2
1
1
1
1
0
2
0
1
0
2
1
1
1
2
0
0
0
0
1
1
2
1
1
1
1
1
1
0
0
0
2
0
0
1
2
0
2
1
0
0
0
3
1
1
1
0
1
0
5
1
0
1
0
0
0
3
1
0
2
2
1
0
1
0
0
2
1
1
1
0
0
0
1
1
1
1
0
0
2
2
0
0
1
1
1
0
1
1
2
1
0
2
1
1
2
2
1
0
0
0
2
2
0
2
0
0
0
1
1
1
0
2
1
0
0
2
2
0
2
0
1
0
1
0
3
0
0
0
2
1
2
1
1
1
1
1
0
1
1
0
1
0
1
0
1
2
0
2
0
1
0
0
1
0
0
1
0
0
0
0
2
2
0
1
0
1
1
0
2
0
0
1
1
2
1
0
2
2
0
2
2
3
1
1
0
1
2
1
1
0
0
2
1
1
1
0
2
1
1
0
1
2
1
3
2
2
1
2
1
1
1
1
1
1
0
1
1
1
0
0
0
1
1
1
0
1
1
0
2
1
3
1
2
1
2
0
2
1
1
1
1
0
1
0
1
1
2
1
1
0
0
0
2
2
0
1
0
0
1
1
1
1
1
1
1
0
1
1
1
1
1
2
1
1
1
0
1
0
2
2
0
1
2
1
1
1
0
1
1
0
2
0
0
0
2
2
0
1
1
1
2
1
1
1
1
1
1
1
0
0
0
1
1
2
2
1
1
0
1
1
1
2
0
1
1
1
1
1
2
1
0
1
0
1
0
0
1
1
2
0
1
0
1
0
1
0
2
1
1
1
1
1
1
2
2
0
0
3
1
1
2
2
1
1
0
0
1
2
1
0
1
0
1
2
2
2
1
1
1
1
0
1
1
2
1
1
2
1
0
1
0
0
1
1
1
2
1
0
1
1
1
1
1
1
2
0
0
1
0
0
1
0
1
1
2
1
1
0
0
0
1
1
1
1
0
1
0
1
3
1
1
2
1
0
0
0
2
1
0
2
1
2
1
1
3
1
1
1
0
0
0
0
1
0
1
1
2
1
1
1
1
0
1
1
0
1
1
0
1
2
1
0
0
1
1
0
0
1
1
0
1
1
2
1
1
0
2
0
0
2
1
0
1
1
3
2
0
1
0
1
1
1
1
1
3
1
1
1
2
1
0
1
1
0
0
1
1
1
2
1
0
1
0
2
1
0
0
1
0
1
3
1
1
0
1
0
0
1
1
1
2
2
2
0
1
1
0
2
1
2
0
1
2
1
0
2
0
1
1
0
1
1
0
2
0
0
1
0
0
1
1
2
1
0
0
1
0
1
0
1
1
0
0
1
1
0
0
2
2
2
1
1
0
1
1
0
0
1
0
1
0
1
0
1
0
1
0
0
1
0
1
0
1
1
0
2
1
2
2
1
0
1
1
1
2
2
0
2
1
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
1
0
1
1
1
2
2
1
1
2
0
0
2
0
2
2
1
1
1
0
1
2
0
1
1
1
2
0
2
0
1
1
1
0
0
2
0
2
1
2
1
4
2
0
0
0
0
2
1
2
1
1
1
1
1
2
1
0
0
2
1
1
0
1
1
1
2
1
0
3
1
1
2
1
1
1
1
0
0
1
1
1
2
0
0
0
2
1
3
1
1
1
1
2
0
1
2
2
0
2
1
1
2
1
1
2
1
1
0
0
0
1
2
1
1
1
2
0
1
0
0
1
0
0
0
0
2
1
0
0
1
1
0
2
1
1
1
0
0
2
1
1
2
1
2
1
0
1
1
1
0
1
0
0
1
1
2
2
0
1
2
0
1
1
1
1
1
0
1
0
2
0
0
0
1
1
1
1
0
3
1
0
1
0
0
1
1
0
2
0
1
1
1
1
0
0
1
0
1
1
2
0
1
0
2
0
1
1
1
0
0
1
0
2
0
0
1
0
1
1
1
0
0
0
0
2
2
0
1
0
0
1
1
1
2
1
2
0
2
2
0
0
2
1
0
2
2
0
1
0
0
1
2
1
1
2
2
1
2
2
0
2
0
2
1
2
0
1
1
0
0
1
2
2
1
1
2
2
1
0
1
1
1
0
1
1
0
0
2
0
0
2
1
1
2
1
0
2
2
1
1
2
1
1
0
1
1
1
1
1
1
0
3
1
1
2
1
0
1
0
2
1
1
2
2
0
2
1
0
1
1
2
1
0
2
1
0
1
1
2
0
1
1
1
0
0
1
0
0
2
1
1
2
1
0
1
2
1
1
2
0
0
2
0
1
1
0
0
1
2
1
1
3
0
0
0
0
1
2
0
1
2
1
2
0
0
1
2
1
0
1
2
1
1
0
0
2
1
1
0
1
2
0
0
1
1
1
1
2
0
1
1
0
2
2
1
1
0
1
1
1
0
2
1
1
0
1
1
1
1
2
0
1
1
1
2
0
0
0
2
0
0
1
1
1
1
1
2
2
2
1
0
1
1
1
2
2
1
2
1
3
0
1
1
0
0
1
1
0
2
0
1
1
1
2
1
1
1
2
1
1
1
1
1
0
0
0
1
0
1
2
1
1
2
2
0
0
1
0
1
0
2
2
1
1
1
0
0
1
2
1
2
2
1
1
1
2
1
1
2
0
1
0
2
1
1
2
2
1
0
1
1
1
1
2
0
1
2
0
1
1
0
1
1
6
1
1
2
2
1
2
1
1
2
0
2
0
0
0
1
2
1
2
0
1
0
0
1
1
1
1
1
1
0
2
0
0
2
1
1
1
1
0
2
1
2
0
1
2
1
1
1
1
1
2
1
0
0
0
0
2
0
1
1
1
1
0
1
2
0
0
2
2
2
1
0
1
1
1
1
0
0
1
1
2
0
1
1
1
1
1
0
1
0
2
6
3
0
2
0
1
0
2
2
2
1
1
2
0
2
2
0
2
1
2
2
1
2
0
1
0
2
0
0
1
0
1
1
1
1
1
1
0
2
0
2
2
2
1
2
0
2
0
1
0
1
1
0
2
0
1
1
0
1
0
2
2
1
0
1
2
1
2
1
1
0
1
2
1
0
0
0
0
1
1
0
1
1
0
1
2
0
1
1
0
0
0
0
1
1
0
0
1
1
1
0
3
1
0
2
1
0
1
1
1
1
0
0
2
1
1
1
2
0
1
1
1
1
0
2
0
1
2
0
1
1
1
1
2
0
1
0
1
1
1
1
1
1
1
1
1
0
1
0
0
2
1
1
1
1
0
1
0
2
2
0
2
0
1
2
1
0
1
1
2
0
1
1
0
0
2
0
1
1
1
1
3
1
1
0
2
1
0
1
0
1
2
2
1
1
1
0
1
0
0
1
1
1
3
1
0
0
1
0
0
1
2
2
0
1
0
1
0
2
2
1
0
1
2
1
1
1
0
1
1
1
1
1
0
0
2
1
2
0
3
1
0
1
0
1
1
2
1
1
0
1
1
1
1
1
1
0
0
2
1
1
1
0
2
1
2
0
0
1
0
1
0
1
1
0
1
1
4
1
2
0
2
0
1
1
0
1
1
2
1
0
1
1
0
1
1
1
1
0
1
0
2
2
1
1
0
2
2
1
1
2
1
0
0
1
0
0
1
0
1
1
1
1
0
1
4
0
1
0
0
1
1
2
0
1
1
2
0
0
0
1
2
1
1
0
1
1
1
3
1
1
1
2
1
1
1
1
0
1
1
1
1
2
1
0
2
1
1
1
2
2
0
0
0
2
0
1
1
0
0
2
0
1
1
2
3
1
1
0
2
3
2
2
1
1
2
0
1
0
0
1
0
2
2
0
0
1
2
2
0
0
0
0
0
2
1
2
1
0
1
0
1
2
2
0
1
1
2
0
0
1
1
1
1
0
1
2
1
2
0
0
1
2
2
1
1
3
1
1
2
1
1
1
0
1
1
0
2
1
0
1
0
1
1
0
1
0
3
0
0
1
1
1
1
1
0
1
0
2
1
1
1
1
1
0
1
2
0
0
1
1
2
0
1
1
1
2
1
0
1
0
1
0
1
1
1
0
1
1
1
1
1
2
0
1
0
1
2
1
1
1
0
0
0
1
1
1
2
1
2
2
0
0
0
1
1
1
2
1
2
0
1
0
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
0
1
1
1
1
2
2
1
2
1
1
0
2
0
2
1
1
1
0
1
1
1
2
0
0
0
1
1
0
1
0
1
2
1
1
0
1
0
1
2
0
0
2
2
1
1
0
2
0
2
2
0
1
1
2
0
1
2
0
1
0
1
0
1
2
0
1
0
1
1
1
0
0
2
2
1
1
1
1
2
0
0
0
0
0
1
2
1
1
1
2
2
0
0
1
2
0
1
2
1
2
1
1
0
1
2
1
1
1
1
2
0
0
1
2
1
1
1
2
1
2
1
1
2
0
0
1
1
0
0
2
2
1
1
2
1
2
1
1
1
1
0
0
0
1
1
1
1
2
0
2
1
1
1
1
0
0
0
0
1
0
2
1
1
0
0
0
0
1
1
1
3
0
1
2
2
2
1
0
2
2
1
1
1
0
3
1
0
1
2
2
0
1
1
1
1
2
1
1
0
0
1
1
0
2
2
1
1
0
1
1
1
1
1
3
0
2
0
2
0
0
7
1
2
0
0
1
1
0
1
1
1
0
1
1
1
1
1
1
0
2
1
1
2
1
2
1
2
2
2
1
2
2
0
1
2
1
1
1
2
0
1
0
0
0
0
0
0
2
1
2
0
2
3
3
1
1
2
2
2
1
2
1
1
0
1
1
0
1
1
2
1
0
1
2
1
0
2
0
1
2
0
1
1
0
2
1
1
1
0
2
0
0
1
1
2
1
1
1
1
0
0
0
0
0
1
1
0
1
0
2
4
1
1
1
1
1
1
1
1
1
1
0
0
1
0
0
0
1
1
0
2
2
0
1
1
1
0
1
2
1
2
1
1
2
0
2
1
2
2
0
0
2
2
0
1
0
2
0
3
1
1
1
0
1
0
1
1
0
2
0
1
2
0
0
1
1
0
0
0
1
0
3
1
3
1
2
1
0
1
0
1
1
1
2
1
0
0
0
2
0
2
2
0
0
1
1
0
0
1
2
0
1
1
1
0
1
0
1
0
0
0
2
1
2
0
2
1
1
0
0
2
2
1
2
1
0
2
1
2
2
2
1
0
0
0
0
2
0
0
1
0
2
1
1
2
2
0
2
1
1
1
1
1
0
0
1
1
1
2
1
1
0
2
0
1
1
2
0
0
0
1
1
0
0
0
1
1
5
2
1
2
2
0
1
0
1
0
0
1
2
0
0
2
2
2
1
1
0
1
2
1
0
1
0
1
0
0
0
1
1
1
1
0
1
0
1
2
2
1
2
1
0
2
0
1
1
0
1
0
2
1
2
0
1
2
1
2
1
0
0
1
0
0
1
2
2
0
2
1
1
2
0
1
0
1
1
2
2
0
0
1
2
0
0
1
1
0
2
2
1
1
0
1
1
1
1
0
1
1
0
1
1
2
0
1
1
0
1
1
1
1
1
1
1
1
0
1
1
2
1
2
1
2
0
0
1
0
1
1
2
1
0
1
2
1
1
2
1
2
2
0
0
0
2
1
0
1
2
2
0
1
2
1
1
1
1
0
0
1
1
0
2
1
1
1
0
1
0
2
0
1
2
1
2
1
2
1
0
2
1
0
0
0
1
1
3
1
1
0
1
1
2
1
0
1
2
0
1
3
2
1
1
1
1
0
1
0
2
0
2
0
0
1
0
1
1
2
0
1
2
1
1
2
2
1
1
1
1
1
2
1
2
0
1
1
3
1
1
0
2
0
1
2
1
1
1
2
0
0
2
1
1
0
2
2
2
0
1
0
2
0
2
1
0
2
1
1
2
1
1
2
0
1
1
1
3
0
1
1
3
1
1
1
1
1
1
1
0
2
2
1
2
0
1
1
2
2
1
3
1
0
2
0
1
1
1
1
1
1
0
1
1
0
1
0
2
1
1
2
1
1
2
0
1
1
1
1
0
0
0
0
2
2
0
2
2
2
0
1
0
0
1
2
1
0
1
1
1
2
1
1
1
0
0
1
2
1
1
1
1
2
0
2
2
1
0
2
1
1
0
0
2
0
1
1
2
0
0
1
1
2
0
0
0
0
1
0
1
1
0
1
0
1
2
2
1
2
1
1
0
0
2
2
1
1
0
1
1
1
0
0
2
0
0
0
1
3
1
0
0
2
2
2
1
1
2
0
2
0
2
1
0
0
0
1
1
2
1
2
1
1
0
2
2
1
1
0
0
1
0
0
2
1
1
0
0
0
2
0
1
2
1
1
1
1
1
2
0
2
1
1
2
0
0
2
1
0
0
1
0
1
1
1
1
1
1
1
0
0
0
1
0
0
0
1
1
2
2
1
1
2
1
0
1
0
1
2
1
0
0
1
1
2
1
3
0
2
1
2
1
2
0
1
1
0
1
0
0
1
0
2
1
0
0
1
0
1
1
0
1
0
1
0
0
2
1
2
2
1
1
2
0
1
1
0
0
0
1
0
0
1
0
1
0
2
0
0
1
0
0
1
2
0
1
1
0
2
0
0
0
2
1
0
1
1
1
1
1
1
2
2
1
1
2
1
1
1
1
1
2
1
1
1
1
0
1
2
2
1
2
3
1
0
2
1
1
1
0
0
2
2
0
1
2
1
1
2
0
0
1
2
1
2
0
1
1
1
2
1
1
0
1
0
1
1
0
2
0
0
0
2
1
4
0
1
1
1
1
1
2
1
2
2
1
1
1
1
2
0
1
0
0
1
1
0
0
1
1
1
1
2
2
0
0
0
1
1
1
2
0
1
1
2
2
2
0
1
1
1
2
1
0
1
1
1
2
1
0
0
2
3
0
1
1
1
2
2
1
1
0
2
0
1
1
1
1
1
1
1
1
1
2
0
1
1
1
2
1
1
1
1
1
2
2
0
1
1
2
1
1
1
2
0
1
1
2
1
2
0
2
0
0
1
1
1
1
1
1
3
1
1
1
2
2
1
2
1
0
1
1
1
1
1
0
2
2
0
0
2
1
0
1
0
1
1
2
1
2
2
1
0
1
0
1
0
1
1
0
0
1
1
0
2
2
1
0
1
0
1
1
2
0
1
2
1
0
0
1
0
1
1
0
1
1
1
1
1
1
0
1
1
0
0
1
2
2
1
1
1
0
1
4
2
1
1
0
1
0
1
1
0
0
1
1
2
0
1
0
0
1
0
1
1
1
2
3
2
2
1
0
1
3
0
0
1
0
1
1
0
0
1
1
0
0
1
2
0
0
1
0
2
1
1
1
1
2
0
1
1
2
2
3
0
1
1
2
0
0
1
1
0
0
1
0
1
1
1
2
2
0
2
1
0
2
0
1
2
1
0
0
2
2
2
2
1
0
0
0
1
1
0
1
1
0
1
1
1
2
0
2
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
0
0
1
1
1
0
2
0
0
1
2
0
2
1
0
0
1
0
2
0
1
1
2
1
3
2
0
0
1
2
2
2
0
2
0
1
0
0
0
1
0
1
1
0
5
1
2
1
2
0
2
1
0
0
1
2
0
1
0
1
1
0
2
1
0
1
1
0
2
1
2
1
0
0
1
2
2
2
2
1
1
2
1
2
2
2
0
1
1
0
1
1
1
0
0
1
1
1
1
1
0
1
1
1
2
1
0
0
1
1
1
2
0
1
1
2
1
2
1
1
1
0
0
2
1
1
2
4
1
1
1
0
2
1
0
2
0
2
2
1
2
1
1
0
1
0
2
2
0
1
0
1
0
2
0
1
1
1
1
0
0
2
2
1
2
1
1
1
1
1
1
0
2
2
1
1
1
8
1
0
0
0
1
1
1
1
1
1
2
1
1
0
2
2
1
1
0
1
0
1
1
2
2
2
0
1
2
1
1
2
1
1
2
0
1
1
2
2
1
1
1
2
2
0
0
1
0
1
1
0
1
2
1
1
2
1
1
2
1
0
1
1
1
2
0
0
1
0
1
0
1
2
0
1
1
2
0
2
1
1
0
1
1
0
1
1
2
0
1
0
2
0
0
0
2
2
0
1
1
2
2
2
0
1
1
0
2
1
2
0
0
0
0
2
1
1
1
2
0
1
0
2
1
0
0
1
1
1
1
1
1
0
1
0
1
0
1
1
1
1
1
0
0
3
4
1
3
0
2
2
0
2
2
2
2
1
0
2
1
1
1
0
1
0
0
1
1
1
0
0
1
1
0
1
1
0
1
0
1
0
1
1
1
0
0
1
0
1
2
1
2
0
0
0
2
1
0
0
1
0
0
2
1
2
1
1
1
1
0
1
2
1
2
0
2
0
1
1
0
0
1
1
1
1
1
2
1
0
1
0
1
2
4
1
1
0
1
1
1
1
2
1
1
1
0
0
1
1
0
0
3
1
0
2
1
1
1
0
2
2
1
1
2
2
0
0
0
0
1
0
0
1
1
0
1
1
0
1
1
1
0
1
1
1
2
1
1
1
1
2
1
1
2
1
1
0
1
0
0
1
1
2
1
1
1
0
1
1
1
1
1
1
0
1
0
0
2
1
1
1
0
2
0
1
2
0
2
1
1
1
0
0
0
1
1
0
1
0
1
0
2
1
1
0
0
0
1
0
2
1
1
1
2
0
0
0
1
2
2
1
0
0
2
1
0
1
0
0
1
2
0
2
0
1
0
0
2
1
1
0
2
2
2
0
1
1
1
0
1
1
0
0
0
1
1
2
2
3
2
1
1
2
0
1
0
1
1
0
0
1
0
1
1
1
2
2
1
1
1
0
0
1
2
0
0
2
2
1
2
4
1
0
1
3
2
1
1
0
0
2
1
2
0
1
1
1
2
1
0
0
1
1
0
4
1
0
1
1
1
2
1
2
2
0
0
2
1
0
2
0
1
0
1
1
0
1
2
1
1
0
1
2
0
1
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
2
2
1
2
0
1
2
0
2
1
1
1
0
1
1
1
1
0
1
0
0
1
2
1
3
0
1
1
1
1
2
0
2
0
0
2
1
0
0
1
1
1
1
0
1
1
0
1
1
1
2
1
0
2
1
0
2
1
2
1
1
1
0
1
0
2
1
1
2
1
1
1
1
0
1
0
2
1
1
1
1
0
1
2
0
1
0
2
1
0
0
1
0
0
1
2
0
1
1
0
2
1
1
1
0
1
1
0
0
1
1
2
2
1
1
1
0
1
0
1
0
1
1
1
1
0
1
1
0
0
1
1
2
1
1
0
2
1
0
0
1
1
1
2
1
2
2
1
2
0
2
1
1
0
0
2
2
1
1
1
1
1
1
1
2
1
1
2
1
0
2
0
0
1
2
1
2
1
1
1
1
1
1
0
0
1
0
2
2
1
2
0
1
2
0
1
2
2
0
0
2
1
2
1
1
2
3
1
3
1
0
1
1
2
2
2
1
2
1
0
1
0
1
1
0
1
0
1
1
1
2
1
0
1
2
0
1
2
1
1
0
1
0
2
0
1
2
0
1
0
2
2
1
0
0
2
0
1
2
1
2
0
1
0
3
2
1
2
0
1
0
2
1
0
1
2
1
1
2
0
1
0
2
0
0
2
1
0
1
0
1
0
0
2
2
0
1
0
1
1
1
0
2
1
1
2
2
1
0
1
2
0
0
0
2
0
1
0
1
1
2
2
0
1
0
4
1
2
2
0
0
2
1
3
2
1
0
1
1
1
2
2
0
0
2
1
1
0
0
0
1
1
1
1
0
0
1
1
1
1
0
0
1
0
2
0
2
0
1
0
1
1
1
0
0
1
1
1
1
1
1
1
1
0
1
1
1
1
2
1
1
2
2
0
0
1
1
0
2
2
1
3
0
1
2
0
0
2
2
0
1
2
0
2
0
0
2
0
1
1
2
2
1
0
0
2
1
1
0
0
2
1
1
2
1
1
1
1
2
1
1
1
1
0
2
0
1
1
2
0
0
2
1
2
1
1
2
1
2
0
2
1
1
1
1
0
2
1
1
0
1
1
1
1
6
0
1
0
1
1
3
0
1
1
1
1
0
1
1
1
1
1
0
1
1
0
1
0
1
1
1
0
2
1
1
0
2
1
1
1
0
1
1
1
2
1
2
1
1
3
1
1
0
2
1
1
1
0
1
0
2
1
1
1
1
1
0
1
2
1
0
1
1
1
1
2
0
1
2
4
0
1
1
0
1
2
0
1
1
0
1
0
1
1
2
2
2
2
1
1
1
1
2
1
1
0
1
1
1
1
0
1
0
1
1
0
0
0
1
2
0
1
0
0
1
0
0
1
1
0
1
1
1
1
1
2
2
1
1
2
1
2
2
1
2
0
2
0
2
1
2
2
2
1
0
1
1
2
1
1
1
0
1
0
1
2
0
0
2
1
2
1
1
0
1
1
2
1
2
2
1
0
2
2
2
1
0
1
1
1
2
1
1
0
1
3
2
0
0
0
0
0
1
2
0
0
0
2
0
1
0
1
2
0
0
0
1
0
1
1
2
1
0
0
1
2
1
3
1
1
1
1
2
0
2
1
1
1
1
1
1
3
0
0
1
2
0
1
0
1
1
1
1
2
1
1
1
2
2
1
1
1
2
0
1
1
0
1
2
0
1
0
0
0
0
2
1
1
1
1
1
3
2
1
1
1
1
1
1
1
2
1
1
1
1
1
0
0
2
1
2
1
0
1
1
2
2
0
1
2
2
1
1
1
2
1
1
0
1
2
1
1
1
2
1
0
1
1
1
1
1
1
0
2
2
2
0
2
0
1
2
0
1
0
0
1
1
1
1
1
1
1
1
1
1
1
1
0
1
0
1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
2
2
0
2
2
2
1
1
1
2
0
1
1
4
2
1
2
2
0
0
1
2
0
1
3
2
1
0
1
0
1
2
1
1
0
2
1
1
1
0
1
1
0
1
0
2
2
1
0
1
2
0
1
0
1
1
0
2
1
1
1
1
0
2
0
2
2
0
1
1
1
2
1
2
0
0
1
1
1
2
1
0
0
1
1
1
0
0
1
0
1
0
2
0
1
1
1
3
1
1
1
1
0
0
0
1
2
1
1
1
4
1
1
1
1
0
1
2
1
0
0
0
2
0
2
1
0
1
0
2
1
1
1
1
1
1
1
0
2
1
1
0
1
0
1
1
2
1
0
0
2
2
2
1
2
2
2
3
0
3
2
1
0
2
0
0
0
0
0
1
0
1
1
1
2
2
0
0
2
2
1
0
0
1
1
0
0
1
1
1
1
1
1
1
1
0
1
1
1
2
2
1
2
1
1
1
1
2
0
1
1
2
0
1
1
2
1
0
0
1
0
0
1
0
2
0
0
0
0
1
0
1
0
0
1
1
1
1
1
0
1
1
1
2
1
1
0
0
2
1
1
1
1
0
1
0
1
2
1
1
2
1
1
1
1
2
0
2
1
0
1
0
1
1
2
1
0
1
0
1
1
1
2
2
1
0
1
1
0
1
1
0
1
2
1
1
0
1
0
1
1
2
2
1
1
1
1
1
1
1
2
0
1
1
2
1
0
1
0
2
2
2
1
1
2
2
0
2
1
2
2
1
2
1
2
1
5
2
1
0
1
1
1
1
1
0
1
0
2
1
0
1
0
0
0
1
1
1
1
1
1
1
1
2
2
0
1
2
1
0
1
0
0
1
0
2
1
0
1
1
0
1
0
2
0
2
1
2
0
2
1
1
2
1
2
0
1
1
0
2
1
2
1
1
2
1
1
0
1
1
0
0
1
0
0
1
2
1
1
1
1
1
0
1
0
1
0
0
1
1
1
1
1
1
0
1
0
1
1
0
1
0
1
1
1
1
2
2
1
1
2
0
0
2
2
0
1
0
2
1
0
1
2
3
2
0
2
0
1
0
1
0
1
1
0
1
2
1
0
0
1
0
0
0
1
1
0
1
2
0
1
2
0
0
1
1
1
2
0
1
2
1
0
0
1
1
0
1
1
1
0
1
2
1
1
2
2
0
2
0
1
0
1
0
1
1
1
2
0
1
1
0
1
1
1
0
1
1
2
1
0
1
1
2
1
1
1
1
2
1
0
0
0
1
0
1
2
0
2
0
1
1
1
1
1
1
0
0
1
2
1
0
2
1
0
0
1
0
0
1
1
1
2
0
1
2
0
1
2
1
0
1
1
2
2
2
0
1
1
0
2
2
1
1
1
2
1
1
1
1
1
0
1
2
1
2
0
1
0
1
4
1
0
1
1
1
0
1
2
1
0
1
0
1
0
1
0
2
1
1
2
2
1
2
1
1
0
2
2
2
2
1
0
1
1
0
1
0
1
0
1
1
0
1
1
1
1
1
2
1
3
0
1
0
0
2
0
1
0
1
0
1
1
1
1
1
1
1
1
1
1
2
0
0
2
2
1
0
2
2
0
1
0
5
1
2
0
0
2
1
2
3
2
1
1
1
1
1
1
0
0
1
2
1
0
2
1
0
1
1
1
1
1
0
1
2
1
0
1
1
0
1
2
0
0
1
1
1
2
0
1
1
0
0
0
1
1
0
1
1
1
2
1
1
0
1
1
1
0
2
1
2
0
0
1
1
2
2
1
1
1
1
1
0
1
1
0
1
0
2
0
1
0
1
1
2
1
0
0
0
1
1
2
1
0
0
0
1
1
2
0
1
1
1
1
0
1
0
0
0
2
1
0
2
5
1
2
0
1
1
2
1
2
1
1
2
0
0
2
1
0
0
1
1
1
1
0
1
0
1
0
2
1
0
1
0
0
1
0
1
0
1
2
0
1
1
2
0
0
0
1
2
1
2
0
0
1
2
1
1
2
0
1
1
1
2
1
1
0
0
1
1
1
1
0
0
1
0
2
1
1
0
1
1
1
1
1
2
0
0
1
2
0
1
1
1
2
1
1
0
0
0
1
1
1
2
1
0
2
2
0
1
2
0
1
1
1
1
1
1
1
1
0
1
1
2
1
2
0
1
0
0
2
1
1
1
2
2
1
0
1
0
1
1
0
0
2
0
0
0
1
3
1
1
0
1
1
1
1
0
1
0
3
2
3
1
1
0
1
0
1
2
1
0
2
2
2
0
1
1
2
1
2
0
0
1
1
2
0
0
0
1
1
2
1
1
1
1
0
0
0
0
2
0
1
1
0
1
2
0
1
2
1
0
0
0
1
0
1
1
1
0
1
1
0
2
2
1
2
0
0
1
1
0
1
1
0
2
1
2
1
2
2
0
0
1
0
1
2
1
2
1
1
1
2
0
2
1
2
2
0
1
1
2
1
0
2
0
0
1
0
1
0
1
0
0
1
0
2
2
3
1
0
1
1
2
2
2
1
1
2
0
0
1
1
0
2
1
1
1
2
1
1
1
0
1
1
1
0
1
2
0
0
1
4
2
0
0
2
1
1
0
1
0
2
2
1
1
0
1
2
2
0
1
1
0
1
3
2
2
2
2
1
0
0
1
1
0
1
2
0
1
1
0
0
1
0
2
0
1
0
1
4
1
1
5
1
1
0
1
0
1
1
0
1
0
0
0
2
1
1
1
0
1
0
0
0
1
0
1
1
1
0
1
0
1
0
0
1
0
2
1
0
0
2
1
1
2
2
2
0
0
1
1
1
0
1
2
1
0
2
2
0
1
1
1
0
0
0
0
1
2
1
1
0
1
2
1
1
1
1
1
1
1
1
0
1
2
1
1
0
0
2
0
1
2
0
2
1
2
2
0
0
2
2
0
0
1
0
1
1
0
2
0
2
2
2
1
1
0
1
1
2
3
1
1
0
1
1
1
2
1
2
1
0
1
1
0
0
0
1
1
1
1
2
1
1
0
1
1
0
1
0
1
0
0
1
1
1
1
1
0
2
1
0
1
1
2
2
1
1
2
0
2
0
1
1
1
1
0
1
2
2
1
1
1
1
1
1
2
2
1
1
1
2
0
1
1
0
2
1
0
1
1
1
1
2
0
1
1
1
2
1
1
0
0
0
1
1
1
1
0
3
1
2
1
2
1
1
0
2
0
2
2
0
2
2
1
1
1
0
1
0
1
2
1
0
2
1
1
1
0
1
1
2
1
1
0
0
1
0
0
2
1
0
1
1
1
1
2
2
0
0
0
2
2
0
0
0
1
1
0
3
2
1
1
1
2
0
1
1
1
2
0
1
1
0
1
2
1
1
2
1
2
1
0
2
1
0
1
0
0
1
0
0
1
1
0
1
1
1
0
2
1
2
2
2
2
1
2
0
2
1
0
1
0
2
1
1
2
2
2
1
0
0
1
1
0
0
1
0
1
2
1
2
0
0
2
0
1
1
1
2
1
1
1
0
1
1
1
1
1
0
1
1
1
1
1
0
0
3
0
1
2
1
1
1
0
0
0
1
1
1
0
2
2
1
0
2
1
2
2
0
1
1
0
1
1
1
1
1
1
2
2
0
2
1
0
1
1
2
0
0
1
1
1
0
1
0
1
1
2
0
1
1
1
0
2
2
0
1
0
1
0
1
1
2
0
0
0
1
0
0
1
0
1
1
1
0
1
2
0
1
1
1
1
0
1
1
0
1
0
2
1
2
0
2
1
1
1
0
0
2
1
1
0
1
1
0
0
1
1
1
1
0
1
1
0
0
2
2
1
1
1
0
0
0
1
0
2
1
2
0
1
0
1
0
1
1
0
1
2
0
1
2
2
1
2
1
2
1
0
0
0
1
1
1
1
1
0
2
1
1
2
1
1
2
1
0
1
1
0
0
2
0
0
1
0
1
1
1
2
1
1
1
3
0
2
1
1
0
1
1
1
1
2
2
2
0
0
2
2
1
1
0
2
1
1
1
1
1
2
1
1
1
0
1
1
1
0
0
1
0
1
1
3
1
2
1
2
1
2
2
1
0
0
0
1
2
0
1
1
2
1
0
0
0
1
1
0
2
1
0
0
1
0
0
1
1
0
0
1
1
1
0
1
0
2
0
0
1
2
2
1
1
1
0
1
1
0
2
1
1
1
2
1
1
2
1
1
0
1
0
2
1
1
1
1
1
1
0
1
0
0
1
0
1
0
1
2
1
1
2
0
2
2
2
1
1
2
1
2
1
1
1
0
1
0
1
0
2
0
1
0
0
2
1
0
1
0
0
1
1
1
2
1
1
2
0
2
1
1
0
1
2
2
2
2
0
2
0
0
0
2
2
2
2
1
1
1
1
1
0
0
1
0
2
1
1
1
1
1
0
0
3
0
2
2
2
0
1
1
1
0
1
1
0
1
0
1
0
0
0
2
1
0
2
0
1
0
2
1
0
3
0
1
1
1
0
2
1
1
1
2
2
1
1
0
1
1
0
1
1
0
1
0
1
2
1
1
1
1
1
0
2
1
2
1
0
1
0
0
2
0
1
0
1
2
0
1
3
0
2
0
1
2
3
1
2
1
1
0
0
2
2
0
0
0
2
1
0
2
1
1
2
1
0
1
1
1
1
1
1
1
1
2
0
1
2
1
2
1
3
0
1
1
2
1
0
1
2
0
2
1
1
1
2
2
1
1
1
1
1
1
0
2
1
2
1
1
0
1
0
0
1
0
2
1
0
1
0
1
1
1
1
2
1
2
1
2
1
2
0
1
2
2
2
2
0
0
1
0
1
0
2
2
1
0
2
1
1
1
0
0
1
1
1
2
1
1
2
1
3
1
3
1
1
1
1
0
0
2
2
0
1
1
2
2
2
1
2
1
1
0
1
1
0
1
2
2
0
1
1
0
1
1
1
1
1
1
0
0
0
1
1
0
1
1
0
1
0
1
2
0
1
1
2
2
2
1
0
1
1
1
2
0
1
0
0
0
2
1
1
1
1
2
0
2
1
2
1
1
2
0
2
1
2
0
0
2
2
2
1
2
0
2
1
1
4
1
1
2
2
1
2
1
1
2
1
1
1
1
2
0
0
1
2
1
1
1
0
1
1
1
2
0
2
0
2
2
0
1
1
1
0
1
1
0
0
1
1
0
0
0
1
1
1
1
1
0
1
1
2
0
2
2
1
0
1
2
1
2
1
0
0
2
2
2
2
0
1
2
1
1
1
2
1
2
1
1
2
1
0
2
1
2
1
2
2
1
1
0
1
0
1
1
0
0
1
0
2
2
1
1
1
4
0
1
2
1
0
0
0
0
1
0
0
2
0
1
1
1
2
0
1
1
2
0
1
2
2
1
1
2
0
0
2
1
2
0
1
0
0
2
1
0
1
0
0
1
2
1
1
2
0
2
1
1
0
0
0
0
0
1
1
2
0
1
1
1
0
1
0
0
0
0
0
1
0
1
1
0
0
1
1
1
2
2
0
1
2
1
2
0
1
1
1
1
0
0
1
2
0
2
1
0
1
0
1
0
1
2
1
1
1
2
1
1
1
1
1
2
0
1
1
0
1
0
2
1
1
0
1
2
0
2
0
0
2
0
2
1
1
0
1
0
3
2
1
0
0
1
1
0
1
1
0
0
1
1
1
2
0
0
1
0
1
0
1
0
0
0
1
0
1
1
1
0
1
2
1
0
2
0
1
0
2
1
1
1
1
1
1
2
0
0
1
0
2
0
1
0
1
1
0
1
2
3
2
0
1
1
2
1
1
0
2
2
1
2
2
1
1
0
1
2
1
0
1
2
0
3
1
1
1
0
0
0
2
0
1
2
0
0
0
2
1
1
2
1
2
0
0
2
2
0
1
0
1
1
2
0
2
2
1
2
1
0
2
1
1
1
2
2
1
2
1
1
0
1
1
2
0
0
1
0
1
1
1
1
2
1
1
1
0
1
2
1
0
1
0
1
1
1
1
1
2
2
0
2
1
0
0
1
1
2
2
0
1
2
1
1
0
2
1
0
1
0
1
1
1
1
0
1
1
2
0
1
1
1
1
1
2
0
1
1
1
2
1
0
1
0
1
1
0
0
0
2
1
2
2
1
1
1
1
1
0
1
1
1
1
1
1
0
1
1
1
1
1
2
1
2
2
1
1
1
0
2
0
0
0
0
0
1
1
2
2
0
2
1
1
2
2
1
0
0
1
1
1
1
0
0
1
0
0
1
0
1
0
0
2
2
1
1
0
1
1
3
1
2
2
1
1
1
1
0
1
1
1
0
1
2
2
1
1
1
0
1
1
0
1
0
1
2
1
1
2
1
1
0
0
0
1
1
1
0
1
1
1
1
0
1
0
0
0
1
0
0
1
0
0
0
0
1
1
2
0
2
1
1
1
1
2
1
1
0
3
2
0
1
1
0
0
1
1
1
1
0
2
0
1
1
0
0
1
2
0
2
1
1
1
0
0
1
0
1
2
1
0
1
1
1
2
1
1
1
2
0
0
1
0
0
0
1
0
0
1
0
1
2
2
2
0
1
1
2
1
0
1
2
0
1
0
2
1
1
3
0
1
1
2
0
1
1
1
2
0
1
1
2
0
2
1
1
2
1
0
1
0
1
2
1
2
0
3
2
1
2
1
1
0
1
0
0
0
0
0
1
2
1
2
2
1
1
2
0
1
1
1
1
0
1
0
1
1
0
1
1
2
2
0
0
1
1
0
1
0
1
1
1
1
0
1
1
0
1
1
0
1
1
0
2
1
2
1
2
0
0
1
2
1
1
0
1
2
0
2
1
1
1
1
1
0
2
1
0
1
1
1
0
2
3
1
1
0
1
0
1
1
0
2
0
1
0
2
2
0
0
1
2
1
0
2
1
1
2
1
1
2
1
0
1
0
2
2
1
0
2
1
1
1
0
0
1
1
0
2
2
1
0
3
2
0
1
1
0
1
0
2
1
0
2
0
2
0
0
0
1
1
2
1
1
1
3
0
1
1
0
2
0
1
1
0
2
1
0
2
0
0
1
1
2
2
1
2
2
1
1
0
1
1
0
0
0
1
0
2
1
1
2
0
1
0
0
0
2
2
0
0
1
1
1
0
1
0
1
2
1
1
1
1
0
1
0
0
0
1
2
1
0
0
1
1
0
0
2
1
1
1
2
2
0
2
1
1
1
1
1
0
1
2
0
2
2
1
1
1
1
1
0
0
1
0
1
0
0
1
1
0
2
1
0
2
1
0
0
2
3
2
2
0
0
2
0
1
0
1
2
1
2
1
1
2
1
0
0
1
4
1
1
1
2
0
1
1
1
0
2
1
2
1
1
1
1
1
2
1
1
1
1
1
0
2
1
1
2
0
1
2
1
1
1
2
2
2
2
0
2
0
0
0
1
2
0
1
1
1
0
0
0
1
1
1
2
2
0
1
1
1
1
1
1
1
1
1
0
0
2
0
0
1
0
2
2
1
1
2
0
0
2
1
1
2
6
0
1
0
0
1
1
1
1
1
4
2
0
0
1
1
1
0
0
1
1
1
1
0
1
2
0
1
2
0
1
0
2
1
0
1
1
1
0
1
2
1
1
2
1
1
2
3
1
1
2
2
4
1
0
1
0
1
0
1
1
0
1
2
1
0
1
2
1
2
1
1
2
2
1
0
1
0
0
2
2
1
2
1
1
1
1
1
2
2
0
2
2
2
2
0
1
0
1
0
2
2
1
0
1
1
1
1
1
8
0
0
0
1
0
1
0
1
1
0
1
1
0
1
1
1
1
1
1
1
2
1
1
1
0
2
0
0
2
1
1
1
2
1
1
1
1
0
1
1
2
0
3
0
2
2
1
0
1
0
1
1
0
1
0
0
1
2
1
0
2
0
2
2
0
1
1
2
2
2
2
1
1
1
1
2
1
1
0
0
1
1
2
1
1
2
0
1
2
2
0
2
1
2
2
1
0
2
1
2
1
0
1
2
1
2
1
0
2
1
1
1
1
1
2
0
1
1
0
1
0
0
1
0
2
2
1
1
0
1
1
1
0
0
1
0
0
2
1
0
1
1
1
1
2
1
1
1
0
2
2
2
2
0
2
0
0
2
1
0
1
1
1
1
2
1
2
1
1
1
1
0
2
0
0
1
0
1
1
2
1
0
1
0
1
1
1
3
1
0
2
1
1
2
2
2
2
1
1
1
2
0
0
1
1
0
0
2
1
1
2
0
2
0
0
2
1
1
2
2
2
2
0
1
1
1
2
1
1
2
0
2
1
0
1
1
2
0
0
0
1
1
1
0
1
0
2
1
0
1
1
1
0
0
1
1
2
2
1
0
2
1
1
0
1
1
1
0
1
0
1
1
2
2
1
2
2
0
2
0
0
1
2
1
1
1
0
1
0
1
0
0
2
0
1
2
1
0
2
2
0
1
1
0
3
2
1
2
0
0
2
0
1
0
1
1
0
0
1
1
0
1
1
2
2
0
0
1
0
2
0
1
1
1
1
2
1
0
0
2
1
1
1
1
0
0
1
2
0
1
0
1
1
0
1
1
2
1
1
1
0
0
0
0
1
0
0
0
2
1
0
1
3
0
2
1
0
2
2
0
0
1
1
2
0
0
2
2
2
0
0
0
0
1
2
1
0
2
1
0
0
0
1
0
2
2
2
0
0
3
0
0
0
1
0
1
2
1
2
1
1
2
1
1
2
1
0
2
2
1
2
2
0
2
0
2
3
0
1
1
1
1
0
0
2
1
1
1
1
2
1
0
1
1
0
1
0
0
1
0
0
2
0
2
1
1
2
0
1
1
1
1
1
1
1
0
0
3
1
1
0
1
2
0
1
1
1
1
1
1
1
1
1
1
0
1
2
2
2
0
1
1
2
1
1
0
1
0
0
1
0
1
1
1
1
0
3
2
2
1
0
1
1
1
1
1
1
0
0
1
1
2
0
2
0
1
1
1
0
0
1
2
1
0
0
1
2
2
0
1
1
0
0
1
1
0
2
1
1
0
2
2
2
1
2
1
1
2
1
1
1
1
2
1
2
2
2
1
0
1
1
1
0
1
1
0
1
1
1
1
2
1
0
0
2
0
0
2
2
0
1
0
1
1
0
0
0
2
0
1
0
0
1
0
1
0
2
3
0
2
1
2
0
0
0
1
2
6
2
0
1
0
1
0
0
2
1
1
1
1
1
1
0
0
1
1
1
1
2
0
1
0
1
0
1
0
1
0
2
0
1
2
2
0
2
1
2
1
0
1
0
2
1
2
0
1
2
1
0
1
1
1
1
0
1
1
1
2
1
3
2
1
1
2
2
0
1
1
2
0
0
1
1
1
1
1
2
1
1
1
0
1
0
1
1
2
1
2
2
1
0
2
0
1
1
2
0
0
0
1
4
1
2
1
1
1
6
2
1
0
1
1
1
0
1
1
2
1
2
1
1
1
1
1
1
1
2
0
1
3
2
0
1
1
0
1
1
1
0
1
1
0
1
1
0
1
1
1
1
1
1
4
2
1
1
1
2
2
0
0
2
0
0
0
2
0
0
1
2
1
0
1
1
1
3
2
0
1
0
1
2
0
1
1
3
0
2
0
0
0
1
1
1
0
2
0
1
2
1
2
1
0
0
2
1
1
1
0
0
1
1
1
0
0
1
1
1
1
0
1
0
1
0
1
2
1
1
0
0
1
1
0
1
2
2
0
0
2
1
1
6
1
1
0
2
0
0
1
0
1
1
1
2
1
0
1
0
1
1
2
0
2
1
1
1
2
1
1
0
1
1
1
0
0
1
0
0
2
0
0
1
1
0
2
1
0
2
1
3
2
1
1
0
2
0
2
2
2
1
0
1
1
1
1
3
1
1
0
1
2
2
0
1
1
1
1
0
1
3
0
1
2
1
1
0
1
0
1
2
1
2
0
1
1
1
0
1
1
1
1
1
0
2
1
1
0
1
1
1
0
1
1
2
1
1
1
1
0
0
1
1
1
2
3
0
1
0
1
0
1
3
0
0
1
2
1
0
2
0
1
2
2
0
1
0
1
1
1
1
0
1
2
1
1
2
0
0
0
1
0
2
1
0
2
0
1
1
1
1
0
1
0
3
2
0
0
2
8
2
1
1
2
2
1
0
0
2
0
1
1
1
0
0
0
2
1
0
1
1
2
0
0
0
1
1
1
2
1
1
1
0
2
1
1
0
1
1
1
0
2
1
2
2
1
0
1
0
2
0
2
1
1
0
1
2
1
3
1
1
1
0
2
1
0
0
1
2
2
2
2
0
2
0
1
1
1
1
1
1
2
1
3
2
2
2
2
0
2
1
1
1
1
0
1
1
1
1
1
2
0
0
1
1
0
2
2
2
1
1
1
1
2
0
0
1
0
0
1
1
0
0
1
1
1
0
2
1
1
0
2
1
2
1
1
1
0
2
1
2
0
1
2
0
0
1
2
2
0
0
2
1
0
2
2
2
1
2
1
0
0
2
2
1
0
2
3
3
0
2
1
2
0
0
0
1
2
0
1
0
0
2
0
1
2
1
2
2
1
0
2
0
0
0
0
1
0
2
1
0
1
2
1
0
1
2
1
2
1
0
3
1
2
1
1
0
1
2
2
2
1
1
0
1
1
2
1
2
1
0
0
1
1
0
0
1
1
1
0
2
1
0
1
2
1
0
0
2
2
2
1
1
0
1
1
0
3
2
1
1
2
0
0
0
2
0
0
1
0
1
0
1
1
0
1
2
1
0
2
1
0
2
1
0
2
0
2
1
3
0
2
1
0
0
2
0
0
0
0
1
2
0
0
0
0
0
1
2
0
1
1
1
0
0
0
1
1
1
0
0
0
0
1
0
2
0
2
1
0
1
2
1
0
1
2
2
0
1
1
1
1
3
1
2
4
1
1
0
2
2
2
0
1
2
1
1
2
1
1
0
1
2
1
1
2
0
1
1
0
1
0
0
2
1
0
1
1
1
2
0
1
1
2
1
1
0
0
0
0
1
0
1
0
2
4
2
1
1
1
1
1
0
0
1
0
0
1
1
2
0
1
1
0
1
0
1
2
0
1
1
2
0
0
1
1
2
0
2
2
1
1
1
0
1
1
2
1
1
2
1
4
1
1
1
2
0
2
1
0
1
1
1
1
1
0
2
2
1
1
1
0
1
0
1
1
1
1
2
0
2
1
0
0
1
0
0
1
1
0
4
0
1
2
1
1
1
2
1
1
1
1
1
0
1
1
1
0
1
2
1
1
2
1
0
1
2
0
1
2
1
1
2
2
2
3
1
1
0
1
0
0
1
3
1
1
1
0
2
2
1
2
0
1
2
1
0
1
0
1
0
2
2
1
2
0
1
0
2
1
0
1
0
0
1
1
1
1
0
1
1
1
0
2
1
0
0
2
0
1
0
1
1
2
0
1
0
0
1
1
1
0
1
1
1
2
0
1
1
2
2
1
0
1
1
0
6
0
1
0
1
2
1
1
1
1
2
2
1
1
1
1
0
1
3
0
0
1
1
2
2
1
0
0
0
2
1
0
2
1
1
0
0
1
1
1
0
0
0
1
1
1
1
1
1
1
2
1
0
0
1
0
0
0
1
1
2
1
0
0
2
0
1
1
1
0
0
1
1
2
0
2
2
1
1
1
1
0
0
1
2
1
1
1
1
1
1
0
1
0
0
1
1
1
1
0
1
1
1
1
1
1
2
2
1
2
1
1
0
1
1
0
0
2
3
1
0
1
0
2
1
0
1
1
0
2
2
1
0
1
1
0
1
1
1
0
0
1
1
0
1
0
1
1
0
1
1
1
1
2
1
2
0
1
1
0
2
1
1
0
2
1
2
1
1
1
2
0
1
2
1
2
1
1
0
2
1
1
0
1
2
1
2
1
1
1
2
0
1
0
1
1
2
1
2
1
4
1
1
2
0
1
2
0
0
2
2
1
1
2
2
1
3
0
1
2
1
2
0
2
1
2
2
1
0
1
0
2
0
0
2
0
2
2
2
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
3
0
0
2
1
1
2
2
2
1
1
0
0
2
2
0
1
1
0
1
1
1
0
2
1
0
0
2
1
1
1
1
1
0
1
1
2
1
4
2
1
1
1
1
2
2
2
2
1
2
1
2
2
1
0
0
0
2
0
1
1
0
0
2
2
1
0
2
1
1
0
0
1
1
0
1
0
1
0
0
1
1
0
1
1
1
1
1
1
1
0
1
2
1
0
2
3
2
3
0
1
0
1
1
1
0
0
1
0
1
1
1
2
0
1
1
0
2
1
0
1
1
2
1
1
0
1
0
0
0
1
2
1
2
2
0
0
0
0
1
2
1
0
2
1
1
2
0
1
1
1
2
2
1
1
0
2
1
4
1
1
0
8
2
1
2
0
1
1
0
1
1
2
0
0
2
1
1
0
2
1
1
1
1
2
0
2
2
2
0
1
0
0
0
1
1
1
1
0
0
2
1
1
1
1
1
1
1
1
0
1
1
0
1
0
1
2
1
2
1
0
1
2
0
0
1
2
1
1
2
1
2
1
1
2
1
1
2
1
1
0
0
0
1
0
2
1
0
2
1
1
0
1
2
1
2
0
0
1
2
0
1
0
1
2
0
1
2
1
1
0
1
0
1
2
1
1
1
1
1
1
0
1
1
1
1
0
0
1
1
2
1
0
1
2
1
1
1
0
1
2
0
1
2
1
1
0
1
1
3
0
1
0
0
1
0
1
2
0
3
1
1
0
1
1
2
1
2
1
0
1
1
1
1
2
0
1
1
2
1
2
0
0
0
1
0
2
0
1
3
0
0
1
1
1
1
2
1
0
1
2
1
0
1
1
1
0
0
0
1
1
1
1
2
0
2
1
3
1
1
1
1
0
1
1
1
0
0
1
3
1
2
1
1
1
1
1
0
0
1
1
1
2
1
1
1
0
1
1
1
1
0
2
0
1
0
0
2
0
1
1
1
0
1
1
1
1
0
0
2
1
1
1
0
1
1
1
1
1
0
2
0
0
1
0
1
0
1
0
0
1
0
2
1
3
2
1
1
2
1
0
1
1
1
0
1
0
0
0
1
0
1
0
0
0
0
2
1
1
2
1
1
1
1
1
1
1
1
3
1
1
0
1
1
2
0
1
1
2
1
1
0
1
1
1
1
0
2
2
0
2
0
2
1
2
1
0
2
0
0
1
0
0
2
1
1
3
1
1
2
1
1
1
0
0
2
1
0
0
2
1
0
1
0
1
2
1
2
0
1
0
2
2
2
2
0
1
1
0
2
0
1
1
1
0
1
0
1
1
2
2
0
0
0
2
1
1
2
1
0
0
2
0
1
1
0
2
0
2
1
1
0
2
1
1
3
0
3
0
2
0
0
1
2
2
2
1
2
0
0
2
0
3
1
1
1
1
0
2
1
1
0
2
0
1
0
1
2
1
1
1
0
0
2
1
0
1
0
1
2
2
2
2
2
1
1
0
1
0
0
2
0
2
1
0
1
0
1
2
1
1
1
0
0
0
2
0
1
0
2
2
1
2
1
0
2
0
2
2
0
2
1
1
2
0
1
1
1
2
1
1
1
0
3
0
1
0
0
0
0
1
1
0
1
0
1
1
0
2
2
1
1
0
1
1
0
1
1
1
2
1
0
1
2
0
0
2
1
1
0
2
0
3
2
1
0
1
2
2
1
1
1
0
1
0
2
1
1
1
1
1
2
0
1
2
0
1
1
2
0
2
2
1
1
0
1
2
2
1
0
2
1
4
1
1
1
1
1
0
1
0
0
0
1
1
0
1
0
0
0
1
0
3
1
1
1
1
0
1
1
1
0
0
2
1
2
0
0
0
1
0
2
2
1
2
0
1
0
0
0
2
1
2
1
2
1
0
0
1
2
0
2
4
2
1
1
0
0
1
1
1
1
1
1
1
0
0
1
0
1
1
1
1
0
2
0
0
1
2
1
1
1
1
1
2
2
0
1
0
1
1
2
2
1
1
3
2
2
0
0
1
2
2
0
0
1
0
1
0
0
1
0
2
0
2
1
1
0
2
0
1
0
1
1
0
1
1
2
1
1
2
1
1
1
1
1
1
1
0
1
1
0
0
2
2
2
1
1
1
1
1
1
1
0
1
2
2
2
1
1
1
0
1
1
1
2
1
0
0
0
1
2
2
2
1
0
2
0
1
0
1
1
1
0
0
0
1
1
1
0
2
1
1
1
2
1
2
1
1
1
1
2
0
0
0
1
2
1
2
1
1
0
1
1
1
2
0
2
1
2
1
2
2
2
1
1
0
2
2
1
1
1
0
1
1
1
1
0
1
1
1
1
0
0
0
1
2
1
1
2
1
1
0
1
0
0
1
0
0
0
1
0
1
1
2
0
1
1
0
1
1
0
1
1
1
0
1
1
1
0
1
0
0
1
1
1
1
1
1
0
1
0
0
1
1
2
1
1
0
1
0
2
1
2
0
2
1
0
0
2
1
1
1
3
2
2
1
0
1
2
1
0
2
2
2
2
2
1
1
1
2
2
2
0
1
1
2
1
1
0
2
0
0
1
1
0
0
0
1
2
1
1
0
0
1
2
1
2
1
1
1
2
0
1
0
1
1
1
0
0
1
1
1
1
0
1
1
1
1
0
2
0
0
1
0
2
2
2
1
0
1
0
2
1
1
0
1
0
1
1
2
1
1
1
1
0
0
0
0
1
2
1
0
1
1
1
1
1
1
0
2
4
1
1
2
0
0
2
2
1
1
2
1
0
0
0
2
1
0
1
0
1
0
1
1
1
1
1
1
1
0
2
1
1
1
0
1
1
2
2
1
2
2
0
1
1
1
2
1
2
1
1
1
1
2
2
1
1
2
0
0
1
1
0
1
2
0
2
1
1
3
3
2
1
1
0
1
1
1
0
1
1
1
1
1
1
2
2
2
2
0
0
0
0
2
1
0
2
1
1
1
0
1
1
0
0
1
1
0
1
0
0
1
1
0
0
2
0
1
1
2
1
1
1
2
2
0
0
1
1
2
0
0
1
1
1
1
1
0
1
2
0
0
2
2
1
2
1
2
2
0
0
2
1
0
1
2
1
0
0
1
0
7
1
0
0
2
1
2
1
2
1
1
0
1
1
1
2
0
1
0
0
1
1
1
1
1
0
2
0
3
1
1
1
2
1
1
0
1
1
2
0
1
1
0
2
2
1
0
1
1
2
1
1
1
0
0
2
1
1
0
0
0
1
1
0
0
0
2
0
0
1
2
1
1
0
1
2
1
0
1
1
1
2
2
1
1
2
2
1
2
0
2
1
1
1
0
1
2
1
0
0
0
1
1
0
1
2
1
0
1
2
1
0
2
1
0
1
1
0
1
1
1
0
1
1
1
2
0
2
3
1
1
1
1
1
1
2
1
1
0
0
1
1
0
1
0
1
1
1
1
2
1
1
1
1
1
0
2
0
1
0
0
0
1
0
1
0
2
0
8
1
0
0
2
0
0
1
0
2
1
2
2
0
0
2
2
0
0
0
1
1
0
2
0
0
0
1
1
1
1
2
0
0
2
1
1
1
2
0
2
2
2
1
0
1
2
1
0
1
2
2
1
0
1
1
1
2
2
0
0
1
1
1
0
1
3
1
1
0
1
1
1
0
1
1
1
2
0
1
2
0
2
0
1
0
1
0
1
1
0
0
0
1
1
1
1
1
2
1
2
1
1
0
2
0
0
0
1
1
1
0
0
2
1
1
0
1
2
2
1
0
2
2
1
1
0
1
2
1
1
1
0
0
2
1
0
1
0
0
1
0
0
1
1
1
1
0
0
0
2
1
2
0
1
0
1
0
0
0
1
0
0
1
1
1
1
0
0
0
2
1
2
0
0
1
0
9
2
1
0
1
0
1
0
2
0
2
1
0
1
1
0
0
1
1
2
0
1
1
2
0
2
1
2
1
2
1
2
1
0
1
2
0
2
1
2
2
1
0
0
0
1
1
1
1
2
3
1
2
1
1
0
0
1
1
1
1
0
1
1
1
0
1
2
1
0
0
1
2
0
3
1
1
1
1
0
0
1
1
1
2
0
1
2
1
0
0
2
1
0
0
3
1
0
2
1
1
1
0
0
0
1
1
1
1
1
0
1
2
1
0
0
1
2
1
1
0
2
0
2
0
0
1
1
1
1
0
2
0
1
1
1
1
0
2
1
0
1
1
1
1
0
1
1
2
1
2
1
1
0
1
2
1
1
0
0
2
1
1
0
0
1
1
1
1
1
2
1
1
1
1
0
1
1
0
0
0
0
0
0
1
1
0
1
1
0
1
0
1
1
1
2
1
1
1
0
1
1
1
1
2
0
1
0
2
1
0
1
1
0
1
1
2
1
0
1
2
2
1
1
1
1
1
1
5
1
1
0
0
2
0
2
1
2
0
2
2
0
1
0
1
1
1
1
1
0
1
0
0
0
1
1
1
1
1
2
2
0
1
2
0
0
1
0
4
1
0
0
1
1
2
1
2
2
1
0
0
0
0
1
0
2
1
2
1
0
1
1
2
0
1
0
2
2
0
1
1
0
0
0
1
1
2
0
1
0
0
1
0
1
1
0
1
0
1
1
0
1
1
1
1
1
4
0
1
0
2
1
1
1
0
2
1
0
1
1
1
1
1
2
1
1
1
2
1
1
2
2
0
0
1
1
1
2
0
0
1
2
0
2
2
1
1
0
2
1
1
0
0
0
1
0
1
1
0
0
2
2
1
0
2
1
2
1
0
2
1
0
2
0
1
1
1
1
1
2
0
2
1
1
1
0
0
2
2
0
1
1
1
1
1
3
1
2
1
1
1
0
1
1
1
1
2
2
1
0
1
0
0
0
1
1
0
1
1
1
2
2
3
1
2
2
0
1
0
0
1
0
4
0
0
1
0
0
0
2
1
0
1
0
2
0
0
1
0
0
1
2
1
2
0
1
0
1
1
0
1
1
1
0
1
1
2
0
0
1
1
1
1
0
1
2
0
1
2
0
2
1
0
0
2
1
2
1
2
1
2
0
1
1
0
0
1
1
1
1
0
2
0
2
1
2
0
1
1
1
2
1
1
0
2
1
0
3
0
1
0
0
1
0
1
0
1
0
1
0
0
1
1
1
2
1
1
0
0
1
0
0
1
1
1
3
0
1
2
0
1
1
0
0
1
1
0
2
2
0
1
1
1
1
1
1
2
1
0
1
2
1
0
2
0
2
1
1
1
2
2
0
2
1
1
2
2
0
0
1
0
2
2
1
0
0
1
1
0
0
1
1
1
1
2
2
0
1
2
0
1
0
0
1
2
1
1
0
1
0
2
1
2
1
0
2
1
0
2
1
1
2
0
1
1
1
1
1
1
0
3
1
1
1
1
1
2
1
1
1
0
1
1
0
0
0
1
1
1
0
1
1
1
0
2
0
1
0
1
1
0
0
0
0
0
0
1
1
0
1
0
1
0
1
0
2
1
1
0
2
2
0
0
1
2
2
0
1
1
1
2
1
2
2
0
0
1
0
2
0
0
0
1
0
3
0
0
1
0
1
0
1
0
0
0
1
0
2
0
2
0
0
0
0
1
0
0
1
2
1
2
0
2
1
0
0
1
2
1
2
1
1
1
0
1
1
1
3
0
1
1
1
1
0
2
2
0
1
2
1
1
0
1
1
1
0
2
1
1
2
2
1
0
1
2
1
1
0
1
1
0
0
2
0
1
1
1
1
0
1
1
2
1
1
0
0
0
1
1
2
1
1
1
1
0
0
1
1
1
1
2
1
2
1
1
2
1
0
1
0
1
1
0
0
2
0
2
2
1
1
0
1
2
1
1
1
1
1
1
1
0
1
1
0
1
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
0
0
1
1
1
2
1
1
0
1
0
0
0
1
1
1
1
0
1
1
1
1
1
1
0
1
2
1
1
0
0
0
0
1
1
1
0
0
1
0
2
2
1
2
1
2
2
0
0
1
0
1
0
1
1
1
0
0
2
2
1
1
0
1
1
2
1
1
1
2
0
2
2
0
1
0
2
0
2
0
2
1
1
2
3
2
1
0
1
0
2
0
1
0
1
0
1
1
1
0
1
1
2
0
1
1
2
1
0
2
1
0
1
2
2
1
2
1
0
1
1
1
1
0
1
1
0
1
1
1
4
1
0
1
0
0
0
1
2
1
1
1
0
1
0
0
2
2
0
0
1
0
2
2
2
2
0
1
1
1
0
1
2
1
1
1
2
0
2
2
0
1
2
1
1
0
1
1
0
1
0
0
0
0
0
0
1
0
1
0
0
2
1
1
3
0
2
1
0
0
1
0
2
1
1
2
1
2
0
0
0
1
2
0
2
1
1
1
0
1
0
1
2
1
1
1
1
0
2
0
1
0
1
1
2
1
1
2
0
1
1
2
0
2
1
1
1
1
1
0
1
1
1
2
2
0
0
2
0
0
1
1
1
2
0
1
2
1
0
2
0
1
1
1
0
2
1
0
0
1
0
1
0
1
1
0
0
2
1
2
3
2
1
1
1
2
0
0
1
2
0
0
2
0
2
0
0
1
2
0
2
1
1
2
0
1
2
0
0
1
1
2
1
0
0
2
2
1
1
0
1
1
2
1
0
1
0
2
2
1
2
1
1
1
1
1
1
0
1
1
4
0
0
1
2
0
1
0
0
1
1
1
0
0
0
0
0
3
0
1
1
0
1
1
1
2
1
1
0
2
0
0
2
1
1
1
0
0
0
2
1
1
1
1
1
0
1
3
2
1
2
1
2
2
1
1
0
0
4
0
2
0
0
0
1
2
2
2
0
1
1
1
0
0
0
2
1
0
1
0
1
0
1
1
0
1
0
0
1
0
1
1
2
0
2
1
2
1
1
1
1
2
0
1
0
2
1
2
2
2
1
1
0
0
0
1
1
0
0
1
0
1
0
0
1
0
1
1
1
0
0
1
1
1
1
0
1
0
1
1
2
1
2
1
2
1
2
1
2
1
2
0
1
1
0
2
0
1
2
1
0
2
1
0
0
1
1
2
1
2
3
0
1
1
1
1
0
1
1
0
1
0
1
0
2
1
1
1
1
1
0
1
1
1
1
2
1
2
2
1
0
1
1
1
0
1
0
1
1
2
1
0
1
1
1
2
2
2
1
0
1
0
0
2
1
0
1
2
0
1
2
0
1
2
1
1
0
0
2
1
1
1
0
0
3
1
0
1
0
1
0
0
1
0
1
1
1
1
0
2
1
1
1
0
2
0
0
0
0
1
1
2
0
0
0
0
0
0
1
0
1
1
2
0
2
1
2
0
1
0
1
0
1
1
1
1
2
1
0
1
2
2
0
1
0
2
0
1
0
1
1
2
1
1
2
1
1
0
5
0
0
1
2
2
2
1
2
1
1
1
0
1
1
1
2
1
1
0
2
0
1
2
1
0
1
0
0
0
1
1
1
2
0
1
2
2
1
1
1
2
0
0
1
1
0
2
2
0
2
0
0
2
1
1
1
0
1
0
0
1
1
0
2
1
2
2
2
2
2
0
1
0
0
1
1
0
0
0
1
1
1
0
2
1
1
2
2
2
0
2
1
0
0
1
0
0
0
3
1
0
1
1
2
1
1
0
1
1
2
2
2
1
1
2
2
1
1
1
0
1
1
1
1
2
2
1
0
2
0
2
0
1
0
0
2
0
1
1
0
1
1
2
2
0
1
2
2
1
1
2
1
0
2
0
0
2
1
1
1
2
0
1
1
1
7
1
0
0
0
0
0
2
2
2
2
1
1
0
0
0
1
0
1
1
1
0
1
0
1
2
1
1
1
0
1
1
0
1
2
1
1
2
1
1
2
0
1
0
1
0
0
1
1
2
1
1
0
0
0
2
0
2
1
0
0
2
1
1
0
1
0
2
1
0
1
1
0
1
1
1
1
0
0
0
2
2
1
2
0
3
1
1
1
2
1
2
0
2
2
1
1
2
0
0
2
1
1
2
0
0
1
1
1
1
1
1
0
2
1
1
1
0
0
1
1
1
2
1
0
1
1
1
0
2
1
1
0
1
2
2
0
1
1
0
2
0
1
1
1
0
1
1
0
5
0
1
1
0
2
7
1
2
2
1
1
1
2
0
1
1
2
0
2
1
2
1
2
1
2
1
1
1
0
1
0
0
1
1
0
0
0
0
1
1
0
0
0
2
2
0
1
0
1
1
1
0
1
0
1
1
0
0
0
0
1
1
2
2
1
1
2
1
0
1
1
2
2
0
0
1
1
1
1
2
2
1
1
2
1
1
1
1
2
1
0
1
2
0
0
2
1
0
0
0
0
2
1
1
2
2
1
1
2
1
0
1
2
2
2
1
1
3
0
0
2
1
1
2
1
1
1
0
0
0
1
0
1
0
2
1
0
1
2
0
1
0
1
1
1
1
0
0
0
2
0
2
0
1
2
2
2
1
0
1
0
1
1
1
1
1
1
2
1
2
2
2
2
2
0
1
1
0
2
0
2
2
2
1
0
0
0
2
1
1
3
1
0
2
0
0
1
1
1
0
2
1
1
2
1
1
0
2
1
1
1
2
1
0
2
0
0
1
0
1
1
1
1
0
1
2
1
0
1
1
0
2
0
0
0
1
1
2
1
0
0
1
1
0
2
0
2
0
1
0
2
1
1
1
0
0
0
1
1
0
2
1
1
2
1
1
0
0
0
2
1
1
1
1
0
1
1
0
1
1
1
1
0
1
1
0
0
1
1
0
1
1
1
2
0
2
2
0
1
2
1
0
1
2
1
1
1
1
1
0
1
1
0
0
2
1
1
2
0
0
2
1
2
1
1
1
2
1
1
2
1
0
2
2
2
1
0
0
5
0
0
2
1
1
0
0
1
1
0
2
0
0
2
0
0
2
1
1
1
1
1
2
1
1
1
1
0
1
2
1
1
1
1
1
0
2
1
1
0
0
1
1
4
2
1
1
1
2
2
1
0
1
0
0
1
3
1
1
0
2
1
1
1
2
1
1
1
1
0
2
0
2
1
1
1
1
3
2
1
0
1
0
1
1
0
1
0
0
1
2
1
0
2
0
1
1
1
1
0
2
0
0
2
2
0
1
0
1
0
2
4
1
1
2
1
0
1
1
0
1
1
1
1
1
0
0
0
2
2
0
0
1
1
1
1
1
1
0
1
1
0
2
0
2
0
1
0
1
0
0
1
1
2
0
1
1
2
1
2
0
1
0
1
1
0
2
0
1
0
1
0
2
1
1
0
0
0
2
0
1
1
1
1
1
1
0
0
0
0
1
1
1
0
1
1
1
4
1
0
1
1
0
2
0
2
2
0
1
0
2
1
1
2
0
1
1
0
0
1
1
1
0
2
1
1
1
2
1
1
1
1
0
1
1
0
2
1
1
1
0
1
1
2
0
1
0
2
2
1
1
1
1
1
2
1
0
0
1
2
1
2
0
0
1
2
1
1
0
1
1
1
1
2
1
1
1
1
2
1
1
2
0
2
2
2
1
2
1
0
2
0
1
2
0
1
2
2
1
0
0
1
1
0
1
2
2
1
2
0
1
2
1
0
1
1
0
1
1
1
1
1
2
0
2
0
1
2
0
1
1
1
1
0
0
2
1
0
2
1
0
2
1
2
1
0
0
1
1
3
1
1
1
2
1
0
0
1
0
1
2
1
2
2
0
1
1
2
3
0
1
2
1
0
3
1
0
1
1
0
0
1
3
1
0
1
0
2
0
0
1
0
0
2
0
1
0
1
2
1
2
2
0
1
2
2
0
0
1
0
1
0
0
0
2
0
1
3
0
2
1
1
1
1
0
0
1
2
0
1
1
0
0
2
2
0
0
1
0
1
0
0
1
0
0
0
1
1
0
0
1
0
2
1
3
1
1
1
1
2
0
0
2
1
1
1
2
0
1
1
0
1
1
1
0
0
2
1
0
2
0
1
1
0
1
0
1
2
1
2
1
0
1
0
2
0
1
0
1
1
1
2
1
0
1
0
2
1
1
1
0
1
1
1
1
0
2
1
2
2
1
1
0
1
1
2
0
2
0
0
1
1
1
1
0
1
1
1
2
1
1
2
2
1
1
1
0
1
0
1
2
2
0
2
1
1
0
1
1
0
2
0
1
1
2
1
2
0
1
1
1
0
0
0
2
1
2
1
1
1
0
0
0
1
0
2
1
0
1
1
1
0
0
0
0
3
0
0
0
1
1
0
1
2
1
1
1
1
2
0
1
1
1
0
1
2
1
1
2
1
1
0
1
0
1
1
0
1
1
1
2
2
1
0
2
1
0
1
1
1
1
2
0
0
2
0
0
1
2
0
0
0
0
1
2
1
1
1
0
1
0
2
1
1
2
3
1
1
0
0
1
0
1
1
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
1
5
0
1
1
1
2
1
1
2
2
0
1
0
1
1
1
0
0
2
1
0
0
1
2
0
1
2
2
0
2
1
2
2
0
1
1
0
1
0
1
1
0
1
1
2
1
1
1
2
1
1
1
0
2
1
2
1
2
0
1
0
1
1
0
0
1
1
1
0
1
0
2
1
1
1
0
1
2
0
2
2
0
0
0
1
1
2
0
2
2
1
1
1
2
2
0
0
1
2
3
1
0
0
2
1
1
2
1
0
0
2
1
1
2
0
1
3
0
0
2
2
1
1
1
1
0
0
0
2
0
1
1
2
1
1
2
1
1
0
3
0
0
1
0
1
1
1
0
0
0
1
1
0
1
1
1
0
1
2
0
2
2
1
0
2
0
1
1
1
2
1
1
1
1
1
1
1
0
1
1
1
2
0
1
1
0
0
1
1
1
2
1
8
0
1
1
2
1
2
2
2
0
2
0
1
1
1
0
1
1
0
0
0
1
2
1
0
2
0
0
0
0
1
0
2
1
2
1
2
1
2
0
2
1
0
2
2
1
1
1
2
0
1
2
2
1
1
1
0
0
0
1
1
0
0
1
1
0
1
2
0
0
0
0
1
2
1
1
1
1
2
1
0
1
1
1
1
0
0
2
0
1
0
0
1
1
1
0
1
1
1
1
1
1
2
0
1
2
2
2
0
1
1
1
1
1
1
0
1
1
0
1
0
1
0
1
0
1
1
2
6
0
1
1
1
1
0
0
2
1
1
2
2
0
2
1
0
2
0
1
0
1
2
1
0
0
1
0
1
1
1
1
1
1
1
1
2
2
0
1
3
2
1
2
0
0
1
1
1
1
0
0
1
2
2
3
1
1
1
2
2
0
2
1
0
1
1
0
1
2
1
0
1
0
2
2
2
2
0
2
0
1
2
0
1
1
0
1
0
0
0
1
0
1
2
2
1
1
2
0
0
1
1
1
2
0
2
1
1
2
1
0
1
2
1
1
2
2
1
1
1
1
1
0
0
1
1
1
2
1
0
2
0
0
0
1
2
1
1
0
1
2
2
2
0
0
1
1
1
1
1
1
1
0
2
0
2
1
0
1
0
2
1
1
1
0
2
1
1
2
0
1
0
0
0
1
1
0
0
2
0
0
2
1
1
1
1
1
1
0
0
0
2
1
1
1
0
0
1
0
1
0
5
1
1
1
1
1
0
2
0
2
1
1
1
0
1
2
1
2
2
2
1
1
1
2
0
1
1
0
1
1
1
1
0
2
2
0
0
2
0
2
1
0
0
1
1
0
1
1
2
1
1
2
0
2
1
1
0
1
1
1
1
1
1
2
0
0
1
0
2
2
1
1
1
0
1
1
2
2
0
1
1
1
0
2
1
1
1
1
2
1
1
0
2
1
1
0
0
1
1
2
1
1
1
0
1
2
2
1
1
1
2
1
2
1
1
1
1
1
0
0
0
1
2
1
1
0
0
1
2
2
1
2
1
0
1
1
1
1
1
1
1
0
0
2
1
0
1
0
1
0
0
2
0
2
0
1
1
1
2
2
2
1
1
2
2
0
0
0
0
0
2
1
0
1
2
2
1
0
1
1
1
0
2
1
1
1
1
1
0
1
0
1
2
0
0
0
2
2
1
1
2
1
1
0
1
1
0
2
0
2
0
1
0
2
1
1
1
1
1
1
1
2
1
2
1
2
0
0
1
1
0
1
1
2
0
1
0
3
0
1
2
2
0
1
0
0
1
1
0
2
3
0
1
1
0
1
1
0
0
1
0
1
1
0
1
1
3
1
1
1
1
1
2
1
2
0
0
1
0
0
1
0
1
0
1
0
1
2
1
4
0
1
1
1
2
2
1
0
1
0
2
1
1
1
1
1
0
2
2
0
0
2
1
2
1
0
2
2
0
2
0
2
2
0
1
0
0
2
0
1
2
0
0
1
1
2
1
1
0
1
0
0
2
2
0
1
0
2
0
1
1
2
0
2
1
0
0
1
1
2
2
1
1
0
2
1
2
1
1
2
1
1
4
1
2
1
1
0
0
1
2
1
2
1
2
2
2
0
2
1
0
0
1
2
1
2
1
0
0
1
0
2
2
1
1
0
1
1
2
1
2
1
1
0
0
0
1
0
2
3
1
1
1
1
1
2
1
2
1
1
2
0
0
1
0
1
2
1
1
1
0
2
0
1
2
2
2
1
1
0
2
0
0
1
1
1
0
1
1
1
0
1
0
1
0
1
1
0
1
0
0
2
1
1
1
2
2
0
0
1
1
1
2
1
2
1
1
0
1
2
1
0
0
0
1
2
2
0
0
2
0
0
1
1
1
2
0
0
2
1
2
2
1
2
1
1
0
2
2
1
2
1
1
1
0
1
1
0
0
1
1
0
1
2
1
1
1
1
0
2
2
1
2
2
1
1
1
1
1
1
1
1
1
0
0
0
1
0
2
1
1
1
1
1
1
1
1
2
2
0
1
1
1
0
2
2
2
0
0
0
1
2
1
1
0
1
1
0
1
2
1
1
2
2
1
2
1
2
0
0
0
2
1
2
0
1
2
1
1
1
3
1
1
1
1
2
0
2
0
4
1
0
2
1
2
2
1
1
1
1
1
0
2
2
1
1
1
0
2
1
1
1
1
1
0
0
1
0
0
1
1
1
1
1
1
1
1
0
1
0
0
0
0
1
1
0
1
2
1
0
2
1
1
1
1
2
1
2
1
1
0
1
1
2
1
1
3
0
1
1
2
0
1
2
1
1
1
1
1
1
1
0
0
2
0
1
1
0
0
1
1
0
0
2
0
0
2
1
1
2
0
0
0
2
1
2
1
0
2
2
0
1
0
2
2
1
0
0
0
2
2
2
1
0
0
2
0
2
0
3
1
0
2
0
2
0
1
2
2
1
0
1
0
1
2
3
2
2
0
2
1
0
0
1
1
0
0
1
1
0
1
1
2
1
1
1
0
2
2
2
1
0
0
1
1
2
2
1
0
1
0
3
0
0
1
0
1
3
1
1
1
3
2
2
1
1
1
0
1
0
1
1
2
0
1
1
1
1
1
1
0
1
1
2
0
1
0
0
0
1
0
0
1
0
2
2
2
0
1
1
2
1
1
0
1
1
1
1
0
0
0
2
1
0
1
1
2
0
0
0
0
0
0
1
2
2
0
1
1
2
1
0
0
0
1
0
1
0
0
0
2
0
3
0
2
1
2
1
1
1
0
1
0
0
1
2
2
1
0
1
1
0
1
1
1
1
1
1
2
0
2
1
0
0
1
1
1
1
1
0
1
1
1
1
1
0
1
0
1
1
0
0
1
0
1
1
0
1
1
1
0
0
1
1
2
1
2
0
1
1
1
1
1
2
1
2
1
1
0
1
1
2
0
0
2
2
1
1
3
0
1
1
0
1
1
1
1
1
1
1
1
2
1
2
1
1
2
0
0
1
0
0
1
1
1
0
1
0
1
0
0
1
0
1
0
1
1
2
1
1
1
2
2
1
1
0
1
0
1
0
1
1
1
2
0
2
2
1
1
1
1
1
1
1
1
0
1
1
2
0
0
1
0
1
2
0
2
0
1
0
0
1
1
1
2
1
0
1
0
1
2
2
1
1
2
1
0
1
2
1
0
1
2
1
1
1
2
1
0
1
1
2
1
1
1
0
0
0
0
2
2
2
2
1
0
0
1
1
1
2
1
2
0
2
0
1
1
1
0
0
1
1
1
1
0
1
2
2
2
0
1
2
1
1
1
0
1
1
0
1
0
0
0
2
1
1
3
1
0
1
2
2
1
2
0
2
1
0
1
1
0
1
1
0
1
0
2
0
1
1
2
0
1
5
1
0
0
1
2
2
2
2
1
1
1
1
2
1
2
2
0
1
0
0
0
1
2
1
0
2
1
0
2
0
2
1
1
1
1
1
1
0
2
0
0
2
0
1
0
1
0
2
0
0
1
0
1
1
2
0
1
1
0
1
2
2
2
1
0
0
1
0
0
0
1
0
1
2
1
1
1
0
1
2
0
1
1
2
1
2
0
1
2
1
0
5
1
2
2
0
2
1
1
0
1
1
1
1
1
2
1
1
2
0
0
1
0
1
1
1
1
1
2
2
1
1
2
1
1
1
1
2
0
0
1
2
0
1
2
4
0
1
1
1
0
0
1
1
1
0
1
1
2
1
2
0
1
0
2
1
1
2
2
0
1
2
1
1
2
2
2
2
1
0
0
1
0
0
1
1
0
0
1
1
0
0
1
1
1
0
2
1
0
2
2
1
0
0
1
1
1
2
1
2
0
1
0
0
1
0
2
3
1
0
1
2
2
1
1
1
1
1
1
2
2
2
0
0
0
0
1
2
1
1
1
1
1
1
1
1
2
0
1
1
2
1
0
0
1
1
2
2
0
0
0
2
1
2
2
1
1
1
2
1
2
1
0
2
2
1
1
1
2
1
1
0
0
1
1
1
1
1
0
0
1
0
2
2
2
0
1
2
0
1
2
2
1
1
0
1
0
0
1
2
1
2
2
1
2
1
1
0
1
1
0
1
1
2
1
2
0
2
1
2
1
1
1
0
0
1
0
1
1
0
0
0
1
0
0
1
1
2
0
0
1
1
0
1
1
1
1
1
1
1
1
1
1
1
2
0
1
1
1
1
2
0
1
0
0
0
1
1
0
0
0
2
0
1
0
1
1
0
1
1
2
2
4
0
0
2
1
2
0
0
2
0
1
2
1
0
1
2
0
2
0
1
0
0
2
2
1
0
1
2
1
0
1
0
2
1
2
1
1
1
1
1
0
0
2
2
1
1
2
0
1
0
2
2
2
2
0
1
1
0
1
1
0
0
0
1
0
1
2
1
2
1
1
1
0
1
1
1
1
1
1
0
2
0
1
1
0
0
0
1
1
1
0
0
1
2
1
0
1
1
0
0
1
0
2
1
2
2
0
1
1
0
0
2
1
1
0
0
1
0
1
2
1
1
1
1
0
1
3
0
1
1
1
0
1
1
2
0
2
0
1
2
2
1
1
1
1
1
0
0
2
1
2
1
1
1
1
2
1
2
1
0
0
2
1
1
0
0
1
0
1
1
2
0
1
1
1
1
1
0
1
1
0
4
2
0
2
1
1
1
2
0
0
0
1
1
1
2
1
2
1
2
2
1
2
0
2
0
0
3
0
1
1
0
1
0
0
0
2
2
0
1
1
0
0
1
2
2
0
2
1
2
1
0
1
0
0
1
1
2
2
0
2
1
2
1
0
0
0
1
0
0
1
1
1
1
1
2
1
0
0
1
0
0
1
2
1
1
1
0
2
0
1
1
2
0
1
0
0
1
2
2
0
1
1
0
2
0
2
1
1
1
2
2
2
1
2
0
0
1
0
1
1
0
2
0
1
1
1
0
0
1
1
2
0
0
3
1
0
2
1
1
0
0
1
1
0
1
0
2
0
2
0
1
1
3
0
1
1
0
0
2
0
0
1
2
2
0
1
0
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
0
2
1
1
1
1
1
2
2
1
1
0
2
2
0
1
1
2
1
1
0
2
3
2
1
2
0
0
2
2
1
1
1
1
1
0
1
0
1
1
0
1
0
1
0
0
0
1
1
3
1
1
1
2
2
1
2
0
2
1
0
1
0
1
1
1
0
0
2
1
0
0
1
1
1
2
0
1
0
1
1
0
1
1
0
2
1
1
1
1
0
2
0
0
1
0
1
1
2
0
0
0
1
0
1
0
1
1
1
0
1
1
2
1
0
0
0
2
0
1
2
0
0
3
0
1
1
2
1
1
5
0
1
2
1
1
2
0
3
1
2
1
1
1
1
0
2
1
1
1
1
1
2
2
0
1
1
1
0
2
0
1
1
0
1
0
0
2
1
2
2
1
0
3
1
2
2
2
0
1
2
1
1
8
1
1
1
0
0
1
1
2
1
1
1
1
1
2
1
1
1
1
0
2
0
1
1
1
2
2
1
0
1
2
1
0
0
0
0
3
2
4
0
2
1
1
1
1
2
0
1
0
0
2
2
1
1
1
0
1
0
2
2
1
0
2
1
1
1
1
1
0
1
1
0
0
2
0
2
1
1
1
0
1
0
3
0
1
2
1
1
0
1
1
0
2
1
1
2
2
2
0
0
3
1
2
2
1
3
1
1
1
1
2
2
1
0
1
1
2
0
1
2
2
1
1
1
1
0
2
2
1
2
0
2
1
0
1
1
1
2
2
1
2
1
2
2
2
0
0
0
0
1
0
1
1
0
2
2
0
2
2
1
0
1
1
2
0
1
2
1
1
1
0
1
2
0
0
2
0
1
3
1
2
1
1
1
0
1
1
2
1
1
0
1
1
1
0
1
0
0
0
0
1
1
0
0
1
0
1
0
1
1
1
1
1
0
1
0
2
1
1
1
1
1
0
0
1
0
4
1
0
1
0
0
1
2
0
1
1
1
1
0
1
2
1
1
0
1
2
1
0
0
1
2
0
2
1
1
1
0
0
0
0
1
1
0
1
1
2
1
1
0
2
1
1
1
0
2
0
1
0
1
1
1
3
1
0
2
0
2
0
1
2
0
3
0
1
0
1
0
1
2
1
2
2
1
0
1
2
1
2
1
1
1
1
0
2
2
1
2
1
1
0
1
0
0
1
2
1
2
1
1
1
0
0
1
2
2
1
2
1
0
2
2
0
1
0
1
2
1
2
0
1
0
1
0
0
2
2
0
1
2
1
0
1
1
2
2
0
0
1
3
1
1
0
1
1
0
0
1
2
1
1
0
1
0
2
1
2
1
2
0
0
1
2
1
2
2
0
0
2
0
1
1
2
1
2
1
2
0
0
2
0
0
1
0
2
2
0
0
1
2
0
0
0
2
1
1
1
1
1
1
0
2
0
1
0
1
1
1
2
0
2
1
2
1
0
0
2
1
2
1
0
0
1
1
1
2
1
0
1
1
0
1
0
1
1
1
3
1
2
1
1
1
0
2
0
1
3
0
1
1
0
0
0
0
0
2
0
2
0
0
0
2
1
0
0
0
0
0
1
1
1
0
1
0
1
1
0
2
1
0
0
1
0
1
3
1
0
0
1
1
1
2
1
0
1
0
1
4
3
2
1
1
1
0
1
2
0
0
1
0
1
1
1
1
1
1
0
1
2
1
1
1
2
1
2
1
0
1
1
3
0
0
1
1
0
1
0
1
1
1
0
2
1
1
1
2
2
2
2
0
1
1
2
0
1
1
2
1
2
1
0
1
2
2
0
1
1
1
1
2
0
0
2
0
0
1
1
0
1
1
1
2
0
3
0
0
2
0
1
1
0
3
1
2
0
0
1
0
1
0
2
0
1
0
1
1
0
1
1
0
1
0
1
1
0
2
2
0
0
0
1
1
1
1
1
2
2
0
1
0
1
0
1
1
1
0
1
0
2
1
1
1
1
1
0
2
1
0
1
2
1
1
2
2
0
2
2
0
1
1
1
2
1
0
1
0
0
2
0
1
0
2
0
1
0
0
0
2
1
1
0
0
0
2
2
0
1
1
0
1
2
3
0
1
1
2
0
2
2
1
2
1
0
1
1
1
2
1
2
0
1
1
2
1
1
2
1
1
1
0
1
1
1
1
1
1
0
1
1
0
1
1
2
1
1
1
1
0
2
1
0
0
1
0
0
0
0
1
0
1
0
0
1
1
1
2
1
1
1
0
2
2
1
2
0
1
1
1
0
3
1
1
1
0
0
0
0
1
3
0
1
1
1
0
1
0
0
0
1
1
1
0
2
0
1
1
1
2
1
2
1
0
2
2
2
2
1
1
0
1
1
0
1
1
1
0
1
2
0
1
1
2
0
1
1
0
0
2
1
2
1
1
1
1
1
1
1
0
0
1
1
1
1
3
0
1
0
1
2
0
0
0
1
1
1
2
0
1
2
0
0
1
1
1
0
0
1
1
0
2
0
2
1
1
2
1
0
1
0
1
2
1
0
2
0
1
1
1
1
2
1
0
2
0
1
1
1
1
1
1
1
0
2
0
0
0
1
1
0
1
1
1
1
1
2
1
3
1
1
0
4
1
1
1
1
0
1
1
1
1
2
2
0
2
2
1
2
1
0
1
4
1
1
0
1
1
1
0
1
0
0
0
0
2
1
1
1
1
2
1
2
2
1
0
1
1
0
1
1
1
2
0
1
1
2
1
1
0
1
1
0
2
0
0
2
1
1
1
1
2
1
0
2
2
2
1
1
0
1
1
0
1
0
0
0
1
1
0
0
0
0
2
0
2
1
2
1
1
1
1
1
0
0
1
1
0
0
1
1
1
0
1
2
1
1
1
1
1
1
2
2
2
2
0
0
1
1
1
2
1
1
2
1
2
0
0
1
1
1
1
1
2
1
1
2
0
1
0
1
0
0
1
1
1
1
1
2
0
1
0
1
0
1
1
1
1
1
1
2
0
2
0
0
1
1
0
2
1
2
3
0
1
1
1
2
1
1
1
2
0
3
1
3
0
0
0
0
1
1
1
1
2
2
2
1
1
0
0
2
2
2
1
1
1
1
1
0
0
0
1
1
2
1
1
0
0
2
2
2
1
2
1
1
0
1
1
1
0
1
0
2
1
1
1
1
0
0
0
0
1
0
1
0
3
2
1
1
1
0
0
1
2
0
2
1
1
1
2
1
2
1
0
1
0
2
0
1
1
0
2
0
2
2
1
0
0
2
1
0
2
2
0
0
0
2
1
1
1
1
2
1
2
2
0
1
0
1
1
0
0
2
1
1
1
1
1
2
2
1
0
0
1
2
0
1
1
1
0
0
0
1
1
0
2
0
0
1
1
0
1
1
1
0
0
2
0
0
0
2
1
0
0
2
0
2
2
1
0
2
3
2
2
1
0
0
2
1
0
1
1
2
0
0
2
1
1
1
1
2
1
0
1
1
2
0
1
1
1
1
0
0
2
0
1
0
0
0
1
2
0
2
2
0
0
1
2
2
2
0
1
2
1
2
1
1
0
2
1
1
0
2
0
1
1
2
0
0
0
2
2
1
2
1
1
2
1
0
0
2
0
1
1
1
2
1
1
1
0
2
0
0
0
1
0
1
1
2
2
1
2
0
1
0
1
2
2
1
2
0
0
3
1
1
1
0
0
1
1
1
2
1
1
1
0
2
0
1
0
1
2
0
2
2
1
1
1
1
0
0
0
0
1
2
1
2
1
1
1
0
1
0
0
1
1
2
1
1
1
0
1
0
1
1
2
0
1
1
1
1
2
1
0
3
0
1
2
1
1
0
0
2
1
0
2
1
2
1
1
1
1
0
1
2
2
0
1
2
2
1
1
1
1
0
1
2
0
2
0
0
2
1
0
0
2
0
1
0
0
1
1
1
1
1
1
1
1
1
1
0
1
2
0
0
1
0
1
2
1
3
1
1
0
0
0
1
1
1
2
1
1
0
1
0
1
1
0
0
1
2
0
0
2
2
1
1
1
0
0
1
1
2
0
1
1
1
1
0
1
0
1
0
0
2
0
1
2
1
1
2
0
1
1
2
0
0
1
1
1
0
1
1
0
0
1
1
2
2
1
1
0
1
1
0
1
0
1
0
0
2
2
1
2
2
1
0
2
1
2
1
1
0
1
1
1
0
0
2
1
1
0
2
1
0
0
1
1
0
0
1
0
0
1
0
2
2
1
1
0
0
1
2
1
4
2
1
0
1
1
1
0
1
0
0
2
0
1
1
2
1
0
0
0
1
2
2
1
2
2
1
0
1
0
1
1
1
1
1
3
0
1
1
1
0
0
2
2
1
1
2
0
0
0
0
0
2
0
1
1
1
1
2
2
1
2
0
0
1
0
1
1
1
1
0
2
1
0
2
0
1
1
1
0
1
0
1
0
0
1
0
1
0
0
1
2
2
2
0
2
0
1
0
2
1
1
1
2
1
1
2
2
1
2
1
1
1
2
2
1
0
0
1
0
0
1
1
2
0
0
1
1
1
1
0
1
1
1
1
2
2
0
1
1
1
0
1
0
1
1
2
0
1
1
0
0
1
0
1
0
1
1
0
1
2
1
0
1
1
1
1
2
1
2
1
1
2
1
0
0
1
1
1
0
2
1
1
1
2
0
0
0
0
1
1
2
1
1
1
1
1
1
0
2
1
1
0
1
1
1
1
1
4
1
1
1
0
1
2
2
1
1
0
1
1
0
1
2
1
0
1
0
2
1
1
0
0
1
0
1
2
2
1
2
2
1
1
1
1
1
1
1
0
1
1
1
2
1
2
1
0
1
0
1
0
1
0
1
0
1
2
1
1
2
2
0
0
0
1
0
1
0
1
1
0
0
1
2
0
3
0
1
0
1
1
2
1
0
1
2
2
2
3
1
0
2
1
0
1
0
2
1
0
0
0
1
0
2
2
0
1
1
2
1
2
0
1
0
0
1
0
1
2
2
1
0
1
1
1
1
2
1
2
0
2
2
1
2
1
0
1
1
2
1
1
2
1
2
2
1
0
1
1
0
0
2
1
0
1
2
0
1
0
1
0
1
1
0
0
1
0
0
1
1
1
0
1
1
2
0
2
1
1
0
1
0
1
2
2
0
2
2
0
1
2
2
3
0
3
2
0
1
0
1
1
0
2
1
0
1
1
1
2
2
0
2
2
1
0
1
2
1
1
0
2
1
2
1
0
3
0
1
1
2
0
2
1
0
1
0
0
1
0
0
2
1
2
1
1
2
1
1
2
0
0
2
2
1
1
1
1
1
1
2
2
1
2
1
1
1
1
0
2
1
2
1
1
0
1
1
1
0
0
2
1
2
1
2
1
1
1
1
3
2
1
2
3
1
0
0
1
0
1
1
1
1
2
1
0
0
0
1
2
1
0
0
0
0
0
0
1
2
0
1
0
2
1
1
0
1
1
1
1
0
2
1
1
2
0
0
2
1
2
1
1
2
1
1
0
1
1
1
0
1
2
1
2
1
0
0
1
1
1
1
1
0
0
1
2
1
0
1
1
0
0
0
0
1
1
2
2
0
0
1
1
1
0
1
1
1
1
0
2
1
2
1
0
1
1
1
0
1
1
1
2
0
2
0
0
1
2
1
1
2
1
1
2
1
1
0
0
1
1
0
1
1
0
2
0
0
0
1
2
1
0
0
1
1
0
1
2
0
1
1
0
2
1
1
3
1
1
1
1
2
0
2
1
0
0
1
0
1
0
1
2
0
1
0
1
2
1
0
1
0
1
1
1
0
1
0
0
2
1
0
1
1
0
1
0
0
2
1
1
1
0
2
2
2
0
1
0
1
0
2
2
0
2
1
2
0
1
1
0
0
1
1
0
2
1
0
0
0
1
0
1
0
1
2
2
2
1
1
1
1
2
0
1
1
1
0
2
2
1
1
0
1
1
1
0
2
1
1
0
2
2
3
2
2
0
2
1
1
1
1
1
1
1
1
1
0
2
1
1
1
1
1
1
0
2
0
0
2
0
0
2
1
2
1
2
0
0
0
0
1
1
1
1
1
2
2
0
0
1
2
1
1
2
1
1
0
0
0
1
2
0
2
1
2
0
0
1
0
1
1
2
2
1
2
0
1
0
1
1
1
1
0
1
0
1
1
3
1
1
0
0
1
2
0
1
0
0
1
2
3
1
1
2
1
2
1
0
1
1
1
0
1
0
0
1
1
1
1
0
1
2
0
1
2
1
1
1
2
2
1
2
2
0
2
0
0
1
1
1
1
0
0
1
1
0
1
1
1
0
0
1
2
1
1
0
0
1
1
2
2
2
0
2
1
1
1
1
2
1
0
2
1
2
0
1
2
0
1
1
0
1
2
2
0
0
1
0
0
2
1
1
1
0
2
2
1
1
1
1
2
1
1
1
1
2
1
2
0
2
2
1
0
2
1
2
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
0
1
0
1
1
2
1
1
1
0
1
1
0
1
1
0
1
2
1
2
0
1
0
1
0
0
1
0
1
3
1
2
0
1
2
2
0
1
0
0
1
0
1
1
1
0
1
0
1
2
1
1
1
2
1
1
0
1
0
1
2
2
0
2
0
1
1
0
1
2
2
2
1
1
1
1
0
0
1
2
2
2
1
2
1
0
1
1
2
1
1
0
0
1
2
1
2
0
1
1
0
1
1
0
1
1
2
2
1
1
0
0
2
1
1
1
0
1
1
1
1
1
0
0
0
0
1
0
2
1
2
1
1
0
1
1
1
1
1
0
0
0
0
1
1
1
0
1
1
1
0
1
2
1
1
1
1
1
1
1
0
1
0
1
1
0
0
1
1
1
1
1
1
0
2
0
2
0
0
0
0
2
2
0
1
1
0
1
0
1
2
1
0
0
1
0
0
0
1
1
1
0
0
0
2
1
0
1
0
0
0
1
1
0
0
1
1
2
0
0
1
3
1
1
1
3
2
1
0
2
2
0
0
1
0
1
1
1
0
0
0
0
0
2
1
1
0
1
0
1
0
2
2
1
0
2
1
1
2
0
1
2
0
1
0
1
1
2
1
0
2
1
1
0
0
0
1
0
0
2
2
1
1
2
0
1
2
0
2
1
2
0
0
1
2
1
2
1
1
1
2
0
0
1
0
1
1
1
0
0
0
0
2
0
2
1
1
2
3
1
1
2
1
1
1
1
1
1
2
2
1
3
2
2
2
0
1
1
2
2
0
1
2
1
0
0
1
1
1
1
1
0
1
1
0
0
4
0
1
2
0
1
1
0
1
0
2
1
0
0
2
1
2
2
1
2
1
1
2
1
1
1
0
1
1
0
0
2
1
3
1
0
1
0
2
2
1
2
0
1
1
2
2
1
3
1
2
1
2
2
0
0
1
0
0
0
2
1
1
2
0
1
1
2
1
0
0
0
0
1
1
2
1
1
0
2
0
3
1
1
1
0
0
0
1
2
1
1
1
1
2
2
0
1
0
1
2
1
2
1
2
0
1
2
0
1
2
0
0
1
1
0
1
1
1
2
1
1
1
2
2
0
2
2
1
2
1
1
0
0
0
0
1
1
0
0
0
2
0
0
0
1
1
0
0
1
0
0
2
0
1
1
1
1
0
2
1
1
1
1
2
2
1
1
1
2
0
1
1
2
0
2
2
0
1
1
1
1
1
2
0
0
2
1
1
1
2
0
1
2
0
0
1
0
0
2
1
0
0
1
0
0
0
2
0
0
1
0
0
1
4
0
1
1
1
1
2
1
0
0
2
2
1
1
0
2
1
1
2
0
0
1
1
0
2
0
1
2
1
1
1
1
1
0
2
0
1
2
1
0
2
1
0
0
1
1
1
1
2
0
1
1
1
2
2
1
0
1
0
2
1
0
1
1
1
1
1
1
1
1
1
0
2
1
2
1
2
2
1
1
0
1
0
1
1
0
1
1
1
2
1
1
0
1
1
1
2
1
1
2
0
3
1
1
2
2
0
1
2
1
1
5
0
2
0
1
1
2
0
1
2
0
1
2
2
1
0
1
0
1
2
3
1
0
0
0
1
2
1
1
1
2
0
2
1
2
1
1
2
1
1
1
1
0
1
2
1
2
2
1
1
2
1
0
1
0
0
1
1
1
0
2
0
1
1
2
2
1
1
0
1
0
1
0
1
1
2
1
1
1
0
1
0
1
1
0
1
1
1
1
2
0
0
1
0
1
1
1
1
2
0
1
1
2
0
0
0
2
1
0
1
1
1
1
0
1
0
2
1
0
1
1
0
1
1
0
2
1
1
0
1
1
0
2
1
2
0
0
1
1
1
2
0
1
2
1
1
1
0
1
0
1
0
1
1
2
0
1
1
0
2
0
0
0
1
0
0
1
1
1
0
0
0
0
1
1
1
0
1
2
1
1
0
1
1
1
2
1
2
1
2
0
0
2
1
0
1
1
1
1
1
0
0
2
2
1
1
1
1
0
1
2
1
2
2
1
0
0
0
1
0
3
1
1
0
1
0
2
2
1
1
2
0
2
0
0
0
1
0
1
2
1
3
1
0
2
0
0
0
1
1
1
1
0
1
1
0
2
1
1
0
0
0
0
0
0
0
2
1
0
2
0
0
2
1
2
0
1
1
2
1
1
0
0
0
1
0
0
1
1
0
1
1
1
2
1
2
1
0
1
2
1
0
1
2
1
1
1
0
1
1
1
2
1
1
2
1
0
1
1
1
1
0
2
0
2
1
1
1
2
1
2
2
2
0
0
1
1
1
1
1
0
1
2
0
0
1
1
1
2
0
2
0
2
2
1
0
0
1
0
1
1
2
2
2
1
1
0
0
0
0
1
0
1
1
0
1
0
0
1
1
2
0
2
1
0
1
2
1
1
0
1
2
0
1
1
2
1
1
1
1
2
0
1
0
2
4
1
0
1
1
1
2
2
2
1
1
0
0
2
1
1
1
1
1
0
2
0
1
2
1
0
3
2
0
2
1
2
0
2
1
1
1
1
1
0
2
0
1
2
1
1
1
0
1
1
0
1
0
3
0
0
0
1
0
1
1
2
1
0
0
0
1
2
2
1
1
0
1
1
1
0
1
0
1
1
2
0
0
1
1
1
1
2
0
1
1
2
0
1
1
0
0
1
1
2
1
0
0
2
1
1
0
1
1
2
1
0
1
0
1
1
0
1
0
2
2
1
1
2
0
1
2
1
0
2
0
1
1
1
0
2
1
1
1
2
1
1
2
1
2
1
1
0
1
0
3
2
0
1
2
1
1
1
1
3
1
6
1
2
2
1
2
1
2
2
2
1
1
1
0
1
1
0
1
1
1
1
1
1
1
2
2
0
2
0
1
2
0
0
1
1
1
2
1
2
1
1
1
2
3
1
1
2
1
0
2
1
1
0
1
1
1
1
2
0
1
1
1
1
0
0
2
1
0
1
1
1
2
1
1
1
1
0
0
1
0
2
1
1
1
0
0
0
0
2
0
2
0
1
1
1
1
2
0
1
1
1
2
1
1
2
1
0
2
0
2
2
1
0
1
1
0
0
1
1
0
1
1
1
2
0
1
0
0
1
2
1
1
1
2
2
0
2
1
0
0
0
1
0
1
1
0
0
1
0
1
2
1
1
2
0
0
1
1
1
2
0
0
0
0
1
2
1
0
0
1
2
1
1
2
1
0
1
1
0
1
1
0
1
0
1
2
0
2
0
0
0
1
0
0
2
1
0
1
0
1
1
1
1
2
1
0
0
2
1
1
1
1
1
2
0
0
2
1
1
1
0
2
2
1
2
0
1
0
2
2
1
0
2
1
2
1
2
1
0
1
2
1
1
1
2
1
1
2
2
0
1
0
0
2
1
0
0
1
1
1
0
1
0
0
0
0
1
1
2
1
0
1
2
2
0
0
0
0
0
1
1
2
0
1
0
1
1
2
1
1
2
1
1
1
1
2
2
0
0
2
2
2
2
1
0
0
1
0
0
1
1
1
2
2
0
1
2
1
1
1
0
1
0
2
0
1
0
0
0
0
1
1
3
0
0
1
0
2
0
1
1
0
0
1
2
0
1
2
0
0
0
0
0
1
1
1
1
1
1
1
2
1
1
2
1
2
0
1
2
1
0
1
2
0
1
1
0
0
0
1
3
0
1
0
0
1
1
0
3
0
1
1
1
2
2
2
1
0
2
1
1
0
1
1
0
2
0
2
0
1
0
1
2
1
2
1
1
1
2
2
1
1
0
1
0
2
1
1
2
1
2
1
2
0
0
0
1
0
0
2
1
2
2
2
2
1
0
1
2
1
0
0
0
0
1
1
2
1
1
1
0
2
0
1
0
2
0
0
1
0
2
0
1
0
3
0
1
1
1
1
2
1
0
0
0
1
1
1
1
1
2
0
1
1
2
1
1
1
1
2
0
1
2
1
1
0
1
0
1
2
2
1
1
1
2
1
2
2
1
1
1
0
0
0
0
1
1
1
0
2
0
2
0
1
0
1
0
1
0
1
0
0
1
1
1
0
2
1
0
1
2
0
1
1
0
1
2
3
2
1
1
4
2
1
0
0
2
1
0
1
0
1
1
0
0
0
1
0
0
1
2
1
0
0
2
0
0
1
1
2
1
0
2
0
2
0
2
0
1
1
2
1
1
1
0
2
1
1
1
1
1
1
1
2
1
1
0
1
2
1
0
1
1
1
2
1
1
0
2
2
2
0
1
2
1
1
2
2
1
2
1
1
2
1
0
2
0
1
1
1
2
2
3
0
1
2
0
1
0
0
0
1
2
1
1
1
1
2
1
1
1
1
2
1
0
1
1
1
0
2
0
0
2
0
1
1
2
0
1
1
2
2
1
1
1
2
1
0
0
0
1
2
1
1
0
1
1
0
0
1
0
1
0
0
0
0
0
0
2
0
0
2
2
1
1
2
1
2
1
1
1
1
0
2
0
1
1
1
1
0
3
1
3
2
1
1
2
2
1
2
1
1
0
1
0
1
1
0
1
0
0
0
1
1
0
1
0
0
2
2
0
1
2
1
1
2
0
1
1
0
0
2
0
2
1
2
2
1
1
1
0
0
0
1
1
2
0
1
0
1
1
0
0
1
1
2
0
1
1
1
1
2
0
1
0
2
1
1
1
1
0
1
1
1
1
1
0
0
1
0
2
3
1
0
1
1
0
1
1
1
2
2
0
0
3
0
1
1
1
2
0
0
0
0
2
1
0
0
1
1
2
1
2
0
1
2
1
1
1
1
1
1
0
0
1
0
0
0
4
1
0
0
1
1
1
1
1
0
2
2
0
0
0
0
3
1
1
1
0
1
0
0
1
1
0
2
0
0
1
1
0
0
2
2
0
1
2
2
0
0
0
1
0
1
1
0
1
0
1
2
1
2
2
1
2
2
2
0
2
1
0
2
0
1
2
1
2
2
1
2
1
1
1
1
1
1
1
1
1
0
1
0
0
1
1
1
0
2
0
0
0
2
2
2
2
1
0
0
1
1
2
1
1
1
2
1
1
2
1
2
0
0
1
0
2
2
0
1
0
1
0
2
1
0
0
2
0
0
1
1
0
2
1
2
1
1
1
2
0
0
0
1
1
0
1
0
0
0
1
2
3
2
3
0
0
1
0
1
1
1
1
2
2
1
0
2
0
1
1
1
3
1
0
2
1
1
4
1
2
0
1
2
2
0
1
1
2
1
0
0
0
1
1
0
1
0
0
2
2
0
1
1
1
1
0
1
1
1
1
2
2
0
1
1
1
1
0
1
1
2
1
1
1
0
2
2
2
2
2
0
0
1
0
1
0
1
2
2
1
0
1
0
0
1
2
0
0
1
0
1
0
1
2
1
2
1
2
0
2
1
1
1
2
0
1
1
0
1
0
2
0
1
1
1
2
2
1
0
0
2
0
1
2
2
1
1
1
0
2
1
1
0
0
2
1
1
1
1
0
1
2
1
2
0
1
1
1
1
1
1
0
1
0
0
0
0
0
1
1
0
0
0
1
1
0
1
0
1
1
0
0
2
2
1
0
2
1
2
0
1
2
1
0
0
1
1
1
1
0
1
1
0
1
1
0
0
1
1
0
1
1
0
0
1
2
0
1
0
1
1
1
1
1
0
2
2
0
0
1
2
1
2
1
2
1
1
1
1
0
0
0
2
2
1
0
2
0
1
0
2
6
2
2
0
1
2
2
1
1
2
0
0
4
1
1
0
2
0
1
1
1
1
1
1
0
2
1
0
0
0
1
0
1
2
0
1
2
2
2
0
0
2
1
2
1
0
0
1
2
0
1
1
1
1
3
1
2
0
0
1
2
1
1
1
2
0
1
1
1
0
2
2
0
0
0
2
0
1
1
1
0
0
1
1
1
1
1
1
0
1
2
1
0
1
2
1
0
1
0
0
2
1
2
0
3
1
0
1
0
1
1
1
1
1
1
1
0
1
0
0
1
1
1
2
0
1
1
1
0
1
1
3
1
0
0
1
0
1
1
0
1
0
1
0
1
1
1
1
0
0
1
0
0
1
0
1
0
0
1
0
0
1
1
0
1
0
1
1
1
2
2
0
2
1
2
1
1
0
0
1
0
0
0
0
1
1
1
0
2
1
1
2
1
2
1
2
1
1
0
1
0
0
2
1
0
0
0
0
1
1
0
1
1
1
0
2
0
1
2
0
1
1
2
0
0
0
1
0
1
1
2
0
1
1
0
1
0
1
2
1
1
0
5
2
0
0
1
2
1
1
4
1
1
1
1
0
1
1
0
1
0
2
0
0
2
0
1
0
1
2
1
0
2
2
2
2
2
1
1
1
0
2
0
1
1
1
0
2
1
2
3
2
1
1
2
1
2
2
1
2
2
1
1
0
1
1
0
1
1
1
1
1
2
1
2
1
2
0
2
1
1
0
1
1
2
1
2
1
0
0
0
1
1
1
0
1
2
1
0
0
2
0
0
2
1
0
1
0
1
1
1
1
0
2
1
1
1
2
1
2
0
1
0
1
1
1
3
0
2
1
2
0
1
1
2
1
0
0
1
1
1
2
1
1
1
1
0
0
2
1
0
1
2
2
1
1
1
1
1
1
1
1
0
1
1
0
0
2
1
1
1
0
0
0
2
2
0
3
1
0
0
0
1
2
0
2
2
2
1
1
1
1
0
1
0
3
2
1
1
1
0
0
2
0
0
1
2
1
0
0
2
1
2
1
2
0
0
1
2
1
0
1
0
1
1
1
2
1
0
1
1
0
1
0
0
1
1
0
1
0
1
1
1
1
2
2
0
1
0
2
3
1
2
2
1
0
1
0
0
1
2
1
1
1
3
1
2
2
0
0
1
2
0
2
0
2
0
0
1
1
1
0
1
2
1
0
1
1
0
0
1
0
1
2
0
2
1
1
0
2
0
0
0
2
1
2
1
3
0
1
1
2
0
1
0
0
0
1
0
1
2
1
1
1
1
0
2
1
0
1
1
0
0
1
2
0
0
1
1
1
0
0
0
1
2
1
1
2
0
1
1
0
2
1
0
0
1
1
1
1
2
2
0
0
2
0
1
2
0
1
2
2
0
1
0
1
1
0
1
0
1
2
2
0
0
1
1
2
1
0
1
1
0
1
1
2
1
2
2
1
0
1
1
1
1
1
2
2
0
1
1
2
0
1
0
1
1
0
1
0
1
0
1
2
0
2
1
2
3
2
1
1
0
0
1
2
0
2
2
2
0
1
0
0
1
2
0
1
0
0
1
1
2
1
1
0
1
1
1
2
2
0
2
0
0
2
0
0
1
1
2
0
1
1
1
0
2
1
0
1
1
1
1
1
1
0
0
0
1
2
0
0
1
0
1
1
0
0
2
2
3
0
1
1
1
0
1
0
0
1
1
1
1
1
0
0
0
0
1
1
1
1
2
0
1
1
1
2
0
1
2
1
1
1
2
2
1
0
1
2
1
3
0
0
2
1
2
0
0
0
0
1
0
1
2
0
1
1
3
1
1
2
1
0
0
2
2
1
0
3
1
1
0
2
1
0
1
1
1
1
1
1
0
1
1
0
1
2
2
1
1
1
0
0
1
0
1
1
1
1
2
1
0
0
1
2
1
0
0
0
0
0
1
0
1
2
0
1
1
1
0
0
1
1
0
1
0
1
0
1
0
2
0
2
2
0
0
1
1
1
1
1
1
1
1
1
2
2
0
1
0
0
2
1
1
0
0
0
1
1
1
0
0
2
1
1
1
0
1
0
1
1
1
1
1
2
2
1
0
1
1
1
1
0
1
0
1
2
1
0
0
1
1
1
1
0
0
1
1
0
1
0
0
1
1
2
1
1
2
1
0
2
0
0
1
3
0
1
3
2
2
1
1
1
2
1
0
0
2
1
0
2
3
1
1
0
1
0
1
2
1
2
1
0
1
0
1
0
1
1
2
0
1
0
2
0
2
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
2
0
1
1
1
2
0
1
1
1
1
1
1
2
1
1
2
1
2
1
0
1
2
2
1
0
1
2
0
0
1
1
1
2
1
1
1
0
1
1
0
1
0
0
0
1
1
1
1
1
2
2
1
2
0
0
2
0
0
2
1
0
1
0
1
1
1
0
1
2
0
1
1
0
1
1
2
0
1
1
1
2
1
0
1
1
1
1
1
2
1
2
1
1
1
2
2
2
0
0
0
1
2
1
0
0
0
0
0
1
1
1
0
1
0
2
1
2
1
1
0
1
0
2
0
0
1
1
0
1
0
1
0
0
0
1
1
1
1
2
2
1
0
0
1
0
0
0
0
0
2
2
2
2
0
1
2
0
2
1
1
1
1
1
2
1
0
0
2
1
0
2
0
0
0
1
0
2
0
3
1
1
1
1
0
1
1
2
1
0
1
1
2
0
1
0
1
1
1
0
2
1
2
2
1
2
0
1
0
2
1
1
1
2
2
1
1
0
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
0
0
0
1
0
0
1
1
2
1
1
2
1
1
2
1
1
1
0
2
0
1
1
0
1
1
0
1
1
1
3
1
1
1
1
0
1
1
1
1
2
1
1
2
2
2
2
2
1
0
1
0
0
2
2
2
2
0
1
1
2
0
0
0
1
1
1
1
1
1
0
2
1
2
0
0
3
2
2
2
1
1
1
1
1
0
2
1
2
1
0
1
2
5
0
0
2
2
2
1
1
1
0
1
2
1
1
1
1
1
1
1
1
2
0
1
2
1
1
1
1
1
0
2
1
0
2
1
1
2
2
1
1
0
1
1
0
1
2
2
0
2
2
1
2
0
0
1
2
2
0
4
1
2
1
1
0
1
1
0
1
1
2
0
0
0
2
1
1
1
0
1
1
1
1
1
1
0
1
0
0
0
1
1
1
1
1
0
2
0
0
1
1
0
0
1
1
1
0
0
1
2
2
1
1
1
2
0
1
0
0
1
0
2
1
1
0
1
1
1
1
0
1
1
0
0
1
0
1
0
2
0
0
0
0
0
1
2
1
0
1
1
1
1
2
2
0
1
1
1
2
2
3
1
1
1
1
1
0
1
0
1
1
1
0
0
1
1
1
0
1
0
1
0
2
2
1
1
2
0
1
0
1
1
1
2
1
2
2
2
1
2
1
0
2
2
0
2
1
1
1
1
1
1
1
0
0
1
0
2
1
2
0
1
0
1
0
0
1
1
1
2
1
0
0
0
1
2
2
2
0
0
2
1
0
0
2
1
0
1
0
2
0
0
1
0
1
0
0
0
1
0
2
1
1
0
3
0
1
2
0
0
2
0
2
1
4
2
1
2
2
0
1
0
0
1
2
1
1
1
0
0
1
0
2
1
0
0
2
1
2
1
1
1
0
1
1
1
0
1
0
2
0
2
1
2
0
1
1
2
0
1
1
0
0
1
3
0
0
0
1
1
1
1
1
2
1
2
1
0
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
0
0
3
0
0
1
0
1
0
1
1
1
0
2
1
1
0
1
0
0
2
1
1
1
2
1
1
0
0
2
0
1
1
0
0
1
1
1
1
2
1
1
2
0
2
0
1
0
2
1
1
1
1
2
1
1
2
0
0
1
0
2
2
2
1
1
1
1
0
1
0
1
2
0
0
2
1
0
0
0
0
1
2
0
0
1
2
1
0
1
0
1
0
1
0
1
1
1
1
2
0
1
1
1
1
0
1
0
1
0
0
3
1
2
1
2
2
1
2
1
1
1
1
1
2
1
2
0
0
0
0
1
1
0
1
0
3
1
1
1
0
0
2
1
0
2
1
2
0
1
2
1
1
1
1
0
1
2
1
0
1
2
0
0
0
4
2
2
1
0
1
1
0
0
1
1
0
0
1
2
2
2
1
0
2
0
2
1
1
1
2
1
1
1
0
1
1
2
1
2
1
3
2
1
1
3
1
1
0
1
0
1
1
0
2
1
2
1
0
1
1
2
2
0
1
1
1
1
2
2
0
1
1
1
0
1
1
0
0
1
0
0
1
2
0
1
2
1
1
2
1
1
1
0
0
1
1
1
0
1
1
1
1
1
1
0
0
1
2
1
0
1
0
2
1
2
2
1
1
2
0
1
1
1
1
1
2
0
1
1
1
0
1
1
0
1
1
2
1
1
1
0
1
2
2
0
0
1
1
0
1
3
1
1
0
1
1
0
0
0
0
1
0
2
1
1
1
1
0
1
1
1
0
2
1
1
1
0
1
2
2
2
1
0
1
1
1
2
2
0
1
1
2
0
0
1
2
1
1
1
1
1
1
2
2
1
1
1
2
2
0
0
1
2
1
2
0
2
0
1
0
1
1
0
1
0
2
2
0
0
2
2
2
0
1
0
0
1
0
1
0
2
1
1
2
0
0
1
0
1
1
0
0
3
0
1
1
1
2
1
1
0
0
1
2
1
1
0
2
2
0
1
2
1
1
1
0
2
1
2
0
1
1
0
1
0
2
2
1
1
1
0
2
2
1
1
1
0
1
1
2
2
1
3
1
1
1
0
2
1
1
1
2
2
1
1
1
3
1
1
3
0
2
0
2
1
0
1
1
1
1
1
1
1
1
1
2
1
1
0
1
1
2
0
1
1
2
0
1
2
2
1
1
1
1
1
1
0
1
0
1
2
1
1
2
1
3
1
2
0
2
1
3
2
0
0
2
0
1
1
2
2
0
0
1
0
0
2
1
1
1
0
0
2
0
0
0
1
1
1
0
2
0
1
1
2
0
0
1
2
0
2
0
1
0
0
2
1
1
1
1
1
1
1
2
1
0
1
2
2
0
2
1
1
1
1
0
2
1
2
0
1
0
1
0
0
1
0
0
0
1
1
1
2
2
1
1
0
1
1
1
0
0
0
2
1
0
1
2
2
0
1
1
1
2
1
1
2
0
1
1
0
0
1
0
2
0
1
1
0
1
1
2
0
0
1
1
1
0
1
1
2
0
0
1
0
1
0
1
0
1
0
1
2
0
3
1
0
0
1
0
1
1
1
0
0
1
1
0
2
1
1
0
0
2
0
1
2
1
0
0
1
1
0
0
2
1
1
0
2
5
0
1
2
1
1
0
1
0
1
2
1
0
2
2
0
1
2
2
0
2
2
0
0
2
0
1
1
1
0
1
0
0
2
1
1
2
0
1
1
1
0
0
1
1
1
1
1
2
0
1
1
0
1
0
1
0
1
1
1
1
0
2
0
0
1
0
1
2
2
2
1
1
1
0
0
0
0
1
0
0
1
1
0
1
2
1
1
0
0
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
0
1
2
0
0
0
2
1
1
1
1
0
2
1
2
2
2
1
1
1
0
2
2
2
1
1
1
1
0
1
1
2
0
1
1
1
1
1
0
2
1
1
2
0
0
1
2
1
1
1
0
0
1
1
1
1
0
0
1
1
1
1
1
1
1
1
0
0
1
1
2
0
0
2
1
2
1
1
2
0
0
2
0
2
1
1
1
0
1
1
2
0
1
0
1
0
1
1
0
2
1
0
0
1
0
1
0
1
0
1
0
0
1
2
1
0
2
0
1
2
1
0
1
0
1
1
0
1
0
1
1
1
0
2
1
0
2
0
0
1
2
1
1
0
0
0
1
1
2
0
1
1
1
1
1
1
0
0
2
1
1
0
1
2
0
0
1
1
0
1
1
0
1
0
2
1
0
1
2
1
1
2
0
1
1
1
1
1
2
1
1
3
0
0
1
1
1
0
0
1
1
1
2
0
0
0
2
1
1
1
1
0
0
2
2
1
1
2
1
1
1
1
0
1
1
2
2
1
1
1
1
1
1
0
1
0
0
1
1
1
0
0
2
1
2
0
2
0
1
1
1
1
1
1
2
1
0
1
0
1
0
1
1
2
1
2
1
2
1
0
2
0
1
0
0
0
0
0
0
2
1
1
1
0
2
1
0
2
0
1
1
2
1
2
2
1
0
1
0
1
1
1
1
0
1
1
2
1
1
1
1
1
1
1
1
0
2
1
1
1
1
0
2
1
0
1
0
0
1
0
1
1
2
2
0
1
2
1
2
2
0
0
0
2
2
2
0
1
1
2
1
1
2
1
1
1
0
1
0
0
1
0
1
3
0
0
2
0
1
1
2
0
2
1
0
1
1
1
1
0
0
1
0
0
0
2
0
0
2
1
2
1
1
1
2
1
1
2
1
2
1
2
1
2
1
3
0
2
1
1
2
4
0
1
0
0
2
1
2
1
0
0
1
2
1
0
1
1
1
0
0
1
0
1
2
1
1
2
0
1
0
0
2
1
0
1
2
2
0
1
2
1
2
2
0
0
2
2
2
1
1
1
1
1
1
2
3
0
1
1
2
3
0
0
2
0
2
0
0
1
0
1
3
1
1
1
0
0
2
0
2
2
1
1
1
2
1
1
0
0
2
2
2
0
0
0
1
1
1
0
0
1
2
2
0
1
2
2
2
2
0
1
1
1
0
0
1
0
1
0
0
2
0
2
2
2
2
1
2
0
0
2
1
2
0
1
1
0
1
1
0
0
1
1
0
1
1
2
1
0
4
1
2
1
0
1
0
1
1
0
1
1
0
2
1
0
1
0
1
0
0
2
1
2
0
2
1
0
0
1
1
1
2
1
2
2
1
1
0
0
1
1
1
2
1
0
2
1
1
1
1
3
0
0
1
1
1
1
1
2
0
0
0
1
2
1
1
2
0
1
0
0
1
0
1
0
0
1
1
0
0
1
0
1
2
1
0
1
0
1
2
1
3
1
4
2
1
1
1
0
2
1
0
2
0
0
2
1
1
1
2
1
0
1
1
2
2
1
1
2
1
1
2
1
2
1
0
0
1
0
1
0
1
0
1
2
2
1
0
0
1
1
0
0
0
3
0
1
2
0
2
1
1
0
1
1
0
0
1
1
1
0
0
2
2
2
1
0
1
1
1
0
0
1
1
1
0
2
0
0
0
0
1
1
2
2
1
2
0
1
1
1
0
0
2
1
1
2
1
1
2
1
1
1
0
0
2
2
1
1
0
1
0
0
0
1
1
1
1
1
1
2
1
1
2
1
1
1
0
1
0
1
0
2
0
0
0
2
0
0
2
0
1
2
1
2
5
2
0
1
1
0
1
2
1
0
0
0
1
11
1
1
1
0
0
1
1
1
0
0
1
0
1
3
2
0
1
1
1
1
1
1
0
0
2
0
2
1
1
0
1
1
1
1
1
1
0
1
1
2
1
1
1
0
1
1
1
2
0
0
0
0
1
1
2
2
0
0
1
0
1
0
1
1
2
1
1
2
0
2
0
2
2
1
0
2
0
0
1
1
2
1
1
0
2
1
2
0
2
1
0
1
1
2
1
0
1
0
0
0
1
1
1
1
1
0
1
0
0
0
1
1
1
0
0
1
1
2
1
1
3
2
0
1
1
0
0
1
2
1
1
1
1
0
0
0
0
1
1
1
1
1
1
1
0
1
1
1
2
1
1
1
0
0
2
1
2
0
3
1
0
0
0
0
0
2
2
1
1
2
0
2
1
0
1
1
0
0
1
0
0
1
0
1
1
1
2
0
0
1
1
1
0
2
1
2
0
2
1
0
0
1
1
2
0
2
2
0
0
2
0
2
0
3
1
1
2
0
0
1
0
2
1
3
0
0
0
1
1
1
0
0
2
3
1
2
1
0
2
2
1
2
1
1
1
1
0
0
0
0
0
0
0
1
0
2
1
1
2
0
1
0
1
1
2
1
1
0
2
1
1
1
2
3
3
1
2
1
0
1
0
1
0
2
2
1
2
1
1
1
1
0
0
0
0
1
1
2
1
2
0
1
1
1
0
1
0
0
2
0
2
0
2
0
1
0
2
0
1
2
1
0
2
0
1
2
0
0
0
1
1
2
0
1
2
2
2
0
1
1
1
1
1
0
0
0
0
2
1
2
1
1
0
0
1
1
0
1
0
0
1
1
1
0
1
3
1
1
2
1
1
1
1
1
1
2
1
1
0
1
3
2
0
0
0
3
1
3
2
2
0
1
1
0
1
0
1
1
0
1
0
2
1
1
0
0
1
0
1
1
1
0
1
0
1
0
1
2
0
0
2
1
2
2
0
2
2
1
1
2
0
1
2
0
0
1
1
0
1
1
2
1
0
2
0
0
0
0
2
2
1
1
1
0
1
0
0
2
1
1
1
1
1
0
1
1
2
2
1
2
0
1
1
1
2
1
1
0
1
0
0
1
1
2
3
2
0
1
2
2
1
1
0
2
1
0
0
0
0
1
1
1
0
0
1
1
1
1
1
2
0
0
0
0
2
0
1
1
1
0
1
0
1
1
1
0
2
1
2
0
1
1
1
0
1
1
2
0
0
1
1
1
2
2
0
0
2
0
1
1
1
2
1
2
1
0
1
0
0
1
1
0
1
0
0
0
1
2
2
1
2
1
1
0
0
2
1
0
1
2
1
1
1
0
1
1
1
1
2
2
0
1
0
0
0
0
0
0
1
0
5
0
1
0
1
2
0
1
0
1
0
1
0
1
1
0
0
0
1
2
2
1
1
3
0
1
1
2
1
1
1
2
2
0
2
0
0
1
0
1
0
0
0
0
1
1
2
1
1
1
0
0
2
2
2
1
2
2
0
1
2
1
1
1
2
1
2
2
0
0
1
1
0
0
2
2
0
1
1
1
1
5
1
1
1
2
1
1
2
1
0
1
0
0
1
1
2
1
2
1
0
2
2
2
1
0
1
2
1
0
1
1
1
2
0
0
0
0
1
1
0
1
1
1
1
1
2
2
0
1
0
2
1
0
1
1
1
0
0
0
0
1
1
1
0
0
1
1
1
1
2
1
0
1
1
1
0
0
3
1
0
2
1
0
1
2
1
1
3
1
1
3
1
1
1
1
0
0
0
2
0
0
0
2
2
0
2
2
1
1
1
0
1
1
2
1
2
2
1
2
1
2
0
1
1
1
0
0
0
1
0
0
2
1
0
1
0
1
2
1
0
0
1
1
0
2
2
0
0
1
0
0
0
0
1
1
0
1
2
2
2
0
1
1
0
1
1
1
2
0
0
0
2
1
0
1
1
1
1
1
1
1
1
1
1
2
0
1
2
1
2
2
1
1
1
2
0
1
1
4
1
1
1
1
0
0
1
1
0
0
0
0
1
0
0
1
1
1
0
2
2
2
0
1
0
0
1
2
2
0
2
1
1
1
0
1
1
1
2
2
0
1
0
2
1
1
1
1
1
0
1
1
1
2
2
3
2
0
1
1
1
1
2
1
0
1
0
1
1
2
1
2
1
1
1
0
1
1
1
1
1
0
0
2
4
1
1
2
0
0
1
1
1
2
1
0
0
3
0
1
1
2
1
0
0
0
2
1
1
0
1
1
0
2
1
0
0
2
1
2
0
2
1
0
2
1
2
1
0
0
2
0
1
2
1
1
2
0
1
0
0
1
1
1
1
2
2
0
1
0
2
0
1
0
0
1
1
2
1
1
1
1
0
1
2
1
1
1
0
1
2
2
1
0
1
1
0
0
1
1
1
1
0
2
1
2
2
0
1
2
1
2
1
1
2
1
1
1
2
0
0
1
2
1
2
0
2
0
2
2
1
1
1
0
1
1
1
0
0
2
1
1
0
1
1
0
1
1
0
1
0
0
1
1
2
1
1
1
0
0
1
1
1
1
1
0
1
0
1
0
2
0
2
2
1
2
0
0
1
2
1
0
2
3
1
1
1
1
1
1
1
0
0
0
0
1
0
2
2
0
1
1
1
1
2
2
1
0
1
2
0
1
0
1
2
2
3
0
0
0
2
1
1
2
1
2
2
0
0
1
1
0
2
0
1
0
1
1
1
4
0
1
1
1
2
1
1
1
0
1
0
2
1
1
0
1
2
0
1
1
1
2
2
1
0
2
1
1
1
1
2
1
1
1
2
1
0
2
1
0
2
1
0
2
2
1
1
2
1
0
1
2
1
1
0
1
2
1
0
0
2
1
2
0
0
1
1
1
0
1
1
2
1
1
1
1
1
0
1
1
0
1
2
2
3
1
2
1
1
0
1
1
2
0
0
1
0
0
1
2
1
2
1
0
1
2
2
1
1
1
1
0
0
1
2
1
2
2
1
1
1
0
1
2
1
1
1
2
0
1
0
0
1
1
0
0
2
1
2
1
1
1
1
1
2
0
5
1
2
1
1
1
0
0
1
0
1
1
2
0
0
1
2
0
0
1
1
2
2
1
1
2
1
1
0
0
0
1
0
0
2
0
1
1
0
0
2
0
0
1
1
1
1
1
1
0
2
1
1
2
1
1
1
1
0
2
0
1
1
1
0
0
0
1
0
0
0
1
1
2
2
1
1
1
0
1
0
2
1
1
2
1
2
0
0
1
1
1
3
2
2
1
1
0
1
1
1
2
0
2
1
1
2
2
2
1
1
1
1
1
1
0
1
0
1
0
1
1
2
1
1
1
1
0
2
0
2
0
2
1
1
1
2
2
1
1
1
1
1
1
0
1
1
0
1
0
0
2
0
0
1
1
1
2
1
0
1
1
0
1
0
1
0
1
1
1
1
2
1
2
0
2
2
2
0
0
0
0
1
1
2
1
1
0
0
2
2
1
1
1
0
0
2
0
2
2
1
0
0
1
0
1
0
0
1
1
1
1
2
0
0
0
1
3
2
2
0
0
1
2
1
0
1
1
0
0
1
1
0
2
0
0
1
1
2
0
2
0
1
1
1
0
2
2
1
2
2
0
0
2
1
1
1
1
0
2
0
0
2
1
0
1
0
0
0
1
2
0
1
1
1
2
1
2
1
1
1
2
1
1
1
1
3
2
0
2
2
1
2
1
1
0
0
0
0
1
1
1
1
1
1
0
1
0
2
1
0
2
2
1
1
0
0
1
1
1
0
1
0
2
0
1
1
2
2
1
0
0
0
0
1
1
1
2
1
1
1
1
0
3
0
1
0
1
2
0
1
1
0
2
1
1
2
1
1
1
1
0
2
0
1
0
1
1
1
0
1
1
1
1
1
1
1
2
2
0
2
0
0
1
2
1
0
0
2
0
0
1
1
2
1
1
0
0
1
1
1
1
0
0
1
2
2
0
1
0
0
1
1
1
1
0
1
2
0
1
1
1
2
2
1
1
1
0
1
1
1
1
1
0
1
1
2
0
0
2
1
1
0
0
1
1
1
3
3
2
1
0
0
1
2
1
0
1
0
2
1
1
1
0
1
3
0
1
3
2
1
0
1
1
1
1
2
2
0
3
1
1
1
1
2
2
2
1
2
2
1
0
1
1
0
1
0
0
0
1
1
0
2
1
1
1
0
1
1
0
1
1
2
2
8
1
0
0
1
1
2
0
1
0
1
0
1
0
0
1
2
1
0
1
0
1
1
0
2
1
2
1
0
1
1
2
1
1
1
2
2
1
2
0
2
2
1
2
1
1
0
1
1
0
2
1
0
1
0
2
1
2
1
2
2
1
1
0
2
1
1
0
1
1
1
2
2
1
0
1
0
2
1
0
3
2
0
0
2
2
2
1
0
1
1
0
1
0
1
1
2
1
1
3
0
0
1
1
2
1
2
0
1
1
1
1
0
1
0
2
1
0
2
0
2
1
0
0
0
2
1
1
2
1
0
1
3
0
2
2
1
2
1
0
2
0
0
1
1
0
1
0
2
0
1
0
1
0
1
0
0
2
0
0
1
2
0
1
1
0
1
1
1
1
2
1
0
1
1
2
1
2
2
1
2
2
1
1
1
0
2
2
1
2
1
1
1
0
2
2
1
0
0
1
0
1
1
0
1
0
1
3
1
2
1
1
0
0
1
2
0
0
1
1
1
1
2
1
1
2
1
1
1
2
2
1
0
2
0
1
0
1
2
1
1
0
2
1
0
0
1
1
1
1
0
2
1
1
1
0
0
1
1
0
1
2
1
0
1
2
1
1
2
1
1
1
1
2
1
1
2
1
1
0
0
1
1
1
1
1
2
1
2
1
0
2
1
0
0
1
1
0
1
0
0
0
1
1
0
1
1
0
1
2
0
2
1
1
1
3
1
1
1
2
0
1
14
0
1
1
0
2
2
2
0
1
0
0
1
1
1
0
1
1
1
0
1
1
2
1
1
2
1
1
1
1
0
2
1
1
0
1
1
1
1
2
1
0
2
1
2
0
0
0
1
1
0
2
0
2
2
1
0
1
1
0
2
1
0
0
2
2
2
0
0
2
1
1
1
0
1
2
0
1
1
1
0
1
1
2
0
2
2
1
2
1
2
1
1
0
2
1
1
1
2
1
2
1
0
1
1
1
1
2
1
0
1
0
1
1
1
1
2
0
2
0
1
1
1
1
1
1
1
0
1
0
1
0
0
1
0
0
0
2
1
1
1
1
1
0
0
2
1
1
0
1
1
0
2
2
1
1
1
0
0
1
0
2
1
0
1
1
1
0
1
0
0
1
1
1
2
1
0
1
2
1
0
0
0
1
1
2
1
0
1
0
0
1
0
0
1
0
1
0
0
2
1
1
1
1
1
0
0
2
2
2
1
1
3
1
1
1
1
2
2
2
1
0
0
2
0
0
1
0
1
1
1
1
1
0
0
1
2
1
1
0
1
0
0
0
2
1
0
0
0
1
0
1
1
0
2
1
1
1
1
2
2
1
0
1
1
1
1
0
1
1
0
1
1
1
1
1
2
1
2
0
0
2
1
0
2
0
1
1
0
1
1
1
0
0
1
0
2
1
0
2
1
1
0
2
0
0
1
0
1
1
0
1
2
0
0
1
0
1
1
0
1
0
2
2
2
1
1
2
0
0
1
2
1
4
2
0
1
0
1
1
1
2
0
1
0
1
1
0
1
1
1
2
0
1
1
2
0
1
1
2
1
0
2
0
2
0
0
2
0
1
0
1
1
2
1
2
1
1
0
1
0
0
1
2
1
1
1
1
1
1
0
1
1
1
1
2
2
2
0
2
2
1
0
1
1
0
0
1
1
2
1
0
1
2
1
2
1
1
1
0
1
0
2
1
1
1
0
2
1
1
1
0
1
0
0
0
1
0
0
1
0
0
1
0
2
2
2
0
1
0
0
0
2
2
1
0
1
1
0
0
1
2
2
1
0
2
2
1
0
1
1
8
1
1
1
0
2
1
0
0
1
3
2
1
1
1
2
1
1
0
1
1
1
2
2
0
0
0
1
1
1
2
2
1
0
1
1
0
0
0
4
0
1
0
1
1
0
0
1
1
1
1
0
1
1
1
2
1
1
0
2
2
0
1
1
1
1
1
1
1
1
0
1
0
0
1
2
2
1
0
1
0
2
1
0
2
0
0
0
1
0
0
1
1
1
0
1
0
1
2
3
1
2
1
1
0
1
0
1
0
0
2
2
0
2
0
1
2
0
2
2
3
0
0
0
1
1
1
0
0
1
2
2
0
1
2
2
0
1
1
1
0
0
1
0
0
1
1
1
2
2
2
2
0
2
1
0
1
0
1
1
1
1
0
0
0
1
1
0
0
1
1
1
1
2
1
0
1
1
1
0
1
0
1
1
0
2
2
0
0
1
2
1
2
1
1
1
1
2
1
0
2
1
1
0
1
0
1
1
2
1
1
1
0
1
0
1
0
0
2
1
0
1
0
0
1
3
1
1
2
1
0
0
0
0
2
1
1
0
1
1
1
1
2
1
2
1
1
0
0
2
2
1
2
1
0
0
1
2
2
2
1
1
0
1
1
1
1
1
1
2
0
2
1
1
2
1
0
1
2
0
1
1
0
1
0
2
0
1
2
1
1
1
1
1
1
1
2
0
0
1
0
0
0
3
0
0
2
1
1
2
1
1
1
0
2
1
1
3
2
2
1
2
1
0
0
1
1
0
0
2
0
2
2
1
1
1
1
0
2
0
2
1
0
0
2
2
0
1
1
1
2
1
1
1
2
1
1
2
1
2
1
1
1
0
1
1
1
1
0
0
1
1
1
2
2
1
1
0
0
1
1
1
1
2
0
1
2
0
0
1
1
1
1
2
2
2
1
1
1
0
1
1
0
2
2
1
1
1
0
1
2
0
0
1
1
1
1
1
1
0
1
2
1
1
0
2
1
1
1
1
1
0
1
2
1
0
1
2
2
2
1
0
0
2
0
1
1
1
1
1
1
1
1
2
0
1
2
0
2
1
0
1
1
0
0
0
0
1
1
1
2
2
1
2
2
0
2
1
2
1
1
1
0
1
0
1
2
0
0
2
1
1
1
2
1
0
1
1
1
1
1
2
1
2
0
0
1
0
1
0
2
0
1
2
1
1
0
2
1
2
0
0
1
1
2
1
1
2
1
1
0
1
0
1
1
2
0
1
2
1
1
0
1
0
2
1
0
1
1
1
0
1
1
0
1
2
0
0
2
2
1
0
1
1
1
0
2
1
0
1
2
0
1
2
0
0
1
2
1
1
2
0
1
1
1
0
0
2
2
1
1
1
2
1
1
2
0
0
1
1
2
1
2
0
0
1
0
2
2
1
2
0
0
1
1
1
2
1
1
2
2
1
2
0
2
1
0
1
1
0
1
1
1
1
0
1
2
1
1
2
0
2
1
1
0
2
1
0
2
1
1
2
0
1
1
1
1
1
0
0
0
3
0
0
2
0
1
1
0
1
1
0
0
0
1
1
1
0
2
2
3
0
1
1
0
2
1
2
1
0
1
1
2
1
0
2
2
1
0
1
0
0
2
0
1
1
1
0
0
2
2
2
0
0
1
0
1
1
1
0
0
0
1
1
1
1
1
1
1
2
3
1
0
0
2
2
1
1
0
1
0
0
1
1
0
2
0
0
2
2
2
1
1
1
1
0
1
1
2
1
0
0
1
2
1
0
0
0
0
0
1
1
0
1
2
1
2
2
0
1
1
1
1
0
0
2
1
0
2
3
1
0
2
2
0
1
2
0
2
0
0
0
1
1
1
2
1
2
0
1
1
1
1
1
1
2
0
1
2
0
0
1
0
3
1
2
0
1
1
2
1
1
1
2
2
2
0
1
0
0
1
0
0
1
1
0
0
1
2
2
1
1
0
1
2
1
0
1
1
0
0
1
0
2
1
2
1
0
1
2
0
1
1
1
1
3
2
1
0
0
0
0
2
1
0
2
1
0
2
2
1
1
0
0
1
0
1
1
1
2
2
0
1
0
2
0
0
2
2
1
1
0
2
1
0
1
3
1
1
0
2
0
1
1
0
1
0
1
1
2
0
0
1
0
2
1
1
1
2
1
0
0
1
1
1
1
1
1
1
2
2
1
1
1
1
1
0
2
1
1
0
1
1
1
1
0
0
0
0
1
1
1
0
2
0
0
1
1
0
1
1
0
2
0
1
1
0
1
1
1
2
2
3
0
1
1
1
0
2
1
0
2
4
2
2
0
0
2
1
11
0
0
0
1
1
3
0
2
0
0
1
2
1
2
2
1
0
1
1
0
2
0
2
1
0
0
2
1
2
2
2
0
1
2
1
1
1
1
0
1
0
1
1
2
0
0
1
2
1
2
0
0
0
2
0
1
1
0
1
0
0
1
1
2
1
1
1
1
2
1
0
0
0
1
2
0
0
1
1
1
0
2
0
1
1
1
0
2
1
2
0
0
2
2
1
0
1
2
0
1
0
1
1
0
1
1
1
1
1
0
2
0
2
3
0
1
1
1
0
1
0
1
1
0
2
1
0
2
0
2
0
2
0
3
0
0
1
2
2
0
2
2
1
0
3
1
2
2
1
0
0
1
1
2
0
0
1
1
0
0
1
2
1
0
3
0
1
0
1
2
1
1
2
0
2
1
2
1
1
1
4
2
0
1
1
1
1
1
0
1
1
0
0
1
1
1
0
0
1
0
1
0
1
1
2
2
0
0
1
1
0
0
1
1
2
2
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
1
1
0
2
2
2
1
1
0
1
2
0
1
0
1
1
1
1
0
1
0
0
0
2
0
1
2
1
2
1
0
3
1
2
1
1
0
0
2
1
0
2
1
0
1
2
2
1
1
2
2
0
0
1
1
2
1
1
0
1
1
2
1
1
2
1
1
2
1
0
1
1
1
1
1
1
1
2
0
1
1
1
1
1
1
2
0
2
1
1
1
1
1
0
1
0
0
1
0
0
1
2
1
0
2
2
1
0
2
1
1
1
1
1
1
0
1
0
1
0
1
4
0
1
1
0
0
0
2
0
2
1
0
0
1
0
2
1
2
2
1
0
1
2
0
0
0
2
0
0
0
1
2
0
1
1
0
0
1
1
1
1
2
1
0
1
0
1
0
1
2
0
1
0
1
2
2
1
2
0
0
2
2
0
2
1
1
0
1
0
0
2
1
1
1
1
1
0
0
1
1
0
1
1
1
0
1
1
0
0
0
0
1
2
1
1
1
2
0
0
2
1
0
1
2
0
2
2
0
0
1
1
0
0
1
2
1
1
2
0
2
1
1
0
0
1
1
1
0
0
0
1
1
2
0
2
1
0
0
0
1
1
2
1
0
0
1
1
2
1
1
1
1
2
0
1
0
0
0
2
1
2
0
0
1
1
1
0
1
2
0
2
1
1
0
2
1
1
1
2
1
0
1
1
1
0
0
1
2
2
0
1
1
2
0
2
0
1
2
2
0
0
1
1
1
1
1
0
1
0
0
2
3
1
1
1
1
3
1
0
1
0
1
1
1
1
1
1
0
0
1
1
1
1
1
1
2
0
1
0
1
0
1
0
3
2
1
1
0
1
1
2
1
2
1
1
1
2
2
1
0
0
0
0
2
0
1
0
1
2
0
2
1
0
1
2
2
0
2
2
1
1
1
0
1
0
2
2
1
0
1
1
0
0
1
1
1
2
0
1
2
1
0
2
1
0
0
1
0
1
1
0
1
0
1
1
1
0
0
1
1
3
2
2
2
2
1
1
1
2
0
2
2
2
0
1
2
0
0
0
1
0
2
0
1
0
0
1
1
2
0
1
0
1
2
0
0
2
2
1
2
1
0
2
1
1
1
1
1
2
0
2
1
2
1
0
1
1
2
0
1
1
1
0
1
1
1
0
1
0
2
0
0
1
0
1
2
1
2
0
0
1
2
0
2
1
1
0
1
1
1
0
1
1
1
1
2
0
2
1
2
0
0
1
2
0
1
1
0
1
2
0
1
2
1
1
2
1
1
0
2
0
1
2
0
1
0
0
1
1
2
1
0
2
1
1
0
0
2
1
1
0
0
2
0
0
2
1
1
0
2
1
0
1
0
1
2
1
2
1
1
1
1
0
0
1
0
1
2
1
0
0
1
0
1
3
1
1
1
0
2
1
1
0
0
2
0
2
0
1
0
1
1
2
1
1
0
2
1
0
2
1
2
0
0
1
1
2
2
1
1
2
2
1
1
0
1
1
1
2
1
0
0
0
1
1
1
0
0
1
2
0
1
2
2
2
0
0
0
1
1
0
0
2
0
1
0
0
0
1
1
0
1
0
0
0
1
1
3
1
0
1
1
0
2
2
1
1
0
2
2
0
0
0
1
0
2
0
1
0
0
1
1
1
0
0
1
2
2
0
1
1
0
0
1
0
0
0
0
1
1
0
3
0
0
2
2
0
2
1
3
2
0
1
1
1
0
2
2
1
1
1
1
4
0
3
0
1
2
2
1
1
1
1
0
0
1
0
1
0
1
2
2
1
1
1
0
1
1
1
0
1
2
2
2
1
0
0
1
1
1
0
0
0
0
1
1
1
1
0
2
2
1
0
1
1
1
1
0
2
1
1
1
1
0
0
2
1
1
2
0
0
1
2
0
0
0
2
2
1
1
0
1
1
1
0
1
1
1
0
0
1
2
1
2
2
1
0
0
1
1
2
0
2
1
1
0
2
0
1
2
1
1
0
2
0
2
1
0
0
2
1
0
2
0
1
2
1
0
1
1
1
2
2
2
0
1
1
1
1
0
2
2
2
1
0
0
1
2
0
0
0
0
0
2
2
1
1
1
2
2
2
3
1
0
1
1
1
1
2
0
1
0
1
0
2
1
2
1
0
1
1
1
1
1
2
1
0
1
0
2
1
1
1
0
1
1
0
0
0
1
0
1
1
0
2
2
1
0
1
1
0
0
0
0
0
1
1
0
0
1
1
2
0
0
1
1
1
0
0
1
1
1
1
1
1
2
1
1
0
1
2
1
0
1
1
1
3
2
0
0
1
1
0
1
0
1
1
1
1
1
1
1
0
5
0
2
1
1
1
0
1
1
0
0
0
0
2
2
2
1
0
2
0
2
0
1
1
0
0
1
2
1
0
1
1
0
1
1
0
1
1
1
2
2
0
1
1
0
2
0
0
1
2
1
1
1
0
1
2
2
1
2
1
1
1
2
1
1
0
0
1
1
2
2
1
0
2
1
1
2
1
1
2
2
4
1
1
1
0
1
1
1
1
0
0
0
2
2
1
1
1
0
1
1
0
0
1
1
1
1
1
1
0
3
2
1
1
2
1
0
1
1
0
1
2
2
1
0
1
1
2
2
0
0
1
1
2
2
0
2
0
0
1
0
0
2
1
0
2
0
2
1
2
2
1
0
1
0
1
1
1
1
2
2
0
0
0
2
0
1
1
2
2
2
0
1
2
0
1
0
0
1
0
1
1
1
1
1
1
1
0
1
1
1
0
0
0
1
2
1
1
1
1
0
1
1
1
2
0
2
1
2
0
0
1
2
2
2
0
2
0
0
1
0
0
1
1
2
1
1
0
0
2
0
2
2
1
0
1
1
2
1
1
1
1
1
1
0
1
1
0
0
0
0
0
1
1
2
1
2
0
1
0
1
1
1
0
2
0
2
1
0
0
1
1
2
1
2
0
0
1
0
1
1
0
1
2
1
1
2
1
0
2
0
0
1
1
1
1
2
0
2
0
0
1
1
0
2
1
0
2
1
0
2
0
2
1
1
1
0
1
2
0
2
1
2
0
1
1
0
2
2
1
2
2
1
1
1
2
2
0
0
0
1
1
0
0
2
0
0
1
1
2
2
1
0
1
1
2
1
0
1
2
2
1
3
3
0
1
0
1
0
0
1
0
0
2
0
0
1
2
2
0
0
0
2
2
0
2
0
1
1
0
0
2
0
0
0
1
1
0
1
2
1
1
0
1
1
2
1
0
1
0
1
1
1
2
1
1
1
0
1
1
1
1
1
1
1
0
2
0
2
1
0
0
2
0
1
0
1
2
1
1
0
1
1
1
0
1
1
1
0
0
1
0
0
1
0
1
0
0
1
1
1
1
0
1
0
1
0
1
1
1
2
2
1
2
1
1
9
0
2
1
0
1
0
0
0
2
1
1
1
0
2
1
0
1
0
0
1
1
1
0
1
2
1
1
0
0
0
1
2
1
0
2
0
1
0
1
2
0
8
2
1
0
0
2
0
0
2
4
0
1
1
2
1
1
2
1
2
1
1
2
1
1
1
2
1
2
2
1
1
0
0
1
2
1
1
1
2
2
1
1
0
2
0
2
0
1
1
1
2
1
2
0
1
0
1
1
0
1
1
1
1
1
0
0
0
0
1
1
0
1
2
2
1
0
2
1
0
1
2
0
1
0
1
2
0
1
1
1
1
2
1
0
1
0
0
1
1
0
1
1
2
0
2
0
2
1
0
0
2
3
0
1
4
1
2
2
0
1
0
2
0
0
1
0
2
1
2
2
1
2
1
2
1
1
0
1
2
1
1
1
0
1
1
1
0
1
1
0
1
1
0
0
1
1
2
1
2
1
2
0
2
1
1
1
0
0
0
1
1
2
0
0
0
2
2
0
0
2
0
2
2
7
0
0
1
0
1
0
1
1
0
1
0
0
1
1
0
0
1
0
0
2
2
0
0
0
1
1
0
0
1
4
0
2
1
0
2
0
1
2
2
1
1
0
1
0
2
1
1
1
1
0
2
0
0
1
2
0
1
1
1
0
0
0
1
0
2
0
2
2
0
0
2
1
0
2
1
1
1
1
0
1
1
1
1
2
1
0
1
1
2
0
2
2
1
1
2
2
0
0
1
2
1
1
1
3
1
0
1
1
0
1
1
1
2
2
1
0
1
1
0
0
0
1
0
2
1
1
1
2
1
0
1
0
2
2
1
1
1
1
1
1
1
0
0
2
1
0
1
1
2
3
1
1
1
1
2
2
1
0
2
1
1
0
1
2
1
2
2
0
0
1
0
3
1
0
0
3
3
2
0
1
1
2
1
1
1
1
2
1
1
0
2
1
1
1
1
1
2
0
2
1
0
2
0
1
1
1
2
1
1
0
1
1
0
1
2
1
1
2
0
1
2
1
2
2
1
0
1
1
2
1
1
1
1
1
1
0
1
1
1
2
1
1
1
1
0
1
0
1
1
2
2
0
2
1
1
0
2
0
0
2
2
1
0
1
1
2
0
1
0
1
1
1
1
1
0
1
1
0
0
0
0
0
0
0
0
1
1
1
1
0
0
1
1
0
1
0
2
2
0
1
0
1
1
2
0
1
0
0
2
1
1
2
0
1
1
2
2
1
1
0
2
1
1
1
0
1
2
1
1
0
2
1
1
1
2
2
0
2
2
2
2
1
3
1
0
1
1
0
1
1
2
0
1
2
1
2
1
1
0
0
2
2
1
5
0
0
1
1
2
1
0
1
1
0
2
0
1
2
0
0
1
2
1
0
2
2
0
2
2
0
1
1
2
0
0
1
0
1
2
1
1
2
2
2
3
1
1
0
1
1
1
1
2
1
0
1
1
1
0
2
0
0
1
1
1
0
1
1
2
1
2
0
1
0
1
0
2
0
1
1
0
2
0
1
1
0
1
2
0
0
1
0
2
0
0
0
1
1
1
1
1
1
1
2
1
1
1
1
1
1
0
1
0
0
0
1
2
1
1
2
1
2
1
1
2
2
2
2
1
1
1
2
1
1
0
1
1
1
2
1
0
2
0
0
1
1
1
1
0
2
1
0
1
0
0
0
1
0
1
0
1
2
2
1
1
1
0
1
1
0
1
1
1
0
0
1
1
0
0
1
3
1
1
1
0
1
1
1
0
0
2
1
1
1
1
2
0
0
1
0
1
1
0
0
2
1
2
1
1
1
0
0
1
1
1
1
1
1
1
0
0
2
2
1
1
1
1
1
1
1
2
0
0
1
2
2
3
2
0
1
1
1
1
2
1
1
1
0
2
2
1
0
0
2
1
2
1
2
0
2
2
0
1
1
0
0
1
1
1
1
0
1
0
2
1
0
0
0
1
1
1
1
1
0
1
2
0
2
1
1
2
1
0
1
0
0
2
0
0
0
0
1
0
2
0
1
1
0
1
0
0
1
0
2
0
0
0
1
1
0
0
2
1
1
0
1
2
1
0
1
2
0
1
1
1
2
0
0
1
1
2
0
2
1
1
1
2
0
1
0
0
1
1
2
1
0
1
1
1
0
2
2
2
2
2
1
0
2
1
2
0
0
1
0
1
2
1
0
1
1
2
0
1
1
1
0
1
1
1
0
2
0
0
2
1
1
1
2
0
1
2
0
2
0
0
1
2
1
0
0
2
1
1
2
1
0
1
0
0
1
1
1
1
2
0
2
2
2
0
0
0
0
2
2
1
3
2
2
0
1
1
1
0
1
1
0
1
0
1
0
0
2
1
2
0
2
1
0
2
2
0
1
2
2
2
1
1
1
0
1
1
2
1
2
0
0
0
0
2
0
1
2
6
1
3
1
0
1
0
1
2
2
1
2
1
0
1
2
0
1
0
0
0
1
1
1
1
1
1
2
1
0
2
0
0
1
1
2
1
0
1
1
0
1
1
1
1
1
2
0
0
2
0
0
2
1
0
1
1
0
1
1
1
0
1
1
1
2
2
0
1
0
1
0
0
2
1
0
1
1
1
1
2
2
2
2
0
1
2
1
0
1
2
0
2
1
1
0
0
2
1
1
1
0
1
0
1
0
1
1
1
1
2
1
0
0
2
0
0
1
1
2
1
1
1
1
1
0
1
1
0
1
1
1
0
1
1
3
1
1
2
1
0
1
1
1
1
2
2
2
2
1
0
3
1
0
1
1
0
1
0
1
0
0
1
0
1
1
1
1
1
1
0
1
0
2
1
2
1
2
2
1
1
0
0
1
1
0
1
0
0
2
2
1
2
0
1
1
0
1
1
1
1
2
2
1
1
2
0
0
0
1
2
0
0
1
1
1
2
0
1
1
1
2
0
1
1
1
3
1
2
2
0
2
1
2
2
1
0
0
0
2
0
1
2
1
1
1
1
1
1
0
1
1
0
1
1
0
1
2
1
1
1
2
1
2
1
2
1
1
2
0
2
0
1
1
0
1
0
1
1
1
0
1
0
2
3
2
0
0
0
1
0
0
2
0
1
1
2
1
1
2
1
1
0
1
0
1
1
2
1
0
2
0
1
1
1
2
1
1
1
1
1
2
1
0
0
2
1
1
0
1
0
0
1
2
1
2
1
0
1
1
1
2
1
1
1
1
0
0
2
0
2
3
0
0
1
0
1
2
0
1
1
1
1
0
1
1
1
2
0
1
1
1
1
2
1
0
2
1
1
0
0
1
1
1
2
0
0
6
0
0
0
2
0
0
4
1
1
1
1
1
1
2
2
1
0
1
1
0
1
0
0
1
1
1
0
0
0
1
1
1
1
2
1
0
1
1
0
2
0
1
1
0
2
0
1
2
2
2
1
0
1
1
1
1
1
1
1
0
1
1
0
0
0
3
2
2
2
2
2
1
0
0
0
1
1
2
0
2
2
1
1
2
1
0
0
1
0
0
1
0
1
1
2
2
1
1
1
1
0
1
1
2
0
1
2
1
0
1
1
1
1
1
1
0
0
0
0
0
0
1
1
1
0
1
1
1
2
1
0
0
2
1
1
0
2
2
0
1
2
1
1
0
1
2
1
0
1
1
0
1
2
0
1
1
2
1
2
0
0
1
0
2
0
1
0
2
0
2
1
1
1
1
1
2
1
1
1
2
3
0
2
1
2
1
1
2
0
2
0
2
2
2
3
0
0
1
1
1
1
1
1
0
1
1
1
1
0
1
1
0
1
0
1
1
1
1
1
2
0
1
2
1
2
1
2
1
1
0
1
0
1
1
2
1
1
2
2
0
0
1
1
3
0
0
1
1
1
1
1
0
1
1
1
1
2
1
3
2
0
2
1
2
1
1
2
1
0
1
1
0
1
1
2
0
1
1
2
2
1
2
1
0
2
1
1
1
1
2
1
1
1
2
0
3
1
1
1
1
2
2
0
0
0
1
1
0
0
1
0
0
1
2
2
1
2
2
0
0
1
0
0
2
1
0
1
2
2
1
0
1
1
1
0
3
0
0
1
1
1
1
2
9
1
0
1
0
1
1
1
0
1
0
1
2
2
1
0
1
1
0
1
0
1
0
1
1
3
1
2
1
1
0
2
1
0
1
1
0
0
2
0
0
1
1
2
2
1
1
1
2
1
1
1
0
0
0
1
0
1
1
0
2
0
1
2
2
2
2
0
0
0
1
1
1
1
1
0
0
1
0
2
0
1
1
0
1
1
2
2
0
0
1
0
1
0
2
1
0
1
1
0
2
0
2
1
2
1
0
3
2
2
0
1
1
1
0
1
2
2
1
0
0
0
2
2
0
2
1
1
2
0
1
1
0
1
0
0
2
1
0
0
1
1
1
1
2
1
0
1
1
1
1
1
1
0
1
2
0
0
1
1
1
2
1
0
1
0
2
1
1
1
1
1
2
0
1
1
2
1
1
1
2
0
1
1
1
1
0
2
5
1
0
0
0
1
2
1
1
0
1
1
1
2
0
1
2
4
2
0
0
0
1
1
0
1
2
1
1
0
1
1
0
1
1
1
1
1
2
0
0
1
1
0
0
0
2
1
2
0
2
2
1
2
2
2
0
2
0
2
1
0
0
1
1
1
1
1
1
2
2
1
1
0
2
0
1
1
0
0
0
2
2
1
1
0
0
1
1
0
0
0
0
0
1
0
1
0
0
1
1
1
0
0
1
1
1
2
0
2
2
1
1
2
1
2
1
2
2
0
1
1
2
2
2
1
1
1
1
1
1
1
1
1
0
1
1
2
2
0
0
1
1
0
0
1
2
0
1
1
0
3
1
0
0
2
1
1
1
1
2
1
1
1
1
0
1
1
0
2
0
1
0
0
2
1
0
2
1
1
1
0
2
0
1
0
1
0
1
1
1
0
2
0
1
1
2
1
1
2
1
2
1
0
1
2
0
0
2
1
2
1
2
1
0
0
1
1
0
0
2
0
1
2
1
0
2
1
2
1
0
1
1
2
0
1
1
2
0
1
2
2
1
1
1
1
1
2
1
0
0
1
1
2
1
1
2
2
1
1
1
1
1
2
1
1
1
0
1
0
0
1
1
2
1
2
1
1
1
0
0
2
1
2
1
1
1
0
0
2
2
1
1
2
1
2
1
1
0
0
2
2
1
0
0
1
0
0
1
3
4
2
0
2
2
1
1
2
0
0
0
1
1
3
1
1
1
2
1
2
1
0
1
0
1
0
0
0
1
1
1
1
0
2
2
1
0
1
0
2
1
1
1
1
1
0
0
0
2
1
2
1
1
1
0
0
1
1
0
0
0
0
1
1
1
0
1
2
0
2
1
1
1
3
0
1
0
2
1
1
1
0
1
1
1
0
0
1
2
0
0
0
1
1
2
1
2
2
1
2
2
0
0
0
1
1
1
1
1
1
1
2
0
1
1
0
0
0
1
1
1
0
1
1
2
0
1
2
1
0
0
1
2
0
0
1
1
2
2
1
1
1
2
1
2
0
1
1
1
0
1
2
2
1
1
1
2
1
1
2
3
0
1
1
1
0
1
1
2
0
1
0
0
1
1
1
2
0
0
1
0
0
1
2
1
1
0
2
1
0
1
1
1
2
1
1
1
2
0
0
1
1
1
2
1
1
1
0
1
1
2
1
1
0
1
1
0
0
0
2
2
1
1
1
2
1
0
1
2
0
0
0
2
2
1
1
1
1
1
1
1
0
1
1
1
1
2
3
0
1
1
1
0
1
1
1
0
0
2
0
0
0
1
1
1
1
1
1
0
1
2
1
2
2
0
0
1
1
0
2
1
2
2
2
0
1
0
0
0
2
0
1
1
0
2
2
1
0
2
1
0
0
0
0
2
1
2
1
1
2
1
2
1
0
1
1
0
1
2
1
1
0
2
0
1
1
1
1
0
1
1
1
1
1
0
0
0
1
2
1
1
1
2
0
1
1
2
1
2
0
0
0
1
1
1
1
0
1
2
1
1
1
2
1
1
1
1
3
0
2
0
0
1
0
0
0
1
2
1
1
1
1
1
2
1
0
1
1
0
0
0
2
2
2
1
0
0
1
2
0
0
1
0
1
0
2
1
2
1
0
1
1
1
2
1
1
1
0
0
1
0
0
0
1
0
0
1
0
2
2
1
2
1
2
0
1
2
1
0
1
1
0
2
1
1
1
1
1
2
0
2
2
0
1
1
0
1
0
1
2
0
0
2
1
1
0
1
1
1
0
2
2
0
2
2
1
2
1
0
1
0
2
0
0
2
0
0
1
0
2
2
1
0
0
1
2
1
1
1
3
0
0
0
1
2
2
0
0
2
1
1
2
2
0
0
1
1
1
1
0
0
1
0
0
0
1
0
0
0
0
1
1
2
1
0
1
1
0
0
0
1
2
0
0
1
2
2
1
1
1
2
0
2
0
2
1
1
0
2
2
1
1
0
1
1
0
2
2
1
2
1
0
0
2
1
1
2
2
1
2
3
0
2
1
1
2
1
2
1
0
1
1
1
1
0
0
0
1
1
2
1
0
1
0
0
1
1
1
0
1
1
2
0
1
0
2
0
1
2
1
0
1
0
0
0
1
0
1
1
2
1
0
1
0
1
0
1
1
0
1
0
1
1
2
2
0
0
2
1
2
0
1
2
0
0
0
0
1
1
0
1
1
1
0
0
1
1
1
0
0
3
1
1
1
0
1
2
1
0
0
1
1
1
0
1
2
1
1
0
2
1
2
1
1
1
0
2
2
2
0
0
0
0
1
1
0
2
3
0
1
0
1
1
1
2
0
1
1
3
1
1
1
0
0
1
0
1
1
0
0
0
1
0
1
2
2
0
1
2
0
2
0
2
2
0
0
1
1
1
1
0
1
2
1
0
1
0
1
1
2
1
0
1
2
0
1
0
1
1
0
1
0
2
0
0
0
0
0
2
1
1
0
0
1
0
1
3
2
2
2
0
2
1
0
2
0
1
1
0
1
2
1
1
2
1
2
1
1
0
2
1
1
1
0
1
2
2
2
2
1
2
1
2
1
1
0
1
1
1
1
2
1
0
0
2
0
0
0
0
2
1
1
1
0
1
1
1
1
2
0
1
1
1
2
1
2
0
2
2
0
0
1
1
1
0
1
0
1
0
1
2
0
1
0
1
1
2
0
0
1
0
0
0
1
0
1
0
2
0
1
0
1
1
1
0
1
0
1
2
0
2
2
1
1
1
2
0
2
1
0
2
2
1
1
2
0
1
2
1
2
0
1
0
1
0
2
1
2
0
1
0
1
2
0
1
1
2
2
0
2
1
2
1
1
1
0
0
1
2
2
0
1
0
1
0
0
0
2
0
1
0
1
1
0
0
2
1
0
1
1
0
2
0
0
1
1
1
1
1
2
1
1
1
0
1
1
0
3
2
2
1
2
2
1
0
1
2
1
2
0
0
1
1
1
1
0
0
1
1
1
1
1
1
1
1
1
1
0
3
2
1
1
1
1
2
0
1
0
1
0
2
1
4
1
1
1
0
1
2
0
1
0
1
1
1
0
1
2
2
1
2
1
1
1
1
1
1
0
2
1
1
1
0
2
1
1
0
1
1
1
1
0
1
3
1
0
2
1
0
2
0
1
0
1
0
2
0
1
0
1
1
2
1
1
3
1
1
0
1
0
0
2
0
0
1
1
2
1
2
0
1
1
1
2
1
0
1
2
1
0
0
1
0
1
1
0
0
1
0
0
0
1
1
1
1
2
2
1
2
0
0
1
1
1
1
1
1
2
0
1
0
1
1
1
1
1
2
1
1
0
0
2
1
1
0
1
0
1
1
0
1
0
1
1
0
2
1
1
2
0
0
0
0
0
1
1
1
0
0
1
0
1
2
0
1
2
1
0
1
0
1
0
2
0
0
1
0
0
0
1
0
0
1
2
2
1
0
2
0
1
2
1
2
1
2
0
0
0
1
0
0
1
1
1
1
1
2
2
2
1
0
1
0
2
1
2
1
2
1
2
3
1
1
3
2
0
2
2
0
0
1
1
1
1
0
1
0
1
1
1
0
0
1
0
0
2
0
1
0
0
1
1
2
2
2
0
1
1
0
1
3
1
0
0
0
1
1
1
1
1
2
1
2
0
0
1
0
1
1
2
1
2
1
1
1
0
1
1
2
1
2
0
0
0
1
0
1
1
0
0
0
2
0
1
1
1
1
2
1
2
1
2
1
1
1
3
1
1
1
1
0
2
1
1
3
1
2
0
0
2
1
1
1
1
1
0
1
1
0
1
0
1
1
2
2
2
2
1
2
0
2
0
0
1
2
2
0
2
1
1
1
1
1
1
1
0
1
1
0
2
1
0
0
2
0
0
0
0
0
0
1
0
0
1
2
1
0
3
1
0
0
1
2
0
1
0
2
1
1
1
0
1
1
0
1
2
2
0
2
1
2
0
0
0
1
1
2
0
0
0
0
1
1
1
0
2
1
1
1
0
1
1
0
1
2
1
1
1
1
1
0
2
0
2
2
0
1
0
2
1
1
2
1
2
1
0
0
1
1
1
2
0
2
1
1
0
2
2
1
2
1
0
0
2
2
0
1
1
0
2
1
1
1
1
1
0
2
2
2
1
2
0
2
1
0
1
1
2
0
0
2
0
1
0
1
1
1
0
1
1
2
1
3
1
1
1
1
1
1
2
1
1
1
2
0
2
0
1
2
2
2
1
1
2
1
1
0
1
1
1
1
3
1
1
1
1
1
2
1
1
0
0
1
2
1
1
1
2
1
1
1
0
1
2
0
2
0
2
1
2
1
1
0
1
1
0
0
1
1
2
2
2
2
0
0
2
0
1
1
1
1
1
2
0
0
2
0
1
0
1
1
1
0
0
1
2
1
0
2
1
2
1
2
1
1
2
1
1
1
0
0
1
0
2
0
1
0
1
0
1
1
1
0
1
1
0
1
1
1
0
2
0
1
1
1
1
2
2
2
0
1
1
0
0
0
2
0
3
0
1
1
1
1
1
2
1
2
1
2
1
0
2
1
1
1
0
0
0
2
0
1
0
2
1
2
2
0
1
1
1
1
0
1
1
1
1
1
1
1
0
1
1
0
0
1
0
0
1
0
0
1
1
1
1
1
1
2
1
1
1
2
0
1
1
0
1
1
0
0
0
1
1
1
1
1
0
0
1
1
1
1
0
2
1
0
1
1
0
0
1
3
1
0
0
1
2
1
1
1
0
0
0
0
1
1
0
0
3
1
0
0
1
0
2
1
0
1
1
0
2
1
0
0
1
2
1
0
0
0
1
2
2
1
1
1
0
0
3
1
1
1
0
0
2
1
0
1
0
0
1
1
0
2
0
1
1
2
1
2
1
2
1
1
0
0
0
1
2
0
2
0
2
3
1
2
1
1
2
0
1
1
2
1
1
1
1
2
1
1
1
0
1
0
0
2
1
1
0
0
3
1
1
1
1
2
0
1
2
1
2
1
4
1
0
1
0
1
1
0
2
1
2
1
0
1
2
1
0
0
1
2
3
3
0
1
1
1
1
2
1
2
1
2
0
1
0
1
2
0
2
1
1
2
1
2
1
2
1
0
1
2
0
0
2
1
1
1
0
1
1
1
0
0
1
0
2
3
0
1
0
0
2
1
1
1
1
0
0
2
2
1
2
2
2
0
2
1
0
1
1
0
1
1
1
1
2
2
0
1
3
1
1
1
2
1
0
1
1
1
1
1
2
0
0
0
3
1
1
1
1
2
2
0
2
0
1
1
2
1
2
0
0
0
1
1
1
1
0
1
1
0
1
1
0
1
0
1
1
2
2
0
1
1
0
1
0
2
2
1
1
0
0
2
1
1
1
0
0
1
1
1
1
0
0
0
0
1
2
0
1
1
1
1
1
2
2
2
1
1
0
2
0
1
1
1
0
1
1
0
1
1
1
1
0
1
2
0
1
1
0
1
1
0
0
1
2
0
2
1
1
1
0
1
2
1
2
1
2
0
0
1
1
0
1
1
1
2
2
2
2
0
2
1
1
1
2
0
0
2
0
1
1
2
1
1
1
0
2
0
1
0
1
0
1
1
1
2
1
3
1
2
1
1
1
1
0
1
0
2
2
1
1
1
1
1
0
0
1
1
1
1
1
1
1
2
0
1
1
2
1
0
1
1
2
0
1
1
0
2
1
1
0
2
0
2
0
1
0
2
2
1
2
2
2
2
2
1
1
0
2
1
0
0
1
2
2
1
1
0
2
1
1
0
0
2
2
0
0
0
1
0
1
1
0
0
1
0
0
1
1
5
1
1
1
2
2
1
1
2
2
1
1
0
1
2
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
2
2
0
0
2
1
1
0
1
1
1
2
1
1
2
0
1
1
0
2
0
1
0
1
1
2
2
1
1
2
1
0
0
1
1
2
1
1
0
2
1
0
1
2
0
0
2
1
0
1
1
1
0
2
2
1
0
0
0
1
1
1
1
0
1
1
1
2
1
1
1
2
0
0
0
1
1
0
2
1
1
0
0
1
2
1
2
0
0
0
1
0
0
1
1
0
1
2
1
2
0
1
2
1
2
0
1
0
2
1
1
2
1
1
2
0
0
1
0
1
1
0
1
1
1
1
1
0
1
2
0
2
2
2
1
0
1
2
2
0
1
0
1
0
0
1
0
1
0
3
1
1
1
0
1
0
1
1
1
0
2
2
1
1
2
1
0
1
1
0
1
1
0
2
0
0
1
1
5
2
0
1
2
2
0
1
0
1
1
2
2
1
2
0
1
0
1
0
0
1
1
2
1
0
2
0
1
0
0
2
0
0
2
2
1
1
1
2
1
1
3
1
1
2
1
1
1
0
0
0
1
1
0
1
2
1
1
1
0
0
2
2
1
2
0
0
0
1
0
2
1
2
1
1
0
2
1
1
0
1
2
1
0
0
2
1
0
0
0
0
2
1
1
1
1
1
1
0
2
1
1
1
1
2
0
1
2
0
0
1
2
1
0
0
0
1
1
0
1
0
0
1
1
2
0
1
1
2
1
2
1
2
1
1
2
0
1
2
1
2
1
0
4
0
2
1
2
1
1
0
0
0
2
1
1
2
1
2
0
2
2
1
2
1
1
2
1
0
1
1
1
2
2
2
1
0
1
0
1
0
0
1
1
0
2
1
1
1
1
2
2
2
1
1
1
0
1
1
1
0
0
0
2
1
0
0
1
2
0
3
1
1
1
1
1
0
1
1
2
1
2
0
1
1
1
0
0
1
1
0
0
1
0
1
2
0
0
0
2
0
2
1
1
0
0
2
1
0
1
1
1
1
0
1
1
1
1
0
2
0
1
1
1
0
1
1
1
3
0
1
2
1
1
0
0
1
0
1
3
1
1
1
0
1
1
2
0
0
0
1
2
1
0
0
0
1
1
2
1
1
2
1
0
2
1
1
1
0
2
0
1
1
1
1
0
1
1
1
2
1
1
2
1
0
2
2
1
1
0
2
2
4
2
0
0
0
1
0
0
1
1
1
0
0
0
2
2
2
1
0
0
1
1
0
0
1
1
0
1
2
0
0
0
2
2
0
0
1
0
2
1
1
2
0
1
2
2
0
2
1
1
1
1
2
1
1
1
2
0
3
1
0
2
2
1
2
2
2
0
1
1
1
1
0
1
0
0
1
0
1
0
2
2
1
2
0
1
2
0
2
2
1
1
0
0
1
0
0
2
0
2
0
1
2
0
0
0
1
1
1
1
0
1
1
1
1
2
2
2
0
1
2
0
0
0
0
1
2
0
3
0
2
0
1
1
1
1
1
2
2
1
1
2
2
0
2
0
0
1
1
2
0
0
1
1
1
0
1
2
0
1
1
0
1
1
1
0
1
0
2
2
1
2
2
2
1
1
0
1
2
1
0
1
1
1
2
2
1
1
1
1
1
0
0
1
2
2
1
2
0
1
1
0
2
1
0
1
0
0
2
1
1
0
0
1
0
1
2
0
2
0
2
1
0
2
2
1
0
1
1
1
0
0
1
0
0
2
1
1
0
0
1
2
1
2
1
1
0
1
0
0
2
2
0
2
0
0
1
1
4
1
1
0
2
1
2
1
0
2
1
0
1
1
0
2
2
1
2
1
0
1
1
1
0
2
1
2
1
1
0
2
2
1
1
2
2
1
1
2
0
1
2
1
1
2
3
2
1
0
1
1
2
0
1
0
1
1
0
1
1
1
0
0
1
1
0
0
1
0
1
0
1
0
1
1
1
0
2
1
1
1
1
1
0
2
2
0
2
1
1
2
1
2
0
1
1
2
0
0
1
1
1
1
1
1
2
2
1
0
1
0
1
0
2
1
1
0
0
1
0
2
1
1
2
1
0
0
2
1
2
2
1
0
0
1
1
0
1
0
0
1
2
1
1
1
1
1
1
1
0
0
1
1
2
2
2
1
1
0
0
0
0
1
1
1
0
2
2
0
2
1
0
0
2
0
0
1
1
0
1
1
2
1
0
1
1
0
1
1
2
1
0
2
1
2
1
1
0
1
0
2
1
1
0
2
1
2
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
2
0
0
4
2
1
2
0
0
2
2
0
2
0
1
0
2
1
1
1
1
2
2
1
1
1
1
1
2
1
0
1
1
0
2
0
1
0
0
1
1
0
2
1
1
3
0
1
1
1
1
1
0
1
1
1
0
0
1
1
0
2
0
2
1
1
2
1
0
2
1
0
0
2
1
2
1
0
1
1
1
0
1
0
2
0
0
0
2
0
0
0
2
1
0
1
0
1
2
1
1
1
1
1
2
1
0
2
1
1
0
0
2
0
1
0
0
2
0
1
0
1
1
0
1
0
1
1
1
1
2
2
2
1
2
1
0
1
1
0
0
1
2
1
2
0
2
2
0
1
0
1
2
1
2
0
0
0
1
0
2
2
1
1
0
1
0
2
1
3
1
2
2
0
0
0
1
2
2
1
2
1
1
1
2
2
0
0
1
1
2
1
2
1
2
1
1
2
2
2
0
0
0
2
1
0
2
0
2
2
1
2
0
1
1
1
2
1
0
1
0
2
1
1
1
0
0
0
1
1
0
1
0
0
0
0
2
0
2
1
0
0
1
2
1
0
0
1
0
1
0
2
1
0
1
0
1
0
0
1
2
1
1
0
2
0
2
0
1
0
3
1
0
0
1
1
0
0
0
2
1
0
2
0
2
1
0
2
1
1
0
0
1
0
2
0
1
1
0
2
0
2
1
0
1
1
1
1
0
2
1
1
0
1
1
0
1
1
1
1
2
1
0
0
2
2
2
0
0
0
1
2
0
1
0
1
0
0
1
4
0
1
1
1
1
1
2
0
0
1
0
2
1
2
1
1
1
0
1
1
0
1
1
0
1
2
1
1
2
1
2
0
2
0
2
1
0
0
1
0
1
1
0
1
0
2
0
0
1
0
1
1
2
1
0
0
0
1
1
2
1
1
1
1
2
1
0
1
1
1
1
1
0
1
2
1
3
2
2
1
1
1
0
2
0
1
2
1
0
0
1
1
1
0
0
1
1
2
2
0
0
1
0
1
1
1
1
0
2
0
2
0
1
0
0
0
2
1
0
2
1
1
0
1
1
0
1
2
1
2
1
1
0
0
2
0
0
0
1
1
2
3
1
1
1
1
0
1
0
1
1
1
0
0
2
1
2
0
1
1
0
2
1
2
0
1
0
1
1
1
0
0
0
0
1
2
1
1
2
2
1
2
1
0
1
2
2
1
1
1
0
1
0
1
1
1
0
2
0
0
1
1
1
1
2
1
2
1
1
1
1
1
2
1
3
1
2
1
1
1
1
1
0
2
1
0
1
1
0
0
0
2
0
1
1
0
2
1
0
2
1
0
0
0
0
0
0
1
1
1
2
1
2
0
1
1
1
2
1
1
0
1
1
2
2
0
3
1
0
0
0
2
1
2
0
1
0
1
3
1
1
1
0
2
0
0
2
1
1
2
1
1
1
0
2
1
1
0
0
2
1
1
0
1
2
1
1
1
1
2
2
0
0
2
1
1
1
3
2
0
1
0
0
0
0
0
1
1
0
1
1
0
0
1
1
0
1
1
1
0
4
1
1
2
2
2
2
1
1
2
1
3
2
1
0
2
0
2
1
2
1
1
2
1
0
0
1
0
0
1
0
1
0
1
0
2
0
0
0
1
0
1
0
1
1
3
1
0
1
2
1
1
1
0
1
1
1
0
2
0
1
2
1
1
2
1
1
2
1
1
0
0
1
1
1
2
2
1
0
1
1
1
0
1
1
0
1
0
1
0
0
1
1
1
0
2
1
2
0
0
1
1
0
0
2
1
2
1
1
2
0
1
2
2
0
1
1
2
0
2
1
1
2
1
0
0
1
2
1
1
1
1
0
1
1
2
2
0
1
1
0
2
1
3
1
1
1
1
2
1
0
0
2
0
2
2
2
1
1
1
1
2
2
0
1
0
1
0
1
3
0
0
2
2
0
2
1
0
0
1
1
0
1
1
1
1
0
1
1
1
2
0
0
1
2
0
0
1
0
0
1
1
0
0
2
2
0
0
0
1
0
1
0
2
0
1
2
2
0
2
1
0
1
2
2
0
0
1
1
1
1
0
1
1
0
2
1
1
1
1
0
0
0
0
1
2
1
1
1
1
1
1
0
1
1
1
1
2
1
0
1
0
2
2
0
1
2
1
0
2
0
1
0
1
3
0
1
1
2
1
0
1
1
1
0
0
2
1
1
1
2
0
1
1
1
2
0
0
2
0
2
1
1
2
2
2
2
0
0
1
0
2
0
1
2
0
2
2
2
1
2
1
1
0
1
0
1
0
0
1
1
1
0
2
1
0
0
1
1
0
1
1
1
2
0
0
2
1
1
0
1
1
0
1
0
0
0
2
0
1
0
0
2
1
0
2
0
2
0
0
1
0
1
1
0
2
0
1
2
1
1
3
1
1
2
1
2
1
0
0
1
0
1
2
1
1
2
1
1
1
1
2
0
2
1
1
1
0
1
1
0
0
2
1
1
2
2
1
0
1
1
1
0
2
0
0
1
1
1
2
1
1
2
1
1
1
1
0
1
0
1
1
0
2
2
2
1
1
0
0
1
2
0
0
1
0
1
0
1
2
1
1
1
0
1
1
0
2
2
1
0
0
0
0
2
2
2
1
2
1
0
1
1
0
1
1
1
0
1
2
0
0
2
0
2
1
1
0
0
1
1
0
1
1
0
1
1
1
1
1
0
1
1
3
2
0
0
0
2
0
1
0
1
0
1
0
1
2
1
1
1
0
0
0
1
2
1
1
0
1
0
1
1
1
0
0
1
0
1
1
1
2
1
1
1
1
1
0
1
1
0
1
1
2
1
1
2
1
1
0
2
1
0
1
1
0
1
2
2
0
0
0
1
2
2
1
1
0
0
0
1
2
0
0
1
1
1
1
1
1
1
0
1
1
0
1
0
1
0
1
2
1
1
4
2
1
0
2
0
0
1
2
1
0
0
0
1
0
1
2
1
1
0
1
1
0
1
1
1
1
0
1
0
0
0
0
0
0
1
1
1
1
1
0
0
2
0
1
2
1
0
1
1
1
1
1
0
1
1
1
2
0
1
1
1
4
1
2
1
2
1
0
1
1
1
0
1
3
1
1
1
0
0
2
1
1
1
2
1
2
1
0
0
1
1
1
0
2
1
2
0
1
0
0
1
2
0
1
0
0
0
0
2
2
1
2
1
0
1
1
1
0
2
1
1
0
2
2
0
1
1
1
1
1
1
0
0
0
1
1
1
1
2
1
0
0
2
1
0
1
0
1
0
2
0
1
0
0
2
2
1
0
1
2
0
0
1
1
2
1
0
1
1
2
2
2
1
1
1
0
0
0
0
0
2
1
1
1
0
1
1
0
2
2
2
0
0
1
2
1
0
2
1
0
2
1
2
0
1
1
5
0
2
1
1
0
1
1
2
0
1
2
0
2
1
0
0
0
1
0
0
0
1
1
0
1
0
2
2
0
1
1
0
2
2
1
1
0
2
0
1
0
2
1
0
0
1
2
2
1
1
1
0
1
0
1
1
1
1
1
2
0
1
2
0
2
1
0
1
0
1
1
0
0
2
0
0
2
0
0
1
2
1
0
1
1
1
1
1
2
1
1
1
1
1
1
0
0
0
2
1
1
2
2
2
0
0
0
1
2
1
0
1
1
0
0
2
1
1
1
1
1
0
2
0
2
2
0
2
0
1
1
1
0
1
1
0
1
0
2
0
1
0
0
1
0
1
1
2
1
1
0
1
1
0
1
1
1
1
0
0
1
0
0
2
1
2
2
0
1
2
1
1
1
0
1
0
1
1
2
1
0
1
1
1
2
1
0
2
1
1
1
1
1
1
1
2
1
1
0
0
1
1
0
0
1
1
1
0
0
2
2
1
0
1
1
0
1
1
1
0
1
0
1
1
0
3
1
1
1
0
1
0
2
2
1
1
0
1
1
1
1
1
0
1
0
1
2
2
0
0
3
2
1
1
1
2
1
2
1
1
2
2
2
1
1
0
1
0
1
0
1
1
0
1
1
1
0
1
0
1
1
1
0
0
0
1
0
1
1
0
2
1
1
0
0
1
0
1
1
0
1
0
0
1
1
2
1
1
2
1
1
1
1
1
0
0
1
0
1
1
1
1
0
0
1
1
2
1
0
0
1
1
1
1
1
1
1
0
0
0
0
1
0
0
1
0
1
1
2
1
1
1
0
1
1
1
1
2
0
2
1
1
1
1
1
1
1
0
1
2
2
1
2
0
1
2
1
1
1
1
1
0
0
6
1
0
1
1
1
0
1
2
0
0
1
1
2
1
0
2
0
1
1
0
1
1
0
0
1
0
1
1
2
2
1
1
0
0
1
1
1
1
0
2
1
2
1
0
0
0
2
0
1
0
0
1
1
2
0
1
0
2
0
1
2
0
2
1
1
1
1
0
0
1
1
1
0
2
1
0
1
0
0
0
1
1
2
2
1
2
1
1
0
0
2
1
1
1
1
0
1
2
1
0
1
1
1
2
0
2
1
0
1
1
0
2
1
1
1
1
0
0
0
3
1
1
1
0
1
2
1
0
1
2
0
0
1
0
0
2
0
1
0
1
0
1
1
1
1
1
1
0
1
1
1
0
0
1
1
1
1
0
1
1
2
2
1
1
1
0
1
0
2
0
0
0
0
2
2
0
0
1
1
1
2
0
0
1
0
1
2
2
1
1
1
0
1
1
1
2
2
1
0
1
0
1
0
8
2
0
1
2
0
0
0
1
2
2
3
0
1
1
2
1
2
1
2
0
1
0
2
0
0
1
0
1
3
1
1
0
1
2
1
1
1
2
1
1
1
0
2
0
2
2
1
3
0
1
1
1
1
1
1
0
1
2
2
1
1
0
1
0
0
2
1
2
2
1
1
2
0
1
1
2
1
2
1
0
0
1
2
0
1
1
1
1
0
0
0
0
2
2
1
2
1
1
0
1
2
1
2
1
0
2
2
1
1
1
1
0
2
2
2
1
1
1
0
1
1
1
0
1
1
1
0
2
1
0
1
1
2
1
1
1
2
0
1
0
1
1
2
1
0
0
0
2
1
1
0
1
0
1
0
1
1
1
3
2
0
1
1
1
2
2
1
2
3
0
0
1
0
2
0
0
0
2
0
1
1
1
2
0
1
1
0
1
1
1
1
1
1
1
0
2
1
1
1
2
2
2
0
2
0
0
0
1
1
1
1
0
0
2
0
1
0
2
0
2
1
1
0
2
2
0
2
2
1
1
2
1
2
2
2
1
2
1
1
1
2
2
1
0
2
2
1
2
0
2
0
1
0
1
0
1
0
0
1
1
1
1
1
0
5
0
0
2
1
1
1
2
1
1
1
0
1
0
2
0
1
2
2
1
0
2
0
1
1
1
1
2
1
1
1
1
1
2
0
0
0
1
0
1
0
1
0
1
1
0
1
0
0
1
2
0
1
1
1
1
0
0
0
2
1
1
0
2
1
0
0
1
0
1
1
2
1
1
1
0
0
1
2
1
2
1
1
2
2
1
2
1
1
0
2
1
0
1
0
0
1
1
1
0
1
1
1
2
0
1
2
0
1
1
2
0
1
2
3
1
0
1
1
1
0
1
1
0
0
1
0
0
0
2
0
1
0
0
1
0
1
3
1
0
1
1
1
0
2
1
2
1
0
1
1
0
3
0
0
1
0
0
0
1
0
0
1
0
1
2
1
0
1
0
1
1
2
1
0
0
1
0
1
1
2
0
2
2
3
0
0
1
0
3
0
1
1
1
2
1
1
3
0
0
2
1
1
0
0
2
1
0
3
1
2
1
0
1
0
1
2
1
3
0
2
0
0
0
1
0
2
1
2
1
1
1
1
1
1
2
2
1
1
0
0
1
1
1
1
2
1
0
0
2
1
0
1
2
1
2
1
0
0
2
1
1
2
1
0
0
1
0
0
0
1
1
1
0
0
0
1
1
0
1
0
2
2
2
1
2
0
0
2
2
1
1
1
4
1
0
1
1
0
1
1
1
1
1
2
1
0
1
0
1
2
1
1
1
0
0
0
2
1
1
0
0
1
1
0
2
2
1
0
2
0
2
1
1
1
0
1
2
0
0
2
1
1
1
2
1
1
1
0
3
2
1
1
0
2
1
2
1
1
2
0
0
1
0
1
1
1
1
2
0
1
2
0
1
2
2
2
1
0
1
0
3
2
2
1
2
1
0
0
0
0
1
0
1
1
0
1
0
0
1
0
0
1
1
1
1
0
1
1
2
1
0
1
1
1
2
1
1
1
0
2
1
1
2
1
1
1
2
1
1
2
1
0
1
1
1
0
1
0
2
0
0
1
0
0
0
1
1
1
0
2
0
1
1
1
1
1
1
1
1
1
2
0
0
0
1
0
2
2
0
1
0
1
0
1
2
2
0
2
0
2
0
2
0
1
1
1
2
1
0
2
0
0
0
2
1
2
1
0
0
1
1
5
1
2
1
0
1
1
1
1
0
1
2
2
2
1
1
0
0
1
1
2
1
0
1
1
1
0
0
0
1
2
4
0
1
0
1
2
1
1
0
1
0
3
2
1
1
1
2
1
1
0
1
0
2
0
0
1
1
0
1
1
0
1
1
1
1
2
1
2
1
1
2
0
2
1
0
1
1
1
2
0
0
2
1
0
0
0
0
1
0
0
1
3
0
1
0
1
1
1
0
0
1
0
0
1
0
1
2
1
1
2
1
1
2
1
3
1
0
2
1
1
1
2
0
2
2
1
1
1
1
1
1
1
0
1
1
0
2
1
1
1
1
0
1
1
0
0
2
1
0
2
2
0
0
5
0
2
1
0
1
0
1
1
0
1
2
0
0
1
1
0
2
0
1
2
1
1
2
1
1
2
0
0
0
1
2
0
2
1
1
1
1
1
2
1
1
0
2
1
1
0
0
0
2
0
1
1
1
0
0
1
2
1
1
2
2
0
1
0
1
0
0
0
1
0
2
0
1
0
1
0
2
1
1
0
1
2
0
2
1
1
0
2
0
2
2
2
1
1
2
1
1
1
1
0
1
2
2
1
1
1
0
1
1
1
2
1
1
3
2
2
1
0
2
1
1
2
1
1
2
1
1
1
0
1
0
0
2
1
1
1
2
1
1
1
1
2
2
1
0
0
2
0
0
0
1
2
1
1
1
0
1
0
1
2
2
1
1
0
2
2
2
0
1
0
0
0
1
0
0
1
2
1
2
1
1
1
1
0
1
1
2
1
1
0
1
2
1
0
1
0
1
0
1
1
2
2
0
2
0
2
1
1
0
1
1
1
0
0
1
1
0
1
1
3
0
1
0
2
1
1
1
0
1
1
2
6
1
1
0
1
1
1
0
2
2
1
0
1
0
0
0
0
0
1
1
0
2
0
0
1
2
0
2
0
1
1
1
0
2
0
0
0
1
0
1
0
0
0
1
1
0
1
0
1
2
3
0
1
1
1
1
1
2
1
1
1
2
1
0
1
2
1
2
1
1
2
1
0
2
1
2
1
1
0
0
0
1
0
1
1
0
1
1
1
0
1
1
2
0
2
1
2
1
1
0
1
1
2
2
1
2
2
2
3
0
0
0
1
0
0
0
1
2
1
2
2
2
1
1
1
1
0
0
1
1
2
1
0
0
2
2
2
1
0
3
0
1
0
0
1
0
1
2
0
1
0
1
0
2
1
1
1
0
2
1
0
0
0
2
2
2
0
1
1
1
1
1
2
0
0
1
1
1
1
0
1
0
0
1
2
2
1
1
1
2
1
1
2
2
1
2
1
1
2
1
1
1
1
0
0
1
1
1
1
2
0
1
1
1
1
1
2
1
0
1
2
0
0
1
0
0
1
1
1
2
2
1
2
0
2
1
1
1
2
1
1
1
0
1
1
1
1
1
1
1
0
1
1
1
1
0
2
0
1
1
0
0
1
1
0
1
0
1
1
1
0
1
0
0
0
0
1
0
0
1
0
1
1
1
2
2
2
1
1
1
1
0
2
2
1
2
2
1
1
1
0
1
0
0
1
0
3
0
0
0
1
1
1
1
1
0
1
1
1
0
0
0
2
1
1
1
2
0
1
2
1
1
1
0
1
1
1
1
1
0
1
0
0
0
0
2
1
1
1
2
0
0
1
2
1
0
1
0
1
1
2
2
1
0
2
1
2
0
0
2
2
1
1
1
1
1
1
1
0
1
0
0
2
0
0
2
1
1
1
1
1
1
2
0
1
1
0
1
4
1
2
1
1
2
2
0
1
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
1
0
2
2
0
2
0
2
0
1
1
1
1
0
1
1
1
1
0
1
1
2
2
2
1
1
0
0
0
1
0
1
0
1
1
1
1
1
2
1
1
0
2
0
1
0
0
1
1
1
0
1
0
1
1
1
1
0
1
2
0
1
1
1
2
0
1
0
2
0
2
1
2
0
0
0
2
1
3
2
1
1
2
0
1
2
0
1
2
2
1
1
0
1
1
1
1
0
1
0
1
1
0
1
1
0
1
0
1
1
0
0
0
0
1
2
1
1
0
2
1
1
1
1
1
1
0
1
1
0
1
2
0
1
2
2
0
1
2
1
0
2
2
0
1
1
0
1
1
0
1
0
2
0
1
1
3
0
0
1
0
0
1
0
1
0
1
2
1
1
1
0
0
2
1
1
0
0
1
1
0
1
0
1
1
0
2
1
1
1
0
1
1
1
0
0
1
0
0
0
2
0
2
1
1
1
0
1
0
0
1
2
2
0
1
1
1
1
2
0
1
1
2
2
1
1
3
0
1
1
2
1
1
2
1
1
0
0
1
0
1
2
2
1
0
0
1
0
1
1
1
1
2
0
1
1
2
0
2
0
0
1
1
1
2
0
0
1
3
0
0
1
1
1
1
1
1
0
1
1
1
1
1
2
0
1
2
2
0
2
1
1
1
0
1
1
0
2
1
2
1
1
0
0
1
0
2
2
0
1
1
1
2
0
3
1
1
2
1
0
1
0
1
2
0
1
0
2
2
2
1
1
2
1
2
0
1
2
1
0
1
1
2
0
1
1
0
1
1
2
2
1
1
0
0
1
1
0
0
2
0
1
0
1
2
0
2
1
1
0
0
2
2
2
2
0
1
2
0
1
0
1
1
0
1
1
1
0
0
0
0
2
2
1
0
2
1
1
2
2
2
2
2
2
0
1
1
0
1
1
0
2
1
0
4
3
1
1
1
0
2
2
2
1
1
0
2
1
2
1
2
1
1
0
0
0
2
1
1
0
1
2
2
1
1
1
1
1
0
0
4
2
1
1
0
0
1
1
1
2
0
2
1
0
1
2
1
1
1
0
0
1
0
2
1
1
0
2
1
0
1
0
0
0
0
1
1
1
0
4
2
0
0
0
1
2
2
0
3
0
0
1
2
1
1
1
1
2
2
2
2
2
1
2
2
2
1
2
1
1
1
2
0
1
0
1
2
2
2
1
1
1
2
2
1
0
2
1
1
1
1
0
1
1
0
0
4
2
1
1
1
1
0
1
1
1
1
1
1
1
0
0
1
1
0
1
0
2
1
1
1
1
1
1
1
1
1
0
0
1
1
0
0
1
1
1
0
2
0
1
0
0
5
0
1
1
2
0
2
0
2
0
0
0
0
2
1
0
0
1
1
1
1
2
1
1
1
2
2
0
2
0
0
1
0
1
1
0
1
2
1
2
1
1
1
0
0
0
1
1
0
1
1
1
1
0
0
2
0
0
1
1
0
2
1
2
1
1
1
0
1
0
2
0
1
1
0
2
0
1
1
2
1
1
2
1
2
1
0
0
1
2
1
0
1
2
1
1
1
1
2
1
1
1
1
0
1
2
2
0
2
2
1
2
2
0
0
2
1
1
1
4
1
0
0
1
0
1
1
1
0
0
2
0
1
2
1
0
0
2
2
1
1
2
1
1
1
0
1
0
1
0
1
1
0
0
0
1
0
1
1
1
0
2
1
0
2
9
0
2
1
2
0
0
1
1
1
4
2
0
1
2
3
1
1
2
1
1
1
2
0
0
1
1
1
0
1
0
1
2
2
1
1
0
1
1
1
1
0
0
1
2
1
1
0
2
2
0
2
0
1
1
2
0
0
0
1
0
0
2
1
1
1
1
1
1
1
1
1
0
1
1
2
0
1
0
1
1
0
0
0
2
1
1
1
0
2
0
1
2
1
1
1
0
2
2
0
1
2
1
0
0
2
1
1
0
1
2
0
0
0
1
0
2
0
1
0
2
1
1
0
1
1
0
1
0
1
2
1
2
2
1
2
1
0
2
1
2
1
1
1
0
0
0
0
1
2
1
1
1
1
0
1
0
0
1
2
0
1
2
2
0
1
2
0
2
0
1
1
1
2
3
2
1
1
0
1
2
0
1
1
0
0
1
0
0
1
1
1
1
0
0
1
2
2
1
0
0
2
1
1
0
2
1
2
2
1
1
2
1
1
2
2
2
1
1
2
2
1
1
1
1
0
1
2
3
0
1
0
0
2
2
0
1
2
2
1
0
1
1
0
2
1
2
1
1
1
1
2
2
0
1
1
1
1
0
1
0
1
1
0
0
1
1
1
1
0
1
2
1
1
1
0
1
2
1
0
2
2
1
1
0
1
1
0
2
1
2
1
1
0
0
1
1
0
2
1
2
0
1
5
2
1
0
1
1
1
1
0
2
1
0
0
1
1
1
0
1
0
0
2
1
2
1
0
1
1
2
0
1
1
0
0
1
1
1
0
1
2
0
1
2
1
1
2
2
1
1
1
2
2
1
0
2
1
0
1
0
2
1
0
1
1
0
0
1
2
2
1
1
1
1
1
1
1
0
2
0
1
1
2
1
2
2
1
0
2
1
0
1
1
1
1
0
1
1
2
1
2
0
3
2
1
0
2
0
0
1
1
1
0
1
2
1
2
2
1
0
0
1
1
2
2
1
1
0
1
2
2
1
1
4
1
1
0
0
1
1
0
0
0
0
0
0
0
2
1
2
2
1
0
2
1
0
1
3
0
0
1
2
1
0
0
1
1
2
1
1
2
2
0
1
0
1
1
1
0
1
1
0
1
3
2
1
1
0
0
1
0
1
2
1
0
0
2
1
1
1
2
2
1
0
1
2
1
1
2
1
0
0
1
1
1
1
0
1
2
0
1
1
1
0
1
1
1
2
2
1
1
0
1
2
1
2
1
0
1
0
2
1
0
2
2
1
1
1
1
1
1
0
1
1
2
0
0
3
0
1
1
2
1
1
2
0
1
2
1
2
1
1
1
2
0
0
1
2
0
0
1
1
0
0
0
2
1
1
0
1
0
0
2
1
1
0
2
2
1
0
1
2
1
0
0
0
0
0
2
1
2
2
1
2
1
1
1
2
0
2
2
1
0
0
1
0
1
2
1
2
1
1
0
1
1
1
1
2
0
2
1
0
1
2
2
1
0
0
0
1
0
1
2
0
1
2
0
1
2
2
0
0
2
2
1
1
0
0
1
0
1
1
0
1
0
0
1
1
1
1
1
1
1
1
1
1
1
2
0
0
1
1
1
1
0
1
1
0
2
2
1
1
2
1
1
1
1
0
0
0
1
2
1
1
1
2
2
1
1
1
2
0
0
0
1
2
1
0
1
1
2
1
1
1
0
1
0
0
2
1
0
1
0
0
0
0
2
1
2
0
1
1
2
2
1
2
1
2
1
1
1
1
0
2
2
0
2
0
1
0
1
1
3
2
2
2
0
1
1
1
1
1
1
2
0
2
1
1
1
3
1
2
1
1
0
3
1
2
1
0
1
0
0
2
0
0
0
0
0
1
1
0
1
0
0
2
0
2
0
2
2
1
0
0
1
2
0
1
2
1
1
4
2
1
1
1
1
1
2
1
1
2
1
2
1
2
1
1
1
1
1
0
0
0
1
0
1
1
0
1
1
0
0
2
2
1
1
1
1
1
0
1
1
1
0
2
0
0
2
1
2
2
1
2
0
0
1
2
1
2
1
2
1
1
0
2
2
1
1
1
1
1
1
2
1
1
2
2
1
2
2
1
1
1
1
1
2
1
1
0
0
2
2
1
1
1
1
2
2
2
2
1
1
1
2
1
1
2
0
1
1
2
0
0
0
0
1
2
1
1
0
0
2
0
1
0
1
1
1
1
0
3
1
1
1
1
2
0
1
0
0
1
0
0
1
1
2
1
2
1
1
1
0
1
1
1
1
1
0
2
0
2
0
1
1
0
0
1
0
1
1
0
1
0
1
1
2
1
1
0
1
1
0
2
0
1
2
0
0
1
0
2
1
1
1
0
1
1
1
2
0
2
3
1
1
1
1
0
1
0
1
1
1
1
1
0
1
0
4
0
1
0
1
2
2
0
1
1
1
2
1
0
1
1
2
1
0
1
1
0
0
1
2
2
2
2
1
2
0
1
1
1
2
1
0
1
0
0
1
0
1
2
2
2
1
0
1
1
1
0
1
1
1
1
2
1
1
2
2
0
1
1
1
1
3
0
2
1
2
2
1
1
2
0
1
1
1
1
2
2
2
0
2
1
0
0
0
0
1
1
1
0
1
0
0
1
0
0
2
1
1
0
0
1
0
1
0
2
1
1
1
0
0
0
0
2
0
1
1
2
1
0
1
2
2
2
1
1
1
0
2
1
1
1
1
1
1
0
1
1
2
2
1
0
2
1
0
0
0
0
2
0
1
0
1
1
0
2
0
1
1
1
1
0
0
0
2
1
1
0
0
2
2
1
1
0
2
2
2
1
1
2
0
1
2
1
2
0
0
1
1
1
0
1
1
0
2
1
1
0
2
0
1
0
1
0
2
2
1
1
1
2
1
2
0
1
1
1
1
1
2
1
2
1
0
0
1
1
1
2
1
1
0
0
2
2
1
0
1
1
0
0
1
0
0
1
1
2
0
0
0
1
1
1
1
0
0
1
0
2
1
1
1
1
2
0
0
1
1
1
1
0
2
1
2
0
1
2
1
0
1
1
1
0
0
2
0
0
1
0
1
2
1
0
1
0
1
0
2
1
0
2
0
1
2
1
1
1
2
0
0
1
0
0
0
0
1
1
1
1
0
5
0
0
0
0
1
2
0
0
1
1
3
1
1
0
0
1
0
0
0
1
1
2
1
1
0
2
0
1
2
0
2
0
1
0
2
0
2
1
1
1
3
0
0
2
1
0
0
0
1
1
0
1
1
1
2
0
1
0
1
0
2
1
0
0
1
1
0
0
2
1
0
1
1
2
1
2
1
1
1
2
0
1
1
0
1
0
2
0
2
0
1
0
0
1
1
1
1
1
0
1
0
0
1
0
1
2
1
0
1
0
2
1
0
1
1
0
0
1
1
1
1
1
1
2
0
1
2
1
0
1
2
0
1
1
1
1
1
1
4
1
1
1
0
0
1
1
3
0
0
1
1
2
0
0
1
1
1
1
2
2
2
1
1
2
1
1
0
1
1
2
0
1
1
1
2
1
1
1
1
1
1
2
4
1
3
2
1
1
2
2
1
2
2
1
0
1
1
1
0
3
1
0
0
1
0
1
0
2
0
0
1
1
2
2
0
0
0
0
1
1
1
0
2
2
0
1
0
1
0
1
1
1
1
0
2
1
4
1
1
1
2
1
0
1
1
0
1
0
1
1
1
2
1
0
0
2
0
0
1
2
1
2
2
1
2
1
1
0
1
2
0
1
0
2
1
0
0
1
1
1
0
2
2
0
1
1
2
0
1
1
1
0
1
2
0
1
2
2
2
1
0
0
1
0
1
1
2
1
0
1
0
2
0
2
0
1
1
1
1
2
1
0
0
0
2
1
1
0
2
0
1
1
0
0
2
1
2
1
2
0
2
0
1
1
2
1
0
1
1
0
0
1
1
0
3
2
2
0
0
1
0
0
0
1
1
2
0
1
2
1
1
1
0
4
1
1
1
1
1
1
1
0
0
2
2
2
0
2
1
1
1
2
1
0
0
0
1
1
1
0
0
1
2
1
1
1
1
2
1
0
1
2
0
1
0
1
0
1
1
2
1
1
1
1
1
1
1
5
0
1
0
1
4
0
1
2
1
2
1
2
1
1
0
1
2
2
0
0
1
1
0
1
0
1
1
1
1
0
0
2
1
1
1
1
0
2
1
0
1
1
1
1
2
1
1
1
1
0
2
2
0
1
0
2
1
0
2
0
1
0
2
2
0
1
2
0
1
1
1
1
1
1
1
1
1
0
1
0
2
2
1
1
0
2
2
0
0
2
1
1
1
0
2
0
1
0
1
1
0
1
0
0
1
1
1
1
0
0
0
0
0
0
1
1
1
1
2
0
0
1
1
1
1
0
1
1
0
0
0
3
2
2
1
1
0
0
1
2
1
2
1
0
1
2
1
2
2
0
1
0
0
0
0
0
2
1
1
1
1
0
1
2
0
1
1
1
1
0
3
0
1
1
1
0
1
1
0
0
0
1
0
1
1
0
1
0
0
1
0
1
1
1
0
2
2
2
1
1
1
1
1
0
2
2
2
1
1
1
2
1
0
2
2
3
1
1
2
2
1
0
0
1
2
0
0
2
0
1
1
1
2
1
2
1
1
0
0
2
2
2
1
1
0
2
1
2
0
2
1
2
1
2
0
0
2
0
2
0
0
0
1
1
2
0
1
1
2
0
2
0
0
1
0
2
2
1
1
1
0
1
1
1
1
2
1
1
0
0
1
0
0
0
1
2
2
1
2
2
2
0
1
1
0
2
0
1
0
2
2
0
0
1
1
1
0
2
1
1
2
1
2
1
0
1
2
1
1
1
0
1
1
0
2
1
0
1
0
1
2
0
2
1
1
0
1
2
1
2
2
1
1
2
0
0
0
1
1
1
2
0
1
0
0
1
1
1
2
0
0
1
1
1
0
0
0
1
1
1
2
1
0
2
0
1
1
2
1
1
0
0
2
1
1
0
0
0
0
1
0
1
0
1
0
0
1
1
1
1
1
2
0
1
2
1
0
0
2
1
1
0
0
0
0
0
1
0
2
0
3
2
1
1
0
1
1
0
1
1
1
2
1
1
2
1
1
1
1
0
0
2
1
1
1
1
0
0
0
1
0
1
2
1
1
0
1
0
1
1
2
1
0
1
1
1
0
2
1
1
0
2
1
0
1
1
0
1
1
2
1
1
2
0
1
1
1
1
2
0
0
0
1
1
2
2
2
0
0
0
1
2
1
1
1
1
2
1
1
1
1
1
0
2
2
1
0
0
2
1
2
0
1
0
0
1
1
0
0
1
1
0
15
2
1
1
1
1
2
2
1
2
0
2
1
0
0
0
1
1
0
1
0
2
0
0
2
0
2
1
0
2
1
1
1
2
1
1
0
2
0
1
1
0
1
2
1
0
1
1
0
0
1
2
0
1
1
3
1
0
1
0
1
0
1
1
1
0
1
1
0
2
0
1
2
0
1
0
0
1
1
1
0
0
0
1
1
2
1
0
1
0
1
1
1
3
0
1
1
0
0
0
0
1
2
1
1
0
0
2
0
2
1
0
1
2
0
1
0
0
1
0
2
1
0
1
1
1
1
1
0
0
1
1
2
2
0
1
0
3
1
0
1
1
1
2
1
2
0
0
2
0
1
2
1
0
0
1
0
0
0
1
2
2
0
0
2
1
0
1
1
0
1
0
1
1
0
1
1
2
1
2
1
1
2
2
1
3
0
1
2
1
4
0
1
0
1
1
1
1
1
0
1
1
0
2
1
1
1
2
1
1
0
1
1
0
0
1
2
2
2
1
0
1
1
2
1
1
0
0
1
1
1
1
1
1
0
1
1
1
2
1
0
0
0
1
2
1
1
1
0
2
1
1
0
2
1
0
1
1
1
2
0
0
1
0
1
1
0
0
1
1
0
1
2
1
0
1
1
1
1
2
2
0
1
1
2
0
0
1
0
0
1
1
0
1
1
1
0
1
1
3
0
1
1
1
1
0
1
0
1
1
1
1
0
1
1
1
3
1
1
1
1
0
1
1
1
2
2
1
1
0
1
0
0
0
0
1
2
4
1
1
1
1
1
2
0
2
0
2
1
1
0
1
1
0
2
1
1
1
1
1
2
1
1
2
0
0
2
1
1
1
1
1
1
0
1
1
2
1
1
0
2
2
1
1
0
1
1
0
1
0
1
2
0
0
2
1
1
1
1
0
0
0
0
1
1
1
1
0
0
0
1
0
1
1
0
1
1
1
0
1
2
0
0
0
1
1
0
1
1
0
2
1
2
2
1
1
2
0
0
1
0
0
1
1
0
2
0
1
2
2
1
1
0
1
1
0
1
2
1
0
1
1
0
2
1
2
1
1
1
3
1
1
0
2
1
1
0
1
1
1
1
1
1
2
0
1
1
1
1
0
1
0
0
1
2
1
1
1
1
2
0
1
1
2
0
1
1
1
1
0
0
1
1
1
1
1
0
1
0
1
1
0
0
1
1
0
2
0
2
2
0
0
1
1
1
0
0
0
1
1
0
1
0
2
2
1
1
1
2
1
1
2
1
0
1
0
0
1
2
0
4
0
0
1
1
0
1
2
1
1
2
0
1
2
0
0
2
1
1
2
0
1
2
1
2
0
1
0
0
0
1
0
0
2
1
2
1
1
2
2
1
1
2
2
3
1
1
0
1
0
1
1
0
0
0
1
0
1
2
1
1
1
0
1
0
1
1
1
0
0
1
0
0
0
1
1
0
1
1
0
1
0
0
2
2
1
2
1
0
0
7
1
1
0
1
0
1
0
1
2
0
0
1
1
1
1
2
2
1
1
1
0
0
1
1
2
1
1
1
0
1
2
1
0
1
2
2
1
1
0
1
1
0
1
0
1
2
1
1
2
0
1
1
1
2
1
1
1
0
0
1
1
1
1
2
2
2
2
1
1
1
0
0
2
1
0
2
1
0
1
0
0
1
0
1
0
0
0
1
2
0
1
1
1
0
2
1
1
2
1
0
0
1
2
2
1
3
1
1
1
2
1
1
1
1
0
0
1
2
1
0
1
1
2
0
2
1
1
0
2
1
0
0
2
2
2
1
1
0
0
0
1
2
1
2
2
0
1
1
0
0
1
1
0
1
1
1
1
2
1
0
3
1
1
1
0
1
0
1
0
1
0
1
1
1
1
1
1
1
1
2
2
2
0
0
0
2
1
0
2
0
3
1
1
0
0
0
1
0
1
2
2
2
1
0
2
2
0
1
1
1
2
2
4
0
1
2
2
2
0
1
0
1
1
0
1
2
1
2
1
1
0
0
0
0
1
1
0
0
2
2
0
2
1
0
1
0
0
0
1
1
1
2
0
1
1
1
2
1
2
1
1
2
2
2
2
1
0
1
1
0
3
1
1
1
1
2
2
0
0
1
2
1
1
2
0
1
2
1
0
1
1
1
1
1
0
2
0
2
0
0
1
0
1
2
0
0
1
1
0
0
2
1
1
2
2
0
0
1
0
1
1
2
0
2
0
0
1
2
0
0
1
2
2
0
1
1
0
2
1
1
0
1
0
1
1
1
4
0
3
1
1
0
1
0
0
2
0
0
1
1
1
1
1
0
1
0
1
1
1
1
1
2
0
0
1
0
4
1
0
2
1
2
1
1
0
2
0
1
0
1
1
1
0
1
2
2
2
1
1
2
1
1
1
1
2
1
2
1
0
0
1
4
1
1
2
1
1
0
0
1
1
1
1
2
1
2
1
3
0
2
1
1
1
2
0
1
2
1
0
1
1
1
2
1
1
1
0
0
2
0
2
1
1
7
2
0
3
1
2
0
0
1
1
0
1
0
0
0
1
1
2
0
1
0
0
1
0
3
1
0
0
1
2
1
1
2
0
1
1
1
1
3
2
0
1
2
2
1
0
1
2
1
1
0
1
2
0
1
3
1
1
1
0
1
0
2
1
0
0
2
0
2
2
0
0
0
0
2
1
1
2
0
1
0
1
1
0
1
1
1
1
0
2
0
2
0
2
2
1
0
0
0
1
1
1
2
1
1
1
2
1
1
2
0
2
0
1
1
1
1
1
0
2
1
1
0
2
0
1
2
0
1
2
0
2
0
0
1
0
1
2
0
0
1
1
1
0
0
2
0
1
1
1
1
2
1
1
1
1
2
1
0
1
0
0
0
1
2
0
1
2
1
1
1
1
1
2
1
2
0
2
1
3
1
1
1
1
1
0
0
0
1
2
0
2
1
1
1
1
2
1
1
2
2
1
1
2
1
0
2
2
2
0
2
3
2
2
0
0
1
2
2
1
2
0
1
0
0
1
0
0
0
0
1
0
0
0
2
1
0
2
1
0
1
1
0
1
3
1
0
0
0
0
1
1
3
1
1
1
0
1
3
0
1
1
1
1
0
2
1
1
0
2
3
0
1
1
1
1
1
0
1
2
1
0
1
1
1
0
1
1
0
0
1
2
0
1
2
2
0
0
0
1
1
1
1
1
1
2
0
0
0
1
1
1
2
1
1
0
0
1
2
0
2
2
1
0
2
2
1
0
2
0
0
3
1
1
0
2
1
2
1
0
1
1
3
1
1
1
1
2
1
1
1
0
2
0
1
2
0
0
2
1
0
0
0
1
1
2
1
0
0
2
1
1
1
0
2
1
0
2
1
2
0
2
0
0
0
0
2
1
1
2
1
2
2
0
1
1
2
1
1
0
0
0
1
1
1
1
1
0
1
2
0
4
1
1
1
0
1
2
1
0
2
1
1
1
0
2
0
1
3
2
1
1
0
2
1
0
0
1
1
0
0
0
1
1
1
1
0
1
1
2
1
1
0
1
1
0
0
1
1
1
0
1
1
1
0
1
1
1
0
0
2
2
2
1
0
2
1
1
0
0
5
1
2
0
0
1
1
0
2
1
1
2
3
0
0
1
0
0
0
1
2
1
0
0
1
0
1
1
1
0
0
1
0
0
0
2
0
2
0
1
2
1
1
0
1
1
0
0
0
1
1
2
3
2
2
1
1
0
1
2
1
2
0
0
0
1
1
1
1
0
2
1
0
1
1
1
1
3
0
1
1
1
2
1
0
1
0
1
2
1
0
0
1
0
2
1
2
1
1
1
1
2
1
2
1
1
0
0
2
2
1
0
1
0
0
1
1
1
2
2
1
1
0
2
1
0
0
0
0
2
1
2
0
1
2
0
2
1
0
1
0
1
1
0
1
0
0
0
3
0
0
1
1
0
1
1
1
1
1
1
0
0
1
1
1
1
1
0
0
1
0
2
0
1
1
0
2
0
1
1
1
1
1
1
0
1
0
1
2
0
1
1
0
2
1
1
1
2
1
0
1
2
1
1
1
1
2
1
1
1
0
1
0
1
2
1
2
0
1
1
1
1
1
0
1
0
1
0
1
0
1
1
1
2
1
0
0
0
1
1
2
0
2
1
0
1
0
1
2
0
0
1
2
0
2
0
0
1
1
1
1
1
1
1
1
0
2
1
1
1
1
0
1
2
1
1
1
0
2
1
0
0
1
0
1
1
1
1
2
0
1
1
2
0
1
1
2
1
1
2
2
2
0
1
1
1
1
1
1
0
2
1
0
1
2
1
2
1
2
2
1
2
2
1
1
1
1
1
1
1
0
1
1
1
1
0
1
2
3
0
1
1
1
1
0
0
0
1
1
1
1
2
1
1
0
1
2
2
0
2
0
0
1
0
1
2
0
1
0
2
2
0
2
0
0
1
2
2
1
1
1
2
0
2
1
0
1
0
2
0
0
1
1
0
0
1
0
1
1
1
1
1
1
2
0
1
1
1
1
0
1
0
1
1
2
1
0
0
0
1
1
1
2
0
2
2
1
1
1
0
1
0
1
1
1
0
2
1
2
1
1
2
1
2
2
2
0
0
1
1
1
0
0
1
1
0
0
1
1
1
2
0
0
1
1
1
0
2
1
1
2
1
1
1
0
1
0
0
0
1
0
1
0
2
2
1
0
1
1
1
0
1
1
2
2
1
0
1
0
2
0
1
1
2
0
1
1
0
0
2
1
0
0
2
1
1
2
0
1
0
1
2
2
2
1
1
1
1
1
1
1
1
0
0
0
1
1
0
2
1
2
0
2
1
1
2
0
2
1
1
0
1
2
2
1
1
1
1
0
2
1
1
0
2
1
0
2
1
1
2
0
0
3
0
0
0
0
0
1
1
0
1
0
2
1
1
2
3
1
0
1
1
1
1
0
1
1
1
0
1
0
1
0
0
0
1
1
0
0
2
1
1
2
2
0
1
2
0
2
1
2
1
2
1
1
1
0
0
0
1
1
0
2
1
1
0
0
1
1
2
1
1
1
1
2
2
0
2
1
6
0
0
0
2
0
0
0
1
2
0
1
0
3
0
2
1
2
1
1
1
0
1
1
1
2
0
2
0
0
1
0
0
1
2
0
1
2
0
1
2
2
2
0
1
1
2
0
0
1
0
1
0
0
1
0
1
0
0
1
1
1
2
0
1
1
1
2
1
0
0
1
0
1
1
1
1
1
1
2
1
2
0
1
2
2
1
2
2
1
0
1
1
0
0
0
2
0
1
1
1
1
1
1
2
1
0
1
1
1
1
1
0
1
0
2
1
0
1
0
0
1
0
0
1
1
0
0
1
0
1
2
0
0
2
0
2
0
1
1
0
1
1
1
1
1
0
1
0
3
2
1
0
1
0
0
1
0
2
0
0
0
2
1
1
3
2
2
1
1
2
0
1
1
1
1
1
2
1
1
1
0
1
0
2
0
2
2
2
1
2
1
2
1
0
1
0
0
2
1
0
0
1
0
0
1
1
2
0
1
2
1
2
0
0
2
1
1
0
0
1
1
0
1
0
2
1
0
2
1
0
1
1
0
1
2
1
2
0
0
2
1
1
2
1
1
0
2
1
2
1
0
1
1
1
2
2
0
0
1
1
0
1
1
0
1
1
1
2
1
0
1
1
1
1
0
1
3
1
0
1
1
2
0
2
0
0
1
1
1
0
1
2
2
0
0
1
0
2
1
2
0
2
2
1
1
1
0
1
2
1
0
1
1
1
1
0
2
1
1
2
0
0
1
2
2
2
1
0
0
2
1
1
2
1
1
0
1
2
3
2
1
2
0
1
2
2
1
4
0
1
1
0
1
2
1
0
1
0
1
0
1
1
2
2
0
1
0
2
1
2
0
0
0
2
1
1
1
0
0
0
0
1
1
2
0
0
0
0
0
2
1
0
2
1
0
3
0
1
1
0
0
2
0
1
2
1
1
0
2
1
1
0
0
1
2
1
1
1
1
1
2
1
2
0
2
1
2
0
2
0
3
0
0
1
0
1
0
0
1
2
0
1
0
1
1
1
1
0
0
0
2
2
0
2
2
1
2
1
2
1
0
1
1
1
1
2
0
1
3
1
1
1
1
0
1
2
1
2
0
0
2
2
0
1
1
1
1
1
0
1
1
1
1
2
1
0
0
1
1
0
1
2
1
0
1
1
0
0
1
0
2
2
0
1
1
3
0
1
2
2
1
1
0
0
2
0
1
0
2
0
0
2
1
0
1
0
1
0
2
2
2
0
0
0
2
0
2
2
1
1
1
1
1
1
1
1
0
1
1
2
0
1
1
0
1
2
1
1
0
1
3
0
1
2
1
3
0
2
1
0
0
1
0
1
1
2
1
2
2
0
0
1
3
1
1
2
1
1
2
0
1
2
1
1
1
7
1
1
1
2
2
2
2
2
1
2
1
0
1
2
0
1
0
1
1
0
1
1
1
2
2
0
1
1
1
1
0
1
2
0
0
1
1
1
1
1
0
0
1
2
1
0
1
1
0
2
1
1
3
2
1
1
2
1
1
1
2
1
1
1
1
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
1
2
0
1
1
1
1
1
1
1
2
0
1
2
1
1
0
0
0
2
0
0
1
1
0
0
1
1
1
0
0
1
1
2
2
1
0
1
0
1
0
0
1
1
1
2
1
0
1
2
0
1
1
1
2
2
0
0
0
1
1
1
1
1
1
0
2
0
1
0
0
2
0
0
1
2
1
1
1
2
0
1
1
0
1
0
2
2
1
1
1
1
1
1
1
0
1
0
1
0
2
2
2
0
1
0
1
1
0
1
2
2
2
2
2
1
0
1
1
1
1
2
0
1
2
0
1
0
2
2
0
1
2
4
1
1
0
2
2
0
0
1
1
1
0
1
1
1
1
1
2
0
2
1
0
1
2
1
1
2
1
0
2
0
1
1
0
0
1
0
1
1
2
2
0
1
1
1
1
0
0
1
1
2
1
1
1
0
2
1
0
1
1
1
1
2
0
2
0
1
1
2
1
0
1
1
0
3
1
2
2
1
1
1
1
1
1
1
0
2
0
0
1
1
0
0
1
0
0
2
2
1
0
2
1
2
0
2
0
2
0
2
2
2
0
0
2
0
0
1
1
1
0
1
1
2
1
0
1
2
0
0
2
5
1
0
1
1
1
1
1
0
1
1
2
1
2
1
1
0
0
0
0
2
0
2
1
0
2
1
2
1
1
1
2
2
1
1
1
0
2
0
0
1
2
1
4
0
1
0
1
0
0
1
1
2
2
0
1
2
1
2
1
1
2
2
1
0
1
0
2
2
1
1
1
0
2
1
1
0
0
0
0
1
0
0
0
1
1
1
1
0
1
1
0
1
1
1
1
0
1
0
2
2
1
2
0
2
2
2
0
1
3
1
0
0
0
0
1
0
2
0
2
2
1
1
1
2
2
2
0
1
2
0
1
1
1
0
1
0
0
1
1
0
1
0
1
1
1
0
1
1
2
2
1
1
1
0
2
0
0
2
2
1
2
2
1
1
1
1
2
1
2
0
2
2
1
2
1
2
1
0
0
1
1
1
1
1
2
2
0
0
2
0
0
1
0
0
1
0
0
1
2
1
1
1
1
0
2
1
1
2
0
0
1
1
1
1
0
0
1
1
1
1
0
1
1
0
1
3
0
1
1
0
0
1
1
1
2
1
1
1
1
0
0
1
0
2
1
0
1
0
3
0
2
0
2
2
0
0
1
0
0
1
1
2
1
0
2
1
1
0
1
2
1
1
0
0
1
1
2
2
1
1
1
1
1
2
0
0
1
0
1
1
2
1
1
1
2
0
2
0
1
0
0
0
0
0
0
0
2
3
1
0
0
1
2
1
0
1
0
1
2
2
1
2
1
2
1
0
0
1
1
1
1
1
1
1
0
1
1
1
2
2
1
2
0
1
1
1
1
1
1
1
1
1
1
1
0
2
1
0
1
0
1
1
0
0
2
1
0
2
1
1
1
0
2
1
0
2
1
1
1
1
2
1
0
0
0
2
0
1
1
1
1
2
2
0
0
2
2
1
1
1
1
1
1
0
1
1
2
2
1
2
1
2
1
0
1
1
2
0
0
0
0
0
3
0
0
0
1
1
1
0
2
2
0
0
2
1
1
0
0
1
1
0
1
0
1
1
0
0
0
1
0
1
0
0
1
2
0
0
1
2
2
1
0
0
0
0
1
2
2
1
1
0
1
2
1
0
2
0
0
1
1
0
2
1
2
1
1
1
1
2
0
1
1
0
2
1
2
2
1
1
2
2
1
1
2
2
1
1
0
0
1
0
1
0
1
1
1
2
0
1
0
1
1
1
1
1
1
1
1
2
0
1
1
2
1
1
2
1
1
1
0
1
0
0
0
0
1
1
2
1
1
1
1
1
1
1
1
0
2
1
2
1
0
1
0
1
1
1
1
1
1
2
1
2
0
1
1
1
0
0
0
2
1
0
0
1
0
0
2
1
1
0
2
1
0
0
2
3
1
0
0
1
0
2
0
0
1
2
1
2
2
0
2
1
0
0
0
1
2
0
0
1
1
0
1
1
2
1
1
1
1
1
1
1
0
1
0
1
1
1
1
2
0
0
1
0
1
1
1
0
2
2
0
1
1
1
1
1
0
0
1
1
2
1
1
1
0
0
2
0
1
2
0
1
2
0
2
0
1
2
2
0
1
0
1
2
1
2
0
1
1
1
1
2
1
1
1
0
1
1
1
1
0
2
2
0
0
1
5
0
0
2
3
1
1
2
2
0
0
2
2
1
0
2
1
1
1
0
0
2
1
0
2
3
2
1
1
1
1
2
0
1
1
0
1
1
1
0
2
1
1
1
1
0
0
2
1
1
1
0
1
0
1
1
1
0
0
0
1
0
1
1
0
1
1
1
1
2
2
1
1
2
2
1
0
1
1
1
1
1
2
2
2
0
1
1
0
0
2
1
1
0
0
1
1
1
1
0
1
1
2
0
2
1
1
1
0
0
1
1
2
1
1
0
0
0
1
2
1
1
0
2
1
1
0
2
0
2
2
0
0
0
1
0
1
1
1
1
2
3
0
1
0
3
1
1
0
2
0
0
1
1
0
1
1
0
2
0
2
1
1
0
0
0
0
2
0
2
0
0
2
0
1
1
1
1
2
1
2
0
2
2
0
1
0
1
2
2
1
1
0
2
1
1
1
0
1
0
1
0
0
1
1
2
1
0
1
1
1
1
1
2
1
1
0
1
0
1
1
2
2
1
2
1
2
0
2
1
1
0
0
1
0
1
2
2
2
1
0
1
1
0
0
0
1
1
1
1
1
1
0
2
2
2
2
1
0
0
1
1
2
2
1
1
1
1
2
2
0
1
0
1
0
2
1
2
0
0
2
3
1
2
0
1
2
0
1
1
2
1
1
1
0
0
0
1
0
0
1
2
1
0
1
1
0
0
1
2
0
0
1
1
0
2
2
1
2
1
2
1
1
3
1
1
2
0
1
1
1
2
0
1
0
2
0
0
0
1
0
1
2
1
0
0
1
0
1
2
1
1
0
0
1
1
1
0
1
1
0
2
1
1
0
1
1
1
0
2
1
1
3
1
2
2
0
1
1
1
0
0
0
1
1
1
1
0
0
1
0
1
1
0
1
1
1
0
1
1
1
1
0
0
0
2
1
0
0
1
0
0
0
1
0
0
0
0
1
2
0
1
2
0
1
0
2
1
0
0
0
2
1
0
0
2
0
0
1
2
2
0
1
0
1
0
0
0
0
1
3
0
2
0
1
0
1
0
2
1
2
0
2
1
0
0
1
1
2
2
2
0
0
1
1
2
0
1
1
1
1
0
0
0
1
0
1
1
2
0
0
2
1
0
0
1
1
0
1
2
1
2
1
0
0
1
0
1
0
2
2
2
1
1
2
1
1
1
1
2
1
1
0
1
0
1
2
2
0
2
0
2
0
0
2
1
1
2
1
1
0
2
2
0
1
1
2
1
0
2
2
0
2
1
0
1
2
1
1
2
0
2
1
1
1
2
1
1
1
0
1
2
1
2
2
2
1
2
6
0
1
1
2
1
0
0
1
1
2
1
1
1
1
1
1
0
1
2
1
1
0
0
1
1
0
1
0
1
1
0
1
0
0
2
1
0
0
0
0
1
2
1
2
0
0
0
1
1
2
2
0
0
0
1
2
1
0
0
1
1
0
1
2
2
0
1
1
1
0
2
1
1
0
2
2
2
0
0
0
1
2
1
2
1
2
2
0
1
1
0
0
0
0
0
1
2
0
1
1
1
1
0
1
1
1
1
1
1
2
2
0
2
2
2
1
1
1
1
0
1
1
1
2
1
1
1
1
1
1
2
3
0
0
2
2
2
2
2
1
1
0
1
0
1
1
0
1
2
1
1
0
0
0
0
1
0
1
1
2
1
1
1
2
1
1
0
1
1
0
1
1
1
0
1
2
0
1
1
0
1
0
1
0
4
1
2
1
1
0
0
1
1
1
2
0
2
2
1
1
3
0
1
1
1
0
1
1
1
0
1
1
0
1
2
1
1
1
1
1
1
1
0
1
2
1
2
0
1
0
2
2
0
0
2
2
1
0
2
2
1
0
2
0
0
2
1
1
0
3
1
3
2
1
2
0
0
2
0
1
0
1
1
0
0
2
2
1
0
1
1
1
3
0
0
0
2
2
1
0
2
1
1
1
1
1
1
0
1
1
1
2
2
1
1
0
2
0
1
0
1
1
1
2
1
1
1
3
1
1
1
1
2
1
0
2
1
0
0
1
2
2
0
0
3
0
0
2
1
1
0
0
0
1
1
1
1
2
1
1
2
0
3
1
1
1
1
2
2
2
0
1
2
0
1
2
0
2
1
2
0
1
1
0
2
1
0
2
1
2
1
1
1
0
0
2
0
1
0
2
0
1
1
1
1
1
1
1
0
0
1
0
2
1
1
0
1
2
1
1
0
2
1
2
2
1
1
1
1
2
0
1
1
1
1
0
0
2
2
1
0
0
2
0
2
1
1
1
1
0
2
0
1
0
1
1
1
1
2
1
0
3
1
1
2
1
1
0
0
1
2
1
1
1
0
0
0
1
1
0
1
1
1
2
0
1
1
1
1
1
0
2
1
1
1
1
1
1
1
1
1
2
2
0
1
2
1
0
1
1
1
1
1
2
1
0
0
2
1
2
0
2
1
2
1
0
1
1
0
1
0
1
0
1
1
2
1
1
2
0
0
1
1
0
1
0
1
1
1
2
1
2
0
3
0
0
0
1
1
1
0
1
0
0
1
0
0
2
1
0
1
1
0
2
2
0
0
1
0
1
2
1
1
1
1
1
1
1
1
0
0
1
1
3
1
2
1
2
2
1
0
2
0
1
2
2
1
1
0
1
2
1
0
0
1
1
1
1
1
0
1
0
0
0
2
1
0
2
1
1
1
2
0
2
1
0
1
1
1
1
4
0
2
0
0
1
1
2
1
0
1
1
1
1
0
1
1
2
0
0
1
2
1
0
2
1
2
2
2
0
0
1
1
1
0
0
1
1
1
0
1
2
1
2
1
0
2
0
1
1
1
1
1
0
1
2
0
1
0
2
1
1
1
1
2
1
3
1
1
0
0
0
1
1
0
0
0
0
0
0
1
1
2
0
0
2
0
2
1
0
1
1
0
0
3
1
0
1
0
0
0
1
2
1
2
0
1
1
0
1
1
1
1
0
1
0
1
0
1
1
2
1
1
1
0
2
0
0
0
1
2
5
1
2
1
0
1
1
1
1
1
0
0
1
1
0
1
2
1
1
0
1
0
0
1
1
1
1
0
2
1
1
0
0
1
1
1
1
1
0
1
2
1
0
1
1
6
2
0
1
1
1
2
1
1
2
1
1
1
0
2
0
0
0
0
2
2
1
0
0
0
1
2
1
1
0
1
1
1
1
1
2
0
1
0
2
3
1
1
1
1
1
2
1
0
0
2
6
1
1
0
0
1
1
1
0
2
0
1
2
0
3
2
1
1
1
1
0
1
0
0
1
1
1
1
1
1
1
1
2
0
2
2
1
1
1
0
2
0
2
2
2
1
0
2
1
0
1
1
1
0
1
2
2
1
0
0
2
1
0
1
1
1
0
1
0
2
1
2
1
0
1
1
0
0
1
0
1
0
0
1
2
1
1
2
0
0
1
0
0
1
2
1
1
0
1
1
0
1
2
0
1
1
2
2
1
0
0
2
2
0
1
1
3
0
1
1
1
1
0
1
0
1
2
1
0
0
0
1
2
1
2
0
1
1
2
0
0
1
1
0
0
2
1
1
1
1
0
0
2
0
0
1
1
0
0
0
0
0
1
2
2
2
0
1
3
1
2
1
2
2
1
1
2
0
1
0
0
1
0
2
1
0
0
2
1
2
1
1
2
1
1
0
1
1
2
2
0
2
0
1
0
1
0
1
1
1
1
0
0
2
1
2
2
2
0
1
0
2
1
1
2
2
1
2
2
1
1
2
0
0
1
2
2
1
0
1
1
2
2
0
2
0
2
1
1
1
1
0
2
2
0
1
1
1
0
2
1
1
1
0
0
0
1
2
1
0
0
1
2
1
0
2
2
1
0
1
1
0
1
1
1
1
1
0
1
1
0
1
2
1
3
0
0
2
1
1
1
1
0
1
2
1
2
3
1
2
2
1
1
0
0
0
3
1
0
0
1
1
0
0
2
0
1
0
2
0
0
1
0
1
1
1
1
0
1
3
1
2
1
0
1
1
0
2
0
1
1
1
2
0
0
0
1
1
0
0
1
1
0
2
0
1
0
1
0
0
1
1
1
0
2
1
1
2
1
0
1
4
1
1
1
1
1
0
1
2
0
0
2
0
1
0
0
1
2
1
1
0
0
1
2
1
2
0
1
0
1
1
2
0
2
1
1
0
0
3
1
1
2
0
2
1
1
2
2
1
1
0
0
1
1
1
1
2
3
0
2
0
1
2
1
1
1
1
0
2
1
2
2
1
2
2
2
2
1
1
1
1
2
1
1
0
1
0
2
1
1
2
1
0
2
0
1
2
1
1
1
1
1
1
2
1
0
0
0
2
1
0
0
1
2
0
0
1
0
1
0
1
1
2
0
3
1
1
1
0
4
1
1
1
1
1
1
0
1
2
0
1
2
2
0
2
0
0
2
1
1
1
1
0
1
1
0
0
0
0
2
1
0
2
0
1
1
2
2
0
3
2
0
1
1
1
0
0
3
1
1
0
1
0
0
1
0
1
0
2
1
0
0
2
1
0
0
2
1
0
1
1
2
2
0
0
0
1
1
0
0
0
1
0
0
1
2
1
1
1
3
1
2
1
1
2
2
1
1
2
0
0
0
2
0
1
2
2
0
0
0
1
1
0
1
2
1
1
2
0
2
1
1
0
0
1
1
1
0
1
1
1
0
0
1
1
1
1
1
1
0
1
1
0
0
0
1
2
0
1
2
1
1
2
1
2
0
1
2
1
0
2
1
0
1
2
2
0
2
1
1
1
2
1
2
1
1
0
1
1
1
1
0
1
1
2
0
0
1
2
0
1
2
1
2
2
2
0
1
2
2
0
1
1
2
0
0
1
2
1
0
0
1
2
2
1
2
1
1
1
1
1
1
2
2
0
1
1
1
0
0
1
0
0
0
1
1
2
0
1
1
2
1
1
1
0
0
0
0
1
0
2
2
2
1
2
0
2
1
2
2
0
1
1
1
1
0
1
0
0
1
1
0
0
1
1
0
1
1
0
2
0
1
1
1
1
1
0
1
1
1
1
1
0
2
1
1
1
2
1
1
0
1
0
1
1
2
0
0
0
2
0
1
0
0
1
1
1
1
0
2
0
0
2
1
1
2
2
1
0
0
1
1
1
0
0
1
1
1
0
1
1
1
2
0
1
0
1
1
2
1
1
2
2
1
2
2
0
1
0
1
1
0
0
0
2
0
1
1
1
1
2
1
2
2
0
1
0
0
0
1
1
1
0
0
1
1
0
0
1
2
1
2
1
2
2
2
2
2
1
1
1
2
1
2
1
0
1
0
1
0
1
1
1
0
1
2
2
1
1
1
1
1
0
0
2
0
1
1
1
1
0
1
1
0
0
1
0
0
0
1
1
0
1
2
1
1
0
0
0
1
1
1
2
1
1
1
1
2
2
0
0
0
0
1
1
3
1
1
1
0
1
2
1
2
0
1
1
1
1
0
3
1
1
2
2
0
1
1
1
2
1
1
1
0
1
2
1
2
1
1
2
1
1
1
0
0
1
1
1
1
0
2
2
0
1
1
1
1
1
1
1
0
1
2
0
0
0
2
3
1
0
1
0
1
1
2
1
1
1
0
0
0
1
1
1
1
1
0
2
0
1
0
0
2
0
1
2
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
1
1
1
2
1
2
0
0
1
0
2
1
2
0
0
1
2
1
1
0
0
1
0
0
1
2
2
2
1
2
2
0
0
1
2
1
1
1
2
0
1
1
1
1
0
1
2
1
1
1
0
2
0
1
1
1
0
1
1
2
0
0
0
0
2
1
1
0
0
0
1
2
1
2
1
2
1
2
1
0
0
0
1
1
2
1
2
2
4
1
1
2
0
1
1
1
2
1
1
1
1
0
2
1
1
1
1
1
2
1
0
1
0
0
0
2
2
2
2
0
0
1
0
0
2
1
2
1
2
1
1
2
3
0
1
1
1
2
2
0
1
2
0
1
1
2
0
2
2
0
1
1
1
0
2
0
1
2
0
1
1
0
0
1
2
2
0
1
0
0
1
2
0
0
1
1
1
1
1
1
1
2
0
0
1
1
1
1
2
0
1
1
1
2
0
0
0
1
1
2
0
0
1
2
0
2
1
0
1
0
1
1
1
2
1
1
1
1
1
1
1
0
2
1
1
2
2
0
2
1
0
0
2
2
0
0
1
1
2
2
2
2
1
2
2
3
1
1
1
2
2
0
2
0
0
1
1
3
0
2
1
1
1
0
0
1
0
1
0
0
2
1
1
1
2
1
1
1
1
2
0
0
0
1
1
1
1
2
1
1
1
2
2
1
2
2
4
0
1
0
5
0
0
0
2
1
0
1
1
1
0
2
0
0
1
0
2
0
1
0
1
0
1
2
0
0
2
2
1
2
0
0
2
2
1
1
1
0
1
0
0
1
1
0
2
1
2
1
0
0
1
1
2
0
0
0
1
1
0
2
1
1
1
1
2
0
1
1
1
0
1
0
1
1
1
0
1
0
1
1
2
1
3
1
0
2
1
2
0
1
1
2
2
1
0
0
1
1
1
0
2
1
1
1
0
2
1
1
4
2
1
1
2
2
1
1
1
0
2
1
0
2
1
0
1
0
2
1
1
1
1
1
1
0
2
1
1
0
0
1
0
1
1
0
0
0
1
1
1
0
1
0
0
0
0
1
0
1
0
2
1
2
2
0
0
0
1
1
1
0
2
1
0
1
2
1
2
2
1
2
2
1
0
0
2
0
0
1
2
1
1
2
1
0
0
1
0
1
1
0
2
1
0
2
1
0
0
1
1
0
1
1
1
1
1
2
1
1
0
2
1
0
0
1
0
2
1
0
2
1
1
0
0
1
0
2
0
2
0
0
0
2
1
2
0
1
1
1
0
2
0
1
2
1
0
0
0
1
0
2
1
2
2
2
2
1
1
1
0
0
2
0
1
0
2
2
0
1
2
0
1
1
0
0
1
1
0
1
2
2
0
1
2
1
1
1
0
2
0
2
2
1
2
1
1
2
2
0
0
6
0
0
1
2
2
1
2
2
0
1
1
5
1
0
0
0
1
2
1
1
0
1
1
0
2
0
2
0
0
0
2
0
0
0
2
0
0
0
1
1
0
1
2
2
0
0
2
0
2
2
1
2
2
1
2
2
2
1
1
2
0
0
1
1
0
0
0
0
0
1
1
0
1
0
0
1
1
1
1
0
1
1
1
1
0
1
1
1
1
0
2
1
0
0
1
1
0
2
2
0
1
1
1
1
2
0
2
2
1
2
0
1
1
1
1
1
2
2
2
0
0
1
0
0
1
1
1
1
1
2
2
0
1
2
1
1
0
1
0
0
1
1
0
2
4
2
2
2
1
2
0
1
2
2
0
2
1
1
1
2
1
1
0
3
2
1
1
1
0
2
0
2
2
1
1
1
1
1
2
2
0
1
0
0
3
0
5
1
1
1
1
1
0
0
0
1
1
0
0
1
2
1
1
1
1
0
0
0
0
1
1
0
0
0
2
2
2
1
0
0
0
0
1
1
1
0
0
0
1
0
2
0
0
0
1
1
1
0
1
1
1
1
1
0
1
1
3
0
0
2
0
1
0
0
2
1
0
1
2
1
0
1
2
2
1
1
1
0
1
1
1
2
1
3
1
0
0
0
2
1
2
0
0
1
1
2
1
1
0
1
2
1
1
2
2
1
1
2
1
0
2
2
2
2
1
0
1
0
3
2
0
1
1
1
0
2
0
2
1
1
1
2
0
0
1
0
1
1
1
1
1
0
0
2
0
1
0
0
1
1
2
1
0
3
2
2
1
1
0
0
1
0
2
1
2
2
2
1
2
0
1
1
2
0
2
1
0
0
1
2
1
1
1
2
2
0
2
2
2
1
1
2
0
1
2
0
1
0
1
0
0
2
1
0
2
0
0
0
2
1
1
1
2
2
1
1
0
1
1
0
1
1
1
0
2
2
1
2
2
0
1
2
0
1
1
0
0
1
0
0
2
2
1
0
2
1
1
0
1
1
0
0
1
0
1
1
0
1
1
2
1
0
1
2
1
1
2
1
0
0
1
2
0
1
1
1
1
1
1
0
1
2
1
2
1
1
0
2
2
2
1
0
2
1
1
1
2
0
1
1
2
1
2
1
0
2
1
2
0
1
1
0
0
1
1
2
1
0
1
0
1
1
1
1
1
1
0
3
1
0
0
1
1
1
1
1
0
0
1
1
0
2
2
2
1
0
1
1
1
0
0
0
0
1
2
0
1
0
1
2
1
1
0
2
2
1
0
1
1
0
1
0
2
1
1
1
3
2
1
0
2
2
0
1
1
1
0
0
2
0
2
1
1
0
1
1
1
1
1
2
1
1
1
1
1
1
2
0
1
1
0
2
1
0
1
1
1
1
0
1
2
1
2
1
2
0
2
1
0
2
1
1
1
1
0
0
0
0
1
2
1
0
2
0
1
0
2
1
1
1
0
0
1
1
2
0
0
1
0
1
2
0
2
0
2
0
0
0
0
0
1
2
1
0
2
0
1
2
1
1
1
2
0
0
0
1
1
1
1
1
2
0
1
1
1
0
0
1
1
2
2
1
1
1
1
1
2
0
1
1
1
0
2
1
2
1
1
0
1
2
2
0
1
1
0
1
1
2
2
1
2
0
0
0
2
1
1
0
0
0
1
0
0
2
1
0
2
0
0
3
0
1
0
1
0
2
0
1
1
0
0
1
1
1
0
1
0
0
0
0
1
2
2
1
3
2
1
2
0
1
2
1
0
1
2
2
0
2
0
1
2
2
1
0
2
1
2
1
1
3
0
1
0
1
2
0
2
1
0
1
1
2
1
1
1
1
1
0
0
0
1
2
1
1
0
1
2
1
0
2
2
1
1
1
1
0
2
0
2
1
2
1
2
1
1
0
2
1
0
0
1
0
1
0
1
1
1
1
0
0
2
0
1
0
2
1
2
1
0
1
1
0
1
0
0
0
0
1
1
0
1
1
3
0
0
1
0
0
2
1
2
1
2
1
2
1
1
2
1
1
0
0
1
1
0
1
1
0
0
1
1
0
0
2
1
1
1
2
1
0
1
0
1
2
1
1
1
2
2
1
1
1
1
0
1
0
2
1
1
1
2
1
2
1
2
0
1
2
2
2
1
1
1
0
1
2
2
2
1
2
2
1
1
2
1
1
1
3
0
0
2
2
0
0
1
3
1
2
1
0
1
0
0
0
1
0
0
0
1
1
1
0
0
0
0
1
1
0
5
1
1
1
1
2
1
1
1
0
1
1
1
3
1
2
0
0
1
1
1
1
1
0
2
2
1
0
0
1
0
1
0
2
1
1
2
2
1
0
0
1
0
1
0
2
0
0
0
1
2
1
0
2
0
2
2
1
1
0
2
1
0
2
2
0
2
1
1
1
1
1
1
0
1
1
1
1
0
1
0
2
0
2
2
2
1
1
0
1
1
1
1
0
1
1
2
0
1
2
2
0
1
2
1
2
1
1
1
0
1
2
0
1
0
2
0
1
2
1
0
1
1
2
0
0
3
0
1
1
0
0
0
2
1
1
0
1
1
2
2
0
1
1
1
0
1
1
0
2
0
2
2
2
2
1
0
0
1
1
2
1
1
1
1
1
2
1
1
2
1
2
0
1
2
2
1
1
2
2
0
0
1
1
0
0
1
1
1
2
0
1
2
2
1
1
2
0
1
0
2
0
0
2
0
0
2
1
1
1
1
0
0
1
1
1
0
0
1
1
1
1
1
1
0
1
1
0
0
1
2
2
2
0
0
0
1
1
1
0
1
2
1
0
3
0
1
1
1
0
1
2
0
1
2
1
0
1
2
0
2
0
1
2
0
2
1
1
2
1
1
1
0
2
0
0
1
1
0
0
2
0
1
0
1
0
1
1
0
0
0
2
2
2
0
1
2
2
0
1
0
2
2
2
1
0
0
0
2
1
2
0
1
1
1
0
1
2
1
1
2
2
0
0
1
1
1
1
1
1
0
0
2
1
0
1
1
0
2
1
1
0
0
1
0
1
1
0
1
1
1
1
2
1
1
0
1
1
2
1
1
1
0
0
1
1
2
0
2
1
1
1
2
3
2
1
0
2
0
2
1
1
2
1
0
3
0
1
1
1
1
3
0
1
0
0
1
1
1
1
1
1
1
2
1
1
2
0
1
1
0
1
0
2
1
1
0
0
2
0
1
2
1
0
1
1
1
1
1
0
0
0
1
1
1
0
1
1
1
1
2
0
1
1
0
2
0
2
2
0
1
2
1
1
1
2
0
2
1
1
2
1
2
0
2
2
1
1
1
1
0
1
2
2
1
2
2
0
1
2
1
0
1
1
0
2
1
0
1
2
0
1
2
0
0
2
0
2
1
0
1
2
0
0
2
0
0
2
1
1
2
2
1
2
0
0
2
1
1
2
1
0
1
1
1
0
1
0
0
1
1
2
1
2
1
2
1
1
0
1
1
0
1
1
0
1
1
2
1
2
2
1
0
1
1
1
1
1
1
0
1
2
2
1
1
1
2
1
0
1
1
2
1
1
0
2
1
2
2
1
1
1
0
1
1
2
0
1
0
1
0
1
2
1
0
0
0
2
0
0
0
1
1
2
0
2
0
0
2
2
0
1
0
0
1
2
1
2
1
0
0
0
1
0
0
1
2
2
1
0
1
1
1
0
0
2
1
3
1
0
1
2
1
1
1
1
1
2
1
1
1
1
0
1
2
0
1
1
1
0
0
3
2
0
4
2
1
0
1
0
2
1
0
2
0
1
1
1
1
0
1
0
2
1
0
1
2
1
1
1
1
1
1
0
1
2
1
2
1
2
1
1
0
1
1
1
2
1
1
1
0
1
0
1
2
1
1
0
1
1
2
1
0
0
2
1
0
1
1
1
1
0
2
0
2
1
2
2
2
1
2
1
0
0
1
0
2
1
0
1
1
0
1
1
2
1
2
0
1
1
0
1
0
2
2
0
1
2
1
1
2
2
0
1
0
1
1
1
1
0
1
1
1
1
2
0
2
0
0
2
1
0
0
1
1
1
1
1
2
2
2
1
1
2
1
1
2
2
1
0
1
1
2
0
0
2
0
1
0
2
0
1
1
1
1
1
0
1
1
0
2
0
1
1
0
3
0
1
1
1
0
0
1
1
1
0
1
1
1
2
1
0
1
1
0
0
1
1
2
1
0
0
1
2
0
0
0
1
3
2
2
1
0
1
1
0
1
2
0
1
2
3
1
0
0
0
1
1
0
2
0
3
1
0
0
2
1
0
2
2
2
1
1
1
2
1
0
2
0
1
1
0
0
0
2
1
2
1
0
0
1
2
2
3
0
2
2
0
1
1
1
0
0
2
0
1
2
1
0
1
1
1
2
2
2
0
1
2
0
0
2
1
1
1
1
1
0
0
2
0
1
1
1
1
2
2
1
1
0
0
0
1
0
1
1
0
1
0
1
1
0
2
1
2
1
1
0
0
2
0
0
1
0
1
2
0
1
2
1
3
1
0
0
2
1
3
1
0
1
0
0
2
2
0
0
2
0
2
2
2
2
1
1
1
1
0
2
2
0
1
1
1
0
2
0
0
1
1
1
0
1
2
2
1
2
0
2
1
2
0
0
1
1
0
1
0
1
1
2
1
1
1
1
0
1
1
1
1
0
1
1
1
3
1
1
2
1
0
1
1
1
1
1
1
2
1
0
0
1
0
0
1
0
1
0
0
0
2
0
0
0
0
2
0
1
2
2
1
0
1
1
0
1
0
0
1
2
0
1
0
0
0
0
0
0
1
1
2
0
2
1
0
0
1
0
1
0
0
1
1
2
3
0
0
0
1
2
0
1
0
0
1
2
0
3
1
0
1
1
1
1
2
0
0
1
0
0
1
1
1
1
0
1
2
1
1
0
1
1
2
1
0
3
0
1
0
1
1
0
1
1
1
1
1
1
0
1
1
1
2
2
2
0
1
0
1
0
1
1
2
0
1
1
1
2
0
0
1
0
1
0
1
2
1
1
2
0
1
1
1
1
2
1
0
3
2
1
1
1
1
0
0
1
0
0
0
2
0
1
1
2
0
2
0
1
2
1
0
1
2
1
1
0
0
2
1
1
2
0
2
1
0
1
1
1
1
2
1
2
2
2
2
0
1
0
0
1
2
0
2
0
1
2
1
2
0
1
2
1
0
0
0
0
1
1
1
1
1
1
0
1
1
0
0
1
1
0
2
0
1
1
1
0
1
2
1
1
2
1
1
1
2
1
1
2
1
1
1
1
2
1
0
0
0
1
1
0
1
1
0
1
1
1
1
1
0
2
0
0
1
0
0
1
1
1
1
1
2
0
0
1
1
1
1
1
0
0
1
1
1
1
0
0
1
0
0
1
2
1
2
1
0
1
2
2
0
1
2
1
2
1
1
0
2
2
1
1
0
2
3
0
1
0
0
0
1
0
1
0
2
1
2
0
0
1
1
1
1
1
2
2
1
1
2
1
0
2
2
1
1
1
0
2
1
0
2
1
1
1
2
1
1
1
2
0
1
2
1
0
2
1
2
1
1
1
1
2
0
1
0
1
0
2
0
1
2
1
0
0
0
0
0
0
1
2
0
1
1
1
2
2
1
1
1
2
1
0
1
0
1
1
2
1
1
0
0
1
1
2
2
1
2
2
0
2
0
2
0
0
1
1
1
2
0
1
0
0
1
2
1
1
0
1
0
2
1
1
2
2
1
1
2
0
1
2
2
1
0
0
2
0
0
2
2
0
2
2
1
2
0
2
0
1
2
1
1
0
1
0
1
3
0
1
1
0
1
1
1
1
1
0
1
1
0
1
0
3
1
1
1
2
1
0
2
2
3
0
1
1
1
2
1
1
1
1
2
0
1
0
1
0
0
1
0
1
0
2
1
1
2
1
0
1
1
1
2
0
1
1
2
2
1
0
1
1
1
2
1
1
1
1
1
1
0
0
1
1
0
2
0
0
0
1
2
0
2
1
1
2
0
2
1
1
0
2
2
0
1
1
0
1
0
1
1
3
1
2
0
2
1
1
1
1
1
0
0
2
0
1
0
0
1
4
1
0
2
1
1
1
1
0
1
0
0
1
1
2
1
2
1
0
1
2
1
1
1
2
2
2
1
1
1
1
2
1
1
1
2
1
2
0
0
0
0
1
0
0
1
2
0
1
0
0
0
1
1
1
0
2
2
2
2
1
1
0
0
1
0
1
0
1
1
0
0
0
1
1
0
2
1
2
2
2
1
2
1
1
0
2
0
0
1
1
2
0
1
0
2
1
1
1
0
0
1
0
1
1
0
0
2
1
1
2
1
1
1
1
1
1
1
1
0
1
0
2
0
2
0
1
0
2
0
0
3
0
1
2
0
1
0
3
0
0
1
1
1
1
1
2
1
0
2
1
1
1
1
2
2
1
1
0
0
2
2
0
0
2
2
1
1
0
1
0
0
2
1
2
1
1
2
1
2
1
1
2
1
0
1
1
1
0
2
2
2
0
2
2
2
0
1
0
4
1
0
0
1
0
2
1
1
2
1
0
0
2
1
1
0
1
2
2
0
1
1
3
0
1
1
1
1
0
1
1
1
1
2
1
0
2
1
0
1
1
2
1
0
0
0
2
0
2
1
1
1
0
1
1
1
2
1
0
0
0
3
0
0
0
1
2
0
2
1
2
2
0
2
1
1
2
1
1
1
1
1
0
1
1
0
0
1
2
3
1
0
2
1
0
0
0
1
0
1
0
2
1
0
1
1
2
1
2
1
0
1
1
1
0
1
0
2
2
0
0
1
0
2
0
0
0
2
0
1
1
1
1
1
2
0
0
0
1
1
0
1
0
0
1
1
2
1
1
1
1
0
1
1
0
2
0
0
2
0
0
1
1
0
1
1
0
1
0
1
1
1
3
2
1
2
1
0
0
2
1
1
1
1
0
1
1
0
1
2
2
1
1
1
1
0
0
0
1
1
0
1
2
2
1
2
1
1
0
1
1
1
1
0
1
0
1
1
0
2
1
1
1
1
1
2
3
2
0
1
1
1
0
1
1
1
0
1
2
0
1
0
0
1
0
0
0
0
0
2
1
1
2
2
2
2
1
1
1
2
0
1
1
1
1
0
1
2
0
2
2
0
0
1
2
1
1
0
2
0
1
1
0
1
2
1
0
1
1
0
1
0
0
1
2
1
0
0
2
1
0
1
2
0
1
2
1
0
0
0
1
0
1
1
1
1
1
0
1
1
1
2
2
1
1
0
0
2
1
2
1
0
2
0
1
0
2
0
0
0
1
0
0
1
1
2
2
1
0
1
0
1
0
0
0
1
2
3
1
1
0
0
1
1
2
1
1
2
1
1
1
1
0
2
1
1
0
1
1
1
1
1
0
1
1
1
1
0
1
1
1
1
1
1
1
3
0
1
1
0
0
0
1
2
1
1
1
1
0
0
2
0
1
2
0
1
1
1
2
1
1
1
0
0
0
2
1
2
1
0
1
1
1
2
1
1
0
1
1
2
1
1
2
1
3
1
0
0
1
1
0
1
1
1
2
2
2
1
1
2
0
1
0
4
2
2
1
0
1
0
2
0
0
0
1
0
1
1
0
1
1
1
1
1
0
1
1
0
1
1
1
1
0
2
1
3
1
1
1
1
0
1
1
0
0
2
2
1
0
1
1
1
1
2
1
0
0
0
0
1
1
2
1
0
1
1
1
0
0
1
1
2
1
2
0
2
0
2
1
0
0
2
1
0
2
1
2
1
0
0
1
2
2
1
1
0
1
1
1
0
1
1
1
0
2
0
2
1
1
1
2
0
2
1
0
0
1
1
0
1
2
1
1
1
0
2
1
1
2
1
2
0
1
0
1
2
0
1
0
1
2
1
1
2
1
2
0
0
1
1
1
1
1
0
0
1
2
0
1
0
2
1
0
0
0
1
2
1
2
0
1
0
0
1
0
0
2
1
1
2
1
1
1
0
2
0
2
2
0
1
1
0
2
2
2
2
1
1
1
1
1
1
2
2
2
0
2
2
0
1
2
1
0
3
1
0
0
0
1
0
1
0
0
1
2
0
1
2
2
2
1
0
4
1
0
1
0
1
1
0
0
1
1
0
2
1
1
1
1
0
0
1
1
0
1
1
2
1
1
1
1
0
1
1
1
0
2
1
0
1
0
0
1
0
2
0
1
0
2
1
1
1
0
1
1
1
1
0
1
0
1
1
0
2
1
1
0
1
1
1
1
0
0
2
0
0
1
1
2
1
0
2
1
1
0
1
0
2
1
0
1
1
2
0
2
0
2
0
1
1
1
0
1
0
0
1
1
1
2
1
2
1
0
2
0
2
2
1
2
0
0
1
1
1
2
1
1
1
2
1
2
0
1
0
0
0
1
1
0
2
1
1
0
2
1
1
1
1
1
1
1
0
1
0
1
0
2
2
1
0
1
1
1
0
2
1
1
2
2
1
2
0
0
1
1
2
2
1
1
1
1
1
1
0
0
0
2
1
0
2
3
0
1
1
0
2
2
1
1
0
1
0
1
2
1
2
1
2
0
1
0
1
0
1
0
0
0
0
1
1
1
1
1
2
0
2
1
0
2
2
1
0
0
1
3
1
2
1
2
2
0
0
0
1
0
1
1
1
0
1
1
1
0
0
1
3
3
1
1
0
2
2
1
0
2
1
1
1
1
2
1
1
1
2
1
5
2
2
0
1
1
0
0
1
1
0
1
3
2
1
2
1
2
0
1
1
1
0
2
1
1
0
1
0
1
2
1
1
1
1
1
2
2
1
2
2
0
2
0
0
1
0
1
2
3
0
0
1
1
1
2
1
1
1
1
1
1
0
2
2
2
1
1
1
1
0
1
1
2
1
0
0
2
2
2
1
1
1
1
2
1
1
2
0
0
2
0
1
0
1
1
0
1
0
0
1
0
2
0
1
1
2
0
1
0
1
2
1
2
0
1
2
1
2
3
1
1
0
1
2
1
0
1
2
1
1
1
0
0
1
1
1
1
0
1
0
0
2
0
0
0
0
1
2
1
0
0
1
0
1
1
1
0
2
1
1
1
2
1
0
0
0
0
1
1
1
2
1
1
1
0
0
0
1
1
2
0
0
1
1
3
1
0
1
2
1
1
0
1
1
0
1
1
1
2
0
1
2
0
1
1
0
1
0
2
2
2
0
1
1
2
2
2
2
2
0
0
0
0
1
1
1
2
2
2
2
2
0
1
1
2
1
2
2
1
1
0
0
1
0
1
0
2
0
0
0
1
1
0
1
2
1
1
1
1
2
1
0
2
0
1
2
1
0
1
2
1
1
1
1
1
1
0
2
1
0
0
2
1
1
0
1
1
0
0
1
1
1
1
0
1
1
1
0
2
0
2
1
2
1
1
0
2
1
1
1
0
2
0
0
1
2
1
1
1
0
2
1
1
0
0
0
2
0
1
0
0
0
1
1
1
2
1
2
1
1
0
2
1
0
2
0
0
3
0
0
1
2
2
0
1
0
0
1
3
2
1
1
2
2
1
0
1
2
1
2
1
1
1
0
0
0
2
1
1
2
2
2
1
0
2
2
1
1
0
1
1
0
2
1
2
1
1
1
1
1
1
2
1
2
2
2
0
1
1
0
2
2
1
1
0
1
0
0
1
0
0
0
1
2
1
1
0
1
0
2
1
1
1
0
2
1
0
2
0
0
1
1
0
2
1
1
0
0
2
0
1
2
0
0
0
0
2
0
1
1
2
0
1
2
0
2
0
1
0
0
1
0
1
0
1
2
2
2
0
2
1
1
0
0
0
0
1
1
2
1
0
1
2
2
2
1
1
2
2
2
0
1
0
1
1
2
0
1
0
1
2
0
0
1
1
1
1
0
0
1
1
2
0
0
2
2
1
1
2
1
2
3
1
0
1
0
2
2
0
1
1
2
2
1
1
2
2
1
1
0
1
0
2
0
0
0
0
2
1
2
0
0
1
0
0
1
2
1
0
0
0
2
1
0
1
1
1
1
0
3
1
1
1
1
0
0
2
1
1
0
2
2
1
0
1
2
1
0
2
1
1
1
1
1
1
0
1
2
2
1
0
0
0
2
0
2
2
1
1
0
1
2
1
2
0
0
0
2
1
1
1
1
1
1
2
2
1
0
2
0
1
1
0
0
1
0
1
2
0
1
2
1
0
0
2
1
1
2
2
0
0
1
0
1
1
1
2
1
1
1
2
0
1
1
1
1
1
1
0
0
1
1
2
1
1
0
1
1
0
1
1
1
1
1
1
0
2
1
1
2
0
1
1
1
1
1
1
2
0
1
0
0
1
1
2
1
0
1
1
3
1
1
1
1
1
1
1
0
2
1
1
0
0
2
2
1
2
1
2
2
1
1
2
1
1
1
2
2
2
1
0
1
0
1
2
2
0
2
0
0
1
1
0
0
1
0
0
1
0
0
0
2
0
1
1
0
0
2
1
1
2
1
1
0
1
1
1
0
1
0
1
0
1
1
1
0
1
2
2
1
1
1
0
2
0
0
0
1
1
1
1
2
0
2
2
1
1
1
1
2
0
1
2
0
0
0
0
2
1
1
0
2
1
1
2
1
1
1
1
2
0
1
2
2
0
1
2
1
0
0
0
2
1
0
1
1
0
0
0
0
0
2
1
1
1
1
2
1
1
2
2
1
0
2
0
0
0
0
1
1
1
0
0
0
2
0
1
1
1
0
2
6
0
1
2
0
0
1
1
2
1
2
1
1
2
2
1
0
1
0
1
1
0
2
1
1
0
0
1
2
2
2
2
1
2
1
2
0
2
1
1
0
1
2
0
1
0
0
1
1
1
2
1
0
1
0
0
0
0
2
2
1
0
2
1
0
0
0
1
0
0
2
1
1
1
2
1
2
0
1
0
1
1
1
1
1
1
2
1
1
1
0
1
1
0
2
1
1
1
0
1
0
0
0
0
2
3
1
1
0
0
0
1
2
1
0
1
1
0
2
1
1
2
1
1
2
2
0
1
1
2
1
1
0
0
0
2
1
0
0
1
1
0
2
2
1
1
1
0
2
1
0
0
2
2
0
0
2
0
0
0
0
0
2
1
1
1
0
1
0
1
1
1
1
1
2
1
2
2
1
1
2
0
2
0
1
0
1
0
1
1
2
1
1
0
0
2
2
1
1
1
0
2
1
1
1
0
1
1
1
0
0
1
0
2
1
0
0
2
2
3
1
1
0
1
2
1
1
2
0
0
1
0
1
2
1
1
1
1
0
2
0
0
1
2
1
0
1
1
0
1
1
0
0
1
1
3
1
1
1
0
1
1
2
0
1
0
1
1
1
0
1
1
1
1
1
0
0
2
1
1
1
0
1
1
0
1
1
1
1
1
2
1
1
2
0
1
0
1
1
1
0
0
2
0
1
1
0
2
2
0
1
0
0
1
1
0
2
1
1
2
1
2
1
1
1
2
0
2
0
1
2
1
0
0
0
1
0
1
2
0
1
1
2
2
0
1
0
1
1
1
0
0
0
0
1
2
1
2
2
1
1
5
0
2
1
0
2
0
0
1
2
2
1
1
2
1
2
2
0
1
0
0
0
1
1
0
1
2
0
2
0
0
1
2
1
0
2
2
2
1
2
1
1
0
1
1
0
2
1
0
1
1
0
1
1
2
0
2
1
0
2
0
0
1
1
1
2
1
0
2
2
0
2
2
1
0
0
0
0
1
2
1
1
2
1
0
1
1
1
1
1
1
0
1
1
1
2
2
0
1
1
0
1
2
1
1
1
1
1
2
1
1
0
1
1
2
3
2
1
1
1
1
1
2
1
1
0
1
1
2
1
1
0
2
0
1
1
0
0
2
2
1
1
1
1
2
0
1
1
1
0
0
0
2
1
1
0
1
1
0
2
2
1
1
0
1
1
1
1
0
0
2
2
0
0
1
1
1
0
2
0
0
1
0
1
1
0
0
0
1
1
1
1
0
2
1
2
2
0
2
2
1
0
2
0
2
1
0
1
0
1
0
1
0
1
1
1
1
0
1
1
2
0
1
2
0
2
1
0
1
1
1
2
1
0
1
2
2
1
1
0
2
1
1
1
1
1
0
2
1
1
1
2
1
0
2
1
1
0
2
1
1
1
1
0
1
1
0
1
0
1
0
2
0
0
1
1
0
2
1
1
1
0
2
1
1
1
0
2
0
0
1
0
1
2
1
0
1
2
2
0
0
1
1
1
1
1
1
1
1
2
2
2
1
0
2
2
1
0
1
0
2
0
1
2
1
0
1
1
2
2
1
2
1
1
2
1
0
1
0
1
2
2
0
0
1
2
2
0
0
3
2
1
0
0
2
1
0
0
0
3
0
2
1
1
1
0
1
0
2
1
0
1
0
1
2
1
1
1
1
0
1
0
0
1
0
1
0
2
0
2
0
1
2
0
0
1
1
2
2
0
1
1
1
2
1
3
0
1
0
2
1
1
0
0
1
2
1
1
0
2
2
1
2
1
1
1
1
0
1
2
0
0
1
2
1
2
2
0
0
1
1
0
0
1
0
0
2
0
0
2
2
1
0
0
0
2
1
1
0
1
1
0
0
0
1
1
2
0
1
1
0
1
0
0
1
1
2
2
0
0
2
2
0
1
0
1
1
0
2
1
2
1
2
2
2
0
0
2
0
0
1
0
1
2
2
1
1
1
2
0
0
1
1
0
0
1
1
0
1
0
2
1
0
0
0
0
2
1
1
1
1
1
2
1
1
0
1
0
2
1
1
0
1
0
0
0
0
0
0
2
1
2
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
2
0
0
1
1
0
1
2
0
1
1
1
1
1
0
1
1
1
2
0
0
1
0
3
1
1
2
1
1
1
2
0
1
2
1
0
0
1
1
1
1
0
2
1
1
2
0
1
0
0
1
2
1
2
0
1
1
0
1
0
1
2
0
2
0
0
0
0
2
1
0
1
1
0
2
2
2
0
0
0
2
0
0
0
0
1
1
2
0
1
0
2
2
2
1
1
1
1
0
1
1
1
0
1
1
1
2
1
0
0
1
0
1
2
0
1
0
1
2
2
1
1
0
1
2
2
0
2
1
2
1
1
0
1
1
1
1
0
0
1
1
0
1
0
2
1
0
2
1
1
1
1
0
0
1
1
1
0
1
2
1
1
1
0
1
0
1
2
0
0
0
2
1
1
0
1
1
0
1
1
1
0
2
1
1
0
1
1
1
0
1
0
2
1
1
1
1
0
1
1
2
2
2
0
2
0
1
2
2
1
1
1
1
2
2
2
1
1
0
2
0
0
2
1
1
2
2
1
1
2
1
2
0
0
0
0
0
0
1
1
0
1
2
2
2
3
0
1
1
0
1
1
1
1
0
1
0
1
0
1
1
1
0
1
0
0
2
1
1
0
0
0
1
2
0
0
1
1
2
0
1
2
0
2
2
1
0
1
1
0
2
0
0
1
0
1
1
1
1
1
2
2
0
0
1
2
2
0
0
0
0
1
0
0
0
2
1
0
2
1
1
0
2
1
1
0
0
1
1
2
1
1
2
1
0
1
0
2
1
4
0
1
0
2
1
1
0
0
1
1
1
1
2
1
0
2
1
0
1
1
1
1
2
2
1
1
1
1
0
0
2
1
2
2
1
1
2
0
1
1
0
0
1
1
1
1
0
1
2
0
1
1
1
2
0
0
0
0
1
1
2
2
1
1
1
1
3
0
1
1
0
2
2
1
0
1
1
0
1
0
2
2
2
1
1
2
1
0
0
0
1
2
0
2
1
1
1
2
1
2
2
1
1
1
1
2
0
0
0
0
2
2
1
0
0
1
1
1
0
0
0
1
1
0
1
1
0
2
1
0
0
2
0
0
2
1
1
0
0
1
1
2
0
0
0
3
3
0
1
0
0
2
1
1
1
0
0
0
1
2
1
1
2
0
2
2
2
0
1
1
3
1
0
2
1
2
0
2
1
1
0
1
2
1
0
1
1
1
1
1
1
0
0
1
1
1
1
0
0
2
0
0
3
1
1
1
0
1
2
1
0
0
0
0
0
1
4
0
0
1
1
1
0
0
0
1
2
0
1
2
2
0
1
1
1
2
1
0
2
1
1
0
1
0
1
0
2
0
1
0
0
0
0
2
1
1
2
0
1
2
2
1
0
1
2
1
1
1
0
0
0
1
1
0
1
0
0
2
1
0
2
1
1
1
1
1
1
1
2
1
2
0
0
0
1
1
1
2
2
1
0
2
0
1
0
1
1
1
2
0
0
0
3
1
0
0
0
2
2
1
1
0
0
0
1
1
1
2
1
0
1
2
1
0
1
1
0
0
1
0
0
0
0
0
2
0
2
2
3
1
2
1
1
0
1
0
2
1
1
0
1
2
1
0
0
0
1
0
1
1
2
0
2
1
0
1
0
0
2
0
1
0
2
0
2
1
1
2
1
1
1
1
2
1
1
1
1
3
2
2
0
3
2
0
1
1
1
1
2
1
1
2
1
1
0
1
0
0
1
1
2
2
1
2
1
0
1
2
1
1
0
1
1
2
2
1
0
2
0
2
0
1
2
1
1
1
1
0
1
2
1
3
1
0
0
1
1
0
0
1
0
1
0
2
1
2
2
1
0
1
1
1
1
0
1
2
1
2
0
1
1
1
0
1
1
1
1
1
0
1
0
1
1
0
1
2
1
1
0
0
2
2
0
0
1
0
1
1
0
0
1
1
1
0
1
2
1
1
2
0
1
1
1
0
0
0
1
2
2
0
1
1
2
1
2
3
2
1
0
1
0
0
1
0
0
2
0
2
1
0
2
1
2
2
1
0
0
1
1
1
1
1
1
0
0
0
1
1
0
0
2
0
2
0
0
2
2
0
1
2
2
1
0
1
2
1
2
1
1
0
0
1
0
1
1
1
1
2
1
1
2
0
2
0
0
3
1
1
3
2
1
1
1
2
1
1
1
2
0
2
1
1
1
0
1
3
0
0
1
1
1
1
2
1
1
1
1
1
0
1
0
1
1
1
1
1
1
2
0
0
0
1
0
1
0
1
0
2
1
0
2
1
0
0
1
1
1
1
1
1
1
2
2
1
2
1
2
0
0
2
0
1
1
0
0
0
1
2
2
1
2
2
0
1
2
2
1
1
1
2
0
2
1
2
2
1
2
1
0
1
0
0
0
0
1
2
1
1
2
1
1
0
1
0
1
0
0
2
1
2
1
1
1
1
1
1
1
2
2
1
2
2
0
2
2
1
0
2
1
1
0
0
0
0
1
0
1
0
1
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
1
0
1
0
0
2
2
2
2
3
0
1
1
2
1
2
1
1
1
2
0
1
2
1
1
1
2
0
1
1
0
0
0
2
2
1
2
1
1
1
0
1
2
1
2
0
1
1
1
0
1
0
2
1
1
0
1
2
1
2
0
0
1
3
0
2
2
2
2
1
1
1
2
1
1
2
1
2
2
0
1
2
1
0
2
2
1
2
2
2
0
1
0
1
2
1
1
1
1
1
1
0
2
2
0
4
2
1
1
1
1
1
0
0
2
1
0
2
2
0
1
2
1
1
2
2
2
1
1
2
1
2
1
1
1
1
0
1
2
1
0
2
1
1
4
1
1
0
1
1
1
1
1
0
1
1
1
1
1
2
1
1
0
0
1
1
1
0
0
0
1
1
1
0
0
1
1
1
1
1
0
0
1
0
0
2
1
1
0
1
1
1
1
2
2
0
2
1
0
1
2
0
2
1
1
1
1
0
1
1
1
0
1
1
1
1
0
1
1
0
2
0
1
0
1
0
1
0
1
0
1
1
2
1
2
1
1
0
1
0
0
1
1
1
1
0
1
0
2
0
0
2
2
1
1
1
1
1
0
1
1
1
2
1
0
1
1
2
1
1
1
0
2
0
1
1
1
2
2
0
1
1
1
0
2
0
1
0
2
2
1
0
0
2
2
1
1
1
3
1
1
1
2
1
2
1
0
2
1
0
0
1
0
2
1
0
0
1
2
1
2
1
1
0
2
2
1
1
1
1
0
2
0
1
1
1
2
1
1
2
0
0
1
2
2
1
0
1
1
1
2
1
2
0
2
0
0
1
1
1
2
0
0
0
2
1
1
2
2
0
1
1
0
2
1
1
2
1
1
1
2
2
1
1
2
2
0
0
0
0
2
2
2
0
1
2
1
1
0
1
1
2
2
0
2
1
2
1
0
1
0
1
1
0
1
2
2
1
1
1
1
1
1
2
0
0
2
1
0
1
2
2
1
0
1
1
1
1
1
0
1
0
1
1
0
2
1
0
1
0
1
1
0
1
1
0
2
1
0
0
2
0
2
1
0
0
1
2
0
1
1
1
1
2
2
0
4
2
2
1
1
1
0
1
1
2
1
1
0
2
2
1
1
1
1
0
1
2
1
0
2
2
1
1
1
0
0
1
1
0
2
1
1
1
1
2
0
1
0
0
0
0
1
1
1
2
0
2
1
1
1
1
0
2
1
2
0
2
0
1
0
0
1
2
0
2
0
1
1
1
1
1
0
1
1
2
1
0
2
0
1
2
0
0
1
1
0
1
0
1
2
1
2
1
0
0
0
2
0
1
1
0
1
2
1
1
0
1
0
1
1
1
1
2
1
1
0
1
2
1
0
2
1
1
2
0
2
0
0
2
0
0
1
1
1
1
1
1
2
0
0
2
0
1
0
0
0
1
0
2
1
0
2
1
1
0
1
2
2
0
0
0
0
1
1
1
1
1
2
1
1
3
1
2
2
2
1
1
0
1
2
1
2
0
1
1
1
1
2
1
2
1
2
0
1
0
1
0
1
2
2
1
0
2
1
1
2
2
0
0
1
1
2
1
1
1
1
1
1
0
1
0
0
2
0
1
0
0
0
1
0
2
4
2
1
1
1
2
0
2
1
1
0
2
2
3
1
2
1
2
2
1
1
1
1
1
0
1
1
2
1
1
0
1
0
1
2
0
1
1
1
2
0
1
2
1
1
1
1
0
0
2
2
0
3
1
0
1
1
0
0
0
2
1
1
0
1
0
1
0
0
1
2
2
1
1
1
0
0
2
1
2
1
1
2
0
0
0
1
2
0
1
1
1
0
2
2
2
1
1
2
0
0
1
2
1
0
2
1
0
0
0
0
1
2
1
0
2
0
1
0
0
2
2
2
1
1
1
2
0
2
2
2
0
2
5
1
1
1
1
0
2
2
0
0
1
0
1
0
2
1
0
1
0
1
4
0
0
2
0
1
1
1
1
1
2
1
1
2
1
2
1
1
0
0
1
1
2
1
1
1
1
1
1
2
2
1
1
0
2
0
1
1
0
0
1
2
0
0
0
1
2
1
1
2
1
1
0
1
1
1
1
2
1
1
1
1
0
3
0
0
1
1
2
2
0
1
1
0
2
1
1
0
2
0
0
1
0
1
0
1
0
0
0
1
0
0
1
0
2
1
0
2
2
1
1
1
0
1
1
2
0
0
0
1
1
2
0
1
1
1
1
2
2
1
1
0
1
1
3
0
1
2
1
1
2
2
1
1
0
0
0
0
0
1
0
1
0
2
0
1
1
1
0
1
0
0
1
2
1
0
2
0
1
1
2
2
0
0
1
0
2
2
1
2
1
0
1
1
1
1
1
1
1
0
0
1
1
2
2
2
2
0
2
1
2
1
0
2
1
0
1
1
1
1
2
2
1
0
1
2
1
1
1
1
0
0
2
1
0
2
2
2
1
2
1
0
1
0
0
1
0
0
1
2
0
1
0
1
1
1
2
0
0
2
1
2
0
1
0
1
1
1
0
1
1
1
1
0
1
2
1
4
0
1
0
0
1
0
0
2
1
1
1
0
1
0
1
1
0
1
0
2
0
1
0
1
2
0
1
1
1
0
2
2
0
1
0
0
0
1
0
1
2
1
0
1
2
1
2
0
2
0
0
0
0
1
1
1
0
2
0
0
0
0
1
1
1
0
1
1
1
0
0
1
0
1
1
1
0
0
1
1
1
0
2
1
0
1
1
2
0
0
1
0
1
1
1
1
0
0
0
1
1
1
1
0
1
1
0
1
0
0
0
0
1
1
1
0
0
1
1
0
1
1
0
2
2
0
1
2
2
1
1
0
2
0
2
1
0
1
0
0
2
1
1
1
0
0
2
0
1
1
1
1
1
0
0
1
0
1
2
2
1
0
1
1
2
2
1
2
1
1
0
1
2
1
1
1
0
0
0
2
1
0
2
1
1
1
2
0
2
0
0
1
0
1
1
2
1
1
1
1
2
2
1
1
1
1
0
1
1
1
1
0
0
1
0
1
0
0
1
0
2
1
1
1
1
1
0
0
1
0
2
1
1
0
0
0
0
0
0
2
1
1
2
1
1
1
1
0
2
1
2
2
1
0
1
1
0
1
1
2
0
0
1
0
1
0
0
1
1
1
5
1
1
1
0
1
1
2
0
0
2
1
0
0
2
1
1
0
1
1
2
1
2
1
1
1
2
0
2
0
0
1
1
2
1
1
1
2
1
0
1
0
1
1
1
0
0
2
0
1
2
1
0
1
0
2
1
6
1
2
2
2
0
0
1
2
0
1
2
1
2
0
3
2
1
1
1
0
1
1
0
1
0
1
1
3
1
2
0
1
1
1
0
1
1
0
0
0
0
2
0
0
1
1
2
1
0
1
1
1
2
2
2
0
1
0
0
0
0
1
1
1
1
2
1
1
0
1
1
2
0
0
2
1
2
2
0
1
0
0
1
2
1
1
1
0
0
1
0
1
0
0
0
0
1
0
1
0
1
0
0
1
0
2
1
1
1
1
2
2
2
1
1
0
2
1
0
0
2
1
0
4
1
1
2
1
1
2
2
2
2
0
1
1
1
0
1
1
1
2
0
1
2
2
1
1
1
2
0
1
0
1
1
0
1
1
1
2
0
1
1
0
0
0
1
0
1
2
1
0
1
1
1
0
0
1
0
1
1
2
1
1
2
0
1
2
0
2
2
1
1
0
1
0
2
2
1
3
2
0
0
0
0
1
1
0
1
2
0
1
1
6
1
2
2
0
0
8
0
1
2
1
1
0
0
1
0
0
0
2
1
2
1
0
0
1
2
1
1
1
2
0
1
2
2
0
2
1
1
1
2
0
0
1
1
0
1
0
2
1
1
2
1
1
1
2
0
0
1
1
1
1
0
1
1
1
1
0
0
1
1
1
0
2
0
0
0
1
1
1
0
2
0
0
2
0
0
1
0
2
1
1
0
1
1
1
2
1
0
1
1
1
2
0
0
2
0
1
2
1
1
1
1
1
1
1
2
1
2
2
0
1
1
1
0
0
1
1
0
0
1
1
1
1
1
0
1
1
1
0
2
1
1
1
0
2
1
1
2
1
1
0
0
1
2
0
1
0
0
1
1
1
1
0
1
0
2
2
2
4
0
1
1
1
0
2
0
1
1
1
2
1
1
2
0
0
2
1
0
0
1
0
1
0
0
1
0
0
0
2
0
2
2
1
1
1
2
1
1
1
1
1
0
1
2
1
1
1
1
2
2
1
1
1
2
0
1
1
0
2
1
0
1
0
1
1
1
1
2
0
3
0
1
0
2
1
1
0
2
1
2
1
0
1
1
1
0
0
1
2
1
0
1
1
2
0
0
1
1
1
2
0
1
1
1
1
1
1
0
0
0
1
1
1
0
1
1
1
1
0
2
2
1
0
2
0
0
4
0
0
2
0
0
4
1
1
1
1
1
1
2
0
0
0
0
0
0
1
1
0
0
1
1
1
4
1
1
1
2
1
0
1
1
2
1
1
1
1
0
1
0
0
2
0
1
1
1
1
1
1
0
0
2
1
2
0
0
1
2
1
1
1
1
0
2
2
1
2
0
2
1
1
0
1
1
0
2
2
0
1
2
1
1
0
1
0
2
1
1
1
0
2
0
1
2
2
2
1
0
1
0
1
2
1
1
0
1
2
2
1
2
0
0
2
0
0
1
1
2
1
0
1
1
2
0
0
1
2
1
0
2
0
4
1
2
1
1
2
1
0
1
1
0
1
0
3
1
3
1
1
1
1
2
1
1
0
1
2
1
1
1
0
1
1
2
1
1
0
1
0
2
1
1
1
0
0
1
2
1
1
2
2
1
2
1
1
1
1
1
1
0
0
1
0
0
1
1
1
1
1
0
1
1
1
2
0
1
0
2
0
1
0
1
0
0
0
1
0
1
0
1
1
0
1
0
2
1
1
1
0
1
1
1
1
0
0
0
3
0
1
1
0
0
1
0
1
2
1
1
1
0
1
0
1
0
3
0
1
1
0
1
2
0
2
1
2
1
1
2
0
2
1
1
1
0
0
2
1
1
1
1
1
1
0
0
2
1
1
1
1
0
0
1
1
1
1
1
0
0
1
1
1
0
0
1
2
1
1
0
1
0
1
1
1
1
0
2
2
0
1
1
1
2
0
0
1
1
1
1
2
0
1
0
2
2
2
0
0
2
2
1
1
1
0
2
1
2
1
2
0
1
1
1
1
1
1
1
1
0
0
1
1
0
1
1
2
2
1
0
0
0
0
1
1
0
3
1
1
1
2
0
2
1
2
1
0
1
1
0
0
1
2
1
0
2
1
2
0
2
0
2
1
0
1
0
2
0
0
1
0
2
1
1
1
0
1
1
2
0
1
0
1
1
1
2
2
1
2
0
0
1
1
0
1
1
0
1
1
1
0
1
1
0
1
2
2
1
2
1
1
1
0
2
0
0
0
1
1
1
1
1
2
2
1
0
1
1
1
1
0
0
1
2
2
1
2
2
1
0
0
0
1
2
2
1
0
1
1
0
0
0
1
1
0
2
0
1
1
1
2
1
1
2
1
1
1
2
2
0
1
2
0
0
1
0
1
1
1
1
1
1
2
2
1
0
0
0
1
0
1
0
0
1
1
1
0
1
2
2
1
2
2
1
0
1
1
1
2
1
4
1
1
1
1
2
2
1
2
0
1
0
2
0
0
0
1
0
1
0
0
1
1
2
1
2
0
1
2
1
0
1
2
0
1
1
1
1
1
2
2
0
0
3
2
0
1
0
2
0
1
0
0
1
1
2
1
1
1
2
1
1
1
0
2
1
1
1
0
1
0
1
1
0
1
2
1
0
1
1
0
0
1
1
0
2
1
0
0
1
2
1
0
1
0
1
0
0
2
1
0
1
1
2
1
0
1
0
0
1
1
2
1
0
2
1
2
0
1
2
0
0
0
1
0
1
1
1
1
0
1
1
0
1
2
1
2
1
1
2
0
2
1
1
1
1
1
1
1
0
1
1
1
2
1
0
2
0
2
2
0
2
0
2
2
2
0
0
0
1
1
0
1
0
2
2
0
2
0
1
1
1
2
1
2
2
3
1
1
0
1
0
1
0
2
2
1
2
1
0
1
0
0
1
1
1
2
0
1
0
1
1
2
0
0
0
2
1
1
2
2
0
1
1
2
1
0
0
1
1
2
0
2
0
1
0
1
1
1
0
2
0
1
1
2
2
0
2
1
2
1
0
1
2
2
1
0
1
1
1
0
1
1
2
1
2
0
0
0
0
2
1
2
0
1
0
1
1
1
2
1
2
1
1
1
0
0
1
2
2
1
1
1
1
0
2
1
0
0
1
1
1
0
2
2
0
2
1
1
1
1
1
1
2
0
1
0
1
1
0
1
1
0
1
2
1
1
0
1
0
1
1
2
1
1
1
1
1
1
2
1
0
0
1
0
0
2
1
0
2
0
1
0
0
1
0
1
3
1
2
0
2
1
1
0
3
2
0
1
0
1
2
1
1
1
2
2
1
1
0
2
2
1
0
1
1
0
0
2
0
2
0
1
0
1
0
0
0
1
1
1
1
2
2
0
0
1
2
0
1
0
1
1
2
1
1
0
2
1
1
1
1
1
1
3
0
2
1
2
2
1
0
2
1
1
1
1
1
1
2
0
2
1
2
1
1
1
1
0
1
2
1
1
1
1
1
2
1
1
0
0
0
0
1
1
1
2
1
1
2
0
1
2
2
0
0
0
1
0
0
2
1
2
2
2
1
1
1
1
1
1
0
1
1
1
1
1
1
2
2
0
1
0
0
1
0
1
0
1
0
1
1
1
1
0
0
0
2
1
0
1
0
1
1
1
0
0
1
1
1
1
1
0
0
1
0
1
0
0
1
1
1
0
0
0
2
1
1
1
0
1
1
1
2
1
0
1
2
0
2
2
1
0
0
3
2
0
2
1
2
2
1
1
2
1
1
0
1
1
1
1
2
2
1
1
1
0
1
2
0
0
0
1
1
1
1
1
1
1
2
1
1
0
0
2
0
1
2
0
1
0
0
0
1
1
2
2
2
1
1
2
0
1
2
1
0
1
1
2
1
1
2
0
0
0
2
0
1
1
3
2
0
2
0
1
0
1
0
2
1
2
2
1
2
1
1
1
1
1
1
1
0
1
1
1
0
0
0
1
1
1
1
0
1
1
2
2
1
1
1
2
1
2
1
1
2
0
1
0
0
1
2
1
0
0
1
0
1
1
1
1
0
0
1
2
0
0
1
1
0
0
0
2
0
0
1
1
1
2
2
0
1
0
1
1
0
0
1
0
0
1
0
1
2
1
2
1
1
0
1
1
0
0
0
0
1
3
1
1
0
0
1
1
1
2
0
2
2
2
2
1
1
1
0
1
0
1
0
1
1
1
0
1
0
0
0
1
0
2
1
2
1
3
1
1
1
0
0
1
0
1
0
1
1
0
2
0
2
0
1
2
0
1
1
2
1
2
0
1
1
1
1
0
0
1
0
0
2
1
1
1
0
1
0
2
1
1
1
1
0
1
1
0
1
2
1
1
1
0
1
1
1
1
2
0
1
1
0
2
1
1
2
2
1
0
0
1
2
2
0
2
0
1
1
1
1
2
0
2
1
1
0
3
1
0
2
1
0
0
2
1
1
1
2
2
0
0
2
1
0
0
2
2
0
1
2
0
1
1
0
2
1
1
2
1
1
2
0
2
1
1
1
0
0
1
2
1
1
1
1
1
1
1
0
1
2
0
2
2
1
0
1
1
3
0
1
0
2
2
2
0
1
2
1
1
1
1
1
1
1
0
2
0
2
2
0
1
0
1
0
1
1
2
2
1
2
1
1
0
0
1
2
0
1
1
1
1
0
2
1
1
3
0
0
1
1
2
0
0
2
1
0
1
1
1
0
1
1
1
1
2
1
1
0
1
1
0
0
1
0
2
1
0
3
0
2
0
2
0
1
1
2
0
1
1
0
2
1
0
0
1
0
1
2
2
0
1
1
0
0
1
0
1
1
0
0
1
2
1
4
1
0
0
1
2
1
1
1
2
0
2
1
1
1
1
1
1
0
0
2
2
2
1
2
1
0
1
0
2
2
2
1
1
1
1
3
1
1
1
1
0
1
2
0
1
1
1
0
2
2
2
1
0
1
2
1
2
2
2
0
0
2
2
0
2
3
0
2
1
1
2
1
1
1
0
0
1
1
2
1
2
0
2
1
0
0
2
2
0
1
1
2
1
1
1
1
0
0
1
1
1
3
1
2
1
1
1
1
1
1
2
1
0
2
1
1
1
2
1
1
0
1
3
1
1
0
1
0
2
1
0
2
1
2
1
1
1
1
0
1
1
0
1
2
0
2
1
2
1
0
0
2
1
1
1
2
0
1
2
2
1
1
2
1
1
0
1
2
0
1
1
0
2
2
2
0
1
0
1
2
1
0
0
1
0
1
1
2
2
1
1
0
1
1
1
2
0
1
1
0
0
1
0
0
0
0
1
0
1
0
1
1
1
2
0
0
1
1
1
1
1
1
0
0
1
0
1
0
0
1
2
1
1
0
0
0
1
2
1
1
1
2
1
1
2
2
2
1
1
1
2
0
1
1
1
1
2
2
1
1
2
1
0
1
0
1
2
1
1
1
1
0
0
0
1
2
0
1
1
1
1
1
0
1
0
1
1
0
2
1
1
3
1
1
0
1
0
2
2
0
0
0
0
0
0
0
1
2
1
0
0
2
1
0
1
0
1
1
1
0
2
1
1
2
1
0
2
1
1
1
2
1
0
0
1
1
1
0
1
0
0
1
2
2
1
0
1
2
1
1
1
1
0
0
1
1
0
1
1
1
1
1
1
3
1
1
1
1
2
1
1
0
0
1
1
2
1
0
2
0
2
1
0
0
1
2
2
1
1
1
1
0
1
1
3
0
1
1
0
1
1
1
3
1
1
1
1
1
1
5
0
0
2
1
1
1
0
1
0
2
1
1
2
1
0
1
2
1
2
2
4
1
1
1
0
1
0
0
2
0
2
2
1
0
0
1
0
1
0
2
0
2
1
2
0
1
2
1
1
2
2
1
2
1
1
2
1
1
1
1
1
1
2
1
1
2
1
1
2
2
2
1
1
1
0
1
2
2
5
2
2
1
2
2
0
2
1
0
0
1
2
3
1
0
0
2
1
0
0
2
1
0
1
1
0
0
1
1
0
0
0
1
0
1
1
1
1
1
2
1
1
2
2
0
3
0
0
0
2
1
1
1
2
0
0
0
0
1
0
1
1
2
0
0
1
1
1
2
0
0
1
1
1
0
0
1
1
2
1
1
1
2
2
1
1
0
2
0
1
1
0
1
1
2
1
1
1
2
0
2
0
0
2
1
1
0
0
2
1
0
2
2
1
1
1
1
2
1
0
1
0
1
0
1
2
1
1
0
0
1
1
2
0
2
0
1
0
1
0
2
0
1
0
0
1
0
2
1
1
2
2
0
0
1
1
0
0
1
1
1
0
0
0
2
1
1
0
1
0
1
1
1
2
1
1
1
1
0
2
0
2
1
1
1
0
1
1
2
1
1
1
1
1
0
0
0
0
0
1
0
0
1
1
1
1
0
0
3
1
1
0
2
2
1
1
0
0
2
1
1
1
0
1
1
0
1
1
0
2
2
0
0
0
1
0
0
1
2
1
1
2
0
1
0
2
0
2
2
1
2
2
1
2
1
0
0
1
2
1
0
1
1
1
1
2
1
0
0
1
1
1
0
0
1
3
1
1
1
0
0
0
2
0
2
1
1
1
1
1
0
2
1
3
0
0
0
0
2
2
0
2
0
1
1
0
1
0
0
1
1
0
1
1
0
1
1
0
2
1
1
0
0
1
1
0
0
3
0
0
0
2
0
1
1
1
1
1
2
1
1
1
0
1
1
1
2
1
1
2
2
1
2
1
1
1
1
2
0
2
0
2
2
1
0
0
0
0
0
1
1
1
0
1
2
0
0
0
2
7
1
2
1
1
1
0
1
0
1
0
1
0
2
5
0
1
2
0
1
1
0
1
2
1
2
1
2
1
2
2
0
0
1
1
1
1
2
1
0
1
1
2
2
1
0
0
2
4
0
0
1
1
1
2
1
2
1
0
1
0
2
1
2
1
1
1
1
1
0
1
1
2
2
0
2
4
2
1
1
1
1
2
0
1
0
0
1
2
1
1
1
0
2
1
1
1
0
1
1
1
0
0
1
0
2
0
1
1
1
1
1
0
3
0
0
1
3
0
1
0
1
1
0
1
1
0
1
0
2
1
1
2
0
0
1
1
0
2
0
2
1
0
2
1
0
2
1
2
1
1
0
2
1
1
1
1
1
1
2
0
1
1
0
1
1
1
0
2
1
1
1
0
1
2
2
1
1
2
0
0
1
2
0
2
1
0
1
2
1
1
0
0
1
2
1
2
0
1
1
1
1
1
2
2
1
2
1
1
0
1
1
0
2
1
1
1
1
0
1
1
1
2
1
1
0
0
0
1
1
2
1
1
0
1
0
1
2
1
0
1
1
1
2
1
0
1
1
2
1
1
1
1
1
0
0
6
1
1
0
1
1
1
1
0
1
0
1
2
1
1
3
0
1
1
0
2
0
0
1
2
1
0
2
3
1
1
0
1
2
0
1
1
1
3
1
0
2
2
1
1
2
0
1
0
2
1
2
0
0
0
1
1
0
1
1
3
1
1
0
0
0
1
0
1
0
1
1
1
2
1
0
0
0
2
1
1
1
0
0
1
2
1
1
2
1
0
1
2
2
0
1
0
2
1
0
2
1
1
1
2
1
1
0
0
2
1
1
1
2
0
1
1
0
2
1
1
0
2
2
0
2
2
2
0
1
0
0
2
0
0
0
2
2
0
1
1
1
2
1
1
0
2
1
1
1
2
2
0
1
1
1
2
0
0
1
1
2
0
0
2
1
1
1
0
2
1
1
0
0
1
1
1
0
1
3
2
1
0
3
1
0
0
2
0
0
0
0
3
0
1
0
0
0
2
2
0
0
0
1
1
2
0
1
0
0
1
1
0
2
0
0
3
0
2
1
3
1
1
0
0
1
1
1
2
2
2
2
1
1
0
0
1
1
1
2
1
0
1
1
2
1
2
1
2
1
2
1
0
1
1
1
2
1
2
1
0
1
1
0
0
0
0
5
1
0
0
1
1
1
0
1
1
1
0
2
0
1
1
0
1
0
0
1
2
1
0
0
1
1
2
2
1
0
0
0
1
2
2
1
2
1
1
2
2
0
0
1
0
1
1
1
1
1
1
2
1
1
1
1
1
1
2
2
0
0
2
1
1
1
1
1
1
1
1
2
2
1
0
0
1
1
1
1
0
1
1
1
2
2
1
2
1
2
0
1
2
1
0
2
1
2
0
1
1
2
0
1
1
1
2
1
0
1
1
2
1
2
0
3
0
1
0
0
1
0
1
1
1
0
2
0
1
0
2
1
1
1
0
0
0
1
2
1
1
2
2
0
0
1
1
0
2
1
1
0
0
1
0
1
0
1
2
1
1
1
1
0
1
0
0
2
2
2
0
0
1
1
2
0
0
0
1
1
1
1
1
1
1
1
2
0
1
2
2
0
2
1
1
0
1
1
1
0
1
2
1
1
0
0
1
1
2
0
2
2
0
2
1
1
2
1
2
0
2
1
0
1
2
0
2
1
1
1
2
1
2
1
1
0
0
1
1
1
2
0
2
1
1
1
2
1
2
0
1
1
1
1
0
1
0
2
1
0
1
1
2
0
0
1
1
1
1
0
0
1
2
1
0
1
0
0
1
0
1
1
2
1
2
2
2
0
1
2
2
1
2
1
2
0
1
1
2
1
1
1
1
1
0
0
1
2
1
0
1
0
1
2
1
0
1
1
0
2
0
2
0
2
2
1
1
0
2
2
1
1
0
1
2
1
0
1
0
1
1
1
1
2
2
2
0
0
1
1
1
1
1
2
2
0
2
1
1
1
1
1
1
4
0
1
1
1
0
0
0
2
2
1
1
2
0
0
1
0
2
1
1
0
2
0
1
1
0
0
1
1
2
0
1
2
0
1
3
2
2
1
2
0
1
2
1
1
2
1
0
0
0
5
1
1
0
1
1
1
1
1
0
2
1
2
0
1
2
1
1
1
1
1
1
2
1
0
1
1
0
0
1
1
1
0
2
0
0
2
2
0
1
0
1
1
0
0
1
0
1
0
2
1
1
2
0
2
1
1
1
2
0
0
1
2
1
0
1
2
0
2
0
1
1
1
1
2
1
1
1
1
2
0
0
1
2
0
1
1
1
0
2
0
1
0
1
1
1
2
2
1
1
1
0
1
1
3
0
1
1
3
1
1
1
0
1
2
0
1
2
1
2
1
2
1
0
1
1
1
0
4
2
1
0
1
1
1
1
2
1
0
0
1
0
1
1
1
0
2
0
1
2
1
0
0
2
2
1
1
2
1
0
1
0
2
1
0
2
1
0
2
2
1
0
1
1
1
0
1
0
2
2
2
1
1
2
1
1
2
1
0
2
1
0
1
0
0
0
2
2
1
0
2
0
1
2
2
1
3
1
0
0
2
1
2
1
1
0
1
1
1
0
2
0
4
0
1
0
1
1
2
1
0
0
1
2
0
2
1
0
1
1
0
2
2
1
2
1
0
2
1
2
0
0
1
1
1
1
2
1
2
2
0
2
1
2
0
1
1
1
2
0
2
1
1
0
1
0
0
0
0
1
2
0
0
1
1
1
0
0
1
2
1
0
2
0
0
1
2
2
1
1
1
1
2
2
0
0
1
0
1
0
1
0
1
2
1
1
2
1
0
3
1
1
0
1
0
0
0
1
1
2
1
0
1
2
1
2
2
0
0
0
1
0
1
2
0
1
2
2
2
2
1
1
2
2
0
0
0
2
1
3
0
1
0
1
0
2
1
0
0
0
1
1
1
2
1
0
0
0
0
0
1
1
2
0
2
2
1
1
0
1
1
0
0
1
1
1
2
2
1
1
2
1
1
0
1
1
2
1
1
2
1
0
1
0
1
0
0
0
2
2
2
1
2
1
1
1
0
1
1
1
1
0
1
0
1
0
1
1
0
1
1
1
2
1
1
1
2
1
1
1
1
1
2
1
1
1
2
1
1
0
0
0
1
1
0
1
0
2
0
1
2
1
1
2
1
2
2
1
2
0
1
0
2
1
0
1
1
3
0
1
1
1
1
1
1
2
1
2
2
0
0
0
2
2
1
1
0
2
1
1
1
1
1
1
1
1
1
1
2
1
0
2
1
0
1
1
1
2
1
1
0
1
2
1
2
2
0
1
2
1
0
2
1
1
2
1
1
0
1
0
1
1
0
1
1
1
2
0
1
2
2
2
1
1
2
1
0
2
0
2
0
2
1
0
1
1
2
1
2
2
2
2
1
0
1
5
1
1
0
1
0
1
1
2
1
1
1
0
0
1
1
1
2
1
2
2
2
0
1
1
1
1
1
2
1
1
1
0
0
0
0
2
1
1
1
0
1
1
2
0
0
2
1
2
2
2
1
2
1
0
2
2
0
1
1
0
0
2
1
1
0
1
3
1
1
1
1
0
2
2
0
3
0
1
1
1
0
0
1
1
0
3
1
0
0
2
1
1
2
1
1
1
1
2
2
2
1
1
2
1
1
0
0
1
0
1
2
1
1
0
1
0
1
1
1
1
1
1
0
0
1
1
1
0
0
0
2
1
1
2
0
0
0
1
1
1
2
1
1
1
0
3
0
0
2
1
0
0
0
2
2
0
1
2
2
1
1
2
2
0
2
0
2
1
1
1
0
0
2
1
2
2
0
1
1
0
1
0
1
0
1
1
1
1
1
2
1
1
2
2
0
2
0
0
0
0
1
0
0
1
0
1
2
2
0
0
0
2
2
2
0
1
1
0
2
1
1
1
1
1
0
1
0
0
2
2
0
2
0
2
1
1
0
2
1
0
1
0
2
1
0
1
2
0
1
2
2
0
1
2
1
0
0
2
1
0
2
1
0
2
0
2
1
1
2
1
1
2
2
2
0
0
1
2
2
0
1
1
0
1
2
1
1
1
1
0
1
0
0
1
1
2
2
1
1
0
1
0
1
0
1
1
0
1
0
0
1
1
0
2
1
1
1
0
0
1
1
0
2
0
1
2
1
0
2
0
1
0
1
0
1
2
1
0
1
1
1
0
1
2
1
1
1
1
0
2
2
1
1
1
2
1
1
2
0
1
0
1
1
1
1
0
1
1
1
1
1
0
1
2
1
1
1
2
1
1
1
1
1
2
0
4
0
1
1
0
2
2
1
0
2
0
2
4
0
2
1
1
0
0
2
1
2
1
1
1
0
1
1
1
1
0
2
2
1
1
0
1
1
2
1
0
2
0
1
2
2
2
0
1
1
0
2
0
0
0
3
1
0
2
0
1
2
2
1
1
2
1
0
0
1
1
1
2
1
2
2
2
0
1
0
1
2
1
2
2
0
2
0
1
1
0
1
1
1
0
0
2
0
1
0
1
0
0
1
1
0
1
0
0
0
1
1
1
2
1
1
0
1
1
2
1
1
0
1
0
1
2
4
1
0
1
0
1
1
1
2
2
0
1
1
2
1
1
2
1
1
0
1
1
1
1
1
1
0
2
2
1
1
1
0
0
2
1
2
0
0
2
0
3
0
0
1
2
1
1
2
1
1
0
1
2
0
1
1
1
1
1
0
1
2
1
1
1
0
0
2
0
2
1
1
1
2
1
0
2
2
1
0
2
0
0
2
2
1
1
1
1
1
0
1
3
1
1
2
0
1
1
1
1
1
0
1
2
0
2
0
1
2
0
1
1
1
0
1
1
1
1
0
0
1
1
0
2
2
2
0
0
2
1
1
1
1
0
0
1
2
0
1
0
1
1
0
0
0
2
1
0
1
1
1
2
0
1
2
1
2
0
0
2
1
2
1
0
1
0
2
2
2
1
2
1
2
0
0
1
1
0
1
1
1
1
2
1
0
1
0
2
2
1
0
0
0
2
1
2
0
0
1
0
1
1
0
1
1
3
0
1
2
2
1
1
0
1
0
0
1
0
1
0
1
3
1
1
0
1
1
0
1
0
1
1
2
0
1
1
1
0
1
1
2
0
0
1
1
0
2
2
1
0
1
0
1
0
0
2
0
0
2
1
1
1
1
1
0
1
1
0
1
1
1
1
1
0
2
1
0
1
2
0
1
1
0
1
2
1
1
1
0
1
1
2
1
2
0
1
1
1
2
1
1
0
1
0
1
1
1
0
1
1
1
2
3
1
1
0
1
1
0
0
0
0
2
1
0
0
1
0
0
1
1
1
0
1
2
0
1
1
1
0
2
0
1
0
1
1
0
2
0
0
0
0
0
0
0
0
2
0
1
1
1
1
1
0
0
0
1
0
2
1
1
0
1
0
1
2
0
2
0
0
2
0
1
0
1
1
1
0
1
2
2
2
0
1
1
2
2
0
3
1
0
2
0
1
1
1
1
0
0
1
1
2
2
1
1
0
1
1
1
0
0
1
2
2
1
2
2
2
1
1
0
1
0
0
1
2
1
2
0
1
2
1
1
1
0
2
2
2
1
1
2
1
1
1
0
1
1
0
2
2
1
1
0
1
0
1
2
0
2
0
0
1
2
1
2
2
1
2
1
2
1
2
1
2
1
2
2
1
0
0
0
1
0
1
1
0
0
0
0
1
2
1
0
0
0
0
0
1
0
1
2
2
1
1
2
0
1
1
1
1
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
1
2
2
0
0
2
0
0
0
2
1
0
2
2
1
1
0
0
1
1
1
1
2
2
1
0
1
1
0
0
2
1
1
2
1
0
1
1
0
1
1
2
1
1
1
0
0
0
0
2
1
1
0
0
0
2
0
1
5
0
0
0
1
2
1
1
0
1
1
1
1
0
1
0
0
2
2
1
3
2
1
1
1
1
2
1
2
1
1
4
1
2
0
1
0
1
1
2
1
1
0
1
2
1
1
2
0
2
0
1
2
0
0
2
1
0
1
0
1
1
0
1
1
2
0
1
1
3
0
0
1
1
1
1
1
1
2
0
2
1
1
1
0
2
0
1
1
1
0
2
1
1
0
0
1
0
2
1
1
1
4
1
2
1
1
0
1
1
0
0
2
0
0
1
0
1
0
0
1
0
0
1
2
1
0
0
2
0
3
1
2
0
2
2
0
1
2
1
2
0
1
2
1
2
0
2
2
0
2
1
2
0
2
2
0
1
0
0
2
1
0
0
1
2
0
1
2
0
0
0
2
0
0
1
0
2
2
1
1
0
2
2
2
1
2
1
1
1
0
0
0
2
0
1
2
1
1
0
1
2
2
2
1
1
2
0
0
0
0
2
1
1
1
0
2
1
2
1
1
0
0
0
1
1
0
0
1
0
0
1
0
1
2
0
0
1
1
1
1
3
1
1
1
1
1
2
2
1
0
0
1
1
2
1
1
1
0
2
0
1
1
2
1
2
2
2
0
0
1
0
1
0
2
2
1
0
1
0
0
0
1
0
0
1
1
2
2
1
1
0
1
2
1
1
1
1
0
3
0
0
1
0
1
1
2
1
2
1
2
1
2
2
1
1
0
2
1
0
1
2
1
0
2
1
0
1
1
1
0
1
2
0
1
1
2
1
1
1
2
1
1
0
2
0
1
1
1
1
0
1
1
1
2
1
2
1
1
1
0
2
1
0
0
2
0
1
0
1
1
0
0
2
0
1
2
2
2
1
2
0
2
0
1
0
0
2
0
1
0
3
0
1
2
1
1
2
1
1
1
0
0
0
1
0
2
0
1
0
0
0
0
2
1
0
0
1
2
1
0
1
2
1
1
1
2
1
0
2
1
1
0
1
1
0
2
1
2
0
1
1
1
1
1
1
2
0
2
2
1
1
2
1
1
0
2
2
0
0
1
0
1
1
2
2
1
1
1
2
1
1
1
1
2
1
2
1
1
0
1
2
2
2
0
1
2
1
0
1
1
0
1
1
1
1
0
1
1
1
0
0
2
1
0
1
2
1
1
0
1
1
2
0
1
2
1
0
2
2
1
0
1
0
2
1
2
1
1
0
0
0
2
0
1
2
0
1
1
0
0
1
0
1
1
1
1
1
2
0
1
1
0
0
0
1
2
0
2
2
0
0
1
0
1
0
1
1
2
2
1
1
2
2
0
2
2
1
1
1
0
1
2
0
1
1
0
2
1
1
2
2
1
1
1
0
0
1
0
1
1
2
1
2
1
0
3
0
2
1
2
2
0
1
0
0
1
1
0
1
0
2
0
1
1
2
2
0
0
1
1
1
2
2
1
1
0
1
3
1
1
0
0
0
1
0
0
0
1
1
2
1
1
1
0
1
1
1
0
1
0
2
2
0
0
1
1
0
1
0
0
1
0
1
0
0
0
2
1
1
1
0
1
0
1
0
1
0
1
2
0
1
1
1
1
1
1
1
2
0
2
0
1
0
0
0
1
1
1
0
2
1
1
0
0
2
2
0
2
0
2
0
0
2
0
2
1
1
1
2
2
1
0
1
2
1
1
1
0
1
1
1
2
1
0
1
1
2
1
1
1
1
1
1
1
0
0
0
0
0
1
1
1
0
1
0
1
1
2
1
1
0
1
2
1
2
0
0
1
2
1
1
1
3
1
0
0
1
0
0
0
1
1
1
1
1
0
2
1
2
1
1
3
0
1
1
0
2
2
1
3
1
0
0
1
0
1
1
7
1
2
1
0
1
0
0
1
1
0
0
2
1
1
1
1
2
2
1
2
0
1
2
1
0
2
2
1
1
0
0
1
0
0
0
0
2
2
2
1
1
2
0
0
0
1
1
1
2
0
1
0
1
0
3
1
2
1
0
2
0
1
1
2
1
2
1
1
0
1
2
1
1
1
0
0
2
1
0
3
0
1
1
1
1
2
1
1
1
1
2
0
1
1
0
0
0
1
1
2
2
0
0
0
0
1
1
2
2
0
0
2
0
1
2
0
2
1
0
0
2
2
1
2
1
3
5
2
1
0
2
0
1
0
1
0
1
0
2
1
0
1
2
0
1
2
1
0
1
2
0
2
0
0
1
1
1
2
1
0
0
0
2
1
0
0
0
1
1
0
2
2
0
1
1
1
1
1
0
2
2
1
2
1
1
1
1
2
1
0
1
2
1
0
4
0
0
0
1
1
3
1
2
0
0
0
1
0
0
2
1
1
0
0
2
0
1
0
1
1
0
1
0
0
1
3
2
0
0
1
0
1
0
0
3
1
0
2
1
0
1
2
2
2
2
1
0
0
0
2
2
0
0
1
2
1
1
1
2
3
0
0
1
1
2
1
1
2
2
2
1
1
1
2
2
0
1
0
1
1
2
1
1
1
0
1
2
1
1
0
1
2
2
1
2
2
2
0
0
1
2
2
0
2
1
0
1
1
1
1
1
2
0
0
2
1
1
1
1
1
1
1
0
1
5
0
0
2
1
0
1
1
1
0
2
2
1
0
0
2
1
0
1
1
0
0
1
1
1
2
1
2
0
0
0
2
1
1
2
2
1
1
1
1
0
0
1
2
1
0
1
1
0
1
0
0
1
1
1
2
1
1
0
2
1
0
0
1
3
1
0
1
0
2
1
0
1
0
1
0
1
1
1
2
1
1
1
1
2
1
1
1
0
1
1
1
0
1
1
0
0
2
0
0
2
2
2
2
1
0
1
0
1
1
3
2
0
1
0
1
1
2
2
1
0
2
0
2
0
1
1
2
2
1
2
0
0
0
1
0
0
0
1
2
2
3
1
1
4
0
1
0
0
2
0
2
0
1
1
0
1
1
1
2
0
1
1
1
1
0
2
1
0
1
2
1
0
1
1
0
1
0
1
2
1
2
0
1
2
1
2
1
1
1
0
1
0
2
1
0
1
2
1
2
0
0
2
0
1
1
0
1
0
1
1
0
2
2
1
0
1
2
1
0
1
1
0
2
1
0
1
1
1
0
1
0
0
0
1
0
0
0
1
1
0
0
1
1
0
1
1
1
2
1
2
1
1
2
1
1
0
0
1
1
0
1
1
1
0
1
0
0
1
1
0
2
1
1
1
1
0
1
0
1
1
1
2
1
2
2
1
0
0
0
0
1
1
1
2
2
2
0
1
1
1
2
1
1
0
1
1
2
0
2
1
2
2
0
1
0
1
1
0
1
0
0
1
4
1
0
1
0
2
1
1
2
1
0
0
2
2
1
0
0
2
2
1
1
1
1
1
2
2
1
1
2
2
1
1
0
1
0
1
1
0
0
0
0
2
2
0
0
1
2
0
0
2
1
1
1
1
2
0
0
1
1
1
2
1
1
1
1
1
0
2
1
0
0
1
0
1
0
0
2
0
1
2
3
0
2
0
1
1
1
1
0
0
0
1
0
2
0
0
1
1
0
1
1
1
0
0
1
1
0
2
1
1
1
1
0
2
1
0
1
0
1
1
2
2
0
1
1
2
1
2
2
1
1
1
1
1
0
2
2
0
1
1
1
0
1
1
1
0
0
0
0
1
2
0
2
0
1
0
0
0
1
0
2
0
1
1
1
1
1
0
0
0
1
1
0
1
2
1
1
0
1
3
1
1
1
1
1
0
1
1
1
1
1
1
1
1
3
1
1
1
1
2
2
1
1
0
1
2
0
0
2
0
1
1
2
0
2
1
1
1
1
2
1
1
1
2
1
1
2
0
1
1
0
0
0
2
1
0
1
2
1
1
1
2
1
0
1
0
1
2
1
1
1
2
1
0
1
1
0
0
1
0
1
0
1
1
2
0
0
2
3
0
1
1
0
1
1
1
1
2
2
0
1
0
0
1
2
0
0
1
0
2
1
1
1
1
0
1
1
2
0
0
1
0
1
0
2
2
1
1
1
0
0
1
2
0
1
1
1
0
2
2
1
0
0
1
1
2
2
1
2
2
0
1
1
0
1
0
2
1
0
0
0
0
2
3
1
1
2
1
2
1
1
1
1
1
2
1
2
1
1
2
0
1
1
0
2
1
1
0
1
2
1
1
0
2
1
1
1
1
1
1
2
0
2
0
1
0
2
0
1
5
1
1
0
1
1
1
1
1
2
0
0
1
1
2
0
1
0
2
2
0
3
0
2
2
1
3
1
1
1
0
1
2
0
2
1
2
2
0
2
3
1
1
2
2
0
0
1
1
0
1
0
1
0
2
0
0
2
1
0
1
0
1
0
0
2
0
2
2
1
1
1
0
1
0
1
2
1
0
2
1
1
2
0
1
0
1
2
1
2
2
0
1
1
2
0
1
2
1
1
1
1
1
2
0
1
0
0
0
1
1
0
1
1
0
0
1
1
0
1
0
0
1
1
1
1
2
0
0
0
0
2
2
0
0
2
0
1
1
1
0
2
0
1
1
1
1
1
1
1
2
2
0
1
1
1
0
2
1
0
1
1
2
2
1
0
1
1
0
2
0
1
1
1
0
1
0
0
0
3
1
2
0
0
1
2
0
1
2
1
1
0
0
0
0
1
1
2
0
0
2
2
1
0
0
2
2
1
0
2
1
1
1
2
1
0
0
1
2
1
1
0
1
1
1
0
2
0
1
1
1
1
1
1
1
1
1
0
1
1
0
1
0
0
2
1
1
1
0
1
2
1
1
2
2
1
2
1
0
0
2
0
0
1
2
0
1
1
0
0
0
2
1
1
2
1
1
0
0
1
1
1
1
1
1
0
0
1
1
2
0
0
1
2
0
0
2
2
2
2
1
0
1
1
0
1
2
1
2
0
0
1
0
0
1
0
1
0
1
2
1
1
0
2
0
2
0
1
1
1
0
2
1
1
1
1
1
1
1
0
0
1
1
0
1
0
3
1
2
1
1
0
1
1
1
1
0
2
1
1
1
1
2
0
0
0
1
0
1
2
0
0
2
4
1
0
2
1
2
2
0
1
0
1
0
1
2
1
1
2
1
0
1
1
2
2
0
0
0
1
0
0
1
0
1
0
1
1
1
2
1
0
0
0
0
2
2
0
1
2
1
0
1
2
1
1
0
1
1
0
2
2
2
1
1
1
1
1
1
1
1
2
1
1
0
0
1
1
0
1
1
1
2
1
3
0
1
2
1
0
4
1
2
1
1
1
2
1
1
1
2
0
1
2
1
1
1
1
0
1
0
0
0
0
2
1
0
0
3
1
1
0
2
1
3
1
2
2
2
0
0
1
0
1
1
3
0
0
1
2
1
2
1
1
1
2
2
1
0
1
2
1
1
1
1
0
1
0
1
1
0
1
1
1
1
0
2
0
2
1
2
2
1
1
0
1
2
1
2
0
1
1
1
2
1
0
4
1
1
1
2
0
1
1
0
1
1
1
2
1
0
1
0
0
2
1
0
3
1
0
2
1
1
2
1
1
2
1
1
1
1
2
0
0
2
1
0
0
0
1
0
1
1
1
2
2
1
1
1
1
2
1
0
0
1
2
1
0
0
0
0
1
1
1
1
1
2
2
2
1
0
1
1
1
0
1
2
0
1
1
1
1
0
0
0
0
1
1
1
0
0
1
1
1
1
1
0
0
2
1
0
2
2
0
1
0
1
1
1
2
2
1
2
0
1
0
1
0
1
0
0
1
1
2
2
2
1
3
0
0
1
1
0
1
1
0
2
2
0
0
1
2
0
3
0
0
2
1
0
1
0
2
0
1
1
1
1
2
0
0
1
1
0
2
1
0
1
1
1
1
1
0
1
2
2
1
1
0
1
1
0
2
0
0
1
1
1
0
1
1
1
0
1
1
1
2
2
0
2
1
1
3
0
1
0
0
3
1
0
1
2
2
1
0
2
0
1
2
1
2
1
0
2
1
1
1
0
0
1
2
2
0
1
0
0
1
0
1
2
1
1
1
1
1
1
1
2
2
1
0
1
1
1
0
2
1
1
0
0
0
0
1
0
1
2
1
2
2
1
0
2
1
0
0
2
1
0
2
1
2
0
1
1
1
2
1
2
1
0
0
0
1
1
0
0
2
1
1
0
0
3
1
0
0
0
2
1
2
0
1
1
1
0
1
1
10
1
2
0
0
0
2
1
1
0
0
2
1
2
1
0
0
1
0
1
2
1
2
1
1
1
2
2
0
2
2
1
2
2
1
2
1
1
0
2
2
0
1
2
0
0
1
3
2
1
1
0
0
2
1
1
1
1
2
1
1
0
4
1
0
1
3
0
1
0
1
0
1
1
1
1
0
1
2
1
0
1
1
0
2
0
1
2
1
1
1
1
1
0
2
1
1
1
0
0
1
0
1
1
2
2
2
0
0
1
1
1
2
1
0
1
0
0
0
0
0
2
2
1
2
0
0
1
1
1
1
0
1
0
2
1
1
1
1
0
0
2
1
0
0
4
0
0
0
2
0
0
1
1
0
1
2
0
2
1
0
1
1
1
0
2
1
0
0
0
2
0
0
0
1
1
1
0
0
1
2
1
1
0
0
1
2
0
0
2
1
0
1
2
3
0
0
0
1
1
1
0
2
3
1
1
0
0
2
0
0
1
0
1
1
1
1
1
0
2
0
1
0
0
2
2
0
0
0
1
0
1
2
2
1
1
1
0
1
1
2
0
1
1
1
1
1
1
2
0
0
1
1
1
1
1
1
0
1
0
0
2
2
2
0
0
0
0
2
1
0
1
0
1
0
1
1
1
1
1
1
1
1
0
1
0
2
1
1
1
0
1
1
3
0
1
0
2
0
1
1
1
2
2
0
0
1
0
0
1
2
1
0
1
1
0
2
1
1
2
0
0
0
1
1
3
2
1
1
1
2
1
1
1
2
1
0
1
0
1
3
1
1
1
1
1
1
1
0
2
1
0
1
2
1
2
1
1
1
0
0
1
2
2
0
2
2
2
0
1
2
1
1
1
1
2
1
1
1
1
0
1
1
2
1
0
1
1
0
0
0
1
0
1
1
0
1
0
0
1
2
2
1
0
1
1
2
2
2
1
1
2
2
1
0
0
0
0
0
2
2
0
2
2
0
0
1
2
1
2
2
1
2
0
1
0
1
1
1
2
2
1
2
0
0
3
0
1
1
2
2
1
0
2
0
1
2
0
1
0
0
0
1
1
0
1
2
2
1
0
1
1
1
1
1
0
0
2
0
0
1
1
0
1
2
0
0
1
0
0
1
0
0
1
2
1
1
1
1
1
0
0
1
0
1
1
2
0
1
0
0
1
2
1
1
1
1
2
1
1
0
1
1
1
0
3
1
1
2
1
1
2
0
2
1
0
2
1
1
2
1
0
2
1
0
1
1
0
0
1
0
1
2
2
1
2
1
1
0
2
0
1
1
1
0
0
0
1
1
1
1
1
2
0
1
1
0
1
2
1
1
1
1
2
1
1
1
0
1
0
2
1
0
0
2
1
1
2
0
1
1
1
2
0
1
1
2
1
1
1
0
0
1
0
0
2
1
0
0
0
0
1
1
2
2
0
1
0
0
0
0
1
0
1
0
0
0
1
0
1
2
0
1
1
2
1
0
0
1
0
0
2
2
1
1
1
0
0
0
2
1
1
1
1
1
1
2
0
1
0
0
1
1
0
1
2
0
1
0
1
1
1
1
0
2
1
0
0
0
0
1
1
1
1
0
1
0
2
1
0
1
1
2
1
2
1
0
0
1
2
0
0
0
2
0
1
0
0
0
0
1
0
0
1
0
2
0
0
1
3
2
2
2
2
1
2
4
2
1
0
1
2
2
1
2
2
2
1
1
1
1
1
1
2
1
0
1
2
0
2
0
1
1
1
1
1
0
1
1
2
1
2
1
1
1
0
1
2
1
1
1
2
1
2
0
1
1
0
1
2
0
1
1
0
1
1
1
1
1
0
1
0
1
0
1
1
2
2
1
1
2
0
1
0
0
1
0
1
1
0
1
0
3
2
0
1
1
0
0
1
0
0
0
0
1
1
0
1
0
2
0
2
0
2
2
0
1
2
0
1
0
1
0
1
2
1
2
1
0
1
0
0
1
2
1
2
2
0
4
1
1
0
0
2
0
1
1
2
2
0
1
0
0
0
0
1
0
1
1
1
1
1
1
1
2
1
0
1
0
1
1
0
0
1
1
2
1
1
1
3
2
1
1
2
2
0
1
2
0
2
1
0
1
1
1
1
1
0
0
1
0
1
2
2
0
0
2
1
0
1
0
2
1
0
2
2
1
1
0
1
1
0
0
2
0
1
2
1
2
1
1
1
1
0
1
2
0
0
2
1
1
3
0
2
0
1
2
2
0
2
2
2
0
0
1
2
2
0
1
0
2
0
1
1
0
0
1
0
2
1
0
1
2
1
1
2
0
0
0
1
0
1
2
1
2
1
1
0
0
1
1
1
1
2
2
1
1
1
2
0
0
1
0
1
1
2
1
2
0
2
1
1
0
1
0
2
1
0
1
2
1
1
0
0
2
0
2
1
0
2
1
2
2
1
1
1
1
1
1
0
0
1
0
1
1
1
1
0
2
5
0
0
1
0
0
2
0
1
0
2
2
2
0
1
0
1
1
1
1
1
1
3
0
1
1
1
1
3
0
0
1
1
2
0
0
1
2
2
0
1
1
1
0
0
1
0
1
1
1
1
2
0
0
0
2
1
0
1
1
1
1
0
0
0
1
1
1
0
1
1
1
0
0
2
1
1
1
1
2
1
0
2
0
2
0
2
0
1
2
2
1
1
1
1
0
1
1
1
2
0
1
1
1
1
1
2
1
2
1
1
1
1
0
1
0
0
1
1
1
1
1
1
2
1
2
1
0
1
2
1
2
0
1
1
2
0
0
1
0
1
2
1
0
1
1
2
1
3
1
1
1
1
1
1
1
1
1
1
2
1
1
4
0
1
0
1
0
2
2
0
1
2
1
1
2
2
3
1
0
0
2
1
1
0
1
0
1
2
1
1
0
0
2
1
1
2
1
1
2
1
2
0
1
0
1
0
1
1
0
2
1
0
1
1
2
1
2
0
0
1
2
2
1
1
1
0
2
1
1
0
1
0
0
2
1
0
1
1
3
1
0
1
1
2
1
0
0
0
0
1
1
1
1
0
2
1
1
1
0
2
2
0
0
1
2
0
0
2
0
0
1
2
1
1
0
2
2
2
2
3
0
2
2
1
1
0
0
0
0
0
0
1
2
1
1
0
1
0
0
0
2
1
0
0
2
0
0
2
0
1
1
1
0
0
0
0
1
1
1
1
1
0
0
0
1
2
0
1
1
0
2
1
1
1
1
0
0
1
2
0
1
1
1
2
0
0
2
1
0
1
1
1
1
1
0
0
1
0
0
0
0
1
0
2
0
0
1
2
1
0
0
1
2
0
1
2
1
3
1
1
0
1
1
2
2
1
1
2
1
1
0
1
1
0
2
2
1
2
1
0
1
1
1
0
1
1
1
2
1
0
1
1
0
2
1
1
0
0
1
0
1
0
0
2
0
1
1
2
1
1
2
1
1
1
2
2
2
1
0
1
1
0
1
2
1
0
1
2
1
0
1
1
1
2
0
1
1
8
0
1
1
0
2
1
0
2
0
1
2
1
1
1
1
0
1
1
1
0
0
1
0
1
1
1
1
0
2
1
2
0
0
1
0
0
1
2
1
1
1
1
1
1
1
2
1
0
0
3
1
2
0
0
2
1
1
2
0
1
5
2
2
1
1
0
1
1
0
2
0
1
1
1
0
0
1
1
1
1
0
1
0
1
0
0
2
0
1
1
3
0
1
0
0
2
1
2
0
1
0
1
1
1
1
1
2
1
0
1
0
0
0
1
1
2
2
0
0
1
2
1
2
0
0
1
2
2
1
0
1
2
1
0
1
1
1
1
3
1
0
1
1
2
1
0
1
1
0
0
2
1
0
1
2
1
1
2
1
1
1
1
0
1
1
0
2
0
1
1
0
1
2
1
0
1
4
0
1
0
0
2
2
1
0
0
1
0
1
0
1
0
2
0
1
0
1
1
1
2
2
1
1
1
1
2
2
1
0
1
0
1
2
1
1
0
1
0
1
0
2
2
1
0
0
0
1
2
2
1
0
1
1
1
0
0
0
1
1
0
1
1
1
1
0
1
2
0
0
1
3
1
2
2
2
1
1
2
0
1
2
1
1
0
1
1
1
1
0
0
1
1
0
1
1
2
0
0
1
1
2
1
1
1
2
1
1
0
0
2
1
2
1
1
0
0
1
1
0
1
1
2
0
1
1
1
1
1
1
2
1
0
0
1
0
1
1
0
1
2
0
1
1
1
1
1
2
0
1
1
1
1
1
1
2
0
1
1
1
0
1
2
1
0
2
1
1
2
0
1
2
2
0
1
2
0
1
0
1
0
1
2
2
0
1
2
2
0
0
1
0
1
1
2
1
1
1
1
0
2
0
1
1
1
1
0
1
1
0
0
2
2
1
1
0
3
0
2
1
1
2
2
2
2
2
0
0
2
1
1
1
0
2
1
2
1
2
0
1
1
1
0
2
1
0
1
1
0
0
1
1
2
0
1
1
1
0
0
0
1
2
0
2
0
1
0
3
1
0
4
1
2
1
0
1
2
2
1
1
1
1
0
0
1
2
1
0
2
0
1
0
1
0
1
1
1
0
2
1
3
1
2
2
2
0
0
1
0
2
0
1
1
1
1
0
0
1
2
1
2
1
2
1
0
2
0
1
1
0
1
0
1
0
2
1
1
1
0
0
1
1
2
0
1
1
0
0
1
2
2
4
1
0
1
0
0
2
0
0
1
0
2
0
0
2
0
0
0
2
1
2
1
1
1
0
0
0
2
1
0
1
0
1
1
0
1
2
2
1
2
1
2
2
2
1
1
1
1
0
0
0
0
1
0
1
0
1
1
0
0
0
2
1
0
1
1
1
0
0
0
0
1
2
1
0
1
1
1
1
2
0
0
2
0
2
1
1
2
0
1
1
1
1
1
1
1
0
0
1
0
1
0
0
2
1
2
0
1
2
0
2
2
1
1
0
1
2
1
2
0
1
0
0
2
1
2
0
1
2
1
2
1
2
1
2
1
0
1
1
0
1
1
0
1
2
3
0
0
0
1
0
2
2
1
2
2
0
0
0
1
0
2
1
1
1
1
1
2
2
1
0
0
0
1
2
1
2
0
1
1
1
0
1
1
1
1
1
2
0
1
0
1
1
2
1
0
1
1
2
6
2
2
2
1
0
1
0
0
2
1
2
0
2
2
0
1
0
1
3
1
2
2
1
1
0
1
1
2
0
0
2
1
2
1
2
1
1
1
0
1
1
0
0
1
4
0
1
0
2
1
1
0
0
0
1
1
2
0
1
2
1
1
0
1
1
2
2
1
2
2
2
0
0
1
0
1
0
1
1
1
0
0
0
2
0
1
1
2
1
1
2
0
0
0
1
1
0
0
1
1
2
0
1
0
1
1
1
1
1
0
1
0
0
1
1
1
1
0
1
0
2
1
1
0
1
0
0
3
1
0
0
0
1
0
0
2
1
1
1
1
2
1
0
1
1
2
0
1
1
1
1
1
2
2
2
1
0
1
0
0
2
0
0
1
0
1
0
0
1
0
2
1
0
1
0
1
0
1
2
0
1
2
0
0
1
0
1
0
0
1
1
1
2
0
1
0
0
1
2
0
1
0
2
2
2
0
1
1
0
2
1
0
0
0
1
2
1
1
1
1
1
0
0
1
2
1
1
0
1
0
1
1
0
1
0
2
0
1
1
0
1
1
1
2
2
0
0
1
0
1
1
2
1
1
0
0
0
2
1
1
0
0
3
1
1
0
2
1
0
0
2
1
0
1
1
1
2
0
1
1
1
2
0
2
1
0
1
2
0
1
1
2
0
0
1
1
1
1
1
2
1
1
2
1
1
1
2
0
1
0
0
0
2
0
0
0
0
0
2
1
2
2
1
1
2
0
0
0
1
1
0
1
1
2
0
0
0
0
2
0
0
0
2
0
0
1
2
1
2
2
1
0
1
1
0
2
1
0
1
1
0
2
2
1
0
1
1
0
1
2
0
1
0
1
1
0
1
1
0
0
1
1
1
0
0
0
1
0
1
1
2
1
2
0
2
1
2
1
1
1
2
0
1
1
2
2
1
0
1
0
0
1
2
0
1
1
1
0
1
1
0
2
0
0
0
1
1
1
1
1
1
1
1
1
1
0
1
2
0
1
1
1
0
0
1
1
1
1
2
0
1
2
0
1
1
1
0
0
0
1
2
1
0
2
0
0
0
2
1
0
1
2
0
1
2
0
3
1
0
0
0
0
1
1
1
1
1
1
1
2
2
0
1
2
2
0
2
2
2
1
0
1
1
2
1
1
0
1
0
1
0
0
1
0
2
0
0
1
1
1
1
1
0
1
1
1
1
2
0
0
1
2
1
1
2
1
1
1
0
2
1
0
2
1
1
0
2
1
2
1
0
0
1
0
0
1
1
0
2
1
0
0
0
3
0
0
0
2
1
2
0
0
1
0
1
1
1
0
2
1
1
0
1
1
2
0
2
1
3
2
2
1
2
1
1
1
1
1
0
0
2
0
1
1
2
1
1
1
2
1
0
1
2
0
1
1
0
1
0
1
0
0
2
0
2
1
1
0
1
0
2
1
1
0
1
0
2
1
1
1
0
1
1
2
1
1
1
0
0
1
1
1
2
0
0
2
1
1
0
0
2
1
1
0
1
1
1
1
1
1
1
1
1
1
2
0
0
2
2
1
0
0
1
1
0
2
1
0
1
1
1
1
1
1
2
0
0
2
0
2
1
1
2
2
1
1
1
0
1
2
1
0
0
1
1
1
1
0
1
0
1
0
1
0
1
2
1
1
0
0
1
1
0
2
1
0
1
1
1
0
0
0
1
2
1
3
1
2
1
1
1
0
1
0
0
1
1
1
2
1
1
1
1
0
2
0
2
1
2
1
2
2
1
1
1
1
1
0
1
0
1
1
2
0
1
0
1
2
0
0
0
1
1
0
2
1
2
1
2
2
1
1
1
1
1
1
1
1
0
2
0
1
1
2
1
0
2
2
1
0
2
1
3
2
1
0
0
0
1
1
0
1
2
1
2
1
0
1
2
1
1
0
1
1
1
2
0
1
2
1
0
1
0
2
1
0
1
1
0
2
1
0
0
1
1
2
1
2
1
0
0
0
2
0
0
1
1
1
1
0
0
2
1
1
1
1
2
0
2
1
1
2
1
0
1
1
1
0
1
0
0
2
1
0
0
2
0
0
1
1
1
2
2
0
1
2
1
1
0
0
0
0
1
1
1
1
1
1
1
1
1
1
1
0
0
1
1
0
2
1
1
2
0
1
0
0
0
0
0
1
1
1
1
2
0
1
1
2
1
2
0
2
2
0
0
0
1
0
2
1
2
2
0
1
1
1
2
0
1
1
1
0
1
0
1
2
2
2
2
2
1
0
1
1
1
0
1
1
2
1
1
2
0
2
1
1
0
0
2
0
1
0
2
1
0
1
1
1
1
2
0
1
1
2
2
1
1
2
2
0
1
0
2
1
1
1
1
0
1
0
0
0
1
1
1
1
3
2
0
1
1
0
2
0
0
3
1
2
1
1
1
2
1
1
1
0
0
1
1
1
1
1
0
1
0
0
0
0
1
1
0
1
2
1
2
1
1
0
1
1
1
1
0
2
2
2
1
1
0
0
1
1
1
1
0
0
1
1
1
1
0
1
0
0
1
0
1
1
0
0
0
1
1
1
2
1
0
0
0
1
1
1
0
2
2
1
0
0
2
1
2
1
0
0
2
2
1
0
0
1
1
2
1
2
0
1
2
1
0
0
1
0
0
1
0
1
1
1
1
2
2
1
1
0
2
1
1
1
1
0
1
2
1
2
2
0
1
0
0
1
1
3
2
2
1
3
0
0
2
2
1
0
1
2
1
2
0
0
1
1
1
3
0
0
0
2
1
1
1
0
2
1
0
2
2
1
0
0
0
1
2
1
0
1
2
0
2
1
2
1
1
1
2
1
1
0
0
0
1
0
0
1
0
1
1
0
1
0
0
2
1
2
0
1
2
1
2
1
0
1
0
0
1
1
0
1
2
1
0
1
0
2
0
1
2
0
1
0
0
1
1
2
0
1
0
1
0
1
1
0
0
1
1
1
1
1
1
0
1
0
2
0
2
0
1
0
0
1
0
1
1
1
0
2
1
0
2
0
2
0
2
2
3
1
0
1
1
2
1
0
1
2
1
0
0
2
0
2
0
1
1
1
0
0
2
1
2
1
1
0
0
1
1
0
1
0
0
2
1
1
3
1
1
0
1
1
1
1
1
2
0
0
1
1
2
1
1
2
0
2
1
2
1
2
1
2
1
2
2
1
1
1
0
3
0
2
0
1
2
1
0
1
2
0
0
2
0
0
1
0
2
1
2
1
1
1
1
2
1
0
1
0
1
2
2
0
1
1
1
1
1
0
2
1
1
1
0
0
1
2
0
1
2
1
1
1
0
1
1
0
2
2
1
2
1
0
1
0
1
1
0
0
1
1
0
2
1
0
1
2
1
1
1
2
3
1
0
1
1
1
0
1
1
0
1
2
1
0
1
1
0
2
1
0
2
1
1
1
1
1
1
0
2
0
1
1
1
0
1
1
1
1
1
1
1
2
0
2
2
1
1
1
1
1
0
0
2
3
1
1
2
2
0
0
2
2
2
1
1
1
2
1
2
2
3
0
0
2
1
2
0
1
1
0
1
0
2
1
1
0
0
0
2
1
1
2
0
0
1
1
0
1
1
1
2
1
1
2
0
1
1
0
2
0
1
0
1
0
1
2
0
1
0
0
2
0
1
2
2
0
2
0
2
1
1
1
1
1
0
1
0
0
1
2
0
1
2
1
1
2
0
2
0
2
2
1
0
0
0
1
2
1
1
1
1
1
1
0
3
0
1
1
2
1
0
1
0
1
1
0
1
0
0
0
0
2
1
2
0
0
1
1
1
2
0
0
2
2
2
1
2
0
0
1
1
1
0
2
1
1
0
1
1
2
2
1
2
0
2
1
0
1
1
1
1
1
1
1
2
1
1
1
0
0
1
1
1
1
1
1
1
1
2
1
0
1
2
2
1
0
1
2
2
1
0
1
1
0
0
1
1
1
1
1
0
1
1
1
0
1
1
1
2
2
0
2
1
2
0
1
1
1
2
1
1
0
0
2
1
1
2
0
1
1
2
1
1
2
1
0
1
0
0
0
0
2
2
1
0
1
1
1
2
0
2
1
0
1
3
2
0
1
1
2
2
1
0
1
1
0
2
2
0
1
1
1
0
2
1
1
1
2
1
1
1
0
1
2
1
2
0
1
1
0
1
1
0
3
1
0
2
0
1
1
1
1
1
1
1
0
2
1
0
0
1
0
1
0
2
2
1
1
1
1
1
0
1
2
0
0
2
1
0
2
0
1
1
1
0
0
1
1
1
1
0
1
2
0
2
0
1
0
0
1
1
2
0
1
1
0
1
2
0
2
1
1
0
1
0
1
0
1
1
1
0
0
1
1
1
1
0
2
1
1
0
1
1
1
1
0
0
1
0
1
1
1
0
1
0
2
1
1
0
1
1
1
1
1
0
1
1
0
1
3
2
1
3
1
0
2
0
1
0
1
1
3
1
2
2
1
2
1
1
1
1
1
2
1
0
0
2
1
1
1
0
1
1
0
0
0
0
0
2
1
1
0
1
1
1
2
0
1
0
2
1
0
1
2
0
2
0
0
1
1
1
1
0
1
1
1
1
0
0
0
1
0
2
1
0
0
0
0
1
1
0
1
0
0
0
0
2
2
1
1
0
0
0
1
0
0
1
1
1
0
1
1
1
1
0
0
0
2
1
1
1
0
0
1
1
1
0
0
1
1
1
0
1
1
1
4
2
0
1
1
0
0
0
0
3
1
0
2
0
1
0
1
2
0
1
1
1
1
1
1
1
0
0
0
0
0
0
2
0
1
0
1
0
2
2
1
1
2
0
1
0
2
0
0
2
1
0
2
0
1
0
2
1
0
1
0
0
2
0
0
1
2
0
1
1
1
0
1
1
1
1
0
1
1
1
0
1
2
1
2
0
0
1
0
1
1
4
0
1
1
1
1
0
0
0
1
2
2
0
1
0
1
1
0
1
1
0
0
1
0
0
0
0
1
2
0
0
2
2
1
0
2
1
0
0
2
1
0
1
1
1
0
2
2
0
1
1
1
2
1
1
1
0
1
2
0
1
0
2
1
1
0
1
0
0
1
0
1
1
2
2
1
2
1
3
2
1
1
2
0
0
1
1
1
1
0
1
0
0
1
0
1
1
0
1
2
1
0
1
2
1
1
2
2
0
2
2
1
0
1
1
1
1
0
1
1
1
0
2
1
0
2
0
2
1
2
0
2
2
1
1
1
0
1
0
1
1
2
1
0
1
0
0
0
0
0
2
1
1
1
1
1
0
0
0
1
1
2
1
1
1
2
0
0
0
1
1
1
1
1
0
0
2
1
1
0
1
1
1
0
1
2
1
1
1
1
1
1
1
1
0
1
1
1
1
0
2
0
0
1
1
1
0
1
0
1
1
0
2
0
1
0
2
1
2
0
1
1
0
0
1
1
0
1
3
1
2
2
2
1
0
0
2
0
1
1
1
2
1
0
2
2
1
0
0
1
2
1
0
1
1
1
0
2
2
1
2
0
2
2
1
1
1
1
1
0
0
1
1
1
2
4
2
1
0
1
1
1
1
1
1
0
0
1
0
1
1
2
1
2
0
0
2
0
1
1
2
1
2
1
1
0
0
1
2
1
1
0
2
1
0
1
0
1
0
2
4
1
1
2
2
1
1
1
1
1
0
1
2
1
0
2
2
0
0
1
1
0
1
2
0
0
0
2
0
2
0
1
1
2
1
1
0
1
2
1
2
0
1
0
1
1
2
1
1
1
1
1
0
2
0
2
1
0
1
1
0
1
1
0
0
1
0
2
2
0
0
1
1
1
2
1
1
1
0
2
1
1
2
1
3
1
2
0
1
1
1
1
1
0
1
2
2
1
2
1
2
1
1
1
0
1
1
1
2
1
0
0
1
0
0
0
2
1
1
1
2
1
1
0
0
0
1
1
1
1
1
2
1
1
0
1
0
0
0
1
1
2
0
2
2
0
0
0
2
0
2
0
1
2
1
2
1
0
2
0
0
0
2
0
0
1
2
0
1
1
1
0
0
1
0
1
1
0
1
1
1
1
2
1
0
0
2
0
1
2
0
0
2
0
1
1
1
1
1
0
3
1
2
0
0
1
0
2
3
1
0
1
1
1
2
1
0
2
1
0
0
0
0
2
0
2
1
0
2
1
1
2
1
1
1
1
1
1
1
0
1
0
1
1
2
0
0
1
2
0
0
2
2
0
2
1
1
0
3
1
0
1
1
0
2
1
1
1
2
2
1
1
2
2
1
1
1
1
2
0
2
2
0
1
1
1
0
2
0
0
0
4
1
2
1
1
1
2
2
1
0
1
2
0
1
0
2
1
0
1
0
0
1
0
1
0
0
1
1
2
1
2
1
2
3
2
1
1
1
1
0
1
1
1
1
1
0
0
0
2
1
2
2
2
2
2
1
1
2
2
1
1
0
1
1
3
0
1
2
1
1
1
2
2
1
2
1
1
1
0
1
0
0
1
2
1
1
1
1
1
2
0
0
2
1
2
2
1
1
3
2
1
2
0
0
1
1
0
0
1
0
1
2
1
0
1
0
1
1
1
1
2
0
1
1
2
0
1
1
0
0
2
1
2
0
1
0
1
1
1
2
1
0
1
1
0
1
2
2
2
1
1
1
0
0
1
1
1
2
1
1
1
1
2
0
1
1
1
2
0
2
1
1
1
2
1
1
0
1
2
0
0
2
1
1
3
0
0
0
1
1
1
1
2
2
2
0
1
2
1
1
1
1
0
2
1
0
0
0
0
0
0
0
0
1
1
1
1
2
0
0
2
2
0
1
0
0
0
1
2
0
2
0
0
1
0
1
0
0
0
1
1
0
1
1
1
0
0
0
0
0
0
1
1
1
1
2
1
1
0
2
1
1
2
2
1
1
0
1
0
1
2
2
0
1
2
0
1
1
2
1
1
1
0
0
1
2
2
0
1
1
1
0
0
1
1
0
1
0
1
2
1
1
0
1
1
2
1
1
1
2
1
1
1
1
1
1
1
0
3
0
2
1
0
0
0
2
1
2
1
1
1
0
1
1
0
1
1
1
0
1
2
1
1
1
0
1
1
1
0
1
0
0
2
2
0
2
0
0
1
1
1
0
1
1
1
0
2
1
2
0
2
1
0
1
0
2
1
1
0
1
2
1
2
2
1
1
1
1
1
2
2
2
1
1
1
1
0
0
0
1
1
0
1
1
0
1
1
2
4
2
1
1
1
0
1
1
1
2
1
2
1
1
1
1
1
1
2
1
2
0
0
0
0
1
1
0
1
1
2
1
0
0
0
0
1
1
1
2
1
2
2
2
1
0
1
0
0
0
1
2
0
1
1
2
1
1
0
0
1
2
1
1
0
0
2
1
0
2
1
0
1
1
1
0
0
1
1
1
1
0
1
1
1
1
0
2
1
1
0
0
1
1
0
0
1
2
1
1
1
0
0
1
1
1
0
0
1
0
2
1
2
1
1
1
1
2
0
1
0
0
1
0
1
0
0
1
0
1
0
2
1
1
1
0
1
1
2
0
1
1
0
1
1
1
1
1
1
1
1
0
2
1
3
0
1
1
0
0
1
1
0
2
1
1
0
1
1
1
2
2
1
1
3
1
0
1
2
1
0
1
1
0
1
1
1
0
0
1
1
1
0
2
1
1
0
2
0
1
0
1
0
1
1
1
0
0
1
1
0
0
1
1
1
1
0
1
1
1
0
0
0
1
1
0
0
1
0
0
1
0
2
0
1
0
2
1
0
0
1
1
1
0
0
0
2
1
1
0
0
1
2
2
2
1
1
0
1
0
0
0
2
0
1
1
1
2
2
0
0
1
1
1
0
2
0
1
1
1
0
1
2
1
0
0
2
1
0
2
0
1
0
1
1
0
1
1
1
0
1
1
1
0
1
1
1
1
1
1
0
1
2
1
1
2
0
2
2
2
0
2
0
1
2
0
2
1
0
1
1
0
0
0
1
0
1
0
1
1
0
1
0
1
2
2
0
1
1
1
0
0
2
2
0
0
1
0
2
0
2
0
1
2
0
1
1
2
0
1
0
1
1
1
1
1
0
1
0
2
0
2
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
1
1
1
1
2
0
2
2
2
0
1
0
1
1
1
1
0
2
0
1
1
2
1
0
1
1
1
2
0
0
0
1
1
1
0
1
1
1
2
0
2
0
0
1
2
1
0
2
0
0
1
2
0
1
1
2
0
0
1
1
2
2
1
0
2
1
1
0
2
1
0
1
0
2
1
1
0
1
1
0
1
0
1
1
1
0
2
0
1
1
0
2
0
1
2
2
1
1
1
1
0
0
0
0
1
1
1
2
2
0
0
1
1
1
1
1
0
1
1
1
1
1
1
1
0
1
1
1
1
2
2
2
1
1
1
2
0
0
1
1
2
1
0
0
0
1
1
1
0
2
1
1
1
0
0
0
1
2
1
2
1
1
1
1
2
0
1
1
0
2
0
1
2
0
0
2
1
2
0
1
0
0
1
2
1
0
0
0
0
1
1
1
1
0
1
0
0
0
1
1
2
1
1
2
2
1
0
2
1
1
1
2
2
1
1
0
0
2
0
2
2
0
0
1
1
0
1
2
1
0
0
1
0
0
2
0
1
2
1
1
2
1
0
2
0
0
1
1
1
2
2
2
1
0
0
1
2
2
1
2
2
0
1
1
0
1
0
1
1
0
2
1
0
1
1
1
1
1
0
1
1
1
1
1
2
2
0
2
0
0
1
0
0
1
1
1
2
0
1
1
1
1
0
2
0
1
1
1
0
1
1
1
1
1
1
1
1
0
3
2
2
1
0
1
0
1
1
1
0
0
2
0
1
0
1
0
1
1
1
0
2
2
1
1
3
2
1
1
1
1
0
1
2
2
2
2
1
0
2
1
2
1
2
3
1
1
1
1
1
1
1
1
0
1
1
1
0
2
0
3
0
1
1
1
0
0
1
0
2
1
0
0
2
2
2
1
1
1
1
1
1
0
2
1
1
0
2
0
1
1
1
2
2
1
2
0
0
2
1
1
1
0
1
1
1
1
2
1
1
1
0
1
1
1
1
0
1
0
0
1
2
0
0
1
1
2
0
2
1
0
1
0
1
0
2
1
1
1
0
2
0
2
0
1
0
2
0
2
2
1
1
1
1
1
2
1
0
0
1
1
0
1
0
0
1
2
2
2
1
2
0
0
1
1
0
2
1
1
0
2
0
0
1
0
1
1
0
2
0
2
1
0
0
0
3
2
2
0
0
1
1
1
0
2
1
2
1
0
1
1
0
2
0
0
0
1
1
1
0
1
1
1
1
1
0
0
0
1
2
0
0
0
0
0
2
1
1
0
1
1
1
1
0
1
1
2
0
0
2
0
1
0
0
0
2
1
1
1
2
2
0
0
0
1
2
0
1
2
1
1
1
1
0
1
1
2
2
0
2
2
2
0
0
1
1
0
0
2
2
1
1
0
0
1
1
1
1
2
1
1
0
1
2
1
2
1
1
1
2
2
1
1
1
1
0
0
2
0
0
0
1
1
1
2
1
1
1
0
0
1
2
1
1
2
1
2
1
1
0
1
3
2
2
1
0
0
0
1
1
1
0
1
0
2
1
0
2
1
1
0
1
1
0
2
1
1
0
2
1
0
1
1
2
0
2
2
1
3
1
1
2
0
2
1
1
2
2
1
0
1
1
1
1
0
2
0
2
2
2
2
1
1
1
1
0
1
1
1
0
1
2
1
1
0
0
1
1
1
1
1
1
1
2
1
0
0
1
1
1
1
1
0
1
1
0
1
1
0
0
0
1
1
2
2
1
1
2
1
0
0
2
2
1
1
0
1
0
2
2
2
1
2
2
1
1
1
2
0
1
0
1
2
2
1
1
1
1
1
1
1
0
1
1
1
2
1
1
2
2
0
2
1
1
1
2
1
1
1
2
0
1
1
0
1
1
1
1
1
2
2
1
1
1
0
0
1
0
1
0
0
1
1
1
2
0
2
0
1
0
0
1
1
2
0
1
0
0
2
2
1
2
1
2
2
1
1
1
2
0
0
1
1
1
0
1
2
2
0
0
1
1
2
0
0
1
1
2
0
1
1
1
1
0
0
1
0
1
2
1
0
0
2
1
0
1
1
0
0
1
0
0
1
1
0
1
0
1
1
1
2
1
2
2
0
0
1
1
0
2
1
0
1
1
2
2
1
1
0
1
0
2
1
0
0
1
1
1
1
1
1
2
2
1
0
1
1
1
0
1
2
2
1
3
0
0
0
0
2
0
0
0
1
2
0
1
1
1
0
2
0
1
0
1
0
0
1
1
0
2
2
1
3
0
1
0
1
1
1
1
1
0
2
1
1
2
0
1
1
0
2
0
1
0
0
2
0
1
1
0
2
1
0
1
1
2
1
1
2
0
0
1
1
1
1
2
2
0
0
0
0
0
1
1
0
1
1
0
1
1
1
0
0
1
0
0
1
0
1
1
2
2
1
1
1
2
0
1
1
0
0
1
2
1
0
2
1
0
1
1
2
1
1
2
1
0
0
0
1
1
2
0
1
0
1
1
1
0
0
0
1
2
0
1
1
0
1
1
2
0
1
2
0
1
0
0
1
2
0
2
1
0
2
1
1
0
1
1
2
1
0
2
3
2
2
0
0
2
2
1
0
0
1
0
1
0
1
1
2
1
2
1
1
2
0
0
2
3
1
1
1
1
2
1
0
1
2
0
0
1
0
2
2
0
0
1
1
0
0
1
0
2
1
1
2
1
1
0
1
1
1
0
0
2
1
1
0
1
1
1
0
1
0
2
1
0
0
0
2
1
0
2
0
0
0
0
0
0
2
1
1
1
3
1
1
1
0
2
1
0
0
1
0
1
1
1
3
0
0
1
1
1
1
1
1
0
1
1
0
0
0
1
2
0
1
1
0
1
0
0
1
1
1
0
2
1
1
1
1
2
1
0
2
1
0
0
1
1
1
1
0
1
1
1
0
2
1
1
1
0
0
2
0
0
0
1
1
2
1
1
1
1
0
1
0
1
0
1
1
0
1
0
1
1
1
0
0
2
0
0
1
2
1
2
0
2
1
2
2
1
1
0
2
1
0
1
1
1
2
1
1
1
2
1
0
0
0
0
1
0
0
0
1
1
0
0
2
1
0
1
2
0
1
1
1
1
0
2
0
0
1
0
1
0
0
1
0
1
1
1
2
1
1
0
1
1
2
2
1
1
2
0
1
2
0
1
2
1
0
1
2
1
1
1
1
0
1
1
1
1
1
1
2
1
0
0
1
2
1
2
1
0
2
0
2
0
1
1
0
1
2
0
1
1
1
2
0
1
0
0
1
0
2
0
1
1
1
0
0
0
0
0
0
1
0
1
0
1
1
0
2
1
0
0
0
1
0
1
1
1
1
0
2
1
1
2
0
1
0
0
0
2
0
0
1
2
0
0
0
1
0
1
0
1
0
1
1
0
1
1
1
1
0
2
0
1
0
0
1
1
1
3
0
1
0
0
0
2
2
2
2
1
0
1
1
0
1
1
1
0
1
0
2
0
0
2
1
1
1
2
1
1
2
1
2
1
0
0
1
0
2
1
1
2
1
2
0
2
1
0
0
1
0
1
1
1
1
1
1
0
1
2
0
3
1
1
1
0
2
1
0
2
1
1
1
2
0
1
0
1
0
2
2
2
1
2
1
1
1
1
2
2
1
2
1
2
2
0
1
1
0
0
0
0
1
2
0
1
0
0
2
0
2
0
1
0
1
0
1
1
0
2
0
0
0
0
1
2
0
0
0
0
1
1
1
1
1
1
2
2
1
2
1
1
1
2
1
1
0
0
0
1
0
2
1
2
0
1
1
1
1
1
1
2
2
2
0
0
1
0
1
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
1
2
2
1
1
2
1
2
0
2
0
0
0
1
0
1
0
1
0
1
0
1
1
2
0
2
1
2
1
1
0
1
0
1
1
2
0
1
0
1
2
0
0
1
1
0
1
0
2
1
0
1
1
0
1
2
0
1
0
1
0
0
1
0
2
0
2
2
0
1
1
1
1
0
0
0
0
1
2
1
0
1
2
2
2
4
1
0
2
1
0
2
1
1
0
0
2
2
2
1
1
5
1
0
0
1
1
1
0
2
0
1
1
1
2
2
1
0
2
1
1
1
0
0
0
2
1
1
1
2
1
0
2
1
1
1
0
0
0
1
1
1
1
0
1
1
0
2
1
1
2
2
1
0
1
1
0
1
0
0
2
0
0
0
1
0
1
1
0
0
0
0
0
0
1
1
1
1
0
1
1
2
1
2
1
1
0
1
1
1
1
1
1
0
0
1
1
2
3
1
1
2
2
1
2
1
5
1
1
0
1
0
1
0
1
1
1
3
1
1
0
0
1
0
2
1
0
0
1
2
2
1
0
2
0
1
0
1
2
1
0
0
2
1
0
0
1
1
0
0
1
0
2
3
2
2
2
0
1
1
1
1
1
1
1
2
0
2
1
0
1
1
1
1
1
1
0
1
0
1
0
1
1
0
2
1
0
1
0
3
2
2
1
0
0
0
0
0
1
2
2
0
0
2
2
1
1
2
1
0
0
0
1
2
0
2
0
0
1
0
1
1
1
0
2
1
0
0
0
1
1
7
1
1
0
0
2
0
1
0
1
1
1
0
1
0
1
2
2
1
1
0
1
1
1
0
1
1
1
1
0
0
1
1
1
1
0
1
2
2
1
1
0
0
2
1
1
0
0
2
1
0
1
0
1
2
0
1
1
0
1
0
0
2
1
1
1
1
1
0
1
2
1
2
1
2
0
1
1
3
1
2
2
2
2
1
1
2
0
2
1
1
1
1
0
0
1
1
2
0
1
1
1
1
2
2
0
2
1
2
0
1
1
2
0
1
1
3
1
0
1
1
2
1
1
1
0
1
1
0
0
1
0
1
1
0
0
1
1
2
1
0
1
1
0
0
2
1
0
2
1
2
2
1
1
2
0
1
0
1
1
2
1
2
2
0
2
1
2
1
1
0
2
0
1
1
1
2
0
1
1
1
0
0
1
1
0
1
2
2
0
1
1
1
2
0
1
2
2
2
0
0
1
1
2
1
0
0
2
1
1
1
1
2
1
1
1
2
1
1
1
1
2
1
2
0
2
1
0
0
1
0
0
0
1
1
0
0
0
2
0
1
1
2
2
1
1
1
1
1
2
1
1
1
2
0
1
1
1
0
2
1
2
1
2
0
0
0
1
1
0
0
0
3
0
0
1
0
0
1
1
2
1
0
0
0
1
1
1
2
0
0
3
1
0
0
1
2
1
0
1
1
1
2
1
1
0
0
2
2
1
0
0
0
2
1
0
1
2
0
1
1
0
1
1
2
2
0
2
2
0
2
0
2
1
1
1
1
2
2
1
1
1
1
0
1
3
1
1
1
0
2
1
0
1
1
3
0
1
1
2
0
2
2
1
0
2
1
2
2
1
1
0
0
0
1
3
1
0
1
1
2
1
2
1
1
2
0
0
0
1
0
2
1
2
0
1
2
0
0
1
0
1
1
2
0
1
1
1
2
2
0
1
1
0
0
1
1
0
2
0
1
1
2
1
1
2
1
1
1
1
0
1
1
0
2
2
2
0
2
0
0
0
0
0
2
0
2
0
2
1
1
0
0
3
1
1
0
1
0
1
1
2
0
2
1
1
1
0
1
2
1
0
2
0
2
2
0
1
1
1
2
0
2
1
1
1
2
0
0
1
0
2
1
2
0
0
1
1
0
0
1
0
3
2
1
1
2
1
2
0
1
1
0
2
1
0
1
1
2
1
0
2
1
2
1
2
0
2
0
2
0
1
2
1
1
0
1
1
3
3
2
1
1
1
0
2
1
0
2
2
1
1
0
2
0
0
2
0
0
2
0
1
1
0
0
2
1
0
1
1
0
2
0
1
2
0
0
1
1
1
1
1
1
1
0
1
1
2
1
1
0
1
2
0
0
1
0
1
1
1
1
2
1
1
1
1
0
1
1
1
0
1
1
2
1
0
1
1
0
1
0
2
0
0
1
1
1
1
1
0
0
1
0
2
2
1
1
0
0
2
1
1
0
2
0
2
1
1
2
1
2
0
1
2
1
2
1
1
2
0
2
1
0
1
0
0
0
0
1
0
1
0
1
2
1
1
0
2
0
1
2
2
1
0
0
1
2
1
2
1
0
1
1
1
1
0
1
1
0
0
1
0
2
1
0
2
2
1
2
2
2
0
1
0
0
1
2
1
0
2
3
2
1
1
3
1
2
1
1
2
1
1
1
2
1
2
1
1
2
2
0
1
1
1
1
1
0
1
2
0
1
2
1
1
1
0
0
0
1
1
1
2
2
1
2
0
2
1
2
2
1
1
0
2
0
2
2
2
2
1
1
1
0
1
1
1
1
2
2
0
0
1
1
1
1
1
0
1
1
0
0
0
0
2
2
1
1
2
1
0
1
1
1
0
0
1
1
2
0
2
0
0
1
2
0
0
0
1
0
1
1
1
2
2
0
0
1
0
0
1
1
0
2
1
2
0
1
0
0
0
2
1
1
1
2
2
2
2
0
1
0
1
1
0
2
2
2
1
1
0
1
1
0
0
0
2
1
1
0
1
1
0
2
1
2
2
0
0
1
1
1
2
2
1
2
1
1
0
1
1
0
2
2
1
2
2
1
1
1
0
2
0
0
1
1
1
0
1
0
1
1
1
1
2
2
0
2
0
2
0
0
2
2
1
1
0
0
1
0
0
1
1
0
2
2
2
1
2
1
1
2
1
1
0
0
2
1
1
1
2
1
0
1
0
0
1
2
0
1
2
2
0
2
1
2
1
1
1
1
1
1
1
0
1
0
0
1
1
0
1
1
0
0
1
1
0
2
0
2
1
2
1
0
0
1
1
1
3
0
2
0
2
1
2
2
0
1
2
0
0
0
1
1
2
0
2
1
2
2
3
2
1
0
1
1
0
2
1
1
2
0
2
2
2
0
0
2
1
0
2
1
2
0
1
1
0
1
1
1
0
1
1
1
0
1
1
1
2
1
2
1
2
1
0
1
2
1
0
1
1
2
1
2
0
1
0
1
2
2
1
0
1
3
0
1
1
1
0
0
2
1
2
1
2
1
1
1
0
0
2
2
0
0
1
1
0
1
1
2
2
2
1
1
1
1
0
0
1
1
2
0
0
1
0
2
0
0
1
0
1
2
0
1
1
1
1
2
2
2
1
1
0
1
1
1
1
1
0
0
1
2
1
0
2
0
1
1
1
0
1
2
1
1
2
0
2
0
1
0
1
1
0
1
2
1
0
1
2
1
1
0
0
0
2
1
0
1
1
1
0
1
0
2
0
2
1
1
0
2
2
1
1
0
2
0
0
2
1
0
1
1
1
2
1
1
0
1
1
0
1
1
0
1
0
0
2
1
0
3
2
1
1
2
0
1
2
2
1
0
2
1
0
0
2
1
2
1
1
1
0
1
2
1
1
1
1
1
2
0
1
0
1
1
1
1
0
1
0
1
2
1
0
1
0
1
0
2
1
1
0
0
0
1
0
1
1
0
0
2
0
0
1
1
1
0
2
0
0
2
2
1
0
1
0
0
1
0
1
1
1
1
0
0
4
0
1
1
1
1
2
2
0
1
2
2
0
1
1
0
0
2
2
0
1
0
0
1
2
1
1
1
1
1
2
2
0
2
1
0
1
2
1
2
0
0
1
0
0
1
2
0
1
2
1
3
1
0
1
1
0
1
0
1
0
1
1
0
1
1
1
2
0
0
1
2
1
1
0
2
0
2
1
2
0
1
2
0
1
0
1
0
0
0
1
1
1
1
1
1
2
0
2
1
2
2
0
1
1
0
1
0
1
1
1
2
0
2
0
1
1
0
1
1
0
0
1
0
1
1
1
2
2
1
0
1
2
0
2
0
0
0
2
1
1
2
1
1
1
1
0
2
0
1
1
1
2
1
3
2
2
1
2
0
1
2
2
0
0
1
0
1
2
0
1
2
1
1
1
3
1
0
2
0
0
1
1
1
0
0
1
1
1
1
2
0
0
0
1
1
2
1
0
2
2
0
2
2
1
0
1
2
1
0
1
1
0
1
0
0
1
0
1
1
2
2
1
2
2
0
1
0
1
0
0
1
0
2
0
2
1
1
1
1
1
0
0
1
0
2
0
0
3
0
1
0
1
2
1
0
2
0
1
1
1
0
2
1
1
1
0
2
2
1
2
0
1
1
1
0
1
2
0
0
1
3
1
0
0
0
1
0
1
2
0
1
0
1
1
2
1
1
1
1
0
0
1
1
2
2
2
3
1
1
1
0
0
1
1
1
0
1
1
1
1
2
1
0
2
1
1
1
0
1
0
1
0
1
1
0
0
1
1
2
0
2
1
2
1
0
1
1
0
0
1
1
0
2
1
1
0
0
0
0
0
2
0
0
0
1
0
1
0
1
0
0
2
1
0
0
1
1
2
2
3
2
1
2
1
1
1
0
2
1
2
1
0
1
0
1
1
1
1
0
1
1
0
0
0
1
1
1
0
0
0
1
1
1
0
0
1
0
1
2
2
1
1
0
1
1
0
1
1
1
2
1
0
2
0
2
2
1
1
1
2
1
1
0
2
0
1
0
1
2
1
0
0
0
2
2
0
0
0
0
2
2
0
1
1
2
2
1
1
0
0
1
2
1
0
0
0
0
1
1
1
0
0
1
0
0
1
2
2
2
2
0
1
1
0
1
1
1
1
1
0
0
1
2
0
0
1
1
0
0
2
1
1
3
0
1
1
2
2
0
2
2
1
0
0
1
1
0
0
2
1
1
1
1
1
1
1
2
0
0
2
1
1
1
2
0
1
1
2
2
1
1
1
2
1
0
1
1
0
1
0
2
0
3
1
1
0
2
0
1
0
1
0
1
2
2
1
1
1
1
1
0
1
0
1
1
0
1
1
2
1
1
1
0
2
0
1
0
0
1
2
0
1
1
1
1
0
0
0
1
2
1
1
1
0
0
0
2
0
1
2
1
1
3
0
2
0
1
0
0
1
2
1
0
1
2
1
1
0
0
1
2
0
1
1
1
0
1
2
2
2
1
2
1
0
1
1
2
0
2
1
0
0
2
0
1
0
0
2
0
1
1
0
1
3
1
1
0
0
1
1
1
2
2
2
0
0
1
0
2
1
1
1
1
0
0
2
0
0
0
2
0
1
0
0
1
1
1
1
0
0
2
0
1
1
1
1
1
1
1
2
1
1
0
1
0
1
1
1
0
0
1
1
1
2
0
1
0
1
0
2
1
1
2
1
1
0
0
1
0
0
0
0
1
2
0
1
1
0
1
0
1
2
1
2
1
1
2
0
2
1
1
0
0
2
1
0
0
1
1
1
1
1
2
1
1
1
1
2
0
0
0
1
0
1
1
1
2
1
1
1
0
1
1
1
0
2
0
2
1
2
2
0
2
2
1
1
2
1
1
1
2
1
1
0
1
1
1
1
1
1
2
3
2
0
1
2
0
1
1
1
2
1
2
0
1
1
0
2
1
2
0
1
1
2
2
0
1
0
2
0
2
1
0
1
1
2
1
2
1
0
0
2
3
1
1
1
0
1
1
0
1
1
1
1
2
0
1
0
0
1
1
2
2
0
1
1
1
1
1
2
0
0
2
2
3
1
1
1
1
2
1
1
0
0
0
2
2
1
1
0
2
1
1
1
0
0
1
1
2
0
1
2
2
1
1
1
2
1
1
1
1
2
2
0
0
2
1
1
2
7
1
2
0
2
0
2
0
1
0
0
0
2
1
1
0
0
0
0
0
0
0
2
1
1
1
1
1
0
1
0
1
1
0
1
2
0
1
2
2
2
2
1
1
2
1
1
1
2
1
0
0
0
1
1
0
1
0
0
1
0
1
0
2
1
1
1
2
1
1
1
3
0
1
0
1
0
0
0
0
0
0
1
0
0
1
2
0
0
2
1
2
1
2
0
1
0
0
3
2
2
1
2
0
0
2
1
1
1
2
0
1
1
3
1
1
0
1
2
1
1
2
0
1
1
0
0
1
2
1
0
1
1
1
0
1
1
0
0
2
0
1
0
0
2
1
0
1
1
1
1
1
1
1
0
1
2
1
2
2
2
1
1
2
2
2
3
1
0
0
0
0
0
1
1
0
1
1
1
1
2
1
2
2
2
1
1
0
2
1
2
1
0
1
1
0
0
1
2
1
0
0
1
1
1
0
2
0
1
1
0
1
0
1
2
0
1
0
0
1
1
2
0
0
0
2
1
1
1
0
2
1
0
0
0
1
2
0
2
1
1
2
1
3
2
0
1
2
0
0
1
1
1
0
2
2
1
1
3
1
0
1
1
0
2
1
2
1
0
0
0
0
0
1
2
2
2
0
2
1
2
1
0
1
1
0
0
0
2
1
1
0
1
2
2
1
1
2
0
0
0
0
1
1
0
2
1
1
1
1
0
1
0
1
0
0
1
2
1
0
1
1
2
0
0
0
2
1
1
0
1
0
1
1
1
1
0
2
2
2
1
1
2
1
2
1
0
0
2
1
2
2
2
0
0
0
0
2
0
1
1
0
2
1
0
0
2
1
0
1
2
2
1
1
0
1
0
0
0
2
0
1
1
0
1
1
2
0
1
0
3
0
2
1
2
1
0
1
1
2
1
2
2
2
2
1
1
2
1
1
6
0
1
0
1
2
1
1
1
0
0
1
2
0
1
0
1
1
0
0
2
3
1
2
1
0
1
1
1
1
2
2
1
2
2
1
1
1
0
1
2
1
1
1
0
1
1
0
1
1
0
0
2
1
1
0
1
0
1
1
2
2
1
2
0
2
1
1
1
0
1
0
2
0
1
0
0
2
3
0
0
0
0
2
0
1
1
2
0
1
0
0
1
0
2
1
2
2
1
1
0
1
1
0
1
1
1
1
0
2
1
1
2
0
0
1
0
1
0
0
1
0
1
0
1
1
0
1
1
0
1
2
1
0
1
1
1
1
0
1
1
0
1
2
1
1
0
1
2
1
0
0
2
1
2
0
0
1
1
0
1
2
1
2
0
1
0
1
0
1
1
0
1
2
1
1
0
1
1
0
2
2
1
0
2
0
2
2
1
2
0
1
1
1
2
1
1
1
1
0
0
1
0
0
0
0
0
1
1
2
0
2
2
0
2
1
0
0
1
0
1
1
1
0
2
1
2
0
3
2
0
0
0
0
1
2
0
1
1
1
0
0
0
2
1
0
0
0
1
0
1
1
1
1
1
1
1
2
0
1
1
0
0
1
0
1
0
2
1
1
1
2
1
0
1
0
0
0
0
2
1
0
0
0
1
1
1
0
1
1
1
1
2
2
1
0
2
1
1
2
2
1
1
1
2
2
1
0
1
0
0
1
1
2
2
0
1
0
1
0
0
0
1
0
2
1
0
2
0
1
2
0
2
2
1
0
1
1
1
0
1
0
0
0
1
1
1
1
2
2
0
2
1
0
1
0
1
0
3
1
1
2
1
1
1
0
0
2
1
0
1
2
2
1
0
3
1
0
1
2
1
1
0
2
1
1
2
0
2
0
0
2
1
0
1
1
0
1
0
1
0
1
1
2
0
2
2
2
1
1
1
0
0
1
2
0
0
1
1
0
2
0
0
0
0
1
1
2
0
0
0
2
2
1
0
1
2
0
2
0
1
1
1
1
1
1
0
2
1
1
0
0
2
1
2
1
1
0
2
2
2
0
2
2
1
0
0
0
1
1
1
1
1
2
0
1
1
1
0
2
3
2
0
2
1
1
1
1
1
0
0
1
1
0
1
1
0
0
1
0
1
2
2
1
0
0
0
0
2
2
0
1
1
0
0
2
0
0
0
2
1
0
1
1
1
1
2
1
1
0
0
1
2
0
2
0
1
2
1
1
1
1
1
1
0
0
1
1
1
0
2
0
1
1
2
1
1
0
3
2
0
1
1
2
0
0
1
0
1
1
0
1
1
0
1
1
1
1
2
0
2
0
0
1
1
0
0
0
1
0
0
2
1
1
1
0
2
0
2
1
0
1
0
1
1
1
0
3
1
0
1
2
0
2
0
1
2
0
1
0
2
0
0
1
0
1
1
1
1
0
1
1
0
2
1
0
1
1
0
2
2
1
1
1
1
2
1
1
0
2
2
0
1
0
2
1
2
0
1
1
2
1
1
1
1
1
1
0
1
2
1
1
1
1
0
2
0
0
1
2
1
1
1
0
1
0
1
0
2
1
1
2
2
1
1
2
0
2
0
1
1
1
1
1
1
2
2
2
1
1
1
2
0
1
2
1
0
1
1
0
0
1
0
1
1
1
1
1
2
1
1
0
2
1
1
1
2
1
1
1
0
2
1
1
1
1
0
0
1
2
1
1
1
2
0
0
0
1
0
1
2
1
1
0
1
0
1
0
0
0
0
2
1
0
1
1
1
0
0
0
0
0
1
0
0
1
0
0
2
0
1
3
0
1
0
0
2
1
1
2
1
1
0
1
1
2
0
0
2
0
3
0
0
1
1
1
0
1
1
0
1
1
0
0
1
0
2
1
0
2
0
1
2
1
1
3
0
0
2
1
2
1
2
2
1
0
1
0
2
0
2
0
1
1
1
1
1
2
1
1
1
1
2
2
0
0
0
2
1
2
2
1
0
0
2
1
2
2
2
1
0
1
2
1
0
0
0
1
0
0
0
2
0
1
1
2
0
0
0
2
1
0
1
1
2
1
1
1
1
1
0
1
1
2
1
1
1
2
1
1
0
1
0
0
2
0
1
1
1
1
1
1
0
0
1
0
0
1
3
0
0
1
2
1
2
0
1
2
1
1
1
2
2
1
0
1
0
1
2
1
2
1
1
1
1
1
1
1
2
1
2
1
1
0
0
1
1
0
1
0
0
0
2
1
1
1
0
1
0
0
1
1
1
2
2
1
3
2
1
1
0
1
3
1
1
1
0
1
2
1
2
2
2
0
0
1
0
0
1
0
0
1
2
2
0
1
1
1
0
0
0
1
1
1
1
1
0
0
3
0
2
0
2
1
2
0
1
0
2
2
1
1
1
2
1
2
0
0
0
1
0
1
1
1
1
0
1
1
1
1
1
1
0
2
0
0
0
1
1
2
0
1
0
0
3
1
1
1
1
0
0
0
0
0
1
0
0
1
1
1
1
0
0
0
0
1
1
2
1
1
1
0
1
1
1
1
1
0
1
2
2
2
1
0
0
0
2
0
2
1
1
2
0
1
1
0
1
0
1
1
0
0
1
1
1
0
2
2
2
2
0
2
2
2
1
2
1
0
2
2
0
0
1
0
0
1
2
1
2
1
2
1
0
2
1
2
0
2
0
1
0
2
1
2
0
0
1
1
2
1
0
2
0
0
1
1
0
0
2
2
0
0
1
2
2
1
1
1
0
0
0
0
2
2
0
1
1
0
1
1
0
0
0
1
2
1
0
1
1
1
0
0
1
2
0
0
1
1
2
0
1
0
1
1
0
1
1
0
2
1
1
1
2
1
0
1
0
1
1
0
1
1
1
0
1
2
0
0
1
1
0
0
0
1
2
0
1
0
2
1
0
1
1
1
1
0
0
2
0
1
0
1
1
2
1
1
1
1
0
1
2
2
1
1
1
1
0
1
1
2
1
2
0
2
0
2
1
2
1
1
0
0
2
0
0
1
1
0
0
2
0
1
2
1
1
1
1
0
0
2
0
2
1
2
1
1
2
2
1
4
2
1
1
1
0
1
1
2
1
1
1
0
0
1
0
2
1
1
1
1
2
0
0
1
0
3
1
0
2
1
2
1
2
1
0
2
2
1
1
1
1
0
0
2
1
1
1
1
0
1
0
4
1
1
1
1
4
5
1
1
2
2
0
2
2
1
0
2
2
0
1
1
2
1
0
2
0
1
1
0
2
2
1
2
1
1
1
1
0
0
2
2
0
1
1
1
1
1
2
0
1
0
1
1
1
2
0
1
0
1
1
0
1
0
1
1
0
0
2
2
0
1
0
0
1
1
0
1
2
1
1
1
1
1
1
3
2
0
1
1
2
1
0
0
0
0
1
2
0
1
0
2
1
2
1
1
2
0
2
1
1
1
2
1
1
3
1
0
1
0
2
0
0
0
1
1
1
2
2
1
1
2
2
2
1
1
1
1
2
1
1
0
1
1
0
0
1
1
0
1
1
0
1
2
1
1
2
1
1
1
0
1
2
0
0
2
0
1
0
2
0
0
0
1
3
1
0
0
1
2
2
0
0
1
0
2
1
0
0
1
0
1
2
1
1
2
1
0
0
1
0
1
2
1
0
1
1
0
2
0
0
2
1
2
4
1
0
1
1
0
0
0
0
1
2
1
0
0
0
1
0
1
0
0
1
1
0
0
1
1
1
2
1
0
2
0
0
0
2
2
2
1
1
2
2
1
2
1
1
0
1
0
1
1
2
1
1
1
1
2
1
2
0
0
1
1
1
0
0
1
1
0
0
1
1
1
5
1
1
1
1
1
0
1
2
1
1
2
0
0
1
0
1
0
1
2
2
0
1
1
2
1
2
0
2
1
1
2
2
1
2
0
1
0
0
1
0
2
1
0
0
1
0
2
2
0
1
1
1
0
1
1
1
0
0
1
2
0
1
2
1
1
1
1
1
1
2
0
0
0
2
1
1
2
1
1
0
1
0
1
1
1
2
1
1
2
1
2
1
2
0
1
1
1
0
2
0
1
1
0
2
0
0
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
0
2
0
0
0
1
1
0
1
2
1
1
2
1
2
0
1
1
0
2
2
1
1
1
0
1
1
1
2
1
1
1
1
2
1
1
2
0
2
0
1
0
1
1
1
1
0
1
0
0
1
2
2
1
1
1
1
1
0
1
1
0
1
1
0
2
1
1
1
0
1
2
1
1
1
2
0
1
0
0
1
1
1
2
1
1
0
2
1
1
1
1
1
1
2
1
1
2
0
1
2
1
2
0
2
1
1
1
2
0
1
0
0
1
0
2
1
1
1
1
2
0
1
2
1
1
2
0
2
0
1
2
1
0
2
2
2
0
0
2
0
0
2
0
1
0
1
2
2
0
2
0
1
0
1
1
2
2
0
1
1
1
1
2
2
1
2
1
1
1
2
2
2
1
1
1
1
1
2
2
0
0
1
1
0
1
0
0
2
0
1
1
1
1
2
1
1
0
2
1
0
1
2
2
1
0
1
1
0
2
0
0
1
2
1
2
0
0
1
0
0
1
1
2
0
1
1
2
1
0
0
1
0
0
1
1
2
1
0
1
2
2
0
2
0
1
0
1
2
2
1
2
0
1
1
1
1
0
1
0
0
0
1
1
0
1
2
2
1
1
1
1
1
1
0
0
2
0
1
1
0
1
2
1
0
2
1
1
2
0
2
1
1
2
1
1
0
1
0
0
2
1
2
0
1
0
0
2
0
1
2
1
2
0
0
2
3
1
1
1
2
2
0
2
1
1
0
0
1
1
0
1
1
2
0
0
1
1
0
0
0
1
1
1
1
1
2
1
1
2
1
0
0
1
2
1
0
2
1
1
0
1
0
0
0
1
0
1
0
1
1
3
1
0
0
1
2
0
1
1
2
2
2
1
0
0
1
2
0
0
1
0
2
1
0
1
1
1
0
1
1
0
0
0
1
1
2
1
0
1
1
0
1
1
2
0
1
1
2
0
0
1
2
1
2
1
1
1
2
2
1
1
1
1
1
0
0
1
1
1
2
1
1
1
1
1
2
1
2
2
1
0
1
1
0
2
1
3
0
1
2
0
2
4
0
0
0
1
0
1
1
0
1
1
1
0
0
0
1
1
0
1
1
1
1
1
0
1
1
2
1
1
1
2
1
1
2
1
1
2
0
1
0
1
1
1
1
1
1
1
2
1
1
0
1
1
1
1
1
5
1
0
1
0
1
1
1
1
1
1
0
2
2
2
1
2
0
0
1
1
2
1
0
0
1
0
2
2
1
2
2
0
1
1
1
1
0
1
0
2
1
2
0
0
0
1
1
0
0
1
0
0
1
1
1
0
1
1
1
2
0
1
1
2
0
1
2
1
0
1
0
1
1
2
1
2
1
1
1
1
2
1
0
1
2
0
1
2
1
2
2
1
0
1
0
1
1
1
0
1
1
1
1
1
0
0
1
0
0
1
1
1
1
0
1
0
1
0
1
1
1
1
2
1
2
1
0
1
1
1
0
1
2
1
1
1
1
1
0
0
0
0
1
0
1
3
1
2
1
0
1
1
2
1
4
2
1
1
0
0
1
1
1
1
2
2
1
1
1
1
0
1
2
1
2
1
0
1
1
0
1
1
0
1
0
1
0
0
2
2
0
2
1
1
2
1
0
2
1
0
1
0
1
0
0
0
2
0
1
0
0
2
2
0
2
1
0
2
1
0
2
2
1
0
0
2
0
2
1
2
0
1
1
0
1
1
0
0
0
2
2
0
1
2
2
1
1
1
2
1
1
0
2
1
1
0
0
0
1
0
2
2
0
2
0
2
2
1
1
0
0
1
1
1
2
1
1
1
1
0
0
0
2
1
2
1
2
1
2
1
0
1
0
0
1
1
0
1
1
2
2
2
1
2
1
1
0
2
2
1
1
0
1
0
0
2
1
1
2
1
2
1
1
0
1
1
1
1
1
1
1
0
2
0
0
0
0
1
0
1
1
1
0
2
1
1
1
2
1
2
0
1
1
1
1
1
2
0
1
2
0
1
1
0
1
2
1
1
3
0
1
0
0
0
0
1
1
1
2
2
1
1
0
1
1
1
2
0
1
0
1
2
0
0
1
0
1
0
0
1
0
2
0
0
1
1
1
2
1
0
1
1
1
1
2
0
2
0
1
1
0
1
2
2
2
1
1
1
2
2
1
0
1
3
0
1
0
0
2
1
1
2
2
1
1
1
1
1
1
0
2
1
2
2
0
0
1
2
1
1
2
0
2
0
1
0
1
1
1
0
1
1
3
1
0
1
1
0
2
1
0
1
1
1
2
0
2
2
0
1
0
2
2
2
1
0
2
0
1
1
1
0
1
0
1
1
0
2
0
1
2
1
0
2
0
1
0
0
1
2
1
0
4
0
1
0
0
0
1
2
2
0
0
1
3
1
0
1
1
1
1
1
1
1
2
1
0
1
1
1
1
1
0
0
1
1
1
1
1
1
1
0
1
2
2
1
1
3
1
0
0
1
1
2
1
0
2
0
1
2
1
0
2
2
0
2
2
1
1
0
1
1
1
1
2
1
1
1
0
1
0
0
1
2
1
0
1
1
0
1
1
1
2
1
0
0
1
0
1
0
1
1
1
1
2
0
1
0
1
2
1
2
2
0
1
2
2
1
1
1
0
1
1
1
1
2
1
2
1
1
2
1
2
0
0
1
1
0
1
1
0
3
2
1
1
1
1
2
1
2
0
2
4
0
0
1
1
1
2
2
1
1
2
0
0
0
2
1
1
1
1
1
1
2
1
2
1
1
1
2
1
0
1
2
1
0
1
1
2
1
1
2
1
0
0
1
5
1
2
1
0
1
0
0
3
1
1
0
1
1
1
2
0
1
0
0
2
0
6
1
2
1
1
2
1
0
2
0
0
1
0
1
2
0
0
0
1
1
0
1
0
2
2
1
1
0
1
0
1
0
0
1
2
1
1
1
1
0
1
0
2
1
2
2
0
1
0
1
1
2
1
1
1
0
1
1
2
1
1
0
1
1
2
1
0
2
1
1
1
1
2
1
1
0
2
1
1
0
0
1
2
0
2
0
0
1
1
0
1
1
2
1
1
2
1
0
1
2
1
1
1
0
2
1
2
1
1
1
3
1
2
2
1
1
1
0
2
0
1
1
1
1
2
1
1
1
1
2
1
0
1
1
1
1
1
0
1
1
1
0
2
0
0
1
2
2
0
0
1
2
2
1
1
1
1
2
2
0
0
0
2
1
1
0
0
0
0
1
1
1
1
1
2
2
2
0
1
0
1
1
1
2
2
1
1
1
1
2
1
1
0
1
1
2
2
1
0
0
2
1
1
0
1
2
1
0
2
1
2
2
1
1
1
1
2
1
1
2
2
2
2
1
1
1
1
2
1
1
1
1
3
1
2
1
1
0
2
0
1
0
0
0
2
1
1
0
0
0
0
2
1
0
2
2
1
2
2
1
1
0
1
2
2
1
2
0
2
1
0
0
1
0
0
0
2
1
1
0
1
1
1
2
2
1
2
1
1
2
3
1
0
1
2
2
1
0
0
1
1
2
1
0
0
1
2
1
1
1
1
2
2
1
0
0
0
0
1
0
1
1
1
2
1
1
2
0
2
2
1
1
0
1
0
1
0
2
1
0
0
1
2
1
0
1
2
2
1
0
1
1
1
1
0
1
2
0
1
1
1
1
1
2
1
1
1
0
1
2
1
1
2
0
0
1
0
0
0
1
0
1
1
1
1
1
1
0
1
0
2
1
2
2
1
0
1
0
1
2
1
1
0
0
0
1
0
0
0
0
0
1
3
1
2
1
2
0
1
1
1
0
0
2
1
1
1
2
1
0
1
0
0
0
1
1
1
2
1
0
0
1
0
2
0
1
0
1
2
1
1
0
0
1
1
2
1
1
1
1
2
0
0
2
1
1
0
2
1
0
1
2
2
1
1
1
0
0
1
1
1
1
0
2
1
1
2
1
0
0
0
0
1
1
1
0
0
2
0
1
2
1
1
2
1
0
1
1
1
1
0
1
0
1
1
0
1
1
0
0
0
1
2
1
1
1
1
0
2
1
0
2
0
1
0
2
0
1
0
1
0
1
0
2
1
1
2
1
0
1
2
0
1
0
1
1
2
2
0
1
1
0
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
0
0
1
0
0
1
1
0
0
1
1
0
1
1
2
3
0
2
2
1
2
2
1
0
1
1
0
0
0
1
2
1
1
2
0
0
0
1
2
0
0
0
1
0
2
0
1
0
1
1
0
1
1
1
0
1
1
0
1
2
1
0
0
1
2
2
0
1
1
0
2
1
1
1
0
0
2
0
2
0
2
0
0
0
1
0
2
1
1
2
2
1
1
0
1
1
0
1
1
1
1
1
0
0
2
1
1
1
1
0
0
0
1
1
1
0
1
0
0
0
2
0
0
0
1
0
1
0
1
1
0
1
0
5
1
2
1
0
1
0
0
1
2
1
0
1
2
0
2
1
1
1
1
1
1
1
0
0
0
1
1
0
1
1
0
0
0
0
1
2
0
1
2
2
2
0
1
1
0
0
1
2
1
1
0
0
1
1
0
1
1
2
1
0
1
1
1
1
1
2
1
1
1
1
1
1
3
2
0
1
2
2
0
1
0
1
1
1
1
0
0
0
0
1
0
1
0
1
1
0
0
1
1
1
1
1
0
2
0
4
0
1
1
0
2
0
1
1
1
1
1
0
1
2
1
1
0
1
1
1
1
1
1
0
1
1
2
1
0
1
1
0
1
0
1
0
1
1
2
1
2
1
0
1
2
2
1
0
0
1
0
1
1
2
2
1
2
1
2
0
0
2
1
0
1
0
0
1
1
1
1
1
2
1
1
1
2
1
1
0
2
1
1
1
1
0
2
2
1
1
2
1
1
1
0
1
2
1
0
1
0
0
1
0
1
0
1
1
0
1
2
2
0
1
0
0
1
3
1
0
1
1
1
2
1
1
0
1
1
2
1
2
1
2
2
2
1
2
1
0
1
1
1
1
2
0
2
1
2
0
1
0
1
0
2
2
2
2
1
2
0
1
1
2
0
2
0
0
2
0
1
2
1
0
1
2
2
1
0
1
0
1
0
1
1
1
3
1
1
0
2
2
0
2
1
1
1
0
0
1
0
1
0
0
1
1
2
2
1
1
1
0
1
2
1
0
1
0
1
1
1
0
0
0
2
1
0
1
1
1
2
0
1
1
2
1
0
1
0
0
1
0
1
2
1
0
2
0
1
1
0
1
0
1
0
1
3
1
0
2
2
1
2
0
1
0
1
1
0
0
1
1
1
1
0
1
0
1
0
0
2
0
0
0
1
2
1
0
1
0
2
0
1
1
1
0
2
0
1
1
1
1
2
0
0
1
1
1
0
0
1
1
0
2
1
0
0
1
1
0
0
1
1
1
0
1
2
1
0
0
2
1
1
0
1
1
3
1
1
1
0
1
0
1
1
1
2
2
2
2
1
1
0
0
0
0
0
0
1
1
1
2
1
1
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
2
2
2
1
1
0
0
0
2
1
0
2
1
3
2
0
1
2
2
1
0
1
0
1
1
2
0
1
1
0
1
1
2
1
1
1
2
2
0
0
2
2
1
1
0
1
0
0
0
1
1
1
2
0
1
0
0
0
7
1
1
1
1
1
1
0
2
1
1
1
0
0
0
0
0
1
1
1
0
0
1
1
1
1
0
2
1
1
1
0
1
2
0
0
1
1
1
0
0
1
2
0
0
2
0
1
1
2
2
1
2
2
1
2
1
0
0
2
1
2
1
0
1
1
0
1
1
1
0
0
3
0
1
2
1
1
1
0
0
0
1
0
1
1
0
1
0
1
1
0
1
0
4
1
1
2
1
1
0
1
1
2
1
0
0
1
2
2
0
3
1
0
0
1
1
1
2
1
0
2
1
1
1
0
2
1
0
1
1
0
1
1
1
0
2
0
0
2
0
2
2
0
1
1
2
1
1
0
1
1
1
2
0
2
1
0
1
2
1
1
2
2
1
1
2
2
0
1
2
1
0
0
1
1
0
0
1
2
0
1
0
1
2
0
1
1
1
2
1
1
0
0
0
0
1
1
0
1
1
1
2
2
0
2
0
1
2
1
0
1
0
2
0
1
1
1
0
1
1
2
3
1
3
2
1
1
0
0
0
2
0
1
1
2
1
1
2
1
2
1
0
0
1
2
2
2
1
1
1
1
1
2
2
2
1
3
2
0
0
1
1
2
2
1
0
1
2
1
0
0
1
2
1
1
1
0
0
1
2
1
0
2
2
1
1
1
1
0
1
1
2
1
1
1
2
2
1
0
1
1
1
2
1
0
1
1
0
0
1
3
2
1
2
2
1
1
0
1
2
0
1
2
1
1
0
1
0
1
0
0
1
2
1
0
0
0
0
0
2
0
1
2
0
2
1
1
2
2
0
1
0
1
0
0
2
1
1
1
1
1
1
0
0
1
0
1
1
0
1
1
1
0
1
2
0
2
1
1
1
1
1
2
2
0
1
0
1
0
0
1
2
2
0
0
1
1
1
0
0
1
1
1
0
2
0
2
3
1
2
2
0
2
0
0
0
2
2
1
2
1
0
1
0
1
2
0
0
2
0
2
1
0
1
4
1
3
0
1
2
0
1
1
1
0
2
1
1
2
1
1
1
2
1
0
4
0
0
0
0
1
2
2
1
2
1
2
2
2
1
0
2
2
0
1
2
1
0
0
2
2
0
1
1
2
0
1
1
1
0
1
0
0
0
1
1
1
1
1
1
1
2
2
0
0
0
2
1
0
0
2
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
1
0
1
1
1
0
0
0
1
2
1
0
2
2
1
1
0
0
1
2
1
1
0
0
1
1
1
1
0
1
1
2
0
0
0
2
1
0
7
0
0
1
0
0
1
1
1
1
0
0
2
1
1
1
2
1
1
1
0
1
0
0
1
2
2
2
1
1
1
0
0
0
2
2
2
1
0
0
0
0
1
1
1
2
1
1
1
1
1
0
0
2
0
1
1
2
1
1
1
0
1
2
2
1
0
1
1
0
1
0
1
0
1
0
1
2
1
0
1
1
1
1
1
2
0
0
1
1
2
1
1
1
3
2
1
1
1
0
1
2
0
2
1
1
1
0
1
1
1
1
1
1
1
0
1
2
2
1
2
1
1
1
1
2
0
0
1
0
2
1
1
2
1
2
0
1
0
0
1
1
1
0
1
1
1
1
2
0
1
1
2
1
1
0
1
1
0
1
0
3
1
0
2
1
1
0
2
1
2
1
1
2
1
2
1
1
0
0
0
1
1
0
2
0
1
1
0
0
0
1
0
1
2
2
2
2
4
3
1
1
0
0
0
1
1
0
0
0
1
2
0
1
1
2
1
1
2
1
1
0
1
1
1
0
2
2
0
1
1
1
0
0
2
1
1
0
0
1
0
0
1
0
1
2
1
0
1
2
2
0
0
1
2
2
1
1
1
1
0
0
1
0
2
1
0
1
1
0
0
1
1
2
0
0
2
1
1
1
1
2
0
1
1
0
0
2
1
1
0
2
0
1
1
1
1
1
1
2
0
2
0
2
2
1
1
0
0
1
1
1
1
1
1
1
0
0
1
1
1
0
0
2
3
1
2
2
1
0
1
1
0
0
1
1
0
2
2
0
0
1
0
0
2
1
0
0
0
2
1
1
2
0
1
1
1
2
2
3
1
1
1
1
1
1
3
1
0
2
3
1
1
1
0
0
0
1
1
0
1
0
1
1
1
1
1
1
2
0
0
0
0
2
2
1
1
1
1
2
1
1
1
2
1
0
2
1
1
2
0
0
2
0
1
1
1
0
1
0
1
3
2
1
0
0
1
2
1
1
0
2
1
0
0
1
1
2
1
1
2
0
1
2
0
0
1
1
1
3
1
0
1
1
1
0
1
2
1
1
1
0
0
1
0
1
1
0
2
0
0
0
2
0
1
0
0
0
1
1
1
0
1
0
1
1
1
2
2
0
1
1
1
1
1
3
0
1
0
2
1
1
1
0
0
1
1
2
1
0
1
0
2
0
2
2
0
0
1
2
1
0
0
0
0
1
1
1
1
1
2
1
0
1
0
0
1
0
1
1
1
2
1
1
1
0
1
1
2
1
6
0
1
0
1
0
2
1
1
2
1
0
1
1
1
2
1
1
1
0
1
1
2
2
2
0
1
1
1
2
2
1
0
0
1
0
2
1
0
2
2
0
1
1
1
1
0
1
2
1
2
1
2
1
1
0
1
0
1
1
1
1
2
0
1
2
2
3
0
1
2
1
0
1
1
1
0
1
2
1
3
1
2
1
0
2
2
1
0
1
1
1
0
1
0
1
2
0
0
1
1
1
0
1
0
0
1
0
0
1
1
1
2
0
2
2
0
2
1
1
1
0
2
1
0
2
0
0
1
1
1
0
0
2
0
1
1
0
2
0
1
2
1
3
2
0
1
0
0
2
0
1
1
1
0
0
2
0
0
1
1
0
1
1
1
2
0
0
1
2
1
1
4
1
1
0
1
1
0
1
0
1
2
0
1
2
1
1
1
0
1
2
1
0
2
0
2
0
0
2
0
1
2
1
1
0
1
1
2
0
0
1
0
1
1
1
0
0
0
1
1
1
2
2
1
0
2
0
1
2
1
0
0
0
1
0
0
0
2
2
1
1
1
0
0
0
0
1
1
2
1
2
0
0
1
0
0
1
1
1
0
1
1
1
2
2
1
1
1
0
1
1
1
1
1
1
0
0
0
1
0
0
1
0
1
1
0
1
0
1
2
0
0
0
1
1
2
0
1
1
0
1
1
0
1
0
0
0
1
2
2
2
1
1
0
1
1
1
1
2
2
2
1
0
2
1
1
1
2
1
5
1
0
1
1
1
1
2
1
2
1
1
0
1
2
2
1
0
0
0
2
2
2
0
2
0
0
0
1
0
1
0
0
1
1
1
0
1
1
0
2
2
0
1
0
2
1
2
2
1
1
2
2
2
0
0
0
1
1
1
1
0
0
1
1
2
2
1
1
1
0
0
2
1
2
2
0
0
1
1
1
2
0
1
0
2
1
0
1
1
1
1
0
0
0
1
1
2
1
1
0
1
1
1
1
1
1
1
1
0
0
0
0
2
0
1
2
1
0
1
1
1
2
1
0
0
1
0
2
0
0
1
1
0
0
1
1
1
2
1
0
0
0
2
0
2
0
1
1
1
0
2
1
2
0
2
0
1
0
1
2
1
2
2
0
3
1
2
1
0
1
1
1
2
0
1
2
1
1
0
1
0
0
1
1
0
1
1
1
2
0
1
0
1
0
0
1
0
1
2
0
0
1
0
2
0
0
1
0
2
2
2
2
1
1
2
1
0
0
1
2
1
2
2
0
1
2
0
2
1
1
0
1
1
2
2
2
0
3
1
0
1
1
0
0
1
1
1
1
1
0
0
0
0
0
1
1
0
0
0
0
1
1
2
1
1
0
2
2
1
0
0
1
0
0
0
2
1
1
1
0
1
1
1
1
0
0
0
2
2
0
2
2
1
1
1
1
1
1
1
0
0
1
2
0
2
1
1
0
0
2
0
1
0
2
0
1
1
1
0
1
0
1
2
2
2
0
0
1
1
2
2
2
1
2
0
1
1
1
2
2
0
0
0
1
1
0
0
2
2
2
0
1
0
1
1
2
1
0
1
1
1
0
1
0
0
1
1
0
2
0
2
1
2
1
0
1
2
2
1
1
2
2
1
1
0
1
0
2
1
2
1
1
1
1
1
1
2
1
1
0
1
0
1
0
1
0
1
1
1
2
1
1
0
1
1
0
0
0
1
2
2
0
0
0
1
3
2
1
0
1
0
1
2
0
0
1
0
0
2
1
1
1
1
1
1
1
1
1
0
1
0
0
0
0
1
2
1
0
1
0
1
0
0
1
2
0
1
1
1
0
2
0
1
1
0
0
1
1
0
0
1
2
1
1
0
2
0
0
0
2
0
1
2
1
1
1
1
2
1
2
0
2
1
0
2
0
2
0
0
1
1
1
0
2
1
1
1
2
0
1
2
0
0
5
1
2
2
1
2
2
1
0
1
2
1
1
1
2
3
1
2
1
0
1
2
1
1
0
3
1
0
1
0
3
2
2
1
0
0
0
0
1
0
0
0
1
1
1
1
2
0
2
2
2
1
0
2
0
1
0
0
0
1
2
1
2
1
2
0
1
2
2
1
1
2
1
2
1
1
1
0
2
0
0
2
1
2
0
0
0
1
1
3
1
1
1
1
1
2
0
3
1
0
1
1
0
0
0
0
0
1
1
0
1
1
1
2
1
2
0
1
2
0
1
0
0
2
2
3
2
0
3
0
0
2
0
1
1
0
1
0
1
1
1
0
1
2
2
1
1
1
1
0
1
1
0
0
1
0
1
1
1
2
0
0
1
2
1
2
0
1
2
1
1
2
1
0
2
1
1
1
0
1
0
0
1
1
2
1
1
0
0
1
2
1
0
1
2
1
0
1
0
0
2
1
2
1
0
1
1
1
1
1
0
2
2
2
0
1
3
1
1
1
1
3
2
0
1
3
1
3
1
0
1
1
1
0
0
2
0
1
0
1
0
0
1
1
2
1
1
2
0
0
1
1
1
0
1
2
1
0
1
1
2
0
1
0
1
0
1
0
1
2
1
1
5
1
3
1
0
1
1
5
1
1
0
0
1
2
2
0
1
1
1
2
1
1
0
1
0
1
0
1
1
1
1
0
1
0
1
1
1
0
1
0
0
0
1
1
1
1
0
1
0
1
1
0
1
1
1
0
1
0
0
1
0
2
1
0
1
2
2
1
1
1
1
0
1
1
0
2
0
1
1
0
1
1
1
1
1
2
0
0
2
1
0
1
0
1
1
0
0
0
2
2
2
1
1
2
2
0
1
1
0
1
0
0
0
1
2
2
0
2
0
2
1
2
1
1
0
1
2
2
0
1
1
1
1
1
0
1
1
0
0
0
1
0
0
1
0
2
2
2
2
1
1
1
0
2
1
1
0
1
0
1
1
0
1
0
1
1
6
1
2
2
1
0
2
1
0
1
1
1
0
1
0
1
0
0
1
1
4
1
2
1
2
1
1
1
2
1
0
1
2
0
0
1
1
0
1
1
1
0
2
2
1
2
1
1
1
1
2
1
2
1
1
1
0
1
1
1
0
1
0
2
1
1
1
0
1
2
0
0
0
1
0
1
0
1
1
0
1
1
1
2
0
2
0
0
1
1
2
1
2
2
2
2
1
1
1
0
1
0
2
0
0
0
1
1
1
1
1
1
1
2
1
0
0
1
1
0
0
1
1
1
1
1
2
0
1
1
0
0
3
2
2
0
1
0
1
1
1
1
0
2
2
4
1
1
1
1
2
1
1
0
2
1
0
2
1
1
0
0
0
1
1
2
1
1
1
2
1
0
0
0
1
1
1
1
1
0
1
1
2
4
1
0
0
0
2
1
0
1
1
0
0
2
1
1
2
1
1
1
0
2
0
2
1
0
1
1
1
0
1
1
1
1
1
1
3
2
0
2
1
0
0
0
1
1
3
1
2
2
1
0
0
1
2
1
1
1
1
2
1
1
2
1
0
1
4
1
1
1
2
1
1
1
0
0
0
0
1
0
1
1
0
1
0
1
0
1
1
1
0
1
1
1
1
1
1
1
1
1
0
1
2
1
1
2
1
1
1
1
0
1
1
2
4
1
1
1
1
1
1
0
2
0
1
0
2
1
1
0
2
0
0
1
1
0
0
1
0
1
0
1
1
0
1
0
0
0
0
1
2
0
1
1
1
0
1
0
1
0
1
2
0
1
2
2
1
1
2
1
0
0
1
0
1
2
2
2
2
0
2
0
0
1
1
1
0
1
1
2
2
1
2
1
2
1
0
0
2
1
2
2
2
1
1
2
0
1
2
0
1
0
0
1
2
0
1
1
2
1
1
1
1
1
1
2
0
0
1
0
0
1
1
1
1
0
1
1
1
1
1
0
1
0
0
1
1
0
1
0
1
1
0
1
2
1
2
2
0
1
0
0
0
0
1
2
0
0
1
2
1
0
2
1
1
2
2
0
1
0
1
1
1
2
1
2
1
0
2
2
2
1
0
0
1
2
1
2
1
2
1
1
0
0
1
2
2
0
1
1
0
3
2
1
2
0
0
2
1
1
2
2
1
1
0
1
0
1
2
0
1
2
2
0
1
1
2
1
0
1
0
0
0
1
2
1
1
0
1
1
0
2
1
1
1
2
1
1
1
1
0
1
3
1
0
1
2
1
1
0
2
0
2
2
0
2
0
0
0
1
1
1
2
2
1
2
0
2
1
2
2
1
1
0
0
1
1
1
1
0
1
2
1
2
1
1
1
2
0
1
1
2
2
1
1
0
1
2
1
1
0
1
0
0
1
1
0
1
2
0
2
1
0
1
2
2
2
1
0
0
1
2
1
0
0
0
1
1
1
1
0
2
0
0
2
1
2
1
1
2
0
1
1
0
1
0
0
0
1
0
1
2
2
2
0
3
0
0
1
1
2
2
0
2
1
1
1
1
2
1
1
2
1
2
0
1
2
0
0
2
0
0
1
1
0
2
2
1
2
1
2
1
2
2
0
0
1
0
0
2
1
1
0
0
1
0
1
0
0
0
1
1
1
2
1
0
0
1
1
2
1
1
1
1
0
0
1
2
1
0
1
1
1
1
0
2
1
1
2
1
2
1
0
0
2
0
1
1
1
0
1
1
0
0
0
1
2
1
1
1
1
1
1
0
0
1
1
1
2
2
1
1
2
0
1
1
1
1
0
2
2
1
0
2
1
0
2
2
2
2
0
1
0
1
2
1
1
0
1
0
1
1
2
2
1
1
0
2
0
0
0
0
1
2
1
0
1
0
1
1
1
0
1
0
0
0
2
1
2
1
0
1
0
2
0
1
2
0
0
2
0
2
1
0
0
0
0
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
0
1
1
0
1
1
0
1
1
1
0
0
0
1
1
1
1
1
3
1
1
1
2
1
2
1
1
1
0
0
1
1
1
0
0
1
1
2
0
2
1
0
1
1
0
1
2
1
0
2
1
1
1
4
0
2
0
1
1
1
1
1
2
1
0
2
0
0
2
1
2
2
1
2
1
1
0
1
1
2
2
2
0
0
0
0
1
2
0
2
0
0
1
1
1
0
0
1
1
1
0
0
0
1
0
1
1
2
1
2
2
1
1
0
1
0
2
2
1
1
0
0
1
2
2
0
0
2
0
1
2
2
2
2
0
2
2
1
0
1
1
1
0
0
0
0
0
2
0
2
0
1
0
1
1
2
0
0
2
0
0
1
1
2
2
2
0
0
2
1
0
0
1
1
0
2
0
2
1
1
1
1
0
1
0
2
1
0
1
1
1
2
0
1
0
1
1
0
1
0
1
2
1
2
0
2
1
1
2
1
0
1
0
0
1
1
0
0
1
2
0
1
1
1
1
2
0
2
1
2
1
0
0
0
1
1
0
0
0
1
1
2
1
1
2
1
1
2
2
1
2
1
0
0
1
1
2
1
1
1
1
0
0
0
1
0
0
1
2
2
2
0
1
1
0
1
1
2
0
1
0
2
2
2
1
0
0
1
0
2
1
0
0
1
0
1
2
1
0
0
1
1
1
0
1
2
1
1
1
1
1
2
1
2
1
2
1
1
3
1
1
1
0
1
0
1
1
0
0
0
4
2
0
1
0
1
1
1
0
1
2
1
1
1
1
1
2
0
1
2
2
1
1
2
0
1
1
1
1
2
1
0
1
1
1
1
1
1
0
1
0
2
0
1
1
1
1
2
2
0
0
2
1
2
0
0
0
0
1
0
2
2
0
1
0
2
0
1
1
1
0
0
0
1
1
2
1
0
1
2
2
1
1
1
1
0
1
1
0
1
1
1
0
0
1
0
2
1
1
0
2
3
3
0
2
1
2
1
0
1
1
1
1
2
1
1
0
1
1
0
2
0
1
0
1
0
1
2
0
2
2
0
0
0
2
3
1
0
0
0
0
0
1
0
0
2
0
1
0
1
2
1
0
1
0
1
2
1
1
1
1
1
0
0
1
0
1
1
1
2
1
1
0
1
0
2
1
1
0
2
3
1
1
0
2
2
1
1
2
1
0
0
1
2
1
1
1
1
0
1
0
2
1
0
1
0
0
0
1
1
1
0
0
1
1
0
2
1
2
1
1
0
1
1
0
1
1
1
0
1
0
0
1
1
2
2
0
0
1
1
0
1
1
1
1
0
1
2
1
0
1
1
0
1
1
1
2
2
1
0
1
2
0
1
1
1
1
2
1
2
2
2
1
2
0
0
1
0
1
0
1
0
0
0
1
0
1
0
2
2
2
2
1
2
1
0
0
2
1
1
0
1
1
2
0
1
0
1
0
2
1
1
2
0
0
1
1
0
2
1
2
2
0
0
0
0
1
1
1
0
0
1
3
1
0
0
0
0
1
2
1
1
0
1
0
0
0
1
0
1
1
0
1
0
1
2
2
1
2
1
1
1
0
0
1
1
2
0
2
1
1
1
0
1
0
1
1
1
0
1
1
0
0
1
1
2
1
1
2
2
0
1
0
0
0
1
1
3
1
1
1
0
1
1
0
1
1
1
1
0
1
0
0
1
0
2
2
2
1
1
1
2
1
2
2
1
0
2
1
0
0
0
0
1
0
0
1
2
0
1
1
2
0
1
2
1
1
2
1
1
2
2
0
1
0
2
0
0
0
3
0
2
1
0
0
2
2
1
0
2
0
1
2
0
1
1
1
1
0
0
0
2
2
1
2
0
2
1
0
3
1
1
1
1
4
1
2
1
0
2
2
1
2
1
2
1
0
1
1
2
1
0
1
0
1
1
0
0
1
0
0
3
0
1
2
1
1
2
0
0
0
0
1
2
2
0
0
0
2
1
1
1
1
2
1
1
1
0
2
0
1
1
2
1
0
1
0
1
1
2
2
0
1
2
1
0
0
0
1
0
0
2
0
1
1
1
0
1
1
2
0
0
3
1
1
0
0
1
1
0
1
1
0
0
0
2
3
1
1
0
0
1
1
0
1
0
1
2
0
2
0
0
1
2
1
1
1
1
1
0
2
2
0
0
2
0
0
0
2
1
1
2
2
1
1
1
1
1
1
1
0
1
1
1
0
0
1
2
1
0
0
0
0
2
0
2
0
1
0
1
1
1
1
1
1
0
1
1
1
1
0
0
1
2
0
1
1
1
2
2
1
2
2
0
1
0
2
2
0
1
0
1
2
1
1
0
1
0
1
1
1
2
1
2
0
0
1
2
0
2
0
1
2
1
0
1
1
1
1
1
1
0
0
1
1
1
1
2
1
0
0
0
1
0
2
1
1
0
2
1
1
1
2
1
1
0
1
0
0
1
0
0
1
1
0
1
0
0
2
1
1
0
0
0
2
2
1
2
0
1
2
2
1
0
1
1
0
1
0
1
1
0
1
0
0
2
2
1
2
2
1
1
1
1
2
0
0
1
1
1
0
1
2
1
1
0
2
2
0
0
1
1
0
0
2
1
1
2
1
1
1
1
0
1
0
1
1
0
1
0
0
1
0
1
0
0
2
1
1
0
1
3
1
0
0
1
0
1
1
1
1
1
0
0
1
2
1
1
0
1
0
0
0
1
2
1
1
0
1
1
1
0
1
0
1
1
0
1
1
0
0
1
1
0
1
1
0
0
4
1
1
0
1
1
0
2
1
1
1
1
1
2
0
0
2
1
1
1
2
2
0
1
2
2
2
1
1
1
1
0
0
1
0
1
1
0
2
1
1
0
0
1
1
0
1
0
1
0
1
1
2
2
1
3
1
1
2
2
0
0
2
0
2
2
1
1
2
0
0
2
1
0
0
1
1
2
1
0
1
1
0
2
1
2
1
0
1
2
2
0
0
0
0
2
2
0
0
1
1
2
0
1
1
0
0
0
0
1
0
1
0
0
0
1
1
1
1
1
3
1
0
1
0
1
1
1
0
2
1
2
1
0
2
1
1
2
1
1
0
1
0
1
2
1
0
1
0
1
2
1
0
1
3
0
0
2
0
1
1
0
1
1
2
0
0
2
0
0
1
2
1
1
0
1
1
2
1
1
3
0
1
1
0
2
1
0
0
1
0
2
1
2
1
0
1
0
1
1
1
2
1
1
1
1
2
0
0
2
1
0
0
1
1
0
1
1
2
0
1
1
0
1
1
2
0
2
0
1
1
2
1
1
2
0
0
2
1
2
2
0
0
3
1
0
1
2
0
2
1
0
0
0
2
1
0
0
0
1
2
1
3
2
0
0
1
1
1
0
1
0
1
2
1
1
1
0
1
1
0
0
3
0
1
0
0
2
1
0
1
0
2
0
0
0
1
0
0
1
0
2
0
0
2
0
0
1
0
1
1
0
1
0
0
1
2
0
0
1
1
1
0
0
1
0
1
1
1
0
2
0
0
2
0
1
2
0
2
2
0
0
0
2
1
1
2
0
0
1
1
0
2
2
0
0
0
2
1
1
0
1
2
2
0
1
1
2
1
0
2
2
3
1
0
0
0
2
2
1
1
1
2
2
0
1
1
2
0
2
1
1
1
0
1
1
2
2
2
0
1
1
0
2
1
1
1
1
0
2
2
0
2
0
0
1
1
2
0
0
1
1
2
1
1
1
0
2
0
0
2
2
2
2
0
0
0
2
0
1
1
1
2
1
2
1
1
2
2
1
2
0
1
1
1
2
1
2
0
1
0
2
2
2
1
1
0
2
0
1
1
1
2
1
2
1
2
1
0
1
1
0
0
1
1
0
1
2
1
1
2
1
1
0
1
2
2
0
1
1
1
1
0
1
0
1
1
2
4
1
2
1
1
0
0
2
2
0
2
0
0
2
1
2
0
0
1
1
0
0
1
0
0
1
0
1
1
2
1
2
3
2
1
1
0
1
1
2
1
1
1
2
0
0
1
1
2
0
2
1
1
1
2
0
0
0
1
1
2
1
2
1
0
2
1
1
0
0
1
1
2
1
1
0
2
1
1
1
1
1
1
1
0
0
0
0
1
0
2
1
1
1
1
2
1
2
0
1
1
0
2
0
2
0
0
1
1
1
1
3
2
1
0
0
0
1
2
1
1
0
0
0
2
1
1
2
2
0
0
1
1
1
1
0
0
2
2
0
0
1
0
0
1
1
1
2
2
1
1
1
1
1
2
1
1
0
1
0
0
0
0
1
1
1
0
1
0
1
0
1
1
2
1
1
2
0
1
0
2
0
2
1
1
1
1
2
0
1
1
2
0
1
1
0
0
2
0
2
2
1
2
1
2
2
2
1
1
1
1
2
2
1
2
2
2
1
1
1
2
1
1
1
3
1
0
2
1
0
0
3
1
0
1
0
1
0
1
1
1
1
1
2
2
2
2
0
1
3
0
0
1
1
0
1
0
1
1
0
1
1
1
1
1
1
0
0
1
2
0
0
0
1
0
0
1
2
0
1
0
0
0
1
2
1
0
2
2
2
1
2
0
1
0
2
0
1
0
0
0
1
2
1
1
1
0
0
2
0
1
1
1
1
1
0
1
0
0
2
1
1
0
2
2
0
0
2
2
0
1
1
2
2
1
1
1
2
2
2
0
1
0
1
1
0
1
1
1
0
0
1
0
2
1
1
1
1
3
2
1
0
0
0
0
1
1
2
1
1
2
0
1
1
2
0
2
1
0
2
0
1
1
1
1
0
2
1
0
1
1
1
1
1
1
1
0
2
1
1
0
0
0
1
1
0
1
1
1
2
2
1
0
0
2
0
0
2
1
1
0
1
1
1
1
2
1
0
2
0
2
0
2
2
1
1
2
0
2
1
1
1
1
0
1
2
0
2
1
0
1
1
1
0
2
2
2
1
2
1
2
0
2
2
2
1
1
1
1
2
1
2
0
0
0
1
1
1
2
1
0
1
1
1
1
1
0
1
1
1
2
2
0
1
0
1
1
1
1
1
1
1
0
1
0
0
0
0
1
1
1
1
2
1
0
2
2
0
1
0
1
1
1
1
1
2
2
0
2
2
2
1
1
1
0
1
1
0
1
0
0
0
1
1
2
2
2
1
0
1
1
2
0
2
1
0
1
0
2
2
0
0
1
0
1
1
0
1
0
0
1
2
0
2
2
0
2
0
1
2
1
0
1
0
0
2
2
2
1
2
2
1
1
1
0
0
2
1
1
1
0
1
5
0
1
1
1
1
1
1
2
0
1
1
0
1
0
1
0
0
1
1
0
1
2
0
1
2
2
1
0
1
1
1
2
0
2
1
0
2
0
2
2
2
1
0
0
2
1
1
0
0
0
0
0
1
0
2
1
3
0
1
2
1
1
0
0
1
1
0
1
0
1
1
1
1
0
0
1
2
0
2
2
1
0
1
2
0
0
1
1
1
0
2
1
1
0
2
0
1
1
1
0
2
0
0
1
2
0
0
1
0
1
1
1
0
0
0
0
0
0
0
1
1
1
1
1
0
0
0
1
1
1
0
1
0
1
2
1
1
1
1
1
0
1
0
0
1
0
0
1
2
2
1
0
1
1
0
2
0
2
1
1
1
1
0
1
1
0
1
2
0
1
0
1
0
2
1
1
1
0
2
0
1
2
0
1
0
1
2
1
1
0
0
1
2
1
1
2
1
2
1
0
2
2
1
1
0
2
0
1
2
1
2
1
1
2
0
0
1
0
1
0
1
2
1
0
1
0
2
0
1
0
0
1
2
0
0
1
0
1
0
1
2
1
1
1
0
0
1
0
1
2
0
1
0
1
0
1
2
1
2
2
2
1
1
0
1
1
0
0
0
1
1
1
1
1
0
0
1
2
1
1
2
2
2
1
1
2
1
1
1
0
0
0
1
0
3
1
0
1
0
0
1
0
0
1
2
1
1
1
2
2
0
1
0
1
0
1
2
0
1
0
1
2
1
0
1
1
1
0
2
0
1
1
0
0
2
1
1
2
1
1
1
1
0
2
0
1
2
0
1
0
0
3
1
1
0
2
1
1
1
2
2
1
2
0
2
1
0
1
1
0
2
0
1
2
1
1
1
1
0
1
1
1
1
0
1
1
1
1
1
0
2
1
0
1
0
1
1
0
1
1
0
1
1
0
1
2
2
0
0
0
1
1
0
1
1
1
0
1
2
0
0
1
1
1
1
2
0
2
1
1
1
1
1
0
1
1
0
0
1
0
0
1
0
0
1
1
1
0
0
2
1
1
0
2
1
1
1
1
0
0
0
0
1
0
1
1
2
2
1
0
1
1
1
1
1
0
1
0
1
1
0
0
1
2
0
0
2
2
1
0
1
1
1
1
1
1
0
2
0
2
0
1
0
1
1
2
1
1
1
2
0
0
0
1
0
0
2
1
1
1
1
1
0
0
1
2
1
1
0
1
2
1
1
1
2
0
1
2
1
0
1
2
4
1
1
1
1
2
1
1
1
2
2
2
0
2
2
2
0
1
1
1
1
1
1
2
1
0
1
2
0
0
1
0
1
0
0
2
1
2
1
0
2
1
0
1
2
0
1
2
1
1
1
1
0
0
1
1
0
1
1
2
1
2
2
2
1
1
1
0
0
1
1
0
0
1
1
1
0
2
2
2
0
1
1
0
0
0
2
1
0
1
2
2
1
1
2
1
0
1
0
1
1
2
1
0
2
1
3
0
0
2
1
1
0
1
0
0
0
1
1
1
0
1
0
1
0
0
1
1
1
2
1
0
1
1
1
1
2
0
2
0
2
1
1
1
0
1
1
3
1
1
1
1
0
0
2
3
0
2
2
1
1
2
3
0
0
2
1
0
1
2
1
0
1
0
2
0
1
0
0
1
1
2
1
1
0
1
2
1
1
1
0
0
0
1
0
1
0
0
0
1
1
3
0
0
1
0
0
1
1
1
0
2
0
0
0
1
0
2
2
1
1
2
2
2
1
0
0
1
0
3
2
0
2
0
1
0
3
2
0
1
1
1
1
0
2
1
0
0
0
1
0
0
2
1
2
1
1
1
1
2
0
1
0
0
2
1
0
0
1
1
2
0
1
1
2
0
0
1
2
0
0
0
1
1
0
1
0
1
2
0
1
1
1
1
2
2
2
1
0
1
0
2
1
0
1
1
1
2
1
1
1
1
2
1
2
0
1
0
0
1
0
0
1
0
1
2
1
1
2
0
2
1
0
0
2
1
2
0
1
2
0
1
2
1
1
1
0
1
1
0
2
0
0
1
2
0
1
1
1
1
1
2
1
0
0
2
1
0
1
1
1
1
0
2
0
2
1
1
0
1
2
1
2
0
1
2
2
0
2
1
2
1
2
0
0
1
1
0
0
1
1
2
1
2
0
1
1
1
1
3
1
1
2
0
0
1
2
1
2
0
2
1
1
0
2
0
0
2
1
1
1
2
0
1
0
0
0
0
0
1
1
1
1
1
0
2
1
1
0
1
1
1
0
1
1
2
1
1
1
3
2
3
1
2
1
1
2
2
0
0
1
1
0
0
0
2
1
1
0
1
2
0
1
0
1
1
0
1
2
0
2
2
0
1
0
1
0
2
0
1
1
2
1
1
2
0
1
1
1
0
0
1
1
0
1
0
1
0
1
1
0
1
1
2
0
1
0
0
1
1
1
1
1
1
1
2
1
0
1
1
1
0
0
2
1
0
1
1
1
0
0
0
1
1
1
2
1
2
2
0
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
2
1
2
0
1
1
1
1
2
2
0
2
0
2
2
0
0
2
2
1
1
1
1
1
1
2
1
1
1
1
0
1
2
1
2
0
2
1
0
2
0
1
2
0
2
2
0
1
1
2
1
1
1
1
0
2
2
0
0
2
1
0
2
1
2
1
0
1
0
0
1
0
1
0
1
0
1
0
1
1
1
1
1
1
1
0
1
1
1
0
2
1
0
0
2
2
6
0
0
0
1
0
2
0
2
2
2
2
1
0
2
2
0
0
0
1
0
1
2
1
1
0
1
1
0
0
1
0
0
1
2
1
1
1
2
0
1
0
0
1
1
1
0
2
0
2
1
0
0
2
0
1
2
1
2
1
2
2
0
0
0
0
2
1
0
1
2
0
2
1
1
2
2
2
1
0
1
1
0
1
1
3
1
2
2
1
0
2
0
2
0
0
1
2
0
2
1
1
1
1
1
1
0
2
1
1
2
1
0
0
2
1
1
1
1
0
1
1
1
2
1
2
2
1
0
1
1
1
1
0
2
2
2
0
1
0
1
1
0
0
1
2
1
1
1
2
0
2
0
1
2
1
1
2
1
1
1
1
1
1
0
1
0
2
1
1
1
1
1
1
0
1
0
0
2
1
0
1
0
1
0
1
1
0
1
2
0
0
1
1
0
0
0
1
1
1
0
0
1
0
0
0
0
2
1
2
1
0
0
1
1
0
0
0
2
1
0
1
1
0
0
1
1
1
1
1
1
0
1
1
0
0
2
0
0
4
1
1
0
2
0
2
1
1
0
1
0
1
1
1
1
1
0
2
1
2
1
0
0
1
2
1
0
1
1
0
0
1
1
0
2
1
1
2
0
1
0
2
1
1
2
1
1
1
1
0
1
2
0
1
2
1
2
2
1
0
1
2
0
2
1
1
0
0
1
1
0
0
0
1
0
2
2
0
0
2
1
2
1
1
1
0
1
0
1
1
0
1
2
2
0
1
1
1
1
2
0
1
0
0
0
1
0
1
1
0
1
1
0
0
1
0
0
2
1
1
1
1
2
1
1
2
1
2
2
0
1
2
1
1
2
2
0
1
1
2
1
2
2
1
1
1
0
1
1
2
1
1
1
1
1
1
1
1
1
1
0
0
2
1
2
1
1
2
2
0
1
1
0
1
0
0
2
1
1
1
1
0
2
2
0
0
1
1
1
0
1
0
2
2
0
5
1
1
3
2
2
0
0
1
1
2
1
1
1
0
1
1
0
0
1
2
0
1
0
0
0
2
1
2
2
1
3
1
1
0
2
1
1
2
1
2
1
0
1
0
1
0
0
1
1
1
0
0
1
0
1
1
2
1
1
1
1
2
1
1
0
1
0
2
0
0
1
1
0
2
1
2
1
2
1
0
1
2
2
2
0
0
0
0
0
0
1
1
1
1
0
2
1
1
2
1
1
0
1
1
0
2
2
1
0
2
1
0
3
1
1
1
1
1
1
1
1
0
1
0
2
2
2
0
1
1
0
1
2
1
1
1
1
0
0
0
2
0
1
0
1
1
1
0
1
1
1
2
2
2
0
1
0
1
0
1
1
0
2
1
0
1
0
2
2
1
2
0
2
1
1
1
2
1
0
2
1
2
1
2
2
2
2
1
2
0
1
2
1
0
1
0
2
1
1
0
2
1
0
1
2
0
2
1
0
0
2
0
1
2
1
1
0
0
1
2
2
0
1
0
2
0
0
2
2
1
2
1
0
0
2
0
1
0
0
1
1
1
0
1
0
0
1
1
2
1
2
0
1
1
1
2
1
1
1
0
1
4
1
1
1
0
3
0
0
1
0
1
1
0
2
1
2
2
0
0
1
1
1
2
2
2
0
2
1
1
1
2
1
1
1
0
0
1
1
1
0
2
1
2
1
1
2
1
3
2
1
1
0
0
1
1
1
1
1
1
0
1
1
0
1
2
1
1
1
0
1
1
2
1
1
2
2
2
1
2
2
1
1
1
1
2
2
2
0
1
1
1
1
1
2
1
1
1
1
0
0
2
0
1
1
1
1
1
0
0
1
1
2
1
0
1
2
0
2
0
1
0
1
1
1
0
0
1
1
1
0
2
1
0
2
1
1
0
1
1
1
0
1
1
1
2
0
1
2
1
2
2
1
1
1
1
3
2
0
1
0
1
1
1
0
2
2
1
2
0
1
1
0
0
1
1
0
1
0
1
1
2
2
1
2
1
1
0
1
0
1
2
1
1
2
1
1
0
1
0
0
1
1
0
1
0
1
2
0
0
0
2
2
1
1
0
1
1
0
0
1
0
1
0
1
1
2
1
1
1
1
1
1
2
1
2
1
1
0
1
1
2
0
1
1
1
2
1
2
0
0
2
1
1
0
0
0
0
1
1
0
1
1
1
1
1
0
1
1
1
0
0
1
2
1
0
1
4
0
1
1
2
1
1
2
0
0
0
0
2
1
0
1
0
0
1
1
0
1
0
0
0
1
1
1
0
0
1
0
0
1
2
1
0
1
1
0
1
2
3
2
1
1
1
1
1
2
2
2
0
0
1
2
2
0
1
1
1
3
0
0
1
0
0
0
2
1
2
1
0
0
1
1
1
1
1
1
1
1
1
2
1
1
1
0
1
1
1
1
0
1
0
2
2
1
2
1
1
1
1
1
1
1
2
1
1
1
2
1
1
2
1
1
0
1
1
2
0
2
1
1
1
0
1
0
1
1
2
1
1
1
1
1
1
1
1
1
0
1
0
1
1
0
1
1
1
1
1
0
0
1
1
1
0
0
2
2
0
1
0
0
0
0
1
1
1
1
0
1
0
2
2
0
0
0
1
1
1
1
2
1
0
0
0
1
0
1
1
0
2
1
2
0
1
0
1
1
1
0
0
0
1
1
2
1
2
1
2
1
1
0
0
0
1
0
0
1
0
2
2
1
1
0
0
2
1
1
0
0
1
1
3
2
0
0
1
1
1
0
0
0
1
0
1
2
2
0
0
1
1
3
1
0
0
1
1
0
0
1
2
1
2
3
0
1
0
1
1
1
0
0
0
0
0
1
0
2
0
1
0
1
2
1
0
1
1
0
2
0
1
0
2
3
1
0
0
0
0
1
2
0
0
2
1
2
2
0
0
2
1
1
1
0
1
0
1
1
0
0
1
1
1
0
0
1
1
1
0
1
1
1
1
1
1
2
0
1
1
0
2
0
0
0
1
1
1
1
4
2
0
2
3
2
0
1
1
4
0
2
0
1
0
1
1
2
0
0
0
1
0
1
1
1
0
0
1
2
1
2
1
2
1
2
1
2
0
2
0
0
0
3
2
0
0
1
2
1
0
0
1
0
1
1
1
0
2
2
0
1
1
1
0
1
2
1
1
1
0
1
1
3
4
1
1
1
0
0
1
1
2
0
1
2
0
1
0
1
3
0
1
1
0
0
2
1
0
0
3
0
1
0
1
0
2
1
2
0
1
1
1
2
0
0
2
1
1
1
2
1
0
0
3
2
0
1
1
1
1
1
0
1
0
0
3
2
2
1
1
0
1
0
1
1
1
0
2
1
1
1
0
0
1
0
1
1
0
0
1
1
1
2
1
1
1
0
0
1
0
1
0
1
0
1
0
2
2
1
1
1
1
1
0
1
1
1
1
2
0
2
1
2
0
2
2
1
1
1
0
1
3
0
1
0
1
1
2
0
2
1
1
2
1
1
1
0
0
1
1
1
2
1
1
1
2
1
1
2
1
2
2
1
0
2
1
1
0
1
2
1
1
0
1
0
1
1
0
0
1
0
1
1
1
1
2
0
1
0
2
1
2
0
0
1
0
0
2
1
1
1
1
2
1
1
3
1
2
1
1
0
0
2
2
1
1
2
1
1
2
1
3
1
2
1
1
0
1
1
1
1
0
1
1
0
1
0
0
1
0
2
1
1
1
1
1
1
1
1
1
1
2
1
0
2
1
0
1
0
0
2
1
2
2
1
1
2
1
1
0
0
1
1
0
0
1
2
1
2
1
0
0
8
1
2
2
0
0
1
2
2
2
2
1
1
0
0
0
1
0
4
0
0
1
1
1
1
1
1
1
0
2
0
0
1
1
0
2
1
0
1
2
0
0
1
1
0
1
1
1
1
0
0
1
0
3
1
1
0
0
1
0
2
2
0
0
0
1
0
0
0
2
3
2
1
1
1
2
1
1
0
1
0
2
0
0
2
1
0
0
1
0
0
0
2
2
0
1
1
0
0
2
1
0
0
0
1
2
1
2
0
0
0
0
0
1
2
3
1
1
1
0
2
2
1
0
1
2
1
2
1
0
1
1
1
2
1
0
0
1
1
1
0
0
1
1
1
1
0
1
1
1
2
1
1
0
2
0
2
1
0
1
0
1
0
1
1
0
0
1
2
1
1
0
1
0
0
1
1
0
0
1
1
1
1
1
1
0
1
2
1
2
0
0
2
0
1
0
0
1
1
2
1
0
3
1
0
1
1
1
0
1
0
2
0
0
1
1
1
0
2
0
1
1
0
1
2
1
0
1
2
1
0
3
0
0
2
1
1
2
0
0
1
2
0
0
1
0
1
1
0
2
1
1
1
0
1
1
1
0
2
0
0
0
1
2
1
1
0
1
0
0
1
1
1
1
1
1
2
0
1
1
0
1
0
0
0
2
0
1
1
1
1
0
0
1
0
1
0
1
1
1
0
1
0
1
1
1
0
1
0
0
4
1
1
2
1
1
1
1
1
2
1
0
2
2
1
0
1
0
1
2
1
1
1
0
1
2
0
2
0
0
0
1
2
1
2
0
0
1
0
0
0
1
4
2
0
2
1
1
1
2
1
1
1
1
1
0
2
1
0
1
1
1
0
0
1
2
1
2
0
1
1
2
1
1
1
0
1
0
2
1
1
1
2
1
1
1
0
2
0
0
2
1
2
1
2
0
1
2
2
2
4
0
0
2
0
0
0
0
0
2
1
2
2
2
1
1
5
1
2
1
1
0
1
2
1
1
1
0
1
0
1
1
1
1
1
0
1
1
1
3
0
1
1
1
2
1
2
2
0
1
0
1
1
0
2
0
2
1
2
1
0
2
2
0
0
0
1
1
1
0
0
2
1
1
1
2
1
0
0
1
0
0
1
0
2
1
1
1
1
1
0
2
2
0
2
1
2
1
0
1
2
2
1
0
2
2
2
0
1
0
0
1
0
0
1
0
1
2
0
0
0
0
1
1
0
1
1
1
2
2
2
1
1
1
1
0
2
2
0
2
1
1
1
0
0
0
1
1
2
1
1
1
0
1
1
0
2
1
1
1
1
0
1
1
0
2
2
1
1
1
1
1
0
2
1
1
2
0
2
2
1
0
1
0
1
0
1
1
0
1
1
2
1
2
1
0
1
1
1
0
2
2
0
1
0
0
1
1
1
2
0
0
2
0
1
0
0
1
1
0
0
0
1
2
1
1
1
2
1
0
0
2
1
1
1
1
1
0
1
0
1
0
2
1
1
1
2
0
0
0
1
1
0
2
0
1
2
2
1
0
0
1
0
2
1
1
2
2
0
2
2
1
0
2
0
1
1
1
2
0
2
0
0
0
1
1
1
0
0
0
2
1
0
1
1
2
1
1
1
0
1
1
1
1
1
1
1
1
0
1
0
1
1
1
0
1
1
0
2
1
2
1
2
1
2
2
1
0
2
1
1
1
0
1
1
0
0
2
0
0
1
2
1
1
1
1
1
0
2
1
2
1
2
1
2
1
2
4
1
1
2
2
1
0
1
1
1
0
0
1
1
1
2
2
2
1
1
0
0
2
1
0
1
0
1
2
1
0
1
0
0
1
0
1
0
1
1
1
1
0
1
1
1
2
1
2
0
1
2
1
1
0
0
0
1
0
2
1
1
0
1
1
1
1
0
0
1
1
3
0
1
2
0
0
0
1
1
2
2
2
2
1
2
1
1
0
1
1
1
2
1
2
0
0
1
1
1
0
2
1
0
1
1
0
2
1
0
1
1
1
1
1
1
1
1
0
1
2
1
1
1
0
0
2
1
1
1
1
2
2
1
2
2
1
1
1
2
1
0
0
1
1
1
1
1
1
0
1
0
1
2
1
1
1
0
2
1
1
0
0
2
1
2
2
0
0
1
0
0
1
0
0
1
1
0
2
1
1
0
2
0
1
1
0
1
1
2
0
1
1
0
3
1
0
0
1
1
0
1
2
1
1
2
1
1
0
0
0
2
1
1
2
1
1
1
0
3
0
0
0
1
1
1
1
0
0
1
1
1
1
2
1
2
1
1
1
0
1
0
2
0
0
1
2
0
0
1
0
2
2
1
0
1
1
1
2
0
1
0
3
1
0
0
0
2
1
2
0
1
0
1
1
0
1
1
1
1
0
1
2
1
0
1
1
0
1
1
2
1
1
1
1
1
2
0
0
1
1
1
1
1
2
1
1
1
0
1
0
0
2
1
1
1
0
2
0
2
1
0
1
2
1
1
1
1
2
0
0
0
1
1
1
1
0
0
1
0
1
2
1
0
1
0
1
0
2
1
1
2
1
0
1
1
0
1
1
2
2
1
1
1
0
1
1
0
1
1
0
1
2
1
1
0
1
1
0
1
2
0
0
1
0
1
0
1
1
2
0
1
0
2
2
1
1
2
1
0
1
1
2
1
1
0
1
1
1
0
0
1
0
1
1
1
0
2
2
0
1
1
0
1
0
0
1
0
0
0
0
5
0
0
1
0
2
1
2
1
2
2
1
2
1
1
1
1
0
0
0
0
0
0
4
3
2
1
1
2
1
0
1
1
0
2
1
1
1
1
0
0
0
1
1
2
0
2
0
1
1
0
1
1
0
1
0
1
2
2
2
1
1
2
2
1
0
2
0
1
1
1
3
1
1
2
0
1
2
1
2
0
2
1
1
1
0
2
1
1
0
0
3
1
2
3
1
2
0
1
2
1
1
1
3
0
2
1
0
0
1
1
1
1
2
0
0
0
0
0
1
0
1
2
0
1
1
1
0
0
0
1
1
1
1
2
1
1
0
0
1
0
1
1
5
2
0
1
2
0
1
1
1
0
1
1
1
1
2
2
1
1
0
1
2
2
0
1
1
2
1
2
0
2
1
0
0
1
1
1
0
1
0
0
2
1
1
3
2
1
2
1
2
1
1
0
1
1
1
2
1
1
1
1
1
2
0
0
1
0
3
1
2
0
0
0
0
1
2
2
0
2
1
0
1
2
0
1
1
0
0
1
1
2
1
0
2
2
1
2
2
0
0
1
1
0
2
0
1
1
0
1
0
3
0
2
1
1
1
0
1
1
1
1
1
2
1
1
0
2
2
2
1
1
1
0
1
2
2
0
0
2
1
1
1
2
1
1
1
1
1
0
0
0
0
0
1
1
0
0
0
1
2
1
1
1
2
1
2
0
1
0
1
1
1
1
2
1
1
0
0
0
0
1
1
2
0
1
1
0
0
1
0
1
1
1
2
2
2
1
1
1
2
0
1
1
0
0
2
0
1
0
2
1
0
1
2
1
1
1
1
1
1
1
0
1
1
1
0
1
2
2
0
1
2
2
0
1
0
2
2
2
2
1
1
2
0
1
0
2
0
1
2
2
1
0
2
1
1
1
1
1
0
0
1
1
2
1
1
0
1
0
0
2
0
3
2
0
1
1
2
0
1
1
1
1
0
0
1
1
1
1
2
1
0
1
0
0
1
1
1
1
1
0
1
1
0
2
1
2
0
1
1
1
1
0
0
0
1
1
2
0
2
1
1
1
1
1
2
2
1
0
0
1
0
2
1
2
1
1
0
1
0
0
1
1
1
1
1
0
2
0
1
1
2
1
2
2
1
1
0
1
0
1
2
3
1
0
1
1
0
2
2
0
0
0
1
0
1
0
1
1
1
0
2
0
0
1
0
1
0
1
0
0
1
1
1
2
1
2
2
1
1
0
1
1
1
1
1
1
1
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
1
1
0
0
2
1
1
1
1
2
2
0
0
0
0
1
0
1
0
0
1
2
1
2
1
1
1
1
0
1
1
1
1
0
1
0
1
1
2
0
2
2
1
0
0
0
2
1
1
1
1
0
0
1
0
1
1
0
0
1
1
0
1
2
1
0
2
1
1
1
1
1
2
0
1
1
2
1
0
1
3
1
2
1
2
1
1
2
1
2
2
0
1
1
1
1
1
1
0
3
0
1
0
1
1
0
2
1
1
1
0
1
1
1
1
2
1
2
1
0
1
1
1
0
0
1
1
1
0
0
1
2
0
0
1
1
1
1
2
0
1
0
1
0
1
0
1
1
1
1
1
0
1
1
0
0
1
1
1
1
2
1
1
1
1
1
0
0
0
1
1
1
1
1
1
1
0
1
0
1
0
2
1
1
2
1
0
0
2
0
1
1
0
1
1
0
1
1
4
2
0
3
1
1
0
0
1
1
1
0
1
1
2
2
1
1
1
2
1
0
2
1
1
0
1
0
1
0
1
0
1
0
2
1
0
0
2
1
0
1
1
1
1
0
0
1
2
0
1
1
0
2
1
1
1
2
1
3
1
0
2
0
2
1
1
2
1
2
0
0
0
1
0
1
0
2
0
1
1
2
1
1
1
1
2
0
0
1
0
1
2
1
0
1
2
1
2
1
1
1
0
1
1
2
1
1
0
2
0
0
1
1
0
1
1
0
0
1
2
0
0
1
0
1
1
1
2
1
2
1
2
1
1
0
0
2
0
0
1
0
2
2
1
2
0
0
1
2
1
1
2
1
1
1
2
1
1
2
2
0
0
2
0
0
1
0
1
0
2
1
1
1
0
1
1
2
0
1
0
1
1
1
2
2
1
2
2
1
0
2
2
0
2
0
1
1
2
0
1
1
1
1
1
1
0
1
2
0
0
1
2
1
0
0
1
2
2
0
0
1
1
2
0
1
2
1
1
0
1
0
2
0
2
1
1
2
0
1
1
0
2
2
2
0
1
0
0
1
0
1
0
2
0
1
2
1
1
0
0
1
2
1
0
0
2
2
1
2
2
1
0
1
2
0
1
1
2
1
2
1
1
1
1
1
0
0
0
1
1
2
2
1
1
1
0
1
1
0
1
1
0
1
1
0
1
1
2
0
2
4
2
1
0
1
1
0
1
2
1
1
1
2
1
1
0
1
0
0
1
1
0
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
2
2
1
1
0
0
0
2
0
0
1
1
1
0
2
0
1
2
0
1
1
1
1
0
0
1
1
0
1
1
0
1
0
0
1
5
0
2
1
1
0
1
1
2
0
0
1
2
0
1
1
2
0
2
1
2
2
1
0
1
1
1
0
2
1
1
2
0
0
1
0
1
1
0
0
2
1
1
2
2
0
1
1
0
1
2
1
0
2
1
1
1
2
0
1
0
1
0
3
1
1
0
0
0
0
2
0
2
1
1
1
2
2
1
1
1
0
1
1
0
2
0
1
1
0
1
2
1
0
0
0
0
1
2
1
0
0
1
1
0
1
0
2
1
1
1
1
0
1
1
0
0
1
2
2
0
1
2
0
0
1
1
1
2
1
1
1
0
2
1
1
1
0
0
1
2
1
1
0
1
1
0
1
1
1
1
0
1
1
0
1
1
3
1
1
2
1
1
1
1
1
2
1
1
0
1
1
0
0
0
1
0
1
1
0
0
2
2
1
1
2
2
0
0
0
1
1
1
1
1
0
0
2
1
0
1
0
1
0
0
0
0
1
0
0
2
1
2
2
2
1
0
0
0
2
0
1
1
2
2
0
0
1
0
0
1
1
1
1
1
1
1
0
2
0
1
1
0
1
1
2
1
1
1
2
0
1
2
1
1
2
2
1
0
1
0
0
0
1
0
2
0
1
2
1
2
2
2
2
2
2
0
1
1
1
1
0
0
1
1
2
1
2
2
2
2
1
1
1
1
0
1
2
2
2
1
0
1
0
2
0
1
0
1
1
2
2
0
1
1
0
0
1
1
0
0
2
0
1
2
1
2
0
1
1
1
2
0
1
1
1
0
2
0
2
0
2
1
1
1
3
0
2
2
1
1
1
2
1
0
1
1
0
3
0
0
0
2
1
0
1
1
1
1
2
0
1
0
0
1
0
0
1
0
1
1
1
0
1
2
1
1
1
2
1
1
1
0
0
0
1
0
0
0
2
1
1
2
1
2
2
1
0
0
0
1
0
1
1
1
1
2
2
1
1
0
1
1
1
1
2
1
6
1
0
1
2
1
1
2
0
1
1
0
2
1
1
1
1
1
1
2
1
1
2
2
2
1
1
0
1
1
1
3
1
1
0
0
1
1
0
2
1
1
1
0
2
0
0
2
1
0
2
2
0
0
2
0
1
0
1
0
2
2
2
1
0
1
1
1
1
1
0
1
1
2
2
2
0
1
2
1
1
1
1
1
0
2
2
2
0
1
1
0
1
2
2
1
0
1
1
1
1
2
1
2
1
0
0
1
0
2
1
1
0
0
1
2
1
1
1
1
2
1
1
1
0
2
2
2
0
2
2
1
1
2
0
1
2
0
1
1
2
1
1
1
0
0
0
0
2
1
0
1
1
1
2
1
0
1
1
2
1
0
1
2
3
0
1
2
1
2
2
0
0
1
0
1
1
2
0
1
0
0
1
1
0
1
1
1
1
1
1
2
2
1
2
1
1
0
1
2
0
1
2
1
2
1
0
2
0
0
0
1
0
0
1
0
1
1
0
2
1
1
2
1
1
0
0
1
0
1
2
1
0
1
2
1
3
3
1
0
0
2
1
1
1
1
0
1
1
1
0
1
1
1
1
2
0
2
1
1
1
1
0
0
1
2
0
4
2
1
1
1
0
0
0
1
0
1
0
1
1
0
0
1
1
1
1
2
2
1
0
2
1
2
2
1
2
2
0
1
1
2
2
1
1
3
1
1
1
1
1
2
0
1
1
2
1
2
1
2
1
0
0
0
1
2
2
2
1
2
1
1
1
2
2
1
0
1
1
0
1
1
0
1
0
0
1
1
1
1
1
0
2
2
2
0
1
1
0
0
0
2
2
1
1
1
0
1
0
0
0
2
0
0
0
1
0
1
0
0
1
0
2
2
1
1
0
1
1
1
0
0
1
0
0
1
1
1
0
0
1
0
1
1
1
0
1
1
2
1
2
0
2
2
2
0
0
2
1
0
0
0
0
1
2
2
1
1
1
2
0
0
1
1
1
1
0
1
1
1
1
1
1
1
1
0
1
1
0
1
1
0
0
2
1
0
2
1
1
1
2
0
1
4
1
1
1
0
1
0
1
0
0
1
0
2
2
1
0
0
0
0
1
1
0
1
0
1
0
2
2
1
0
0
2
1
1
2
0
1
1
0
2
2
0
1
2
1
1
2
1
1
0
1
2
0
1
1
1
0
0
1
1
1
2
0
2
1
1
1
1
1
2
0
1
1
1
1
1
1
2
4
0
0
0
1
1
2
1
2
2
2
1
1
0
1
1
0
2
1
5
0
2
1
0
1
1
2
1
1
1
0
1
0
1
1
2
1
2
0
1
0
2
1
1
0
0
0
1
0
1
1
0
1
1
2
1
1
2
1
0
0
0
1
1
2
2
1
1
1
1
1
2
1
3
1
0
0
1
1
2
1
1
0
2
1
1
0
1
2
2
1
0
0
1
0
1
0
0
1
0
0
0
1
2
0
1
1
0
2
1
0
2
1
0
2
1
1
0
1
1
1
0
2
0
2
1
1
0
1
1
0
0
0
1
0
2
1
1
0
2
1
1
0
1
1
1
2
0
0
2
1
0
1
1
1
1
0
1
2
1
1
1
1
0
2
1
1
0
0
0
1
1
1
0
2
1
2
2
0
1
1
1
0
1
1
1
0
1
2
0
0
2
1
1
2
1
2
1
1
0
1
1
2
1
0
0
0
1
0
0
1
0
1
0
0
0
0
2
1
2
1
1
2
0
0
0
0
1
0
0
0
1
1
0
2
1
0
1
1
0
0
1
1
2
0
0
2
1
1
2
1
0
1
1
1
0
1
0
0
1
2
2
1
1
2
3
2
1
0
1
1
1
2
1
2
0
0
1
2
2
0
1
0
0
2
0
1
2
2
0
1
1
2
1
1
1
1
1
1
0
2
2
2
1
1
0
1
1
1
1
1
1
0
1
1
1
1
2
1
2
0
1
1
2
1
1
2
0
1
0
0
1
2
2
1
1
2
1
1
1
1
1
1
0
1
1
1
2
1
1
2
2
1
0
1
0
1
1
1
0
1
1
1
0
1
0
1
2
0
1
0
1
1
1
1
1
2
0
0
1
1
2
1
1
2
0
0
2
0
1
1
1
0
0
1
0
0
1
1
1
1
0
2
1
1
1
1
0
2
1
2
1
0
1
0
2
0
0
1
1
0
2
1
1
0
2
0
2
0
0
1
2
2
2
3
0
1
1
1
1
0
1
1
1
0
2
0
1
1
1
0
0
1
1
0
0
2
1
1
2
0
0
0
1
1
2
2
1
2
2
1
2
0
1
0
2
0
2
0
1
0
1
0
1
0
2
2
1
1
0
1
1
1
1
0
1
1
0
0
1
0
1
0
2
1
1
2
0
1
2
2
0
1
1
0
0
0
2
0
1
0
1
1
0
2
0
0
1
1
1
1
2
1
2
1
1
1
1
0
0
1
2
3
1
1
1
1
2
2
2
0
1
0
1
0
1
1
0
1
2
1
1
1
2
1
0
2
0
1
0
1
2
4
1
0
1
0
1
2
0
1
1
1
0
2
1
1
1
1
0
0
1
1
1
0
0
2
1
2
2
1
2
1
1
2
0
0
1
0
1
0
0
0
2
1
1
2
1
0
2
1
0
1
1
1
1
1
1
0
0
0
2
2
0
0
1
2
0
1
0
0
1
0
0
0
1
0
3
0
1
1
1
0
1
3
1
2
1
2
0
2
1
2
0
1
2
1
0
2
0
1
1
1
2
1
0
1
1
1
0
0
0
1
1
1
0
2
1
1
1
0
1
1
2
0
1
1
2
0
1
0
0
1
0
2
2
2
2
0
0
1
1
1
0
1
0
0
0
0
1
1
0
0
0
1
0
1
1
1
0
1
1
0
1
1
0
0
1
1
1
2
1
1
2
1
1
0
2
1
0
0
1
1
1
0
1
0
1
2
1
2
0
2
1
1
1
2
0
1
1
0
0
0
1
1
1
1
0
2
1
0
2
0
0
0
1
0
2
1
2
1
0
1
1
1
1
2
0
1
2
0
1
1
2
2
1
1
1
2
1
2
0
1
0
3
1
1
1
1
2
2
0
1
1
2
1
1
1
1
1
1
1
0
2
1
1
1
1
1
2
0
2
1
2
2
1
3
1
1
2
1
1
2
2
1
0
0
2
3
1
0
0
2
1
2
0
1
1
1
0
1
0
0
2
1
0
0
1
0
0
1
1
2
0
0
1
1
1
2
1
2
1
1
0
0
1
1
1
1
0
0
1
1
0
2
2
1
1
0
1
1
1
0
1
0
1
1
0
0
1
1
2
0
0
2
1
0
1
2
1
1
0
2
1
1
1
1
1
1
0
2
1
1
1
1
2
2
2
1
0
2
1
1
0
1
0
0
2
1
2
0
1
1
2
0
1
1
1
2
1
2
0
0
1
2
1
1
2
1
2
2
1
0
2
1
1
1
1
1
1
2
2
1
0
1
1
0
2
0
1
2
2
1
2
1
0
2
0
0
0
1
1
2
0
0
0
0
1
0
2
2
0
1
1
1
3
0
1
2
2
2
0
0
1
1
2
0
2
0
1
1
2
0
2
1
1
0
1
2
1
0
1
0
0
1
2
0
1
1
2
1
1
0
1
1
0
0
1
1
2
1
0
1
0
0
0
0
0
1
0
3
1
1
1
1
2
2
2
0
1
1
1
1
1
0
1
0
0
2
2
0
0
2
1
2
0
2
0
2
0
1
8
1
1
1
0
0
1
0
0
2
1
0
1
1
0
1
1
0
2
1
2
1
2
0
0
1
1
0
2
2
1
1
1
3
0
1
1
2
2
1
1
1
1
0
0
1
1
0
1
1
0
1
0
1
2
2
1
2
1
1
2
2
1
0
1
2
1
1
1
2
1
0
1
2
1
0
2
2
2
1
0
0
1
0
0
0
0
1
0
1
0
0
1
1
2
1
2
0
0
2
1
0
0
0
2
0
0
1
2
1
1
1
1
0
1
1
1
1
1
2
2
2
1
0
0
1
0
1
1
1
1
1
0
2
2
1
2
1
0
0
0
0
1
1
2
2
1
0
1
1
1
2
0
0
0
3
1
1
0
1
1
0
0
0
1
1
2
0
1
2
1
1
0
0
4
2
0
1
2
0
1
1
0
1
1
2
1
1
2
1
1
2
0
1
2
0
2
2
2
1
0
0
0
1
2
1
1
0
1
1
2
0
2
1
1
2
2
2
0
1
0
1
1
1
1
2
1
1
1
0
1
1
1
1
1
0
0
2
1
0
0
1
0
1
1
2
1
1
1
1
1
1
0
1
2
2
3
1
2
0
1
1
0
0
0
0
0
1
0
2
1
3
0
1
0
2
1
1
2
1
0
2
1
0
2
0
1
1
2
1
2
1
1
1
0
1
1
1
2
1
1
1
0
0
1
1
2
1
1
0
1
2
0
0
1
0
1
1
1
2
2
1
1
0
1
0
1
3
1
1
1
2
0
2
0
1
0
0
1
0
1
1
0
0
0
0
1
0
0
1
1
1
2
2
1
1
2
1
0
0
1
2
1
1
2
4
0
0
0
2
0
0
1
1
3
2
2
2
2
1
1
1
0
0
1
0
1
1
1
2
1
1
1
1
2
1
0
0
5
2
0
2
2
0
1
1
2
0
1
2
2
1
1
2
1
1
0
1
1
1
2
1
1
1
1
0
1
1
2
4
1
1
2
1
1
0
0
1
1
0
2
1
1
0
1
1
1
2
0
1
0
0
0
2
1
2
1
1
1
1
0
1
1
0
1
1
1
0
1
1
1
0
1
2
0
1
0
1
1
2
1
1
1
1
1
1
1
1
1
0
0
1
0
2
2
1
1
0
1
2
1
2
0
1
1
2
0
2
2
0
1
2
2
1
1
0
0
1
1
1
2
0
0
1
1
0
1
1
0
1
0
1
2
1
0
2
0
2
1
0
0
1
1
1
1
1
2
0
0
1
1
1
0
0
2
0
0
1
2
1
0
2
1
0
1
1
0
0
2
2
1
2
2
0
0
0
1
1
0
2
0
1
0
1
1
1
1
1
1
1
1
0
2
1
2
1
1
1
2
2
1
1
2
2
1
0
0
0
0
1
0
2
1
3
1
1
1
1
0
3
0
0
0
2
1
1
1
1
2
1
1
1
1
1
0
1
0
0
1
0
1
1
0
0
1
0
0
2
1
0
1
0
0
1
2
1
1
1
1
2
1
1
1
1
1
1
1
0
4
1
1
1
1
1
2
1
2
0
1
1
1
1
1
0
3
2
1
1
0
1
1
0
1
0
2
2
2
1
1
2
2
2
0
0
1
1
1
0
1
1
0
1
1
1
0
1
3
2
1
1
0
1
0
2
2
1
0
1
0
2
0
2
1
1
1
0
0
0
2
0
1
0
2
1
1
1
3
1
1
2
0
1
1
1
0
1
1
1
2
0
1
0
1
0
0
0
0
0
1
2
0
2
0
1
1
2
0
1
2
0
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
0
1
1
2
2
1
1
1
0
1
0
1
2
1
2
0
0
1
0
2
1
1
1
1
1
1
1
2
2
0
0
1
1
0
4
2
2
2
1
0
1
2
2
1
2
1
2
0
0
1
0
0
1
0
1
1
1
2
1
2
1
1
0
0
1
1
1
2
1
2
1
0
2
0
1
0
2
1
0
0
0
1
1
1
2
2
1
2
1
1
1
0
1
1
0
0
0
1
1
1
2
1
1
1
0
1
0
0
2
0
0
2
1
1
0
0
0
1
0
0
2
2
0
2
2
4
1
1
2
1
1
2
2
1
1
3
2
0
0
1
0
2
1
1
0
2
0
2
2
2
1
2
1
0
2
1
0
1
1
0
1
0
0
2
0
0
0
1
0
1
2
2
0
1
1
0
1
1
1
0
2
0
1
2
0
0
1
1
0
1
1
0
1
1
1
3
1
2
0
1
2
2
1
0
1
2
1
1
1
1
1
0
1
0
1
1
1
2
1
1
0
0
2
1
1
1
3
0
0
0
1
0
1
2
0
1
0
2
1
1
0
2
0
1
0
1
2
1
1
0
0
2
1
1
2
1
1
1
1
2
1
1
1
0
0
0
2
0
2
1
1
1
2
1
0
1
3
1
1
2
0
0
0
1
1
0
2
0
0
2
4
0
2
0
1
3
1
0
0
1
1
2
1
2
1
0
1
0
0
2
1
0
1
0
2
2
1
1
1
0
1
0
1
2
1
0
1
2
1
1
0
0
1
2
0
0
2
1
0
1
2
2
1
1
1
0
1
0
0
0
0
1
2
1
1
2
1
0
2
2
0
1
1
1
1
1
1
1
0
2
1
2
0
0
0
2
1
0
0
1
1
2
1
0
1
0
0
0
1
1
0
0
0
0
1
2
1
1
0
0
2
0
1
0
1
0
1
1
2
2
0
0
2
1
1
0
2
0
0
1
1
1
1
0
0
1
2
1
0
2
0
2
2
2
1
2
0
1
2
0
0
1
0
0
1
1
1
1
2
2
1
0
1
0
2
1
1
1
0
2
2
1
2
1
0
0
1
0
2
1
2
0
1
1
2
1
1
2
1
1
1
0
0
1
0
0
1
0
0
1
0
0
2
2
0
0
2
0
0
0
0
0
0
2
1
0
0
2
1
1
1
1
1
1
0
2
1
1
2
2
2
1
2
0
0
1
0
1
2
1
0
1
1
2
2
0
2
1
2
1
1
1
1
2
1
1
0
1
1
1
1
1
2
2
2
2
0
1
1
1
0
1
0
1
0
1
0
1
1
1
2
0
1
1
1
1
1
2
1
2
1
1
2
2
2
0
1
2
0
0
1
1
2
1
1
1
1
1
2
2
1
1
1
1
1
1
2
1
2
1
3
1
0
0
1
1
1
2
1
0
1
0
1
0
1
1
2
2
2
1
0
0
1
1
1
1
0
0
0
1
0
2
2
0
1
1
1
1
2
0
2
0
1
1
1
1
1
3
1
2
1
1
1
1
0
1
1
0
2
2
1
2
1
1
0
1
0
1
1
1
0
1
2
1
1
1
0
1
1
2
2
1
1
0
0
0
1
0
0
1
2
1
2
0
0
0
0
1
1
1
0
0
0
1
0
2
2
0
1
0
0
1
1
0
0
1
2
0
3
1
1
1
1
1
1
1
2
1
0
1
1
1
2
0
0
1
0
0
0
1
0
0
1
1
0
2
1
0
1
0
1
1
2
0
1
2
0
2
1
0
1
2
1
1
0
0
1
0
2
1
2
1
1
1
0
0
0
0
2
0
2
0
0
2
0
1
1
1
2
1
2
0
0
1
1
1
0
1
2
1
1
1
1
2
2
1
0
0
0
0
1
0
2
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
2
1
2
3
0
1
0
0
1
2
0
2
1
0
1
2
2
0
2
0
0
1
0
2
1
1
1
0
2
2
1
0
0
1
2
1
1
2
0
2
1
0
1
0
0
0
1
0
0
3
0
1
1
1
1
1
0
1
2
1
2
1
0
0
1
1
1
1
2
1
0
1
2
0
1
1
1
0
1
1
2
1
2
1
1
2
1
1
0
2
1
1
1
2
0
1
1
1
0
1
1
2
1
2
0
2
2
0
0
1
1
1
1
1
1
1
1
1
1
4
0
2
1
0
1
0
2
0
1
1
2
2
1
2
2
0
1
1
0
0
1
1
0
2
1
0
0
0
2
1
1
2
0
1
1
2
1
1
2
2
1
0
1
0
1
1
1
0
0
1
0
1
0
1
1
0
0
2
0
2
0
0
1
1
2
0
0
0
1
0
0
2
1
1
2
1
0
1
0
0
1
0
0
1
0
2
0
0
1
0
0
1
0
1
2
2
0
1
0
1
0
1
0
1
0
1
1
0
0
0
0
1
0
0
0
1
1
0
2
0
2
1
1
2
2
0
1
2
2
2
2
0
0
1
1
2
1
0
1
0
0
1
4
1
1
2
0
0
0
1
1
2
1
1
2
1
0
2
0
1
1
2
0
2
0
0
2
1
0
1
1
2
1
2
0
1
2
1
2
1
1
1
0
0
2
1
2
2
1
1
2
0
2
1
2
0
1
1
1
1
1
0
0
1
1
1
1
1
1
1
0
1
1
2
1
1
0
2
0
1
1
0
1
0
1
1
2
0
1
2
1
1
1
1
0
1
0
0
2
1
1
0
0
2
1
0
2
2
0
1
0
0
0
0
2
1
1
0
0
1
1
0
1
0
0
0
0
2
0
0
1
1
0
2
0
2
1
2
1
0
0
1
1
0
0
2
1
0
0
0
1
1
2
2
1
1
0
1
2
2
2
1
2
1
0
1
2
1
1
0
0
0
1
0
1
0
2
1
2
0
0
1
0
0
0
0
1
0
0
0
2
1
0
2
2
2
2
1
1
1
1
1
1
1
0
1
2
0
0
1
2
2
1
1
1
0
1
2
1
2
0
1
0
0
2
1
0
2
1
2
1
2
1
1
2
2
0
2
2
0
1
0
0
1
1
2
1
0
2
0
2
1
0
1
2
1
1
1
0
0
2
2
1
0
0
1
2
0
2
0
1
4
0
0
1
1
1
2
1
2
1
0
1
1
0
0
0
2
1
2
2
1
0
2
1
1
1
1
0
1
0
3
2
0
0
0
2
0
2
1
1
0
1
4
1
0
1
2
1
1
0
0
1
0
1
1
1
1
1
0
1
1
0
1
0
1
2
2
1
1
1
1
0
0
1
0
1
0
1
2
1
1
1
2
2
0
0
1
0
1
2
0
1
0
2
1
1
1
2
1
0
0
0
1
0
2
1
1
1
2
0
1
0
0
2
1
1
1
2
1
1
1
1
1
2
0
1
1
0
0
1
1
1
0
1
1
2
1
2
0
1
1
0
1
1
0
2
1
0
2
0
1
1
1
0
0
1
2
1
1
1
1
1
1
1
1
1
2
1
0
1
1
0
0
1
2
1
0
1
0
4
0
1
0
1
2
1
0
1
1
0
1
1
0
2
0
0
2
1
1
1
1
2
2
1
1
0
2
1
0
1
0
1
0
1
1
2
2
1
0
2
1
2
0
1
0
2
1
2
2
1
0
1
2
2
1
0
0
2
0
0
1
0
0
1
2
1
1
2
1
0
0
1
1
2
0
0
2
1
1
1
1
0
0
1
1
0
0
2
3
0
0
1
1
2
2
1
1
0
0
1
1
0
0
0
1
1
0
0
0
0
2
2
2
0
1
0
1
2
0
2
1
2
1
2
1
0
1
0
0
1
1
1
1
2
2
0
0
0
0
1
1
1
2
0
1
0
2
2
2
1
0
1
0
1
0
2
1
2
1
0
1
0
2
1
0
0
1
1
1
1
1
0
1
1
1
0
2
1
0
1
1
1
1
1
2
1
0
2
0
2
1
0
1
1
0
0
0
0
0
1
2
0
1
0
2
2
1
2
2
1
0
0
1
0
2
1
1
0
1
1
1
0
1
2
1
1
0
2
2
1
0
2
1
2
1
1
2
0
1
0
0
2
0
1
1
0
1
0
0
1
1
1
0
1
1
1
2
2
2
2
1
1
1
0
1
2
0
1
0
1
2
1
1
0
0
1
1
2
2
1
2
2
1
1
2
0
0
0
2
0
2
0
0
0
1
1
1
2
1
1
0
1
0
2
1
0
0
1
1
0
2
0
0
0
4
0
1
1
1
1
0
2
1
1
1
0
0
2
1
2
0
2
1
0
2
0
1
0
0
0
0
0
1
1
0
1
1
0
0
1
2
0
1
1
0
1
2
1
0
1
1
0
1
0
2
1
0
1
0
1
0
1
1
1
1
0
2
2
0
0
1
1
2
2
0
2
1
0
0
0
2
2
0
0
2
1
1
0
0
0
2
1
1
0
1
1
1
1
1
1
1
0
1
0
2
0
2
1
2
0
0
0
1
4
0
1
0
1
2
1
1
0
1
0
0
0
1
3
1
0
1
1
1
2
2
1
1
1
1
2
1
0
0
0
2
1
1
2
0
2
1
2
2
2
0
2
2
1
0
2
0
2
2
3
1
1
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
2
2
0
0
2
0
1
2
0
0
1
1
1
1
1
1
0
1
0
0
2
0
0
1
3
2
1
1
1
1
1
0
2
2
0
1
0
2
1
2
2
2
1
1
1
0
2
0
0
0
1
1
0
1
1
0
2
1
1
1
0
1
1
1
1
0
0
1
1
1
2
1
1
2
0
2
1
1
0
1
1
1
2
2
1
2
1
0
0
2
1
0
1
1
1
2
2
1
1
1
1
0
1
3
1
0
0
2
1
1
1
0
1
1
0
2
1
2
1
0
1
2
1
0
0
1
2
2
0
2
0
0
0
1
0
1
0
1
1
2
0
0
1
2
1
2
0
1
1
2
2
1
1
0
0
1
0
1
0
2
0
2
1
2
1
1
1
1
1
0
1
1
1
2
1
0
0
1
1
2
2
0
1
1
0
1
0
0
1
0
0
3
0
2
1
1
1
2
1
0
1
1
1
1
1
1
1
0
1
1
1
0
0
0
0
1
2
0
0
0
0
0
1
2
1
0
1
1
2
1
1
0
1
1
0
0
1
0
1
1
2
2
1
2
0
0
2
0
2
1
1
1
1
1
1
2
0
1
1
0
1
1
1
2
2
1
2
0
2
0
1
0
0
1
0
0
0
1
2
2
2
2
2
3
2
1
0
2
0
1
0
1
2
0
0
1
1
1
2
1
2
0
1
1
1
0
1
0
0
1
1
0
0
1
0
2
2
1
2
0
0
1
1
2
1
2
1
0
2
1
1
1
1
0
0
2
2
0
1
1
1
2
1
1
1
2
1
1
0
0
2
1
0
0
1
1
0
1
0
2
1
0
0
1
0
1
1
0
0
1
1
0
2
1
1
2
4
2
2
1
1
1
3
0
2
1
1
0
1
0
0
2
1
1
0
0
4
1
0
1
1
1
1
1
1
1
0
1
1
1
1
0
1
1
0
1
2
1
2
2
0
1
0
0
1
1
0
0
1
0
2
2
1
0
2
1
1
1
3
0
0
0
2
2
0
0
0
1
1
1
0
0
1
0
1
2
1
0
0
0
1
0
2
1
1
2
1
1
2
0
0
0
2
2
1
1
0
1
1
2
2
2
1
1
0
0
0
2
2
1
1
2
1
1
0
0
1
0
3
2
0
1
1
1
1
1
1
2
1
1
0
0
0
2
1
1
1
0
1
0
1
1
2
0
2
1
0
1
1
0
1
1
2
1
0
1
2
1
1
1
0
2
1
0
5
1
2
0
2
2
1
1
1
1
1
0
1
0
2
1
1
0
0
1
1
1
1
0
1
1
2
2
0
0
1
1
0
2
2
1
0
1
0
1
1
2
0
1
0
2
1
1
2
1
2
2
1
2
1
1
0
1
0
1
0
3
0
1
0
1
1
0
0
0
1
1
0
1
1
1
1
1
1
3
2
2
0
2
1
0
2
2
1
2
0
0
1
2
0
1
1
2
1
0
1
2
2
1
0
0
2
1
1
1
1
0
2
1
0
0
1
0
1
0
0
2
0
1
0
1
0
0
2
2
0
0
1
1
2
1
4
0
0
1
0
0
0
1
0
0
1
1
1
1
1
0
0
1
1
2
1
1
1
1
1
0
0
1
1
0
0
1
1
0
1
1
2
1
3
1
0
0
0
1
2
2
2
0
2
1
1
1
1
2
0
2
1
1
2
1
0
1
2
2
0
1
0
0
1
1
1
1
0
0
2
0
1
0
1
0
2
1
2
1
1
1
0
2
0
1
0
1
0
1
0
0
0
2
2
1
1
0
2
0
0
2
1
2
1
1
0
0
0
2
1
1
1
2
2
0
0
1
1
0
2
1
2
0
2
1
1
1
1
1
1
0
2
0
1
0
2
0
1
0
3
1
2
1
1
0
1
2
1
2
1
1
2
1
2
2
1
1
1
1
1
2
1
0
2
1
2
0
3
1
2
1
1
0
2
2
2
2
0
0
1
2
0
2
2
1
2
1
1
0
0
0
0
0
0
1
1
1
1
0
1
2
1
1
1
1
2
0
1
1
1
1
1
1
1
1
1
0
0
0
0
0
1
2
1
1
2
0
1
1
1
0
1
1
1
1
0
0
1
2
1
1
1
1
0
0
1
0
0
0
1
1
1
1
1
0
0
1
0
0
1
1
1
0
1
2
1
1
0
0
0
2
1
1
1
0
1
1
1
2
0
0
2
2
1
1
2
1
1
1
1
1
1
1
0
1
1
1
2
2
1
2
1
2
0
2
1
0
3
2
1
1
2
1
2
0
1
1
1
0
1
0
0
1
2
1
0
1
1
1
1
1
1
2
0
2
1
1
1
2
1
1
1
0
1
1
0
1
1
1
2
1
0
2
0
1
0
1
1
0
1
1
1
1
2
1
2
2
1
0
1
1
1
2
2
0
2
1
0
1
2
1
0
1
0
2
0
1
1
1
1
1
0
0
1
1
2
2
0
1
2
1
1
0
1
1
2
2
1
0
1
1
2
0
1
2
1
2
1
0
1
1
0
1
1
1
1
1
0
1
1
0
0
2
1
1
1
2
2
2
1
1
2
1
2
1
3
1
1
2
1
2
0
2
2
0
4
1
2
1
1
1
1
7
2
1
1
1
1
1
1
1
2
0
2
2
2
1
0
0
0
1
1
2
1
1
1
0
2
2
2
1
1
0
0
3
1
0
0
1
1
1
0
0
0
1
1
1
2
3
2
0
2
0
0
0
1
0
1
1
1
0
0
0
1
1
0
1
1
1
0
1
0
2
0
0
2
2
0
1
2
0
1
0
1
0
0
0
1
0
1
1
0
1
2
0
2
0
0
1
1
1
2
1
1
1
1
1
2
1
2
1
2
2
0
2
0
2
0
2
0
2
2
1
2
1
1
2
1
1
1
2
1
1
2
2
1
1
0
2
1
4
1
0
1
1
0
1
0
2
2
2
1
1
1
1
0
0
1
0
1
0
2
0
1
1
2
2
1
0
0
2
1
3
3
1
0
0
1
2
0
2
1
2
1
0
1
1
1
1
2
0
2
1
1
3
1
1
1
0
0
2
0
2
1
1
0
1
2
1
0
2
1
1
1
1
0
1
0
3
1
1
1
1
1
2
1
1
2
0
1
0
2
1
0
0
1
0
0
0
2
2
2
2
0
1
0
0
2
1
1
2
2
1
3
0
1
1
0
0
1
0
0
1
1
0
2
0
1
2
2
1
1
0
2
2
1
0
0
3
0
1
0
0
0
1
1
0
1
1
2
1
2
2
2
2
2
1
0
1
1
1
1
3
2
1
2
2
0
1
1
2
2
2
1
2
1
1
2
2
0
0
2
0
0
1
1
1
1
1
2
0
1
3
0
1
0
2
0
2
0
0
1
0
1
1
1
0
1
1
2
0
1
1
0
1
1
1
2
0
0
1
1
1
1
2
0
0
0
1
1
2
2
1
1
1
1
0
3
0
0
2
0
2
0
2
1
0
0
0
1
0
2
1
0
1
1
1
2
2
1
0
1
2
1
0
0
1
1
0
1
2
1
2
0
1
1
0
1
1
0
2
1
0
1
1
1
0
1
0
2
2
1
2
2
2
0
0
1
2
0
1
1
1
0
0
1
2
2
2
1
1
1
1
1
1
2
0
0
1
0
0
0
0
1
2
0
2
1
1
0
0
0
2
1
1
1
0
2
2
1
1
1
2
2
2
1
1
1
0
1
2
2
2
1
1
1
0
0
2
1
1
1
0
0
1
1
0
2
0
2
1
1
0
0
0
1
0
1
0
0
0
1
2
0
1
2
0
2
0
0
0
1
1
1
1
2
1
1
2
1
1
1
1
1
1
0
1
2
1
0
1
1
1
1
3
1
1
1
1
1
0
1
2
2
1
2
0
0
2
1
1
2
1
0
0
2
1
0
0
2
1
1
1
0
0
2
0
1
1
1
0
1
1
0
0
1
1
1
1
2
2
1
0
0
2
1
1
2
0
0
0
1
3
2
0
1
1
0
0
1
2
0
1
0
1
1
2
1
2
0
0
1
1
0
0
0
1
1
1
0
0
1
0
2
0
1
0
0
0
2
2
1
0
0
4
1
1
2
1
0
2
0
2
1
1
1
2
0
0
0
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
0
0
0
0
0
0
2
1
0
2
1
2
2
2
0
0
2
1
1
1
0
1
2
1
1
1
2
1
1
1
0
0
1
1
2
2
1
1
2
0
1
1
1
1
0
1
0
0
1
1
1
0
2
1
1
1
1
2
0
2
0
0
1
0
1
1
0
3
2
1
1
1
2
0
1
1
2
1
2
0
1
1
1
0
0
0
2
0
1
2
2
4
2
0
2
2
2
1
1
6
0
2
2
0
1
3
1
1
0
2
1
1
0
0
0
0
0
1
1
0
1
1
0
0
0
1
1
2
1
0
1
0
1
0
2
2
1
0
1
3
0
1
0
0
0
0
0
0
0
0
1
3
1
0
1
2
0
1
1
0
1
1
1
1
0
0
1
1
0
1
1
2
1
2
0
0
0
2
1
2
1
1
1
1
2
0
1
1
1
0
1
1
1
1
1
2
0
1
1
1
0
1
0
1
1
1
1
1
0
0
1
0
0
1
1
0
0
1
1
1
2
2
0
0
1
1
0
1
0
1
2
1
2
0
1
1
0
1
1
1
1
2
0
0
0
1
1
0
0
1
0
0
1
2
0
1
4
0
2
2
1
1
0
1
1
0
2
1
1
0
1
0
2
1
1
1
1
2
0
1
0
2
0
0
3
0
1
0
0
1
1
2
0
0
1
0
2
0
0
0
1
2
1
1
1
1
2
1
1
1
1
0
0
0
0
1
1
0
1
0
1
1
0
2
2
1
1
1
0
0
1
1
0
0
1
1
0
2
2
2
1
1
0
2
2
1
0
1
1
0
1
1
1
1
0
0
1
0
2
1
2
1
0
1
2
1
0
2
0
1
0
1
0
1
2
1
1
0
2
0
1
1
2
0
1
1
2
0
2
0
1
2
2
0
1
0
1
1
1
0
1
0
3
1
0
1
0
2
1
0
0
1
0
1
2
1
1
1
0
0
1
1
1
0
2
0
1
2
2
0
0
1
0
1
1
2
1
1
2
0
1
1
1
1
1
1
1
0
2
0
1
1
1
0
1
1
1
0
1
2
0
0
1
2
2
1
1
0
2
0
2
2
1
2
2
2
1
2
1
1
2
1
0
1
1
1
1
1
2
2
0
1
0
1
0
0
1
1
0
1
1
2
2
0
2
1
0
1
1
1
0
0
1
1
0
0
1
1
0
0
0
0
1
1
1
0
0
2
2
1
1
0
0
2
1
1
0
1
2
1
2
1
0
0
0
1
2
1
0
1
2
1
0
2
1
1
2
0
0
2
0
1
1
0
1
1
0
0
1
1
1
1
2
0
1
2
0
2
1
1
1
0
1
1
1
1
0
1
1
1
1
2
2
1
2
1
1
1
1
1
4
1
0
2
0
1
1
2
0
0
2
2
0
0
0
2
2
2
1
2
1
3
1
0
0
0
1
1
1
0
2
0
1
2
0
1
1
3
1
2
2
2
1
1
1
0
2
1
0
2
3
0
1
1
2
0
0
2
2
0
0
1
1
1
1
0
1
1
1
0
2
1
1
0
2
2
1
1
0
2
0
0
0
1
0
1
0
1
0
2
0
0
1
2
0
1
0
1
1
0
0
1
0
1
2
1
0
0
1
0
1
1
1
0
0
2
2
2
1
0
0
1
2
1
0
1
2
1
1
0
1
2
1
1
1
0
2
2
0
2
2
1
1
1
2
1
1
0
0
0
1
0
1
0
0
1
1
1
2
1
0
0
0
2
1
1
0
1
0
0
1
2
0
1
0
0
1
0
2
1
1
1
1
0
0
0
0
2
0
1
2
1
1
3
0
1
2
0
0
0
1
1
1
0
2
1
1
1
1
0
1
0
2
1
2
1
1
2
0
0
2
0
2
2
2
0
2
0
0
2
1
2
2
1
0
0
1
1
0
2
2
1
2
0
0
2
1
0
2
2
2
1
0
1
1
0
1
2
1
2
0
1
0
1
0
2
0
1
1
0
1
1
1
2
1
1
2
0
1
0
0
1
1
0
1
0
1
2
1
0
0
2
1
2
1
1
1
1
1
0
1
0
1
2
1
0
1
1
2
0
1
1
2
0
4
0
2
2
0
1
0
0
1
2
0
0
1
0
1
2
0
0
1
1
1
0
1
0
1
1
0
0
1
1
1
1
2
1
2
0
0
2
0
1
0
0
4
1
0
0
1
0
1
0
0
0
1
0
2
0
1
1
0
0
2
0
1
0
0
1
0
1
0
0
0
2
1
0
1
1
1
1
0
2
1
0
0
0
1
1
1
1
0
1
2
1
1
1
2
0
1
0
1
0
1
2
1
1
2
1
1
0
1
0
0
1
0
1
1
1
1
1
0
2
1
0
0
0
1
0
1
1
0
1
0
0
1
0
1
0
1
1
0
1
2
0
2
0
1
1
0
1
1
0
1
2
1
1
0
1
1
2
2
2
2
0
0
1
0
1
1
1
2
1
2
2
1
0
1
1
2
1
1
2
1
1
2
1
4
1
0
0
1
1
0
1
0
1
2
2
1
1
1
1
1
2
1
2
0
1
1
1
1
2
1
1
0
1
1
1
0
1
0
0
0
0
2
2
1
0
2
0
1
0
0
2
0
0
3
1
2
1
2
0
1
1
1
2
1
1
0
1
1
1
0
0
2
1
0
0
1
3
1
0
0
1
1
0
1
2
4
0
1
0
2
1
1
2
1
1
1
0
1
2
1
1
2
1
1
1
1
1
0
0
1
1
1
2
0
2
1
0
0
0
0
1
3
1
1
2
1
0
1
2
0
2
1
1
1
0
1
0
0
0
2
0
2
1
1
2
2
1
1
1
0
2
1
1
1
1
1
1
0
1
1
0
0
0
0
0
0
1
1
1
1
0
1
1
2
1
1
1
2
0
2
2
1
2
2
1
1
1
2
1
0
1
1
1
1
0
2
1
1
1
6
0
0
0
1
0
1
1
2
1
1
0
1
2
1
1
2
2
1
1
2
2
1
2
2
1
1
0
1
1
2
1
0
1
2
1
2
1
0
2
1
0
1
0
1
1
2
0
0
0
1
1
1
0
1
1
1
1
0
1
1
0
2
2
1
1
1
1
1
1
2
0
1
1
0
1
0
1
1
2
1
1
0
1
1
1
1
1
0
0
2
0
1
0
1
1
1
0
2
3
1
0
2
2
1
1
0
2
1
1
1
0
0
0
0
0
1
0
1
0
2
0
1
1
2
1
2
2
1
1
1
1
1
0
1
2
0
1
1
1
2
2
0
1
0
2
1
0
0
1
1
1
1
2
2
1
1
0
0
1
2
1
1
1
0
1
1
0
2
2
0
2
0
0
0
0
0
1
2
1
2
1
2
0
2
1
2
2
1
0
1
1
0
0
0
0
0
0
0
1
2
1
0
1
0
1
1
1
3
1
0
1
1
2
0
0
2
0
0
1
1
2
1
0
2
0
1
2
0
0
0
2
1
2
2
1
1
0
3
1
0
0
1
0
1
0
0
1
0
1
1
0
1
2
0
1
1
2
2
2
2
2
0
1
1
0
1
1
1
0
0
2
1
0
0
2
1
1
0
3
0
3
0
1
1
0
1
2
1
0
1
1
3
1
0
1
1
0
0
1
1
2
0
1
0
1
1
1
1
0
2
0
0
2
1
0
2
2
2
1
1
0
1
1
0
0
0
0
1
0
1
1
5
0
0
0
0
0
0
0
2
1
2
1
0
0
0
0
1
1
0
1
0
1
1
1
0
1
1
0
0
2
1
1
1
0
3
0
1
0
1
0
0
1
1
0
1
1
1
1
1
1
2
2
0
1
1
1
2
0
1
0
1
1
1
1
2
1
1
2
0
1
0
2
1
1
1
0
2
1
1
0
1
1
1
0
0
1
2
1
1
0
2
0
1
1
0
1
2
2
0
0
2
1
2
1
5
1
1
0
1
1
0
1
2
1
1
2
2
0
1
0
1
1
2
1
1
1
1
1
2
0
1
1
2
1
1
0
1
2
2
1
1
1
1
1
1
0
0
0
2
1
0
0
1
1
2
1
1
1
0
1
2
2
1
1
1
0
1
0
0
1
2
2
1
1
2
1
1
0
1
1
0
2
1
1
1
1
2
1
2
1
0
2
2
1
1
1
1
2
1
0
1
0
1
0
1
0
1
1
1
1
2
1
1
1
0
1
1
0
0
2
2
2
1
1
1
1
2
1
1
2
0
1
1
1
1
3
1
0
1
2
2
1
1
2
0
1
1
2
0
1
1
0
1
1
1
2
1
1
1
0
0
1
2
2
1
2
2
2
2
0
3
1
2
2
0
1
2
0
0
0
1
1
1
0
1
1
1
1
2
0
1
2
0
0
1
1
1
1
2
0
0
0
0
0
1
0
2
0
1
0
0
1
2
2
2
0
2
1
2
0
1
1
2
3
0
2
2
1
0
0
1
1
1
0
1
1
1
1
1
0
1
1
1
0
0
1
1
1
1
1
2
1
1
0
2
2
1
2
0
1
1
1
2
1
1
2
1
0
0
1
2
1
2
1
0
0
3
0
2
0
1
2
1
0
1
2
1
2
1
1
1
0
2
1
0
2
1
2
1
0
2
1
1
1
1
1
0
2
0
1
0
0
1
1
1
0
2
2
1
2
1
2
2
2
2
1
0
2
0
1
1
1
1
0
0
2
0
1
0
1
0
2
0
2
2
1
1
0
2
1
0
0
1
0
0
0
2
2
2
1
0
1
0
2
1
1
1
0
1
0
0
2
1
0
1
0
1
2
1
2
0
1
2
1
2
2
1
0
1
1
0
0
1
1
0
1
1
1
1
1
0
1
1
1
1
0
1
0
0
1
0
2
2
2
0
1
2
1
0
2
1
1
0
2
1
0
1
2
2
1
1
0
2
1
0
1
0
2
2
0
0
2
2
1
2
2
2
0
1
1
1
1
0
2
1
2
1
2
1
2
1
2
0
0
1
0
0
0
0
0
1
2
0
0
2
1
1
1
0
1
2
0
0
0
1
1
2
1
1
1
1
1
1
1
0
2
1
1
2
1
1
1
2
1
0
1
0
1
0
1
1
0
0
1
0
2
2
0
0
1
2
1
2
0
0
1
0
1
2
0
2
1
2
0
1
0
0
0
1
1
0
0
0
1
1
2
0
1
1
2
2
0
0
2
2
1
2
0
2
1
1
0
0
2
0
2
1
1
2
1
1
0
1
2
1
1
2
2
2
1
2
1
1
0
0
1
1
0
0
0
0
1
0
0
0
2
1
1
1
2
1
1
0
0
0
1
1
0
0
2
2
0
0
2
1
1
1
1
1
1
2
1
1
2
1
1
1
0
0
0
1
1
1
1
1
0
2
1
1
2
2
0
0
2
2
2
0
2
1
0
1
0
1
1
2
2
0
0
0
0
0
2
0
1
2
1
0
2
1
1
0
1
0
0
0
1
2
1
0
1
0
0
1
1
1
1
0
1
0
2
1
1
0
0
2
0
1
1
1
1
1
1
0
1
0
0
1
2
0
2
1
0
0
0
1
3
2
2
1
2
2
2
2
0
2
2
0
1
3
1
0
2
2
1
2
0
2
1
2
0
2
2
1
1
0
2
2
0
1
1
1
1
1
0
1
2
2
0
1
2
2
1
2
0
0
1
0
0
1
1
0
0
0
2
1
2
0
2
1
0
0
0
0
1
2
1
1
0
2
0
1
2
1
0
1
0
1
3
0
1
1
0
1
1
2
1
0
1
0
1
2
0
1
2
2
1
2
1
2
1
1
1
1
2
1
1
1
0
2
2
1
1
3
1
2
0
1
1
1
1
0
1
0
1
0
0
2
0
1
1
1
2
0
1
1
2
0
1
2
0
1
0
0
0
0
2
1
0
0
0
0
2
2
1
1
2
1
1
1
1
0
1
0
0
1
1
1
0
1
1
0
1
2
1
2
1
0
1
1
1
1
0
2
1
2
1
2
0
1
1
2
2
0
1
3
1
0
1
0
1
1
0
1
0
1
1
1
0
2
1
1
2
0
0
0
2
1
0
1
2
0
0
1
1
1
1
2
1
1
1
0
1
0
1
1
1
0
0
1
1
1
1
0
1
1
0
2
1
1
2
0
0
2
0
2
1
1
1
1
1
1
2
0
0
1
1
0
0
0
1
0
2
1
0
2
1
1
1
0
1
1
1
0
0
0
1
2
1
3
1
2
0
0
1
1
2
1
1
1
0
1
1
1
1
1
0
0
1
1
0
1
0
0
1
2
2
1
1
1
1
1
2
2
0
0
1
2
0
1
1
0
1
0
2
0
0
2
0
2
1
1
1
0
1
1
2
1
2
2
1
1
1
0
1
2
2
0
1
2
2
2
1
1
1
1
3
0
1
0
1
2
0
0
2
0
1
0
2
1
1
1
0
0
1
1
1
1
3
0
1
0
1
1
1
1
2
1
1
0
2
1
0
0
2
0
0
1
2
2
1
0
0
1
2
0
1
1
1
2
2
2
1
2
0
1
1
1
1
0
1
0
1
1
1
0
1
0
1
2
1
1
1
0
1
0
1
0
1
1
1
1
0
1
0
1
2
0
0
0
0
0
0
1
1
1
2
0
1
1
1
1
2
1
1
2
2
1
2
1
0
0
1
2
2
1
1
1
1
2
1
1
0
1
1
1
1
0
0
1
2
0
2
1
0
0
0
0
0
1
1
1
1
1
1
1
0
1
0
1
1
1
1
2
0
0
0
0
2
1
0
1
1
0
0
0
1
3
1
0
0
1
0
0
1
1
0
1
1
2
1
1
2
0
2
1
1
0
1
1
0
1
2
1
1
1
1
0
1
2
2
1
2
1
1
1
1
0
0
0
1
0
1
1
0
1
2
1
1
1
0
0
2
3
1
0
2
1
1
1
0
1
0
1
1
0
1
1
2
2
0
2
0
1
1
0
2
2
0
1
2
2
1
1
0
1
2
1
2
1
0
1
1
2
1
2
0
2
0
0
1
1
0
1
2
1
1
0
0
1
1
1
1
1
3
2
1
0
1
1
2
2
1
1
1
0
0
1
1
2
0
1
2
2
0
3
0
1
0
1
0
0
2
1
1
1
2
1
1
1
1
0
0
2
2
0
1
1
2
0
1
1
0
1
0
2
1
2
1
0
0
1
1
0
2
0
1
1
1
1
0
0
1
1
0
1
3
0
1
1
2
3
1
0
1
1
2
1
0
2
3
1
1
1
2
2
1
1
0
2
2
1
1
1
0
2
0
1
0
1
1
18
1
0
0
2
1
1
1
0
1
2
0
1
2
2
0
0
1
0
1
1
1
0
0
1
0
1
1
1
0
2
2
1
1
1
0
1
2
0
0
0
0
0
1
1
0
0
1
1
0
1
2
1
2
2
2
3
1
0
1
2
0
1
0
0
0
1
0
1
0
0
0
2
1
1
1
0
2
2
1
0
2
1
1
2
1
2
0
0
0
0
2
0
3
1
2
2
1
1
0
1
1
1
1
1
2
0
0
1
2
2
1
1
2
1
0
0
2
2
0
0
1
0
0
1
1
1
0
1
1
1
2
2
1
1
0
0
0
1
1
2
0
0
1
0
0
0
1
0
0
1
0
0
1
1
1
1
1
2
2
1
2
0
1
0
0
1
1
2
2
1
0
1
1
0
1
2
1
2
1
3
1
2
2
1
0
0
2
1
1
2
1
1
1
1
0
1
1
0
1
1
1
0
0
0
1
2
0
1
0
0
1
1
0
0
0
1
2
1
1
1
0
0
1
1
0
2
0
1
1
1
1
2
2
1
2
1
1
1
1
0
1
0
2
1
1
2
0
1
2
1
2
1
0
0
0
1
1
1
1
1
0
1
1
1
6
2
1
2
1
1
0
0
2
1
2
0
0
0
1
2
0
1
0
0
1
1
0
1
0
2
1
2
1
1
2
2
0
0
0
1
1
1
0
1
1
1
0
2
1
2
2
1
3
2
2
1
2
2
1
1
2
0
0
1
0
0
0
1
1
1
1
0
1
1
1
1
0
0
0
2
2
1
1
1
1
1
2
0
2
1
1
1
2
0
1
1
2
0
1
2
2
2
1
1
2
2
1
2
2
0
2
0
0
1
1
2
0
0
1
1
0
0
1
1
1
0
1
0
1
1
1
1
1
1
1
1
1
0
0
1
2
0
1
0
0
1
0
1
1
2
0
2
1
1
1
1
2
1
1
0
0
1
0
1
1
1
1
1
0
1
1
2
1
1
1
1
2
1
1
2
2
0
0
1
1
1
1
1
1
1
2
2
0
0
2
0
2
0
1
1
0
0
1
1
1
1
1
1
0
1
1
1
2
1
1
1
0
2
2
0
1
2
1
0
2
1
0
0
1
1
1
0
0
1
2
0
1
0
1
1
0
1
1
0
0
1
1
1
1
1
2
2
1
1
2
1
2
2
2
1
1
0
1
0
1
1
2
0
0
0
1
0
0
1
0
2
2
2
1
2
1
1
2
2
0
2
1
1
1
1
0
2
2
1
1
2
0
2
0
0
1
1
0
0
0
1
0
1
1
0
1
1
1
1
1
2
2
1
0
1
1
0
2
1
0
2
0
0
2
1
0
1
2
0
0
2
3
2
0
2
0
1
2
0
1
2
0
0
0
0
2
1
1
0
1
1
1
0
1
2
0
3
2
1
0
1
1
0
1
1
0
0
0
0
2
2
1
1
1
0
2
1
0
1
1
1
2
1
0
0
1
2
0
1
1
0
0
1
1
2
1
1
2
1
0
0
1
1
1
2
1
0
1
1
0
1
1
1
1
1
1
0
0
1
2
1
1
1
1
0
1
1
0
0
1
1
1
2
0
1
1
1
1
0
1
2
2
0
2
0
0
0
1
0
1
1
1
1
1
2
1
1
2
2
1
1
0
2
3
1
1
2
2
1
0
1
1
0
2
0
1
1
1
1
2
2
0
1
1
2
2
1
1
0
2
0
2
0
0
1
2
2
0
2
1
0
1
1
0
1
0
0
0
0
2
1
1
2
2
3
1
0
1
0
0
5
1
1
1
1
0
1
1
1
1
0
1
0
0
0
1
1
1
1
1
2
2
0
1
1
0
1
1
0
0
0
1
2
1
0
0
2
2
4
1
1
0
1
0
1
1
1
2
2
1
0
2
1
0
2
0
0
0
0
2
2
1
2
1
2
1
2
2
2
2
2
2
2
0
1
0
0
1
2
0
1
2
0
2
2
1
0
0
1
2
1
1
1
1
0
1
0
1
2
1
2
1
1
2
1
0
1
0
1
0
2
0
2
1
1
1
1
1
0
0
2
1
1
5
1
1
0
1
0
1
1
1
1
1
1
1
0
1
1
0
0
1
2
2
1
0
1
2
1
1
2
0
0
0
1
2
0
0
0
0
1
1
2
0
1
0
2
1
0
0
1
0
0
0
2
2
0
1
0
5
2
1
2
2
0
0
0
0
1
1
1
2
0
2
0
1
1
2
1
2
2
3
2
2
0
2
0
0
1
0
2
1
1
0
1
0
2
1
2
2
1
0
0
1
1
0
1
1
1
2
2
2
1
0
1
1
1
1
2
0
0
0
1
1
1
2
0
1
2
1
0
0
0
0
1
0
2
0
1
1
2
1
2
2
1
1
0
0
0
1
2
1
1
0
0
2
0
0
0
0
1
0
0
1
1
1
1
0
1
0
2
2
1
2
0
1
0
2
0
0
2
1
2
1
1
1
1
1
1
1
1
2
0
1
0
0
1
1
2
1
0
2
2
0
0
1
1
2
0
1
1
1
0
1
1
0
0
0
1
1
1
0
0
1
2
1
1
0
1
1
1
1
2
0
1
0
1
1
1
2
0
1
0
0
0
1
0
2
1
2
0
1
1
2
0
0
1
1
1
2
0
1
1
0
1
2
0
2
0
1
1
0
0
0
1
1
0
0
0
0
1
5
1
1
0
2
1
1
1
2
2
1
2
3
0
2
1
1
0
0
1
1
1
2
1
0
2
0
1
1
2
1
2
1
0
2
0
1
1
2
0
1
0
0
1
1
0
0
2
2
2
1
1
0
1
0
2
2
0
0
2
0
1
0
0
1
2
2
1
1
1
1
2
1
0
1
0
1
0
1
2
1
0
1
1
1
0
0
0
1
0
0
2
1
1
0
1
0
2
1
0
0
2
0
1
1
1
1
1
1
1
0
3
0
1
2
2
1
0
2
1
0
1
1
1
1
1
0
0
0
0
2
2
0
0
1
1
0
1
2
2
2
0
1
0
1
0
1
1
2
1
1
1
1
0
1
0
2
2
0
0
2
1
4
2
0
1
0
0
2
0
0
0
1
2
1
1
0
1
0
2
0
1
1
1
0
1
1
1
1
2
1
0
1
0
0
0
0
0
1
1
0
3
1
2
1
0
1
0
1
2
1
1
0
1
0
0
1
2
1
0
2
1
2
0
1
1
1
1
2
2
2
2
0
0
1
1
0
1
2
2
1
1
1
1
2
1
1
1
1
1
0
0
0
3
0
2
1
2
1
1
2
0
1
2
2
1
0
0
1
0
1
0
2
1
0
0
0
1
0
1
1
1
2
0
0
1
1
0
1
0
0
1
0
1
0
1
1
0
2
1
0
1
0
0
1
0
1
1
1
1
1
1
1
1
1
0
0
1
0
2
1
0
1
2
1
1
1
1
0
2
1
1
0
2
0
1
1
0
1
1
1
0
1
2
1
1
1
1
1
0
1
1
0
2
1
1
1
1
1
1
0
1
0
1
0
1
2
1
0
2
1
2
1
0
0
0
1
1
1
1
2
0
2
1
0
2
0
0
2
1
1
1
1
1
1
1
0
1
0
0
1
0
0
0
0
2
1
1
1
1
1
0
2
1
0
0
1
1
0
1
1
1
1
0
0
1
0
0
0
1
1
2
0
2
1
0
2
2
2
1
1
0
0
1
0
1
1
1
2
0
1
1
1
1
0
0
1
2
1
0
2
3
0
0
1
2
2
2
2
1
1
0
1
2
1
1
2
1
0
1
2
2
2
2
1
1
1
1
1
0
1
1
1
1
2
1
1
1
1
0
1
1
1
1
0
0
0
0
0
0
1
1
1
1
0
0
2
1
1
1
1
1
1
1
0
2
1
1
2
2
0
1
1
1
1
1
0
0
0
0
0
2
1
1
1
1
1
1
1
2
0
1
1
1
2
2
0
2
1
2
0
2
1
1
2
2
2
1
0
1
2
2
1
1
3
1
2
2
2
0
1
0
0
1
0
1
0
0
1
1
1
2
0
0
2
0
1
0
1
2
1
1
1
1
0
0
1
0
0
1
1
1
1
1
0
1
0
1
1
2
0
2
1
2
1
0
1
1
1
1
1
0
2
1
0
2
1
0
1
0
2
2
2
2
1
1
0
0
0
0
1
1
0
1
1
1
1
1
1
1
1
3
2
2
0
0
2
0
0
2
1
2
1
1
0
1
1
3
2
2
1
0
1
2
3
0
2
0
1
2
0
0
0
1
1
0
1
2
0
1
0
1
0
0
1
1
1
1
0
0
2
1
2
2
2
1
1
1
1
0
2
0
2
0
0
2
1
1
1
0
2
1
1
2
1
1
2
1
0
1
1
2
1
0
1
0
1
2
1
0
2
1
1
2
1
0
0
1
1
0
1
1
1
1
1
1
0
1
0
1
1
0
2
1
0
0
1
2
0
0
0
2
0
1
1
3
1
1
2
2
0
1
2
1
1
0
0
2
2
0
1
0
1
1
3
1
0
2
1
0
2
0
1
0
1
2
1
0
2
1
0
1
2
1
2
2
0
2
0
2
2
1
0
2
0
2
0
1
1
0
2
0
1
1
1
1
2
2
1
1
1
1
1
1
1
0
1
2
0
1
1
1
2
1
2
1
0
1
1
0
1
2
1
0
1
1
1
1
2
1
0
0
1
1
0
0
1
0
1
1
2
1
0
0
0
1
0
0
2
2
0
2
1
1
1
0
1
1
1
0
0
0
1
1
1
0
1
1
1
1
0
1
0
1
0
3
1
1
1
0
1
6
1
1
2
1
1
0
1
1
2
2
2
0
1
0
1
1
0
2
1
1
2
0
1
0
2
1
1
1
2
3
1
2
1
0
2
1
1
0
1
1
1
1
2
1
0
2
1
2
0
0
0
0
0
2
1
1
2
0
2
1
1
1
1
0
1
0
1
1
1
1
1
1
2
0
0
1
2
1
1
1
1
2
2
1
1
0
2
0
1
0
1
0
2
0
0
2
0
2
1
0
0
0
1
1
2
2
2
1
0
0
2
2
2
1
1
0
2
1
1
2
2
0
1
0
1
2
0
0
0
2
1
2
0
0
1
1
1
2
1
1
0
0
0
0
1
1
1
1
1
1
1
0
1
1
0
1
1
1
2
2
1
2
0
1
1
1
2
1
0
1
0
1
1
0
1
1
0
0
0
2
2
1
1
0
1
1
1
2
1
3
0
1
2
1
1
1
1
1
1
1
2
3
1
2
0
4
0
1
0
1
0
0
0
2
0
1
1
1
1
1
0
1
1
1
1
0
2
1
1
0
1
2
1
0
1
3
1
2
0
1
2
2
3
0
0
0
2
0
1
1
2
0
0
1
0
0
0
0
1
0
0
1
0
0
1
1
1
0
0
2
2
2
1
0
1
1
2
1
1
2
1
2
1
0
1
2
2
1
1
0
0
0
0
0
1
1
3
1
2
2
0
0
0
2
1
0
0
1
0
1
2
1
1
1
2
0
1
2
2
1
0
0
2
0
0
1
1
1
1
1
1
1
1
0
1
1
3
0
2
0
2
0
1
0
2
2
1
2
0
0
0
1
1
0
1
4
0
2
1
0
1
2
0
2
2
1
1
0
2
1
0
1
1
1
2
2
1
1
1
1
1
0
1
2
0
1
1
1
1
1
0
0
1
0
0
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
0
2
1
0
1
1
0
2
0
2
0
1
1
1
0
0
0
1
1
2
3
1
1
1
1
1
1
0
0
0
0
1
1
1
0
1
0
0
2
1
1
2
0
1
1
0
1
0
1
0
1
1
5
1
0
0
0
5
1
1
1
1
1
0
1
2
3
2
1
1
0
2
1
1
2
1
1
0
2
2
1
2
1
0
2
0
0
1
1
1
1
1
3
2
1
2
2
0
0
0
1
0
1
0
0
1
2
1
0
0
0
1
2
1
1
1
3
1
2
1
1
1
1
2
2
0
1
0
1
1
1
1
1
1
2
2
1
0
1
0
2
0
2
0
0
0
2
0
0
1
0
1
1
0
1
1
1
0
2
2
1
0
1
0
1
1
2
0
0
0
1
1
0
1
0
1
2
0
1
2
2
1
0
1
1
2
2
1
0
1
1
0
1
0
1
1
0
2
1
0
1
1
0
2
1
2
2
0
1
2
0
0
1
2
1
0
2
1
0
0
0
2
1
0
0
2
2
1
0
1
1
1
1
1
0
0
1
1
2
0
3
0
2
0
0
1
2
1
0
2
1
1
0
1
1
1
2
2
1
0
1
1
1
2
2
0
0
1
0
1
1
0
1
0
2
2
0
1
1
0
1
1
1
0
1
2
1
0
2
1
1
0
3
1
2
1
1
0
1
2
1
0
0
1
1
0
1
1
0
2
2
1
1
1
0
1
1
1
1
2
2
2
1
0
0
2
0
2
1
2
1
3
1
2
1
1
1
0
1
2
2
1
1
1
1
1
0
1
1
1
2
0
1
0
2
1
0
0
1
2
0
1
0
0
2
0
0
1
0
1
0
2
0
2
1
2
0
1
0
2
1
1
0
2
1
2
1
2
0
1
1
0
1
0
1
2
1
1
1
1
0
1
1
2
1
0
2
0
1
0
2
0
0
1
1
3
1
1
1
2
1
1
1
1
2
1
0
2
1
0
1
1
1
0
2
2
2
1
2
1
1
0
1
0
1
2
0
1
1
1
2
2
1
0
2
0
2
1
1
1
2
0
1
2
1
2
3
2
1
0
1
1
1
2
2
3
2
1
1
2
1
0
2
0
1
0
2
0
1
1
0
1
2
1
0
1
0
1
0
0
2
1
0
1
2
1
2
1
1
0
1
1
1
0
1
1
0
2
0
1
0
0
2
1
0
1
1
1
2
0
0
0
0
1
0
0
1
0
1
1
1
2
1
1
0
1
1
0
0
1
0
0
2
1
1
1
1
1
0
1
2
2
2
2
0
1
0
1
1
1
1
1
1
0
1
0
1
2
1
1
1
2
1
2
1
0
2
1
1
0
1
0
1
2
2
0
1
1
1
0
1
1
2
0
2
0
1
2
1
0
1
0
2
0
1
2
2
0
1
1
1
2
0
0
2
1
1
2
1
1
2
0
0
2
0
1
2
1
1
1
2
2
0
2
1
1
1
1
1
1
0
1
1
0
1
1
1
2
1
1
1
0
2
1
1
2
0
0
1
2
2
2
3
0
1
1
0
0
2
0
0
1
0
2
2
0
2
1
1
2
1
1
1
0
0
3
0
1
0
2
0
1
1
2
2
1
1
3
1
1
1
1
2
0
1
1
1
0
0
1
1
1
2
0
0
1
2
0
1
2
1
1
1
1
0
1
0
1
1
2
2
2
4
1
6
1
0
2
2
1
0
1
1
0
1
0
0
2
1
2
1
2
2
1
1
0
2
0
1
1
0
4
0
1
2
2
1
1
1
1
1
1
0
1
1
0
0
1
0
0
0
2
0
0
0
2
0
1
0
1
1
2
0
1
1
0
1
1
1
1
1
0
1
1
0
0
1
0
1
2
0
2
0
1
2
1
0
1
1
2
0
2
1
0
0
3
1
2
1
1
0
3
1
1
0
1
2
2
1
1
0
0
1
1
0
0
0
1
1
0
1
2
1
1
1
1
0
0
0
0
1
1
1
0
1
1
1
0
1
1
1
0
2
2
1
1
0
2
0
0
1
1
0
0
1
0
1
1
1
0
1
1
0
0
0
1
1
2
2
1
0
1
0
1
0
1
1
0
0
1
1
0
1
0
0
0
0
1
0
2
1
2
2
1
0
2
2
2
2
1
1
0
1
1
2
1
1
1
0
1
1
1
1
0
0
2
0
0
0
1
1
0
0
1
0
0
0
2
0
0
1
2
1
2
1
2
2
1
0
2
2
1
1
1
2
2
1
2
2
2
1
0
0
0
1
0
1
0
0
1
0
2
0
1
2
2
2
0
1
1
0
2
1
0
1
1
1
0
1
1
2
1
1
1
1
1
2
0
1
0
1
1
0
2
1
1
1
1
1
1
1
0
1
2
2
0
2
1
2
1
2
1
1
0
1
1
1
1
1
1
1
1
0
0
1
0
1
0
0
1
1
1
1
0
2
1
3
1
1
2
1
0
2
0
1
0
1
1
1
2
1
0
0
2
3
1
0
2
0
1
1
1
1
1
0
1
0
3
0
2
0
0
1
1
0
1
1
0
0
1
0
0
0
0
0
1
1
1
0
1
1
0
0
1
2
2
0
0
1
0
1
2
1
1
1
0
0
1
1
1
0
1
2
1
1
2
0
1
1
1
2
1
2
1
2
1
1
1
1
1
1
0
0
1
1
0
1
0
2
1
0
0
1
1
1
0
1
2
1
0
0
1
0
0
4
2
1
2
1
2
1
0
2
1
2
0
2
1
1
1
1
1
1
1
2
0
1
2
1
1
2
0
2
0
1
2
1
1
0
0
1
2
1
2
1
1
3
0
0
1
0
0
0
0
1
1
2
0
3
0
1
1
1
1
0
1
0
2
1
2
1
1
1
2
1
0
0
0
1
2
0
1
0
1
2
0
1
2
0
2
1
0
1
1
1
1
2
2
1
1
1
2
1
0
1
1
2
1
1
2
0
0
2
1
1
1
1
0
0
1
1
0
0
1
2
1
1
0
1
0
1
2
1
1
1
1
0
2
0
1
2
1
1
1
1
1
1
0
1
1
1
0
0
4
3
2
1
1
1
2
2
2
0
0
2
1
1
1
0
2
1
1
0
0
2
1
1
1
0
1
1
2
0
1
2
1
0
0
1
1
0
1
2
1
0
1
1
2
1
1
0
1
0
2
1
1
2
0
2
1
1
1
1
2
0
2
1
0
0
1
0
0
1
1
1
0
1
1
1
1
1
2
1
1
0
1
1
2
0
1
0
1
0
0
2
1
1
1
2
2
0
1
1
0
0
0
0
1
1
0
1
2
2
1
1
0
0
1
0
0
1
0
1
0
0
1
0
2
1
1
0
2
1
1
3
1
1
1
2
0
1
1
1
2
2
1
3
1
0
1
2
0
0
0
1
2
2
2
2
1
2
2
0
0
1
1
2
1
2
0
0
2
0
2
1
2
0
1
1
1
0
2
2
1
0
1
0
1
1
0
1
2
0
1
1
2
0
1
0
2
0
1
1
2
1
1
2
1
1
0
0
2
0
2
2
1
1
1
1
1
0
1
1
1
1
0
0
0
1
0
1
1
2
2
2
1
0
2
1
0
2
1
0
2
1
0
1
1
0
1
0
1
1
0
0
1
1
0
1
1
1
1
1
2
1
1
0
0
0
1
1
0
2
1
1
1
1
1
1
0
0
1
1
1
1
1
0
3
0
1
2
1
1
0
2
0
2
1
0
1
1
1
0
1
1
1
1
0
2
0
0
0
2
3
0
1
1
0
1
0
2
1
0
0
0
1
0
0
2
0
0
2
0
1
1
1
2
1
1
0
1
1
2
1
0
1
0
1
2
1
1
0
1
1
1
0
1
1
0
2
1
0
0
1
3
0
1
0
1
0
2
2
2
0
2
2
1
1
0
1
1
1
2
1
1
1
1
0
2
4
0
1
1
2
2
0
1
1
1
1
0
0
0
0
1
1
1
2
2
1
0
1
0
0
0
1
0
0
0
1
1
1
2
1
0
2
1
0
2
2
0
1
0
1
0
0
1
0
2
2
2
1
1
0
0
0
2
2
0
2
1
1
1
2
2
1
2
2
1
2
0
1
0
1
2
0
1
0
2
0
0
1
1
0
1
0
1
0
2
1
2
0
0
2
1
0
1
2
1
1
0
0
0
3
1
2
0
0
0
1
1
2
0
0
0
2
0
1
2
1
2
2
0
1
0
0
0
1
1
0
0
0
0
2
1
0
1
1
1
1
1
1
1
1
1
0
2
1
1
1
2
1
1
2
1
1
1
0
2
0
1
1
0
2
0
1
1
1
1
1
0
1
1
2
1
2
0
1
1
1
2
0
2
0
2
2
1
2
1
2
1
2
1
1
1
0
2
2
1
2
2
2
2
1
1
1
1
2
0
0
1
1
1
1
1
1
1
0
1
1
4
0
2
0
0
2
0
1
0
2
1
2
0
2
1
0
1
0
0
1
2
1
2
0
0
1
2
1
1
1
0
0
2
1
1
1
2
0
0
1
0
2
0
0
0
0
2
1
2
1
2
1
1
1
0
2
2
2
1
1
1
1
1
0
0
0
1
2
2
0
1
0
0
2
1
1
1
1
1
2
2
1
0
2
0
0
1
0
2
0
1
0
0
1
0
2
0
0
0
1
1
2
0
2
1
2
2
1
0
2
1
0
1
0
0
0
1
1
1
1
1
2
2
0
1
0
1
0
2
1
1
1
1
2
0
3
2
1
0
0
0
0
1
1
0
0
1
0
1
4
1
0
0
2
1
1
2
2
0
1
0
2
1
2
0
0
0
0
1
2
2
1
0
1
1
1
1
1
2
1
1
0
1
0
1
1
0
1
2
1
1
1
0
3
1
0
1
1
2
0
1
1
0
2
1
0
1
1
2
2
0
1
1
0
0
2
1
2
0
1
1
1
0
1
1
0
2
1
2
1
0
2
1
2
0
0
1
0
0
0
1
2
1
1
1
1
0
0
1
2
1
1
0
2
1
2
1
0
2
2
1
1
1
2
1
0
1
2
0
0
2
1
1
1
1
0
1
1
0
0
0
1
1
1
1
0
0
1
1
3
0
1
1
1
2
1
2
0
1
0
1
0
1
1
1
0
1
2
0
1
0
0
1
1
1
1
1
2
0
1
0
2
1
1
1
1
1
0
1
1
2
2
2
1
0
1
0
2
0
0
2
1
2
2
1
1
1
2
1
0
1
0
0
2
1
2
0
2
2
0
1
1
1
0
0
1
1
2
0
1
1
1
2
1
0
2
0
1
2
1
0
1
1
0
1
1
0
2
1
0
1
3
1
1
1
2
2
1
0
0
1
0
0
0
0
1
1
0
0
2
1
1
3
1
0
1
1
0
0
1
1
1
2
2
0
2
0
0
1
0
1
1
4
1
0
0
3
2
1
1
1
0
2
1
0
0
0
1
1
4
0
1
1
2
1
1
1
0
1
2
0
1
1
0
2
2
2
2
2
0
1
1
1
1
1
1
2
1
1
1
2
0
0
1
0
0
1
1
1
1
1
0
0
1
0
1
1
1
0
1
1
2
0
2
0
1
2
1
0
1
1
1
1
1
1
1
0
1
0
3
0
2
1
1
1
1
0
0
2
2
2
1
1
0
1
0
0
0
2
1
0
1
0
0
0
2
2
0
0
1
1
1
0
1
0
1
0
2
1
1
0
0
1
1
1
1
2
1
1
1
0
0
2
1
1
1
0
2
0
0
0
0
1
1
0
1
2
1
1
1
1
1
1
2
1
1
2
1
1
2
1
0
1
0
1
2
2
0
0
1
1
1
0
1
2
1
1
2
2
2
1
1
1
2
1
3
0
2
1
1
0
1
6
0
3
1
0
0
1
0
0
1
2
0
0
0
1
1
0
1
1
2
1
2
1
0
2
0
0
2
1
1
1
0
0
0
2
0
1
1
1
2
1
1
1
1
1
1
0
1
1
2
2
1
1
1
2
0
2
0
0
0
0
1
0
1
1
1
1
0
2
2
3
1
0
2
0
0
1
1
0
2
1
2
1
1
2
0
1
1
0
2
0
2
1
1
2
1
0
2
0
0
1
0
0
2
0
1
2
0
0
1
1
1
0
0
0
0
1
0
1
1
2
1
1
0
1
0
0
0
2
0
0
0
2
0
1
3
2
1
0
1
0
1
0
1
0
1
1
0
1
0
1
1
1
1
1
2
0
2
0
1
1
1
2
0
1
2
1
0
0
1
2
1
0
0
1
2
1
1
1
0
1
1
1
0
2
3
0
1
0
1
1
0
1
2
2
0
0
2
1
0
0
0
1
1
1
1
0
1
1
0
2
2
0
2
1
1
1
2
1
1
1
1
0
2
5
1
0
1
1
2
2
1
3
0
1
0
1
1
0
1
3
1
1
0
0
2
0
0
0
1
1
1
0
1
1
0
0
0
2
1
0
0
1
1
1
2
1
1
1
1
2
0
1
1
2
0
0
2
0
1
2
2
1
1
1
0
3
0
0
2
1
1
0
1
0
0
0
1
1
1
0
2
0
0
0
0
1
1
1
1
1
1
2
1
0
0
1
0
0
1
2
0
1
1
2
0
1
0
0
1
0
0
1
2
0
1
1
1
1
1
1
0
1
1
0
1
0
0
1
0
0
2
2
1
1
2
1
0
1
2
0
2
1
2
0
1
1
0
1
1
2
1
0
0
1
1
1
0
0
1
1
2
1
0
1
2
1
2
1
1
3
2
1
1
0
1
0
1
2
0
0
2
0
1
1
1
2
1
0
1
1
2
1
2
1
2
1
1
0
2
0
1
0
0
2
0
1
0
2
1
1
1
1
1
0
3
1
0
0
1
2
1
0
1
0
0
1
1
1
1
1
1
1
1
0
1
0
0
0
0
0
1
0
1
2
1
1
2
0
0
0
0
2
1
2
0
1
1
2
0
1
2
1
0
0
2
2
1
1
2
0
2
2
1
2
2
0
1
2
0
0
0
2
2
0
0
2
0
1
1
2
1
0
0
2
2
1
1
1
1
1
2
1
2
0
1
0
0
0
1
0
1
1
0
3
0
0
1
0
2
0
1
2
1
2
1
0
2
0
2
0
1
2
2
1
0
1
2
1
2
2
1
0
1
1
2
1
1
0
0
2
1
0
2
14
1
1
1
0
2
2
0
0
1
1
1
0
0
1
1
1
1
1
0
0
1
1
0
0
1
0
1
0
0
1
0
0
0
1
1
0
2
0
0
0
0
0
1
0
2
0
1
1
0
1
1
0
0
0
1
2
1
0
2
1
0
2
2
0
1
0
2
1
2
1
0
0
2
0
1
1
2
1
2
0
1
1
0
1
1
0
1
0
2
1
0
2
0
1
0
2
0
0
1
0
1
1
1
1
1
1
1
1
0
1
0
1
0
0
1
1
1
1
2
1
1
1
1
1
0
0
2
0
0
1
1
0
1
1
2
1
0
0
1
2
0
1
2
1
2
2
0
2
1
1
0
0
1
1
1
0
0
1
2
0
1
2
0
2
0
1
2
1
1
1
0
1
1
2
0
0
0
0
1
1
1
2
2
1
0
1
0
1
1
0
1
1
0
0
0
0
2
0
0
1
2
2
1
1
1
0
0
0
2
1
1
1
0
0
0
1
0
0
1
0
4
2
1
2
1
2
0
2
2
1
2
1
1
0
1
1
2
1
0
0
1
0
1
3
0
2
2
0
2
0
3
1
1
2
5
0
2
1
0
1
2
1
2
1
1
2
0
2
2
0
1
2
2
0
0
2
0
1
0
0
2
1
1
1
0
0
3
0
2
1
1
0
1
1
1
0
1
1
1
0
1
1
1
2
0
2
1
1
2
0
1
1
2
1
1
1
0
1
0
0
1
1
1
1
1
0
2
0
1
1
0
2
0
0
1
1
0
2
1
1
0
1
1
1
1
1
0
0
0
0
1
0
0
1
0
1
1
1
1
0
1
0
0
2
0
0
1
1
1
0
1
1
1
2
1
1
1
1
0
2
0
1
1
2
0
0
1
2
1
0
1
0
0
1
3
2
1
2
0
1
2
1
0
0
1
0
2
0
1
2
1
2
0
1
2
1
1
0
0
2
0
1
0
1
1
0
1
1
2
2
1
0
1
0
2
2
0
1
1
0
0
0
2
2
1
0
0
1
1
1
1
0
2
2
0
0
2
1
1
2
0
0
1
0
2
1
1
1
1
0
0
1
1
1
1
1
0
1
1
0
2
1
0
2
1
1
1
0
2
0
0
0
0
1
0
0
2
0
0
2
1
0
2
0
2
0
2
1
1
1
0
1
1
1
2
1
0
2
1
2
2
2
1
2
0
1
1
1
2
1
1
1
0
2
0
1
1
1
2
2
2
1
2
1
0
0
1
1
1
1
2
2
2
0
1
1
2
2
2
1
1
2
0
2
2
1
2
0
3
1
1
1
1
1
2
1
1
1
1
0
1
0
0
0
0
1
0
0
0
0
2
1
1
0
1
1
1
0
2
1
2
0
1
0
0
2
1
1
1
1
0
2
2
0
0
2
1
1
1
0
0
0
2
1
1
3
0
2
1
2
0
2
0
0
0
1
0
1
2
0
1
0
1
0
1
2
0
2
0
1
1
2
1
1
5
0
0
0
1
2
0
0
2
1
1
2
1
1
3
0
2
2
0
0
1
0
2
1
0
0
0
2
2
0
2
0
1
0
0
0
0
2
1
0
1
0
1
0
1
2
1
1
1
1
0
0
2
1
1
1
1
1
0
2
1
1
1
1
0
0
1
0
0
2
0
1
0
1
1
2
2
1
1
2
1
0
0
1
1
1
0
1
1
4
0
2
2
0
2
1
1
0
1
0
0
2
1
2
0
1
0
1
0
2
1
2
1
1
1
2
0
2
2
1
0
1
1
1
1
1
1
2
2
0
1
0
2
0
2
0
1
0
1
1
1
1
0
1
1
1
2
0
1
2
1
0
0
1
1
1
1
1
2
2
0
0
1
2
2
1
0
0
0
1
2
0
1
1
1
0
0
2
1
1
0
3
1
2
0
0
0
0
2
1
0
2
2
0
0
1
1
1
1
1
2
2
1
0
1
1
0
2
2
0
2
0
0
1
2
1
0
1
0
0
2
2
0
1
0
1
1
1
1
1
2
1
0
0
0
1
1
2
1
2
2
1
1
2
0
0
1
1
1
1
1
1
2
0
0
1
1
1
0
0
1
2
2
2
2
1
3
1
0
2
1
2
0
0
1
0
0
0
1
0
1
0
2
0
0
2
0
2
0
1
0
1
0
0
1
1
1
1
1
1
0
1
2
1
0
1
0
1
0
2
1
0
1
0
2
0
0
0
1
1
0
0
0
2
1
0
1
1
1
0
0
1
2
0
0
1
0
0
2
1
2
1
1
1
2
1
1
2
2
0
0
2
0
2
2
1
1
2
1
2
2
0
1
0
2
1
1
0
1
0
1
2
2
1
2
2
0
1
1
1
0
2
0
1
1
2
2
1
1
0
1
3
0
1
1
0
1
0
0
2
1
1
0
2
1
1
0
1
1
1
0
2
1
1
0
2
1
0
0
2
0
1
2
1
0
1
0
0
2
1
2
1
0
1
1
2
0
0
1
0
0
1
2
2
1
0
0
0
2
0
2
0
1
0
0
0
0
1
1
0
1
2
2
2
1
2
2
0
0
1
0
2
0
1
1
2
2
0
1
0
1
0
0
1
0
1
0
1
1
1
4
1
2
2
2
0
1
1
1
2
1
1
1
1
0
3
1
1
0
0
1
0
1
2
2
0
1
1
1
0
2
0
0
2
0
1
0
1
1
1
0
0
2
2
1
0
3
2
2
0
0
0
1
0
1
0
0
2
1
2
0
2
1
1
2
1
0
1
0
0
2
1
2
0
1
2
1
1
1
2
2
1
1
0
1
1
1
1
1
0
2
0
1
0
1
1
1
1
0
1
1
0
1
0
0
1
0
2
2
0
2
1
1
0
1
2
2
1
2
0
0
1
2
0
1
2
0
0
0
1
2
2
2
1
0
1
1
1
1
0
2
1
1
1
1
1
2
2
1
1
0
0
2
2
1
0
2
2
2
0
1
2
1
0
2
0
2
1
2
1
1
2
0
0
1
1
2
1
0
3
1
1
1
1
0
1
1
1
2
1
1
0
0
1
1
2
1
0
0
1
0
2
0
2
2
1
1
1
0
0
0
2
0
0
2
1
1
1
1
3
1
0
2
2
2
2
0
2
1
2
2
2
2
1
1
0
1
0
0
0
1
1
0
0
2
0
1
1
0
1
1
2
1
2
1
1
1
2
1
2
1
1
2
1
2
2
2
1
0
2
1
1
2
0
2
0
1
2
1
1
2
1
0
1
2
1
1
1
1
1
0
1
0
0
0
2
0
0
2
0
0
1
2
1
1
2
0
1
0
0
2
1
1
0
2
1
1
0
1
0
0
1
0
1
1
2
2
2
1
0
0
2
0
1
2
0
1
1
2
2
1
0
2
2
2
2
1
0
1
1
1
1
1
1
0
1
1
2
0
1
1
1
0
2
1
0
0
1
1
2
2
0
1
2
0
0
1
1
1
1
0
1
0
0
1
0
1
2
1
1
2
1
0
0
3
0
2
1
1
3
2
0
2
0
1
1
0
1
2
1
1
1
1
1
2
1
0
0
2
1
2
1
0
1
0
0
1
1
2
2
0
2
1
1
1
1
2
0
1
1
1
1
1
0
2
0
1
1
0
2
1
1
1
0
1
1
2
0
1
1
0
0
2
0
1
0
2
0
0
1
2
0
0
1
1
2
0
1
2
1
1
1
2
1
0
1
2
0
1
0
0
0
1
1
1
2
2
0
2
1
0
1
1
1
2
0
1
0
0
1
2
0
1
1
2
1
2
1
1
1
1
0
1
1
0
2
0
2
0
1
1
0
2
1
1
0
5
0
1
1
1
2
1
0
0
0
1
0
0
0
2
1
1
1
2
2
2
1
2
0
0
1
2
1
0
1
0
1
1
0
2
0
0
2
0
1
1
1
2
1
2
1
2
2
1
0
0
1
0
2
3
0
0
0
1
1
2
1
2
1
1
0
0
0
1
1
0
1
1
0
1
0
1
0
1
2
1
2
1
0
0
2
1
0
2
1
1
1
0
2
0
3
1
0
1
0
0
1
0
0
0
2
1
0
1
1
0
1
1
0
1
1
1
1
1
1
1
1
2
1
1
1
0
1
2
2
1
2
1
1
1
1
1
0
1
1
0
1
2
0
1
1
0
0
2
1
1
1
0
0
0
1
1
0
1
2
2
1
1
0
0
0
1
2
1
1
1
2
0
1
0
1
1
0
1
0
0
1
0
1
2
0
2
2
1
1
0
1
0
1
1
0
1
1
1
0
0
1
2
0
2
2
0
2
0
0
2
2
2
0
0
0
1
0
0
1
0
0
1
1
1
2
0
0
1
1
0
1
1
1
1
1
2
1
0
1
2
2
0
1
1
0
1
1
2
1
3
0
0
1
1
0
0
0
0
1
0
2
2
0
2
1
1
1
2
0
0
2
1
1
2
2
0
1
1
1
1
2
0
2
0
1
1
1
0
1
1
1
2
1
0
1
2
1
1
1
0
1
1
1
1
1
0
0
1
1
1
2
2
1
1
1
3
1
0
1
1
1
2
1
2
1
1
2
0
0
2
2
2
1
1
1
1
0
2
1
1
1
0
1
1
0
1
3
1
0
2
0
0
2
1
1
1
0
1
1
1
2
0
2
1
2
1
2
1
1
2
1
2
1
1
2
0
1
1
1
1
2
0
1
2
0
0
2
2
1
1
2
0
2
0
1
2
1
2
1
0
0
2
0
0
1
1
0
1
2
0
0
0
0
1
1
1
0
1
1
2
0
1
1
1
1
2
2
1
1
0
4
1
1
1
2
0
0
0
1
1
0
1
1
1
0
0
2
0
1
2
2
2
1
1
1
0
1
2
0
1
1
0
1
0
0
1
1
1
2
2
1
0
0
0
2
2
1
2
2
1
2
0
2
0
0
1
1
0
0
2
0
0
0
1
0
3
1
1
1
1
2
0
0
1
0
1
0
1
1
1
0
1
0
2
2
1
1
1
1
0
1
2
1
1
2
1
1
0
2
2
1
1
2
0
0
0
1
0
0
2
1
0
1
1
2
0
0
2
0
2
1
1
2
0
2
0
2
0
1
1
0
0
1
0
1
2
0
1
1
0
0
0
1
2
2
1
1
1
1
2
1
0
2
2
0
1
1
0
0
1
0
1
2
1
1
2
2
2
1
0
0
0
0
0
1
2
1
0
0
1
2
2
1
1
1
1
1
0
0
1
2
1
1
2
1
1
0
3
1
2
2
0
3
0
1
0
2
0
2
0
1
0
1
1
1
1
1
5
1
1
1
3
1
0
0
1
0
1
1
2
0
2
2
1
1
0
1
2
1
0
1
0
1
0
1
1
1
1
0
1
0
2
2
1
1
1
0
1
0
2
2
2
1
2
0
0
2
0
2
2
0
2
1
0
1
0
1
0
2
2
1
1
0
0
1
0
0
0
1
3
1
2
1
0
2
1
2
2
1
2
2
1
3
1
0
0
0
0
1
0
2
2
3
1
0
1
0
1
0
1
0
0
1
0
1
0
2
1
1
0
2
1
0
1
1
1
2
1
2
2
0
0
1
1
1
1
1
2
1
1
0
3
2
1
1
1
1
1
0
0
0
1
2
0
2
1
0
1
1
0
2
1
0
1
0
2
1
0
1
1
2
2
1
1
0
0
3
0
1
0
2
0
0
0
2
2
2
2
1
2
1
2
2
0
0
0
0
2
1
1
0
2
2
2
0
1
1
0
5
1
1
2
0
1
0
0
0
1
0
1
1
1
0
1
1
1
0
2
1
1
2
0
0
2
2
2
1
2
1
2
1
2
1
1
1
2
0
1
1
1
1
1
2
0
0
1
1
1
2
1
2
0
2
1
2
1
1
1
1
1
1
1
0
2
1
1
2
1
1
0
1
1
1
1
1
1
0
1
1
2
1
1
1
2
0
2
0
2
0
0
0
3
1
0
0
1
1
0
2
0
0
1
1
0
1
1
1
0
1
1
1
1
0
1
0
0
0
1
1
0
0
2
0
1
1
1
1
2
1
0
2
0
1
1
0
2
0
0
1
2
1
1
0
1
1
1
0
0
2
0
1
0
1
0
1
2
1
0
1
0
1
1
1
1
1
1
1
1
1
0
1
0
1
2
0
1
2
1
1
1
2
0
0
2
2
2
1
1
0
0
2
1
0
1
0
1
1
0
2
0
0
1
2
0
0
2
2
4
0
0
1
0
1
1
1
2
0
1
0
0
0
2
1
1
0
1
0
0
0
1
2
0
1
1
1
1
0
0
0
1
1
2
2
1
1
0
1
0
2
0
1
1
3
2
1
1
1
1
0
1
0
1
1
1
0
0
2
0
5
1
1
1
1
1
1
2
1
0
1
0
1
1
2
1
1
1
1
1
1
3
0
2
1
1
1
0
0
1
1
0
1
0
0
0
3
0
0
0
2
1
1
0
0
1
0
1
1
0
0
0
1
0
0
1
0
1
1
1
0
1
1
1
1
1
2
1
0
0
0
2
0
2
0
2
1
1
2
0
0
1
0
1
1
1
2
2
2
2
1
1
1
0
0
2
0
0
0
1
0
0
0
2
1
2
2
1
1
1
2
1
1
1
1
0
1
1
0
0
2
0
0
0
0
2
1
1
0
1
0
1
1
2
2
1
0
1
1
1
1
0
1
0
1
1
1
2
0
1
1
3
1
2
1
0
1
2
1
1
1
1
1
2
0
0
1
0
1
2
0
0
0
1
0
0
2
2
1
0
0
2
2
1
2
1
1
0
0
0
1
1
2
2
1
1
0
1
1
1
0
2
1
0
1
1
0
2
1
1
1
1
2
1
2
2
1
1
0
1
1
2
1
1
1
2
1
0
1
1
0
2
1
2
1
1
1
0
1
1
0
1
1
1
1
1
0
0
2
0
2
0
2
0
2
0
0
1
2
1
1
0
1
1
2
2
1
0
0
1
1
1
1
0
0
1
3
1
1
0
1
1
0
0
2
0
1
3
1
1
1
0
0
2
2
2
0
1
1
1
1
1
1
0
1
1
0
1
0
1
1
0
1
2
1
2
0
0
1
1
2
1
1
1
0
1
1
0
2
2
0
0
0
2
2
0
0
0
1
3
2
1
1
3
1
1
1
1
0
0
1
1
1
1
1
0
1
5
1
1
3
0
1
0
1
1
0
0
2
0
2
1
1
1
1
2
0
2
1
1
1
0
2
0
1
1
1
0
0
0
0
0
2
1
0
2
2
2
2
2
1
0
0
2
1
0
2
2
0
2
2
2
1
1
1
2
0
1
1
1
1
1
2
0
0
1
1
1
0
1
1
2
1
1
1
1
1
0
1
2
2
1
2
1
1
2
2
1
1
1
2
1
0
1
1
1
0
1
2
2
0
1
0
4
1
1
1
1
0
2
1
0
2
0
2
0
2
2
2
1
1
0
2
2
1
1
1
0
1
0
2
2
1
0
1
1
1
1
1
0
1
0
0
1
1
1
2
0
1
1
0
2
1
1
2
1
2
0
2
2
2
1
1
0
2
1
1
0
1
2
1
1
1
1
0
2
1
0
1
1
0
1
1
0
2
2
2
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
0
7
2
1
1
2
1
0
0
2
2
0
2
5
2
1
2
0
1
2
2
0
1
1
1
2
1
4
0
1
1
2
2
1
0
1
1
1
1
0
1
1
2
0
2
2
0
2
0
2
1
1
2
2
1
1
2
0
2
1
0
0
2
1
0
2
0
1
0
0
0
0
0
2
2
1
0
3
0
1
2
1
1
0
1
1
1
2
1
1
2
1
0
1
0
1
1
0
1
0
0
2
2
1
1
2
0
1
0
0
0
1
0
1
1
3
2
0
5
1
1
0
1
0
0
1
0
1
1
2
1
0
2
0
0
0
1
1
1
3
2
2
0
1
2
1
1
0
2
0
0
1
1
1
1
1
1
1
1
1
1
1
0
1
2
1
2
1
1
2
1
2
0
1
0
1
0
2
1
1
1
1
2
0
1
1
2
2
1
1
1
2
1
1
1
1
0
1
1
2
1
1
2
2
2
1
1
0
2
1
1
0
1
1
1
2
0
1
1
1
1
1
1
2
0
1
0
0
1
0
0
1
0
2
1
2
0
1
0
1
2
1
0
1
0
2
1
1
1
1
0
1
1
1
1
0
1
1
1
0
2
1
1
1
1
2
0
2
0
1
0
1
2
0
0
1
0
2
1
1
1
1
0
2
2
0
1
1
1
1
1
1
1
1
1
0
1
0
1
1
2
0
2
2
1
2
2
0
1
0
0
2
0
1
1
2
0
1
1
2
1
2
4
1
2
0
1
2
2
1
0
1
0
1
1
1
1
1
3
1
0
0
1
0
1
1
0
0
2
2
0
0
0
0
1
3
0
0
0
2
0
0
3
2
0
1
0
0
1
0
1
2
3
1
1
1
1
1
1
1
1
1
1
1
2
0
0
0
2
2
1
1
1
2
1
1
0
1
2
2
0
2
1
0
0
2
1
1
2
0
0
0
1
1
1
0
1
1
0
2
1
1
2
2
1
0
1
0
5
2
2
0
1
3
1
0
2
1
1
1
2
1
3
2
0
0
1
2
1
0
0
0
2
0
1
1
3
1
1
0
0
2
1
2
2
0
2
1
1
0
2
1
1
1
0
0
2
1
1
0
1
0
1
1
2
0
0
2
1
1
3
1
2
1
0
1
1
0
2
1
1
3
1
2
1
1
2
0
0
1
1
0
1
1
2
0
2
1
0
1
1
0
0
1
1
1
0
0
2
0
1
1
2
0
1
1
0
1
0
1
0
1
1
0
2
2
1
0
2
1
1
1
0
0
0
3
1
1
1
1
2
1
1
0
0
1
2
0
2
1
1
0
1
0
2
0
0
1
1
2
1
1
0
1
1
1
0
2
0
1
0
2
1
0
1
0
0
2
0
1
2
1
1
2
1
1
0
1
1
1
0
2
0
1
2
1
2
0
3
1
1
0
0
0
1
1
0
2
0
1
2
2
1
2
2
0
0
1
0
2
1
1
0
0
2
1
1
1
1
0
1
1
4
0
0
0
0
2
0
2
1
0
0
0
1
1
1
1
0
1
2
2
1
2
1
1
1
1
0
0
1
2
0
2
1
0
0
2
0
2
1
1
1
1
2
0
2
0
1
0
2
1
1
1
3
0
1
1
2
0
1
1
1
1
1
2
0
2
1
1
0
1
1
0
2
1
1
2
2
1
0
1
2
1
0
1
2
2
0
1
0
0
1
1
1
0
1
0
1
2
1
0
0
1
0
1
1
0
1
2
0
0
1
1
1
1
2
0
0
3
1
1
2
0
1
0
1
1
1
0
0
0
1
2
0
0
2
0
0
1
1
1
1
1
1
2
0
0
0
1
2
2
1
0
1
2
1
2
0
0
2
2
0
0
1
0
0
0
0
0
2
2
1
0
1
0
1
1
0
2
0
1
2
1
1
1
1
1
1
1
0
1
0
1
0
0
3
0
0
2
5
0
0
0
1
0
2
0
0
1
2
1
0
1
1
1
0
1
0
1
1
2
1
0
1
2
1
1
2
1
2
1
0
0
0
1
2
1
3
0
2
0
1
3
1
0
0
1
2
2
0
2
1
1
1
0
2
1
1
2
1
2
1
2
2
0
1
1
1
0
2
1
2
1
1
2
1
0
1
1
1
1
1
0
2
0
2
1
0
2
2
1
2
0
2
2
1
0
0
1
1
0
1
2
0
1
1
1
1
0
1
2
1
0
1
0
2
2
0
2
1
2
2
1
1
1
2
2
1
2
1
0
2
0
2
1
2
1
2
2
0
2
2
1
1
0
0
1
0
0
1
0
2
1
0
0
1
0
1
1
1
1
2
1
0
0
1
0
3
1
2
0
2
0
0
1
1
2
0
0
2
1
0
0
1
1
1
0
0
1
1
2
0
2
1
1
1
1
1
2
0
0
1
1
1
2
2
1
2
0
1
2
1
1
0
1
2
0
1
1
1
2
0
2
2
1
2
2
0
0
0
1
0
1
0
1
0
1
0
0
3
2
1
0
2
1
2
1
2
0
2
0
1
1
1
0
1
1
2
2
2
0
0
0
1
0
4
0
1
1
1
2
2
1
0
2
1
2
1
2
1
2
0
0
0
1
1
0
0
0
1
1
1
0
1
1
1
0
0
0
2
1
0
0
0
1
0
1
0
0
1
1
1
1
1
0
1
1
1
2
1
2
0
1
2
1
0
0
0
2
1
3
1
1
1
1
1
1
1
1
2
1
0
1
1
1
0
1
0
1
1
1
1
1
1
2
2
2
0
2
0
1
2
1
1
1
1
0
1
1
1
0
0
1
0
2
1
1
1
0
0
1
2
1
0
0
2
2
0
1
1
1
0
2
0
0
2
0
1
3
1
1
1
1
0
1
2
1
0
1
0
2
0
1
0
0
0
2
1
0
0
0
1
0
3
1
1
1
3
1
1
0
1
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
2
2
1
2
1
1
0
2
0
1
1
0
1
1
1
1
1
2
1
2
2
1
0
1
1
1
0
1
1
1
2
0
1
1
2
1
2
3
1
2
1
1
1
1
2
1
2
1
1
2
1
1
0
2
0
1
2
4
1
0
0
1
1
1
1
1
2
0
0
2
2
1
0
1
1
2
2
1
2
1
0
1
1
0
2
1
1
1
0
2
0
0
1
0
1
0
1
1
1
1
2
0
1
0
1
1
1
1
0
1
0
0
0
0
0
1
0
1
0
0
1
2
0
0
2
2
0
0
0
1
2
2
0
1
2
1
1
1
0
0
0
0
1
0
2
2
1
1
2
1
0
1
0
1
1
1
1
0
0
1
1
1
0
0
1
2
0
2
0
1
1
1
2
1
2
1
1
2
0
0
0
2
2
0
2
2
1
0
3
0
2
0
1
0
0
3
1
0
0
0
0
0
1
0
2
0
0
2
1
0
1
1
1
0
0
0
0
1
0
0
2
2
1
1
1
1
1
0
0
0
1
1
2
0
1
1
1
0
2
0
2
2
1
2
0
0
0
0
1
0
1
3
1
2
1
1
0
0
1
1
2
0
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
0
0
1
0
0
2
1
0
0
1
1
1
1
0
2
2
1
1
1
1
0
1
1
1
1
1
1
1
1
1
3
0
2
1
1
1
1
2
4
1
1
1
1
2
0
0
2
1
0
1
1
0
2
2
0
2
1
1
1
0
1
2
1
0
0
1
1
1
1
1
1
0
0
0
2
0
1
1
1
1
0
0
2
1
1
0
1
0
1
0
1
1
1
2
1
1
0
1
0
2
1
0
1
1
1
1
2
6
2
1
1
0
2
0
1
0
1
2
1
0
1
0
0
1
1
0
1
1
1
1
0
1
1
1
1
0
0
1
1
0
2
1
0
1
0
1
0
1
0
2
0
0
0
1
0
2
0
2
1
1
0
0
2
2
1
1
1
1
1
1
1
1
2
1
2
0
2
0
1
1
0
1
0
2
0
1
3
1
0
2
2
1
1
2
1
1
2
2
2
1
1
1
0
1
0
2
1
2
0
2
0
2
1
1
1
0
0
1
0
1
0
0
2
1
2
1
1
1
0
1
1
2
0
2
1
1
2
0
1
1
0
0
1
0
0
1
0
0
2
1
0
2
2
2
1
1
1
1
0
1
2
2
1
1
0
0
1
1
0
0
2
1
1
1
1
1
2
1
1
1
0
2
3
1
1
0
2
0
0
1
1
0
2
1
1
1
2
2
0
2
1
1
2
0
0
0
1
1
2
1
1
1
0
1
0
2
1
2
2
1
1
0
1
0
1
0
2
1
0
1
1
1
0
1
2
1
0
0
0
1
1
0
1
0
1
1
1
1
0
2
6
2
2
2
2
2
0
1
0
2
0
0
1
0
1
1
2
0
0
0
1
1
1
1
1
0
2
2
1
1
2
0
2
1
1
0
0
0
1
0
0
2
1
2
2
0
0
0
0
1
0
0
1
3
0
0
1
0
0
2
1
0
1
1
1
2
1
1
0
1
1
2
0
1
1
1
2
1
3
0
2
0
0
0
1
1
3
1
1
1
2
2
1
0
2
2
1
1
2
0
0
0
1
0
1
0
2
1
3
2
1
2
1
1
0
1
1
2
1
1
2
1
1
1
0
0
1
2
1
1
1
2
0
0
1
1
1
1
0
0
1
0
1
0
1
0
1
2
0
2
1
1
0
0
2
1
1
0
2
1
2
2
2
1
0
0
0
1
0
2
0
1
0
1
0
2
0
0
1
0
0
1
1
0
3
1
1
1
1
1
1
0
2
2
2
1
0
2
1
0
1
1
1
0
2
1
2
1
0
1
1
1
0
1
0
1
1
2
2
0
1
1
1
1
1
1
0
2
1
2
1
1
0
0
0
0
0
2
0
8
1
0
2
0
2
1
1
1
1
2
1
2
0
1
2
2
1
0
0
1
2
0
1
2
1
2
1
0
2
1
1
1
1
2
0
1
0
1
0
2
0
2
0
1
1
1
1
2
1
1
3
1
1
1
0
0
2
1
1
2
1
1
1
1
2
0
0
2
0
1
0
0
2
1
0
1
1
0
1
1
1
1
0
1
1
1
2
1
1
1
1
1
1
1
0
1
3
1
2
2
0
0
2
1
0
1
2
0
1
2
1
0
0
1
1
0
2
1
2
0
1
0
1
2
1
1
1
0
0
0
0
1
2
1
0
0
1
0
1
1
1
0
0
1
1
2
2
1
0
2
2
1
2
1
2
1
0
1
1
1
0
1
2
2
1
1
0
1
0
2
0
1
1
1
1
0
2
1
2
1
1
0
1
0
1
0
2
2
1
1
1
1
2
1
1
0
1
0
1
3
1
0
1
0
1
1
0
1
1
2
0
0
1
1
0
4
1
1
2
1
2
1
1
1
0
1
1
2
0
1
0
1
1
2
2
1
0
1
1
0
1
1
2
1
1
2
1
0
1
0
1
0
2
0
0
1
0
0
1
1
2
0
0
1
0
1
1
1
0
1
2
1
0
1
0
0
1
1
1
1
2
1
2
0
1
2
2
1
0
1
1
0
2
1
2
0
1
1
1
0
0
2
1
2
2
1
1
2
1
1
1
1
3
2
0
2
1
0
1
0
1
0
0
2
0
1
1
1
1
0
2
1
2
0
0
2
0
1
1
1
2
2
0
1
0
0
1
1
1
1
2
2
1
1
1
1
0
1
2
1
1
0
0
2
1
0
0
1
2
0
1
2
1
1
0
1
2
1
0
2
2
2
1
1
1
2
0
1
2
0
0
1
1
1
1
2
1
0
0
2
1
2
0
1
2
1
2
0
0
1
1
0
2
0
1
0
1
1
1
2
0
1
2
0
0
2
1
2
1
1
1
0
0
1
0
0
2
0
1
1
0
1
1
0
1
1
1
1
0
1
1
1
1
1
0
1
2
1
0
2
0
0
1
0
0
0
1
1
0
0
0
1
0
1
2
0
1
0
1
1
1
1
2
0
0
2
0
2
1
1
1
1
0
0
1
1
0
0
0
0
1
1
1
1
2
1
1
2
2
1
1
2
0
3
2
0
1
1
1
0
0
1
1
1
1
0
1
0
0
1
0
0
1
1
0
0
2
2
0
0
0
1
1
1
1
0
1
1
0
1
2
0
2
1
1
2
1
0
1
0
0
1
1
1
0
0
1
2
1
0
0
0
0
1
1
1
2
0
2
2
1
1
0
1
2
1
2
0
0
1
1
0
0
0
2
1
2
3
2
2
1
0
1
0
1
0
1
1
0
0
1
1
0
2
2
1
1
2
1
1
1
2
1
1
2
0
0
0
0
2
0
0
1
2
2
0
0
1
1
0
0
0
0
2
0
1
2
2
1
1
2
0
0
2
0
0
1
0
1
2
1
1
0
0
1
0
1
1
0
2
0
2
1
0
0
0
1
1
2
1
0
1
1
0
0
1
1
2
0
2
2
0
1
2
0
1
1
2
1
2
2
0
0
2
2
1
0
0
0
1
1
1
1
1
2
1
0
0
0
1
1
1
0
0
2
1
0
4
0
1
0
1
1
2
3
0
1
0
0
1
1
1
0
0
1
0
0
0
1
1
0
1
2
1
0
2
1
1
1
2
1
2
1
1
0
0
0
1
0
0
0
2
1
1
0
1
1
1
1
1
0
2
1
1
0
0
0
2
1
1
1
0
1
1
1
0
0
2
0
2
0
1
1
2
1
1
1
2
2
0
1
1
1
1
1
1
1
1
0
2
1
2
1
1
1
0
2
1
2
0
1
0
1
0
0
1
0
1
0
0
1
0
2
0
2
1
0
1
0
2
1
1
1
2
1
0
1
1
2
1
2
0
0
0
0
0
1
1
1
1
1
2
0
2
1
0
0
0
2
2
2
0
0
1
1
0
1
1
0
1
0
1
1
0
1
0
2
1
2
1
0
1
2
2
2
2
1
2
1
1
1
1
0
0
2
1
1
0
1
0
0
1
0
1
1
1
2
0
2
0
0
0
2
1
0
1
1
2
1
2
1
1
1
1
2
1
1
2
1
0
0
1
0
1
0
2
0
1
0
0
0
2
0
1
1
0
2
2
0
0
2
2
1
1
0
1
0
2
2
1
3
2
0
1
0
1
0
0
1
1
1
1
1
1
1
1
1
1
2
0
0
2
0
1
1
2
1
0
1
1
0
2
0
2
1
0
1
0
0
2
1
0
1
1
0
0
2
1
0
0
2
0
0
1
0
1
1
1
1
1
0
1
1
2
2
1
0
1
1
0
0
0
1
1
1
1
0
2
1
0
0
0
1
0
1
1
1
1
0
1
0
1
1
1
2
1
1
2
2
1
0
0
1
2
0
0
2
0
0
1
0
2
2
1
0
1
1
1
2
1
2
2
0
0
1
1
0
1
1
0
1
1
0
0
1
2
2
2
0
1
0
0
0
1
0
1
0
1
1
0
0
0
1
1
0
1
2
1
1
0
0
0
1
0
0
1
1
1
1
0
1
1
0
1
0
1
0
1
0
0
0
1
1
1
0
1
0
2
1
1
1
0
1
0
0
0
1
1
1
1
1
2
0
1
0
0
2
1
1
0
0
3
2
0
2
0
2
1
1
1
0
0
1
0
2
0
1
0
1
1
0
2
0
1
1
3
1
0
0
2
0
1
0
2
1
2
1
1
0
0
1
1
1
0
1
1
1
0
2
1
1
0
2
2
2
2
0
0
0
1
0
2
2
1
1
1
2
2
0
0
2
1
2
1
1
2
2
2
1
1
1
2
2
2
2
2
1
0
1
0
1
0
1
0
0
2
0
1
0
1
1
2
2
1
1
1
3
1
0
1
1
1
0
0
1
1
1
1
0
0
1
0
0
1
1
0
1
1
0
2
2
0
0
2
1
2
2
0
2
1
0
2
1
1
1
1
1
2
1
0
1
0
0
1
2
4
0
0
0
1
1
1
1
2
2
0
2
0
1
0
1
0
1
2
0
2
1
2
1
2
2
1
1
0
1
1
1
1
1
1
0
1
1
0
1
1
1
2
2
1
0
1
1
2
2
1
2
0
2
0
1
3
1
1
2
0
0
1
0
1
2
0
0
1
1
0
1
1
2
0
0
1
1
1
1
1
0
2
1
0
1
1
1
1
2
1
1
1
1
2
2
1
1
0
0
2
1
2
1
1
1
1
0
1
0
1
1
2
1
1
1
2
2
0
0
2
2
1
1
2
1
0
1
0
0
2
2
1
1
1
1
1
1
2
2
1
2
0
0
0
1
1
2
0
1
4
2
2
0
2
1
2
2
0
1
1
1
1
2
1
1
2
1
0
1
1
1
0
1
4
1
0
0
1
1
1
1
1
1
1
1
2
0
1
0
1
1
1
1
2
0
0
1
2
0
0
1
2
1
2
1
0
2
1
2
0
0
1
0
1
1
0
1
2
2
1
2
0
0
1
0
1
0
0
0
0
0
1
1
0
1
0
1
0
1
0
2
2
1
2
1
2
2
1
0
3
0
0
1
1
0
0
1
1
1
2
0
1
1
1
2
1
2
0
0
0
0
0
2
2
1
1
1
1
0
1
2
2
1
1
1
1
1
2
2
1
0
1
0
1
0
1
1
2
0
0
2
3
0
0
0
2
0
1
1
1
2
2
0
2
1
1
1
1
0
2
1
1
0
0
1
0
0
2
1
1
1
0
1
1
2
1
1
2
2
0
1
0
1
2
3
1
1
0
1
1
1
0
1
1
1
0
2
0
1
0
0
1
1
1
2
2
2
1
0
1
2
1
0
3
1
2
1
1
1
1
1
0
1
1
0
2
0
1
1
2
1
1
1
2
1
2
1
1
0
1
1
0
1
2
0
1
1
0
2
1
1
2
1
2
1
2
1
1
1
1
1
1
2
1
1
0
1
2
1
0
3
1
0
1
1
1
0
0
2
2
1
1
1
0
2
0
2
1
1
1
2
1
0
0
1
1
2
1
1
2
0
0
1
0
0
1
1
1
0
1
2
2
0
1
1
2
2
1
2
1
1
3
0
0
1
1
1
1
1
0
1
1
1
1
1
2
1
1
0
2
1
0
1
1
1
1
0
2
1
2
2
0
1
2
1
1
1
1
2
0
1
0
0
2
0
2
1
2
1
1
0
1
1
1
1
2
0
1
1
0
0
2
1
0
2
2
0
1
1
1
0
0
2
1
1
0
0
0
0
1
3
1
0
1
1
2
0
1
0
1
2
1
1
1
1
1
0
0
0
1
0
0
1
1
1
1
1
0
2
1
1
0
1
0
1
1
2
1
2
1
1
0
0
1
1
1
0
2
0
0
1
0
2
0
1
1
0
0
1
1
1
2
0
1
0
2
2
1
1
1
2
1
1
1
1
1
1
1
2
2
1
1
0
0
1
1
0
2
2
1
1
1
0
1
1
2
1
1
2
1
1
0
2
1
0
2
1
1
1
0
2
1
0
0
0
1
3
0
2
1
1
1
1
1
1
2
1
1
1
1
0
0
0
2
0
1
2
2
0
1
2
2
1
0
2
2
0
0
3
2
1
0
2
1
0
1
0
1
1
1
0
2
0
1
0
2
2
1
2
0
0
0
1
2
1
1
1
0
1
1
0
1
0
0
0
1
1
0
2
1
1
1
1
2
0
0
0
0
2
2
1
1
1
0
0
1
2
0
3
0
0
1
1
0
1
1
0
1
1
0
2
2
0
1
0
0
2
2
1
2
1
0
2
1
0
0
1
0
0
2
1
1
1
2
1
0
0
1
0
2
0
0
1
2
1
1
1
1
0
1
2
1
2
0
2
1
1
2
0
0
0
1
1
1
1
2
2
1
0
2
2
2
1
1
1
0
0
1
0
0
1
0
1
1
0
0
1
0
1
0
2
0
1
0
2
2
1
0
0
2
1
0
1
0
0
1
2
1
2
2
1
0
0
2
0
1
0
0
0
1
0
1
1
2
0
1
1
1
1
0
1
1
0
1
1
0
1
2
2
2
1
0
1
0
1
1
2
2
1
0
2
0
1
1
1
2
2
1
0
0
2
1
6
1
1
1
0
0
1
4
2
2
0
2
0
0
2
2
0
1
0
2
1
1
2
1
2
0
0
2
1
1
1
1
0
2
2
0
0
0
1
2
1
2
0
1
0
0
0
0
0
1
1
2
2
2
1
0
0
1
1
0
1
0
0
1
2
2
0
0
1
1
0
3
0
1
0
0
2
0
0
0
1
0
0
2
1
1
1
1
0
1
2
0
1
0
1
1
2
0
1
0
1
0
1
1
2
1
0
1
1
0
1
2
2
0
0
0
0
2
2
0
1
0
0
1
2
1
0
2
2
0
2
2
1
3
0
1
1
2
2
0
1
1
0
1
1
2
3
2
1
2
0
0
2
1
2
1
0
4
1
0
0
2
2
0
1
2
1
0
1
0
1
0
1
1
1
1
0
2
2
0
1
1
1
0
0
0
2
1
0
0
2
0
0
1
2
0
0
1
0
2
0
2
0
1
2
2
2
1
1
1
1
0
4
0
1
1
2
1
0
1
0
0
0
1
0
1
2
2
2
1
0
0
2
2
1
0
2
0
0
0
0
0
0
0
1
0
2
1
1
0
0
0
1
0
0
2
1
1
1
2
1
1
1
0
1
2
2
1
0
1
0
1
0
1
0
2
2
0
0
0
0
2
1
1
1
1
2
2
2
1
2
0
0
0
2
0
1
0
1
2
1
1
2
0
1
2
2
0
0
0
0
1
1
1
1
0
2
1
1
1
0
1
1
1
1
1
0
1
1
0
0
0
1
2
2
2
2
1
0
1
5
2
1
0
2
1
0
1
2
2
1
1
1
2
0
1
1
1
1
0
0
1
1
2
0
1
2
1
2
1
0
1
1
0
1
2
0
0
0
1
1
0
2
1
0
2
1
2
1
2
2
2
2
0
0
1
0
1
2
1
2
0
0
1
1
0
0
1
1
0
2
1
1
1
1
0
2
3
2
1
1
2
2
0
0
1
0
0
0
2
0
1
1
1
1
0
1
0
2
1
1
0
1
1
1
0
2
1
1
0
2
0
2
0
2
1
2
1
0
0
2
0
1
0
1
1
0
0
2
1
2
1
1
2
1
1
1
0
0
1
1
0
0
0
0
2
2
0
1
2
1
1
1
2
0
1
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
2
0
2
1
1
0
1
1
0
0
0
0
0
0
2
1
0
0
1
2
0
1
0
0
2
2
1
1
0
2
1
1
1
0
1
1
1
1
2
0
0
2
1
2
3
0
1
0
2
0
1
1
1
2
0
0
0
1
1
1
0
1
1
1
0
0
0
1
1
2
1
1
2
1
1
1
2
1
0
2
0
2
0
2
1
1
2
2
1
2
1
0
2
1
0
1
1
2
0
1
1
0
1
1
1
1
0
1
1
2
2
1
1
2
0
0
1
0
0
1
2
2
2
0
0
1
1
1
1
1
2
1
0
2
1
2
0
2
1
0
2
1
0
1
2
1
1
1
1
0
1
0
0
2
1
1
2
0
1
0
2
1
0
1
1
0
1
0
1
1
0
2
0
0
1
1
2
1
1
0
0
0
1
4
0
1
0
1
1
1
2
1
0
0
1
2
0
1
1
0
0
2
2
2
2
0
2
2
0
0
3
2
0
2
1
2
2
0
1
1
0
1
0
1
0
2
0
2
1
2
1
0
2
1
2
1
1
0
1
1
1
0
1
2
0
0
0
1
2
0
1
2
1
2
1
2
1
0
0
0
0
1
1
1
1
1
1
1
0
2
1
0
1
1
0
1
0
0
1
1
0
2
1
1
1
2
0
1
1
2
0
0
2
1
0
1
1
1
1
1
1
2
0
1
2
0
0
2
1
0
2
0
0
1
2
1
0
0
1
1
2
1
2
0
1
1
2
1
0
1
1
1
1
0
0
1
0
1
2
1
1
0
1
1
1
0
0
1
2
0
3
1
1
0
1
0
1
0
1
0
2
1
0
1
1
1
4
0
1
1
1
1
1
0
1
1
0
1
0
1
0
1
0
1
0
0
2
0
4
1
1
1
2
0
1
2
1
0
1
2
2
1
1
1
0
1
0
1
0
0
0
1
1
0
0
0
0
0
1
1
0
2
1
1
1
1
1
1
2
0
0
1
0
0
1
1
0
0
1
0
1
2
2
0
2
2
2
2
0
2
2
2
1
1
2
1
1
0
0
1
1
3
0
1
0
0
1
1
0
1
2
0
0
1
1
2
2
0
0
0
1
1
1
1
1
1
0
0
0
1
1
1
2
2
1
4
0
1
2
1
1
2
1
1
0
1
0
0
1
0
1
1
2
2
0
1
2
0
0
1
0
1
1
2
1
2
0
1
1
0
2
5
3
1
2
0
2
1
0
1
2
2
2
1
2
2
0
1
1
1
2
1
1
1
0
0
1
2
0
1
1
1
1
0
0
1
0
1
2
1
2
1
1
0
1
1
0
1
2
0
0
1
0
0
0
1
1
0
0
0
0
2
2
0
0
1
2
0
0
1
1
1
2
0
0
1
0
0
2
2
0
1
1
0
1
1
0
0
2
0
1
1
2
1
2
2
1
0
1
0
1
2
0
1
0
0
0
2
0
0
1
0
1
1
1
1
2
1
2
0
1
0
1
1
0
1
2
1
2
2
0
6
1
1
2
1
1
1
0
0
2
0
0
1
1
0
1
2
1
1
1
0
1
1
2
2
2
1
2
1
1
1
2
0
2
2
2
1
0
1
2
1
2
1
0
1
2
1
0
1
1
1
0
1
1
2
1
1
1
0
0
1
1
2
2
1
2
2
1
0
2
1
0
2
0
2
1
2
0
0
1
1
1
2
0
1
0
0
1
2
1
1
1
0
1
0
2
1
0
1
2
1
1
1
0
1
2
1
2
1
1
0
0
1
1
1
1
1
0
1
2
1
0
0
1
1
1
0
4
1
0
0
0
1
0
1
0
1
1
1
1
0
0
1
0
2
1
0
0
4
1
1
0
0
1
0
1
0
0
1
1
1
1
1
1
0
0
2
1
2
0
1
2
1
2
1
2
1
1
3
2
1
2
0
0
0
1
1
1
1
1
1
0
0
2
0
1
1
1
1
0
1
1
2
0
1
0
3
2
1
0
1
0
2
1
1
1
2
0
1
0
1
1
2
1
1
1
1
0
1
0
2
1
0
1
1
0
1
1
0
1
2
0
2
2
1
2
1
2
0
1
1
0
1
0
1
0
1
0
1
1
1
1
0
1
1
1
0
0
2
1
2
0
0
2
1
1
0
1
1
1
1
1
1
0
1
1
1
2
2
3
0
1
0
0
1
2
0
1
1
2
1
0
1
1
1
0
0
2
0
0
3
2
0
1
0
0
0
1
2
0
1
1
1
2
1
1
1
2
1
1
1
1
2
2
1
2
1
0
0
1
1
1
1
0
1
1
2
1
1
2
2
1
2
3
2
1
1
0
1
0
2
1
1
1
1
1
3
1
1
1
1
0
1
1
1
2
1
0
2
1
1
0
0
1
0
2
1
0
2
1
2
2
0
1
1
0
1
2
1
1
1
0
0
3
1
1
2
2
2
3
0
0
1
1
0
1
1
1
0
0
1
1
1
1
1
1
1
2
1
1
2
1
1
0
2
0
1
0
1
2
0
2
2
0
0
0
0
0
1
1
1
1
1
1
1
1
1
0
1
2
1
2
1
1
2
1
2
2
3
1
0
1
0
2
0
0
1
0
1
1
0
1
0
3
1
1
2
2
0
0
2
1
1
1
0
1
0
0
0
2
0
1
2
1
2
1
1
1
0
1
2
0
2
1
0
2
0
0
0
0
1
1
1
0
1
2
0
0
1
2
1
0
2
0
0
1
1
1
1
2
2
0
0
1
0
2
0
0
3
2
1
1
1
2
2
0
1
1
1
0
0
1
2
1
1
1
0
2
0
1
2
1
1
2
1
2
2
2
1
1
2
0
2
1
0
2
0
0
1
2
1
1
2
2
1
2
2
1
1
1
0
1
1
0
1
2
0
3
0
1
0
0
1
1
1
0
1
1
1
0
1
1
1
1
2
1
1
1
1
1
1
1
1
0
1
0
1
0
0
1
1
0
2
1
2
1
1
1
0
0
1
1
0
1
1
2
2
0
2
0
0
1
1
1
3
0
1
1
0
0
0
1
1
0
2
2
1
1
2
0
1
0
1
1
0
0
1
0
1
1
1
2
1
0
6
0
1
2
1
1
1
0
0
1
1
2
0
1
2
1
1
2
1
1
1
1
1
1
1
0
1
1
0
1
1
1
0
1
2
1
0
0
1
1
2
1
1
2
1
1
2
0
0
1
1
0
2
3
3
2
1
1
0
1
0
1
1
2
0
1
1
2
1
1
0
2
1
1
0
1
2
0
0
1
1
0
0
1
0
2
2
0
1
1
0
0
2
2
1
1
1
0
2
0
2
1
0
1
2
2
0
2
0
1
1
0
0
1
1
0
1
1
1
4
2
2
1
2
0
0
1
1
0
1
0
1
1
1
0
0
1
0
0
2
1
2
1
0
0
1
1
0
0
1
2
1
2
1
0
2
1
2
0
1
1
2
1
1
2
1
0
1
3
1
0
1
1
0
0
0
0
1
1
1
2
0
0
1
2
1
1
1
0
2
2
2
1
0
1
0
1
2
0
2
1
1
1
0
1
2
1
0
1
0
1
0
1
1
0
0
1
0
3
1
0
0
2
2
1
0
1
1
1
1
0
2
2
1
0
1
0
2
3
1
0
1
1
2
1
1
0
1
0
0
0
1
2
1
2
1
2
1
0
1
1
1
0
1
0
2
0
1
1
0
2
2
0
2
2
1
2
0
1
2
0
2
1
1
1
2
1
1
2
0
1
1
0
0
1
1
2
1
0
0
1
1
0
2
1
0
0
1
2
3
0
1
1
2
1
2
1
1
1
1
0
1
0
0
1
0
2
1
2
0
1
1
2
0
2
0
2
0
1
0
0
2
1
1
1
0
1
1
1
0
1
2
1
1
1
0
2
1
0
1
1
1
1
1
2
1
1
0
1
2
1
1
1
0
1
1
0
1
2
1
2
1
2
0
0
2
2
1
1
0
1
2
2
0
0
0
0
1
1
1
1
1
1
1
1
1
1
0
0
0
2
2
0
2
0
2
1
1
1
1
2
1
2
2
2
1
2
2
1
2
1
0
1
0
1
1
1
2
0
1
0
0
1
0
1
1
1
2
0
2
2
2
2
2
2
1
0
0
0
2
1
0
1
2
0
0
0
1
1
1
1
0
1
0
0
0
0
0
0
2
0
2
1
1
1
1
1
1
2
1
2
0
2
1
0
1
2
1
1
1
0
2
1
1
1
0
1
2
1
2
2
2
1
2
1
1
1
1
2
2
0
0
0
1
2
0
2
0
1
1
0
0
1
1
0
1
1
1
2
1
2
1
1
2
1
0
0
1
1
1
0
1
1
1
0
0
1
0
2
2
1
0
1
0
1
0
0
0
1
1
1
1
2
0
1
1
1
0
0
0
1
1
0
0
1
2
0
2
1
2
1
1
0
0
0
1
0
1
1
2
0
1
2
1
0
1
2
1
0
1
1
1
0
1
1
0
1
2
1
1
2
1
1
1
0
0
1
1
0
1
1
1
2
0
0
1
2
0
1
2
1
1
0
2
1
1
1
2
2
1
2
1
2
1
1
0
0
0
1
2
2
1
1
0
0
1
2
0
1
2
0
0
1
0
1
0
1
2
1
0
1
2
2
1
1
1
3
1
1
1
1
2
1
1
0
1
2
0
2
1
1
1
1
0
0
1
1
2
0
0
2
2
1
1
0
0
0
1
1
1
2
2
0
0
0
0
2
1
0
0
0
0
1
2
2
1
1
2
2
0
2
2
0
0
1
1
1
0
0
1
0
0
0
1
2
1
2
2
2
1
1
1
1
2
0
1
2
1
1
1
0
1
0
2
0
2
1
1
0
1
0
0
1
1
1
1
2
0
1
1
1
0
2
1
2
0
1
2
0
0
1
2
2
1
1
1
0
0
2
0
2
0
1
1
2
1
0
2
1
1
1
1
2
0
0
1
1
2
1
0
1
0
2
0
1
1
2
0
3
0
0
1
0
0
2
1
3
1
2
1
2
1
1
0
2
0
1
1
1
0
1
1
0
1
0
0
2
2
1
0
0
1
1
1
2
3
1
1
0
1
1
2
1
1
0
2
1
0
1
2
0
1
1
1
2
0
1
1
0
1
0
0
1
3
2
1
1
1
1
1
1
2
1
1
0
0
0
1
1
0
1
1
1
1
2
1
1
1
0
0
1
0
0
2
1
0
1
1
1
1
0
0
0
1
1
1
1
0
1
1
0
1
1
1
0
1
1
1
1
0
1
0
5
1
0
1
0
1
2
1
1
1
1
1
1
0
1
1
1
0
0
0
0
2
2
0
2
1
1
2
2
0
1
1
2
0
1
0
2
1
0
0
1
0
0
0
1
1
0
0
1
1
1
1
1
0
1
1
1
0
1
1
0
1
1
1
2
1
0
0
0
0
2
0
1
1
2
0
1
1
0
2
1
0
1
1
1
0
0
1
2
1
2
0
1
0
1
1
1
0
0
0
0
1
2
0
0
1
1
0
2
1
1
1
0
0
1
0
1
0
1
1
1
2
1
1
0
2
2
1
0
0
1
2
1
2
0
1
2
2
4
1
2
0
2
1
1
1
0
0
2
0
2
1
2
4
1
1
0
0
2
1
1
0
1
1
0
1
1
1
0
0
1
2
1
0
2
2
0
1
1
0
1
0
2
1
0
1
2
3
1
1
1
1
0
1
0
1
1
0
2
1
1
0
2
2
1
0
1
1
2
1
1
0
0
0
1
1
3
0
0
1
0
0
1
0
1
1
1
1
1
0
1
2
0
0
0
2
1
0
1
1
1
2
2
1
1
0
1
1
1
1
1
1
0
0
0
0
0
2
1
1
1
0
0
1
0
1
1
1
1
2
2
0
1
0
0
1
1
2
1
0
2
1
0
2
1
1
0
0
0
2
2
2
0
1
1
0
1
1
1
0
1
0
0
1
0
0
2
2
0
1
2
1
0
0
0
0
1
2
1
0
1
6
0
1
1
1
1
1
1
1
0
1
0
0
1
2
1
1
1
0
1
0
1
1
1
4
1
1
1
1
1
0
2
1
0
1
1
2
1
0
0
1
1
2
1
1
1
0
2
1
2
0
1
0
0
1
1
1
1
1
1
1
0
0
1
2
2
2
1
1
1
0
0
0
0
1
2
2
1
0
1
0
0
0
2
1
1
1
1
1
0
0
1
2
1
1
0
1
1
2
1
1
1
1
1
0
2
1
1
0
1
1
1
1
1
0
0
2
2
1
1
3
1
0
1
0
1
2
1
1
1
0
0
1
2
0
0
0
0
0
0
2
1
0
1
1
0
0
1
1
1
1
0
0
0
0
0
0
0
1
2
1
1
1
0
1
1
0
1
2
0
0
2
3
1
1
0
0
1
2
0
1
2
0
1
1
1
1
2
1
0
0
0
0
0
0
1
0
1
0
1
1
1
1
2
1
0
1
2
0
0
1
0
1
0
1
1
1
0
1
0
1
0
2
2
0
2
0
1
2
1
1
1
2
1
2
2
1
1
2
0
1
2
2
1
2
0
1
1
0
1
0
0
0
0
0
1
0
1
0
1
0
2
0
1
1
2
1
1
1
2
0
1
0
2
1
1
1
1
0
2
1
0
1
0
1
1
0
1
2
2
0
1
0
1
1
1
2
1
1
0
0
1
0
2
2
1
1
2
1
1
0
1
0
0
0
1
2
1
0
2
2
2
1
2
0
1
1
1
0
1
2
0
2
0
2
1
1
2
0
1
1
0
1
1
2
2
1
1
1
0
1
0
0
0
1
1
1
1
1
1
2
1
1
0
1
0
1
2
1
1
0
2
1
2
1
2
2
0
2
1
1
1
2
0
0
1
2
1
0
0
1
1
0
1
0
1
0
0
2
0
1
0
0
2
0
1
1
2
1
2
0
2
2
1
0
1
1
0
1
0
2
2
2
1
1
1
1
1
1
1
1
0
1
1
1
1
0
1
0
1
0
0
0
0
2
1
1
2
1
0
1
1
2
2
0
2
1
1
2
1
2
1
2
2
1
0
1
1
1
2
1
0
1
1
1
0
2
1
0
2
0
1
1
2
0
1
4
1
0
0
1
1
0
1
2
0
0
0
1
1
0
2
2
0
6
2
2
2
1
1
1
1
0
2
2
2
1
1
0
0
0
2
1
1
0
3
1
0
1
0
0
1
1
0
1
1
2
2
1
1
0
0
0
2
2
1
0
1
0
1
3
1
2
0
1
0
0
2
1
0
1
1
1
1
2
0
0
2
2
0
1
2
1
0
0
2
0
1
1
0
1
2
2
2
1
0
1
1
1
1
0
0
3
1
1
1
0
1
1
1
0
0
0
0
1
2
1
0
1
1
1
0
2
1
1
2
1
1
2
1
1
4
1
0
1
0
0
0
2
0
1
1
0
0
1
2
1
2
0
1
0
1
0
1
1
1
1
1
0
1
0
0
1
0
1
0
2
1
0
0
0
2
1
2
1
1
2
2
3
1
2
1
2
1
1
2
1
0
1
1
1
0
2
1
2
1
2
0
0
0
1
0
2
1
1
1
1
1
0
0
3
1
1
0
2
1
1
1
0
1
0
1
0
0
1
1
1
1
1
0
0
1
1
1
1
1
1
1
0
2
0
1
0
1
0
0
1
1
0
0
1
2
0
2
0
1
1
1
1
0
1
1
1
2
1
1
1
2
0
1
0
1
1
4
0
1
2
2
2
1
2
1
1
1
1
0
1
0
1
2
1
2
1
2
1
0
0
0
0
0
2
1
2
0
1
1
0
0
0
1
1
2
0
1
2
0
0
2
2
1
1
0
1
2
0
1
2
1
1
3
0
1
1
0
1
2
1
1
1
1
2
1
1
0
1
0
1
1
1
0
2
2
0
2
1
0
0
1
1
0
0
2
2
0
0
3
1
0
2
2
1
1
2
2
0
0
1
1
2
1
0
2
1
1
1
1
1
1
1
1
2
0
1
0
0
0
1
0
2
1
0
1
0
1
2
1
0
0
0
0
2
1
1
1
0
1
2
2
1
0
1
0
2
0
1
0
0
2
0
1
2
1
1
0
0
1
1
2
1
0
2
0
2
2
1
1
1
0
1
1
1
1
2
1
0
2
0
1
1
2
0
2
1
1
2
0
2
2
1
3
2
2
1
2
0
0
2
0
1
2
1
2
1
0
0
1
1
2
1
0
1
1
1
1
0
1
0
0
1
0
0
1
0
1
1
1
0
1
2
1
1
0
1
0
1
1
1
1
0
1
2
1
1
1
1
1
0
0
1
1
1
1
1
1
0
0
0
1
0
0
1
2
1
1
1
1
0
1
1
0
0
1
0
0
0
1
1
0
2
1
1
1
0
0
1
1
1
0
2
1
1
2
1
1
0
0
1
1
1
0
0
1
1
0
0
2
2
0
0
1
0
0
1
2
0
0
0
2
1
1
2
1
1
2
1
1
0
1
1
0
1
1
1
1
1
2
0
1
2
0
2
0
1
2
1
2
2
2
0
1
2
1
0
1
1
0
1
0
2
0
3
2
2
2
1
1
2
1
1
0
1
1
0
0
2
0
1
1
2
2
1
1
0
1
1
1
2
1
1
1
1
1
1
1
1
0
0
1
1
1
1
0
0
1
0
1
0
0
0
0
0
1
0
1
1
1
1
1
0
2
1
1
0
0
0
1
1
0
1
1
1
2
1
2
0
1
3
0
1
2
0
0
0
1
0
1
1
2
0
1
2
0
2
2
1
0
2
0
1
1
0
2
1
1
1
0
0
1
0
2
1
2
0
0
0
1
0
0
1
1
1
0
0
1
0
1
0
0
1
0
1
2
2
1
2
1
2
0
0
0
1
2
2
2
2
0
1
1
0
1
0
1
0
0
0
2
0
2
2
1
0
0
1
2
1
1
2
2
2
1
1
0
1
1
2
1
1
0
1
1
2
0
0
0
1
0
0
1
2
2
2
0
1
1
0
2
0
1
2
0
1
1
1
2
3
1
1
0
1
1
1
1
0
0
0
0
2
0
1
2
1
0
0
1
0
2
0
0
1
1
1
1
0
0
2
2
0
0
3
1
1
0
0
2
1
1
1
1
2
0
2
2
1
2
1
0
1
0
0
0
2
2
2
0
2
0
1
0
1
0
0
0
0
2
1
1
1
1
1
1
2
0
1
1
1
1
1
0
2
1
2
1
2
1
0
0
0
1
1
0
1
0
0
0
0
3
1
1
0
0
0
2
2
1
0
2
0
2
2
1
0
1
1
0
1
0
1
2
2
2
1
0
1
2
1
1
1
1
0
1
0
1
1
0
0
1
2
1
0
2
0
0
1
1
0
1
1
1
3
0
1
1
1
1
1
1
1
2
1
2
1
2
2
2
2
1
1
0
0
0
1
2
1
2
1
1
0
0
0
2
0
2
1
1
2
1
0
1
0
1
1
0
0
1
2
0
1
1
1
2
2
1
2
1
1
1
0
0
0
0
0
0
1
2
1
0
0
0
0
2
1
1
2
2
2
0
2
1
1
0
1
3
2
0
1
6
0
1
1
1
2
1
1
1
2
2
1
0
1
0
1
0
0
2
1
2
0
1
1
0
1
1
1
2
1
0
1
1
0
2
1
0
1
1
1
0
1
0
1
1
0
2
0
2
2
1
0
0
0
1
0
1
2
0
2
1
2
1
0
0
0
0
1
1
0
2
1
1
1
1
1
1
2
0
2
0
1
2
1
2
1
1
0
2
0
0
2
1
0
0
0
1
2
2
1
0
0
1
1
1
1
1
2
1
3
2
2
1
1
0
2
1
1
1
0
2
0
1
2
1
2
0
0
1
2
1
2
2
2
1
0
0
0
0
1
0
3
1
0
1
1
1
0
1
0
3
0
1
1
0
2
1
0
2
0
1
1
0
1
1
0
1
2
0
1
1
1
1
0
0
1
1
1
1
0
1
0
1
2
0
1
0
1
0
0
2
1
1
1
1
1
0
1
1
2
2
0
2
1
1
0
1
2
0
0
1
1
1
1
0
1
1
1
1
1
2
0
1
2
1
1
0
1
1
0
1
1
1
1
1
0
2
0
1
2
1
1
1
0
1
2
0
1
0
1
2
0
0
1
1
0
1
1
2
1
1
1
2
0
3
1
2
0
1
0
2
0
2
2
1
1
0
2
1
2
0
0
0
1
1
1
0
2
1
0
0
1
1
1
0
0
0
0
1
0
0
1
0
2
0
1
0
0
0
2
0
0
1
1
0
1
0
2
1
1
0
2
0
1
0
1
2
1
1
0
1
2
2
1
1
1
0
2
0
1
2
0
1
0
1
1
0
1
0
2
1
1
1
1
0
2
1
1
0
1
1
0
1
1
1
1
0
1
1
1
1
2
1
1
1
0
1
1
1
1
1
0
1
0
1
1
1
0
1
1
1
2
1
1
0
1
1
1
1
2
1
0
1
0
0
2
2
1
1
0
0
0
0
0
0
1
2
1
1
0
0
0
1
0
1
1
0
0
1
2
1
2
2
3
0
1
0
1
0
2
2
0
1
0
0
1
1
0
0
1
1
0
1
2
1
1
0
2
1
1
1
0
2
1
1
0
1
0
0
1
1
1
0
1
0
0
0
1
1
0
0
2
1
1
1
1
1
0
1
1
1
1
2
0
1
4
1
1
0
1
0
2
0
0
2
4
1
1
0
1
2
0
0
0
1
1
2
1
1
1
0
1
1
0
1
0
1
0
0
1
1
1
1
1
2
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
2
1
1
1
1
1
0
0
0
1
1
1
1
1
0
0
1
1
1
6
1
1
1
0
1
1
2
2
1
0
1
1
2
1
1
2
0
1
2
1
1
1
2
1
1
2
1
1
1
1
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
1
2
1
1
0
2
0
0
1
2
0
0
2
2
1
0
0
1
1
1
1
2
0
0
1
1
1
1
0
0
1
1
1
0
0
0
0
0
2
1
1
0
1
1
2
0
0
2
0
0
1
1
0
2
2
2
0
2
1
1
2
2
1
1
1
0
1
0
0
2
1
1
0
2
2
0
1
1
0
1
1
2
1
1
1
1
1
1
1
0
2
0
1
1
1
2
1
1
1
1
1
1
0
1
2
2
1
1
2
1
0
2
2
1
0
0
1
2
0
5
1
0
1
1
2
0
1
1
1
0
1
1
1
1
1
0
2
1
2
0
0
1
0
1
0
2
0
1
0
3
0
1
0
2
1
2
1
0
1
1
0
1
0
2
1
1
1
1
1
0
1
2
1
1
1
0
1
1
1
1
0
2
2
0
0
0
0
2
2
0
2
5
1
4
2
0
0
0
0
0
0
2
1
0
1
1
1
2
1
1
2
1
1
1
1
0
0
2
2
0
2
1
0
2
1
1
2
1
0
1
0
1
1
2
1
1
0
0
0
0
0
1
1
1
2
1
1
1
1
1
0
1
1
0
1
1
1
0
2
1
2
1
0
2
1
1
0
1
0
2
0
2
1
1
0
1
1
1
0
0
0
1
1
1
1
0
1
1
2
0
1
2
2
2
1
0
1
1
0
0
1
0
0
0
1
2
0
0
0
1
1
1
1
0
1
1
0
1
1
0
1
0
1
1
0
2
0
1
1
1
1
1
1
2
2
1
0
1
0
1
1
0
1
1
1
1
1
1
3
1
0
0
1
1
1
1
1
0
1
1
1
3
1
0
0
0
1
2
0
2
1
0
0
0
0
1
0
1
2
1
1
1
1
1
1
1
1
0
1
1
2
0
1
2
2
0
0
2
0
2
1
0
2
1
0
2
1
1
2
1
2
0
1
0
1
1
0
1
1
0
0
0
1
1
0
0
3
2
2
2
2
0
2
2
1
2
0
1
1
1
0
0
0
2
1
1
0
0
0
0
2
0
1
2
1
1
2
0
2
1
1
0
0
1
2
0
1
2
1
2
2
2
1
0
1
0
2
0
2
0
2
0
1
1
1
0
1
4
1
2
1
1
1
1
1
0
1
2
2
1
2
1
1
1
0
2
1
0
0
1
1
1
1
2
1
0
0
2
1
1
2
1
0
3
2
2
0
1
1
1
0
1
2
1
0
0
0
1
2
1
2
2
1
1
2
1
1
0
1
1
0
0
1
2
0
1
2
0
1
0
1
1
1
2
1
2
2
2
0
1
0
0
1
2
1
2
1
2
2
1
0
0
1
0
2
1
0
0
1
0
1
0
0
0
0
1
1
1
1
1
0
0
2
0
2
1
0
0
1
0
1
1
1
1
1
0
1
2
1
1
1
2
1
2
2
3
1
0
1
0
1
1
1
1
1
1
1
2
0
1
1
1
3
2
1
1
0
3
0
1
1
2
2
1
2
1
2
0
2
0
1
1
0
2
2
0
1
0
0
1
1
1
0
0
0
1
1
2
1
0
1
2
1
1
2
3
0
1
0
0
1
0
1
1
0
1
0
1
2
2
0
0
1
1
1
2
1
1
0
1
1
1
1
0
0
1
1
0
1
0
2
0
1
1
0
1
2
1
1
2
0
2
1
1
0
1
0
1
1
1
1
0
1
1
1
1
0
1
0
0
2
1
0
2
0
0
0
1
2
1
1
1
2
2
2
2
1
1
2
0
1
2
1
0
0
2
0
1
0
1
1
1
0
1
0
0
1
2
1
2
2
1
1
1
1
0
1
0
0
1
0
1
1
0
2
1
2
1
1
0
0
2
1
1
0
1
1
0
1
2
1
2
2
0
0
1
0
0
2
1
1
1
2
0
1
0
1
1
0
1
1
1
2
1
0
1
1
2
2
1
0
2
0
1
1
0
0
0
0
1
1
0
0
2
0
2
1
1
1
1
1
2
1
0
1
1
1
1
4
0
2
0
1
2
0
1
0
1
2
1
2
1
1
1
1
0
0
1
1
1
2
1
0
0
0
0
1
0
1
2
0
2
0
2
1
1
1
1
1
0
1
1
1
0
1
0
0
1
2
1
1
1
1
0
1
1
0
1
1
0
1
0
0
1
2
0
2
1
1
1
1
2
1
1
1
0
0
2
2
2
1
2
0
2
1
2
1
1
0
0
1
0
0
2
0
2
0
0
1
1
0
1
1
0
1
0
1
1
2
3
2
2
1
2
0
0
1
1
2
1
0
2
0
0
1
1
1
0
1
0
1
1
1
0
1
1
1
2
0
0
1
0
2
0
0
3
2
1
1
1
1
1
1
1
0
1
1
1
0
1
1
0
2
1
0
1
0
1
1
1
0
1
1
0
1
2
2
0
2
1
1
0
0
0
0
1
1
0
1
1
0
1
1
0
0
1
1
1
1
0
2
0
2
0
1
0
2
1
2
2
0
2
1
6
1
1
2
0
0
0
1
0
1
0
2
0
0
1
2
1
1
1
0
2
1
2
3
2
2
0
1
0
2
1
1
2
3
0
2
0
2
1
0
1
0
1
1
2
1
1
2
0
1
1
1
0
1
1
0
1
1
1
2
2
0
1
1
0
1
1
1
1
0
1
2
2
0
2
1
1
0
0
1
0
0
1
0
3
0
1
2
2
1
1
0
0
2
0
1
0
2
0
0
2
1
3
0
0
1
1
1
2
0
1
1
0
1
1
1
2
1
1
0
1
2
1
1
0
0
1
1
1
2
1
1
2
1
1
1
3
0
1
1
1
1
1
1
1
2
2
0
2
1
1
1
1
0
0
0
0
1
0
1
1
0
1
1
2
1
2
2
2
1
1
0
0
0
1
0
2
1
1
1
0
2
1
1
0
0
2
0
0
0
0
2
1
0
2
0
1
1
1
0
1
1
0
1
0
1
1
0
0
3
0
0
0
0
1
2
1
1
0
1
2
0
1
1
0
1
1
2
2
0
1
1
0
1
0
1
0
1
0
1
1
0
0
1
1
0
2
1
2
1
0
2
0
0
2
1
0
1
0
1
0
0
1
1
2
2
0
1
2
0
1
0
1
1
0
1
1
1
2
1
0
0
1
2
1
1
0
3
0
1
1
1
0
0
2
1
1
2
1
0
1
2
2
2
1
1
0
2
3
1
1
0
1
1
1
1
1
2
0
1
1
1
0
0
2
1
2
1
0
1
1
0
0
1
0
0
1
2
1
1
0
2
1
1
1
1
2
0
1
1
1
0
1
1
0
0
0
1
0
1
1
1
1
1
1
2
2
1
1
2
1
1
0
1
2
1
1
1
1
1
0
1
0
2
1
0
2
1
1
0
1
1
1
2
2
0
0
1
4
1
0
2
0
1
0
1
2
1
0
1
1
0
1
0
1
2
2
0
1
2
2
2
1
0
0
1
1
1
3
1
2
1
0
1
1
1
1
2
1
0
1
2
1
0
1
1
0
1
1
0
0
2
1
0
2
0
2
2
0
1
1
1
1
1
2
0
0
1
2
2
2
2
2
2
1
0
1
2
0
2
0
1
2
2
1
0
1
1
1
0
1
0
1
1
1
0
0
1
0
1
1
2
1
0
1
2
2
0
1
2
0
0
0
1
2
0
1
1
0
1
1
0
0
1
1
1
0
1
1
2
2
0
2
2
1
2
2
2
0
0
2
2
2
1
0
1
1
1
1
1
1
1
1
1
2
1
2
1
1
0
1
1
0
0
2
2
2
0
0
2
1
0
0
1
0
1
2
0
2
1
1
1
1
0
1
2
0
2
2
0
0
2
1
1
1
0
1
0
0
1
0
0
2
1
1
2
2
1
1
1
1
1
0
1
3
1
2
0
1
1
2
1
1
0
1
1
2
1
1
2
1
1
0
1
1
2
2
2
1
2
1
1
0
1
2
1
1
1
0
1
1
2
1
2
0
1
2
0
1
1
0
1
0
1
1
1
1
1
0
0
1
0
0
2
1
1
1
1
1
0
0
0
1
1
2
1
1
1
2
1
1
2
1
2
1
2
0
1
1
1
1
1
2
2
0
0
1
1
2
2
1
1
2
1
1
1
0
2
2
0
2
2
0
2
2
0
0
1
2
0
2
3
2
1
2
2
1
0
0
2
1
0
0
1
0
1
0
2
2
0
1
1
0
1
1
0
1
1
0
2
1
1
0
0
1
0
1
1
0
2
2
2
2
1
1
1
2
1
0
1
1
0
1
0
1
0
2
2
0
2
2
1
0
2
1
0
1
1
2
2
2
2
1
0
0
1
2
0
1
0
1
0
1
1
2
1
0
0
1
1
1
2
2
1
2
1
3
1
1
2
1
0
1
2
2
1
1
1
2
1
0
2
0
1
1
2
2
0
2
0
0
0
0
1
2
2
1
1
1
1
1
2
0
1
1
1
1
0
2
0
1
1
1
1
2
1
1
0
0
1
2
0
1
0
0
0
2
1
1
0
0
1
0
1
1
0
0
1
1
1
2
0
1
0
1
1
2
2
3
1
0
1
1
1
1
1
1
0
1
2
1
1
0
2
1
2
0
1
1
2
1
2
1
0
0
2
1
1
2
1
2
0
0
1
0
1
1
1
1
0
0
1
1
1
0
1
0
0
2
0
1
1
2
1
0
2
1
0
2
0
1
0
1
1
0
1
0
1
2
1
2
2
0
0
2
2
1
1
0
1
1
2
0
0
0
1
1
1
1
2
0
1
2
0
0
1
1
2
2
2
0
0
2
2
1
0
1
0
2
2
1
1
1
3
1
1
1
0
2
0
1
1
1
2
0
0
1
0
2
1
2
1
1
2
1
1
0
1
1
2
0
3
1
1
1
0
2
1
2
2
0
2
1
1
0
1
2
3
2
3
0
1
2
0
0
1
1
1
1
0
1
1
1
2
1
0
0
0
1
0
2
1
0
1
1
1
0
1
2
0
0
2
1
0
1
1
0
0
1
1
1
0
1
2
2
1
0
2
1
2
1
1
1
1
1
1
3
0
2
1
2
1
2
0
0
0
2
0
1
0
0
1
0
1
1
1
2
2
0
2
2
2
1
1
1
1
1
0
1
1
1
1
1
2
0
4
1
0
0
0
0
1
1
2
2
0
1
0
0
1
0
1
1
2
0
0
0
2
1
0
1
2
0
2
0
0
1
2
0
0
1
1
1
1
1
2
1
0
0
0
1
1
0
0
1
1
2
1
2
1
0
1
1
1
2
2
1
1
1
1
1
2
1
1
1
0
0
1
1
1
0
2
0
1
1
0
2
0
1
1
2
0
0
2
0
2
2
2
1
1
1
2
2
0
1
1
0
1
1
1
2
1
3
1
0
0
1
0
2
1
1
2
1
0
0
2
2
0
1
0
2
0
0
1
1
1
0
2
1
0
0
0
2
2
1
2
2
1
0
0
0
2
2
0
1
1
1
3
0
1
0
0
0
0
1
0
1
1
1
1
0
1
1
1
1
1
0
2
1
0
0
0
1
1
2
1
1
1
1
1
0
1
1
1
0
0
0
0
2
2
0
1
0
3
3
1
1
2
1
0
0
2
0
1
1
1
2
2
1
0
1
1
1
1
0
0
0
0
0
0
0
1
1
1
1
2
1
1
0
0
1
1
1
2
1
0
1
1
0
0
3
1
1
2
1
0
0
0
0
0
1
0
1
0
1
1
0
1
2
0
0
2
1
2
2
0
2
0
1
2
0
0
1
1
0
1
1
2
1
0
2
1
2
1
0
1
1
1
2
1
2
0
1
0
0
2
1
1
0
3
1
2
1
0
2
1
1
1
1
0
1
1
0
1
1
0
1
2
1
1
1
1
1
1
1
1
2
2
1
1
0
1
1
2
2
0
1
0
2
0
1
1
0
1
1
5
0
0
0
1
0
0
1
0
1
2
2
2
1
1
1
0
1
2
0
0
0
2
1
0
1
1
0
0
0
2
1
1
2
1
1
2
1
2
0
0
1
3
0
0
0
1
0
1
0
1
0
1
0
0
1
1
0
2
1
2
0
1
1
2
1
0
0
2
1
1
1
1
0
1
1
2
3
0
1
1
1
1
1
0
1
1
1
1
1
1
2
0
2
1
2
1
1
2
2
1
0
0
0
2
0
1
0
1
1
1
1
1
1
0
1
0
2
1
1
1
1
1
1
0
1
1
2
0
2
0
0
1
1
1
0
2
0
2
1
0
0
0
2
1
0
0
1
0
0
1
2
0
2
1
1
2
2
1
2
0
0
1
0
0
0
1
0
1
0
2
0
0
1
2
1
2
0
1
1
0
0
1
2
2
2
0
1
2
1
0
1
0
1
1
1
2
1
2
0
6
1
0
0
1
0
1
2
2
1
1
0
1
0
2
1
1
1
1
1
0
2
2
2
2
0
1
1
2
1
1
2
0
1
0
0
0
2
2
2
0
1
0
1
2
1
0
1
1
2
0
0
1
0
1
1
3
1
0
0
2
1
1
2
2
0
2
1
1
1
1
2
1
2
2
2
1
0
1
1
0
0
1
1
0
0
0
2
2
0
0
1
0
1
0
1
1
0
0
1
1
1
1
0
0
2
1
1
2
1
1
1
0
1
0
0
1
2
1
1
2
0
0
1
1
1
2
0
1
1
2
0
1
2
1
0
1
0
0
1
0
1
1
1
0
2
0
2
0
1
0
1
1
2
2
0
1
1
2
1
1
2
0
1
1
1
0
0
1
2
0
0
1
2
0
0
0
0
2
1
1
0
0
1
1
0
1
1
0
1
0
1
2
1
0
1
1
0
0
0
1
1
1
1
0
1
1
0
1
0
2
1
1
1
0
1
0
0
1
0
2
0
1
2
0
0
0
0
1
1
0
1
2
1
0
0
2
2
0
0
2
1
2
1
0
1
0
2
0
2
1
1
2
0
1
1
0
1
1
1
0
1
0
0
2
3
0
1
2
1
1
0
1
0
1
1
1
0
0
2
3
0
2
1
0
0
1
1
4
1
1
1
2
1
0
1
1
2
1
1
2
1
0
0
1
2
2
2
1
0
1
0
2
2
1
1
1
2
2
0
0
0
1
1
1
1
2
2
0
1
0
0
1
2
0
1
1
0
0
0
1
1
0
0
0
1
2
1
1
0
0
0
1
1
0
1
1
2
1
0
1
1
1
0
2
2
1
0
0
2
1
1
2
2
1
1
1
0
3
2
0
0
1
0
0
0
0
2
1
0
2
0
0
1
1
0
1
2
2
0
0
1
2
1
1
0
1
0
1
0
0
1
1
1
1
0
0
0
0
1
1
2
1
2
1
0
1
0
1
0
0
1
1
1
1
0
0
2
0
2
1
1
1
1
1
0
1
1
0
1
0
0
1
0
1
0
0
0
0
1
1
2
0
0
0
0
0
2
0
0
2
2
0
1
0
1
2
1
2
2
1
1
1
1
0
2
0
1
1
1
1
0
1
0
1
0
1
0
1
1
1
2
1
0
1
2
1
2
1
1
0
1
1
1
2
0
1
1
2
0
2
1
1
0
0
0
1
0
0
1
0
1
1
1
1
0
1
1
1
0
0
1
1
0
0
2
2
2
0
2
1
0
0
0
2
1
1
1
1
1
1
0
1
0
2
0
0
0
1
2
1
0
0
0
2
1
1
0
1
1
1
0
1
1
1
1
1
2
1
3
2
0
0
0
1
2
0
0
1
2
0
1
1
2
2
1
2
2
0
1
1
0
1
1
0
0
1
1
0
0
1
1
2
1
2
1
1
0
1
0
1
0
2
2
0
0
1
0
1
1
0
1
0
1
2
1
2
1
1
1
0
0
1
1
0
1
0
0
1
2
0
1
1
1
0
2
2
0
0
1
1
1
0
2
2
1
0
1
1
1
0
2
0
0
0
2
1
2
2
1
0
1
3
1
1
1
0
0
0
1
1
1
0
0
1
0
1
1
1
1
1
0
1
2
0
2
0
1
2
1
0
0
1
1
1
1
0
1
2
1
1
1
1
1
0
2
1
2
0
2
0
1
0
0
0
2
1
0
2
1
1
2
2
0
1
1
2
0
0
2
1
2
1
2
0
1
2
1
0
1
0
0
0
0
0
1
1
1
0
1
1
2
1
2
0
0
1
2
1
1
2
1
2
0
2
1
2
1
0
1
1
1
0
1
0
1
1
2
2
0
0
2
0
1
2
0
1
1
0
1
1
2
1
1
1
1
2
0
1
1
1
2
1
1
2
1
1
1
2
1
2
1
1
2
1
2
1
2
1
1
2
1
1
1
0
0
1
0
1
1
1
0
0
1
0
0
2
1
0
0
0
2
0
2
0
1
0
0
1
0
2
0
1
1
2
0
1
1
1
3
1
2
0
1
1
1
1
0
1
1
1
1
1
0
1
1
0
2
1
2
1
1
1
1
1
1
0
1
0
1
0
2
2
2
0
1
0
2
3
2
1
1
1
0
2
1
0
1
0
2
2
2
0
2
0
1
2
1
0
1
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
4
1
0
2
1
0
1
0
0
0
0
2
2
1
1
1
1
2
2
1
2
1
0
2
1
2
0
5
0
1
1
0
2
1
0
0
2
1
1
1
0
1
1
2
1
0
0
0
0
1
1
1
1
1
0
0
1
1
0
0
0
2
1
0
0
1
3
1
2
1
2
2
1
1
2
1
1
0
0
1
2
0
1
1
1
0
1
0
1
1
0
1
1
1
1
2
1
1
2
2
0
0
0
0
0
1
0
1
1
2
0
0
0
0
1
1
2
1
1
1
0
2
3
1
0
1
0
1
0
0
0
1
0
0
0
2
2
2
1
2
1
0
1
2
1
0
1
0
2
1
1
1
0
2
1
1
0
0
1
2
1
2
1
1
2
1
1
2
1
1
2
0
0
0
1
0
0
0
0
1
2
1
2
2
2
1
2
1
0
1
0
0
1
1
0
0
0
0
0
2
2
0
1
2
2
1
2
1
1
1
1
2
2
1
1
0
1
1
0
2
1
1
1
3
1
2
0
1
0
1
2
1
1
1
2
0
0
0
1
1
1
1
0
0
1
0
1
1
2
0
0
0
2
1
0
0
1
2
0
1
1
0
1
2
1
1
1
1
1
1
0
1
2
0
2
1
0
1
1
0
2
1
1
2
1
0
1
0
1
3
2
1
1
1
1
0
0
2
1
1
2
0
0
1
2
1
0
2
2
0
0
1
0
1
1
2
1
1
1
1
1
1
1
0
2
0
1
1
1
0
0
2
2
0
0
0
0
1
2
1
1
0
1
1
1
0
0
1
1
3
0
1
0
1
2
1
1
1
2
2
0
1
2
1
1
2
0
1
2
1
2
1
1
1
1
0
1
0
0
0
1
1
1
1
0
1
1
1
0
1
1
0
2
1
2
1
0
1
1
0
0
1
1
0
2
0
0
2
2
0
1
1
0
0
0
0
0
0
0
1
0
2
1
1
1
2
0
0
1
1
1
2
1
0
1
1
0
1
1
0
0
1
1
2
1
1
2
2
0
1
0
0
1
1
2
0
1
1
1
2
0
1
1
1
2
2
1
1
2
0
2
1
2
1
1
2
2
1
1
1
0
1
1
1
0
1
0
0
2
1
2
1
2
1
0
1
1
1
1
1
0
3
2
1
0
0
1
1
0
1
0
1
2
1
1
0
0
2
0
1
1
0
1
1
2
1
1
1
1
1
0
1
1
0
1
0
1
0
2
0
0
1
1
0
0
1
1
2
1
0
1
1
2
0
1
1
0
1
1
0
2
0
1
0
2
2
2
1
1
2
0
2
0
0
1
2
0
0
0
1
1
1
1
1
1
2
1
1
1
2
1
2
1
2
1
0
2
0
1
2
2
0
1
2
1
0
1
1
0
2
1
0
0
0
2
1
1
0
0
0
1
1
0
0
0
1
0
1
2
1
1
2
1
1
1
0
1
1
1
1
2
1
1
1
1
0
1
0
2
0
1
0
1
0
0
0
0
1
1
0
3
1
1
0
1
1
1
0
2
1
2
1
1
1
2
1
1
1
1
0
0
0
2
2
0
0
1
1
3
2
2
1
2
1
0
2
0
2
1
1
1
0
1
1
0
0
2
0
2
1
1
1
1
1
1
2
2
0
1
1
0
2
1
1
1
0
2
2
2
0
2
1
1
1
1
2
0
1
1
0
0
0
1
2
1
1
1
1
1
2
1
0
0
1
1
1
0
2
2
0
1
0
1
1
0
1
1
0
1
0
1
1
1
2
2
0
1
1
1
1
2
2
0
1
1
2
1
1
0
0
1
0
1
0
1
4
1
1
2
1
1
1
0
1
0
0
1
0
1
2
0
0
1
0
1
0
0
1
0
2
2
0
0
0
0
0
0
0
2
2
1
1
1
1
1
2
0
1
1
1
1
0
2
1
1
2
1
1
2
0
0
1
2
1
0
2
1
0
1
0
1
0
2
1
2
1
1
1
1
2
1
2
1
0
1
2
1
1
0
0
0
1
0
2
1
2
2
1
2
0
1
1
1
0
1
2
1
1
0
1
1
1
1
0
1
1
1
0
2
1
0
0
0
1
0
0
1
1
0
2
2
0
1
2
1
1
1
1
1
2
0
1
2
3
0
0
0
1
0
1
1
1
0
1
0
0
1
1
0
1
0
1
2
0
3
0
0
1
1
1
1
1
0
2
0
1
2
0
1
1
2
1
0
0
1
1
0
1
2
1
0
1
0
2
1
0
1
2
0
2
2
0
0
1
1
1
1
1
1
1
0
1
1
0
0
2
0
1
0
2
1
2
2
0
4
0
1
0
2
0
0
1
1
1
1
2
1
1
1
0
1
2
0
2
0
1
1
2
2
1
1
1
1
1
1
0
0
0
1
1
1
1
0
1
1
1
0
2
0
0
0
1
0
2
1
0
2
1
2
1
0
2
2
1
0
2
1
2
1
1
1
1
1
2
2
0
0
0
0
1
1
2
0
2
1
1
1
1
1
0
1
1
1
1
0
2
1
2
0
1
2
1
2
1
1
1
1
1
0
1
2
2
0
0
1
2
3
0
1
1
2
1
2
1
0
0
2
0
0
1
1
1
1
1
1
1
1
1
1
2
1
2
1
2
2
0
1
0
2
1
0
2
0
2
1
0
1
0
1
1
0
1
1
1
0
2
2
0
1
1
2
1
1
0
1
1
1
0
1
1
1
1
3
1
1
2
0
0
1
1
2
1
0
1
0
0
1
2
1
1
1
2
1
2
0
0
0
1
1
1
0
0
2
1
1
1
0
0
2
2
0
1
1
1
0
1
0
2
1
0
0
0
0
2
0
2
0
2
2
0
0
0
0
1
2
1
1
3
2
1
1
1
2
1
1
0
0
1
1
0
0
1
2
1
1
2
0
1
0
2
1
0
0
1
0
1
0
1
0
1
1
0
1
2
0
0
1
1
3
1
2
1
0
1
0
1
0
1
0
0
0
1
0
2
2
2
0
1
1
1
0
1
0
2
1
1
0
2
1
1
2
1
1
1
2
2
1
2
2
2
3
0
0
0
1
2
1
1
1
0
1
1
1
1
2
1
0
1
0
0
1
2
0
2
0
1
1
1
0
0
1
1
1
1
2
1
2
1
1
1
1
0
1
1
0
1
1
1
5
0
1
0
4
1
0
0
1
0
0
1
0
0
0
2
0
0
0
1
1
0
1
2
0
0
0
0
0
1
2
1
2
0
0
1
2
0
1
0
2
1
1
2
1
1
1
0
0
2
2
1
0
1
1
1
2
2
1
1
0
1
1
1
0
0
0
1
1
0
0
1
2
1
1
1
2
0
1
2
1
1
2
2
1
2
0
1
1
1
2
1
0
2
1
1
1
1
1
2
1
2
0
1
0
1
1
1
2
2
0
2
1
1
2
2
1
2
0
1
0
2
1
0
0
0
2
1
1
1
2
1
1
1
0
2
1
1
0
1
3
0
1
2
1
1
2
2
1
1
2
0
2
1
1
0
0
2
1
2
0
0
2
3
1
2
2
2
0
0
0
1
0
0
1
0
0
1
1
1
2
2
0
1
2
1
0
0
0
2
0
1
2
2
1
0
1
0
2
1
1
0
2
2
2
1
1
0
1
1
1
0
0
1
1
1
0
1
1
0
0
1
0
2
0
1
1
0
0
1
0
1
1
0
1
1
1
0
2
2
2
0
0
1
0
1
2
1
0
1
3
2
1
1
2
0
1
1
2
1
1
2
0
1
0
1
0
1
0
0
2
3
0
1
1
1
1
0
1
1
1
1
1
1
3
1
2
0
0
0
0
0
0
0
0
1
1
1
1
1
1
0
1
1
2
1
0
0
1
1
2
2
1
2
2
1
1
1
1
1
2
1
0
1
0
0
1
1
1
1
1
2
0
0
0
1
1
0
1
1
0
0
1
0
1
2
1
1
0
2
1
0
0
1
1
1
1
0
1
1
1
0
3
2
1
2
1
1
1
2
2
1
2
1
1
0
0
1
2
1
1
2
1
0
0
1
0
0
3
1
1
0
1
2
3
1
0
0
1
1
2
0
0
1
1
1
1
0
2
2
1
1
1
1
1
0
0
0
1
0
0
1
0
2
2
2
1
0
1
1
1
0
1
1
2
1
2
1
1
1
0
1
2
1
0
0
1
2
0
1
1
1
0
0
1
0
1
1
0
1
1
0
0
1
2
1
0
1
1
2
1
1
1
2
2
0
1
2
1
1
0
1
0
0
0
1
1
1
1
2
1
0
0
2
1
0
2
2
2
0
1
2
0
0
1
0
2
2
1
1
2
2
2
1
2
0
0
2
0
1
1
1
0
0
1
1
1
0
0
0
1
1
1
2
0
1
0
1
0
0
1
0
1
0
2
0
1
1
1
1
0
0
1
2
1
1
1
1
2
1
2
1
2
1
0
0
2
2
2
1
1
2
0
0
0
1
0
1
2
1
1
2
1
2
2
1
0
1
2
1
2
0
1
1
2
1
1
0
2
2
1
0
0
1
0
0
0
1
0
0
0
2
2
0
1
1
0
0
1
1
2
1
1
2
1
1
2
0
0
1
1
1
0
1
1
1
1
1
1
1
0
1
0
1
1
2
2
0
0
1
1
2
1
1
1
1
0
3
1
1
1
1
1
1
1
1
0
2
0
0
0
0
1
2
0
1
0
0
1
1
2
3
1
0
1
1
1
0
0
2
1
1
1
0
2
1
0
1
0
1
1
2
0
1
0
1
1
0
1
1
0
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
2
1
0
1
1
1
1
1
2
1
2
1
1
0
0
1
1
2
0
1
2
1
1
2
0
2
2
1
1
0
1
0
1
2
0
0
1
1
0
1
0
0
0
2
1
0
1
1
0
2
2
0
1
2
0
1
2
0
0
1
1
2
1
0
0
1
0
0
1
1
2
1
2
1
2
1
2
1
0
1
1
0
1
1
1
0
0
0
1
0
2
1
0
0
2
2
1
2
0
0
1
0
0
0
2
0
1
1
1
1
1
0
0
0
0
1
1
2
1
0
1
0
0
0
1
1
1
0
1
2
2
1
0
1
1
1
1
1
1
3
2
0
2
1
1
1
0
1
0
2
1
1
0
2
1
1
1
1
1
2
1
0
1
1
1
0
2
1
0
1
1
1
1
1
0
2
1
1
0
0
2
1
1
2
1
0
1
1
1
1
1
1
0
1
1
1
1
1
0
1
2
1
1
0
1
2
2
0
2
2
0
0
0
0
2
2
2
2
2
0
1
1
0
0
1
2
1
1
1
1
1
0
1
2
1
1
1
0
1
0
0
0
1
2
1
1
0
1
0
1
1
1
2
0
1
1
1
1
1
1
1
0
0
0
0
1
1
1
0
2
0
0
1
0
1
2
1
0
0
1
2
0
1
1
1
1
2
0
1
0
0
1
1
1
1
1
1
2
1
2
1
2
1
1
2
1
1
2
0
0
0
1
0
0
2
1
0
1
0
0
1
1
1
1
0
1
0
1
1
1
1
2
0
1
2
2
1
2
0
1
0
0
0
0
1
1
2
0
1
1
1
0
0
2
1
7
1
0
2
1
0
0
2
1
0
1
0
1
0
1
3
2
1
1
1
0
0
1
1
0
1
1
1
2
0
1
1
2
0
0
0
1
2
0
2
1
2
2
1
1
1
1
0
1
0
1
1
0
0
0
0
0
2
2
1
0
2
1
1
2
1
1
0
1
1
1
1
2
2
2
0
1
1
0
0
2
0
0
0
3
1
0
0
0
1
1
1
1
0
1
1
1
2
1
0
1
2
0
2
1
2
0
1
1
2
0
2
1
0
1
0
2
0
1
1
2
1
1
0
1
1
1
2
1
1
0
1
2
1
1
2
2
1
1
1
1
1
2
0
3
2
1
1
0
0
1
1
1
2
1
1
0
1
0
2
1
1
0
0
0
1
1
2
0
0
2
2
2
1
0
0
0
1
1
0
1
1
0
1
0
0
0
2
1
1
0
2
0
2
2
1
1
0
1
1
1
1
1
1
1
0
2
1
2
0
1
1
2
0
0
2
2
2
1
1
1
1
1
1
1
2
0
1
0
1
0
2
0
0
0
0
0
1
0
1
1
1
2
1
1
1
0
0
0
2
2
1
0
0
1
0
1
2
1
0
1
2
0
0
2
1
1
1
2
2
2
0
1
2
0
0
1
2
2
1
0
0
2
1
0
1
0
0
0
1
0
0
2
2
1
1
1
2
1
0
1
0
1
2
1
0
2
1
1
2
1
0
0
1
2
1
1
1
1
2
0
1
2
0
1
0
1
2
2
2
2
0
1
1
0
0
1
2
1
2
0
1
0
1
1
1
0
0
2
0
1
1
0
1
2
2
1
1
4
1
1
1
1
1
0
2
1
1
2
0
1
1
2
1
4
0
1
2
0
0
2
0
2
2
2
1
2
1
2
2
0
0
0
2
1
2
2
0
2
1
0
0
1
0
1
1
0
1
2
1
2
1
0
0
3
6
1
1
0
1
1
3
1
1
0
1
0
1
1
0
1
1
1
1
1
1
2
1
0
1
0
1
1
0
1
0
0
2
1
0
0
2
0
0
0
1
0
0
2
1
0
0
1
0
0
1
1
1
2
1
0
2
2
1
1
1
0
2
2
1
1
0
0
1
0
1
2
1
1
1
1
0
1
1
1
0
0
1
1
0
2
1
2
1
1
1
1
1
1
1
2
0
1
2
1
2
1
1
1
1
1
1
1
0
1
0
1
1
1
1
3
1
0
0
1
1
1
0
1
0
2
2
1
1
0
0
2
0
1
2
1
0
2
2
0
2
0
1
1
1
2
1
0
2
2
0
2
1
0
2
2
1
1
2
1
1
1
2
1
0
1
1
0
0
0
1
1
1
1
0
1
1
1
1
0
2
2
1
2
2
0
2
1
1
1
0
0
2
0
1
1
1
0
2
1
1
0
0
1
1
1
0
0
1
1
0
1
2
2
0
0
2
0
0
1
0
0
1
1
0
1
0
0
1
2
0
0
1
1
1
0
1
2
0
0
0
0
1
1
1
6
1
1
0
1
1
2
0
1
2
2
0
1
1
1
0
1
1
2
0
2
1
0
2
1
1
7
0
3
1
2
1
1
2
1
0
0
1
0
1
1
2
2
2
1
1
3
1
3
1
0
0
2
1
2
0
1
1
1
1
1
0
1
1
2
0
1
2
0
1
0
0
0
3
0
1
1
1
1
1
0
0
1
1
1
1
1
1
1
2
1
0
1
1
1
2
0
2
2
2
0
0
2
1
1
2
2
1
2
2
2
2
0
1
1
1
2
0
1
0
3
1
2
0
0
0
1
1
0
0
0
1
1
1
1
0
1
0
0
2
1
2
0
0
0
1
0
2
0
1
1
1
0
0
8
0
1
1
0
1
1
1
0
1
1
1
0
2
1
2
0
2
1
2
1
1
1
1
1
1
2
1
2
2
0
0
1
1
2
2
1
1
0
1
0
1
1
3
2
0
0
0
1
1
1
1
0
0
0
1
1
2
0
0
1
0
2
0
0
0
1
1
1
1
0
0
1
2
0
0
1
1
2
1
1
0
0
1
2
2
1
2
1
1
0
1
1
2
0
0
2
0
0
1
0
2
3
0
3
1
0
2
0
0
2
1
0
0
1
1
2
0
0
0
2
1
2
1
0
0
1
0
2
1
1
0
0
1
0
1
2
1
1
0
1
1
1
1
0
1
0
1
1
0
1
0
2
2
1
1
0
0
1
0
2
1
2
0
1
2
1
1
1
0
0
1
2
1
1
1
0
1
1
0
2
1
1
0
0
4
1
1
2
1
1
2
1
1
1
2
1
0
0
0
1
1
0
1
1
0
1
1
0
1
0
2
2
1
0
0
0
2
1
1
1
0
0
2
1
3
0
0
0
1
1
1
1
1
1
1
1
0
1
2
1
2
0
1
1
1
2
1
1
0
1
0
1
2
1
0
0
2
3
1
0
0
2
0
2
2
1
1
0
1
2
0
2
1
1
2
0
2
1
1
0
0
2
1
1
1
0
0
1
2
0
2
1
3
1
0
2
1
1
1
0
1
0
1
0
1
0
0
0
2
1
0
2
1
1
2
0
1
1
1
1
0
1
1
1
0
1
1
2
2
0
0
0
2
1
1
2
1
0
1
1
0
2
0
0
0
1
2
1
0
0
1
2
2
1
1
1
1
2
0
19
1
0
1
2
1
2
0
0
0
2
2
2
2
1
2
0
2
0
0
1
0
0
1
2
1
0
1
0
1
1
1
1
0
0
0
2
1
1
1
0
3
0
1
0
2
0
2
2
1
1
1
2
1
0
0
1
0
1
0
1
1
1
0
1
0
2
1
1
2
0
0
2
2
1
0
1
0
0
0
2
0
0
2
4
0
0
1
1
1
1
0
1
1
1
1
2
1
1
1
0
1
0
0
0
1
1
1
0
1
2
0
1
0
2
0
1
1
0
1
1
1
1
1
1
1
0
1
0
1
1
1
1
0
2
0
2
1
1
1
1
1
2
0
1
1
1
1
1
1
1
1
1
0
0
0
1
1
1
0
2
1
1
1
1
2
1
1
1
1
1
1
0
0
2
1
0
1
0
2
0
1
1
0
0
2
0
1
2
0
2
1
1
1
1
2
1
1
1
0
1
0
2
0
3
2
1
2
2
1
1
0
2
1
1
1
1
1
1
1
1
2
0
1
1
2
0
1
2
1
1
0
2
1
2
0
0
0
0
1
1
2
0
1
1
0
0
1
1
0
1
1
0
1
2
1
0
1
1
2
1
2
1
0
1
1
0
1
0
1
3
1
1
1
1
0
0
2
2
1
2
2
1
1
1
2
1
0
2
2
0
2
0
0
1
0
0
1
1
1
0
1
1
0
0
2
1
1
1
0
1
2
1
1
1
1
2
1
1
0
2
2
0
2
0
2
1
0
0
1
0
0
1
0
1
2
1
2
1
2
1
1
1
0
2
2
0
1
1
2
2
1
0
0
0
2
1
2
1
0
0
1
2
2
2
2
1
1
2
1
1
2
1
1
2
2
2
2
1
0
1
2
1
1
1
1
0
2
0
2
2
2
1
1
1
1
1
1
1
2
1
0
1
0
2
0
1
2
1
1
1
2
0
1
2
1
0
3
1
1
2
3
1
1
1
1
1
2
1
2
1
2
1
1
1
2
2
1
1
2
2
1
1
1
2
0
1
0
1
2
1
0
1
1
2
1
1
1
1
1
1
1
1
0
1
1
0
2
1
2
0
0
1
2
0
1
2
1
1
1
0
1
0
0
2
0
1
0
0
0
1
0
2
2
0
1
0
2
0
0
1
1
1
0
1
1
1
2
1
1
1
1
2
1
0
0
1
1
2
1
1
2
2
1
2
2
1
2
0
1
1
2
0
1
0
1
1
1
2
0
0
0
1
0
0
0
2
2
0
1
1
1
1
1
1
0
1
1
1
1
1
2
2
2
2
0
2
1
1
1
0
1
2
0
0
0
1
1
1
1
0
0
1
0
1
2
1
9
0
2
0
2
1
2
1
0
2
1
1
2
2
0
0
0
1
2
2
1
2
1
2
1
0
2
1
2
4
1
1
1
0
1
0
1
0
2
1
2
1
0
1
1
1
1
1
0
1
1
1
1
2
1
0
0
1
1
2
0
0
1
1
4
1
0
1
0
1
0
0
1
1
0
1
0
1
1
1
1
1
0
0
1
1
1
0
1
1
2
0
2
1
1
1
1
1
0
1
1
1
2
2
1
1
0
2
0
0
1
2
1
0
1
2
2
2
0
0
1
0
1
0
0
0
1
0
1
0
0
1
0
0
1
1
4
2
2
0
2
0
1
0
1
1
1
1
1
1
2
1
2
2
1
1
1
1
0
1
1
1
1
0
0
1
0
1
1
0
1
0
0
1
0
0
1
1
1
0
1
1
1
1
2
1
0
1
3
1
1
0
1
0
1
0
0
0
2
2
0
1
1
0
0
0
1
1
1
0
1
1
0
2
0
2
1
2
2
0
1
2
2
1
1
1
2
2
1
0
2
1
2
2
1
1
2
1
2
0
1
1
0
0
1
1
2
1
2
2
3
1
0
1
2
2
1
2
1
0
1
0
1
0
2
1
3
1
1
1
0
0
1
0
1
1
2
1
1
1
0
1
1
1
2
0
0
1
1
0
1
1
0
0
0
2
3
0
0
0
1
2
0
0
1
0
3
1
1
1
0
0
1
1
0
1
2
0
0
0
1
1
1
1
1
1
1
0
1
1
2
1
2
2
1
2
2
1
1
0
2
0
1
1
2
2
1
2
0
1
1
1
0
1
2
0
0
1
0
1
3
1
1
1
0
1
0
1
1
2
0
2
1
0
0
0
2
2
1
2
1
0
2
0
1
1
0
2
2
1
0
2
2
0
1
0
0
0
1
1
0
1
2
0
2
0
1
1
2
0
1
0
0
2
2
1
1
2
1
2
0
2
1
1
1
1
1
0
0
1
1
1
1
0
1
1
0
0
2
0
1
2
0
0
2
1
0
1
1
1
2
2
1
1
0
2
1
1
0
0
2
1
1
2
1
0
0
2
1
2
2
2
0
1
1
1
0
2
0
1
2
1
0
1
2
2
1
2
0
1
1
1
0
3
1
2
2
1
1
1
1
0
1
1
0
0
1
1
2
0
2
2
1
1
1
1
0
2
0
3
1
2
1
0
1
0
2
0
2
1
0
1
2
0
0
2
0
1
0
1
2
1
1
0
0
1
0
2
3
1
2
1
0
1
0
1
3
0
1
1
1
1
1
0
0
2
0
1
0
0
2
2
0
1
0
0
2
0
2
0
2
0
2
1
2
1
1
2
0
1
0
0
1
3
0
2
4
1
0
1
0
0
0
1
1
1
1
2
0
1
0
1
0
2
1
0
1
1
1
0
2
1
2
2
1
1
1
0
1
1
0
1
1
0
2
1
1
0
1
1
2
0
1
2
2
1
2
0
0
2
2
1
1
1
2
1
3
1
2
0
1
0
0
1
1
2
0
1
0
1
0
1
1
1
2
1
2
3
0
2
1
0
1
2
1
0
3
0
1
2
1
2
2
2
0
1
0
1
0
1
1
1
0
1
1
1
2
0
1
1
0
0
0
1
2
0
1
1
2
1
3
0
2
1
1
2
0
1
2
2
1
1
1
0
1
0
1
2
1
0
2
1
0
2
2
2
0
1
1
1
1
1
1
0
0
1
1
0
1
1
1
1
1
2
0
0
0
1
0
2
1
1
2
0
0
1
2
0
1
1
0
2
1
1
0
1
2
1
0
2
2
1
3
1
2
1
1
2
2
1
0
2
0
1
0
1
1
0
2
2
0
1
0
1
0
0
1
1
1
1
2
2
0
1
1
1
1
0
1
2
2
0
1
1
2
0
2
0
1
1
0
1
1
3
0
0
1
4
1
1
1
0
0
2
0
1
1
2
2
1
2
1
1
0
1
0
1
0
2
1
0
0
0
1
1
0
2
0
2
0
1
0
1
0
0
1
1
1
1
1
0
1
1
1
2
2
1
0
1
2
0
2
1
0
1
1
1
2
0
0
1
1
0
0
2
1
0
1
0
0
1
0
1
1
1
0
2
0
1
1
1
1
2
1
1
1
1
1
1
1
1
0
1
2
2
2
1
0
0
1
1
1
2
0
1
1
1
0
0
0
0
0
1
0
1
2
2
1
0
1
0
0
2
2
0
2
2
1
1
0
2
2
1
0
0
2
2
2
0
2
2
2
0
0
1
2
0
2
1
1
2
1
0
0
1
1
0
1
1
1
2
1
1
1
0
1
0
1
1
1
1
1
0
2
1
2
0
0
0
0
0
0
1
0
2
1
0
1
1
0
0
1
1
0
0
2
0
0
1
1
0
0
1
1
1
1
1
2
0
1
2
0
0
2
0
0
1
0
1
0
0
1
1
1
1
2
2
0
1
0
2
0
2
1
0
2
2
1
0
0
2
2
1
0
0
1
1
2
1
2
1
0
1
0
2
1
1
1
0
1
0
1
1
0
2
1
1
2
0
1
1
0
0
1
1
1
1
2
1
0
1
1
2
2
1
0
0
0
0
0
0
1
1
0
1
1
0
1
1
1
0
2
2
2
0
1
1
1
2
1
0
0
0
0
0
0
1
2
4
0
1
1
0
2
1
1
1
1
1
2
2
2
1
0
2
1
0
2
2
0
2
0
1
0
1
1
2
1
1
0
0
0
0
1
0
0
1
1
1
1
2
1
0
1
1
2
1
0
2
0
2
1
0
0
0
0
0
1
2
1
2
2
1
2
1
0
2
2
1
2
1
1
1
2
1
0
1
1
1
1
1
2
1
1
2
1
0
1
1
1
1
2
0
2
0
1
2
2
2
2
1
1
4
1
0
2
1
0
1
0
2
1
0
1
0
1
1
1
1
0
0
1
0
0
1
2
2
0
2
0
1
2
1
1
2
1
1
1
1
0
2
0
0
0
0
1
1
1
0
1
2
1
1
1
1
2
1
1
1
2
0
2
0
2
2
1
2
3
0
1
0
1
1
0
1
1
1
1
1
0
1
1
0
2
3
0
1
0
1
0
2
1
1
0
0
1
1
0
1
2
1
0
2
1
2
1
0
1
0
0
1
0
2
1
1
0
2
1
0
1
2
0
1
1
0
2
2
0
1
2
0
0
0
1
0
1
1
0
1
1
2
1
1
2
1
1
3
3
0
1
1
1
0
0
0
1
1
1
0
2
0
1
1
2
1
1
2
2
0
0
0
0
1
1
1
1
1
2
1
1
2
0
1
1
2
0
1
0
2
1
0
0
1
0
2
0
1
0
2
0
1
1
1
2
0
2
2
1
0
2
1
0
1
1
2
0
1
0
2
1
1
2
1
0
1
1
1
0
1
1
0
0
0
2
1
2
1
1
2
0
2
0
0
1
0
0
1
2
1
2
2
0
2
0
1
1
1
0
0
0
1
1
1
0
0
2
0
1
2
1
1
2
1
1
1
2
1
1
0
1
1
1
0
2
1
0
2
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
8
2
1
0
2
1
1
1
1
0
0
0
1
0
2
2
1
1
0
0
0
2
2
1
1
2
1
1
1
0
0
0
0
1
1
1
0
1
2
1
1
1
1
0
1
1
0
2
1
1
1
0
0
1
2
1
1
0
1
1
2
0
2
1
1
2
2
0
1
1
0
1
0
1
1
0
2
0
0
0
0
0
0
2
2
1
0
0
0
1
0
0
0
1
2
1
1
2
1
2
1
1
1
0
1
0
1
0
0
0
0
2
1
1
1
1
0
1
1
2
2
1
1
2
1
1
2
0
2
1
2
1
2
1
2
1
1
1
1
1
2
1
0
3
1
1
1
1
1
1
1
0
2
2
1
1
1
2
0
1
1
2
1
1
1
1
0
2
2
1
0
1
2
2
1
0
1
2
0
1
1
0
2
0
1
0
1
2
2
0
1
1
1
0
1
0
1
0
1
2
1
2
2
0
1
1
2
0
2
1
0
1
2
2
2
1
2
2
2
1
1
2
0
2
0
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
0
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
0
0
0
0
2
2
0
1
1
2
1
0
0
1
0
1
0
0
1
3
1
0
1
1
0
0
1
1
0
0
2
2
1
1
0
1
2
0
1
2
1
2
1
1
0
0
0
0
1
1
0
0
0
2
1
1
0
1
1
3
1
0
0
0
1
1
2
0
3
2
0
2
0
0
1
2
1
1
0
1
2
2
1
2
1
0
1
2
1
2
1
1
0
1
1
2
2
1
2
0
0
1
0
2
2
0
0
0
0
1
1
0
2
0
2
2
2
0
1
1
2
1
1
1
1
1
1
1
1
2
2
1
0
0
1
0
1
0
0
2
2
0
1
1
0
1
1
1
1
1
1
1
0
1
0
2
1
2
1
1
1
0
2
2
1
1
2
0
1
0
1
0
2
0
2
2
1
1
1
0
0
1
1
0
1
0
0
0
0
0
0
1
3
0
1
1
0
2
1
0
2
1
0
2
2
2
0
1
0
2
0
0
1
0
1
1
1
2
2
0
1
1
2
2
0
1
1
1
0
1
0
0
1
1
1
0
1
0
2
1
1
1
1
2
0
0
2
2
1
2
1
0
1
1
2
0
1
0
0
1
2
0
1
1
0
0
1
3
0
0
0
1
1
2
3
0
0
2
1
1
0
2
1
1
1
1
1
1
1
2
1
1
1
1
2
1
3
1
1
1
2
1
1
1
2
1
0
3
1
0
1
1
2
1
0
1
0
1
1
0
0
1
1
1
1
1
0
0
1
1
0
1
3
1
1
2
1
1
0
0
0
1
0
0
1
2
2
1
1
0
0
1
0
1
0
2
1
2
1
1
1
2
0
1
1
2
1
0
1
2
0
2
1
2
0
1
2
0
1
1
0
0
1
1
2
2
1
1
1
1
1
1
2
1
1
0
1
1
1
1
2
1
0
0
1
0
1
1
1
0
0
0
1
0
0
1
1
1
1
0
2
1
2
1
0
1
1
2
0
1
0
0
0
3
1
0
0
0
0
2
1
0
1
1
1
1
0
1
2
1
2
0
3
1
1
1
1
2
1
1
1
1
1
0
2
1
2
1
2
2
0
2
2
0
0
1
0
0
1
2
1
2
0
0
1
1
1
1
2
1
2
1
1
2
0
0
0
2
2
2
1
2
1
0
0
2
1
1
1
0
2
0
1
1
0
0
0
1
2
1
1
1
0
0
1
1
1
1
1
0
0
1
2
2
1
0
0
1
2
0
1
2
1
0
0
0
2
1
0
1
1
2
1
0
1
0
1
1
0
2
1
1
0
2
1
1
0
2
1
1
1
0
1
0
0
1
0
0
1
0
0
2
0
0
2
1
1
1
1
2
0
1
0
1
1
0
1
1
1
1
0
1
2
0
1
1
2
0
0
2
0
0
2
1
0
3
0
2
1
0
1
1
1
1
2
1
1
0
2
1
2
2
0
2
1
0
1
0
0
0
1
0
2
2
0
1
1
0
2
1
1
1
2
0
1
1
2
0
0
2
1
1
1
2
1
2
1
0
2
0
2
1
1
1
1
2
0
2
1
0
1
1
1
1
1
0
3
1
0
0
0
1
0
0
1
2
1
0
1
1
0
0
0
1
0
0
1
0
1
0
1
1
1
1
2
1
1
0
1
1
1
0
0
0
2
0
1
1
0
1
1
1
0
1
0
1
2
0
3
1
1
1
1
1
2
1
1
0
0
1
1
0
1
1
0
1
2
0
0
0
2
1
1
1
2
1
1
1
1
0
3
1
2
0
0
2
1
1
2
0
1
1
2
0
1
1
1
0
2
1
2
1
2
1
1
0
1
0
2
0
0
1
1
1
1
0
1
2
2
0
1
0
1
1
1
0
1
1
2
3
1
1
0
1
5
1
2
1
1
1
0
0
1
1
1
0
1
1
0
1
2
0
1
1
0
1
0
1
1
0
2
0
2
1
0
1
4
1
2
0
2
0
1
0
0
1
0
0
2
0
0
1
0
1
1
1
1
0
2
0
1
1
0
0
0
1
1
0
0
0
0
0
0
1
2
1
0
1
1
1
0
1
3
1
2
1
0
1
0
1
0
2
0
1
1
0
0
0
1
2
0
1
3
0
2
1
1
1
0
2
0
2
1
1
0
0
1
1
2
1
2
1
1
1
0
2
0
0
1
0
0
2
0
4
2
2
0
0
0
2
2
1
1
2
2
1
2
2
1
1
1
1
1
2
0
0
2
0
2
0
0
0
1
1
1
1
0
2
1
0
0
4
0
0
0
1
0
0
0
0
1
1
1
1
0
2
2
2
1
1
2
1
2
1
1
1
0
1
1
0
2
0
1
2
1
1
2
2
1
1
1
0
1
0
3
1
0
0
2
2
2
1
1
1
0
1
1
1
2
0
1
0
0
1
1
2
1
1
2
1
1
1
1
0
2
2
1
1
1
0
1
2
1
1
0
1
0
1
1
2
1
1
0
0
2
1
2
2
1
1
0
0
1
2
0
1
2
0
1
1
1
1
1
1
0
1
1
0
1
1
1
1
1
0
0
1
1
1
1
0
3
1
2
2
2
1
1
1
2
1
2
2
0
1
1
0
1
0
1
1
1
2
1
0
0
0
1
1
1
0
0
1
1
2
0
1
2
1
2
2
0
1
1
0
0
0
1
0
1
2
0
1
1
0
1
1
0
0
2
0
1
0
2
1
0
0
1
1
1
1
1
1
0
2
2
0
0
1
1
0
1
0
1
1
1
2
1
1
2
1
1
1
0
0
1
1
2
1
0
1
0
2
2
1
3
2
1
1
0
0
1
0
0
0
1
1
0
0
3
1
3
1
1
1
2
1
2
1
1
1
2
1
0
0
0
0
2
0
0
2
1
1
1
1
1
0
1
1
1
1
1
1
1
0
1
1
3
1
0
1
0
1
1
2
1
2
1
1
1
4
2
0
1
1
0
2
1
0
1
2
1
1
1
1
2
1
2
0
0
1
1
1
0
1
1
0
1
1
2
0
1
0
0
2
1
1
1
0
0
1
1
1
2
1
0
2
2
0
1
1
1
2
2
1
1
1
1
0
0
1
0
0
0
1
1
2
2
1
0
2
0
2
2
0
0
3
1
1
0
0
0
1
0
1
2
0
1
1
0
0
1
1
1
1
0
0
1
1
1
2
2
2
1
2
1
0
0
0
1
1
0
2
2
2
2
0
1
2
2
1
1
1
1
0
0
2
1
2
1
3
0
1
2
0
1
0
2
0
2
0
1
0
0
1
0
1
1
1
1
1
0
1
0
0
1
0
2
1
0
1
1
1
0
0
0
2
1
1
0
1
1
1
2
0
1
0
1
3
0
1
2
0
1
0
0
0
0
1
0
2
1
3
1
1
2
1
1
1
1
1
2
0
2
0
1
1
0
1
0
1
1
1
0
0
1
0
0
0
0
0
1
0
2
2
0
1
2
1
0
1
1
1
1
2
2
1
2
0
1
1
1
2
1
1
0
1
0
0
1
1
1
2
0
2
1
1
1
0
0
1
0
2
1
1
1
1
1
0
1
2
0
0
2
2
2
1
2
0
1
0
1
1
1
1
2
2
2
0
1
1
2
0
1
1
5
1
0
0
2
0
0
0
1
1
2
1
1
1
2
0
1
0
2
0
1
1
2
0
0
0
1
1
3
0
1
1
1
3
1
0
1
1
0
0
0
1
0
1
1
2
0
2
2
2
1
0
1
0
0
1
0
0
3
0
1
1
0
0
1
0
1
1
0
0
0
1
0
0
1
1
0
1
0
1
1
2
1
0
1
1
0
2
1
1
1
2
1
1
0
1
0
1
1
1
1
1
1
1
1
2
2
0
0
1
2
1
2
0
1
0
1
0
2
1
1
0
0
1
0
2
1
0
2
1
1
2
3
0
1
0
1
2
2
2
0
1
1
1
1
0
1
2
1
1
2
1
0
1
1
1
1
1
0
2
2
0
0
2
1
0
1
0
1
1
1
2
0
0
0
3
0
0
1
0
2
0
1
0
1
1
0
1
1
1
1
0
1
1
0
1
2
0
0
0
1
1
4
0
0
0
0
0
1
1
0
0
0
1
1
2
1
1
1
0
1
1
2
1
0
2
0
0
2
1
1
0
2
1
1
2
1
0
1
1
2
1
3
0
2
1
0
2
0
2
2
0
1
1
1
0
0
1
1
0
1
1
2
2
2
2
1
1
1
1
1
0
1
1
1
1
1
1
1
0
0
2
2
1
1
1
2
1
0
2
1
2
2
1
1
1
1
0
2
2
0
2
2
0
2
1
0
1
0
1
0
1
1
1
1
0
0
1
2
2
1
0
2
2
1
0
1
2
1
0
1
1
1
2
0
0
2
2
1
2
0
1
1
1
0
0
2
1
1
1
0
1
1
0
0
2
1
1
2
1
0
0
1
1
2
2
1
1
0
1
0
2
1
1
1
2
0
1
1
1
1
1
3
1
1
2
0
2
2
1
0
1
1
0
1
1
1
2
1
1
0
2
1
1
0
1
0
0
1
2
1
0
1
0
2
1
1
0
0
1
1
1
1
2
1
1
0
0
2
1
0
2
2
0
1
2
0
1
2
2
0
1
1
2
0
1
1
2
2
1
1
0
1
2
2
2
1
1
0
1
1
1
1
1
4
2
1
2
1
0
1
0
1
1
2
1
2
0
1
2
0
0
1
2
1
1
1
1
1
1
1
2
0
2
1
2
2
1
0
1
1
0
0
0
1
1
0
1
1
1
1
1
1
1
2
0
1
0
1
1
0
1
2
2
2
1
1
1
2
0
0
2
2
0
1
1
0
1
0
0
1
2
1
1
0
0
1
2
2
1
0
1
1
0
2
0
0
1
1
0
0
1
0
0
2
0
2
0
0
0
1
1
0
1
2
2
2
1
1
1
1
0
1
0
1
1
0
2
0
1
2
1
2
1
0
0
1
0
0
0
0
1
0
1
1
0
0
1
0
1
2
0
0
1
0
1
2
1
1
0
2
1
0
1
1
0
2
2
2
0
1
1
1
1
0
0
2
1
1
2
0
1
0
2
2
1
1
2
1
1
1
2
1
1
1
1
2
0
4
0
2
1
1
0
0
0
2
1
1
0
2
1
1
1
2
2
0
0
1
1
0
1
2
1
2
0
0
1
0
1
1
2
1
2
0
1
1
0
1
1
1
1
0
0
1
0
0
0
1
2
0
1
1
1
2
2
1
0
0
2
1
0
1
1
1
0
1
0
2
0
1
0
0
1
1
1
0
0
1
1
0
0
2
1
1
1
1
0
3
2
0
2
1
0
2
1
2
0
0
0
2
1
2
1
1
0
2
2
0
0
1
1
0
0
0
0
0
1
1
2
0
0
0
1
1
2
1
1
2
1
1
2
1
1
0
2
1
0
0
1
1
1
1
1
0
1
0
2
1
1
1
1
1
1
0
0
1
2
1
2
1
1
1
1
1
1
2
0
0
0
2
1
0
0
0
1
1
0
2
2
1
1
0
1
1
1
2
2
1
2
0
1
1
1
0
1
0
1
1
0
0
1
2
1
1
0
2
2
1
0
2
0
1
0
1
1
1
0
1
0
1
0
1
1
0
1
2
3
1
1
1
1
1
1
0
1
1
0
1
1
2
1
0
2
2
0
0
1
1
0
2
2
0
2
2
1
1
0
1
1
1
1
0
1
2
1
0
1
0
1
2
1
2
0
0
1
2
0
0
1
1
2
2
1
0
0
0
1
0
1
0
1
0
0
2
0
2
1
0
0
1
2
1
0
1
1
0
1
1
1
1
0
1
0
1
3
1
1
0
1
1
1
1
1
1
1
2
0
0
2
0
0
2
0
1
0
1
0
2
0
1
0
1
1
0
1
0
2
2
1
2
2
0
0
0
0
1
2
0
1
2
0
1
0
1
1
1
2
0
0
1
2
2
1
1
0
0
2
0
2
1
2
1
2
1
1
1
1
0
1
1
1
1
1
3
0
1
2
1
0
2
1
1
1
1
0
1
1
2
2
2
2
0
0
2
1
2
1
0
0
1
0
3
1
0
0
1
1
1
0
1
1
0
1
2
1
2
2
0
2
2
1
1
0
1
0
2
1
1
2
1
0
1
1
1
2
0
0
1
1
2
1
1
2
2
0
1
2
1
9
0
1
2
1
1
1
2
1
0
1
1
0
0
1
1
1
1
1
1
2
2
2
0
0
1
0
0
1
0
2
2
1
1
0
0
1
1
1
1
0
0
1
0
2
0
2
1
0
2
0
0
1
2
2
0
1
2
1
1
1
1
1
1
2
1
2
1
1
0
0
0
1
1
1
0
2
1
1
2
2
0
0
1
1
0
1
0
2
0
1
1
1
0
1
1
2
0
1
2
2
1
2
1
2
1
1
1
1
0
1
1
0
1
2
2
0
1
1
1
1
1
1
1
0
1
1
2
1
0
2
0
2
0
0
1
0
2
2
1
0
1
2
0
1
1
0
2
2
0
1
0
0
1
0
2
1
2
1
0
1
1
3
2
1
0
1
0
2
1
1
2
0
0
0
1
0
2
1
1
2
1
1
0
0
1
2
1
2
2
1
0
0
0
0
0
1
1
1
1
2
2
0
1
0
3
0
0
0
1
1
1
1
0
0
1
0
0
0
1
0
0
2
1
2
2
2
0
1
0
2
1
1
2
1
0
1
1
2
2
0
1
1
0
0
1
2
0
0
0
2
3
1
0
2
0
1
2
2
1
1
1
1
0
0
1
1
1
0
3
1
0
1
1
1
0
1
2
2
3
0
0
1
1
3
1
0
1
1
2
1
1
2
0
0
1
1
3
1
1
1
1
1
1
2
2
1
1
2
1
0
1
1
0
4
0
0
1
0
2
1
1
0
2
1
2
1
0
1
4
1
0
1
1
1
2
1
2
0
1
0
0
0
1
0
0
1
0
0
2
1
2
1
0
2
2
0
1
1
0
0
0
0
0
1
2
1
0
1
2
0
2
1
1
0
0
0
0
1
1
0
2
1
1
1
1
0
3
1
1
0
2
1
1
0
0
1
1
0
0
1
1
0
1
1
0
1
1
1
1
1
9
1
1
1
2
1
1
1
0
1
1
1
2
1
0
2
3
0
3
2
0
1
1
0
2
1
2
0
1
1
1
2
2
1
1
0
1
0
1
1
1
1
2
1
0
1
2
0
1
1
0
1
1
2
0
1
2
2
1
0
1
1
1
1
1
1
2
1
0
1
1
1
2
1
1
0
1
2
0
1
1
0
3
1
2
1
2
1
0
2
1
2
0
2
1
1
2
2
1
0
2
0
1
1
1
0
1
1
2
1
1
1
0
1
1
1
2
2
1
0
0
2
0
2
1
0
2
1
1
0
1
1
1
0
1
1
1
2
1
2
0
1
1
2
1
2
1
0
2
1
1
0
1
1
0
2
1
1
2
1
1
0
1
1
0
2
1
0
2
0
1
0
2
2
1
2
2
1
1
1
1
2
2
4
2
1
1
0
2
2
1
1
2
2
0
0
0
1
2
2
2
1
1
1
0
0
1
1
0
1
2
2
0
1
1
0
1
2
2
1
2
2
1
0
1
2
1
0
2
0
3
0
0
1
0
1
1
2
0
1
1
1
0
1
1
1
1
2
0
0
1
0
1
1
1
0
1
0
0
2
1
0
1
2
1
2
0
0
0
2
2
0
0
2
1
2
2
2
1
0
2
2
0
1
0
2
1
1
0
1
1
1
1
1
1
1
1
0
1
1
1
2
1
0
0
0
1
2
0
1
0
2
0
2
2
1
1
1
1
1
0
2
1
1
0
1
1
1
1
0
0
1
1
1
1
1
2
0
2
2
1
1
0
0
3
1
2
0
0
1
1
1
0
2
1
1
2
1
1
1
0
0
1
2
2
1
1
0
0
1
1
1
0
0
1
1
1
1
1
1
1
1
2
1
0
1
1
1
1
1
1
1
1
3
1
0
0
1
0
1
2
1
1
0
0
1
3
1
1
1
0
0
1
1
1
2
0
1
1
1
0
0
2
2
0
0
1
1
1
0
2
1
0
0
0
0
1
2
0
0
1
0
1
1
3
2
2
1
0
0
0
2
0
1
2
1
1
0
1
2
1
1
2
1
0
2
1
1
0
1
1
0
0
0
1
1
1
2
1
1
0
2
1
1
1
1
0
1
0
1
1
0
0
2
0
0
0
1
0
1
1
2
1
1
1
2
0
0
1
1
1
1
1
0
1
1
0
2
0
2
2
1
0
2
1
2
1
2
1
0
1
1
2
0
1
0
2
1
1
1
0
1
1
0
1
1
2
1
1
1
0
1
4
1
1
2
0
1
1
2
0
1
1
1
0
1
0
0
1
0
0
0
0
1
0
1
1
0
1
1
1
1
0
1
2
1
2
0
0
2
2
1
0
0
1
0
1
0
2
0
1
0
1
1
0
1
1
1
1
0
0
1
2
0
0
1
1
1
1
1
2
2
2
1
1
0
1
0
1
1
0
1
1
1
1
0
1
1
2
0
0
1
0
1
2
1
1
1
0
1
1
0
0
0
0
0
2
1
1
1
1
0
2
0
2
0
0
1
0
1
0
1
2
0
0
1
2
1
1
2
1
1
1
0
1
1
0
1
2
1
0
2
0
0
1
0
1
0
2
1
0
1
1
2
1
1
1
1
0
3
2
2
0
1
0
1
0
1
0
1
0
1
2
1
1
2
1
1
0
1
2
1
2
1
0
0
0
1
1
1
0
1
0
0
0
3
0
1
1
1
0
1
0
2
2
1
0
1
1
0
0
2
1
0
2
1
0
1
2
0
1
1
1
2
1
1
1
1
0
2
2
0
1
1
2
0
1
2
0
3
1
1
1
1
1
1
0
1
1
2
1
2
1
1
1
2
2
1
1
1
0
2
0
1
0
2
1
1
1
1
1
1
0
0
0
0
2
1
1
1
2
1
1
0
0
0
1
0
0
1
1
0
2
1
0
1
1
1
0
2
1
1
1
0
0
1
1
0
2
1
1
1
1
2
1
0
2
0
0
1
1
0
0
0
1
2
0
3
1
2
1
1
1
1
1
2
0
2
0
2
1
2
2
2
1
0
0
1
0
2
2
1
0
2
0
2
1
1
1
0
1
1
0
2
1
2
1
0
1
0
0
1
1
1
0
1
1
1
0
1
1
1
2
2
1
1
1
2
0
1
1
1
0
1
1
0
0
3
2
1
1
1
1
2
0
1
0
2
0
1
0
1
0
1
0
1
1
0
0
2
1
2
1
2
1
0
1
2
1
2
2
1
0
1
1
1
1
2
1
2
0
2
2
0
1
1
1
2
2
2
2
1
1
0
1
1
0
1
0
1
0
1
0
0
1
1
0
1
0
2
1
1
1
0
2
2
1
1
0
2
1
0
1
1
1
2
1
2
1
1
0
0
1
1
2
2
2
1
1
1
1
1
0
2
0
2
4
2
1
1
1
1
1
2
2
0
1
1
3
1
0
0
1
2
0
1
1
2
2
1
0
0
1
1
1
1
1
2
0
1
1
1
0
1
1
0
1
0
0
0
1
2
1
1
3
1
1
0
1
0
0
0
2
0
1
3
1
1
1
2
2
1
0
1
1
1
1
0
1
1
1
0
0
1
1
1
1
1
4
1
1
0
0
1
1
1
1
1
1
0
2
0
1
2
1
1
2
0
2
2
0
1
1
1
1
0
2
1
2
2
0
0
0
2
0
2
0
1
2
2
1
0
2
1
0
2
1
0
2
1
0
2
2
0
0
2
1
0
2
1
1
1
0
1
2
1
1
1
2
2
0
0
0
1
0
2
1
1
1
0
1
2
2
0
2
0
0
1
1
0
0
1
1
2
1
2
2
1
1
0
1
1
1
0
0
1
2
1
0
2
0
2
1
2
1
0
0
2
1
1
1
1
1
0
3
1
1
0
0
1
1
1
1
1
0
1
1
1
0
1
0
2
1
1
1
0
1
0
1
1
2
0
1
1
0
1
1
1
0
2
0
2
1
1
1
1
0
1
1
0
1
1
1
1
2
1
0
1
2
2
1
0
1
2
2
2
1
0
2
1
2
2
1
1
2
0
1
0
0
1
1
0
0
0
1
1
0
0
2
1
2
2
2
0
2
1
1
1
1
2
0
2
1
1
0
2
2
1
2
1
0
1
0
2
1
1
0
1
1
1
1
2
2
1
1
1
1
0
0
1
2
0
0
1
0
0
0
1
1
1
1
0
0
1
0
0
1
2
1
1
1
1
1
2
0
2
0
1
0
1
1
2
0
2
1
1
0
2
0
0
0
1
1
1
1
0
1
0
1
0
1
1
1
1
1
1
0
1
1
1
0
0
0
1
1
15
2
1
0
2
2
1
1
1
2
2
2
1
3
2
2
1
1
0
3
0
0
1
0
1
1
0
1
0
1
0
1
0
1
2
1
1
1
0
1
2
0
6
1
0
1
0
1
1
2
3
2
1
0
2
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
2
2
1
1
1
2
0
1
1
0
1
1
0
1
1
0
1
1
0
0
1
1
2
0
2
0
1
1
2
1
1
0
0
1
2
0
0
0
1
1
0
1
3
0
0
1
0
1
0
1
1
1
2
1
1
1
2
0
1
2
1
1
1
0
1
0
1
1
1
1
0
1
1
2
0
2
2
1
1
0
1
1
0
2
1
2
1
2
2
0
1
1
2
1
0
0
1
1
0
2
1
0
2
2
1
0
1
1
0
1
0
1
1
1
1
0
2
3
2
2
1
1
2
1
0
2
0
1
8
2
1
2
1
0
1
1
0
0
2
0
1
0
1
2
0
0
0
0
0
1
1
2
1
0
2
0
2
1
1
1
1
0
2
0
1
2
1
1
0
2
1
0
0
1
0
1
0
0
1
1
1
1
1
1
1
1
0
0
1
0
1
0
2
2
1
0
1
0
1
0
2
0
1
1
1
1
0
1
1
2
1
0
1
0
2
0
2
0
2
1
0
2
0
1
1
1
1
1
0
2
1
2
1
0
1
1
0
0
1
1
4
2
1
2
1
1
2
2
1
0
2
2
0
0
0
1
0
1
1
0
0
1
1
1
0
1
0
1
1
1
1
1
1
3
2
0
0
2
1
0
0
1
2
1
1
0
1
1
1
2
1
1
1
0
1
1
2
2
1
2
0
1
0
0
0
1
1
2
1
1
4
2
1
1
1
0
1
1
0
1
0
1
0
1
1
2
2
0
1
0
1
2
2
1
1
1
0
0
3
0
1
0
1
2
1
0
0
1
1
0
0
0
1
1
1
1
1
1
1
1
1
1
0
0
3
2
1
1
1
1
2
2
2
2
1
3
2
0
1
1
2
0
0
2
1
2
1
1
2
0
1
1
1
2
2
1
0
0
1
2
2
0
1
1
1
2
0
1
0
2
1
2
0
1
1
2
2
1
1
1
0
1
2
1
1
1
1
2
2
1
1
1
2
2
1
1
0
0
1
2
1
2
1
2
2
1
0
1
1
2
0
1
0
1
1
1
1
0
0
0
0
1
0
0
3
2
1
2
0
2
1
0
1
1
0
1
0
0
1
2
1
0
1
2
0
1
1
2
2
1
1
0
2
1
1
1
1
0
2
1
1
1
1
2
0
1
3
1
3
2
0
1
1
1
1
1
2
1
1
1
0
1
1
1
5
1
1
2
2
2
1
1
0
2
2
1
2
1
2
1
2
0
2
1
0
1
1
1
1
1
1
2
0
0
0
2
0
2
0
1
2
1
2
0
2
2
2
0
0
1
0
1
1
1
0
1
0
0
1
0
1
1
0
2
1
0
1
0
1
3
1
0
1
1
2
2
1
1
1
2
1
2
0
0
1
1
1
2
1
1
1
0
0
1
1
2
1
1
2
1
2
1
0
1
1
0
1
0
1
0
2
3
1
7
2
0
1
2
1
1
2
1
0
2
1
2
1
1
0
1
1
0
2
0
1
2
1
1
1
1
1
2
2
1
1
2
0
1
1
0
1
1
1
2
2
3
2
1
2
1
1
0
1
0
1
2
2
2
1
1
0
2
0
0
0
1
0
0
0
0
0
0
1
1
8
0
0
2
2
1
2
0
1
1
2
0
1
2
0
1
2
1
1
1
1
1
0
1
0
0
0
2
2
0
1
1
0
1
1
1
2
1
1
0
2
0
2
0
0
2
1
0
0
1
0
1
0
0
1
2
1
0
0
1
3
2
1
2
1
1
0
4
1
1
0
0
1
0
2
0
1
1
0
1
1
1
3
2
0
1
2
1
1
0
1
1
0
1
0
0
1
2
0
2
0
1
1
1
0
1
1
1
0
2
1
0
1
0
2
1
0
0
1
2
2
2
1
1
1
2
0
0
0
2
1
1
1
1
2
1
1
1
0
1
1
0
0
0
1
0
0
0
1
0
2
1
0
1
5
1
2
1
2
1
0
0
1
2
1
1
0
0
1
2
1
0
0
2
2
1
1
1
1
2
0
2
1
0
2
0
0
1
4
2
2
0
0
0
1
1
2
1
1
2
2
1
1
1
1
2
2
2
1
0
0
1
0
1
2
0
0
3
0
0
0
0
1
1
1
2
2
0
0
2
2
1
2
0
1
1
2
1
1
1
0
1
0
0
1
2
2
0
1
0
0
1
2
2
1
0
1
0
0
0
1
1
2
0
1
2
2
1
1
1
1
0
1
1
0
1
1
0
2
1
0
0
2
2
1
1
1
0
1
2
1
0
0
1
0
1
1
1
2
1
0
1
1
1
1
1
0
0
1
0
1
2
0
1
1
0
0
0
0
1
2
1
1
1
2
7
1
2
1
2
1
0
2
0
1
1
1
0
1
2
2
2
0
1
0
1
2
1
2
1
1
1
1
1
1
1
2
0
0
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
2
1
0
2
1
0
2
1
0
1
1
2
1
0
1
2
1
0
0
0
1
2
1
2
1
2
1
2
0
1
1
0
0
1
1
1
1
1
1
1
1
0
2
2
1
1
2
1
1
0
1
1
0
1
2
2
2
2
0
0
1
1
2
1
1
1
2
1
1
0
2
0
2
2
1
2
1
2
2
2
0
0
2
1
1
2
1
0
1
1
2
0
2
1
1
2
1
2
1
0
1
1
1
2
1
0
1
2
1
0
1
0
1
1
1
2
0
4
0
1
1
0
1
0
1
1
2
1
0
0
2
2
1
0
0
2
1
2
1
1
2
1
1
0
2
2
2
1
1
1
0
0
1
0
0
1
1
0
2
1
0
0
2
0
1
1
2
2
1
1
2
0
1
1
2
2
0
0
0
0
3
2
1
2
1
0
2
2
2
0
1
0
2
1
0
1
1
1
2
0
1
1
1
0
0
0
1
1
1
2
0
0
0
2
0
1
0
1
0
0
1
0
1
2
1
0
1
1
1
2
2
1
1
3
1
0
2
2
0
0
2
0
1
0
1
0
0
1
0
1
1
1
2
0
0
3
1
1
0
1
1
1
2
1
3
1
2
1
1
2
1
1
2
1
0
0
2
1
2
1
0
1
2
0
0
0
2
0
2
0
1
1
2
0
1
1
0
1
1
0
0
1
1
2
2
1
1
2
0
1
0
1
1
1
1
1
1
0
1
1
0
1
1
1
2
2
0
1
0
1
2
1
1
1
2
1
1
0
1
0
1
1
1
1
0
2
1
1
1
0
1
2
0
1
1
1
1
2
2
1
0
1
0
1
2
2
1
0
1
0
0
1
0
2
1
0
1
3
1
0
2
1
0
1
1
1
2
1
1
1
1
1
2
2
0
0
1
0
1
2
0
1
0
0
0
1
1
1
0
1
1
1
1
1
0
1
1
1
2
1
0
0
0
1
1
2
1
0
1
1
0
1
1
2
1
0
1
1
1
1
1
2
0
0
2
0
1
1
1
1
1
1
1
1
1
1
0
0
0
0
1
1
2
2
2
0
1
1
2
0
1
1
0
1
1
1
0
0
2
1
1
1
1
2
2
2
1
2
0
1
1
1
0
0
1
1
0
1
1
1
0
1
1
1
2
2
2
1
1
1
1
1
1
1
1
0
2
1
0
0
2
0
1
1
0
0
1
1
1
0
0
1
2
1
1
0
1
1
1
4
2
1
0
1
0
0
2
1
1
2
0
2
1
1
1
1
0
1
1
0
0
1
1
2
2
1
1
0
2
2
1
1
1
1
1
1
1
0
1
2
1
0
0
0
2
1
0
1
0
1
1
1
0
2
1
0
0
1
0
1
1
1
1
0
1
1
0
1
0
1
1
0
1
0
1
2
1
1
1
1
1
1
3
2
1
1
0
1
2
1
1
1
1
2
0
2
1
0
2
2
2
0
0
1
0
1
1
2
0
2
0
1
1
1
1
1
1
0
0
2
2
0
2
0
0
1
1
0
1
1
0
1
1
1
3
1
1
1
0
2
0
2
0
1
2
0
0
1
0
1
1
1
0
1
0
2
1
0
1
1
0
2
1
0
0
0
1
0
1
1
1
1
0
1
3
0
1
1
1
2
0
0
0
2
2
1
4
0
1
0
1
1
1
0
2
0
1
1
2
2
1
2
1
1
0
1
1
0
1
1
0
1
2
1
0
1
1
0
1
2
1
0
0
2
1
1
2
1
1
1
2
0
1
0
2
2
0
0
1
1
0
1
1
0
1
0
0
1
0
1
2
2
0
0
0
1
0
0
1
2
1
1
1
1
1
0
1
1
0
0
1
0
1
1
0
1
1
1
0
1
1
0
1
0
0
1
1
0
2
2
3
2
0
2
0
0
1
1
1
1
2
1
0
1
1
2
0
1
1
4
2
0
1
0
0
1
0
1
1
1
1
1
2
0
0
1
1
2
0
1
0
0
2
1
3
1
0
1
1
2
0
1
1
1
2
1
2
1
1
1
2
0
1
2
0
1
1
1
0
1
2
0
1
2
1
1
1
2
2
1
1
0
1
1
1
1
1
0
0
1
1
2
0
0
1
1
3
1
2
1
1
2
1
0
0
0
2
2
0
1
2
0
0
2
0
1
1
1
0
2
1
1
1
0
1
1
0
2
3
2
0
1
0
1
1
1
1
0
1
0
0
1
0
0
2
0
1
0
2
1
0
2
1
1
2
2
2
0
1
0
1
2
0
2
0
0
1
1
1
2
3
2
1
0
2
1
0
1
1
1
2
0
2
1
0
0
1
2
1
2
2
1
2
2
2
1
1
1
2
0
1
1
0
1
0
2
1
2
1
1
1
2
2
2
1
1
1
0
1
1
0
0
1
1
1
1
2
2
1
1
2
2
1
1
0
1
0
0
2
0
0
2
1
1
1
0
1
0
0
1
0
2
1
0
0
1
0
2
0
2
1
0
1
1
1
1
0
1
1
1
1
1
2
0
0
1
2
1
0
1
1
0
1
1
0
1
1
1
0
0
0
2
1
0
1
1
1
1
1
1
1
0
3
1
1
1
1
2
1
1
2
0
3
1
0
0
0
1
0
1
1
2
1
1
1
0
2
0
0
1
1
2
1
1
1
1
0
1
1
0
1
1
0
0
0
2
1
1
1
1
0
1
0
0
1
1
2
0
2
1
2
0
1
1
2
0
0
2
1
2
0
0
0
1
1
2
1
1
1
1
0
1
2
1
2
1
2
2
2
0
1
1
1
0
1
1
1
1
3
1
1
1
0
0
1
1
0
1
0
2
1
1
0
1
2
0
2
1
0
2
2
0
1
2
2
2
3
0
0
0
4
0
1
2
0
1
1
2
0
0
2
0
0
2
1
2
1
1
1
0
1
0
1
1
0
1
1
2
0
0
1
0
1
0
1
1
2
2
0
0
1
1
1
0
1
0
1
1
1
0
0
1
0
0
1
1
0
0
0
2
1
2
0
1
0
1
0
1
1
2
1
1
1
1
0
2
1
2
2
1
1
1
1
1
1
1
2
1
1
0
0
2
1
1
0
0
1
1
1
0
1
1
0
2
1
2
1
2
2
2
1
1
1
2
2
0
0
1
2
2
0
2
1
1
1
0
0
0
1
1
1
1
1
2
0
0
2
0
0
1
0
0
1
2
1
1
1
3
1
2
3
1
2
1
1
1
1
0
2
1
1
0
1
0
1
1
2
1
1
1
3
1
0
1
2
1
1
1
2
2
1
1
0
1
0
0
2
2
1
0
1
2
0
2
0
2
0
3
1
0
1
1
1
2
1
2
1
2
0
0
1
1
0
1
1
0
1
0
1
1
1
0
1
0
0
1
1
3
1
2
0
0
0
1
2
2
1
2
0
1
1
1
0
2
0
1
2
1
0
0
0
2
3
2
0
1
0
1
1
0
1
0
0
0
2
1
0
2
1
1
1
0
1
1
0
0
1
0
1
1
1
0
0
1
0
2
0
0
2
1
1
1
0
1
0
2
1
1
0
0
0
1
1
0
0
1
1
1
0
1
0
1
0
1
1
0
2
1
2
1
0
0
2
1
1
1
1
1
1
1
1
0
0
1
0
0
0
0
1
0
1
1
1
2
0
1
0
1
1
1
0
2
1
1
0
1
2
1
1
0
1
0
0
2
2
1
0
2
0
1
1
2
0
0
0
1
2
1
0
0
0
0
0
0
1
1
1
0
1
1
0
0
0
1
1
1
2
1
1
1
1
1
1
1
1
0
0
1
2
0
0
1
1
0
1
2
0
0
0
1
0
1
2
0
0
1
1
1
1
0
1
1
2
0
1
1
0
2
1
1
2
0
0
1
1
1
0
1
0
1
0
1
2
2
0
1
1
0
3
1
1
1
0
2
0
1
1
0
2
0
1
1
0
1
1
1
2
1
2
0
0
2
1
1
1
2
0
1
0
1
0
0
1
1
0
1
0
0
1
1
1
1
0
1
0
0
0
2
1
1
2
0
1
1
1
2
0
0
2
0
2
1
3
2
2
1
1
1
0
0
0
0
1
0
1
2
1
1
2
1
0
1
2
2
1
1
0
1
1
1
1
0
0
2
1
1
1
0
2
0
0
1
1
0
0
0
0
0
2
1
2
0
0
1
1
0
1
2
2
0
0
2
1
1
1
2
0
1
1
1
1
2
1
1
2
0
2
0
1
1
1
1
0
2
0
1
1
1
0
0
0
1
1
2
1
0
1
2
1
1
0
1
0
2
1
1
3
0
0
0
0
1
2
0
0
1
0
2
2
2
1
1
1
2
2
1
0
1
2
1
1
1
1
1
2
0
2
0
2
1
1
1
2
1
2
2
1
1
1
1
1
1
0
1
0
1
0
2
2
1
1
0
0
1
1
1
1
0
1
1
1
1
1
1
1
2
1
1
2
2
2
0
2
1
1
2
0
1
1
1
0
1
1
0
1
2
1
1
0
1
1
0
0
1
0
2
1
1
2
0
1
4
1
0
2
0
1
1
2
0
1
2
0
2
0
1
1
1
1
2
1
1
1
0
1
1
2
1
2
1
1
0
2
1
0
2
1
1
1
1
0
1
2
2
0
1
1
1
1
1
1
0
1
1
2
1
1
1
1
0
0
1
0
0
0
0
1
1
0
1
1
1
1
1
2
0
0
1
1
1
1
2
1
1
1
1
1
3
0
1
0
1
0
1
1
2
1
1
1
1
2
1
2
0
0
0
0
0
2
2
1
0
2
1
0
1
1
1
0
1
0
0
0
0
2
2
1
1
0
2
0
2
1
1
0
2
0
0
1
1
1
1
1
1
0
1
1
1
2
0
1
2
0
1
0
0
0
1
0
0
0
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
0
1
0
1
1
0
1
2
1
1
1
2
2
0
1
1
0
0
1
1
2
0
2
1
2
0
1
1
2
2
1
1
0
2
1
1
0
1
1
1
1
0
2
1
1
1
0
2
1
1
2
2
2
2
1
0
1
0
0
1
1
0
1
1
0
1
0
0
1
0
1
0
3
0
0
1
1
2
0
1
1
1
1
0
2
2
1
2
0
1
0
1
1
1
0
1
1
1
1
0
1
2
2
2
0
1
1
1
1
0
2
2
0
2
0
1
2
1
2
1
0
0
1
1
1
2
0
1
0
0
0
0
0
2
2
1
1
2
0
2
0
1
0
0
1
2
2
2
0
1
1
1
1
2
1
0
0
0
2
1
0
2
1
2
1
2
1
0
0
2
1
1
2
2
2
2
0
0
0
1
0
0
0
0
2
0
1
1
2
2
1
1
0
1
1
1
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
3
2
1
3
0
1
0
1
0
1
0
1
2
2
1
1
1
0
1
1
0
0
3
0
0
1
2
1
1
0
1
0
1
2
1
1
1
0
1
0
0
3
2
0
1
1
0
1
1
1
0
1
0
2
0
0
2
0
1
1
2
1
2
2
1
1
1
0
2
1
0
2
1
0
1
0
0
1
1
1
0
2
1
1
0
0
2
1
0
1
2
0
2
0
0
2
1
0
1
1
1
1
2
1
2
1
1
1
0
0
1
1
1
1
1
2
0
0
1
2
1
1
1
0
1
0
1
1
1
1
1
1
0
2
0
0
0
1
0
1
1
2
2
1
1
1
1
1
0
2
2
0
1
2
0
2
1
2
2
1
1
1
0
1
0
2
1
0
2
1
0
1
2
2
3
0
0
1
1
2
1
1
0
2
1
1
1
1
1
0
0
0
1
2
1
0
1
2
1
0
1
2
1
0
1
0
0
1
1
0
0
2
2
1
1
0
1
1
2
0
2
1
2
1
1
1
0
2
1
2
2
1
1
0
1
1
1
2
1
1
2
1
1
0
1
1
2
1
1
1
1
0
2
1
2
0
2
2
0
1
1
1
1
1
1
1
1
1
0
0
2
1
0
1
1
2
1
1
1
2
1
0
2
2
1
1
0
0
0
1
0
1
2
0
1
2
1
1
0
2
2
2
1
1
1
1
0
0
2
2
1
0
0
0
1
1
0
0
0
0
2
2
1
1
2
2
2
2
0
1
1
0
2
2
2
1
0
1
0
0
0
2
1
2
1
0
2
2
2
0
0
2
1
1
0
1
2
1
1
0
2
1
0
1
0
2
1
1
2
0
1
1
1
1
0
1
0
1
2
1
1
0
1
0
1
0
6
2
1
1
0
2
1
2
1
1
1
0
1
2
0
1
2
0
1
0
1
1
1
1
0
0
0
1
2
1
1
1
1
1
1
1
0
1
1
1
1
0
2
1
1
2
2
0
2
0
2
1
2
2
1
0
2
1
1
2
2
1
0
0
0
0
1
0
1
0
1
2
0
0
0
0
2
0
2
1
0
0
1
0
1
0
1
1
1
1
1
1
0
3
1
1
2
0
0
2
2
1
1
0
0
1
0
0
1
0
0
2
1
2
1
2
0
3
2
0
1
1
2
1
0
1
1
0
1
1
1
0
1
0
0
0
1
1
0
1
1
0
0
1
0
1
0
0
0
2
0
0
0
1
1
0
0
1
2
2
1
1
0
0
2
1
2
2
1
0
1
0
2
1
1
1
2
0
1
0
1
1
0
0
1
0
0
1
1
1
1
1
2
0
1
1
1
0
1
2
2
2
0
0
0
1
1
2
1
1
1
1
0
1
0
1
2
2
0
0
2
2
1
0
0
0
1
1
1
1
2
0
1
1
1
1
2
1
2
2
1
0
0
1
1
2
0
0
1
1
2
1
0
1
1
2
1
1
1
1
2
0
0
2
0
1
1
1
1
0
2
1
2
0
1
1
1
1
0
0
1
2
1
0
1
1
0
1
0
1
0
1
2
2
1
0
2
0
1
2
1
1
1
2
0
1
2
1
1
1
1
1
0
1
0
2
1
1
2
1
2
1
2
2
1
0
1
0
1
1
1
1
2
1
2
1
1
0
0
1
2
2
1
1
1
0
0
0
0
1
1
0
0
1
0
1
0
2
1
2
0
1
2
1
1
2
0
1
1
2
2
0
1
1
1
0
0
0
0
0
0
0
0
0
1
1
2
1
1
1
1
1
1
2
1
0
1
2
1
2
1
0
1
1
1
0
1
1
1
2
0
2
0
2
1
0
2
2
1
0
3
1
2
1
1
2
1
2
0
1
0
0
2
2
1
1
0
0
0
1
0
0
1
0
0
1
0
0
1
1
1
1
0
2
0
0
0
2
1
1
0
1
0
2
0
1
1
1
1
0
1
1
1
2
2
1
1
2
2
0
1
1
1
1
0
2
1
2
1
0
0
1
1
1
0
1
1
1
1
1
1
0
1
1
1
2
0
0
0
0
0
2
1
0
1
1
0
1
0
1
1
0
2
0
1
2
2
1
2
2
8
0
1
1
2
2
0
1
0
2
2
0
1
2
1
1
3
0
1
0
1
1
2
0
1
0
0
2
0
1
0
0
1
0
0
1
0
1
2
0
2
0
0
2
2
0
1
2
1
2
0
1
1
1
0
1
0
1
0
2
0
0
1
1
1
1
1
1
1
0
2
1
2
0
1
2
0
0
1
0
1
0
2
2
2
1
0
0
1
1
1
0
1
2
1
2
0
2
0
0
2
1
2
1
1
0
1
2
1
1
1
2
2
1
0
1
1
1
1
1
1
0
0
2
2
1
0
0
2
1
1
2
1
0
1
1
2
1
1
1
0
2
0
1
0
2
1
3
0
1
2
0
2
0
1
0
0
2
0
1
0
1
1
1
1
0
1
1
1
0
0
0
0
1
2
1
1
0
2
2
2
3
1
1
1
2
1
1
0
0
0
1
0
1
0
0
1
1
1
1
1
1
2
1
1
1
1
1
1
1
0
0
2
0
0
0
0
0
2
1
0
0
0
2
1
1
1
2
1
1
1
1
1
1
0
0
1
1
2
1
0
2
0
1
1
2
1
1
2
2
0
1
0
2
1
2
1
2
1
1
1
1
2
1
0
2
0
0
1
1
1
0
0
1
1
1
1
0
0
0
1
1
0
2
1
1
0
1
3
1
0
0
1
1
0
1
0
3
1
2
1
1
2
2
2
1
1
0
1
0
0
1
2
1
2
2
1
2
1
0
0
2
1
1
1
0
1
0
0
0
1
0
0
2
0
1
2
2
0
1
2
1
1
0
2
2
1
0
0
2
1
0
0
0
0
1
2
2
2
1
2
2
2
0
2
4
0
2
0
1
1
1
0
0
0
1
1
1
2
2
1
1
0
1
1
2
2
0
1
0
1
0
1
2
2
0
1
2
0
1
0
2
1
2
2
1
0
1
1
1
2
0
0
1
1
2
0
2
0
0
5
2
0
2
1
2
1
2
0
2
0
0
1
2
0
1
2
2
1
1
1
2
1
1
0
0
1
1
1
0
2
1
2
2
0
2
1
1
0
1
2
1
1
1
2
0
0
1
0
1
0
0
3
0
2
0
1
0
1
1
1
0
1
1
2
2
2
1
1
2
0
0
1
2
2
0
0
0
2
1
2
1
1
2
1
0
0
1
0
0
2
2
0
0
1
1
1
0
1
1
2
1
1
2
0
0
0
1
1
0
2
0
2
0
2
1
1
0
0
1
0
0
1
1
2
2
1
1
2
0
1
1
2
1
0
0
1
1
1
1
0
0
1
1
2
0
2
1
1
0
2
1
1
1
0
0
1
2
1
1
1
2
0
1
1
1
0
0
1
2
1
0
0
1
0
0
2
1
1
1
0
1
1
1
1
2
1
0
0
0
1
1
0
0
1
2
1
2
0
2
1
2
1
0
0
1
2
1
1
3
0
1
2
1
2
1
0
0
1
0
1
0
2
1
1
0
1
0
1
1
0
0
1
0
1
1
1
1
0
1
1
1
0
1
2
2
1
1
0
0
1
1
1
1
0
0
0
2
1
4
2
0
2
1
2
0
1
2
0
0
1
1
2
1
1
0
1
0
1
2
1
1
2
6
1
1
0
1
2
0
2
1
2
2
0
0
0
1
0
1
0
1
3
2
1
0
2
1
1
2
2
1
1
1
1
0
0
0
0
2
0
0
2
1
1
0
1
0
1
2
2
2
2
1
0
2
1
1
0
1
2
1
0
1
0
0
2
0
2
0
2
1
0
2
0
1
1
0
1
1
1
5
1
0
1
0
2
1
1
1
0
2
1
1
1
2
1
0
1
1
0
1
1
1
2
2
0
1
1
1
1
0
0
0
1
1
1
0
1
1
0
0
0
2
0
0
2
1
1
1
2
0
1
2
1
0
1
1
0
0
0
1
1
0
1
1
0
1
0
1
1
0
1
1
0
0
1
1
1
2
2
1
1
3
2
1
2
2
0
0
1
0
1
0
0
0
1
1
1
0
1
1
0
1
1
1
2
1
0
0
1
2
1
0
0
2
2
1
1
1
1
1
1
2
1
2
2
2
2
1
1
3
2
1
1
1
0
2
0
0
2
0
2
2
1
2
1
2
1
1
1
1
1
1
1
0
2
0
0
1
0
0
1
1
0
2
0
0
2
1
0
1
1
2
1
1
1
0
1
1
0
1
1
2
2
2
1
1
2
1
1
2
2
1
0
2
1
2
0
2
0
0
0
1
1
0
0
1
0
0
1
2
1
0
0
1
2
0
2
2
1
1
1
1
1
1
1
0
1
1
1
0
1
1
2
2
1
1
0
0
0
2
0
0
1
1
0
1
1
1
0
1
1
0
1
1
1
1
0
1
0
1
2
2
1
0
1
1
2
0
2
1
2
1
1
2
1
0
1
2
2
1
1
2
0
1
0
2
2
1
2
1
1
1
1
1
0
1
1
0
1
1
1
1
0
0
1
1
0
1
2
1
0
0
1
1
1
0
1
2
1
0
0
1
1
1
3
1
2
3
2
1
1
0
1
1
0
1
0
0
2
2
0
1
2
2
2
0
1
0
2
1
1
1
0
1
1
0
1
1
1
0
1
1
1
0
1
0
1
1
1
2
1
1
2
1
2
1
1
2
1
0
1
1
1
0
4
2
1
2
0
1
0
1
1
1
1
1
1
0
0
1
2
2
1
1
0
0
3
1
2
0
1
1
2
1
0
1
2
0
0
1
1
0
1
1
1
1
2
1
1
1
2
0
1
0
1
1
0
0
1
0
0
1
1
0
1
0
1
1
0
1
1
0
1
1
2
2
4
2
2
1
2
0
1
0
1
1
0
2
0
2
0
1
0
1
1
1
1
1
0
1
0
1
0
1
1
2
2
1
1
1
2
1
0
1
1
1
0
2
0
0
0
1
0
2
1
1
2
0
1
1
0
1
2
1
2
0
1
1
1
1
0
0
1
2
1
2
1
0
0
1
1
1
2
1
1
0
0
1
1
0
2
3
1
1
2
0
0
1
0
0
1
1
1
1
1
1
1
0
1
0
0
1
0
2
1
0
0
2
1
2
1
2
2
0
2
0
1
1
0
2
1
1
2
0
1
1
0
1
1
1
1
1
1
0
1
0
1
1
1
0
1
2
1
1
1
1
1
2
1
1
3
2
1
1
2
2
2
0
0
1
1
2
1
0
2
2
2
1
0
1
0
1
1
1
2
2
0
1
1
1
1
2
1
1
0
1
1
1
1
2
1
2
1
2
2
2
0
2
2
0
2
0
0
1
0
2
0
1
2
1
1
1
0
0
0
1
1
0
0
1
0
1
1
2
0
0
2
0
0
1
1
1
0
0
1
0
0
0
1
1
0
1
0
0
1
2
1
1
1
2
0
1
1
2
1
0
1
1
1
1
0
1
2
1
2
2
2
2
1
1
1
1
0
0
2
1
1
0
0
0
1
0
0
1
0
1
1
0
0
2
1
1
0
1
1
2
2
1
2
2
2
1
2
1
1
1
1
1
0
1
0
1
1
1
1
2
3
1
1
2
0
0
2
1
3
0
1
1
1
1
2
1
1
0
0
1
1
1
0
1
1
0
2
1
0
0
1
2
1
2
1
1
1
2
0
0
0
0
0
1
1
1
1
0
1
0
1
1
0
1
2
1
1
1
1
2
1
1
1
1
0
2
2
0
1
2
1
2
1
0
1
2
0
1
0
1
1
0
1
1
1
0
0
1
1
2
0
0
0
2
0
1
0
1
0
2
1
1
0
1
0
2
1
2
1
1
1
0
1
1
1
0
0
1
0
0
2
1
1
0
0
0
0
1
2
2
1
1
1
1
1
0
0
0
0
1
2
2
0
0
0
0
1
1
1
1
1
0
0
1
1
1
1
0
1
0
0
1
0
1
1
2
2
1
1
1
1
1
0
1
0
1
1
2
2
1
1
0
2
1
0
1
2
0
1
0
2
1
0
2
2
1
2
2
1
2
1
1
1
2
2
1
1
1
2
0
2
0
0
1
2
2
2
1
1
2
1
2
0
0
1
2
0
2
1
0
1
1
2
1
1
1
0
0
1
2
1
0
0
2
1
0
2
0
2
1
0
0
2
0
1
1
1
0
0
1
1
1
1
1
0
1
1
1
0
1
0
0
1
2
1
0
0
0
1
0
2
2
0
1
1
0
2
2
1
0
1
1
0
1
0
1
1
1
0
8
1
1
1
2
2
1
0
1
2
2
1
2
0
1
0
1
1
1
2
2
1
0
0
1
0
1
2
0
0
2
0
6
0
3
0
0
0
2
1
2
1
2
2
1
1
2
1
1
0
0
1
1
2
1
2
1
0
1
2
1
1
0
1
3
0
0
5
1
1
1
1
0
2
1
0
0
1
1
2
1
0
1
0
1
0
1
2
0
1
1
2
1
0
1
2
2
2
1
2
1
2
0
1
1
2
0
3
2
2
1
0
2
1
0
2
1
0
2
0
2
0
1
2
0
1
1
1
0
1
1
1
1
0
1
2
2
1
1
1
1
1
0
1
2
1
1
0
2
1
2
1
1
0
1
1
2
2
0
0
0
3
2
1
1
0
1
2
0
1
2
0
1
2
1
0
2
1
2
1
2
1
0
1
1
1
1
0
0
2
1
0
2
1
2
2
0
1
0
0
2
2
0
2
1
2
1
0
0
1
2
0
1
1
0
2
1
0
1
0
3
2
1
0
2
0
1
1
1
1
2
1
0
1
0
0
1
0
0
1
1
0
2
1
2
1
2
1
0
1
1
1
2
1
1
2
1
1
1
1
2
1
1
0
2
0
0
0
0
2
1
1
2
0
2
1
1
2
2
0
0
0
1
0
1
1
1
0
1
0
0
1
1
1
2
1
0
0
1
1
1
1
0
0
1
0
0
0
3
1
1
1
0
2
2
0
1
1
1
1
2
1
0
0
1
1
0
2
1
0
2
0
0
1
3
1
2
0
0
1
0
1
2
2
2
1
1
0
1
1
1
2
1
1
1
0
2
1
0
1
1
1
0
0
0
2
2
2
1
0
1
1
1
2
1
0
1
2
0
1
2
2
2
1
0
1
2
0
0
0
0
2
0
2
1
1
3
1
1
1
1
1
0
1
1
0
1
0
1
0
1
1
2
0
1
1
4
1
1
0
2
0
1
1
1
2
1
1
1
0
1
0
2
1
1
0
0
2
1
0
0
1
2
1
1
1
1
1
1
1
1
1
1
3
1
0
0
1
2
0
1
1
0
2
2
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
1
0
1
1
0
1
0
1
0
1
1
0
2
2
1
0
1
1
0
2
2
2
1
0
1
2
2
2
1
1
0
0
1
1
0
1
2
1
1
0
0
1
1
0
1
1
0
0
1
0
1
1
2
0
2
1
1
0
1
2
1
1
0
1
2
2
0
1
0
0
0
1
0
2
1
0
1
0
2
1
2
1
2
1
0
0
1
1
0
1
1
1
2
1
0
1
1
1
0
2
0
1
1
1
0
1
1
1
1
0
1
1
1
1
0
0
1
2
2
2
2
1
1
2
0
1
1
1
1
1
0
1
0
1
1
1
2
1
2
2
1
1
0
2
1
0
0
0
1
1
2
1
2
0
0
1
2
1
1
2
0
0
1
2
1
0
1
1
1
0
1
0
1
0
1
0
1
1
0
1
1
1
1
1
1
2
1
1
1
1
0
2
1
0
0
0
0
1
2
2
0
1
2
1
1
1
1
0
0
2
0
0
0
1
1
0
1
1
0
1
1
0
0
2
2
2
0
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
0
1
0
2
1
2
0
1
0
1
2
0
2
0
0
1
0
0
0
2
1
1
1
2
2
1
0
2
1
1
1
0
0
1
1
2
2
2
1
1
0
1
1
1
3
3
0
1
1
0
1
0
1
0
2
2
1
0
2
0
3
0
0
2
1
1
1
1
1
1
1
0
0
3
1
1
1
1
0
0
0
2
1
1
1
1
0
0
2
2
0
1
1
1
1
1
1
1
2
1
0
2
1
1
1
2
1
0
0
1
2
0
2
1
2
1
2
1
2
1
1
2
1
0
0
1
0
1
2
1
1
1
2
0
0
0
1
1
1
1
0
0
1
2
2
1
1
1
1
2
1
0
1
1
1
2
1
0
2
1
0
0
1
2
1
0
1
0
0
0
0
1
0
1
0
0
1
2
1
1
0
1
0
1
2
0
0
0
1
2
0
0
2
2
1
2
0
2
1
0
2
1
0
0
2
0
0
2
1
1
1
1
1
0
2
1
2
1
1
1
2
2
0
3
1
1
2
1
0
1
1
1
1
2
2
1
0
1
1
1
2
1
1
0
1
1
2
0
0
2
1
2
1
1
1
1
0
0
1
0
0
0
1
1
0
1
0
1
1
1
1
0
1
2
0
1
1
1
0
0
1
0
2
2
1
1
0
2
0
1
1
2
0
1
1
2
2
1
1
0
2
0
2
0
3
1
1
1
0
2
1
0
1
1
0
2
0
2
1
2
1
0
2
2
1
0
1
1
2
2
1
1
2
0
2
0
1
1
1
1
1
1
0
1
0
1
1
1
0
1
1
1
0
1
1
1
1
1
1
1
2
1
1
2
1
2
4
1
0
3
1
1
2
2
0
0
0
1
2
2
0
0
0
1
0
0
0
0
0
0
2
1
0
0
2
2
2
1
1
0
2
1
1
0
1
0
1
2
3
1
0
0
1
0
0
1
0
1
1
1
0
1
0
0
2
1
3
2
2
1
2
1
1
1
1
0
0
1
1
0
1
1
1
2
2
1
1
1
0
1
1
1
1
1
1
1
1
2
2
2
0
2
2
1
1
1
0
0
1
1
1
1
2
0
1
1
1
1
2
0
0
1
2
1
1
1
2
0
3
0
0
2
1
0
2
0
2
2
1
0
2
1
1
2
2
0
1
1
0
3
2
1
1
2
1
0
1
1
0
0
2
0
1
0
2
2
1
0
0
1
0
1
0
1
0
1
1
1
2
1
1
2
1
1
0
1
1
0
1
0
1
1
2
0
1
1
3
0
2
1
1
0
1
1
2
0
0
2
2
0
1
1
2
1
1
1
0
0
0
2
0
0
1
1
2
2
0
1
1
0
0
2
1
3
0
2
2
0
0
0
1
1
1
1
0
1
1
0
1
1
1
1
1
1
1
1
0
2
1
1
2
0
1
0
0
0
1
1
0
0
1
1
1
2
1
0
2
0
1
2
0
0
1
2
1
0
0
1
1
1
1
0
1
1
1
2
2
0
1
1
1
0
1
1
2
1
2
1
1
0
1
0
1
1
0
1
0
1
1
2
1
2
1
1
1
2
2
0
2
2
1
0
0
1
0
1
0
1
0
1
2
1
0
1
3
2
0
0
1
0
0
2
2
0
1
2
1
2
1
0
0
1
2
0
1
0
1
1
1
0
2
1
0
1
1
0
0
2
1
3
1
1
1
1
2
1
2
1
0
1
1
1
0
1
1
2
2
1
0
0
1
1
2
1
2
0
1
1
3
2
1
2
1
2
0
1
1
2
1
1
1
2
2
1
1
1
1
0
0
1
1
1
0
2
0
2
2
2
1
1
2
2
2
0
0
1
0
0
0
1
2
2
0
2
0
0
0
1
0
0
1
0
1
1
0
2
1
1
2
1
2
0
2
1
1
0
0
0
0
2
0
1
0
1
1
3
0
2
1
0
1
0
1
0
0
1
0
0
1
0
1
1
0
1
0
1
1
0
2
0
1
1
2
1
1
1
2
0
0
0
2
1
2
1
1
0
0
2
0
1
1
1
1
2
1
0
0
2
1
2
1
0
0
0
1
1
0
0
2
0
0
2
1
0
2
1
0
1
1
1
1
2
1
1
0
1
2
0
0
1
1
0
1
2
2
1
1
2
1
1
2
1
2
1
1
2
1
2
1
2
1
1
2
2
1
1
0
1
1
1
1
1
0
1
1
0
0
0
2
2
1
2
1
1
1
1
0
2
1
0
1
1
3
0
0
2
1
2
1
1
1
1
2
0
1
1
2
1
0
1
1
0
2
0
1
1
1
1
0
2
1
0
1
0
1
1
1
2
1
1
1
1
2
0
1
2
0
1
1
0
0
1
1
1
2
1
1
1
0
2
0
0
0
1
1
0
1
1
0
1
1
1
1
0
1
0
2
1
0
0
2
1
2
1
0
0
2
2
1
2
2
0
2
1
1
1
2
0
1
1
2
1
0
0
0
0
2
1
1
0
1
1
3
1
2
1
1
1
0
0
2
1
1
1
1
2
0
2
1
1
1
0
1
1
1
2
0
1
2
0
0
0
1
1
1
1
2
1
1
0
0
2
1
1
0
0
0
1
1
1
0
1
1
1
1
0
0
0
1
1
1
1
0
1
0
0
1
1
0
2
0
1
1
0
1
0
1
1
0
1
0
0
1
0
1
0
1
1
1
2
1
1
2
2
2
1
0
0
3
1
1
1
1
0
0
3
0
1
0
1
0
1
0
1
1
1
2
2
2
0
1
2
1
0
1
1
2
1
0
1
1
0
1
0
0
1
3
0
1
1
1
0
1
0
1
1
1
1
1
0
0
0
1
0
2
1
1
0
1
0
2
1
1
1
2
0
1
1
1
2
1
0
1
0
0
3
1
1
0
2
1
1
0
2
0
1
0
0
1
0
1
1
0
1
1
1
1
1
1
0
2
1
1
0
1
0
0
1
2
0
2
0
3
2
0
2
1
1
1
2
0
2
2
0
2
0
1
0
2
0
0
2
2
1
0
0
2
1
4
2
0
1
1
0
1
2
1
1
2
2
1
1
1
2
2
1
2
0
0
0
0
1
2
0
1
2
1
0
0
0
1
0
0
1
2
0
0
1
1
1
2
0
1
1
2
1
0
0
1
1
0
1
1
2
1
2
2
2
0
0
0
1
0
1
2
1
1
1
0
2
0
1
1
0
1
1
2
1
2
0
1
1
0
2
1
1
1
3
1
0
0
1
0
1
3
1
1
0
1
1
2
0
1
2
0
2
1
2
1
0
1
1
1
1
1
0
0
2
0
1
0
0
1
0
0
2
1
0
1
1
1
1
1
1
1
0
1
2
2
0
0
1
1
2
1
1
2
0
0
1
2
0
1
1
1
2
2
1
0
2
2
0
0
1
0
2
1
0
2
2
2
0
0
0
1
1
1
0
0
2
1
2
1
2
0
1
2
0
1
1
1
0
0
2
0
0
0
0
1
2
2
2
1
2
1
0
1
2
1
0
2
1
1
1
1
2
1
1
0
2
1
0
0
0
1
2
1
1
1
0
1
2
1
2
2
2
1
1
1
0
1
1
0
1
1
0
0
1
1
0
0
0
0
0
1
2
2
1
1
0
0
0
2
0
2
0
2
1
2
2
1
0
0
1
1
1
0
1
0
3
0
0
2
1
0
0
1
1
1
1
1
2
1
1
0
1
2
1
2
0
1
1
1
1
0
0
1
1
0
2
1
1
0
1
1
2
1
1
2
1
2
1
0
1
1
2
1
0
1
1
1
1
0
0
1
1
2
1
0
0
1
0
2
0
1
2
1
1
0
1
1
2
0
0
1
0
2
2
1
0
2
0
2
0
0
2
1
0
1
0
0
0
1
1
2
1
1
0
2
2
2
1
1
1
2
1
2
1
0
0
1
1
0
2
0
0
2
1
1
2
0
1
2
0
1
1
1
0
1
2
0
1
0
3
1
1
2
0
2
0
1
1
0
1
1
0
0
1
0
1
2
1
0
1
2
1
0
2
0
1
1
5
1
0
3
1
1
1
2
2
0
1
2
0
1
0
0
1
1
1
1
1
2
1
0
1
0
0
1
1
1
2
0
0
0
0
2
2
1
0
2
2
1
0
0
1
0
2
1
3
0
1
1
2
1
1
1
1
0
2
1
0
2
1
0
0
0
1
0
1
0
1
1
1
1
1
0
1
0
1
2
0
0
0
1
2
1
0
2
1
2
2
2
2
1
2
2
2
2
1
1
1
0
0
1
0
1
0
1
1
0
1
0
1
1
2
1
1
1
0
0
2
1
0
1
2
0
0
0
0
0
2
1
0
1
0
2
1
1
0
2
2
0
1
1
1
1
1
1
2
2
2
0
3
0
0
0
1
1
1
2
1
1
2
1
1
0
0
0
2
0
0
1
1
1
0
1
2
0
1
2
1
0
1
0
1
1
1
0
0
0
2
2
0
1
1
0
0
1
1
1
0
1
1
0
2
2
2
0
2
0
2
0
1
0
2
1
1
2
1
0
0
1
1
1
0
1
1
0
1
1
1
0
1
2
0
2
0
1
1
0
0
2
2
1
0
1
2
0
1
2
0
0
0
1
1
1
1
1
0
1
1
1
1
0
1
1
1
0
1
2
1
2
2
2
1
0
2
1
2
1
2
0
1
0
1
0
2
1
1
0
2
0
2
0
1
1
0
1
0
1
1
1
1
0
0
1
0
0
1
1
1
0
1
2
2
0
1
3
0
1
0
2
0
0
0
0
1
2
1
0
1
1
1
1
2
1
1
1
2
0
0
1
0
2
2
1
0
0
1
1
1
1
0
0
2
1
2
0
0
0
0
1
0
1
1
1
1
0
1
1
2
0
0
2
1
0
0
1
1
1
2
1
1
1
2
1
0
0
0
1
2
1
2
1
0
1
1
0
0
1
1
2
1
0
1
0
1
1
1
0
2
2
1
1
2
1
0
1
1
0
0
2
2
1
2
2
1
1
0
1
0
1
0
0
1
0
0
1
1
0
1
2
1
3
2
1
1
1
2
1
1
2
0
1
1
1
0
1
1
1
1
1
1
2
1
1
1
0
2
1
2
1
0
2
1
2
0
1
1
2
1
0
0
2
2
1
1
1
0
1
1
0
2
2
1
1
1
1
1
0
1
2
0
1
1
0
1
0
0
0
0
1
1
2
0
1
0
0
1
1
0
2
1
2
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
1
2
0
1
2
1
0
1
1
1
0
0
1
0
0
1
2
1
0
0
1
0
1
1
0
2
0
0
0
1
2
1
0
2
0
2
1
2
1
1
2
0
1
1
1
0
0
2
0
1
2
1
1
1
2
0
1
1
2
0
0
0
0
1
1
0
1
1
1
2
1
1
2
2
0
2
1
0
1
2
2
1
1
1
2
0
2
1
1
2
1
2
0
1
1
2
2
1
2
0
1
0
1
2
0
2
0
1
1
0
1
0
0
0
2
1
0
1
1
1
1
2
1
2
0
0
1
1
1
0
0
2
0
1
1
1
1
1
1
2
1
1
0
2
2
2
1
1
0
0
1
0
1
0
1
0
2
0
0
1
2
1
2
2
1
2
1
2
1
1
0
1
1
2
1
1
1
1
0
1
1
0
1
0
1
1
1
1
0
2
1
2
1
0
0
1
0
0
1
1
0
1
2
1
2
1
0
2
0
0
1
1
0
0
0
2
0
1
0
1
0
1
2
2
1
1
1
1
1
1
0
3
1
0
1
1
1
0
0
0
1
1
1
1
0
0
2
2
0
1
2
1
0
1
2
1
2
1
1
2
0
2
1
0
1
1
1
1
2
2
1
1
1
1
0
1
0
0
0
1
1
1
0
0
0
1
1
0
1
2
2
1
1
2
0
1
0
1
1
0
2
2
1
1
1
1
2
1
1
0
1
0
1
1
2
1
1
1
0
1
1
1
1
2
0
1
1
1
0
0
1
0
2
1
2
2
2
1
2
1
1
1
1
0
1
0
2
2
1
0
1
1
1
0
1
1
0
1
0
0
1
1
1
0
1
1
0
0
1
2
3
1
1
1
1
2
1
1
0
3
0
1
0
1
1
1
2
0
2
2
2
0
1
1
0
0
1
2
0
1
2
0
1
1
1
2
2
0
2
2
1
0
0
0
1
1
2
0
1
1
1
1
1
1
0
2
0
0
1
1
0
2
2
1
0
1
1
1
0
0
0
0
0
0
1
1
2
0
3
1
1
1
1
1
1
2
0
0
1
1
1
0
1
0
1
1
0
2
2
0
2
2
1
1
1
0
2
1
1
1
0
0
2
2
1
2
1
0
2
0
0
2
1
1
2
0
1
1
1
1
1
0
1
1
1
0
2
1
2
1
0
1
0
2
1
2
1
0
0
1
1
2
1
2
0
1
1
0
0
2
1
0
2
0
1
1
1
1
0
1
1
2
0
0
1
1
0
1
0
1
1
2
1
1
2
2
1
0
1
2
0
0
1
1
1
1
0
1
1
2
0
1
1
2
1
2
0
2
0
0
0
1
0
1
1
1
0
2
2
2
0
0
2
0
2
1
1
1
0
0
2
0
1
1
0
2
1
0
2
1
1
1
1
0
2
1
0
1
2
1
1
0
1
1
2
0
0
1
1
2
2
1
1
2
1
1
1
1
2
1
2
0
2
0
0
0
0
1
0
1
2
0
2
2
0
1
1
2
0
1
1
0
2
1
2
1
2
2
2
1
2
2
0
1
1
0
0
1
1
1
0
1
1
1
1
0
0
1
0
2
2
1
0
0
0
2
1
0
1
1
1
3
2
2
2
0
1
0
1
1
0
1
1
1
2
1
0
1
2
0
1
1
1
1
1
1
0
0
1
1
1
1
2
1
1
1
1
0
1
0
1
1
1
1
0
1
2
0
2
1
1
2
1
0
0
1
1
0
1
1
1
1
1
0
0
1
1
1
1
0
2
1
1
1
0
0
1
1
0
0
1
1
1
1
0
0
1
1
0
1
0
2
1
1
1
2
2
0
0
2
0
2
1
1
1
3
1
0
0
2
0
0
2
0
1
0
0
1
1
2
2
1
1
0
1
0
2
1
1
1
0
1
1
2
0
3
1
1
0
2
1
1
1
2
1
2
0
1
1
0
1
0
2
0
0
0
2
0
2
2
1
2
1
0
1
1
0
1
0
1
0
0
1
1
0
1
1
0
2
3
1
2
0
0
0
2
0
1
0
2
1
1
2
0
0
1
3
2
1
2
1
0
0
0
0
2
0
1
2
1
0
1
2
0
1
1
1
2
0
1
0
0
1
0
1
1
4
0
1
0
1
1
0
1
0
1
0
1
1
0
2
2
2
0
0
0
0
0
2
1
1
2
1
0
2
2
1
1
0
1
1
1
1
0
1
1
0
1
1
1
0
0
0
0
1
1
2
0
2
1
0
1
0
2
1
0
0
1
1
0
0
1
0
0
0
0
1
2
2
1
1
1
0
1
1
0
1
2
1
1
0
1
2
1
3
1
0
1
2
0
1
0
1
1
3
1
1
0
2
1
1
2
2
1
2
1
1
1
1
0
1
2
2
1
0
1
1
1
2
1
0
1
0
1
2
1
2
0
2
1
1
0
1
1
1
1
2
1
2
2
0
0
0
3
1
0
2
2
1
0
1
1
0
0
0
1
0
0
1
1
0
1
1
2
1
1
0
0
0
1
1
1
1
2
2
0
0
0
1
2
2
0
1
0
2
2
1
1
2
1
2
0
1
1
1
1
0
2
2
2
1
0
1
1
2
2
1
0
2
2
1
1
1
0
1
0
0
1
1
1
2
0
0
0
1
0
0
2
1
2
0
1
1
1
1
0
2
1
0
1
1
0
0
1
1
1
1
1
0
1
0
2
1
1
0
1
0
1
1
1
1
1
1
0
0
2
2
1
1
1
2
1
0
0
1
0
0
0
1
1
0
1
1
1
1
1
0
1
0
0
1
0
2
0
1
1
1
0
0
0
1
0
1
2
0
0
0
1
1
2
0
2
1
0
1
0
2
2
1
1
0
0
1
1
0
2
1
1
1
0
1
2
1
1
1
0
1
2
2
1
1
0
1
0
1
2
1
2
1
1
1
1
2
0
1
2
1
2
2
0
2
1
1
1
0
2
1
1
1
0
2
0
1
2
1
2
1
0
1
1
2
1
1
1
1
0
1
1
1
3
2
0
1
2
1
1
2
0
0
1
0
0
1
0
2
2
0
0
1
1
1
1
0
0
0
0
1
1
0
1
3
0
0
2
0
1
1
1
1
0
2
1
1
2
2
0
0
2
0
2
0
1
1
3
1
1
1
0
0
1
3
1
2
1
0
1
0
6
1
4
1
0
1
0
1
1
1
1
1
1
2
0
2
2
1
1
1
0
1
0
0
1
0
1
2
1
1
0
2
1
0
2
2
1
2
1
1
1
2
1
0
0
2
2
1
1
1
1
0
0
0
0
2
4
1
1
2
1
2
2
2
1
1
1
1
2
2
1
1
0
1
2
1
1
2
1
1
1
1
0
2
1
0
1
1
0
1
0
0
0
1
1
2
1
0
0
1
0
2
1
0
1
2
2
1
0
0
1
1
1
0
0
0
0
0
0
2
0
1
1
1
2
0
1
1
2
2
1
2
2
0
0
1
0
1
1
1
1
0
1
0
1
0
2
0
2
2
0
1
0
0
1
1
2
0
0
2
2
1
0
2
1
2
1
1
1
0
2
2
0
2
0
1
1
1
2
1
2
4
0
2
1
2
1
0
2
0
1
1
0
0
1
1
0
1
1
2
0
1
0
1
2
1
2
1
1
0
1
2
1
0
1
1
1
1
1
0
0
0
0
0
1
1
1
1
1
2
0
1
0
2
0
1
1
1
1
0
2
1
0
2
0
0
0
1
0
0
1
0
2
1
1
0
1
1
1
1
2
1
1
2
1
2
2
1
1
1
1
0
0
1
2
1
1
2
1
1
0
2
0
2
2
0
1
3
0
1
0
2
1
1
1
0
0
1
1
0
1
2
2
1
1
2
2
1
2
0
1
2
1
1
2
0
1
2
2
0
0
0
1
2
1
2
2
0
2
0
0
1
1
0
2
2
1
0
2
1
4
2
1
0
1
2
0
0
2
0
0
1
0
0
1
2
1
0
1
1
2
2
0
1
1
1
1
2
1
0
0
0
1
2
1
1
3
0
0
0
1
0
1
1
1
0
0
1
0
2
1
1
1
0
0
2
1
1
0
0
0
2
2
2
0
0
2
0
0
1
1
1
1
1
0
1
0
1
0
2
1
1
2
2
2
0
3
1
2
0
1
0
1
1
1
2
1
1
1
2
1
2
1
1
3
1
0
2
1
1
3
0
0
2
0
1
0
1
1
1
1
2
0
0
2
1
2
1
1
0
1
2
3
1
1
0
1
1
1
1
2
1
1
1
1
1
1
0
1
2
1
1
1
0
0
0
0
0
2
2
1
0
0
1
1
1
0
2
0
1
1
1
0
2
0
0
0
2
1
2
0
1
1
0
0
1
0
1
2
0
0
3
0
0
0
1
0
1
0
0
0
1
1
0
1
1
1
0
1
1
0
2
1
1
2
0
1
2
0
1
2
1
1
2
0
2
1
0
1
0
1
0
0
2
0
1
1
0
0
0
1
1
1
2
1
2
1
1
1
1
2
0
1
1
1
1
0
2
1
1
1
1
0
1
1
2
0
0
1
1
1
0
1
2
2
2
0
0
2
1
0
0
2
0
2
1
0
1
0
1
1
0
1
1
1
1
1
1
3
1
0
2
0
1
1
1
1
0
2
1
1
1
0
0
2
1
0
1
0
0
0
1
0
1
0
1
0
0
1
0
1
2
1
1
1
0
1
0
0
0
1
1
2
1
2
2
1
0
2
2
1
1
2
0
0
2
0
2
0
0
2
0
1
1
1
0
1
1
2
1
2
0
2
1
0
1
1
1
1
1
1
1
1
1
0
1
1
0
1
1
0
0
1
0
0
2
1
1
1
0
2
0
1
0
0
1
1
1
0
2
2
1
0
2
1
2
2
1
0
1
0
0
0
1
2
0
0
1
2
0
0
3
0
0
0
1
1
1
0
1
1
1
2
1
0
0
0
1
2
1
2
1
1
0
1
2
1
0
2
1
1
0
2
0
1
0
1
2
2
0
1
1
0
2
2
0
1
1
1
0
1
1
1
1
1
2
1
2
2
0
2
1
2
2
2
1
1
1
1
0
1
1
0
1
1
1
1
1
1
2
1
2
4
2
2
1
0
0
0
1
0
1
1
1
1
3
2
1
0
1
1
1
0
2
2
1
1
0
2
2
0
1
1
1
2
1
0
1
1
2
1
1
0
0
1
2
1
1
0
1
1
1
2
1
0
1
2
0
0
1
1
1
0
0
0
0
1
2
2
0
1
1
1
1
1
0
0
0
1
0
1
0
2
1
1
0
2
1
2
1
1
0
1
2
1
0
2
0
0
1
2
0
1
2
0
3
2
0
0
2
1
1
1
2
1
2
1
1
0
1
0
1
0
1
1
1
0
0
2
1
0
0
2
2
2
0
1
1
0
2
0
1
1
1
1
1
1
1
0
0
0
1
1
0
0
0
0
2
1
2
0
1
0
0
2
0
1
0
1
1
0
1
1
1
0
2
0
1
0
1
1
1
1
1
0
0
2
1
1
1
2
2
0
2
1
1
0
2
2
0
2
1
1
0
2
1
1
0
2
1
1
1
2
1
1
1
2
1
2
0
2
0
1
1
0
0
1
1
2
1
1
2
0
2
2
1
1
1
2
2
1
0
1
1
0
1
0
0
1
2
1
1
2
1
2
2
0
1
1
1
0
2
1
2
0
2
0
0
0
1
1
0
0
0
1
2
0
2
1
1
1
1
2
2
0
1
0
1
3
0
1
0
1
1
1
1
1
0
1
2
4
1
0
1
1
1
2
1
2
2
0
1
1
1
1
1
1
0
1
0
1
2
4
0
1
1
0
1
1
1
3
2
1
0
1
2
1
0
2
2
2
1
1
1
1
2
1
2
0
1
1
1
0
1
1
2
2
1
2
1
0
0
2
1
0
0
2
0
1
0
0
3
1
1
1
0
1
2
1
1
1
2
1
1
0
2
1
2
0
0
0
1
1
4
1
0
2
2
0
0
1
1
0
0
1
2
0
1
1
2
2
0
1
1
1
1
1
1
0
1
1
2
1
0
1
1
2
1
2
0
1
1
1
0
0
1
0
2
1
1
1
2
1
1
0
1
2
1
0
1
2
1
0
1
2
0
1
0
1
1
0
0
1
1
1
1
0
2
0
0
0
2
1
1
2
1
1
0
1
1
2
0
1
0
0
0
2
1
1
1
0
1
0
2
1
1
0
0
0
2
1
1
2
1
2
2
0
0
0
0
2
0
1
2
0
2
2
0
0
0
0
0
0
0
1
0
0
0
1
0
1
2
1
1
1
0
1
2
2
1
0
1
1
1
0
1
1
1
2
0
1
2
1
0
2
0
0
3
1
2
0
0
1
2
1
0
2
0
1
1
1
1
1
2
4
1
0
1
1
2
1
0
1
0
1
0
0
1
0
0
2
0
0
2
1
1
1
1
2
1
0
1
2
1
0
2
1
1
0
0
0
1
2
1
1
1
1
1
3
0
0
1
1
0
0
1
1
0
1
2
2
2
1
0
1
0
0
0
5
0
0
2
1
1
0
1
0
0
0
1
1
0
0
1
0
1
1
0
2
1
2
1
1
0
2
1
1
1
1
0
1
1
0
1
1
1
2
1
1
0
2
0
1
1
0
1
0
0
0
0
0
1
1
0
1
1
1
1
2
1
0
2
1
2
1
1
1
1
0
2
1
2
2
0
2
1
1
1
1
1
0
1
0
0
1
1
1
1
1
1
1
2
1
0
2
2
0
1
2
3
1
4
2
0
0
1
1
1
1
1
1
2
1
2
2
1
1
1
1
2
1
2
0
2
1
0
0
1
0
1
1
0
0
1
1
1
1
1
1
1
1
2
0
0
2
1
1
2
0
2
0
1
0
1
1
2
1
0
0
0
0
1
1
2
1
2
0
2
0
0
1
1
2
1
0
1
2
1
0
0
2
1
0
1
1
1
1
1
1
2
1
1
1
0
1
0
0
0
1
1
1
1
0
2
0
0
2
1
0
0
0
0
0
2
1
1
0
1
2
4
1
2
2
1
1
0
1
1
1
0
2
2
2
0
1
2
0
2
1
2
0
1
1
0
1
0
2
1
2
2
2
1
0
1
0
1
2
1
0
1
3
1
0
1
1
1
1
0
1
2
1
2
2
1
0
0
0
1
0
1
0
1
0
1
0
1
1
1
1
0
2
1
0
1
1
1
1
2
0
0
0
0
0
1
1
1
1
1
1
0
2
0
0
1
1
1
1
0
2
0
0
0
0
1
0
1
1
1
1
1
0
1
1
2
1
1
1
1
0
0
1
1
0
1
0
0
2
2
1
1
2
0
0
1
0
0
2
2
2
0
0
2
0
2
1
0
2
0
1
2
0
1
0
0
0
1
0
2
2
1
0
0
0
1
2
1
1
1
1
2
2
1
2
1
1
1
0
1
1
1
1
0
1
1
2
1
2
1
1
2
0
0
1
1
2
2
0
0
1
0
0
2
0
2
2
1
1
0
1
1
1
2
1
1
1
0
2
0
1
0
1
2
0
1
1
2
1
2
0
0
1
0
2
1
2
0
1
0
2
2
0
1
2
0
1
1
1
1
1
1
1
2
1
1
2
2
0
1
0
1
1
1
2
0
1
1
1
1
1
1
0
2
2
1
1
1
2
0
1
1
2
1
0
1
0
2
1
0
1
2
1
2
0
0
1
1
0
0
0
1
0
0
1
2
2
2
0
0
0
0
2
0
0
0
0
2
2
0
3
1
1
0
2
0
0
2
1
0
0
1
1
1
0
1
0
0
2
1
1
0
1
2
2
2
2
1
0
0
0
1
1
1
1
2
1
1
1
0
2
0
2
2
1
0
1
1
3
1
1
2
0
1
0
0
1
0
1
0
2
2
1
1
0
0
2
1
1
1
1
2
2
1
1
1
0
1
1
1
2
1
1
0
1
0
0
2
1
1
0
1
0
0
0
1
0
2
0
2
2
2
0
1
1
2
0
1
2
1
1
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
2
1
0
1
0
2
1
0
1
2
0
1
1
1
0
0
1
0
1
3
2
2
1
1
2
1
0
1
2
0
1
1
2
1
0
0
2
0
1
2
1
1
1
1
1
2
2
0
0
3
1
2
1
1
1
1
1
2
0
0
2
0
2
0
0
0
0
0
2
1
1
3
1
0
1
0
1
2
2
2
2
1
0
1
1
0
0
2
0
0
0
0
0
0
1
1
1
0
2
1
1
1
1
2
1
1
1
0
0
0
1
1
1
0
0
2
0
1
0
0
0
1
0
2
0
2
1
1
1
1
1
2
0
1
1
2
0
0
1
0
2
0
1
0
1
1
1
2
1
2
2
0
1
0
1
1
1
2
2
1
0
2
1
0
2
1
1
1
0
1
2
0
1
1
1
1
1
0
0
1
1
1
0
1
0
1
1
1
1
0
0
1
1
0
1
0
0
3
2
1
1
1
0
1
1
1
0
2
2
2
2
0
1
0
1
1
1
0
0
0
1
1
3
1
2
1
3
0
0
0
0
2
1
0
2
0
1
0
2
1
1
0
1
1
1
1
1
0
0
1
2
0
0
1
1
1
1
1
0
0
1
1
2
2
0
0
2
1
1
1
1
6
1
2
2
2
1
0
1
3
2
1
1
1
0
1
1
1
2
2
1
1
1
2
2
1
1
1
4
1
0
1
1
1
1
2
0
1
0
2
1
2
1
1
0
1
4
1
1
2
0
0
0
2
0
2
1
1
1
0
0
1
2
1
2
2
1
1
0
2
0
1
2
0
1
0
3
1
1
1
0
2
0
1
0
2
1
0
0
1
1
1
1
0
1
0
0
1
0
1
1
0
3
0
1
1
1
1
0
2
1
2
1
0
1
2
1
0
1
1
1
0
1
1
0
1
2
1
0
0
0
2
2
1
1
2
2
1
0
1
1
0
2
1
2
0
2
1
1
0
1
2
1
1
1
1
0
1
1
0
0
1
0
1
2
0
1
0
0
1
1
2
1
1
1
1
2
2
0
2
0
2
2
1
2
0
1
2
0
1
0
1
1
1
1
0
1
0
0
1
1
1
1
1
1
1
0
2
1
2
1
1
0
0
1
0
1
1
0
1
0
0
1
1
0
0
1
0
1
0
1
2
0
0
0
1
0
0
1
2
2
2
1
1
1
1
0
1
1
2
1
0
2
2
2
1
5
1
2
0
1
1
1
1
1
0
0
1
1
1
1
1
0
1
1
1
1
1
3
1
0
0
1
0
2
0
2
0
0
1
1
1
2
2
0
1
0
1
1
1
1
0
2
1
1
1
1
1
1
2
3
0
1
1
0
2
1
1
1
2
1
0
2
2
2
2
1
2
1
0
1
1
0
1
2
1
1
1
0
0
0
1
0
2
1
2
1
1
0
2
2
1
1
1
2
2
2
2
0
1
2
0
1
1
2
0
1
0
1
1
1
3
1
0
1
1
1
1
0
2
2
0
1
0
1
1
0
0
1
0
0
1
0
0
1
1
2
1
2
1
1
0
2
1
1
2
1
1
2
1
2
2
1
1
0
2
1
1
1
1
2
1
1
0
2
2
0
0
1
1
2
2
2
3
1
1
0
0
1
1
1
2
0
2
2
2
1
0
1
0
1
2
1
0
0
1
1
2
1
2
1
2
1
1
0
1
3
2
1
1
2
1
1
1
1
2
0
1
0
0
1
0
2
1
1
0
0
2
0
2
1
1
0
0
2
1
0
1
2
0
1
1
2
2
1
1
1
1
0
2
1
1
0
1
2
2
1
1
0
2
0
1
1
2
2
1
0
0
0
2
1
1
1
1
1
1
0
1
2
1
1
1
0
2
1
2
0
0
2
0
1
1
2
2
1
0
1
0
1
0
1
1
0
2
0
1
1
0
0
1
2
0
1
1
0
1
2
0
1
2
1
0
1
0
1
2
0
2
0
2
0
1
2
0
2
2
2
1
1
1
0
0
0
0
2
0
1
0
0
1
0
1
2
1
1
2
1
1
0
0
2
2
2
2
0
0
1
1
0
1
0
0
1
2
0
1
2
1
0
0
1
0
1
1
1
0
3
2
0
2
1
2
1
1
1
2
2
1
2
0
2
1
2
1
2
0
1
1
1
1
1
1
0
0
2
2
2
0
2
0
0
2
1
1
0
0
1
1
1
1
1
1
1
0
2
0
2
2
2
1
1
0
0
0
1
2
2
0
0
1
2
2
0
2
2
2
2
0
1
1
0
0
1
2
2
0
1
2
1
2
0
0
0
1
1
1
1
0
1
1
1
1
2
1
1
2
2
1
1
1
1
1
0
0
1
1
1
1
0
1
0
0
1
1
1
0
1
0
0
0
0
1
0
1
0
1
0
3
1
2
0
2
0
2
1
0
1
1
0
1
0
1
0
1
0
1
2
3
2
0
1
0
0
0
0
1
1
1
1
1
2
0
2
0
0
0
2
0
0
1
1
1
2
0
2
1
2
0
2
2
1
2
2
2
1
0
1
1
0
0
0
1
1
1
1
1
0
1
2
1
1
1
0
1
1
2
1
0
0
1
2
1
2
1
0
0
1
0
1
1
0
0
2
1
0
2
1
1
2
1
2
1
0
1
0
1
2
2
1
0
2
1
2
0
1
1
0
0
2
0
1
1
1
2
0
2
0
0
0
1
1
2
1
1
2
1
2
1
1
0
1
2
0
1
0
1
0
0
1
0
0
1
1
0
1
1
1
1
1
2
0
0
0
2
1
1
1
1
0
1
2
0
0
0
1
1
2
1
1
2
1
1
1
0
1
0
1
1
0
1
2
1
2
2
1
1
1
0
1
2
1
1
0
2
2
0
2
2
0
2
2
1
1
1
1
0
0
0
1
1
0
1
2
2
1
0
2
1
0
2
1
0
0
0
1
1
1
1
1
2
2
1
1
2
1
2
0
2
0
0
1
1
1
2
1
2
1
0
2
1
2
3
0
2
2
2
1
1
0
2
0
1
2
2
1
1
0
0
1
0
1
3
1
1
1
1
1
0
1
0
1
1
3
0
2
1
0
1
0
2
0
1
2
1
1
1
2
2
1
1
0
6
2
0
0
1
0
1
1
2
0
1
0
1
1
1
2
1
2
1
1
1
1
1
1
1
1
2
1
2
1
0
0
1
0
2
2
2
1
2
1
1
1
0
1
1
2
0
1
0
1
1
1
0
1
1
2
1
1
2
2
1
1
1
1
1
1
2
1
2
1
0
0
2
2
0
0
0
1
1
0
2
0
1
1
1
1
1
2
1
0
1
1
1
2
1
0
0
0
1
2
0
0
1
1
1
1
0
8
0
1
1
0
0
0
1
0
3
2
1
0
0
1
0
1
1
2
3
2
2
0
0
2
0
1
2
0
1
1
1
0
0
1
0
0
1
1
1
2
1
0
2
1
1
2
2
1
2
1
0
0
1
0
3
2
2
1
1
1
2
2
1
0
0
2
1
0
1
1
0
0
2
2
2
0
2
1
1
1
2
0
1
1
0
2
0
1
1
1
0
1
1
1
0
3
0
0
0
1
0
0
0
1
0
1
0
2
0
0
2
0
1
1
1
1
0
1
2
2
2
1
1
1
1
1
0
1
1
1
1
1
1
0
0
1
0
4
1
0
1
0
0
0
1
1
0
1
1
2
1
0
0
0
0
1
1
0
0
1
0
1
2
0
2
0
1
1
1
1
1
2
1
1
0
1
1
1
2
0
1
0
2
1
1
2
2
1
1
0
0
1
1
1
1
1
0
0
0
1
0
0
0
1
0
0
0
1
2
0
1
0
1
1
2
1
2
1
1
1
0
1
1
1
1
2
1
1
1
0
2
1
1
0
0
0
1
0
2
1
0
1
1
0
2
2
1
0
1
0
2
1
2
2
0
1
2
1
0
2
1
0
1
2
1
0
1
1
0
1
1
2
1
1
2
0
1
1
0
1
0
1
0
0
1
0
2
0
2
0
1
1
2
1
2
2
2
1
0
2
1
1
0
1
0
0
1
0
0
1
0
0
1
0
1
1
0
0
1
0
1
2
0
0
0
2
2
0
0
0
2
1
2
0
0
1
1
0
1
0
1
2
0
1
0
1
0
3
1
2
0
1
0
0
2
1
0
2
0
1
1
1
1
0
2
2
1
1
2
0
1
1
2
3
0
1
1
2
0
1
0
2
2
1
0
0
0
1
1
2
0
1
1
1
2
0
1
0
0
1
2
2
1
0
0
1
1
2
1
0
0
2
1
0
1
1
0
0
1
1
1
0
1
2
0
0
1
1
2
2
1
1
1
1
1
1
0
1
1
0
1
1
1
3
0
1
0
1
0
1
0
1
1
1
2
0
0
2
0
0
1
1
1
1
1
1
0
1
1
0
1
2
2
1
1
1
1
2
1
1
1
1
0
2
1
0
0
1
1
0
0
0
1
1
2
1
0
1
1
2
1
0
1
1
2
2
0
1
0
0
1
0
1
0
1
1
0
2
2
1
1
1
2
0
2
0
0
1
2
1
1
1
0
1
0
1
1
1
1
3
1
0
1
1
0
0
1
0
1
1
0
0
0
0
0
1
1
0
1
0
1
0
1
1
0
2
2
0
1
0
1
2
2
1
1
2
1
1
0
0
1
1
2
1
1
1
1
2
6
1
2
0
1
1
1
0
2
1
1
2
1
1
2
1
1
1
1
0
0
1
0
0
0
0
0
1
0
1
0
1
2
0
0
0
0
2
2
1
0
1
0
0
0
2
1
1
0
1
1
2
2
1
2
1
0
1
1
2
0
1
1
2
2
0
1
2
1
1
1
3
0
0
1
0
1
1
1
0
1
0
1
0
0
1
1
2
0
0
2
0
2
0
1
3
0
1
1
2
1
0
0
5
1
1
1
0
0
0
2
1
0
1
0
0
1
2
1
0
0
0
1
2
2
0
1
1
2
1
0
0
3
0
1
1
1
1
0
0
0
1
2
1
2
2
1
1
2
1
2
1
1
1
1
1
0
1
0
2
1
1
0
1
1
0
1
1
1
0
2
2
0
1
2
1
1
1
1
2
2
2
0
0
2
1
1
0
1
0
1
0
1
1
1
0
2
2
1
2
1
1
1
1
0
0
1
1
0
1
0
0
1
1
1
1
2
2
0
2
0
2
1
0
1
1
2
1
1
1
0
2
1
1
2
2
1
2
1
1
1
1
1
0
1
0
1
0
1
3
1
1
2
1
2
0
0
1
1
1
1
0
1
0
1
1
2
1
1
2
2
2
1
1
1
1
0
0
0
1
1
1
1
0
0
0
1
1
0
1
0
2
1
1
1
1
0
1
1
0
2
0
2
1
0
2
1
0
0
1
2
1
1
0
1
0
0
0
2
1
1
2
0
2
1
1
1
2
1
0
2
0
1
1
2
0
2
0
1
2
2
0
0
3
0
1
2
1
1
2
1
2
0
0
2
0
0
1
0
2
1
1
1
0
1
1
1
2
0
1
1
1
0
0
3
0
1
0
2
1
0
1
0
2
1
2
3
0
0
0
1
0
0
4
1
5
1
1
0
2
1
0
0
1
1
0
0
2
1
2
2
1
1
1
1
1
1
0
1
1
1
1
0
1
1
2
0
1
0
2
1
0
0
0
0
1
0
1
0
1
0
1
1
0
1
1
1
1
1
0
1
1
1
1
1
1
2
0
2
0
2
2
2
1
0
2
0
1
1
2
0
2
1
1
0
0
1
2
1
1
0
2
1
0
0
1
1
2
0
1
1
1
1
1
0
1
0
1
1
1
0
0
0
0
1
1
0
0
0
1
1
1
1
0
1
2
2
2
3
2
0
1
1
1
0
0
0
0
1
1
0
1
1
0
0
0
0
1
1
0
2
0
2
2
1
2
3
0
2
1
1
0
1
1
0
2
0
1
1
1
1
0
1
1
2
0
2
1
0
2
1
0
2
1
1
0
2
0
2
0
2
0
1
1
0
1
0
1
0
2
1
1
2
0
1
1
0
1
0
1
1
2
2
1
1
0
0
1
2
1
2
1
1
1
1
0
1
2
1
1
0
2
2
1
1
1
1
1
1
1
1
0
0
1
1
0
0
2
1
1
1
0
0
0
0
1
1
1
0
0
1
2
2
0
0
0
1
0
2
2
1
1
2
1
1
0
0
1
1
0
1
2
2
1
0
2
1
2
1
0
2
1
1
0
3
2
0
2
0
2
0
0
1
1
1
1
0
1
0
2
1
1
1
2
0
1
1
1
2
1
1
1
1
0
0
2
0
2
1
3
2
2
1
1
3
1
1
1
1
2
0
0
2
5
1
0
0
0
1
1
0
1
0
2
2
2
2
2
0
0
1
1
1
1
1
1
1
0
1
1
2
1
1
1
0
1
1
2
3
1
1
0
3
1
0
2
2
0
2
1
0
1
1
2
2
1
2
1
0
1
2
0
1
2
1
0
0
1
0
1
1
0
2
0
2
1
1
0
2
2
1
2
0
0
2
0
2
0
1
2
1
2
0
0
1
0
0
1
1
0
0
2
1
3
2
1
2
0
2
1
1
0
1
1
0
1
0
2
0
1
2
0
3
1
1
0
2
0
0
1
0
1
0
2
0
0
1
1
1
1
1
0
0
0
2
2
1
1
1
0
1
1
0
1
1
1
0
0
2
1
1
1
2
2
1
0
1
2
1
1
0
1
1
1
0
1
2
2
0
0
0
1
0
1
0
2
1
1
1
1
1
0
1
1
1
2
1
0
1
1
0
0
0
1
1
0
3
2
0
1
2
0
1
1
2
0
1
1
1
1
0
1
1
1
1
2
1
2
1
0
1
1
1
2
0
2
2
2
1
0
0
2
0
1
1
1
0
1
1
0
2
1
1
0
1
1
1
1
0
0
0
1
1
2
1
2
0
0
0
1
1
0
2
0
1
1
0
1
1
1
2
0
1
2
1
1
1
0
2
1
2
1
1
2
1
1
1
1
1
1
2
2
1
0
0
2
1
1
2
1
1
1
1
2
1
0
0
1
1
1
2
2
1
1
0
0
2
1
1
1
1
1
0
1
1
2
0
1
1
2
1
0
1
1
1
1
1
0
1
1
0
2
1
0
0
2
1
1
1
1
1
1
0
2
1
2
0
1
0
2
3
1
8
1
1
1
1
1
1
0
0
1
2
1
1
2
1
1
2
1
1
2
1
0
1
1
2
1
1
1
1
1
0
2
2
0
1
1
2
1
1
1
1
2
1
0
1
0
0
0
0
1
2
1
0
1
0
1
2
2
1
0
1
0
2
0
1
2
1
0
2
2
1
2
1
2
0
0
0
1
1
1
2
1
1
1
0
1
0
0
0
1
2
2
1
0
1
0
1
0
0
0
2
2
1
1
1
1
1
1
0
0
1
1
2
1
0
1
1
0
1
0
2
1
2
1
2
2
0
1
0
1
1
1
2
1
1
0
1
1
0
2
0
1
1
0
1
1
2
1
1
0
0
1
0
1
1
1
2
2
0
1
1
1
1
2
2
0
0
1
2
0
1
0
2
1
0
0
2
1
2
0
0
0
1
0
0
0
0
1
1
0
1
1
2
1
0
1
1
1
1
1
2
1
2
0
1
1
1
0
0
1
0
0
0
0
2
1
2
0
1
1
1
1
0
1
2
0
0
2
2
0
0
0
0
0
0
1
0
0
1
0
0
0
1
2
1
3
1
2
1
2
0
1
1
0
1
0
1
1
0
0
0
1
1
1
0
1
0
0
1
1
0
1
1
0
2
1
0
1
1
1
0
2
1
2
2
1
1
0
1
1
1
1
1
2
0
2
1
0
0
1
1
2
1
0
0
0
0
1
1
1
1
2
1
0
0
0
1
1
2
2
0
0
0
2
1
2
0
1
2
1
1
2
0
1
1
1
2
2
1
1
0
1
1
1
1
1
1
1
1
2
1
0
2
1
1
1
0
0
1
0
1
1
1
0
1
2
1
1
1
0
1
0
0
0
1
0
0
1
0
0
2
1
1
1
0
1
1
0
1
1
2
2
1
1
0
1
0
0
0
1
0
0
2
0
2
0
2
0
1
1
1
1
1
2
2
2
0
2
3
2
1
2
0
0
0
0
0
0
1
1
2
1
1
1
0
1
1
2
1
1
1
0
0
1
0
1
1
2
0
1
1
1
1
2
2
2
2
0
2
0
1
0
1
1
0
1
0
1
1
0
1
2
2
0
0
2
2
1
1
1
1
0
1
1
0
1
0
1
0
1
1
1
0
1
0
1
0
1
1
1
2
0
2
1
1
0
2
1
1
1
1
1
1
1
0
2
2
2
2
2
1
0
2
0
1
0
0
1
0
2
0
2
1
2
0
2
2
1
0
0
2
2
1
0
1
2
1
1
0
1
0
1
0
1
1
1
0
1
2
0
1
0
1
1
2
2
0
1
0
4
2
1
0
2
2
2
2
2
2
1
1
1
0
2
0
1
0
2
1
0
0
0
1
2
0
0
0
2
2
0
1
2
2
0
2
0
0
2
1
0
1
2
1
2
2
0
0
0
0
0
2
0
1
2
0
1
0
1
0
1
1
0
0
0
1
1
1
2
2
3
0
1
2
0
0
2
2
1
1
2
1
1
1
2
1
2
1
1
0
2
1
1
1
0
0
0
1
0
2
1
0
0
2
2
0
0
2
1
0
1
2
2
2
2
1
0
0
1
0
1
1
1
1
1
2
0
2
0
0
0
1
2
0
0
1
1
1
0
0
4
2
1
2
2
1
0
1
2
2
1
1
1
0
1
2
1
1
2
0
0
0
2
0
0
2
1
0
0
0
1
0
1
3
0
2
0
1
2
1
1
1
1
0
0
1
2
2
1
2
0
2
1
1
2
2
0
0
1
2
1
1
1
1
2
0
1
0
1
2
1
1
3
0
2
1
1
2
1
2
1
0
1
1
1
1
2
1
1
1
1
1
1
1
1
1
0
1
2
0
2
0
1
1
1
1
2
0
1
0
1
1
1
0
0
1
1
2
1
2
0
1
0
1
0
1
0
0
0
1
2
1
1
2
1
1
1
2
2
3
2
2
0
1
0
1
1
1
2
1
1
0
0
1
1
1
1
0
1
0
0
1
0
0
2
1
1
2
1
1
1
1
0
2
1
1
1
1
1
0
1
0
1
1
2
2
1
0
0
0
1
1
2
0
0
1
1
0
0
0
2
0
1
1
2
0
0
0
0
0
1
1
1
1
1
0
1
1
2
2
2
0
1
2
1
2
0
1
1
2
1
1
1
0
1
1
1
1
0
0
1
1
2
2
0
1
2
1
2
0
2
0
1
1
0
2
2
2
2
3
1
1
1
1
2
2
0
1
1
2
0
1
1
2
0
2
1
1
1
0
1
1
0
2
0
0
1
1
0
1
2
2
0
2
1
0
1
3
1
1
1
0
0
1
1
0
0
1
2
1
0
2
0
1
2
2
1
1
0
1
1
1
2
1
0
2
1
1
0
1
1
1
3
2
0
2
0
2
0
1
2
0
1
0
2
1
1
1
0
0
1
1
0
0
1
0
1
1
1
1
1
1
0
1
1
0
1
1
1
1
2
0
2
2
1
1
1
1
1
0
0
1
1
1
1
1
2
1
1
2
0
2
0
1
1
0
2
2
2
1
1
1
1
1
0
2
1
1
0
0
1
0
2
0
2
0
1
1
0
1
0
1
0
0
0
2
3
2
0
1
1
1
0
1
1
0
0
1
1
1
1
1
2
0
0
0
1
1
1
0
1
1
0
0
1
0
0
2
2
1
0
1
0
0
1
1
1
1
0
1
0
2
0
1
2
1
2
2
0
2
2
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
2
1
2
2
2
1
2
1
1
1
2
1
0
0
1
0
0
0
0
1
3
2
0
0
1
0
1
0
0
1
0
0
0
1
0
1
1
1
1
1
2
0
2
0
0
0
1
0
1
0
2
1
0
0
0
1
0
1
1
0
1
2
1
1
0
2
0
0
1
0
0
2
1
0
1
0
1
1
1
2
2
1
1
0
1
1
1
1
1
1
1
0
2
1
1
1
2
1
1
2
1
0
0
1
1
4
0
0
1
1
1
1
1
1
0
0
2
2
1
1
0
1
1
2
0
1
2
2
2
0
0
2
0
0
1
1
2
1
2
1
1
0
1
1
0
0
0
0
2
1
2
2
0
0
1
1
1
1
1
2
0
1
0
0
0
0
1
0
0
1
0
1
0
1
0
1
0
1
1
1
1
2
2
1
1
1
2
0
1
2
0
0
0
1
1
1
1
1
1
1
0
0
0
0
0
0
0
2
2
1
0
2
1
2
1
1
2
2
0
2
2
1
1
0
1
0
2
0
1
1
1
2
2
0
1
1
1
1
1
2
1
1
1
1
2
1
1
0
1
1
1
0
0
0
0
1
1
2
1
1
1
1
1
0
1
2
0
0
2
2
2
1
1
1
0
2
0
1
1
2
2
0
1
0
0
1
0
2
2
1
2
0
0
2
0
1
1
1
0
1
2
1
0
0
1
2
0
7
4
1
1
0
0
1
1
0
0
1
0
2
1
0
1
0
2
1
1
1
0
2
0
0
2
1
1
0
2
0
2
1
1
0
2
0
0
0
2
0
1
0
2
1
2
1
1
0
0
2
1
1
1
1
2
0
2
0
1
1
1
1
2
1
1
1
0
0
0
0
2
1
2
1
0
1
0
1
1
0
1
1
1
1
2
1
0
1
0
0
1
0
0
1
1
0
1
1
1
1
2
0
1
2
1
1
0
2
0
2
2
1
1
2
2
0
2
2
2
1
4
1
1
1
0
1
2
1
0
1
2
1
2
1
1
0
0
1
1
1
2
2
0
1
2
1
1
0
1
1
2
2
0
1
1
1
1
2
1
2
1
1
0
0
0
1
2
1
1
2
1
1
0
1
1
0
1
2
0
2
1
2
0
3
1
1
1
0
1
3
2
0
1
1
1
3
1
0
1
1
0
0
2
1
2
1
2
1
0
1
1
1
1
0
1
1
1
0
1
1
2
0
1
0
1
1
1
1
1
0
1
1
2
2
0
1
1
0
1
0
0
1
0
0
1
0
2
1
1
1
1
0
1
1
0
2
1
0
1
2
1
0
1
4
2
0
0
0
0
1
0
1
2
3
1
0
1
1
1
0
2
1
0
0
1
1
2
1
1
1
0
1
1
1
2
1
2
0
0
2
1
1
1
2
1
1
2
0
1
2
0
1
1
1
0
1
1
2
1
0
1
1
1
1
1
1
0
0
3
1
0
1
1
1
2
0
1
0
1
2
1
1
1
1
2
0
1
2
0
0
1
2
1
1
2
3
2
2
1
4
2
1
1
1
2
1
0
2
1
0
0
1
1
0
1
0
1
1
0
0
0
1
0
2
1
3
1
1
1
0
2
0
1
1
1
1
2
1
1
2
1
1
0
1
1
2
0
2
0
0
0
0
1
2
1
0
1
1
1
1
2
1
1
1
0
1
1
0
0
1
2
1
1
1
0
1
1
0
1
1
1
1
2
1
1
0
1
0
0
1
0
0
1
0
1
1
1
2
1
2
1
1
1
0
0
0
1
1
1
1
0
0
0
2
2
2
1
1
0
1
0
0
0
1
1
1
1
1
1
1
0
0
3
2
1
2
1
0
2
1
0
1
1
0
1
1
1
1
2
2
1
2
2
1
1
0
1
1
1
1
2
1
1
2
0
1
1
1
2
1
1
1
2
2
0
1
0
1
0
0
2
1
0
1
0
1
3
1
1
2
1
0
2
1
0
0
1
2
1
2
0
2
1
0
2
1
0
0
1
1
2
0
1
3
2
1
1
2
0
1
1
2
2
2
1
0
0
1
2
0
0
4
1
0
0
1
1
2
0
0
0
1
0
1
0
0
0
0
2
0
1
0
0
2
1
1
1
1
1
1
1
1
0
0
0
1
2
1
0
1
1
1
0
0
2
0
0
1
1
1
2
1
2
1
1
1
1
1
1
0
1
2
0
0
1
0
1
2
0
0
1
1
1
1
1
0
1
1
1
1
0
2
1
1
1
1
1
1
1
1
1
1
1
1
0
0
0
1
1
1
1
1
1
1
1
1
2
0
0
0
0
2
1
2
0
0
1
0
1
0
1
1
1
1
2
0
1
0
1
0
0
0
1
0
1
1
0
1
1
2
2
2
0
1
0
1
0
0
0
1
2
0
1
2
0
4
2
0
2
2
0
0
0
0
2
1
1
1
0
0
1
0
2
4
1
1
0
0
2
1
1
0
0
0
2
2
0
0
1
1
1
1
0
1
0
0
1
2
1
1
2
0
3
1
1
1
1
1
1
0
1
2
0
1
0
1
0
2
0
1
2
1
0
2
1
2
1
1
2
0
1
2
0
1
0
1
0
0
0
1
1
0
0
0
1
2
0
1
0
1
1
0
0
0
1
1
3
2
0
0
1
0
0
1
0
1
2
0
1
0
0
1
1
0
2
1
0
0
2
1
1
2
1
1
1
1
0
1
2
2
0
0
0
1
2
1
0
0
0
0
2
0
0
0
2
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
0
2
0
2
0
0
1
1
1
0
0
2
0
1
1
2
1
2
0
1
0
0
1
0
0
1
2
1
0
0
0
0
2
0
1
1
1
2
0
3
1
1
0
1
1
0
0
1
1
1
1
2
1
1
1
1
2
0
0
2
1
0
2
1
1
1
2
1
1
0
0
2
0
0
1
1
2
1
3
0
1
2
0
1
1
1
2
1
0
2
0
0
1
0
0
2
1
2
0
2
0
2
0
1
1
2
1
1
0
0
2
0
1
0
1
1
1
2
0
1
0
1
3
0
1
0
0
2
0
0
3
0
2
1
2
2
1
1
1
1
0
1
1
2
3
1
0
1
0
1
1
1
1
2
0
1
1
0
1
2
0
2
0
2
1
1
0
0
1
2
0
1
0
1
0
0
1
0
2
0
2
1
2
0
2
1
2
2
0
0
0
0
1
1
2
0
1
1
0
1
0
0
1
2
1
1
2
0
0
1
0
1
1
1
0
2
0
1
1
1
2
1
0
0
1
2
3
3
0
1
1
1
1
1
0
1
2
1
0
3
1
0
1
1
1
0
1
1
0
0
0
1
0
1
2
1
0
1
0
0
1
2
1
0
0
2
2
0
2
1
0
0
0
1
1
1
1
0
0
2
0
1
2
1
2
1
1
0
1
1
1
2
0
1
3
2
1
0
1
2
0
1
0
6
1
1
0
0
4
1
1
2
2
1
1
0
1
0
1
2
0
1
1
1
0
2
1
1
1
1
2
1
4
0
0
2
0
1
1
1
2
0
2
1
1
0
1
2
2
1
1
1
0
2
0
0
1
0
0
2
0
1
0
0
1
2
1
1
0
0
0
0
0
0
0
2
1
1
1
0
1
1
2
1
1
2
1
1
1
0
1
2
0
1
1
0
0
2
0
1
2
2
1
0
1
1
0
1
1
1
1
2
0
2
2
2
0
2
2
1
2
2
1
2
0
2
1
1
1
1
2
0
1
1
1
1
0
1
2
0
1
1
1
0
0
2
1
1
1
1
0
1
0
1
1
1
0
0
2
0
2
1
1
1
1
0
1
3
2
1
1
0
0
1
0
1
1
0
0
1
4
1
1
1
1
1
1
2
2
0
2
1
1
1
0
1
1
1
2
2
0
2
1
2
1
2
1
0
1
0
1
0
0
1
1
0
2
2
1
0
0
1
1
2
1
2
2
0
2
1
1
1
2
0
1
0
1
1
1
1
1
1
2
2
0
2
0
1
1
1
1
0
1
0
0
2
2
1
1
2
1
2
1
0
1
0
1
0
1
1
2
1
0
0
1
0
1
2
1
0
2
1
0
0
1
0
1
1
2
1
1
2
1
1
2
1
2
1
0
0
0
0
0
2
1
1
2
0
1
2
1
0
2
2
1
0
0
0
1
0
0
0
2
2
1
0
0
1
1
1
0
0
1
1
0
1
1
1
1
2
0
2
2
0
1
1
0
0
1
1
0
2
0
2
1
1
6
0
0
0
0
1
1
2
0
2
2
0
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
0
2
0
2
0
1
2
2
0
2
1
1
0
1
0
1
0
0
0
0
2
1
2
1
0
0
0
2
1
2
1
0
0
2
1
1
1
1
1
0
1
1
1
0
0
2
2
0
1
1
0
0
2
2
0
2
1
1
1
1
1
0
0
1
0
1
0
0
1
1
2
0
1
1
0
1
2
0
0
1
1
1
1
0
1
2
1
2
2
1
1
2
2
2
2
1
1
1
0
0
1
1
0
1
1
3
1
1
0
2
1
1
1
2
1
1
2
1
1
0
2
1
2
0
2
1
1
1
2
0
1
1
0
0
2
0
1
0
1
2
1
1
0
0
0
0
1
1
1
2
2
0
1
2
1
2
1
2
1
1
1
0
2
2
1
0
0
0
2
2
1
1
2
1
0
1
0
1
1
0
0
1
2
2
1
2
2
2
0
0
1
1
2
2
2
2
1
2
1
1
0
1
1
0
0
2
1
0
2
1
1
1
0
1
1
0
1
0
2
2
0
0
2
0
1
1
0
1
0
1
1
1
1
0
2
1
1
2
2
0
2
2
1
1
1
0
1
2
1
2
1
1
3
1
1
1
1
1
2
1
1
2
2
2
1
1
1
1
2
0
1
1
1
1
2
1
1
1
1
0
1
0
1
1
0
0
1
1
1
1
0
1
1
0
0
1
1
0
1
0
0
2
0
2
2
0
1
2
1
1
1
0
0
2
1
1
1
1
0
0
1
2
1
1
0
1
0
1
1
1
1
0
1
2
2
0
1
1
2
2
1
2
0
0
1
1
0
1
1
2
1
1
1
1
2
1
1
1
1
0
2
0
0
1
0
1
0
1
0
1
1
5
0
0
1
0
1
1
0
1
2
0
1
0
1
0
1
1
2
1
0
2
2
0
0
0
0
0
0
1
1
2
2
0
1
2
0
1
2
1
1
0
1
1
1
2
1
0
2
1
1
1
2
1
0
0
0
2
1
2
1
0
0
0
0
0
1
0
0
0
2
1
2
1
2
0
1
1
0
0
1
3
1
1
1
2
0
0
1
2
2
1
1
1
2
0
2
2
1
1
0
2
1
1
1
1
0
0
2
0
1
0
1
2
2
0
2
2
1
2
0
0
1
1
1
1
1
0
1
1
0
2
1
1
1
2
0
2
0
0
1
1
1
1
1
1
1
2
2
2
0
1
2
1
0
1
1
0
2
1
0
0
0
2
0
2
1
1
1
2
0
2
1
1
1
1
1
1
1
0
1
1
1
1
0
1
0
0
2
1
1
2
1
1
1
1
1
0
1
1
0
1
0
1
2
2
2
0
2
1
2
1
2
1
0
1
1
1
2
0
2
0
1
0
2
3
1
1
2
1
1
2
2
1
1
1
1
1
1
2
0
1
0
1
0
0
0
0
2
0
0
1
0
2
0
1
2
1
1
3
1
1
0
0
1
1
1
0
1
0
1
0
1
2
0
0
2
1
1
0
2
0
0
0
0
1
1
1
0
0
1
0
1
1
1
1
0
0
0
0
0
0
1
2
1
0
1
0
1
1
1
1
1
2
2
1
1
0
1
0
2
1
1
1
0
1
1
1
2
1
1
3
2
2
1
2
2
0
1
0
1
1
1
1
0
1
1
2
1
0
2
1
0
2
0
1
0
1
1
0
2
1
2
0
2
0
0
2
1
1
1
0
0
1
0
0
1
0
2
0
0
1
0
1
2
1
1
0
2
2
0
1
0
0
2
0
0
1
1
0
1
0
0
1
1
1
2
2
0
0
1
0
0
0
0
1
1
2
1
0
1
0
1
0
0
1
1
0
1
1
0
0
1
0
0
1
0
1
1
2
2
0
0
0
0
2
0
2
0
1
0
0
0
2
0
1
1
0
1
1
0
2
1
2
1
1
2
2
1
2
0
2
0
0
2
1
2
1
2
1
2
0
1
1
1
1
0
0
2
1
1
1
1
1
0
1
2
0
1
2
0
1
1
2
1
1
1
1
1
1
0
2
0
0
1
1
1
1
1
0
1
0
0
1
0
0
2
0
1
1
1
1
1
2
0
0
0
2
0
0
1
1
2
1
0
0
1
2
1
1
1
1
1
0
1
0
1
0
2
1
0
1
1
0
0
1
1
2
0
1
0
1
1
1
2
0
1
0
1
0
2
3
0
1
1
2
2
0
0
0
0
1
1
0
0
1
1
1
1
1
0
1
0
3
1
1
1
2
1
1
2
1
2
2
0
0
1
1
3
1
1
0
0
0
1
2
1
0
0
0
0
1
0
1
1
0
1
0
0
1
0
2
0
1
0
0
0
1
2
2
2
1
1
1
0
1
0
1
0
1
1
1
0
1
0
0
3
1
1
1
1
2
1
0
1
2
2
1
0
1
2
2
1
2
1
1
1
0
1
0
1
1
2
1
1
1
1
0
1
0
0
0
1
1
0
0
1
0
1
0
0
1
2
2
0
1
1
0
1
0
2
2
0
1
1
0
1
1
1
1
2
2
1
1
0
1
0
0
1
2
0
2
1
0
0
1
1
1
0
1
2
2
2
1
1
1
2
1
1
0
1
1
0
2
1
0
1
2
1
0
0
1
3
2
1
0
1
1
0
3
1
1
0
1
3
1
1
0
2
1
1
0
0
1
2
1
0
1
2
3
0
0
1
2
0
1
0
0
1
2
2
2
2
2
2
1
0
2
0
1
1
1
1
2
0
1
1
1
2
0
0
1
1
2
1
1
1
1
2
1
2
1
1
1
1
2
2
0
1
0
1
1
1
2
2
1
1
2
1
1
2
0
2
1
2
0
2
1
0
2
0
1
1
2
2
1
0
0
0
1
2
2
2
4
0
2
2
1
2
1
0
1
1
0
0
0
2
2
1
0
1
0
2
2
0
1
2
0
1
1
0
0
1
1
1
1
1
1
2
0
0
2
0
1
1
2
2
0
14
1
0
2
2
0
1
0
2
2
1
1
1
1
0
0
2
0
1
0
5
2
1
2
0
0
1
1
1
0
0
2
1
0
0
2
1
1
2
2
1
1
1
0
0
1
0
0
2
2
1
1
0
1
1
0
0
0
0
1
2
1
2
2
0
0
2
1
2
2
0
0
0
1
1
0
1
0
1
0
0
1
1
3
0
0
1
1
2
0
1
1
2
3
0
1
0
1
0
0
2
2
1
1
0
1
0
0
1
0
0
0
1
2
1
1
1
2
2
2
2
3
0
1
0
0
2
0
1
1
1
1
1
2
2
2
1
0
1
0
0
2
1
2
0
1
1
1
2
0
0
2
1
1
1
1
3
0
1
1
2
0
1
3
0
0
0
2
1
0
0
0
2
1
2
1
1
2
0
0
2
2
2
0
1
1
0
1
0
0
0
0
1
1
1
1
1
2
1
1
2
1
0
2
1
1
1
0
0
1
2
1
1
0
1
1
1
1
1
0
1
0
1
1
1
2
2
0
2
0
1
0
1
1
0
0
1
1
1
0
0
1
1
1
1
1
2
1
0
0
0
1
0
1
1
0
1
0
0
2
0
1
0
2
1
1
0
2
2
1
0
1
1
1
1
0
1
0
1
1
0
2
2
1
1
1
1
2
1
0
1
0
2
2
1
0
1
0
1
1
1
2
1
1
1
0
0
0
0
0
1
0
1
0
1
2
2
0
1
0
1
1
2
1
1
2
1
1
0
0
1
0
0
1
1
0
1
1
1
0
2
1
2
1
1
0
0
0
0
3
1
1
0
1
1
1
2
1
1
1
1
1
1
2
2
1
1
2
0
1
2
2
3
0
1
1
1
1
0
1
1
1
0
2
1
1
1
0
0
2
1
1
0
0
1
1
1
2
1
2
0
1
1
2
2
0
1
0
2
1
1
1
1
2
1
2
1
0
1
1
0
1
1
0
0
0
2
1
0
2
1
2
1
0
1
1
2
1
0
0
1
2
0
1
0
1
0
2
0
2
1
0
1
0
2
1
0
1
2
0
0
2
0
2
2
2
1
2
2
1
1
0
0
1
2
1
1
1
2
1
1
1
2
0
0
1
2
2
0
1
1
0
0
2
2
0
0
0
1
0
1
0
1
1
0
1
1
1
0
0
1
0
1
2
1
0
1
2
1
2
1
2
0
1
2
0
0
2
1
0
1
0
1
1
1
0
2
2
0
1
0
2
1
1
0
1
0
2
1
1
0
1
1
2
0
0
1
1
0
1
1
1
2
1
1
1
0
1
0
1
2
0
1
1
1
0
1
0
1
1
1
1
2
1
2
1
1
2
0
1
1
0
1
0
0
1
2
2
1
1
0
4
0
2
0
1
2
2
1
1
2
2
1
0
1
1
2
1
2
1
1
2
2
2
1
0
1
2
0
1
0
1
1
1
1
1
0
0
1
0
2
0
1
1
1
2
0
1
2
1
1
0
0
0
1
1
1
1
1
2
1
0
1
2
1
1
1
2
1
1
1
2
1
0
1
2
1
1
2
0
1
1
0
1
2
1
1
2
1
0
0
1
2
1
0
1
1
0
1
0
0
1
1
0
1
0
1
1
2
1
0
1
0
1
1
0
1
0
1
0
1
0
1
0
0
1
0
0
1
1
1
1
1
0
1
0
1
0
2
0
1
1
0
0
2
1
2
1
0
0
2
1
0
1
0
2
1
0
2
2
1
2
2
2
4
1
0
1
0
2
0
0
1
2
2
1
1
0
0
1
0
0
1
0
1
1
0
1
1
1
1
0
1
2
1
1
4
1
1
1
1
4
1
0
0
1
1
4
1
2
2
1
0
0
1
1
2
1
0
1
1
1
1
1
0
1
1
0
1
0
1
0
1
0
1
1
0
1
0
1
2
2
1
0
1
1
0
0
2
1
1
0
1
1
1
1
1
0
0
0
1
1
0
0
1
1
0
1
0
1
1
1
0
1
1
1
5
1
1
0
1
1
1
0
0
1
0
2
0
1
1
1
1
1
1
2
2
2
0
0
0
0
2
0
0
2
0
1
2
1
1
1
1
2
2
1
0
1
1
1
2
1
1
1
0
1
0
3
0
0
2
0
1
1
1
1
0
0
1
0
0
0
1
1
1
1
0
0
1
3
1
1
0
1
1
2
2
2
2
2
2
1
2
1
1
1
0
1
1
1
2
1
0
0
1
0
1
1
2
1
2
1
1
1
1
1
0
0
1
2
1
1
0
2
1
1
0
1
2
1
0
0
0
1
1
2
2
0
2
0
1
0
1
1
1
0
2
2
2
0
1
0
2
2
1
1
0
1
1
0
1
2
1
1
1
0
2
0
2
1
1
1
2
1
0
1
1
1
0
2
1
0
0
1
2
2
1
2
2
1
0
2
1
2
1
1
1
1
2
1
1
0
0
0
0
0
1
1
2
1
0
1
1
2
2
1
1
1
0
1
2
0
1
2
0
2
1
1
2
0
2
0
1
1
0
0
1
1
2
1
1
0
0
0
1
1
0
2
2
1
0
0
1
2
2
0
1
1
2
1
1
1
2
1
1
2
0
3
0
2
1
0
1
1
1
2
1
1
0
2
2
0
2
0
1
2
1
2
1
1
3
0
1
0
2
1
1
2
0
1
2
1
1
0
0
2
0
0
0
1
2
2
1
1
0
1
1
1
1
1
1
0
0
1
1
1
0
1
1
2
2
0
1
2
0
0
2
2
0
0
2
1
0
1
1
0
0
1
1
0
0
0
0
1
0
2
1
1
0
0
2
1
1
3
1
1
1
1
1
2
2
1
0
1
1
1
2
0
1
0
1
2
1
1
1
1
0
2
0
0
1
1
1
0
2
0
1
1
1
2
1
0
2
1
1
1
1
1
1
1
1
1
1
3
1
1
0
2
1
2
1
1
2
1
1
2
2
0
1
1
0
2
1
1
0
2
1
0
2
1
1
1
2
1
1
2
1
1
0
2
2
1
1
2
0
1
0
0
2
1
1
0
1
0
2
1
4
0
1
2
0
3
2
0
1
1
1
2
0
0
1
2
1
1
1
1
1
1
1
0
2
0
2
0
2
1
1
1
0
0
0
0
2
1
0
1
1
1
1
0
0
0
0
0
1
0
2
1
0
2
0
1
2
0
0
2
2
0
1
0
2
0
1
0
2
0
1
2
0
1
2
1
0
2
2
1
0
1
1
0
1
1
1
0
1
0
2
1
1
1
0
2
1
1
1
0
0
2
0
2
1
0
1
1
1
1
1
1
1
2
1
2
1
1
0
1
1
2
1
0
1
2
1
0
1
1
0
2
0
1
1
1
1
1
1
0
2
2
1
1
2
0
2
0
2
1
1
1
1
1
0
1
1
0
1
2
0
1
0
2
1
0
1
1
0
1
0
0
0
0
1
1
1
2
1
0
1
2
0
0
0
1
1
2
1
0
1
1
1
2
2
0
0
1
2
1
1
1
1
2
2
0
1
1
2
2
0
0
0
0
0
1
2
1
1
1
2
1
2
1
0
1
0
2
0
1
1
1
1
1
2
2
5
0
2
0
2
1
1
1
1
2
0
1
2
0
2
1
1
0
0
1
1
1
2
0
0
1
0
1
0
1
1
1
0
1
2
1
1
1
2
2
0
2
1
2
0
1
2
2
1
0
1
1
2
2
1
0
0
2
0
1
2
2
2
1
1
1
0
1
0
0
2
2
2
1
1
2
1
6
0
0
0
1
1
0
1
1
0
1
1
1
1
1
1
0
1
1
1
1
1
0
1
1
0
2
2
1
1
0
1
1
2
2
1
1
1
0
0
1
1
2
1
1
0
1
2
0
1
0
1
1
1
1
1
1
1
1
2
1
1
2
2
0
1
1
0
1
1
1
0
1
2
2
2
1
2
2
1
1
0
1
1
2
2
1
1
1
1
1
1
0
1
0
2
1
1
2
1
2
1
2
1
1
1
2
1
1
0
1
1
0
2
1
1
1
0
0
0
1
0
0
1
1
1
2
2
1
1
1
1
1
0
2
1
0
0
1
2
0
1
1
1
0
0
2
1
0
1
0
1
1
1
1
0
0
1
0
1
2
0
2
1
1
2
1
0
0
0
2
1
0
0
0
1
1
2
0
0
0
0
0
1
0
1
0
1
1
2
1
1
1
1
2
1
1
2
1
1
2
2
0
1
0
1
1
2
1
1
0
0
0
1
1
1
2
1
1
2
1
2
1
2
1
0
2
1
1
2
1
1
0
1
2
1
1
2
2
2
1
1
1
1
1
0
1
1
0
1
2
1
2
1
1
0
0
2
1
1
0
2
4
1
2
2
1
1
1
2
1
3
1
2
0
1
1
1
1
2
1
0
2
1
1
1
1
2
1
1
1
1
1
0
0
0
0
2
1
1
0
2
2
1
1
1
1
2
1
2
1
1
1
1
1
0
0
2
2
0
2
2
0
1
0
1
1
0
0
2
0
1
1
2
1
0
1
0
0
0
2
0
2
1
2
1
0
1
1
1
2
1
2
0
1
0
0
1
1
1
0
1
2
0
1
0
1
0
1
1
1
1
1
1
2
0
0
2
1
0
1
2
0
1
1
1
3
1
1
1
1
0
2
1
1
1
1
1
0
1
0
0
1
0
1
2
2
1
0
0
1
1
0
2
3
0
1
2
0
0
0
1
2
2
1
1
1
1
1
0
1
2
3
1
1
2
0
1
0
0
1
0
0
2
0
2
0
1
1
2
1
1
1
2
3
1
1
1
0
1
1
1
1
0
1
0
1
1
0
0
1
1
2
1
1
1
2
0
0
2
2
0
1
2
1
1
2
0
2
0
2
1
0
1
1
2
1
1
2
0
1
0
0
2
1
1
0
1
2
0
1
2
0
1
0
2
1
2
2
0
1
0
2
1
2
2
1
1
0
1
1
1
2
1
0
7
1
0
1
1
1
1
0
2
0
0
1
0
0
2
0
1
2
1
0
0
0
1
0
2
0
1
1
1
1
0
2
1
0
2
2
0
2
0
2
0
2
1
1
1
0
0
1
1
2
1
1
0
2
1
1
1
1
2
1
0
1
0
1
1
2
2
1
1
0
1
2
1
1
0
1
1
2
1
0
0
0
1
1
1
1
1
1
2
1
0
1
2
1
2
1
1
1
1
1
0
1
1
1
1
1
1
1
0
1
0
0
1
1
1
1
0
1
2
0
1
1
3
0
2
1
1
2
2
1
2
2
2
1
1
0
1
0
2
2
1
2
0
1
2
0
1
1
0
1
0
1
1
1
1
0
1
1
1
1
0
2
1
0
0
0
1
1
1
1
0
0
2
0
1
1
0
2
2
2
1
1
1
0
2
0
0
0
1
1
0
1
0
0
1
1
1
1
1
1
2
0
1
1
0
0
1
1
2
0
0
3
0
1
0
0
2
0
1
0
0
2
2
1
2
1
1
1
2
2
1
0
1
1
2
1
1
1
1
1
0
1
1
1
1
4
1
2
1
0
1
2
1
0
0
1
0
1
3
0
1
2
1
1
1
2
2
1
2
0
0
1
1
1
2
1
1
1
1
1
1
1
0
0
2
0
0
1
0
1
1
1
1
1
2
1
1
1
1
1
1
2
0
1
1
3
1
1
1
2
1
1
0
1
2
1
2
0
2
0
1
2
0
1
1
0
0
0
0
1
1
0
2
0
0
0
1
0
1
0
0
1
1
0
1
0
1
0
1
0
1
0
2
1
2
2
0
2
0
1
1
2
3
1
1
2
0
1
0
0
1
1
0
1
1
1
1
1
2
0
0
2
1
0
2
1
2
0
1
2
0
2
0
1
2
0
0
1
1
0
1
0
1
1
0
0
2
0
2
1
1
1
0
1
1
1
2
2
0
0
2
0
0
1
1
1
1
2
1
1
2
2
1
1
2
0
1
2
1
1
0
1
0
1
1
2
0
1
1
3
1
0
2
1
0
0
0
0
1
6
1
1
0
1
1
0
0
1
1
1
0
0
2
1
1
1
2
1
0
1
1
2
1
2
3
1
2
0
1
1
0
1
1
0
1
1
1
1
1
2
2
1
2
1
1
11
1
1
2
1
1
1
1
1
0
0
1
0
2
1
0
0
0
1
0
1
1
1
1
1
0
1
1
1
2
0
0
1
0
0
0
1
1
0
1
0
0
1
0
2
0
1
2
1
0
0
1
1
0
1
0
1
0
1
0
0
2
1
0
1
0
1
1
1
1
1
2
0
2
0
2
1
2
1
1
2
1
3
1
2
2
2
2
2
0
1
0
2
1
1
2
1
2
2
0
1
0
2
1
0
0
2
1
1
0
0
0
1
0
1
0
1
1
1
1
2
3
1
1
1
1
1
1
1
1
2
1
2
1
1
1
3
1
1
0
2
1
2
0
1
2
1
2
1
0
1
0
1
2
1
1
1
1
1
1
2
1
0
2
0
0
2
0
0
2
0
1
1
2
0
0
1
2
0
1
0
1
0
0
2
1
1
0
1
1
2
0
0
1
0
2
0
0
0
1
1
1
1
1
2
1
2
2
1
2
1
2
2
2
0
2
0
1
1
1
1
0
2
1
1
1
1
1
1
1
1
0
1
1
1
1
1
2
1
1
0
1
1
0
0
0
2
0
0
0
0
1
0
1
0
0
2
1
1
2
2
2
0
2
0
1
2
1
2
0
0
0
1
2
1
0
2
1
1
0
0
1
1
0
2
0
1
0
1
0
2
2
2
2
1
1
1
1
0
1
1
0
0
0
1
0
1
1
1
1
1
1
1
2
1
0
1
1
2
1
1
2
1
0
0
1
3
2
0
0
1
1
1
0
2
1
1
0
1
2
1
1
0
2
1
1
1
1
0
1
2
1
2
0
0
1
1
2
1
2
0
1
1
1
1
1
1
2
0
3
1
1
0
2
1
1
1
2
1
0
2
1
0
1
0
0
1
2
2
2
2
0
0
1
2
1
0
1
1
0
1
1
0
2
1
1
0
0
2
1
2
2
1
0
1
2
0
1
0
2
0
1
1
1
1
2
2
1
1
0
2
2
0
1
1
0
2
0
1
1
2
1
2
1
1
2
2
1
0
1
3
0
2
0
1
1
0
1
0
1
1
1
2
2
1
1
4
0
0
0
0
1
1
0
2
1
2
0
0
1
1
1
1
2
0
1
1
1
0
0
1
3
0
1
0
1
1
1
1
1
1
2
1
0
0
1
0
1
0
1
0
0
1
0
0
0
1
1
2
1
0
0
1
2
1
2
0
2
2
1
2
2
1
1
0
1
2
1
0
0
1
0
1
2
3
2
1
2
4
0
2
1
1
0
2
1
1
0
0
1
2
0
0
0
1
1
1
1
0
0
0
1
0
0
0
1
2
0
2
1
1
1
1
2
0
2
1
1
1
0
0
1
2
0
1
1
1
1
0
1
0
2
1
0
2
1
1
1
0
0
1
2
2
1
0
1
1
1
1
1
0
0
1
1
1
1
2
0
1
0
0
1
1
0
0
2
1
0
1
1
1
1
0
2
0
0
1
1
2
0
1
0
1
0
2
1
2
2
0
0
0
0
0
0
1
2
1
1
1
2
1
1
0
1
1
1
2
2
0
1
2
2
2
2
1
2
2
2
1
1
0
1
1
2
1
1
0
0
1
1
1
0
2
2
2
1
2
0
0
1
1
1
1
2
2
2
1
1
2
1
0
2
0
1
1
1
1
2
0
1
2
0
1
0
0
1
1
1
1
0
1
1
0
0
0
2
1
2
2
0
1
1
0
0
1
2
1
2
0
1
1
1
1
0
1
0
1
2
2
1
0
1
0
1
0
1
2
1
1
1
1
2
0
0
0
1
1
2
0
0
1
0
1
2
2
0
0
0
2
0
2
2
0
1
1
2
2
2
1
0
1
1
1
2
2
0
0
0
1
2
2
2
1
2
2
1
1
0
2
2
1
1
2
1
1
2
1
3
1
0
1
0
0
0
0
1
2
1
0
0
1
2
2
1
1
0
1
1
2
2
0
0
2
2
0
0
2
0
1
1
2
0
1
2
1
1
1
0
0
1
1
1
2
0
0
1
1
1
1
1
1
2
1
1
2
2
1
1
1
0
0
2
1
2
0
2
1
0
1
0
1
0
0
0
0
0
2
1
1
1
2
1
2
1
0
1
1
1
1
0
1
0
2
0
1
1
2
1
0
0
1
2
1
1
4
1
1
1
1
0
2
1
2
1
0
1
1
2
0
0
0
1
1
1
1
1
0
0
1
0
1
1
2
1
0
1
2
1
1
2
1
0
1
0
1
0
1
1
1
2
2
0
1
0
1
0
1
0
1
0
1
1
1
2
2
1
1
1
0
2
2
0
1
1
1
2
0
2
0
1
0
1
1
0
1
1
4
2
2
0
0
2
1
1
1
0
1
1
1
0
2
0
0
1
1
0
1
1
0
1
1
0
0
2
1
1
0
1
0
1
2
0
3
1
2
1
2
1
1
1
0
0
0
2
1
0
1
1
0
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
0
2
1
2
1
0
1
1
0
1
1
3
0
1
0
2
0
1
1
1
1
0
1
1
1
0
2
1
2
0
2
1
2
2
2
2
0
2
3
1
2
1
0
0
1
2
1
0
2
1
2
1
1
2
0
2
0
0
2
0
1
1
0
1
2
0
1
1
2
1
1
2
1
0
2
2
1
1
1
1
0
1
1
0
1
1
1
2
1
1
2
2
0
2
1
2
1
1
1
1
0
1
0
0
1
1
1
0
0
2
1
2
2
2
0
2
0
0
1
2
2
0
2
0
0
1
0
0
2
2
1
1
1
2
0
1
0
0
2
0
1
2
2
1
0
1
1
1
1
0
0
1
2
1
2
1
2
0
0
1
1
2
0
0
0
0
0
1
0
1
1
0
0
0
0
2
1
0
1
2
0
2
1
1
1
2
0
2
2
0
1
1
2
2
1
2
2
2
1
0
2
2
1
1
1
2
0
0
0
1
1
2
0
1
2
1
0
1
1
0
1
1
1
2
2
1
1
2
1
0
0
2
0
1
1
2
0
1
2
2
1
2
0
1
1
1
1
1
2
2
1
1
2
0
1
1
0
2
1
0
1
1
1
0
0
1
1
1
0
1
1
0
1
0
0
1
2
0
2
2
0
1
1
0
0
1
0
0
1
1
0
2
1
0
1
1
1
1
1
1
0
0
2
2
1
2
1
1
0
1
1
0
0
1
0
2
2
2
0
2
1
1
0
0
1
1
0
0
1
1
1
1
1
1
2
2
2
2
2
0
2
1
0
1
1
0
0
1
2
1
1
1
3
0
1
0
1
1
1
0
2
1
2
1
0
1
0
0
2
1
2
4
0
1
2
1
0
1
2
0
0
2
0
0
2
1
1
2
2
0
1
1
1
0
0
0
2
2
2
1
0
0
1
1
1
1
0
0
1
0
0
0
1
1
0
0
1
1
1
2
1
0
0
2
1
2
1
0
1
1
0
1
1
0
0
1
0
0
0
0
0
1
0
2
2
2
1
1
2
1
2
1
2
1
1
1
1
0
0
1
0
2
0
0
1
1
1
2
1
0
0
0
1
1
1
1
1
1
2
1
1
0
0
1
1
0
0
2
0
1
1
0
0
2
1
1
2
1
1
2
0
1
2
0
1
1
1
2
2
0
1
0
2
1
1
1
2
1
1
1
0
1
1
1
2
0
2
1
1
2
0
2
1
1
1
1
1
1
1
1
0
1
2
1
0
0
1
1
0
1
0
0
0
0
0
2
1
1
2
1
0
1
1
1
1
0
2
0
0
1
2
1
0
0
2
0
2
1
1
2
1
1
1
1
1
2
1
0
1
1
1
2
0
1
1
3
2
0
1
0
1
1
1
2
0
1
1
1
1
0
1
1
1
0
1
1
0
0
1
1
1
1
2
0
1
1
2
1
0
1
0
1
0
0
1
2
2
1
2
0
1
0
1
2
1
0
0
0
0
0
1
0
0
0
1
1
1
1
1
0
0
1
1
1
1
1
0
1
1
1
5
1
0
0
0
1
1
1
1
2
1
0
3
1
0
2
0
2
0
0
0
2
2
1
1
1
1
1
0
2
1
0
1
0
1
2
1
1
2
1
1
3
1
0
2
0
0
1
2
2
1
2
2
1
0
1
1
1
1
0
0
2
1
1
0
0
2
1
0
1
2
0
0
0
1
1
1
1
2
1
2
0
1
0
1
1
2
0
2
1
0
1
1
1
0
1
1
0
1
1
0
0
1
1
0
1
0
2
0
1
1
0
2
1
0
2
2
1
0
0
0
2
1
1
1
1
1
2
2
1
0
1
0
2
2
1
1
2
1
0
1
2
0
1
2
1
2
0
2
0
1
1
0
2
1
1
1
1
1
1
1
1
1
1
1
0
3
1
1
1
1
1
1
1
1
0
0
0
0
0
2
2
1
1
1
0
0
1
1
1
1
1
0
2
0
0
2
1
2
0
1
1
1
0
0
1
0
0
1
0
1
0
1
2
0
2
1
1
0
1
2
2
0
1
1
2
1
1
1
1
0
1
2
0
2
1
1
3
1
1
2
3
1
0
1
2
0
1
1
0
1
1
1
0
0
0
1
1
1
1
0
0
2
1
2
1
0
1
0
2
2
2
0
2
2
1
0
0
1
2
1
1
1
0
1
1
1
1
1
1
0
0
1
1
1
0
0
1
2
1
1
2
0
2
0
1
0
0
0
1
1
2
1
1
1
1
1
1
1
0
0
2
1
1
0
1
1
0
1
0
0
0
1
1
1
0
1
0
0
1
1
0
1
1
1
2
1
1
1
0
1
0
1
1
0
2
1
1
2
1
1
1
0
1
2
1
0
0
0
1
0
0
1
1
1
0
1
2
1
1
0
0
2
0
2
1
0
0
1
0
0
1
1
1
2
0
1
1
2
0
0
1
0
2
0
1
1
2
1
1
0
0
0
0
0
1
1
1
1
2
2
1
1
1
0
0
1
0
2
0
2
2
1
1
0
2
1
0
2
0
1
0
2
0
1
1
1
2
2
1
2
1
2
1
1
6
1
1
1
2
0
0
2
1
1
2
2
2
2
3
2
0
1
2
1
1
2
1
1
1
0
0
0
0
0
1
1
0
2
0
2
1
0
2
0
1
1
0
1
1
2
0
1
2
0
0
1
1
0
1
0
1
1
0
0
0
1
0
1
1
0
0
2
1
2
0
0
1
1
2
0
0
1
1
2
1
0
3
0
2
2
2
0
1
0
1
1
1
0
0
0
2
1
1
2
0
1
2
1
1
2
1
2
0
2
1
0
0
1
0
0
1
1
1
0
0
2
2
0
2
1
1
0
1
1
1
0
1
0
0
2
1
0
0
3
1
0
0
1
0
1
1
1
0
1
2
2
2
1
1
0
2
1
1
1
1
1
2
1
0
0
2
2
0
1
0
2
1
1
1
0
1
0
0
0
2
0
0
1
2
0
1
0
0
1
1
2
0
0
1
0
1
0
0
2
2
2
1
1
1
2
1
0
1
1
1
0
2
1
0
1
1
1
2
2
1
2
1
0
2
1
2
1
0
0
2
2
0
2
1
1
2
1
1
1
1
2
1
1
1
0
2
0
2
1
1
0
0
2
1
2
1
2
1
1
1
2
1
1
2
1
2
0
2
0
0
1
1
1
2
1
1
1
0
2
2
1
1
1
1
1
0
1
1
2
1
0
0
1
1
0
2
0
1
1
0
0
1
0
0
1
0
0
0
2
1
0
2
2
0
0
2
1
1
2
1
1
0
2
2
0
0
0
1
1
0
0
1
2
2
0
2
1
2
0
0
0
0
0
0
1
1
1
2
1
1
1
0
1
1
0
1
2
1
1
1
1
0
1
0
1
1
0
0
1
2
2
2
0
0
1
2
1
1
0
1
0
1
2
3
0
0
0
2
0
1
2
0
1
0
1
1
1
1
0
2
2
0
1
1
1
0
1
0
1
0
1
1
1
0
1
1
2
2
2
1
0
1
0
2
2
0
1
0
1
1
0
2
2
1
0
2
2
2
0
0
2
0
0
0
1
2
2
1
2
0
1
1
0
0
0
0
1
0
0
1
1
0
1
0
1
1
1
2
2
2
1
1
2
0
1
1
0
1
1
2
2
1
0
0
1
0
1
1
1
1
1
1
2
1
0
2
1
1
1
2
1
1
0
0
1
1
2
0
0
1
0
1
2
1
1
1
1
1
2
1
2
1
1
0
2
1
0
2
1
9
2
0
0
1
1
1
1
1
0
0
1
0
1
0
1
2
1
1
2
0
0
1
1
2
1
2
1
1
1
1
1
2
0
2
2
1
0
0
1
2
2
0
0
3
0
1
1
1
2
1
0
1
2
0
0
1
0
0
1
0
2
2
2
1
1
0
1
0
1
1
1
1
0
1
1
1
1
0
1
2
1
0
0
1
0
1
1
0
1
0
2
2
3
1
0
0
1
1
0
1
1
1
2
0
1
0
1
1
1
0
0
2
1
1
3
0
1
1
1
1
1
1
2
1
1
2
1
1
0
0
0
1
3
0
1
0
0
0
1
2
0
2
0
0
2
1
1
0
1
1
1
2
2
0
0
1
1
1
1
0
0
1
0
2
2
1
2
0
0
2
2
0
1
0
0
2
0
1
2
1
0
2
1
0
2
0
1
0
1
0
1
1
0
2
0
0
0
1
1
2
0
0
2
1
3
1
1
1
1
0
1
0
1
1
1
1
1
2
2
1
0
1
1
2
1
0
0
1
0
0
1
1
0
1
2
0
0
2
0
1
2
1
1
1
1
1
0
1
1
1
0
1
0
1
2
0
0
1
0
2
2
2
1
0
1
2
0
2
0
1
1
0
1
1
0
0
0
0
1
1
1
1
1
2
1
1
0
0
1
1
1
2
1
1
1
0
1
2
1
1
2
0
2
1
1
1
2
1
1
1
1
1
0
0
2
2
1
1
0
1
1
2
1
1
2
0
1
0
0
0
0
0
0
2
1
1
1
0
1
0
2
1
1
0
1
1
2
1
0
0
1
1
1
2
1
1
0
1
1
1
1
0
2
0
0
7
0
0
1
1
1
0
0
0
0
0
0
1
2
1
0
0
2
0
0
0
2
0
0
3
1
0
1
0
1
0
0
1
0
1
1
2
0
1
2
0
0
1
1
0
0
1
2
0
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
2
1
1
0
1
0
1
0
1
1
2
2
0
1
2
0
2
1
2
1
2
1
1
1
1
1
1
0
1
0
1
2
1
1
0
0
1
2
2
0
1
0
0
2
1
2
0
0
1
1
2
1
0
1
1
1
0
0
1
0
2
2
0
2
1
1
2
1
1
0
0
0
1
1
1
1
1
1
1
1
1
0
1
0
0
1
0
1
1
0
1
1
4
1
0
0
0
0
1
1
1
0
2
1
1
2
1
0
1
0
0
1
1
1
0
0
0
1
1
2
2
0
0
2
2
1
1
2
0
0
1
0
1
2
0
1
2
0
0
1
0
2
2
1
0
0
0
1
1
1
0
0
0
2
1
0
2
0
1
1
0
0
2
2
0
1
0
1
0
0
1
0
0
1
2
2
2
3
0
1
0
2
2
1
1
0
1
1
1
1
1
1
0
1
2
0
1
0
0
1
2
0
1
2
3
1
1
0
1
1
2
2
1
0
0
1
1
0
1
0
0
1
0
0
1
2
2
1
1
0
0
1
2
0
1
1
2
0
2
1
2
1
1
0
0
2
2
0
1
0
0
2
1
1
1
0
1
1
1
2
1
4
2
1
0
0
1
0
2
0
1
0
0
1
1
1
1
1
2
1
0
2
2
1
1
0
0
1
0
2
1
2
2
0
2
2
1
0
1
1
2
1
1
1
0
1
2
0
1
0
1
2
2
1
0
0
1
0
0
1
1
2
2
1
2
1
0
0
1
1
1
0
1
2
1
1
0
1
1
0
2
1
1
0
1
1
2
1
0
0
1
1
2
0
2
3
2
0
1
0
0
2
2
1
1
1
2
1
2
3
2
1
1
0
2
1
0
0
1
1
1
1
0
1
1
2
1
0
1
3
0
0
1
0
1
0
1
1
0
1
0
0
1
0
1
1
2
0
1
0
1
1
0
0
1
0
1
0
0
2
1
1
0
0
1
1
0
2
2
0
1
0
1
2
1
0
1
1
0
1
1
2
1
1
1
2
0
1
0
1
2
1
2
2
2
0
0
2
2
0
0
0
0
0
1
0
0
1
1
1
1
1
1
1
0
1
1
2
1
1
1
0
0
1
2
3
1
1
2
1
2
0
0
0
1
1
2
0
1
1
0
2
1
1
1
2
1
1
2
0
0
2
0
2
1
0
2
2
0
1
2
1
0
0
0
0
2
1
6
1
2
0
1
1
1
2
0
2
1
1
0
1
2
0
1
1
2
2
0
1
2
2
1
4
0
2
1
1
1
0
1
1
2
0
1
1
1
0
1
2
0
1
0
1
2
0
2
0
1
1
0
2
2
3
0
2
2
0
1
0
1
1
1
0
1
2
1
1
2
0
1
1
1
1
0
0
1
1
2
1
1
0
0
0
2
1
2
1
2
1
1
1
0
1
2
0
1
2
0
1
0
0
0
0
0
1
0
2
1
2
1
2
1
0
1
1
2
1
1
1
1
2
1
0
1
1
1
2
0
1
0
1
1
2
0
0
1
1
1
3
2
1
1
1
1
2
1
2
1
1
2
1
0
0
1
1
1
1
0
2
1
2
2
2
1
0
0
1
0
0
2
0
2
2
0
1
0
1
0
2
1
1
0
1
0
1
2
2
0
1
0
1
0
2
0
2
0
0
1
0
2
3
2
0
1
1
0
1
0
2
0
2
0
1
1
0
1
0
0
2
1
0
1
2
0
0
2
1
0
1
1
0
1
0
0
0
2
1
0
2
1
1
0
2
0
1
2
1
2
1
2
1
2
0
1
0
2
1
1
1
1
1
0
0
2
2
2
1
2
1
1
2
1
2
0
1
1
1
0
1
0
0
1
0
1
1
1
2
2
1
1
2
0
1
2
0
1
1
1
3
0
1
0
0
0
2
0
2
2
2
0
0
1
0
1
1
1
2
1
0
1
1
2
1
2
1
1
1
2
2
2
2
0
0
0
1
1
1
0
1
1
2
2
1
1
1
0
1
0
1
2
1
1
1
1
0
1
1
1
0
0
0
0
1
0
1
0
2
1
2
2
1
0
1
1
1
1
0
0
1
1
2
2
0
0
2
0
0
0
1
0
2
0
1
1
1
1
2
2
0
0
2
1
1
0
3
2
1
1
1
0
1
1
0
1
2
1
2
1
0
1
2
1
0
1
2
0
0
2
2
2
1
2
1
1
0
0
2
1
2
1
2
0
2
0
0
2
0
1
1
0
0
0
1
1
0
0
1
1
0
0
2
2
0
1
1
0
2
1
1
1
0
0
1
0
1
2
1
1
2
1
0
0
1
1
0
1
2
1
1
1
1
0
0
2
0
1
0
0
1
1
0
0
2
1
0
0
1
1
0
0
0
1
0
1
1
1
1
2
0
1
1
1
2
1
2
2
1
2
0
0
1
1
2
1
0
0
0
1
1
2
1
0
0
3
1
1
1
2
1
1
5
0
1
0
1
2
2
0
1
1
1
0
1
0
1
2
0
1
1
1
1
1
1
0
0
1
1
2
1
1
0
2
0
1
1
1
1
2
1
1
0
0
0
1
1
1
0
1
2
0
0
1
1
1
1
1
2
0
0
1
2
1
0
1
1
0
2
3
1
1
0
2
1
2
1
1
0
0
0
0
0
0
2
2
1
1
2
2
1
0
1
2
0
3
1
1
0
1
1
1
0
1
2
1
1
0
0
1
1
2
0
1
1
1
1
1
2
2
2
1
1
1
2
1
1
0
1
2
1
2
0
1
2
1
0
0
1
1
1
1
2
1
1
0
1
1
1
0
2
0
1
0
1
1
1
1
1
3
2
2
2
0
1
2
2
2
2
0
0
1
2
0
0
0
0
0
0
0
1
0
1
1
0
0
1
1
1
0
1
0
2
0
1
1
2
1
0
2
0
0
2
1
0
1
1
2
1
1
3
0
2
1
2
0
2
1
1
1
1
0
0
0
1
1
0
1
1
2
1
1
0
1
2
2
1
1
1
0
1
1
0
1
0
2
1
1
2
1
0
1
2
1
0
1
2
1
1
0
2
1
2
2
1
1
1
0
1
3
1
1
2
1
1
0
1
1
1
1
1
0
0
1
1
0
1
2
0
1
1
1
1
2
0
1
2
1
0
1
1
0
1
2
0
2
1
1
1
1
1
0
0
1
1
2
2
1
0
2
2
0
0
3
0
1
0
1
1
2
0
1
0
1
2
2
0
1
3
2
0
1
2
2
1
2
1
0
1
2
2
2
0
1
0
2
1
0
0
0
0
1
2
2
2
0
1
0
2
2
0
0
0
2
0
1
2
1
1
1
2
2
1
3
1
0
0
2
0
2
1
1
1
2
2
1
2
2
2
1
4
1
0
1
0
1
1
0
2
1
2
1
0
0
1
3
1
0
2
1
1
0
0
2
2
1
0
1
1
1
0
0
1
2
1
2
1
0
0
1
1
2
0
2
0
1
1
1
0
0
0
1
0
2
2
0
0
1
1
2
2
1
0
0
1
2
0
2
2
1
1
1
0
0
1
2
1
0
1
1
0
0
0
0
2
1
2
1
1
1
1
1
1
0
2
1
1
1
1
1
1
1
2
2
1
2
5
1
0
1
2
1
3
0
2
1
0
0
1
0
1
2
1
1
0
1
2
0
0
0
3
0
1
1
0
0
0
1
0
1
1
1
1
1
1
2
2
2
1
1
1
0
0
0
0
0
1
2
2
1
0
1
1
0
0
1
0
1
2
2
1
1
2
1
0
2
1
1
1
2
0
1
0
2
0
0
1
1
1
1
2
1
1
2
2
4
2
1
2
2
1
1
2
2
2
0
0
0
0
2
0
1
0
2
1
1
1
1
1
0
1
1
2
0
1
1
0
1
0
0
1
0
1
1
1
2
2
0
1
0
1
1
2
1
1
2
1
0
2
1
2
0
2
1
0
1
0
2
1
0
1
2
1
1
2
1
0
1
1
1
2
2
2
1
0
2
0
3
1
1
1
1
2
1
1
0
1
1
1
0
1
0
1
2
2
1
2
2
1
2
2
1
1
1
2
0
2
1
2
0
1
0
1
2
7
0
0
0
3
1
2
1
2
1
0
2
1
0
0
1
1
0
2
1
1
0
2
0
2
0
1
2
1
0
2
1
0
2
0
1
2
2
1
0
1
2
1
0
1
2
1
0
2
0
0
0
1
0
1
1
0
1
0
0
0
2
2
0
1
0
0
2
0
1
2
2
1
1
0
1
1
1
1
0
0
1
0
0
0
1
0
0
4
2
1
1
1
1
0
1
1
0
2
1
0
0
1
1
1
1
1
0
0
1
2
0
2
2
1
1
1
0
2
1
0
1
1
0
0
0
2
1
1
0
0
0
1
1
0
1
0
2
2
0
2
2
0
1
1
1
2
0
2
0
2
1
0
2
1
0
0
1
1
2
0
1
0
0
2
0
1
2
1
1
1
0
2
1
0
2
1
0
1
2
2
0
0
0
1
0
2
0
3
1
0
1
1
1
1
0
0
2
1
1
1
1
1
1
1
0
0
0
0
1
2
1
0
1
1
0
1
3
1
1
1
1
1
1
2
0
2
0
1
1
2
1
0
0
1
0
1
0
0
1
1
1
0
1
0
1
1
1
1
2
1
1
0
1
1
1
1
1
2
0
2
1
1
2
0
1
1
1
2
1
0
2
2
2
1
2
1
2
2
1
1
1
1
1
1
0
1
0
2
0
2
1
0
1
3
1
2
1
1
1
1
1
1
0
2
1
2
2
2
0
1
1
1
3
2
1
0
2
0
0
0
0
2
2
1
1
0
1
1
1
2
1
1
1
2
0
1
1
1
3
0
1
1
1
1
0
1
2
0
1
1
1
1
1
1
1
0
2
0
1
3
1
1
1
0
1
1
2
0
0
2
1
2
1
1
1
0
2
1
0
1
1
0
2
1
1
0
1
2
0
2
1
1
1
1
1
2
2
2
1
1
1
0
0
1
0
2
2
0
0
1
0
1
2
1
0
1
0
3
1
1
0
2
0
1
2
0
0
3
1
2
1
1
1
0
0
1
1
0
1
1
1
1
2
0
2
1
1
1
2
0
1
1
1
1
2
2
0
0
1
1
1
0
1
1
1
0
1
1
2
1
1
1
0
1
1
1
2
2
0
1
1
2
2
0
1
2
0
0
0
1
1
1
1
2
2
1
1
0
1
2
1
1
1
0
0
0
1
1
2
0
1
0
1
1
2
1
2
0
0
2
1
2
0
1
0
1
2
0
2
1
1
0
0
1
0
0
1
1
1
3
0
1
1
2
1
1
0
0
1
0
2
0
2
1
2
1
1
1
1
2
0
1
2
1
1
0
2
0
5
2
0
0
0
0
1
0
0
1
0
1
1
1
1
0
1
1
0
0
2
2
0
2
1
1
1
2
0
2
1
2
1
0
0
2
2
2
0
0
0
2
2
2
1
1
1
1
1
2
0
0
1
2
0
0
1
1
1
1
1
2
2
2
0
1
1
2
2
1
3
1
0
1
2
2
1
1
1
0
0
0
1
0
0
0
0
1
1
2
1
1
1
2
2
0
2
1
0
0
1
0
0
2
1
1
2
1
2
0
1
0
1
0
2
1
1
1
1
1
0
0
0
2
1
1
2
1
1
2
1
2
1
1
1
2
1
2
2
1
1
1
0
2
0
1
1
2
1
0
1
0
0
0
1
2
0
0
2
1
0
1
0
2
2
1
2
1
1
2
1
0
0
0
2
1
1
2
2
1
0
1
0
0
1
0
1
1
2
2
0
2
0
1
0
2
0
1
1
4
0
1
1
1
1
2
0
0
3
2
0
2
2
1
1
2
2
1
1
0
0
1
1
1
2
0
1
1
1
2
1
2
1
1
2
1
1
0
2
0
0
1
1
0
2
1
0
1
0
0
2
1
1
1
1
1
1
1
0
0
0
1
0
0
2
0
1
1
0
2
0
0
2
2
1
1
2
1
1
0
1
2
1
3
2
0
0
1
0
1
1
1
0
1
1
0
1
1
2
1
1
0
0
2
1
1
1
0
1
1
0
0
2
1
1
0
0
2
2
1
1
3
1
2
2
1
2
1
2
1
2
1
7
0
0
2
0
0
0
2
2
3
1
0
2
1
1
1
2
1
2
1
1
1
0
0
3
0
0
1
1
0
1
1
0
0
2
1
1
1
1
1
0
2
1
1
2
3
0
0
1
3
1
1
1
0
1
0
0
2
2
0
2
1
1
0
0
1
1
2
1
1
2
0
1
0
1
0
2
1
1
2
2
1
0
1
0
1
1
1
1
1
0
0
2
0
0
1
0
0
0
1
1
1
1
2
1
1
0
2
2
0
2
2
0
0
1
1
2
2
1
2
1
1
0
1
1
2
1
2
0
1
1
2
1
2
1
1
2
0
1
1
0
0
0
0
1
1
1
1
0
0
2
0
2
1
1
1
1
1
1
1
0
1
2
2
2
0
1
1
2
0
1
0
1
2
0
0
1
1
2
2
0
1
1
2
0
0
0
0
1
1
2
2
3
0
1
1
1
2
1
0
0
1
1
1
1
1
1
0
1
2
1
1
1
0
1
1
1
0
0
0
1
0
0
1
0
1
1
1
0
2
2
3
1
0
2
0
0
1
1
0
1
0
1
1
1
2
1
1
0
2
0
1
1
2
1
1
0
1
1
0
0
0
1
1
2
1
0
1
1
2
0
1
0
0
2
0
2
2
0
2
1
0
1
1
2
1
0
2
0
1
0
1
2
0
2
2
1
1
2
1
1
2
0
0
1
1
2
0
1
1
2
2
1
0
1
1
1
1
0
1
2
1
1
1
0
1
0
1
1
2
1
0
0
0
2
1
0
1
2
0
2
1
1
0
2
0
0
1
1
2
0
0
3
0
0
1
2
1
2
1
1
1
1
2
1
2
2
1
0
2
1
2
1
2
1
2
0
1
1
2
2
1
1
0
1
0
0
0
0
0
1
0
1
0
1
0
0
1
1
1
2
2
1
1
1
1
2
1
0
1
1
1
1
1
1
1
0
0
0
0
1
0
1
1
1
2
2
0
0
0
1
2
2
1
0
0
0
2
2
0
1
1
1
1
1
1
0
0
0
0
0
0
1
1
0
0
1
2
1
1
1
0
0
1
0
0
1
0
1
3
1
1
2
1
1
1
0
1
1
0
1
2
0
0
0
2
2
1
2
0
0
2
2
0
0
1
0
1
0
1
1
2
1
0
2
1
0
0
1
2
1
0
1
0
1
1
1
2
1
1
0
2
0
1
0
2
2
2
0
1
0
0
0
1
0
2
2
1
1
1
1
1
0
0
1
1
1
0
2
2
1
0
0
0
1
0
0
0
0
0
0
2
0
1
0
1
0
0
1
0
1
1
1
1
1
0
0
2
0
1
2
1
0
1
1
0
1
1
0
1
0
1
0
1
1
0
0
1
0
1
0
1
2
2
1
1
1
1
1
1
1
1
3
2
2
1
0
0
0
1
1
1
0
0
2
1
2
1
1
2
0
0
2
1
1
2
0
2
1
0
2
0
0
2
0
2
1
1
2
1
1
0
1
1
1
0
2
1
1
1
0
0
0
1
2
2
4
2
1
2
0
0
1
2
1
2
1
1
2
2
1
0
1
1
1
0
1
1
1
1
0
1
1
1
1
0
1
1
0
0
2
1
1
1
0
1
1
0
1
0
1
0
0
2
1
1
2
2
1
0
0
1
2
1
0
2
0
2
1
2
2
2
1
1
1
2
1
2
3
0
1
0
0
1
0
1
1
2
3
2
2
1
0
0
0
2
0
0
2
1
2
1
1
0
1
0
1
0
2
0
2
1
1
1
0
1
0
0
1
0
2
1
1
2
2
0
0
0
2
1
1
2
1
1
1
2
1
0
2
1
1
2
2
1
1
0
2
1
2
1
1
1
1
2
0
1
1
1
1
1
2
0
0
1
0
1
1
1
1
0
2
1
0
0
1
0
1
1
2
0
1
0
1
0
1
1
1
1
1
2
1
1
1
1
2
1
0
0
0
0
0
0
0
1
1
0
2
0
1
1
0
1
1
1
1
1
1
1
0
0
0
0
0
1
3
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
2
1
0
2
0
1
1
0
1
0
2
1
0
2
0
0
1
0
0
1
1
0
1
1
1
1
1
1
1
0
2
3
1
2
1
1
2
2
0
1
2
1
1
1
1
2
1
1
0
2
0
4
2
1
0
2
1
2
1
0
1
1
1
0
1
2
2
1
2
2
0
1
0
2
0
1
3
0
1
1
2
2
2
2
1
2
1
0
1
1
1
0
0
1
2
2
1
2
1
1
1
2
2
0
1
1
1
1
2
0
0
1
0
0
1
0
1
0
1
1
0
0
0
2
1
1
2
0
0
0
1
0
2
1
2
2
1
2
1
2
2
1
0
1
1
1
1
2
1
1
0
0
1
0
2
0
0
1
0
0
2
2
1
0
0
0
2
0
1
2
1
0
0
0
1
0
0
1
1
0
1
0
1
1
0
1
0
1
1
0
2
0
0
0
1
2
0
1
2
0
1
1
0
1
2
1
0
0
2
1
1
0
2
1
2
1
0
0
0
1
1
0
1
2
2
1
1
2
1
2
0
1
1
1
1
1
0
1
0
0
1
0
2
2
0
2
2
1
2
1
0
1
4
0
1
2
1
1
1
1
0
1
1
1
0
0
1
1
0
0
0
1
1
1
0
1
2
1
1
1
2
2
2
0
0
1
0
2
0
2
0
1
1
0
2
1
0
2
2
0
2
1
1
1
1
2
1
1
2
1
1
0
1
1
1
2
2
0
1
0
1
1
0
1
1
2
1
0
0
0
0
0
1
1
1
1
2
0
2
2
1
1
1
2
2
0
0
1
1
0
1
0
1
1
1
0
1
1
1
1
1
1
1
2
0
0
1
1
2
1
1
2
1
0
0
0
0
1
0
2
2
2
1
2
1
1
2
1
1
0
2
1
0
2
1
0
0
0
1
1
0
0
1
0
1
1
0
2
2
1
1
1
0
2
0
0
0
1
0
0
3
0
1
1
0
0
1
0
0
2
1
1
1
2
1
1
1
0
0
0
1
2
0
0
2
1
0
1
1
1
1
2
2
0
2
1
0
0
1
0
1
1
0
2
2
1
0
1
5
1
0
1
1
2
2
0
0
1
1
0
1
0
2
3
1
1
0
1
1
1
1
1
2
1
1
0
1
1
2
1
1
2
0
1
2
1
1
0
1
1
0
1
2
1
1
1
0
1
0
1
1
0
1
1
1
1
0
1
1
1
0
0
1
1
1
1
1
1
1
1
0
2
1
0
1
0
0
0
0
1
0
0
1
1
2
0
1
0
1
0
0
0
1
0
2
2
2
2
1
1
2
0
3
0
1
1
0
1
1
1
2
2
0
0
1
1
1
1
1
1
2
1
2
0
0
0
1
0
1
1
2
3
1
1
2
1
1
2
1
1
1
0
1
3
0
1
1
1
0
0
0
1
1
1
0
1
1
0
0
1
1
1
1
2
2
0
0
1
2
1
1
0
0
0
2
1
1
0
1
1
2
0
5
0
1
2
2
1
2
1
1
1
1
1
1
0
2
1
2
2
2
1
2
1
0
1
0
0
2
0
1
0
1
0
1
1
0
0
0
0
1
0
2
1
1
0
0
2
1
0
1
2
1
0
1
2
1
0
1
0
2
0
3
2
0
0
1
0
1
2
2
0
2
1
3
0
1
1
1
1
2
1
1
0
1
1
0
1
1
0
0
1
0
0
1
1
0
1
2
1
0
1
1
0
0
2
1
1
1
1
0
1
2
1
2
2
2
0
1
1
1
0
1
1
0
1
1
1
1
2
1
1
0
0
3
0
2
1
1
1
1
2
1
0
0
2
1
1
2
0
0
1
1
1
0
0
1
2
1
0
1
1
0
0
0
1
1
2
1
0
2
2
2
1
0
1
2
0
0
0
0
2
1
0
1
2
1
1
0
2
0
1
1
2
1
1
0
1
1
2
1
0
1
1
1
0
0
1
1
2
2
1
1
1
2
1
0
1
2
1
2
1
0
1
0
0
1
2
2
0
1
2
1
1
0
2
0
1
1
2
0
0
1
2
1
0
1
2
1
0
0
0
1
0
1
1
0
1
0
0
1
0
1
0
0
1
2
0
2
1
1
1
1
0
1
0
1
1
1
0
0
1
2
1
1
0
0
0
1
1
2
3
0
1
1
0
0
1
1
0
1
2
2
1
0
1
1
2
0
1
1
1
1
1
1
2
0
2
2
0
0
1
1
0
2
2
1
0
0
1
0
1
0
1
1
0
2
0
2
1
0
1
1
2
1
0
0
1
1
0
1
1
0
1
2
1
1
1
1
1
0
2
1
1
1
0
2
1
1
1
2
1
2
1
1
1
0
1
1
1
0
1
2
2
0
1
0
1
0
1
1
1
3
1
2
0
1
1
0
2
1
0
0
1
1
2
0
0
0
1
1
2
3
1
0
0
1
1
0
0
1
0
2
2
1
1
0
0
1
1
1
1
1
1
0
1
2
1
0
2
2
1
1
1
2
1
1
1
1
0
2
1
1
2
1
1
0
1
0
2
0
1
1
1
0
0
3
1
1
0
2
2
0
2
2
2
0
1
0
0
1
1
1
1
1
1
0
1
0
2
1
0
1
1
2
0
1
0
1
2
0
1
0
1
1
1
1
1
0
2
1
2
1
0
1
1
2
0
1
1
1
1
1
1
1
0
0
2
0
1
2
1
1
1
1
1
1
1
1
1
2
1
0
0
1
0
1
0
2
1
2
1
0
0
1
2
2
1
2
1
1
1
1
1
2
2
1
1
0
2
2
1
2
1
1
2
1
0
0
1
1
1
0
1
1
1
1
0
0
1
1
2
1
1
1
1
0
0
1
2
1
1
1
1
0
0
1
0
0
2
1
1
0
2
1
2
1
1
1
0
1
1
1
3
3
1
2
2
1
1
0
1
2
2
1
0
1
0
0
1
1
0
2
2
1
0
0
1
0
0
0
0
0
1
1
2
1
1
1
0
0
2
0
1
1
2
2
0
2
2
1
2
1
2
1
0
1
1
0
1
2
2
1
0
0
0
1
1
0
1
2
1
0
0
1
1
1
1
0
1
0
0
0
1
0
0
1
0
1
1
0
1
0
2
2
0
0
1
1
1
1
2
0
0
0
0
1
3
0
1
0
1
1
1
1
1
1
2
0
1
1
0
1
1
0
1
0
1
1
0
2
1
1
2
4
2
1
2
1
1
2
3
1
0
1
2
0
3
1
2
1
1
3
0
0
1
0
0
2
0
2
1
0
1
0
1
1
1
1
1
0
1
0
0
2
2
0
1
2
1
1
1
2
0
2
1
1
1
0
1
0
1
1
1
2
1
0
2
1
0
0
1
1
0
0
2
2
1
2
1
1
0
1
1
0
1
0
0
0
1
1
0
1
1
0
2
0
0
2
2
1
1
1
1
0
1
1
1
0
0
2
0
1
1
2
0
1
1
0
1
0
2
2
0
1
1
0
2
2
1
0
2
0
0
1
2
1
1
0
1
1
1
1
2
0
0
2
1
0
1
1
0
1
2
1
2
0
0
1
0
0
0
1
1
1
1
0
2
2
1
2
0
2
5
0
1
2
2
1
1
1
1
2
1
2
2
1
1
0
1
0
0
1
0
1
1
0
2
1
0
0
2
0
1
1
1
1
2
2
2
1
0
1
1
1
2
1
3
0
0
0
1
2
2
0
1
2
0
0
2
0
2
1
1
1
1
0
1
2
0
0
0
0
1
0
0
1
1
0
0
1
1
1
2
3
1
0
2
0
2
3
2
1
1
0
2
1
1
0
2
2
1
1
1
2
2
0
1
0
2
2
2
1
0
0
1
0
1
1
0
1
1
1
1
0
2
1
2
2
1
2
0
2
1
1
3
1
1
0
2
1
1
0
2
1
0
2
2
1
1
1
2
1
1
0
2
1
0
1
2
1
1
1
1
1
0
2
2
1
2
1
2
1
0
0
0
2
0
0
0
0
1
0
1
0
0
2
0
1
0
1
0
2
1
1
2
1
1
0
0
1
2
1
2
1
0
1
0
1
2
1
0
1
0
2
2
1
2
1
1
0
1
2
2
0
1
1
1
1
2
1
0
2
1
0
1
1
1
6
1
1
1
0
2
1
1
2
2
1
0
1
1
0
1
2
2
2
0
1
0
2
2
1
1
1
1
1
1
0
0
2
0
1
0
1
1
2
1
1
2
1
1
1
0
0
2
2
0
2
0
3
0
0
0
0
0
1
0
1
2
2
3
1
0
1
0
0
1
2
1
1
1
1
1
1
1
0
0
1
2
1
1
0
2
2
1
1
0
2
2
1
0
1
0
1
3
0
0
0
2
1
0
2
2
1
1
2
0
0
0
2
0
2
1
0
1
0
1
1
1
0
1
1
1
1
1
0
0
1
1
2
3
2
1
1
1
1
0
2
0
1
1
2
1
2
5
0
2
2
1
0
0
0
1
0
0
1
0
1
2
0
0
1
0
1
1
1
0
1
2
0
1
3
1
2
0
1
1
0
2
0
1
0
2
0
0
0
1
1
1
2
2
1
1
0
0
0
0
1
0
0
0
0
0
1
1
3
0
0
0
0
0
1
0
1
0
2
0
0
1
1
0
1
2
2
1
0
1
1
2
1
0
1
1
1
1
0
0
2
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
2
1
1
2
1
0
1
1
0
0
2
1
1
1
1
1
2
2
1
0
1
0
1
1
1
1
0
0
1
2
0
1
0
0
1
1
0
2
0
0
2
0
0
0
0
0
2
1
1
1
0
0
1
1
1
1
1
1
2
0
0
0
1
1
0
1
2
1
1
1
0
0
0
0
2
0
1
2
1
0
2
1
2
1
0
0
1
2
2
1
1
1
0
1
2
2
2
1
1
1
1
0
0
2
1
1
1
1
1
1
0
0
1
1
0
1
0
0
1
2
1
1
0
1
0
1
0
1
0
1
1
2
1
2
1
0
0
0
1
0
2
1
0
1
1
2
0
0
2
0
3
2
1
1
1
0
1
2
0
0
0
0
1
1
2
0
1
2
12
1
2
0
1
2
0
2
1
1
1
4
1
1
1
0
1
1
1
0
0
0
0
1
1
0
2
1
1
1
0
1
1
1
2
1
0
2
1
1
0
0
1
0
1
1
0
0
1
2
1
2
0
0
0
1
0
0
1
0
1
1
1
1
2
1
2
1
0
0
0
0
1
2
0
0
1
3
1
1
2
2
0
1
0
0
0
3
3
0
1
1
1
2
1
0
2
2
1
1
1
1
0
2
0
1
2
2
1
0
2
0
1
1
1
0
3
2
0
1
1
1
1
0
2
0
1
0
0
0
2
0
1
2
1
1
1
0
3
1
1
2
1
0
2
0
0
0
1
0
1
1
1
0
2
2
1
1
3
1
1
2
2
0
0
0
0
2
1
0
1
1
2
1
1
3
0
0
0
0
0
1
1
1
3
1
0
0
2
0
0
1
1
1
1
1
0
2
1
1
0
2
1
0
0
1
1
1
1
1
2
1
2
1
1
5
0
1
1
0
1
0
1
2
1
0
2
2
1
1
2
1
2
0
0
0
0
2
2
2
2
0
0
0
1
1
2
1
1
0
1
1
0
1
0
2
2
1
0
0
0
2
1
1
1
1
0
1
1
0
0
1
0
2
1
0
2
0
1
1
1
0
0
1
2
2
1
1
1
2
0
1
1
2
1
2
0
1
0
2
2
1
2
1
1
1
0
0
1
1
0
1
0
1
1
2
0
3
1
1
1
0
1
1
2
1
2
0
0
1
1
0
2
0
0
0
2
1
1
0
2
1
0
1
1
1
0
0
2
1
0
1
1
1
1
0
1
0
4
2
2
0
1
1
1
2
0
2
0
1
1
2
1
1
0
1
0
2
0
1
0
1
0
0
0
1
1
1
0
2
1
0
2
1
0
1
2
1
0
1
1
2
2
1
1
0
0
0
0
0
0
1
1
2
0
1
2
1
0
1
0
1
2
1
0
1
1
0
1
1
1
0
2
1
1
0
1
0
1
3
1
2
1
1
1
3
0
1
0
1
2
0
1
1
2
0
1
1
1
2
0
0
2
1
2
1
1
1
1
2
1
1
1
0
2
1
1
0
1
0
0
1
0
1
2
0
3
1
1
3
1
2
1
0
0
0
1
0
1
2
2
0
1
1
1
0
1
1
1
2
1
1
2
1
0
1
1
2
0
1
0
1
0
0
1
1
0
1
3
1
0
1
1
1
2
0
2
2
1
0
2
1
0
1
0
0
0
1
1
2
1
0
1
1
1
1
1
0
1
2
2
1
0
2
1
2
1
1
1
0
1
0
1
2
2
1
1
0
1
1
1
1
3
1
2
1
1
0
1
0
0
1
0
0
1
1
3
0
0
1
1
1
1
0
2
2
2
1
1
2
0
2
1
1
2
1
1
1
1
2
1
0
2
1
1
1
2
2
0
2
2
0
4
0
1
0
0
0
0
1
1
1
0
1
0
0
0
1
1
1
1
2
2
1
0
2
0
1
0
0
1
1
2
1
0
2
1
1
1
1
2
0
2
0
0
2
1
0
1
1
1
2
1
1
1
0
2
1
0
2
1
2
1
1
1
2
0
0
1
2
1
2
1
1
0
1
1
0
1
1
1
1
2
0
0
1
6
1
2
0
0
1
2
1
1
0
1
1
0
1
2
2
1
0
0
1
0
0
1
1
1
1
0
3
0
2
4
0
0
1
2
1
0
0
1
1
1
0
0
1
1
2
1
2
1
1
0
2
0
1
2
1
1
2
2
1
1
1
1
1
2
1
1
2
0
1
1
1
1
2
0
0
1
1
0
2
2
1
2
1
0
1
2
1
1
1
0
0
1
0
1
2
1
0
1
1
1
1
1
2
2
2
0
2
4
1
1
2
2
1
0
0
2
1
1
2
2
0
1
1
0
2
0
1
2
2
1
1
2
0
0
1
0
1
1
2
0
1
0
0
0
0
2
0
0
0
0
0
2
1
0
1
1
1
0
1
1
1
1
0
0
1
0
1
0
2
1
2
0
0
2
0
1
0
0
2
3
1
2
1
1
0
0
1
1
1
2
2
1
1
0
0
2
1
1
1
1
1
0
1
0
0
2
1
2
1
1
2
0
1
2
1
2
0
1
1
1
0
1
1
0
1
1
1
1
1
0
0
1
2
0
1
2
1
1
0
1
1
0
2
1
0
1
0
1
1
3
1
2
0
0
1
2
1
1
1
2
1
0
0
1
1
2
1
1
0
2
2
0
1
0
1
1
1
1
0
0
1
2
2
0
1
1
1
1
0
0
1
1
1
1
1
1
0
0
1
0
1
1
0
1
1
2
1
1
1
1
0
0
1
1
0
0
0
2
0
1
1
2
2
0
1
2
2
1
1
0
1
1
0
1
0
2
2
0
1
0
1
1
0
1
0
0
0
1
1
0
0
1
1
1
1
1
1
0
1
1
0
2
1
2
1
1
0
2
2
1
1
2
2
0
1
2
1
2
0
1
1
1
1
2
0
2
0
1
1
0
0
2
2
1
1
0
1
1
2
0
0
2
0
1
1
0
1
2
2
0
0
0
1
2
2
2
1
0
0
1
1
0
1
0
2
1
0
1
1
0
1
1
0
1
1
2
0
1
2
0
0
1
1
2
2
2
1
1
2
2
0
0
2
1
0
1
2
0
0
0
0
1
0
0
0
1
0
1
0
1
1
2
0
2
0
1
3
2
1
0
0
1
1
1
0
1
0
2
2
2
0
0
1
1
1
1
1
2
4
0
0
0
2
1
0
0
0
1
1
1
3
1
1
0
1
2
1
1
0
1
1
2
2
1
2
2
2
1
1
1
2
1
1
0
1
0
2
0
2
0
2
0
1
0
1
0
1
0
1
1
1
0
0
1
1
1
0
2
0
1
1
0
1
0
0
0
2
1
0
2
1
0
0
1
1
1
1
1
1
1
0
1
2
0
1
2
1
0
2
1
1
0
1
1
1
1
1
0
1
0
3
1
2
1
1
0
1
1
1
0
0
1
1
1
0
2
0
1
2
1
2
1
1
2
0
0
1
0
1
1
1
1
0
0
1
2
0
0
1
1
1
0
1
1
0
1
1
1
0
1
1
0
1
2
1
0
0
1
0
0
1
2
0
1
2
0
2
0
0
2
1
2
1
4
2
1
1
1
2
1
1
1
1
2
0
0
1
0
0
1
2
0
1
1
1
1
0
1
0
1
1
2
1
1
0
1
0
1
0
1
0
1
0
1
0
1
1
5
0
1
1
2
2
1
2
1
0
1
0
2
2
2
1
1
0
1
2
0
0
1
1
0
2
2
1
2
1
2
0
1
0
1
0
1
1
2
1
1
1
1
0
2
0
1
0
2
1
2
1
1
1
1
2
0
1
1
1
2
0
0
1
2
0
2
0
0
1
2
0
1
0
0
2
2
0
1
1
2
2
1
1
2
0
2
1
0
1
0
1
1
0
2
1
2
0
1
0
1
1
4
2
2
1
1
2
1
0
1
1
2
1
0
1
1
1
1
0
2
4
1
1
1
1
0
0
1
2
0
0
0
1
0
2
1
0
2
0
1
1
1
0
1
1
1
1
1
2
0
0
2
2
0
0
1
1
1
0
1
1
2
1
1
2
1
1
1
0
1
2
0
2
0
1
0
1
0
1
0
1
1
1
2
0
1
0
1
2
2
2
2
1
0
0
0
0
0
1
1
2
1
0
2
1
1
2
0
1
0
0
1
1
2
1
1
1
1
1
1
1
0
1
0
1
0
2
0
1
1
1
0
0
1
0
1
0
1
1
1
1
12
0
2
1
2
0
0
1
1
0
1
1
0
1
0
2
0
0
1
0
0
1
1
2
0
2
1
0
1
0
1
2
2
1
1
1
0
1
1
0
2
2
1
0
0
1
1
1
1
0
1
0
1
1
1
1
0
2
0
1
1
2
0
1
2
1
1
1
1
2
2
0
1
0
1
1
2
1
1
2
0
0
2
1
3
0
1
2
1
1
1
2
0
2
0
1
1
1
2
1
0
2
2
2
0
1
1
1
1
1
2
1
2
2
2
0
2
1
1
0
1
0
0
1
0
1
0
1
2
1
1
1
0
1
0
1
1
1
2
2
2
0
2
2
0
2
1
1
0
0
3
1
1
1
0
0
2
1
0
2
2
1
2
1
2
1
1
1
1
2
0
0
1
2
1
1
0
1
1
0
2
2
1
0
1
0
0
0
1
0
0
0
1
1
2
1
0
0
0
2
1
1
1
1
1
2
0
2
1
1
1
1
1
2
1
1
0
0
1
1
0
2
1
0
0
2
1
0
1
1
1
0
1
1
1
1
1
2
2
1
4
1
2
1
0
2
2
1
0
0
2
2
2
0
1
0
2
1
0
0
2
0
0
2
2
2
1
0
0
0
0
2
0
1
2
0
1
0
0
2
0
1
0
1
1
1
2
2
0
0
2
2
1
2
0
1
0
0
1
1
2
1
1
2
1
0
0
2
2
1
1
2
1
1
2
0
0
1
1
0
1
1
0
1
0
0
0
1
2
0
0
1
0
0
0
0
0
1
2
0
1
1
1
1
2
1
3
0
1
1
2
1
2
0
2
0
1
0
1
2
1
1
2
0
0
2
1
1
0
0
1
3
2
0
1
0
0
2
1
0
1
2
0
2
2
1
2
2
0
1
1
2
1
2
0
1
1
1
0
0
2
1
1
1
1
1
2
2
1
0
0
2
2
0
1
0
1
0
2
2
0
0
2
0
2
1
0
1
0
0
0
1
0
1
2
0
1
0
0
2
1
2
0
2
0
0
1
0
1
2
2
1
0
1
0
0
1
0
0
0
0
0
1
2
0
1
0
1
1
1
1
2
0
1
0
0
0
0
1
2
1
1
1
0
1
1
2
1
0
0
2
2
0
2
0
1
1
1
0
1
1
2
0
0
1
2
0
1
1
1
2
2
2
1
0
2
1
1
0
0
1
1
2
1
0
0
1
1
0
1
0
0
1
0
0
1
1
1
0
1
0
2
2
0
0
0
1
1
0
3
1
1
1
1
1
2
1
1
2
2
1
1
1
0
1
1
1
2
1
0
1
2
1
2
0
0
0
1
1
0
3
1
1
1
0
1
1
1
1
1
2
0
2
2
1
0
1
1
0
0
1
1
1
1
2
1
1
2
0
1
0
1
1
2
0
2
2
1
2
1
0
1
0
1
1
1
1
2
0
2
1
1
0
1
1
1
0
2
0
0
0
0
0
2
0
1
2
2
1
2
1
1
1
0
2
1
0
2
2
1
2
1
1
1
1
2
1
1
1
1
2
0
0
1
0
1
1
2
1
1
1
1
2
4
2
2
0
1
1
0
1
2
1
1
3
3
0
0
0
0
1
0
0
1
3
0
2
1
3
0
0
1
1
1
1
1
2
1
1
1
0
1
1
0
1
1
0
1
0
1
0
1
1
1
2
0
1
1
1
0
0
0
2
0
0
1
0
0
2
1
2
1
2
1
0
1
2
0
2
1
0
0
1
1
0
0
0
1
1
0
2
1
2
0
0
1
1
1
1
1
1
1
1
1
1
1
1
2
0
1
1
0
2
1
0
0
2
0
2
1
0
1
0
2
0
2
0
1
1
1
2
1
3
0
2
1
1
1
1
0
1
0
0
1
1
1
0
1
1
2
1
0
1
1
0
1
2
1
0
1
0
0
1
5
0
1
1
1
0
0
2
2
1
0
1
0
2
1
0
1
2
2
0
1
1
1
1
1
1
1
2
1
1
0
1
0
1
1
1
0
2
0
1
0
1
0
0
1
0
2
0
1
1
1
2
1
0
1
1
0
1
0
0
0
2
1
0
1
1
1
1
0
0
1
0
2
1
1
1
0
1
1
2
0
1
1
1
0
1
1
1
1
0
1
1
1
0
0
1
0
2
1
0
0
1
1
3
2
1
1
0
1
2
2
0
2
2
1
1
0
1
1
2
0
0
1
0
2
0
1
1
0
1
1
1
0
1
1
0
1
0
2
0
2
1
0
1
0
0
1
1
1
1
2
2
1
0
1
1
1
2
1
0
0
1
1
1
2
1
0
1
2
0
1
1
2
2
1
1
0
1
1
1
2
0
0
0
0
2
1
1
2
0
0
0
2
0
2
2
1
2
2
0
1
2
2
0
0
2
0
1
1
1
1
1
1
0
0
0
1
2
1
1
1
2
1
1
1
1
0
2
0
2
2
2
0
1
1
1
0
1
0
0
2
1
1
2
2
1
1
1
1
0
1
0
1
1
1
1
0
4
2
1
1
2
0
0
2
1
0
0
1
0
0
2
1
1
1
0
1
2
0
1
1
1
1
2
0
1
1
0
2
1
0
1
1
0
1
1
0
0
0
2
1
1
1
2
1
1
1
1
1
1
0
2
1
2
1
0
1
1
0
1
0
2
0
0
1
1
0
1
0
1
2
1
1
1
0
0
1
1
2
1
1
2
2
3
1
1
2
1
0
1
1
0
0
1
1
1
2
1
1
1
0
1
2
0
1
0
1
0
2
1
3
2
1
1
1
1
0
2
0
0
0
1
0
0
0
0
0
1
1
0
1
1
0
0
2
1
1
1
1
0
0
1
2
0
1
0
0
1
1
1
0
1
1
2
1
1
2
0
0
1
1
0
1
0
1
0
1
2
2
0
1
0
1
0
0
0
2
0
1
2
1
1
2
0
1
1
0
1
2
0
1
2
0
0
1
0
2
0
1
0
1
0
1
0
2
2
2
2
1
1
2
1
1
1
0
1
0
2
1
1
1
0
1
1
0
3
0
0
2
1
0
0
1
1
0
1
1
0
1
2
1
0
2
1
1
2
1
0
2
0
1
1
0
1
0
1
1
1
0
2
2
1
0
0
2
1
2
1
1
0
1
1
0
0
2
1
1
2
1
2
0
1
1
2
1
1
1
1
1
1
1
0
0
1
2
1
1
0
2
2
1
1
1
1
1
1
1
1
3
2
0
2
1
1
0
1
1
0
1
0
1
0
1
1
1
1
2
1
0
3
1
0
1
0
0
0
1
1
2
0
0
1
2
0
1
0
0
1
0
1
1
0
0
0
1
1
0
1
1
0
0
1
1
1
0
1
0
1
2
1
1
0
1
1
1
1
1
1
2
1
1
0
2
1
0
1
1
2
1
0
0
0
1
2
2
0
1
0
0
2
1
0
2
1
1
1
0
0
1
0
1
1
0
2
1
2
1
1
2
0
1
1
1
1
0
1
0
0
1
2
0
2
1
1
2
2
0
0
5
1
0
0
2
0
0
1
0
2
1
2
0
0
0
1
0
1
1
0
0
0
1
1
0
2
1
2
2
2
0
1
0
1
2
2
2
1
1
1
1
2
1
1
1
0
1
1
2
1
0
0
1
1
2
0
1
0
0
0
1
2
1
1
1
0
1
1
2
2
2
0
1
1
0
1
0
1
0
2
0
1
1
2
1
1
1
1
2
0
2
2
1
1
0
1
0
0
2
0
1
1
1
0
2
2
1
2
2
2
2
1
0
1
1
2
1
2
1
1
1
1
0
2
2
1
1
1
1
2
2
0
1
1
1
1
0
2
1
1
1
2
0
1
1
1
1
1
0
0
0
0
0
2
2
1
0
2
1
2
0
0
3
0
0
1
3
1
2
1
0
0
1
0
0
1
0
2
1
1
2
0
1
1
0
0
1
0
1
0
2
1
1
1
0
0
2
1
0
2
2
2
0
0
1
2
0
2
1
0
1
1
2
1
1
0
1
1
1
0
1
0
1
2
2
1
0
1
1
1
1
2
0
0
1
0
1
0
1
1
0
0
1
0
1
2
0
1
1
1
0
2
1
1
0
2
0
1
0
1
2
1
1
1
1
0
1
1
3
0
1
0
1
1
0
2
0
1
1
1
1
0
2
1
0
2
0
0
0
1
1
1
0
0
1
2
1
1
1
0
1
2
1
1
1
1
3
0
0
1
1
0
2
1
1
0
2
1
1
1
0
1
0
0
2
1
2
1
0
1
1
2
0
1
1
0
2
1
1
2
1
0
1
1
0
2
1
1
0
1
1
0
0
1
1
1
2
2
2
2
1
2
1
1
2
1
2
1
0
1
0
1
1
0
1
0
1
1
1
0
1
0
1
2
0
1
0
1
1
1
1
1
0
1
0
0
2
1
1
0
0
1
1
2
0
1
2
1
0
1
0
0
1
1
1
1
1
0
0
0
3
1
2
0
0
1
1
2
2
0
0
1
1
2
1
1
2
0
2
1
1
1
1
2
1
0
2
0
1
0
1
2
0
1
1
1
0
0
3
1
0
3
1
1
1
2
1
0
1
1
1
0
1
5
1
1
0
1
1
0
1
1
1
1
1
1
0
3
2
5
1
2
1
1
0
2
0
0
1
0
0
0
1
1
0
2
1
1
1
2
2
2
2
1
1
1
1
1
1
0
0
2
2
1
2
2
1
1
1
0
1
1
1
1
1
2
0
0
1
0
2
1
1
1
2
0
0
2
0
2
1
1
1
0
1
1
1
0
0
1
0
2
0
1
0
2
1
0
0
0
2
2
1
0
0
0
1
2
1
0
1
0
1
1
2
1
0
1
1
0
0
1
1
1
1
0
2
2
0
0
1
2
1
1
0
0
1
1
1
1
0
0
2
2
1
1
1
1
0
0
1
1
2
0
0
1
1
1
2
1
0
1
0
0
2
1
0
1
0
2
0
0
0
1
1
1
1
1
1
2
2
1
2
0
0
3
0
2
1
2
2
1
1
2
1
0
0
1
2
1
1
1
2
0
1
0
1
1
1
2
1
1
0
1
1
2
1
2
1
2
0
0
2
1
0
0
0
0
1
0
1
0
1
2
2
1
1
1
0
1
1
2
1
0
2
0
3
1
1
1
1
2
1
1
2
1
1
1
1
0
0
0
0
1
1
0
1
1
0
0
2
0
2
1
1
0
1
0
1
2
2
0
2
2
0
0
1
0
1
2
1
2
2
0
3
0
1
1
1
2
1
3
2
1
2
2
0
2
1
1
0
1
0
1
0
2
2
1
0
2
0
1
0
1
1
1
2
2
0
2
1
1
0
1
1
2
1
0
1
0
0
0
1
1
1
0
1
1
2
1
0
1
1
1
1
1
2
2
1
1
2
0
0
1
2
1
2
0
0
1
1
1
2
1
0
2
0
0
1
0
1
1
1
1
2
0
0
1
2
0
1
3
2
1
0
1
0
1
0
0
2
2
1
1
2
2
1
1
1
0
2
0
2
1
0
0
3
0
1
2
0
1
1
1
0
1
0
0
0
2
1
1
0
1
0
2
0
2
0
2
1
1
0
2
1
0
1
0
1
0
1
1
1
1
1
1
1
2
1
0
2
0
2
1
0
1
1
1
0
1
1
0
0
1
1
1
0
1
0
0
1
1
2
1
2
2
1
2
2
0
1
0
0
2
1
1
1
2
1
0
0
0
1
1
2
2
0
1
1
0
1
0
0
1
1
1
1
1
1
2
1
2
1
0
1
2
1
1
0
0
1
0
0
1
1
1
1
1
0
1
1
1
1
1
0
1
0
0
1
2
1
0
1
1
0
1
1
1
0
2
1
0
1
0
1
0
1
1
2
0
0
1
1
1
1
0
0
1
1
2
0
1
1
1
1
1
0
2
1
2
1
1
2
1
1
0
0
0
2
1
2
0
0
1
0
0
0
0
0
2
1
2
2
1
0
0
2
1
1
2
1
2
2
0
2
2
2
1
2
0
1
1
0
1
1
2
0
1
2
0
2
0
2
1
0
1
1
1
0
0
2
1
0
0
1
0
2
1
0
1
1
0
1
1
1
1
2
1
0
1
1
1
2
1
0
2
1
2
1
2
1
0
1
1
0
1
2
1
0
0
2
1
1
1
0
2
1
0
2
2
0
1
1
1
1
1
1
0
1
1
1
2
1
1
1
1
2
2
0
2
1
1
2
0
2
3
2
2
2
2
1
1
1
1
2
0
1
0
1
1
0
1
2
0
1
1
2
1
1
2
0
1
0
0
1
1
1
0
0
0
0
1
0
2
1
0
1
1
1
1
3
1
0
1
2
1
1
1
1
1
2
1
2
1
1
0
0
2
0
0
1
0
2
1
0
2
1
1
3
1
1
1
2
0
1
1
0
2
1
2
1
2
2
1
2
2
2
1
0
0
1
2
2
0
0
2
1
2
2
0
0
1
2
1
1
1
0
2
0
2
1
2
3
1
1
0
1
0
1
0
0
1
2
1
0
1
1
0
1
1
0
1
1
1
1
1
0
1
1
0
2
0
2
1
1
0
0
1
0
1
0
1
1
0
0
2
0
3
1
2
1
1
0
0
1
1
2
1
2
0
0
0
0
1
1
1
1
1
1
2
1
1
1
0
1
1
0
2
0
1
0
1
1
0
1
1
0
0
2
1
3
1
0
2
0
0
1
0
2
1
1
0
1
1
0
1
1
2
1
2
1
1
1
1
1
2
2
1
1
0
2
2
0
1
0
1
0
1
0
2
1
0
1
1
3
3
1
1
0
0
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
2
3
2
1
1
1
1
0
1
0
2
1
1
3
0
0
1
0
1
0
0
1
0
0
2
1
0
1
2
0
1
2
2
0
0
1
0
1
1
0
0
0
2
3
2
2
0
1
0
1
0
1
1
1
2
1
2
1
2
1
1
2
2
1
0
2
2
1
2
2
1
2
1
0
0
1
0
1
1
0
1
1
1
0
1
1
0
2
2
0
0
1
0
3
1
0
0
2
1
0
2
2
0
0
1
1
1
0
0
1
0
0
1
1
1
2
1
0
1
1
0
0
1
0
1
1
1
2
1
0
2
1
0
2
2
1
0
0
1
0
1
2
1
0
2
2
1
1
0
2
0
1
1
1
0
0
1
0
1
2
2
0
4
0
0
0
2
1
1
1
0
2
1
1
1
1
2
2
2
0
1
1
1
1
0
2
0
0
0
0
1
1
1
1
1
1
2
1
2
1
2
0
0
1
2
1
3
1
0
3
1
1
1
1
2
0
1
1
0
1
1
0
0
0
2
3
1
0
2
1
1
2
1
2
0
0
0
2
2
2
1
0
1
1
0
1
1
1
3
0
1
0
0
1
2
3
0
2
1
1
0
1
2
1
0
0
1
1
1
0
1
1
1
0
1
1
1
1
0
1
2
2
0
2
0
1
1
2
0
1
0
1
1
0
1
0
1
1
1
2
0
2
1
0
1
0
1
0
0
2
1
2
0
0
1
0
0
1
2
0
2
1
2
1
1
0
2
1
2
0
2
0
1
1
1
0
1
1
1
1
1
1
0
1
0
1
1
1
0
0
0
1
0
1
0
0
1
2
0
1
1
1
2
0
1
1
0
2
1
1
1
1
0
0
1
2
0
1
1
0
1
2
2
0
2
0
1
1
1
0
1
1
2
2
1
1
1
2
2
2
1
1
2
1
2
2
1
2
1
1
1
5
1
0
1
2
1
0
0
1
0
1
1
1
1
1
1
0
2
1
1
1
2
1
2
1
0
1
1
1
1
0
0
2
1
1
1
2
0
2
0
1
0
2
0
2
1
2
1
2
0
2
2
1
0
2
0
0
0
0
0
1
2
0
1
0
1
1
1
1
2
0
1
0
1
1
0
1
1
1
0
1
1
0
0
0
1
0
1
1
1
2
2
0
1
1
1
2
0
1
1
0
1
1
1
1
1
1
1
1
3
1
0
3
1
0
0
0
0
0
1
0
2
0
4
2
2
2
0
2
0
1
1
1
1
0
0
1
0
2
1
1
0
2
0
1
0
0
1
1
1
1
0
1
1
1
2
0
1
1
0
1
0
0
0
0
1
1
1
1
1
1
2
2
1
1
0
0
1
1
1
0
0
0
1
1
0
1
0
2
2
0
1
1
1
1
1
0
0
0
1
0
1
1
1
0
0
0
1
2
1
1
1
1
1
1
2
1
1
0
0
2
0
3
0
2
3
0
0
1
1
1
1
0
1
2
1
1
1
0
0
2
2
0
0
1
1
0
1
2
2
2
2
1
1
1
2
0
1
1
1
0
0
2
1
1
0
0
3
1
1
0
0
0
1
2
1
0
1
1
2
2
2
1
0
0
2
1
1
1
0
2
1
1
1
1
0
2
0
2
1
0
1
1
0
0
1
0
0
1
0
0
0
2
1
1
1
0
0
1
0
1
1
0
2
3
0
1
2
0
1
0
2
0
0
1
1
0
0
1
0
1
0
1
0
0
0
1
1
1
1
1
0
1
0
0
2
0
2
0
1
1
1
1
1
0
2
2
0
1
0
1
1
2
1
1
1
1
2
1
2
0
0
1
2
0
1
1
1
0
1
1
1
1
0
1
1
0
1
0
1
1
1
1
1
1
2
2
1
1
2
0
2
0
2
0
1
0
0
1
2
1
0
0
1
2
1
2
1
2
1
2
2
1
1
1
2
0
1
0
0
0
0
2
1
1
1
0
1
1
0
1
0
0
1
0
2
1
2
2
0
2
2
1
1
0
0
1
2
1
1
2
2
1
1
2
2
0
1
0
0
1
2
0
1
1
1
1
1
1
2
0
2
1
0
1
2
1
1
0
1
0
0
0
2
1
2
1
0
1
2
1
1
1
1
1
1
1
0
1
2
1
1
1
1
0
1
1
0
1
1
1
0
0
1
0
0
0
2
2
2
0
1
2
0
1
0
0
2
1
0
1
1
0
1
0
1
0
1
0
0
1
1
0
2
0
0
1
1
0
1
0
1
1
1
1
0
2
0
1
1
1
0
0
1
1
0
0
1
1
1
1
1
0
2
1
0
0
0
1
0
1
0
1
2
2
2
1
1
2
1
0
0
2
2
2
1
1
2
1
1
1
1
0
1
1
1
0
0
1
1
1
2
1
2
0
0
2
0
2
1
1
1
2
1
1
0
1
1
0
1
2
1
0
1
1
2
2
1
1
1
2
1
0
2
1
0
1
1
2
2
0
2
1
2
0
1
0
1
1
0
1
2
0
2
0
1
1
0
0
1
0
0
1
0
2
2
2
1
0
1
2
2
1
1
2
1
0
0
0
1
0
1
2
0
2
1
1
1
1
1
1
2
0
1
0
1
0
1
0
1
2
1
1
1
1
1
2
2
0
2
1
1
1
1
0
2
1
1
1
1
0
1
1
1
0
2
2
1
1
1
0
2
1
2
0
1
0
1
0
1
1
0
0
0
0
0
1
1
2
1
1
1
1
1
1
1
1
1
0
1
1
1
0
1
2
1
1
1
1
2
1
1
1
2
0
1
0
1
1
0
1
0
1
0
0
0
2
1
1
2
1
1
1
0
1
1
0
1
0
1
1
1
1
1
1
0
2
1
0
1
2
0
0
1
1
2
0
2
1
0
1
9
0
1
1
0
2
0
1
0
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
0
0
2
0
1
1
0
1
1
0
0
1
0
0
2
1
1
2
0
1
2
1
1
0
1
2
0
1
1
1
2
2
0
0
0
1
1
1
0
1
0
1
2
1
0
1
0
1
0
2
0
2
1
0
1
1
1
2
1
1
0
0
2
2
0
1
1
2
1
2
1
2
1
0
1
0
0
1
2
0
1
1
1
2
1
1
1
2
2
0
1
0
0
0
0
1
1
2
2
1
1
3
1
0
2
2
0
0
2
1
1
2
0
1
1
0
0
0
1
0
1
0
1
1
1
2
0
1
0
1
1
0
2
0
1
1
0
0
1
0
1
0
1
1
1
0
1
2
1
1
0
1
1
1
0
0
2
1
0
2
1
2
1
2
0
1
1
1
1
1
1
0
1
2
0
2
2
1
1
1
1
1
1
1
2
0
0
0
0
1
1
2
0
1
0
1
1
2
0
1
0
0
2
1
1
1
4
1
0
1
1
1
2
1
0
1
2
1
0
0
0
1
1
2
0
1
0
1
1
2
1
0
1
0
0
2
1
1
1
0
0
1
0
2
0
1
1
1
1
1
1
1
1
1
1
0
1
1
2
1
3
1
0
1
1
0
1
0
1
1
0
2
1
0
2
1
0
1
1
1
1
1
1
1
1
0
1
1
0
0
0
1
1
1
0
0
2
0
0
2
0
1
0
0
2
2
0
2
2
1
0
0
2
0
3
0
0
2
1
0
1
0
0
0
1
1
0
0
1
1
0
2
0
1
1
1
0
0
1
0
2
2
1
1
1
1
1
1
1
0
1
0
0
1
1
1
0
1
1
2
0
0
0
2
1
1
1
0
1
1
1
1
2
2
1
1
2
0
2
1
1
1
1
2
1
1
0
0
1
0
2
0
0
0
1
1
0
2
2
0
1
1
1
1
1
1
1
0
1
2
0
0
0
0
0
1
1
2
0
2
1
1
1
1
1
1
1
1
2
1
2
2
0
1
0
2
1
0
0
2
0
1
1
1
0
2
2
1
1
1
0
0
1
1
1
2
2
2
0
0
0
1
1
1
1
2
1
1
0
1
1
0
1
1
1
1
1
1
0
1
2
1
1
1
2
5
2
0
0
1
2
2
0
1
1
2
1
1
0
2
2
2
2
1
0
1
1
0
2
1
1
2
2
0
1
0
1
2
2
0
2
1
1
3
0
1
1
2
1
1
1
1
0
1
1
1
1
1
1
2
1
1
3
0
1
1
1
1
0
0
2
1
0
0
1
1
1
1
2
1
1
2
1
1
1
0
1
0
1
0
2
1
1
2
1
2
1
2
2
1
1
0
2
0
1
2
2
1
1
1
0
0
1
0
1
1
0
1
1
1
0
2
0
1
2
0
2
1
2
1
3
0
1
0
0
0
1
0
0
4
2
1
2
0
1
1
1
1
0
1
0
2
2
2
1
1
0
2
1
0
0
0
0
0
1
2
0
1
1
1
1
2
1
1
0
1
1
1
3
1
2
0
1
1
0
2
1
1
1
1
3
0
1
1
1
1
1
0
1
1
1
1
1
1
0
0
1
2
1
1
0
1
1
2
0
1
2
0
2
2
2
1
1
1
0
0
0
0
1
0
1
1
1
2
0
1
0
1
2
1
1
2
1
1
2
1
0
2
1
0
0
1
1
1
2
1
1
1
2
1
2
0
1
2
1
1
1
0
2
2
0
1
3
2
1
0
0
0
1
1
2
1
0
2
2
2
1
0
0
2
2
2
1
1
0
1
0
0
2
0
1
2
0
0
1
0
1
1
1
2
2
2
1
1
1
0
0
0
1
1
0
1
1
0
0
2
1
2
0
1
1
1
1
2
0
0
1
1
2
0
0
1
3
1
2
0
2
1
0
1
0
1
1
1
2
2
2
2
1
2
1
0
1
1
1
2
1
2
2
1
2
1
0
2
0
2
1
0
0
1
1
2
0
2
2
2
1
2
1
1
1
1
0
1
2
0
1
1
2
1
1
0
0
1
1
2
1
1
1
1
1
1
0
1
0
0
1
1
1
1
0
2
1
2
1
0
0
1
2
1
1
2
1
1
0
1
0
1
0
0
2
2
0
1
1
0
1
1
1
0
2
0
2
1
1
1
1
1
1
0
2
2
1
1
0
1
0
2
1
1
0
2
1
0
1
1
2
1
0
1
0
1
1
1
1
1
1
0
2
0
1
1
0
0
1
1
0
1
1
0
2
0
0
1
2
0
0
1
1
2
1
2
1
1
1
1
0
1
0
1
1
1
1
2
4
1
0
1
0
2
2
1
1
1
1
0
1
0
1
2
2
1
2
2
1
1
1
1
1
2
0
0
2
1
1
1
0
2
0
2
2
1
0
1
1
1
1
1
2
0
2
0
0
0
0
1
1
1
0
3
0
2
1
1
1
2
2
2
0
1
2
0
0
0
1
0
0
0
2
1
1
2
1
0
2
1
1
1
2
3
2
2
1
0
0
1
2
1
1
1
1
0
0
1
0
1
0
0
1
1
0
0
2
0
2
1
1
1
2
2
2
1
0
1
3
0
1
0
1
0
1
0
2
1
2
0
1
0
2
0
2
2
0
0
2
1
1
2
0
1
1
0
2
1
0
0
1
0
1
1
1
2
1
0
1
1
0
1
1
2
0
0
1
0
1
0
2
1
1
2
0
0
0
0
1
2
1
0
1
0
0
0
0
0
2
0
0
1
2
1
0
1
0
1
1
1
0
1
0
1
1
0
1
1
1
0
1
1
3
1
0
0
1
1
0
1
0
1
2
0
1
0
1
1
1
1
1
2
1
1
0
2
2
2
2
1
2
2
1
1
0
2
2
1
1
0
1
0
0
2
0
1
1
0
1
1
1
2
0
2
1
2
0
1
0
0
2
0
2
1
0
0
1
1
0
2
1
0
1
1
1
2
1
1
1
1
0
2
1
1
0
1
1
2
2
1
1
0
1
0
0
1
0
0
0
1
0
1
0
1
0
1
0
2
1
2
2
1
0
1
0
2
1
2
1
0
0
1
2
2
2
2
0
1
1
1
1
0
0
2
1
0
1
0
0
2
0
1
2
1
3
1
1
1
2
1
1
1
0
0
1
1
1
2
0
1
1
1
0
2
0
2
0
2
1
2
0
1
0
5
0
1
1
1
1
0
1
2
2
0
1
0
7
0
2
1
1
0
1
0
1
0
1
1
0
0
0
1
1
1
1
2
1
0
1
1
1
0
1
0
0
1
1
1
2
0
1
1
0
1
2
1
6
0
2
0
0
0
1
1
1
0
1
1
1
1
1
0
1
1
1
2
0
1
0
0
1
1
1
0
0
1
2
1
0
0
2
1
1
1
2
1
1
1
2
2
1
1
1
0
2
0
1
0
0
1
2
1
0
0
1
2
0
0
0
0
2
1
1
2
1
0
1
0
1
0
1
1
1
0
0
0
1
0
0
1
1
2
1
1
0
1
1
0
1
0
1
1
1
1
0
2
1
1
0
1
1
2
0
1
1
2
0
0
1
0
0
1
1
2
1
1
2
0
0
1
2
1
2
1
1
1
1
1
2
0
0
2
2
0
0
0
1
1
1
1
2
1
0
1
2
2
1
1
1
1
1
0
3
1
0
1
0
0
2
1
4
0
0
1
0
2
1
1
0
1
3
1
0
1
0
2
1
1
0
1
1
1
2
0
0
0
2
0
0
1
0
0
1
2
1
1
1
1
2
3
1
2
0
0
0
1
2
0
2
1
3
1
2
2
0
1
0
0
1
1
1
1
0
1
1
1
1
1
0
1
0
2
1
1
1
1
2
2
1
0
0
0
1
2
0
0
0
1
2
1
0
2
1
0
1
1
1
0
2
1
1
1
0
1
1
1
1
2
1
2
1
0
0
1
1
0
2
1
2
1
3
1
1
2
1
1
2
1
1
0
0
2
1
1
0
0
1
1
0
1
2
1
1
1
1
0
3
0
2
1
0
1
0
0
1
0
2
2
2
1
1
1
1
2
2
1
1
1
1
2
0
0
2
0
0
1
2
1
1
0
2
1
1
2
1
1
1
0
1
0
1
1
3
0
1
1
1
0
1
0
1
0
1
1
0
2
1
0
0
1
2
0
1
0
0
0
2
1
1
0
2
2
1
2
2
1
1
1
1
0
0
1
2
1
1
3
1
1
1
0
1
2
2
0
2
1
1
1
1
1
0
1
1
2
1
1
2
2
0
0
2
2
2
1
0
0
1
1
1
1
1
0
1
2
2
1
1
1
0
2
0
1
2
0
1
1
2
2
1
1
0
1
2
1
2
1
1
1
1
0
1
2
0
0
0
0
2
1
1
2
1
0
0
1
2
2
3
1
2
0
0
0
1
1
1
1
1
0
1
1
1
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
2
2
0
2
0
2
1
1
2
1
2
0
2
0
0
0
2
1
3
1
0
0
1
0
1
0
2
0
0
1
1
1
1
0
1
1
1
1
0
1
1
2
1
1
0
0
1
1
0
1
1
1
0
0
1
1
2
1
2
0
1
1
1
1
0
1
1
0
1
1
1
1
1
0
1
1
1
0
1
0
2
0
1
1
2
1
2
2
2
2
2
0
1
1
0
2
2
1
1
3
1
2
2
1
2
1
1
2
1
1
1
1
0
1
2
2
0
1
2
3
2
1
2
1
2
0
0
0
2
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
0
1
1
1
0
1
1
0
2
1
2
1
1
0
2
0
1
1
0
1
0
2
3
0
0
3
1
1
2
1
0
0
1
1
1
1
1
1
2
1
2
1
0
1
1
1
1
1
0
1
1
2
0
3
4
2
0
1
1
0
2
2
1
0
0
2
0
0
1
1
2
1
0
0
2
1
1
2
1
0
1
2
0
1
0
0
0
0
1
1
1
1
1
1
0
1
2
1
1
2
2
1
1
2
1
0
2
2
1
2
1
2
0
1
1
1
0
2
0
1
1
0
2
1
2
2
2
0
0
1
2
1
2
0
0
0
0
2
2
2
1
0
3
1
0
1
0
1
1
0
1
1
1
0
0
1
1
0
1
0
0
1
0
1
0
2
2
1
0
2
2
1
1
2
2
1
0
0
2
1
0
1
2
0
1
0
0
0
1
1
1
2
3
0
1
1
0
2
1
0
1
1
1
1
0
1
2
1
1
1
3
1
1
1
2
0
1
0
1
1
1
1
1
1
0
1
1
0
0
2
1
2
1
1
2
0
1
1
2
0
0
1
1
0
1
2
0
0
0
1
1
1
3
2
1
2
1
0
0
0
1
0
1
1
0
1
2
1
3
1
2
0
1
2
0
1
1
0
1
1
0
2
0
1
1
1
1
1
0
0
1
1
0
1
1
1
3
1
0
2
1
0
0
2
2
0
1
1
1
0
1
1
2
1
1
1
1
2
0
0
0
1
0
0
1
2
1
0
1
0
0
2
0
1
1
0
1
1
1
1
2
0
0
1
2
1
0
1
0
1
1
0
1
0
0
2
0
1
0
1
0
0
1
2
1
0
0
0
0
0
1
1
1
1
0
1
1
0
2
1
0
1
1
1
2
0
1
1
0
1
0
1
1
2
1
2
1
1
1
2
2
1
1
1
5
1
0
2
1
0
1
0
1
1
0
3
1
1
1
2
2
1
2
0
2
0
1
2
1
4
2
1
1
0
0
2
2
1
0
0
1
1
2
0
2
1
0
1
1
1
0
0
0
1
3
1
2
2
0
2
0
0
1
0
1
1
2
0
1
1
1
0
1
0
1
0
1
1
0
1
1
1
0
2
1
2
1
1
0
1
1
0
1
2
0
0
0
1
1
0
2
0
0
0
0
0
1
1
0
2
1
1
1
1
2
1
2
2
0
2
1
1
1
1
0
0
1
2
0
1
0
2
1
0
0
0
2
2
0
1
1
0
1
0
1
0
0
2
0
0
0
2
1
0
1
1
1
2
0
0
1
0
2
2
1
0
0
2
0
1
2
2
2
1
2
2
0
1
0
0
1
0
0
1
1
0
1
2
1
1
2
0
1
1
0
1
2
2
2
1
0
1
1
2
2
2
1
1
2
2
0
1
0
1
1
1
2
0
1
1
1
0
2
0
1
0
0
1
1
1
0
1
1
0
0
1
1
1
2
2
1
0
1
2
0
0
1
0
2
0
2
1
5
1
1
2
2
1
1
1
1
1
0
1
1
2
0
2
1
1
1
0
1
2
1
2
0
2
1
0
2
2
2
2
2
1
1
2
1
1
1
2
1
0
1
0
1
0
0
0
1
0
0
0
0
1
0
1
0
1
1
2
1
2
0
2
1
2
0
1
1
2
2
2
1
2
0
1
1
0
0
0
2
1
1
2
2
1
1
1
0
1
1
0
0
2
2
2
1
1
0
1
1
2
1
0
2
0
1
1
2
0
1
1
1
1
0
1
1
0
0
0
1
2
1
2
0
2
2
0
1
2
2
0
1
1
1
1
1
0
0
0
0
2
0
0
0
1
2
2
1
1
1
1
3
0
1
1
2
1
0
0
1
2
0
1
0
1
1
1
2
0
0
1
1
1
0
1
0
2
2
1
3
0
2
2
1
1
0
1
2
0
2
2
1
1
1
1
1
1
2
2
1
1
1
0
0
1
2
2
1
2
1
1
1
1
0
0
1
1
1
0
1
1
0
1
1
2
0
1
2
0
2
0
1
1
1
1
4
0
2
1
1
1
2
0
1
1
2
0
1
1
0
1
1
1
1
2
1
1
2
0
0
2
1
1
0
1
1
2
0
1
1
1
2
2
1
1
2
2
1
1
2
1
0
0
1
2
0
0
0
1
0
1
0
2
2
2
1
2
1
1
1
0
1
1
0
1
1
6
0
1
1
2
1
2
1
2
2
1
1
0
0
2
1
0
1
1
1
2
1
0
1
0
0
0
0
1
1
0
1
1
1
1
2
0
0
1
1
1
0
1
1
0
1
2
1
1
1
2
2
2
2
1
1
2
0
0
1
0
2
1
1
0
0
1
0
2
0
0
1
1
1
0
2
1
0
1
1
1
0
0
0
2
1
2
1
1
0
1
2
1
1
1
1
0
2
1
1
1
1
0
0
2
0
1
2
0
0
0
1
1
1
1
2
1
1
1
0
1
0
2
0
2
1
1
0
0
2
0
0
2
0
0
1
0
1
0
0
2
0
1
1
0
1
2
1
1
1
1
1
1
1
1
0
2
2
1
1
0
1
1
1
2
0
0
0
2
0
2
2
1
1
0
0
1
0
2
1
0
1
0
0
1
1
1
2
2
1
1
0
0
2
2
1
2
3
1
1
0
0
1
1
1
1
3
1
2
0
0
0
0
0
1
0
2
0
0
1
1
2
1
1
1
0
2
0
0
1
0
0
1
1
1
0
2
2
1
1
2
1
1
1
1
0
2
0
0
1
1
0
1
0
0
1
2
1
0
1
2
1
1
2
1
0
0
2
0
1
1
1
2
0
0
1
1
2
1
2
1
1
1
0
1
2
2
0
1
0
0
1
1
2
1
2
0
0
0
1
0
1
0
0
1
1
1
1
2
2
2
2
1
1
2
0
1
2
0
1
1
0
0
2
0
1
0
1
2
0
1
0
0
1
2
0
1
1
1
0
1
0
0
1
3
2
0
2
1
1
0
1
1
2
1
2
1
1
0
1
1
1
1
0
1
1
0
0
1
1
1
1
0
1
2
0
1
1
0
1
2
1
0
2
1
0
1
1
0
1
1
1
0
0
1
1
1
1
0
0
1
0
1
2
1
1
1
1
2
1
0
0
1
0
2
0
1
2
1
0
0
0
1
1
0
0
1
1
0
0
1
1
1
2
0
0
0
0
1
1
1
0
1
0
0
2
0
0
0
0
1
1
2
3
1
0
0
0
0
2
1
2
1
2
1
0
1
1
0
2
1
2
1
0
1
2
0
1
1
2
1
1
1
1
1
2
0
0
0
1
0
2
0
0
1
2
2
0
0
0
1
0
1
2
1
1
2
1
2
1
1
2
0
0
0
2
2
1
2
1
1
1
1
1
0
1
1
0
1
2
1
1
1
1
1
1
0
2
0
2
1
1
1
1
1
2
0
0
1
1
1
2
1
0
0
1
1
1
1
0
0
1
0
2
0
0
1
1
0
2
1
2
0
1
1
2
1
1
1
0
1
0
1
0
1
1
0
0
1
0
2
2
0
1
1
0
2
1
2
0
1
1
1
0
2
2
1
2
0
1
1
3
1
2
0
3
0
1
2
0
0
2
1
1
1
1
0
2
0
0
0
1
0
3
3
1
1
0
0
2
1
1
1
0
2
1
0
1
2
1
1
1
0
1
1
2
0
0
0
1
0
2
0
1
1
2
1
1
0
1
1
1
1
0
0
1
1
1
0
2
1
2
0
1
0
2
1
0
2
2
0
1
0
0
1
2
1
0
0
0
0
0
1
0
3
1
4
1
0
1
1
1
1
2
0
2
2
1
0
1
2
2
1
1
3
1
0
0
0
0
0
0
1
1
1
0
1
1
0
1
2
1
1
2
1
0
1
0
1
0
0
0
1
1
1
2
2
1
0
1
0
1
0
2
2
2
0
2
0
1
1
2
0
0
2
1
1
0
1
2
2
2
0
1
0
1
1
0
0
1
2
1
1
1
2
1
1
2
0
0
1
1
0
1
1
1
2
1
1
2
0
1
1
1
2
2
2
1
0
0
2
2
0
0
2
1
2
0
1
1
1
2
1
1
0
1
1
1
2
0
1
2
2
1
0
1
2
1
0
1
1
0
0
1
1
1
0
2
1
1
0
2
1
3
2
1
3
1
1
1
0
1
1
1
0
2
1
1
0
1
1
2
0
1
1
2
0
1
2
1
2
1
1
0
1
0
0
0
2
1
1
1
1
0
0
0
1
1
1
1
2
2
1
1
2
0
0
0
2
0
2
1
0
2
1
1
0
2
1
1
2
1
1
0
0
1
0
0
0
1
1
1
1
0
1
1
1
1
1
1
2
1
0
1
1
1
1
0
1
0
1
2
1
0
3
0
1
2
2
1
0
1
0
1
1
1
0
2
2
1
2
1
0
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
0
3
0
4
1
1
2
2
1
1
2
1
1
0
1
1
1
1
1
1
0
1
1
2
1
1
0
1
1
0
0
1
1
1
2
1
1
1
2
3
1
2
1
2
0
2
0
1
1
0
2
1
1
0
0
2
1
1
0
1
1
1
1
2
0
1
2
1
0
1
2
0
1
1
0
1
1
1
2
1
0
2
1
0
2
1
1
0
1
0
2
2
2
0
1
0
1
2
1
0
0
0
2
1
2
0
2
2
2
0
1
0
1
2
2
0
0
1
1
2
0
1
2
1
2
1
2
0
2
0
1
0
0
0
1
1
1
1
1
0
0
1
0
2
2
2
2
0
1
1
1
0
1
2
1
2
1
1
1
2
1
1
1
1
0
2
1
0
1
0
1
2
1
0
0
1
2
1
1
2
1
1
0
2
2
1
2
2
1
1
1
0
0
0
1
1
1
0
0
1
2
1
1
1
1
1
1
0
1
1
0
1
1
0
1
1
0
1
2
0
0
0
2
1
2
1
0
2
3
0
0
2
0
1
2
0
1
0
0
0
1
1
1
2
1
2
1
1
0
1
2
2
1
0
1
0
0
0
0
0
1
1
0
0
1
1
0
0
1
4
1
1
1
1
2
1
0
2
0
2
2
0
1
0
1
1
1
0
0
2
1
0
0
0
1
1
2
1
1
1
0
1
0
0
2
2
1
1
1
0
2
1
1
2
1
1
1
1
2
2
2
1
0
1
1
1
1
1
0
2
0
1
2
1
1
0
1
0
0
1
0
0
1
2
0
1
0
1
1
1
2
1
1
1
0
0
0
0
1
1
1
1
1
2
0
0
1
0
1
1
1
0
1
0
0
1
1
1
1
0
1
1
0
0
0
0
1
1
0
1
1
2
2
2
2
0
2
1
1
0
0
0
0
0
0
0
1
1
2
2
1
2
2
0
2
1
1
2
0
1
1
2
0
0
1
2
0
1
2
1
2
1
0
1
0
0
0
1
0
2
0
2
1
0
2
0
0
0
0
1
0
0
0
1
1
1
0
1
3
1
2
1
2
0
0
0
1
0
0
2
0
2
1
0
0
2
1
2
2
1
1
2
2
1
1
1
2
0
2
0
0
0
3
1
0
0
0
4
1
0
3
2
1
1
0
1
2
1
2
1
1
1
0
0
1
2
0
1
0
0
0
2
0
0
0
1
1
0
0
2
1
0
2
1
1
0
0
0
0
1
1
2
2
1
1
2
2
2
1
1
1
1
1
1
2
2
2
1
1
2
0
2
1
0
1
1
0
0
1
0
1
2
0
2
2
1
1
0
2
0
0
2
1
2
1
0
1
1
0
1
3
0
2
1
0
1
1
1
1
3
2
1
0
0
0
0
0
1
2
3
1
1
1
1
0
0
0
1
1
1
1
0
2
1
0
1
1
1
1
2
1
0
1
0
0
2
1
0
0
2
0
1
1
1
0
0
0
1
2
0
1
1
0
0
0
1
2
0
1
1
1
0
0
1
0
1
1
1
1
0
0
1
0
0
1
1
1
1
1
0
0
1
1
1
1
0
1
1
0
0
0
2
0
1
2
0
0
2
2
1
1
2
1
1
0
1
0
2
2
1
1
2
1
2
2
1
0
0
1
1
1
2
1
0
1
0
1
0
2
1
0
2
1
0
1
1
3
0
1
0
2
1
1
2
1
0
2
1
2
1
0
2
1
1
1
1
0
1
1
1
3
1
1
2
2
2
0
1
2
1
2
1
1
0
1
0
0
0
2
1
0
0
0
2
2
0
0
2
2
1
1
1
0
1
0
2
2
1
1
0
0
1
1
2
0
2
1
0
0
0
0
0
1
1
1
0
1
1
1
0
1
2
1
0
2
2
1
1
1
0
0
2
1
0
0
1
2
1
0
1
1
1
0
0
2
0
1
2
2
0
2
1
0
2
1
4
1
1
2
1
1
1
1
0
1
2
1
1
1
0
1
2
2
0
5
3
1
0
1
2
0
1
1
0
1
2
2
1
1
1
1
1
1
0
2
1
2
1
0
1
2
2
1
1
0
0
1
1
0
1
0
0
0
0
0
1
0
1
1
0
2
2
0
0
0
2
2
2
0
1
2
1
2
2
0
2
0
1
2
1
0
2
1
1
0
0
0
2
1
2
2
1
0
0
1
0
0
1
0
0
1
1
1
0
1
2
1
2
0
1
1
1
1
1
2
0
1
2
0
1
1
2
0
2
1
0
1
2
2
0
1
0
0
1
2
1
1
1
2
1
1
0
1
1
0
1
1
0
2
1
0
1
2
1
1
2
0
1
2
0
1
1
1
2
2
0
2
1
1
1
2
2
1
1
0
0
0
1
2
1
0
0
1
1
2
1
3
1
0
0
1
0
1
1
1
0
1
1
1
2
1
1
0
2
1
0
2
0
1
2
2
1
1
1
0
0
0
2
2
0
1
1
1
1
1
2
0
2
2
2
0
1
1
1
1
1
0
1
0
2
2
0
2
0
1
1
1
1
0
1
2
1
2
1
1
1
1
1
4
2
0
0
0
1
1
1
0
1
0
0
1
0
1
1
1
0
1
2
0
0
0
2
1
1
0
0
0
1
0
0
0
1
0
0
2
1
1
1
0
2
0
0
1
1
1
1
2
2
0
1
1
1
2
1
2
1
2
2
1
2
1
2
2
0
0
2
1
0
0
0
1
1
2
1
2
0
0
1
1
2
1
0
1
0
0
0
1
1
0
0
1
1
1
2
2
1
1
0
0
2
0
0
0
0
1
2
1
2
1
1
1
0
0
1
0
0
3
2
1
0
1
0
1
0
1
2
0
1
0
1
1
1
0
0
1
1
0
1
1
0
1
1
1
1
1
2
2
0
0
0
2
1
1
1
1
0
0
2
2
0
2
1
1
2
1
0
0
1
2
2
1
0
1
2
1
2
2
0
1
2
1
1
1
1
1
1
0
1
1
1
0
1
2
2
1
0
1
1
0
0
1
2
1
0
1
1
2
1
1
1
0
1
1
1
1
1
1
1
1
1
1
2
1
1
1
0
1
1
1
0
2
2
0
1
0
2
2
2
0
1
3
2
0
1
0
0
1
0
0
1
0
1
1
0
0
0
2
1
1
2
1
1
1
1
1
0
0
0
0
1
1
1
1
1
0
2
0
1
1
1
1
1
0
1
1
0
1
0
2
1
1
2
2
0
2
1
2
1
1
2
1
1
0
0
3
2
1
1
1
0
1
2
1
0
0
1
2
1
1
2
4
0
0
0
1
1
0
1
1
1
3
2
2
1
1
0
2
0
1
1
2
0
1
1
1
0
1
1
1
2
2
1
2
0
2
1
1
1
2
2
1
1
4
0
0
2
0
1
2
1
0
2
2
1
0
0
2
2
3
2
0
2
0
1
1
1
0
0
0
1
1
0
2
1
1
1
1
1
1
1
2
2
2
2
0
1
1
1
1
1
1
0
0
0
1
0
0
1
2
1
4
2
1
1
2
2
1
1
0
2
1
2
0
1
0
0
0
1
2
2
1
2
2
0
2
1
1
0
2
1
0
0
2
0
2
1
1
0
2
1
0
1
1
1
2
2
1
0
0
2
1
1
2
1
2
1
0
0
1
0
0
2
1
1
1
0
0
1
1
1
0
2
1
2
0
1
1
2
1
0
1
1
1
0
1
1
1
1
1
2
1
0
1
1
3
1
0
2
0
1
0
1
0
0
0
1
1
1
2
1
0
1
0
1
0
1
2
1
0
1
0
2
1
1
1
2
2
1
0
0
1
0
2
0
1
1
1
1
1
2
1
1
2
0
0
1
1
0
0
1
0
2
1
1
0
0
1
1
0
1
0
0
2
0
2
0
0
0
2
2
2
1
2
4
0
0
2
0
1
2
2
2
1
0
0
0
2
0
1
1
0
2
0
2
0
0
1
0
0
2
0
1
2
1
0
0
1
1
2
0
1
0
0
1
1
1
0
2
1
1
1
0
1
2
1
0
1
0
1
2
0
1
1
1
2
3
3
1
0
1
1
1
2
1
1
1
1
0
0
0
1
0
1
0
2
1
2
0
1
1
0
1
0
0
1
0
0
1
2
2
2
2
0
1
0
2
1
0
1
1
1
0
0
1
1
0
1
0
1
1
3
0
0
3
1
0
0
0
1
0
1
0
2
2
0
1
1
1
1
1
1
2
0
1
1
1
0
0
2
1
1
0
1
1
1
1
2
2
0
0
0
1
0
0
1
0
2
1
2
2
1
0
0
0
0
1
1
0
1
1
1
1
2
1
1
2
2
0
1
1
0
1
0
0
1
0
0
2
1
1
1
1
1
1
1
1
1
1
1
2
0
0
1
2
0
1
1
2
1
2
1
2
2
1
1
2
1
1
0
0
2
1
1
0
1
2
1
0
2
1
0
1
0
1
1
2
2
2
2
1
0
1
0
1
1
1
2
2
1
2
1
1
1
0
1
1
2
1
1
1
2
2
2
0
0
1
2
1
1
4
0
1
0
2
1
0
1
0
1
2
0
1
0
1
1
1
2
1
1
1
2
1
2
2
1
1
1
1
1
0
0
0
0
1
2
2
1
0
0
1
2
1
0
0
1
2
1
1
1
1
2
0
2
2
1
0
0
1
2
0
2
1
0
1
1
2
0
1
1
0
1
0
1
0
0
2
2
1
1
3
1
1
2
1
0
3
0
2
0
1
2
2
1
0
1
0
1
0
0
0
0
5
0
1
1
2
0
1
0
0
1
1
1
1
0
0
0
1
1
1
1
1
2
1
4
0
2
0
0
2
1
0
1
0
1
1
0
0
0
2
2
1
1
3
2
2
1
2
1
3
2
2
1
0
1
0
2
1
1
0
1
2
0
2
0
0
0
2
2
0
1
2
2
1
0
2
0
2
1
1
1
1
2
2
1
1
0
2
0
2
0
1
1
2
0
1
0
0
1
0
0
1
1
1
1
2
2
0
2
0
1
1
1
1
1
0
1
2
1
2
2
2
0
1
0
2
2
1
1
0
1
1
0
0
1
0
0
2
1
0
1
0
0
0
1
2
0
1
1
0
2
1
1
0
0
0
1
1
2
2
0
0
1
1
2
0
2
0
2
0
1
1
1
0
4
3
1
1
0
2
1
0
0
1
2
2
2
0
1
0
1
2
2
1
2
1
0
0
0
2
2
0
1
1
0
3
1
1
2
1
1
1
1
1
2
5
0
0
2
1
0
1
2
1
0
0
1
2
0
1
1
2
0
0
0
1
1
1
0
0
1
2
0
1
1
1
1
0
1
2
1
1
1
1
1
1
0
1
2
1
0
0
1
0
2
0
1
3
1
0
0
1
1
1
1
1
1
1
1
1
1
1
0
0
2
2
0
2
0
1
1
2
1
2
1
1
0
2
2
1
1
1
0
1
0
0
1
1
1
1
2
2
1
0
2
0
1
0
1
0
0
2
2
1
0
3
2
1
1
1
0
0
1
1
1
0
1
1
1
1
0
1
0
1
1
1
1
1
0
1
2
2
1
0
0
2
0
2
2
1
1
2
0
1
0
0
2
0
1
0
0
1
1
0
0
2
2
2
1
0
1
1
1
1
1
0
1
1
0
2
2
0
1
0
1
1
0
2
1
0
1
1
2
0
2
2
1
0
0
2
2
2
1
4
0
2
2
1
0
0
1
1
0
0
2
0
0
0
1
1
0
1
2
1
1
0
1
1
2
2
1
1
0
0
1
1
1
1
1
1
1
0
1
0
1
2
1
1
1
0
1
0
0
0
1
0
1
0
0
0
0
2
1
2
1
1
0
0
2
0
2
2
0
1
1
0
1
0
1
2
0
1
1
2
0
0
1
2
0
1
1
1
0
1
2
0
1
1
1
3
2
1
1
0
1
0
1
1
0
1
0
0
0
1
1
0
0
0
0
1
1
0
2
2
1
2
1
2
1
1
3
1
1
0
1
1
0
2
1
2
2
0
0
3
1
1
1
1
3
1
2
2
0
1
2
0
1
2
1
1
1
1
2
1
2
1
0
0
1
0
1
1
1
1
2
1
2
0
0
0
0
1
1
2
0
1
2
0
1
1
1
1
0
1
1
1
0
2
0
0
2
0
1
0
0
0
2
1
0
1
2
1
1
1
0
1
1
1
1
1
0
1
1
0
0
2
2
1
1
2
1
1
2
1
1
0
1
1
1
1
0
2
2
2
0
1
0
1
2
1
2
1
1
1
1
2
0
2
1
2
1
2
1
2
0
1
0
1
0
0
1
1
1
2
0
1
0
1
2
2
0
0
1
0
2
1
0
0
1
2
0
2
0
2
1
1
1
0
2
2
2
0
2
1
1
1
0
1
1
1
2
0
1
0
1
1
1
0
1
1
1
0
1
0
1
1
0
1
0
0
2
1
0
1
1
2
3
1
1
0
1
1
0
1
1
1
0
0
0
1
1
0
2
1
2
2
1
2
0
0
1
1
2
1
1
1
0
1
1
2
1
0
1
3
1
0
0
2
1
2
2
0
0
0
1
2
1
0
0
0
1
2
1
2
2
1
0
0
1
2
1
0
0
1
1
2
0
2
0
1
1
0
0
0
1
0
0
0
0
1
1
0
2
1
2
1
1
0
2
1
1
1
0
0
2
2
1
1
0
1
0
0
1
1
0
1
2
1
0
0
0
1
0
1
1
1
0
1
1
0
1
0
1
1
0
1
1
1
0
1
2
2
1
2
2
0
2
0
0
1
0
1
0
1
1
1
1
3
0
1
1
0
2
0
0
1
0
2
1
1
2
0
2
0
1
1
2
1
1
2
0
1
2
0
0
1
0
0
0
0
1
2
0
0
0
2
1
0
0
1
2
1
0
1
1
0
1
2
2
1
1
0
0
1
1
0
2
1
1
2
0
1
0
1
2
0
1
2
1
0
1
0
1
1
0
0
0
0
0
1
1
1
0
1
1
1
0
0
1
1
0
1
1
0
1
2
0
2
1
1
1
1
1
1
1
0
2
1
0
0
1
1
1
0
1
2
2
2
0
0
2
1
0
2
1
2
1
1
0
1
2
2
1
2
1
2
2
0
1
1
0
0
1
1
1
0
1
0
1
1
2
2
0
0
1
1
2
2
0
1
1
2
2
1
0
1
0
1
0
2
1
0
0
0
2
1
1
0
2
0
1
1
0
1
2
1
2
1
0
2
0
1
1
1
2
1
1
2
2
1
1
2
2
1
1
1
2
1
0
1
0
1
1
0
1
2
0
0
1
0
0
1
0
1
1
0
1
0
1
1
1
0
1
1
1
1
1
0
1
1
0
3
1
1
0
0
0
1
1
2
1
2
1
1
1
1
2
2
1
0
0
2
1
1
0
1
0
1
2
2
1
1
0
1
2
2
1
0
3
0
2
1
1
0
0
1
2
0
0
1
3
1
0
2
1
2
2
1
1
0
1
0
1
1
2
1
2
1
1
1
0
1
2
1
1
1
1
1
0
0
1
2
1
1
0
1
1
2
1
1
0
1
0
1
0
1
2
1
1
0
2
1
0
2
1
3
0
1
1
2
0
1
1
0
1
1
0
1
1
0
1
0
2
2
1
1
1
2
0
1
1
1
1
1
1
1
0
1
0
0
1
1
2
1
1
1
0
2
2
1
0
2
1
2
1
1
1
0
1
0
0
1
1
1
1
1
0
0
0
0
0
0
1
0
1
1
0
1
1
2
1
2
2
1
1
1
0
1
0
1
1
0
2
2
1
0
0
0
3
1
1
1
0
1
0
1
1
2
1
2
1
1
0
1
1
1
1
1
1
1
1
2
1
3
1
0
2
1
0
0
2
1
1
1
1
1
1
1
2
1
0
1
1
1
1
0
1
1
2
0
2
1
0
1
2
1
1
1
2
0
0
2
1
1
2
1
2
1
1
1
0
1
0
0
1
1
2
0
2
0
1
0
0
1
2
1
2
1
0
1
0
0
2
1
0
1
2
2
1
1
2
1
1
0
1
1
2
1
1
1
0
1
0
0
2
1
0
1
1
1
1
2
1
2
1
0
0
1
1
1
1
1
1
0
1
1
0
0
2
2
0
0
1
1
1
1
0
0
0
2
0
0
0
1
0
0
1
0
0
1
0
1
1
0
1
0
0
0
1
0
0
0
1
2
0
2
0
2
1
1
2
1
1
1
2
1
0
1
1
2
1
2
0
1
0
1
1
0
2
2
2
1
2
2
2
1
1
1
2
0
1
0
1
0
0
1
1
2
1
1
2
1
0
0
2
1
0
1
0
1
1
0
1
0
0
2
2
1
2
1
2
0
0
0
1
1
1
1
5
0
2
1
2
1
2
0
0
2
1
0
0
1
0
1
0
1
2
1
1
2
1
0
0
1
1
1
1
1
1
2
1
1
1
2
2
0
1
1
1
1
0
2
2
1
0
1
1
2
1
0
1
1
0
0
2
0
1
1
0
2
1
2
2
1
2
2
1
1
0
2
0
1
0
1
2
2
2
1
0
1
1
0
2
1
2
1
1
0
1
1
1
1
1
0
0
0
1
0
1
2
1
1
2
2
1
1
0
2
0
0
0
1
0
0
2
1
1
2
0
3
2
0
1
0
0
1
0
0
0
0
2
1
1
0
1
0
2
2
1
0
1
0
1
0
1
1
1
1
0
1
1
1
0
2
2
1
0
0
0
1
0
1
1
0
2
1
2
1
1
0
1
0
1
1
1
1
0
1
1
2
1
1
2
3
0
1
0
2
1
1
0
1
2
0
1
0
0
1
0
0
1
1
1
0
2
0
5
1
0
1
1
1
0
1
1
1
1
1
1
1
0
2
2
1
0
1
1
0
0
0
1
2
1
1
1
1
1
0
0
1
0
0
1
2
2
1
1
2
1
1
1
1
2
0
1
1
2
0
2
2
2
1
2
1
1
0
0
0
1
0
1
0
1
2
0
1
0
1
0
2
1
1
1
1
1
1
1
0
1
2
0
2
1
0
1
2
1
2
1
2
0
2
0
0
1
2
2
1
1
2
1
0
2
1
1
1
1
1
2
1
1
0
0
1
1
1
0
2
0
1
1
1
2
1
2
1
0
0
1
2
1
0
1
0
0
1
0
0
2
0
0
1
0
0
0
2
1
1
0
1
0
0
0
1
1
1
0
1
0
2
2
0
1
0
1
0
0
1
1
1
1
1
1
1
0
0
0
0
1
1
1
1
0
1
0
0
0
1
0
1
1
0
1
1
0
1
0
0
0
2
0
2
0
0
1
0
1
0
1
1
1
0
0
0
0
2
2
0
0
1
1
0
2
1
0
0
1
1
1
0
1
1
0
1
1
1
0
1
0
0
2
1
0
1
1
0
2
0
0
0
1
1
1
1
0
0
0
0
1
1
1
2
0
0
1
2
1
1
1
2
1
0
1
0
1
1
0
1
0
1
0
0
1
1
2
2
2
2
0
1
1
1
0
1
0
2
1
1
1
0
2
0
0
1
2
0
0
1
1
1
1
0
3
2
0
1
1
1
1
2
2
1
0
1
2
2
2
0
0
0
1
1
0
1
1
1
0
0
1
2
2
1
0
1
1
0
0
2
1
1
0
1
1
2
1
1
0
1
1
0
1
0
1
1
1
2
0
2
1
1
1
1
1
0
2
1
0
0
1
2
1
1
1
0
0
1
2
1
1
1
0
1
0
3
1
0
1
1
0
1
1
0
2
1
1
0
2
2
0
1
0
2
0
1
1
1
0
2
1
0
1
2
1
0
2
1
0
0
1
0
1
1
0
0
0
0
2
1
0
0
0
0
1
2
0
2
2
2
0
2
1
0
0
1
0
1
0
1
1
1
1
1
1
0
1
1
1
1
2
0
1
1
0
2
1
1
1
1
3
0
2
1
0
1
1
2
1
1
1
1
1
0
0
1
1
1
2
1
1
2
1
0
0
2
0
1
0
2
1
0
0
0
2
1
1
0
2
1
1
0
0
1
0
1
0
0
0
4
1
1
1
1
2
2
1
1
0
2
0
2
1
3
1
2
1
0
1
1
2
1
1
1
1
1
1
0
2
1
1
1
1
1
0
2
1
2
1
0
1
1
0
0
0
1
1
2
2
1
1
1
1
2
0
1
1
1
0
0
2
1
1
1
2
0
0
1
0
1
1
1
0
1
1
1
0
1
2
2
1
2
0
1
0
0
1
2
2
0
1
2
2
0
1
2
0
2
2
0
2
2
2
1
1
2
1
1
0
2
1
0
0
2
2
0
0
2
1
0
0
1
1
2
0
2
2
1
1
1
1
2
0
1
0
0
2
1
1
0
1
1
2
1
1
2
0
2
0
0
1
1
2
2
0
1
2
1
2
1
0
0
2
1
1
1
0
1
0
0
1
2
1
0
1
0
1
1
1
2
1
0
0
1
0
1
1
1
0
1
1
0
0
0
1
1
1
0
1
0
2
1
1
1
1
1
0
2
2
0
1
1
1
0
1
1
2
1
0
0
0
1
1
0
2
2
4
2
2
0
1
0
0
1
1
1
1
0
0
1
3
2
0
2
0
2
1
1
2
2
1
1
2
1
2
0
2
0
1
0
1
2
0
2
0
1
1
1
3
1
0
1
0
1
0
1
0
1
1
1
1
0
0
2
1
1
0
0
1
0
1
1
2
1
1
2
0
2
2
1
2
0
0
1
1
2
0
1
2
2
1
1
1
0
1
1
1
0
0
1
0
0
1
0
1
1
0
1
0
1
1
2
1
1
1
1
0
1
0
1
0
0
0
1
1
2
0
0
1
1
1
1
0
1
1
0
2
1
2
1
2
1
1
1
0
0
1
1
1
0
0
1
0
1
0
1
2
1
2
0
1
1
1
0
2
0
0
2
2
2
2
1
2
0
1
0
0
1
1
0
1
1
1
0
0
0
2
1
1
0
0
1
1
1
0
1
1
0
2
1
1
1
0
1
1
2
1
1
2
1
1
0
2
5
1
1
1
1
1
0
1
3
1
1
0
1
0
1
0
1
1
2
1
1
1
0
0
1
1
2
0
1
2
1
1
2
0
1
2
1
2
1
0
0
2
2
0
1
0
2
0
1
2
2
1
2
0
0
0
2
1
0
0
0
0
1
1
1
1
0
1
1
1
0
0
1
1
1
1
1
1
2
1
3
1
0
0
1
1
0
1
2
0
2
1
0
1
0
1
1
1
1
1
0
1
1
0
2
1
0
1
1
2
0
1
0
1
0
1
0
2
1
0
1
0
2
1
2
1
1
2
2
1
0
2
2
0
1
1
0
1
0
1
1
1
0
2
1
3
1
4
1
1
1
0
1
1
1
0
0
0
0
1
1
2
0
2
1
0
3
0
2
0
0
2
1
0
2
1
2
1
0
1
1
1
0
0
1
0
0
1
1
1
1
1
0
2
2
0
0
2
1
1
0
0
0
2
0
1
1
1
1
1
0
0
2
2
1
1
1
0
2
0
0
1
1
1
0
0
2
1
2
1
2
1
1
0
2
1
2
1
1
1
2
2
1
1
0
2
1
0
0
1
2
0
3
1
1
2
0
0
2
0
1
1
2
0
1
0
4
1
0
1
0
0
2
0
2
1
2
2
0
1
2
2
1
1
2
1
1
0
0
1
2
0
1
3
0
1
1
2
0
1
0
0
1
2
0
0
0
0
1
0
1
0
1
1
2
0
0
1
1
1
0
2
2
1
2
0
2
2
2
0
2
0
2
2
1
2
1
2
0
0
1
0
0
3
1
1
1
0
2
2
1
1
0
1
0
2
1
1
1
1
0
1
1
0
1
0
0
1
1
1
0
2
3
0
1
1
0
1
0
1
1
1
0
2
1
1
1
1
2
1
0
2
1
2
1
0
1
2
2
1
2
1
0
0
0
1
0
0
1
2
2
1
1
0
0
1
0
1
0
1
2
2
2
0
1
2
1
1
0
0
1
1
1
2
0
0
0
0
0
0
2
1
0
2
1
1
2
1
0
2
1
1
1
0
1
0
2
1
1
1
2
2
0
0
2
1
0
2
2
1
1
0
0
1
1
1
1
1
3
0
2
1
0
0
1
0
0
1
0
1
2
0
0
2
0
0
3
3
4
0
1
0
0
1
0
1
1
2
1
2
1
2
1
3
1
0
0
0
2
0
0
1
0
1
1
1
1
1
1
0
1
2
2
1
0
0
1
1
0
0
2
0
0
1
2
3
1
1
1
1
2
0
1
2
2
2
1
0
0
2
1
1
1
1
0
1
0
2
1
1
1
1
1
1
2
1
0
3
1
1
0
1
0
2
0
2
1
2
1
0
1
1
2
1
0
1
2
0
0
1
1
1
2
1
1
2
2
1
0
1
2
2
0
1
2
0
2
2
1
2
2
1
1
1
0
0
1
1
2
2
1
1
1
0
2
0
2
2
1
0
2
0
0
0
2
1
2
1
1
0
0
1
1
0
1
2
2
2
2
1
0
2
1
0
2
1
2
1
0
1
0
1
1
1
0
2
2
1
3
0
1
1
1
1
2
1
1
0
1
0
0
2
0
1
1
0
1
2
1
2
2
0
0
2
0
0
1
1
0
0
1
1
1
1
2
0
1
2
2
1
0
0
2
1
1
2
0
1
1
1
1
1
2
2
1
2
0
0
1
1
1
1
0
1
0
1
0
0
0
1
1
1
2
1
2
2
1
0
2
1
0
0
0
0
1
1
1
0
1
0
0
1
1
0
1
2
1
1
1
1
1
1
1
1
0
1
1
0
1
1
0
1
0
1
2
1
1
1
1
1
2
0
0
1
1
2
1
2
1
1
0
0
0
0
1
0
2
1
1
0
0
2
1
0
0
1
2
1
2
1
1
0
2
1
0
0
0
1
2
1
2
2
3
0
1
1
0
2
0
1
2
1
0
1
1
1
1
1
1
2
1
0
1
1
0
1
1
1
1
2
1
1
1
0
0
2
1
1
0
0
1
1
1
1
0
1
1
2
1
0
1
1
2
1
1
1
1
1
1
2
1
1
0
0
0
1
1
0
1
1
1
0
1
1
4
2
2
1
1
1
1
0
0
2
0
2
1
0
1
1
2
1
0
2
1
2
2
0
2
2
0
1
0
1
1
1
3
1
1
1
0
1
0
1
2
2
2
0
2
0
1
1
1
1
1
1
0
1
1
0
0
1
0
0
0
1
0
1
1
2
0
2
0
2
0
2
2
1
1
1
2
0
1
0
2
0
1
1
1
2
1
0
1
1
2
2
0
1
1
2
0
1
1
1
1
1
1
1
2
2
0
2
2
1
1
2
1
0
0
2
0
2
0
1
1
2
1
2
1
2
1
1
1
2
1
1
1
0
0
0
1
1
0
1
1
2
1
1
0
1
1
1
1
1
0
1
1
1
0
1
0
1
1
1
1
0
2
2
2
0
1
1
1
0
0
1
0
1
1
2
1
1
1
0
1
1
1
1
1
0
1
2
1
0
1
1
2
2
1
1
1
2
2
1
1
1
0
1
2
0
0
1
1
0
2
1
1
1
0
1
2
0
1
1
0
2
3
2
1
1
2
2
1
2
0
2
0
1
1
1
0
1
0
1
1
2
1
1
0
1
1
0
1
1
1
2
1
0
0
2
1
0
1
2
0
1
1
2
1
1
0
1
0
2
2
0
1
1
2
2
0
0
2
1
2
1
1
0
1
1
0
2
1
2
1
1
0
2
0
0
2
1
1
0
0
2
1
0
3
2
0
1
2
0
0
0
1
0
1
1
2
0
0
2
0
2
2
0
1
1
1
0
1
1
0
0
2
0
0
1
1
0
1
4
0
2
0
1
0
2
1
2
1
0
1
0
1
1
0
0
1
2
2
2
1
0
1
1
2
2
2
0
1
1
1
2
1
2
1
0
1
0
1
1
1
1
1
0
1
1
1
2
1
1
1
1
1
1
0
1
1
1
0
2
1
0
1
0
2
0
2
1
2
2
2
2
0
3
0
2
2
1
0
2
2
1
1
0
0
2
1
1
1
0
0
1
0
0
1
1
1
1
1
1
1
0
0
0
2
0
0
2
0
1
0
1
1
1
2
1
2
0
0
2
2
1
1
1
3
1
2
0
1
0
1
0
0
1
1
2
0
2
0
0
1
0
2
0
1
1
0
1
0
1
1
1
1
1
1
0
2
1
0
2
2
2
1
1
0
1
1
1
4
1
2
1
0
2
1
1
1
0
1
2
2
2
0
0
1
0
1
0
0
1
0
2
2
0
2
1
2
1
0
1
1
1
2
1
2
2
2
2
1
0
1
0
1
0
0
2
0
0
1
1
0
1
1
0
2
0
0
1
2
1
1
1
0
0
2
0
1
0
2
1
0
0
1
2
0
1
1
0
2
1
1
1
1
0
1
1
1
1
1
1
1
1
0
1
1
1
1
1
0
0
0
1
2
2
2
1
1
2
1
0
1
0
1
1
1
2
2
0
1
1
0
1
0
1
1
0
1
1
1
0
2
0
3
0
1
0
2
1
1
1
2
2
0
1
2
2
1
1
1
1
1
1
1
0
1
0
2
1
1
1
0
1
1
0
2
0
1
1
0
1
0
0
1
2
1
0
1
0
1
2
1
1
1
0
1
1
1
0
1
0
2
1
2
2
1
1
0
1
0
1
1
0
1
0
1
1
1
0
0
1
0
2
2
0
2
0
1
2
1
0
0
1
0
1
1
2
1
2
1
1
1
1
2
1
1
2
0
1
0
0
0
0
1
0
1
0
0
1
1
0
1
1
2
3
0
1
1
2
1
2
0
0
0
1
0
1
0
2
2
0
1
1
0
0
2
2
0
0
1
1
2
1
2
1
0
1
1
1
2
1
2
1
1
0
0
1
1
2
0
0
2
0
0
0
0
2
1
1
2
0
0
0
1
2
1
1
1
1
2
0
1
2
1
2
1
0
0
1
1
1
0
0
1
1
1
0
1
2
0
1
0
1
1
2
1
2
1
1
1
0
1
1
2
2
1
2
1
1
1
1
0
0
2
2
2
1
1
0
2
1
1
0
1
0
1
1
1
1
1
0
0
1
1
2
1
1
2
1
0
2
2
1
1
1
2
1
3
2
0
0
1
0
0
1
2
1
1
1
0
0
1
1
1
1
1
1
1
1
1
0
2
1
2
1
2
1
0
1
1
0
0
2
1
0
1
0
0
1
1
2
1
1
1
2
1
2
0
1
1
1
1
0
0
1
2
0
0
2
1
1
2
1
1
1
1
0
2
2
0
2
2
0
0
1
0
1
1
2
1
2
1
0
2
2
1
1
0
1
1
1
0
1
0
2
1
1
1
0
0
1
1
1
0
1
0
2
1
2
1
2
2
0
2
0
1
0
0
1
1
0
1
1
2
1
1
1
1
0
1
2
1
1
3
1
1
0
1
1
2
1
0
0
1
1
0
1
1
0
0
0
1
0
2
2
1
1
1
1
1
1
0
1
2
0
2
0
1
1
0
1
1
2
1
0
2
0
1
1
2
1
2
1
1
1
0
0
0
2
0
1
1
2
1
0
2
1
1
1
1
1
1
0
2
0
0
0
1
2
0
0
1
0
2
0
0
0
2
1
1
2
0
2
1
1
1
1
0
1
0
2
0
0
2
1
1
1
1
1
2
2
1
1
0
2
0
1
1
1
1
2
2
2
2
1
0
0
0
2
0
0
0
0
0
1
1
2
2
1
2
1
2
2
1
1
1
1
2
1
1
1
2
0
1
0
0
2
0
1
0
2
2
1
0
1
1
1
0
2
1
2
1
0
2
1
2
1
1
0
2
1
1
1
1
1
1
0
0
1
2
0
1
2
2
0
1
2
1
1
1
0
1
2
0
0
2
0
0
1
1
1
2
1
1
0
1
0
1
0
0
2
0
0
2
1
1
1
2
1
1
1
0
2
2
1
1
0
1
0
1
1
0
3
1
1
1
0
0
3
2
1
2
1
1
0
0
1
0
0
0
1
1
0
2
2
0
1
1
0
3
0
1
1
0
1
1
0
0
2
0
0
1
1
0
0
1
0
2
1
1
1
0
2
0
2
2
1
1
0
1
1
0
2
2
1
1
0
1
2
1
0
0
1
2
1
0
0
1
1
0
0
1
1
2
1
0
1
1
2
0
1
1
2
1
0
1
0
1
2
1
0
2
2
1
2
0
0
1
1
0
1
1
1
0
1
1
0
0
1
2
1
1
2
1
0
1
1
0
0
1
0
0
0
1
0
2
1
1
0
0
1
1
1
2
2
1
1
0
0
0
1
1
2
1
2
0
1
1
0
2
2
0
0
1
0
1
0
2
0
0
1
1
1
0
0
0
1
1
2
0
1
1
0
1
0
1
0
0
1
1
2
1
0
1
1
0
1
1
2
1
2
2
2
0
1
1
2
1
1
0
0
0
0
0
0
0
2
1
1
2
0
0
2
1
1
1
1
1
0
2
0
0
0
1
1
2
0
1
1
2
2
0
0
2
0
1
2
1
2
2
2
0
0
1
0
0
2
1
0
0
0
2
1
1
1
1
2
1
0
1
1
0
1
2
2
1
1
1
1
1
1
0
2
2
1
0
1
1
2
1
1
1
1
2
1
0
0
0
0
1
1
1
0
1
2
0
1
1
0
1
0
1
2
1
1
2
0
0
2
1
0
0
1
1
1
2
1
2
2
0
2
0
3
3
1
2
1
0
0
1
1
1
2
1
0
0
1
0
1
2
1
2
1
1
0
2
1
0
1
2
0
2
2
1
0
1
1
1
0
1
1
0
2
1
0
1
2
2
1
1
1
0
1
2
0
0
2
2
1
2
1
0
1
0
2
2
2
1
1
1
1
1
2
0
1
1
0
1
0
1
1
2
0
0
1
2
1
1
1
1
1
0
0
0
1
0
1
0
2
0
2
1
1
1
1
2
1
1
0
0
0
0
2
1
1
1
2
1
0
1
0
1
0
2
1
2
0
2
2
0
2
3
1
1
1
0
0
2
2
2
1
0
0
2
1
1
1
2
2
2
2
2
1
0
1
1
2
2
0
0
1
1
0
1
0
0
0
2
2
0
1
0
1
1
1
1
1
1
1
0
0
1
0
2
1
0
0
2
2
0
1
1
1
0
1
0
0
1
1
0
2
1
1
1
2
1
1
1
2
1
1
2
0
0
0
0
0
2
1
0
0
2
0
0
1
2
2
1
2
2
0
3
1
1
0
2
1
0
2
0
0
1
1
1
0
1
1
0
0
1
0
1
0
2
2
2
1
0
3
1
2
0
1
1
1
2
1
1
1
1
0
0
2
1
1
2
2
2
1
0
0
2
0
1
1
1
2
1
1
0
1
0
1
0
1
1
1
2
0
1
1
2
1
2
1
2
1
1
1
1
1
1
0
0
1
1
1
0
2
0
1
1
2
0
1
1
2
0
1
2
3
2
1
0
1
0
1
1
2
0
1
0
1
0
0
0
1
0
1
2
2
0
0
1
1
1
1
0
0
0
2
1
1
1
1
0
1
2
1
2
0
1
1
0
2
1
0
1
1
0
1
0
1
2
0
2
0
0
1
0
1
0
1
1
1
0
1
2
1
1
1
0
1
0
1
1
0
1
1
2
0
2
1
2
1
1
1
2
1
0
1
1
0
1
0
2
1
2
1
0
2
2
1
0
2
1
0
1
1
1
1
0
1
1
0
1
1
2
0
1
1
0
2
1
0
0
1
0
1
2
1
2
1
2
1
2
1
1
0
1
1
2
1
1
0
1
1
2
1
2
1
1
1
2
2
1
1
2
1
0
2
2
0
1
3
2
3
2
1
0
1
0
1
0
2
0
1
1
2
1
2
1
1
0
1
0
0
1
0
0
1
1
1
1
1
0
1
2
0
0
1
2
2
1
0
0
1
2
0
0
2
1
1
2
1
1
1
2
1
0
1
1
1
3
0
1
0
0
1
2
0
1
1
1
1
0
1
0
0
0
0
0
0
1
1
0
0
0
2
1
1
0
0
0
2
0
0
1
1
2
1
2
1
1
2
0
1
1
2
1
1
0
1
0
2
0
1
2
2
2
1
0
0
0
1
1
2
0
1
0
1
0
0
0
3
1
0
1
2
0
0
1
1
0
2
1
1
1
2
1
0
1
0
2
0
1
2
1
2
2
1
0
0
0
2
1
1
1
1
0
2
1
0
1
1
0
2
1
0
2
1
1
1
1
0
1
1
1
1
2
2
0
1
0
2
1
0
2
0
2
2
0
2
0
0
0
1
2
0
1
1
2
0
2
1
2
0
2
1
1
1
2
0
1
0
2
1
0
2
2
1
1
1
2
0
1
2
0
1
2
0
1
0
1
0
2
0
2
1
1
1
1
1
1
1
0
2
1
2
2
0
1
2
2
1
1
0
2
2
1
1
0
4
1
0
2
0
1
0
3
0
0
0
1
1
1
0
0
1
0
2
0
0
1
1
2
1
1
0
1
0
0
0
1
1
1
0
2
1
3
1
1
1
1
2
1
1
1
0
0
1
2
0
1
1
1
1
1
1
1
1
1
2
1
1
1
0
1
1
4
1
0
0
1
1
1
2
1
2
0
0
1
0
1
1
2
0
2
2
0
1
0
1
0
2
1
1
1
0
1
1
1
2
1
1
0
1
2
1
1
0
0
0
1
1
1
1
2
1
0
1
2
0
0
1
1
0
1
2
0
2
0
1
0
0
1
1
1
1
0
1
2
2
1
0
1
2
0
1
1
2
0
1
1
1
1
0
1
2
1
0
1
2
0
0
0
0
0
0
0
0
1
0
1
1
1
1
0
2
1
2
0
1
0
0
0
0
2
2
0
0
0
1
1
1
2
0
0
2
0
2
2
2
2
0
0
1
2
1
1
1
0
1
1
1
0
1
3
0
1
2
0
1
2
1
2
0
1
2
2
2
1
0
2
1
0
0
2
2
1
0
0
1
1
0
1
1
1
1
2
2
0
0
1
0
0
1
2
1
2
0
0
1
1
1
0
1
0
1
1
0
0
0
1
1
0
0
0
1
0
1
0
1
0
1
2
0
2
0
2
0
1
1
0
1
0
1
1
2
1
1
1
2
0
2
1
1
2
0
2
1
2
1
1
2
1
1
1
2
2
1
1
0
0
0
1
0
1
1
1
2
1
2
0
2
0
1
1
0
0
2
1
0
0
2
1
2
0
1
1
1
0
0
2
1
1
2
1
1
2
2
0
2
1
1
0
2
0
0
0
1
0
2
2
0
1
0
0
2
0
1
1
0
2
1
1
1
2
1
0
1
1
0
1
2
2
0
1
0
1
1
1
0
2
2
1
1
2
1
1
1
0
1
0
0
1
2
2
1
2
0
1
1
2
1
1
2
0
1
0
1
2
2
2
2
1
1
1
0
0
1
1
1
0
1
0
1
0
0
1
2
2
1
1
1
2
1
1
1
1
0
0
1
2
1
1
0
1
0
0
0
0
0
2
0
1
2
3
3
1
1
1
2
0
0
1
1
1
1
1
2
2
1
0
2
2
1
1
1
2
1
1
1
0
1
0
0
0
0
2
1
0
0
1
2
0
1
2
1
0
1
1
1
0
1
4
2
0
2
0
0
2
2
2
0
0
2
1
0
0
1
1
1
2
1
0
1
2
1
2
0
0
0
1
1
1
0
1
0
0
0
1
2
1
2
1
2
0
1
2
2
0
1
1
0
1
1
1
1
1
1
1
0
2
0
1
1
0
1
0
2
2
1
1
1
0
2
1
1
2
1
0
2
1
2
0
0
0
2
1
1
1
0
1
1
2
3
2
1
0
1
0
2
0
2
3
1
1
2
1
2
1
1
1
2
0
2
0
0
1
2
1
2
1
2
0
0
2
1
2
2
0
1
0
2
1
0
1
2
1
1
2
1
2
1
1
2
7
0
1
0
0
0
0
1
0
2
2
0
1
0
0
1
1
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
1
0
1
0
0
1
0
0
1
0
1
1
1
2
1
2
1
1
0
1
1
0
1
0
0
0
2
0
1
1
2
0
2
0
2
1
1
1
0
1
2
0
1
1
1
1
2
0
1
1
1
0
1
2
2
2
0
2
1
2
1
0
1
0
1
1
1
2
0
2
2
1
0
1
2
0
1
2
1
1
1
1
2
0
0
1
1
1
0
2
1
1
0
1
1
0
0
0
1
1
2
1
2
0
1
1
2
0
1
1
0
1
2
1
0
1
1
1
2
1
1
1
0
1
1
2
2
1
0
0
1
0
1
2
0
1
0
1
0
1
2
1
0
1
1
1
0
0
1
0
1
2
0
0
0
0
1
2
0
2
0
0
2
3
0
1
1
1
1
2
2
0
2
0
0
0
0
1
2
0
1
1
1
1
3
1
1
0
0
2
1
1
1
1
0
1
1
0
0
2
1
0
1
2
1
2
0
2
1
2
1
1
2
2
1
2
1
1
1
1
0
0
0
1
1
2
2
1
0
1
0
1
1
0
1
3
0
0
0
3
0
2
2
1
1
0
2
2
1
1
2
2
0
1
0
1
2
2
1
1
1
1
0
2
1
0
0
0
2
0
1
1
1
1
1
0
1
2
2
2
1
1
1
0
2
1
1
0
1
1
1
0
1
1
0
2
0
1
1
1
1
1
0
0
0
0
0
1
1
0
2
3
0
0
2
2
1
0
1
1
1
1
1
0
0
0
1
1
2
1
2
0
2
0
1
1
0
2
0
0
1
1
1
1
0
1
1
0
0
2
2
0
0
3
1
1
1
1
0
1
0
1
1
1
1
0
0
2
2
1
1
1
1
1
1
1
1
1
2
0
2
1
1
2
1
1
1
2
1
1
0
1
1
1
2
1
1
1
1
1
2
2
0
0
0
1
2
0
1
2
1
1
2
2
1
1
2
1
1
2
0
1
1
2
1
0
0
1
2
1
2
0
2
1
2
0
2
1
1
0
2
1
1
0
0
1
0
2
2
2
0
1
1
1
1
1
1
0
0
1
0
2
0
1
1
1
0
0
0
0
0
0
0
2
0
1
0
1
1
2
0
1
1
0
1
0
0
1
0
1
1
0
1
2
2
0
2
1
2
1
1
2
0
0
1
1
1
2
0
0
2
1
2
0
1
0
2
0
0
0
0
1
0
1
1
1
1
3
0
1
0
1
0
1
2
0
2
1
1
0
1
1
0
1
0
1
2
1
2
1
2
2
0
0
1
1
1
1
1
1
1
0
0
2
2
0
2
0
1
2
0
2
0
0
0
1
1
1
1
1
2
2
1
0
1
0
1
0
0
1
1
0
1
2
0
1
0
0
0
1
0
1
2
1
2
0
1
3
2
1
0
0
0
2
0
2
2
2
1
2
0
1
1
0
1
1
2
1
1
1
1
1
0
1
0
0
0
2
1
1
1
0
1
0
0
2
2
0
1
0
0
0
1
1
0
1
1
2
1
1
1
2
0
0
0
1
3
1
2
1
1
0
1
0
1
1
2
1
2
1
0
1
1
1
0
1
3
1
0
1
1
1
1
2
2
1
0
0
1
2
1
1
0
1
1
2
2
2
2
1
1
5
0
1
0
1
1
1
1
0
1
2
1
1
1
2
0
0
0
2
0
1
0
0
0
0
1
1
0
2
3
1
0
1
1
1
2
1
0
2
2
4
0
0
0
2
1
1
2
0
1
2
0
2
2
0
2
2
0
0
1
1
1
2
2
1
1
2
2
0
1
0
1
2
0
1
1
2
1
2
2
2
2
1
1
0
2
1
3
0
0
1
0
1
0
2
1
1
2
2
1
1
2
2
0
2
1
1
2
2
0
2
0
1
2
0
0
1
0
1
1
2
0
1
0
0
1
1
1
1
1
2
1
1
0
0
0
1
1
1
0
2
2
2
1
1
1
0
2
2
1
1
2
2
2
2
1
2
1
0
0
0
1
2
1
1
1
3
1
1
2
2
0
2
1
0
1
2
0
1
0
0
1
1
1
1
0
2
0
0
1
1
0
1
2
1
1
2
1
1
1
1
1
2
1
0
0
0
1
1
1
0
0
0
0
1
1
2
1
0
1
1
1
2
1
2
0
1
1
0
1
1
1
4
1
0
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
2
0
0
1
0
1
1
0
0
0
0
0
1
1
2
0
0
1
2
2
0
1
1
0
1
1
1
0
3
1
0
2
2
2
0
1
1
1
0
2
1
1
1
1
1
1
2
2
0
0
0
2
1
1
1
1
1
3
2
1
2
2
1
2
0
1
2
1
2
2
0
1
1
0
0
0
0
2
1
0
0
0
1
0
2
0
1
1
1
1
1
1
0
2
1
0
1
1
1
1
1
1
1
1
1
2
1
1
0
1
0
0
1
1
1
1
1
2
2
0
1
1
1
0
2
1
2
2
1
2
1
1
1
1
1
0
0
1
2
2
1
1
2
2
1
1
1
1
1
0
2
1
0
1
1
0
2
1
0
1
0
1
0
1
1
1
0
1
1
0
2
0
2
0
0
1
2
1
1
1
1
1
1
1
2
2
2
1
0
1
2
1
1
2
1
1
1
1
0
1
2
1
0
1
1
1
1
2
2
4
2
0
2
1
1
1
1
1
1
0
1
1
1
0
1
1
1
1
0
1
2
1
0
0
1
1
1
1
2
2
1
0
0
0
2
0
0
1
0
1
2
0
1
1
1
1
0
0
1
1
1
0
1
0
0
2
0
1
2
2
1
0
1
0
0
0
1
1
1
0
0
1
0
2
1
0
1
1
2
0
0
1
0
0
0
0
1
1
1
1
1
1
1
2
0
0
0
1
0
0
1
0
1
1
1
1
2
1
0
0
1
1
0
1
1
1
1
0
0
1
0
1
1
1
2
1
2
1
0
0
0
2
1
0
0
1
2
0
1
1
0
1
2
1
1
0
2
0
1
1
1
1
1
2
1
1
1
2
1
0
0
2
0
2
0
2
0
1
1
2
1
1
1
1
1
1
0
1
1
1
0
0
1
2
0
1
0
1
0
0
1
1
2
1
2
1
0
1
1
1
0
2
1
1
0
1
1
1
1
1
0
1
1
0
1
1
0
2
2
1
1
0
2
0
0
2
1
0
2
1
2
2
0
2
1
1
0
0
2
1
2
1
2
0
1
1
0
1
1
1
0
1
1
2
1
2
0
1
0
1
1
0
2
0
1
1
1
0
1
2
2
1
2
1
2
0
1
1
0
1
1
0
1
0
1
1
1
2
1
1
1
1
0
1
1
1
1
1
1
1
1
1
2
0
0
1
0
1
0
0
1
1
2
0
1
1
1
2
4
0
1
1
0
1
1
0
1
1
1
1
0
0
2
0
2
0
1
1
0
1
1
0
0
0
0
0
1
1
1
1
2
0
0
1
0
1
2
1
0
1
0
2
2
2
1
1
1
1
1
1
0
1
1
1
0
1
1
1
1
2
1
1
0
1
1
1
1
0
1
1
2
1
1
0
2
1
0
2
2
2
1
2
2
2
0
1
2
1
0
1
0
0
1
1
1
2
0
1
0
2
0
0
1
0
1
0
1
3
1
1
0
1
1
4
1
1
0
0
0
1
1
1
0
2
1
0
1
1
1
3
1
1
0
1
2
0
1
0
1
1
0
2
0
1
0
0
1
0
1
1
2
0
2
0
1
2
2
0
0
0
1
1
0
1
1
1
2
0
1
0
0
2
0
0
0
1
0
1
0
1
0
1
1
0
1
1
0
0
0
1
1
1
2
1
1
1
2
1
0
0
1
0
1
2
0
1
0
1
1
1
1
0
1
1
1
1
0
0
0
1
2
2
3
0
0
2
1
1
0
4
1
0
2
2
0
1
1
1
2
0
0
2
0
0
1
2
0
0
1
0
3
2
2
1
1
2
1
1
2
1
2
2
1
0
0
1
2
0
1
2
0
2
2
2
0
1
1
1
0
2
1
1
2
1
0
1
0
1
1
0
0
2
1
1
1
0
2
1
0
1
0
1
0
0
1
0
0
1
1
1
1
1
1
1
2
3
1
0
1
2
0
0
1
0
0
1
2
2
1
2
2
1
2
2
0
0
0
1
0
3
1
2
1
1
0
0
1
0
1
2
0
0
2
0
0
1
0
1
0
1
1
1
1
0
1
1
2
1
0
1
0
3
0
0
0
1
2
2
2
1
0
0
2
1
2
0
2
0
1
0
1
0
1
1
1
1
0
0
2
0
0
3
0
2
1
2
1
0
0
2
1
1
2
1
2
0
2
1
2
2
1
2
0
0
0
0
0
1
1
1
1
1
0
1
0
2
1
0
1
1
1
1
1
0
1
0
2
2
1
2
2
1
1
1
2
1
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
1
2
0
2
0
0
0
1
1
2
1
0
0
0
2
1
0
1
1
0
0
1
0
2
0
0
1
1
2
1
2
2
1
0
0
1
1
1
1
0
1
0
1
1
2
2
1
1
1
2
2
1
1
0
2
1
1
1
1
1
0
1
0
1
1
0
1
0
1
1
0
2
1
0
0
1
1
1
2
2
1
1
0
2
1
2
1
0
1
1
1
1
2
0
1
1
1
0
0
0
2
1
2
2
2
2
0
1
2
0
0
1
2
0
0
2
1
0
0
2
0
2
1
0
2
0
0
1
1
1
0
1
0
2
1
0
1
1
2
0
0
1
1
0
1
2
1
0
2
0
0
0
1
1
1
1
2
1
2
1
1
1
1
2
2
3
2
1
2
2
0
0
0
1
1
1
0
0
2
0
1
0
0
1
2
0
1
1
2
0
1
2
1
0
1
1
0
3
1
0
1
0
1
1
0
1
1
0
0
0
0
1
2
3
1
2
1
0
1
0
0
0
0
1
1
0
2
0
1
2
0
2
1
0
1
1
1
1
0
2
1
1
2
1
1
1
0
1
2
1
1
0
1
0
1
1
1
1
1
1
0
1
1
2
2
2
0
2
2
0
1
0
1
2
0
1
2
1
0
0
0
0
0
1
0
0
1
1
2
1
2
2
1
2
1
1
0
1
0
2
0
1
0
0
2
2
0
0
2
1
2
1
1
0
1
1
1
2
1
1
1
0
0
0
1
1
2
1
1
1
1
0
1
1
1
0
1
0
0
2
0
1
2
1
1
0
0
2
1
0
1
0
2
1
1
1
0
0
1
0
1
1
1
2
1
0
2
0
0
1
2
0
1
0
1
1
1
1
2
2
1
1
1
1
1
0
0
1
2
1
2
1
0
0
1
0
0
1
2
1
0
1
2
1
0
2
1
0
0
1
1
1
1
2
1
1
0
2
0
0
1
1
1
1
0
1
1
1
2
1
2
0
2
1
0
1
1
1
2
1
2
2
1
1
1
2
1
1
0
1
0
2
1
0
0
2
3
1
1
2
0
0
0
0
0
2
0
0
1
1
0
3
1
1
0
1
0
0
0
2
2
0
1
1
2
2
1
0
2
2
3
1
2
2
1
1
1
2
0
1
1
1
1
0
1
0
1
1
1
2
1
1
2
1
1
1
1
0
1
1
1
1
2
1
1
0
2
0
1
0
2
0
2
1
0
2
2
0
1
1
1
1
1
1
1
1
2
0
1
0
1
1
2
1
0
0
0
0
0
1
0
1
1
0
0
1
0
2
0
1
0
1
1
2
1
2
0
1
0
0
1
0
1
1
0
1
1
0
0
0
1
1
0
2
0
1
1
0
0
0
0
1
2
1
2
2
2
1
4
1
1
1
0
2
1
0
1
0
1
1
0
2
2
1
0
0
0
2
0
1
2
0
0
1
1
1
1
1
2
1
0
1
0
1
0
1
2
1
1
1
1
1
0
1
0
1
1
1
0
0
3
1
0
1
0
0
1
2
1
1
1
2
0
1
2
1
0
0
1
0
1
0
2
1
3
1
2
2
1
1
1
1
1
1
0
1
0
0
0
1
0
1
0
1
1
1
1
1
2
0
0
2
0
0
0
0
1
1
2
1
1
0
0
1
2
0
0
1
0
1
1
1
0
0
1
0
0
0
0
1
2
0
1
0
1
2
1
2
1
2
1
0
0
0
0
0
2
1
0
0
0
1
2
1
2
1
1
2
1
0
0
1
0
3
1
0
0
1
0
0
2
1
0
0
1
0
2
1
2
0
0
1
1
1
1
1
1
0
0
0
1
1
0
2
0
0
1
1
2
0
1
2
0
2
2
0
0
2
1
1
1
0
0
0
2
1
0
0
1
0
0
0
2
2
2
1
2
2
2
1
0
0
2
1
0
3
0
0
1
0
0
1
1
0
0
0
1
2
0
1
1
1
0
0
1
1
0
1
0
0
0
1
1
2
2
1
0
1
1
1
1
1
1
1
0
1
1
1
1
0
1
2
2
1
0
2
2
1
2
1
0
1
0
1
1
0
1
1
1
1
0
1
1
0
0
1
1
2
1
2
2
0
1
1
0
1
1
2
1
1
1
0
2
1
1
2
1
2
2
0
0
1
0
2
2
0
0
2
1
1
1
2
1
2
0
0
1
1
2
1
2
1
1
1
0
1
1
1
1
1
1
1
2
2
1
1
1
1
2
0
1
2
2
1
0
4
3
1
0
2
2
1
3
0
0
1
1
1
0
2
1
1
0
2
1
1
1
0
2
1
2
0
1
0
2
0
0
1
0
2
1
1
0
0
1
2
0
2
1
1
1
0
1
0
1
0
0
2
1
1
2
1
1
1
0
0
0
0
0
1
0
1
0
2
0
2
0
0
0
1
1
1
0
1
1
1
0
1
1
0
1
1
0
1
1
1
0
1
1
1
0
2
1
1
1
0
1
1
1
1
1
0
1
1
1
0
2
0
1
1
1
1
1
0
2
0
1
0
1
2
0
2
1
1
0
2
0
0
2
2
2
2
1
1
0
0
0
1
2
1
1
2
1
0
1
0
0
0
2
1
1
1
0
1
1
1
0
2
1
0
1
0
2
1
1
1
1
0
0
1
1
0
0
3
0
1
1
1
0
1
0
0
1
1
1
0
1
2
0
1
0
1
0
1
2
1
2
0
1
0
2
1
1
0
0
0
1
1
0
0
1
3
0
1
0
2
1
0
1
2
0
0
2
1
1
2
0
2
2
1
2
0
1
1
0
0
1
1
0
1
1
1
0
2
2
0
2
2
2
2
2
1
0
1
1
2
1
2
1
1
1
1
1
1
2
2
0
1
2
2
0
1
0
1
0
1
1
0
0
2
1
2
0
1
0
1
1
1
1
2
2
0
1
1
0
2
2
0
1
0
1
1
1
1
1
1
1
2
1
0
1
2
0
1
1
2
2
1
0
1
1
2
1
1
0
2
0
2
2
2
1
1
2
2
2
1
1
0
1
1
0
2
2
2
0
1
1
0
1
0
2
1
1
2
1
1
2
2
1
1
0
1
2
0
1
0
1
1
0
1
1
1
1
2
1
1
1
1
2
3
0
1
0
2
1
1
0
1
2
0
0
1
0
2
3
1
2
0
1
0
1
1
2
0
0
2
2
2
2
1
2
1
1
1
0
2
0
1
1
0
3
1
2
2
2
0
0
1
2
1
1
1
1
0
1
1
2
1
1
2
1
1
2
1
0
0
1
0
0
2
1
1
1
0
1
1
1
2
1
0
0
0
1
0
1
1
2
0
1
1
1
1
1
2
0
0
0
0
3
1
0
1
2
1
2
1
1
0
2
1
1
0
0
1
1
2
0
1
1
1
0
0
0
0
0
0
1
1
1
2
0
0
0
1
0
1
0
1
1
1
0
1
2
0
2
0
1
0
1
1
3
1
1
1
0
1
2
0
1
0
1
2
0
1
1
0
1
1
0
0
2
1
1
0
0
1
0
13
1
1
1
3
0
1
1
2
2
0
0
2
0
2
0
0
1
0
2
1
0
0
1
1
0
2
1
0
1
0
1
0
1
1
0
2
1
1
1
0
1
1
1
0
1
1
1
0
1
0
0
2
0
1
0
2
0
2
2
0
1
2
0
0
2
1
0
0
0
0
2
0
1
1
0
1
1
1
1
0
1
1
0
0
0
2
1
1
1
1
1
1
1
2
0
1
1
0
1
0
0
1
1
1
1
2
1
2
0
0
1
1
0
1
1
0
0
1
0
1
1
1
1
1
2
0
2
2
1
1
1
2
0
1
1
2
2
1
0
1
2
0
2
1
0
0
1
2
2
1
2
1
2
0
1
0
1
1
0
1
1
1
3
0
0
0
1
2
1
1
1
2
1
1
2
1
0
1
2
1
1
1
2
1
1
0
1
2
1
1
2
2
2
2
1
3
1
2
0
2
2
1
1
0
2
1
1
1
1
1
1
1
1
1
1
0
1
1
1
0
0
2
0
2
0
0
1
2
1
3
2
0
1
1
1
1
1
1
1
1
0
0
0
0
1
1
1
2
0
1
1
1
1
2
1
1
1
1
2
1
2
0
1
1
2
1
0
0
2
0
2
1
0
1
2
0
1
1
0
1
1
1
0
0
0
1
0
2
2
2
2
1
0
0
0
1
1
1
0
1
0
0
2
0
1
1
1
1
1
0
1
1
1
2
1
0
0
1
0
3
1
1
1
2
0
1
1
0
1
1
1
2
1
0
2
1
1
2
0
0
2
2
1
1
1
1
1
2
0
1
2
1
1
0
1
0
1
1
0
0
2
10
1
0
1
2
2
0
1
2
0
2
0
2
0
0
0
0
1
0
0
1
0
0
0
1
1
1
2
1
2
0
0
1
1
1
1
1
1
0
0
0
2
1
3
0
1
1
0
2
1
1
1
0
1
2
0
2
0
1
2
1
1
1
1
2
0
1
1
1
0
0
2
1
1
0
1
1
2
0
1
0
1
2
2
1
0
0
0
0
2
1
1
1
1
1
1
0
1
4
1
0
1
1
0
1
0
1
1
1
2
1
1
1
1
2
1
1
1
2
1
2
1
0
1
1
1
0
1
1
0
2
0
0
1
0
0
0
2
2
0
0
1
2
1
0
1
1
1
2
2
0
2
2
0
1
1
1
2
2
1
2
0
0
0
0
1
1
1
5
2
1
2
2
1
1
1
2
1
2
0
2
1
2
1
1
2
1
2
2
1
0
2
2
1
0
0
1
1
1
5
2
1
1
1
0
0
1
1
1
2
1
2
1
2
0
1
1
1
2
2
1
1
1
2
0
2
1
1
0
0
2
0
1
2
1
2
1
1
1
0
1
2
0
1
3
0
0
0
1
1
2
1
2
1
1
1
2
0
2
1
0
3
2
2
2
0
1
1
0
1
1
1
0
2
0
0
2
1
0
1
1
0
2
1
2
1
2
0
1
1
0
0
2
1
2
2
2
2
0
0
0
1
1
1
1
1
2
2
0
0
0
0
1
1
2
1
0
1
1
0
1
1
1
0
2
1
2
2
0
1
1
1
1
0
1
0
0
0
1
0
0
1
0
1
0
1
0
1
1
2
1
0
2
2
1
1
0
0
1
2
1
0
0
0
1
0
0
1
2
0
1
2
1
1
2
2
2
1
1
2
0
1
1
0
1
2
0
2
1
1
0
1
2
1
0
0
2
0
2
1
1
1
1
0
0
1
2
0
1
0
1
1
1
1
2
1
0
0
1
0
0
2
0
1
2
1
0
1
0
3
2
0
2
1
1
1
2
1
3
2
0
4
1
1
0
0
1
1
2
1
1
1
1
1
1
2
2
1
1
0
0
1
1
1
0
0
1
1
1
2
2
2
0
2
1
1
0
1
0
1
0
0
0
1
0
2
2
1
0
2
2
1
2
1
1
1
2
1
2
0
0
1
2
0
1
3
1
1
0
1
2
0
0
1
1
1
2
0
1
1
1
1
1
0
1
2
2
2
1
0
0
1
1
1
1
2
1
1
1
1
0
2
1
0
1
1
1
1
1
2
2
2
1
0
0
1
2
0
2
2
1
0
2
1
1
2
1
1
2
1
1
1
3
1
1
0
4
0
1
1
0
1
1
1
0
0
0
0
2
2
2
1
0
1
1
1
0
2
0
1
1
0
0
1
0
0
2
2
1
2
1
1
1
1
0
1
0
1
2
1
1
1
0
0
1
0
1
2
1
0
0
0
1
1
3
2
1
2
1
1
1
1
2
1
1
0
2
1
2
0
0
1
0
1
1
1
2
2
0
1
0
2
1
0
0
1
1
0
2
2
0
2
2
2
1
1
2
1
2
2
0
1
0
1
0
1
0
1
1
1
1
2
1
0
1
0
0
2
1
1
2
1
0
1
1
2
0
3
2
1
2
1
1
2
1
0
1
1
1
1
1
2
2
1
1
1
1
0
1
0
1
2
1
0
1
1
0
2
0
2
1
1
1
2
1
2
1
0
1
1
0
1
4
2
1
1
1
0
2
1
0
0
1
1
2
1
1
2
0
2
2
0
1
1
1
0
1
0
0
1
0
2
1
0
2
1
2
1
0
0
1
1
1
2
1
0
1
2
0
2
3
1
3
1
1
0
0
1
1
0
1
2
0
0
0
1
1
0
1
2
0
3
0
1
0
1
2
2
0
2
1
0
2
0
1
1
1
0
1
0
1
2
2
0
0
1
1
0
1
0
2
1
0
2
1
0
1
1
2
0
1
1
1
1
2
1
0
2
0
0
2
1
0
0
0
1
2
2
1
2
0
1
0
2
0
0
0
0
1
2
0
1
1
0
0
0
1
1
2
2
1
2
0
3
0
1
1
0
1
1
0
0
1
1
0
0
1
0
2
1
1
1
0
1
1
2
1
0
1
2
0
0
1
2
0
1
1
0
0
0
2
1
0
1
1
1
2
2
1
1
0
1
1
1
3
1
0
1
1
3
2
2
0
4
0
0
1
2
1
0
0
2
1
1
2
0
1
2
2
1
2
1
0
1
1
0
2
0
1
0
0
2
0
0
2
1
2
1
2
1
1
2
2
0
0
0
0
1
1
1
1
0
1
0
2
0
2
1
0
1
0
1
1
2
0
2
0
1
1
1
2
1
1
2
2
1
1
1
0
2
1
0
0
0
1
0
1
1
1
2
2
1
1
1
1
1
1
1
0
1
1
0
1
2
0
0
1
0
1
1
0
1
1
0
1
1
1
1
2
0
0
1
0
1
2
0
0
1
2
1
0
1
0
1
2
2
1
1
2
1
1
1
1
1
1
2
2
0
1
0
2
2
2
1
3
2
1
2
1
1
1
2
1
1
2
0
1
1
1
1
1
0
0
1
1
0
1
2
0
1
1
0
1
1
1
0
2
1
1
1
1
1
1
2
1
1
0
1
1
1
2
2
0
2
2
1
0
1
0
1
1
1
1
0
0
0
2
1
1
1
0
0
0
1
2
1
2
0
3
2
0
2
1
0
1
0
1
2
0
1
1
0
0
2
0
0
1
1
0
2
0
1
0
1
0
1
1
1
0
0
1
3
2
1
0
1
2
0
1
1
2
1
1
1
1
2
0
2
2
0
2
1
1
2
1
1
1
0
5
0
0
2
2
1
1
1
0
1
2
0
2
2
1
2
1
2
2
2
1
2
2
1
0
2
1
0
0
1
1
1
1
0
2
1
2
1
0
2
1
0
1
0
1
0
0
0
2
1
0
1
1
0
1
1
1
1
1
1
1
1
3
1
2
0
0
2
0
0
5
2
2
2
1
0
0
2
1
0
1
1
1
2
0
0
2
0
2
1
2
1
0
2
0
1
2
1
1
0
0
1
1
1
0
1
1
2
1
0
0
0
1
2
1
1
1
2
0
1
2
1
1
1
0
1
0
0
1
2
1
1
2
0
0
0
1
1
3
3
1
0
1
0
1
2
1
2
0
1
1
3
0
0
1
1
1
2
2
1
2
1
0
1
2
0
1
2
0
2
1
0
2
1
2
2
1
2
0
1
2
2
1
0
0
0
1
0
1
1
1
0
1
1
1
0
1
2
1
0
2
1
1
1
0
0
1
2
0
0
1
2
0
1
1
2
2
1
1
0
0
1
0
1
1
1
1
1
1
0
1
0
0
1
0
0
2
1
0
0
0
0
2
2
0
2
1
2
1
0
2
0
2
0
1
2
1
2
1
1
2
0
1
0
0
0
0
2
1
0
2
1
2
2
0
0
0
1
0
1
2
0
0
0
0
1
1
4
1
2
0
0
1
1
0
1
1
2
1
0
0
2
1
0
1
1
2
0
0
0
1
1
0
2
1
1
2
2
1
1
1
1
1
1
0
2
3
0
1
1
2
1
1
1
0
1
0
1
2
2
0
1
1
1
1
1
0
1
1
0
1
0
2
1
0
2
1
1
1
1
0
1
1
1
1
1
2
1
1
0
0
1
0
2
2
0
1
2
2
2
2
1
2
1
0
2
2
0
1
1
1
0
1
1
0
2
1
0
1
1
2
1
0
0
3
1
0
2
0
2
0
0
1
1
0
1
0
2
2
1
1
1
3
0
1
1
0
2
0
2
1
1
2
0
0
1
1
1
1
1
2
1
0
2
0
0
1
0
1
0
0
0
1
0
2
2
2
1
0
0
1
1
1
1
1
1
1
1
1
1
2
1
1
2
0
1
0
2
0
1
1
1
1
1
2
1
0
2
0
0
1
1
2
1
2
1
1
0
1
0
1
0
2
0
2
1
2
2
0
1
0
1
1
1
1
2
0
1
1
0
2
1
1
0
1
2
1
2
0
1
1
1
0
0
2
0
2
2
0
1
2
1
2
1
1
0
1
0
1
0
0
1
1
2
2
2
0
0
1
1
1
1
2
0
1
0
1
2
0
2
2
1
1
2
2
2
2
1
0
1
0
1
0
0
0
0
0
2
0
2
1
0
0
1
1
2
2
1
0
2
2
1
0
0
1
1
1
1
0
2
0
0
1
0
1
0
0
1
1
1
1
0
1
1
2
0
4
1
1
2
1
0
2
0
0
2
1
1
2
0
1
1
0
1
1
1
0
1
0
1
2
0
2
1
2
1
1
1
1
1
1
0
1
2
3
1
0
1
1
0
0
1
1
1
1
2
2
2
0
1
1
2
1
1
3
2
2
2
0
0
2
1
1
2
1
0
1
0
1
2
3
0
1
0
0
2
1
0
0
0
1
1
0
1
1
1
0
0
1
1
1
1
1
1
1
0
2
0
0
0
1
1
0
0
2
2
0
0
2
1
2
1
1
0
1
1
1
1
1
1
0
0
1
1
2
2
1
5
1
1
1
1
0
1
1
1
0
3
0
2
2
0
1
0
0
1
1
3
3
1
1
1
0
0
1
0
0
1
1
1
1
1
0
1
1
1
1
2
0
1
0
1
1
0
0
0
0
1
1
2
1
0
1
0
0
0
2
3
2
2
2
1
0
1
1
0
0
2
2
1
0
1
2
1
0
0
0
2
2
1
1
2
2
2
2
2
1
0
1
1
1
2
0
1
2
1
0
2
2
1
1
0
2
0
0
1
2
0
1
1
1
0
1
2
1
1
0
1
0
1
1
1
2
1
1
0
1
1
1
0
1
1
6
1
1
2
0
0
2
1
2
1
1
1
0
0
1
2
1
1
2
1
1
1
1
1
0
2
0
0
2
0
1
1
2
1
2
1
1
0
1
4
2
1
1
1
0
1
1
1
0
2
2
1
0
1
1
1
0
1
1
1
0
1
1
1
1
2
0
1
2
0
1
1
1
1
1
0
0
1
0
1
1
1
0
1
0
2
1
2
1
1
1
0
1
1
0
1
0
2
0
1
1
2
0
1
1
1
1
1
1
2
0
1
0
1
1
0
0
2
0
0
0
1
1
1
2
0
2
1
1
0
2
0
1
0
0
2
0
1
2
1
0
1
0
1
2
0
0
1
2
0
1
0
0
2
1
1
1
1
1
1
1
0
0
1
2
1
0
1
1
2
1
1
1
0
1
0
2
0
0
2
0
2
1
2
2
1
1
2
0
0
0
0
1
2
3
0
1
1
1
1
1
1
2
2
2
1
1
2
0
2
2
1
1
1
0
1
1
1
0
2
1
1
0
1
2
0
1
2
1
1
2
1
2
2
1
1
1
1
0
2
1
2
2
1
2
0
0
1
1
0
2
2
1
1
0
0
0
2
0
0
1
0
1
0
2
0
0
0
2
0
1
2
1
1
1
1
0
0
2
1
1
2
2
0
1
0
1
2
1
1
1
1
2
2
2
1
1
2
0
1
2
1
1
1
1
1
1
0
0
2
2
1
1
1
1
2
0
0
0
0
0
0
1
0
1
1
1
1
0
1
1
1
1
2
0
1
0
2
0
2
1
2
0
2
0
0
1
0
0
0
1
1
0
0
2
1
1
1
2
2
1
2
0
0
0
1
0
2
0
0
0
1
1
2
0
2
1
1
0
0
1
1
0
0
1
2
0
2
2
0
1
1
1
0
1
1
2
0
2
1
0
1
0
0
2
1
1
2
1
2
2
1
1
1
1
0
1
1
0
1
0
0
0
1
1
1
1
2
1
2
2
1
1
2
1
1
1
0
1
1
1
0
1
1
0
0
0
1
0
0
1
1
0
0
0
1
1
1
1
1
0
1
1
0
2
1
0
1
1
0
0
0
1
0
1
1
2
0
1
1
2
1
2
1
1
0
0
1
1
1
1
1
0
0
1
0
0
0
0
1
1
1
2
1
0
1
1
1
0
1
1
0
1
0
1
1
1
1
0
2
2
0
1
1
0
1
1
1
1
1
1
1
0
1
0
0
1
1
1
0
2
0
0
0
1
1
1
1
0
0
1
0
2
1
1
2
0
1
1
2
1
0
2
1
1
0
1
2
1
0
2
0
0
0
1
1
0
0
2
0
1
1
3
2
2
0
2
2
2
2
0
3
2
1
0
1
1
1
0
2
1
1
2
0
0
1
1
1
1
1
0
2
0
2
0
0
1
1
1
1
2
1
2
1
2
0
1
1
0
1
1
1
1
0
2
0
0
2
1
1
0
1
1
2
0
2
1
1
1
0
0
2
1
0
1
1
0
0
2
0
0
1
1
0
1
1
0
0
1
2
0
1
0
0
1
0
0
1
2
1
2
3
2
0
0
2
2
3
1
1
0
0
1
1
0
1
1
1
1
0
1
1
1
0
0
0
1
1
0
2
0
0
1
1
1
2
1
0
1
2
1
2
0
1
0
2
1
1
1
2
1
0
0
1
0
0
0
1
2
1
0
1
0
2
0
2
1
1
2
1
0
2
4
0
1
2
1
0
1
0
0
1
0
1
1
0
2
1
0
1
0
0
0
2
1
0
2
1
0
0
0
1
1
0
0
1
1
1
1
0
1
1
1
1
0
0
0
1
1
2
1
1
1
0
0
1
1
2
0
1
0
1
1
1
1
1
2
2
1
2
0
0
0
1
2
2
0
1
4
2
1
1
1
1
1
0
1
2
2
2
0
3
1
0
1
2
0
0
0
1
0
0
1
1
1
0
1
0
0
0
0
1
0
1
2
0
0
1
0
1
0
0
0
1
1
1
2
0
2
1
1
0
0
0
0
1
1
1
1
0
1
2
1
0
1
1
0
1
2
2
1
1
0
0
2
1
0
1
1
1
0
1
1
2
1
1
1
1
1
1
0
1
0
1
2
1
1
2
0
2
0
0
0
1
1
1
0
2
1
1
1
0
1
1
2
0
2
2
2
1
2
0
1
1
2
1
1
1
2
0
2
0
2
3
2
2
1
1
1
1
2
1
1
2
2
1
1
1
2
2
1
0
0
2
0
1
1
1
0
2
1
1
0
1
2
0
1
1
0
2
0
0
0
0
1
1
0
1
2
1
1
0
1
1
1
1
1
1
0
1
1
0
1
1
2
1
0
1
2
1
1
1
1
1
0
2
1
1
1
1
2
0
1
1
2
1
1
0
0
1
0
2
1
2
1
2
0
2
2
0
1
3
1
2
1
1
0
0
3
1
0
1
1
0
0
0
0
2
0
0
0
1
0
2
1
0
1
2
1
1
2
0
2
0
0
0
2
0
0
1
1
2
1
2
0
0
0
0
1
1
0
0
1
0
0
0
0
0
2
1
0
2
0
1
1
1
0
1
1
0
0
0
2
3
1
1
0
0
2
0
1
1
2
2
1
0
2
1
1
0
1
1
1
2
0
0
1
0
2
2
2
1
1
2
2
1
0
1
0
2
0
2
1
3
1
0
1
2
1
1
1
1
0
1
0
2
2
0
0
0
2
2
1
0
0
1
1
2
1
2
2
0
0
1
0
0
1
1
0
0
0
1
0
2
0
1
1
1
1
0
0
2
0
2
1
0
1
1
2
1
1
0
0
0
2
1
2
0
0
1
2
1
2
1
0
0
1
1
0
1
0
2
0
0
0
2
0
0
0
1
2
0
2
0
1
2
0
0
0
1
1
1
1
1
0
2
2
2
0
1
2
0
0
1
1
0
0
1
2
0
1
0
1
1
1
1
1
0
1
0
1
2
0
2
2
0
2
1
1
0
1
3
2
1
0
0
0
1
0
2
0
0
1
2
2
1
0
1
1
1
0
1
1
1
1
1
1
2
0
1
1
1
1
0
1
0
2
2
1
0
1
2
2
0
1
1
0
1
1
1
1
0
1
1
1
0
2
2
2
1
0
0
1
1
2
1
0
2
2
0
1
0
0
1
2
0
0
1
1
0
0
0
1
0
1
1
1
2
1
1
1
1
1
1
0
2
2
2
1
1
0
0
1
1
2
1
1
2
1
1
1
0
1
0
1
2
1
2
1
1
2
1
1
0
0
0
1
1
0
2
2
2
1
0
1
1
0
1
2
0
0
1
2
1
0
1
1
0
1
1
1
1
1
0
1
0
2
2
1
0
0
1
2
2
1
1
0
1
1
1
1
1
1
0
2
1
1
1
0
0
2
0
1
0
0
0
4
2
1
2
0
1
2
1
0
1
1
0
1
2
0
1
1
1
0
0
0
0
0
3
1
2
1
2
0
2
0
1
1
2
1
1
0
1
2
0
0
1
1
0
1
2
1
2
2
1
0
2
1
2
0
1
0
0
2
1
2
2
0
0
1
1
1
0
0
0
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
0
0
1
1
0
1
0
1
0
1
0
0
0
1
0
1
2
1
1
1
1
0
2
1
2
1
0
0
2
1
2
1
1
1
1
2
1
1
2
0
2
1
0
1
2
2
1
1
0
0
0
0
0
2
1
1
0
1
1
1
1
0
1
1
1
2
2
1
0
1
1
1
1
1
1
1
1
0
1
1
0
1
1
0
1
0
2
0
0
0
2
0
2
2
0
0
3
2
1
0
1
0
1
0
1
0
2
2
0
1
2
0
0
2
1
1
0
1
1
0
1
1
2
0
1
1
1
0
2
2
2
0
2
1
2
0
2
1
1
0
2
3
0
0
2
1
1
1
0
1
2
2
0
0
1
2
1
1
1
1
2
0
1
2
1
2
0
0
1
0
2
0
1
0
1
1
2
2
1
0
1
1
0
1
2
1
0
2
0
0
0
1
2
2
1
0
1
0
1
1
1
0
1
0
3
1
1
1
0
1
2
1
1
2
0
1
2
1
0
1
0
1
1
1
1
2
1
2
0
0
1
2
1
0
1
2
2
2
0
1
0
0
1
1
1
0
0
1
2
0
0
1
2
0
2
2
0
2
0
0
1
0
1
1
0
0
1
1
1
1
1
1
1
1
1
0
2
1
1
1
0
2
2
1
0
0
0
38
0
1
0
2
0
1
0
1
1
1
0
0
0
1
1
1
1
1
1
0
0
1
1
1
1
1
2
1
0
0
1
0
1
0
0
2
1
1
1
1
1
0
1
1
1
3
0
1
0
1
1
0
1
2
1
0
2
1
3
0
1
0
0
0
1
0
0
1
2
2
1
1
2
1
2
1
2
2
1
1
2
2
1
1
2
1
1
1
0
2
0
1
2
2
1
2
0
1
1
1
1
2
2
0
2
1
2
2
0
0
1
0
2
1
0
1
1
0
1
2
0
2
0
0
2
1
1
1
0
1
0
2
2
1
1
1
0
0
0
1
1
1
1
1
0
2
0
2
0
2
1
1
1
1
0
1
0
0
0
1
2
0
1
1
1
0
0
0
1
1
0
2
0
0
0
1
0
1
0
1
1
1
0
1
1
0
2
0
0
0
1
1
0
2
1
0
1
1
1
2
0
1
2
0
1
0
1
1
2
1
1
2
0
16
0
0
1
1
1
1
2
2
1
1
1
2
1
0
0
2
0
2
1
0
1
2
0
0
0
0
1
0
1
2
0
1
2
2
1
1
0
1
1
1
1
0
1
2
0
0
1
2
1
1
1
0
0
1
1
1
2
1
1
1
0
1
0
1
1
0
0
1
2
1
1
1
1
1
1
1
1
2
0
1
1
0
0
2
0
0
1
1
1
1
0
0
1
0
2
2
2
0
1
1
0
0
0
2
1
1
0
2
0
1
0
1
1
0
1
1
1
1
1
0
0
1
1
1
0
1
0
2
1
1
1
0
0
1
2
1
1
2
1
0
2
1
0
0
1
1
2
1
0
2
0
2
1
1
2
0
1
1
2
1
1
1
1
2
1
2
1
2
0
2
1
1
1
0
1
2
0
0
2
1
1
1
1
1
0
1
2
1
2
2
0
1
1
1
2
3
2
2
0
1
1
0
2
1
2
0
0
2
0
1
1
1
1
1
0
0
1
0
0
1
1
1
2
0
0
2
2
1
0
1
1
0
0
1
1
1
1
2
2
1
2
1
2
1
2
1
1
0
3
1
1
1
1
0
0
2
0
0
0
1
1
1
0
1
2
1
0
2
1
0
1
0
1
2
1
1
0
0
1
1
1
0
0
2
2
1
1
2
0
2
2
1
0
1
2
2
0
1
0
1
1
2
0
0
0
1
0
1
2
1
0
2
1
0
1
0
0
0
3
2
1
2
0
0
1
1
0
0
2
0
0
1
2
0
1
0
0
2
0
0
1
0
0
0
0
0
2
0
1
1
1
1
2
1
1
1
1
1
0
1
1
0
1
1
0
0
0
1
2
0
2
1
2
2
1
1
1
1
2
2
0
1
1
1
0
0
0
1
4
2
2
2
1
0
1
0
1
0
2
1
1
1
0
0
1
0
0
2
1
1
1
0
1
0
0
0
0
1
2
2
2
1
0
0
0
1
0
0
1
0
0
0
2
1
1
0
0
0
1
2
1
1
0
1
1
2
1
1
2
1
1
2
1
2
1
2
1
3
0
1
0
2
0
0
2
0
1
1
1
2
1
2
2
1
1
0
0
0
1
1
1
0
1
1
1
0
0
1
1
0
1
2
1
2
1
3
3
1
1
1
1
0
1
2
0
2
1
2
0
1
0
1
1
1
1
1
1
2
0
0
0
1
0
1
1
1
2
1
1
0
0
1
2
1
1
2
1
1
1
0
1
2
0
0
0
1
0
0
1
2
1
1
1
0
1
1
0
0
2
1
2
2
1
0
0
1
1
1
0
1
2
2
1
1
2
0
1
1
1
0
0
1
2
2
1
2
1
1
1
0
1
1
2
2
0
0
2
0
2
2
0
2
1
2
1
1
1
2
2
0
1
0
1
2
2
1
0
0
0
1
1
0
0
0
2
1
1
0
0
2
0
2
1
1
2
1
1
0
2
1
1
2
0
2
0
1
0
0
2
2
1
2
2
1
1
0
2
1
0
1
1
2
2
0
1
0
1
1
2
2
1
1
1
0
0
2
1
2
1
1
1
1
0
2
1
1
1
0
0
1
0
1
1
2
1
0
1
0
2
0
2
0
1
2
1
1
2
0
0
1
2
0
0
1
0
1
3
0
2
0
1
2
3
1
2
0
1
1
1
1
2
1
1
1
1
0
1
0
0
2
3
0
0
2
0
0
1
1
0
0
1
0
1
1
2
0
1
0
0
0
1
0
0
0
0
2
1
2
0
1
2
1
0
2
1
0
2
1
1
2
0
0
0
0
1
0
0
0
1
1
2
1
1
0
1
1
1
2
1
0
1
2
10
0
0
2
0
2
0
1
2
2
1
2
1
2
2
1
0
0
0
1
2
1
0
1
2
2
0
0
1
1
0
0
2
3
1
2
0
2
2
0
2
0
1
2
1
1
1
2
1
0
0
1
2
1
0
1
1
1
0
0
0
2
2
1
0
1
2
1
2
1
1
0
0
0
0
1
1
1
2
1
2
0
0
0
1
1
2
1
1
1
1
1
0
1
1
1
0
0
1
3
2
0
1
2
0
0
1
1
1
2
1
0
1
0
0
1
2
0
2
1
1
2
2
1
0
2
3
0
1
1
1
2
1
1
1
0
1
1
0
1
0
0
0
1
0
2
1
2
1
1
1
2
2
1
2
2
2
1
0
0
0
1
1
1
1
1
0
0
1
0
0
1
1
1
0
1
1
1
2
2
1
2
2
0
1
0
0
2
2
2
0
1
3
0
2
1
1
0
1
0
2
2
2
1
1
0
0
2
3
1
0
1
1
2
1
1
0
1
1
1
1
0
1
0
0
0
0
0
1
0
0
1
1
2
0
1
1
0
2
0
1
0
0
2
1
1
0
0
1
2
1
0
2
0
1
1
1
0
1
1
0
2
0
0
0
1
0
1
0
0
1
0
0
2
2
0
0
2
1
0
0
0
1
1
0
0
2
0
1
0
2
1
1
0
0
1
1
1
1
0
2
0
1
0
2
1
1
1
2
1
0
1
1
0
2
1
1
0
0
0
0
2
0
2
0
1
2
1
2
1
1
1
1
0
0
1
1
1
1
1
2
0
1
1
0
2
1
1
2
0
0
2
0
0
2
1
1
1
0
0
1
3
2
0
2
1
1
0
0
1
1
0
1
2
2
0
0
2
0
1
1
1
1
0
2
0
0
0
0
0
1
0
1
1
1
1
1
0
0
1
1
2
0
1
2
2
1
0
1
1
1
0
1
2
0
1
0
0
1
1
0
1
1
1
1
0
1
2
2
1
1
0
1
1
0
0
0
0
1
1
1
1
1
2
2
0
2
2
1
2
1
0
0
1
0
2
1
0
0
0
2
1
2
1
2
2
0
1
1
0
1
2
1
1
2
0
1
0
0
0
0
1
1
0
1
2
2
0
1
1
0
1
1
1
2
1
1
2
0
0
1
0
2
2
3
2
0
1
0
2
0
1
1
0
1
1
0
1
2
1
0
1
1
1
1
2
1
1
0
1
0
0
1
0
0
1
0
0
2
2
2
2
1
1
2
1
0
1
2
1
1
1
0
1
1
2
1
0
1
1
0
1
0
1
1
2
3
2
0
1
1
0
2
2
2
0
1
0
0
0
0
0
1
2
2
1
0
1
2
4
2
2
1
2
0
0
2
0
1
1
1
0
0
2
1
0
0
2
1
0
1
1
2
0
1
2
1
1
0
1
1
1
1
0
0
1
1
0
1
0
2
0
1
0
0
1
1
0
2
2
0
2
0
0
0
1
1
0
2
0
0
1
0
0
0
2
1
2
0
0
0
2
1
0
2
0
1
1
2
1
2
2
1
0
1
2
2
2
0
1
1
0
2
1
1
2
0
0
2
2
1
2
1
1
0
1
2
1
1
1
2
0
1
1
2
0
2
1
1
1
0
0
1
2
2
1
1
1
1
2
2
2
1
1
2
0
0
1
1
0
0
2
1
1
0
2
1
2
1
0
1
1
2
1
2
1
2
1
0
1
1
0
1
0
0
1
0
1
1
0
0
1
1
2
0
0
0
1
1
1
3
2
1
0
1
0
1
1
1
2
0
1
1
0
1
0
1
1
2
1
1
0
2
1
0
0
2
0
0
1
1
0
0
0
0
2
0
0
2
2
1
2
0
1
0
1
0
2
1
0
0
1
1
2
2
2
3
1
0
1
0
1
1
1
0
1
0
0
0
0
1
2
0
2
0
1
1
0
2
0
1
0
0
2
1
2
2
0
1
0
1
0
1
0
1
0
1
1
2
0
1
1
0
2
1
1
0
0
0
1
2
2
1
1
0
0
1
0
2
1
0
1
1
0
1
0
1
0
2
1
0
2
1
0
0
0
2
2
1
0
1
1
0
2
0
0
0
0
1
1
0
2
0
1
0
2
1
1
2
2
2
0
0
2
0
1
0
1
1
1
1
1
1
1
1
1
0
1
1
1
0
2
0
2
2
1
3
2
1
1
0
1
2
0
1
0
2
1
1
1
1
1
0
0
1
1
0
1
0
0
2
2
1
0
1
2
0
0
1
1
2
2
1
2
0
1
1
0
0
1
0
1
2
0
2
2
0
1
2
0
0
1
1
1
1
2
2
0
0
2
0
3
0
0
1
1
1
1
1
0
0
1
1
0
2
2
1
1
0
0
0
2
0
1
0
1
1
1
1
1
1
1
1
0
1
1
1
2
0
1
1
1
1
2
1
0
2
1
2
1
2
1
0
1
1
0
1
0
0
0
1
0
0
0
1
1
0
0
2
0
2
1
0
1
2
0
1
0
1
2
2
2
0
1
2
1
2
2
1
0
2
0
0
1
2
1
1
1
0
0
1
2
2
2
0
1
1
0
1
1
1
1
2
1
2
1
2
1
1
1
2
3
0
0
0
1
1
0
2
2
1
1
0
2
1
1
1
1
0
1
1
2
0
1
1
0
2
1
1
3
1
0
1
0
1
1
0
1
1
0
5
1
1
1
1
1
2
1
2
0
1
2
2
2
2
0
1
0
2
1
0
0
0
0
1
1
2
0
0
1
1
1
0
1
2
2
1
2
1
1
1
2
2
2
2
1
2
1
0
1
1
1
2
1
2
1
1
1
2
2
2
1
2
1
1
0
1
1
0
0
1
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
2
1
1
0
0
1
2
0
1
0
1
0
2
1
2
1
0
2
3
2
0
1
0
0
0
0
0
1
1
1
1
1
0
0
1
2
0
1
0
2
1
1
2
1
0
0
2
1
0
1
0
0
1
2
1
1
0
0
2
1
1
2
0
0
0
0
1
1
1
2
0
1
0
0
0
2
0
5
2
0
0
2
1
0
1
1
0
1
0
1
1
0
1
2
0
0
2
0
0
2
1
1
1
1
0
0
1
1
0
2
1
0
1
0
1
1
2
2
1
0
1
0
1
1
2
0
0
1
1
4
2
1
0
1
3
0
0
1
1
2
1
1
1
2
0
2
1
1
2
1
1
2
2
0
1
1
1
2
0
1
0
1
1
2
2
1
1
1
0
1
2
0
1
1
2
0
0
2
0
0
2
1
2
1
0
2
1
1
1
1
1
2
1
2
0
1
1
1
0
1
1
1
1
1
0
1
1
2
1
0
1
0
1
0
0
2
1
1
0
0
0
0
0
2
1
1
1
1
1
1
1
1
1
1
0
2
1
1
2
2
0
0
0
1
2
1
2
1
1
0
0
0
2
1
0
2
2
2
1
1
1
2
0
1
1
1
1
2
0
1
0
0
2
1
1
0
0
0
1
3
0
1
0
1
0
1
2
2
0
0
1
0
0
2
0
1
1
0
1
1
1
1
2
0
1
0
1
0
0
1
2
1
1
1
0
2
1
1
1
1
0
1
1
1
1
1
0
1
0
0
1
2
0
2
1
1
1
0
2
0
2
1
0
0
0
2
0
1
1
1
0
0
1
0
0
2
1
0
2
2
1
1
1
2
0
1
0
1
1
0
1
1
1
1
1
2
0
2
0
0
1
0
0
0
0
1
2
1
1
0
0
2
1
2
1
1
1
0
1
1
1
1
0
0
1
2
1
0
0
1
0
1
2
1
1
1
0
2
2
2
1
1
1
1
0
0
2
0
2
1
1
2
0
1
1
1
1
1
0
0
1
1
2
1
1
1
0
2
0
1
1
1
2
2
1
0
0
2
2
2
2
4
2
2
1
2
1
1
1
0
2
1
1
2
1
1
2
1
2
2
0
0
0
0
1
2
0
1
2
1
1
1
0
1
0
0
1
2
0
1
1
2
0
0
1
1
0
2
1
1
1
2
1
0
1
0
1
0
2
2
1
0
1
1
1
0
1
1
1
1
1
2
0
2
1
2
0
0
2
1
2
1
2
1
1
0
1
0
2
1
1
2
1
0
1
0
1
0
2
0
0
0
1
0
1
2
0
0
0
1
2
0
0
0
2
0
0
2
0
0
1
1
0
1
1
1
2
2
1
1
1
2
0
1
0
2
0
1
0
0
0
2
1
1
2
1
1
1
1
0
2
0
0
0
2
0
0
0
1
1
1
2
1
0
1
1
3
1
2
1
1
0
1
1
2
1
6
1
2
1
0
1
1
0
1
1
0
1
2
1
2
1
1
1
0
1
2
1
1
0
0
0
2
1
1
0
0
1
1
1
2
1
0
1
1
1
0
1
0
0
2
0
0
0
2
1
1
1
1
2
2
0
0
0
1
1
0
0
1
1
1
2
1
1
2
0
0
0
1
1
1
1
0
2
1
1
0
1
0
0
2
1
0
1
2
2
1
0
1
0
0
0
0
1
1
0
1
0
0
0
1
0
1
0
0
1
0
0
1
0
2
1
1
0
1
2
2
0
0
0
0
0
1
0
1
1
1
2
3
2
2
1
0
0
1
2
1
2
1
1
0
2
1
0
0
0
2
0
1
1
2
1
0
0
0
2
1
1
1
1
1
1
1
1
1
1
0
1
0
1
2
0
0
0
0
2
1
1
0
1
1
1
1
0
1
0
2
1
1
1
2
0
0
1
1
3
0
0
0
1
0
1
0
1
1
1
1
0
0
2
0
0
1
1
2
0
0
0
2
2
1
2
2
0
2
1
2
0
2
1
1
2
0
1
1
0
2
1
0
2
1
2
3
2
1
0
1
2
0
1
2
2
2
0
0
0
1
0
0
2
1
0
1
1
1
1
0
3
0
1
1
1
0
1
1
0
0
1
0
0
1
1
2
0
1
2
1
2
2
0
0
1
0
1
1
0
0
0
0
1
1
1
0
2
1
0
1
1
1
0
1
1
2
0
1
1
1
0
0
1
1
1
1
1
1
1
1
0
2
1
0
0
0
2
1
0
2
1
1
0
1
1
1
2
0
1
0
0
1
1
1
1
0
2
0
1
1
0
1
0
1
0
1
1
2
0
2
1
1
1
1
0
1
2
1
2
1
1
2
0
0
1
0
2
2
0
0
0
1
2
1
2
1
0
0
1
0
2
0
1
0
1
0
1
1
1
2
1
1
1
2
1
0
1
1
1
1
1
0
1
1
0
0
1
0
0
1
1
3
2
1
0
2
0
1
0
0
0
0
2
1
1
1
1
0
0
0
1
1
0
1
1
0
1
0
2
1
0
1
0
1
0
0
2
1
1
2
1
1
2
1
0
1
0
0
0
1
1
0
0
1
1
1
1
1
2
2
0
0
1
1
0
0
0
2
2
2
1
1
2
2
1
1
2
0
1
1
1
1
1
2
0
1
1
1
1
0
1
2
2
1
1
2
2
0
1
2
0
1
1
1
1
0
1
1
1
1
2
0
0
1
2
1
0
2
0
0
1
2
0
1
1
0
0
0
1
2
1
1
1
2
0
2
2
0
1
1
1
2
2
1
2
2
2
1
1
3
0
2
0
1
1
1
2
1
0
0
2
0
2
1
1
0
0
0
2
2
1
2
0
0
2
1
0
0
1
1
1
1
1
2
0
2
0
1
0
0
3
3
1
2
0
1
1
2
0
0
1
1
1
2
1
0
1
0
2
1
2
1
1
1
1
1
1
2
0
1
0
1
2
1
1
5
1
1
0
0
2
1
2
0
0
0
1
2
0
3
1
2
2
1
0
1
2
1
1
0
2
1
0
1
0
1
0
2
1
0
1
1
0
0
1
1
1
0
0
1
2
1
0
1
1
1
1
1
0
1
1
1
1
0
1
0
0
1
1
1
0
2
1
1
0
1
1
1
0
2
2
2
0
0
1
0
1
2
2
1
1
1
0
1
1
1
2
0
0
2
0
1
1
2
1
0
1
1
0
1
2
1
2
0
1
0
0
1
1
2
0
1
1
0
0
0
2
0
1
1
1
2
0
1
2
2
2
1
1
1
0
2
1
1
1
1
1
0
1
1
0
1
2
0
1
0
1
1
0
2
1
1
2
1
1
1
1
2
2
2
2
1
1
1
1
1
1
1
2
1
0
0
2
1
0
0
1
1
1
0
1
2
0
2
1
0
2
1
2
3
0
0
0
1
1
1
1
1
1
2
0
1
1
1
1
0
0
0
1
1
3
1
2
1
2
0
1
0
1
1
0
0
2
1
1
1
1
1
1
0
2
2
1
1
0
2
0
0
0
1
0
1
1
0
0
0
1
1
0
1
1
0
1
1
1
1
1
0
1
1
1
0
0
1
2
1
0
0
1
0
2
2
0
0
2
0
1
1
0
1
0
1
2
1
0
0
1
1
1
1
2
0
0
1
0
1
1
2
1
2
0
2
1
0
0
1
1
1
0
1
0
0
0
0
0
1
1
1
0
0
2
1
1
0
2
2
0
2
2
1
0
0
2
1
1
1
1
2
1
1
0
0
0
0
1
0
1
0
0
2
0
2
0
0
1
1
2
3
4
1
1
0
2
1
1
1
2
0
1
1
1
2
0
1
2
1
2
1
1
2
0
1
0
1
2
1
0
1
0
1
1
2
3
1
2
1
2
0
1
1
1
3
1
0
2
1
1
2
1
2
1
0
0
0
0
1
0
0
2
1
2
1
1
0
0
0
1
0
2
1
1
1
1
0
0
0
0
1
2
0
1
0
0
0
1
1
1
2
1
1
2
1
1
2
2
1
2
1
2
1
0
2
2
1
3
1
0
2
0
0
1
2
2
1
0
0
2
2
0
2
1
1
1
2
0
1
0
0
0
1
1
2
2
1
2
1
0
0
0
0
1
1
0
0
1
1
1
1
1
1
2
1
1
0
7
3
0
1
0
1
1
1
1
1
1
0
0
1
0
1
0
0
0
2
0
0
2
1
1
1
2
1
1
2
1
1
2
0
1
0
1
1
1
1
0
0
1
1
1
1
1
0
0
0
0
0
1
2
0
0
1
2
1
1
0
0
1
0
0
0
2
2
2
1
0
0
2
1
0
2
1
0
0
1
1
0
1
2
0
1
1
1
1
1
0
2
0
2
2
1
2
1
1
1
0
1
2
0
1
0
1
1
1
0
1
1
0
0
0
0
2
1
1
2
1
0
2
1
1
1
0
1
2
1
0
1
1
2
2
1
0
0
2
2
2
1
0
1
0
1
0
0
2
1
1
1
2
1
1
1
1
2
1
1
1
1
0
2
1
1
2
0
2
1
0
1
1
0
1
0
1
1
1
3
1
2
0
0
1
1
0
1
1
0
0
1
0
1
0
1
1
1
1
1
1
0
1
1
1
2
2
2
1
1
0
1
2
1
2
0
0
1
1
1
2
0
2
2
1
1
2
0
1
2
0
0
2
1
0
1
1
2
1
0
1
2
2
1
2
1
1
1
2
2
1
0
0
1
2
2
0
0
1
0
1
0
1
0
1
0
1
0
1
1
1
0
0
3
1
1
1
2
0
1
1
1
0
1
0
1
0
0
2
2
2
2
0
2
0
1
1
1
1
0
1
1
0
0
0
1
2
1
0
1
1
0
0
1
1
1
1
1
1
2
0
1
0
1
1
0
1
1
1
0
0
2
0
1
2
2
1
0
1
1
0
1
1
2
1
1
1
1
2
1
0
2
1
0
1
1
1
2
0
2
2
2
1
1
1
1
2
2
0
1
1
1
0
1
0
0
2
2
3
1
0
1
1
1
1
0
0
1
1
0
0
1
1
0
2
1
1
2
0
0
1
1
1
1
2
0
0
1
0
1
0
1
1
1
3
1
2
1
1
1
0
1
1
0
2
0
1
1
0
1
1
1
1
0
1
0
1
1
1
0
1
2
1
2
0
2
1
1
1
0
0
1
0
0
2
2
1
0
1
2
0
2
0
1
1
0
1
2
0
0
1
2
1
1
2
0
1
1
2
0
1
1
2
1
1
1
1
2
1
1
1
1
1
1
2
1
2
3
1
0
2
1
1
0
1
2
0
0
1
1
0
1
1
2
1
0
0
1
1
1
0
1
1
0
0
2
1
1
1
1
1
2
0
1
1
0
2
0
0
1
1
0
1
0
0
1
1
1
0
0
1
2
0
0
1
1
0
1
0
1
1
1
1
0
1
1
0
0
1
0
2
0
1
0
2
3
1
2
0
1
1
0
1
1
1
0
0
1
0
1
1
1
1
1
2
0
3
1
1
0
0
0
0
1
1
2
0
0
1
1
1
2
1
0
1
1
2
1
0
1
0
2
1
1
3
2
2
1
0
0
0
2
1
1
0
1
1
1
2
1
1
0
2
2
3
0
0
1
1
1
0
0
0
1
1
2
4
1
2
0
1
2
1
0
2
0
1
1
2
0
1
2
0
2
0
1
1
0
1
1
0
0
1
1
1
0
0
1
0
0
0
1
1
1
1
0
0
1
1
0
0
5
0
0
1
1
1
1
0
0
1
0
0
0
2
0
1
0
1
2
1
0
0
1
1
1
1
1
1
0
0
2
1
1
1
1
2
1
1
1
1
1
1
0
2
2
1
3
1
2
1
2
1
1
1
1
1
1
2
1
2
0
2
0
2
0
0
2
0
1
1
2
1
0
0
1
2
0
0
0
0
2
0
1
1
1
1
0
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
0
0
1
1
0
1
0
0
1
1
1
0
2
0
1
2
0
2
0
0
1
0
0
1
1
0
2
1
1
0
1
2
1
1
2
4
2
1
2
0
2
1
0
2
1
0
1
0
1
0
2
1
2
0
1
0
0
2
0
1
1
0
2
1
0
1
1
1
1
2
1
2
2
1
0
1
0
2
0
1
1
1
2
1
0
1
1
0
1
2
1
2
2
1
2
0
1
2
0
0
1
2
2
0
2
2
1
1
0
0
1
0
0
1
2
2
0
2
1
2
1
1
2
0
1
2
0
0
2
1
0
1
0
2
1
2
1
1
2
0
1
2
0
0
1
1
1
0
2
1
0
1
1
0
1
2
0
3
1
0
2
5
1
0
1
1
1
0
2
2
1
0
0
0
1
1
1
1
2
0
1
1
2
0
1
1
1
1
0
0
1
1
1
1
1
1
2
2
1
0
2
1
1
2
1
1
0
0
0
1
1
2
1
0
3
0
2
2
0
1
1
1
0
1
2
1
2
2
1
1
1
0
2
1
1
1
1
1
1
1
0
0
2
1
1
0
2
2
1
2
2
0
0
0
0
0
0
1
1
0
0
1
1
1
1
0
1
1
3
1
1
2
1
1
2
1
0
1
2
0
1
1
1
0
1
1
1
1
1
2
1
2
1
0
1
2
0
1
1
2
1
1
0
1
3
2
1
1
1
0
2
1
0
1
0
1
0
1
0
2
0
1
1
2
2
1
1
1
1
1
3
0
0
1
2
1
0
2
0
0
1
0
1
1
1
1
1
1
1
1
0
1
0
2
0
1
0
4
0
1
1
2
0
1
2
3
0
1
1
1
0
1
1
1
1
1
1
2
0
1
0
1
2
0
0
0
0
1
1
1
2
0
2
1
0
2
1
1
1
0
0
1
0
1
1
2
1
0
2
1
1
0
1
1
0
1
0
1
0
1
1
0
0
0
1
1
1
1
1
2
2
2
2
1
1
1
0
0
1
1
1
0
3
0
1
1
0
1
1
2
1
0
0
0
0
1
2
1
1
1
1
1
0
0
1
0
1
1
0
1
0
2
1
1
0
2
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
1
1
1
0
1
0
2
1
0
0
1
1
0
1
2
2
2
1
4
1
1
2
2
2
1
0
1
1
2
1
0
2
1
0
2
1
1
1
0
1
0
0
1
0
2
1
0
1
1
1
0
0
1
0
1
3
2
2
0
1
2
1
1
3
1
1
0
1
0
2
2
0
4
1
0
1
2
1
0
1
1
0
2
2
0
2
2
1
2
1
1
0
2
1
0
0
1
0
1
1
1
2
0
1
1
0
1
1
2
1
1
2
0
2
1
0
0
1
0
2
1
0
1
1
0
1
0
0
0
0
1
0
1
0
2
2
0
1
0
0
1
1
1
1
0
0
1
0
2
1
1
1
1
2
9
0
1
2
2
1
1
0
1
0
2
0
1
0
0
0
1
0
0
0
1
2
0
1
1
1
3
0
0
1
1
1
2
1
1
1
1
1
2
1
1
0
0
0
2
0
1
1
2
2
2
0
1
1
0
0
1
2
0
2
0
2
1
0
1
2
1
1
1
0
1
0
1
1
2
0
1
2
1
0
0
0
1
0
0
2
2
1
1
1
2
1
2
0
1
0
1
0
1
2
2
0
0
0
2
1
1
1
2
0
1
1
1
1
1
0
1
2
0
1
1
0
0
2
2
2
0
1
2
0
0
1
6
0
1
1
1
2
0
2
0
1
1
0
1
0
2
1
0
0
2
0
1
1
1
0
2
0
1
1
0
1
1
2
1
1
2
1
0
0
0
2
0
1
2
3
0
0
0
1
1
3
0
1
2
1
0
0
1
0
2
2
1
1
0
0
2
0
1
0
2
0
0
0
0
1
2
2
0
0
2
1
1
1
2
0
2
1
0
0
1
0
1
1
0
1
1
3
2
1
1
1
1
1
1
0
0
1
2
3
2
0
1
0
2
0
2
1
1
1
0
0
1
1
1
1
1
2
0
1
1
2
0
0
0
2
0
1
0
1
2
1
1
1
0
2
0
0
1
2
1
1
1
0
2
2
4
2
1
1
1
1
0
0
2
1
0
1
0
1
1
2
1
1
2
1
0
2
0
0
1
0
0
1
1
1
1
0
1
1
1
0
1
0
0
1
2
0
0
1
1
0
0
2
2
0
1
1
1
4
2
2
2
1
0
1
1
0
1
0
1
1
0
2
1
3
1
1
0
0
0
1
0
2
2
1
1
1
1
1
1
1
1
0
1
0
1
2
0
1
1
1
1
1
1
0
1
0
2
2
1
2
1
1
0
0
0
1
1
2
1
1
0
0
1
1
0
0
0
1
1
1
1
0
1
0
1
2
0
0
1
0
2
0
2
1
2
1
2
1
0
1
1
0
1
2
1
1
1
2
1
2
2
2
2
1
0
0
0
0
1
1
1
1
1
0
1
0
1
2
2
1
0
1
1
1
0
2
0
0
2
0
2
2
1
1
0
0
0
1
1
1
1
1
0
0
0
2
1
2
1
0
2
2
2
2
1
2
2
1
1
1
1
2
2
1
1
2
3
2
1
2
1
1
2
0
1
1
0
1
1
0
1
0
1
0
0
0
1
0
2
0
0
0
1
2
0
0
0
0
2
2
0
0
0
1
1
0
1
1
0
1
1
0
1
0
2
0
1
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
1
2
2
2
1
2
1
1
1
0
1
1
1
0
0
1
0
1
0
1
2
1
1
1
2
2
0
0
1
1
1
0
2
0
2
1
2
1
0
1
1
0
1
1
1
0
0
2
1
0
1
1
0
0
1
2
2
1
1
1
1
1
1
2
2
1
1
0
1
2
1
1
1
1
1
1
1
2
2
1
2
1
0
2
1
0
1
1
1
2
1
0
2
1
0
1
1
0
2
1
1
1
1
0
1
0
1
0
0
0
0
2
1
0
1
1
0
1
1
1
2
1
1
1
0
0
1
1
0
2
2
1
2
0
1
1
1
3
1
1
1
0
2
0
0
2
0
1
1
1
1
1
2
2
2
0
0
1
1
1
1
0
2
1
2
0
0
0
0
1
2
1
0
2
1
1
2
1
1
3
0
2
0
1
1
0
0
1
2
0
1
1
2
1
0
0
1
2
2
0
0
2
2
2
1
1
2
0
1
0
0
1
1
1
2
2
0
0
1
0
2
0
1
2
1
0
1
1
0
2
1
0
1
1
1
1
0
1
1
1
1
1
0
0
1
0
1
0
0
1
1
2
1
2
0
1
0
1
1
2
1
0
1
1
2
0
2
1
2
1
1
1
1
1
2
0
1
1
2
0
0
1
0
0
0
1
0
1
1
0
1
0
0
0
0
1
2
1
0
0
1
1
2
1
2
0
2
1
0
1
1
1
1
2
2
1
2
1
1
1
0
2
0
1
0
0
0
1
1
0
2
1
1
1
3
1
0
1
1
1
2
1
0
1
3
1
2
0
1
0
0
0
1
2
0
0
1
0
1
0
2
3
2
1
0
0
2
2
2
1
0
1
0
2
0
1
4
1
2
0
1
0
0
0
1
0
0
0
1
1
2
0
2
1
1
0
2
1
1
1
1
2
0
0
0
0
1
0
1
1
1
2
1
1
0
0
0
1
1
1
2
1
1
1
0
3
2
0
1
2
0
0
2
2
1
1
1
0
2
1
1
1
0
0
0
2
0
1
1
1
1
0
0
3
2
2
2
1
1
2
0
1
2
1
1
0
2
2
0
1
0
1
1
1
1
2
0
2
0
0
0
1
1
1
0
1
2
2
1
0
2
0
0
0
2
1
4
0
0
2
0
1
1
1
1
1
1
0
0
1
1
2
0
1
1
0
1
3
1
0
0
0
1
1
0
1
1
0
0
1
1
0
2
0
1
1
1
1
1
1
1
2
0
2
0
0
0
0
1
0
0
0
4
2
0
1
1
0
2
1
0
0
1
2
1
0
1
2
0
1
1
0
2
2
1
1
1
0
0
1
1
1
1
1
0
1
0
0
1
1
0
1
1
0
1
1
1
1
1
1
0
3
1
2
1
1
1
1
1
2
2
2
0
1
0
1
0
0
1
1
1
1
0
2
0
0
1
2
1
1
1
1
1
0
1
2
1
0
0
1
1
0
1
1
0
0
1
1
2
0
2
0
2
0
1
0
1
1
0
0
1
0
1
1
1
0
1
1
1
1
0
0
1
1
1
1
1
0
0
0
2
0
1
0
1
1
0
1
2
2
1
0
0
0
0
2
0
2
0
2
0
0
0
1
0
1
0
0
1
0
0
1
2
0
1
1
0
1
0
4
0
0
2
2
0
0
0
0
1
2
2
0
1
1
2
0
1
1
1
0
2
1
1
0
2
1
1
1
1
3
1
2
0
1
0
1
2
1
1
0
0
0
2
1
1
1
2
1
1
1
0
1
1
0
1
1
1
2
0
0
1
1
0
1
1
0
2
1
2
1
1
1
2
1
1
1
1
2
0
3
1
1
1
1
0
1
1
1
0
1
1
1
0
2
2
1
2
1
1
0
2
3
1
1
0
2
1
0
1
1
1
1
1
1
1
1
0
1
3
1
2
0
2
0
2
0
0
0
0
1
1
1
2
1
0
2
2
0
1
0
1
1
0
0
0
0
1
1
0
1
0
1
1
0
0
1
1
1
1
0
0
1
0
1
1
0
1
0
0
0
1
0
2
1
1
2
1
1
2
1
0
0
0
2
1
1
2
1
0
0
0
1
1
1
2
2
0
2
1
0
0
0
0
1
0
2
2
0
1
0
2
0
1
1
1
1
0
0
1
2
1
0
2
1
1
3
1
1
0
0
0
0
0
2
1
0
0
2
0
2
1
1
0
1
1
1
1
1
0
1
1
1
1
1
0
2
1
1
1
0
1
1
2
0
1
1
0
1
1
0
1
0
0
0
0
2
0
2
1
1
0
0
2
2
3
1
0
1
2
1
0
1
1
1
1
0
2
0
1
1
0
1
1
0
1
1
2
0
1
0
1
2
1
2
0
1
1
1
2
1
1
2
0
1
0
0
0
1
0
1
0
2
0
1
0
1
1
1
0
1
0
1
2
1
0
1
1
1
2
1
2
0
0
1
1
1
1
1
1
0
3
1
0
0
0
0
2
1
1
2
1
0
0
0
0
2
1
1
0
0
1
1
0
1
1
1
1
0
0
1
0
1
0
1
1
2
2
2
2
2
0
2
2
0
2
1
1
1
2
0
1
0
1
1
1
0
0
1
0
2
1
1
0
1
0
0
2
1
1
1
1
2
1
2
1
1
0
1
0
2
1
1
1
0
1
0
2
0
1
2
1
1
2
0
0
1
1
1
1
4
1
1
0
1
1
1
1
1
1
0
1
0
0
0
1
0
0
0
1
1
0
1
0
0
1
1
0
2
1
0
0
1
1
2
0
0
2
1
1
0
1
1
1
2
0
1
0
0
1
1
1
1
1
1
2
2
0
2
1
1
0
1
2
1
2
0
1
1
0
1
0
1
2
0
2
1
2
0
2
1
1
0
2
1
3
1
2
1
1
1
0
0
0
0
1
1
0
2
0
1
0
2
2
1
0
0
1
1
0
2
0
2
1
1
1
1
1
0
0
2
1
0
2
1
1
1
0
2
2
0
2
0
0
1
2
2
0
0
2
1
1
1
0
0
1
1
1
0
0
2
2
2
1
0
0
1
2
1
2
2
1
3
3
1
0
0
2
0
1
1
1
2
1
1
2
0
1
0
1
1
1
1
1
2
0
2
2
2
2
1
0
1
1
1
0
3
1
2
1
1
1
0
2
1
1
0
0
1
2
1
2
1
0
1
0
0
1
0
1
2
1
0
2
1
1
2
1
0
1
0
1
3
2
1
1
2
1
1
2
0
1
2
2
0
0
0
0
1
1
0
1
2
1
1
0
1
1
0
0
1
0
0
1
1
0
0
1
1
0
1
1
1
1
1
2
2
1
1
0
1
2
1
0
0
1
2
1
0
1
0
0
1
1
2
2
1
1
0
0
1
1
2
1
1
0
2
1
1
1
2
0
1
2
0
1
0
2
1
2
1
1
0
1
0
2
0
1
1
0
1
2
1
1
1
1
0
1
0
1
2
1
0
1
1
1
0
1
1
1
2
1
0
0
1
0
0
1
1
1
2
1
0
1
1
1
1
1
0
0
2
1
0
0
0
1
0
1
1
0
2
1
1
1
1
2
1
0
1
1
1
0
1
1
1
1
1
1
0
2
0
0
1
2
1
1
1
2
1
1
2
0
1
0
2
2
0
1
1
3
0
1
0
0
0
1
1
1
4
2
0
1
0
2
2
1
0
0
2
3
0
0
0
0
1
1
1
1
2
1
2
0
2
0
1
2
1
1
1
3
0
0
1
0
1
1
0
2
2
1
1
1
1
1
1
0
1
1
1
2
1
0
1
0
2
2
2
0
0
2
2
1
1
0
0
3
0
2
1
1
1
1
2
1
2
2
1
0
0
1
1
0
2
1
1
1
1
0
1
0
1
1
0
1
1
2
0
2
1
0
1
2
1
2
2
0
0
2
0
0
0
0
1
0
2
0
0
0
0
1
0
2
1
2
0
0
1
1
0
0
2
3
0
0
0
1
1
2
1
0
1
3
0
1
1
0
0
2
1
0
2
2
2
2
2
0
0
0
0
0
0
0
2
1
0
0
1
1
2
1
2
1
0
1
0
0
1
2
2
2
1
0
1
1
3
0
1
0
2
0
1
2
1
0
2
2
1
1
1
2
0
0
1
1
1
2
1
2
0
0
2
1
1
0
0
1
3
1
2
1
0
1
1
0
0
2
1
1
1
1
1
1
2
1
0
2
0
0
0
0
1
1
1
1
1
0
1
2
2
1
1
0
1
2
2
2
1
0
1
0
1
1
1
1
0
1
1
1
3
1
2
1
2
1
1
1
1
0
0
1
2
1
0
2
0
1
0
1
1
2
1
1
1
0
1
0
1
2
1
2
2
1
2
2
1
0
1
0
0
0
1
1
2
1
1
0
0
1
0
0
1
2
0
2
0
4
0
1
1
1
1
1
0
0
1
2
1
2
2
2
1
1
1
1
2
0
1
2
0
1
0
2
2
0
1
1
0
0
1
0
2
2
1
1
0
1
1
0
1
2
1
0
2
1
1
0
0
1
1
1
2
5
1
1
1
1
1
1
0
1
0
1
1
1
1
1
1
1
4
1
1
0
1
2
2
2
1
2
1
1
0
0
0
2
0
1
1
1
0
1
2
2
2
2
0
0
1
1
2
3
2
1
1
3
2
1
0
1
2
1
1
1
0
0
0
0
0
0
1
1
0
0
1
0
3
1
0
1
1
1
0
1
2
0
0
2
2
0
0
2
1
2
1
2
3
0
0
0
2
0
0
1
1
1
2
1
1
0
1
1
1
1
1
0
2
0
1
1
1
1
1
0
1
2
0
1
1
1
1
1
2
1
0
2
0
2
2
1
0
1
0
1
1
0
0
1
1
0
0
2
0
1
1
0
0
2
1
1
1
2
1
1
1
0
1
1
0
0
1
1
1
1
0
1
2
1
2
1
1
2
1
1
1
2
0
1
2
0
1
0
1
1
1
0
2
2
1
2
1
2
0
1
1
2
1
2
3
0
0
0
2
2
0
0
1
1
1
1
1
1
0
2
2
2
1
0
0
1
1
1
2
2
1
1
0
2
0
2
2
1
2
2
1
1
2
0
0
1
2
0
1
1
1
2
0
2
2
0
1
2
1
2
0
0
1
0
1
0
0
0
0
0
0
1
2
1
1
1
2
1
0
1
0
1
1
2
1
0
2
1
1
0
0
3
1
2
1
1
2
1
1
1
1
2
0
1
0
1
1
1
1
0
1
1
1
1
2
2
2
1
1
0
1
0
0
1
1
1
2
3
2
1
1
1
0
3
0
2
0
1
1
0
2
1
1
2
1
1
1
0
1
1
0
1
0
1
0
0
0
1
0
0
1
1
1
0
1
1
0
7
0
1
1
0
2
1
1
1
0
0
1
0
2
1
1
0
1
2
1
2
0
0
0
1
1
0
0
1
1
1
1
1
2
1
1
0
1
0
0
1
0
1
1
0
1
1
0
0
1
0
1
2
0
2
0
1
2
2
2
1
1
1
0
1
0
1
1
2
1
2
1
0
1
1
0
0
0
1
0
1
1
2
1
1
1
0
1
0
2
0
1
1
2
2
0
1
2
0
1
0
0
1
1
0
1
1
0
0
1
1
1
2
1
1
1
1
2
1
0
0
0
0
1
0
0
0
1
0
1
1
0
0
1
0
1
0
0
1
1
1
1
0
1
2
0
1
1
0
0
1
2
0
1
1
2
1
2
2
2
0
0
2
0
0
1
0
0
1
1
0
2
0
2
0
0
0
1
0
2
0
2
1
1
1
0
1
0
2
1
1
1
1
1
2
2
2
0
1
0
2
1
2
1
2
0
1
1
0
0
0
2
0
1
0
1
0
1
0
0
0
2
1
2
3
0
1
1
0
0
2
1
1
1
1
0
1
2
1
2
1
1
0
0
1
1
2
0
1
1
0
2
1
4
2
0
1
0
1
1
1
2
1
2
0
2
0
0
0
1
2
0
1
0
3
1
1
1
1
1
2
1
0
0
0
0
0
0
1
1
1
1
1
1
1
3
2
2
1
1
0
0
2
0
1
0
2
1
0
1
1
0
0
2
0
1
1
1
3
1
1
0
0
1
0
3
2
1
0
2
0
1
1
0
1
1
0
1
1
0
1
1
2
1
2
2
1
1
0
1
0
0
2
1
0
0
0
1
0
1
2
1
1
1
1
0
0
0
1
0
1
2
0
1
0
1
1
1
0
0
2
0
2
1
1
1
1
0
0
1
1
0
1
1
0
1
1
0
0
0
2
0
0
1
1
0
0
1
0
2
0
0
2
1
1
0
2
1
2
3
1
1
1
1
2
1
1
0
0
0
0
1
3
1
0
1
2
0
2
1
2
2
1
0
0
1
2
1
2
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
0
1
1
0
1
2
0
0
1
2
1
0
1
0
1
1
2
0
1
0
2
1
2
1
6
1
2
1
2
0
2
0
0
1
1
0
0
0
0
0
1
2
0
1
0
0
0
1
0
2
0
1
1
1
0
1
1
0
2
0
1
1
2
0
1
2
1
0
1
1
2
0
1
2
1
0
0
1
1
0
1
1
2
0
2
1
0
1
1
2
2
1
0
1
2
0
1
2
1
2
1
3
1
2
0
2
1
0
0
2
0
2
1
1
1
0
1
2
0
2
2
1
1
0
0
0
0
1
0
0
1
2
0
1
2
3
1
0
0
2
2
0
1
1
1
0
1
1
0
1
0
2
4
1
1
0
1
1
2
2
1
0
2
0
1
2
1
0
0
1
2
2
0
0
1
2
2
0
1
0
1
0
1
0
2
1
1
2
0
1
1
1
2
1
2
2
2
1
2
2
1
2
2
1
1
1
1
1
2
1
1
2
0
1
1
1
0
0
1
1
2
1
1
2
1
0
1
1
0
0
2
1
0
1
2
0
1
0
1
0
0
0
2
1
0
0
0
0
2
1
0
0
0
1
2
2
1
2
1
1
0
0
2
0
1
1
1
1
0
1
1
1
2
0
2
0
1
1
1
0
2
1
0
1
1
1
0
1
1
1
1
0
2
2
4
1
2
2
2
1
2
2
1
1
2
1
0
2
1
2
2
1
2
0
3
0
0
1
0
1
2
2
0
0
0
2
1
1
1
0
0
0
0
1
1
2
1
0
1
2
1
2
1
0
0
1
1
1
1
1
1
0
0
1
1
0
2
0
2
1
0
0
1
1
2
1
1
0
1
1
2
2
1
2
1
0
2
1
2
1
1
2
0
1
0
1
1
0
0
0
0
0
0
2
0
0
2
1
2
1
1
0
0
0
1
2
1
0
0
0
1
2
1
1
1
2
1
1
2
1
1
2
2
1
1
1
1
1
1
1
1
1
1
0
0
1
1
1
0
1
0
1
0
1
2
1
1
0
1
0
2
1
1
1
1
2
2
0
1
1
0
1
0
1
0
1
1
0
1
1
0
0
1
0
1
0
2
2
1
2
1
0
1
3
0
1
1
1
1
1
1
0
1
0
1
1
2
1
0
0
2
1
2
2
1
1
0
1
1
1
1
1
0
1
1
1
1
0
1
1
1
0
2
0
0
2
1
0
0
0
0
0
2
1
0
1
1
1
0
1
1
1
0
1
0
1
1
1
1
1
1
1
1
2
1
0
0
0
0
1
0
2
0
1
1
2
1
2
2
0
3
1
2
0
0
1
0
1
1
1
2
1
1
2
0
0
1
1
1
2
0
0
2
2
1
0
1
2
0
0
2
0
1
0
1
1
0
1
0
0
1
0
1
2
0
1
1
1
1
1
0
1
0
0
0
0
1
0
1
1
0
0
0
1
0
2
2
1
2
0
0
1
1
2
2
1
2
0
2
0
2
2
1
0
2
2
2
1
1
0
1
1
0
3
1
1
1
1
1
2
1
2
0
1
1
0
0
0
1
1
0
1
0
2
1
2
0
2
0
1
1
0
0
1
2
1
2
1
1
1
2
0
1
1
7
0
0
1
0
0
2
0
1
1
0
0
1
0
0
0
1
1
0
0
2
1
0
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
0
1
2
1
1
2
1
1
1
1
1
0
0
1
0
0
1
1
1
2
0
1
1
1
0
2
2
1
1
2
2
2
1
1
2
0
2
0
2
0
1
0
1
2
1
1
1
0
1
2
1
2
1
3
0
0
0
2
2
0
1
1
2
0
0
1
0
1
0
1
0
1
2
1
1
1
2
2
0
2
0
0
2
2
1
2
0
4
0
0
1
1
1
1
1
0
1
0
0
2
2
1
2
2
1
1
0
0
0
1
1
3
0
3
0
2
0
2
0
1
1
1
0
0
1
1
0
2
0
2
1
0
1
0
1
0
2
1
1
0
0
0
1
3
0
1
1
2
1
1
0
1
1
1
0
2
0
0
1
2
1
2
1
2
1
1
1
0
1
2
1
2
2
0
0
2
2
1
2
1
1
1
1
1
1
2
1
0
1
2
2
1
0
2
0
1
1
1
0
0
2
2
0
1
2
1
1
2
1
0
1
2
2
1
2
1
0
2
0
1
1
1
1
0
1
1
2
0
0
0
0
0
2
2
0
1
2
0
0
0
1
1
1
1
1
0
2
1
2
0
3
0
1
1
1
0
0
1
1
2
0
1
1
0
1
2
0
0
2
2
0
1
1
0
0
2
2
1
0
2
1
0
0
1
1
1
2
1
1
0
1
2
3
1
3
2
2
0
0
1
2
0
2
1
3
0
1
1
1
1
1
0
2
0
0
0
1
0
0
0
0
1
1
1
1
1
1
1
0
1
2
1
0
2
1
2
0
1
1
1
2
1
0
1
0
1
1
2
2
2
0
3
2
0
2
1
1
1
0
0
0
1
1
1
0
2
1
0
2
3
1
1
2
2
1
1
2
1
0
2
1
1
0
1
0
1
1
1
0
1
2
1
0
1
0
0
2
2
2
1
1
0
3
2
1
3
2
2
0
0
1
0
1
0
1
0
2
1
1
2
0
1
1
0
1
2
2
0
1
1
2
2
1
2
0
0
0
2
0
0
1
2
2
2
0
1
1
0
1
1
1
1
1
1
0
0
1
0
1
0
0
0
0
0
1
2
1
1
0
1
2
1
0
0
1
1
0
1
1
1
1
2
2
2
1
1
2
2
0
0
1
2
1
0
0
1
1
1
1
2
1
1
1
4
0
1
9
2
1
0
1
1
1
1
2
1
1
0
0
1
1
1
1
2
0
0
2
2
1
0
0
1
1
1
1
0
0
1
1
1
0
3
2
1
0
1
1
0
0
1
1
0
1
1
1
1
2
0
1
0
2
1
1
0
1
2
2
1
1
1
0
0
2
1
1
0
1
1
0
0
1
1
1
1
1
3
1
1
2
1
1
0
1
2
1
1
0
1
1
0
2
2
0
0
1
1
0
0
1
2
1
1
2
0
2
2
1
0
1
2
1
0
0
0
0
1
1
0
0
1
1
1
0
1
1
1
1
1
0
1
1
0
1
2
0
2
0
0
0
2
1
1
1
0
1
1
0
1
1
2
2
0
2
1
0
1
1
0
1
2
0
1
0
1
1
1
1
1
0
2
0
1
0
1
1
0
2
0
0
0
1
1
2
0
1
0
1
1
1
2
0
1
2
2
1
1
2
0
0
2
3
1
1
1
2
0
0
1
0
1
0
1
0
3
0
0
0
1
0
3
2
0
1
1
1
1
3
1
1
1
1
0
1
1
0
0
1
1
1
1
1
0
1
2
1
2
1
1
1
1
1
0
2
1
1
0
1
1
0
1
2
1
1
1
2
2
1
2
0
2
1
1
1
0
0
0
3
0
1
0
2
2
0
1
1
1
0
1
1
0
1
1
1
0
1
0
1
0
1
0
1
1
1
1
0
1
2
1
2
2
1
1
0
1
0
0
1
1
0
1
3
0
1
2
0
0
0
1
0
0
0
1
1
1
1
1
1
1
2
1
2
1
1
1
0
2
0
0
1
1
1
0
1
2
1
0
1
1
0
1
1
1
1
1
0
2
1
1
1
1
0
1
2
0
2
0
1
1
0
0
2
2
1
1
1
0
2
1
2
0
0
1
1
0
3
2
1
1
1
1
2
2
0
1
2
2
1
0
1
1
1
1
1
1
1
2
1
1
0
1
0
1
1
2
1
1
2
0
1
1
0
2
1
0
1
2
0
1
0
1
1
0
0
1
0
0
0
1
0
0
1
0
1
2
1
1
1
1
1
0
1
2
1
1
0
0
2
1
0
1
2
0
1
1
1
1
0
1
0
2
1
1
1
2
1
2
0
0
1
0
1
1
0
1
2
2
1
2
1
1
1
1
2
2
2
1
0
1
0
1
0
2
1
1
2
2
1
0
0
1
1
1
0
1
1
0
2
0
2
1
1
1
1
1
1
0
1
1
1
2
1
1
2
0
1
2
2
0
0
1
0
0
1
0
1
2
0
1
0
1
0
0
2
0
1
1
0
1
1
1
0
0
0
1
2
1
0
1
0
1
0
1
1
2
0
0
1
0
1
1
1
1
2
1
0
1
1
0
1
1
1
1
0
1
1
0
2
0
1
0
1
0
0
2
0
0
0
0
2
1
1
2
0
1
2
0
1
2
0
1
1
1
1
2
1
1
2
2
2
1
0
1
1
2
1
1
2
2
1
2
3
0
4
1
1
2
2
1
2
1
2
0
0
1
2
2
1
1
1
0
0
0
0
1
1
1
2
2
1
2
1
2
2
0
0
1
1
2
0
0
0
1
0
1
1
2
2
0
2
2
0
1
1
0
2
1
2
0
0
2
0
1
2
0
1
2
2
1
0
0
1
2
0
1
0
1
1
1
1
2
2
1
0
0
0
0
0
1
0
2
2
1
0
3
0
1
1
2
1
0
1
1
1
2
0
1
1
1
0
0
1
1
0
1
2
2
0
1
0
1
0
0
1
2
1
0
1
1
1
0
0
1
1
2
1
1
0
0
1
1
1
1
1
1
1
1
1
4
1
1
2
1
0
0
1
0
2
1
2
0
1
1
0
1
0
0
1
1
3
0
1
1
1
1
1
0
1
1
0
0
0
2
1
1
1
0
0
1
1
1
1
0
1
0
1
1
0
1
0
1
1
1
0
1
0
0
0
1
1
0
1
0
2
1
2
2
0
0
1
1
2
0
1
1
0
1
0
2
1
0
0
1
2
1
2
1
1
1
2
4
2
1
0
1
2
1
1
2
0
2
2
2
1
0
1
2
1
0
1
2
1
1
2
1
0
1
1
2
1
1
0
1
1
1
1
2
0
0
0
1
1
1
1
0
0
1
0
0
1
0
0
0
2
2
0
1
0
0
1
1
1
1
2
1
0
1
0
0
0
0
0
2
1
8
1
1
0
0
1
2
2
2
1
1
1
1
2
1
0
2
0
2
0
2
0
0
1
0
0
1
1
2
1
2
0
1
1
1
0
1
1
0
0
0
1
0
1
2
1
0
1
1
2
2
0
2
1
1
1
1
1
1
0
0
2
1
0
0
1
0
0
1
1
0
1
2
2
1
0
0
0
1
1
1
1
1
1
1
0
1
0
2
0
1
0
1
2
1
0
0
2
0
1
1
1
2
1
0
2
0
1
1
1
2
0
1
1
0
0
0
1
1
1
2
0
0
1
0
0
0
1
1
1
1
2
0
1
2
3
0
1
1
0
0
1
1
1
2
0
1
1
1
1
1
0
0
2
2
2
1
2
2
1
1
1
1
2
0
0
2
0
2
0
1
0
2
1
1
0
0
1
3
2
2
0
0
1
2
2
1
1
0
1
0
1
2
2
0
1
0
1
1
3
3
0
0
2
1
1
1
0
2
0
1
0
1
1
1
1
1
1
0
0
1
0
1
1
1
1
2
1
1
2
0
0
1
1
1
0
0
1
1
1
2
0
1
1
1
0
2
1
1
1
1
1
0
1
0
0
1
0
1
0
0
1
0
0
1
2
1
0
2
1
0
2
1
2
0
2
0
2
1
2
1
1
0
1
0
1
1
0
2
1
2
0
2
2
2
2
1
0
0
1
1
1
0
2
0
1
1
2
0
0
0
5
0
0
2
0
1
0
1
1
1
1
0
1
1
2
1
1
1
1
1
1
2
1
0
0
1
1
0
0
2
0
1
0
1
1
2
1
1
1
1
0
1
0
2
1
0
0
0
1
1
1
0
0
2
0
3
1
1
1
1
2
1
1
1
1
2
0
1
1
1
1
1
0
0
0
2
2
0
0
0
1
2
1
1
1
1
2
2
1
0
0
1
0
1
0
2
0
0
1
2
2
0
0
1
1
1
1
2
0
1
1
2
0
1
0
1
1
1
1
0
1
0
0
0
0
1
2
0
1
2
2
0
0
1
2
2
1
0
2
1
2
1
1
0
1
2
1
2
0
0
1
0
2
0
1
1
0
1
0
2
1
0
1
0
1
0
1
1
2
0
2
2
1
2
0
0
1
2
0
0
1
1
0
1
1
2
1
0
2
0
1
2
1
1
1
0
0
2
1
1
1
0
1
2
1
1
1
1
0
0
1
1
0
1
2
2
1
1
1
1
1
1
1
1
1
0
0
1
1
0
0
0
1
1
1
1
1
2
0
0
1
1
2
1
1
2
0
0
2
2
1
1
1
0
1
2
0
1
0
2
0
1
0
1
1
1
2
0
2
1
2
2
2
1
1
0
0
2
0
1
1
2
1
2
0
2
2
2
2
1
1
0
1
1
2
1
0
0
0
1
2
0
1
1
0
0
2
0
1
2
1
0
3
1
1
1
1
0
0
2
0
0
2
1
1
0
2
1
2
0
1
0
1
1
2
1
0
1
2
2
2
2
2
1
2
0
0
1
1
1
2
2
2
1
1
2
2
1
0
1
1
1
1
0
1
0
0
0
1
1
2
1
1
1
1
0
0
0
2
2
0
1
1
1
1
0
0
1
1
1
1
0
1
1
1
1
1
2
1
1
2
1
0
0
1
0
1
1
1
1
1
2
0
1
1
0
1
0
1
2
1
1
1
1
2
0
1
0
1
1
2
1
2
0
1
1
1
2
2
0
0
0
0
0
2
0
2
1
1
1
1
1
1
0
1
2
2
1
1
0
0
0
0
1
1
1
1
2
0
1
1
1
1
1
0
1
0
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
2
0
1
2
0
2
2
0
0
1
0
2
0
1
1
1
0
2
1
1
1
1
0
2
2
1
1
2
2
1
1
1
1
0
0
0
1
2
1
1
1
1
1
0
2
0
1
2
1
2
2
1
2
1
3
0
1
1
0
1
0
2
1
0
0
1
1
0
0
1
0
1
2
2
1
1
1
1
1
1
2
2
2
2
2
1
1
0
1
0
2
1
0
2
2
0
1
2
2
0
1
1
1
0
1
0
3
0
1
2
1
1
0
2
1
0
1
0
2
2
1
0
1
1
1
0
1
1
1
2
1
1
1
1
2
1
1
1
0
2
1
1
2
1
2
0
0
0
1
2
0
0
1
2
0
1
0
1
1
2
0
0
1
1
0
2
0
1
1
2
1
1
1
1
1
0
1
1
0
1
0
1
1
1
1
0
2
1
2
3
0
2
1
1
2
2
1
1
1
1
0
1
1
0
0
1
2
1
1
0
1
2
1
1
0
0
0
1
0
1
0
1
1
1
1
1
1
1
1
2
0
2
1
2
0
1
1
0
0
0
2
1
2
1
1
0
2
1
2
1
1
1
1
2
1
1
2
1
2
1
2
0
0
1
0
1
1
0
1
0
2
1
0
2
0
0
2
2
1
1
0
0
0
1
2
1
2
1
2
2
1
2
1
2
1
2
1
1
0
2
0
2
0
0
1
2
1
0
1
0
1
1
1
1
3
1
1
2
0
0
1
0
2
0
2
0
1
0
1
1
0
1
0
1
2
1
0
1
1
1
0
1
2
0
1
1
1
0
0
1
0
1
1
0
2
0
0
2
0
1
1
0
1
2
1
2
2
1
0
2
1
1
2
2
0
1
0
2
2
1
0
1
0
0
0
0
1
2
0
0
1
1
1
0
1
0
1
0
4
1
1
0
1
1
1
1
1
1
6
0
0
1
0
1
2
0
0
1
1
1
0
2
1
1
1
2
1
0
2
1
2
2
1
0
0
1
2
1
2
1
0
2
2
1
0
0
2
1
1
1
2
0
2
0
0
0
0
0
1
1
0
2
2
1
1
0
2
2
0
2
2
0
2
0
1
1
1
0
1
2
1
1
0
2
1
1
0
1
0
1
1
1
0
0
2
1
1
0
1
2
1
1
0
0
2
1
1
2
2
1
1
0
1
1
1
1
1
0
1
1
0
1
0
0
1
1
1
0
3
0
1
1
0
1
1
1
0
1
0
0
1
0
0
1
2
0
1
1
2
2
0
0
0
2
1
1
0
1
0
0
2
1
0
0
2
2
1
0
1
0
2
2
0
2
1
1
1
0
2
0
1
1
2
0
0
1
0
1
1
0
1
1
2
1
1
1
1
0
1
1
2
0
0
2
1
1
1
1
2
2
0
1
1
1
2
1
0
1
2
2
0
0
0
1
1
1
2
1
0
1
2
0
1
1
1
1
1
0
1
2
0
3
0
1
1
2
1
1
1
1
1
0
1
0
0
0
1
1
0
0
3
1
0
1
1
0
0
2
1
1
2
1
1
0
2
0
1
0
0
2
1
2
0
1
0
1
1
0
0
0
2
1
1
1
1
2
1
0
0
1
1
1
0
1
1
0
1
0
1
0
1
2
2
1
1
1
1
0
0
1
1
2
1
1
0
1
2
1
2
1
2
3
0
0
1
1
1
1
0
1
1
1
0
1
0
1
1
1
1
1
2
1
2
0
2
1
0
1
1
2
1
2
1
1
0
2
1
1
2
0
1
1
1
4
1
1
0
2
1
1
1
1
0
1
2
1
0
2
1
0
1
1
0
1
1
0
0
0
1
1
2
1
1
2
0
1
1
2
1
1
0
0
4
1
1
0
1
1
1
1
0
1
0
1
1
1
0
1
0
1
2
0
0
1
0
0
1
1
1
1
1
0
2
1
1
0
0
1
1
1
1
1
0
2
0
0
2
2
0
1
1
0
0
1
1
2
1
2
0
2
1
2
0
1
1
0
0
0
1
0
2
1
0
1
0
0
2
0
2
1
1
1
0
1
1
1
3
0
4
2
0
1
0
1
1
1
2
1
0
1
0
0
1
1
0
1
2
2
1
2
1
0
2
1
1
2
0
0
0
0
2
1
2
2
2
1
0
1
1
1
1
0
1
1
1
3
0
0
1
0
1
1
0
1
0
2
2
2
1
1
1
1
1
0
1
2
0
1
0
0
1
0
2
1
1
2
0
0
2
0
2
1
1
1
2
1
0
1
1
1
0
0
1
0
1
0
1
1
1
0
2
0
0
1
1
3
1
0
0
1
2
1
2
1
2
0
1
1
2
1
1
1
3
0
1
1
2
0
1
2
2
1
0
1
1
1
1
1
1
1
0
0
1
2
0
1
1
1
1
0
2
1
0
3
0
2
1
0
0
2
0
2
2
1
1
2
0
0
0
1
0
1
2
0
1
1
2
2
1
1
0
1
0
2
1
0
4
2
2
1
0
1
0
2
1
1
2
1
1
1
2
0
1
1
0
0
2
1
1
4
0
0
2
0
1
0
2
3
1
2
1
1
2
0
2
1
2
0
2
2
0
1
1
1
2
0
4
0
2
0
1
1
1
1
0
0
1
0
1
0
0
1
1
2
2
0
1
0
1
1
2
0
1
3
0
0
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
0
2
0
1
0
1
2
2
1
1
0
0
1
1
2
0
0
0
0
1
2
1
1
1
1
1
2
1
0
2
0
0
1
1
0
0
1
0
1
1
1
1
0
1
2
1
2
1
0
2
2
3
1
2
2
1
1
0
1
1
1
1
0
1
1
2
0
1
1
0
0
0
1
2
1
1
0
0
2
1
1
2
2
0
0
1
0
0
1
1
0
1
1
1
1
1
1
1
0
0
0
1
2
2
1
1
0
1
0
2
0
2
1
2
0
2
0
1
0
1
1
1
0
2
1
0
0
1
1
0
1
0
1
1
1
1
0
1
1
0
1
0
0
0
1
0
1
1
0
0
1
1
2
1
1
0
1
1
1
1
1
2
0
2
0
2
1
1
1
1
1
2
0
1
0
2
1
1
1
1
1
1
2
1
0
1
0
1
1
1
2
1
1
2
0
0
0
1
1
3
2
1
2
1
0
1
2
0
2
2
1
1
0
0
0
0
0
2
1
1
0
1
1
3
1
0
0
0
1
0
0
1
1
2
1
1
2
0
0
2
1
2
1
1
0
2
1
0
1
1
1
2
1
1
2
1
1
2
2
0
0
2
2
2
0
0
0
3
2
0
1
0
2
2
2
1
0
0
1
0
1
2
1
2
1
2
0
0
1
1
1
0
1
1
1
0
1
0
1
0
1
1
1
2
2
0
2
1
1
0
2
1
1
0
1
1
1
0
1
2
0
1
4
2
1
0
1
2
1
2
0
1
0
0
0
1
1
1
0
0
1
0
1
1
1
0
2
1
1
0
1
2
1
0
1
0
0
1
2
0
0
0
3
0
0
2
1
1
2
0
1
1
0
0
1
1
1
1
2
1
0
1
2
0
0
0
0
0
0
2
0
1
1
1
2
1
1
0
1
1
1
1
6
1
0
1
0
1
1
1
0
1
0
1
3
0
1
0
2
1
1
1
1
0
2
1
1
0
1
1
1
0
1
3
2
1
1
2
0
1
1
1
1
1
1
0
0
1
0
1
0
0
2
2
0
1
1
1
1
1
1
0
1
1
2
0
1
1
0
2
1
1
0
2
1
1
2
0
0
1
1
1
0
1
1
2
2
1
0
1
1
1
2
0
0
1
1
1
2
1
0
2
0
2
1
1
1
0
1
1
1
1
1
1
2
0
0
0
1
1
0
1
1
1
1
1
4
1
1
0
0
0
0
1
1
1
1
0
1
1
1
0
1
0
1
0
2
2
0
0
2
1
1
1
1
1
0
0
0
2
0
1
1
0
0
1
0
2
0
0
2
1
1
0
1
2
1
1
2
1
2
1
0
1
0
1
0
2
1
0
2
1
1
2
0
0
0
1
1
2
0
2
1
1
1
1
0
1
0
1
0
0
0
0
1
2
0
1
1
2
1
3
2
0
2
1
1
1
0
1
1
1
0
0
1
0
2
2
0
1
0
1
1
4
0
0
6
1
1
1
1
2
1
0
0
4
1
0
1
0
0
0
1
2
1
2
2
1
1
1
1
2
1
0
0
1
0
1
2
0
2
1
0
0
2
2
2
1
2
0
1
1
0
2
0
2
1
0
0
1
0
1
1
0
0
1
1
1
1
0
1
1
2
0
0
1
2
1
1
2
1
1
1
1
1
2
1
3
2
1
2
2
1
1
2
0
1
1
0
1
1
2
1
0
2
0
1
1
1
2
0
2
2
0
1
1
0
0
0
2
0
0
2
2
1
2
2
1
1
2
1
0
1
1
0
0
1
1
1
2
0
2
1
1
2
2
2
1
0
0
0
1
0
1
2
1
1
2
1
1
2
1
1
2
1
1
0
1
1
0
2
1
2
2
1
1
1
1
0
3
1
0
3
1
0
0
1
2
1
1
1
1
0
1
0
0
1
0
2
0
1
1
2
1
0
1
1
2
2
1
0
1
2
1
2
0
1
0
4
0
1
1
1
1
3
0
1
1
0
1
1
2
0
1
1
0
2
0
2
1
2
1
4
1
1
2
0
1
0
0
0
0
1
1
1
1
2
0
1
1
0
0
0
2
0
1
0
1
1
1
0
2
2
1
1
1
1
1
1
2
2
1
1
2
1
2
1
1
1
1
0
2
2
2
1
1
0
0
1
0
1
1
2
1
0
0
0
1
1
2
1
2
1
1
1
1
1
0
1
2
1
1
2
0
1
1
2
0
0
0
1
0
1
1
2
1
1
1
0
0
1
0
1
0
2
1
1
0
1
1
0
1
1
1
1
1
2
0
2
2
1
1
2
1
1
1
1
0
0
2
2
0
0
0
1
0
1
0
1
1
0
1
2
1
0
1
2
0
0
2
0
0
0
2
0
0
1
2
0
2
1
1
2
1
0
0
1
3
0
1
2
1
0
1
1
0
1
1
0
1
1
1
1
1
1
1
2
2
2
1
3
1
1
0
2
0
1
0
2
1
1
1
1
1
0
1
0
1
2
1
1
1
2
2
1
0
0
0
1
2
3
0
0
1
2
1
2
2
1
1
1
0
1
1
0
1
1
1
2
2
1
1
1
1
1
1
0
0
0
0
1
1
1
2
2
1
0
1
0
0
1
1
1
1
1
1
0
1
1
0
1
1
1
0
2
0
1
2
2
1
1
1
0
0
2
1
0
0
5
0
1
2
2
0
1
1
0
0
2
1
1
2
0
1
1
1
0
1
0
1
1
2
2
2
0
0
1
2
1
1
1
0
1
2
1
0
0
1
2
1
2
1
2
2
0
0
1
1
0
1
0
1
0
2
1
1
1
0
1
1
0
1
0
2
0
1
1
2
1
0
1
1
1
1
1
1
1
0
1
0
0
1
1
1
1
1
1
1
0
2
0
1
0
1
4
0
2
0
2
1
2
2
1
2
0
0
1
3
2
0
2
1
0
1
0
1
1
1
3
2
1
2
1
1
1
1
0
1
1
4
1
1
2
1
2
2
1
0
0
1
1
0
0
0
1
1
1
0
1
0
1
0
1
4
2
0
0
1
2
0
2
0
0
1
0
3
0
0
1
2
0
2
2
2
1
0
1
0
1
1
2
1
2
0
0
1
0
1
0
2
2
0
0
1
1
0
1
0
2
0
1
0
0
2
1
1
0
1
1
1
1
2
0
1
2
1
1
0
0
2
0
0
1
2
0
2
2
1
2
3
1
0
0
1
1
0
2
2
2
1
1
0
0
1
0
0
1
2
1
2
2
0
2
2
1
1
1
1
1
2
1
2
1
2
2
0
1
0
2
1
1
0
0
2
1
2
1
1
2
1
0
2
1
1
1
1
0
2
1
1
1
1
1
1
1
1
2
0
2
0
1
3
2
2
1
0
1
2
1
1
1
1
2
1
0
3
1
0
2
2
0
1
1
0
1
0
1
0
2
1
1
0
1
1
1
1
1
2
1
1
2
2
1
0
0
1
1
1
2
2
0
1
1
0
1
4
1
1
1
0
1
0
1
0
0
1
0
1
1
2
1
1
2
2
1
0
0
2
0
0
1
1
2
2
2
0
0
2
2
3
3
1
1
0
1
0
2
0
1
0
2
1
0
1
1
2
1
1
2
1
1
1
0
1
2
2
1
1
2
2
2
0
2
1
1
1
1
1
0
0
2
1
1
0
0
1
2
2
0
1
1
0
1
0
2
1
2
1
1
1
2
1
2
1
1
1
0
1
2
1
2
0
1
1
1
1
1
1
1
0
2
0
0
1
2
0
1
0
1
0
2
2
1
1
0
1
0
0
1
1
0
0
2
1
2
1
2
1
1
0
1
0
1
2
2
1
2
1
1
0
2
1
1
0
2
2
1
0
2
0
1
1
2
0
1
0
1
0
1
1
2
0
1
1
0
0
1
1
1
0
0
0
1
1
0
1
2
1
2
1
1
1
1
1
1
1
0
2
0
1
1
0
1
1
2
1
1
0
1
1
1
0
1
2
1
0
1
1
1
0
2
1
0
0
1
0
0
1
0
1
1
1
0
2
0
0
1
2
0
0
1
0
2
1
1
2
1
0
1
0
1
2
2
1
1
1
0
0
2
2
2
1
2
0
0
1
2
2
2
2
2
1
1
1
0
1
1
0
0
1
0
2
1
1
1
0
0
1
2
1
2
1
1
1
1
1
0
1
1
2
2
0
1
1
1
1
0
2
3
1
1
1
1
0
0
1
1
1
1
1
1
1
1
2
1
0
1
1
3
0
1
1
2
2
0
1
1
1
2
0
0
2
1
0
0
0
0
1
1
0
1
2
0
2
1
0
0
0
1
1
0
0
1
1
1
2
1
2
1
2
1
1
0
0
0
1
0
1
1
1
0
3
1
0
0
1
0
2
1
0
0
1
1
1
1
1
1
1
1
2
2
1
1
1
1
0
1
0
1
2
0
1
0
1
2
0
1
1
1
1
1
0
0
1
1
0
1
0
1
1
1
0
1
2
2
1
0
2
1
1
2
2
2
0
1
2
1
1
1
0
0
2
0
1
1
1
0
1
1
1
1
0
0
2
0
1
0
1
0
2
0
0
2
0
1
1
0
1
0
1
0
2
0
1
1
0
2
1
1
2
2
0
2
2
0
1
1
0
0
1
1
0
0
0
0
0
0
1
0
1
0
2
1
1
2
0
1
0
1
2
2
0
0
2
2
0
0
1
1
1
0
1
1
0
2
0
2
0
1
0
0
1
0
1
1
0
0
2
1
1
1
0
0
2
0
2
0
2
0
0
1
0
0
0
0
2
0
2
0
0
0
1
0
0
1
1
2
1
0
1
1
0
1
1
0
1
0
2
2
1
0
0
2
1
1
1
1
1
1
1
1
1
0
2
1
1
0
1
1
1
2
1
2
1
0
1
2
0
0
1
2
2
0
1
1
2
1
0
2
1
0
0
1
1
1
2
0
0
0
0
1
1
1
0
1
0
2
2
1
1
0
1
1
2
2
1
1
1
1
0
2
0
1
1
0
1
1
1
0
0
1
1
1
1
1
2
0
1
0
1
2
1
0
0
2
0
1
1
0
0
1
1
1
1
2
2
2
3
0
2
1
0
0
0
1
0
1
2
0
1
1
1
2
1
2
2
0
1
2
1
1
2
1
0
1
0
2
1
1
1
2
2
2
0
0
0
1
1
2
1
2
0
2
1
0
1
1
2
1
1
1
1
1
0
1
0
2
1
1
1
1
1
1
1
0
0
2
0
0
2
1
2
0
0
0
1
1
0
2
2
1
0
0
1
1
0
1
1
0
1
0
0
1
1
1
1
0
1
1
0
1
1
0
0
1
2
1
1
1
2
2
2
0
2
0
0
1
0
1
3
2
0
0
2
3
1
0
1
0
1
1
1
0
2
1
1
0
1
2
1
2
1
1
2
3
2
2
0
2
1
1
2
1
2
0
1
1
1
1
0
1
0
2
2
0
1
0
1
0
1
1
1
0
1
1
1
0
4
1
1
1
1
0
0
2
1
0
0
0
0
1
0
0
1
1
1
2
2
2
2
0
1
0
1
0
0
2
0
1
0
0
1
1
1
0
2
1
0
2
2
0
0
1
1
1
1
1
1
2
1
1
0
2
0
2
0
2
1
0
0
2
1
2
2
2
2
1
0
1
1
1
0
0
1
1
1
1
1
1
0
2
2
1
1
2
1
0
1
0
1
1
1
0
0
0
0
0
1
1
1
1
0
0
0
1
0
1
1
0
0
1
1
1
1
0
0
1
1
1
0
0
2
0
0
0
2
0
1
2
4
1
0
0
1
0
2
1
1
1
0
0
1
1
1
1
0
0
1
2
1
1
1
0
1
1
1
1
2
0
1
1
1
2
0
1
1
2
1
2
0
2
0
2
1
2
0
1
0
1
2
2
1
2
2
1
2
0
0
1
1
0
0
1
2
0
0
2
0
2
0
1
1
1
2
1
2
0
0
1
0
0
2
1
0
2
0
1
1
1
2
1
0
0
0
2
0
2
0
0
0
0
0
0
2
0
1
2
2
2
1
1
0
1
0
1
1
1
1
0
0
1
1
2
0
2
0
0
1
1
1
0
0
1
0
0
1
0
1
0
1
2
0
2
1
2
1
0
1
0
0
2
1
2
0
1
0
0
1
1
0
0
0
1
1
0
1
2
0
1
2
1
1
0
0
0
0
0
0
1
0
2
1
0
0
2
4
2
1
0
0
1
1
0
1
0
1
1
1
0
1
1
2
1
1
1
0
1
0
3
0
0
0
1
2
1
1
1
0
1
0
1
0
0
2
1
0
0
1
1
0
0
2
1
2
0
2
3
0
1
0
0
2
1
0
1
1
2
1
0
2
2
1
2
1
1
1
0
1
1
0
0
2
2
0
0
1
0
1
0
1
0
1
3
0
0
2
1
1
1
1
2
0
1
2
1
0
2
0
0
1
2
1
1
1
2
2
0
2
1
1
1
0
0
1
0
2
0
1
1
1
1
2
1
1
1
0
0
0
0
2
0
0
2
2
2
1
0
1
1
1
1
2
1
1
0
2
2
2
2
2
1
1
1
2
0
0
0
2
0
1
0
2
2
1
1
0
2
0
1
1
7
0
0
1
1
2
1
0
0
0
2
1
0
1
0
1
1
2
2
2
0
0
1
1
1
2
2
1
2
3
1
0
1
1
1
1
0
1
1
1
0
0
0
2
1
1
0
3
1
2
2
1
1
1
0
1
1
0
0
0
0
0
1
1
1
2
0
1
1
0
1
1
2
1
0
2
2
0
1
3
0
0
0
0
2
0
1
1
1
0
2
1
1
1
2
2
1
2
1
2
1
1
1
2
0
0
0
1
0
2
2
0
1
1
1
1
0
2
1
1
2
2
2
1
1
2
1
1
0
1
2
1
1
1
1
1
0
2
0
1
0
1
1
0
1
1
0
0
2
1
1
2
1
1
0
2
0
1
0
2
0
1
1
1
0
1
2
0
1
0
1
1
0
2
1
1
2
0
1
0
1
0
1
0
0
0
3
2
1
1
1
1
1
0
2
2
0
2
1
1
1
1
2
1
1
1
2
1
0
0
1
2
0
1
2
1
0
2
1
1
0
1
0
0
0
1
1
1
0
0
0
1
0
0
1
0
1
0
1
2
0
1
2
2
2
1
0
0
1
0
0
1
0
2
1
1
2
2
2
1
1
2
0
1
1
1
0
0
1
0
1
1
1
0
1
1
2
2
1
0
1
1
1
0
1
0
1
1
0
0
1
1
0
0
1
1
0
0
1
1
0
2
0
0
1
1
1
0
2
1
1
0
2
1
1
1
2
1
1
0
1
3
1
2
1
1
1
1
2
0
1
1
2
1
1
0
1
0
0
1
2
0
1
0
1
1
1
0
1
0
1
3
1
0
0
4
2
0
0
1
1
3
2
1
1
0
1
0
1
0
2
1
1
0
2
0
1
0
0
0
1
0
1
1
2
1
1
1
2
1
0
2
0
0
0
1
2
0
0
1
1
1
1
1
2
3
0
0
0
1
0
1
1
0
1
1
1
0
1
2
1
0
1
2
1
0
1
2
1
1
1
2
0
1
2
2
1
1
1
1
0
1
1
1
0
1
1
0
0
0
1
1
1
0
1
1
1
0
2
2
2
0
0
1
1
1
1
1
2
1
0
1
0
2
2
1
1
1
1
1
0
1
0
2
2
1
0
1
0
0
1
1
1
0
1
0
1
2
0
1
1
1
1
4
2
0
1
1
1
2
2
1
2
0
1
2
1
1
1
1
0
0
0
0
0
2
1
0
5
1
1
0
0
2
0
0
1
2
2
1
1
0
2
2
1
1
1
1
1
2
0
0
0
1
1
0
1
0
0
2
1
1
2
0
0
1
2
1
1
2
0
2
2
0
1
1
1
1
0
1
1
0
2
1
3
1
2
1
2
2
0
1
1
2
1
1
2
0
0
0
2
0
0
1
0
2
0
1
0
0
1
1
1
2
1
2
0
0
1
0
0
2
0
0
1
1
1
2
1
2
1
2
2
0
0
1
1
1
1
1
1
0
2
1
2
1
1
0
2
2
1
1
2
0
0
0
2
1
2
2
0
2
0
0
0
0
0
2
1
0
1
1
1
1
0
0
1
1
2
1
1
1
0
1
2
0
1
2
1
3
1
1
4
1
0
0
1
1
0
2
0
0
1
1
0
1
0
2
0
2
0
1
0
2
1
0
1
0
1
1
1
1
0
0
1
1
2
1
1
1
0
1
0
2
1
1
0
2
1
1
1
1
3
1
2
1
1
1
0
0
0
1
1
1
0
2
1
0
1
1
2
0
2
0
1
2
1
2
1
1
5
0
0
1
2
0
2
1
1
1
0
2
1
1
0
1
1
0
1
1
1
1
1
1
1
3
1
1
1
2
1
1
2
2
1
0
1
1
3
1
0
0
1
2
0
2
1
0
1
1
0
0
0
0
2
1
1
0
1
1
1
0
1
1
0
1
1
0
1
1
1
1
1
0
2
0
0
3
0
1
0
2
1
1
1
2
2
0
0
0
2
2
2
1
1
1
1
0
0
1
2
1
2
0
1
1
2
1
2
1
1
0
1
1
2
0
1
2
0
1
2
1
1
1
0
1
1
0
1
2
1
1
0
0
2
1
0
1
0
2
1
1
0
2
2
1
0
0
1
0
0
1
1
1
0
1
2
1
1
1
1
1
1
1
1
2
1
0
0
1
0
1
1
1
1
2
2
1
0
0
1
0
1
2
1
2
2
1
1
2
0
1
0
1
3
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
1
1
1
2
1
1
0
0
1
2
0
0
0
0
1
1
2
1
1
0
1
1
1
2
0
5
0
1
2
1
1
1
1
2
0
2
1
1
0
0
1
1
0
0
2
1
2
1
0
1
0
0
0
0
1
1
0
2
2
2
4
1
2
1
2
0
2
1
0
2
0
0
0
1
0
0
0
1
1
2
0
1
0
2
2
1
1
2
1
1
1
1
0
1
0
0
1
1
1
0
1
1
1
1
1
1
0
3
0
2
2
2
0
2
1
1
1
1
0
2
1
1
0
0
1
2
1
0
1
0
1
1
0
1
2
2
1
0
1
0
2
3
1
1
1
1
0
2
0
0
1
1
1
1
1
0
1
0
6
2
1
0
0
2
2
1
1
0
0
0
1
1
0
1
0
1
3
2
2
1
1
1
1
2
0
1
1
0
0
2
1
1
1
2
4
0
1
1
1
1
1
2
2
1
1
0
1
2
0
0
1
1
0
1
1
0
1
1
1
0
1
2
2
1
0
0
0
0
0
1
2
2
1
2
2
1
0
2
2
1
1
1
1
1
1
0
0
1
0
2
1
0
1
1
2
0
1
1
1
1
1
2
0
1
1
0
1
2
2
1
2
0
2
1
0
1
1
0
0
1
2
2
3
2
1
1
0
0
2
1
0
0
1
1
0
0
2
1
2
0
0
2
4
0
0
1
0
0
0
0
1
1
2
2
0
0
1
0
1
2
0
1
1
2
0
0
0
0
1
0
1
0
1
1
1
2
1
2
0
0
1
2
0
1
0
1
0
0
2
0
1
0
1
1
2
1
1
0
1
0
1
2
1
1
1
0
0
0
2
1
0
0
0
2
1
0
0
0
2
1
4
0
1
1
1
2
1
0
1
0
0
2
1
1
0
1
1
1
0
1
1
1
2
1
2
1
1
2
0
1
1
1
1
1
1
0
1
2
2
0
1
1
0
2
1
2
0
1
0
1
1
2
1
1
1
0
1
0
1
0
1
0
1
4
1
1
1
0
1
1
1
2
2
0
0
0
1
2
1
2
1
1
0
1
0
0
2
1
0
0
2
1
1
1
0
1
0
2
1
2
0
1
1
2
1
1
0
2
1
2
0
1
0
1
0
0
0
0
1
1
1
2
2
0
2
0
1
1
2
0
1
2
2
2
2
0
1
2
1
1
0
1
0
1
1
1
3
1
0
1
2
0
2
2
0
1
1
0
2
1
1
1
0
2
1
1
0
0
1
0
1
2
1
1
0
0
1
1
0
1
1
0
1
2
0
1
1
0
0
0
1
0
0
0
0
2
0
3
0
1
1
1
0
1
1
1
0
0
1
2
1
0
1
0
1
1
0
1
1
1
1
1
0
0
0
1
1
0
0
1
2
1
1
1
1
2
1
1
2
0
0
1
2
0
0
2
0
0
2
0
1
0
2
0
1
1
1
0
1
2
2
0
0
2
2
1
1
3
1
1
0
1
1
1
1
0
0
1
1
1
1
1
1
1
2
1
0
1
1
1
1
2
1
2
1
0
0
0
0
1
1
1
2
2
1
0
0
0
1
2
2
0
1
1
1
0
2
0
1
1
0
1
1
1
1
1
1
1
0
1
1
1
1
2
0
0
2
0
2
1
1
1
1
1
0
0
0
2
1
1
1
1
1
1
2
1
1
1
1
2
0
1
1
0
1
1
1
0
2
2
0
1
0
0
3
0
1
1
2
0
1
1
0
2
0
1
2
0
0
1
2
0
1
1
1
0
2
1
1
1
1
0
1
2
0
0
1
1
1
0
1
0
1
1
2
1
1
2
2
1
2
0
1
2
1
0
1
0
0
1
0
1
2
1
1
0
0
1
0
0
0
0
1
1
0
1
1
1
1
2
2
1
0
1
0
1
1
2
1
0
1
1
1
1
2
1
2
2
2
0
0
0
1
0
1
0
1
3
0
1
1
0
1
1
1
0
0
1
0
1
1
0
1
1
1
1
0
1
0
1
0
2
0
1
4
0
2
0
0
2
0
1
1
2
1
0
2
1
1
0
2
1
0
1
0
1
0
0
0
1
1
1
0
2
2
3
2
0
0
1
0
3
1
1
1
1
1
1
0
0
1
3
2
1
1
1
0
1
1
0
1
0
0
0
1
1
0
1
0
1
1
1
1
1
0
1
0
0
1
1
0
0
0
1
1
2
1
1
2
1
2
0
1
0
1
0
0
1
1
2
1
1
0
0
1
1
0
2
0
2
1
2
0
2
1
0
1
1
2
2
2
1
0
2
1
0
1
1
0
0
1
0
1
0
2
2
0
0
1
2
1
1
1
0
1
1
0
1
0
1
0
0
0
1
1
0
0
1
1
0
0
0
1
1
2
1
2
1
1
1
0
2
1
1
2
1
2
0
2
1
2
1
1
1
1
0
1
2
1
0
1
0
1
0
1
1
1
1
1
1
0
0
0
0
1
2
2
2
2
1
1
1
1
1
1
1
1
2
1
0
0
1
3
0
0
0
1
0
1
2
0
1
1
2
2
0
2
1
0
0
2
1
1
1
2
1
1
2
1
2
1
1
0
2
2
2
2
1
0
1
2
0
1
0
0
1
2
1
0
1
2
2
0
2
0
2
1
1
2
0
1
1
1
2
1
0
1
1
0
0
1
0
1
2
0
1
1
2
1
1
2
1
0
0
2
0
1
1
1
2
1
1
1
1
0
1
0
0
0
1
1
0
1
0
2
2
1
0
1
1
0
0
0
0
1
0
1
2
2
0
0
0
2
2
2
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
0
1
1
1
2
0
1
1
0
0
1
1
2
1
2
2
1
1
0
1
2
0
1
1
1
1
1
1
1
2
0
0
1
1
2
2
2
1
0
1
2
1
0
1
0
1
2
3
1
0
0
1
0
1
1
1
0
0
0
0
1
0
0
0
0
1
2
0
0
1
1
1
0
1
0
1
2
1
1
1
1
1
1
1
1
0
1
0
1
2
0
2
1
1
1
2
0
1
1
1
1
0
2
0
1
1
1
2
0
1
0
0
0
2
2
1
0
2
2
2
0
3
2
0
0
1
0
1
2
0
0
0
1
1
1
1
0
1
2
0
0
0
1
0
1
0
1
2
1
0
1
0
1
0
0
0
2
1
0
1
1
0
0
1
0
1
1
1
1
0
3
0
1
1
1
2
0
1
1
1
0
2
1
0
0
0
2
1
1
0
0
2
0
1
1
1
2
2
1
1
3
0
1
1
2
1
2
1
1
1
0
2
1
2
1
2
1
2
2
0
1
1
0
1
0
1
0
1
2
2
1
2
0
1
0
0
2
1
0
1
1
1
0
2
1
2
2
2
2
1
1
1
1
2
1
0
1
1
1
1
2
2
2
1
1
1
1
1
0
2
0
1
1
1
0
0
1
2
3
0
1
0
0
1
2
1
2
1
1
1
1
0
1
2
0
2
0
0
0
0
1
2
3
1
1
3
0
0
2
1
1
2
1
1
0
0
0
1
2
2
1
2
0
0
1
0
2
1
1
2
0
1
1
1
2
0
1
2
2
1
1
0
1
2
1
0
1
2
0
2
2
1
0
1
2
1
1
2
1
2
1
0
1
1
2
1
1
1
0
1
2
0
0
1
1
0
0
1
1
1
3
1
1
1
1
1
1
1
1
1
1
1
1
0
0
1
1
1
2
1
2
1
1
0
2
1
1
0
1
1
1
0
0
0
0
1
1
1
1
1
1
1
1
1
0
0
2
1
0
2
2
1
1
1
2
2
1
0
1
1
1
0
2
0
2
1
0
2
1
0
1
2
0
2
1
2
0
0
0
1
1
1
1
1
1
0
0
2
2
0
2
1
0
1
1
1
1
1
1
0
0
1
1
2
1
1
0
2
1
0
1
1
1
1
0
0
2
0
1
0
1
2
1
2
0
1
1
0
0
0
0
1
1
2
0
1
2
1
1
0
2
0
0
1
1
0
0
1
0
0
2
0
1
1
0
1
0
1
1
2
1
0
1
3
1
1
0
1
1
1
2
1
1
2
1
1
1
0
1
1
0
2
0
1
1
0
0
2
2
1
1
0
1
0
1
1
0
1
1
1
0
0
0
1
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
0
0
2
1
1
2
2
2
0
0
2
0
1
1
1
0
0
0
2
1
2
0
2
0
1
1
2
1
2
1
0
1
1
2
0
0
1
0
1
1
2
1
1
1
2
1
0
3
0
2
0
0
1
2
1
1
0
0
0
1
1
0
2
2
2
0
0
1
1
1
1
0
0
2
1
1
1
1
2
2
1
0
1
1
0
2
1
1
0
2
1
0
2
2
1
2
0
1
0
2
2
2
0
0
2
0
2
0
1
0
1
1
2
1
0
1
1
1
1
0
4
0
0
0
2
1
3
0
2
2
1
1
2
1
0
0
0
2
0
1
1
0
0
2
1
0
2
0
1
2
2
1
1
1
0
2
1
1
1
0
1
1
2
1
1
2
1
1
1
0
0
3
0
1
1
1
2
1
0
3
4
2
2
0
1
1
1
0
1
1
1
2
1
2
2
1
1
0
0
2
0
2
1
2
1
2
0
1
0
0
2
1
1
2
0
0
0
1
2
2
1
1
0
2
2
2
1
2
1
1
1
2
1
0
0
3
1
0
0
1
1
1
0
0
4
3
2
2
1
2
2
0
2
2
1
1
0
1
2
0
2
1
1
2
2
1
1
1
1
2
1
1
0
1
2
1
1
2
2
1
2
1
1
0
0
2
0
2
0
0
1
2
0
2
3
1
1
0
1
1
2
2
1
2
0
1
1
2
2
2
1
1
1
1
1
2
2
2
2
2
0
0
1
0
1
1
1
1
2
0
0
1
0
0
1
2
2
1
1
1
0
0
1
1
3
1
0
0
0
1
1
0
2
1
2
0
0
0
1
2
0
1
0
1
1
1
0
2
0
2
0
0
2
2
2
0
1
0
0
0
0
1
2
2
0
1
0
1
1
1
1
0
0
0
2
0
1
0
1
0
0
1
1
0
0
1
1
1
1
0
1
1
0
1
1
1
0
1
1
1
1
2
1
0
1
0
0
1
2
1
0
1
0
0
1
2
1
3
1
1
2
1
0
2
0
1
0
0
0
0
1
1
2
2
0
0
0
0
0
0
1
2
1
0
2
1
1
1
0
1
2
2
1
1
2
0
1
0
1
1
2
1
1
0
1
1
1
2
1
1
1
0
0
0
1
2
2
1
1
0
1
1
1
1
1
1
1
1
1
0
0
0
2
1
1
1
1
1
3
2
1
2
2
1
2
0
1
2
1
2
1
1
1
1
1
1
1
2
1
0
1
2
1
1
1
1
2
0
1
3
1
1
1
1
1
1
0
0
1
0
0
1
1
1
0
0
2
1
1
1
1
2
1
0
0
1
2
1
1
2
1
1
1
1
0
1
1
1
0
0
2
0
1
1
0
2
1
2
0
1
1
1
2
1
0
0
1
0
0
2
2
0
1
1
1
1
0
2
2
0
0
1
2
1
1
1
0
1
1
1
1
0
1
1
1
1
1
1
2
1
0
1
1
2
1
1
1
0
1
3
2
0
1
1
1
1
1
5
0
1
0
2
2
0
0
2
1
0
2
1
0
0
2
0
1
2
1
1
2
0
0
0
0
0
1
1
2
1
1
1
1
0
1
2
0
2
0
1
1
0
2
1
1
0
2
2
1
0
1
1
0
0
1
0
0
0
1
1
2
0
1
2
0
1
2
0
0
2
1
1
0
1
0
2
1
0
0
0
1
1
0
0
1
1
2
1
0
0
0
0
2
0
1
1
2
1
0
1
0
1
0
2
1
1
1
1
0
1
1
1
2
1
1
1
1
1
2
3
1
0
0
1
2
0
0
1
1
6
1
0
2
1
1
1
0
1
2
0
0
2
1
1
2
1
1
1
0
1
1
0
1
1
1
2
1
0
1
0
0
1
0
0
0
1
1
0
1
2
1
2
1
2
0
0
0
2
1
2
0
0
1
1
1
1
1
0
1
2
2
0
4
2
1
2
1
2
1
0
1
1
1
0
2
0
2
0
2
2
0
1
1
1
0
1
1
1
1
1
0
0
1
1
1
2
1
0
0
2
0
1
1
1
1
2
0
2
1
2
1
0
1
0
1
0
2
0
1
1
1
0
0
0
1
2
5
0
1
1
2
0
1
0
1
1
1
0
2
1
0
0
0
2
2
1
0
0
3
1
0
0
1
0
0
1
0
1
1
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
1
2
1
2
1
2
2
2
1
0
1
1
4
0
2
0
1
0
2
1
0
0
2
2
1
0
1
1
1
0
1
2
2
1
1
1
0
2
1
0
1
1
0
1
0
1
1
2
1
2
0
0
0
1
2
0
1
1
1
2
1
1
1
0
0
1
1
0
1
1
1
1
2
0
0
0
0
1
1
1
2
0
0
1
1
2
2
0
0
1
0
0
0
1
2
2
1
0
0
1
0
2
0
2
3
1
0
1
2
0
1
0
0
3
1
1
1
1
2
1
0
2
2
1
1
1
1
2
0
1
2
1
2
1
2
1
1
0
4
0
0
1
0
2
0
1
1
1
2
0
1
2
1
2
0
2
2
2
0
1
1
0
1
4
0
0
0
2
2
1
0
1
1
0
2
0
1
2
0
2
1
1
0
1
2
1
1
0
0
1
2
0
1
2
0
2
1
0
2
0
2
0
1
1
1
1
0
0
1
1
2
1
2
0
1
2
0
1
2
2
2
0
1
0
1
3
0
0
1
1
1
2
0
2
1
1
1
0
1
2
0
1
0
1
1
1
1
0
0
0
1
1
1
1
1
1
1
2
1
1
0
0
1
1
1
1
0
0
1
3
1
1
1
0
0
1
2
0
2
1
0
4
1
1
1
1
1
2
1
0
2
1
1
0
2
2
2
1
1
2
1
2
0
0
0
1
2
0
2
0
0
1
1
2
0
3
0
1
2
2
0
1
1
0
0
2
2
2
0
0
1
2
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
0
0
1
0
0
1
1
2
0
1
1
1
1
2
1
2
0
1
2
1
0
1
0
0
0
1
1
1
1
2
1
0
2
0
1
1
0
2
0
1
1
0
2
1
1
2
2
0
1
0
1
1
3
0
2
0
0
0
1
2
1
2
2
1
0
1
1
1
1
1
1
1
2
1
0
1
0
0
1
1
1
1
0
1
2
0
0
1
1
1
1
2
0
2
1
1
1
1
1
0
2
1
2
0
0
2
1
2
0
1
2
1
1
1
1
0
1
0
2
0
2
0
0
1
1
2
1
1
1
0
1
0
1
0
1
0
2
0
1
0
0
0
1
2
0
1
0
0
2
1
1
2
1
0
1
1
1
0
1
1
0
1
2
2
1
0
0
3
2
1
2
1
1
1
0
0
1
1
1
1
1
0
2
0
0
0
1
1
0
2
0
1
1
1
0
0
2
1
1
0
0
1
0
1
0
2
6
1
0
0
1
1
1
0
1
2
1
1
2
0
1
1
0
2
0
1
1
1
0
2
1
2
2
0
0
0
0
2
2
1
1
0
1
1
2
0
0
0
1
0
2
2
0
1
1
1
1
2
1
1
1
1
0
1
1
2
0
0
2
2
0
2
0
0
0
2
1
1
1
1
2
2
2
0
2
1
1
1
2
0
2
2
3
2
1
0
1
0
0
5
0
1
1
2
2
0
0
1
1
2
1
1
0
2
2
1
2
1
2
3
1
0
0
1
1
1
1
2
1
1
0
1
0
1
1
8
0
0
1
2
1
1
0
1
1
2
2
2
1
2
2
1
2
1
0
3
1
1
2
0
1
2
0
0
1
1
2
0
0
0
0
0
0
2
0
1
2
2
2
1
0
0
2
2
1
2
2
1
0
4
0
1
1
3
2
1
1
0
0
2
1
1
1
1
0
2
1
2
2
1
0
1
0
0
1
2
0
1
1
0
1
1
1
0
2
0
2
2
1
3
0
2
2
1
0
2
1
1
0
1
1
1
1
0
0
1
1
1
0
2
0
1
0
1
1
1
0
1
1
1
1
1
0
2
2
2
0
1
1
1
1
1
1
1
1
2
2
0
1
1
1
1
1
1
0
1
1
1
1
1
1
2
2
0
2
0
2
2
1
0
0
1
2
2
1
0
1
0
1
0
1
0
1
2
1
0
0
2
0
2
1
2
1
2
2
0
1
2
1
2
0
0
2
1
0
2
1
2
1
2
1
0
2
0
0
0
2
0
2
0
2
1
2
1
1
1
1
2
1
0
1
2
2
0
0
0
1
1
0
1
1
1
2
0
0
2
2
2
0
2
1
1
1
2
1
2
1
1
1
2
1
0
1
1
1
1
0
1
0
0
1
0
0
0
1
1
0
2
1
0
0
0
2
2
1
3
1
2
0
2
1
1
1
1
1
0
0
0
0
0
1
2
1
1
1
2
1
1
1
1
0
2
0
6
2
1
1
1
1
0
1
0
1
2
1
1
1
1
1
1
0
2
2
0
0
1
0
2
2
1
1
2
0
1
1
2
1
0
1
1
0
1
1
1
1
1
2
0
0
1
0
2
1
2
1
2
1
1
2
2
0
1
0
1
0
2
0
1
2
1
0
1
2
1
0
0
1
4
1
1
1
1
0
0
1
1
1
1
1
0
0
2
1
2
1
2
1
1
0
0
0
1
0
0
1
0
2
1
0
2
0
2
0
1
0
0
0
4
0
1
2
1
1
1
0
2
3
1
2
2
1
0
3
0
1
0
2
2
0
2
2
0
1
1
1
1
2
0
1
2
0
3
2
0
1
2
2
0
0
1
2
2
2
1
1
0
1
0
2
1
1
0
2
0
0
1
1
0
0
0
0
1
2
1
1
1
0
0
0
0
1
0
0
2
2
2
0
0
1
0
1
1
1
0
1
1
1
1
1
1
1
1
1
1
0
0
4
2
1
1
1
0
1
1
0
0
0
1
0
1
1
1
0
2
2
2
1
1
1
1
2
1
1
1
0
2
1
2
0
1
1
1
1
0
1
1
1
2
2
0
2
0
1
1
0
2
0
2
2
1
1
1
0
1
1
2
1
2
1
1
1
1
2
1
0
0
1
1
1
1
1
0
0
1
0
0
0
1
0
1
3
1
0
1
1
1
1
0
0
1
1
0
3
0
1
1
0
1
1
0
1
1
1
0
2
1
1
1
1
1
2
1
2
0
2
1
1
2
0
1
1
1
0
1
0
0
2
1
2
0
1
1
2
0
2
2
1
1
2
2
0
0
0
0
1
1
1
1
0
1
2
1
1
2
2
1
1
1
0
0
0
0
0
1
1
0
1
2
2
2
1
0
1
2
0
1
2
2
1
1
1
2
1
1
2
0
1
1
1
2
1
1
1
2
1
0
1
0
5
1
2
2
1
0
0
1
1
1
1
3
0
0
2
1
1
1
1
2
0
1
1
1
1
0
1
1
1
2
2
0
2
1
1
1
0
1
1
2
2
0
0
2
1
2
1
0
0
1
2
1
1
1
2
0
0
1
0
1
2
1
3
0
1
0
2
1
1
0
0
2
0
1
1
1
2
0
0
1
0
0
1
1
1
0
2
2
1
0
2
0
1
1
1
1
0
2
0
2
1
1
1
2
1
2
1
1
2
2
0
1
2
2
1
0
1
1
2
0
2
1
2
1
2
1
1
1
0
0
1
2
1
1
2
0
1
0
2
1
1
2
2
0
2
1
1
2
1
1
1
1
2
1
0
1
0
0
2
0
0
0
2
0
1
1
1
2
2
1
0
1
1
2
0
1
1
1
0
1
1
1
0
0
2
1
1
1
1
0
1
0
1
1
1
1
0
1
1
0
2
1
1
0
1
0
1
1
2
4
1
1
0
2
0
2
1
1
2
0
3
0
0
1
1
1
0
0
0
0
2
1
0
1
2
2
0
0
1
2
0
0
0
0
0
1
2
1
2
1
2
2
0
0
1
0
2
1
1
2
1
1
2
1
2
1
1
0
1
0
0
0
0
0
1
1
1
2
1
1
1
0
1
2
1
0
1
1
0
2
1
2
0
1
2
0
2
0
1
1
1
2
2
0
0
1
0
1
2
0
1
0
2
2
1
2
0
1
0
2
0
1
1
1
1
1
0
0
0
0
0
0
2
1
0
1
2
1
1
2
1
1
0
1
1
0
1
1
1
0
2
1
1
2
1
1
0
1
1
1
1
1
1
1
1
1
1
1
2
0
0
0
1
1
0
0
1
2
2
1
0
2
0
0
0
1
0
1
1
1
0
0
0
1
0
1
4
2
0
2
2
2
1
1
1
2
0
2
1
1
0
1
1
0
0
0
1
0
1
0
1
0
0
0
2
1
0
1
2
2
0
0
3
1
1
1
2
3
2
1
1
1
1
2
0
1
1
2
0
1
0
0
2
1
1
2
1
0
0
2
2
1
1
1
0
1
1
1
1
0
1
1
0
2
2
1
1
1
0
1
1
1
1
1
0
2
2
0
1
1
2
0
1
1
0
1
1
0
2
1
0
1
1
2
1
0
0
1
1
0
1
1
0
1
1
0
1
0
1
1
0
2
1
1
2
1
2
1
0
1
0
0
1
2
1
1
3
2
2
1
2
0
1
2
0
0
1
1
1
1
2
0
1
1
1
1
1
2
1
2
2
1
1
1
0
0
1
2
1
1
2
1
0
0
2
0
1
2
1
0
0
1
0
1
0
1
1
0
1
1
2
2
2
0
1
2
1
1
0
1
1
1
1
2
0
1
0
1
0
1
1
1
0
0
1
0
1
0
2
2
0
2
1
0
2
1
1
2
0
1
2
2
0
1
2
0
1
1
0
0
1
1
1
0
0
0
0
0
2
1
2
1
2
3
1
1
1
0
1
1
1
0
1
1
2
2
2
2
1
0
1
0
0
0
2
1
3
1
2
1
1
0
1
2
1
0
2
1
1
1
0
1
2
0
2
0
1
1
0
2
2
0
1
2
1
0
0
1
1
2
1
1
0
0
1
1
2
0
0
1
1
0
0
2
2
1
1
2
1
1
1
0
3
0
0
0
2
0
1
1
0
1
2
1
1
1
1
1
1
2
0
1
1
0
1
1
3
1
0
1
0
1
2
1
1
3
0
2
0
0
1
1
2
1
2
0
1
0
0
0
0
1
1
0
0
2
0
0
1
2
3
2
2
0
1
1
1
1
2
0
0
1
0
2
3
1
2
1
0
1
2
0
1
0
1
1
9
1
1
1
1
2
0
6
1
0
1
3
1
1
0
1
1
0
1
0
1
2
1
1
0
0
2
1
0
0
1
2
1
2
1
0
2
1
1
1
2
1
2
0
2
1
2
1
0
2
1
4
0
2
1
1
1
1
1
2
1
0
1
2
1
1
1
0
0
0
0
1
1
0
0
2
2
0
0
1
0
1
2
0
0
0
1
2
0
2
2
0
0
1
1
1
0
1
1
1
1
0
1
0
1
0
1
0
0
0
1
1
1
0
0
2
1
2
0
0
0
1
0
0
1
2
0
1
2
0
1
2
1
2
0
2
2
1
0
0
2
1
1
1
1
1
1
1
0
2
1
0
2
1
1
0
0
1
1
0
0
1
0
1
1
3
2
1
2
1
1
1
0
1
1
2
1
1
1
0
1
1
0
1
1
0
1
2
0
1
0
2
0
2
1
1
1
0
0
2
0
1
2
2
2
2
1
1
0
1
1
1
2
0
0
1
0
2
0
1
1
0
0
0
2
1
0
1
0
1
1
1
1
1
1
0
1
0
0
2
1
0
0
0
0
2
2
0
0
1
2
0
2
2
0
2
0
1
0
4
2
1
2
0
1
1
1
0
1
0
1
2
1
0
2
1
0
0
1
1
1
2
1
0
2
1
0
0
1
2
1
1
2
1
0
0
0
1
2
0
2
2
1
0
2
2
1
2
1
1
1
1
1
1
0
1
0
1
1
2
2
1
1
1
1
1
0
1
0
1
0
0
1
2
0
0
0
1
1
1
2
1
1
2
0
0
0
1
0
1
0
2
2
2
2
2
1
0
0
0
0
1
1
0
1
1
0
1
2
1
1
1
1
2
2
0
1
2
2
2
1
0
0
0
1
1
1
1
1
2
0
0
1
1
1
1
0
0
0
2
0
0
0
1
0
0
1
1
1
1
0
1
1
1
2
1
1
1
0
0
1
0
1
1
1
1
0
1
1
1
0
0
1
1
2
1
1
2
0
1
1
0
0
2
2
0
1
1
1
0
1
0
1
1
1
1
0
1
2
2
0
1
1
1
1
2
2
2
2
1
2
2
2
2
0
0
1
1
1
0
1
1
1
1
2
1
1
0
1
0
0
0
1
1
1
1
0
1
1
1
1
1
2
1
1
2
2
0
2
2
2
1
0
0
1
2
2
5
1
1
1
1
0
0
0
1
2
0
1
2
2
0
1
2
2
1
0
2
1
1
1
1
0
1
1
2
1
0
0
0
1
1
1
0
1
0
0
1
0
1
2
0
1
2
1
0
2
0
1
2
1
0
5
2
1
1
1
0
2
1
1
0
0
1
1
1
2
2
1
1
1
1
1
2
2
0
1
1
1
1
1
2
0
1
0
1
0
0
1
0
0
1
0
2
1
1
1
1
3
0
0
1
2
1
0
1
3
1
0
1
1
1
0
2
1
0
2
0
0
1
0
0
0
0
1
0
1
1
0
1
1
0
1
1
2
1
0
1
2
1
2
0
0
1
1
1
0
1
2
1
2
0
0
2
0
3
1
1
3
2
1
0
2
1
0
2
1
1
1
1
1
0
1
1
0
0
1
0
3
1
1
1
1
2
1
2
2
0
2
2
1
0
0
0
1
1
0
0
0
1
1
2
1
0
2
1
0
1
1
3
2
0
0
1
0
0
0
1
1
0
1
0
1
1
2
1
0
2
2
0
1
0
0
1
1
0
0
1
2
1
0
1
1
0
2
1
1
1
2
2
0
2
1
1
0
2
0
0
1
1
1
1
1
2
1
1
2
1
1
2
0
1
0
0
1
1
0
1
1
0
1
1
0
0
1
0
1
1
3
1
0
0
1
0
1
2
1
1
0
1
1
1
1
1
0
1
2
1
1
1
2
0
1
1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
0
2
0
2
1
1
1
3
1
0
1
1
0
1
0
1
1
0
1
0
2
1
1
2
1
1
1
1
1
2
3
1
2
0
0
1
0
2
1
0
2
0
0
1
1
1
0
0
0
0
1
0
0
1
1
0
0
1
2
1
1
1
2
1
1
0
0
1
1
2
1
0
1
2
1
2
2
0
1
0
1
0
1
2
1
0
2
1
0
1
0
1
1
1
1
0
1
0
1
3
0
0
1
1
0
0
0
1
3
0
0
1
2
1
1
0
0
1
2
1
1
0
0
1
3
0
1
0
1
0
2
1
1
1
1
1
3
1
1
1
0
1
2
1
0
1
1
0
1
1
0
2
0
2
0
0
1
1
0
2
0
1
2
1
0
0
1
0
2
0
0
1
2
2
2
1
1
1
2
1
1
1
2
1
1
1
2
2
1
1
2
1
0
0
0
0
1
1
0
1
1
0
1
0
0
2
1
0
1
2
1
1
1
1
1
2
1
0
0
1
0
1
0
2
1
2
0
1
3
0
1
2
2
1
2
0
1
1
0
1
1
0
0
1
0
2
1
2
0
0
2
1
1
2
0
0
2
2
0
0
0
2
1
1
2
1
1
0
1
1
0
1
1
1
2
1
2
1
2
2
2
0
1
0
2
1
0
1
0
1
1
1
2
2
0
1
2
3
0
1
0
0
0
0
1
1
1
1
1
1
1
1
1
0
0
1
2
1
1
1
0
0
1
0
1
1
0
0
1
1
0
1
1
0
1
2
1
2
0
1
0
2
0
1
1
0
1
1
1
0
1
1
0
2
2
0
2
0
0
2
1
1
0
2
1
2
2
0
3
0
1
0
0
0
0
1
1
0
1
0
0
0
1
1
1
1
1
1
1
0
2
1
1
0
0
2
1
0
1
0
1
1
1
1
1
0
0
1
2
0
1
0
0
1
3
2
1
1
2
0
1
2
1
2
0
0
2
0
2
1
2
0
1
0
1
1
2
2
0
2
0
1
1
1
0
1
2
0
2
2
2
2
2
1
1
0
0
2
0
2
1
2
1
0
1
0
1
1
1
1
1
1
2
1
0
2
1
2
0
2
0
2
1
1
0
0
1
0
0
0
1
0
0
1
4
1
5
2
0
1
1
1
0
1
0
1
1
0
2
2
1
0
1
1
0
1
2
3
1
2
0
2
1
0
0
0
2
0
0
0
0
1
1
0
1
2
1
1
1
2
1
0
1
1
1
2
2
0
1
1
1
1
0
2
0
1
0
1
0
1
0
1
0
2
0
2
0
2
0
2
1
1
1
1
1
0
2
1
1
2
2
2
0
1
1
0
2
0
0
0
0
1
0
1
0
1
0
1
1
1
0
0
0
1
1
1
1
1
1
1
1
0
1
1
1
2
1
1
1
1
1
1
2
2
1
1
2
1
0
2
0
1
0
2
2
0
0
0
1
0
2
0
2
1
2
0
1
1
1
1
2
0
1
1
2
0
1
1
1
1
1
1
2
2
0
2
1
0
0
2
1
0
0
3
2
1
0
0
1
0
1
0
2
1
1
2
1
0
1
0
0
1
1
1
0
1
3
1
2
1
1
0
0
0
1
1
0
2
2
1
3
0
1
1
2
0
1
2
1
0
0
2
1
1
1
1
1
1
0
1
2
1
2
2
0
0
1
0
2
0
0
1
2
1
0
1
2
1
0
1
2
0
1
1
2
1
2
1
1
0
1
1
0
0
2
1
0
0
1
0
1
2
0
0
2
1
0
0
0
1
1
0
3
2
0
1
0
1
0
1
1
0
2
1
2
1
1
0
0
1
2
1
0
1
1
1
1
0
0
1
0
0
1
0
2
2
0
1
0
1
0
0
2
2
0
0
0
2
0
2
0
1
2
2
1
0
0
0
1
0
0
0
2
0
2
1
0
1
1
1
2
2
0
1
0
2
0
1
1
0
0
2
1
2
0
1
4
1
1
2
1
1
1
0
0
2
1
2
1
1
2
1
2
1
1
1
0
1
1
1
2
2
0
0
2
2
1
1
1
0
0
1
0
1
1
1
1
0
2
1
1
1
0
1
1
0
1
1
1
2
0
1
1
2
1
1
1
1
2
0
3
1
1
0
1
2
1
0
0
3
1
2
0
1
0
0
1
1
1
0
1
2
0
2
1
2
1
1
0
0
1
3
1
1
2
1
2
0
2
0
0
2
1
1
0
2
1
2
0
1
2
2
2
2
0
2
1
1
1
0
1
0
1
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
1
1
0
1
0
2
1
1
2
1
2
3
0
1
1
0
1
1
0
1
1
2
1
1
2
0
1
0
1
1
1
1
1
1
2
1
2
2
1
0
2
2
1
0
0
1
1
1
1
2
2
0
1
1
1
1
0
1
2
1
1
1
1
0
0
0
1
2
1
1
1
2
1
1
1
2
1
0
1
1
1
2
2
1
1
2
2
2
2
1
1
1
1
1
0
0
1
1
0
0
1
1
0
2
2
0
2
1
0
0
1
0
0
1
0
2
1
0
0
1
0
0
2
0
0
1
1
1
1
1
1
2
0
1
0
2
1
1
2
2
1
1
1
0
0
0
0
0
1
2
2
2
1
0
1
0
0
0
1
0
1
2
0
0
0
0
0
2
0
1
2
1
0
1
1
1
2
1
0
1
1
0
0
1
0
0
2
1
1
1
2
0
0
2
0
1
1
1
0
1
0
0
1
0
1
0
1
2
0
2
1
1
2
2
0
0
2
2
0
0
1
0
2
0
4
1
0
2
2
2
2
0
0
1
1
0
1
1
1
1
1
0
2
0
0
1
1
1
1
2
1
2
1
1
0
1
0
0
0
3
2
1
2
1
1
1
3
1
2
0
0
1
1
1
0
1
0
2
0
0
1
0
0
1
0
1
2
2
0
0
1
1
1
1
0
1
2
1
2
0
1
1
0
1
2
0
2
2
2
2
0
0
0
2
1
1
0
1
2
2
1
2
1
2
2
0
0
0
0
1
1
2
0
1
1
0
1
1
1
0
1
2
1
0
1
0
0
0
1
1
2
1
2
1
1
0
2
0
2
1
1
0
1
1
2
2
0
2
1
1
1
1
1
0
1
2
0
1
0
1
1
1
1
1
1
0
2
0
1
0
1
1
1
2
1
1
2
1
1
1
0
1
1
2
2
0
0
1
1
2
0
0
0
1
0
0
1
0
0
2
0
1
2
1
0
2
0
0
0
1
0
1
2
2
2
0
1
0
1
0
0
2
2
1
2
1
1
1
2
0
0
1
0
1
1
0
0
1
1
0
1
2
0
2
1
1
1
1
2
0
0
2
1
1
1
1
1
1
2
1
0
2
2
0
0
1
1
1
0
0
2
2
0
1
2
2
2
0
1
1
0
0
1
1
0
2
1
0
0
0
1
2
1
0
0
1
0
1
1
0
2
0
1
1
1
2
1
1
1
0
0
0
2
1
1
1
2
1
1
2
1
1
1
0
2
1
1
2
1
0
1
0
1
2
0
1
1
0
0
0
1
1
1
2
2
1
1
0
0
2
0
1
1
1
0
1
1
1
1
0
2
0
0
2
0
1
2
0
1
5
0
1
1
1
1
2
1
3
0
1
0
0
1
2
1
1
1
1
1
0
0
0
0
0
2
0
0
1
1
2
0
1
1
2
2
2
2
1
1
0
1
1
1
1
0
1
2
0
2
0
1
0
0
1
2
1
1
0
0
1
0
2
2
0
2
1
1
1
0
0
2
1
1
1
1
1
1
2
1
1
0
1
0
2
1
0
0
1
2
3
2
1
2
1
0
0
0
1
0
1
2
1
0
1
2
1
1
1
1
0
1
0
1
2
1
1
2
1
1
1
1
0
2
2
1
1
0
0
2
0
1
0
1
2
1
1
0
1
1
1
2
0
1
1
0
1
3
1
2
1
0
2
2
1
1
1
0
0
1
0
2
0
1
1
1
0
0
2
0
1
1
1
0
2
1
1
3
0
0
0
0
0
1
0
3
0
1
1
0
1
1
0
2
2
1
0
1
0
1
1
1
2
0
1
1
0
2
0
2
1
0
0
0
1
1
1
0
2
1
2
1
0
2
1
0
1
0
1
0
2
2
1
0
1
1
2
1
0
1
1
1
2
2
1
1
0
1
1
1
1
2
1
1
0
1
1
1
1
1
2
2
1
2
1
0
1
1
2
1
0
1
0
0
1
0
1
1
1
1
0
0
2
0
1
0
2
3
1
0
1
1
1
1
0
0
1
1
2
2
1
2
1
0
2
1
2
1
0
0
0
0
1
1
0
0
0
0
2
1
0
0
1
1
1
1
0
2
2
2
0
0
0
1
1
0
1
2
0
2
1
2
2
2
1
2
1
0
1
1
1
2
0
0
1
1
1
0
0
1
3
1
2
1
1
0
1
0
0
1
0
0
1
1
1
1
0
1
0
0
0
2
2
1
1
0
0
0
2
1
0
2
2
1
0
1
1
0
1
1
0
1
1
1
2
1
2
0
1
1
2
2
1
0
1
1
2
2
0
2
1
1
0
0
1
3
1
2
0
1
0
1
1
1
1
0
1
1
0
1
2
1
2
1
0
0
1
0
1
1
0
0
1
2
0
1
0
1
2
0
0
2
1
1
1
1
0
1
0
1
1
0
0
1
1
2
0
2
2
1
1
0
0
1
1
0
2
0
2
1
2
1
1
1
1
0
2
0
1
0
2
1
1
0
2
1
0
1
2
3
1
0
1
1
1
2
1
2
2
0
1
2
1
0
2
1
0
0
0
1
1
1
1
1
1
1
0
1
2
0
3
1
0
0
0
1
1
2
1
0
0
1
2
1
0
0
1
1
0
1
2
1
2
1
2
0
1
1
1
1
2
1
0
1
0
1
1
0
2
1
0
0
0
0
1
1
0
0
0
0
2
2
2
1
1
1
1
1
1
1
0
0
2
0
1
1
1
2
0
0
1
0
1
1
0
0
1
1
0
0
0
0
1
1
2
1
0
1
1
1
2
0
2
1
2
2
2
0
0
2
1
1
0
0
1
2
2
2
0
0
1
1
1
2
1
2
1
1
0
0
1
0
1
1
0
2
1
2
1
0
1
2
0
1
0
1
0
1
2
1
1
0
0
2
0
1
2
1
1
0
1
0
0
1
1
0
1
1
0
1
0
0
2
0
1
0
0
1
1
1
1
0
0
2
2
1
0
1
1
1
1
1
1
2
2
0
0
1
2
1
2
2
2
0
2
1
1
1
1
0
0
2
2
1
1
1
0
0
1
1
0
0
2
1
2
0
1
1
1
0
0
1
0
1
0
2
2
0
1
0
1
0
0
1
2
2
2
1
1
2
1
0
0
2
0
1
1
1
3
0
1
1
1
1
2
2
1
1
1
2
1
1
1
0
1
0
2
0
2
0
0
1
0
1
0
0
1
1
1
0
0
0
2
1
1
0
0
1
1
2
1
1
1
1
0
0
0
2
1
2
1
0
0
1
0
2
2
2
0
2
2
1
2
1
0
2
0
1
2
0
0
0
0
1
1
0
1
0
2
0
0
1
0
1
1
1
1
0
0
1
4
1
0
0
0
1
1
2
1
2
1
1
1
0
1
2
0
1
1
1
0
1
2
0
0
3
1
1
0
1
2
0
1
2
2
0
0
2
0
0
2
2
0
1
1
0
4
1
0
1
2
1
2
0
2
1
0
2
0
2
1
1
0
1
0
0
1
0
1
1
0
1
0
1
0
2
1
0
1
1
2
2
1
2
2
2
1
2
3
1
2
0
3
2
2
0
1
1
0
1
0
0
0
2
0
1
2
0
1
1
1
0
2
0
2
2
2
2
0
1
1
0
0
1
1
1
1
1
1
3
1
2
2
1
1
0
1
2
0
1
0
2
1
2
1
1
1
2
1
0
2
1
1
0
1
2
0
2
0
1
0
1
2
2
2
1
0
2
1
1
2
2
0
2
1
1
0
1
1
2
1
1
1
1
1
0
0
1
2
1
0
1
1
2
0
1
1
0
0
0
1
1
0
2
1
0
1
1
0
0
1
2
1
1
0
1
2
2
1
1
0
0
1
1
0
2
1
1
1
1
1
1
0
2
1
1
1
1
1
0
2
1
0
1
1
0
2
2
0
1
0
1
1
0
1
1
4
1
1
0
0
1
0
2
2
1
0
2
0
1
0
1
1
0
1
1
0
2
1
0
0
0
0
1
1
0
1
0
1
2
0
0
0
1
2
1
1
1
0
1
1
1
0
1
0
0
1
2
3
0
1
1
2
0
1
1
0
1
1
0
2
1
0
0
2
1
1
1
1
0
0
1
0
1
0
0
1
0
0
2
0
0
0
0
1
0
2
1
1
1
2
1
1
2
1
2
1
0
0
0
1
1
0
1
1
2
0
1
2
1
1
2
1
0
0
2
0
0
2
1
0
1
1
2
1
1
1
1
1
1
0
0
1
0
1
1
1
0
0
0
1
1
1
2
0
2
1
0
4
1
1
2
0
0
1
1
0
0
2
1
1
0
0
0
0
1
0
2
2
1
2
1
0
0
1
0
0
2
1
1
1
4
1
0
1
0
2
1
0
1
1
0
0
2
0
0
1
2
0
1
0
1
1
0
2
1
2
2
1
3
2
2
1
0
1
1
2
2
0
0
1
1
1
1
0
0
3
1
2
0
0
1
0
1
0
2
1
0
2
1
1
1
1
0
1
1
1
2
1
1
0
1
1
2
1
1
1
2
2
2
0
0
2
0
1
1
0
2
1
0
0
1
1
0
0
1
2
1
1
2
1
0
2
2
2
2
1
2
0
2
1
0
1
1
0
0
1
1
0
0
0
1
2
0
1
1
1
1
1
1
1
3
0
0
0
0
1
2
1
2
1
1
1
1
0
2
1
1
2
0
1
1
0
2
1
1
0
1
1
2
1
2
3
1
1
1
0
0
0
2
1
0
1
2
1
1
1
1
1
2
2
0
1
2
1
0
1
2
0
1
1
2
1
1
2
1
0
0
1
1
2
0
0
0
1
0
2
0
0
2
2
1
1
1
1
1
0
0
1
1
1
1
2
2
1
0
1
2
1
1
0
1
0
2
1
2
0
2
0
2
1
1
1
1
1
0
1
1
1
1
2
1
1
2
1
1
1
1
2
0
1
1
3
2
1
1
1
0
1
2
0
2
1
1
2
2
2
1
2
0
2
0
0
0
1
1
2
1
1
2
0
2
0
1
2
0
0
1
1
2
1
0
2
1
1
0
1
2
0
0
2
1
1
1
2
0
2
1
2
0
2
2
1
2
1
0
2
0
1
1
1
1
0
1
1
0
2
1
0
2
0
1
1
2
0
0
2
1
1
0
0
0
2
1
0
1
1
0
1
1
0
1
1
2
1
2
2
2
1
0
2
1
1
1
1
2
2
2
1
1
2
1
0
0
2
2
2
0
2
0
1
1
1
0
1
0
2
0
1
0
1
2
0
1
1
2
1
2
1
0
0
2
1
1
0
0
0
1
1
2
2
0
0
1
1
0
0
0
0
2
1
0
1
1
1
0
1
1
0
0
0
0
1
1
0
0
0
0
0
1
1
0
1
1
0
0
0
2
1
2
0
0
0
1
0
0
2
2
1
0
0
0
2
1
2
1
1
0
2
3
0
1
0
1
1
2
2
2
0
2
1
2
0
2
1
1
1
1
1
1
2
2
0
1
1
1
3
2
1
0
2
1
1
1
2
0
0
1
0
0
2
0
1
0
0
1
0
1
1
1
2
0
2
1
0
0
2
1
0
0
1
2
3
1
0
2
2
0
1
1
1
3
1
2
0
0
1
0
0
2
0
0
0
1
2
2
2
0
0
1
0
2
0
0
1
0
2
2
1
0
1
0
1
1
2
1
0
0
2
0
1
0
1
1
0
0
1
2
0
1
1
1
0
0
1
0
1
1
2
1
1
1
2
2
0
2
0
1
0
1
1
0
0
1
1
0
0
2
0
2
0
0
0
1
1
1
1
1
0
2
0
0
1
1
0
1
1
1
1
1
0
2
1
1
1
0
2
2
1
3
2
2
3
0
2
0
0
2
2
2
1
2
1
0
0
1
1
0
1
0
1
1
2
2
2
2
2
1
0
0
1
2
2
2
0
1
1
1
1
0
0
2
1
0
1
1
0
0
1
0
0
1
1
0
0
1
1
2
2
0
2
1
1
0
0
1
1
2
1
2
1
1
0
2
0
5
1
0
1
1
0
1
0
1
0
1
0
2
0
1
2
2
1
1
1
1
0
2
2
0
0
2
2
2
1
1
1
0
2
1
0
1
1
2
2
2
0
2
2
1
1
0
1
2
0
1
0
1
1
2
1
2
1
1
0
0
1
1
2
1
1
2
1
1
0
1
2
0
2
1
2
0
2
0
1
2
0
2
2
0
2
1
0
0
2
1
1
0
2
0
2
2
2
2
1
1
0
0
1
0
2
1
2
5
0
1
1
1
1
0
0
1
0
1
2
1
1
0
2
0
1
0
0
2
1
1
0
1
0
1
0
0
2
2
0
0
0
2
1
3
0
2
1
4
2
2
1
0
1
0
1
1
0
2
0
1
0
0
2
0
1
1
1
3
2
1
2
0
1
2
1
1
1
1
1
0
0
1
1
1
1
1
1
1
1
2
0
1
1
1
0
1
1
0
1
0
1
1
0
1
1
1
2
2
2
2
1
0
1
2
0
0
0
1
1
0
1
2
2
3
1
1
1
0
1
1
4
1
2
0
1
1
2
1
1
1
0
2
2
0
2
0
1
2
1
1
1
1
1
1
1
0
1
0
1
1
1
2
2
1
1
0
1
1
2
2
1
1
1
1
0
1
1
0
1
1
0
1
2
0
0
0
0
0
1
1
0
0
0
0
1
1
1
2
2
2
1
0
0
0
1
2
1
1
2
2
0
2
0
0
1
0
0
2
0
1
0
2
0
1
1
1
1
1
0
0
1
2
1
1
0
1
2
3
1
1
1
1
1
1
1
0
1
1
0
2
0
1
3
0
1
0
0
0
0
1
1
2
0
0
1
0
2
2
0
2
0
0
0
2
1
1
0
1
0
1
0
0
0
1
1
2
1
1
0
1
1
1
1
1
2
3
0
2
0
0
0
1
1
2
1
2
1
2
2
1
1
0
2
1
2
1
1
1
0
1
0
1
0
1
2
1
2
1
2
1
0
2
0
0
1
0
0
0
0
1
0
1
0
1
2
1
1
1
1
0
2
1
1
2
0
1
1
0
1
1
0
1
2
2
1
1
1
1
0
2
0
1
0
1
1
2
3
2
0
1
1
2
3
1
2
1
0
2
1
2
1
0
2
0
1
0
1
2
1
0
1
1
1
1
0
0
1
0
1
1
0
2
1
0
2
1
0
1
2
2
0
1
1
0
0
2
1
1
0
2
1
1
2
1
2
2
0
0
1
1
2
1
0
1
1
1
1
0
2
1
3
1
1
2
1
2
1
1
0
1
0
0
0
2
2
0
1
3
0
3
1
1
0
1
1
2
1
0
1
1
0
0
2
0
0
2
1
1
2
1
1
0
0
1
2
0
1
3
0
0
0
2
0
2
0
0
1
1
1
2
0
1
0
1
2
0
1
2
1
0
0
1
2
1
0
2
0
1
0
1
1
1
2
2
0
1
1
0
0
1
1
0
1
1
0
1
1
0
1
1
1
1
0
0
0
2
0
1
0
2
1
0
2
2
0
2
1
1
1
1
1
3
2
1
2
0
1
1
1
1
2
0
1
1
1
1
1
1
1
1
0
1
1
1
0
1
0
1
1
0
2
0
1
0
1
0
2
1
1
0
1
0
1
1
0
2
1
3
1
2
0
1
0
0
2
1
0
1
1
1
2
1
1
0
1
1
1
0
1
1
0
2
2
0
0
0
1
1
0
0
1
0
2
2
1
2
1
1
0
1
1
0
0
1
0
0
1
1
1
1
1
1
2
0
0
0
2
1
2
0
1
2
1
1
1
2
0
1
0
1
0
0
1
1
2
2
1
2
2
1
0
1
1
2
2
0
0
2
0
0
1
1
1
1
5
1
1
2
1
1
0
1
1
1
2
2
1
0
1
1
1
2
3
2
1
1
2
1
1
2
0
1
2
0
0
1
3
3
2
1
1
0
0
1
0
1
0
0
1
1
1
2
2
2
1
1
2
1
2
2
0
1
1
1
0
0
2
0
1
1
0
0
0
1
1
0
2
0
1
1
0
1
2
0
1
0
0
0
2
1
1
1
0
0
0
0
0
0
0
0
0
0
2
0
1
1
1
1
0
1
1
0
2
1
0
0
1
1
2
0
0
0
1
0
2
1
0
1
0
2
0
0
0
0
0
0
1
0
0
1
1
2
0
1
2
0
1
0
2
1
0
1
2
2
2
2
0
0
1
1
0
1
1
2
2
1
0
1
0
0
1
0
1
0
2
2
1
1
1
1
2
1
1
1
1
1
2
3
0
1
0
0
2
1
0
0
2
1
1
0
2
0
0
0
1
2
1
1
2
1
2
2
0
3
0
2
0
1
0
1
2
2
1
1
2
0
2
1
0
0
1
2
1
1
0
1
1
1
2
0
1
1
1
2
1
2
0
0
0
1
1
2
1
0
0
1
0
1
1
1
1
1
0
0
2
1
1
1
1
0
2
0
2
1
0
1
0
0
2
0
0
1
1
0
2
0
0
1
2
0
3
3
1
0
2
1
1
0
1
2
3
2
0
1
1
0
0
1
2
0
0
2
1
1
2
0
0
1
1
2
0
0
1
2
1
1
0
0
1
1
2
2
1
0
0
1
1
0
0
2
1
2
0
1
2
2
1
1
2
1
1
2
1
0
0
0
0
1
1
1
1
1
1
1
0
1
0
2
0
2
1
0
1
0
0
0
2
1
0
1
0
1
1
0
1
2
0
0
0
2
0
1
1
1
1
1
2
0
2
2
1
0
1
0
1
1
1
0
1
0
0
0
1
1
0
1
0
0
1
0
0
0
0
1
1
0
0
0
1
1
0
0
3
2
0
1
2
1
1
1
1
1
1
1
1
0
2
1
0
1
0
2
1
1
2
2
0
1
2
1
2
2
2
2
1
0
2
0
0
1
2
1
1
1
1
2
1
0
1
1
0
1
2
1
0
1
2
1
2
1
1
0
1
1
1
1
0
1
1
2
0
1
0
1
2
2
2
2
0
1
2
0
0
0
0
1
2
0
1
0
2
1
1
1
0
0
2
2
2
1
0
1
1
1
0
2
1
1
2
1
0
0
1
2
1
0
0
0
1
0
1
2
1
1
1
1
2
1
1
1
2
1
1
1
1
2
2
2
1
0
0
1
1
0
1
0
1
1
1
0
1
2
0
0
0
2
2
2
1
0
3
2
1
1
1
0
2
1
0
0
0
1
1
2
2
1
1
0
0
2
1
1
1
0
1
1
2
1
1
0
1
0
0
1
2
1
2
0
1
2
0
1
1
1
1
2
0
0
0
1
2
0
2
2
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
1
1
1
1
2
2
1
1
2
0
0
0
0
1
1
1
2
1
2
1
1
2
1
1
0
1
1
1
1
1
0
2
0
2
0
0
0
1
0
2
1
1
1
1
1
0
0
1
1
0
0
0
0
2
1
0
2
1
2
2
1
1
0
2
0
1
1
0
2
1
1
2
0
1
1
1
1
1
2
1
0
1
1
1
1
0
1
1
1
1
0
2
0
1
1
1
0
1
3
2
2
1
2
0
0
1
1
1
1
2
2
1
1
0
0
0
1
0
2
2
0
1
3
0
1
2
2
2
1
2
1
0
0
1
0
1
0
0
1
1
1
1
1
1
2
0
1
0
1
1
1
1
1
2
1
2
0
1
1
1
0
1
2
1
1
0
1
3
2
0
0
1
0
1
2
1
1
2
3
0
1
0
1
0
2
1
1
1
2
2
1
0
1
0
1
1
1
0
0
1
2
1
1
1
1
0
1
1
1
0
2
0
0
1
1
0
1
2
2
0
1
0
2
1
2
1
1
0
2
2
1
0
0
1
1
1
1
1
1
2
0
2
1
1
2
0
1
0
1
1
2
1
0
0
1
1
1
1
1
0
1
1
1
0
1
1
0
0
0
1
0
2
2
1
2
2
1
0
0
0
0
0
1
3
2
0
1
2
1
0
1
0
1
2
0
1
0
2
0
1
0
1
1
0
0
2
1
1
1
0
2
1
1
1
2
0
1
2
2
1
0
2
1
1
2
0
1
0
0
0
0
1
2
0
1
1
2
1
1
0
1
1
0
2
2
1
1
0
1
1
1
1
1
2
1
3
0
0
2
1
1
1
1
1
2
2
0
1
0
2
1
2
1
1
1
1
0
1
2
2
0
1
1
1
1
2
0
1
1
0
1
0
0
2
2
1
1
1
1
1
0
0
1
2
1
0
2
1
1
0
1
2
2
1
2
0
1
2
1
1
1
2
0
0
1
1
1
2
1
0
2
1
0
0
1
2
0
1
0
1
0
2
2
3
2
1
2
0
1
1
1
1
1
1
1
0
2
1
0
1
1
0
0
0
0
1
1
1
1
0
0
0
0
2
0
1
1
0
0
2
1
1
2
1
1
2
1
1
1
0
1
2
1
0
2
0
1
1
0
1
0
0
2
4
2
1
0
1
1
1
0
1
2
1
2
1
0
1
1
0
2
2
1
1
1
1
1
0
1
2
1
2
1
1
1
0
1
0
0
2
2
0
0
1
1
0
2
1
1
1
0
1
2
1
1
1
1
1
1
1
0
0
1
0
1
1
0
0
1
1
1
0
1
0
1
1
1
2
1
1
2
1
1
1
1
1
0
2
0
1
1
1
2
2
1
1
0
2
0
1
0
0
0
2
0
2
0
1
2
0
2
1
0
1
1
0
1
1
2
1
1
2
1
1
2
2
1
1
1
2
1
1
1
2
1
0
1
2
2
0
0
1
1
0
2
1
1
1
1
0
2
2
2
0
0
2
1
1
1
2
0
2
2
0
0
0
1
0
2
0
1
0
1
0
1
2
0
0
1
1
1
0
2
1
0
0
1
0
2
1
1
1
2
1
1
0
1
2
0
2
0
1
0
1
0
2
2
0
2
1
0
0
1
1
1
0
1
1
0
1
0
2
1
0
2
1
2
1
1
2
0
0
0
1
0
0
1
1
3
1
2
0
1
1
0
2
2
2
1
2
0
0
1
2
1
0
2
1
1
1
0
0
0
0
1
0
1
1
1
1
0
0
1
0
0
0
1
0
0
0
0
0
2
0
1
1
2
1
1
1
1
2
1
1
1
2
0
1
0
1
0
0
1
2
1
1
2
2
1
1
1
0
1
0
1
1
0
1
2
1
1
1
0
0
1
1
1
0
1
1
1
0
2
2
2
2
1
2
1
0
1
2
0
0
3
0
2
0
3
1
1
0
1
1
0
1
2
0
2
2
2
0
0
0
0
0
0
1
2
1
1
3
1
1
1
1
1
0
1
0
1
1
1
1
2
1
1
1
1
0
2
0
1
2
1
1
0
1
0
1
0
0
1
1
0
0
1
0
2
2
1
1
1
1
1
1
1
1
0
0
1
0
0
1
2
2
0
0
1
0
1
1
0
0
0
2
2
0
1
1
0
0
1
1
2
2
1
0
0
0
1
1
2
0
2
1
3
0
0
1
2
0
2
1
1
1
1
1
0
1
1
0
1
1
0
1
1
2
0
1
0
1
1
3
1
1
2
0
2
1
0
1
0
1
1
2
1
1
0
0
1
0
0
3
1
1
0
1
1
1
1
0
1
1
1
2
2
1
2
0
1
3
0
1
0
2
2
1
1
3
0
1
1
2
1
2
2
1
1
1
0
1
1
2
1
1
2
1
1
1
0
1
0
2
1
1
2
1
1
1
2
1
1
0
1
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
1
1
0
1
1
1
2
1
2
0
0
1
0
1
0
1
1
2
1
1
1
1
2
1
1
1
0
1
0
1
0
2
2
2
1
2
1
1
1
1
0
2
1
2
1
1
2
0
1
0
1
1
1
0
1
1
1
1
0
2
1
1
1
1
1
1
0
1
2
1
1
1
1
1
1
1
0
1
1
0
1
1
2
1
0
1
0
1
2
1
1
2
1
0
1
0
0
0
1
1
1
1
1
1
1
1
2
1
1
1
2
1
0
1
0
1
0
1
0
1
0
1
1
0
1
0
2
0
2
1
0
1
1
0
0
1
1
0
4
1
1
0
1
1
1
1
1
2
0
1
2
1
2
0
2
0
0
1
0
0
0
1
0
1
2
0
0
2
2
1
2
0
1
1
2
2
1
0
1
1
0
0
0
1
0
1
0
0
0
1
1
1
1
2
1
1
1
1
0
0
1
1
0
1
0
1
2
1
0
1
1
1
1
1
0
1
1
2
1
0
1
2
1
1
1
1
1
2
0
0
1
1
1
2
1
0
1
1
1
2
1
2
1
0
2
0
0
1
1
0
1
1
0
0
1
2
2
0
2
1
1
1
0
2
1
1
0
0
2
1
1
0
0
1
0
1
2
2
2
2
0
1
0
1
0
2
0
0
0
0
0
0
1
2
2
1
4
2
0
1
0
2
2
1
2
1
0
1
1
1
0
1
0
1
1
3
1
0
1
0
1
0
1
0
0
1
0
2
0
2
0
1
2
2
1
1
1
1
2
1
1
0
1
1
0
1
1
0
0
1
0
2
0
1
1
2
0
0
1
0
0
1
2
1
0
2
1
0
2
1
1
2
0
1
1
2
1
1
1
1
1
2
0
1
1
2
0
2
0
0
2
0
0
0
1
0
1
1
1
1
1
0
0
0
1
1
1
1
0
0
1
1
0
1
2
2
1
1
1
1
1
0
0
1
1
2
1
0
2
1
1
0
1
2
2
1
1
0
0
0
1
1
2
1
2
2
2
1
0
0
2
1
1
1
1
1
1
0
0
1
0
1
0
2
0
2
0
1
2
0
2
0
1
0
1
1
1
2
0
0
2
0
0
1
1
0
1
0
1
3
1
7
0
1
2
1
2
2
1
1
2
2
1
0
1
0
0
0
1
1
2
1
3
0
0
0
0
1
2
1
0
1
1
2
2
1
3
2
1
1
1
0
0
0
1
1
0
2
1
1
1
2
2
3
1
0
1
2
0
0
1
1
0
0
1
0
0
1
1
0
2
1
1
2
1
2
0
0
0
1
0
1
2
1
5
2
0
0
0
1
0
1
2
1
1
0
0
2
1
1
0
1
0
0
0
0
1
1
2
1
1
1
1
0
0
1
2
1
0
0
1
1
0
1
1
1
0
1
1
1
1
0
1
1
2
0
0
0
1
0
2
1
0
1
1
1
1
1
1
2
0
1
1
2
1
1
1
1
2
0
2
1
0
0
1
0
1
1
2
1
2
0
1
0
1
0
1
2
0
1
0
1
2
1
1
1
2
1
1
1
1
1
0
0
1
1
1
2
0
0
1
0
1
1
7
1
1
1
1
0
2
0
2
0
2
1
2
1
1
1
0
2
0
1
2
1
1
1
1
2
1
2
2
0
0
0
2
2
0
0
1
0
2
2
2
0
1
0
2
2
4
0
2
1
2
2
2
0
2
2
2
1
2
1
0
1
0
2
2
1
1
0
2
0
0
1
1
1
2
1
1
0
1
1
1
0
1
2
1
0
1
2
1
0
0
1
1
0
2
1
0
1
1
2
2
0
1
1
1
1
0
1
2
1
0
1
0
1
2
2
0
0
1
0
1
0
1
1
1
0
1
1
2
0
0
0
0
1
0
1
1
1
1
0
1
0
0
1
1
0
1
0
1
2
2
1
1
1
1
1
0
1
0
1
1
0
2
0
1
2
0
0
1
0
0
1
0
0
1
1
2
1
2
1
1
2
0
0
1
1
2
0
2
1
1
1
0
1
1
0
0
1
2
1
4
2
1
3
0
1
2
2
2
1
1
2
0
1
0
1
1
1
1
0
0
1
0
3
1
2
3
1
1
1
2
2
2
0
2
1
1
2
0
1
1
2
0
2
0
2
1
2
0
0
1
0
1
0
0
2
1
1
2
2
0
1
1
0
0
0
2
2
2
1
1
0
2
1
1
1
1
1
2
0
1
0
0
2
1
1
1
0
0
1
1
1
1
1
2
1
2
1
1
0
1
0
2
1
1
2
1
1
1
2
2
0
0
2
2
1
1
2
0
1
0
1
0
1
1
1
0
2
0
1
0
1
1
1
1
0
1
1
0
0
1
2
0
1
0
2
1
0
0
2
1
0
1
0
0
0
1
1
1
1
1
1
1
1
0
0
0
1
1
1
1
0
0
0
2
1
1
1
1
0
2
1
0
0
0
0
1
1
2
1
0
2
1
1
0
0
1
2
1
1
2
2
1
2
1
2
1
1
0
2
0
1
0
1
0
1
1
2
0
0
1
1
1
0
5
2
1
0
2
0
0
0
0
1
1
1
1
0
2
1
1
0
0
1
0
1
1
0
1
1
1
2
0
0
1
0
2
1
0
0
1
3
0
1
0
0
1
2
2
1
0
2
1
2
0
1
1
2
1
0
1
2
2
1
0
1
1
1
1
1
1
0
1
1
0
0
0
1
1
1
0
0
1
0
1
0
1
0
1
0
1
1
2
1
0
1
1
0
1
1
1
1
1
0
1
0
1
0
1
1
0
1
2
0
0
1
1
1
1
0
1
1
1
0
0
2
0
1
0
1
0
1
1
1
1
1
0
0
0
0
1
1
1
1
1
2
2
1
2
1
2
2
0
0
0
1
0
1
1
1
0
1
1
2
1
0
1
0
1
1
2
0
0
1
2
1
1
0
2
1
1
0
1
0
2
1
0
1
1
0
1
0
2
0
0
2
1
1
1
0
0
1
1
1
1
2
2
1
1
0
1
1
1
2
2
2
1
1
2
0
2
1
0
1
2
1
1
1
1
0
0
2
1
1
1
1
0
1
1
0
1
1
2
0
0
0
3
2
0
2
0
0
0
1
2
1
1
1
0
0
2
1
2
4
1
1
1
2
1
2
1
0
1
1
1
1
1
1
1
0
2
1
0
0
0
1
2
1
1
2
1
2
1
0
1
2
0
1
3
0
0
1
2
0
2
0
1
1
0
0
0
3
0
2
1
0
0
1
2
1
1
0
1
1
0
2
0
1
2
0
2
1
0
2
1
1
1
0
1
1
2
1
1
2
0
2
0
2
0
0
2
1
0
1
2
1
1
0
1
1
2
1
2
2
2
1
0
1
1
1
0
0
0
1
1
0
2
1
0
0
0
2
0
1
2
2
1
0
2
0
0
1
1
0
2
0
1
0
1
0
0
0
2
0
2
0
1
1
1
1
1
1
2
1
0
0
1
0
1
0
1
2
1
1
2
1
1
2
2
0
1
2
2
2
1
0
0
1
0
0
0
0
0
0
0
0
3
2
0
1
1
2
2
2
2
0
0
2
0
0
2
2
3
1
1
2
1
1
0
1
1
1
3
0
0
1
1
0
2
0
1
0
1
0
1
0
1
1
2
0
2
1
2
1
0
1
1
1
0
1
1
1
1
0
0
0
1
3
1
1
1
1
0
0
1
1
1
1
1
1
0
1
1
1
0
2
2
0
1
0
1
1
2
2
1
0
2
1
2
1
1
0
2
2
1
1
1
2
0
0
1
0
2
1
1
1
0
0
2
0
1
1
0
2
0
1
2
2
2
1
1
2
3
0
2
2
2
2
1
1
0
1
1
1
1
2
3
1
1
2
1
1
0
0
0
3
1
1
1
2
2
1
1
0
0
2
1
0
1
0
1
0
1
1
0
2
0
1
1
2
1
0
0
1
0
1
1
1
2
0
1
1
1
1
0
1
0
1
1
0
2
0
1
2
1
0
1
1
0
3
1
2
0
1
0
0
0
1
1
1
0
0
0
1
1
0
1
1
2
0
1
1
0
2
0
1
1
2
2
0
1
0
2
0
1
0
0
0
2
0
1
0
0
1
1
1
2
0
2
0
0
1
1
0
1
1
0
1
1
1
1
3
1
1
1
2
0
1
2
0
2
1
0
1
1
2
0
0
1
0
2
1
1
1
2
1
2
1
0
1
1
1
1
1
0
2
2
1
0
1
2
1
1
1
1
1
2
2
0
0
0
0
1
0
2
0
3
1
1
0
0
0
0
2
0
0
0
1
2
1
1
2
2
1
1
1
1
2
0
1
1
2
1
0
0
2
3
0
3
1
2
1
1
0
2
0
2
1
2
0
2
1
1
1
2
1
1
1
1
1
0
2
1
1
2
2
0
0
1
1
1
0
1
2
0
0
1
0
0
1
1
2
1
0
1
2
1
2
1
1
1
0
0
0
1
1
0
1
2
1
1
0
1
1
0
1
2
1
1
0
0
1
1
0
2
1
1
2
0
1
0
0
0
1
1
1
0
0
0
0
0
2
1
0
1
1
3
1
1
0
1
0
1
1
1
1
1
2
1
0
2
1
1
1
1
0
1
0
1
1
2
1
1
0
1
1
0
0
0
0
1
1
2
2
1
0
1
0
0
4
0
0
2
2
0
0
1
0
1
0
0
2
0
1
1
0
1
1
0
2
2
0
1
1
0
1
0
0
1
1
1
2
0
2
2
0
0
1
0
0
1
1
1
0
1
1
1
0
1
2
1
4
0
1
1
1
2
0
0
2
0
1
1
0
1
2
1
0
2
2
1
0
2
1
0
1
2
1
2
1
1
2
0
0
0
1
4
1
1
2
0
0
1
1
0
1
1
1
1
0
0
2
0
1
2
1
1
2
1
2
0
0
0
1
2
0
1
2
1
1
1
2
0
1
1
2
1
1
1
0
0
1
2
1
1
0
1
1
0
2
0
1
0
2
1
1
2
3
0
1
1
0
0
1
1
1
1
1
0
1
1
1
0
0
2
1
0
1
2
0
0
1
1
1
2
0
0
1
1
2
0
0
2
1
0
0
1
1
1
1
1
0
4
1
1
0
0
0
0
1
2
2
0
1
0
1
1
1
1
0
1
0
1
0
0
0
0
0
1
1
1
1
1
2
2
0
2
0
1
1
0
0
1
2
1
0
1
1
1
1
0
0
0
0
1
1
0
0
0
3
1
1
1
1
2
0
0
1
1
1
2
1
1
2
1
0
1
1
0
1
0
1
1
1
1
1
0
0
0
1
2
1
0
2
2
0
0
1
3
1
1
2
2
0
1
2
1
1
0
2
1
1
0
0
1
2
1
3
1
2
0
1
1
1
1
0
2
2
1
2
0
1
0
2
2
0
1
0
1
0
1
1
1
2
2
2
1
1
2
1
1
0
1
1
1
0
0
0
0
1
1
1
1
0
1
0
1
0
1
1
0
1
0
2
2
0
2
2
2
2
0
1
1
2
1
0
0
0
3
1
2
1
0
0
0
2
2
1
1
0
1
0
2
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
1
0
2
1
1
0
1
0
1
0
1
1
0
2
2
1
1
0
0
1
0
1
1
0
0
1
2
1
0
2
1
0
1
0
2
0
2
1
1
1
1
1
1
1
0
2
2
2
2
0
1
0
2
1
1
1
1
1
2
1
0
1
1
1
0
1
2
0
1
1
0
0
0
0
0
2
0
2
2
1
0
1
0
0
1
0
0
0
1
1
2
2
1
1
0
0
0
1
0
1
1
1
1
2
1
1
2
2
1
0
0
0
1
0
1
0
2
1
2
1
0
1
1
3
0
2
0
1
0
0
1
1
0
2
1
1
1
1
1
0
1
0
0
1
1
1
0
1
1
2
1
0
0
1
0
0
0
0
1
1
1
2
1
2
0
1
2
0
1
0
1
1
2
1
2
1
1
2
0
1
2
1
1
1
2
2
0
2
0
2
2
1
1
0
1
2
1
1
0
0
2
4
1
1
0
1
1
1
1
0
1
0
1
2
1
1
0
1
1
0
1
0
1
1
1
0
2
2
1
0
1
2
0
1
0
2
2
0
1
1
0
0
0
1
2
2
2
1
1
1
2
0
0
1
2
0
0
1
1
1
1
2
1
1
2
1
2
0
2
0
1
0
0
1
1
1
3
2
0
2
1
0
0
1
0
2
0
1
2
1
0
1
1
0
0
2
1
1
1
0
1
0
0
0
0
0
1
0
2
2
1
1
1
1
1
2
0
0
2
2
0
0
3
2
1
2
2
2
0
1
1
1
0
1
2
2
1
1
1
2
0
1
1
1
1
0
0
1
1
1
2
1
1
1
0
2
0
0
1
0
1
1
0
0
0
2
1
0
0
0
0
2
1
1
1
1
2
1
2
2
1
1
1
0
0
2
1
0
1
1
2
0
1
1
2
1
0
2
0
0
0
2
1
1
1
2
0
1
0
1
1
0
1
0
1
1
2
0
0
1
1
1
0
0
1
1
1
4
1
1
1
1
2
1
2
3
0
0
0
0
0
0
0
3
1
1
1
0
0
3
0
2
2
0
3
2
0
0
1
2
0
0
1
2
1
1
1
1
1
3
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
1
0
0
3
1
1
1
1
2
1
1
1
0
1
1
2
0
1
0
0
0
2
1
2
0
0
2
1
1
0
1
2
1
1
2
3
1
1
1
2
0
0
2
0
1
1
1
1
1
0
1
1
1
0
1
2
0
2
1
0
1
1
0
2
0
1
0
0
0
1
1
2
1
0
0
3
2
0
1
1
0
0
2
0
0
1
0
2
1
2
0
1
0
0
2
0
0
1
1
1
0
1
10
1
0
2
1
1
1
0
0
0
0
1
1
1
1
0
1
0
0
2
1
1
1
2
1
1
1
1
0
1
1
1
1
0
1
1
1
1
2
3
0
1
0
2
0
0
1
1
2
0
1
0
1
2
1
3
0
1
0
2
0
1
1
0
2
2
2
1
2
1
1
1
1
1
2
0
2
1
1
0
0
1
1
0
1
0
0
0
0
1
1
1
2
1
2
0
1
0
1
0
0
1
1
1
1
2
0
2
5
1
2
1
1
0
1
1
2
0
1
0
1
1
2
0
0
1
0
2
0
2
0
1
0
0
1
1
1
0
1
1
1
1
1
1
1
1
2
0
1
2
1
0
3
0
2
1
0
0
1
1
0
1
0
0
0
0
1
2
0
1
1
0
2
1
0
1
0
0
2
0
1
0
0
1
2
2
1
1
0
1
0
1
0
3
1
2
1
0
0
1
1
1
1
2
0
1
2
0
1
1
1
1
2
1
1
1
0
2
0
2
1
1
0
0
1
1
1
1
1
1
3
1
1
0
0
1
2
1
1
1
1
1
1
0
0
2
2
0
1
1
0
2
1
0
0
2
1
1
1
0
2
2
2
1
2
0
0
2
1
1
1
1
2
1
2
1
2
1
2
1
2
1
0
0
0
0
2
0
0
0
2
0
0
1
1
0
1
1
0
0
2
1
1
0
2
1
2
1
0
2
0
1
1
2
1
1
0
0
1
0
1
1
0
0
1
0
1
0
0
2
0
1
2
1
1
1
0
1
1
2
2
1
1
1
1
0
1
0
1
0
2
2
2
1
2
0
1
1
2
1
0
1
1
2
0
0
1
0
1
1
2
1
0
0
1
2
0
0
2
1
1
0
0
1
1
1
2
1
1
0
0
0
1
2
2
2
0
1
1
0
0
0
1
2
1
0
1
0
1
0
2
1
1
1
0
0
1
0
1
0
1
2
1
2
1
0
1
0
2
1
0
1
1
0
0
1
0
1
1
1
2
2
1
1
0
1
0
2
0
0
1
0
0
1
1
0
1
1
2
1
4
0
2
0
1
0
1
0
0
1
3
0
1
1
1
1
2
2
0
2
2
1
0
0
0
0
1
1
0
2
1
2
1
0
0
1
1
1
1
0
0
0
1
2
0
0
1
0
0
2
2
1
1
1
1
1
1
1
1
2
1
2
0
0
0
2
1
1
1
2
1
1
1
1
0
2
0
2
1
1
2
2
1
0
0
1
1
1
1
1
2
2
0
1
1
2
2
1
1
1
2
1
1
2
2
0
0
2
0
1
1
0
1
2
1
0
0
1
1
1
0
1
1
1
2
1
1
0
2
0
1
1
0
1
1
1
1
1
1
1
1
1
1
0
0
1
1
1
2
2
0
1
1
1
0
2
1
1
0
1
0
0
1
0
1
1
1
2
1
2
0
1
2
1
1
1
0
1
1
2
1
2
1
0
0
0
1
2
1
0
1
1
1
1
1
1
0
0
1
2
2
2
2
1
1
1
2
2
1
1
2
2
4
1
1
1
7
2
1
2
1
1
0
1
2
0
0
2
2
1
2
0
1
3
0
0
1
0
3
0
2
2
0
1
4
0
0
1
0
0
1
1
2
0
1
0
1
1
2
2
1
1
1
1
1
0
1
1
2
2
0
1
1
0
2
1
1
1
1
1
2
1
0
2
1
1
2
1
1
1
1
2
0
0
1
1
1
1
1
1
2
1
1
2
1
1
3
1
0
1
0
2
1
0
0
1
1
0
1
1
1
1
0
0
1
1
1
0
1
0
1
0
1
1
2
0
0
1
1
0
0
1
1
0
0
1
0
2
0
2
2
1
1
4
2
2
4
0
0
0
2
2
1
1
0
2
1
0
1
1
4
2
2
1
1
2
2
1
0
0
1
0
2
2
1
1
0
0
0
0
1
1
0
2
1
1
1
0
1
0
1
2
1
2
3
1
1
0
0
1
1
1
0
1
2
1
0
2
1
0
1
1
1
1
1
1
1
0
1
0
1
0
1
1
0
2
0
1
1
0
0
0
0
1
1
1
2
0
1
0
0
0
0
0
1
0
0
1
1
0
1
1
2
1
1
1
1
1
2
0
1
1
2
2
1
2
2
1
0
2
1
1
2
1
1
1
0
1
2
0
0
1
1
1
1
0
0
1
1
1
1
1
1
1
1
1
1
1
0
2
2
1
1
1
2
1
0
0
1
1
0
0
0
1
1
0
1
1
1
1
1
1
0
1
1
1
1
1
0
0
2
1
1
1
0
0
1
2
2
1
2
0
2
1
0
1
2
0
1
1
1
0
1
0
2
2
1
0
0
0
3
0
1
2
1
1
0
1
2
1
2
2
0
1
2
0
2
2
0
0
2
1
2
0
1
2
1
0
1
0
1
1
1
1
0
2
1
0
0
1
1
1
0
1
0
0
1
2
0
1
1
2
1
2
0
1
1
1
1
2
1
1
0
1
1
1
0
1
0
2
1
1
2
2
0
2
0
1
2
2
1
1
0
0
0
0
3
1
1
1
0
0
2
0
0
0
0
1
1
1
2
1
0
1
1
1
1
0
0
1
1
0
0
0
1
0
0
1
1
0
2
0
1
0
1
1
2
2
1
1
2
0
0
0
0
1
7
1
1
1
0
1
2
2
1
0
2
1
0
1
0
1
1
2
1
1
0
0
0
1
2
1
0
1
1
1
1
1
1
0
0
1
0
0
1
1
1
1
0
1
1
1
1
1
1
1
2
2
0
1
2
1
1
2
2
0
2
2
1
2
1
0
1
1
1
0
0
1
1
2
1
1
0
0
2
2
1
2
2
1
0
2
0
1
2
1
2
2
0
2
2
0
0
1
0
0
2
0
2
1
1
2
3
2
2
0
0
0
1
0
1
2
2
2
2
1
2
1
1
0
1
1
1
2
4
1
2
2
1
1
0
2
1
1
2
1
1
0
1
2
1
0
2
1
1
1
1
0
2
0
1
1
2
0
1
1
2
1
0
0
2
0
1
0
0
1
2
1
1
1
2
1
0
1
3
0
1
1
0
1
2
2
0
2
2
1
1
1
1
1
1
1
1
0
0
1
1
2
0
2
2
1
1
0
1
1
2
2
2
1
0
1
1
1
2
0
1
1
2
1
2
1
0
1
1
2
2
3
1
1
2
2
1
1
0
0
0
1
0
1
1
0
0
0
1
1
0
0
0
1
0
1
1
0
0
0
2
2
1
0
0
2
0
0
1
1
1
2
2
0
1
0
1
0
0
0
0
0
2
1
0
1
1
2
0
1
0
1
0
1
1
1
1
1
1
1
0
1
2
0
1
2
2
1
1
1
0
0
1
1
0
1
1
1
1
2
0
0
2
1
1
2
2
2
0
1
1
1
0
0
3
1
2
0
0
0
0
0
1
1
1
1
1
2
1
1
0
1
1
1
1
2
1
1
2
1
1
1
1
2
0
2
0
1
1
2
2
0
1
1
1
2
1
1
0
2
0
1
1
1
0
2
1
1
0
1
1
1
2
0
0
1
0
1
0
1
1
0
2
0
1
0
2
3
2
2
1
1
0
1
1
0
2
2
1
0
1
1
1
1
0
1
0
1
1
2
1
0
0
0
1
1
0
1
0
1
1
0
2
2
1
1
2
1
1
1
1
0
0
0
2
1
2
1
1
2
1
1
0
2
0
1
0
1
1
2
0
0
0
1
0
0
0
2
1
0
1
1
1
0
0
1
0
0
1
0
1
1
0
0
0
2
1
0
5
1
1
2
1
1
2
1
0
1
2
1
1
1
2
2
1
0
1
0
2
1
1
2
1
1
0
1
0
0
0
0
0
2
0
1
2
1
1
1
1
1
0
1
1
1
0
1
1
1
1
1
1
1
1
2
0
0
1
1
1
0
2
2
1
0
0
1
1
0
1
0
1
1
0
0
1
1
1
1
1
1
0
2
1
0
0
2
1
2
1
1
1
0
0
1
1
2
0
2
1
1
0
1
0
1
0
1
1
1
3
1
1
0
1
1
0
1
0
0
1
2
2
1
1
1
0
1
1
0
2
1
0
1
1
2
0
1
0
1
1
2
0
1
1
1
2
1
0
1
1
1
0
1
2
1
2
0
1
1
1
0
0
2
1
1
1
1
2
0
2
0
0
2
0
2
1
1
3
0
1
2
0
1
2
1
1
1
1
0
1
2
1
1
1
1
0
2
1
1
1
2
2
1
1
1
1
3
1
0
0
0
1
0
2
1
0
1
2
0
2
2
1
0
1
1
0
0
2
1
3
0
1
0
1
2
1
2
0
0
0
2
1
1
0
1
1
2
1
2
1
0
0
1
0
2
1
2
2
2
0
0
1
1
0
0
2
0
0
0
1
0
1
2
1
1
0
1
0
1
1
0
0
1
0
0
1
2
1
2
1
0
5
0
2
0
0
0
0
1
3
2
1
0
2
2
0
2
1
4
0
0
1
0
1
0
1
0
1
1
0
1
2
1
1
2
0
2
1
0
1
3
1
1
0
1
1
2
2
1
0
0
1
0
1
2
2
1
1
1
2
1
1
0
0
1
2
1
0
1
2
1
1
0
1
1
2
1
1
2
0
1
1
2
0
2
1
1
0
2
0
0
1
0
1
1
0
0
1
1
1
1
0
0
1
0
2
1
1
0
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
0
0
1
1
2
1
0
1
1
1
0
1
2
2
0
0
1
0
2
1
2
1
1
1
1
0
1
0
0
1
2
0
1
1
2
1
0
0
1
1
1
2
0
1
1
1
1
0
1
0
1
1
0
0
1
1
2
2
1
1
1
0
0
0
1
1
2
2
1
1
0
1
1
0
0
2
1
1
1
1
1
1
1
1
0
2
0
1
1
2
0
0
1
0
0
1
1
1
0
1
1
1
2
2
1
2
1
0
1
2
1
1
0
0
1
1
1
0
1
2
1
3
0
1
1
2
1
0
0
0
0
2
2
0
2
1
1
0
1
0
1
1
1
2
1
1
1
0
0
0
2
1
1
0
2
1
0
1
1
1
1
0
0
1
0
1
1
1
0
0
1
1
2
1
2
2
2
0
0
0
3
1
0
0
1
0
1
1
1
1
1
0
2
1
0
1
2
0
1
0
1
0
2
1
2
2
1
1
1
2
2
1
2
1
1
1
0
2
0
2
1
1
2
2
2
0
0
2
0
1
1
2
0
1
2
1
0
0
1
1
1
2
1
2
1
1
1
0
2
2
0
1
0
0
2
0
1
2
2
0
0
2
0
1
1
0
1
0
1
1
2
0
0
1
0
0
0
1
1
1
2
2
3
1
2
0
0
0
1
0
0
2
1
1
1
2
0
2
1
1
2
1
1
1
2
1
1
1
1
0
0
1
0
0
1
1
2
0
2
1
1
0
5
2
2
1
0
2
2
0
1
0
1
0
2
1
0
1
1
2
0
2
0
0
1
2
1
1
1
0
1
11
1
3
1
1
1
1
1
2
3
1
0
1
1
0
0
2
0
0
2
1
2
0
0
3
2
0
0
2
2
1
0
1
3
1
1
2
0
0
0
1
0
1
0
0
1
0
0
0
2
1
1
2
1
1
1
1
1
1
0
1
2
2
0
1
2
1
1
2
0
0
0
0
0
2
0
1
0
1
2
0
0
0
1
0
1
1
2
0
1
1
1
0
0
0
1
1
2
2
1
1
1
0
1
2
2
1
0
0
0
1
1
2
0
0
1
0
0
2
0
1
1
0
2
1
0
2
2
1
0
2
1
0
0
1
0
1
2
1
1
0
1
1
1
1
2
0
0
2
0
1
0
1
1
0
2
0
0
0
1
1
1
0
2
1
2
1
1
0
1
0
1
2
1
1
1
0
1
0
0
1
1
0
0
1
0
1
1
1
1
0
1
0
0
1
1
1
0
2
2
1
0
1
0
1
1
0
0
0
1
1
1
1
0
1
1
1
1
2
0
0
1
2
2
0
2
2
2
1
0
1
2
0
0
1
0
1
0
0
2
1
0
3
2
1
2
1
0
1
1
0
1
2
0
1
1
1
2
2
0
0
1
1
1
1
0
1
0
0
1
1
1
0
0
1
1
1
1
1
1
1
0
1
2
3
1
0
1
0
1
2
2
1
0
2
1
0
1
1
0
1
1
1
0
2
1
1
0
1
0
1
0
0
1
1
0
0
1
1
1
0
1
0
0
2
2
1
0
1
0
1
1
1
0
1
0
1
0
0
1
0
1
3
1
1
0
2
1
1
1
0
2
1
1
0
1
0
2
0
2
1
2
0
0
1
1
2
3
2
1
0
0
2
2
0
2
2
2
1
2
1
1
0
1
1
1
0
0
0
1
1
2
1
0
0
2
0
1
2
0
1
0
1
1
0
2
2
1
2
1
0
0
1
2
2
1
0
0
0
2
2
0
1
0
1
2
0
1
0
2
1
1
0
1
0
1
1
1
0
2
2
1
1
1
1
0
1
1
1
2
2
0
1
1
1
2
1
2
3
2
2
1
1
0
1
1
2
0
2
2
2
1
2
1
1
1
0
2
2
0
1
1
2
1
1
0
1
0
1
1
2
1
2
0
0
1
2
0
0
1
2
1
1
1
2
1
1
1
1
2
2
0
1
0
0
0
1
0
2
0
2
2
1
3
2
1
0
2
1
2
2
0
1
0
2
1
0
1
1
0
0
2
1
1
0
4
0
0
3
1
1
3
2
3
1
1
2
1
1
0
1
0
0
2
2
2
1
1
1
1
1
2
0
0
1
1
0
1
2
1
0
0
2
0
0
0
1
1
0
1
2
0
1
2
1
1
1
1
2
3
2
1
2
1
1
1
1
1
1
0
2
1
1
0
0
0
1
0
4
1
2
0
1
0
1
0
1
1
0
1
0
1
1
0
1
2
1
1
0
0
0
1
0
0
1
2
1
1
1
2
2
2
0
1
0
1
1
0
2
1
2
0
0
1
2
0
1
1
1
2
2
0
1
1
2
2
1
2
2
0
2
3
2
2
2
0
1
2
1
2
2
1
2
2
2
1
0
1
1
0
0
1
1
2
1
0
2
1
0
1
0
1
1
1
2
0
2
0
1
1
2
1
1
1
0
0
0
0
1
1
1
1
2
0
2
1
0
0
0
1
2
1
0
1
0
1
1
0
0
0
1
1
1
1
1
0
1
2
1
2
1
2
0
1
2
1
1
1
1
1
2
1
2
1
0
2
0
1
1
1
1
1
0
2
2
2
1
2
0
0
1
1
1
0
1
2
0
2
2
0
1
1
1
1
1
1
2
0
0
0
1
1
2
1
2
1
1
0
1
1
2
2
0
1
0
2
0
1
0
1
1
2
0
0
1
1
2
2
1
1
2
0
1
0
1
2
2
0
0
1
1
2
3
1
1
1
1
1
1
1
0
3
0
2
1
0
0
1
1
1
2
1
0
2
2
1
2
1
1
1
0
0
1
1
1
1
1
1
0
1
0
0
2
0
0
1
1
0
2
1
2
2
0
1
0
2
0
1
0
0
2
3
2
0
1
5
2
1
1
0
2
0
1
0
1
2
1
1
0
1
1
0
2
0
0
1
1
0
0
0
2
1
0
0
1
1
0
2
2
1
1
1
0
1
1
0
1
2
0
1
0
0
1
1
1
2
2
1
1
0
1
0
1
1
0
1
1
0
1
0
0
1
1
1
2
1
1
1
1
1
1
2
2
2
1
4
1
2
1
2
1
1
1
1
2
2
2
1
0
1
2
2
1
1
0
2
2
2
0
0
1
1
2
1
0
1
0
0
0
1
2
2
0
0
1
1
1
1
1
0
2
1
0
0
0
0
0
2
0
1
1
1
0
2
1
1
1
1
1
2
1
0
0
0
1
2
1
1
1
2
5
2
0
1
2
1
2
1
4
1
0
1
0
2
1
2
1
1
1
0
2
1
0
1
0
1
1
1
1
1
1
2
2
2
2
0
1
1
0
1
1
2
1
1
2
1
1
0
1
0
1
0
0
1
1
2
1
2
0
1
2
1
0
0
1
1
0
0
1
1
1
0
0
0
1
1
1
0
0
2
3
1
1
1
1
1
1
2
1
2
0
1
2
1
1
2
1
1
0
0
2
0
1
0
0
0
2
0
1
2
1
1
1
0
1
1
1
0
1
0
1
1
1
0
1
1
1
1
0
1
2
1
1
0
1
1
2
1
2
0
1
2
0
1
1
1
0
0
0
1
2
1
1
1
1
2
2
0
0
0
2
1
2
2
1
1
1
0
1
1
0
1
0
0
1
2
1
1
1
1
1
1
1
0
0
0
1
1
0
1
2
0
0
1
0
1
1
1
2
1
0
2
1
1
2
0
1
0
0
1
1
1
1
1
2
0
2
2
2
1
0
0
0
2
1
1
1
1
2
1
2
2
0
0
1
1
2
0
1
1
0
1
0
2
0
1
1
1
0
1
0
0
0
1
1
1
1
2
0
2
0
0
1
1
1
1
1
0
2
1
1
3
1
0
2
1
0
1
2
3
1
0
1
2
0
2
1
0
2
1
1
0
0
1
1
1
2
2
1
1
1
1
0
0
2
0
1
2
2
0
2
0
1
0
1
0
2
2
1
0
0
1
1
0
1
2
1
1
2
1
1
0
0
1
1
2
0
2
0
1
1
1
1
0
2
2
0
2
3
2
0
0
2
0
1
1
0
0
1
1
2
1
2
1
1
1
1
2
2
0
0
2
0
1
0
1
2
1
0
0
2
0
1
0
1
2
2
2
1
1
0
0
1
1
2
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
2
1
1
0
0
0
0
1
1
1
1
1
0
2
2
1
1
0
1
1
2
1
2
1
1
0
1
1
0
1
2
0
2
1
2
0
2
0
1
2
2
1
0
2
1
2
1
1
1
1
1
1
2
1
0
0
0
1
1
1
0
1
2
0
1
0
1
1
1
0
0
0
0
3
1
1
2
0
1
0
1
1
1
1
1
1
1
2
0
2
2
0
2
0
1
2
0
0
0
1
1
2
2
1
2
1
1
2
0
2
0
1
0
1
2
2
1
2
1
2
0
0
2
1
1
2
0
2
2
1
2
1
2
1
1
0
1
1
0
2
1
0
1
2
0
1
1
0
1
1
1
1
1
1
0
1
1
0
1
1
2
1
1
1
1
0
2
1
1
2
1
2
1
0
2
1
0
1
0
1
1
0
2
1
1
2
1
1
1
1
0
1
1
1
0
2
1
2
0
0
1
0
1
0
1
1
2
1
1
1
0
1
1
1
0
0
1
0
1
1
0
0
0
0
1
0
1
1
1
0
1
2
2
1
1
1
2
2
1
2
0
2
1
1
2
0
0
2
1
2
1
1
2
1
1
0
2
2
0
1
1
0
2
1
0
1
1
3
1
1
1
1
1
0
1
0
1
0
1
1
1
2
0
1
1
3
1
2
1
2
1
0
1
2
1
2
0
1
1
1
2
0
1
0
0
1
1
1
2
2
1
2
1
1
1
0
0
1
1
2
1
1
1
0
2
0
0
1
2
1
0
1
1
0
0
2
2
2
1
2
1
1
1
1
0
2
0
2
2
0
0
0
1
0
2
0
0
1
0
2
2
3
2
0
0
1
1
1
1
1
0
0
2
2
1
1
0
0
1
0
2
2
0
2
1
1
1
2
1
1
3
1
1
1
0
0
1
2
0
1
2
2
1
1
0
0
0
0
1
0
0
1
0
1
0
2
2
0
1
3
1
1
0
1
0
1
0
0
1
1
0
0
0
0
2
1
0
1
1
0
1
2
1
1
1
2
1
1
0
2
1
0
1
1
1
0
0
1
1
0
0
0
1
1
0
1
1
0
1
1
0
3
1
1
2
0
1
1
1
1
2
0
2
1
0
2
1
1
1
1
2
1
1
2
1
1
2
0
2
1
1
2
1
2
0
1
0
1
1
1
1
0
0
0
1
1
0
1
2
0
1
0
1
2
2
0
1
1
0
0
0
1
0
1
1
2
0
0
1
1
1
1
0
0
0
1
0
0
1
0
0
1
1
1
1
1
0
1
2
2
1
1
1
2
0
1
1
0
0
2
0
1
1
1
2
1
2
1
1
1
0
1
0
0
1
1
0
0
2
1
0
0
1
1
1
0
1
0
2
0
1
0
1
2
0
1
1
0
0
1
1
0
4
1
1
0
0
0
1
0
1
0
1
0
0
1
0
0
1
1
0
1
1
2
1
2
1
1
1
1
1
2
2
1
0
1
1
0
0
1
2
1
3
1
1
0
0
1
1
0
2
1
1
1
2
0
1
1
2
1
1
0
0
0
1
0
1
2
1
1
0
1
1
1
2
0
1
1
1
0
0
0
0
1
0
2
0
0
2
1
2
1
2
2
1
0
1
0
1
0
1
0
0
0
0
1
1
0
2
1
0
2
1
0
0
1
0
2
2
1
0
0
2
1
2
2
1
1
1
1
2
1
1
0
2
1
1
0
0
2
0
1
1
2
2
1
0
2
1
0
1
0
0
0
0
0
1
1
0
1
1
1
1
2
0
0
2
1
0
1
2
2
1
2
0
0
0
1
2
2
1
1
0
2
1
1
1
2
1
1
2
2
2
2
1
0
2
1
0
2
0
1
1
2
1
0
1
0
0
0
1
0
1
1
0
1
0
1
2
1
1
1
2
1
1
0
2
1
1
0
0
1
2
1
0
1
0
1
1
2
0
1
1
1
0
1
1
1
1
2
1
0
1
2
0
1
1
1
0
1
1
1
0
4
1
0
1
0
1
0
0
1
2
0
0
1
1
2
1
2
0
2
1
0
0
2
1
1
0
0
0
2
0
0
1
2
0
1
0
2
1
2
1
0
0
1
1
1
1
1
1
1
1
2
1
0
1
1
2
1
1
1
0
2
1
1
0
0
1
1
2
0
0
0
1
1
1
1
0
2
0
1
1
0
0
0
2
2
2
0
1
2
2
2
1
2
0
2
2
1
0
0
2
0
1
2
1
0
1
0
1
0
2
0
0
1
1
2
2
2
1
1
3
2
0
0
2
1
1
2
0
1
3
1
0
0
1
1
2
0
2
0
5
2
1
2
0
1
1
2
0
2
2
1
0
2
2
1
0
1
0
1
0
0
1
0
1
1
0
2
2
0
1
2
1
1
2
1
2
2
2
1
0
2
2
1
1
1
1
1
1
0
1
1
1
1
1
0
0
1
0
0
1
1
2
0
2
1
1
0
0
1
1
1
0
1
1
0
1
1
1
2
0
1
1
1
1
0
2
0
2
1
2
1
0
1
1
1
2
0
1
1
1
1
1
0
1
0
0
0
1
0
0
0
1
2
1
1
2
2
1
1
1
1
0
1
1
1
1
1
2
1
2
0
2
1
1
0
0
0
1
1
0
0
1
1
0
0
0
1
0
1
2
1
2
1
2
1
2
0
0
1
0
1
0
0
0
1
0
2
2
2
1
2
2
1
4
0
1
0
0
0
1
1
1
1
1
1
1
2
1
1
1
0
2
1
1
1
1
0
0
1
0
1
1
0
0
2
1
1
1
1
2
2
1
0
0
1
1
0
0
1
2
1
1
1
2
0
0
1
1
0
0
2
1
0
1
0
1
1
0
0
1
2
0
1
0
0
1
2
1
0
0
0
1
1
2
1
1
1
1
0
1
1
1
0
1
0
1
2
2
1
2
2
1
2
0
0
0
0
1
1
1
1
1
0
0
2
1
2
2
0
2
1
1
1
2
0
1
0
1
2
1
1
1
2
0
1
0
0
1
1
2
1
0
0
2
1
1
1
2
1
0
1
0
0
2
2
1
0
2
0
0
1
1
2
1
0
0
0
1
0
1
1
1
2
0
0
1
1
1
1
1
0
0
0
1
1
2
1
0
1
1
1
2
0
3
1
2
1
1
1
1
1
1
2
0
2
0
2
0
2
2
1
2
1
2
4
0
1
0
0
1
0
2
1
1
2
2
1
1
0
1
0
1
0
1
1
1
2
1
1
1
0
0
1
1
1
1
0
2
0
0
2
0
1
0
0
2
1
1
1
0
1
0
0
0
3
1
1
1
0
2
2
1
1
2
0
2
1
0
2
2
0
1
2
0
0
1
1
1
1
1
2
2
0
0
0
1
1
2
0
1
1
2
1
0
1
0
1
1
1
2
0
0
3
1
0
0
1
0
1
1
1
0
0
1
2
0
1
1
0
1
1
1
1
2
1
2
1
0
0
1
1
0
1
1
1
0
2
0
1
1
2
1
1
0
3
2
2
0
2
0
0
2
0
0
2
1
2
2
0
0
0
2
2
0
2
1
2
0
1
1
2
1
1
1
1
2
3
2
1
1
0
1
0
2
1
0
2
2
2
0
1
0
1
0
1
2
2
0
2
1
3
0
2
0
2
1
1
2
0
0
0
0
0
2
1
2
1
2
0
2
0
2
2
1
2
1
0
0
2
1
1
0
0
1
0
2
1
1
0
1
0
1
0
0
1
0
1
2
0
2
2
1
0
2
1
2
0
0
1
1
1
1
0
1
2
1
1
1
1
1
1
1
0
1
1
1
2
0
1
0
0
1
0
0
0
1
2
1
2
1
0
0
2
1
0
2
0
1
1
1
0
1
1
0
1
0
0
1
1
1
2
1
1
0
1
1
2
0
2
1
2
1
1
1
0
1
0
2
1
2
1
1
0
1
2
0
1
2
1
2
2
1
0
1
2
2
1
2
2
1
1
1
0
0
0
1
1
2
1
1
2
0
1
2
0
1
2
1
1
1
1
1
1
0
0
1
1
0
2
1
0
1
1
0
2
4
1
2
0
2
1
0
1
0
0
3
0
1
2
0
2
0
1
0
2
2
1
2
1
1
2
0
1
3
2
1
1
1
0
2
1
0
0
0
1
1
1
1
1
1
2
2
0
0
2
1
0
0
1
2
0
2
0
1
1
0
2
1
1
1
1
1
1
2
1
1
0
0
2
0
0
1
2
1
0
2
1
2
0
2
1
1
1
1
1
3
1
2
1
0
1
0
1
0
0
0
2
1
0
0
1
0
1
1
0
2
1
1
1
0
1
1
0
0
0
0
0
1
2
1
1
0
0
0
0
1
1
1
1
0
1
0
0
2
1
1
0
1
1
2
1
1
2
2
1
1
0
2
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
2
1
0
1
1
1
1
0
2
0
1
1
0
0
0
0
0
0
1
1
0
2
1
2
0
2
0
0
1
0
1
1
1
0
0
1
0
1
1
1
1
0
0
0
1
0
1
2
1
0
2
0
1
0
0
0
0
1
0
2
0
0
2
2
0
1
1
0
0
1
1
0
1
0
0
0
0
1
0
0
1
0
0
0
1
2
2
1
0
2
4
2
1
1
1
0
2
2
1
1
1
2
1
1
1
1
0
1
0
1
0
1
1
1
0
2
2
1
1
2
2
0
1
2
0
0
1
1
1
2
1
2
1
0
1
0
2
2
1
1
0
1
1
1
0
0
0
1
2
1
0
0
2
1
1
0
2
0
0
1
0
0
3
2
0
0
1
0
1
1
1
0
1
2
1
1
1
1
0
1
2
1
1
0
3
2
0
1
3
0
1
1
0
0
2
0
1
1
0
1
1
0
0
1
3
1
1
2
1
0
0
2
1
0
0
2
2
4
1
1
1
0
1
0
1
1
1
1
0
0
1
0
1
0
1
1
6
1
1
1
2
1
0
1
1
0
1
0
1
2
0
0
0
0
1
1
0
2
1
2
2
0
4
2
0
0
0
1
1
1
2
1
1
0
1
1
1
0
2
3
1
2
1
0
0
1
1
1
1
2
2
1
0
2
2
2
1
0
0
0
1
2
1
3
1
0
1
0
2
0
2
2
1
1
1
2
1
1
1
0
1
1
0
1
0
0
2
0
0
2
2
1
1
0
1
1
1
0
0
0
1
1
2
0
1
1
2
1
0
1
0
1
1
2
1
1
0
0
1
1
0
1
2
1
2
3
1
1
1
0
2
0
0
2
1
2
1
0
2
0
0
0
1
2
1
0
2
2
1
1
2
0
0
2
2
2
1
2
0
2
1
0
2
1
1
1
0
2
1
1
2
1
1
2
2
1
2
0
1
2
0
0
0
1
2
1
1
2
2
2
1
1
0
0
1
0
0
1
2
1
1
1
0
0
1
1
0
1
0
2
2
1
0
2
1
1
0
1
1
0
1
1
1
0
1
1
1
0
1
1
1
1
1
1
1
0
1
0
1
1
2
1
1
2
2
1
0
2
2
1
0
1
1
0
0
2
1
0
0
1
2
1
1
1
0
2
1
0
1
1
1
1
0
2
1
0
1
1
2
0
2
0
0
1
1
1
1
2
1
1
0
2
1
0
2
0
2
1
2
2
1
2
2
2
0
2
2
1
1
0
0
1
2
1
1
2
1
1
0
2
2
0
1
2
2
3
2
0
1
1
1
1
1
2
1
0
2
0
1
0
0
1
1
1
2
0
1
0
1
0
2
0
0
2
1
0
0
1
1
1
1
1
1
2
1
0
1
2
1
1
1
2
2
0
1
1
0
1
2
2
2
0
0
0
1
1
1
1
1
1
0
0
0
1
1
2
1
0
0
2
0
1
0
1
2
1
0
1
0
1
0
0
1
1
2
2
1
1
1
2
1
1
1
0
0
1
0
0
2
2
1
0
1
2
1
1
0
2
1
0
0
0
0
0
1
0
2
1
1
0
1
1
2
1
1
2
0
2
1
1
1
0
1
2
0
0
0
2
1
0
1
0
1
0
3
0
1
0
1
1
2
0
1
1
1
1
0
1
0
0
0
1
0
2
1
2
1
2
2
1
0
1
1
2
2
2
1
1
1
2
1
2
1
0
1
1
0
4
2
0
1
1
1
0
0
0
1
2
0
1
2
0
1
1
2
1
2
0
2
1
1
1
1
2
2
0
2
2
1
1
2
2
0
1
1
2
1
0
1
2
2
0
1
1
2
0
1
1
0
1
1
2
1
0
0
0
2
2
0
2
3
2
0
1
0
1
1
1
1
0
0
1
1
1
2
1
0
2
1
1
1
1
1
0
1
2
0
1
1
1
2
1
1
2
1
2
2
2
1
1
1
0
1
1
1
1
2
0
1
1
0
2
1
0
0
2
2
1
0
1
1
0
2
2
2
1
0
1
1
1
1
0
1
0
0
2
1
2
2
1
1
2
1
2
1
1
0
1
1
0
1
0
1
2
1
1
1
1
1
1
1
1
0
0
1
1
0
2
1
2
0
1
0
2
2
0
1
1
0
0
1
2
1
1
1
0
1
0
0
0
0
1
1
1
2
0
0
0
0
1
2
2
0
2
0
1
2
2
0
0
0
0
0
1
1
0
1
1
1
0
2
0
0
0
0
1
1
0
0
1
0
0
0
1
0
2
1
0
1
1
1
0
1
1
1
1
0
0
1
1
2
0
1
1
2
2
1
0
0
1
2
0
1
0
2
0
1
0
0
0
1
0
1
2
1
1
1
0
0
1
1
0
0
1
0
2
0
1
1
1
1
1
0
1
0
1
0
0
0
2
2
0
2
0
1
1
1
1
1
2
1
2
2
2
2
1
1
0
2
2
2
2
0
1
1
1
2
4
1
1
1
0
0
0
0
1
0
1
0
2
0
2
2
2
0
1
2
0
1
0
1
2
0
2
0
2
0
0
2
1
1
1
1
1
1
1
1
1
0
1
1
2
0
1
1
1
0
0
0
1
1
0
2
0
0
1
1
1
1
1
1
1
2
0
0
1
1
0
1
2
0
0
0
1
1
0
1
2
2
1
0
2
1
0
2
1
1
0
1
1
1
1
1
0
1
0
1
1
2
1
0
0
0
0
1
0
0
0
1
0
2
1
0
1
0
1
1
2
2
0
2
3
0
1
0
2
1
1
1
2
1
1
0
1
1
1
2
0
1
2
0
2
2
1
0
0
1
0
2
2
2
2
1
0
0
1
1
0
2
1
0
0
1
10
1
0
0
1
1
1
1
2
1
1
1
2
2
1
0
0
1
1
1
1
2
2
1
2
0
1
0
1
1
1
0
2
1
2
0
1
1
0
0
1
0
0
0
1
1
2
3
1
1
2
0
0
0
1
1
0
1
2
0
1
0
1
0
2
1
0
1
0
1
2
2
0
0
0
1
1
1
1
0
1
1
1
0
0
1
0
1
1
2
0
1
1
0
0
0
2
1
1
2
1
1
2
0
1
1
1
1
1
0
1
2
1
1
1
1
1
1
0
0
1
0
1
1
1
0
1
1
1
2
1
2
1
0
1
1
2
0
1
0
1
0
1
0
2
1
1
1
1
0
0
0
2
1
1
1
0
1
1
1
0
0
1
1
0
0
1
1
1
1
0
0
1
0
0
0
1
1
2
1
1
0
0
0
2
0
0
2
1
1
0
1
0
1
1
0
1
0
0
2
2
1
0
2
2
0
1
0
1
0
1
2
0
1
1
1
0
1
2
2
0
0
2
0
0
2
1
1
1
1
1
0
2
0
0
1
1
2
1
0
2
1
1
1
3
2
2
2
2
0
1
0
0
1
0
1
0
1
2
1
1
1
1
0
1
1
0
0
1
0
1
2
6
2
2
1
1
2
1
2
0
1
0
1
0
0
2
2
1
0
1
1
1
1
1
0
1
0
1
1
2
0
1
0
0
1
0
0
0
1
2
2
1
1
1
1
1
1
1
1
0
2
0
2
2
0
2
0
2
2
0
0
2
2
1
3
1
2
0
1
2
0
1
1
0
2
0
1
2
1
0
2
1
1
2
1
1
1
1
2
1
1
2
1
2
1
1
1
1
3
3
2
1
1
1
0
3
1
0
1
1
2
1
2
1
1
1
1
1
1
0
1
0
2
1
1
0
2
1
1
0
2
1
2
1
1
1
0
0
0
2
2
2
1
2
1
2
1
2
1
2
1
2
0
0
1
2
2
0
1
1
1
0
0
1
2
1
2
2
0
0
0
1
2
1
2
1
1
1
1
0
1
1
1
1
1
0
1
0
0
2
0
2
2
0
0
1
2
0
0
0
0
1
2
0
0
0
2
1
1
1
1
1
2
2
2
2
1
1
0
0
2
1
1
2
2
2
0
1
1
0
0
1
2
2
1
1
1
1
1
1
0
2
0
1
2
0
2
0
2
1
0
1
0
0
2
0
1
0
2
2
1
0
0
2
1
0
1
1
1
0
1
2
0
2
1
2
0
0
1
1
2
0
0
1
1
2
2
2
0
2
1
0
2
1
1
1
0
1
1
0
2
2
0
0
1
2
0
1
1
1
0
2
2
0
1
1
0
0
0
2
1
1
0
2
1
4
1
2
2
1
1
2
2
1
1
1
1
2
6
2
2
1
1
1
1
1
1
0
0
0
1
1
1
0
1
0
1
1
0
0
0
1
1
2
2
0
1
0
2
2
2
0
1
1
2
2
1
1
0
2
0
0
0
2
1
0
1
0
1
0
1
0
2
0
1
2
1
1
1
1
0
2
2
1
0
2
1
1
2
1
1
1
1
1
0
1
0
1
2
0
1
1
0
0
1
1
0
1
2
1
0
1
1
3
1
2
1
1
2
2
0
0
1
2
1
1
1
1
0
2
1
1
0
1
2
2
0
1
2
1
0
0
1
0
1
1
1
0
0
0
3
1
1
0
0
0
1
1
0
0
1
0
0
1
1
1
0
0
0
0
2
0
1
1
1
0
0
0
1
0
1
1
0
1
1
0
1
1
1
1
0
1
2
1
1
0
1
2
0
0
0
1
0
2
1
1
0
2
0
2
0
1
0
1
1
1
0
0
0
0
1
2
0
1
2
1
1
0
1
0
1
2
0
1
1
1
0
2
1
1
1
0
1
2
0
1
1
1
1
1
2
1
1
1
1
1
1
1
2
2
2
1
1
1
2
0
1
0
2
1
1
1
0
1
0
1
2
0
1
2
0
1
1
0
0
1
0
0
1
2
1
1
2
0
1
0
0
0
1
1
0
1
1
1
1
0
1
1
0
0
1
2
2
1
1
2
3
1
0
1
2
0
0
0
1
2
0
2
1
1
0
1
2
1
1
1
0
1
1
1
2
0
1
0
1
2
0
1
2
2
1
1
1
1
2
1
1
2
0
0
0
0
0
1
3
0
1
0
0
1
1
2
1
2
1
1
0
1
1
0
0
1
0
1
0
1
0
2
0
0
2
1
2
2
3
2
1
0
0
1
0
2
1
0
2
0
2
0
2
1
0
0
1
0
1
3
0
0
1
1
2
1
2
2
2
0
1
0
0
0
1
0
0
1
1
0
1
1
0
1
1
2
0
1
2
1
2
1
4
0
1
0
0
0
1
0
0
1
1
0
0
1
2
0
1
1
0
1
0
1
1
2
1
0
1
0
2
0
1
1
1
0
2
0
0
2
1
1
2
1
0
1
2
2
1
0
1
1
0
0
2
2
2
1
0
1
1
2
0
2
1
1
2
1
1
1
1
2
0
1
1
2
2
0
1
1
0
2
1
0
1
1
1
2
2
1
1
0
1
3
2
0
2
0
0
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
2
1
0
2
1
2
1
2
0
2
1
0
1
1
2
1
0
0
0
1
1
0
0
0
1
0
0
0
2
2
0
2
1
1
1
2
1
0
1
2
0
2
1
3
1
0
2
0
1
0
0
2
1
0
0
1
1
1
0
1
2
1
0
0
1
1
1
1
0
0
2
0
1
0
2
0
1
1
1
1
1
0
0
3
2
0
1
0
1
2
2
0
1
0
1
2
1
0
1
1
1
2
2
1
0
0
1
0
1
0
1
1
1
0
1
0
1
1
1
3
2
1
3
2
1
1
2
2
2
0
2
0
2
1
2
0
1
1
2
1
0
1
2
1
1
1
0
1
1
2
0
1
1
1
2
2
1
0
1
0
2
1
0
1
0
0
0
1
1
0
1
1
0
1
1
2
0
0
1
0
2
2
1
1
1
0
0
1
1
1
2
0
1
0
0
1
1
2
1
0
2
1
2
1
1
1
1
2
0
2
0
1
1
0
1
2
1
1
0
0
1
2
2
1
0
1
1
2
2
0
1
1
2
2
0
0
2
2
0
1
0
1
1
0
2
2
0
2
2
2
0
0
1
1
2
1
1
1
0
0
0
2
1
2
1
0
1
1
2
0
1
0
1
2
0
1
2
1
1
0
2
0
2
0
1
1
1
1
0
1
1
2
1
2
0
1
0
2
1
2
1
0
1
1
1
1
0
1
1
1
0
1
0
0
0
1
0
2
0
1
0
0
0
1
1
1
2
1
1
1
0
0
1
0
1
2
2
0
0
1
0
2
1
0
1
1
1
0
1
2
1
0
1
0
0
1
1
1
1
2
1
2
1
2
2
0
0
0
2
0
0
1
1
2
0
1
1
0
0
2
1
2
1
4
0
1
1
1
0
1
1
0
0
0
1
2
2
0
1
2
1
0
1
1
0
0
0
1
2
2
0
1
0
0
2
0
2
1
1
0
0
1
0
0
0
0
1
0
2
1
1
2
0
1
0
1
1
2
0
1
0
1
2
1
0
0
1
0
0
2
0
1
0
1
1
1
1
2
1
0
0
0
1
1
1
1
1
0
1
2
1
1
1
1
1
0
2
1
2
0
1
0
2
0
2
2
1
1
2
0
0
0
1
0
1
1
0
2
1
1
0
1
0
1
2
1
1
2
1
1
4
2
0
1
0
2
2
1
1
1
2
1
1
1
1
1
1
0
0
2
1
0
0
3
1
1
0
2
2
2
0
0
0
1
2
1
1
2
1
3
0
1
1
1
2
2
1
1
1
0
1
1
1
2
1
1
2
0
2
1
2
2
1
1
0
0
0
0
0
1
2
0
0
1
2
1
2
2
0
0
0
1
1
1
4
2
1
0
0
0
1
1
1
1
2
1
0
0
0
2
0
1
0
2
1
0
0
1
2
0
0
2
1
1
1
0
1
2
1
1
2
2
1
2
2
2
1
1
1
0
1
1
1
1
1
1
1
2
0
0
0
0
0
0
1
0
1
1
2
1
1
0
1
1
1
1
1
1
2
0
0
0
0
2
1
1
2
1
0
1
1
0
1
0
0
1
0
0
1
0
0
1
1
1
2
1
1
1
0
0
1
2
2
1
0
1
2
1
0
0
0
1
1
0
0
1
1
1
1
0
1
1
2
1
1
0
0
2
2
0
0
1
0
1
0
1
0
1
0
1
1
0
0
1
0
2
1
0
1
1
1
1
2
1
0
1
0
0
1
0
3
1
2
0
0
1
2
1
0
2
2
0
1
0
1
1
1
1
1
2
1
1
1
1
1
1
0
1
3
0
1
1
1
1
0
0
2
1
1
1
2
2
0
1
1
2
1
2
1
0
1
0
0
0
1
1
0
1
1
2
1
1
1
0
2
0
1
2
1
0
0
0
0
1
0
1
2
1
1
0
1
2
0
1
0
2
1
1
2
1
2
1
1
1
0
0
0
1
0
0
1
0
0
1
0
2
2
1
0
0
0
1
2
1
1
0
0
1
0
1
1
2
1
1
1
2
1
1
1
2
1
1
0
2
1
0
0
1
2
1
2
2
2
1
0
1
1
0
1
1
1
0
1
1
1
1
2
1
1
2
2
0
0
0
1
2
0
0
0
0
1
1
2
0
2
1
1
2
1
1
1
0
1
1
1
1
2
1
1
2
1
1
2
2
0
0
1
1
2
2
0
1
2
1
1
1
0
1
1
1
2
0
0
1
1
1
0
2
1
1
1
0
1
2
2
1
2
2
0
1
1
1
0
1
0
2
1
1
2
2
1
0
0
0
0
2
1
0
1
0
1
1
1
0
2
7
2
1
1
2
1
1
0
2
0
0
1
1
2
1
2
0
1
2
0
1
0
1
1
1
2
0
0
1
0
1
1
0
1
1
0
1
0
0
1
0
1
2
1
2
2
0
1
1
2
0
2
1
1
0
1
2
0
1
0
1
1
1
2
0
0
1
2
2
1
1
1
1
0
1
1
1
2
2
3
1
1
1
1
0
2
1
2
0
1
0
2
0
0
1
2
0
1
1
1
0
1
1
2
2
0
0
0
2
0
0
0
4
2
2
1
1
1
1
1
1
2
1
1
1
1
0
0
0
2
1
1
1
1
1
2
2
0
2
1
1
0
2
0
2
1
0
2
1
4
0
0
1
3
2
1
2
0
0
0
2
2
2
0
1
0
0
1
0
1
0
0
1
0
2
2
1
1
0
0
2
2
1
3
1
1
0
1
0
2
2
0
0
1
0
2
0
0
1
0
1
0
2
1
0
1
1
0
1
0
0
1
0
0
2
0
1
0
1
1
1
1
1
2
1
1
1
2
0
1
1
2
2
0
1
1
1
1
1
0
1
0
1
2
2
1
0
0
0
1
2
0
0
1
1
1
1
1
0
1
2
0
1
1
1
0
1
1
1
2
1
1
0
1
2
1
2
1
2
0
0
1
0
1
1
1
1
1
0
1
1
1
1
0
1
0
2
1
1
2
1
0
1
0
2
1
1
1
1
1
1
1
2
2
1
1
1
1
0
2
0
0
1
1
1
1
1
1
2
1
2
1
1
1
1
2
1
0
0
0
0
1
1
1
1
1
0
2
2
0
0
0
0
0
1
1
2
1
1
2
1
1
0
0
0
0
1
0
0
2
0
1
1
1
1
1
1
0
1
2
1
0
1
1
0
1
2
2
2
1
2
0
0
1
1
2
1
2
0
1
1
1
0
2
1
1
1
2
0
0
1
0
1
0
0
0
0
0
1
1
1
1
0
2
2
2
0
0
1
2
1
1
0
1
1
0
0
1
0
0
0
2
1
1
0
1
0
0
1
0
2
1
2
2
2
0
2
1
0
2
2
2
1
1
0
1
1
2
0
0
2
1
2
1
1
0
2
1
1
0
3
0
0
0
1
0
2
1
0
1
0
1
0
1
0
1
1
1
1
1
1
1
1
1
1
0
1
1
0
1
2
0
1
2
0
1
1
0
1
1
0
2
1
1
1
0
2
0
0
1
1
1
0
1
0
2
1
0
2
1
0
1
1
1
2
1
2
2
1
2
1
1
3
0
1
1
1
0
1
1
1
1
2
0
1
1
1
0
0
2
2
1
2
2
1
2
1
2
1
1
1
0
0
1
0
0
1
1
0
1
1
2
0
3
0
0
0
2
2
1
0
0
2
2
0
1
0
1
0
1
0
1
2
0
0
1
1
0
0
1
0
2
2
1
0
2
2
0
2
1
2
1
0
0
1
1
1
0
0
2
0
0
0
2
1
0
2
1
1
2
0
0
0
0
1
2
1
1
2
0
0
1
0
2
0
2
0
0
1
0
1
2
1
1
1
1
1
0
0
1
0
1
0
1
2
2
1
2
1
1
0
1
1
2
0
1
1
0
2
1
1
2
0
1
1
1
0
0
2
2
1
0
0
1
0
1
0
1
1
2
0
1
2
0
2
1
1
2
2
1
1
2
1
2
1
0
0
1
0
0
2
1
1
1
0
1
1
1
0
0
0
1
1
1
1
1
1
1
1
1
0
1
0
1
1
0
2
1
1
1
2
1
0
1
1
2
2
0
1
1
0
1
1
1
2
0
0
0
0
2
1
0
1
1
0
3
1
2
1
1
2
0
1
2
1
0
1
2
1
0
0
0
1
0
1
0
1
1
0
0
1
1
1
2
1
0
2
0
1
1
1
1
1
0
1
1
2
1
1
1
0
2
1
0
0
1
1
1
1
1
2
0
1
1
0
1
0
1
1
1
0
0
3
0
1
1
1
0
0
1
0
1
1
0
1
0
1
1
1
1
0
0
2
1
1
0
0
1
2
1
1
0
0
0
1
1
1
1
0
1
0
0
1
1
2
0
1
0
0
2
1
0
1
0
1
1
0
3
1
0
1
1
1
1
0
0
0
1
1
0
0
1
2
1
0
1
1
0
1
0
1
1
2
1
1
1
1
0
1
1
1
1
0
0
1
2
0
2
0
2
1
1
1
1
0
0
1
0
0
0
1
1
0
0
1
2
2
1
2
0
0
1
1
1
1
1
2
0
1
2
1
1
0
1
1
2
2
0
1
0
1
1
1
0
2
2
1
0
0
2
1
2
0
2
0
0
0
0
1
1
2
1
0
0
0
1
2
2
1
1
1
0
0
1
2
1
1
0
1
1
0
2
1
1
1
1
1
1
3
1
0
2
1
2
1
1
2
1
0
0
2
0
2
2
1
0
0
2
2
2
1
0
1
1
1
1
2
0
1
1
0
2
0
1
1
0
1
0
2
0
1
0
2
0
0
1
1
1
0
0
1
1
0
1
0
0
0
2
0
2
1
1
1
0
2
1
1
1
2
0
1
1
1
2
1
1
0
0
0
2
0
2
1
1
1
0
2
1
0
0
2
1
4
0
1
1
1
2
1
1
2
1
2
2
0
2
0
1
0
0
1
1
0
1
0
1
1
0
1
1
0
0
0
0
1
0
1
1
1
2
1
0
0
0
0
0
1
0
0
1
3
2
2
2
1
1
1
1
2
2
1
0
1
2
2
0
2
2
2
1
0
0
1
1
1
2
2
0
1
0
0
2
1
1
1
0
2
1
1
1
0
1
0
0
2
2
2
1
0
2
1
1
1
1
0
0
1
2
2
1
0
0
2
1
2
2
1
1
1
0
0
2
1
1
1
0
1
1
1
2
1
1
0
1
0
0
2
1
1
1
1
2
1
1
1
1
0
1
1
1
1
2
2
0
0
2
2
2
1
1
1
1
1
2
0
1
1
1
0
2
1
1
1
0
0
2
2
1
2
1
0
2
1
2
1
2
0
0
1
2
1
1
1
0
1
1
1
2
1
0
1
0
1
2
1
3
0
2
2
1
1
0
1
0
2
1
1
1
1
0
1
1
1
2
1
0
0
2
1
2
1
1
0
0
1
0
2
2
0
0
2
1
2
1
1
0
0
2
1
0
1
0
1
0
2
1
0
1
1
0
1
2
0
0
2
1
1
1
0
1
0
1
0
2
0
1
0
2
1
1
1
3
2
2
1
1
1
2
2
2
1
0
0
1
1
2
2
1
0
1
1
1
0
1
1
2
0
2
2
0
1
1
1
1
1
2
1
3
1
1
1
1
1
2
0
0
1
1
0
1
1
0
1
1
2
0
2
1
2
0
1
1
2
2
1
2
0
0
2
1
2
1
1
1
0
1
1
1
1
1
1
1
2
1
0
1
1
0
1
1
1
2
1
0
2
0
1
0
0
1
2
1
0
1
1
1
1
1
0
1
0
0
2
2
2
1
1
1
0
0
2
1
0
0
0
0
2
1
1
1
1
1
2
2
0
0
0
0
2
1
0
2
2
2
0
1
0
0
0
1
2
2
1
1
1
2
1
0
2
0
0
0
0
2
1
0
0
2
1
1
1
1
0
1
1
0
2
2
1
1
0
1
0
1
0
0
0
2
1
1
0
0
1
1
0
1
1
1
1
2
0
1
0
1
1
0
0
1
1
0
1
1
1
1
1
2
2
0
2
1
0
0
0
0
1
0
0
1
1
2
2
0
0
0
3
1
1
2
2
1
0
0
1
2
0
1
1
0
1
1
1
2
1
2
1
0
1
1
2
1
1
2
0
0
0
1
2
1
1
1
0
1
0
0
1
1
1
0
1
1
0
1
2
0
1
0
2
1
2
0
1
1
2
0
1
1
1
1
1
2
1
1
2
1
1
1
2
2
0
1
1
0
0
1
1
2
1
0
1
0
2
0
2
2
0
0
0
0
1
0
1
1
1
1
0
1
0
2
1
2
0
0
0
1
0
1
2
1
2
2
1
1
1
2
1
0
0
1
0
1
1
1
1
1
2
1
1
2
0
1
0
2
0
0
2
0
1
1
1
1
0
0
1
1
1
1
1
1
1
0
1
1
0
0
1
1
1
2
1
1
1
1
0
1
1
1
2
1
1
2
0
1
1
0
0
0
2
1
0
1
1
3
0
1
1
1
1
0
1
1
2
0
1
0
1
1
1
1
2
2
1
1
1
2
0
0
1
2
2
0
0
1
1
1
2
1
0
0
0
2
2
2
1
0
1
1
2
1
5
1
2
2
0
1
0
0
0
0
0
2
1
2
1
0
0
1
0
0
1
1
0
1
2
0
2
2
1
2
1
1
1
2
1
1
1
0
0
2
1
2
0
1
1
3
0
0
1
2
0
1
1
1
2
2
0
1
0
0
1
2
0
1
1
1
0
1
2
1
0
0
2
2
1
1
1
2
1
2
0
1
2
0
1
1
1
2
1
1
0
0
2
1
1
0
1
1
0
1
0
1
0
1
0
2
0
1
1
1
2
2
0
1
1
2
1
0
2
0
2
1
2
1
1
1
1
1
0
2
0
0
0
1
1
1
0
0
1
1
1
1
0
0
1
1
1
0
0
0
0
1
0
0
0
1
2
1
1
1
1
2
1
2
2
1
0
0
0
0
2
0
0
0
1
1
1
2
1
1
1
0
2
1
1
2
1
2
0
0
0
1
3
1
0
0
1
0
1
1
1
2
1
1
0
2
1
0
2
0
2
1
2
0
1
2
1
0
1
1
1
2
2
1
1
1
0
1
1
1
0
0
1
0
1
0
2
0
0
1
0
1
0
0
0
1
1
2
2
1
3
2
2
2
1
1
1
0
0
1
1
1
1
1
2
2
0
0
0
1
1
1
1
1
1
1
0
1
1
2
2
1
2
1
1
1
0
2
1
0
2
2
1
0
1
1
1
2
0
1
1
1
2
0
0
1
2
2
1
0
1
0
1
1
2
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
1
1
1
2
1
2
0
2
1
1
2
0
3
1
0
0
0
1
2
0
0
0
0
1
2
1
0
1
0
2
1
0
0
1
0
0
0
0
1
2
0
2
1
0
0
2
2
0
0
1
2
1
0
1
0
1
1
1
0
1
1
1
1
0
1
2
2
0
2
2
1
2
2
2
0
1
0
2
1
1
1
1
1
0
1
1
0
0
0
1
0
1
0
1
2
1
1
1
1
2
2
2
1
1
1
1
1
2
0
1
0
0
1
1
0
1
1
2
2
1
0
1
1
0
1
1
2
0
2
1
2
0
0
1
0
0
2
1
1
1
1
1
1
2
0
2
1
1
2
1
1
1
1
2
0
1
1
0
2
2
0
2
1
0
0
2
2
1
1
1
2
29
2
2
1
2
0
1
1
1
0
0
1
1
0
1
2
2
0
1
2
0
0
1
1
1
2
1
0
0
0
1
1
1
0
0
2
1
2
1
2
1
1
1
0
0
3
0
0
1
1
2
1
0
2
0
1
1
1
1
1
2
0
0
2
0
2
2
1
2
1
1
1
0
1
1
0
8
1
1
1
2
1
2
1
0
1
2
0
1
1
1
0
1
2
1
0
2
1
1
1
2
1
2
1
2
1
1
0
1
2
1
0
1
1
0
0
1
1
1
0
2
0
1
1
1
0
0
0
2
0
1
1
0
1
0
1
1
0
0
1
2
1
1
2
1
2
2
2
0
2
1
1
2
1
2
1
0
0
1
1
2
2
0
1
1
0
0
1
0
2
1
2
1
0
1
1
0
1
0
2
0
1
1
1
0
2
1
2
2
0
2
1
1
1
2
1
1
3
0
2
0
1
2
0
1
1
0
0
1
0
2
2
1
0
1
2
1
1
0
2
1
0
2
2
0
2
2
2
1
0
0
1
2
2
2
1
1
0
0
0
2
0
2
1
1
1
1
1
2
1
1
3
1
0
1
0
2
1
1
1
2
0
2
0
1
2
1
0
1
2
1
1
0
1
4
1
1
3
1
0
2
0
1
2
1
1
2
2
2
1
0
0
0
1
2
1
0
0
2
2
1
0
0
1
1
0
2
0
0
0
1
1
2
1
1
1
2
2
1
0
1
0
1
1
0
0
1
1
2
2
0
2
1
2
1
2
1
0
2
5
1
2
2
1
1
0
0
0
1
2
0
2
1
0
2
0
1
0
1
2
1
2
2
0
2
2
1
1
1
3
1
1
1
0
0
1
1
0
1
0
2
0
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
0
2
1
0
1
1
1
1
1
1
0
1
1
3
1
1
1
1
1
1
1
1
0
2
1
1
0
0
1
1
2
1
0
1
1
2
2
1
0
0
2
2
0
0
0
0
0
2
2
2
0
1
1
2
0
1
0
1
2
1
0
1
1
1
1
1
0
1
2
1
0
1
2
1
1
1
1
1
1
0
2
1
0
2
1
0
0
1
1
0
2
0
0
2
1
1
1
1
2
1
1
1
1
2
0
0
1
2
2
0
1
1
0
0
2
1
1
3
0
2
1
1
0
0
2
5
1
1
1
0
1
0
1
0
1
0
0
0
0
1
0
0
0
1
2
1
2
2
2
2
0
0
2
2
1
3
2
2
3
1
0
0
1
1
1
1
5
1
1
1
1
1
0
2
0
0
1
1
1
1
0
0
0
2
0
0
1
1
0
1
0
1
1
1
0
1
1
2
1
2
0
0
2
2
1
1
2
1
0
2
1
1
1
1
1
1
1
1
1
2
1
1
1
0
8
0
1
1
0
1
0
1
1
1
0
1
1
0
0
1
0
0
2
3
1
1
1
0
1
0
1
1
1
0
2
1
2
0
2
1
1
1
2
1
0
2
1
1
1
0
1
2
1
2
0
0
0
0
1
0
1
1
0
1
2
2
0
1
0
2
1
0
1
1
0
2
2
1
0
0
1
0
1
1
0
0
1
2
0
1
0
0
1
1
2
2
0
1
1
1
2
1
1
1
2
2
2
0
1
0
0
0
0
0
2
3
1
0
0
0
1
0
0
2
1
0
2
1
0
1
2
1
0
1
1
1
0
0
0
1
2
0
0
0
0
2
0
1
1
1
0
1
0
2
1
2
0
1
1
1
1
2
0
1
0
2
0
0
0
2
0
1
1
2
1
0
1
0
1
2
2
2
1
1
2
1
1
0
0
1
1
0
1
0
1
2
1
1
2
0
1
1
1
0
1
2
0
2
1
0
1
1
1
1
0
0
0
1
1
1
2
1
2
1
1
0
0
1
1
1
1
1
0
0
2
2
1
1
1
1
0
1
1
1
2
1
2
0
2
1
0
1
0
2
0
1
1
1
1
0
1
0
1
2
0
0
0
1
1
1
2
1
0
1
0
0
0
0
0
1
1
2
1
2
2
2
2
0
1
1
1
1
1
2
1
1
1
0
1
1
1
0
0
0
1
0
1
2
1
1
1
2
1
1
1
0
0
0
1
2
0
0
1
1
1
1
0
2
0
1
1
1
1
2
1
0
0
0
1
2
1
0
1
1
0
2
2
2
1
2
2
1
0
1
0
0
2
0
1
0
1
1
1
0
1
2
1
1
2
0
1
0
1
1
1
1
0
1
1
0
0
0
1
0
0
1
1
2
1
1
1
1
2
2
0
1
0
1
2
3
2
2
2
2
0
0
0
2
0
1
1
0
2
1
1
0
1
1
2
0
1
1
0
1
1
2
0
2
2
0
1
0
1
2
1
2
1
1
0
1
1
0
0
1
1
1
1
1
0
1
1
1
4
1
2
2
2
0
0
1
1
0
1
2
0
0
0
1
1
2
1
1
0
0
0
1
0
0
0
0
1
0
0
1
1
0
2
0
1
0
0
0
0
1
1
0
1
1
1
0
1
1
1
0
1
1
1
0
1
1
1
1
2
0
0
2
1
3
1
0
1
0
1
2
0
0
1
2
2
0
0
0
0
1
2
0
1
1
0
1
1
1
0
1
1
0
2
0
0
1
0
0
0
1
0
2
2
0
2
1
0
1
1
2
1
2
1
1
0
1
1
0
2
2
2
0
0
2
1
0
2
2
2
1
1
0
2
2
2
0
2
2
1
0
2
2
2
0
1
0
2
0
0
1
0
1
3
0
1
0
1
1
1
2
2
1
1
1
1
1
1
0
2
0
1
1
2
0
1
1
1
0
1
1
2
2
1
1
1
0
0
1
1
2
0
1
1
0
1
1
1
0
0
0
1
3
1
1
1
2
1
0
1
2
0
1
0
1
1
1
1
0
0
1
0
1
2
1
0
2
0
1
0
1
1
0
0
1
1
1
0
0
0
0
1
2
0
1
2
0
1
1
2
0
1
1
0
1
1
2
1
1
0
2
1
1
2
0
2
1
1
1
1
0
1
1
2
2
1
0
2
2
1
1
1
1
1
1
1
1
0
1
2
1
1
0
2
0
2
1
1
0
2
0
0
1
0
1
1
1
1
0
0
1
0
2
0
0
1
1
0
1
1
0
0
1
1
1
2
1
1
1
1
2
1
2
0
2
0
2
1
1
1
2
0
2
1
1
0
0
0
0
1
0
0
1
0
0
1
2
1
5
1
1
0
2
1
0
1
0
1
1
2
0
0
1
1
1
0
1
1
0
2
1
2
1
1
1
1
1
1
1
1
0
2
1
2
0
2
2
1
1
1
1
0
0
1
0
1
2
1
2
0
0
1
1
1
0
1
0
1
0
1
1
1
0
0
0
1
1
1
1
0
1
0
2
0
0
1
2
2
1
2
2
0
0
2
1
1
0
1
2
1
0
1
2
1
0
0
1
2
2
1
0
3
1
1
1
0
0
2
0
0
1
0
2
0
0
1
2
1
2
2
1
0
1
1
0
1
2
1
2
2
2
1
2
1
1
0
1
1
2
1
2
2
1
1
1
0
0
0
1
2
2
0
1
3
0
0
0
0
2
0
1
0
0
0
0
1
0
1
1
1
1
0
0
2
1
2
0
0
1
2
1
0
1
0
1
1
1
0
0
1
2
2
2
0
0
1
2
0
2
1
1
0
1
2
0
2
0
0
1
0
0
1
1
1
1
0
0
1
1
1
0
1
1
2
0
2
1
1
1
0
1
2
1
2
1
2
0
1
2
0
1
1
0
2
0
1
2
1
2
1
0
1
0
0
3
0
1
1
1
2
1
2
2
0
0
1
0
1
0
1
0
2
0
1
1
1
0
1
0
1
1
0
0
2
1
1
0
2
2
2
1
0
1
0
1
1
1
1
0
1
1
0
1
1
0
1
1
1
1
2
2
1
1
2
2
0
1
2
2
1
1
2
1
1
0
1
1
1
0
1
0
1
1
2
1
2
0
0
0
0
0
0
1
0
0
0
1
1
0
2
1
1
1
1
1
0
1
2
2
2
0
1
1
1
2
2
0
1
0
2
1
1
1
1
0
1
1
1
3
0
1
1
1
2
1
1
0
0
1
1
1
0
0
0
2
1
2
1
1
1
0
1
1
1
2
1
1
1
0
1
1
0
2
1
1
0
1
1
1
5
0
2
0
2
0
0
2
1
2
1
1
0
1
1
0
2
0
2
1
1
1
1
0
2
0
0
1
2
1
1
0
2
1
2
2
1
2
2
1
0
0
1
2
1
0
0
1
0
0
0
1
1
0
0
0
2
2
2
2
1
1
1
2
2
2
2
1
0
0
3
0
2
0
2
0
0
2
1
0
1
0
0
1
1
2
1
0
1
2
1
1
2
0
1
0
2
1
1
2
1
1
1
2
2
1
2
0
2
4
1
1
0
1
1
1
0
1
1
1
1
1
1
1
0
0
1
1
0
1
0
1
0
0
0
0
1
1
2
1
1
1
0
1
1
1
0
0
0
2
2
1
1
2
0
1
0
0
2
1
2
1
2
0
0
2
0
0
0
1
1
1
1
0
1
1
2
1
1
1
0
1
1
1
0
1
3
0
1
1
1
0
2
1
0
1
1
1
1
0
2
0
2
2
2
1
0
2
0
1
0
1
0
2
2
0
2
0
1
0
0
2
0
1
1
0
2
1
1
1
0
0
2
1
2
2
1
0
0
1
1
2
0
0
2
1
2
1
1
2
2
1
1
1
1
0
1
2
1
2
0
1
2
1
2
1
1
1
1
1
1
0
0
1
0
1
2
2
1
2
0
0
1
1
1
1
1
2
0
2
3
2
1
0
1
0
1
1
2
0
0
2
1
0
0
1
0
1
0
0
0
0
2
1
1
0
2
1
2
2
1
0
0
0
1
1
0
0
5
0
2
1
1
1
1
2
1
1
2
0
0
1
1
2
0
1
1
0
1
0
2
0
0
1
1
0
2
1
2
1
1
0
1
0
0
1
2
0
1
1
0
1
1
0
0
0
1
1
1
2
2
1
1
1
2
1
0
0
1
0
2
2
1
0
1
2
1
1
2
1
1
1
1
0
1
0
1
0
0
2
0
2
0
0
1
1
1
0
1
1
0
1
1
0
2
0
0
0
1
0
1
2
0
1
2
0
0
1
1
2
1
1
1
1
2
1
1
0
2
1
1
1
2
1
1
2
1
1
1
1
2
0
2
1
0
1
1
1
2
1
0
1
1
1
1
0
1
1
1
1
2
1
1
0
0
0
2
2
1
2
1
0
1
0
0
1
1
0
1
1
1
0
1
1
0
0
1
1
1
2
1
1
0
1
1
2
2
2
2
1
1
0
0
1
1
1
1
0
0
0
2
2
1
1
0
1
2
0
1
1
0
1
0
0
1
1
0
1
1
1
1
1
1
2
0
0
0
2
2
0
1
2
1
3
0
0
0
0
0
0
1
0
1
2
1
0
1
1
1
2
1
0
1
1
1
0
1
0
2
1
2
1
0
2
1
2
1
0
1
0
0
1
1
0
2
1
0
2
0
0
1
1
1
1
0
0
1
1
1
1
1
1
1
1
1
1
0
2
1
1
1
2
1
0
1
0
1
1
2
0
1
1
1
1
3
0
1
0
0
1
1
1
1
1
1
1
0
2
0
2
2
2
1
1
2
0
0
2
1
0
1
1
1
0
1
0
1
1
0
0
1
1
1
0
1
1
1
0
1
0
0
1
1
1
1
1
0
2
0
2
1
1
0
1
0
0
0
2
0
1
2
1
1
2
1
0
1
0
2
1
1
1
0
2
1
0
0
1
1
1
2
2
2
0
0
0
1
1
0
2
1
1
0
1
1
1
1
2
1
1
2
2
1
1
0
1
0
1
0
2
1
1
2
0
2
1
2
1
1
1
1
2
1
2
2
1
0
1
2
0
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
0
2
0
0
0
0
1
2
1
2
2
2
2
1
0
0
2
2
2
0
2
0
2
2
1
0
2
1
1
1
1
2
1
0
2
1
2
2
2
0
1
1
1
2
0
0
1
1
0
2
2
0
2
0
0
1
0
2
1
2
1
0
0
2
1
0
1
1
2
1
0
2
1
1
0
1
0
1
1
1
1
2
3
1
0
1
0
2
0
2
1
1
1
2
1
1
0
2
1
1
0
1
2
1
2
1
0
1
0
1
1
0
1
1
1
0
2
1
2
1
0
0
1
3
1
2
1
0
2
0
0
3
0
2
0
2
2
0
2
0
0
2
2
1
2
0
2
2
0
1
2
0
0
1
0
1
2
1
1
2
1
1
0
2
1
2
1
1
1
0
0
0
1
1
2
1
1
1
0
1
0
0
0
0
0
0
1
0
1
3
1
0
2
2
1
1
1
2
0
1
2
1
1
1
0
1
1
1
2
1
1
1
1
1
0
0
1
4
1
0
0
1
1
1
2
0
1
1
1
1
1
1
2
2
1
1
2
2
2
1
1
1
1
1
1
0
1
1
1
2
0
0
1
1
1
1
2
1
1
0
2
1
0
0
1
1
1
11
1
0
1
1
0
2
0
2
1
1
1
1
0
1
1
3
0
1
1
1
1
0
1
2
2
0
1
1
2
1
1
1
0
1
1
0
1
1
0
2
1
1
2
2
1
0
1
1
1
2
1
1
2
0
0
1
0
2
0
1
1
0
0
2
0
1
0
0
2
2
0
1
1
1
0
1
0
2
1
2
0
2
0
2
1
0
2
1
0
1
0
1
1
1
0
1
0
0
1
1
1
0
2
2
0
1
0
1
0
1
0
1
1
1
1
1
2
2
1
2
0
0
1
1
1
0
1
1
1
1
1
1
1
1
1
2
0
1
1
0
0
1
1
2
0
2
3
1
2
0
0
1
1
1
2
1
2
2
1
2
1
0
0
1
0
2
2
1
1
2
0
2
1
0
1
0
2
1
0
2
1
2
1
1
1
0
0
2
0
2
0
0
1
0
2
1
1
1
1
1
1
1
1
2
1
1
1
1
0
2
0
0
0
0
1
1
1
2
2
1
0
1
1
0
1
1
1
1
2
1
0
1
0
1
1
1
1
0
0
1
1
2
1
2
1
0
0
2
0
1
0
2
1
1
1
2
2
2
0
1
1
1
1
1
1
0
1
2
4
1
2
0
1
1
0
1
2
1
1
2
1
1
0
0
0
1
2
1
0
2
0
0
1
1
0
1
0
1
1
1
1
1
1
1
1
0
2
1
1
2
2
1
2
2
0
2
2
0
1
0
0
1
1
1
1
1
2
1
1
1
0
0
2
1
1
2
1
1
0
1
2
0
1
1
2
0
1
1
1
1
2
1
0
1
1
0
1
2
2
0
1
2
1
1
1
0
1
1
0
1
0
1
1
1
3
1
1
2
3
2
3
0
0
1
1
0
1
1
1
1
1
1
2
0
1
2
1
1
0
0
1
1
2
1
2
0
2
1
0
2
1
2
0
2
1
2
1
0
1
1
1
1
1
1
0
1
0
1
0
1
1
1
0
0
2
1
1
1
2
2
2
1
1
2
2
2
1
1
0
2
0
0
1
0
2
0
2
1
1
2
2
0
1
1
1
2
1
1
1
2
1
0
2
1
1
1
1
1
0
0
2
1
0
0
1
2
1
1
2
3
0
1
1
1
1
0
0
2
1
0
1
0
1
1
1
0
0
1
0
2
2
0
0
2
1
1
1
1
1
0
0
1
2
0
1
1
1
0
1
1
2
0
0
2
0
2
0
3
1
1
2
0
2
1
1
0
2
2
0
2
1
3
1
2
0
2
2
2
1
1
1
1
1
2
2
2
1
2
1
1
2
0
0
2
0
1
2
0
1
1
1
0
0
0
0
1
1
0
0
1
1
1
1
0
1
1
1
2
0
1
0
1
0
0
0
0
1
0
1
0
1
0
1
1
1
1
1
1
2
1
0
2
1
2
1
0
3
0
4
0
3
2
1
2
1
0
0
1
0
0
1
1
1
0
2
0
1
0
0
0
1
2
0
1
1
0
0
0
1
0
2
0
1
1
1
1
0
1
2
1
1
0
2
1
2
0
0
2
1
1
1
2
1
1
1
0
0
1
2
1
1
0
1
0
1
0
0
2
0
0
2
1
2
1
0
2
1
0
1
2
2
1
2
1
1
2
1
2
1
1
2
0
2
0
1
2
0
1
1
0
1
1
0
0
1
1
1
1
1
1
1
0
0
0
1
0
2
1
2
1
1
0
1
0
0
1
0
0
0
1
2
1
1
0
1
1
0
0
2
0
2
2
1
1
0
1
1
2
1
0
1
2
1
1
1
2
1
0
0
1
0
2
0
1
0
2
2
0
1
0
1
1
2
1
1
0
0
1
0
1
1
2
1
2
1
0
1
1
0
0
1
1
8
0
1
2
0
0
0
1
1
2
0
1
0
0
1
1
0
1
1
0
1
1
0
0
2
1
1
1
0
2
1
1
2
1
0
2
2
0
2
2
0
2
2
0
1
1
0
1
0
1
1
2
1
0
2
1
1
1
0
1
1
1
0
1
1
1
0
2
0
1
1
0
0
0
0
1
2
1
1
1
1
1
1
1
1
0
2
1
1
1
1
1
1
1
0
0
0
1
1
2
1
2
1
1
2
2
0
0
1
1
0
0
1
2
0
0
1
2
0
0
0
1
0
1
1
1
1
2
1
2
0
0
2
4
2
0
0
0
1
2
1
2
2
1
1
1
0
0
1
4
0
1
2
3
1
1
1
1
1
1
1
1
1
2
0
1
0
0
0
2
0
2
1
0
1
1
1
0
2
1
2
1
2
2
0
0
1
1
1
0
0
0
2
1
1
0
1
0
2
1
1
2
0
0
4
0
0
2
2
0
0
1
2
0
0
2
0
2
1
2
1
1
1
0
1
1
1
0
1
1
1
0
1
1
1
2
1
1
1
1
2
1
0
1
1
1
0
1
0
2
0
1
0
2
0
1
0
0
1
0
1
1
1
0
0
0
0
2
1
0
1
1
0
2
1
2
1
1
1
0
2
1
0
0
1
1
0
1
2
1
2
0
0
2
0
1
1
1
2
1
2
2
1
0
1
1
0
0
1
1
0
2
2
1
2
1
2
2
2
1
2
2
0
0
0
1
0
1
1
1
0
2
0
0
1
0
1
0
2
1
1
1
1
1
1
1
0
2
1
1
1
1
2
1
0
0
2
1
1
0
1
0
1
2
1
0
1
1
1
0
0
1
0
1
1
4
0
1
1
0
2
1
1
2
0
0
2
1
2
2
1
0
2
2
0
2
1
2
2
0
1
2
1
1
2
1
1
1
1
1
0
1
0
1
1
1
1
0
1
1
1
1
0
0
0
0
1
2
1
1
0
1
1
1
0
0
1
2
0
1
0
0
1
0
2
0
2
1
1
1
1
0
1
0
1
1
0
0
0
0
1
1
2
0
0
1
0
2
2
3
2
2
0
0
1
1
1
1
0
1
1
1
1
2
1
0
2
2
1
2
1
0
0
1
1
0
1
1
1
1
1
1
1
0
1
0
1
2
0
0
1
1
0
3
2
0
0
1
1
1
1
0
0
0
0
0
1
0
2
1
1
1
0
1
1
0
0
2
1
2
1
1
1
1
2
0
0
1
2
1
0
1
1
1
1
0
2
1
1
2
0
0
0
0
0
1
1
1
2
0
1
1
1
1
1
3
2
0
1
1
0
2
2
2
2
1
2
1
0
0
0
0
1
0
1
2
2
0
2
0
1
2
1
2
0
1
2
1
1
1
0
0
0
0
0
1
1
0
2
1
0
1
1
0
1
1
1
2
1
2
1
0
1
0
0
2
0
1
0
2
1
1
0
2
0
1
2
1
2
2
0
0
1
1
2
1
1
0
1
1
1
1
1
0
1
0
1
1
1
1
0
1
2
1
1
2
2
1
1
1
1
1
2
1
1
1
2
1
0
0
2
0
3
2
1
0
1
1
0
0
2
2
1
0
1
0
0
0
2
1
2
2
0
2
0
2
2
0
2
1
1
0
2
2
1
0
2
2
2
1
0
2
1
1
1
0
2
1
2
2
0
1
0
0
0
2
2
0
0
1
0
0
2
1
0
0
1
1
1
0
1
0
1
0
1
2
2
4
1
1
2
0
1
2
0
0
1
0
0
1
0
0
2
0
0
1
2
1
0
1
0
0
2
1
1
0
2
1
0
2
1
2
2
0
2
1
0
0
1
0
0
0
2
2
1
2
0
1
2
2
2
2
2
0
2
1
1
1
1
1
2
1
2
1
2
1
2
1
0
0
0
1
0
1
1
2
0
1
0
2
0
1
1
2
1
2
1
2
2
1
1
3
2
2
1
2
1
1
1
2
1
0
0
0
0
0
0
1
1
0
1
1
1
0
0
2
0
0
0
1
1
1
2
0
1
1
1
0
1
2
2
1
1
1
1
1
1
0
1
1
2
0
2
1
1
1
0
1
0
1
1
0
1
1
1
1
2
1
0
1
0
0
2
1
1
1
2
1
0
4
1
1
0
2
1
1
1
0
1
1
1
1
2
1
1
0
1
1
1
1
1
2
1
2
1
1
0
0
1
2
1
0
1
1
2
1
1
1
0
1
0
1
1
2
1
0
1
1
2
1
1
2
0
0
2
1
2
0
2
1
1
1
0
0
1
0
1
2
1
0
1
1
2
1
2
3
0
1
0
1
1
0
0
0
1
0
1
2
1
1
1
2
0
2
0
1
2
1
0
2
0
1
0
0
0
1
2
0
0
1
0
0
2
1
1
1
2
2
2
0
1
0
0
2
1
0
1
0
0
1
0
0
2
1
2
0
2
3
0
0
0
2
1
0
2
0
3
2
0
1
2
0
1
0
2
0
2
1
0
0
2
1
0
2
1
1
1
1
3
1
0
0
2
0
1
0
2
2
1
0
2
2
2
0
1
1
0
2
1
0
0
0
0
2
2
0
1
1
1
0
1
1
1
0
1
1
1
1
2
1
0
2
1
2
1
1
1
0
0
1
1
0
1
1
1
2
1
0
1
3
1
1
2
2
0
0
1
1
1
0
0
0
1
1
1
0
2
4
1
1
1
1
1
0
2
2
1
1
1
1
1
0
2
1
1
0
1
1
1
1
2
1
0
0
2
2
2
1
0
0
1
1
3
1
0
0
1
0
2
2
1
0
1
1
0
2
0
2
1
1
1
2
2
2
1
0
2
1
0
1
2
2
0
2
2
0
1
2
0
0
1
1
1
2
1
1
1
0
2
1
1
0
1
0
0
2
0
1
1
1
0
1
2
1
1
1
1
1
2
1
0
0
1
2
0
0
2
1
0
0
1
1
0
1
1
1
1
1
0
1
2
0
1
2
1
1
1
0
1
0
2
0
0
1
1
2
1
1
0
1
0
0
0
1
1
0
2
2
0
0
1
2
1
1
0
1
0
0
1
0
1
1
0
1
2
0
2
1
0
2
0
1
1
1
1
0
1
0
0
0
0
1
1
2
2
2
1
0
1
1
0
1
1
1
1
2
1
1
1
1
0
1
2
0
1
1
3
2
0
1
1
1
2
0
2
1
2
0
0
1
1
1
1
0
2
0
3
1
0
1
2
2
1
2
0
1
1
1
1
1
0
1
1
1
1
1
0
1
2
0
1
0
1
1
0
0
1
1
0
2
2
1
1
0
2
1
0
1
1
0
1
1
1
2
0
1
0
2
1
1
1
0
1
0
2
1
2
1
1
1
0
1
1
0
0
0
1
2
1
0
0
0
0
1
0
1
0
0
1
0
1
1
1
1
1
2
1
1
1
1
1
1
2
2
1
0
0
1
0
0
1
0
1
1
1
1
1
1
0
1
0
7
1
2
0
0
1
0
2
0
0
2
1
1
2
0
0
0
2
0
1
2
1
2
1
1
0
0
1
1
1
0
1
0
1
1
1
0
2
1
1
0
1
1
1
2
1
1
1
3
0
2
1
0
2
0
1
1
2
0
0
2
2
1
1
1
1
1
1
0
1
1
0
1
2
1
0
2
1
0
1
2
0
1
2
0
1
0
0
1
2
2
0
1
1
1
2
0
0
2
0
1
1
1
1
1
0
2
1
2
0
1
0
2
1
2
1
1
1
2
0
1
0
4
0
0
0
1
1
0
0
0
0
0
0
0
1
3
1
2
0
2
1
2
1
0
2
1
1
0
2
1
1
1
0
0
0
1
1
0
0
1
1
0
2
0
0
2
2
1
0
1
0
2
1
1
2
0
1
0
1
1
1
1
1
0
1
2
1
0
1
1
1
0
1
2
1
1
1
0
3
1
1
1
1
1
0
1
0
2
0
1
2
1
1
0
0
1
1
1
1
2
0
0
2
1
0
1
0
0
0
0
1
2
1
1
0
1
1
1
1
0
2
0
1
1
2
0
1
1
1
1
1
1
0
1
1
1
2
0
1
1
1
0
2
3
2
0
2
0
0
0
1
2
0
1
1
1
0
1
1
1
1
2
0
0
2
0
2
1
1
1
0
1
1
1
2
0
1
0
1
0
1
2
1
2
0
2
0
3
2
2
1
1
1
0
0
0
0
0
1
1
1
1
1
1
2
0
1
0
1
0
2
2
0
2
2
1
2
2
0
1
1
1
1
1
2
1
2
0
2
1
2
0
2
0
1
0
2
0
1
1
1
1
1
1
0
1
3
0
3
0
1
0
2
1
2
0
0
1
1
1
1
0
3
1
0
1
1
0
2
1
0
1
2
1
1
1
0
0
1
1
1
1
0
2
0
2
1
1
2
2
0
2
0
2
0
0
1
1
0
1
2
1
0
1
1
0
3
1
0
3
1
1
2
0
0
0
2
2
0
1
2
0
1
1
1
2
2
2
1
2
0
2
2
0
2
1
1
0
2
2
1
0
2
0
1
1
2
1
0
1
2
1
0
1
1
1
2
0
1
0
0
0
2
1
0
1
0
1
1
1
1
1
0
1
1
1
0
2
1
2
0
1
0
1
2
1
1
1
1
2
1
1
1
0
0
1
1
1
0
2
2
2
2
0
1
0
0
3
0
1
1
1
0
2
2
0
1
0
1
1
4
0
0
1
0
0
2
3
1
0
2
2
1
1
1
0
2
1
2
0
0
1
1
1
0
2
2
2
2
0
0
1
1
0
0
1
1
0
2
2
2
1
1
0
1
1
2
2
0
1
1
1
0
1
1
2
0
2
0
0
1
0
1
0
1
1
0
2
0
0
0
1
1
2
0
1
1
2
1
0
1
1
0
0
1
2
2
1
1
1
0
0
1
1
1
2
1
1
2
1
0
0
1
2
1
1
0
1
1
0
0
2
2
0
2
1
1
1
1
0
1
0
1
1
0
1
0
2
1
0
1
1
1
1
0
1
1
1
0
2
0
0
1
0
0
0
0
1
1
0
1
1
2
1
1
1
0
2
0
2
1
1
2
2
0
0
2
0
2
2
1
1
1
1
0
0
1
1
1
0
0
2
1
0
2
1
0
0
1
0
1
0
2
1
0
2
2
0
0
2
0
1
0
2
0
2
1
0
2
1
1
0
1
2
0
0
1
0
2
0
1
1
1
0
0
0
0
0
2
2
1
1
0
1
0
0
1
1
2
1
0
2
1
1
1
0
2
2
1
1
1
1
0
0
1
1
1
1
1
0
0
1
1
0
0
0
0
0
1
1
2
2
1
2
2
1
1
0
1
0
2
0
0
1
1
0
2
2
1
1
1
2
0
0
2
2
1
1
0
1
1
2
1
0
2
0
1
0
1
1
2
0
0
1
0
1
1
1
0
1
1
1
1
0
1
0
1
0
1
0
1
1
1
1
2
2
0
1
0
1
1
0
2
2
1
1
1
1
0
1
0
1
1
1
0
1
0
1
1
1
0
0
1
1
1
0
1
2
1
2
2
2
6
2
1
1
0
0
0
1
0
0
0
0
1
1
2
0
1
0
0
1
1
1
1
1
0
0
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
0
2
0
2
1
2
1
2
1
2
1
1
1
1
3
0
0
1
1
1
1
1
1
1
1
0
2
1
2
1
0
0
1
0
2
1
0
1
1
2
1
0
0
2
0
1
1
2
1
3
2
0
1
2
1
0
0
0
0
0
2
0
1
1
2
0
3
0
1
2
0
0
2
1
2
0
1
1
1
1
0
1
0
2
2
0
0
1
2
1
1
1
1
2
0
0
2
1
0
1
1
2
1
1
1
0
1
1
0
1
1
1
0
0
0
1
0
1
0
1
0
1
1
1
0
1
2
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
0
0
1
1
1
1
1
2
0
1
0
0
2
1
2
0
0
1
0
0
0
0
0
2
1
1
0
2
0
2
1
1
2
1
0
1
1
0
1
0
2
2
1
2
0
0
0
1
0
1
0
2
0
0
2
0
2
2
1
1
1
0
1
1
0
1
1
1
1
0
0
0
2
2
0
0
1
1
1
1
1
1
1
1
2
1
0
1
3
2
2
1
1
2
0
1
1
0
0
2
1
2
1
1
1
0
0
0
1
1
2
0
1
0
1
1
1
2
1
2
0
1
1
1
2
1
1
0
0
3
2
0
2
1
1
0
1
1
2
0
0
1
1
0
1
0
0
2
0
1
1
1
0
2
0
2
0
0
1
0
1
1
1
0
0
1
1
1
1
0
0
0
0
0
1
1
2
1
1
0
2
0
2
0
2
1
1
1
0
0
1
0
1
0
1
1
1
0
2
2
1
1
2
0
1
1
2
2
2
1
1
0
0
1
1
0
2
0
1
0
0
0
1
0
0
1
1
2
0
2
0
1
2
0
0
1
2
1
1
1
1
0
2
2
1
1
3
0
2
1
0
1
1
0
1
1
1
1
1
1
0
1
0
1
0
1
0
2
1
2
0
0
0
1
1
1
0
1
1
1
2
3
0
0
0
0
0
1
0
1
2
2
2
2
0
1
2
1
1
1
0
1
1
1
1
0
0
0
2
1
1
1
1
1
1
1
2
0
2
2
1
2
1
1
0
1
0
1
0
0
0
1
2
1
1
0
1
1
1
1
2
0
1
2
2
0
1
1
1
2
1
0
0
1
2
1
1
1
0
0
2
1
1
0
0
1
0
1
1
0
2
2
0
1
1
0
1
1
2
1
1
1
0
1
0
2
1
1
1
1
2
0
2
1
0
1
0
1
3
1
0
0
0
1
1
1
1
1
1
1
1
0
0
2
2
1
1
0
1
0
2
1
0
0
0
0
1
2
0
1
2
1
0
1
0
0
0
1
2
2
0
1
0
1
0
1
1
1
1
2
1
1
0
1
2
0
1
0
2
0
0
1
1
2
1
1
1
2
0
2
1
0
2
1
2
1
1
0
1
1
0
1
0
1
1
1
1
0
0
1
2
1
0
2
1
2
0
1
2
0
0
1
1
1
0
1
0
1
0
1
2
0
1
0
1
0
1
1
1
0
0
0
1
1
1
1
1
1
1
1
2
1
1
0
2
0
1
1
0
2
1
0
0
0
1
1
0
1
2
0
0
0
2
1
2
1
2
0
0
0
0
1
2
2
0
0
1
2
1
1
1
1
2
1
2
1
1
1
1
0
1
0
0
2
0
1
1
2
0
0
1
0
0
2
2
2
1
1
2
0
1
1
1
1
2
1
0
2
0
1
1
1
1
0
2
1
1
1
0
1
1
0
1
1
1
0
2
2
1
0
1
6
2
1
2
1
1
0
1
1
0
0
0
1
0
1
2
1
0
1
1
0
0
1
2
0
1
2
0
2
2
2
0
1
0
1
2
1
1
2
1
1
0
2
1
2
1
0
1
0
1
1
0
1
2
2
1
1
0
1
0
1
1
1
0
1
2
2
2
1
2
1
0
2
1
1
1
2
0
1
2
1
1
0
0
0
3
0
2
2
0
2
0
2
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
2
0
1
1
1
3
1
1
3
1
1
1
0
0
1
2
1
0
1
0
1
1
0
0
2
2
0
0
2
0
2
1
1
2
1
2
1
0
1
1
1
1
1
1
2
0
1
1
1
1
1
0
2
0
0
5
1
0
1
2
0
2
1
0
2
0
0
1
2
1
2
1
1
1
2
1
2
0
1
0
0
1
0
2
1
1
0
2
2
0
1
1
1
0
0
1
1
1
2
0
2
1
0
0
2
2
3
1
0
2
1
2
1
1
0
0
0
1
0
0
0
1
0
1
2
1
0
2
0
0
1
1
1
2
0
1
0
1
2
2
1
2
1
2
0
1
1
2
1
1
1
2
1
1
2
2
1
0
1
0
1
1
1
2
1
2
1
1
1
1
2
1
1
0
2
1
0
1
1
1
2
0
2
0
2
2
0
1
0
2
2
1
2
2
1
0
0
0
0
0
1
2
2
2
2
1
2
0
2
2
1
0
1
1
1
1
0
2
1
1
0
2
2
2
0
1
0
1
1
0
2
2
0
1
0
1
2
1
1
0
2
1
0
0
1
0
1
0
1
1
0
1
1
1
2
1
1
1
1
2
1
0
0
2
0
0
1
1
0
0
2
2
2
2
0
1
0
2
0
1
1
3
1
1
1
1
2
0
0
1
1
1
2
1
1
2
1
2
1
2
0
0
2
0
0
0
0
1
1
0
1
0
0
2
0
1
1
0
0
1
1
4
0
1
0
2
0
0
0
1
1
0
2
1
0
1
0
0
1
2
1
0
0
2
0
0
2
0
1
1
2
0
1
1
1
2
2
1
1
1
0
2
0
0
1
1
0
1
0
0
0
1
2
1
0
1
1
1
1
1
1
1
0
1
0
0
1
1
1
1
1
2
0
0
1
5
1
1
0
1
0
0
2
0
0
0
1
0
1
4
5
0
0
2
2
0
0
1
2
0
3
1
1
3
1
0
0
0
1
2
3
1
1
1
1
0
2
0
1
1
2
1
0
0
0
1
1
1
1
0
0
1
0
1
0
0
1
2
2
1
0
0
1
2
1
1
1
2
3
1
3
1
2
2
2
0
2
1
0
1
1
4
1
0
1
1
0
1
1
1
0
2
2
0
1
1
2
0
1
1
1
0
1
0
1
0
0
0
0
1
1
0
0
2
1
1
0
1
0
1
1
0
0
1
1
2
2
0
1
1
1
0
1
1
1
2
0
2
2
2
1
2
1
0
0
2
1
0
2
1
0
1
0
1
1
1
0
0
0
1
0
0
0
1
0
2
2
2
1
0
1
1
2
1
1
0
1
0
2
1
0
1
1
2
1
1
0
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
1
1
2
1
1
1
2
1
1
1
2
0
1
0
1
1
0
1
2
1
2
2
2
1
2
0
2
2
0
2
3
1
2
2
0
1
2
1
1
1
1
1
1
1
2
1
1
0
1
0
0
1
0
2
1
1
1
0
3
1
0
0
2
2
0
2
0
1
1
1
1
0
1
0
0
1
0
1
1
1
1
2
1
1
0
0
1
2
1
1
1
1
0
1
1
1
1
2
1
2
0
2
0
1
2
1
1
1
2
1
2
1
1
0
2
2
1
1
1
1
0
1
2
0
1
2
2
1
0
1
0
0
1
1
1
1
1
1
1
1
0
1
2
4
0
1
1
3
0
1
2
1
0
1
0
2
1
1
2
1
2
0
2
1
2
0
2
2
0
2
0
1
0
1
1
1
1
1
0
1
1
0
1
0
2
1
1
2
1
0
2
1
1
1
1
1
2
3
0
0
0
1
1
2
0
0
1
0
2
0
0
0
2
1
1
1
1
1
2
1
5
1
1
1
1
2
2
1
2
2
2
1
1
0
0
0
1
1
0
1
1
0
0
1
0
0
2
2
0
0
1
2
2
2
1
1
1
1
1
1
2
1
1
4
2
1
1
3
2
1
2
1
1
1
1
1
0
0
1
0
1
1
1
1
0
2
0
0
1
0
1
2
1
0
3
2
0
2
1
0
1
4
0
0
0
2
0
2
0
2
1
2
2
0
0
3
2
2
0
1
2
0
1
0
2
0
1
1
0
0
1
1
0
0
0
0
1
1
0
1
0
1
0
0
2
4
2
1
0
3
1
0
0
1
2
1
1
1
0
0
2
0
1
0
1
1
2
1
1
2
0
1
1
0
1
1
2
1
1
0
1
1
1
1
0
2
1
0
0
0
2
2
1
1
1
1
3
1
1
1
0
1
0
1
0
1
1
1
0
1
2
2
0
2
2
1
2
0
0
2
1
1
1
1
1
1
1
1
1
0
1
0
2
0
0
0
0
2
0
1
2
0
1
1
1
1
1
1
1
2
0
2
1
1
1
2
1
2
0
1
0
2
0
1
4
1
0
1
2
2
1
0
2
1
2
2
1
2
0
1
1
2
1
0
1
1
2
1
0
0
0
1
0
0
1
1
1
1
0
0
1
1
1
2
0
1
0
0
2
0
0
3
2
0
1
1
1
1
1
0
1
1
0
5
0
1
0
1
0
1
1
1
1
1
2
1
2
0
2
1
0
0
1
1
1
1
1
1
1
0
0
1
1
1
1
1
1
0
1
1
1
0
1
0
2
1
1
0
0
1
0
0
0
0
2
0
1
0
1
1
0
1
1
0
2
1
1
1
0
1
1
0
0
1
1
1
1
1
1
1
2
1
1
1
1
1
1
0
0
2
0
2
0
1
0
1
2
1
0
1
1
1
0
1
0
1
2
1
0
0
0
1
2
1
1
1
0
0
1
1
0
0
0
0
1
0
0
1
0
0
1
0
1
0
1
0
2
0
0
2
0
1
2
0
2
0
2
0
2
2
0
2
1
1
1
0
0
0
0
0
0
0
1
1
0
1
1
1
2
0
2
2
2
1
0
1
0
2
0
0
1
0
1
0
0
2
1
1
2
1
1
0
2
1
1
1
0
1
1
0
0
0
1
0
1
0
0
2
0
0
2
1
1
1
1
0
1
0
0
1
1
3
1
1
1
0
1
0
1
1
2
1
0
2
2
2
0
1
1
2
0
2
2
1
1
1
0
1
1
1
2
1
0
0
0
0
1
0
0
1
1
1
0
1
2
1
0
1
1
1
1
1
0
1
0
1
1
1
1
0
2
1
2
0
0
2
1
1
0
1
1
1
1
1
1
2
2
2
0
0
1
1
0
0
0
1
1
2
0
1
1
0
1
2
0
0
1
2
1
1
1
0
1
1
1
3
2
2
2
0
2
1
1
1
0
0
1
1
1
0
2
0
1
1
1
1
2
2
1
2
0
0
0
0
2
1
0
1
0
0
0
2
0
1
2
1
0
1
0
1
0
0
1
1
0
1
2
0
2
0
1
2
1
1
0
1
0
0
2
2
1
1
1
0
1
2
1
1
4
2
1
1
2
2
1
2
2
1
1
0
1
2
0
0
0
1
1
2
0
1
1
1
1
2
0
1
0
2
0
2
1
2
2
1
2
1
2
2
1
1
1
1
1
0
0
2
0
1
1
1
2
1
0
1
0
0
1
2
2
0
2
1
0
1
1
1
1
2
1
1
2
1
1
1
2
2
1
2
1
0
1
1
1
1
1
1
2
3
0
1
1
1
1
2
1
0
2
2
1
1
0
1
1
2
1
2
1
2
1
0
0
1
1
2
0
1
0
1
1
1
1
0
1
1
1
0
0
1
0
1
1
0
0
0
1
2
2
0
2
0
1
0
1
1
2
2
2
0
1
1
0
0
1
1
0
2
2
1
2
1
0
2
0
1
1
1
0
0
0
1
0
0
1
1
1
1
0
0
1
1
0
1
2
1
1
1
1
1
1
1
0
0
2
1
0
2
1
0
1
1
1
0
2
2
0
2
1
2
2
0
1
2
2
1
1
1
1
2
1
0
2
0
2
0
0
1
1
0
1
1
2
2
1
1
1
1
0
0
1
0
2
1
2
1
0
1
0
1
2
1
0
1
1
1
1
1
0
2
1
1
2
1
0
2
0
2
1
1
1
1
0
1
1
0
1
0
1
0
0
1
0
1
2
2
1
1
1
1
2
0
0
1
1
0
2
1
2
0
2
0
2
2
1
1
2
2
1
1
0
3
2
0
1
1
2
0
0
1
1
2
2
1
2
1
2
0
2
2
1
2
1
5
1
0
1
2
1
1
0
1
1
0
1
0
0
1
0
1
1
1
0
1
0
0
1
1
2
0
1
1
0
0
1
0
2
0
1
1
1
2
0
1
1
1
1
1
0
1
0
0
0
0
2
0
2
2
1
1
1
1
0
0
0
1
1
1
2
1
2
2
0
1
0
1
1
0
1
1
0
1
2
0
2
1
2
2
1
1
2
1
0
0
0
2
1
1
1
0
1
1
1
1
1
0
1
1
0
1
0
2
1
1
0
0
2
1
0
2
1
1
1
1
1
1
0
2
0
0
1
0
2
1
1
1
0
0
0
0
2
0
2
1
0
2
1
0
0
1
0
1
1
0
1
0
1
1
0
1
1
0
0
0
1
1
0
1
1
2
0
1
0
0
0
2
1
1
2
0
0
0
1
2
0
1
1
2
1
0
1
1
1
1
2
0
1
0
1
0
0
2
1
1
0
2
2
2
0
0
0
1
0
1
0
1
2
2
1
2
1
0
1
1
0
0
3
2
2
1
2
2
1
0
1
2
2
2
1
1
1
0
3
1
1
1
1
1
0
1
0
1
2
0
0
1
1
1
0
1
1
0
2
1
2
1
0
0
3
0
1
2
1
0
1
2
0
0
2
1
1
0
1
2
0
0
1
0
1
0
0
0
2
0
0
1
1
1
1
1
1
1
1
0
1
0
0
1
1
0
2
2
1
1
1
1
0
2
0
1
1
0
2
0
1
1
2
2
0
2
2
1
0
0
0
1
1
1
0
1
0
2
2
2
1
1
1
1
1
0
2
1
1
2
2
0
0
0
1
2
1
2
1
0
2
1
2
2
3
2
1
1
1
2
1
3
1
0
0
1
1
1
1
1
2
1
1
2
1
1
0
1
2
0
1
1
0
0
0
1
1
1
1
1
1
1
0
1
1
0
0
1
1
2
0
0
2
2
1
2
2
0
0
1
2
1
0
1
1
1
2
1
1
2
0
1
1
1
1
1
2
0
0
3
0
0
1
1
1
0
1
1
1
4
2
0
1
1
0
0
0
0
1
0
0
1
1
1
1
0
2
1
1
1
2
0
0
2
2
1
2
0
2
0
0
1
1
0
0
1
1
0
2
1
0
0
2
2
1
0
0
1
0
2
0
0
1
0
2
1
2
0
0
1
0
1
1
0
1
1
1
0
1
1
0
2
2
2
1
1
2
1
1
2
1
1
0
1
2
0
0
1
0
1
1
2
2
2
0
0
0
0
0
0
1
0
1
1
0
3
0
1
2
1
1
2
2
1
1
0
0
1
1
1
0
0
1
0
0
1
0
0
1
0
1
1
1
1
1
1
0
1
1
2
1
2
1
1
0
1
1
0
1
1
3
1
1
2
0
1
1
0
1
1
1
3
0
0
1
1
2
0
0
1
0
0
1
2
0
0
1
0
0
0
2
2
0
0
2
2
1
1
1
0
0
1
1
1
2
2
1
0
2
0
1
2
1
1
0
0
1
0
0
2
2
1
1
1
1
1
0
0
0
2
2
1
0
1
0
1
0
1
1
1
1
2
0
1
0
0
0
2
1
2
0
1
1
1
0
0
0
0
0
1
2
2
0
0
0
2
1
1
1
1
2
2
1
2
2
1
0
1
1
1
1
1
1
1
2
1
1
0
1
2
1
1
0
1
1
0
1
1
1
1
1
1
2
2
2
1
0
1
1
1
2
0
0
1
1
1
0
1
0
1
2
0
1
1
1
2
1
2
1
1
3
1
1
1
1
2
1
1
0
0
1
1
1
1
0
1
0
1
1
2
1
1
0
2
1
7
2
2
1
0
1
2
0
0
0
0
2
1
0
2
1
1
2
2
0
1
0
2
1
1
1
1
1
1
1
0
0
0
0
1
1
1
0
0
0
0
2
1
1
1
0
1
1
1
3
2
2
1
2
1
0
0
2
1
1
0
1
0
1
2
1
1
0
0
0
1
0
0
2
1
0
0
0
2
0
1
0
0
1
1
2
0
1
0
0
2
0
1
2
1
0
1
0
1
0
2
1
0
1
0
1
1
0
0
1
1
1
1
1
1
1
0
1
1
0
0
1
2
0
2
1
0
0
0
1
0
0
1
2
0
2
0
0
1
1
1
0
1
0
1
1
1
1
1
2
1
1
2
2
0
0
1
0
2
2
0
1
0
0
0
1
1
1
0
2
2
0
1
1
1
1
1
1
0
2
1
1
0
0
1
0
0
1
0
0
2
1
0
0
1
0
1
0
0
0
2
0
0
1
1
2
0
1
1
1
1
1
0
0
2
1
2
1
2
0
2
0
1
0
1
0
2
1
1
1
0
1
0
1
2
2
0
4
1
0
1
1
0
2
0
1
0
0
0
1
0
1
0
1
1
0
1
2
0
1
1
1
0
1
1
2
0
1
0
0
1
0
1
2
4
0
0
1
0
2
1
1
0
1
0
2
1
0
2
0
1
1
2
1
1
0
1
2
1
2
0
0
1
0
2
1
1
1
1
2
1
1
2
0
2
1
1
0
1
1
1
1
0
1
2
2
0
0
0
0
1
0
1
1
2
0
0
0
0
0
0
1
2
0
1
0
0
2
1
1
1
1
1
0
2
2
1
1
1
1
4
2
0
2
1
0
2
2
1
1
2
1
1
2
2
1
3
1
0
1
0
2
2
1
2
0
0
1
1
0
0
1
2
1
1
2
1
0
0
0
1
2
0
0
0
0
2
2
3
2
1
0
1
0
1
0
1
0
1
1
2
2
1
0
1
0
1
1
1
2
1
0
2
1
0
2
0
1
1
0
1
1
2
2
2
1
0
0
0
1
0
1
1
2
1
0
1
2
0
1
0
1
1
2
0
1
2
0
0
0
0
2
2
0
1
0
1
1
0
1
0
1
1
0
0
0
1
2
2
1
0
1
1
1
2
2
1
0
0
1
0
1
1
0
1
0
1
0
2
1
1
1
2
1
0
1
1
2
1
1
2
0
1
1
1
0
2
1
2
2
1
0
0
1
1
0
2
0
0
0
0
1
0
1
1
2
0
2
1
1
0
2
0
1
2
1
1
1
1
0
0
1
0
0
1
0
1
0
0
2
0
2
2
1
1
1
1
2
3
0
1
2
0
1
2
2
0
1
1
1
0
0
0
1
0
2
1
0
3
1
3
0
0
1
0
0
1
2
2
1
1
1
0
1
1
1
2
1
1
1
0
0
0
1
1
1
2
1
0
2
0
1
1
4
1
1
0
1
1
2
0
0
2
1
0
1
1
2
1
2
1
0
1
1
0
1
2
1
1
1
2
2
1
0
1
0
2
2
0
0
0
1
0
0
1
2
1
2
0
2
1
2
1
0
1
1
1
1
2
2
1
2
0
0
2
1
1
0
0
1
3
1
1
0
1
1
0
2
1
0
1
1
1
1
1
0
2
1
2
2
2
1
0
0
1
1
2
1
0
1
2
0
0
1
2
2
1
1
1
1
0
2
1
1
2
3
1
0
1
0
1
1
1
0
0
0
1
1
1
1
0
1
0
0
1
2
1
1
3
1
0
2
1
1
1
2
1
0
0
0
1
0
1
0
1
0
1
0
1
0
0
0
0
1
1
1
0
1
2
0
1
0
1
1
0
2
2
0
1
1
2
1
2
1
2
1
2
1
1
2
1
1
1
1
1
0
2
0
2
0
1
1
0
1
1
0
1
0
1
3
0
2
1
0
1
1
2
1
1
1
1
2
2
0
1
2
1
1
1
1
0
1
1
0
1
2
1
1
0
1
0
1
2
2
0
0
2
1
2
2
0
1
1
1
2
1
2
2
0
1
0
1
0
2
1
1
1
2
2
1
0
3
0
2
0
0
2
1
1
1
1
0
1
1
0
0
2
1
1
1
1
2
2
2
1
2
2
1
2
0
0
0
1
1
1
1
2
1
0
0
0
0
0
0
1
0
0
1
0
1
1
1
1
2
0
2
1
1
1
1
1
2
1
1
1
0
0
1
1
2
1
0
0
1
0
2
0
2
1
2
1
0
0
1
0
1
1
2
1
1
2
2
0
1
0
0
0
1
1
1
0
1
2
2
1
0
2
0
0
2
0
1
1
1
0
1
2
1
1
0
0
1
1
1
1
1
1
1
0
2
1
1
1
0
2
1
1
0
0
2
1
1
0
2
1
1
0
0
1
0
1
2
1
2
0
1
2
2
2
0
1
2
1
2
1
2
1
0
1
0
2
1
4
1
1
2
0
0
2
0
1
1
2
0
1
1
2
1
1
1
1
0
1
2
1
1
1
0
1
1
0
1
1
2
1
0
2
1
0
0
0
0
0
1
1
1
0
1
1
1
0
1
0
1
1
1
1
1
1
0
1
1
0
0
1
1
1
1
1
1
2
0
0
0
1
0
1
1
1
1
1
2
0
2
1
1
1
0
1
0
0
1
1
0
2
0
0
1
1
2
2
1
0
1
1
2
0
1
2
0
2
2
2
1
2
1
2
0
1
2
2
1
1
2
1
1
2
1
1
2
0
0
0
2
1
0
1
0
0
0
0
2
0
0
1
2
0
2
1
2
0
0
0
1
2
0
0
2
0
0
1
0
1
1
1
0
1
2
1
1
1
1
0
2
0
0
1
2
2
0
0
0
1
2
1
1
1
2
0
2
0
2
2
0
2
0
1
1
1
1
1
2
0
1
2
0
1
2
0
1
1
1
0
1
0
0
0
2
0
1
0
1
0
1
1
0
0
1
1
1
2
1
1
0
2
1
1
0
1
0
0
2
1
1
0
0
2
2
0
0
1
1
0
1
1
1
1
1
2
0
1
2
0
1
1
0
2
0
1
1
0
0
1
0
1
2
1
1
1
2
1
2
0
0
0
1
0
1
1
2
2
1
0
0
1
1
1
0
0
2
1
1
0
2
1
1
0
1
1
2
1
0
1
1
0
0
0
0
2
0
0
1
1
1
1
1
0
0
1
2
1
1
0
0
0
1
1
2
7
1
1
0
2
0
1
1
1
2
0
0
1
0
0
0
1
1
3
1
1
2
1
0
1
0
1
1
0
3
0
0
0
2
1
2
1
0
1
1
1
2
0
2
0
3
0
2
1
2
0
1
0
2
1
0
1
0
0
1
1
0
0
0
2
2
0
3
1
1
0
0
1
0
1
2
2
1
0
1
1
1
1
1
2
2
1
1
2
0
1
0
0
3
2
0
2
1
1
1
1
1
0
2
0
1
0
0
0
2
0
3
2
1
1
0
1
2
2
1
0
0
0
1
1
2
1
0
1
1
0
0
2
0
1
2
2
0
2
2
0
1
1
0
1
1
0
2
0
1
0
2
0
0
1
2
0
0
0
1
2
2
0
0
1
1
1
0
1
2
1
0
1
1
2
0
1
1
1
1
0
0
1
2
1
2
2
0
1
1
1
1
1
0
2
1
2
1
1
0
0
1
2
2
1
0
1
0
1
0
1
2
1
0
1
1
1
2
0
1
3
1
1
1
1
1
1
2
2
1
1
2
0
1
2
0
1
2
1
2
0
2
2
0
0
2
1
1
0
1
1
0
0
0
1
0
1
1
1
0
0
1
0
1
0
0
1
1
1
1
1
1
2
2
1
1
1
0
0
1
2
1
2
0
0
1
0
2
1
2
2
1
0
2
1
1
1
1
1
0
1
2
2
0
1
2
2
0
1
1
2
2
1
0
0
1
1
0
0
0
1
1
1
1
1
1
1
1
1
1
1
1
13
1
0
1
2
1
2
1
2
1
2
1
1
1
2
1
2
1
1
1
0
0
2
0
0
0
0
1
0
1
1
1
0
1
0
2
0
0
1
0
1
1
1
2
0
2
1
2
1
0
1
2
0
1
1
2
1
0
1
0
0
0
1
2
2
0
1
0
1
0
1
2
0
2
0
2
2
2
2
0
1
0
2
0
1
1
1
0
0
1
1
0
2
2
0
1
0
1
0
0
2
0
1
1
1
1
1
1
1
2
0
0
0
1
0
1
2
1
0
2
0
1
1
1
0
1
2
0
1
0
0
1
1
0
0
1
1
0
1
0
1
1
1
2
2
1
1
1
1
0
1
2
2
1
2
1
1
2
0
1
0
1
2
0
2
1
1
1
1
0
1
0
0
2
1
1
0
2
0
1
2
1
0
0
1
1
1
1
1
1
1
0
1
1
1
1
0
1
1
1
1
1
1
1
1
1
2
0
2
0
0
1
1
1
1
1
1
2
0
2
1
0
1
1
2
2
0
1
0
1
0
1
0
1
0
2
1
2
2
0
0
1
1
2
2
1
2
0
0
2
1
0
0
0
0
1
1
1
0
2
0
2
2
0
2
1
0
1
2
1
1
1
2
1
0
2
1
1
1
0
1
0
0
0
2
2
2
2
1
2
3
0
1
0
0
2
0
2
1
0
0
1
1
1
5
1
2
1
0
0
0
0
3
1
1
1
1
1
1
1
0
1
2
1
1
0
1
1
1
1
2
1
0
2
1
1
1
1
0
1
1
0
0
2
1
2
1
0
0
1
0
1
1
2
2
1
1
0
0
1
0
0
1
1
2
0
2
2
0
0
1
2
1
0
2
1
1
1
2
1
1
0
2
2
1
0
1
1
0
0
0
1
0
0
0
2
0
1
1
1
1
1
1
0
0
1
2
1
2
0
2
0
1
1
1
0
1
1
0
1
1
0
1
1
0
1
0
2
1
1
2
2
1
1
1
0
2
0
2
2
0
0
1
2
1
2
0
1
0
1
2
1
1
1
0
2
2
2
1
2
0
1
1
2
1
1
1
0
0
0
1
1
2
1
0
2
0
0
0
0
0
0
1
1
1
1
2
1
1
2
0
1
1
2
1
1
1
1
1
1
2
0
0
1
2
1
0
1
1
2
0
2
3
1
1
2
1
1
2
0
2
0
0
1
2
0
0
0
1
0
0
0
2
0
1
1
0
1
1
1
0
2
0
0
1
0
0
1
1
0
1
1
1
1
2
1
2
1
1
1
1
1
0
0
1
0
1
0
1
1
0
1
0
1
1
2
0
2
1
1
1
1
2
1
1
1
1
1
2
1
0
2
1
0
2
2
0
1
0
2
0
2
1
2
2
0
1
0
1
1
2
1
1
2
1
0
0
1
0
3
2
1
1
1
1
0
2
0
1
0
1
2
1
0
0
2
1
1
1
2
2
1
1
1
2
0
1
0
2
1
0
1
0
0
1
2
0
1
1
1
1
1
1
1
2
1
0
0
1
0
0
1
1
1
1
1
1
2
0
1
2
2
0
1
0
2
1
1
0
1
0
2
0
0
0
2
2
2
2
0
1
1
2
1
1
1
0
0
1
0
1
0
0
2
0
2
1
2
0
1
1
1
0
1
1
1
0
1
2
1
0
2
1
0
2
2
1
1
0
2
0
0
2
2
0
1
1
1
0
1
0
0
0
2
0
1
1
0
2
0
0
0
2
2
3
1
2
1
0
2
2
0
1
2
2
2
1
1
1
2
0
0
0
1
2
0
0
0
2
2
0
1
0
2
2
0
1
0
1
0
2
0
2
0
1
2
1
1
1
1
1
2
0
1
2
0
1
2
1
1
1
2
1
1
2
1
0
1
2
2
0
3
0
2
1
1
1
0
3
1
0
1
1
2
1
0
1
1
1
0
1
1
0
0
1
1
1
1
1
0
0
2
0
2
2
1
1
2
1
1
1
1
1
1
0
1
1
0
0
1
1
2
2
0
2
1
0
0
0
0
0
2
0
1
1
2
2
1
1
1
0
2
1
0
0
0
2
1
1
2
2
2
2
1
1
0
1
2
2
1
1
1
0
1
1
0
1
1
1
0
2
1
1
0
1
1
0
2
1
0
0
2
0
1
1
1
0
0
0
0
2
0
2
1
0
2
1
2
0
1
2
2
1
1
1
2
2
1
0
2
0
1
1
1
1
0
1
0
1
2
0
1
2
2
0
1
1
0
0
1
1
1
0
0
1
1
0
1
2
1
0
0
0
1
0
2
0
1
1
3
1
0
1
1
0
2
1
1
2
2
0
1
1
0
0
1
2
2
1
1
0
2
0
0
1
2
1
0
1
0
1
5
1
1
0
0
0
2
2
2
1
1
0
1
1
0
2
1
0
0
0
1
0
1
0
1
2
1
2
0
2
1
1
1
2
1
2
0
0
1
0
1
0
1
0
2
1
1
1
1
1
1
1
2
1
1
1
0
1
1
0
1
1
1
1
1
1
0
2
1
1
2
2
0
2
2
2
0
0
1
2
0
0
1
1
0
1
1
0
2
0
0
3
1
0
1
1
2
0
2
2
1
2
2
1
0
1
4
1
2
1
1
0
2
1
0
0
1
1
0
0
0
0
1
0
2
1
1
2
1
1
2
2
1
1
1
0
1
1
1
1
1
0
0
2
1
1
1
1
2
2
0
2
1
5
2
1
0
0
2
1
2
0
1
0
0
3
1
1
2
1
1
2
1
0
2
0
1
2
2
1
2
0
0
0
1
0
2
1
1
0
2
0
1
2
2
1
1
0
2
1
1
0
0
0
0
0
0
0
2
1
0
1
2
1
0
1
0
1
0
0
1
1
1
1
0
0
0
0
0
0
1
2
2
1
0
0
0
0
1
0
1
1
1
1
0
1
1
1
0
1
1
0
1
2
1
1
1
2
1
2
1
1
0
2
2
2
0
1
1
1
2
0
0
0
0
1
1
1
2
1
1
2
1
1
1
0
1
2
2
1
0
1
2
1
0
0
0
1
3
1
1
1
1
0
0
1
0
1
1
1
2
3
1
0
1
0
1
1
1
1
2
1
1
2
0
1
0
2
1
1
1
2
1
1
2
0
1
0
1
2
0
2
0
1
1
1
0
1
2
2
1
1
1
1
1
1
1
2
0
1
0
1
0
1
1
1
0
2
2
2
2
1
1
1
1
0
1
0
1
1
2
0
1
2
1
1
1
1
1
1
1
1
0
2
1
2
1
0
1
0
1
1
1
1
0
2
1
0
0
1
1
2
2
0
1
0
1
1
2
2
2
1
0
2
1
0
1
0
1
1
1
0
0
0
2
0
0
0
2
0
0
1
1
2
1
0
1
0
0
0
1
1
1
1
2
0
2
1
2
0
1
0
0
2
1
0
1
2
2
2
0
1
1
1
0
1
1
0
3
1
2
1
1
0
2
0
1
2
0
1
1
1
0
0
0
1
0
1
1
0
0
0
2
2
1
0
0
0
0
1
0
2
1
0
0
1
2
1
2
2
0
1
0
0
0
0
1
2
2
0
1
2
1
0
1
1
2
0
0
1
1
2
0
0
1
1
2
0
1
0
1
0
2
0
1
1
2
1
2
1
1
0
0
2
1
1
2
1
2
2
1
2
2
0
1
1
0
1
1
0
0
1
0
0
1
0
1
0
0
1
1
1
1
1
1
1
0
1
0
0
2
1
2
2
0
0
1
0
1
0
1
0
1
1
1
0
1
2
1
0
1
1
1
1
1
1
1
0
0
2
1
0
0
2
1
1
1
0
1
0
0
1
0
1
1
1
1
0
0
1
2
2
0
1
1
1
1
1
2
1
1
1
2
1
2
1
0
0
1
2
0
2
4
0
2
2
1
1
0
2
0
1
0
0
0
1
1
2
2
0
2
0
1
1
0
1
0
0
0
1
1
1
1
2
0
1
2
2
1
0
2
0
0
1
0
1
1
0
1
2
1
1
0
0
1
0
0
1
0
0
2
2
2
1
1
0
1
1
0
1
3
1
1
1
1
0
0
1
1
0
2
1
0
1
1
0
2
1
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
2
2
1
3
1
2
1
2
0
3
1
0
0
1
0
2
3
2
3
0
1
1
0
1
2
0
1
1
0
2
1
0
0
0
0
1
0
0
1
1
2
2
0
2
1
0
1
0
1
1
0
1
2
0
1
1
1
1
1
1
0
1
1
2
0
1
2
2
2
1
0
0
1
0
2
2
1
1
0
1
3
0
1
2
1
1
2
1
1
0
1
0
1
1
1
2
0
2
1
1
1
1
2
1
1
2
0
2
0
1
2
0
0
2
2
1
1
2
1
1
3
2
1
1
2
1
1
2
1
1
3
0
1
1
0
1
0
0
0
1
1
1
1
0
1
1
1
0
1
1
1
2
0
2
0
1
0
1
0
2
1
1
0
0
1
0
1
1
0
0
0
1
4
0
2
0
2
0
1
1
2
0
0
0
2
2
0
1
1
0
0
2
1
1
2
0
1
0
1
1
0
0
1
0
0
0
1
0
1
1
2
0
0
2
2
1
2
0
0
0
1
1
0
2
1
1
2
1
2
1
0
1
0
3
1
0
2
1
1
1
2
2
0
2
0
0
1
1
0
0
0
0
2
0
0
1
1
1
0
2
1
0
2
2
2
0
0
0
1
1
0
5
1
1
1
1
1
2
0
0
1
1
1
0
0
1
1
2
1
0
2
1
1
0
1
1
2
2
1
2
0
2
0
0
0
1
0
2
1
2
0
1
0
2
0
0
0
2
1
1
1
0
1
1
2
0
1
1
1
0
0
2
2
1
1
0
2
1
1
1
1
2
1
1
1
1
1
0
0
1
0
2
0
2
1
2
0
0
1
1
0
0
0
0
2
2
0
1
1
1
1
1
3
1
2
1
1
1
1
1
2
0
2
1
2
2
1
1
2
1
3
1
0
1
1
0
2
0
2
0
1
0
1
0
1
2
2
0
0
2
1
1
1
1
1
1
0
0
1
1
1
1
0
1
0
2
2
1
4
2
2
1
1
1
0
0
1
2
2
2
1
0
1
1
0
0
2
0
1
1
1
0
0
1
1
0
1
1
1
0
1
2
2
2
2
0
1
0
0
2
2
1
1
2
0
1
2
1
2
0
1
1
0
0
1
1
2
1
1
1
1
1
0
2
2
0
0
0
1
2
2
1
1
1
0
0
1
2
2
0
1
3
0
2
2
1
1
1
1
1
0
0
1
1
1
1
0
0
2
0
0
1
1
0
0
1
2
1
0
0
1
1
1
2
2
2
0
1
1
1
0
0
0
1
0
0
0
1
2
2
1
2
3
1
1
2
1
1
2
1
1
2
0
0
1
2
2
1
1
2
0
1
1
2
1
1
1
1
0
0
1
2
1
0
1
4
0
1
1
1
2
1
2
2
0
2
2
1
0
1
2
0
2
2
1
1
0
1
0
1
2
0
0
1
2
2
1
1
1
0
1
1
1
1
0
1
2
0
1
1
0
2
0
1
2
1
1
0
1
1
1
2
1
1
1
1
3
1
0
1
2
1
1
0
1
1
1
1
2
3
0
1
1
0
1
1
0
2
1
1
0
1
0
1
1
1
0
0
2
0
2
1
0
1
1
0
1
1
1
2
2
1
1
1
1
1
1
2
1
2
1
2
1
2
1
1
2
1
3
1
1
0
3
1
1
3
0
0
0
1
0
0
0
1
1
1
1
1
2
2
1
1
1
1
1
1
1
2
0
0
1
1
1
0
4
2
1
0
1
2
1
1
2
0
1
2
0
0
1
0
0
0
1
0
2
2
0
0
1
0
0
0
2
2
0
1
1
0
1
2
2
1
2
1
0
0
0
1
0
0
0
1
1
1
2
0
1
0
2
2
2
1
0
1
2
1
2
1
0
1
2
1
0
1
2
2
1
1
1
0
1
1
1
2
1
1
0
1
2
1
1
1
1
1
0
0
1
0
0
1
1
0
1
0
0
1
0
2
0
2
0
1
1
1
1
2
1
2
1
2
0
1
0
1
2
2
0
2
1
0
1
1
1
0
1
1
1
1
1
0
1
0
1
2
0
0
0
1
1
1
1
0
1
0
1
0
2
0
0
1
1
1
0
2
2
1
2
0
2
3
2
0
0
1
2
2
1
1
2
0
1
1
0
0
1
1
2
1
0
1
1
1
2
3
1
2
2
0
0
2
0
0
0
1
0
1
0
0
1
1
1
1
1
0
0
2
1
1
2
0
1
0
1
1
1
2
2
0
0
0
1
0
0
2
0
1
0
2
0
1
0
1
1
0
0
1
1
1
1
0
2
2
0
0
2
1
2
0
2
1
2
0
1
0
1
0
2
0
1
1
1
2
2
2
2
2
1
0
1
1
2
1
0
0
1
0
0
1
0
1
4
1
0
0
1
1
0
1
2
1
2
1
0
0
1
3
2
1
1
0
1
2
0
2
1
1
0
0
1
0
0
1
1
0
1
1
1
1
1
2
0
2
0
0
1
2
1
1
2
1
1
2
0
1
1
0
1
1
1
2
0
2
1
1
2
0
1
2
1
2
1
1
0
2
2
0
1
0
2
1
2
1
0
1
0
1
1
2
1
0
1
1
1
2
2
1
0
1
1
0
2
2
1
2
2
1
1
1
1
0
1
0
0
0
0
1
2
1
0
0
1
1
2
1
0
1
0
2
2
1
2
1
0
0
1
0
1
2
1
1
2
0
1
1
1
2
1
1
1
1
0
0
1
2
1
1
1
2
0
1
0
2
2
1
2
1
1
1
0
0
2
2
0
0
2
1
1
0
0
0
1
1
1
0
0
1
1
1
0
1
0
2
1
0
2
1
0
1
2
0
0
1
1
0
0
1
1
0
0
1
0
1
1
1
0
2
2
2
0
1
2
2
2
0
1
0
1
1
1
0
0
1
0
0
2
1
1
1
2
0
0
0
1
1
1
0
1
1
1
0
0
2
2
0
2
1
1
2
1
1
1
0
0
0
1
0
0
2
1
0
2
1
1
2
0
0
2
1
1
2
2
1
0
1
0
3
0
0
2
0
1
2
1
0
1
2
1
0
1
1
0
2
1
2
0
0
1
0
2
0
0
2
0
1
0
1
1
2
0
0
0
0
1
1
0
0
1
1
1
1
0
1
2
1
2
0
0
0
2
0
2
2
1
1
0
1
2
1
0
0
1
1
0
0
0
0
1
2
0
2
1
1
1
1
0
0
0
1
1
0
2
0
0
0
1
1
1
3
0
0
1
2
2
1
1
0
0
1
2
2
0
0
0
0
1
0
0
1
1
2
2
0
2
3
0
0
1
1
0
0
1
1
0
0
2
1
0
1
0
0
1
0
2
1
1
0
1
1
1
2
0
1
2
0
0
0
1
1
0
1
1
1
0
2
1
0
2
2
1
2
0
2
0
0
1
0
1
2
1
0
1
1
1
1
1
1
0
2
2
1
0
2
0
1
2
2
2
1
0
1
0
0
0
0
1
2
0
0
1
0
1
1
1
2
1
0
1
2
1
1
1
1
0
0
1
0
1
0
1
1
0
0
2
1
1
1
2
2
1
1
1
1
3
2
2
2
1
1
2
1
1
0
2
0
1
0
1
0
1
0
2
0
1
2
1
2
2
2
3
0
2
0
0
0
1
2
1
0
1
1
1
1
1
1
2
2
1
2
2
0
0
1
0
1
1
0
1
0
1
2
0
1
2
0
0
1
0
1
0
0
1
1
1
0
1
1
2
2
2
1
1
0
1
1
1
0
1
0
0
2
1
0
0
0
0
1
0
0
0
2
1
1
1
2
2
0
0
0
1
0
0
2
1
0
0
1
1
2
2
2
0
2
2
2
1
2
1
0
1
0
1
1
1
1
2
0
1
1
2
0
2
1
0
0
3
0
1
2
1
1
0
1
1
0
2
2
1
1
2
2
0
1
1
2
0
2
0
2
0
0
1
1
1
2
1
0
1
0
2
0
0
1
2
0
1
1
0
0
2
1
1
0
0
1
1
2
0
1
0
2
1
2
1
0
1
1
1
1
1
1
0
2
2
2
1
1
2
3
0
1
1
1
0
1
0
1
1
2
1
2
0
2
1
1
1
1
0
1
0
1
1
0
2
1
0
0
2
0
2
0
1
1
7
1
1
2
1
0
0
1
1
2
1
2
0
1
1
2
0
0
0
1
1
1
2
2
2
2
0
1
1
2
3
0
2
0
0
0
1
0
1
0
2
0
0
2
1
0
1
1
1
1
1
2
0
1
0
1
2
1
2
1
1
2
1
1
0
1
0
1
1
1
0
1
2
2
1
0
1
0
0
2
2
0
0
0
0
1
1
2
0
2
2
2
1
2
0
1
1
0
1
0
1
2
0
1
1
1
1
2
0
1
1
0
1
0
1
2
1
2
1
1
2
0
1
1
2
0
1
0
0
0
1
1
0
0
0
2
2
1
2
0
2
2
0
1
0
0
0
1
0
1
0
2
1
1
2
2
1
1
1
0
2
1
0
0
1
1
0
0
1
2
1
2
1
0
2
1
1
1
1
0
0
1
1
1
0
1
1
2
1
2
2
1
0
1
1
2
1
1
0
1
0
1
0
0
1
2
1
1
1
1
1
1
0
1
0
0
0
0
0
0
2
0
1
0
1
1
1
1
1
1
1
0
1
1
2
0
0
1
2
0
1
1
1
2
2
1
0
2
0
1
1
0
0
2
1
1
1
0
0
1
2
0
3
2
2
1
1
0
0
2
1
2
2
2
0
1
2
2
2
0
2
1
1
1
1
0
0
2
0
1
1
2
0
2
1
1
0
1
1
1
0
0
2
1
1
0
1
2
1
1
2
1
0
3
2
1
1
2
1
2
0
1
0
0
2
1
0
1
1
2
1
1
2
0
0
1
1
1
1
1
1
1
1
1
1
2
1
1
0
0
3
0
1
1
1
2
1
0
1
0
1
2
1
1
1
1
1
2
2
1
1
1
1
2
1
0
1
1
0
1
2
0
1
0
1
1
1
1
1
0
1
1
0
1
1
0
1
1
2
2
0
0
0
0
2
0
2
3
0
1
0
0
0
1
2
1
0
2
0
0
2
1
0
0
1
0
0
2
1
1
2
0
1
1
1
2
2
1
0
1
1
1
0
0
0
1
2
1
1
1
2
0
1
2
2
2
0
0
1
0
0
0
1
2
2
1
2
1
0
6
0
0
1
1
0
0
2
0
0
1
2
1
1
1
2
1
0
2
1
1
1
1
2
0
0
1
2
1
1
2
2
1
2
2
0
2
1
1
2
0
1
1
2
0
0
2
1
0
1
2
1
1
2
1
2
1
2
1
1
0
0
2
2
2
1
2
0
0
1
0
1
0
0
0
1
1
1
2
0
0
1
2
1
1
1
1
1
1
2
1
2
1
0
0
0
0
1
1
0
1
1
2
1
1
0
1
1
0
2
0
0
2
2
1
0
0
1
0
1
1
0
2
0
0
1
1
4
0
3
2
0
0
1
0
0
1
1
0
1
1
2
0
1
0
1
1
2
2
0
2
1
2
2
1
1
2
0
1
1
2
1
2
1
2
2
1
0
0
1
2
1
1
1
1
0
1
0
0
0
1
2
2
0
2
1
2
0
0
0
1
1
2
0
1
1
2
2
0
1
1
1
1
2
0
0
1
0
1
1
1
1
1
1
1
2
0
1
0
1
1
3
0
0
2
2
2
0
1
2
1
1
0
1
0
3
0
0
1
2
0
0
2
1
1
0
0
0
1
2
1
1
0
0
1
1
1
1
1
0
0
1
1
2
2
1
2
1
2
0
1
1
1
1
2
2
0
2
0
2
2
1
2
0
1
2
0
0
0
2
2
2
1
1
0
2
1
1
1
1
1
1
0
1
1
0
1
1
1
0
1
2
0
1
1
0
1
0
2
0
0
1
1
2
0
1
0
0
0
1
2
2
2
0
1
1
1
1
0
0
0
0
1
1
0
2
1
0
0
0
2
1
1
0
0
2
0
2
0
0
1
1
2
1
0
1
2
1
1
1
0
1
1
0
1
1
0
0
1
0
1
0
0
1
1
1
1
0
2
1
1
1
1
1
1
1
0
2
1
0
2
1
1
0
0
0
2
1
0
2
0
0
1
1
0
2
1
2
1
0
1
1
1
2
0
1
1
0
2
1
0
2
3
2
1
2
0
1
1
1
2
1
2
0
2
1
2
0
2
0
0
1
2
1
1
1
1
1
1
1
2
0
0
2
0
0
1
1
0
1
0
0
2
3
0
2
1
2
2
1
0
0
0
0
2
2
1
2
0
1
0
2
1
0
2
1
1
0
1
1
0
2
1
1
0
0
1
2
0
2
0
1
1
0
2
2
1
0
2
1
1
1
1
2
1
2
0
1
1
0
1
1
2
1
0
1
1
0
2
1
1
1
1
1
1
1
1
1
1
0
0
1
1
1
0
0
0
0
0
1
1
0
0
2
0
2
0
0
1
1
1
1
0
2
4
1
2
1
0
0
1
0
2
2
0
0
1
2
1
0
2
1
1
2
0
0
0
0
2
2
2
0
2
3
0
1
0
1
0
0
0
1
0
2
1
0
2
2
0
2
2
0
0
0
0
1
1
2
2
1
0
1
0
0
0
2
1
1
0
2
3
1
0
1
1
0
0
0
0
0
1
0
1
0
0
2
2
1
0
3
0
1
0
1
1
0
0
1
0
0
2
0
2
0
0
1
0
2
0
1
1
1
0
1
0
1
1
1
1
1
1
1
2
2
2
1
0
0
2
1
0
0
0
0
0
2
1
1
1
0
1
2
1
1
2
2
1
0
1
2
1
1
0
2
1
0
2
1
1
1
1
1
1
1
0
0
0
1
1
0
1
1
2
1
1
2
2
2
1
0
0
0
0
0
2
2
1
1
1
1
0
2
2
0
2
2
2
0
1
1
0
1
1
1
1
0
1
1
1
1
1
1
1
1
1
0
2
4
1
1
1
0
2
0
0
1
2
2
2
0
0
1
2
1
1
2
2
1
2
0
0
2
1
1
0
0
1
3
1
1
1
3
0
0
0
2
0
1
2
1
1
1
1
0
0
1
1
2
0
0
2
1
2
1
0
2
2
1
1
2
1
0
0
0
1
1
1
1
2
2
0
1
1
1
0
0
1
0
2
1
0
0
2
1
1
2
1
0
1
2
0
0
2
1
2
2
2
0
0
2
1
0
2
1
1
2
2
1
1
1
0
2
0
2
1
2
1
2
1
1
1
2
0
0
0
1
0
1
1
1
2
1
1
0
1
2
1
2
1
2
0
0
2
0
2
0
1
0
1
1
1
1
2
1
2
1
1
1
0
1
0
2
2
0
0
0
0
1
2
0
1
1
1
0
0
1
2
1
1
1
1
1
1
1
0
1
0
3
1
1
1
1
1
1
0
2
1
2
1
2
2
1
2
0
2
1
0
0
0
1
1
0
1
2
1
1
2
2
1
1
2
2
1
0
0
0
1
1
1
2
0
2
1
1
0
1
1
1
0
0
0
1
1
1
1
1
1
1
1
0
0
0
0
0
2
0
1
2
0
1
2
0
2
0
1
0
1
1
0
0
2
1
1
1
1
1
1
1
1
1
0
0
2
0
0
1
0
0
1
0
1
1
0
1
2
0
1
1
0
0
0
1
1
1
2
2
1
0
1
1
2
0
0
1
1
0
2
2
2
1
0
0
1
2
1
1
1
1
0
2
2
1
2
2
2
1
0
0
0
1
1
0
0
2
0
1
1
1
1
0
2
1
2
2
1
1
0
1
0
2
1
0
0
1
2
0
0
2
2
0
0
0
0
1
1
1
1
1
2
1
0
1
2
1
0
0
1
1
1
2
1
1
1
1
1
0
1
1
2
0
1
1
1
1
0
1
0
1
0
0
1
0
0
0
3
2
0
0
0
1
1
3
2
2
2
2
0
0
2
0
1
2
2
0
0
0
2
0
1
0
2
1
2
1
2
1
2
1
1
1
2
0
1
0
1
0
0
1
0
0
1
0
0
0
1
1
1
3
0
2
0
2
1
1
0
1
0
0
2
2
2
1
1
1
1
1
2
0
0
1
0
1
2
2
1
1
0
0
1
1
0
0
0
1
3
2
1
0
0
0
0
2
2
2
0
1
0
2
1
1
0
0
0
1
0
2
2
2
1
0
1
1
1
1
1
2
1
0
2
0
1
1
0
1
0
2
0
2
0
0
1
1
0
1
2
2
1
0
1
1
4
1
0
0
0
1
0
1
0
0
0
2
0
0
0
1
1
0
0
0
2
2
2
2
1
2
0
1
2
1
0
1
1
0
1
2
0
1
2
0
0
0
1
0
0
3
1
0
1
1
1
2
0
1
1
2
0
2
1
1
0
1
0
0
1
2
0
2
0
0
0
1
0
0
1
2
1
1
0
3
0
0
1
2
0
1
2
2
1
0
0
0
0
1
1
0
1
0
2
1
0
1
2
0
1
1
0
1
0
1
1
0
1
0
0
1
0
1
1
1
0
1
1
1
0
2
2
1
0
0
1
1
0
1
2
2
0
1
1
1
2
0
2
0
1
1
2
1
0
1
1
1
0
1
2
2
2
1
0
1
1
0
0
1
1
2
1
0
1
0
1
1
0
1
0
0
2
0
2
1
1
1
2
2
2
1
2
1
2
2
0
1
2
1
2
0
1
1
0
0
1
1
1
0
2
1
2
1
1
0
2
0
0
1
1
0
1
0
1
1
0
0
0
1
1
1
2
2
2
2
2
1
0
1
1
2
1
2
0
0
0
2
2
0
1
2
0
2
2
0
0
0
2
0
1
1
1
1
1
1
2
0
2
0
1
1
1
5
1
1
1
1
1
0
0
0
1
1
0
0
1
2
1
1
2
0
0
1
0
2
0
1
0
1
0
0
1
1
1
0
2
0
1
0
2
0
1
1
0
0
1
1
1
1
1
0
0
0
2
1
0
1
1
2
0
1
1
2
1
1
1
1
0
2
0
0
1
1
0
1
2
1
0
1
3
1
1
0
1
2
1
0
1
0
1
2
0
1
0
0
2
0
1
1
0
2
1
1
1
0
0
2
2
2
0
0
0
1
1
1
1
0
1
2
1
0
1
0
0
2
1
2
1
1
1
1
1
1
2
1
1
0
1
1
0
0
1
1
0
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
2
1
0
2
1
1
2
1
0
1
1
0
1
0
1
1
0
0
2
2
1
2
1
2
0
0
0
1
0
0
1
0
1
0
1
2
1
2
1
0
1
0
0
0
3
0
1
1
0
2
1
0
1
1
1
1
1
0
1
1
2
0
1
1
1
1
0
0
2
0
0
1
1
2
0
3
0
1
0
2
0
2
1
0
1
1
1
0
2
2
1
1
1
1
1
1
1
2
1
1
1
2
1
2
1
2
2
1
0
0
2
1
1
1
2
0
0
2
2
1
0
0
1
0
1
2
0
1
1
1
1
1
1
1
1
1
2
0
0
0
1
1
0
0
1
2
0
1
0
1
1
2
1
0
0
2
1
0
0
0
2
2
0
1
1
0
0
2
1
1
2
0
1
0
0
1
1
4
1
1
0
2
2
2
1
0
1
1
2
1
1
1
1
1
0
1
1
0
1
1
1
1
1
0
1
0
2
1
0
0
0
1
1
0
1
0
1
0
2
2
2
0
1
1
1
1
0
1
1
1
1
1
1
1
1
0
1
0
0
1
1
1
2
1
0
2
1
0
0
1
1
1
1
1
2
0
1
2
2
1
0
0
0
0
1
1
1
1
1
1
0
2
1
1
1
1
0
1
2
0
0
0
2
1
1
0
2
2
2
1
0
1
1
1
0
1
0
1
1
1
1
2
1
0
1
0
1
2
2
1
1
1
2
0
0
0
1
0
1
1
1
2
2
0
1
1
1
0
2
2
0
2
2
1
1
0
1
0
1
1
0
1
0
0
2
0
2
1
1
0
1
1
0
1
1
0
2
2
0
1
2
1
0
1
2
1
0
1
1
1
1
1
3
0
0
1
1
1
1
1
0
2
1
1
1
1
1
2
1
2
0
0
2
2
0
1
2
3
2
2
1
2
0
2
1
1
0
1
1
2
0
0
0
2
2
0
0
1
1
2
0
0
1
1
4
1
1
1
2
0
1
2
0
1
2
1
1
0
2
1
2
0
1
1
2
1
1
1
1
1
1
1
2
0
0
1
0
2
2
0
1
0
0
1
1
1
0
1
0
1
0
1
2
2
1
2
0
0
1
1
1
2
1
0
1
2
0
1
0
0
1
1
1
0
1
2
0
0
1
1
0
0
1
1
0
2
1
1
1
1
2
1
1
0
2
1
2
1
0
2
0
0
2
2
2
1
2
1
2
1
2
1
1
1
0
1
2
1
2
1
0
1
0
2
1
1
0
2
0
1
1
1
1
1
1
2
0
0
2
0
0
1
0
1
2
2
1
1
0
1
1
1
1
0
0
2
0
2
1
1
2
1
2
1
2
1
2
0
2
1
0
0
1
1
2
0
1
2
0
1
1
1
1
1
1
1
0
1
0
0
1
1
1
2
1
0
1
1
2
2
2
2
1
1
2
0
2
2
2
1
1
1
0
0
0
1
0
2
1
2
2
1
2
2
1
2
1
0
0
1
1
1
1
1
0
1
2
1
1
0
1
2
2
0
1
0
0
2
2
2
2
0
0
0
1
1
1
1
0
1
2
2
1
1
0
0
1
0
0
0
0
1
1
4
1
0
1
0
0
1
0
2
2
1
1
0
1
1
2
2
1
1
1
1
0
2
2
0
1
1
1
1
0
1
1
2
1
1
0
2
0
0
1
2
0
0
0
1
0
1
2
2
2
0
1
0
1
2
1
0
0
0
0
0
0
1
1
0
1
1
0
2
2
0
1
1
1
1
1
0
1
1
0
1
1
0
0
2
0
0
1
1
1
1
2
1
0
2
0
2
1
1
0
2
1
2
1
1
1
0
2
1
2
0
1
1
1
0
0
1
2
1
1
2
1
0
1
1
2
1
2
0
1
0
0
1
1
2
0
0
2
1
0
2
0
0
0
2
2
1
0
1
0
1
1
0
1
0
1
1
0
1
1
0
1
0
0
1
0
1
0
1
1
1
0
0
1
1
0
0
1
1
0
1
2
0
0
2
0
1
1
0
1
2
1
0
1
1
0
1
0
1
5
2
2
0
0
0
1
2
0
1
1
1
1
1
1
0
0
1
2
1
1
1
0
1
2
0
1
1
2
1
1
0
2
0
0
1
1
1
0
1
0
1
1
1
2
0
0
1
0
0
1
0
0
1
0
1
0
0
1
0
0
1
1
1
1
2
0
1
0
2
0
0
1
0
2
2
0
1
1
1
2
0
0
1
2
1
1
0
0
1
1
2
0
1
2
1
0
1
0
1
0
1
2
1
2
1
0
2
0
0
0
1
1
1
1
2
1
1
1
1
2
0
0
0
2
0
1
1
2
0
0
1
2
0
0
1
1
1
1
1
2
1
1
2
0
1
1
1
0
2
1
1
1
1
1
0
1
0
1
2
1
2
0
1
1
2
0
0
1
2
1
1
0
0
1
1
1
1
0
0
2
0
2
1
0
1
2
1
1
2
1
1
1
1
0
3
0
1
0
2
0
0
0
0
2
2
1
1
0
2
1
1
1
1
2
1
1
0
1
2
1
4
1
2
1
1
1
2
2
1
2
1
2
1
2
0
1
2
1
1
1
2
0
1
1
1
0
1
0
0
0
0
0
1
0
1
0
1
0
2
1
2
1
0
0
0
0
1
1
1
1
1
0
2
1
1
2
2
1
1
0
0
0
1
0
1
1
0
0
2
2
1
1
1
0
1
0
1
0
1
1
1
0
1
0
0
2
2
3
1
2
0
0
1
0
1
1
1
1
2
0
0
1
1
0
2
0
2
2
1
0
0
0
0
0
0
2
2
2
1
2
1
1
1
1
0
1
2
2
1
0
1
1
2
2
2
1
0
1
2
1
2
1
0
1
1
2
2
1
1
1
2
2
2
1
0
0
0
1
0
2
0
4
1
2
0
1
2
0
0
0
0
1
2
0
2
2
0
1
0
1
1
1
2
1
2
1
0
0
1
1
1
1
1
0
1
1
0
1
0
1
2
1
2
0
1
2
2
0
0
2
0
1
0
1
2
1
1
2
0
1
0
1
0
1
1
1
2
0
2
1
0
1
0
2
1
1
2
1
1
0
1
0
2
0
2
2
2
0
0
5
2
0
1
1
1
2
0
2
2
2
0
1
2
1
1
2
3
0
1
2
1
3
1
1
0
3
2
1
1
2
1
2
0
1
2
1
0
2
2
2
0
0
3
0
3
1
0
1
0
1
0
2
1
0
0
0
0
2
1
0
2
1
2
1
1
2
3
0
1
1
1
1
2
1
1
2
2
1
0
1
1
0
2
0
1
1
0
1
1
0
0
1
0
2
1
2
1
1
0
2
2
2
0
2
1
2
1
2
0
0
1
1
1
2
1
1
1
0
1
1
1
0
3
0
1
1
1
1
1
0
1
1
0
2
3
1
0
1
1
2
1
1
0
2
2
1
0
2
0
0
1
2
3
0
0
1
1
1
1
1
0
1
1
1
2
1
0
2
2
1
1
1
1
1
1
2
1
0
2
2
0
0
1
0
2
2
1
2
1
1
2
0
0
1
1
2
1
1
0
0
1
0
1
0
3
1
1
0
1
1
1
2
1
0
1
1
0
1
0
0
0
0
0
2
2
1
0
1
1
0
1
1
1
0
1
1
0
1
1
0
1
0
0
0
0
0
1
0
1
2
1
1
2
0
0
1
0
0
1
0
1
1
2
1
2
1
0
1
0
0
0
0
1
0
1
2
0
2
0
0
1
1
0
1
0
0
1
0
2
1
1
1
1
2
0
0
0
1
1
1
0
1
1
1
1
0
1
2
2
0
1
2
1
0
1
2
1
1
1
1
0
1
2
1
0
2
2
0
0
1
2
1
1
0
1
0
0
0
0
0
1
1
1
2
0
2
0
1
1
1
1
0
1
0
2
1
0
1
0
2
0
1
1
2
1
2
2
1
1
1
1
1
1
1
2
2
2
1
1
0
1
0
0
1
1
2
1
0
1
1
1
2
1
0
1
0
0
2
1
1
0
1
1
0
2
2
2
2
1
1
2
1
1
0
1
1
2
1
1
2
1
1
1
0
0
0
1
1
3
0
1
1
0
1
0
1
0
1
2
1
1
1
1
2
0
1
2
1
1
0
1
0
1
1
0
1
2
1
1
2
1
1
0
1
2
0
0
0
1
1
1
2
1
2
1
0
2
1
1
1
1
1
1
0
1
1
1
1
1
0
0
2
1
0
1
1
1
2
1
1
0
2
2
0
0
2
1
1
0
2
1
1
2
1
1
1
2
0
1
0
0
1
1
1
1
1
2
1
0
0
1
1
1
1
0
2
1
0
0
2
1
0
0
2
1
0
1
0
1
1
1
0
0
1
0
0
0
2
1
2
0
1
1
1
0
1
1
1
1
1
1
0
2
1
1
4
2
1
1
1
0
0
1
1
0
1
2
2
1
2
1
0
1
1
2
1
0
1
1
1
2
1
0
1
1
0
1
1
1
0
1
2
2
0
1
0
2
2
0
2
2
1
0
2
1
1
0
1
2
1
2
1
2
1
0
1
1
1
1
2
2
1
0
0
0
1
1
1
1
1
1
1
1
1
1
1
0
1
1
0
3
0
1
0
0
0
1
1
1
2
0
2
1
0
0
2
0
2
1
2
2
2
2
0
1
1
1
1
0
1
1
2
1
1
2
1
0
0
0
1
1
1
2
1
1
0
2
2
1
1
1
1
0
1
1
1
1
0
1
1
1
2
0
1
1
1
2
4
2
1
1
1
2
1
1
0
1
2
0
2
0
1
1
2
0
1
2
0
1
3
0
1
1
0
1
3
1
2
2
0
0
1
1
1
5
1
1
1
1
0
1
0
1
1
0
0
1
2
1
0
1
0
0
0
1
0
2
0
2
2
2
1
0
0
0
2
1
1
0
1
0
1
3
0
2
0
0
1
0
1
1
0
2
0
1
1
1
1
2
1
1
1
1
1
1
2
1
2
2
1
2
1
1
1
1
0
0
0
1
0
1
2
0
2
2
1
0
2
2
2
2
1
1
0
0
1
1
0
1
2
1
0
1
1
1
2
1
1
2
1
2
0
0
2
0
1
1
2
0
1
1
1
1
1
1
0
1
0
0
0
0
1
2
1
1
0
0
1
0
2
1
0
1
2
0
1
1
1
1
0
1
0
0
2
1
1
1
1
0
0
1
2
2
1
1
0
1
1
2
1
2
0
1
0
0
1
1
1
0
0
1
2
2
0
1
1
0
1
2
1
0
2
1
0
2
0
1
1
0
0
1
1
1
0
1
5
2
1
1
2
1
0
1
0
1
1
1
0
1
2
0
1
0
1
1
0
1
1
2
0
1
2
1
1
2
1
0
1
1
0
1
1
0
0
1
1
1
0
0
1
1
1
2
0
1
1
2
1
0
0
1
3
0
0
1
1
1
1
0
1
1
1
0
1
3
0
1
0
1
3
1
2
1
0
0
0
2
2
2
2
1
2
0
2
1
1
1
0
0
1
0
2
0
0
1
0
0
0
1
1
0
0
0
1
1
1
2
1
1
0
2
0
1
0
1
1
1
1
2
0
1
0
0
1
1
0
2
1
0
0
1
0
1
1
1
0
0
2
1
0
0
1
1
1
1
0
1
0
1
1
1
0
1
2
0
1
0
0
0
1
1
1
2
0
1
1
1
1
0
0
1
1
2
1
1
0
2
1
0
1
2
2
0
2
1
1
1
0
2
2
0
2
1
1
1
1
0
0
1
1
0
2
1
1
0
1
9
1
1
1
0
2
1
2
2
2
2
2
2
1
2
1
1
1
2
1
2
0
0
1
0
0
1
2
0
1
1
0
1
0
2
2
1
0
3
0
0
1
0
0
0
2
2
0
2
1
2
2
0
1
1
0
1
0
1
0
1
2
2
0
1
0
2
1
0
1
0
0
0
1
1
0
1
0
2
0
0
0
1
0
1
0
1
1
2
2
1
1
1
1
2
1
0
0
1
2
2
2
3
0
0
1
0
0
0
2
1
1
1
2
0
0
0
1
0
0
1
2
1
1
2
1
1
1
1
1
1
1
2
2
1
1
0
0
2
0
1
2
1
2
2
2
1
1
1
1
1
0
0
2
1
1
1
2
2
2
0
1
0
0
2
0
0
2
0
0
1
0
0
1
0
1
0
2
0
1
2
2
2
1
1
1
1
0
2
1
2
2
0
2
1
1
1
1
1
1
2
0
1
2
0
1
1
1
2
0
0
2
2
0
0
1
1
1
0
2
1
1
1
2
0
0
2
2
1
1
0
0
2
1
0
1
2
1
0
1
3
1
1
2
1
0
0
0
0
1
1
1
0
1
1
0
1
0
1
0
0
2
0
1
2
1
2
1
0
0
1
0
1
1
2
1
2
1
0
0
1
2
2
1
0
3
1
1
1
1
2
2
0
0
1
2
1
0
1
0
0
1
0
1
1
2
1
2
1
0
0
1
1
1
1
2
2
1
0
0
2
1
1
2
1
1
1
1
0
0
1
2
1
2
0
0
0
0
2
1
1
0
1
0
1
1
0
1
1
0
0
2
1
1
0
2
1
2
0
1
1
2
1
0
1
2
1
0
1
0
0
1
1
1
1
0
0
0
0
1
0
0
0
1
1
0
2
1
1
0
1
1
1
1
1
1
1
0
0
1
1
1
1
1
0
0
1
0
1
1
2
1
0
0
1
0
2
1
1
0
1
0
1
2
0
1
1
0
1
1
1
1
1
2
1
0
0
0
0
0
1
1
1
2
1
2
0
0
1
0
1
0
1
0
0
0
2
3
2
2
1
1
0
1
0
1
0
2
2
1
2
1
1
3
4
0
1
0
3
1
1
2
1
0
0
0
2
0
1
1
0
1
4
1
0
2
2
1
0
0
0
1
1
2
1
0
1
0
1
1
1
1
0
2
2
1
1
2
0
0
2
2
0
0
1
0
2
0
2
2
0
2
1
0
1
0
1
1
2
1
2
0
2
0
0
1
0
1
2
1
0
2
0
1
1
1
2
3
1
0
1
2
2
1
1
2
0
2
0
0
0
1
1
2
2
1
2
1
1
1
1
1
1
0
1
0
2
1
1
0
1
1
1
1
0
1
1
0
0
1
1
1
0
1
2
2
1
3
1
0
1
2
2
1
2
1
2
1
2
0
0
1
0
1
0
1
2
0
1
1
1
0
0
1
0
0
1
0
1
1
2
1
0
1
0
2
0
0
0
1
2
1
2
1
2
0
0
2
0
3
0
0
1
0
1
2
2
1
0
1
1
0
1
2
1
2
1
1
1
1
1
2
0
0
1
0
1
1
5
1
1
2
1
1
1
1
0
0
1
1
0
1
0
1
1
0
2
1
2
1
4
2
0
0
0
2
1
1
0
1
1
0
1
0
1
0
1
1
0
1
0
2
1
2
0
1
2
0
0
1
0
1
0
0
1
0
1
2
1
2
1
2
2
1
1
0
1
0
0
0
0
2
0
1
2
1
2
0
1
0
3
1
1
1
0
1
0
1
0
0
1
0
1
1
0
1
1
2
0
0
1
0
1
2
1
1
1
1
0
0
2
1
2
0
0
0
1
1
0
1
1
2
1
1
1
1
2
1
1
1
0
1
0
0
1
0
1
2
1
1
1
0
2
1
1
0
1
0
0
1
1
1
2
0
1
0
0
1
2
3
1
1
1
1
2
0
1
1
2
1
1
1
0
1
1
1
2
2
1
2
1
2
2
1
1
0
0
2
0
2
2
0
0
0
0
2
1
1
1
1
1
1
0
2
1
1
0
0
0
0
1
3
2
0
2
1
2
1
1
2
1
1
0
0
1
1
0
4
1
0
2
0
0
0
2
0
1
0
0
1
1
1
0
1
1
0
1
1
1
0
1
1
2
0
1
2
2
1
5
1
0
0
3
1
0
2
2
1
0
0
2
2
1
0
0
1
2
0
1
1
2
1
0
1
2
2
3
0
2
1
1
0
2
1
0
1
0
1
0
0
1
0
1
1
0
1
2
0
1
2
0
0
1
1
0
2
1
0
1
0
0
0
1
0
1
0
2
0
2
0
2
1
1
2
1
0
1
0
3
1
1
1
2
2
1
2
1
0
2
0
0
1
1
2
0
0
2
1
1
1
0
0
2
1
0
1
0
1
1
1
0
1
1
2
1
0
0
1
0
2
2
2
1
1
0
2
0
2
1
2
0
1
1
2
0
0
2
1
1
1
1
0
1
1
0
1
0
0
1
0
0
1
1
0
0
0
2
2
1
2
1
0
0
1
1
2
0
1
2
2
0
2
1
0
1
2
0
0
1
1
1
0
2
1
1
0
2
1
2
1
0
2
1
1
2
1
1
2
1
1
1
2
1
2
1
1
1
2
2
0
2
1
2
0
1
0
0
0
0
2
1
0
1
0
2
0
1
2
1
1
1
0
2
0
0
0
0
0
1
0
1
1
0
2
0
0
3
1
0
1
0
2
2
1
1
1
0
2
1
2
1
1
2
1
1
1
0
1
0
0
1
0
1
0
0
1
0
0
1
0
1
1
2
0
2
1
0
2
1
1
2
1
0
2
0
0
1
2
2
1
1
2
1
1
1
1
1
0
0
0
0
1
1
0
2
2
2
1
1
2
1
1
0
1
1
0
1
1
0
1
1
1
2
1
0
1
2
0
0
1
1
0
0
2
1
2
1
0
0
2
0
1
0
1
2
1
0
2
0
0
0
0
1
2
0
1
0
1
1
0
0
0
1
1
1
0
1
1
1
0
0
1
1
2
0
1
2
1
1
1
1
1
0
1
2
0
0
1
1
2
1
2
2
1
1
1
1
0
1
1
1
0
1
1
2
2
1
0
2
0
2
2
0
2
1
1
1
1
0
1
1
0
1
2
0
0
1
0
3
1
0
1
0
2
0
0
2
1
1
2
1
2
2
2
1
1
2
0
0
1
0
2
2
2
2
0
2
2
2
0
0
1
1
1
1
1
1
1
1
0
2
0
2
2
0
0
1
2
1
2
1
1
1
2
2
1
2
1
1
2
1
0
1
2
0
1
0
2
0
0
2
1
1
1
1
1
1
1
2
2
0
1
1
0
2
3
1
1
1
0
0
0
1
1
0
1
1
0
2
1
1
2
1
1
1
1
1
0
2
1
1
1
0
7
1
0
1
1
1
0
1
1
0
0
1
1
2
1
0
2
2
2
2
1
1
1
1
2
1
0
1
1
1
1
2
0
2
2
2
1
1
1
1
1
2
0
2
1
0
1
0
1
1
2
1
0
0
2
2
1
0
0
1
1
2
0
0
1
0
2
0
1
2
1
0
1
1
1
1
1
0
1
1
1
0
1
1
0
0
2
0
1
0
1
2
1
0
0
1
0
0
1
2
0
1
1
0
1
1
0
2
1
2
1
1
1
0
1
1
2
1
0
1
0
1
2
0
0
0
0
1
0
1
2
0
2
0
2
1
1
0
0
2
2
1
2
0
2
2
0
1
1
1
1
1
2
0
1
1
1
2
1
0
1
0
0
2
1
0
0
0
2
1
1
0
2
0
0
1
1
1
1
1
1
0
1
0
2
0
1
1
2
2
0
0
1
1
0
1
2
1
1
1
0
0
1
2
1
0
0
0
1
1
0
1
2
2
1
0
0
2
1
0
1
1
1
1
1
0
1
0
0
1
1
1
2
2
0
1
1
2
0
1
1
2
0
1
0
1
1
2
1
0
2
1
1
1
0
0
1
1
0
1
1
0
2
2
1
1
1
0
1
0
1
0
1
0
0
2
1
2
1
0
1
2
2
1
1
1
1
1
0
1
2
1
1
1
2
1
1
1
0
1
2
0
1
2
0
2
2
0
0
1
0
2
2
1
1
0
1
1
1
0
0
2
1
1
0
1
1
0
0
1
1
0
1
2
1
0
1
1
0
2
0
2
1
2
0
0
0
1
0
2
1
1
0
0
2
2
1
0
0
0
1
0
1
1
1
2
0
0
1
2
0
2
0
1
2
2
1
0
1
0
1
1
0
1
1
1
0
1
0
2
0
0
1
0
0
0
1
2
1
0
1
1
0
1
0
1
1
1
0
0
1
0
0
0
1
2
2
0
1
1
1
0
0
2
1
2
2
0
0
0
1
1
0
1
1
2
0
0
1
2
3
1
2
0
1
1
0
0
1
0
0
0
0
0
0
2
1
1
1
2
1
2
1
2
0
2
1
1
1
0
2
0
0
1
0
0
1
2
2
2
2
2
2
0
1
0
1
1
2
1
2
1
2
1
1
0
1
1
1
0
0
2
1
2
0
1
1
1
2
0
1
0
1
0
1
1
0
3
1
0
2
1
1
0
1
2
0
1
1
1
2
1
1
1
2
2
1
1
0
0
1
0
1
1
1
2
1
1
1
0
1
1
2
1
2
2
0
2
2
2
2
1
0
0
2
2
0
2
1
1
2
1
0
1
1
1
0
1
2
1
0
3
3
0
0
0
2
1
0
2
1
0
2
1
0
2
1
2
1
1
0
0
1
1
0
1
1
0
1
1
1
2
0
0
1
2
0
1
1
0
2
0
2
0
0
1
1
1
1
1
1
1
1
0
0
0
1
0
2
2
2
1
0
0
1
0
1
1
2
3
1
0
2
1
2
0
1
1
1
1
1
0
1
1
1
0
2
0
1
1
2
2
0
2
2
2
2
0
1
0
2
1
0
2
1
0
0
2
1
0
2
1
1
0
1
1
2
0
0
0
2
1
0
0
0
0
1
0
2
1
1
1
0
1
1
1
0
0
0
1
0
0
1
1
2
2
0
1
0
1
1
1
1
0
0
2
0
1
2
4
1
1
1
0
1
0
1
0
1
2
1
2
2
2
1
0
2
1
1
1
1
2
1
2
2
1
1
0
0
0
2
1
0
1
0
0
1
2
1
1
0
0
1
1
0
0
0
0
0
0
1
1
1
1
2
1
1
0
0
1
2
2
0
2
1
1
0
1
1
2
0
0
2
2
0
1
2
0
0
1
0
1
1
1
1
2
0
0
0
2
1
0
1
0
1
1
1
0
0
0
1
0
1
1
0
2
0
0
1
0
1
1
2
4
1
1
0
1
1
1
1
1
1
0
1
1
1
0
1
2
3
2
1
2
0
0
2
0
0
0
2
1
1
0
1
1
1
2
1
2
1
1
2
3
1
2
2
2
2
1
0
1
2
1
1
0
2
3
1
1
1
2
1
2
1
0
0
0
0
1
2
4
1
2
4
2
0
1
2
1
2
1
0
0
2
1
2
2
1
1
1
1
0
1
1
1
1
0
1
0
1
0
0
0
0
1
1
2
0
1
1
0
0
1
2
2
1
2
1
1
1
5
2
0
1
1
3
1
1
1
1
1
2
3
2
1
2
1
1
0
1
2
1
2
0
0
1
1
0
0
1
0
1
1
2
1
2
0
1
2
1
1
0
1
1
0
0
1
1
0
0
1
1
1
0
1
0
1
2
2
1
1
0
0
0
1
1
1
0
0
2
2
2
1
0
1
1
1
1
1
2
0
0
0
1
0
1
1
1
2
1
0
0
2
1
0
0
1
0
1
1
2
0
1
0
1
1
2
0
0
2
2
0
1
0
2
2
0
0
1
1
0
0
1
2
1
0
0
1
2
1
2
0
9
1
1
0
1
2
2
2
1
2
0
2
0
1
2
2
0
1
1
0
2
2
1
0
0
1
0
0
2
1
0
0
0
1
1
1
1
1
1
1
0
2
1
0
1
1
0
1
1
0
2
0
1
2
0
2
0
2
1
0
1
0
1
1
1
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
2
2
0
1
1
2
0
1
1
2
0
2
1
1
0
2
2
1
1
1
1
2
1
1
1
2
1
1
2
1
1
0
1
1
2
1
2
0
1
1
1
2
1
0
0
2
1
0
1
1
1
2
0
1
1
0
2
1
1
0
0
2
1
1
0
2
0
1
0
0
1
0
1
2
0
1
0
1
1
2
0
2
0
1
1
1
1
0
2
1
0
1
1
1
2
2
0
0
2
0
1
2
3
0
1
0
0
1
1
2
0
1
0
1
1
1
0
1
1
0
1
1
1
2
1
1
1
1
1
1
1
2
0
1
1
1
2
1
1
0
2
0
1
3
0
0
0
0
2
1
3
0
1
0
1
2
0
1
1
1
1
0
1
0
1
0
1
1
1
1
1
0
0
1
0
0
0
0
3
1
1
2
2
2
0
1
1
1
2
1
0
2
0
0
0
1
1
1
2
1
1
1
1
1
1
1
1
2
1
3
2
0
0
1
1
0
1
0
0
0
0
1
2
0
2
1
1
2
1
2
1
2
2
2
0
2
1
0
1
1
1
1
1
1
0
1
0
1
1
0
2
0
3
1
0
1
1
1
0
0
1
0
1
1
3
2
2
1
1
0
1
0
1
0
0
2
1
2
1
1
1
1
2
1
0
1
1
2
1
1
1
1
0
1
1
0
0
1
1
0
1
1
1
0
1
0
2
2
0
1
0
0
0
2
1
1
0
2
1
1
1
1
0
2
1
1
1
2
0
2
1
1
1
2
0
1
1
1
0
1
2
2
0
2
1
1
1
2
0
1
0
1
1
1
2
1
0
1
0
1
0
2
0
1
2
1
0
0
2
0
2
0
2
0
0
1
1
1
2
0
2
1
0
0
0
4
1
2
0
0
1
1
2
0
1
0
2
1
2
1
4
1
1
2
0
0
0
2
1
1
1
0
1
3
0
0
1
1
2
1
1
1
0
1
1
1
2
2
0
0
0
1
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
1
2
1
1
2
0
2
1
1
2
2
1
0
0
2
1
0
2
0
2
0
1
1
1
0
1
2
0
1
2
1
1
0
1
2
1
1
1
0
1
2
0
1
2
1
0
2
2
0
2
1
1
1
0
1
0
0
2
1
2
0
0
0
2
0
1
1
0
1
2
3
0
1
1
2
1
1
1
1
2
1
1
1
2
0
1
0
1
2
1
1
2
0
0
1
2
1
1
1
1
2
1
0
2
1
0
2
1
0
0
1
1
0
1
1
1
2
2
2
0
1
0
2
2
1
1
2
0
0
1
2
1
2
1
1
1
2
0
2
1
1
1
6
0
1
1
2
2
0
1
3
1
0
0
1
0
0
2
0
0
1
0
1
0
1
1
1
1
2
1
1
1
1
0
2
0
1
1
1
1
0
2
2
0
1
0
1
2
0
1
1
2
2
1
1
0
2
0
1
0
0
1
1
0
1
2
2
0
0
1
0
2
1
2
1
1
2
0
1
1
1
1
2
0
2
1
2
1
0
1
0
0
0
0
2
1
0
0
1
2
0
1
2
1
1
1
0
1
1
1
0
2
0
2
0
1
2
1
0
0
1
1
1
0
1
0
2
1
1
0
2
1
2
1
1
2
0
1
2
1
1
2
1
1
1
1
1
1
1
1
1
0
0
1
0
2
1
1
1
1
0
1
0
0
0
1
1
0
1
1
2
1
1
2
2
0
1
0
1
2
0
2
2
1
2
2
2
1
0
2
0
0
0
1
2
2
1
0
1
1
0
1
1
1
0
2
1
2
1
2
1
0
1
2
2
0
1
2
1
1
0
1
2
0
1
0
0
1
0
1
0
1
1
1
2
1
0
0
1
2
0
1
2
1
1
1
1
2
1
2
0
0
0
1
0
0
1
0
1
1
2
1
1
1
1
2
1
0
1
2
2
2
1
2
1
0
0
1
0
1
0
1
2
1
1
1
0
0
0
0
0
2
1
2
1
1
3
1
2
1
2
0
1
1
1
1
0
3
2
1
0
1
0
0
0
0
0
1
2
1
1
1
0
1
1
0
1
1
2
0
1
1
1
2
1
1
1
2
1
2
2
1
1
1
1
1
1
1
0
1
1
0
2
1
2
1
1
1
1
3
1
0
1
1
1
1
2
0
1
0
1
0
1
2
0
1
1
0
1
2
0
0
2
0
2
2
0
1
0
1
0
2
2
0
1
1
0
0
1
1
0
0
2
0
0
2
1
2
2
1
1
0
0
1
2
1
0
0
1
1
1
1
0
1
1
0
2
1
1
0
0
1
1
2
2
0
1
2
1
1
1
1
2
0
2
1
0
2
2
1
2
1
2
1
1
2
2
1
2
1
1
0
0
1
0
2
2
0
1
2
0
2
1
2
1
0
1
1
2
2
2
0
0
1
2
1
2
1
0
0
1
0
2
1
0
1
1
2
1
0
0
0
2
1
1
0
2
0
1
1
1
1
0
1
0
0
1
1
0
0
3
1
2
0
0
1
0
0
2
1
0
1
0
1
2
1
2
1
0
2
2
1
1
2
0
1
1
2
1
1
0
2
1
1
1
1
8
2
1
0
2
1
1
0
0
0
1
1
2
1
2
0
2
2
1
0
0
1
0
1
1
0
0
1
0
0
2
1
2
1
0
2
2
0
0
1
1
1
2
0
1
0
1
1
1
2
2
1
1
1
0
2
1
1
0
1
1
2
1
0
0
1
0
2
0
1
1
1
2
2
1
1
0
0
0
0
1
0
2
1
2
1
1
1
1
0
1
0
0
1
2
0
1
2
0
1
1
0
0
1
1
0
1
1
0
1
2
0
2
1
3
1
0
2
0
2
1
0
2
2
0
2
1
1
2
1
1
1
1
0
1
0
1
0
0
4
0
1
1
1
1
1
1
1
0
1
1
2
1
0
1
0
1
0
0
2
0
1
0
0
1
1
1
1
0
2
0
1
1
1
1
1
2
0
1
1
2
1
1
1
1
0
1
2
1
2
2
2
0
1
2
1
0
1
1
0
1
0
2
1
1
2
1
1
2
1
1
1
0
1
0
2
0
1
2
0
2
1
3
1
2
0
1
0
2
1
2
1
1
0
1
1
0
0
2
1
0
0
1
0
1
2
0
1
1
0
1
1
1
4
0
1
0
1
1
0
1
1
2
0
2
1
1
1
0
1
0
2
2
3
2
1
1
0
1
0
1
2
2
1
1
0
0
1
1
2
1
1
1
1
2
1
0
2
0
1
1
2
1
2
0
2
1
3
2
1
0
0
1
0
1
0
0
0
1
1
0
1
1
0
1
0
1
2
0
1
0
1
0
0
1
1
0
1
1
1
0
2
0
1
2
1
1
0
0
1
0
1
0
0
2
2
0
1
0
1
0
2
0
1
2
1
0
0
1
1
2
1
1
1
0
2
0
2
1
0
1
1
0
0
1
2
0
0
1
1
1
1
2
1
0
0
0
2
1
1
2
1
1
1
0
1
2
1
1
0
1
2
2
2
1
1
0
1
1
0
2
0
1
1
2
0
1
4
1
0
0
1
1
1
0
1
0
0
1
1
2
2
0
1
1
1
1
2
0
1
2
1
1
0
1
1
1
1
0
2
1
2
1
0
1
2
1
0
1
1
2
2
1
0
1
1
1
1
0
0
1
0
1
1
1
2
1
0
1
2
1
1
1
0
1
0
2
0
0
0
2
0
0
1
2
1
1
1
1
0
0
0
1
1
2
1
1
2
1
2
2
1
0
0
0
0
1
2
0
2
1
1
1
1
1
2
1
0
1
2
1
0
2
1
1
1
1
0
0
1
1
0
2
2
1
1
2
1
1
0
0
1
2
0
2
0
1
1
1
2
0
1
2
1
1
1
0
2
2
1
0
1
2
1
1
1
1
0
1
1
0
1
1
1
2
1
2
0
1
1
1
0
1
1
1
2
1
0
1
1
1
1
0
1
2
1
1
1
1
1
1
1
2
0
0
1
2
0
1
0
0
1
1
0
1
2
1
1
1
2
0
0
1
1
0
2
0
0
2
1
0
4
1
1
1
1
1
0
1
0
1
1
1
1
1
2
3
1
1
0
1
2
0
2
0
1
0
2
2
1
1
2
2
0
1
0
0
2
1
0
0
2
2
0
1
0
1
0
1
0
0
2
1
1
0
0
1
0
1
2
0
1
1
1
1
1
3
1
0
0
1
1
1
0
2
2
0
1
0
0
1
0
0
1
2
1
1
0
0
0
1
2
1
1
0
0
0
1
0
2
2
0
1
0
0
1
1
0
2
2
0
1
0
1
0
1
1
1
2
1
0
1
1
0
1
0
1
1
2
1
1
1
2
1
0
0
0
2
1
1
0
0
1
1
1
1
0
2
1
0
1
2
2
2
1
2
2
2
1
1
1
2
1
1
1
1
2
1
1
1
1
2
1
0
2
0
2
1
0
2
2
2
2
0
1
2
1
0
1
0
1
0
2
2
0
1
0
3
3
1
1
2
2
1
1
1
0
1
1
0
2
1
1
1
0
2
1
2
3
1
2
3
2
1
1
0
2
1
0
2
1
1
1
1
1
1
2
1
1
0
1
1
0
0
1
0
1
1
0
2
1
4
1
1
0
1
1
0
1
2
2
0
1
0
2
1
0
0
2
0
1
0
2
1
1
1
2
1
1
0
1
2
1
1
0
0
0
0
0
2
1
1
2
1
2
2
2
0
2
0
1
1
0
2
0
2
1
0
1
0
0
0
0
2
0
1
1
1
2
1
1
0
2
2
1
0
2
1
1
3
1
0
1
3
2
2
2
0
3
2
0
0
1
1
0
2
2
1
1
2
0
1
0
1
1
2
0
2
0
0
0
1
2
1
0
1
1
2
2
0
1
2
2
1
1
0
3
2
0
1
1
0
0
2
1
0
0
3
1
2
1
1
1
1
2
2
1
1
2
0
1
0
1
1
1
1
1
1
1
1
2
0
0
1
2
0
1
0
1
0
1
1
0
1
0
0
2
1
1
1
2
1
1
2
1
2
1
1
0
1
0
1
0
1
0
0
0
1
2
2
0
0
1
0
1
1
2
2
2
1
2
1
1
0
1
2
1
0
2
2
2
0
1
1
2
1
0
0
1
2
0
0
0
0
1
2
1
0
1
1
1
1
1
1
1
2
2
0
1
2
1
0
0
1
1
1
2
1
0
1
1
2
1
1
1
1
0
1
1
1
1
2
1
2
2
2
1
2
1
1
0
2
1
0
0
2
0
1
1
0
0
1
0
1
0
1
1
1
1
0
0
1
2
2
1
0
2
1
1
1
0
2
0
0
1
1
1
1
2
1
1
2
1
2
2
1
1
1
1
0
2
1
1
1
1
1
0
1
1
1
1
2
1
0
1
0
1
0
1
0
1
1
2
0
1
1
1
1
0
0
1
2
0
0
1
2
2
2
3
1
1
0
1
0
0
0
2
1
1
2
2
2
2
0
0
1
2
2
0
2
2
1
0
1
0
2
1
0
3
1
0
2
2
1
0
2
2
1
0
1
0
2
1
1
0
0
2
1
0
0
1
1
1
0
2
0
2
0
0
1
1
2
2
0
1
2
1
1
2
1
2
1
1
0
0
1
2
1
1
0
0
0
0
0
1
1
1
1
2
0
1
1
2
1
0
1
1
0
1
0
2
2
1
1
2
2
0
0
1
1
1
2
2
2
2
1
1
1
0
1
1
1
0
1
1
0
1
0
2
1
1
1
1
0
1
1
1
1
2
1
1
2
0
2
2
0
1
0
2
0
1
0
0
0
0
0
0
2
1
2
1
1
0
1
2
0
1
0
2
1
2
2
1
0
0
0
2
0
0
1
1
0
2
1
0
2
2
0
1
2
1
1
0
0
1
1
0
1
0
1
0
0
2
1
1
1
1
2
0
1
3
1
0
1
0
1
2
1
0
1
2
1
1
1
1
0
2
1
2
1
0
2
1
1
1
2
1
0
1
0
1
2
1
0
0
0
1
2
1
2
0
0
1
0
0
1
1
1
0
0
2
1
1
2
1
2
0
2
2
0
2
1
2
2
0
0
1
1
1
0
1
2
1
1
1
2
2
2
0
1
1
0
1
2
1
0
0
1
1
2
0
0
1
0
1
0
1
1
0
0
1
0
0
1
2
1
1
1
0
0
1
1
1
1
1
0
1
1
1
1
1
1
2
1
1
1
1
3
1
0
2
1
1
0
2
1
0
1
1
1
1
0
1
2
2
0
0
0
2
1
1
3
1
2
0
1
2
1
7
1
1
2
0
1
0
0
1
2
2
0
1
1
0
2
2
1
2
0
2
0
1
1
0
2
1
0
1
1
1
1
2
1
0
1
1
0
2
1
0
0
2
1
1
0
0
0
1
2
1
2
0
2
1
0
0
1
2
4
1
0
0
2
0
0
1
0
1
0
2
2
1
1
0
1
1
3
2
0
0
1
1
0
1
1
2
1
1
2
2
2
0
0
2
2
0
0
1
0
1
0
0
0
1
1
0
3
0
1
1
2
1
1
1
0
1
0
0
2
0
2
1
1
0
2
0
0
1
1
1
0
1
0
1
0
1
2
1
0
2
1
2
1
1
0
1
0
4
2
2
0
2
2
1
0
0
1
2
1
0
1
1
1
0
0
1
0
1
1
0
0
0
1
0
2
1
0
2
2
0
2
1
1
1
0
0
1
2
1
0
0
0
0
1
1
1
1
0
2
1
1
0
0
1
0
0
2
0
2
1
1
1
2
1
2
0
1
0
1
0
1
0
0
0
1
0
1
2
0
2
0
1
0
0
0
1
0
1
2
1
1
0
0
0
0
1
2
1
1
1
0
1
3
2
1
2
1
1
1
1
2
2
1
1
2
1
1
1
1
1
0
2
0
0
1
1
1
1
0
2
0
0
2
1
1
0
1
1
0
2
0
1
1
2
1
0
0
2
2
1
2
0
2
0
1
1
0
0
1
1
1
2
0
2
1
2
2
0
2
1
0
1
2
1
1
0
3
1
2
3
1
1
0
1
2
1
1
1
1
0
0
0
0
2
1
0
1
1
1
2
1
2
0
2
2
0
1
0
2
0
1
2
0
2
1
1
0
0
1
2
1
0
1
0
2
1
1
1
2
1
1
2
0
0
0
2
1
1
1
0
0
0
0
1
1
0
0
1
2
1
2
4
1
0
0
1
2
1
1
1
2
1
0
0
2
2
1
1
2
2
1
1
1
0
1
0
1
0
2
0
0
2
2
1
0
0
0
1
1
1
2
2
2
1
1
2
1
1
0
2
2
1
1
1
2
2
1
0
0
3
0
1
2
2
1
0
1
0
0
2
1
1
0
0
0
1
0
1
0
0
1
2
0
1
2
2
1
1
1
2
2
1
0
1
1
0
1
1
1
2
1
0
0
1
1
1
1
1
1
1
1
2
2
0
2
1
0
2
2
0
0
2
0
0
0
1
1
0
1
2
3
2
1
0
1
1
1
1
1
1
1
0
0
2
0
1
1
1
1
1
0
0
1
0
1
1
1
3
2
2
1
1
1
0
2
0
1
1
1
2
0
1
1
1
0
1
1
1
1
0
1
1
2
2
0
1
0
0
2
1
0
1
1
1
2
1
0
1
1
1
1
1
0
2
1
0
0
2
2
2
1
2
1
1
2
0
2
0
0
1
1
0
2
1
1
2
1
1
2
0
0
0
1
1
0
1
2
0
1
2
2
0
0
1
2
1
0
0
2
0
0
2
0
1
1
1
1
0
2
2
2
0
0
0
1
1
2
2
1
0
1
2
1
1
2
0
0
0
0
0
1
0
0
1
1
3
2
1
1
0
1
2
1
1
2
0
0
3
1
1
1
1
1
0
0
1
1
2
0
0
1
1
2
1
1
2
1
1
0
1
2
0
1
0
1
2
1
0
0
0
0
0
1
2
1
2
1
2
1
1
1
1
1
0
1
1
2
0
2
1
0
2
2
2
1
1
3
1
2
1
1
0
1
2
0
0
1
2
1
1
1
1
2
1
0
0
2
1
1
2
0
0
1
2
1
1
1
1
0
1
2
0
1
2
1
2
1
1
0
1
0
1
0
1
1
1
1
1
1
0
1
1
0
2
1
2
1
2
0
1
0
0
2
1
1
0
0
0
1
1
2
1
1
1
1
1
1
2
0
1
2
1
1
1
0
1
0
1
1
0
0
2
0
1
0
1
0
2
2
0
0
1
0
1
1
1
1
0
3
2
1
0
2
1
0
0
2
1
0
1
1
0
2
0
0
0
1
1
2
1
0
1
0
0
2
0
0
1
0
2
0
1
2
0
1
1
0
1
0
1
0
1
1
1
0
1
1
1
1
1
2
2
1
2
1
1
2
2
0
1
1
1
1
1
1
2
2
0
1
0
0
0
1
1
2
1
0
2
1
2
2
1
1
1
1
2
2
0
2
1
2
1
1
1
0
0
0
1
1
1
1
0
1
0
0
0
1
1
0
2
2
2
1
1
0
0
0
2
2
2
2
2
1
2
0
1
0
1
0
1
2
2
1
1
1
1
1
1
1
2
1
1
1
2
2
0
0
0
1
1
0
1
1
0
1
1
1
1
2
1
2
1
2
1
2
1
1
1
2
0
0
2
0
1
0
1
2
2
2
1
2
0
0
1
1
0
0
1
0
1
1
0
1
1
0
2
0
2
0
0
1
2
0
1
1
1
0
2
0
0
1
1
1
1
1
0
0
1
1
2
1
0
1
2
2
2
1
0
1
1
0
1
2
0
0
2
0
2
2
1
2
2
1
1
0
0
0
2
1
0
0
2
0
1
0
0
0
1
1
0
0
1
1
1
1
0
0
0
0
1
1
0
0
2
2
1
0
0
1
1
1
1
1
1
1
3
0
1
0
1
2
2
1
0
0
1
1
1
0
1
0
1
0
0
0
1
0
2
1
0
1
0
4
1
1
1
0
0
0
0
0
1
0
1
1
1
1
0
1
0
0
1
2
1
1
1
1
1
0
2
2
0
1
0
1
1
2
1
1
0
1
1
0
0
0
2
2
2
0
1
2
0
0
1
2
1
2
1
0
2
1
2
1
1
2
0
2
0
0
0
2
2
1
1
1
2
1
1
1
1
2
0
1
0
1
1
2
1
1
0
1
0
0
1
0
1
0
1
0
3
0
0
0
0
0
1
0
1
0
2
1
0
1
1
1
2
1
0
0
1
2
1
1
0
1
1
1
0
2
1
2
1
1
1
0
4
1
2
0
0
0
2
1
1
2
0
1
1
0
2
2
1
2
1
1
0
1
2
1
1
1
0
1
0
0
2
0
1
0
0
2
2
1
2
1
1
1
1
0
1
0
3
1
0
1
2
0
0
0
2
1
0
2
2
1
0
0
2
1
1
1
0
0
1
1
1
1
0
0
2
0
2
0
1
1
0
0
1
1
1
1
1
1
1
2
2
2
0
2
1
1
1
0
0
0
1
2
1
1
1
1
2
1
0
2
0
2
2
1
1
1
2
1
2
0
1
1
0
2
0
0
1
0
2
1
2
1
0
1
0
0
2
1
2
1
0
0
1
2
0
0
1
1
0
1
1
1
1
3
1
1
0
1
1
0
2
2
1
0
1
0
2
1
1
2
0
1
0
0
0
1
2
1
1
2
0
0
2
1
1
1
2
2
0
1
0
1
2
1
0
0
1
1
1
2
1
0
1
0
2
0
1
0
2
2
0
0
0
1
1
0
2
1
1
2
1
1
1
0
1
1
0
0
1
0
0
1
1
2
0
0
1
1
2
1
1
1
3
1
1
1
1
1
1
2
2
1
0
1
1
0
2
1
1
2
2
1
2
2
1
0
1
1
2
2
1
1
1
2
1
1
0
2
0
0
1
3
1
2
1
1
1
1
0
1
1
1
0
0
0
1
1
1
2
0
2
0
0
1
1
2
1
0
1
0
0
1
2
1
2
0
0
1
3
2
1
0
1
0
2
2
1
1
2
0
2
1
0
0
0
1
0
0
1
1
0
0
0
1
1
0
1
2
1
1
2
0
0
0
1
0
0
1
2
1
1
1
1
0
1
2
2
0
0
0
1
1
1
0
1
3
1
0
2
0
0
1
1
1
1
2
2
0
3
1
1
1
1
2
1
0
1
1
0
2
1
1
0
1
1
1
0
0
0
0
2
1
2
1
1
1
1
0
1
2
1
1
0
0
1
0
2
1
1
0
1
0
1
1
1
0
0
1
1
2
1
0
2
0
2
1
1
1
0
2
1
0
0
2
1
1
1
2
2
0
2
1
1
0
1
1
1
0
0
2
1
2
0
1
2
2
2
1
1
0
2
1
0
1
0
0
0
0
0
0
2
0
2
0
1
2
2
1
1
0
1
0
0
0
3
1
2
2
1
2
3
0
0
1
0
1
1
1
1
2
1
2
1
2
1
1
0
1
2
2
0
1
0
1
1
1
0
0
0
0
0
0
1
2
1
2
1
0
1
1
1
1
4
2
0
1
0
0
1
0
1
0
0
1
1
0
1
1
2
0
1
0
0
1
1
0
1
1
1
1
1
2
2
1
1
0
2
1
1
1
0
1
1
0
0
2
2
0
0
2
1
1
0
0
1
0
1
2
0
1
2
1
1
1
2
2
1
2
1
2
0
0
1
0
2
0
0
1
0
2
1
1
1
2
2
1
1
0
0
1
1
1
0
0
1
1
2
2
1
1
1
1
1
2
0
0
0
1
1
1
1
2
0
1
3
0
2
11
0
0
1
2
1
1
0
1
0
2
2
0
2
1
1
0
2
0
1
1
0
0
2
1
1
2
2
1
1
0
0
1
4
0
2
1
1
2
1
2
2
0
1
1
1
0
1
1
1
1
2
2
3
2
1
1
1
1
1
1
0
1
1
1
0
0
0
1
0
1
2
5
0
1
2
1
2
1
1
1
0
0
0
2
1
1
1
1
1
1
1
1
0
0
1
1
2
0
1
2
0
1
0
1
0
2
0
0
1
1
2
1
1
1
1
1
2
1
2
0
1
1
2
1
1
2
2
1
0
0
2
0
2
1
1
1
0
0
0
1
1
1
2
1
2
1
2
0
0
2
1
0
0
1
0
1
0
1
1
1
2
1
2
1
0
1
1
1
2
1
1
2
2
1
0
1
1
0
1
1
1
1
1
0
0
1
1
0
0
0
2
1
1
1
0
1
0
0
0
1
1
1
1
0
1
1
1
0
0
0
0
0
1
2
1
0
2
3
0
0
1
1
1
1
1
2
0
3
1
1
0
0
1
1
1
1
2
0
1
0
0
2
2
5
1
1
2
1
1
0
0
2
1
0
0
1
1
2
1
1
0
2
2
0
0
1
1
0
2
2
1
0
1
0
1
1
1
1
2
1
1
1
1
2
0
1
1
1
1
2
1
3
1
1
0
2
1
1
1
2
0
1
1
0
1
1
1
1
1
1
0
2
0
0
0
1
2
1
2
0
2
0
2
1
0
0
2
1
0
1
1
0
2
2
0
0
2
2
1
1
2
1
1
1
1
1
2
0
1
0
1
1
0
1
1
0
0
2
0
0
2
2
1
1
2
2
2
1
1
2
1
1
0
2
1
0
1
1
2
1
1
0
0
0
2
1
0
1
2
0
0
2
0
0
1
2
2
2
1
2
1
1
1
2
1
0
0
2
1
1
0
0
3
1
1
1
1
2
2
1
1
3
1
0
1
1
0
0
1
1
1
0
1
1
1
2
3
2
0
0
2
1
2
1
3
1
2
1
2
1
1
2
1
1
1
0
0
2
0
2
1
0
2
2
1
0
1
1
1
0
2
0
2
0
0
1
0
1
1
2
0
2
2
1
0
0
1
1
3
1
1
0
1
0
2
2
0
2
1
1
1
0
0
2
0
1
0
1
1
1
1
0
1
0
1
1
2
1
1
1
1
1
1
0
1
1
1
1
0
1
1
0
1
1
1
1
0
2
0
0
2
2
0
1
0
0
0
0
1
2
1
2
2
0
1
1
2
0
0
0
2
1
2
0
2
2
1
1
3
2
1
1
0
0
1
2
1
2
2
1
2
0
0
2
1
1
2
2
2
1
1
1
1
1
0
0
2
0
1
1
2
2
1
1
2
0
1
2
2
1
2
1
1
1
1
0
3
0
1
1
0
1
2
1
1
1
1
0
1
0
2
1
2
1
0
1
0
1
0
1
2
2
1
0
1
1
2
2
1
1
0
0
1
0
0
1
1
1
2
2
1
2
1
1
2
2
1
1
2
1
0
0
0
2
0
1
1
1
1
0
1
0
1
1
0
1
0
1
1
0
1
1
0
1
2
2
0
0
1
0
1
0
0
2
0
1
0
1
0
0
2
1
3
0
1
2
2
0
0
0
0
0
1
1
0
1
0
1
2
1
0
1
1
1
1
1
0
1
1
0
1
1
1
2
0
1
1
2
0
0
0
1
0
1
2
2
1
0
1
2
1
1
0
1
2
1
2
0
1
1
1
1
1
2
1
1
2
1
1
1
1
2
1
0
2
0
0
1
0
0
0
5
1
0
0
1
0
1
1
1
1
0
2
3
0
0
1
0
1
2
1
1
1
1
1
1
2
1
1
1
2
2
2
0
0
0
4
1
1
2
2
0
1
2
0
0
0
1
0
2
1
1
1
2
2
2
2
1
0
1
1
1
2
0
1
0
1
1
1
1
1
0
2
2
1
2
1
1
1
0
0
1
2
1
2
1
1
2
2
1
0
2
1
1
0
1
1
0
1
1
1
1
0
2
1
1
1
1
0
1
0
0
2
0
0
0
1
0
1
1
0
2
1
0
0
2
1
1
2
1
2
0
1
1
0
0
0
1
1
2
1
3
4
1
1
0
1
0
1
2
1
1
2
0
0
1
1
1
1
1
2
0
0
0
1
2
1
4
1
1
2
1
1
0
1
1
1
0
1
0
0
2
0
1
1
1
1
1
0
0
0
0
1
2
1
0
1
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
0
0
0
1
2
1
2
0
1
3
1
1
1
1
1
2
0
2
0
1
0
1
1
0
0
1
0
2
1
3
0
2
1
1
2
2
1
0
1
1
1
1
1
1
1
0
0
1
1
0
0
1
2
1
0
1
0
1
0
0
2
0
0
1
0
0
1
0
1
0
0
1
0
0
1
0
0
1
1
1
1
1
1
2
0
1
1
0
1
1
2
0
1
1
1
1
0
1
1
0
0
2
2
0
0
2
1
2
1
0
1
2
0
0
0
0
1
1
2
3
2
1
0
0
1
1
0
0
0
0
0
1
1
2
0
0
2
1
2
1
1
1
0
2
2
0
2
0
0
0
1
1
1
4
0
2
2
1
0
1
2
0
0
1
0
1
0
2
1
1
2
0
1
0
0
0
0
2
1
1
0
1
1
1
0
2
0
2
1
2
2
0
0
1
1
1
1
2
1
0
1
1
2
1
0
2
1
0
1
2
0
2
1
1
2
3
2
1
0
1
2
1
1
1
0
0
0
1
0
1
2
2
1
1
1
1
0
1
0
1
2
0
1
1
0
0
2
1
0
1
0
0
1
2
0
1
0
0
0
1
1
2
0
1
2
1
1
2
1
2
0
2
1
1
0
1
1
1
1
2
2
1
1
1
3
1
0
0
2
0
0
0
1
1
2
1
0
1
1
1
1
2
0
2
2
2
2
2
0
1
1
1
2
2
1
1
1
0
1
0
0
0
1
0
3
0
1
0
1
1
1
2
0
2
3
1
0
0
1
2
4
2
0
0
0
0
1
3
1
1
0
0
1
0
1
2
1
1
1
0
1
1
1
1
3
0
2
1
1
0
2
0
2
1
1
1
1
1
1
1
1
0
0
2
0
0
0
4
2
1
1
0
1
1
1
1
0
1
2
0
2
1
1
1
1
1
0
2
2
1
0
1
1
2
2
1
1
1
2
0
1
0
2
0
2
0
0
1
1
0
0
2
1
2
2
0
1
0
0
1
1
2
2
0
0
2
1
2
1
2
0
0
1
2
2
1
1
0
1
1
1
0
2
2
2
1
0
0
0
0
0
2
0
2
1
2
0
1
1
0
0
1
2
0
1
0
1
1
1
1
0
2
2
2
1
1
0
0
1
2
1
0
1
1
0
0
1
1
0
2
2
1
0
1
0
1
0
1
1
1
0
2
2
2
1
0
2
1
1
1
1
1
1
0
1
1
0
0
1
2
1
1
2
0
2
1
1
1
1
1
0
1
1
1
1
0
0
1
1
1
1
1
1
1
1
1
2
1
1
0
2
2
1
1
0
0
1
1
1
1
0
0
2
1
1
1
0
0
1
0
1
1
1
0
0
2
0
0
0
0
1
1
0
2
2
0
1
2
2
1
1
1
1
0
1
1
2
1
1
1
1
0
1
1
1
1
2
1
1
2
1
2
0
0
1
0
0
1
1
1
0
2
1
0
0
1
1
1
1
1
1
2
1
0
1
0
1
1
3
1
0
0
1
2
1
1
3
2
1
1
0
0
1
1
0
1
1
1
2
2
0
1
2
1
1
0
2
1
1
5
2
1
1
1
1
0
2
0
0
0
2
1
1
0
2
0
2
0
1
1
2
2
0
1
1
1
1
0
1
1
1
2
2
0
1
2
2
2
0
0
0
1
1
0
0
0
1
1
1
0
1
1
2
2
1
0
0
0
1
0
1
0
1
2
0
0
1
1
2
1
1
0
0
0
1
0
1
2
0
1
2
1
1
0
0
1
0
0
0
0
2
0
0
2
2
0
3
0
2
1
0
2
0
0
1
0
0
5
2
0
1
2
1
2
0
0
1
6
1
1
1
2
1
1
1
2
0
1
1
2
2
0
1
0
0
1
0
2
1
0
1
1
0
1
3
2
0
0
0
2
2
1
1
2
0
1
0
1
2
0
0
0
0
0
2
2
3
2
1
0
1
0
0
0
2
1
1
1
1
0
0
0
0
1
0
0
1
1
2
0
1
1
0
0
0
2
0
2
0
1
0
1
1
0
1
0
1
2
0
0
1
0
1
0
1
2
2
0
1
0
1
2
1
2
1
1
0
2
0
2
2
1
1
2
1
1
1
0
1
2
1
1
1
1
1
0
0
0
2
2
0
0
1
2
1
2
1
1
1
1
2
1
1
0
2
0
0
1
0
2
0
1
1
0
0
1
2
1
1
2
0
1
1
1
1
2
1
1
2
1
2
2
2
3
2
1
2
0
0
0
1
1
0
0
0
2
0
0
0
2
2
2
2
0
0
1
0
1
1
1
2
2
1
1
1
1
0
0
1
0
1
1
2
2
1
0
0
0
1
0
1
2
0
0
1
0
1
1
0
1
1
2
0
1
0
0
2
1
1
0
2
1
1
0
2
1
0
2
1
1
1
1
0
1
0
0
1
2
2
0
1
1
2
2
1
1
1
0
2
2
2
1
0
0
0
2
2
1
0
1
0
2
1
1
0
1
1
1
0
1
0
2
1
1
1
0
1
0
0
2
1
1
0
2
1
1
2
1
0
1
0
1
1
0
0
1
2
2
1
1
2
1
1
0
1
1
0
1
0
1
0
1
2
2
0
1
1
2
1
1
2
0
2
0
2
1
0
2
0
1
1
1
0
0
1
0
2
1
3
0
0
0
1
2
0
1
1
0
1
1
1
2
1
1
0
1
1
1
0
1
0
0
0
1
0
1
1
0
2
2
1
0
2
1
1
0
0
0
2
1
1
0
0
0
1
0
1
1
0
1
1
1
0
2
0
1
0
0
2
0
1
0
0
1
1
0
2
1
0
1
0
1
2
2
1
1
2
2
2
2
1
0
0
2
1
0
0
1
1
1
2
0
1
0
0
0
1
2
0
3
0
1
1
1
1
1
1
2
1
1
0
2
1
0
2
0
1
1
1
0
0
1
0
1
1
1
0
1
1
2
0
1
2
0
0
1
2
0
1
1
1
0
2
2
2
1
0
2
0
1
1
1
1
1
1
1
2
0
0
1
1
2
1
1
2
2
0
2
0
2
0
1
1
0
0
1
1
1
1
1
1
0
3
1
1
0
1
1
2
0
0
1
1
1
2
1
2
1
0
0
2
1
1
1
2
0
0
2
1
0
0
3
0
2
2
2
0
0
1
1
0
1
1
1
1
0
0
0
2
1
0
1
0
2
1
2
2
1
1
0
1
0
1
1
1
0
0
1
0
0
0
1
1
1
1
2
1
2
1
2
1
2
2
0
1
1
0
1
0
1
2
1
1
2
1
2
2
1
1
1
1
2
0
0
1
0
2
2
1
1
1
0
1
2
1
1
0
1
0
0
1
1
2
1
1
1
0
0
2
1
2
2
2
1
1
0
2
0
1
1
1
0
2
0
0
1
1
2
1
0
0
0
0
2
1
1
1
1
2
0
1
1
2
0
1
4
1
2
0
1
1
1
0
0
1
0
2
1
2
2
1
1
0
1
0
1
2
0
1
2
2
2
1
2
0
1
2
1
1
2
0
2
1
2
0
1
2
1
1
1
1
2
0
0
2
1
2
2
1
1
2
2
0
0
0
2
2
0
1
2
0
1
1
0
2
0
1
1
0
1
1
0
2
1
0
2
2
0
0
1
1
1
1
0
0
1
0
1
1
1
0
1
0
1
0
1
1
1
1
2
1
2
0
1
2
2
1
1
1
1
1
1
1
0
2
1
1
1
4
0
1
0
1
2
1
1
1
1
2
0
1
1
1
0
1
2
1
1
1
1
0
2
2
0
1
1
1
1
2
0
0
1
2
1
2
1
1
1
0
0
1
0
1
0
1
1
1
1
1
1
2
1
0
0
1
1
1
1
0
3
1
0
2
1
0
0
1
2
1
1
0
1
2
1
0
1
1
0
1
1
2
0
1
2
0
0
1
1
2
2
1
2
1
2
0
1
1
2
0
0
1
1
1
1
1
0
3
1
0
2
1
2
2
1
0
2
0
2
0
0
1
4
1
1
2
1
0
1
0
1
1
2
1
2
1
0
2
0
1
0
1
2
2
2
2
2
0
2
4
0
2
1
0
1
0
1
1
2
0
0
1
1
0
2
1
0
0
2
1
2
1
0
0
0
1
1
1
0
2
0
0
0
1
0
3
1
2
0
9
0
2
0
1
1
0
0
1
1
1
2
1
0
0
0
1
1
0
2
1
2
1
1
1
1
1
2
1
0
1
2
1
0
1
0
1
1
1
1
0
0
1
1
0
0
1
0
2
1
0
1
1
2
1
2
0
1
1
2
0
1
2
1
1
0
0
0
2
0
0
1
1
0
1
1
0
1
0
1
2
2
0
2
0
2
0
1
1
0
2
0
0
1
0
1
1
1
0
2
1
0
0
1
1
0
0
2
0
1
1
1
2
2
1
0
1
2
2
2
1
1
2
1
1
0
1
1
1
0
1
2
1
1
2
1
1
0
2
0
0
1
1
1
1
2
0
0
0
2
1
0
2
3
1
1
1
0
1
0
0
1
2
0
0
0
1
0
2
1
0
0
2
0
0
2
1
0
1
1
1
2
1
1
1
1
1
0
1
0
0
0
1
2
1
0
2
2
1
0
0
2
0
2
1
1
1
2
2
0
1
2
1
1
1
1
0
2
0
2
1
1
2
2
0
1
1
2
0
1
0
1
2
0
1
1
1
1
0
1
2
1
1
1
2
1
1
0
2
1
2
2
1
1
0
2
0
1
1
1
0
0
0
0
1
2
1
1
2
0
0
1
1
1
0
0
0
1
0
1
1
1
0
1
2
1
1
1
1
2
1
1
1
1
1
1
0
1
1
1
0
1
2
0
1
2
2
1
1
1
1
0
0
1
1
0
1
0
1
2
2
1
1
1
1
1
0
0
1
1
0
0
1
1
0
0
3
1
0
0
2
0
0
1
2
0
1
2
1
0
2
0
0
0
0
0
1
1
1
1
2
0
2
2
0
1
1
1
1
0
1
1
1
0
1
0
1
1
1
1
0
1
3
2
1
1
1
0
1
1
1
0
1
3
0
1
0
2
1
1
1
1
1
1
1
2
1
0
1
1
0
2
2
2
1
1
1
0
1
0
1
1
1
0
1
1
0
1
0
2
0
0
0
0
0
0
2
1
1
1
0
1
0
0
1
0
1
1
1
2
2
1
1
0
0
0
2
1
1
1
0
0
0
2
0
1
1
0
2
2
0
2
1
2
1
2
2
1
1
0
1
0
2
0
3
2
0
0
1
1
1
0
1
0
0
1
2
1
0
0
2
1
0
1
1
1
1
1
2
1
0
0
1
0
2
1
0
0
1
1
0
1
0
5
2
0
1
0
1
1
1
2
1
2
1
0
1
0
1
1
0
1
1
1
0
2
1
3
0
0
1
0
0
1
1
0
1
0
1
0
2
1
0
1
1
0
1
0
2
3
0
0
0
1
1
1
2
1
1
1
1
0
1
0
0
1
2
1
1
1
0
0
1
1
0
0
2
1
1
1
2
0
2
1
0
1
1
3
2
1
0
0
1
1
0
2
1
0
0
1
0
1
2
1
2
1
0
1
1
1
0
1
1
1
0
0
0
1
0
1
1
1
1
1
0
0
1
2
1
0
1
2
0
1
0
2
0
1
0
1
0
1
1
1
2
1
2
1
0
0
1
2
1
1
0
0
1
1
0
1
1
2
2
1
1
1
2
2
1
1
5
0
0
1
1
1
1
0
1
0
1
0
1
2
0
1
2
1
1
1
1
0
0
1
1
1
1
2
0
2
1
2
1
1
0
0
1
1
0
1
0
3
0
1
0
0
2
0
0
1
1
2
1
0
1
1
0
0
1
0
1
1
2
2
1
2
1
0
1
1
1
1
2
1
2
1
0
1
1
1
1
1
0
1
1
1
2
1
1
1
1
1
0
2
0
1
0
0
0
2
0
0
2
2
1
2
4
1
0
0
1
2
0
1
2
2
0
2
1
0
1
1
1
1
2
0
1
2
2
1
1
1
0
1
2
1
1
1
2
1
2
1
1
0
2
1
1
0
0
2
2
0
1
1
1
0
0
2
0
1
2
1
1
1
1
1
0
1
2
1
2
0
1
1
0
0
2
1
1
1
1
0
0
2
0
0
0
0
1
1
1
0
1
0
0
0
2
2
1
0
0
2
0
1
2
2
2
0
1
0
0
1
1
0
0
1
1
0
0
2
0
2
1
1
1
0
1
1
1
0
1
1
1
1
0
0
0
0
1
0
1
0
1
2
1
3
3
1
2
0
1
0
0
1
0
2
1
1
1
1
2
0
0
1
0
1
1
0
0
2
2
1
1
1
3
2
2
2
0
0
2
0
1
2
1
2
0
0
1
1
0
1
0
0
1
2
1
0
0
2
2
1
2
1
1
1
1
1
0
0
1
2
1
2
2
0
1
2
2
0
2
1
1
2
1
0
0
0
0
1
0
1
1
0
1
0
2
1
2
1
0
2
1
0
3
0
2
1
1
1
1
0
2
1
1
1
2
2
0
0
0
0
0
2
0
0
2
0
0
1
0
1
1
2
1
0
1
1
0
1
0
1
2
0
0
1
1
1
2
1
0
0
1
1
1
0
1
2
1
2
1
2
1
1
1
0
2
0
0
1
1
1
1
1
1
1
2
1
1
2
2
0
1
1
0
2
2
1
0
0
0
0
1
3
1
2
1
0
0
0
0
2
1
1
1
0
1
1
1
0
0
3
1
0
2
0
0
1
3
1
1
0
0
0
0
1
0
1
1
0
1
0
2
0
0
2
1
2
1
0
0
1
0
1
1
1
1
0
1
0
1
1
1
1
1
2
1
0
1
1
0
1
0
1
1
0
1
0
0
1
2
1
1
0
0
1
1
1
0
1
4
1
0
0
0
2
1
2
1
2
2
1
1
0
1
0
0
2
1
1
1
1
2
2
2
2
1
0
0
1
2
0
1
0
2
1
1
2
1
1
1
1
1
1
0
2
1
2
0
3
2
1
0
1
1
1
1
1
0
1
0
1
0
0
0
1
0
1
5
1
1
1
1
2
1
2
1
0
1
0
1
1
1
5
0
1
2
1
1
1
1
1
2
0
0
0
1
1
0
0
0
2
1
0
2
2
1
0
0
2
2
2
2
1
2
0
2
0
0
0
0
1
2
2
0
2
0
1
1
1
2
1
1
3
1
1
2
2
2
1
1
0
1
2
0
0
2
0
0
0
1
0
1
0
0
0
2
1
1
1
1
1
1
1
0
1
2
2
1
1
2
2
2
2
2
1
0
1
1
0
0
0
0
1
1
0
1
2
1
2
2
1
0
2
0
0
1
2
0
1
1
1
0
2
0
1
1
1
1
1
1
3
0
1
1
0
1
2
2
1
0
1
1
2
1
2
0
2
1
0
0
0
2
0
1
2
0
0
1
1
0
0
1
3
1
1
1
1
1
1
1
1
1
0
2
1
0
1
0
1
1
1
1
0
1
0
0
0
0
0
2
1
1
0
1
0
1
3
1
0
1
1
0
0
1
0
0
0
0
0
1
1
1
1
1
0
1
0
0
0
1
0
0
2
1
1
1
2
1
1
0
0
1
0
0
1
1
2
0
0
2
1
1
2
1
0
2
2
0
1
1
1
1
1
1
0
2
0
0
1
0
1
1
0
1
2
0
1
1
0
0
0
1
1
1
1
0
1
1
2
2
1
1
2
2
1
0
1
1
1
0
0
0
2
1
0
4
2
0
3
0
1
1
0
1
1
2
1
1
1
1
1
1
0
0
0
2
0
1
1
1
0
1
1
0
0
2
0
2
1
0
2
1
1
0
1
0
1
1
2
1
0
1
2
1
2
1
1
1
0
2
2
2
2
2
1
1
0
1
1
1
1
0
1
2
1
0
4
0
0
0
0
3
1
0
1
0
2
0
0
2
1
1
2
1
1
2
3
0
1
1
0
2
1
0
0
1
0
0
1
1
4
0
1
1
2
0
0
2
1
0
2
0
1
1
1
2
0
0
2
2
2
0
1
1
1
2
1
1
0
1
1
1
1
0
1
2
2
1
1
1
1
1
0
1
1
1
3
0
0
1
0
2
1
1
0
0
0
0
1
0
2
1
2
0
1
0
2
1
2
1
1
2
1
2
3
0
2
1
2
0
2
0
1
1
1
1
1
2
2
1
0
0
0
0
1
0
0
1
2
0
1
1
0
0
1
0
2
0
0
0
1
1
2
2
2
0
0
1
1
0
1
2
1
1
2
1
0
1
2
1
1
2
2
1
1
0
1
2
1
1
1
1
1
0
0
1
0
1
1
2
1
1
0
0
1
2
0
0
1
5
0
2
1
2
1
2
0
2
0
0
2
2
3
2
2
0
1
2
1
0
1
1
1
0
1
1
0
1
0
1
1
1
0
1
1
1
1
0
0
1
2
0
1
1
0
3
1
1
0
2
1
0
2
1
0
1
1
1
1
1
1
0
2
1
0
0
1
2
1
0
1
2
0
1
0
1
1
1
2
0
1
0
0
1
0
2
1
0
0
1
0
2
0
1
0
2
2
1
1
1
0
1
0
0
1
0
2
0
1
1
1
1
2
1
2
1
1
1
1
1
1
0
0
1
1
1
1
1
1
0
1
0
0
2
2
1
1
0
1
1
0
1
3
0
2
1
1
2
0
0
1
0
0
0
0
1
1
0
2
2
1
1
1
3
1
0
0
3
1
0
1
2
1
1
2
1
1
2
1
3
2
0
1
0
1
2
3
1
0
0
1
2
0
0
0
1
0
1
0
2
1
1
0
1
2
1
2
0
1
1
1
0
1
0
0
0
1
0
2
1
1
2
0
1
2
1
0
2
0
2
2
2
2
1
0
1
0
1
2
2
3
0
2
1
3
2
1
0
0
1
1
1
2
1
2
0
0
1
1
1
1
2
0
2
1
0
1
0
2
1
1
1
0
1
0
0
3
2
2
1
1
1
1
0
0
2
2
2
2
1
0
0
2
1
1
2
0
0
1
1
1
1
0
1
1
1
2
1
1
0
1
1
1
1
1
3
1
0
0
2
0
2
0
0
0
1
2
1
0
0
0
1
1
1
0
1
0
2
1
2
1
1
2
2
2
2
1
0
0
0
1
1
2
0
1
1
1
1
1
0
0
0
2
1
1
1
0
1
1
1
1
0
1
2
2
0
0
0
0
1
2
1
0
0
1
2
1
1
2
0
1
1
1
0
1
1
2
1
2
2
1
1
1
2
1
1
0
1
1
2
1
1
0
1
0
1
0
1
1
1
0
3
1
2
2
0
0
1
1
0
1
2
2
2
1
0
3
2
1
2
1
2
2
1
0
1
1
2
1
1
1
1
3
2
0
0
1
2
1
1
1
0
4
1
1
0
2
1
2
3
2
0
1
0
2
1
1
1
1
1
1
2
0
0
2
0
2
1
1
2
2
1
0
0
0
1
2
0
0
1
1
0
2
1
0
1
0
2
1
1
2
1
1
1
1
2
0
0
2
0
1
1
0
1
2
1
1
2
1
0
1
1
0
1
1
3
0
2
0
0
2
1
0
0
0
2
1
0
0
0
1
1
1
1
0
1
2
1
1
2
0
1
0
1
1
1
1
0
0
1
1
0
1
2
0
1
2
0
1
0
1
2
2
2
0
2
1
1
2
2
1
0
1
0
2
2
1
0
0
1
1
1
1
0
2
1
1
2
0
0
1
2
0
1
0
2
0
0
0
0
2
2
0
2
1
2
1
2
3
1
1
1
0
0
1
1
0
2
2
0
0
0
2
1
1
0
1
1
1
1
1
0
1
2
1
1
2
0
1
2
0
1
1
2
1
1
0
1
0
0
1
2
2
1
0
2
1
0
1
2
0
1
0
0
2
1
1
2
0
1
1
1
1
2
0
1
0
1
0
1
1
1
1
0
1
1
1
0
1
1
2
0
0
0
3
1
1
2
1
0
0
0
0
1
1
1
1
0
1
1
2
1
1
1
1
1
2
1
1
0
2
2
1
1
0
2
0
2
2
1
0
1
1
1
1
2
1
1
0
0
0
1
1
1
0
0
0
1
1
2
2
2
1
1
1
0
2
2
1
1
2
2
1
2
2
1
1
0
1
1
0
1
0
0
0
2
1
1
1
1
1
0
1
0
1
1
1
1
1
0
1
2
1
1
0
1
2
0
0
2
2
1
2
0
2
0
1
1
1
1
2
1
0
2
1
4
0
1
0
0
1
0
1
1
2
1
2
0
1
0
2
1
1
1
1
0
0
1
0
2
1
1
1
0
1
2
1
3
1
2
0
1
1
1
0
2
0
0
1
2
1
0
0
0
1
1
0
3
2
1
2
1
2
1
0
2
1
2
1
1
2
0
2
1
1
1
1
2
1
0
1
0
1
1
1
1
0
0
1
0
0
0
2
1
0
1
1
0
0
1
2
1
1
0
1
1
1
1
1
0
2
2
0
1
2
0
4
2
0
1
2
2
2
1
1
0
2
0
1
2
1
0
0
2
2
2
2
1
2
0
1
2
1
1
0
2
0
2
2
1
1
0
1
0
2
1
0
0
0
0
1
0
6
1
2
1
0
0
0
0
1
1
0
0
1
1
2
0
2
0
1
0
1
0
2
0
1
0
1
1
1
0
0
2
1
1
2
0
1
2
0
1
1
0
1
1
1
1
1
1
1
0
2
1
1
0
2
0
1
1
0
2
1
1
0
1
0
1
1
1
1
2
0
1
0
0
1
1
2
1
2
1
2
0
1
0
1
0
1
1
1
1
0
1
0
1
1
0
1
1
1
2
2
2
1
0
0
1
0
2
2
0
2
1
2
0
1
2
1
2
1
0
1
0
1
1
1
1
2
4
1
2
1
1
2
0
1
2
1
2
1
2
2
1
2
2
2
1
1
1
2
0
1
0
0
0
2
1
0
1
1
0
0
0
2
2
1
1
1
1
2
2
0
2
1
1
1
0
0
1
1
2
1
1
1
2
1
0
0
2
5
1
1
1
1
1
2
2
1
0
1
1
1
2
0
1
1
1
1
2
1
0
1
0
1
2
1
1
0
0
2
1
1
1
1
1
0
1
0
1
2
2
0
1
2
1
1
2
2
0
0
0
2
0
2
1
1
1
0
0
1
1
1
1
0
1
2
1
1
1
1
0
2
2
1
1
2
1
0
0
2
0
1
0
0
1
1
1
2
0
1
0
1
2
0
0
2
2
2
1
2
1
0
2
0
1
2
1
1
1
1
1
0
2
0
1
0
2
1
2
1
1
1
2
1
1
1
2
1
0
2
2
1
2
2
0
2
0
0
2
0
2
1
1
0
0
2
1
0
0
0
1
0
0
0
1
0
0
1
0
1
1
1
0
1
1
1
0
2
2
1
0
0
2
2
0
1
0
0
1
2
1
0
0
1
2
1
1
1
0
1
0
0
0
1
1
1
2
2
1
1
1
0
0
0
0
1
1
1
1
1
2
1
0
1
1
1
1
1
0
1
1
2
2
0
1
1
0
2
1
0
1
0
0
1
1
0
1
2
1
1
1
0
0
2
1
1
1
1
0
0
2
1
1
2
1
0
0
0
0
1
2
1
1
1
2
0
0
1
1
1
1
1
0
2
1
0
0
0
1
1
1
0
0
2
1
2
1
1
0
1
1
0
2
1
2
0
1
0
1
1
0
1
1
1
2
1
1
2
2
1
1
0
0
1
2
1
1
1
1
0
1
2
1
2
0
0
0
2
2
1
2
1
0
2
1
1
1
0
2
2
1
0
0
1
1
0
0
0
0
2
1
1
1
0
1
2
1
2
1
1
1
1
0
2
0
2
1
2
1
2
1
0
0
2
1
1
0
2
1
2
0
0
0
1
1
1
1
1
1
1
1
0
2
0
1
0
0
1
1
0
1
1
1
1
0
0
2
2
1
1
1
2
1
1
0
1
0
0
1
1
0
1
2
0
0
1
1
2
1
0
0
1
0
4
2
2
1
0
0
1
3
2
1
2
2
0
1
2
2
1
0
1
0
0
0
2
1
2
1
2
2
1
1
1
1
2
0
2
0
1
1
1
1
0
0
2
1
1
1
2
1
0
1
4
2
0
1
0
0
0
0
0
0
1
2
1
1
0
2
1
1
1
0
1
1
2
1
1
1
2
1
0
1
1
0
1
0
2
1
1
2
1
1
0
0
2
2
1
2
0
1
0
1
4
0
0
1
0
0
1
2
0
1
1
0
2
1
5
1
1
0
1
2
0
1
2
1
0
2
1
1
1
2
1
2
2
2
1
0
0
0
2
1
0
0
2
4
2
1
2
0
2
2
0
2
1
2
2
0
2
2
1
1
2
2
0
3
1
1
1
2
1
0
0
1
0
0
1
0
1
0
0
2
2
2
1
0
0
0
1
1
2
2
0
1
1
1
0
1
2
0
0
2
1
0
1
0
1
1
3
1
0
1
1
0
0
1
1
1
1
0
2
2
1
0
0
1
1
2
1
1
0
0
2
1
0
0
0
2
1
0
0
3
1
2
0
0
1
2
3
0
1
1
1
0
1
1
1
0
0
1
0
1
0
1
4
2
2
2
0
1
2
1
3
0
0
1
0
2
0
2
1
0
1
2
0
2
1
2
2
0
1
0
2
4
1
2
3
0
0
1
1
1
0
0
0
2
0
0
1
0
1
1
1
1
0
0
1
1
0
0
2
1
0
0
0
1
0
1
1
1
1
0
0
1
2
1
2
0
1
2
1
1
0
0
1
2
1
1
2
1
1
3
0
1
2
1
0
1
1
1
2
0
0
1
3
1
1
1
0
1
1
0
0
0
1
1
0
1
1
1
5
1
1
2
2
3
1
0
1
1
0
0
1
1
1
0
1
0
0
2
1
2
0
0
1
0
0
1
1
1
1
0
1
3
1
0
1
1
2
1
1
2
2
1
1
1
1
1
0
2
1
2
0
2
1
0
0
0
0
1
1
0
1
3
1
1
1
0
2
0
1
1
1
0
1
2
1
1
1
1
0
1
2
1
0
1
0
0
2
0
0
0
0
2
0
2
0
1
1
1
0
1
1
0
1
2
0
0
1
1
1
0
0
1
1
1
2
1
0
1
1
2
0
2
1
1
0
1
0
1
2
1
0
0
0
2
0
0
1
1
2
2
0
1
1
1
2
2
0
2
0
0
1
0
0
1
1
1
0
0
1
1
1
0
0
1
0
1
2
1
1
0
1
0
1
1
0
1
0
2
0
1
2
1
1
0
1
1
1
1
1
1
0
0
1
2
1
2
1
0
0
0
1
0
1
2
2
1
2
0
1
1
0
1
0
0
0
1
2
1
1
1
0
1
0
0
0
1
2
2
1
1
2
2
0
1
1
0
1
0
2
1
0
0
2
0
1
0
2
1
1
1
1
0
1
1
0
0
0
0
0
1
1
0
2
2
0
1
1
2
2
2
1
0
2
2
2
2
1
0
0
1
1
0
0
0
0
0
3
1
2
2
2
1
1
1
2
1
1
0
0
2
1
1
1
0
0
1
0
0
1
1
0
1
1
0
1
0
0
1
2
2
1
2
1
2
0
2
1
0
2
0
0
1
0
1
1
0
1
0
0
1
0
0
3
1
2
0
0
0
0
1
2
1
0
0
2
1
0
0
1
2
2
0
0
1
2
1
1
0
2
2
1
2
0
0
2
1
1
1
0
1
1
0
2
4
0
2
0
0
0
1
1
1
0
1
1
0
1
0
3
2
0
1
1
2
1
0
0
0
0
0
1
0
1
1
1
2
2
1
0
0
0
0
1
2
0
1
2
0
0
1
0
1
0
1
1
0
1
2
2
2
2
2
0
1
1
1
1
0
1
2
1
0
2
0
0
0
0
0
2
3
1
1
2
1
1
2
2
0
1
1
2
1
1
0
0
2
0
1
1
1
0
1
1
1
1
0
1
1
1
1
0
1
1
1
1
0
0
2
2
1
0
0
0
2
0
1
2
1
2
0
1
1
2
2
1
0
0
1
2
0
2
1
2
1
2
1
1
0
1
1
1
2
2
1
1
2
1
0
1
2
1
1
2
0
1
0
0
0
2
1
1
2
2
1
0
0
1
0
2
1
1
2
1
1
1
1
0
0
0
1
2
1
1
0
1
0
2
1
1
2
2
1
2
1
1
0
1
5
2
0
0
0
1
1
0
0
1
1
2
0
1
1
0
1
2
1
1
1
0
0
1
1
1
0
0
0
1
0
1
0
1
0
1
0
2
1
1
1
1
1
1
2
0
0
0
1
1
0
2
0
1
1
1
1
1
1
1
0
0
0
0
0
1
1
1
0
2
0
1
0
0
2
0
0
1
1
0
1
0
2
0
1
0
0
1
1
1
0
2
1
0
1
1
2
1
1
1
0
1
1
2
1
0
0
2
2
2
0
1
2
1
2
1
1
1
1
2
0
1
1
1
1
2
1
0
2
1
1
1
2
1
0
0
0
0
1
2
1
2
1
1
1
1
2
0
1
1
1
2
2
1
1
1
0
1
2
2
1
0
1
2
1
2
1
1
0
1
1
0
0
1
0
2
1
1
2
1
1
0
1
1
0
1
0
2
2
0
1
0
4
1
1
0
1
0
1
1
1
2
1
1
1
0
1
1
0
1
0
1
2
2
1
0
1
0
1
2
0
1
1
1
1
0
0
2
0
1
1
2
2
1
0
1
2
0
0
2
2
1
0
1
1
1
2
1
1
1
1
2
0
3
1
2
2
1
2
2
0
2
1
0
0
2
0
2
2
2
2
2
2
2
1
2
1
0
0
0
1
0
2
1
0
1
2
2
2
0
2
1
0
1
0
1
2
1
0
2
1
0
1
0
2
2
0
1
2
0
0
1
1
1
0
1
1
1
1
0
2
0
2
0
1
1
0
1
1
1
0
1
2
0
1
1
1
0
1
1
0
1
1
0
1
1
1
2
1
2
0
2
1
1
1
1
0
0
1
2
1
0
0
1
2
0
1
1
1
1
0
2
0
0
1
0
0
1
0
0
2
1
0
1
1
2
0
1
1
1
1
0
1
1
2
0
1
2
1
1
3
1
0
1
1
1
1
2
0
1
1
2
2
0
1
0
0
1
2
0
2
1
1
1
2
1
0
0
0
0
2
2
0
0
1
2
1
1
1
0
2
1
0
1
0
0
1
1
1
0
0
1
1
1
1
2
1
1
0
1
1
2
1
1
2
0
1
2
1
0
1
2
0
1
1
1
1
0
0
2
0
1
1
1
0
0
0
1
2
0
1
0
2
1
0
0
1
2
0
0
0
3
1
0
1
1
2
2
1
2
1
2
1
2
1
1
0
1
2
1
2
2
1
2
0
2
0
1
0
1
2
2
1
0
1
1
1
0
2
2
1
1
2
2
1
2
1
1
2
0
0
1
1
2
0
2
1
1
2
0
0
1
1
0
1
1
2
1
0
2
1
2
1
1
1
1
1
1
1
0
1
0
2
0
0
1
1
1
0
1
1
0
1
0
0
1
1
0
1
0
1
2
1
0
2
1
2
0
1
0
1
1
1
0
0
1
1
1
2
1
1
1
2
0
1
1
2
0
0
0
2
2
0
1
1
2
2
2
0
1
1
1
0
1
0
1
0
0
0
0
0
0
2
1
1
0
1
0
0
1
1
2
1
1
0
1
0
2
2
1
0
1
0
0
0
1
0
1
2
1
0
0
0
2
2
1
0
2
0
0
1
0
1
1
1
1
2
2
0
1
2
2
0
1
0
0
2
1
1
2
1
2
1
0
2
1
1
1
1
1
0
0
2
1
0
0
2
1
0
1
2
1
0
5
1
1
0
1
1
2
1
1
2
1
1
0
1
0
2
0
1
0
1
2
2
1
1
1
1
1
2
1
0
2
2
1
2
2
0
2
1
1
2
1
0
0
1
1
1
2
0
2
1
0
1
1
1
1
2
1
0
1
2
0
0
1
0
2
1
0
1
0
1
1
2
1
1
1
1
0
0
2
1
2
1
2
0
1
0
0
1
0
1
1
1
2
1
1
0
1
1
0
1
0
1
1
1
1
0
0
1
0
0
0
2
2
1
1
0
0
1
1
2
1
0
0
1
1
1
1
0
1
1
0
0
1
1
1
0
1
0
1
1
0
0
2
1
1
1
2
1
1
1
1
1
0
1
0
1
2
1
1
1
2
0
1
0
2
2
0
1
1
0
2
0
1
0
1
1
1
0
1
0
1
1
1
0
2
0
2
1
0
2
1
2
0
0
0
1
0
1
0
2
2
0
1
1
1
1
1
2
2
0
2
1
1
1
1
0
2
0
1
1
1
0
1
0
1
2
1
0
1
2
0
2
2
1
1
0
1
0
1
2
1
1
0
0
0
2
1
1
1
0
0
2
2
2
0
0
2
1
1
0
1
2
1
0
1
2
0
2
2
1
1
0
0
2
0
1
1
0
1
2
2
1
1
1
1
1
0
1
1
2
0
2
1
0
2
2
2
1
2
0
0
1
1
1
2
0
2
1
1
1
2
1
1
1
2
2
0
0
1
2
1
0
0
0
0
2
0
1
0
1
1
1
2
2
0
0
1
1
1
2
1
0
2
1
3
1
1
2
1
2
1
1
0
1
0
2
0
0
2
1
1
1
1
1
1
0
2
2
0
1
1
2
1
2
1
2
0
1
0
2
1
1
1
1
1
0
1
1
0
2
0
1
0
2
0
1
1
1
0
0
2
2
1
1
0
1
0
2
1
1
1
1
1
1
0
1
0
1
0
1
0
1
1
1
2
2
0
1
0
1
1
1
0
1
1
1
0
1
0
0
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
0
1
2
0
2
0
1
1
1
1
0
1
2
2
1
1
1
1
1
2
1
1
1
1
1
1
0
2
0
2
0
1
1
0
2
1
1
2
0
1
2
1
1
0
1
0
1
0
1
1
1
3
2
0
0
1
1
2
0
1
2
0
0
0
1
0
3
0
2
1
0
1
0
1
3
1
2
0
2
0
1
0
1
2
1
1
2
1
2
1
0
0
0
1
2
2
1
1
0
1
0
0
1
1
0
1
1
2
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
2
1
1
0
1
2
0
0
1
1
1
1
1
1
0
2
2
1
3
0
1
1
0
1
1
0
0
0
0
1
0
2
0
0
1
0
1
1
1
2
2
2
1
1
0
0
1
2
1
1
2
0
1
0
0
1
1
0
2
2
0
2
0
2
0
2
2
1
2
1
1
0
2
1
2
1
2
1
2
1
2
2
1
1
1
0
1
2
0
2
1
0
1
1
0
1
1
1
1
2
0
0
1
1
1
0
1
2
1
0
0
4
1
1
2
0
0
1
1
0
1
1
1
2
0
1
0
1
1
1
1
2
0
0
2
1
1
2
0
2
0
0
0
1
1
0
2
1
2
0
1
0
1
0
1
1
2
0
2
1
2
1
2
1
1
1
2
1
1
2
2
1
1
1
1
1
1
1
0
2
0
1
1
0
1
1
2
2
0
3
1
1
1
1
2
0
2
2
1
1
0
1
1
0
1
3
1
1
1
0
0
0
0
2
1
2
2
0
0
1
1
1
1
1
1
0
1
0
1
1
1
3
1
1
2
0
2
1
1
0
1
2
2
2
0
1
2
0
0
0
0
1
1
0
2
0
2
1
1
1
1
2
0
2
1
2
2
0
1
1
2
0
0
2
1
1
2
0
1
1
0
1
0
0
1
0
1
1
1
1
1
2
0
1
1
0
1
1
2
2
1
1
2
0
2
1
2
1
1
0
0
0
0
0
0
2
1
1
2
2
1
2
1
2
1
2
2
1
0
1
2
0
1
2
1
0
2
0
0
0
0
2
0
0
0
1
6
1
1
1
2
0
2
0
0
0
1
1
1
1
2
1
2
1
1
0
0
0
2
1
0
1
0
1
0
0
0
2
0
2
2
0
1
2
1
0
1
1
1
1
0
1
2
1
1
1
2
1
0
2
1
1
0
1
2
2
2
1
1
1
0
0
1
0
2
2
1
0
1
2
2
1
1
0
0
1
1
3
0
0
0
2
1
2
2
0
1
1
1
0
1
0
2
1
1
1
1
0
1
0
0
1
1
1
1
0
1
2
0
1
0
1
0
1
1
0
0
1
1
0
1
0
0
1
1
0
2
1
0
1
1
0
2
1
2
1
0
2
0
2
2
1
1
1
1
1
1
1
1
0
1
1
1
2
2
2
1
1
1
0
0
2
2
1
1
0
2
0
2
1
2
0
2
1
1
2
2
1
1
1
1
1
1
0
1
1
1
1
1
1
0
3
2
0
1
1
2
2
1
1
1
2
0
1
0
1
1
2
1
0
0
1
1
1
0
1
2
2
1
0
2
0
1
2
1
1
1
0
1
1
0
2
1
0
1
2
1
0
2
1
0
1
2
1
2
1
2
2
0
2
0
1
1
1
1
1
0
1
1
2
1
2
0
2
0
1
2
2
1
2
1
1
1
0
1
0
4
1
1
0
3
0
2
2
1
1
1
0
2
1
0
2
0
0
0
2
0
1
1
0
2
1
1
0
0
0
1
2
2
2
0
2
1
0
1
1
2
0
0
0
1
0
1
1
3
0
0
0
1
0
1
2
2
1
1
2
1
1
1
1
2
0
2
1
0
1
0
0
2
1
2
1
1
0
1
2
0
1
1
1
1
2
1
2
2
0
2
0
0
2
1
2
1
2
2
1
1
2
0
1
0
1
1
0
2
1
0
0
0
1
1
1
1
2
1
1
1
0
1
0
1
1
1
1
0
0
1
1
1
1
0
1
1
1
1
0
0
1
1
0
1
2
1
0
1
1
0
1
1
1
1
1
1
1
1
1
1
2
0
1
2
2
1
1
2
0
1
1
1
1
1
2
2
0
0
0
0
0
0
1
1
2
1
0
1
1
0
1
0
0
1
1
1
1
2
1
1
1
1
1
0
1
0
3
0
0
1
2
1
1
0
0
1
0
1
1
1
0
1
1
1
0
2
1
1
1
1
1
1
0
2
2
1
2
2
2
2
0
1
1
2
0
0
1
0
0
1
1
0
1
1
0
0
3
1
1
0
1
0
2
0
2
1
1
1
1
2
2
1
5
0
0
2
1
0
1
1
1
0
1
1
0
0
1
2
3
2
2
1
1
1
0
0
1
1
1
2
0
1
1
1
1
2
1
1
1
1
0
0
1
2
2
2
1
2
1
1
1
1
2
2
1
3
0
1
1
0
2
1
1
1
2
0
0
0
1
1
0
2
1
0
0
1
0
0
2
1
0
1
0
2
1
2
0
0
1
2
0
1
1
0
0
1
1
1
2
1
1
1
3
2
1
0
1
1
2
1
2
0
1
1
0
0
2
1
0
1
1
1
0
0
1
2
1
1
2
1
0
1
1
1
1
1
0
1
1
1
2
1
1
1
1
2
1
1
1
2
2
1
0
1
1
1
0
2
2
1
2
4
0
1
0
2
1
1
1
2
1
0
1
0
1
0
2
2
1
1
1
0
1
2
1
1
0
1
2
0
1
2
1
2
1
0
2
1
1
0
1
0
0
1
2
1
1
0
2
0
0
1
0
1
1
0
1
2
1
0
2
1
1
1
1
1
1
0
2
0
0
1
1
0
1
2
2
1
2
2
1
0
0
0
1
1
0
1
1
0
1
1
1
2
1
1
0
0
2
2
0
2
0
0
1
0
2
2
1
2
0
2
0
2
1
1
0
1
2
1
0
1
2
2
2
1
1
1
2
2
0
0
1
1
0
0
1
1
0
1
2
1
2
2
2
1
0
1
1
1
1
0
1
1
1
0
1
1
1
1
1
1
0
2
1
0
1
0
2
2
1
1
0
0
1
1
0
2
0
0
0
0
0
0
0
1
0
1
2
0
1
2
2
1
1
0
2
0
1
0
1
1
2
1
0
0
2
2
0
2
1
0
1
0
1
1
1
1
0
0
1
1
0
0
1
1
1
1
0
0
0
0
2
2
0
1
2
2
2
2
0
1
1
0
0
0
2
1
1
0
1
1
1
3
0
0
1
0
0
0
2
0
0
1
1
1
0
1
1
2
2
0
2
1
2
1
1
0
1
2
0
1
1
0
1
1
1
0
0
0
2
2
0
1
1
0
0
2
0
1
0
1
1
0
0
0
1
1
1
1
1
1
1
2
1
1
0
0
0
0
1
1
0
0
1
1
1
1
0
0
1
1
3
1
2
0
1
0
0
1
2
0
1
0
0
1
0
1
3
0
0
1
5
0
2
2
0
1
2
2
2
0
0
1
8
0
2
2
2
0
0
0
1
0
0
1
1
0
1
2
0
3
1
2
2
0
1
2
0
2
1
1
0
1
2
2
1
0
0
1
1
0
0
1
1
0
0
1
0
0
2
0
0
0
2
1
0
2
0
1
2
1
1
0
1
2
0
1
0
1
1
2
1
1
1
0
1
1
0
2
0
1
1
0
1
1
1
1
0
1
0
0
2
1
1
0
0
2
0
1
0
1
3
1
0
1
1
0
1
2
1
2
0
0
0
1
1
0
1
2
2
1
0
0
0
0
2
0
2
2
1
1
2
1
2
2
2
1
0
0
0
1
1
1
1
2
2
1
1
2
0
1
1
2
0
0
2
2
0
1
2
0
0
1
0
0
0
1
0
1
0
1
1
0
1
0
1
0
0
1
0
1
2
2
0
0
2
0
1
3
0
0
1
0
1
2
0
1
0
2
3
1
1
1
1
1
2
0
1
0
2
1
0
1
1
1
1
2
0
0
0
0
1
1
1
2
1
0
1
1
1
2
2
1
2
1
1
2
2
0
2
2
2
1
0
1
1
2
1
0
2
1
1
2
1
1
0
1
2
0
0
0
1
0
2
0
1
1
1
1
3
0
1
0
0
1
1
0
1
1
1
0
0
0
1
2
2
1
2
1
1
1
2
3
1
0
0
0
1
1
2
1
2
0
0
0
1
0
2
0
1
2
1
1
1
2
0
1
1
0
0
2
1
1
2
4
1
1
1
0
2
0
1
1
0
2
1
1
1
2
1
2
1
0
1
2
1
2
1
1
0
2
1
1
2
1
1
1
1
0
2
2
2
0
1
0
0
0
2
2
1
1
2
0
1
0
2
1
1
2
0
0
2
1
1
1
0
1
0
2
2
2
1
0
0
1
1
1
1
1
1
0
0
0
1
0
0
0
0
1
2
2
2
1
1
1
0
0
0
0
0
1
0
2
1
1
1
1
1
2
1
0
2
2
2
0
0
0
1
1
1
1
1
0
2
1
1
0
1
3
2
0
0
1
1
2
0
1
1
1
1
1
2
1
1
1
1
0
1
1
2
1
1
1
2
2
1
2
1
2
0
1
1
0
2
0
0
0
1
1
0
2
2
2
0
1
1
1
1
0
0
1
2
2
1
0
1
1
3
1
1
0
1
0
0
2
0
1
1
2
0
1
1
0
0
0
0
1
1
0
2
1
0
2
1
1
0
1
1
1
2
2
1
0
1
1
0
0
2
1
1
2
2
1
1
1
2
1
1
1
1
1
0
1
0
1
2
0
1
2
1
0
1
1
1
1
1
0
2
1
1
0
1
1
1
1
0
2
0
1
1
1
0
1
0
0
0
2
0
2
2
0
0
0
3
1
0
1
0
3
3
1
0
0
1
1
2
0
0
2
2
2
2
2
1
0
1
3
1
1
1
2
1
0
2
0
1
0
2
1
1
1
1
1
2
1
0
1
1
0
1
0
0
0
2
1
2
1
2
2
2
1
2
1
1
2
0
0
0
2
0
1
1
1
1
1
1
0
1
1
1
2
1
2
0
2
1
1
2
1
1
0
1
0
1
0
1
2
0
2
1
2
1
0
1
2
0
1
1
0
1
1
1
1
0
0
0
1
1
0
1
1
1
0
1
0
0
2
0
0
1
0
2
1
1
2
1
3
1
1
0
2
2
0
0
0
1
1
1
0
2
1
1
1
0
1
0
1
0
1
2
1
0
2
1
0
0
1
1
2
0
1
0
0
1
0
1
1
2
0
1
3
1
0
1
1
0
0
1
2
0
0
1
2
2
1
1
0
0
0
1
0
2
0
1
2
1
2
0
2
1
1
2
2
2
1
1
1
3
0
1
0
1
1
0
2
1
1
0
1
2
0
1
0
2
1
2
0
1
0
0
1
1
2
0
1
2
2
1
1
1
2
1
0
0
1
1
1
1
2
1
1
2
1
1
2
1
2
1
0
0
0
0
1
0
1
0
1
2
0
2
0
1
1
1
1
0
0
1
1
2
2
1
1
1
1
1
1
0
3
1
2
2
2
2
1
1
1
1
2
1
0
0
1
1
2
1
0
1
1
1
1
0
1
2
1
0
1
0
2
2
1
1
0
0
1
3
0
0
1
1
1
1
1
2
0
0
0
1
2
2
2
1
0
0
0
0
0
1
0
1
2
3
0
1
1
2
0
0
0
1
1
0
2
1
0
1
1
2
1
1
1
0
2
0
2
2
0
1
1
1
1
3
1
0
1
2
1
1
0
2
2
0
0
0
2
1
1
1
1
1
0
1
2
1
1
2
1
0
1
1
1
1
2
0
2
0
0
1
1
1
2
2
1
2
2
1
1
2
1
1
1
1
0
1
0
1
2
0
1
1
1
1
1
1
2
3
2
1
2
2
1
1
0
1
2
2
2
0
2
1
2
1
1
0
1
0
1
1
2
2
1
0
2
0
1
1
0
0
1
2
2
1
1
1
1
2
0
1
1
3
1
1
2
1
1
1
1
2
2
0
1
1
1
3
2
0
1
2
1
1
0
1
1
1
2
0
0
1
1
1
1
2
0
1
2
1
1
2
0
0
1
1
3
1
0
4
2
0
2
2
1
1
3
2
2
0
1
1
0
1
1
2
0
0
0
2
2
2
2
1
2
1
2
0
1
1
1
1
0
1
0
1
2
2
1
1
0
1
0
2
0
1
1
1
1
0
2
1
0
0
0
2
2
1
1
2
1
0
1
1
1
2
2
0
0
1
2
2
2
1
2
2
0
2
0
1
0
0
2
2
2
1
1
0
0
1
1
2
0
0
1
0
1
0
1
1
0
0
1
1
1
2
1
0
0
1
0
1
1
1
0
2
0
1
1
1
1
0
2
1
1
1
2
1
1
1
1
2
2
1
1
1
1
1
0
1
2
0
1
0
1
2
2
1
1
2
1
2
2
1
2
0
0
0
1
1
1
2
0
0
1
2
2
1
2
0
2
1
0
2
2
0
0
0
0
1
2
1
0
2
1
0
1
1
0
2
1
1
2
2
0
0
0
1
0
1
1
1
1
1
0
2
0
0
2
1
1
2
0
1
0
1
1
1
1
1
1
2
1
0
1
1
1
2
3
1
0
1
1
0
0
0
0
2
1
1
1
0
0
2
1
2
1
1
0
0
1
2
0
1
1
1
0
2
1
0
1
1
1
0
0
2
1
0
1
0
0
0
1
1
1
0
0
1
2
1
2
1
1
0
2
1
1
2
2
0
2
1
0
0
2
2
0
0
1
0
1
1
0
2
2
0
1
2
1
2
0
1
1
1
0
0
2
0
0
0
2
0
1
0
2
1
2
1
0
2
1
2
1
0
1
1
0
1
0
2
2
2
2
2
0
0
1
1
1
0
0
0
1
2
0
1
0
1
2
0
1
0
1
0
0
2
1
1
0
0
0
3
1
1
1
1
2
0
2
0
0
0
0
1
2
1
0
1
2
2
0
2
1
1
0
2
1
2
1
2
1
0
1
0
1
1
0
2
1
2
1
2
1
1
2
1
2
0
1
1
1
1
1
0
0
0
0
1
2
2
2
1
1
1
1
1
0
0
0
1
0
13
1
0
1
0
0
1
2
0
0
0
2
1
0
0
0
1
1
0
1
3
2
1
1
0
0
1
0
2
1
1
0
3
1
0
1
1
0
1
1
2
0
0
2
0
3
0
0
0
1
2
1
2
1
0
2
1
1
1
1
1
1
1
2
0
2
1
1
4
1
0
1
2
0
1
1
1
0
1
3
1
1
0
2
0
0
2
1
0
2
2
3
2
1
1
1
0
1
0
1
1
1
2
2
1
0
1
0
0
1
0
1
1
1
2
0
2
1
1
1
1
1
1
1
0
1
1
2
1
1
2
1
1
0
1
1
1
1
1
0
2
0
0
0
1
1
0
2
0
1
1
0
1
0
1
2
1
2
1
0
2
1
0
1
0
3
1
2
1
1
1
0
1
2
1
2
2
1
1
0
0
1
2
0
2
1
1
2
1
1
0
0
2
2
1
2
2
0
1
1
0
0
0
1
0
1
0
2
1
2
5
2
0
1
0
1
1
1
1
0
0
1
0
2
2
0
0
1
0
0
1
1
0
0
0
1
1
1
1
1
1
2
0
2
2
2
1
1
2
1
1
1
1
1
0
0
0
2
1
0
2
0
0
1
1
1
3
1
2
0
1
0
2
1
0
3
1
0
2
2
0
0
0
1
1
0
0
1
1
1
0
0
1
0
1
0
0
1
2
0
1
1
0
2
1
1
1
1
2
1
1
1
0
0
0
0
0
2
2
1
0
1
0
1
1
0
0
2
0
2
0
1
2
1
1
1
2
0
2
0
0
2
1
0
0
1
1
0
1
2
2
2
2
1
0
0
0
1
1
1
0
2
1
1
1
1
1
0
1
1
0
1
2
1
2
1
0
1
1
0
1
2
1
1
0
0
2
0
0
1
1
1
4
2
1
1
2
0
2
1
0
0
2
1
1
0
0
1
1
1
0
2
2
2
1
1
2
2
3
1
0
0
1
3
1
1
0
0
0
1
2
1
0
2
0
1
0
0
0
0
2
1
1
0
0
1
1
0
1
1
1
0
1
3
2
1
2
1
1
1
0
2
1
0
1
1
1
2
0
0
0
2
1
1
0
1
1
1
1
1
2
2
0
2
0
1
1
1
0
0
1
1
2
1
1
1
3
1
2
2
1
0
2
0
0
0
1
2
3
0
0
0
2
0
1
0
0
1
1
1
1
2
3
1
2
1
0
0
1
0
1
0
2
2
3
3
2
2
2
1
1
1
1
2
3
0
0
0
1
0
2
1
2
2
2
2
0
0
2
2
1
1
1
0
0
2
1
1
0
0
2
1
2
1
1
1
1
2
2
0
0
1
1
1
1
1
2
2
1
2
0
4
0
1
2
2
0
3
2
2
2
0
1
1
0
1
2
1
0
1
2
1
1
1
2
0
0
1
1
0
1
1
1
1
1
2
1
0
2
0
2
1
2
3
0
0
1
2
1
1
1
2
1
1
1
0
2
0
1
1
0
1
0
1
1
1
1
1
2
0
0
3
0
0
1
1
0
2
1
1
1
0
2
2
1
1
0
1
2
1
1
1
1
0
2
1
1
1
2
0
1
0
1
1
3
0
1
0
2
1
1
1
1
2
4
1
1
1
2
1
4
1
1
1
1
1
0
2
0
0
0
0
2
1
0
2
1
0
1
1
1
2
1
1
1
2
2
1
1
0
2
2
0
2
1
1
1
0
1
1
1
0
1
0
1
1
1
1
2
0
1
1
0
1
1
1
0
1
1
1
0
1
0
1
2
0
2
1
1
1
1
1
0
2
2
1
0
1
0
1
1
1
1
2
1
0
0
0
1
0
0
2
0
1
1
1
0
0
0
0
1
1
1
2
0
1
0
0
3
1
0
0
2
1
1
1
0
0
1
1
2
0
1
0
0
1
0
1
2
0
0
0
1
1
1
1
1
1
2
2
2
1
1
0
1
2
2
0
0
0
1
0
0
1
1
1
1
1
1
3
2
2
0
0
0
1
1
1
1
1
1
1
0
1
0
1
1
0
2
1
1
1
0
2
1
2
1
2
0
2
0
1
2
0
1
1
2
0
2
0
2
1
1
1
0
1
0
2
1
1
1
1
2
0
2
1
2
1
1
0
1
1
2
0
0
1
0
2
1
1
1
0
1
1
0
0
0
1
0
1
1
1
1
1
1
0
2
1
1
1
1
1
3
1
0
2
1
3
1
1
0
1
1
0
0
1
1
0
1
2
1
0
1
0
0
1
0
2
1
1
1
1
0
1
2
1
0
3
2
0
1
0
2
1
1
2
1
1
1
2
0
1
1
1
2
0
2
0
0
2
0
1
1
0
1
1
0
0
1
1
0
0
1
1
0
2
1
0
2
0
0
1
1
1
0
0
2
1
1
0
1
0
0
0
1
0
1
1
1
2
0
3
1
1
1
1
2
1
2
2
0
2
0
0
2
2
1
3
0
0
1
2
1
1
1
0
1
1
0
2
0
2
2
3
1
1
0
1
1
1
0
0
0
2
1
1
1
1
1
0
1
1
0
1
1
1
1
2
1
0
1
1
1
1
1
1
0
2
0
1
1
0
0
1
0
0
3
0
1
2
1
2
1
0
0
0
1
0
0
0
1
1
1
0
1
0
0
2
1
2
1
0
0
0
1
1
1
1
0
2
1
1
1
1
0
1
0
0
0
2
1
0
1
2
0
0
1
0
0
1
0
1
1
0
2
0
2
1
0
0
1
2
1
0
1
0
1
0
0
1
0
1
0
1
0
1
0
0
1
1
2
1
2
1
0
1
2
0
0
2
1
1
1
1
1
0
0
2
2
2
1
0
0
0
1
1
2
0
0
0
1
0
1
2
2
2
1
1
3
0
1
1
1
1
2
1
0
0
2
3
1
1
0
1
2
2
1
1
0
1
1
1
2
2
1
1
0
2
0
2
0
0
0
1
2
3
0
1
2
1
0
1
1
0
2
0
0
2
1
1
1
2
1
1
3
0
1
1
1
1
2
1
1
0
1
1
0
0
1
0
0
0
2
1
0
0
2
1
1
1
1
2
1
0
1
1
2
1
0
1
1
1
1
1
2
0
1
2
1
0
0
0
1
1
1
1
2
0
0
1
0
2
2
2
1
1
1
0
0
2
2
1
0
1
1
0
1
1
1
2
0
1
0
2
3
1
1
0
2
0
2
1
1
2
2
1
0
0
1
1
1
1
0
2
0
2
1
1
0
1
1
1
0
1
0
1
2
1
1
1
5
2
2
1
1
3
1
0
2
1
3
0
0
1
1
0
0
0
1
1
1
1
0
0
1
1
1
2
2
1
2
1
1
2
1
0
1
2
0
1
0
1
0
1
1
1
1
2
1
0
1
0
0
0
0
1
0
2
1
1
1
1
1
1
2
0
1
1
1
1
1
0
0
1
1
0
1
2
1
2
0
1
0
0
1
0
0
0
1
1
1
0
1
1
1
1
1
2
1
2
0
1
1
2
1
0
1
1
1
1
0
0
1
1
0
1
1
1
0
2
0
0
0
1
2
3
0
1
0
1
0
0
1
1
2
1
0
2
1
2
1
1
0
0
1
1
0
0
0
1
1
2
1
1
0
2
0
1
1
1
4
0
1
1
1
2
0
0
0
0
1
1
1
0
1
2
1
0
1
0
1
1
1
2
1
1
2
2
1
1
0
1
0
2
0
1
2
1
1
1
0
0
0
1
1
1
1
2
1
0
1
0
0
1
0
0
1
2
1
0
0
4
1
1
0
1
2
4
1
1
1
1
0
1
0
1
1
0
1
2
1
1
0
1
0
2
0
1
2
2
1
1
0
0
2
1
0
1
2
0
2
0
2
0
1
0
2
0
1
0
1
0
0
1
1
2
2
2
0
1
2
3
2
0
1
0
1
0
2
0
1
0
0
0
0
2
2
2
1
2
2
1
0
1
1
1
2
0
2
1
1
0
0
2
1
1
1
2
0
0
1
1
0
2
1
0
0
2
1
1
0
2
0
0
0
0
2
1
2
0
2
0
0
1
2
0
2
1
1
1
1
0
2
0
0
0
2
0
1
1
2
1
2
1
1
3
0
0
1
1
0
0
0
2
1
1
1
0
2
2
2
1
1
2
2
2
0
0
0
1
0
0
1
1
1
1
1
1
1
1
0
0
1
1
2
1
1
0
1
1
1
2
2
1
0
2
1
2
1
1
3
1
0
0
0
0
0
1
0
1
1
0
0
0
1
2
0
1
3
1
1
2
2
2
0
0
0
1
2
1
1
0
1
2
0
2
2
1
1
1
2
1
0
0
1
2
1
1
2
0
1
1
0
1
1
0
0
0
0
1
0
1
1
1
1
1
0
2
1
1
0
0
1
0
2
1
0
0
0
0
1
1
2
0
0
0
2
1
2
0
1
0
2
2
1
1
1
0
1
2
0
0
1
1
1
1
0
1
0
0
0
1
1
2
1
1
0
0
1
2
2
2
1
1
2
1
1
1
1
0
2
1
1
0
0
1
2
0
1
2
1
1
2
2
1
0
1
1
2
1
0
2
1
2
2
0
1
0
0
1
2
2
2
0
2
1
1
1
1
1
0
2
2
1
1
0
2
1
1
0
1
0
1
0
0
1
0
1
1
2
2
0
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
0
2
2
0
2
1
0
1
1
2
0
0
1
1
0
1
1
0
1
2
0
1
2
1
0
0
1
1
1
2
1
0
2
1
1
1
0
1
1
1
1
1
1
0
2
0
2
0
1
0
0
1
2
0
2
1
0
1
0
0
0
1
2
2
1
1
1
0
2
2
1
1
1
1
0
1
1
0
1
0
0
1
0
1
2
2
1
2
0
1
1
0
0
1
3
2
0
0
0
1
0
0
1
1
1
0
0
0
1
2
1
2
2
0
2
2
1
2
0
1
1
1
0
2
0
1
1
0
1
1
0
0
0
0
0
1
1
1
0
1
1
1
0
0
2
2
0
1
2
1
0
1
0
0
0
2
1
0
0
1
1
2
1
0
2
1
0
0
2
1
1
1
2
1
1
0
0
0
0
0
0
0
0
1
1
0
1
2
2
0
2
2
1
1
0
1
3
0
1
0
2
1
0
0
1
3
2
0
2
2
0
1
0
1
0
1
1
0
1
1
0
0
1
1
2
1
1
1
0
2
2
1
0
1
0
2
0
0
2
0
1
0
1
0
1
3
0
2
1
0
0
0
1
1
1
0
1
1
0
1
0
0
0
1
1
2
2
1
1
1
2
1
0
1
2
1
0
1
1
2
1
0
1
1
1
2
0
1
1
1
1
0
2
1
1
0
2
2
3
1
0
1
0
3
1
1
0
1
1
0
2
1
1
1
0
1
0
2
0
0
1
1
0
1
1
1
1
0
0
2
1
2
1
1
1
1
1
0
1
1
2
0
1
2
1
2
0
2
0
2
0
0
0
0
1
1
0
0
1
1
1
1
1
1
1
1
0
0
0
0
1
1
2
0
0
1
2
2
0
0
1
1
1
2
0
2
0
1
0
0
0
1
1
2
2
0
0
2
2
2
0
1
0
2
1
2
1
1
2
0
1
1
1
1
1
0
0
0
0
1
1
0
2
1
1
0
1
2
1
0
1
0
0
1
0
1
2
0
0
2
2
1
1
0
1
1
1
1
1
2
2
1
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
2
1
0
1
2
1
1
2
1
1
1
0
3
2
1
1
1
1
1
2
0
2
1
1
2
2
1
1
1
1
2
2
1
2
0
1
2
0
2
1
0
0
1
2
1
0
2
0
1
1
2
0
0
1
2
1
0
1
1
0
1
0
1
1
1
1
2
2
2
0
2
0
1
1
1
1
1
1
2
0
0
0
3
2
0
1
1
2
1
1
0
1
0
0
1
1
1
2
1
1
0
1
2
1
1
1
1
1
1
1
2
0
1
2
2
2
2
0
0
2
0
3
1
1
1
1
2
0
1
1
1
1
1
0
1
2
0
0
1
2
1
1
1
2
0
1
0
2
2
1
2
2
1
0
0
0
1
1
2
2
1
2
1
3
2
2
1
0
1
1
2
0
0
0
2
7
1
1
1
0
2
1
1
2
1
1
2
1
2
1
0
1
1
1
0
0
1
0
2
2
1
0
0
0
1
1
1
1
2
1
2
0
1
3
1
0
1
1
0
1
0
0
1
1
2
1
2
1
2
2
2
1
0
0
2
0
0
1
2
0
1
1
1
1
2
1
1
1
0
1
1
0
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
2
1
1
1
0
2
1
0
0
1
1
0
2
2
0
1
1
0
0
1
1
2
0
0
1
0
1
1
1
0
1
1
1
1
1
1
1
1
1
1
2
0
1
2
2
0
1
0
2
1
2
0
2
0
0
2
1
2
0
1
1
0
2
1
1
2
0
2
1
1
1
1
1
1
1
0
1
0
2
1
0
1
3
1
0
0
2
0
0
0
1
0
0
1
1
1
3
0
1
2
1
0
0
1
1
2
1
1
1
1
1
0
0
1
0
1
0
0
0
2
2
1
1
0
1
1
1
0
0
1
0
0
1
1
2
1
0
0
1
1
1
0
0
0
1
1
2
0
0
1
1
0
1
1
0
2
0
1
1
2
1
1
1
1
0
1
2
2
2
2
0
2
0
0
1
0
1
0
0
1
1
0
1
1
1
1
1
1
0
1
2
1
2
1
0
0
0
0
2
0
0
0
1
1
0
1
1
2
0
2
0
1
1
2
1
1
2
1
0
2
0
2
1
4
3
1
1
1
2
2
1
1
0
0
1
2
1
1
1
1
0
1
1
0
2
1
0
1
2
2
1
1
2
2
0
1
2
2
1
1
0
3
2
1
1
1
0
0
1
1
3
0
1
1
0
2
0
0
3
1
0
1
2
1
1
1
1
0
1
0
1
0
0
0
1
0
1
0
1
1
1
2
2
2
0
2
1
1
1
0
1
1
1
1
1
0
0
0
2
2
1
0
1
1
0
0
1
0
0
1
1
0
0
0
0
2
1
1
1
1
1
2
1
2
0
0
0
0
0
1
0
1
1
0
1
0
1
0
0
0
0
0
1
2
1
1
0
2
1
2
1
1
1
1
1
1
1
1
1
0
0
1
2
2
1
1
0
0
1
0
0
0
1
1
1
0
0
1
1
0
0
1
0
0
0
1
1
0
0
2
2
0
0
1
1
0
1
1
2
1
2
0
1
1
2
0
1
1
1
0
1
0
2
0
0
1
2
1
2
2
2
0
0
2
1
0
1
0
1
1
0
2
1
3
0
0
1
2
2
2
0
1
1
1
0
0
1
2
2
2
0
0
1
0
0
1
2
0
2
2
1
2
0
1
1
1
1
2
0
2
1
1
2
0
0
1
2
2
0
0
1
0
0
1
1
0
2
1
1
0
0
0
1
1
2
0
0
2
2
1
1
0
0
1
2
1
1
2
0
1
1
0
1
1
1
1
1
1
1
2
1
2
1
0
1
0
1
1
1
1
0
1
2
2
1
1
2
2
1
1
0
0
1
2
2
0
0
0
1
1
1
3
0
1
2
1
0
0
0
2
0
1
1
1
1
1
1
0
0
2
1
2
0
3
1
2
2
1
1
1
2
0
1
2
2
1
0
1
1
2
0
1
1
1
2
0
1
1
0
2
2
3
0
0
0
2
0
1
0
0
2
1
0
0
0
0
1
0
0
0
1
0
1
0
2
2
1
0
2
0
1
0
2
2
1
1
0
2
0
2
1
1
0
1
0
2
1
0
1
1
0
1
1
2
1
2
1
1
0
0
0
2
2
2
1
2
1
0
1
2
2
0
1
2
0
1
1
0
0
1
1
1
1
1
2
2
1
1
1
1
1
1
0
1
1
1
0
1
0
0
1
1
1
2
2
1
2
0
1
0
1
2
0
2
1
2
2
2
1
1
1
0
2
0
1
0
1
1
0
0
1
0
0
2
1
0
1
1
1
2
0
1
1
1
1
1
1
2
0
1
1
2
0
2
0
0
0
1
0
0
1
1
1
0
3
0
0
1
1
2
1
0
1
2
0
2
2
2
1
2
2
2
1
2
1
1
1
2
0
1
0
0
2
0
2
2
1
1
1
0
1
1
0
1
1
0
2
0
0
0
0
1
0
0
1
1
0
2
0
1
1
0
1
1
2
0
0
1
0
1
0
2
0
1
0
1
1
0
1
2
1
0
1
1
1
0
0
1
1
1
0
2
2
0
2
1
1
0
1
0
2
1
0
1
0
0
2
1
2
1
2
1
2
0
2
1
1
2
1
1
0
1
0
1
2
2
1
1
0
1
2
0
1
0
2
1
2
1
0
2
1
0
0
1
1
2
1
1
0
1
1
1
0
1
1
1
1
0
2
1
2
1
0
2
1
1
1
0
0
0
1
1
1
0
1
1
0
0
1
2
0
2
2
1
0
1
2
0
0
1
0
1
1
1
0
1
1
0
0
1
1
1
1
1
2
0
2
0
2
1
0
1
0
1
1
0
0
0
1
2
0
2
3
0
2
0
0
2
3
1
0
1
1
2
1
1
1
0
1
1
1
1
1
1
0
1
0
1
2
3
0
2
1
1
0
0
0
2
1
2
1
1
2
0
1
1
0
0
0
0
2
1
2
2
1
2
2
0
0
0
0
0
1
1
1
1
1
1
0
0
2
1
2
2
0
0
0
1
0
0
1
1
1
0
2
1
1
0
0
1
1
1
0
2
0
2
0
3
1
2
2
1
0
0
1
0
2
0
1
1
1
0
0
2
1
1
1
1
1
1
1
0
0
0
0
1
1
0
1
1
1
1
1
0
0
0
0
0
1
1
2
1
2
1
1
0
0
1
0
0
1
2
0
1
1
1
1
1
0
1
2
0
3
0
2
2
0
1
1
0
1
0
0
2
1
1
1
1
1
2
0
1
0
1
1
1
0
1
2
1
1
0
1
1
1
2
0
1
1
1
1
0
0
0
2
1
1
2
0
1
0
1
1
1
0
1
2
1
3
0
2
1
1
1
2
0
2
0
1
0
2
0
2
1
0
1
0
0
2
0
0
0
1
0
0
0
1
0
1
1
0
1
0
1
1
1
1
2
1
1
0
0
1
1
0
2
1
1
1
0
1
1
0
0
2
0
1
1
1
1
1
2
0
0
2
1
1
1
2
1
0
2
1
1
1
1
1
0
1
1
0
0
1
2
2
0
1
1
1
2
2
3
1
0
2
0
1
1
2
1
2
1
0
1
2
1
1
2
0
1
0
2
1
0
0
1
1
0
0
2
0
0
1
1
3
0
2
0
1
2
1
0
2
1
0
1
2
1
1
0
2
1
1
2
2
1
0
2
1
0
0
1
0
1
0
1
2
0
2
0
2
1
0
1
1
1
2
1
2
1
1
0
0
0
2
1
1
1
2
1
0
2
1
1
1
0
1
2
0
0
2
1
2
1
2
2
2
1
0
0
1
1
1
1
2
2
0
0
2
1
0
0
2
1
1
2
0
0
1
0
1
0
1
0
1
1
1
0
2
0
2
1
1
1
0
2
2
2
0
2
2
2
1
0
2
1
1
1
0
2
1
1
2
0
1
1
2
2
1
1
2
0
2
0
2
0
2
2
0
1
1
1
0
1
1
2
1
0
1
1
2
1
1
2
0
1
3
0
0
1
2
0
0
1
2
1
0
2
2
0
2
1
2
0
2
2
1
1
1
1
1
1
2
1
1
0
1
1
1
1
0
1
1
1
0
1
0
2
1
1
2
2
1
0
2
2
1
2
1
2
1
0
1
1
1
2
0
2
2
0
1
3
2
0
2
1
0
2
1
0
1
0
0
2
2
1
2
2
1
2
1
1
2
1
0
2
0
2
0
1
1
1
0
1
1
2
0
2
1
1
3
0
1
2
1
0
1
1
0
0
0
0
2
1
0
2
2
2
1
0
1
0
1
0
2
1
0
1
1
0
2
0
1
1
0
0
0
1
0
2
1
2
0
0
0
0
1
2
1
2
0
0
0
0
1
0
1
1
0
2
2
1
1
2
1
1
1
1
0
1
1
2
0
1
0
0
2
0
0
0
0
2
1
1
2
0
1
1
1
1
0
1
0
1
1
1
1
1
1
0
0
2
1
1
1
2
1
0
2
0
2
1
2
0
1
0
1
1
2
1
2
0
1
0
1
2
0
1
0
1
1
1
0
0
2
1
2
1
2
0
2
0
0
1
2
0
1
1
0
1
1
1
2
0
1
1
1
2
0
0
2
1
1
1
0
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
0
1
1
1
1
2
3
1
0
2
1
1
2
0
1
2
1
1
0
0
1
2
1
2
0
1
0
1
1
2
2
0
1
1
1
1
1
2
0
2
0
0
1
2
2
1
1
1
0
0
2
1
1
2
2
2
2
1
2
3
2
2
0
0
0
1
2
1
2
1
1
1
1
0
1
1
2
1
1
0
2
1
2
2
1
3
0
0
2
0
1
1
0
0
1
1
0
1
1
1
1
0
0
1
1
1
1
1
1
1
0
0
1
1
0
1
0
2
1
1
0
2
1
0
1
1
0
0
0
1
1
0
0
1
2
1
1
2
1
0
0
1
2
2
1
1
0
0
0
1
1
1
3
1
1
1
1
0
2
0
0
1
2
0
0
1
1
1
2
0
0
1
2
2
0
1
1
1
1
0
2
0
1
1
2
1
0
0
1
0
2
1
1
1
1
2
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
2
0
2
5
1
2
0
2
1
2
1
1
1
2
1
1
1
1
0
1
1
0
0
1
0
2
2
2
0
1
0
2
0
1
1
1
1
0
2
1
2
1
1
1
0
2
1
2
1
1
1
1
2
1
2
1
2
1
0
1
1
1
0
1
2
2
1
2
1
1
2
0
0
1
1
1
1
1
1
1
1
2
1
1
1
2
0
1
2
0
1
2
2
0
0
1
0
1
0
1
1
0
0
2
1
1
2
1
0
1
1
0
0
0
0
0
0
1
1
0
0
2
0
1
1
1
3
1
0
0
2
1
1
0
1
1
0
0
1
1
1
1
2
0
1
1
2
1
1
2
1
0
0
1
1
1
1
1
1
2
0
1
2
1
0
1
1
1
1
1
0
2
1
0
0
1
0
0
0
0
1
0
1
1
2
1
1
0
1
1
2
2
1
0
1
1
0
1
1
0
0
0
0
1
0
2
0
0
0
1
1
1
1
0
1
0
0
0
0
1
2
0
1
2
0
2
1
1
1
0
1
1
1
0
2
1
1
2
1
1
1
1
0
1
2
2
1
1
2
1
1
1
1
2
0
0
0
2
0
1
1
1
0
1
1
0
1
1
2
1
1
1
1
1
2
2
0
0
2
1
0
1
0
0
0
0
1
1
0
0
2
1
1
1
0
1
1
1
0
0
2
0
1
0
2
0
1
0
0
0
0
2
1
0
0
1
1
0
2
0
0
1
2
1
0
1
1
2
1
1
2
0
1
1
2
2
0
0
2
1
0
1
1
1
0
0
1
1
1
1
1
1
2
1
0
2
1
1
2
1
0
2
2
2
1
1
1
0
2
1
2
0
0
1
1
2
2
2
0
1
1
2
1
1
1
1
1
2
2
1
2
1
1
0
0
2
1
0
1
0
0
0
0
2
2
0
1
1
1
1
0
1
2
2
1
1
1
1
0
1
1
1
0
1
1
1
0
0
1
1
2
1
1
1
0
1
2
0
2
1
1
1
1
0
1
1
0
2
2
0
1
0
0
1
0
2
1
1
1
0
1
0
0
2
0
0
2
1
0
1
2
0
1
0
0
1
1
1
0
1
1
0
1
1
1
1
1
1
0
0
0
1
1
0
0
0
0
1
1
0
1
2
2
0
0
0
0
0
2
2
2
1
0
0
1
1
1
1
0
1
1
0
1
0
0
2
0
0
0
1
2
2
1
1
1
1
1
1
2
0
2
0
1
0
1
0
1
1
1
0
1
2
0
1
1
1
0
0
1
0
2
1
1
3
1
1
1
1
0
1
1
0
0
0
1
0
1
1
2
0
1
1
1
2
1
1
1
1
1
3
1
1
2
0
3
1
0
0
1
0
1
1
0
1
2
1
1
0
2
1
1
1
2
1
1
0
1
0
0
1
1
0
0
0
1
1
1
1
3
2
2
1
2
1
3
1
1
2
1
4
0
3
0
1
1
1
0
0
0
1
2
0
0
0
1
0
1
2
0
1
1
2
2
0
1
2
0
2
0
0
2
2
2
2
1
0
1
0
0
0
3
2
2
0
1
0
1
1
0
1
1
1
0
2
0
0
1
1
0
0
1
1
1
1
1
1
0
0
2
2
1
1
1
2
0
1
1
1
1
1
1
1
1
1
0
1
2
0
1
2
1
0
0
0
1
2
1
2
2
1
2
0
2
0
1
2
2
0
0
1
0
3
1
2
0
0
0
2
1
1
0
0
0
0
1
1
1
1
1
0
0
1
2
1
2
0
1
1
0
0
1
2
1
0
0
0
0
1
1
2
2
0
1
0
2
1
2
1
2
1
1
2
0
0
1
0
1
0
2
1
0
1
0
1
0
0
1
1
1
0
1
1
2
1
1
1
1
2
1
2
2
1
1
0
1
1
1
1
0
0
1
2
2
0
1
0
0
0
1
2
0
0
0
0
2
0
2
0
0
1
0
1
0
1
1
0
1
0
1
1
1
0
0
0
2
0
1
0
2
1
1
0
1
2
1
2
1
1
2
1
1
1
0
1
1
0
1
0
0
1
0
1
1
4
1
1
3
1
0
0
0
1
1
2
1
3
0
1
2
2
0
0
0
0
1
1
1
1
0
0
1
1
1
1
1
1
2
1
1
1
0
0
0
0
2
1
0
2
1
2
0
0
2
1
1
0
1
0
2
1
0
1
2
2
1
2
1
0
0
1
1
0
1
1
0
2
0
1
2
0
1
0
1
2
1
0
0
1
1
3
2
0
0
1
1
1
1
0
2
0
1
2
1
0
1
1
1
4
1
0
2
1
1
0
1
0
0
1
1
1
1
1
1
0
1
0
2
2
1
1
1
1
2
1
1
1
0
1
1
1
1
0
2
0
0
0
1
1
0
1
0
1
1
1
1
0
0
1
0
0
2
2
0
0
2
2
1
0
1
0
1
0
0
1
2
1
1
2
2
0
1
2
1
0
0
2
1
1
1
2
2
1
0
1
2
1
1
1
2
1
0
1
0
1
1
2
1
0
0
2
2
2
2
1
0
1
1
1
0
2
0
0
0
1
1
2
2
0
2
2
0
2
1
1
1
0
1
2
1
0
1
1
1
2
1
0
2
0
2
0
0
1
1
1
2
2
1
2
0
2
1
1
1
1
1
0
3
0
2
1
1
2
1
2
1
1
1
0
2
2
1
1
2
2
0
1
0
1
2
0
0
1
0
2
1
1
0
0
0
0
0
1
1
1
1
0
0
1
3
0
1
1
0
0
1
2
1
1
1
1
1
0
0
0
2
0
0
1
0
1
0
2
0
1
2
2
0
0
1
1
0
1
1
1
1
1
1
1
1
2
1
0
0
1
1
0
1
0
2
0
2
2
0
1
1
0
0
1
1
1
1
0
1
2
1
2
2
1
1
1
0
0
2
0
1
0
2
0
0
2
1
2
1
2
0
1
2
1
2
0
1
0
1
1
1
0
1
1
1
2
0
0
1
2
1
0
2
0
2
0
1
0
1
2
0
1
1
0
1
1
1
0
0
0
1
1
1
1
0
1
1
2
2
1
2
2
1
1
1
0
2
0
2
0
2
2
1
1
0
1
0
1
0
0
1
1
1
2
1
1
0
2
1
1
1
2
1
1
1
0
1
1
2
1
2
0
2
1
1
1
0
0
1
1
2
1
0
0
1
0
1
0
0
1
1
1
0
2
2
3
0
0
1
0
2
0
0
1
2
1
1
0
2
2
2
1
2
1
0
0
2
2
1
0
0
2
1
0
3
2
0
0
0
0
0
1
1
1
1
1
1
1
1
0
0
1
1
0
1
0
1
0
2
1
0
1
0
1
0
2
2
1
1
1
2
1
2
1
1
1
0
2
0
0
2
1
0
0
0
0
0
0
2
2
0
0
1
0
1
1
1
0
2
1
0
0
0
2
0
0
0
1
1
0
0
1
2
0
0
1
1
0
1
2
0
1
1
1
2
2
0
2
1
1
0
1
1
0
0
2
2
0
1
1
0
1
1
0
0
0
2
2
2
0
1
2
1
3
2
1
1
2
2
1
0
0
1
1
0
1
1
1
1
1
2
2
2
0
0
0
2
0
1
0
0
0
0
0
0
1
0
1
0
0
2
2
2
2
1
1
0
1
1
1
1
1
2
0
2
1
0
1
2
2
1
1
1
1
0
2
1
1
0
1
1
1
1
1
0
0
1
2
0
0
1
1
1
1
1
3
2
1
2
1
2
1
1
1
0
3
1
0
0
1
2
2
1
0
0
2
0
1
3
0
0
1
1
0
1
1
0
2
1
2
0
1
2
0
1
0
1
2
0
2
2
1
2
1
0
1
1
1
1
0
0
1
2
1
1
0
2
1
0
1
0
2
1
0
1
2
1
2
0
1
0
0
0
2
0
1
1
2
3
2
1
1
0
0
0
1
0
1
2
0
1
2
1
1
1
1
2
0
1
1
1
2
0
0
1
1
0
1
0
0
1
1
0
2
1
1
2
2
0
2
1
0
0
0
1
1
0
1
0
10
1
0
3
1
0
1
0
1
0
2
0
1
2
0
2
2
2
1
1
1
1
0
0
1
1
2
2
0
0
1
1
1
0
2
1
0
1
2
2
0
1
0
2
0
1
1
1
1
0
2
0
2
2
0
0
0
2
2
1
0
1
2
0
2
1
2
1
1
2
1
0
0
6
1
2
1
0
1
1
0
1
1
0
1
2
0
2
1
1
1
1
0
2
1
1
1
1
2
0
0
0
2
1
0
1
1
2
2
1
1
1
2
2
0
0
1
1
0
0
1
1
1
0
0
1
1
2
2
1
1
0
2
1
1
0
0
1
0
2
1
1
1
1
0
3
1
1
1
1
0
1
1
0
2
1
2
3
0
1
1
1
0
0
0
1
1
2
1
2
0
1
2
0
0
1
1
2
1
2
2
2
1
1
0
1
1
1
2
2
1
2
2
2
1
0
0
0
0
0
1
0
0
1
2
1
2
2
0
2
2
1
1
2
1
1
2
1
2
1
2
2
0
0
0
1
1
1
1
1
1
0
1
1
0
0
0
1
1
0
1
2
1
1
0
1
0
2
1
1
1
1
1
0
1
0
0
1
0
2
2
1
1
0
1
2
1
1
1
2
0
1
2
1
0
2
1
1
0
2
1
1
1
1
1
0
1
0
0
0
0
0
2
2
0
0
0
0
1
1
1
2
1
2
3
1
0
0
0
2
2
1
2
1
1
1
0
0
1
2
1
1
2
0
0
2
1
1
2
0
2
0
1
2
2
1
0
2
0
1
0
2
2
1
1
0
1
2
1
1
1
1
0
1
0
3
2
1
2
1
1
1
1
2
1
1
0
1
3
1
2
0
3
2
1
1
2
1
1
1
1
1
0
2
1
2
0
0
0
0
0
2
1
1
0
1
0
0
2
1
1
1
1
1
1
1
0
2
1
2
1
1
0
2
2
0
1
2
0
2
1
0
1
2
0
0
2
1
1
1
2
2
0
2
1
0
1
1
2
2
0
0
2
1
0
0
1
0
1
1
0
2
2
0
1
0
2
0
1
1
2
0
0
1
1
1
0
2
0
2
1
0
0
2
1
0
2
0
1
1
1
1
0
0
0
0
1
0
1
0
2
2
1
1
2
1
1
0
1
1
0
1
0
1
0
2
0
0
1
0
0
1
1
2
0
1
1
1
1
2
1
0
0
0
2
0
0
1
1
1
1
1
0
2
0
2
0
2
2
1
0
0
2
0
2
1
1
0
1
1
0
1
0
0
1
0
2
0
0
1
2
0
2
1
2
2
0
2
0
1
1
0
1
1
0
1
2
2
1
0
0
1
1
1
0
2
1
1
2
0
2
1
2
2
0
0
2
2
0
0
0
1
3
0
2
2
1
2
2
1
0
1
2
2
1
1
0
0
1
0
1
0
1
1
0
1
1
0
1
1
1
0
0
2
0
0
1
0
1
0
1
0
2
2
1
2
0
2
1
1
2
0
1
1
1
0
1
1
0
1
0
1
2
1
2
1
1
2
0
1
1
1
1
1
0
1
1
0
2
1
1
0
1
1
1
0
1
1
0
1
1
1
1
0
1
1
1
0
0
1
1
1
1
0
0
0
1
1
1
2
2
2
0
1
0
1
1
0
0
0
0
1
1
1
0
1
2
2
1
0
0
2
0
2
1
1
1
0
2
1
2
0
0
1
1
1
0
2
1
1
2
0
0
1
1
1
2
1
0
2
2
1
2
0
1
1
1
1
0
1
1
0
2
0
0
2
1
0
0
1
0
1
0
2
2
2
1
1
2
2
1
0
1
0
2
0
1
0
2
2
1
2
1
0
1
0
2
2
2
2
1
1
1
2
2
1
1
0
0
1
1
1
0
1
1
1
0
3
1
2
0
1
0
1
0
1
0
0
0
2
1
3
0
2
1
2
2
3
2
1
1
4
1
1
2
2
1
0
1
1
1
1
0
0
2
1
1
1
0
1
0
0
1
0
1
0
0
1
1
1
1
0
1
0
1
1
1
1
1
0
0
2
1
2
0
3
1
0
1
1
1
1
1
2
0
0
1
3
0
2
0
0
2
2
0
2
1
1
0
1
0
1
0
3
1
2
2
0
1
1
1
1
2
1
0
1
1
1
1
1
0
1
0
1
2
1
2
1
0
2
1
2
1
0
1
0
2
1
2
1
2
1
0
1
1
3
2
1
0
0
0
0
1
2
1
0
1
1
0
0
0
2
1
2
2
1
1
2
2
0
0
1
1
2
1
1
1
1
1
2
1
2
1
2
2
1
1
1
1
2
1
0
1
0
0
2
1
1
0
1
1
0
1
1
0
1
0
0
0
0
0
2
1
0
1
1
0
1
2
2
1
0
3
1
0
1
1
2
0
0
1
1
2
1
1
2
0
1
0
2
0
2
0
2
2
1
0
1
0
0
1
0
0
2
0
1
1
1
1
0
1
1
0
0
2
1
0
0
2
2
1
1
0
1
0
2
1
2
1
1
1
0
1
1
1
1
2
1
0
0
2
1
1
0
2
1
1
0
0
2
2
0
0
0
0
2
1
1
0
0
1
1
2
0
1
2
0
1
1
0
1
1
1
0
2
0
0
1
2
2
1
1
1
3
0
2
2
0
1
2
1
1
2
2
1
0
1
2
1
0
0
0
1
0
0
1
0
0
2
1
2
2
2
1
1
0
1
1
2
3
1
1
0
1
1
2
1
1
1
1
0
2
1
0
2
0
2
1
1
2
2
1
1
2
0
0
1
1
1
1
1
0
0
0
1
0
0
1
0
0
0
1
1
2
2
2
1
1
1
0
2
1
0
2
7
2
1
1
1
1
1
2
0
2
1
1
1
2
2
0
1
1
2
1
0
1
1
1
2
2
1
1
1
1
0
0
0
2
2
1
0
0
1
2
0
0
1
0
1
0
0
0
1
2
1
1
2
1
0
1
1
0
0
0
1
0
2
1
0
1
1
0
1
0
0
0
1
1
0
0
0
2
0
2
2
2
2
0
2
1
1
1
2
0
1
3
1
2
1
0
1
2
1
0
1
0
1
1
2
1
0
1
0
2
0
2
1
1
1
0
1
2
2
1
0
1
2
3
1
0
0
0
0
0
1
1
1
1
1
0
1
1
0
1
0
1
2
0
1
2
1
1
0
1
1
1
1
1
2
0
0
0
1
1
1
3
1
2
2
0
2
0
1
1
0
1
0
1
2
2
0
0
1
1
1
1
1
2
0
0
0
1
0
0
0
1
2
1
0
0
1
3
1
0
2
2
0
1
0
0
1
2
0
3
1
0
1
1
2
1
1
0
1
1
0
0
1
2
0
2
0
0
2
1
1
2
1
0
2
1
1
0
1
0
1
1
0
1
2
1
2
2
1
3
2
2
0
0
0
2
1
0
2
0
2
0
0
1
1
2
1
1
1
2
0
1
2
1
1
1
1
0
1
1
1
2
0
2
1
1
2
0
1
1
2
1
0
2
0
1
0
3
2
0
1
2
0
0
2
0
2
1
0
1
0
1
2
2
1
1
2
1
0
0
1
1
1
0
2
1
1
2
1
0
1
1
0
1
1
0
1
0
2
0
1
1
0
1
1
2
1
1
1
0
2
0
1
1
1
1
1
2
0
2
0
2
1
0
0
1
1
0
1
3
0
2
1
1
2
2
1
0
2
1
1
1
0
1
2
0
2
1
0
0
3
1
1
1
0
1
2
0
2
1
1
0
1
2
1
0
1
2
2
0
1
0
0
0
1
1
1
1
1
0
1
1
1
2
0
0
1
0
0
1
0
1
1
1
2
2
0
0
0
0
1
0
1
2
1
0
0
1
2
2
1
1
1
1
1
0
1
2
1
0
1
2
1
1
2
2
1
0
1
1
0
0
1
1
1
2
0
1
2
0
0
0
2
2
0
2
0
1
2
2
0
0
2
1
0
1
1
0
0
1
0
0
1
2
0
1
0
0
0
2
1
2
1
2
0
1
1
1
0
1
2
0
1
1
0
2
0
1
1
2
1
2
4
2
0
2
1
0
1
1
0
0
0
0
1
2
1
1
1
0
1
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
1
3
1
0
2
1
0
1
2
4
1
2
1
1
2
1
1
1
1
1
0
2
1
1
1
1
0
0
2
2
0
1
2
1
0
1
0
1
0
1
1
1
2
1
0
0
1
0
0
1
2
2
0
0
3
0
1
2
0
0
1
2
2
0
0
2
2
0
1
0
0
0
2
2
0
1
1
0
1
1
0
1
2
2
0
0
2
2
1
0
1
1
2
1
2
0
2
1
1
0
0
0
1
1
0
0
2
1
0
2
1
0
2
2
2
0
2
1
2
3
2
1
2
1
0
1
1
0
2
0
0
2
2
0
0
0
1
1
1
1
1
0
0
0
2
1
0
1
1
2
1
1
0
1
0
1
0
0
1
0
2
2
0
2
2
1
0
2
1
0
0
1
0
0
2
1
1
0
1
0
1
0
0
0
1
0
1
1
1
0
1
2
0
1
1
1
1
1
0
1
1
1
1
0
1
0
1
1
0
0
0
2
0
1
1
0
0
0
2
0
0
1
1
0
1
0
2
2
0
2
1
0
2
1
1
1
0
0
1
0
2
2
0
0
2
1
1
1
2
1
0
0
1
0
2
0
1
1
0
0
0
2
1
1
0
1
0
1
0
1
0
1
0
1
1
0
2
0
1
2
1
2
0
2
1
1
2
0
1
0
0
1
1
1
0
1
1
0
2
0
1
2
2
2
1
0
1
1
1
1
2
0
1
0
0
0
2
2
0
2
0
1
0
1
2
0
1
2
1
0
1
1
0
2
1
2
1
1
1
1
1
2
2
1
1
0
0
1
1
1
2
2
0
2
0
1
0
2
1
2
0
0
1
1
0
1
1
1
1
0
1
1
0
1
1
0
0
1
1
1
0
1
0
1
1
3
1
1
3
1
1
0
1
1
0
1
1
0
1
2
0
1
1
0
1
0
0
0
1
1
1
1
0
2
0
1
1
1
0
2
1
1
1
0
0
0
2
0
0
0
1
2
0
1
1
1
1
1
2
0
1
1
0
0
1
1
0
1
0
1
2
1
0
0
1
1
0
1
0
1
2
1
0
0
1
1
0
0
0
2
1
1
0
1
1
1
0
1
2
1
1
1
1
2
1
1
2
1
2
1
2
2
1
1
1
0
1
1
0
0
1
1
1
1
6
2
2
1
1
1
2
1
0
1
2
0
1
1
2
1
0
2
1
2
0
1
2
2
1
1
1
2
1
5
0
2
1
0
1
3
1
0
0
1
1
0
2
0
2
1
1
1
1
2
1
0
2
0
1
2
0
2
1
1
1
2
0
1
3
0
1
1
1
2
2
1
0
1
1
1
2
2
0
0
1
1
1
0
1
1
1
0
2
2
1
0
2
1
2
2
1
1
1
0
1
1
0
0
1
0
1
1
1
2
2
1
0
0
0
2
0
2
0
1
1
1
0
1
2
1
2
2
0
0
2
2
1
1
2
2
0
1
1
0
1
1
0
1
0
0
0
1
0
1
1
1
2
1
0
0
2
1
0
0
0
0
2
1
0
1
0
1
0
1
3
2
1
0
1
2
1
0
1
0
2
2
0
1
1
1
1
2
1
1
2
1
2
2
1
1
1
0
1
1
1
1
1
1
1
2
1
1
1
0
1
0
1
0
1
0
1
1
0
1
1
1
1
1
1
2
0
1
1
1
2
0
1
0
1
0
2
1
1
1
1
0
0
0
2
0
2
2
1
0
2
1
0
2
2
0
0
2
0
1
1
0
1
2
0
1
1
2
1
0
0
0
3
1
1
2
1
2
0
1
0
1
2
0
0
0
1
1
1
2
2
1
0
2
1
1
1
1
1
1
0
2
1
0
5
1
2
1
0
1
0
1
1
1
1
1
1
1
1
1
0
1
2
0
1
1
1
2
1
0
0
1
1
1
2
1
2
0
0
1
2
1
1
2
0
1
0
1
1
0
0
1
0
2
2
1
0
1
0
2
1
0
1
2
2
1
2
2
2
2
1
0
2
0
2
0
0
1
0
0
1
1
1
2
2
2
1
2
1
1
0
2
0
1
0
0
0
1
0
1
1
2
1
1
0
1
1
1
2
0
2
2
0
2
0
3
0
1
1
1
1
1
2
0
1
1
2
1
0
0
0
1
0
1
0
2
2
2
1
2
1
1
1
0
1
1
1
1
1
1
1
1
2
1
0
0
2
0
1
1
2
1
2
1
2
0
1
0
2
1
0
2
2
0
0
1
1
0
0
1
2
1
0
0
0
1
2
1
1
1
2
1
0
2
1
2
1
1
1
0
0
2
1
1
1
1
1
2
0
1
2
0
1
1
0
1
1
2
0
0
1
1
3
0
0
1
0
2
0
2
1
0
0
1
0
1
2
2
1
2
0
1
1
1
0
1
1
1
1
1
1
2
0
1
1
1
1
1
1
1
2
1
0
0
2
1
0
2
0
1
1
0
1
0
0
2
2
1
1
1
1
0
2
2
1
0
2
3
1
2
0
2
1
1
1
0
0
0
1
0
0
0
1
0
0
1
1
2
0
0
1
2
0
1
0
1
1
0
2
1
1
2
1
2
1
0
0
0
1
0
2
1
1
2
0
1
0
1
0
0
1
0
1
3
2
0
1
2
1
0
0
0
1
1
0
2
1
1
1
0
1
1
0
3
1
0
0
2
0
1
0
2
0
1
1
1
0
1
1
1
3
1
1
0
1
1
1
0
1
1
0
2
0
2
1
0
2
2
2
1
2
0
0
1
0
1
3
0
2
2
0
1
2
1
1
1
1
1
1
2
2
0
0
2
1
2
2
1
0
0
1
0
0
0
1
2
1
1
0
2
1
1
0
1
1
1
1
0
0
2
1
1
2
2
1
1
0
0
1
2
2
2
0
1
1
2
0
1
2
0
2
0
1
2
3
1
1
1
0
1
2
1
0
2
2
0
1
0
0
1
2
1
0
1
2
1
2
2
1
0
1
1
1
2
1
1
1
0
0
1
1
1
2
1
1
0
0
1
1
0
1
1
1
1
1
0
0
0
0
1
1
1
1
1
0
1
1
1
1
0
1
1
2
1
1
1
1
0
1
1
1
0
1
2
1
0
2
2
0
2
1
2
1
0
1
0
0
1
2
1
0
1
2
1
1
1
1
0
2
1
0
0
2
1
0
2
2
1
1
1
1
1
1
1
0
1
1
1
1
0
1
0
1
1
1
0
0
6
0
1
0
0
2
0
4
1
1
1
1
0
0
1
2
0
0
1
1
2
0
2
2
1
1
1
0
1
2
1
1
2
2
1
0
0
1
0
1
0
0
1
2
0
0
1
0
0
1
0
0
2
2
2
0
3
2
1
1
1
1
1
0
0
0
1
1
0
0
0
2
1
1
2
1
1
0
3
0
0
0
0
1
1
0
0
1
0
2
1
0
1
2
2
0
2
1
1
1
0
2
0
0
1
0
1
0
2
1
1
1
2
1
0
1
1
1
0
1
1
1
1
1
2
2
0
0
1
1
0
1
1
1
1
0
2
2
2
1
1
1
0
2
1
0
2
2
1
2
0
1
1
0
2
1
1
2
1
0
1
1
1
1
2
2
0
1
0
0
1
0
0
1
0
1
2
0
1
0
1
0
2
0
2
2
1
0
0
2
0
2
0
0
1
1
1
1
0
1
1
0
2
0
0
2
0
1
2
1
0
1
0
0
1
1
0
2
1
1
1
0
1
1
1
0
1
1
0
3
0
2
1
0
1
0
1
0
4
2
0
0
0
0
1
1
1
1
2
1
1
2
0
1
1
0
1
1
1
3
0
2
0
0
2
2
1
0
2
0
1
0
1
1
1
0
1
0
2
1
1
0
2
1
2
1
1
1
1
1
1
2
0
0
2
1
2
2
1
0
0
1
0
2
0
1
0
0
2
0
1
2
1
1
1
1
0
1
1
2
1
0
0
1
1
1
0
1
1
1
1
2
2
1
1
0
1
2
1
0
1
2
0
2
1
0
2
0
0
2
2
0
0
0
1
1
1
1
1
0
0
1
1
2
1
2
0
1
0
1
2
0
0
1
0
0
2
0
2
1
1
1
1
1
1
2
0
1
2
0
0
2
1
0
1
2
0
2
1
1
0
1
1
1
0
2
1
0
1
1
1
0
2
1
0
1
2
2
0
1
1
0
0
0
1
0
1
0
0
1
1
2
1
2
0
2
0
0
1
2
1
0
0
1
0
1
4
3
1
0
0
1
1
0
1
0
0
1
1
1
1
1
2
1
1
0
0
0
1
1
1
2
2
1
1
0
1
0
1
0
2
1
1
0
1
1
1
1
1
2
0
0
1
0
1
2
5
1
2
1
2
1
1
0
2
2
1
2
1
1
2
2
1
1
0
2
1
1
0
1
1
1
1
1
1
0
0
2
1
0
1
1
1
1
1
1
2
2
1
0
1
1
1
0
2
2
0
2
2
0
1
1
2
2
1
1
0
2
2
1
2
2
1
0
1
2
1
1
0
0
0
2
0
1
1
1
2
2
1
0
1
1
2
1
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
1
0
0
1
2
2
2
0
1
1
0
0
3
0
1
1
1
0
0
2
0
1
0
2
1
2
0
0
0
1
1
1
1
0
2
1
1
2
1
2
1
2
1
1
2
1
1
1
1
2
2
0
2
0
2
2
2
1
0
1
1
0
0
2
2
2
1
0
1
1
2
0
1
1
2
0
1
0
0
1
0
1
1
1
1
1
0
1
0
1
1
1
1
0
1
1
1
1
1
1
1
0
0
0
1
1
1
1
1
2
0
1
2
2
0
0
1
2
1
1
0
2
1
2
0
1
0
0
1
1
1
1
1
1
1
1
1
1
2
2
1
0
1
2
2
1
1
1
1
1
1
2
0
1
0
0
1
0
0
1
1
1
0
1
1
1
1
1
0
0
2
2
2
1
1
2
1
3
1
1
1
3
1
0
0
2
1
1
1
1
1
1
1
1
3
1
2
2
0
0
0
1
0
1
1
0
1
1
2
1
1
1
1
1
0
0
2
2
1
1
1
1
1
0
0
1
0
0
0
0
1
1
2
0
1
0
1
2
1
1
1
2
1
2
0
2
0
1
0
1
0
1
1
1
1
2
1
2
1
2
1
0
2
1
1
2
1
1
0
0
1
0
0
1
1
1
1
1
2
2
0
2
3
1
1
1
1
1
2
0
0
2
0
1
1
1
0
1
0
1
2
0
2
0
2
2
2
2
1
1
2
1
0
1
1
1
0
0
0
0
0
1
2
1
1
0
2
1
0
0
0
1
2
1
1
1
2
1
2
0
2
1
1
1
0
1
2
1
2
1
2
1
1
1
1
0
0
1
1
2
2
0
1
2
1
2
2
2
1
1
0
2
1
2
2
1
0
2
0
2
1
1
1
1
1
2
1
1
0
1
1
1
1
0
0
2
0
1
2
0
3
2
2
1
1
0
0
0
0
0
1
0
1
1
2
1
0
1
1
1
1
1
1
1
1
0
1
0
0
2
2
2
1
2
0
1
1
0
1
1
1
2
2
1
1
1
2
0
1
2
1
2
2
1
1
1
1
0
1
0
1
1
0
1
1
1
1
1
0
1
0
2
1
1
2
1
1
2
0
0
1
0
1
0
2
0
0
1
1
2
1
1
0
2
1
1
2
1
1
0
1
0
0
0
1
2
1
0
1
0
2
1
2
0
0
2
1
1
0
2
2
2
0
1
2
0
1
1
0
0
0
2
1
1
0
1
1
1
1
2
2
0
0
0
2
0
1
2
0
1
1
1
0
1
0
1
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
0
0
1
1
0
2
0
1
2
0
2
1
1
2
1
2
1
0
0
0
1
1
2
0
1
2
0
0
1
3
0
2
0
0
0
1
1
1
0
0
0
1
0
0
1
0
1
0
2
0
1
3
1
0
1
0
1
0
2
1
1
1
1
0
2
1
1
0
2
0
0
1
0
1
2
1
1
1
0
1
1
0
0
1
2
1
1
0
0
2
1
1
1
1
0
0
1
0
1
1
2
3
1
1
1
1
1
0
0
0
0
2
1
1
1
1
2
1
1
0
0
0
1
0
1
2
1
0
1
0
1
1
1
0
1
1
2
1
0
1
2
0
2
2
0
1
2
0
1
2
1
1
0
0
0
0
1
1
2
2
2
0
0
1
0
2
1
2
2
2
0
1
1
0
0
1
0
0
1
1
0
2
1
0
1
0
1
0
1
0
1
1
1
1
2
1
1
2
0
2
2
0
1
2
2
2
1
0
0
1
2
2
0
0
1
0
2
1
1
1
1
0
0
2
2
0
1
1
1
0
0
0
0
2
0
2
1
0
2
0
0
0
0
0
1
0
2
1
1
1
1
1
0
1
1
0
1
1
1
0
0
1
1
1
1
1
0
0
0
1
2
1
0
0
1
1
1
2
1
2
2
0
1
0
1
2
2
1
1
0
1
0
0
2
0
2
1
1
2
1
0
2
2
2
0
2
2
2
1
1
2
1
0
1
0
1
2
1
1
0
2
0
3
0
0
1
1
1
0
1
1
0
2
0
0
1
0
0
1
0
2
2
0
1
1
0
2
0
0
0
0
1
1
1
1
1
2
1
1
0
1
0
1
1
1
1
1
1
1
0
1
0
2
0
1
1
1
1
1
1
2
0
0
2
2
1
3
1
0
0
0
2
2
1
1
2
1
1
1
2
0
1
1
1
0
0
1
1
1
0
2
0
1
1
1
0
1
1
1
1
2
1
1
2
1
1
2
1
0
0
0
2
1
3
2
0
0
2
1
2
1
1
1
0
0
0
1
1
0
1
0
0
1
1
1
0
0
0
1
0
2
0
1
1
0
0
0
1
2
0
0
2
0
0
2
1
1
1
1
1
1
1
2
0
0
0
2
1
0
2
2
1
1
0
2
0
1
1
2
0
1
1
1
2
0
0
1
1
1
0
0
1
0
1
1
2
1
0
1
1
2
1
1
1
1
1
1
1
0
1
1
0
1
2
0
0
2
2
1
0
2
0
0
0
1
2
0
2
0
1
1
2
0
2
0
0
2
1
1
3
0
0
1
0
2
0
2
0
1
1
0
1
2
2
0
1
0
1
0
1
2
1
1
1
0
2
0
1
1
1
1
2
0
1
2
1
0
2
2
0
1
1
1
1
2
1
3
1
0
1
0
1
1
0
2
0
0
1
1
1
2
1
1
0
1
1
2
1
1
1
1
0
1
1
0
1
1
0
1
0
1
1
0
0
1
1
1
0
1
2
1
1
2
1
0
2
1
0
1
1
0
1
2
0
1
0
0
1
2
1
2
3
1
1
1
1
1
2
0
1
1
1
1
1
1
1
0
0
1
1
1
2
0
2
0
1
2
2
0
0
2
0
2
2
1
1
1
1
1
0
1
0
0
1
1
0
1
1
2
2
1
3
2
0
1
1
1
0
0
1
1
0
0
1
1
2
0
0
0
1
1
1
0
1
0
0
0
0
1
1
2
0
1
1
1
2
1
1
1
0
0
1
1
2
2
1
0
1
0
1
1
1
1
0
0
1
2
1
2
1
1
1
0
1
2
2
3
0
1
1
2
1
2
1
0
0
2
0
0
1
1
1
0
1
0
2
0
1
0
1
0
0
1
1
1
2
0
2
1
2
0
1
1
0
1
1
3
0
0
2
0
1
0
1
0
0
1
1
1
1
1
2
0
1
1
0
2
0
0
1
2
0
0
0
0
0
2
1
1
2
0
1
1
4
1
2
1
0
1
1
2
2
0
0
3
1
0
0
1
2
1
1
2
1
1
1
0
1
1
1
0
2
1
1
1
2
1
1
1
0
1
0
1
1
0
0
0
1
1
0
1
2
2
0
1
1
2
0
0
1
0
0
1
1
2
2
2
2
1
0
1
0
1
2
1
1
1
0
1
2
1
1
0
2
1
1
1
0
1
0
2
2
2
1
1
2
0
0
1
1
0
0
2
2
0
0
0
0
0
2
0
2
0
1
0
1
1
1
1
0
0
0
1
0
1
1
0
1
0
0
1
0
1
1
2
1
1
1
2
1
1
2
1
0
2
1
0
2
0
1
2
0
2
1
0
0
1
2
2
2
0
2
1
1
1
2
0
1
1
2
0
1
2
0
1
1
0
1
0
1
0
2
1
1
2
1
1
1
0
0
1
2
1
0
0
0
1
1
2
1
1
1
0
0
0
0
1
0
2
2
1
0
1
0
1
0
0
0
6
2
0
0
0
0
2
0
0
1
2
1
0
2
1
1
0
2
0
0
1
2
1
1
1
2
1
0
3
1
1
0
2
0
0
2
1
1
0
1
2
0
0
1
1
1
2
1
0
0
1
0
2
2
1
1
0
1
1
1
1
1
0
1
0
1
1
0
0
0
1
0
0
5
1
0
1
0
1
2
2
0
1
1
1
2
2
0
1
2
0
0
1
0
2
1
2
1
0
0
1
1
0
1
1
0
1
1
1
1
0
3
2
0
1
0
0
2
2
1
0
1
2
2
1
1
1
0
2
0
0
0
1
2
0
1
1
1
2
2
1
1
1
1
1
1
0
1
0
1
1
1
1
1
1
0
2
1
2
2
1
2
0
0
0
0
1
0
2
1
1
1
2
0
2
2
0
0
1
2
2
1
0
0
0
1
2
1
1
0
0
0
1
0
1
1
1
2
3
1
0
0
1
1
0
0
0
0
0
1
1
1
1
2
1
0
1
0
1
2
0
1
2
1
2
1
1
1
1
0
0
1
0
2
1
1
0
0
1
2
1
1
0
1
1
0
0
2
1
1
2
0
1
0
0
0
3
2
2
1
1
0
0
0
0
0
1
2
1
1
1
1
1
1
0
2
0
0
1
0
1
3
2
0
1
1
1
0
0
1
0
2
1
0
2
2
0
2
0
1
1
1
0
1
0
0
1
1
1
2
0
2
0
1
2
2
1
2
1
2
0
1
1
3
2
1
0
1
1
1
1
1
2
1
1
0
1
1
1
2
0
1
1
0
1
1
1
1
0
0
0
2
1
0
1
1
0
2
0
2
1
1
1
2
0
1
0
0
0
1
1
1
1
1
1
0
1
1
1
2
2
1
1
1
2
1
1
1
1
0
0
2
0
1
2
3
1
2
1
1
1
1
2
0
1
1
2
0
1
1
0
0
3
1
2
0
0
1
2
2
1
2
1
1
0
1
1
2
0
1
0
1
1
0
1
0
1
0
1
0
1
1
0
1
1
0
0
1
1
1
1
1
0
0
2
0
2
1
1
1
2
2
2
1
2
2
1
2
0
1
0
0
0
1
3
0
0
1
1
1
2
1
2
0
0
0
1
1
1
1
1
1
1
1
1
0
1
1
2
1
0
1
0
1
1
0
0
0
0
0
1
1
1
1
1
0
1
0
2
1
0
1
0
1
2
1
1
1
2
1
1
2
0
1
1
2
0
0
0
1
1
2
2
2
0
1
0
1
1
0
1
1
1
2
2
2
1
1
1
0
1
1
0
1
1
1
1
2
2
0
2
2
1
2
1
1
0
2
0
1
1
0
0
2
1
1
2
0
1
2
1
1
0
2
0
0
1
2
1
2
2
1
1
0
1
2
0
0
0
0
0
1
1
1
1
1
1
2
1
1
1
1
0
0
1
2
0
1
0
0
0
2
0
1
2
1
2
1
2
1
2
2
2
1
0
1
2
1
2
1
2
1
1
1
1
2
1
1
0
2
0
2
1
0
1
1
2
1
0
1
1
1
1
1
0
2
1
2
2
0
1
1
0
1
1
0
2
2
2
0
1
2
1
1
1
1
1
0
0
2
1
1
1
1
2
1
2
1
1
0
1
3
1
1
0
0
1
1
3
0
1
0
1
0
0
1
1
0
1
0
0
1
1
0
1
0
1
0
0
1
1
1
1
1
2
0
1
1
2
0
2
1
1
2
2
0
2
1
2
1
1
0
0
1
2
1
1
2
0
0
0
1
1
0
2
0
1
0
1
0
1
0
2
1
1
3
2
0
1
0
1
0
1
2
2
0
1
1
1
0
0
1
1
1
1
2
1
1
1
0
2
1
0
1
1
1
3
1
1
1
0
1
1
0
0
1
2
1
1
0
1
1
2
1
2
2
2
1
1
0
0
0
0
0
1
1
1
2
1
2
1
1
2
1
0
1
1
1
1
2
2
0
1
1
1
1
1
1
1
0
2
0
1
0
0
2
1
1
2
0
2
0
2
0
1
1
1
0
0
2
0
0
0
1
0
1
0
0
1
0
0
1
1
1
1
1
1
0
1
1
2
1
1
0
2
2
1
1
2
2
2
0
1
0
0
1
0
2
0
1
0
1
0
2
1
0
1
0
2
0
0
0
0
1
2
1
0
1
2
1
1
0
3
0
2
1
1
2
1
0
2
1
1
1
2
1
0
2
0
0
0
1
1
1
1
0
0
0
1
2
0
0
1
0
0
2
0
1
1
1
0
1
0
2
2
1
1
1
0
1
0
1
1
1
0
0
0
0
2
1
1
1
1
1
2
0
1
0
1
1
1
2
0
1
1
1
0
0
2
0
1
1
1
2
1
1
1
1
2
1
0
1
2
1
2
2
1
1
1
1
1
1
0
2
1
0
4
0
0
2
1
1
2
1
2
1
2
1
2
2
0
1
1
1
0
1
0
2
2
2
1
1
0
0
1
2
0
1
2
1
2
0
1
0
1
1
0
1
1
0
1
1
1
0
1
2
1
1
1
1
0
0
0
2
2
1
0
1
2
0
1
1
2
0
0
2
1
0
2
2
0
0
1
1
2
0
0
2
2
0
1
2
2
2
0
0
2
0
0
0
1
2
1
1
2
0
0
1
1
1
1
1
1
1
2
0
1
1
1
0
1
0
1
0
1
2
2
0
2
1
1
2
0
1
1
0
2
1
1
3
1
1
2
0
1
0
0
0
0
0
2
0
0
1
2
1
2
1
1
0
0
2
0
0
1
1
1
0
0
1
1
1
1
2
0
1
0
2
1
1
1
2
2
2
1
2
2
0
1
1
1
1
1
0
1
1
1
1
1
2
3
0
1
2
2
2
0
1
2
1
0
0
0
2
0
0
1
0
0
1
0
1
1
1
0
2
1
0
0
1
2
1
0
1
2
0
1
0
1
0
1
1
1
0
0
1
0
1
1
0
0
1
2
0
1
1
1
0
1
1
0
0
1
1
2
0
2
0
1
0
1
2
0
1
1
2
0
1
2
1
1
1
1
2
0
2
2
2
1
1
1
1
0
1
0
2
1
1
0
0
0
1
2
1
0
2
1
1
0
2
1
0
2
0
1
0
0
0
1
1
3
1
1
1
1
0
2
1
1
0
1
0
2
0
1
1
0
1
1
0
3
2
2
0
1
1
2
0
1
1
0
1
1
0
0
1
1
2
1
1
0
0
0
1
0
2
1
2
2
1
1
0
1
1
0
1
2
0
2
0
0
1
1
0
1
1
2
1
1
2
1
1
0
0
1
1
2
1
2
1
2
2
2
0
1
1
1
1
2
1
2
2
1
0
0
2
1
0
0
0
0
1
1
1
1
1
1
1
2
1
0
1
0
1
1
2
0
1
1
1
1
2
2
4
1
1
1
2
2
1
1
1
0
1
2
0
1
1
2
1
1
1
1
1
1
2
0
2
1
1
1
1
2
0
2
2
0
2
1
2
0
0
1
2
1
1
0
2
0
2
1
0
3
2
1
1
1
1
1
1
1
0
2
1
2
1
1
1
1
2
0
1
1
1
2
0
0
1
1
1
1
1
0
2
2
1
1
2
1
1
0
1
1
1
0
1
1
0
0
1
1
0
0
1
1
2
2
1
2
1
0
1
0
1
2
1
2
2
1
0
2
0
0
2
0
2
1
1
1
1
0
0
1
2
2
1
1
2
1
0
3
1
0
0
1
1
1
2
1
1
0
1
1
1
1
1
1
0
1
0
1
0
0
1
2
0
1
0
1
0
1
2
0
2
1
1
2
1
1
0
2
0
0
0
0
0
1
0
1
1
1
0
0
1
0
1
1
2
0
0
2
1
0
0
1
0
0
1
1
2
2
1
1
2
2
0
1
1
1
2
0
0
1
1
1
1
2
1
2
1
2
1
1
1
2
3
1
1
1
2
3
2
2
0
1
3
0
1
2
1
0
1
0
1
1
0
0
0
1
0
1
0
1
1
0
1
1
0
0
1
1
1
2
0
1
0
0
1
0
1
1
1
2
1
0
0
0
1
2
1
0
2
1
2
0
1
1
2
2
2
0
1
1
1
1
1
1
2
0
2
1
0
0
0
2
1
0
1
1
2
2
2
1
0
2
1
1
1
1
1
2
1
0
1
1
1
2
1
1
1
1
2
1
0
2
0
0
2
2
2
1
1
1
2
0
1
2
2
2
1
2
1
2
0
0
0
1
1
1
1
0
1
1
2
2
1
1
1
0
0
1
1
2
3
2
1
2
2
0
1
2
2
0
2
0
1
0
1
0
1
0
2
0
2
1
1
1
1
1
2
1
1
2
2
3
0
2
1
0
1
2
0
1
0
0
1
0
1
1
0
2
0
0
2
0
2
1
2
1
2
0
0
0
0
1
0
1
0
1
3
2
2
1
1
1
2
0
1
2
0
1
2
2
0
1
1
1
1
1
2
0
1
2
2
1
2
0
1
0
1
0
0
1
0
2
1
2
1
0
3
2
1
2
1
2
1
1
0
1
2
2
1
0
1
2
0
1
1
1
2
1
1
1
2
1
1
1
2
1
1
0
1
1
1
1
1
0
1
1
0
1
1
1
1
1
2
1
1
2
0
0
0
1
2
1
0
1
1
2
2
0
2
2
1
0
0
1
0
1
2
1
1
2
2
0
0
1
1
1
1
1
1
0
2
0
0
0
1
1
1
0
2
0
0
0
0
1
0
2
1
2
0
1
1
2
0
1
2
1
0
1
2
2
1
1
0
0
2
1
2
1
1
0
2
2
2
2
0
1
2
0
0
5
0
0
1
0
1
1
0
0
0
2
2
2
1
1
1
1
0
1
2
0
2
0
0
1
2
1
1
1
1
2
1
0
0
0
1
0
0
0
1
1
0
1
1
0
0
1
3
1
0
1
1
2
1
0
1
0
2
1
0
0
1
1
2
0
1
0
0
2
0
0
0
2
2
2
2
0
2
2
1
2
0
1
1
0
2
0
0
0
1
1
0
0
1
2
1
1
4
1
2
0
1
0
1
1
1
0
1
1
0
1
0
2
1
0
0
0
0
0
0
2
1
2
2
1
1
1
1
1
0
1
1
1
0
0
0
0
1
1
1
0
1
0
2
1
1
1
0
0
1
1
2
0
1
0
2
1
1
0
1
0
0
1
0
1
2
1
0
0
1
0
1
1
1
0
1
1
2
1
2
1
2
0
1
2
0
0
1
1
1
0
2
1
1
1
1
1
0
1
1
0
1
2
1
0
0
1
1
2
1
1
1
0
1
0
1
0
1
2
1
0
2
0
2
1
1
1
2
0
1
1
0
1
0
1
0
1
1
1
0
1
0
1
1
0
0
0
0
1
1
2
0
1
2
0
0
1
0
1
1
2
0
2
1
1
0
0
1
1
1
1
1
1
0
1
1
2
0
1
1
1
2
1
0
1
2
1
1
1
0
1
1
1
0
2
0
1
1
1
2
0
1
1
0
0
0
1
1
0
1
0
0
0
2
1
2
2
1
1
1
2
2
2
1
0
2
0
0
0
1
0
1
2
1
2
1
0
2
0
2
1
1
2
0
1
1
1
1
1
1
1
1
1
0
1
1
0
0
1
2
1
1
1
0
1
1
1
0
1
2
0
1
1
2
1
1
1
0
2
1
1
1
0
1
0
1
0
1
1
2
2
2
0
1
1
0
0
2
1
1
2
1
1
1
1
1
0
1
1
0
1
0
1
1
1
1
0
2
1
2
1
1
1
1
1
0
1
1
0
0
2
1
2
1
1
1
1
0
2
2
1
2
2
2
0
2
2
0
1
0
2
0
0
0
0
1
1
1
0
1
1
0
1
1
1
1
2
0
1
2
0
1
1
1
0
2
1
2
0
2
1
1
0
2
1
0
1
1
1
1
1
1
0
0
1
0
1
0
1
1
1
2
0
1
1
1
1
1
2
0
1
0
2
1
1
1
2
0
0
1
1
2
0
2
0
0
1
1
0
0
1
1
2
0
1
1
1
1
1
2
1
1
0
1
1
2
0
0
1
1
0
0
0
2
2
1
2
0
3
1
2
1
1
1
0
1
2
0
0
1
0
1
0
1
1
0
2
0
1
0
0
0
1
2
2
0
1
1
1
1
0
2
0
1
0
0
1
1
1
0
1
0
1
1
2
2
2
1
1
1
1
1
1
2
0
1
0
1
0
0
1
0
1
0
0
0
0
1
2
1
1
0
0
0
1
2
0
1
1
2
1
1
2
1
0
0
0
2
1
0
0
2
1
1
1
0
1
1
1
0
1
0
1
1
1
2
1
1
2
1
1
0
2
2
1
0
1
0
1
1
1
0
1
1
0
0
1
2
1
1
0
2
2
1
0
0
1
1
2
2
1
2
0
0
1
2
1
1
2
1
2
0
0
2
1
1
2
1
2
0
1
1
1
0
1
1
0
1
1
1
0
0
1
1
3
2
2
1
0
1
1
2
0
1
1
0
1
1
1
0
2
3
2
1
1
1
2
0
0
1
0
1
0
1
0
0
0
2
1
1
2
0
0
2
0
0
2
1
0
1
1
0
2
2
1
0
1
1
1
1
1
1
1
1
0
0
0
1
2
0
1
0
2
1
0
2
3
2
2
1
1
1
2
1
0
0
1
2
2
2
1
0
2
2
1
1
2
1
1
1
2
2
1
1
2
2
2
0
1
1
1
1
0
2
2
0
2
2
1
1
1
0
1
1
1
0
0
0
1
2
1
0
1
2
2
2
1
2
0
0
2
1
2
2
1
0
1
1
0
0
1
0
1
1
0
0
1
0
0
1
2
0
2
0
0
2
1
1
2
1
1
0
2
2
1
0
2
0
0
2
4
1
0
1
1
2
2
1
2
1
0
1
0
0
0
2
0
1
1
1
1
1
0
2
1
1
1
0
2
0
2
1
0
0
1
2
0
2
0
2
1
0
0
1
1
2
1
1
0
0
0
1
1
1
2
2
0
1
0
2
2
0
0
1
3
0
1
1
2
2
0
1
0
2
0
0
2
1
0
0
2
0
1
0
1
1
0
1
1
1
0
0
2
1
0
1
0
0
2
0
2
1
2
0
1
0
0
0
1
0
1
1
1
0
1
2
1
0
2
2
0
1
0
1
2
1
1
1
0
2
2
0
1
0
0
2
0
0
1
0
1
2
1
2
1
1
0
1
1
2
1
1
0
2
2
0
1
2
2
1
1
4
0
1
0
1
1
1
1
1
1
2
0
2
1
2
2
0
1
0
0
1
0
1
1
2
0
1
0
1
1
1
1
2
0
0
0
0
2
1
2
2
2
0
0
2
1
1
1
2
1
1
0
1
2
1
1
0
0
1
1
0
1
0
0
1
0
1
1
2
1
0
1
2
1
2
1
0
0
1
2
0
2
2
1
2
1
0
1
2
0
1
1
0
1
2
1
1
1
1
2
2
0
2
1
0
1
1
1
1
0
1
1
1
1
2
2
0
1
1
1
1
1
2
0
1
1
1
1
2
0
0
1
1
0
2
1
0
1
1
1
0
1
1
0
2
0
1
0
1
1
0
0
1
0
2
0
0
1
2
1
2
2
2
0
0
2
1
2
1
0
2
1
1
0
1
1
1
2
1
2
1
2
1
0
2
1
1
1
0
2
2
2
1
0
0
1
1
1
0
0
2
0
0
1
1
2
0
1
1
0
1
1
1
0
0
0
2
0
0
2
1
1
2
1
0
0
1
2
1
1
0
0
1
0
1
0
1
2
2
0
2
1
0
0
2
0
1
0
0
0
2
0
1
2
0
1
0
2
0
1
1
1
2
1
0
1
1
0
0
0
1
0
1
1
1
1
0
1
0
0
0
2
2
2
1
0
1
1
2
0
4
0
0
0
1
1
0
1
0
1
1
1
1
1
1
3
2
1
2
1
2
0
1
1
2
0
0
1
0
1
1
1
0
1
1
1
1
2
0
2
0
1
0
0
2
1
1
1
1
2
0
1
1
1
2
1
0
1
2
0
1
2
1
0
1
0
1
2
3
1
2
2
1
0
0
1
1
1
0
1
0
1
0
0
2
2
0
1
0
1
1
1
2
1
0
1
1
1
0
1
1
2
0
1
2
2
1
2
0
1
2
2
1
1
1
1
1
1
1
1
1
1
1
0
1
2
2
1
1
1
2
1
2
2
1
2
0
0
1
0
2
2
1
2
2
2
0
1
1
0
1
2
2
0
1
0
1
1
2
1
1
3
0
2
1
1
0
0
2
1
0
0
0
0
1
1
1
0
0
2
0
0
0
0
1
1
1
0
0
0
1
1
0
1
1
0
1
1
0
2
2
2
1
1
1
0
0
0
0
0
2
2
2
0
3
2
2
1
1
0
1
1
2
1
1
2
0
2
1
0
0
0
2
0
1
2
1
1
2
1
1
3
1
0
1
1
0
0
1
1
1
0
2
0
1
0
2
1
0
2
2
1
0
2
1
0
1
1
0
2
0
1
2
0
1
0
1
1
0
1
1
1
1
1
2
0
2
0
0
1
0
2
1
1
1
2
2
0
2
1
2
1
1
1
0
2
3
1
1
1
1
0
2
1
1
0
1
1
1
1
2
0
0
2
1
1
0
1
1
1
1
0
1
1
2
1
1
1
1
1
0
0
5
0
2
1
1
2
0
0
1
0
0
2
0
0
0
2
0
1
2
0
0
1
2
1
2
0
0
1
1
1
2
1
0
2
1
0
0
0
1
2
1
0
1
0
1
0
1
0
1
0
0
1
0
2
1
2
1
2
2
1
1
0
2
0
1
1
0
1
0
0
3
0
0
0
1
2
0
1
0
1
1
1
1
2
0
1
0
1
0
2
0
0
2
1
2
0
1
2
2
1
1
1
0
0
1
0
1
0
1
2
0
2
2
0
0
0
1
1
1
0
1
1
1
1
2
1
2
1
1
2
1
1
1
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
1
1
1
0
1
0
2
1
1
1
2
0
1
1
2
0
1
1
2
0
0
1
2
1
0
2
2
2
1
1
0
2
2
1
0
1
1
1
2
1
3
0
1
0
2
0
2
2
0
0
1
1
1
1
1
1
2
2
1
0
0
2
0
0
1
2
0
2
1
2
2
1
0
2
2
1
1
0
1
1
1
0
1
2
1
1
1
0
2
0
2
0
1
0
1
2
1
2
0
0
0
1
1
1
4
1
1
2
0
0
0
2
0
2
0
0
2
2
1
1
1
0
1
2
1
0
0
1
1
0
1
1
0
0
0
1
0
2
1
0
1
2
2
1
1
2
0
2
0
0
0
0
1
2
0
1
2
1
2
1
1
0
2
0
0
2
1
1
1
1
1
1
1
1
0
1
1
1
1
1
0
1
0
0
1
0
0
0
1
0
1
1
1
0
0
0
1
1
2
1
1
1
2
0
0
0
1
1
1
0
1
2
2
1
1
1
0
0
2
1
0
0
2
1
0
1
1
0
1
0
0
1
2
0
0
2
0
2
1
0
2
2
1
1
0
0
2
2
1
2
0
1
0
0
1
2
0
1
1
0
0
1
1
2
1
1
0
1
0
3
0
1
1
1
1
1
0
2
1
2
0
1
2
1
3
1
1
0
1
1
0
0
0
1
1
2
0
1
1
1
1
1
1
1
2
2
2
1
1
1
1
0
1
2
1
1
2
2
1
0
0
1
2
3
1
0
1
0
0
2
1
2
0
1
0
1
2
1
0
1
2
0
2
1
2
1
1
2
2
2
2
1
0
1
1
0
1
1
1
1
2
0
2
1
1
0
1
1
1
2
1
1
0
1
0
2
0
1
0
1
0
1
1
1
1
1
2
1
0
1
1
1
0
2
0
1
1
2
1
1
2
1
1
2
1
1
1
1
2
0
0
0
2
0
0
2
2
1
1
1
2
0
1
0
2
1
0
1
1
1
0
0
1
0
1
1
0
1
1
0
0
0
1
2
1
1
1
0
0
2
1
1
0
0
2
1
2
1
1
2
0
1
1
1
1
0
1
0
1
2
1
1
2
1
1
1
2
4
0
2
1
2
1
2
0
2
0
2
0
1
2
0
0
1
1
2
2
2
2
1
0
0
1
2
0
0
1
1
2
2
0
2
0
0
1
2
2
0
1
0
1
1
0
1
2
0
1
1
2
1
2
0
0
1
0
1
2
2
0
0
0
0
1
0
0
0
2
2
1
1
2
1
0
0
1
1
1
1
1
0
2
1
0
0
1
1
1
1
0
1
0
1
2
0
0
1
1
0
2
2
1
2
0
1
1
2
0
1
1
1
1
1
2
2
0
0
0
2
1
2
0
1
1
0
0
1
2
1
1
0
1
1
1
0
1
1
0
1
2
0
1
3
1
3
2
1
1
1
1
1
0
0
1
1
2
1
2
1
3
1
0
1
0
1
0
2
1
0
0
1
0
0
2
1
2
1
2
0
1
1
2
1
0
2
1
2
2
1
0
2
0
0
0
0
1
1
3
2
0
1
1
0
1
1
1
0
2
0
0
1
0
0
0
1
1
1
0
1
1
1
2
0
1
2
1
0
0
0
0
1
1
0
1
1
1
0
0
1
1
0
2
1
1
0
1
1
0
2
2
1
2
1
1
1
1
1
0
1
1
1
1
0
1
1
1
0
1
2
0
2
0
2
1
1
0
2
1
1
1
2
0
2
1
0
0
2
1
1
1
0
1
0
2
1
0
1
0
3
4
0
2
1
0
1
0
0
2
0
1
1
1
1
0
1
2
2
1
0
1
0
0
1
1
0
0
1
1
2
1
0
1
0
0
0
1
2
1
0
0
0
0
1
0
0
2
0
0
0
1
0
0
2
0
1
0
0
1
1
0
1
1
0
2
1
0
2
0
1
0
1
2
0
1
1
1
0
2
0
1
1
1
1
1
0
0
2
1
1
0
0
1
2
1
0
1
1
0
1
0
0
1
1
2
0
2
0
0
0
1
2
0
1
3
1
1
1
1
2
1
1
1
1
1
1
1
1
0
0
1
2
1
1
1
2
1
1
2
1
1
1
2
0
1
1
2
1
0
1
1
1
1
1
1
1
1
1
1
2
0
2
0
0
1
2
1
0
0
2
0
1
1
0
0
0
1
4
1
1
0
0
1
0
2
2
0
1
0
0
0
1
0
2
2
0
1
1
0
1
4
1
1
1
2
2
1
2
0
0
1
0
0
1
2
1
1
2
3
0
1
0
2
1
1
1
2
1
1
1
1
0
0
1
2
0
0
2
1
2
2
1
1
0
2
1
1
0
2
1
0
1
0
1
2
0
0
1
1
0
2
1
0
2
1
0
2
0
1
1
1
1
1
1
2
2
1
1
2
1
0
1
2
1
1
1
0
1
0
1
2
0
0
2
2
0
1
1
0
2
0
1
1
1
0
1
0
2
1
2
1
0
1
0
1
1
1
2
1
0
1
2
0
1
2
1
0
0
1
2
0
0
2
2
0
1
1
1
1
1
1
1
0
2
0
0
0
2
2
0
2
0
2
0
1
1
0
1
0
2
0
1
1
0
1
2
1
1
2
1
1
1
0
0
0
1
1
1
1
1
1
2
2
0
2
2
1
0
0
1
1
1
1
1
2
0
1
0
1
2
0
2
0
0
1
1
2
1
0
1
0
1
1
1
1
1
1
1
1
0
0
0
2
1
0
1
2
0
0
0
1
1
2
1
1
0
0
0
1
0
0
1
1
1
0
1
0
0
0
2
2
0
1
2
1
0
2
3
1
0
0
2
1
2
1
2
0
1
1
1
0
1
1
1
1
2
1
0
0
0
1
2
1
1
1
1
2
2
0
0
1
0
0
0
2
2
1
1
2
3
2
2
1
2
1
3
1
2
2
2
0
0
1
3
1
2
1
1
0
1
2
1
2
1
0
1
2
0
1
1
2
1
1
2
1
1
1
0
2
2
2
1
0
2
1
1
4
0
2
1
0
0
0
0
2
1
1
1
1
2
0
4
2
2
0
1
0
0
2
1
1
1
0
0
1
1
3
2
0
0
2
2
1
1
1
1
1
2
1
2
2
1
0
0
2
0
0
1
1
1
1
1
0
0
0
2
1
0
1
2
0
1
0
1
1
0
3
0
1
1
1
3
2
1
4
0
1
0
1
1
1
2
1
1
1
2
0
1
1
2
2
1
0
1
1
0
0
1
1
2
0
0
2
0
2
1
0
2
0
0
1
1
1
2
1
1
0
2
0
2
0
2
1
0
1
2
1
1
0
2
1
2
2
2
1
1
1
3
1
1
0
0
1
1
0
0
2
1
2
2
1
0
1
0
2
1
0
2
0
2
2
1
1
2
0
2
2
2
1
1
0
2
1
1
1
1
0
1
1
1
2
1
1
1
1
2
1
1
1
2
1
2
2
2
1
1
1
1
0
1
1
2
1
1
1
0
1
0
2
2
1
0
1
1
0
0
0
0
2
1
2
0
0
1
0
1
1
1
1
0
1
0
0
1
3
2
1
0
0
1
1
2
1
1
0
1
1
0
1
2
0
2
1
0
0
1
2
1
1
1
1
0
2
3
0
0
2
2
1
2
0
1
1
0
1
1
1
1
0
2
0
0
0
1
1
0
1
1
1
1
1
1
0
2
1
0
1
1
1
1
2
1
0
0
0
1
2
12
0
1
1
1
1
1
2
0
1
1
1
0
2
1
0
1
2
2
2
2
1
1
2
1
1
1
0
0
0
0
2
1
1
0
1
1
0
0
1
0
0
1
0
1
0
1
0
0
2
1
1
0
2
1
1
0
0
0
1
1
2
1
1
2
0
2
1
1
2
2
0
1
0
1
0
0
0
1
0
0
1
1
1
1
0
0
1
1
1
1
1
0
1
1
1
0
0
0
2
0
0
0
0
2
2
1
2
1
1
1
1
0
2
1
0
1
2
0
1
1
1
2
1
2
1
1
2
1
2
0
2
0
1
2
1
1
0
1
1
1
3
1
1
0
1
0
0
2
2
2
0
1
1
2
1
1
1
2
2
0
1
0
0
0
0
0
1
1
1
1
2
0
1
1
1
0
1
2
1
1
0
0
0
2
2
1
1
2
0
0
0
0
2
0
1
1
0
0
1
0
2
0
0
0
0
2
2
2
0
1
2
1
0
0
0
0
1
1
0
2
0
1
0
0
1
0
2
2
1
1
1
2
1
0
2
1
1
0
1
0
2
0
0
2
1
0
1
1
2
1
1
1
2
1
0
1
0
0
0
0
0
1
3
1
1
1
2
2
0
1
0
0
2
0
0
2
1
0
0
0
1
2
0
2
1
1
0
1
1
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
1
2
2
1
2
2
1
0
0
1
2
0
1
2
1
2
1
1
0
1
1
1
1
0
0
0
0
1
1
0
1
1
0
1
0
1
0
0
0
0
0
0
1
1
0
1
0
1
0
1
0
1
2
1
0
0
1
0
2
1
1
1
1
2
1
1
0
1
1
1
1
0
1
1
1
1
0
1
0
1
2
1
1
2
1
1
1
1
1
1
0
0
1
0
1
1
0
2
2
1
2
1
1
2
0
1
0
2
1
0
2
1
1
1
0
1
1
0
1
0
1
2
2
0
0
1
1
1
1
2
1
1
0
0
2
0
0
1
1
1
0
1
0
1
0
0
1
1
1
1
0
1
2
1
0
1
1
0
1
1
0
1
1
1
1
2
1
1
0
1
2
2
1
0
2
3
1
1
0
1
1
1
0
1
2
1
0
0
1
0
1
1
0
1
2
2
0
0
1
2
1
1
1
2
1
0
0
0
2
0
0
1
1
1
1
2
1
0
1
1
1
1
0
2
0
1
1
0
2
0
1
3
1
1
1
1
1
0
2
0
1
2
0
1
2
0
1
1
0
0
0
1
0
1
5
1
1
1
0
0
1
0
0
1
1
0
1
0
1
0
2
1
0
1
0
0
1
2
1
3
1
1
1
0
3
1
1
0
0
1
0
2
2
2
0
1
0
1
1
1
1
1
1
2
0
1
0
1
0
1
2
0
1
0
1
1
0
1
2
0
0
1
1
1
1
0
0
1
0
1
2
2
1
1
1
2
0
1
1
2
2
1
2
1
0
1
1
3
1
2
1
2
1
2
2
1
1
2
0
1
1
2
1
0
2
0
1
0
0
2
1
0
2
1
0
0
2
1
1
1
2
1
2
1
0
1
1
2
1
1
0
0
1
2
1
1
2
1
1
1
0
0
1
2
1
1
1
1
1
1
1
2
2
1
1
0
3
0
1
1
1
1
1
2
1
1
1
1
1
1
1
0
0
0
1
1
1
1
2
2
1
1
2
0
1
2
2
1
1
2
0
0
1
1
1
0
2
0
0
0
0
1
2
2
1
2
1
2
1
0
2
2
0
1
1
2
1
1
1
0
1
1
1
2
1
1
0
2
1
0
1
2
1
0
2
1
0
0
2
2
1
2
1
1
0
0
0
2
2
1
1
1
1
1
0
2
2
2
1
0
2
2
2
0
1
2
1
0
0
0
1
1
1
1
1
0
0
0
2
1
1
2
0
0
1
1
0
0
1
1
1
1
0
0
0
0
0
2
0
1
1
0
1
0
1
0
1
2
0
2
1
1
0
2
0
2
1
2
2
0
0
0
0
1
1
1
2
1
1
1
1
0
1
1
2
2
1
2
2
1
2
1
1
0
1
0
0
1
0
1
1
1
1
0
1
2
0
0
0
1
1
0
1
2
2
1
1
0
0
2
2
0
2
2
1
0
0
2
1
1
1
0
1
0
2
1
0
1
0
1
1
1
1
1
0
2
0
1
1
1
2
0
2
1
1
1
2
1
2
1
0
0
0
1
0
1
2
1
0
0
1
0
2
2
0
0
2
0
0
2
1
0
0
3
5
0
0
0
1
2
1
2
1
2
1
1
1
1
1
1
0
2
1
1
0
1
1
1
1
0
1
1
2
1
1
2
2
0
2
1
0
2
1
0
1
0
2
0
2
1
2
2
1
0
1
1
2
1
1
2
1
0
1
0
1
1
1
0
1
1
2
2
2
0
3
1
0
2
0
2
0
1
0
1
1
2
1
0
0
2
2
1
0
0
1
1
1
0
0
0
1
1
2
1
1
1
0
2
1
0
1
0
0
1
1
1
2
0
2
2
0
1
0
1
1
1
1
1
2
1
1
3
1
1
0
1
1
1
1
2
2
0
1
1
2
0
0
1
1
0
1
1
1
0
1
1
1
2
2
2
1
0
1
1
2
1
1
1
1
0
0
2
1
2
1
0
1
1
0
0
0
0
1
1
1
1
0
1
0
1
2
1
2
1
1
0
1
1
1
0
1
2
1
1
0
1
0
0
0
1
1
0
1
1
1
2
1
2
1
0
0
1
1
2
1
0
1
0
1
1
0
2
2
2
1
0
1
0
2
0
1
0
1
2
1
0
1
0
0
1
1
1
1
2
0
2
1
1
2
1
1
1
2
1
1
2
0
2
0
2
2
0
1
1
0
0
1
1
0
1
1
0
2
1
2
7
1
0
1
2
1
1
0
1
1
0
1
0
0
1
0
1
0
1
1
2
1
2
1
1
2
0
0
1
2
2
0
0
0
0
1
0
0
2
0
2
2
1
1
1
1
0
1
0
1
2
0
1
0
1
1
1
0
0
0
1
1
1
2
1
2
2
1
0
1
1
1
1
0
1
1
1
0
0
0
0
1
0
1
2
1
1
0
0
2
1
1
1
0
0
1
0
2
1
0
1
2
4
0
0
1
0
0
2
0
2
2
0
0
2
0
1
1
0
0
1
1
1
2
0
0
2
0
0
2
1
1
2
1
0
2
1
1
0
1
4
0
0
2
0
2
0
1
2
1
2
1
2
0
0
2
1
2
3
2
2
2
0
1
1
1
1
2
2
1
1
1
2
0
1
0
1
1
1
0
0
0
1
1
0
1
1
1
1
1
0
0
2
1
1
2
1
0
2
1
1
1
1
1
1
1
1
1
1
0
0
1
1
1
0
1
1
1
1
1
1
1
0
0
1
0
0
1
2
1
0
2
0
1
1
0
2
1
1
0
1
0
0
2
1
1
1
0
4
0
0
1
1
2
1
1
0
0
2
2
0
0
0
1
0
0
1
2
0
1
0
2
0
1
2
1
1
1
1
0
0
2
2
2
0
0
0
2
1
1
2
0
2
1
0
1
1
1
2
1
1
0
1
1
2
2
2
1
2
1
2
1
2
0
0
1
1
1
1
2
1
1
1
0
1
0
1
0
1
2
1
2
1
2
0
1
2
0
0
1
2
1
0
2
0
2
0
1
0
1
0
1
0
0
0
1
1
0
0
0
0
0
2
0
0
0
1
2
0
2
0
1
2
0
1
0
0
2
0
2
2
0
1
0
1
1
1
0
1
1
0
0
1
2
0
1
1
2
0
1
0
2
2
2
0
2
1
1
1
0
2
2
1
0
1
0
1
1
1
1
2
1
1
0
0
0
2
0
1
1
0
1
1
1
1
0
0
1
0
1
2
0
1
1
1
0
1
1
1
0
1
1
0
2
1
0
0
1
0
0
1
0
1
0
1
2
1
1
2
2
2
0
1
1
1
0
1
0
2
0
1
1
1
2
1
0
1
1
1
0
0
0
1
1
0
0
2
1
0
0
2
1
1
1
1
0
1
2
0
1
2
0
1
0
0
2
1
0
0
1
1
2
0
2
2
1
0
2
1
0
1
1
0
1
2
1
0
0
1
1
3
1
0
1
1
2
1
1
2
1
0
1
0
1
1
1
0
1
1
0
1
2
1
2
0
0
2
2
0
1
0
2
1
0
0
2
0
0
1
1
0
2
2
2
0
2
0
1
0
1
1
0
1
1
1
1
1
0
0
1
1
1
0
1
0
2
1
1
2
0
1
1
2
0
0
1
1
0
2
1
1
0
0
1
1
1
1
1
2
1
2
0
0
2
1
1
0
1
2
0
2
1
0
0
1
1
1
2
0
1
2
0
1
0
2
0
3
2
2
0
1
1
1
1
3
0
1
2
2
0
0
4
2
2
0
1
0
0
0
0
3
1
1
1
1
0
1
2
0
2
0
1
1
0
2
0
1
1
0
1
0
2
2
0
0
1
1
1
1
0
2
0
0
1
1
0
2
0
1
2
1
1
0
1
2
2
1
1
0
0
2
0
0
0
0
0
1
0
1
1
0
1
0
0
0
1
2
1
0
2
2
0
2
1
0
1
1
0
1
0
0
1
1
1
0
0
1
0
0
2
1
2
1
2
1
1
1
3
1
0
1
1
2
2
2
2
1
0
2
2
0
1
1
0
0
1
1
2
1
1
0
1
0
0
0
1
2
1
0
0
2
2
1
1
2
0
0
1
1
1
2
3
2
1
1
0
1
0
0
1
1
2
0
1
1
2
0
1
1
2
0
0
1
1
2
0
1
2
1
0
0
1
0
1
2
2
1
2
1
1
1
1
0
1
2
0
1
1
1
1
0
1
0
0
1
2
0
1
2
0
1
1
0
0
2
0
0
1
0
2
0
0
1
1
1
0
1
2
2
1
0
0
1
1
0
0
0
2
0
0
0
0
3
0
2
0
1
1
1
2
1
1
1
0
2
0
2
1
1
1
0
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
0
2
0
1
1
1
0
0
1
1
0
1
1
2
1
1
1
2
0
0
2
0
2
0
0
1
0
1
1
2
0
1
0
1
0
1
0
1
1
0
1
1
1
1
0
0
2
1
0
1
1
1
1
0
1
0
0
1
2
0
2
1
1
0
2
0
1
2
0
1
1
0
1
1
0
1
1
0
1
0
2
1
1
1
2
1
0
2
1
1
1
1
0
1
2
1
1
0
2
0
1
0
1
0
0
1
1
0
2
2
0
0
2
1
1
1
1
0
1
2
1
2
1
0
2
1
1
1
0
1
0
1
2
4
1
2
2
1
1
1
2
1
1
0
0
2
1
1
0
1
1
1
2
2
1
0
1
0
1
1
1
1
2
2
0
1
0
2
1
0
0
2
1
0
1
0
0
1
2
1
1
0
1
0
1
0
0
1
2
0
1
1
2
0
0
1
0
0
0
1
0
1
0
1
1
2
1
1
1
1
0
0
2
2
1
1
1
2
1
1
1
2
0
0
2
1
1
1
2
2
1
0
2
0
1
2
1
0
1
1
2
0
0
0
0
0
1
1
0
1
1
0
1
1
0
1
1
2
1
1
1
2
1
0
1
0
1
1
2
0
0
0
1
0
1
3
1
1
0
1
0
1
1
1
1
1
1
1
0
2
2
0
0
1
0
0
1
1
1
1
0
1
1
0
1
1
0
0
2
1
2
1
2
0
2
0
0
2
0
0
1
2
1
2
0
1
1
1
0
0
1
0
1
1
0
0
1
1
1
3
1
0
0
0
1
1
1
1
0
3
1
0
0
1
1
0
1
1
1
1
1
1
1
0
1
0
1
1
2
1
1
0
1
1
1
1
2
0
1
1
0
2
1
1
0
1
0
2
1
1
2
0
2
0
2
2
0
1
0
0
2
2
0
0
1
1
2
1
1
1
1
1
1
1
1
0
1
0
0
2
0
0
2
2
0
2
2
1
1
1
0
0
2
1
1
1
1
0
1
0
1
0
2
0
1
2
1
2
2
1
1
0
0
0
1
2
2
0
2
1
2
2
1
0
1
1
0
1
2
1
0
2
2
2
1
3
1
0
0
0
2
1
2
1
2
1
0
0
2
2
1
0
1
0
1
1
0
1
2
1
1
2
0
0
0
1
0
0
0
1
2
1
1
2
1
1
1
0
0
2
1
1
1
1
0
1
0
2
2
1
0
1
2
0
1
0
2
1
2
1
1
0
1
1
2
2
2
0
1
0
1
1
0
0
2
1
1
2
2
1
0
2
1
1
0
1
1
1
1
1
0
0
0
2
1
0
1
0
0
0
1
2
0
0
1
1
1
0
0
2
1
1
0
1
1
0
0
1
2
2
1
1
2
2
1
0
1
1
2
0
1
2
1
1
1
2
2
2
0
1
1
1
1
1
1
1
0
2
2
2
2
0
2
1
2
0
1
1
2
0
1
3
1
0
2
0
0
0
0
0
3
0
0
0
1
1
1
2
2
2
2
0
1
2
1
2
1
0
1
1
2
1
1
0
0
0
1
1
1
1
1
2
1
2
1
1
3
2
1
0
1
2
3
1
2
1
1
1
0
2
0
2
1
0
1
2
3
0
2
2
1
0
1
1
0
1
0
1
0
1
1
2
0
1
1
1
1
1
1
0
1
1
1
1
1
0
0
0
0
2
1
0
1
1
0
0
1
0
1
0
0
0
2
0
1
1
1
1
2
1
2
0
1
0
1
0
1
1
0
1
0
1
1
0
2
2
1
0
2
1
1
1
0
0
1
2
0
1
0
2
0
1
0
0
1
0
6
1
2
2
2
1
1
0
0
2
1
0
1
1
0
1
1
0
1
2
1
1
1
1
0
2
0
1
3
0
2
1
1
2
1
1
1
1
0
1
2
1
2
1
0
1
2
1
1
2
2
1
1
2
1
1
1
1
2
0
1
0
0
0
1
0
1
2
0
1
1
1
2
0
2
2
1
0
0
2
0
0
0
1
2
0
1
0
0
1
1
0
2
0
2
1
1
0
1
1
1
1
1
1
0
0
2
0
1
1
1
1
1
1
2
1
2
0
1
1
2
1
2
2
2
1
2
0
2
0
1
0
2
2
2
1
2
2
0
1
1
1
2
0
1
1
1
2
1
1
2
1
0
1
0
1
2
1
2
0
0
2
0
0
2
0
0
0
0
1
0
0
1
0
1
0
1
1
0
1
1
1
1
2
1
2
0
0
0
1
1
0
2
3
2
2
1
1
0
1
0
0
1
0
1
0
0
1
1
1
1
1
1
0
1
0
1
1
0
2
0
1
1
1
0
1
1
1
0
0
1
0
1
1
0
2
0
1
2
0
2
0
2
0
0
1
1
4
1
1
1
1
2
1
1
0
2
1
0
1
1
1
0
0
1
1
0
0
1
0
1
1
1
1
1
1
1
1
0
0
1
2
1
1
1
1
1
0
2
0
1
1
0
1
2
1
2
0
1
0
1
0
1
0
0
2
0
0
2
0
1
1
1
1
1
0
0
0
0
1
1
1
2
1
1
1
0
0
2
1
1
2
1
1
2
0
1
1
1
0
2
0
1
0
3
2
2
1
0
1
1
2
1
2
3
0
1
1
1
2
1
0
2
2
1
1
1
2
2
1
2
0
1
1
1
1
1
1
0
2
1
0
0
0
1
1
1
2
2
0
1
1
1
2
1
3
1
0
0
2
1
2
0
0
1
2
1
1
2
1
0
1
0
1
1
1
2
1
2
0
1
0
0
1
0
0
0
1
2
1
1
1
0
1
1
1
1
0
1
2
1
1
1
1
1
0
1
1
2
1
2
1
2
0
2
0
0
2
0
2
0
0
0
2
3
1
1
0
0
0
2
1
0
1
1
1
2
2
2
0
1
1
2
0
1
1
0
1
2
0
2
1
1
1
0
0
1
1
2
1
2
1
2
2
1
2
2
0
1
2
2
0
1
0
0
1
0
0
2
0
0
1
1
1
1
0
1
0
1
2
0
2
1
1
0
2
1
1
1
2
0
1
0
0
1
1
1
1
1
1
0
2
0
1
2
0
0
0
2
0
0
2
1
0
0
1
2
0
0
1
1
2
1
1
1
1
2
1
2
2
1
1
0
1
0
1
1
1
0
1
2
1
2
1
0
0
2
0
0
1
2
1
1
1
1
2
1
1
1
2
2
2
1
1
1
1
0
1
2
2
1
2
0
1
1
1
1
0
1
1
0
0
1
2
0
2
0
0
1
0
1
1
2
0
1
1
0
1
1
1
0
2
0
2
0
2
1
0
2
1
0
1
2
2
2
2
0
0
1
0
1
2
1
1
1
1
2
0
1
0
2
0
2
0
1
1
0
1
2
1
1
1
0
1
2
0
1
1
1
1
1
1
1
0
1
1
1
1
1
1
0
0
0
1
1
0
2
2
1
1
0
2
1
2
1
0
1
1
1
1
1
1
0
1
0
1
2
0
1
1
1
1
0
1
0
0
1
0
1
1
0
1
1
0
0
2
1
0
0
0
1
1
1
1
0
2
3
1
0
1
2
1
3
1
1
0
0
0
1
1
0
0
0
1
1
0
0
0
1
2
2
0
1
1
2
0
1
1
2
1
0
2
2
1
1
0
1
1
2
1
2
1
1
1
1
1
1
1
0
0
2
1
1
0
1
1
2
1
1
1
1
1
0
1
0
0
2
1
1
1
1
1
0
1
0
1
0
0
2
2
1
2
1
6
0
1
1
0
1
2
1
1
1
0
2
1
2
2
1
2
2
1
1
2
1
1
1
2
1
1
0
1
1
0
1
1
1
2
1
1
0
1
1
0
1
1
1
0
0
1
0
0
1
1
1
2
0
0
2
0
1
0
2
1
1
2
2
0
2
0
1
1
1
0
2
1
2
1
2
1
1
2
1
2
1
2
2
2
1
2
2
2
1
1
0
1
1
1
1
3
1
2
1
1
0
0
1
1
1
1
0
1
0
1
1
1
0
2
0
2
4
2
1
1
3
1
0
2
0
1
1
0
1
1
1
1
0
1
1
0
1
0
2
0
2
1
0
1
1
1
1
1
1
2
2
1
1
0
1
1
0
2
0
1
1
1
0
2
0
1
1
1
1
0
1
2
1
2
1
4
0
0
1
0
0
1
1
1
2
1
1
2
2
0
0
2
0
2
1
3
0
1
1
0
1
1
1
2
1
0
1
1
1
2
1
1
1
1
1
1
0
0
2
0
2
1
0
1
1
2
0
3
2
1
1
0
1
1
1
2
1
0
2
2
1
0
1
0
2
1
1
0
1
1
1
1
1
1
0
0
1
0
0
1
0
1
0
2
1
1
0
0
1
1
1
0
3
1
1
1
2
2
1
1
1
0
1
1
0
1
1
1
0
0
0
0
1
1
2
0
0
1
1
1
0
1
0
2
0
0
1
1
1
1
0
0
0
1
1
1
1
1
1
2
0
1
2
1
0
2
0
1
1
2
1
1
0
1
1
1
1
0
1
1
0
1
0
0
1
2
0
1
1
1
0
0
2
0
1
1
1
1
1
1
1
0
1
1
2
1
1
1
3
1
1
1
0
1
1
1
1
1
0
0
0
0
2
1
1
0
1
2
2
1
2
1
1
0
0
1
0
1
1
0
2
1
1
2
1
0
0
1
2
0
0
0
0
1
1
1
0
1
1
2
1
1
1
1
1
1
2
2
0
1
2
2
0
1
1
2
1
2
0
0
1
1
2
0
1
2
1
1
0
3
0
2
0
2
1
0
0
1
2
1
0
3
1
1
0
1
2
1
1
1
1
0
2
0
0
0
0
1
1
2
1
1
0
0
2
0
3
2
0
1
0
0
2
1
1
1
0
1
1
0
2
1
1
2
2
1
1
1
1
2
1
1
1
2
1
2
1
2
1
1
0
1
0
1
0
2
1
2
2
1
1
0
2
1
1
0
1
0
1
1
0
1
1
2
1
0
1
0
1
1
1
1
1
1
2
2
1
0
0
1
1
0
2
1
2
0
1
1
0
1
2
0
0
1
1
1
1
1
1
0
0
1
1
1
0
0
1
1
2
1
1
1
0
1
1
0
2
1
1
1
1
0
1
1
1
2
0
0
1
2
2
1
1
1
2
1
1
2
1
2
2
2
1
0
2
0
0
0
1
0
0
0
1
0
0
2
1
0
1
0
0
0
0
1
0
1
0
0
1
1
1
0
1
2
1
1
2
0
1
1
1
1
2
1
1
2
1
2
1
0
1
1
1
1
0
0
1
2
1
1
1
5
1
1
1
0
1
0
0
0
0
1
2
1
1
0
0
1
1
0
0
1
1
1
0
0
0
0
1
0
1
1
1
0
2
1
2
2
1
2
0
0
1
0
1
0
2
1
1
2
1
1
0
1
1
0
0
1
0
1
1
0
2
1
1
2
0
1
1
0
0
0
2
1
1
1
0
1
1
1
0
2
1
2
1
2
1
2
1
0
0
1
0
0
1
1
2
0
0
0
1
2
2
1
1
2
1
1
1
0
0
2
0
0
2
2
1
1
2
1
1
2
0
1
0
2
1
0
1
1
1
1
1
2
2
1
1
0
1
1
2
2
1
2
2
1
1
0
2
0
1
1
0
1
0
1
2
2
1
1
1
1
1
0
1
0
1
0
2
2
0
1
0
0
0
0
0
2
0
1
0
3
0
2
1
0
0
1
2
2
1
0
0
2
1
3
0
1
0
1
0
1
2
3
2
0
1
2
2
0
0
1
1
0
1
1
1
1
1
1
2
1
1
0
2
0
1
1
0
1
1
1
0
1
2
2
0
0
1
0
1
0
2
1
2
1
1
0
1
1
0
0
1
1
1
0
0
0
1
1
1
0
0
2
2
2
0
3
0
0
2
1
1
2
1
1
1
0
1
1
2
1
1
0
1
1
1
1
1
2
1
0
2
0
2
0
0
0
0
0
0
0
2
0
1
1
2
1
0
1
0
1
1
2
2
1
0
1
1
2
1
0
2
1
1
1
1
2
1
1
1
2
0
1
2
0
0
0
1
2
0
0
3
2
1
1
1
1
1
1
0
0
0
0
1
1
0
1
0
1
0
1
1
0
2
1
1
2
0
0
0
1
0
0
0
1
2
2
0
0
0
1
1
1
3
0
1
1
0
1
1
0
2
0
1
0
0
1
0
0
0
0
1
2
2
1
2
1
1
1
0
1
1
1
1
0
0
2
1
1
0
1
1
0
0
0
1
1
2
0
2
2
2
1
1
2
2
1
2
1
0
1
0
1
0
1
1
0
1
0
1
0
2
1
2
1
0
1
0
1
1
0
1
1
1
2
0
1
2
1
1
2
1
1
1
0
1
1
2
0
1
4
0
1
0
1
0
1
1
1
1
1
1
1
2
2
1
1
0
3
1
1
2
1
0
1
0
1
0
1
0
0
1
1
1
0
0
1
1
1
0
0
1
0
1
1
1
0
1
2
0
1
1
0
2
1
0
2
2
0
1
1
2
0
0
1
1
1
1
1
1
2
0
2
1
1
2
2
0
2
1
1
0
0
0
2
0
1
2
1
0
1
1
2
0
1
1
2
2
1
1
1
1
1
0
0
0
1
1
2
1
0
2
1
2
1
2
1
1
1
0
2
1
1
1
1
1
1
1
1
0
2
0
0
2
1
0
0
2
2
1
0
1
0
0
0
0
0
1
1
1
0
2
1
0
1
0
1
2
0
1
2
2
1
1
1
0
1
0
1
1
2
2
1
2
1
1
1
1
1
0
1
0
0
0
1
1
2
1
2
1
1
1
3
1
0
0
0
2
0
1
1
0
0
1
1
1
0
0
0
1
2
1
2
1
1
1
1
2
0
0
1
0
1
1
0
0
1
0
0
1
2
1
1
0
0
0
2
2
2
0
0
1
1
1
0
1
1
0
1
1
0
1
0
1
0
0
1
2
1
1
2
2
1
0
2
0
1
1
2
2
1
1
1
1
1
1
0
0
1
0
0
0
2
0
0
0
0
1
2
1
0
1
1
1
2
1
2
0
1
1
2
1
0
2
1
2
0
1
1
2
1
0
1
1
1
2
0
1
2
2
0
1
2
2
0
1
2
1
1
1
2
0
1
2
1
0
1
0
2
1
0
1
1
0
0
1
0
0
0
2
0
1
0
1
1
1
1
0
1
0
0
1
0
1
1
2
0
1
0
1
1
1
0
1
0
0
0
1
0
1
0
1
2
0
0
2
1
2
0
0
0
1
1
1
2
0
1
2
1
1
1
2
1
2
2
0
0
2
2
1
3
1
0
0
0
1
0
0
1
1
0
1
1
1
0
0
0
1
0
1
0
1
0
2
1
1
0
0
0
2
1
0
2
1
1
0
1
0
1
2
2
1
1
1
0
0
1
0
1
1
1
1
1
1
0
1
0
0
2
2
0
1
1
2
1
0
0
1
1
1
1
0
0
0
1
1
1
1
2
0
1
0
1
1
1
0
1
0
1
1
2
0
0
2
0
1
1
1
0
1
0
2
2
3
1
2
0
0
2
0
0
1
1
0
2
1
1
2
1
0
1
1
1
1
1
0
1
1
0
2
2
0
0
0
0
2
1
2
1
0
0
1
2
2
0
1
0
0
0
2
1
4
1
0
0
2
0
0
1
0
0
1
2
1
0
1
1
0
2
1
0
1
2
1
0
1
1
2
0
0
1
2
1
1
1
1
1
0
0
1
1
2
1
0
2
0
2
4
1
0
0
1
0
2
1
2
1
2
0
3
1
2
0
1
2
1
1
1
0
0
1
0
1
2
1
1
0
0
1
0
1
2
1
1
1
2
0
0
1
1
1
0
2
0
1
0
1
0
0
3
3
7
2
1
0
1
1
0
1
0
1
1
1
1
2
1
2
2
0
0
1
1
0
1
1
2
1
2
0
4
0
2
0
1
1
0
1
1
0
3
1
0
1
1
1
1
1
0
2
2
0
1
0
1
2
1
1
1
1
0
2
1
1
1
1
0
0
1
4
1
0
1
0
2
2
1
1
0
1
0
2
1
0
1
1
2
1
1
1
1
0
2
1
1
1
1
1
0
1
1
0
2
1
0
1
1
1
0
0
0
0
2
0
0
1
0
1
0
0
2
2
1
2
0
1
1
0
1
1
0
1
0
2
1
1
1
2
1
0
0
2
1
1
1
0
1
1
0
0
0
1
0
0
0
2
0
2
2
3
2
1
1
3
2
1
0
1
0
0
1
1
2
1
0
0
0
1
1
1
1
1
2
0
0
0
3
1
2
1
1
0
1
1
0
1
2
0
1
1
0
1
1
0
0
0
1
0
1
1
0
1
1
2
0
2
1
1
0
1
0
3
1
1
2
1
1
1
0
1
2
0
1
2
1
1
1
0
1
0
2
2
1
0
0
1
1
1
2
0
1
3
1
1
1
2
2
2
1
0
1
1
2
1
1
1
1
1
1
0
1
1
0
1
0
0
1
1
1
2
2
1
1
1
0
1
1
1
0
2
1
1
1
1
1
1
2
1
0
1
2
0
0
1
0
1
0
1
1
1
1
0
0
1
2
2
0
1
2
0
1
0
1
1
0
1
1
2
1
2
2
2
1
1
1
1
1
1
2
0
1
1
1
0
1
1
1
1
0
0
1
2
0
1
1
2
1
1
0
1
1
1
1
1
1
0
1
2
1
1
0
1
2
0
1
1
1
1
1
1
2
1
0
1
1
1
0
1
1
1
1
1
0
1
2
0
1
1
2
0
0
2
1
1
0
0
1
1
3
0
0
0
0
1
1
0
0
2
1
1
2
1
1
2
0
1
1
0
3
1
1
1
0
0
0
2
0
1
1
1
0
1
0
2
1
2
1
1
1
0
2
0
0
2
2
0
0
0
1
1
1
2
0
2
2
1
0
3
0
0
0
2
2
1
1
0
1
2
0
2
1
2
1
1
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
2
2
0
0
2
1
1
1
2
3
1
1
0
1
1
1
0
1
2
2
0
2
0
2
1
1
0
1
2
1
2
0
0
2
2
0
1
1
0
2
0
1
0
2
18
0
1
1
1
0
0
0
1
1
0
2
2
3
0
2
0
0
0
0
1
2
1
0
1
1
0
1
1
1
0
0
2
2
0
1
0
2
0
1
1
0
1
2
1
1
0
1
1
1
2
1
0
1
0
0
0
1
1
2
2
1
1
1
1
0
1
1
1
2
0
1
0
0
4
1
2
1
0
1
0
2
1
2
2
1
0
1
2
1
2
1
1
0
0
0
1
1
1
2
1
1
1
0
3
1
1
1
1
0
0
1
1
1
0
1
1
2
1
0
1
1
2
1
1
1
1
2
0
0
2
2
0
1
1
1
2
2
2
1
1
0
0
2
0
1
2
1
0
1
0
1
1
1
1
1
1
1
0
1
1
0
2
1
1
0
0
1
0
1
1
1
1
2
0
2
2
1
1
0
1
1
2
1
0
1
3
2
1
1
2
1
0
0
2
1
0
2
1
0
1
1
0
1
1
2
1
1
0
0
1
2
1
2
2
0
0
1
0
1
3
0
1
2
2
0
2
1
0
0
2
2
3
0
1
0
1
1
1
0
0
0
1
1
1
0
0
0
1
1
1
2
0
0
1
1
0
2
2
0
2
2
0
2
1
1
1
1
1
1
2
1
2
2
0
2
1
1
0
1
1
2
1
2
1
3
1
1
0
2
1
1
0
2
1
1
2
0
1
1
0
0
2
0
1
1
2
1
0
1
2
0
2
0
0
1
2
1
1
1
1
0
0
1
1
2
1
0
0
2
0
0
0
1
0
1
0
1
0
0
0
2
0
0
2
1
1
2
0
1
1
2
1
0
0
1
0
0
0
2
3
1
0
2
0
2
1
0
0
4
1
1
2
2
1
2
1
0
1
0
0
1
0
0
0
1
3
0
1
0
0
1
0
1
0
0
1
1
2
1
1
1
2
1
1
2
2
1
1
2
0
0
0
0
0
1
1
0
2
0
1
2
1
2
2
2
1
2
2
1
1
1
0
2
1
1
0
1
0
2
1
1
2
1
1
0
2
0
0
1
2
0
2
0
0
0
1
0
0
1
1
1
2
1
1
1
0
1
0
1
1
2
0
1
1
0
0
1
0
1
1
1
1
1
2
1
2
2
0
2
1
0
1
0
2
1
1
1
2
0
0
2
2
1
0
1
0
1
0
1
1
1
0
1
2
1
0
0
1
0
2
2
1
0
1
2
0
1
2
2
2
0
0
0
2
0
1
0
1
1
1
0
1
1
0
0
2
0
2
0
2
1
2
0
1
1
2
0
2
2
0
0
1
1
0
0
2
0
0
2
1
0
0
0
1
1
0
1
2
1
1
0
0
0
2
1
1
1
2
1
1
1
1
0
0
2
1
0
1
1
1
1
1
0
1
1
2
2
2
2
0
0
0
1
1
1
1
1
0
1
1
1
1
0
0
0
0
0
2
1
1
0
0
2
0
0
1
2
1
2
0
1
1
1
0
1
0
1
0
1
1
0
0
1
1
1
0
0
1
0
1
0
0
0
0
0
1
1
1
0
1
1
2
2
1
1
2
1
2
0
2
1
1
2
1
1
0
1
2
0
1
1
2
2
1
1
0
2
1
1
2
2
1
2
1
1
2
1
2
1
0
2
2
1
0
0
1
1
0
0
2
0
2
2
1
2
1
1
2
0
2
1
2
0
1
2
1
2
0
1
3
0
0
2
1
2
0
2
0
0
1
1
0
1
2
0
2
1
2
2
3
0
0
0
1
2
1
2
0
1
1
1
0
2
1
1
2
2
1
0
0
0
0
1
2
2
2
0
1
2
0
1
2
1
1
0
1
1
1
1
2
1
2
1
2
1
1
1
2
1
0
1
2
0
0
1
1
1
0
2
1
2
2
2
1
1
0
1
1
1
1
1
1
0
2
1
1
1
1
1
1
1
1
0
0
1
0
0
2
2
1
0
1
1
2
1
0
0
2
2
1
0
2
1
1
1
0
1
0
1
0
0
1
1
1
1
2
1
0
0
1
1
1
1
0
1
1
0
1
1
1
0
1
2
1
1
3
1
0
0
2
0
3
1
1
2
1
0
0
0
3
1
0
0
2
1
2
1
1
1
1
0
1
0
2
1
2
0
0
0
1
1
1
1
1
1
1
2
0
2
1
1
0
1
1
2
2
1
2
1
1
0
1
2
1
0
1
1
0
1
2
0
2
1
1
0
2
1
0
1
2
0
2
0
3
0
1
1
1
1
1
1
2
1
0
0
1
1
1
3
1
0
0
0
2
1
1
2
1
2
2
0
2
1
0
0
2
1
2
1
1
1
0
2
0
0
1
0
0
0
0
2
1
2
1
1
1
2
2
2
2
1
2
1
2
1
2
2
1
2
1
0
0
2
0
1
2
1
2
1
1
3
0
1
1
1
2
0
0
2
1
2
0
0
0
0
2
1
1
0
0
2
0
1
0
1
1
0
0
1
0
0
0
2
1
1
2
1
1
2
1
1
1
0
1
0
2
0
1
0
0
2
2
1
0
0
2
0
1
1
0
1
1
1
0
2
1
2
2
2
0
0
0
1
0
1
1
2
0
0
0
1
0
1
1
0
1
1
0
1
0
0
0
1
2
1
1
0
2
1
1
0
1
0
0
0
1
1
2
2
0
2
1
1
2
1
1
1
0
1
0
1
0
2
1
0
2
2
1
0
2
0
1
1
0
0
2
2
1
2
0
1
1
2
1
1
2
2
0
1
2
1
1
1
2
1
2
2
0
0
3
2
2
2
1
2
2
0
1
1
0
1
1
2
2
0
0
2
2
1
1
1
1
1
1
1
1
0
1
0
1
0
2
1
0
1
2
2
2
2
1
1
1
0
2
1
2
1
2
0
1
0
1
2
1
1
1
1
2
0
1
2
1
1
1
0
0
1
0
2
2
0
2
0
1
1
1
0
0
2
1
2
0
0
1
2
2
1
1
2
1
1
0
2
1
1
2
0
1
0
1
2
2
1
2
2
2
1
1
0
0
1
1
1
1
2
0
1
2
4
2
0
1
1
2
1
0
0
0
0
1
1
0
0
0
1
1
0
0
1
0
4
2
0
1
2
2
2
1
0
1
1
1
1
0
2
1
1
1
1
1
1
1
0
2
2
1
1
1
0
2
1
1
2
1
1
0
1
2
1
2
0
1
0
1
1
0
1
2
2
1
0
0
0
2
0
2
1
1
1
3
0
4
0
2
0
1
0
1
1
2
0
1
2
2
0
1
0
1
2
0
1
1
1
1
2
0
1
2
2
2
1
2
2
1
0
1
1
1
1
2
1
0
2
1
2
1
1
1
2
0
1
2
1
0
1
0
0
1
1
1
1
1
0
0
0
2
0
1
2
2
2
0
1
1
0
1
1
2
1
1
1
2
1
0
0
1
0
1
0
1
1
2
1
0
1
0
1
1
0
0
2
1
0
1
0
1
2
2
2
0
0
1
0
1
1
1
1
0
1
1
1
1
0
1
2
0
0
1
1
2
2
0
1
0
1
1
1
2
0
3
0
1
2
0
1
0
1
0
1
2
3
1
0
0
0
2
0
2
2
2
0
1
0
2
1
0
1
1
0
1
0
1
3
0
1
2
0
0
1
0
1
0
0
0
1
1
1
2
0
1
2
0
1
1
0
1
2
1
0
2
0
0
0
3
1
0
0
0
1
1
1
1
2
1
2
2
1
0
0
1
1
0
1
1
2
1
1
1
1
1
2
0
1
1
1
0
2
0
1
1
0
0
0
1
0
1
1
1
0
1
1
1
1
0
1
1
1
1
2
1
1
1
0
0
0
0
1
1
0
1
1
0
0
1
0
0
1
1
1
1
0
2
1
1
1
1
2
0
1
1
0
1
2
1
0
1
1
0
1
1
1
1
1
2
0
1
0
1
0
1
1
1
0
2
4
0
0
2
0
2
1
0
2
2
2
1
0
0
0
3
1
2
0
0
1
1
1
1
0
1
0
0
1
1
1
0
1
1
1
1
2
1
2
0
1
2
0
1
0
0
0
2
1
1
1
1
2
0
3
0
1
1
2
1
1
1
2
2
1
1
1
0
0
0
1
0
1
0
1
1
1
0
1
0
1
0
0
0
2
0
0
1
1
1
0
2
1
2
2
0
1
1
1
0
2
2
0
2
0
0
1
1
1
0
0
2
0
1
1
0
1
1
2
0
0
1
3
1
2
1
0
0
1
1
1
1
2
2
0
1
1
0
1
0
0
2
1
2
1
1
0
2
0
1
2
1
1
0
0
1
1
1
2
2
0
3
1
0
2
0
0
1
1
0
2
1
0
2
1
1
2
2
0
0
0
0
0
0
1
0
1
1
2
3
1
2
0
2
1
0
1
0
1
2
0
2
1
1
2
0
0
0
1
1
1
0
0
0
1
0
1
1
1
0
1
0
1
2
2
1
2
1
1
2
0
1
1
1
1
0
0
1
2
0
1
1
2
2
0
1
1
0
0
1
1
2
0
0
0
1
1
1
1
1
1
1
1
2
1
2
0
2
1
2
0
1
1
1
1
2
0
1
1
0
2
0
2
1
0
1
1
0
1
1
0
2
1
1
1
1
1
1
0
2
2
1
1
1
0
1
0
1
0
2
1
1
1
0
0
1
0
1
0
1
4
2
1
1
1
1
2
1
1
0
1
0
0
1
1
1
0
1
1
2
0
2
0
1
2
2
1
0
1
1
1
1
0
0
0
0
1
1
1
1
1
0
2
1
1
0
1
2
1
2
2
1
1
2
1
2
1
1
0
1
0
2
0
0
0
1
1
2
1
1
0
1
1
0
2
0
0
1
1
0
0
1
1
1
0
1
1
1
2
1
1
1
1
0
1
1
1
2
0
1
2
1
2
2
1
1
0
1
2
1
3
2
2
1
1
2
1
1
0
1
1
1
0
1
1
1
1
1
1
2
2
0
0
1
1
0
1
2
1
1
1
1
0
1
1
1
2
1
0
2
0
1
2
1
1
0
1
0
1
1
0
1
0
1
0
1
0
1
1
0
1
2
1
1
0
2
0
1
0
1
1
1
2
0
1
1
2
0
1
0
0
0
2
1
2
1
2
1
0
1
0
1
1
0
1
0
1
4
0
0
0
1
1
1
1
0
1
1
0
1
1
2
2
2
1
0
1
0
1
2
1
1
2
2
1
1
2
2
1
1
0
0
1
3
2
6
0
1
1
1
1
2
1
2
2
0
1
1
1
0
1
2
1
1
0
1
0
1
2
0
1
1
1
2
1
0
1
1
0
0
2
1
1
1
1
2
1
2
0
0
0
0
1
0
0
2
1
2
1
1
0
1
0
0
1
0
0
2
1
0
2
1
0
1
0
1
1
0
1
1
2
1
2
2
1
1
0
1
0
1
2
3
0
0
2
1
0
0
0
1
1
1
1
1
1
2
2
3
3
1
0
0
2
1
1
2
1
1
1
0
0
2
2
1
1
2
1
1
2
1
0
2
0
1
1
1
1
1
0
1
1
1
0
0
2
0
1
1
2
2
0
0
0
1
0
0
1
1
1
1
1
1
0
2
1
1
1
0
1
0
0
0
0
0
0
0
1
2
1
1
1
2
1
0
0
0
0
1
1
2
1
2
0
2
1
0
1
0
1
1
0
1
2
1
1
1
0
1
0
1
2
0
1
1
0
1
1
1
5
0
1
0
0
2
1
2
2
0
1
2
2
0
1
0
1
2
1
3
1
0
1
3
1
0
1
1
0
2
0
1
1
1
1
2
1
1
1
2
1
1
1
0
2
0
1
1
1
1
1
2
1
0
2
1
1
1
3
2
1
1
0
2
1
1
0
1
0
1
1
2
1
2
1
0
0
1
0
1
1
1
0
0
1
1
0
0
0
0
1
1
1
0
1
1
0
0
0
1
1
1
1
0
1
0
3
1
1
1
1
2
1
0
1
1
0
2
0
1
2
2
1
1
2
0
0
1
1
1
2
0
0
2
1
1
1
2
2
2
2
2
0
1
1
1
1
1
2
1
2
0
2
0
0
1
1
2
0
1
0
2
2
2
0
0
0
0
0
2
1
2
0
0
1
1
2
2
1
1
0
1
1
1
0
0
1
1
1
2
2
1
2
2
1
1
0
1
0
2
1
0
1
0
0
1
0
1
0
1
2
0
1
2
1
1
1
0
1
2
1
0
2
0
0
2
1
1
1
2
1
0
2
1
1
2
0
0
1
1
1
1
2
0
0
0
0
0
1
1
1
0
1
2
0
1
1
2
1
2
2
1
1
1
1
1
0
1
2
0
0
1
1
2
0
1
1
2
2
2
2
2
2
1
0
0
0
1
1
0
0
0
2
3
2
1
0
0
1
1
2
3
1
1
1
1
1
0
1
1
1
1
1
1
1
1
0
0
1
2
1
0
1
0
1
3
1
3
1
0
0
1
2
0
2
1
0
1
0
0
1
1
1
1
1
0
2
0
1
1
1
2
1
1
1
2
0
1
2
0
0
0
0
1
0
2
1
2
1
2
2
0
3
1
1
2
1
1
0
1
0
0
1
1
2
4
1
2
0
0
1
0
2
1
2
1
1
1
1
0
1
0
0
1
1
1
0
0
0
1
2
1
0
2
1
1
1
1
1
1
2
1
2
0
0
1
1
1
1
1
0
1
1
0
0
1
0
1
1
3
1
1
1
1
0
1
1
1
3
1
1
1
1
1
1
0
2
0
1
0
2
0
0
0
1
2
2
0
2
3
2
0
1
1
1
0
1
0
0
1
2
1
1
0
0
2
2
3
1
2
1
1
0
0
0
2
2
2
1
0
0
0
1
1
1
1
1
0
2
0
0
2
0
1
1
1
2
0
2
1
2
0
1
1
1
1
0
0
0
0
1
0
1
1
1
0
1
2
1
0
1
1
1
1
1
1
2
0
1
1
2
0
2
1
0
1
1
0
1
3
1
1
1
0
0
1
1
2
1
1
1
2
1
1
0
1
0
2
2
1
1
2
0
1
1
1
1
0
1
1
1
1
2
1
0
0
0
1
2
1
0
1
0
1
1
1
0
0
2
1
1
1
2
2
1
2
2
1
1
2
1
2
1
1
2
1
1
1
0
1
0
1
0
0
1
1
1
1
1
0
1
0
2
0
1
0
2
2
0
1
0
2
2
1
2
1
0
2
3
2
2
1
0
1
1
1
1
1
1
0
0
1
1
2
1
2
2
0
0
2
1
1
0
2
1
2
0
0
2
1
1
1
2
1
1
0
1
1
0
1
1
0
1
2
2
0
2
1
1
1
1
0
1
0
1
1
0
2
2
0
1
3
1
1
1
1
3
0
0
2
1
0
1
2
0
2
1
1
0
2
1
2
1
1
0
2
1
1
0
2
1
0
0
0
0
2
0
2
1
0
2
0
1
0
2
0
0
0
0
0
0
1
2
1
1
1
0
1
1
0
1
0
0
0
2
1
1
3
2
2
2
1
2
1
0
1
0
1
2
1
2
2
2
1
1
2
0
0
0
1
0
1
1
0
2
1
1
1
1
1
0
2
1
1
0
0
2
0
2
1
1
0
0
2
1
0
0
1
1
0
0
1
2
0
0
2
1
0
1
1
1
0
1
2
1
1
0
1
2
0
1
1
1
1
0
1
1
0
0
2
2
1
0
0
1
0
0
2
1
2
2
1
0
0
0
1
1
0
1
0
1
1
0
0
2
0
0
1
0
0
1
2
0
1
1
1
1
0
0
0
3
1
1
0
0
0
1
0
1
1
1
0
1
1
1
1
1
2
1
1
1
1
1
1
1
0
1
0
0
2
1
0
2
2
1
4
1
1
0
2
2
1
1
1
1
2
1
0
1
2
0
1
1
1
1
1
0
1
2
2
1
1
1
1
2
0
0
0
1
1
0
0
1
2
1
2
1
1
1
2
2
1
1
2
1
1
1
0
1
0
2
1
0
0
1
3
1
1
1
1
1
1
0
2
0
0
1
0
1
1
2
2
0
0
1
1
1
0
0
0
2
1
0
1
2
1
0
2
2
1
0
0
2
1
0
1
0
1
1
0
0
2
2
2
0
1
1
1
1
2
0
0
2
1
2
0
1
2
2
2
0
1
0
0
2
1
1
1
1
2
0
1
2
1
1
1
1
2
5
1
1
1
0
1
1
0
1
0
0
0
2
1
0
0
1
1
1
0
2
2
0
0
1
1
1
1
1
1
0
0
1
0
1
1
1
1
0
0
0
1
1
1
2
1
1
2
1
0
2
1
1
1
2
1
0
1
1
1
1
2
1
1
1
0
1
0
1
1
0
1
1
0
1
1
1
0
0
1
0
0
0
1
1
1
1
1
0
1
1
1
1
1
2
1
0
1
1
2
0
0
1
1
2
2
2
1
1
1
1
1
1
1
2
1
1
1
6
1
2
0
0
0
1
0
0
2
1
0
1
0
0
0
2
2
2
1
0
1
0
2
2
2
0
1
2
0
0
1
2
1
1
2
0
1
2
4
1
1
0
1
0
1
1
2
1
2
1
1
0
0
0
1
1
0
1
0
1
1
2
0
0
0
1
2
1
1
1
1
1
0
0
1
3
0
0
0
1
1
2
1
2
1
1
1
0
1
0
0
1
0
2
2
2
0
0
1
0
1
2
0
1
2
2
1
0
1
1
2
2
1
2
0
0
1
0
1
1
2
0
2
1
2
0
2
0
1
1
1
1
1
0
0
2
0
2
1
1
0
1
0
1
0
0
0
2
2
2
0
3
1
1
1
1
1
1
2
0
1
0
0
0
0
1
1
1
0
0
1
1
0
1
0
2
1
0
2
1
1
0
1
0
0
1
1
1
2
1
0
2
1
2
1
0
1
0
0
1
1
0
2
0
1
1
2
0
1
1
1
0
2
1
1
1
0
1
2
1
1
1
1
2
2
0
2
2
1
0
1
0
0
1
1
0
0
1
1
1
2
0
2
1
3
1
2
1
1
2
0
1
0
2
0
1
2
0
0
1
1
0
1
1
2
2
1
1
1
0
1
0
1
0
1
1
2
0
2
0
0
1
1
1
1
0
0
3
0
0
1
2
2
2
1
0
0
1
1
1
1
1
1
1
0
1
1
1
2
1
0
1
1
0
0
2
1
1
1
1
1
1
0
1
2
2
2
2
2
2
0
0
1
0
1
2
0
0
1
0
3
0
0
0
1
0
1
1
2
1
0
0
2
2
1
0
2
0
1
0
2
1
2
2
2
0
0
1
1
1
2
0
0
1
2
1
1
1
1
2
1
2
0
2
0
1
1
0
1
1
1
1
1
2
0
1
1
0
1
1
1
3
1
1
1
0
1
0
1
1
2
1
0
2
1
1
1
0
1
2
0
1
1
0
2
1
1
2
0
1
1
0
1
1
1
1
1
1
1
0
2
1
0
1
1
1
1
1
0
0
2
1
0
1
1
2
1
2
0
0
2
1
0
1
0
1
1
0
1
1
0
2
2
1
0
0
1
1
2
2
1
1
1
1
3
0
1
2
2
1
0
1
1
1
1
2
1
1
1
0
2
2
0
1
1
1
1
1
2
0
1
1
1
1
1
0
2
1
8
1
0
1
1
0
3
1
0
1
0
1
0
2
2
1
1
0
2
0
1
0
0
0
2
0
3
1
1
1
1
1
2
1
0
2
1
2
0
1
1
0
0
0
2
2
0
2
0
0
2
0
1
0
1
1
2
2
2
1
2
0
1
0
1
0
2
1
1
0
0
2
1
0
0
1
1
1
1
0
2
1
1
1
1
1
0
1
1
0
1
1
2
1
1
0
1
0
0
0
1
0
1
1
1
1
1
1
0
1
1
2
2
2
1
0
1
0
1
1
1
0
1
1
1
1
1
0
0
1
1
1
1
0
1
1
0
2
2
2
0
1
0
2
2
1
1
2
1
0
0
0
2
0
1
1
1
1
2
0
1
2
1
1
1
1
1
1
2
2
1
1
2
1
0
1
1
1
1
1
1
1
0
1
1
0
0
2
0
1
0
1
0
0
1
1
2
1
0
1
2
1
2
0
1
0
2
0
0
1
1
1
0
0
1
2
0
0
1
0
2
0
0
1
0
0
1
0
1
1
1
3
1
1
0
2
2
1
0
2
1
0
2
1
2
0
1
2
1
0
2
1
2
1
1
1
0
2
0
4
0
0
1
0
3
4
1
2
1
1
0
0
1
1
1
2
0
1
1
0
0
1
0
1
2
1
0
3
0
2
1
0
1
1
1
2
2
0
1
1
0
0
1
2
0
0
1
1
1
0
1
2
1
1
0
0
0
2
0
0
1
1
1
1
0
0
1
1
2
1
3
0
1
1
1
4
1
1
1
1
1
0
3
2
2
0
2
1
1
1
1
1
2
1
1
2
1
0
0
1
0
0
0
1
1
0
2
1
1
2
2
1
0
0
1
1
1
2
1
1
1
2
1
1
2
2
0
2
0
0
1
2
1
2
0
2
2
0
0
2
2
0
1
1
0
1
1
1
1
1
1
0
0
1
1
0
0
2
1
0
1
3
1
2
0
1
2
2
0
0
2
1
0
1
1
0
0
1
0
2
1
1
1
1
0
1
2
2
1
1
0
0
1
1
1
2
1
0
0
1
1
1
4
1
0
1
2
0
2
2
2
2
0
1
2
0
1
0
0
0
1
2
1
0
4
1
1
0
1
1
2
2
1
2
0
1
1
1
1
0
1
2
1
1
0
1
1
0
4
0
1
0
1
0
1
2
0
2
0
1
1
0
2
2
1
1
2
2
0
1
1
0
2
2
1
0
1
1
1
0
2
2
0
2
1
2
0
1
1
0
2
0
0
1
2
1
0
1
0
0
1
1
1
2
1
2
0
2
1
1
0
1
2
1
0
0
2
1
1
2
0
0
1
2
1
0
0
1
2
1
0
2
0
2
2
1
0
1
2
0
0
1
1
0
1
3
1
1
1
1
1
2
1
2
2
0
1
1
2
0
0
1
2
1
1
1
1
0
2
2
1
1
1
2
0
1
0
0
1
2
1
1
1
1
0
2
1
0
1
0
1
2
1
2
0
0
0
2
1
2
1
1
1
0
0
1
1
1
1
0
2
1
0
1
0
1
0
1
1
1
0
1
2
2
1
0
1
0
1
0
0
1
1
1
0
0
0
1
2
1
1
1
1
0
1
1
1
0
0
2
1
0
1
0
2
1
1
0
0
2
1
1
1
2
0
1
1
0
1
0
0
1
1
1
1
0
2
1
1
0
2
0
1
1
1
2
2
1
1
0
1
1
0
0
1
1
1
1
1
2
3
1
1
2
2
2
1
0
2
0
2
2
0
0
2
1
1
0
1
1
2
0
1
1
1
2
1
2
1
1
0
0
0
0
1
0
2
0
1
2
0
0
0
1
1
1
2
1
1
0
0
1
1
2
1
1
1
1
0
0
1
1
1
1
1
1
0
1
2
1
1
2
0
0
1
0
1
1
0
1
1
0
2
2
1
0
2
0
0
0
0
0
0
0
1
1
0
2
2
1
1
0
2
1
1
2
1
2
0
2
0
0
1
0
1
0
0
0
1
2
0
2
1
0
0
1
1
2
1
2
1
0
0
1
1
1
0
1
0
2
3
1
1
1
5
0
1
2
1
1
1
0
0
1
0
0
1
2
2
1
0
1
2
3
2
1
2
2
2
1
0
1
1
2
1
0
2
1
1
0
1
0
2
1
2
1
2
0
1
1
0
0
0
2
0
0
1
2
0
1
0
1
0
1
0
0
0
0
0
1
2
1
1
2
0
1
1
2
0
1
3
1
1
1
0
0
1
1
2
1
2
0
2
1
1
2
1
2
2
0
1
1
0
1
1
0
2
2
1
1
2
0
0
1
1
1
0
1
0
1
0
1
1
1
1
0
2
1
1
1
0
2
0
0
0
0
0
0
0
1
0
0
1
2
0
1
0
0
0
1
1
0
0
1
1
1
0
0
0
1
1
1
1
0
0
1
1
1
1
1
1
0
0
1
1
0
1
2
1
1
0
1
0
1
1
0
2
1
1
1
0
1
2
1
1
3
0
1
0
0
0
1
3
1
0
0
1
0
2
2
1
1
1
1
1
1
1
0
1
1
0
0
1
1
2
0
1
1
0
3
0
1
1
2
2
0
2
1
1
0
2
1
1
2
0
0
0
1
0
2
2
0
0
1
1
1
1
0
0
1
1
1
1
1
1
1
0
1
0
0
1
1
0
2
0
1
0
1
1
1
1
0
1
1
1
3
2
1
3
1
1
2
0
0
0
1
0
2
0
1
1
1
1
1
1
2
1
2
0
1
0
2
2
0
1
1
1
1
1
0
1
2
1
1
2
0
1
2
1
2
0
1
2
2
1
1
1
0
1
0
2
1
0
1
0
1
2
1
1
0
0
1
1
1
1
1
1
2
1
2
1
0
1
0
0
1
1
1
1
1
1
1
1
1
1
1
0
1
0
3
1
0
1
1
2
0
1
1
2
2
2
1
0
2
1
2
1
1
2
1
0
0
1
0
1
2
0
0
0
0
2
1
0
1
0
0
0
1
0
0
2
0
2
0
2
1
1
1
1
2
0
1
2
2
2
1
1
2
0
0
0
1
0
2
1
0
0
1
4
1
1
1
1
0
0
1
1
1
2
0
1
2
2
1
0
2
1
1
1
1
0
2
1
2
1
1
2
1
1
2
2
1
0
1
1
2
0
0
1
1
2
1
1
1
0
1
0
0
0
0
2
1
1
0
1
2
1
0
0
2
1
2
2
0
1
0
0
0
0
1
1
2
0
1
0
2
1
0
2
0
1
1
0
1
0
1
2
2
0
1
1
2
1
2
0
1
0
2
2
1
1
2
2
1
0
0
1
2
2
1
1
2
0
0
2
0
1
1
2
0
1
1
1
0
1
2
1
0
1
2
1
0
2
2
2
0
2
1
2
1
2
1
1
0
1
0
0
0
1
1
0
2
1
0
0
0
0
2
1
0
0
2
1
2
1
1
1
0
1
0
1
1
1
0
0
1
1
1
1
1
0
1
1
0
2
1
0
1
0
2
1
0
2
0
0
1
0
0
2
2
0
0
0
1
0
0
1
2
0
1
2
1
1
1
1
1
1
0
0
1
0
1
0
0
2
1
2
0
1
1
1
0
0
0
0
2
0
0
1
0
2
0
1
1
1
0
1
1
0
1
0
1
0
1
0
2
0
2
0
2
1
1
1
1
1
2
0
1
2
2
0
3
0
0
0
0
0
0
1
0
2
1
1
2
0
0
0
1
2
1
1
1
0
2
2
1
0
1
3
0
2
1
1
2
0
1
1
1
1
2
0
2
2
2
1
0
1
1
2
0
0
1
3
0
0
2
0
2
1
1
1
0
0
0
2
1
1
0
1
1
1
2
1
1
2
1
1
2
0
1
0
1
2
0
1
0
1
0
4
1
2
1
1
0
2
1
1
2
2
3
0
1
1
0
1
2
1
2
1
2
0
0
0
0
1
0
0
2
2
1
1
0
1
0
1
3
1
1
1
1
1
2
2
0
2
1
0
1
2
1
1
1
0
2
0
2
1
2
2
2
2
0
1
1
1
1
1
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
1
2
1
2
2
1
1
2
1
0
1
0
0
2
1
1
1
1
0
1
0
1
0
0
0
2
1
1
1
1
0
1
1
1
0
1
1
0
0
1
1
1
1
1
1
1
1
2
0
2
1
1
0
1
0
1
2
0
2
0
0
1
9
0
1
2
1
1
0
2
0
0
2
1
1
0
2
0
0
0
2
0
2
1
2
1
2
1
1
2
2
1
2
1
0
1
0
0
0
0
1
2
1
0
2
0
2
1
0
2
1
1
0
1
1
1
1
1
1
0
2
3
0
2
3
0
0
1
2
2
1
0
0
1
1
0
0
0
0
1
2
1
1
0
1
0
2
1
2
1
0
2
1
2
1
2
0
1
1
0
1
0
1
2
2
1
0
1
0
2
1
0
1
1
2
0
0
2
1
0
2
1
1
2
0
0
1
0
2
2
0
2
0
0
2
2
1
1
2
2
1
0
1
0
1
0
1
1
0
0
1
2
1
1
1
0
0
1
0
1
1
2
0
0
0
1
1
0
1
2
1
1
0
1
1
1
1
2
0
1
0
2
0
0
2
2
1
1
1
1
0
2
2
1
2
1
1
2
1
2
0
1
0
0
0
0
0
0
1
1
1
1
2
0
1
1
0
0
0
2
1
2
1
2
2
0
2
0
1
1
1
0
2
2
1
1
0
2
0
0
1
0
1
1
2
0
1
2
1
0
2
0
0
2
2
0
0
1
1
0
2
0
0
1
0
1
0
1
1
1
2
0
1
2
0
0
0
0
1
1
0
0
0
1
1
1
1
1
1
0
2
0
1
2
2
1
0
1
0
0
0
0
0
1
1
2
0
0
0
1
1
1
0
1
1
1
1
0
1
1
1
1
0
0
2
1
1
2
1
2
1
2
1
0
0
1
0
1
0
1
0
2
0
0
0
1
0
1
0
2
1
2
0
2
1
1
0
1
1
2
0
1
1
2
1
0
1
0
0
1
0
1
0
1
1
1
3
1
1
1
0
0
0
1
0
1
1
2
4
1
0
1
1
1
0
1
1
0
1
2
0
1
1
0
0
1
0
1
1
0
2
1
0
0
1
1
2
1
2
1
1
1
0
1
1
1
0
1
0
1
0
1
1
0
3
2
1
1
1
1
2
1
1
1
0
0
1
1
0
1
1
0
1
1
1
1
1
2
0
2
0
0
0
2
0
1
1
1
1
0
0
1
1
2
1
0
1
0
0
1
2
0
1
0
0
1
0
3
2
0
2
1
1
2
1
1
1
1
1
1
1
1
0
1
1
1
1
0
0
2
2
1
2
2
1
1
0
1
1
0
1
1
1
1
0
0
1
1
0
0
1
1
1
2
1
1
1
0
0
2
1
2
1
0
0
3
1
0
1
1
1
2
2
1
2
1
1
0
2
1
1
0
2
1
2
3
2
1
0
2
1
1
0
2
1
0
0
1
1
0
4
1
1
1
1
1
2
3
0
1
1
0
3
0
2
1
0
0
0
2
2
0
1
1
1
1
2
0
1
1
0
1
2
0
1
2
2
3
0
1
1
2
0
0
0
1
2
2
1
2
1
1
0
1
1
1
0
0
1
0
1
0
0
1
2
0
0
0
1
1
2
1
1
2
1
0
1
2
1
0
0
0
1
1
2
0
1
0
1
1
1
1
2
0
1
2
0
1
1
1
1
1
1
1
0
1
2
1
2
0
1
1
0
0
1
2
0
1
2
1
1
1
1
1
1
0
1
1
2
0
0
0
1
0
1
1
1
0
1
0
0
1
1
1
1
0
2
1
2
2
1
1
1
1
1
2
0
1
1
2
2
0
1
3
0
0
2
1
2
2
2
1
0
1
1
1
2
1
1
0
1
1
0
1
1
0
1
1
2
2
1
2
0
0
2
2
1
1
1
2
1
1
1
0
0
2
1
1
2
0
1
2
1
1
0
1
0
1
1
1
0
0
0
0
0
1
3
2
0
1
0
3
1
1
1
1
2
3
2
0
0
0
1
1
1
1
1
1
0
2
1
0
1
1
0
2
1
1
0
1
2
1
2
1
3
1
1
1
2
1
0
0
0
0
1
2
0
1
1
1
0
1
2
1
0
1
1
0
0
2
1
1
1
0
0
1
7
1
2
2
2
2
1
1
0
0
1
0
2
1
0
0
2
1
2
1
0
0
2
0
0
0
0
1
0
2
2
1
0
2
1
2
0
3
0
1
1
1
0
1
1
3
1
1
0
0
1
0
1
1
2
0
2
0
1
0
1
0
0
2
0
2
0
0
1
1
1
0
1
0
0
1
0
1
0
2
0
2
1
1
1
7
1
0
1
1
1
1
0
0
0
1
6
1
0
0
10
0
0
0
1
0
0
0
1
1
0
1
0
2
1
2
0
1
0
0
1
0
0
1
1
0
1
0
0
1
1
2
1
2
1
1
1
0
1
0
0
1
2
0
1
3
2
1
1
0
0
2
1
2
0
2
2
1
1
0
1
0
0
2
1
2
1
0
0
1
0
1
1
2
0
2
0
0
2
0
1
1
0
0
0
0
2
0
1
1
0
1
1
2
1
1
3
1
2
1
1
2
2
0
2
2
1
0
0
1
0
2
3
3
1
1
1
1
0
0
2
1
0
2
1
2
0
1
1
0
2
0
2
2
1
1
0
0
1
0
1
1
0
0
1
1
2
2
1
1
0
0
1
0
1
1
0
0
0
1
0
1
0
0
0
0
2
2
2
1
1
1
4
1
2
1
2
1
1
2
0
1
1
0
3
2
1
1
1
1
0
0
0
1
1
0
2
1
1
1
0
2
0
2
2
0
1
1
2
0
1
0
1
2
2
0
0
0
2
4
0
1
1
1
2
0
0
1
1
2
0
1
2
1
1
1
1
1
1
2
0
1
1
2
1
1
1
2
1
3
1
2
0
0
1
0
0
1
2
2
2
0
1
0
0
0
1
0
1
2
0
0
1
0
2
1
2
0
1
0
1
0
3
0
0
1
0
1
1
1
0
1
1
1
0
1
2
0
1
1
0
2
2
1
2
1
1
1
2
2
2
2
1
1
0
1
1
1
0
1
2
2
1
1
0
1
1
1
0
1
1
1
1
1
2
1
2
2
1
1
1
1
2
2
2
1
1
1
0
2
0
2
2
2
2
1
0
2
1
1
0
2
0
1
0
0
0
1
1
2
1
0
2
0
2
1
0
0
1
0
0
2
1
2
1
0
0
1
2
1
2
0
2
0
0
1
1
0
0
2
0
2
0
4
1
0
1
1
2
1
2
1
1
0
2
0
0
1
1
2
1
1
0
1
0
1
0
2
1
1
0
1
1
1
1
1
1
1
0
1
2
2
1
1
1
2
3
1
0
2
2
1
0
1
0
0
0
0
2
0
0
1
1
1
0
1
1
2
2
1
0
0
0
1
1
2
1
0
0
1
2
1
1
1
0
1
0
2
0
0
1
1
0
1
1
0
1
1
0
2
1
0
1
1
0
1
2
2
2
1
0
1
1
1
0
1
0
1
1
2
0
1
1
0
1
1
0
2
1
1
1
1
1
1
1
2
1
1
0
1
2
2
2
1
0
0
0
1
0
2
1
2
1
2
1
0
1
1
1
0
2
1
2
0
3
2
2
1
0
1
2
0
1
0
0
1
0
0
0
1
0
0
2
1
1
0
1
0
2
1
0
1
0
2
0
0
3
0
1
1
0
2
0
1
1
0
0
2
2
0
1
1
0
0
1
1
2
1
1
1
2
1
1
1
0
2
2
1
0
0
0
2
0
2
1
1
0
1
2
0
1
1
2
1
1
0
1
5
0
0
2
2
1
1
2
0
2
2
2
0
1
0
0
1
1
2
0
1
0
1
1
2
1
2
0
1
1
1
2
0
1
1
2
2
1
1
2
1
2
2
2
1
1
0
0
0
0
2
1
1
1
1
1
1
1
2
2
1
0
1
4
0
1
0
1
1
1
1
2
1
0
2
1
0
1
0
0
1
2
2
3
0
2
0
1
2
1
1
1
2
2
2
0
1
1
1
3
2
1
1
1
1
2
0
0
0
2
0
1
0
1
1
0
1
1
1
1
2
0
0
0
1
0
2
1
0
1
1
0
1
1
2
0
0
1
1
2
1
2
0
0
0
1
1
2
0
2
0
1
0
2
1
1
1
1
1
1
2
2
1
1
0
0
0
0
2
0
1
2
0
1
1
1
1
1
0
0
1
0
1
0
1
1
1
1
1
0
1
0
2
2
0
1
1
1
1
1
1
0
2
2
0
1
0
1
1
0
1
1
1
1
1
0
2
0
1
1
1
0
2
0
1
0
0
0
2
0
1
1
1
2
0
1
0
1
0
2
2
1
0
0
1
4
0
2
2
1
0
1
1
2
0
0
0
1
0
0
1
1
1
0
1
0
1
0
2
2
1
1
0
1
0
1
1
0
1
1
0
1
1
1
2
0
2
1
1
1
2
0
1
1
0
0
2
0
1
0
1
2
1
0
0
0
2
1
2
0
1
1
0
1
0
1
2
1
1
1
0
1
2
1
1
0
1
1
2
0
2
0
0
2
0
0
1
1
0
0
1
0
2
1
1
2
1
2
2
1
1
1
0
0
1
2
0
1
1
1
0
1
0
0
1
2
2
1
1
2
0
1
0
1
1
0
2
0
0
1
1
0
1
2
1
1
1
0
1
2
1
1
0
1
1
0
1
0
0
2
1
0
1
1
1
2
2
0
2
0
1
0
0
1
1
1
1
0
1
1
0
1
1
2
0
1
1
2
1
1
2
0
3
1
1
1
0
1
0
0
1
1
0
1
1
2
0
1
0
2
2
2
0
1
0
1
1
0
0
1
0
0
1
1
3
0
1
0
0
1
1
1
1
1
0
1
2
2
1
1
1
1
0
0
2
1
2
2
2
0
0
0
1
2
0
2
0
1
1
2
2
2
0
1
1
0
0
1
2
1
0
1
1
1
0
1
0
0
2
1
1
1
1
0
1
1
1
0
0
0
1
1
1
0
1
0
1
0
0
1
1
1
0
1
1
0
1
1
1
2
1
0
0
0
1
0
1
1
1
2
0
0
1
2
1
0
0
0
1
0
1
4
0
0
0
0
1
0
1
0
0
1
1
0
1
1
2
0
0
0
1
2
3
1
0
1
1
1
0
0
2
0
1
0
1
0
0
1
1
2
1
0
1
1
3
1
0
0
2
1
1
1
0
1
1
0
1
1
0
1
1
0
1
1
2
2
0
2
1
1
2
0
1
0
1
1
1
1
0
2
1
1
2
1
1
0
1
1
0
0
2
0
1
2
0
0
1
0
0
0
2
1
1
1
1
1
1
2
2
1
1
0
0
1
0
0
1
1
1
1
3
1
0
1
1
0
1
0
1
2
1
0
1
2
0
0
0
1
0
2
0
2
1
1
2
0
1
2
0
0
2
1
0
1
0
1
1
1
1
1
0
1
0
1
2
2
1
2
1
2
2
1
1
2
2
0
1
1
2
1
2
1
1
1
1
1
2
0
2
2
2
1
1
0
0
1
0
0
0
1
1
1
1
1
1
1
1
0
1
1
2
1
1
1
1
0
2
2
2
0
0
1
0
1
1
0
1
1
1
0
1
0
0
0
1
2
1
1
1
0
1
1
2
2
1
0
1
0
0
1
0
2
0
1
2
2
2
1
0
1
2
1
2
1
2
1
2
0
3
1
0
0
0
0
0
0
1
1
0
1
1
1
0
0
1
2
2
2
0
1
2
1
1
1
1
0
1
0
2
0
2
0
0
1
1
2
0
1
0
0
0
1
0
0
1
1
2
0
1
1
1
0
0
0
2
0
2
0
0
0
2
3
2
2
0
1
1
0
1
0
0
2
2
1
0
2
0
0
2
2
0
1
1
1
1
2
1
1
1
4
1
0
1
1
2
1
0
0
2
0
2
0
1
1
1
1
1
1
2
1
1
2
1
1
2
1
1
0
0
1
1
1
0
1
0
1
2
2
1
1
2
0
2
0
0
1
0
1
0
0
0
2
1
2
0
2
2
0
1
1
1
2
1
0
1
6
0
0
1
0
1
2
2
2
0
1
2
2
1
2
2
1
1
1
1
2
0
2
2
0
0
1
1
2
0
1
1
1
1
1
0
1
1
1
0
1
1
0
1
1
0
0
2
0
0
1
0
1
0
1
0
1
3
1
0
0
1
1
1
0
2
1
1
0
0
2
1
0
1
1
0
2
4
1
1
1
0
1
0
0
1
2
1
0
1
1
0
2
1
2
2
1
0
0
1
1
0
0
1
1
1
1
1
0
2
1
1
0
1
1
0
2
0
3
1
2
1
1
0
0
0
2
2
1
1
1
2
0
2
1
1
1
1
0
1
1
1
1
1
2
3
1
1
0
0
1
0
2
0
1
1
1
1
1
1
2
2
0
1
1
1
2
1
1
0
1
2
1
0
2
1
1
1
1
0
0
0
0
0
1
0
2
1
1
1
0
0
1
1
1
0
1
1
0
1
1
0
2
2
0
0
2
2
1
1
1
1
1
1
0
1
1
1
0
0
2
5
2
1
1
2
2
2
0
1
2
1
1
0
0
1
2
2
2
2
1
1
1
0
1
2
1
1
1
1
0
2
0
1
0
1
1
0
1
2
1
1
2
1
1
1
1
2
1
0
1
1
0
2
1
0
1
3
0
1
1
2
1
0
0
1
0
0
2
1
1
1
2
1
0
2
0
1
2
0
0
0
2
1
0
2
1
1
0
2
1
1
0
0
1
1
1
1
0
0
2
1
0
0
2
0
1
1
1
1
1
1
1
1
0
2
3
0
1
1
0
1
2
1
0
0
1
1
1
0
0
0
0
0
0
1
1
1
1
2
1
0
1
1
0
2
1
1
1
0
1
1
2
0
1
0
0
0
1
1
0
2
1
0
2
1
0
2
1
1
0
0
1
1
1
2
0
1
0
1
2
1
2
1
1
2
2
1
1
0
2
1
3
0
0
0
1
1
1
0
2
1
1
1
1
0
0
1
0
2
1
1
2
1
1
1
2
1
0
0
1
1
2
1
1
0
1
2
1
0
2
1
0
2
1
1
1
0
2
1
0
2
1
1
0
1
0
1
0
1
1
2
1
0
0
0
0
0
1
1
0
1
0
1
2
1
1
0
2
1
1
0
2
2
2
1
0
1
1
1
1
0
0
1
1
1
1
2
1
2
0
1
1
1
3
2
1
1
0
1
1
1
0
1
2
1
2
0
0
0
0
1
0
1
0
0
0
1
2
1
1
1
0
1
3
2
0
1
0
2
1
0
0
0
0
0
1
1
6
0
1
1
1
0
0
2
2
1
2
0
0
1
1
1
1
0
1
1
1
1
1
1
0
0
2
1
1
1
0
1
0
1
1
0
1
2
0
1
2
0
1
2
1
2
1
0
1
2
2
3
0
0
0
1
0
1
1
1
0
1
1
1
0
0
2
1
0
1
2
2
0
1
0
1
0
1
1
1
2
0
2
1
2
0
1
2
0
0
2
1
0
1
1
3
1
0
1
0
1
2
1
0
1
0
0
0
0
2
1
0
1
1
1
2
0
1
0
2
1
1
1
2
0
1
2
1
2
1
1
2
1
1
0
1
1
0
0
0
0
0
2
1
1
0
1
1
2
2
1
1
0
1
1
1
2
1
1
1
0
2
1
1
2
1
2
1
1
0
1
0
2
0
3
2
1
2
1
2
1
2
0
1
1
2
0
0
1
2
0
2
2
1
1
0
1
0
1
2
2
2
2
0
1
0
0
0
1
2
2
0
2
0
0
1
0
0
1
2
0
2
0
2
1
1
2
0
0
0
0
2
1
1
0
2
1
0
0
1
2
1
1
1
1
1
2
2
0
1
1
0
1
0
1
0
2
2
1
1
1
1
2
0
0
0
2
1
1
2
0
1
2
1
0
0
1
1
0
2
0
2
0
0
0
0
2
1
1
2
0
1
0
2
2
1
1
1
1
1
2
0
2
1
1
2
1
0
1
1
1
1
0
1
1
1
1
1
1
2
0
1
0
2
0
2
1
0
1
1
0
2
0
1
0
1
1
1
1
0
2
1
1
1
3
0
1
0
1
1
1
1
2
2
1
0
1
1
2
1
1
1
2
0
1
0
0
1
1
1
0
1
1
1
1
1
2
3
1
0
2
0
0
0
2
1
1
1
0
1
2
1
2
0
1
1
1
0
1
0
1
2
2
0
1
0
1
2
0
0
1
0
1
1
1
0
1
2
1
2
1
1
1
1
1
4
1
0
1
1
0
1
1
0
2
0
1
0
2
1
0
0
3
0
1
1
1
0
2
1
0
2
1
0
1
2
0
1
3
3
1
0
1
0
0
1
0
2
1
1
4
1
0
1
0
0
2
1
1
1
1
1
1
1
2
1
0
0
2
0
0
0
1
2
1
1
1
1
0
1
0
0
0
1
2
0
0
0
1
1
0
1
0
2
0
1
1
0
0
2
1
1
2
0
2
1
2
2
0
1
1
0
1
2
1
1
1
2
0
1
1
2
1
0
1
1
0
0
0
1
0
1
0
0
1
0
1
2
1
1
2
0
0
2
1
1
1
0
0
1
0
2
1
4
0
0
1
0
0
2
2
0
2
2
2
2
0
1
0
0
2
2
2
2
1
1
1
0
2
2
2
3
2
1
0
2
0
1
1
2
0
0
1
0
1
1
2
1
1
1
0
0
1
2
1
1
1
1
0
1
2
0
0
1
0
1
2
2
2
0
0
1
1
0
1
1
1
0
1
1
1
0
1
2
1
1
1
0
2
0
1
2
2
1
0
0
0
0
0
0
1
2
0
1
0
0
1
0
2
2
1
2
0
1
1
1
1
1
1
2
0
0
0
0
0
1
0
1
2
0
2
2
1
1
1
1
0
1
1
2
1
1
1
1
0
1
0
1
1
0
1
0
1
0
1
1
1
1
0
1
2
1
1
1
2
2
0
0
1
0
1
0
0
2
1
2
1
0
1
2
0
0
1
1
0
0
0
1
1
1
1
2
1
2
2
2
1
1
0
1
1
1
3
1
0
1
1
1
1
0
1
1
0
2
0
1
1
0
0
1
1
1
0
1
0
1
0
1
0
1
2
3
1
1
0
0
0
1
1
0
1
0
2
2
0
1
1
1
0
1
0
1
1
0
1
2
2
0
1
0
2
1
1
1
1
2
0
0
1
0
2
3
1
0
2
0
1
0
1
1
1
2
0
0
1
1
2
1
0
0
0
0
1
1
1
1
1
1
1
0
1
0
1
0
0
2
2
1
0
1
0
0
1
0
1
1
1
0
2
0
1
1
1
1
0
0
1
1
1
2
1
1
1
2
1
1
1
1
1
0
2
2
1
2
2
1
1
1
1
0
2
2
1
0
1
1
1
1
1
1
1
0
2
0
2
3
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
1
1
1
1
1
1
1
1
0
0
1
1
0
2
0
1
1
0
0
2
1
1
1
1
2
0
0
0
1
1
2
2
2
0
1
1
1
1
3
0
2
0
0
2
0
1
0
2
2
0
2
1
0
1
1
1
1
1
0
2
1
1
1
2
2
0
0
1
1
0
1
0
2
2
1
0
2
1
1
0
1
1
0
2
2
1
2
1
1
1
1
1
0
1
1
1
2
3
1
2
1
1
0
2
1
1
0
0
1
1
1
1
1
1
2
1
1
0
1
0
2
1
0
0
1
0
0
1
2
2
2
1
0
1
1
0
2
1
1
1
1
1
0
1
1
2
0
1
0
1
0
1
1
2
1
1
1
1
2
0
1
1
1
0
0
1
1
1
0
1
1
0
2
0
2
1
1
0
2
1
0
1
2
1
1
0
0
1
1
1
2
0
0
0
1
0
2
0
1
0
1
1
0
1
1
1
1
1
1
1
1
1
1
2
1
2
1
0
1
1
2
0
0
1
0
1
0
1
1
2
1
0
0
1
1
1
0
1
0
1
1
1
1
0
2
0
0
1
1
1
2
1
1
0
2
2
2
1
0
2
2
2
0
0
1
2
2
1
0
2
2
0
0
0
0
1
0
0
0
1
1
2
2
0
0
2
1
0
1
1
2
0
0
2
1
0
0
2
2
2
1
1
0
2
0
2
2
1
1
1
2
1
1
0
2
1
1
1
1
2
0
0
2
2
1
1
0
1
2
0
1
0
2
2
1
1
1
2
2
1
1
1
0
1
1
1
1
2
1
0
0
2
0
0
1
1
2
1
1
1
0
1
1
0
1
1
1
0
2
1
2
1
2
1
0
1
0
1
0
1
0
3
0
1
1
0
2
2
0
2
2
0
0
1
2
2
0
0
2
2
0
0
2
2
2
2
2
1
1
1
0
1
0
0
0
1
3
2
1
1
0
2
0
0
2
2
1
1
0
2
0
1
0
1
0
1
1
1
1
0
0
1
0
1
1
0
1
0
1
2
1
1
1
2
2
1
1
2
0
1
0
1
1
0
1
0
1
2
1
2
1
2
2
1
0
1
2
1
0
1
1
1
1
1
0
2
2
1
1
1
1
0
0
1
0
2
1
2
2
1
1
0
1
1
1
0
0
1
1
6
0
0
2
1
1
1
0
0
1
1
1
0
2
0
0
0
2
0
0
1
0
1
2
1
1
1
1
2
1
1
1
0
2
1
2
2
2
0
1
1
2
0
1
1
1
1
1
0
0
0
1
2
1
1
1
0
0
1
1
0
1
0
0
1
1
1
0
1
1
1
1
1
2
1
1
1
1
0
1
0
1
2
1
2
1
1
0
1
1
1
2
2
2
1
0
0
1
1
1
1
1
2
1
0
1
0
1
1
0
2
1
1
0
0
0
2
1
0
0
0
2
2
2
1
0
2
0
1
1
2
2
1
0
1
2
2
0
2
1
1
1
2
2
0
1
1
1
1
1
1
1
1
1
1
1
1
0
2
1
0
1
1
0
1
1
3
2
1
0
1
0
2
2
2
0
0
1
0
2
1
0
1
1
2
1
1
1
1
1
0
1
0
0
1
2
1
1
2
0
0
1
0
1
0
0
1
0
2
1
1
0
1
1
0
0
1
0
2
2
1
2
1
0
1
1
2
0
0
3
1
0
1
2
1
2
1
2
0
1
1
0
1
0
0
2
1
1
1
2
1
2
1
2
1
0
2
1
2
2
1
1
2
2
3
1
1
0
2
1
1
1
1
0
2
1
1
0
0
2
3
1
1
1
0
1
0
0
0
0
0
1
1
1
1
2
0
0
0
2
1
2
2
2
1
1
0
1
0
1
1
2
0
0
1
2
1
0
1
1
1
0
1
0
1
2
1
1
2
1
0
1
0
1
1
2
2
1
1
2
1
1
1
2
1
2
1
1
2
2
1
1
1
1
0
2
1
0
0
1
2
1
0
0
1
2
0
0
1
0
0
2
0
0
1
1
2
1
0
2
1
1
2
1
0
1
1
0
1
2
2
0
1
1
1
2
2
0
1
2
2
1
2
1
0
2
1
1
0
1
0
1
2
1
0
0
3
2
3
0
2
2
4
2
0
2
0
1
0
1
1
1
0
2
0
1
1
2
1
1
1
1
0
3
1
2
2
1
0
2
0
2
0
1
0
0
2
0
0
2
3
0
0
1
1
1
0
2
1
1
0
0
2
2
1
1
0
1
3
0
2
0
1
0
1
0
2
0
1
0
1
2
1
1
0
0
1
0
1
2
1
1
1
1
2
0
2
2
0
0
1
1
1
1
0
1
1
1
0
2
2
0
1
2
0
0
1
1
2
0
0
0
0
2
2
1
1
2
1
0
1
1
1
0
0
1
1
1
0
2
0
2
2
0
1
2
1
1
1
3
1
1
0
1
0
2
1
2
2
1
0
0
1
0
1
0
1
2
2
1
1
0
1
1
1
1
0
2
1
2
0
2
0
0
1
1
1
0
1
1
2
2
0
1
0
1
0
1
1
1
1
1
1
2
2
0
1
1
1
1
1
2
1
0
2
1
2
2
2
2
1
1
0
1
0
0
1
1
2
1
2
1
1
3
1
0
2
0
0
0
1
2
1
1
2
2
1
0
3
0
1
2
1
1
0
1
0
0
0
2
0
2
0
1
0
0
0
1
1
3
0
2
1
1
1
1
0
1
3
2
0
0
1
0
1
2
1
0
0
2
0
2
2
0
2
2
1
1
2
3
1
0
1
0
2
0
1
0
1
0
1
0
0
2
1
1
2
0
0
2
1
1
0
0
1
0
1
1
3
2
0
1
2
0
1
2
0
1
1
1
0
0
0
0
0
1
0
0
1
2
2
1
0
1
2
0
1
1
0
2
0
1
0
0
1
2
1
0
1
2
1
1
1
0
0
3
0
2
1
1
0
0
1
2
2
1
2
1
1
1
1
0
0
1
1
1
2
2
1
1
0
0
0
0
0
2
1
0
1
1
1
0
2
1
1
1
1
0
2
1
1
0
0
0
0
0
0
1
1
2
0
1
0
1
0
1
1
2
1
1
1
0
1
2
2
2
0
2
2
2
1
1
2
0
2
2
1
1
1
0
2
0
1
2
1
1
2
0
1
2
1
2
2
1
2
2
0
1
1
1
2
0
0
2
0
1
1
0
1
1
1
0
2
1
1
1
1
1
0
2
1
1
2
0
0
1
1
0
1
0
2
0
1
2
0
1
0
1
0
0
0
1
0
1
2
1
1
1
1
1
0
0
2
1
1
1
3
0
1
1
1
1
1
1
0
1
1
1
0
1
2
0
1
1
0
0
1
1
2
1
2
0
1
1
1
3
2
1
1
0
0
2
0
1
1
1
2
0
2
1
0
1
0
0
2
2
0
2
2
1
0
1
1
2
1
0
2
0
1
0
1
0
0
1
0
0
1
2
0
1
1
1
0
1
1
1
1
1
1
2
0
0
2
2
1
0
1
1
1
1
2
1
1
1
2
0
1
0
0
0
2
1
1
2
0
0
0
1
0
1
0
0
1
1
2
1
1
1
1
1
1
2
1
0
0
2
0
1
1
2
1
2
1
0
0
1
1
1
0
0
0
2
2
0
0
0
0
0
1
1
1
1
1
0
1
2
1
0
2
3
1
2
1
1
0
1
0
1
1
1
2
2
1
1
1
1
1
0
0
1
0
2
1
1
2
1
0
0
0
1
1
0
2
1
1
1
2
0
2
1
1
2
2
1
1
2
2
0
1
1
0
1
0
0
0
1
1
2
2
1
1
2
0
1
0
0
2
0
0
1
1
0
1
1
2
1
0
1
0
1
2
1
1
0
2
2
0
2
0
1
1
1
0
0
3
2
0
0
1
0
0
2
1
2
1
0
0
1
1
0
1
1
0
0
1
0
1
0
1
1
0
1
0
0
0
1
0
1
1
0
1
2
0
0
0
2
0
1
1
1
0
1
0
2
0
0
2
1
2
0
1
1
3
1
0
0
1
0
0
2
1
1
0
1
0
2
1
1
1
2
1
1
1
1
1
0
1
2
0
2
0
0
3
1
1
1
1
0
2
2
1
1
2
0
0
1
2
1
1
1
1
0
0
1
0
2
3
1
1
1
1
0
1
1
1
0
0
1
1
1
1
1
1
1
0
1
2
1
1
1
2
1
0
2
0
1
2
0
0
0
1
0
1
0
1
2
0
2
2
0
2
1
1
2
3
2
1
1
1
2
0
1
0
2
0
2
2
1
0
1
0
1
0
0
1
1
1
1
1
0
0
0
2
1
2
1
0
0
0
1
2
0
2
1
4
2
0
0
1
2
4
7
1
1
0
0
1
2
1
2
0
2
0
0
2
1
1
2
0
1
1
0
1
1
1
1
1
1
2
0
2
0
1
0
2
0
1
1
0
0
0
2
1
2
0
0
2
0
2
1
1
1
0
2
1
0
1
1
0
1
0
2
1
2
0
0
2
2
1
2
2
1
1
1
1
1
2
2
1
0
1
1
0
1
1
2
1
1
1
1
1
1
1
2
2
1
1
1
0
2
1
1
2
0
2
0
0
1
1
0
0
1
1
1
1
1
0
1
0
0
0
0
0
1
1
1
1
2
1
1
0
2
2
1
0
2
1
1
1
2
2
1
0
2
0
1
1
1
1
0
1
0
1
0
1
1
1
1
1
0
2
1
2
0
0
1
1
1
2
0
2
0
0
0
1
2
0
4
0
0
1
1
0
1
1
1
0
2
2
1
3
1
2
0
0
0
1
1
1
2
2
0
0
0
0
1
1
1
2
1
1
1
0
0
0
0
1
2
0
1
1
1
1
1
0
0
1
1
0
0
0
1
0
1
1
2
1
0
2
2
1
1
0
1
2
0
1
2
1
1
0
2
1
1
2
0
2
1
2
1
0
1
2
1
2
1
1
1
1
0
4
0
0
0
2
0
1
0
2
2
2
0
1
1
0
1
1
0
2
1
2
0
0
1
0
0
0
3
2
1
0
1
1
2
1
1
0
0
2
1
0
1
1
2
0
0
1
0
1
1
1
1
2
0
0
2
2
0
0
1
1
1
3
1
1
2
0
2
1
0
1
1
1
1
0
0
4
0
0
1
1
0
0
1
1
2
1
2
1
0
0
2
1
1
1
1
0
1
1
1
0
1
0
0
1
1
1
2
1
1
0
2
0
0
0
1
0
1
2
1
1
2
1
0
1
1
0
1
1
1
1
1
2
0
0
0
0
8
0
1
0
2
2
0
0
0
1
2
1
1
0
1
0
0
2
0
0
1
0
1
0
0
1
2
1
0
1
2
0
1
2
1
1
1
1
0
2
0
2
1
1
0
1
1
1
1
1
0
0
2
1
1
1
1
1
2
0
1
2
1
1
2
1
1
0
0
0
2
1
1
2
1
1
0
1
1
2
0
1
1
1
0
0
2
1
1
2
1
2
2
1
1
0
0
4
1
3
2
2
2
1
0
0
0
2
0
3
1
0
1
1
0
2
1
2
0
1
1
1
1
1
0
2
0
1
0
0
2
1
1
2
1
1
1
2
1
2
0
1
2
1
1
2
0
0
1
2
0
1
1
0
1
0
2
0
0
1
1
1
0
0
0
0
0
1
1
0
1
1
2
1
1
2
0
1
0
2
1
1
1
1
1
2
1
1
1
1
1
0
2
0
1
1
0
2
2
1
1
0
1
0
0
0
2
1
2
0
1
1
2
0
1
1
1
1
0
0
0
2
1
2
1
0
2
0
0
1
2
0
1
0
1
1
2
0
1
2
2
2
0
1
1
1
1
2
0
0
2
1
1
1
0
3
0
1
2
2
0
0
2
2
1
1
1
0
2
2
1
0
0
0
1
1
1
0
2
0
0
2
2
1
2
1
2
1
0
1
1
1
1
1
1
0
2
1
0
2
1
1
0
1
1
1
0
2
1
0
1
0
2
1
1
1
1
0
1
2
2
0
2
0
1
1
1
1
0
0
1
1
3
2
1
2
2
3
0
3
0
2
1
0
2
2
1
2
1
1
1
0
2
0
0
1
1
1
1
1
0
0
1
1
0
1
0
1
1
1
1
1
0
1
1
0
1
1
1
1
0
2
0
2
0
1
1
0
1
1
0
0
0
1
2
1
1
1
1
2
0
1
1
0
1
1
0
0
1
1
1
2
0
1
0
0
2
1
2
2
2
1
2
2
1
1
1
1
1
1
1
1
0
1
0
0
1
2
1
1
1
0
3
0
0
1
1
0
1
2
0
0
1
1
1
2
3
1
1
1
1
1
0
1
0
1
2
0
2
0
1
1
1
0
0
0
1
0
1
1
0
1
4
0
1
0
2
0
1
2
1
1
2
1
1
1
2
0
3
2
1
1
0
2
2
1
0
1
0
1
1
1
0
0
1
0
0
0
0
0
1
0
0
1
2
0
0
0
2
1
1
1
1
1
2
0
1
1
2
0
1
1
1
1
1
1
0
3
2
1
1
1
0
0
0
0
1
1
2
1
2
3
0
1
1
0
0
2
1
2
1
0
1
1
1
1
1
1
1
1
2
0
1
2
2
0
0
1
1
1
1
2
1
0
1
1
2
1
1
0
1
2
0
0
1
1
1
1
2
0
0
0
2
2
1
2
0
1
1
1
0
2
2
2
1
0
1
0
1
0
0
1
2
0
1
0
1
1
2
0
0
1
1
0
1
2
0
1
0
1
1
1
1
0
1
3
1
1
1
1
2
0
1
0
2
1
1
1
2
2
1
1
0
3
1
0
1
0
2
1
0
1
1
0
0
3
0
0
1
0
0
2
0
0
0
1
0
1
1
1
1
1
1
0
1
0
1
1
1
0
1
0
2
2
0
1
1
1
2
2
0
2
1
0
0
1
1
1
1
1
1
1
0
1
1
0
1
0
2
1
0
2
1
0
1
2
0
2
1
3
1
1
0
0
1
0
1
1
1
0
0
1
2
1
0
0
0
0
1
0
1
2
1
0
0
0
0
2
1
2
1
1
0
2
2
1
0
1
3
1
2
1
1
2
1
0
1
1
1
0
2
0
1
0
1
0
1
0
2
3
1
0
0
2
1
1
1
2
2
0
2
0
1
1
1
1
1
0
0
1
0
0
2
2
0
2
2
0
0
1
1
1
1
3
2
0
0
2
1
2
2
2
1
2
1
1
0
2
1
1
1
1
1
1
0
1
0
1
1
0
2
0
0
1
1
1
0
0
0
2
0
0
1
0
0
0
0
2
1
3
1
0
2
1
1
0
1
2
1
1
1
1
0
1
1
2
2
1
1
1
1
1
1
0
1
1
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
1
0
0
2
0
0
1
2
1
1
1
1
1
2
2
1
1
1
1
0
1
1
1
1
0
1
0
1
0
0
2
2
1
2
1
0
0
1
2
0
1
0
1
1
1
1
0
0
0
1
0
0
2
1
1
1
0
1
1
2
1
0
0
0
1
1
2
1
1
0
1
0
2
1
0
1
2
1
1
0
0
2
1
0
1
1
0
0
0
2
2
0
0
0
0
1
2
2
2
1
0
2
1
0
1
4
2
2
1
0
0
0
0
0
1
2
1
3
1
1
1
0
1
1
1
0
1
0
1
0
0
0
0
0
1
1
1
1
1
1
2
0
1
2
0
1
2
1
1
1
0
0
1
2
0
2
1
1
2
1
1
1
2
1
0
1
1
2
1
1
0
1
1
1
1
1
1
3
2
1
0
1
2
1
0
2
1
1
1
1
1
2
1
1
1
0
3
1
0
1
1
0
1
1
1
0
0
1
0
2
0
2
1
2
2
1
2
1
2
1
0
0
2
0
1
3
1
0
0
1
2
0
1
1
1
1
0
2
0
1
1
1
0
0
0
1
1
0
2
0
1
2
1
1
0
1
0
2
0
0
1
0
1
0
1
1
0
2
1
1
0
0
0
1
1
0
1
1
1
2
0
2
1
0
0
0
1
2
2
1
1
0
2
0
0
3
0
1
0
1
3
1
2
1
0
2
0
0
2
1
2
0
1
0
1
1
0
0
0
2
1
1
0
0
1
0
2
0
2
0
0
0
2
0
0
2
0
2
2
1
1
1
2
1
1
0
1
1
1
0
1
0
1
1
0
0
1
2
1
1
0
2
1
1
0
1
2
1
1
1
1
0
1
0
2
1
2
2
1
0
2
1
0
0
1
1
1
2
0
1
2
1
1
1
0
1
0
0
1
2
0
2
2
1
0
2
0
1
1
2
0
0
1
0
1
0
1
1
0
2
2
1
1
2
1
1
1
2
0
2
0
1
2
1
1
0
2
1
2
1
1
1
1
1
1
1
1
2
1
2
2
0
1
1
0
2
1
1
1
1
1
0
0
2
0
2
1
0
2
1
0
2
0
0
0
0
0
1
3
1
0
0
2
3
0
0
0
0
2
0
0
1
0
1
0
1
1
0
0
2
1
0
1
1
0
1
1
0
2
0
3
0
1
1
0
0
0
0
0
0
2
2
0
1
0
0
1
0
1
2
1
0
1
1
0
0
1
0
0
1
0
2
0
2
2
2
1
2
2
1
1
0
1
2
2
1
1
1
0
1
2
2
1
1
0
1
2
0
1
1
2
1
0
1
0
2
0
1
1
2
1
2
1
1
1
2
1
0
0
1
1
2
1
2
1
1
2
1
2
2
1
0
1
1
2
1
0
2
1
0
0
2
0
2
0
0
2
0
1
0
1
2
0
1
2
3
0
1
1
1
1
0
1
0
0
0
1
1
0
1
1
1
1
1
0
0
1
1
0
1
1
1
1
2
2
1
0
1
1
2
0
2
1
2
1
2
0
2
1
1
1
1
1
1
2
1
2
0
1
0
1
1
1
1
2
2
1
1
0
3
3
2
1
0
0
2
1
0
0
1
1
1
1
1
1
1
1
4
2
2
1
1
0
1
1
2
0
1
1
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
1
1
2
1
1
4
0
1
0
0
0
1
1
0
2
0
0
0
1
1
1
1
1
0
1
0
1
1
1
0
3
2
1
1
1
1
1
0
2
1
1
0
1
1
1
0
0
0
1
2
1
1
1
2
0
1
1
2
0
1
1
0
0
0
1
0
1
0
0
1
1
0
2
1
0
0
2
0
0
1
0
2
0
1
1
0
2
1
1
3
1
1
3
0
1
1
2
1
0
0
1
1
3
1
1
1
0
0
0
0
0
0
1
0
0
1
1
1
1
1
1
0
2
0
0
1
0
1
0
1
0
0
1
0
1
1
1
2
1
0
1
1
1
1
1
0
0
1
1
1
0
1
2
0
2
0
1
1
0
1
0
0
2
1
1
1
1
0
1
1
1
0
1
1
1
2
0
0
1
2
0
1
0
1
2
1
2
0
2
2
0
0
1
0
0
0
2
0
0
1
2
1
2
1
1
1
0
1
2
1
1
0
1
1
0
1
0
0
1
0
0
1
1
1
1
0
0
1
2
1
1
0
1
1
0
2
2
0
0
2
2
1
0
2
2
1
1
1
1
2
2
1
1
1
1
2
2
1
1
1
1
2
2
2
0
2
0
1
1
1
0
2
1
2
0
0
1
1
2
0
1
0
1
1
1
0
0
1
2
0
1
1
1
1
0
1
2
1
0
1
0
1
0
1
1
0
1
2
1
0
1
0
2
2
1
1
1
1
1
2
1
0
1
1
0
2
1
1
1
1
0
2
0
0
2
1
1
1
2
1
0
0
1
1
1
0
0
1
0
0
1
0
2
2
1
2
1
1
1
1
0
2
1
1
1
1
2
1
1
0
1
0
2
1
2
1
1
1
1
1
0
0
1
2
2
2
1
2
2
0
2
2
2
0
1
1
1
0
1
0
1
1
0
1
0
1
1
1
0
1
1
0
2
2
0
1
0
1
1
1
1
1
1
3
0
1
0
0
1
2
2
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
2
0
1
1
1
1
0
1
0
0
1
2
1
2
2
0
0
1
0
0
1
0
2
1
1
1
1
1
2
1
0
1
0
2
3
1
4
1
2
1
1
1
1
0
1
2
0
1
1
0
1
0
1
1
0
1
1
1
1
1
0
0
2
1
1
2
1
1
1
1
1
1
2
1
1
0
0
2
0
1
1
1
2
2
0
1
1
1
1
1
0
2
2
2
1
2
0
2
0
1
1
1
1
0
1
2
1
1
0
1
2
0
0
0
0
1
9
1
0
1
2
3
2
1
0
0
1
1
2
2
0
0
0
0
0
1
2
1
2
0
0
0
1
0
2
1
3
0
0
1
1
1
1
1
2
2
1
1
1
0
3
1
1
1
1
2
2
0
1
1
1
1
0
0
0
1
1
0
0
1
0
2
1
2
1
2
1
1
0
0
1
1
1
1
1
1
2
1
1
0
1
0
2
1
1
1
2
0
1
2
1
0
1
2
1
1
0
0
1
1
1
1
0
1
2
1
0
2
2
1
0
1
1
1
1
2
1
2
0
1
1
2
2
0
1
1
0
2
1
1
1
1
2
2
1
1
2
1
2
0
0
0
1
1
1
0
1
2
3
0
0
1
0
0
1
1
0
2
2
2
0
0
2
0
2
1
1
0
1
0
2
1
1
2
2
0
1
2
2
1
1
1
1
0
0
0
2
2
1
1
0
1
1
2
1
0
1
0
2
1
0
0
0
1
2
2
0
1
2
1
2
2
1
0
1
2
1
0
0
0
1
1
0
2
2
2
1
2
2
3
2
1
1
1
0
2
1
1
3
0
1
2
2
0
1
0
1
2
0
0
1
2
1
1
1
2
0
1
1
1
2
2
0
1
1
1
1
2
0
0
0
1
0
2
0
3
0
0
2
2
1
1
0
1
2
0
2
1
1
1
1
2
1
0
1
1
0
1
0
1
1
2
0
1
1
1
1
1
2
1
1
0
1
0
0
2
3
1
1
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
1
2
0
1
2
0
1
2
1
1
1
2
0
1
2
1
1
0
1
1
1
2
2
1
2
2
1
1
1
1
1
1
2
1
1
1
0
3
1
0
0
6
2
0
1
1
0
0
1
0
1
2
1
0
2
1
0
1
2
1
1
0
0
0
0
1
2
1
2
0
2
0
0
1
1
1
2
1
1
1
1
1
1
1
1
0
0
3
1
0
1
0
0
1
2
1
0
1
1
2
0
0
0
1
0
1
1
1
0
0
2
0
1
0
2
0
1
3
0
2
0
2
1
0
1
1
2
1
1
1
2
2
1
0
1
2
0
0
0
0
1
0
0
0
0
0
1
0
2
3
1
0
0
2
2
0
0
1
2
1
0
0
0
0
1
1
1
1
1
0
1
0
1
0
2
1
1
1
1
0
1
2
1
2
0
1
0
1
2
2
0
1
0
1
0
1
0
1
1
1
1
1
1
1
0
1
1
0
0
2
2
1
2
0
0
1
0
0
2
0
0
1
1
0
1
1
2
0
0
1
1
2
0
2
2
1
1
2
0
1
0
2
0
1
0
0
1
0
1
0
1
0
1
1
0
1
0
0
1
1
0
0
2
0
1
0
1
1
1
1
2
1
0
1
0
1
1
1
2
2
1
0
1
1
2
1
1
1
1
1
0
2
0
1
0
3
1
1
1
1
0
1
1
1
1
0
1
0
1
0
1
2
0
2
1
2
1
2
0
1
2
0
2
0
0
1
0
2
2
2
1
2
1
1
1
2
0
0
1
1
1
1
0
2
1
0
1
2
1
1
1
0
2
0
1
0
1
2
0
1
0
0
1
0
1
1
1
0
1
2
2
2
0
0
1
0
0
2
1
0
2
0
2
0
1
0
1
2
0
2
1
2
0
2
1
0
0
1
0
2
1
2
1
1
1
0
1
1
0
0
2
2
1
0
1
0
0
1
4
1
1
0
0
0
1
0
2
1
0
0
1
0
1
0
1
1
2
1
1
1
0
2
2
1
0
0
0
0
1
0
2
2
1
0
2
2
0
0
0
1
0
1
1
3
2
1
0
0
1
0
0
1
1
0
2
1
0
1
0
1
1
1
1
1
1
2
1
1
0
1
1
3
2
0
3
1
1
1
0
0
1
1
2
2
0
0
1
1
1
1
1
0
2
0
0
0
1
2
1
2
2
0
0
0
2
2
1
0
2
0
0
0
0
1
0
2
0
1
1
2
1
2
1
2
2
1
0
2
1
0
0
1
0
2
1
1
0
0
2
1
0
1
2
1
1
1
1
0
1
0
1
1
0
1
1
1
1
1
0
1
1
0
2
0
1
0
0
0
0
2
1
0
1
0
1
1
0
1
0
2
3
1
3
2
1
2
1
1
0
0
2
0
1
1
1
2
2
2
1
1
1
1
1
0
1
1
1
2
1
1
1
1
0
0
1
2
1
0
4
1
2
1
1
1
0
0
0
0
0
0
2
1
0
3
2
2
0
1
0
0
1
1
1
1
1
1
1
0
1
2
0
0
1
0
1
0
0
0
2
1
0
2
1
1
2
1
0
0
1
1
1
3
0
1
0
1
1
1
1
1
0
2
1
1
2
2
2
1
1
2
2
0
1
0
0
0
0
1
1
1
1
2
1
0
1
2
1
2
0
1
1
1
0
1
1
1
1
1
1
0
1
0
1
0
0
1
2
0
1
1
1
1
0
0
0
1
1
1
0
1
0
0
1
0
2
1
2
1
0
0
1
1
1
2
0
1
0
1
2
1
1
2
1
0
1
1
2
0
2
2
1
1
1
2
2
0
1
2
1
1
0
0
1
1
1
1
0
1
1
1
0
1
0
1
1
2
1
1
0
0
2
1
1
1
1
2
2
1
0
1
2
1
1
1
1
1
0
0
1
0
1
0
1
1
0
2
0
0
2
0
0
2
2
1
0
0
2
0
0
0
0
0
0
1
1
1
0
1
1
0
1
0
2
1
0
0
0
1
2
0
1
3
0
0
3
1
0
2
0
0
1
1
0
0
0
0
0
1
1
1
2
1
1
0
1
0
2
1
0
0
1
2
0
0
1
1
2
0
1
3
0
1
1
1
2
1
1
0
0
1
1
6
2
0
0
2
1
1
1
1
0
1
1
1
1
2
0
0
1
0
1
1
1
1
2
2
0
2
1
2
1
2
1
0
1
1
2
1
4
0
6
0
1
2
0
0
1
1
2
1
2
1
1
0
0
0
2
1
1
2
1
1
0
0
1
2
0
1
1
0
1
1
1
0
3
1
1
2
0
1
1
0
1
2
1
1
0
0
0
0
2
1
2
0
2
2
1
0
1
0
0
0
0
2
0
2
2
0
1
1
1
1
2
0
1
2
0
1
0
0
2
0
1
2
2
0
1
1
1
4
1
0
1
1
1
0
1
0
2
2
1
0
0
0
0
2
1
1
1
1
0
0
2
1
1
0
2
1
1
0
2
0
1
0
2
1
2
2
0
1
2
0
2
2
1
1
1
0
1
0
1
2
0
0
1
0
2
1
0
2
0
0
0
2
0
2
1
1
1
1
0
2
0
0
0
1
0
1
1
1
0
0
2
2
0
1
1
0
0
1
2
0
2
0
2
1
1
1
0
1
1
1
0
1
1
1
1
0
1
3
0
1
1
1
2
0
1
0
0
2
1
1
2
0
2
1
0
0
0
2
1
0
1
1
1
2
1
2
0
2
1
0
0
1
1
0
1
1
0
1
0
0
1
1
1
2
1
1
1
1
0
0
1
0
1
1
2
0
1
1
0
1
2
0
1
0
2
1
1
1
1
1
0
0
1
2
0
0
1
0
0
1
1
1
0
1
1
0
0
0
1
1
0
1
0
2
1
1
2
0
1
1
1
2
1
2
1
2
0
2
1
3
0
1
1
2
0
1
0
1
0
0
1
1
0
1
1
2
0
2
2
0
1
1
1
2
1
0
2
1
1
1
1
1
0
1
1
0
0
1
4
1
0
1
1
1
0
1
1
1
1
1
0
0
1
1
1
2
2
0
2
1
1
1
0
0
0
0
1
0
2
2
1
1
1
1
1
2
1
3
1
0
0
1
2
1
1
0
0
1
0
2
1
0
2
1
2
1
0
2
1
2
0
2
0
0
1
0
1
2
1
1
1
0
0
1
0
0
2
0
2
1
1
1
1
1
0
2
2
2
1
1
1
2
2
1
0
1
1
0
2
0
1
2
1
1
1
1
2
0
0
2
2
1
0
1
1
0
0
0
0
2
1
0
0
1
1
1
0
1
1
1
1
1
2
2
0
0
0
1
0
2
2
1
2
0
1
0
1
1
2
0
0
1
1
1
0
0
1
2
1
1
2
0
2
0
2
2
1
1
1
1
0
2
1
1
1
0
1
0
1
1
1
1
1
0
1
1
2
1
2
1
1
0
1
0
0
0
0
1
2
0
0
1
2
0
0
0
1
1
1
0
0
1
1
1
0
2
1
2
2
1
2
0
0
2
2
4
0
1
0
1
1
2
1
1
2
2
1
1
1
0
1
0
1
2
1
1
0
0
1
1
2
0
0
1
0
2
2
1
0
1
2
1
0
1
1
2
0
2
0
1
2
1
1
1
1
1
0
0
2
1
1
1
0
1
2
1
0
1
1
0
1
2
1
1
2
1
1
0
1
0
1
1
1
0
0
1
2
0
2
0
1
2
1
0
1
0
2
1
2
1
1
2
1
1
2
0
1
0
0
1
2
2
1
1
0
1
2
2
0
1
1
2
1
1
1
2
1
1
1
2
2
1
1
3
0
1
0
2
1
1
2
1
1
0
0
2
1
2
0
0
1
1
0
1
2
0
0
0
1
2
2
0
1
0
1
0
0
1
1
0
1
1
0
1
2
1
1
2
0
0
0
5
1
1
1
0
0
2
1
1
0
1
0
2
1
2
2
0
0
1
1
1
1
0
2
2
1
1
1
2
2
2
1
2
1
0
4
0
1
4
1
1
1
0
1
0
0
1
1
0
1
2
1
0
0
1
1
0
1
0
1
2
2
0
1
0
1
2
1
2
1
1
0
1
0
1
2
1
2
1
2
0
1
1
1
0
1
1
2
1
0
0
1
1
0
1
3
1
2
0
0
0
0
1
2
2
0
0
1
0
1
2
1
0
0
2
2
0
1
1
2
2
1
1
1
1
2
0
1
1
1
2
0
1
1
0
1
2
1
0
1
1
2
1
2
0
1
0
0
1
1
0
1
0
0
1
1
2
1
1
1
1
0
1
0
2
1
1
1
1
1
0
1
2
2
1
0
1
0
1
1
1
2
2
2
0
0
2
1
0
0
2
1
0
1
0
2
0
0
0
1
1
1
1
1
0
1
0
2
1
0
2
0
0
1
2
0
1
0
1
1
0
0
2
3
1
0
0
2
0
2
1
2
2
0
1
1
1
1
2
1
2
1
0
2
1
2
1
0
0
1
0
2
1
1
1
0
0
1
1
1
1
1
0
2
2
1
0
0
0
2
1
1
0
2
3
0
0
1
0
0
1
1
0
1
1
0
0
1
0
2
1
2
1
1
0
1
2
2
1
1
2
2
1
0
2
0
1
0
0
1
0
1
2
1
1
0
0
2
2
2
2
2
0
0
2
0
0
1
1
0
1
0
1
2
1
1
2
1
0
2
1
0
2
1
1
1
0
0
0
2
1
1
1
1
2
1
1
1
0
0
1
1
0
2
2
0
0
0
2
1
0
0
0
0
1
0
1
1
1
1
1
0
0
2
1
1
1
1
1
0
2
2
0
2
1
1
0
2
2
1
3
2
0
1
2
0
2
1
0
2
1
1
0
0
1
1
1
2
0
1
1
0
0
1
2
0
1
1
1
2
2
1
1
1
2
1
1
0
2
1
0
2
2
0
1
2
0
2
1
2
2
0
2
0
1
0
1
1
3
1
0
1
0
1
1
2
2
2
2
1
0
0
0
1
0
2
0
0
1
2
1
1
1
1
1
0
0
1
2
1
0
1
1
0
2
2
0
1
1
1
0
2
2
1
0
0
1
0
1
2
1
1
0
2
0
2
1
1
1
1
1
1
1
0
1
1
1
2
1
1
1
2
1
1
1
0
1
0
0
0
1
1
3
1
1
1
1
1
1
0
0
1
2
2
1
1
1
1
0
1
1
0
1
0
1
1
2
0
1
1
0
0
0
1
1
1
0
1
1
0
1
1
1
0
0
1
0
0
1
1
1
0
1
0
1
1
2
0
1
1
0
1
1
1
1
0
2
1
1
2
1
2
1
0
1
0
1
1
0
1
1
0
0
1
2
3
0
1
2
0
2
0
1
0
1
1
0
1
1
0
1
1
1
1
0
2
2
1
1
1
2
0
0
1
0
2
1
0
1
2
1
0
1
1
1
1
1
1
0
2
1
2
0
1
1
0
0
2
1
0
1
0
0
0
1
2
0
1
0
1
1
0
2
1
1
0
0
1
0
0
1
2
0
0
1
1
1
0
0
0
0
0
0
2
1
0
0
2
0
1
2
1
1
1
1
1
0
1
1
1
0
0
0
0
2
1
1
1
0
2
2
2
1
2
1
0
1
0
2
2
0
1
1
3
1
2
1
0
0
0
1
1
1
0
1
1
1
1
1
0
1
0
0
0
0
2
1
0
0
1
2
2
0
2
2
0
1
0
0
1
0
2
0
1
1
0
0
1
1
1
1
0
2
1
1
1
1
1
1
1
0
1
1
1
0
1
2
1
0
0
1
1
1
1
2
2
0
0
3
0
1
2
0
1
1
1
1
2
1
0
1
0
2
0
1
0
0
2
2
1
2
3
2
1
0
1
0
0
1
2
1
0
0
1
2
1
0
0
1
1
2
1
2
1
2
2
0
0
0
1
1
1
0
1
0
1
0
1
1
0
0
2
0
1
2
1
1
0
1
1
0
1
0
1
1
0
1
1
0
1
1
1
0
1
0
0
1
2
0
1
1
1
1
1
1
1
1
2
0
0
0
2
1
1
0
1
2
1
0
2
2
1
1
0
0
1
1
1
1
1
0
1
4
1
2
1
0
2
0
1
1
0
1
1
1
0
1
1
0
1
1
0
1
1
1
1
0
1
1
1
0
2
0
1
0
0
0
0
0
0
0
1
1
1
0
1
1
1
1
1
1
0
0
1
2
0
2
1
0
0
1
0
0
1
1
1
0
1
1
1
2
0
0
0
1
0
1
1
1
2
2
1
0
1
1
2
1
1
1
1
1
0
0
0
0
1
0
0
2
0
2
1
0
2
0
2
1
0
1
1
0
0
1
1
0
1
2
1
0
1
1
2
0
0
1
1
1
0
1
0
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
0
1
1
1
2
2
2
2
0
1
1
0
2
2
1
0
1
2
1
1
1
0
0
2
1
1
1
1
1
2
1
1
1
1
2
0
1
2
2
1
1
1
0
1
1
1
2
0
1
2
1
0
1
1
1
0
1
0
0
1
1
0
1
1
1
0
1
1
2
1
1
2
1
1
2
0
2
1
2
0
1
1
2
3
1
1
0
1
2
1
0
2
2
0
2
0
1
1
0
1
0
2
0
3
1
1
0
1
0
2
2
0
0
1
0
1
1
1
1
1
1
0
0
1
1
1
1
0
1
0
2
2
1
0
2
0
0
1
1
1
2
0
1
1
1
1
2
1
0
0
1
2
0
1
0
0
1
2
1
1
0
1
1
1
2
0
0
2
0
2
1
1
1
0
1
1
0
0
0
0
1
0
1
0
1
0
1
0
0
0
1
1
0
1
1
2
4
3
1
0
1
1
0
1
0
2
2
0
0
1
0
2
0
0
0
1
0
0
1
0
0
2
0
1
2
1
0
1
0
1
0
1
0
2
4
2
1
2
1
1
0
1
1
1
0
1
2
1
0
1
1
2
1
1
1
1
2
2
1
0
2
1
0
1
2
1
1
0
1
1
1
0
2
0
2
1
0
1
1
1
0
0
0
1
0
0
1
1
2
0
0
0
1
1
2
1
0
1
0
0
2
2
1
1
2
1
3
0
0
0
0
1
2
1
1
1
0
1
2
0
1
1
0
1
0
2
0
1
2
0
0
0
1
1
1
2
1
1
0
4
0
1
1
2
2
1
1
1
1
1
1
0
2
1
1
0
0
3
2
2
0
1
2
0
0
0
2
2
1
1
2
2
1
1
0
0
1
1
2
1
1
0
0
1
1
1
0
1
1
0
2
0
1
0
1
0
0
1
1
1
1
1
1
1
1
1
0
3
1
1
1
0
2
1
0
0
2
0
1
1
1
1
0
2
0
1
1
0
1
1
1
0
1
0
0
1
1
1
1
1
1
1
0
1
1
1
0
0
1
1
1
1
1
1
1
0
1
0
0
1
1
1
1
1
2
1
1
2
2
2
0
0
2
0
0
0
2
1
0
1
1
0
2
0
1
1
1
0
0
0
0
1
1
0
0
1
2
0
1
1
0
1
2
1
2
1
2
0
1
1
0
1
0
1
0
1
1
1
0
1
0
0
0
0
1
1
1
0
1
0
0
2
1
2
1
1
0
0
1
0
2
0
1
0
0
1
1
0
1
0
0
1
1
1
1
1
1
0
0
1
0
4
1
1
1
0
0
2
0
2
1
1
1
1
1
0
1
1
1
1
0
0
2
2
1
2
1
1
2
1
0
1
3
1
1
0
0
2
3
3
1
1
2
0
1
0
1
0
1
1
1
1
1
1
1
1
1
1
1
2
1
1
0
0
1
0
0
1
0
1
1
1
1
2
1
1
1
0
1
1
1
1
1
0
1
0
1
1
0
2
2
1
1
0
0
2
1
1
1
0
1
2
1
1
1
0
0
1
1
1
1
1
1
1
1
2
2
2
2
1
1
2
1
0
1
0
0
1
0
0
0
2
1
0
1
0
1
1
1
2
0
1
0
2
2
1
0
1
1
0
0
2
1
2
2
1
0
1
0
1
0
0
1
2
1
0
1
1
1
0
2
0
1
2
2
1
0
2
0
1
2
2
1
0
1
1
1
1
0
1
0
2
1
1
1
1
2
1
2
2
2
1
1
2
2
1
1
2
1
0
2
1
1
2
1
2
2
1
0
0
1
2
2
1
2
2
1
1
0
2
0
1
1
0
1
2
1
1
1
2
1
1
0
2
0
1
0
0
0
1
1
2
1
1
0
1
1
1
1
2
2
2
2
2
2
0
1
1
1
1
0
1
1
1
1
1
2
1
0
1
0
0
0
0
1
1
2
1
1
1
1
1
2
2
1
1
2
0
2
2
0
0
1
1
0
0
0
1
1
0
1
1
1
0
0
1
1
0
0
1
1
1
1
0
0
1
1
1
2
2
1
2
0
2
1
0
1
1
2
1
2
0
1
1
1
0
1
2
1
1
3
0
0
1
0
0
0
1
2
1
2
1
1
1
0
1
0
2
0
2
0
2
1
1
3
1
1
0
2
0
1
0
1
1
1
1
1
1
1
0
1
2
0
0
1
2
1
0
1
1
0
1
1
1
1
2
1
0
2
1
1
1
2
1
1
0
0
1
1
2
0
1
1
1
0
1
2
0
1
1
2
1
2
2
0
0
2
1
1
1
1
1
1
0
1
0
1
0
2
1
1
1
1
0
2
2
2
3
1
1
0
1
1
0
1
1
2
0
0
1
0
2
2
1
1
2
0
0
2
3
3
0
1
1
0
1
0
1
2
1
0
2
0
0
1
2
1
1
1
1
1
0
2
1
1
1
0
1
2
1
2
1
0
0
2
0
2
0
0
2
2
0
1
0
1
2
1
2
2
1
0
1
1
1
3
1
1
0
0
1
0
1
1
1
0
0
0
1
2
0
0
0
0
1
1
1
0
0
1
1
2
1
1
1
0
0
0
2
1
2
0
1
2
2
2
2
0
0
0
1
2
1
1
0
0
1
0
2
1
1
1
0
0
2
0
1
0
0
0
0
2
1
0
1
1
1
0
1
1
1
1
2
0
2
1
2
2
1
1
1
1
0
1
1
2
0
2
0
1
0
2
2
0
1
1
1
1
0
2
0
3
0
1
1
0
1
2
1
1
0
0
1
0
2
1
1
1
1
1
0
0
0
0
0
0
1
0
4
3
1
3
0
2
1
1
1
0
1
2
0
0
1
0
2
0
0
1
0
2
2
2
0
1
1
1
2
1
0
2
1
1
1
2
2
1
1
1
0
0
0
0
0
3
2
0
0
1
1
0
1
1
1
1
1
1
2
0
0
1
2
1
2
2
1
0
0
0
1
0
1
1
0
0
1
2
1
0
0
1
1
0
2
1
0
2
2
0
1
0
1
2
1
1
1
0
2
0
1
0
2
1
1
2
1
1
3
1
2
0
0
0
2
0
0
1
1
1
0
0
0
0
2
0
1
2
1
0
2
1
2
1
2
2
2
2
2
4
1
0
2
0
2
0
0
1
1
1
1
0
2
0
0
1
0
0
2
0
2
0
0
0
1
0
1
1
1
1
1
2
2
0
1
1
1
2
1
0
1
2
1
1
1
0
1
0
2
0
1
1
3
2
0
1
1
1
1
0
0
0
1
1
1
1
0
1
1
0
1
1
1
0
1
1
1
0
1
1
1
0
2
1
0
0
1
2
1
0
1
1
2
2
0
0
1
0
0
1
0
0
0
1
1
0
2
1
1
0
0
0
1
1
1
1
2
0
1
2
1
1
1
2
2
1
0
1
0
1
2
1
1
1
1
2
1
1
2
1
0
2
1
0
0
0
0
0
2
1
1
1
0
1
0
1
0
0
2
0
1
1
0
1
2
1
1
1
1
2
0
2
1
0
1
0
1
1
1
0
1
2
1
0
1
1
1
1
0
0
2
2
0
0
1
2
0
0
0
1
1
1
0
0
2
1
1
1
2
2
1
1
1
2
1
0
1
1
0
0
1
0
2
1
0
1
0
0
1
0
1
2
0
0
0
2
0
2
1
1
2
1
2
2
1
0
2
1
2
1
0
2
2
5
0
1
2
2
1
0
2
0
2
1
1
1
2
1
0
2
0
3
2
0
1
1
1
1
1
1
1
2
2
1
1
0
1
2
1
2
2
0
1
0
1
1
0
1
2
2
1
0
1
1
0
1
1
1
1
0
2
0
3
1
1
0
0
1
1
2
1
1
0
0
0
1
0
0
1
1
2
0
0
0
0
1
0
1
1
1
0
0
1
2
2
0
1
1
2
1
0
1
3
1
2
0
0
2
2
1
1
1
2
0
0
1
1
1
1
1
1
1
2
1
0
2
2
1
0
0
1
0
0
1
1
1
1
1
0
2
2
1
1
2
0
1
0
0
2
2
3
2
0
2
1
0
0
1
2
2
1
2
0
2
1
0
1
2
1
1
2
1
1
1
2
2
0
1
0
0
1
2
2
0
0
2
2
1
2
0
1
1
2
1
2
0
1
1
1
2
0
1
0
1
0
1
1
0
2
1
0
1
1
0
1
1
2
2
1
1
0
0
0
0
1
1
1
2
2
1
1
1
2
0
2
1
1
1
1
1
2
1
2
1
1
1
1
0
0
0
1
0
1
2
1
2
2
0
0
1
0
1
2
6
1
0
1
1
2
1
1
1
0
1
2
1
2
1
0
1
2
1
1
0
0
0
0
1
1
2
1
2
1
2
0
2
1
1
1
2
1
2
1
0
2
1
1
1
0
0
3
1
2
1
0
0
2
2
2
1
0
1
1
1
0
2
2
0
5
1
0
1
0
0
0
2
0
1
2
2
2
0
2
0
2
2
2
0
1
2
1
1
1
1
1
1
1
1
1
1
2
0
1
1
0
1
1
1
1
0
1
2
2
1
1
2
1
1
0
0
2
2
0
1
2
1
1
0
1
1
0
2
0
2
2
1
0
1
1
0
1
1
1
0
1
1
1
2
0
2
1
0
2
0
1
1
1
1
2
1
4
0
2
3
1
0
0
0
1
1
2
0
2
0
1
2
1
0
2
1
0
0
2
1
2
1
2
0
1
2
2
0
1
2
0
0
0
0
0
1
1
1
0
2
2
1
0
0
2
1
0
3
1
0
0
1
0
2
0
0
1
0
1
1
1
0
1
1
0
0
1
1
1
1
1
1
0
1
0
0
0
1
0
2
2
0
1
1
2
2
0
1
1
0
0
2
0
1
1
0
2
1
0
1
0
2
1
2
2
0
0
3
5
1
2
1
0
1
1
0
2
0
1
0
0
2
1
1
0
1
2
0
0
1
1
0
0
2
2
1
2
0
1
1
1
1
0
1
1
0
0
2
0
1
1
0
1
0
0
1
1
0
0
0
0
1
0
1
1
1
0
0
1
0
1
2
2
1
4
1
0
0
2
1
1
1
1
0
0
2
2
1
2
2
0
1
1
2
0
1
1
0
2
0
1
1
2
1
2
2
1
2
0
1
0
0
1
1
1
0
0
1
1
0
1
1
1
0
2
0
1
1
2
0
1
1
1
1
0
1
1
1
0
0
1
2
0
2
0
1
2
0
1
2
1
2
2
2
1
2
0
6
0
1
0
1
1
1
2
2
1
0
1
1
2
2
0
0
1
1
2
1
1
1
2
1
1
2
1
0
1
1
0
1
1
1
1
1
0
1
0
1
1
0
0
0
2
2
0
0
0
0
1
1
2
0
1
2
2
1
1
2
0
1
1
1
1
1
1
2
1
0
0
1
2
0
1
2
1
2
2
1
1
0
1
0
1
1
2
0
2
1
0
1
1
1
0
0
2
1
0
0
1
2
1
1
1
1
1
1
0
1
1
2
0
0
0
2
2
0
2
0
2
0
1
1
1
0
2
1
1
0
0
1
0
0
1
2
1
0
1
0
0
1
2
0
1
1
1
1
0
1
0
1
0
2
1
2
0
1
1
1
1
1
2
1
0
3
1
1
2
0
3
0
2
0
1
2
0
1
2
2
1
1
2
0
0
0
0
0
1
1
0
0
3
1
1
0
2
1
1
0
0
1
1
2
0
0
0
1
2
2
1
1
2
2
1
1
1
2
1
0
1
0
2
2
0
1
1
1
2
0
1
1
1
2
1
1
1
1
0
2
0
1
2
3
2
0
1
2
2
1
2
0
0
0
1
2
1
2
1
0
1
2
1
2
1
1
2
2
1
1
2
0
1
0
0
1
0
2
2
2
1
2
1
2
1
0
1
1
1
0
2
1
2
2
1
1
0
2
0
1
0
1
1
2
1
0
1
2
0
1
0
0
0
0
0
1
1
1
1
2
2
0
1
1
2
1
1
2
0
0
0
2
2
0
1
2
1
1
1
1
1
1
1
4
2
1
1
1
1
2
1
0
1
2
0
1
2
1
0
2
0
2
0
0
1
1
1
1
1
1
0
0
1
1
0
2
1
2
1
1
1
0
0
2
2
2
1
1
2
0
0
1
1
0
1
0
1
1
1
1
1
0
3
1
1
0
1
2
1
0
0
0
1
1
2
0
2
1
1
2
1
1
1
0
0
0
2
1
0
3
1
0
1
1
1
2
1
1
1
0
0
2
2
1
0
1
2
1
0
0
1
2
1
1
1
1
1
0
2
1
0
1
1
0
0
1
1
1
1
0
1
0
0
1
1
0
0
0
0
1
1
1
1
0
1
3
0
2
1
1
1
1
0
2
0
0
0
2
1
0
0
2
0
1
0
0
2
1
0
2
0
1
1
1
0
0
1
0
1
0
5
2
2
2
0
1
2
0
2
2
1
0
1
0
2
2
1
0
0
0
1
1
0
1
1
1
0
1
1
2
2
1
2
1
2
0
1
0
1
1
1
2
3
0
1
1
2
1
1
1
0
0
1
1
0
2
1
0
1
2
1
2
4
1
1
1
1
0
0
1
1
1
0
1
2
0
1
0
1
2
1
1
1
1
1
0
1
1
2
2
1
0
1
2
0
1
1
1
1
0
0
0
0
0
1
1
2
1
2
1
0
1
2
1
1
0
1
1
2
0
3
2
1
0
2
2
1
1
0
1
6
0
1
0
2
1
1
2
2
1
1
1
0
0
2
2
0
1
2
1
0
1
1
0
0
0
1
2
1
1
1
0
0
2
0
0
1
2
1
2
2
0
1
1
0
0
1
1
0
1
0
2
0
1
3
1
0
0
1
1
0
0
0
0
2
1
2
2
1
1
0
1
0
0
0
0
1
1
8
1
0
1
1
2
1
1
0
1
1
0
0
1
0
3
0
0
0
1
1
0
0
2
0
1
0
0
1
5
1
1
1
1
1
0
1
1
2
1
2
2
2
0
1
1
0
2
0
0
1
0
0
2
2
1
1
0
0
1
2
0
0
1
1
3
2
0
0
2
0
1
1
0
1
2
0
0
2
1
1
2
2
0
1
1
1
1
0
1
1
1
0
0
1
1
1
2
1
0
1
1
0
1
1
1
0
1
0
2
1
2
1
1
1
0
2
1
2
0
2
0
0
2
1
1
2
0
0
1
1
1
0
0
2
0
2
1
1
2
1
2
2
1
2
2
1
0
1
0
1
2
1
2
0
2
1
2
1
1
2
0
0
0
0
0
1
0
1
1
3
2
1
2
0
0
2
2
1
0
1
0
1
2
1
0
2
0
2
1
1
1
1
1
0
1
1
1
1
1
0
1
1
3
1
0
1
0
1
0
3
0
1
1
1
2
1
0
1
0
0
0
1
1
1
0
1
0
1
1
1
1
1
1
1
0
1
0
1
2
2
2
3
1
0
1
2
2
0
1
0
0
1
0
1
2
0
1
0
2
1
0
0
1
1
1
1
2
1
2
1
0
0
1
1
0
0
0
1
1
2
2
1
2
0
2
1
2
2
0
1
1
0
0
0
0
0
2
0
1
1
0
1
1
0
0
0
1
2
1
2
2
0
2
2
2
0
1
1
1
0
1
0
1
1
1
2
2
0
1
1
2
1
1
1
2
2
1
1
0
2
1
1
1
0
1
0
1
1
0
0
1
0
1
2
1
0
1
1
0
0
1
1
2
2
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
0
2
0
1
0
0
2
0
0
0
0
0
2
0
2
2
1
0
2
1
1
0
1
1
1
1
1
1
0
1
1
0
1
2
0
2
2
0
0
1
1
2
0
2
2
1
1
1
0
0
0
1
1
1
0
0
0
2
0
2
1
0
0
2
1
0
2
1
0
1
0
2
2
0
1
2
2
1
2
1
1
1
2
0
0
2
0
1
1
0
2
0
1
2
1
2
1
0
2
2
1
0
0
0
2
0
0
1
2
2
1
2
1
0
2
0
1
1
0
0
1
2
1
0
2
1
1
2
1
0
2
0
1
0
1
1
1
1
1
1
1
1
1
1
0
0
1
1
1
2
0
0
1
1
1
2
1
1
0
0
0
0
1
1
0
0
0
1
1
1
0
1
2
0
1
0
1
1
2
1
2
2
1
2
1
2
1
1
1
0
0
1
1
0
0
1
2
1
0
0
1
1
1
0
0
0
1
0
1
0
1
1
1
0
1
3
1
1
0
1
1
1
2
1
0
1
1
1
1
1
1
0
2
0
1
1
1
2
0
0
1
1
1
1
1
1
1
2
1
0
2
2
2
2
1
0
1
1
1
0
1
1
1
0
2
0
1
2
2
2
1
1
2
1
1
1
1
2
2
1
2
1
0
0
0
1
1
0
1
1
1
0
0
0
2
1
1
1
2
1
0
2
1
1
1
0
0
0
1
4
1
0
0
2
1
2
0
0
0
2
1
1
2
0
1
2
1
1
2
4
1
1
0
2
0
0
0
2
2
0
1
1
2
0
1
0
2
1
1
0
0
1
1
1
0
0
1
0
0
0
2
1
1
0
2
0
2
0
1
0
1
1
1
1
0
1
1
2
2
0
1
1
0
1
1
0
0
1
1
2
3
2
1
0
1
1
1
1
1
1
2
2
2
1
1
0
1
1
0
1
1
0
1
1
0
1
1
1
2
1
0
0
1
2
1
2
1
0
2
2
2
1
2
0
2
1
0
1
1
1
1
2
0
1
1
1
2
1
0
2
0
0
1
1
1
0
2
1
1
1
0
1
1
0
0
0
1
1
1
1
0
1
1
2
1
1
1
0
0
1
1
1
1
2
1
1
0
2
2
0
1
1
1
0
0
1
1
0
0
3
2
2
1
1
0
0
1
1
0
1
0
1
0
2
0
0
1
3
1
0
1
1
2
3
0
0
1
1
0
1
1
1
1
2
0
0
1
1
1
0
1
1
1
0
1
2
1
0
0
0
2
2
0
0
1
1
1
0
0
2
2
2
1
1
1
2
1
3
1
2
0
0
3
0
1
2
1
0
1
1
1
1
1
3
1
0
0
1
1
1
0
1
1
0
0
1
0
1
0
1
1
0
0
1
0
2
0
1
0
1
1
0
0
0
1
0
1
2
0
1
0
2
2
0
0
0
2
0
0
1
1
2
2
2
0
0
0
2
1
0
2
1
0
0
1
0
1
2
0
2
0
1
0
1
2
0
1
1
1
1
2
1
0
0
1
1
2
0
0
1
1
1
0
1
1
1
2
1
0
1
1
1
1
1
0
1
0
1
0
2
0
2
1
1
1
0
2
1
2
0
0
0
0
0
0
2
1
1
0
0
0
0
0
1
1
1
0
0
2
0
1
1
1
2
0
1
2
0
0
1
1
0
0
1
1
1
1
1
2
0
0
2
1
1
1
1
1
1
0
1
1
2
2
1
2
1
0
0
0
2
1
0
0
1
0
0
0
1
0
2
1
0
1
1
0
1
1
1
1
1
0
1
1
1
0
2
2
1
0
0
1
0
2
1
1
2
0
1
1
1
1
0
1
2
2
0
2
2
1
0
2
1
0
0
1
0
1
1
1
1
1
1
1
1
0
1
1
1
0
1
0
1
1
0
1
1
1
3
0
1
1
0
1
0
1
0
0
2
1
1
0
1
1
1
0
3
1
1
0
0
1
1
2
1
1
1
3
0
1
0
2
0
1
0
1
2
1
1
1
1
0
1
2
0
2
1
0
1
2
1
0
0
0
1
2
2
1
2
0
0
1
0
2
1
1
2
1
2
1
2
2
2
1
1
1
2
2
0
0
0
0
1
2
1
2
1
1
2
1
1
1
2
0
1
2
1
0
2
1
1
0
1
2
1
1
2
1
2
1
2
2
1
1
0
1
0
1
1
1
1
1
1
1
1
1
0
1
1
1
1
0
2
0
1
0
2
2
2
1
0
1
1
0
0
2
1
2
1
0
1
1
2
2
1
1
2
0
1
1
1
2
1
2
2
1
0
2
2
0
1
1
0
1
1
0
0
2
1
1
1
1
0
0
1
0
0
0
1
3
0
0
2
2
1
0
0
0
1
1
2
0
2
1
1
0
8
1
1
2
1
1
2
1
0
2
0
1
2
0
0
1
2
2
0
1
0
1
0
0
1
1
2
2
2
1
1
0
1
1
0
2
0
2
1
1
1
2
2
0
0
2
0
1
1
0
1
2
1
0
1
1
1
2
1
0
1
1
1
2
0
0
2
2
2
0
0
1
0
0
1
2
0
2
1
1
2
1
1
2
2
2
0
1
0
1
1
1
1
1
0
0
2
1
1
1
1
1
1
1
0
1
1
0
1
1
0
2
1
1
0
2
2
1
1
1
2
0
0
2
1
1
2
1
0
1
0
1
1
1
1
1
0
0
2
2
0
1
1
1
2
2
0
1
1
2
1
2
1
2
1
0
0
0
1
2
1
0
1
0
1
1
1
0
0
1
1
2
0
1
2
1
1
1
2
2
1
0
0
1
1
0
1
0
1
1
0
2
1
2
0
2
2
1
0
1
1
2
2
0
1
0
1
1
0
3
0
1
4
1
0
1
2
1
1
2
0
0
0
1
2
2
2
1
0
1
0
1
0
1
1
1
2
1
1
2
1
1
2
0
0
1
1
1
1
1
0
0
0
0
0
0
1
0
2
2
0
3
1
0
1
0
2
0
1
1
1
2
1
1
2
0
1
1
1
1
1
0
0
1
0
1
2
0
1
1
2
1
1
2
0
2
1
1
0
2
0
1
0
0
0
2
0
1
0
1
2
0
1
1
1
1
1
1
0
1
1
2
1
1
1
2
1
0
0
2
1
1
2
1
2
0
2
1
2
1
2
1
0
0
1
2
2
1
1
1
0
0
1
0
0
0
1
1
2
2
0
1
0
1
1
0
0
0
1
1
1
1
1
2
0
0
2
0
0
1
2
1
1
1
2
2
0
1
0
0
1
0
2
1
2
1
1
1
2
0
0
0
0
2
0
0
2
1
1
2
0
0
1
1
2
2
0
1
0
1
1
1
1
1
1
1
0
3
1
0
2
1
0
1
1
2
2
2
1
1
1
1
2
1
1
1
2
1
1
0
2
1
1
0
1
2
0
0
0
0
2
1
2
1
2
1
1
1
1
0
0
1
0
1
1
0
2
0
1
2
1
1
2
1
0
0
2
1
1
0
1
0
1
0
0
1
0
1
2
2
1
1
2
0
1
0
1
0
1
1
1
0
1
1
0
3
0
0
1
1
2
0
0
1
1
1
0
1
2
1
1
1
0
2
2
1
2
2
0
1
1
2
0
1
0
2
1
2
0
3
2
0
1
0
0
1
1
1
1
1
1
1
0
2
1
1
2
2
0
1
2
0
1
1
0
2
1
1
0
0
1
0
0
2
0
1
0
1
1
2
1
0
1
0
0
1
1
0
0
1
2
0
0
2
1
1
0
1
1
0
1
2
1
0
0
0
0
2
1
1
0
1
1
1
0
2
2
1
0
0
0
0
0
2
0
0
0
2
1
1
0
0
0
0
2
0
0
0
0
1
3
2
1
0
1
1
1
0
0
1
1
2
1
2
1
2
0
0
1
0
2
1
0
1
1
1
2
0
0
1
0
2
2
1
2
1
1
2
1
1
1
0
2
0
1
2
2
1
1
1
1
1
0
1
0
1
1
2
1
1
1
0
1
1
2
1
0
1
1
1
1
4
1
0
1
2
0
0
1
1
2
0
1
0
2
0
2
1
1
2
1
1
2
2
0
1
2
0
2
1
1
0
0
2
1
1
2
1
1
0
1
2
1
1
1
2
0
0
1
1
1
2
2
0
2
2
0
2
0
0
1
2
1
1
1
1
1
1
0
0
2
2
2
2
1
1
2
1
2
1
0
2
2
0
2
0
1
1
2
1
1
1
1
1
0
2
2
1
0
2
2
1
1
2
2
1
1
1
1
2
1
1
2
0
0
1
0
0
1
0
2
1
2
2
0
1
0
1
0
1
2
0
1
2
1
0
0
0
1
0
0
1
1
0
1
0
0
1
2
1
1
1
1
1
1
1
1
1
0
2
2
2
1
0
1
1
0
0
1
1
0
1
0
0
1
2
1
1
1
0
1
1
1
0
0
0
1
1
2
1
1
1
0
1
1
0
1
0
0
1
0
0
1
1
1
2
7
1
2
0
0
1
1
1
1
0
1
1
2
1
1
1
1
1
1
0
0
2
0
0
1
1
2
0
0
1
0
1
1
0
2
1
2
1
2
1
0
1
1
0
2
2
1
1
1
0
0
0
2
1
2
0
2
2
0
2
1
1
1
2
1
1
2
1
0
1
1
1
1
2
0
1
0
1
1
2
1
1
0
2
2
0
2
2
2
1
1
1
0
1
0
3
1
1
2
0
2
1
0
1
0
2
2
0
1
1
2
0
2
1
1
1
1
3
2
1
1
2
1
2
1
1
1
2
2
0
2
1
0
0
0
0
1
1
1
1
1
2
1
1
1
0
1
1
1
2
1
1
2
0
0
1
0
1
2
2
1
2
1
1
1
2
2
1
2
1
1
1
0
1
1
1
1
1
0
1
2
1
1
1
1
2
1
0
0
2
1
1
1
0
0
2
1
1
1
1
1
2
1
0
2
0
2
1
1
0
2
0
1
2
1
0
1
1
1
2
0
2
1
1
1
0
1
1
1
2
2
0
0
1
1
1
1
1
2
1
1
0
2
0
0
1
1
1
1
0
0
1
0
2
1
1
1
0
2
4
1
1
1
3
1
1
0
0
0
1
2
1
0
2
0
1
2
0
2
0
1
0
0
0
1
0
1
1
1
1
1
0
2
1
0
2
0
0
1
1
1
1
0
0
2
1
1
0
2
0
2
1
2
1
1
2
1
1
1
0
0
2
1
0
0
0
1
1
0
0
1
0
0
1
1
1
1
1
1
0
2
1
0
4
0
1
1
0
2
0
1
0
2
1
0
0
2
2
2
0
1
1
2
1
0
0
1
1
0
1
1
1
1
0
2
2
0
0
1
2
0
1
2
1
0
2
0
1
1
2
1
0
1
2
2
0
0
1
0
2
1
2
2
1
1
2
1
0
1
1
0
1
2
2
0
0
0
0
1
0
1
0
1
1
2
0
1
1
1
1
1
2
1
2
2
2
0
1
2
2
1
0
1
0
2
1
0
1
1
2
0
0
1
2
1
0
1
2
1
1
0
0
1
1
2
2
0
1
1
1
0
2
5
2
1
0
1
1
0
2
1
1
1
1
1
0
2
0
0
0
2
1
0
1
1
0
1
0
0
1
1
2
1
1
0
1
1
1
1
0
1
1
0
0
1
1
1
1
1
1
0
2
0
1
0
1
0
1
1
1
1
1
2
2
1
1
1
2
0
0
2
0
1
1
0
1
1
1
2
0
2
0
0
1
2
0
0
2
0
0
3
0
1
1
0
1
2
1
2
0
1
0
1
0
0
1
2
2
1
1
1
2
0
0
1
0
0
1
0
1
1
0
2
0
0
2
1
1
1
0
1
1
2
1
0
2
1
0
1
1
0
1
1
0
1
0
0
0
2
0
0
0
1
0
2
1
1
1
0
1
1
0
2
1
0
0
1
1
2
1
2
0
1
1
0
2
1
0
0
1
2
1
1
0
2
1
1
2
1
0
0
1
1
1
2
2
0
1
2
1
1
1
1
1
1
2
1
1
2
1
3
2
0
2
1
2
0
0
2
0
2
1
1
1
1
0
1
1
0
0
0
1
1
2
2
2
2
1
1
0
2
2
0
1
1
0
2
1
0
1
1
1
0
2
1
0
1
1
0
0
1
6
1
0
2
1
1
1
0
1
0
2
1
1
1
2
0
1
1
0
1
1
0
0
2
1
1
1
1
2
1
0
2
1
1
1
0
2
1
2
2
1
1
1
2
1
2
0
1
0
0
1
0
2
1
1
0
1
1
0
0
2
2
2
0
0
0
1
1
1
1
2
2
0
1
0
2
0
1
1
1
0
0
3
0
0
0
0
2
0
0
2
2
1
0
1
2
0
1
1
2
2
2
0
0
1
0
2
2
0
0
1
1
1
0
0
0
0
1
2
2
1
2
1
1
0
1
0
0
1
1
2
1
1
1
1
1
1
1
0
0
2
1
1
1
0
1
0
0
2
1
1
0
0
0
1
1
0
1
0
1
2
1
1
1
0
1
1
1
1
0
0
0
2
0
1
0
0
1
1
0
3
1
0
0
2
1
1
1
0
0
0
1
2
1
1
1
1
0
1
0
1
2
1
0
0
1
0
2
3
0
2
2
1
3
2
2
1
1
0
2
2
1
1
1
1
1
3
2
0
2
0
1
0
1
0
1
1
0
1
0
0
2
0
0
1
1
0
1
2
0
0
1
1
1
0
1
0
0
1
0
0
0
1
1
1
2
2
2
2
0
0
1
2
1
0
1
1
1
2
2
0
2
1
2
2
1
1
2
0
1
2
0
0
1
1
0
2
0
1
1
1
0
2
0
2
0
1
0
1
0
1
1
0
0
2
0
0
2
0
1
0
1
1
2
1
1
2
1
1
2
0
0
1
0
1
0
1
2
0
0
1
1
2
1
2
2
1
1
0
0
0
1
0
1
2
1
2
2
1
2
0
0
2
1
1
1
1
2
1
1
1
2
0
0
1
1
0
1
1
2
1
2
0
2
0
0
1
1
1
2
2
2
0
1
2
1
2
0
1
0
1
0
1
1
1
1
1
0
0
2
1
0
0
1
1
1
1
1
0
1
1
0
1
0
2
1
1
1
0
0
1
2
0
1
1
1
0
0
0
2
1
1
0
0
1
0
2
1
1
2
0
1
1
2
2
2
2
0
2
2
1
1
1
0
2
1
0
0
0
2
0
0
1
3
1
1
0
0
1
1
2
1
2
1
1
0
2
1
1
1
2
2
2
1
2
1
1
0
0
0
1
1
2
1
1
0
1
1
1
1
0
2
0
0
1
1
1
2
1
1
2
2
0
0
0
2
1
1
1
1
1
0
0
1
1
1
1
2
2
1
2
0
2
1
0
1
1
0
1
1
3
2
1
0
0
0
1
0
1
1
0
1
1
2
1
0
1
0
1
1
2
1
0
1
2
0
0
1
0
0
0
2
1
0
0
1
1
0
0
2
1
0
1
0
3
1
2
1
1
1
1
2
0
1
2
0
1
0
1
2
0
0
1
2
0
0
1
2
2
1
2
2
0
2
0
1
1
0
1
0
0
2
0
1
1
1
2
2
1
2
0
2
1
1
1
1
2
1
1
2
0
1
0
1
1
0
1
1
2
2
1
1
2
1
0
1
2
0
0
0
0
1
2
2
1
0
1
0
1
2
1
0
2
0
0
0
0
0
1
0
0
1
0
0
1
1
1
2
0
2
2
2
1
1
1
1
1
0
1
2
1
0
2
1
0
1
2
0
1
1
1
1
2
0
1
0
1
0
2
2
0
2
0
2
0
1
1
1
0
2
0
0
1
1
0
1
1
1
1
1
1
2
0
0
1
1
1
0
1
0
0
1
1
1
1
1
1
0
1
1
1
0
0
2
3
1
2
1
1
1
1
2
0
2
1
0
1
0
0
1
1
2
2
1
2
0
2
0
2
0
0
1
0
1
1
1
2
0
0
1
2
0
2
1
2
0
1
2
1
1
0
2
0
0
2
3
2
0
1
1
2
1
1
0
1
2
0
1
2
0
1
1
2
1
1
1
0
1
1
2
1
0
2
1
2
0
0
1
1
0
2
0
2
1
0
2
1
1
1
2
2
1
0
1
0
2
2
1
1
0
1
0
1
1
2
1
0
2
1
1
1
1
1
2
1
1
1
0
1
0
0
1
2
1
0
0
0
0
0
2
2
0
0
1
1
1
0
1
1
2
0
1
1
1
1
2
0
1
1
1
0
0
0
0
0
0
0
0
1
2
0
1
1
1
1
0
0
0
1
1
0
0
1
1
2
3
2
2
1
0
2
1
1
1
0
2
1
1
1
1
0
1
0
1
1
1
2
2
1
0
2
2
0
1
1
1
1
1
1
2
2
1
1
2
1
0
1
1
2
0
1
1
1
2
2
1
1
0
2
2
1
1
1
0
1
2
0
2
1
0
0
0
1
0
1
1
1
1
0
1
1
0
3
0
0
0
1
1
2
0
1
0
0
0
0
1
0
1
1
0
1
1
0
0
1
1
1
0
0
0
1
0
1
2
1
2
0
2
2
1
1
1
1
1
1
2
2
2
1
1
1
0
1
0
0
1
2
0
1
1
2
0
0
2
2
0
2
1
1
0
0
2
1
1
0
1
1
0
1
0
0
1
1
1
1
1
1
0
1
0
1
0
2
1
0
0
2
1
1
0
1
0
2
0
2
1
1
2
1
0
2
1
0
1
0
1
1
1
0
0
1
0
0
1
1
0
1
2
2
0
3
2
1
1
0
1
1
0
1
1
2
0
1
2
1
2
1
0
0
4
1
0
2
1
1
0
0
1
0
1
1
1
1
3
2
0
0
1
0
0
1
1
0
2
1
1
0
0
1
2
0
1
0
1
1
0
2
1
1
0
1
0
0
1
1
1
1
0
0
1
1
2
1
1
0
1
1
1
1
0
2
1
1
1
1
2
1
1
1
2
1
0
1
0
0
1
0
0
0
2
2
1
0
1
2
2
1
1
0
1
0
1
1
1
0
0
0
1
1
0
1
2
0
2
2
0
1
0
0
2
1
1
1
0
1
2
1
1
2
0
1
1
2
1
2
1
1
0
0
0
0
0
0
1
0
2
0
0
0
3
2
1
2
1
2
1
0
2
1
0
0
0
0
1
2
1
1
1
0
0
2
0
0
1
1
1
1
0
1
2
1
0
0
0
0
1
3
0
1
2
0
0
2
1
0
2
1
2
1
2
0
1
1
2
1
0
1
0
1
2
0
1
1
0
0
2
1
0
2
1
2
1
2
0
2
1
1
0
1
2
1
1
1
1
2
1
2
1
1
2
1
0
1
2
0
2
0
1
1
1
0
0
0
1
0
2
0
0
2
3
2
0
2
2
2
1
1
1
1
0
1
1
2
0
1
1
0
2
0
1
0
1
1
1
0
1
2
1
1
1
0
1
1
1
0
0
0
0
1
1
0
0
2
1
1
1
1
1
1
0
0
1
1
2
0
0
1
2
1
0
1
0
1
0
1
1
0
0
2
0
1
1
2
1
1
1
1
2
1
1
1
1
2
0
1
1
2
0
0
1
1
0
0
0
1
1
1
1
0
0
1
3
2
1
0
2
1
0
2
1
1
0
1
1
6
1
1
1
2
1
0
1
0
1
1
0
0
0
2
1
1
0
1
0
0
0
1
0
1
0
2
0
2
1
1
2
1
1
2
1
1
1
0
1
0
1
0
2
0
0
1
0
0
0
1
0
1
1
0
1
1
1
2
2
0
0
1
1
2
0
2
2
2
1
1
2
1
0
2
1
0
1
2
1
0
2
1
1
0
1
2
1
1
2
0
1
1
2
0
1
2
1
1
1
1
1
1
1
2
2
1
1
1
1
0
1
2
0
0
0
0
1
1
0
0
1
0
1
1
1
0
2
1
1
1
0
1
1
1
1
1
2
1
3
1
2
1
2
0
1
0
1
1
0
1
2
2
0
2
0
2
1
0
2
0
1
2
0
2
2
2
0
1
0
2
1
0
0
0
2
2
1
2
1
2
1
0
1
0
1
1
1
1
0
1
2
0
0
1
0
1
1
0
1
0
1
0
0
1
1
1
2
1
0
1
0
1
1
1
1
2
1
2
0
0
2
0
0
0
1
0
1
0
1
1
2
1
1
1
1
1
0
2
0
1
2
0
1
1
1
0
1
1
0
2
1
0
2
1
0
1
1
1
0
0
1
1
0
1
0
1
2
1
0
1
0
0
1
1
2
2
1
0
0
2
1
0
0
2
0
2
2
0
0
1
2
2
0
1
0
0
1
0
2
2
1
1
1
2
2
2
2
2
2
1
1
0
0
1
1
2
1
0
0
1
1
0
0
1
0
1
1
0
1
0
1
0
1
2
2
0
1
0
2
1
1
2
0
0
1
0
1
1
0
2
0
0
2
1
1
2
1
0
0
1
1
0
1
1
1
2
1
1
0
1
2
0
1
1
1
0
0
1
0
1
1
0
1
1
1
1
2
1
0
1
1
1
1
1
1
0
0
1
2
0
2
1
1
2
0
1
1
2
1
1
1
0
2
2
1
1
1
0
0
0
0
0
1
0
0
1
1
1
1
2
2
1
1
1
1
0
0
0
1
2
0
1
1
0
2
1
1
1
2
1
0
0
1
2
0
1
1
1
2
1
0
1
0
2
0
1
2
1
1
1
0
0
2
0
0
1
2
0
0
2
1
1
0
1
1
1
1
1
0
1
0
0
1
1
1
2
2
1
1
2
1
1
1
0
0
4
2
0
2
2
1
1
1
2
0
0
0
1
1
0
0
1
0
1
0
1
2
2
0
2
2
0
2
0
1
2
1
1
2
1
0
2
2
0
0
2
1
2
1
0
1
0
0
2
1
0
1
2
4
2
1
1
0
1
2
0
3
0
0
0
0
1
1
2
0
1
1
0
1
1
2
0
1
2
1
0
0
0
1
1
0
1
2
1
0
2
0
1
0
1
1
1
1
2
1
0
1
1
1
1
2
1
1
0
0
0
0
1
1
2
0
2
0
0
0
0
0
0
1
0
1
0
1
1
0
0
1
1
1
1
0
1
2
1
0
1
1
1
0
0
1
1
0
2
0
1
1
1
0
1
2
0
1
3
1
1
0
1
0
0
0
0
2
2
0
1
2
1
1
2
1
2
1
0
0
3
1
0
0
2
0
0
2
1
1
0
1
0
0
0
1
2
0
2
2
0
0
1
1
3
0
0
1
1
1
1
1
1
2
0
0
2
2
2
0
0
0
4
2
1
0
1
0
1
2
2
1
1
2
0
2
1
0
1
1
2
1
1
1
1
0
1
2
0
1
1
2
0
1
1
0
2
1
1
1
1
0
2
0
0
0
2
0
1
1
1
2
1
0
0
1
1
1
2
1
1
1
0
1
4
1
1
1
0
0
1
1
2
1
1
1
2
0
0
2
2
2
2
0
2
2
0
1
2
1
0
0
1
2
1
1
0
1
0
3
1
2
1
0
1
0
1
0
0
0
0
0
0
1
1
1
0
0
1
1
1
0
1
1
2
1
2
2
1
1
2
1
1
2
1
0
0
0
0
0
0
0
0
0
1
2
1
0
2
2
2
0
0
0
1
2
0
0
1
1
1
1
1
0
0
1
1
1
1
1
2
2
1
0
1
0
1
1
1
0
0
0
1
2
0
1
2
1
1
0
2
1
1
0
2
2
2
1
2
0
1
1
2
2
1
2
0
1
1
0
2
2
1
1
1
0
1
0
0
1
0
1
1
0
0
1
1
0
1
2
0
0
0
2
1
1
1
1
1
2
2
0
1
0
0
1
1
1
2
2
2
1
2
2
2
0
1
0
0
1
0
2
1
0
0
0
2
0
1
2
1
1
2
0
1
0
1
2
2
1
0
1
1
0
1
1
0
1
1
1
1
1
0
2
1
1
2
1
2
1
1
0
0
1
0
2
2
0
2
0
1
2
2
1
2
1
0
0
1
4
3
1
0
1
0
1
2
0
2
2
2
2
1
1
0
1
0
1
1
2
1
0
0
1
1
0
0
1
2
1
1
1
0
2
0
2
0
1
1
1
1
0
1
1
1
2
0
1
0
0
2
1
0
2
0
1
2
0
0
1
0
1
0
0
0
1
1
1
0
2
0
1
1
0
2
0
1
1
0
1
1
1
0
1
2
1
1
0
1
1
1
2
0
1
2
1
0
2
1
1
1
2
2
1
0
1
2
0
0
1
1
1
0
1
0
1
1
0
0
0
0
2
2
1
0
2
0
2
1
1
1
2
1
1
0
2
2
2
2
2
1
0
1
1
1
0
1
2
1
1
0
1
0
0
0
0
1
1
0
1
1
2
1
1
1
0
1
1
0
1
2
2
2
1
1
3
1
0
1
0
1
1
0
2
1
1
1
1
0
0
1
1
0
2
0
2
0
0
0
1
1
2
0
1
0
2
0
2
1
1
2
1
1
2
1
0
1
1
1
2
1
3
2
1
1
1
1
1
1
2
1
1
0
1
1
2
1
1
2
1
1
0
0
1
1
1
2
2
0
1
0
1
0
0
2
1
0
1
1
0
1
1
1
2
0
2
1
1
1
0
0
1
1
1
2
0
1
1
0
2
0
1
1
0
0
1
1
1
3
2
1
1
2
0
1
2
1
1
1
1
1
0
0
0
1
2
0
1
1
1
0
1
1
2
0
1
1
1
0
1
1
1
0
0
0
0
0
1
0
1
0
1
1
0
2
0
0
0
1
1
1
1
1
0
1
0
0
1
2
1
1
0
0
0
0
2
0
1
0
1
1
1
1
0
1
2
2
1
0
3
0
1
1
2
1
2
0
1
2
2
1
1
0
2
1
2
1
0
1
1
0
0
1
0
1
1
0
0
0
1
1
2
2
1
2
1
1
0
0
1
1
1
1
0
1
0
1
0
2
2
1
1
1
0
0
1
1
1
2
1
1
2
2
2
1
0
1
1
2
0
0
0
0
1
0
1
0
0
0
1
2
3
3
1
0
1
1
2
1
1
1
0
1
2
2
1
1
3
1
1
2
2
1
0
0
1
1
2
0
1
4
0
1
1
1
1
1
3
0
1
0
1
0
0
1
0
2
1
0
1
1
1
1
1
1
1
1
1
1
0
1
1
0
2
0
1
0
4
1
1
2
2
1
0
0
2
1
1
2
1
1
2
1
2
3
0
0
2
1
1
1
1
1
1
1
0
1
0
0
0
1
0
1
2
0
1
0
2
1
2
0
0
1
1
1
1
1
1
0
1
0
2
0
1
1
0
1
0
2
1
2
0
0
1
1
2
0
1
1
0
2
1
1
1
0
2
1
1
1
1
2
1
2
1
0
0
1
1
2
2
1
1
1
1
0
1
2
0
1
0
1
1
0
2
2
2
1
0
2
0
2
0
0
0
2
1
1
1
1
1
2
0
2
0
1
2
0
1
1
0
1
1
2
1
2
1
1
0
1
2
1
1
1
1
1
1
1
2
0
2
1
1
3
0
0
2
0
0
2
2
1
1
0
0
2
1
1
0
1
0
0
2
0
0
1
1
0
1
2
0
1
1
1
2
1
1
2
2
0
1
1
2
1
1
0
1
1
1
1
1
1
0
0
0
1
1
0
1
0
1
0
0
1
1
0
1
1
1
1
0
1
0
2
0
0
0
2
2
2
0
1
2
1
0
2
2
1
1
2
1
0
2
1
2
2
0
0
0
0
0
2
1
1
2
0
1
0
0
0
0
1
1
0
0
1
1
2
3
2
1
1
0
2
1
2
0
1
2
2
2
1
1
2
0
1
1
1
0
0
0
1
0
1
2
0
1
1
0
1
0
1
1
1
0
1
2
1
0
4
1
1
2
2
0
0
2
1
0
1
1
0
2
0
2
0
2
0
1
2
0
0
1
1
2
2
0
1
0
0
0
1
3
2
1
1
1
4
1
1
1
2
1
0
1
2
1
0
0
1
0
1
2
1
1
1
0
1
1
0
0
2
0
1
0
0
2
2
2
1
1
0
0
2
2
2
1
1
1
1
0
1
2
0
1
0
1
2
0
2
1
1
1
1
0
1
1
1
1
2
1
0
1
1
2
0
1
1
1
2
1
1
1
0
0
0
1
1
1
0
1
2
1
0
1
1
0
1
0
1
0
0
1
1
0
1
1
1
1
0
1
1
2
1
0
0
2
2
2
1
1
1
2
1
0
0
2
2
1
0
0
1
3
1
1
0
0
0
1
2
0
0
1
1
1
0
1
1
1
0
1
1
0
2
1
0
1
2
0
0
0
0
2
1
0
0
1
1
0
3
0
0
0
0
3
1
1
1
1
1
1
1
1
2
2
1
1
1
3
0
2
1
0
1
2
1
0
1
1
1
1
1
1
1
1
1
2
1
0
1
0
0
2
0
2
1
2
0
2
0
1
1
2
1
0
2
0
2
1
0
1
0
2
1
0
2
1
0
0
2
0
1
2
1
0
1
0
0
1
1
2
1
1
1
0
1
0
0
1
1
1
1
2
1
1
0
0
0
1
2
2
1
0
0
0
0
0
1
1
0
0
2
0
2
0
2
1
1
1
1
0
2
1
1
0
0
2
1
1
0
2
0
0
1
0
1
2
2
3
2
0
2
1
1
2
0
0
2
0
0
1
2
1
1
0
1
0
1
0
1
1
1
1
1
2
0
1
0
2
1
0
2
0
1
1
1
1
3
1
1
0
0
1
1
0
2
2
2
1
1
1
0
0
1
1
0
1
0
1
2
0
1
1
1
0
1
0
2
1
0
0
0
1
0
1
2
1
2
1
0
0
0
2
2
0
2
0
1
2
0
2
2
1
2
0
1
2
1
2
1
0
1
1
0
2
4
2
1
0
1
2
0
1
2
0
1
1
1
1
1
0
1
2
1
1
0
1
0
0
1
2
1
0
0
0
1
0
1
0
1
1
1
2
1
2
0
1
1
1
1
1
0
0
0
0
0
1
2
0
1
0
2
1
2
1
1
2
0
0
1
1
1
2
1
1
1
2
1
1
1
2
2
2
0
2
1
2
2
1
0
2
1
1
1
0
0
1
2
2
2
0
1
2
0
1
0
0
3
2
2
0
2
2
1
2
0
2
2
1
1
1
1
2
0
1
2
1
1
1
2
1
1
2
2
1
2
1
1
0
1
2
2
1
2
0
1
1
2
2
0
1
1
0
1
0
2
0
0
1
1
1
0
1
1
1
1
1
1
1
1
2
1
1
2
0
1
3
1
0
1
1
1
1
2
0
2
1
1
1
2
0
1
1
0
2
0
0
1
1
2
0
1
1
0
2
2
0
0
2
0
1
3
1
2
0
1
1
1
1
2
0
1
1
0
0
1
2
0
1
1
0
2
3
1
1
1
0
1
1
2
1
1
1
0
2
0
1
0
2
2
2
0
1
1
0
1
0
0
0
2
0
1
1
2
1
2
1
0
1
0
1
1
0
0
1
0
1
1
2
1
1
0
2
0
1
0
1
2
0
1
0
2
1
1
2
1
0
1
0
0
0
1
1
0
1
0
0
1
2
2
1
0
2
0
2
1
2
1
0
0
0
1
1
1
0
2
1
1
1
1
0
1
0
1
0
0
2
1
1
1
0
1
7
0
1
1
1
0
3
1
1
0
0
2
2
2
2
1
1
2
0
0
0
1
2
1
1
2
1
1
0
0
1
1
1
2
1
0
0
1
2
1
0
2
0
0
2
2
0
1
2
2
1
1
1
1
1
1
1
0
1
0
2
1
1
1
0
0
2
2
2
0
1
0
0
0
1
2
3
1
1
0
1
0
0
2
0
0
2
1
0
2
1
1
1
0
0
2
0
1
1
1
1
0
2
0
1
1
0
2
1
0
0
1
1
1
1
0
0
1
0
0
1
1
2
2
3
2
1
1
0
2
2
1
2
1
1
1
0
0
0
2
1
1
0
2
1
0
0
0
0
0
1
2
0
1
1
1
0
0
0
2
1
0
1
1
1
1
0
0
7
1
0
0
0
1
0
2
1
1
0
2
1
1
0
2
2
1
1
1
1
2
2
0
2
0
1
2
1
6
1
1
0
1
1
1
1
2
1
3
2
1
0
0
1
2
0
0
1
2
1
0
1
1
0
0
0
1
1
1
1
0
1
2
1
3
0
2
1
1
0
1
0
1
2
0
0
1
1
0
0
1
0
1
1
1
0
1
0
1
0
2
1
0
3
2
0
0
1
0
0
1
1
1
1
1
1
1
2
1
1
0
2
0
1
0
2
0
2
1
1
1
1
2
1
2
0
1
1
1
1
0
1
1
1
2
0
0
1
1
0
1
2
2
0
1
0
0
1
0
0
2
1
2
1
0
0
2
0
0
2
1
2
1
1
0
3
0
3
0
0
0
1
1
1
0
1
1
2
1
1
1
0
1
1
0
2
1
1
1
0
0
0
1
1
1
1
2
2
1
0
1
2
2
1
4
1
0
1
1
1
0
2
1
2
1
0
1
1
0
1
0
1
0
1
2
1
0
0
1
1
1
1
4
2
1
5
0
1
3
3
2
0
1
1
1
0
4
0
1
0
1
0
0
0
1
0
1
2
1
1
0
3
0
0
1
2
1
2
0
2
0
1
1
0
0
0
0
1
1
1
1
1
1
0
2
1
1
1
1
0
2
1
2
0
1
2
2
1
1
1
0
1
1
0
1
2
1
2
1
1
1
1
2
1
0
0
1
0
1
1
1
1
2
1
1
1
2
0
1
1
0
0
1
1
1
1
2
1
2
1
1
1
1
0
1
1
1
0
1
0
1
0
0
1
1
1
1
0
0
1
0
2
0
0
1
0
1
0
0
2
1
0
1
1
2
2
2
1
2
2
1
1
0
0
0
1
1
1
0
1
0
0
1
1
0
2
1
0
0
1
0
0
1
0
0
0
1
0
1
1
0
1
2
1
2
1
2
1
1
0
1
2
1
1
1
0
0
1
0
0
1
2
2
1
3
2
1
1
2
2
1
1
0
0
1
0
1
0
0
1
1
1
0
0
0
2
2
1
2
1
1
0
1
0
1
1
2
1
0
0
2
2
1
1
1
1
2
0
1
2
1
1
0
1
1
1
1
1
3
1
1
1
0
0
1
0
1
1
2
0
0
0
0
1
0
0
1
0
2
1
1
1
0
1
1
1
0
1
0
1
1
2
1
0
1
2
1
1
0
1
2
0
1
0
2
2
1
2
2
1
0
1
1
0
2
0
1
1
0
2
1
1
0
1
1
0
1
0
1
1
1
2
1
0
1
2
0
2
2
1
1
0
1
0
1
0
1
0
1
0
2
1
1
1
0
1
1
0
1
1
0
2
1
1
0
1
1
0
1
0
0
1
1
2
2
1
2
0
1
1
2
1
1
1
1
1
1
1
1
1
1
1
0
0
0
0
3
1
0
0
0
1
0
0
1
1
1
1
1
0
0
0
0
2
1
1
2
1
1
1
0
1
2
1
1
1
1
1
2
2
0
1
1
1
0
1
2
2
0
2
1
0
0
0
1
1
1
1
1
3
0
2
1
3
0
1
1
0
1
1
1
2
1
0
0
0
1
0
1
0
1
2
1
2
0
2
2
2
0
1
1
0
1
1
1
1
0
0
1
1
0
2
1
2
0
1
0
2
2
2
0
1
1
0
2
1
1
1
1
1
0
0
0
2
0
2
2
1
0
1
1
0
1
2
2
0
4
2
0
1
1
1
0
0
1
1
1
0
2
1
1
1
1
1
2
1
0
0
3
2
1
1
1
1
1
1
1
2
0
0
1
0
2
2
0
0
1
1
1
1
0
2
2
0
2
1
1
1
2
1
0
1
0
1
1
0
1
1
0
1
2
1
2
2
0
1
1
1
1
0
2
1
0
0
0
1
1
0
2
1
1
1
1
2
1
0
0
2
0
1
0
1
0
1
2
1
1
1
2
2
0
1
2
1
1
0
3
2
0
0
1
2
1
1
1
1
2
4
1
1
1
0
1
1
2
2
2
1
0
1
0
1
0
0
1
1
2
1
1
1
0
0
2
0
0
1
1
1
1
1
2
0
0
1
0
1
1
0
0
1
1
1
2
0
1
1
1
2
2
1
0
1
1
0
1
1
0
1
0
0
2
1
0
0
1
2
1
1
1
0
0
0
1
1
1
2
1
0
0
1
0
0
0
1
1
2
2
1
1
0
1
0
2
1
0
3
0
1
1
1
2
1
1
0
1
0
1
1
0
1
1
2
1
1
0
0
1
1
0
0
1
1
1
2
1
1
4
0
1
2
0
2
1
1
2
0
2
1
1
1
1
1
1
1
2
1
2
2
1
1
2
2
2
2
0
2
0
1
1
0
1
0
1
1
3
1
1
2
1
1
0
0
1
1
1
1
1
1
1
1
2
0
1
1
2
2
0
1
1
1
1
1
0
1
0
2
2
1
0
2
1
0
0
0
0
1
1
1
1
0
1
1
2
1
0
1
0
1
1
1
2
1
2
2
1
0
1
1
0
2
0
1
0
0
1
2
2
0
2
0
1
1
1
1
1
1
2
1
1
0
0
2
0
1
1
1
0
1
2
2
2
0
0
1
1
0
0
1
1
0
1
1
0
0
0
0
0
1
1
0
1
1
0
2
2
3
1
2
0
2
2
0
0
2
1
2
1
1
1
2
0
0
1
0
1
2
1
2
1
1
1
1
0
2
1
1
0
1
1
0
0
1
1
2
1
1
1
0
0
0
1
1
1
2
2
0
2
1
1
0
2
2
1
0
1
1
6
0
1
0
1
1
2
1
2
1
0
1
1
0
0
0
1
2
1
0
0
2
1
1
2
1
0
0
2
2
1
1
1
0
2
1
1
1
0
1
1
1
1
0
0
1
1
1
1
0
2
0
0
1
1
0
2
1
1
1
0
0
2
0
0
0
2
0
1
2
1
0
2
0
0
0
0
1
1
1
1
0
1
2
1
1
0
0
0
1
0
0
0
1
0
1
0
1
1
1
2
1
0
1
0
1
1
0
2
1
1
1
2
0
1
0
0
1
2
0
0
1
1
1
1
1
3
1
0
1
1
1
1
0
2
2
0
0
0
1
2
1
6
0
2
1
1
2
0
0
0
1
0
1
0
1
3
2
1
4
2
1
1
0
1
2
0
1
1
1
1
1
2
2
0
1
0
0
0
1
1
1
1
1
0
0
0
0
0
0
1
1
1
0
0
2
2
1
1
0
0
1
2
1
3
1
0
1
1
1
1
1
0
0
1
2
1
1
1
2
2
1
1
2
1
1
1
0
1
2
0
1
0
1
1
2
0
0
2
2
0
1
2
2
1
1
1
1
2
1
1
0
1
0
2
0
0
1
1
0
1
2
1
0
0
1
1
0
1
2
1
2
1
0
2
1
0
1
1
0
1
1
1
0
1
1
2
0
1
1
2
1
1
3
2
1
2
1
1
1
2
2
0
0
2
1
1
1
1
1
2
1
0
1
1
1
1
2
2
0
0
0
0
0
1
1
0
1
1
0
1
0
0
1
0
1
0
1
1
2
0
1
0
2
0
0
1
2
0
1
1
1
1
0
1
1
1
2
0
2
0
0
1
2
1
1
1
1
1
0
1
0
2
1
2
2
1
2
2
1
2
2
1
0
1
2
1
2
1
0
2
1
1
2
2
0
1
0
0
1
2
1
0
1
1
1
1
1
0
2
0
1
0
0
2
2
0
0
1
1
2
1
0
0
0
1
1
0
1
0
0
1
1
0
0
2
0
1
1
0
0
1
1
1
1
1
0
1
1
1
1
1
1
1
2
0
2
1
0
2
2
2
0
0
1
2
2
1
3
1
1
2
1
1
1
1
1
2
1
1
0
2
1
1
1
2
1
1
1
0
0
2
1
3
0
0
1
0
0
1
1
1
0
2
0
2
1
1
0
1
1
1
0
1
2
1
2
1
0
1
3
1
1
1
1
2
0
0
1
0
1
1
0
1
1
1
0
1
2
1
1
2
0
1
1
1
0
5
1
2
1
1
0
1
0
1
0
2
1
1
0
2
0
1
1
0
0
2
0
0
0
1
1
1
2
2
1
1
0
1
2
2
1
1
0
2
1
1
0
1
2
1
2
0
2
2
1
0
1
2
1
1
1
1
2
0
0
3
0
1
0
0
1
3
0
1
1
2
1
2
0
1
1
0
0
1
0
2
1
1
1
1
1
1
0
1
1
2
2
2
0
2
1
0
0
0
0
1
0
1
1
2
1
0
1
1
1
2
2
0
1
1
0
2
2
0
0
1
1
1
0
1
1
1
0
0
2
1
1
1
1
2
1
0
2
0
1
1
0
1
2
0
1
2
2
0
1
2
2
2
1
1
2
0
1
1
1
0
0
2
1
2
1
0
0
2
0
1
0
0
1
1
1
1
0
2
0
2
1
1
1
0
0
1
2
1
2
1
0
2
0
2
3
0
0
1
1
0
1
0
0
1
2
1
0
0
1
2
0
1
1
0
1
2
1
2
0
2
0
2
1
0
0
0
1
1
1
3
1
2
1
0
0
1
1
1
1
1
0
2
4
0
2
1
1
0
0
1
1
2
2
1
1
2
0
1
1
2
0
2
2
0
1
0
0
1
0
2
1
0
0
1
1
1
1
0
0
1
2
1
0
0
0
1
1
0
1
2
1
0
1
1
0
1
0
1
1
1
0
0
2
1
1
1
1
2
1
1
1
0
2
0
2
2
1
2
1
2
0
1
0
0
0
1
2
1
1
0
1
0
1
0
2
2
2
1
0
1
0
0
0
1
1
1
2
0
0
0
1
1
1
2
1
1
1
2
0
0
2
1
1
1
2
5
1
0
1
2
0
1
0
1
1
1
1
0
1
2
0
2
1
1
1
0
1
2
0
0
2
0
1
1
1
1
1
1
0
0
1
1
0
1
2
1
0
0
1
0
1
1
0
1
2
0
0
0
0
0
0
1
0
1
1
0
1
0
1
0
0
1
1
1
4
2
1
1
1
1
1
1
1
2
2
2
0
0
0
3
1
1
2
2
0
1
0
2
1
1
1
1
0
2
0
0
1
1
1
0
1
1
0
0
0
1
1
1
0
1
2
0
0
1
0
0
1
0
1
2
0
2
1
0
0
1
2
4
1
0
2
0
2
1
1
1
2
1
0
1
1
1
1
2
1
1
1
1
1
0
2
2
2
1
1
1
2
2
1
2
5
1
2
1
2
2
0
2
2
1
1
1
0
1
1
0
0
0
1
0
0
0
0
2
0
2
1
2
2
2
1
0
1
0
0
1
0
1
1
0
0
2
1
0
2
2
0
1
0
0
1
0
1
2
1
1
2
1
0
0
2
2
0
0
0
2
1
1
2
2
1
1
2
1
1
2
0
2
1
2
0
2
1
0
1
1
0
1
2
1
1
1
2
0
1
2
1
1
0
1
2
1
1
1
0
1
0
2
0
1
2
1
1
0
1
0
0
1
0
1
0
1
1
1
2
1
0
2
1
2
1
1
2
1
1
2
0
1
0
0
1
0
1
2
2
1
1
0
1
0
0
0
1
2
1
2
1
1
2
2
2
0
1
1
2
0
1
2
1
0
0
0
0
0
1
1
2
2
1
0
1
1
0
2
2
0
1
0
1
1
1
1
1
1
0
1
0
0
1
0
1
1
1
0
0
1
0
1
2
1
2
0
0
0
1
1
0
1
0
0
1
1
0
0
0
1
1
2
2
1
0
0
1
1
0
0
0
2
1
1
1
0
1
1
1
2
2
2
1
1
0
2
1
0
0
1
0
2
1
0
2
0
0
0
1
2
1
1
2
2
0
0
0
1
0
2
0
1
1
0
0
2
1
2
2
1
2
0
1
2
1
1
0
1
0
0
1
2
2
1
2
0
2
1
0
1
1
3
1
0
1
1
1
0
0
1
1
0
2
0
2
1
1
1
0
0
0
1
2
0
1
0
2
1
1
1
2
1
2
1
2
1
2
1
1
1
1
2
1
2
1
1
2
1
1
1
2
1
3
1
0
1
1
1
0
1
0
1
2
1
0
0
1
1
1
1
1
0
2
1
0
1
1
1
2
1
1
1
2
0
1
1
1
1
1
1
2
0
1
2
1
1
1
0
3
0
3
2
1
0
0
1
2
0
1
1
1
1
0
1
2
0
0
0
2
0
1
2
1
0
1
0
1
1
1
1
0
1
2
0
0
1
1
0
0
1
1
1
0
0
0
2
0
1
0
1
1
2
0
0
2
0
1
0
0
0
1
0
2
2
1
1
1
1
1
1
0
2
1
0
2
1
1
1
2
2
2
0
0
1
0
0
1
2
1
2
2
1
1
0
2
1
2
0
0
1
1
0
0
0
2
1
0
0
1
2
1
1
1
1
1
2
2
1
0
3
1
0
0
1
1
0
0
1
0
0
1
1
0
0
0
1
2
1
2
0
1
1
1
1
0
1
1
0
1
1
2
2
0
1
0
0
1
1
1
1
1
1
2
1
0
1
1
0
1
1
1
0
1
1
0
0
0
0
0
0
1
2
1
1
1
1
1
2
0
0
1
1
1
0
1
0
0
1
1
1
2
1
2
1
2
2
0
1
1
2
0
1
1
1
2
0
1
1
0
0
1
1
1
1
1
1
0
1
2
0
0
0
1
1
0
1
0
1
2
0
0
1
1
1
1
0
2
1
2
2
2
0
1
0
2
1
1
2
0
0
0
1
1
1
0
1
2
1
0
0
1
0
1
0
1
1
2
0
1
1
2
2
1
0
1
1
1
1
2
1
1
1
0
0
0
0
1
1
1
2
1
0
1
1
1
1
0
3
1
1
2
1
0
0
2
1
0
2
1
1
1
1
1
1
0
2
0
2
1
1
1
0
1
0
1
0
2
0
1
0
1
0
0
0
1
0
1
2
0
0
1
1
0
1
0
0
2
0
1
1
0
2
1
0
2
1
0
1
0
1
1
0
1
1
2
1
2
1
1
1
0
2
1
1
1
1
0
0
0
2
1
1
0
0
2
2
1
0
0
1
1
1
2
1
2
1
0
2
2
0
1
1
1
2
0
0
1
0
2
0
0
2
1
2
0
1
0
2
2
1
0
1
1
0
3
2
1
0
0
1
1
1
1
2
1
0
0
1
2
0
1
0
1
0
2
0
1
2
0
0
1
1
2
1
0
1
0
1
1
3
1
1
0
0
0
1
1
1
1
1
0
0
1
1
1
2
1
2
1
1
1
0
1
0
2
1
0
0
1
2
1
1
2
3
1
3
2
0
1
1
2
1
1
0
1
1
0
1
0
1
1
1
0
2
2
1
0
0
0
1
1
1
2
2
0
2
2
2
1
1
2
1
0
0
1
1
0
0
0
0
0
1
1
1
0
2
2
1
0
1
1
0
0
0
1
1
1
1
0
2
2
1
0
2
2
1
0
1
1
1
1
1
2
0
2
1
1
1
0
1
0
2
1
2
0
1
0
0
0
1
2
0
1
0
1
1
2
0
1
2
0
1
1
1
0
1
0
0
2
1
2
0
1
1
1
0
1
1
0
0
1
1
2
2
0
0
2
1
1
1
2
1
2
2
0
2
1
1
1
2
1
0
1
1
2
1
0
0
2
1
0
0
0
2
1
0
1
0
1
2
1
0
2
1
1
1
0
1
1
1
1
0
1
2
2
1
1
0
1
0
1
1
1
2
1
1
1
0
1
0
1
2
2
1
1
1
1
2
1
1
2
1
1
2
1
0
1
0
1
1
1
1
2
2
2
1
1
1
1
2
0
1
0
2
1
0
2
2
2
2
1
0
1
0
1
2
1
0
0
0
2
1
1
1
0
0
0
0
1
0
1
1
1
2
2
0
2
0
4
0
0
1
1
2
2
1
2
0
0
1
0
1
2
2
1
0
1
1
2
1
0
0
0
0
1
1
0
1
0
0
2
1
0
1
0
1
2
2
1
1
0
0
1
0
2
2
0
1
2
1
1
2
2
0
2
2
0
1
0
2
1
1
1
1
1
0
1
1
2
2
1
1
2
0
0
0
2
2
1
1
0
0
0
1
2
2
0
1
1
1
1
0
0
1
2
1
2
1
0
1
1
1
1
2
2
1
2
0
2
0
0
0
2
1
2
1
1
1
0
0
1
7
1
1
2
0
0
2
0
0
0
1
2
0
2
0
0
1
2
1
1
0
1
1
1
0
0
1
0
2
0
1
0
2
2
2
0
1
1
1
1
2
1
1
0
1
2
2
0
1
0
2
1
0
0
1
2
1
2
1
2
1
0
1
1
2
0
1
0
1
1
1
0
0
1
1
1
0
4
0
2
1
2
1
0
0
1
1
0
0
1
2
0
1
2
3
1
0
2
1
2
1
1
1
0
2
0
0
1
3
1
2
1
0
2
1
0
1
1
0
1
2
0
2
2
0
0
1
0
2
0
2
0
0
0
1
2
2
1
2
2
0
1
2
1
0
1
1
2
1
0
1
1
0
2
2
1
2
1
1
1
0
0
2
0
0
1
1
1
1
0
1
0
1
2
3
1
0
3
1
2
1
0
1
1
1
0
2
1
2
1
0
0
2
2
0
2
1
1
1
1
0
1
1
0
0
1
1
0
0
2
0
1
1
1
1
1
2
1
0
2
0
2
0
1
0
0
1
1
2
2
2
0
1
1
2
1
1
0
1
1
1
2
1
0
2
0
1
1
2
1
1
0
0
0
2
1
0
1
1
2
1
0
0
1
2
2
1
2
2
3
1
2
2
2
1
1
2
1
1
1
1
0
1
1
0
0
0
2
1
1
2
0
0
0
0
1
2
1
1
1
1
0
0
1
1
1
1
2
1
1
0
1
2
2
1
1
2
1
2
2
1
0
1
1
1
3
0
2
1
2
1
1
1
1
1
2
1
0
0
3
1
3
1
2
1
2
0
0
2
2
0
0
5
1
2
1
1
0
0
1
1
1
0
1
0
1
1
2
1
1
1
1
0
0
0
0
2
0
2
0
0
2
1
1
2
1
0
0
0
1
1
1
2
1
1
1
1
0
1
1
1
1
0
0
0
1
1
1
0
2
2
1
0
0
0
0
1
0
0
0
1
0
1
0
1
0
1
0
1
1
0
0
0
2
4
0
0
3
0
0
2
0
2
1
1
2
1
2
2
0
2
1
1
0
0
1
0
2
2
0
1
1
1
1
0
1
1
0
1
0
0
1
3
2
1
1
1
0
0
0
2
1
1
0
0
1
1
1
2
1
0
1
1
0
1
0
0
1
0
0
2
1
1
2
1
2
0
0
1
2
1
1
0
1
2
2
0
1
2
0
1
1
1
0
2
1
0
0
0
1
0
1
0
1
1
0
0
1
0
2
2
2
1
1
1
0
1
0
1
1
1
1
1
0
1
3
0
1
0
2
2
2
1
2
2
1
1
2
1
0
1
2
0
0
1
1
0
0
1
1
0
1
1
0
2
0
2
1
0
1
1
0
0
1
1
1
1
1
0
1
0
1
0
0
0
0
0
2
2
0
1
1
2
1
1
2
1
2
2
3
0
0
2
1
1
1
1
0
0
1
0
0
1
0
1
2
0
2
2
0
2
0
0
1
1
2
1
1
1
0
0
6
1
0
0
1
1
0
1
1
1
0
0
1
0
1
1
1
1
0
0
2
1
1
2
1
1
1
1
0
0
2
1
0
0
0
1
0
2
0
0
1
1
1
1
1
0
1
0
3
0
0
0
1
0
1
1
0
1
1
0
0
3
1
0
0
1
1
0
1
2
1
0
1
2
0
0
2
1
0
1
2
0
0
1
1
1
5
1
0
2
2
0
0
1
1
1
2
2
2
1
1
1
0
1
2
1
0
0
1
2
0
0
1
0
2
1
2
0
0
0
1
2
2
0
2
1
1
0
1
2
0
1
1
1
0
1
0
0
1
0
1
0
2
2
2
1
0
1
0
2
1
2
1
3
1
0
0
1
1
1
0
0
0
1
0
1
2
0
1
2
3
2
2
0
2
1
0
1
1
0
0
2
1
0
2
0
1
1
0
1
2
1
2
1
0
1
1
1
1
0
2
0
1
0
0
1
0
1
0
2
1
2
0
0
1
2
2
1
0
1
1
1
1
1
3
2
1
1
2
0
0
1
0
1
2
1
1
0
1
2
0
1
0
0
0
0
0
0
0
0
1
2
1
1
2
1
0
0
0
0
2
0
1
1
1
0
0
2
0
0
1
1
0
1
1
2
2
0
0
1
0
0
1
1
1
1
0
1
1
0
0
1
3
1
2
1
0
2
0
1
1
1
0
2
0
1
2
1
1
1
2
1
1
2
1
1
0
1
1
0
0
1
0
2
0
1
0
0
0
1
0
1
1
1
0
1
1
1
0
2
1
0
0
0
0
1
1
0
0
1
1
1
0
2
1
1
1
2
2
0
1
1
0
1
1
3
1
2
0
2
1
1
2
2
1
1
1
1
1
2
1
0
0
1
0
0
1
0
0
2
1
1
0
0
1
1
1
0
1
1
0
0
1
1
1
1
1
0
0
0
1
1
2
1
0
0
0
1
1
1
0
1
0
1
2
2
1
1
1
0
1
1
1
2
0
2
2
2
1
1
1
1
2
0
2
2
1
0
2
2
1
1
1
1
1
2
3
0
2
1
0
1
0
0
0
1
2
2
2
1
2
1
0
2
2
2
1
0
0
0
2
0
1
1
1
1
1
1
0
2
1
1
1
1
1
0
2
0
0
0
0
0
4
1
1
1
0
1
2
1
0
0
1
2
1
0
1
0
1
2
1
0
1
2
2
2
0
0
1
2
0
1
2
0
0
1
1
0
2
1
1
1
0
1
1
1
0
0
0
2
1
0
1
2
2
1
2
2
0
0
0
0
0
0
1
2
2
2
1
1
0
0
3
0
1
0
1
1
2
0
1
1
1
1
2
2
0
1
1
1
1
1
1
1
1
0
1
2
1
1
2
1
1
2
0
0
2
2
2
0
2
0
1
1
0
1
0
1
1
2
2
2
1
0
1
1
2
5
2
0
0
1
1
1
1
1
1
0
0
0
0
4
1
2
2
1
0
1
0
1
0
2
1
0
5
1
0
2
1
1
1
2
2
2
0
1
2
1
0
2
1
1
0
0
0
1
1
2
1
1
1
1
0
0
1
0
1
0
1
1
0
1
1
2
0
2
1
1
1
2
0
2
0
2
2
1
1
2
0
1
0
2
1
1
0
1
2
1
0
0
0
1
0
0
1
1
0
1
1
0
0
1
2
2
0
1
2
2
0
0
0
1
0
0
3
1
1
3
1
2
1
0
0
1
1
1
0
2
2
1
2
0
1
1
2
0
1
2
0
1
0
0
0
1
0
1
1
0
0
0
1
1
1
1
0
1
0
1
2
1
1
2
0
0
1
0
0
0
2
0
1
1
0
1
1
2
1
0
1
1
1
0
2
0
0
1
1
0
1
2
1
1
1
0
0
2
1
2
1
0
0
1
1
0
1
0
1
1
0
1
1
1
0
0
1
0
1
1
1
0
2
2
1
0
0
1
1
1
0
0
1
0
0
1
1
0
2
1
0
0
1
1
1
1
1
0
0
0
1
1
0
1
0
0
2
0
0
1
0
1
2
0
0
2
2
1
0
1
1
2
1
1
0
0
0
1
1
2
0
1
1
4
0
1
0
0
0
1
1
1
1
1
1
2
1
0
0
1
2
2
0
0
0
1
1
2
1
3
1
0
0
1
2
0
0
1
0
1
1
2
1
2
0
0
0
0
3
1
0
0
0
1
1
0
0
2
2
1
2
0
2
2
2
0
0
2
2
2
0
1
0
1
1
1
1
2
1
1
1
0
1
0
1
0
0
0
0
1
0
0
2
1
0
1
1
1
1
0
0
2
1
1
1
1
0
1
1
1
1
0
0
1
2
0
2
2
0
2
0
2
0
0
1
2
1
2
1
2
1
0
1
1
0
1
1
1
1
1
2
1
0
0
2
1
2
0
0
0
1
2
0
1
1
1
1
2
1
1
0
1
0
2
0
0
1
2
1
0
1
0
1
1
1
0
0
0
1
4
1
0
1
1
1
1
0
2
1
2
1
1
1
0
2
1
1
2
1
1
0
0
2
1
1
0
0
1
2
0
1
1
2
1
2
2
2
0
3
1
1
2
0
0
0
2
1
1
1
2
1
2
2
0
1
0
0
2
1
1
0
2
0
1
1
2
1
0
2
0
2
1
1
1
1
3
1
1
1
0
0
2
1
0
1
2
2
0
0
1
1
0
1
2
2
2
2
2
2
1
2
0
2
1
1
2
0
3
0
1
0
2
0
0
1
2
0
2
1
1
1
1
1
1
0
5
1
1
0
2
0
1
1
1
1
1
0
0
1
1
2
0
1
2
1
1
2
1
0
1
1
1
2
2
1
1
2
0
1
1
2
1
2
1
0
1
0
1
0
2
0
0
2
0
0
0
1
2
0
0
0
1
1
0
1
1
1
0
0
0
0
1
1
1
2
1
0
0
1
1
0
0
1
2
1
1
1
1
1
1
1
1
1
1
1
1
0
0
1
2
2
2
0
1
0
2
1
0
0
1
2
2
2
1
2
1
2
1
0
1
2
2
2
1
1
0
2
1
1
1
0
0
1
0
1
2
1
2
0
1
1
1
1
1
2
1
1
0
1
2
1
2
1
0
1
1
1
1
2
0
1
2
1
2
0
2
2
1
1
0
1
0
1
2
0
2
1
0
2
0
0
1
1
2
2
0
2
1
1
1
0
1
1
0
2
1
1
1
1
0
1
2
0
1
2
0
0
0
0
1
1
0
1
1
1
2
2
2
0
1
2
1
1
1
1
0
1
3
1
1
0
0
0
1
0
0
1
0
0
2
1
1
1
2
0
1
0
1
2
0
1
1
2
1
1
1
2
1
1
2
0
1
0
1
0
1
0
1
1
0
1
1
0
1
0
1
2
0
1
1
0
2
0
0
0
0
1
3
1
2
1
0
0
1
0
0
1
0
0
1
1
2
2
1
1
1
0
0
1
1
1
2
1
1
1
1
1
1
2
0
0
1
1
1
1
1
1
0
1
2
0
1
1
2
1
0
1
0
0
1
1
1
1
0
0
1
1
2
0
0
1
1
1
2
2
4
1
0
0
2
2
0
2
1
1
1
2
2
1
0
0
0
0
0
2
2
0
1
3
2
2
1
2
0
0
1
1
0
2
1
2
0
1
1
0
1
3
0
1
1
2
2
1
1
0
0
0
1
2
1
1
0
2
1
0
1
1
0
1
1
2
2
1
1
1
1
3
2
0
0
0
1
1
0
0
1
0
0
0
1
1
1
2
1
1
2
1
1
1
1
1
1
1
0
1
2
1
2
1
2
2
0
1
0
1
1
0
2
0
1
0
2
0
1
1
1
1
1
1
2
2
2
1
2
1
0
2
0
0
1
0
2
1
0
2
2
1
0
2
1
1
3
0
0
0
1
1
0
0
1
2
2
1
2
2
1
0
1
0
2
0
1
0
1
1
1
0
1
0
1
1
1
1
0
1
1
1
0
1
1
1
2
2
1
2
2
1
2
2
0
1
1
2
0
1
1
1
2
0
2
1
3
1
0
0
0
2
1
1
1
1
2
0
1
1
2
0
2
1
0
0
0
2
0
0
0
1
1
0
1
0
0
1
2
2
0
0
0
2
2
1
1
1
1
1
0
1
0
1
0
1
2
0
0
0
2
1
2
1
2
0
2
0
0
0
1
0
2
1
1
0
2
1
2
2
2
1
2
3
1
2
1
1
0
1
0
2
0
1
0
1
2
1
0
2
2
2
1
0
0
0
0
1
2
2
2
2
1
1
2
0
0
2
4
2
2
1
1
1
0
0
1
1
0
1
3
2
0
1
2
0
1
1
1
1
2
1
1
1
0
1
2
2
1
2
2
2
0
1
0
2
1
1
2
0
1
1
2
1
1
1
0
1
2
2
4
1
1
1
1
2
2
0
1
1
1
0
1
0
2
0
0
0
0
0
0
2
0
1
1
1
2
1
2
1
2
1
1
0
2
1
1
1
1
1
2
1
1
1
1
1
0
2
1
0
0
1
2
1
2
1
2
1
1
0
2
1
0
1
1
0
2
1
2
2
1
1
0
1
0
0
1
0
1
0
1
0
1
1
0
0
2
1
1
1
2
0
0
0
2
2
2
2
1
1
1
1
2
1
0
1
1
0
0
0
0
0
0
1
2
1
2
2
2
1
1
1
0
1
1
2
2
1
1
0
0
1
0
2
0
1
0
2
1
0
0
1
0
0
0
0
1
1
1
1
2
1
0
0
2
0
0
0
1
0
2
1
0
1
0
1
1
0
1
1
1
1
0
1
1
1
0
0
0
1
0
1
0
2
1
1
1
1
1
1
0
1
2
0
2
0
0
2
2
2
3
0
1
1
0
1
0
1
1
2
2
1
0
0
0
2
1
0
2
0
2
0
2
1
2
0
1
2
0
1
1
0
0
2
1
2
0
1
0
0
1
2
0
1
1
2
1
1
1
1
1
2
1
2
1
1
0
1
1
0
1
0
0
1
1
2
1
0
2
2
0
2
0
2
0
1
3
1
1
1
1
2
0
1
0
0
1
1
2
0
0
2
0
0
0
1
1
0
1
1
0
1
1
1
0
0
0
1
0
0
1
2
1
1
2
1
2
0
0
1
1
0
1
1
2
0
2
1
1
2
0
2
2
0
1
0
1
1
0
1
0
1
1
1
1
1
0
0
2
1
2
0
0
1
0
1
1
1
0
2
0
0
2
0
0
2
1
0
1
1
1
1
2
0
1
0
2
0
1
1
1
1
1
2
0
2
1
1
0
0
1
2
1
1
2
0
0
0
2
2
1
1
0
3
2
0
0
1
1
0
0
1
1
2
1
1
1
2
1
2
1
1
0
1
0
1
0
1
1
3
1
1
1
0
1
0
1
1
0
0
0
1
2
1
0
1
2
2
1
2
2
0
1
1
1
1
1
1
1
2
1
0
1
2
0
2
0
1
2
2
1
1
1
0
1
1
0
1
0
1
0
2
1
1
1
0
1
1
1
1
1
1
0
1
2
1
1
2
0
1
1
0
1
0
1
0
0
1
1
0
0
2
1
0
2
0
1
1
1
1
0
2
0
1
0
2
2
0
0
1
0
2
0
1
0
1
0
2
2
0
0
1
2
0
0
0
1
2
1
0
1
2
0
1
2
2
0
2
1
0
2
1
2
0
1
1
0
1
1
0
1
2
1
2
0
0
0
2
1
0
2
2
1
0
0
0
3
2
1
1
2
1
1
2
0
1
1
2
0
1
1
0
1
1
1
1
0
0
1
1
0
1
0
2
2
0
1
2
1
1
0
1
1
1
2
0
0
1
1
0
1
0
2
0
1
0
2
2
1
0
1
1
0
1
2
2
0
0
2
0
1
1
1
1
1
0
0
0
0
0
2
1
2
2
0
2
0
2
2
1
0
1
0
2
0
0
2
1
3
0
0
0
1
0
1
2
0
1
1
1
2
2
1
1
0
1
1
1
0
1
0
0
1
1
0
1
1
0
2
1
0
2
1
1
1
2
1
1
2
1
2
2
0
1
0
1
0
1
2
0
1
1
0
0
1
0
0
2
1
1
1
1
0
1
1
1
2
1
0
0
2
1
2
1
1
1
0
1
1
0
1
0
2
1
3
1
1
2
2
0
2
2
1
1
1
0
1
1
2
0
2
1
1
1
1
0
1
0
1
1
2
0
2
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
2
1
1
2
0
0
0
1
0
1
2
2
1
0
1
0
1
1
0
0
1
1
1
2
1
1
0
1
1
2
1
1
2
0
1
2
2
0
1
0
1
1
2
2
1
1
2
1
0
0
1
1
2
1
0
5
1
2
0
1
1
1
2
1
1
0
0
2
0
1
0
1
1
0
1
2
1
0
1
0
1
1
1
1
1
1
2
0
1
1
1
1
1
0
1
0
0
1
1
2
1
1
1
1
1
1
1
1
0
2
1
1
0
1
1
2
1
2
1
1
0
1
1
1
1
1
0
1
0
1
2
1
1
0
0
0
1
2
1
1
1
1
2
0
2
1
0
0
0
1
1
0
1
2
0
1
0
2
1
0
2
1
1
1
1
1
1
1
0
1
1
1
1
1
0
1
0
2
0
0
1
0
0
1
1
0
1
1
1
1
0
1
2
1
1
0
2
0
1
0
2
2
2
1
1
2
1
1
0
0
2
0
2
1
1
1
1
0
1
1
0
1
0
2
2
0
0
0
0
1
1
0
1
1
1
0
2
0
1
1
1
2
0
1
0
1
1
1
0
1
2
1
0
1
1
0
1
1
1
2
0
1
1
2
1
2
1
3
2
1
1
2
1
1
0
1
2
0
2
1
2
2
1
0
1
0
0
1
0
0
1
0
0
2
1
1
1
1
0
0
2
1
1
0
1
0
0
2
0
1
2
0
2
0
1
1
1
2
1
0
0
1
0
1
1
1
0
0
0
1
0
2
2
1
1
0
1
2
2
1
2
0
0
1
1
0
0
1
1
1
2
1
0
0
1
1
0
1
2
2
1
0
1
0
1
1
0
1
1
0
2
0
2
1
1
2
1
1
1
0
1
1
1
2
1
1
1
2
1
1
2
2
2
2
1
0
0
1
2
0
1
1
1
1
1
1
2
2
2
1
0
1
1
1
0
1
0
1
2
1
1
0
0
2
1
1
1
2
0
1
0
1
1
1
1
0
1
0
1
0
1
1
2
2
1
1
0
0
2
0
0
1
0
1
1
1
2
0
1
1
2
2
1
1
1
1
2
2
0
1
2
1
1
1
1
1
1
2
1
0
1
1
1
1
1
1
1
1
1
0
0
2
1
1
1
1
2
1
0
1
0
4
0
1
0
2
1
0
0
1
1
2
0
0
1
1
1
1
2
1
1
0
1
0
1
2
1
3
0
2
0
1
1
1
1
1
2
2
2
1
1
0
2
0
1
0
2
0
1
1
0
1
0
0
1
1
1
1
1
2
1
2
1
1
1
0
1
0
1
1
2
1
1
0
1
1
1
1
0
1
1
1
1
0
1
1
1
0
1
1
0
1
1
1
0
1
3
0
2
0
1
0
2
1
0
2
1
1
2
0
2
0
1
0
2
0
0
1
0
0
0
1
1
1
1
0
0
1
2
2
0
1
1
0
1
1
2
0
0
0
1
1
2
1
2
1
1
2
1
2
1
1
1
0
1
0
1
2
0
2
2
1
1
2
1
1
0
1
2
1
1
0
2
2
1
2
1
1
3
0
0
2
0
0
1
0
2
0
2
2
0
0
2
2
0
1
0
1
1
0
1
1
1
2
1
0
0
1
0
1
1
1
1
0
0
1
1
0
2
0
0
0
0
0
2
0
0
1
0
1
2
1
1
2
0
2
2
1
0
0
1
2
1
1
2
1
1
0
1
1
0
1
0
0
1
0
1
1
1
1
1
1
0
0
1
1
0
0
1
2
2
0
1
0
1
1
0
1
2
0
0
1
0
1
0
0
2
1
0
3
2
1
0
3
1
1
1
1
2
1
1
2
2
2
1
1
0
0
2
1
1
0
0
1
1
0
2
1
0
2
0
0
0
1
0
2
0
0
1
0
1
1
1
1
2
2
2
1
2
2
2
0
1
0
1
0
1
0
2
2
1
0
1
1
2
0
1
1
2
0
2
1
0
2
2
1
3
2
5
1
1
1
0
2
1
0
1
1
1
2
2
0
5
2
0
1
1
1
2
2
0
1
0
2
0
1
1
0
1
1
0
1
1
1
1
0
1
1
0
1
0
1
2
1
1
1
0
0
2
2
2
1
1
1
2
0
0
2
2
2
0
1
1
2
0
2
1
0
1
1
1
2
2
1
1
2
2
0
0
0
2
0
1
1
2
0
0
0
0
1
0
0
1
0
1
1
0
0
3
1
2
1
2
1
1
0
2
2
0
1
1
0
0
1
1
0
1
1
0
2
3
1
2
2
1
1
0
1
2
1
2
1
1
0
0
0
1
1
1
3
1
0
0
1
2
1
2
0
1
0
1
1
2
1
2
1
1
0
1
2
0
1
2
2
2
0
2
2
0
1
1
2
1
0
1
4
0
1
1
1
0
2
1
1
0
0
0
2
3
1
1
1
0
0
2
2
0
1
0
1
0
1
0
1
0
0
1
2
2
0
3
0
0
1
1
2
0
1
0
2
1
1
1
2
1
2
0
0
1
0
0
1
1
1
1
0
1
0
0
2
0
0
0
0
0
2
0
0
2
2
1
0
1
0
2
2
3
1
1
0
2
0
2
2
1
1
1
1
1
1
1
1
1
1
2
0
0
2
1
0
1
3
2
0
2
2
3
2
0
0
0
2
1
1
0
0
2
0
2
0
1
1
1
0
2
0
2
1
2
2
0
1
2
1
0
0
2
1
0
1
0
0
0
1
1
2
2
1
0
0
0
1
0
0
2
1
1
1
1
2
1
2
1
0
0
2
2
0
1
2
1
0
1
1
1
1
1
0
1
1
1
1
1
1
0
2
1
1
1
1
1
1
1
1
0
0
1
1
1
1
2
1
0
0
1
2
0
0
1
3
1
1
2
2
1
2
0
0
1
0
2
1
0
1
1
0
0
1
4
0
1
2
2
1
0
1
3
2
1
2
2
1
0
1
1
0
1
2
1
2
0
0
1
1
1
0
1
2
1
1
0
2
2
1
0
0
1
2
0
1
1
1
2
0
1
2
2
1
2
1
1
0
1
0
3
0
2
0
0
2
2
2
1
1
1
0
0
2
0
2
1
2
1
2
1
1
1
2
1
0
0
1
0
0
1
0
0
1
0
0
1
2
1
1
1
0
1
2
0
1
1
0
1
1
1
2
1
0
0
0
1
1
1
1
3
1
1
2
1
1
0
1
0
1
0
1
1
2
1
0
0
0
0
2
1
1
0
2
1
2
0
0
1
0
1
1
0
0
0
0
0
0
2
1
0
0
0
3
0
2
1
0
0
1
1
1
1
0
1
1
2
2
1
0
0
1
1
2
2
2
0
1
1
0
1
0
1
1
0
2
0
1
1
0
2
0
1
1
0
1
2
1
2
1
2
1
1
1
1
1
2
1
1
1
0
0
0
2
2
0
2
0
1
0
1
0
1
0
1
1
2
2
0
1
2
1
2
2
0
0
0
0
1
0
1
1
1
2
1
0
0
0
1
1
2
2
0
1
2
1
1
1
1
1
0
1
0
1
1
2
2
1
0
0
1
1
1
0
0
1
0
1
1
1
0
1
2
1
1
2
1
1
1
1
0
1
1
1
2
0
0
1
1
1
1
1
1
1
0
1
0
3
1
0
0
1
1
0
1
3
1
1
1
1
1
1
0
1
2
2
1
1
1
2
1
0
1
1
1
0
0
1
2
0
0
1
1
2
2
1
2
1
2
2
1
1
1
3
0
2
2
1
0
1
2
2
0
0
0
0
0
0
0
0
2
1
1
0
2
1
1
0
1
0
1
1
2
2
1
1
1
1
0
2
0
2
1
0
1
1
2
0
1
0
0
1
1
1
2
1
1
1
0
0
3
1
0
10
1
1
2
2
1
2
0
2
1
0
0
2
1
0
1
0
1
1
1
2
1
1
1
0
2
2
0
0
0
1
1
0
1
1
0
1
2
1
2
0
0
0
2
2
0
1
0
2
2
0
2
1
1
1
1
1
2
1
2
2
1
0
0
1
1
2
2
0
0
1
3
1
0
1
1
2
1
1
1
2
2
3
1
0
1
1
0
1
2
0
2
1
0
0
1
0
0
0
1
1
0
1
0
1
1
1
2
0
1
2
0
1
1
0
2
1
1
0
1
0
2
0
1
2
0
0
2
2
1
2
1
0
0
0
2
1
1
2
1
0
1
0
0
2
1
2
1
1
0
1
1
2
1
1
0
0
1
0
1
1
0
0
0
0
1
1
1
1
0
1
0
1
1
1
1
3
2
0
3
0
0
1
0
1
2
1
1
1
1
0
2
1
1
2
2
0
0
0
1
1
1
0
0
0
1
2
1
1
1
0
1
2
1
0
1
0
2
1
1
0
0
0
3
0
2
2
0
1
1
0
0
1
2
1
0
0
1
0
1
0
1
0
3
2
1
0
2
1
1
1
0
0
0
1
0
2
0
0
1
0
0
2
0
0
2
0
1
2
2
1
1
2
0
0
2
0
1
1
0
2
1
2
3
0
0
0
2
1
1
1
1
1
2
1
0
1
1
0
1
0
1
1
2
2
0
0
2
0
0
2
0
0
1
1
1
1
1
2
1
0
1
1
0
0
1
0
1
1
2
0
2
1
1
0
1
1
2
1
1
1
1
1
1
1
2
1
0
1
2
1
0
1
1
1
2
0
1
2
2
1
4
0
3
1
1
1
1
0
2
1
0
0
0
1
1
1
2
1
0
0
2
1
1
1
2
1
1
1
0
1
1
1
0
1
0
0
0
1
0
2
1
0
6
1
1
1
2
1
1
1
1
1
0
1
2
1
1
0
1
1
0
3
2
4
0
0
2
2
0
0
1
1
1
2
0
1
0
2
1
0
1
1
0
0
1
0
1
0
0
1
1
0
0
2
1
1
1
0
1
1
0
1
1
0
1
1
0
1
1
1
2
1
0
1
0
0
1
0
1
1
1
2
1
0
1
2
1
1
0
2
1
2
0
1
1
0
2
1
1
2
1
1
1
2
1
2
0
1
1
1
1
0
1
1
2
1
0
0
0
0
1
1
1
1
2
0
0
0
2
2
0
0
1
2
0
1
0
1
1
1
2
1
2
1
0
1
3
1
0
1
1
1
2
1
1
0
1
1
0
3
0
0
2
0
0
1
2
1
0
1
1
2
1
1
0
2
1
2
1
1
1
0
1
2
2
1
2
2
0
0
1
0
2
1
0
1
2
0
1
1
1
2
1
1
1
0
1
1
1
1
1
0
2
0
0
0
1
0
1
1
2
2
2
1
1
0
2
1
1
1
2
1
1
2
0
2
0
1
2
2
0
0
0
1
1
0
0
1
2
1
0
0
0
2
2
0
1
1
2
0
0
0
1
1
1
2
1
1
1
2
1
0
1
0
0
2
2
0
1
2
1
1
0
2
1
1
3
2
0
1
1
1
1
1
1
1
2
2
1
0
0
1
2
1
1
1
2
1
0
1
2
0
1
1
1
0
1
0
0
2
2
1
0
1
1
1
0
1
1
1
1
1
2
1
0
1
1
0
2
0
0
0
1
2
1
0
0
1
1
1
1
2
1
1
0
5
0
1
1
0
1
0
1
0
0
1
1
1
2
2
1
0
0
1
1
1
0
0
1
1
1
1
1
2
0
2
2
0
2
2
0
1
0
0
2
0
1
3
4
0
2
0
3
0
1
1
1
0
2
1
2
0
0
1
2
0
2
1
1
0
1
1
0
3
1
0
2
1
0
0
0
1
1
0
2
1
1
1
1
1
0
0
1
1
1
0
1
0
0
0
1
0
2
1
2
1
0
0
2
0
0
0
0
0
1
1
1
1
1
1
2
1
1
1
2
0
2
0
0
1
0
2
2
1
0
1
1
1
1
2
1
2
0
0
0
1
1
1
1
1
2
1
1
0
0
0
0
2
1
2
2
1
1
1
1
1
0
2
0
1
2
0
1
0
1
1
0
0
1
1
2
0
0
0
1
1
0
2
1
1
1
2
0
0
0
1
1
0
2
1
2
1
1
1
1
0
2
1
1
1
1
1
2
2
1
2
1
0
1
2
1
1
1
1
0
0
0
1
2
0
1
0
1
2
1
1
0
0
1
0
0
1
1
1
0
1
2
1
1
0
2
2
2
1
1
2
0
1
0
0
1
1
2
2
0
1
2
1
0
1
0
1
1
2
1
2
1
0
1
2
2
1
0
1
1
0
1
0
2
1
1
1
0
1
0
1
1
2
0
1
1
0
1
0
0
3
2
1
2
2
0
0
1
2
2
0
1
1
0
1
2
0
1
1
0
0
1
0
2
1
1
1
0
0
3
2
2
2
0
0
1
2
2
0
0
0
1
2
0
1
1
1
2
0
1
2
1
1
2
1
1
2
1
2
1
1
1
2
1
0
0
0
1
0
1
1
1
0
1
0
0
2
2
1
0
0
0
2
2
0
4
2
1
0
1
1
1
2
1
0
0
0
0
3
1
1
1
2
0
1
0
3
0
0
2
1
1
2
1
1
0
0
0
0
1
1
0
0
1
1
0
0
1
0
2
1
0
2
1
2
0
3
0
2
1
1
1
1
1
0
2
0
1
0
2
0
1
2
1
1
2
1
0
1
1
0
0
2
0
0
1
2
0
1
1
0
1
0
2
0
1
1
1
0
0
1
0
1
1
1
2
2
1
2
1
1
0
0
2
1
1
1
0
2
0
4
0
1
1
0
1
1
2
1
2
3
1
2
0
1
2
1
0
2
2
0
0
1
1
2
1
1
0
2
1
1
0
1
1
0
0
1
1
0
0
1
2
0
1
0
0
0
1
0
1
1
1
2
1
1
1
2
2
0
1
1
0
1
2
1
0
1
1
0
1
0
1
2
0
2
0
1
0
0
1
1
1
1
1
1
0
1
1
1
1
1
0
0
0
1
1
1
1
1
1
4
1
1
2
1
1
0
1
0
0
1
1
1
0
3
0
1
0
0
1
0
1
1
0
1
0
1
0
2
2
1
1
0
2
1
2
0
2
1
2
1
0
1
0
2
1
1
1
0
1
1
1
1
0
2
0
1
1
1
1
1
1
0
2
2
1
0
0
0
1
1
0
1
1
1
1
2
0
2
0
1
1
1
1
2
0
2
0
1
2
1
0
2
2
1
0
0
2
1
2
2
2
0
2
1
2
0
2
0
2
2
1
2
1
0
1
1
1
2
2
3
1
2
0
0
0
1
1
1
2
1
0
0
1
2
0
0
0
0
2
2
0
0
1
0
2
1
1
0
0
1
1
0
1
0
0
0
0
2
1
1
1
1
2
0
1
1
2
0
1
0
1
2
1
1
0
0
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
0
1
2
0
1
1
2
2
0
1
3
2
1
1
0
2
1
1
0
0
1
0
1
1
1
1
1
0
0
2
1
0
1
0
0
1
2
0
2
1
1
2
1
2
0
1
2
2
1
1
0
0
1
1
1
0
3
2
1
1
3
0
1
2
2
2
0
2
0
1
0
0
1
2
0
1
1
2
0
0
0
1
2
0
1
1
0
2
1
1
1
1
0
1
1
0
0
1
0
2
0
0
0
2
1
2
0
1
0
2
0
0
1
0
1
2
3
1
1
2
2
0
0
0
1
0
1
0
0
1
0
1
1
1
0
1
0
0
1
1
0
0
2
0
0
2
1
1
1
1
2
1
0
2
1
1
1
1
0
1
1
1
1
0
1
2
1
1
1
1
2
1
0
2
0
1
1
0
1
1
1
2
1
0
0
1
0
0
1
0
0
1
0
1
0
2
1
1
0
1
0
1
2
1
0
0
0
1
1
1
2
0
2
0
2
0
1
0
0
2
1
0
0
0
0
0
1
2
1
0
1
2
2
0
2
1
1
0
1
0
0
1
1
1
1
1
0
1
1
0
0
0
2
2
0
2
1
1
0
1
1
1
0
2
0
1
0
1
2
1
0
3
0
1
2
0
2
0
1
1
0
2
0
2
2
0
0
1
0
2
1
1
2
1
3
1
2
1
2
2
0
0
2
0
2
0
0
0
0
2
1
0
0
0
2
2
1
2
0
1
1
1
0
3
0
1
1
1
0
1
0
1
0
1
1
0
0
2
1
2
0
2
1
0
0
2
1
1
0
0
0
1
1
1
1
2
1
1
1
1
0
1
1
2
0
0
0
1
0
1
1
1
0
1
1
0
0
1
1
1
0
1
1
0
1
0
2
1
1
0
1
1
1
1
0
1
1
1
1
1
1
2
1
2
0
1
1
0
1
2
1
0
1
0
1
0
1
1
1
1
1
1
1
0
0
0
0
1
2
0
0
2
1
0
0
0
0
2
1
1
1
1
1
1
0
2
1
2
2
1
1
1
1
0
3
0
1
2
1
1
0
0
1
1
2
1
2
1
1
1
1
0
0
0
0
1
1
1
0
2
2
1
3
1
2
2
0
0
0
1
1
1
1
1
0
1
1
1
2
2
1
0
1
0
1
2
1
1
0
0
0
1
2
1
1
2
1
1
0
0
1
2
1
1
0
2
0
1
1
1
1
1
1
0
0
1
0
0
1
0
2
2
1
1
2
2
1
0
0
1
1
1
1
1
1
2
2
2
1
1
1
1
1
0
2
1
2
1
1
1
1
0
1
0
1
2
0
0
1
1
2
1
1
2
1
1
0
1
1
1
0
0
0
1
3
1
1
1
3
2
1
0
1
1
0
1
1
1
0
1
1
1
0
0
2
3
1
2
0
1
2
2
2
1
0
1
0
0
0
0
1
1
0
0
1
1
1
1
2
0
0
1
0
0
2
1
2
2
2
2
1
2
0
1
2
2
0
0
0
1
1
0
0
1
1
1
1
2
1
1
1
2
0
1
1
1
1
1
0
0
1
2
1
0
1
0
2
1
1
1
0
2
0
0
1
0
1
2
0
1
1
0
2
1
0
2
2
1
1
0
1
1
0
1
1
0
1
2
0
1
0
0
0
1
2
1
0
1
1
1
1
1
0
1
1
2
2
2
1
1
1
1
0
0
2
2
2
1
1
1
0
1
1
0
0
0
2
0
1
0
0
0
0
0
2
1
0
1
0
0
1
0
0
1
0
1
1
0
0
1
0
1
0
1
1
0
1
2
0
1
0
1
0
2
1
1
0
1
0
1
1
1
0
2
2
0
1
6
1
1
1
1
0
1
1
4
0
1
1
1
0
2
1
2
1
1
1
2
0
1
0
1
1
2
1
1
2
1
1
1
0
1
2
2
1
1
0
1
0
2
0
2
1
1
0
0
0
1
2
0
0
0
2
0
1
1
1
2
1
0
0
0
1
0
0
0
1
0
1
0
0
0
2
0
2
1
2
1
1
2
0
0
1
0
1
1
0
1
1
0
0
2
1
1
1
2
0
0
2
1
0
2
0
1
1
0
1
0
0
0
0
1
0
0
1
0
1
2
1
1
2
1
2
0
0
0
1
1
1
0
0
1
2
0
1
2
0
1
1
1
1
2
1
0
1
0
2
1
0
0
2
0
1
0
0
2
1
0
0
0
1
0
0
2
2
2
1
1
0
1
1
0
1
2
0
0
1
1
1
2
2
2
0
0
1
0
1
1
2
1
2
0
0
2
1
1
1
2
1
0
0
1
1
1
0
0
0
1
2
4
0
2
1
0
1
0
2
0
1
2
1
1
1
2
1
1
2
2
2
1
0
0
1
1
1
1
1
2
2
1
1
1
2
0
0
1
1
1
1
2
0
0
1
1
1
1
1
1
1
0
0
2
0
0
1
0
1
2
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
2
2
1
1
0
1
0
1
1
1
0
1
1
0
1
2
0
1
1
1
2
0
0
2
2
1
1
1
2
2
1
1
1
1
0
0
2
1
1
2
1
1
0
1
2
1
1
2
0
1
0
0
2
1
0
2
0
0
1
0
5
1
1
0
0
1
1
2
2
2
1
0
1
1
1
1
2
1
1
2
2
0
0
1
1
0
2
3
0
1
1
1
1
0
1
0
0
0
1
1
2
0
1
0
1
2
0
0
1
1
3
0
0
2
2
1
0
0
0
2
1
0
1
2
1
2
2
0
1
1
0
1
2
2
1
2
1
0
1
2
1
2
0
0
0
0
1
0
0
1
2
1
0
2
0
2
1
0
1
2
1
0
1
0
1
0
1
1
0
1
1
1
2
1
0
1
1
0
0
1
1
1
1
1
0
0
0
2
0
0
3
1
2
1
1
2
2
1
1
1
2
2
1
0
1
0
1
2
2
0
0
1
2
1
0
1
0
2
1
1
1
0
0
1
1
1
0
1
2
1
3
1
2
2
2
1
1
2
1
1
2
0
0
0
0
2
1
1
2
1
2
0
0
2
1
2
1
1
1
0
1
0
1
2
1
1
0
1
2
0
1
1
1
0
1
0
2
0
2
1
0
1
0
1
1
2
2
0
1
1
0
1
2
1
1
1
2
1
0
1
2
1
0
1
1
1
0
2
1
1
1
0
2
1
1
1
2
1
1
1
2
1
0
1
1
0
2
1
1
4
1
0
1
0
2
1
1
0
0
1
1
1
2
2
1
1
0
0
2
1
0
1
2
0
2
0
1
2
1
1
2
1
2
1
0
2
0
2
1
1
0
1
2
2
1
0
1
0
2
1
1
1
0
0
2
1
1
1
2
1
1
1
1
1
2
1
1
1
2
2
1
0
0
1
0
1
1
1
0
0
0
1
1
1
0
1
1
2
1
0
1
1
1
2
1
1
1
2
0
1
1
2
0
0
1
0
1
1
0
0
1
0
0
1
0
0
2
0
1
2
0
1
0
0
1
1
1
1
0
1
2
0
2
1
1
1
1
0
1
1
1
1
0
0
1
0
0
0
0
1
1
1
1
2
2
1
2
0
2
1
0
0
2
1
1
2
2
0
0
1
1
2
1
1
0
2
0
1
2
1
1
0
0
0
1
2
1
1
0
1
1
0
0
1
1
2
1
0
0
1
1
1
1
0
1
2
2
1
1
0
2
1
0
0
1
1
0
0
0
1
1
1
1
1
1
3
0
1
3
0
2
1
1
1
1
2
1
1
0
0
1
1
1
0
1
0
1
2
2
0
0
1
0
0
0
1
0
1
1
1
1
1
0
0
0
0
2
1
1
0
1
1
1
1
1
1
0
2
1
0
1
0
2
1
1
1
0
0
0
2
2
1
0
0
1
0
1
1
1
0
1
2
1
0
2
0
3
2
0
1
0
2
0
0
1
1
0
1
3
1
1
2
1
1
2
1
2
0
0
2
0
1
1
1
1
2
2
1
1
1
1
2
1
1
1
2
0
0
0
1
1
0
2
1
2
1
2
1
1
0
0
2
0
2
3
0
0
0
0
2
1
0
1
0
0
0
0
1
0
0
1
0
2
1
1
1
1
0
1
1
2
1
1
1
1
0
1
1
1
0
1
2
1
0
1
1
1
0
2
1
2
2
1
0
1
1
1
1
2
1
1
0
0
1
1
1
2
2
0
2
2
0
0
1
1
0
0
2
0
1
1
2
0
1
1
0
0
1
0
0
1
1
0
0
0
1
2
1
2
0
1
0
0
1
1
2
2
1
2
1
1
0
0
2
0
1
1
1
2
2
0
2
1
1
2
1
1
0
2
1
1
1
1
0
1
1
2
1
1
0
1
2
0
0
0
1
1
1
0
0
2
1
1
1
1
2
1
1
1
1
1
1
0
2
2
1
1
2
2
0
0
1
1
2
1
1
1
2
2
0
1
1
1
1
1
0
0
2
0
0
2
2
1
1
1
0
1
2
1
1
0
0
1
1
1
2
0
1
0
1
1
1
1
1
0
0
1
0
0
1
2
1
1
2
1
1
2
0
0
1
1
1
1
2
2
1
0
1
1
2
2
2
0
2
3
1
0
0
2
1
0
0
1
1
2
2
2
0
0
0
0
0
0
0
2
2
0
1
1
1
2
1
2
2
1
0
1
1
1
2
1
0
2
1
1
2
0
1
1
1
1
1
1
1
0
1
0
0
0
1
1
2
3
1
1
1
1
2
0
1
1
1
1
2
1
2
1
1
1
0
2
1
1
1
0
0
0
0
0
1
2
1
2
0
2
0
1
0
1
1
1
1
1
1
0
4
0
1
1
2
1
1
0
0
0
0
1
1
0
1
2
1
0
0
0
2
0
1
2
1
1
2
1
1
1
0
1
0
0
1
0
0
1
1
1
2
2
1
1
2
1
0
1
1
1
1
2
1
1
0
1
0
1
0
2
2
2
0
0
2
1
0
2
0
0
0
2
2
1
1
1
0
0
0
0
1
1
1
1
0
1
0
0
1
1
1
0
1
0
0
1
0
1
1
0
1
0
1
1
2
1
0
1
2
0
1
1
1
0
1
0
1
1
0
0
2
0
0
1
2
1
1
1
2
0
1
0
0
0
0
1
0
0
1
1
1
2
1
0
0
1
1
2
0
1
1
2
0
1
1
0
1
1
0
1
2
1
0
1
2
0
1
2
2
2
1
1
1
0
1
0
2
1
1
2
4
1
1
0
0
2
2
1
1
1
1
1
3
0
1
1
1
1
1
1
0
0
1
1
2
2
2
0
1
1
0
0
1
1
0
0
1
2
1
1
0
0
0
1
0
0
1
0
1
0
1
1
0
0
0
0
1
0
0
1
2
1
1
1
2
1
1
1
0
0
0
0
2
1
2
0
1
2
2
0
1
1
2
0
0
1
1
1
2
1
1
2
1
1
1
1
0
1
1
1
2
1
1
0
1
0
1
0
1
2
2
1
0
0
1
1
1
1
0
0
2
1
1
1
3
1
1
1
0
0
1
0
0
1
0
1
2
0
0
1
1
1
1
1
3
1
1
0
1
2
1
1
0
0
1
0
0
0
2
1
1
1
0
0
1
1
2
1
0
0
2
0
0
1
1
2
0
1
1
1
2
1
1
1
1
2
0
0
1
1
1
0
0
0
1
0
1
1
1
2
1
0
1
0
1
1
0
0
1
0
0
2
0
0
1
1
2
2
2
0
2
1
1
2
1
1
2
0
0
1
0
3
0
1
1
0
1
1
0
1
1
2
0
1
2
1
0
1
0
0
2
0
2
1
0
1
1
0
0
0
1
1
0
2
1
1
0
2
1
0
0
0
1
1
1
1
1
1
1
0
1
0
2
1
2
0
2
2
0
0
2
2
2
1
2
1
1
0
2
2
0
0
2
1
1
0
2
2
0
1
1
5
1
0
0
1
2
1
1
1
2
0
2
1
1
2
0
1
2
2
2
0
1
1
3
2
3
0
0
2
2
0
0
1
0
2
1
2
0
1
0
0
0
2
0
1
2
1
0
1
1
1
1
0
0
1
2
2
2
3
1
0
1
1
0
1
0
1
1
1
1
0
0
0
0
1
2
0
1
1
2
0
1
1
0
2
1
1
0
1
1
1
3
0
1
0
0
1
0
0
0
0
0
1
1
2
1
2
1
0
1
1
0
0
1
1
0
0
2
1
1
1
2
2
0
0
1
0
2
1
0
2
1
1
1
0
2
1
1
1
1
0
0
0
2
1
1
0
1
2
1
3
0
0
0
1
0
3
1
2
0
2
1
1
0
2
1
0
0
2
1
1
1
0
1
0
0
2
0
1
0
0
1
0
1
0
2
1
0
2
1
0
2
1
0
2
1
0
1
1
1
3
0
1
0
2
1
1
1
0
1
0
0
1
2
1
2
1
2
1
2
2
1
1
1
0
1
2
1
0
2
0
1
1
1
0
1
0
1
0
0
1
1
0
0
1
1
1
1
1
1
0
2
1
2
1
0
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
2
2
2
0
0
1
2
0
1
2
1
1
1
2
1
0
2
1
2
1
1
2
1
0
0
1
0
1
0
2
0
2
1
0
2
0
0
0
1
1
0
1
1
2
0
1
0
1
2
0
1
1
2
1
0
2
4
2
0
1
2
2
0
1
0
1
1
1
1
1
1
2
1
1
1
1
1
0
1
0
0
1
0
2
1
1
0
2
1
0
0
1
2
1
0
0
0
1
0
1
0
2
1
1
1
1
1
4
1
2
1
0
2
2
2
0
1
0
0
0
1
0
1
1
0
0
0
0
1
1
0
0
1
0
2
1
2
2
1
1
2
1
1
0
1
0
0
0
1
0
1
1
0
1
1
2
1
1
1
0
1
1
0
1
1
1
2
2
1
0
2
0
0
0
1
1
1
1
0
0
0
1
1
1
1
2
0
1
1
1
0
1
0
2
1
0
1
0
1
1
2
0
0
0
0
0
0
1
1
2
0
1
2
0
2
1
1
0
2
1
1
0
2
1
0
2
0
1
3
1
0
1
0
0
0
0
1
2
1
0
1
1
1
1
0
1
1
1
1
1
1
0
1
1
1
0
2
2
0
0
0
1
0
1
1
1
2
1
1
1
0
2
1
2
1
1
3
0
0
0
1
1
0
1
2
1
0
1
2
1
1
1
2
1
0
1
1
0
0
0
0
1
1
1
1
2
1
1
1
1
1
2
0
0
2
1
2
1
0
1
1
1
1
0
2
1
0
1
1
1
1
1
3
1
2
0
1
1
1
1
2
1
2
2
1
0
4
1
1
0
1
2
0
0
2
3
2
1
2
0
1
1
1
2
1
1
0
0
0
1
1
2
0
0
1
1
0
1
2
0
1
4
2
0
1
1
1
1
1
2
2
0
1
1
2
1
1
0
2
1
1
0
1
1
0
1
0
0
1
0
1
0
0
0
1
1
1
2
1
0
0
2
1
2
1
0
0
0
1
1
1
0
1
2
2
3
0
1
1
0
1
2
1
2
2
2
0
1
1
1
0
1
1
1
1
1
2
0
1
2
2
2
2
1
0
1
1
0
1
0
0
1
2
1
1
0
2
1
1
0
2
1
1
0
1
1
1
0
2
0
1
1
2
1
0
2
1
1
1
1
0
1
1
1
1
2
0
1
3
0
1
0
0
0
0
2
0
2
0
2
1
2
1
1
1
0
1
2
2
0
1
0
1
1
2
1
0
1
0
2
1
1
2
1
0
2
1
1
0
0
2
2
2
1
0
2
0
0
1
0
2
0
1
0
0
2
2
0
1
2
1
0
1
0
1
2
1
0
2
1
0
1
1
1
1
1
0
1
1
1
1
0
0
1
0
2
1
2
0
0
0
1
1
0
1
0
0
1
1
1
2
0
1
0
1
0
1
1
0
3
0
1
1
1
1
0
2
2
2
0
2
0
1
2
1
1
1
0
1
1
2
2
0
0
1
2
1
1
1
0
1
2
0
0
1
1
1
0
1
1
0
2
0
1
0
2
0
0
1
2
0
0
2
0
0
0
0
1
1
2
1
2
0
0
1
0
2
1
1
0
2
2
1
2
0
0
2
2
1
2
1
1
1
0
1
0
1
0
0
0
0
0
0
1
1
1
1
1
0
0
0
0
2
1
2
1
2
1
2
2
0
2
1
1
2
0
2
1
0
1
1
0
0
2
1
1
1
2
0
1
0
2
0
0
2
1
2
1
0
2
0
0
1
0
0
1
0
1
2
1
0
0
0
2
1
1
0
1
2
1
1
1
1
2
1
1
0
3
1
1
1
0
2
1
3
1
0
1
1
1
2
1
1
1
1
1
1
1
0
1
0
0
1
0
1
1
2
1
0
1
1
2
0
2
0
0
0
1
2
2
1
0
2
1
2
2
2
0
1
0
0
0
1
1
0
2
1
1
0
1
1
0
0
0
1
2
0
1
0
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
0
1
1
0
1
0
2
1
1
1
0
0
1
1
1
1
1
1
1
1
2
2
1
2
2
2
1
0
1
1
2
1
1
0
0
1
0
0
1
0
1
1
2
1
1
1
2
2
0
0
1
2
1
0
2
1
1
2
2
1
2
0
2
1
1
1
1
1
2
0
0
1
0
2
1
0
0
0
1
0
1
2
1
0
2
1
2
1
1
1
1
1
0
1
1
1
1
1
0
1
1
1
0
0
2
1
1
0
2
0
1
0
1
0
1
1
1
0
1
1
0
1
1
0
0
0
2
1
0
0
0
1
0
1
1
3
0
1
0
1
1
1
1
1
0
2
2
0
1
2
1
1
0
0
2
2
1
1
0
2
1
1
0
1
1
1
0
1
0
1
1
0
1
2
0
0
2
1
1
1
0
1
0
0
1
2
0
0
2
2
0
1
1
0
2
0
1
1
1
1
1
0
2
0
0
2
1
2
0
0
1
0
0
1
0
0
2
1
2
0
1
3
1
0
0
0
0
2
2
0
1
1
0
2
2
1
1
2
2
1
0
0
1
2
1
1
2
0
0
2
1
1
1
0
0
3
3
0
1
1
1
1
0
1
1
1
1
2
0
0
1
1
1
1
2
1
2
0
0
2
1
1
1
1
0
1
0
0
0
1
1
2
0
1
1
0
2
1
2
0
0
1
0
2
3
2
0
0
0
0
1
1
1
2
0
0
0
1
1
1
2
1
0
0
2
2
1
1
1
0
1
0
0
2
0
2
1
1
1
2
1
1
2
1
0
1
2
1
1
2
0
1
0
0
1
1
0
1
2
2
0
1
1
2
0
1
2
1
0
0
0
0
1
0
0
1
1
1
1
0
1
1
1
1
2
1
0
2
0
0
1
2
0
0
1
0
1
1
0
0
1
1
1
0
1
0
0
2
2
1
1
1
0
0
1
1
0
1
0
1
2
0
0
1
2
2
1
5
1
2
1
2
1
0
1
1
0
0
0
2
1
1
2
1
1
0
1
1
2
0
1
2
0
0
2
0
2
0
0
1
1
2
1
1
0
2
1
1
2
1
1
0
1
0
0
0
1
1
1
1
0
1
0
0
2
2
2
2
0
0
0
1
0
1
1
0
2
0
0
0
0
2
1
2
1
2
0
0
2
1
1
0
1
2
1
0
1
1
2
1
2
1
2
1
2
1
1
1
0
0
0
0
0
2
1
1
2
0
1
1
0
1
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
1
1
1
1
1
0
2
1
1
1
1
1
1
2
0
1
1
1
0
1
0
0
0
0
1
1
1
1
1
1
1
0
0
0
1
2
1
2
1
2
0
1
2
1
1
0
1
1
0
0
2
1
2
1
0
0
0
3
1
0
0
0
0
1
2
1
1
1
1
0
1
0
1
2
1
0
2
5
2
1
1
0
1
0
0
0
1
0
1
1
0
2
0
1
0
1
0
1
1
1
3
0
0
0
1
1
3
1
1
1
0
1
0
3
1
0
1
1
3
0
1
2
1
0
1
1
0
0
2
1
0
1
1
0
1
2
1
0
1
1
1
1
0
2
1
1
2
1
1
1
0
1
1
1
1
2
2
1
1
1
0
2
2
2
1
2
1
1
1
0
1
1
2
0
2
0
1
1
2
1
0
0
1
1
0
1
2
0
2
0
1
2
3
1
0
0
1
0
1
1
1
2
1
1
2
1
1
0
1
0
0
0
2
2
0
1
3
2
1
0
0
0
0
1
1
1
2
2
0
0
2
2
0
1
2
0
1
0
0
2
0
1
1
2
0
0
0
1
1
2
1
1
0
0
1
0
0
1
2
0
1
1
2
0
0
2
0
0
0
1
2
0
1
1
1
0
1
1
1
0
2
1
1
0
2
1
0
0
2
2
1
2
1
0
2
0
0
1
1
1
2
0
0
1
1
1
1
1
1
1
1
0
2
0
1
1
1
1
1
1
0
2
1
0
0
2
2
1
0
0
1
1
1
1
1
0
2
2
0
1
2
0
1
1
1
0
1
0
0
3
0
2
0
0
1
1
2
2
1
1
1
1
1
1
1
0
0
0
0
1
1
0
0
1
2
0
0
1
1
1
0
1
0
2
2
0
1
2
1
1
1
1
1
2
1
0
1
1
1
1
0
2
2
1
2
1
0
1
1
0
2
1
2
1
1
0
2
1
2
0
2
0
2
2
0
1
1
1
1
0
0
2
1
2
1
0
3
0
1
1
0
0
2
1
2
1
1
0
1
1
0
1
1
1
1
0
2
1
0
1
0
2
1
1
0
0
1
1
2
1
2
1
0
1
0
1
1
1
5
0
1
2
0
1
1
1
1
0
2
3
1
0
1
1
1
0
1
2
1
1
2
2
1
0
1
2
1
3
2
1
1
1
0
1
2
1
1
2
1
0
0
0
0
1
2
1
2
0
2
2
2
2
0
0
1
1
1
2
1
2
1
1
2
1
1
0
1
0
1
2
1
0
0
2
1
3
0
1
0
1
2
1
2
1
1
0
0
0
1
2
2
1
1
2
1
1
1
0
0
0
1
1
1
1
1
0
0
2
1
1
0
5
0
2
1
1
2
1
2
1
0
2
1
1
0
1
0
1
0
1
0
1
0
0
0
2
2
2
1
1
0
0
2
2
1
1
2
1
0
0
2
1
0
1
1
1
0
1
0
2
1
2
1
1
2
1
1
0
4
0
2
1
0
1
1
1
1
1
1
2
0
0
2
2
2
0
0
1
1
1
1
1
0
1
2
0
2
1
1
1
1
1
1
0
1
1
0
1
1
0
0
1
2
2
0
1
0
0
0
2
2
0
1
1
1
1
0
1
1
0
1
2
0
1
0
1
1
1
0
1
1
0
1
1
2
1
1
1
1
2
0
2
0
0
1
1
0
2
0
1
2
0
1
0
0
1
1
0
0
1
1
0
1
2
1
1
2
0
2
2
2
0
1
2
1
1
1
1
0
0
1
2
0
1
0
2
0
2
0
1
2
0
0
2
1
2
1
1
0
1
1
0
2
1
2
2
2
1
1
0
1
1
0
1
1
2
2
1
1
1
0
2
0
0
1
1
0
1
0
0
1
0
1
0
1
1
1
2
0
0
1
0
2
0
1
1
0
2
1
1
0
1
0
0
1
0
0
1
2
3
1
1
1
7
2
0
1
0
1
1
1
0
1
2
0
1
1
0
0
2
2
1
1
1
1
2
3
2
0
0
2
1
0
2
0
0
0
2
0
0
1
1
2
1
1
1
0
1
1
1
1
1
2
1
1
2
0
1
2
1
1
1
1
2
1
0
1
3
0
1
1
0
0
1
1
2
1
0
1
0
1
2
0
0
1
0
2
2
0
1
1
2
2
0
2
1
0
0
2
1
2
0
1
3
1
1
1
2
1
0
2
0
0
2
0
1
0
0
0
1
0
1
3
0
1
1
2
2
0
2
1
2
2
1
1
3
1
1
1
0
0
1
2
0
0
0
1
0
1
0
2
1
1
0
1
1
1
1
1
1
0
1
1
0
1
1
2
1
2
0
0
1
1
3
1
1
0
1
1
0
0
1
1
2
1
1
0
1
2
1
0
1
1
1
2
2
1
2
2
1
1
0
0
1
1
1
0
1
1
4
2
1
1
2
2
1
1
0
0
1
1
2
1
0
3
2
1
1
2
0
0
0
2
1
0
1
1
1
2
1
0
2
1
1
2
1
2
1
3
1
1
0
0
1
1
0
1
0
1
0
1
2
1
0
0
0
1
1
1
2
1
1
1
1
2
2
1
1
0
1
1
2
2
2
0
1
0
0
0
3
1
1
1
1
1
2
1
1
3
0
0
2
0
1
1
1
1
1
2
1
1
2
0
0
0
1
1
1
0
1
2
2
1
1
1
1
0
2
2
1
2
1
1
0
2
2
1
1
1
0
1
0
1
2
1
2
0
2
1
1
1
1
0
1
1
2
2
2
0
2
0
2
1
1
1
2
1
1
0
0
2
1
1
1
0
0
0
1
1
0
2
0
0
0
1
1
1
0
0
2
1
0
1
0
2
1
0
0
0
1
1
1
0
0
0
1
1
2
1
2
2
0
2
0
1
0
1
1
1
1
2
1
1
1
5
0
2
1
0
0
0
1
1
1
1
1
1
1
0
0
0
3
0
0
2
2
1
0
1
1
1
0
2
2
1
1
2
2
1
1
1
1
1
2
1
1
2
1
0
2
2
0
2
4
0
2
1
1
2
0
2
1
0
0
2
0
0
2
0
1
1
1
0
0
2
0
1
0
0
0
0
2
2
0
1
1
0
1
0
1
0
1
0
0
2
1
1
2
2
2
0
1
1
1
2
2
1
1
0
1
1
0
1
0
0
0
2
1
2
0
1
0
2
1
0
1
2
1
1
1
1
2
1
2
0
1
1
1
2
2
0
0
0
0
1
1
0
3
0
2
1
2
1
0
2
1
0
2
1
1
2
0
0
0
3
1
1
2
2
1
1
1
2
1
1
2
2
1
1
0
0
1
1
1
1
1
1
0
0
1
1
0
0
0
1
0
0
1
1
0
2
2
3
0
1
0
2
1
1
1
0
0
1
2
1
1
1
0
1
1
1
2
0
1
2
1
1
2
1
0
1
0
1
0
1
1
2
1
2
1
0
0
0
0
1
2
2
2
4
1
3
0
1
0
0
2
1
0
1
0
0
1
2
2
2
2
0
2
1
1
1
1
1
0
0
0
2
0
1
2
0
0
2
2
0
0
1
2
1
2
0
0
1
1
1
1
1
3
0
1
1
1
0
2
1
0
1
0
2
2
0
1
1
0
1
1
0
0
1
2
1
1
2
1
1
1
1
1
2
2
1
0
0
2
1
1
2
1
1
0
1
1
1
0
1
1
1
1
1
0
0
0
0
1
0
1
0
1
1
1
0
1
1
0
1
0
1
0
2
1
5
0
1
1
1
1
3
2
0
1
0
1
0
1
0
0
0
1
1
0
0
1
2
1
2
0
1
1
2
0
0
2
2
1
0
1
2
7
0
1
1
0
0
1
1
2
2
2
3
1
1
1
1
1
3
1
1
0
0
0
0
1
0
0
1
0
1
2
0
1
1
3
1
0
1
1
1
2
0
2
1
1
2
2
1
0
1
1
1
0
1
2
1
1
0
2
2
2
1
0
1
1
1
0
2
1
1
1
0
2
2
0
0
2
0
1
0
0
1
2
1
2
0
2
1
0
0
1
0
0
1
2
0
0
1
1
0
1
0
0
1
2
1
2
0
2
0
1
2
0
0
0
0
1
1
0
2
0
2
1
0
1
0
0
0
0
2
1
2
0
0
1
2
0
1
2
1
1
3
1
1
0
1
0
1
2
0
0
0
0
1
1
1
2
1
2
2
1
0
1
1
1
1
1
2
0
1
2
0
2
0
2
2
1
0
1
1
1
1
0
1
2
0
1
0
1
0
1
2
2
0
1
0
1
1
0
1
3
1
2
0
1
0
2
2
2
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
2
0
0
0
0
1
2
1
0
2
0
1
0
0
0
0
2
1
0
1
0
0
1
2
2
0
2
2
2
1
3
1
1
1
1
1
0
2
1
1
1
0
1
2
2
1
0
1
0
0
0
0
0
0
0
1
0
1
2
1
0
2
0
2
1
2
1
0
0
1
0
0
0
1
0
0
0
1
1
1
0
2
0
1
0
1
1
0
1
1
0
1
1
0
1
1
1
1
0
1
2
1
1
2
2
0
2
1
1
1
1
0
2
0
0
2
0
1
1
0
0
1
1
0
0
0
0
1
0
0
1
1
1
0
2
1
0
2
1
0
0
1
1
1
1
2
2
2
1
2
1
1
1
0
1
1
3
1
1
0
1
1
1
1
1
1
1
0
2
0
2
1
1
1
2
2
2
0
0
2
1
1
2
0
1
1
0
0
2
0
1
1
0
1
1
2
1
0
1
1
2
1
1
2
1
2
2
1
0
1
1
1
0
2
1
1
0
2
2
0
2
1
1
1
1
1
0
1
0
1
0
1
0
1
1
2
2
1
1
1
1
1
1
2
0
0
1
2
1
1
0
1
0
1
1
1
2
0
1
1
2
1
3
0
0
1
1
1
1
1
2
2
2
0
2
1
0
0
1
2
1
1
2
1
2
1
0
1
1
1
0
1
1
1
1
0
1
1
0
1
1
2
0
1
0
0
1
2
2
1
1
0
0
0
0
1
1
1
0
0
0
1
1
0
1
2
1
1
0
2
1
1
2
1
1
2
2
0
1
1
2
1
0
0
0
2
2
1
1
1
1
2
2
1
0
1
0
1
2
0
2
1
1
1
1
1
0
3
2
0
0
1
1
0
2
1
1
2
2
1
0
2
2
2
2
0
0
0
0
1
1
0
1
0
0
0
1
1
2
0
1
1
0
1
1
1
1
0
2
0
1
0
2
2
0
1
1
0
0
2
0
2
0
0
0
2
1
0
1
0
1
1
2
2
0
0
0
2
1
0
1
1
1
1
7
0
0
1
0
0
0
0
0
1
1
2
2
1
0
3
1
1
2
1
0
3
1
1
0
0
0
1
0
1
1
1
1
1
0
0
1
2
0
1
0
2
2
0
2
0
1
0
1
1
1
0
0
0
0
1
0
0
2
2
1
0
2
0
0
2
1
0
1
2
0
2
0
1
1
1
0
0
1
2
1
5
0
1
1
4
2
0
0
1
2
2
0
1
2
1
2
1
2
1
2
0
0
2
2
1
1
1
3
2
0
1
0
0
1
1
1
0
1
1
0
1
1
2
2
1
2
2
1
0
1
0
1
2
1
2
1
1
1
0
1
1
2
1
2
3
1
1
1
1
1
0
2
2
0
2
0
1
1
1
1
0
2
1
2
1
1
1
0
1
0
1
1
1
0
2
0
1
0
0
1
0
2
1
0
1
0
0
2
2
2
2
1
1
0
1
0
1
4
0
1
0
0
1
2
0
0
1
2
0
2
0
1
1
2
0
1
1
1
2
2
2
1
1
2
1
1
0
1
1
0
1
1
0
2
1
0
1
1
2
2
1
1
1
1
2
0
0
2
0
1
1
0
1
1
1
0
0
0
0
1
0
1
2
1
0
2
1
0
1
0
1
1
1
1
2
0
1
0
1
0
1
2
1
0
1
1
1
0
2
0
1
1
1
1
0
1
0
1
0
1
2
1
2
2
1
1
1
1
0
1
2
2
1
1
0
2
1
1
0
1
0
1
1
1
2
1
0
2
1
1
1
1
0
1
0
0
2
2
2
0
0
1
2
2
0
1
0
2
1
2
1
1
3
0
1
1
2
1
1
1
1
1
1
1
1
1
0
2
1
2
0
2
2
0
1
0
3
2
2
0
1
0
1
0
0
2
1
1
2
1
1
1
1
0
2
0
1
1
2
0
1
2
0
0
0
0
0
0
1
1
0
2
1
0
2
0
0
1
1
1
2
1
1
0
1
2
1
0
0
0
0
1
2
0
1
1
1
2
0
0
1
0
1
1
0
2
1
2
1
0
0
1
2
0
1
1
2
2
2
0
1
1
1
2
0
1
1
0
1
1
0
1
0
0
0
0
1
1
1
2
1
1
1
1
0
0
1
0
1
1
1
1
1
1
0
0
0
0
1
1
0
1
0
1
0
1
0
1
1
1
0
2
0
2
1
1
1
0
0
1
1
4
1
0
0
1
0
1
1
0
1
1
0
1
1
2
1
0
2
0
1
2
0
0
0
1
1
1
1
1
3
2
2
1
2
2
0
1
2
1
1
1
0
3
1
2
2
2
1
1
0
1
1
1
0
1
0
1
1
1
1
0
0
2
1
2
0
0
1
1
1
0
1
0
1
2
1
2
0
1
2
1
0
0
0
2
0
0
2
2
2
1
2
1
1
1
1
0
1
1
0
0
0
1
2
2
2
1
1
2
0
1
1
0
1
1
1
2
1
0
0
1
2
2
2
0
1
2
2
2
0
1
1
1
1
1
2
1
1
1
0
0
0
1
2
0
2
0
2
2
1
2
1
1
1
1
0
0
1
1
0
1
1
1
2
1
1
1
1
2
1
1
1
0
1
1
2
2
0
0
2
1
1
1
2
1
2
1
2
1
0
1
1
0
1
0
1
2
1
2
1
0
0
2
1
1
1
0
1
1
1
2
2
1
0
1
2
2
1
0
1
1
1
0
1
1
0
2
1
1
1
0
0
0
0
0
0
2
2
0
1
1
0
2
2
0
1
1
0
1
1
1
0
1
0
0
1
0
1
0
1
2
0
0
1
1
2
0
1
1
0
0
3
0
0
0
0
1
1
2
0
0
1
2
2
0
0
0
1
0
1
1
0
1
1
1
1
2
1
2
0
1
1
2
0
1
0
1
0
0
0
0
1
1
1
0
0
0
1
2
0
2
0
1
2
0
2
2
1
1
0
1
0
0
2
1
1
2
1
1
2
0
2
2
1
2
1
2
2
1
1
1
2
0
1
0
2
0
1
0
1
2
1
2
2
2
0
1
1
0
1
2
0
1
1
2
0
1
1
1
2
0
0
2
0
1
0
2
1
1
1
2
2
0
1
2
1
1
0
1
1
0
1
1
2
0
2
0
1
2
1
2
1
1
1
0
0
1
2
0
1
0
1
0
1
1
1
1
1
0
1
1
1
0
2
1
1
2
1
1
2
0
0
1
1
1
2
0
1
1
0
2
0
1
0
0
0
0
1
1
0
1
0
0
1
2
2
0
1
0
0
0
1
0
2
0
1
1
1
0
2
1
1
1
1
1
0
1
0
1
3
1
2
1
0
0
1
0
1
1
0
0
2
1
0
0
0
1
0
1
1
0
1
0
1
1
1
0
2
0
1
0
2
1
1
0
2
1
2
0
1
1
1
2
0
1
1
1
2
1
1
1
0
1
1
0
0
1
2
2
3
1
0
1
0
0
1
0
1
1
0
0
2
0
1
2
0
0
1
1
0
1
0
2
0
0
1
1
2
2
2
1
2
1
1
0
1
1
0
2
0
2
2
1
1
1
1
0
1
1
2
2
0
1
0
1
1
0
1
2
2
0
1
0
1
0
1
0
0
0
1
0
3
2
1
2
1
0
0
2
0
1
0
0
1
0
1
1
0
1
2
0
1
1
1
2
1
0
1
1
0
0
1
0
1
1
1
1
1
2
2
2
1
0
0
1
1
1
2
3
1
2
1
1
0
2
0
0
0
1
1
1
0
0
1
1
1
0
0
1
0
2
1
0
0
2
1
1
1
0
0
1
1
2
2
0
2
2
1
0
1
0
1
1
1
0
1
2
1
1
0
0
2
0
0
0
1
2
1
0
1
1
1
0
1
0
1
2
1
1
1
1
2
2
2
0
1
0
1
0
1
1
1
1
2
1
0
1
1
1
1
2
0
2
1
2
1
0
2
0
1
1
1
0
1
1
0
0
1
1
1
0
0
0
1
1
0
1
0
2
2
8
1
3
1
1
0
0
1
1
1
1
1
0
2
1
0
0
0
1
0
0
0
1
1
1
0
2
2
2
1
1
0
1
1
2
1
0
0
1
2
1
2
0
1
0
1
1
1
1
1
1
1
1
0
1
1
0
0
0
1
2
0
0
1
1
0
0
1
1
0
1
1
0
1
1
2
2
1
1
1
2
0
0
1
0
2
2
1
0
1
0
0
0
0
4
0
2
1
2
1
0
0
1
1
1
0
0
1
0
1
1
1
1
1
1
1
1
2
2
2
0
1
2
1
1
0
1
1
1
1
0
0
1
2
1
1
1
0
2
1
1
0
1
1
0
1
2
2
2
1
1
2
0
1
2
1
1
1
1
1
1
2
0
1
1
0
2
1
1
1
2
2
1
2
2
1
1
2
2
0
1
2
1
2
1
2
0
2
1
2
1
0
2
1
0
0
1
5
2
1
2
1
0
0
0
2
1
1
1
1
0
2
2
1
1
1
1
0
1
1
4
0
2
0
1
1
0
1
0
0
1
1
3
2
1
0
1
1
2
2
1
0
1
2
2
1
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
1
2
1
0
0
1
2
1
0
2
1
1
1
1
1
1
0
1
2
0
2
1
0
1
2
0
2
1
0
0
1
1
0
1
0
1
1
2
1
2
0
0
1
0
1
0
0
1
0
1
1
1
2
1
1
1
0
1
1
1
1
0
0
2
1
1
2
4
1
1
1
2
0
1
2
1
1
0
0
1
2
0
0
0
0
1
2
0
1
2
2
1
1
2
0
1
1
1
1
1
1
0
1
1
0
1
0
1
0
3
1
2
1
2
1
1
1
1
1
0
0
2
0
1
0
1
1
2
0
2
1
0
0
1
0
0
2
0
1
0
2
0
0
0
3
0
1
1
1
2
0
0
1
0
2
1
2
2
1
2
1
0
1
0
2
1
1
0
0
2
1
0
0
1
0
0
2
2
1
2
0
2
2
2
2
1
1
1
0
1
3
1
1
1
1
1
2
1
1
0
0
2
3
1
0
1
2
1
0
2
0
1
1
0
1
0
1
1
2
1
1
0
1
0
1
0
2
0
1
1
2
0
0
1
2
1
1
0
1
0
2
0
1
1
2
1
1
0
1
1
1
0
0
1
2
0
1
0
2
2
1
2
2
1
1
1
0
0
1
2
0
0
0
1
1
1
0
0
2
1
1
1
1
0
0
1
2
1
1
1
0
1
1
1
1
2
1
1
1
1
0
0
1
2
1
0
1
1
0
0
2
2
2
1
2
2
1
1
0
1
1
0
1
0
2
1
1
0
2
1
1
1
1
1
2
1
0
0
1
2
1
1
1
2
1
1
1
2
0
0
0
0
1
1
1
0
0
1
1
0
2
0
1
2
1
1
1
0
0
1
1
2
0
0
0
0
1
1
2
1
2
0
2
1
1
0
2
1
1
0
1
1
0
1
2
2
0
1
1
1
0
1
1
0
1
0
2
1
1
0
1
0
2
1
1
0
2
0
0
2
0
1
1
1
0
0
0
0
2
1
2
3
0
1
1
0
2
0
1
1
0
0
1
1
1
1
1
1
0
1
0
2
1
0
0
4
0
2
2
0
2
2
1
1
1
2
2
2
1
1
0
1
1
0
0
0
1
1
1
1
1
0
0
2
0
1
1
1
1
1
1
1
0
1
0
1
0
0
1
1
1
0
1
1
1
1
0
0
0
0
0
2
0
1
2
0
1
0
0
2
0
1
2
0
1
0
1
0
0
1
1
1
2
2
0
0
1
2
0
1
0
1
2
0
0
1
1
2
1
1
1
0
0
0
1
1
0
2
0
0
0
2
1
2
1
1
0
0
1
0
0
0
0
1
1
1
1
2
0
7
0
1
2
1
1
0
1
2
0
0
0
1
0
0
1
1
1
1
1
2
2
0
0
1
1
0
2
0
1
0
2
1
0
1
1
0
1
0
0
1
1
1
1
1
0
0
1
0
0
0
0
1
1
1
0
1
1
2
0
1
0
1
2
1
2
2
1
2
0
1
2
1
1
2
1
1
1
0
1
1
2
0
1
1
0
1
2
0
0
0
0
0
1
1
1
0
1
0
0
0
2
1
3
2
2
1
2
0
0
0
2
2
1
1
1
1
2
0
1
0
2
2
0
1
2
1
1
2
0
1
1
1
0
0
1
2
2
1
1
1
1
1
0
0
1
1
0
1
2
0
0
0
1
2
2
0
1
1
0
2
0
2
1
0
2
2
0
1
1
1
3
1
0
1
1
0
0
0
1
1
1
1
0
1
1
0
1
1
1
1
1
2
0
0
2
0
0
0
0
1
1
0
1
1
1
1
2
1
1
0
1
3
2
0
0
3
2
3
0
1
1
1
0
1
2
1
0
2
1
1
1
0
0
2
2
2
0
1
1
1
0
1
1
0
1
2
2
1
2
0
0
2
1
1
0
1
0
0
2
2
2
2
1
2
0
1
0
1
1
0
0
0
1
1
1
1
2
2
1
1
1
2
0
1
2
3
0
0
0
1
0
2
1
0
2
1
0
1
1
1
0
0
1
0
2
1
0
1
1
1
1
0
2
1
0
0
1
2
2
2
2
0
0
2
2
2
1
2
1
0
1
1
1
2
1
0
1
0
0
0
2
0
2
0
0
1
2
0
1
1
2
1
2
0
1
1
1
1
0
3
1
1
1
0
0
1
1
2
2
1
1
0
1
1
1
1
1
1
0
2
2
3
2
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
1
1
0
1
1
1
1
1
2
2
0
2
4
1
2
1
1
1
0
1
1
0
1
1
1
1
2
1
1
2
2
1
1
1
1
1
1
1
1
1
0
0
0
0
2
0
1
0
1
2
1
1
0
0
0
0
2
0
0
0
1
2
1
1
1
1
1
0
0
2
0
1
0
2
2
0
0
1
1
1
2
1
2
0
0
0
1
1
1
1
2
0
1
2
0
1
2
2
1
1
1
1
3
2
0
2
2
1
0
0
0
0
0
1
1
0
2
1
1
2
1
0
1
1
1
1
1
1
2
2
2
1
1
0
2
1
0
1
2
0
0
2
1
1
1
1
1
0
7
1
0
2
0
2
2
2
1
1
2
0
0
0
0
1
1
0
2
1
21
1
1
0
2
1
2
1
0
0
1
0
1
1
0
1
1
1
1
0
2
1
0
2
0
0
1
1
1
1
0
0
1
1
1
0
0
2
1
1
1
2
1
1
1
2
1
2
0
0
1
1
1
0
1
1
0
0
2
0
0
0
1
1
2
0
0
1
1
1
2
1
2
0
0
0
1
0
1
2
0
1
2
3
1
2
1
0
0
1
2
1
1
0
1
0
0
1
1
2
0
2
0
2
1
1
1
2
0
1
1
0
1
2
1
0
1
0
0
0
2
0
2
0
1
0
1
1
0
0
1
2
0
2
2
1
1
2
1
0
2
0
1
0
2
2
1
1
2
1
1
2
1
2
1
1
0
0
1
1
0
0
1
1
0
2
1
1
1
2
2
2
2
4
1
1
1
0
2
0
0
1
1
2
1
0
1
1
1
1
1
1
2
0
2
1
1
1
2
0
1
0
2
1
1
2
0
1
0
1
2
5
2
0
0
3
1
1
1
0
1
1
0
0
1
1
1
0
1
2
0
0
1
0
0
1
2
2
1
1
1
0
1
0
1
0
0
0
1
1
2
2
2
1
0
2
1
0
1
0
1
0
2
1
2
2
1
0
0
1
1
2
0
2
1
0
1
1
1
1
1
1
1
1
1
0
2
1
2
0
1
0
2
1
1
2
2
1
0
0
1
2
1
2
1
2
1
1
1
0
1
1
4
0
1
1
0
2
0
1
2
2
2
2
1
1
1
0
2
0
1
2
0
0
1
1
1
1
0
1
1
1
2
3
0
2
6
0
1
1
1
0
0
1
2
0
2
0
1
0
1
2
1
0
0
2
1
0
1
1
1
1
1
0
0
1
1
3
1
1
2
1
1
1
0
1
1
1
2
1
1
1
1
1
1
2
1
2
0
0
0
2
1
1
0
1
1
0
2
0
2
1
0
2
1
0
1
1
2
0
1
1
0
1
2
0
4
1
0
0
1
1
1
1
1
1
1
1
1
0
2
0
2
0
1
1
1
1
2
1
1
2
1
1
1
0
1
2
1
2
2
2
2
0
3
2
0
1
8
0
1
0
0
1
2
2
0
2
2
0
2
1
1
2
0
1
0
2
0
2
0
2
0
0
0
0
0
0
1
2
1
1
2
1
2
2
0
1
1
2
0
1
1
1
2
0
1
2
1
0
2
0
0
1
1
2
2
2
0
2
0
0
0
1
0
4
0
0
0
1
0
1
0
1
0
0
1
1
1
1
1
0
0
1
1
1
1
1
2
1
1
0
1
1
2
1
0
1
0
0
2
1
1
0
2
1
0
1
0
2
1
2
1
0
1
2
1
1
0
1
1
1
1
1
2
2
0
0
0
1
0
0
1
0
2
1
0
2
0
1
1
2
2
2
0
1
4
1
1
1
1
0
2
2
0
2
1
1
2
1
1
2
2
0
2
0
1
0
1
1
1
1
1
0
0
1
0
1
1
1
0
1
1
2
1
1
2
1
2
0
0
1
1
1
1
1
2
1
0
1
1
2
0
1
2
1
2
0
1
1
0
0
2
1
1
1
1
0
0
1
2
2
2
2
0
1
1
1
0
1
1
2
1
1
0
1
1
1
1
1
2
1
1
1
0
1
1
2
2
1
0
2
2
1
1
0
1
1
0
0
0
0
1
0
0
1
1
1
1
1
1
1
0
2
2
2
1
0
2
1
2
0
0
1
1
1
2
1
2
0
0
1
0
2
2
1
2
0
2
0
2
0
1
1
2
0
0
0
0
2
2
1
1
0
0
1
0
0
1
1
2
1
2
3
1
1
0
2
1
2
1
2
2
1
2
0
2
1
0
1
2
2
2
2
1
2
0
1
1
1
0
1
1
1
1
0
1
2
1
1
0
0
1
0
1
1
1
0
0
2
2
0
1
2
2
2
2
0
0
0
1
1
1
1
1
0
0
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
2
0
1
0
1
1
2
2
2
0
1
0
2
1
0
1
2
1
2
0
1
1
2
0
2
1
1
2
0
1
1
2
1
1
1
0
2
1
4
1
2
1
5
1
1
1
1
0
1
1
2
0
2
1
1
1
1
2
1
1
2
0
2
1
0
1
0
0
1
2
1
1
1
1
1
1
1
1
1
0
1
1
1
1
2
1
2
0
0
1
1
1
1
0
0
1
0
2
3
2
1
1
1
2
1
2
2
2
2
0
2
2
1
2
0
0
0
0
1
1
1
0
0
1
0
1
2
1
1
2
2
0
1
2
0
0
2
0
2
2
2
2
1
0
0
2
1
0
0
0
0
2
1
3
2
2
3
0
2
0
1
0
1
1
0
1
1
4
1
1
0
0
1
0
1
0
2
0
1
0
1
1
1
2
1
0
1
1
1
1
1
1
1
1
2
0
1
1
1
0
0
0
1
1
1
0
0
2
4
1
1
1
2
1
1
1
0
1
1
0
1
0
1
1
1
2
2
0
1
0
4
1
0
1
0
2
0
2
1
2
1
1
1
1
1
1
0
0
4
1
1
2
2
2
1
1
1
1
2
0
1
0
1
1
0
0
1
1
1
0
2
1
1
0
1
2
1
0
1
1
0
0
1
0
1
2
1
0
1
1
0
2
2
2
2
1
0
1
0
1
1
2
0
1
3
0
2
2
0
1
1
0
1
1
2
0
1
0
1
0
0
0
0
1
0
2
0
0
1
1
1
1
0
1
1
1
1
0
0
1
2
2
1
2
1
0
2
1
2
0
0
0
0
1
0
0
0
1
1
1
0
2
1
1
0
0
0
1
0
2
2
1
1
1
1
1
1
1
0
0
0
1
1
2
0
1
0
1
0
1
1
1
1
2
1
1
0
0
0
1
1
1
2
2
1
0
0
2
1
0
0
1
1
0
0
1
1
2
0
0
1
1
1
0
1
2
0
0
0
2
1
0
0
1
1
1
1
1
1
0
1
0
0
1
2
1
2
0
0
1
1
2
2
0
0
0
1
0
2
0
1
0
0
1
2
1
2
1
1
1
0
1
1
1
1
1
0
1
1
1
0
1
3
1
0
1
0
0
1
0
1
1
0
1
2
1
0
0
1
0
0
1
2
1
2
0
0
0
2
0
2
2
1
2
1
1
1
1
1
1
2
0
2
1
1
1
2
1
2
2
2
0
2
0
1
1
1
0
1
0
0
1
0
0
0
1
0
0
2
3
0
0
2
1
1
0
2
1
1
2
1
2
2
1
0
1
0
1
1
0
0
1
0
2
1
0
1
0
1
1
1
1
0
1
0
1
2
1
2
1
2
1
0
1
0
1
0
1
1
1
1
1
0
1
1
0
1
1
1
2
1
0
1
0
1
1
0
1
3
2
0
0
1
1
0
1
0
1
0
0
1
1
0
0
2
0
2
2
2
1
2
1
2
0
1
0
1
0
1
1
0
1
0
0
0
1
1
0
0
0
0
2
2
1
1
1
1
2
0
1
0
1
1
0
1
3
0
1
1
2
0
1
1
0
1
1
1
2
0
2
2
0
1
0
0
1
1
1
1
0
1
0
2
1
2
0
0
2
0
1
0
0
0
2
1
3
1
0
1
1
0
2
0
1
1
2
2
1
1
1
0
1
0
1
2
2
2
1
0
1
2
1
1
0
1
1
1
1
0
0
1
1
1
1
0
1
1
1
0
1
1
0
2
2
0
2
0
2
1
1
0
4
1
1
1
1
1
0
0
1
1
1
1
1
0
0
2
1
1
0
0
1
0
1
0
2
1
1
1
2
0
0
2
1
1
1
1
0
0
1
1
1
1
0
1
1
2
0
0
1
1
1
1
0
2
2
1
2
0
1
0
0
0
0
2
0
1
1
0
1
0
2
1
0
1
2
1
1
0
3
0
0
1
0
1
0
1
1
1
1
1
1
0
1
1
1
2
1
0
1
1
1
2
0
1
0
0
0
0
0
0
2
0
0
0
2
1
0
0
2
1
0
1
2
0
0
1
2
2
1
1
1
0
1
2
1
2
2
2
1
1
1
4
0
2
1
2
0
2
2
1
1
0
1
2
1
0
0
2
0
0
1
1
2
0
1
1
2
2
0
1
1
0
2
2
0
0
0
0
1
0
2
0
0
2
1
2
0
0
0
1
2
2
1
0
1
0
0
0
2
1
2
1
0
0
1
0
2
2
1
1
2
1
2
1
2
2
1
2
2
2
1
1
1
0
0
1
1
0
2
2
1
1
2
1
1
0
1
0
0
2
0
1
0
0
1
0
1
2
2
1
1
1
1
0
0
2
1
1
0
0
1
1
1
0
0
1
2
1
0
0
2
2
0
1
1
3
0
0
1
1
1
1
1
2
1
2
1
1
1
0
2
1
0
1
1
0
2
1
0
2
1
1
1
2
0
1
1
0
1
0
1
2
1
1
0
1
1
1
1
1
1
1
1
2
1
1
1
1
1
0
2
1
0
1
0
1
2
1
1
1
1
0
2
0
1
1
0
1
1
0
3
2
1
1
2
0
1
1
1
1
1
0
1
2
1
1
1
1
1
1
2
1
3
2
2
1
1
2
1
1
1
1
1
1
1
2
0
1
1
0
0
1
1
0
1
0
1
1
2
1
0
1
0
0
0
2
0
2
1
2
0
0
2
1
0
2
0
2
0
1
1
1
1
0
0
1
2
1
1
2
1
1
0
0
0
2
2
1
2
1
2
1
1
1
2
1
1
2
1
2
2
0
1
1
0
0
1
0
0
0
1
1
0
0
2
2
1
0
0
2
1
1
1
1
1
2
0
2
1
0
1
0
0
1
0
1
1
0
1
0
2
1
0
2
0
1
1
0
0
2
1
1
1
1
1
1
2
1
1
1
0
2
2
2
1
1
1
1
1
0
2
0
0
0
1
1
1
1
1
1
0
0
1
1
1
0
0
0
0
1
2
1
1
1
1
0
2
1
1
1
2
1
0
1
1
0
2
0
1
0
1
0
1
0
0
1
2
2
2
1
0
1
0
2
0
1
1
1
1
1
0
2
2
2
2
1
1
2
1
0
0
1
1
1
1
1
1
2
0
1
0
1
1
0
1
1
0
2
1
0
0
2
1
1
1
1
0
1
2
2
1
1
0
1
2
0
0
2
0
0
1
1
2
0
1
0
0
0
1
1
0
0
1
0
1
0
1
0
1
0
2
2
2
0
0
0
1
1
1
1
2
1
1
0
1
2
0
2
2
1
1
1
0
2
0
1
0
2
1
0
1
0
2
0
1
0
2
2
0
1
1
0
1
0
0
2
2
1
0
1
2
1
0
1
2
1
1
0
1
1
2
1
1
1
1
2
1
0
1
0
1
0
1
1
2
1
1
1
1
1
1
1
1
2
0
0
1
1
1
1
2
1
0
1
1
1
0
1
2
2
0
1
0
0
0
1
1
1
0
0
1
1
2
0
0
2
0
1
1
0
1
2
2
1
2
1
1
1
2
1
1
2
1
1
0
1
1
1
2
1
1
1
1
1
1
0
1
1
1
0
1
1
1
1
2
2
1
1
0
1
0
0
2
5
1
1
0
2
1
0
1
2
1
1
1
1
1
1
1
1
1
0
1
0
1
1
0
1
2
0
2
0
0
1
1
0
1
0
1
0
2
1
1
1
2
0
2
0
1
0
0
1
0
2
1
1
1
2
0
1
0
5
1
0
2
4
1
0
3
1
0
1
1
2
0
1
1
2
1
0
0
0
0
1
0
0
0
0
0
2
0
2
2
2
1
0
2
2
2
0
0
2
1
2
1
1
0
1
0
1
1
1
2
2
2
1
1
1
0
0
0
1
2
1
2
1
1
0
1
2
2
1
0
0
1
1
0
1
1
2
2
1
0
1
1
1
0
1
0
0
1
2
0
0
1
1
0
0
1
0
1
1
1
1
1
1
0
1
1
1
0
0
2
0
0
0
2
0
1
2
0
0
2
1
1
1
1
1
1
1
0
2
2
0
3
0
0
1
1
0
1
1
4
1
0
2
2
1
1
2
1
1
0
1
1
0
1
0
2
1
0
1
1
1
1
2
2
2
1
2
2
0
1
1
1
0
1
0
1
0
1
0
0
2
4
0
1
2
2
1
0
2
0
1
0
0
2
1
1
1
1
1
1
2
0
2
2
2
0
0
1
1
1
0
0
0
1
0
0
0
1
2
1
1
1
2
0
0
0
1
0
0
1
0
0
0
1
0
0
1
1
0
1
1
0
2
2
1
0
2
1
1
0
0
1
1
3
2
0
0
0
0
1
0
2
1
1
1
0
0
1
1
1
1
0
1
0
2
1
1
1
2
0
0
1
1
0
1
2
1
1
1
2
0
2
0
3
1
2
2
1
0
1
2
1
2
3
2
2
0
2
1
0
2
1
0
0
1
2
2
2
2
0
0
0
1
0
0
0
0
0
1
1
2
2
1
0
1
1
0
0
2
1
2
0
0
1
1
0
1
2
1
2
3
0
1
1
1
0
2
1
1
1
0
1
1
0
1
0
2
1
1
1
0
1
2
0
0
1
2
0
2
1
1
1
0
0
0
1
0
0
0
1
0
1
0
1
1
0
1
1
1
0
0
1
0
2
0
0
0
0
0
1
0
1
0
2
1
0
1
0
0
0
1
0
1
1
2
1
1
0
2
1
1
1
0
1
2
1
1
1
1
1
2
1
1
1
0
1
1
2
1
0
0
1
0
1
1
1
1
0
1
1
1
2
0
1
0
0
0
0
0
0
2
1
1
1
0
0
2
1
1
1
0
2
1
1
1
1
2
1
1
0
1
1
2
1
0
0
2
0
0
1
2
0
0
1
1
1
1
0
1
1
0
0
1
1
0
2
1
2
1
2
1
2
0
1
2
0
1
1
0
1
0
2
0
0
1
1
1
0
1
1
1
0
1
1
2
1
1
0
1
0
0
2
1
2
2
1
2
0
0
2
1
2
2
2
1
2
1
1
1
1
1
0
0
0
0
1
1
2
2
1
1
1
1
1
0
1
1
1
1
1
0
0
1
1
1
0
0
1
0
0
2
2
1
1
0
1
1
0
1
2
1
0
2
2
0
1
1
0
2
1
2
2
0
1
1
1
0
2
0
0
1
1
0
2
1
1
0
1
1
1
2
1
2
0
2
0
1
1
1
1
1
0
0
1
0
1
0
1
1
1
2
1
0
1
1
1
3
2
0
0
0
0
2
1
0
1
2
1
0
0
0
0
1
2
0
0
2
0
0
0
1
0
0
0
0
1
0
0
1
1
1
2
1
1
0
0
2
1
1
2
1
0
0
1
2
0
1
0
1
1
2
0
0
1
2
2
1
1
2
2
1
1
1
2
0
0
1
0
0
0
1
0
1
1
1
1
1
2
0
0
0
1
1
1
1
0
1
1
1
1
2
0
2
1
1
1
1
0
1
1
2
1
0
1
0
1
0
1
2
2
1
1
0
0
2
0
1
1
1
1
1
1
0
2
0
2
1
0
1
1
0
1
2
1
1
2
0
0
1
0
1
1
1
1
1
0
1
1
1
2
0
2
2
1
1
1
1
1
1
1
2
1
0
1
1
1
1
1
2
1
0
1
1
2
0
0
1
1
1
2
0
2
2
0
1
2
1
2
1
2
1
0
2
1
0
2
1
1
2
0
1
1
2
1
1
0
2
2
0
4
2
1
1
1
2
1
1
1
2
2
2
1
0
0
0
0
1
0
1
0
2
1
1
1
0
2
1
0
1
1
0
2
2
0
1
1
1
0
0
2
0
2
1
0
0
1
1
1
2
2
2
0
0
2
2
0
0
1
0
0
1
1
0
2
1
0
1
1
0
1
2
1
0
2
0
2
1
0
0
0
2
1
0
1
1
1
1
1
0
0
2
1
0
1
2
0
2
0
1
2
3
2
0
2
3
1
2
1
1
0
1
0
0
1
0
1
1
3
2
0
1
1
1
0
1
0
0
0
1
0
2
0
1
1
0
0
0
1
1
1
1
1
0
0
2
2
1
1
0
1
1
1
1
0
0
0
1
0
0
0
0
2
0
1
2
1
2
0
0
0
0
1
1
1
2
1
2
1
1
1
0
1
0
1
1
2
1
1
1
1
1
0
0
2
1
1
0
2
0
1
2
1
1
1
0
1
1
1
0
0
1
0
1
1
1
1
0
2
0
0
1
1
2
1
1
0
1
1
2
1
1
0
1
0
0
1
2
1
1
0
1
0
1
3
2
2
0
0
1
0
3
0
2
1
1
0
2
0
0
1
0
1
1
1
2
1
1
0
1
2
0
1
1
2
2
0
2
2
0
2
1
0
0
0
1
1
1
2
0
0
2
1
1
0
0
2
0
0
0
0
2
1
0
2
0
0
0
1
0
1
0
0
1
2
0
1
0
0
1
1
2
1
0
1
1
2
1
1
2
1
1
1
1
0
1
0
0
1
1
0
2
1
0
0
0
1
2
2
1
1
3
0
0
2
1
1
1
1
1
2
2
2
1
0
1
1
0
1
0
1
1
0
2
1
1
1
0
0
0
1
3
1
0
1
1
2
1
0
1
1
0
2
2
1
1
1
2
0
1
2
1
0
1
0
2
2
0
1
0
0
1
1
0
2
0
0
0
2
0
0
2
0
2
1
0
2
1
2
1
1
0
1
0
2
2
1
0
1
2
2
0
2
5
1
0
1
1
0
2
1
0
0
2
0
1
1
2
0
2
2
2
1
0
1
0
1
0
0
1
2
1
0
0
2
0
0
1
1
2
1
0
1
1
2
2
0
2
0
1
1
0
0
2
3
1
0
0
1
0
2
0
0
1
1
2
0
1
1
0
0
0
2
2
2
1
2
0
2
2
1
2
2
1
0
0
0
1
0
1
1
2
1
2
0
2
1
2
1
0
1
1
1
2
0
0
1
1
1
0
1
2
2
1
1
0
1
1
0
1
0
2
1
0
1
2
1
1
1
0
3
1
2
2
1
1
1
0
2
1
0
0
2
1
0
1
1
0
0
1
0
1
2
1
0
1
2
0
1
0
1
2
1
0
0
1
2
2
1
0
0
1
0
1
1
1
1
1
1
0
0
0
0
0
2
0
0
0
1
2
1
2
1
2
1
1
0
0
0
2
0
2
1
2
0
2
2
2
0
0
2
0
0
1
0
2
1
1
0
2
0
2
1
1
1
1
1
1
1
0
0
1
0
1
1
0
1
1
1
1
2
1
1
2
1
2
0
0
1
1
0
1
2
1
1
2
1
1
1
1
1
0
2
2
0
1
0
1
1
1
0
1
2
1
1
0
1
2
0
0
0
1
1
1
1
0
0
2
1
0
1
2
2
0
2
1
1
1
1
1
2
0
0
1
1
2
2
1
2
1
2
0
0
1
3
2
0
2
1
0
1
1
2
1
1
0
1
0
1
1
1
1
1
1
1
1
1
2
1
2
2
2
2
1
3
0
1
1
1
2
1
2
0
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
0
0
0
1
1
0
1
2
0
0
2
1
1
1
1
2
2
1
0
1
1
0
2
1
0
1
1
1
1
1
1
2
2
1
1
0
0
1
0
0
0
0
2
3
0
2
0
2
0
1
0
1
2
2
1
0
0
0
1
2
1
2
1
1
1
4
1
0
0
1
0
0
1
1
1
0
0
1
0
2
0
2
0
1
2
0
1
3
1
0
2
1
1
0
1
2
1
0
1
0
1
1
1
0
1
1
1
1
1
2
0
1
1
1
0
1
1
1
0
0
0
1
1
2
1
0
1
2
2
1
2
0
1
1
1
0
1
1
1
1
0
0
1
2
1
1
1
1
1
1
1
3
1
2
1
0
0
0
0
1
2
0
1
1
1
0
1
0
1
1
1
0
2
0
0
2
0
2
0
1
1
1
1
1
1
2
3
2
0
1
0
1
0
1
1
1
1
1
1
0
0
1
2
2
2
1
2
1
1
1
0
0
1
1
0
0
1
2
1
0
0
0
2
0
2
3
0
0
0
0
0
1
1
0
1
0
1
1
1
1
1
1
1
1
1
0
1
1
2
1
1
1
2
1
1
1
1
1
0
1
1
0
1
1
1
1
1
0
2
0
2
1
0
2
0
0
1
1
1
0
0
1
1
0
1
1
0
2
0
1
1
0
0
1
0
0
1
1
2
1
0
2
2
1
0
0
1
0
2
1
0
1
0
1
2
2
2
0
0
0
1
2
1
0
2
1
2
1
1
1
2
1
1
0
1
2
1
1
0
2
0
1
1
2
1
2
1
1
1
2
1
0
2
1
2
0
1
1
1
1
0
0
1
1
0
0
0
1
0
1
1
0
2
3
1
1
0
1
0
2
0
1
1
2
0
1
0
0
1
0
2
2
0
1
2
1
1
2
1
1
1
1
1
1
1
0
1
1
1
0
1
2
1
0
2
0
2
1
0
2
0
2
1
1
0
0
2
2
1
4
1
0
1
1
1
4
2
0
1
1
1
0
2
1
1
0
1
2
0
1
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
2
0
1
0
0
1
0
1
0
0
1
1
0
1
1
1
1
0
0
0
0
0
1
2
1
0
0
1
0
1
1
2
2
2
1
1
2
2
2
2
0
1
1
3
0
0
0
1
0
1
0
1
0
2
1
2
0
1
1
1
1
2
1
0
1
2
1
1
0
2
1
1
0
0
0
2
1
1
1
1
0
0
0
1
2
1
4
0
1
2
0
0
0
1
2
0
1
1
1
0
1
1
0
0
1
1
2
2
0
1
1
1
0
0
0
1
1
1
0
0
0
1
1
1
0
0
1
0
1
2
1
0
0
1
0
1
1
2
1
0
0
1
1
2
0
0
1
1
1
1
1
0
1
0
1
1
1
2
1
0
0
2
1
1
1
1
1
0
0
2
0
1
0
1
0
1
0
0
1
2
1
2
1
0
1
1
0
1
2
2
1
0
1
1
0
0
2
1
0
1
0
1
0
1
2
0
1
1
1
0
1
2
2
1
0
0
1
1
1
0
0
1
2
0
1
1
1
1
2
0
1
1
1
1
2
1
2
2
1
2
0
1
0
1
1
0
0
1
1
1
1
2
1
0
2
1
0
1
0
1
0
1
0
0
1
0
1
2
1
1
1
2
0
0
1
1
1
0
2
0
0
0
0
0
1
2
2
1
1
1
1
1
1
2
2
0
0
0
2
0
0
1
4
0
2
2
0
1
0
1
1
1
1
2
1
1
0
1
1
2
1
2
0
2
2
0
2
0
2
1
1
1
1
2
0
0
1
2
0
1
0
0
1
0
0
2
1
1
0
1
1
1
1
1
3
0
0
1
2
2
0
0
2
0
2
2
0
1
2
1
0
0
0
2
1
1
0
2
0
1
2
3
2
0
1
1
0
2
1
1
1
1
2
1
0
0
1
2
3
0
0
0
2
2
0
1
1
1
0
2
1
1
0
0
1
2
1
2
1
0
2
1
3
1
1
1
1
1
1
0
1
0
1
1
1
1
1
2
0
4
1
1
1
2
2
0
0
1
1
1
1
2
0
1
0
2
0
0
0
0
0
1
0
1
0
0
1
1
2
1
0
1
3
0
1
0
0
2
1
1
1
1
1
0
0
0
0
3
1
1
0
2
2
0
1
1
1
2
2
1
0
0
2
3
1
1
0
0
0
2
1
1
1
0
1
2
1
0
0
2
1
1
0
1
1
2
2
0
0
1
0
0
2
0
0
1
0
2
1
0
0
1
0
2
0
0
1
2
0
1
2
1
2
0
1
0
2
2
0
1
2
2
0
2
1
2
2
2
0
1
2
0
1
0
2
0
1
0
2
1
0
0
1
3
0
2
2
1
1
0
0
2
2
0
0
1
0
1
2
1
1
0
0
0
2
0
1
1
0
2
2
1
1
1
1
2
1
1
0
2
2
1
0
1
1
2
1
0
0
1
1
2
2
1
0
1
0
0
1
1
1
1
0
0
1
2
2
0
1
1
1
1
1
1
2
0
0
0
2
1
1
1
0
1
1
1
1
0
1
1
1
1
2
0
0
1
1
0
1
1
1
1
1
1
1
1
1
2
0
1
0
0
2
1
1
2
2
0
0
2
0
2
2
1
2
1
1
0
0
1
0
0
1
2
0
2
0
1
2
1
1
2
2
1
1
2
1
1
1
2
1
1
2
0
0
0
2
0
2
1
0
1
1
0
1
1
1
1
2
0
1
0
0
1
1
1
1
1
1
2
2
2
1
1
1
1
2
1
0
1
0
1
1
2
1
1
2
2
0
2
1
1
1
0
1
1
0
1
0
1
0
2
3
1
0
1
1
2
2
2
2
1
1
0
1
0
0
1
2
1
1
1
0
1
1
1
1
0
1
0
1
0
2
1
1
0
2
1
1
1
1
2
0
1
1
0
1
1
0
0
0
1
0
1
2
1
0
1
0
0
1
0
1
0
2
0
2
1
2
0
0
1
1
1
2
1
1
1
1
2
2
2
1
0
1
0
0
1
2
0
2
1
2
1
1
1
1
1
1
0
1
1
2
0
1
1
2
1
2
1
0
0
0
0
0
2
2
1
1
0
0
1
1
0
2
1
2
2
0
1
1
0
0
0
1
1
0
1
1
1
0
1
3
1
0
2
2
1
2
2
0
0
0
1
2
0
2
0
0
2
0
1
2
1
0
0
0
1
2
2
4
1
1
1
0
0
1
2
2
1
0
0
1
1
1
0
2
1
0
1
1
1
0
0
0
1
1
1
1
1
0
1
1
0
1
1
0
1
0
2
0
1
0
2
0
1
2
1
1
1
0
1
1
2
1
2
2
1
1
1
2
0
1
2
0
0
2
1
2
1
2
1
0
0
0
2
0
0
1
1
2
1
1
4
1
0
2
1
0
1
1
0
1
1
4
1
1
2
2
0
2
2
2
1
2
4
1
0
2
1
2
0
0
1
1
1
0
1
1
2
1
1
0
0
2
0
2
2
2
2
1
1
0
1
0
0
3
2
1
0
2
1
1
1
1
1
1
1
1
2
2
2
2
1
2
0
0
2
0
2
0
1
2
0
1
1
1
0
2
0
1
0
1
1
0
2
1
1
2
0
1
0
0
1
1
1
1
2
0
0
2
0
1
1
1
0
1
0
1
1
1
1
1
1
1
5
1
0
1
2
0
1
1
2
1
1
0
1
2
1
0
1
0
2
1
1
1
0
1
1
1
0
1
0
1
1
1
1
1
2
0
1
1
0
2
1
0
2
1
1
1
0
2
2
2
0
0
0
2
1
0
0
0
1
0
0
2
1
1
1
1
0
1
0
1
0
1
2
1
1
0
1
1
1
1
1
1
0
1
1
1
2
1
0
1
0
0
1
2
0
1
1
1
0
2
0
0
1
1
1
0
1
1
0
0
1
0
1
0
1
1
1
1
1
0
0
0
1
2
0
1
2
1
1
2
2
2
2
0
2
0
1
1
1
1
1
0
1
2
1
2
1
1
0
1
1
2
1
2
1
2
0
0
2
1
0
2
1
0
1
1
1
1
1
0
1
1
0
1
0
0
1
1
0
2
0
1
1
0
0
1
2
2
0
0
0
1
1
1
0
2
0
1
1
0
1
1
0
0
3
1
0
1
2
0
2
0
0
0
2
2
2
0
2
1
2
1
2
0
2
0
0
1
2
2
1
1
2
1
0
1
0
0
2
0
1
1
2
0
1
1
1
1
1
0
2
1
0
0
1
0
0
0
1
2
2
1
0
0
0
2
2
1
0
1
2
2
1
0
1
1
0
2
1
1
0
0
1
0
1
0
0
2
1
1
0
0
0
0
1
2
1
2
1
1
2
0
1
0
0
0
3
2
0
0
0
0
2
1
2
1
1
2
2
0
0
2
2
1
1
2
0
0
0
1
1
1
2
2
1
2
0
0
1
1
2
0
0
2
2
2
1
1
2
2
1
0
1
1
0
1
1
1
1
1
1
2
2
1
1
1
1
1
0
1
1
2
2
0
2
0
2
2
2
0
1
1
4
1
0
0
0
1
0
0
2
1
0
1
2
0
1
2
1
2
2
0
1
1
1
1
0
1
1
2
1
1
2
2
0
1
0
1
0
1
0
1
1
1
1
0
0
1
0
0
0
2
0
1
3
2
0
1
1
1
2
2
0
1
1
1
1
2
0
1
0
1
0
1
0
2
1
1
2
0
1
1
1
1
0
0
1
0
0
1
1
1
1
0
2
2
0
1
0
1
1
0
1
1
0
1
0
2
1
0
0
0
2
2
1
1
0
0
1
1
2
0
0
1
2
0
0
1
0
1
2
0
0
2
2
2
0
0
2
2
0
0
2
1
1
0
0
0
1
0
2
0
1
1
2
0
1
0
1
1
1
0
0
1
0
0
2
1
0
1
2
1
1
0
2
1
1
1
1
0
1
1
0
1
0
1
2
0
0
1
1
1
0
2
1
0
0
2
1
2
1
1
2
1
0
0
0
2
0
1
2
2
2
1
2
1
0
0
0
2
1
1
1
1
1
2
1
0
1
1
0
2
0
0
2
0
0
0
1
0
2
2
0
1
1
0
1
0
0
1
2
1
0
0
1
0
2
1
2
0
1
0
1
1
1
0
1
0
2
1
2
0
1
1
1
1
1
5
1
0
2
0
1
2
3
1
2
0
0
0
1
2
0
0
1
0
1
2
0
1
1
2
1
0
1
0
2
0
2
1
1
0
0
2
1
0
0
1
1
1
2
1
0
1
1
2
1
3
1
0
2
2
1
0
0
1
2
2
1
0
1
0
0
1
1
1
1
1
1
1
1
1
2
2
2
2
1
1
1
0
1
1
0
0
0
1
1
2
1
0
0
1
0
1
2
1
0
1
0
1
0
0
0
0
1
0
1
0
0
0
1
0
1
1
1
1
0
0
1
1
0
1
2
1
2
0
1
1
2
1
0
2
1
1
1
1
1
1
0
2
3
2
0
1
1
1
0
0
0
2
0
1
0
1
2
0
1
2
0
2
2
1
2
2
1
2
2
1
1
1
1
2
1
0
1
1
0
1
0
1
1
0
0
2
0
0
1
2
1
2
1
1
1
1
0
1
0
0
2
0
1
0
1
2
0
0
0
1
2
1
0
1
0
1
1
0
0
1
1
2
1
1
1
0
1
0
0
1
0
2
0
0
0
1
1
0
1
1
1
1
0
1
0
1
1
1
0
1
2
0
1
1
2
2
2
1
0
1
1
0
1
2
0
0
0
0
2
0
2
1
2
0
0
2
1
3
2
1
0
1
1
1
2
2
1
2
0
2
1
1
0
2
1
1
0
1
1
0
0
0
1
0
1
1
1
1
2
2
2
1
2
0
2
1
0
1
2
0
0
2
1
0
0
1
0
1
2
0
2
2
1
1
1
2
2
0
2
2
0
0
0
1
2
1
2
0
1
0
1
1
1
1
0
0
1
0
1
1
0
0
1
0
0
0
1
0
2
2
2
1
0
0
0
0
1
2
1
0
1
1
1
1
1
1
1
1
1
0
2
2
1
1
0
0
1
0
1
1
1
1
1
0
1
2
2
1
0
1
1
0
2
1
2
1
1
1
1
1
1
1
2
2
1
1
0
2
1
2
0
1
0
1
1
1
1
1
2
0
0
1
1
1
0
2
0
0
1
1
0
1
0
0
2
0
0
0
1
0
0
1
1
2
1
1
0
0
2
0
0
0
0
1
1
1
1
0
2
0
0
1
1
2
0
1
1
0
2
1
1
1
1
2
0
1
1
1
1
1
2
0
1
6
2
0
1
1
1
2
1
0
1
1
1
0
0
1
0
1
1
2
2
0
2
0
1
0
1
0
0
0
2
2
0
1
2
1
1
2
1
1
1
2
0
0
2
1
1
1
0
0
0
0
1
0
0
2
1
2
1
0
0
0
0
0
2
1
0
1
0
1
0
2
0
2
2
1
1
0
2
2
1
1
1
2
2
1
2
0
1
1
0
1
1
1
1
0
0
3
0
2
2
1
1
1
0
1
2
0
0
1
0
0
2
1
1
2
1
1
1
1
2
2
1
1
1
2
1
1
0
2
1
2
0
1
1
0
2
1
1
0
1
1
0
0
1
0
1
1
0
2
0
1
1
2
0
0
0
1
2
1
1
2
1
0
0
1
1
2
2
0
1
1
0
2
0
1
0
1
1
0
1
1
1
0
1
1
1
2
2
0
1
1
2
0
0
2
0
1
0
0
1
2
0
1
1
1
0
1
2
2
2
0
0
1
1
1
1
1
1
3
0
2
1
2
0
1
0
1
2
1
0
2
2
1
1
0
0
1
0
2
0
1
1
1
0
2
1
2
1
0
0
1
0
0
0
0
0
2
0
0
1
2
1
0
2
0
1
0
0
0
1
2
1
0
0
1
1
1
0
1
1
1
1
0
2
1
2
0
1
2
0
1
2
1
1
1
0
1
2
0
0
1
1
0
0
2
0
1
0
0
0
2
2
1
1
1
0
2
1
2
1
1
1
1
2
2
1
1
1
2
1
2
0
1
1
1
0
2
3
1
2
2
0
1
2
1
0
0
1
1
1
0
1
0
0
0
0
1
2
0
2
1
0
2
1
1
2
2
0
1
1
1
0
1
1
1
0
1
2
0
2
1
1
0
1
1
1
2
1
0
0
2
0
1
1
0
0
1
0
2
0
1
2
0
2
0
1
1
0
2
0
0
0
1
1
1
1
1
1
3
0
1
2
2
1
0
1
1
0
2
1
3
1
0
1
1
1
2
1
1
0
1
0
2
1
2
1
2
1
0
0
1
0
1
1
1
1
1
0
1
0
0
0
2
1
2
0
0
0
2
0
1
1
0
1
0
0
0
2
1
2
2
3
0
0
0
1
1
0
1
2
1
0
1
2
1
2
1
1
2
1
1
1
1
1
0
1
1
0
1
2
1
1
1
1
1
2
1
0
0
0
1
1
2
0
1
0
1
1
2
1
1
2
2
1
0
2
2
1
0
0
0
0
1
1
2
0
1
1
1
0
2
0
2
2
3
3
1
1
2
0
0
1
1
0
1
1
0
1
0
0
1
0
1
1
1
1
0
1
2
0
1
1
0
0
1
0
0
2
0
0
1
1
0
1
1
1
1
1
1
2
0
0
1
0
2
0
1
1
2
1
0
0
2
2
1
1
0
1
1
2
0
1
1
0
2
1
1
2
2
1
2
1
1
2
1
1
0
0
1
2
0
2
1
1
0
2
1
2
2
1
1
2
0
1
0
0
2
0
0
2
1
0
1
1
0
2
0
1
1
2
1
0
2
0
1
0
1
0
0
2
1
0
1
1
2
1
0
0
0
1
2
2
1
1
0
1
1
2
0
1
1
1
0
1
1
1
2
0
0
0
0
1
0
0
0
1
1
2
0
0
1
1
1
1
1
2
0
0
2
2
0
1
1
2
0
0
1
1
2
1
1
0
1
2
0
1
2
2
1
1
2
2
0
1
1
1
0
0
0
1
2
2
0
2
1
2
0
0
0
2
0
0
2
0
1
1
1
0
0
2
1
1
1
1
1
0
1
0
2
4
1
0
1
1
1
1
0
1
2
2
1
1
1
1
0
1
1
2
1
0
0
0
0
2
1
2
1
2
0
2
2
0
2
1
1
1
1
2
2
1
1
1
0
1
1
2
2
1
1
1
1
2
1
1
0
0
1
1
1
2
1
1
1
1
0
0
1
1
1
0
2
2
0
0
2
1
1
0
1
0
1
2
0
1
0
1
2
1
0
0
1
3
0
1
0
0
2
0
0
1
2
1
1
1
1
1
1
2
0
1
1
1
1
1
1
1
2
2
0
0
2
1
0
1
0
0
1
1
1
2
0
2
0
0
1
0
1
2
0
2
2
0
1
0
2
1
1
1
1
1
1
2
2
1
1
1
0
1
1
0
1
2
1
1
1
2
1
1
0
0
0
2
0
0
0
1
1
1
3
0
0
1
1
0
0
0
1
0
0
1
2
1
1
1
1
0
0
1
1
0
0
1
0
4
1
2
2
1
0
0
0
2
1
1
1
1
1
1
2
1
1
0
2
0
2
1
0
0
0
1
2
2
1
2
0
0
2
1
0
2
1
1
0
1
2
1
0
1
0
0
0
1
0
2
0
0
1
1
0
1
1
1
1
2
1
1
0
1
1
2
2
1
0
1
1
0
1
1
1
1
2
1
1
2
1
0
2
0
1
1
1
2
2
2
1
2
0
1
0
0
2
0
2
1
1
0
0
0
1
1
2
0
1
0
1
0
0
0
0
0
1
1
1
1
1
0
2
1
0
1
0
0
0
1
0
1
1
1
1
2
1
1
1
0
1
1
0
2
1
0
0
0
2
1
1
1
0
2
2
2
0
1
1
2
2
2
0
1
0
1
1
1
0
1
0
1
0
1
1
2
3
1
2
1
0
0
1
1
0
0
0
2
0
1
1
1
0
1
0
0
2
2
2
1
0
0
1
2
1
2
1
0
1
1
1
0
1
2
2
0
2
1
0
1
1
1
0
1
1
1
1
0
1
2
0
1
2
0
1
1
1
1
0
1
1
0
1
1
0
0
2
1
1
1
0
0
1
1
0
0
2
0
0
1
2
1
0
1
2
2
0
2
1
1
2
0
2
1
0
1
1
0
1
1
0
1
1
2
0
1
1
2
1
0
5
1
1
1
0
2
2
2
1
2
0
0
1
1
0
1
1
0
0
2
1
2
2
1
0
2
1
0
3
1
1
0
1
0
0
1
0
2
1
0
2
1
1
0
1
1
0
1
2
0
1
3
0
1
2
2
2
1
0
2
2
3
0
0
0
0
3
2
0
0
0
1
2
1
1
1
0
1
0
0
0
1
1
1
0
1
0
1
0
3
1
0
1
1
1
2
1
1
1
1
2
2
1
0
0
2
2
1
2
1
1
2
1
2
1
0
0
1
2
0
2
0
1
1
0
1
1
2
1
1
0
0
0
2
0
1
1
1
1
0
1
0
2
0
0
1
1
2
2
0
0
1
0
2
1
1
0
2
0
1
1
2
1
2
0
0
1
2
1
2
2
1
0
2
1
0
2
1
0
2
0
1
1
1
1
1
2
1
1
4
3
1
0
2
0
1
2
0
0
1
2
1
1
2
0
0
1
0
2
0
2
1
1
0
1
0
1
1
2
1
1
1
0
0
1
2
1
0
0
0
0
2
1
0
2
0
1
3
1
1
1
1
2
1
1
1
0
1
1
0
2
0
0
0
0
0
0
0
1
1
1
1
1
1
1
0
0
1
1
0
1
1
0
2
1
1
2
1
2
1
0
1
1
2
0
1
0
2
1
1
1
0
0
0
1
2
2
1
2
3
1
1
2
1
2
1
1
1
0
2
3
1
1
0
1
0
0
1
0
1
2
1
2
1
2
1
0
0
0
2
0
2
0
2
1
1
1
3
2
1
2
2
2
0
1
0
2
0
1
0
1
1
1
1
0
1
0
0
1
2
2
0
1
1
0
1
2
1
0
1
2
0
0
0
1
0
1
0
1
1
2
0
2
1
2
1
2
0
2
1
0
1
0
1
0
1
0
1
1
0
0
1
2
0
2
0
0
2
2
1
1
0
0
1
0
1
2
1
1
1
1
0
1
1
1
2
1
0
0
1
2
2
2
2
1
1
1
1
0
2
2
1
1
1
1
0
1
1
1
0
0
0
2
2
0
2
2
1
2
2
0
1
1
1
2
1
0
1
1
0
2
0
2
0
1
2
1
0
2
1
1
0
0
1
1
2
1
0
0
0
1
1
0
1
1
0
1
1
1
2
0
1
0
0
1
1
1
0
2
0
2
3
0
0
0
1
0
1
1
1
2
2
1
0
2
1
2
2
1
1
0
0
1
0
1
2
2
0
0
0
1
0
1
0
3
0
1
0
1
1
0
1
0
0
1
2
1
1
2
0
2
2
2
0
2
0
1
2
1
1
1
1
1
1
1
0
0
0
1
2
2
1
1
0
1
0
1
1
0
2
1
2
1
0
1
0
0
2
3
1
1
0
0
0
1
2
0
0
1
0
1
2
0
2
0
1
1
0
1
1
0
1
0
2
3
1
1
1
1
1
1
2
1
1
1
2
0
2
1
1
0
1
2
1
2
2
0
1
1
2
2
2
3
2
5
2
2
1
0
0
1
0
0
1
1
1
0
1
1
1
0
1
2
1
1
2
1
2
1
1
1
0
1
0
1
2
1
2
0
0
0
2
2
1
1
0
0
0
1
2
1
1
0
0
1
0
0
0
0
1
0
0
0
2
1
2
1
1
0
2
0
2
1
2
2
2
1
1
2
1
0
0
0
1
1
2
1
2
1
0
1
1
2
1
2
0
1
1
1
2
1
3
0
0
0
1
1
0
1
2
1
1
1
1
1
1
0
3
2
1
1
0
1
1
0
1
0
1
0
1
1
1
1
1
1
1
0
1
0
2
0
1
1
1
1
2
1
1
1
1
2
2
0
0
0
2
1
0
0
0
1
0
1
1
1
1
2
0
2
1
1
1
1
2
1
1
0
1
0
1
2
1
2
1
2
1
1
2
1
1
1
0
0
1
2
1
1
1
0
1
0
1
0
2
1
0
1
2
2
1
2
1
2
2
1
0
2
2
0
0
1
0
1
0
0
2
0
2
2
0
1
1
1
2
1
1
0
1
0
0
1
1
0
1
1
0
2
1
1
1
1
1
2
0
0
1
1
2
0
2
0
1
1
1
0
0
1
0
1
0
1
0
1
1
0
0
2
0
2
2
0
1
0
1
0
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
0
1
0
1
1
0
2
1
0
1
0
1
1
0
2
1
0
3
2
1
0
1
1
1
2
0
2
1
1
1
1
1
2
1
2
0
1
1
0
0
0
0
0
0
0
0
1
1
0
1
0
1
2
1
2
1
1
1
1
2
1
2
0
0
2
1
0
1
1
0
2
1
0
1
1
0
1
0
1
1
1
1
0
1
2
2
1
0
0
1
0
1
2
1
2
2
1
1
1
0
2
2
0
1
0
2
0
1
1
1
0
1
2
1
1
1
1
0
1
0
0
1
1
1
3
0
1
0
0
1
0
1
1
2
0
1
0
2
5
1
1
1
0
1
1
0
2
0
1
1
1
0
2
0
2
1
2
3
1
1
0
1
0
0
2
2
1
0
0
2
1
2
1
0
1
1
1
2
0
2
1
0
1
0
0
0
0
1
2
3
2
1
0
2
2
1
1
1
0
1
1
0
1
2
1
0
2
2
1
1
1
3
2
0
2
2
1
2
0
0
2
0
2
0
1
0
1
1
2
1
1
0
0
2
0
0
0
1
0
1
1
1
0
5
1
0
1
0
0
0
3
1
0
3
1
1
0
1
2
0
2
1
3
1
2
0
2
0
0
1
1
1
0
1
2
1
2
0
1
1
1
0
0
1
2
2
1
0
1
1
0
2
0
1
1
0
0
0
2
2
2
1
1
2
1
6
2
1
1
1
0
0
0
0
0
2
2
2
0
1
0
1
1
1
0
0
1
2
2
0
1
0
1
0
1
0
0
1
0
2
0
0
1
2
4
0
1
1
2
0
1
2
0
0
2
2
1
1
1
0
1
2
0
0
2
0
1
2
3
0
0
2
1
0
1
1
2
1
1
1
0
1
0
1
1
0
1
1
2
2
2
0
1
1
2
0
1
0
1
0
0
0
1
1
2
1
0
0
0
2
0
0
1
0
1
1
2
0
1
0
1
0
2
0
0
1
0
1
0
1
0
1
2
1
2
1
0
2
1
0
2
1
1
0
2
0
0
0
1
1
1
1
1
0
1
0
0
2
2
0
1
0
0
1
2
1
0
1
1
0
1
1
1
1
0
2
0
2
1
0
1
1
2
0
0
2
2
1
1
2
0
2
0
2
2
2
1
2
1
0
2
1
1
2
1
2
0
1
0
1
1
2
1
1
0
2
2
1
2
1
1
0
1
1
2
0
1
1
0
1
2
0
2
2
1
2
0
1
2
0
0
0
2
1
1
1
2
2
0
1
2
1
0
2
0
1
1
0
0
0
1
0
1
0
1
2
2
1
1
1
0
2
1
1
0
1
2
1
2
0
0
1
0
2
1
0
0
1
0
1
1
1
0
0
0
0
2
1
1
1
1
0
2
2
0
1
2
1
1
0
1
0
1
1
1
0
0
1
1
1
1
1
2
2
2
1
1
2
1
1
0
0
1
0
1
1
0
1
0
1
2
1
0
0
0
1
1
2
3
1
1
2
2
0
0
1
1
1
1
1
3
2
2
0
0
0
1
2
2
2
1
1
0
1
1
2
1
0
0
2
1
1
0
0
0
2
1
1
1
0
2
1
1
0
2
2
1
0
0
1
2
0
0
0
0
1
1
2
1
0
0
1
1
0
2
0
2
1
0
0
1
1
2
0
1
2
2
1
0
1
0
0
2
0
1
0
1
1
1
0
0
2
1
1
0
1
2
2
2
1
0
1
1
0
1
0
0
1
1
1
2
1
0
1
0
2
2
2
1
0
1
2
0
1
0
1
2
0
0
1
0
1
0
1
1
2
0
1
0
2
2
1
1
2
1
2
0
1
2
0
2
1
2
1
0
1
0
1
1
0
1
0
2
0
2
1
2
1
1
0
1
1
0
0
1
2
1
2
1
1
0
0
1
1
1
1
0
2
1
1
0
0
2
1
1
1
0
0
1
0
2
1
2
1
1
1
0
1
1
1
0
2
2
1
1
1
0
0
1
1
0
1
1
1
1
2
1
0
2
0
0
1
2
0
0
1
2
0
0
1
0
1
0
1
2
2
0
1
0
2
1
2
0
0
1
1
2
2
2
1
1
0
1
1
1
1
1
1
0
0
0
0
2
0
1
2
0
0
2
0
1
1
1
1
1
0
0
1
2
2
0
0
0
0
1
1
1
1
1
1
1
2
1
2
0
2
1
2
1
0
1
2
0
0
0
0
1
1
2
1
1
1
0
1
1
1
1
0
1
1
0
0
0
0
1
1
1
2
1
1
2
1
0
2
3
2
2
0
0
2
2
0
1
2
2
1
0
1
2
0
1
1
1
0
0
0
2
1
1
1
1
2
2
0
0
1
1
2
2
1
1
1
2
2
0
0
2
2
1
2
2
0
2
1
1
1
0
2
1
0
2
1
2
1
0
1
1
2
0
0
0
0
0
0
0
1
2
1
0
0
2
1
2
2
1
1
0
1
0
0
2
1
0
1
0
1
2
1
1
1
0
1
0
1
1
1
1
2
1
2
0
0
0
0
2
2
2
0
1
0
1
1
1
2
1
0
1
0
0
1
2
0
2
3
0
0
1
0
0
2
0
0
1
0
1
1
2
1
1
1
1
0
2
0
1
1
2
1
2
1
1
0
2
2
0
1
1
0
0
1
2
1
0
1
2
1
1
1
0
0
0
1
1
0
0
1
1
1
1
2
0
1
0
2
1
2
0
1
1
0
2
2
0
1
0
1
1
2
2
0
1
1
1
1
1
0
2
2
0
1
0
0
1
2
0
1
1
2
2
1
1
1
1
1
1
0
1
1
1
0
1
1
0
1
1
2
1
0
2
0
0
1
2
0
0
1
1
1
2
0
2
1
1
1
2
1
1
1
1
2
1
1
1
2
2
1
0
1
1
1
1
1
2
2
2
0
2
1
1
1
5
1
1
2
0
0
1
0
1
1
2
1
2
1
1
1
1
0
2
1
1
2
0
2
2
1
1
2
2
2
1
1
0
0
1
0
0
1
2
2
1
1
1
0
0
1
1
1
1
0
0
1
0
0
1
2
1
0
1
0
1
1
1
2
0
0
1
1
2
0
1
2
0
0
3
0
0
2
2
2
1
1
1
0
0
0
1
1
1
0
1
1
1
0
1
0
1
0
1
2
0
1
0
0
2
1
0
1
1
2
0
2
1
1
2
0
1
0
0
1
0
2
0
0
0
1
1
3
1
5
2
0
1
1
1
0
2
0
1
1
2
0
1
2
1
1
1
0
1
1
2
1
0
0
1
0
0
1
0
1
1
1
1
0
0
1
1
2
1
1
0
2
2
3
1
0
0
2
0
0
0
2
3
1
1
1
1
1
1
1
2
1
1
1
1
0
0
2
0
0
0
1
2
2
1
2
1
0
0
0
0
0
1
1
0
1
2
1
0
2
0
0
1
0
2
0
0
1
2
1
0
2
2
1
0
1
1
0
1
0
0
2
2
2
0
0
1
2
1
2
0
1
1
2
0
0
0
2
2
0
0
2
1
0
1
1
0
0
0
2
0
0
0
1
0
1
1
2
2
1
1
1
2
1
1
2
1
2
2
2
1
0
2
0
1
0
1
0
1
1
1
0
0
1
1
1
0
1
0
1
0
3
1
0
1
1
1
0
1
1
2
2
1
1
0
2
1
0
2
0
1
0
1
2
0
0
2
0
2
1
2
1
1
1
0
0
0
1
0
1
0
0
1
2
1
0
1
0
2
2
2
1
1
2
0
1
0
0
1
1
0
0
3
1
1
1
1
2
1
2
1
0
0
0
2
2
0
1
2
1
0
1
1
0
1
4
3
2
0
1
0
1
0
0
2
1
2
1
1
2
2
2
0
2
2
1
2
1
2
0
1
0
0
1
0
1
1
0
1
1
0
1
1
2
0
1
0
0
0
0
1
1
1
1
0
2
2
1
2
0
1
1
1
1
3
1
2
0
1
0
0
0
0
2
1
0
0
1
0
2
0
0
0
0
0
0
1
2
1
1
1
1
2
1
1
0
1
1
0
0
2
2
1
2
1
1
2
0
1
1
1
2
0
2
2
0
1
0
2
2
0
0
1
1
3
0
0
2
0
0
1
0
2
1
2
1
0
1
1
2
1
2
0
0
1
0
1
0
1
0
1
1
2
1
3
1
2
1
0
0
1
0
1
0
1
2
0
2
1
2
1
2
0
1
1
0
0
2
0
1
0
0
2
1
0
0
0
0
0
0
0
1
0
1
0
2
1
2
1
1
0
1
1
3
0
2
2
1
1
0
1
0
0
0
1
0
0
0
2
1
0
1
0
2
1
0
1
1
0
1
2
1
0
2
1
1
2
1
1
0
2
1
2
1
1
1
0
0
2
3
2
1
1
0
1
1
2
1
2
2
1
2
2
0
1
1
1
2
0
1
0
0
1
0
0
2
1
1
0
0
1
0
1
2
0
1
0
2
0
0
2
2
0
1
2
2
2
0
0
0
0
1
2
1
1
2
0
0
1
1
1
0
2
0
1
1
1
0
1
1
0
0
1
1
2
1
2
1
0
1
2
1
0
1
3
1
1
2
2
1
1
0
2
0
2
0
0
1
3
0
0
0
2
1
0
1
1
2
0
0
0
1
0
2
2
1
0
1
2
1
0
1
0
0
0
2
2
1
0
0
1
1
1
2
2
2
2
1
2
0
1
1
1
2
2
0
1
0
1
1
2
0
1
1
1
3
0
0
0
0
2
1
0
0
2
2
0
1
1
1
0
0
1
2
1
2
1
1
0
1
0
2
0
2
2
1
2
2
0
1
1
1
2
1
2
1
0
0
1
1
0
1
1
2
1
2
0
0
2
1
1
1
2
0
0
1
2
1
1
0
0
0
1
2
0
2
0
1
1
2
0
0
2
1
0
2
2
1
1
0
1
1
2
1
0
1
1
2
1
1
2
1
1
1
2
0
0
2
0
0
0
1
2
1
0
1
1
1
1
0
1
0
0
1
0
2
1
2
1
1
1
2
1
1
1
0
1
0
2
1
1
2
1
2
2
1
0
0
0
1
1
0
1
1
1
0
1
1
3
1
2
0
1
1
1
0
2
0
1
0
1
0
2
0
0
1
2
1
2
2
2
1
2
1
2
1
2
0
1
2
0
0
1
0
2
0
2
0
1
1
0
0
1
2
0
1
2
1
1
0
0
1
0
1
1
0
2
2
0
1
1
1
1
2
2
1
0
2
0
1
2
0
2
0
1
0
0
1
0
0
1
1
1
0
1
2
1
2
1
1
2
0
1
0
1
1
1
0
0
2
1
2
2
0
2
0
0
1
0
0
0
1
0
1
0
0
1
1
0
1
0
2
2
0
0
0
1
1
1
2
0
1
1
0
1
1
2
1
1
1
1
1
1
1
1
0
0
1
1
0
0
2
1
1
0
1
2
1
2
0
0
2
1
0
2
1
1
1
0
1
1
0
0
1
1
1
1
0
0
0
0
0
2
1
2
0
2
1
0
1
1
1
2
2
2
0
2
0
0
1
1
0
2
0
2
2
2
1
0
1
2
1
1
1
0
0
1
0
1
2
0
1
0
0
2
0
1
1
1
1
0
1
0
2
1
0
2
2
2
0
1
1
0
1
0
1
0
0
0
1
1
0
1
0
3
2
1
0
0
2
0
1
2
0
2
1
1
1
0
2
1
2
1
0
0
0
1
0
1
2
0
2
1
1
0
1
1
2
1
1
0
0
0
1
1
1
0
2
2
1
2
1
0
1
1
0
2
2
0
1
0
2
0
0
0
0
1
1
1
1
1
1
1
2
0
1
1
1
1
2
0
0
1
0
2
0
0
1
1
0
0
1
1
0
1
0
1
1
1
2
2
0
0
0
0
0
0
0
0
2
0
2
2
0
1
1
0
0
1
1
1
1
0
1
1
0
0
0
1
2
1
2
1
1
2
1
0
0
1
0
1
1
2
1
2
0
1
1
0
0
1
1
1
1
2
1
1
0
1
0
1
0
0
0
2
1
0
0
1
2
1
1
1
1
2
0
1
2
1
1
2
1
2
0
1
1
1
0
1
2
2
2
1
0
2
1
0
1
1
1
0
1
1
1
1
2
1
1
0
1
2
1
1
2
1
1
2
2
2
1
1
2
1
1
0
1
2
0
1
6
4
0
1
2
1
1
0
1
0
2
1
0
1
0
1
0
0
2
1
1
2
0
2
2
2
0
1
0
1
0
1
0
1
1
0
0
2
0
1
1
2
0
0
1
1
1
1
0
1
1
0
2
0
2
2
1
1
1
1
1
2
1
1
1
1
2
0
3
1
0
0
1
2
2
0
1
1
1
0
0
2
1
2
0
1
1
0
1
1
1
0
2
0
1
0
2
2
1
1
1
0
1
1
0
0
2
1
1
1
0
0
1
0
1
0
0
2
0
0
0
1
1
1
1
0
2
0
1
2
1
1
1
2
1
2
2
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
1
0
2
1
0
2
0
2
1
1
1
1
1
1
2
1
2
1
1
0
1
1
0
0
2
1
2
2
0
2
4
1
0
2
0
0
1
2
1
1
1
1
1
1
0
1
1
2
1
2
2
0
2
2
0
0
1
2
2
1
1
1
0
1
1
2
0
0
0
0
2
1
1
1
1
0
2
1
0
0
1
0
1
0
0
0
1
1
2
2
1
2
0
1
1
2
2
0
1
1
1
0
1
1
1
0
1
0
0
1
1
0
1
0
1
0
2
2
2
1
0
0
1
0
1
1
1
1
0
0
1
1
2
1
0
0
1
1
2
0
1
0
2
1
2
2
0
1
1
0
0
2
1
3
0
1
0
2
0
1
0
1
2
1
2
0
0
2
1
2
0
1
0
1
1
3
0
1
0
1
1
2
2
0
1
1
1
2
2
1
2
0
2
1
0
1
2
0
3
1
1
1
1
1
1
1
0
1
0
0
2
1
1
0
2
2
1
2
1
2
0
1
1
0
0
1
0
1
1
0
2
2
0
1
1
1
1
0
0
1
2
2
0
1
1
1
1
1
1
0
0
2
1
1
1
1
2
0
0
2
1
2
0
1
1
2
0
1
0
1
1
2
1
2
1
0
1
1
1
1
1
0
3
1
2
3
0
0
1
1
0
1
1
0
1
0
0
1
1
0
2
2
1
1
1
1
2
1
0
0
0
1
0
1
1
1
1
0
0
0
2
2
2
0
0
0
1
0
2
2
0
2
2
1
1
1
1
1
1
2
1
0
0
0
1
2
0
0
1
2
0
2
2
0
2
1
0
2
1
1
1
0
1
2
0
1
1
2
0
2
1
1
1
1
0
0
2
1
2
0
0
1
2
0
0
1
2
2
1
1
1
2
0
0
2
1
2
0
1
2
0
0
1
0
0
2
1
3
1
1
2
1
1
2
2
1
2
1
0
1
0
0
0
1
1
1
1
0
2
1
1
1
0
0
0
1
1
2
1
1
1
0
2
1
1
1
1
1
0
2
0
1
1
1
0
1
1
0
0
1
2
0
1
1
3
1
1
0
1
0
0
1
0
1
0
2
2
1
3
1
0
1
0
1
1
0
1
1
1
1
0
1
1
1
0
2
1
1
2
1
1
0
0
0
1
1
1
3
0
1
1
1
1
0
0
2
0
1
0
2
0
1
1
1
1
2
2
1
2
1
1
0
1
1
0
0
1
1
2
0
2
1
1
0
0
2
1
1
0
0
0
0
1
1
2
1
1
1
0
1
2
1
4
2
0
2
1
0
2
0
1
0
0
0
1
1
1
0
0
1
1
1
1
1
0
0
1
0
0
2
1
1
1
0
0
1
1
0
0
2
2
1
1
1
1
0
1
0
1
1
2
1
1
0
1
0
0
0
1
0
2
1
0
1
1
0
0
1
2
1
1
0
1
0
1
0
0
1
0
1
0
2
1
1
1
0
1
1
1
1
0
1
2
1
0
0
2
5
2
0
1
1
2
1
2
0
1
0
2
1
1
0
1
1
1
1
1
1
0
1
2
1
1
1
0
0
0
0
1
1
0
1
1
2
0
0
2
0
2
1
1
0
4
0
1
1
1
2
0
0
1
1
0
0
1
1
1
1
0
2
1
1
1
1
1
1
0
2
0
1
2
1
2
2
1
2
1
1
1
1
0
1
1
0
1
1
1
2
1
0
0
0
1
1
1
1
1
0
1
0
1
0
2
1
2
0
1
1
0
1
0
0
0
0
0
1
0
0
1
0
2
2
0
1
2
2
0
0
1
1
0
1
2
0
1
2
0
2
0
0
1
1
1
0
2
1
1
2
1
1
1
2
2
0
1
1
0
2
1
2
1
0
1
1
1
1
0
0
0
0
0
1
0
1
0
1
0
2
0
0
0
0
1
0
0
0
1
0
3
1
0
1
1
2
1
0
2
0
2
1
1
0
0
1
2
1
0
2
1
1
1
1
1
0
0
1
0
1
1
1
1
1
1
2
1
1
1
2
1
2
1
0
0
1
1
1
2
2
0
1
1
2
0
2
1
1
0
1
1
0
2
2
0
2
2
2
1
1
0
0
1
0
1
0
0
0
1
3
2
2
0
1
1
0
2
2
0
2
1
1
1
0
1
2
1
0
0
1
0
0
0
1
0
1
0
1
1
1
1
0
0
0
0
0
1
0
0
2
0
1
1
0
1
0
1
1
1
2
2
1
1
2
1
0
0
1
1
0
1
1
0
2
0
1
2
0
1
0
2
0
1
1
0
2
1
1
1
0
1
0
0
1
1
2
1
1
2
0
2
1
1
1
2
0
0
1
0
2
1
0
1
1
1
1
0
1
1
0
2
1
0
1
1
1
2
0
2
1
2
0
0
2
0
0
1
1
1
1
2
0
1
1
2
0
0
0
0
0
2
2
1
1
2
1
0
1
0
1
0
2
1
1
0
0
0
1
1
3
1
1
0
1
1
2
1
0
2
3
0
3
4
1
1
0
0
0
2
1
1
1
0
1
2
1
1
2
1
3
0
0
0
1
2
2
0
2
1
0
0
2
0
1
0
1
0
1
1
1
1
2
1
1
0
0
0
1
1
1
0
0
1
2
2
1
1
2
1
0
2
2
1
1
1
0
0
1
1
1
2
0
0
2
2
1
0
0
2
2
1
1
0
0
1
0
1
0
1
1
1
0
1
1
1
4
1
1
1
1
0
0
4
1
2
1
1
1
0
1
0
1
2
1
2
1
1
0
2
0
0
1
0
1
0
1
0
2
0
0
3
1
3
1
0
0
2
0
0
1
0
0
2
1
1
1
1
0
0
2
1
1
1
2
0
1
0
0
0
2
0
0
1
2
2
2
1
2
0
0
1
2
1
0
1
1
0
1
1
0
0
1
0
0
0
2
1
0
2
1
1
2
1
0
2
0
2
3
2
1
2
0
0
0
1
2
2
1
1
0
1
1
0
0
0
1
2
2
0
1
1
0
1
1
0
1
2
1
1
0
0
2
1
0
1
0
0
1
0
1
1
1
2
2
2
0
1
1
2
1
0
0
2
0
1
0
2
1
2
1
1
0
2
0
0
1
1
2
0
1
0
1
1
0
1
0
1
0
1
1
1
0
1
1
0
1
1
0
2
0
1
0
1
1
0
0
0
2
1
2
1
1
1
0
1
2
1
0
0
1
2
1
1
2
0
2
0
0
1
1
0
1
0
1
1
1
2
1
0
0
1
1
0
0
1
2
2
1
1
0
1
2
1
0
1
2
1
3
1
2
0
0
1
0
2
2
2
2
1
1
3
1
0
2
0
0
1
2
1
1
1
2
1
0
1
2
2
0
2
0
0
0
1
0
1
0
1
0
1
0
1
2
1
2
1
1
1
0
0
1
2
0
0
1
1
2
1
0
0
1
2
1
0
1
1
1
0
1
0
2
1
2
4
2
1
0
0
0
0
1
1
6
2
2
2
0
1
2
0
1
1
2
0
1
1
1
1
1
1
1
0
2
2
2
1
2
1
2
0
2
0
0
1
1
2
1
1
1
2
1
0
1
2
2
1
1
1
1
1
1
0
1
1
2
1
0
0
1
1
2
1
2
2
1
0
1
0
0
1
0
2
2
1
2
0
1
1
1
1
1
0
0
0
0
1
3
0
0
0
0
0
1
1
1
1
1
0
0
0
0
1
1
1
0
2
0
0
1
2
2
0
1
1
2
1
1
1
0
0
0
0
0
1
2
1
1
1
1
1
1
0
1
0
1
4
1
1
1
1
0
1
2
2
2
1
1
2
0
1
1
2
0
0
0
2
0
1
0
2
2
1
0
2
0
0
0
0
0
0
2
1
1
1
1
1
1
1
0
1
0
1
1
1
1
1
1
1
0
1
1
1
0
2
1
1
2
1
1
1
1
0
2
1
0
1
0
0
1
0
2
2
1
0
2
1
0
1
2
2
1
2
1
2
2
2
3
1
1
0
0
1
0
0
0
1
0
0
0
1
0
1
1
1
2
1
0
0
1
1
1
1
2
1
1
0
0
1
1
1
1
1
2
1
0
1
1
0
1
1
1
1
1
0
0
1
2
2
1
1
2
0
1
2
1
0
2
1
0
1
0
2
0
1
2
2
1
2
1
0
0
2
1
1
1
0
0
1
2
2
0
0
1
1
1
2
1
1
0
1
0
1
1
2
1
1
1
0
2
1
2
0
1
4
1
1
1
0
1
1
0
1
0
0
0
0
1
2
1
2
0
1
1
1
0
1
2
0
2
1
0
0
0
1
1
2
2
2
0
1
0
0
1
2
1
2
1
2
0
1
1
1
1
1
0
1
1
0
0
1
0
1
1
1
0
1
0
0
2
1
2
0
0
1
2
1
2
1
1
1
1
1
0
1
1
2
0
1
1
1
1
1
2
0
0
1
0
1
1
3
2
0
1
2
1
1
1
1
2
0
1
1
0
1
1
5
0
1
0
0
1
1
1
0
0
0
1
2
1
1
1
3
0
0
1
1
2
2
0
1
0
0
0
1
1
1
0
2
1
1
2
0
0
1
0
0
2
0
1
1
1
2
0
0
1
1
1
0
1
2
1
1
1
1
1
1
0
2
1
2
3
0
1
2
1
0
0
1
2
1
0
1
1
0
0
2
2
2
1
1
1
1
0
1
1
2
0
1
0
1
1
0
1
2
1
0
0
1
2
1
1
2
1
1
0
1
1
0
1
1
2
1
1
0
1
0
0
0
1
0
1
1
0
1
1
1
0
0
1
1
2
1
1
0
1
1
0
1
1
2
1
1
2
2
1
2
0
3
1
2
3
1
2
0
1
0
1
1
0
1
2
1
1
2
1
0
1
1
1
1
0
2
2
2
2
0
0
0
2
0
2
1
1
1
1
2
1
0
1
1
2
2
0
1
0
0
0
0
0
2
1
2
1
0
0
0
0
0
2
1
0
0
1
1
0
1
0
0
0
0
0
0
1
1
2
1
2
1
1
0
1
2
0
0
2
0
0
1
1
1
7
0
1
2
1
0
1
2
0
1
1
1
2
0
1
2
1
1
1
1
2
2
2
1
2
0
0
0
1
0
1
1
1
2
1
0
0
0
2
0
1
0
1
1
2
1
1
0
1
1
0
0
2
0
1
0
0
1
0
1
1
2
0
1
0
2
0
1
1
1
2
1
0
2
1
1
0
2
0
1
0
1
0
2
1
2
1
1
0
1
1
1
1
2
0
0
2
2
1
1
0
1
1
0
1
2
1
0
1
1
2
1
0
0
1
0
2
1
0
2
2
0
1
1
1
1
2
1
0
2
1
0
1
1
1
2
0
1
1
2
0
1
1
1
2
1
2
1
0
2
1
2
1
1
2
0
1
2
2
1
0
1
2
1
0
1
2
0
2
1
0
0
1
0
1
1
2
1
2
0
0
2
0
1
2
1
0
1
0
3
2
0
1
1
1
1
0
1
0
0
0
1
0
0
0
1
0
1
0
2
0
0
1
1
1
2
1
2
1
0
2
3
0
1
0
0
0
0
2
2
0
2
1
2
2
0
0
1
2
2
2
2
2
1
2
2
1
0
1
1
0
1
0
0
1
0
0
2
0
0
0
0
0
0
1
0
1
2
1
0
0
1
0
0
0
0
0
1
1
1
2
2
2
0
2
1
1
0
2
1
2
2
0
0
2
0
0
0
0
1
1
0
1
1
2
1
1
0
0
1
2
0
2
0
0
1
1
0
1
2
1
0
2
2
0
0
1
0
2
0
1
0
0
1
1
1
0
1
1
2
0
1
2
0
1
1
1
1
1
0
1
0
1
1
1
0
1
2
2
0
1
1
2
0
1
1
2
1
1
1
1
1
0
0
1
2
2
1
1
1
0
2
1
1
0
1
0
0
1
0
1
1
2
0
1
1
0
1
1
1
1
2
0
0
2
0
1
0
0
0
1
1
0
2
0
0
1
1
1
2
2
1
1
0
1
0
0
1
2
1
1
1
1
1
1
2
2
0
0
0
2
0
1
0
2
0
0
1
1
0
1
1
0
0
0
2
2
1
1
1
1
1
1
0
2
0
2
0
1
2
1
1
2
1
2
1
1
1
3
0
0
2
0
0
1
1
0
0
1
1
1
0
2
1
1
1
1
2
1
2
0
2
2
1
0
1
0
0
0
0
1
0
1
1
0
1
2
1
2
2
1
2
1
2
1
2
1
1
1
0
1
1
0
0
2
1
1
0
1
0
2
1
2
1
1
1
1
1
0
1
2
1
1
1
2
1
1
0
0
2
0
2
0
1
0
1
2
1
1
0
0
1
2
0
0
0
0
1
2
1
1
2
1
0
1
1
1
1
0
1
2
0
0
0
2
2
1
1
2
2
1
0
1
0
1
2
2
0
2
0
1
1
0
0
0
0
1
1
2
1
0
1
1
0
1
1
2
1
0
1
1
0
1
1
2
0
1
1
2
1
1
0
2
1
1
1
1
0
2
1
0
0
2
1
1
1
0
1
1
0
1
1
2
1
2
2
1
1
2
2
1
1
1
1
0
1
1
2
2
0
1
0
1
1
1
0
1
1
0
0
1
1
1
1
1
1
0
2
1
1
0
0
0
0
1
2
0
1
0
0
0
0
1
2
2
1
1
0
1
1
2
1
1
1
2
0
1
1
0
0
0
0
0
0
1
1
1
0
2
1
1
2
1
1
2
1
0
1
2
0
1
2
0
0
0
1
1
1
1
0
0
0
1
1
0
0
1
0
2
0
1
1
0
1
1
0
2
1
0
0
1
1
0
1
0
1
1
0
1
2
1
1
2
1
1
1
1
0
0
0
0
0
1
1
0
2
2
1
2
1
1
0
1
1
0
2
2
2
1
0
2
2
1
1
1
0
0
0
1
3
0
2
2
2
0
0
1
0
1
1
1
0
1
2
3
1
1
1
1
0
1
6
0
0
2
2
0
1
2
1
0
0
2
1
0
0
1
1
1
1
1
0
1
1
1
1
0
0
1
1
0
1
2
1
0
1
1
1
2
0
1
1
1
2
1
2
0
1
0
0
2
1
1
1
1
2
0
0
1
1
2
1
1
1
1
1
1
1
0
0
2
0
0
0
1
2
0
1
2
2
1
1
1
1
2
0
0
0
1
1
0
1
1
1
2
4
2
0
1
0
2
1
3
1
0
1
3
0
1
1
1
1
1
0
2
1
1
1
1
1
0
0
1
0
1
1
0
0
1
0
0
1
1
1
0
2
1
2
0
0
1
0
1
1
2
1
1
1
1
0
1
1
1
0
0
0
0
0
1
0
0
3
3
2
1
0
1
0
0
0
0
1
2
1
0
2
0
1
2
1
0
0
1
1
1
1
1
0
0
0
0
0
1
0
1
0
2
1
2
0
1
0
0
0
1
0
2
1
2
0
1
0
2
1
0
2
2
1
0
1
2
1
2
2
1
1
0
1
1
1
1
0
1
2
0
1
1
0
1
0
2
2
3
0
1
2
0
0
1
2
2
1
1
2
1
0
1
2
1
2
1
1
1
1
2
0
1
2
0
0
1
1
1
0
0
0
1
2
1
1
0
0
1
1
2
0
1
2
0
1
1
0
1
1
0
1
4
1
0
1
1
2
1
0
2
1
1
1
2
0
1
1
2
2
2
1
2
1
1
1
1
0
1
1
0
1
0
2
1
0
2
0
1
1
0
1
1
0
0
0
0
1
2
1
0
0
2
1
1
0
2
0
0
0
1
0
1
2
1
0
0
1
1
1
0
3
1
0
0
1
0
1
1
0
1
1
0
2
2
1
0
2
0
0
0
1
1
0
0
0
1
2
1
0
0
0
0
2
1
2
1
0
0
1
1
2
0
1
0
1
2
2
0
1
1
2
0
0
0
0
0
1
1
1
1
0
1
0
0
0
1
0
2
1
2
3
1
1
1
0
0
4
1
0
0
0
0
0
0
1
1
0
1
1
1
1
1
0
1
0
1
2
2
1
2
1
0
1
0
0
0
0
2
1
1
2
0
0
0
2
0
0
0
2
3
1
2
0
1
0
0
0
2
2
1
1
1
1
2
1
0
1
1
1
1
1
0
0
2
1
2
1
1
1
0
0
0
2
1
1
0
1
0
2
1
1
2
1
0
1
1
1
0
1
1
1
1
1
1
1
0
1
2
1
0
1
2
2
0
2
1
1
1
0
0
0
1
1
2
1
0
1
1
0
0
2
1
2
1
0
2
1
0
0
0
2
0
1
2
1
1
2
1
1
3
0
0
1
3
0
2
1
0
1
0
1
1
1
1
1
0
3
1
2
1
0
2
1
0
1
1
1
1
1
0
1
1
0
0
0
1
1
2
1
1
1
3
0
0
1
2
1
0
1
0
0
2
0
0
0
0
0
1
1
1
1
1
1
2
2
0
1
0
1
0
1
1
1
1
1
1
0
1
0
2
1
1
2
2
1
0
1
1
2
0
0
1
0
0
0
2
0
1
1
0
1
1
1
2
2
0
1
3
0
1
1
1
0
1
2
2
1
1
0
1
1
2
2
1
0
0
2
1
0
0
1
0
1
1
0
0
1
1
1
2
1
2
1
1
2
1
1
2
1
0
2
1
0
1
0
1
0
1
2
1
1
1
0
1
1
1
0
1
1
2
0
1
0
0
0
0
1
1
1
2
1
0
2
0
1
2
1
0
1
1
0
1
1
0
1
1
2
1
0
1
2
2
0
0
0
1
2
1
1
2
2
1
1
0
1
1
0
3
1
1
2
2
2
1
1
2
2
0
1
0
0
1
1
0
1
0
2
0
0
2
0
2
1
1
0
1
0
0
1
1
1
2
0
2
0
1
1
1
1
0
1
1
2
1
0
1
2
1
1
2
1
0
1
0
2
0
0
1
0
0
1
1
1
0
3
1
1
1
1
1
2
1
1
1
2
0
1
2
2
2
2
2
1
2
1
0
3
2
0
1
2
1
1
1
1
2
0
1
1
2
0
1
1
2
0
1
2
1
1
1
0
0
2
1
1
0
1
1
1
1
1
2
0
1
1
2
2
2
3
1
1
0
1
1
2
1
2
2
3
3
1
0
1
0
0
1
1
1
1
1
0
1
0
1
1
2
1
2
0
1
1
1
0
0
2
1
2
1
0
1
0
1
1
1
0
0
1
0
1
1
1
1
0
0
2
0
0
1
0
1
2
1
2
2
1
2
0
1
1
1
0
1
1
0
1
1
1
1
0
1
1
1
0
2
1
1
1
1
1
0
1
1
0
0
1
2
0
2
1
0
1
2
1
2
1
0
1
0
1
2
1
1
1
0
1
1
1
1
0
1
1
1
2
1
1
1
0
0
1
1
0
2
0
0
2
0
0
1
0
2
1
0
1
1
0
0
1
2
0
2
0
2
0
0
0
1
2
1
1
2
2
1
1
1
0
1
1
2
0
0
1
0
1
2
0
1
0
1
1
1
1
1
0
1
1
1
2
1
0
1
1
2
0
1
0
1
0
2
0
2
1
2
2
0
0
1
0
0
2
1
1
0
1
2
0
1
0
1
0
0
0
1
2
0
2
1
1
0
0
0
2
1
2
1
1
2
2
2
2
1
0
1
0
1
1
0
1
0
2
1
0
2
0
2
1
0
1
2
1
2
2
2
0
2
1
0
1
1
2
1
1
1
1
0
0
0
0
2
1
1
1
1
0
1
1
2
1
1
0
2
1
1
1
1
1
1
3
1
0
1
1
2
2
1
1
1
1
0
1
1
1
2
1
1
2
1
2
1
1
0
0
0
1
2
1
0
2
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
1
0
0
2
1
0
1
0
1
1
1
2
1
1
1
1
1
1
0
1
2
0
1
2
0
2
1
0
0
1
1
0
1
1
2
1
2
1
1
0
2
1
2
1
1
1
2
1
0
1
1
2
1
1
0
0
1
2
1
0
1
1
2
0
1
1
1
2
1
0
0
0
1
0
2
0
0
2
1
1
1
0
1
1
0
2
1
1
2
1
0
0
0
2
0
0
0
6
2
0
1
1
1
1
2
1
2
2
0
1
0
1
1
0
1
0
1
1
1
0
1
2
1
2
6
0
1
0
1
1
0
1
0
0
1
1
0
1
2
0
1
1
2
1
2
0
2
0
0
0
0
1
0
1
0
1
1
2
1
1
1
1
0
0
2
2
1
1
2
0
2
0
1
0
1
1
0
1
2
1
0
0
1
0
1
2
1
1
1
2
0
0
1
2
0
1
0
0
2
2
1
0
1
1
1
2
0
3
1
1
0
0
1
1
0
1
1
2
2
1
0
1
3
2
0
2
1
1
1
0
1
0
1
0
2
0
2
1
0
0
0
1
1
1
2
0
4
0
2
1
2
1
1
1
1
1
2
2
1
0
2
1
2
1
0
0
2
1
2
2
2
0
2
1
1
1
2
1
2
2
2
0
0
1
2
2
0
1
1
1
3
1
0
0
1
0
1
2
0
1
2
2
0
1
1
2
1
1
1
1
1
0
0
0
0
1
1
0
1
2
2
1
0
2
2
2
1
1
2
1
0
0
0
0
0
1
1
0
0
1
0
0
1
1
2
0
1
1
1
1
2
1
1
2
0
1
1
2
1
0
2
2
2
2
1
1
1
0
2
1
0
1
1
0
1
1
1
1
1
1
1
0
1
2
0
0
1
2
2
0
1
2
1
0
0
1
0
1
1
1
1
1
0
2
0
1
1
2
1
1
1
1
1
1
1
0
2
0
1
1
2
1
0
0
1
1
0
0
1
2
1
0
1
2
1
0
1
2
1
1
0
2
2
1
1
2
0
0
1
0
1
2
1
1
0
0
1
0
0
0
0
1
1
0
2
1
2
3
1
2
1
2
1
0
1
2
1
1
1
0
2
1
2
1
1
1
1
0
1
2
0
0
1
1
0
0
0
1
1
2
1
1
0
1
0
0
2
1
1
0
0
1
1
0
1
2
0
1
0
1
1
1
0
0
0
0
0
1
0
1
1
0
2
2
1
1
0
0
1
0
0
1
2
0
0
1
2
0
0
0
1
1
1
0
0
1
0
2
0
1
2
0
1
2
1
1
1
0
0
1
1
1
2
0
1
0
2
0
1
1
1
1
0
3
1
2
0
2
1
2
0
2
0
1
1
0
1
0
1
1
2
1
1
2
1
0
3
0
1
0
1
1
0
1
2
1
0
2
2
0
1
1
1
2
1
0
0
1
0
1
1
1
0
1
1
0
2
1
1
0
1
1
0
0
0
0
5
2
1
0
1
2
1
1
0
1
0
0
1
1
1
2
0
2
0
1
2
1
1
1
0
0
0
1
0
1
1
0
1
0
0
2
1
2
0
1
1
1
1
1
0
1
2
1
1
2
2
0
1
1
0
1
2
1
1
0
1
0
0
1
0
0
1
0
2
0
1
1
1
1
0
1
1
0
1
2
2
0
1
1
1
2
0
1
2
1
0
0
1
0
1
0
0
0
2
1
1
5
0
0
0
1
1
1
0
0
1
0
1
1
1
1
1
1
0
1
2
1
1
0
2
1
0
2
0
0
1
1
1
0
1
2
1
3
0
2
0
0
3
0
1
1
1
0
0
0
1
1
0
2
0
1
1
1
0
0
0
1
0
1
0
2
2
0
0
0
2
2
0
2
1
1
2
1
1
0
0
0
0
1
2
2
0
3
1
1
1
1
0
1
1
0
1
0
1
2
0
0
2
0
0
0
2
0
2
1
2
3
1
3
1
2
1
0
2
1
0
0
2
0
1
0
0
0
0
1
0
2
0
0
1
2
1
1
1
2
1
1
0
2
0
1
0
2
1
2
1
0
1
0
1
1
0
1
1
0
2
0
1
1
1
1
1
0
2
1
1
0
0
0
2
2
1
2
0
1
1
0
1
1
0
0
1
2
2
1
0
2
2
2
3
0
2
0
1
2
1
2
1
0
0
0
2
1
1
1
2
1
0
1
0
2
1
3
1
0
0
1
0
2
0
1
0
1
2
0
2
1
1
1
2
2
0
2
0
1
0
1
1
1
1
2
0
1
0
1
2
1
1
0
2
0
2
2
1
0
2
1
2
1
2
2
2
2
2
2
2
1
2
1
2
2
0
2
1
1
1
0
1
2
2
0
1
1
0
1
1
2
3
1
1
2
1
0
1
0
0
1
2
2
1
1
2
1
1
1
1
0
0
0
0
0
1
0
2
0
2
0
0
1
1
0
0
2
1
0
0
2
0
1
1
2
1
0
2
2
1
2
0
1
1
1
1
1
1
0
0
1
1
1
1
0
1
2
0
2
1
1
1
1
1
2
2
0
2
1
1
1
2
0
0
1
0
2
2
2
1
2
1
1
1
0
0
1
2
1
2
0
1
2
2
0
1
0
0
0
0
2
0
1
2
0
1
1
2
1
1
0
1
1
1
1
1
0
2
1
0
1
1
0
0
1
1
1
1
1
1
0
2
0
0
1
0
0
0
0
0
0
1
0
1
0
2
1
3
0
1
2
2
2
1
2
0
1
2
3
0
1
0
0
1
0
1
1
0
0
0
1
2
1
0
0
0
0
1
1
1
2
2
0
1
1
0
1
0
1
0
1
1
1
0
0
0
1
1
0
0
2
2
1
1
1
1
2
2
2
2
0
0
0
1
2
2
0
1
1
0
1
1
1
0
2
2
1
1
2
0
0
1
0
1
1
1
1
1
2
1
1
0
1
2
2
0
0
2
0
2
1
0
1
1
1
2
1
1
1
3
0
1
2
0
0
1
0
0
1
2
3
1
0
1
1
2
2
1
1
0
1
2
0
0
2
0
0
1
0
2
1
0
2
1
0
1
0
1
1
1
1
2
1
0
0
0
1
0
1
0
0
1
1
1
0
1
0
2
2
1
2
1
0
2
2
2
2
1
3
0
2
1
1
1
2
4
0
1
1
1
1
1
1
1
0
0
2
1
1
0
2
0
1
2
1
1
1
2
0
2
0
1
1
1
1
2
1
0
1
2
0
0
1
1
1
1
2
0
0
0
1
3
1
1
2
0
0
1
1
2
0
1
1
2
1
2
0
1
0
1
1
2
1
2
0
1
1
2
2
1
2
2
2
1
1
1
1
1
0
2
2
0
2
2
0
0
0
0
1
0
1
2
2
1
1
2
0
0
0
0
1
2
1
0
0
2
1
1
0
0
0
0
0
0
0
0
0
1
1
1
2
1
2
1
1
1
1
0
1
1
1
1
1
1
0
0
2
0
0
1
0
0
2
1
1
2
1
2
2
2
1
0
1
1
0
2
1
0
0
1
1
1
1
2
0
0
0
2
2
2
1
1
0
1
0
2
2
0
0
1
0
1
1
0
1
0
1
1
2
1
1
1
0
0
0
2
1
2
1
0
0
1
1
1
2
1
1
0
1
1
1
2
2
0
1
1
0
1
2
1
1
0
2
0
1
0
0
1
1
0
1
1
0
0
2
2
1
0
0
0
2
2
1
1
2
1
0
1
0
0
1
2
0
0
2
1
1
2
0
1
0
0
1
1
1
2
1
0
0
1
2
0
0
1
1
2
2
1
1
0
0
1
0
2
0
1
0
0
1
0
2
2
0
1
2
1
1
1
1
1
1
2
2
0
1
0
0
0
2
0
1
0
0
1
0
1
0
2
1
0
1
1
1
2
1
0
1
1
2
1
1
2
1
0
1
0
0
1
1
1
0
2
0
1
2
1
1
0
2
0
1
1
1
1
1
1
1
0
0
1
1
1
1
1
3
1
1
2
0
2
1
1
1
1
2
1
2
0
0
0
2
1
1
0
1
1
1
1
1
1
2
1
1
1
4
0
0
0
2
1
1
2
1
2
0
1
1
1
1
1
1
2
1
2
1
0
0
0
0
1
1
1
0
3
1
1
0
2
0
1
0
0
0
1
1
0
0
1
2
1
2
0
1
1
1
1
0
2
0
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
0
2
1
1
1
2
2
1
1
2
1
1
1
1
1
1
0
1
1
0
1
2
1
1
0
0
1
2
3
2
1
0
1
1
0
1
2
1
0
1
0
1
0
1
1
1
0
0
1
1
2
0
1
2
1
1
1
0
0
1
1
0
1
2
2
2
0
2
1
1
1
1
1
1
0
0
0
0
0
1
1
2
0
0
2
0
2
0
0
2
1
1
2
0
1
0
1
2
0
2
1
1
1
1
0
2
2
1
0
1
0
0
0
1
0
2
2
0
0
1
2
2
0
1
1
1
2
2
0
1
1
2
1
1
1
1
1
2
1
1
0
1
1
1
1
0
0
2
1
1
2
1
0
1
1
1
0
0
1
1
1
0
2
0
1
1
1
1
1
1
0
1
0
1
2
2
1
2
1
2
0
0
2
1
0
4
0
0
2
1
2
1
2
1
1
1
2
1
0
1
2
1
0
0
0
0
1
0
1
1
0
1
2
2
0
0
2
0
1
0
1
1
0
1
2
1
0
2
3
1
1
2
0
1
1
1
0
1
1
1
0
1
0
1
1
1
0
0
1
1
0
1
0
0
1
2
1
2
2
1
2
0
0
1
2
2
1
2
0
1
1
2
1
2
2
1
0
0
1
1
3
1
0
0
0
2
1
1
2
0
1
1
2
0
2
1
0
0
1
0
1
0
0
1
2
0
1
0
1
1
1
0
0
0
1
1
2
1
2
1
2
2
4
1
1
0
1
0
2
2
1
1
1
2
1
1
1
1
1
0
0
0
1
1
0
0
2
1
2
2
1
1
1
1
1
0
2
2
1
1
2
0
1
0
2
1
0
0
1
1
2
1
0
2
0
1
0
0
0
1
0
1
1
1
1
1
0
1
0
1
0
0
0
1
2
1
1
0
0
2
0
1
1
0
1
0
2
0
1
2
1
1
0
1
2
1
2
1
1
1
2
2
1
1
1
0
2
1
1
1
0
0
0
1
0
2
1
0
0
0
1
0
0
1
0
0
2
1
2
1
1
0
0
2
4
0
1
0
1
1
1
0
2
0
0
1
1
1
0
1
2
1
1
0
1
1
3
1
0
0
1
0
1
2
0
1
2
1
1
1
1
1
2
2
1
1
1
1
1
0
1
0
1
2
1
0
1
0
0
0
2
1
1
1
2
1
0
1
1
1
2
0
1
0
1
1
1
1
2
4
0
3
2
0
0
1
2
1
0
1
1
1
2
2
2
1
2
1
1
2
1
2
1
2
0
1
0
0
1
1
0
0
0
0
1
1
2
0
1
0
1
1
0
0
0
1
1
1
0
1
2
1
0
0
1
6
2
0
2
0
1
1
0
1
0
1
0
0
2
1
0
1
0
1
1
0
1
1
0
1
1
2
1
1
1
1
2
0
1
1
1
2
2
2
1
0
0
0
2
0
2
1
2
1
0
0
2
0
0
1
0
1
1
3
1
0
0
1
0
2
1
1
0
2
0
0
2
2
0
2
2
1
1
0
1
2
1
1
1
1
0
2
1
1
2
1
2
2
1
1
1
2
1
0
1
1
1
0
1
1
2
1
0
1
1
0
1
0
2
0
0
1
1
2
2
1
1
0
1
1
1
1
1
2
0
0
2
0
0
0
0
0
1
1
1
1
0
2
0
0
1
0
0
1
0
1
0
0
2
1
2
2
1
1
1
2
2
1
1
1
0
1
1
0
1
0
1
1
2
1
2
0
1
2
5
0
1
1
1
1
1
2
1
1
1
0
0
0
2
0
2
1
2
2
1
1
0
0
1
1
1
0
3
2
0
0
2
2
0
0
1
0
2
1
2
2
1
1
2
0
2
1
1
2
0
1
1
2
1
0
2
2
2
1
1
2
1
1
0
2
0
0
1
0
1
1
1
0
2
2
1
0
2
1
2
1
2
1
0
2
0
0
1
1
1
1
1
0
1
0
1
1
2
1
1
0
1
0
1
1
0
1
1
2
1
1
0
1
1
0
1
2
1
0
2
1
2
1
2
1
1
0
2
0
1
1
0
0
1
1
1
1
0
2
0
2
1
1
2
0
0
1
2
1
1
2
0
1
1
0
2
1
0
1
1
0
1
1
1
2
1
0
2
1
1
1
1
1
0
1
0
0
1
2
0
1
0
1
1
2
1
0
1
0
0
1
1
1
1
1
1
1
1
1
1
1
0
2
2
1
3
1
0
0
1
0
1
2
1
1
0
0
1
0
1
2
2
2
1
0
2
0
2
0
2
0
0
0
1
0
1
1
0
0
1
1
2
1
2
1
2
2
1
3
1
1
2
0
0
2
2
1
0
1
0
3
0
0
2
2
0
0
2
2
1
2
0
0
1
1
1
1
2
1
0
1
1
0
0
1
1
0
1
2
0
0
1
1
0
1
1
1
1
1
0
2
1
2
1
0
1
1
0
1
1
0
0
0
1
1
1
1
1
1
0
0
1
1
1
0
0
3
2
1
0
0
1
0
1
1
2
2
1
1
2
1
3
0
2
2
1
1
2
2
3
1
2
1
0
0
1
0
1
0
1
2
1
2
0
2
2
0
1
2
0
2
1
1
0
0
2
1
2
0
1
1
0
2
1
1
0
1
2
1
2
0
2
1
1
0
1
0
0
0
1
2
2
3
0
1
1
0
0
2
1
1
0
1
1
1
2
0
2
0
0
0
1
1
0
1
1
1
1
0
0
1
1
1
1
2
1
2
2
0
1
1
0
0
1
0
0
2
2
0
2
1
1
0
1
0
0
1
1
1
1
1
2
1
2
1
1
0
1
2
0
2
0
0
1
1
0
2
1
1
0
0
2
0
1
0
0
1
3
0
1
3
1
0
1
0
3
1
1
1
1
2
1
1
2
1
0
0
0
1
1
1
0
1
0
0
2
1
1
1
1
1
0
1
3
0
1
4
0
1
0
1
1
1
1
0
1
1
2
0
1
1
2
1
0
1
1
0
0
0
0
2
0
0
1
2
1
0
1
2
0
2
1
1
1
1
1
1
0
0
0
0
1
2
1
1
1
1
0
0
2
0
1
0
0
0
0
0
1
1
1
2
2
0
0
1
1
1
1
1
2
1
2
2
0
0
0
1
2
1
2
1
2
2
1
0
0
2
1
1
1
1
2
0
1
1
0
1
2
2
0
2
2
1
0
2
0
0
2
2
0
2
0
3
2
0
1
0
2
2
0
2
0
2
0
2
1
1
2
1
0
2
1
0
1
2
0
2
2
1
2
0
0
1
1
2
2
0
2
0
1
1
2
1
1
0
1
0
0
0
0
2
0
2
1
1
1
1
1
0
0
1
1
0
2
0
0
0
2
1
1
1
0
1
0
0
1
1
1
0
1
1
1
0
1
1
0
0
1
2
1
2
1
2
1
0
2
0
2
1
1
0
2
2
0
0
1
2
0
1
1
0
1
2
1
1
1
1
1
0
1
1
2
1
1
1
2
1
2
2
0
1
1
1
0
0
1
2
1
2
1
1
1
1
2
0
2
1
1
0
0
2
1
0
0
1
1
1
0
1
1
1
1
1
0
2
1
2
1
0
0
1
0
1
1
0
3
2
1
1
1
0
1
2
2
0
1
2
0
1
0
2
1
0
1
2
1
1
2
2
1
0
2
1
0
2
1
0
2
1
2
0
0
1
2
1
1
0
1
0
1
1
2
1
2
2
1
0
2
2
1
0
1
1
1
1
0
1
1
1
0
2
1
1
0
1
0
1
0
2
2
1
1
0
0
2
3
1
1
0
1
1
0
0
0
1
0
0
0
1
1
1
1
2
0
0
0
2
2
1
0
1
0
4
0
3
1
1
1
1
0
1
2
1
1
1
1
1
1
0
1
1
1
0
1
0
2
0
1
1
0
2
1
0
0
1
1
2
0
1
0
1
1
2
2
0
0
0
1
1
1
1
0
0
2
0
0
0
2
1
0
1
0
1
1
0
1
1
1
1
1
2
2
2
1
0
0
2
1
1
1
1
0
2
2
19
1
1
1
1
2
2
1
1
1
0
1
0
2
1
0
1
1
1
1
0
1
1
0
2
0
2
1
2
0
1
2
0
1
2
2
1
1
1
1
2
2
1
2
1
0
1
0
2
1
0
2
1
0
1
0
1
0
2
0
0
1
0
0
2
0
1
0
1
1
1
0
1
2
1
2
1
1
1
0
1
2
0
0
0
1
1
1
0
1
0
2
0
0
0
1
0
1
1
0
1
1
0
1
1
0
1
0
2
2
1
2
1
0
0
1
2
1
1
1
0
1
1
1
2
4
1
0
0
1
1
1
2
1
0
0
1
1
1
1
1
0
0
0
2
1
0
1
1
2
1
1
2
2
0
1
0
0
2
1
0
1
1
2
0
1
1
0
0
1
1
0
1
1
0
0
2
0
0
1
2
1
2
1
2
1
1
1
0
1
1
2
2
1
1
2
1
1
2
2
1
1
2
2
0
2
2
1
1
0
0
1
2
1
2
2
1
1
1
1
1
2
1
2
1
1
0
1
0
1
2
1
1
1
1
2
1
0
0
1
1
0
1
5
1
1
1
1
1
0
1
0
0
0
0
1
0
1
1
0
1
2
2
0
0
0
1
0
0
1
1
0
0
1
2
1
1
2
0
1
1
2
0
1
1
1
1
0
1
2
0
1
1
1
0
1
2
0
0
2
2
0
1
2
0
1
0
1
1
0
1
0
2
1
1
1
1
2
1
2
1
1
1
0
1
0
2
0
1
1
1
1
1
0
0
2
1
1
0
0
0
1
2
0
2
0
1
2
3
0
1
2
1
1
2
1
0
1
0
1
0
0
0
0
0
0
0
0
1
1
2
0
0
1
1
1
0
0
0
0
0
2
0
1
0
0
0
1
2
0
0
1
0
1
1
2
0
1
1
0
0
0
0
2
1
0
0
0
0
1
0
0
0
2
1
1
1
1
2
1
1
2
2
1
1
1
1
0
1
1
0
0
2
0
0
2
2
2
2
0
0
0
1
0
0
0
2
2
1
0
0
1
2
0
0
1
2
1
2
1
0
1
1
1
0
1
0
0
2
1
1
1
0
2
2
2
2
1
1
0
1
1
2
0
1
1
1
1
1
1
0
1
1
1
2
0
0
0
0
2
0
1
2
1
0
1
0
2
1
1
0
1
0
0
1
0
1
1
1
1
0
2
2
1
0
1
1
2
0
1
2
2
1
1
0
2
1
1
1
2
1
1
0
0
1
3
0
1
0
1
0
0
1
1
2
0
1
2
2
0
0
0
0
0
1
1
4
1
0
1
1
0
0
0
2
1
1
1
1
2
2
1
1
2
0
3
1
0
1
1
2
0
0
0
2
0
1
0
2
0
0
2
0
1
1
1
1
0
1
2
1
1
1
0
1
0
0
1
2
0
3
0
2
1
0
2
1
0
1
1
1
0
1
2
1
2
0
2
1
0
1
0
0
1
0
2
1
1
1
1
1
2
1
2
1
0
2
1
2
2
0
0
0
1
0
0
0
1
2
1
0
1
2
1
1
0
2
0
1
1
1
0
1
0
0
0
1
2
2
1
0
1
1
0
0
1
0
0
1
1
1
2
0
1
0
1
0
1
1
0
1
0
0
1
0
0
2
1
0
0
0
2
0
1
1
1
1
2
1
0
1
0
1
1
1
1
1
0
1
2
1
2
1
0
2
3
1
0
1
2
2
2
2
1
1
2
0
1
0
0
0
0
0
0
1
1
1
1
0
1
1
2
0
1
0
0
0
0
1
1
0
0
1
1
0
1
2
0
0
0
1
0
2
0
1
0
1
2
2
1
1
0
1
0
1
0
1
1
3
2
1
1
1
0
0
1
0
0
0
0
1
0
2
1
1
1
0
0
1
1
1
0
0
1
1
1
0
1
2
0
2
0
1
0
0
1
1
0
0
1
0
0
0
1
0
1
2
0
1
1
0
0
1
1
1
0
1
1
2
0
1
2
2
1
1
2
0
2
0
1
2
2
0
1
0
1
1
1
1
2
1
1
2
1
0
0
2
0
1
1
1
1
0
1
0
2
0
2
2
1
1
1
3
0
2
0
1
1
0
1
1
2
1
1
3
1
1
0
0
2
0
1
1
0
1
1
1
2
2
2
0
1
0
0
0
2
1
0
0
1
0
0
0
2
0
2
0
1
0
0
1
2
1
0
1
1
1
0
2
2
0
0
2
1
0
0
0
2
1
2
1
2
1
1
0
1
1
1
1
1
0
0
1
1
0
2
2
0
1
0
0
1
1
2
0
1
0
2
1
2
1
1
0
0
1
1
0
2
2
1
0
0
2
1
0
2
1
0
1
1
1
0
2
1
0
1
1
0
0
0
1
0
1
2
0
1
1
2
1
2
0
1
2
1
0
0
0
1
2
1
0
1
1
1
1
1
1
1
0
1
1
1
0
1
1
2
2
0
0
2
2
0
2
0
1
0
0
0
1
2
0
1
1
1
0
0
0
0
1
1
0
1
2
1
2
2
2
2
2
0
0
1
1
2
1
1
0
0
1
1
0
1
1
1
1
0
1
1
1
2
1
1
1
3
0
0
2
0
1
1
1
1
2
1
2
2
1
0
0
0
1
2
0
0
0
1
2
1
1
0
0
1
1
1
0
2
1
1
2
2
1
0
0
1
0
1
0
1
1
1
1
1
0
2
1
0
1
1
1
0
1
2
1
1
2
0
2
2
0
3
1
2
1
1
2
0
1
2
2
0
2
1
2
1
0
1
1
1
0
0
0
2
1
1
2
1
1
1
1
2
0
0
0
2
0
1
0
0
2
1
2
0
0
1
1
0
2
1
1
1
0
0
2
0
1
0
1
0
3
0
1
1
1
1
1
2
1
2
1
1
0
1
1
1
1
2
2
0
1
0
0
0
2
0
0
0
1
1
2
1
1
1
2
1
1
1
0
1
1
1
1
1
1
0
1
0
0
1
1
1
2
1
0
0
1
3
0
1
1
0
1
0
1
2
1
1
1
1
0
0
1
0
1
1
1
1
1
0
0
1
0
1
0
1
1
0
3
1
0
2
0
0
0
0
1
2
1
0
3
1
1
2
0
0
1
0
2
0
1
1
2
1
1
2
0
1
1
0
1
1
0
2
1
0
2
0
2
1
1
2
2
0
0
1
1
2
1
2
2
0
1
1
1
1
2
0
1
1
1
1
2
0
2
1
2
0
1
0
0
1
2
1
2
0
0
0
1
1
0
0
0
1
0
0
1
0
0
1
0
1
2
0
1
2
0
2
2
1
2
1
1
0
0
2
1
1
0
1
1
0
1
1
2
2
0
0
3
1
1
2
2
2
0
2
0
2
1
1
0
2
2
2
1
1
1
2
1
0
2
0
0
2
1
0
2
1
1
1
1
2
1
0
1
0
1
1
0
1
1
1
0
2
1
1
0
1
0
1
0
1
1
1
1
1
0
0
1
1
1
0
0
2
2
1
1
1
2
0
1
2
2
0
1
1
1
0
3
0
1
0
0
2
2
1
2
0
1
1
1
0
0
0
2
1
1
0
2
1
1
2
0
2
1
2
1
1
1
2
0
1
2
1
1
2
2
0
1
2
0
1
2
1
1
1
0
2
2
2
1
0
1
0
2
0
0
0
1
1
0
0
1
1
2
1
1
1
1
0
0
1
1
1
0
2
2
1
1
0
0
1
1
0
2
1
2
0
1
0
0
2
1
0
1
1
2
1
1
2
2
1
0
2
1
1
3
0
1
0
0
1
1
2
1
2
1
2
1
1
1
0
0
1
1
2
1
1
2
1
0
0
1
0
0
1
2
1
0
1
0
1
2
2
1
0
1
0
0
1
1
0
1
1
1
0
2
1
2
0
2
1
2
1
0
1
0
0
2
1
1
0
1
1
0
0
0
1
0
1
8
1
0
2
1
2
2
1
1
0
1
1
1
1
3
0
2
2
1
2
2
2
2
1
1
1
2
1
1
1
1
1
0
1
1
1
1
1
0
1
1
1
1
2
0
2
1
0
0
0
0
1
1
1
1
1
0
0
1
0
0
0
0
0
0
0
2
1
1
0
0
1
0
1
1
1
1
2
1
1
1
1
0
1
1
1
1
2
1
2
1
0
1
1
2
1
2
1
1
1
1
1
1
3
0
1
1
2
1
0
2
2
0
0
1
1
1
1
0
1
1
0
1
1
1
1
1
1
0
0
2
0
0
1
1
2
1
1
0
2
1
3
2
1
1
1
1
1
0
1
2
1
0
2
1
0
1
1
2
0
2
2
1
0
0
1
0
1
1
2
2
1
1
1
2
2
1
4
0
1
1
1
2
0
1
1
0
2
2
1
1
0
1
1
2
1
1
2
1
1
1
1
1
1
1
2
1
1
0
0
2
2
0
1
1
0
4
1
0
2
2
1
0
1
0
1
1
1
1
1
2
1
0
0
0
1
2
1
1
0
2
1
1
2
1
2
1
0
2
2
0
0
1
0
2
0
1
1
2
0
1
0
1
1
0
0
1
1
0
1
1
1
0
4
0
1
0
1
2
1
0
1
0
0
2
0
1
2
1
1
0
1
0
2
0
0
1
1
1
0
1
0
1
1
0
1
2
1
0
1
1
1
0
0
0
2
1
2
1
1
1
0
0
1
1
1
1
0
0
1
2
0
1
0
1
1
0
2
1
2
0
1
1
0
2
2
3
0
2
1
1
2
1
2
0
1
1
0
1
1
0
0
0
0
1
1
1
1
1
1
1
0
1
0
1
2
1
1
0
2
2
0
1
2
0
2
1
0
0
1
2
1
1
1
0
2
1
2
0
1
0
1
1
2
0
0
1
1
2
2
0
1
1
0
2
0
1
0
1
0
0
1
1
2
2
4
1
1
0
1
1
1
2
1
1
2
0
1
4
0
0
1
1
0
1
2
2
0
0
0
0
1
0
0
1
1
2
2
1
1
2
1
1
0
2
0
0
1
0
0
1
1
1
0
0
1
0
2
0
2
2
0
2
1
2
1
0
2
0
0
0
3
1
1
2
1
2
0
1
2
0
0
0
2
2
0
0
1
0
2
1
1
1
1
0
1
0
1
0
1
1
1
2
1
0
1
1
2
4
1
0
0
1
0
1
1
0
2
0
0
2
1
1
1
1
0
2
1
0
1
0
0
2
1
0
0
2
1
1
1
1
2
0
2
2
2
1
0
1
1
1
1
2
1
1
1
1
0
1
1
2
0
1
1
1
2
0
2
0
1
0
2
0
1
0
1
1
1
1
1
0
1
1
0
0
2
1
0
1
1
2
0
1
1
2
2
0
2
1
1
0
0
0
2
0
0
1
1
0
1
1
0
1
0
1
1
1
0
2
0
0
1
0
0
2
1
0
2
0
2
1
2
2
2
1
1
1
1
1
0
2
0
1
0
1
1
0
0
0
1
1
1
2
1
0
1
2
1
1
0
0
1
2
1
1
1
0
2
1
1
1
0
0
1
0
1
1
0
1
1
1
2
1
3
0
2
0
1
1
2
0
1
0
1
0
0
0
2
0
1
1
1
1
1
1
1
1
0
0
2
1
1
0
0
0
1
1
1
1
0
1
1
1
1
0
0
1
3
2
1
2
0
0
2
0
1
0
0
0
1
2
0
1
0
1
0
2
1
1
1
0
2
0
1
1
2
1
1
0
0
1
2
0
1
0
1
0
1
2
2
0
2
1
1
2
2
0
1
0
1
0
1
0
0
2
1
0
0
1
0
1
1
1
1
2
1
3
0
1
2
1
0
2
1
0
0
0
0
0
2
0
1
1
2
1
2
1
1
0
1
1
0
0
1
0
1
1
1
3
1
1
1
2
1
1
0
0
1
1
0
1
1
1
1
1
1
0
2
0
0
1
0
2
0
2
1
2
1
1
1
0
1
1
0
2
1
1
1
2
0
1
0
1
1
1
1
1
0
1
1
1
2
0
0
1
1
1
0
3
0
1
1
2
0
1
2
1
1
1
1
0
0
2
1
2
1
1
1
0
0
0
0
1
1
0
2
1
1
2
1
0
1
2
0
2
2
1
1
0
2
1
0
2
2
1
1
0
0
1
2
2
1
0
0
2
1
1
1
1
0
0
1
1
2
1
0
0
1
2
0
0
0
1
1
1
1
2
1
1
2
1
1
2
0
1
2
0
2
1
1
2
0
2
2
0
2
1
0
0
0
0
2
1
1
1
0
3
0
0
2
0
2
1
2
1
1
2
0
1
0
0
1
0
1
0
1
1
1
1
1
2
0
0
1
2
0
4
0
2
1
1
2
3
2
1
0
1
1
2
0
2
0
1
0
1
2
1
1
1
1
1
0
1
1
0
0
2
2
1
1
0
1
0
1
1
1
0
2
1
1
1
0
0
0
1
1
0
0
1
0
1
0
2
0
0
1
2
1
2
2
2
1
1
1
2
0
0
1
1
2
2
1
0
1
2
1
1
1
1
0
0
0
0
0
0
1
1
1
1
0
2
1
1
1
1
2
2
0
1
2
0
2
1
1
0
2
1
0
1
1
2
0
1
1
1
0
2
1
0
0
2
1
0
2
0
1
1
1
0
1
0
1
2
1
0
1
0
1
0
0
0
1
1
1
2
2
3
2
1
1
1
0
0
0
1
1
0
2
0
1
0
2
1
0
2
1
1
0
0
2
2
2
1
0
0
2
1
2
1
0
1
0
0
2
1
0
1
0
1
1
1
1
1
2
1
0
0
1
0
2
0
1
1
2
1
1
0
2
0
1
2
0
1
1
2
0
1
2
1
1
0
1
2
0
1
2
1
1
0
0
1
1
0
1
0
1
1
1
1
0
1
0
2
1
1
1
2
0
0
2
3
0
1
1
0
1
1
1
0
0
0
2
1
2
0
1
1
1
1
1
2
2
0
1
2
3
0
0
2
1
0
1
2
0
0
1
1
1
1
2
1
1
1
0
1
0
1
1
1
1
2
1
1
1
0
0
0
1
0
1
0
1
1
0
0
1
0
2
1
0
0
2
1
3
1
0
2
2
0
2
1
1
1
1
2
1
0
0
1
1
0
1
1
0
2
2
2
1
0
2
2
0
0
1
2
0
0
1
2
1
2
1
1
2
0
1
1
1
1
3
1
0
2
1
0
1
1
0
1
1
2
2
1
0
2
1
0
0
1
1
1
2
1
0
0
1
0
1
1
1
1
0
0
2
1
1
1
1
2
1
1
0
1
1
1
0
0
0
0
1
1
0
2
1
0
1
1
0
2
0
0
1
3
1
0
1
0
0
0
1
1
1
2
2
1
2
1
1
2
1
2
1
0
2
2
0
1
3
1
2
2
1
1
1
1
0
0
1
1
1
0
0
0
1
1
0
2
2
0
2
3
1
1
2
0
1
0
4
1
2
1
0
2
1
3
4
1
0
2
0
2
1
2
1
1
0
0
0
0
1
2
1
1
1
1
0
1
0
1
1
2
1
2
1
1
1
1
3
1
1
1
0
0
0
1
0
2
0
0
1
2
1
0
2
0
1
1
1
2
0
2
1
2
1
0
1
1
1
0
1
1
2
2
1
1
2
1
1
0
1
0
0
0
2
0
0
1
1
1
1
1
3
3
1
0
0
0
0
2
1
0
2
0
0
0
1
2
1
1
0
0
2
1
1
0
0
1
2
1
1
0
1
1
2
2
2
0
1
1
0
2
1
2
1
0
0
0
0
0
0
1
0
2
1
2
1
1
0
2
2
0
2
1
2
1
1
1
1
1
0
1
1
4
0
0
0
1
1
1
1
1
1
2
1
0
0
2
1
0
0
1
1
0
1
0
0
1
1
2
1
0
0
1
2
1
1
2
0
1
3
3
0
2
1
1
1
0
0
0
1
2
1
2
2
1
0
1
2
1
2
1
1
0
1
1
2
3
0
1
1
1
0
2
0
2
0
1
1
1
1
0
2
1
2
2
0
1
0
0
0
1
1
0
1
1
1
0
1
4
1
1
3
1
1
1
0
0
2
0
0
0
1
1
0
2
1
1
2
1
0
0
1
2
1
1
0
1
0
2
1
2
1
0
1
2
3
1
1
1
0
0
1
2
0
1
1
1
0
1
0
2
2
2
0
2
0
0
2
1
1
2
2
1
1
2
0
1
2
1
0
1
2
0
1
0
0
1
2
1
1
1
0
1
2
0
1
0
1
0
1
0
1
0
0
1
1
0
2
0
2
0
1
1
0
2
1
0
0
1
0
2
0
0
0
1
0
1
0
0
2
1
2
1
1
1
1
1
0
1
1
1
1
1
1
2
1
1
1
1
1
1
0
4
1
1
0
1
1
1
2
1
1
1
1
0
1
2
0
0
2
1
2
1
0
0
1
1
1
2
1
2
1
3
0
1
1
1
0
1
1
0
1
0
1
1
1
0
0
2
1
0
0
2
0
0
0
1
1
1
1
0
1
3
1
1
0
0
1
0
1
1
1
2
0
1
0
1
2
2
1
1
1
0
1
1
0
0
1
1
1
1
0
1
1
1
1
1
1
1
1
0
1
1
0
2
2
1
2
0
2
1
1
1
2
0
1
1
1
1
1
1
1
2
1
0
2
0
1
1
1
0
1
1
3
1
2
2
0
1
1
0
1
2
0
2
0
1
0
2
1
1
0
2
1
1
1
1
0
2
2
1
0
1
1
1
1
0
1
1
1
2
1
1
1
2
1
2
1
2
1
1
2
2
2
2
0
1
1
2
0
1
1
0
0
2
0
0
0
1
2
1
2
1
2
1
0
0
3
0
0
0
2
1
1
0
0
1
1
2
7
1
0
0
1
2
0
1
0
1
1
0
0
0
1
1
1
1
0
1
0
2
0
0
0
1
1
0
0
1
1
3
0
2
0
0
1
1
1
1
2
1
1
0
1
0
0
2
1
1
2
3
0
0
2
0
0
0
1
1
1
1
0
0
0
1
0
2
2
3
1
0
0
0
1
1
0
1
0
1
1
1
0
0
1
1
3
2
0
1
0
0
0
2
2
0
1
1
1
2
1
1
1
0
0
0
1
0
2
0
1
1
1
0
1
1
0
1
1
2
1
1
1
0
2
0
1
1
2
2
0
1
1
0
1
0
2
1
1
0
1
1
2
1
0
1
0
1
0
1
0
1
1
1
0
1
1
0
0
2
1
0
1
1
0
3
0
0
1
0
2
1
1
1
1
1
2
1
0
2
1
0
2
3
1
1
1
1
0
0
0
0
0
1
1
1
1
1
1
0
0
0
0
1
0
1
1
0
0
2
1
0
0
1
0
3
1
2
1
0
0
1
2
0
1
1
0
1
0
1
1
0
1
0
0
1
2
0
1
1
1
2
0
2
1
1
1
1
1
1
1
1
2
1
3
1
1
2
1
2
1
0
1
1
2
2
0
1
0
2
2
1
1
0
0
1
0
0
2
1
1
2
1
1
1
0
2
1
2
1
2
1
2
0
0
2
1
0
0
1
1
1
1
1
1
1
2
2
0
2
0
0
1
2
1
0
1
1
1
1
0
0
0
1
2
1
2
1
1
1
1
2
1
0
1
2
0
0
1
0
1
1
0
1
1
0
1
0
2
0
3
2
1
1
1
1
0
1
0
1
2
1
1
0
0
1
1
0
1
0
1
0
0
1
2
1
1
1
2
1
1
0
1
2
1
1
1
0
2
0
0
1
0
1
0
0
0
1
0
2
5
0
1
0
0
2
1
1
1
2
2
2
1
1
2
1
1
2
2
2
0
1
1
0
1
1
2
1
1
0
0
1
1
2
1
1
0
1
2
2
1
1
1
1
0
2
2
0
2
1
0
2
2
2
0
0
2
2
1
2
1
2
2
1
2
1
1
1
0
0
1
2
1
0
0
1
2
1
2
0
1
2
2
0
1
1
0
1
1
0
0
2
1
1
1
0
1
1
1
2
1
2
0
2
1
0
1
2
0
0
1
1
0
2
1
1
1
0
0
1
1
0
1
0
0
0
1
1
0
2
0
0
1
1
1
0
4
0
0
0
1
2
2
0
1
1
0
1
0
1
1
2
1
0
1
1
1
0
1
0
1
1
2
0
1
1
0
1
1
1
1
1
1
1
1
0
1
1
0
1
0
0
3
1
0
1
1
0
2
1
1
0
0
0
0
1
2
1
0
1
2
1
0
1
2
1
1
0
1
0
0
1
0
0
1
0
0
1
0
2
1
1
1
1
2
1
2
0
0
1
1
1
2
0
1
1
1
2
0
1
1
1
1
1
1
2
1
1
2
1
1
1
2
0
2
0
0
1
0
2
1
0
1
0
0
1
1
0
1
0
1
1
0
1
3
0
0
1
1
1
0
1
1
2
0
1
1
1
0
2
0
2
0
1
2
0
0
1
1
2
0
0
1
0
1
1
2
2
2
0
2
0
1
0
0
1
0
1
1
1
0
0
1
0
1
1
0
2
1
0
0
0
0
1
1
0
1
1
1
0
2
0
0
1
2
1
0
1
0
1
2
2
1
1
1
1
1
2
2
1
2
1
2
2
0
1
2
2
2
1
0
1
0
1
2
0
0
1
0
0
1
1
2
0
0
1
0
4
0
1
3
0
0
0
0
2
2
2
1
2
1
1
1
1
1
1
0
0
2
2
0
2
0
0
2
1
2
0
1
1
1
0
1
2
1
2
0
0
0
2
0
1
1
0
0
0
1
0
1
1
1
0
1
1
2
0
1
0
0
0
1
0
2
1
0
1
1
1
0
1
1
0
2
1
1
0
0
1
1
0
1
2
1
1
0
0
1
2
2
0
1
2
2
0
1
0
1
2
2
0
1
2
0
1
0
0
1
1
0
0
0
1
2
0
1
0
1
1
1
1
1
1
0
1
0
2
1
1
1
2
1
1
2
1
0
0
1
0
2
1
2
0
1
1
1
0
1
1
1
0
1
0
2
2
2
1
1
0
1
0
1
2
4
1
1
0
0
0
0
2
0
2
1
1
1
1
0
2
1
1
1
0
2
1
1
0
1
1
0
2
0
0
1
1
0
1
2
2
5
0
1
0
1
0
1
2
1
2
1
1
1
2
2
0
3
2
1
1
1
0
1
1
2
1
2
1
1
1
1
1
0
2
0
2
0
1
1
0
1
2
2
0
2
1
2
0
1
2
0
2
0
2
0
1
1
0
1
0
0
0
1
1
2
0
1
0
0
0
1
0
1
6
1
0
2
0
1
1
1
0
1
1
0
0
1
0
1
0
2
2
2
0
1
1
0
1
0
2
1
1
0
3
2
1
2
0
1
0
1
0
1
1
1
1
2
2
1
2
1
0
1
1
1
0
0
0
0
0
1
0
1
0
1
2
1
0
0
0
0
0
1
0
1
0
1
1
0
2
1
2
0
0
1
1
1
0
2
1
1
2
2
0
0
2
2
1
1
1
1
4
2
2
0
1
1
1
2
0
0
0
0
2
0
1
1
2
0
1
1
2
1
1
1
1
0
0
0
1
1
1
2
0
0
0
2
0
1
2
3
1
2
1
2
2
1
1
1
2
0
1
1
1
1
1
0
1
2
1
1
1
1
1
1
2
1
0
3
0
2
1
0
1
0
0
1
1
0
3
0
1
1
0
1
1
1
1
3
0
0
0
1
0
0
1
0
1
0
2
1
2
2
0
1
1
0
2
1
1
0
0
2
0
1
2
2
2
2
2
1
2
1
1
1
2
0
2
0
0
1
2
1
1
0
0
1
0
1
2
1
1
2
1
0
0
0
2
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
0
1
2
0
1
1
0
2
1
1
2
2
1
1
1
2
1
0
2
2
1
1
0
0
2
1
1
0
2
0
0
1
2
1
0
3
0
3
2
0
2
1
3
0
0
1
2
2
1
0
2
2
0
4
1
0
0
0
0
1
1
1
1
1
2
2
1
2
0
2
1
1
2
0
1
1
0
0
0
0
0
1
2
1
0
0
2
1
0
1
0
0
1
0
1
2
0
1
2
0
0
0
1
1
1
0
1
2
1
1
1
0
1
1
2
1
2
1
1
1
2
0
2
2
1
1
1
2
1
2
2
1
3
0
0
1
0
0
0
1
0
2
2
0
0
0
1
0
2
0
0
0
1
1
1
1
1
1
1
2
1
1
2
1
0
1
0
1
0
1
2
2
0
1
2
1
1
2
2
2
1
0
0
0
2
2
0
0
0
1
0
1
2
1
1
1
0
1
1
2
1
0
0
1
1
1
0
1
1
0
1
0
2
1
1
2
0
1
1
2
1
1
2
0
0
0
0
1
1
0
1
1
1
1
1
0
1
0
1
2
2
1
1
1
1
1
2
2
1
0
0
2
0
2
0
0
1
1
0
2
0
2
0
2
0
2
2
1
1
1
0
1
1
1
1
0
1
1
0
0
1
1
1
1
1
2
2
0
1
0
0
1
0
0
1
0
2
1
2
0
0
1
2
1
1
1
0
2
1
1
1
2
0
1
0
0
0
1
2
0
0
1
1
1
0
1
1
1
1
3
0
1
0
1
1
2
1
0
1
1
0
2
2
0
1
1
0
1
1
0
1
1
0
0
1
0
0
1
2
2
2
0
0
1
0
2
2
0
0
0
0
1
2
1
1
1
2
0
1
0
0
2
1
1
1
1
1
0
1
1
2
1
1
1
1
0
0
0
1
0
1
1
1
1
1
2
0
1
1
0
1
1
1
2
0
0
1
0
2
1
1
2
0
1
3
1
0
0
1
2
1
0
2
2
2
1
0
0
1
0
1
1
1
2
1
2
0
3
1
0
0
1
2
1
1
0
1
2
0
0
0
1
0
0
1
2
1
0
0
1
0
0
0
2
2
0
0
1
2
0
0
2
1
1
2
2
2
1
0
0
1
1
1
0
1
1
1
1
1
2
0
1
1
0
1
0
1
2
2
0
0
2
2
0
0
1
0
1
0
2
1
0
1
1
1
2
0
2
1
0
1
1
1
2
0
1
1
1
0
1
0
1
1
1
0
1
0
1
2
0
1
1
1
1
0
2
1
1
1
1
2
1
0
0
0
0
1
0
1
2
1
0
2
1
0
2
1
0
2
0
0
0
2
0
2
0
2
0
1
0
0
0
0
1
0
1
0
1
1
1
2
1
0
0
0
2
1
1
1
1
1
1
1
2
0
2
1
0
1
2
3
0
0
1
1
1
0
1
0
1
0
0
1
0
0
1
2
1
0
1
2
2
2
2
0
0
1
1
1
0
0
2
2
1
2
0
0
2
2
0
1
1
1
1
2
1
2
1
1
0
1
1
1
0
1
2
2
2
1
1
1
1
0
2
1
1
1
0
0
2
2
0
2
1
2
0
0
0
0
2
0
1
0
1
1
0
1
0
0
0
1
1
2
1
0
2
1
2
1
0
0
1
0
1
1
1
0
0
1
0
2
1
2
0
1
1
2
1
1
0
2
3
0
2
2
0
1
2
1
1
1
0
1
0
0
0
2
2
1
2
1
1
0
0
1
1
2
1
0
2
1
1
2
2
0
0
2
1
1
2
0
1
1
1
1
2
1
0
1
0
1
2
1
0
0
0
1
1
1
0
2
0
1
0
0
0
0
2
1
1
1
1
2
1
1
1
0
1
2
1
0
1
2
3
0
0
0
0
1
0
1
1
0
1
1
2
1
2
1
0
1
1
2
0
1
2
1
1
0
1
1
0
0
0
0
1
0
1
1
0
2
0
0
0
2
0
2
1
1
1
2
0
2
1
0
2
1
2
0
0
1
0
1
0
1
0
2
2
1
2
1
2
2
1
1
0
0
1
0
2
2
2
0
1
1
1
1
1
1
0
0
1
1
0
0
0
0
1
4
2
1
1
1
0
1
0
1
1
1
0
1
0
2
1
1
2
2
1
1
0
2
0
0
1
1
2
1
0
1
2
1
0
1
0
1
1
1
1
2
1
0
0
2
1
1
0
1
1
1
1
0
3
0
1
2
1
0
1
0
1
1
1
1
1
0
1
1
1
1
0
0
0
0
1
3
2
1
1
0
0
0
1
0
1
0
1
1
0
2
1
1
1
2
2
1
1
1
0
1
0
1
1
1
0
2
0
1
1
1
1
2
0
1
2
1
0
1
1
1
1
1
2
1
2
2
0
1
2
1
0
2
1
2
1
2
2
0
1
0
0
0
1
1
2
2
2
1
1
1
1
0
1
1
0
1
2
0
0
0
0
2
2
2
1
0
0
2
1
1
0
1
1
2
1
1
2
2
1
0
0
1
1
1
2
1
0
2
3
1
0
2
0
1
0
0
0
1
1
0
0
1
1
1
0
2
0
0
2
2
1
0
0
0
0
2
0
0
2
0
1
3
1
1
1
0
2
1
1
1
2
1
1
0
1
2
0
0
1
1
0
1
1
0
1
1
1
2
0
0
2
1
1
0
2
1
0
0
2
1
0
0
1
1
1
0
2
2
1
2
1
2
1
1
1
1
0
0
1
1
1
1
0
1
1
0
1
0
1
0
0
1
0
1
2
2
1
1
2
1
2
0
0
1
1
1
2
1
0
0
0
1
1
1
0
1
2
0
1
3
2
1
3
0
1
1
2
0
0
0
0
1
1
0
2
2
0
0
1
0
0
2
1
2
2
2
2
0
0
2
1
2
1
1
0
0
2
0
1
1
0
0
0
2
0
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
0
1
1
1
2
0
1
1
2
1
0
1
1
1
1
0
0
1
0
0
0
0
3
1
1
1
2
1
2
1
0
0
1
2
1
1
2
2
0
2
0
2
1
1
1
2
0
1
1
2
1
2
0
1
1
1
1
2
1
0
2
1
1
1
0
2
1
2
1
0
1
2
2
0
0
1
0
0
0
2
0
3
1
0
0
0
2
1
2
1
1
1
1
1
1
0
1
0
1
0
1
0
2
0
1
1
0
0
1
2
1
1
1
0
0
0
1
2
1
1
1
0
0
1
0
1
1
0
3
0
2
1
2
0
0
0
1
2
1
1
0
1
0
1
1
1
2
1
1
3
0
2
1
3
0
1
1
1
1
1
0
0
0
1
1
0
2
0
0
0
3
1
1
1
0
1
0
1
0
1
0
0
1
1
1
1
1
1
1
1
0
1
0
2
1
2
1
2
0
1
0
0
2
0
2
0
0
1
1
2
2
0
0
1
1
0
1
2
0
0
0
0
2
0
0
1
0
0
0
1
1
1
1
0
2
1
0
0
1
0
1
2
1
2
1
0
2
0
0
0
1
0
2
1
0
1
2
1
1
0
1
0
1
2
1
1
1
1
0
1
2
1
1
2
1
1
2
1
1
1
2
1
1
1
1
0
2
1
1
1
0
2
1
0
2
0
1
1
2
2
1
1
2
0
1
1
0
1
1
1
1
1
1
0
1
1
1
1
1
1
0
1
2
0
1
1
0
2
2
0
0
0
0
1
0
1
2
0
0
1
0
0
1
1
1
1
1
2
1
0
2
1
0
0
0
1
0
1
2
0
2
2
1
2
0
2
1
0
1
2
1
1
0
1
2
1
1
0
1
1
2
1
0
0
1
2
2
1
0
1
1
1
2
2
0
2
1
1
1
2
1
0
0
2
2
1
0
2
0
0
2
1
1
1
2
0
2
1
0
3
1
1
1
1
0
0
0
1
0
2
2
1
0
1
1
0
0
2
1
1
0
2
1
1
1
0
0
2
2
1
0
0
0
1
0
1
2
0
0
0
1
0
0
1
3
0
1
1
0
1
1
1
1
0
0
1
0
2
0
1
0
1
0
0
1
1
0
1
1
0
1
0
0
1
0
2
1
1
1
0
0
1
2
1
1
0
0
0
2
0
0
2
0
1
1
1
1
0
1
0
0
0
2
0
1
0
0
1
0
2
1
0
0
0
1
2
1
2
1
0
1
2
1
1
1
0
0
0
0
2
2
0
0
2
2
2
0
0
0
1
1
1
1
0
0
1
1
2
0
2
2
0
1
0
1
1
0
0
6
2
0
1
0
2
2
2
0
0
0
0
0
1
1
1
1
1
0
0
2
0
2
1
0
0
2
1
2
0
1
1
2
1
0
2
1
2
0
1
0
0
1
1
0
0
2
0
0
1
2
1
1
1
1
1
1
1
2
1
0
1
1
2
1
1
1
2
0
0
2
1
2
0
1
0
1
0
1
2
1
1
1
2
1
0
1
0
2
2
0
0
1
2
2
5
0
1
0
0
0
2
0
2
1
2
1
1
1
0
0
2
0
0
1
0
0
1
1
2
1
1
1
0
0
4
1
0
0
2
2
0
0
2
0
2
1
0
2
2
1
1
2
1
0
0
2
0
0
1
2
2
1
1
2
0
1
0
1
0
0
2
2
1
1
2
1
1
2
0
0
1
2
0
1
0
2
1
1
1
1
2
0
1
0
0
0
0
2
1
2
2
0
2
1
2
1
1
0
1
1
1
1
0
1
0
0
1
1
1
1
2
0
1
0
1
2
1
0
0
0
2
0
0
1
1
2
1
1
1
1
1
0
2
0
1
1
1
1
1
2
2
0
2
2
1
1
0
0
1
0
0
0
0
1
2
1
0
0
2
1
0
2
0
1
0
0
1
1
2
1
0
1
1
1
2
1
0
1
2
2
1
2
1
0
0
0
0
1
0
0
1
1
1
1
1
1
0
0
1
2
0
0
2
2
1
2
0
1
2
2
1
2
2
2
2
2
2
1
1
1
0
2
2
1
0
1
0
0
1
1
1
1
2
2
1
0
1
0
3
2
1
2
0
1
1
1
1
1
0
1
1
1
1
1
1
0
0
1
1
1
0
0
2
0
1
0
2
0
0
2
0
0
1
2
1
1
0
0
0
1
0
1
2
0
0
1
2
2
2
0
1
1
0
2
0
2
0
1
0
1
1
1
2
1
1
0
1
0
1
1
0
0
1
0
1
2
2
1
1
1
0
1
1
1
1
1
0
0
1
1
0
3
1
1
1
0
3
1
2
1
0
1
1
0
0
1
0
0
1
0
0
2
1
0
1
1
1
0
2
0
1
1
0
1
2
1
0
2
1
1
0
0
1
1
0
1
0
2
0
1
1
0
2
1
2
1
1
1
1
0
0
0
2
1
1
1
1
0
1
0
2
2
1
2
6
1
2
0
3
1
0
1
0
1
0
0
1
0
1
0
1
2
2
1
0
1
0
1
2
2
0
0
1
2
0
0
1
1
1
0
1
1
1
2
1
0
1
1
1
2
2
1
1
1
1
1
1
2
1
2
1
1
2
2
1
0
1
1
0
1
0
1
1
1
1
0
1
1
1
0
2
1
2
2
1
2
2
2
1
2
0
1
1
1
1
1
2
0
1
0
2
0
1
1
0
2
1
1
1
1
0
0
1
0
0
0
1
0
0
1
2
2
1
1
0
3
0
1
1
0
1
0
0
1
1
1
2
1
1
2
2
1
0
1
2
0
1
0
1
2
1
1
0
0
0
0
1
1
0
2
0
1
1
0
1
2
1
1
1
1
1
1
1
0
0
0
0
0
0
1
1
3
0
0
1
0
1
0
0
1
0
1
2
2
1
2
2
0
1
0
0
2
1
1
0
0
2
0
1
2
1
0
2
0
1
0
0
0
1
1
0
0
1
0
0
1
1
1
2
0
1
1
1
1
0
2
1
1
1
1
1
0
0
2
1
0
1
1
2
1
0
1
2
2
2
1
0
1
0
1
1
2
1
1
0
1
0
2
2
1
0
0
1
1
1
2
2
0
0
1
0
2
2
2
0
0
0
2
1
1
2
0
1
3
1
1
0
1
1
2
0
0
2
1
1
0
0
0
1
1
0
0
1
0
1
1
0
1
0
0
2
2
1
0
2
1
2
2
2
1
1
0
1
1
1
0
0
2
1
2
1
1
0
1
0
2
0
0
5
1
1
2
1
2
0
1
0
1
1
0
0
1
2
2
1
0
0
0
2
1
2
1
1
1
0
0
2
2
1
1
0
1
1
1
2
2
1
0
0
1
0
0
0
1
1
0
0
2
1
2
1
11
2
1
0
2
1
0
2
1
0
0
0
0
1
0
1
2
1
2
2
2
2
0
1
0
2
2
1
1
0
1
1
0
1
1
2
2
1
1
1
1
2
1
0
1
1
1
0
0
1
1
2
1
2
0
1
1
1
0
0
1
2
0
1
0
1
0
1
1
1
1
0
0
1
1
1
0
1
1
2
1
2
1
2
1
1
2
0
1
1
0
2
1
0
1
2
1
0
2
2
0
1
2
0
1
1
2
0
2
1
2
1
0
0
1
1
1
2
0
1
1
1
1
1
2
0
1
0
0
1
0
1
0
1
1
0
0
1
1
1
1
0
1
1
2
2
0
3
1
1
1
1
1
0
0
2
1
2
2
1
2
2
1
2
0
0
0
2
0
1
1
0
1
2
1
0
1
2
1
1
0
0
0
1
1
2
1
0
1
1
2
2
0
1
1
1
0
2
2
1
2
1
0
1
1
0
1
0
0
1
1
0
1
1
0
1
0
1
1
1
1
1
2
1
1
1
1
1
1
1
0
1
1
0
1
1
1
2
1
0
0
2
3
0
1
1
1
0
2
0
1
1
1
0
2
2
2
2
0
2
1
1
0
2
0
2
1
1
0
0
2
0
0
0
1
0
2
0
1
1
2
2
1
0
0
1
1
2
2
1
0
1
2
1
2
0
0
1
1
1
1
2
1
1
1
0
1
1
0
2
1
1
1
0
1
1
1
1
2
1
0
2
0
0
1
0
2
1
2
1
1
0
0
2
0
2
2
2
0
1
1
0
1
1
2
1
2
2
1
2
1
1
0
0
0
1
1
0
1
0
1
1
0
2
1
1
0
0
0
2
2
0
1
2
1
0
1
2
2
1
2
1
1
1
2
1
1
1
1
4
0
0
2
1
0
0
2
0
1
0
1
1
0
2
1
2
1
0
0
1
2
1
1
2
0
0
1
0
0
1
0
1
2
2
0
2
0
0
1
2
0
1
1
2
2
0
2
1
0
1
0
0
1
1
4
0
2
1
1
0
2
0
1
1
0
0
0
1
0
0
0
2
0
2
1
1
2
1
0
1
2
1
1
1
0
0
1
0
0
0
0
2
2
1
0
1
0
1
2
2
0
2
2
0
0
2
2
0
1
2
0
1
1
1
2
1
0
1
0
2
2
0
1
1
1
2
1
0
0
3
1
1
1
0
1
1
1
0
3
2
0
1
1
2
0
1
0
2
1
1
3
1
1
0
1
0
0
1
0
0
2
1
1
0
0
2
1
1
0
2
0
1
2
0
1
2
1
1
1
0
2
0
2
0
0
1
0
0
0
1
1
1
1
0
0
0
1
1
2
1
1
0
2
1
2
1
1
0
1
0
2
1
2
1
1
2
2
1
1
1
1
1
1
0
1
2
1
1
1
1
1
2
0
1
2
0
0
2
2
1
1
2
2
1
2
2
1
2
1
0
1
1
1
1
1
1
2
0
2
0
0
0
1
1
0
1
2
0
1
0
0
0
1
2
1
1
2
1
3
0
0
0
1
1
1
1
1
2
1
0
2
1
2
1
0
0
1
1
0
1
2
1
0
2
2
1
0
1
3
0
2
1
0
2
1
2
1
1
0
1
1
1
1
0
0
0
0
0
0
1
1
1
0
1
0
0
2
1
1
0
1
1
0
1
0
0
0
0
2
2
1
1
2
1
0
1
4
1
1
1
1
1
1
2
1
1
0
1
1
0
0
1
2
1
0
1
1
1
1
0
1
0
1
1
0
1
0
1
1
1
0
2
1
1
2
1
1
2
0
1
1
1
1
2
0
0
0
3
1
0
1
1
1
1
1
0
0
0
1
2
1
1
1
1
1
1
2
2
1
2
1
1
2
1
0
1
1
1
1
1
1
2
1
1
2
2
1
1
2
0
1
1
2
0
0
0
1
0
1
0
0
0
0
1
0
1
1
2
3
0
1
2
0
0
2
2
0
1
1
1
2
0
1
0
2
1
0
2
0
1
2
1
2
1
2
0
0
0
1
0
1
1
2
0
1
0
1
2
1
1
2
1
0
1
1
1
1
2
1
0
2
1
0
1
2
0
1
1
0
0
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
2
1
3
0
1
1
1
1
1
1
1
0
1
2
0
4
0
1
2
1
0
1
0
1
0
1
1
1
1
2
0
1
1
1
0
1
1
2
0
1
1
2
2
0
1
0
0
2
0
2
0
2
2
0
0
1
2
1
2
2
0
1
2
1
0
1
1
0
1
0
1
2
1
0
0
2
2
1
1
0
0
1
1
1
1
2
0
2
1
1
1
2
0
2
1
0
0
3
0
2
0
1
1
1
2
0
0
2
1
0
1
0
0
1
0
1
0
0
0
2
1
2
0
2
2
0
1
0
1
2
0
0
0
0
1
0
1
0
0
2
1
1
0
1
0
2
1
2
0
1
1
0
0
0
1
1
1
0
2
1
0
0
1
1
0
2
2
1
1
1
2
1
1
0
0
1
1
1
1
3
1
2
1
1
0
2
1
2
1
1
2
2
0
0
2
0
0
1
0
2
2
2
1
1
0
0
0
1
2
0
1
0
0
1
1
0
2
2
3
1
1
0
0
2
0
2
1
2
1
1
0
2
1
1
1
2
0
2
0
0
2
1
1
0
0
1
1
2
1
0
0
1
1
1
1
0
1
0
1
1
1
0
1
2
1
1
2
0
0
2
3
0
2
1
0
2
1
2
0
2
0
2
0
2
1
1
1
0
0
2
0
1
1
2
2
0
1
1
2
2
1
1
2
2
1
0
1
1
1
0
1
1
1
2
1
1
1
0
1
1
1
1
1
1
0
1
1
2
3
1
1
1
1
1
2
0
0
2
0
1
1
0
1
1
0
2
0
1
1
2
2
1
1
1
2
0
1
2
1
0
0
1
2
0
0
1
1
1
1
1
1
0
1
1
1
2
2
1
1
2
2
1
1
2
1
1
1
2
1
1
1
1
0
1
1
2
3
2
0
0
1
1
1
2
1
0
0
1
1
1
1
0
2
2
1
0
1
0
2
0
1
0
1
1
2
2
1
2
1
2
0
1
0
1
2
1
1
0
0
2
3
0
2
2
2
1
0
1
2
1
1
0
2
2
0
1
0
1
1
2
1
0
0
2
1
1
1
1
1
0
1
1
1
0
0
2
1
1
1
0
0
3
0
2
0
0
0
1
1
0
1
0
1
1
1
1
1
3
0
2
0
0
3
2
2
1
1
1
1
0
2
1
0
0
0
1
1
0
1
0
2
0
1
1
1
1
1
0
0
1
1
0
4
0
0
1
1
2
0
2
1
0
0
1
0
1
0
0
0
1
1
0
2
1
1
0
1
1
0
0
0
1
1
1
2
1
0
1
1
1
0
1
0
1
1
1
2
2
2
1
1
1
1
1
2
3
0
1
0
1
1
0
2
1
1
2
0
2
1
0
1
0
0
1
2
0
0
1
1
0
2
2
0
0
0
1
0
0
0
0
1
2
1
1
0
0
1
1
2
0
1
1
0
0
1
1
1
1
2
0
3
2
1
1
0
0
1
2
1
2
1
0
1
0
0
1
1
2
1
0
2
1
1
1
1
1
0
0
1
0
2
1
1
1
0
0
0
1
0
1
2
1
0
1
1
1
1
2
0
2
3
1
2
2
1
2
1
1
2
2
2
1
2
1
2
0
2
1
0
1
1
1
1
2
0
2
0
1
2
1
0
1
0
2
1
2
0
0
1
2
2
2
1
1
2
0
1
1
0
1
2
1
0
0
1
1
0
0
1
0
0
0
1
0
1
1
1
1
2
2
1
2
2
1
2
1
0
2
0
1
1
1
1
0
2
1
0
1
0
1
0
0
0
2
7
0
1
2
1
0
0
0
1
0
0
1
0
1
1
1
0
2
0
0
0
1
0
2
2
2
0
0
1
0
1
2
1
1
0
0
2
0
0
1
2
0
1
1
2
0
2
2
1
1
2
2
1
0
1
0
0
1
1
1
2
1
0
1
0
2
1
0
0
4
0
1
2
2
1
1
1
1
1
1
2
0
3
1
1
1
2
0
0
1
2
2
2
0
1
0
2
0
2
2
0
0
2
0
1
1
0
2
1
0
2
1
1
1
2
0
1
1
0
2
1
0
0
1
2
1
2
0
1
1
1
3
0
1
2
2
2
1
1
1
1
1
0
0
1
1
0
0
1
2
1
2
1
1
1
2
1
1
1
2
1
1
2
1
0
1
1
1
0
1
0
1
1
1
1
1
0
2
1
1
0
1
0
1
1
2
0
0
2
0
0
1
2
0
1
1
0
1
0
1
0
2
1
1
1
1
0
1
1
2
1
1
1
1
2
1
3
0
1
1
2
0
2
0
0
0
0
2
1
0
1
1
0
0
0
1
1
0
2
1
1
0
2
1
0
0
1
2
1
1
1
0
2
0
0
1
1
0
1
1
2
1
1
2
0
2
1
1
2
1
1
0
0
1
0
0
2
2
2
2
0
1
2
2
2
0
1
2
2
1
1
0
2
1
1
1
2
0
1
2
1
0
2
1
1
0
1
1
0
2
1
1
1
1
0
2
2
1
1
1
1
1
1
0
2
2
0
0
2
1
2
1
1
2
1
0
1
1
1
1
1
1
1
0
2
0
2
2
1
1
1
1
0
0
0
2
0
3
1
2
2
1
1
0
1
1
2
2
2
2
0
2
0
2
1
1
0
2
2
1
0
0
2
1
2
1
1
1
1
1
1
1
1
0
2
0
0
2
1
2
1
0
2
1
1
0
2
0
1
2
1
1
2
1
1
1
0
2
1
2
1
1
0
1
0
1
2
0
0
1
1
2
1
2
1
1
0
0
2
1
0
1
2
1
0
0
0
1
1
2
2
1
0
1
2
1
1
2
5
2
2
1
0
1
1
0
1
2
1
2
0
1
0
2
1
6
0
2
0
0
0
0
2
1
0
1
0
2
1
0
1
0
2
2
2
0
3
1
1
1
1
0
1
0
1
1
1
2
2
0
2
1
1
0
0
1
1
1
1
2
2
0
1
2
0
0
2
1
2
1
0
2
1
0
2
1
1
1
0
2
2
1
1
3
1
0
0
1
1
0
0
1
1
1
2
0
1
1
0
2
2
1
1
0
1
1
0
0
1
0
1
1
0
2
0
0
1
1
2
0
0
0
2
0
2
2
1
0
0
1
1
2
2
1
2
1
0
1
1
0
2
1
1
0
0
0
1
1
2
0
2
0
2
1
3
0
2
1
0
1
1
1
1
1
1
0
1
0
2
1
0
2
0
1
0
1
2
0
2
2
0
0
2
1
1
0
0
1
1
1
0
0
1
0
1
0
0
2
1
1
2
0
0
2
2
2
0
2
2
2
1
0
2
0
2
0
0
0
2
1
1
0
1
1
1
0
0
1
0
2
0
0
1
2
1
1
0
0
0
1
2
1
2
1
0
1
1
1
1
1
1
2
2
0
0
0
1
0
0
2
2
1
1
0
1
1
0
0
3
2
1
1
2
2
1
0
0
0
1
0
2
2
1
0
1
0
2
1
0
1
1
0
0
0
1
1
1
1
0
2
0
1
2
0
0
2
0
1
1
1
0
1
1
0
0
1
1
1
1
0
0
2
2
1
0
0
1
0
1
1
1
1
1
0
0
1
0
0
1
2
0
2
2
1
1
2
0
2
1
2
1
2
0
1
0
1
0
0
1
1
0
1
1
2
1
0
0
0
1
1
0
1
1
2
0
1
2
2
1
0
1
0
1
1
2
0
1
1
2
0
1
2
1
1
1
2
0
0
2
1
1
0
2
1
1
1
1
0
0
0
0
1
1
1
1
2
1
2
2
2
1
0
1
1
2
0
1
2
1
2
2
1
0
1
1
0
1
0
2
1
2
0
0
1
2
1
0
0
1
0
0
2
1
1
2
2
0
1
1
1
2
2
0
1
2
1
1
0
0
0
1
1
0
2
1
2
1
0
0
0
0
1
2
0
2
1
0
1
0
0
1
2
1
2
2
2
1
1
1
0
1
1
1
0
0
0
1
2
1
1
1
1
1
1
1
1
1
0
1
1
1
2
0
2
0
0
1
2
0
2
1
1
1
2
0
0
1
2
0
2
1
0
1
2
1
1
2
0
0
1
0
0
1
1
3
0
1
1
1
0
0
1
1
1
1
1
0
2
1
0
2
2
2
3
0
1
0
1
3
2
0
0
1
1
0
1
2
1
1
0
1
1
0
0
0
0
2
0
0
0
0
1
0
1
1
2
1
0
1
1
2
2
0
0
0
1
0
1
1
0
2
1
1
0
0
1
0
1
0
0
1
1
0
0
1
1
1
1
0
2
1
1
1
0
0
0
0
1
2
1
1
0
0
0
1
0
0
0
1
2
0
0
0
1
1
0
0
1
4
2
1
0
0
0
0
1
2
0
1
0
1
1
0
1
2
1
0
1
1
1
1
2
1
1
1
0
0
1
1
2
1
1
2
0
1
1
1
1
0
1
0
1
1
2
0
1
1
0
2
1
1
0
1
3
0
0
2
0
1
1
1
1
0
0
0
1
0
3
3
0
1
1
1
0
1
3
1
2
1
1
1
1
0
2
2
0
0
1
1
1
1
1
0
1
1
0
1
1
0
3
2
0
1
1
0
0
2
1
2
1
2
1
0
1
2
1
0
0
1
2
1
3
1
0
1
0
0
0
1
0
1
0
1
0
2
0
1
0
1
1
2
2
0
4
2
0
0
1
1
2
2
0
1
1
0
2
0
0
1
1
1
0
2
0
2
1
0
0
2
1
1
2
1
0
3
2
2
2
4
1
0
0
2
1
1
0
0
1
1
0
1
0
1
2
0
0
1
3
0
1
1
2
2
2
1
2
2
1
2
0
1
1
0
2
2
2
1
2
0
0
0
1
2
1
1
0
0
1
1
0
2
1
1
1
1
3
0
0
2
1
1
1
1
1
1
3
1
0
0
1
0
2
1
2
1
1
0
2
3
4
0
0
2
1
0
0
0
1
2
2
0
1
2
2
0
1
1
1
1
1
1
2
1
1
2
2
1
1
1
1
0
0
1
0
0
2
1
2
0
1
1
1
0
1
1
0
1
0
2
2
1
2
0
1
2
0
1
1
2
2
2
0
1
1
0
1
1
0
1
0
1
2
2
0
1
1
2
1
2
1
2
0
1
2
1
0
1
2
2
0
0
0
0
1
1
0
0
0
2
1
0
0
0
2
0
2
0
0
1
1
0
1
1
1
0
0
1
1
0
2
2
1
0
1
0
0
0
1
1
2
1
1
0
0
0
1
1
1
0
1
0
0
1
1
0
0
1
0
0
1
2
0
1
0
0
2
1
0
0
0
2
1
0
0
1
0
0
0
1
1
0
1
0
1
0
2
0
2
0
0
2
0
0
2
2
1
1
2
0
1
2
0
1
0
2
0
1
1
2
1
1
2
2
1
1
1
1
1
2
0
0
2
0
0
1
1
2
2
0
1
1
1
1
2
1
1
0
1
1
1
2
1
0
2
1
1
1
1
2
0
0
0
0
1
1
1
1
1
2
2
0
1
1
1
1
1
0
2
1
0
1
2
1
2
0
0
1
2
1
0
0
0
1
1
1
2
1
5
1
1
0
0
1
0
1
0
2
0
1
1
0
1
1
1
0
1
1
0
1
2
1
2
0
0
3
1
2
1
1
2
1
1
0
1
1
0
0
4
0
2
0
0
0
1
1
1
2
1
0
0
1
1
1
2
2
0
1
1
1
0
2
0
1
2
2
0
2
1
2
0
1
1
2
2
2
1
1
1
1
3
2
0
0
1
2
1
1
3
2
0
0
1
0
1
1
1
1
0
1
0
1
1
3
2
1
3
1
1
1
1
0
2
1
1
0
3
1
0
0
2
0
2
2
1
1
2
1
1
2
1
0
2
0
1
1
2
0
1
1
0
0
1
0
1
1
1
1
1
2
1
0
1
0
1
0
1
0
1
1
1
1
1
0
1
1
1
1
0
0
2
1
2
1
0
2
1
1
1
1
0
2
1
0
1
1
0
0
0
0
2
1
1
1
1
2
1
1
0
4
0
1
1
0
2
2
2
2
1
1
0
0
1
1
0
0
2
1
2
2
2
1
1
1
1
2
1
1
0
0
1
1
1
0
1
0
1
1
1
2
2
0
0
2
0
1
1
1
0
0
0
1
0
0
0
1
0
1
1
3
1
0
0
2
1
3
1
1
1
0
2
1
2
1
0
0
0
1
1
2
2
2
0
1
1
1
0
1
1
1
0
2
1
1
0
1
1
2
0
0
1
2
1
1
0
1
2
2
0
1
0
1
1
0
1
2
1
0
1
2
2
0
0
1
2
2
1
2
1
2
0
2
1
0
1
1
0
1
0
1
1
1
2
1
1
1
2
2
0
0
1
2
0
0
2
1
1
1
2
1
2
2
0
0
0
0
0
2
1
2
1
0
0
0
2
0
0
2
0
0
2
0
1
1
0
1
1
3
1
1
0
0
1
2
0
1
1
2
1
1
1
1
2
2
1
1
1
1
0
2
1
2
0
0
1
1
1
1
1
1
0
2
2
1
2
0
1
2
1
0
1
2
1
0
0
0
2
3
2
1
0
1
2
2
0
0
0
0
1
1
1
1
0
2
0
1
1
2
0
1
0
1
1
0
1
1
1
0
2
0
1
2
1
0
2
1
1
2
1
1
3
0
2
1
0
2
0
0
1
1
0
1
0
2
1
1
1
1
1
1
2
1
1
1
0
1
0
1
1
2
1
0
2
2
2
0
1
1
0
2
1
1
1
2
0
3
1
0
1
0
1
1
2
0
1
2
0
0
1
0
0
1
1
0
1
2
0
2
2
0
1
0
1
1
1
2
0
0
0
1
2
0
0
1
1
1
0
1
2
1
1
1
0
2
1
1
1
1
2
0
1
0
1
0
0
1
1
1
0
1
1
0
1
2
0
3
0
2
2
1
1
2
2
1
2
2
2
2
1
1
1
1
1
1
0
0
0
2
2
0
1
1
1
1
1
0
1
0
1
1
0
1
0
1
1
0
2
1
2
2
0
1
0
1
1
2
2
0
2
2
2
1
1
1
1
0
2
1
0
2
2
1
1
1
1
1
1
0
0
2
0
0
1
1
1
1
2
0
1
0
1
1
1
3
1
1
1
0
2
2
1
1
1
0
0
0
2
1
1
1
2
0
2
2
2
2
2
0
0
1
1
1
1
1
2
1
2
0
0
1
2
0
1
1
0
0
1
0
2
2
1
0
0
1
1
1
1
1
2
0
0
1
1
1
0
0
2
1
1
0
1
1
1
1
1
0
0
1
0
1
1
1
2
0
0
0
1
2
1
2
1
1
1
1
1
2
2
1
1
2
2
0
1
1
1
0
2
1
2
2
0
0
1
0
1
0
0
0
0
0
1
2
2
0
0
1
0
0
2
2
2
0
0
3
1
0
1
0
0
0
1
1
1
1
1
1
0
1
0
0
1
2
0
1
1
0
0
1
0
1
0
0
0
1
1
0
2
0
2
1
1
0
0
0
0
2
1
1
1
0
1
2
2
0
0
2
1
1
2
1
1
0
2
0
1
2
1
2
2
0
2
1
0
1
1
0
1
1
1
0
1
1
0
0
1
1
2
1
0
0
0
2
1
1
0
1
1
1
2
1
2
0
1
1
2
0
1
1
0
1
2
1
1
3
1
0
2
1
0
0
0
0
2
1
0
1
1
2
2
0
1
0
1
0
1
4
1
2
2
2
2
0
1
1
2
0
2
1
1
0
2
0
0
1
1
2
1
1
0
1
0
1
0
1
1
2
1
2
0
2
1
1
1
1
1
1
0
2
1
2
1
0
1
2
0
1
1
1
1
0
1
0
1
1
1
0
1
2
1
0
1
2
1
0
2
0
0
2
0
1
0
0
1
1
1
0
0
1
1
1
0
0
1
1
1
0
1
2
0
1
1
2
1
1
2
0
2
0
0
1
0
1
2
2
0
1
2
2
2
3
1
1
2
2
1
1
0
1
1
2
2
1
2
0
0
2
1
1
1
1
1
0
0
1
0
1
1
0
0
1
1
0
1
0
1
2
0
1
0
1
0
0
1
1
2
1
1
0
2
2
0
0
1
1
1
1
2
1
1
1
1
0
0
2
0
1
1
0
1
3
2
1
0
0
1
1
0
1
1
0
2
2
2
0
1
0
0
5
0
1
1
1
0
0
1
1
1
2
0
1
0
0
1
0
1
1
1
0
1
1
1
1
2
0
2
0
0
1
1
0
1
2
1
1
0
1
0
0
2
0
2
1
0
6
1
0
0
1
1
2
5
2
1
0
1
1
0
1
0
0
1
1
0
0
4
0
0
0
0
1
1
1
0
2
1
1
1
1
1
1
1
2
1
1
1
0
0
0
0
2
1
0
2
2
2
1
1
2
1
2
1
1
2
1
2
0
1
0
1
1
1
1
1
0
2
1
0
2
0
0
0
0
1
1
1
2
1
1
1
1
1
1
1
1
0
0
0
1
2
1
2
1
1
1
1
1
0
1
0
0
2
1
2
0
1
0
1
1
0
0
1
1
0
2
1
2
0
0
1
2
3
1
0
1
0
1
1
1
0
1
0
0
1
2
0
1
1
0
1
1
0
2
1
1
0
3
1
2
3
0
2
0
0
0
0
0
2
2
2
0
2
1
1
0
2
0
1
0
2
1
4
1
2
1
1
1
2
1
2
2
0
1
0
1
0
1
1
0
0
0
0
1
2
0
1
0
1
0
0
0
2
1
2
1
2
1
1
1
0
1
1
2
0
1
2
0
0
0
2
3
2
1
2
1
2
1
1
1
2
0
0
0
1
0
0
1
0
1
0
1
1
2
1
0
1
1
1
0
1
5
0
1
1
1
1
2
0
1
1
2
1
1
1
1
0
2
1
1
0
0
0
1
0
1
1
2
0
2
2
1
3
2
1
0
1
2
1
0
1
0
2
0
1
0
0
1
0
0
2
1
0
0
0
1
3
0
1
1
2
1
1
7
1
1
1
2
2
1
1
0
1
0
0
2
0
1
1
1
1
1
1
0
1
0
2
1
0
1
1
1
2
1
2
1
1
1
1
2
0
1
1
1
2
1
1
1
2
2
1
1
1
1
1
0
0
0
1
2
2
2
0
0
1
2
0
1
0
1
1
0
1
1
1
1
2
0
0
1
0
2
1
2
1
1
0
2
2
1
1
0
1
0
0
0
1
1
1
1
0
0
1
1
1
0
0
1
2
2
2
2
1
0
1
1
1
1
0
1
0
0
1
0
1
1
1
1
0
0
2
1
0
0
0
0
0
1
1
1
1
0
3
1
1
2
0
1
1
0
0
1
1
2
0
0
0
0
1
2
0
1
1
1
4
1
2
1
0
1
1
1
0
2
1
2
1
2
0
1
0
1
6
2
0
1
1
1
0
0
1
2
0
0
1
0
1
0
2
2
0
1
0
2
0
2
1
1
1
1
0
2
0
1
2
1
0
1
1
1
0
2
2
2
1
1
2
1
1
1
2
2
0
1
0
1
1
0
0
0
1
0
1
2
1
1
2
2
1
1
0
2
2
1
1
0
1
1
0
2
1
0
0
2
2
1
1
1
2
0
0
1
0
1
0
2
1
2
0
0
1
1
0
1
1
1
1
1
1
1
2
0
0
1
2
2
2
0
2
1
1
1
1
1
2
1
2
0
0
1
1
2
1
2
1
0
2
1
0
1
2
0
2
1
2
1
1
0
1
2
0
0
0
2
0
1
1
1
1
1
1
1
0
2
1
2
1
1
0
1
0
1
1
1
2
0
2
0
2
1
1
2
1
2
1
1
1
1
1
0
2
0
2
0
2
1
1
1
2
1
2
0
1
0
1
2
1
2
2
0
0
3
0
1
1
0
0
1
0
0
0
0
1
2
0
2
0
2
1
1
1
1
0
2
1
1
1
2
1
0
1
1
0
1
1
1
1
0
1
0
1
1
1
0
0
1
1
2
1
2
0
0
1
1
0
1
0
1
1
1
1
1
0
1
0
2
2
2
1
1
0
0
1
1
1
1
1
1
0
0
1
1
0
1
1
0
0
1
0
1
1
0
0
1
1
1
1
1
2
0
2
3
0
1
1
2
1
0
3
0
2
1
0
1
2
3
1
1
2
1
1
0
0
0
2
1
1
2
2
1
0
0
1
1
1
1
0
1
2
0
2
1
1
0
1
1
1
1
1
0
0
1
0
2
1
0
1
1
2
2
0
1
2
1
0
2
1
2
0
1
1
1
1
2
1
1
3
1
1
1
1
1
1
2
1
1
0
1
2
2
0
1
1
2
0
0
1
0
1
1
1
1
2
1
1
0
0
0
1
2
1
0
1
2
2
1
1
1
1
1
2
1
1
1
2
2
1
1
2
0
2
2
2
0
1
1
1
1
1
1
1
1
0
2
1
0
0
1
1
0
0
1
1
0
1
1
2
1
0
1
0
0
1
2
1
2
1
1
0
0
2
2
2
1
1
1
1
0
1
1
1
0
1
1
2
0
1
1
1
1
1
0
2
2
1
2
2
1
0
1
1
0
2
1
1
0
1
0
1
0
2
1
0
1
0
3
0
0
2
1
1
2
0
2
2
1
2
1
0
1
2
1
0
2
1
0
1
1
0
1
1
0
1
1
1
1
2
2
0
0
1
1
0
1
2
2
1
1
1
0
1
2
1
1
0
1
0
2
1
1
0
1
2
2
1
1
1
0
1
0
1
1
1
1
2
2
0
1
2
1
2
1
1
2
0
1
1
1
1
1
1
0
0
1
0
1
0
0
0
2
2
1
0
1
2
0
1
0
0
1
1
1
2
1
1
1
0
1
1
1
2
1
0
0
1
1
0
1
1
0
2
1
2
0
2
1
0
1
1
1
0
1
0
1
1
0
1
0
0
1
0
2
1
0
1
1
1
0
1
1
2
3
4
1
2
1
2
2
1
1
1
0
1
0
1
1
1
1
0
1
1
2
1
2
2
0
0
1
0
0
1
1
2
0
1
2
1
1
2
0
0
2
0
1
0
2
0
0
2
1
1
1
1
2
2
0
2
2
2
0
1
1
2
1
1
1
1
1
1
2
2
1
0
0
1
0
1
2
2
1
1
1
0
1
1
1
0
2
2
0
1
1
0
0
0
2
1
1
1
0
2
0
1
1
1
0
0
0
1
2
0
0
0
0
0
2
1
1
0
0
2
1
0
2
2
1
1
1
1
2
0
2
0
2
1
3
1
2
0
0
3
1
1
2
1
1
1
2
1
0
2
0
1
2
1
0
2
1
1
2
0
1
1
1
0
1
1
2
2
1
1
2
0
0
1
0
2
1
0
1
0
0
2
1
0
1
1
1
2
1
2
0
0
3
1
2
0
2
0
2
1
0
1
0
1
2
2
1
1
0
0
1
1
0
2
1
1
2
1
1
1
2
1
2
1
1
2
0
1
0
1
1
1
1
2
1
0
0
0
0
0
1
0
1
1
0
0
2
0
1
1
2
0
2
0
0
1
1
1
2
1
0
2
1
0
2
1
0
1
1
0
2
1
0
0
0
0
1
0
0
0
0
1
1
0
1
1
1
1
1
1
0
0
2
2
2
1
2
1
1
1
2
1
2
0
1
0
1
0
0
1
0
0
1
6
1
2
1
1
1
1
1
1
0
1
1
1
1
1
2
0
0
1
2
1
1
2
0
1
0
0
1
2
1
1
1
1
0
0
2
2
0
1
2
2
1
1
1
1
1
1
0
1
2
1
1
0
1
2
0
1
0
2
0
1
2
0
0
0
0
0
2
0
2
1
1
0
0
2
2
1
2
2
1
0
1
1
1
0
0
0
0
0
1
1
2
0
0
1
0
1
0
1
1
0
1
0
5
2
1
3
0
0
2
2
1
2
1
2
2
1
1
0
1
0
1
0
0
0
1
1
1
2
1
0
0
2
1
1
0
0
1
1
2
1
0
1
1
0
2
0
2
0
1
0
1
0
2
1
1
1
1
0
1
2
2
0
2
1
1
2
1
2
1
1
0
0
1
1
2
3
1
0
1
1
0
1
1
1
1
1
2
1
0
1
1
1
1
1
0
0
0
1
2
0
0
1
1
1
1
0
1
1
0
0
3
1
2
1
0
0
1
1
2
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
2
1
0
2
1
1
1
1
0
1
1
1
0
1
1
0
0
0
1
0
2
1
0
2
1
2
0
0
0
1
0
0
1
1
0
1
1
2
1
1
0
0
1
2
1
0
2
1
1
1
2
0
1
1
1
1
0
1
0
0
1
0
0
1
1
1
0
2
0
2
1
1
0
1
0
2
2
0
0
1
1
0
1
0
2
0
1
1
1
1
1
1
1
0
2
0
0
1
0
2
1
1
1
1
1
1
0
2
1
1
3
1
1
0
2
2
2
2
0
2
1
1
1
1
0
2
1
1
0
1
1
1
1
2
2
0
1
0
1
1
0
0
1
0
0
1
2
0
1
1
1
1
1
1
0
1
1
2
0
0
0
2
0
2
0
0
0
1
2
1
0
2
2
1
0
0
1
1
0
1
0
2
3
2
1
2
1
4
0
2
1
1
0
0
2
1
0
0
1
0
0
0
2
0
1
1
2
1
1
1
0
2
1
1
0
2
0
3
3
2
2
0
3
1
2
0
2
1
0
0
1
0
2
0
2
1
1
2
2
1
1
2
2
0
0
0
0
1
2
0
2
1
1
1
2
2
0
1
1
1
0
1
2
2
1
2
2
1
1
0
1
0
0
1
2
1
0
1
1
1
2
1
1
2
1
1
1
0
2
1
1
1
1
2
2
1
0
1
0
1
0
1
0
0
2
1
1
0
2
1
0
1
0
1
1
1
1
0
1
1
2
0
0
1
0
1
2
1
2
1
2
0
1
1
2
1
0
0
1
1
1
1
3
1
2
1
2
0
0
1
2
2
0
1
0
0
1
1
1
1
1
2
2
0
1
1
1
0
1
1
0
1
1
1
2
0
1
2
3
1
0
2
0
1
2
1
1
0
2
0
1
0
2
2
2
0
1
0
0
1
1
0
0
1
2
2
0
0
1
1
1
1
0
2
0
0
2
0
1
1
0
0
2
1
1
0
1
1
1
0
1
1
1
2
1
1
1
0
1
0
0
0
1
2
1
1
1
1
0
0
1
0
0
0
2
1
1
1
2
1
2
1
0
1
0
1
1
0
1
1
0
0
2
2
2
0
1
0
0
1
2
1
2
0
1
2
0
1
2
1
0
1
0
1
1
2
1
1
2
1
1
1
1
3
1
1
1
2
1
1
0
0
2
2
1
1
0
1
0
3
2
0
0
2
0
0
1
1
2
2
0
1
1
0
2
2
1
1
1
0
0
2
2
1
1
0
0
2
0
0
1
0
0
1
1
0
1
1
0
1
2
1
0
1
0
1
0
1
0
0
1
1
1
1
2
1
1
1
0
1
3
1
0
1
0
1
0
1
0
2
1
1
0
2
1
0
2
1
1
2
1
0
1
1
1
1
0
2
2
1
0
0
1
2
2
0
0
1
1
2
2
0
1
1
1
1
1
1
1
2
0
1
0
1
0
0
2
0
2
2
8
1
2
3
2
1
0
2
0
1
5
0
0
2
1
1
2
1
0
1
2
1
1
1
0
0
1
2
0
0
1
0
1
0
2
1
1
1
2
3
0
1
1
1
0
1
2
2
0
0
1
1
0
0
0
2
3
1
1
1
0
2
0
1
2
1
0
0
0
1
0
1
1
1
2
1
0
1
1
0
0
2
1
1
1
2
0
2
2
1
1
2
1
2
1
0
0
0
1
1
0
1
1
0
0
0
0
1
2
2
0
2
0
1
2
1
0
2
2
2
0
0
1
2
0
0
1
2
1
1
0
1
2
1
0
0
0
4
1
4
2
0
1
1
0
1
1
1
0
2
2
0
1
3
1
0
1
2
1
0
1
1
1
1
0
2
0
1
2
0
1
0
0
2
1
2
1
2
2
2
2
2
2
1
1
1
1
0
1
1
3
2
1
1
1
0
0
1
3
0
1
0
1
0
2
2
1
1
1
0
1
2
1
0
1
1
0
0
1
0
1
0
1
1
0
1
0
0
1
1
0
0
1
0
1
2
0
1
1
1
1
0
1
2
0
0
1
0
2
1
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
1
1
1
1
0
1
1
1
2
1
2
2
0
1
1
1
1
0
0
1
1
1
4
1
1
1
1
0
2
0
1
0
0
0
0
1
0
0
1
1
2
1
0
2
0
2
1
2
2
0
1
0
2
1
1
1
1
0
1
3
0
0
0
0
2
0
2
1
1
1
0
1
1
2
1
1
0
1
1
7
0
1
1
1
1
0
1
0
1
2
1
0
2
2
0
1
0
1
1
1
1
0
0
0
1
0
1
1
1
2
1
1
3
1
1
0
1
2
4
2
0
2
1
0
1
1
0
1
1
1
1
1
1
1
1
1
0
1
1
0
0
1
0
0
2
1
2
0
0
0
1
0
0
1
2
0
0
6
0
2
0
2
1
1
1
0
1
0
1
0
2
0
1
0
1
1
1
1
0
1
0
1
1
2
1
0
1
2
1
2
2
0
0
2
1
0
1
0
1
2
1
0
0
1
0
1
1
1
1
0
1
0
1
1
1
1
6
2
0
1
0
1
1
2
1
0
0
1
2
1
1
0
0
2
0
3
1
0
0
0
2
0
0
2
1
0
2
1
0
1
1
1
0
2
1
2
0
2
0
1
1
0
0
3
2
0
1
1
2
1
1
1
2
2
2
1
1
2
1
0
0
2
0
1
2
2
0
0
3
0
1
2
0
1
0
0
2
0
1
1
0
2
1
2
2
1
0
1
1
1
1
2
1
1
1
2
1
2
0
0
0
1
2
1
1
3
1
1
0
1
1
1
0
2
3
0
1
0
0
2
0
0
1
1
1
0
1
2
0
0
2
0
1
1
2
0
1
0
1
1
1
1
2
1
1
2
2
0
1
3
0
0
1
1
2
0
1
1
1
1
2
0
0
3
1
1
1
0
0
2
1
1
1
0
1
1
0
0
2
0
1
2
1
0
1
0
2
0
0
0
1
1
2
0
1
2
2
1
2
0
1
1
2
1
1
1
0
0
0
2
2
1
1
2
0
1
1
1
1
1
1
1
2
1
1
0
2
1
0
2
1
2
1
0
1
3
1
1
1
1
0
0
1
2
1
2
1
1
1
2
2
2
0
0
1
1
1
3
2
0
1
1
1
0
2
1
2
0
0
1
1
1
2
1
1
1
0
1
2
1
1
3
2
1
2
0
1
2
0
2
0
1
0
0
1
1
1
0
1
2
1
0
4
1
1
2
0
1
1
2
2
0
0
1
0
2
1
1
1
2
0
1
1
2
1
3
0
2
0
0
1
2
1
0
2
1
1
2
0
2
1
1
0
0
0
0
0
2
2
1
1
2
0
1
0
4
1
1
2
1
1
1
1
0
2
1
0
1
1
4
1
0
0
0
0
2
2
1
2
1
1
1
0
1
1
2
1
0
2
0
2
2
2
0
1
1
1
1
1
2
1
1
2
1
1
0
1
1
0
0
2
2
2
1
1
0
1
0
2
1
1
0
1
1
2
2
1
1
0
1
2
0
2
2
1
0
0
1
2
1
0
1
1
0
0
1
0
2
1
1
1
2
0
2
1
1
2
1
2
0
0
0
1
2
0
1
0
1
1
1
2
1
2
0
0
0
1
1
0
2
1
0
0
2
1
1
1
0
1
2
0
0
1
1
1
1
1
2
2
0
3
1
1
0
2
2
1
2
2
1
0
1
0
1
2
0
0
2
0
2
1
0
0
1
2
1
0
2
1
1
1
0
0
1
0
2
1
1
0
1
1
2
1
0
1
1
1
1
1
3
1
0
1
1
1
1
0
2
0
1
0
2
2
1
2
1
2
1
1
2
1
1
0
1
1
1
1
2
2
2
0
0
1
0
0
0
0
0
2
1
2
0
1
0
1
0
1
1
0
2
1
2
2
0
2
0
2
1
1
0
4
2
0
2
0
0
1
1
1
1
1
0
1
2
0
0
1
0
1
1
1
1
1
1
1
2
0
0
0
1
1
0
0
1
1
0
1
1
2
2
2
0
1
1
2
0
1
1
0
1
1
2
1
1
0
1
1
1
2
0
0
1
1
1
0
1
1
1
1
1
0
0
1
1
0
1
1
2
0
2
1
2
0
1
0
0
0
0
2
2
1
0
0
2
0
1
1
2
0
2
1
1
1
0
2
0
2
1
2
1
2
1
1
1
1
1
1
0
1
0
1
0
0
1
1
1
1
1
1
1
2
1
2
0
1
2
0
0
1
1
2
2
2
1
2
1
1
2
1
2
1
0
0
1
0
1
0
2
0
1
2
2
1
0
1
2
1
1
1
1
1
1
2
1
2
1
1
1
1
1
1
1
1
1
0
1
1
0
1
0
1
2
1
2
1
2
1
2
0
1
1
0
0
2
2
2
0
2
2
1
0
0
4
1
1
1
1
0
0
1
1
1
0
2
3
2
0
0
1
0
2
2
1
1
0
0
1
2
0
0
2
1
1
1
2
1
1
1
1
2
1
0
1
2
0
1
1
1
2
1
0
1
2
0
1
2
1
2
0
2
1
0
2
3
1
1
2
0
1
0
2
0
0
1
1
2
1
0
2
1
2
1
2
0
0
2
1
2
1
1
0
0
1
0
2
0
1
1
1
0
0
0
0
1
1
1
1
2
0
0
1
1
1
1
1
2
0
0
1
0
2
1
1
2
2
1
0
0
0
1
0
2
1
1
3
0
1
1
0
1
2
1
0
1
1
1
1
0
0
1
0
0
0
2
1
1
1
1
1
2
1
1
0
1
1
2
0
1
1
1
1
0
0
2
1
0
1
1
2
0
0
1
2
0
1
0
0
0
0
1
1
0
1
1
2
1
0
2
1
0
0
0
2
0
0
1
1
0
2
1
0
1
2
2
0
1
0
2
0
2
1
1
1
0
2
1
1
0
1
2
0
1
1
2
0
1
0
1
0
0
0
0
1
1
0
0
1
1
1
1
2
2
1
0
0
1
0
0
1
2
1
1
0
1
0
0
0
1
1
0
1
1
0
1
0
2
0
1
0
0
0
0
1
2
1
1
1
2
0
2
1
1
1
1
1
0
1
1
1
1
1
0
0
0
2
0
1
0
2
1
2
1
1
1
1
2
1
0
2
2
0
0
0
2
2
1
2
1
1
0
1
1
1
0
2
1
1
1
0
1
0
1
1
1
0
0
2
0
0
2
1
1
0
0
0
0
2
2
1
1
2
2
1
1
1
1
1
2
0
0
1
0
1
2
1
0
1
0
2
2
0
1
1
1
0
2
0
1
2
1
2
1
1
1
2
1
2
1
1
1
0
0
0
0
1
2
2
1
1
1
0
1
1
1
1
1
0
1
1
1
0
0
0
1
0
1
1
1
2
2
1
1
1
1
2
1
1
2
2
0
1
0
1
0
0
2
1
1
0
0
1
0
1
1
1
0
1
1
2
2
0
1
1
0
0
0
0
0
0
1
1
3
2
0
1
1
1
2
1
1
0
0
1
2
2
1
0
1
2
1
1
1
1
1
0
0
1
1
0
2
2
2
1
0
1
2
1
2
1
1
0
0
1
0
1
0
0
2
1
0
1
1
2
1
1
0
1
1
1
1
0
2
0
2
1
1
1
1
2
2
1
0
0
1
0
0
0
0
0
2
0
1
0
0
1
1
1
1
2
1
2
1
1
2
1
0
0
2
1
1
2
0
2
1
1
1
1
0
0
1
0
1
0
1
0
0
0
0
2
1
0
1
1
1
2
0
1
1
1
1
1
1
2
4
0
1
1
1
0
1
0
1
1
0
1
0
0
2
0
1
0
1
1
0
1
0
0
1
2
0
0
0
1
1
2
2
1
1
0
0
2
0
1
1
0
2
0
0
1
2
0
1
2
0
0
1
1
0
2
0
2
1
1
0
0
1
0
1
1
1
1
2
1
2
0
2
2
2
0
1
0
0
1
1
2
1
1
1
1
0
2
0
1
2
0
1
0
1
2
2
1
0
0
1
1
0
0
1
2
0
2
0
1
2
2
0
2
1
0
1
1
0
0
0
1
1
2
0
0
1
2
2
2
1
1
2
2
0
0
2
0
0
3
2
0
0
2
1
1
2
0
2
1
2
1
0
1
0
0
2
2
1
0
0
1
1
1
0
1
1
1
1
0
0
1
1
2
1
0
1
1
1
1
2
2
1
2
1
0
1
0
1
1
0
1
1
1
1
1
0
1
2
2
1
0
2
2
1
0
1
2
0
1
2
1
1
0
1
1
2
1
1
1
2
1
0
1
1
1
0
1
1
2
0
2
0
0
0
2
3
0
2
1
2
0
2
2
0
1
0
1
0
1
2
1
2
2
1
0
0
1
0
0
0
1
1
2
0
1
0
2
0
0
2
1
1
1
0
0
0
1
0
0
1
1
1
1
0
1
2
2
0
1
2
1
2
0
1
0
2
0
1
0
1
2
1
2
2
0
2
1
0
1
1
0
1
0
1
1
0
2
2
0
2
1
2
1
0
1
1
0
1
0
0
2
1
1
1
0
1
1
0
2
1
1
1
1
1
0
0
0
2
2
0
0
0
0
1
1
1
1
0
0
2
0
1
2
1
1
2
0
0
1
0
0
1
2
2
0
1
1
1
1
1
1
0
0
0
1
1
0
2
1
2
0
1
2
0
1
0
0
2
1
1
1
0
1
2
0
1
0
1
1
2
0
0
1
2
2
1
0
0
1
1
0
0
2
0
0
0
1
0
0
0
0
1
0
2
1
0
0
1
0
1
0
1
0
0
2
0
1
1
1
1
1
0
2
2
2
2
0
1
1
1
2
0
0
0
1
1
0
0
2
2
2
1
0
1
1
2
0
0
0
0
2
2
2
1
1
1
0
0
1
1
0
2
1
0
1
0
0
0
1
0
0
1
2
1
2
1
2
1
0
2
1
1
4
0
0
1
0
1
1
2
1
2
1
2
1
0
0
2
2
0
0
1
0
1
0
1
1
1
2
1
0
0
1
0
0
0
0
1
0
1
1
1
1
1
2
0
2
2
2
2
1
1
0
0
1
1
1
0
1
1
1
1
1
1
3
1
0
3
0
1
1
1
1
0
0
2
2
0
0
2
1
0
0
1
0
2
1
1
1
0
1
0
0
1
0
2
2
2
1
0
2
0
1
3
0
0
1
1
0
1
1
1
0
1
0
2
0
1
1
0
1
1
1
1
2
2
1
3
0
1
0
0
1
1
2
1
0
0
0
2
1
2
1
2
1
1
1
0
1
1
1
2
0
0
1
2
1
1
1
1
0
1
1
0
2
1
1
2
2
2
0
2
0
0
2
1
1
1
0
1
1
1
1
1
1
2
2
1
2
0
1
2
2
1
1
2
1
1
2
3
2
3
2
0
0
1
2
2
2
0
1
2
0
1
2
2
2
1
0
2
1
2
1
1
0
2
0
2
0
1
0
0
1
1
1
0
1
0
2
0
1
2
0
0
1
2
2
0
1
0
2
0
0
1
0
1
1
0
1
2
0
2
1
1
1
1
1
1
2
0
1
2
1
0
1
1
2
0
3
2
0
1
1
1
1
1
1
1
0
0
1
1
1
1
0
2
1
2
2
0
1
1
2
2
0
0
1
0
1
1
0
1
1
0
0
1
0
0
1
1
0
1
1
0
1
1
0
1
0
0
1
0
0
1
2
1
2
2
1
1
2
1
1
1
0
4
1
1
0
2
1
1
0
0
2
1
1
1
0
2
0
0
1
1
1
1
1
1
1
0
1
0
1
1
1
0
2
2
0
1
2
2
0
1
1
1
2
1
2
2
1
2
1
2
1
1
0
0
1
1
2
0
1
2
1
0
1
1
2
0
1
2
1
2
1
0
1
1
0
2
1
2
1
1
1
0
1
0
1
1
0
1
2
0
0
1
1
1
0
1
1
1
1
1
0
1
0
2
1
1
1
0
0
1
0
2
1
0
1
0
0
0
0
1
2
0
1
1
0
0
1
0
1
2
1
1
1
1
0
0
0
2
2
0
2
0
1
2
1
2
2
0
2
1
2
0
1
1
1
2
1
1
1
1
0
0
2
0
1
1
2
0
0
1
2
0
4
1
1
0
1
1
1
0
0
1
1
2
1
2
1
1
0
2
1
1
0
1
0
1
2
2
0
0
1
0
1
1
2
1
0
2
0
0
2
1
1
0
1
1
1
0
2
1
1
2
1
1
2
0
2
2
1
0
0
0
1
1
1
2
1
1
0
1
1
1
2
0
0
0
1
1
0
1
1
1
2
2
0
0
1
1
1
0
1
3
1
1
2
1
2
1
1
0
1
1
1
1
2
1
2
0
2
1
1
1
0
0
0
2
2
1
1
2
1
0
0
0
1
2
0
1
0
0
1
0
2
1
0
1
1
0
2
0
1
2
1
2
2
1
1
1
2
2
1
1
1
0
2
1
1
0
0
0
1
0
2
1
1
1
0
2
0
1
2
0
1
0
1
0
1
1
1
2
1
1
0
1
1
2
1
0
2
2
1
0
1
0
0
0
1
0
1
2
1
2
1
2
1
1
1
2
0
0
1
1
2
1
1
1
0
0
2
0
2
1
0
1
1
1
1
1
0
1
1
0
2
1
1
2
1
2
1
1
0
0
0
0
1
1
2
1
1
0
1
1
1
0
2
1
1
0
1
1
1
1
1
0
1
0
1
0
0
1
1
1
0
2
1
1
0
2
1
1
2
3
1
0
1
2
1
0
1
1
2
0
0
1
0
0
5
3
1
0
2
0
0
1
1
0
0
0
1
1
1
1
2
1
0
1
2
0
0
0
1
0
1
2
1
2
0
2
1
0
2
1
0
1
0
0
1
1
1
1
0
0
1
0
1
1
0
1
0
1
2
1
1
1
0
0
1
1
1
2
0
0
2
1
2
1
1
0
1
1
2
1
0
0
1
2
1
2
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
1
0
0
0
2
0
0
1
0
0
1
0
0
0
0
1
2
1
1
2
0
1
1
1
1
0
1
1
0
1
0
1
1
1
1
0
0
2
0
2
1
1
1
1
1
1
1
1
1
0
1
1
0
2
0
1
2
1
1
1
1
1
1
1
0
1
1
0
1
1
1
0
1
1
0
1
1
1
0
0
2
1
1
2
1
1
1
1
1
1
1
2
2
1
0
1
0
1
2
2
1
1
0
1
0
2
2
0
1
1
0
1
0
2
0
2
1
1
1
1
1
1
0
1
1
0
1
0
0
2
2
0
1
3
0
1
1
1
1
0
1
0
1
2
0
2
1
3
1
1
0
1
2
0
0
1
2
0
1
2
0
0
1
0
1
0
2
0
0
0
1
1
2
1
2
0
1
0
2
2
0
1
2
0
1
0
2
1
0
1
0
0
0
2
0
2
2
1
1
1
1
1
0
1
2
2
1
0
1
1
2
1
0
1
0
1
0
2
1
1
1
0
0
0
2
1
2
0
1
2
1
0
2
1
0
1
1
1
0
1
1
0
2
2
1
2
1
1
2
1
1
0
0
0
0
1
1
0
2
1
2
0
1
2
0
2
1
2
0
1
0
1
1
1
2
1
1
0
1
2
1
0
2
2
0
1
0
1
1
0
1
2
2
0
1
0
1
0
1
0
1
1
0
0
0
0
0
0
2
2
0
0
0
0
1
1
0
0
1
0
3
1
2
0
1
2
0
2
0
0
1
0
0
2
2
0
0
1
0
2
0
1
0
3
0
2
0
4
1
0
1
1
2
2
1
1
2
0
1
1
1
0
1
0
0
0
2
0
0
1
0
0
1
1
1
1
1
1
0
0
0
2
0
2
1
2
0
1
2
2
1
1
0
0
2
1
0
0
2
0
0
0
1
0
1
0
1
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
2
0
0
0
0
2
1
1
1
2
0
1
0
2
1
2
2
1
1
2
1
1
0
0
1
1
1
2
2
0
1
1
1
0
2
0
2
1
0
1
2
1
1
1
1
1
0
0
2
0
2
0
2
0
2
0
2
1
0
1
1
1
0
0
1
2
0
0
1
1
1
2
0
1
0
1
1
2
1
1
1
0
1
0
0
1
1
1
2
2
1
2
2
0
1
1
2
3
1
1
0
1
1
1
2
2
1
1
1
0
0
0
0
2
0
1
1
0
0
1
1
1
0
1
2
0
2
0
0
0
1
1
0
1
0
1
2
1
2
0
1
1
2
1
0
1
2
0
1
2
2
0
1
1
1
3
1
1
0
2
2
2
0
0
0
1
1
1
0
0
1
2
2
2
0
1
1
1
0
1
0
0
2
1
1
0
2
0
2
2
1
2
0
0
0
1
2
0
0
1
1
1
1
2
2
1
2
0
2
1
1
0
1
2
1
0
2
1
0
1
1
1
2
2
1
0
1
2
1
1
0
0
1
1
0
1
2
1
1
0
0
0
0
2
2
1
1
2
1
2
1
1
1
2
0
2
0
0
0
0
2
0
1
0
1
2
2
0
0
1
1
0
2
1
0
1
2
1
0
1
0
0
0
0
0
0
2
0
1
0
1
2
0
0
0
2
2
2
1
0
0
1
2
0
1
1
0
2
2
0
0
1
2
0
2
1
0
1
0
1
1
0
0
1
1
0
0
1
1
0
1
0
1
1
2
0
0
0
0
2
1
0
1
1
2
1
1
1
1
0
0
2
0
0
0
1
0
2
0
1
0
1
1
0
1
1
0
2
1
0
1
1
0
1
1
1
1
3
1
0
0
2
2
1
1
0
1
1
0
0
1
1
1
0
0
0
2
2
1
1
1
0
0
1
1
2
1
1
0
0
1
1
2
1
0
1
0
0
2
1
0
0
2
2
0
1
3
1
1
2
0
1
1
1
0
1
1
1
2
0
2
2
1
1
1
1
0
1
2
1
0
2
0
2
1
2
0
1
0
1
2
1
0
3
2
1
2
2
2
1
1
1
2
1
1
0
0
0
0
0
2
0
1
0
0
2
2
0
2
3
1
0
0
0
1
0
0
0
2
1
0
0
1
2
0
0
1
1
1
1
0
0
2
2
1
1
2
1
0
0
0
1
0
1
0
1
0
1
0
1
1
1
0
2
2
1
1
0
0
2
3
1
2
1
1
0
2
1
1
1
3
2
2
2
2
1
1
0
2
0
1
0
1
0
2
2
1
1
1
1
2
0
0
1
0
2
2
0
1
1
0
1
1
1
1
1
0
2
1
2
0
1
2
1
0
0
1
1
0
0
2
1
0
1
1
0
1
1
1
1
0
2
3
1
1
2
1
0
0
1
0
0
0
1
2
0
1
1
1
1
2
2
2
1
1
5
0
1
2
1
1
1
0
2
1
0
1
1
1
0
0
0
0
0
2
1
1
1
2
0
1
1
0
1
1
1
1
3
1
1
1
1
2
2
1
0
1
1
2
1
1
0
1
0
1
2
0
1
1
1
2
1
2
1
2
1
1
0
1
2
2
0
1
1
1
1
1
0
2
0
1
0
1
2
0
1
1
1
1
0
0
0
0
0
1
2
0
0
1
2
0
1
0
2
1
1
0
1
0
2
0
1
0
0
0
1
2
2
1
1
2
1
0
1
2
1
0
0
2
2
1
2
2
1
2
0
3
1
1
1
2
0
2
1
0
1
1
2
1
0
1
1
1
2
1
2
0
1
0
2
1
1
1
1
1
2
1
0
1
1
0
2
1
0
1
1
1
0
2
2
1
1
0
0
0
0
0
2
1
1
0
1
0
1
1
2
1
1
2
1
1
0
2
2
1
0
1
2
2
1
0
0
0
1
1
0
1
1
0
1
1
1
1
1
1
2
0
0
1
1
1
2
2
0
1
2
1
1
0
2
1
1
0
3
1
0
2
3
1
1
0
0
1
1
1
1
1
0
1
0
2
0
0
0
2
2
0
1
0
2
1
1
1
1
2
1
2
1
1
0
1
1
1
1
1
1
0
1
1
1
1
0
0
0
1
1
2
2
0
1
1
1
2
0
1
0
1
0
0
1
2
1
1
0
0
1
0
1
1
1
1
2
2
0
1
2
0
0
1
0
2
1
2
1
2
1
1
0
1
0
0
2
0
1
1
1
1
0
1
3
0
0
1
1
0
0
0
1
3
1
0
1
2
1
1
3
0
1
1
0
0
1
1
1
1
0
1
0
0
1
1
1
0
2
1
0
2
0
1
0
2
1
1
0
1
2
0
1
0
1
1
0
1
1
1
0
1
2
2
1
0
1
1
2
1
2
1
0
2
1
1
1
0
1
0
2
2
0
1
2
0
0
1
1
1
0
2
0
1
1
1
1
1
1
1
2
0
2
1
1
0
0
0
0
1
1
0
0
0
1
1
1
1
1
2
1
1
1
1
1
1
2
0
2
1
1
2
1
0
2
1
0
1
1
1
2
1
0
2
1
1
1
1
1
0
2
0
1
1
1
1
1
1
2
0
1
1
1
0
2
2
0
2
1
1
0
1
2
0
0
0
1
1
1
0
2
0
1
2
0
0
2
1
1
1
0
1
2
0
0
2
0
0
1
1
1
1
1
1
3
2
0
2
0
1
1
2
2
1
0
2
1
1
1
0
0
2
1
1
1
1
1
1
1
1
1
1
1
2
1
2
0
2
0
0
1
2
1
1
2
1
0
1
1
2
0
0
1
1
0
2
0
2
2
0
2
1
1
2
0
0
2
2
0
1
1
1
1
1
2
0
1
2
1
2
1
1
1
1
1
1
2
1
0
1
1
1
1
0
1
0
1
1
1
3
0
1
1
2
1
0
0
0
2
0
2
0
2
2
0
1
2
1
0
2
1
1
2
1
1
1
1
2
0
0
0
1
0
2
1
0
0
0
0
2
0
0
1
1
3
1
1
0
2
1
0
1
1
1
0
1
2
2
1
0
1
0
0
1
2
1
1
0
1
1
2
1
0
2
1
1
2
1
2
0
1
1
1
3
1
1
1
0
1
1
0
2
2
2
1
1
2
0
0
0
1
1
1
0
1
2
2
4
0
1
2
2
0
0
1
1
0
2
0
1
1
1
0
2
1
1
0
2
0
1
0
1
2
0
0
1
1
2
2
0
0
1
1
1
1
0
1
1
0
2
0
2
1
1
1
2
0
0
0
0
1
1
2
1
0
1
1
0
0
2
1
1
1
2
2
1
1
1
0
1
2
2
2
1
2
1
0
2
1
0
0
1
0
1
2
0
2
1
1
0
1
1
1
1
2
1
1
1
1
2
1
2
1
2
3
1
1
0
4
1
1
2
1
2
1
0
1
0
2
1
1
0
1
0
2
2
2
1
0
1
0
0
1
1
0
0
0
0
1
1
0
0
2
1
0
0
1
1
1
2
0
1
2
2
0
1
0
1
7
0
0
2
3
1
0
0
1
3
2
2
1
2
1
1
2
0
2
1
0
2
1
2
0
1
1
0
2
1
1
0
1
0
0
1
1
0
0
0
1
1
2
1
1
0
1
0
0
1
2
1
2
1
1
0
2
0
0
0
1
2
1
0
1
0
2
0
2
1
0
2
0
1
0
2
3
1
2
2
1
1
1
0
0
1
1
0
1
1
0
1
2
2
1
1
0
2
0
2
2
0
1
2
0
1
0
1
2
2
0
1
1
1
1
1
0
1
2
1
1
2
2
0
1
1
1
2
1
1
1
2
1
1
1
1
0
1
2
2
0
1
0
2
0
0
0
2
1
0
1
1
2
1
0
1
0
1
1
1
0
1
2
1
1
2
1
0
2
0
1
2
1
0
2
1
0
1
2
1
1
0
2
1
0
2
1
1
1
2
0
1
2
2
2
2
0
1
2
0
0
0
2
1
1
0
0
2
1
1
0
1
1
1
1
0
2
1
1
0
0
1
0
0
1
1
0
1
2
1
2
2
1
1
1
1
1
1
1
2
1
0
1
1
0
1
2
1
1
1
1
1
1
1
1
0
1
0
0
1
1
1
2
1
0
1
1
2
1
2
0
2
0
0
1
0
0
1
1
3
0
2
0
0
1
0
0
0
1
0
1
0
0
2
2
1
1
0
2
2
1
2
0
1
1
1
1
1
0
0
0
0
2
1
0
2
1
1
0
2
1
2
1
2
1
2
2
1
3
1
2
2
0
1
2
2
1
1
2
0
1
0
2
0
0
1
1
2
1
0
1
1
0
0
1
1
1
0
0
0
1
0
0
2
1
0
2
0
0
0
1
2
1
1
0
1
0
2
2
0
2
1
1
1
0
4
0
1
1
0
1
2
0
0
1
0
0
0
0
0
1
1
1
1
1
2
0
0
1
2
0
0
0
0
0
1
2
0
0
1
2
1
1
1
2
0
1
0
2
1
2
0
0
2
0
0
0
1
1
2
1
1
1
0
2
1
1
1
1
0
0
0
1
2
0
1
1
1
1
1
1
1
1
1
2
0
0
1
1
1
1
0
1
1
1
0
0
1
0
1
0
0
1
1
1
0
0
1
2
0
0
1
0
1
1
1
1
2
0
0
2
0
1
1
1
2
2
2
2
1
1
0
0
2
2
2
1
0
2
1
0
1
0
0
1
0
3
0
2
1
0
1
1
1
1
1
1
0
2
0
0
1
0
0
0
2
1
2
0
1
1
2
0
2
1
1
1
0
1
1
2
1
1
2
0
1
1
2
0
0
2
2
2
2
0
1
2
1
3
0
1
2
0
1
0
2
0
1
0
1
1
1
1
2
1
0
2
0
1
0
0
0
1
1
1
0
1
0
2
2
2
1
2
2
2
0
1
2
0
2
0
1
1
1
1
1
1
1
1
1
2
2
2
0
1
2
2
0
0
2
1
2
2
1
0
0
0
0
1
0
0
1
1
0
1
1
0
1
0
0
0
0
0
0
1
1
2
1
2
1
2
1
2
0
0
2
0
0
2
1
0
1
1
1
0
1
2
2
1
0
1
1
1
1
1
1
2
0
0
2
0
1
1
0
1
0
0
2
1
0
0
1
1
1
2
1
1
2
0
2
0
1
2
1
1
1
0
1
1
0
2
1
1
1
2
0
0
2
1
0
0
0
1
1
1
0
0
1
1
1
0
0
0
1
0
1
0
1
2
2
2
2
0
1
2
2
1
1
1
1
1
1
1
2
1
1
1
3
2
1
1
0
0
1
0
1
2
1
0
0
2
1
1
0
1
0
1
1
0
0
1
0
0
1
1
1
2
2
1
2
1
2
0
1
2
2
1
2
2
1
1
2
2
1
1
1
1
0
1
1
1
1
1
1
2
1
0
2
0
0
1
1
1
1
1
1
1
0
2
1
0
1
1
1
1
1
1
1
0
2
1
1
2
2
1
1
0
0
2
1
1
2
0
1
1
0
0
2
0
0
1
1
2
0
0
1
0
0
3
1
2
0
2
1
3
1
2
1
0
1
1
0
1
1
2
1
0
1
0
0
0
2
1
2
1
2
2
0
0
2
1
0
0
2
1
1
1
1
1
1
0
0
2
1
1
2
1
1
1
1
2
2
1
0
1
1
1
2
1
0
1
1
2
1
0
0
1
0
1
0
1
1
1
0
1
0
2
1
2
2
0
0
0
1
1
0
2
2
0
1
1
0
1
2
1
1
0
0
2
2
1
1
0
0
0
1
2
0
1
0
0
0
1
2
0
0
2
1
1
1
2
1
0
1
0
2
1
0
1
1
0
1
2
1
0
1
0
2
0
1
0
0
1
1
2
1
1
0
2
1
2
0
2
0
2
1
2
2
2
2
1
3
0
0
1
2
2
1
1
1
2
0
2
1
1
1
0
0
0
2
0
0
2
0
0
2
0
1
0
0
2
0
1
1
1
1
2
1
2
1
2
1
2
1
2
0
0
0
1
2
2
1
1
0
0
1
2
0
3
0
1
1
1
1
1
1
2
1
1
0
1
1
0
4
1
1
2
1
1
2
2
0
2
1
1
2
0
2
1
1
1
1
2
1
1
1
2
0
0
1
0
1
0
1
0
1
3
1
1
0
1
0
2
2
0
1
0
1
0
1
1
1
2
1
2
2
2
2
1
2
0
2
2
0
1
1
0
2
2
2
2
1
1
1
1
0
1
1
0
1
1
1
0
0
0
0
3
1
1
1
1
1
1
1
2
0
2
1
1
1
2
0
0
1
1
1
1
0
0
0
1
1
0
1
2
1
0
0
2
0
1
3
1
1
2
1
2
1
1
1
1
1
0
1
1
0
2
1
1
1
2
0
1
2
2
2
1
0
2
1
2
2
0
0
0
1
1
1
1
2
1
0
1
0
0
1
1
1
0
1
0
1
1
0
0
2
2
1
0
1
1
1
1
0
1
1
0
2
4
0
0
0
1
1
1
1
1
1
1
2
1
0
2
1
0
1
1
1
1
1
1
1
0
0
0
0
1
0
1
2
0
1
1
1
2
2
1
2
0
0
1
0
1
1
0
0
2
0
0
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
2
0
1
2
0
0
0
2
2
1
0
1
0
2
1
3
0
0
0
1
0
1
1
1
0
1
1
0
1
1
0
0
1
1
1
0
0
1
0
2
2
2
1
0
0
1
1
1
2
0
0
3
0
0
1
2
2
2
1
0
1
3
1
2
1
1
2
0
0
1
2
1
0
2
1
0
1
1
0
0
0
2
1
1
0
2
0
1
0
0
1
1
0
0
0
1
1
0
1
1
1
1
1
2
2
1
1
1
2
2
0
1
0
1
2
1
1
1
2
0
2
1
1
2
1
0
2
3
2
1
0
0
2
0
2
1
1
1
2
0
0
1
1
2
1
1
2
1
1
1
1
1
1
1
0
1
1
1
2
1
0
2
2
0
1
2
1
1
1
0
0
1
0
0
1
1
1
2
2
2
0
2
1
0
1
1
0
1
1
2
0
1
1
1
1
0
0
1
1
0
0
1
1
0
1
0
0
1
1
2
1
1
1
0
0
1
2
2
1
2
1
1
1
0
0
1
2
0
1
1
0
0
1
1
0
0
1
0
2
1
1
1
1
2
2
1
1
0
1
1
0
1
1
1
1
2
0
1
2
0
1
1
1
0
0
0
0
0
1
1
0
1
1
0
1
2
0
3
1
0
1
1
0
1
1
1
0
1
2
2
1
0
1
0
1
0
0
1
0
1
0
0
0
2
1
1
1
0
0
2
1
2
1
2
1
0
1
2
0
2
3
0
2
2
1
2
2
0
0
1
1
0
0
1
2
1
0
0
1
1
1
1
0
2
0
0
0
2
1
0
2
0
0
0
1
0
1
0
1
1
2
0
2
1
1
1
1
1
1
0
2
0
2
2
1
1
0
1
1
1
0
0
2
0
0
1
0
1
2
1
0
5
2
0
2
1
2
0
1
1
0
2
1
0
1
2
4
0
1
0
1
0
1
0
1
3
0
0
2
3
1
1
2
1
0
2
1
1
2
0
1
0
1
0
0
1
1
1
0
0
0
1
2
1
1
2
0
0
1
1
0
1
1
0
2
0
0
2
2
1
2
1
2
2
0
0
0
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
0
1
0
1
1
0
0
0
2
0
0
1
1
0
1
1
1
1
0
0
3
1
0
0
1
1
2
1
1
2
1
0
2
1
2
1
2
1
0
2
1
2
1
2
1
2
1
1
0
1
1
0
0
2
1
1
0
0
1
0
1
1
2
1
0
2
1
0
0
1
0
1
2
0
0
0
0
1
1
1
0
0
2
1
3
1
1
1
0
2
1
0
2
0
0
2
1
2
0
1
1
1
0
0
0
1
0
1
2
0
1
1
1
2
1
1
1
1
0
2
1
2
0
1
2
0
0
1
0
1
1
0
1
0
0
0
2
0
1
0
0
2
0
1
1
2
1
2
1
1
1
0
1
1
3
1
1
2
0
0
0
1
0
2
0
0
2
2
1
0
2
1
0
2
1
2
0
2
1
0
2
2
1
1
1
0
2
0
1
1
0
2
0
1
2
1
1
1
2
1
0
0
0
1
0
2
0
0
1
1
0
2
1
1
2
1
0
1
2
0
1
2
1
2
1
0
1
1
0
0
1
1
1
1
0
1
0
2
2
2
1
0
0
0
0
1
0
0
1
0
2
2
2
1
0
0
1
0
1
1
0
1
0
1
2
0
2
2
1
0
1
2
2
1
1
0
1
1
2
1
2
1
0
2
1
0
1
2
0
2
1
1
1
0
0
2
1
6
0
1
1
1
1
1
1
1
1
2
0
0
0
1
1
1
1
0
1
0
0
2
5
1
1
2
1
1
0
2
0
1
0
1
0
2
0
1
0
0
2
1
1
2
1
0
0
0
0
1
0
0
0
1
2
2
0
1
1
1
3
0
0
1
1
0
3
0
0
2
1
1
1
2
1
0
1
0
0
1
1
1
1
1
1
1
0
0
0
1
1
1
1
1
0
1
1
2
2
1
0
0
1
1
0
3
1
2
2
0
1
1
2
0
1
0
2
3
1
1
1
1
1
2
2
2
1
0
1
0
0
2
1
1
1
0
0
2
0
1
1
0
0
1
2
1
1
1
1
1
0
2
2
0
2
1
2
1
1
1
0
0
1
2
1
1
1
0
2
2
1
1
1
1
0
1
2
2
0
1
0
0
1
1
1
1
0
0
0
1
0
2
2
0
2
1
1
0
0
0
2
2
2
0
1
0
0
1
1
0
1
1
0
0
0
1
1
1
1
2
2
1
2
0
1
1
1
0
1
1
1
0
1
2
1
2
1
1
1
1
2
0
0
2
1
0
2
2
0
1
0
1
2
1
1
2
1
1
1
0
0
1
0
2
0
2
0
1
0
0
1
1
4
1
0
0
0
1
2
2
2
2
1
1
1
0
0
1
0
0
2
1
1
0
2
1
0
0
1
1
2
0
2
1
0
1
1
1
1
2
0
2
0
2
1
1
1
0
0
2
1
1
1
1
2
1
1
1
0
1
1
0
2
1
3
2
2
2
2
0
1
1
1
2
1
1
0
2
1
1
1
1
2
1
1
2
1
2
0
2
0
0
0
1
0
5
0
1
0
1
2
0
1
1
2
0
1
1
1
0
1
0
2
0
1
1
0
1
0
0
1
0
1
1
1
2
1
1
0
1
0
1
2
1
1
0
0
1
1
0
2
0
1
1
2
2
1
1
1
3
1
1
1
0
1
1
0
2
1
1
1
2
2
1
0
1
1
1
1
0
1
2
1
2
1
0
2
1
2
2
2
2
1
1
0
1
2
1
0
0
2
1
1
1
1
1
0
2
2
0
2
1
0
0
2
1
1
0
1
1
1
2
2
1
1
0
2
2
1
1
1
0
0
2
0
0
2
1
0
0
1
2
1
0
0
1
1
2
2
1
0
1
2
1
2
0
0
1
0
2
1
1
2
1
0
0
0
1
1
2
2
0
0
0
1
0
1
1
1
1
0
0
1
1
1
0
0
0
1
1
1
1
1
2
1
1
1
1
0
1
1
1
1
1
1
2
1
0
1
2
0
2
2
2
1
0
1
1
1
2
1
1
0
2
1
1
1
0
2
0
0
4
1
0
1
0
0
2
1
1
2
2
1
1
0
1
0
2
1
1
1
1
1
2
0
0
0
0
0
1
1
1
1
1
0
0
2
2
1
0
1
1
0
0
2
2
1
2
1
0
2
0
1
1
0
0
2
1
2
1
1
1
0
1
1
1
0
1
1
0
1
0
1
0
0
1
1
1
0
0
0
2
1
0
0
0
2
0
1
1
1
2
0
2
2
1
1
0
1
1
1
0
0
1
0
0
1
1
1
0
0
1
2
1
1
1
0
1
1
1
1
0
0
2
2
1
1
2
0
1
1
0
0
3
2
1
2
1
1
0
1
0
2
0
0
2
0
2
0
0
1
1
1
2
2
0
0
0
1
0
1
0
1
0
1
0
2
1
0
1
2
1
1
1
0
0
1
1
0
2
0
0
2
0
2
0
0
2
0
1
0
0
0
0
2
1
0
0
2
1
1
1
2
0
1
1
2
1
2
1
0
1
1
2
0
0
0
2
0
0
1
1
1
0
1
0
2
2
0
0
0
0
1
1
0
1
1
0
0
1
2
0
0
1
2
2
1
1
0
1
1
0
1
0
0
2
1
1
0
1
1
1
2
1
1
2
0
1
1
0
0
1
1
1
2
2
2
1
0
1
0
0
1
0
2
1
2
0
2
1
0
1
0
0
1
1
2
2
2
1
2
0
1
0
0
1
1
0
0
1
1
0
0
2
1
0
1
0
1
2
0
2
1
2
2
1
1
2
1
0
2
0
2
2
1
1
1
1
1
1
0
1
1
2
1
0
1
0
0
0
2
2
1
1
1
2
1
0
0
1
2
4
1
1
0
1
0
1
0
2
3
0
2
1
2
0
0
2
2
1
1
1
1
0
1
2
2
2
2
0
2
1
0
1
1
2
1
2
1
1
1
2
0
0
2
1
1
0
0
0
1
1
0
1
1
0
1
2
1
2
2
1
0
0
0
1
0
2
1
0
1
2
0
1
1
2
1
1
1
0
1
1
0
2
0
0
2
0
1
1
2
0
1
1
4
0
1
1
0
1
0
0
0
0
2
0
1
1
1
0
1
2
2
2
0
1
2
1
1
2
1
0
1
0
4
0
1
2
0
1
1
1
1
0
2
1
0
1
1
0
3
1
1
1
1
1
1
2
1
3
1
1
2
0
0
2
2
1
2
0
1
0
1
0
2
1
1
2
2
0
1
2
1
1
2
1
1
0
1
0
1
1
0
0
1
1
1
1
1
2
2
2
0
1
1
0
1
1
1
0
0
0
1
0
1
0
2
1
1
1
1
1
0
0
1
1
2
0
0
1
1
0
1
2
1
1
0
2
1
1
0
2
1
0
1
0
0
0
1
1
0
2
1
1
0
0
1
1
1
1
1
2
1
1
0
0
0
1
0
0
1
0
2
1
3
0
0
2
1
2
1
1
0
1
1
1
2
0
1
0
0
0
1
1
0
1
0
1
0
0
1
0
1
2
1
0
2
2
1
2
2
1
0
0
1
1
2
2
1
0
1
3
2
1
2
1
1
1
2
2
0
2
0
1
0
0
2
1
1
1
1
0
1
1
0
1
1
1
0
1
1
1
1
1
0
1
0
0
0
1
0
2
2
1
0
2
1
0
0
0
1
1
1
1
1
1
1
2
1
1
2
0
1
1
1
1
0
0
1
1
1
0
1
0
1
0
3
0
0
2
0
0
1
1
0
1
2
1
2
1
1
0
1
1
0
3
1
1
0
1
1
1
1
2
0
0
4
0
1
0
0
1
1
1
0
1
0
1
2
0
1
0
2
1
3
2
1
0
1
2
2
1
2
1
1
0
1
0
1
1
0
1
1
0
0
0
0
1
0
7
0
1
0
2
1
2
1
2
1
1
2
0
1
1
2
2
2
1
1
0
2
0
0
0
1
0
3
0
1
0
1
0
1
2
1
1
1
0
0
2
2
1
1
1
0
0
1
1
1
2
2
1
0
1
1
0
1
1
0
1
1
1
2
0
2
1
1
0
0
1
0
12
0
2
1
2
0
0
2
2
0
1
2
1
1
1
1
0
2
2
2
2
0
0
0
2
0
1
2
1
1
0
2
1
1
0
0
1
2
0
0
1
2
2
0
2
2
0
0
1
1
0
1
0
2
0
1
1
0
2
0
1
1
0
1
1
1
0
0
2
0
0
0
2
0
1
2
1
0
0
2
1
0
0
0
2
0
2
2
2
0
0
2
0
0
1
0
0
0
1
0
2
0
2
1
2
1
3
1
0
0
0
1
1
1
0
1
2
1
0
1
2
0
2
1
0
1
1
0
0
1
0
1
1
0
2
1
3
0
1
2
2
1
1
2
0
1
1
0
0
1
1
0
1
1
0
2
1
1
0
0
1
1
0
0
1
1
0
0
1
0
0
1
2
0
0
1
2
0
1
0
1
1
2
1
1
1
2
2
2
0
0
0
2
1
1
0
1
1
0
0
0
2
1
1
3
1
1
1
2
2
1
0
0
0
1
1
1
1
2
1
1
1
1
0
1
2
0
2
1
2
2
1
1
2
1
1
3
1
1
4
0
2
0
2
1
0
0
1
1
0
2
0
0
1
0
2
0
1
1
2
1
1
1
0
0
0
1
0
0
0
1
1
1
1
1
0
0
0
1
0
2
0
0
0
1
2
1
0
2
1
2
1
1
1
0
0
0
3
0
2
0
0
1
0
2
2
0
0
1
1
1
1
1
0
1
0
1
1
1
0
1
0
0
1
2
1
1
0
1
0
0
1
1
1
0
2
2
0
1
1
2
1
0
2
2
1
0
2
1
2
2
0
0
2
2
2
1
0
1
1
0
1
0
1
1
0
1
2
1
0
2
1
2
1
1
0
0
1
0
2
0
1
0
0
2
1
2
0
1
2
2
0
1
0
1
2
0
1
1
1
0
0
2
1
1
1
0
1
2
2
1
0
2
1
1
2
0
0
2
0
1
2
1
1
1
2
1
0
1
0
2
1
0
1
1
1
1
1
0
1
0
2
0
1
0
1
1
2
0
0
2
0
0
0
1
0
1
0
2
1
1
1
1
1
2
0
2
0
1
0
1
0
0
1
1
1
3
2
0
1
1
1
1
0
1
2
1
1
1
1
0
0
0
0
1
2
2
2
1
0
0
2
2
2
0
0
0
1
0
1
0
2
1
0
1
2
0
4
0
1
0
0
0
2
1
1
1
0
1
0
1
2
1
2
0
1
1
1
1
2
0
1
1
1
1
2
2
0
1
0
1
3
0
0
0
0
1
0
2
1
1
0
0
1
2
0
1
0
0
0
1
1
0
2
1
1
0
0
1
1
1
0
1
1
1
2
2
1
1
0
1
0
1
0
0
0
0
0
1
1
2
1
1
0
0
1
1
1
1
0
1
2
2
3
0
2
1
2
0
0
0
1
0
1
1
2
0
1
1
1
1
0
1
2
0
0
0
2
1
1
1
0
1
0
1
2
3
0
2
2
1
0
1
0
0
1
1
1
0
0
1
1
1
1
1
1
0
0
1
0
1
0
0
0
2
0
1
1
1
2
0
1
1
1
0
2
1
2
6
1
1
0
2
0
0
1
2
1
1
1
1
2
2
1
0
1
0
0
2
0
1
2
1
2
0
0
1
1
1
1
1
1
2
1
2
1
2
0
1
1
2
0
0
1
1
1
1
2
0
1
0
1
1
0
1
1
2
1
1
1
2
0
2
0
1
2
0
1
1
1
2
2
0
0
1
3
2
1
0
2
2
0
0
0
2
1
1
0
2
1
0
1
0
0
0
1
0
3
1
0
1
2
1
2
2
1
0
1
1
1
1
0
0
0
1
1
1
1
0
2
1
0
0
1
2
0
1
0
0
2
1
1
1
0
2
2
0
0
2
1
2
1
0
3
0
1
2
0
1
1
1
1
1
1
0
2
0
2
2
1
1
0
1
0
1
1
1
1
1
2
1
1
0
2
1
0
1
0
2
1
2
3
0
1
0
0
0
1
3
1
2
1
1
0
1
2
1
1
0
0
0
0
1
1
2
1
0
2
2
1
1
1
5
0
1
1
1
0
1
2
2
1
1
0
1
1
1
1
1
1
1
0
2
1
1
1
2
2
0
2
1
0
1
1
1
1
2
1
1
1
2
1
0
1
4
2
1
2
0
1
1
0
2
2
1
1
0
0
2
2
0
1
2
1
1
2
1
1
1
1
1
1
2
1
2
2
1
1
1
0
1
1
1
1
1
0
0
0
1
2
1
0
1
0
2
1
1
1
1
0
1
2
0
0
0
1
2
2
2
1
1
0
0
1
2
1
2
1
0
1
1
1
0
1
2
0
1
1
1
1
0
1
1
2
1
1
2
0
1
0
1
1
1
1
0
1
1
1
0
5
0
2
1
1
0
1
1
0
2
1
1
1
1
1
0
1
1
2
0
1
1
1
1
1
2
1
0
1
2
0
1
1
1
1
1
2
1
1
1
0
0
1
1
0
0
1
1
2
0
2
0
2
0
2
0
1
0
0
1
1
1
2
2
2
1
2
1
1
0
0
1
0
1
1
2
2
2
2
0
2
1
0
1
1
1
2
1
1
0
2
0
1
0
0
2
1
1
1
1
1
0
0
1
0
1
1
1
2
0
0
1
0
2
1
0
1
1
2
1
2
0
1
0
1
1
1
0
0
0
1
0
1
1
0
2
2
2
0
2
0
2
0
1
1
0
2
1
0
0
0
2
2
1
1
2
0
0
2
1
0
1
0
2
2
0
0
1
1
1
0
0
0
3
1
0
0
0
2
0
1
1
0
1
0
1
1
0
2
1
1
1
0
1
3
1
1
0
1
2
0
1
0
1
0
1
1
2
1
0
2
0
0
0
2
1
0
1
1
1
0
2
1
1
1
1
0
1
1
1
1
1
0
1
1
1
1
2
2
0
0
0
0
0
0
0
1
0
1
1
1
0
2
1
1
2
1
1
1
1
0
1
0
1
0
0
1
0
1
1
1
2
2
0
2
0
0
1
1
0
1
1
1
1
1
0
2
1
1
0
0
0
0
0
1
3
1
1
0
2
0
1
0
0
0
2
1
2
1
1
1
1
0
1
1
0
0
1
1
1
0
1
1
0
1
1
1
2
0
0
1
0
1
1
1
2
0
2
0
2
0
1
1
0
0
0
0
1
1
1
1
0
0
1
1
2
0
0
1
1
2
1
1
0
0
0
1
0
1
1
2
0
2
1
2
2
1
2
0
0
2
1
1
2
0
0
1
3
0
1
2
0
1
1
0
2
0
0
1
1
2
2
1
1
1
3
1
1
0
1
0
0
2
0
0
1
0
1
1
3
1
1
1
1
0
0
2
1
1
0
1
2
1
0
1
2
0
2
0
2
0
0
2
0
2
0
1
0
1
2
0
1
2
1
0
1
0
1
2
0
0
1
1
1
1
1
2
1
2
0
0
1
1
0
0
1
1
2
1
2
1
0
0
1
1
0
0
0
1
1
0
2
1
2
1
1
1
1
1
1
1
1
0
0
0
0
1
1
1
1
0
2
0
0
1
2
1
0
1
1
1
1
0
0
0
0
0
0
2
0
2
1
1
2
0
2
0
1
0
1
1
1
1
2
2
2
1
0
1
0
0
3
2
2
1
1
2
1
1
1
3
0
2
0
0
0
2
0
1
1
3
2
1
0
1
0
0
1
1
1
2
1
0
0
1
1
2
2
2
0
2
0
2
1
1
0
0
1
0
2
1
7
1
2
1
1
0
2
0
1
0
1
1
0
1
1
1
2
0
0
1
1
0
1
0
2
0
1
1
0
2
0
1
1
1
0
0
0
0
1
1
1
2
0
1
2
1
1
1
1
1
1
0
0
0
1
0
2
0
1
1
0
1
1
1
1
1
1
0
0
1
0
1
1
1
0
1
1
0
2
1
0
0
1
1
1
1
2
1
0
1
1
0
1
0
0
0
2
1
1
1
1
0
1
0
0
0
0
1
1
1
0
0
1
0
1
1
0
2
1
1
1
0
1
1
0
0
0
0
2
2
1
1
1
0
0
0
2
1
1
1
1
1
1
1
0
0
0
1
1
0
1
0
1
2
0
1
0
0
1
1
0
1
1
1
2
1
0
1
2
1
0
0
0
0
1
1
1
0
0
1
0
0
1
2
1
0
1
1
1
1
2
1
2
1
2
0
0
1
0
0
0
1
0
1
0
0
1
0
2
2
2
1
2
1
1
1
0
0
0
1
0
2
0
0
2
1
1
1
1
1
2
2
0
2
1
1
1
0
1
2
1
0
1
1
2
1
0
0
0
1
1
0
1
0
2
2
1
1
2
1
1
2
1
1
1
4
2
1
1
2
0
1
0
1
1
1
0
0
1
0
0
1
0
1
1
2
1
1
2
0
0
1
0
1
0
1
2
1
0
0
1
0
1
1
0
1
0
1
0
1
2
1
0
1
0
0
1
0
0
2
1
0
2
1
1
0
1
2
0
1
3
0
2
1
1
0
0
1
0
0
1
1
1
1
1
2
2
1
1
2
0
2
1
2
2
0
0
1
2
0
0
2
1
1
0
1
0
2
0
2
0
1
0
1
2
0
0
1
0
0
0
1
0
0
2
1
1
0
2
2
1
2
1
1
0
0
1
1
0
0
0
1
1
1
0
1
1
1
1
2
1
2
1
0
0
0
0
0
0
1
2
0
0
1
2
0
1
2
1
2
1
2
2
1
1
3
1
2
2
2
1
2
10
1
1
0
1
2
1
0
2
2
1
1
2
0
0
0
1
1
1
1
2
1
2
0
0
0
1
2
0
1
0
0
2
2
2
1
1
2
1
2
1
0
0
0
2
1
1
0
1
0
0
0
1
2
2
1
0
1
1
1
1
0
1
2
1
0
1
1
0
1
2
1
1
2
1
2
0
1
3
0
0
1
1
1
0
2
0
1
0
1
0
1
1
1
0
0
1
1
2
0
1
2
1
0
1
0
2
1
0
2
0
1
1
1
0
1
0
2
2
0
1
1
2
0
0
0
0
1
1
2
0
0
0
3
1
1
1
0
2
2
0
1
1
2
1
1
1
0
1
2
0
1
1
1
2
0
0
2
1
0
1
1
1
2
1
1
0
1
1
2
1
2
1
0
0
1
1
0
2
1
1
1
1
2
0
1
0
1
0
0
1
0
0
1
2
2
1
1
2
2
1
0
1
0
1
0
1
1
1
2
1
0
0
1
1
1
0
2
1
1
1
0
0
0
2
0
1
2
1
0
0
2
0
1
1
1
0
0
2
0
1
0
0
0
0
2
0
0
2
1
1
1
3
0
0
2
2
1
0
1
0
1
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
1
1
0
1
1
1
1
0
2
0
1
1
2
0
1
1
2
2
0
1
0
1
1
2
1
0
1
2
1
0
2
1
0
0
0
2
0
1
1
1
1
1
0
2
1
2
3
1
0
1
0
1
0
1
1
1
0
0
0
0
1
2
2
3
0
1
0
1
1
0
0
1
0
3
2
1
0
2
0
2
1
2
0
1
1
1
0
2
0
1
0
1
0
0
1
1
1
0
1
1
0
1
2
0
2
1
2
0
1
0
1
2
0
1
1
1
0
0
0
2
0
0
1
1
2
0
0
1
1
2
1
1
2
2
1
0
1
1
7
2
1
1
0
1
2
0
1
0
2
0
2
1
0
0
1
1
1
1
1
1
0
2
0
1
1
1
1
2
0
1
2
0
1
2
0
1
2
1
0
1
0
2
1
1
0
2
0
0
2
0
2
2
0
0
1
1
0
1
1
0
2
0
1
1
2
1
1
1
2
2
1
1
1
1
1
0
1
1
2
0
0
1
1
1
2
0
1
2
0
1
1
0
0
1
1
0
1
2
0
0
1
0
1
0
1
0
0
1
1
0
1
0
2
1
0
2
1
0
1
0
2
2
1
0
1
1
1
1
2
1
1
0
1
2
0
2
0
0
0
1
1
2
0
2
0
1
1
1
0
2
0
2
1
2
2
1
1
1
1
1
1
1
0
0
1
1
0
1
1
1
1
0
1
1
2
0
2
1
0
2
1
1
3
1
1
1
1
2
0
2
3
2
0
0
1
0
0
1
1
1
1
2
1
1
0
2
2
2
1
1
2
0
0
1
1
2
1
1
2
0
1
0
0
2
0
2
2
1
0
0
2
2
0
0
1
1
2
1
1
1
1
0
0
2
0
2
1
0
2
1
0
0
1
1
0
1
1
0
1
1
0
1
3
1
0
1
1
0
1
1
0
1
1
0
0
1
2
2
2
0
0
1
1
2
1
1
1
0
1
1
2
1
0
0
2
1
1
1
2
1
1
0
0
0
2
2
0
1
2
0
0
2
0
1
1
0
1
1
2
2
1
1
2
2
1
1
0
1
1
0
0
2
0
1
2
2
1
0
0
2
2
2
2
1
1
2
0
0
1
0
2
2
1
0
1
2
2
0
2
1
1
1
0
0
1
2
1
1
0
0
2
0
0
1
1
1
0
1
2
0
0
0
2
1
1
1
0
0
2
1
1
1
1
1
2
0
0
2
3
1
0
1
1
2
1
1
3
0
2
0
0
0
0
1
0
0
0
0
2
1
1
1
1
1
1
1
1
2
1
2
4
1
1
2
1
0
1
1
1
2
1
1
1
1
1
1
0
2
1
2
0
1
2
0
1
1
6
0
1
1
0
1
1
0
1
0
1
0
0
1
2
0
1
1
1
1
2
1
0
1
2
0
0
1
0
1
0
1
0
1
0
2
1
1
2
0
1
1
1
1
2
1
2
1
2
1
2
1
0
1
1
1
1
0
3
2
1
2
1
1
2
1
1
2
0
1
0
0
1
1
1
1
0
2
3
1
0
0
0
1
2
1
1
0
1
1
0
1
1
0
0
1
2
1
0
2
1
1
1
2
2
2
2
1
0
0
1
2
1
2
1
1
1
0
2
0
1
1
2
2
1
1
2
1
2
1
2
0
1
1
2
1
2
0
1
2
2
0
2
1
1
1
2
2
3
0
2
2
1
1
1
1
1
1
1
1
0
2
2
1
0
1
1
2
0
2
0
1
1
1
1
0
0
2
1
2
2
2
1
0
0
1
1
3
0
1
0
1
0
2
0
1
2
0
2
2
1
1
0
0
0
1
1
2
0
2
2
1
2
0
0
0
1
1
2
1
1
1
1
2
0
1
1
2
2
0
1
2
0
1
3
1
1
2
0
2
2
1
1
0
1
0
0
1
0
1
2
0
0
2
1
0
1
1
1
1
0
1
2
1
2
0
1
0
0
1
1
1
0
1
2
1
1
1
3
1
4
1
1
1
0
0
3
2
0
1
0
1
0
1
0
1
2
0
0
4
2
1
1
1
2
1
1
0
2
2
1
1
0
2
1
1
0
3
2
3
1
1
1
0
0
2
0
1
1
0
1
0
0
0
1
1
1
1
1
1
0
1
1
1
1
1
0
4
2
2
1
0
0
0
0
2
1
1
1
1
2
1
2
2
1
0
0
1
0
1
0
1
0
1
1
1
0
2
1
1
0
2
1
1
2
2
0
1
0
1
1
0
1
1
0
2
0
2
1
1
1
1
1
2
2
1
1
1
0
0
1
1
2
2
2
0
1
1
1
2
2
0
1
0
0
1
1
0
1
1
0
0
1
2
1
1
2
1
1
1
2
0
1
0
0
0
2
1
1
1
2
2
0
2
0
0
0
2
0
0
0
1
0
1
1
1
0
2
2
0
1
1
2
1
1
2
0
1
1
2
1
1
1
1
1
1
2
1
1
0
1
1
3
1
0
1
0
0
2
1
2
1
0
1
2
2
1
1
0
0
0
2
1
0
1
0
1
1
3
1
2
0
2
1
2
1
0
0
1
0
0
0
2
1
1
0
0
2
2
0
1
1
2
2
1
0
0
1
2
1
0
1
2
0
0
0
2
1
1
1
2
0
0
0
0
1
0
0
1
0
2
1
0
1
0
1
0
1
1
1
1
0
2
1
1
0
1
0
0
1
1
2
2
1
1
2
1
0
0
0
2
1
1
0
0
1
1
1
0
2
1
1
1
1
0
1
0
1
1
0
1
1
0
0
1
0
1
1
1
1
0
1
1
0
1
1
0
0
1
1
1
1
1
2
0
1
0
1
1
2
2
0
2
1
0
0
1
0
1
1
1
1
2
1
1
0
1
2
1
1
3
1
2
2
0
0
0
1
1
0
1
1
1
1
0
0
0
2
1
1
2
2
1
2
0
0
1
3
2
1
2
2
2
2
0
1
2
1
1
1
1
1
2
1
0
0
1
0
1
0
0
0
1
1
2
1
1
1
1
1
0
0
1
2
0
1
2
0
0
0
1
1
0
0
0
2
0
0
2
1
2
0
1
2
1
0
0
2
1
1
1
1
1
2
1
0
1
1
1
1
2
1
0
1
0
1
2
0
1
1
1
2
0
2
0
2
0
2
1
1
0
1
2
0
2
1
1
1
0
2
0
1
0
0
2
0
1
1
1
0
0
1
0
0
2
0
0
1
2
1
2
0
0
1
2
2
1
1
1
1
0
0
1
2
1
0
0
2
1
2
0
1
0
0
2
0
1
1
0
2
1
2
2
1
0
0
1
2
0
1
2
1
1
1
0
2
1
2
1
1
0
0
1
1
0
0
0
0
1
1
1
0
1
1
0
6
2
1
1
0
2
1
0
1
0
0
1
0
1
1
1
0
1
1
0
0
1
1
1
0
1
1
2
1
0
2
0
2
1
2
1
1
1
2
1
1
2
1
0
0
2
0
2
0
2
2
0
0
2
1
0
0
1
1
4
2
0
1
2
1
1
0
1
2
2
2
0
2
1
2
0
1
0
0
1
2
1
0
0
2
0
0
1
5
2
1
1
2
1
1
2
2
1
1
0
1
1
1
2
2
1
0
1
0
1
0
2
2
3
2
2
1
0
1
2
0
0
1
1
1
2
1
0
1
1
1
1
0
0
0
1
0
0
0
0
1
1
0
1
2
0
1
1
1
1
1
0
1
1
0
2
0
1
1
1
1
0
0
1
1
2
1
2
1
2
0
1
0
1
0
2
3
1
0
1
1
1
1
1
1
0
0
1
0
1
0
1
1
0
1
1
0
1
1
1
1
1
1
2
1
2
0
1
0
1
1
2
0
0
1
1
1
2
1
0
1
1
0
2
0
0
1
0
1
2
0
2
1
1
2
1
2
0
1
2
1
1
2
1
1
1
2
2
2
1
1
3
0
1
1
0
1
1
0
0
2
0
1
1
0
2
1
0
0
0
1
1
2
1
1
2
0
2
1
1
2
0
2
1
1
2
1
0
0
1
2
3
1
1
1
3
2
1
1
0
2
2
0
0
1
1
1
1
1
0
1
2
1
2
1
1
1
2
0
3
0
0
1
1
0
1
0
1
0
2
0
0
0
1
0
1
0
2
2
1
0
2
1
0
1
0
2
1
1
2
0
0
2
1
2
1
1
2
1
2
1
1
1
1
0
0
2
0
2
1
2
1
1
0
0
2
0
1
1
1
0
0
0
1
0
0
0
0
1
1
1
0
0
2
1
1
0
0
2
0
1
1
1
2
0
0
2
0
0
1
0
2
0
0
0
2
2
1
2
1
1
1
1
0
2
1
0
1
1
0
1
0
1
1
1
1
0
0
0
2
1
1
0
1
0
1
1
2
0
0
0
1
0
0
2
1
1
0
0
2
1
3
0
2
2
1
1
0
0
0
0
0
1
1
0
1
0
1
0
2
0
1
1
0
2
1
0
0
1
0
1
0
2
1
1
1
1
2
1
0
2
2
0
1
1
2
1
1
1
1
2
0
2
1
1
2
1
0
2
0
0
2
1
1
1
3
1
1
1
0
0
1
1
1
1
1
1
0
1
2
2
1
1
2
1
0
1
0
0
2
0
1
1
1
0
1
1
0
2
0
0
1
1
1
1
2
0
0
1
0
1
1
0
0
2
2
2
1
0
1
1
1
0
2
1
0
0
1
1
0
1
1
0
2
1
0
2
0
1
1
0
1
1
1
1
0
0
0
3
1
2
1
1
0
0
1
0
0
1
2
2
1
2
2
0
0
0
1
0
1
0
2
1
0
1
1
1
2
0
2
2
0
1
1
1
2
0
1
1
1
2
1
0
1
1
0
0
1
0
1
1
1
2
2
1
1
1
2
0
2
1
0
0
0
0
1
1
0
0
2
1
0
2
2
0
2
0
0
1
1
1
1
2
0
0
0
1
0
2
1
1
2
1
0
1
2
0
0
1
1
1
1
2
1
0
0
1
0
2
0
0
2
1
2
1
2
0
0
1
1
1
0
1
2
1
1
1
1
2
2
1
0
1
1
2
1
1
0
0
1
0
0
1
2
0
1
1
2
2
0
1
2
2
1
1
0
1
1
2
1
2
1
1
1
1
0
1
2
2
1
2
1
1
0
2
1
1
1
1
1
0
1
0
1
0
1
2
2
0
2
1
0
0
1
1
1
0
1
2
0
0
0
1
0
1
2
1
1
2
1
0
0
1
0
0
1
0
1
0
0
0
0
1
2
3
2
0
1
2
0
2
0
1
0
2
2
1
0
1
1
1
0
0
1
0
1
2
2
0
1
2
0
2
1
2
1
0
2
0
0
1
0
0
1
0
0
0
0
1
1
2
2
1
2
2
1
1
2
1
1
0
1
0
0
1
1
1
1
1
0
0
1
1
0
1
0
0
1
1
1
1
1
0
0
1
0
2
1
1
1
0
1
1
3
0
1
1
1
1
0
1
1
1
1
3
2
1
1
1
2
0
2
1
1
0
2
0
2
1
1
0
1
0
1
0
0
0
0
0
1
0
0
2
2
1
2
1
2
1
1
0
1
1
1
0
2
0
1
1
1
1
1
1
0
1
1
0
0
1
2
0
0
2
0
1
1
0
2
2
0
0
1
2
1
0
0
1
1
1
1
1
2
1
0
0
0
1
1
0
0
1
1
0
1
1
2
1
2
1
2
0
0
0
1
0
0
2
0
0
1
1
1
0
2
1
1
0
0
1
1
2
1
0
1
0
0
1
0
1
0
0
5
1
0
2
0
1
0
0
0
0
2
1
0
1
0
1
2
1
0
1
1
1
0
1
0
0
0
0
1
0
1
1
1
2
1
2
1
1
0
0
1
0
2
2
1
0
2
0
1
0
0
3
1
1
0
0
0
1
0
2
0
2
2
0
1
1
0
2
1
2
2
1
1
1
1
1
1
2
1
2
0
2
1
0
1
1
0
1
0
1
2
1
2
1
0
2
1
1
2
2
0
0
2
1
0
2
2
1
0
2
1
1
1
0
1
1
1
0
1
1
2
0
0
2
0
1
1
2
1
1
0
1
0
2
0
0
2
0
1
0
2
1
0
0
1
0
1
2
0
1
0
2
1
1
1
1
1
0
1
0
0
1
1
2
3
0
0
0
1
1
1
1
1
0
1
2
1
1
0
2
1
0
0
2
1
0
1
1
1
0
0
1
0
1
0
2
1
2
2
1
1
1
2
1
0
0
2
0
1
0
1
2
0
1
0
0
0
0
1
0
1
0
0
1
0
1
1
1
0
1
1
1
0
0
0
0
2
0
1
2
3
0
0
0
2
2
1
1
2
0
1
0
2
1
1
0
0
1
0
0
1
2
2
1
1
2
0
1
0
0
1
0
2
2
0
0
1
1
1
0
0
1
1
1
1
1
1
1
1
1
2
1
1
0
2
1
2
1
0
1
1
1
0
0
1
2
0
1
1
1
1
2
1
2
1
0
1
1
2
1
0
0
0
2
1
1
1
0
1
0
1
0
1
2
1
0
1
1
1
1
1
1
1
3
1
1
1
2
1
0
1
1
1
0
0
2
2
1
1
1
1
0
2
0
1
0
1
0
2
3
1
0
0
1
1
1
1
1
1
2
0
1
1
0
0
0
0
0
1
0
0
1
1
0
0
0
1
1
0
0
2
1
1
1
2
2
0
1
1
1
1
1
2
1
1
0
2
0
1
1
1
1
0
2
1
1
1
2
2
1
1
1
1
1
2
1
1
0
1
1
1
1
1
1
1
0
1
1
1
1
1
0
1
0
0
2
1
1
1
3
1
1
1
0
0
2
2
1
1
1
1
2
3
1
1
0
2
1
1
1
1
0
2
2
1
1
2
1
3
1
0
0
0
1
1
1
1
0
0
2
2
1
1
1
1
1
0
2
1
0
1
0
1
1
3
0
0
2
0
0
0
0
1
2
1
0
1
1
0
1
2
1
1
0
0
1
0
1
2
1
2
2
0
0
1
2
1
1
0
0
1
0
1
0
2
0
1
1
1
1
0
0
0
1
2
2
1
0
1
0
2
1
0
1
1
1
0
0
1
2
1
2
0
1
2
2
2
2
0
1
1
1
2
2
0
0
1
1
1
1
0
2
0
2
2
0
1
2
1
0
0
1
2
1
0
1
1
0
0
1
1
1
0
1
0
1
0
2
0
2
1
0
0
0
1
1
1
0
0
0
2
1
0
2
1
0
1
0
0
0
2
1
1
0
0
0
2
1
0
0
1
2
0
1
1
1
2
1
1
1
0
2
0
1
1
0
1
1
0
0
2
1
1
1
0
0
1
2
1
2
1
0
1
2
0
1
0
1
2
0
2
1
1
1
1
2
0
2
2
0
0
1
0
1
1
0
0
1
1
2
1
3
1
1
2
1
1
0
1
2
0
1
0
1
2
2
0
2
0
0
1
0
1
0
2
0
1
0
1
1
0
1
1
2
2
0
1
1
2
2
1
2
2
1
1
2
2
1
1
1
1
0
0
2
1
1
1
0
0
1
2
1
1
0
1
0
0
1
2
2
1
1
0
0
1
2
1
1
2
1
2
1
1
1
1
1
1
0
0
0
1
2
0
0
0
1
1
2
2
1
1
1
1
2
1
1
0
2
0
1
0
0
1
1
2
1
2
1
0
1
1
2
2
1
1
1
1
0
0
0
1
1
0
1
0
1
1
1
1
2
2
1
2
2
1
1
1
1
1
1
0
0
1
0
1
2
1
1
0
0
1
0
1
1
0
1
0
1
1
0
0
2
0
1
1
1
2
1
1
1
1
0
2
1
1
0
1
2
1
2
2
1
1
1
1
1
0
2
1
1
1
0
1
1
0
0
0
0
1
0
0
0
3
0
0
0
0
2
1
2
0
1
1
0
3
0
0
0
0
2
2
0
1
1
2
2
2
1
1
2
1
1
0
2
1
1
0
1
1
2
0
1
1
0
1
0
1
2
2
1
1
1
1
0
1
0
1
1
1
0
1
0
1
0
1
2
1
0
0
0
2
1
2
0
1
1
2
1
1
1
0
0
0
1
0
1
2
1
2
0
2
0
1
0
0
0
0
3
2
0
2
1
2
2
1
0
1
0
1
0
2
2
1
1
0
2
1
1
1
0
1
1
1
1
2
0
2
0
2
1
1
0
0
1
1
0
2
2
0
1
1
0
2
1
1
2
1
2
1
2
0
1
0
0
1
2
1
0
1
2
1
0
2
2
0
1
1
1
1
1
1
2
0
0
2
2
2
0
2
0
2
0
2
0
0
0
0
1
1
1
1
1
0
1
1
1
0
2
0
2
1
1
2
1
0
0
2
2
1
2
0
0
0
1
1
1
3
1
1
1
0
2
2
1
1
1
1
0
0
1
2
1
0
1
1
1
1
2
0
0
1
3
1
1
0
1
2
1
0
0
1
1
1
1
0
1
2
2
0
0
1
1
1
1
1
0
1
2
1
2
1
1
0
1
2
1
1
0
1
1
0
0
0
0
0
2
0
0
2
1
1
1
2
2
2
1
1
0
0
1
1
0
0
1
1
0
0
2
1
1
0
1
1
1
2
1
2
0
0
1
1
1
1
0
1
2
1
1
2
0
1
0
2
2
2
0
0
0
1
0
1
1
2
1
2
0
2
0
0
0
2
0
1
1
0
0
2
0
0
0
0
0
1
1
0
0
1
0
2
1
1
0
0
2
0
1
1
1
1
2
2
1
2
2
0
0
0
1
1
0
0
0
1
0
1
0
1
2
1
1
1
0
0
0
0
1
0
2
1
0
0
0
1
2
2
2
0
0
1
0
2
0
1
0
1
1
1
1
1
1
1
2
1
2
0
2
1
1
0
1
0
0
1
2
0
1
2
2
1
1
1
0
1
0
2
1
1
0
2
1
0
1
1
0
0
1
0
2
2
0
2
2
1
1
0
1
0
1
0
1
2
0
0
0
2
1
1
0
1
0
0
1
1
1
0
4
2
0
1
1
0
1
1
0
0
0
1
0
1
1
2
2
2
0
1
2
0
1
1
1
0
0
1
2
1
1
0
2
1
0
2
2
0
0
1
1
0
0
1
0
2
2
0
1
1
1
1
1
2
2
1
1
0
1
1
1
2
2
1
6
1
1
2
0
1
0
1
1
2
1
0
2
1
1
1
1
0
1
1
1
1
2
1
1
1
0
2
4
0
1
1
2
1
1
2
0
1
0
0
0
1
1
0
1
1
0
2
2
2
2
1
2
2
1
1
0
2
1
0
1
1
2
0
1
1
1
2
0
2
1
0
1
1
1
0
1
0
1
1
1
1
2
0
0
1
1
0
2
1
2
2
0
1
3
0
1
0
0
1
2
2
1
1
0
0
0
1
1
0
1
1
2
0
1
2
2
2
1
0
1
1
1
1
1
1
2
2
1
1
0
1
1
0
1
1
0
0
1
1
2
1
2
2
0
0
2
1
0
3
2
1
1
1
1
0
1
1
1
2
2
0
0
2
1
1
0
1
1
0
0
0
0
0
1
2
1
0
1
2
0
2
0
1
1
0
2
0
0
1
1
1
1
1
1
1
0
1
1
0
1
1
0
1
1
1
1
1
0
1
2
0
2
0
1
0
1
1
1
1
0
1
2
0
2
0
0
1
2
2
0
0
1
0
0
1
2
1
0
1
0
1
0
2
1
2
2
1
1
0
1
1
0
1
0
1
0
0
3
1
1
0
2
0
2
0
2
0
1
0
1
2
0
1
1
1
1
1
0
1
0
2
0
1
2
1
0
1
1
1
2
1
0
1
1
2
1
1
2
1
0
1
1
2
0
1
1
0
0
0
1
0
1
2
0
1
1
0
1
2
0
0
0
1
1
1
0
1
2
3
2
2
0
0
3
2
0
0
1
2
1
1
2
0
0
0
0
1
0
1
2
2
1
1
1
2
0
2
1
0
1
0
0
0
0
2
2
0
0
1
1
0
0
0
2
0
0
1
1
0
1
2
1
1
0
2
1
0
1
1
0
0
1
0
0
1
1
1
0
1
1
2
2
0
2
0
1
1
0
2
1
2
2
0
2
1
2
2
1
0
1
2
0
0
1
2
1
0
1
1
1
0
2
2
1
1
1
0
1
0
0
1
1
0
0
0
0
1
0
0
2
1
2
0
2
1
2
1
1
1
1
0
2
0
0
2
1
1
0
1
1
1
0
1
1
0
2
2
2
0
0
1
1
1
1
0
1
2
2
0
2
3
1
2
1
2
1
1
0
0
1
1
0
0
2
1
0
1
1
1
1
0
0
1
2
0
0
1
2
0
2
1
1
0
0
2
1
1
1
1
0
0
2
0
2
0
0
0
1
1
0
2
2
2
1
2
0
2
0
1
2
2
0
0
2
1
1
1
0
1
0
0
0
0
1
0
1
0
1
0
1
0
2
1
1
0
0
1
1
0
1
0
1
0
1
1
1
0
0
3
2
1
0
0
1
0
1
1
1
1
0
1
1
1
2
0
0
1
1
2
0
1
1
0
0
2
0
0
1
1
1
2
1
1
2
2
5
0
0
1
1
0
1
1
1
0
0
1
0
1
2
1
2
0
0
0
0
1
1
0
1
1
0
1
2
0
2
0
0
0
1
2
0
0
1
1
2
0
1
1
2
2
2
2
0
2
0
0
1
2
1
0
0
1
0
1
2
0
1
1
1
0
2
1
0
2
2
1
1
1
1
0
1
2
2
1
1
1
2
1
1
1
0
0
2
2
1
1
1
1
1
0
1
1
0
0
2
1
1
0
1
1
2
2
2
0
1
1
1
2
0
1
1
0
0
0
0
1
1
1
2
1
0
1
1
1
2
2
0
1
1
1
0
2
1
1
1
0
2
1
0
1
1
1
0
1
1
0
1
1
1
2
1
0
2
1
0
1
0
0
1
1
1
1
1
2
1
1
2
2
0
0
1
1
1
0
1
0
1
2
1
0
1
1
2
0
1
1
0
1
2
1
0
1
1
0
0
1
0
2
1
0
2
1
1
2
0
2
2
1
0
2
1
2
1
2
0
2
1
2
2
2
0
1
0
1
0
1
1
2
1
1
0
1
1
2
0
1
1
0
3
0
0
1
0
1
2
1
0
2
1
1
0
1
1
0
1
1
0
0
0
0
1
0
1
1
0
0
2
0
1
0
2
0
2
0
0
1
0
1
2
0
1
0
1
1
2
1
2
0
0
1
2
1
0
1
0
1
0
1
1
1
2
2
0
2
2
0
0
2
1
0
2
2
0
2
2
1
1
1
0
1
1
1
2
1
2
1
1
2
2
2
0
1
1
1
0
0
1
0
1
0
0
0
1
2
2
1
1
2
0
0
2
0
2
1
0
2
0
0
0
0
2
0
1
0
0
0
1
0
1
1
1
2
0
0
1
2
0
1
1
1
2
1
0
1
2
0
0
0
2
0
0
0
1
1
1
0
1
2
1
1
2
2
2
1
0
1
2
1
1
1
0
2
0
2
0
1
0
0
0
0
0
0
0
4
0
1
0
2
2
1
1
0
0
0
2
0
1
2
1
1
0
1
1
2
1
1
0
0
0
2
1
2
2
1
1
2
2
2
1
2
2
0
2
0
0
1
1
1
0
1
1
1
1
5
2
1
1
0
1
0
2
1
1
1
1
1
0
1
2
2
1
1
0
0
0
0
0
1
2
1
1
2
2
0
1
0
1
1
2
3
0
2
0
1
0
1
2
0
1
1
0
1
1
1
1
0
2
0
1
1
1
0
1
2
1
1
1
1
1
1
2
0
2
0
0
1
0
0
0
1
1
1
1
1
1
2
1
1
0
2
1
0
1
1
0
2
1
0
0
0
1
0
1
1
1
1
0
1
2
0
0
2
0
1
0
0
1
1
1
0
1
0
0
0
1
1
0
0
0
1
0
2
2
2
2
2
2
1
1
1
0
0
1
1
2
0
1
2
1
1
0
0
1
1
0
0
0
0
0
1
0
1
1
0
1
1
1
1
1
1
2
1
0
1
0
1
1
0
0
0
1
2
0
1
2
2
1
0
1
0
1
2
0
1
1
1
2
1
1
0
1
1
1
0
1
1
1
1
2
2
2
1
1
0
1
2
2
0
0
1
0
0
2
1
0
4
1
2
0
1
0
1
1
1
1
1
1
0
1
1
1
1
1
2
1
1
2
2
1
0
2
1
1
1
2
2
1
2
1
1
1
0
1
1
0
2
1
1
0
1
2
0
1
2
2
1
0
1
1
2
0
1
0
1
0
0
0
1
2
2
2
0
1
1
2
1
0
1
0
1
2
1
1
0
1
1
1
0
1
0
0
1
2
1
1
0
0
0
1
1
1
1
1
0
1
1
0
1
1
1
0
2
0
2
0
2
2
1
0
3
0
0
0
0
1
1
2
0
0
2
1
1
0
0
1
1
2
0
1
1
1
2
1
0
2
1
0
1
2
2
3
1
0
1
1
0
1
1
0
1
1
1
0
0
0
0
2
1
2
1
0
1
1
1
1
1
1
2
2
1
1
1
1
0
1
2
2
0
1
0
0
1
1
1
1
0
1
1
0
1
1
2
1
0
2
1
1
0
1
1
1
3
0
2
0
2
0
1
1
2
1
2
1
5
1
1
0
1
0
2
0
0
2
1
1
2
0
0
0
1
1
0
0
2
1
2
0
2
0
0
1
1
2
2
1
2
1
1
0
0
0
0
1
1
0
0
0
1
2
1
1
0
1
0
2
1
0
1
0
0
0
0
1
1
0
1
0
0
1
2
0
0
0
1
1
1
0
1
0
2
2
1
1
1
2
1
2
1
0
1
0
1
1
2
2
0
2
0
1
1
1
0
0
1
0
0
0
1
0
1
2
0
1
1
1
1
0
1
1
2
0
1
0
0
1
2
1
1
0
0
1
1
0
1
2
1
2
1
0
2
1
0
1
1
0
2
1
0
0
1
0
1
0
1
0
1
1
1
0
1
1
0
0
0
2
1
1
0
1
0
1
0
1
0
0
1
1
0
2
0
0
0
0
1
2
1
0
0
1
1
1
0
1
0
1
1
2
1
1
1
0
0
1
0
1
2
1
0
1
0
1
0
0
2
2
1
2
0
1
0
0
1
0
0
1
1
1
0
1
0
0
0
1
1
1
0
0
1
0
2
1
0
0
2
0
2
0
0
0
1
1
1
1
1
2
2
1
2
1
1
0
0
1
0
0
1
1
3
1
2
1
1
2
1
0
1
1
1
1
1
0
2
3
0
1
2
1
2
2
1
1
4
2
2
1
1
0
2
2
1
1
0
0
0
1
0
1
1
1
0
1
1
1
3
0
1
1
2
2
0
1
1
0
0
1
0
1
2
1
2
3
1
0
0
1
0
1
3
1
1
1
2
0
0
0
1
0
0
1
1
2
0
1
1
2
2
1
1
1
0
0
2
2
1
2
1
1
2
0
1
1
0
1
0
1
1
2
1
1
1
1
0
3
1
0
1
1
2
1
2
0
2
2
1
4
2
2
1
1
1
2
1
2
0
0
0
2
2
0
1
0
0
0
1
2
0
0
0
1
0
1
0
1
1
0
0
1
2
2
0
1
0
0
1
1
2
1
0
1
2
2
0
1
1
1
0
1
2
2
1
1
3
0
2
0
0
1
1
1
0
2
0
1
1
1
0
0
0
1
1
0
0
1
2
0
1
2
1
0
1
1
0
2
2
1
2
0
0
2
1
1
2
1
2
1
1
1
0
1
0
0
0
1
1
0
0
1
1
0
2
1
1
2
0
1
0
0
2
2
3
1
0
1
2
0
1
1
0
0
0
1
0
2
1
0
0
1
2
0
2
0
2
0
0
1
2
2
1
1
0
0
1
1
1
0
2
1
2
0
1
2
2
1
0
0
1
0
1
0
1
2
3
1
2
2
0
3
1
0
1
0
0
0
1
1
0
1
1
1
2
2
0
1
1
1
1
0
1
1
0
2
1
1
1
2
1
2
3
0
0
2
2
1
1
0
1
1
1
1
0
1
1
1
2
1
1
0
0
1
1
0
1
0
1
1
0
2
0
1
1
0
0
2
2
1
1
1
2
1
0
0
1
1
0
1
1
2
1
0
1
1
2
0
1
0
1
1
1
2
0
0
1
1
0
0
3
0
1
1
2
1
0
1
1
1
1
1
1
1
0
1
2
1
1
1
2
2
2
2
2
0
0
0
1
0
1
0
0
3
0
1
2
1
1
1
1
1
2
2
2
1
1
1
2
1
1
0
2
1
1
1
1
1
0
1
2
1
1
1
2
2
1
1
0
0
2
2
1
1
2
0
0
2
1
0
1
1
0
0
0
2
1
1
0
0
1
0
1
0
1
0
1
2
1
1
1
2
1
1
2
0
0
0
2
0
1
1
1
1
0
1
0
2
1
1
1
0
1
1
0
2
0
0
0
0
2
1
1
1
1
0
2
0
1
2
1
1
2
1
0
1
0
1
1
0
0
1
1
1
1
2
1
0
1
1
2
0
0
2
2
2
2
0
0
1
2
2
1
2
1
1
0
1
1
0
0
1
2
1
0
0
0
1
0
0
0
1
1
1
1
1
2
1
1
2
1
0
0
2
0
1
1
1
0
1
2
2
1
0
0
2
2
0
0
1
2
1
1
0
0
0
2
1
0
0
0
0
0
0
1
1
0
1
0
2
0
1
1
1
1
0
2
1
1
0
2
1
0
1
1
1
1
0
0
0
1
0
2
1
2
0
2
1
2
1
1
1
2
2
1
1
1
1
1
0
1
1
0
2
2
0
1
0
2
1
1
0
1
1
1
1
2
1
0
1
0
1
1
0
1
0
1
1
1
1
1
0
1
2
1
2
1
2
2
1
1
1
2
1
2
1
0
1
1
1
1
0
0
0
2
1
1
4
2
0
4
1
1
1
2
1
1
2
0
1
1
0
1
1
0
0
2
2
0
1
1
1
1
0
2
1
1
2
1
0
2
1
1
1
1
2
1
1
1
0
2
1
1
0
1
1
1
1
1
1
2
1
1
1
0
0
0
0
2
0
1
0
0
0
2
1
0
1
1
2
1
1
2
0
0
1
1
0
1
0
0
0
1
1
0
2
1
2
0
2
1
0
1
1
0
1
0
0
1
1
2
1
1
0
0
1
1
1
2
0
1
1
1
0
0
0
0
1
0
2
1
0
1
0
1
2
0
0
0
2
3
2
1
2
1
0
1
0
2
1
0
0
0
2
1
0
1
1
0
2
1
1
1
0
2
0
2
1
1
0
0
1
0
1
1
0
2
1
2
1
0
2
0
2
2
1
1
1
1
0
1
1
2
0
0
0
1
1
0
0
1
1
2
0
1
1
0
1
2
1
1
1
2
1
1
1
2
2
0
0
1
3
0
0
0
1
2
1
2
1
1
0
1
0
1
1
0
1
2
0
2
1
0
1
0
1
2
2
2
0
0
1
1
0
1
0
0
1
1
1
1
2
2
2
0
2
0
1
2
1
1
2
1
2
0
1
0
0
0
1
1
1
1
1
1
2
1
1
1
1
2
1
1
0
2
1
0
1
1
0
1
0
2
0
1
1
1
0
2
1
0
2
1
0
1
1
1
1
1
1
0
0
2
0
1
2
0
1
2
0
0
0
2
0
0
3
0
1
1
2
1
2
1
2
1
0
1
0
2
1
1
2
0
1
1
1
2
0
1
0
2
1
0
2
0
2
0
0
1
1
1
2
0
2
1
0
1
1
0
0
1
1
0
1
0
0
1
0
0
1
2
2
1
1
2
1
1
1
3
1
2
1
0
0
1
2
1
1
0
1
0
2
0
0
0
0
1
2
1
1
1
2
2
0
0
1
0
0
0
1
0
0
2
0
1
1
0
2
1
1
1
2
2
0
1
0
0
1
1
1
2
2
2
1
1
1
0
1
0
1
0
2
2
1
1
2
1
4
2
0
1
0
0
1
2
2
1
0
0
0
0
1
1
1
1
2
2
0
0
0
1
1
0
2
0
1
1
1
1
0
2
0
1
1
2
1
2
2
2
1
1
1
3
2
1
0
1
0
1
2
2
0
0
0
0
1
1
1
1
2
2
1
1
2
0
2
0
1
1
1
0
2
2
1
1
0
1
2
1
0
0
2
1
4
1
1
1
0
1
0
0
0
2
1
2
1
1
4
1
0
1
2
2
0
1
0
1
1
0
2
1
1
1
2
0
1
0
0
1
0
1
1
1
2
1
1
1
1
2
1
0
2
1
0
4
1
1
2
1
0
0
1
0
0
0
0
1
0
1
0
2
0
1
0
0
1
0
0
0
0
0
1
1
1
1
1
2
0
1
1
0
2
1
1
1
1
0
0
1
2
0
0
1
2
1
2
0
1
2
0
0
0
2
0
1
1
1
1
2
0
2
1
1
2
2
0
3
0
1
2
1
1
1
1
1
0
1
2
3
0
0
1
1
1
2
2
0
0
1
1
2
1
1
0
1
0
1
0
2
1
1
1
0
1
0
1
0
2
2
1
1
1
1
0
0
0
1
2
1
1
1
1
1
2
0
1
0
1
1
1
0
1
0
0
1
2
1
1
2
1
2
0
0
1
1
4
1
1
0
2
2
1
1
1
2
2
2
2
0
1
1
1
1
0
1
0
2
1
0
1
1
1
1
0
0
0
1
1
1
1
2
1
0
1
1
0
2
0
0
2
1
0
1
1
1
1
0
1
1
0
1
0
1
0
2
1
2
0
1
1
1
1
1
0
1
2
1
1
0
0
1
0
0
1
0
0
1
0
0
2
2
1
2
1
2
1
1
2
2
0
1
1
1
2
1
0
2
2
1
2
1
2
1
1
0
1
1
1
2
1
3
0
0
1
1
0
0
0
1
1
3
2
3
0
1
1
1
1
0
2
2
2
2
2
2
2
2
1
1
0
2
1
1
1
1
1
1
2
1
0
2
1
1
1
2
0
2
1
2
1
2
1
1
2
0
2
2
1
0
2
1
2
0
0
0
1
2
0
2
0
3
1
2
1
1
0
1
1
0
1
1
0
1
0
1
1
0
1
1
1
0
2
0
1
2
0
2
0
1
1
0
1
3
0
2
0
0
0
2
1
0
2
1
1
1
1
1
1
1
2
2
1
2
0
1
0
0
0
2
2
1
0
1
1
2
0
1
1
1
0
0
1
1
1
1
0
1
0
0
2
0
1
0
0
2
1
0
2
1
1
1
1
1
1
2
1
0
0
0
2
2
0
1
0
2
1
0
1
2
0
1
1
1
1
1
0
0
2
2
0
1
0
1
0
2
0
2
1
2
2
1
2
0
1
0
1
1
1
2
1
0
0
2
9
2
0
1
2
0
1
0
1
2
1
1
1
1
1
1
0
0
1
2
0
0
0
1
0
0
0
0
2
2
1
2
0
0
1
2
1
1
2
0
1
1
0
0
1
0
2
2
0
1
0
0
0
1
1
0
1
1
2
1
1
1
0
2
1
1
0
1
0
1
1
1
0
1
1
0
0
1
1
1
1
2
2
2
0
1
1
1
1
2
0
0
2
1
0
0
1
1
2
1
0
1
1
1
2
1
0
2
1
2
2
1
1
1
1
0
2
2
1
1
2
0
1
1
1
2
1
1
1
0
2
1
2
0
2
0
0
2
0
1
0
0
1
1
1
1
1
0
1
0
0
0
0
2
0
0
0
2
1
1
2
0
1
0
2
1
1
1
0
0
1
1
0
1
2
0
2
1
1
1
0
0
2
1
0
2
2
2
1
1
2
0
1
1
2
0
1
0
1
1
1
1
0
1
0
0
1
0
1
0
0
2
1
0
1
2
0
0
0
2
1
0
1
0
1
1
0
0
0
1
1
2
1
1
0
1
1
1
2
0
0
1
1
2
0
1
2
1
2
1
2
1
0
2
1
1
1
1
1
2
1
0
1
1
1
0
0
0
0
0
2
0
2
0
1
2
0
1
2
1
2
1
0
0
2
1
0
1
1
0
0
1
0
1
0
1
1
2
0
0
0
0
1
0
0
0
1
0
1
1
2
1
1
1
1
2
1
1
1
0
0
1
0
1
1
0
0
1
1
0
1
1
1
0
0
2
1
0
0
0
1
0
1
1
0
0
1
0
0
2
2
1
1
1
0
1
1
0
1
2
1
1
1
1
2
0
1
1
1
1
2
1
1
2
1
0
1
0
1
2
2
1
0
0
1
0
1
2
1
3
1
2
1
1
1
0
1
0
0
1
1
0
0
3
0
0
1
0
0
1
1
0
1
1
2
1
2
0
2
1
1
0
1
2
0
0
1
2
2
1
2
0
1
1
2
2
1
2
1
0
0
1
1
1
1
1
0
0
0
2
0
2
2
0
1
0
1
0
1
2
1
2
1
2
0
2
2
0
0
1
0
1
1
2
1
0
0
1
1
0
2
2
1
1
1
2
2
1
1
1
0
1
2
0
1
1
0
1
2
1
1
1
1
0
2
0
2
1
1
1
1
1
2
1
2
1
1
2
2
2
0
2
1
1
1
1
0
1
0
0
1
0
2
0
1
1
2
1
1
1
0
1
1
1
1
1
0
0
1
1
1
2
2
2
0
0
2
0
1
0
1
2
0
1
1
2
2
0
0
0
0
1
0
2
0
2
2
1
1
0
0
0
0
0
1
2
0
1
2
0
1
1
1
1
1
1
1
2
1
1
1
0
1
0
1
1
0
2
1
2
0
0
2
0
0
1
0
1
2
2
2
1
1
0
0
1
1
0
1
1
1
0
1
0
2
0
1
1
1
0
0
2
1
1
0
1
1
0
2
0
1
2
0
0
0
1
1
0
2
0
2
1
2
1
1
1
2
1
2
0
3
0
2
0
2
2
0
2
1
0
1
1
0
1
0
0
2
1
0
1
0
1
1
1
1
0
1
1
0
2
0
0
1
0
1
2
1
1
1
2
1
2
1
2
1
0
1
0
2
0
2
0
0
1
0
2
1
0
1
2
1
1
2
0
0
0
0
0
1
1
2
2
0
1
2
0
1
1
0
0
1
0
1
0
0
1
1
1
1
1
2
0
1
1
0
0
1
0
0
0
2
2
0
1
2
0
2
0
0
0
2
0
1
1
1
1
1
1
1
0
2
0
1
0
0
2
1
0
1
0
0
0
1
0
1
1
1
0
0
0
1
0
1
1
0
0
3
0
2
2
1
1
2
1
0
2
2
1
2
0
1
2
2
0
1
0
1
2
1
1
1
2
0
1
0
1
2
0
1
0
2
1
2
1
0
2
1
1
1
2
0
1
1
1
2
2
1
2
1
1
0
2
1
1
1
1
0
0
1
0
1
1
1
0
0
0
0
0
0
2
1
0
1
2
2
0
1
1
1
1
1
1
1
1
0
0
0
1
1
0
1
2
0
1
0
1
0
0
0
1
2
0
3
1
1
0
2
1
1
0
1
1
2
0
1
0
0
1
0
3
1
0
1
2
1
0
0
1
0
1
0
2
1
1
1
1
0
1
2
2
1
2
1
1
0
1
1
1
2
1
0
1
0
1
2
1
0
0
1
1
0
2
1
1
1
0
1
0
2
0
2
1
1
1
1
1
2
1
2
1
4
0
0
2
1
4
0
1
2
1
1
1
1
2
2
0
1
0
1
0
0
2
0
0
1
0
0
1
1
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
2
2
0
1
0
0
1
1
1
0
0
1
0
2
1
1
1
0
0
1
0
0
1
1
0
0
0
0
0
2
1
0
1
1
1
0
1
0
0
2
1
0
0
1
2
5
2
0
1
0
3
1
0
0
0
1
2
1
7
0
1
0
0
2
2
1
1
1
1
1
1
1
2
1
0
1
0
1
2
1
1
1
0
2
1
1
2
0
1
1
1
1
0
1
1
1
2
0
1
0
0
1
1
1
2
2
1
1
1
2
1
2
0
2
1
0
0
0
1
0
0
1
1
0
1
0
0
1
1
1
1
2
1
1
1
2
2
0
1
1
1
1
0
0
1
1
1
3
1
2
1
1
1
1
1
1
1
1
0
2
2
0
1
1
0
1
1
0
1
2
0
1
1
1
1
0
0
1
1
2
1
1
2
0
0
1
1
1
1
2
1
1
1
0
1
1
0
0
1
1
1
2
2
1
1
0
1
1
1
2
1
2
1
0
1
2
1
2
2
0
2
0
2
0
0
1
1
0
0
1
2
1
1
1
0
1
2
3
0
1
0
0
0
2
1
1
2
1
2
0
0
1
1
0
1
0
1
1
1
1
1
1
1
1
0
0
0
0
0
0
2
1
2
1
2
1
0
1
1
0
1
0
1
2
0
2
0
1
0
1
0
1
0
0
1
0
2
0
1
2
3
0
1
0
1
0
1
2
1
1
0
1
0
2
1
1
0
1
0
1
1
1
0
0
2
1
0
2
2
2
1
1
0
1
0
1
0
2
2
1
1
1
2
2
2
2
1
1
0
2
2
1
2
2
1
1
1
1
0
2
2
2
0
1
1
0
0
1
1
2
1
2
1
2
3
0
4
1
1
2
1
0
1
2
1
2
1
1
1
1
1
0
0
1
2
0
0
1
2
1
1
1
1
2
0
1
2
3
0
0
0
2
1
1
2
2
2
1
1
0
1
1
2
0
1
2
1
1
1
2
1
2
0
1
1
2
0
0
2
1
1
2
0
0
1
0
0
0
1
1
0
2
1
1
1
1
0
0
2
0
1
1
1
0
0
1
1
1
2
1
1
1
1
0
1
0
2
1
0
0
0
1
0
1
0
1
0
1
2
2
2
1
0
0
1
1
0
1
2
2
0
2
1
2
1
2
2
0
1
1
0
0
1
1
0
1
0
1
1
0
2
1
1
1
0
1
2
1
1
1
1
2
1
2
2
2
0
1
1
1
1
1
1
1
1
0
2
1
0
1
0
0
1
2
1
1
1
1
2
1
1
0
1
1
2
1
1
2
2
2
1
1
0
0
1
1
1
1
1
1
1
1
0
0
1
0
0
0
1
2
2
2
1
0
2
2
1
2
3
1
1
0
2
1
0
1
1
2
1
1
0
0
0
1
1
0
1
0
1
1
1
1
1
0
1
1
2
1
1
0
1
0
1
0
1
1
0
0
0
1
0
1
0
1
1
2
1
1
0
0
1
1
2
1
0
2
0
0
1
1
2
4
0
1
2
1
2
1
1
0
0
1
1
2
1
1
0
0
2
3
1
1
1
2
1
0
1
0
1
0
2
0
0
0
0
0
1
1
1
2
0
1
1
1
2
1
1
0
1
1
0
0
0
0
0
1
1
0
3
2
1
1
1
1
0
1
1
1
1
2
1
2
1
0
2
1
2
0
2
1
2
1
1
2
1
1
0
0
1
0
1
0
1
2
2
2
2
1
1
2
1
2
2
2
0
1
1
1
1
1
1
1
1
1
1
2
0
0
0
0
2
2
2
2
1
1
1
1
1
0
2
1
1
1
1
1
1
0
0
1
1
0
0
1
0
2
2
0
0
1
0
1
0
2
0
1
1
1
2
1
0
1
0
1
1
1
2
0
0
0
0
2
0
3
1
1
1
1
0
1
1
2
1
1
0
1
0
1
1
0
1
1
1
1
2
1
0
1
1
0
1
1
1
0
2
1
0
2
0
1
0
0
1
0
0
1
0
1
0
1
1
1
1
1
1
1
1
0
0
0
2
2
2
0
2
0
1
0
0
2
1
2
1
0
2
2
1
1
0
1
1
1
1
0
1
0
3
2
1
2
0
1
1
1
1
0
1
1
1
3
0
0
1
1
0
1
2
0
1
0
1
0
1
2
2
1
0
3
0
4
1
1
2
0
0
0
1
1
1
1
1
1
2
1
0
0
0
1
2
1
0
0
0
2
1
0
1
1
0
0
1
0
1
3
1
1
0
0
0
2
1
2
0
1
0
1
1
1
1
0
1
1
2
1
0
1
2
0
1
0
1
1
0
1
1
1
1
0
1
2
2
2
1
0
2
2
0
1
2
0
1
2
1
1
1
1
0
2
0
2
1
1
1
1
1
2
1
1
0
1
2
0
1
1
2
1
2
1
2
0
2
3
0
1
0
0
1
1
1
8
1
1
2
1
0
2
0
1
2
1
0
0
0
2
1
1
1
0
0
0
1
0
1
2
1
2
0
1
0
0
1
1
1
0
1
1
0
2
1
0
1
1
0
1
1
0
1
1
1
2
0
1
0
1
1
1
2
1
1
0
1
0
1
2
1
2
2
2
1
1
0
1
0
0
0
3
1
0
1
0
2
1
2
0
1
0
0
0
1
1
1
1
1
2
1
0
0
1
1
2
1
0
0
0
1
0
2
1
1
1
1
1
2
0
2
0
1
0
1
1
0
0
1
1
2
1
0
1
0
2
2
1
2
1
0
0
0
1
0
1
2
1
1
2
0
0
0
0
1
3
3
2
0
1
1
1
1
1
0
1
1
2
2
2
1
1
1
2
1
0
1
1
1
2
1
2
2
0
1
0
2
0
0
2
1
0
0
2
1
1
1
1
1
1
2
1
2
1
0
1
1
2
0
2
1
1
2
1
1
1
2
1
1
2
1
0
1
1
1
1
2
1
0
1
0
2
2
1
0
0
0
1
1
0
0
1
2
0
0
1
0
0
1
1
1
1
0
0
1
0
2
0
1
1
0
1
2
0
1
2
1
1
0
2
0
1
2
0
1
1
2
2
2
0
0
0
1
2
0
0
0
1
2
0
0
1
0
0
2
2
1
2
0
1
1
0
1
0
0
0
2
1
1
2
0
2
0
2
3
2
1
2
0
0
2
0
0
2
1
1
1
0
1
1
1
2
2
2
1
0
0
0
0
1
2
1
0
1
1
2
0
0
0
0
1
2
0
0
2
0
0
1
2
1
2
2
1
0
1
1
0
0
2
1
0
0
2
0
0
1
4
1
0
0
1
1
2
1
2
1
0
0
2
2
0
1
1
2
1
0
0
2
1
0
1
0
1
0
1
2
2
1
0
1
1
0
1
2
1
0
0
1
0
0
2
2
2
0
1
2
1
1
0
0
1
2
1
1
0
0
0
1
1
1
2
0
1
1
2
1
0
1
0
1
1
0
1
1
1
1
0
1
0
0
0
1
1
0
0
2
0
2
0
0
2
0
1
2
2
2
1
1
2
1
1
0
0
2
2
2
1
0
2
0
2
1
2
0
0
0
2
1
1
0
1
1
0
0
1
1
0
2
1
0
1
1
1
0
2
1
1
3
1
1
0
1
1
1
2
2
1
1
0
0
1
1
1
2
0
0
1
1
0
2
1
0
1
0
1
1
1
2
0
1
1
2
2
1
0
0
1
1
0
0
0
2
1
0
0
1
0
1
2
1
2
2
0
1
2
1
2
2
0
0
2
0
1
3
0
0
1
1
0
1
0
2
1
1
2
2
1
2
1
1
0
1
1
2
1
1
1
1
0
1
2
2
1
0
1
2
0
0
1
1
0
2
0
2
0
1
2
1
1
0
0
2
1
1
2
2
0
1
0
1
0
2
1
1
2
2
0
0
2
0
0
1
1
1
1
1
2
0
1
0
0
1
0
0
1
2
1
0
1
1
1
0
0
1
1
1
0
2
0
0
0
3
0
0
1
1
0
1
0
0
1
0
1
0
0
1
1
1
2
2
0
0
1
0
1
2
1
1
2
1
1
1
1
1
0
1
2
1
1
0
1
1
0
0
1
1
1
0
0
0
1
1
0
1
1
0
1
1
0
2
1
0
0
1
0
2
0
2
2
1
1
2
1
1
1
2
2
1
0
2
2
0
0
0
1
2
2
1
0
0
1
1
2
0
1
0
1
2
2
2
0
0
1
1
2
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
2
1
1
2
2
1
0
0
0
1
0
2
1
1
0
1
0
0
1
2
2
2
2
0
0
0
1
0
0
0
0
0
1
1
2
0
1
1
2
2
2
2
0
1
0
0
1
0
0
2
0
0
0
0
0
1
2
0
2
0
0
2
1
1
0
2
2
1
1
1
1
0
1
1
0
1
0
0
1
2
1
0
0
1
0
1
1
1
2
1
1
1
1
3
2
2
1
1
1
1
1
2
2
1
0
1
2
1
1
1
1
2
0
0
1
1
1
1
1
0
1
2
1
2
2
2
1
2
0
2
1
2
0
0
1
2
1
2
1
1
0
1
1
1
2
1
3
0
1
1
3
1
2
1
1
1
0
1
2
2
0
0
1
0
1
2
1
1
1
1
1
2
1
0
2
0
2
0
1
1
0
0
0
1
2
1
0
1
1
2
1
1
2
2
1
2
1
2
1
1
1
0
1
1
1
2
0
2
2
1
1
0
2
0
0
1
1
1
2
0
0
0
2
1
2
1
0
2
1
2
1
0
1
0
0
1
1
0
1
1
2
1
1
0
1
1
1
1
2
2
1
2
1
2
1
1
1
1
1
1
1
2
1
1
0
0
1
1
1
1
0
1
1
0
0
1
1
2
1
1
0
1
2
2
1
1
0
1
1
0
1
2
0
1
2
1
1
1
0
1
1
1
1
1
0
1
0
2
2
2
1
4
0
2
0
1
1
2
0
1
0
0
0
2
1
1
2
1
2
0
2
0
0
1
1
1
0
1
0
0
0
1
0
0
1
1
1
0
2
2
4
2
1
0
1
1
0
2
1
2
2
0
1
2
0
0
2
2
0
1
1
0
1
1
1
2
0
0
2
2
0
0
2
1
0
1
1
0
0
2
0
2
0
2
1
0
2
1
0
1
1
0
0
1
0
0
2
2
1
1
0
1
1
0
1
2
2
0
7
0
1
1
0
4
1
1
0
2
2
1
0
1
2
1
0
1
1
1
0
0
0
0
1
0
1
2
1
1
3
2
0
0
2
0
2
1
0
1
1
2
2
0
1
0
0
0
0
0
0
2
3
0
2
2
0
0
1
1
2
0
1
2
1
1
2
2
0
0
1
1
1
2
3
0
0
1
1
0
1
1
1
0
1
0
0
1
1
0
1
1
1
0
1
0
0
0
1
0
0
1
1
0
2
1
2
1
0
0
2
0
2
2
1
0
0
0
1
2
2
1
3
1
1
1
0
0
3
1
1
0
0
2
0
1
2
1
1
1
0
1
2
2
0
0
2
1
0
1
2
2
1
0
0
2
1
2
2
1
1
2
1
2
1
0
1
2
1
0
2
2
0
0
2
1
1
1
1
3
0
1
0
1
0
2
1
3
0
2
1
1
1
0
0
0
2
1
2
0
0
1
0
0
1
2
2
0
0
1
0
1
0
2
0
1
1
1
2
1
0
1
2
1
1
0
1
0
0
2
2
2
0
1
2
1
0
2
2
2
0
2
0
0
1
0
1
0
1
1
2
1
1
2
0
1
1
0
1
2
2
0
1
1
2
1
1
1
1
0
3
0
1
2
1
1
0
3
1
0
1
1
0
0
0
0
1
1
2
2
1
2
0
1
1
0
0
1
2
0
1
0
1
0
6
0
1
1
1
1
0
0
0
0
1
2
1
1
1
0
1
2
0
1
0
1
0
2
2
0
1
1
0
1
1
2
0
2
0
1
2
0
1
1
1
1
0
2
0
0
0
0
0
2
1
0
1
0
1
1
2
1
1
1
2
1
1
0
1
2
1
2
2
1
0
0
0
1
0
1
0
1
2
1
0
2
0
1
0
1
1
1
2
2
0
1
1
0
1
2
0
1
0
2
1
0
0
0
3
0
1
1
1
2
2
2
1
0
0
0
3
2
1
1
1
2
0
2
0
1
1
2
1
1
2
0
3
2
0
1
1
2
0
1
0
0
1
1
1
0
1
1
1
1
0
1
2
0
0
3
0
1
2
2
2
2
1
1
0
0
2
2
0
1
2
1
0
1
0
0
1
2
1
1
0
1
3
0
0
1
2
1
1
1
0
1
0
1
0
1
1
2
1
0
0
0
1
2
2
1
2
0
0
1
0
1
1
2
2
0
2
2
1
0
2
0
1
1
0
5
0
0
2
1
1
2
2
0
0
0
1
2
0
1
1
2
0
1
2
2
1
1
1
0
1
0
0
1
0
1
1
1
1
0
1
0
0
1
1
0
1
0
0
1
1
2
1
2
1
5
2
0
0
1
1
2
2
1
1
1
1
0
0
1
1
0
1
1
0
1
2
1
1
1
2
1
0
2
1
1
1
1
2
2
1
1
1
0
2
1
1
1
1
2
0
0
2
1
0
1
0
2
1
1
1
0
1
0
0
0
0
1
1
2
2
1
1
1
0
0
0
0
2
1
1
4
2
1
1
1
2
1
0
0
0
1
0
1
0
2
1
1
1
0
0
2
0
1
1
1
2
1
1
4
0
0
0
2
0
2
1
0
1
0
2
1
0
0
1
2
1
1
1
1
2
1
1
1
1
0
1
2
1
1
1
1
0
1
1
0
2
2
1
1
1
1
2
1
1
2
2
2
2
1
2
0
0
2
2
2
1
1
1
1
1
0
1
1
1
2
0
3
2
0
0
0
0
0
0
0
0
1
0
0
2
1
1
1
0
1
0
2
2
1
1
0
1
1
0
0
0
0
0
0
1
1
2
2
0
1
1
0
0
1
1
0
1
0
1
1
0
0
2
0
2
0
2
1
1
0
0
1
0
0
0
2
2
0
2
1
1
1
1
2
0
1
0
0
1
0
1
0
1
2
0
1
1
0
1
1
2
0
1
2
0
1
1
1
2
2
0
0
1
0
1
2
2
4
0
1
1
0
1
1
2
1
1
1
1
1
1
2
0
2
2
0
2
1
1
1
2
1
1
0
1
1
1
1
1
1
0
1
0
0
0
1
2
0
1
0
1
0
2
1
1
0
1
1
0
1
2
2
2
1
2
0
1
2
0
0
2
0
2
0
0
0
1
0
1
0
0
0
1
0
1
1
0
2
2
1
2
1
1
0
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
0
2
1
2
1
1
0
0
1
2
1
1
1
1
2
2
1
1
2
0
1
1
1
0
1
0
1
1
1
0
2
2
1
2
1
1
0
1
1
2
1
0
0
1
1
0
1
2
3
1
1
1
1
1
2
2
2
3
0
0
0
2
1
1
0
0
2
1
1
1
1
2
2
0
0
1
1
0
0
2
2
2
0
1
1
2
2
0
2
1
0
1
0
0
0
1
0
0
1
1
2
1
1
1
0
1
0
2
0
1
2
0
1
0
1
1
0
2
1
1
1
2
1
1
0
2
1
0
0
1
0
0
1
0
1
0
0
1
2
1
1
0
0
1
1
0
1
2
0
0
1
3
0
1
1
2
0
0
1
2
1
1
0
0
0
0
1
0
2
1
2
2
2
1
1
0
1
1
0
0
0
1
2
3
4
1
1
1
1
0
1
0
1
0
1
1
2
0
2
0
1
1
1
0
1
2
1
0
0
1
2
0
1
0
1
1
2
1
1
1
1
2
1
1
0
1
1
2
2
0
0
1
2
0
1
0
1
0
0
1
0
1
0
1
1
1
1
2
1
0
2
0
0
1
1
2
1
0
0
2
0
1
1
1
0
1
1
1
0
0
1
1
1
1
0
0
0
0
1
2
0
2
1
0
0
0
1
1
0
1
1
0
1
1
1
0
0
1
0
0
0
1
0
1
0
1
1
1
0
1
0
0
0
0
0
0
1
1
1
1
0
2
0
0
0
2
2
0
1
1
0
2
1
0
0
1
1
1
0
2
2
0
0
2
2
1
1
2
2
2
1
3
2
2
2
0
1
0
0
1
1
0
2
1
1
0
0
1
1
1
0
0
1
1
2
1
1
2
2
1
1
0
1
0
1
0
1
1
1
1
1
0
1
2
1
1
0
2
0
2
2
1
1
1
2
1
0
0
1
1
2
2
1
2
0
1
2
0
0
0
1
1
1
1
1
1
0
1
0
1
1
2
0
2
0
0
0
2
1
2
0
0
1
0
1
0
0
2
1
1
0
0
2
0
1
1
0
3
1
1
0
1
0
0
1
2
0
1
1
1
1
1
1
1
2
0
1
2
1
2
1
2
0
1
1
1
4
0
1
1
1
1
2
2
0
1
0
1
2
1
1
1
1
1
2
0
1
1
1
1
0
1
0
0
0
2
0
1
1
0
2
2
0
1
0
0
1
1
2
1
1
2
0
0
1
1
0
3
2
2
1
1
0
0
1
2
0
0
0
2
1
2
0
0
2
0
1
2
1
2
1
1
0
0
1
0
0
1
1
1
2
0
2
0
2
1
2
2
2
0
1
1
2
1
1
2
1
0
0
1
2
1
1
1
1
1
1
2
0
1
0
2
1
2
0
0
2
0
0
2
1
1
1
1
0
1
2
2
1
0
1
1
0
2
2
1
1
2
0
2
1
0
1
1
0
1
2
0
1
1
1
1
1
1
0
1
1
1
1
0
0
0
1
1
0
1
0
1
1
1
1
0
2
1
1
2
1
0
0
1
2
2
3
0
1
0
2
1
0
0
2
0
2
0
1
0
1
0
2
1
1
1
0
3
1
1
1
0
1
2
1
1
1
1
1
2
0
1
1
1
1
0
2
0
0
1
0
0
0
1
0
0
0
1
1
0
0
1
1
1
1
1
1
1
1
1
1
0
0
1
1
1
2
1
1
1
1
1
1
1
1
2
1
0
1
1
2
1
0
0
1
1
1
1
0
0
2
2
0
0
1
0
1
2
1
1
1
1
2
0
1
0
0
1
1
1
1
1
0
2
0
0
1
2
0
2
1
0
1
2
1
1
1
0
1
0
1
1
1
0
2
1
1
2
2
1
1
2
1
0
1
1
2
1
1
1
0
0
2
1
0
0
0
1
1
0
0
0
1
1
0
0
0
1
2
3
1
2
0
2
0
0
0
1
2
1
1
0
1
1
1
0
0
1
1
1
0
1
1
1
1
1
0
2
1
1
0
2
0
0
1
1
2
1
0
2
1
1
1
0
2
2
1
1
1
0
1
2
1
1
2
0
1
0
1
0
1
1
0
2
1
1
0
0
0
2
2
2
0
1
1
1
1
2
1
2
1
2
0
0
2
1
1
0
2
1
2
1
0
0
1
1
2
2
1
1
1
1
0
0
0
0
1
1
1
0
1
1
0
1
1
2
0
1
2
1
1
2
2
0
1
0
0
0
0
1
1
0
1
0
1
1
0
1
2
0
0
1
0
1
1
2
0
1
1
1
2
1
2
1
0
1
1
2
0
0
0
0
0
0
0
0
2
0
1
1
2
0
1
1
1
1
0
1
1
1
0
0
0
1
2
2
1
0
1
0
0
0
1
1
2
0
1
1
2
1
0
2
1
0
2
0
1
0
0
2
0
1
1
2
2
2
1
0
0
2
1
1
1
2
0
1
1
2
1
0
1
1
1
1
2
2
2
0
1
2
1
1
1
1
0
2
1
1
1
0
1
1
1
1
0
0
1
1
1
0
1
1
1
1
0
0
2
0
2
1
1
1
0
2
1
0
1
0
0
2
1
1
1
0
1
1
0
1
2
0
1
2
1
1
0
0
0
1
2
1
0
1
2
1
1
1
0
1
2
0
2
0
1
0
2
0
1
0
2
0
2
3
0
0
0
0
2
2
1
0
0
2
2
1
0
1
0
1
2
0
1
2
0
0
1
0
1
1
1
1
2
1
0
0
2
0
1
1
1
0
0
1
1
1
0
2
0
1
0
1
3
1
2
1
1
1
2
0
1
1
0
2
2
0
2
0
1
1
2
2
1
1
0
2
1
1
0
0
1
1
0
2
1
0
0
1
0
2
2
0
0
1
2
2
1
1
2
0
1
0
0
1
2
1
2
1
0
0
0
1
0
1
1
1
1
1
1
0
1
1
0
1
1
2
1
0
0
0
1
1
1
0
1
0
1
0
1
2
1
0
0
0
0
1
2
2
1
1
0
2
1
0
0
0
1
0
0
1
1
2
0
1
0
1
0
1
2
1
2
0
1
1
0
1
0
0
1
1
1
1
1
0
0
1
3
0
0
1
1
1
0
1
1
0
2
1
2
1
0
1
1
1
1
1
1
2
2
1
1
1
2
2
1
1
0
2
0
1
0
1
2
0
0
2
1
2
0
1
0
1
0
0
1
1
0
1
3
1
1
1
1
0
0
0
1
0
0
0
1
2
1
1
0
1
1
0
0
1
1
0
2
0
1
1
1
0
1
0
0
1
2
1
1
0
1
1
1
0
1
0
0
0
1
1
2
2
2
1
0
1
1
0
2
1
0
1
2
0
1
2
1
2
0
1
0
0
0
2
1
0
1
1
1
1
1
1
1
1
1
2
2
1
1
2
0
2
0
1
2
1
2
2
1
1
0
0
1
1
1
0
2
0
0
0
1
1
1
1
1
1
1
1
2
0
1
1
0
1
0
0
1
4
1
1
0
0
1
1
1
0
1
1
2
0
1
2
1
0
0
1
1
0
0
0
0
1
0
1
1
2
2
2
1
1
1
1
2
1
1
1
1
0
1
1
1
1
1
0
1
0
1
1
0
1
1
1
0
0
1
2
2
1
0
0
1
2
0
0
1
0
1
1
0
2
0
0
1
1
1
2
0
2
2
1
2
1
0
0
1
1
1
1
1
2
1
0
0
1
1
2
1
0
0
0
0
1
1
0
2
1
0
1
0
2
1
1
1
0
1
1
1
1
1
2
1
1
2
1
0
1
0
1
1
1
2
2
0
1
0
1
0
0
2
1
0
0
2
1
1
0
1
1
1
2
2
0
1
1
2
0
1
2
2
1
2
1
1
1
3
0
1
2
0
2
1
1
1
0
2
1
1
0
1
1
1
2
1
0
1
1
0
2
1
3
1
1
0
0
2
2
2
1
0
1
1
1
1
0
2
0
1
2
3
1
1
0
1
2
1
1
1
1
0
0
2
2
1
2
0
0
2
1
1
1
2
1
2
0
1
0
0
1
2
1
1
1
1
2
2
2
1
0
3
1
1
1
1
1
4
1
2
1
2
0
1
0
0
0
2
2
0
0
0
1
0
1
2
2
1
0
0
1
2
0
1
0
2
0
1
1
1
0
2
0
2
1
0
0
2
1
0
0
2
1
1
2
1
1
0
1
1
1
1
0
1
0
2
2
1
1
1
1
1
1
2
0
0
0
0
1
1
0
1
1
1
1
0
2
2
1
2
1
1
0
1
2
1
0
2
0
0
2
2
0
1
2
1
0
0
1
0
1
2
2
1
1
0
1
0
1
1
0
2
1
0
2
1
1
0
3
2
0
0
1
0
0
0
1
2
1
0
1
2
1
2
0
2
1
0
0
1
1
0
2
1
0
0
0
3
1
1
2
1
0
2
4
2
0
2
2
0
0
1
0
1
3
0
0
0
1
1
0
1
0
1
1
0
2
2
1
2
0
1
1
0
2
2
0
0
1
0
0
1
1
2
0
0
1
1
0
1
0
1
0
1
2
1
2
0
1
1
0
4
1
0
0
2
1
0
0
0
1
0
0
0
0
2
1
1
1
0
1
1
1
1
1
1
1
1
0
0
0
1
4
1
1
0
1
1
1
0
0
2
1
2
2
0
0
1
0
0
1
0
1
0
1
2
0
1
0
0
0
0
0
0
1
1
1
1
0
1
2
0
1
0
2
1
0
0
0
1
0
1
1
0
2
3
1
0
2
2
0
0
0
0
0
0
2
2
1
2
2
1
2
0
1
0
2
1
1
1
1
2
2
2
1
3
0
1
1
0
1
0
1
1
1
2
0
1
2
1
2
0
1
0
1
1
0
0
1
2
1
1
1
1
2
1
2
2
0
1
1
0
1
1
1
1
0
2
2
1
2
1
1
0
0
0
0
0
2
0
1
0
1
1
2
1
0
0
1
1
1
1
1
2
0
1
2
1
1
1
1
1
2
1
1
1
1
2
1
1
0
1
0
0
1
2
0
1
0
0
1
2
1
2
2
1
0
2
1
1
1
1
0
1
1
0
0
1
0
1
2
2
1
0
1
2
2
0
1
1
0
3
1
1
1
1
2
1
1
1
1
1
2
1
1
2
1
0
0
0
2
1
1
2
2
1
2
0
2
2
0
1
2
0
0
1
0
1
1
0
0
2
1
1
2
0
1
1
2
2
2
0
2
2
0
1
0
0
1
1
1
1
1
2
2
1
1
1
1
0
2
1
2
1
1
1
1
1
1
1
2
2
2
1
2
2
0
0
2
2
2
1
1
2
0
1
1
1
1
1
1
0
2
2
2
0
1
0
2
1
1
1
2
2
1
2
0
0
1
1
0
1
1
0
1
1
1
1
0
0
0
0
1
2
2
1
2
1
0
0
1
1
1
1
0
1
0
0
1
1
1
0
0
3
2
0
2
1
1
1
0
2
2
0
0
1
0
1
1
1
0
0
0
1
1
1
1
0
2
1
1
1
2
1
2
2
1
1
1
1
1
2
1
1
0
1
2
2
0
0
1
1
2
1
1
0
2
2
1
0
1
1
0
2
1
1
1
1
1
1
2
1
1
1
2
1
1
3
1
2
0
0
0
2
1
2
0
2
0
2
1
0
0
0
1
1
1
1
2
0
0
2
1
1
2
1
3
0
1
0
1
1
1
0
1
2
1
1
1
1
1
1
0
2
0
1
1
0
2
0
0
0
0
2
2
0
0
1
0
2
1
2
1
2
1
2
0
0
1
0
0
2
1
0
2
1
1
3
1
1
0
0
0
0
1
1
2
0
1
1
1
0
1
1
1
0
0
0
2
0
1
0
0
1
2
0
2
1
0
2
1
1
1
0
1
2
2
2
1
2
0
2
0
2
2
0
1
0
2
1
1
2
1
2
0
0
0
1
1
0
2
2
1
1
2
2
0
1
2
2
0
0
0
2
2
1
1
0
0
1
1
1
2
1
1
0
1
1
1
1
1
1
2
2
0
1
1
0
0
1
4
0
1
1
1
0
1
1
0
1
0
0
1
2
2
1
1
2
1
2
1
2
2
1
0
0
1
1
1
0
0
1
1
1
1
0
1
1
0
0
1
1
2
1
1
0
2
1
1
0
0
1
2
1
1
0
1
1
0
0
0
3
0
1
2
1
2
2
0
0
1
1
1
2
1
1
1
1
1
0
1
2
2
1
1
0
2
1
1
0
1
0
2
1
0
1
1
0
2
0
0
2
1
2
1
2
0
2
1
1
0
0
0
2
1
2
1
1
2
1
0
0
0
2
0
1
1
0
1
1
0
2
1
1
1
2
1
2
2
1
0
2
0
1
2
0
0
1
1
1
1
1
1
2
2
1
1
2
0
0
1
2
0
0
0
2
1
1
1
1
2
1
1
1
1
0
1
2
1
0
1
1
0
2
1
0
1
0
1
0
1
0
0
1
1
1
1
1
0
1
2
1
0
1
0
1
1
0
1
2
1
2
2
0
2
1
0
1
1
1
2
0
0
1
2
2
3
0
1
0
2
2
1
1
0
0
1
0
0
1
0
1
0
1
1
2
0
1
1
0
2
0
0
1
1
1
1
2
0
1
0
2
1
1
1
0
0
1
0
2
1
0
3
1
2
1
1
2
0
1
1
0
0
0
1
1
0
0
1
0
0
1
1
0
0
0
1
1
0
1
0
1
2
1
0
1
1
2
2
1
1
0
1
0
1
0
0
0
0
2
2
1
2
1
0
2
0
1
1
1
1
0
1
2
1
0
0
1
0
1
1
3
0
0
1
1
1
1
2
1
1
0
1
2
1
1
0
0
1
0
1
0
2
1
0
1
1
1
1
1
2
2
0
0
2
1
2
2
0
0
1
1
0
1
0
2
1
1
2
3
1
1
2
0
2
2
0
1
2
2
0
0
2
1
1
0
1
2
1
1
1
2
0
1
1
1
1
2
2
0
1
2
1
2
1
2
2
1
2
1
1
2
0
1
0
0
0
1
0
0
1
1
0
2
5
1
0
1
2
1
1
0
0
2
1
1
0
1
0
1
1
1
2
1
1
0
0
0
1
2
0
0
1
1
1
1
0
1
0
1
1
1
0
1
0
1
2
0
0
1
1
0
2
1
0
0
1
1
0
0
1
0
5
1
2
2
2
1
1
1
0
1
1
2
2
0
0
0
1
1
1
1
2
0
0
3
0
1
0
1
0
0
1
0
0
1
0
1
0
1
2
2
1
2
0
1
0
1
0
0
2
1
1
0
1
1
1
0
1
0
1
1
1
2
1
3
1
0
0
1
1
1
1
1
2
0
1
1
2
2
1
0
1
1
0
2
1
0
1
0
0
0
2
2
1
2
1
0
0
1
2
1
1
0
1
1
0
1
1
1
0
0
0
1
1
1
1
0
0
0
0
2
2
2
0
1
1
1
1
1
1
1
1
0
2
1
1
0
0
2
0
1
1
0
1
0
2
1
0
2
0
1
1
0
0
0
1
1
1
1
1
2
2
1
1
0
0
0
0
1
2
1
0
0
0
1
2
1
1
0
1
0
1
1
2
1
0
0
1
0
2
1
1
1
1
1
0
1
1
1
0
1
1
0
0
0
1
2
1
1
0
0
1
1
1
1
2
0
1
1
1
0
0
1
0
0
1
2
0
1
0
0
1
3
1
2
0
0
2
0
0
1
2
1
2
0
1
0
0
0
2
2
0
1
1
0
0
0
1
1
1
0
2
1
1
2
2
0
2
2
0
0
1
0
0
0
1
2
0
0
1
1
0
2
1
1
1
1
1
1
1
1
0
1
2
2
0
1
1
1
0
2
0
1
2
2
2
2
1
0
0
0
0
2
0
1
1
1
1
0
1
1
2
0
1
0
1
1
2
2
1
1
1
1
1
2
0
2
0
1
1
1
3
0
1
2
1
1
2
1
0
0
1
2
2
0
2
1
1
2
2
1
0
1
0
1
1
1
0
1
1
1
1
0
1
2
0
0
1
1
1
1
1
0
0
1
1
1
2
1
1
0
4
1
0
1
1
1
0
1
0
1
2
0
3
1
2
3
0
2
2
1
1
2
1
2
2
1
1
0
0
1
0
1
2
1
2
1
1
0
0
2
1
0
1
2
0
1
0
0
2
1
0
0
2
1
2
0
2
1
0
1
1
1
1
0
0
3
2
0
2
1
1
2
0
1
0
0
0
1
1
0
1
1
2
0
0
0
0
1
0
1
1
1
0
0
2
3
0
0
0
1
1
1
0
1
1
0
2
1
0
0
1
1
0
2
1
1
2
0
0
1
2
1
0
1
1
2
2
1
1
1
0
1
0
1
2
0
2
2
1
4
2
2
0
0
2
1
1
1
1
1
1
0
2
1
0
0
2
1
2
0
0
2
2
2
2
0
1
1
2
2
1
0
0
1
1
1
1
2
0
1
0
0
2
0
2
2
2
1
1
2
0
1
1
1
3
0
1
1
0
2
1
1
1
1
2
0
2
1
0
1
1
2
1
0
1
1
0
0
0
0
1
1
2
1
2
2
1
1
1
2
2
1
1
2
2
0
0
2
2
0
0
0
2
2
0
2
1
1
0
0
2
2
1
0
1
1
1
1
1
0
1
1
1
0
0
1
1
1
1
1
0
0
0
2
0
0
2
0
2
2
1
0
0
0
0
1
2
1
0
2
0
1
1
4
0
2
1
2
1
0
1
0
1
1
0
1
1
0
1
1
2
2
1
0
0
3
1
0
1
0
1
1
0
0
0
1
2
1
1
2
0
0
0
0
2
1
0
1
0
1
0
1
0
2
2
1
1
1
0
0
1
1
2
2
1
0
1
1
1
1
1
1
2
0
0
0
2
1
2
1
0
1
0
1
1
2
0
0
2
2
2
1
1
1
1
1
2
0
1
1
1
0
1
2
0
0
1
0
1
2
1
2
1
0
0
1
2
2
0
1
1
1
0
0
0
1
1
1
1
0
1
1
2
5
2
0
2
0
0
1
0
2
1
0
1
1
1
2
2
1
1
1
2
2
2
2
2
0
1
0
0
1
1
1
0
1
0
1
0
1
1
1
0
2
1
1
1
0
2
1
0
2
2
0
0
1
2
1
0
0
0
0
1
1
1
0
0
0
0
2
1
1
1
1
0
0
1
0
1
0
2
1
1
1
1
1
1
0
0
1
0
1
1
0
2
1
1
2
0
1
1
0
0
0
1
1
1
1
2
1
0
0
2
1
0
0
2
1
0
1
0
2
1
2
1
2
0
0
0
1
1
0
0
1
3
0
1
1
1
1
2
0
1
0
1
0
1
1
1
0
1
1
1
1
1
1
1
1
1
2
0
0
0
1
1
2
1
0
0
0
0
1
1
1
1
0
2
0
1
1
0
1
0
1
2
0
0
0
0
1
2
1
2
2
3
1
1
2
0
0
0
1
1
1
0
1
1
1
0
1
1
1
1
0
1
2
2
0
0
0
1
1
0
1
0
1
1
1
1
2
1
0
0
2
1
1
1
1
1
1
0
1
2
0
1
1
1
1
0
1
0
0
0
0
1
2
0
1
1
1
0
1
2
1
2
2
0
0
2
1
4
1
0
1
1
0
0
0
1
0
2
1
0
1
1
1
1
2
1
1
0
1
0
0
0
2
1
2
0
2
0
1
1
1
2
2
1
1
1
0
0
1
0
0
2
1
1
1
0
0
1
0
1
1
0
1
1
1
1
1
1
1
1
1
2
2
0
1
1
1
0
2
0
0
2
1
0
1
1
0
2
2
3
2
2
1
0
2
2
0
1
2
1
2
1
1
1
2
0
2
1
1
1
1
1
1
1
1
2
0
1
0
0
1
1
0
0
2
0
1
0
2
2
0
2
1
1
1
1
1
0
3
1
0
2
0
0
1
3
1
0
0
1
1
1
0
0
0
2
2
1
1
0
1
3
2
1
1
1
1
0
2
1
1
0
1
1
1
1
1
2
2
1
2
0
1
0
0
0
1
0
0
1
1
0
0
0
2
2
1
1
2
2
1
1
2
1
0
1
2
1
2
0
1
0
1
2
1
2
1
2
1
1
1
0
0
0
2
1
1
0
1
0
1
0
0
1
0
1
1
1
1
2
0
1
1
1
1
2
0
0
1
2
1
1
0
0
1
1
1
1
1
1
2
2
0
2
1
0
0
2
1
2
2
1
2
1
0
1
2
1
0
2
1
1
0
0
0
0
0
1
1
1
0
1
0
0
0
2
2
0
1
1
1
2
0
2
2
2
1
1
1
2
2
0
2
0
0
0
2
1
2
2
0
1
1
1
0
2
1
1
1
1
0
2
0
2
1
0
2
1
1
1
0
1
2
1
0
0
2
1
0
2
1
1
1
0
2
0
0
1
0
0
1
1
1
1
0
0
1
1
0
0
2
1
1
1
0
2
1
2
1
1
1
0
2
0
1
2
1
1
1
2
2
1
1
0
1
1
1
1
0
0
2
1
0
1
0
1
1
0
2
1
1
2
0
1
0
1
0
2
2
0
2
0
1
2
0
0
2
0
3
2
2
1
1
0
1
2
0
0
0
1
1
2
0
1
0
1
1
2
1
3
0
0
1
0
0
1
2
1
0
0
1
1
1
0
3
0
2
1
0
0
1
1
1
2
1
0
0
0
1
1
1
1
1
1
1
1
2
1
1
1
0
0
1
1
2
0
2
2
1
3
1
2
0
1
0
2
2
1
0
2
0
0
1
2
0
0
1
1
0
1
1
0
2
2
0
2
1
0
0
2
1
0
1
2
2
2
1
2
1
2
1
1
0
1
1
1
1
1
0
1
0
0
1
1
1
2
1
1
0
2
2
1
1
2
1
0
0
1
1
0
2
1
1
2
1
2
2
1
1
0
0
0
0
1
2
0
0
0
0
1
1
0
1
1
2
1
1
0
2
1
1
4
1
2
2
1
2
2
0
1
1
1
1
0
1
2
0
0
0
1
0
2
1
0
1
0
1
1
2
1
1
0
1
0
0
1
0
0
2
1
2
1
0
0
0
0
1
1
2
1
1
2
0
0
0
1
0
1
1
2
0
1
2
0
0
1
1
1
0
2
2
1
1
6
1
0
1
1
0
0
0
1
1
1
0
1
1
1
0
2
2
1
1
2
1
1
0
2
0
1
1
2
0
1
0
2
1
1
2
1
0
0
2
1
1
1
0
0
0
1
2
2
0
1
2
3
1
0
0
0
1
1
2
1
0
1
1
0
2
1
0
1
0
1
1
2
2
0
0
0
0
2
1
2
1
1
2
0
0
1
0
2
1
2
1
1
1
1
1
1
2
2
1
2
1
0
0
1
2
0
0
0
2
1
0
1
0
0
0
0
1
1
1
1
0
1
2
2
1
0
0
0
1
1
1
1
1
1
0
1
0
1
0
2
2
1
0
0
1
0
1
1
1
1
0
1
1
0
0
0
2
2
1
1
1
1
1
0
2
1
2
2
3
0
0
1
0
2
1
0
1
1
2
1
0
0
1
1
0
2
2
1
0
0
0
1
2
0
0
1
0
0
2
1
1
1
1
2
0
1
1
1
1
1
1
1
2
1
2
2
1
1
2
1
1
1
1
1
1
0
1
2
0
0
1
0
1
1
0
0
2
1
1
1
2
0
1
0
0
2
2
0
1
0
1
2
1
1
0
2
2
2
1
0
0
1
1
1
2
1
2
0
1
2
1
0
0
1
1
2
1
1
2
1
1
0
1
1
1
1
1
1
0
1
1
0
1
1
5
0
0
2
0
2
0
1
1
0
1
0
2
1
1
1
2
0
2
0
1
2
2
0
1
1
2
2
1
1
1
2
1
0
0
1
1
2
2
2
0
1
1
0
0
1
0
0
1
1
1
1
1
0
1
1
0
0
0
0
2
0
1
1
1
1
1
0
2
0
0
0
0
1
2
0
1
0
1
1
2
1
1
1
2
1
0
2
1
1
1
2
0
1
1
2
1
1
1
1
2
0
1
1
1
1
1
1
2
1
1
0
2
0
1
0
2
1
2
1
0
0
0
0
0
3
1
1
1
0
0
0
1
2
2
0
1
0
1
4
2
2
1
2
2
1
0
5
1
1
1
0
0
1
0
0
1
0
1
1
0
1
0
2
1
0
2
1
1
1
1
1
0
2
1
1
2
1
0
1
0
0
1
1
2
1
1
1
1
2
0
0
4
1
0
2
2
2
1
2
1
2
2
2
2
0
1
1
1
0
1
1
2
1
0
1
1
3
0
0
0
2
0
1
0
0
1
0
1
1
0
2
1
0
0
1
2
2
0
1
1
1
0
2
0
2
1
1
0
2
2
0
1
2
0
1
2
1
0
1
1
1
1
0
1
0
1
0
0
1
0
2
1
0
0
0
1
1
1
0
3
0
4
0
1
0
0
2
0
2
0
1
1
1
2
0
0
1
2
1
2
0
1
1
2
1
1
1
0
1
0
2
1
2
1
1
1
2
0
1
0
1
0
2
1
0
1
1
2
1
1
1
0
0
2
0
2
1
2
1
0
0
2
0
1
0
1
0
2
1
1
1
2
1
2
1
1
0
0
1
1
0
2
2
1
1
1
0
0
1
1
0
1
1
1
0
0
2
1
0
0
1
0
3
0
0
1
1
0
1
1
1
1
0
1
1
1
0
1
2
1
1
0
0
3
1
1
1
1
2
1
1
1
0
2
1
2
1
2
2
1
0
0
1
2
0
1
1
0
2
0
0
2
1
2
1
2
1
1
1
1
0
2
0
1
2
1
2
2
0
1
2
2
0
1
2
1
2
0
1
1
1
0
1
2
1
0
0
1
0
0
1
1
0
0
2
2
0
2
2
1
0
1
0
1
1
2
1
2
0
1
2
1
0
2
0
0
0
0
0
3
1
2
2
2
2
2
0
0
0
3
1
0
0
2
2
1
1
2
1
0
0
2
1
1
1
0
0
1
2
1
2
1
1
2
2
1
2
1
1
1
1
2
0
1
0
2
1
0
1
1
0
1
1
2
2
3
0
1
0
0
0
2
2
0
1
2
0
1
1
0
1
2
1
2
1
2
1
2
2
1
1
2
0
1
0
1
1
2
1
0
0
0
0
1
0
1
2
0
1
1
0
2
4
1
0
2
2
2
0
1
0
1
0
0
1
1
1
2
2
1
0
1
1
1
2
0
2
1
1
1
1
1
0
5
1
0
1
0
0
1
0
0
1
1
1
2
0
1
0
1
1
0
1
1
2
2
1
1
0
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
2
0
0
1
0
2
0
1
3
2
1
0
1
2
0
1
1
1
1
1
2
1
0
1
0
0
2
1
1
1
2
2
1
1
1
0
2
1
1
0
0
1
0
2
2
0
1
0
3
1
1
0
0
1
1
2
3
1
0
1
1
1
1
2
1
0
0
1
0
1
1
0
1
1
1
0
0
1
0
2
0
2
2
2
0
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
0
2
0
1
1
0
1
1
1
1
0
0
3
1
0
1
0
1
1
0
1
1
0
0
1
2
1
1
0
0
2
0
0
1
1
2
0
1
0
0
1
0
0
2
2
1
2
0
2
0
1
0
1
0
1
2
0
1
3
2
1
2
0
0
1
0
1
2
0
2
0
1
0
2
0
2
1
1
2
0
0
1
1
1
1
0
1
1
2
1
0
0
0
2
1
1
0
1
1
2
0
1
2
0
1
1
0
2
1
1
2
0
1
1
1
2
1
0
1
0
2
1
1
1
0
0
0
0
0
1
1
0
0
1
0
1
2
1
2
2
1
0
1
2
1
2
2
0
0
1
0
0
2
1
2
0
0
0
0
1
0
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
1
0
2
1
1
0
1
1
1
0
0
0
1
1
0
1
0
1
0
0
1
1
1
1
0
0
1
0
1
1
2
0
0
0
2
0
2
0
2
0
0
2
1
1
0
0
0
0
1
1
0
0
2
2
3
1
1
1
2
0
1
1
2
2
1
1
2
2
1
3
0
2
2
1
1
1
1
0
1
1
2
1
0
1
1
2
0
2
0
1
1
0
1
0
1
1
1
2
0
0
1
0
2
1
1
1
0
1
2
1
2
1
1
0
2
0
1
0
1
0
1
1
1
2
0
1
1
0
2
1
2
0
1
0
2
0
2
1
1
1
1
0
0
0
1
1
1
1
2
2
1
1
0
1
0
1
0
0
1
1
1
3
2
0
1
1
2
1
1
1
0
1
0
0
2
2
1
2
1
2
3
1
2
2
1
2
1
0
1
1
1
2
0
0
3
0
0
1
1
0
1
0
1
1
2
0
0
1
0
0
2
2
1
1
1
0
0
0
2
2
1
1
0
1
0
1
2
0
2
1
1
1
1
0
1
2
1
0
1
1
0
0
0
1
1
1
1
1
1
0
1
0
0
2
1
2
0
1
2
2
1
1
1
0
2
2
1
2
0
1
0
0
1
0
1
0
1
1
1
2
2
1
2
0
1
1
0
2
1
0
1
2
0
0
0
2
1
0
2
0
1
0
2
0
2
1
1
2
0
1
0
1
1
1
1
0
1
0
2
1
1
1
0
0
0
1
1
0
1
2
2
1
2
0
1
2
0
1
0
1
0
1
2
1
1
0
4
1
1
0
0
0
0
2
2
0
1
1
0
0
1
0
2
0
0
0
1
2
1
0
1
2
0
0
1
1
1
0
1
0
1
0
0
1
0
1
1
1
1
1
1
0
2
1
1
1
1
1
1
2
2
1
2
2
1
2
2
2
1
1
1
2
2
3
2
1
0
2
2
0
1
1
1
0
1
2
1
0
0
1
0
1
1
1
1
2
1
1
1
0
2
1
1
1
3
1
4
0
1
0
0
1
1
1
2
1
0
0
2
0
0
0
1
1
1
0
2
0
1
0
1
1
0
1
2
1
1
1
1
0
1
2
0
1
0
1
1
1
1
2
2
1
1
1
0
1
0
2
2
1
0
1
0
1
1
1
1
1
1
1
1
2
1
0
0
2
1
1
1
2
1
1
1
2
1
1
1
1
0
3
2
0
1
2
2
1
0
1
2
2
3
1
1
1
0
0
1
2
0
0
2
1
1
0
1
1
1
1
1
1
2
1
1
2
0
2
2
1
1
1
1
0
2
0
1
2
2
0
2
2
2
0
2
0
2
1
2
1
1
1
1
1
0
1
2
1
0
1
1
3
0
0
1
0
1
0
0
1
2
0
0
2
1
1
1
1
2
2
0
0
0
2
0
1
0
1
2
2
1
2
0
0
1
1
1
2
1
1
2
2
1
1
0
1
1
0
0
2
1
0
0
2
1
1
0
0
1
1
0
2
2
2
2
1
2
2
0
1
1
1
1
1
1
1
0
2
0
1
0
1
0
0
0
2
0
1
0
0
1
1
1
0
1
0
2
1
0
1
0
2
2
0
2
1
0
1
1
1
1
0
2
2
1
2
2
2
1
2
1
0
1
3
1
1
1
1
2
1
1
0
0
2
1
1
1
0
1
1
0
0
0
2
1
0
0
1
2
1
1
1
1
0
2
1
2
0
2
0
0
2
2
2
1
1
2
2
1
2
0
0
1
0
4
1
2
1
1
1
0
0
0
2
1
1
1
0
0
1
1
1
1
2
1
2
3
1
2
1
0
2
0
0
1
1
0
2
1
1
0
0
1
2
1
2
1
1
0
2
3
2
1
1
1
2
2
1
0
1
2
0
2
1
0
1
1
1
1
0
0
1
1
1
0
0
0
0
1
1
0
1
0
1
2
1
0
0
0
1
2
1
1
1
0
0
2
2
1
1
2
1
0
1
0
1
1
2
2
1
1
1
0
2
1
1
1
2
1
3
1
2
2
0
1
2
2
1
2
0
0
2
2
1
1
2
1
0
0
1
0
2
0
1
1
1
1
1
0
1
0
2
1
1
0
2
0
2
0
1
0
1
1
1
1
1
1
1
2
1
0
1
0
1
1
1
0
1
1
1
1
0
1
1
0
2
2
0
1
1
1
1
2
2
0
0
1
1
0
1
1
0
2
1
2
1
0
2
1
0
0
0
0
2
3
0
0
0
0
1
1
0
0
1
1
2
1
1
1
0
1
0
0
1
0
1
2
0
0
1
1
3
0
0
0
1
1
0
0
0
1
1
1
1
0
1
1
0
0
0
1
2
1
1
0
0
1
1
0
2
3
1
1
2
0
0
0
0
1
0
1
1
1
1
0
1
1
1
2
0
1
2
1
1
0
1
0
0
1
1
0
0
0
1
2
2
0
2
2
1
2
1
0
0
0
2
1
2
1
1
0
1
1
1
1
1
2
0
2
1
0
1
1
1
1
1
0
1
1
2
1
0
1
1
1
1
0
0
1
2
2
0
0
0
1
0
1
1
1
0
1
1
1
1
1
1
0
0
1
0
1
2
1
3
0
0
0
1
1
0
0
0
0
0
0
0
1
2
0
1
0
2
1
1
1
2
0
0
2
0
1
2
1
2
1
0
0
1
1
1
1
0
0
1
1
2
0
0
1
0
3
2
1
1
1
0
0
2
0
0
1
0
0
2
1
1
1
1
0
1
0
1
2
1
2
1
1
1
0
2
1
1
3
0
2
1
1
2
1
2
1
0
2
1
1
1
1
0
0
1
1
0
2
1
0
0
1
2
0
1
0
2
0
2
0
0
0
0
0
1
2
2
1
1
2
3
1
0
1
1
0
0
0
3
1
0
0
2
2
1
2
0
2
1
1
1
1
0
2
1
0
0
1
1
2
1
0
1
2
0
1
0
1
0
0
0
1
1
1
1
0
1
0
0
0
2
2
0
0
1
1
0
1
2
0
1
1
0
2
0
1
0
2
2
1
2
0
0
2
0
1
1
2
0
2
0
1
1
0
1
2
0
0
0
1
2
0
1
2
0
3
2
0
1
1
2
2
0
1
1
1
1
1
0
1
0
0
2
0
1
1
2
0
2
1
0
2
0
1
1
1
0
1
2
1
0
1
1
2
1
0
1
1
0
1
1
2
0
1
0
1
0
1
0
0
1
2
1
1
1
1
0
2
2
0
1
2
0
1
1
2
2
2
1
1
0
2
1
1
1
1
0
2
2
1
0
1
2
0
1
1
0
1
1
1
0
1
2
0
1
1
1
1
1
1
1
0
1
0
1
0
1
1
1
1
2
2
2
2
2
2
1
1
2
2
1
1
2
1
1
1
1
0
4
0
1
1
1
1
2
2
1
0
1
1
1
2
1
2
1
1
1
1
0
1
1
0
2
1
1
2
1
0
1
0
1
1
1
0
1
1
2
1
3
2
0
1
0
1
2
2
0
1
1
1
2
0
0
1
0
1
1
2
0
1
1
2
0
1
1
0
2
1
1
0
1
0
2
0
2
1
1
2
2
2
0
1
0
0
1
0
1
0
0
2
1
0
1
0
1
1
0
1
1
2
1
2
2
2
1
1
1
0
2
1
2
1
1
2
1
0
1
0
0
1
2
1
1
0
2
1
0
0
1
1
1
1
1
1
1
0
1
2
1
1
1
1
2
1
1
1
1
0
1
0
0
1
1
2
1
1
1
1
0
1
2
0
1
1
1
1
0
2
0
1
2
2
0
0
1
1
0
0
1
2
2
0
1
1
0
2
2
1
2
2
0
1
2
0
1
0
0
1
0
0
2
0
2
0
1
1
1
1
0
0
1
0
2
2
2
1
1
0
1
1
1
2
1
0
0
1
2
0
2
1
1
0
0
1
1
1
0
2
2
0
1
1
1
1
2
1
1
0
1
1
1
1
1
0
2
1
0
1
1
0
2
1
1
0
2
1
1
1
0
0
1
1
1
1
1
1
2
1
1
1
0
1
1
1
1
1
2
1
2
1
0
1
3
0
1
1
1
2
1
0
0
1
1
0
2
0
0
1
1
0
1
2
0
1
1
0
1
0
0
1
1
2
2
1
0
0
0
2
0
2
1
0
1
2
1
1
1
1
1
1
1
1
0
1
0
1
1
2
1
2
1
0
0
1
1
1
0
2
1
0
0
0
0
2
0
0
0
7
2
0
0
1
1
1
1
0
0
2
1
1
1
2
1
1
0
1
0
0
1
1
0
0
0
2
2
1
0
1
0
1
0
1
2
1
1
1
0
1
1
2
1
0
1
1
0
1
0
0
2
2
0
1
1
1
0
1
0
0
1
1
1
1
0
1
2
0
3
1
0
0
2
2
0
1
1
0
0
1
1
2
2
0
0
3
0
2
1
0
1
0
0
1
1
1
1
1
1
0
0
0
2
1
0
0
1
0
0
0
1
1
1
1
1
1
1
1
1
0
0
1
2
1
2
3
0
1
1
1
0
0
1
2
2
1
2
1
1
1
2
0
1
1
1
1
0
1
1
1
0
0
0
0
1
1
0
1
0
0
0
1
0
1
0
1
1
1
1
3
1
1
1
1
0
0
1
1
1
0
2
1
1
2
0
1
2
1
2
1
1
1
2
0
1
2
2
2
0
1
1
1
1
1
0
0
0
2
0
0
1
1
0
0
0
1
2
1
1
1
0
1
0
2
1
1
0
0
0
0
1
0
1
0
1
0
1
1
2
1
0
1
0
0
1
0
1
2
4
1
0
2
1
0
0
1
1
1
1
0
1
1
1
1
1
0
1
0
3
2
1
1
0
2
0
1
0
0
0
1
0
0
0
1
1
0
1
1
0
0
0
0
2
0
1
0
0
2
1
1
1
0
1
1
1
3
1
0
0
2
1
2
2
2
0
0
2
1
1
1
0
1
1
1
0
0
0
1
2
0
0
0
0
2
0
0
2
1
1
1
1
2
2
2
0
0
0
1
0
1
0
1
1
1
1
1
2
1
0
1
1
1
2
0
1
1
0
0
2
2
0
2
1
0
0
1
2
1
1
1
1
0
1
1
1
1
0
0
1
0
0
1
0
1
2
1
2
1
1
3
2
1
0
2
0
2
0
0
2
0
1
2
1
0
0
0
0
1
0
1
1
2
1
0
2
0
4
0
0
2
0
2
1
1
0
1
1
1
1
2
2
2
1
2
1
1
1
0
2
0
0
1
1
1
2
0
0
0
2
1
1
1
1
0
1
2
0
1
1
1
1
1
1
0
2
0
0
0
1
1
0
1
1
2
2
2
2
0
2
1
1
0
0
1
2
0
1
1
1
1
1
1
0
1
3
0
0
1
2
1
1
0
1
0
2
0
1
0
1
2
0
1
2
1
0
0
0
0
0
2
0
1
0
1
1
0
0
2
1
1
2
0
1
2
0
2
1
0
0
1
1
0
1
1
0
0
2
0
1
2
5
1
2
1
1
2
1
2
1
2
1
2
2
1
1
0
1
1
0
1
0
2
2
1
1
0
1
1
1
1
0
1
1
2
0
1
0
2
1
1
0
0
0
0
1
1
1
1
0
0
1
1
0
0
0
1
1
0
1
0
1
0
0
0
2
0
2
1
1
1
0
1
1
1
3
1
2
1
1
2
0
1
1
1
1
1
2
2
2
1
1
2
1
2
2
2
1
1
0
1
1
2
1
2
0
1
0
0
1
1
1
3
1
0
2
0
2
1
1
0
1
0
0
1
2
1
2
0
2
1
2
0
0
0
1
0
2
2
1
0
0
0
0
1
2
0
1
0
0
1
0
0
2
1
1
0
2
0
0
2
2
1
1
0
0
0
1
2
0
1
0
1
2
1
1
2
1
0
1
2
2
0
1
0
1
2
3
1
1
1
0
1
0
0
1
0
1
0
1
1
1
1
2
0
1
1
1
0
0
0
2
2
1
2
2
1
1
0
1
1
0
0
3
1
1
2
0
0
0
1
1
2
2
2
2
2
0
0
1
1
1
1
0
1
0
0
1
2
2
0
2
1
2
2
2
0
3
1
0
1
1
2
0
1
2
1
1
2
1
0
1
1
0
1
1
0
1
1
1
2
2
1
2
2
0
1
3
0
2
1
1
0
1
2
1
1
2
1
1
1
0
0
3
1
2
0
1
0
2
1
0
1
1
1
0
1
2
0
1
1
2
1
1
1
0
2
0
0
0
2
2
1
0
1
0
0
1
0
2
0
1
2
0
1
1
1
1
2
2
1
0
1
0
2
1
2
3
0
2
0
1
0
1
1
0
1
1
0
1
2
1
0
2
0
0
1
0
2
0
0
0
0
1
2
2
0
2
1
1
1
2
1
2
0
1
0
1
1
1
0
1
0
0
2
1
1
2
2
1
2
1
0
0
1
2
1
1
1
1
0
2
2
1
0
1
1
1
0
1
2
1
2
1
0
0
1
1
0
0
0
0
1
0
2
1
0
0
0
1
1
2
1
1
0
1
1
2
0
0
2
1
2
1
0
2
0
0
1
0
1
0
2
1
1
1
1
0
1
1
2
1
0
3
1
1
0
0
1
1
1
2
2
0
1
3
2
2
0
1
1
0
2
2
2
1
0
1
0
1
3
0
0
0
0
1
2
1
1
1
1
1
0
0
0
1
1
1
0
0
0
0
2
2
1
2
1
2
0
1
1
1
0
2
1
0
0
0
2
0
0
2
1
0
0
2
0
0
1
1
2
1
0
1
1
1
1
2
1
1
0
1
0
0
1
2
0
1
0
1
1
0
0
1
0
0
1
2
0
1
1
1
2
1
1
3
1
0
0
0
1
0
1
1
1
1
2
0
0
0
0
2
1
1
2
1
0
1
0
1
0
0
0
0
2
0
0
1
1
0
0
1
0
1
2
0
2
2
1
0
1
1
1
1
2
2
1
0
0
0
0
1
1
1
2
1
0
1
1
2
0
1
1
0
0
1
1
2
0
1
1
2
2
1
2
1
2
0
0
2
1
1
1
0
0
2
2
2
0
1
3
1
1
2
1
1
1
1
2
1
0
0
3
0
1
1
2
2
1
1
1
1
2
2
2
1
1
0
1
0
1
1
1
1
0
2
0
1
0
1
1
2
1
1
1
0
2
1
2
0
2
1
1
1
0
2
1
1
1
2
0
0
3
1
2
0
1
0
0
2
1
2
0
1
1
2
1
1
1
2
1
1
0
1
0
1
1
2
2
0
1
0
0
0
2
1
1
0
1
0
1
2
2
2
0
0
1
2
1
6
1
0
0
0
1
1
2
1
2
0
0
0
1
1
1
0
2
1
1
1
1
2
1
1
2
2
0
2
0
2
2
2
1
1
2
0
1
1
1
1
1
1
1
1
0
2
0
2
0
1
2
1
0
0
0
1
2
1
1
0
1
1
1
0
0
1
1
1
1
0
2
1
0
0
2
0
2
2
0
1
0
0
1
1
2
1
1
0
1
0
1
1
0
1
0
1
1
0
1
1
0
1
2
0
0
0
1
2
1
0
1
1
1
0
0
1
0
1
0
2
2
0
0
0
1
1
1
0
1
0
1
2
0
4
1
0
2
1
0
1
1
1
0
2
1
1
1
1
1
1
0
0
0
2
1
2
0
1
2
0
1
2
2
2
1
0
2
2
1
1
1
0
0
0
1
1
1
1
0
3
0
1
1
0
1
1
0
2
1
1
1
1
2
0
0
2
1
1
1
2
0
1
1
0
1
2
0
1
3
0
1
2
0
2
0
1
1
0
1
1
1
1
1
1
2
0
2
1
2
2
1
0
1
1
0
0
1
1
0
0
0
2
2
0
1
0
1
0
1
1
0
0
0
1
0
1
2
0
0
0
2
2
2
2
1
1
1
1
1
1
0
1
0
0
2
0
2
1
1
1
0
2
1
0
2
2
1
1
1
0
1
1
1
1
1
1
0
3
0
0
1
3
0
2
1
1
0
0
0
0
2
2
2
1
0
0
1
0
1
0
0
0
2
1
1
1
2
1
1
1
1
1
0
1
0
1
2
1
2
0
2
0
1
2
1
0
0
2
2
3
0
0
1
2
0
0
1
2
1
1
2
2
1
1
0
1
0
1
1
2
1
0
0
1
1
2
1
2
0
1
1
0
0
1
1
1
2
2
0
2
0
1
0
2
1
1
2
0
1
1
0
2
1
2
1
2
1
0
2
0
2
0
2
1
1
0
2
1
1
0
0
1
1
0
1
1
1
0
2
1
0
0
1
0
1
2
2
1
1
1
1
0
0
1
1
0
1
0
2
0
1
0
1
1
1
2
1
2
1
0
1
1
1
0
2
1
1
1
1
1
0
0
2
1
2
2
2
0
1
1
1
1
1
0
1
2
1
2
2
1
2
1
1
1
0
1
0
0
1
1
1
0
0
2
0
2
1
1
1
0
0
0
0
1
0
1
1
1
0
0
1
2
0
0
1
1
0
1
1
0
0
1
1
0
0
2
0
1
2
0
1
0
0
0
1
1
1
0
0
0
1
1
2
1
0
1
1
2
1
0
1
1
2
1
4
1
1
0
0
1
2
0
1
1
1
1
1
1
1
1
1
1
1
1
0
1
0
1
1
2
2
2
1
1
0
2
0
2
1
0
1
1
0
1
0
0
2
0
2
1
1
0
2
1
0
1
1
0
1
0
1
2
1
1
0
0
2
1
1
1
0
2
0
1
1
1
2
0
1
1
1
1
1
2
1
1
2
1
1
1
2
2
0
0
1
1
1
1
0
2
1
2
1
0
1
0
1
0
2
2
1
0
1
0
2
0
1
0
0
1
1
1
1
2
1
1
1
0
0
1
0
1
1
0
0
2
1
3
1
1
1
2
0
0
1
1
0
1
3
0
0
0
0
1
1
0
0
0
0
0
1
1
1
2
0
1
0
0
1
2
0
0
1
1
2
1
1
0
2
0
0
0
0
0
2
0
0
0
1
2
0
0
1
2
0
0
2
1
2
2
1
0
2
1
0
0
1
1
1
1
1
0
2
1
0
1
1
1
1
1
1
0
1
0
1
0
0
2
2
3
1
1
0
1
1
1
0
2
1
1
1
0
1
0
0
0
0
2
2
1
0
1
0
0
1
1
1
0
0
2
2
1
0
2
1
0
0
0
0
1
1
1
0
2
2
2
2
1
2
1
0
0
0
1
1
0
0
0
1
1
0
2
1
0
2
0
2
0
2
1
1
1
1
1
0
2
0
0
1
2
1
1
0
1
2
1
1
2
1
1
1
2
1
0
3
1
1
1
0
0
1
2
1
0
1
0
0
1
2
0
2
1
2
0
2
2
0
1
1
0
1
1
2
1
0
1
1
1
0
1
1
1
1
2
1
0
2
1
2
0
0
0
1
2
1
2
0
2
0
0
0
0
2
0
2
2
2
2
1
0
1
1
2
2
0
2
2
2
2
1
1
2
1
1
0
0
2
1
1
1
2
2
1
1
1
1
0
0
1
1
1
0
1
0
2
0
1
0
1
1
5
1
0
1
0
1
0
1
1
0
0
0
1
0
0
2
2
2
0
2
1
1
0
1
0
1
1
1
1
1
1
1
0
0
2
2
0
1
0
0
0
2
1
2
1
1
2
0
0
0
0
2
1
1
0
1
0
3
0
1
1
0
0
1
0
2
0
2
1
0
0
0
1
1
1
0
0
2
2
1
0
1
1
0
3
1
0
2
1
1
2
1
2
1
0
0
1
0
2
0
1
1
0
1
1
0
1
2
2
2
0
0
1
1
2
1
0
1
0
1
0
1
0
2
2
0
2
1
1
1
0
0
1
0
1
0
1
1
0
2
1
0
0
1
1
1
2
1
0
1
0
1
1
0
0
2
0
1
1
2
1
1
0
2
0
0
1
1
1
2
0
1
0
3
0
1
1
1
0
2
3
2
1
1
2
1
0
1
2
1
1
1
1
1
2
2
2
0
0
1
2
1
2
0
0
2
0
2
1
0
1
1
1
1
3
0
1
0
1
1
0
1
0
1
2
4
2
0
2
1
0
1
1
2
1
2
0
4
0
1
0
0
1
1
1
0
0
0
0
1
2
1
0
2
1
0
1
1
0
1
2
1
1
0
0
3
3
1
2
2
0
0
0
1
1
0
2
2
0
0
1
0
1
0
0
0
1
1
0
1
2
1
0
1
2
0
0
0
0
0
0
1
2
0
0
1
1
2
1
0
0
0
0
0
2
0
2
1
0
1
0
0
1
0
0
1
0
1
2
0
1
0
1
2
0
2
1
2
1
0
2
2
1
1
0
0
1
2
1
0
2
2
1
1
1
2
2
1
2
1
2
2
1
0
1
2
3
1
1
1
0
2
2
0
1
1
0
0
1
1
1
2
0
1
0
0
0
0
0
0
1
1
0
0
2
1
1
1
0
3
0
0
1
2
1
0
2
1
1
0
1
2
0
1
1
1
0
1
1
3
1
1
1
2
1
1
2
2
2
2
0
1
1
0
1
1
0
1
0
2
0
2
1
2
1
0
2
1
2
1
1
2
1
1
2
2
0
2
2
1
1
1
1
0
1
1
1
2
1
1
2
0
1
1
0
1
1
1
2
1
1
1
1
0
0
0
5
1
1
2
1
0
1
0
1
0
1
1
0
0
2
0
2
2
0
2
1
0
1
2
1
0
2
1
0
0
0
2
0
0
0
1
1
1
0
1
2
1
1
0
1
1
0
1
1
0
0
1
1
1
0
1
0
2
2
1
1
0
2
1
1
2
1
1
2
0
1
1
1
1
1
0
1
2
0
0
1
0
0
1
2
0
0
1
0
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
0
2
0
2
0
2
1
0
1
2
1
2
0
0
0
1
2
1
1
0
0
1
0
0
0
1
0
0
0
0
0
2
0
2
1
1
1
2
1
1
2
1
1
2
0
1
0
0
0
1
2
0
2
1
2
1
0
1
0
2
0
2
1
0
1
1
2
2
0
1
0
2
1
0
0
1
0
1
0
1
0
1
2
0
1
1
1
1
1
1
0
1
2
2
1
2
1
2
1
0
0
0
0
1
0
1
0
1
2
2
1
0
1
1
0
1
2
0
0
2
1
4
1
2
0
2
1
0
1
1
1
0
3
2
1
0
0
2
0
0
0
0
1
0
1
1
1
1
2
2
0
0
2
1
2
1
0
1
1
3
1
1
1
2
1
0
2
1
0
0
0
2
0
2
0
2
3
1
0
0
1
1
0
0
2
1
0
1
1
0
2
1
0
0
1
0
1
2
2
1
0
1
1
1
0
0
2
0
1
0
0
2
0
0
0
4
0
2
0
1
1
0
0
0
1
0
1
2
2
0
2
0
1
1
0
0
1
1
0
2
2
0
1
1
2
1
0
1
0
0
2
0
1
0
1
2
2
2
1
0
1
2
2
1
1
2
0
0
2
0
2
2
2
1
1
1
0
0
2
2
2
0
2
1
0
0
0
1
1
0
1
1
1
1
0
0
0
0
1
1
2
0
0
0
2
1
1
0
2
1
0
1
0
0
0
1
1
0
0
2
2
1
1
1
0
0
0
1
1
1
1
1
0
2
0
1
2
0
2
2
2
0
0
0
1
1
0
2
1
1
1
2
1
1
0
2
2
0
0
2
1
0
2
0
0
1
0
1
2
0
0
1
2
3
0
1
0
2
0
2
0
0
1
1
1
1
0
1
2
2
0
1
0
1
1
0
0
0
0
1
0
1
0
0
4
0
2
1
1
2
1
1
1
2
2
1
1
0
1
2
1
0
1
1
0
0
2
1
2
2
1
2
0
2
1
2
0
1
1
0
0
2
1
1
1
1
0
2
1
0
0
0
1
1
0
0
0
2
0
1
1
1
0
1
1
2
1
0
0
2
1
2
1
0
1
0
1
1
1
1
0
1
0
1
3
0
0
1
0
0
0
1
2
1
0
1
0
1
1
1
2
5
2
1
1
1
1
0
2
1
0
3
0
0
1
0
1
2
0
0
1
2
0
1
2
1
0
0
2
1
0
2
1
2
1
1
2
0
0
0
1
1
1
1
0
2
0
3
1
1
2
0
1
1
0
0
1
1
0
0
0
1
1
1
1
2
0
2
1
0
0
2
0
1
0
0
0
2
2
2
1
0
0
2
0
1
0
0
0
1
1
0
0
1
0
2
1
0
0
2
2
2
1
0
1
0
0
0
2
1
1
0
2
0
2
1
0
2
0
1
3
1
0
1
1
0
1
1
1
1
2
0
0
1
1
2
1
1
1
1
0
2
0
0
1
2
1
1
0
0
1
2
2
1
1
1
3
1
1
1
2
2
0
0
1
0
0
2
1
0
0
1
1
1
1
1
0
1
1
2
0
1
2
1
1
1
1
0
1
1
7
0
0
0
1
4
1
1
1
1
1
0
1
0
2
0
2
1
0
2
1
0
0
1
0
1
1
1
1
2
0
1
0
0
2
1
1
1
2
0
2
2
1
3
0
1
1
0
2
2
1
1
0
1
1
0
0
1
1
0
2
3
0
1
2
1
1
0
1
0
1
1
2
0
2
0
1
1
1
0
0
1
1
0
1
1
0
0
1
2
2
1
0
1
1
2
1
0
0
0
2
2
1
1
1
1
1
2
1
2
1
2
1
1
2
1
1
1
1
0
0
0
2
2
1
2
0
1
1
0
1
2
2
1
1
0
1
0
1
2
0
1
2
1
1
0
1
0
0
0
1
0
0
1
0
2
0
1
0
1
0
0
0
0
1
3
0
1
0
1
1
1
2
0
1
3
0
1
1
2
2
3
1
1
1
0
2
1
2
2
0
1
1
0
2
2
0
2
2
0
2
3
2
0
1
2
0
1
0
2
2
0
0
1
0
0
0
0
0
1
2
1
0
1
3
2
2
2
2
1
0
0
0
2
1
2
0
0
2
1
1
0
0
1
0
1
2
1
0
1
4
0
2
1
1
2
1
2
1
1
0
0
0
2
1
1
1
1
2
1
1
1
2
1
0
0
2
1
0
0
1
1
1
0
1
1
2
1
2
3
1
1
1
2
1
1
1
1
2
0
1
1
1
1
0
0
0
1
0
2
0
0
0
1
1
1
0
1
1
1
0
1
1
2
0
1
1
0
2
0
1
0
1
2
1
1
0
1
0
0
1
1
0
1
0
1
2
1
0
0
0
0
2
0
1
1
0
1
0
1
1
1
0
1
0
0
1
1
1
0
2
1
1
0
2
1
2
0
1
0
1
2
0
2
1
1
2
1
1
0
2
2
0
2
1
0
1
2
0
0
1
1
0
2
0
1
1
1
1
1
1
1
0
1
0
1
1
0
1
2
0
1
2
1
2
1
1
0
1
1
1
0
1
0
1
0
1
1
2
0
1
1
1
0
1
1
2
0
1
1
2
0
1
2
2
3
0
2
1
1
2
1
1
2
1
1
1
2
0
0
1
1
2
0
1
2
2
1
1
1
2
0
2
0
1
1
1
2
1
1
2
1
1
0
0
0
1
1
0
2
1
2
1
2
1
2
1
1
8
0
0
2
1
2
1
1
2
0
1
0
0
2
2
0
2
0
1
1
1
2
2
1
1
0
1
0
6
1
0
1
1
2
1
2
1
0
0
0
1
1
1
1
0
1
3
1
1
1
2
0
1
1
1
2
0
2
0
0
0
1
1
0
2
2
2
0
0
0
1
0
2
2
1
0
1
2
1
1
1
3
1
0
1
0
0
0
1
0
0
2
0
0
1
1
0
2
1
2
1
2
1
0
0
0
1
1
1
1
1
0
1
0
1
1
1
1
1
0
2
2
0
1
0
0
1
0
3
0
0
0
1
2
1
0
1
0
0
1
1
0
0
1
0
1
0
1
1
1
0
1
0
1
1
2
0
1
1
1
2
0
1
1
0
1
0
0
0
0
1
0
2
1
0
2
0
1
0
1
2
1
2
2
4
1
2
0
1
0
1
0
2
0
1
2
1
1
1
0
0
1
1
0
0
2
2
0
1
1
1
2
1
1
2
0
0
0
0
0
0
2
1
2
0
0
1
2
2
0
3
2
1
0
0
1
1
1
1
0
0
1
0
1
1
2
0
0
1
1
2
1
0
0
0
2
2
1
2
1
1
0
0
2
1
0
1
2
0
2
0
0
1
0
1
2
0
2
0
0
0
2
2
1
1
2
1
0
1
1
1
2
1
1
1
0
1
3
3
0
0
2
0
1
1
4
1
2
2
1
0
1
0
2
2
2
2
1
2
1
1
1
1
2
0
1
5
0
1
0
1
1
0
2
1
4
0
0
1
1
0
2
1
0
2
2
0
2
1
0
1
0
0
0
1
0
2
0
1
2
0
0
1
0
1
1
0
1
0
0
2
0
0
1
0
2
1
2
3
1
1
1
1
1
1
0
0
1
1
2
1
0
0
0
0
1
0
0
1
1
2
2
1
0
2
0
1
2
1
2
2
1
0
1
0
1
2
2
1
0
2
2
1
2
2
1
1
1
1
0
0
2
0
2
1
2
1
0
1
1
1
2
1
1
2
1
2
1
1
2
1
1
1
1
1
0
1
1
1
1
2
0
1
0
1
2
0
1
1
1
0
1
1
1
1
2
2
1
0
0
1
1
2
1
2
1
1
2
0
0
1
0
2
1
1
2
1
1
2
0
1
1
1
1
1
1
2
2
0
2
0
0
2
1
2
1
1
0
1
2
1
1
2
1
0
1
1
1
0
1
0
0
1
0
1
0
0
2
0
0
1
0
1
0
0
1
2
0
1
2
0
0
0
0
0
0
1
0
1
2
0
0
1
0
1
1
1
1
1
2
0
1
1
1
2
1
2
2
1
0
0
1
1
0
1
1
2
0
0
0
0
0
1
0
0
0
1
1
0
1
1
0
1
1
0
1
1
1
0
2
2
0
0
0
0
2
0
1
0
1
0
1
2
0
1
2
0
0
1
1
0
1
1
2
1
1
0
1
2
2
0
0
1
2
0
0
1
1
2
2
1
1
0
1
1
2
1
1
2
0
1
0
0
1
0
0
1
1
1
1
1
0
0
0
1
0
2
1
0
0
2
1
1
0
1
2
1
2
1
1
0
1
2
2
0
1
2
3
1
2
1
2
1
1
1
1
1
1
1
1
0
2
1
1
0
1
0
0
0
1
1
1
1
0
1
1
1
1
2
0
0
1
1
2
0
2
0
1
1
0
2
1
2
0
1
0
0
1
0
1
1
0
1
0
2
2
1
0
0
0
1
2
1
1
0
1
1
1
1
0
1
2
0
0
0
1
0
1
1
2
1
1
1
1
1
1
1
1
1
2
0
1
0
2
1
2
1
2
1
0
0
1
1
1
0
2
0
1
2
2
0
1
0
1
1
0
0
1
0
0
1
1
2
0
2
2
2
1
2
0
0
2
1
1
1
0
2
1
1
2
1
0
1
1
0
0
0
1
1
1
1
1
2
1
1
1
0
0
1
2
0
1
2
0
2
1
1
0
0
0
2
0
1
1
1
0
1
0
1
0
1
2
2
1
0
1
0
1
1
2
0
0
1
0
0
2
1
1
2
1
0
2
0
1
3
2
0
0
1
1
0
0
0
2
0
1
1
1
0
2
1
1
1
1
1
0
0
1
1
0
2
0
1
2
0
1
1
1
0
0
0
0
0
1
0
0
1
0
1
2
0
1
1
1
1
3
0
2
0
2
1
1
0
1
0
0
0
0
3
2
0
1
0
2
0
0
1
0
0
12
0
1
2
1
2
2
1
0
2
1
2
1
0
1
2
1
2
2
1
0
1
2
1
0
1
1
1
2
1
2
0
1
2
1
1
1
1
1
2
2
1
2
1
1
0
0
0
0
0
1
0
1
0
2
1
1
1
1
1
0
1
2
0
0
1
0
2
2
1
0
0
1
0
1
2
3
2
0
0
1
0
2
0
1
0
0
0
1
0
0
0
0
0
1
0
0
2
1
0
1
1
2
1
1
1
0
2
1
2
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
1
2
1
0
0
0
2
0
0
1
1
1
1
0
0
1
1
1
0
0
0
1
2
0
2
0
1
0
1
1
0
1
1
0
1
0
1
0
0
0
2
1
1
1
2
1
1
0
2
1
0
1
0
0
1
1
2
1
2
0
1
0
1
1
1
0
0
1
1
1
0
1
2
1
1
1
0
2
0
1
1
2
0
1
0
1
1
0
2
1
2
1
1
1
1
2
1
1
1
1
1
0
1
1
2
1
1
1
0
1
0
0
0
3
2
2
0
1
1
1
1
1
1
2
0
1
0
0
1
0
0
1
2
1
1
1
0
1
0
2
0
2
1
0
1
2
1
0
1
0
1
0
0
2
2
1
1
0
1
1
1
2
0
0
1
1
1
1
0
2
1
0
0
0
1
1
1
1
1
0
0
1
2
1
1
2
2
3
2
2
0
0
1
1
1
1
2
1
1
2
1
2
2
0
1
1
1
2
0
0
2
1
1
1
1
0
1
0
1
2
0
1
0
0
1
1
0
1
0
0
1
1
1
0
3
0
0
1
0
1
0
1
0
0
1
2
1
1
2
1
2
1
2
1
1
0
1
0
2
2
1
0
1
1
0
0
1
0
2
1
1
0
1
2
2
2
1
1
2
1
1
2
0
0
2
1
1
0
0
0
1
0
1
1
0
0
0
2
2
0
2
1
0
0
2
1
1
1
0
0
0
2
1
3
1
1
1
0
1
1
2
0
0
0
1
1
0
0
0
1
2
1
2
2
0
1
1
1
0
0
0
1
2
2
2
1
2
1
0
1
1
1
1
0
1
1
2
1
0
0
1
1
1
1
0
2
1
1
3
2
2
2
1
1
0
1
0
0
2
0
1
2
1
2
0
0
1
0
0
2
0
1
2
2
1
0
0
1
1
1
1
1
2
0
1
1
1
1
1
1
1
0
2
2
0
1
2
0
0
1
0
2
0
2
1
2
1
2
0
0
1
1
2
1
1
0
0
1
1
0
2
1
1
2
2
0
0
0
0
0
0
2
2
0
2
1
2
0
1
0
1
0
1
2
1
0
1
0
2
2
0
0
0
1
2
1
0
1
0
0
0
0
1
0
0
1
1
1
2
0
1
3
2
2
2
2
0
1
0
1
0
0
0
2
2
2
1
0
0
0
1
1
0
1
1
2
1
1
1
0
1
0
1
1
1
0
0
0
1
1
1
2
1
2
0
0
1
1
0
1
1
0
1
2
1
3
0
1
1
1
0
1
0
1
2
1
1
0
0
0
0
1
0
1
1
2
0
1
1
1
0
0
1
1
1
2
0
2
0
2
1
0
1
0
0
2
2
0
1
0
2
0
0
1
2
0
2
1
1
1
0
2
2
1
2
0
1
0
0
1
0
2
2
0
1
2
1
1
2
2
1
0
1
2
2
0
3
1
1
0
0
1
2
2
1
1
1
0
2
1
1
0
0
0
1
1
0
0
0
1
1
2
1
1
1
2
2
1
2
1
1
0
1
3
1
1
0
1
0
0
1
2
1
3
2
1
1
0
1
1
1
0
1
0
1
2
1
0
1
1
1
0
2
0
1
1
0
2
1
1
1
1
1
1
1
0
1
1
0
1
0
1
2
0
1
1
2
1
1
0
0
1
0
2
1
2
1
0
1
2
1
0
1
1
1
0
2
2
1
0
1
2
1
2
0
0
1
1
8
0
0
2
1
0
1
1
0
1
0
1
0
1
1
2
1
1
0
0
1
1
1
0
2
0
1
2
1
1
1
1
2
2
2
1
1
1
1
1
1
1
1
1
0
1
1
0
0
1
1
0
1
0
1
2
2
0
0
1
2
2
1
1
1
1
0
2
2
1
1
0
2
0
1
0
0
2
0
1
0
2
1
1
0
0
0
0
1
2
1
0
2
1
0
1
1
0
2
0
2
2
2
1
1
0
1
0
0
0
0
1
2
1
1
2
0
1
2
0
2
0
0
1
2
1
0
1
1
0
1
1
0
0
0
0
2
1
0
1
0
0
2
0
1
1
1
0
1
1
2
1
2
1
0
1
2
0
0
2
1
0
0
1
0
1
0
1
0
2
0
1
1
2
0
2
1
0
0
0
2
2
0
1
2
0
0
0
1
1
0
1
1
1
1
2
2
0
1
0
3
2
1
1
1
2
1
1
1
2
1
1
0
1
2
0
0
1
1
1
1
0
1
1
1
1
0
1
0
2
0
2
3
0
0
1
0
2
0
0
0
1
2
2
1
1
1
2
0
2
1
1
2
0
0
1
1
0
2
2
0
0
1
1
2
2
1
0
0
0
1
1
0
2
2
2
1
1
1
1
2
3
2
1
1
1
2
0
1
1
3
0
1
1
1
1
1
1
0
0
0
1
2
1
1
1
1
1
0
0
1
1
1
2
0
1
1
0
2
1
1
0
2
0
0
1
0
0
1
1
0
2
0
1
3
1
1
0
0
0
2
2
2
0
1
0
1
1
1
1
0
0
1
0
2
1
1
0
0
0
0
2
1
1
1
1
1
1
2
2
1
2
0
1
2
2
1
2
0
2
0
1
1
0
1
2
1
2
0
1
2
1
2
1
0
0
0
1
1
0
1
0
2
0
1
1
0
2
3
0
2
0
2
1
1
0
0
1
1
0
2
1
2
2
0
1
0
1
0
1
2
1
0
1
1
3
0
2
1
0
0
0
0
1
1
0
2
0
2
1
1
0
1
1
2
0
2
1
2
0
1
1
0
1
1
2
1
1
0
3
1
1
0
1
0
0
1
0
1
1
2
1
3
2
0
0
2
0
1
1
2
1
1
1
1
1
2
0
1
0
1
1
1
1
1
0
1
1
0
1
2
1
1
0
2
1
1
0
1
0
1
1
1
0
1
1
1
1
0
1
1
1
2
1
2
0
1
2
1
2
0
1
0
0
0
0
1
1
2
2
2
1
1
0
1
1
0
0
1
1
1
1
2
2
1
1
1
1
0
1
1
2
2
0
1
2
1
1
1
1
1
1
0
1
1
1
2
2
1
0
1
1
0
1
1
1
2
2
1
1
2
2
1
1
0
1
1
1
2
1
1
1
2
2
2
0
1
1
1
0
1
1
0
0
2
1
0
1
0
2
0
1
2
1
0
2
0
2
1
0
1
1
2
1
0
1
2
0
1
0
1
0
0
0
0
1
0
2
0
1
1
2
0
0
1
0
1
2
0
1
0
0
0
1
1
1
1
1
1
0
2
0
1
0
0
2
1
1
1
3
2
0
1
2
0
2
2
0
1
0
1
2
0
1
1
0
1
0
1
0
2
2
1
0
2
1
1
0
0
0
2
2
1
2
0
1
1
1
0
0
1
1
0
0
0
0
0
0
0
1
1
2
0
0
0
1
2
2
0
4
0
0
1
0
1
1
0
0
2
2
0
2
1
1
1
0
0
1
1
1
1
0
2
0
1
1
2
1
2
0
1
1
1
0
1
1
2
1
2
1
0
1
1
1
0
1
1
2
1
1
1
1
1
0
2
0
0
0
1
1
2
1
1
2
0
0
2
1
1
0
0
1
0
1
1
1
0
1
2
0
2
4
1
0
0
2
1
1
1
1
2
0
2
0
1
1
1
1
1
2
0
1
1
1
1
2
0
2
0
1
0
1
0
1
0
1
2
1
2
1
0
1
0
1
0
1
0
0
2
0
2
0
1
0
0
0
1
2
2
0
0
0
1
1
1
2
2
1
2
0
0
2
1
1
0
2
1
0
1
0
0
1
1
1
1
1
2
0
2
2
1
2
1
1
0
1
0
2
0
0
0
1
2
0
1
1
1
1
1
1
1
0
1
0
1
1
2
2
0
2
0
1
2
1
0
0
1
0
0
2
0
0
2
2
2
1
1
2
1
1
0
1
2
1
0
1
1
2
1
2
0
2
0
1
1
0
0
1
1
0
1
2
1
0
1
2
3
2
1
2
0
0
0
0
0
1
1
1
1
1
1
1
2
0
0
1
1
1
2
2
1
1
1
0
1
1
1
2
1
3
1
1
1
2
0
2
1
2
0
0
0
0
1
1
1
0
2
1
0
1
1
0
2
0
1
0
2
2
1
1
1
1
0
0
2
2
0
2
1
1
0
1
0
2
1
1
1
0
0
2
2
2
0
1
1
1
1
0
2
2
1
1
0
1
1
1
2
2
0
1
0
0
0
1
0
2
1
2
0
0
1
1
1
0
1
2
1
1
1
2
1
1
0
1
1
0
1
0
1
1
1
1
1
1
1
0
1
1
0
0
1
1
0
1
1
1
1
2
1
0
2
0
2
1
1
0
1
0
1
0
1
0
1
2
2
2
0
0
1
1
2
0
0
1
1
1
0
1
0
0
2
1
3
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
1
2
0
1
0
0
1
2
2
1
0
2
1
0
0
1
1
1
0
0
1
2
1
1
1
1
2
0
1
0
1
1
0
1
2
0
0
1
2
2
1
2
0
1
1
1
2
2
1
1
2
0
1
1
1
1
1
0
1
1
1
1
1
1
0
1
1
1
1
2
1
1
0
1
1
2
2
0
2
1
0
0
1
0
1
1
2
1
0
0
1
1
1
1
0
0
0
1
2
0
1
2
0
0
1
1
1
1
1
0
1
0
0
2
1
2
1
1
0
1
2
2
1
0
2
2
1
1
1
1
0
2
1
1
0
0
0
0
1
1
1
0
2
0
1
1
1
0
2
0
1
1
1
0
1
0
0
0
1
0
2
1
1
0
1
1
0
0
1
1
0
1
1
1
1
0
0
0
3
1
2
2
2
1
0
1
2
0
0
1
1
2
2
1
0
1
0
2
1
1
1
1
2
1
1
1
1
2
1
1
0
0
1
1
1
1
2
2
1
1
0
1
2
1
0
1
1
0
1
0
2
1
1
2
1
2
1
1
0
0
1
0
1
1
0
1
1
1
0
0
1
1
3
1
2
1
1
0
1
2
0
2
2
3
1
1
2
2
1
1
1
0
0
2
2
0
2
1
0
1
0
1
1
1
1
0
0
2
1
1
2
1
1
1
1
2
0
1
0
0
1
2
0
1
2
1
1
1
1
1
2
1
0
0
1
1
1
2
2
0
2
2
2
0
0
0
3
0
0
2
0
2
0
2
2
2
1
1
2
1
0
1
1
1
1
1
1
1
1
0
0
2
2
0
1
0
2
1
1
1
1
1
1
1
1
1
1
1
2
2
1
0
2
1
1
0
2
0
1
2
1
1
2
1
2
1
0
2
2
0
0
1
0
1
2
1
1
1
0
1
1
2
0
2
1
2
1
0
2
0
2
2
3
1
2
1
1
2
0
1
2
0
0
0
2
2
0
1
1
1
1
1
2
0
0
1
1
1
1
0
0
1
1
1
0
0
1
2
0
2
1
0
0
0
2
1
2
0
1
0
1
1
0
1
1
1
1
1
2
2
1
1
1
0
0
1
2
2
0
0
1
1
1
1
1
1
0
1
0
0
1
2
2
1
2
1
1
1
1
1
1
1
1
0
1
2
1
1
0
1
1
0
2
1
1
1
0
1
0
0
1
1
1
1
1
0
2
0
0
0
0
1
1
1
2
1
0
0
0
4
0
0
1
2
1
0
2
2
0
1
1
2
1
0
1
1
0
1
1
0
1
1
1
1
0
0
2
1
2
0
0
1
1
0
2
1
1
0
2
1
1
0
1
0
2
1
1
2
1
1
1
2
2
1
0
0
1
1
0
0
1
1
1
0
2
1
0
1
2
2
1
1
1
0
0
1
1
0
2
0
2
0
2
0
1
1
1
2
1
0
0
1
0
1
1
2
0
1
0
0
2
1
1
1
0
1
1
0
1
1
1
2
2
2
2
1
0
1
0
1
0
2
0
0
1
0
1
2
1
1
1
2
0
1
2
2
0
0
2
1
1
1
1
2
0
0
1
3
1
0
1
0
2
1
2
1
0
1
0
1
0
2
1
1
2
1
2
2
2
0
2
1
1
1
2
1
1
1
1
2
1
2
2
1
2
0
2
2
1
1
0
0
1
1
1
2
0
2
3
1
2
0
0
1
2
0
1
2
1
0
0
0
0
0
1
0
1
0
3
2
1
0
0
1
2
1
1
2
1
1
0
0
0
1
1
1
1
1
0
2
2
2
0
0
0
1
0
0
0
1
0
1
1
2
3
2
1
1
0
0
1
2
1
1
1
1
1
2
0
1
1
2
0
2
1
0
0
1
0
0
0
1
1
1
1
0
2
1
0
0
2
2
2
1
1
1
1
2
1
1
0
1
2
0
1
0
2
1
1
1
1
0
0
0
0
1
1
0
2
1
2
1
3
1
0
2
0
2
1
1
0
2
0
2
0
1
0
0
1
1
0
0
0
1
2
0
1
1
1
2
0
0
1
1
0
1
1
0
2
0
1
2
2
2
1
0
0
1
0
2
1
0
1
1
1
1
1
1
1
1
0
1
0
2
1
0
2
1
2
0
2
0
1
1
0
1
1
0
2
1
1
1
0
0
1
1
1
1
1
2
0
2
1
2
1
2
1
1
0
0
0
0
0
0
1
1
1
1
1
0
0
1
0
0
1
1
0
2
0
1
1
0
1
1
1
2
2
2
1
1
1
1
0
2
1
2
1
0
1
1
1
0
1
1
0
1
1
2
0
1
2
1
1
1
3
0
1
1
1
1
0
1
0
1
1
1
0
0
2
2
1
1
1
0
1
1
1
1
1
1
1
0
0
1
1
1
1
2
0
2
1
0
1
0
1
2
1
0
1
1
1
1
2
4
1
1
2
1
1
2
0
2
1
2
2
1
2
3
1
1
1
1
0
3
0
0
1
0
1
0
1
2
2
2
1
1
1
0
1
2
0
1
0
1
0
0
1
0
1
1
0
2
0
1
0
1
1
1
1
2
3
1
0
2
1
2
1
0
1
0
2
1
2
0
1
1
0
2
2
0
1
1
0
1
0
2
1
2
1
2
1
1
1
1
0
0
1
1
2
1
2
0
0
1
1
1
1
1
2
1
2
1
2
1
1
1
1
2
0
0
2
1
0
4
2
2
5
2
2
1
1
1
1
1
2
1
0
1
1
0
0
1
2
0
1
2
2
1
1
0
1
1
0
1
0
1
1
1
1
0
1
1
1
2
2
1
0
0
1
2
1
2
0
1
1
1
1
1
0
1
0
2
2
1
0
2
1
0
1
2
0
2
1
0
1
0
1
1
0
1
0
2
0
1
1
1
1
1
1
3
1
1
2
2
0
0
0
2
1
0
1
2
1
1
0
1
1
2
1
1
2
1
1
0
0
0
10
0
0
0
2
1
0
1
2
1
1
2
2
0
2
0
2
2
2
1
0
0
1
1
0
0
0
1
2
2
1
1
1
0
1
1
0
1
1
0
0
2
0
2
0
1
0
1
1
0
1
1
0
1
1
0
0
1
3
1
1
2
2
1
0
1
2
1
2
1
0
0
1
1
1
0
1
1
1
1
1
1
0
1
2
1
0
1
1
0
0
2
1
0
2
1
3
0
2
0
1
1
1
1
1
1
2
0
0
1
1
0
0
1
1
1
0
0
1
2
2
2
0
2
2
2
1
1
0
0
0
0
0
0
0
1
2
1
0
2
0
0
2
1
0
2
0
2
0
1
2
1
0
2
1
1
3
1
2
0
0
1
1
0
2
0
2
0
2
2
2
0
2
1
1
2
1
2
1
0
0
1
0
2
1
0
1
1
2
2
1
1
1
0
0
1
1
1
2
0
1
0
0
1
1
0
1
0
0
1
0
0
1
0
2
1
1
1
2
0
0
1
3
1
1
1
0
1
1
1
2
2
1
0
1
2
2
2
0
1
1
1
2
0
2
2
1
6
1
1
2
1
1
0
2
1
0
1
0
1
0
1
1
1
1
1
0
1
0
2
2
0
0
2
1
1
1
0
1
1
1
2
0
2
1
0
2
0
0
0
1
1
1
0
1
0
1
1
2
2
2
1
0
2
2
1
1
1
1
1
2
0
2
1
0
2
2
1
2
0
2
1
2
2
1
1
1
1
0
1
1
0
0
0
1
0
0
0
0
0
2
2
0
2
0
1
2
0
0
0
0
2
0
1
2
3
0
1
2
2
1
0
0
1
1
0
0
2
0
1
0
2
1
0
1
1
1
1
1
2
2
1
1
2
1
0
3
1
1
1
1
1
2
1
1
2
1
1
0
2
1
0
0
1
1
1
3
1
0
2
0
1
1
1
2
1
1
2
0
0
0
2
0
1
1
0
1
1
3
1
1
1
0
2
3
0
2
0
1
5
0
2
1
0
0
1
2
2
1
0
2
0
0
1
1
0
1
1
1
0
0
1
0
1
1
1
1
0
0
3
1
0
1
2
1
0
1
0
0
1
0
2
2
2
1
1
0
1
0
0
0
0
1
0
2
1
2
2
1
0
1
0
1
1
0
1
2
1
0
0
2
1
0
1
2
2
0
0
1
2
2
0
0
2
0
1
1
0
0
1
0
0
0
1
0
1
1
1
1
0
2
1
1
2
0
1
2
1
1
2
1
0
0
1
1
0
1
1
0
0
2
3
2
2
1
2
1
2
0
0
1
0
1
2
0
1
0
2
0
0
2
2
2
1
0
2
2
1
0
1
2
0
2
0
2
1
1
1
3
0
1
1
1
0
0
1
0
0
2
1
0
2
0
1
0
0
3
0
2
0
4
1
2
1
2
0
1
1
0
2
2
1
1
1
2
2
1
0
1
1
0
0
3
1
2
1
2
0
0
1
0
1
1
1
1
0
1
1
0
0
2
0
0
2
0
0
2
0
1
0
1
0
1
2
0
0
1
1
0
1
1
2
0
0
1
0
0
2
0
1
1
0
3
2
0
1
1
1
1
1
1
0
0
1
0
2
1
0
11
1
2
1
1
2
1
1
1
2
1
1
0
1
1
2
1
0
1
1
0
0
0
2
0
1
0
1
1
0
1
2
2
0
1
0
1
2
2
0
1
1
1
1
2
1
0
0
0
0
2
0
1
2
2
1
0
2
1
1
1
0
0
1
1
1
0
1
2
0
1
0
2
2
1
1
3
0
2
1
1
2
2
2
1
1
0
0
1
0
1
0
0
0
1
1
1
0
2
2
2
2
1
1
2
1
1
0
0
0
2
0
0
0
0
1
2
0
0
1
0
0
1
1
0
1
0
0
0
2
0
2
0
0
1
1
2
1
1
0
2
0
0
0
0
2
1
0
1
1
1
0
1
2
1
1
0
2
0
0
0
0
1
0
2
0
1
0
1
0
1
1
0
1
1
2
2
1
0
0
0
0
0
1
1
1
1
1
1
1
1
2
1
1
2
1
1
0
2
2
1
0
1
2
1
0
1
0
0
0
2
2
3
2
0
2
0
1
3
1
1
2
2
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
1
1
0
0
0
0
2
0
0
0
2
0
0
1
1
1
1
1
1
2
1
2
1
1
0
1
1
2
0
1
0
2
1
0
1
1
2
1
1
0
2
2
2
0
0
0
1
1
2
0
0
1
1
1
2
2
2
2
1
0
2
0
1
1
2
2
1
1
1
1
1
1
1
1
1
2
0
2
2
1
2
0
1
0
1
1
0
0
0
0
0
0
0
2
0
2
0
2
2
0
1
1
2
1
2
0
0
1
2
1
0
1
1
0
0
2
1
0
0
1
0
1
0
0
3
1
2
2
0
1
0
2
1
1
1
1
2
2
1
1
2
0
2
2
0
1
2
2
0
2
3
1
0
2
1
0
0
0
1
1
0
1
0
1
2
0
1
0
2
2
0
0
1
1
1
1
2
2
0
0
1
2
1
0
1
1
1
2
1
1
0
1
0
0
0
1
1
1
1
0
1
0
2
0
0
2
1
0
0
0
1
2
2
3
1
0
0
0
1
1
2
2
2
1
2
1
2
3
2
2
0
1
0
0
1
1
1
2
0
1
1
2
0
1
1
2
1
1
0
1
3
2
2
1
1
0
1
1
1
2
1
1
0
0
1
0
0
1
0
0
2
2
0
1
1
1
1
2
0
1
1
2
2
1
0
0
2
2
1
2
1
0
0
2
2
0
2
1
1
0
1
1
0
2
0
2
0
1
3
1
0
2
1
1
0
2
0
2
2
1
1
1
1
1
1
1
1
1
0
1
1
1
1
0
1
0
1
0
2
1
1
0
2
0
0
1
1
1
2
0
2
1
1
0
1
1
1
0
0
1
1
2
0
1
1
0
0
0
0
2
0
0
1
0
2
2
2
1
1
2
0
1
1
0
0
2
1
0
0
1
2
2
1
1
2
1
1
0
1
1
1
1
2
1
2
0
1
2
1
1
2
0
2
1
2
0
1
1
1
2
1
2
1
2
0
0
1
2
1
2
0
0
1
1
3
1
1
2
2
1
1
1
0
0
0
1
1
2
1
0
1
1
1
2
0
0
2
1
1
1
1
1
0
1
2
2
0
2
0
1
0
1
1
0
1
0
0
2
0
1
0
0
1
1
2
0
1
2
2
2
1
0
1
1
1
1
0
1
1
0
1
0
1
1
2
2
2
1
2
1
0
2
0
0
0
1
1
1
0
1
1
0
0
0
0
1
0
1
1
1
0
0
0
1
1
1
1
2
0
2
1
2
2
0
0
0
0
1
0
2
1
2
0
1
0
1
0
1
1
0
1
2
1
1
1
1
2
0
1
0
1
1
1
0
0
1
2
2
1
0
1
1
2
0
2
1
1
1
2
0
1
0
1
1
0
1
2
2
0
1
1
0
0
1
1
1
1
0
2
1
2
1
0
1
0
0
1
1
2
1
0
0
2
1
0
1
0
0
2
2
1
0
1
1
0
1
1
0
2
1
2
1
2
1
0
3
1
2
0
1
2
2
2
1
0
0
1
1
2
1
1
1
1
1
1
1
1
2
1
1
2
2
2
0
1
0
1
0
0
1
2
1
1
0
3
0
2
0
1
2
0
2
1
1
3
0
1
0
1
1
0
0
0
1
2
0
0
2
1
1
0
1
1
0
1
1
1
1
1
1
2
1
2
1
1
2
2
0
1
1
2
1
2
1
0
1
0
0
0
1
2
1
0
1
0
0
1
1
1
1
0
0
0
1
0
1
2
0
0
1
0
1
0
2
1
1
2
0
0
1
1
1
1
1
0
1
0
2
2
2
1
2
0
1
2
0
1
0
1
0
0
0
1
0
2
0
0
0
1
0
0
1
0
1
1
1
0
2
2
1
0
1
1
1
1
0
0
0
1
1
2
1
1
2
1
1
0
0
0
1
1
1
0
1
2
2
0
1
1
1
0
2
2
2
0
2
0
2
1
1
1
2
0
2
0
1
1
1
2
1
1
1
2
1
2
0
2
2
0
2
2
1
2
2
1
1
0
0
0
1
2
2
2
1
1
0
1
1
1
0
0
2
0
3
0
2
2
3
0
1
1
2
1
2
2
0
1
1
1
2
1
0
1
0
1
0
1
2
1
1
0
0
0
0
2
1
1
0
1
1
1
1
0
0
0
2
1
0
0
0
1
2
1
2
2
2
0
1
1
0
1
0
0
0
2
0
0
0
2
2
1
1
0
0
0
1
1
1
2
1
2
1
1
0
1
0
2
2
1
1
3
1
0
0
1
0
1
0
2
2
0
1
1
4
0
2
0
2
0
1
1
0
1
0
0
0
0
2
0
2
0
2
1
1
1
1
1
0
0
2
3
1
2
2
0
2
1
0
2
1
2
0
2
0
0
0
2
0
1
2
1
1
1
1
1
1
0
1
1
3
1
1
0
1
2
1
1
2
0
1
0
1
1
1
1
0
2
0
1
2
0
1
0
1
1
0
0
0
2
0
1
0
1
0
0
1
0
0
1
1
0
1
2
1
1
1
1
0
0
1
1
1
0
2
0
0
0
0
1
2
1
3
1
0
0
0
5
1
0
0
0
2
0
1
1
3
0
0
0
0
1
0
2
1
1
1
1
2
1
2
1
1
1
1
2
0
0
1
0
2
1
2
0
1
1
0
1
2
0
0
2
0
2
1
1
0
1
1
0
0
2
0
2
1
0
0
2
1
1
1
1
1
1
1
1
1
1
2
0
1
1
2
1
1
1
1
0
0
0
1
1
1
1
0
0
2
1
1
2
0
0
1
1
1
0
1
1
0
0
0
2
2
2
0
0
0
1
1
1
2
0
1
2
2
2
0
2
1
2
0
2
2
1
0
1
1
0
1
2
0
0
1
1
0
0
1
1
1
0
0
2
2
2
1
2
0
1
0
0
1
1
2
2
1
2
4
2
1
1
2
1
1
0
1
0
0
1
1
3
1
1
0
2
0
1
1
0
3
0
1
1
1
3
1
2
1
2
0
0
0
1
2
1
0
2
1
1
0
0
1
0
2
2
2
1
0
0
1
0
1
2
1
1
1
0
1
1
1
1
0
0
1
2
0
1
0
2
0
0
2
1
0
1
1
1
1
1
0
2
1
1
1
0
0
1
1
1
0
1
2
2
1
0
0
0
0
1
2
1
1
1
0
0
0
1
0
0
1
1
0
1
1
1
1
0
2
0
2
0
2
0
1
2
0
0
2
1
1
2
1
1
1
1
2
0
2
2
1
0
0
1
0
0
0
0
2
2
0
0
0
0
2
1
3
1
2
0
0
1
0
1
0
1
1
1
1
0
1
1
0
2
1
1
1
1
0
1
1
2
1
2
2
0
4
0
1
0
0
0
2
0
0
2
1
1
1
1
0
0
2
1
2
2
0
0
1
0
1
2
1
0
1
2
2
0
2
2
1
0
2
1
1
2
0
0
2
0
1
0
1
0
0
1
2
0
1
1
1
1
1
1
0
1
2
0
1
1
1
1
1
0
0
2
0
0
1
1
3
1
5
2
1
2
1
0
1
1
1
1
1
1
2
1
1
0
1
1
2
2
1
2
0
2
2
2
1
0
0
1
1
1
0
0
1
1
1
0
2
0
0
1
1
1
1
1
0
1
2
0
0
2
1
1
1
1
1
1
2
0
1
0
2
1
0
1
0
1
0
1
0
0
0
0
0
2
0
2
2
1
1
0
0
1
1
2
3
0
2
0
1
0
0
1
2
3
1
2
1
0
1
1
1
0
1
2
1
0
1
1
1
2
0
1
1
2
2
1
2
0
1
1
0
1
0
1
0
0
2
0
0
2
1
1
2
1
0
0
1
0
0
1
0
1
0
0
2
1
1
1
0
0
1
1
0
0
3
0
2
1
0
0
1
2
5
0
3
0
0
1
0
1
0
0
0
0
2
3
2
0
1
1
2
2
0
1
2
0
1
2
2
2
1
1
2
0
1
1
1
1
1
0
0
1
2
0
0
2
0
1
1
1
2
3
2
1
1
0
0
0
2
0
0
2
1
0
0
0
1
1
2
0
0
0
0
1
0
1
2
1
2
1
1
0
0
1
0
1
1
0
2
1
1
1
0
1
2
0
1
0
2
1
0
0
0
1
0
0
1
0
1
2
0
1
1
1
1
2
0
0
1
1
2
1
1
0
1
1
0
1
2
1
1
1
2
0
2
2
0
0
0
0
1
2
1
1
1
2
0
1
0
1
1
1
1
0
1
0
2
1
3
0
1
2
0
0
0
2
0
2
0
0
1
0
1
2
2
0
1
0
0
2
2
0
1
2
2
2
1
1
2
1
0
0
1
0
2
2
2
0
2
1
0
0
1
1
0
1
2
0
0
1
0
1
1
1
1
1
1
3
2
1
0
2
2
1
1
3
1
1
0
1
2
1
2
2
0
1
0
1
1
1
1
1
1
1
1
0
2
2
1
1
2
1
2
2
0
1
0
1
2
2
1
0
1
0
1
1
1
0
1
2
1
1
1
0
1
0
2
2
0
0
1
1
0
0
2
2
0
1
0
0
1
1
1
1
1
1
2
1
2
1
1
1
2
1
1
0
0
1
1
1
0
2
2
2
1
0
2
1
2
0
0
2
0
0
1
1
2
2
1
2
1
1
1
0
1
0
1
0
0
2
0
1
2
2
0
1
1
0
1
1
1
0
2
2
0
2
2
1
2
1
0
0
0
2
0
1
0
0
2
1
1
2
0
0
1
1
2
0
1
1
0
0
0
1
2
0
1
1
1
1
1
0
1
0
1
1
2
2
2
1
0
1
1
1
1
1
0
1
0
0
1
2
1
0
1
3
2
0
2
1
0
0
0
0
1
0
0
1
1
2
2
1
1
1
0
0
1
1
0
1
1
1
0
2
0
2
3
0
3
1
1
1
1
1
1
0
2
1
1
1
0
2
0
2
1
0
1
0
1
0
1
0
0
2
1
2
0
2
1
2
1
1
1
2
2
0
2
2
0
1
1
1
1
0
2
0
0
1
1
1
0
0
0
0
1
0
1
0
0
1
1
3
2
1
0
1
1
2
1
0
1
1
0
1
1
2
0
1
2
0
0
2
1
1
1
1
0
1
0
2
1
0
1
0
1
1
0
1
0
1
1
1
1
1
0
0
1
1
1
1
0
2
0
0
1
2
1
1
1
2
1
1
2
0
1
1
1
3
0
2
1
0
2
1
0
1
1
2
0
0
1
0
1
2
0
0
1
2
1
1
2
1
1
0
0
2
1
1
2
0
0
0
3
2
0
1
1
2
1
1
0
0
1
0
1
1
1
2
1
1
2
2
0
1
2
2
1
1
1
1
0
2
0
1
2
1
1
1
2
0
0
1
0
1
1
0
1
2
2
0
1
1
2
1
1
2
1
2
0
0
1
0
2
0
1
2
1
1
1
2
1
0
2
3
6
2
1
2
3
1
0
1
1
0
0
1
0
2
0
3
1
1
0
2
1
2
2
2
0
0
2
1
1
2
1
0
1
1
1
1
0
1
2
0
1
2
1
0
1
1
1
0
1
2
2
0
1
1
1
0
0
1
0
1
2
0
2
0
1
1
0
2
0
1
1
0
1
1
1
0
1
1
3
0
1
0
1
1
2
1
1
1
1
1
1
0
0
2
0
2
0
1
0
2
0
0
1
1
2
0
0
1
0
0
0
2
1
1
1
0
1
1
3
1
2
0
2
0
2
0
2
1
1
0
1
1
0
0
1
1
1
1
1
0
1
1
0
0
1
2
1
1
2
0
0
0
3
1
2
0
0
0
2
1
0
0
2
1
0
0
1
2
2
1
1
3
2
2
1
0
0
1
0
1
1
1
1
0
1
2
1
1
0
1
1
1
1
1
2
0
2
0
0
1
2
0
1
1
0
2
2
1
2
0
1
3
2
2
1
2
2
2
0
1
1
1
0
0
2
2
2
1
1
0
2
0
0
2
1
2
0
0
1
1
2
1
2
1
0
0
2
2
2
1
1
2
0
0
1
0
1
0
1
2
2
0
0
1
1
1
0
0
2
0
2
0
0
0
1
1
1
0
2
2
2
2
0
1
2
0
1
1
1
1
1
1
1
1
1
2
0
2
1
3
0
2
1
0
1
0
2
1
0
0
1
1
0
1
1
2
0
1
1
1
1
0
2
1
2
2
2
1
0
0
0
1
1
1
1
1
0
2
2
2
1
2
1
2
1
0
2
0
1
2
0
1
0
2
1
1
0
1
0
0
0
0
2
1
1
1
0
0
2
0
2
0
1
1
1
1
0
2
0
0
1
1
1
0
1
1
0
1
1
0
0
2
1
2
0
1
0
1
0
0
3
0
1
0
0
1
1
0
0
0
1
1
0
2
0
2
0
1
0
1
0
0
0
2
2
2
1
0
1
1
1
1
1
1
1
1
1
2
0
2
0
1
2
1
2
2
1
0
0
1
2
2
1
1
0
0
1
1
2
0
0
1
0
1
2
1
1
1
2
1
0
1
1
0
0
1
1
2
2
1
1
1
1
1
2
0
1
0
1
2
1
1
0
0
1
1
1
0
1
1
1
0
2
1
1
1
1
0
0
0
0
2
0
1
2
2
1
0
1
1
0
0
2
1
1
0
1
1
1
0
0
0
1
1
1
1
2
1
1
1
0
0
0
1
0
2
1
0
2
1
1
1
2
2
1
2
3
0
0
2
0
0
2
0
2
1
1
0
0
2
2
0
0
0
1
0
0
0
2
1
0
0
1
0
2
2
0
0
1
0
1
1
2
0
0
0
2
1
1
1
1
1
1
0
1
1
1
0
3
1
1
1
2
1
1
2
2
0
1
1
2
1
0
1
1
1
1
2
0
0
1
2
1
0
0
1
0
0
0
1
0
0
2
1
2
1
3
1
0
0
1
0
0
0
1
1
2
0
0
2
1
0
1
1
2
0
2
1
0
2
0
1
1
2
2
0
0
0
1
0
1
1
0
1
0
2
1
1
1
0
3
0
1
2
0
1
1
2
1
1
0
1
0
1
1
0
1
2
0
0
0
1
2
0
0
1
2
2
2
1
1
0
1
1
1
1
2
1
1
1
1
1
2
1
1
0
3
1
1
1
0
0
1
1
1
1
1
0
2
1
1
1
0
1
1
1
1
1
1
0
0
0
0
0
0
1
1
1
1
1
1
0
1
0
0
2
0
2
1
1
1
0
1
1
0
2
2
1
2
2
0
0
1
1
2
0
1
0
1
0
0
2
0
0
1
1
0
1
1
0
1
0
2
1
2
1
1
1
1
1
0
1
2
0
0
1
0
2
0
0
1
0
1
1
1
1
1
2
0
1
3
1
0
1
2
2
1
1
1
1
1
2
2
2
1
0
1
1
0
2
1
1
1
0
1
1
2
1
1
1
1
1
1
1
1
1
2
0
0
0
1
0
1
2
0
1
1
0
2
1
1
1
1
0
1
1
2
1
1
1
1
2
0
1
2
2
1
2
1
1
2
1
0
0
1
1
2
1
1
0
2
1
2
2
0
0
0
1
1
1
0
0
0
1
0
1
1
1
0
2
1
1
2
1
1
0
0
1
1
0
0
0
0
2
0
1
0
1
0
0
0
0
0
1
1
1
1
1
1
2
0
1
1
1
0
1
1
0
1
1
0
1
1
0
0
2
1
2
2
2
1
1
1
0
1
1
1
1
0
1
2
1
2
2
2
0
0
1
1
1
2
1
1
2
1
1
1
1
2
1
1
0
1
1
1
1
0
1
0
0
2
1
2
0
1
1
1
1
1
0
0
1
1
1
0
2
0
2
1
0
0
2
1
1
2
0
3
0
1
1
1
1
1
1
0
1
0
1
0
0
1
2
0
1
2
1
0
2
2
2
1
1
2
1
0
1
2
0
3
1
1
1
0
2
1
0
1
1
2
1
0
2
0
0
0
1
0
1
1
0
0
1
0
1
1
1
1
0
2
0
0
1
1
0
0
1
2
1
2
2
1
0
0
2
2
1
1
0
2
1
0
0
2
0
1
0
0
1
1
0
2
1
1
0
0
2
1
0
1
1
1
1
0
0
1
1
0
2
2
2
2
2
2
0
1
1
0
0
0
2
1
2
2
0
1
1
0
1
0
0
1
1
1
0
0
0
1
0
1
1
2
1
0
0
0
1
1
1
0
1
0
0
2
2
0
0
1
3
0
1
0
1
1
1
1
2
1
1
1
0
1
1
1
1
1
2
1
0
1
0
1
2
2
2
2
0
0
1
0
2
0
1
1
1
1
1
1
1
0
1
2
1
0
0
0
0
0
0
1
0
1
1
1
1
2
1
1
1
1
0
1
1
1
0
0
0
1
2
0
1
1
0
0
2
0
0
0
0
1
1
0
0
0
0
1
2
2
0
3
0
1
1
2
1
2
2
1
1
3
1
1
2
1
1
0
1
1
0
1
2
0
1
0
2
0
1
0
0
2
2
0
0
3
0
0
0
0
1
1
1
0
1
0
1
0
0
0
0
2
2
1
1
0
1
1
1
1
1
2
2
1
2
1
0
0
1
1
1
0
0
0
1
0
0
0
1
0
1
1
0
1
0
1
1
2
0
3
1
0
1
1
2
1
1
2
0
1
1
1
0
0
1
0
1
2
1
1
1
0
0
1
2
1
1
1
2
2
2
2
1
1
0
0
1
2
0
2
1
1
1
1
1
1
0
0
1
1
0
2
2
2
2
1
4
1
2
1
1
1
0
1
1
1
0
1
1
2
0
2
2
1
1
1
1
2
2
1
0
0
1
0
2
0
1
0
2
2
2
1
1
1
2
1
1
1
0
0
0
1
1
0
0
2
1
1
2
1
1
0
1
2
0
3
1
1
1
1
1
1
2
2
1
0
1
2
2
2
1
0
1
0
0
2
2
1
1
0
1
2
0
2
0
1
0
0
1
1
0
0
2
0
1
1
2
2
0
2
0
2
1
1
1
1
0
1
1
0
0
0
5
0
0
0
0
2
2
1
1
1
2
0
1
0
0
1
2
2
0
0
0
0
2
1
2
1
1
0
1
2
1
2
1
2
1
1
1
1
0
1
1
0
0
1
2
1
2
1
1
0
0
0
2
0
2
0
1
1
1
1
0
2
1
0
2
3
0
0
2
1
0
2
2
2
1
2
1
0
0
1
0
1
0
0
2
0
0
1
0
1
1
2
0
0
2
0
1
1
2
1
0
2
1
1
0
2
1
2
0
1
2
0
1
1
0
1
0
0
1
2
0
1
1
1
2
0
2
1
1
0
1
2
0
2
1
2
1
3
0
0
1
0
1
0
1
0
0
0
1
1
0
1
1
1
2
0
0
2
1
1
1
2
0
2
2
0
1
1
1
1
1
2
0
2
2
0
0
0
1
1
0
0
1
1
0
2
0
1
0
2
1
0
1
0
2
1
2
0
0
1
2
0
0
1
2
1
0
1
2
3
2
2
0
1
1
0
1
0
1
1
0
1
1
2
1
1
1
1
0
1
1
2
0
1
1
1
1
2
1
1
1
1
1
1
0
1
1
1
0
1
0
0
1
1
0
0
0
1
2
1
0
2
0
1
1
0
1
0
0
1
0
2
1
0
1
2
0
1
0
0
0
0
2
1
2
1
0
0
1
2
0
2
1
0
1
1
0
0
0
3
0
1
2
1
0
4
0
1
1
0
1
1
1
0
0
1
1
0
2
1
0
2
0
1
2
1
1
0
1
2
1
1
1
0
0
0
2
0
1
1
1
2
1
3
0
2
0
2
0
0
0
1
2
2
2
0
0
0
1
1
1
1
1
1
2
1
0
2
2
1
0
1
0
0
1
2
1
1
1
0
2
1
1
0
2
1
0
0
1
0
2
1
2
1
1
0
1
0
1
0
2
1
1
1
1
2
1
2
1
1
3
2
1
1
0
1
1
0
1
1
1
0
2
0
0
0
0
1
1
1
1
0
0
1
0
1
0
1
2
1
1
0
1
0
0
2
1
0
1
2
2
1
2
2
2
0
0
2
1
0
1
1
0
1
2
0
2
0
2
1
1
1
1
1
2
1
1
1
1
1
0
1
0
1
1
1
0
1
2
1
1
2
2
2
0
1
2
0
2
0
2
0
1
2
3
1
1
2
0
0
1
1
2
2
0
0
1
1
1
1
0
0
0
2
1
2
0
1
1
1
0
1
1
2
6
1
1
1
0
0
0
2
2
1
1
1
1
1
0
1
0
0
1
1
1
0
0
1
1
2
0
1
1
0
0
1
1
1
0
2
2
0
1
1
0
0
2
1
1
0
0
1
0
1
0
0
1
0
0
1
1
1
0
0
0
1
1
2
1
1
2
1
0
0
1
1
1
1
0
1
1
1
1
0
2
2
1
0
2
1
2
1
1
1
1
1
1
0
2
2
1
0
1
0
1
2
0
0
1
1
2
2
0
1
0
1
1
1
2
1
0
0
0
2
0
0
1
1
0
0
2
2
0
1
0
1
1
0
2
1
0
0
0
0
0
1
1
1
0
0
1
1
1
0
1
1
0
2
2
0
2
1
1
0
2
1
0
0
2
2
1
0
1
2
1
1
2
0
1
2
1
2
1
1
1
0
0
1
1
1
0
2
2
1
2
2
0
0
0
1
3
2
0
2
0
2
0
1
1
1
1
2
1
1
0
1
1
1
1
1
0
0
2
1
2
0
1
1
2
1
2
2
0
0
0
1
1
1
1
1
0
1
1
2
1
1
1
2
0
1
2
2
1
0
2
1
0
0
1
1
2
2
2
0
2
2
1
2
2
2
1
0
2
2
1
2
2
1
0
1
1
1
2
1
1
1
1
2
1
2
0
1
2
1
1
0
1
1
2
1
0
1
1
0
0
1
2
1
2
2
0
2
1
1
2
0
2
0
2
1
0
2
0
2
1
0
0
1
1
2
0
1
1
1
0
0
1
2
0
2
1
1
2
1
0
2
2
2
1
2
1
1
2
2
1
0
2
2
0
0
1
0
1
1
2
2
1
0
2
1
2
2
1
2
2
1
3
0
0
2
0
2
0
0
1
1
1
1
0
0
1
0
1
1
1
1
2
1
1
0
1
0
1
1
1
2
2
0
0
0
0
0
1
1
1
1
1
0
1
2
1
1
1
1
0
0
1
1
1
1
2
2
2
0
1
2
0
1
0
1
1
1
2
0
0
1
0
0
0
1
2
1
1
1
1
0
2
0
1
0
0
2
1
2
2
1
2
0
0
0
2
1
1
0
1
0
2
0
1
2
2
1
0
0
0
2
1
0
1
1
1
1
0
0
0
0
1
0
1
1
0
1
0
0
1
1
0
1
2
1
0
1
2
0
1
1
2
1
2
1
1
1
1
0
1
0
1
2
1
1
2
2
0
1
0
2
0
3
1
0
0
1
1
0
2
1
2
1
0
0
1
1
1
1
1
0
2
2
2
2
1
2
2
1
0
1
1
1
1
1
2
2
2
1
1
1
1
0
0
1
1
0
0
0
2
0
0
1
2
1
0
1
1
0
0
1
0
0
1
0
0
1
0
1
1
2
2
1
0
1
1
1
3
1
1
0
0
0
0
0
0
0
1
1
1
1
1
0
0
1
2
1
0
1
3
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
2
2
1
1
2
1
2
1
1
0
0
2
1
1
0
1
1
1
1
0
1
2
0
2
0
0
0
0
1
2
0
2
1
1
2
1
0
1
1
2
2
0
0
1
0
1
2
0
2
1
0
1
0
2
0
2
0
2
1
1
1
1
1
1
1
1
1
0
1
0
1
1
2
0
1
2
2
0
2
0
0
1
2
0
1
0
1
0
0
0
1
2
2
0
0
1
1
1
2
1
0
1
1
2
1
0
0
0
0
1
1
0
1
1
1
0
1
2
2
0
2
1
1
1
2
2
1
2
3
1
1
1
2
1
0
0
1
0
2
1
1
1
2
0
2
1
1
2
1
0
0
1
0
0
1
1
0
2
1
0
1
2
2
0
2
0
1
2
1
0
0
2
1
1
2
1
3
2
1
1
2
1
1
3
2
0
1
2
0
0
1
2
1
1
0
0
0
1
1
0
3
2
1
1
1
0
2
1
0
0
1
0
1
1
0
0
2
2
1
0
1
4
1
0
1
2
1
1
0
1
1
0
0
1
0
1
1
1
0
0
0
0
0
1
1
1
2
1
2
0
0
1
1
2
0
1
1
0
2
2
1
2
2
1
1
0
1
2
0
0
0
0
2
0
0
0
1
0
2
1
1
0
1
1
0
2
1
2
2
1
1
2
1
0
1
2
0
2
0
1
1
0
0
0
0
1
0
1
0
1
2
1
0
1
1
1
1
0
1
0
2
1
2
1
1
0
0
0
2
1
0
2
1
2
2
1
2
1
4
1
3
0
1
2
2
2
1
1
0
2
2
0
0
0
0
2
1
0
1
1
0
0
1
1
2
1
1
0
1
0
1
1
1
0
0
0
1
1
1
0
1
2
2
1
1
0
1
1
1
1
1
1
1
1
0
1
2
1
1
0
1
2
1
1
2
0
2
1
0
2
0
2
0
0
1
0
2
1
0
0
2
0
1
1
1
1
3
2
1
1
0
1
2
1
1
0
2
1
2
3
2
2
2
1
1
0
2
1
2
0
1
0
2
1
2
1
0
1
1
0
0
1
0
1
1
0
1
1
1
1
2
0
2
0
0
1
0
1
2
0
0
0
1
2
0
0
0
1
1
1
1
0
1
1
0
2
1
1
2
0
1
1
2
0
1
2
2
0
0
1
1
1
0
2
1
0
2
0
2
1
1
1
0
1
2
1
0
1
1
1
1
0
1
2
2
0
1
1
2
0
1
0
0
2
1
1
0
0
2
0
0
0
1
1
1
1
0
0
1
0
1
0
2
0
2
7
1
2
0
0
0
2
0
2
0
1
0
0
0
1
0
0
2
1
0
0
0
2
0
2
2
1
0
0
0
1
3
0
0
3
1
2
1
1
1
0
1
0
1
1
1
1
2
1
0
1
1
2
1
2
2
0
0
1
1
0
0
2
1
0
0
0
2
0
1
0
2
1
1
1
0
2
2
2
1
2
1
0
1
1
0
0
2
1
0
2
1
2
1
1
0
0
0
1
2
1
1
0
0
1
1
1
2
0
0
1
1
0
1
1
1
2
1
0
1
1
1
1
2
2
0
1
2
1
2
0
1
0
0
0
1
2
1
0
1
0
2
1
2
1
0
1
1
0
0
0
1
2
0
0
0
1
1
1
0
2
1
3
2
0
1
2
1
1
3
2
2
1
1
1
1
0
1
1
1
2
1
0
0
1
0
0
2
2
1
2
0
0
1
0
1
1
2
1
2
2
1
0
0
0
0
1
1
2
1
2
2
2
0
2
0
1
0
0
1
1
2
1
0
0
1
0
0
0
1
2
1
2
1
0
2
0
1
1
0
1
0
1
1
1
0
0
1
0
3
0
1
1
1
0
0
2
0
1
0
1
1
1
1
1
1
2
0
1
0
0
1
1
1
1
0
1
1
1
1
0
1
1
1
1
1
1
1
2
1
1
1
0
0
2
2
1
1
1
1
0
0
0
1
1
1
1
0
1
2
2
1
0
0
2
0
1
1
2
1
1
2
2
0
0
1
0
2
0
0
0
1
1
1
1
1
0
0
2
1
2
1
0
1
0
0
1
2
2
0
0
1
1
1
0
0
1
1
0
1
2
1
0
1
0
1
2
1
1
0
1
0
2
1
1
1
2
1
0
0
0
1
1
1
0
1
1
0
0
2
0
1
1
1
1
1
0
2
1
1
1
2
0
0
2
1
2
2
0
1
1
0
1
1
0
1
1
1
1
0
0
0
2
2
0
2
1
1
1
1
2
0
0
0
0
0
1
1
0
2
2
2
0
1
1
0
2
1
2
0
1
1
1
2
1
1
1
0
1
3
0
0
0
0
0
1
0
1
1
0
2
1
0
0
1
2
0
1
0
3
2
2
4
0
1
0
1
0
1
1
2
0
1
1
1
1
0
1
1
0
1
2
1
1
2
2
1
1
1
0
1
2
1
1
1
1
1
1
0
0
2
1
1
2
1
0
1
0
1
1
1
1
0
2
0
0
2
2
0
2
1
1
1
0
0
1
1
0
0
0
1
0
1
1
1
0
2
2
1
1
0
0
2
0
2
1
1
0
1
1
1
0
1
0
1
0
1
1
0
1
2
0
1
2
1
2
1
0
1
0
1
0
1
3
1
1
1
2
1
2
0
1
2
1
1
0
0
0
2
0
0
0
1
0
0
1
1
1
1
2
0
1
2
2
0
1
1
0
1
1
1
1
1
0
0
1
1
0
1
0
0
0
2
1
1
2
1
2
0
2
0
2
0
0
1
1
1
3
0
1
2
2
1
1
1
0
1
1
0
1
1
1
1
0
2
1
0
0
2
0
1
1
1
0
1
2
2
1
1
1
3
0
1
1
0
0
1
3
0
1
2
1
1
2
0
2
1
1
0
0
0
2
0
0
1
0
4
0
0
1
1
1
0
1
1
0
1
1
1
2
3
0
1
1
1
1
1
1
1
1
0
1
0
0
2
1
1
1
1
1
1
0
1
2
0
1
1
1
2
0
0
2
2
1
2
0
1
1
1
0
0
0
1
0
1
0
0
2
1
1
1
2
0
1
1
2
1
1
1
0
0
1
2
1
2
1
0
1
1
1
1
1
2
0
1
1
0
2
1
1
2
1
2
2
0
1
1
0
0
1
2
1
0
1
1
0
0
0
1
1
1
0
1
2
2
1
1
1
1
2
2
0
1
3
1
2
0
2
0
2
0
1
1
1
2
0
1
1
0
1
3
0
2
1
0
0
1
1
0
1
2
2
0
0
1
0
1
1
0
0
2
2
1
0
0
0
0
0
2
1
0
0
1
2
0
1
2
0
2
2
0
1
0
0
1
1
2
1
3
1
0
0
0
1
1
1
1
1
1
1
0
1
1
3
0
0
0
0
1
2
0
0
0
3
0
0
2
1
1
0
2
2
2
3
1
1
1
1
0
1
1
1
2
2
1
0
1
1
0
0
2
2
1
2
2
1
0
0
2
0
2
0
1
2
0
1
0
1
0
1
1
2
0
0
1
2
1
1
2
0
0
1
1
2
0
0
1
0
2
2
1
1
0
1
1
0
2
1
0
1
1
0
0
1
1
2
1
3
2
0
1
1
2
0
0
2
1
1
2
2
0
1
1
2
1
1
2
2
1
1
1
0
1
0
0
1
1
1
1
1
1
0
1
2
2
1
1
0
2
0
2
1
0
1
0
1
2
1
1
1
0
1
2
1
0
1
0
1
2
0
1
0
2
1
0
1
2
1
0
1
1
1
1
2
1
2
0
0
1
1
1
0
0
1
0
1
2
2
0
1
0
1
2
1
0
1
0
0
1
1
1
1
0
2
2
0
1
2
1
1
1
0
1
1
1
1
0
0
1
1
1
1
0
0
0
0
0
0
0
1
0
1
2
0
1
0
0
1
0
1
0
1
1
0
2
0
1
2
0
3
1
0
1
0
2
2
0
2
0
1
1
1
0
1
0
0
0
1
0
0
0
2
2
1
0
2
1
1
1
0
2
1
1
1
1
1
1
0
1
2
0
0
0
1
2
0
1
1
0
1
1
1
2
3
0
0
0
1
2
1
2
1
2
2
0
1
0
1
0
1
2
0
1
2
1
0
2
0
1
1
0
1
1
0
1
1
1
2
1
0
1
1
1
1
1
1
2
1
1
1
1
1
1
0
0
1
2
2
1
0
2
2
2
2
1
0
1
1
0
1
1
1
2
0
1
2
2
0
0
0
1
1
1
2
0
0
0
2
1
1
0
0
2
1
0
2
0
2
2
1
2
2
1
2
1
1
1
0
0
1
2
1
0
1
1
1
0
2
1
2
1
1
0
1
2
0
1
1
1
0
1
1
2
1
0
1
0
0
2
0
0
0
0
1
1
1
0
0
0
1
1
1
0
2
0
0
1
2
0
2
1
1
0
0
1
1
1
1
0
0
1
1
1
2
2
1
1
1
2
1
0
0
1
0
2
0
1
1
0
2
0
1
0
1
0
0
1
2
2
1
1
0
2
0
0
1
0
1
2
2
1
1
0
2
2
1
1
0
1
1
2
1
1
1
2
1
0
0
1
0
1
1
1
1
1
1
0
0
1
2
1
2
0
1
1
0
1
1
0
0
1
0
1
2
1
2
2
0
2
1
0
2
2
0
1
0
1
3
1
0
3
0
0
2
0
0
0
0
1
2
0
1
1
1
0
1
2
2
0
0
0
2
1
1
0
0
2
0
0
1
2
1
0
2
2
0
0
1
1
0
1
0
1
0
0
1
2
2
0
1
1
1
0
0
2
2
2
1
1
1
0
1
0
1
0
1
2
2
2
1
1
1
2
0
1
2
0
2
1
2
1
0
2
1
0
0
0
0
1
2
2
2
1
1
2
1
0
1
1
0
1
0
2
1
1
3
0
0
1
1
0
0
1
1
1
0
1
0
1
1
0
0
0
1
1
0
1
1
1
2
1
0
0
0
0
1
0
2
2
2
0
1
2
1
2
0
2
0
2
1
1
0
0
0
0
2
0
0
1
1
1
2
1
0
0
0
2
1
1
0
0
2
0
0
2
1
0
2
0
1
1
1
1
1
2
1
4
1
3
2
0
1
2
0
0
1
1
0
0
1
2
1
2
1
0
0
0
1
0
0
2
0
2
1
1
1
1
0
1
0
2
1
0
2
1
0
1
2
0
0
1
1
1
0
1
1
0
2
1
0
2
1
1
2
2
0
2
1
1
1
1
1
2
0
1
1
2
1
1
0
0
1
0
2
1
0
1
2
0
1
1
1
0
1
2
1
2
0
1
2
1
2
2
1
2
2
1
2
0
2
2
1
1
1
0
1
1
2
1
1
2
0
1
1
1
0
0
1
1
0
1
2
1
0
2
2
0
0
1
0
1
1
1
0
2
0
2
1
3
1
1
1
2
2
1
0
1
1
2
0
1
1
0
1
0
1
0
0
1
2
0
2
0
2
0
1
0
2
1
1
0
0
0
2
0
0
2
1
0
0
1
1
2
2
0
2
2
1
1
2
2
1
0
2
2
1
1
1
0
0
0
0
0
1
0
1
1
1
0
0
1
1
2
2
2
1
0
1
0
0
1
1
2
1
0
1
1
1
1
1
1
2
2
1
1
2
2
2
1
1
1
1
1
0
0
0
2
2
3
0
1
1
2
1
1
0
1
0
2
2
1
1
1
1
2
1
2
0
1
2
2
1
0
0
0
1
1
0
0
0
1
2
0
1
0
0
2
0
1
1
1
1
2
0
1
1
1
0
3
1
1
2
0
0
1
0
0
1
1
0
2
1
1
0
2
0
2
1
0
1
14
0
2
1
2
1
1
0
0
0
1
1
0
0
2
0
1
2
0
1
0
1
1
0
0
0
0
1
0
1
0
2
0
0
1
0
1
0
1
1
2
0
2
0
1
2
0
2
1
1
2
1
1
0
2
2
1
1
0
0
1
1
1
1
0
0
0
0
2
0
2
2
0
1
1
0
1
1
0
0
1
0
1
1
1
1
4
1
1
1
2
1
0
2
2
1
1
1
1
2
1
1
1
0
0
3
1
1
0
1
1
0
1
2
0
0
1
2
1
2
1
1
2
1
0
1
1
0
2
0
0
0
0
1
0
0
2
0
2
1
0
0
0
1
0
0
0
1
0
1
2
1
1
2
1
0
0
1
1
2
1
1
2
0
1
0
1
0
0
0
1
2
1
1
0
1
0
0
0
0
1
0
1
0
1
0
1
2
1
1
0
1
1
2
2
2
2
1
0
0
1
0
1
0
2
1
1
2
1
1
2
5
1
0
0
1
1
1
0
1
1
0
0
1
1
0
0
0
0
1
2
2
0
0
3
2
0
1
1
0
2
0
2
2
1
2
1
1
2
1
0
0
0
1
1
1
0
1
0
1
0
1
0
0
1
2
0
0
2
1
1
3
2
1
2
2
1
1
1
0
1
0
1
0
0
2
0
2
0
1
1
2
0
1
2
1
1
1
0
0
2
2
1
2
2
0
1
2
0
1
2
2
4
3
0
2
1
0
1
1
3
0
0
1
2
0
2
2
0
2
0
1
2
3
1
2
2
1
0
1
0
1
1
0
2
0
2
1
1
0
0
1
2
1
2
1
0
2
1
0
0
0
2
1
0
0
2
0
0
2
0
0
2
1
1
1
2
1
1
0
0
0
2
0
2
1
0
2
0
2
1
1
1
0
1
0
0
1
0
3
2
1
1
2
2
2
1
1
0
0
1
1
0
1
1
1
2
0
1
0
1
2
2
1
1
2
0
2
1
0
2
1
2
1
1
1
0
2
1
1
1
0
0
0
2
0
3
1
0
1
1
1
0
1
1
0
1
1
1
1
1
2
2
1
1
2
1
1
0
1
1
1
0
2
1
1
0
2
1
2
1
1
0
1
0
2
0
0
0
1
2
1
1
1
1
0
0
0
1
2
1
0
2
1
0
1
2
1
2
2
0
0
2
1
1
1
2
0
0
2
3
1
2
0
1
0
1
2
0
2
2
0
2
1
1
1
1
0
1
1
0
2
2
1
2
1
0
1
0
1
1
2
0
0
0
2
0
0
1
1
2
1
0
1
1
0
1
3
1
1
2
2
2
2
1
1
0
1
3
2
1
0
1
3
1
0
1
0
1
0
1
1
1
2
0
1
2
2
1
2
1
2
0
1
2
2
1
1
2
0
0
1
2
2
1
0
0
0
0
2
1
1
1
1
0
1
1
0
2
2
1
1
0
1
0
1
1
1
0
0
1
2
0
0
0
1
2
1
0
2
1
2
2
1
2
1
1
1
2
1
0
1
2
0
2
2
1
2
1
0
1
2
1
2
1
1
0
0
6
1
2
1
3
2
2
2
2
0
0
1
3
1
1
1
1
1
0
1
2
1
1
1
0
0
0
1
1
1
1
1
0
1
0
2
1
1
0
2
1
1
1
0
0
1
2
1
0
0
1
0
1
0
1
0
1
1
1
1
1
1
0
1
2
0
0
2
1
1
0
0
1
1
1
0
0
1
0
1
1
0
1
0
0
2
1
0
0
0
1
1
2
0
1
1
1
0
2
1
1
1
1
1
1
1
0
2
2
0
4
0
0
1
1
0
1
0
0
1
2
0
1
1
0
1
1
1
0
1
0
1
0
0
1
3
0
1
1
0
0
1
1
0
1
1
2
1
0
0
1
0
1
1
1
1
1
2
0
2
2
1
1
1
0
0
0
1
1
1
1
1
2
1
0
1
2
0
0
0
0
1
1
1
0
0
1
0
2
3
0
0
0
2
1
0
2
0
2
2
1
4
1
1
0
2
1
2
0
0
1
1
2
2
1
3
1
1
1
1
0
1
0
1
0
2
2
1
1
0
0
1
2
2
2
0
0
1
5
0
1
1
1
2
1
1
0
1
1
1
2
2
0
2
0
1
1
1
2
2
0
1
1
1
0
0
1
2
0
1
0
2
1
1
0
0
0
1
0
1
1
0
2
1
1
1
1
0
0
2
0
0
0
1
0
0
1
1
2
1
1
1
0
1
1
0
0
1
1
1
2
0
1
1
1
0
2
1
0
1
1
0
1
1
1
1
0
1
0
2
1
0
0
2
0
1
0
1
2
1
0
1
0
1
2
0
1
1
1
2
1
0
0
1
1
1
0
2
1
1
0
0
0
1
1
0
0
1
0
2
1
0
1
1
1
1
1
0
1
2
2
1
1
0
1
0
0
1
0
0
0
2
1
1
0
0
1
1
0
0
1
1
2
1
0
1
2
1
1
0
1
1
2
1
2
1
1
0
0
1
1
2
0
2
1
1
1
0
0
1
0
0
1
1
1
1
1
2
1
1
1
1
0
0
3
0
2
0
1
1
1
1
1
1
0
1
0
0
1
1
0
1
1
1
2
0
1
1
1
0
1
0
2
1
0
1
0
1
1
1
2
0
1
0
2
0
1
1
1
6
0
0
2
1
1
0
1
1
1
2
1
0
1
2
2
2
1
1
1
1
1
1
0
1
1
2
0
0
2
1
2
1
0
0
1
1
0
0
0
2
1
1
0
1
0
1
3
1
0
0
1
0
0
1
0
2
1
0
1
1
1
0
1
1
1
1
1
0
0
1
1
0
2
0
0
2
2
0
1
1
2
1
2
1
2
1
1
1
0
1
0
2
0
0
2
0
0
1
1
0
1
2
1
2
0
1
0
2
2
0
1
1
1
0
0
1
1
2
1
2
1
1
0
1
0
1
0
2
1
2
0
1
2
1
1
3
2
0
0
2
1
1
0
2
1
1
0
0
1
0
2
2
0
2
1
0
2
1
0
0
1
0
1
1
2
2
1
0
2
0
1
1
1
1
1
2
1
2
1
1
1
0
0
1
2
1
2
1
2
2
1
1
1
4
0
2
2
3
2
2
0
0
1
2
1
1
1
2
1
2
1
1
1
1
2
2
1
1
1
2
0
0
2
0
1
1
0
2
2
3
0
0
1
0
1
0
0
0
1
1
1
1
1
1
0
0
1
0
1
1
1
1
1
0
2
0
1
2
0
0
2
1
2
1
1
0
1
1
1
1
2
0
1
1
1
0
2
0
2
2
0
0
1
2
1
0
0
1
4
2
1
1
1
1
1
0
1
1
1
0
0
0
0
0
1
0
2
0
2
2
0
0
1
1
3
0
1
1
0
0
2
2
0
0
2
0
0
2
2
1
0
0
1
1
2
0
1
0
0
2
0
0
1
1
1
0
1
2
2
2
0
0
1
1
1
2
2
3
1
3
2
1
1
1
1
2
0
1
2
2
1
0
1
0
2
0
2
1
2
1
0
2
0
1
1
2
1
2
1
0
0
0
0
0
1
0
1
1
1
0
0
0
0
2
1
0
1
1
2
2
1
3
0
0
1
2
1
2
0
0
1
0
0
0
0
1
1
2
2
0
0
1
1
2
0
2
0
1
0
0
1
0
1
1
0
1
1
1
1
0
2
1
2
0
0
0
2
2
1
3
2
0
0
1
0
0
0
1
0
1
1
1
0
1
1
1
1
0
1
0
0
1
0
2
2
1
2
1
1
2
0
1
0
1
1
1
1
2
2
1
0
1
1
1
1
2
1
1
1
2
2
0
1
1
0
0
1
0
0
0
0
0
2
1
1
1
1
1
1
1
0
0
2
0
0
2
1
1
0
0
3
1
1
1
0
1
3
2
0
1
2
0
0
0
1
2
2
0
1
2
0
0
1
1
0
2
1
0
0
0
2
0
2
1
1
0
1
2
2
0
1
1
1
0
1
1
0
3
2
1
1
0
2
0
1
1
2
1
1
2
0
2
1
1
1
1
1
1
3
0
0
1
1
1
0
2
1
1
2
0
0
0
0
1
1
2
0
0
1
2
2
0
1
0
2
2
0
1
0
1
2
0
2
1
1
1
1
1
1
1
0
2
1
1
0
2
0
2
2
0
2
1
1
1
1
1
1
3
1
0
0
0
2
1
0
0
2
1
0
0
1
2
0
2
1
0
2
1
1
1
2
1
0
1
0
0
0
2
0
0
1
0
0
2
2
1
0
2
2
2
2
1
1
2
2
1
2
1
1
2
0
1
2
1
1
0
0
0
2
1
2
2
1
0
1
1
2
0
0
1
1
2
1
0
1
1
2
3
1
1
2
0
0
0
0
2
1
1
0
0
1
1
2
1
1
1
0
1
0
1
1
1
1
1
2
0
1
1
1
2
2
1
1
1
0
1
1
2
2
2
1
1
0
1
1
1
0
2
2
1
1
0
2
0
0
0
1
1
0
0
1
1
2
1
1
0
1
1
2
2
1
1
1
1
2
1
1
1
2
2
1
1
1
0
1
0
1
1
2
0
1
1
2
0
1
2
0
0
2
0
1
1
1
1
0
3
1
1
1
1
1
2
1
1
1
2
2
1
1
1
3
2
2
1
2
1
2
0
0
1
0
0
2
1
0
2
1
2
0
1
2
1
0
0
1
0
1
0
1
1
1
2
1
1
0
1
0
0
0
0
0
0
1
1
2
0
0
1
0
0
1
0
0
2
0
1
1
0
3
1
0
1
0
1
2
0
1
0
2
1
1
1
1
0
1
0
1
1
2
0
0
1
1
0
1
0
0
1
1
1
1
2
1
2
1
0
1
0
1
1
0
1
1
0
1
0
1
0
2
0
0
2
1
0
1
1
0
1
1
0
1
1
1
2
5
2
1
0
1
1
1
0
0
6
1
1
1
3
2
0
3
1
1
0
1
1
1
1
0
1
1
2
1
1
0
0
0
1
0
1
1
0
1
1
0
0
0
1
2
2
1
2
1
1
1
1
1
1
1
2
2
1
0
1
1
0
1
2
1
1
0
0
1
2
1
1
0
1
1
1
2
1
1
2
2
2
1
1
1
2
2
1
0
0
0
0
0
1
1
1
0
0
0
1
2
2
1
1
0
0
1
0
0
0
1
0
1
2
2
0
1
0
1
1
2
1
0
1
1
0
2
0
1
0
0
2
1
1
0
0
1
1
0
0
1
0
1
0
2
1
2
0
2
0
0
1
1
0
1
1
1
2
0
2
0
0
1
2
1
2
0
1
1
1
1
0
2
3
0
1
2
0
0
0
2
0
1
2
2
0
1
2
1
0
0
1
1
2
1
0
0
1
1
1
0
1
2
1
0
1
1
2
1
0
0
0
1
2
2
1
0
1
0
1
1
1
1
1
0
1
1
0
1
1
1
1
2
0
2
0
2
1
0
1
0
0
0
2
0
1
1
0
2
0
2
2
1
2
2
1
0
0
1
2
0
2
1
2
1
0
0
1
2
1
0
2
2
1
0
2
1
0
1
0
2
1
0
1
1
1
1
2
1
0
2
1
2
1
1
1
1
0
1
1
0
3
1
0
1
0
2
0
1
0
1
0
0
1
1
0
1
1
1
0
1
1
1
1
1
2
0
1
1
1
0
0
2
1
2
2
0
0
1
1
0
1
1
2
2
2
1
2
1
1
1
2
0
1
0
1
2
1
1
2
1
1
0
1
0
0
1
1
0
2
1
2
1
2
0
1
0
1
0
1
0
3
0
1
2
1
0
0
1
0
2
0
0
1
0
1
1
1
0
1
2
1
2
2
1
0
1
2
1
1
2
2
1
3
2
0
2
0
1
0
1
0
1
1
1
0
1
1
8
1
0
1
2
1
1
1
2
1
1
0
1
1
0
1
1
0
0
2
1
0
1
0
1
1
1
1
1
0
1
0
3
1
1
1
1
1
1
1
0
0
0
1
2
2
0
2
2
0
0
0
1
0
0
0
0
1
1
0
2
2
0
1
0
2
1
1
2
1
1
2
2
2
0
1
0
1
0
1
1
2
0
2
1
0
0
2
2
0
0
2
2
0
0
2
0
1
1
1
1
0
4
1
0
0
1
0
1
2
1
1
0
1
0
1
0
1
1
2
0
2
1
1
1
0
0
1
1
1
0
1
4
0
0
0
1
2
2
0
0
2
1
0
1
1
1
2
0
1
1
2
0
2
0
0
0
3
0
1
2
2
1
1
1
0
2
1
1
1
0
0
2
1
2
1
1
0
0
0
2
1
0
1
1
0
1
2
1
1
2
2
0
1
1
3
0
0
2
0
2
0
1
2
1
0
0
1
0
1
0
0
1
1
1
0
0
0
0
1
2
0
1
1
2
0
2
1
2
0
0
1
1
2
2
2
2
1
0
0
0
1
1
2
0
1
0
0
1
1
0
2
0
1
1
2
1
0
0
1
1
0
1
0
1
1
2
2
1
2
0
1
2
0
0
0
0
1
0
1
1
1
1
2
2
1
1
1
3
1
0
1
1
0
1
1
0
1
0
1
0
1
1
2
0
2
0
1
1
1
2
3
0
0
1
1
0
1
1
0
1
1
1
0
0
2
2
2
1
0
1
2
0
1
1
3
0
1
1
0
0
1
0
1
2
1
1
1
1
0
0
0
2
1
2
1
0
0
0
2
4
0
1
2
1
1
2
1
0
1
1
1
1
1
0
2
1
0
0
0
0
0
2
0
1
0
0
1
1
1
1
2
0
1
1
0
0
1
1
2
1
1
1
1
0
1
2
2
1
2
1
0
0
1
2
2
1
1
1
2
0
1
2
0
1
0
2
1
1
2
1
0
2
1
1
2
0
1
1
1
0
2
1
3
1
2
2
2
0
1
2
0
1
0
3
1
0
1
0
2
1
2
1
1
1
1
1
0
0
3
2
1
1
1
2
0
2
0
1
1
1
2
1
1
1
1
2
0
1
0
0
0
1
1
1
0
0
1
0
1
2
2
0
1
0
1
0
0
2
1
0
1
0
2
1
0
0
2
1
1
1
1
2
1
1
0
0
2
1
1
1
2
1
1
1
0
1
1
1
0
1
2
1
1
1
1
1
1
1
1
2
1
0
1
0
1
1
1
0
1
2
1
1
1
1
0
0
2
2
2
1
2
0
1
1
1
1
0
1
1
2
1
2
1
0
1
1
1
1
0
1
1
2
1
1
0
2
0
1
0
1
2
1
0
1
2
1
0
0
2
4
0
0
0
1
0
1
0
0
1
2
1
1
1
1
1
1
1
1
0
2
1
0
0
0
0
1
2
0
2
0
1
0
0
2
1
1
2
1
2
0
2
0
3
1
1
0
1
1
1
0
1
1
2
1
2
1
0
0
1
1
1
0
0
1
1
1
0
0
1
2
1
0
1
1
2
1
1
1
1
1
0
1
1
2
1
1
0
0
1
2
0
0
0
0
1
1
1
1
0
1
0
0
1
2
2
0
1
0
1
0
0
1
1
1
0
0
2
0
2
1
2
1
2
1
0
0
1
0
1
2
1
0
0
2
2
0
1
0
2
0
1
2
0
1
2
2
3
1
0
2
3
1
0
2
1
2
2
2
1
1
0
1
0
2
0
2
2
1
1
1
1
0
0
0
1
0
1
0
1
2
0
1
0
1
1
2
2
0
1
0
0
1
1
0
1
2
1
2
1
0
1
0
1
0
1
1
1
2
1
0
0
1
0
2
0
1
0
0
2
2
2
1
0
0
0
2
2
3
0
0
0
1
0
0
1
1
2
0
1
0
2
2
1
1
1
1
2
0
1
1
0
0
1
1
1
2
2
0
2
1
1
0
1
0
2
1
1
0
1
1
3
0
1
0
0
0
0
0
2
1
1
1
1
2
0
2
2
1
1
1
0
2
1
1
1
2
2
1
1
0
1
0
1
0
0
1
1
1
2
0
0
0
3
1
0
2
0
0
0
0
1
1
1
1
0
2
1
2
2
2
0
1
0
1
0
0
1
0
0
2
1
1
1
0
2
2
2
1
1
0
1
2
0
2
0
2
0
1
1
1
2
1
0
0
0
1
1
0
2
0
1
1
1
1
0
0
1
0
1
2
1
0
1
2
0
2
1
1
0
0
0
1
0
1
1
1
1
1
2
1
1
2
1
2
2
1
1
1
1
0
2
0
0
0
3
0
1
1
0
0
0
0
0
0
1
1
0
1
1
0
0
2
3
2
1
1
0
1
0
1
2
2
0
0
1
1
0
2
0
1
1
2
0
0
1
2
2
2
1
0
1
0
1
0
2
1
0
0
0
0
4
0
1
1
0
2
2
1
1
2
1
0
1
1
1
1
1
2
1
0
2
1
1
2
2
2
0
2
1
1
2
2
1
1
2
1
1
2
1
2
1
1
0
1
1
0
1
1
2
1
1
2
1
2
2
0
1
0
0
0
1
1
1
1
1
1
1
3
1
1
1
0
1
1
0
2
2
0
0
0
0
0
1
0
1
2
0
0
2
1
0
1
1
1
0
2
0
1
3
2
0
1
0
2
0
1
1
1
1
2
1
2
1
1
0
0
0
2
1
1
2
1
1
2
1
0
2
2
4
2
2
2
1
1
1
1
0
0
2
2
1
1
1
1
2
2
1
2
1
0
2
1
0
0
0
0
2
0
1
2
1
1
1
0
2
1
2
0
2
1
1
1
1
0
0
2
2
0
0
2
0
0
0
2
1
1
1
2
0
1
2
1
2
1
1
1
0
0
0
2
1
1
1
1
0
0
1
1
1
0
0
0
0
2
2
0
1
0
0
0
1
1
1
0
1
1
1
1
2
1
2
2
0
0
0
0
2
0
1
1
0
0
0
0
1
1
2
0
2
1
1
1
1
1
0
1
0
0
0
1
0
0
0
2
2
2
1
2
1
1
1
1
0
0
0
1
0
1
2
2
1
0
0
0
1
1
1
1
0
2
2
0
1
1
2
1
1
0
1
0
0
1
0
1
1
1
1
0
1
0
1
1
1
1
2
3
0
2
0
1
1
2
2
0
0
1
0
0
1
1
2
0
2
0
1
0
0
0
3
1
1
1
1
0
2
0
3
2
0
0
0
1
2
1
1
2
0
1
1
0
1
1
1
1
0
0
0
0
1
1
0
0
1
0
2
2
0
0
1
1
1
1
1
1
1
0
2
1
0
1
1
1
2
2
2
1
2
2
2
0
0
0
0
0
2
1
0
1
1
1
0
0
0
1
0
0
1
1
1
1
0
0
1
1
2
0
1
0
2
0
4
0
0
1
0
1
1
2
1
0
0
1
1
1
1
0
0
2
0
2
0
1
2
2
0
2
0
0
1
0
0
0
0
0
1
1
1
1
1
1
1
2
2
1
1
1
1
2
1
1
2
0
1
0
0
0
1
0
2
1
2
0
1
1
1
2
0
0
1
2
0
1
2
0
2
0
0
2
0
1
2
2
0
1
0
1
0
1
2
1
1
1
0
2
0
0
0
1
0
0
2
1
1
0
0
1
1
2
2
1
1
2
1
1
0
1
2
0
1
1
0
0
2
1
0
1
1
1
2
2
1
1
0
2
1
0
0
0
1
1
0
1
0
1
1
2
0
2
0
0
1
1
1
1
1
1
1
1
0
2
0
1
0
2
0
1
1
2
0
2
0
1
1
2
1
0
1
1
2
1
3
2
1
1
0
0
0
1
2
1
1
1
1
1
0
1
1
1
0
2
0
1
2
1
1
2
0
0
1
0
1
2
0
1
1
1
0
0
1
1
0
0
2
1
1
1
0
2
2
1
1
1
0
0
1
2
1
1
1
5
1
0
1
0
2
2
0
1
1
0
1
0
0
1
1
1
1
2
1
1
0
2
1
0
1
1
1
2
1
1
1
1
1
2
0
2
2
1
1
1
1
2
1
1
0
0
0
1
2
1
0
1
0
1
0
1
2
1
1
1
0
2
0
0
1
1
1
0
1
0
0
1
0
0
2
0
1
0
1
0
0
0
2
1
1
1
0
1
1
2
2
1
0
0
0
1
1
1
1
1
1
1
2
1
2
0
0
0
0
1
0
0
0
1
0
1
2
2
0
2
2
1
1
2
1
0
0
0
0
0
1
1
1
0
1
0
0
1
3
1
0
0
0
1
2
3
2
1
1
2
1
0
0
1
1
1
2
0
1
1
0
0
0
0
1
0
2
1
2
0
0
0
1
1
1
2
1
1
1
2
2
1
2
0
1
2
0
1
0
0
0
0
0
1
0
0
1
1
1
1
0
0
1
0
2
3
0
1
0
1
0
1
0
1
1
0
3
1
2
1
1
0
0
0
0
1
0
1
1
1
1
0
1
2
1
1
0
0
4
1
1
3
0
0
1
0
1
1
0
0
0
3
0
0
2
0
1
1
1
0
2
0
2
1
2
1
3
0
0
0
0
2
1
1
0
2
0
2
0
1
1
0
1
2
1
0
1
1
0
2
2
0
2
1
1
1
1
1
1
2
1
1
0
0
2
1
1
1
0
0
0
1
2
2
0
0
1
1
0
1
0
1
1
1
1
0
1
1
2
0
1
1
0
2
1
0
1
0
1
0
0
2
0
0
1
2
1
1
1
0
0
1
2
0
1
1
1
1
0
0
0
1
1
2
1
2
1
2
1
1
4
1
1
1
1
1
1
2
0
1
1
1
0
2
1
2
1
2
2
1
2
1
1
2
1
1
1
1
0
0
1
0
1
0
1
1
0
0
1
1
0
1
2
1
1
1
1
0
2
1
1
0
0
1
1
1
0
1
1
0
1
2
2
0
0
1
1
1
0
0
2
0
0
2
2
1
0
1
2
1
1
1
0
2
1
2
1
0
1
1
1
0
1
0
0
0
1
1
2
0
2
2
1
1
1
1
0
1
0
0
0
1
1
0
2
0
0
1
0
0
1
1
1
1
1
1
2
0
1
0
0
2
1
2
0
0
1
1
1
2
2
1
2
1
1
1
1
2
1
0
0
0
1
0
1
0
1
2
0
0
1
1
2
0
1
1
1
0
0
1
1
0
0
0
1
1
1
2
1
2
2
0
0
1
0
1
1
1
2
1
2
1
0
1
0
2
1
1
2
2
1
1
1
1
0
1
1
2
2
1
2
1
1
1
0
2
1
2
4
1
0
1
0
1
2
2
0
1
0
1
0
0
2
1
1
0
1
1
2
1
1
0
0
1
1
1
0
0
2
1
1
1
2
1
1
0
1
1
0
1
0
1
1
1
1
2
1
0
0
1
1
0
1
1
2
1
0
1
1
0
2
2
1
0
1
1
0
1
2
1
1
0
0
1
1
0
0
2
0
1
1
0
2
0
0
0
2
1
0
1
3
0
0
0
1
2
1
1
1
0
1
0
1
2
1
0
1
1
2
0
0
1
0
1
2
0
2
0
1
1
2
1
1
1
2
1
0
1
1
0
0
0
0
2
0
0
1
1
0
2
1
1
1
1
1
0
2
0
2
2
2
1
0
1
1
1
2
1
1
1
1
3
0
2
1
1
1
0
1
0
2
3
0
0
1
0
0
1
2
2
2
2
2
1
0
2
0
2
1
0
2
0
1
0
1
1
1
1
0
1
1
0
1
1
3
0
1
1
2
0
0
2
2
1
1
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
1
2
1
0
0
0
1
1
1
0
1
1
1
1
1
1
0
1
1
1
1
1
2
0
2
1
1
1
1
1
0
0
0
1
1
0
0
2
2
1
1
0
0
1
0
1
0
2
0
3
0
0
1
1
2
1
1
0
0
1
1
0
1
2
0
1
1
2
0
1
1
3
1
0
0
2
1
1
2
0
1
0
1
0
0
3
1
0
2
0
1
2
2
1
1
0
2
2
1
2
1
0
0
1
2
1
0
2
3
0
1
2
2
1
2
0
2
1
1
1
1
0
1
1
1
1
1
0
0
0
1
0
2
1
0
0
0
0
1
1
0
0
1
1
1
1
1
1
0
1
3
1
1
1
2
2
0
2
0
1
0
2
2
2
2
0
2
2
0
1
0
0
0
1
0
1
1
2
0
2
2
0
1
2
1
2
0
1
0
0
2
0
2
0
1
0
2
1
1
1
1
1
1
1
0
1
1
1
1
1
3
0
1
0
0
2
1
1
1
0
1
1
2
1
0
1
1
1
0
1
0
1
1
1
0
2
0
2
0
2
1
1
1
1
0
2
0
0
1
1
1
0
0
1
2
2
1
1
1
0
1
2
2
1
2
0
2
0
2
1
1
0
1
2
1
0
0
1
1
2
0
1
1
1
1
1
0
1
1
1
0
0
0
0
0
2
1
2
1
1
2
0
1
1
0
1
0
1
2
1
2
1
0
0
1
1
1
2
2
0
0
2
1
2
1
2
0
1
2
2
2
0
1
1
0
2
1
0
2
2
1
1
0
0
0
0
0
1
2
0
1
2
2
1
1
1
1
0
1
2
0
0
1
0
1
2
2
1
1
1
1
1
0
0
0
1
1
1
2
1
1
0
0
1
1
1
1
2
0
1
2
1
0
2
1
0
1
1
1
0
1
1
2
0
1
2
0
0
0
0
2
1
0
1
0
0
0
1
0
1
0
2
1
1
1
1
1
1
0
0
2
0
1
0
1
0
2
0
1
1
1
1
1
0
1
2
3
1
1
2
1
1
1
0
2
1
2
1
1
0
1
0
1
1
2
0
0
0
0
2
2
2
0
0
1
0
2
1
2
2
1
1
0
1
1
0
0
1
1
1
1
1
1
1
2
2
0
1
0
2
1
1
1
0
0
0
0
0
1
1
0
0
0
1
1
0
1
0
0
1
0
1
0
2
1
2
0
1
0
1
2
1
0
1
1
2
1
1
1
1
1
1
2
1
1
1
1
1
0
0
2
1
0
0
1
2
0
4
1
0
2
1
1
2
0
1
1
0
1
1
0
1
2
2
1
2
2
0
0
1
1
0
0
1
1
1
0
2
2
2
0
0
0
1
1
0
0
1
1
2
1
1
2
1
1
1
1
0
1
1
1
1
1
1
11
1
2
1
1
1
1
1
2
1
1
1
1
1
0
2
4
1
2
1
1
1
0
1
0
1
1
0
2
1
0
1
1
0
0
1
2
1
1
1
1
0
1
1
2
1
1
2
1
1
1
0
0
1
1
0
0
0
1
0
1
2
1
0
0
0
2
2
1
0
0
1
0
0
1
2
1
1
1
1
1
1
1
0
1
1
1
1
1
1
2
1
0
2
1
1
0
1
1
1
0
3
3
1
2
0
1
2
0
2
2
3
2
1
0
1
1
2
1
1
2
1
1
1
2
0
1
1
2
1
1
2
1
1
1
0
0
1
2
1
0
1
1
0
1
1
2
0
1
0
2
1
0
1
0
0
1
0
0
2
0
0
0
1
2
1
1
0
1
1
1
2
1
1
1
0
1
1
2
1
2
0
1
2
2
2
0
1
0
0
2
1
2
1
1
0
1
1
0
1
1
0
0
1
2
1
1
2
0
0
0
0
3
1
1
0
1
2
2
1
0
1
1
1
1
1
2
1
1
2
0
2
0
0
0
2
1
0
2
0
1
1
1
1
1
2
1
1
0
2
1
0
0
1
1
2
1
1
0
1
2
1
0
1
0
2
0
2
2
2
1
1
1
0
1
1
2
0
1
1
0
0
2
1
0
1
2
0
0
1
1
2
0
0
1
1
1
2
2
1
0
2
2
0
0
2
1
1
1
2
2
1
0
0
2
1
1
0
0
1
2
2
2
2
0
1
1
1
0
1
1
1
2
1
3
1
2
1
1
1
0
1
1
1
2
1
2
0
0
2
0
1
0
1
1
0
2
0
1
1
2
1
1
1
1
1
2
2
1
2
1
1
0
2
1
1
1
1
1
1
1
1
0
1
1
0
1
0
2
0
0
0
0
2
2
2
2
1
1
2
2
0
0
1
0
0
1
1
1
1
1
2
0
1
0
1
0
0
1
0
1
1
1
1
2
1
1
0
2
0
1
2
0
1
1
1
1
1
1
1
2
0
1
0
0
0
2
1
1
1
0
0
0
1
1
0
1
0
0
1
2
1
0
0
0
1
0
0
2
0
0
2
0
3
1
1
0
1
1
0
1
2
1
0
0
1
0
0
0
1
1
1
1
0
1
1
2
1
1
0
2
2
0
2
0
0
1
1
0
0
1
2
1
0
0
2
2
0
1
2
0
2
1
1
1
0
2
1
1
1
1
2
1
2
0
1
1
2
0
0
0
1
0
1
1
0
0
1
1
1
1
2
1
0
0
1
1
1
1
1
1
2
1
2
1
2
0
0
2
0
2
2
1
1
2
0
2
1
1
1
2
1
1
2
2
0
1
0
1
0
1
0
2
1
1
1
1
1
0
1
3
0
0
1
0
0
0
2
0
1
0
1
1
1
0
1
1
2
0
0
0
0
1
1
1
0
1
1
0
1
1
1
1
1
0
1
1
1
1
2
1
1
1
1
1
0
0
1
1
1
1
1
1
1
0
0
0
2
0
0
0
1
1
3
2
2
1
1
2
0
1
0
0
0
1
1
1
0
2
0
1
1
0
1
1
1
1
1
1
1
0
2
0
0
1
1
1
1
1
1
0
0
0
2
1
1
1
2
1
1
0
0
1
1
0
0
1
1
1
1
1
4
1
0
2
1
0
0
1
1
1
0
1
2
2
1
1
1
1
1
2
1
0
0
2
1
1
1
1
1
1
1
0
1
1
0
2
0
0
1
2
2
0
0
1
0
1
0
1
0
1
2
3
0
2
1
2
1
0
0
1
2
1
1
0
1
2
1
3
1
2
1
0
1
2
2
0
1
0
1
0
1
1
2
0
1
2
2
1
0
0
0
1
0
1
2
1
1
1
1
1
1
1
0
2
4
1
1
0
0
2
0
2
2
0
0
0
1
1
2
1
0
0
0
0
1
2
2
2
1
2
1
1
1
2
0
1
0
0
0
1
0
0
2
1
1
1
2
0
1
1
1
1
1
1
2
0
2
1
2
1
0
2
2
0
0
2
1
0
0
1
2
2
2
1
1
1
0
0
0
0
1
0
0
2
1
0
1
1
0
1
1
2
3
1
3
0
1
0
1
0
0
0
0
1
0
0
2
1
0
2
1
2
1
1
2
1
2
0
1
0
1
2
1
1
1
2
1
0
0
0
2
1
0
1
1
2
1
1
1
1
0
1
0
0
2
3
2
0
1
2
0
1
0
1
0
1
1
0
1
1
2
1
0
2
1
2
1
2
0
0
0
0
0
2
1
0
1
0
2
0
0
1
1
1
1
1
1
0
3
2
2
0
1
0
0
1
1
1
2
1
1
1
1
1
0
2
1
2
1
3
2
0
2
0
0
2
0
2
1
1
1
0
1
0
0
1
1
1
1
2
2
0
1
0
1
2
2
1
0
2
0
1
0
1
1
1
1
2
1
1
2
2
0
1
1
1
1
0
1
1
0
0
1
2
2
0
1
0
2
0
1
1
1
0
1
0
1
2
2
1
2
2
1
1
2
1
2
2
1
0
3
2
1
0
2
1
2
1
1
1
0
2
1
2
0
0
0
2
0
1
1
0
1
1
0
1
0
1
2
1
1
0
2
0
2
1
1
0
1
1
1
1
1
1
1
1
1
1
0
1
2
1
0
1
1
1
1
1
0
1
0
2
1
0
1
2
1
0
1
1
1
1
2
1
2
1
0
1
0
1
1
0
1
0
1
1
1
2
0
1
2
1
0
2
1
1
0
0
0
1
0
0
1
2
0
1
1
1
0
0
3
2
1
0
2
1
1
0
2
1
1
0
1
2
0
1
1
1
1
1
1
1
1
1
1
2
0
1
2
0
0
1
0
2
2
1
2
1
0
0
1
1
2
1
1
0
1
1
1
1
0
2
2
1
2
2
1
1
2
0
0
1
1
1
1
2
0
1
2
0
0
0
1
1
2
1
2
3
1
1
2
2
1
2
1
2
1
0
2
0
2
2
0
1
0
1
0
1
1
0
2
1
1
2
2
1
5
1
1
1
0
1
1
2
1
1
2
1
0
1
0
1
1
2
2
2
0
0
1
1
0
1
2
1
2
2
1
0
2
0
2
2
2
1
0
0
1
2
0
1
1
0
0
2
0
2
0
2
2
1
1
1
2
1
1
1
0
0
1
1
1
2
0
1
1
0
0
2
2
1
1
1
2
1
1
0
0
0
0
0
1
1
0
2
1
1
2
2
1
1
0
2
0
0
1
1
2
1
0
1
1
0
1
2
0
2
1
0
1
2
0
0
0
2
1
2
2
0
0
2
0
6
1
1
1
1
1
1
1
0
1
0
1
0
0
1
2
0
2
0
1
1
2
1
2
0
0
1
2
1
1
1
0
1
0
1
0
1
1
0
1
1
1
1
2
1
1
0
0
1
1
1
2
2
1
1
1
1
1
2
0
0
1
0
2
3
0
1
1
0
2
1
1
1
2
0
1
2
0
0
0
1
1
0
1
1
1
0
0
1
1
0
0
1
0
0
0
0
1
1
0
0
0
0
1
1
1
2
0
1
2
0
0
1
0
2
0
1
0
1
2
1
1
1
0
2
1
2
0
1
1
1
0
2
1
1
2
0
2
1
0
1
1
1
1
0
2
1
1
0
0
2
1
2
1
1
2
2
1
0
1
1
0
1
1
1
0
0
1
0
1
1
0
0
1
1
0
0
0
1
0
1
0
2
0
1
0
0
1
1
0
1
1
2
0
2
1
1
1
1
1
0
0
2
1
1
1
1
2
0
1
1
1
1
0
1
1
0
0
2
2
0
1
1
1
0
0
7
2
0
2
1
0
0
1
1
1
2
2
1
2
1
1
0
1
2
1
1
1
0
0
0
2
1
0
2
2
0
1
1
2
1
1
1
2
0
0
1
1
0
1
2
1
2
1
2
1
2
0
0
1
0
1
0
0
0
0
1
1
2
1
1
0
2
0
1
2
1
0
1
1
1
2
2
1
1
1
0
1
1
0
0
1
0
2
1
0
1
1
0
2
2
1
1
2
1
1
1
1
2
1
1
1
1
1
2
2
1
1
0
2
0
0
0
0
1
1
1
0
2
0
1
1
0
1
1
1
2
0
0
0
2
0
2
2
0
1
1
0
1
0
1
0
1
0
2
1
1
1
0
2
0
0
1
1
1
1
1
1
1
0
1
2
2
1
0
0
1
1
2
0
2
1
2
1
1
2
2
1
1
1
1
1
1
1
2
0
0
2
1
1
1
1
0
0
2
0
2
1
0
0
2
0
2
2
1
0
0
0
1
2
1
1
1
3
1
1
1
1
1
3
0
2
1
2
0
1
1
1
1
0
2
2
0
1
0
2
1
2
1
1
2
1
2
1
1
0
1
0
1
1
0
1
1
1
0
2
1
2
2
1
1
1
0
1
1
1
2
2
1
2
1
2
0
1
2
2
1
1
2
1
1
1
0
2
2
1
1
2
1
1
1
1
1
0
1
0
1
3
1
1
0
1
2
0
0
0
2
1
1
1
1
2
1
0
0
0
2
5
1
1
0
2
0
1
2
1
2
1
1
2
2
1
1
0
0
0
1
0
0
1
1
1
1
1
1
0
0
1
0
0
2
0
1
0
1
1
0
0
0
1
2
2
1
0
2
0
2
1
1
1
1
0
1
2
0
0
1
1
3
1
0
1
2
0
1
1
0
0
1
0
0
2
0
1
2
0
2
2
2
1
1
0
1
2
1
0
2
2
0
1
1
1
2
2
0
0
1
1
2
1
0
0
2
0
2
1
0
0
1
2
1
1
2
1
1
0
0
1
1
2
1
1
0
1
1
2
1
1
1
3
1
2
0
1
1
1
2
0
2
2
1
0
2
2
1
0
1
1
1
1
2
2
0
1
1
1
1
0
2
1
0
1
1
1
1
0
2
0
0
1
0
0
1
2
2
2
2
0
2
1
1
1
2
1
1
1
0
0
0
1
0
1
2
1
1
0
2
2
1
2
2
1
1
0
1
0
2
1
0
2
0
1
1
0
1
1
1
0
1
0
0
0
2
2
1
1
0
1
1
0
2
1
1
2
0
0
0
1
0
1
0
1
2
2
1
1
1
1
0
2
2
1
1
0
1
1
0
1
0
1
1
2
1
1
0
0
1
0
1
0
1
1
1
1
2
2
0
0
0
0
0
0
0
1
1
1
3
1
0
0
0
1
0
2
1
1
0
2
0
1
2
1
2
2
0
1
1
2
1
1
1
1
1
0
1
0
0
1
1
0
1
2
1
1
1
1
0
1
2
2
0
1
0
2
1
1
1
1
2
1
2
1
0
1
1
1
0
1
2
1
2
2
1
0
1
0
1
1
0
2
1
2
1
1
0
0
0
2
1
1
1
2
1
1
1
2
2
1
1
1
1
2
2
4
1
1
3
2
1
0
3
2
1
0
1
1
0
2
1
1
1
0
2
1
1
1
2
1
1
0
2
1
1
2
1
0
2
0
0
1
0
2
0
1
1
1
1
1
1
0
1
2
1
0
2
0
4
0
2
2
1
0
0
0
1
1
1
0
1
3
1
1
1
0
0
0
2
1
1
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
4
0
0
1
2
0
2
1
1
0
2
1
0
1
2
1
2
1
0
2
0
2
1
1
2
3
2
1
1
1
2
0
2
1
0
0
1
0
1
2
2
1
1
2
1
0
0
1
1
0
1
2
1
0
1
0
0
1
0
1
0
0
0
0
1
1
1
2
1
1
2
0
1
0
0
1
2
0
4
1
0
0
1
0
0
2
1
1
0
1
1
2
1
0
0
2
1
1
1
1
1
1
0
0
1
0
1
1
1
0
1
1
1
0
1
1
2
1
1
2
0
0
2
0
1
0
2
1
2
0
1
1
2
2
1
0
0
1
2
1
2
1
1
0
1
1
2
0
1
2
0
0
0
0
0
1
0
0
1
0
0
1
1
1
1
1
0
1
1
0
0
2
1
1
0
2
0
0
0
0
2
2
1
1
2
1
1
1
1
2
0
1
1
2
2
0
0
1
1
1
1
1
3
1
0
2
1
0
2
1
2
1
2
0
1
1
0
0
1
0
2
1
1
2
0
1
0
2
1
1
1
1
1
2
1
0
1
0
0
1
1
0
2
2
0
0
2
1
0
0
1
2
1
2
0
2
1
2
1
1
2
1
1
0
1
0
0
1
1
1
1
1
1
1
1
1
0
2
1
0
1
0
2
1
1
0
0
2
1
1
1
2
1
1
1
1
1
2
0
1
2
1
0
0
1
1
1
0
0
2
0
0
0
0
2
1
0
1
0
1
0
2
1
3
0
1
0
1
1
0
0
0
0
1
3
2
0
1
2
3
1
1
0
2
1
1
0
1
1
0
2
2
1
1
1
1
0
1
0
0
0
0
1
0
1
2
0
2
1
1
1
2
0
1
2
1
2
1
2
1
1
1
0
1
1
1
0
2
0
0
1
1
1
1
1
3
1
1
1
1
0
1
1
1
1
0
0
0
0
0
0
1
0
1
0
1
2
2
1
1
0
2
2
1
0
2
0
2
0
1
2
1
0
1
1
1
2
0
1
0
2
1
2
3
2
2
0
1
0
3
1
0
1
2
0
1
1
3
1
0
1
0
2
1
2
0
1
0
0
1
0
1
0
1
1
0
1
0
1
2
2
2
1
1
0
0
2
1
1
2
0
0
1
1
2
2
1
0
1
1
1
1
2
2
1
0
0
1
2
0
1
2
1
1
1
0
0
1
1
1
1
2
1
0
2
1
1
2
0
1
0
1
1
2
1
2
1
1
1
1
2
1
1
1
0
1
1
1
0
0
1
1
0
1
1
1
1
1
1
1
2
1
0
2
0
1
2
1
1
1
1
1
0
1
0
2
1
0
1
0
1
1
0
0
1
1
0
1
2
0
2
2
2
4
1
0
0
0
1
2
1
1
0
1
1
2
0
1
1
1
1
2
1
2
0
0
0
1
0
1
2
0
0
0
1
1
0
2
0
3
1
1
2
1
2
1
1
1
1
0
1
1
1
1
1
1
1
1
2
0
1
1
1
0
0
1
1
1
2
2
1
1
1
1
0
0
0
2
0
2
1
3
0
1
1
0
1
1
2
1
0
0
1
1
1
0
1
0
1
0
0
1
0
1
2
0
2
1
1
2
0
2
1
2
1
1
2
1
2
1
0
0
1
2
0
1
0
1
0
1
1
0
1
0
0
1
1
2
1
1
1
0
1
1
2
1
1
1
0
1
0
0
1
0
0
1
2
0
2
1
1
1
2
2
0
0
1
1
1
2
1
0
0
1
0
1
2
2
1
2
1
1
0
1
1
1
1
0
1
2
0
1
1
1
1
1
0
0
1
0
2
2
1
0
0
0
1
2
0
0
1
0
1
2
1
1
0
0
0
1
0
0
3
1
1
2
0
0
0
0
2
1
0
3
1
1
0
0
0
2
1
0
2
1
1
1
1
2
1
2
0
0
2
0
0
0
2
0
1
1
2
0
1
0
1
2
0
2
2
1
0
2
1
2
0
0
1
1
1
0
1
4
1
0
0
1
1
2
1
2
1
0
1
0
1
1
1
2
1
0
1
0
2
1
2
1
1
0
1
0
2
2
1
1
0
0
2
1
0
1
1
1
0
2
2
1
1
0
0
0
2
2
0
2
2
0
1
2
1
1
1
1
1
2
0
2
1
2
1
0
0
0
1
1
1
1
0
0
0
1
2
1
1
1
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
2
0
2
1
1
0
1
1
0
1
0
0
2
0
0
1
1
2
0
2
0
2
0
1
1
0
1
1
2
0
0
2
1
0
1
1
0
0
0
1
2
1
1
1
1
1
0
1
0
2
1
1
2
0
0
0
1
1
1
0
0
1
1
2
1
0
1
1
1
1
1
1
0
2
1
1
0
2
1
1
2
3
1
1
0
0
0
0
1
1
1
2
2
2
2
0
0
1
1
2
1
1
2
2
1
0
1
0
0
1
1
0
1
2
1
2
1
0
1
1
1
0
1
1
1
1
3
2
2
2
2
1
0
0
1
1
1
1
0
1
2
1
3
0
0
0
1
0
1
0
0
2
1
1
1
1
1
0
0
1
1
0
0
0
1
0
0
1
1
1
0
0
0
0
1
1
0
4
1
2
2
0
1
1
0
0
0
1
4
2
0
1
1
1
1
1
0
1
0
1
0
1
1
1
2
0
1
0
2
1
1
1
2
1
0
2
0
1
1
2
0
0
2
0
1
0
2
1
1
0
2
0
1
1
2
1
2
1
1
2
1
0
0
1
0
1
1
1
0
1
1
0
0
2
1
1
0
1
0
1
0
1
2
1
0
2
1
0
1
0
2
1
2
0
1
1
1
1
0
2
1
2
0
0
2
0
2
0
2
1
2
1
1
2
0
1
1
0
1
2
1
1
1
0
1
1
1
1
2
1
0
2
1
2
1
3
0
1
0
0
1
1
0
1
1
1
0
0
0
1
1
1
2
0
2
0
2
1
0
0
1
0
1
1
1
0
2
0
0
1
1
0
2
0
1
1
0
1
1
2
0
2
0
1
1
0
2
0
0
2
1
1
1
0
2
2
0
1
1
0
0
1
2
0
1
0
1
1
0
1
0
1
1
0
0
0
2
2
2
1
0
1
1
0
2
1
0
1
2
1
1
0
2
2
0
1
1
0
2
2
1
1
0
1
0
1
1
0
1
1
1
0
2
0
2
1
1
2
1
0
1
0
1
1
0
0
2
1
0
0
0
1
2
0
0
1
1
0
1
0
2
2
1
1
0
1
1
0
0
1
0
1
1
1
0
1
1
2
2
0
1
1
0
0
0
1
1
2
0
0
0
1
0
0
1
0
2
1
1
2
1
1
2
1
1
1
1
0
1
0
1
2
1
1
1
2
2
2
2
1
0
2
0
0
2
0
2
0
2
1
0
0
0
1
2
1
1
0
0
1
1
1
1
0
2
1
1
0
1
2
1
1
0
2
1
0
1
2
1
2
1
0
0
0
1
1
1
1
4
0
2
2
2
1
0
0
2
1
1
1
1
1
1
2
0
2
1
0
1
0
1
0
1
1
0
1
3
0
1
0
1
2
0
2
2
0
1
4
1
2
0
1
1
2
0
1
0
1
1
1
0
1
1
0
2
2
2
0
0
2
0
2
0
1
2
0
1
1
0
0
0
1
1
1
1
1
2
1
2
0
2
0
2
1
2
1
0
0
2
1
2
0
0
0
2
1
0
0
3
1
2
0
0
0
1
1
1
0
0
0
2
1
1
1
2
1
1
2
1
2
0
1
1
2
2
2
0
0
1
2
1
1
1
0
2
2
2
2
1
1
1
1
1
1
1
1
1
0
1
1
1
2
1
0
2
0
2
0
2
2
1
2
1
1
1
2
1
0
2
0
1
0
2
2
0
1
1
1
0
0
0
2
0
1
1
1
1
2
1
1
0
1
1
0
2
1
0
1
1
0
2
0
0
0
2
2
1
1
2
1
1
1
1
2
1
1
0
1
1
0
2
2
0
2
1
2
1
2
0
2
0
0
0
1
0
1
1
2
1
1
0
0
1
0
2
1
0
1
2
2
2
1
1
1
1
0
2
0
1
1
0
1
1
1
1
2
1
2
0
1
2
0
0
0
1
1
1
1
1
2
0
0
3
1
0
1
0
1
1
0
0
1
1
1
2
1
0
2
0
1
1
1
0
1
1
1
2
2
2
1
0
0
0
1
1
1
0
1
0
0
0
4
0
0
1
0
1
0
1
2
1
2
0
1
1
3
4
1
0
1
2
1
1
1
1
1
1
1
0
0
1
1
1
1
1
1
0
1
1
2
1
1
0
1
2
2
0
2
1
1
2
0
0
0
2
1
1
2
1
2
0
1
1
0
0
0
0
1
0
0
0
2
0
1
1
1
2
1
1
2
1
1
2
1
1
0
0
1
0
0
0
1
0
2
2
1
1
1
1
0
0
1
0
0
2
1
1
1
2
1
0
0
0
0
0
0
2
2
2
0
1
1
1
0
1
1
1
2
1
1
1
2
2
0
1
0
0
0
0
2
0
0
0
1
0
0
2
1
2
2
2
0
0
0
1
1
1
2
1
2
2
0
1
1
0
2
2
1
1
1
1
0
0
0
1
1
0
1
1
0
2
0
0
1
0
1
1
1
0
2
1
2
0
1
1
1
0
1
0
2
1
0
2
0
0
1
0
1
0
0
0
0
1
2
0
1
2
1
1
2
1
0
1
1
0
2
0
1
0
1
0
0
0
1
0
1
0
2
0
1
1
1
1
1
2
0
0
1
1
1
2
2
1
1
1
1
0
0
1
2
0
0
2
0
0
1
0
1
1
0
1
1
0
2
1
0
1
0
2
0
1
2
2
0
1
0
2
0
2
1
0
1
1
2
1
1
2
0
1
1
0
2
1
2
1
1
1
1
0
1
1
1
1
0
1
0
1
2
2
2
2
1
1
1
2
1
2
1
0
1
2
1
2
1
1
1
0
0
2
1
1
1
1
0
1
2
1
1
0
1
0
1
2
2
1
1
1
2
1
2
1
1
0
2
1
2
0
0
2
2
1
0
1
0
0
1
1
0
0
1
0
1
2
0
1
0
1
0
2
0
1
2
4
1
1
2
1
1
1
1
2
0
0
2
0
0
0
1
1
0
1
1
0
1
1
1
1
1
1
1
1
2
1
1
0
2
2
0
0
1
0
0
1
1
1
1
0
1
2
1
1
0
0
1
1
1
1
1
0
0
3
1
0
1
1
2
0
0
1
2
0
1
0
0
2
0
1
3
1
1
1
0
1
3
1
2
2
1
1
1
1
1
1
2
0
1
1
1
1
1
1
2
1
1
0
1
1
2
2
0
2
1
2
1
1
2
0
1
1
1
0
0
1
1
1
1
0
1
0
1
2
2
1
2
1
0
2
2
1
0
1
2
1
2
2
0
1
2
0
0
2
1
2
1
1
1
1
2
0
2
2
1
0
1
1
0
2
0
1
0
2
0
1
2
0
1
0
1
1
2
2
2
2
2
2
1
2
0
1
1
2
0
0
0
1
2
2
1
0
2
3
1
2
0
1
2
0
0
2
1
1
2
0
2
0
0
1
0
2
0
0
0
0
1
0
0
2
1
0
1
0
0
2
0
1
2
1
1
2
1
2
1
2
0
0
0
0
0
1
0
0
2
0
1
1
1
2
0
0
1
2
1
0
0
1
0
0
1
1
2
1
2
1
0
2
2
0
1
0
1
1
1
1
2
1
1
0
1
2
2
2
2
0
1
2
0
0
0
0
1
1
1
1
2
0
0
1
0
0
1
0
0
1
0
1
1
1
1
1
0
1
1
0
0
1
1
0
2
2
0
1
1
1
0
2
1
0
1
1
1
1
1
3
1
1
1
1
1
0
0
1
1
2
1
2
2
0
1
0
2
1
0
0
1
2
0
1
1
0
3
1
0
2
0
1
0
1
1
1
1
1
0
0
1
2
1
1
0
0
0
2
0
0
2
2
1
1
1
0
4
1
0
3
2
1
1
2
0
2
1
0
2
0
2
1
0
2
2
0
2
1
1
0
0
1
0
1
0
1
1
0
2
1
1
0
2
1
1
0
1
1
2
0
1
1
1
0
1
3
1
0
2
2
3
0
2
2
0
1
1
0
0
1
1
1
2
2
1
0
1
1
2
0
1
1
1
1
0
1
0
1
2
1
0
1
0
0
1
1
0
1
0
2
0
0
2
1
0
0
1
1
0
2
1
1
0
1
1
0
1
0
2
1
2
0
1
0
0
1
1
1
1
1
2
0
1
0
1
2
0
2
2
0
1
0
0
0
0
1
1
0
0
2
1
0
0
0
0
0
1
2
1
1
2
2
0
1
0
1
1
0
0
2
1
1
0
1
1
0
0
1
0
0
0
1
0
1
1
1
0
1
0
1
0
1
1
0
0
1
1
1
0
1
1
2
1
1
1
1
0
1
1
2
2
1
1
1
1
3
2
2
0
1
1
1
1
0
1
2
1
2
2
1
1
0
1
1
2
1
0
0
2
1
1
1
0
0
1
0
1
0
2
1
1
1
1
1
1
2
0
0
1
1
0
1
0
1
0
2
1
2
0
1
2
1
1
1
1
0
2
2
1
1
1
1
0
1
1
1
1
1
2
1
0
1
1
0
1
2
1
0
0
1
2
1
1
1
1
1
0
0
0
1
1
0
0
1
1
2
1
0
0
0
0
0
2
1
1
0
0
1
0
0
2
1
2
0
1
0
1
0
0
2
2
1
2
2
0
1
1
0
0
2
1
1
0
1
0
1
0
1
1
1
1
1
0
1
1
1
1
2
2
1
1
1
0
0
1
2
0
0
1
0
1
1
1
1
2
2
1
0
1
2
0
0
3
0
1
1
0
0
2
0
1
1
0
2
2
0
1
1
2
2
0
2
0
1
0
1
1
1
0
1
1
2
1
0
1
0
1
0
1
1
2
0
1
1
1
2
1
1
2
1
1
0
1
0
0
0
0
2
1
1
1
1
2
0
2
1
0
2
2
1
1
1
0
0
2
0
1
2
1
0
0
1
2
1
0
0
0
1
1
0
1
2
1
2
1
2
1
0
2
0
2
1
0
2
2
1
1
1
1
2
1
1
0
2
2
1
0
0
0
1
2
1
0
1
0
2
1
1
1
0
0
2
0
0
1
0
2
2
0
1
0
0
1
0
0
1
2
1
1
1
1
3
0
0
0
2
1
2
0
2
2
3
1
1
2
1
1
1
2
0
0
1
1
1
0
0
1
0
0
1
3
1
1
1
0
2
1
1
1
2
1
0
2
0
1
1
2
0
2
2
0
2
0
1
1
0
1
1
1
0
1
2
1
1
3
2
1
0
1
1
1
1
0
2
1
1
1
1
1
2
0
0
1
2
2
1
2
2
1
0
1
1
1
1
0
2
1
0
0
1
1
1
1
2
1
1
1
1
1
0
1
3
3
2
0
1
1
1
0
1
2
0
2
1
1
2
2
0
2
1
1
0
1
1
1
0
1
2
1
1
1
0
2
0
0
2
1
1
1
1
2
2
0
2
2
2
1
2
1
1
1
0
1
0
1
2
0
3
1
2
1
0
0
2
0
0
0
1
2
0
0
1
0
1
2
0
0
1
0
0
0
1
1
1
1
0
2
1
0
2
2
1
1
1
1
1
0
1
0
0
1
0
0
2
0
1
2
0
1
2
0
0
1
0
0
2
2
2
1
1
1
0
1
1
0
1
0
0
2
2
0
0
1
0
2
1
1
2
2
0
0
0
2
0
0
2
2
0
2
1
2
2
2
1
0
0
1
1
0
1
1
0
1
1
1
2
1
1
0
1
0
0
0
0
2
0
2
0
0
1
2
1
1
2
2
1
2
1
0
0
1
1
2
1
0
2
0
2
0
1
1
1
0
1
1
2
1
0
1
1
0
1
0
1
0
0
0
1
0
1
1
0
1
1
9
0
2
0
0
1
1
0
0
1
2
0
0
3
1
0
2
0
1
0
0
1
1
0
1
1
0
1
1
0
0
0
0
2
0
2
0
1
1
0
0
0
2
0
1
2
0
1
0
2
1
2
1
1
1
0
1
1
0
1
1
1
1
2
1
2
1
0
1
0
2
1
0
0
1
2
0
2
1
1
1
2
1
2
2
0
2
1
2
1
2
0
1
1
0
1
2
1
1
0
0
1
1
0
2
1
1
2
2
1
0
2
0
1
1
2
0
2
1
1
1
1
2
1
1
2
0
2
1
1
1
1
1
1
1
1
2
0
2
0
0
1
1
2
0
0
2
1
0
2
1
2
1
2
0
1
0
2
1
0
1
0
0
0
1
0
1
0
1
0
1
1
1
0
0
0
1
2
1
2
1
1
0
0
1
1
1
0
1
0
2
2
2
1
1
1
0
0
1
1
0
0
2
1
0
1
0
0
2
1
1
1
1
2
1
2
2
0
0
0
1
0
0
0
0
1
0
2
1
1
2
1
2
1
0
1
1
1
1
0
1
2
1
1
1
0
1
2
0
1
1
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
2
1
1
1
1
0
2
1
1
1
2
0
0
1
2
0
1
2
1
2
1
1
1
0
1
1
0
0
1
1
0
1
1
2
2
0
1
1
0
1
1
2
0
2
1
0
0
1
1
1
2
0
1
1
1
0
0
1
1
0
1
0
0
1
1
1
1
0
0
2
1
2
0
0
1
1
0
0
2
1
0
1
1
1
1
0
0
0
1
1
0
0
1
1
1
1
0
1
2
0
0
1
1
0
1
0
0
1
1
0
1
1
2
2
1
2
1
0
1
1
2
0
1
2
1
0
2
2
1
1
2
1
1
1
1
2
1
1
1
0
1
0
2
1
2
1
2
0
1
0
0
2
2
1
0
0
1
2
1
0
1
2
0
1
1
1
1
0
0
0
0
0
2
1
0
0
0
2
1
1
4
1
1
0
1
1
1
0
1
0
2
1
2
1
1
0
1
0
1
1
2
0
1
0
2
1
1
1
0
2
0
1
1
1
2
0
2
1
1
2
0
1
0
0
2
1
1
1
0
0
2
0
2
2
2
2
0
2
2
1
2
2
1
0
1
1
1
1
1
1
1
1
0
0
1
0
1
1
2
0
1
2
1
1
0
1
2
2
1
0
1
0
1
1
2
3
0
2
2
0
1
1
1
0
0
2
1
0
1
1
0
1
3
2
1
1
1
1
2
0
0
1
0
2
2
1
2
0
1
1
1
2
3
0
1
0
1
1
2
0
0
0
2
0
2
0
1
1
1
2
0
0
0
1
2
1
0
0
0
1
1
2
6
1
0
2
0
1
1
0
0
0
1
1
2
0
1
1
0
0
2
1
1
0
1
1
0
1
0
0
1
0
0
2
0
2
0
1
0
2
1
2
1
2
1
1
1
0
1
0
0
1
2
0
1
1
2
1
2
0
0
0
2
1
1
1
2
0
1
0
1
2
1
0
1
2
0
0
0
1
1
1
1
1
0
0
1
0
1
1
0
0
2
0
1
0
0
2
1
1
1
0
0
1
1
1
1
1
0
0
1
2
2
1
1
2
0
2
2
3
1
1
1
1
3
0
1
2
1
2
1
0
1
1
0
2
1
1
1
1
0
1
0
1
1
1
1
2
0
0
0
1
0
1
0
0
2
1
0
2
0
0
1
1
1
0
0
1
1
1
1
1
0
0
0
0
1
0
1
1
1
0
0
1
0
2
1
0
1
1
1
1
0
2
0
1
2
1
2
0
2
1
0
1
1
1
1
1
1
1
1
2
1
0
1
0
0
2
1
2
1
1
1
0
1
2
2
1
0
0
0
1
1
0
2
2
0
0
0
2
1
0
1
0
0
2
0
1
0
1
0
0
2
2
2
1
0
0
0
0
2
2
1
1
0
2
1
2
0
1
0
2
2
1
0
0
1
1
2
1
0
1
2
0
1
0
1
1
2
0
1
3
0
0
3
1
2
1
1
0
1
1
1
1
1
2
0
1
0
0
0
2
2
1
1
1
0
1
0
0
1
0
0
0
1
1
1
1
1
0
1
2
0
1
0
0
2
0
1
0
0
1
2
1
2
2
1
3
0
0
0
2
1
0
1
1
0
1
0
0
2
2
0
0
0
0
1
0
0
1
1
1
0
2
2
1
2
0
0
2
1
1
1
4
0
1
2
1
1
2
0
1
1
0
1
0
1
2
0
1
2
2
1
0
2
0
2
0
2
0
1
0
2
0
0
1
1
0
1
1
1
0
0
1
1
1
2
0
1
0
1
1
2
1
0
2
2
1
2
1
1
1
1
1
1
0
0
0
0
2
2
0
0
0
1
1
0
2
0
0
0
0
0
0
1
2
1
0
1
1
1
1
0
1
1
2
1
1
1
3
1
1
2
1
2
1
0
2
2
0
2
1
0
1
1
0
1
1
2
2
1
1
0
2
1
2
0
2
1
1
2
1
0
1
1
0
0
2
2
1
2
2
0
0
0
1
0
0
1
0
0
1
1
1
0
0
1
0
1
0
1
1
1
1
2
0
1
0
2
1
1
2
0
1
1
0
1
1
0
0
2
0
1
1
1
2
0
1
1
0
0
1
1
1
2
2
0
2
1
1
1
1
1
2
0
1
2
0
1
1
0
2
1
2
0
1
2
1
1
0
2
2
0
1
0
0
1
2
1
1
1
1
0
1
0
0
2
0
0
0
1
2
0
1
0
0
2
1
2
0
1
0
1
1
1
3
1
1
1
1
1
1
0
0
1
0
0
1
2
1
0
1
4
0
1
2
0
1
1
2
2
1
1
1
1
0
1
0
0
1
0
1
0
1
0
2
1
1
2
2
0
1
1
0
0
1
0
0
2
0
1
0
1
1
1
0
1
1
1
0
1
0
0
1
2
1
2
1
0
0
2
1
1
1
0
0
0
1
1
1
2
1
0
2
0
0
0
1
1
2
0
1
2
2
2
2
1
0
1
1
2
2
0
1
2
2
1
2
1
1
0
1
0
2
2
1
1
1
0
0
2
0
0
0
2
1
1
1
1
0
1
1
2
1
3
1
0
2
1
0
0
1
1
2
1
1
1
1
1
1
0
1
0
1
1
1
2
0
1
0
0
1
1
0
1
1
1
1
2
1
2
1
1
1
0
0
1
1
1
0
1
2
0
1
1
3
0
2
1
2
2
1
2
2
1
1
2
2
0
1
0
1
0
2
0
1
1
2
2
3
0
2
1
0
0
0
0
2
1
1
2
1
0
1
0
1
1
0
1
2
0
0
1
0
2
1
0
0
0
1
1
0
1
1
0
0
1
1
0
1
1
2
1
1
1
4
3
1
2
1
2
1
2
1
0
1
1
1
0
1
1
1
0
1
2
0
0
0
1
0
1
0
0
1
0
2
1
2
0
1
0
2
0
0
2
1
2
1
0
0
2
0
1
0
0
3
0
2
0
2
2
1
1
1
1
2
0
1
1
0
1
1
1
0
1
1
0
0
0
1
0
2
1
1
0
0
1
1
2
0
0
0
1
1
0
1
0
1
0
0
0
1
1
0
1
2
2
1
1
0
2
1
2
1
3
1
0
1
0
2
2
2
1
1
1
2
1
0
2
1
2
1
1
1
1
0
2
1
0
2
0
4
2
3
2
1
0
2
0
2
1
0
2
1
0
1
2
0
1
1
1
0
1
0
1
2
1
0
1
1
1
2
0
0
1
1
1
1
0
0
1
1
1
1
1
0
1
2
1
0
1
0
1
1
0
0
2
0
1
1
0
1
0
1
0
1
1
2
1
0
1
1
2
0
0
0
1
1
0
1
1
0
0
1
1
1
1
1
2
1
1
2
1
1
1
0
1
1
2
0
0
0
2
2
1
1
2
3
1
1
0
1
2
0
2
4
0
1
0
1
1
1
1
1
0
2
1
0
2
1
0
0
1
1
2
1
1
1
1
2
1
1
1
1
2
1
2
1
1
1
1
1
1
0
2
2
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
1
1
1
0
2
1
1
1
0
0
0
0
1
1
0
1
1
0
0
1
0
0
0
0
1
1
2
0
1
0
1
1
0
1
1
0
0
2
1
0
0
1
0
2
1
1
1
0
0
1
0
0
2
0
2
1
0
0
1
1
2
2
2
0
0
1
1
0
0
2
2
1
1
2
2
2
1
0
1
0
1
2
1
0
2
2
1
1
1
1
2
1
1
0
1
1
1
0
1
1
2
0
1
1
1
1
0
2
1
1
0
1
1
0
0
1
1
0
0
0
1
0
0
0
1
0
0
2
0
1
1
1
2
0
2
1
1
0
1
1
1
1
2
1
2
2
2
1
0
2
1
2
1
0
0
0
2
1
1
1
0
2
0
2
0
0
0
0
1
1
2
1
1
0
2
1
1
1
1
1
0
2
1
1
1
0
2
0
1
1
0
0
0
0
0
0
0
5
2
0
2
0
0
2
2
1
1
0
1
2
1
0
1
1
0
1
1
1
2
2
1
2
1
1
3
2
0
1
0
2
1
0
0
0
1
0
1
1
1
2
1
0
1
1
2
2
2
0
2
1
1
2
0
0
1
1
0
2
0
2
0
2
1
1
1
0
2
0
1
1
1
1
1
1
2
1
2
2
1
2
1
1
2
1
2
0
2
2
1
0
1
0
1
2
0
1
1
0
1
1
1
0
2
0
1
1
0
0
1
0
2
0
1
1
0
0
0
1
0
1
1
0
1
1
2
1
1
0
0
0
1
1
0
0
1
1
1
1
0
0
2
1
0
2
2
1
1
1
0
1
0
1
0
1
0
0
1
0
1
1
0
0
1
2
1
0
2
1
1
0
0
1
2
0
0
0
2
1
1
0
0
0
2
3
0
0
0
0
0
1
1
1
2
1
1
1
1
1
2
1
1
0
0
0
1
1
0
0
3
1
2
1
1
1
0
0
3
0
1
1
0
0
0
1
0
0
1
1
2
2
2
0
2
0
2
1
0
0
1
1
0
0
2
2
1
1
1
0
1
0
2
1
2
2
2
1
2
1
1
1
0
0
1
1
1
0
2
0
2
1
1
2
1
1
0
0
1
2
2
2
1
2
1
0
0
1
1
1
2
0
0
2
2
1
2
1
1
1
0
1
0
2
1
2
1
1
2
2
2
2
0
1
0
0
0
1
1
1
0
0
0
0
3
1
1
0
3
2
0
0
2
0
2
1
0
1
0
0
0
0
2
1
1
1
2
1
2
0
0
1
1
1
1
1
0
1
1
2
1
2
0
0
1
0
2
1
1
2
0
2
2
0
2
1
1
1
0
1
1
0
1
1
2
1
2
1
2
1
2
1
1
0
0
1
1
0
1
2
0
1
1
1
0
1
2
1
2
1
2
1
2
0
1
1
1
1
1
3
0
0
0
0
1
1
1
2
2
1
2
1
1
3
0
1
0
1
1
0
2
2
0
0
0
2
2
2
1
0
1
0
1
2
2
0
0
0
2
2
2
1
1
1
2
0
2
1
2
1
1
2
1
0
0
1
0
0
1
1
0
1
0
1
2
2
2
0
1
0
1
0
2
2
0
0
1
1
0
1
1
2
0
1
1
1
2
2
0
0
2
0
2
2
0
1
1
2
1
0
0
1
2
0
0
1
1
1
0
0
0
0
1
2
1
0
1
2
0
1
1
0
1
1
2
1
1
0
2
2
0
2
2
2
0
1
0
0
1
0
2
2
1
1
1
0
0
1
1
1
2
1
0
1
2
1
0
1
1
2
0
1
2
3
1
0
0
0
0
1
2
1
1
1
1
1
0
1
0
2
1
1
0
1
2
2
0
2
0
0
0
0
0
0
0
0
1
1
0
1
0
1
1
0
1
1
0
2
1
1
0
3
2
0
2
1
1
0
0
2
1
1
1
0
0
0
1
1
0
1
0
2
1
0
1
2
1
0
0
0
0
1
0
2
0
0
1
0
2
1
3
0
0
0
0
2
1
2
1
2
2
1
0
0
2
1
2
0
1
1
1
0
1
0
1
1
0
0
2
0
2
0
1
1
1
1
2
1
1
1
1
1
2
2
2
0
1
2
2
0
1
1
0
1
1
0
2
1
0
1
0
3
0
2
1
1
1
0
2
1
0
1
1
0
1
1
2
0
0
1
0
0
1
0
2
2
0
2
2
1
1
1
1
2
1
1
0
1
1
1
0
0
3
1
0
2
1
1
1
1
0
1
1
0
1
0
1
1
2
0
1
1
2
1
1
2
1
2
2
2
2
1
0
1
1
2
1
1
0
0
0
1
1
1
1
1
1
0
1
1
2
1
2
0
1
1
2
0
2
1
1
1
0
2
1
1
0
0
0
1
1
1
2
0
1
1
0
0
1
0
1
0
0
2
1
1
1
2
1
0
0
0
0
1
1
1
2
1
1
1
1
2
0
0
1
2
2
1
2
2
1
2
1
0
1
1
0
1
1
3
2
1
1
1
1
0
1
2
0
0
0
0
0
0
1
1
0
1
2
2
0
1
1
0
1
2
0
3
2
0
0
2
1
0
1
1
0
1
0
5
2
1
1
1
2
1
0
1
2
0
1
1
2
0
1
2
1
1
2
0
1
1
2
2
1
1
0
1
1
1
0
2
1
0
0
2
0
3
0
1
0
1
0
2
2
0
0
1
0
1
1
1
0
1
1
0
1
0
0
0
1
2
1
2
1
0
1
0
1
0
2
1
2
2
0
1
2
1
0
1
1
0
0
1
1
1
0
1
2
6
0
0
0
3
0
2
1
1
3
1
1
1
0
1
2
0
1
2
1
0
1
1
0
1
0
1
0
2
1
1
1
1
2
1
1
2
0
2
2
2
1
1
0
0
1
1
2
1
2
0
1
0
1
0
1
2
1
0
1
2
0
2
0
2
0
1
0
0
2
1
0
2
1
0
0
0
0
0
2
0
1
1
1
2
1
2
1
0
2
0
1
2
0
1
2
1
0
2
2
2
0
1
0
0
0
1
1
1
1
2
1
1
0
1
0
1
2
2
1
2
0
1
3
0
1
3
1
1
2
1
0
1
1
2
0
2
2
1
0
0
1
2
0
2
1
0
0
0
1
0
0
1
1
1
1
1
1
1
0
2
1
1
0
1
0
0
1
0
1
1
0
0
2
0
0
0
1
1
1
0
1
2
0
1
1
1
1
1
1
0
1
0
1
4
2
1
0
0
2
2
0
1
2
0
2
0
0
0
0
0
2
1
1
1
1
0
1
2
2
2
1
0
2
0
0
0
0
1
1
1
0
0
1
3
0
2
0
0
1
0
0
1
2
2
0
1
1
1
1
0
0
1
0
2
1
1
1
1
1
0
2
0
2
2
0
0
2
1
2
1
2
1
1
1
1
1
1
0
0
2
1
1
1
1
0
1
1
2
1
1
1
2
0
2
0
2
0
1
1
0
1
1
1
2
3
0
1
0
0
1
0
0
0
1
2
1
2
0
1
0
1
1
2
0
0
0
1
2
1
4
0
2
2
1
1
1
1
1
0
2
2
1
1
0
1
0
2
1
1
2
1
1
1
1
1
1
1
2
2
1
1
2
2
5
1
0
1
2
0
0
1
0
0
0
1
1
0
1
0
1
1
1
1
1
1
1
1
1
1
2
0
0
0
1
0
1
1
2
2
2
1
1
2
1
2
0
2
1
0
0
0
1
2
1
2
2
1
1
1
2
1
0
0
1
2
2
1
1
2
1
0
1
1
1
0
1
0
0
1
0
1
2
1
2
2
1
1
2
1
0
0
1
2
1
1
1
1
0
1
2
0
1
1
1
0
1
0
2
1
1
0
1
1
0
1
0
0
0
0
1
1
1
2
0
1
2
2
1
0
0
1
2
1
1
0
1
0
1
1
2
1
1
1
2
1
1
1
1
0
0
1
0
1
1
1
1
0
1
2
1
0
0
1
1
1
1
2
2
0
1
3
1
0
0
0
1
1
1
2
2
1
0
1
2
1
0
0
1
0
1
1
0
0
3
0
2
1
2
1
2
1
0
1
0
0
0
2
2
2
1
1
1
1
1
0
1
0
0
2
1
0
2
0
1
1
2
2
2
1
0
2
1
0
2
0
0
2
0
2
0
2
1
1
2
1
0
2
0
1
0
0
0
1
1
2
2
2
2
0
1
1
1
1
1
2
3
0
1
0
2
0
1
3
0
1
0
1
2
1
0
1
0
1
0
1
1
0
2
0
0
2
2
1
1
0
0
2
1
0
0
1
3
1
2
1
1
0
0
1
1
1
2
1
1
1
1
1
0
0
0
1
1
1
1
1
2
1
1
1
1
1
1
0
2
0
1
1
1
1
1
1
1
1
0
0
1
0
0
0
1
2
2
0
1
1
0
1
0
1
0
1
1
1
0
2
3
2
1
1
0
0
1
0
1
1
2
0
1
2
1
1
0
1
2
1
1
1
0
1
1
0
1
1
1
0
0
0
2
0
1
1
1
0
2
1
0
1
1
0
0
1
0
0
0
0
1
3
0
1
0
1
1
1
0
1
0
0
2
1
1
1
2
1
1
3
1
1
1
0
1
0
0
1
0
2
1
1
1
0
0
1
1
2
1
0
1
2
1
2
0
0
0
1
0
2
1
0
1
2
2
1
0
0
1
0
1
2
1
1
1
1
0
2
0
0
2
1
2
1
1
2
0
2
1
1
0
0
1
2
2
1
0
1
1
2
0
1
1
1
1
0
2
2
2
0
1
2
1
2
0
1
2
2
2
2
0
0
1
1
0
0
1
2
1
1
0
1
1
0
0
0
1
1
0
1
0
0
2
0
0
1
2
2
1
2
0
0
2
1
2
2
1
0
1
1
1
0
0
1
1
1
1
2
1
2
0
1
4
2
2
0
1
0
1
2
1
2
1
0
1
0
1
1
1
0
0
0
2
1
2
1
1
1
1
0
0
1
2
0
1
0
1
2
2
1
0
1
2
2
0
1
0
1
1
0
2
2
1
1
1
1
2
0
1
0
0
0
1
1
2
0
1
2
0
0
1
0
0
2
0
0
0
0
1
0
1
1
0
0
1
0
0
0
1
2
1
2
0
1
1
1
2
0
2
1
2
1
2
0
1
1
2
1
0
1
1
0
1
1
1
0
0
0
1
0
1
2
0
0
3
0
2
1
1
0
0
2
2
0
1
2
1
2
1
2
1
2
1
1
2
3
2
1
2
0
0
2
1
0
1
1
2
1
2
0
1
2
1
1
1
0
3
0
1
0
1
1
1
1
2
2
2
0
1
1
1
2
2
0
0
1
1
0
0
2
2
0
1
2
2
0
1
1
1
1
0
1
1
1
1
1
1
0
1
2
2
0
1
1
2
1
0
1
1
0
2
1
1
1
1
1
0
1
1
1
1
1
0
1
0
1
0
2
2
1
1
0
1
2
0
0
2
1
1
2
0
0
1
0
1
1
1
1
2
2
0
2
1
0
0
1
1
0
1
1
0
1
0
2
0
1
1
0
0
0
0
0
1
2
1
1
1
0
2
1
1
2
0
2
0
2
0
0
1
1
0
1
0
0
2
0
0
2
1
2
1
2
2
1
0
0
0
2
1
1
2
1
1
0
0
1
1
1
1
0
0
2
1
0
0
0
1
1
0
1
2
1
1
1
1
1
0
1
1
1
1
1
1
1
2
1
1
1
1
0
0
0
1
1
0
0
1
1
0
2
0
2
1
1
1
1
1
0
2
0
1
2
2
2
1
2
1
0
2
1
0
1
2
0
0
1
1
0
0
2
2
0
2
1
1
0
1
2
0
1
0
1
0
0
1
0
1
1
0
2
1
1
0
1
2
1
0
1
3
1
0
2
3
0
0
0
1
0
1
0
2
1
2
2
0
2
3
2
2
1
1
2
1
1
0
0
1
0
1
1
2
2
2
2
2
1
1
0
0
1
1
2
2
0
1
1
2
2
0
1
0
0
1
1
1
0
1
1
2
1
1
0
1
0
0
2
0
1
2
1
0
0
0
1
1
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
1
1
3
0
0
0
1
0
1
2
1
1
2
1
0
0
0
0
0
0
0
2
1
1
0
0
1
1
0
2
2
0
0
2
1
1
2
1
0
0
0
0
1
2
1
1
0
1
0
0
0
1
2
0
0
2
0
1
1
0
1
2
1
2
0
0
1
1
0
1
0
1
1
0
1
1
2
1
1
1
1
1
0
1
2
2
2
2
0
1
1
1
1
0
1
2
0
0
1
1
1
1
2
0
0
1
1
1
6
2
1
0
1
0
0
0
1
1
0
1
1
1
0
1
1
0
1
0
1
2
0
1
0
1
1
2
1
2
1
0
1
1
1
4
1
0
1
2
1
1
1
0
2
0
0
1
1
1
2
0
0
1
1
1
1
0
1
1
0
1
2
2
1
0
0
0
0
3
0
1
2
2
0
1
2
2
1
1
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
1
2
1
1
1
1
1
0
2
2
1
0
1
1
1
1
1
2
1
0
0
1
1
1
0
2
0
0
1
1
1
0
1
1
0
1
2
0
0
1
2
1
1
1
0
1
2
1
0
0
0
1
1
1
0
0
1
1
1
1
0
0
2
2
1
0
1
1
1
1
0
1
2
0
2
1
2
0
0
0
0
0
1
0
1
1
1
0
0
0
1
2
1
1
0
2
2
0
2
2
0
1
1
1
2
0
1
3
1
0
0
1
1
1
3
1
1
0
1
0
0
0
0
1
1
0
1
1
2
0
0
0
1
1
0
0
1
2
1
1
0
1
0
0
0
0
2
2
1
1
2
0
0
1
1
1
0
0
2
0
1
1
0
1
1
1
1
2
2
1
0
1
1
0
2
1
1
2
2
0
1
1
1
0
0
1
1
0
1
1
1
0
0
2
1
2
1
2
1
2
1
1
2
0
1
2
2
1
1
2
1
2
2
1
2
2
1
1
3
2
0
1
2
0
1
1
1
0
1
3
0
1
1
1
0
2
2
0
0
1
0
0
1
1
1
2
0
1
1
2
1
2
0
0
2
2
0
1
0
1
1
0
1
0
1
0
0
1
0
2
2
0
1
1
0
1
0
1
1
1
2
0
1
1
0
0
0
1
0
1
0
2
1
0
1
0
1
0
1
1
1
1
0
0
0
0
1
2
1
1
1
2
2
1
0
1
3
0
0
0
0
0
2
2
2
2
0
2
2
0
0
1
1
1
0
1
1
1
0
0
1
1
1
1
0
0
1
2
1
2
2
1
2
0
1
1
0
1
1
1
0
2
0
2
1
1
1
1
2
0
1
1
2
2
1
1
1
2
1
0
0
1
1
1
1
1
0
1
1
1
1
1
1
1
0
1
1
0
0
0
0
1
1
1
1
0
1
1
0
1
0
1
1
1
1
0
2
2
1
2
0
0
2
1
2
1
1
1
1
2
1
0
1
2
0
1
2
5
1
1
0
2
1
2
1
0
0
0
0
1
1
0
2
1
1
1
1
1
2
0
2
2
2
3
0
0
1
0
1
1
0
1
0
1
0
2
0
2
2
2
1
1
0
1
0
1
0
1
1
2
2
0
1
0
2
1
0
1
2
0
0
2
0
0
0
2
1
2
0
0
0
0
1
2
0
0
1
2
1
1
1
1
0
1
0
0
0
1
2
1
2
0
2
2
1
1
0
0
0
1
1
0
2
1
1
1
1
1
1
1
1
0
1
1
0
0
0
1
1
0
0
0
1
0
1
0
2
1
2
0
1
2
1
1
1
1
1
2
1
0
1
1
1
1
1
1
2
0
1
2
0
1
1
0
0
1
0
1
1
1
1
0
2
2
2
0
1
1
1
1
1
1
2
1
0
1
1
1
1
1
1
1
0
1
0
0
2
1
0
1
0
1
2
1
1
1
1
0
0
1
1
1
2
1
1
0
0
0
1
1
1
0
1
1
2
1
1
1
0
0
0
1
1
1
2
2
0
1
0
2
0
1
0
1
2
1
1
0
1
0
0
1
0
0
1
0
1
1
1
2
1
0
1
1
0
1
0
1
2
1
1
1
1
0
1
2
1
0
2
1
2
1
1
0
2
2
0
1
1
0
0
0
0
1
0
2
2
2
0
4
1
1
2
1
0
0
2
1
1
2
0
2
1
1
1
1
1
1
0
2
1
2
1
1
2
1
0
0
1
1
0
1
0
0
0
2
0
2
1
0
2
2
1
0
1
0
1
0
2
1
1
0
1
1
1
1
1
3
0
2
1
0
1
2
0
1
1
1
0
1
1
0
2
1
1
1
1
1
1
1
1
2
2
7
1
0
1
2
1
1
0
1
0
3
1
1
0
0
1
1
0
2
0
2
0
1
0
2
2
0
0
2
0
2
1
0
1
0
0
1
0
0
1
0
1
1
1
0
2
0
2
0
1
1
1
1
1
0
1
0
1
0
0
1
0
1
1
1
2
0
2
0
1
0
1
0
0
0
1
1
1
1
2
2
2
0
0
0
1
0
2
1
2
1
1
2
0
0
2
0
1
1
2
2
0
1
2
1
1
0
1
1
1
1
0
0
0
1
2
0
2
0
1
2
2
1
1
0
2
1
0
2
0
1
0
2
0
1
2
0
0
2
1
1
0
1
0
1
0
0
1
1
0
1
1
1
1
1
1
0
0
2
2
1
1
1
1
1
1
1
0
1
1
1
0
1
0
0
1
1
0
3
0
1
0
1
2
0
0
1
0
2
0
2
1
1
0
0
3
0
1
1
0
2
0
2
2
2
1
0
1
1
1
0
2
1
2
0
0
1
0
1
0
1
0
1
2
1
0
2
1
2
0
2
0
0
1
1
0
1
1
1
0
2
1
1
1
1
2
0
0
1
0
0
2
1
1
0
2
1
0
2
0
1
2
1
0
0
1
0
0
1
0
1
0
1
0
0
2
1
0
1
1
0
1
0
2
0
2
2
2
0
1
1
1
2
2
0
0
2
0
1
1
2
0
2
1
2
0
2
1
2
1
0
1
1
1
2
1
3
1
1
1
0
0
2
0
1
0
0
2
1
2
1
1
1
1
1
2
2
2
1
0
0
0
2
1
1
1
0
0
1
0
0
1
1
2
1
1
1
1
0
0
1
1
1
0
0
0
1
1
1
2
1
1
1
0
1
2
1
0
1
1
1
0
1
1
0
2
1
1
0
1
0
0
1
0
1
2
2
0
2
1
2
1
2
0
1
3
2
1
2
1
1
0
0
0
1
1
2
1
1
0
1
0
1
0
0
1
2
2
1
0
1
1
1
1
0
0
3
2
0
0
0
1
1
0
1
1
1
0
1
0
1
0
1
0
1
0
0
0
0
1
1
2
1
0
0
2
2
1
0
1
1
1
1
2
1
1
2
1
0
4
0
1
3
0
1
0
1
0
0
1
0
1
2
2
0
1
1
0
1
1
1
1
0
1
2
2
1
2
1
1
0
0
1
0
1
0
1
0
1
1
1
0
0
2
0
1
1
1
1
1
2
2
1
0
1
0
2
1
1
1
0
1
0
0
0
1
1
1
1
0
0
1
2
1
1
2
0
2
0
1
0
0
0
0
1
2
1
0
2
1
0
0
0
0
1
1
1
1
1
1
1
0
2
1
1
0
1
2
2
1
0
0
1
1
1
2
0
1
1
1
0
1
1
1
0
1
0
1
0
0
1
2
0
0
1
1
0
1
1
0
2
1
2
0
2
1
2
0
1
1
0
0
2
3
1
1
1
1
7
1
2
1
2
1
0
1
1
0
2
2
1
1
0
0
0
1
1
1
2
0
0
0
5
2
1
0
0
2
3
0
2
1
1
1
1
1
0
0
0
1
0
2
2
1
2
0
0
0
0
2
0
2
1
0
0
2
1
2
1
2
1
1
1
1
2
1
2
1
0
1
0
1
0
0
2
0
0
1
1
2
1
0
0
2
1
1
1
0
1
2
1
1
0
2
0
1
1
1
1
2
2
1
0
1
2
1
2
0
2
0
0
1
1
1
1
0
0
2
1
1
1
2
1
1
1
0
1
0
1
0
1
3
1
1
0
1
1
2
2
1
0
0
0
0
2
1
2
1
1
0
1
0
2
1
2
1
1
1
0
2
1
1
1
0
0
0
0
1
2
0
1
2
0
1
1
2
0
2
0
0
1
0
2
1
1
1
1
2
2
0
2
1
2
1
0
0
2
0
1
1
0
2
1
1
1
2
1
1
2
1
0
0
1
1
0
0
1
0
1
0
1
0
2
0
0
2
1
1
1
2
0
1
1
0
0
1
1
1
1
1
1
2
0
0
1
1
1
1
1
1
0
0
0
2
0
1
0
0
0
0
2
1
0
1
0
2
1
1
2
1
2
0
0
1
1
0
0
1
2
0
1
4
1
0
0
0
1
0
1
1
2
1
0
2
0
2
1
1
1
0
1
1
0
1
1
2
0
0
1
0
2
2
1
0
0
0
2
1
1
0
1
1
1
2
1
2
0
1
1
1
1
0
1
0
2
2
2
0
0
0
2
2
1
0
1
2
0
0
1
1
0
0
0
0
2
1
1
0
2
2
2
2
0
1
2
2
0
0
2
1
1
0
1
0
1
1
1
0
1
0
2
2
0
3
2
1
2
2
1
2
1
1
1
2
0
1
1
0
0
2
1
1
2
0
2
0
1
2
0
0
0
1
0
2
1
0
0
1
1
0
0
2
1
3
0
2
2
1
0
1
1
0
0
2
1
2
1
2
0
0
1
0
1
1
2
1
0
0
1
2
1
1
0
1
0
2
1
2
2
0
1
0
2
1
2
1
1
2
2
1
1
0
2
1
1
0
0
0
1
1
0
2
2
1
1
0
1
0
1
0
1
1
2
1
0
0
1
2
1
0
2
1
0
0
1
0
1
1
1
2
1
0
2
0
1
1
1
1
2
2
0
0
0
1
0
2
1
1
0
1
0
1
2
0
0
1
1
1
1
1
0
2
0
1
0
0
1
2
1
0
0
1
1
0
0
1
1
1
2
0
0
1
1
1
1
2
2
1
1
2
0
2
0
2
2
0
0
1
1
1
1
1
0
0
1
0
1
1
2
1
2
1
1
0
2
0
1
1
2
0
2
1
2
3
0
0
1
1
1
1
0
0
0
0
1
2
2
0
2
2
1
3
0
1
0
1
2
2
0
1
0
1
0
1
1
0
2
1
0
1
1
1
1
2
2
1
0
0
2
0
1
2
1
1
0
1
0
2
2
2
1
1
2
3
1
0
0
0
0
2
2
0
1
2
2
0
1
2
2
1
2
2
0
1
1
0
3
1
1
1
2
0
1
1
2
1
0
2
1
1
0
2
1
0
0
1
1
1
1
1
3
1
2
2
2
1
0
1
1
0
2
0
2
0
0
2
1
0
1
0
0
1
2
1
0
2
1
0
2
1
1
2
1
0
2
0
0
0
1
1
2
1
0
0
0
1
0
0
1
0
0
1
1
0
0
0
1
2
2
1
2
2
1
0
2
1
1
1
1
1
1
2
2
1
0
0
0
1
1
0
0
1
0
1
0
1
0
1
1
1
2
1
2
3
2
1
1
1
1
0
2
0
0
2
2
0
0
1
0
2
2
1
1
1
3
1
1
2
1
2
1
2
1
1
0
0
2
0
1
1
1
1
1
0
0
1
1
1
0
0
1
0
1
2
3
1
1
1
0
1
3
1
1
2
1
0
0
1
1
0
1
1
1
1
1
0
0
1
1
1
0
1
1
0
0
1
1
1
1
1
0
2
0
1
2
1
1
1
2
1
1
2
1
0
2
2
1
2
2
1
1
1
2
0
1
1
0
0
1
1
3
1
1
0
2
0
1
0
0
1
2
1
1
1
0
0
1
1
0
1
1
0
0
1
1
1
1
2
2
2
1
0
1
2
2
2
1
1
1
0
1
0
0
0
1
2
2
1
2
2
1
1
0
0
1
0
0
0
1
2
1
1
1
0
0
0
1
1
2
0
1
1
2
0
1
1
2
0
0
0
0
2
0
0
1
1
0
2
2
1
1
1
1
2
1
0
2
0
0
0
1
0
1
0
1
1
0
1
1
1
0
1
0
0
0
1
0
0
1
1
1
0
1
1
1
2
1
1
1
0
0
0
0
1
1
0
2
1
1
1
0
2
2
0
0
1
1
0
0
2
1
1
0
0
0
3
2
1
1
1
2
1
0
1
0
1
0
0
1
0
2
1
2
1
1
1
0
0
0
3
0
2
2
0
1
1
1
2
2
0
2
1
0
0
1
2
1
0
0
5
1
1
1
2
1
1
0
0
0
0
0
2
1
0
1
2
1
2
1
0
1
1
1
1
0
1
2
2
1
2
1
1
0
1
2
0
1
1
0
0
2
0
1
4
1
0
1
2
1
0
2
1
2
1
2
2
1
0
0
1
0
1
1
0
0
2
0
1
2
1
0
2
1
2
1
0
2
2
0
0
2
1
0
2
0
1
1
1
1
1
2
1
1
1
2
0
0
1
0
1
1
2
0
0
1
1
1
0
1
2
2
1
0
0
1
2
1
1
1
2
0
1
1
2
0
1
0
1
1
1
1
1
2
1
0
0
2
1
1
1
0
2
0
0
0
1
0
1
1
1
1
2
2
2
0
0
0
0
0
1
0
2
1
2
2
2
1
1
0
0
1
2
2
1
2
0
1
0
2
1
1
1
0
2
3
1
1
0
0
1
2
0
1
0
2
1
2
1
1
0
1
1
1
0
1
2
1
1
0
0
2
0
1
1
0
1
1
0
1
2
1
0
1
1
0
1
1
2
2
1
2
0
0
1
0
0
1
1
0
1
2
1
1
1
1
1
0
1
2
2
1
2
1
1
1
0
1
2
0
1
0
1
1
0
1
1
0
0
1
1
0
1
1
0
0
2
3
0
0
1
1
1
2
0
2
0
1
1
0
0
1
2
1
1
0
1
1
1
0
1
0
1
1
0
1
0
0
1
1
1
0
0
1
1
0
1
1
2
0
2
0
1
1
2
0
0
0
0
1
2
1
0
0
1
1
0
0
1
1
0
2
1
0
0
1
2
1
0
0
1
0
2
2
1
2
2
2
1
0
1
1
1
0
0
2
0
2
1
1
0
0
0
0
0
2
1
0
2
1
2
0
1
1
2
1
1
1
2
0
0
1
4
1
2
2
1
2
2
2
1
2
0
1
0
2
1
0
0
1
3
1
2
1
0
1
1
1
0
2
1
1
2
2
0
1
1
2
1
3
1
1
1
0
1
1
1
1
1
2
1
0
0
2
2
1
1
0
1
1
1
1
1
1
2
1
1
3
1
2
1
2
1
1
2
1
0
1
0
2
0
2
1
1
2
2
0
1
1
1
1
0
0
1
1
0
2
1
1
2
1
0
1
1
0
0
0
1
1
1
4
1
0
0
0
1
1
0
0
2
0
0
1
1
2
0
1
0
1
2
2
3
1
0
0
0
1
1
1
1
0
1
1
1
1
0
1
2
1
1
1
0
0
1
1
1
0
0
2
0
1
0
0
1
1
0
2
2
0
0
2
1
2
1
1
1
1
2
0
1
0
2
0
0
0
0
2
0
1
1
0
1
2
2
2
0
2
0
0
0
1
1
1
0
0
0
1
1
1
1
1
1
0
1
1
0
2
1
2
1
0
0
1
1
2
2
1
3
1
1
3
2
0
1
0
1
0
1
1
1
1
1
0
0
0
2
1
0
1
0
2
1
1
0
0
1
1
1
1
1
1
3
6
0
1
0
0
0
0
0
0
0
2
0
1
1
1
1
1
0
0
0
1
3
1
0
1
2
0
0
1
2
2
1
0
1
1
0
0
0
1
1
1
0
0
2
1
2
2
0
2
1
1
1
2
1
1
1
3
0
0
2
1
0
2
1
1
1
1
0
1
0
0
1
1
0
1
1
0
2
0
1
1
1
1
0
1
1
0
1
1
0
1
1
1
0
0
1
1
2
3
3
0
1
1
2
0
0
1
0
0
1
0
2
1
2
1
4
0
1
2
2
1
1
0
1
1
1
2
1
1
0
2
2
1
0
1
1
1
2
2
0
1
1
0
1
0
1
2
0
1
1
1
0
0
1
2
0
2
1
1
0
0
0
0
0
1
1
1
1
1
1
2
1
2
0
1
1
2
0
1
0
1
1
1
0
1
0
4
2
0
2
2
1
2
0
0
2
1
2
0
2
1
0
1
2
1
1
0
0
2
1
2
2
2
1
0
0
1
0
0
1
0
1
1
1
2
0
0
1
1
1
0
0
2
1
0
0
1
1
2
0
0
0
1
2
1
3
2
3
0
1
1
2
0
1
2
1
2
1
0
0
1
2
0
1
0
1
1
1
1
0
1
1
1
1
1
1
1
1
1
2
0
0
1
3
1
0
0
1
1
1
1
0
1
2
0
1
1
2
2
1
1
1
2
1
1
1
1
0
1
1
1
0
1
1
1
1
1
1
1
0
1
2
1
1
0
1
0
0
1
0
2
2
1
2
2
0
0
1
1
2
1
0
1
2
1
2
1
2
1
1
0
2
0
1
0
2
1
1
1
2
0
0
1
0
2
2
1
0
1
0
0
1
0
0
2
1
2
1
0
1
0
0
1
2
1
1
1
1
1
2
2
0
0
1
1
2
0
0
0
1
1
1
2
1
2
2
1
1
0
1
1
0
1
1
0
0
0
1
0
2
1
1
0
0
1
1
1
0
1
0
2
2
1
0
2
2
0
1
0
0
0
2
0
1
1
0
1
2
0
2
1
2
1
0
0
2
2
1
1
1
1
2
1
2
0
1
0
0
1
3
2
2
1
0
0
1
1
0
2
0
1
1
0
2
1
1
1
0
0
0
1
1
1
2
2
1
1
1
2
2
2
1
0
1
1
1
0
2
1
1
1
0
2
1
0
0
1
0
1
2
0
0
0
1
0
1
1
0
1
1
1
0
1
1
0
0
1
0
1
1
1
1
1
0
0
2
1
1
0
0
2
1
1
1
1
0
2
1
1
1
1
1
0
0
1
1
0
2
1
1
2
1
0
1
0
2
1
0
1
1
1
2
2
0
1
1
1
1
2
1
1
1
2
0
2
2
0
2
1
2
2
0
0
0
1
0
1
1
1
1
2
0
2
0
1
2
0
0
1
1
2
0
0
0
1
2
2
1
1
0
1
1
2
2
0
1
2
2
0
2
2
2
1
2
1
2
1
1
2
1
1
0
0
2
2
2
2
0
1
2
2
2
2
1
1
1
2
0
0
0
1
2
1
2
1
0
0
1
1
1
1
1
1
0
2
2
1
0
0
1
1
0
1
1
1
2
0
0
2
1
1
2
1
0
1
0
0
0
2
1
1
1
1
1
2
0
1
1
1
0
2
0
2
1
1
2
1
1
1
0
2
1
1
0
0
0
2
1
1
2
0
2
1
1
0
0
1
1
2
1
1
1
2
0
1
1
0
1
1
0
1
1
0
2
2
0
1
1
1
1
1
2
2
1
1
0
0
1
5
1
2
0
2
0
0
2
1
1
2
0
1
0
1
0
1
1
1
0
0
1
1
0
1
2
1
0
2
0
1
1
1
0
1
0
1
0
1
1
1
0
0
1
2
2
2
1
1
1
2
1
2
1
2
0
0
1
1
0
1
1
2
1
1
2
2
1
1
0
1
3
1
2
1
0
1
0
1
1
1
0
1
2
0
1
0
1
2
1
1
1
2
0
2
1
2
0
1
1
1
0
2
2
2
0
1
2
0
2
2
1
1
0
1
1
3
2
1
1
1
1
1
0
2
1
2
1
1
0
1
1
2
1
1
1
1
1
0
1
1
0
0
0
3
0
2
1
2
2
1
1
0
0
1
1
0
0
2
1
2
0
2
1
1
1
1
2
1
2
0
2
0
1
2
2
0
0
1
0
1
0
1
0
1
1
1
0
1
1
1
0
2
2
0
1
0
3
2
2
1
1
1
2
2
1
1
1
1
2
1
1
1
1
2
1
1
1
0
2
1
2
2
2
0
1
1
0
0
0
1
1
0
2
1
0
0
2
1
0
2
1
1
0
1
0
0
0
0
1
1
2
1
2
1
0
0
0
1
1
1
2
0
2
0
1
0
0
0
2
1
1
0
0
1
1
1
2
1
0
1
0
2
1
2
0
1
1
1
2
2
2
1
0
1
1
0
1
3
1
0
0
1
2
0
2
0
1
1
0
1
1
0
1
0
2
2
3
0
1
1
1
0
1
1
1
0
2
0
0
1
2
2
1
2
1
0
0
0
0
0
0
1
2
2
0
0
0
0
2
0
1
1
1
1
2
2
1
1
0
1
0
0
2
0
2
1
0
2
0
1
1
1
1
1
0
2
0
2
0
0
1
0
1
1
1
0
1
1
0
0
2
0
1
2
2
0
1
1
1
1
1
1
2
2
1
1
0
2
1
0
0
1
1
0
1
0
1
1
0
1
1
1
2
0
0
1
0
2
0
0
0
0
0
1
2
0
1
0
1
0
2
2
2
1
1
0
2
2
0
0
2
1
2
0
0
1
2
2
2
0
2
2
1
0
0
2
1
0
1
1
1
1
2
1
1
0
0
0
1
0
2
0
2
1
1
1
0
1
1
2
1
1
0
0
2
1
1
1
0
0
0
2
0
0
2
1
0
1
1
0
0
0
1
0
1
1
0
2
2
2
1
0
2
1
1
2
1
0
1
1
1
2
1
0
2
0
2
2
2
0
1
1
0
1
2
1
1
2
0
1
1
0
2
1
2
1
1
2
0
2
2
1
1
2
1
1
1
0
2
0
2
2
2
0
1
1
2
1
1
2
1
1
2
2
2
0
2
1
1
0
0
1
1
1
1
0
0
1
0
2
0
1
3
2
1
0
1
1
0
5
1
0
0
2
2
0
1
1
0
1
2
2
2
0
1
1
0
0
2
1
1
1
2
1
0
1
2
0
1
2
2
0
2
2
0
1
1
1
1
0
0
1
0
1
0
1
2
0
2
1
2
0
1
1
1
2
1
1
0
0
0
1
1
0
2
0
1
1
1
1
1
1
0
1
1
1
2
0
1
1
2
1
1
0
1
1
1
2
1
2
1
1
0
1
0
1
0
0
0
2
1
1
2
1
1
2
0
1
2
0
1
1
1
1
1
2
1
1
0
0
2
1
1
2
0
1
1
1
2
0
0
0
1
1
1
2
1
0
0
0
2
1
2
0
2
0
1
1
2
1
0
0
2
2
1
0
2
1
0
1
0
1
2
1
0
2
1
2
2
2
2
2
2
1
1
2
1
0
3
0
0
1
1
2
0
0
0
1
0
0
0
0
1
0
1
2
1
1
2
2
2
0
2
0
1
1
0
1
1
0
1
2
1
0
0
0
2
0
0
1
0
0
0
0
1
0
1
1
2
1
0
0
1
1
2
2
1
0
0
1
2
2
0
2
1
0
0
0
0
1
0
2
0
0
0
2
1
1
0
0
0
2
1
2
0
2
1
0
1
1
0
0
0
2
0
0
0
1
1
1
0
1
0
1
0
1
1
2
2
0
0
0
2
1
1
1
2
1
2
1
2
0
0
0
1
1
0
2
1
0
1
0
0
1
1
0
2
1
1
0
2
0
1
2
0
1
0
2
1
0
0
2
2
1
2
0
1
0
2
1
1
1
1
2
0
1
0
0
1
1
1
2
1
1
0
2
2
1
1
2
1
1
0
1
2
2
0
1
0
2
2
3
1
1
0
1
1
1
1
1
2
2
1
0
1
1
1
0
1
0
0
2
0
0
1
1
1
1
1
1
0
1
2
0
1
1
0
2
2
0
1
1
0
1
1
0
2
0
1
0
1
1
2
0
1
0
2
0
1
2
1
2
0
2
2
1
0
0
1
2
0
1
1
1
2
1
1
2
0
0
1
0
2
2
0
0
1
1
0
2
0
2
0
1
1
1
0
1
1
2
0
0
1
1
2
2
1
0
2
2
2
1
1
2
2
1
1
1
2
2
1
1
1
0
0
0
2
2
2
0
1
1
2
2
1
1
1
1
1
1
1
2
1
1
2
0
1
1
1
0
0
1
1
1
1
0
2
1
0
1
1
0
0
0
1
0
1
0
0
0
1
1
1
2
2
0
1
1
0
0
1
1
2
0
2
2
1
1
0
1
0
0
0
1
1
2
1
2
0
2
2
1
2
0
0
0
0
1
0
1
0
1
0
1
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
2
4
3
1
0
1
1
1
1
1
1
0
1
1
2
1
2
1
2
1
2
2
1
2
1
1
2
1
0
1
0
1
3
1
2
1
1
1
0
1
1
2
1
1
2
1
1
2
0
0
2
1
0
0
1
2
0
1
1
1
0
0
1
1
1
1
0
1
2
1
1
1
0
1
1
0
1
0
0
0
1
0
2
0
2
0
0
1
2
2
1
0
2
0
0
1
2
1
0
0
2
0
0
2
1
2
1
1
0
1
0
0
1
1
0
0
0
1
0
2
1
1
1
0
0
2
1
0
0
1
0
2
1
2
0
0
1
1
1
1
2
0
0
0
1
1
0
0
2
2
2
0
1
2
0
3
0
1
2
1
0
1
1
1
1
0
0
2
1
0
2
1
1
1
0
2
0
0
0
2
0
2
0
1
1
1
1
2
0
0
1
0
0
1
1
0
0
1
2
2
1
0
0
1
0
0
2
2
0
0
0
1
1
2
1
1
0
0
1
2
1
0
0
1
2
1
0
1
3
2
0
0
1
2
0
2
1
1
0
1
1
0
0
2
1
0
2
1
2
0
1
0
2
0
2
1
1
0
0
2
0
1
1
2
0
1
0
1
0
0
0
0
1
1
1
1
1
2
1
2
0
2
1
0
1
1
1
2
0
1
2
0
1
1
1
1
1
1
1
0
2
1
2
0
1
2
1
0
0
1
0
1
1
1
1
0
0
0
0
1
1
2
2
1
1
2
0
1
0
1
1
4
0
2
0
1
1
0
1
1
1
1
0
0
0
2
2
1
0
0
2
0
0
0
1
2
1
2
1
0
1
2
1
2
0
0
2
1
0
0
0
1
1
1
1
0
1
0
0
2
0
0
0
1
0
1
2
2
2
1
1
2
1
0
2
1
0
1
2
0
1
0
2
1
1
0
1
0
1
1
0
0
1
1
1
1
2
1
0
0
1
2
0
1
2
2
0
1
1
0
2
1
1
1
1
2
2
1
1
2
0
0
1
2
0
1
2
3
2
2
1
1
1
1
0
0
1
2
2
0
2
2
0
1
2
2
0
0
1
6
1
3
0
0
1
0
1
1
1
1
1
1
1
0
0
1
0
0
1
1
1
2
1
1
2
0
1
0
1
1
2
1
0
1
1
0
0
0
1
0
1
1
1
0
1
0
0
2
0
1
0
1
2
1
1
1
2
1
0
2
1
0
1
0
2
1
0
1
1
1
0
0
2
2
1
1
0
1
1
1
0
1
1
2
1
0
0
0
2
0
1
3
0
3
0
1
1
1
1
1
1
0
2
0
1
1
0
0
2
1
0
1
1
1
2
1
0
0
0
0
0
0
1
0
2
0
2
1
0
1
0
3
0
2
2
0
1
0
1
0
0
0
1
1
1
2
2
2
0
3
2
1
1
1
0
2
1
2
1
0
1
0
0
0
0
0
1
0
1
0
1
2
1
0
1
0
2
1
1
1
0
1
0
0
2
0
0
0
2
1
2
1
1
2
1
2
0
1
0
1
1
0
1
2
1
2
1
0
1
1
2
0
1
1
0
1
0
0
0
2
1
1
1
1
1
4
1
1
1
0
0
2
2
1
1
1
2
0
0
0
1
2
0
0
1
1
0
0
1
2
1
1
1
1
1
1
0
0
1
0
1
0
1
1
2
1
3
1
2
1
1
1
0
1
2
2
1
0
0
2
0
1
1
0
1
1
0
0
2
1
0
0
0
0
1
2
0
0
2
0
0
1
2
1
0
1
1
0
2
1
0
1
0
0
1
0
0
0
0
1
0
2
1
0
2
1
0
0
1
0
1
2
1
1
1
1
1
2
0
1
0
2
1
1
1
0
0
0
2
0
1
1
1
1
1
1
0
1
1
1
1
1
0
1
0
1
0
1
0
1
0
1
3
1
0
1
1
1
0
2
1
0
1
0
2
1
2
2
2
0
0
2
1
1
1
2
2
2
1
0
1
2
1
0
0
1
1
2
0
1
0
1
0
1
2
0
1
3
1
2
1
1
1
1
2
2
2
0
0
0
0
0
1
0
0
1
0
0
2
1
0
1
1
2
0
1
3
0
1
1
1
1
1
1
0
2
2
3
1
1
0
2
0
0
0
0
1
0
0
1
1
1
1
1
0
0
1
1
2
1
1
1
0
0
1
0
0
0
1
2
2
0
0
0
2
1
1
1
2
2
0
1
0
1
1
2
1
0
1
0
0
0
1
3
0
0
2
0
1
1
1
1
1
1
2
0
1
1
1
1
1
0
2
1
0
1
0
0
0
1
1
0
0
0
1
2
1
1
1
0
0
0
2
0
0
1
0
3
1
2
1
2
2
1
1
0
1
0
1
1
2
1
2
0
1
2
2
1
1
1
1
2
0
2
1
1
0
1
0
3
1
2
1
1
2
0
1
1
1
2
0
0
1
0
2
1
1
0
2
0
1
0
2
1
0
0
0
1
0
1
2
2
0
0
0
1
0
1
0
2
0
1
0
1
1
1
1
1
1
1
1
1
1
0
2
2
2
2
0
1
2
2
1
1
1
0
2
2
1
2
0
1
0
1
0
1
1
1
2
1
0
2
1
0
3
0
1
1
2
1
1
1
0
0
0
3
2
0
1
2
0
1
3
1
0
2
2
1
1
1
0
0
1
2
0
1
1
1
1
1
1
1
1
0
0
0
1
0
1
1
1
0
0
1
1
0
0
2
0
0
0
1
2
0
2
1
2
2
2
0
1
1
1
0
3
1
1
1
1
3
1
1
3
0
0
1
0
1
2
2
1
1
2
1
2
1
0
2
0
0
0
1
3
0
2
1
0
1
1
1
2
2
0
1
0
1
2
2
1
1
1
2
1
1
1
1
1
1
0
1
1
2
1
1
0
1
2
2
0
0
1
0
1
2
0
1
1
1
1
2
0
0
1
1
2
1
2
1
0
2
2
3
0
2
0
0
0
0
1
1
1
1
1
2
1
0
1
0
2
1
1
2
1
0
1
2
0
2
2
1
1
1
1
2
2
2
0
0
2
1
1
1
0
1
1
0
2
2
1
2
2
2
2
0
0
1
2
1
1
0
0
1
0
3
0
1
0
1
1
0
0
1
1
1
1
0
2
0
0
0
1
0
0
1
0
0
0
1
3
2
1
1
1
1
0
1
1
2
0
1
1
0
1
0
0
1
0
1
1
1
0
1
0
0
0
1
0
1
0
0
0
0
1
2
1
0
1
2
1
2
0
0
1
0
1
0
0
0
0
1
1
2
5
3
0
0
2
1
1
0
1
2
2
1
2
1
1
1
1
0
0
0
0
2
0
2
2
2
1
1
2
0
0
0
0
1
1
1
2
1
1
0
2
1
0
1
1
0
1
1
1
1
1
1
1
1
0
2
1
2
2
0
1
1
1
0
1
1
2
2
4
0
1
1
2
0
1
0
1
1
1
2
1
1
1
2
0
0
1
1
1
0
2
2
1
1
0
0
2
1
0
1
1
1
2
1
0
2
2
0
1
0
2
5
0
2
4
1
0
2
1
0
1
1
2
2
1
1
1
1
1
1
1
0
2
2
1
0
1
2
1
0
2
1
1
0
0
1
1
0
2
0
0
0
0
0
1
0
0
1
0
1
1
0
2
1
1
0
2
2
1
1
1
1
0
2
0
1
0
0
0
1
0
0
1
0
0
1
0
2
0
2
1
2
1
2
2
0
1
1
0
1
0
2
0
0
1
0
1
0
2
0
4
0
1
0
2
1
1
0
0
1
0
2
0
0
0
1
0
1
1
1
1
1
1
1
0
1
1
0
0
2
0
0
1
2
2
1
2
1
2
1
2
1
2
0
2
1
2
0
0
1
1
1
1
1
1
0
1
1
2
2
2
1
0
1
1
1
0
1
1
1
2
1
0
0
1
1
0
1
1
2
2
1
1
2
0
1
2
2
0
1
2
2
1
0
2
1
2
2
4
1
1
2
2
2
2
1
1
0
1
2
2
3
2
1
2
0
0
1
0
1
0
0
1
0
0
2
0
2
0
0
0
0
0
1
0
1
3
2
0
0
2
1
2
1
0
1
2
1
0
0
0
0
1
2
0
0
1
1
0
0
2
1
2
2
0
1
0
0
0
1
1
1
1
1
2
1
1
2
1
2
0
1
2
2
1
2
2
3
1
0
1
2
2
1
2
2
0
2
0
1
2
1
0
2
1
1
2
0
1
1
2
2
0
0
0
0
1
2
2
1
1
1
1
0
2
0
0
1
0
0
0
2
1
1
2
2
1
0
2
0
2
0
1
0
0
1
1
1
0
0
1
2
1
2
1
1
0
2
1
2
2
1
2
1
1
2
1
2
1
1
0
0
1
0
1
2
1
1
2
1
0
0
1
1
0
2
2
0
0
0
2
1
0
0
1
2
1
0
1
2
1
0
1
2
1
1
0
0
1
1
1
0
1
0
1
1
0
1
0
0
1
0
2
0
1
1
1
1
2
1
1
1
1
1
0
0
1
1
0
2
1
0
0
2
0
0
0
1
1
0
1
0
2
1
0
1
1
2
0
1
0
1
1
0
1
1
0
1
1
2
1
2
2
0
0
2
0
1
1
1
1
2
1
2
1
0
1
1
0
0
1
2
1
2
0
0
0
0
1
0
0
1
0
1
1
2
0
1
0
1
1
1
1
2
1
0
1
0
1
0
0
2
1
0
1
0
0
1
1
2
0
2
1
0
0
1
0
1
0
2
0
0
1
0
1
0
0
1
1
1
0
1
1
0
0
1
0
1
0
0
1
0
1
3
0
1
2
1
1
2
1
1
0
2
0
1
0
1
1
0
2
0
0
0
1
1
1
0
0
1
1
1
0
1
1
1
0
1
1
5
1
1
0
3
0
2
2
1
0
0
0
1
1
0
1
0
1
1
2
0
2
2
0
1
1
0
1
2
1
0
1
1
2
1
0
1
1
1
1
2
0
0
2
2
2
0
0
2
0
3
1
1
2
1
1
2
0
0
1
1
0
1
2
1
0
2
2
1
0
0
2
1
0
1
1
1
0
0
0
1
1
0
1
1
0
0
1
0
1
0
0
0
0
1
2
2
0
1
0
0
2
1
0
2
1
0
1
2
0
1
1
1
1
0
1
2
4
1
1
1
0
0
1
1
0
1
0
2
0
2
2
1
3
0
0
0
2
1
1
1
2
1
0
0
2
1
1
2
1
2
1
1
2
2
2
1
0
1
0
1
1
1
2
2
2
1
1
0
0
1
0
2
1
2
1
2
1
1
0
1
0
1
2
1
0
1
0
1
1
0
1
0
1
2
1
0
1
2
2
1
2
0
2
1
2
1
0
2
0
0
1
1
1
1
2
1
0
0
1
1
1
1
1
1
0
0
0
0
1
0
2
1
2
2
0
0
0
2
0
0
2
2
1
1
1
0
1
1
0
2
1
1
2
1
0
1
1
1
0
2
1
0
1
0
2
0
0
2
2
2
2
0
1
0
0
2
0
2
2
0
1
1
0
1
1
1
1
0
0
0
0
0
0
1
1
1
0
0
0
1
1
1
1
1
1
1
2
2
1
1
1
1
0
2
2
1
0
0
3
1
0
1
2
1
1
2
0
2
1
2
2
1
1
3
1
2
2
1
0
1
0
1
3
0
0
0
0
1
2
0
0
1
0
0
2
2
1
1
0
1
3
1
0
1
1
1
0
0
0
0
0
2
1
2
0
0
1
3
1
1
1
1
0
2
1
0
1
2
0
1
0
2
2
1
0
0
1
0
2
1
1
0
0
1
1
2
2
1
2
0
3
3
0
0
2
0
1
3
0
1
2
0
1
1
1
2
0
2
0
1
1
2
1
1
0
0
1
1
1
0
2
2
1
0
2
1
1
1
2
0
1
1
1
2
1
1
0
2
2
0
2
1
0
0
2
1
1
2
0
0
2
0
1
0
0
2
1
1
0
1
0
0
2
2
1
1
0
0
1
1
0
1
1
1
2
0
0
1
1
2
2
2
1
1
3
0
0
0
0
1
1
1
0
1
1
1
1
2
0
1
2
1
2
1
1
1
0
2
1
1
2
1
1
0
0
1
0
2
1
2
2
2
0
0
2
1
0
1
1
1
0
1
1
1
1
0
0
3
1
1
1
0
1
0
0
0
0
1
0
1
0
0
2
2
1
0
2
1
2
0
1
2
2
1
0
2
1
0
0
0
1
0
1
1
0
2
0
2
1
1
0
1
2
0
1
0
2
0
2
2
1
0
1
0
0
0
1
0
0
1
0
1
1
0
8
0
1
0
2
1
2
0
1
0
1
0
1
0
0
0
1
1
0
2
0
2
1
1
1
2
0
0
1
0
0
1
0
2
1
1
1
0
1
2
0
1
0
1
1
0
1
0
2
0
2
1
0
1
0
0
1
1
1
0
0
0
2
2
1
1
0
1
2
0
0
0
1
1
1
2
0
0
2
1
1
1
2
0
2
0
1
0
2
1
1
3
1
0
1
1
1
2
2
0
1
2
2
0
0
0
1
0
1
1
0
0
2
1
0
2
1
0
2
1
1
0
1
2
2
2
0
1
0
0
0
1
1
0
2
0
0
1
3
1
1
1
1
2
0
2
1
1
1
2
2
1
2
0
1
1
2
2
2
1
1
1
0
1
2
1
1
0
0
1
0
0
1
1
0
2
0
0
1
1
2
0
1
2
2
2
0
1
1
1
1
1
1
1
0
1
0
0
2
1
2
1
2
2
2
1
1
1
0
2
0
0
1
1
1
0
1
0
1
2
2
0
1
1
2
1
1
1
2
0
1
0
2
1
1
2
2
1
0
1
2
2
1
0
2
2
0
0
1
0
0
0
1
1
0
1
1
1
0
0
2
1
3
1
1
2
0
1
1
0
0
0
1
0
1
2
1
0
2
2
0
1
0
2
1
0
1
2
1
0
1
1
2
2
1
1
1
2
0
0
2
0
0
0
0
0
1
1
1
0
1
2
1
1
0
1
1
2
2
1
2
0
0
0
1
1
1
1
1
0
1
1
0
1
1
2
1
2
2
0
0
2
0
1
1
2
2
1
1
0
2
0
0
1
1
1
1
1
2
1
1
2
0
0
1
1
1
1
0
1
0
1
1
1
2
2
0
0
1
0
5
1
0
1
2
2
1
1
1
1
0
0
1
0
0
1
1
0
0
1
2
0
0
1
1
2
2
1
2
0
1
6
1
1
2
1
0
1
2
0
0
2
0
0
2
1
2
0
2
1
2
1
2
0
2
1
1
1
1
2
0
0
1
2
0
2
2
1
0
1
2
1
2
0
0
2
1
1
1
2
1
0
1
0
0
0
2
1
0
2
0
0
1
2
2
0
1
0
0
0
1
2
1
1
1
0
0
1
0
1
1
0
0
0
2
1
2
2
0
0
1
0
1
1
1
1
0
1
2
1
2
0
0
0
0
2
1
0
3
1
2
1
0
1
0
1
0
1
1
2
1
1
1
0
1
2
1
0
0
1
0
0
0
1
1
0
1
0
0
1
2
0
0
0
2
0
2
1
0
2
1
0
1
0
2
2
1
0
1
0
0
1
0
0
1
0
0
1
0
1
0
1
2
0
0
1
0
2
1
0
0
1
0
1
1
0
2
2
0
0
1
1
1
0
1
3
0
0
1
1
1
2
1
0
2
0
1
1
0
2
0
1
0
0
1
1
1
1
1
1
0
2
1
1
2
2
2
0
1
2
1
1
1
0
0
1
1
0
1
0
3
1
1
0
1
0
2
1
2
0
0
0
1
1
1
0
1
0
2
1
1
1
2
1
0
0
1
1
2
1
1
2
0
1
0
2
3
0
1
1
2
0
0
0
0
0
0
0
1
1
0
0
2
0
0
1
1
2
1
1
0
0
1
1
0
1
1
1
0
1
2
1
1
1
2
0
0
1
0
0
2
1
0
0
0
0
1
2
1
0
1
0
0
1
2
1
1
0
1
0
1
1
3
1
1
1
1
0
0
1
0
1
0
0
1
1
0
1
1
2
0
1
2
0
1
1
1
1
2
0
1
0
0
1
1
1
2
0
3
1
1
2
1
2
1
0
1
1
0
0
0
1
0
0
1
2
1
0
2
0
0
1
0
2
0
0
1
2
2
0
1
0
0
0
1
0
2
0
1
0
6
0
1
0
2
1
1
1
1
0
1
1
1
0
2
2
2
0
0
1
1
3
1
2
2
3
2
0
1
2
1
0
0
2
1
1
1
0
1
0
1
1
2
2
1
1
1
0
1
1
1
0
1
2
1
1
1
1
1
1
1
0
0
4
2
1
2
1
0
2
0
0
2
1
0
0
1
1
1
0
0
1
1
1
0
1
2
1
2
0
1
1
0
1
0
0
0
0
1
1
1
0
1
1
0
1
1
1
1
1
1
0
1
0
2
0
0
2
2
1
0
0
0
0
0
1
1
1
1
1
0
1
1
0
2
2
0
1
1
1
2
1
0
1
1
2
1
0
2
0
1
0
1
1
0
0
2
1
0
1
1
0
2
0
0
1
1
0
0
2
1
1
0
1
2
0
1
0
0
1
1
1
0
2
0
0
0
0
2
0
0
2
2
1
0
2
2
0
2
2
1
0
0
0
1
1
0
2
0
2
1
2
0
1
4
2
0
0
0
0
0
0
2
1
1
0
0
2
1
2
0
1
1
0
0
0
0
2
1
2
1
0
3
2
1
1
1
1
1
0
2
1
0
1
1
1
1
1
1
2
1
2
2
2
1
1
0
2
1
0
1
2
0
0
1
1
1
1
1
0
1
0
1
0
1
2
0
1
1
1
2
2
1
2
1
1
1
1
1
0
0
2
1
2
1
1
0
1
1
0
2
0
2
0
2
0
1
1
1
1
1
2
1
0
1
1
2
2
0
0
1
1
1
0
0
1
0
0
0
2
0
2
2
2
1
1
0
1
1
1
1
1
1
1
0
1
1
0
1
1
1
1
2
1
1
2
0
0
0
2
1
1
1
0
0
1
0
1
1
1
1
0
1
1
2
2
0
2
1
1
1
0
0
2
0
2
2
2
1
3
1
0
0
2
0
1
0
1
0
1
2
0
1
1
1
0
2
0
0
0
1
1
2
2
1
0
1
1
1
2
1
1
2
2
0
0
2
1
1
2
1
0
1
1
1
1
0
1
0
0
0
1
2
0
0
1
1
2
1
2
2
2
0
0
1
2
1
1
2
0
1
0
0
1
0
1
1
0
0
1
1
1
1
1
1
0
1
1
1
1
2
2
2
0
0
2
0
0
1
1
1
1
0
0
0
0
1
2
2
1
2
2
3
0
2
1
2
1
2
1
1
0
4
1
0
0
1
0
1
0
2
0
0
0
1
1
1
0
0
1
0
2
0
1
2
0
0
1
1
1
3
1
0
1
0
0
1
2
1
1
0
1
1
1
0
0
0
0
1
1
0
2
1
2
2
0
1
0
0
1
0
2
1
1
1
0
1
0
1
1
1
2
0
0
0
0
1
3
0
1
2
0
1
0
0
3
2
1
2
0
0
1
1
1
1
1
2
1
0
1
2
0
0
0
1
1
0
2
2
0
0
2
1
1
1
1
0
2
1
2
0
3
2
1
3
2
0
0
1
1
0
0
1
1
1
2
1
1
1
2
1
3
1
1
1
1
1
1
0
2
0
1
0
1
0
0
0
1
0
2
1
1
0
0
0
0
0
2
0
1
0
1
1
1
1
0
1
2
1
1
0
1
0
0
0
0
1
2
2
2
0
2
1
1
2
1
0
2
1
1
0
0
0
1
1
2
2
2
2
0
1
2
2
2
1
1
2
2
0
0
1
2
1
1
2
0
1
0
0
1
1
0
1
0
2
2
0
1
1
1
1
2
1
2
0
1
1
1
2
1
0
1
1
0
1
2
0
1
0
1
1
0
2
0
1
2
2
1
1
0
2
0
0
5
1
0
1
1
1
5
1
1
1
0
1
1
2
0
0
2
2
0
0
1
2
0
2
2
0
0
1
1
2
2
1
0
0
1
1
0
0
1
0
1
2
1
2
1
4
0
1
1
2
1
1
1
1
1
1
0
2
0
1
2
2
1
1
0
0
0
2
2
2
2
1
1
0
0
0
0
2
1
1
2
1
3
2
0
1
1
0
1
0
1
0
0
1
1
2
1
1
1
0
2
1
1
1
0
0
2
1
2
1
0
1
1
1
2
2
0
0
1
1
0
1
2
1
2
1
2
0
2
0
0
1
0
2
2
2
1
1
2
1
1
0
1
0
0
0
0
2
0
1
2
1
0
0
1
1
2
0
2
0
1
0
2
0
0
0
0
2
1
0
0
0
0
1
1
1
0
1
0
0
0
2
2
1
0
1
0
0
0
0
1
2
1
1
1
2
0
2
0
0
1
2
0
1
0
2
2
0
2
0
1
1
1
1
2
1
0
2
0
0
1
1
1
1
2
1
1
1
0
1
0
2
2
0
1
1
1
0
1
0
1
1
2
0
0
2
1
2
1
0
1
0
0
0
0
1
0
1
0
0
0
2
1
1
1
0
2
0
0
2
1
1
0
1
0
2
2
0
0
0
1
0
0
0
0
2
1
1
0
0
1
1
1
1
1
1
1
2
2
1
1
1
0
1
0
1
2
0
0
2
1
0
1
2
1
3
0
0
0
0
1
0
1
1
1
0
0
1
2
1
0
1
0
1
2
1
1
0
0
1
2
0
2
2
1
0
1
1
0
0
1
1
1
1
0
0
0
3
1
2
0
1
1
0
1
1
2
0
0
1
0
1
0
2
0
1
0
1
2
1
1
1
0
0
1
2
1
1
1
0
1
2
2
0
2
0
2
1
0
1
1
1
1
2
1
2
0
0
2
1
1
2
0
1
0
0
1
0
2
2
2
2
1
2
1
0
1
1
1
1
2
0
2
2
1
0
0
1
2
1
1
1
2
1
1
0
0
1
2
0
1
1
2
0
2
0
1
0
0
0
1
2
1
2
1
2
1
1
2
0
0
1
2
0
2
2
2
1
2
1
2
2
0
1
1
1
2
0
2
1
0
0
1
1
2
0
0
0
1
1
0
0
1
1
1
1
0
0
0
1
1
0
0
1
0
2
2
1
2
1
1
1
1
0
0
1
1
3
2
0
1
1
0
2
0
1
0
1
0
0
1
1
1
2
1
0
1
2
0
1
0
1
0
1
0
2
0
1
1
0
2
1
1
1
0
2
1
1
1
0
0
2
0
0
1
0
0
0
1
1
1
1
1
1
0
0
0
1
2
2
1
1
2
0
2
1
0
0
2
1
1
1
1
1
1
1
0
2
1
1
1
2
2
0
1
1
1
1
2
1
1
0
0
1
2
2
2
2
2
1
0
0
1
1
2
0
0
2
0
0
0
0
3
1
2
1
1
1
0
0
0
1
1
2
1
2
1
2
1
1
2
2
2
1
2
1
2
0
2
1
1
1
2
1
0
0
1
1
4
2
1
0
2
1
2
1
1
1
0
2
1
1
1
1
2
0
0
0
1
1
0
0
2
2
1
0
0
1
0
2
0
0
0
0
0
2
1
1
0
1
0
1
1
1
1
1
1
0
2
2
2
0
1
1
3
1
1
1
2
2
2
1
1
1
2
1
1
2
0
2
1
1
1
0
1
1
0
0
1
1
1
2
2
1
1
1
1
2
2
1
1
2
2
1
0
1
1
1
0
1
0
1
2
2
0
1
0
2
2
1
2
2
0
2
0
1
1
2
0
1
1
0
2
0
1
1
0
2
2
1
1
1
1
0
1
0
1
2
2
0
0
2
2
0
0
0
0
2
1
1
2
1
2
1
1
1
0
0
0
0
1
2
2
2
0
1
0
2
0
1
1
0
0
1
1
1
1
1
0
0
1
0
1
2
1
0
1
1
2
1
0
2
2
2
2
0
0
1
0
0
0
0
2
0
0
0
0
3
1
1
1
2
0
3
1
0
0
1
1
1
1
2
0
2
0
1
0
2
1
0
0
0
0
1
0
2
2
1
1
1
0
1
1
1
0
1
1
1
2
2
2
0
2
0
1
0
2
1
0
1
1
2
1
1
0
0
0
1
1
2
1
1
1
0
1
0
1
2
1
0
0
1
2
1
1
1
0
1
0
2
1
2
0
1
0
0
1
0
1
0
1
0
0
0
1
2
1
1
0
2
1
0
0
0
1
1
1
0
2
2
2
1
0
1
1
3
1
0
3
1
1
0
1
2
0
1
0
1
1
1
2
2
1
0
1
0
0
0
0
1
2
1
1
1
1
1
1
0
2
1
1
1
2
1
2
0
1
2
2
1
2
0
2
0
3
2
2
0
0
0
0
1
1
0
1
1
1
0
0
0
1
0
0
1
2
0
2
0
1
1
1
0
0
4
2
0
1
1
0
0
1
1
0
0
1
1
2
1
1
2
1
0
1
2
1
1
1
1
0
0
1
3
1
2
1
1
0
2
1
2
1
0
0
1
2
1
0
2
2
1
2
2
2
1
0
1
0
0
2
0
2
0
1
2
0
0
0
0
2
1
1
0
0
0
1
0
1
1
0
1
0
1
0
1
1
1
0
1
1
1
1
1
1
0
2
1
0
1
0
2
2
2
0
0
0
1
2
0
2
1
0
1
0
0
0
1
2
2
0
2
2
2
0
0
1
1
1
0
2
0
0
0
2
1
1
0
1
0
1
1
0
1
1
1
1
1
2
1
0
2
0
1
1
1
1
1
2
0
0
0
0
1
0
1
1
1
2
0
2
1
1
1
1
0
2
1
0
0
1
0
0
0
2
2
0
0
0
0
2
2
0
1
1
2
1
0
0
2
2
0
0
0
1
1
0
1
0
1
2
0
1
1
2
0
0
0
1
1
0
1
2
0
0
2
1
0
0
2
2
0
1
1
2
0
2
2
2
1
1
0
1
0
0
0
1
0
1
0
2
1
1
1
0
1
1
1
1
1
2
1
2
1
0
0
0
0
2
1
2
1
1
0
1
1
1
0
1
1
1
1
2
1
1
1
2
1
0
2
2
2
2
2
1
0
1
0
0
1
0
1
0
1
1
1
1
1
0
0
4
1
1
2
0
1
0
1
0
1
2
0
2
0
1
1
1
1
0
0
1
0
0
1
1
1
1
1
1
0
1
1
0
2
1
0
1
1
1
1
1
1
0
1
0
0
0
1
2
1
1
2
1
1
1
1
1
0
0
1
3
1
0
1
2
0
0
1
0
1
0
2
3
0
0
0
2
4
0
1
1
2
1
0
1
0
2
2
0
0
2
0
0
0
1
1
1
1
0
1
0
0
2
2
1
2
0
1
2
1
0
2
0
1
1
0
0
1
0
0
1
0
1
1
1
0
1
2
1
0
1
0
1
2
2
1
0
2
1
1
2
1
0
0
1
0
1
2
2
0
0
2
0
2
2
2
0
0
0
0
0
2
1
2
1
1
1
2
1
0
3
1
0
0
2
1
2
1
0
2
1
1
1
3
2
2
2
2
1
0
1
0
1
0
2
2
2
1
0
1
1
1
0
1
0
1
0
0
2
0
1
1
1
2
1
2
1
2
1
1
1
0
0
3
1
0
0
1
0
0
2
2
0
0
2
0
1
1
0
0
2
1
0
1
1
6
0
1
0
0
0
1
1
2
1
1
2
0
0
1
1
1
0
1
1
0
0
2
1
2
0
1
0
1
0
1
1
1
1
1
0
1
1
3
4
0
2
2
2
1
1
1
0
1
1
1
0
2
1
1
1
2
0
1
1
0
0
2
1
1
1
0
1
1
0
0
2
0
1
1
1
2
2
1
3
1
0
2
0
1
0
2
2
1
1
1
2
1
1
0
2
1
0
1
0
1
1
1
0
0
1
1
1
1
2
1
1
0
0
2
2
0
0
1
1
1
3
2
2
0
1
0
0
1
1
2
1
2
2
2
1
0
2
2
0
1
2
2
0
0
1
1
0
2
1
0
2
2
1
0
1
1
1
1
1
2
2
1
1
0
0
0
1
1
0
0
2
0
0
1
2
1
1
1
2
1
0
1
2
1
2
0
0
0
2
1
1
2
2
2
1
1
1
1
2
0
1
0
1
0
1
2
1
0
2
2
1
2
0
1
1
2
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
2
1
1
0
0
1
1
2
1
1
1
1
1
1
2
1
2
2
0
1
2
1
0
1
2
2
0
1
0
2
1
1
1
0
1
1
0
2
1
2
2
1
1
2
1
1
1
1
1
2
0
0
1
2
1
0
1
2
1
0
1
0
0
1
1
2
1
0
2
0
2
2
2
0
0
0
0
1
1
0
0
1
1
2
3
1
1
0
1
1
0
1
2
0
1
0
0
0
0
0
0
2
1
2
1
1
1
0
1
0
1
1
0
1
1
1
1
1
0
0
1
0
0
0
3
1
1
0
0
1
1
2
0
1
2
2
0
0
1
0
1
2
1
0
0
0
1
0
1
0
2
0
0
0
2
1
2
1
1
2
1
0
0
1
0
2
1
0
2
1
0
1
2
2
2
0
1
0
0
1
1
1
0
1
0
1
0
0
2
1
1
1
1
3
0
2
1
1
0
2
1
0
1
1
1
2
0
1
1
1
2
0
0
1
1
0
0
1
1
1
1
0
1
0
2
1
1
1
2
1
0
1
1
1
0
1
1
0
2
1
4
0
1
0
2
0
2
0
1
2
1
1
2
0
1
0
1
0
0
0
1
0
0
1
2
1
1
1
2
2
1
0
0
1
2
0
0
2
1
0
0
2
2
1
1
0
0
2
2
1
0
1
1
0
1
2
1
2
1
1
1
0
2
0
1
2
2
2
1
1
2
4
0
1
1
0
2
1
1
0
1
1
2
1
1
1
0
1
1
0
2
1
2
0
1
1
0
1
1
1
2
2
0
0
1
1
2
1
1
1
1
0
2
0
1
1
2
1
1
1
2
0
0
1
0
0
1
0
1
0
0
1
2
1
1
2
2
1
1
0
1
1
2
0
1
0
2
1
2
2
1
1
1
1
1
1
1
1
0
0
0
1
0
2
1
0
2
1
1
0
0
1
1
1
1
2
1
2
0
0
1
1
1
2
2
1
0
1
1
0
1
1
0
2
2
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
1
2
2
2
2
1
2
1
1
1
1
0
2
1
2
2
2
0
0
0
0
1
1
0
1
1
0
0
1
1
1
0
2
1
2
1
1
0
2
0
0
1
2
1
0
2
1
3
0
2
2
1
2
1
1
0
1
2
2
0
2
0
1
2
0
0
2
1
1
1
0
1
1
0
1
1
1
1
2
2
2
2
1
1
1
2
0
1
2
1
2
1
0
1
1
1
0
0
0
0
0
1
2
0
1
1
0
1
1
3
1
0
1
1
2
0
2
1
1
0
0
0
2
1
0
1
1
0
2
1
1
1
2
2
1
0
1
2
1
0
1
1
2
0
2
2
0
0
2
0
2
2
1
0
0
0
1
0
1
0
2
1
2
0
2
0
2
1
2
1
2
1
1
2
0
1
2
2
2
1
2
2
0
1
6
0
2
1
1
1
0
2
1
0
1
1
2
1
0
0
1
1
1
1
1
0
0
2
0
2
1
1
1
0
0
1
1
1
1
2
0
0
0
0
1
2
2
0
0
1
1
0
1
2
2
1
1
0
1
1
2
0
1
1
0
1
0
0
1
0
1
0
0
1
1
0
1
1
2
1
2
0
2
2
1
1
2
1
0
1
1
0
0
2
0
0
3
1
2
2
0
0
2
0
0
1
1
1
1
1
1
0
1
0
1
1
1
0
0
1
1
1
0
1
0
0
1
0
1
0
1
1
2
1
0
1
2
0
1
1
1
1
1
2
0
0
0
0
1
1
1
1
0
1
0
1
1
0
1
1
1
1
2
0
1
0
2
0
0
1
0
1
0
2
2
0
0
1
0
0
1
1
1
1
2
5
1
2
0
0
0
2
0
1
2
2
1
1
0
1
2
0
0
0
2
2
3
1
0
0
0
0
1
1
1
1
1
1
1
0
1
1
1
1
1
0
1
1
0
1
1
2
2
0
1
0
2
1
1
1
1
0
0
1
0
1
0
1
1
1
0
0
0
2
2
1
1
0
1
2
1
2
0
1
1
2
1
0
0
0
1
1
1
0
1
4
1
0
1
0
0
0
0
0
0
1
0
2
2
1
0
3
2
0
0
0
1
1
0
0
1
2
1
1
1
1
1
1
2
2
1
1
1
0
1
1
2
1
0
2
2
2
1
0
0
1
1
2
0
2
1
1
0
0
2
2
2
1
0
1
0
1
0
0
0
1
0
2
0
1
0
1
2
1
1
3
0
2
1
0
2
1
2
1
0
1
2
1
0
2
0
1
2
1
0
1
2
0
1
0
2
1
1
0
1
1
2
1
1
2
1
2
0
1
1
0
0
0
1
2
0
1
1
1
2
2
1
2
1
0
1
0
1
2
1
2
1
1
1
2
2
1
1
5
1
2
2
0
2
1
2
0
2
2
1
0
0
0
0
1
0
1
1
2
1
0
0
2
0
0
1
0
1
0
1
1
1
0
1
1
0
0
0
0
0
2
2
0
2
0
1
0
1
3
2
1
1
2
0
1
0
1
0
0
0
2
2
1
1
2
2
1
2
1
1
1
1
2
0
1
1
0
1
1
1
1
1
1
2
0
1
1
0
0
1
1
2
1
0
0
0
1
0
0
1
0
2
2
0
2
1
1
0
0
1
2
1
1
1
0
1
0
1
1
0
1
2
0
0
1
1
2
1
1
0
1
1
1
1
1
0
1
0
2
4
0
0
1
1
0
2
0
1
0
1
0
1
0
1
0
1
1
1
0
0
1
0
1
1
1
1
1
0
0
2
3
0
0
1
1
1
2
2
0
0
1
4
1
1
0
0
1
1
1
0
2
1
0
1
2
0
0
0
1
0
2
2
1
0
0
2
0
1
0
1
0
1
1
0
2
0
3
0
0
1
2
2
1
1
1
0
1
1
2
0
1
0
0
0
1
0
0
0
1
2
1
1
1
1
0
1
0
2
1
1
0
2
0
2
1
1
1
1
1
2
1
2
0
0
0
0
1
0
2
2
1
2
0
1
0
0
0
2
1
1
2
1
0
0
0
0
1
1
1
1
0
1
1
0
2
2
1
1
1
1
1
0
1
2
2
3
2
1
0
0
0
1
1
0
2
0
0
2
2
0
0
0
1
0
0
0
1
1
1
0
1
0
1
1
0
1
0
1
1
1
2
1
1
2
1
0
0
0
1
1
1
2
0
1
2
1
0
0
0
0
1
1
0
1
1
0
0
3
0
1
3
0
0
0
0
0
1
1
2
1
0
2
0
0
1
2
2
0
2
1
1
0
1
0
1
1
1
0
1
2
0
1
1
1
0
0
0
2
1
1
0
2
0
1
0
0
2
2
0
2
2
0
0
0
1
0
1
1
2
1
0
0
1
1
2
1
1
1
1
0
1
1
1
0
1
0
0
1
0
2
0
0
4
1
1
1
1
1
0
1
1
0
0
1
0
1
2
1
1
1
1
1
2
0
0
1
0
0
0
2
1
1
1
0
0
1
1
1
2
1
1
0
1
1
0
1
1
2
0
0
2
1
1
2
1
1
1
1
1
1
1
1
0
1
1
0
4
0
1
1
1
2
2
1
1
0
1
2
2
2
1
2
0
1
0
2
0
0
0
1
1
1
0
0
0
1
1
1
1
1
1
1
1
1
1
0
1
1
0
2
0
0
1
1
0
2
0
2
1
2
2
2
1
0
1
1
2
2
3
1
2
1
1
1
0
1
0
0
0
0
0
1
0
1
1
1
0
1
1
0
1
0
1
2
2
1
1
1
2
2
1
1
1
1
2
0
0
1
1
1
0
2
0
1
1
1
1
1
1
1
2
0
1
0
2
1
2
2
1
2
1
1
2
0
0
0
0
1
0
1
0
0
0
1
2
1
1
1
1
2
1
0
1
2
2
0
1
1
0
2
1
2
1
1
2
2
2
0
2
1
0
1
2
1
2
1
2
2
2
1
0
2
0
0
2
2
1
1
0
2
1
3
2
1
2
1
1
1
0
0
1
0
1
2
1
2
1
3
1
1
0
1
0
2
1
0
0
1
1
0
1
1
2
2
2
3
1
2
2
1
1
2
2
0
1
1
2
0
1
1
1
1
1
3
1
0
1
0
0
1
1
2
1
2
2
0
2
2
1
1
1
2
1
2
0
0
0
0
1
0
1
2
0
1
0
2
1
0
1
0
1
1
2
1
0
2
0
1
2
2
1
1
2
0
1
1
1
0
1
1
1
1
2
1
0
0
0
0
2
1
2
2
2
0
1
1
0
0
0
1
2
2
2
1
1
1
0
1
1
1
0
1
1
1
0
1
0
0
0
0
1
1
0
0
0
2
0
0
1
2
0
1
1
0
1
1
1
1
0
0
2
0
2
1
1
0
0
0
2
1
1
1
1
1
1
1
0
1
0
1
5
1
0
2
1
1
1
0
1
2
0
0
0
2
0
1
2
1
1
2
0
1
1
1
1
2
0
1
1
0
1
2
0
1
0
2
0
2
1
1
1
1
1
1
0
1
2
0
1
2
1
1
1
1
1
2
2
2
1
0
0
2
0
0
1
1
0
1
1
0
1
1
2
0
1
0
1
1
1
1
2
1
2
1
0
0
1
2
2
0
1
1
1
0
1
3
0
1
1
3
2
2
2
0
1
1
1
2
0
1
2
0
1
0
1
1
0
0
1
1
2
0
0
0
1
1
1
0
0
0
1
0
1
2
0
1
1
2
0
0
0
1
0
2
1
1
1
0
2
2
0
0
2
0
1
2
1
1
2
1
3
1
1
1
0
0
0
0
1
0
2
2
1
1
1
1
1
0
1
1
1
0
2
1
1
2
1
0
2
1
0
1
0
1
0
0
2
0
1
0
1
1
1
0
1
2
1
0
0
2
0
2
1
0
0
2
2
1
2
2
0
1
1
0
0
0
0
1
1
1
1
1
1
0
1
1
1
1
2
2
1
1
2
1
2
0
2
1
2
1
0
1
0
1
2
1
1
2
2
2
1
0
1
0
0
0
2
2
0
1
1
1
1
1
0
0
2
1
0
1
0
2
1
1
2
1
1
1
0
1
1
1
2
2
0
1
0
1
0
0
0
2
1
1
2
0
1
2
1
2
1
0
0
0
0
1
1
2
2
1
0
0
0
1
1
2
1
2
2
1
1
0
1
2
0
1
2
0
1
1
0
0
2
1
1
2
2
2
1
1
0
0
1
0
1
1
1
1
1
2
1
2
1
1
1
1
0
1
0
2
1
1
1
1
1
0
0
1
0
2
3
2
1
1
1
0
1
1
1
2
0
0
0
2
2
0
2
1
1
0
1
3
0
0
1
1
1
2
1
1
1
0
1
1
2
1
1
1
0
2
2
1
2
1
0
1
1
0
0
1
1
2
1
1
2
0
1
0
1
0
1
0
2
2
2
0
1
1
2
2
2
1
1
2
0
1
0
1
1
2
0
1
2
1
1
1
0
0
2
1
0
0
0
1
1
1
0
1
0
0
0
1
0
2
2
1
1
0
2
1
0
0
0
0
0
2
1
0
0
1
0
1
0
1
0
0
2
1
1
0
2
0
1
0
1
0
2
0
0
2
1
0
2
0
1
1
1
0
0
2
1
1
0
1
3
1
0
1
1
0
1
2
2
2
1
0
0
0
2
0
1
0
1
0
2
1
1
1
1
1
1
0
1
1
1
1
0
1
1
1
1
1
1
2
1
0
0
1
1
2
1
0
2
1
0
1
2
0
1
1
1
1
1
2
2
1
1
0
1
1
0
1
2
1
1
1
2
2
0
2
0
2
1
1
1
0
1
2
1
0
2
2
0
1
0
1
0
0
0
2
1
0
0
1
0
1
1
1
1
1
1
1
0
1
1
0
1
2
2
1
0
1
0
2
1
2
0
0
1
1
2
0
1
2
0
0
0
2
0
2
1
0
1
0
0
2
2
2
1
1
1
1
1
2
1
3
2
1
2
1
2
1
1
0
1
0
0
2
0
1
0
0
1
2
0
1
2
1
2
0
0
2
1
1
1
1
1
0
1
1
2
1
0
0
2
2
0
1
2
0
1
1
0
1
0
1
0
0
1
1
1
0
2
1
1
2
1
0
0
1
0
1
1
0
1
1
0
0
1
0
0
0
1
1
0
1
1
1
1
1
2
2
2
0
0
0
0
2
2
1
1
2
1
2
1
2
0
1
2
1
1
2
2
0
1
1
0
1
1
2
0
1
1
0
1
1
1
2
0
0
2
2
1
2
1
0
2
0
1
1
0
0
2
0
1
2
0
0
1
0
0
1
1
1
1
0
0
0
1
0
2
1
1
1
1
2
2
2
0
2
2
2
1
1
2
1
0
1
1
2
1
0
2
0
1
0
2
0
1
1
0
0
0
1
2
1
1
0
1
1
0
2
2
0
0
0
2
0
1
0
1
0
2
0
0
2
2
1
0
1
2
2
0
1
1
1
1
1
1
0
2
1
1
1
1
1
0
2
1
0
1
2
2
2
1
1
1
1
2
2
0
2
3
1
0
1
1
1
0
0
0
2
2
0
1
1
1
1
2
1
0
0
1
1
0
1
2
1
2
0
0
0
1
1
0
2
1
1
0
1
2
0
0
1
0
1
1
2
1
0
1
0
1
0
0
0
1
1
0
0
0
1
1
1
1
1
1
2
0
0
1
1
1
0
1
1
1
2
2
0
0
1
1
0
0
0
2
1
2
2
1
1
1
2
0
2
0
1
1
1
0
1
0
1
0
0
2
0
2
1
0
1
0
1
1
0
1
1
5
0
0
0
0
1
1
0
0
0
0
1
2
1
0
1
1
1
0
1
1
0
1
1
0
2
1
1
1
1
1
0
1
0
2
0
0
1
0
2
2
0
1
0
2
1
1
1
1
1
2
1
1
2
0
2
1
0
0
2
2
1
0
0
0
0
0
2
0
0
0
1
2
1
1
0
2
0
1
0
0
1
1
0
2
0
1
0
2
1
0
0
1
2
0
0
2
1
2
1
2
2
2
1
1
1
0
2
0
0
0
1
1
1
2
1
2
2
2
1
2
0
0
2
1
1
1
1
2
2
2
1
2
2
1
0
0
2
1
1
0
1
0
2
2
1
2
1
1
1
1
1
0
1
1
0
0
1
1
2
1
1
1
0
0
2
0
1
0
0
1
0
1
2
2
0
2
2
2
0
1
0
3
1
0
1
1
1
1
0
2
0
1
0
0
0
0
0
0
1
1
0
1
1
1
2
2
1
0
0
1
3
0
0
0
1
3
1
1
1
1
1
0
1
1
1
0
1
0
0
2
1
1
1
1
1
0
1
2
2
0
2
1
1
1
1
1
1
0
1
1
1
0
2
1
0
2
1
1
1
2
0
1
1
1
1
1
1
1
1
0
0
0
1
0
1
2
0
1
1
1
1
2
0
2
0
2
2
1
0
2
0
1
2
2
2
1
0
0
2
1
2
1
2
1
0
2
0
1
0
0
1
0
2
0
1
1
0
1
1
0
0
0
1
2
2
0
1
2
1
1
1
0
1
1
1
1
0
0
1
1
0
1
0
2
1
0
1
1
1
2
0
0
0
1
2
0
1
0
1
0
1
1
1
0
1
1
1
0
1
2
0
1
1
2
1
1
0
1
2
1
0
1
1
1
2
2
1
1
0
1
1
0
1
0
1
1
1
1
2
1
0
1
2
0
0
1
1
0
2
1
0
0
0
1
2
1
1
2
0
2
1
0
1
1
0
1
0
0
0
0
0
1
0
2
0
0
1
2
1
0
2
1
0
1
0
0
2
0
1
0
0
1
2
0
1
1
1
1
0
0
0
0
0
0
1
1
1
2
0
2
1
2
0
1
1
0
2
0
0
0
2
1
0
1
1
1
1
0
3
1
1
1
1
0
1
1
0
2
2
2
2
1
0
1
1
1
2
2
2
1
1
2
3
0
1
0
1
0
1
0
0
0
2
0
1
0
1
2
1
1
0
1
0
2
0
1
1
1
0
1
1
1
1
0
1
3
1
1
0
1
3
0
0
1
1
0
2
1
0
1
1
2
2
1
0
0
0
1
1
2
2
0
0
1
2
0
0
2
1
1
1
0
0
1
1
0
2
1
2
2
0
1
0
0
6
0
1
1
1
1
2
2
2
2
1
1
2
0
0
2
0
0
1
0
1
1
1
2
2
0
0
1
0
0
1
0
1
0
0
0
0
1
1
0
1
0
1
1
2
1
2
1
1
2
2
1
0
1
2
3
1
1
0
2
1
1
1
2
0
0
0
2
0
0
0
2
1
0
1
1
2
1
1
1
0
2
1
1
0
0
1
0
1
1
0
1
0
1
0
1
1
2
2
1
1
1
0
1
0
0
1
1
1
3
0
2
0
2
1
2
0
1
2
0
0
1
1
0
2
1
0
2
1
1
0
4
1
1
0
1
1
2
1
2
2
1
0
1
0
1
1
1
1
2
1
2
1
2
2
0
0
1
1
1
2
2
1
0
0
0
0
0
0
0
1
1
1
1
1
1
0
0
1
2
1
1
0
1
0
0
2
1
0
2
1
1
0
1
1
0
0
0
2
2
1
1
2
0
2
1
0
0
1
1
1
1
1
0
2
1
1
2
1
0
2
0
1
1
0
1
2
1
2
2
1
0
1
0
1
1
0
1
1
1
0
3
0
0
0
1
0
0
1
0
1
0
1
2
1
1
1
0
2
1
1
0
0
1
0
2
1
2
0
0
1
0
1
1
2
0
1
3
0
0
0
1
2
2
1
1
2
0
2
1
0
1
2
0
0
0
2
1
0
2
2
0
0
0
1
1
2
2
0
0
1
2
1
1
0
1
2
2
1
1
0
0
0
0
1
0
0
2
1
1
1
1
2
1
1
0
1
0
1
0
2
0
1
1
1
0
1
1
2
2
0
1
1
0
1
1
0
1
2
2
0
0
0
2
1
0
1
1
2
1
4
2
1
2
1
1
1
2
1
0
2
1
1
0
1
1
2
0
2
2
2
2
1
1
1
1
0
1
0
2
1
0
1
0
1
1
0
0
0
1
1
1
1
0
1
1
2
1
2
0
0
0
1
1
1
0
0
0
0
1
2
2
0
1
2
2
0
0
1
0
1
0
0
1
0
0
0
1
1
2
1
2
1
2
0
2
1
1
1
1
1
1
2
1
0
1
2
1
2
1
1
3
1
1
1
1
1
0
3
1
1
2
1
1
1
0
2
1
1
1
1
0
0
1
1
0
1
0
0
1
2
0
0
1
2
0
0
1
0
2
0
2
0
0
2
2
0
0
2
0
1
1
0
1
1
1
1
0
2
2
1
0
0
1
1
0
1
1
2
0
1
2
1
2
0
1
1
0
2
1
0
2
0
1
2
1
1
1
0
1
2
1
0
1
0
0
1
0
2
2
2
0
1
0
0
2
1
1
0
0
0
0
0
2
1
2
1
0
0
2
1
0
0
1
1
2
0
0
0
1
1
1
0
0
1
1
0
5
2
1
0
0
0
0
1
0
1
1
1
1
1
0
1
1
0
0
1
2
1
2
2
1
2
1
2
1
0
1
0
1
0
0
1
0
1
0
0
1
0
0
1
1
0
1
1
0
1
0
1
1
2
1
0
1
2
1
0
1
1
1
1
0
3
0
1
1
1
0
0
0
1
1
1
1
0
2
1
1
0
0
1
1
1
1
1
0
1
2
0
1
0
0
1
2
1
1
2
1
1
1
0
1
2
2
0
1
0
1
1
0
0
1
1
0
0
0
1
2
1
0
0
1
1
0
1
0
0
1
0
2
0
1
1
2
1
2
1
1
1
1
0
0
2
2
0
2
5
0
1
0
0
0
0
0
2
1
1
2
1
0
0
1
0
1
1
0
1
1
1
0
1
1
0
2
1
0
1
0
2
0
0
1
1
1
1
1
2
0
1
1
1
1
2
2
1
0
2
1
1
1
0
0
2
0
0
1
1
1
2
0
1
1
1
1
2
1
1
2
1
1
1
0
2
1
0
2
0
2
2
1
2
1
1
1
1
2
0
3
1
1
0
1
1
0
0
0
0
0
1
2
2
0
1
2
1
1
1
2
0
2
0
1
2
0
0
1
1
2
1
1
0
2
1
1
2
0
2
2
1
1
1
2
2
0
1
0
2
0
1
0
1
0
1
0
2
2
2
1
1
1
2
0
0
1
1
0
2
1
0
0
0
0
0
0
2
0
1
1
2
0
1
0
2
1
0
0
1
2
2
0
1
0
2
0
1
0
0
1
0
0
0
1
1
1
2
1
1
2
2
0
1
1
0
1
0
1
2
0
2
1
2
2
1
2
1
1
0
1
0
0
1
0
2
1
1
0
1
1
1
2
0
1
1
1
0
0
1
1
1
1
0
0
2
1
1
0
2
2
2
0
2
1
1
1
1
1
1
0
0
2
1
0
1
0
1
1
1
1
1
2
1
0
1
2
1
2
2
1
0
1
1
2
0
1
1
0
1
1
0
1
1
1
0
1
0
2
2
1
1
3
1
2
0
2
1
1
1
0
1
2
1
1
0
1
1
2
1
2
0
1
1
1
1
2
1
0
0
1
2
1
1
1
1
1
1
1
2
0
1
3
1
1
0
0
1
0
1
1
1
0
2
1
0
2
2
2
0
2
0
0
1
3
2
1
0
1
1
0
4
1
2
1
1
1
1
1
1
2
1
1
0
2
1
2
1
1
0
0
1
0
1
1
1
1
2
2
0
1
2
2
1
2
1
1
1
2
0
2
1
0
1
1
2
2
2
1
1
0
1
1
1
1
2
1
0
1
0
1
0
1
2
0
1
1
1
0
2
1
1
1
0
1
2
2
2
0
1
1
2
0
1
1
0
0
1
0
2
3
0
0
2
0
0
2
1
0
2
0
1
0
0
1
1
1
1
1
2
1
1
2
1
2
1
0
1
1
2
2
1
1
2
0
0
1
2
0
2
2
1
1
1
1
1
0
1
0
1
2
0
1
2
1
2
1
8
1
1
0
2
2
2
1
1
1
0
2
1
0
2
2
2
1
3
1
1
1
2
2
1
1
2
2
0
2
0
0
1
1
0
2
1
1
2
1
1
1
2
0
0
2
0
1
2
1
1
1
2
0
0
1
0
0
1
0
1
1
1
1
2
1
1
1
2
2
2
1
1
1
0
0
0
0
2
1
0
0
2
1
2
1
1
1
1
1
1
2
1
1
2
0
0
0
0
2
2
1
0
0
1
1
0
0
2
1
1
0
1
0
2
1
1
0
1
1
0
2
1
2
1
1
1
2
1
2
0
1
1
1
0
1
2
0
1
2
2
1
1
0
1
0
2
2
2
0
2
1
0
0
0
1
1
1
2
1
2
1
1
1
0
1
1
1
2
2
2
0
1
1
0
1
2
1
0
1
1
2
1
2
1
1
1
1
2
1
1
0
1
1
0
1
1
2
0
0
0
1
1
1
1
1
1
1
1
1
1
2
0
2
2
5
0
1
1
0
1
1
2
1
0
1
3
0
1
1
0
2
0
0
2
2
1
0
1
2
1
1
1
1
2
1
1
0
0
0
2
2
0
2
1
1
2
0
0
2
2
2
1
1
0
1
1
0
0
2
0
0
0
1
0
2
1
1
1
0
2
0
0
0
1
0
2
2
2
0
1
1
1
0
1
1
0
2
2
0
2
0
0
2
1
1
1
0
2
0
0
1
0
1
0
1
0
1
2
1
0
1
1
0
1
1
0
1
0
0
0
1
1
0
1
0
1
0
1
1
2
1
2
0
2
1
0
1
0
1
1
2
0
1
1
2
1
1
1
1
1
1
0
1
1
0
0
1
5
0
1
0
1
1
0
2
1
1
2
0
0
1
2
0
1
2
0
1
1
0
1
1
0
1
2
0
2
0
2
2
2
1
0
1
0
2
1
1
0
1
0
2
1
0
1
0
1
0
1
1
0
0
0
1
1
0
0
1
2
2
0
0
2
0
1
1
0
1
0
0
1
1
0
1
2
1
2
1
1
1
1
2
2
1
1
0
1
2
2
1
1
1
1
2
0
1
1
0
0
0
1
1
1
1
1
0
0
0
1
1
1
1
1
0
2
1
0
2
0
0
0
2
0
1
1
1
1
0
0
0
2
2
2
1
1
2
0
1
0
2
1
0
0
1
1
0
1
0
2
2
0
1
2
0
1
1
2
0
2
1
1
2
0
0
2
0
2
1
1
0
1
2
1
1
1
1
1
0
1
2
0
1
1
2
1
2
0
0
1
1
2
1
0
0
0
0
2
1
1
0
0
1
1
1
0
1
0
2
1
0
1
1
0
0
1
2
2
0
0
0
2
0
1
0
2
1
1
0
2
1
2
0
2
1
1
1
1
2
1
2
1
2
1
2
0
1
1
0
0
2
0
0
0
1
0
1
1
0
2
0
1
1
0
1
1
1
2
1
1
0
1
2
1
0
0
2
1
1
0
0
0
1
0
1
1
2
2
1
1
2
1
2
0
0
0
0
1
0
1
1
0
0
0
0
1
1
1
2
0
1
0
0
1
2
3
1
2
0
0
1
2
1
1
1
0
2
1
1
2
1
1
2
0
0
1
0
2
1
1
1
3
0
1
2
1
1
1
1
0
1
2
2
1
2
0
0
0
1
0
2
1
1
0
1
2
1
3
1
1
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
2
1
1
2
1
1
3
0
0
1
2
1
0
3
0
0
1
0
1
0
0
0
0
0
0
2
2
2
0
1
1
1
1
0
0
0
1
1
1
2
1
0
2
0
1
0
1
1
2
0
2
2
1
2
1
0
2
1
2
1
1
1
2
1
0
1
1
0
0
1
0
1
2
1
0
0
2
1
1
1
1
0
4
2
1
1
0
1
1
2
0
1
0
1
2
0
2
1
0
1
0
1
1
0
1
1
1
0
1
1
1
1
1
2
0
0
2
1
2
0
1
1
1
1
1
2
0
2
1
1
1
1
2
2
0
1
1
0
1
1
0
0
1
1
0
2
0
0
1
0
1
1
1
0
1
2
2
1
0
1
2
1
2
2
2
0
1
2
0
0
0
0
1
2
0
1
2
1
1
1
1
0
1
2
0
1
2
1
0
0
0
0
0
0
1
0
0
0
0
1
2
2
2
2
1
1
1
0
0
2
1
1
1
0
2
1
0
2
0
1
1
1
0
1
1
1
2
1
2
2
0
0
0
1
1
0
0
1
1
2
0
1
2
0
1
0
1
0
1
1
0
1
2
1
1
2
0
1
0
1
0
0
1
0
0
1
0
0
0
1
2
2
2
1
1
0
2
1
2
1
2
1
0
0
1
1
0
1
0
1
0
0
1
2
0
0
2
1
2
1
2
2
0
0
1
2
1
0
0
0
1
1
1
0
1
1
1
1
0
0
2
1
0
1
0
1
1
0
0
2
1
1
0
1
1
2
0
0
0
1
0
0
2
1
1
0
0
1
0
2
0
2
2
0
1
1
3
1
1
2
1
2
2
0
2
1
1
0
2
1
1
0
0
1
2
1
2
1
0
0
0
1
0
1
1
2
1
1
1
2
1
1
0
2
2
1
1
1
0
1
2
2
2
1
1
1
1
1
1
2
0
3
1
1
1
0
0
1
0
0
0
0
2
0
1
2
1
2
1
1
1
0
1
1
0
1
1
1
2
1
0
1
2
0
2
0
0
0
1
1
1
0
2
2
2
1
1
1
1
1
1
1
2
1
0
1
1
1
0
0
1
1
0
1
2
1
1
1
1
1
2
1
0
0
0
1
1
2
2
0
1
0
0
0
0
0
0
2
1
1
0
1
1
0
1
2
1
3
1
0
0
1
1
0
1
2
1
0
0
2
1
1
2
1
0
1
0
2
2
1
0
2
1
0
1
0
2
0
2
1
1
3
1
2
1
1
0
1
1
0
0
1
1
1
1
2
1
0
1
1
1
2
2
1
0
1
0
0
2
0
0
2
2
1
1
1
2
0
2
1
0
1
1
1
2
0
0
0
2
0
0
2
2
0
1
1
2
1
0
1
0
3
0
1
1
1
1
0
2
2
0
1
0
0
2
1
1
1
3
0
1
2
1
2
2
2
1
0
3
1
0
1
1
2
2
2
0
3
2
1
2
0
5
0
1
0
0
2
1
1
2
2
0
0
2
1
0
1
1
1
1
2
1
0
0
1
0
0
0
2
1
0
1
2
1
0
1
0
1
1
1
1
0
2
2
1
1
1
0
0
1
1
0
1
0
2
0
1
1
1
0
1
1
2
2
1
1
2
0
1
0
0
1
1
2
2
0
0
1
2
0
0
0
1
1
1
0
1
0
2
0
1
0
1
1
1
2
1
0
0
1
1
2
2
1
1
1
1
1
1
1
1
0
1
2
0
0
1
1
1
1
1
1
0
2
1
0
1
0
0
0
2
0
1
2
1
2
1
2
1
1
2
1
2
0
1
1
1
1
1
1
2
1
0
1
0
2
0
2
1
2
0
1
0
2
1
1
0
0
1
0
1
0
1
1
0
2
2
2
2
1
0
2
1
0
0
1
0
0
0
1
1
1
0
2
1
2
0
1
0
2
1
2
1
0
2
1
0
2
1
2
3
0
1
1
1
1
1
1
2
2
0
1
1
1
2
1
0
1
0
1
0
1
1
1
0
0
0
1
1
1
0
0
1
1
1
0
2
0
1
0
0
0
1
0
2
0
0
2
0
2
1
0
1
1
1
0
1
0
0
0
2
1
0
1
0
1
3
2
1
0
1
1
1
0
1
1
1
2
1
2
0
0
1
1
1
2
1
0
2
1
2
0
1
0
2
1
0
1
1
0
1
0
1
0
3
1
1
2
1
1
1
0
1
1
1
2
0
0
1
2
1
2
0
1
1
0
1
4
1
0
1
0
2
1
0
2
0
0
1
0
1
1
0
0
1
0
2
1
1
1
1
1
0
2
1
0
0
1
2
0
2
1
0
0
1
1
1
1
2
2
1
2
0
0
1
1
0
0
0
0
2
0
1
0
2
1
0
0
0
0
1
1
0
1
0
0
1
1
0
2
1
2
1
1
2
1
1
1
0
0
2
1
0
2
0
1
1
1
1
2
1
0
1
1
0
1
1
2
1
2
1
0
1
0
2
4
0
1
0
2
0
0
1
2
1
1
0
1
0
2
3
1
2
1
2
0
1
0
1
1
0
2
0
0
2
2
1
0
1
0
1
1
2
2
2
2
1
1
1
1
1
0
1
2
0
0
2
2
1
1
1
1
2
2
0
1
1
0
2
1
1
1
1
1
2
0
0
1
0
1
2
0
1
1
2
2
1
2
0
1
1
0
2
1
1
1
1
1
1
1
1
1
0
1
1
0
1
1
1
2
1
1
0
1
1
7
2
1
1
1
0
1
0
1
1
2
1
1
1
2
2
1
1
2
1
0
0
2
0
2
0
1
1
1
0
2
2
0
0
1
1
2
1
0
1
1
0
0
0
0
1
1
1
2
2
1
0
1
0
2
0
1
1
1
0
1
0
1
1
1
1
2
1
1
1
0
1
0
2
1
1
1
1
1
0
2
1
2
1
2
1
2
1
1
2
0
1
1
2
1
0
0
2
1
1
1
1
1
2
1
0
1
0
0
0
2
0
2
1
0
0
1
2
1
0
0
1
1
1
0
0
1
1
0
0
0
1
2
1
0
1
2
2
0
0
1
1
1
1
1
1
2
1
1
3
2
0
2
2
1
1
1
1
1
1
1
2
2
2
2
1
1
1
1
0
0
1
2
1
0
1
1
0
1
2
0
2
1
1
1
2
0
1
1
1
0
2
1
0
0
1
1
0
2
0
1
1
1
1
0
1
1
1
1
2
0
0
1
1
1
3
0
0
2
1
0
1
1
1
1
0
1
0
0
2
1
2
1
1
2
0
1
2
1
2
0
0
0
1
1
2
0
1
2
2
1
0
1
0
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
0
2
1
1
1
2
1
1
2
1
1
0
0
1
0
1
2
0
0
0
2
1
0
1
2
1
0
1
1
1
0
1
0
1
0
2
0
1
1
2
2
1
1
1
1
1
0
2
1
0
1
1
1
2
0
1
2
1
1
2
1
1
1
1
1
0
0
2
1
0
1
2
2
0
2
1
1
0
0
4
1
1
0
1
0
1
0
2
2
1
1
1
2
2
0
0
0
2
1
1
0
0
1
1
2
1
1
0
1
0
2
1
1
2
0
2
1
1
2
2
1
1
1
1
1
1
0
2
0
0
1
0
0
1
0
1
1
0
1
1
0
0
0
1
0
0
1
1
1
2
1
1
0
2
1
0
1
1
2
0
1
2
1
1
0
1
0
1
2
1
0
1
0
1
1
1
1
1
1
0
1
0
0
1
1
0
1
1
2
2
2
1
0
1
1
1
0
1
0
1
2
0
1
1
0
1
2
0
0
2
1
0
2
0
4
1
2
1
2
1
2
0
0
0
1
2
0
0
2
0
1
0
1
2
1
0
2
0
0
0
1
0
1
1
2
2
1
1
2
1
2
2
2
1
1
2
3
0
1
1
0
0
0
1
2
1
1
1
0
0
1
0
1
1
1
0
0
0
1
1
1
0
2
2
1
1
1
0
2
0
0
0
1
1
0
2
0
1
0
0
1
0
0
1
1
0
1
1
1
1
2
1
2
0
1
0
2
1
1
3
0
1
0
0
1
2
1
1
0
0
0
1
1
0
1
1
2
1
1
2
1
0
1
1
0
2
1
0
1
1
0
0
1
1
1
1
1
0
4
1
2
1
0
1
0
2
2
1
0
2
0
0
1
0
0
1
2
0
1
1
1
0
0
0
2
1
2
1
1
2
1
2
0
0
2
0
0
0
0
1
1
1
1
1
0
2
0
2
2
0
0
1
0
1
1
1
1
0
1
1
1
1
2
2
2
2
1
1
1
0
0
0
1
1
0
0
1
1
1
1
1
1
1
0
2
1
1
0
2
1
1
0
1
1
1
0
1
1
1
2
0
0
0
0
1
0
1
1
1
1
2
0
1
1
0
1
1
1
2
0
1
0
2
2
1
0
0
0
0
2
0
3
0
0
1
1
1
2
0
1
1
0
1
0
0
2
1
2
0
0
0
1
0
1
0
2
0
0
2
1
1
2
1
1
1
1
1
1
1
1
0
1
0
2
2
0
2
1
0
1
1
1
1
2
1
1
1
2
1
0
1
1
0
0
2
2
0
2
0
2
1
1
2
2
1
1
0
1
0
1
0
1
0
1
2
0
1
1
2
2
0
2
1
1
2
0
0
0
1
0
1
1
0
1
1
2
0
1
1
1
2
2
0
1
2
3
0
0
1
1
2
0
1
0
1
0
1
1
2
2
1
0
0
1
1
0
0
2
1
0
5
0
2
0
1
1
1
1
1
1
1
0
2
1
1
1
0
0
1
2
1
2
2
1
1
0
0
1
0
0
0
0
1
1
0
2
2
0
1
1
1
0
3
0
1
1
0
0
0
0
2
1
1
1
1
2
2
0
2
1
2
2
0
0
1
0
0
0
1
2
2
1
2
2
1
0
2
1
1
0
0
0
2
0
1
2
1
1
0
2
2
1
1
1
0
1
2
1
1
0
0
1
0
0
2
1
1
2
2
1
0
0
2
1
1
0
0
2
2
2
1
0
0
0
1
0
2
1
1
1
0
1
1
1
2
2
2
0
0
2
0
1
1
1
1
1
0
2
1
3
0
2
1
1
1
0
0
1
1
1
0
1
2
2
1
1
1
1
1
0
0
1
0
1
1
2
1
0
2
1
2
2
1
0
1
1
1
0
1
1
1
2
1
1
2
1
0
2
0
0
1
1
0
2
0
2
0
1
1
2
2
0
1
0
2
0
2
1
1
0
0
1
1
1
1
1
1
0
1
1
1
1
0
1
1
0
1
1
0
1
2
0
2
0
0
2
3
2
0
1
1
0
1
1
1
1
0
2
1
0
2
1
3
1
0
0
0
1
1
1
0
0
1
2
1
0
0
0
1
1
2
1
3
1
0
1
1
2
1
0
1
1
1
2
0
0
1
1
0
1
0
1
0
1
1
2
0
1
1
0
1
2
0
1
2
1
1
1
0
1
0
2
2
1
6
0
0
1
0
2
2
2
2
1
0
1
1
0
1
2
2
2
0
0
0
1
1
1
0
2
2
0
2
1
2
2
0
0
1
0
0
1
2
0
0
2
1
0
1
0
2
0
0
2
1
1
2
0
1
0
1
0
1
2
1
1
0
1
0
1
1
0
1
2
1
0
0
1
2
2
0
0
0
2
1
1
2
1
1
1
1
1
2
0
2
1
0
1
0
0
0
0
0
1
0
0
0
2
1
1
1
1
1
1
1
0
0
1
1
1
0
2
2
0
0
0
2
1
1
0
0
2
6
0
2
1
0
1
1
1
1
0
0
0
2
1
0
1
0
1
1
2
1
1
0
1
2
1
1
0
0
4
1
1
1
1
1
0
1
0
0
0
2
0
1
0
1
1
1
0
1
1
0
0
0
1
1
2
1
0
1
1
1
0
2
2
1
3
0
1
2
1
2
0
0
0
2
2
1
1
1
2
1
1
2
0
1
1
2
1
0
2
1
0
0
1
1
0
2
1
1
2
0
2
1
1
1
2
2
0
0
1
0
1
0
2
0
0
0
0
2
1
2
1
0
1
1
1
1
1
1
1
1
2
0
2
1
2
0
0
1
1
1
1
2
1
0
1
0
0
0
2
0
1
1
2
2
0
1
2
0
1
1
0
0
0
1
0
1
1
2
3
1
1
0
0
1
2
1
0
1
0
1
1
1
1
1
1
1
1
2
1
0
1
0
0
1
0
1
0
1
1
0
1
1
0
0
0
2
1
0
0
0
1
0
1
1
1
1
0
1
0
1
0
0
0
0
1
2
1
1
1
1
1
2
0
3
2
1
3
1
2
0
0
1
1
2
0
1
1
0
0
2
1
2
1
1
2
1
2
2
0
1
0
2
1
1
1
7
0
1
2
2
1
1
2
2
0
2
1
1
0
0
2
2
1
0
0
1
1
0
0
1
1
1
1
1
0
1
1
1
2
0
1
1
0
1
0
1
2
1
1
0
1
1
1
0
0
1
1
1
0
0
1
2
2
0
2
1
1
0
1
0
0
1
2
1
1
0
1
1
1
0
1
1
0
1
0
2
0
2
1
1
0
0
0
0
1
2
1
1
0
0
1
1
1
2
0
0
0
2
0
0
1
0
2
1
1
1
1
0
0
0
0
1
2
1
1
1
0
0
1
2
0
0
0
1
2
1
0
0
2
0
0
0
0
1
0
0
1
0
1
1
1
2
1
1
1
0
0
1
0
1
1
1
2
2
1
1
0
0
1
1
0
1
1
0
1
1
0
2
0
0
0
3
2
0
2
1
0
1
1
1
1
0
0
3
1
2
0
1
0
1
1
2
2
0
1
1
1
1
1
0
1
0
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
0
0
2
2
1
2
2
2
1
2
1
1
1
0
1
0
2
0
0
2
0
2
1
1
1
1
1
1
2
0
1
1
2
0
0
1
1
1
1
1
0
2
0
0
1
1
1
1
1
1
2
2
2
0
1
2
1
1
0
2
1
1
0
2
2
1
0
0
2
0
1
2
2
2
0
1
0
1
1
0
0
1
1
1
1
1
2
1
1
0
1
1
1
1
1
1
2
0
0
2
0
0
0
0
1
2
2
1
1
1
0
0
0
1
0
0
0
2
1
1
0
1
2
1
0
1
2
1
0
1
2
2
2
0
2
0
1
1
1
2
0
1
1
0
0
2
1
0
0
1
1
1
0
0
2
0
1
2
1
0
1
2
0
1
1
1
1
1
1
0
0
0
0
1
0
1
1
1
0
1
2
1
0
0
0
2
1
1
1
1
0
0
1
1
0
0
0
0
0
2
0
3
1
0
1
2
2
1
1
1
0
1
1
0
2
2
2
0
1
1
0
1
1
1
4
2
0
0
0
1
2
1
2
0
0
0
0
1
1
0
1
1
3
1
1
1
4
0
0
1
0
1
1
1
0
0
1
1
1
1
1
1
0
1
2
1
0
1
1
0
0
1
1
2
1
1
0
0
0
2
1
0
2
1
3
0
0
2
3
1
1
1
1
0
1
1
3
0
2
0
2
1
0
1
1
2
2
1
1
0
2
2
1
1
2
1
1
0
1
2
1
1
0
2
1
1
1
1
0
1
1
2
1
1
0
1
2
2
0
0
1
1
1
1
2
0
0
0
1
2
2
0
2
2
0
1
0
1
2
1
2
2
1
2
0
0
0
1
1
2
0
1
0
0
2
0
1
0
4
1
2
1
2
2
0
1
0
2
1
1
0
1
4
1
0
0
0
0
0
0
0
1
1
2
0
1
1
1
2
2
2
2
1
1
1
1
0
0
1
2
1
1
1
0
0
0
1
1
1
2
1
2
5
2
0
1
0
1
1
0
0
2
1
2
1
0
1
0
1
0
2
0
0
2
2
1
2
1
1
1
1
0
0
2
1
0
0
1
2
0
1
2
0
1
2
1
0
1
2
1
0
2
1
0
0
1
0
1
1
1
1
1
0
2
2
1
1
2
0
2
0
1
2
2
1
1
1
1
1
0
1
2
2
2
2
1
0
0
0
0
1
3
2
1
1
1
1
1
1
0
0
1
1
0
2
1
0
1
1
1
0
0
2
2
1
1
0
0
2
1
2
2
1
0
0
1
1
1
1
1
2
1
0
0
0
2
0
1
0
2
1
0
1
0
1
0
0
1
1
2
1
0
1
0
0
0
1
2
0
1
1
1
2
2
1
0
2
1
1
1
2
0
0
1
1
2
1
0
0
1
0
0
1
2
1
0
2
1
1
2
2
2
1
0
1
1
1
1
2
1
1
2
2
0
1
1
2
1
1
1
1
3
0
1
0
1
0
1
1
1
2
0
0
0
1
1
0
1
1
2
2
0
1
0
3
1
2
1
0
2
0
2
1
0
1
2
2
0
1
0
1
1
1
0
0
2
0
0
1
2
2
1
0
1
1
0
0
1
1
0
1
1
0
1
0
2
1
1
1
1
2
1
1
1
2
1
1
0
1
2
2
2
2
2
1
1
2
1
1
1
1
2
0
1
1
1
1
1
1
1
0
0
1
0
1
0
1
2
2
0
2
0
1
1
1
2
0
1
2
0
1
2
2
1
1
1
1
0
1
0
1
2
1
2
2
2
1
2
1
2
1
1
1
0
1
1
1
1
2
1
2
1
2
1
2
0
1
2
1
2
1
1
1
0
1
4
1
0
0
1
1
2
1
0
1
1
1
1
2
4
1
1
1
0
0
2
1
1
1
2
2
0
0
0
1
2
2
3
0
1
1
1
0
1
0
1
1
1
1
1
0
2
0
2
1
1
1
0
1
2
1
0
1
1
2
1
0
2
1
2
2
0
4
2
2
1
2
1
0
0
1
0
0
1
1
1
0
0
2
1
0
0
1
0
1
0
1
2
1
2
0
2
2
1
1
2
0
0
2
1
0
0
1
0
1
1
0
1
1
0
1
2
0
0
1
1
1
1
0
1
0
0
2
1
0
2
1
1
2
0
2
0
0
2
0
0
1
0
1
2
1
2
0
1
0
0
1
1
2
1
1
1
1
1
0
2
1
0
1
0
1
0
0
1
0
0
0
1
0
1
1
1
0
1
0
1
1
1
2
0
0
2
2
0
1
1
0
1
0
2
0
0
0
1
1
0
1
1
0
2
1
0
1
1
1
0
1
1
1
1
2
1
1
0
0
2
0
0
0
1
1
2
1
1
1
0
2
1
0
1
1
0
1
1
1
1
1
0
0
0
1
0
0
1
2
0
1
0
1
0
0
0
1
1
2
2
1
0
1
0
1
1
1
1
2
1
2
2
1
0
0
2
0
0
1
2
1
0
2
1
0
1
2
2
0
0
0
1
1
1
1
0
1
2
2
1
0
1
0
1
1
0
1
1
1
2
0
2
2
2
1
1
0
1
2
0
0
2
0
2
0
0
1
1
2
1
1
1
2
1
2
1
1
0
1
0
1
0
1
0
0
1
1
0
1
0
2
3
1
3
2
0
1
1
0
1
1
2
0
2
1
2
1
0
0
8
2
0
1
1
0
1
2
2
0
0
1
1
1
1
2
0
3
1
0
0
1
1
0
1
3
0
0
1
0
1
1
1
0
2
0
1
2
2
1
2
2
2
1
0
1
1
1
2
0
1
1
1
1
1
1
2
1
1
1
3
2
0
1
1
1
0
1
1
0
0
1
1
0
0
0
0
1
1
0
0
2
1
0
2
2
2
2
0
2
1
1
5
2
1
0
1
1
1
2
1
2
0
2
2
0
0
2
1
0
0
0
1
1
1
1
1
2
0
1
0
0
0
1
2
0
1
0
0
2
0
0
2
1
0
0
2
0
1
0
0
1
1
1
2
1
0
1
1
0
2
1
2
1
2
0
0
1
1
1
0
1
0
1
0
1
1
0
1
3
1
0
2
0
2
1
2
0
1
2
1
1
2
2
0
2
1
2
2
2
2
1
0
2
2
1
0
1
1
2
0
2
0
2
2
2
0
0
0
1
2
0
1
0
0
2
1
0
0
1
0
1
2
1
2
2
1
1
2
2
1
1
0
0
1
0
1
0
0
1
1
1
1
0
1
0
0
2
0
1
1
1
1
0
0
1
0
2
0
1
1
1
0
1
0
0
2
1
1
1
1
0
1
1
0
2
0
1
1
0
2
0
1
1
0
1
2
0
0
2
2
0
0
1
0
2
1
0
0
1
1
2
1
1
0
0
1
1
0
1
2
1
1
1
0
0
1
1
1
0
1
0
1
1
2
0
2
1
1
0
1
2
1
1
2
1
0
1
1
2
0
3
2
2
1
0
1
2
0
1
1
2
1
0
2
1
1
0
2
1
2
0
2
1
1
0
0
2
3
1
2
1
0
1
1
1
0
0
1
0
1
1
1
1
2
1
0
1
2
1
2
1
0
0
3
1
2
1
1
0
2
1
0
0
2
1
0
0
0
0
2
2
1
0
0
0
2
0
0
1
0
2
0
1
0
0
1
2
1
2
1
0
1
1
1
1
2
1
2
1
2
1
1
0
1
0
1
0
3
0
1
1
2
1
0
0
2
2
2
0
0
1
1
0
0
1
0
2
0
1
0
1
2
1
2
0
2
1
1
1
1
0
2
1
1
1
1
1
0
1
0
0
1
0
0
1
0
1
0
1
0
2
2
0
4
0
1
0
2
0
1
0
2
2
0
2
1
1
1
1
0
1
0
0
2
2
2
0
0
0
2
0
0
1
1
1
1
1
0
1
2
1
1
1
2
1
1
0
2
1
0
0
1
1
2
0
2
1
1
2
2
2
1
4
1
1
0
2
2
2
0
1
2
1
1
0
1
1
1
0
2
0
0
1
1
2
0
2
0
0
2
1
0
1
1
1
0
0
1
1
0
2
0
0
0
0
1
0
1
0
2
0
0
3
0
1
2
1
2
2
0
2
1
0
2
2
2
1
0
1
2
1
0
2
2
0
1
1
0
2
0
1
0
1
1
1
1
1
0
2
0
1
1
0
1
1
1
2
1
0
0
2
2
2
0
0
2
2
1
2
2
1
0
1
1
1
1
2
1
2
0
4
2
0
0
1
0
1
1
0
1
1
1
2
1
0
1
2
1
1
2
1
0
1
1
0
1
0
1
1
1
1
1
1
0
5
0
0
1
2
1
1
1
1
1
0
1
0
1
0
2
1
1
0
1
2
0
1
2
1
0
1
1
0
2
2
2
0
2
0
2
2
0
2
1
1
2
2
0
1
2
2
2
2
0
0
1
1
0
2
2
2
1
3
2
1
2
1
1
1
1
1
2
2
0
2
1
1
1
2
1
2
0
1
0
0
1
1
1
0
2
1
2
2
2
2
0
1
0
1
1
0
2
1
1
1
1
0
0
1
1
1
1
1
0
0
2
1
0
0
1
2
2
0
0
1
1
0
0
1
0
0
0
1
2
2
2
0
0
1
2
0
0
1
1
1
0
2
3
2
0
1
2
0
1
2
1
0
1
0
1
0
0
1
2
0
0
0
1
2
0
0
0
0
0
1
1
3
1
2
1
0
2
2
1
0
1
1
0
0
0
2
0
1
2
0
1
0
0
1
3
0
0
1
1
1
1
2
1
2
2
1
2
1
3
0
0
2
1
2
2
1
1
2
1
1
0
2
1
0
2
3
0
1
2
1
1
0
0
0
0
0
0
1
0
1
1
0
2
0
3
2
1
0
1
2
2
0
1
2
0
0
0
1
0
1
2
1
0
1
1
0
0
2
0
1
0
1
0
2
1
2
3
1
2
2
2
2
0
0
1
1
1
0
1
0
1
2
1
2
1
2
1
2
1
2
0
0
2
2
2
0
0
0
2
2
2
1
0
1
1
1
1
1
0
1
1
0
1
1
2
1
1
0
0
0
2
1
1
1
0
0
0
1
2
0
2
2
0
0
1
0
0
1
1
0
1
1
1
1
0
0
0
1
1
1
2
0
1
1
1
1
1
0
0
1
0
1
2
0
1
1
1
0
1
1
1
0
2
1
1
0
0
1
1
1
1
0
1
1
1
1
0
1
2
1
1
2
3
1
2
2
0
0
2
0
1
0
1
0
0
0
2
1
0
0
2
1
1
1
1
0
0
1
1
3
1
2
1
1
2
2
2
1
0
1
0
1
1
1
1
1
0
2
0
0
1
0
1
1
1
2
0
2
2
0
2
2
1
1
0
1
1
0
0
0
0
1
0
2
0
1
0
1
1
0
0
1
1
1
2
1
0
0
0
2
2
1
0
0
0
1
0
1
1
2
0
1
0
0
1
1
0
1
1
1
0
2
1
4
1
0
1
2
0
2
1
0
1
2
1
0
0
1
2
1
1
1
2
2
1
1
0
1
1
2
0
1
3
1
2
0
0
0
1
2
0
2
1
0
2
2
1
2
2
2
1
1
1
1
1
1
1
1
1
0
0
1
0
0
2
1
3
1
0
1
1
1
1
0
2
1
1
1
0
1
1
1
0
1
1
1
0
1
1
1
2
1
2
1
2
2
0
0
1
1
0
0
1
1
0
0
0
0
0
1
1
2
1
0
1
2
2
0
2
0
0
0
0
0
1
1
1
1
2
1
2
0
0
1
1
1
1
1
2
2
1
1
0
1
2
1
0
0
2
0
1
0
1
0
0
1
1
0
1
1
1
1
0
0
1
0
1
0
2
2
1
0
1
1
2
2
0
2
2
1
3
1
1
1
0
1
0
5
1
0
0
1
1
0
0
0
2
0
1
1
2
2
1
0
1
0
2
2
1
1
1
0
0
0
1
0
2
1
0
1
1
1
0
1
1
0
1
1
2
0
0
1
1
2
1
2
0
1
2
1
0
2
1
1
0
0
2
0
1
0
1
0
1
0
2
1
1
1
0
2
0
1
0
1
2
1
1
1
1
0
0
1
1
1
1
0
0
2
1
1
1
0
2
0
0
0
1
1
1
2
1
1
1
0
0
0
1
2
1
0
1
0
0
0
1
0
0
2
1
1
2
1
2
0
0
0
1
1
0
2
2
0
1
2
1
1
0
0
1
1
2
2
2
0
0
1
1
2
1
1
0
2
2
1
1
1
1
1
1
1
2
0
1
1
1
1
1
0
2
0
1
2
0
1
2
2
1
1
0
2
1
1
2
3
1
0
2
0
1
2
0
0
2
0
0
0
1
1
1
2
0
1
0
2
0
1
2
0
1
2
1
1
0
1
0
2
1
2
1
1
1
0
0
2
2
1
1
1
0
2
2
0
0
0
0
3
1
2
2
1
2
0
2
0
2
0
0
1
0
0
0
1
1
1
1
2
1
1
2
1
0
0
2
0
1
2
1
1
2
1
1
0
1
2
1
1
0
0
1
0
1
1
1
0
0
0
1
1
0
1
0
2
0
1
1
0
1
1
1
1
0
2
2
1
0
0
2
2
1
0
0
2
0
2
0
1
0
0
6
0
1
1
0
1
0
1
1
0
0
1
2
1
4
1
1
0
1
2
1
1
1
1
1
2
2
2
1
3
1
1
0
1
1
1
2
1
0
0
1
0
0
2
0
0
0
2
0
1
0
0
1
1
1
1
2
4
0
1
0
1
0
1
1
2
2
1
4
1
2
2
0
0
1
2
1
1
1
1
1
2
0
2
1
1
1
0
0
0
1
1
0
2
1
2
1
2
0
1
2
2
1
2
0
1
0
2
1
2
1
0
0
1
0
0
2
0
0
0
0
2
1
1
1
0
1
0
1
1
2
1
0
2
2
1
1
1
2
1
1
1
1
0
0
1
1
2
2
2
2
0
2
1
0
1
1
1
0
1
1
2
0
1
1
2
1
1
1
0
0
1
0
1
1
0
1
1
2
0
2
1
3
0
1
0
1
1
2
0
1
2
0
1
0
3
0
1
1
2
1
2
2
1
1
0
1
1
2
2
0
1
1
1
1
0
0
1
0
1
1
0
0
1
1
0
2
0
1
2
0
1
0
0
1
0
0
2
1
2
0
1
0
0
2
0
0
1
1
1
0
1
2
3
0
1
1
1
1
2
1
1
2
2
1
2
1
1
1
0
1
1
1
1
1
1
1
0
1
1
0
0
1
0
0
0
0
0
2
2
1
1
1
0
2
2
1
2
1
1
0
2
2
0
1
1
0
0
1
2
1
1
0
1
1
1
0
0
1
1
1
2
0
0
1
0
1
1
1
1
0
2
2
1
1
0
2
2
1
0
1
0
0
1
0
2
0
0
0
0
2
2
1
1
0
2
0
1
0
1
3
0
1
2
1
1
0
1
0
1
1
2
1
1
1
1
1
2
0
0
1
1
2
0
1
2
1
0
1
1
0
0
2
0
0
2
1
1
1
1
1
0
2
0
0
0
0
1
1
1
0
1
1
1
1
1
1
1
0
1
2
0
3
2
0
1
1
1
1
1
0
0
0
0
0
0
0
0
2
2
1
1
2
1
1
1
2
2
1
1
1
1
1
2
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
1
1
2
1
0
0
1
0
1
2
0
1
0
1
2
2
2
1
2
2
0
0
2
2
0
0
0
1
1
1
1
1
1
0
0
1
1
2
1
1
1
1
1
0
2
2
0
0
0
1
2
1
1
1
1
0
2
0
0
0
1
0
2
0
1
1
0
1
1
7
0
0
1
2
0
1
1
0
1
2
1
1
1
2
1
0
0
2
1
1
2
0
1
1
1
1
1
2
1
0
2
0
1
0
0
2
1
1
0
0
0
0
1
1
1
1
1
1
0
2
0
0
0
0
2
0
2
0
1
2
1
0
2
0
2
2
0
2
0
0
2
0
0
0
1
1
0
1
0
2
0
1
1
0
2
2
1
1
1
1
1
1
1
1
1
1
2
2
0
0
2
1
2
1
1
1
2
1
1
1
1
0
1
0
1
0
2
1
1
1
1
1
1
0
2
0
0
2
2
0
0
1
0
0
2
1
2
2
1
4
0
1
1
1
1
0
0
2
1
1
2
2
1
0
1
2
2
1
0
1
0
0
1
2
1
1
0
0
1
1
1
1
0
0
2
0
1
2
2
2
1
1
1
0
0
2
1
0
0
0
0
0
2
2
1
1
1
1
1
0
0
1
0
0
1
1
1
2
0
0
2
1
1
1
0
2
0
2
2
0
2
1
1
2
0
2
0
4
2
1
1
0
2
1
0
0
2
0
0
0
1
1
1
0
1
1
0
2
1
0
0
4
0
0
2
1
1
0
1
0
2
1
1
1
0
0
1
2
1
1
1
1
0
2
1
0
1
1
1
0
1
0
1
0
2
2
1
0
1
2
0
1
0
0
1
0
1
1
0
0
2
1
1
2
2
1
1
1
1
1
2
0
2
1
1
1
1
1
1
1
0
1
0
0
1
0
1
1
0
1
2
1
2
1
1
1
0
0
0
0
1
1
0
1
1
1
2
1
0
1
1
1
2
1
0
1
1
2
2
1
0
0
0
0
2
1
2
1
1
0
1
0
1
0
1
0
2
2
1
1
3
0
1
1
2
1
2
1
1
0
0
1
1
1
1
2
0
3
0
2
0
0
1
1
1
2
1
1
1
2
1
1
2
0
2
2
0
1
1
0
0
1
1
2
1
0
1
1
1
1
1
2
0
0
1
0
2
1
0
2
0
1
2
0
0
0
0
0
0
0
1
2
1
3
1
1
1
1
2
0
0
0
0
1
0
2
2
2
0
1
1
1
0
1
0
6
0
1
1
2
0
1
1
1
1
1
0
1
1
0
1
0
0
1
1
0
1
2
2
0
1
1
0
1
2
1
0
2
2
1
1
2
1
0
2
2
0
1
1
2
1
1
1
0
0
1
1
1
1
1
2
2
2
0
1
0
0
0
1
0
1
1
1
0
0
1
1
1
2
1
1
1
0
1
1
0
1
2
1
1
0
2
2
1
0
1
1
2
1
0
0
0
0
1
1
0
1
3
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
0
0
1
0
1
2
1
1
1
1
1
2
1
1
1
1
1
1
2
2
1
2
0
1
0
1
0
1
0
1
2
1
0
1
1
1
1
1
1
2
0
2
1
1
1
1
1
1
2
2
0
0
1
0
0
0
1
0
1
1
0
3
2
1
1
1
0
1
2
0
1
1
2
1
1
2
1
2
1
1
0
1
0
0
1
0
2
2
0
1
1
0
1
2
1
2
1
0
0
1
0
0
1
1
0
2
1
1
1
2
2
0
1
1
0
1
0
1
0
0
1
2
1
1
0
1
0
2
0
1
1
2
2
2
0
1
1
1
0
2
1
1
2
0
2
1
0
0
0
1
1
2
2
1
2
0
0
1
1
0
1
0
0
0
1
1
1
1
1
2
0
0
1
1
1
0
0
0
1
0
1
0
0
2
1
0
2
1
1
2
2
2
1
0
0
2
2
1
0
1
1
1
1
0
0
1
0
1
2
0
1
1
0
1
0
2
2
2
1
3
1
2
1
1
0
1
0
1
1
0
1
1
0
2
1
0
1
2
1
1
2
3
1
2
0
1
0
1
1
0
1
0
1
2
2
1
2
2
1
1
1
2
2
1
1
0
1
1
2
0
1
2
1
1
1
1
1
1
1
0
0
0
0
0
1
1
0
0
1
1
1
1
0
1
1
2
0
2
1
0
0
1
2
0
0
2
0
1
1
1
1
0
1
1
2
1
1
1
2
1
2
1
0
1
0
1
1
0
2
0
1
0
1
0
0
1
1
1
1
2
1
1
2
1
1
1
2
2
1
2
1
1
1
1
0
0
0
1
1
0
0
1
0
0
1
1
1
2
1
0
0
1
0
1
1
1
3
2
0
3
1
0
1
0
1
1
0
0
2
1
0
2
2
0
1
2
0
0
0
0
0
1
1
0
0
1
1
0
2
1
0
1
1
0
1
2
2
2
1
2
2
0
1
2
1
1
1
1
0
1
0
1
2
0
0
2
0
1
1
0
1
1
2
1
1
0
1
1
1
1
0
0
0
1
1
1
1
0
2
2
1
1
0
1
2
2
0
1
1
0
1
1
1
0
2
0
1
1
1
0
1
1
2
1
1
1
0
2
1
1
0
1
0
0
2
1
0
1
0
1
1
0
1
1
2
1
1
1
2
1
1
1
2
1
0
2
0
2
1
1
2
0
1
2
0
0
2
1
0
2
4
2
0
1
1
2
0
1
1
0
0
3
1
0
0
0
1
1
0
2
0
1
0
1
0
0
1
1
2
1
0
1
1
0
2
1
1
1
1
1
0
1
1
1
4
1
0
1
2
0
0
0
1
0
0
0
1
1
1
0
0
0
0
1
1
2
2
2
0
0
1
2
1
0
2
0
2
1
2
0
0
0
0
2
2
4
1
1
0
2
0
0
2
2
0
0
0
0
2
2
1
1
1
1
0
0
1
1
2
0
1
1
2
1
1
1
0
1
0
1
5
0
1
1
1
0
1
1
1
1
0
2
1
0
0
0
1
1
1
0
1
0
2
0
0
1
2
0
2
0
1
1
2
1
1
0
0
0
2
1
0
3
1
0
1
1
1
0
1
1
1
2
1
0
2
1
1
0
1
0
2
1
5
1
2
0
0
1
1
1
0
4
1
0
1
0
2
2
0
0
1
2
1
1
1
0
0
1
1
1
0
2
0
1
0
2
2
0
1
0
1
0
3
2
1
3
1
2
1
1
0
0
0
0
2
0
0
0
1
1
1
2
1
2
0
2
2
1
0
0
1
1
2
1
0
0
2
0
2
2
0
1
2
0
0
2
1
1
2
1
2
0
1
1
1
1
1
1
0
0
0
2
1
1
1
0
0
2
2
2
0
3
1
0
2
1
0
1
0
0
2
1
0
0
3
1
1
1
1
1
4
2
1
1
1
2
1
1
0
1
1
0
1
2
1
0
2
3
1
1
1
0
1
2
2
0
0
1
0
1
0
2
2
1
1
0
1
2
1
2
1
0
2
0
0
2
2
1
1
1
2
0
1
1
1
1
1
1
1
0
1
0
2
0
1
0
0
1
0
0
0
3
0
0
0
0
0
1
2
0
1
0
1
2
0
1
2
1
2
0
2
2
0
1
1
0
0
1
0
2
2
1
0
1
0
1
2
1
1
0
0
2
1
0
2
0
0
0
2
2
0
1
1
0
0
1
0
1
0
1
1
0
1
1
2
2
1
1
2
0
1
1
0
2
0
2
0
0
2
1
0
1
2
0
1
2
1
2
0
0
2
0
0
1
0
1
1
0
1
1
0
1
2
1
0
0
1
2
0
2
1
0
0
2
2
1
0
0
1
2
1
1
2
1
0
2
1
1
1
2
0
1
2
1
1
0
1
1
0
1
0
1
1
0
3
0
0
0
0
1
1
0
2
2
1
2
1
0
2
0
1
0
0
1
0
1
1
1
1
1
0
1
0
1
2
1
0
2
0
1
1
2
1
1
0
1
2
1
2
1
0
1
1
0
1
1
2
0
1
0
1
2
0
2
1
1
0
1
0
2
0
1
1
2
1
1
0
1
2
0
2
2
1
2
0
1
0
1
1
1
2
2
2
0
1
2
3
0
1
2
1
1
1
2
1
0
1
0
1
1
1
2
0
1
0
0
2
2
1
2
1
1
1
0
1
2
1
1
1
2
1
2
0
1
1
2
1
0
1
1
1
0
2
0
2
1
0
0
1
1
1
1
0
1
1
2
1
0
0
0
1
0
2
1
2
1
1
1
0
1
2
1
0
1
1
0
0
0
1
1
2
0
1
0
1
0
2
2
2
2
1
2
0
1
1
0
1
0
1
1
1
2
2
0
0
0
1
0
2
1
1
0
1
1
0
1
1
2
1
2
1
1
0
0
1
1
2
2
1
1
0
1
0
0
1
0
0
1
1
0
2
1
1
2
1
0
0
0
1
0
1
2
1
1
1
1
1
1
0
0
0
1
1
1
0
1
0
2
1
0
0
0
1
0
1
2
2
0
1
0
2
0
1
1
1
1
0
0
1
1
0
1
1
0
2
2
1
2
1
2
2
1
2
0
0
0
0
0
1
1
1
2
1
2
1
0
0
1
2
1
0
1
0
2
1
1
2
1
1
1
1
2
1
0
0
0
0
0
0
0
0
2
1
3
1
0
1
2
0
0
1
1
2
0
2
2
1
1
0
2
2
3
1
0
1
2
1
1
1
1
0
2
0
0
0
1
2
1
1
1
0
1
2
1
0
1
0
1
1
0
1
2
1
2
1
0
0
1
2
2
1
1
0
0
1
1
2
2
1
0
1
2
0
0
1
1
1
1
3
1
0
2
1
1
3
1
1
2
1
2
0
1
2
2
0
0
0
2
1
1
1
1
2
2
1
2
2
1
0
1
0
2
1
1
0
0
2
1
0
1
1
1
2
1
1
2
2
1
2
0
1
1
1
0
2
0
2
1
1
1
2
2
1
1
1
2
0
1
2
1
1
0
1
2
1
2
0
2
1
2
2
1
0
1
1
2
2
1
1
1
1
0
1
1
1
0
1
2
0
0
1
1
2
2
0
0
0
4
0
1
0
1
0
1
0
0
0
1
1
2
3
0
1
2
1
0
3
2
1
0
0
1
0
1
2
1
1
0
2
0
1
0
0
0
1
0
2
1
0
0
1
0
1
1
1
2
1
1
0
0
0
1
2
1
1
2
2
1
0
1
1
1
2
1
0
1
3
2
1
0
2
2
1
1
1
0
2
1
1
1
1
2
1
1
1
1
0
2
2
1
1
1
1
1
1
0
1
1
2
1
0
1
2
1
1
2
1
2
0
1
2
1
0
1
1
1
1
0
2
0
0
1
0
1
3
0
1
1
0
1
1
0
0
1
1
0
0
2
0
1
1
0
1
1
0
0
0
0
1
0
1
0
1
0
0
1
1
0
0
1
0
1
0
2
2
1
1
1
1
1
2
1
2
0
1
2
1
1
2
1
1
0
0
0
0
0
1
1
1
1
0
1
0
2
1
0
2
0
1
2
1
2
0
0
1
0
1
2
0
1
0
1
2
0
1
1
0
0
1
1
2
1
1
2
3
0
0
2
0
0
2
1
1
0
2
0
2
0
1
1
0
2
1
0
0
1
0
0
0
2
1
2
1
2
1
0
1
3
0
2
1
1
2
0
1
2
1
2
2
1
1
0
1
1
1
1
0
0
0
1
1
3
0
1
1
2
2
0
2
1
0
1
1
1
1
2
0
0
0
0
2
2
0
0
0
1
2
2
2
0
1
0
1
1
1
1
1
1
1
1
0
0
1
1
0
1
0
1
3
2
1
2
1
2
1
2
1
2
0
2
1
0
0
0
2
0
1
1
1
1
2
2
1
1
0
1
1
1
1
0
0
0
0
1
0
1
0
0
3
0
0
2
1
1
1
2
2
0
1
1
0
1
2
1
0
0
0
0
1
0
2
2
0
1
1
0
0
0
2
2
1
2
0
0
1
1
1
1
1
1
2
1
1
1
1
2
0
0
2
0
0
0
0
1
0
1
2
0
1
2
1
1
2
2
1
2
0
0
1
1
0
0
1
2
1
1
2
1
1
0
0
0
0
2
0
1
1
1
1
0
0
2
2
0
1
1
0
0
1
2
1
2
1
1
2
0
0
1
0
0
0
1
0
1
1
1
1
1
0
0
0
2
3
1
0
1
1
1
0
2
2
1
1
1
1
0
1
1
0
0
1
4
0
0
1
0
1
0
1
1
0
1
0
0
2
2
0
1
0
0
0
1
1
2
2
1
2
1
0
1
1
0
2
0
1
1
1
2
2
1
0
0
0
1
1
0
1
2
0
1
0
1
1
2
2
1
2
1
0
0
0
1
1
0
4
1
0
1
0
2
0
2
2
2
1
2
0
1
0
2
2
1
1
2
1
0
2
0
0
0
1
1
0
1
0
1
0
0
1
0
2
1
0
2
0
1
0
0
1
0
1
2
0
1
0
1
1
0
0
1
0
1
1
0
1
2
1
1
1
0
0
1
1
1
2
0
1
2
2
1
1
1
2
1
2
1
1
0
2
2
1
0
1
0
0
0
1
0
2
1
1
1
2
1
0
1
1
1
2
1
2
0
1
1
1
1
1
0
2
1
1
1
2
1
1
2
2
0
2
3
2
2
1
1
2
0
2
1
2
1
2
1
1
1
1
1
1
0
0
1
2
2
1
1
1
0
0
1
2
1
1
1
2
1
1
1
1
2
0
0
2
2
0
0
0
0
2
1
0
1
2
1
1
0
0
2
2
1
2
0
1
1
0
0
1
1
1
1
2
2
1
1
1
0
1
1
1
1
1
2
1
1
2
2
1
0
2
1
0
2
0
1
2
1
0
0
2
0
0
0
0
0
0
1
0
2
1
2
0
2
1
1
0
0
1
1
2
0
0
0
1
2
0
1
1
1
2
1
1
1
2
2
0
2
0
0
1
1
4
1
0
0
2
1
1
1
1
0
0
1
0
1
2
1
2
1
2
1
0
0
2
0
2
3
2
0
0
1
1
1
0
1
0
0
2
1
0
1
1
1
1
1
0
1
2
2
1
1
0
2
1
0
2
1
2
2
2
1
1
0
2
1
1
0
1
2
0
0
1
1
1
0
1
1
1
0
0
1
2
0
2
0
2
2
1
1
1
1
1
1
2
0
1
0
0
0
2
2
1
1
0
0
0
0
2
0
2
1
1
2
0
1
2
1
2
1
1
0
1
2
0
1
0
2
1
1
1
1
1
2
0
2
2
0
0
0
2
1
1
0
2
1
2
0
1
0
1
1
0
1
0
1
0
0
1
1
1
1
1
0
0
2
1
1
0
0
1
0
1
1
1
0
1
2
0
1
1
2
0
1
1
0
0
1
1
0
1
0
1
1
2
1
1
0
1
1
1
1
0
1
2
1
2
0
1
1
1
1
1
1
1
0
1
1
2
1
2
2
1
2
0
0
0
1
1
2
1
1
1
0
0
1
1
1
0
1
1
1
0
2
1
1
2
1
1
2
1
0
2
2
1
1
0
2
0
1
1
1
1
1
1
0
0
2
1
2
0
1
1
1
1
1
1
1
1
1
0
2
2
0
2
1
2
0
0
1
1
1
1
0
0
1
0
1
1
1
2
2
2
0
0
1
2
0
2
1
0
0
2
7
1
1
1
0
2
2
1
2
0
2
2
0
1
2
1
2
1
1
2
0
1
2
0
1
0
2
2
0
1
1
0
1
1
1
1
0
1
0
0
1
1
1
1
1
1
0
3
2
0
0
2
0
2
1
2
2
1
1
1
2
0
1
1
2
1
1
0
0
0
2
1
1
0
2
1
2
1
1
2
1
1
1
2
1
1
1
2
1
0
1
1
1
1
0
0
1
2
1
1
1
2
1
1
2
0
0
2
1
1
0
2
1
1
0
1
1
1
1
0
0
1
2
0
1
2
0
2
0
0
1
0
0
1
1
1
1
1
0
0
2
1
2
0
2
5
0
2
0
1
0
1
2
1
3
0
1
0
0
1
1
2
1
2
1
2
1
1
2
3
1
1
2
0
0
1
0
0
0
1
0
1
1
0
1
1
1
2
1
0
1
2
1
2
1
0
1
0
1
2
1
1
1
0
0
2
2
1
1
2
2
0
1
2
2
1
1
1
1
2
0
0
2
2
1
0
1
0
2
1
0
2
2
0
0
1
0
1
0
1
1
0
1
1
0
0
1
1
0
1
0
2
1
2
0
0
1
1
1
1
1
1
1
0
0
2
3
0
1
0
0
0
0
2
0
1
1
1
1
1
1
2
1
2
0
0
1
2
1
2
1
0
2
2
0
0
2
1
1
2
2
1
2
1
2
0
1
2
1
0
0
2
0
1
1
0
0
0
0
1
2
0
1
1
2
1
2
2
2
0
2
2
1
0
0
0
0
1
1
2
1
0
1
1
2
0
1
0
0
2
0
1
1
0
0
2
1
1
1
0
0
1
2
0
1
0
1
2
1
0
1
0
1
0
1
1
0
0
0
1
1
1
1
2
0
0
2
0
1
1
0
0
1
0
1
1
0
2
0
0
1
0
0
1
1
0
1
0
2
2
0
0
2
0
1
1
0
1
0
2
1
0
0
1
1
0
1
2
1
1
1
2
0
0
2
2
0
1
0
0
2
0
2
2
0
1
0
1
1
2
1
0
0
1
1
1
0
2
1
0
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
0
0
0
1
2
2
1
1
1
2
2
0
1
0
1
1
0
2
0
1
1
2
1
0
1
1
2
2
1
1
1
3
0
1
0
1
1
0
0
1
0
2
1
2
1
1
0
1
1
0
2
1
1
1
2
0
0
0
0
0
1
1
0
0
2
2
1
1
1
2
0
0
1
0
0
1
1
1
0
1
2
2
0
0
1
1
2
2
0
3
2
0
0
1
0
0
0
1
1
0
1
1
1
2
1
1
0
3
1
0
1
1
0
0
2
0
1
1
1
0
1
0
2
1
2
1
1
2
0
1
1
1
0
2
1
0
1
0
0
2
2
2
1
1
1
0
0
1
2
1
0
1
1
1
2
1
0
2
0
2
2
1
0
1
2
2
1
0
1
0
0
2
0
1
1
1
1
1
1
0
0
0
2
1
0
1
0
1
0
1
1
0
1
0
0
0
1
1
2
0
1
1
0
1
0
1
1
0
1
0
0
0
0
1
0
0
0
1
0
0
1
1
2
0
0
2
1
1
1
0
1
0
0
1
1
0
1
1
2
1
1
0
1
1
2
1
2
2
0
0
1
1
1
0
2
2
1
1
1
1
1
1
0
0
1
2
2
0
1
1
4
0
0
0
0
1
1
1
1
2
1
1
1
0
1
0
1
1
2
0
1
0
1
1
1
1
2
1
1
0
0
2
0
1
2
0
2
1
2
1
0
1
0
1
1
1
0
0
0
1
1
1
1
0
1
1
2
1
1
0
0
2
1
0
0
1
1
0
1
0
1
0
2
1
1
1
2
1
2
0
1
1
0
0
1
1
0
1
1
2
0
1
0
2
0
0
0
1
1
1
1
1
0
1
1
0
1
1
1
0
0
0
0
1
1
1
1
1
2
0
0
0
0
1
0
0
0
0
2
1
1
0
0
1
1
2
1
0
1
1
2
1
2
1
1
1
2
1
1
1
0
1
1
2
1
1
2
0
1
1
1
2
1
0
1
2
1
0
2
0
1
0
1
1
2
1
0
1
0
2
1
0
0
0
1
1
1
1
1
0
1
0
1
0
2
1
1
3
0
0
2
1
2
0
1
2
0
1
0
1
0
2
1
0
1
1
1
0
2
1
1
0
2
0
2
1
0
1
1
1
1
2
1
2
1
1
1
1
1
2
0
1
2
1
0
0
2
0
2
1
1
1
1
1
0
0
1
1
0
1
1
1
1
2
0
1
0
0
1
2
0
1
0
1
1
0
1
1
1
2
2
0
1
1
2
2
2
1
1
1
1
1
1
0
2
1
1
0
3
2
2
0
2
1
0
1
2
1
1
1
0
2
2
2
0
0
2
0
1
1
1
2
1
0
1
1
0
0
1
0
0
1
1
0
1
1
0
1
0
1
0
1
1
1
1
0
0
1
1
0
1
0
1
1
2
1
1
1
2
4
2
0
1
1
1
1
0
2
0
1
0
0
1
0
2
1
1
0
2
0
2
2
0
2
1
1
1
2
0
2
2
2
0
0
0
0
2
1
1
0
0
1
1
0
1
2
1
0
0
1
0
1
0
0
0
1
0
0
1
0
1
0
1
0
0
1
0
1
2
1
2
0
0
0
2
1
2
2
2
0
0
1
1
1
2
1
2
2
0
0
0
0
2
2
0
1
2
2
2
1
0
2
2
1
0
2
0
0
0
1
1
1
3
1
1
1
1
1
0
1
1
1
0
2
0
1
1
0
1
1
0
3
1
1
1
1
1
1
1
0
0
2
2
0
1
1
0
1
1
1
1
0
1
0
1
1
0
1
2
2
2
1
1
1
2
1
1
2
3
0
1
0
2
2
0
2
1
0
0
2
1
1
0
1
0
0
2
1
2
1
2
0
0
0
1
1
1
1
2
1
0
1
1
1
0
0
0
0
1
0
2
1
2
0
1
1
0
1
1
3
2
1
0
2
2
1
6
1
0
1
1
0
2
2
0
1
2
1
0
1
2
1
2
0
1
1
1
1
1
1
2
0
0
1
0
2
1
1
2
2
1
1
1
1
0
2
0
2
2
2
0
1
0
2
1
1
1
0
0
0
0
1
1
4
1
1
2
0
1
0
2
0
0
0
2
2
1
1
0
1
0
2
1
1
2
1
2
2
2
1
0
2
1
1
1
1
1
1
1
2
0
3
0
2
0
2
0
2
1
0
2
2
0
0
0
2
5
0
1
2
0
2
2
0
1
2
1
2
1
1
0
2
1
1
1
0
2
2
0
1
10
1
1
1
1
0
1
1
1
0
0
1
1
0
0
0
2
3
1
0
2
1
1
1
1
0
0
0
1
1
0
1
0
1
2
2
0
0
0
0
0
1
1
0
0
0
1
1
1
1
0
1
2
1
1
1
0
2
0
1
0
0
1
1
0
0
0
0
2
2
0
0
1
1
0
0
1
1
1
0
0
1
0
1
2
1
3
1
1
2
0
2
1
1
0
1
2
2
1
1
0
0
2
2
0
1
1
2
1
1
1
0
2
1
1
1
1
1
2
1
0
0
2
1
0
1
0
2
2
2
0
2
2
1
1
0
0
1
0
1
1
0
2
1
2
1
2
1
2
1
2
1
1
0
0
1
0
0
1
1
0
0
1
1
1
0
0
2
0
0
1
2
0
1
2
0
1
1
1
1
0
2
1
1
0
1
1
2
0
0
0
1
1
2
0
2
1
2
0
1
1
0
1
2
2
3
1
1
1
1
0
1
1
1
0
0
1
1
0
0
2
1
1
2
0
2
1
2
1
1
0
1
1
1
1
1
1
1
1
0
1
0
0
1
0
2
2
2
0
0
0
1
2
1
0
1
1
1
0
1
0
0
1
1
1
0
1
1
0
2
1
0
1
2
0
2
2
0
1
0
2
1
1
1
1
0
2
1
1
0
1
1
2
0
1
0
1
2
1
2
1
1
2
1
1
0
0
1
1
1
2
1
0
1
1
1
2
0
1
2
1
2
2
1
1
1
2
2
3
2
1
1
2
0
0
0
2
2
1
1
0
0
1
0
0
2
0
0
1
0
2
0
2
0
0
0
0
1
1
1
1
2
0
0
0
0
1
0
0
1
3
1
0
0
0
0
2
0
1
0
0
0
1
2
1
1
0
2
1
1
1
1
1
0
1
2
1
0
1
2
2
1
0
1
0
0
2
0
1
1
0
1
1
1
1
2
0
1
1
0
0
0
0
1
0
0
2
0
1
0
1
2
2
1
2
2
1
0
2
0
2
1
1
1
0
1
1
0
1
0
0
1
1
1
1
0
1
2
1
1
0
0
1
1
2
1
1
2
0
2
0
1
1
0
0
0
1
1
0
0
2
2
1
1
0
0
2
0
3
0
1
0
0
1
1
0
1
1
0
0
0
0
0
0
1
2
2
1
0
1
1
0
0
1
1
0
0
1
0
0
1
1
1
0
1
1
0
0
0
2
0
0
2
0
0
1
2
0
1
2
0
1
2
1
1
2
0
2
1
2
0
2
1
2
1
1
1
2
1
2
1
0
1
2
0
1
1
1
1
0
0
2
1
1
1
2
0
0
2
0
0
1
1
2
0
0
1
0
1
0
1
0
1
1
1
2
0
1
0
2
0
1
2
2
2
1
1
0
1
1
1
0
2
1
1
0
1
0
0
1
0
0
1
0
0
2
1
1
1
1
1
1
1
2
1
1
1
0
0
0
1
1
1
0
1
2
0
1
1
1
2
0
1
0
2
1
2
1
1
1
0
1
0
1
2
2
2
1
1
1
0
0
1
1
2
1
0
0
1
1
1
1
1
2
0
2
1
0
1
1
1
2
1
0
1
1
0
0
2
2
0
1
2
0
1
1
1
1
0
1
0
2
1
1
0
2
0
1
1
1
2
1
1
0
1
1
1
1
0
0
0
1
0
1
1
2
2
1
2
0
1
2
2
1
0
1
0
2
1
1
1
1
1
2
1
1
1
1
1
1
1
0
1
0
0
1
2
1
2
1
2
0
1
0
1
1
1
0
2
1
1
2
0
1
1
1
0
1
0
0
2
0
2
1
1
0
0
0
1
0
1
1
1
1
0
1
0
0
1
0
0
0
0
2
2
0
1
1
2
2
0
2
0
0
2
1
2
1
2
1
0
1
0
0
0
0
0
0
0
0
0
0
1
2
2
1
1
0
0
2
0
0
2
1
1
1
0
2
2
1
1
4
1
0
2
1
1
2
3
0
1
2
0
1
0
1
3
1
0
0
1
1
1
0
1
1
1
1
0
2
2
1
1
2
1
0
0
1
1
1
1
0
1
2
0
2
1
0
0
2
1
0
0
1
1
1
0
2
1
1
2
2
0
0
3
0
2
0
2
2
2
2
2
0
1
1
1
0
1
0
1
2
0
0
0
2
0
1
1
1
0
1
0
1
0
1
0
1
2
0
0
1
1
2
1
0
0
0
1
1
1
0
1
0
0
1
1
2
0
1
1
1
2
0
1
1
0
1
0
2
0
0
2
2
0
0
2
1
0
2
2
0
2
0
2
1
0
0
0
2
0
0
1
1
0
1
2
2
0
1
0
2
1
1
0
1
0
2
1
1
1
0
0
0
0
0
0
1
1
0
1
0
1
0
2
0
1
2
2
2
1
2
0
2
0
2
1
2
0
0
1
1
1
0
0
0
1
2
1
1
2
0
1
0
2
0
0
0
0
2
2
0
0
1
1
2
1
1
2
1
1
2
1
1
0
1
2
0
1
0
2
1
0
1
0
1
1
1
0
1
0
3
2
0
1
1
0
2
1
0
1
1
1
1
0
1
2
1
0
0
2
0
2
1
0
0
0
1
0
0
0
0
1
1
2
1
1
2
0
1
1
0
1
2
2
0
1
3
1
2
1
1
1
2
2
1
0
2
1
1
0
1
0
0
2
1
0
1
0
2
0
1
1
0
4
1
1
2
1
1
2
1
2
1
1
1
0
1
1
0
2
0
2
2
1
2
1
1
0
0
1
0
0
1
1
0
0
1
1
2
1
1
1
2
0
0
1
0
0
1
2
1
2
0
2
0
2
0
2
1
1
2
1
2
1
1
1
0
1
2
1
2
0
2
2
1
0
0
1
0
2
1
1
1
1
2
1
1
1
1
1
0
6
1
1
1
0
2
1
1
2
1
1
1
2
1
0
0
1
2
0
2
2
1
0
1
2
1
2
0
1
2
2
1
0
0
1
1
1
3
1
1
0
1
1
1
1
1
1
0
0
1
1
1
2
0
1
0
0
2
0
0
0
0
2
0
2
0
1
2
1
1
0
0
0
1
3
0
0
1
0
2
2
0
1
0
2
2
0
1
2
1
1
1
0
0
2
1
2
1
0
2
1
2
1
0
1
2
1
1
1
1
1
0
2
0
1
1
1
1
0
0
0
0
0
0
2
0
0
1
0
2
1
1
2
3
0
0
1
1
0
0
2
0
1
2
0
1
2
1
0
0
2
2
1
0
1
2
0
1
2
2
0
3
1
2
1
1
0
2
1
1
1
1
2
0
1
2
1
1
0
1
2
1
1
0
2
1
0
1
2
2
0
3
1
1
1
2
1
1
1
1
0
1
2
0
1
0
1
0
1
1
1
0
2
0
1
1
1
1
0
1
0
1
1
1
1
1
0
1
0
1
1
0
0
2
2
1
0
1
2
2
1
0
2
2
6
0
1
0
1
1
0
1
0
1
1
1
0
2
0
0
2
2
0
2
0
0
0
1
2
2
1
2
0
1
2
0
1
0
0
1
2
1
0
2
0
1
1
2
0
1
2
0
2
1
1
0
1
1
2
0
1
2
0
1
0
0
1
0
1
2
1
1
0
0
0
0
1
1
2
2
2
2
1
4
0
2
1
1
1
1
0
1
1
1
1
2
1
0
0
1
0
0
0
3
1
2
1
2
1
0
1
2
0
1
2
0
0
2
1
2
2
1
1
2
0
1
0
0
2
2
0
2
0
1
2
2
1
2
0
1
1
0
1
0
0
1
1
1
2
1
0
1
2
1
0
0
2
1
3
0
3
1
2
1
1
0
1
1
0
2
1
0
0
1
1
2
0
1
1
0
2
0
0
0
2
2
1
1
0
1
0
0
1
2
2
1
1
1
1
2
1
0
0
1
0
0
0
2
0
0
0
1
2
1
0
0
0
2
1
0
1
1
2
1
1
2
1
0
2
1
2
2
2
0
1
1
0
0
5
1
2
1
0
3
1
0
2
1
1
0
2
0
2
1
1
1
2
0
1
1
0
1
1
1
0
0
1
0
0
2
0
2
1
2
1
1
2
1
1
0
1
2
0
1
1
0
0
0
2
2
1
2
2
1
0
0
1
0
2
1
1
2
2
0
2
1
1
2
1
0
2
0
1
1
1
0
2
2
2
0
1
0
0
0
2
2
1
2
2
0
0
1
1
0
0
1
1
0
1
2
0
1
0
1
0
1
1
0
2
1
0
1
1
0
1
2
1
1
1
0
2
1
1
1
0
1
2
0
2
0
2
0
1
1
1
1
1
0
1
1
1
0
0
2
1
1
1
2
0
0
1
1
2
1
1
0
0
1
0
1
1
0
0
1
1
1
0
0
2
1
2
0
1
1
1
1
3
2
1
1
1
0
0
2
1
0
2
2
2
1
1
0
1
2
1
2
2
1
1
2
1
1
1
2
2
2
1
1
1
2
1
2
0
1
1
2
1
2
1
1
1
0
1
1
1
1
2
2
1
2
1
1
1
1
1
0
1
1
2
0
1
0
2
0
0
1
1
2
1
0
1
0
0
1
2
1
2
0
1
1
1
1
1
1
1
1
0
2
0
1
0
1
1
1
0
0
1
2
0
0
2
2
1
0
1
2
1
1
0
0
1
0
1
0
1
1
0
1
2
3
0
1
1
2
0
2
0
2
2
0
1
2
1
1
1
1
0
0
0
0
1
0
2
2
2
0
1
1
0
2
0
0
1
2
2
1
0
0
2
0
1
2
1
0
2
1
0
1
1
1
1
2
1
2
1
2
2
1
1
1
1
0
2
1
1
1
0
1
1
0
1
1
1
1
2
0
1
2
0
2
2
0
1
2
2
2
2
0
1
1
2
1
2
1
1
1
0
1
1
1
2
0
1
0
1
0
0
2
0
1
1
0
1
0
1
1
1
1
1
0
2
1
0
2
0
0
0
2
1
0
0
1
2
0
0
2
1
0
0
1
0
1
0
0
2
1
1
1
1
0
0
1
0
2
0
2
0
1
1
0
2
0
1
0
1
1
1
0
1
0
1
0
1
0
0
1
0
2
1
0
0
0
0
0
1
1
0
0
0
1
1
1
2
0
2
1
0
1
1
0
0
0
2
1
0
1
1
1
2
2
1
1
1
0
0
1
2
1
1
1
2
2
0
0
0
0
2
1
2
1
1
1
0
2
1
1
1
0
2
1
1
1
1
1
2
1
2
0
0
1
0
2
0
1
1
1
0
1
1
1
2
0
0
0
0
1
1
1
0
1
1
1
0
1
0
1
1
1
1
1
1
0
0
1
0
1
1
0
1
1
1
1
2
3
0
1
1
2
1
1
1
1
1
0
1
1
1
2
1
2
1
1
1
2
0
2
0
2
1
2
1
0
2
2
0
1
2
1
0
1
1
1
1
0
0
0
1
0
1
2
0
1
1
1
1
2
2
1
0
2
1
1
1
1
2
3
0
1
1
1
2
1
2
1
0
2
0
0
1
3
0
1
1
0
1
1
2
1
1
1
1
0
2
0
1
2
1
0
1
1
0
0
2
0
1
1
1
2
0
1
1
1
1
2
2
1
0
1
0
1
1
0
0
0
1
1
1
0
1
1
2
2
0
2
0
2
2
0
2
2
2
1
1
1
2
0
1
1
0
2
1
0
1
1
0
0
1
0
1
1
0
1
0
1
2
1
1
0
2
0
1
0
1
2
0
1
1
1
0
0
1
1
0
0
0
1
1
2
1
1
1
1
2
1
1
1
1
1
1
1
3
2
1
1
1
1
2
1
0
1
0
1
0
1
0
0
0
1
3
0
1
0
2
0
0
0
1
1
1
0
1
0
2
4
2
1
1
1
2
1
0
2
0
1
1
3
1
1
2
1
1
0
1
1
0
1
0
1
0
0
1
1
0
0
2
1
1
2
1
1
1
1
1
1
1
0
1
1
1
0
1
3
0
1
0
1
2
0
2
1
1
1
2
1
1
2
0
2
1
1
1
2
0
1
1
0
0
2
2
1
2
1
2
2
1
1
1
1
0
1
1
2
2
0
0
1
2
0
2
1
1
1
1
1
2
0
2
0
0
2
2
0
0
1
1
0
1
0
1
1
2
1
0
0
1
0
1
0
0
2
2
2
2
0
2
1
1
1
1
0
1
1
0
0
1
0
2
1
0
0
1
3
0
1
2
0
1
0
1
1
1
3
2
1
0
1
0
0
2
2
1
1
1
1
0
1
0
0
1
0
2
0
2
1
0
1
1
2
1
1
1
2
2
2
2
1
1
1
0
2
2
1
1
0
2
0
1
1
1
1
1
0
2
0
0
1
1
1
0
1
1
0
2
1
0
1
0
0
2
2
1
1
1
0
1
2
1
0
2
2
1
0
1
1
1
2
1
1
2
2
1
1
0
1
0
1
0
1
2
0
1
2
1
2
2
2
1
0
1
2
2
1
2
0
0
0
1
1
1
1
1
0
2
1
2
0
0
0
0
1
1
1
1
1
1
0
2
3
1
1
0
2
2
2
1
1
1
1
2
1
2
0
0
0
0
0
1
1
1
1
2
1
0
1
2
1
2
1
0
2
0
1
0
2
2
0
1
2
2
1
1
1
0
2
0
0
2
0
2
1
0
1
1
0
1
2
0
2
0
2
1
1
2
1
1
1
1
1
4
0
2
0
1
0
1
1
2
1
0
1
0
2
0
0
2
1
2
3
1
1
1
0
1
1
0
1
0
1
2
1
0
1
0
1
1
2
1
1
0
1
1
1
1
0
1
1
0
0
2
1
5
1
0
1
0
1
1
2
0
0
1
1
0
1
0
1
1
0
1
0
1
0
0
1
0
1
1
2
2
1
1
2
1
0
0
1
1
0
0
1
2
1
2
1
1
1
2
0
2
2
1
1
1
0
1
1
1
0
1
2
0
0
1
0
2
1
0
2
2
1
1
1
1
1
2
2
1
2
0
1
1
1
0
0
0
0
2
0
0
0
0
2
1
0
0
0
1
1
2
1
1
1
2
1
1
1
0
2
1
0
2
0
2
0
2
0
1
1
0
1
2
2
0
0
1
2
0
2
0
1
2
0
2
1
1
1
1
1
1
0
1
2
0
1
2
3
1
0
0
0
1
1
1
1
0
1
0
1
0
0
1
0
2
1
2
0
2
2
0
0
2
1
2
2
1
2
0
1
4
0
2
1
2
0
0
0
0
1
1
2
0
2
0
2
1
1
0
0
1
1
1
0
2
2
1
1
2
1
1
1
2
1
1
0
0
1
1
0
0
0
1
2
0
2
1
1
0
0
1
0
2
2
2
1
1
2
2
0
0
0
1
2
1
1
2
1
0
1
0
1
1
0
2
0
1
0
5
1
2
2
2
1
1
1
1
2
2
0
0
1
2
1
0
0
1
0
0
1
1
1
0
3
0
2
1
0
1
1
1
0
1
1
0
0
1
0
1
0
0
0
1
1
1
1
1
0
1
0
1
0
1
0
1
2
0
2
0
0
1
1
1
0
0
1
1
2
1
2
2
1
1
1
0
1
2
1
2
1
1
0
1
0
1
0
2
2
1
0
1
0
1
0
1
1
1
0
1
1
0
0
0
1
1
0
0
0
1
2
1
1
2
0
0
1
2
2
2
1
1
2
0
0
1
1
1
1
0
2
1
0
1
0
1
0
0
1
0
0
2
0
0
1
1
1
1
2
0
0
0
1
0
0
0
2
1
1
2
0
2
2
2
0
0
2
2
0
1
0
1
1
3
1
0
1
1
0
1
1
3
1
2
2
0
0
1
0
1
0
1
1
2
1
1
2
1
2
2
1
0
1
1
2
1
1
1
0
2
2
1
2
1
0
2
1
1
1
0
1
0
2
0
0
0
1
2
1
1
1
1
1
0
0
0
4
1
0
1
0
1
2
0
2
1
0
0
1
2
1
0
0
3
0
0
0
2
2
0
0
0
1
1
1
0
0
0
1
1
1
1
0
0
1
1
0
0
0
0
1
1
2
1
1
1
0
0
2
1
0
2
1
2
1
0
1
1
0
2
1
2
1
0
1
0
2
0
1
2
0
2
0
2
2
1
1
1
1
1
1
0
1
1
0
1
1
0
0
0
0
2
2
2
0
0
0
0
2
2
1
1
1
2
1
1
0
0
1
1
0
1
1
1
2
1
2
0
0
2
2
1
1
2
1
1
2
1
1
1
1
1
1
1
0
1
1
0
1
0
2
2
1
0
1
1
0
2
1
0
1
1
1
1
0
1
1
0
1
1
1
1
0
0
1
0
0
1
2
2
1
1
3
1
1
1
1
1
1
0
1
1
1
1
0
1
1
2
2
2
1
2
1
1
1
1
1
1
0
2
0
0
0
2
2
0
2
1
1
1
2
1
2
1
1
2
1
0
2
2
0
2
1
0
2
2
1
1
0
2
0
0
2
0
0
0
1
1
0
1
1
0
1
0
1
1
0
1
0
2
0
2
0
0
0
0
2
2
1
0
2
0
1
0
1
1
3
0
1
1
1
2
1
1
2
1
0
1
1
2
1
2
1
1
0
2
1
1
1
1
0
1
0
2
2
1
0
1
1
1
1
2
1
0
1
1
2
0
1
2
1
1
2
2
0
0
0
2
1
1
0
1
0
1
2
0
1
2
0
0
2
1
2
1
1
2
1
0
2
1
2
0
0
0
1
0
0
2
0
1
0
0
0
2
1
0
1
1
1
0
0
0
1
1
0
2
1
0
1
1
0
1
1
1
2
1
1
0
0
2
1
0
2
1
0
1
1
0
2
1
0
1
1
0
1
3
2
0
1
0
0
0
1
1
2
1
2
1
0
1
0
1
2
2
0
0
2
2
0
1
1
1
2
1
1
1
1
0
0
1
1
1
1
0
1
2
1
1
1
2
1
0
0
0
0
2
1
1
2
3
2
0
1
0
2
4
1
2
1
0
0
1
0
2
1
2
0
1
1
1
2
0
1
2
1
0
1
0
1
0
2
0
0
2
2
2
1
0
0
0
3
3
1
0
1
1
2
1
0
0
1
2
1
0
1
1
0
2
1
1
0
1
1
0
1
0
1
0
2
2
1
1
1
1
1
1
1
2
0
0
2
2
1
2
1
1
1
0
0
1
1
1
0
1
0
1
1
1
0
0
1
0
1
0
2
1
2
1
1
0
0
1
0
1
1
0
1
0
0
1
1
1
1
0
2
1
1
0
1
1
0
1
0
1
1
2
2
1
0
2
1
2
0
2
0
1
2
2
1
0
1
0
1
0
1
1
1
1
0
2
0
4
1
0
0
2
0
1
1
1
2
1
2
0
2
0
0
1
2
0
0
2
1
2
1
2
0
1
1
1
0
1
1
0
0
0
1
0
0
1
0
2
2
0
1
1
0
1
1
1
1
1
1
0
1
1
1
0
0
0
0
1
1
0
1
0
0
1
1
1
1
2
2
1
0
0
2
1
1
0
1
2
1
1
1
3
0
1
2
0
0
0
0
0
1
1
1
2
2
1
1
2
1
0
2
0
0
1
1
1
1
0
1
1
1
1
0
0
1
2
1
0
1
1
0
0
1
1
0
2
2
1
2
1
1
1
0
1
1
1
1
1
1
1
1
0
0
1
2
1
0
1
1
2
1
1
2
0
1
1
1
1
2
2
0
1
2
1
1
0
1
1
0
0
0
1
1
2
1
1
1
2
1
0
1
1
1
2
2
1
1
2
2
1
3
1
2
0
2
1
2
0
1
1
0
1
0
1
2
1
1
2
2
0
0
0
1
3
1
2
1
0
2
2
0
1
1
1
1
1
1
1
0
0
1
1
0
2
0
1
1
1
2
0
1
1
2
3
1
0
1
1
1
2
1
1
0
2
2
1
0
1
0
1
0
2
1
1
1
0
1
1
1
1
0
0
0
0
2
0
0
1
1
1
1
1
1
1
0
1
0
1
1
2
0
2
0
1
1
1
0
0
2
0
1
0
1
1
0
1
1
2
2
1
1
1
1
0
1
0
0
1
2
1
0
1
0
1
1
2
1
1
1
2
0
2
2
2
1
2
2
1
0
2
2
1
0
1
2
1
2
2
1
1
1
0
0
6
0
1
0
2
1
0
0
2
2
2
2
1
2
1
1
1
2
0
1
2
0
1
1
2
1
1
1
0
2
2
0
1
1
0
1
1
1
1
1
1
1
0
1
1
0
1
1
0
2
1
1
1
1
1
2
0
2
0
1
2
0
0
0
0
2
2
0
1
2
0
1
0
2
0
1
0
2
1
2
1
0
0
0
1
0
2
1
0
1
0
2
0
0
2
1
2
2
1
0
2
2
2
0
1
0
1
1
1
1
1
1
4
2
1
1
1
1
0
0
1
1
2
1
0
0
1
2
1
0
1
3
1
1
0
2
1
0
0
0
0
0
0
1
1
0
2
1
0
1
0
0
2
1
1
1
2
2
0
1
2
1
1
0
0
1
2
0
0
0
1
1
1
0
0
0
0
1
1
0
0
1
2
2
2
0
0
1
1
1
1
0
1
1
1
0
0
1
1
1
1
0
0
2
0
1
1
2
1
0
1
1
2
1
2
1
0
0
1
1
2
2
0
2
0
0
1
0
0
1
2
2
1
1
1
1
0
0
0
2
1
1
2
2
2
0
0
0
1
0
0
1
2
1
2
0
0
1
1
2
1
1
0
2
0
0
1
1
1
0
1
1
1
0
1
2
1
1
0
1
0
1
1
1
1
0
1
1
0
1
1
2
1
2
0
0
1
0
0
1
3
1
1
1
1
1
0
1
2
1
0
0
2
1
0
0
1
0
0
1
1
1
0
1
0
0
1
0
1
1
2
1
1
0
0
0
0
1
1
2
0
1
0
2
0
0
0
1
0
0
1
1
2
0
0
1
1
1
0
1
2
2
0
2
0
1
2
3
1
1
0
1
0
0
0
1
1
1
2
1
1
2
1
2
1
1
1
1
1
0
0
0
2
1
0
1
0
0
0
3
1
2
0
1
1
1
1
2
2
0
2
1
0
1
1
2
1
0
1
1
1
1
1
1
1
1
1
1
0
0
0
1
1
3
1
0
0
2
1
2
0
0
1
0
2
1
1
1
1
0
1
2
1
1
2
0
1
4
2
0
2
2
0
1
2
1
1
1
2
0
1
2
1
2
0
0
1
2
2
0
1
0
1
1
1
1
0
1
1
0
2
1
0
1
1
1
0
2
2
2
2
0
2
1
1
1
2
1
0
0
1
1
2
1
2
1
1
2
1
0
0
1
1
2
4
1
0
1
0
1
2
0
1
1
1
2
1
1
1
2
0
1
2
0
1
1
0
1
1
1
1
1
2
0
0
2
3
1
2
2
1
1
1
0
1
0
0
1
0
1
1
1
1
1
0
1
0
0
1
1
2
1
2
1
0
2
1
1
0
1
1
0
0
1
1
1
0
0
2
1
0
1
1
2
1
2
1
1
1
2
0
1
0
0
0
1
0
1
1
0
1
1
0
1
0
2
0
1
1
1
1
0
2
2
1
2
2
1
0
1
0
1
1
1
1
0
1
1
1
2
1
1
0
2
2
0
0
1
2
1
0
1
0
0
1
0
0
1
1
1
1
0
0
2
1
2
0
0
1
0
0
1
2
1
1
0
2
0
2
2
0
2
0
0
2
0
1
0
0
1
1
2
1
0
1
1
2
1
0
1
1
1
0
1
0
0
1
0
0
1
2
1
3
2
2
0
1
0
0
1
0
1
1
1
3
0
1
0
1
2
1
0
0
0
1
1
1
1
2
0
1
1
1
1
1
1
0
1
0
2
2
0
2
0
1
0
0
1
0
1
2
1
2
2
1
2
1
0
3
1
0
0
2
1
0
0
0
1
0
0
1
1
2
0
0
0
0
1
2
1
1
1
2
1
0
0
1
1
1
0
1
1
1
1
1
2
1
1
0
1
1
1
0
0
0
0
2
1
0
0
1
1
1
2
2
1
1
0
1
1
2
2
1
0
0
2
2
2
0
1
1
1
1
1
1
1
1
1
1
3
1
0
1
1
0
1
2
1
1
1
0
1
2
2
0
1
0
0
0
2
1
0
1
2
2
0
1
0
0
1
0
2
1
1
1
1
2
2
2
2
1
2
1
1
2
1
1
0
1
1
1
1
0
0
0
1
2
2
0
1
0
1
0
1
0
0
0
1
0
1
1
1
1
2
1
0
0
1
1
0
1
1
1
1
1
2
0
1
2
2
2
1
0
1
1
2
0
1
1
0
1
0
0
2
1
1
1
0
0
0
2
0
1
1
1
0
1
0
1
0
1
1
0
0
0
0
0
0
1
0
1
2
0
2
2
1
1
0
0
1
1
1
1
1
0
2
1
2
1
0
0
1
0
0
2
1
0
0
1
1
2
1
2
1
0
1
0
2
0
1
2
1
2
2
1
1
1
0
2
0
0
0
1
0
1
1
1
1
0
1
0
0
0
1
0
2
1
2
2
1
1
1
2
1
0
0
2
1
0
2
1
0
1
1
0
0
0
0
1
2
1
1
0
1
1
1
0
1
0
1
2
2
1
0
0
0
0
0
1
0
0
1
1
0
1
1
2
2
1
2
1
1
0
0
1
0
1
1
2
2
0
1
0
0
1
0
1
1
1
1
1
2
2
2
1
0
1
1
0
1
2
2
2
0
1
1
1
0
0
1
1
0
0
1
1
2
0
2
0
1
0
1
1
1
1
1
1
0
1
0
1
1
1
0
1
0
0
2
2
1
1
1
0
1
1
0
1
1
0
2
2
2
1
1
1
0
0
0
1
2
2
0
1
2
1
1
0
0
2
0
0
2
1
2
2
1
1
0
0
0
1
0
1
2
2
1
1
2
1
1
0
1
0
0
0
1
1
2
1
1
0
0
1
1
2
1
0
0
1
1
0
1
0
1
0
1
0
0
1
0
2
2
1
0
0
1
1
0
2
0
2
2
1
2
2
2
0
1
0
0
2
0
1
1
0
0
1
0
3
1
1
2
1
1
0
2
0
1
1
2
1
0
0
0
2
1
1
2
3
1
2
0
1
1
1
2
3
1
1
1
1
1
0
0
1
0
0
0
0
1
0
0
2
1
1
2
1
2
0
1
0
1
0
2
1
2
2
0
0
1
1
2
2
1
2
0
1
0
2
0
0
2
2
2
2
2
1
0
0
2
2
0
0
1
0
1
0
1
2
2
0
1
2
1
2
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
0
0
2
1
1
1
0
1
2
2
0
0
0
1
2
1
1
0
0
1
0
0
2
0
1
0
1
2
1
2
1
0
3
2
0
1
0
1
1
0
0
0
2
0
1
2
0
0
0
2
1
2
1
1
2
1
1
0
0
1
0
2
1
0
0
0
1
0
1
0
0
1
0
0
1
1
1
0
1
1
0
1
0
0
0
0
1
1
1
2
0
3
0
1
1
1
2
0
1
2
0
0
0
2
2
1
0
1
0
1
1
1
1
0
1
2
1
2
1
2
1
0
2
1
0
1
1
3
1
1
0
1
1
1
1
1
0
0
2
1
0
3
1
0
0
0
1
0
3
1
2
0
2
0
0
1
0
1
0
1
1
0
0
1
1
2
1
0
1
1
2
0
0
0
2
2
0
0
0
1
2
1
2
1
1
1
0
1
2
1
0
1
0
1
2
1
2
2
1
2
0
1
1
0
1
4
2
0
0
0
0
0
1
2
2
1
1
1
2
1
2
2
0
1
0
1
0
2
2
0
2
1
1
1
0
2
0
1
0
1
2
0
1
1
1
1
0
0
1
0
1
1
0
0
0
0
2
2
1
0
1
1
2
0
1
1
1
0
0
1
1
2
2
1
2
1
1
0
1
1
2
0
0
2
2
1
1
0
2
1
0
2
1
0
0
2
1
1
1
1
0
0
2
0
0
1
2
0
0
2
2
0
2
1
1
1
2
1
2
1
2
1
1
2
0
0
1
2
1
2
1
1
1
0
1
1
2
1
0
1
0
0
1
2
2
0
1
1
0
0
1
0
0
0
0
0
2
0
0
1
0
1
2
0
3
2
2
1
2
1
1
1
1
1
2
1
2
1
0
1
1
0
1
1
1
1
0
0
0
1
0
1
0
1
2
0
1
2
1
0
2
0
1
1
0
1
0
0
1
1
1
1
1
0
2
1
0
1
1
2
1
1
1
0
5
1
1
1
1
0
1
0
1
1
0
1
1
2
0
1
0
0
0
1
1
1
1
1
0
0
2
1
0
0
1
2
0
0
0
0
1
2
0
1
0
0
1
1
1
1
1
1
0
1
0
2
1
1
1
1
1
0
1
1
0
1
1
1
1
1
0
2
0
1
1
1
0
1
2
2
0
2
2
1
0
0
0
1
1
2
2
1
2
2
0
0
0
1
1
1
0
1
2
1
0
1
2
1
2
1
0
1
0
0
0
1
1
0
1
1
1
1
2
1
0
2
1
0
0
2
0
0
0
1
1
0
2
2
0
2
0
2
1
1
1
2
0
1
0
0
0
1
0
2
2
0
1
0
0
2
1
0
0
1
0
2
2
1
0
1
2
2
1
0
1
0
1
0
1
2
1
1
0
0
2
2
2
2
1
0
1
1
1
1
1
2
2
1
1
1
1
2
2
1
0
1
0
2
2
5
0
1
0
1
0
2
0
1
0
1
2
0
2
2
1
1
0
1
1
0
0
0
2
1
0
1
0
1
0
0
1
2
1
0
0
0
2
0
1
2
0
2
0
1
1
1
1
1
1
0
0
2
1
1
1
2
1
2
1
0
0
0
1
0
0
2
2
1
1
1
1
1
0
0
0
0
0
1
0
1
2
1
1
1
1
1
1
1
1
0
1
1
1
0
1
0
2
1
1
0
1
0
1
1
1
2
1
2
1
2
0
2
2
1
2
2
0
0
1
0
2
0
1
2
1
0
0
1
2
1
1
1
0
2
0
0
1
0
2
1
1
2
1
1
1
2
0
0
1
0
1
1
2
0
0
1
0
1
0
0
2
0
1
1
0
3
0
0
1
2
1
1
1
0
1
1
0
1
1
1
1
1
1
2
0
0
0
0
1
1
0
1
1
0
0
0
1
1
0
1
0
0
1
0
0
2
1
2
2
0
0
0
0
1
2
0
0
1
0
0
1
1
0
1
2
1
1
1
0
0
2
2
1
1
1
1
0
0
1
1
1
0
1
1
0
1
2
0
2
3
1
0
0
0
1
2
1
1
2
0
1
1
1
2
0
2
2
1
0
2
1
0
1
0
0
1
0
0
1
0
1
0
1
0
1
2
0
0
2
2
0
2
2
1
1
0
1
1
0
1
1
0
2
2
1
1
2
1
1
2
0
0
1
1
2
0
1
1
2
1
1
1
2
2
0
0
1
1
0
1
3
2
1
0
2
3
1
1
0
0
1
1
0
2
1
1
1
0
1
0
2
1
1
2
1
2
0
2
2
2
1
1
2
2
1
0
0
1
1
1
1
2
1
1
1
1
0
1
2
1
2
1
1
1
1
0
2
1
1
0
0
2
2
1
0
2
1
1
1
3
0
1
1
1
1
0
2
1
0
1
0
1
1
0
1
0
1
2
0
2
1
0
0
2
1
0
1
0
0
1
2
0
1
1
0
2
0
0
1
2
0
0
1
1
1
1
0
2
1
0
0
0
1
1
1
0
2
2
0
1
0
1
1
0
0
0
1
0
0
0
0
1
2
1
0
1
0
1
1
1
0
1
1
0
0
0
2
1
1
1
1
2
1
0
2
1
0
1
2
0
1
0
0
0
0
0
1
0
0
0
1
1
0
2
2
0
2
1
1
2
2
1
2
0
0
1
2
2
1
1
2
2
0
0
2
1
0
1
1
2
2
0
1
0
2
2
0
2
1
1
0
0
1
2
0
0
0
1
0
1
1
0
1
1
2
1
0
0
0
0
2
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
0
1
0
1
2
2
2
1
1
0
2
1
0
1
2
1
2
0
2
0
1
2
0
1
1
0
1
1
2
1
2
0
1
2
0
1
1
4
2
0
1
3
0
1
0
1
1
2
1
2
1
1
1
1
2
2
1
0
1
0
1
1
1
2
2
1
2
1
2
0
1
1
1
2
2
0
1
1
0
1
0
2
1
1
2
2
1
0
1
1
1
2
0
1
0
2
1
2
2
1
0
1
1
2
0
1
0
0
1
0
1
1
0
1
0
1
2
1
1
0
0
0
0
2
0
0
2
2
1
2
0
0
2
0
1
2
0
2
1
1
1
1
0
1
1
2
1
2
1
1
2
1
2
2
0
1
0
0
1
0
2
2
0
1
0
0
0
0
0
1
2
1
1
2
2
1
1
2
1
1
0
1
1
0
1
1
2
0
1
0
1
1
0
1
0
0
0
1
1
1
0
1
0
1
0
1
4
2
0
2
1
1
0
1
1
1
3
1
1
1
1
0
3
1
1
2
2
1
1
1
1
0
1
0
0
1
0
1
1
2
0
3
1
2
1
1
1
0
0
1
2
0
0
1
1
1
2
2
1
1
0
1
0
1
2
2
1
1
1
0
0
2
2
2
1
0
2
1
0
0
2
0
0
0
1
1
0
1
1
2
1
1
1
1
1
1
0
0
2
1
0
0
0
2
0
1
2
0
2
1
2
0
2
0
1
1
2
1
0
2
1
1
1
0
0
1
2
0
1
0
0
1
1
1
1
0
1
1
0
0
2
2
3
0
0
1
0
0
0
2
0
0
1
1
1
1
2
1
0
1
0
1
1
1
1
1
1
1
0
4
2
1
2
1
1
1
1
1
1
1
0
1
0
1
1
0
1
0
1
2
0
1
1
1
2
0
0
2
1
0
0
2
1
0
1
1
1
2
2
1
1
1
1
2
1
1
1
0
1
1
0
1
1
1
0
3
3
0
2
2
1
1
4
1
1
0
1
2
0
0
0
2
1
0
1
0
1
1
0
0
0
1
0
1
1
0
1
2
0
2
0
5
1
0
1
1
1
0
0
0
2
2
3
0
0
1
0
2
0
1
2
2
2
1
1
1
0
2
0
0
0
1
1
1
1
0
2
1
2
0
2
1
0
0
1
1
1
1
0
1
2
1
0
0
0
2
2
2
0
1
0
1
1
1
1
2
1
1
2
0
1
0
1
2
0
1
0
3
0
1
1
0
1
0
1
0
1
0
2
1
1
0
0
1
1
2
1
1
0
0
0
1
0
2
1
0
1
1
1
2
1
2
3
1
1
1
1
0
1
0
1
0
1
2
1
1
10
2
0
0
1
3
1
1
0
0
0
0
0
1
0
2
1
0
2
1
0
2
2
2
4
1
0
2
1
1
0
1
1
1
1
1
1
1
0
1
0
1
1
0
0
1
0
2
2
1
1
1
0
1
2
1
1
2
0
1
1
1
1
1
0
1
1
1
1
1
1
1
0
0
2
0
2
1
1
1
1
0
0
0
0
2
1
2
0
1
0
1
0
2
1
1
2
2
1
0
1
0
1
2
0
0
1
2
0
1
0
0
0
1
2
1
0
2
0
1
2
1
1
1
1
0
2
0
0
0
1
1
2
1
1
1
0
1
0
1
0
0
3
0
1
1
0
0
2
1
0
0
1
1
2
0
1
2
0
1
1
1
0
0
2
1
2
1
0
1
2
2
1
1
0
1
0
2
2
0
1
1
1
1
2
0
1
1
0
3
0
2
0
1
0
1
2
0
0
2
2
1
1
1
1
1
0
1
0
1
2
1
2
0
0
0
1
1
0
0
0
1
2
1
1
1
1
0
1
0
1
0
1
1
2
1
0
1
1
2
1
2
1
2
1
0
1
2
1
2
0
3
1
1
2
0
3
0
0
1
0
0
0
2
0
2
2
1
0
7
0
1
1
2
1
1
1
2
2
2
2
1
2
1
2
0
1
1
0
0
0
1
0
2
1
1
0
0
1
0
0
0
2
1
2
1
1
0
0
2
1
1
1
0
1
1
0
1
1
1
0
1
2
1
1
2
1
2
0
0
2
2
1
1
2
0
1
2
2
1
1
1
1
0
1
0
1
0
1
1
1
0
2
0
0
0
0
0
1
2
1
2
1
1
0
0
2
2
1
1
0
0
1
1
0
1
2
0
1
0
1
1
0
2
0
1
1
2
1
2
2
0
1
2
2
0
0
1
0
2
1
3
2
1
1
1
0
1
1
2
0
1
2
0
2
1
0
1
1
1
1
0
2
1
1
2
2
0
0
0
2
0
1
0
0
1
1
0
1
1
2
2
1
0
1
1
1
0
0
2
0
1
1
1
1
0
1
1
1
2
0
1
0
2
2
1
0
2
1
1
2
1
1
2
0
1
0
1
2
1
0
1
0
0
1
0
2
1
2
0
2
1
2
0
0
1
1
2
2
0
0
1
2
1
1
2
2
1
0
1
1
2
0
2
1
0
1
2
2
1
0
2
0
2
0
1
0
1
1
0
0
1
1
1
1
2
0
1
1
0
1
2
1
0
1
0
0
1
1
0
1
1
0
1
1
2
1
4
0
1
2
2
0
1
1
0
0
0
2
0
1
0
2
1
1
0
0
1
0
0
3
1
1
1
1
1
0
2
1
0
0
1
1
1
1
0
2
1
0
0
0
0
1
1
0
0
2
1
0
0
1
1
1
0
1
1
0
1
1
2
1
0
1
1
0
1
1
2
1
1
2
1
1
1
1
1
1
1
0
1
0
1
1
2
1
1
1
1
1
2
0
1
1
1
1
1
1
1
2
1
0
1
0
1
0
1
1
1
1
0
1
2
0
0
1
1
2
2
3
2
1
1
0
2
1
1
1
0
1
2
1
0
2
1
1
1
1
2
0
1
0
1
1
0
0
2
2
1
1
1
2
1
1
1
2
1
0
1
0
1
0
0
0
1
0
2
0
1
1
0
2
1
0
0
0
0
0
0
1
0
0
0
1
2
0
0
1
2
0
0
1
1
0
0
2
0
0
1
2
0
1
2
1
1
2
1
1
2
0
0
0
1
1
0
1
1
1
2
0
1
1
0
1
1
0
1
0
0
0
2
1
1
2
2
0
0
2
0
2
1
2
2
1
1
1
1
2
1
0
1
1
1
0
1
1
1
0
1
1
0
1
0
0
1
1
0
1
0
0
0
1
3
1
0
2
1
1
2
2
2
1
1
0
1
1
1
0
1
1
0
0
0
0
0
0
0
3
2
1
0
2
1
1
1
0
0
0
0
0
2
1
2
0
0
1
1
0
2
1
0
0
1
2
0
0
2
1
2
0
2
2
1
1
1
0
0
0
1
0
0
0
2
2
1
0
2
1
1
2
2
1
2
0
0
1
0
1
0
2
1
1
0
1
2
1
0
1
0
0
1
1
1
1
1
1
1
1
1
1
0
1
1
0
1
1
0
2
6
1
1
2
0
0
0
1
0
2
1
1
0
2
2
0
1
1
1
1
0
1
1
0
1
1
1
0
1
1
1
0
0
0
1
2
1
0
1
2
1
0
0
0
1
1
0
0
1
1
1
1
2
0
1
0
1
2
0
1
1
0
0
2
1
2
0
2
1
0
1
2
2
1
3
0
0
2
1
1
0
0
0
0
0
1
2
2
1
0
0
2
1
2
0
1
0
1
0
1
1
1
1
1
1
0
2
1
0
0
0
1
1
2
1
1
0
2
1
1
2
1
1
0
1
1
1
2
1
0
1
1
0
1
0
0
1
0
0
1
0
1
1
1
0
1
0
0
0
2
0
2
2
0
1
0
2
2
1
1
1
1
0
1
1
0
1
1
1
0
1
1
1
2
1
0
1
0
0
2
2
1
1
1
0
1
1
1
2
2
2
1
1
2
0
1
1
1
0
2
0
0
2
1
0
0
1
0
0
0
2
1
2
1
1
1
1
1
1
1
1
0
0
0
0
0
2
0
0
2
1
0
1
1
1
1
0
0
0
2
1
2
1
0
1
1
1
1
1
0
0
2
2
1
1
0
2
0
0
2
6
0
1
1
2
0
1
1
0
1
1
0
0
1
1
0
1
0
1
0
1
1
0
2
1
1
1
1
2
2
2
2
0
1
1
1
1
1
1
0
2
1
0
1
1
1
1
2
1
1
1
1
1
1
0
0
1
0
1
0
2
1
1
0
1
1
0
0
0
1
2
1
1
1
0
1
1
1
0
3
1
2
1
1
1
1
0
2
2
1
1
1
1
1
1
2
2
1
1
2
0
0
1
1
2
1
1
0
0
2
1
1
1
0
0
0
2
2
2
0
0
0
2
1
1
2
0
2
1
1
0
0
1
1
2
0
0
1
1
0
0
0
0
1
2
1
2
1
3
1
1
0
1
1
2
0
1
2
1
0
2
0
0
2
1
2
1
2
2
1
2
1
2
0
2
1
0
1
1
1
0
0
2
1
3
2
1
3
1
1
2
0
2
1
1
1
1
0
1
2
2
1
1
1
0
1
1
2
1
1
0
2
0
0
1
1
0
1
0
0
1
1
1
1
2
1
0
2
1
2
0
1
0
2
0
1
4
0
1
2
1
0
0
1
2
2
0
0
1
0
0
0
0
1
0
0
0
1
0
1
2
0
2
1
0
0
0
1
0
2
1
0
1
2
1
0
1
0
2
1
4
1
0
2
1
1
1
1
0
0
1
2
1
2
1
0
0
0
0
0
1
0
1
0
1
2
0
1
2
0
0
1
0
1
1
1
1
0
2
1
1
0
1
0
1
1
1
1
1
0
2
0
0
2
2
1
2
0
0
2
1
2
2
0
1
2
1
2
2
2
0
1
0
2
0
2
2
1
2
1
1
1
1
2
1
1
1
1
2
1
2
2
1
0
1
1
1
0
1
2
0
0
0
0
2
0
0
1
1
0
2
0
0
1
1
1
1
2
0
1
2
1
1
0
1
1
0
0
0
0
1
0
1
1
1
1
0
0
2
2
1
0
1
0
2
1
1
1
1
1
0
2
0
1
3
1
3
1
1
0
0
1
1
1
1
0
0
1
0
1
0
1
1
1
0
1
3
1
0
1
1
1
2
2
2
0
1
1
1
2
1
2
2
0
0
0
0
1
0
1
2
2
1
2
0
1
1
0
1
2
0
2
0
1
0
1
1
0
1
0
2
0
0
2
0
0
1
1
0
2
1
1
0
1
2
1
2
1
1
2
1
1
1
0
1
0
0
0
0
1
0
0
1
0
1
1
1
0
2
1
1
1
2
1
2
2
1
2
0
1
1
0
0
0
1
1
2
1
1
1
1
2
1
0
1
2
0
1
0
1
0
0
1
0
0
1
1
0
1
0
0
1
1
1
0
2
0
2
4
0
0
0
2
0
1
0
1
1
0
0
1
1
0
0
0
2
2
1
2
1
1
0
1
1
1
1
2
0
0
1
0
1
1
1
2
1
0
1
2
2
0
1
1
2
2
2
1
0
0
1
1
1
2
1
0
1
1
1
1
0
2
0
0
0
0
2
1
1
2
0
0
1
1
2
2
0
1
0
1
0
1
0
2
0
1
0
0
1
1
1
2
0
1
2
0
0
1
2
0
0
0
2
0
1
1
1
2
1
0
0
0
1
0
2
2
1
0
0
0
2
0
0
1
1
0
0
1
2
0
1
1
0
1
0
2
0
0
1
1
0
0
1
1
2
1
0
0
1
1
0
2
0
1
1
0
0
1
1
2
0
2
0
0
2
1
2
0
2
0
0
1
1
1
1
2
2
1
1
1
2
0
2
1
1
1
2
1
1
1
0
1
0
1
2
2
1
2
0
1
1
0
0
0
1
0
0
2
1
0
0
2
1
1
2
0
2
1
1
2
0
2
1
1
2
1
0
0
0
0
0
1
0
2
1
0
2
1
0
1
0
1
0
0
2
2
1
1
1
2
1
1
1
1
1
2
0
0
0
1
1
0
0
1
0
1
1
1
0
1
1
1
2
1
1
1
1
0
0
2
1
2
2
1
2
1
0
0
2
1
0
1
0
1
1
1
1
2
1
2
1
0
1
1
1
1
1
0
2
2
2
1
1
0
1
1
2
0
2
1
1
1
1
2
1
1
1
0
1
1
1
1
2
1
2
1
2
1
0
0
1
1
0
1
1
1
2
1
0
2
2
2
0
0
1
0
1
2
0
2
1
0
2
1
0
1
0
1
0
1
1
1
0
1
0
2
0
1
1
0
1
2
0
2
0
0
2
0
1
1
2
0
0
0
2
0
0
0
1
2
0
0
1
1
1
0
1
1
1
2
2
1
1
0
2
2
0
1
0
1
1
0
2
2
2
1
1
1
1
2
0
1
2
2
1
0
1
0
1
2
1
1
0
2
0
1
0
1
1
1
1
1
1
2
2
1
1
1
0
1
1
2
0
1
2
1
1
1
1
1
0
0
0
1
1
2
2
0
2
2
0
1
0
0
1
1
2
2
1
0
2
1
2
1
1
1
0
0
1
2
1
0
0
1
1
1
0
3
0
1
2
0
1
0
0
1
2
0
2
1
2
1
0
0
1
0
1
1
1
0
0
2
0
1
0
1
1
0
1
1
1
1
0
0
0
2
3
0
0
1
2
1
0
1
1
1
1
2
1
1
1
1
1
2
2
0
0
1
1
2
1
0
1
1
0
0
2
1
0
0
1
1
2
1
2
1
1
1
2
1
2
2
1
1
0
1
2
1
0
0
0
2
3
1
1
0
1
1
1
0
2
0
1
1
1
1
2
0
0
2
0
2
0
0
0
2
2
2
0
1
1
1
0
1
0
0
0
2
0
0
2
1
2
2
1
1
2
1
1
1
0
2
1
1
0
0
2
0
1
1
0
2
1
1
0
2
1
1
1
1
1
3
0
1
1
1
1
2
1
0
2
2
0
1
0
1
1
1
0
1
0
2
1
1
0
1
1
1
2
0
0
1
0
1
1
2
2
1
0
2
2
1
0
1
2
2
1
0
1
0
0
2
2
0
1
1
1
2
1
1
1
1
0
2
0
1
1
0
1
1
1
1
0
2
2
1
0
1
1
2
2
1
1
0
1
0
0
1
0
0
1
2
1
0
1
0
1
2
0
1
2
0
1
1
2
0
0
0
2
1
1
0
1
0
2
1
1
0
1
0
0
1
0
1
0
1
1
1
0
0
0
0
1
0
0
1
1
1
0
1
1
2
1
1
1
0
1
0
1
1
1
1
1
1
0
0
1
2
0
0
2
1
0
0
1
0
1
2
1
2
1
1
0
1
1
2
2
2
2
1
0
0
0
0
2
0
0
1
1
0
1
1
1
0
2
0
0
1
1
0
1
1
2
0
0
2
2
1
1
1
0
1
1
2
1
2
1
0
1
1
0
1
0
1
0
0
0
1
1
1
1
1
2
0
0
3
1
0
1
1
0
1
1
0
0
1
0
2
1
2
1
1
0
1
1
2
0
1
2
1
1
2
2
0
2
0
0
0
0
1
1
0
1
1
2
1
2
1
1
1
1
0
1
0
2
1
0
0
1
1
1
1
0
0
2
1
1
1
0
0
1
0
0
1
0
1
2
0
1
1
0
1
1
1
1
1
0
0
2
1
2
0
0
0
1
2
0
1
1
1
1
0
1
1
3
0
1
0
0
1
1
2
2
2
0
1
0
1
0
2
1
1
1
0
1
1
0
0
1
0
1
1
1
1
2
1
2
2
1
1
1
2
0
0
0
2
2
0
0
2
0
1
1
1
1
0
1
1
1
1
0
0
1
1
2
1
0
2
1
2
1
0
0
2
0
1
0
0
0
2
0
1
2
2
1
0
0
1
2
2
1
3
1
2
2
0
0
2
0
2
3
2
1
0
0
0
1
1
0
1
0
2
0
1
1
0
2
2
0
1
0
0
2
2
0
2
1
1
2
2
2
1
0
2
2
2
0
0
2
2
2
1
0
2
0
0
2
0
1
1
0
1
0
1
2
1
1
1
1
2
2
0
0
1
2
0
1
0
2
0
1
0
0
1
1
0
1
1
1
2
1
0
1
0
0
0
1
1
1
1
0
2
0
2
1
0
2
1
2
1
1
2
1
0
0
2
1
1
1
1
1
0
0
0
0
1
1
1
2
1
2
1
1
1
0
1
1
1
1
1
0
1
2
1
0
0
0
0
2
2
1
1
1
0
1
0
2
0
0
2
1
2
0
1
3
1
0
2
0
0
0
1
1
2
1
1
0
4
1
2
3
0
1
2
0
0
0
0
0
1
0
0
0
1
1
0
1
1
1
1
0
0
1
1
0
1
1
0
1
0
0
1
1
0
2
0
0
0
1
1
0
0
0
2
1
1
1
2
0
1
0
1
1
1
2
2
2
0
0
2
0
2
1
2
2
0
1
0
3
0
1
0
1
1
0
2
1
2
0
0
2
0
1
2
0
2
0
1
1
0
0
0
2
1
0
0
1
1
2
2
0
0
1
0
1
1
0
0
2
2
0
2
1
2
2
1
1
1
0
1
0
1
1
1
0
1
1
1
1
0
1
2
1
1
0
2
2
2
0
0
1
1
3
0
2
2
0
2
1
1
1
1
1
2
1
0
0
0
1
0
0
2
1
1
0
2
1
1
0
1
0
0
0
1
1
1
1
2
0
2
1
2
0
1
0
1
2
1
0
1
1
0
2
2
0
3
1
2
2
1
1
2
1
2
2
2
0
1
1
1
0
0
1
0
1
0
1
1
0
0
2
1
0
1
0
0
0
0
0
2
1
1
1
2
1
1
0
1
0
1
0
2
0
0
1
1
2
1
0
1
0
1
1
1
1
1
1
1
0
0
2
0
4
0
1
1
1
1
2
1
0
0
0
1
1
0
1
1
1
1
0
0
2
1
0
1
0
1
1
2
2
1
1
1
1
2
2
1
0
1
1
1
0
0
1
2
1
0
0
0
0
0
1
1
1
2
0
2
1
1
0
0
0
0
0
1
1
4
2
0
1
0
0
1
0
2
1
1
0
5
1
1
1
0
0
1
1
2
0
1
0
0
1
1
0
1
0
2
2
0
1
2
0
1
1
1
2
0
0
1
1
0
1
2
0
0
0
1
1
1
1
0
1
1
1
1
1
1
1
1
2
0
1
1
2
1
1
0
0
1
1
1
1
0
0
1
2
1
1
0
1
1
1
0
1
2
1
0
0
0
1
1
2
0
0
1
3
1
1
0
0
1
1
2
0
0
2
1
1
1
2
1
2
0
1
1
3
1
2
0
0
0
1
2
1
0
2
1
0
1
1
1
2
1
1
2
0
0
0
0
1
1
0
0
1
1
1
2
2
0
2
1
0
2
0
2
0
0
1
0
0
1
0
2
0
1
0
0
1
2
1
1
0
1
2
1
0
0
0
1
2
5
0
1
1
2
1
2
1
0
4
1
1
1
1
2
1
1
1
1
2
2
3
2
1
1
1
2
0
2
0
1
0
1
1
0
2
1
0
2
1
1
3
1
2
1
2
1
2
1
0
1
1
1
2
0
1
1
1
2
2
0
1
0
0
2
1
2
1
0
1
1
1
0
1
1
2
0
0
2
1
0
1
1
1
1
0
0
3
0
1
0
1
0
1
0
1
2
2
1
1
1
0
2
1
1
2
0
1
2
1
0
0
1
1
2
0
2
2
0
1
0
3
1
1
0
2
1
1
1
1
1
2
1
1
1
1
1
0
1
1
1
0
1
1
1
1
0
1
1
1
1
0
0
1
2
1
1
0
2
0
0
1
0
0
2
1
2
0
1
1
1
1
1
0
1
1
0
0
0
1
2
0
0
1
0
0
2
1
0
1
0
1
0
2
1
1
1
0
3
1
1
1
2
0
2
1
0
1
1
0
1
0
1
1
1
0
0
1
2
0
1
1
0
0
0
1
1
0
1
3
2
0
2
2
1
3
2
1
0
2
1
2
1
1
0
0
0
1
0
1
1
1
1
0
0
1
0
1
0
1
1
1
1
1
1
2
0
2
0
1
2
1
2
0
0
1
0
1
0
1
1
0
0
1
2
0
2
1
1
2
1
0
1
0
2
0
1
0
1
1
1
1
2
2
1
0
0
2
0
0
0
0
1
0
2
1
2
0
1
0
2
0
1
1
0
0
1
1
0
1
1
1
0
0
0
2
0
1
2
1
0
0
0
2
1
0
1
0
1
1
1
0
1
2
1
0
1
1
1
1
1
0
2
0
0
1
2
0
1
0
1
1
1
1
1
0
1
1
0
2
0
2
0
1
2
1
0
1
2
2
2
2
4
1
0
1
1
1
2
0
2
0
2
1
2
1
2
1
1
2
1
0
0
1
0
1
2
2
1
2
0
1
1
1
0
1
0
1
0
0
1
2
1
1
1
0
1
2
2
0
0
0
1
0
2
0
0
1
0
4
0
1
1
0
1
3
1
0
0
1
0
1
1
1
1
1
0
2
0
1
1
2
1
0
1
2
0
1
2
2
1
0
0
1
5
1
1
0
0
0
2
1
1
1
1
1
2
3
1
0
0
0
0
1
2
0
2
1
1
0
2
1
2
1
0
2
1
1
2
0
1
2
2
0
1
1
0
1
2
2
0
1
1
1
1
1
1
0
0
1
1
0
0
0
2
0
2
1
1
1
1
0
1
0
1
1
2
2
1
0
0
1
1
0
1
3
1
1
2
1
1
2
0
2
1
1
2
0
2
1
1
2
0
0
2
1
0
1
2
1
2
1
4
1
2
1
0
2
0
2
1
2
0
1
0
0
1
0
1
0
2
0
1
0
0
0
2
1
1
2
4
1
1
1
1
1
1
1
0
2
0
1
1
2
0
2
2
1
2
0
1
0
2
0
2
1
2
0
0
1
0
1
1
1
1
1
2
2
0
2
2
1
1
1
2
1
1
0
0
1
0
0
1
1
2
0
2
0
1
0
0
1
2
1
1
1
1
2
2
0
1
1
1
1
0
0
1
1
0
1
1
2
1
2
1
1
1
1
1
1
1
1
0
2
0
1
2
1
3
1
1
1
1
0
1
2
0
1
0
1
1
1
2
1
1
0
1
1
0
1
0
2
1
1
1
0
2
1
1
1
0
1
1
1
0
2
1
1
1
2
1
1
1
1
0
1
2
0
0
4
0
0
0
2
0
2
2
0
0
0
0
0
0
0
2
0
1
1
1
1
2
1
4
1
1
1
1
0
0
1
1
0
1
0
0
0
1
2
3
1
2
1
1
0
1
2
0
1
1
1
0
0
1
1
2
2
1
1
0
1
1
1
2
1
2
1
0
1
1
1
0
0
1
2
1
0
1
3
0
1
0
2
0
0
2
0
0
1
1
1
0
1
1
0
1
0
1
0
0
1
1
0
0
0
1
2
1
0
1
0
1
1
0
1
0
1
0
1
1
1
1
0
0
0
1
1
2
1
0
1
1
1
1
1
1
1
0
1
1
2
3
1
2
0
1
1
1
1
0
0
0
1
1
0
0
1
0
0
2
0
0
1
1
0
1
0
1
1
1
1
1
1
2
1
1
0
1
1
0
2
0
0
1
0
1
1
1
2
0
2
2
1
1
2
0
2
2
1
0
1
1
1
2
1
2
2
0
0
1
1
2
2
1
2
0
1
0
0
1
2
0
1
0
1
1
1
0
2
2
2
1
1
1
1
1
0
0
2
2
0
0
1
0
0
1
2
0
0
0
0
1
1
1
1
0
0
0
0
1
1
1
1
0
2
0
0
2
0
0
1
1
0
2
2
0
2
0
0
1
1
0
0
1
0
2
1
2
0
0
2
1
1
1
1
1
2
1
2
0
0
1
2
1
1
0
1
1
1
2
1
2
0
0
1
1
0
2
1
1
1
2
2
1
1
1
0
2
2
1
0
1
0
0
0
2
0
1
0
0
0
0
1
1
1
2
0
1
1
2
0
1
1
0
1
1
0
0
0
1
1
0
1
2
0
1
0
1
2
1
2
0
1
0
1
2
1
1
0
1
2
2
0
0
0
1
0
1
0
1
2
0
0
2
0
0
1
0
1
0
1
1
1
2
2
0
0
1
1
0
1
0
4
2
2
1
0
0
1
0
0
1
2
1
2
1
1
0
2
0
2
0
1
1
1
0
1
2
1
0
0
2
2
1
2
1
2
2
2
0
0
0
1
2
2
0
1
1
0
1
0
2
0
0
0
0
1
1
1
0
2
1
0
1
0
1
0
2
0
2
1
1
1
1
1
0
4
2
1
0
1
1
1
1
0
2
2
0
2
1
3
2
1
2
1
0
0
0
2
1
1
2
2
0
1
0
1
1
2
0
0
1
0
1
1
1
1
0
0
0
2
1
1
1
0
0
2
1
2
0
0
1
1
0
2
1
1
0
0
1
1
0
1
2
1
1
0
1
1
1
1
1
0
2
0
0
1
2
1
0
1
0
0
2
2
2
3
0
1
2
0
2
1
2
2
1
1
1
0
2
2
1
0
1
0
1
2
0
1
1
1
2
2
0
2
0
2
2
1
1
0
8
1
1
1
0
0
2
0
1
2
1
2
1
2
0
0
1
2
2
2
1
0
1
2
1
0
1
1
1
1
1
1
1
2
1
2
0
1
1
0
1
0
0
1
1
0
1
1
1
1
0
0
1
2
2
2
0
2
1
2
1
0
2
0
1
1
2
1
1
2
0
2
0
2
1
1
1
2
1
0
0
0
1
1
1
2
1
0
0
0
0
1
1
0
1
1
2
2
2
1
1
1
0
0
2
2
1
1
0
0
1
0
1
0
1
1
0
2
0
0
0
0
0
1
1
1
0
1
1
2
1
0
2
3
2
1
0
0
0
2
1
0
0
0
0
0
0
0
1
1
1
1
0
1
2
0
1
1
1
2
1
1
0
0
1
1
1
0
2
1
2
0
1
1
0
1
1
0
2
2
0
2
2
1
2
1
1
1
1
2
1
0
2
2
0
2
2
1
0
1
0
1
1
2
2
2
2
0
0
2
1
1
1
1
0
0
1
1
0
1
1
1
1
1
1
3
0
0
1
0
3
1
0
2
0
1
0
1
2
2
2
0
1
1
1
1
0
0
0
0
1
1
2
1
0
1
2
0
1
1
0
2
1
1
1
0
0
0
1
1
2
7
1
0
0
2
0
1
1
0
0
1
1
2
1
1
2
1
1
2
0
1
1
0
1
2
2
1
2
1
1
0
0
1
0
1
1
0
4
1
2
2
0
1
1
2
2
1
0
1
0
1
1
0
2
0
0
1
1
1
1
1
0
1
1
2
2
1
2
1
1
0
1
1
1
2
2
1
1
0
0
0
1
0
1
2
0
0
2
0
2
1
2
0
1
1
2
1
0
0
1
1
0
0
1
1
0
1
1
1
1
1
1
1
1
2
2
1
1
2
1
0
1
0
0
1
1
2
2
1
1
1
1
0
2
0
1
1
0
0
1
2
1
1
1
1
0
0
1
0
1
1
0
0
1
1
0
1
0
0
0
0
0
1
1
0
1
1
2
1
1
1
1
1
0
1
1
1
0
1
0
1
0
1
2
1
2
0
1
0
0
1
0
0
1
0
0
2
1
1
0
1
2
2
1
0
1
0
0
1
0
2
0
1
2
0
1
1
2
1
0
0
0
2
1
1
1
0
0
2
1
1
1
1
0
0
2
1
1
1
1
2
1
2
1
1
1
0
2
1
2
2
1
0
0
0
1
2
1
1
1
0
1
1
1
1
2
2
0
3
2
2
1
2
2
1
0
1
0
2
0
0
1
1
0
2
2
1
1
1
2
1
0
1
1
1
0
1
2
1
0
3
1
1
0
0
1
2
0
2
1
0
1
1
1
2
0
0
0
0
2
1
2
2
1
1
0
2
0
1
2
0
1
0
0
1
1
1
1
2
1
1
2
0
0
1
1
0
0
1
0
1
1
2
0
1
2
1
1
0
0
2
1
1
5
1
1
1
0
2
2
2
0
0
1
0
0
1
1
1
1
0
1
1
2
2
2
1
1
0
0
0
2
0
0
1
1
1
1
1
0
1
0
0
7
0
0
1
1
1
2
1
1
1
1
2
1
0
2
1
1
1
2
1
2
2
1
1
1
1
1
0
1
0
1
2
1
0
1
0
0
1
2
1
1
1
1
1
1
2
1
1
1
0
1
0
2
1
0
2
2
3
1
0
1
1
1
1
1
0
2
0
0
1
2
0
0
0
0
0
1
1
0
1
1
1
3
0
1
1
1
0
0
1
2
1
2
1
1
2
1
1
1
1
0
0
0
1
1
1
1
1
0
0
1
3
1
0
2
0
2
1
1
0
0
1
1
0
0
1
1
1
1
1
1
0
1
1
1
2
0
1
1
0
1
0
1
1
2
1
2
2
3
1
1
2
0
1
2
0
0
2
2
1
1
1
0
1
1
0
0
0
2
1
0
0
1
1
1
1
0
3
1
2
1
2
0
1
0
2
1
1
1
1
0
1
3
0
1
0
0
1
2
1
1
2
0
1
0
1
1
1
1
0
1
1
1
1
1
0
1
1
0
0
1
1
2
2
2
0
0
0
1
1
1
1
0
2
1
0
2
1
1
2
1
0
0
1
2
2
1
0
2
0
1
2
1
1
0
1
1
0
1
1
1
1
2
1
1
0
1
1
0
1
1
2
1
5
0
2
2
1
1
0
0
1
2
0
0
2
2
0
1
1
1
0
1
0
1
0
1
2
0
0
0
1
1
1
1
0
2
2
0
1
1
0
2
1
0
1
1
2
1
1
1
2
1
0
0
0
2
0
0
1
2
1
1
0
1
1
2
1
2
2
2
1
1
2
0
1
0
1
2
2
2
2
1
2
1
2
1
0
1
1
1
1
0
1
0
0
0
0
1
2
2
0
0
0
1
0
1
0
0
0
1
1
1
0
0
1
0
1
0
2
2
0
1
1
0
1
0
2
1
2
0
1
1
0
1
1
1
2
1
1
1
2
0
1
2
2
1
0
0
2
1
0
0
0
0
1
1
0
0
0
1
1
2
1
0
1
0
1
0
2
1
1
1
0
0
0
2
0
2
2
2
0
1
0
2
1
0
0
1
0
2
2
1
0
0
1
0
1
3
1
1
1
0
0
0
1
1
1
1
0
0
1
2
1
1
0
2
0
2
1
1
0
1
1
1
1
3
0
2
1
0
1
1
0
1
2
1
1
1
2
1
0
0
1
1
1
2
1
0
1
1
2
2
1
1
2
1
1
2
1
1
0
0
1
1
0
2
1
1
2
1
2
1
1
1
1
2
0
1
0
1
0
1
3
0
0
0
0
1
6
0
1
0
0
2
2
1
1
1
1
1
0
2
0
0
1
2
1
1
2
0
0
2
0
2
2
0
1
1
1
1
2
1
0
0
0
1
0
1
3
1
0
1
2
2
0
0
1
0
1
1
1
2
2
2
2
1
1
1
1
1
0
2
1
0
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
0
2
2
1
2
1
1
1
1
2
1
0
0
2
0
0
1
2
0
0
1
1
2
2
2
1
1
0
0
1
2
0
0
1
1
1
2
1
1
0
2
0
1
2
0
1
1
1
0
2
2
2
1
1
1
2
2
0
0
1
0
1
1
2
0
1
0
2
3
2
0
1
0
2
1
0
0
1
1
0
0
1
2
2
1
1
2
1
2
0
1
1
0
2
1
0
0
1
1
0
2
1
2
2
0
2
1
1
0
0
1
0
0
2
2
1
0
1
0
2
2
1
2
2
0
2
2
2
1
2
1
1
1
1
1
2
2
1
1
0
0
0
1
2
2
0
2
2
1
0
1
2
2
1
0
1
1
1
0
1
1
2
1
0
0
1
1
2
1
1
0
1
1
3
2
2
1
0
1
0
1
2
2
1
1
0
2
1
2
1
1
1
1
2
1
1
0
2
1
2
1
1
0
1
0
1
1
0
1
0
0
1
1
1
2
0
1
0
2
2
0
1
1
0
0
0
0
0
1
1
1
2
0
1
0
0
1
2
0
1
0
2
1
0
0
0
2
2
1
0
0
1
0
1
2
0
0
0
0
1
1
0
2
2
2
2
1
1
0
0
1
1
1
1
1
0
0
3
1
1
0
1
0
1
0
1
2
2
1
0
1
1
2
2
2
1
0
2
1
2
0
0
0
1
1
0
1
1
2
0
1
2
2
0
2
1
1
1
1
1
2
2
1
0
1
1
1
1
1
1
1
2
1
1
1
1
2
0
1
0
0
1
0
2
0
1
1
2
2
0
2
1
1
1
1
1
2
1
1
0
1
1
1
1
1
2
0
1
0
1
1
1
1
1
1
1
1
0
1
1
1
0
0
1
1
0
1
1
2
1
2
0
0
2
1
2
1
0
0
2
3
2
0
1
0
0
0
0
1
0
0
0
0
0
1
2
1
1
1
1
0
0
2
0
1
2
1
0
1
0
0
0
3
0
0
2
2
1
2
0
1
2
1
2
1
1
2
2
0
1
1
0
1
1
0
1
1
0
1
1
2
1
1
1
2
1
2
2
2
1
1
0
2
1
0
1
1
0
1
0
1
0
2
1
0
1
0
0
0
1
1
4
1
1
1
1
0
1
1
1
1
1
1
0
1
1
2
2
0
0
1
2
1
2
4
0
0
0
1
1
1
1
2
0
2
2
1
1
1
1
0
1
1
0
1
0
2
0
1
1
0
0
1
0
0
2
0
0
0
1
0
1
1
0
0
0
1
2
1
0
0
0
0
0
1
1
1
1
1
2
1
2
2
2
2
1
1
2
1
1
1
1
1
2
1
0
0
2
0
1
2
1
0
2
0
0
0
2
0
0
0
3
0
1
0
1
1
0
2
2
0
2
0
0
2
1
2
2
0
1
0
0
2
0
2
1
0
2
1
1
1
1
0
0
0
1
2
2
1
0
0
0
2
1
0
1
5
1
1
0
0
3
0
2
1
0
0
1
0
1
1
1
1
1
1
0
0
1
2
2
1
2
1
0
1
0
1
2
0
0
1
0
2
2
0
1
1
0
2
0
2
0
1
0
1
1
1
1
0
1
0
0
2
1
0
1
0
2
0
0
2
2
0
1
3
1
1
0
1
1
1
0
1
0
1
1
0
2
0
0
2
0
2
2
1
0
0
1
1
3
2
0
0
1
1
2
1
2
0
2
1
2
0
1
0
1
2
1
1
1
0
2
2
0
1
0
1
4
2
1
1
2
1
0
0
0
0
1
1
1
2
2
0
1
0
0
0
0
1
1
0
0
2
1
0
1
1
2
3
0
0
0
2
1
1
1
0
1
0
0
1
0
1
1
1
2
1
1
0
1
1
1
1
1
0
2
0
1
0
1
1
1
0
1
2
0
1
1
1
0
3
1
1
1
0
1
1
0
1
1
1
1
0
0
1
1
1
0
1
1
2
2
1
1
1
1
2
1
2
1
2
1
1
0
2
2
2
0
1
0
1
1
0
2
1
0
1
1
1
1
1
2
1
0
2
1
1
1
1
2
2
2
1
1
0
0
2
1
1
0
0
2
1
0
0
0
0
1
1
2
2
2
1
2
2
0
1
0
0
0
0
1
1
0
1
0
1
1
1
1
2
0
1
1
1
0
1
0
1
1
2
2
1
2
0
0
0
2
1
0
1
1
1
1
1
1
1
0
1
0
1
1
2
2
0
0
2
1
0
2
0
1
0
0
0
0
0
2
1
0
0
2
2
1
1
4
0
0
1
1
0
0
0
1
1
1
0
0
2
1
1
2
0
0
0
1
0
1
0
1
2
0
1
1
2
1
1
1
0
0
1
2
2
1
0
1
0
0
0
1
0
0
0
1
2
1
1
2
0
1
1
0
1
1
2
0
2
1
2
1
1
1
1
1
1
0
2
1
0
1
0
0
2
0
1
0
0
2
1
1
0
0
2
0
1
2
1
1
2
0
2
1
1
0
0
2
1
0
0
0
1
1
1
1
0
1
1
1
0
1
1
1
1
0
1
0
0
1
2
1
0
3
0
1
0
2
2
1
1
0
1
1
1
1
2
1
1
0
1
0
1
1
0
0
1
1
0
2
1
0
0
1
0
1
0
0
0
1
1
2
2
1
1
0
0
1
0
1
2
1
1
2
1
2
0
1
0
1
1
0
1
1
0
1
2
1
2
2
1
0
3
1
1
0
1
0
1
0
2
0
2
1
1
3
2
1
2
0
1
2
1
0
0
0
2
1
2
1
2
2
0
1
0
2
0
1
1
1
0
1
0
0
2
0
1
1
1
1
1
1
1
0
1
1
1
0
2
2
1
1
0
1
1
0
2
2
1
0
1
1
1
0
0
2
1
0
2
1
1
1
0
1
2
0
3
2
1
1
1
1
0
0
3
1
1
1
1
0
0
1
0
1
1
1
1
1
2
2
1
2
1
1
2
0
0
0
1
0
1
2
0
0
2
1
1
1
1
0
2
0
0
0
0
2
1
1
1
1
2
0
1
1
0
1
1
2
1
0
1
2
1
0
1
1
0
1
2
2
1
0
1
2
1
0
0
0
1
0
1
1
2
0
1
1
2
1
0
1
0
1
0
0
0
1
1
2
1
2
2
1
2
1
0
0
0
1
1
0
0
1
1
0
2
2
1
1
1
1
2
0
1
1
1
2
0
0
0
1
1
0
0
1
1
2
0
1
0
0
3
2
0
0
1
1
0
0
1
0
0
1
0
0
0
2
1
1
0
2
1
2
3
0
1
1
1
3
1
1
1
1
0
1
1
1
2
1
2
0
2
1
1
0
2
0
2
1
1
1
2
0
2
1
1
1
1
1
1
2
1
0
0
0
1
2
0
1
1
0
2
1
0
0
1
2
0
1
0
2
2
0
0
1
0
1
2
0
1
0
1
0
1
1
1
1
1
0
4
1
1
2
2
0
2
0
2
0
1
0
1
1
1
2
2
1
0
3
1
0
2
2
0
2
0
1
2
1
0
2
0
0
0
2
0
2
1
1
2
0
1
2
1
1
0
2
1
1
1
1
1
0
1
0
1
0
0
0
2
0
2
1
1
2
2
2
1
1
1
2
2
0
2
0
1
0
0
0
2
0
0
0
2
0
1
2
1
1
1
0
2
1
1
0
1
1
0
0
2
2
1
2
2
1
1
2
0
1
0
1
1
0
1
1
0
1
0
1
1
1
0
1
1
1
2
0
2
2
0
0
0
2
1
0
1
1
0
1
0
1
0
2
2
2
2
1
0
2
1
0
2
1
1
0
1
1
2
2
1
0
2
0
1
1
0
1
0
1
0
0
0
1
2
0
2
0
0
1
2
1
3
0
1
2
0
0
1
2
1
2
1
2
1
0
0
1
0
0
0
1
1
1
0
2
1
1
1
0
1
0
2
2
0
0
0
1
2
0
2
1
2
1
1
1
0
1
1
0
1
1
1
1
2
0
1
1
0
0
0
0
2
1
1
0
2
2
1
2
2
2
0
1
1
1
0
0
3
1
2
0
2
1
1
0
1
1
2
2
0
1
0
1
0
1
2
1
1
1
1
1
1
0
0
2
1
1
1
0
1
2
1
1
1
2
2
0
0
0
0
0
1
1
1
1
1
2
1
2
1
1
1
1
0
0
0
1
1
0
1
1
0
1
1
2
2
2
1
2
1
1
0
1
0
0
3
2
1
1
0
1
2
2
1
1
1
1
2
1
1
1
1
0
0
2
1
2
0
2
0
1
2
0
1
2
0
0
0
1
1
0
1
0
1
2
0
1
1
2
2
0
1
1
2
1
2
1
0
1
0
1
1
0
1
1
1
0
2
0
0
0
1
2
1
1
1
1
0
0
1
0
0
1
1
1
1
1
1
1
2
2
1
1
3
0
2
2
2
1
2
1
1
2
1
0
0
1
1
1
2
3
1
2
0
2
0
1
2
2
0
0
1
0
0
1
1
0
2
2
2
0
0
1
1
0
1
0
1
0
1
1
0
2
1
1
1
2
1
0
1
1
0
0
0
2
0
1
1
0
2
0
1
2
1
1
2
0
0
2
1
1
0
1
2
1
0
0
2
1
0
2
1
2
2
0
0
2
2
0
0
2
0
1
1
0
2
1
1
0
2
1
1
1
2
0
1
0
0
2
1
2
1
1
2
1
2
2
1
0
1
2
1
0
2
1
1
2
2
1
1
1
1
2
1
1
0
0
1
1
2
0
0
0
2
0
0
3
1
2
2
0
1
0
1
1
1
1
1
2
1
2
1
2
1
3
1
1
1
0
0
2
2
1
1
0
0
0
2
2
1
1
2
1
1
0
0
1
1
0
1
2
1
2
1
0
2
1
0
1
1
1
1
0
1
0
1
1
1
1
0
1
0
0
0
0
1
1
1
1
1
2
0
0
1
0
0
1
2
1
1
0
1
0
0
0
2
0
1
1
0
0
0
1
2
1
1
1
1
2
0
0
0
2
0
0
2
0
3
1
1
1
0
1
1
1
2
1
1
1
2
2
0
0
0
2
0
1
2
1
2
0
2
0
1
2
3
1
2
0
0
2
1
0
0
1
2
2
2
2
2
0
0
1
1
2
1
0
1
0
2
1
0
2
1
0
0
1
1
1
1
1
1
2
3
1
2
1
1
0
1
2
1
2
1
1
0
2
2
2
0
1
1
2
1
2
3
0
1
2
0
2
1
0
0
1
0
2
1
2
0
0
1
1
0
1
0
0
1
2
1
1
1
0
1
1
2
1
1
1
0
1
0
2
1
1
0
0
1
0
0
1
1
1
0
0
3
1
2
1
1
0
2
0
1
0
0
1
0
0
1
0
1
1
2
2
0
2
1
0
1
2
1
0
2
2
1
1
2
0
0
1
1
1
1
1
1
2
1
1
1
0
0
1
0
1
0
0
1
1
0
1
1
1
1
2
0
0
0
1
0
2
1
0
0
1
1
2
1
2
1
1
0
1
1
2
1
0
0
0
1
0
3
2
1
2
2
1
0
0
1
0
0
1
2
2
1
3
1
0
2
0
0
1
2
0
1
1
1
1
0
1
0
0
1
0
1
1
0
0
0
0
0
1
2
2
0
2
1
2
2
2
0
0
1
2
2
1
0
0
0
0
1
0
1
1
1
1
1
1
0
0
1
1
1
1
1
2
0
1
0
2
0
1
2
2
2
2
0
1
1
0
1
1
2
1
1
0
0
0
0
0
1
1
0
1
1
0
1
2
0
2
2
2
0
0
1
3
4
1
2
0
0
0
0
0
1
2
0
1
0
1
0
0
2
0
1
1
2
1
1
2
0
4
2
0
0
2
1
1
1
1
1
2
1
0
2
1
1
1
1
1
0
1
1
0
1
2
1
1
1
2
1
1
0
1
1
0
1
2
0
1
3
1
2
2
0
2
0
1
1
2
0
0
1
1
1
1
2
1
1
1
1
1
1
0
1
1
0
0
0
1
1
0
1
0
2
1
1
2
1
2
1
2
1
0
0
1
1
1
0
0
0
1
0
1
0
1
1
2
1
0
0
1
2
1
0
0
2
0
2
0
0
2
0
2
0
1
1
0
1
1
2
0
1
1
1
1
0
2
2
0
1
1
0
2
0
3
0
1
2
1
1
1
2
2
1
1
1
1
0
1
1
0
1
0
0
1
2
1
2
0
2
0
1
0
1
2
2
2
0
1
2
0
0
1
2
1
1
1
0
2
1
1
0
1
1
0
2
2
1
0
0
1
1
1
1
2
1
1
1
2
1
1
2
1
1
2
2
1
1
0
0
0
1
2
1
1
2
1
2
0
1
0
2
1
0
0
1
2
0
1
0
0
1
1
0
2
1
2
2
0
0
2
2
1
1
1
1
1
2
1
2
0
0
1
1
0
1
1
0
1
0
0
1
1
1
1
0
0
0
2
1
1
1
0
2
1
0
0
2
1
0
1
0
1
0
1
2
0
1
0
1
0
1
0
2
2
2
2
1
0
0
2
2
2
0
0
0
1
2
2
1
1
0
1
0
0
1
1
0
2
0
0
0
0
2
0
2
1
2
0
0
0
1
2
2
0
1
1
2
1
2
1
0
2
1
0
2
1
2
2
2
0
1
1
1
1
0
1
1
1
1
1
1
0
2
1
1
1
2
1
1
1
0
2
0
2
2
2
2
1
0
1
1
0
1
0
0
0
4
0
0
2
2
1
1
0
1
0
0
0
0
0
1
2
1
1
1
2
1
1
0
1
1
2
0
1
1
2
1
1
2
2
1
0
5
1
0
1
1
0
1
1
1
1
1
1
1
1
2
0
1
1
1
0
2
1
0
0
1
0
1
0
1
2
0
2
2
0
1
1
0
0
0
1
2
2
2
2
0
0
1
0
0
2
1
1
0
0
1
1
0
1
2
1
2
1
0
1
2
1
1
3
2
1
0
1
2
1
1
1
0
1
1
1
0
1
2
0
1
2
0
0
0
0
0
2
1
1
2
0
1
0
3
1
1
1
2
1
1
1
2
0
1
1
2
1
1
1
1
2
0
0
2
1
0
0
0
0
1
1
2
0
2
1
3
1
2
1
0
1
0
0
2
2
1
1
1
1
2
0
2
1
1
1
1
0
1
0
1
2
1
1
0
1
2
2
0
0
0
1
3
0
1
0
1
0
0
0
0
2
1
1
1
1
1
0
0
1
2
2
1
1
1
2
1
2
1
1
1
0
2
1
2
1
0
0
2
1
0
1
0
2
1
0
1
1
2
2
0
2
2
1
0
0
2
0
1
1
0
1
1
1
2
0
1
1
0
0
0
2
2
1
1
0
0
1
1
0
1
0
1
0
0
0
0
0
1
2
2
0
2
1
1
1
0
1
1
1
1
1
0
2
1
1
1
2
2
1
2
0
0
0
0
1
0
1
1
0
0
0
1
0
1
1
0
1
0
2
1
1
2
1
0
2
1
2
0
0
2
0
0
1
1
0
1
0
0
3
1
1
1
0
1
2
2
1
2
0
1
0
1
0
2
1
1
0
2
1
2
1
1
2
1
0
0
1
0
1
2
1
1
1
0
1
0
2
1
2
0
0
0
1
0
1
0
2
0
1
0
0
2
1
0
0
2
1
1
1
0
1
0
1
2
0
0
0
0
2
0
1
1
1
0
1
1
1
2
1
1
0
2
0
2
1
1
0
0
0
0
0
1
2
1
1
1
3
1
1
3
0
1
1
0
2
2
1
0
1
1
2
0
0
1
2
1
1
1
1
1
0
1
0
1
2
1
0
1
1
0
1
1
1
1
0
0
1
2
1
0
1
1
1
1
2
1
1
1
2
0
2
1
0
1
1
1
0
2
1
1
1
0
0
2
2
1
0
0
2
0
1
1
1
2
2
1
3
2
2
0
0
0
1
2
1
0
1
0
0
1
0
1
0
0
0
0
1
0
2
0
0
2
1
0
2
1
1
2
1
0
1
0
0
1
2
1
0
2
0
0
1
2
0
1
0
0
1
0
1
1
0
1
1
0
0
1
0
0
0
2
1
1
2
1
1
1
1
0
2
2
1
1
0
2
1
0
1
1
1
2
1
0
1
0
0
2
1
0
0
1
0
0
1
1
1
0
2
1
0
0
0
1
0
2
1
1
1
1
0
0
2
2
2
0
0
0
1
1
2
0
0
1
1
1
0
0
0
0
1
1
1
2
1
2
2
0
1
0
1
2
0
1
1
2
1
2
2
1
2
0
1
0
0
1
1
1
1
1
1
1
0
1
2
0
1
2
1
1
0
0
2
2
2
1
0
0
1
1
2
1
0
2
1
1
2
0
1
2
1
2
2
2
2
0
1
2
1
0
2
1
1
1
1
2
1
1
2
1
0
1
2
2
1
0
4
1
1
1
0
2
0
1
0
0
2
2
0
0
1
1
0
1
1
2
2
1
0
0
2
1
0
2
0
2
1
0
1
1
1
1
2
3
1
0
1
0
1
2
1
0
1
1
1
2
1
0
0
0
0
1
0
1
1
1
0
0
2
1
0
1
0
0
0
1
0
2
2
2
0
1
2
1
1
0
2
0
1
0
2
1
1
1
1
0
2
1
2
0
0
0
1
1
1
1
1
1
1
2
0
0
0
1
1
1
1
2
2
1
0
2
1
0
1
1
2
0
2
1
0
1
1
2
1
0
1
1
0
0
1
1
0
1
2
1
0
1
1
1
1
2
1
1
1
2
1
1
0
1
1
0
0
1
2
2
1
0
1
2
1
1
1
0
0
2
1
0
1
0
0
1
1
1
2
0
1
1
3
0
2
2
0
1
0
1
1
1
0
1
1
1
1
2
1
1
1
0
0
2
2
1
0
0
1
1
0
0
2
1
0
0
0
0
0
0
1
1
0
1
2
2
1
1
1
1
1
1
2
0
1
0
2
1
1
2
2
0
1
0
0
0
0
1
0
2
0
1
1
0
0
0
1
1
2
0
0
0
1
1
1
0
2
2
0
1
2
0
2
0
1
1
0
1
2
2
1
4
1
1
1
1
2
1
2
0
1
2
1
2
1
2
1
1
0
0
0
0
1
1
0
1
0
0
1
0
0
2
1
0
0
0
1
1
2
0
2
2
1
1
1
1
0
1
0
2
2
1
1
1
1
1
3
1
1
0
1
2
0
1
0
1
1
1
0
0
0
0
1
1
0
1
2
2
1
0
2
1
2
1
2
2
1
1
1
0
2
1
0
2
0
0
2
1
1
0
0
0
0
1
0
1
1
2
1
0
2
0
1
1
2
1
0
0
2
0
0
0
1
0
0
1
0
2
1
0
0
2
1
1
1
1
2
2
2
2
0
1
0
0
0
1
1
2
0
1
0
2
1
1
1
9
0
1
0
0
1
1
0
0
0
0
1
1
0
1
1
1
1
1
2
1
1
1
2
0
1
2
0
2
1
0
0
2
2
2
2
0
0
2
0
0
1
1
6
0
0
0
2
2
1
2
2
1
1
1
0
0
1
0
0
1
0
1
1
1
0
1
1
2
1
0
0
2
0
1
0
0
2
0
0
2
2
0
2
0
1
1
2
0
0
0
0
0
1
0
1
2
0
1
2
0
1
2
1
0
1
0
0
1
2
1
2
1
1
1
1
1
2
2
1
1
2
2
3
1
0
1
1
1
1
2
2
0
0
1
0
0
4
0
1
1
1
1
1
1
2
0
1
2
0
1
1
1
2
1
0
2
1
2
2
2
0
1
1
0
1
2
0
2
3
1
1
1
0
1
1
0
2
0
1
2
1
1
0
0
1
0
1
2
0
1
1
2
0
2
2
0
0
2
1
1
1
2
2
1
0
1
1
2
2
1
0
3
0
0
0
2
1
1
0
1
1
2
0
2
0
0
2
1
1
1
0
1
1
0
0
1
0
1
1
2
0
2
1
1
1
2
1
0
2
1
1
1
0
2
1
0
1
1
1
1
2
1
1
1
0
1
1
1
1
0
1
2
0
0
1
2
0
2
1
0
1
1
1
1
0
1
2
1
2
0
2
1
0
0
0
1
2
2
3
1
2
0
1
1
0
1
1
0
1
2
1
1
1
2
0
1
3
1
1
0
0
1
0
1
0
0
1
0
0
1
1
1
0
1
0
0
1
2
0
0
2
0
2
0
1
1
1
1
0
1
2
1
0
0
2
3
1
1
0
0
0
1
2
0
1
0
1
1
0
1
0
0
1
1
2
0
0
2
1
1
0
1
1
1
1
1
1
0
2
1
0
2
1
1
0
2
0
2
1
1
2
2
0
1
2
2
1
2
2
4
1
1
1
0
1
1
1
2
0
0
1
1
1
1
1
0
1
1
1
0
0
0
0
0
1
0
0
1
2
2
2
0
0
1
2
0
2
2
2
1
1
1
2
0
0
1
0
1
1
1
0
0
1
0
1
0
1
0
0
0
1
0
1
1
1
1
1
2
0
0
1
1
1
1
1
1
2
2
2
0
2
0
1
1
1
1
0
1
1
1
2
1
1
3
1
0
0
1
2
1
1
2
0
0
1
0
0
2
1
2
2
1
1
0
2
1
0
1
2
0
0
2
1
1
1
0
1
2
0
1
1
0
1
4
1
1
2
1
0
0
0
1
0
1
2
1
0
2
1
0
1
2
0
1
2
0
1
1
2
2
3
2
0
2
0
1
1
1
0
0
0
1
1
1
2
1
1
0
2
1
2
2
1
0
2
0
1
1
1
2
2
2
2
0
2
1
1
2
0
0
2
0
0
1
0
1
2
0
2
2
0
1
1
0
1
1
0
1
1
0
1
3
2
1
0
0
0
0
0
2
1
0
2
2
1
0
2
1
0
0
2
1
1
0
0
1
1
0
1
0
1
6
2
1
1
1
0
1
2
1
1
2
0
2
1
2
2
0
1
1
2
2
1
1
1
0
2
0
1
2
0
0
0
1
1
0
2
0
0
1
1
2
2
0
0
1
2
1
2
0
0
2
2
0
0
2
2
2
1
0
2
1
0
2
1
0
2
0
0
0
1
1
1
0
1
0
0
1
0
0
1
1
1
1
4
0
1
1
2
1
1
2
1
0
0
4
1
0
0
1
0
2
0
0
1
1
1
0
1
1
1
2
1
2
1
1
1
0
1
1
2
0
1
2
0
2
1
0
0
0
2
0
0
1
1
1
0
0
1
0
1
6
0
1
1
2
0
0
1
0
1
0
2
2
1
0
1
0
1
1
0
1
2
1
1
2
0
2
0
1
0
2
0
0
1
2
2
0
2
1
1
2
0
1
1
2
1
2
2
2
0
1
1
1
2
1
0
1
1
0
0
1
1
0
1
0
1
1
1
1
0
1
0
0
1
1
0
0
0
1
0
0
1
0
2
0
1
0
1
1
1
0
1
1
1
0
1
2
0
0
0
2
1
1
2
1
2
1
0
0
0
0
1
0
1
1
1
0
1
0
0
2
0
2
1
1
2
2
1
2
1
1
0
2
2
1
1
0
1
0
1
2
0
1
1
1
2
0
0
0
1
0
1
0
0
0
1
1
1
1
0
1
1
1
2
1
1
1
2
0
0
1
1
0
1
1
1
0
3
1
1
1
1
2
0
0
2
1
1
0
1
2
1
0
0
1
0
1
2
2
1
0
1
1
1
0
1
1
1
0
1
2
0
1
2
0
1
2
0
0
0
1
2
0
2
1
1
2
1
0
2
1
0
2
1
0
1
2
2
0
0
0
1
2
0
1
2
1
1
1
1
2
2
0
1
2
1
1
0
0
2
1
1
0
1
2
0
1
2
0
1
1
2
0
1
1
0
1
0
1
3
0
2
0
0
1
0
1
1
1
0
0
0
2
1
0
1
2
1
1
2
1
0
1
1
3
0
1
1
1
0
2
0
0
0
2
0
2
0
1
0
1
2
2
1
1
1
2
2
1
1
1
0
1
2
0
1
0
1
1
1
2
1
1
1
2
0
1
0
0
2
0
1
2
1
0
1
1
0
2
1
0
0
1
1
1
3
1
0
1
1
1
0
1
0
1
0
1
1
2
2
1
2
4
0
0
1
2
1
2
1
0
0
1
2
0
0
1
1
1
1
1
1
0
1
2
2
1
1
3
1
2
0
1
2
1
1
2
1
2
1
1
1
2
1
0
1
1
0
2
0
1
0
1
1
1
2
2
2
1
0
0
1
1
1
2
2
2
1
0
2
0
2
2
2
1
0
2
1
1
1
2
2
2
0
1
0
2
0
0
0
2
1
0
0
0
1
2
1
2
2
0
0
0
2
1
1
1
1
0
1
1
0
1
2
0
2
2
1
0
1
1
1
0
1
1
1
1
2
1
2
2
1
0
1
0
1
0
3
0
0
1
1
1
1
0
0
1
0
1
0
1
1
0
0
1
1
1
1
0
1
1
1
1
0
0
2
0
0
1
2
1
0
0
0
3
2
1
0
1
1
0
2
2
0
2
0
0
0
2
1
1
0
0
1
1
1
0
2
0
2
2
0
2
0
2
1
0
0
1
1
1
1
1
1
0
1
2
2
1
1
0
0
1
0
1
0
2
2
2
1
0
1
1
0
0
0
1
1
0
0
1
0
3
0
3
1
0
2
1
0
1
1
0
2
1
0
1
1
0
1
3
0
0
0
1
1
1
0
1
1
2
1
2
1
2
0
0
0
0
1
1
1
2
0
1
1
0
0
3
0
1
0
1
1
1
1
0
0
2
0
2
1
1
1
2
1
1
2
2
2
0
1
2
0
0
1
0
0
2
0
2
2
1
1
1
2
1
0
2
1
1
1
1
0
2
1
0
2
1
0
2
0
2
2
0
2
0
1
2
2
0
0
2
0
0
1
1
0
0
0
0
1
3
2
1
0
1
2
1
2
0
2
2
0
1
1
0
1
1
1
2
1
1
2
2
1
1
0
0
0
0
1
1
1
0
1
1
1
3
1
2
1
0
1
1
0
2
2
2
2
1
1
0
3
1
2
1
2
1
1
1
1
0
0
1
1
1
2
2
1
0
1
2
0
1
1
2
1
1
2
0
0
0
2
1
0
0
1
2
0
0
1
1
0
0
1
2
0
2
1
0
2
0
1
0
1
0
0
2
0
1
1
0
0
2
0
2
1
0
2
0
2
0
2
1
1
0
0
1
0
2
1
1
0
1
0
1
2
1
0
1
0
0
0
0
1
0
2
2
1
2
0
1
0
1
2
1
0
1
0
1
1
1
2
0
1
1
1
3
1
1
0
1
0
1
1
0
1
0
1
1
0
1
0
1
2
1
1
0
2
0
2
1
2
1
1
1
1
0
0
1
1
0
2
1
0
0
1
7
1
1
2
3
1
0
1
0
2
2
1
0
1
0
1
0
1
1
0
0
1
1
2
4
0
2
1
0
1
1
1
1
0
0
1
1
2
0
0
2
1
0
0
1
1
1
1
1
1
2
1
2
1
0
0
1
1
1
1
0
0
2
1
1
1
0
0
2
0
2
1
2
1
1
0
1
1
1
0
1
1
1
0
0
1
2
0
0
1
1
0
0
1
0
1
1
0
2
1
3
0
1
2
1
0
2
0
2
1
0
0
1
2
0
2
1
1
2
0
0
2
1
1
1
1
1
1
2
1
1
0
3
2
2
0
1
1
1
2
1
1
1
0
1
2
0
1
4
1
1
1
1
1
0
0
0
1
2
0
1
1
0
2
1
2
1
2
2
0
2
1
1
1
0
1
0
1
3
1
3
0
1
1
2
0
0
1
1
1
2
1
0
0
0
0
1
0
0
1
0
1
0
2
2
0
1
2
0
1
0
1
2
2
1
1
1
1
0
1
1
1
1
0
2
0
0
1
0
1
3
2
2
1
0
1
1
0
1
0
1
1
1
1
1
1
0
2
1
0
0
1
2
1
0
0
2
1
1
1
1
0
0
1
2
1
1
1
1
1
0
1
0
1
1
1
1
0
1
0
1
0
0
2
1
1
2
1
0
0
1
0
2
1
2
1
1
1
1
0
1
0
0
1
2
2
2
0
1
0
0
2
1
2
0
1
0
2
1
0
0
0
1
1
0
2
0
0
0
0
0
0
2
2
0
0
2
1
2
0
1
1
2
0
0
0
0
1
2
0
1
0
0
2
4
1
1
1
1
1
0
0
0
2
1
2
0
2
2
0
1
2
2
1
0
0
1
2
1
0
1
0
1
2
1
1
2
2
1
1
1
3
0
0
1
0
1
1
1
1
2
2
3
1
2
1
1
1
0
1
1
1
1
0
1
1
1
1
0
1
0
0
1
2
1
0
0
1
0
1
0
0
1
1
1
1
0
0
1
1
1
4
1
2
1
0
0
2
1
1
1
1
2
1
2
1
1
0
2
0
1
0
0
1
1
1
1
0
0
2
1
0
0
0
0
0
2
0
0
1
0
2
1
0
0
2
1
0
2
0
0
0
2
0
0
0
2
1
2
1
0
0
0
3
0
1
1
2
1
1
0
1
1
2
1
0
2
1
1
0
2
0
1
1
2
1
2
1
2
2
1
1
0
0
2
1
0
0
2
1
0
0
2
1
1
0
2
1
1
2
2
0
0
2
0
0
2
1
2
0
2
0
1
0
1
2
1
2
1
2
1
0
0
0
0
2
0
0
1
2
1
1
2
0
1
2
0
1
1
1
1
1
2
1
1
2
2
0
1
2
1
1
2
1
0
2
0
0
0
1
1
0
2
1
0
0
0
1
1
1
2
1
0
2
1
1
0
3
1
2
0
1
2
1
0
1
0
1
1
0
2
2
2
0
2
1
2
2
3
1
1
0
1
1
7
1
2
1
1
2
0
1
1
1
1
1
1
1
1
1
1
0
1
2
1
2
1
1
0
0
1
1
2
1
1
2
1
3
2
0
2
0
0
0
0
1
0
0
1
1
0
1
0
1
0
1
1
2
0
1
0
1
2
3
1
0
1
1
0
2
0
0
1
0
2
2
0
0
0
1
1
1
2
0
0
2
0
1
0
1
1
1
1
1
0
0
1
1
1
1
1
0
2
2
3
1
0
1
0
1
0
2
2
1
2
0
2
0
1
1
2
2
1
1
2
1
0
0
0
1
1
0
1
2
1
2
1
1
2
2
0
0
2
0
1
1
2
2
1
0
1
1
2
1
0
1
2
1
2
0
0
0
2
1
2
1
0
1
1
2
2
0
1
1
1
2
0
1
1
2
1
0
0
1
0
1
3
2
0
1
0
2
1
2
0
0
1
0
1
2
1
0
0
1
1
1
1
0
0
1
1
1
0
0
0
1
2
1
0
1
1
1
1
1
1
2
0
1
0
1
0
1
1
2
1
1
1
1
2
1
1
1
1
0
0
0
1
0
0
0
1
3
1
2
0
1
1
1
0
1
2
1
1
1
1
2
0
1
2
1
0
0
2
0
0
1
1
1
1
2
0
0
1
0
0
1
1
1
1
1
1
1
0
1
0
2
0
1
2
2
1
2
0
1
0
0
1
0
1
1
1
1
0
0
1
0
1
1
1
1
0
1
0
0
1
1
1
1
1
1
1
1
0
1
1
1
3
1
2
0
0
1
0
0
2
1
1
1
1
0
2
1
1
1
2
2
1
0
0
1
2
0
1
0
1
0
0
0
0
0
0
1
0
0
2
1
1
0
1
1
0
0
0
0
2
2
1
2
1
2
1
2
1
1
2
1
1
0
2
2
2
2
0
0
2
2
1
1
2
1
2
1
1
1
2
1
0
2
2
0
1
1
1
0
1
0
0
0
0
2
1
2
1
1
1
0
0
1
1
2
2
2
2
0
0
0
1
0
0
2
0
1
1
1
1
2
0
2
0
2
1
0
2
0
1
0
1
0
0
0
1
2
1
1
0
0
1
0
1
1
0
0
2
0
0
2
2
2
0
1
1
2
1
1
0
2
1
1
1
1
1
0
1
1
1
0
2
1
1
1
1
1
1
1
0
0
0
1
2
1
0
1
0
1
1
1
0
1
0
1
1
2
0
2
0
0
0
0
1
1
1
0
1
1
1
1
2
0
2
2
1
1
0
1
1
2
2
2
0
0
0
0
2
1
1
0
1
1
0
1
2
1
1
0
1
0
1
2
2
1
0
0
1
1
1
1
1
0
1
1
0
1
0
2
2
1
0
2
1
0
0
1
1
2
0
0
1
1
1
0
0
1
3
2
1
1
1
2
0
1
2
2
0
1
1
2
1
1
1
2
10
2
1
0
1
1
2
1
0
0
2
1
0
0
1
1
1
1
2
0
1
2
1
2
0
1
1
1
1
2
0
0
0
2
2
2
0
1
1
1
1
0
2
1
1
1
2
0
0
0
1
1
1
0
1
2
1
1
2
1
1
2
0
1
1
1
0
1
1
0
0
1
1
1
1
0
0
2
1
1
0
0
1
2
1
0
0
0
0
1
0
0
0
0
2
2
1
1
2
1
0
2
1
1
1
1
2
2
1
1
0
0
1
1
0
0
2
0
2
1
1
1
0
1
0
0
2
1
0
2
0
0
1
1
1
1
0
1
1
0
1
0
1
0
0
2
2
0
2
1
0
1
1
0
0
0
1
1
2
1
0
1
1
1
1
1
1
0
0
1
1
1
1
2
1
1
1
2
2
1
0
0
1
1
2
0
0
0
1
2
0
1
1
1
1
1
2
0
2
1
1
0
1
0
2
3
0
1
1
2
0
1
2
1
1
2
1
0
1
1
0
0
2
0
1
0
0
1
0
0
1
1
0
2
0
3
0
1
0
1
1
0
1
1
1
2
2
0
2
2
1
1
0
1
0
1
0
1
1
1
2
0
0
0
1
1
1
1
1
1
1
1
0
1
1
0
0
0
3
0
0
1
2
1
1
1
1
1
0
1
1
0
2
2
2
2
0
1
1
1
0
1
1
1
0
1
0
2
1
0
0
1
0
2
1
0
0
2
1
1
1
0
1
0
0
2
1
0
1
0
1
2
0
2
1
1
1
1
2
0
2
1
0
1
0
1
1
1
1
1
1
0
1
1
1
1
0
0
2
0
1
0
1
1
0
2
1
0
2
0
2
0
0
1
2
0
1
1
0
1
0
0
1
0
0
0
1
0
0
2
2
1
2
0
1
1
2
1
1
1
1
2
0
1
0
1
2
1
0
1
1
1
1
1
2
4
2
1
1
0
1
2
1
0
2
2
1
1
1
1
1
1
1
1
2
0
1
1
1
0
1
1
1
0
1
1
1
2
2
2
1
2
0
1
0
1
0
1
0
2
2
1
2
0
1
2
2
1
2
0
1
1
0
1
0
0
0
1
0
1
1
0
0
0
0
2
1
0
1
2
1
1
1
1
0
0
1
1
2
2
1
3
1
1
0
0
1
2
1
0
0
0
2
1
1
2
2
2
1
1
0
2
0
0
1
2
0
3
2
3
1
2
0
0
1
0
2
0
2
1
0
2
1
1
1
1
1
1
1
2
0
1
0
0
1
1
0
2
0
0
0
2
1
0
1
1
1
0
1
1
2
1
0
2
1
0
0
0
2
2
1
0
0
2
1
0
0
1
1
0
1
0
2
1
2
1
2
1
0
2
2
1
1
0
1
1
2
2
1
0
1
1
0
1
1
1
0
1
1
2
0
0
1
2
0
3
0
2
0
2
2
2
0
0
1
0
2
1
0
2
0
0
1
1
1
2
1
1
2
1
0
1
1
0
1
1
2
1
0
0
2
0
1
0
1
1
2
0
1
1
1
2
0
1
0
0
1
2
1
2
1
1
1
2
0
0
2
0
2
2
2
0
1
1
2
0
1
1
0
1
1
1
1
1
1
2
0
0
1
0
1
0
1
1
0
0
0
2
1
1
1
1
1
0
0
0
1
0
2
1
2
1
2
1
0
1
0
0
1
2
1
0
1
2
1
1
0
0
1
0
0
1
0
1
2
0
1
0
1
0
0
1
1
1
2
1
1
1
0
2
1
1
0
0
1
1
0
0
1
1
2
2
0
1
1
1
1
1
0
1
1
1
1
2
1
0
0
1
0
1
3
0
1
0
1
0
0
1
0
1
0
2
0
1
2
2
1
1
1
1
1
1
0
0
1
1
1
1
1
0
1
1
1
0
0
0
1
1
1
1
0
1
1
2
0
1
0
1
2
0
1
1
1
1
0
1
1
1
1
1
2
1
2
0
2
2
1
1
1
2
1
0
1
1
2
0
0
1
1
1
0
0
1
1
1
2
2
2
1
2
1
1
1
1
1
2
0
1
0
0
1
1
2
0
2
0
0
1
1
2
0
0
1
0
1
0
1
2
1
1
1
1
0
2
1
0
0
0
0
2
1
2
1
0
0
1
1
1
1
2
2
0
0
0
0
0
2
0
1
1
0
0
0
1
0
1
2
2
0
0
1
1
1
1
2
2
0
0
0
1
1
1
0
0
0
0
1
2
1
2
0
1
1
2
1
1
1
1
0
2
1
0
0
1
1
1
1
0
1
2
0
0
2
1
0
2
0
2
2
0
0
2
1
1
1
1
1
1
2
1
0
0
2
1
0
1
1
1
0
1
1
0
0
1
0
0
1
1
1
0
0
1
0
1
2
1
1
2
2
1
0
2
2
1
1
0
1
1
1
1
2
1
0
0
0
1
0
1
0
0
1
0
0
0
0
2
0
0
1
2
1
0
2
1
1
1
0
0
2
0
0
0
0
2
1
0
0
1
2
1
1
0
0
0
2
0
0
2
2
0
2
1
1
0
2
1
2
2
0
1
0
1
2
1
0
0
0
2
0
1
1
0
2
0
1
0
0
2
0
0
1
2
0
0
0
2
0
2
0
2
2
0
0
1
0
0
0
1
0
0
1
0
1
1
1
2
0
1
2
0
0
0
2
0
0
1
1
2
1
2
1
2
1
1
0
1
0
0
2
1
2
2
0
0
1
1
0
0
1
0
1
1
1
1
0
2
2
1
0
1
0
1
0
1
1
2
2
1
0
1
0
1
1
1
3
0
0
1
1
2
1
0
1
1
3
1
0
1
1
1
0
1
1
0
0
0
0
1
1
0
2
1
1
1
0
1
0
0
1
2
2
1
1
1
0
2
1
1
1
0
0
2
1
0
1
1
0
1
1
2
0
0
0
2
0
1
0
1
1
1
1
0
0
1
2
1
1
0
0
0
1
1
1
0
0
0
1
0
2
1
1
0
1
0
0
1
0
0
2
2
0
0
0
1
1
2
1
0
0
1
1
1
1
2
2
0
2
1
0
0
0
2
0
0
0
0
1
1
1
1
0
1
1
0
1
2
2
0
0
1
0
2
2
0
0
0
1
1
1
0
0
0
1
0
0
0
0
1
0
1
0
0
2
1
1
0
1
0
1
0
0
2
0
1
1
2
1
0
2
1
1
0
1
1
2
1
2
0
0
0
2
2
2
1
0
2
2
2
1
2
1
1
1
2
0
1
1
1
1
0
1
1
0
0
3
1
2
1
1
1
0
0
1
1
1
1
0
0
1
2
0
1
2
1
1
1
2
0
1
1
1
1
1
1
2
1
1
0
1
0
0
1
1
0
2
2
2
0
1
0
1
1
0
2
0
1
1
1
1
1
2
1
1
1
2
2
1
1
3
1
1
2
1
1
1
0
1
0
0
0
2
1
1
1
2
0
0
1
0
1
0
0
2
1
1
1
1
0
4
1
1
0
0
2
0
1
0
1
2
2
1
2
0
2
1
0
1
1
1
1
0
0
0
0
1
1
1
0
0
0
1
2
1
1
2
2
1
0
2
0
0
2
0
0
0
0
0
1
0
2
0
2
2
1
0
1
0
1
2
1
0
1
1
1
0
1
1
2
0
2
1
1
0
2
1
1
2
0
1
0
0
0
2
1
0
2
1
0
1
0
1
2
0
1
1
1
1
0
1
1
0
2
1
0
0
1
1
1
0
0
0
1
2
1
1
2
1
1
0
3
0
0
1
0
0
2
1
1
0
2
0
2
2
0
1
2
2
1
1
1
1
0
1
2
1
0
0
0
1
1
0
3
0
0
0
1
2
1
1
0
1
0
0
2
2
2
0
1
1
0
1
1
0
2
0
2
1
0
1
1
0
2
1
1
0
0
1
0
2
1
0
1
1
1
2
0
0
2
2
1
1
1
1
0
1
0
2
1
0
0
0
0
1
1
0
1
1
1
1
2
0
2
1
2
2
1
1
2
0
0
1
1
1
0
0
0
1
1
0
0
1
0
2
1
1
0
1
2
0
1
1
2
1
0
1
1
1
2
2
1
1
1
1
0
0
1
1
0
0
0
1
1
1
0
1
1
1
2
1
1
1
1
0
2
0
1
1
1
0
0
0
2
0
0
1
3
1
2
0
1
2
0
1
0
0
0
1
1
2
1
1
4
1
0
1
2
2
1
1
1
1
0
1
1
1
0
0
0
2
0
1
0
2
2
0
2
0
1
1
1
1
1
1
2
1
2
2
1
1
0
1
0
0
1
1
1
1
1
1
0
0
1
0
1
1
0
0
2
1
0
1
0
0
0
1
1
2
2
1
1
1
0
0
1
1
1
1
2
1
2
1
1
0
0
2
0
0
1
1
2
1
1
1
0
2
1
0
2
0
1
1
1
0
0
2
1
0
2
1
2
1
1
1
0
2
1
2
1
1
0
1
1
1
0
2
1
0
0
2
0
0
2
0
1
2
0
0
2
1
0
0
1
1
1
0
0
1
1
0
2
0
1
2
0
1
1
0
0
0
0
1
2
1
1
1
1
0
1
0
0
1
0
0
2
1
2
0
2
1
0
2
2
1
1
2
1
2
2
1
0
2
1
1
1
0
1
2
1
1
1
0
1
1
2
1
1
0
2
2
0
1
1
1
1
0
0
1
0
0
1
0
2
1
1
0
0
2
0
1
0
1
2
1
1
1
0
0
2
1
1
0
0
2
0
1
0
0
0
1
1
2
1
1
1
1
1
0
0
0
0
0
2
1
1
1
1
0
1
0
1
0
1
3
0
0
3
2
1
0
2
1
2
0
2
0
1
0
1
1
0
1
1
1
0
1
1
0
1
1
1
1
1
0
0
1
1
2
1
1
0
3
0
0
1
1
2
0
0
1
2
0
1
2
1
1
1
1
1
1
2
1
2
0
0
0
1
0
1
0
0
1
1
1
1
2
1
2
1
1
2
1
2
0
1
0
1
0
1
2
1
0
0
0
0
0
0
1
0
0
1
1
2
0
0
0
1
0
1
1
1
0
1
1
1
2
0
1
0
1
3
1
0
1
1
2
2
2
0
0
1
2
0
0
1
1
2
2
2
1
2
0
1
2
0
1
2
1
0
2
0
2
1
0
1
0
1
1
2
0
0
1
2
2
1
0
0
2
1
1
2
0
0
0
2
1
1
0
1
1
0
0
2
1
1
1
1
2
0
0
2
0
1
2
0
0
1
1
0
1
1
1
1
1
1
2
0
2
0
0
0
1
1
2
0
1
2
1
1
1
1
2
0
2
0
1
1
2
0
0
0
1
1
0
2
0
0
1
0
2
0
1
0
1
0
1
1
2
0
0
1
0
1
0
1
1
1
0
3
1
1
0
1
0
3
1
1
1
0
2
0
0
1
1
0
0
2
1
2
2
2
2
1
0
0
1
1
1
0
0
0
1
2
1
0
0
1
1
0
2
0
0
1
1
0
1
1
2
2
0
1
5
1
1
1
0
1
1
2
0
0
2
0
0
1
2
0
2
0
1
2
2
1
1
0
1
0
1
1
1
0
0
2
0
2
0
1
2
0
0
0
0
1
1
1
1
1
0
2
0
2
2
1
0
0
1
1
1
1
2
1
0
2
1
0
2
0
2
4
0
0
2
2
0
0
2
0
0
1
1
1
1
2
1
2
1
0
2
0
1
2
0
0
2
2
2
2
1
0
1
2
1
2
1
1
1
1
1
1
1
2
1
1
0
1
1
2
0
0
1
1
0
1
1
0
1
1
1
1
1
0
2
1
2
0
1
2
0
2
2
1
2
2
1
0
0
1
2
1
0
1
2
2
1
0
1
1
2
1
0
2
0
0
0
1
1
0
1
1
0
1
1
0
1
1
0
1
0
1
1
0
1
1
1
1
1
1
1
2
1
1
1
1
1
0
2
1
0
1
0
0
1
1
1
0
1
1
0
0
2
1
2
2
1
2
1
2
1
1
0
0
2
1
1
1
0
1
1
0
1
0
1
1
1
1
2
2
3
2
0
0
2
2
2
0
1
1
2
0
0
2
1
2
2
1
0
0
1
0
2
1
1
2
2
0
1
2
1
0
1
1
1
2
1
1
1
2
0
1
0
1
0
1
1
1
2
0
1
0
1
1
1
0
1
1
1
1
1
0
1
0
1
1
1
0
1
1
1
2
1
0
0
1
1
0
0
0
2
0
2
2
1
1
1
2
2
1
1
0
1
1
1
1
2
0
2
1
2
0
2
1
1
2
1
0
0
0
0
1
1
0
0
7
1
1
1
2
1
0
0
0
1
1
3
1
1
0
1
0
2
2
0
0
0
0
0
0
1
0
2
1
1
1
1
1
0
1
1
0
1
2
1
2
1
2
1
0
0
0
1
0
1
0
1
4
0
1
2
3
1
2
1
1
0
0
0
2
0
3
1
0
2
1
1
1
0
0
1
1
1
1
2
0
1
1
0
1
2
1
0
1
2
0
1
0
0
0
0
0
0
2
1
2
1
1
0
0
0
0
0
0
1
2
2
1
1
2
0
1
1
1
1
0
0
1
0
0
0
1
1
1
0
2
1
1
1
1
0
1
0
1
1
1
2
2
1
2
2
2
2
0
2
0
1
1
0
2
2
0
0
1
1
2
0
2
0
1
1
0
2
1
1
0
0
1
1
0
2
0
1
0
1
1
0
1
2
1
1
1
1
0
0
1
1
0
1
0
0
1
1
0
1
2
0
1
2
1
0
0
1
1
1
0
1
2
0
0
1
0
1
0
0
2
0
1
0
0
0
2
2
2
2
0
1
0
1
1
1
1
1
1
1
2
1
3
1
0
1
0
2
1
1
0
1
1
0
0
2
0
1
0
1
1
1
0
1
2
2
2
0
1
1
1
2
2
1
1
2
1
1
1
2
0
0
1
2
2
0
0
1
1
0
0
0
2
0
1
1
0
1
1
0
1
2
0
1
0
1
1
0
2
1
1
2
0
2
2
2
2
2
2
0
1
1
1
1
1
1
1
0
2
1
1
1
1
1
1
1
0
2
0
1
2
1
0
2
0
1
1
2
2
1
0
1
1
1
1
1
3
0
2
0
1
1
1
0
2
1
1
0
1
2
0
1
1
0
2
0
2
2
0
2
1
0
1
0
2
1
1
1
0
0
1
2
0
1
2
0
2
0
0
2
1
1
1
0
0
0
1
1
2
0
0
1
2
0
0
1
1
1
2
2
1
2
1
1
2
2
1
1
2
1
1
1
1
0
1
1
2
2
1
1
0
1
0
1
0
2
1
3
2
2
2
0
1
1
0
2
0
1
1
0
1
2
1
1
0
1
1
1
2
0
0
2
0
1
1
3
0
1
1
1
0
5
0
1
2
2
2
0
2
0
0
1
2
1
1
0
2
1
2
0
1
0
2
0
2
2
0
1
0
2
0
2
0
0
1
1
1
0
0
0
3
1
0
2
0
1
2
2
1
1
1
1
0
1
2
1
2
2
2
0
2
2
0
2
2
0
0
1
1
0
1
0
0
1
1
0
0
1
2
1
2
2
1
0
0
0
1
1
0
0
0
1
1
2
2
1
1
0
2
0
1
0
0
1
1
0
0
2
2
0
3
1
0
1
2
2
1
2
1
0
2
1
0
1
1
1
0
1
1
0
6
2
1
1
0
1
0
2
0
1
2
0
1
1
1
2
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
2
2
0
0
1
1
1
0
1
2
1
1
2
2
0
0
2
0
2
2
1
0
0
2
1
1
0
1
1
0
0
1
0
0
2
1
1
0
0
1
1
1
0
0
1
2
2
0
0
0
0
1
1
0
0
1
0
0
1
1
2
3
1
1
0
1
1
0
2
2
0
2
0
0
1
0
0
0
1
1
1
0
1
1
0
0
2
0
2
0
1
2
0
1
2
1
0
1
2
2
1
1
2
1
1
2
0
1
1
2
1
1
1
1
1
1
0
0
1
0
1
1
2
1
0
1
1
0
0
1
0
2
1
2
0
1
0
1
1
1
1
0
1
1
2
1
1
1
1
0
0
2
2
2
0
1
2
1
2
1
2
1
0
2
1
0
0
0
1
1
1
0
1
1
1
1
0
1
1
0
1
2
0
0
1
2
1
2
1
5
1
2
0
1
3
2
2
1
0
0
1
0
1
1
2
1
0
1
0
1
1
1
0
2
0
0
0
0
4
2
0
0
1
0
2
2
1
1
0
0
2
0
2
1
2
0
1
1
0
0
1
1
0
0
2
0
1
1
0
1
1
1
1
0
1
1
0
1
0
1
2
2
0
0
0
0
0
1
1
2
2
1
1
0
0
2
2
2
0
1
1
1
1
2
0
1
1
2
2
2
0
1
1
0
1
0
1
0
0
0
1
1
1
0
0
1
0
0
0
2
0
1
2
1
1
2
1
1
1
0
2
1
1
0
2
1
1
1
0
1
1
1
0
2
0
2
0
1
1
1
0
2
0
0
0
2
1
0
0
0
3
1
0
1
1
2
0
2
1
1
1
0
3
1
1
0
0
0
0
1
2
0
0
2
1
0
1
1
0
2
1
0
1
0
1
1
0
2
1
1
1
0
0
2
1
2
1
1
1
0
1
1
0
1
0
1
2
2
0
0
2
2
1
1
1
1
0
1
0
1
3
2
1
0
0
0
1
1
2
2
0
2
1
1
2
0
3
1
2
1
0
1
2
2
1
0
2
0
1
2
0
2
1
2
0
0
1
1
1
1
1
1
1
0
2
2
0
1
1
0
0
1
0
1
2
0
2
2
0
1
0
0
0
1
0
2
1
1
1
2
1
1
2
2
0
1
1
0
0
2
1
0
0
1
1
2
2
2
0
2
2
1
2
2
2
0
2
0
2
0
1
2
2
0
2
0
0
1
2
0
2
0
2
1
2
1
0
1
1
0
1
0
1
1
0
2
2
0
2
0
0
1
0
0
1
2
2
0
1
1
2
1
1
1
1
2
2
0
2
0
0
1
1
0
0
2
1
1
0
1
0
0
0
2
0
1
2
1
0
2
2
1
0
1
0
0
1
0
1
0
1
1
2
0
1
2
1
1
2
0
1
2
1
0
0
1
0
2
1
1
2
4
2
4
1
1
0
1
0
1
0
1
0
1
2
0
2
0
1
0
0
1
2
2
0
1
2
2
2
2
2
0
1
2
1
1
1
0
0
1
2
2
1
0
1
0
1
1
1
1
1
1
2
1
0
0
2
1
1
1
2
0
1
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
1
3
1
2
1
1
2
1
2
1
0
2
2
0
0
2
0
0
0
0
2
1
1
2
1
2
1
0
1
0
1
1
1
2
2
2
1
2
0
1
0
3
1
1
1
1
0
0
1
0
0
1
3
0
1
2
1
0
0
0
0
1
1
1
2
0
0
0
2
2
2
0
0
1
1
1
1
1
1
1
0
2
0
0
2
0
1
1
1
2
0
1
1
0
1
0
1
1
0
1
1
1
0
0
2
0
1
1
1
1
2
2
1
0
0
2
0
2
1
1
0
1
1
1
2
2
1
1
1
0
2
0
1
0
1
0
1
0
1
1
1
0
0
2
1
1
0
2
1
1
1
1
2
2
1
1
1
0
1
0
0
0
1
2
0
0
0
1
2
0
1
1
1
3
1
1
2
1
1
0
1
2
1
2
2
1
1
1
1
0
0
2
2
2
1
2
1
1
1
0
0
1
0
0
0
0
1
1
2
1
1
1
1
0
3
1
0
1
0
1
2
1
1
0
0
1
0
2
0
0
1
1
1
1
0
1
1
0
0
1
2
0
1
0
0
0
1
1
1
0
0
1
1
2
1
0
0
0
1
1
1
0
1
1
0
1
0
1
0
2
1
1
2
1
1
0
2
1
0
0
1
0
1
0
0
0
2
1
1
0
1
0
2
0
2
1
0
1
1
2
2
0
1
1
1
1
2
0
0
0
2
1
1
0
2
1
1
1
0
1
0
0
1
1
2
0
1
1
1
1
0
2
2
1
1
1
0
1
0
0
1
0
0
0
1
0
2
1
0
2
1
2
1
1
0
0
0
2
0
1
0
1
1
2
2
0
1
0
0
1
0
0
1
1
2
0
2
1
0
1
1
1
0
2
2
1
1
1
1
0
0
1
1
2
1
1
0
2
2
0
2
0
1
1
1
0
1
1
0
0
2
2
2
1
1
0
2
1
0
0
1
1
1
1
0
2
0
1
0
0
1
2
1
1
0
1
1
0
0
1
1
1
0
1
1
3
0
2
2
1
2
1
0
1
1
2
2
1
2
1
1
1
1
1
0
0
0
1
1
1
1
1
0
0
1
0
0
2
1
1
0
0
0
1
1
0
1
0
0
0
1
1
1
1
0
1
1
0
0
0
1
0
0
1
2
1
0
2
0
1
1
1
0
2
2
0
0
1
2
1
0
2
1
0
1
1
0
1
0
2
1
0
1
1
1
2
2
1
0
1
0
2
1
1
0
0
0
1
1
1
1
1
0
0
0
1
2
0
0
0
1
0
0
0
1
1
0
0
1
1
1
0
0
1
2
2
0
0
1
2
2
2
0
0
1
1
1
1
2
0
0
2
1
2
1
1
0
0
1
1
2
1
1
1
1
2
1
0
2
1
0
1
2
0
0
0
1
2
1
1
1
2
1
1
1
2
0
1
2
1
0
1
0
1
2
4
1
0
1
1
1
0
0
0
3
2
3
2
1
0
0
1
2
1
1
0
2
1
1
2
1
1
0
2
1
0
0
2
1
2
1
1
1
2
1
1
0
0
0
1
1
1
2
1
1
1
1
1
1
0
0
1
0
0
1
2
2
1
2
1
1
1
0
1
0
1
5
1
1
1
2
1
1
0
1
1
0
1
1
1
0
1
0
0
2
1
2
2
0
1
1
2
1
0
2
0
0
1
2
1
0
1
1
1
1
0
0
2
0
1
0
1
1
2
0
2
2
2
0
1
2
1
1
2
1
0
1
0
0
1
1
1
2
0
0
2
2
1
1
1
1
1
1
1
0
0
1
0
1
1
0
1
2
1
0
0
2
1
1
2
1
0
3
1
1
1
1
0
0
0
0
3
0
1
1
0
1
1
0
1
0
0
1
1
1
0
1
2
0
0
1
1
1
1
1
1
1
2
1
1
0
0
0
1
1
1
0
0
0
2
2
0
2
0
0
1
2
1
2
1
1
0
1
1
1
0
1
1
1
1
1
0
0
1
2
2
0
2
2
1
0
0
0
1
0
2
0
1
2
2
2
0
1
0
0
1
1
0
0
2
1
0
0
2
2
2
0
1
1
1
1
2
2
1
1
0
2
1
0
0
0
2
1
1
2
2
0
1
0
0
2
0
1
1
1
1
2
0
1
1
1
1
0
1
1
3
2
0
0
0
0
0
2
0
0
1
1
0
0
5
1
0
0
0
1
0
0
0
2
0
1
0
2
1
2
1
2
0
0
1
2
1
0
0
0
2
1
0
1
2
1
1
1
1
1
2
2
1
2
1
0
1
1
1
1
1
0
1
0
2
1
1
0
0
3
1
0
2
0
2
1
3
3
0
0
1
1
2
2
1
2
1
0
1
1
1
2
0
2
1
2
1
0
1
2
1
0
0
0
0
1
1
0
2
2
1
2
1
2
0
1
1
1
1
0
1
0
0
1
1
1
2
0
0
0
1
2
3
1
0
0
0
2
2
1
1
0
0
2
0
2
0
0
1
1
1
1
2
1
1
2
1
0
1
2
1
1
1
2
1
0
1
4
1
4
1
1
0
2
0
2
0
1
0
2
1
2
0
2
2
2
2
1
1
1
1
1
1
0
0
1
0
1
1
1
1
0
1
1
0
1
2
0
2
1
1
2
2
1
2
0
2
0
1
0
1
1
1
0
1
0
0
1
1
0
0
2
0
2
1
1
0
1
0
0
0
0
2
1
1
1
0
1
0
0
0
2
0
2
0
0
1
1
0
2
0
1
0
1
1
0
2
1
2
1
0
1
1
0
0
0
0
2
1
0
0
1
2
1
1
2
1
0
1
1
1
1
1
1
2
0
0
1
1
1
2
1
1
1
0
0
0
0
1
3
0
1
2
2
2
2
0
1
2
1
0
0
1
1
1
0
1
1
1
0
1
1
0
0
2
0
1
0
0
0
2
1
0
0
1
0
1
2
2
2
1
2
1
1
2
0
2
1
1
1
1
1
1
1
0
2
2
2
1
0
1
3
1
0
3
2
1
1
1
2
0
0
1
1
1
2
2
0
1
0
0
1
0
1
1
1
0
0
0
1
0
3
0
13
1
1
1
0
2
0
0
0
1
1
0
1
1
2
1
1
0
2
1
0
1
2
1
0
2
0
0
1
1
1
2
1
0
0
2
1
0
0
1
2
2
0
1
0
2
0
2
1
1
2
2
0
1
1
1
1
1
0
1
1
2
2
1
1
0
1
1
0
1
1
2
1
2
1
1
2
1
2
0
0
1
1
0
0
0
2
1
0
0
1
0
0
2
0
1
0
1
1
1
1
1
1
0
1
1
0
2
0
1
0
1
1
1
1
1
1
2
2
2
1
2
2
2
0
0
1
1
1
1
2
1
1
2
1
1
0
2
1
1
1
2
0
1
2
1
0
0
2
1
2
1
1
2
0
2
0
0
1
0
1
2
2
1
2
2
1
1
0
0
0
0
1
1
0
3
0
1
2
1
0
1
1
0
1
2
2
0
1
1
0
1
1
0
0
0
2
1
1
1
1
0
1
0
0
1
0
2
2
1
0
1
1
0
1
1
0
1
1
2
0
0
0
2
1
0
1
1
2
1
1
2
0
2
1
1
1
0
2
2
2
1
0
0
1
0
0
2
1
0
1
1
1
1
0
1
1
0
1
0
2
1
0
1
1
0
1
2
1
0
0
1
0
0
2
0
1
0
0
1
0
2
1
1
0
1
1
0
1
0
1
2
1
0
0
1
1
0
1
2
1
1
1
0
0
1
1
2
1
0
0
3
1
0
0
2
1
1
1
0
1
2
2
1
2
2
1
1
0
2
0
1
0
0
0
2
0
0
0
1
2
1
1
1
0
0
1
1
1
2
1
2
0
1
1
0
1
0
2
0
0
1
0
2
1
0
0
2
0
0
1
1
2
1
1
1
1
2
1
1
0
1
1
0
1
0
2
1
0
2
0
1
0
1
0
1
0
1
1
0
1
2
1
1
0
2
0
1
1
1
1
1
0
1
1
1
0
1
1
0
0
0
0
1
0
1
1
2
0
1
1
1
0
0
2
1
0
1
0
1
1
1
0
1
1
1
1
1
0
0
1
2
2
1
1
1
0
0
0
1
1
0
1
1
1
1
1
1
1
1
2
0
1
1
1
0
0
1
0
0
0
0
0
1
1
0
0
2
2
1
1
1
1
1
2
0
1
1
1
2
2
0
0
1
1
0
1
1
0
1
0
1
1
2
1
1
2
0
2
1
0
1
3
0
2
1
1
0
2
2
0
2
1
0
2
2
1
1
1
1
2
1
2
1
0
0
0
2
2
0
0
1
1
2
1
1
2
0
0
0
0
1
0
1
0
1
1
2
0
1
0
1
3
0
0
0
2
0
0
2
0
1
1
2
1
0
0
1
2
1
2
1
3
0
1
1
0
1
1
2
2
1
2
1
1
1
1
0
0
2
1
2
1
1
1
1
0
1
1
0
0
1
1
0
1
1
0
1
1
2
0
2
0
1
0
1
2
0
0
2
1
0
0
1
0
1
1
0
1
0
0
0
1
1
1
0
1
1
1
0
1
2
1
1
1
1
1
2
0
0
0
0
1
0
0
1
0
1
0
1
1
0
1
1
2
2
1
1
0
1
1
1
0
2
0
2
1
2
1
0
1
1
0
1
0
1
1
0
0
2
1
2
0
1
0
0
1
2
0
2
1
1
2
0
0
0
1
1
1
1
2
1
1
1
1
0
2
1
0
1
2
0
1
0
2
1
2
1
1
1
1
1
0
1
1
0
0
1
1
1
0
1
1
3
0
2
1
1
1
0
1
2
3
1
0
0
1
3
2
0
2
0
1
0
2
1
1
2
1
0
2
2
0
1
2
2
1
0
1
1
1
1
2
0
1
2
0
2
0
1
2
0
1
1
3
2
1
0
2
1
1
0
1
3
1
0
2
2
1
1
2
2
0
1
1
0
0
1
0
1
0
0
2
1
2
0
0
1
2
1
2
2
2
0
0
0
0
1
2
1
1
1
1
1
1
2
0
1
0
0
1
2
1
1
0
2
2
2
2
0
1
0
2
1
2
1
1
1
1
1
1
0
1
0
1
0
3
1
1
2
0
1
0
1
1
1
0
0
1
1
1
1
0
2
2
1
2
1
0
0
0
0
0
0
2
2
1
1
1
1
1
4
0
1
0
1
1
2
2
1
0
2
0
1
2
1
2
2
1
2
1
1
0
1
2
1
2
2
0
1
1
0
1
2
1
1
1
1
3
1
0
1
1
2
1
2
1
0
1
1
0
1
1
1
1
0
2
2
1
1
1
1
2
1
1
2
2
0
0
1
2
1
0
2
1
1
2
1
1
0
1
0
2
2
1
2
1
2
2
2
9
1
1
1
1
1
1
1
0
0
1
0
0
2
2
0
0
2
0
2
1
0
1
1
1
0
1
0
2
2
1
2
1
0
1
2
0
2
1
0
0
0
0
1
0
1
1
1
0
1
4
2
1
2
0
0
0
2
1
1
0
0
0
1
0
0
1
2
2
1
0
1
0
1
2
0
0
0
1
1
2
2
0
1
0
1
1
1
0
0
2
1
0
1
2
1
2
0
1
1
1
1
2
0
2
1
1
1
1
0
2
1
0
2
0
1
2
1
1
1
1
2
2
3
1
1
2
1
1
0
1
2
2
1
0
1
0
1
2
1
2
1
1
0
2
0
0
1
0
0
1
1
1
2
0
0
2
0
0
2
0
1
1
0
1
1
2
1
1
1
1
0
0
1
1
1
2
0
0
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
1
0
1
0
0
2
1
1
1
1
2
1
2
1
1
1
1
0
2
1
0
1
1
1
2
0
1
1
1
1
2
0
2
3
1
1
2
1
1
2
2
2
1
1
1
1
1
1
1
2
0
2
1
1
0
0
0
2
1
0
0
1
1
1
1
0
2
0
1
0
1
0
1
1
0
1
1
1
1
2
2
1
0
0
0
0
1
1
2
2
2
1
1
0
2
0
1
0
0
1
1
0
2
0
1
2
2
0
1
0
1
1
2
1
0
2
2
0
0
0
2
2
1
0
1
0
1
1
1
1
1
1
0
1
0
2
1
1
1
0
1
2
0
0
0
0
2
1
1
1
2
0
2
2
0
1
1
0
0
0
1
1
1
2
1
0
2
1
0
1
1
2
2
1
1
0
2
2
1
0
1
2
0
1
2
1
1
0
0
0
1
1
1
1
0
0
2
1
1
1
0
0
2
2
2
1
1
1
1
0
0
0
1
2
6
0
1
2
0
1
2
2
4
1
0
2
2
1
1
1
0
1
0
0
0
2
0
1
1
0
0
1
0
0
0
1
2
1
0
1
2
1
0
0
1
0
1
0
2
0
1
2
2
0
1
3
1
1
1
0
1
0
1
0
2
0
0
1
2
1
2
1
0
0
1
1
2
1
0
0
0
0
0
1
1
0
1
2
2
1
0
0
1
2
0
0
1
1
2
2
1
1
0
2
0
0
1
0
3
2
1
1
2
1
2
1
1
2
0
0
1
1
2
1
2
1
0
3
0
1
0
2
1
0
0
0
0
0
1
2
1
0
1
0
2
1
0
0
1
1
0
1
1
1
2
2
2
2
1
0
1
2
0
1
1
0
0
1
0
0
0
2
1
1
2
2
0
1
0
3
1
0
0
0
1
2
2
1
2
1
0
0
1
0
2
0
0
1
1
0
2
2
0
2
1
0
0
1
0
1
0
2
0
2
2
1
1
0
0
1
1
3
1
1
0
0
0
1
1
0
0
2
1
0
2
0
0
0
2
2
2
1
2
2
3
0
1
0
1
3
0
1
0
2
1
0
0
0
1
1
1
1
1
0
1
0
0
0
1
1
2
2
1
1
1
1
1
1
2
1
1
0
1
1
0
1
1
1
1
1
1
2
0
1
1
1
2
0
0
1
1
1
0
0
1
5
0
1
2
1
1
2
0
0
0
1
1
0
1
2
2
0
0
2
2
1
0
1
1
0
1
0
0
0
2
2
0
1
0
1
1
2
1
1
0
1
1
1
0
1
0
2
1
2
0
0
3
1
1
0
1
0
2
1
1
3
0
1
2
1
0
1
0
1
1
0
1
0
0
0
0
1
4
0
2
0
2
1
1
0
0
1
1
0
0
0
1
0
1
1
1
0
1
0
2
1
1
1
1
0
1
0
1
1
1
0
0
1
1
1
0
1
0
1
0
1
1
1
2
2
0
1
1
0
1
1
1
0
1
1
0
0
1
2
0
1
1
0
1
0
2
1
1
2
0
1
1
0
1
0
0
0
4
0
0
0
0
5
0
0
1
2
1
0
1
1
0
0
2
0
0
2
1
2
1
1
1
2
0
0
0
1
1
0
1
1
2
0
1
1
1
1
2
0
1
1
0
1
2
1
2
0
2
1
1
0
0
1
1
1
1
2
1
1
1
0
2
2
1
0
2
1
1
0
0
1
2
2
0
1
1
1
2
1
1
0
0
2
0
0
2
1
1
1
1
1
1
2
0
1
0
2
0
2
2
2
1
0
1
1
1
1
1
0
2
0
1
1
2
1
1
1
0
1
1
1
1
2
2
0
1
3
1
0
2
2
1
1
1
1
0
2
1
0
2
2
2
2
1
0
0
1
1
0
0
0
0
2
1
1
1
1
2
0
0
1
1
2
1
1
1
1
1
2
2
1
1
1
1
1
1
0
0
2
0
0
0
0
2
1
3
1
0
2
3
1
1
1
1
1
0
2
0
0
1
0
0
2
1
2
0
2
1
2
2
1
1
1
2
1
2
1
1
0
2
2
2
1
2
0
1
0
0
1
0
0
2
1
2
1
0
0
0
1
2
0
1
2
0
0
1
1
0
1
1
0
0
1
1
1
1
1
0
1
0
2
1
0
2
1
1
0
1
0
1
1
2
0
1
2
1
0
0
1
1
0
0
0
0
1
2
0
1
2
2
0
1
1
1
1
1
1
0
2
1
0
2
1
1
1
2
1
1
2
0
0
0
1
1
2
1
0
2
0
0
1
2
2
0
0
2
2
1
1
0
2
1
0
1
1
1
1
1
1
0
1
2
2
1
1
1
0
1
2
1
0
0
2
2
1
1
2
1
1
1
0
0
1
1
2
1
2
1
0
1
2
0
2
0
1
2
1
1
1
0
0
1
1
1
1
2
1
0
1
1
0
1
1
1
2
2
0
0
1
1
1
2
2
2
1
2
1
1
0
3
1
1
0
2
1
1
0
1
2
1
0
1
1
0
0
1
0
1
0
1
1
1
0
1
1
1
2
1
0
0
1
0
1
1
0
0
1
0
1
0
1
2
2
0
1
1
0
2
0
1
0
1
2
1
2
2
1
0
2
0
2
0
0
1
1
0
1
1
1
0
0
1
1
0
1
1
1
1
1
2
1
1
1
0
0
0
0
2
2
0
0
2
0
0
0
2
1
2
2
1
1
0
0
2
1
3
0
1
2
1
0
2
1
2
1
0
1
1
1
0
2
2
1
0
1
0
2
2
1
1
0
1
1
1
1
1
1
2
1
1
0
1
2
1
0
1
1
0
0
0
1
2
1
2
1
2
2
1
2
1
2
1
0
1
1
1
1
2
2
0
1
1
2
1
2
2
0
2
1
0
1
0
0
0
0
0
0
0
1
0
2
2
1
1
1
1
0
2
2
2
0
0
2
1
1
1
2
0
1
1
1
0
2
2
0
1
1
0
2
2
2
1
1
1
1
1
1
1
0
1
2
1
0
1
1
2
0
0
1
0
1
2
2
0
2
1
0
0
0
1
1
1
0
2
0
0
1
0
1
2
0
0
1
0
0
2
0
1
2
2
1
0
2
1
2
3
0
1
2
2
2
2
2
2
1
0
1
1
0
0
1
2
2
1
1
2
1
1
1
1
0
1
1
1
2
0
1
1
1
1
3
0
1
2
1
0
1
2
0
0
1
1
1
1
0
1
0
1
1
1
0
2
2
2
2
1
1
0
2
1
0
0
1
2
1
1
1
0
0
1
2
2
1
0
1
1
1
0
0
2
2
1
0
1
1
2
2
0
0
0
1
1
2
2
1
0
0
1
1
1
0
1
1
1
0
1
0
1
1
1
2
1
0
2
1
1
0
1
1
2
0
1
1
1
0
0
0
1
0
1
2
1
1
1
2
1
1
0
0
3
0
0
0
1
0
0
0
0
1
1
3
0
1
1
0
2
1
1
0
2
0
0
0
2
2
2
0
1
0
2
1
0
2
1
1
0
1
0
0
1
1
2
1
0
0
2
2
0
1
2
0
0
1
1
0
2
0
1
2
1
1
2
0
1
1
1
0
2
1
0
2
0
0
1
1
2
0
1
1
0
0
0
2
2
2
0
1
1
1
0
1
1
0
1
2
1
1
2
1
0
1
0
0
1
1
0
1
1
1
0
1
1
1
1
0
0
1
0
2
2
0
0
2
0
0
2
0
1
0
1
1
0
0
2
0
0
1
1
0
0
1
1
0
1
1
0
0
1
1
0
1
1
1
1
2
2
1
2
0
1
0
1
0
0
0
2
1
2
0
0
0
0
2
1
1
1
2
0
1
1
1
1
1
1
0
0
1
1
0
2
1
2
0
1
1
2
1
0
2
1
2
2
1
0
0
2
2
0
1
2
2
0
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
2
1
1
1
0
4
1
0
1
2
0
0
0
0
2
1
0
0
1
0
0
2
1
0
0
2
2
0
1
0
2
0
1
1
2
0
1
1
1
1
2
1
2
0
0
1
0
0
2
2
1
1
1
1
2
2
0
0
0
1
2
1
0
0
0
2
0
2
0
2
1
1
0
1
0
1
1
1
0
1
1
0
1
1
0
0
0
2
1
0
1
1
1
0
0
1
0
1
0
1
0
0
1
2
1
0
1
0
1
0
1
2
2
0
1
1
1
2
1
1
0
1
1
0
0
0
0
1
1
1
1
1
1
1
1
0
0
1
1
2
1
0
0
0
2
0
0
1
1
1
0
1
1
1
1
1
0
1
0
1
2
0
0
2
0
2
0
1
1
0
0
0
0
1
0
1
0
0
2
1
2
2
1
0
1
1
1
0
0
0
1
0
1
0
0
1
2
0
0
0
1
0
1
1
0
1
2
2
0
0
0
1
2
1
0
1
1
1
1
0
2
1
1
2
2
1
2
1
2
1
1
1
2
1
1
1
2
2
2
0
2
2
0
0
1
2
1
0
3
0
1
1
1
2
0
0
2
1
1
2
1
1
0
2
2
0
2
1
2
1
1
0
1
0
2
2
3
0
1
1
0
1
1
2
0
1
1
1
1
0
2
1
3
0
4
2
0
0
0
2
0
2
1
0
1
1
2
1
0
1
1
1
1
2
1
1
0
1
0
1
0
0
2
1
1
2
2
0
0
0
0
0
1
1
1
2
0
2
0
2
0
0
1
0
1
1
1
1
2
1
2
1
0
2
0
1
0
1
0
0
1
1
1
1
1
1
0
1
0
1
1
1
0
0
0
1
1
0
0
0
2
0
2
1
0
0
1
0
1
0
1
1
2
1
0
0
1
1
0
2
1
1
0
2
2
1
1
1
1
0
1
0
1
2
1
0
1
1
2
1
0
2
0
1
1
0
0
1
2
0
2
0
2
2
0
0
0
1
1
1
0
1
1
0
1
1
0
1
0
2
0
1
0
1
1
0
0
1
0
2
0
2
0
0
1
0
1
0
1
0
1
1
0
0
0
1
1
0
1
1
1
1
0
2
2
1
1
1
0
0
3
0
0
0
0
0
0
0
1
1
1
1
1
1
2
2
0
1
1
0
1
1
1
0
1
1
0
2
1
0
2
1
1
1
1
0
2
1
1
1
0
1
1
1
1
0
1
1
0
1
1
1
2
0
0
1
0
2
0
2
2
0
1
1
1
1
2
2
0
0
1
3
1
0
0
1
2
2
1
0
1
1
1
0
1
0
3
2
3
1
4
0
1
1
1
4
4
0
2
1
0
1
2
1
0
0
0
2
1
0
0
0
0
0
0
0
1
1
2
1
1
1
1
0
1
0
1
0
2
1
0
0
0
1
1
1
1
0
2
3
0
0
0
1
0
2
0
0
0
1
0
0
1
0
1
0
0
0
2
4
1
2
1
2
0
3
1
0
2
0
1
1
2
0
1
0
0
2
3
1
1
2
0
0
1
2
0
1
2
3
1
1
0
1
0
1
1
1
0
1
1
0
3
0
2
0
0
1
2
2
5
0
1
2
1
2
1
0
1
0
1
3
0
1
2
1
1
0
2
0
1
0
1
1
2
1
1
0
1
1
1
1
2
0
1
2
2
2
0
2
1
2
0
1
1
0
0
2
0
3
1
1
1
1
2
1
0
1
2
2
0
2
3
0
2
1
2
1
2
1
1
1
1
1
2
1
0
2
2
0
2
1
1
1
0
1
1
0
1
1
2
0
1
1
1
1
0
2
1
1
1
1
1
1
2
0
1
0
1
1
2
0
1
2
2
0
1
0
1
0
0
1
1
1
1
0
2
0
0
3
0
1
1
0
1
1
1
2
0
2
2
1
1
1
1
1
1
1
2
1
0
2
1
0
1
0
1
1
3
1
1
0
1
0
2
1
1
2
0
0
0
0
1
1
1
1
1
2
0
0
0
1
2
1
1
0
0
0
1
1
1
1
1
1
2
1
1
2
2
1
1
1
0
0
1
2
0
0
1
0
1
1
2
2
0
1
1
1
0
2
0
0
0
1
1
0
0
0
1
2
2
1
0
1
1
1
0
0
2
1
3
1
0
1
2
1
1
0
1
1
2
0
2
1
1
2
0
1
3
1
0
1
1
1
1
3
2
1
0
1
0
0
1
1
0
1
0
1
1
0
2
1
0
1
1
3
0
0
1
2
0
1
0
1
1
1
1
0
0
2
0
2
1
1
2
0
1
0
1
1
1
0
0
0
1
2
1
2
0
3
0
2
0
0
0
0
1
2
1
1
0
0
5
0
0
1
0
2
2
1
0
0
1
0
3
1
1
1
1
1
2
0
2
0
1
1
1
2
1
1
0
1
1
0
0
0
1
0
0
1
1
0
1
1
1
2
1
2
0
1
0
1
0
0
0
0
0
0
1
2
1
1
1
2
0
1
2
0
1
0
2
0
1
0
1
2
0
1
2
1
2
1
0
0
2
0
2
1
2
1
1
1
0
1
1
1
1
1
1
0
0
1
0
1
0
1
0
0
1
1
1
2
0
2
1
1
0
1
2
1
1
0
1
0
2
0
0
1
0
2
2
0
1
0
1
2
1
0
0
1
1
0
1
0
1
0
1
0
1
1
2
2
0
1
2
1
1
2
1
0
0
1
0
1
2
1
0
2
1
1
0
0
1
1
2
1
0
1
1
1
1
1
0
2
1
1
0
0
1
2
1
1
1
1
0
2
1
1
1
2
0
2
1
2
0
1
0
1
2
2
0
0
2
2
0
0
1
1
2
0
0
0
1
1
0
0
0
0
1
1
2
1
1
1
2
0
2
1
1
0
2
1
1
0
1
1
2
0
1
1
1
2
2
1
0
1
1
0
1
0
2
2
0
2
2
1
0
2
1
0
1
0
1
1
1
0
1
2
1
2
1
0
0
2
0
0
0
1
0
0
2
0
1
0
0
1
1
2
1
1
3
0
1
2
1
1
2
1
1
0
2
1
1
2
0
0
0
1
0
2
0
0
0
0
2
1
1
1
0
0
0
0
1
0
1
1
0
1
0
1
0
0
3
2
1
0
0
0
1
1
1
0
0
1
0
1
0
1
1
1
1
1
1
2
1
2
2
2
1
0
1
0
0
0
1
1
1
2
0
2
2
1
1
0
0
0
1
0
0
1
1
0
1
0
1
1
0
1
1
1
1
1
1
2
0
1
1
1
1
2
1
0
0
1
1
1
0
0
1
0
1
0
0
2
0
2
2
1
2
1
1
0
2
0
0
1
1
2
0
1
2
1
1
3
1
2
2
2
1
0
1
1
1
1
1
0
1
0
1
1
1
1
2
1
1
1
1
0
1
0
0
1
0
0
1
1
2
0
2
1
1
1
1
2
2
0
0
1
0
1
0
3
0
1
2
1
1
2
3
1
0
1
2
2
1
2
0
3
1
1
1
0
1
3
0
1
0
2
2
1
0
1
1
1
0
1
1
2
0
0
1
2
1
0
1
0
2
0
1
1
1
1
1
1
2
1
3
0
0
1
0
0
0
0
1
1
1
1
1
0
1
0
2
2
1
1
0
5
1
0
0
1
1
2
1
1
0
0
1
1
0
1
2
1
0
0
1
1
2
1
2
1
2
2
1
0
2
2
1
2
1
0
2
1
1
1
0
0
0
0
2
1
1
2
0
2
0
0
1
1
2
1
1
0
0
2
1
0
1
1
1
1
1
1
1
1
0
1
0
2
1
2
1
1
0
1
1
0
0
2
0
0
0
1
1
1
0
2
0
1
1
0
1
1
1
0
2
1
1
0
0
1
1
0
0
0
1
1
0
0
2
3
1
0
1
0
0
0
1
2
1
1
0
1
1
0
0
1
2
2
2
1
0
0
1
1
1
0
0
1
2
1
1
1
0
0
0
1
0
1
1
1
1
2
2
0
2
1
1
1
2
1
0
1
3
0
0
2
1
0
0
2
0
0
0
0
0
0
1
3
2
1
1
1
1
0
1
1
2
2
1
1
0
2
1
1
0
1
1
1
1
1
0
3
1
1
0
1
1
0
0
0
0
1
1
1
0
0
1
1
2
1
0
0
0
1
0
1
1
1
2
1
1
1
0
2
1
1
1
0
1
2
0
1
1
1
0
0
0
0
0
0
1
0
2
0
1
1
4
1
2
2
0
1
0
1
2
1
0
1
2
2
1
0
2
1
0
0
2
1
0
1
2
1
0
2
1
2
1
0
1
0
1
1
0
2
1
0
0
0
2
2
1
1
2
0
2
2
1
0
2
1
1
1
0
1
0
0
1
1
0
0
1
1
0
2
1
0
1
1
2
0
0
0
1
2
0
1
2
1
1
0
1
1
1
0
2
2
1
1
1
1
2
2
1
0
1
0
1
1
1
2
0
1
0
1
1
2
0
0
2
2
2
2
2
2
0
0
1
0
1
1
1
1
1
2
0
1
1
1
2
2
0
0
1
0
1
0
0
0
0
1
1
0
1
1
2
1
2
1
1
2
1
0
1
0
1
1
1
0
0
1
0
4
1
1
0
1
2
1
0
0
1
0
0
1
1
1
1
1
1
1
2
0
1
0
0
0
1
2
1
1
0
1
0
0
2
2
0
3
1
3
1
0
0
2
0
1
1
1
0
0
0
0
1
1
1
0
2
0
0
0
3
1
2
1
0
1
1
0
0
1
0
1
0
1
0
0
0
2
2
1
0
2
1
2
1
0
1
1
0
1
0
1
1
2
1
2
0
1
2
1
2
1
3
0
1
1
1
2
0
0
1
2
0
2
1
1
1
0
2
2
0
1
0
0
1
1
1
0
2
2
1
0
1
2
1
2
1
2
0
1
0
0
1
0
1
1
1
0
1
1
0
2
2
1
1
1
1
2
2
2
2
1
1
1
0
0
1
1
1
1
2
1
1
0
2
0
0
1
0
2
1
0
1
1
0
1
0
1
0
0
0
1
1
2
1
2
2
1
0
2
0
1
1
1
0
2
1
0
2
0
0
2
1
1
1
1
1
2
1
1
2
1
1
1
0
1
1
0
0
0
3
1
1
1
1
1
2
0
0
0
2
0
2
0
2
0
1
0
2
2
2
2
1
1
1
2
1
1
1
1
0
1
1
1
0
0
1
2
1
1
0
1
0
0
1
0
1
2
0
2
0
0
1
1
0
2
2
1
0
2
0
1
0
1
1
0
1
2
1
1
2
1
0
0
2
2
1
2
1
2
0
1
1
1
0
0
0
0
2
1
1
0
1
1
0
2
2
1
1
1
1
2
0
0
1
1
0
0
2
0
0
1
1
0
1
1
1
0
0
0
1
2
1
1
1
0
2
1
3
0
1
0
1
0
1
1
2
3
0
2
2
0
1
1
0
1
1
1
1
2
0
1
1
2
0
0
1
2
0
1
1
1
1
0
1
1
0
0
0
1
1
0
1
1
0
1
0
0
2
1
2
2
2
0
1
0
1
0
1
2
0
0
0
1
2
1
0
1
1
1
0
1
1
1
1
1
0
1
0
1
1
0
1
2
1
1
2
1
1
2
2
0
3
0
1
0
2
1
0
0
1
1
0
1
0
2
2
1
3
0
1
2
0
1
1
1
1
1
1
2
1
1
0
1
1
1
1
2
0
1
0
1
2
1
2
0
0
0
2
0
2
2
2
0
1
0
0
0
1
2
1
1
1
1
2
1
0
0
1
0
1
1
2
1
0
1
0
1
0
1
1
0
2
2
0
1
1
1
2
1
0
1
1
0
0
0
0
0
1
1
2
2
0
0
0
1
0
3
1
0
0
0
1
2
1
1
2
0
2
0
0
1
2
0
1
1
2
2
0
1
2
1
1
2
1
2
0
1
2
2
1
1
1
1
0
0
1
2
1
0
0
1
0
1
2
1
2
1
2
3
1
0
1
0
1
2
1
2
0
0
1
0
1
1
0
1
1
2
1
1
1
0
0
1
0
0
0
1
1
1
0
1
0
1
1
1
0
3
0
0
0
1
1
1
0
1
1
0
1
0
0
2
1
1
2
0
1
1
2
2
2
1
1
1
0
2
0
1
1
1
2
0
1
0
2
0
1
1
2
0
1
0
0
1
1
1
0
0
2
1
0
0
1
1
2
1
0
0
1
2
2
2
1
0
0
1
1
0
1
1
0
0
0
2
2
1
0
1
0
0
1
1
2
1
1
0
1
0
1
1
0
1
2
0
1
0
2
0
4
0
1
1
1
1
1
2
1
1
0
1
1
1
3
1
0
1
1
1
0
1
2
2
1
0
1
0
2
1
1
0
0
2
1
0
0
0
2
0
1
0
0
2
1
0
0
2
2
0
0
0
0
0
0
0
1
0
1
3
2
2
1
1
2
1
2
1
0
1
1
0
1
2
1
0
1
1
2
1
1
0
0
0
1
0
1
3
1
1
0
1
0
0
1
0
1
0
0
1
1
1
1
0
1
1
1
0
0
1
1
1
2
1
1
1
1
2
0
1
1
2
1
0
0
2
2
1
0
2
1
1
1
0
0
0
1
0
1
1
2
0
0
1
0
0
2
2
1
2
1
1
1
1
0
0
1
2
1
1
1
1
1
2
1
1
0
1
1
1
2
1
3
2
1
0
0
1
1
0
3
1
1
2
0
1
0
1
0
1
1
0
0
1
0
0
0
2
0
2
1
1
0
1
0
0
1
0
0
2
1
1
2
1
0
1
1
1
0
1
4
0
1
0
1
0
2
2
1
2
2
1
1
1
1
0
1
1
1
2
0
0
1
2
0
2
1
0
2
1
1
0
0
1
1
1
0
0
1
1
2
0
0
1
1
0
1
2
1
0
1
2
1
0
1
2
1
0
1
0
1
2
1
2
1
0
2
1
1
0
0
0
1
0
0
0
1
1
1
0
0
2
0
1
1
1
0
1
1
1
1
1
1
0
1
2
1
0
1
0
1
0
1
0
2
3
1
1
2
2
1
0
0
2
2
2
0
1
1
1
1
2
1
0
2
0
1
2
2
2
9
2
1
0
1
1
1
0
1
2
1
0
0
1
1
2
2
0
0
0
1
2
1
1
0
1
2
0
2
1
1
0
2
0
1
2
0
2
0
2
2
1
0
2
1
1
0
2
0
0
1
2
1
1
0
0
1
3
0
2
1
1
0
1
0
0
1
0
2
0
1
1
1
1
0
2
2
0
1
0
2
2
0
2
1
0
1
2
1
1
1
2
1
0
2
1
1
1
0
0
1
1
1
2
1
3
1
1
1
1
0
1
1
1
0
0
1
1
1
1
0
1
2
0
2
1
1
2
2
1
0
0
0
0
2
2
0
1
2
1
1
1
2
0
1
1
2
1
1
1
2
1
2
1
1
1
2
1
0
1
0
2
0
0
1
2
0
0
1
2
0
0
0
1
0
0
0
0
2
1
0
1
0
0
2
1
1
0
1
2
1
2
2
1
1
1
1
0
0
2
0
0
0
0
0
2
1
2
1
0
1
1
0
1
2
2
0
2
0
1
0
0
2
0
1
0
2
1
2
2
0
2
1
2
2
0
0
0
2
1
1
2
2
1
1
0
1
1
1
1
2
0
0
2
1
0
0
2
0
1
1
2
1
0
0
1
1
1
0
1
7
1
2
1
2
1
0
0
2
1
2
0
1
2
1
1
2
2
1
0
3
1
0
1
1
0
1
0
1
0
1
1
2
0
0
2
2
2
1
0
0
1
1
1
0
1
3
2
2
3
1
0
2
0
2
1
2
0
1
1
1
1
1
0
2
1
1
0
1
2
0
0
1
1
1
1
1
0
1
1
0
0
1
0
1
0
0
1
1
1
1
1
1
1
0
0
1
1
1
2
0
0
2
1
0
0
1
1
1
1
1
1
0
1
1
2
1
1
1
0
1
1
1
0
0
2
1
1
1
2
1
1
1
1
0
0
1
0
0
2
1
0
1
0
0
1
1
0
1
0
0
1
0
0
1
0
1
0
0
1
0
1
1
2
2
1
2
1
1
2
0
2
1
1
2
0
2
0
0
1
1
0
0
0
0
1
1
2
1
1
0
0
1
1
1
0
1
0
0
1
1
0
2
1
0
2
1
0
1
1
2
0
0
1
0
1
0
1
0
2
2
0
0
1
1
2
1
3
2
1
1
3
0
0
1
4
1
1
0
1
1
1
1
1
1
1
0
2
1
0
3
0
0
1
1
0
1
1
0
1
1
0
1
0
0
2
1
1
0
1
1
2
1
1
1
1
0
0
2
1
0
3
0
1
0
2
2
2
0
1
1
2
1
1
1
0
1
1
1
3
0
0
1
1
0
1
1
1
1
2
1
0
1
1
1
1
2
1
1
0
2
1
0
2
0
1
1
1
1
1
2
0
1
1
0
1
2
2
3
1
0
2
2
1
0
0
0
1
0
2
0
1
3
1
2
2
2
1
0
0
0
1
2
1
3
0
1
1
1
2
2
2
2
0
0
0
0
0
0
1
4
0
1
1
0
1
1
2
0
0
0
2
1
2
2
1
1
2
1
0
1
1
1
0
1
1
0
0
2
1
1
1
0
1
0
1
1
2
0
0
0
1
0
1
2
1
2
2
2
1
1
1
1
1
0
1
1
1
2
2
1
1
2
0
1
1
2
0
0
1
0
0
1
1
0
1
2
2
1
1
0
1
1
1
1
1
0
1
1
1
1
1
0
1
1
1
0
0
1
1
1
0
0
1
0
0
1
1
1
2
0
2
0
2
1
0
1
1
1
1
1
1
2
2
1
1
2
2
0
0
1
1
2
1
2
1
1
1
0
0
1
1
2
1
0
2
1
1
0
0
0
2
0
1
1
0
2
1
0
1
1
0
2
1
1
1
0
1
0
0
0
1
0
1
0
1
0
0
1
2
0
1
0
3
2
1
1
0
1
0
1
1
2
0
0
1
1
0
1
1
1
1
1
0
2
1
1
2
0
1
2
1
0
0
1
0
1
1
0
1
1
0
1
0
1
0
1
1
0
0
1
1
2
1
1
1
0
1
0
2
2
1
0
0
1
0
2
0
0
1
1
1
0
0
2
1
0
2
1
2
2
1
1
1
1
1
2
2
2
1
1
1
3
0
2
2
0
1
0
1
0
1
0
2
1
2
1
0
1
1
1
1
2
2
0
0
1
0
0
1
1
1
1
0
1
0
1
2
1
1
0
0
1
1
0
1
1
0
0
2
1
2
1
2
2
0
1
2
2
1
1
0
0
1
0
1
2
2
1
0
1
0
1
0
2
2
1
0
0
1
0
0
1
0
2
2
0
0
0
0
1
1
2
0
1
0
2
1
1
1
1
0
1
1
2
1
2
1
0
0
0
0
1
1
1
1
0
0
2
0
1
1
1
0
0
1
0
0
0
3
1
2
1
2
0
0
1
0
2
1
0
1
2
0
0
1
1
1
0
0
2
1
0
1
1
0
6
1
0
1
2
0
1
1
1
1
0
1
1
1
0
0
3
2
1
1
2
1
1
2
2
2
0
0
0
1
0
1
1
1
2
2
0
1
1
0
0
2
1
2
1
2
1
0
2
2
0
1
0
0
0
0
0
1
0
1
1
1
0
1
2
0
1
0
0
0
2
0
0
0
2
1
1
1
0
2
2
1
1
2
1
0
1
0
2
2
2
0
2
0
0
2
2
0
1
0
3
1
0
1
1
0
0
0
2
1
0
0
0
0
1
1
0
0
1
0
2
1
0
1
1
2
0
0
0
1
1
1
0
1
0
0
0
2
2
0
1
1
1
2
1
2
1
0
2
2
1
1
1
2
1
0
0
0
0
1
1
0
0
0
1
2
0
1
1
1
0
1
2
1
1
0
1
0
1
0
1
1
1
1
1
1
1
1
0
0
1
1
0
2
0
0
1
1
2
2
1
2
2
0
1
2
0
2
1
0
1
2
1
0
1
2
2
2
1
0
0
1
1
0
1
1
2
2
1
3
1
1
0
1
1
0
0
1
1
1
1
2
2
0
0
2
0
0
0
0
2
0
2
2
0
0
2
1
1
2
1
1
1
0
0
0
2
1
1
1
0
0
2
0
1
2
0
0
1
2
1
0
1
2
0
1
0
1
1
0
1
2
0
0
1
0
0
1
2
2
2
0
0
1
3
1
2
1
0
0
0
0
1
0
0
1
1
0
1
1
1
2
1
0
2
1
1
2
2
0
0
0
0
2
1
1
0
1
0
1
2
1
1
0
2
1
0
2
1
0
4
0
0
1
2
2
0
1
1
2
1
2
3
0
1
0
1
0
2
1
1
1
1
1
1
2
0
0
1
2
1
1
1
0
0
1
0
1
1
0
1
1
0
1
0
0
1
0
1
0
1
2
0
2
2
1
1
0
1
1
0
1
0
1
0
2
0
0
1
0
0
1
1
1
2
0
1
0
0
0
1
1
0
1
1
0
1
0
1
0
2
0
1
1
2
1
0
1
0
1
0
0
2
2
0
1
2
1
1
0
1
1
1
0
2
2
1
0
1
0
1
0
1
0
2
1
2
2
1
1
1
2
0
2
3
9
1
1
1
0
1
0
1
0
1
1
2
2
1
1
1
1
1
1
2
1
0
0
1
1
0
1
1
1
1
1
2
2
1
0
1
1
1
1
1
1
0
1
0
2
0
2
0
1
0
1
2
2
0
0
1
2
0
1
2
0
2
0
0
1
1
1
2
2
2
1
2
0
2
0
0
1
1
1
0
2
0
0
0
1
1
1
0
1
1
0
0
0
0
0
1
1
1
2
1
2
0
0
0
0
0
1
2
1
2
0
1
1
1
0
1
1
1
1
0
2
2
1
1
0
1
1
0
2
1
0
1
0
1
2
1
1
1
1
2
0
1
1
0
1
1
2
4
0
1
1
1
2
0
1
2
0
2
0
0
2
1
1
0
1
0
1
2
0
2
0
0
1
2
1
3
1
1
0
2
0
1
0
0
0
0
0
0
1
1
1
1
0
0
0
1
1
0
1
2
0
1
0
1
1
2
1
1
2
1
2
2
2
1
0
0
2
1
1
0
1
1
2
1
2
1
1
1
1
0
2
0
0
3
0
2
0
1
2
2
0
1
0
0
1
2
1
1
1
0
2
2
0
2
2
2
2
1
1
0
2
1
2
0
0
1
2
1
1
0
1
2
1
1
0
1
1
1
1
1
1
0
1
2
2
1
0
2
0
1
2
3
1
2
1
2
1
2
1
1
0
0
1
1
2
1
0
0
1
0
1
0
0
1
1
0
3
1
0
2
4
0
1
0
0
3
1
2
1
1
1
0
2
1
0
0
0
0
0
1
1
2
1
1
0
2
1
0
1
1
1
1
1
1
1
2
2
1
0
1
1
1
1
1
1
2
2
0
0
1
1
1
0
0
1
2
0
0
1
1
1
0
0
2
1
1
1
2
2
2
0
2
3
1
1
0
1
2
2
2
0
1
0
0
1
0
0
1
0
1
1
0
2
1
1
2
2
1
1
0
2
0
1
1
1
1
2
0
1
1
0
0
0
2
1
2
1
3
0
1
0
4
2
0
2
1
0
0
1
2
2
1
0
0
1
2
1
1
1
1
0
0
1
0
1
2
1
2
0
3
0
1
1
0
2
2
2
1
0
1
1
3
0
2
1
0
2
2
1
0
0
1
1
1
1
1
1
2
1
2
0
1
1
0
1
0
0
1
1
1
1
1
4
0
0
0
0
2
1
0
0
0
1
2
1
0
1
1
0
1
3
0
1
1
1
1
0
0
0
2
0
2
0
0
1
1
1
1
2
1
0
0
0
0
2
1
2
1
1
1
1
0
1
3
2
1
1
1
1
0
1
0
1
0
2
2
1
1
1
2
2
1
1
2
1
0
0
2
1
0
1
2
0
2
1
2
2
2
1
2
2
2
2
1
2
1
3
1
2
0
1
1
1
1
2
2
1
3
0
2
2
0
2
0
0
0
0
0
0
1
0
1
1
2
1
0
0
2
1
0
1
1
1
0
0
1
2
0
2
2
3
1
1
1
2
1
2
1
1
1
1
1
1
2
0
1
0
1
1
0
1
1
1
0
2
0
3
1
1
0
1
1
0
0
0
1
1
0
0
0
0
0
1
0
2
0
2
2
1
1
1
0
1
1
0
2
2
0
2
1
2
2
0
0
1
1
1
1
1
0
1
0
1
2
2
1
1
1
1
2
2
1
2
0
1
2
1
1
1
0
0
1
1
0
1
0
0
0
1
1
2
0
1
1
1
1
2
1
1
0
2
2
0
0
0
0
0
1
1
1
2
0
1
1
1
1
1
2
0
1
0
2
0
2
1
1
2
1
0
3
0
1
2
1
0
1
0
0
1
1
0
2
1
0
1
2
2
0
1
1
1
1
2
1
1
0
2
0
0
0
1
0
1
0
0
0
2
2
2
1
1
1
1
0
0
1
0
0
1
1
1
0
0
1
0
1
2
1
2
2
0
1
1
1
1
1
2
0
1
1
2
1
0
0
0
0
1
0
1
1
1
0
2
1
1
2
1
2
1
0
1
0
1
0
0
0
1
1
0
0
0
2
1
1
1
0
1
2
1
1
1
0
1
1
1
2
1
0
1
2
0
0
0
1
0
1
1
1
1
0
1
0
0
0
2
0
1
1
2
1
0
1
1
0
2
2
0
2
1
1
2
1
3
0
2
1
0
2
1
1
1
2
2
0
1
2
2
1
0
1
0
2
0
0
0
2
1
2
1
1
0
0
2
1
1
0
1
0
0
0
0
2
1
1
0
2
1
2
0
0
0
0
0
1
1
1
1
1
2
2
3
0
1
1
1
1
1
1
1
2
1
0
0
1
1
1
1
1
0
3
2
2
1
1
1
1
2
0
1
1
2
1
3
0
2
0
2
0
1
2
1
1
1
2
1
1
1
2
1
2
1
1
0
0
0
2
2
2
1
1
1
2
1
1
1
1
0
1
1
2
0
0
1
0
2
1
1
1
2
2
0
0
2
2
1
3
0
2
0
0
1
0
1
0
1
0
1
2
1
0
1
4
0
1
2
0
1
1
2
0
0
0
2
1
1
2
1
1
1
1
0
1
0
1
1
1
0
1
2
0
1
2
0
2
2
2
1
0
1
0
2
1
1
0
1
1
1
1
1
1
1
2
0
2
0
0
0
1
1
2
0
2
1
1
2
1
1
1
2
1
1
2
0
1
0
1
0
2
1
2
0
2
2
0
2
0
1
0
2
1
0
1
1
0
1
1
1
0
0
1
1
1
1
1
2
0
1
1
0
0
2
2
2
0
1
0
1
0
0
0
1
0
1
0
1
0
1
0
0
1
1
1
1
0
1
1
2
1
0
1
1
0
3
4
0
0
1
0
0
0
0
1
1
1
0
1
2
1
2
0
1
0
1
1
0
0
2
0
1
0
2
1
0
1
0
1
1
1
1
2
2
2
0
1
1
1
0
2
1
0
1
1
0
0
0
0
1
2
1
2
1
1
0
0
1
0
0
2
0
1
1
1
1
1
1
2
0
0
0
0
1
1
1
2
0
1
0
2
0
2
1
1
1
1
1
2
2
1
2
2
2
2
2
1
2
1
1
1
2
2
0
0
1
1
1
1
0
1
0
2
0
0
0
0
1
1
0
1
1
0
0
0
2
1
1
1
1
0
1
0
0
1
1
1
0
3
1
1
2
1
0
2
2
0
0
1
0
2
2
0
0
1
1
3
1
1
2
2
0
1
2
1
2
1
1
0
1
2
1
1
1
0
2
2
1
1
0
0
0
1
1
0
2
1
0
1
1
1
0
1
1
0
2
2
1
1
1
0
0
1
0
2
1
2
1
0
1
0
1
1
0
0
2
0
0
0
0
1
0
1
1
0
2
1
0
2
0
1
1
1
1
4
2
0
2
1
0
0
2
0
2
2
1
0
0
1
0
1
1
1
2
0
1
1
1
1
3
0
0
1
1
2
3
1
0
1
0
1
0
2
1
1
0
0
2
1
2
1
1
1
2
1
1
0
1
0
2
0
2
1
1
2
1
1
0
2
0
1
0
2
1
0
0
2
0
1
0
1
1
2
1
1
1
0
2
1
1
1
1
2
3
1
1
2
0
0
0
2
1
0
0
2
1
1
2
2
2
0
0
0
1
2
2
1
1
1
2
2
0
1
0
0
0
0
1
0
0
1
1
1
0
0
0
1
1
1
1
1
0
0
1
2
0
1
1
1
1
2
1
0
2
0
1
2
0
0
1
0
0
1
1
1
1
2
0
2
2
1
1
2
2
1
0
1
0
0
0
1
0
0
0
1
0
1
1
2
2
0
0
1
0
0
2
1
0
0
2
1
0
1
1
1
0
1
0
3
0
0
1
2
1
1
1
2
1
1
0
0
0
1
1
0
1
1
0
0
0
2
1
2
0
0
1
1
1
1
2
0
1
1
0
0
0
0
0
1
1
0
1
2
2
1
0
0
2
1
1
1
1
1
1
1
1
1
1
2
0
1
0
0
0
2
1
0
0
0
0
1
0
0
2
0
1
2
1
1
1
0
1
1
2
0
1
0
0
2
1
2
1
0
1
1
1
1
1
0
1
1
0
1
0
1
0
0
0
1
0
1
0
0
2
2
1
3
0
0
2
2
0
1
2
0
1
0
1
0
0
0
1
2
3
1
1
1
2
1
1
1
0
1
0
0
0
0
0
1
0
0
1
2
1
0
2
1
1
2
0
1
2
1
1
0
0
1
0
1
0
1
0
1
0
2
2
0
1
1
0
1
0
1
0
1
1
0
0
3
2
0
1
1
1
0
0
1
2
0
1
1
0
2
0
1
1
0
0
1
0
0
2
1
0
0
1
1
0
1
2
1
1
0
0
2
2
1
0
2
1
1
0
0
1
1
0
0
1
2
1
0
1
1
0
0
1
1
2
2
2
1
1
0
0
1
1
1
1
1
0
1
2
2
2
0
1
0
1
0
0
1
0
1
2
0
1
0
1
3
2
1
0
0
2
2
0
1
0
1
2
0
2
0
1
1
0
0
0
0
0
1
2
3
1
0
1
2
1
2
2
2
0
1
1
0
3
3
0
1
1
0
3
1
0
0
1
1
0
0
1
1
1
2
2
1
0
0
1
0
1
1
1
1
1
2
1
1
1
1
1
1
1
1
0
1
1
2
0
0
1
0
3
2
2
1
1
0
1
2
1
0
0
1
1
1
1
1
1
2
0
1
0
1
1
1
1
0
2
1
1
0
1
2
1
0
1
0
0
1
2
1
0
1
0
0
1
1
0
2
2
1
1
0
1
0
1
2
1
1
1
1
0
0
0
1
0
2
0
0
3
0
1
1
0
1
0
1
1
1
1
2
1
1
2
1
1
0
0
2
2
2
2
1
1
1
2
2
2
1
1
0
1
0
1
0
1
0
1
2
1
0
1
0
1
2
1
1
1
1
2
2
1
1
1
2
1
1
1
0
1
2
0
0
1
2
1
1
0
0
1
0
1
2
0
1
2
1
0
2
0
0
0
1
1
0
1
0
0
0
2
2
2
1
0
0
0
2
0
1
0
2
2
1
1
1
1
2
0
5
0
1
1
1
1
2
2
1
3
2
1
1
0
1
1
1
1
2
1
1
0
1
0
0
1
1
0
1
1
1
1
1
0
0
1
0
1
1
1
1
2
0
0
0
1
2
1
1
0
1
1
0
1
1
1
0
0
2
2
4
0
1
0
1
0
0
0
1
2
0
1
1
0
1
0
0
1
1
0
1
1
1
1
1
0
1
0
1
1
1
1
0
1
2
1
1
0
1
1
1
0
1
0
2
2
2
0
1
0
3
2
1
0
2
1
1
1
3
1
0
1
2
1
1
1
2
2
1
1
1
1
1
0
0
0
0
1
0
0
0
1
1
1
1
1
0
1
2
1
1
1
1
0
0
0
2
2
1
1
0
1
0
1
1
2
1
1
1
2
0
1
1
1
0
0
1
1
0
1
1
1
0
1
1
2
0
0
2
1
2
2
2
1
1
1
1
1
1
2
2
1
2
0
2
1
0
1
0
0
2
1
2
2
0
2
0
1
2
1
0
0
1
1
2
1
0
0
0
0
1
1
0
2
1
0
2
0
2
1
0
2
1
2
1
2
1
1
1
1
2
1
0
1
1
1
5
2
0
0
1
2
0
2
0
1
1
1
2
1
1
0
1
0
0
1
1
2
1
1
2
2
1
1
1
0
1
1
1
0
1
1
0
1
0
1
1
0
1
1
0
0
2
0
1
1
0
1
1
2
1
1
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
2
0
0
2
1
0
0
0
1
0
1
0
0
0
1
0
1
2
1
0
1
1
2
2
1
2
1
0
1
1
1
1
1
0
0
1
1
2
2
0
1
2
1
0
2
0
2
0
0
0
1
2
1
0
0
0
1
0
2
1
2
2
1
1
2
0
0
1
1
1
0
3
0
0
2
1
1
1
1
1
1
0
2
1
0
0
2
1
0
0
2
0
1
2
0
1
0
2
0
1
0
0
0
0
1
2
0
1
0
0
2
1
1
2
1
0
1
1
0
1
0
1
0
1
0
1
1
1
2
1
0
2
2
1
1
0
0
1
2
0
0
1
2
0
2
1
1
1
1
0
2
0
0
0
2
0
1
1
0
2
1
0
1
1
2
1
1
0
1
0
1
0
1
1
1
1
2
0
2
1
1
0
1
1
2
0
1
2
0
1
2
1
2
2
1
1
0
2
1
0
0
1
2
1
1
0
2
1
1
1
2
2
0
2
2
2
1
2
2
2
0
0
0
2
1
1
2
1
2
0
1
1
1
1
0
0
0
2
1
2
0
2
1
3
2
1
1
2
1
2
0
0
1
1
1
0
0
1
2
2
1
1
1
0
2
1
2
2
0
0
0
1
0
1
2
1
1
0
0
2
1
2
0
1
1
0
0
1
2
1
1
1
1
1
1
1
1
0
1
1
0
0
4
1
1
1
2
0
1
1
0
1
1
0
0
0
1
2
0
0
1
1
1
1
1
0
1
1
0
1
1
0
2
0
0
1
1
0
0
1
1
2
2
2
0
0
0
1
0
1
1
1
2
0
1
0
1
0
1
1
2
2
0
1
2
1
1
0
0
0
2
2
2
0
2
1
1
1
1
0
2
1
1
2
0
0
1
1
0
1
0
2
1
2
1
1
4
0
0
2
1
2
1
1
2
2
0
2
0
1
1
1
0
1
1
2
1
0
1
0
1
1
1
0
1
0
1
1
1
0
0
1
1
1
0
2
0
1
0
0
1
0
0
2
1
0
0
2
1
2
1
0
1
0
2
1
0
2
2
1
1
1
2
2
1
1
1
1
1
1
0
0
1
1
1
1
1
0
2
0
0
0
1
0
2
1
1
1
0
0
1
0
2
1
2
1
2
1
1
0
1
1
1
1
1
0
1
0
1
1
2
0
0
1
0
0
2
0
0
0
0
2
3
0
1
1
1
2
0
0
2
0
1
0
0
1
0
1
1
0
1
0
0
2
1
1
2
1
1
1
1
2
1
0
1
0
0
0
0
0
0
1
0
2
0
1
2
2
2
1
0
1
0
1
0
1
0
0
1
0
2
2
1
1
1
2
1
1
1
0
1
1
2
1
1
1
2
0
1
1
2
1
0
1
1
0
1
1
2
1
2
2
1
1
2
1
1
2
0
1
2
1
0
1
2
0
0
0
0
0
3
0
0
1
2
0
5
2
0
0
0
0
1
1
0
0
0
2
1
0
2
0
2
1
1
1
1
2
2
2
0
2
1
2
0
2
1
1
0
0
2
1
1
1
1
3
1
1
1
2
0
2
2
1
0
1
2
1
0
1
2
4
0
1
2
0
0
0
0
2
0
1
1
2
0
1
0
0
1
2
1
1
2
2
1
2
1
2
2
0
0
1
1
2
1
2
2
0
0
1
0
2
1
0
0
1
2
0
1
2
0
0
3
0
0
2
1
2
1
2
2
1
0
0
1
0
0
0
1
1
0
1
1
0
2
0
0
0
2
1
1
1
0
0
3
2
1
0
1
0
0
1
0
0
0
6
1
1
1
2
1
0
2
1
1
1
1
1
2
0
1
4
2
0
2
2
0
0
1
2
0
1
0
2
1
2
1
0
0
0
2
0
2
0
1
1
1
1
2
0
1
2
1
1
2
0
1
1
0
1
3
2
0
1
1
1
2
2
1
2
0
0
1
1
0
0
1
1
0
1
1
2
0
1
0
1
2
2
0
1
2
1
2
1
0
1
1
2
2
0
2
0
0
0
1
0
2
0
0
1
1
0
1
1
2
1
3
1
0
1
1
2
1
1
2
1
0
1
1
1
0
0
1
0
0
1
0
1
2
0
1
0
2
1
2
0
1
2
2
1
3
1
0
0
2
0
0
0
2
1
2
1
1
1
0
1
0
1
0
1
1
4
0
1
0
2
0
1
1
0
0
0
1
0
1
0
0
1
1
1
1
2
1
2
1
0
2
0
1
0
3
0
1
0
1
2
2
0
1
0
1
1
0
1
1
0
0
1
0
1
2
1
1
1
1
0
2
1
1
0
0
2
0
1
2
1
1
1
2
2
1
2
1
0
0
2
0
1
2
0
1
0
0
1
0
0
0
2
1
2
0
2
1
1
1
1
1
1
1
1
1
1
1
4
1
1
3
0
1
1
1
1
1
0
0
1
0
3
1
0
2
0
1
1
1
1
0
2
1
1
1
1
0
1
1
1
0
1
2
0
0
2
2
3
0
1
1
1
2
2
1
2
0
1
0
0
2
0
2
0
0
0
2
0
0
1
1
0
1
1
5
1
2
0
0
0
0
1
2
0
0
4
0
2
1
0
1
1
2
1
2
1
1
1
1
0
0
1
2
0
1
1
2
2
1
0
1
1
1
2
1
2
1
1
0
0
2
2
0
0
2
1
1
1
0
0
0
1
1
1
0
2
0
0
2
1
1
0
0
1
1
2
2
1
1
1
2
1
1
0
2
1
1
1
2
2
2
3
1
0
1
0
2
2
0
1
1
2
1
1
2
1
2
2
0
3
3
2
0
1
0
1
0
2
1
0
0
0
1
2
1
0
1
2
0
2
0
2
1
0
0
2
0
0
0
1
1
1
0
2
1
0
1
0
0
0
1
1
0
1
2
1
2
0
2
0
1
2
0
0
0
1
1
1
0
2
0
2
1
1
0
0
0
2
0
1
1
0
1
2
1
1
1
1
0
2
1
1
1
1
0
1
2
2
1
0
1
2
0
1
0
1
1
1
0
2
0
0
0
0
1
1
0
0
1
1
1
1
1
1
1
2
0
0
1
0
1
1
2
1
2
0
1
1
0
2
0
0
0
0
0
2
0
0
1
1
1
1
0
0
1
1
1
0
3
2
0
0
0
1
0
1
1
2
0
0
0
0
0
0
1
0
1
1
0
2
1
2
1
1
6
0
0
2
1
0
2
0
0
0
1
1
0
1
1
1
3
1
1
1
1
1
1
2
1
1
1
2
2
1
0
2
0
2
1
0
2
1
1
1
1
2
1
1
0
2
0
1
1
1
0
1
0
1
0
1
1
0
2
0
1
0
1
0
1
0
1
0
0
1
0
1
2
1
1
1
1
1
1
1
1
3
2
0
1
2
1
1
0
0
2
0
1
1
2
3
1
2
0
2
2
0
0
0
1
1
1
0
0
1
1
0
2
2
1
2
1
1
0
1
2
0
0
0
0
1
2
1
1
2
2
0
0
0
0
1
2
1
1
0
0
1
0
2
1
1
1
0
1
0
1
0
0
0
1
1
1
1
2
0
3
1
0
0
0
1
0
0
1
2
0
1
1
0
0
0
0
2
1
0
2
0
2
0
1
1
0
0
1
1
0
1
0
2
1
2
1
1
2
0
0
2
1
0
0
1
1
1
2
1
1
0
2
1
1
1
1
0
2
1
0
0
0
0
0
0
1
0
1
4
1
0
1
2
2
1
0
1
1
0
1
0
1
1
1
4
0
1
0
2
2
0
1
1
0
1
1
1
1
0
3
1
1
0
0
0
0
0
1
0
0
2
0
2
1
1
0
1
0
1
1
0
0
1
2
0
0
1
0
1
1
2
2
1
0
1
1
0
2
2
5
2
0
1
2
2
1
1
2
1
2
2
2
1
3
1
1
1
2
0
2
1
1
1
2
1
1
0
1
2
1
0
1
2
0
1
1
0
2
1
0
1
1
1
0
0
2
0
1
0
1
2
2
0
0
1
0
1
1
2
2
1
1
2
2
1
1
1
1
1
1
1
2
2
2
2
1
1
0
1
2
2
1
2
1
2
1
2
2
2
1
0
0
1
2
0
0
0
1
0
2
2
0
1
0
0
1
2
0
1
1
2
1
1
2
1
1
2
1
0
0
1
2
2
2
0
0
0
1
0
1
1
0
1
1
1
0
1
1
0
0
0
0
2
1
1
0
4
1
2
1
1
0
1
1
1
1
0
0
0
0
0
1
1
2
0
0
1
0
0
2
2
1
1
0
1
1
0
0
1
0
1
1
2
1
1
1
1
0
0
0
0
1
3
1
1
1
2
1
0
0
1
3
2
2
0
0
1
0
1
1
1
0
1
0
0
1
0
2
2
1
0
1
1
1
0
0
1
2
2
1
0
1
0
2
1
2
1
2
0
1
0
1
0
1
1
1
1
0
2
2
2
0
2
1
0
0
1
1
0
0
0
1
1
2
1
1
0
1
1
1
1
1
1
1
1
1
1
1
2
1
0
0
0
0
1
2
0
1
2
0
1
2
0
0
0
2
1
0
1
1
0
0
1
0
0
3
0
0
0
0
0
1
2
0
0
0
1
0
2
4
1
1
1
1
1
1
0
1
1
0
0
0
1
0
0
1
0
3
0
1
1
1
0
1
1
0
1
1
0
0
0
1
1
2
1
1
0
1
0
1
1
1
0
2
0
1
0
0
0
1
0
1
0
1
0
1
2
1
1
1
1
1
1
1
2
1
1
2
0
0
0
0
1
1
0
0
1
1
0
0
0
2
0
2
1
0
1
1
0
0
1
2
1
1
0
2
0
2
1
2
2
0
0
1
0
2
0
0
1
2
2
0
0
2
1
0
2
1
1
2
1
3
2
3
1
1
2
1
1
2
0
2
1
0
0
1
0
1
1
1
0
0
1
1
2
2
1
2
1
0
1
1
1
0
1
1
1
0
0
0
0
1
2
1
2
1
0
1
1
2
1
1
0
1
1
1
1
3
0
0
0
0
0
1
1
0
2
1
1
0
0
0
1
2
0
1
0
0
1
1
1
1
0
2
1
2
0
0
1
2
0
1
1
2
1
2
1
0
2
2
0
1
0
1
1
0
1
1
1
0
0
1
0
1
0
1
0
0
1
2
0
2
1
2
0
0
0
0
0
1
0
1
0
0
0
0
2
0
1
0
0
0
1
1
0
1
0
2
1
0
1
2
1
0
1
1
0
1
0
1
0
1
0
1
2
1
1
2
1
0
0
1
1
1
2
2
2
0
0
0
1
0
0
0
2
0
1
0
2
1
2
1
0
0
1
0
2
1
1
1
0
1
1
1
0
2
0
1
1
1
0
1
1
2
0
3
1
2
0
0
2
1
2
1
2
0
0
1
0
1
0
0
2
2
1
1
1
0
1
0
1
1
1
0
0
1
2
2
0
1
2
1
0
0
2
0
1
1
1
1
1
2
1
0
1
0
2
0
1
0
0
1
2
1
1
0
0
2
1
0
1
2
1
1
1
1
0
1
0
2
0
0
2
2
2
4
1
0
1
0
0
2
1
0
1
0
1
0
1
1
1
1
2
1
1
2
2
1
1
2
0
3
0
1
1
2
1
2
0
2
0
1
1
0
0
1
2
2
0
0
0
0
2
2
1
1
1
0
1
0
0
1
0
1
0
2
0
2
0
0
1
1
2
0
0
0
0
0
1
1
2
0
1
1
1
2
1
2
1
1
2
0
0
0
2
0
1
0
0
1
2
0
1
2
0
1
1
2
1
1
2
2
2
1
2
1
0
1
1
2
0
1
1
1
2
0
1
0
1
1
1
1
2
1
0
1
2
1
2
2
2
1
2
1
1
2
0
0
1
1
2
1
1
1
0
2
0
1
2
1
2
1
1
0
0
1
1
1
2
0
0
2
1
1
2
1
3
1
0
1
2
3
0
1
1
1
0
1
0
0
1
0
1
1
1
1
2
2
1
1
1
2
1
0
1
1
1
2
0
1
1
1
1
1
1
1
0
1
1
2
0
1
2
0
0
1
2
2
0
2
1
1
0
1
1
0
1
1
2
1
2
2
1
2
1
1
1
0
0
0
1
1
1
1
2
0
0
2
0
2
1
2
0
1
1
1
1
2
1
2
4
1
1
1
1
1
2
1
1
1
1
0
1
1
0
2
1
1
1
0
1
1
1
0
2
0
0
1
0
1
0
1
0
1
0
1
0
1
1
0
2
1
0
3
0
2
1
0
0
1
0
0
0
0
0
2
1
0
1
1
1
1
2
2
2
1
1
1
2
0
0
1
1
0
1
1
1
0
2
1
2
0
1
2
0
1
0
1
1
1
1
0
0
0
1
1
1
0
1
1
1
1
1
1
1
1
0
1
1
1
0
1
1
1
1
2
0
1
1
1
0
1
1
2
0
0
0
0
1
1
0
2
0
2
1
2
3
0
1
0
1
1
2
2
1
0
2
1
2
1
1
0
0
1
0
0
1
1
0
0
1
0
2
1
1
0
1
2
0
1
1
1
1
0
0
2
0
1
2
2
0
0
1
0
0
0
0
1
0
2
2
1
0
1
0
0
2
1
1
1
1
0
2
1
0
0
1
0
1
1
0
1
0
1
0
1
0
2
2
1
3
0
0
2
1
2
0
0
0
2
1
1
2
1
2
0
1
2
0
1
2
0
1
2
1
2
0
1
1
0
0
0
0
0
0
2
0
1
0
0
1
0
2
1
1
1
1
1
1
1
1
1
2
1
1
1
0
2
0
2
0
2
0
1
0
1
1
1
1
1
0
1
1
1
1
2
1
1
2
0
1
0
1
2
1
2
1
1
2
1
1
1
0
0
2
1
2
0
0
2
2
1
2
1
0
1
6
0
2
0
1
0
0
1
1
2
2
0
0
1
1
1
0
1
0
2
2
1
1
0
0
1
2
0
1
1
1
2
1
1
1
2
0
0
1
2
1
1
0
3
0
1
1
0
1
0
0
1
1
1
0
1
2
0
2
0
0
1
2
1
1
1
2
2
2
1
3
0
1
0
1
2
2
0
0
1
1
1
2
1
0
1
2
1
0
1
1
2
1
2
1
1
2
1
2
0
2
1
0
2
0
2
1
0
2
0
1
1
1
2
2
0
0
2
2
1
1
2
0
0
2
0
1
1
2
0
2
2
1
1
2
2
1
1
2
0
0
2
1
1
0
0
0
1
1
1
0
1
1
0
0
1
1
0
1
0
1
1
0
1
4
2
2
0
0
0
1
0
3
2
2
1
1
3
0
1
0
1
2
1
0
1
0
0
1
2
1
1
1
1
2
1
1
1
0
1
1
0
0
0
1
2
0
2
2
1
0
1
2
0
0
2
1
1
1
0
0
1
4
1
1
1
1
1
1
2
0
2
0
0
0
0
1
0
1
1
1
2
1
1
0
0
0
2
2
2
2
1
2
0
1
0
1
1
1
2
1
1
0
0
2
2
1
2
2
0
1
0
0
0
0
2
5
1
1
2
2
1
2
0
3
0
1
0
2
1
0
0
1
2
1
0
1
0
1
0
2
0
0
1
2
2
0
0
0
0
1
1
1
2
1
0
2
1
0
1
1
1
1
0
1
1
2
0
0
3
1
2
0
1
1
1
0
2
0
2
1
1
1
1
0
1
1
0
2
1
2
2
1
2
2
2
2
2
0
0
1
0
1
1
2
1
0
2
0
2
1
1
1
0
0
0
0
2
0
0
0
1
2
1
1
1
1
1
0
0
0
2
0
4
0
0
1
1
0
0
1
2
1
2
2
0
0
0
0
0
0
1
1
1
1
1
0
1
0
0
1
2
2
1
0
1
2
0
0
0
2
0
0
1
1
1
0
1
1
0
2
2
0
1
2
0
1
2
1
2
0
1
1
1
0
0
1
1
1
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
1
2
2
0
1
0
2
1
0
2
0
1
1
0
1
0
1
2
1
1
1
0
0
1
1
0
1
0
1
2
0
2
2
0
1
1
1
1
1
0
0
1
1
0
1
2
2
0
0
2
1
1
1
1
1
1
1
0
1
0
0
1
1
0
1
1
1
1
2
0
1
1
1
0
1
1
1
0
0
1
2
0
1
1
0
1
2
0
1
1
1
0
1
1
0
1
0
1
0
0
0
1
2
0
1
0
1
1
0
2
1
0
0
0
2
2
0
1
0
1
1
1
0
2
2
1
0
1
2
2
1
1
1
2
1
1
2
0
1
2
2
2
1
2
1
1
0
2
0
1
0
0
1
1
1
0
1
0
0
1
3
2
1
0
2
0
1
1
1
1
1
1
0
1
1
1
1
0
0
0
2
1
1
2
0
1
1
0
0
1
1
0
0
0
0
2
1
2
1
1
0
1
2
1
1
1
1
2
1
2
1
0
0
1
1
1
0
2
2
2
1
1
1
0
0
0
0
1
1
2
0
0
2
2
1
0
2
1
1
0
2
1
1
1
1
0
0
2
1
2
0
0
2
1
2
1
2
0
0
2
1
0
1
1
1
2
1
0
1
1
2
1
0
1
0
1
2
1
0
1
1
0
1
1
1
1
1
0
1
0
1
1
3
1
1
1
1
0
2
0
0
2
1
1
2
2
1
2
1
0
1
1
0
0
1
1
2
2
1
0
1
1
0
1
2
0
0
1
1
2
1
2
0
2
1
0
2
1
2
1
2
1
1
0
2
0
0
1
1
2
0
0
2
1
0
0
2
0
1
1
1
1
1
0
0
1
0
0
0
1
0
1
1
2
1
0
1
0
1
0
2
1
1
2
1
1
0
0
2
0
1
2
1
0
2
1
1
2
1
1
0
1
1
2
0
1
1
1
1
2
1
1
1
0
1
1
2
1
1
1
1
1
1
3
2
0
2
1
2
1
0
0
2
0
1
1
1
0
1
1
3
0
0
3
1
1
1
1
1
0
0
1
2
1
1
2
2
2
2
1
2
2
0
0
1
1
1
1
0
0
1
1
1
1
0
1
1
1
1
2
0
1
1
0
1
1
0
2
1
1
1
0
2
1
0
0
0
1
2
1
0
1
0
1
1
1
1
0
0
0
0
2
0
0
1
1
1
0
2
2
1
2
2
0
1
2
2
0
1
1
1
0
0
0
0
0
0
0
1
0
1
0
1
1
1
1
1
0
1
1
0
2
2
1
2
1
1
0
1
1
1
1
0
1
1
1
1
0
0
1
1
0
1
2
3
2
1
1
1
2
1
0
2
1
0
2
1
0
0
3
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
1
0
2
1
0
1
2
0
1
2
0
1
2
1
1
2
1
2
1
0
0
2
0
2
2
2
1
2
2
1
1
2
1
2
1
1
1
0
0
1
0
0
1
1
0
0
2
2
1
1
0
0
1
0
2
0
0
1
1
1
0
0
0
2
0
1
0
1
0
1
1
1
1
1
1
0
0
0
1
2
0
1
1
0
1
0
2
2
2
1
1
0
2
2
1
1
1
2
1
2
1
1
1
1
1
1
1
1
2
1
0
1
1
2
1
1
0
1
1
1
1
0
2
1
0
1
2
1
2
0
1
7
2
0
1
2
1
0
1
0
1
1
1
1
2
1
1
0
0
1
1
3
1
1
0
1
2
1
1
0
1
0
3
2
1
1
1
1
2
1
1
1
2
1
1
0
1
1
1
1
0
2
0
2
2
0
0
0
1
1
0
1
0
1
0
2
1
0
0
1
0
2
1
3
0
2
1
1
2
1
1
0
1
2
1
1
1
1
0
0
1
1
2
0
0
2
2
1
0
0
1
0
1
0
1
1
1
2
0
2
1
2
0
0
0
0
1
2
0
1
0
2
1
1
1
1
3
2
0
0
1
0
1
0
0
1
0
1
1
0
1
1
1
1
2
0
1
2
1
1
0
0
0
0
0
0
0
1
1
1
1
0
1
2
2
0
0
1
1
0
1
1
0
2
1
4
2
1
3
0
0
1
0
1
2
2
2
0
0
1
2
1
1
1
0
0
2
0
0
1
2
1
1
0
1
0
1
1
1
1
1
0
1
1
1
1
0
1
1
1
0
2
1
2
3
1
2
2
2
2
2
0
1
3
1
1
1
1
2
0
2
1
2
2
0
0
1
2
1
0
4
0
1
1
0
1
0
0
1
0
0
1
1
1
8
0
1
1
0
0
1
0
0
0
0
2
0
1
1
1
0
1
0
3
1
1
0
1
1
2
0
0
0
1
1
2
1
1
0
1
0
2
1
2
2
0
0
0
1
1
0
2
0
0
2
0
0
1
1
0
3
2
0
1
1
2
1
1
2
1
0
1
2
0
1
1
1
0
0
1
1
1
1
0
2
1
1
1
2
1
1
1
2
0
0
2
1
1
1
0
2
1
3
1
2
2
0
3
2
1
1
0
0
0
0
0
1
0
0
2
0
2
0
2
1
2
2
0
1
0
0
1
2
1
0
1
2
0
0
0
1
1
2
0
1
1
2
1
1
1
2
0
1
0
0
0
0
1
1
0
0
0
1
2
2
0
2
0
1
1
0
0
1
0
0
1
0
0
2
0
2
1
0
1
2
0
1
1
1
1
1
1
0
0
0
1
2
0
1
1
2
1
2
0
0
0
1
2
1
1
2
0
1
2
0
1
1
1
1
0
2
0
0
0
0
0
2
1
1
0
1
0
1
1
2
1
1
2
1
1
1
1
2
2
0
0
0
1
1
1
1
1
2
2
1
1
0
2
2
0
2
0
0
1
1
0
1
1
1
0
1
2
1
1
2
2
0
0
0
1
1
1
1
1
0
1
0
0
2
0
0
1
0
1
1
1
2
1
0
0
1
1
1
0
1
1
1
1
0
0
0
2
1
2
1
1
1
2
1
2
2
2
0
1
0
1
0
1
0
1
1
0
1
2
1
0
0
0
5
1
1
0
2
0
2
1
1
1
1
0
2
0
2
0
2
0
0
1
1
1
0
0
1
0
3
1
1
0
1
0
1
1
1
1
1
2
0
2
1
2
2
2
1
1
1
1
0
0
1
0
0
2
0
2
1
3
1
2
2
0
0
1
1
0
0
0
0
0
0
1
1
1
2
1
0
1
0
1
1
3
0
1
1
0
1
1
1
2
0
0
2
0
1
1
1
1
2
1
0
0
1
0
2
1
0
1
0
1
1
2
0
0
2
2
1
1
0
1
1
0
1
0
1
1
2
0
0
1
1
1
2
0
2
0
0
1
1
0
2
0
0
0
2
1
0
6
1
1
0
1
0
2
1
1
0
0
1
0
0
1
1
1
0
2
0
0
1
0
1
1
0
1
1
1
0
2
2
2
0
2
2
0
0
0
1
0
0
2
2
1
1
0
2
0
2
0
2
1
0
2
2
1
1
1
2
1
1
2
1
1
0
1
0
1
1
1
1
1
0
0
1
1
0
1
2
0
0
1
1
2
1
1
0
1
1
0
1
1
2
2
0
1
0
0
1
1
2
0
2
0
0
0
1
1
2
1
1
2
0
0
0
1
2
1
3
1
2
1
0
1
1
0
0
3
1
0
2
2
1
0
0
2
0
1
1
1
1
1
0
1
3
1
2
1
0
1
1
0
0
0
1
2
0
2
1
1
0
1
1
1
0
2
1
0
0
2
0
2
2
1
1
1
1
2
0
1
1
2
1
2
1
1
1
1
0
2
0
1
1
1
2
1
1
2
2
1
1
1
1
0
0
2
1
1
2
0
0
1
1
0
1
1
2
0
1
0
2
2
1
2
2
1
0
2
1
2
1
1
2
2
2
0
2
0
1
0
0
0
1
0
1
2
2
0
1
0
1
3
2
0
0
2
0
2
1
0
0
1
0
1
0
2
1
1
1
0
0
1
1
2
1
0
1
1
1
0
2
1
1
1
2
1
1
0
0
2
0
0
1
0
1
1
1
0
1
1
0
0
0
1
2
0
2
1
2
2
0
0
4
2
2
0
0
1
2
0
0
1
2
1
2
0
0
1
0
1
1
2
2
2
0
1
2
2
0
0
1
0
0
1
2
1
1
2
2
1
0
1
2
1
0
0
1
1
0
0
1
0
1
0
0
1
0
1
2
0
1
1
2
2
0
0
0
1
1
0
0
0
0
1
1
1
1
0
1
1
0
1
0
1
2
1
1
0
1
1
2
2
1
1
1
0
2
0
1
1
1
1
0
0
0
1
2
1
1
1
1
1
1
1
2
2
0
0
1
0
0
2
1
0
2
2
2
2
3
1
1
1
1
2
0
1
2
1
0
2
1
0
2
1
1
1
0
2
0
1
0
1
2
2
0
1
0
2
2
1
2
1
3
1
2
1
1
2
1
1
2
0
0
1
2
0
0
1
0
1
0
1
1
1
1
1
1
1
1
1
2
0
2
0
1
1
0
0
0
0
0
1
2
1
2
0
2
1
0
1
2
0
0
1
1
1
0
1
0
0
0
1
3
1
1
0
0
2
1
0
1
1
2
0
1
2
1
1
1
0
0
2
1
1
1
1
2
0
2
1
3
0
0
2
2
0
1
0
0
2
1
2
1
1
0
0
1
1
0
2
1
2
1
1
1
1
1
2
2
2
2
1
2
0
1
0
2
1
2
0
0
2
1
0
0
1
1
2
2
0
0
0
0
2
2
3
2
0
0
2
0
1
1
1
1
2
2
0
2
0
1
0
1
0
1
1
0
0
0
1
3
1
3
1
1
1
2
2
1
0
0
0
2
1
1
1
1
1
0
1
2
1
0
1
0
2
1
1
1
1
0
1
1
1
0
1
1
1
1
1
0
1
1
1
1
2
1
1
1
0
0
2
0
0
2
1
1
1
2
0
1
1
2
1
1
1
1
1
2
0
1
1
0
0
0
1
2
2
1
1
1
0
0
2
1
0
2
0
0
2
2
2
0
0
0
0
1
2
0
2
2
2
1
1
0
0
0
0
1
2
2
1
0
1
0
1
1
2
1
1
1
2
0
0
1
2
1
0
1
1
1
6
0
2
0
1
2
1
2
1
1
2
0
1
0
1
1
2
0
0
0
0
1
1
2
1
0
2
0
1
1
1
1
0
2
0
1
2
1
0
1
0
2
1
2
1
1
1
2
0
2
2
2
1
1
1
0
1
1
1
0
1
1
2
2
1
2
1
0
0
2
1
2
0
0
1
0
1
1
0
0
1
2
2
1
1
2
0
2
1
0
1
2
1
1
1
1
1
1
0
1
0
0
2
1
2
0
1
2
2
0
1
2
0
1
0
1
0
1
1
0
0
1
0
0
1
0
0
1
1
2
1
2
2
2
1
1
1
0
0
0
1
0
1
0
1
0
2
0
1
0
1
0
1
2
1
0
2
0
0
2
1
0
0
2
0
2
2
0
1
2
2
2
2
0
1
1
1
2
1
2
1
2
2
1
1
0
1
2
1
2
0
0
1
2
0
1
1
0
2
1
2
2
0
1
0
1
0
0
1
1
1
0
1
1
2
2
1
0
0
0
0
1
0
0
0
0
0
2
1
1
0
0
2
0
0
0
1
0
1
0
0
1
0
1
2
2
0
0
1
1
1
2
1
1
0
0
0
1
2
1
1
0
1
1
0
0
2
1
1
0
1
2
1
1
0
2
1
1
1
0
1
2
2
0
1
1
0
1
1
2
2
2
1
0
0
0
0
0
0
0
1
2
0
0
0
2
0
1
0
0
1
1
1
0
2
1
0
2
1
2
1
0
0
1
1
1
1
1
1
2
2
2
1
0
1
2
0
1
1
1
2
0
1
1
0
1
1
0
0
0
1
0
0
0
2
1
1
1
1
0
2
2
0
1
0
1
1
0
0
0
2
2
1
1
0
2
2
2
1
1
2
1
2
1
1
1
1
0
2
1
0
1
0
2
1
1
1
1
2
2
1
1
0
2
1
2
1
0
0
2
1
1
1
1
1
2
0
2
2
2
2
2
0
1
1
0
1
2
0
1
0
1
2
2
0
1
1
1
0
2
2
1
0
0
0
1
1
1
2
1
1
0
1
0
0
0
1
0
0
2
2
1
1
0
1
0
0
0
0
1
0
0
0
2
1
1
1
2
1
1
0
1
1
1
1
2
2
1
3
0
1
1
0
1
1
0
2
2
0
2
0
1
0
1
1
1
1
2
0
0
0
2
0
1
1
1
0
1
0
2
1
2
0
3
2
1
0
1
1
1
1
2
1
1
1
2
0
1
0
1
1
0
2
2
1
2
0
0
1
1
1
1
1
1
1
0
1
0
2
1
3
1
1
1
2
1
0
2
2
2
1
1
2
1
2
0
1
1
0
1
1
1
0
0
1
1
1
2
1
0
0
1
0
2
1
2
1
0
2
2
0
1
1
0
1
1
1
2
0
1
1
1
2
0
2
2
0
2
2
1
1
1
2
1
1
1
1
0
2
0
1
3
1
0
2
1
0
0
0
0
0
0
1
2
1
0
0
1
1
1
2
0
0
3
1
1
2
0
0
1
2
1
2
0
1
1
0
1
5
1
1
0
0
1
1
1
1
1
1
0
1
0
2
2
1
2
1
0
0
1
0
1
1
0
0
0
0
1
1
1
1
1
1
2
0
2
1
1
0
1
2
1
2
1
1
0
2
0
0
1
1
1
2
0
1
0
0
0
0
1
1
0
2
1
1
0
1
1
2
1
1
0
1
1
1
1
2
2
2
0
1
1
1
1
1
2
1
0
0
0
1
1
0
0
0
2
1
1
1
1
1
0
2
0
2
1
0
0
1
2
1
2
2
0
0
2
0
0
2
1
1
2
0
0
1
0
0
1
1
1
0
1
1
1
2
0
1
1
1
0
1
0
0
1
0
0
0
1
1
2
1
0
0
2
0
0
1
0
2
2
1
0
0
0
1
0
1
0
2
0
0
0
0
1
1
1
2
0
1
0
0
1
1
1
0
1
2
1
0
1
0
1
2
1
2
2
0
1
1
0
2
1
2
1
0
0
2
2
2
1
0
1
0
2
0
0
1
2
2
1
0
0
1
0
1
2
0
2
0
0
0
0
2
0
0
0
0
1
2
0
1
1
2
2
0
1
1
1
0
1
0
1
0
0
1
0
1
2
0
0
2
1
1
1
1
2
0
1
1
0
0
0
0
1
1
2
0
0
0
1
3
2
1
1
0
1
0
2
1
0
1
1
0
0
1
1
2
2
2
0
1
0
0
1
1
0
2
1
1
0
1
2
0
1
1
1
0
1
1
1
1
0
0
1
1
1
2
0
2
1
2
1
0
0
2
0
1
0
1
2
1
1
1
2
1
0
0
0
2
1
2
2
1
1
1
1
0
0
0
1
1
0
0
1
0
1
1
1
2
1
1
1
0
1
1
0
1
1
0
0
1
0
1
1
0
1
0
1
2
2
1
1
1
2
1
1
1
0
0
0
1
1
2
3
2
2
2
1
0
0
1
2
1
1
1
1
0
0
0
0
1
1
1
0
1
0
1
1
0
0
1
2
1
0
1
0
0
0
0
1
1
0
2
2
2
0
1
1
2
0
2
0
0
1
0
1
1
0
2
2
1
1
1
1
0
1
1
1
0
0
1
1
0
1
1
1
3
2
1
0
2
0
2
1
0
0
1
1
1
1
1
1
1
1
1
1
2
1
0
1
3
1
2
0
1
1
2
1
2
1
0
2
1
0
2
2
0
1
0
1
2
0
1
1
0
2
1
1
2
1
0
0
0
0
1
0
1
0
1
1
0
0
1
2
0
1
1
0
1
1
2
0
0
1
0
1
0
0
0
2
1
0
1
1
2
0
2
1
0
1
1
2
1
1
1
1
1
1
2
0
1
2
6
0
0
0
0
0
1
2
2
2
2
0
2
2
1
1
1
2
0
0
0
0
2
0
1
1
1
1
1
1
0
0
2
0
0
2
0
1
2
0
0
1
0
0
1
0
0
1
2
1
1
2
0
0
2
1
1
1
0
2
1
1
1
0
1
2
0
1
1
0
1
0
1
1
0
0
0
1
0
1
2
1
0
1
0
1
1
1
1
1
0
1
1
1
1
0
0
0
1
2
0
1
0
1
3
1
1
1
2
7
1
2
0
1
2
1
0
1
0
2
2
0
1
1
1
2
0
1
2
1
1
2
0
0
2
2
1
0
1
0
1
2
1
2
1
2
0
0
0
1
0
2
2
1
1
1
0
1
0
0
2
0
1
0
1
1
0
0
1
0
1
1
0
1
1
1
2
0
1
0
1
2
1
0
0
2
1
0
0
1
1
1
1
1
0
2
0
0
1
0
3
0
2
1
1
1
1
0
1
2
2
1
2
2
1
1
0
1
0
1
2
0
1
1
2
3
2
0
1
1
1
1
1
1
2
0
2
2
1
1
1
1
0
0
2
1
1
2
2
2
2
0
1
1
1
2
0
0
0
1
2
0
1
1
0
2
1
0
2
1
1
0
0
2
2
2
0
1
2
0
2
0
1
0
1
1
1
1
1
2
2
2
1
1
1
0
1
1
0
2
0
0
0
1
2
1
1
2
3
1
1
1
1
0
1
1
0
1
1
0
1
1
1
0
0
0
0
2
0
1
2
1
1
1
1
0
1
0
0
0
0
1
1
1
0
1
0
1
1
0
0
0
0
2
4
1
0
1
0
0
1
1
1
0
1
2
1
1
2
2
1
2
1
0
1
3
1
0
1
1
0
2
1
1
1
2
1
1
1
2
0
1
0
0
2
1
0
1
0
1
0
0
1
1
0
1
2
1
0
1
1
1
2
1
1
2
0
1
2
1
1
0
0
0
1
1
1
1
2
0
2
1
1
1
1
1
1
2
1
0
0
1
2
0
0
0
1
2
2
1
1
1
0
1
0
2
2
0
0
0
0
1
1
1
1
2
2
1
0
1
0
0
1
1
1
1
0
1
1
1
1
0
2
1
1
0
1
2
0
2
3
2
2
2
2
1
1
0
0
1
2
1
2
0
0
0
2
0
1
2
0
1
1
1
2
1
1
1
1
1
0
2
1
0
1
0
1
2
0
0
0
2
0
2
0
1
0
1
1
2
0
1
2
0
1
0
0
2
1
0
1
1
1
0
0
0
1
1
2
1
2
2
0
0
1
1
1
1
1
0
0
3
0
0
1
0
1
1
0
2
2
0
0
1
2
3
1
2
1
0
0
2
1
0
1
2
2
1
0
0
1
1
0
2
2
3
0
1
2
0
2
1
1
0
0
2
1
1
1
1
3
1
1
2
1
1
1
1
0
2
0
2
1
1
1
2
2
1
2
0
1
1
2
2
2
1
0
1
0
0
1
1
2
0
2
3
2
1
0
2
2
3
1
1
0
1
2
1
0
1
2
0
2
2
2
2
2
1
0
1
0
1
0
1
0
2
1
1
0
1
2
1
2
0
0
0
0
1
2
0
0
1
0
0
1
0
2
1
1
2
1
0
0
1
0
1
2
2
1
0
1
0
0
0
1
0
1
1
1
1
0
1
0
0
2
0
0
0
2
1
1
0
1
1
1
2
2
1
1
1
0
2
1
1
0
2
0
1
1
0
1
0
0
0
0
0
1
1
0
0
1
1
1
1
1
2
0
0
1
2
2
1
1
1
1
2
0
2
1
0
1
0
0
0
2
0
1
0
2
0
1
2
0
2
0
0
0
1
0
0
2
1
1
0
2
0
1
0
0
0
0
0
1
1
1
1
0
0
1
1
2
0
1
1
0
2
1
2
1
0
2
0
0
1
1
1
0
2
2
0
0
2
0
1
1
2
1
0
2
0
0
0
1
1
1
1
2
0
0
0
2
1
2
1
1
1
1
1
1
2
0
0
2
2
2
2
2
1
2
1
0
0
2
0
2
0
1
1
1
1
1
1
1
1
1
0
2
1
1
0
0
1
1
0
0
0
0
1
1
2
1
0
1
0
2
0
2
1
1
0
1
2
0
2
1
0
2
2
0
0
1
1
1
2
0
0
0
1
1
1
1
1
1
2
1
1
1
0
1
0
0
0
1
0
1
0
2
0
1
0
0
0
2
1
0
1
0
0
1
0
1
2
1
0
0
1
0
1
0
1
0
1
1
1
2
1
1
0
2
1
1
0
0
0
1
0
2
1
1
1
1
2
0
1
1
1
0
0
1
1
0
1
0
1
0
1
2
0
3
3
1
2
2
0
0
2
1
1
1
1
1
2
0
0
2
0
1
2
1
1
0
2
1
0
3
1
0
1
1
0
0
1
1
0
3
1
1
0
1
1
1
1
1
1
1
0
2
2
1
0
0
2
2
1
1
2
1
2
2
1
1
2
0
1
0
0
1
2
2
1
1
2
1
1
1
0
1
2
0
2
0
1
0
1
1
2
0
0
0
1
2
1
2
1
3
0
0
1
1
0
2
2
2
0
2
0
1
0
2
1
0
1
2
0
0
1
0
2
2
1
1
1
0
0
1
1
1
0
2
2
0
2
1
3
1
1
0
1
2
1
0
1
0
2
1
1
1
0
3
2
2
0
1
1
1
0
0
2
1
1
2
0
2
2
0
1
1
2
1
1
1
0
1
1
1
1
1
1
1
1
0
0
1
0
2
1
0
0
2
0
2
2
0
1
1
2
2
2
0
0
1
2
0
0
0
0
1
1
1
0
0
2
0
3
2
1
1
0
2
2
1
1
1
1
1
1
0
1
1
2
0
0
1
0
0
0
2
1
1
1
1
2
0
1
0
0
2
1
1
1
2
0
1
0
1
0
2
2
1
1
2
2
3
2
2
1
1
0
1
2
1
1
0
2
1
0
1
1
0
1
2
1
2
3
1
2
2
1
0
1
1
0
0
2
1
0
0
2
1
1
0
1
0
0
0
1
1
2
2
2
0
1
0
1
2
3
0
2
2
2
1
0
1
1
0
0
2
0
0
1
1
1
2
0
1
1
1
1
1
0
2
1
0
0
0
0
1
2
0
1
0
2
2
0
2
0
1
2
2
1
1
2
1
2
1
0
1
1
2
0
0
0
1
0
1
2
2
0
0
0
0
0
1
1
0
1
1
0
1
0
1
1
2
1
1
0
1
1
0
2
2
1
2
2
1
1
0
2
1
2
1
0
0
1
0
1
1
1
1
0
2
0
1
0
1
1
0
2
2
1
1
2
1
2
1
2
0
0
2
0
2
1
2
0
0
1
1
2
0
1
2
0
2
2
2
0
2
1
2
2
1
2
0
2
1
0
3
2
1
0
0
1
1
2
2
1
1
0
0
0
1
1
0
1
1
1
2
2
2
0
1
1
2
0
0
0
2
2
2
1
5
0
1
1
0
1
2
1
1
1
0
2
1
1
0
0
2
0
2
2
1
1
0
0
2
3
0
2
2
0
0
1
1
0
1
2
1
1
0
1
1
0
0
2
0
0
1
1
0
2
1
2
1
0
1
0
1
0
1
0
1
0
1
1
1
2
2
2
1
2
2
0
0
1
1
1
1
0
2
0
2
0
0
2
1
1
0
1
1
1
1
1
2
3
0
1
0
2
0
0
0
1
1
1
1
0
1
0
0
1
1
0
0
0
0
2
1
0
0
0
0
0
0
1
0
2
0
2
0
0
1
1
0
0
1
0
1
2
0
1
0
1
0
2
2
1
2
0
0
0
1
2
1
2
1
2
1
0
1
2
0
3
0
1
2
0
2
1
1
0
0
2
1
0
2
4
0
0
1
2
0
0
1
1
0
0
1
1
1
1
2
1
1
0
1
1
2
1
1
2
1
0
1
2
0
0
0
1
0
0
1
1
1
2
1
0
1
1
2
1
2
1
1
2
2
1
1
1
1
2
1
1
1
1
0
1
2
0
1
2
2
1
2
3
1
1
2
1
0
1
2
0
1
1
1
2
1
2
3
0
1
2
2
1
2
0
1
0
0
0
1
1
1
1
1
2
0
0
0
1
1
2
0
2
0
2
2
0
0
0
0
0
1
1
0
1
0
1
1
1
0
1
1
1
0
1
2
2
1
2
0
0
3
1
1
1
0
0
1
0
3
0
1
1
2
1
0
1
1
1
0
2
0
1
0
0
0
1
0
0
1
1
1
0
1
5
2
0
1
0
2
0
0
1
1
0
1
0
0
0
0
2
0
0
1
1
0
1
1
0
1
1
2
1
2
2
1
0
1
1
3
0
0
0
0
0
1
1
0
0
2
2
0
0
1
0
0
0
2
1
0
0
0
2
2
2
0
2
0
1
1
0
0
2
2
2
2
1
1
0
5
0
0
1
0
2
1
0
1
2
2
1
2
1
1
0
1
2
0
1
1
2
0
1
1
0
2
1
1
2
1
1
1
2
1
0
1
2
1
0
0
1
1
1
1
0
2
1
0
2
0
1
3
1
0
2
2
2
2
1
1
1
1
2
1
2
1
1
1
2
0
2
0
1
0
0
0
0
1
1
1
1
2
1
2
0
2
2
2
0
0
0
0
1
1
0
0
0
1
0
0
1
2
0
2
1
0
1
2
1
2
1
1
1
0
2
1
0
2
1
1
0
0
2
1
2
0
1
1
2
1
1
2
0
1
1
0
1
1
2
0
0
0
2
1
1
2
2
1
1
0
1
1
1
1
1
1
2
0
0
1
2
2
1
2
0
1
1
1
0
0
0
1
0
2
1
2
1
0
1
3
2
1
1
0
1
0
1
2
2
0
1
1
1
0
1
2
1
1
1
2
0
2
1
1
1
1
0
1
2
1
1
1
0
1
1
2
2
1
0
1
4
1
1
0
1
0
1
1
0
0
0
0
2
2
1
1
1
0
2
1
1
1
0
0
2
2
1
1
1
0
1
0
1
2
0
1
2
0
2
1
0
1
2
0
8
2
0
1
1
0
0
1
1
0
0
2
0
1
0
1
0
0
1
2
0
0
1
0
0
1
2
0
0
0
0
1
1
1
0
0
1
1
1
1
0
0
2
0
2
1
0
0
1
0
2
0
2
1
1
0
1
0
1
0
1
1
0
1
1
1
0
1
1
1
1
0
1
1
1
1
1
0
0
1
0
0
2
1
1
1
0
1
0
0
1
1
1
1
1
2
1
2
2
1
0
1
0
0
1
2
1
0
1
0
2
2
2
1
0
2
1
1
1
0
0
2
1
1
1
2
1
0
1
1
0
1
0
2
1
1
0
2
0
0
2
2
0
1
1
1
0
1
2
0
1
1
2
0
1
2
1
1
0
1
0
1
1
1
1
0
0
0
2
1
1
1
0
1
1
1
1
1
1
0
2
1
0
1
0
0
2
0
1
2
2
1
1
0
2
1
1
0
0
1
1
1
1
0
0
1
1
1
1
2
0
0
1
1
2
0
1
2
0
0
1
0
1
0
1
1
3
1
0
0
2
1
1
0
2
1
1
1
0
2
1
0
0
0
1
1
1
1
0
1
1
1
0
0
1
2
1
1
0
1
1
0
1
1
1
2
1
0
2
2
0
1
1
1
7
0
1
0
1
1
0
1
2
0
1
0
1
1
2
0
1
1
1
1
2
2
4
1
0
2
1
1
0
0
0
1
0
1
1
0
1
2
6
1
2
1
1
1
0
1
0
0
2
1
2
0
1
1
0
1
0
1
2
1
2
1
2
1
1
0
1
1
0
0
0
0
0
1
2
0
3
1
1
1
1
1
1
0
0
1
1
1
2
1
1
1
1
1
2
0
2
2
1
2
2
2
1
2
0
1
0
1
1
1
0
1
3
1
2
0
1
2
1
1
2
2
0
1
1
4
1
1
2
0
1
0
2
1
0
2
1
2
1
0
0
0
0
1
1
1
1
2
0
1
2
1
1
1
0
1
1
1
0
1
1
2
0
1
2
0
1
1
2
0
0
1
2
1
2
0
4
0
0
0
0
1
3
1
0
0
2
0
2
1
1
1
1
1
0
0
1
2
0
2
0
2
1
1
1
1
1
2
0
1
0
1
1
0
2
0
1
1
0
1
2
1
1
2
1
1
2
0
1
0
0
1
1
1
0
0
0
1
0
1
1
0
1
1
1
0
1
0
1
2
1
1
0
2
1
0
2
6
0
1
1
1
0
1
1
0
0
1
0
1
1
1
1
0
0
2
1
1
0
1
1
2
0
1
2
2
1
2
0
2
0
2
2
0
1
0
1
3
2
0
2
1
0
1
0
1
1
1
1
1
0
1
1
1
1
2
1
2
0
0
1
1
2
2
0
2
0
0
1
0
0
2
1
0
2
1
1
1
1
1
0
2
1
1
1
2
1
0
1
1
1
1
2
1
1
0
1
2
2
1
1
1
0
1
2
0
1
2
1
1
0
0
0
0
1
1
1
1
0
2
1
1
1
1
2
1
1
1
2
2
2
1
0
0
1
1
1
0
1
0
1
0
1
1
0
1
2
1
1
1
0
1
1
2
1
2
0
0
1
3
1
0
2
2
2
1
1
1
0
1
1
0
1
0
2
1
2
0
2
1
2
0
0
0
1
2
0
1
2
0
2
0
0
2
1
2
0
1
0
0
0
1
1
2
2
0
1
0
0
2
1
0
2
0
0
1
1
0
1
2
0
1
0
1
1
1
1
1
1
0
0
0
0
2
2
2
0
1
0
2
1
1
2
1
1
0
2
2
2
0
1
2
0
0
1
1
0
1
0
1
1
0
1
1
0
2
2
0
1
1
0
1
1
1
1
2
0
2
1
1
0
1
1
0
2
0
2
0
1
2
0
2
1
1
1
0
2
0
0
0
1
1
1
1
0
0
0
1
2
1
1
1
1
2
1
1
0
1
1
0
0
2
0
1
1
0
1
0
0
2
1
0
1
0
2
2
1
2
1
2
1
2
2
0
1
1
0
2
0
1
1
1
1
1
2
0
0
0
0
0
1
0
0
2
2
2
1
1
0
1
0
0
0
1
1
2
0
1
0
0
1
2
0
2
0
2
2
1
1
2
0
1
0
1
1
0
1
5
1
1
1
0
1
3
1
0
1
0
1
1
2
2
0
1
0
2
1
1
2
1
1
0
0
1
1
0
0
1
1
0
1
0
1
0
0
1
1
1
1
1
0
3
1
1
2
0
1
0
1
0
0
1
2
0
2
1
0
1
1
0
1
0
1
1
1
2
2
1
2
0
2
1
0
0
1
1
1
1
1
0
0
1
2
1
1
1
1
0
1
1
1
1
2
1
0
0
0
1
2
0
0
2
2
1
0
1
2
2
1
0
1
2
1
1
4
2
1
0
0
1
1
1
1
2
0
0
0
0
1
2
1
1
0
1
1
0
1
2
2
0
2
1
2
1
1
0
1
0
1
0
0
0
0
1
2
1
0
1
1
2
2
1
2
0
1
0
2
1
0
0
0
0
0
2
1
1
0
0
1
1
1
1
1
1
1
1
0
0
0
2
0
1
1
1
0
1
1
2
1
1
1
1
2
0
2
1
2
1
1
1
2
1
2
5
1
3
2
0
0
0
1
2
1
0
1
0
0
1
1
2
1
0
1
0
0
1
3
0
1
0
3
0
2
1
1
2
1
0
0
0
2
1
1
2
0
0
1
1
1
1
1
2
1
1
1
1
1
2
2
0
1
1
2
0
0
0
2
0
1
0
1
2
1
2
2
1
1
1
0
1
1
2
0
0
0
0
0
0
1
1
0
2
0
1
1
1
2
1
1
1
1
1
0
0
2
1
2
2
1
2
1
0
0
1
0
1
1
0
1
1
2
1
1
1
2
2
0
0
1
1
0
2
1
0
1
0
2
0
1
1
0
2
1
0
1
1
1
1
1
0
0
0
2
0
1
1
1
1
0
1
1
0
1
1
2
1
1
1
2
0
0
0
1
2
0
2
1
0
0
0
1
1
1
1
1
0
1
0
0
1
0
0
1
2
1
0
1
0
0
0
0
0
1
1
0
2
1
0
2
0
1
1
2
0
0
2
1
0
0
1
2
0
2
0
2
0
0
0
0
1
0
0
2
0
0
0
1
0
1
0
2
1
1
0
0
0
0
0
1
0
2
1
0
1
2
0
2
3
1
2
1
1
0
0
2
0
2
1
0
2
0
2
2
1
2
1
0
1
1
1
0
1
1
0
1
1
1
2
1
1
1
0
0
1
2
0
2
1
2
2
0
2
0
2
2
1
0
0
0
1
0
0
0
0
1
2
1
0
0
0
1
1
0
1
1
0
1
1
2
2
0
1
0
2
1
0
1
2
1
0
0
2
1
0
1
0
0
2
2
0
1
0
1
1
1
0
1
2
2
0
2
1
1
1
2
1
0
1
2
1
1
1
0
2
0
1
1
1
0
1
0
1
0
1
0
2
1
0
1
0
2
0
1
1
0
2
0
1
2
1
1
2
0
0
1
1
1
0
1
1
2
2
1
2
1
1
2
1
0
1
0
2
1
0
1
1
0
2
1
0
1
2
1
1
0
1
0
1
0
0
2
1
1
0
0
2
2
1
0
1
0
2
1
1
0
0
2
0
1
0
1
2
1
1
0
1
1
1
1
1
2
0
0
0
1
0
2
0
1
1
2
3
1
0
1
1
1
1
0
0
0
1
1
2
1
2
0
0
0
0
1
2
0
2
1
0
1
1
0
0
1
0
0
0
2
1
1
0
0
2
0
1
1
0
1
0
2
1
2
1
0
0
1
2
2
1
1
1
0
2
1
2
0
0
1
1
0
2
1
1
1
0
2
1
1
0
2
0
1
0
0
1
1
0
0
1
1
1
0
2
1
1
2
1
1
1
1
0
1
0
0
1
1
2
0
1
1
0
1
1
2
1
1
0
0
2
2
1
2
1
1
0
1
1
0
0
1
0
0
0
1
1
0
1
0
1
0
2
0
1
0
1
0
1
0
2
1
0
2
2
1
2
2
0
1
1
1
2
0
3
0
2
2
0
1
1
2
1
1
1
0
0
2
1
2
1
0
2
0
1
1
1
0
2
0
1
1
1
2
1
1
0
2
2
2
0
1
2
1
1
1
3
1
2
1
1
1
1
1
2
1
2
0
0
2
1
2
2
1
0
1
1
0
2
1
2
1
1
0
2
0
2
1
0
0
2
1
0
2
1
1
0
0
0
0
2
0
0
1
0
4
1
1
0
1
0
3
0
1
0
1
1
0
1
1
1
2
1
2
1
1
1
1
1
2
2
2
1
2
1
2
1
0
0
2
0
1
2
0
1
0
0
1
0
0
2
0
0
0
1
1
1
1
1
1
0
3
0
1
0
1
0
2
2
0
0
1
0
3
1
0
2
1
0
2
2
0
1
2
0
1
2
1
1
1
2
1
0
0
2
2
1
2
1
1
1
0
0
2
0
2
2
0
1
0
0
2
0
1
0
2
1
1
0
2
2
3
1
1
0
1
1
2
0
0
0
3
0
1
0
3
1
1
0
1
0
1
0
1
2
2
1
1
1
1
0
0
1
1
1
1
0
1
1
0
0
1
1
1
1
2
2
0
0
2
0
0
1
1
0
0
1
3
1
0
1
1
0
0
1
1
1
0
1
2
0
1
0
2
1
0
1
2
1
0
2
1
0
1
0
0
1
0
1
0
0
0
2
1
0
2
2
1
1
2
1
2
1
1
0
0
1
2
2
1
0
0
1
1
1
1
0
1
0
0
1
2
0
0
1
0
1
1
0
0
0
2
1
0
1
1
0
2
2
2
2
0
0
0
0
1
2
0
1
0
2
1
1
1
0
0
1
2
2
0
1
2
2
0
1
0
0
0
0
1
2
1
1
0
0
0
1
0
0
2
1
1
0
1
1
2
2
1
1
0
3
1
0
2
2
0
0
0
1
0
0
0
1
0
1
1
1
1
2
1
0
0
2
1
1
0
0
2
1
1
1
2
0
2
2
0
2
1
0
2
1
1
0
0
2
2
0
2
1
0
1
0
0
0
1
1
1
2
0
0
3
1
1
0
1
1
2
0
1
1
0
0
1
2
0
2
0
1
0
1
0
1
2
2
1
2
0
1
0
1
1
0
1
1
2
1
2
1
0
0
1
1
1
1
2
0
1
0
0
1
1
0
2
2
2
0
0
1
1
2
1
1
0
0
2
0
1
1
3
2
1
1
2
0
2
0
0
0
0
0
1
0
0
2
1
0
0
1
1
0
0
1
1
1
0
0
1
1
2
1
0
1
0
1
1
1
2
0
0
1
1
1
1
2
0
0
2
0
0
0
2
0
1
0
0
0
0
1
0
1
1
2
0
1
1
2
0
1
1
1
0
0
1
1
0
2
1
1
0
0
0
0
1
1
0
2
1
2
1
2
1
0
2
1
2
1
2
1
2
0
0
2
0
1
0
2
1
0
0
1
1
2
2
2
1
0
0
1
0
0
2
0
0
3
1
1
2
0
0
1
1
2
0
0
1
1
2
1
2
1
1
3
2
2
0
2
2
2
0
0
1
0
0
2
0
1
2
1
1
1
0
2
2
1
1
1
2
2
7
1
1
2
1
0
1
1
1
2
1
1
1
0
2
0
2
1
1
1
2
2
0
2
1
0
1
2
1
0
1
0
0
0
0
1
1
1
1
1
0
0
2
1
1
1
1
1
1
0
2
0
2
2
0
1
1
1
1
0
1
1
2
0
0
2
2
1
0
2
1
2
0
0
2
0
1
2
1
0
1
0
1
1
1
0
1
1
0
1
2
1
1
2
1
1
2
1
0
1
0
0
1
2
0
2
2
0
0
2
0
0
1
0
0
1
0
1
3
0
1
2
1
1
2
0
1
0
1
1
2
0
1
3
0
0
1
2
1
1
1
0
1
1
1
0
0
2
0
2
2
1
1
0
0
0
2
1
0
1
1
0
1
1
0
0
1
0
1
2
2
1
0
1
0
1
1
0
1
2
1
1
0
0
1
0
2
1
0
1
1
1
1
0
0
1
1
0
2
0
1
1
0
0
1
1
2
2
0
1
0
1
0
2
0
1
1
2
1
0
0
0
1
1
1
0
1
3
1
0
1
0
0
0
0
1
2
0
2
1
2
1
0
2
1
1
1
1
1
2
2
2
1
1
1
0
1
2
1
0
1
1
1
1
1
0
2
1
0
0
1
2
1
0
1
2
2
2
1
0
1
0
1
1
1
0
1
1
1
1
2
0
2
0
0
1
1
1
0
1
1
1
1
1
1
1
2
0
2
2
1
2
2
0
2
0
1
1
2
0
1
0
1
1
1
2
1
2
1
1
0
1
0
1
1
1
1
0
0
1
1
0
0
2
1
0
0
1
0
0
1
1
1
0
1
0
0
0
2
2
1
1
1
0
1
1
0
0
1
1
1
4
1
2
0
1
1
1
2
0
1
0
0
2
0
0
2
1
1
1
0
2
1
0
0
1
0
3
1
2
0
1
0
1
1
1
1
1
1
0
1
1
0
0
2
2
0
2
0
2
2
0
2
2
0
1
1
2
0
1
0
1
0
0
0
0
1
0
0
3
1
1
1
1
1
1
1
0
1
1
0
0
1
0
1
1
0
1
1
1
2
0
2
1
1
1
1
2
0
0
0
1
1
1
1
2
1
0
0
1
1
1
2
1
1
2
1
1
1
1
0
1
1
0
0
1
2
1
1
1
1
0
0
1
2
0
2
1
1
0
1
1
0
1
2
1
1
1
1
1
0
1
0
1
0
2
1
0
1
1
2
0
1
1
1
1
2
1
1
1
0
0
0
2
0
2
1
2
2
1
2
0
0
2
2
2
0
2
0
0
1
1
0
1
2
1
2
2
2
0
0
1
2
1
0
1
2
1
1
2
1
2
2
1
0
1
1
1
2
2
1
2
1
2
1
2
0
1
1
0
1
1
1
0
2
1
0
1
1
0
0
2
3
2
1
1
0
2
1
0
1
2
2
0
1
1
2
1
2
2
0
0
2
1
1
1
0
0
0
0
0
1
1
0
2
2
1
0
1
3
0
0
0
2
2
0
1
0
1
2
2
0
0
2
0
0
0
2
1
1
0
0
1
2
0
0
1
0
1
3
0
0
0
1
0
1
1
1
2
1
0
1
1
1
1
1
1
1
1
2
3
1
1
2
1
2
1
0
0
0
1
1
2
1
1
1
1
2
2
0
1
0
0
1
2
0
1
0
0
2
0
1
0
1
1
2
2
0
1
0
2
1
1
1
2
1
1
0
1
0
1
0
0
0
0
2
1
1
0
0
2
0
2
1
0
0
2
1
0
1
1
1
1
2
1
1
0
0
2
0
0
1
1
2
1
1
1
0
0
1
1
2
1
1
1
0
1
0
1
0
0
2
2
1
1
1
1
1
0
0
1
0
0
0
1
1
0
2
2
1
0
1
0
0
0
0
3
1
2
1
1
2
1
2
1
0
1
1
2
1
1
1
2
2
1
0
2
1
1
1
1
2
2
1
1
1
0
1
1
1
1
2
2
0
0
2
1
0
2
1
3
0
1
1
0
1
1
1
1
1
1
2
0
0
0
0
2
0
1
1
1
1
0
1
2
2
0
2
0
2
2
1
0
1
2
1
0
1
1
0
1
1
1
1
0
1
2
2
2
0
0
1
1
1
1
1
1
1
0
1
1
1
1
0
2
2
2
1
1
0
0
2
0
0
1
1
0
0
1
1
0
0
1
1
0
0
0
1
1
0
0
1
2
1
0
2
0
1
1
1
1
1
1
2
1
0
1
1
0
0
1
1
1
3
1
2
0
2
1
1
2
0
0
2
0
0
1
2
2
1
0
0
1
1
2
1
0
0
0
1
1
0
1
0
2
1
2
1
1
1
1
0
1
1
2
1
0
1
0
0
0
2
2
0
0
0
2
0
0
1
0
2
0
1
2
1
2
1
0
1
1
1
2
2
2
0
0
1
0
0
1
3
1
0
0
1
0
2
1
0
0
2
0
3
0
1
1
2
1
1
0
1
3
0
1
1
1
0
2
1
0
2
1
0
1
1
1
1
1
0
3
0
2
1
1
2
1
0
1
2
2
1
1
1
3
2
1
0
0
1
1
1
2
1
1
0
2
0
1
0
0
4
0
0
1
1
0
1
1
3
1
1
2
1
2
0
0
2
2
0
0
1
0
1
2
2
0
2
2
2
1
0
2
1
1
1
1
0
0
1
1
0
1
1
2
1
0
2
0
1
1
1
1
0
0
1
1
1
1
1
1
1
0
1
0
0
1
2
0
2
1
2
2
1
0
1
0
0
1
1
1
1
1
1
2
1
1
3
2
1
1
1
1
1
0
1
0
2
2
1
2
1
1
2
2
1
1
2
1
2
1
0
0
0
1
0
1
0
1
0
1
0
1
1
1
1
0
1
2
1
0
2
1
1
0
0
1
1
2
0
1
0
2
2
2
0
1
1
1
1
1
0
1
0
1
2
1
1
0
2
1
1
1
0
2
2
1
2
1
1
0
1
2
0
2
0
0
2
0
1
1
1
0
0
2
0
1
2
0
2
0
0
1
1
1
2
1
0
2
1
1
2
0
7
0
1
0
0
0
1
0
0
1
0
1
1
0
1
0
2
1
1
2
2
0
0
0
1
0
1
1
1
1
2
0
1
1
1
0
0
2
1
1
0
1
2
1
2
1
0
1
1
2
0
1
3
1
1
0
1
2
1
1
1
1
2
1
2
0
1
1
1
1
3
0
1
1
1
1
2
0
0
0
1
0
1
1
0
1
2
0
0
1
1
1
1
1
1
0
1
1
0
1
2
1
2
2
1
1
1
1
1
0
0
0
1
0
2
0
0
1
1
3
2
0
1
0
1
0
0
4
2
0
0
1
0
0
2
1
2
1
1
0
1
0
1
0
1
0
0
0
1
1
1
0
2
1
0
0
0
1
2
1
0
0
0
0
1
0
1
1
0
1
1
0
2
1
1
1
2
0
1
1
1
0
0
1
2
2
2
0
1
0
1
2
1
1
1
0
0
0
0
1
1
2
1
1
0
0
2
0
2
0
1
2
1
2
1
1
2
0
1
1
2
1
0
1
1
1
0
0
0
2
2
1
1
0
2
0
1
0
1
1
2
1
1
1
1
0
2
1
1
2
2
1
0
1
1
1
0
1
2
0
1
0
2
1
0
1
1
0
1
0
1
2
1
0
0
0
1
1
0
2
1
0
0
0
1
1
1
2
1
0
1
0
1
1
0
1
1
1
1
2
1
1
0
1
0
1
0
1
1
0
4
1
1
1
1
1
1
1
0
1
2
1
1
1
0
0
0
2
0
1
0
2
0
0
1
0
2
1
0
2
1
0
1
0
2
1
1
1
1
0
0
0
0
0
1
2
2
2
2
2
1
0
1
2
1
0
1
1
0
0
1
1
1
1
1
2
1
0
1
1
1
1
2
0
1
1
1
1
2
1
1
1
0
0
3
2
1
1
2
1
1
0
0
0
0
1
2
2
0
2
1
1
4
0
2
1
2
0
1
1
2
1
0
0
1
2
0
0
1
2
1
2
0
1
1
2
2
1
2
2
3
0
3
2
0
1
0
1
1
1
0
1
0
1
2
1
0
0
1
0
1
1
1
1
0
2
2
2
1
1
1
2
2
1
0
0
1
0
1
2
1
0
1
1
0
1
1
1
2
1
1
1
2
1
0
1
0
2
1
1
0
1
2
2
0
1
1
1
0
0
1
1
1
0
1
1
2
1
1
0
0
1
0
1
3
1
0
1
1
1
4
1
2
0
0
1
0
2
1
0
1
2
0
0
1
0
1
1
1
1
0
0
2
1
0
2
2
0
2
0
2
1
1
0
2
0
0
1
1
0
2
1
1
0
0
0
1
0
0
2
0
1
2
2
1
1
0
0
1
2
2
1
1
1
1
1
1
0
1
2
1
2
1
1
1
0
0
1
0
1
1
0
1
0
0
2
0
0
0
0
1
0
1
0
0
2
2
1
1
1
0
1
0
2
1
0
1
0
1
0
1
1
2
1
0
1
0
0
0
1
0
0
1
0
1
0
1
1
1
1
2
1
0
2
0
2
1
1
0
0
1
2
0
1
0
1
0
2
1
1
2
1
3
1
1
2
1
1
1
0
0
2
0
2
2
1
0
0
1
1
1
1
1
0
2
2
1
1
0
1
1
1
2
0
1
0
0
0
1
1
1
0
0
2
1
2
2
0
1
2
1
2
2
1
1
1
2
0
0
0
0
1
0
1
1
1
0
2
0
1
0
1
1
0
1
0
1
0
1
0
0
1
0
0
1
1
0
0
2
2
1
1
2
0
0
2
2
3
1
2
1
0
0
2
0
2
2
1
0
2
2
0
2
0
2
1
1
0
0
1
1
1
2
1
1
1
0
1
1
2
0
0
0
1
1
0
1
1
3
0
2
2
0
1
1
0
2
1
1
0
3
1
1
0
1
1
1
2
2
1
1
1
0
1
1
2
2
0
0
0
0
0
1
0
1
0
1
0
1
1
0
1
2
2
1
0
1
1
1
2
2
2
0
1
2
1
1
1
1
2
1
0
2
1
3
2
0
0
3
1
2
2
0
1
1
0
1
0
0
0
2
2
0
1
1
1
1
0
0
1
2
1
2
0
1
0
2
1
2
1
1
1
1
0
1
1
1
0
1
2
1
0
1
0
0
0
2
1
0
2
1
0
0
0
1
1
1
0
0
1
2
0
0
1
1
0
0
1
1
1
0
0
2
2
0
0
0
2
2
0
1
1
0
1
1
1
0
2
3
2
2
1
0
2
2
2
0
1
1
1
1
1
1
1
1
0
1
0
1
1
0
0
2
2
0
1
1
2
0
0
2
0
1
0
1
0
1
2
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
2
0
2
1
0
1
3
2
1
0
1
2
1
1
1
0
2
2
1
0
0
2
0
0
0
2
1
1
1
0
1
0
2
1
1
1
0
2
3
2
2
1
1
4
0
2
1
0
1
1
0
1
2
1
1
1
0
0
2
0
1
0
1
1
1
0
0
2
4
1
1
1
1
1
1
0
1
0
2
2
4
0
2
0
1
1
2
1
1
1
2
2
1
0
2
2
1
2
0
1
0
1
1
2
1
1
0
0
1
1
0
0
1
1
1
3
2
0
1
1
3
1
2
0
0
0
0
0
1
1
0
0
0
0
2
1
0
1
0
2
0
2
1
0
0
1
2
2
2
0
1
1
2
0
7
1
0
2
1
0
1
1
2
0
1
1
2
2
0
0
0
1
0
3
1
3
1
1
1
1
3
2
2
1
1
0
0
0
1
1
0
0
1
1
0
0
0
1
2
0
1
1
0
2
0
0
0
2
0
1
1
1
0
1
0
2
0
0
0
1
0
1
0
1
1
0
0
1
1
1
2
1
1
1
1
0
1
1
0
2
0
1
1
2
2
3
0
2
0
0
1
1
0
0
0
2
1
2
1
0
1
1
2
1
1
1
1
1
1
1
0
2
2
0
1
1
2
0
1
1
3
0
1
2
2
0
0
2
2
1
2
2
1
1
1
0
2
0
1
1
0
2
2
2
0
1
1
0
2
1
0
1
1
1
2
0
0
2
1
2
1
1
1
1
1
1
0
1
0
1
0
1
1
0
2
1
2
1
1
1
1
1
0
2
0
0
1
2
0
2
0
1
2
0
1
1
1
1
2
1
1
1
1
2
2
1
1
0
1
1
0
1
1
2
1
1
0
1
0
1
1
2
2
2
1
1
1
1
2
0
1
4
2
0
0
2
0
0
1
0
1
1
0
1
1
0
0
0
1
2
2
0
2
1
0
2
0
2
0
0
1
4
0
1
1
1
1
1
0
2
0
0
2
0
0
2
0
1
0
3
1
0
1
2
1
1
1
1
2
1
0
1
0
1
2
0
1
1
1
1
1
0
1
1
2
1
0
1
2
1
1
1
1
1
1
1
0
0
1
0
2
1
1
1
2
1
2
0
0
1
2
2
0
0
0
1
1
0
1
2
1
2
0
1
2
2
2
0
1
0
0
2
0
2
1
0
0
2
1
0
0
0
0
2
0
2
2
1
1
1
1
0
0
1
0
1
0
2
1
1
0
0
2
2
2
1
1
2
1
2
2
0
2
0
2
1
1
2
2
2
1
2
1
0
0
1
1
1
1
1
1
1
1
1
0
1
0
2
0
0
1
2
2
0
1
0
0
0
1
0
1
0
2
2
0
2
2
1
1
2
2
1
1
1
1
1
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
2
2
0
2
0
1
1
1
0
1
2
2
0
0
1
0
0
1
0
0
0
0
1
0
1
1
2
1
3
0
0
2
1
0
1
2
0
2
2
0
0
0
1
1
1
2
3
1
0
0
1
1
2
0
1
0
2
0
2
2
0
2
1
2
2
1
1
2
2
0
1
1
0
0
0
2
1
1
1
2
2
0
1
0
0
0
2
3
3
1
1
0
1
1
1
1
2
2
2
2
0
2
2
1
1
1
0
1
2
0
2
1
0
2
2
2
0
2
2
1
1
1
0
2
2
1
1
2
2
2
0
0
0
0
1
2
0
0
1
0
1
0
2
1
0
2
1
1
1
1
0
0
0
1
0
0
1
0
2
0
1
1
0
1
1
0
0
0
0
2
1
0
1
1
0
1
0
1
0
0
2
1
2
1
0
0
2
2
0
1
2
2
0
1
0
0
1
1
1
0
0
0
1
2
1
2
0
0
1
1
0
0
2
1
1
0
1
0
7
1
1
1
1
1
1
2
2
0
2
2
2
0
0
0
2
0
2
0
2
1
1
1
1
0
1
0
1
0
0
1
1
0
1
0
2
2
0
0
2
2
0
1
1
2
1
1
1
1
0
1
0
1
1
2
1
0
2
2
0
1
2
1
2
0
1
2
0
0
0
1
1
1
1
1
2
1
2
0
1
0
0
0
1
0
2
1
1
2
2
0
2
0
2
3
2
1
2
2
0
2
0
0
1
0
0
1
0
1
0
0
1
0
0
1
1
0
0
0
2
2
1
0
1
1
0
2
1
1
0
0
0
0
1
3
2
0
1
0
1
1
1
1
1
0
1
1
0
2
2
0
2
0
0
0
1
1
1
1
1
2
3
0
2
1
1
1
1
1
2
0
0
0
1
0
0
3
1
0
1
2
2
1
1
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
2
2
2
1
1
1
1
2
1
1
1
0
0
1
1
1
1
0
0
1
1
0
0
2
0
1
0
1
1
2
1
0
1
1
1
0
1
1
0
1
1
2
0
0
2
1
2
2
0
1
1
0
1
1
0
1
2
2
1
1
2
1
0
2
1
2
1
1
1
0
1
0
0
2
1
1
2
1
2
2
1
1
0
2
0
2
1
1
0
1
1
2
0
1
0
1
1
0
0
1
1
2
1
1
1
2
2
1
1
1
1
1
0
1
2
1
1
1
1
2
1
1
1
1
1
0
1
1
1
0
2
0
1
2
1
0
0
1
1
0
2
0
0
1
2
1
2
0
1
2
0
2
1
1
1
1
2
0
0
1
1
1
0
0
2
0
1
2
1
0
0
0
2
1
0
1
1
1
1
2
0
1
0
1
0
1
1
0
2
1
1
2
1
2
0
1
2
0
0
1
1
1
0
1
2
2
2
1
1
0
1
0
0
0
1
0
2
2
1
1
1
1
1
1
0
1
1
1
2
2
1
1
1
1
0
0
1
1
0
1
2
1
0
2
1
0
0
1
0
0
1
0
1
0
8
1
1
0
1
2
0
0
0
0
0
1
1
2
0
0
0
0
1
1
0
0
1
0
1
1
0
2
1
0
1
2
2
2
1
1
1
1
0
0
2
0
1
0
1
0
1
2
0
2
1
2
0
2
0
0
0
1
0
1
1
1
0
1
0
2
1
2
1
0
0
0
1
0
0
2
0
0
1
0
2
0
1
0
0
0
0
1
0
2
1
1
1
1
1
1
1
2
0
1
2
2
3
0
2
1
0
3
1
1
1
0
0
0
1
1
1
0
2
1
1
0
1
1
1
0
0
2
0
0
1
2
1
0
0
0
1
1
0
1
2
2
1
1
1
2
1
1
0
0
1
1
0
0
0
1
1
1
2
2
1
1
2
1
0
2
0
0
0
2
1
2
0
0
0
0
1
2
1
1
1
2
1
1
1
2
0
1
0
1
0
2
1
2
0
0
0
2
1
1
0
1
1
2
1
0
1
1
0
1
1
2
1
0
2
2
1
1
0
0
2
2
2
1
2
0
1
1
1
1
0
0
0
0
0
1
1
0
0
2
1
0
0
1
2
1
1
0
1
1
3
1
0
2
0
0
0
0
0
1
1
1
1
0
0
2
1
1
1
2
1
1
1
1
1
0
0
1
0
0
1
1
1
1
0
1
0
1
0
1
1
1
1
1
1
0
1
0
1
2
0
0
0
1
0
0
2
1
0
1
3
2
1
1
2
1
0
2
1
1
1
2
1
2
1
1
2
1
1
2
1
1
1
2
0
0
1
0
0
2
2
1
1
0
1
1
1
2
1
0
1
1
2
1
1
2
1
1
1
1
1
2
2
1
0
0
0
1
1
0
2
0
0
1
1
2
0
1
1
1
0
0
1
1
1
1
1
1
0
0
1
0
1
3
1
1
0
0
1
3
0
1
0
1
2
1
2
1
1
1
0
2
2
1
0
0
0
1
0
1
0
1
1
0
1
1
2
0
0
2
2
0
1
0
1
0
1
0
0
0
1
0
1
0
2
1
0
2
0
0
0
0
1
2
0
1
0
1
1
0
0
1
1
1
0
2
1
0
0
1
1
1
0
0
0
0
0
2
1
2
1
3
3
1
1
2
3
0
2
2
0
1
0
1
1
1
1
1
0
1
1
2
2
2
1
1
0
0
0
0
1
2
2
0
1
1
1
0
0
2
1
0
1
3
1
1
1
1
1
0
1
2
0
0
1
1
1
1
1
1
2
1
0
1
1
0
1
2
0
2
2
1
0
0
1
1
0
0
2
1
2
1
1
1
0
0
1
1
1
1
2
0
0
2
2
1
0
1
2
2
1
0
2
2
0
0
3
0
2
2
2
1
2
0
1
0
0
2
1
2
0
1
0
1
1
0
1
2
2
0
1
2
1
0
1
0
2
1
2
1
0
2
2
1
0
2
2
2
2
2
1
1
1
1
0
1
1
1
2
0
1
0
0
1
2
0
0
2
0
1
1
2
1
2
0
0
0
1
0
2
0
1
2
1
2
2
0
1
1
2
1
0
0
2
0
2
2
1
1
1
1
2
1
2
0
1
1
0
2
1
2
0
0
0
1
0
1
2
2
0
1
1
1
1
0
0
1
0
1
2
3
1
0
0
2
1
1
0
2
0
1
1
1
0
1
0
2
1
1
0
0
0
2
2
1
1
2
1
1
0
2
1
1
0
0
0
1
0
1
2
1
0
1
2
2
2
1
1
0
0
1
0
1
0
1
1
0
1
0
1
2
1
1
2
0
0
2
2
0
1
2
1
2
1
1
2
1
1
1
1
1
1
0
0
1
1
1
0
1
1
1
1
1
1
2
1
1
2
1
1
1
0
1
0
3
1
0
1
0
0
1
2
1
1
1
2
0
0
1
2
1
2
1
1
0
0
1
2
0
2
0
0
1
1
0
2
1
1
1
2
1
1
1
2
2
0
0
2
1
2
2
1
1
1
1
0
1
1
1
2
0
2
1
2
0
1
1
1
1
0
1
1
1
2
1
2
0
0
1
1
1
2
1
2
2
1
0
1
2
0
0
1
1
1
3
0
1
0
0
1
0
2
1
0
2
1
1
0
0
2
1
0
2
0
1
1
0
2
1
2
0
2
1
2
0
0
2
0
0
0
1
0
1
1
0
0
1
2
0
1
0
0
0
2
1
1
2
1
1
0
0
1
1
0
1
0
1
2
0
0
0
0
1
2
0
0
2
2
1
1
1
2
1
0
0
0
0
1
2
0
2
1
0
2
1
1
0
0
0
1
1
2
2
0
0
0
0
1
1
1
0
0
0
2
1
1
0
1
0
0
1
1
1
1
0
1
1
1
0
1
0
0
2
1
2
0
1
0
1
2
1
0
2
1
2
0
1
1
1
0
1
2
1
1
1
1
0
2
2
1
1
1
0
0
1
2
1
1
1
0
2
0
2
0
1
0
0
1
1
1
0
1
2
2
1
1
0
1
1
1
0
2
2
1
0
0
1
0
1
0
2
1
0
0
1
1
2
0
4
2
0
0
0
0
2
1
1
2
2
2
1
2
0
2
0
0
1
0
0
1
2
1
1
0
0
1
1
1
2
1
1
2
1
0
2
2
0
1
2
1
1
1
0
1
1
1
1
0
1
1
1
2
0
0
2
1
1
1
1
1
1
2
0
1
2
2
1
0
0
1
0
2
2
0
2
1
1
0
2
1
1
0
1
0
2
1
1
1
2
2
1
1
0
1
2
1
0
0
1
1
1
2
2
1
2
0
2
2
0
2
0
2
1
1
1
2
2
1
0
0
1
0
1
1
2
0
0
2
1
1
0
0
1
1
1
2
2
2
0
1
0
0
2
0
0
0
1
0
0
1
2
2
2
1
2
1
1
0
0
1
0
1
0
1
2
1
1
0
0
0
2
0
2
1
1
1
1
1
0
2
2
0
0
1
1
1
1
0
0
0
1
0
2
1
1
2
1
1
1
1
0
0
0
0
0
0
1
1
2
2
1
2
1
1
1
0
1
2
1
0
1
1
1
2
1
0
1
2
0
1
1
2
1
2
1
2
1
0
2
2
0
1
1
1
1
1
1
1
1
0
1
2
2
2
1
2
1
1
1
0
0
0
1
0
0
0
1
1
2
0
2
0
1
0
1
1
0
0
1
0
2
1
1
1
0
1
2
0
2
1
2
1
0
1
1
1
2
2
0
4
1
0
1
0
2
2
0
1
1
2
0
0
0
1
0
1
0
1
0
0
0
2
1
1
0
2
1
0
1
3
1
4
1
1
0
1
2
0
0
1
2
1
1
0
2
1
2
1
2
0
1
1
2
0
2
2
2
0
1
1
0
0
2
0
0
1
2
1
2
0
1
1
0
0
2
1
1
1
2
1
0
1
0
0
1
1
1
1
0
1
1
1
1
1
0
0
1
1
2
1
1
2
0
0
0
0
0
2
0
1
1
0
2
2
2
0
2
1
1
2
1
2
1
0
0
0
2
0
0
2
0
1
2
0
0
0
1
1
2
0
1
2
1
1
1
1
2
2
0
1
1
1
0
0
0
2
0
1
2
1
1
1
1
0
2
1
0
2
0
1
3
0
1
0
1
0
0
1
1
0
0
2
1
1
0
0
0
2
1
1
2
2
1
1
2
1
1
0
0
1
1
1
1
0
0
1
0
0
1
2
0
1
0
0
1
0
1
4
1
2
2
1
1
2
1
0
1
1
0
1
1
1
0
1
1
1
0
0
0
0
2
1
1
0
2
0
1
2
0
2
0
0
3
0
1
2
1
0
0
3
1
0
1
2
0
0
0
1
0
1
1
1
2
2
1
1
0
1
1
1
1
2
0
1
0
1
1
0
1
1
0
0
1
0
2
2
1
0
0
1
1
0
0
0
1
1
2
1
1
0
0
1
1
1
0
2
1
1
1
2
1
0
2
0
0
2
0
1
2
1
1
2
2
2
1
2
0
0
1
1
0
1
1
1
1
0
0
2
1
1
1
1
0
2
1
1
1
1
2
2
0
0
2
2
1
1
0
0
2
1
0
1
2
1
1
0
2
0
0
1
1
4
0
2
2
2
1
1
0
0
2
0
0
1
2
1
0
1
0
1
1
1
1
0
2
1
1
0
1
1
0
0
1
0
1
0
0
1
1
2
1
0
1
2
1
1
2
2
2
1
1
1
2
1
1
2
1
0
0
0
1
1
1
0
2
0
1
1
1
1
0
2
2
1
0
0
1
1
1
1
1
0
1
0
0
1
0
1
0
1
1
2
1
0
0
1
0
0
0
1
0
2
1
0
1
0
0
1
0
0
1
1
0
1
1
1
1
0
0
3
1
1
2
1
1
1
0
1
0
2
1
1
1
0
1
0
0
2
1
2
1
0
1
1
0
2
1
0
1
1
1
1
1
0
2
1
1
0
1
1
1
2
3
0
1
1
0
0
2
2
0
1
1
1
2
1
2
2
1
2
2
1
2
0
1
3
2
0
2
0
0
1
1
1
1
2
0
1
0
0
1
3
2
0
1
1
0
1
1
2
1
1
0
1
1
0
0
0
1
1
0
1
0
1
1
2
1
1
1
1
1
1
2
0
2
0
0
0
2
2
1
2
1
2
0
2
2
1
1
1
1
1
1
1
0
1
1
1
0
1
1
0
1
0
0
2
1
0
1
0
2
1
0
1
1
1
0
3
0
0
0
1
1
2
0
1
2
1
1
1
0
0
1
0
0
1
0
0
1
1
1
2
0
2
1
1
1
0
2
0
1
1
1
2
2
1
1
6
0
2
1
1
0
1
0
1
1
1
0
1
1
0
1
0
0
2
0
2
1
1
1
0
1
0
1
1
1
1
0
0
1
1
1
0
2
1
0
1
2
1
0
1
8
0
0
1
1
1
0
0
1
1
3
1
0
0
1
1
2
1
0
1
0
0
1
1
1
1
0
0
1
1
1
1
0
2
0
1
1
0
1
1
0
0
0
2
1
0
1
0
1
1
1
1
2
3
1
0
1
1
0
1
1
2
0
0
1
1
2
1
1
1
2
2
1
2
0
1
0
0
1
1
3
1
1
2
1
0
2
0
2
1
2
1
0
1
0
0
0
1
0
1
2
1
2
1
1
2
0
0
1
0
0
1
2
1
1
1
0
0
1
1
0
1
1
1
0
1
1
1
2
1
0
0
2
0
0
0
0
1
2
2
1
0
0
0
1
0
0
1
3
2
0
2
0
1
0
2
1
2
2
0
2
0
1
1
2
0
2
2
0
1
2
0
2
0
0
0
1
1
1
1
1
0
2
1
1
0
2
1
1
1
0
0
2
0
1
1
1
1
1
1
1
0
1
2
2
0
1
2
1
0
1
0
1
2
2
1
0
0
0
1
0
0
1
1
2
0
1
1
0
0
0
1
0
2
2
1
1
3
2
1
2
0
1
1
2
4
1
1
1
0
0
0
0
1
5
1
1
1
2
1
1
0
2
1
0
2
2
0
1
0
1
0
2
1
1
2
2
2
1
1
0
1
2
2
1
0
0
2
0
2
0
1
0
2
2
2
0
1
1
1
2
1
1
0
2
1
1
0
1
2
0
0
0
1
2
0
2
2
1
0
2
1
3
0
2
1
2
1
1
2
0
1
1
1
0
1
1
1
1
1
2
0
1
1
1
2
2
1
1
2
1
1
1
0
1
0
1
2
2
1
0
1
1
1
0
1
1
1
0
0
1
1
1
1
2
1
1
2
0
2
2
1
2
2
3
1
0
2
1
1
0
1
1
1
0
2
2
2
1
2
1
2
1
0
1
0
2
1
1
2
2
0
0
1
2
1
1
2
2
1
0
1
0
1
2
1
2
1
1
1
0
2
1
0
0
0
0
1
1
0
0
1
2
1
2
0
0
2
1
1
2
0
2
1
1
1
0
0
1
1
2
3
1
2
0
1
1
2
1
1
1
0
0
1
1
1
0
0
0
0
2
1
1
0
0
2
1
1
2
0
0
0
1
1
0
0
0
0
1
1
2
0
0
1
2
0
1
1
0
2
1
0
2
0
0
0
0
0
1
0
1
1
2
0
0
1
0
1
1
1
0
1
2
1
0
1
1
0
2
2
0
2
2
0
2
0
0
0
0
1
2
1
0
2
1
0
1
0
0
1
0
0
1
1
2
1
1
0
0
2
0
1
0
1
1
1
0
1
1
1
1
2
1
0
1
1
0
0
2
1
1
2
2
1
1
1
1
2
1
0
0
0
0
1
1
1
2
1
1
2
1
1
0
1
1
2
2
2
1
1
0
1
0
0
1
2
2
0
0
1
2
2
1
1
1
0
0
1
2
1
2
1
0
1
2
2
1
1
1
1
0
0
1
2
0
2
1
0
0
0
1
0
0
0
3
2
0
0
1
1
1
2
1
0
1
1
1
1
1
2
0
2
1
1
2
1
2
1
2
1
2
1
0
1
1
0
1
1
1
0
1
1
0
1
2
1
0
0
0
0
0
1
1
2
1
1
1
0
0
1
1
0
0
1
1
1
1
2
2
2
0
1
0
0
2
0
1
2
1
0
1
0
0
1
0
0
0
1
0
1
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
1
1
1
0
2
2
1
0
1
1
2
2
1
2
1
0
1
0
1
0
0
1
0
2
0
1
1
1
1
0
0
1
0
1
0
2
0
1
0
1
1
1
1
0
1
0
0
2
1
2
2
2
1
1
1
0
0
2
0
0
0
2
1
2
1
0
0
1
1
0
3
1
1
0
1
0
1
0
1
1
0
0
1
1
0
0
1
0
2
1
2
1
2
0
1
1
1
0
1
2
1
0
1
1
1
1
2
1
1
0
0
1
1
2
1
1
2
2
1
2
2
2
0
1
1
3
1
1
2
1
2
0
1
1
0
1
1
0
1
2
2
2
1
1
0
1
2
0
0
0
1
1
1
0
2
0
1
0
1
2
0
1
1
0
1
0
1
0
1
1
1
2
2
1
2
1
0
0
1
1
0
1
2
1
0
0
1
0
1
0
3
2
1
0
1
1
0
0
2
1
1
1
0
0
1
0
1
0
1
0
1
0
1
0
0
0
1
1
1
1
0
2
2
1
1
1
1
1
1
0
0
1
1
1
1
1
2
1
2
2
1
1
1
0
3
1
0
1
1
1
0
1
2
1
2
2
0
2
1
0
2
0
0
2
0
0
0
2
0
0
3
0
0
0
0
2
0
0
1
1
1
1
0
1
1
1
2
0
2
2
1
1
0
0
0
0
1
2
1
1
0
1
0
0
0
1
0
0
3
1
0
2
2
0
1
2
1
1
1
1
0
1
2
0
1
0
1
2
1
1
0
0
1
1
1
1
1
1
1
1
2
3
1
0
1
0
1
1
0
2
2
1
2
1
1
0
1
0
2
2
1
1
0
0
1
1
1
1
1
2
0
0
0
0
1
2
2
1
2
1
0
1
2
0
0
1
1
1
1
1
1
1
1
0
0
2
2
0
0
2
1
0
2
0
1
0
1
1
2
1
1
1
3
2
2
0
0
0
0
1
1
1
2
2
2
0
1
1
1
1
2
0
1
1
2
0
0
0
1
0
1
1
2
2
1
0
0
1
1
2
1
2
1
3
0
1
2
1
0
0
1
1
0
1
1
0
2
1
1
1
1
2
1
1
1
0
2
2
1
1
2
2
1
0
1
0
0
1
0
1
1
2
1
2
1
0
0
0
1
2
1
0
1
0
2
0
1
0
2
1
1
1
1
0
1
0
2
0
2
0
1
1
2
1
0
1
1
0
1
0
0
0
2
1
1
1
1
0
1
0
1
0
1
2
1
1
0
2
0
1
1
2
2
0
0
1
0
1
1
3
1
0
1
1
0
2
2
1
0
1
0
2
2
0
1
1
0
1
2
1
1
0
1
2
0
1
2
0
0
2
0
0
1
0
1
1
1
0
1
0
0
1
1
2
1
1
1
2
0
2
1
1
1
0
0
2
1
1
1
1
1
1
1
2
1
0
0
1
2
0
1
1
1
1
2
1
1
2
2
1
2
1
0
2
0
1
1
2
0
1
0
1
0
2
0
0
0
1
0
0
1
0
1
0
1
0
1
2
0
2
0
1
0
1
0
1
2
0
1
0
0
2
1
1
0
1
1
0
0
0
2
2
2
0
1
1
2
1
1
0
1
0
1
2
0
1
0
1
2
1
1
0
1
0
1
0
1
0
2
2
1
1
2
0
1
2
2
3
1
0
0
1
2
2
2
0
2
0
4
2
0
0
1
1
0
0
1
0
1
1
1
1
0
2
1
1
0
2
1
1
1
1
1
1
0
2
1
1
1
0
2
0
1
1
0
0
2
1
1
1
0
1
1
1
0
2
2
0
1
2
1
1
1
0
0
1
0
1
1
0
2
1
0
0
0
0
2
1
0
0
0
0
1
1
1
0
1
1
1
2
1
1
1
1
1
2
0
1
1
1
1
1
2
0
0
0
2
0
2
2
1
2
1
1
0
2
1
0
2
0
1
0
3
1
0
0
1
0
1
0
1
0
1
1
1
0
0
1
1
0
1
0
0
1
0
1
2
1
1
1
2
0
1
0
1
2
0
0
1
1
0
2
1
1
2
0
0
1
0
1
1
1
2
0
0
1
1
0
0
1
1
0
1
1
0
1
1
2
1
0
1
0
1
1
0
1
0
2
2
2
2
0
1
0
1
2
1
1
0
2
0
0
1
1
1
1
0
0
1
2
1
0
0
1
0
2
0
3
2
1
4
1
1
1
0
0
2
2
1
1
1
3
2
2
1
1
2
1
1
2
2
1
0
0
0
0
1
0
1
2
0
2
1
1
0
2
0
1
1
0
0
0
1
2
1
0
1
1
2
2
0
1
0
1
0
1
1
2
1
1
2
0
2
1
0
1
2
0
2
1
2
0
0
2
1
1
2
0
0
1
0
0
0
0
1
2
0
2
0
1
2
1
1
1
1
0
1
1
0
0
0
0
1
0
1
0
0
1
0
1
0
1
1
1
0
1
0
1
1
0
1
0
0
0
1
0
0
1
1
1
2
1
1
0
0
1
3
0
1
0
2
2
2
2
0
1
1
0
1
1
1
0
1
2
1
1
1
0
1
1
1
0
1
1
1
0
0
2
1
2
0
2
1
1
0
0
2
2
0
0
1
1
1
1
1
2
2
2
2
2
0
1
1
2
1
1
0
1
1
1
1
1
2
1
1
0
1
0
0
2
1
2
0
1
1
1
0
0
1
0
0
0
0
0
1
1
0
1
1
1
0
0
0
2
0
1
0
2
0
1
0
2
0
1
2
0
1
1
1
1
2
1
2
2
1
0
1
2
2
1
1
2
2
0
1
1
1
0
0
0
0
0
1
0
0
1
0
0
1
2
2
2
0
1
1
0
1
2
0
0
1
0
1
1
0
0
2
1
0
2
1
1
1
2
1
0
1
1
1
1
1
1
1
1
2
1
0
0
1
0
1
1
0
1
0
1
1
0
1
0
0
0
1
0
0
1
1
1
1
1
0
1
1
1
0
1
1
1
1
1
2
1
1
1
1
2
0
2
1
1
1
0
1
1
2
0
1
1
0
2
2
0
0
0
1
0
1
0
0
1
0
2
3
1
1
1
2
1
0
0
0
2
0
2
2
1
0
1
0
0
3
1
1
0
0
0
1
0
0
1
1
0
1
0
1
1
0
0
2
2
1
0
2
1
1
2
0
0
1
0
1
1
1
0
1
0
2
0
1
1
0
2
1
0
2
2
1
3
2
0
0
0
1
0
1
1
1
1
0
1
1
0
3
1
0
0
2
1
1
0
2
0
0
1
1
2
0
1
0
1
1
1
1
1
1
2
1
0
0
2
0
1
1
2
0
1
1
0
2
0
1
1
2
2
0
2
1
1
0
1
1
1
2
0
0
1
0
1
0
2
0
1
0
1
0
0
0
1
0
2
0
0
2
1
1
0
1
1
1
0
1
1
1
1
1
1
1
1
2
1
1
1
2
0
0
2
0
0
1
1
0
0
2
0
0
1
0
1
1
0
0
0
1
3
0
0
0
2
0
1
1
1
1
0
0
2
0
1
2
1
0
1
1
0
0
0
0
0
1
1
1
1
2
1
0
0
1
0
1
1
1
0
0
1
2
0
1
0
0
1
2
1
1
1
2
0
1
0
1
0
0
2
1
2
1
1
0
2
1
0
0
0
1
2
0
1
0
1
2
0
0
0
1
1
0
0
0
1
0
0
1
2
0
0
1
0
0
0
1
2
1
0
0
1
1
1
1
0
1
2
0
0
1
1
1
2
1
0
2
1
1
2
0
0
1
1
0
2
1
0
2
1
1
2
0
0
1
2
1
3
0
1
1
1
2
1
1
0
1
1
1
2
2
2
1
0
2
0
0
0
2
0
1
1
0
0
1
0
0
0
0
1
0
1
1
1
1
0
2
0
1
1
2
1
1
1
0
0
1
0
1
2
1
1
1
0
0
1
2
0
1
1
0
0
0
1
0
2
0
1
1
3
1
0
1
2
1
1
2
0
1
0
2
2
0
0
0
1
0
0
1
4
1
0
2
1
0
1
3
0
2
0
1
2
0
0
1
2
2
1
2
0
0
0
0
0
1
1
0
1
1
1
1
1
1
2
1
1
0
0
0
1
1
0
0
1
2
1
0
0
0
1
1
1
0
0
0
0
0
2
0
2
0
0
1
0
1
1
2
0
1
1
0
1
1
1
1
1
0
1
1
1
0
0
0
1
0
1
2
0
2
1
2
1
1
1
2
1
1
1
1
1
2
0
0
1
1
1
2
2
1
0
0
0
1
1
1
1
0
1
1
2
1
0
0
1
1
1
0
1
2
1
1
1
2
0
1
1
0
0
1
1
0
1
2
1
1
1
0
1
1
3
0
3
0
0
0
1
1
2
1
2
1
2
1
0
1
2
1
0
1
1
1
2
2
0
0
2
0
0
1
1
0
1
1
1
0
0
0
1
1
2
1
0
1
0
0
0
1
2
1
1
2
0
1
2
2
0
1
2
1
1
1
1
1
1
1
1
0
1
1
1
1
0
1
2
0
1
0
1
0
2
2
0
1
0
1
2
3
2
1
0
0
3
1
1
1
3
0
1
0
1
1
1
0
0
2
0
1
0
3
1
0
1
1
1
3
0
2
1
0
2
2
2
2
0
2
1
2
1
2
0
2
1
0
2
0
2
0
1
1
1
2
1
0
0
2
1
1
1
1
2
0
1
1
1
2
1
0
1
1
1
2
0
1
1
4
1
2
1
1
1
0
0
0
1
1
1
2
0
0
2
2
1
0
2
1
0
1
1
0
1
0
2
2
2
1
2
1
1
1
1
1
1
1
1
1
1
2
0
1
2
1
1
2
2
2
0
0
0
1
1
0
1
2
1
2
2
1
1
1
0
0
0
1
1
1
0
2
2
0
0
2
0
0
1
1
3
1
1
0
0
1
0
1
0
1
1
0
0
2
1
1
0
0
0
1
0
0
2
1
1
1
2
1
2
2
1
1
1
1
2
1
0
0
0
1
2
2
1
0
1
1
1
1
0
3
1
0
1
0
0
1
1
2
1
1
0
1
2
2
1
2
1
2
2
1
1
1
0
2
1
0
3
2
1
0
0
2
1
0
0
1
1
1
2
0
0
0
2
2
2
0
1
0
0
0
1
1
1
1
0
0
1
1
0
1
1
0
0
1
0
1
1
1
0
0
0
2
0
2
1
0
0
2
1
1
0
1
0
1
1
2
0
1
1
1
2
1
0
2
1
2
1
1
0
0
1
0
1
0
1
0
0
2
1
1
2
1
1
1
1
1
0
0
1
0
2
0
0
2
1
1
1
0
2
1
1
2
1
0
1
2
1
1
1
0
0
1
2
1
1
2
2
1
1
1
2
0
2
0
1
0
0
1
0
1
1
1
0
0
2
1
2
0
1
2
2
1
0
0
2
1
0
1
1
1
0
0
2
1
1
0
1
0
0
1
2
0
2
2
2
1
2
1
0
0
1
2
1
0
2
2
0
1
0
2
0
2
1
2
1
1
1
2
0
2
1
0
2
1
1
2
2
1
0
0
0
1
0
2
2
2
1
2
1
1
2
0
1
0
2
0
0
2
1
0
1
1
4
2
1
1
1
0
0
1
2
2
1
0
1
0
0
1
2
0
1
1
1
1
2
1
1
2
3
1
1
1
1
0
3
1
0
2
2
0
0
1
0
1
0
1
1
1
2
0
1
1
1
1
0
1
1
2
2
1
0
0
0
0
0
1
0
1
1
0
1
1
0
1
1
2
1
0
0
0
2
1
0
2
1
2
1
3
1
0
2
0
1
1
1
1
1
2
2
1
0
2
1
1
0
1
0
0
0
2
1
2
1
2
1
1
0
1
4
1
0
1
0
0
0
1
0
1
0
2
1
1
1
2
0
0
6
2
2
1
0
1
1
1
2
1
2
2
0
0
2
1
1
0
2
0
0
0
2
0
0
0
0
0
1
3
1
0
0
1
0
0
1
2
1
1
2
1
0
1
0
2
2
0
1
0
0
1
1
1
2
1
2
1
0
0
1
1
1
1
0
1
1
1
2
1
1
1
1
1
4
1
0
1
0
0
0
2
3
2
1
0
1
2
1
1
1
0
0
1
1
2
1
1
2
0
1
2
0
1
2
1
1
2
1
1
1
0
1
1
1
1
1
2
0
1
1
1
0
1
0
1
0
0
0
0
2
1
1
1
0
1
1
2
2
1
1
1
0
0
1
2
2
1
1
0
3
0
0
1
2
2
0
0
1
0
1
2
1
1
2
1
0
1
1
0
3
1
2
1
0
1
1
1
2
2
1
0
1
1
2
1
1
2
1
1
2
2
1
0
1
2
1
1
1
1
0
1
1
0
1
1
1
0
1
1
1
1
0
1
0
1
0
0
0
1
1
2
1
2
1
1
0
0
1
1
1
0
1
2
1
0
2
0
1
0
1
1
0
1
1
1
1
2
2
1
0
0
1
2
0
0
1
1
1
0
2
2
1
2
0
2
1
2
0
1
0
2
1
2
0
0
1
1
1
1
1
0
1
0
0
0
0
2
1
0
2
1
1
1
1
2
0
2
1
0
0
0
0
0
1
1
1
0
1
1
1
1
2
0
0
0
0
1
2
0
1
1
1
0
1
0
1
1
1
1
0
0
0
0
2
1
1
2
0
0
2
1
0
2
1
1
1
2
2
4
1
1
0
1
0
1
0
3
0
1
1
2
2
0
1
2
1
1
0
0
2
0
0
2
1
0
1
1
0
1
1
2
1
1
1
0
0
1
2
1
0
1
0
1
1
1
2
1
2
2
2
1
1
0
1
1
1
1
1
0
0
0
0
1
1
0
0
2
1
2
1
1
1
1
1
1
1
0
2
1
1
0
1
0
0
2
0
0
1
0
0
1
0
0
0
0
1
0
1
0
1
1
1
2
1
1
1
2
0
0
1
2
1
2
1
0
0
1
0
1
1
5
1
0
1
0
2
0
2
0
2
2
3
0
2
1
0
2
2
0
0
1
0
0
1
1
1
0
0
1
1
0
3
1
0
1
1
2
2
2
0
1
2
1
1
2
0
1
1
2
1
2
1
2
0
0
2
1
0
2
1
2
2
0
1
2
2
1
0
0
0
0
0
1
2
1
1
2
0
0
1
1
0
1
0
1
1
1
1
1
1
2
0
1
1
1
0
2
2
1
2
2
0
0
1
1
0
2
2
1
2
1
1
0
0
2
1
1
2
0
0
1
1
1
2
1
0
1
0
1
0
2
1
2
2
1
2
1
0
1
2
0
1
1
2
1
2
0
1
1
1
2
2
0
1
2
2
2
0
2
0
0
0
0
2
2
1
1
2
0
1
1
1
1
1
0
1
1
0
1
2
0
0
1
1
0
0
1
2
2
1
0
0
2
2
0
2
1
0
1
0
1
0
1
1
1
1
1
1
1
1
0
1
1
1
0
1
1
2
0
2
0
0
2
2
1
2
0
0
0
1
0
1
1
2
2
1
0
1
0
1
1
1
1
0
2
1
0
0
1
2
0
0
1
1
0
2
2
1
1
2
0
1
2
0
1
1
1
0
2
1
1
1
1
2
1
1
1
1
0
1
1
1
0
2
1
0
1
0
1
2
2
1
0
0
1
2
0
2
1
0
0
1
0
1
0
1
1
0
0
0
1
2
1
0
1
2
2
1
1
0
0
2
0
2
1
0
0
0
0
1
0
0
1
1
0
0
1
2
0
0
2
1
2
2
0
0
2
2
0
1
2
1
2
2
0
1
2
0
1
1
1
1
1
1
1
2
2
1
1
1
0
1
0
2
2
1
1
0
1
0
1
1
1
1
1
0
1
0
1
1
2
0
2
1
1
0
1
1
0
0
1
0
1
1
1
1
1
0
0
1
1
0
1
1
2
1
1
1
1
2
0
1
1
1
1
1
0
0
1
0
1
1
1
2
0
2
1
0
2
1
2
1
2
0
0
1
1
0
1
1
0
0
1
1
0
3
1
1
0
2
1
2
2
0
1
0
0
1
0
0
1
0
0
0
0
0
2
0
1
1
2
0
1
2
2
2
0
0
1
1
1
1
0
0
1
1
1
3
0
3
1
2
2
0
2
0
2
1
1
0
1
0
0
0
0
2
0
2
0
2
2
2
0
0
0
1
0
1
2
2
1
1
1
0
1
0
2
2
0
1
1
0
2
0
2
2
0
0
0
0
0
2
0
0
0
2
0
2
2
1
0
1
0
4
1
2
2
2
2
0
1
1
1
2
1
1
1
1
1
0
1
0
1
0
0
0
0
2
1
0
0
1
2
1
1
1
0
1
1
2
0
2
1
0
1
1
0
1
3
0
2
2
1
1
0
0
0
1
1
0
1
0
1
1
1
0
0
0
1
1
0
1
1
1
1
1
1
2
0
1
0
1
0
0
2
0
2
2
1
1
0
2
1
0
0
1
1
1
1
1
1
1
1
0
2
1
2
2
2
0
1
1
1
2
1
1
2
0
2
1
0
3
0
0
2
0
0
1
0
2
1
0
1
3
1
0
0
1
1
1
0
1
1
0
1
1
0
1
1
0
1
1
0
0
0
2
0
1
1
1
1
0
2
1
1
0
1
1
0
2
0
1
2
2
1
1
0
2
1
1
1
1
1
1
0
1
0
1
2
2
1
2
1
0
1
0
2
2
1
0
1
0
1
0
0
1
0
2
1
2
2
1
1
0
1
1
1
0
2
1
1
0
1
1
1
0
1
1
2
1
0
2
1
0
1
1
0
5
0
1
0
1
1
0
0
0
2
1
0
0
2
1
1
1
0
1
1
0
1
3
1
0
1
1
0
0
0
2
2
0
1
2
1
2
0
1
1
1
2
2
2
2
2
0
1
2
1
0
0
0
1
0
0
0
1
0
0
1
0
1
2
1
1
2
1
0
0
0
1
0
2
2
1
0
0
1
2
2
1
2
0
2
1
1
1
1
0
1
1
1
2
2
2
1
1
0
1
1
0
2
1
0
0
1
1
2
2
3
1
1
1
0
2
2
2
1
1
0
0
1
0
1
0
0
3
1
1
0
1
1
1
2
1
2
1
1
2
2
1
2
1
0
0
1
1
2
2
0
1
0
1
0
0
1
1
0
1
0
2
0
1
1
0
1
1
2
1
1
0
1
0
0
1
0
2
0
1
1
1
0
0
1
2
2
2
2
1
1
0
0
1
1
0
0
0
1
2
3
2
2
1
1
1
1
1
0
2
1
0
0
0
2
0
3
2
0
1
2
1
1
0
3
0
2
2
0
0
1
1
0
3
2
1
1
0
1
1
2
0
1
0
0
0
0
1
0
0
0
1
1
1
2
0
1
0
1
0
2
2
2
0
1
1
1
2
1
0
0
0
2
2
2
2
1
2
2
1
1
0
2
0
0
0
2
1
0
1
0
1
0
1
2
1
1
2
2
2
2
1
1
0
0
2
1
1
0
1
0
0
1
2
1
1
1
1
2
3
2
1
1
0
1
1
0
0
1
1
1
1
1
0
1
0
0
1
1
1
1
1
0
1
3
0
1
0
2
1
1
0
1
0
1
2
1
0
2
0
2
0
0
2
1
0
2
2
2
0
1
0
2
1
2
0
0
1
1
2
0
1
1
1
0
1
0
0
2
2
2
2
1
0
1
0
1
1
1
2
0
1
0
1
1
2
1
1
0
3
1
1
1
1
1
1
1
2
2
0
2
2
0
2
0
0
0
2
2
0
1
0
1
1
1
2
1
1
1
0
2
1
3
1
1
2
2
0
0
2
2
1
0
1
0
1
0
1
1
1
1
0
1
1
3
0
0
1
2
2
0
1
1
1
0
1
2
1
1
2
0
1
1
1
0
3
1
1
1
2
0
2
1
1
1
1
1
2
1
0
1
2
1
0
2
1
1
1
0
2
0
1
1
2
0
0
2
0
0
1
2
1
1
2
2
2
1
0
1
1
1
1
0
1
1
0
1
0
2
0
1
0
1
1
1
1
0
1
0
1
1
1
1
0
1
0
1
1
2
2
0
0
1
1
2
2
1
0
0
1
0
1
1
2
1
1
2
0
1
0
1
0
1
1
0
0
0
1
0
2
0
2
0
1
2
1
2
1
1
0
2
0
0
1
0
0
0
0
2
1
1
0
1
1
1
0
1
1
0
1
0
1
1
1
0
0
1
0
1
1
1
0
1
1
1
0
1
2
1
1
1
0
2
2
2
0
0
1
1
1
0
2
1
1
0
1
1
0
1
1
2
0
2
1
1
1
1
2
1
1
0
0
0
1
1
1
1
2
0
1
1
1
1
1
2
1
0
0
0
0
1
1
1
0
2
1
1
0
1
0
1
0
0
2
0
0
2
1
2
1
0
0
1
0
2
1
1
0
1
2
1
1
1
0
0
0
1
0
2
0
1
2
1
1
1
2
0
0
1
2
1
1
1
1
1
2
2
0
1
1
0
1
1
0
2
1
1
2
2
0
1
1
0
0
2
1
2
1
1
0
0
0
1
1
1
1
1
0
0
2
1
1
0
0
0
1
0
1
0
0
1
2
1
1
0
1
1
2
0
1
2
0
1
0
0
0
2
0
2
0
0
1
1
1
0
0
1
0
0
1
1
1
0
0
0
0
0
0
1
0
2
0
1
0
0
1
0
1
0
0
1
1
0
1
1
0
2
1
0
0
1
2
1
1
1
1
1
1
0
0
0
0
1
1
2
2
3
1
0
0
1
1
1
0
2
1
0
0
2
1
1
0
0
1
0
1
0
1
1
0
0
2
0
1
2
0
2
1
2
1
1
1
1
1
1
0
2
1
0
0
1
2
1
1
4
1
1
1
1
1
1
1
0
1
1
0
1
0
0
1
0
1
1
0
0
0
1
1
1
0
1
2
0
1
1
2
4
1
1
1
0
2
1
0
1
1
1
2
1
0
1
0
2
0
2
0
1
1
2
1
1
2
0
1
2
0
2
4
0
2
1
1
1
1
0
1
0
1
1
0
0
1
1
0
1
1
0
1
1
2
0
2
1
0
0
6
1
0
1
2
1
2
1
1
2
1
0
0
1
1
0
1
1
0
1
1
1
0
1
1
1
2
1
2
1
0
0
0
1
0
2
0
1
1
0
1
1
2
0
0
1
1
1
1
0
1
1
1
1
1
0
1
1
1
0
2
1
2
1
0
0
1
2
0
0
1
3
1
1
1
1
2
2
1
2
1
0
1
2
0
1
0
2
1
1
1
2
0
2
2
1
4
1
0
1
1
1
2
1
0
0
1
0
2
1
2
2
2
2
3
1
2
1
1
1
0
1
0
1
0
1
0
0
1
1
2
2
1
1
0
1
0
1
1
1
4
1
1
1
1
1
2
2
0
0
2
1
1
0
1
0
1
0
0
0
2
1
2
0
0
0
0
2
0
0
0
1
1
1
0
0
0
0
2
1
1
2
0
1
0
0
2
0
0
1
0
0
1
0
1
2
0
0
1
1
1
0
2
1
1
1
2
1
1
1
1
1
1
0
2
2
0
2
1
2
1
2
1
2
2
0
1
1
1
1
1
0
2
0
0
0
0
0
1
0
2
1
0
1
1
0
1
0
1
1
1
2
1
1
2
1
0
1
1
0
1
0
1
0
1
1
0
2
1
0
1
1
2
0
1
0
1
2
0
0
2
2
1
0
1
1
0
1
2
0
0
0
0
1
0
0
2
1
0
0
2
1
0
0
2
0
1
1
1
0
2
1
2
1
1
1
1
0
0
2
0
0
1
2
1
1
1
1
2
0
0
0
2
1
1
0
0
1
1
1
2
2
0
2
0
1
2
1
2
2
0
0
0
1
0
1
0
4
2
1
1
2
0
1
2
1
0
0
1
0
1
1
1
1
0
1
3
0
1
0
2
1
0
0
2
0
1
1
1
0
0
0
2
0
0
2
0
1
0
2
1
1
1
1
0
1
1
0
2
0
1
2
2
1
0
0
0
0
0
1
2
0
0
2
0
2
1
0
1
1
1
2
1
2
1
0
0
0
1
1
1
1
1
0
1
0
1
0
0
2
0
1
1
1
1
1
1
1
2
0
1
1
1
1
1
2
1
2
0
2
0
2
1
0
1
2
1
0
0
0
2
1
1
1
2
1
0
0
0
0
0
1
1
0
1
0
1
2
1
2
0
2
1
0
0
3
2
0
2
0
0
1
2
3
1
1
1
1
1
1
1
1
0
0
2
1
1
1
1
0
1
1
0
0
1
0
2
3
2
1
2
2
1
1
2
2
1
2
2
1
1
0
0
0
0
1
0
1
0
1
0
1
1
1
2
2
1
0
1
2
0
1
0
1
1
1
1
2
1
0
0
1
1
1
1
1
1
2
1
1
1
1
2
1
1
1
0
1
1
0
0
0
1
1
0
0
0
1
0
0
0
2
1
1
1
2
1
1
0
1
2
0
0
2
1
1
1
0
2
1
2
1
2
1
2
0
0
2
0
1
1
1
1
2
2
1
0
0
0
0
0
1
1
2
2
1
3
0
1
1
1
1
1
0
2
1
1
1
2
1
0
1
1
1
0
0
0
3
0
1
2
2
2
1
2
2
0
1
1
0
1
1
1
0
0
2
1
0
1
0
1
1
1
0
2
1
1
0
1
1
0
2
2
1
1
2
1
2
0
2
1
0
2
1
0
0
2
0
0
1
0
1
0
2
2
2
1
0
1
1
2
0
1
0
2
1
1
1
1
0
0
1
2
1
1
1
1
0
0
0
0
2
2
1
1
2
0
2
0
1
1
2
2
0
1
0
1
1
1
1
1
1
1
0
0
1
1
0
0
2
1
2
1
0
2
1
1
2
2
1
0
0
1
0
1
0
0
3
1
0
1
1
2
0
0
0
0
0
1
0
3
2
2
2
1
0
0
1
2
0
0
1
1
2
0
2
1
0
3
1
1
0
0
2
0
0
0
0
2
1
0
1
1
0
2
0
1
1
0
1
0
0
0
2
1
2
1
2
2
2
0
2
2
1
0
1
1
1
1
0
1
1
1
1
0
0
1
0
1
1
1
0
1
1
0
1
1
0
2
0
2
0
0
1
1
1
1
1
0
1
2
2
1
1
1
1
2
1
1
1
0
0
2
2
0
1
0
1
0
2
0
2
1
0
0
0
3
1
1
2
0
1
0
1
0
2
1
2
0
0
1
1
0
0
2
1
2
1
2
2
0
1
1
0
2
0
1
1
1
1
0
1
1
1
0
0
2
0
0
0
2
0
0
0
0
0
0
1
1
0
2
0
0
0
1
1
0
2
1
1
0
1
2
1
1
1
2
0
1
1
1
1
1
1
0
1
0
2
1
1
1
1
0
2
0
2
1
2
0
0
2
1
1
1
1
2
1
0
2
1
0
1
0
2
1
1
1
0
2
1
2
1
1
0
1
1
2
1
0
1
0
1
2
0
0
0
0
0
1
1
2
2
2
0
0
1
2
2
0
2
2
0
0
1
2
1
1
1
2
1
1
1
1
0
1
1
1
0
1
1
0
0
2
2
2
1
2
1
0
2
1
1
0
1
1
0
0
0
1
1
0
2
0
1
1
0
0
1
1
0
0
0
2
1
2
0
1
1
1
1
0
0
0
1
1
2
0
2
1
0
0
0
1
0
0
1
0
1
0
0
2
0
2
0
2
0
0
1
1
1
1
1
0
2
1
0
1
2
2
0
1
0
0
1
1
2
2
0
0
0
0
2
4
0
1
1
2
1
0
1
2
0
0
1
1
2
1
2
1
1
1
1
1
0
2
0
1
1
1
0
1
0
1
1
1
0
1
0
1
1
2
0
1
2
1
0
1
1
0
2
1
1
0
0
2
0
0
2
0
2
0
0
1
0
2
1
0
1
1
2
1
0
1
2
1
1
2
1
1
1
1
1
1
0
0
0
1
1
1
1
0
0
0
0
0
1
1
1
1
1
1
1
2
2
0
2
1
1
0
1
1
1
1
1
1
1
0
0
1
1
2
1
1
1
1
2
2
0
0
1
0
0
1
0
1
0
2
1
1
1
0
2
0
0
0
0
1
3
2
1
2
1
0
1
0
2
1
1
0
1
0
1
1
1
0
0
0
0
2
1
0
1
1
0
2
0
1
1
2
0
0
0
1
0
2
0
1
0
1
2
0
1
1
1
0
0
1
1
2
0
1
1
2
0
1
1
1
2
1
1
2
2
1
1
4
1
1
1
2
1
1
2
1
1
1
1
2
1
1
1
0
0
2
2
1
1
2
3
1
1
0
2
1
1
0
2
1
0
1
1
1
1
1
0
1
1
0
2
1
0
1
0
1
0
2
1
1
2
0
1
1
0
0
1
0
0
1
1
0
2
1
0
1
1
0
0
2
1
0
1
0
1
0
0
0
0
0
0
1
1
1
2
0
1
1
1
0
1
1
1
1
2
0
2
1
0
0
1
2
0
1
1
1
0
1
1
0
3
1
1
2
0
1
2
0
1
3
1
2
1
0
1
1
0
0
0
2
0
1
0
0
0
0
0
0
1
1
1
0
0
2
2
2
1
0
1
2
0
0
1
1
1
1
0
0
0
0
0
1
1
1
1
2
0
0
1
0
1
0
2
1
1
2
0
2
2
1
0
1
3
1
2
1
2
2
2
2
1
1
1
6
0
0
0
0
2
2
1
1
1
1
1
0
1
3
1
0
0
2
1
0
1
0
0
0
1
0
2
1
2
1
2
0
1
1
0
0
2
1
1
0
2
1
0
0
0
0
1
2
2
3
2
0
1
1
1
0
0
1
1
1
0
1
1
2
2
1
1
4
3
2
0
0
1
1
1
3
0
1
0
1
1
0
1
0
2
1
1
0
1
0
0
1
2
2
0
0
0
2
1
0
2
1
1
4
1
1
2
2
1
1
1
0
0
0
2
0
0
1
2
0
1
1
0
0
0
1
1
1
1
1
1
1
1
0
1
0
2
1
2
1
1
1
1
0
1
0
1
0
0
1
1
2
0
1
1
0
0
2
1
1
1
1
2
1
0
3
0
1
2
0
0
2
0
3
1
1
0
0
0
0
1
2
1
1
0
2
0
1
1
0
0
2
2
2
1
2
0
0
1
0
1
0
1
1
0
1
1
0
0
2
0
1
1
0
2
1
1
0
0
0
1
0
0
0
2
0
1
0
1
0
1
8
1
2
1
1
2
0
1
0
1
2
2
0
0
1
1
2
1
2
0
0
1
1
2
0
4
1
0
1
1
1
1
0
0
0
2
0
0
3
0
1
1
0
0
0
1
0
1
2
1
1
0
1
1
0
2
0
0
1
1
0
2
2
0
1
2
1
1
1
0
2
1
1
1
0
1
1
0
1
1
1
0
4
0
3
1
1
1
0
1
1
0
0
0
0
1
0
1
1
1
1
1
1
0
2
1
2
0
0
0
0
1
0
0
1
1
0
1
0
1
0
1
1
2
1
1
1
1
1
1
2
0
2
1
1
2
1
1
1
1
1
1
0
1
0
2
3
2
1
0
1
0
1
0
0
1
1
0
1
1
2
2
2
1
0
0
0
2
0
2
1
0
1
1
1
0
0
1
0
1
1
3
1
1
2
2
2
1
1
1
0
0
0
2
0
2
1
1
1
1
1
1
0
1
0
1
1
1
1
2
2
1
1
0
3
0
1
2
1
2
1
1
1
2
1
1
0
0
0
2
0
0
0
1
1
1
1
1
1
0
2
1
2
4
2
0
1
1
2
1
0
1
1
1
1
0
2
1
1
2
0
1
1
3
1
1
1
1
1
2
1
2
2
1
2
2
0
1
1
2
1
1
0
1
1
0
0
1
1
1
0
2
0
0
1
1
0
1
2
0
0
1
0
2
1
0
0
0
1
1
1
2
3
1
0
1
0
1
1
1
1
2
1
0
2
2
0
0
1
1
0
1
1
1
0
2
1
0
1
0
0
1
0
1
2
0
1
0
2
1
1
2
1
1
2
1
0
1
1
0
2
0
1
2
0
2
0
2
0
1
1
2
1
0
0
2
1
0
1
0
0
2
2
0
0
3
3
0
0
1
1
1
1
1
0
1
1
1
0
1
1
1
0
0
2
2
1
1
0
0
0
1
1
2
1
2
0
1
2
0
2
2
0
0
1
2
2
1
0
0
2
0
2
2
1
0
0
1
2
2
1
1
1
1
1
2
1
2
1
0
0
0
1
0
0
0
1
0
0
2
1
2
1
1
2
1
1
0
2
1
1
2
0
0
1
1
1
1
0
0
0
1
1
2
0
0
1
0
1
1
1
2
1
0
0
1
0
0
1
1
0
2
1
2
2
2
0
0
0
1
2
0
1
0
0
1
1
2
1
0
0
1
0
0
1
1
1
0
1
0
1
4
1
0
0
1
0
1
2
1
1
1
0
0
0
1
1
0
1
0
1
1
1
1
2
1
1
0
0
0
0
0
0
0
0
0
0
1
1
2
1
1
0
2
1
1
0
1
0
1
0
1
0
2
1
0
1
1
0
1
1
4
1
0
2
1
2
0
1
1
0
0
0
1
1
1
0
2
0
2
1
1
0
1
1
1
2
0
1
1
1
0
1
2
1
2
2
2
0
1
1
1
0
0
2
0
1
3
0
1
1
2
1
1
1
0
2
0
0
1
4
1
1
1
3
1
1
1
0
1
1
1
0
1
2
0
1
1
1
0
1
2
1
1
1
0
0
3
2
1
2
1
0
2
1
2
1
0
1
0
1
0
1
1
2
2
0
0
3
2
2
1
2
0
0
0
2
1
0
2
1
0
2
0
1
1
2
2
1
2
1
0
1
0
0
1
0
0
0
1
0
1
1
1
0
1
1
1
0
2
0
1
0
2
1
2
0
2
2
2
0
1
1
2
1
0
1
1
2
2
1
1
1
1
1
1
0
0
1
2
1
1
1
1
2
1
1
1
1
0
1
2
3
0
0
0
2
0
1
0
0
2
1
2
1
1
2
1
0
0
0
0
3
1
1
2
0
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
0
0
2
1
0
0
2
5
1
0
2
2
1
1
1
0
0
1
1
1
1
2
0
1
0
1
2
1
2
1
0
1
1
2
1
1
2
0
2
1
0
0
1
0
0
2
0
2
0
2
1
1
1
1
0
1
1
2
2
1
0
1
1
2
1
1
0
1
1
1
1
2
3
0
1
1
1
1
1
0
0
1
2
1
1
0
2
2
0
0
0
2
1
0
1
2
1
2
1
1
1
2
1
1
0
1
2
0
2
2
1
0
1
1
0
0
2
1
1
1
1
1
1
1
0
0
2
0
1
1
0
1
1
1
1
2
2
1
0
2
2
2
1
0
2
2
0
2
0
2
1
1
0
1
0
2
0
0
2
1
1
1
1
1
1
1
0
1
0
1
2
2
0
0
0
2
2
1
2
1
1
0
0
1
1
1
0
2
1
2
1
1
1
2
0
1
1
2
1
1
2
0
2
1
2
0
0
1
1
2
2
1
1
0
1
0
2
0
0
2
2
2
2
2
0
1
1
2
0
0
1
1
0
1
0
0
1
2
1
0
1
1
1
0
0
1
2
1
2
2
2
2
2
2
1
1
1
1
2
0
0
1
1
1
0
1
0
1
1
1
1
1
1
0
1
1
0
0
2
0
1
0
0
1
0
2
1
2
1
1
0
0
3
1
2
1
0
1
2
0
0
1
2
1
0
1
2
1
1
2
0
1
1
0
1
0
1
0
2
1
1
2
2
0
1
1
3
0
2
1
1
1
0
1
0
2
1
0
2
0
2
2
1
0
0
0
1
0
1
1
1
1
0
2
0
0
1
0
1
0
1
1
1
0
1
0
0
2
2
1
1
1
0
1
1
0
2
1
1
3
1
1
2
2
1
1
1
1
1
2
0
1
1
0
2
0
1
2
2
1
1
1
0
2
2
1
1
0
0
2
0
0
0
1
1
0
1
1
2
2
2
0
1
1
0
0
1
1
2
0
0
1
2
1
0
1
1
1
0
0
2
0
2
2
1
1
2
2
1
0
1
0
1
1
0
4
1
1
1
1
1
2
0
1
1
0
0
2
1
0
1
1
1
2
1
3
1
1
1
1
1
1
2
1
2
0
2
0
0
1
2
0
2
1
2
1
1
0
0
1
1
0
2
0
0
1
1
2
0
2
0
1
1
1
2
1
0
1
1
1
1
1
2
1
1
1
0
1
0
1
0
1
0
2
0
0
2
2
1
0
1
1
0
0
0
2
1
0
1
2
0
1
1
1
1
1
1
0
1
1
1
1
2
0
0
0
2
1
2
1
1
1
1
0
2
0
0
1
2
0
1
1
1
0
0
1
0
1
0
0
0
2
1
1
0
0
1
3
1
1
1
0
1
2
1
1
2
1
2
2
1
1
0
1
0
2
1
1
0
0
1
1
1
2
0
1
1
1
1
1
1
1
1
0
2
1
2
0
0
2
1
1
1
0
2
0
1
2
2
1
1
1
0
0
0
0
2
0
1
1
1
1
0
0
0
2
1
1
1
0
2
0
0
0
4
1
1
1
0
0
1
1
1
2
1
1
0
0
2
0
0
0
1
1
1
1
2
0
1
1
1
0
1
0
1
0
1
2
0
2
0
1
1
2
1
1
0
1
1
0
0
1
2
0
1
0
1
1
1
2
1
1
1
0
0
0
1
1
2
0
1
2
2
0
1
2
0
1
2
0
2
2
1
1
2
1
2
0
0
2
1
1
2
1
0
0
1
1
0
0
1
2
0
0
2
1
1
1
0
1
1
1
2
0
1
2
1
1
1
0
0
2
0
1
1
2
2
1
0
1
2
3
0
1
0
0
2
2
0
0
1
1
1
1
1
1
3
3
0
0
0
1
2
1
2
1
1
2
0
1
2
0
1
2
1
1
0
0
0
1
2
1
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
2
2
2
1
1
2
1
1
1
1
2
1
1
1
1
0
1
0
0
0
1
1
2
1
1
0
1
2
1
0
0
0
0
0
1
2
1
1
2
1
1
1
2
2
2
0
1
0
0
0
1
2
0
2
1
1
0
2
1
2
1
1
0
1
1
1
1
0
1
0
2
0
1
0
0
1
0
1
2
0
1
1
1
1
1
1
1
0
2
2
0
0
2
2
0
1
0
1
1
1
1
0
0
2
1
0
1
1
1
1
2
1
1
1
0
1
1
2
1
1
1
1
0
4
0
1
2
1
0
0
1
2
2
1
0
1
0
1
1
2
0
0
1
0
1
0
1
1
1
0
0
0
0
2
0
1
2
1
1
0
1
0
1
2
1
1
0
0
1
1
2
0
0
2
0
1
2
1
0
0
0
2
3
0
0
1
0
0
0
2
1
0
1
1
1
0
1
0
1
2
2
1
1
1
0
1
0
1
1
1
0
1
2
1
1
0
1
1
2
2
0
2
0
0
1
3
2
1
0
1
0
1
1
0
1
1
2
2
1
1
0
2
1
0
1
0
1
2
0
1
1
1
0
1
1
1
1
0
1
1
0
5
1
2
0
1
0
0
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
2
1
1
1
1
2
1
0
0
1
2
0
0
1
0
0
0
0
0
0
1
0
0
1
2
1
0
0
2
2
3
1
2
1
1
1
0
2
2
1
0
1
1
1
1
2
0
1
0
1
1
1
1
1
2
1
2
0
0
1
0
2
1
1
0
0
0
1
1
1
1
0
2
2
1
2
1
2
1
1
0
1
1
1
1
1
2
0
2
2
3
0
0
2
0
1
2
1
0
0
2
1
0
1
2
1
0
2
2
0
2
2
0
1
0
2
1
1
0
1
0
0
1
0
1
1
1
1
1
2
1
2
0
1
1
0
0
1
0
0
1
0
0
2
1
2
1
1
1
0
2
0
1
2
0
0
0
2
2
2
2
0
1
2
0
2
1
2
1
0
0
0
0
0
1
1
2
1
2
0
2
2
2
1
0
1
1
2
0
0
1
1
0
1
2
2
1
1
0
0
2
0
1
0
2
2
1
0
0
1
1
0
2
0
1
0
1
2
0
1
1
0
1
1
0
0
0
2
0
1
1
1
0
0
0
0
2
1
2
0
0
0
1
1
1
7
0
2
1
0
1
0
2
1
2
0
2
1
0
0
1
0
2
1
0
2
0
1
1
2
1
1
0
0
2
1
2
3
0
1
0
1
1
0
1
0
1
0
1
1
2
0
0
1
0
1
1
1
2
1
2
1
2
1
0
2
2
0
0
1
1
1
3
0
0
1
1
0
1
1
0
0
0
1
1
0
0
0
1
0
1
1
1
1
0
1
0
0
2
0
0
3
1
1
2
1
0
1
0
1
0
0
1
4
1
0
2
2
0
1
1
1
0
1
3
1
0
1
1
1
1
0
2
0
1
1
1
0
1
1
2
0
0
1
1
1
0
2
1
2
1
1
0
1
3
2
1
1
0
2
1
0
1
0
0
1
0
0
1
1
0
0
2
1
1
1
1
1
0
0
1
1
2
0
0
2
2
1
1
0
1
1
0
2
1
1
1
1
1
2
2
0
2
0
1
1
0
2
2
1
0
2
2
0
0
0
2
0
1
1
0
2
1
2
2
1
1
1
0
0
0
1
1
0
1
1
1
0
1
1
2
1
2
1
0
1
1
2
2
1
1
0
2
1
2
0
1
1
1
1
1
0
1
1
1
0
0
0
1
1
1
0
1
3
1
2
1
0
1
1
1
1
1
0
0
2
1
0
0
2
2
2
1
0
1
0
1
1
1
0
0
0
1
1
0
2
0
0
1
1
0
1
2
2
1
1
1
0
1
2
4
0
2
2
1
1
1
1
0
0
0
1
1
1
0
2
1
1
2
2
1
2
1
1
0
1
1
2
0
1
1
1
0
2
2
1
2
0
2
1
2
1
1
1
1
2
1
0
0
1
1
1
0
1
2
1
1
0
1
2
2
0
1
2
2
2
0
1
1
1
0
0
1
1
1
1
1
1
1
0
2
1
1
2
0
1
1
0
2
1
1
1
0
0
2
0
2
2
1
0
1
1
1
0
1
0
1
1
2
1
0
1
0
2
1
1
1
0
0
1
1
1
0
1
0
0
0
1
0
2
0
0
0
0
2
1
1
0
2
1
2
2
1
1
1
1
0
0
1
1
1
0
1
1
0
2
1
1
1
0
0
0
1
0
1
0
1
1
1
0
2
1
1
2
1
1
2
1
0
0
2
1
1
1
1
2
1
1
1
0
2
0
1
0
0
2
1
0
0
2
0
1
0
1
2
1
1
0
0
1
0
0
0
0
1
2
0
1
2
3
1
2
2
1
0
2
1
2
0
0
0
2
2
0
2
1
2
0
1
1
1
0
1
1
0
1
1
0
1
0
3
1
0
4
1
2
0
0
0
1
0
0
1
0
1
1
1
2
2
1
1
1
0
2
1
1
3
1
1
1
0
1
0
0
2
2
2
1
0
0
0
2
1
1
1
1
0
0
1
2
0
1
1
1
1
1
2
2
1
1
1
0
1
2
0
0
0
0
1
1
1
0
1
0
1
1
0
1
1
1
2
0
1
1
1
2
1
2
1
0
0
0
0
2
1
0
2
2
1
1
0
2
1
0
0
1
2
0
0
0
1
0
2
1
2
1
0
2
1
0
1
1
1
1
0
0
1
0
2
1
0
2
1
1
0
1
0
2
2
0
0
0
2
0
3
1
1
1
1
0
0
0
2
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
1
1
2
1
0
1
2
1
1
1
2
1
0
1
1
0
1
2
2
1
0
1
2
1
1
0
2
1
1
2
1
2
0
1
1
0
1
1
1
0
0
1
1
0
1
1
1
2
0
0
0
0
1
1
1
0
1
0
1
1
0
1
1
1
0
1
0
0
2
2
2
0
1
2
0
0
1
1
3
1
0
2
2
2
2
1
2
2
0
1
2
1
2
0
0
2
1
1
2
1
0
1
0
1
1
1
0
1
0
1
0
0
1
0
0
1
0
0
2
1
2
1
1
2
0
1
1
1
0
1
1
1
1
1
0
1
1
0
1
1
1
1
0
2
1
0
2
2
0
1
2
1
0
1
1
0
1
1
1
1
1
0
0
1
1
1
0
3
0
1
2
0
2
1
2
1
1
2
0
0
0
1
3
2
0
0
1
1
0
1
1
2
1
0
2
1
1
3
1
1
2
1
1
0
0
1
1
0
2
2
2
2
2
0
0
0
1
1
2
1
0
1
2
0
0
1
0
0
1
0
0
0
1
2
1
1
0
1
1
0
0
1
1
2
2
0
3
2
0
2
2
2
0
2
0
2
2
1
2
1
1
1
1
2
2
2
1
1
0
1
0
1
1
1
0
0
0
2
1
0
2
1
2
2
0
0
1
1
2
1
1
1
0
2
0
0
0
1
2
1
1
1
0
0
1
1
1
1
0
0
0
2
1
2
2
0
1
2
2
0
1
1
2
1
1
1
0
1
0
1
0
0
1
1
2
2
0
0
1
0
1
1
1
2
0
1
0
0
2
0
0
0
1
1
2
0
0
2
1
2
2
1
0
1
1
0
1
2
2
0
0
1
1
0
0
1
0
0
1
2
1
0
1
2
1
2
1
0
1
2
1
1
0
1
2
0
0
1
0
1
0
0
1
1
2
3
1
2
0
1
1
0
0
0
3
1
1
2
1
0
0
1
1
0
2
1
1
1
2
2
2
0
1
1
1
0
0
0
2
1
0
0
1
0
0
1
0
1
2
0
2
1
2
0
1
1
2
1
1
2
1
0
1
0
0
1
1
1
0
1
1
1
2
0
2
1
2
1
1
1
0
0
1
1
1
1
0
2
0
1
2
2
2
0
1
2
0
2
0
1
1
1
0
0
0
1
1
0
0
1
2
1
2
0
1
2
1
2
2
1
1
0
0
1
1
1
1
0
1
6
1
1
0
2
1
1
0
1
0
1
1
2
0
1
1
0
2
0
0
1
1
1
0
0
2
1
0
1
1
1
0
1
1
1
1
1
1
1
1
0
2
2
0
2
2
0
1
0
1
0
2
2
0
0
2
1
1
0
2
2
0
1
0
1
0
0
0
1
1
0
1
2
1
1
1
0
2
2
2
1
2
0
1
1
0
1
1
2
1
0
0
2
1
2
1
1
1
2
1
0
0
0
1
6
2
1
2
1
0
1
0
2
1
2
0
1
2
2
1
1
1
1
0
1
0
1
0
0
1
1
0
2
0
0
1
0
1
1
1
1
1
1
0
0
1
1
1
1
1
1
0
1
2
2
0
1
0
0
1
1
2
2
1
2
2
1
1
1
1
0
0
1
0
1
0
1
2
1
1
3
2
3
2
0
0
1
2
1
4
1
1
0
0
0
1
0
2
1
1
1
1
2
2
2
0
1
1
0
1
0
1
0
0
2
1
0
1
0
1
1
1
1
0
2
0
0
0
1
0
0
0
0
2
2
1
2
1
0
1
1
0
2
1
0
1
0
0
2
2
1
1
2
1
0
1
0
0
1
0
1
0
0
1
0
2
0
1
2
3
1
1
0
0
0
0
0
2
0
1
1
0
0
1
2
0
0
1
1
0
2
1
1
2
0
1
0
2
2
0
2
0
0
1
2
1
0
1
0
1
1
1
2
0
0
1
2
1
1
0
0
1
1
1
2
2
1
0
0
1
0
2
1
3
1
1
1
0
2
1
0
1
0
1
0
0
1
2
0
0
2
2
2
1
1
1
1
1
0
2
0
0
0
1
1
0
0
0
1
0
1
2
0
1
1
0
0
1
1
2
2
0
1
1
1
0
0
2
1
0
1
2
1
1
2
1
1
0
0
2
1
1
1
1
1
3
0
0
0
0
1
1
0
2
0
1
2
2
2
0
1
2
1
1
2
0
2
0
1
1
1
0
1
0
1
0
1
0
0
1
1
1
1
1
0
2
0
0
1
0
3
0
1
0
1
1
2
1
1
1
1
1
1
0
0
2
1
0
4
1
0
0
2
0
1
2
0
1
1
0
2
2
1
1
2
0
2
0
1
1
1
0
2
1
1
0
1
1
1
0
1
2
1
2
0
0
1
0
1
1
1
1
2
0
1
1
1
1
2
2
2
1
0
0
2
1
1
2
0
5
0
0
0
0
1
1
2
1
1
1
2
2
1
0
1
1
1
2
0
0
1
1
1
0
0
0
2
1
1
1
1
0
1
2
2
1
1
0
1
0
0
1
0
1
1
1
2
1
1
0
1
1
1
0
1
1
1
0
1
2
2
1
1
1
2
1
1
1
1
0
0
2
2
1
1
0
0
0
1
0
2
2
1
1
0
2
2
0
3
1
2
1
0
1
1
0
1
1
1
1
1
0
0
1
0
2
2
1
0
0
1
0
1
1
1
0
1
1
2
0
1
2
1
2
1
0
0
1
0
0
1
2
1
1
1
0
1
2
1
2
0
0
2
2
1
1
1
2
1
0
1
2
2
2
2
1
1
0
0
2
1
1
1
2
2
1
0
1
0
1
1
0
1
0
1
2
1
0
0
2
1
1
1
2
2
0
0
1
0
1
1
0
1
1
3
1
2
1
1
1
2
1
2
1
1
1
1
2
0
2
0
0
0
1
1
2
0
2
1
2
1
1
1
10
0
0
0
2
1
1
2
2
1
0
0
0
1
2
2
1
1
1
2
0
1
2
1
0
1
2
1
1
1
0
1
2
1
0
1
2
0
2
0
2
0
1
0
1
0
1
1
1
0
0
2
0
1
0
1
0
1
0
2
1
0
1
2
2
1
0
1
0
2
0
2
2
1
0
1
1
1
0
1
2
1
0
1
1
0
1
2
1
0
0
0
0
1
1
1
2
1
0
1
2
1
1
1
1
2
2
0
2
1
1
1
2
0
0
1
2
0
0
0
0
0
1
0
2
1
2
1
1
1
1
1
1
0
1
0
0
1
1
0
2
0
0
2
1
0
0
1
0
1
3
1
4
0
0
3
2
0
2
0
0
1
1
0
2
2
2
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
2
1
1
1
0
0
1
2
2
2
2
0
1
1
1
2
1
1
1
0
2
5
0
2
1
1
0
2
2
1
1
1
0
1
0
0
2
1
2
1
0
1
0
1
1
1
1
3
1
0
0
1
1
2
1
2
0
2
1
0
2
1
2
0
0
1
2
1
1
0
0
1
2
1
0
2
1
0
0
1
2
0
0
1
1
2
1
0
1
1
1
0
1
2
2
2
0
2
0
1
0
1
0
1
1
1
1
1
1
1
1
0
0
0
0
1
1
0
0
2
1
1
0
2
1
0
1
1
1
0
2
0
1
0
0
0
1
2
1
1
0
0
0
1
1
1
1
0
1
0
1
2
1
0
2
0
0
1
1
0
1
0
0
1
2
0
1
1
2
0
2
2
0
2
1
1
2
1
1
1
2
2
1
1
1
1
1
1
0
0
0
1
0
1
1
0
1
2
0
1
0
1
2
2
1
2
0
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
0
0
0
0
1
1
0
0
1
0
0
0
1
1
0
0
0
0
1
1
0
2
1
1
2
1
0
0
0
2
0
1
1
2
0
2
1
1
1
1
1
0
0
1
0
1
1
0
2
0
1
0
1
1
2
0
0
2
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
2
2
0
2
1
1
0
1
0
0
0
2
2
1
1
0
1
1
1
1
0
0
0
0
1
0
2
1
2
1
1
1
2
1
1
0
1
0
1
0
1
0
2
1
1
1
2
3
2
1
0
0
2
0
1
2
1
0
0
0
1
2
2
0
0
1
2
1
1
0
1
0
2
1
1
1
1
1
1
1
1
0
2
2
0
1
1
0
2
0
1
2
2
0
0
2
0
0
0
0
1
1
1
2
1
0
2
0
0
2
1
2
2
0
0
0
0
1
0
1
0
2
3
1
0
1
0
1
1
0
1
0
0
1
1
0
1
1
1
0
1
1
0
1
2
1
2
1
2
2
0
0
1
1
2
1
2
1
1
1
1
1
2
1
1
1
2
0
2
1
1
1
2
1
1
2
0
0
0
0
1
0
2
1
1
2
0
0
0
0
1
2
2
1
2
1
1
2
1
1
1
1
1
1
2
2
1
1
1
0
0
0
0
0
1
1
0
0
2
2
1
1
0
2
1
0
1
0
2
2
2
0
1
1
0
0
1
1
2
1
0
1
1
0
0
0
1
1
1
1
1
1
2
0
0
1
1
0
0
2
0
0
1
0
1
2
1
1
0
2
1
0
0
0
2
2
1
0
3
1
1
2
0
1
1
1
1
1
0
1
1
2
1
1
2
1
2
1
1
1
0
0
1
0
2
1
1
0
1
1
0
0
1
0
1
1
2
1
1
0
1
1
2
1
1
0
0
0
0
1
0
1
1
2
2
1
1
1
1
1
0
1
1
0
0
1
1
1
1
2
0
2
1
0
0
1
1
2
1
0
1
2
0
2
1
1
1
0
1
2
1
1
0
0
0
2
1
2
2
1
2
1
0
1
0
1
0
1
2
0
1
0
0
1
2
0
0
1
2
1
0
1
1
0
1
1
1
2
1
2
0
1
1
2
0
0
0
1
0
1
1
0
1
2
0
1
0
1
1
0
0
1
1
0
1
1
2
2
1
1
0
2
1
2
1
0
0
1
2
1
0
2
0
0
1
1
0
1
1
1
1
0
1
0
0
1
1
0
0
0
0
2
1
2
0
2
0
0
1
2
1
0
0
0
0
1
0
2
2
0
2
0
1
2
0
0
0
3
1
1
0
0
1
1
2
2
1
1
1
2
1
2
1
0
1
1
0
0
2
1
0
2
0
0
0
0
1
0
0
0
2
1
1
2
1
2
0
1
1
1
1
0
2
2
1
1
0
1
1
2
1
2
2
0
0
1
1
1
2
0
1
1
1
2
0
0
0
1
1
1
2
0
1
1
2
1
0
0
1
2
1
0
1
1
1
1
0
1
0
0
1
1
2
1
0
2
1
0
1
1
2
2
0
0
0
1
2
1
1
2
1
0
2
1
0
1
1
0
1
2
1
0
1
0
2
1
0
2
0
1
2
2
0
0
1
0
2
1
0
0
1
2
0
1
0
2
0
1
0
0
1
1
2
0
1
0
0
0
2
0
2
2
3
2
1
1
2
1
0
1
2
0
1
0
2
0
1
0
1
2
1
2
0
1
1
1
1
1
0
1
0
1
0
1
3
0
1
1
1
0
1
0
2
0
0
2
1
2
2
0
1
2
2
2
0
1
1
2
1
2
0
0
2
2
0
1
1
0
2
0
0
0
0
2
2
2
1
0
1
0
2
0
0
0
0
2
0
1
1
1
2
2
2
2
2
1
0
2
0
2
1
1
0
2
1
1
0
1
0
1
2
2
1
0
0
1
1
2
1
1
1
1
0
1
3
0
2
1
2
2
1
1
1
0
2
0
2
0
2
0
1
1
2
1
1
1
1
1
1
0
2
0
2
1
1
0
2
1
2
1
2
0
1
0
1
1
2
1
0
0
2
2
1
2
1
2
0
2
2
1
0
2
1
2
0
0
0
1
0
0
1
1
1
0
1
2
1
1
2
1
0
0
0
1
2
0
1
2
0
1
1
1
2
1
2
1
1
2
1
1
1
6
1
1
0
0
0
1
1
1
0
1
0
1
1
1
0
1
2
1
1
2
2
2
1
1
0
0
1
2
0
1
2
1
1
2
0
1
0
1
0
1
2
0
1
0
1
0
2
1
1
2
1
0
1
0
1
1
0
0
2
1
2
1
0
2
1
1
0
0
2
0
2
0
2
1
0
1
1
0
1
0
2
0
1
0
2
0
0
1
0
2
2
1
0
0
0
1
0
0
0
0
2
0
1
2
0
0
1
2
0
1
0
1
1
1
1
2
2
2
1
2
2
1
2
1
1
0
1
0
0
0
4
0
0
1
0
0
1
1
1
0
2
2
1
1
1
2
1
1
1
1
0
1
0
0
0
2
1
2
2
2
1
3
1
1
2
1
1
1
0
1
0
0
0
0
2
1
1
2
2
2
1
2
0
1
1
1
1
0
1
0
1
0
1
1
1
1
1
1
1
2
2
1
2
1
2
1
0
1
1
1
2
1
1
2
1
1
2
1
2
1
1
1
0
1
1
1
2
1
0
1
2
1
1
1
2
2
0
0
1
0
1
1
1
3
2
2
2
0
0
0
1
0
2
1
2
1
1
0
0
1
1
0
0
1
2
0
0
0
2
0
0
1
0
2
1
0
1
0
0
2
1
0
0
0
1
1
0
2
1
2
0
2
2
2
0
1
0
2
0
2
0
0
0
1
0
0
2
1
1
1
1
1
0
1
1
2
0
0
0
0
2
0
1
0
0
0
2
2
0
0
0
2
1
2
2
0
1
0
0
1
1
0
1
0
0
1
1
1
2
2
2
2
1
1
1
1
1
2
2
1
2
1
0
3
1
2
0
1
1
1
2
2
3
1
1
1
1
1
1
0
2
0
1
0
1
0
0
2
1
1
0
0
0
1
1
0
0
0
0
1
1
1
0
1
1
1
1
1
0
0
2
0
2
1
1
0
0
1
2
1
1
0
1
0
1
0
1
2
2
0
1
1
1
0
0
1
0
1
2
3
0
2
1
1
3
1
0
1
0
1
2
0
1
2
2
1
2
2
1
1
2
2
1
0
0
1
1
1
2
1
0
2
1
2
1
2
1
1
0
0
1
0
1
0
1
0
0
0
1
1
2
0
2
0
1
1
1
0
1
1
1
1
0
1
1
0
0
1
2
0
1
0
2
1
1
1
1
1
0
0
0
1
0
0
1
1
1
3
0
2
2
1
1
1
1
1
0
1
1
2
2
1
0
1
1
0
0
2
0
0
1
0
1
1
2
2
1
0
1
1
2
2
0
1
1
2
2
0
1
0
2
0
1
0
3
1
2
0
1
1
1
0
1
1
2
1
2
1
1
1
1
1
2
1
0
1
2
1
1
2
3
0
3
2
1
2
0
1
2
2
1
1
1
2
1
2
2
2
2
0
1
0
0
1
1
1
0
0
1
1
2
0
1
2
1
2
2
1
1
0
1
1
0
0
0
2
1
2
1
0
1
1
1
1
2
0
1
0
0
0
1
1
2
0
0
1
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
1
1
0
1
1
2
1
0
1
0
0
2
2
1
3
1
0
0
2
2
1
2
1
3
0
1
2
1
0
1
0
2
0
1
1
1
1
2
0
2
1
0
0
1
2
1
0
2
1
2
0
0
0
1
0
1
1
1
0
0
2
2
1
2
0
2
0
1
0
0
1
0
2
0
1
1
2
0
0
1
0
1
1
1
0
1
1
0
2
1
1
0
0
1
0
1
0
1
1
1
1
1
1
0
1
1
1
1
0
1
1
2
0
0
1
0
0
1
0
0
0
1
2
0
0
1
0
1
0
1
1
2
1
1
2
2
0
2
2
2
1
1
2
0
3
1
1
1
1
0
1
1
2
0
0
1
2
1
2
1
2
0
1
0
1
2
1
1
0
0
1
1
0
0
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
1
0
2
0
1
3
1
0
0
0
0
1
1
7
1
0
0
1
1
3
1
0
1
2
1
1
2
5
1
0
0
0
1
1
0
1
1
0
2
0
0
0
0
0
2
0
1
0
0
1
1
0
0
1
2
1
1
2
2
1
2
1
1
1
2
1
2
1
2
2
1
1
2
1
1
0
0
1
1
1
0
1
0
2
1
1
1
0
2
1
1
0
0
1
0
0
0
1
2
0
1
0
0
1
1
2
2
0
2
1
1
1
0
0
0
0
1
1
1
0
0
1
1
2
2
0
0
0
1
1
1
0
1
1
2
2
1
1
1
1
0
0
1
1
1
1
0
0
1
0
2
0
1
1
1
1
1
0
1
1
2
1
0
1
0
1
1
0
0
0
1
2
0
0
1
0
1
1
1
2
2
0
1
1
1
0
1
0
0
1
6
0
0
2
0
1
1
0
1
1
2
2
2
2
1
0
1
2
1
1
2
1
0
2
1
1
2
2
1
0
1
1
1
1
1
2
1
0
2
1
1
2
0
1
0
0
0
1
1
1
1
0
3
0
2
0
2
1
2
1
1
0
1
0
2
0
0
1
0
2
1
2
1
1
0
2
1
3
1
0
1
1
0
1
0
2
0
1
2
0
1
0
0
1
2
1
2
0
1
0
1
2
2
1
0
3
0
1
2
1
0
1
2
2
0
0
1
0
0
1
0
1
2
1
2
1
1
1
1
2
1
2
0
0
1
1
0
0
0
4
0
0
0
0
1
1
0
2
1
1
1
1
1
0
2
2
0
1
1
0
0
3
0
2
0
1
1
2
0
1
0
0
0
0
0
0
1
2
0
0
1
1
1
2
3
1
1
0
2
0
0
1
1
1
2
1
1
0
1
1
2
0
0
1
1
1
0
1
2
1
2
2
2
1
1
0
1
2
1
2
0
2
1
1
1
1
1
0
0
0
1
0
0
1
0
0
0
1
2
0
0
2
1
1
1
2
1
1
2
2
1
3
0
1
0
0
2
1
2
1
0
1
2
2
1
0
0
0
2
1
0
0
1
0
1
2
0
1
1
0
2
1
1
1
1
2
1
2
0
2
2
1
2
1
0
1
1
2
1
1
1
0
2
2
1
0
0
2
0
0
2
0
2
1
1
2
1
1
0
1
1
1
0
0
1
0
1
1
1
1
1
1
0
0
2
1
0
1
1
1
0
2
1
1
2
1
2
2
1
1
2
0
0
1
0
0
1
2
1
1
1
1
1
0
1
1
2
0
1
1
1
0
1
1
2
3
1
1
1
0
0
2
0
1
1
0
2
2
1
0
1
0
1
0
1
0
1
1
1
1
0
2
0
2
0
0
1
2
1
2
1
0
0
2
0
1
2
1
2
1
0
0
0
2
1
2
0
1
1
0
0
0
1
0
0
2
1
2
0
0
1
1
0
1
1
1
1
0
0
0
2
0
1
1
0
1
0
2
2
0
1
1
0
2
1
1
0
1
0
0
1
1
0
2
0
1
0
0
0
1
0
1
2
1
0
1
1
1
2
2
1
0
2
0
1
1
0
2
0
1
1
1
1
1
1
1
1
2
1
0
1
2
1
1
1
1
1
0
2
0
1
1
1
1
1
1
1
0
2
1
4
0
1
1
1
1
2
2
1
0
0
1
2
0
0
2
0
2
1
0
1
1
0
0
1
0
1
1
1
1
0
2
1
0
1
0
0
2
1
1
1
1
1
1
1
0
2
0
1
0
0
1
1
1
1
1
0
1
1
1
2
0
2
0
1
0
2
1
1
0
0
1
0
1
1
1
1
2
0
1
0
1
2
0
2
2
2
0
1
1
2
0
0
0
1
0
1
0
1
1
2
1
1
0
1
2
0
0
1
0
1
1
0
0
0
1
0
1
3
1
0
0
1
1
1
2
1
2
1
1
0
1
1
2
1
2
0
1
0
0
1
2
0
0
1
0
2
0
0
0
1
1
2
0
1
0
0
1
0
1
2
2
1
0
1
1
2
0
0
0
2
1
1
1
0
1
1
1
1
2
1
3
0
1
1
0
0
0
1
2
1
0
0
1
0
1
1
1
0
1
1
1
1
2
1
1
0
2
0
0
1
1
1
0
0
1
0
1
0
1
2
0
1
0
2
1
1
1
0
1
1
1
1
2
0
0
2
1
1
1
2
0
1
1
1
1
3
2
2
2
1
2
4
2
2
0
0
2
0
0
0
1
1
3
1
1
0
1
1
2
0
1
0
1
0
1
1
1
3
1
2
1
1
1
1
2
0
1
1
2
2
1
2
0
0
1
1
2
0
0
0
2
1
0
0
1
2
1
0
0
0
1
0
4
2
0
1
1
0
0
2
0
2
1
0
0
0
0
1
0
1
0
2
0
2
1
3
1
0
3
0
0
1
1
0
1
1
1
1
0
0
0
1
1
1
1
1
1
0
0
0
2
1
1
2
0
0
0
0
1
0
2
1
1
0
2
2
1
0
1
1
0
1
2
2
1
0
1
2
0
2
0
0
1
1
0
1
2
2
1
2
0
1
0
1
0
0
1
1
1
1
0
1
2
0
1
2
3
2
1
0
2
0
2
2
0
2
2
1
2
0
1
1
1
0
1
2
1
1
2
1
2
0
1
1
1
2
1
0
1
1
1
1
2
5
2
1
2
0
0
0
1
1
0
0
1
0
1
2
1
1
0
1
0
1
1
1
1
0
0
1
0
0
1
1
0
2
1
1
1
2
1
1
0
0
2
0
2
1
2
0
2
0
1
0
0
0
3
2
2
2
0
2
1
0
1
2
1
2
1
1
2
0
1
2
0
1
1
2
1
1
1
1
0
1
2
1
0
0
2
0
0
2
1
0
0
2
1
1
0
4
1
1
1
2
2
1
1
1
2
2
2
1
3
2
1
0
1
2
1
1
2
1
1
1
1
1
0
0
2
1
0
3
1
1
2
0
2
0
0
2
2
2
2
0
1
0
0
0
0
2
1
1
0
2
0
4
2
1
0
2
2
0
0
2
0
0
2
0
1
2
2
0
0
1
0
0
0
2
0
1
1
1
2
0
0
1
1
0
1
0
2
0
1
0
0
0
1
1
0
1
1
2
1
0
1
1
1
1
2
1
1
1
1
0
0
0
1
0
0
2
1
1
1
1
1
1
0
2
2
1
0
0
1
1
1
0
1
0
1
0
2
0
1
1
1
2
2
1
1
2
0
0
0
0
0
2
1
1
1
2
1
0
0
0
1
1
1
1
0
1
1
0
0
0
0
1
1
0
2
0
2
2
1
0
2
0
1
1
2
1
1
0
0
0
2
1
2
0
1
1
1
2
2
2
2
1
1
0
2
0
2
0
2
1
1
0
4
0
1
1
1
1
2
0
1
2
0
2
2
0
0
2
1
1
1
0
0
0
0
1
1
1
1
0
2
2
2
0
1
0
1
1
0
1
1
0
2
0
1
0
1
1
0
0
2
1
1
0
1
1
1
0
0
1
0
0
0
1
1
0
0
2
1
2
1
1
1
0
1
0
1
3
0
1
2
1
0
2
1
2
1
0
0
2
1
1
1
0
0
2
1
2
2
2
2
0
0
2
2
0
1
3
2
0
2
1
1
1
0
0
2
0
1
1
0
1
1
1
1
2
0
0
0
1
1
2
0
0
1
2
1
0
1
1
0
1
1
2
1
0
1
1
1
0
1
1
2
1
1
2
0
0
0
1
0
2
0
1
1
1
2
1
0
0
0
2
0
0
0
0
1
1
1
1
0
1
1
0
2
0
1
0
2
2
1
2
1
2
1
4
0
0
0
1
1
2
0
2
0
2
0
1
1
1
1
0
2
2
1
1
1
1
1
2
1
1
2
2
1
0
1
2
1
2
0
0
0
2
1
0
1
0
0
0
0
1
1
0
0
0
0
2
2
1
2
1
0
1
0
1
0
1
1
2
1
1
1
1
1
2
0
1
1
2
2
1
1
0
1
1
1
1
1
1
0
1
1
2
1
1
1
2
2
1
2
6
0
2
1
1
0
2
1
1
1
1
0
1
1
0
0
0
0
2
1
2
1
0
1
1
1
1
1
2
2
0
0
1
1
1
1
2
2
1
0
1
2
2
0
1
1
1
2
1
0
2
1
1
2
1
2
0
2
1
0
0
1
2
1
1
1
1
1
1
1
0
1
1
1
1
1
0
0
2
1
1
0
0
0
1
1
2
0
0
1
1
0
0
2
1
0
3
1
1
2
1
2
1
1
0
1
4
0
1
1
1
0
1
2
0
0
1
2
2
1
1
0
0
0
2
0
2
1
1
0
1
2
1
0
1
1
2
2
1
1
2
2
0
0
1
3
2
0
0
1
2
0
0
1
2
2
0
2
2
0
1
1
2
0
0
0
0
1
2
0
3
2
0
1
1
2
2
2
3
2
0
0
1
2
0
2
1
1
1
2
1
0
0
0
0
1
1
0
2
1
0
1
1
0
2
1
1
0
1
2
1
0
1
1
1
1
1
0
1
2
0
0
0
1
0
1
1
0
0
1
0
1
0
0
2
2
1
2
2
0
0
1
0
2
1
2
2
1
1
2
3
0
0
1
1
1
1
0
0
2
0
0
0
2
1
1
1
2
1
2
0
2
1
0
0
1
2
2
0
1
2
0
1
2
2
1
0
1
0
1
0
0
2
1
2
1
1
0
1
0
2
0
1
0
0
0
1
0
1
2
1
0
1
2
0
2
2
1
1
1
1
1
1
2
0
0
0
1
1
1
2
2
3
1
2
1
2
1
1
0
1
2
0
0
1
2
2
2
0
1
2
0
0
1
1
1
1
2
1
1
0
0
2
2
1
1
0
2
1
2
0
1
2
1
2
1
1
0
2
0
0
2
0
1
0
1
1
1
1
2
0
0
0
1
0
2
0
1
1
0
0
2
1
1
1
1
0
1
1
2
1
0
1
1
1
0
1
0
3
1
1
0
2
2
2
0
1
1
1
2
1
0
1
1
1
1
1
1
1
1
0
1
0
1
0
1
0
1
0
0
0
0
1
1
1
1
1
3
1
1
0
1
2
2
2
2
1
2
1
1
1
0
2
0
2
0
2
2
1
1
0
1
2
1
0
1
1
1
2
1
1
2
0
0
2
1
2
0
1
1
0
1
1
0
2
0
1
1
2
0
2
2
0
0
2
2
1
1
0
1
1
1
1
0
1
0
3
1
1
1
1
1
1
1
1
1
2
2
0
0
2
1
0
1
2
1
0
2
0
1
2
1
1
3
2
1
2
2
0
0
2
0
2
0
0
0
2
2
1
0
0
2
0
1
2
0
1
0
2
1
0
1
1
0
1
1
1
2
0
0
2
1
0
0
0
0
1
0
1
0
1
2
1
1
1
1
0
1
2
2
1
0
2
1
0
2
1
1
2
0
0
1
1
0
1
1
1
0
1
2
1
0
0
1
1
1
1
0
1
1
1
1
1
1
0
1
1
0
2
1
2
2
1
0
0
0
2
2
0
0
1
0
1
1
0
1
1
0
1
2
0
1
1
0
1
2
1
0
0
1
2
1
1
0
2
1
2
2
1
0
1
1
1
1
1
1
0
0
2
1
0
0
2
1
0
1
1
0
1
0
1
2
0
2
0
1
2
0
0
2
1
2
0
1
1
2
0
0
0
0
1
1
0
0
1
2
1
2
2
1
0
1
2
2
2
2
1
2
8
0
2
2
1
0
1
0
1
0
0
1
1
3
1
0
1
1
1
0
1
1
1
1
2
0
1
0
1
2
0
1
1
1
0
2
2
2
1
2
0
0
1
0
3
2
1
1
0
0
0
1
0
2
1
1
1
0
0
2
1
1
1
1
1
0
1
1
2
1
2
1
1
1
1
0
3
0
1
0
2
1
2
1
1
1
1
0
0
1
0
0
2
0
0
0
0
2
1
0
0
0
1
1
1
0
4
2
1
1
0
1
0
1
1
2
1
1
0
0
1
1
1
0
1
1
1
2
1
1
1
2
1
1
0
2
1
1
0
1
1
0
0
1
1
2
1
1
0
0
1
0
1
0
2
2
0
0
2
2
1
1
1
0
0
1
2
0
1
2
1
1
0
1
1
0
2
0
0
1
1
0
0
2
0
2
1
1
1
2
1
1
0
2
0
0
0
1
2
2
1
0
0
1
0
0
0
2
1
1
1
1
1
0
2
1
0
0
0
1
0
0
1
1
3
1
2
0
1
2
2
0
0
0
0
2
1
0
0
0
1
1
2
0
1
1
2
1
1
1
2
1
0
1
1
1
1
1
1
1
0
1
0
0
2
2
0
0
0
0
1
2
0
1
1
0
0
1
1
1
2
0
1
8
0
0
1
1
1
0
1
2
2
1
0
1
2
2
0
0
0
0
0
0
2
1
1
2
1
2
1
1
0
0
0
0
1
0
2
1
2
1
0
2
1
1
1
1
0
1
1
1
1
1
0
0
2
0
0
0
1
1
0
0
0
0
0
1
1
1
1
1
1
1
0
0
2
2
1
1
1
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
2
0
2
1
0
0
1
1
0
0
2
2
0
1
2
2
0
0
2
2
0
1
1
2
3
2
0
0
0
0
2
0
2
1
1
0
0
1
1
1
1
1
2
1
0
1
1
0
1
6
2
2
1
2
2
0
1
1
1
0
3
1
1
1
2
1
1
2
1
1
2
0
2
1
1
1
1
0
1
2
0
1
0
0
1
2
0
1
0
1
1
1
1
2
1
1
1
1
1
2
0
0
1
1
0
1
0
1
1
1
2
1
2
1
0
0
0
1
0
0
1
0
2
2
0
0
1
5
1
1
1
0
0
0
1
0
1
1
0
2
2
3
1
1
0
0
1
1
0
1
0
1
0
0
2
2
1
0
1
1
0
1
0
2
2
2
2
1
2
0
0
1
1
1
0
0
0
0
2
1
0
1
0
0
0
1
0
1
1
2
2
1
2
1
1
2
1
2
1
1
0
1
1
0
0
2
0
1
1
1
1
1
0
1
0
1
0
0
1
1
0
1
1
1
0
1
0
2
1
0
0
1
0
0
2
0
2
0
1
1
0
0
1
2
0
1
1
1
0
0
0
1
1
1
1
0
0
2
1
2
1
1
1
1
0
1
2
0
1
2
2
1
0
0
1
1
0
1
1
0
0
0
0
3
1
1
1
1
0
0
1
1
0
1
1
1
1
0
0
2
2
1
2
0
1
2
1
1
1
0
2
1
0
2
1
0
0
0
1
0
0
0
2
2
1
0
0
1
0
1
0
0
1
2
0
2
1
2
1
1
1
0
1
1
1
1
1
2
2
0
1
0
0
2
1
0
1
2
2
2
2
1
2
0
0
1
1
1
0
1
0
2
1
0
0
1
2
1
1
2
1
1
0
0
1
0
2
1
1
1
1
0
0
1
1
1
1
1
0
1
2
2
0
1
2
1
0
1
0
0
1
1
1
1
0
1
0
15
1
2
1
0
1
1
2
1
1
0
0
0
0
2
2
1
0
1
1
1
1
1
1
0
2
1
1
0
2
1
1
1
2
1
2
1
2
1
2
0
0
0
1
2
1
2
1
2
2
1
1
1
0
1
1
1
0
2
0
1
1
2
1
0
0
1
0
2
2
0
0
0
1
0
2
1
2
0
1
1
0
0
0
1
1
0
1
2
1
3
1
1
1
1
1
0
1
2
0
0
0
1
0
1
0
2
0
1
2
1
1
1
2
0
2
1
1
2
0
0
2
0
1
1
1
1
0
1
1
2
0
1
1
0
1
2
1
1
0
2
1
0
0
0
2
1
0
1
1
1
0
2
1
0
2
1
0
2
1
2
0
1
2
1
1
2
1
1
0
1
1
0
0
2
0
1
3
1
0
2
1
1
1
1
2
0
0
3
1
1
1
2
1
0
1
2
2
0
1
1
0
2
1
1
1
1
0
0
0
0
1
1
0
0
0
1
1
1
1
2
2
1
1
0
1
0
0
2
0
1
4
0
1
2
1
1
1
1
1
0
0
1
0
0
1
1
2
2
0
0
2
2
1
1
1
1
1
0
0
1
1
0
0
1
2
0
0
0
0
1
2
0
1
1
1
1
0
1
0
1
0
0
1
1
1
0
0
1
1
0
0
0
1
1
0
2
1
0
3
2
1
1
4
1
0
1
2
1
1
0
1
1
1
2
1
1
1
0
0
1
1
1
1
1
1
0
2
0
2
1
2
0
0
2
0
1
1
2
1
0
5
2
1
0
1
0
1
1
0
1
0
1
2
1
0
0
0
0
0
1
1
2
1
0
1
2
0
2
1
1
1
1
0
2
3
1
2
1
2
0
1
1
2
0
0
1
0
1
0
0
1
1
0
0
1
2
1
2
2
0
1
2
1
1
1
2
1
1
0
1
2
1
1
1
1
1
1
1
0
1
0
1
0
1
1
0
1
0
0
1
1
1
0
0
1
0
0
2
1
1
2
1
0
0
1
1
0
0
1
2
2
0
0
1
0
1
0
1
0
2
2
2
0
1
0
0
1
1
1
2
1
0
1
1
1
1
3
0
1
1
1
1
1
2
1
0
1
2
0
0
1
1
2
0
2
1
1
0
1
0
0
1
2
0
0
3
0
2
0
0
2
1
1
0
0
0
0
0
1
0
2
1
2
1
2
1
1
1
1
1
1
1
0
1
1
0
1
3
1
1
1
0
2
1
1
0
0
0
1
1
2
1
0
1
0
0
1
2
1
0
2
1
0
0
0
1
1
2
2
2
2
0
1
1
1
2
0
0
1
1
1
0
0
1
2
1
1
2
1
1
1
0
1
0
1
1
1
0
2
0
1
1
1
1
0
2
1
0
2
2
0
1
0
1
1
0
2
2
1
0
2
0
1
1
0
0
0
1
1
1
0
1
2
1
1
1
0
2
1
0
0
1
2
1
1
0
1
2
1
2
4
1
0
2
1
0
0
1
0
2
0
0
1
0
1
0
0
1
0
0
2
1
3
1
0
0
1
2
1
1
1
0
0
2
1
1
0
2
0
1
1
1
1
0
1
0
2
1
1
1
1
0
0
1
2
1
1
1
0
0
2
1
1
0
1
1
1
1
2
1
1
0
1
0
1
1
1
1
1
1
0
1
0
1
0
1
0
1
0
0
1
0
0
1
1
1
0
2
0
1
0
0
0
1
2
1
4
2
0
2
1
0
1
1
2
1
2
1
1
0
2
0
1
1
0
1
0
1
2
0
0
2
1
2
1
2
1
1
0
1
0
1
1
1
1
2
1
0
1
0
2
0
0
1
1
2
1
1
2
0
1
1
0
1
0
1
0
2
0
0
1
0
2
0
0
1
2
1
1
0
1
1
0
1
1
0
1
2
1
1
1
0
0
1
2
0
2
0
1
1
0
1
0
0
0
1
1
1
2
1
3
1
0
2
1
1
0
1
0
0
0
2
0
0
4
2
3
0
1
0
0
1
2
0
2
1
2
1
1
1
1
0
2
1
1
1
0
0
1
1
0
0
2
0
0
1
2
0
1
1
1
1
0
0
1
0
1
0
2
1
0
1
1
1
0
0
1
1
2
0
1
1
1
0
1
1
0
0
1
1
1
2
0
1
1
2
1
1
0
1
1
0
1
2
2
2
1
0
2
0
0
0
1
0
2
1
0
1
1
1
2
1
0
0
0
1
0
1
1
1
1
2
1
1
1
2
0
2
1
1
1
1
2
3
1
1
0
1
1
1
1
2
2
1
0
1
1
0
2
2
2
0
0
1
2
0
2
1
0
1
2
1
1
0
1
1
1
2
2
1
1
2
1
2
1
1
1
2
0
1
0
1
1
1
2
1
0
1
0
1
1
2
2
1
2
1
1
1
2
0
1
1
1
0
0
2
1
0
1
0
0
1
1
0
2
1
1
1
0
1
0
0
1
1
1
1
0
0
1
1
0
1
0
1
0
1
0
1
2
1
1
1
2
0
1
1
0
2
0
0
2
1
1
2
0
1
2
1
1
2
0
0
0
1
1
0
2
1
1
2
1
1
0
0
1
1
1
1
2
1
1
0
1
1
2
1
0
1
2
0
2
1
1
0
2
0
0
1
2
2
1
1
1
1
3
0
0
1
0
0
1
1
0
1
0
1
2
1
1
0
0
1
1
0
1
1
1
1
1
0
0
2
0
2
0
0
1
2
0
2
1
1
1
0
1
2
1
0
0
2
2
0
0
0
0
2
0
2
2
0
0
1
0
0
1
0
2
0
2
1
1
1
0
1
1
1
0
1
2
1
2
1
1
1
2
1
0
1
1
2
1
0
0
1
1
1
1
1
1
0
2
1
1
0
0
1
1
0
1
0
1
1
2
0
2
0
2
1
1
1
0
0
2
1
1
0
2
0
0
2
0
0
2
1
1
1
0
3
1
1
2
2
0
2
0
0
0
2
0
0
1
1
2
0
1
3
1
1
1
0
0
1
0
0
0
1
0
0
1
0
1
2
2
2
0
1
1
1
1
0
1
1
2
0
1
0
0
0
2
1
0
1
2
1
1
1
0
0
0
1
2
1
1
1
1
1
0
2
1
0
1
0
0
2
0
2
1
1
1
0
0
0
1
1
1
2
1
1
1
1
0
1
2
2
2
1
0
2
0
1
2
1
0
0
0
1
1
1
1
2
0
2
0
0
0
0
0
1
0
1
0
1
1
1
1
0
0
2
2
0
0
1
1
0
1
2
0
1
2
1
0
1
0
1
1
1
0
1
0
1
1
0
0
0
2
0
2
1
1
1
3
2
1
2
0
1
1
0
3
1
0
0
1
0
0
1
1
1
1
0
1
0
0
0
0
2
0
2
0
0
2
2
2
1
0
0
1
0
1
1
1
2
0
0
0
1
2
1
0
1
1
0
1
1
0
0
3
0
3
1
1
1
1
2
1
2
0
2
1
2
1
1
2
2
0
3
2
1
0
1
1
0
1
0
0
0
1
3
1
1
0
1
1
1
1
1
2
0
0
0
1
0
2
2
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
1
1
2
1
3
2
2
0
0
0
0
1
0
2
1
1
0
0
2
0
0
0
1
1
1
0
0
1
2
0
0
1
0
1
2
1
0
0
0
0
1
1
1
2
1
0
0
1
1
0
0
2
0
2
1
1
0
2
1
0
0
0
0
0
1
1
1
1
1
1
0
0
0
1
2
1
1
1
0
1
1
1
1
0
4
1
2
1
2
1
2
2
0
0
0
1
0
1
0
0
2
0
0
0
2
0
0
2
0
1
1
0
0
1
2
2
1
2
0
0
1
2
1
2
0
1
0
1
0
2
0
0
0
0
0
0
0
0
1
1
1
2
0
1
3
2
2
1
0
1
1
0
2
1
0
1
0
1
0
1
0
1
1
2
1
2
0
1
1
1
1
1
2
0
0
0
0
1
1
1
1
1
1
2
2
3
2
1
2
2
1
2
1
2
1
1
2
0
0
0
0
1
1
0
1
1
0
0
1
0
0
1
0
1
1
1
0
0
0
1
0
1
1
2
1
2
1
1
2
0
1
2
1
2
0
1
0
1
0
0
1
0
1
0
0
1
1
0
1
0
1
2
0
0
2
1
1
0
0
1
0
2
2
1
1
0
1
0
2
1
0
0
2
0
1
0
1
1
1
1
2
0
1
0
0
1
1
1
0
2
1
2
0
1
0
2
0
2
0
2
0
2
1
0
2
1
1
0
1
1
0
2
2
1
1
0
1
1
1
0
0
1
1
2
0
2
1
0
2
2
0
1
1
1
0
0
2
0
0
1
2
0
0
0
1
0
1
2
0
0
1
2
2
1
1
0
0
0
2
0
0
2
2
1
2
1
1
1
0
1
1
1
1
0
1
2
1
1
3
2
2
0
1
0
1
0
1
2
1
1
0
3
2
0
1
1
0
0
0
1
1
2
0
1
1
1
0
1
0
1
0
0
1
2
1
0
2
2
1
2
2
2
1
1
0
2
2
0
0
1
1
1
0
2
1
2
1
1
2
0
1
1
2
1
0
1
2
2
1
1
0
1
1
2
1
1
2
1
2
1
1
1
1
1
0
1
2
2
1
2
2
3
0
1
1
2
1
2
2
0
0
0
0
0
1
0
2
0
2
2
0
2
1
1
1
0
1
1
1
1
1
0
1
0
0
2
1
1
2
2
1
0
0
0
2
2
1
2
0
0
1
1
2
2
0
1
0
0
0
1
1
3
1
1
2
0
0
1
0
1
1
1
2
0
1
1
1
0
0
1
2
2
1
1
0
1
2
2
1
0
0
1
1
1
2
1
0
0
2
0
2
1
1
1
2
0
2
1
1
1
2
1
0
0
1
3
0
1
2
1
1
2
0
3
1
4
0
0
0
0
0
0
0
0
0
3
0
2
0
1
1
0
1
1
1
1
1
1
1
1
0
1
2
2
1
1
0
2
1
0
0
2
1
1
1
1
2
1
0
1
0
0
2
0
2
2
0
1
1
1
2
2
1
0
1
1
1
1
1
2
0
1
2
1
1
0
0
1
1
1
1
1
0
0
0
1
0
0
0
2
0
0
2
2
3
2
1
1
2
1
0
1
0
1
2
1
1
2
0
1
1
1
1
0
0
1
1
1
0
0
1
1
1
1
2
1
1
1
2
1
0
1
2
2
0
1
1
0
2
1
2
2
1
2
3
3
0
1
1
0
1
2
1
1
2
1
1
2
1
0
0
1
1
1
0
1
1
2
0
0
0
1
0
1
1
2
1
1
0
0
1
1
1
1
0
1
1
0
1
1
1
0
0
1
0
0
2
2
1
0
2
1
1
1
1
1
0
0
0
1
0
2
0
1
1
1
1
0
0
1
1
1
0
2
1
1
1
0
1
0
0
2
0
0
1
0
0
2
1
1
2
1
0
1
3
0
2
1
0
0
1
1
2
2
1
1
0
0
2
1
1
1
2
0
1
1
1
2
0
0
1
2
2
1
1
0
1
1
1
0
0
0
2
1
1
2
0
1
2
0
1
0
2
0
1
2
1
2
1
0
2
1
2
1
0
1
1
1
1
1
1
1
0
1
0
1
0
2
0
1
0
0
2
0
0
2
0
1
3
1
1
0
1
1
2
2
1
2
1
2
1
0
2
0
2
1
1
1
0
0
2
1
0
0
2
1
4
0
0
2
1
0
1
0
0
1
1
1
1
2
0
1
1
3
1
0
1
0
2
1
0
0
1
1
1
0
0
0
1
1
1
0
1
1
3
0
2
1
1
2
0
1
0
1
1
0
1
0
2
1
2
1
2
1
0
0
1
1
0
2
2
1
0
1
1
1
1
2
2
0
0
1
0
1
1
1
2
0
0
2
0
1
3
1
0
1
1
2
1
2
1
0
1
0
2
0
1
0
1
2
1
0
0
0
1
1
1
1
2
2
1
1
3
1
1
0
1
3
0
0
0
1
0
1
1
1
1
2
1
0
1
0
1
1
1
2
1
1
1
1
1
2
3
0
0
2
0
1
0
1
2
2
1
1
0
2
2
0
1
0
0
0
1
2
0
0
0
1
3
2
1
2
2
1
0
1
1
1
1
1
1
2
1
1
0
2
0
2
0
1
0
1
2
2
0
1
1
1
1
0
1
0
0
1
2
0
1
1
0
1
0
0
0
0
0
8
1
1
1
1
2
0
1
1
1
1
1
0
0
1
0
1
2
0
0
2
0
1
2
0
1
0
1
1
1
1
0
1
1
1
2
1
1
0
2
1
0
1
1
2
1
0
2
0
1
1
1
0
1
1
1
1
1
1
0
1
2
1
2
0
1
0
1
2
0
1
1
2
2
0
1
0
0
0
1
2
2
1
0
0
1
2
2
1
1
1
2
0
0
2
0
0
1
0
2
1
0
0
1
0
1
0
1
1
2
0
1
0
0
0
2
1
1
2
1
1
1
2
1
1
1
1
1
2
1
1
1
2
2
1
2
0
1
1
2
0
1
0
1
2
0
0
2
1
2
2
2
1
0
1
1
0
1
1
1
0
1
2
0
2
2
1
1
0
1
1
1
0
0
1
0
1
1
1
2
1
0
2
0
1
1
2
1
0
2
0
0
1
0
0
0
1
1
1
1
0
0
1
0
1
1
0
2
1
2
1
2
1
1
0
1
3
0
1
1
1
0
1
1
1
0
1
0
2
2
1
1
1
2
1
1
1
0
1
0
1
0
1
0
2
0
2
1
2
2
3
2
1
0
1
1
0
0
1
2
2
0
1
2
0
0
1
0
1
1
1
0
1
0
0
0
1
0
1
2
1
1
1
0
0
2
2
1
1
1
2
1
0
1
1
2
0
0
1
1
0
2
1
0
2
2
1
0
0
1
0
0
1
2
1
0
1
2
1
1
2
3
1
1
1
2
0
1
1
2
1
0
2
0
2
2
1
1
1
1
3
3
1
1
2
0
1
1
0
0
2
0
1
0
0
1
2
1
1
1
1
1
1
1
0
1
0
3
2
1
0
1
0
1
1
1
1
0
0
0
0
0
0
2
1
1
0
0
0
2
1
2
0
2
1
1
1
0
0
0
0
1
2
0
0
0
1
0
1
1
1
1
0
1
0
1
1
1
2
1
1
2
1
1
1
1
0
2
2
0
1
2
0
1
0
1
1
1
2
0
0
0
1
1
0
0
0
1
1
2
2
0
0
0
2
0
4
0
1
1
2
1
0
0
2
1
0
2
1
0
0
0
2
1
1
0
1
0
1
0
1
0
0
1
0
1
0
1
2
0
0
1
0
1
0
1
2
0
1
0
1
1
1
1
0
2
1
2
1
1
1
2
1
1
1
1
2
0
1
2
0
0
0
1
2
2
0
0
1
0
0
1
1
0
2
1
0
1
1
0
0
1
0
1
1
2
0
0
1
1
0
0
0
0
1
2
0
0
2
2
0
2
1
1
1
0
0
0
2
0
1
1
1
0
2
0
0
1
0
0
0
1
1
2
1
1
1
1
1
1
0
1
0
2
3
1
1
0
1
1
1
1
1
1
1
1
2
2
0
2
3
2
1
2
1
1
1
1
2
1
1
1
2
2
2
1
0
2
2
1
1
0
0
1
0
1
1
0
0
1
2
1
0
0
0
1
2
2
2
1
1
2
1
0
0
2
0
1
0
1
2
0
1
0
2
1
1
0
1
1
0
3
2
1
0
0
0
0
1
1
1
2
2
0
1
0
0
1
1
0
2
0
0
1
2
2
1
1
1
2
2
0
1
1
1
2
0
1
0
2
2
0
0
0
0
0
0
0
1
1
1
2
1
2
1
1
0
0
2
1
2
0
0
0
1
1
1
1
2
1
0
1
1
1
2
0
1
1
1
1
1
2
0
1
2
1
1
0
2
1
1
2
1
2
1
1
1
1
2
0
2
1
0
2
0
1
1
1
1
0
3
0
0
1
0
1
0
3
1
2
1
1
1
0
2
1
0
0
0
2
1
1
2
0
1
3
1
0
1
1
2
1
0
2
1
0
1
2
2
1
0
0
0
0
1
1
1
1
1
0
0
1
1
1
1
0
0
1
2
1
0
0
1
1
2
1
0
0
0
1
0
1
0
0
0
0
0
1
1
3
0
1
0
2
0
1
0
1
1
1
2
1
0
4
0
1
1
1
1
0
0
2
1
2
1
1
2
1
1
0
1
1
0
1
1
2
1
1
2
2
0
1
2
1
0
1
0
2
1
0
0
0
3
1
1
1
1
1
0
1
1
0
0
1
1
1
1
1
0
1
0
0
0
0
0
0
1
2
0
0
0
1
0
1
0
1
1
2
0
1
1
0
1
2
1
0
1
1
0
0
1
1
3
1
1
0
0
1
1
2
2
0
0
1
0
2
2
1
0
1
2
1
0
1
0
2
0
1
0
1
0
2
1
1
1
0
0
2
1
1
2
0
1
1
0
0
0
0
0
0
0
0
0
1
0
2
2
2
1
0
0
1
2
0
0
1
1
2
0
1
0
1
1
0
1
1
1
2
1
1
0
0
0
1
0
0
2
2
0
0
1
0
0
2
1
1
0
2
1
1
0
0
1
2
1
0
0
0
2
0
1
0
1
2
1
0
1
0
0
1
1
1
2
1
0
0
0
0
0
1
2
1
1
2
2
1
1
1
1
2
3
0
1
1
2
2
0
2
1
2
0
0
0
1
1
2
3
0
1
0
2
0
1
1
0
1
2
2
0
2
1
2
1
0
0
2
0
0
2
0
1
1
0
2
2
0
1
0
1
0
1
2
1
0
0
1
1
0
2
0
1
0
1
2
1
1
1
1
1
0
1
1
1
1
0
2
2
1
0
1
0
1
0
2
2
1
1
2
0
2
1
2
1
1
2
1
0
1
1
0
1
0
1
0
2
0
1
1
2
2
1
0
1
2
2
0
1
1
1
2
0
1
0
2
1
2
1
1
2
2
2
2
0
1
1
1
0
0
0
1
0
1
0
2
3
1
1
1
1
0
1
2
1
0
0
1
0
1
0
3
0
1
1
1
1
0
0
1
0
2
0
2
1
2
2
1
2
2
1
1
1
1
0
0
1
0
0
1
0
1
2
1
2
0
1
2
0
0
2
0
1
1
2
1
2
1
2
1
1
1
1
0
2
2
1
1
2
2
0
1
1
1
2
1
0
2
1
2
1
0
2
1
2
0
0
2
1
1
0
1
0
0
1
1
2
1
1
1
1
1
1
1
1
3
1
2
1
0
1
1
0
1
1
2
0
2
1
0
1
0
1
2
2
0
0
2
1
0
2
0
2
0
0
1
0
1
1
2
0
1
1
2
0
1
1
1
1
1
1
1
2
0
0
1
2
0
1
2
1
1
1
0
1
0
0
4
1
2
0
0
2
2
1
1
1
2
1
1
0
1
0
0
2
1
1
1
1
1
0
0
1
0
0
1
0
0
2
1
0
1
2
1
3
0
2
0
3
2
0
1
2
1
1
1
1
0
2
1
0
2
1
2
0
1
0
0
2
1
1
1
0
2
2
3
1
1
7
1
2
2
0
1
2
2
0
1
2
1
0
2
1
2
2
0
1
1
1
0
2
0
1
0
1
2
0
1
1
0
2
1
2
0
2
1
2
2
1
2
1
0
1
1
0
0
0
1
1
1
0
0
1
1
2
1
0
0
0
1
2
1
2
1
0
2
0
0
2
2
1
1
1
1
1
2
2
1
2
3
2
0
0
1
3
2
0
0
1
1
2
0
0
1
0
1
1
0
0
1
2
1
1
0
1
2
1
2
0
1
1
0
1
0
1
0
1
2
3
3
1
1
1
1
1
2
0
2
2
0
1
1
0
4
0
1
1
1
1
2
1
0
0
1
2
2
1
0
0
0
1
1
2
2
1
0
0
0
2
0
2
0
2
2
1
1
0
1
1
0
0
2
0
0
1
1
0
1
1
1
2
0
0
0
0
1
1
0
0
1
0
0
0
0
2
1
1
1
0
0
1
1
1
1
1
1
1
1
1
1
1
2
0
1
0
1
1
0
1
1
0
1
1
0
1
0
5
2
0
1
1
1
0
0
0
2
1
1
0
2
0
0
1
1
0
1
1
1
1
0
2
1
1
2
0
2
0
1
1
0
0
2
0
2
2
2
2
0
1
2
0
1
1
2
0
2
2
1
0
1
2
5
0
0
0
1
2
0
1
0
1
0
1
0
2
2
1
0
2
0
1
1
1
0
1
2
1
1
1
2
1
0
1
1
0
1
0
3
1
1
1
0
2
0
2
0
1
1
0
1
0
2
2
0
0
1
1
2
1
2
0
0
1
1
1
0
0
0
2
1
1
1
1
1
2
1
2
1
0
2
1
2
1
2
2
2
1
1
0
2
0
1
1
0
2
1
1
2
1
0
1
3
2
1
1
1
1
1
0
0
2
0
1
2
4
1
0
1
1
1
0
2
2
1
3
1
0
0
0
0
2
2
2
0
1
1
1
1
2
0
1
0
2
2
2
0
2
1
0
0
0
0
2
2
0
0
0
1
1
1
1
1
2
1
1
1
1
0
0
2
1
2
1
1
2
1
2
2
0
2
2
1
1
2
0
1
0
1
2
0
0
1
2
0
2
2
0
1
2
1
0
1
1
1
1
1
1
0
1
0
0
0
0
2
1
2
1
0
1
1
1
2
0
1
1
0
2
2
1
3
2
1
1
1
0
0
0
0
2
0
1
2
0
1
0
1
1
1
1
0
1
1
0
2
1
1
2
1
0
2
0
0
1
2
0
1
1
1
1
1
1
1
0
2
1
1
2
2
0
1
1
0
0
1
2
2
2
1
1
2
0
1
1
2
2
2
2
1
0
0
0
2
1
1
0
1
1
0
1
1
0
0
0
0
0
0
1
2
1
0
0
2
0
1
1
1
4
0
0
1
1
1
0
0
0
2
1
2
1
1
1
0
0
1
0
0
1
0
1
1
1
0
2
0
2
0
1
1
1
1
0
1
1
0
0
0
1
2
1
0
1
0
1
3
2
0
0
0
0
1
0
1
0
1
0
1
2
1
2
0
2
0
2
0
0
0
0
1
0
2
4
0
0
1
2
1
2
0
2
1
1
1
0
1
0
2
0
2
0
2
1
2
0
1
1
1
0
0
3
1
1
1
2
2
1
1
1
0
0
0
0
0
0
1
2
2
2
1
1
1
1
1
1
0
2
1
2
1
2
1
1
1
2
1
1
1
0
0
2
1
0
0
2
0
0
2
0
2
1
1
1
0
2
2
1
1
1
1
1
0
0
0
1
1
1
1
2
0
0
1
0
0
1
1
0
2
2
0
1
1
2
1
0
1
2
0
1
2
1
1
1
1
1
1
1
0
1
1
1
1
2
1
1
0
2
1
1
2
0
0
2
0
0
1
0
1
2
0
2
0
0
0
1
1
1
0
0
1
1
0
1
1
1
1
0
1
1
2
2
1
0
1
2
2
0
2
0
0
0
2
1
2
2
0
1
1
1
0
1
3
0
2
0
2
0
0
1
1
2
0
1
1
2
0
2
0
2
1
0
1
1
1
1
0
1
1
1
0
0
0
1
2
2
1
1
0
1
2
1
1
2
1
1
1
1
2
1
1
1
1
0
1
0
0
2
1
1
1
1
1
1
2
1
0
2
1
1
1
0
1
1
0
1
1
1
0
1
0
2
1
1
1
1
1
1
1
1
2
0
3
2
2
2
2
0
0
1
1
1
2
1
2
0
0
1
0
2
0
1
1
0
2
1
1
0
1
0
1
1
1
1
2
0
0
1
0
2
0
0
1
2
2
0
0
0
1
0
2
2
2
1
2
1
0
2
1
1
2
1
0
3
0
0
0
2
1
1
2
0
2
0
0
1
2
1
2
0
1
0
0
3
2
1
1
0
1
0
0
1
0
0
1
0
0
0
1
0
1
1
1
0
1
1
2
2
0
0
1
1
0
1
1
0
1
0
1
2
1
1
0
1
2
0
1
1
2
0
2
0
2
1
1
1
1
2
1
0
1
1
0
1
1
1
0
2
2
2
0
2
0
3
0
1
1
1
1
1
0
1
1
2
0
1
0
1
2
1
0
1
2
1
1
0
0
2
0
2
0
2
1
1
1
1
1
1
0
0
1
2
1
2
1
1
1
0
1
0
2
0
2
1
0
2
0
2
1
1
1
0
2
0
1
2
1
1
0
2
1
2
0
1
2
1
1
0
1
2
1
0
0
1
0
0
1
0
1
0
1
1
0
0
1
1
1
0
1
1
1
0
2
2
2
1
2
0
0
1
1
2
1
1
0
1
1
1
1
0
2
0
0
1
0
0
1
2
2
2
1
2
2
2
1
0
0
2
1
1
2
0
0
0
1
2
2
1
2
1
1
0
0
1
0
1
2
1
0
2
1
1
0
2
0
2
1
0
3
1
0
0
1
0
1
0
1
2
1
1
1
2
1
2
1
1
2
0
1
1
1
0
1
1
0
1
1
1
2
1
0
1
0
1
1
1
0
1
1
1
0
1
1
1
1
1
0
0
2
0
1
1
1
2
1
1
0
2
2
0
1
1
0
0
2
1
1
1
0
1
0
0
1
0
0
1
1
0
1
1
0
0
0
2
0
0
1
1
0
0
1
1
0
1
1
1
2
2
1
0
1
0
0
0
2
3
1
1
2
3
2
1
0
0
0
0
1
1
1
0
1
1
1
1
0
1
1
1
0
2
1
1
1
1
1
0
0
0
1
0
1
2
0
1
0
1
1
0
1
1
2
1
2
1
0
1
2
0
1
1
1
1
1
0
1
1
1
1
0
0
2
2
1
2
0
1
1
0
1
2
2
0
2
1
1
1
1
0
2
0
0
0
0
2
2
0
2
0
0
0
0
0
0
1
0
2
2
1
0
0
0
2
2
1
2
1
2
0
2
2
2
1
1
2
2
0
1
1
1
2
2
0
0
1
1
3
0
0
2
0
0
1
2
1
0
3
1
1
0
1
1
0
0
0
1
2
1
1
1
2
2
0
1
2
2
1
1
2
0
2
0
1
1
2
1
1
2
1
1
1
0
2
1
0
1
0
0
2
1
0
1
1
0
2
0
1
1
1
1
2
0
1
0
1
1
1
1
1
2
1
2
2
1
0
1
1
2
1
0
1
2
1
0
1
1
1
1
0
0
0
1
1
1
3
1
1
2
1
2
2
1
0
0
0
0
0
1
0
2
1
1
0
0
2
1
1
2
1
0
0
0
1
0
1
2
0
2
0
1
1
2
0
1
0
0
1
1
1
2
2
1
0
2
1
0
1
0
1
1
0
3
2
2
0
1
0
2
0
0
0
0
2
1
1
0
0
1
0
1
0
2
1
0
0
2
2
1
0
1
1
1
1
1
0
1
2
1
1
0
1
0
1
0
1
3
0
2
2
1
1
2
0
1
0
2
1
1
1
0
1
0
0
0
2
0
1
2
1
0
1
2
1
1
1
1
2
0
0
1
1
0
3
1
2
1
1
2
0
1
0
2
0
2
0
2
1
1
1
0
0
1
0
1
0
2
0
1
1
1
1
1
1
1
2
2
1
0
0
0
1
0
1
2
1
2
0
2
0
1
0
0
0
1
0
1
1
0
1
0
1
1
1
1
3
0
0
2
1
2
1
1
2
1
2
1
0
0
1
1
1
0
1
3
2
2
0
1
0
1
0
1
1
1
0
1
2
1
1
2
0
1
0
1
2
1
2
1
0
0
2
0
1
0
0
0
0
0
0
1
1
1
1
1
0
0
2
2
0
1
0
0
2
1
1
1
0
0
1
1
1
2
0
1
0
0
1
1
1
1
0
2
2
0
1
0
0
2
1
0
0
1
1
2
1
0
0
0
2
2
1
1
2
1
0
0
1
2
0
0
1
3
1
0
1
2
2
1
1
0
1
1
1
2
0
0
2
2
0
1
1
0
1
2
0
3
0
0
1
0
0
3
1
1
3
0
1
0
1
0
1
1
2
0
1
0
2
2
0
1
2
0
0
2
1
2
0
5
3
0
2
1
1
1
2
0
1
2
1
2
1
0
0
1
2
1
0
1
1
0
1
2
0
1
2
2
1
0
1
0
0
0
1
0
0
2
0
1
2
1
1
1
0
2
1
0
1
1
1
2
1
1
1
2
2
0
0
1
1
1
0
1
0
2
1
2
1
0
1
1
0
0
2
1
1
0
1
2
1
2
1
1
1
0
1
1
1
1
1
1
1
2
1
1
1
1
0
1
0
0
0
0
1
1
6
1
1
2
3
2
1
1
0
1
0
1
0
1
1
2
1
0
1
1
0
2
1
0
0
0
1
1
0
2
0
0
1
2
2
0
1
2
2
1
2
2
1
0
1
1
0
1
1
0
0
1
1
1
0
0
1
0
1
1
1
1
2
0
0
1
1
2
2
1
0
0
3
1
1
1
2
0
0
2
0
2
1
0
2
1
1
0
0
1
1
1
0
1
0
1
1
0
2
0
0
2
0
1
0
1
0
3
1
2
0
2
2
1
1
1
1
1
1
2
0
0
1
2
1
2
0
1
1
1
1
1
2
0
0
0
2
1
0
0
0
2
1
0
1
1
3
1
2
1
1
0
1
0
1
1
0
1
1
1
0
2
1
2
1
2
1
0
2
1
1
1
0
0
2
1
1
2
1
1
1
1
0
0
1
1
0
1
1
1
0
0
0
3
2
1
2
0
1
2
1
0
1
1
0
1
1
1
1
0
1
2
0
1
1
1
0
1
0
2
0
0
0
0
0
1
2
0
1
1
0
0
1
0
1
0
0
1
1
1
1
1
0
0
1
0
0
1
0
1
0
1
0
1
1
1
2
3
1
1
0
2
1
1
1
1
3
0
1
1
1
2
0
2
0
2
1
3
0
1
2
2
0
2
0
1
1
1
1
1
0
0
0
1
1
1
1
1
1
1
0
1
0
1
2
1
2
1
0
2
0
0
0
2
1
1
1
1
2
0
1
0
0
2
1
2
0
2
1
0
0
0
1
1
1
2
0
2
0
0
0
2
1
0
1
0
0
0
1
1
1
0
0
1
0
1
0
1
1
1
2
0
1
1
1
1
0
1
1
0
1
1
1
4
2
0
1
1
1
1
1
2
0
0
2
1
1
0
0
0
2
1
2
1
0
0
1
2
1
1
1
2
1
0
0
1
2
1
1
1
0
0
1
1
0
0
0
2
0
2
1
0
2
0
0
0
0
1
2
0
0
1
1
2
1
0
1
1
0
1
0
2
1
0
0
2
0
0
0
2
2
0
2
1
0
1
1
3
1
0
1
1
1
2
2
1
2
1
1
2
1
1
0
1
1
0
1
2
1
1
0
0
1
1
1
0
1
1
2
0
2
1
0
0
1
0
0
1
1
0
2
0
1
0
1
1
1
1
1
2
1
1
0
1
1
0
1
1
1
1
0
2
1
1
0
1
1
2
0
0
2
1
2
1
0
1
1
1
1
0
0
1
1
0
1
0
1
1
0
1
1
0
0
1
0
0
1
0
0
1
2
0
1
0
2
2
1
0
2
2
0
1
0
1
2
1
1
6
0
2
1
1
1
0
1
1
1
1
0
1
5
2
1
2
0
1
1
1
1
0
1
1
1
2
2
2
2
1
1
1
1
0
0
2
0
1
1
0
1
0
0
1
0
0
1
2
0
1
0
1
3
0
1
0
1
0
2
0
2
2
1
1
0
1
1
0
1
0
1
0
1
1
3
2
0
1
0
1
2
1
0
0
0
1
2
0
0
1
1
1
1
1
2
0
1
1
3
0
1
1
1
1
1
0
1
1
0
1
0
2
0
1
1
0
2
1
0
2
1
1
1
1
1
0
0
3
1
1
1
1
0
2
2
0
2
2
1
2
1
1
2
0
1
0
2
1
1
2
0
1
0
1
0
2
0
2
0
1
2
1
2
1
1
0
0
1
2
0
1
1
0
2
0
2
0
1
0
1
2
1
0
1
1
2
2
0
0
0
1
1
2
0
0
1
0
0
1
1
0
1
0
1
1
0
1
0
1
1
0
1
2
1
2
0
2
1
2
1
1
1
1
1
0
0
2
1
1
1
1
2
1
1
1
1
2
0
1
0
2
1
1
1
0
0
1
1
2
0
1
1
1
2
1
2
0
1
3
0
0
4
1
1
1
1
1
0
1
1
1
3
2
2
1
1
1
1
1
1
0
1
0
0
0
0
1
0
0
2
1
0
0
1
0
2
1
0
2
1
0
2
1
0
1
1
1
2
1
0
1
1
1
1
2
1
0
1
2
0
1
0
0
1
2
0
0
1
0
1
0
1
1
0
0
2
2
1
0
1
0
0
2
0
2
0
1
1
1
2
1
2
0
2
1
0
1
0
1
1
1
1
0
1
1
0
2
1
2
1
0
1
1
1
0
1
2
1
1
0
2
1
0
0
2
1
1
1
1
1
1
2
0
0
0
0
1
1
1
2
0
1
0
2
0
2
1
1
0
1
1
0
4
2
1
1
1
0
1
1
0
1
1
2
1
2
2
2
1
0
2
2
0
2
0
0
1
1
1
1
1
0
0
1
0
1
1
1
1
0
0
1
1
1
0
1
1
2
1
1
2
0
0
0
1
0
1
0
0
1
1
1
0
0
0
0
1
0
1
1
0
1
0
0
1
1
2
0
0
0
1
2
1
1
0
1
1
1
0
1
2
2
2
1
1
0
1
1
0
2
1
0
1
0
2
0
2
1
0
1
1
1
1
1
0
1
0
1
2
0
1
0
2
0
1
2
0
1
0
1
1
2
1
1
1
0
1
2
0
0
0
0
0
1
1
0
2
2
1
1
1
1
1
1
0
1
1
1
2
0
0
1
1
0
0
0
1
0
2
1
1
0
1
0
1
1
0
1
1
1
0
1
1
2
2
1
1
1
2
0
1
0
1
0
1
1
0
0
2
1
0
1
1
1
1
1
1
0
2
0
2
1
0
0
1
1
1
0
2
0
0
0
2
1
1
0
1
2
2
3
1
2
1
2
2
0
1
2
1
1
0
1
1
0
0
1
0
0
1
1
1
0
1
1
1
0
2
1
0
0
1
1
0
1
2
0
0
2
1
1
1
1
1
0
1
0
1
0
0
2
2
2
1
1
1
1
0
1
0
1
2
0
2
1
0
0
1
0
1
0
1
2
2
1
0
1
1
2
1
2
0
0
1
1
0
1
0
2
1
1
2
0
0
2
1
0
0
2
1
0
0
1
2
1
1
1
1
0
0
1
1
2
2
0
1
1
1
1
0
2
1
1
1
0
0
0
1
0
1
1
2
2
0
0
0
1
3
1
1
2
1
0
1
2
0
2
2
2
2
1
2
1
0
0
1
0
1
1
0
1
2
0
1
1
1
0
1
0
0
1
0
0
0
1
2
1
3
4
1
2
1
1
0
2
1
2
2
0
0
1
2
2
2
1
2
0
1
1
2
1
0
0
2
0
1
2
1
2
1
0
0
1
2
0
1
2
1
0
0
2
1
0
0
1
1
1
0
2
0
0
2
1
1
1
1
2
4
1
1
0
2
1
4
0
0
0
0
1
1
1
0
0
0
0
1
1
1
1
2
0
0
0
1
2
0
0
1
0
2
1
0
0
1
4
1
0
1
1
1
2
2
2
1
2
5
1
0
1
1
1
0
1
2
2
2
0
2
1
1
0
0
0
0
2
0
0
1
0
2
0
1
2
2
1
1
0
0
0
0
0
1
0
0
1
1
2
2
0
0
0
1
1
1
1
1
1
0
1
0
0
1
0
0
0
2
2
0
0
1
0
0
1
1
1
1
0
0
1
1
1
1
1
2
0
2
0
1
1
1
0
2
0
1
1
0
1
1
2
0
1
0
2
2
1
1
2
2
1
0
0
1
0
2
0
2
1
1
2
1
0
1
1
0
2
1
0
2
0
1
2
1
0
0
1
2
2
1
1
0
0
2
1
0
1
1
0
2
0
1
0
2
1
1
0
0
0
0
0
2
0
0
0
1
1
2
2
0
0
2
1
1
0
2
0
2
1
1
1
0
1
0
0
0
1
2
0
0
0
1
1
0
1
0
1
1
1
1
0
0
0
1
0
2
2
1
0
1
1
0
1
2
0
1
1
1
0
1
2
1
1
1
1
1
1
1
0
3
0
2
0
0
1
0
1
2
1
0
2
1
1
2
1
1
1
0
1
2
0
2
2
2
0
0
2
1
0
1
1
0
1
0
1
0
1
1
2
1
0
0
1
0
0
0
0
1
2
1
2
1
0
1
0
1
0
1
0
1
1
1
0
3
2
0
1
0
0
1
1
0
0
2
0
1
0
2
2
1
1
2
0
2
1
0
3
0
1
1
0
0
0
1
2
1
1
2
1
1
1
2
1
2
2
1
2
1
1
1
2
1
0
0
2
0
0
1
0
0
1
1
1
1
2
0
1
0
1
2
1
0
0
2
0
1
1
1
3
1
2
2
1
1
1
2
1
1
2
1
1
1
1
0
0
1
1
1
1
0
1
2
0
1
2
1
0
1
0
2
2
2
1
1
1
0
1
2
2
2
0
1
2
1
2
0
1
0
0
0
0
2
2
1
1
0
2
2
0
2
1
2
1
2
0
0
2
1
1
1
1
0
0
1
2
2
2
0
1
0
1
1
2
2
0
2
1
1
1
0
1
1
1
1
1
1
2
0
1
0
2
2
2
2
1
1
0
0
1
1
1
1
1
0
2
2
1
2
1
1
2
0
0
1
1
0
2
1
1
0
1
0
1
1
1
0
1
0
1
1
1
1
2
2
0
1
1
3
2
1
1
0
1
2
1
1
0
1
1
1
0
0
1
2
2
2
1
2
1
1
1
0
1
1
1
2
1
1
2
0
0
0
0
2
2
1
1
0
1
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
1
1
1
1
1
2
1
0
1
2
1
0
0
1
1
0
0
0
2
1
2
0
2
1
2
1
2
1
0
1
2
1
1
1
1
1
1
1
1
1
1
0
3
1
1
0
1
1
1
0
1
2
2
1
0
1
1
1
0
2
0
1
2
1
0
1
0
1
0
1
1
0
0
1
2
1
0
0
2
2
0
2
0
0
1
1
3
1
0
0
2
0
0
0
2
0
0
2
0
2
1
2
1
1
0
2
2
0
2
2
2
0
1
0
1
1
0
2
0
1
1
0
0
0
0
1
1
1
0
2
0
0
0
0
1
2
0
1
0
0
1
2
0
1
2
2
3
0
0
1
1
1
0
0
0
1
2
0
1
0
1
1
0
1
0
1
0
2
1
2
0
0
0
1
2
1
2
1
0
1
0
1
1
2
0
1
2
0
2
0
1
1
1
1
2
1
2
0
0
0
0
0
0
2
1
2
1
1
1
1
1
0
0
1
0
1
2
0
1
0
1
1
0
1
0
0
0
1
1
0
2
3
1
0
0
1
1
0
0
0
2
1
1
2
0
2
1
2
1
0
1
0
0
1
1
0
0
2
0
0
0
1
1
1
2
1
2
0
1
1
0
0
1
1
1
1
1
0
1
2
2
1
1
2
0
1
2
0
0
2
2
0
2
2
1
0
0
0
0
0
1
1
0
1
0
1
2
2
2
2
1
0
0
2
2
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
2
1
0
1
0
1
2
0
0
0
2
1
1
1
1
1
3
1
0
2
2
0
1
2
2
0
0
2
2
1
2
0
0
1
1
1
0
1
1
1
1
0
1
2
0
1
1
2
0
0
1
2
1
1
2
2
2
1
1
0
1
1
1
1
1
1
2
0
0
2
1
1
2
1
0
0
0
2
1
1
0
1
2
0
0
1
0
1
2
1
1
0
0
2
2
1
1
2
1
0
0
0
1
1
2
1
0
1
2
0
1
0
0
0
1
2
1
1
2
0
1
1
0
1
1
1
0
4
1
0
2
2
1
1
2
0
1
2
0
0
1
1
1
1
2
2
1
0
2
1
2
0
1
1
2
0
1
0
1
1
1
1
1
0
0
0
1
1
0
1
2
1
1
0
1
2
2
2
0
2
2
0
0
0
2
0
1
0
0
3
1
1
1
0
2
1
1
0
0
0
0
1
2
0
7
0
0
3
0
2
1
0
0
1
0
0
0
1
1
1
0
1
2
1
1
0
1
2
0
1
1
2
1
0
1
0
1
1
1
2
0
1
1
1
1
2
2
2
1
1
0
1
0
0
1
1
1
1
1
1
1
2
0
1
1
1
0
1
0
0
0
0
0
1
1
0
2
0
1
1
0
0
2
1
1
0
1
0
0
1
1
2
0
2
2
3
2
2
0
2
1
1
0
2
1
1
1
1
1
1
1
0
1
1
1
2
1
0
1
0
2
0
1
2
0
1
0
1
1
1
0
2
0
1
1
0
2
2
1
1
0
1
0
1
1
2
1
1
1
2
1
3
1
0
0
1
1
2
0
0
1
1
2
1
1
0
1
1
1
2
0
0
0
1
1
0
1
1
1
1
0
0
1
1
0
0
1
0
3
0
2
1
3
0
0
1
1
2
1
2
0
2
1
1
1
2
1
1
0
0
1
1
2
1
2
0
1
0
0
1
0
0
0
0
0
2
1
0
0
1
2
1
1
0
1
2
1
0
1
2
0
1
1
2
0
0
0
0
0
0
2
1
1
0
0
2
1
1
0
2
1
1
0
1
2
3
1
1
0
1
2
1
0
2
0
2
0
0
0
1
2
2
0
0
1
1
0
1
2
1
0
0
1
0
1
2
0
0
0
1
1
1
0
2
1
1
0
2
0
0
1
1
1
1
0
1
1
0
0
2
0
0
1
1
1
1
1
0
0
0
1
1
1
1
0
1
1
2
1
1
1
1
2
1
2
1
2
1
1
1
1
3
1
0
0
0
0
2
0
2
0
1
2
1
1
1
1
1
2
2
2
1
0
0
3
1
2
1
0
1
1
7
1
2
2
0
0
0
1
0
1
1
1
1
0
1
1
1
0
2
0
0
4
2
1
1
1
0
0
1
1
1
1
0
1
1
1
1
2
1
2
1
1
0
1
1
0
1
1
1
1
0
0
0
1
1
2
0
2
1
1
1
0
3
1
2
1
1
0
0
0
1
1
0
1
0
1
2
1
0
1
2
1
1
0
0
1
1
1
1
1
1
0
0
2
1
2
0
1
1
0
2
2
0
1
2
2
1
1
1
0
0
1
0
1
1
0
2
1
2
2
1
0
0
2
1
0
1
0
0
0
1
0
1
0
1
1
0
2
0
0
2
1
2
1
0
2
2
0
2
1
0
1
1
1
1
2
0
1
0
1
0
1
2
1
0
2
0
1
1
0
2
2
1
1
1
1
1
1
2
1
1
2
2
1
1
0
0
1
3
2
0
0
0
0
1
2
2
1
2
10
1
1
1
0
0
0
1
2
2
2
1
2
2
0
2
1
0
0
2
1
0
2
1
0
0
0
1
0
2
1
0
0
2
3
1
1
2
0
1
1
0
2
2
4
0
1
0
1
1
0
1
0
2
1
0
1
0
0
1
0
0
0
0
2
1
2
1
0
0
2
1
1
1
2
1
0
2
1
1
2
0
0
1
1
1
3
1
1
0
1
0
2
2
1
0
2
1
2
1
1
1
2
1
1
1
1
0
1
1
2
0
0
2
1
1
1
1
1
2
1
1
0
0
1
2
0
1
2
1
2
1
2
0
1
0
1
1
2
0
1
1
1
1
0
1
1
2
1
2
0
2
0
1
1
1
1
0
5
1
1
2
1
1
2
0
0
2
0
1
0
0
0
0
0
2
1
2
0
1
1
1
1
1
1
2
1
1
2
2
1
1
1
1
0
0
1
1
2
0
2
0
0
0
0
0
1
0
2
1
1
0
1
2
0
2
1
2
1
1
1
1
1
0
0
1
0
1
0
1
1
1
2
1
1
2
1
1
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
1
1
2
2
0
0
1
2
1
0
1
1
1
1
0
0
1
1
0
2
0
1
1
0
2
2
1
2
0
0
2
1
0
0
2
1
0
2
1
0
1
2
1
0
1
1
1
1
0
0
1
2
1
1
1
2
1
1
1
1
0
1
1
1
2
2
0
1
1
1
1
1
1
3
0
0
1
1
1
1
1
1
2
0
0
2
1
0
8
2
1
0
1
1
1
1
1
1
2
0
1
2
1
1
1
0
2
1
1
1
0
0
1
2
2
2
1
1
2
2
2
1
1
1
1
1
1
0
2
2
1
1
1
0
2
2
2
1
1
0
1
1
1
1
1
0
1
2
1
2
1
0
0
0
1
2
1
2
1
1
1
0
0
1
1
2
1
0
1
1
1
1
0
1
0
2
1
0
1
1
2
1
1
0
0
1
0
0
1
0
0
2
2
1
2
1
1
1
0
2
1
2
2
2
1
1
2
2
1
0
1
1
0
0
2
1
1
1
1
1
0
0
3
0
2
1
1
1
1
1
1
1
0
0
0
1
1
0
1
1
0
2
1
2
0
1
1
1
1
0
2
1
2
1
2
1
0
0
1
1
1
0
0
1
1
2
0
1
2
1
1
0
0
2
0
2
0
2
1
1
1
2
0
1
0
1
0
1
2
1
1
2
0
1
2
1
1
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
1
2
1
1
1
1
1
2
1
1
2
2
0
0
1
1
1
1
0
1
2
1
1
0
2
1
2
1
0
1
1
2
1
0
2
0
2
1
1
1
0
0
0
1
0
1
2
1
1
0
1
0
0
1
1
0
0
1
1
2
0
2
1
1
2
1
1
1
2
2
1
1
0
0
2
2
1
2
2
2
1
1
1
0
1
0
1
2
2
1
0
1
0
2
1
2
0
0
0
2
2
1
2
1
1
2
0
0
1
2
0
1
3
2
1
2
2
1
1
2
1
1
0
1
0
2
1
1
1
2
2
0
2
1
1
1
0
1
0
1
1
2
2
1
2
0
2
2
1
1
0
2
1
1
1
1
0
0
1
2
2
1
1
0
2
0
0
1
0
1
0
0
0
2
0
2
1
0
1
0
1
1
2
2
1
1
2
2
1
1
0
2
0
2
0
1
1
1
2
0
1
0
1
1
0
1
0
1
1
0
2
0
0
2
1
0
1
1
1
0
2
0
1
4
1
1
1
1
0
1
0
2
1
0
1
2
0
0
1
1
2
1
2
0
0
2
1
1
1
0
1
0
2
0
1
0
1
0
0
0
0
2
0
1
1
1
1
0
0
1
0
1
1
0
1
2
2
0
0
1
0
0
2
2
1
1
0
0
0
2
0
1
1
0
2
1
1
1
1
2
0
1
2
1
1
1
1
1
0
1
1
0
1
2
1
1
2
2
1
1
0
1
1
1
1
0
0
2
2
1
1
0
2
2
0
1
1
2
2
0
1
2
1
0
2
1
2
1
0
1
0
0
1
1
4
0
1
2
0
0
1
0
1
2
1
1
0
1
0
1
0
0
0
1
1
2
0
0
1
1
0
0
2
0
1
1
1
2
2
1
0
0
2
3
1
1
1
2
2
2
2
0
2
1
0
2
0
0
1
0
0
1
1
1
1
2
0
0
0
1
0
1
0
1
0
2
0
0
2
1
1
1
1
1
0
2
1
1
1
1
0
1
2
2
1
0
2
2
2
1
2
0
0
2
0
1
1
0
0
2
1
0
1
0
0
2
2
1
0
2
1
1
2
2
1
1
0
2
0
0
0
1
0
1
1
2
1
2
1
0
1
0
2
0
0
1
0
2
0
2
0
0
1
1
0
1
2
1
1
1
2
1
0
0
0
1
1
2
4
0
0
0
1
2
1
0
1
1
1
2
0
1
1
2
3
1
1
0
1
2
2
0
1
2
2
0
2
1
1
1
1
1
1
0
2
1
1
0
1
1
1
1
1
2
1
1
1
2
1
2
0
0
0
0
1
1
1
1
2
0
1
2
1
1
0
1
2
1
0
1
2
1
0
1
1
1
2
2
1
2
2
1
1
0
1
1
1
0
1
1
1
3
0
0
0
1
0
2
1
1
1
1
1
1
2
0
0
1
0
0
1
2
0
2
1
1
1
2
2
0
0
1
2
0
0
0
0
1
1
1
1
1
1
1
0
0
1
2
0
2
0
2
2
1
1
2
0
1
1
0
0
1
1
0
1
1
0
2
2
0
1
2
1
0
1
0
0
1
0
1
1
1
0
0
1
0
0
1
1
2
1
2
1
1
1
0
1
0
0
2
2
0
2
0
2
1
1
1
1
1
0
2
2
1
1
2
0
2
1
0
0
0
1
2
2
1
1
0
0
1
1
2
1
1
1
2
2
0
2
2
1
1
0
0
1
0
0
1
1
1
1
1
1
0
1
1
2
0
0
2
1
1
1
1
0
0
1
2
2
1
1
2
2
0
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
3
2
0
1
1
0
0
1
0
1
0
1
0
1
2
1
1
2
0
1
1
1
0
0
2
0
1
0
1
2
2
2
1
1
0
2
1
0
2
0
0
0
2
3
0
0
0
1
0
1
0
0
1
1
2
2
1
1
0
1
0
0
1
0
1
1
2
1
0
1
0
2
1
1
1
2
0
2
2
0
1
0
0
2
2
1
1
1
2
0
1
0
1
0
2
0
1
1
2
1
0
1
0
1
1
0
0
1
0
2
1
1
1
1
0
1
0
0
1
2
1
0
1
1
1
1
0
2
0
0
1
0
0
2
0
0
1
0
2
2
2
1
0
0
0
1
0
2
2
2
2
1
2
1
2
1
1
1
1
0
0
2
2
1
3
1
0
2
0
1
2
2
1
2
1
2
2
2
1
0
0
0
0
0
0
1
1
1
1
1
2
0
0
1
2
0
1
0
1
1
0
3
0
0
0
1
1
0
1
1
1
2
2
0
1
2
0
1
1
1
0
4
0
2
2
0
1
2
2
0
1
2
1
0
2
1
0
0
1
2
0
1
1
1
0
0
1
0
1
0
1
2
1
0
2
0
1
0
0
0
1
0
0
1
2
0
1
1
0
0
1
1
1
0
1
1
0
0
1
1
1
1
3
0
1
1
1
0
1
0
2
2
1
1
1
0
2
0
2
1
2
0
0
1
1
2
2
0
1
2
1
2
0
0
1
1
1
2
1
1
1
0
0
1
2
0
0
0
0
0
2
1
0
1
1
0
0
2
0
0
1
2
1
0
2
1
1
1
1
0
1
2
2
2
0
2
2
2
0
1
1
0
1
1
0
0
0
0
0
1
0
2
1
0
1
0
2
1
1
0
1
1
2
1
1
0
2
1
0
1
0
1
1
0
0
1
2
2
0
2
0
1
2
2
1
1
2
1
1
1
1
0
1
1
0
2
1
3
2
2
1
1
1
1
2
1
2
2
1
0
0
2
1
0
3
2
2
0
1
2
1
1
0
1
0
0
1
0
1
1
0
1
1
0
0
0
2
2
3
1
1
1
2
1
0
0
2
1
0
2
2
1
1
0
1
1
1
2
2
1
0
2
1
1
1
1
2
0
1
1
0
2
2
1
1
0
1
2
1
2
1
0
2
1
0
1
2
2
2
1
2
1
1
2
0
1
0
0
1
0
1
1
1
0
2
0
1
0
1
0
1
1
1
0
1
1
1
1
1
0
0
0
0
0
0
0
0
1
0
2
0
1
2
1
1
2
1
1
0
0
2
1
1
0
0
0
2
1
2
1
2
0
2
0
1
0
1
2
1
3
0
2
2
0
0
1
0
1
0
1
0
1
1
0
1
0
1
1
2
1
0
1
0
0
1
0
1
0
1
0
0
0
0
2
0
0
4
0
0
0
1
2
0
1
0
0
2
1
1
3
1
0
0
1
1
0
1
2
0
0
2
0
0
1
0
1
2
1
1
1
1
0
1
0
2
0
2
1
1
2
0
0
1
2
0
1
1
1
0
0
1
1
1
0
0
2
0
0
1
2
1
1
1
1
0
0
1
1
0
1
3
2
2
2
0
2
0
1
1
1
1
2
1
1
1
1
0
4
0
1
1
1
0
0
1
0
1
1
0
2
0
0
1
0
1
1
0
0
2
0
0
0
0
0
1
0
1
2
1
1
0
0
1
2
1
1
2
0
0
1
1
1
1
0
1
0
0
1
1
1
0
0
1
2
0
2
1
1
1
0
1
1
1
1
3
1
0
1
1
0
2
1
1
0
0
2
0
1
1
1
2
1
0
0
2
0
1
1
1
2
0
2
1
0
1
1
1
0
1
3
1
1
0
0
1
2
0
0
0
0
0
2
1
1
1
1
0
0
2
0
0
0
2
2
1
1
1
1
0
0
1
0
1
2
1
2
2
0
1
0
2
0
0
0
1
0
1
0
0
2
1
0
0
1
0
1
1
1
0
2
0
1
0
2
1
1
2
0
0
1
1
1
1
1
1
1
0
1
0
1
1
1
1
0
1
0
0
1
2
2
0
2
1
1
1
0
0
0
1
1
0
0
1
0
0
2
0
1
1
1
2
1
0
0
0
1
1
1
0
1
1
1
2
0
1
1
1
2
1
1
0
1
2
2
1
1
0
0
2
2
1
2
1
1
1
0
1
1
1
2
1
0
1
0
1
0
1
0
0
1
0
0
2
1
0
1
1
1
0
0
1
0
1
0
1
2
0
0
1
0
0
0
0
0
0
2
0
1
0
3
0
0
2
1
1
2
0
1
2
0
0
1
3
1
2
0
2
0
0
1
2
0
0
1
1
1
2
0
0
0
3
2
1
1
1
1
1
0
1
1
1
1
3
0
1
1
0
1
2
0
2
1
0
1
0
1
1
1
1
0
1
1
2
1
1
1
2
0
0
0
1
1
0
2
1
0
0
1
0
1
1
0
2
1
1
0
1
1
2
0
0
1
0
0
1
1
1
1
0
2
1
2
1
4
2
1
1
1
0
1
1
1
1
0
2
3
0
1
1
2
0
1
1
2
9
2
2
0
2
2
1
0
1
1
0
1
0
0
2
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
2
0
2
1
0
1
2
0
1
1
1
1
0
2
1
3
0
1
0
0
0
1
0
2
0
0
0
1
2
1
2
2
1
0
0
2
1
0
2
1
0
1
0
0
1
0
1
1
1
1
0
0
1
2
0
2
1
1
1
2
1
1
0
2
1
1
0
0
0
1
2
1
1
0
0
2
2
2
0
0
1
1
1
0
1
1
1
1
1
1
1
1
0
0
1
1
1
1
1
1
2
3
1
0
1
1
1
2
0
1
2
2
0
2
0
1
0
1
1
1
0
2
0
0
0
1
0
0
1
1
2
0
2
1
0
2
1
2
1
1
1
1
0
2
1
1
0
1
1
1
0
1
1
0
0
0
0
0
0
0
1
1
3
0
0
0
0
0
2
1
1
0
2
0
1
0
1
0
1
2
0
1
1
2
2
0
1
0
1
2
1
1
1
2
0
0
2
0
1
0
0
0
0
1
0
2
0
1
1
0
0
1
0
1
1
1
1
0
2
1
1
2
2
2
0
1
0
1
2
1
2
1
1
1
1
1
1
2
3
2
0
0
0
2
2
1
1
1
0
0
0
2
1
0
1
2
1
1
1
1
0
1
1
0
1
1
2
1
1
1
1
1
2
2
2
1
1
2
1
0
1
1
1
1
0
0
2
2
1
3
0
0
2
1
1
1
0
0
0
0
0
2
2
0
0
1
2
0
1
1
0
0
0
1
0
2
0
2
1
0
2
0
2
0
2
2
2
1
1
0
2
1
2
3
0
2
1
1
0
1
1
2
2
1
1
0
2
0
1
0
1
1
0
1
0
3
0
0
2
1
1
2
1
0
1
0
2
0
0
1
0
0
2
0
0
1
2
1
1
0
1
0
0
2
1
1
0
0
2
1
1
0
0
1
2
0
0
1
1
0
1
0
0
1
1
1
2
1
1
1
0
1
1
2
1
0
1
0
1
0
2
0
0
2
0
0
0
0
1
1
1
1
1
1
1
1
1
2
2
1
1
1
0
0
2
1
1
1
0
0
2
2
0
1
2
1
0
0
2
0
4
1
2
2
2
2
2
1
1
2
1
0
1
0
0
1
2
0
1
2
1
1
3
1
0
0
0
2
0
1
1
1
2
1
2
0
2
1
1
0
2
0
3
0
1
0
0
2
2
1
0
1
1
1
1
0
1
1
1
2
1
1
0
1
2
0
1
2
0
0
1
1
1
2
0
1
0
2
0
0
0
1
1
0
2
0
2
0
1
0
4
0
1
1
1
1
1
0
3
0
1
1
1
1
0
1
3
1
2
1
1
0
1
1
0
0
1
1
1
1
0
1
0
0
2
1
0
1
2
0
1
1
2
1
2
1
1
2
1
0
3
1
0
1
2
0
1
1
0
1
2
1
0
1
1
0
1
0
2
1
0
1
2
1
0
1
1
0
2
1
1
1
1
2
0
0
1
1
1
1
1
2
0
1
0
1
1
0
2
2
3
1
0
2
0
2
0
1
0
0
2
8
1
0
2
1
2
0
2
2
2
0
1
1
1
2
1
1
0
1
0
0
0
1
1
0
2
0
0
1
0
2
0
0
1
0
1
2
1
1
0
1
1
0
1
1
1
0
0
0
0
1
2
1
2
1
1
0
0
0
1
2
0
1
1
2
1
1
2
1
1
1
0
2
1
0
2
0
1
0
0
1
1
0
1
2
1
1
1
0
0
0
1
0
1
2
0
1
1
1
2
2
1
1
2
2
2
2
2
2
0
2
0
0
1
1
1
2
1
0
2
0
0
0
2
1
0
2
0
1
0
0
2
1
1
0
1
1
0
0
0
0
0
1
2
1
1
1
1
0
1
1
2
1
0
0
2
1
1
2
1
1
1
2
1
1
0
1
1
1
2
1
1
0
0
1
2
1
2
0
0
1
1
1
1
0
1
2
2
1
2
0
1
0
1
2
1
1
1
1
1
2
2
1
1
0
2
1
1
0
1
2
0
0
2
0
0
1
2
0
1
2
1
0
0
0
0
1
1
1
2
2
2
1
2
1
0
2
1
1
0
0
1
0
1
1
0
2
1
1
0
1
1
0
1
2
1
0
1
1
0
1
2
2
1
1
1
0
2
1
0
1
0
1
0
0
1
2
1
0
1
1
1
0
2
2
1
1
0
1
1
1
0
0
2
1
0
1
1
1
2
1
1
1
2
1
1
0
1
0
0
1
0
2
0
1
2
2
0
0
0
1
0
0
0
2
2
2
1
0
1
1
0
2
1
0
1
1
1
0
2
2
0
1
0
2
1
0
1
0
1
1
0
2
2
1
2
1
0
0
6
1
1
1
2
1
2
0
2
0
1
1
0
0
2
1
0
1
1
1
4
1
2
1
1
1
1
1
0
0
0
0
1
1
0
0
0
1
1
1
0
1
1
1
0
1
1
3
2
1
1
2
2
2
2
1
2
2
0
1
1
2
1
1
2
1
1
0
1
2
1
1
2
1
1
0
0
0
1
0
2
1
1
0
1
1
0
0
0
1
2
0
1
2
2
1
4
1
1
0
0
1
0
1
0
1
1
1
2
2
1
1
1
0
1
1
1
0
0
2
1
1
0
0
3
0
1
1
0
0
0
2
0
0
1
0
2
1
2
1
1
0
2
1
1
1
1
0
1
1
0
0
2
0
1
2
0
1
1
1
2
1
1
0
2
2
1
0
2
1
0
0
1
0
2
0
2
0
1
0
1
1
2
1
2
2
0
0
0
0
1
1
1
2
1
1
0
2
0
1
1
0
0
2
0
0
1
1
0
2
0
1
0
1
2
2
1
2
0
1
1
0
1
1
1
1
0
0
1
1
0
2
1
1
2
1
1
1
0
2
1
2
0
0
1
1
0
0
1
2
1
0
2
0
1
0
2
0
0
1
0
0
2
0
2
1
1
1
1
2
1
0
2
2
1
1
0
1
1
2
1
2
0
1
2
1
0
2
1
0
1
2
1
1
0
2
0
1
0
1
2
2
1
2
0
0
0
1
2
1
0
0
1
1
1
2
0
1
2
2
0
1
2
0
1
1
1
1
1
1
1
5
1
0
1
0
2
1
0
1
0
0
1
1
1
1
2
1
0
1
2
1
0
0
1
0
1
1
1
0
1
2
1
1
0
1
0
2
1
0
0
0
1
0
1
1
2
1
1
1
1
1
0
0
1
2
0
2
2
0
0
2
0
1
1
2
0
2
1
0
1
1
1
1
1
1
0
1
1
1
1
0
3
1
1
1
2
1
2
0
0
1
1
1
0
2
0
1
1
0
1
0
2
1
1
1
0
0
1
1
0
1
1
0
3
6
1
0
0
1
0
1
0
2
0
1
1
1
1
2
0
1
2
1
1
1
1
0
1
2
1
1
0
1
1
0
1
1
2
1
0
1
1
1
2
1
0
0
2
1
0
1
1
1
0
0
2
1
1
2
1
0
1
2
1
1
0
1
3
0
2
1
0
2
0
1
2
1
1
1
0
1
1
0
0
0
1
2
2
1
1
0
0
1
0
1
2
1
1
3
1
0
2
1
0
1
0
1
2
1
0
1
0
3
0
0
1
1
0
1
1
0
1
1
2
1
1
2
0
1
1
2
1
0
1
0
1
1
0
1
1
1
1
2
0
0
0
1
0
0
2
0
2
0
2
0
0
1
1
0
1
2
1
0
2
1
1
1
2
1
0
0
3
2
1
0
2
1
1
2
0
0
1
1
2
0
1
2
0
2
2
1
1
0
1
1
2
1
0
1
1
1
1
3
2
2
1
2
1
1
2
0
1
3
1
1
1
2
1
1
0
0
1
0
0
1
1
2
2
0
1
1
0
0
2
1
0
2
1
1
1
0
0
2
1
1
1
0
1
0
1
1
1
1
1
1
2
2
1
2
1
0
0
0
1
0
1
0
1
2
1
0
0
0
1
1
0
0
1
0
1
2
0
1
1
0
0
1
1
2
1
0
1
1
1
2
1
1
1
1
1
0
1
1
0
0
1
1
1
0
0
0
0
0
0
1
1
1
2
1
2
2
2
1
2
1
2
1
1
1
3
1
1
2
1
2
0
3
2
1
2
1
2
1
2
0
0
1
1
0
1
1
0
0
0
2
0
1
2
1
1
0
2
2
0
1
1
1
2
1
1
0
0
0
1
0
0
0
1
0
0
2
0
2
0
2
1
1
1
1
1
0
0
0
0
1
1
0
0
0
2
1
2
0
0
1
1
1
0
0
1
0
1
0
0
4
0
1
1
0
2
1
1
0
1
2
2
1
1
1
1
0
1
2
2
2
1
0
0
0
1
0
0
0
1
1
2
1
1
0
1
1
1
1
0
1
1
1
1
2
0
0
1
1
2
1
1
1
0
2
1
2
1
1
1
1
1
0
1
0
2
3
0
0
1
0
2
2
1
1
0
0
1
2
1
0
0
0
0
0
1
1
0
1
0
1
1
3
2
2
1
0
0
1
0
0
0
2
1
2
0
1
0
1
1
0
1
1
1
1
1
1
0
0
2
0
1
0
0
1
1
0
2
1
1
1
2
1
2
1
0
1
1
1
1
2
3
1
1
1
1
2
0
1
1
0
1
1
1
0
0
1
1
1
1
1
2
1
0
2
1
2
1
1
0
1
0
0
1
0
3
1
1
2
1
2
2
0
1
1
2
1
1
1
1
1
1
0
1
0
1
1
1
0
1
0
0
1
1
1
1
1
1
1
1
2
1
1
0
1
1
1
2
0
1
0
0
0
2
1
1
1
1
0
0
2
0
0
0
1
1
1
0
1
2
1
0
1
1
1
0
1
1
0
1
1
1
1
0
0
1
0
0
1
1
1
1
0
2
0
0
1
2
0
1
0
1
1
0
2
0
1
1
1
2
1
0
2
0
0
0
1
0
2
1
2
0
1
1
0
1
1
0
2
2
1
3
0
1
0
1
2
0
1
2
0
1
2
1
0
1
1
1
2
1
0
0
1
1
0
2
0
2
1
1
0
1
1
0
2
0
1
0
0
2
2
1
0
0
2
1
0
1
1
1
1
1
1
2
0
1
0
1
1
0
1
1
1
1
2
1
0
0
0
2
1
0
1
1
0
2
0
1
1
2
0
1
2
0
1
0
1
0
0
1
0
0
2
2
0
1
1
1
1
0
1
2
2
1
1
1
0
4
2
0
1
0
2
0
1
0
0
0
0
0
2
0
2
0
0
1
0
1
1
1
0
0
0
0
0
1
1
1
1
1
0
2
2
0
0
1
1
2
4
1
0
1
2
0
0
0
1
1
1
2
1
1
2
1
0
1
1
0
0
0
0
2
1
1
2
3
0
1
1
0
1
1
0
2
2
1
1
1
1
0
1
2
1
0
1
1
0
0
2
2
0
1
2
1
1
1
0
2
1
1
1
2
1
0
0
0
2
1
2
1
0
0
1
1
0
0
1
2
0
2
1
1
0
1
0
1
1
0
1
1
2
0
1
2
1
0
0
0
0
1
1
1
2
1
1
0
1
1
2
2
1
2
1
1
0
2
2
0
1
1
1
0
1
2
1
1
0
1
1
2
1
1
2
2
2
0
2
0
2
0
0
1
2
0
0
2
0
0
0
1
0
0
1
1
0
2
1
2
2
1
0
0
1
2
1
1
1
1
0
0
1
1
0
0
2
0
2
0
1
2
1
1
0
1
1
0
2
2
1
1
2
1
1
1
2
0
0
1
0
0
1
1
2
1
1
2
2
0
1
1
1
2
2
1
0
1
2
2
1
1
2
1
0
2
2
0
1
0
2
0
1
2
2
0
1
2
1
1
2
2
0
1
2
1
1
1
1
0
1
0
0
2
1
1
0
0
0
1
1
2
2
2
2
1
1
1
1
2
2
1
1
1
1
2
1
0
0
2
0
0
2
0
0
1
1
2
1
1
1
1
1
0
1
1
1
1
2
1
2
1
1
1
1
2
0
2
1
2
2
2
0
1
0
0
1
0
1
1
2
1
0
0
0
1
1
1
0
0
1
1
1
1
0
1
3
1
0
1
0
0
1
2
0
2
0
1
0
2
2
0
2
1
1
1
0
0
1
1
0
0
1
0
1
2
2
1
1
2
1
0
1
0
1
1
1
1
1
1
0
0
1
1
0
1
0
2
2
2
1
2
1
1
0
2
0
2
1
0
0
1
0
1
2
0
2
0
1
0
1
2
1
0
0
2
2
2
1
2
2
0
1
3
1
0
1
0
0
1
0
1
1
1
0
1
2
0
1
1
1
1
1
1
2
2
0
2
1
1
1
1
0
2
1
1
0
0
0
2
1
1
1
0
1
0
0
1
1
1
0
1
1
1
2
1
1
1
1
1
0
1
2
2
0
1
1
0
1
1
0
0
2
3
1
1
0
1
2
1
2
1
2
1
0
2
1
2
0
0
1
0
0
2
2
1
0
1
1
1
1
0
2
2
1
2
0
1
0
1
2
1
2
1
1
0
1
1
1
1
2
0
2
1
0
1
1
1
1
1
0
1
0
1
0
1
1
0
2
1
0
0
1
1
0
0
1
0
1
0
2
0
2
2
1
0
3
2
2
1
1
2
0
0
1
0
2
0
3
1
1
1
1
1
1
0
1
1
2
1
0
1
1
1
1
2
1
2
2
0
1
1
1
1
2
1
1
1
2
2
1
0
2
1
2
1
1
1
0
1
0
0
1
2
1
0
0
2
0
1
0
1
3
0
0
0
1
2
1
2
1
1
0
1
1
0
0
2
1
1
0
2
0
1
1
2
1
1
1
0
0
0
1
1
2
1
1
1
1
0
1
0
3
0
1
1
1
0
0
2
1
0
1
1
0
1
0
0
1
1
0
1
0
1
3
2
1
0
1
2
0
1
2
2
0
3
1
1
2
1
1
0
2
1
1
0
1
1
1
2
2
0
1
1
1
2
1
1
2
2
1
0
2
0
0
0
0
1
1
1
1
0
1
1
1
1
1
1
1
1
1
0
0
2
1
0
2
2
0
1
1
2
2
1
1
1
0
2
2
1
1
2
1
2
2
2
1
0
2
1
1
2
0
1
2
1
1
1
1
0
0
0
1
1
1
2
0
2
0
0
1
1
0
1
1
1
2
1
0
0
1
0
1
2
1
0
1
5
0
0
2
1
1
1
1
1
0
1
0
0
1
1
1
0
1
1
0
0
0
0
0
0
1
2
2
1
1
1
2
0
1
1
0
1
1
0
2
0
1
1
0
2
1
4
1
0
0
1
1
1
0
3
1
1
0
1
1
1
2
1
1
0
2
4
2
1
2
1
1
2
1
1
1
2
1
2
1
2
1
0
1
2
1
1
1
0
1
1
1
1
1
1
2
2
1
1
0
1
0
0
1
1
3
0
1
2
1
1
1
1
1
1
2
2
1
1
1
1
0
0
2
0
2
0
1
0
0
1
0
0
0
1
1
3
0
0
1
1
0
0
0
1
2
0
2
1
1
1
1
1
2
1
1
1
2
0
1
2
1
0
0
1
2
1
0
0
2
0
2
1
1
1
1
0
0
2
1
1
1
5
0
1
0
1
1
3
0
0
1
1
1
0
1
1
1
0
1
2
0
1
1
0
0
1
1
0
1
0
1
0
1
0
0
0
1
1
2
2
1
1
1
2
1
1
1
0
2
0
1
0
3
2
1
2
0
1
2
2
1
0
2
1
1
2
1
1
0
0
1
0
0
0
0
0
0
1
1
1
2
0
0
1
2
1
0
0
0
1
2
1
2
2
1
1
0
1
0
1
0
0
2
1
0
2
1
3
0
0
2
2
1
1
1
1
1
0
1
1
1
0
1
2
1
0
1
0
2
0
2
1
1
2
1
1
2
2
1
1
1
0
2
1
1
0
2
1
1
1
1
2
0
1
0
0
1
0
2
0
0
6
2
3
1
0
0
1
2
0
0
0
0
2
1
1
1
2
0
0
0
1
0
2
2
1
1
0
1
1
2
1
0
1
2
1
0
2
2
0
2
2
0
1
1
2
2
2
1
2
0
0
1
2
1
2
1
0
0
1
0
2
1
2
1
0
1
1
1
2
1
0
1
2
0
1
1
1
0
2
1
2
2
1
2
1
1
2
2
2
1
1
1
1
0
1
1
0
2
1
2
1
0
1
1
2
1
1
1
1
0
0
0
2
0
2
0
2
0
0
1
0
2
0
0
1
0
1
0
1
1
1
2
1
2
1
1
1
2
1
0
0
0
0
0
1
2
1
1
1
1
0
2
2
1
4
1
0
1
1
2
2
1
0
0
1
0
1
0
0
0
0
1
2
0
2
1
1
1
2
0
1
2
1
1
0
1
2
0
1
1
1
0
0
1
1
1
0
1
0
1
1
1
0
1
0
0
1
1
1
1
1
0
1
0
1
0
1
0
1
2
1
1
0
1
2
1
1
0
0
0
0
2
0
0
0
1
1
0
1
2
0
1
1
1
0
0
0
2
0
1
0
2
1
1
1
0
1
0
1
2
1
1
0
1
0
1
1
1
1
3
2
0
0
0
1
1
1
1
0
1
2
2
2
0
0
2
0
1
0
0
1
0
0
1
2
0
1
0
1
0
1
2
1
0
0
1
1
0
0
0
0
2
0
1
1
2
1
0
0
1
0
0
1
2
0
1
2
0
1
1
1
0
0
0
1
2
1
1
2
1
1
0
0
0
2
0
1
1
0
2
1
1
1
1
1
0
0
2
1
0
2
0
0
0
1
2
1
0
0
1
0
0
0
0
1
1
2
2
0
1
1
2
1
2
0
1
2
2
1
1
0
1
0
1
0
2
2
1
1
0
0
0
1
1
1
1
1
0
1
2
1
2
1
0
1
1
0
2
0
2
1
0
1
1
1
0
0
1
1
3
2
0
2
2
0
1
1
2
2
0
2
1
1
0
1
1
0
0
2
0
1
1
2
0
0
1
0
1
2
1
1
0
0
3
0
1
0
0
1
1
1
0
1
0
1
0
1
2
2
2
1
1
0
0
1
2
1
0
1
1
1
1
1
1
2
1
1
0
1
0
1
1
1
0
1
1
0
0
0
2
0
1
1
0
1
1
2
1
1
0
1
0
2
1
1
0
1
0
2
2
2
1
0
1
1
2
0
1
0
1
1
0
1
1
2
1
0
0
2
0
1
0
1
2
0
1
2
1
0
2
1
1
1
2
1
1
1
1
1
1
2
0
1
1
0
1
1
1
0
1
0
1
2
0
2
1
2
1
1
1
2
1
1
0
1
2
2
0
0
0
0
2
2
1
1
0
0
2
0
1
0
3
0
2
0
1
1
0
1
0
0
2
0
1
0
1
1
1
2
2
0
0
1
2
1
1
1
0
1
0
1
1
2
0
0
1
1
0
1
0
0
0
2
1
2
0
1
1
2
1
0
2
0
1
1
0
1
1
2
0
1
0
2
1
1
1
1
0
2
2
1
1
2
1
2
1
2
2
0
1
1
1
3
1
1
1
1
1
1
0
1
1
1
0
1
0
2
3
1
2
1
2
0
0
1
2
1
1
2
0
1
4
2
1
2
1
0
1
0
2
0
1
0
1
0
2
1
0
0
2
1
1
0
1
2
1
1
1
1
1
2
0
1
0
0
1
0
1
1
1
0
0
0
1
0
4
0
2
0
0
1
1
1
1
1
0
1
0
0
2
1
0
2
0
1
1
0
2
1
0
1
1
1
1
1
0
2
2
0
1
1
1
0
0
0
4
0
2
0
1
2
2
2
1
1
2
1
1
1
0
2
1
1
0
1
1
0
0
0
2
1
0
0
2
2
1
1
0
0
2
0
2
2
0
1
0
1
1
0
1
1
0
2
1
2
1
1
1
0
1
1
1
1
0
0
1
0
0
1
1
1
0
1
1
0
0
0
1
1
2
3
2
1
0
1
1
1
2
0
1
0
1
0
1
0
0
1
0
1
2
1
0
0
1
1
1
0
0
0
0
0
0
1
1
2
0
1
1
1
1
1
0
2
1
0
0
0
1
1
1
0
0
1
1
1
1
2
1
0
0
2
2
1
0
1
0
1
0
1
1
0
0
1
1
0
2
0
2
0
1
1
1
4
0
0
0
0
0
1
1
1
1
1
2
2
1
0
0
1
1
0
2
3
0
1
0
2
0
0
1
2
2
1
0
0
2
0
2
1
1
2
1
1
0
2
1
2
1
2
0
2
2
1
1
0
0
0
2
1
1
0
1
1
2
2
0
0
0
1
2
0
1
2
1
1
2
0
2
1
0
1
1
2
0
1
1
1
1
1
0
0
1
2
1
1
1
2
2
1
1
0
2
1
0
1
0
1
1
0
1
0
0
2
0
0
1
2
0
1
1
1
1
1
2
3
0
1
1
2
1
0
0
1
1
1
2
1
2
0
0
2
1
1
0
1
0
1
1
0
0
1
0
2
0
1
0
0
0
0
0
2
0
1
0
2
0
0
1
2
0
1
2
0
0
1
2
2
0
0
2
0
0
2
1
0
1
0
0
0
2
1
1
0
0
1
1
1
1
0
0
1
0
2
0
1
0
2
1
1
0
1
1
0
0
1
2
1
0
1
1
0
1
1
1
1
1
1
2
2
0
1
1
0
0
1
2
0
1
2
0
1
0
1
0
1
2
0
1
0
1
1
0
2
2
0
1
1
0
1
0
1
0
1
1
1
1
0
0
0
1
0
0
2
0
2
3
1
0
0
1
0
1
1
0
2
1
1
2
0
1
1
2
1
1
1
1
1
0
1
1
1
0
0
0
2
0
0
1
0
0
0
1
1
0
0
1
2
0
1
2
2
1
2
2
1
2
1
0
1
0
1
0
0
0
2
0
2
0
2
0
2
0
1
0
0
1
1
1
2
1
1
1
1
0
0
2
0
0
1
1
0
0
1
1
0
2
2
2
1
1
0
1
1
3
1
0
1
1
1
1
0
2
1
0
0
0
2
0
0
1
1
1
1
1
0
0
0
0
0
1
0
1
1
0
0
2
2
1
0
1
2
0
0
0
1
2
2
2
0
0
2
2
1
1
1
1
2
0
1
1
1
1
1
1
2
2
1
0
1
0
1
0
0
1
1
1
1
1
1
0
1
2
1
2
0
0
1
1
1
2
0
2
1
1
1
1
1
1
1
1
1
2
2
1
1
0
1
1
1
1
0
0
0
1
1
2
2
0
0
0
0
2
0
0
0
1
2
0
0
0
2
4
2
2
1
0
1
1
1
0
0
2
1
2
2
2
0
0
1
1
1
2
1
1
0
1
1
0
3
1
2
0
1
2
1
1
1
2
3
2
1
1
1
1
0
1
1
1
2
1
2
1
2
0
1
2
1
0
1
1
1
2
0
2
1
0
1
1
0
2
1
1
0
1
0
1
1
1
0
2
1
2
1
1
1
0
1
1
0
1
1
1
1
1
0
0
1
1
1
1
0
0
1
1
1
0
2
1
1
2
1
0
1
1
1
1
0
1
1
0
1
1
1
3
0
2
1
2
2
0
2
4
2
1
0
1
0
0
1
2
1
1
1
1
2
1
2
0
0
0
1
1
1
0
2
0
1
1
2
1
2
0
0
0
1
1
0
0
0
1
1
1
1
0
2
2
0
2
3
1
0
0
2
0
1
2
0
1
1
0
1
2
2
0
1
2
0
2
2
2
0
0
1
0
1
1
2
2
1
2
1
1
0
1
1
1
0
1
0
2
0
2
0
0
0
0
1
1
1
1
1
1
1
0
1
0
1
1
2
0
2
2
2
0
0
1
1
2
0
1
2
0
0
1
1
1
1
2
1
1
1
0
1
2
2
1
0
1
1
0
0
1
1
0
0
2
1
2
1
2
0
0
1
0
0
2
0
1
2
0
0
1
1
0
1
2
0
1
1
1
1
0
1
2
1
1
2
0
1
0
0
1
1
1
1
2
1
0
0
1
0
2
1
1
1
2
1
1
0
1
1
0
1
1
1
1
0
0
2
1
0
0
1
1
2
0
2
2
1
1
1
1
1
1
1
0
0
0
2
1
2
1
1
0
0
1
2
0
0
0
0
2
0
0
1
1
1
1
1
0
0
2
1
2
2
0
0
1
2
2
1
1
1
0
0
1
1
1
1
1
2
1
1
0
2
0
2
0
1
1
1
1
0
2
1
1
0
2
1
2
1
1
1
1
0
1
2
1
1
1
2
1
3
1
1
2
0
0
1
2
2
1
1
1
1
0
1
0
1
1
2
1
0
1
0
1
1
1
1
2
1
0
0
2
0
1
2
1
1
1
2
1
2
1
1
3
0
0
2
1
1
2
1
0
0
0
0
1
0
2
1
0
2
1
1
1
1
0
1
1
0
1
2
0
1
1
0
1
1
2
1
1
3
0
0
1
2
1
1
0
0
0
1
0
1
2
0
1
1
1
0
0
1
2
1
0
2
1
0
1
2
0
2
1
0
2
1
1
1
0
1
1
0
1
1
0
0
0
1
2
0
2
2
1
0
0
0
0
0
1
0
1
2
0
1
2
1
0
2
1
2
1
0
1
1
1
2
1
1
1
1
1
0
0
0
2
1
0
0
0
0
0
1
1
0
0
1
0
0
2
1
1
2
2
1
2
2
2
1
1
1
2
1
2
1
0
1
0
2
0
1
1
1
1
2
0
1
0
1
1
0
0
1
1
2
0
1
0
1
1
0
2
0
0
0
1
0
0
0
1
2
2
0
0
0
1
1
0
1
0
1
1
2
0
1
4
1
2
4
0
0
1
1
1
0
0
1
1
0
0
2
2
1
2
0
1
0
1
1
1
1
1
2
0
1
1
1
1
0
1
2
0
2
1
0
2
1
1
2
1
1
0
2
2
1
1
1
1
2
0
2
0
2
0
1
0
0
0
0
1
0
1
0
2
2
1
1
2
2
0
0
1
2
2
1
2
0
1
2
0
0
1
1
1
2
1
1
1
0
0
1
1
1
2
0
1
0
1
0
1
1
0
1
2
1
0
2
0
0
1
1
1
0
0
2
1
1
1
0
0
1
0
1
1
3
2
1
0
1
1
1
2
0
0
0
1
0
0
0
0
1
1
0
0
1
1
0
0
1
0
1
2
2
2
1
1
0
1
1
1
0
0
1
1
2
2
1
0
1
1
1
0
0
0
1
1
1
1
1
2
0
0
1
0
1
2
0
2
1
0
1
1
1
0
1
2
1
0
1
0
2
2
1
2
0
0
1
0
10
1
2
0
1
1
1
1
0
1
2
1
1
1
1
1
1
0
2
1
1
1
0
0
1
1
2
2
0
1
2
1
0
1
1
1
0
1
2
1
1
2
1
0
2
2
1
2
1
1
0
0
1
2
0
0
0
1
1
1
0
1
0
2
2
0
0
0
0
1
1
0
1
2
1
2
2
1
2
2
0
1
3
2
0
0
0
1
0
1
2
0
1
0
2
0
1
0
1
1
2
0
1
1
2
0
2
0
1
2
2
1
0
1
0
2
1
1
0
1
0
1
2
1
3
1
2
1
1
1
1
0
1
2
0
2
1
0
1
0
1
1
1
1
2
2
1
1
2
2
0
0
1
0
1
0
1
0
1
2
2
0
0
1
1
0
1
1
1
1
0
1
1
0
2
1
0
1
0
0
0
0
1
2
2
0
1
1
0
0
2
0
1
1
0
2
1
0
0
1
1
0
2
0
1
0
2
0
0
0
1
2
2
0
2
2
0
1
2
1
0
1
1
1
0
0
1
1
1
1
0
0
0
1
1
1
1
2
1
0
1
0
1
0
1
1
1
2
0
0
3
1
2
0
2
1
1
0
1
1
1
2
1
1
0
0
0
0
0
1
1
2
0
1
1
0
0
0
0
2
2
1
0
1
1
1
2
2
0
2
0
2
1
1
1
1
1
0
1
0
1
0
0
1
1
1
0
1
1
1
2
1
0
2
0
1
0
1
1
1
2
1
1
0
1
3
0
0
1
1
1
1
1
0
1
0
1
1
0
1
2
0
1
2
0
1
2
0
1
1
1
1
0
1
1
1
0
1
2
2
0
2
2
1
1
0
0
1
1
1
1
1
2
2
1
2
2
1
1
0
1
1
0
1
1
0
0
1
0
0
1
1
2
1
0
2
2
1
0
2
2
0
1
1
1
0
0
0
1
1
1
0
1
1
2
1
0
0
0
2
0
2
2
1
0
2
0
0
0
2
4
2
2
1
1
1
0
2
0
1
2
1
2
1
0
1
1
0
1
2
1
1
0
1
3
0
0
3
0
1
2
0
0
1
1
1
0
2
1
2
1
1
1
0
1
0
1
1
0
0
2
1
0
2
1
1
1
0
1
1
0
0
0
0
1
0
2
2
0
1
0
1
1
1
0
1
1
1
0
0
1
0
0
0
0
1
1
2
0
0
1
1
1
1
2
1
2
2
0
0
1
1
1
1
1
2
0
0
0
2
1
2
2
2
1
2
1
1
1
0
1
0
0
1
1
1
1
1
0
0
0
2
1
1
1
1
0
1
0
1
2
0
1
1
2
2
2
0
1
2
2
1
2
0
2
1
1
0
1
1
1
1
0
1
2
0
1
0
2
0
0
1
1
1
1
2
0
2
1
1
1
1
1
0
1
0
1
1
0
0
1
0
0
1
1
0
1
0
1
2
0
1
2
2
2
1
1
0
1
1
0
0
1
0
1
2
1
0
1
0
0
0
0
1
2
1
4
1
1
1
2
0
1
0
1
1
0
2
0
0
1
2
1
2
1
0
2
1
1
1
0
1
2
2
0
2
1
1
2
1
1
0
1
2
0
1
6
0
0
1
1
1
0
2
0
0
0
0
0
1
1
0
1
1
1
2
2
1
2
1
2
0
2
0
1
1
0
2
1
2
1
0
1
2
1
1
0
2
0
2
0
0
1
1
1
1
1
1
2
1
2
1
1
2
0
2
0
0
1
0
1
0
1
2
0
1
0
0
1
1
0
0
1
2
1
0
1
0
0
0
2
1
1
2
0
1
1
2
0
1
1
2
0
1
0
1
2
0
1
1
0
0
3
1
1
1
0
0
0
1
1
1
0
1
1
1
1
1
0
2
0
0
1
1
0
1
0
0
1
1
0
1
0
0
0
2
0
0
1
1
1
1
2
0
1
1
0
2
0
0
0
1
0
1
1
1
1
1
0
0
0
1
0
0
1
0
2
2
0
2
0
1
0
2
1
0
2
1
0
2
1
0
2
2
1
0
1
1
1
1
1
0
1
1
4
2
1
0
0
0
0
1
1
1
3
2
1
1
0
1
0
2
1
2
0
1
0
0
2
1
0
0
0
1
1
1
0
1
1
1
0
1
0
1
1
1
1
1
0
1
1
2
0
1
0
2
2
0
0
0
1
1
1
2
0
0
2
0
0
0
2
1
0
2
2
3
2
1
1
2
1
0
0
1
1
1
1
2
0
1
1
1
2
1
1
2
0
0
0
0
2
0
0
0
1
0
1
2
3
1
3
1
2
2
1
1
1
0
1
0
1
1
2
0
0
1
1
1
1
0
2
1
2
0
1
1
1
0
0
0
1
1
0
1
0
1
0
1
0
1
0
2
0
1
1
0
0
0
2
1
0
2
1
2
1
2
2
2
0
1
1
0
2
1
0
0
0
1
3
0
0
1
0
0
2
0
2
1
0
1
2
1
2
2
0
0
2
2
1
2
1
0
0
1
0
0
0
2
0
1
0
2
2
1
1
1
3
1
1
0
2
0
0
2
2
1
1
1
1
2
1
0
1
0
0
2
0
2
0
0
1
1
1
1
0
1
2
1
1
0
1
1
1
1
1
0
0
0
0
2
1
1
1
0
2
1
1
0
2
0
1
1
0
1
1
0
4
1
2
0
0
1
0
0
0
1
0
0
1
1
1
0
3
0
1
1
1
2
0
0
0
1
1
1
1
0
1
1
0
0
1
1
1
2
0
2
1
0
1
1
1
1
1
1
2
1
1
0
1
0
1
0
0
1
1
0
1
0
2
2
1
2
1
0
0
1
1
0
1
1
1
0
1
1
1
1
1
0
2
0
0
1
1
4
0
2
1
0
1
0
1
1
1
1
1
0
0
2
0
3
1
0
1
2
1
0
2
0
1
1
1
1
2
2
2
1
1
1
1
1
0
1
1
1
0
0
1
3
0
2
1
2
1
2
1
1
0
1
2
1
1
1
1
1
2
2
1
1
1
0
1
2
2
0
0
1
0
1
2
0
2
0
1
0
0
0
0
0
0
0
0
1
2
1
0
1
1
1
1
0
1
0
1
0
1
2
1
1
1
2
1
1
1
0
2
1
1
0
1
2
0
2
1
1
0
1
1
1
1
1
1
2
2
1
3
1
0
0
1
2
1
1
0
0
0
0
1
2
1
1
1
1
0
0
1
0
1
1
1
1
2
2
1
1
0
0
2
1
2
0
1
1
0
2
2
1
1
2
0
1
0
2
0
0
1
1
1
2
1
0
2
0
0
1
0
0
1
0
0
1
0
1
0
0
1
1
0
2
0
2
1
0
0
2
0
1
0
1
1
0
1
1
0
0
1
2
1
0
0
1
1
1
0
0
1
2
1
1
0
2
1
1
1
0
0
1
2
1
0
2
0
2
1
1
2
0
1
0
1
1
0
0
0
0
2
2
2
0
0
1
0
1
2
2
1
2
1
1
1
0
0
2
1
0
0
0
0
1
2
1
0
0
1
1
0
1
1
0
2
2
1
2
1
1
1
0
0
1
1
1
0
1
1
1
0
1
0
0
0
2
0
1
2
1
1
0
0
2
2
1
3
1
0
0
1
1
0
1
0
0
0
1
1
2
1
1
0
0
3
2
1
0
0
1
1
0
0
0
0
1
2
4
1
0
1
0
2
1
2
1
1
0
1
1
0
2
1
0
1
1
1
0
0
0
1
2
1
1
2
0
2
2
1
3
0
1
0
0
0
2
1
1
1
2
0
1
0
0
1
1
0
1
1
1
0
1
2
0
0
1
1
1
0
0
1
0
0
2
1
1
0
2
1
1
2
1
1
0
0
2
0
2
0
1
1
0
0
1
0
2
1
1
0
1
2
0
1
1
1
2
1
0
2
1
1
1
0
0
0
0
1
1
0
0
2
0
1
1
0
0
0
1
2
1
1
1
0
2
2
1
2
1
0
1
1
2
1
1
1
1
1
0
1
1
1
2
1
1
2
2
2
1
1
1
1
0
0
2
1
0
0
1
0
2
0
0
1
1
1
0
2
1
0
2
0
1
0
0
0
0
1
0
2
1
0
0
0
1
0
1
1
1
2
2
1
0
0
2
0
1
1
1
2
0
1
1
0
1
2
1
1
0
0
0
0
0
2
0
2
0
1
0
2
2
1
1
1
0
0
3
2
0
2
0
1
1
1
0
2
0
0
1
1
0
2
0
2
7
2
1
2
2
2
0
0
1
1
0
0
1
1
1
0
2
1
1
0
0
0
2
0
0
0
1
1
2
0
2
1
1
1
1
2
0
0
0
1
1
1
0
2
0
1
1
0
1
0
1
1
1
0
1
1
0
1
0
2
1
0
0
0
1
1
2
2
1
2
0
0
0
1
0
0
2
1
1
1
2
2
2
1
0
1
1
0
0
1
1
0
2
2
1
1
0
0
2
1
1
1
0
2
0
4
0
2
2
0
2
0
1
1
0
1
1
0
0
2
2
1
2
2
2
2
1
1
2
1
0
2
1
1
1
1
0
2
1
1
1
1
1
2
1
2
0
0
2
1
1
0
0
1
2
1
0
2
0
1
1
4
1
1
0
0
0
1
0
0
1
0
1
2
1
1
2
1
0
1
2
2
1
2
0
1
1
2
1
1
1
0
1
0
0
0
1
0
1
1
1
2
1
1
2
1
2
1
2
2
0
2
3
0
1
2
0
0
2
1
0
1
1
2
2
1
1
1
1
0
1
0
0
1
0
1
0
1
1
2
0
1
1
2
1
1
0
0
1
1
1
0
0
1
0
0
0
1
1
2
1
1
0
0
2
0
2
1
0
0
2
0
0
1
2
2
0
1
0
2
1
0
0
0
0
3
1
0
0
0
1
2
1
0
0
1
0
2
1
2
1
1
2
1
0
1
0
1
0
1
1
1
1
1
1
0
0
2
0
2
1
0
1
2
1
0
1
0
2
1
1
1
2
1
0
1
1
1
0
0
1
2
2
0
0
1
0
2
0
0
1
0
1
1
1
2
1
1
1
1
0
1
0
2
0
1
1
0
0
1
1
0
0
1
0
2
0
0
0
0
0
1
1
1
1
1
2
2
0
1
0
0
1
2
3
0
0
0
1
1
1
0
0
0
1
1
1
0
1
0
1
0
1
0
0
1
1
4
1
1
1
0
1
1
0
2
2
8
1
2
1
1
2
0
1
1
2
2
1
1
1
1
2
1
0
1
2
1
1
1
0
1
1
0
0
2
1
1
1
1
3
2
0
1
0
0
0
0
1
0
2
0
0
1
0
1
2
1
2
1
1
0
1
0
1
0
1
0
1
0
0
1
2
1
0
0
3
1
2
0
1
1
2
0
2
2
1
1
2
1
1
0
0
1
3
1
1
0
2
1
0
2
0
2
0
2
2
0
2
0
0
1
2
1
2
1
1
1
0
2
1
1
2
4
0
0
1
1
1
2
1
1
2
0
1
2
1
1
0
2
0
1
3
2
0
2
2
1
1
0
1
1
0
2
1
0
0
1
0
2
2
2
1
1
1
0
2
1
1
1
2
0
1
1
2
0
0
0
1
0
1
1
0
1
2
0
1
1
1
1
0
1
0
0
1
1
0
0
1
2
0
1
2
2
1
1
2
0
0
3
1
1
3
1
0
2
0
0
1
0
0
1
0
1
0
1
2
0
3
2
1
1
2
0
2
0
2
1
2
0
2
2
1
2
2
0
1
1
2
1
1
1
1
0
1
1
2
2
0
2
0
1
0
0
2
1
0
0
1
0
1
3
1
1
1
0
1
2
0
2
2
3
1
2
2
0
1
0
0
1
1
1
1
2
1
0
2
2
1
1
1
1
1
0
0
0
2
1
2
1
1
2
1
2
2
2
0
2
0
2
0
1
1
1
1
1
0
2
1
2
0
1
3
1
0
1
0
0
0
2
2
1
0
0
1
2
0
2
0
2
2
0
2
0
1
0
1
1
0
1
0
0
0
1
0
1
2
1
2
2
2
1
2
0
0
0
0
0
0
2
0
0
0
0
0
1
1
1
0
1
4
1
0
0
1
1
2
1
1
1
2
1
2
2
2
2
0
2
2
0
0
1
1
0
1
2
1
1
0
1
2
2
0
1
0
1
1
1
1
0
0
1
1
0
0
1
2
1
2
0
0
2
1
1
1
1
1
0
0
2
0
1
0
2
1
0
2
0
0
0
2
2
0
0
1
1
0
2
1
1
1
2
1
1
1
0
1
1
1
1
2
0
1
1
1
1
2
2
0
1
1
0
0
1
1
2
0
2
0
2
1
0
0
2
2
0
0
0
0
5
1
0
0
0
0
2
1
2
1
1
0
0
1
0
1
2
2
1
1
1
1
1
0
2
0
0
0
0
1
0
1
0
0
2
1
1
0
1
1
0
1
0
0
1
0
1
1
3
1
0
1
2
0
1
1
2
0
0
2
1
1
1
1
1
2
1
1
1
1
2
1
1
1
0
2
1
1
1
0
2
0
1
0
0
0
1
1
2
1
1
0
0
1
1
1
1
1
0
0
0
1
0
0
1
0
1
1
0
1
0
0
0
1
0
1
1
2
0
0
1
1
1
0
1
1
1
2
2
2
0
0
2
2
2
0
1
2
1
1
1
2
1
0
4
0
1
1
0
0
2
0
2
2
1
0
2
0
1
1
0
0
2
0
0
1
1
1
1
1
1
2
2
2
1
1
1
0
1
0
2
0
0
0
1
1
0
0
1
1
2
0
1
1
1
1
0
1
0
1
0
2
2
1
1
2
0
1
2
0
1
1
1
2
2
2
0
1
2
1
0
2
0
1
0
0
0
0
0
0
0
2
1
1
1
2
2
1
4
2
1
1
2
1
0
2
0
0
1
1
1
1
0
2
0
1
1
1
2
0
0
1
1
1
1
2
0
0
1
2
2
2
1
1
2
1
0
1
1
1
1
3
1
0
2
2
1
2
2
1
0
1
2
0
1
0
2
0
2
1
0
0
0
1
0
0
2
1
2
0
1
0
2
2
0
1
1
0
1
0
1
2
1
1
1
1
1
1
1
1
0
1
2
0
0
1
2
2
1
1
0
1
1
1
1
1
1
1
2
1
2
2
0
2
0
1
1
1
1
1
0
1
0
1
0
1
1
2
0
1
1
0
0
1
2
2
0
0
1
0
0
1
0
2
0
2
0
0
1
1
0
0
2
0
2
0
2
1
1
1
0
1
1
0
1
1
2
2
1
0
0
2
0
0
1
0
0
3
1
2
0
0
1
2
2
1
0
2
0
0
0
2
0
0
1
1
1
0
1
0
2
1
1
1
0
0
1
1
2
1
1
2
0
2
1
0
1
1
1
1
0
2
2
0
1
2
0
1
1
1
2
0
0
0
1
2
1
0
1
1
0
1
1
0
3
2
0
0
1
0
1
1
0
0
0
0
1
1
0
2
1
2
0
1
0
1
1
1
1
1
1
1
1
1
1
1
1
0
1
0
1
1
2
0
0
0
1
2
0
0
0
2
1
2
2
0
1
2
0
0
0
1
2
1
1
2
1
0
2
1
0
1
0
2
0
2
2
2
2
0
2
0
0
0
1
1
0
0
0
1
1
0
1
0
1
2
1
1
0
2
2
0
2
1
0
1
1
1
2
1
0
1
0
0
0
1
0
1
0
0
1
0
0
1
0
1
1
1
2
0
1
1
0
1
0
1
0
1
2
1
1
1
1
0
0
1
1
0
0
2
1
1
0
0
1
3
1
2
0
0
0
3
1
0
0
0
1
0
0
2
1
1
2
1
0
0
1
2
2
2
0
1
0
2
0
1
2
1
1
1
1
0
1
0
1
0
1
1
1
0
1
0
2
1
2
0
1
1
0
0
0
1
1
0
2
1
2
1
0
1
2
1
1
1
1
1
0
1
2
0
3
0
2
1
0
1
0
0
2
2
0
0
0
2
0
1
2
1
0
2
0
1
2
2
1
0
0
1
2
2
0
1
2
1
5
1
2
3
0
0
0
0
0
1
2
1
2
2
0
1
2
1
2
1
0
0
1
1
0
0
0
1
1
1
2
0
1
1
1
1
2
0
1
1
3
1
1
0
1
2
1
1
0
1
0
0
2
0
2
1
1
0
1
1
0
0
0
1
1
0
2
1
2
0
0
1
1
0
2
2
3
1
1
1
1
1
0
2
1
2
1
2
1
0
0
2
2
2
0
0
0
1
1
1
1
0
2
1
1
1
0
0
1
1
1
2
2
0
0
1
2
1
0
1
1
1
0
1
1
2
0
0
1
0
2
2
0
0
1
0
1
1
2
0
2
2
1
0
2
1
1
1
1
1
0
1
0
1
1
0
0
1
2
1
2
0
1
1
1
0
2
2
0
0
0
2
1
1
1
1
0
2
1
0
1
0
1
1
0
1
1
2
1
2
0
1
0
1
1
1
1
1
0
1
2
0
2
2
1
2
0
1
1
1
1
2
2
0
1
0
2
1
0
1
1
0
0
0
0
1
1
1
1
0
1
1
2
2
0
1
0
1
1
1
1
0
1
0
1
1
0
0
1
1
0
2
2
1
1
2
0
1
1
0
2
1
1
0
1
2
1
1
0
1
0
0
1
1
1
1
2
2
0
5
2
0
9
0
2
1
1
2
2
1
0
2
1
1
1
2
1
1
2
2
1
2
1
1
3
0
1
1
0
1
1
3
0
3
2
0
0
1
0
2
2
1
0
1
0
0
2
0
0
1
1
2
1
1
1
1
1
2
0
1
0
0
2
2
2
1
0
0
2
2
1
1
2
1
2
0
1
0
1
2
3
1
0
2
0
2
2
1
0
0
0
0
1
2
1
2
1
2
1
1
1
0
0
2
0
0
1
0
0
0
2
1
2
0
0
1
2
2
1
0
0
1
2
1
2
2
2
2
1
0
2
1
0
0
0
2
1
0
1
0
0
1
1
1
1
1
0
0
2
1
1
1
1
1
0
0
1
1
1
0
1
1
0
1
1
1
0
0
1
0
2
0
0
0
2
1
2
0
2
0
2
2
1
2
0
1
0
1
1
2
1
1
0
2
1
2
0
0
1
2
0
1
0
1
0
1
2
1
1
1
1
2
2
2
1
2
0
3
2
1
1
1
0
1
1
1
1
1
2
0
0
0
1
1
1
1
0
0
1
1
1
2
0
1
1
1
2
0
1
2
0
0
1
2
2
0
1
1
1
1
0
0
2
1
2
0
0
1
0
1
1
1
1
1
2
2
0
1
2
0
0
0
1
0
0
1
1
1
2
1
0
1
2
1
4
1
0
1
1
2
0
0
1
0
0
0
1
0
1
2
0
1
1
2
1
3
0
0
2
0
1
1
1
1
1
0
1
2
2
1
0
2
0
2
0
1
0
1
2
2
2
1
1
0
1
1
2
0
2
1
3
0
0
0
1
1
1
0
2
1
3
1
0
1
1
1
1
1
3
0
1
0
2
2
1
1
0
0
1
1
0
1
0
2
0
2
2
2
0
1
1
1
1
1
2
1
1
1
1
0
2
1
0
1
0
2
1
2
1
2
2
1
1
1
1
2
0
1
1
1
0
1
0
0
0
0
1
2
2
0
1
2
2
1
1
0
1
1
1
0
1
1
1
2
0
1
1
2
1
0
2
1
1
0
1
1
1
1
0
1
1
2
2
1
1
0
0
1
1
0
1
0
0
1
0
2
0
1
1
0
0
1
1
1
0
0
1
0
0
0
1
1
0
0
2
1
0
0
2
2
1
1
1
0
1
0
2
2
0
2
1
2
1
0
1
1
1
0
0
0
1
1
2
0
1
0
1
0
2
1
1
1
1
0
0
0
1
1
1
1
0
2
1
0
0
0
0
2
1
0
0
1
0
0
0
1
1
3
0
1
2
3
1
0
2
0
0
2
1
2
1
1
2
2
1
0
0
2
1
0
0
1
0
0
1
0
0
0
1
1
1
1
0
0
2
1
1
1
2
2
0
2
1
1
0
0
0
1
0
1
1
0
1
0
1
1
2
1
1
1
1
2
1
0
1
1
1
0
2
0
2
1
2
2
0
1
2
1
2
1
2
1
0
2
1
0
2
1
0
1
1
1
1
1
0
1
1
0
0
0
2
1
1
0
2
0
0
0
1
2
1
2
2
1
1
1
0
1
0
0
2
1
1
0
1
1
1
0
1
1
0
1
1
2
2
2
2
1
0
1
2
2
1
1
0
2
1
2
2
2
2
2
2
2
1
0
1
1
0
2
0
1
2
0
1
1
2
1
1
1
1
0
3
2
2
1
1
2
1
1
0
0
2
0
0
0
0
0
1
1
1
1
1
1
0
0
2
2
0
0
2
2
0
1
1
0
1
1
2
0
1
0
2
0
1
0
2
1
0
0
0
1
1
0
1
1
0
0
0
0
1
1
1
1
0
1
2
1
0
1
1
0
1
2
0
0
1
2
1
0
0
2
1
2
0
1
1
0
0
0
0
2
1
1
1
1
1
0
1
2
1
1
1
0
1
1
1
0
2
0
1
1
1
1
2
0
1
0
1
2
0
0
1
1
0
0
0
1
0
1
1
2
2
1
0
0
0
1
1
5
0
0
2
2
1
1
1
0
1
2
2
1
3
0
2
1
0
1
0
0
0
2
0
0
1
1
1
1
2
2
2
1
1
1
1
2
2
2
0
0
0
0
0
2
0
0
0
1
1
1
1
0
1
0
2
0
0
1
0
0
1
1
1
1
2
1
0
1
2
0
1
1
0
1
1
2
0
0
2
2
2
0
1
0
0
2
1
0
1
1
1
1
1
1
1
0
0
2
1
1
1
2
0
1
0
1
0
2
1
2
1
1
1
1
0
1
1
2
1
1
1
0
1
1
0
0
2
1
1
0
0
1
1
1
0
1
2
0
2
1
2
0
1
2
1
1
0
0
0
1
0
0
1
0
1
0
0
1
1
2
1
1
1
1
1
2
0
1
1
0
0
0
1
1
1
1
1
0
1
1
1
0
0
2
2
2
0
1
1
2
1
1
1
1
0
0
0
1
1
2
0
2
0
0
1
1
0
1
2
2
1
2
1
2
2
1
1
1
1
2
1
1
1
1
2
2
1
1
0
0
0
1
1
0
2
0
2
1
0
1
1
1
1
2
0
1
0
1
0
1
0
2
0
0
0
1
1
0
2
1
1
1
1
1
1
1
1
1
3
3
0
1
0
1
2
1
1
2
2
1
2
0
2
1
1
0
0
0
0
0
2
1
2
1
1
1
2
1
0
0
0
1
0
1
1
2
5
0
1
0
0
0
1
1
0
0
3
1
1
2
1
0
3
0
0
1
2
2
1
0
0
0
1
0
0
1
1
0
2
0
2
1
1
1
1
1
1
0
0
1
0
1
2
0
0
1
1
2
1
2
0
1
0
1
0
1
1
0
1
0
0
1
1
2
0
1
1
1
1
0
1
1
0
1
0
1
2
2
2
3
2
0
2
1
1
1
1
0
0
0
2
0
1
1
2
2
0
1
0
0
1
2
1
2
1
1
0
1
0
1
0
0
1
1
1
0
0
0
1
0
1
2
1
1
1
2
0
0
1
1
0
2
0
1
1
0
3
1
0
1
2
0
0
1
1
1
0
2
2
1
2
2
2
1
1
1
1
0
0
1
0
1
0
0
1
0
0
0
1
1
2
1
1
0
2
0
1
1
0
0
1
1
0
0
1
2
0
1
2
1
1
1
0
0
1
1
1
1
1
0
2
2
1
1
1
0
1
0
1
0
0
1
0
1
1
0
1
3
2
2
0
1
1
1
0
0
0
0
1
5
1
1
1
1
3
0
0
0
1
1
1
1
0
1
1
2
2
0
0
2
0
0
1
1
1
0
1
0
1
0
1
1
1
1
0
2
1
2
1
1
1
0
0
0
2
0
2
1
1
1
1
1
0
1
2
2
0
0
0
0
1
1
1
0
0
1
2
0
1
0
1
1
1
1
1
0
1
2
1
0
0
1
1
0
2
0
2
0
0
2
0
1
1
1
1
0
0
1
1
1
1
0
1
1
0
2
1
4
2
1
0
1
2
1
2
0
0
1
2
0
1
2
1
1
2
1
2
1
0
1
0
2
1
1
0
2
2
5
0
0
2
2
2
1
1
0
2
1
1
2
0
1
0
2
1
0
1
1
1
0
1
1
0
0
1
1
1
0
0
2
0
2
0
1
0
0
0
0
1
0
0
1
2
1
2
0
1
1
1
0
1
1
1
0
1
0
0
1
0
0
2
0
1
1
1
1
2
0
1
0
1
0
1
0
3
1
1
1
0
2
0
1
1
2
2
0
1
0
2
2
0
0
1
0
1
0
1
1
2
1
1
0
1
0
1
1
0
1
1
1
1
2
0
1
0
1
2
0
1
1
1
1
1
1
0
1
0
2
1
0
0
1
1
0
0
0
0
0
1
2
1
0
2
0
1
2
2
0
1
1
2
0
2
1
1
0
2
1
0
2
0
1
2
0
1
0
0
1
1
0
2
1
1
1
0
1
0
2
0
2
2
1
1
0
2
1
2
1
1
0
0
1
0
3
0
0
1
1
0
0
2
0
0
0
0
2
2
0
0
1
0
2
1
1
2
0
2
1
2
2
0
1
1
1
0
1
1
1
1
0
1
1
0
1
1
0
1
2
0
2
2
1
0
2
2
0
0
2
1
1
2
0
1
1
1
2
1
1
1
1
1
1
1
1
0
0
1
0
2
0
1
1
1
1
0
1
1
1
0
2
1
2
0
1
2
1
0
1
1
0
2
2
1
1
0
1
0
0
2
1
1
1
0
0
2
3
1
0
0
0
0
1
1
1
0
0
2
0
1
1
1
2
1
1
1
0
2
1
0
2
1
0
1
1
0
1
1
0
1
0
0
0
0
1
1
2
0
0
2
1
7
1
0
2
1
1
1
2
1
1
0
1
2
0
1
2
1
1
1
1
0
1
1
1
0
1
0
2
1
1
2
0
2
2
2
2
1
2
1
1
1
0
0
0
1
0
2
1
1
2
0
0
1
1
0
0
2
1
2
1
0
1
2
0
1
1
1
1
1
2
0
1
1
0
1
1
0
1
2
1
0
1
2
0
0
0
0
2
0
0
2
1
2
1
0
2
1
1
1
0
1
1
2
0
0
0
1
2
2
0
1
1
2
1
1
2
0
1
0
0
0
0
0
1
1
1
1
0
1
2
0
2
2
0
1
2
1
1
0
1
1
1
1
1
2
1
0
1
1
1
2
1
2
1
1
1
1
2
2
1
0
1
2
1
2
1
2
1
2
0
1
2
1
2
0
0
0
2
0
2
0
1
1
1
1
0
1
1
0
0
1
0
0
1
0
1
0
2
1
2
1
0
1
0
1
0
1
0
0
0
1
2
1
1
0
1
0
0
0
2
1
2
0
0
0
2
0
2
1
0
0
1
0
0
0
2
2
0
2
0
0
2
1
1
2
1
1
2
1
1
0
1
1
1
2
0
0
0
0
0
2
0
1
1
1
1
2
1
1
1
1
2
2
0
1
0
2
1
1
0
0
0
1
1
1
1
1
2
1
2
1
1
3
1
2
0
1
1
0
0
0
1
2
1
2
0
0
1
1
0
1
0
0
0
0
1
0
1
1
1
2
2
0
0
2
0
0
1
2
1
1
0
1
0
1
2
1
1
1
1
1
1
1
0
2
0
1
0
1
1
2
0
0
1
0
2
0
1
1
1
1
2
0
0
0
1
2
1
2
0
1
2
1
1
0
0
1
1
3
1
1
1
2
0
1
1
0
0
2
1
1
1
0
1
1
0
1
1
2
2
1
0
1
1
1
1
1
1
2
0
1
1
2
1
1
0
0
0
2
1
0
1
0
0
1
2
1
1
2
2
1
0
0
1
1
1
2
0
0
1
2
0
1
2
1
0
0
2
0
2
1
1
1
1
1
0
0
1
0
0
2
2
1
0
0
0
1
1
1
0
2
2
1
1
1
0
1
0
0
0
0
2
1
1
1
4
2
2
1
0
0
1
0
1
0
1
1
1
2
0
4
0
1
1
1
1
1
0
1
1
2
1
0
1
1
0
2
1
0
1
2
1
0
1
1
2
1
1
1
3
1
0
1
0
1
0
0
1
0
1
1
1
1
0
2
1
1
1
1
1
0
1
0
0
1
0
0
1
2
1
1
1
0
1
1
1
0
1
2
0
1
2
0
2
0
2
0
0
0
1
0
0
2
0
1
0
2
4
0
1
0
2
0
0
0
0
2
2
1
1
1
1
2
0
1
0
1
1
1
2
1
0
2
0
0
2
1
0
0
0
1
1
1
0
0
0
1
1
0
1
1
0
1
1
2
0
0
1
1
0
0
1
0
1
2
1
2
0
2
1
1
0
1
2
2
0
1
1
1
1
1
1
0
2
2
0
1
1
1
1
2
1
0
3
1
1
1
2
0
0
2
1
2
0
1
1
0
0
2
1
0
0
2
1
1
1
2
2
1
0
0
1
0
1
0
1
0
0
2
2
2
1
0
1
0
1
1
1
1
1
2
1
2
2
2
0
0
1
1
2
2
1
0
2
1
0
0
2
0
3
0
1
1
1
1
2
0
0
2
2
1
1
0
0
1
0
1
0
0
1
0
0
0
1
0
1
1
1
0
3
0
2
0
0
1
2
0
1
0
2
0
1
2
2
1
1
1
1
1
3
1
2
0
1
2
2
2
0
0
0
2
1
1
1
0
1
0
1
0
2
0
2
0
0
0
2
1
0
0
2
0
1
1
2
2
1
0
0
2
0
1
2
0
2
0
1
2
1
1
2
1
1
0
1
1
0
2
1
2
1
2
0
1
1
0
2
1
2
2
0
1
0
0
1
0
0
0
0
2
0
1
2
2
0
1
0
2
0
1
1
1
0
1
0
2
2
0
1
1
1
0
0
0
1
2
2
1
1
1
0
0
0
2
2
3
1
1
0
1
0
0
0
0
1
2
1
1
0
0
1
0
1
2
0
2
0
0
2
1
1
1
1
2
1
0
2
2
1
0
1
1
1
1
1
1
0
0
2
2
1
4
0
0
0
0
0
1
1
1
0
0
0
0
2
1
3
0
1
5
2
1
2
1
1
1
1
1
0
1
3
0
2
1
0
1
0
1
0
0
0
0
1
0
0
0
1
1
1
0
1
0
4
2
0
0
2
1
2
1
1
1
1
0
1
0
1
2
1
1
0
1
0
1
1
2
0
0
1
1
2
1
0
0
1
0
2
1
2
0
1
0
0
1
0
0
0
1
1
1
0
0
2
0
2
2
2
1
2
0
1
1
1
0
2
1
1
0
1
2
1
1
0
2
1
0
0
1
1
0
0
0
1
1
0
1
1
0
1
1
1
1
2
1
1
1
1
1
2
0
1
0
2
2
2
1
2
0
2
0
1
0
1
0
1
1
1
0
1
1
2
0
1
2
1
0
1
1
1
1
0
1
1
1
0
0
1
1
1
0
0
1
1
0
1
0
1
1
0
1
2
0
0
1
0
1
0
1
1
1
1
2
1
0
1
0
0
0
2
1
2
1
2
0
2
2
3
1
0
1
1
2
1
0
0
1
0
1
3
1
0
0
2
1
0
2
0
0
0
0
1
0
1
1
1
0
0
0
1
1
1
1
0
0
0
1
2
0
0
0
1
1
2
2
1
2
1
2
1
2
1
1
0
0
2
0
0
1
1
0
2
2
0
0
2
1
2
2
1
0
2
1
0
1
0
1
1
3
2
2
1
1
1
1
2
1
0
0
2
0
1
1
0
1
0
1
2
2
1
1
0
1
2
1
1
1
0
0
2
1
1
0
2
1
2
0
0
2
0
0
0
0
2
1
1
0
2
1
0
0
1
2
2
0
1
0
1
0
0
0
2
3
0
0
0
2
1
2
0
0
1
0
2
1
0
0
0
0
1
0
2
0
1
0
3
1
1
1
0
1
0
1
0
0
2
1
1
1
1
0
1
1
1
1
1
1
0
0
1
1
0
1
0
0
1
1
0
1
1
0
1
2
1
1
2
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
0
2
1
3
0
1
1
0
2
0
1
0
1
0
1
1
2
1
1
2
1
1
0
1
1
1
1
1
0
1
1
1
1
0
2
0
1
1
2
1
1
1
2
0
0
0
0
1
2
1
2
1
0
1
2
2
0
0
2
1
0
4
2
2
0
0
1
2
1
1
1
1
1
2
1
0
2
1
2
2
0
1
1
0
0
1
0
2
1
1
0
0
0
11
1
2
2
1
1
0
0
1
1
0
1
1
1
1
1
1
1
0
0
1
2
2
0
1
0
2
2
0
0
1
0
2
0
0
0
1
0
1
1
1
0
1
1
2
1
2
0
0
1
0
2
2
1
0
0
2
2
2
0
1
0
0
0
0
1
2
0
0
0
1
1
0
1
2
2
1
0
0
1
0
0
1
0
1
0
2
2
1
1
1
1
1
2
0
0
1
0
0
0
1
0
0
0
2
2
0
0
1
0
2
2
0
1
1
0
0
1
2
1
0
2
1
2
1
0
2
1
1
0
0
2
2
1
1
1
2
2
1
1
1
1
0
0
0
2
0
1
0
1
0
2
3
1
0
2
1
0
1
2
2
1
0
0
0
0
0
1
0
0
0
1
0
0
1
2
1
2
1
2
1
2
1
1
1
2
1
1
0
3
1
0
0
1
1
2
2
1
0
2
0
2
0
2
2
1
0
0
0
0
3
2
2
0
2
1
1
0
2
0
1
1
1
2
0
2
1
0
1
1
1
0
1
1
0
1
1
1
0
1
13
1
1
1
1
0
2
0
1
1
0
1
1
1
0
1
1
1
2
0
1
1
1
0
1
1
1
1
1
1
1
0
1
1
0
2
0
1
0
0
1
0
0
0
1
1
1
1
2
0
0
1
1
0
2
2
1
1
1
1
0
2
0
0
1
0
0
0
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
2
0
1
1
0
2
1
0
1
0
1
2
2
0
0
2
0
1
0
1
1
0
1
1
0
1
1
1
0
0
1
1
2
0
0
1
1
0
2
1
2
1
2
1
0
1
1
1
1
1
1
0
1
1
1
2
0
1
2
0
0
3
2
1
2
1
0
0
1
0
2
0
0
1
0
1
0
0
1
2
1
1
2
0
1
1
1
2
0
2
0
1
1
1
1
0
0
1
1
0
1
0
1
0
0
1
0
2
0
2
0
0
0
2
0
2
1
1
1
0
0
1
2
0
0
1
0
1
1
1
0
0
1
1
2
0
0
1
2
1
1
1
2
0
2
1
0
1
1
1
2
2
1
1
1
1
1
1
2
0
2
1
2
1
0
1
1
1
0
0
1
0
1
1
0
1
1
1
1
1
3
1
0
2
1
2
0
0
2
2
2
1
1
1
2
1
1
0
1
1
0
2
1
0
1
1
0
0
0
0
0
0
2
2
2
1
2
2
2
1
2
2
0
2
0
1
2
0
1
2
1
0
1
0
0
0
0
1
1
2
2
1
0
1
0
0
1
2
1
0
1
0
0
0
1
1
0
0
1
2
0
1
0
0
2
1
1
0
2
1
1
1
1
1
0
1
0
0
1
0
0
2
0
2
0
1
1
2
2
2
0
1
1
1
1
2
2
0
4
1
2
1
2
0
1
1
0
1
2
1
0
0
0
2
1
0
2
1
4
0
1
1
1
0
0
2
1
0
2
2
1
0
1
3
0
0
1
1
1
0
2
0
0
1
2
1
1
2
2
0
1
1
0
0
1
1
0
1
1
1
2
1
1
0
0
1
0
0
2
1
0
2
0
2
1
1
1
2
0
2
1
0
1
0
1
1
1
1
1
4
1
1
2
0
1
1
0
2
2
1
0
0
0
1
2
1
2
0
2
1
4
0
0
2
1
0
2
3
0
1
1
0
1
1
0
0
2
1
1
1
0
1
0
1
2
1
2
1
1
1
1
2
2
0
0
0
1
2
2
0
2
0
0
1
2
0
0
0
0
2
0
0
2
1
1
1
2
1
1
1
1
0
1
1
0
1
0
0
1
1
1
0
2
1
2
2
1
1
2
0
2
0
1
0
1
1
0
1
1
0
2
0
0
0
2
0
0
2
1
2
1
0
1
2
1
1
2
0
0
2
1
3
1
2
0
1
1
1
2
0
0
0
2
0
0
0
0
1
2
0
1
0
2
1
2
0
0
0
2
2
0
2
0
2
0
0
0
2
2
0
0
0
2
0
0
1
0
1
0
0
1
1
0
0
2
0
1
1
2
0
1
0
0
1
2
1
1
1
2
1
2
1
2
1
0
0
0
1
1
1
0
0
0
1
1
2
2
2
0
0
0
0
1
1
0
0
0
2
2
1
2
1
0
0
1
2
1
0
0
2
1
2
0
1
1
2
1
0
0
1
2
2
0
1
2
2
0
0
0
0
1
0
1
1
2
0
0
0
0
0
1
0
2
1
2
2
2
1
1
2
0
1
2
1
0
2
1
3
1
1
1
1
2
1
1
1
2
1
1
0
1
1
0
1
2
1
0
0
0
1
1
1
2
1
0
1
1
0
0
2
1
1
0
3
1
1
1
2
1
1
2
1
0
0
1
0
1
1
0
2
1
1
1
1
1
0
1
2
1
2
3
0
1
2
1
0
1
0
0
1
0
2
0
1
1
1
1
1
0
0
1
1
1
1
1
2
0
1
1
1
0
0
1
1
2
0
1
1
0
0
2
1
1
2
2
2
1
0
1
2
2
2
1
1
1
1
2
0
1
0
1
0
1
0
1
1
2
1
0
2
1
2
1
0
0
1
2
0
1
1
0
0
2
1
1
2
1
1
1
0
1
2
1
2
1
1
0
1
1
1
1
1
1
2
0
1
1
1
2
1
2
2
1
1
1
0
2
0
1
1
1
0
0
1
2
0
1
0
1
2
0
1
0
0
1
2
1
0
0
0
2
0
0
0
1
1
1
1
2
0
1
2
0
0
2
0
2
1
1
1
2
2
1
1
2
2
1
1
0
1
0
0
1
2
2
1
1
1
1
1
0
0
1
1
1
0
1
1
1
0
1
0
0
2
1
2
2
1
1
1
1
2
1
0
0
1
0
2
2
1
2
0
1
2
2
1
1
1
1
1
0
1
1
0
1
0
1
1
1
2
1
1
2
0
1
2
1
1
2
2
2
0
0
0
2
1
0
1
1
0
3
1
1
2
0
1
2
1
2
2
0
1
0
1
1
0
0
2
1
1
1
0
1
1
1
1
1
0
2
2
1
0
0
1
0
1
1
1
2
1
0
1
1
2
1
2
1
0
2
1
1
1
0
1
1
2
0
0
0
3
0
2
2
2
2
1
1
1
1
1
1
2
0
1
2
0
1
0
2
0
0
0
1
2
1
0
1
1
1
0
2
0
1
1
2
1
1
2
2
0
0
2
0
2
2
1
2
2
2
2
1
1
1
0
0
2
0
2
1
2
2
2
2
1
2
1
1
0
0
1
2
1
0
1
1
0
1
0
0
2
0
1
1
0
2
1
0
2
1
0
0
1
0
1
1
2
0
2
2
0
0
2
1
1
1
3
0
1
0
0
0
0
1
0
1
1
2
1
2
2
0
1
1
0
1
2
0
0
0
0
1
2
0
1
0
1
1
0
1
0
1
1
0
1
1
1
2
1
1
1
1
1
0
1
1
2
0
2
0
0
2
0
0
0
0
0
1
0
1
1
2
1
3
1
1
1
1
0
2
1
2
1
2
2
0
2
1
1
2
0
0
1
0
2
1
0
0
2
2
0
1
1
0
1
1
1
1
1
0
1
1
1
1
1
1
1
2
2
0
2
1
0
1
1
1
0
2
2
1
2
2
1
1
0
1
1
0
1
1
1
1
1
2
2
0
1
2
0
1
2
1
1
1
1
0
1
1
1
1
1
0
1
0
0
2
1
1
0
0
1
0
1
1
1
2
2
1
1
0
0
0
1
0
2
2
1
0
1
1
1
1
1
0
2
1
1
1
1
3
2
1
0
0
1
1
1
1
1
2
0
0
0
1
1
2
0
2
1
1
0
0
1
2
0
2
1
2
1
0
0
0
1
1
2
2
1
0
2
3
2
0
1
1
1
1
1
2
0
1
0
1
1
2
0
1
1
1
0
0
0
1
1
0
0
0
0
1
1
1
2
1
0
0
0
1
2
1
2
1
1
1
1
0
1
1
1
0
1
1
0
1
0
0
1
2
1
0
2
1
1
2
0
0
2
2
2
1
1
1
1
1
2
2
1
1
1
1
2
0
1
1
1
1
1
2
1
1
0
1
1
3
1
1
2
1
1
0
0
0
1
1
0
2
1
0
1
1
1
2
1
1
1
1
1
1
0
2
0
2
0
1
1
2
1
1
0
2
2
1
1
2
0
2
1
0
0
2
0
0
2
0
0
2
1
0
0
2
1
1
1
2
1
1
0
0
1
0
0
1
1
2
2
0
1
2
0
1
1
1
0
1
1
2
0
1
1
0
2
1
0
0
0
0
2
1
0
0
0
1
2
1
0
0
1
0
0
2
1
1
2
0
2
1
1
1
1
1
0
1
1
1
2
0
2
2
0
0
1
1
1
1
2
2
2
1
1
0
0
0
0
0
2
1
1
0
0
2
1
2
1
0
1
1
1
0
1
0
1
1
0
1
1
2
0
2
1
2
0
2
1
1
1
0
1
0
1
1
0
2
2
1
0
1
0
1
0
1
0
1
2
1
1
0
0
0
0
1
1
0
0
1
2
1
0
1
1
0
0
2
0
2
0
0
2
0
1
2
0
0
2
0
0
0
1
2
1
2
2
1
0
0
1
2
0
1
0
2
2
2
1
0
1
2
3
0
1
0
1
2
0
2
1
2
0
0
1
1
0
1
2
0
1
2
1
1
2
0
0
1
0
1
0
0
1
0
2
2
2
2
1
2
0
0
0
1
1
0
1
2
0
0
1
1
1
1
0
1
1
1
1
1
0
0
0
1
2
2
1
1
1
1
1
2
2
1
1
1
1
0
1
2
1
2
0
2
1
1
0
2
1
1
2
1
2
1
1
1
0
1
1
2
1
0
1
0
1
0
0
1
0
0
0
1
0
1
1
2
2
2
2
0
1
1
0
0
0
0
1
2
2
1
1
1
2
2
1
0
1
1
0
1
2
2
0
1
2
1
0
0
1
1
2
0
1
0
0
0
1
0
1
1
1
1
0
0
2
1
1
0
1
1
2
1
1
0
1
1
1
1
1
2
1
0
1
2
0
1
1
0
0
0
0
2
0
2
0
0
2
2
1
1
3
0
1
1
2
2
1
2
0
0
1
1
3
1
0
0
1
1
1
0
0
1
0
1
0
1
2
0
1
2
1
0
2
1
0
1
1
0
1
2
1
0
1
1
1
0
0
0
1
5
0
1
2
2
1
0
0
0
1
1
1
2
2
0
1
0
1
1
1
2
1
1
2
1
1
0
1
2
1
2
0
0
3
1
0
1
1
2
1
1
1
0
1
3
0
1
0
1
2
1
3
2
1
1
1
1
1
2
0
1
2
1
1
0
2
2
1
0
0
1
2
0
1
0
1
0
1
1
0
2
0
0
1
1
2
1
1
0
0
2
0
0
1
1
0
0
0
1
0
0
1
0
2
0
0
0
1
0
1
0
1
1
1
1
1
1
1
1
1
2
2
2
0
2
2
1
2
0
1
0
0
0
0
1
1
2
1
1
0
1
1
2
0
0
1
0
2
0
2
0
1
0
2
1
1
2
3
1
1
1
3
1
1
0
1
1
2
1
1
1
0
0
0
1
2
0
1
1
0
3
1
4
2
1
1
1
0
2
1
1
1
0
0
2
1
0
1
0
2
1
2
1
1
0
1
1
1
1
1
0
0
0
0
2
1
0
2
2
1
1
0
2
1
2
1
1
0
0
0
2
2
1
1
1
1
0
1
0
1
1
2
2
0
1
0
0
1
2
2
1
0
1
0
1
1
1
0
1
1
2
2
1
1
1
1
2
0
1
0
0
1
0
0
1
1
0
1
2
1
2
1
2
0
2
0
1
0
1
2
1
0
0
1
0
1
1
1
2
1
1
2
1
2
2
0
1
1
2
2
1
2
1
0
0
0
0
1
1
0
1
1
1
3
3
1
1
1
2
0
2
0
0
0
1
0
1
0
1
1
1
0
1
0
3
2
1
0
1
1
1
1
1
1
2
2
0
2
0
1
1
0
1
0
1
1
2
2
2
1
2
1
2
0
0
1
1
1
2
1
0
0
2
1
1
1
2
2
2
2
1
0
2
2
2
0
0
1
2
2
1
0
1
2
1
1
1
1
1
2
1
2
1
0
1
2
1
0
0
2
1
2
2
3
1
0
1
1
1
1
1
0
1
2
2
0
0
2
2
1
1
1
0
0
2
2
1
1
0
1
0
2
1
0
1
0
1
1
0
0
0
0
2
2
0
1
1
2
0
1
0
2
1
2
2
2
2
1
2
0
1
2
2
1
2
1
1
1
1
2
2
2
1
1
2
1
2
1
1
1
0
0
2
1
0
2
1
2
2
1
2
1
0
1
0
0
1
1
0
3
2
0
2
1
0
2
0
0
0
0
0
1
0
1
1
0
1
0
0
0
1
0
1
0
1
1
1
1
2
1
0
2
0
1
0
1
0
0
2
1
1
1
1
2
8
1
0
0
2
2
0
2
2
0
0
1
0
1
1
8
0
1
1
0
1
1
0
0
3
0
0
0
2
2
1
2
1
0
2
0
1
1
1
1
0
1
0
0
0
0
2
1
0
2
1
2
0
1
2
1
0
0
1
2
1
2
0
1
1
0
2
2
1
1
1
0
2
0
0
0
1
1
1
2
0
2
1
2
1
0
0
1
2
1
1
0
0
2
2
1
1
0
1
2
2
1
1
0
1
1
0
0
0
2
1
0
0
1
1
0
2
1
2
1
2
2
1
2
0
1
1
0
0
2
1
2
0
2
1
1
0
2
0
0
1
1
0
2
0
1
1
2
1
1
0
2
0
0
10
1
1
2
1
2
1
0
1
1
1
0
1
1
0
1
1
1
0
1
1
1
0
0
1
0
1
1
0
1
1
1
3
0
1
1
1
0
0
1
0
0
0
0
1
2
2
2
0
2
1
1
0
0
2
1
2
2
1
0
0
2
2
1
1
0
0
2
0
1
1
1
0
0
1
1
0
1
0
1
1
1
1
1
1
1
0
0
2
0
1
1
0
1
0
1
0
0
2
1
0
0
2
0
1
1
1
0
1
2
1
2
1
1
0
1
1
2
1
0
1
1
1
2
0
0
2
2
2
0
0
2
1
0
0
2
1
2
1
1
1
1
1
0
2
2
1
1
0
0
0
0
1
1
1
1
2
1
0
2
1
1
1
0
0
1
3
0
2
3
0
1
3
2
2
1
1
2
1
0
2
1
2
1
1
1
2
1
1
2
1
2
1
1
1
2
0
1
0
2
0
1
2
0
2
3
0
2
0
1
0
1
1
0
2
2
1
1
2
2
1
2
1
1
1
0
1
0
2
2
2
0
2
1
0
0
1
1
1
2
0
2
0
1
1
2
1
0
2
1
1
1
0
1
2
1
3
1
0
0
1
1
1
1
1
1
1
0
0
1
1
2
0
0
0
2
0
1
1
0
1
0
1
1
1
0
1
1
1
1
1
0
0
1
1
0
0
0
0
1
1
1
1
0
0
0
2
1
3
1
0
0
1
1
1
0
0
1
0
2
1
1
2
1
0
0
0
1
0
1
0
1
1
2
0
1
0
1
2
0
1
2
2
0
0
1
1
1
0
1
1
0
1
2
2
0
2
1
1
1
0
0
2
2
2
0
1
1
2
0
2
1
1
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
0
1
0
1
1
2
1
1
2
0
1
1
0
2
1
1
2
0
2
1
1
1
0
1
1
1
1
1
1
2
0
2
0
0
1
1
0
0
0
1
0
1
1
2
1
2
1
1
1
1
0
1
1
1
1
2
1
0
0
1
0
2
2
1
0
0
2
2
0
0
1
0
2
1
1
2
1
2
0
1
0
0
1
2
0
2
0
2
1
0
0
3
0
1
1
0
0
2
1
0
0
0
2
1
1
1
0
0
1
0
1
0
1
1
1
0
1
0
2
0
1
2
1
1
1
1
2
1
2
1
0
0
1
2
1
2
1
0
0
1
1
2
1
0
0
2
1
1
2
1
1
2
1
1
1
0
2
1
2
0
1
1
1
0
1
0
0
2
0
0
2
0
1
1
4
1
0
1
1
0
0
1
0
0
0
0
0
0
1
0
2
0
2
1
1
0
0
1
2
0
1
1
1
0
0
0
2
0
1
0
1
1
0
1
0
1
1
0
2
2
0
1
0
1
1
0
2
2
3
0
0
1
0
1
1
1
0
2
1
0
0
2
1
1
0
1
2
1
2
2
1
0
1
2
1
0
0
0
0
1
2
1
2
1
2
1
1
0
2
0
0
0
0
1
2
1
1
1
1
2
2
1
0
0
1
2
2
1
0
2
0
1
2
1
0
0
2
1
1
1
0
0
0
1
1
2
1
2
0
1
0
0
1
0
2
0
2
2
1
1
1
2
0
0
1
1
0
1
1
1
0
2
2
1
1
0
1
1
2
2
2
1
1
0
0
0
0
2
0
2
0
1
0
1
0
0
0
2
0
1
2
1
1
1
2
1
2
2
1
2
2
0
1
2
1
0
1
1
1
1
1
2
0
0
1
1
0
0
1
1
1
1
3
0
0
2
1
0
1
0
2
1
2
0
0
1
1
1
2
2
2
1
0
1
1
1
0
2
0
0
2
0
0
2
0
2
0
1
3
1
2
1
1
1
1
0
1
2
0
0
0
1
1
2
2
1
1
1
0
0
1
1
1
2
0
1
0
0
0
1
1
1
0
0
1
1
0
2
1
1
2
1
1
1
1
0
1
2
0
2
1
1
1
1
1
1
0
1
3
1
1
0
1
1
0
4
1
1
0
1
0
2
2
1
0
1
2
1
0
0
0
0
1
1
1
0
0
1
2
0
2
2
1
2
1
1
0
1
2
0
0
1
0
0
2
1
1
0
1
4
1
1
1
2
1
1
0
2
0
1
1
1
3
0
1
1
2
1
1
2
0
2
0
0
2
1
1
0
0
1
1
1
0
2
0
1
0
1
1
1
2
1
1
2
1
0
1
1
5
0
0
1
1
1
2
4
2
2
0
1
1
0
0
1
1
0
1
2
1
1
1
1
1
2
0
2
1
1
0
1
0
1
1
2
2
1
1
1
1
1
1
0
1
2
2
1
2
1
1
1
0
1
0
1
2
1
2
0
1
1
0
1
1
1
1
2
2
1
0
2
1
0
2
0
1
0
0
2
0
1
1
1
2
0
0
1
1
1
1
2
0
1
0
1
2
1
2
2
1
2
1
1
1
0
1
1
2
0
2
1
0
2
1
1
1
1
2
1
1
1
1
0
1
0
1
2
0
1
1
1
2
1
1
0
0
2
2
2
0
1
2
2
2
0
1
2
0
2
1
0
1
2
1
1
0
2
1
1
0
2
0
1
2
2
0
2
2
0
1
1
0
1
0
1
0
2
2
1
1
1
0
0
3
2
1
0
2
1
0
0
1
2
0
0
2
2
1
1
0
1
1
2
1
1
1
0
0
1
2
0
1
0
2
0
1
0
1
0
0
0
1
1
1
0
1
0
2
2
1
1
1
1
0
1
2
0
2
2
1
1
0
1
1
0
1
0
2
0
1
2
1
1
0
2
2
0
0
1
0
1
1
1
1
1
0
1
1
2
0
0
0
2
1
1
1
0
2
2
1
0
1
3
1
1
1
1
2
0
1
1
0
2
2
1
2
2
2
0
0
0
0
1
0
1
2
2
0
0
0
0
1
0
1
4
1
2
1
1
1
0
1
1
0
1
1
1
2
0
2
1
0
0
0
1
0
0
2
2
0
1
1
2
0
3
2
2
1
1
4
1
0
1
0
2
1
1
0
1
1
0
0
3
1
0
1
2
1
0
1
1
1
0
0
0
3
1
1
0
1
0
1
0
1
1
1
2
1
0
1
1
0
1
1
2
2
1
2
0
2
0
2
2
0
2
0
1
1
2
2
0
1
1
1
0
1
2
0
2
1
1
3
1
0
0
1
0
1
1
0
1
0
1
1
0
0
1
1
1
1
0
1
0
1
1
2
1
0
2
2
1
2
1
1
1
1
0
2
2
0
0
2
3
1
1
0
0
2
0
1
1
1
1
1
1
2
1
2
0
0
0
0
1
1
0
0
0
0
0
1
1
1
1
0
0
1
1
1
1
1
0
0
2
0
0
0
1
2
1
1
2
0
1
2
1
1
2
0
0
1
0
0
2
1
1
1
0
0
1
0
0
0
1
0
1
1
1
0
0
1
2
0
1
2
0
1
1
1
0
2
2
1
1
1
0
1
1
1
1
1
2
1
0
1
2
0
1
1
1
1
0
2
4
1
0
1
0
2
0
1
1
0
0
0
2
1
1
1
0
1
1
2
1
0
0
2
0
0
0
2
1
2
1
3
0
1
1
1
0
0
1
2
0
2
2
1
1
1
0
1
1
2
0
2
2
0
0
0
0
0
0
2
1
1
2
1
2
0
0
1
0
2
2
1
1
0
1
1
1
2
0
1
0
0
0
0
1
0
0
0
2
0
1
1
1
2
1
0
1
2
1
0
0
0
1
0
1
1
0
1
1
2
1
1
0
1
1
1
0
2
1
1
1
0
5
1
2
2
1
1
0
1
1
1
1
2
2
0
2
1
1
1
2
2
2
2
1
1
1
0
2
1
2
1
2
1
1
0
0
2
1
1
1
0
0
0
1
1
0
0
2
0
2
1
1
0
0
1
1
1
0
3
0
2
0
0
1
0
1
0
1
0
1
2
1
1
1
0
1
1
2
2
1
1
2
3
1
1
1
2
0
0
2
1
0
1
1
1
0
2
1
2
1
0
0
0
1
2
1
0
0
2
0
0
0
1
0
1
0
1
1
1
1
2
2
1
2
1
1
2
0
1
0
1
0
2
0
0
2
2
0
0
1
0
0
0
1
0
0
1
1
0
0
1
1
0
0
0
1
0
0
1
1
0
0
1
0
0
2
1
0
1
1
0
1
2
1
1
1
1
1
0
0
1
0
2
0
2
0
0
0
0
1
0
1
2
0
2
0
4
2
1
1
2
1
1
0
0
1
1
1
0
2
0
2
0
1
0
1
1
0
1
0
0
0
1
0
0
1
0
2
0
0
1
1
1
2
0
2
1
0
0
1
1
1
1
1
1
2
1
0
2
1
1
2
1
1
1
2
2
1
0
1
1
0
0
2
1
0
1
1
0
0
1
1
0
3
0
1
2
2
1
2
1
0
0
0
0
1
1
2
0
2
1
2
2
0
0
1
1
1
0
0
0
2
1
1
1
1
2
1
0
0
2
0
0
0
0
1
1
1
0
1
1
1
1
0
2
0
0
1
2
1
1
0
1
1
3
1
2
0
0
1
0
1
0
1
0
1
1
3
1
0
1
1
0
2
1
1
1
1
0
0
2
1
0
1
1
1
2
0
1
0
0
2
2
1
1
1
0
1
1
0
1
0
1
2
1
1
2
2
2
0
0
2
2
0
1
2
0
2
2
2
0
0
1
1
2
1
1
2
1
1
1
0
0
1
2
0
0
2
1
0
2
1
1
2
1
1
0
1
0
2
1
0
1
1
0
0
2
2
0
3
2
1
1
0
0
1
2
1
1
0
1
2
1
1
1
1
1
1
0
1
1
2
1
0
1
1
1
1
1
1
1
1
2
1
0
0
0
0
0
0
0
1
2
1
0
2
2
2
0
1
1
1
0
0
0
0
1
0
1
0
0
1
0
1
3
1
1
0
1
0
0
1
1
1
0
2
1
1
1
0
2
0
1
1
2
2
7
1
2
1
0
1
0
0
1
0
1
0
1
0
0
0
0
0
1
1
0
1
0
2
0
2
1
2
1
1
1
0
0
0
0
0
1
0
0
1
1
1
1
0
0
1
1
1
0
2
0
0
0
1
0
1
0
0
1
0
0
1
1
2
0
2
0
1
1
2
3
2
2
1
1
0
2
0
1
1
1
1
0
1
1
2
2
2
2
0
1
0
2
0
1
1
1
2
1
0
1
1
2
1
0
0
0
2
1
0
0
0
0
0
1
0
1
2
1
0
1
2
0
1
0
1
1
0
2
0
0
0
1
1
1
0
2
1
0
1
0
1
2
2
0
0
2
1
2
0
0
1
1
1
1
1
1
2
0
0
2
0
0
0
1
0
5
0
0
0
1
1
1
1
1
0
1
0
1
1
0
0
1
1
0
1
1
1
2
0
0
1
0
0
3
2
0
1
0
1
1
0
2
0
0
0
0
0
0
1
1
1
0
1
1
1
1
2
1
1
2
1
2
0
1
1
1
1
2
2
0
0
0
1
1
2
0
1
4
2
1
0
2
2
0
0
0
2
0
0
1
0
1
0
1
0
2
1
2
2
2
1
1
2
2
0
0
1
0
0
0
1
0
1
0
1
1
0
0
0
1
1
0
1
2
0
0
0
1
0
0
1
1
1
2
1
1
1
1
2
1
0
0
1
0
2
1
0
1
1
0
2
1
0
2
1
2
1
1
1
1
3
0
1
1
1
1
1
1
1
1
1
1
0
1
0
0
2
2
2
1
1
1
1
1
1
1
0
1
1
1
0
1
1
0
0
2
1
0
1
0
1
0
0
0
1
0
1
1
1
0
1
0
1
0
1
1
2
0
0
2
2
1
1
1
0
1
2
1
0
2
0
2
0
2
1
1
1
0
0
2
0
1
2
1
2
1
0
0
0
0
1
1
0
2
2
2
1
0
0
1
1
0
1
1
1
2
0
2
1
2
0
0
2
0
0
2
1
1
1
2
0
1
1
2
2
0
1
0
1
0
1
1
1
1
1
1
1
1
1
2
1
1
0
1
0
1
1
1
1
1
2
1
1
2
0
0
1
1
2
1
1
0
2
2
0
0
2
0
0
1
1
1
2
1
1
0
1
1
0
1
2
1
1
1
2
0
0
1
0
1
0
2
2
1
1
0
0
1
0
2
0
2
1
1
2
1
2
2
0
0
2
1
1
0
1
2
1
1
1
1
0
2
2
0
1
2
0
1
0
0
0
1
1
2
0
2
0
2
0
1
0
2
1
1
0
2
0
1
0
1
1
1
0
1
2
1
1
1
1
1
2
2
1
1
1
1
1
1
2
0
0
1
1
1
0
0
1
1
0
1
0
0
1
1
1
2
2
1
1
1
2
1
1
1
1
2
1
1
1
2
3
1
1
0
0
2
0
1
1
2
2
2
1
1
0
2
1
1
1
1
2
0
0
2
1
2
1
2
1
0
0
1
1
0
2
2
2
2
2
0
1
0
1
1
2
2
4
1
1
0
1
1
1
0
1
3
0
1
2
0
1
0
2
0
0
0
0
0
1
0
2
1
2
1
1
1
1
2
1
3
2
1
0
1
0
0
1
1
0
3
2
0
3
1
0
1
0
0
1
1
1
1
1
1
1
2
0
0
1
0
0
2
1
2
1
0
2
2
0
0
2
1
2
1
0
1
0
0
1
1
1
0
1
1
0
0
0
0
1
1
0
1
0
2
1
2
2
0
4
1
2
1
1
1
2
1
2
1
1
1
1
0
0
0
1
2
0
0
0
0
1
0
0
1
2
1
1
0
1
1
2
1
2
1
2
1
1
1
1
2
0
0
0
1
2
1
2
2
0
0
2
0
2
1
0
1
1
1
2
2
1
1
1
2
2
2
1
1
2
1
1
1
0
0
1
2
1
1
1
2
2
1
1
1
1
0
2
2
0
0
1
0
1
0
1
2
1
1
2
1
0
1
1
0
0
2
1
2
0
0
0
2
0
1
1
1
0
0
1
0
1
2
1
1
1
1
1
1
0
1
1
0
0
1
0
2
0
1
0
1
2
0
2
2
0
1
1
0
1
2
1
1
2
1
0
0
0
0
2
0
2
2
1
1
2
0
1
0
1
2
0
2
0
2
0
1
0
1
1
2
3
2
2
0
1
0
0
1
0
0
2
2
1
1
1
1
0
1
2
1
0
1
2
1
1
1
0
0
0
1
0
1
1
1
1
0
1
1
1
2
0
1
0
3
0
1
0
0
0
1
0
1
1
0
0
0
1
0
2
1
1
1
1
0
1
0
0
2
0
0
1
2
0
0
2
2
2
2
1
1
1
2
0
1
1
1
0
0
2
1
1
1
0
0
1
0
2
1
0
2
0
0
1
1
1
0
1
0
0
1
1
1
2
2
1
0
2
1
0
1
0
2
0
2
1
1
1
1
1
1
1
0
2
2
1
1
0
1
0
0
1
0
0
1
0
1
0
1
0
0
0
2
1
0
2
0
2
0
1
1
1
1
0
0
1
0
0
1
2
1
1
0
0
0
1
2
1
0
0
2
0
0
1
1
2
1
1
1
1
2
1
0
1
0
0
1
0
0
0
1
2
3
0
1
0
0
1
0
0
1
0
1
0
0
2
0
1
1
1
0
0
2
2
1
1
0
2
2
1
1
0
1
1
1
0
1
2
1
2
0
1
0
0
1
1
0
2
1
0
0
0
2
0
2
0
0
1
1
0
3
1
2
1
2
0
2
1
0
1
4
1
1
1
0
0
0
1
1
2
1
0
1
2
0
0
0
0
1
1
2
2
2
1
1
0
0
1
1
1
2
2
1
2
0
2
1
1
0
1
0
1
1
0
1
2
0
1
0
2
1
1
1
1
2
0
0
1
1
2
0
1
2
1
1
1
3
0
2
2
2
1
1
0
1
0
2
1
0
3
1
1
0
1
0
1
0
1
0
0
2
0
3
2
0
0
1
1
1
2
0
0
0
1
0
3
2
1
1
0
2
0
1
2
1
1
2
1
1
1
1
1
0
2
1
0
0
0
1
1
1
1
0
2
1
0
2
1
0
0
1
0
1
1
1
1
1
1
0
1
1
0
0
3
1
1
2
1
2
2
1
0
1
1
0
2
0
0
0
1
1
1
1
0
1
0
1
2
0
2
0
0
1
1
1
0
0
1
1
1
0
2
0
1
0
1
1
0
0
1
0
1
1
0
1
1
1
2
2
0
0
1
2
1
0
1
0
1
1
1
1
1
1
1
1
0
1
0
2
2
2
0
1
0
0
2
0
2
1
1
1
1
1
0
1
1
0
0
1
0
1
0
0
0
0
2
2
0
2
0
1
0
1
1
0
2
1
0
1
1
1
1
0
0
1
0
0
1
0
1
1
1
0
0
0
1
2
1
1
1
1
1
1
0
2
2
1
3
2
0
0
0
2
0
2
2
1
2
1
0
1
0
1
1
0
1
0
2
1
2
0
0
2
1
1
2
0
1
2
0
0
0
1
0
1
0
2
0
0
0
0
1
2
0
1
1
0
2
0
2
1
2
0
2
0
2
2
0
1
0
0
0
1
0
1
1
1
2
1
1
1
1
0
2
2
0
2
1
1
1
0
1
0
1
0
1
0
0
1
0
1
0
0
1
0
2
2
0
0
1
1
2
0
1
1
0
1
0
2
1
2
0
0
0
1
2
1
2
1
0
0
1
2
2
0
2
1
0
1
2
1
2
0
2
1
0
1
1
1
1
1
1
0
2
1
1
0
1
0
1
0
0
1
1
1
1
2
2
4
0
0
1
0
2
0
1
1
1
0
0
1
2
2
1
0
1
2
4
0
1
0
1
1
0
0
2
0
2
1
2
0
1
1
2
0
0
0
2
2
2
0
2
0
1
1
0
0
0
1
0
1
2
1
1
2
0
2
2
1
1
1
0
2
1
0
0
1
1
1
0
1
0
0
1
2
0
2
1
2
0
2
1
1
2
1
2
3
0
0
1
1
0
1
0
0
2
0
0
2
2
1
1
0
2
2
1
1
1
1
1
0
2
1
1
1
1
0
1
1
1
2
2
2
0
0
1
2
1
0
2
2
1
1
1
1
2
1
2
1
2
1
3
2
0
0
3
1
1
1
1
2
2
1
1
2
1
1
1
0
2
0
1
2
1
2
2
0
1
1
2
2
1
1
1
1
1
1
0
1
1
1
0
0
2
2
0
1
1
1
2
1
2
1
1
3
2
1
2
1
2
0
0
2
1
1
1
0
0
0
1
2
0
1
1
1
2
0
0
1
0
1
1
1
0
1
0
1
0
0
1
0
1
2
1
1
2
1
1
1
0
0
2
2
1
1
1
1
2
1
0
1
0
2
0
0
2
1
2
1
1
1
0
1
0
0
0
1
0
2
1
1
2
2
0
2
0
0
5
2
1
1
0
1
1
1
2
1
1
1
1
2
3
1
1
0
1
1
2
1
1
0
2
1
2
1
1
0
1
2
1
1
1
1
0
0
2
2
2
0
1
0
0
1
0
0
1
1
1
1
2
0
1
1
0
1
2
1
1
0
2
0
2
1
1
1
0
0
0
1
1
2
1
1
0
1
2
1
1
1
0
1
2
2
1
1
0
1
1
0
1
2
0
4
0
0
2
2
0
2
1
0
0
0
1
1
1
2
1
2
0
0
2
0
0
0
1
0
0
2
1
1
0
2
2
0
1
4
0
4
1
0
1
0
0
0
1
1
1
0
0
3
0
1
2
0
1
0
1
2
1
1
1
2
1
2
1
1
0
1
1
1
1
1
1
1
0
2
1
0
1
0
0
0
1
1
0
0
0
0
0
0
1
1
1
0
1
2
0
1
0
1
2
0
1
2
2
0
0
0
1
1
2
1
1
0
0
0
1
1
1
0
2
1
0
0
1
0
2
0
1
1
1
0
1
2
1
0
1
1
1
0
0
1
0
2
0
1
3
0
1
1
0
2
1
0
1
1
0
2
1
1
0
0
2
1
1
1
0
0
1
1
2
2
0
2
0
2
0
0
0
1
2
0
1
0
0
1
1
2
1
1
2
0
2
0
1
2
1
1
2
2
2
0
1
2
1
0
2
1
1
1
1
1
1
0
0
2
1
1
0
1
2
3
2
0
0
2
1
1
0
1
1
0
0
0
1
1
1
1
0
1
0
0
1
1
1
1
1
0
2
1
0
1
0
2
0
0
1
2
2
0
2
0
0
2
0
1
1
1
1
2
1
0
1
1
2
0
2
0
2
0
1
1
1
0
2
2
2
1
2
2
0
0
0
1
0
1
1
1
2
2
0
1
2
0
0
1
0
0
2
2
0
0
2
0
1
0
0
0
2
1
2
0
1
2
2
0
0
0
2
0
1
0
2
1
2
1
0
0
0
1
6
1
0
2
1
1
0
1
1
1
1
2
1
2
2
1
0
0
2
0
2
1
0
1
1
1
1
2
1
1
1
0
2
0
0
1
1
1
0
0
0
0
1
1
1
1
0
0
1
0
0
7
2
1
1
0
0
1
0
1
1
2
0
1
2
1
1
0
1
2
1
1
1
1
0
1
0
0
2
1
0
1
0
2
1
1
2
0
1
0
1
2
1
0
1
0
2
2
1
1
0
1
0
1
1
2
2
0
1
0
1
1
0
1
1
1
1
0
1
2
2
0
2
0
1
2
3
1
1
2
1
0
0
0
0
1
1
1
2
0
1
1
0
0
1
0
0
0
0
2
1
0
1
2
0
1
1
1
1
1
1
1
1
1
0
1
0
1
1
0
0
1
0
0
1
0
0
2
1
0
1
1
1
1
1
0
1
0
0
2
2
0
0
1
1
2
1
1
2
0
2
0
0
2
2
2
1
2
0
0
5
2
0
1
2
0
0
0
1
0
1
1
2
0
0
1
1
1
1
1
1
0
1
0
2
0
0
2
1
1
1
1
1
1
1
0
2
1
1
1
2
1
1
0
2
2
0
1
2
1
0
0
4
1
2
1
1
0
0
1
0
0
1
1
1
0
1
0
0
0
0
1
1
1
1
1
0
1
1
0
2
4
1
2
0
0
0
2
1
1
2
2
1
1
0
1
1
0
0
2
1
0
1
1
0
0
1
1
0
0
2
1
1
1
1
0
1
2
1
1
3
1
2
0
1
0
0
0
2
0
0
0
1
0
2
2
0
2
1
1
1
1
0
1
1
1
1
0
1
1
2
2
1
1
0
1
1
0
1
0
0
1
0
0
3
1
1
2
0
0
0
1
1
1
1
0
0
1
1
0
1
1
0
0
2
0
0
1
2
1
1
0
1
3
1
1
2
0
2
1
1
1
2
0
2
1
1
2
1
0
0
1
2
0
2
3
0
2
1
2
0
1
1
1
1
0
2
0
2
1
1
0
1
0
2
2
2
0
1
2
1
1
1
1
0
1
1
2
0
2
2
2
2
1
2
1
1
1
1
2
0
2
0
3
1
1
0
2
0
0
2
1
0
2
2
0
1
0
0
1
1
0
1
1
2
0
2
0
1
1
1
0
2
2
0
2
0
0
0
1
0
1
2
0
1
2
0
1
1
1
1
0
0
2
1
2
1
1
1
1
1
2
2
1
0
1
1
1
1
1
1
0
0
1
1
1
1
3
0
1
1
1
0
1
2
2
2
0
0
1
1
1
1
0
2
1
2
0
1
1
0
2
1
2
1
1
1
1
1
1
1
2
1
0
0
1
1
0
0
0
1
2
0
1
2
1
2
1
1
1
0
0
0
1
2
0
1
0
0
0
0
2
0
1
1
1
2
0
0
0
0
1
1
1
1
0
1
2
0
1
0
1
1
5
1
1
2
0
1
0
1
1
1
2
1
1
1
1
2
1
3
2
1
1
1
0
2
1
2
1
1
1
0
1
0
1
0
1
0
0
0
2
0
1
1
1
0
2
1
3
1
0
1
2
2
1
1
0
2
0
0
1
0
1
1
1
0
0
2
1
1
2
1
1
2
1
1
1
1
0
2
0
6
2
1
2
0
0
1
0
1
1
1
2
1
1
1
2
1
0
1
1
0
2
1
1
1
1
1
3
1
2
1
2
1
2
1
1
1
0
1
0
0
1
2
0
1
1
1
0
0
0
1
1
0
0
1
0
1
1
0
1
1
2
1
0
2
2
1
1
1
0
2
0
4
0
0
0
1
1
1
1
2
0
1
1
0
1
1
0
0
2
0
0
1
0
0
0
1
2
1
1
0
2
1
1
0
2
2
1
0
0
0
2
1
1
1
0
1
1
1
2
1
0
1
0
2
1
1
2
0
1
1
0
1
1
0
2
1
1
0
0
0
1
1
0
1
0
1
2
1
2
1
0
2
0
0
0
0
1
0
0
2
1
1
1
1
1
2
0
3
1
0
3
0
0
2
1
1
1
0
5
1
1
1
2
1
1
2
1
0
2
0
0
1
1
1
2
3
0
0
1
1
0
1
1
1
1
1
1
2
2
0
0
0
2
3
1
0
0
0
0
0
1
0
0
0
0
1
1
1
1
1
0
2
1
2
1
1
2
2
1
2
1
3
2
2
1
0
2
2
1
1
2
1
1
1
1
0
0
1
1
1
2
0
1
1
1
0
1
0
0
0
0
0
2
1
1
1
2
0
2
0
3
1
0
0
2
2
0
0
2
1
2
1
1
2
2
1
2
1
2
1
0
2
1
2
1
1
1
1
1
1
0
0
1
1
2
2
2
1
1
1
2
0
0
2
1
2
2
1
2
2
0
0
0
0
2
1
0
1
0
1
0
0
0
1
1
2
0
1
1
1
0
2
0
1
2
2
1
1
2
1
1
1
0
0
1
1
0
1
2
0
1
0
2
0
1
1
0
1
1
2
1
0
0
0
1
0
1
0
0
1
2
1
0
2
1
1
1
1
0
2
2
1
2
2
0
0
0
1
1
0
3
1
1
1
1
1
1
1
3
1
1
1
0
1
0
2
0
0
0
2
1
0
1
1
1
1
0
2
1
0
2
0
0
1
1
1
1
1
1
0
2
1
1
2
1
1
1
0
2
1
0
0
0
2
1
1
0
2
0
2
0
1
1
1
2
2
0
2
1
1
1
1
2
1
1
2
1
1
1
1
1
0
2
1
2
1
1
0
1
1
1
0
3
2
1
1
2
2
1
2
1
0
1
1
2
1
2
1
1
1
1
1
1
0
0
2
0
1
0
0
0
2
1
1
1
0
1
1
1
1
0
2
1
0
2
2
0
2
1
1
1
1
2
2
0
2
2
2
1
1
1
1
2
2
0
0
2
0
1
1
0
1
1
1
1
0
1
2
1
0
2
1
2
0
2
0
2
2
0
2
0
0
0
2
1
2
0
1
1
1
1
0
1
0
1
0
0
1
1
1
0
0
0
1
1
1
0
0
0
2
2
2
1
0
2
1
0
0
2
1
2
0
2
0
2
2
0
1
2
1
2
0
1
1
1
1
1
2
0
1
0
1
1
1
0
1
2
2
1
0
0
0
1
2
1
1
0
2
0
1
2
0
0
1
1
0
1
2
1
1
0
1
2
0
1
2
2
1
2
0
0
1
0
0
0
1
2
1
1
1
0
1
2
0
0
1
0
0
2
1
1
0
0
2
2
1
1
1
1
0
0
0
1
1
0
2
0
1
1
2
0
1
2
2
1
0
3
0
1
0
0
0
0
1
0
1
1
1
1
1
0
0
0
1
1
0
0
1
2
1
0
1
0
2
0
3
0
0
0
2
2
1
0
0
2
3
0
1
1
2
1
1
1
0
0
2
0
2
2
2
2
1
0
1
1
0
0
0
0
1
0
0
1
0
0
0
1
1
1
1
1
0
0
1
1
0
1
1
0
1
2
1
0
0
0
1
1
2
2
0
0
1
1
0
1
1
0
1
0
2
2
1
0
2
2
1
0
1
0
0
1
0
0
1
1
2
0
1
0
1
2
1
1
1
0
3
3
1
1
0
1
3
1
3
0
2
0
1
1
0
0
0
1
0
1
2
1
0
1
1
1
2
0
1
2
0
1
1
1
1
0
2
1
2
0
1
0
1
3
1
1
1
2
0
0
2
0
0
2
0
1
2
0
2
2
1
0
1
1
2
1
1
1
2
0
0
0
2
2
0
1
2
0
1
1
0
0
1
1
0
1
2
1
1
1
0
0
1
2
1
1
1
1
0
1
0
0
1
2
1
2
2
2
2
2
2
1
1
2
1
1
1
2
1
2
0
0
1
0
1
0
2
1
1
0
4
1
2
2
1
0
0
0
1
0
2
1
1
0
2
2
1
1
2
1
0
2
2
0
0
0
0
0
1
0
2
3
0
1
1
1
0
1
0
1
2
1
1
1
0
1
0
0
1
2
1
0
2
2
0
2
0
1
1
1
0
2
0
2
1
1
2
1
2
1
0
2
0
0
1
1
2
1
1
2
2
1
0
1
0
0
1
0
1
0
0
0
1
2
1
2
0
0
2
0
0
0
0
1
1
0
1
1
2
1
1
0
1
0
1
1
1
2
1
2
0
1
0
2
1
1
1
0
2
0
1
1
2
1
1
2
0
1
0
0
3
2
0
1
1
0
2
1
1
0
1
2
1
0
3
2
1
1
0
1
0
1
0
0
0
1
0
1
2
2
1
1
2
1
0
2
0
1
1
2
1
2
0
2
0
1
2
1
1
1
1
0
0
0
1
1
1
1
0
1
0
1
0
0
2
1
2
1
1
2
0
2
1
1
2
1
0
2
1
0
2
0
0
1
1
1
0
0
1
0
0
0
0
2
2
0
2
2
1
2
1
1
2
0
1
2
1
1
2
1
1
0
2
1
2
3
2
1
1
0
0
1
2
0
0
1
1
0
1
1
2
1
0
1
1
1
2
0
1
1
1
0
3
1
1
0
1
0
1
0
1
1
0
2
0
1
1
0
1
0
0
1
1
1
1
1
0
1
1
0
2
2
0
1
0
1
0
1
1
0
0
1
1
0
0
0
1
0
1
0
2
1
2
1
0
1
2
1
2
1
2
1
0
0
1
0
0
1
0
0
1
0
1
1
2
1
1
1
2
0
0
0
0
1
0
0
0
1
2
0
1
1
1
0
0
1
1
1
0
2
1
1
1
1
0
1
0
0
1
1
2
3
1
0
0
1
0
2
2
2
0
1
0
0
0
1
0
0
1
0
1
1
1
2
1
1
1
0
2
0
1
1
2
2
1
0
0
2
0
0
1
3
2
2
2
1
1
2
0
2
1
0
1
2
0
0
1
2
1
2
3
0
1
1
3
0
0
0
1
1
0
1
0
2
1
1
0
1
0
1
0
0
0
0
0
1
2
0
0
3
1
0
1
2
1
1
1
2
0
1
1
0
0
0
0
0
0
0
1
2
1
1
1
4
1
1
0
2
1
0
1
1
2
2
0
1
2
1
1
0
2
1
0
2
1
2
2
2
2
0
2
1
0
1
1
0
1
2
1
2
2
0
1
1
0
1
2
1
0
2
0
3
0
1
1
0
0
0
2
1
1
1
1
2
0
1
1
0
1
0
2
1
0
1
2
1
1
0
1
0
1
0
0
1
1
0
0
3
1
1
0
2
1
1
1
2
2
1
0
1
1
0
1
1
1
0
1
2
0
0
2
2
1
2
1
0
1
2
0
2
0
0
0
2
2
1
2
1
1
0
0
1
1
2
0
0
1
2
2
1
1
0
1
0
1
2
1
1
0
1
0
2
0
0
0
1
1
0
2
0
1
2
1
2
2
1
2
0
1
2
1
2
1
2
0
1
1
1
1
1
0
0
2
0
0
0
1
1
0
1
2
2
0
1
0
1
1
1
0
1
0
1
1
2
1
2
2
0
0
1
1
1
2
2
1
0
1
1
1
0
1
1
1
2
0
2
0
0
0
1
2
0
1
0
0
0
1
0
1
1
2
1
1
2
0
0
0
2
1
1
1
1
1
0
0
1
1
2
1
1
0
0
0
1
1
1
2
2
2
0
1
1
0
3
0
1
0
2
0
1
1
0
1
0
1
1
1
1
1
1
0
0
2
2
0
1
1
0
1
1
0
1
1
0
1
1
0
0
0
1
0
0
0
2
0
2
1
1
0
1
1
1
0
0
0
1
2
1
1
2
1
3
1
1
0
0
2
1
1
0
2
0
1
2
0
2
4
1
1
0
1
2
2
1
0
2
1
1
1
1
0
0
1
2
1
0
0
2
2
1
2
2
0
1
2
1
2
1
0
0
1
0
0
0
2
1
1
1
1
0
1
0
1
2
0
0
2
1
1
0
0
0
2
0
1
2
0
1
2
2
0
0
1
0
1
0
2
2
1
0
2
0
2
1
1
2
1
2
2
0
1
2
0
2
1
1
0
1
1
2
1
1
1
0
1
2
1
0
1
1
2
2
1
1
1
2
0
2
1
0
1
0
1
2
0
0
1
1
0
0
1
1
1
0
1
1
1
1
2
2
1
2
0
1
1
1
1
2
1
1
1
1
1
1
0
0
1
2
1
1
1
2
0
1
0
0
1
1
1
1
1
1
1
0
2
1
1
2
1
2
1
2
1
0
1
2
0
1
1
2
1
2
2
2
0
2
1
1
0
0
0
0
1
1
0
2
0
1
1
2
1
2
1
3
1
0
1
0
0
0
0
2
2
1
0
0
0
0
1
1
2
0
0
1
2
0
0
1
1
1
2
1
0
2
1
1
0
1
0
2
0
0
1
1
0
2
0
0
2
1
1
1
0
0
2
1
0
0
2
2
2
2
1
0
2
1
0
0
0
0
1
2
0
0
0
0
1
1
2
1
1
0
1
1
1
3
3
1
1
1
0
1
0
1
1
0
1
1
2
1
0
1
1
1
0
1
2
2
1
0
1
0
1
1
1
0
1
0
1
2
0
2
0
1
0
0
1
1
2
1
1
1
0
0
2
2
1
1
0
2
1
1
2
2
1
1
0
2
1
1
2
2
2
0
0
0
0
0
0
1
0
2
0
1
1
0
0
0
1
3
2
0
1
0
0
1
0
0
2
1
1
1
1
0
0
1
2
1
1
0
1
0
1
1
0
1
0
0
2
1
0
1
0
3
1
1
1
0
1
0
4
0
1
2
2
2
1
1
1
0
0
0
1
1
1
2
1
2
0
1
2
0
0
1
0
3
0
1
1
2
0
1
0
1
1
2
2
1
1
0
0
0
2
2
1
1
1
0
1
1
0
0
2
5
0
1
1
1
1
1
0
1
0
2
1
1
0
1
1
0
2
0
1
2
2
2
1
1
0
2
1
0
2
0
1
1
1
1
1
0
0
1
1
2
2
1
0
0
2
1
1
1
1
0
1
1
0
0
1
1
0
2
2
1
2
1
0
1
1
1
2
1
0
1
1
1
0
0
0
0
1
0
1
3
1
1
2
0
0
1
1
1
0
2
1
1
0
1
9
0
1
0
1
0
0
1
2
2
0
1
1
0
0
0
1
2
1
0
0
1
0
0
1
2
2
0
1
0
0
1
0
0
1
0
2
1
1
0
1
1
0
1
0
1
1
2
1
0
1
1
1
0
1
2
1
1
2
0
2
1
2
1
1
1
1
1
2
0
1
1
1
1
1
2
0
1
0
0
2
1
0
1
2
1
0
0
2
2
2
1
1
2
1
0
1
1
1
1
1
2
1
0
1
2
0
1
1
1
1
0
0
0
0
0
0
1
1
0
0
0
1
0
1
1
1
1
0
0
0
2
2
0
1
1
2
1
1
1
0
2
1
0
1
3
1
0
0
0
0
0
0
0
0
1
2
0
2
0
2
0
2
1
1
1
0
2
1
1
0
0
1
2
1
1
1
2
0
2
2
0
1
1
0
1
1
2
0
2
1
1
2
1
2
2
0
1
1
1
0
1
1
0
0
2
0
1
0
1
1
1
1
2
0
1
2
1
0
1
0
2
0
0
1
1
2
1
1
2
2
2
4
0
1
0
2
0
2
2
1
1
0
2
1
1
1
0
0
2
0
1
0
2
0
0
0
2
0
1
2
1
0
0
1
0
0
1
2
0
0
1
1
0
0
1
2
1
1
1
1
1
0
0
2
1
1
1
1
2
1
2
2
2
0
1
0
2
0
1
2
0
2
0
1
1
0
0
1
1
1
0
1
0
1
2
2
0
1
0
1
1
0
1
0
2
0
1
1
2
0
1
0
2
1
0
2
2
0
2
1
0
1
1
1
1
0
2
1
0
1
0
2
0
1
0
1
0
1
1
2
0
1
1
0
2
0
4
1
1
1
1
1
1
1
0
2
1
1
2
2
0
0
0
0
2
2
1
0
1
0
1
1
2
2
2
1
0
0
2
2
0
2
0
1
2
0
0
1
3
2
1
1
0
1
1
0
0
0
1
1
0
1
0
0
0
1
0
1
1
2
1
0
0
1
2
0
0
1
0
1
2
0
0
1
1
0
0
0
0
1
1
1
1
0
1
0
1
2
1
0
1
2
1
1
2
0
1
2
0
1
1
0
2
2
2
2
1
0
0
1
0
2
2
2
0
0
1
0
0
2
2
2
2
1
2
1
0
0
1
0
1
2
1
2
2
1
0
1
0
0
1
2
2
2
1
1
1
2
0
1
0
1
1
1
1
1
0
2
0
2
2
1
1
2
2
1
1
1
1
1
4
0
0
2
1
1
0
1
0
1
1
0
2
1
1
0
2
1
0
0
0
0
0
2
1
1
0
3
1
0
1
2
1
2
1
2
2
1
2
0
2
1
0
2
0
1
1
1
1
0
1
1
2
1
1
2
1
1
0
0
1
1
0
0
0
1
1
0
2
0
1
1
3
2
2
3
1
0
1
2
2
1
1
0
1
2
1
1
1
2
0
2
2
0
1
1
0
0
0
0
2
0
2
1
2
0
2
1
1
1
1
1
1
2
1
1
0
1
0
2
0
1
2
1
3
0
1
1
0
0
0
0
0
0
2
1
1
1
1
2
1
2
0
2
0
1
2
0
0
0
0
1
1
1
0
1
3
1
2
1
1
0
0
0
0
0
1
1
0
1
5
0
2
2
1
1
1
1
0
0
1
0
0
1
2
1
2
0
1
1
1
1
0
2
2
1
1
1
2
1
0
0
1
0
1
2
1
0
1
2
1
1
1
0
2
1
0
0
1
2
2
2
1
1
1
1
0
0
0
1
2
0
2
0
1
1
1
1
1
1
1
0
2
0
2
2
1
0
0
1
0
2
1
0
0
0
0
0
1
1
1
0
0
1
0
2
1
1
0
0
0
1
0
0
0
0
0
1
0
0
1
2
0
1
2
2
1
2
1
1
2
0
2
1
1
0
1
1
0
1
0
1
3
1
0
0
1
0
1
1
1
0
1
0
1
2
2
1
2
1
0
2
0
16
1
1
1
1
2
1
3
2
0
2
1
1
0
0
0
0
1
1
2
0
1
1
3
1
1
0
0
0
1
1
2
2
2
1
1
0
0
0
0
1
1
1
1
2
0
1
2
0
1
0
1
1
2
1
2
1
0
1
0
1
1
1
1
2
0
1
1
1
2
2
1
1
0
1
0
0
1
1
1
2
1
2
0
3
1
1
1
0
1
1
1
0
3
0
0
1
0
0
2
1
2
1
2
0
0
1
1
1
0
0
2
1
1
0
0
1
2
0
0
1
1
1
0
2
1
0
1
2
2
1
0
1
0
1
2
2
0
0
1
1
0
1
1
2
1
0
2
1
0
1
2
0
1
0
1
1
2
1
0
1
0
0
2
1
1
0
1
1
1
0
2
0
1
0
1
0
1
0
1
0
2
2
1
0
0
1
1
2
2
2
2
1
1
0
0
2
1
0
1
1
1
0
1
2
1
1
1
1
1
1
1
2
0
0
2
1
0
0
1
1
1
2
0
1
2
0
1
2
1
2
1
1
0
0
0
0
2
0
1
1
0
0
1
1
1
0
0
0
0
1
1
1
1
1
1
1
2
0
1
2
0
3
2
1
0
1
1
1
0
1
2
0
2
0
0
0
1
0
2
2
1
0
1
0
2
1
1
1
1
0
1
1
2
2
1
0
1
2
0
1
0
1
0
1
1
1
1
0
1
1
1
2
1
1
1
0
0
1
0
0
1
1
2
2
2
2
1
1
2
0
2
2
0
2
1
1
1
1
0
2
2
1
2
0
2
1
1
1
2
2
0
0
1
1
1
1
0
1
1
2
0
2
4
0
1
0
2
1
1
1
1
2
2
2
2
0
1
1
0
1
1
0
0
0
0
1
0
1
1
1
1
1
1
0
2
0
1
2
2
2
0
1
1
2
1
1
0
1
2
2
2
0
0
0
2
2
2
2
0
0
1
1
0
0
1
1
2
2
1
1
0
1
1
0
2
0
0
1
1
2
0
2
1
1
1
1
0
1
1
1
0
0
1
1
2
1
1
2
0
2
1
1
1
1
1
0
1
3
1
1
1
1
1
0
0
0
0
4
1
0
2
0
0
0
2
2
0
0
2
0
2
1
1
2
0
0
1
1
1
1
0
1
0
0
1
2
1
1
1
3
0
1
1
0
0
1
1
0
2
1
0
2
1
1
1
1
2
0
2
1
1
1
1
0
1
1
1
1
0
0
0
0
1
1
0
1
1
0
2
2
1
2
1
2
2
1
0
2
1
2
0
1
1
0
1
2
2
1
1
1
0
1
0
1
3
1
2
1
2
0
1
0
2
0
0
1
0
1
1
1
2
2
0
2
0
0
0
1
1
0
0
1
1
2
1
2
0
0
0
2
0
2
0
1
0
1
1
1
2
1
0
1
0
0
1
1
1
0
2
1
1
2
1
2
2
0
1
0
0
0
0
0
1
1
1
0
2
0
1
2
0
0
1
2
1
2
1
1
2
0
1
1
1
1
0
2
0
0
1
0
2
0
1
0
1
1
2
2
1
0
1
1
3
1
0
2
0
1
1
1
2
1
1
1
2
0
1
1
2
2
1
0
1
2
2
2
2
1
2
1
2
1
1
0
1
0
0
0
0
0
2
1
1
0
1
2
2
1
1
1
0
1
1
1
0
1
2
1
0
1
4
0
2
0
1
1
0
1
0
1
2
1
2
0
1
1
2
1
2
1
0
1
1
1
1
2
2
1
0
0
2
2
0
0
0
2
0
1
0
1
1
0
1
0
1
2
1
1
1
1
1
0
0
1
1
2
0
2
1
1
1
1
0
0
0
0
1
1
0
0
2
1
0
0
2
1
1
1
1
1
1
1
1
2
1
3
1
2
0
0
1
0
1
2
1
1
0
0
1
2
1
0
2
0
1
1
1
0
2
0
0
0
0
0
0
1
1
1
2
0
1
0
0
1
1
0
0
2
0
0
2
1
2
1
0
2
2
0
1
0
0
1
1
2
1
1
0
1
0
2
0
2
1
1
1
0
1
1
1
2
2
1
1
0
1
1
1
2
2
1
0
1
1
0
1
1
0
0
0
2
1
1
1
2
1
1
2
1
1
1
0
1
0
2
1
1
0
2
1
1
1
1
0
1
0
0
0
1
0
1
0
1
1
0
2
1
1
1
1
1
1
0
2
1
0
0
2
2
1
2
0
1
0
1
2
2
1
1
2
1
0
0
2
0
1
2
2
0
1
1
0
1
2
0
0
2
1
1
2
0
1
2
0
0
0
1
2
0
1
1
0
1
0
1
1
1
0
1
1
1
2
2
1
2
0
1
0
1
2
0
1
0
1
1
0
1
1
1
0
1
1
1
2
1
1
1
1
0
1
2
1
0
2
2
1
1
0
1
0
1
1
1
0
0
1
2
1
0
1
1
0
3
0
1
0
2
0
0
1
1
0
1
2
0
1
2
1
1
0
1
1
1
1
0
1
1
0
1
0
1
0
2
1
1
1
2
1
0
1
1
1
2
1
0
0
2
0
2
1
0
3
0
0
0
0
2
0
1
1
1
2
1
1
2
1
0
0
1
1
1
1
1
1
0
0
2
1
0
1
0
1
1
1
0
0
1
1
0
2
1
1
1
1
1
1
0
1
1
0
2
0
1
2
0
1
1
0
1
0
1
2
1
0
0
0
2
1
2
1
1
1
1
2
2
0
1
1
1
1
1
0
1
0
1
1
1
1
2
2
0
0
1
1
1
0
0
1
2
1
1
1
0
1
2
1
1
0
2
2
2
0
1
1
1
1
1
2
0
1
0
1
0
1
2
3
2
2
1
2
1
0
1
1
1
2
1
1
2
1
0
0
1
1
0
2
2
2
0
1
0
0
0
2
0
2
2
1
1
1
1
0
2
1
1
2
1
0
0
1
1
2
2
2
1
0
0
0
1
2
1
2
0
0
1
1
2
1
1
2
2
0
1
1
1
1
0
0
2
2
0
1
1
1
0
2
1
1
0
0
1
0
1
0
2
2
2
0
1
2
0
2
1
2
2
2
0
1
1
1
0
0
1
4
0
0
0
0
0
0
1
2
0
2
2
1
2
0
2
0
1
1
0
0
2
0
1
0
2
1
0
1
0
1
1
1
0
2
1
1
2
0
2
1
0
1
1
2
2
2
1
0
0
1
0
1
2
0
1
1
0
0
2
0
1
0
0
1
2
1
1
0
0
1
1
2
2
1
0
1
2
0
1
1
2
1
0
1
1
2
1
0
0
0
1
0
1
2
2
0
1
1
1
0
1
0
2
0
1
2
1
2
1
0
0
0
3
0
2
1
0
1
0
2
1
1
0
0
2
2
1
1
0
0
1
1
1
2
2
2
0
2
1
2
2
1
2
1
0
1
2
1
2
0
1
2
1
1
1
1
0
2
1
1
2
1
0
2
2
0
1
0
0
0
0
2
2
0
1
1
1
0
0
0
1
1
0
1
1
1
1
1
1
0
1
0
1
1
0
2
1
2
2
1
0
0
0
0
1
0
1
1
1
0
0
2
1
1
0
1
1
1
1
0
1
0
1
1
0
2
2
0
1
0
1
2
0
1
1
0
0
2
1
0
0
1
1
1
1
1
2
2
0
0
1
1
2
0
1
2
2
1
1
3
2
0
1
0
0
0
1
1
0
1
1
2
1
2
1
1
2
1
0
1
1
1
1
0
0
1
1
2
0
0
1
2
2
1
1
2
3
1
2
1
0
2
1
1
1
1
1
0
1
2
1
2
2
0
1
1
1
1
2
1
0
0
1
1
1
1
0
1
2
1
1
2
1
1
0
0
0
1
0
2
2
0
0
1
3
0
0
1
1
1
1
1
2
1
2
1
0
1
1
2
0
1
2
0
2
0
1
1
0
0
0
2
1
1
2
2
0
1
1
2
1
1
1
1
1
1
0
1
1
2
1
2
2
2
0
1
2
1
1
0
0
1
1
1
1
1
1
0
1
1
1
1
0
1
1
2
1
1
2
0
0
0
1
0
1
1
0
1
0
2
1
3
1
0
0
0
1
1
1
0
0
2
0
0
0
1
1
2
2
0
0
0
0
1
1
1
0
0
0
3
0
1
0
1
1
1
0
0
0
1
1
1
1
0
0
0
2
1
0
0
1
1
0
0
1
1
1
0
1
1
1
1
1
2
0
2
2
1
2
2
0
2
2
1
0
0
1
1
1
1
0
0
0
1
1
0
2
1
1
1
1
0
1
1
0
1
0
1
2
0
1
1
1
1
0
1
1
0
1
1
0
0
0
0
1
5
2
2
2
1
0
1
1
1
0
0
1
1
1
1
1
1
1
1
0
1
2
1
0
1
1
2
2
1
1
1
2
1
1
0
2
2
2
0
1
2
0
2
1
1
1
1
1
0
2
1
1
0
1
2
0
0
2
2
0
0
2
2
0
0
2
0
1
1
2
1
1
0
0
1
0
1
2
0
0
1
0
1
1
0
1
2
1
2
1
1
0
2
1
0
1
1
2
1
2
1
2
0
1
1
0
1
1
0
1
0
1
0
0
1
2
0
1
0
1
1
0
1
2
1
0
2
2
1
2
0
2
2
1
2
2
2
1
2
1
0
1
1
1
1
1
1
1
0
0
1
1
1
1
2
3
2
2
0
0
1
1
1
1
0
1
1
2
2
1
2
1
2
0
0
1
0
0
1
1
2
1
1
1
0
2
1
2
1
0
0
1
0
0
1
0
0
1
1
0
0
0
2
1
0
1
1
1
0
0
2
1
1
0
0
1
1
1
0
1
0
0
2
1
0
1
2
1
2
3
1
1
1
1
0
1
2
2
2
1
1
1
2
0
0
1
4
2
0
0
1
2
0
2
0
0
2
1
0
0
0
0
1
1
2
2
1
1
0
0
0
0
1
0
0
0
1
1
1
1
0
0
1
2
1
1
3
1
2
2
0
0
1
0
0
2
0
0
1
2
2
0
1
1
0
1
2
1
1
0
1
2
1
1
0
2
1
1
1
1
1
0
1
3
1
2
0
1
0
2
0
1
1
0
2
2
0
1
2
2
2
2
0
0
0
0
0
1
2
0
0
2
1
1
2
2
1
1
2
0
0
2
2
1
2
1
0
1
1
1
0
0
1
1
2
1
0
1
0
2
1
1
1
1
1
2
2
0
0
0
0
1
0
0
1
2
2
1
0
1
2
1
0
1
0
1
2
1
1
1
0
2
2
0
1
2
3
1
0
1
0
2
1
0
2
2
2
0
0
0
1
1
1
1
1
2
2
1
0
1
1
1
1
1
1
0
0
1
1
1
1
0
1
0
0
1
1
1
1
0
0
1
1
1
0
1
1
2
1
0
1
1
0
0
0
2
2
2
1
1
1
1
0
1
1
0
2
1
0
1
0
1
1
1
1
0
0
2
2
0
2
1
1
2
0
0
1
1
2
0
1
0
2
0
2
0
1
0
0
0
0
2
1
0
0
2
1
0
1
1
0
1
1
0
0
2
0
0
0
1
1
1
1
1
1
2
0
1
1
2
0
2
2
2
0
1
1
1
1
1
0
0
0
1
2
8
1
2
2
0
1
0
1
1
1
0
1
0
1
1
0
1
2
2
3
1
2
0
0
1
1
1
0
0
1
1
1
1
0
1
0
2
2
0
0
1
1
2
0
2
0
2
2
0
2
0
0
2
1
1
1
2
2
1
1
0
1
0
2
2
0
0
1
0
1
0
1
0
2
0
0
0
1
1
0
0
0
1
1
0
2
1
0
1
1
0
1
0
0
0
1
0
0
2
1
1
0
1
1
1
1
1
0
0
2
2
0
1
3
0
1
1
1
2
0
1
0
1
1
0
1
2
0
1
1
1
0
1
1
0
1
2
0
0
1
1
0
1
1
0
0
1
0
0
1
1
0
1
2
1
1
1
0
1
1
1
1
1
0
3
0
0
1
0
0
0
0
0
1
1
1
1
0
1
1
1
1
1
1
2
1
1
0
0
1
1
0
2
0
0
1
1
0
1
1
1
1
1
0
1
0
1
0
1
1
0
2
1
1
1
1
1
1
1
0
2
1
0
1
1
0
0
1
1
2
0
0
1
1
0
0
0
0
1
1
1
2
0
1
0
1
0
2
1
2
0
2
0
0
1
1
1
1
1
2
0
2
2
2
0
1
1
2
1
1
1
2
0
1
0
0
3
2
2
1
1
1
0
2
1
1
2
1
2
1
2
0
2
2
0
2
2
0
2
1
2
0
0
1
1
0
1
0
0
0
1
2
1
1
0
0
1
0
2
1
1
0
0
1
1
0
1
1
1
1
2
1
0
1
0
1
2
1
1
1
0
2
1
1
0
5
0
1
0
0
0
0
1
0
1
3
1
2
2
2
2
0
3
2
2
1
1
0
1
0
0
2
2
2
0
1
0
1
0
1
1
2
1
1
1
0
0
0
3
0
2
2
2
1
2
2
0
1
2
1
2
0
0
1
1
2
5
0
2
1
2
0
1
1
0
0
0
2
0
0
1
2
0
0
0
0
1
0
1
1
1
0
0
2
1
1
1
1
1
1
2
1
0
2
0
1
1
1
1
1
1
0
1
1
0
0
2
2
2
0
1
1
1
1
0
1
0
1
1
0
2
0
1
0
0
1
1
0
2
0
2
1
0
2
0
1
1
2
1
0
1
2
2
0
1
1
1
1
1
0
0
2
1
0
0
2
0
3
0
1
2
1
1
2
0
1
0
1
0
2
0
0
1
1
1
0
1
0
1
1
0
0
2
1
0
1
1
1
1
1
1
1
1
1
1
0
2
1
1
0
0
1
0
2
2
1
0
1
1
1
0
1
1
0
0
1
1
0
0
1
1
1
1
2
2
1
0
2
0
1
0
1
0
0
1
0
0
1
1
0
2
2
0
1
1
1
0
1
0
2
1
1
1
1
0
1
1
0
2
2
1
1
1
2
2
1
0
1
1
0
0
1
1
2
0
2
2
1
0
2
1
0
1
0
1
1
2
0
3
1
1
1
1
1
1
0
0
1
1
0
0
1
2
2
0
0
0
1
0
0
2
0
2
2
1
1
2
2
2
0
3
1
1
1
0
0
3
0
2
1
1
0
0
1
0
2
1
1
0
2
1
1
1
1
2
2
2
1
0
2
0
1
0
2
2
0
2
0
0
2
1
1
0
1
1
0
1
0
0
0
1
1
0
2
2
1
0
1
1
0
1
1
0
0
1
1
0
0
2
2
1
1
0
1
0
4
1
0
2
1
3
2
0
2
0
1
1
1
1
0
0
1
1
0
0
1
1
0
0
2
1
1
2
1
0
0
1
1
0
2
0
2
1
0
1
2
1
1
1
1
0
0
0
0
2
2
0
0
0
1
2
2
1
0
6
1
1
0
2
1
1
0
1
2
0
2
1
0
1
1
2
0
0
1
1
0
1
0
2
0
0
2
2
2
0
3
1
0
1
2
0
1
1
0
0
2
1
1
0
0
0
2
1
0
2
2
1
2
1
1
2
1
1
2
1
1
1
2
1
2
0
2
1
1
1
2
0
2
2
0
1
1
1
2
1
1
2
1
2
2
1
2
1
1
0
2
2
1
0
0
1
0
2
2
0
2
2
0
1
0
1
1
0
1
1
1
0
1
2
1
1
1
1
1
2
0
1
1
1
1
0
1
1
0
1
1
1
1
2
1
2
0
1
0
2
2
1
2
1
0
2
2
1
1
2
0
1
1
2
1
0
1
1
1
1
0
1
2
1
1
1
1
0
1
1
0
1
0
1
2
1
0
2
0
2
1
1
1
2
0
0
1
1
0
1
2
1
2
1
1
1
1
1
1
1
1
2
0
0
1
1
1
0
1
0
0
1
1
2
0
0
0
0
1
1
1
1
1
0
0
1
2
2
0
0
0
2
0
3
2
1
2
2
0
0
3
1
0
1
1
1
1
0
1
0
0
1
1
2
2
1
1
1
0
1
0
1
1
1
2
2
1
1
1
2
2
1
2
2
2
0
0
2
1
0
1
0
0
1
2
2
0
1
0
1
1
0
2
0
1
1
0
1
1
0
1
0
2
2
2
1
1
0
1
0
2
0
0
2
1
0
1
0
1
0
0
1
1
0
1
1
1
2
0
2
1
1
0
0
1
0
1
0
0
1
1
1
1
1
1
0
0
1
1
1
1
1
2
3
0
1
1
1
0
0
1
2
1
2
2
2
1
1
1
1
2
0
0
2
2
2
1
0
1
2
1
1
1
1
1
2
1
0
1
1
1
2
1
0
1
0
1
0
1
1
1
0
1
0
0
3
2
0
2
0
0
2
2
0
0
1
2
1
0
0
0
1
0
1
1
1
1
0
0
0
1
0
1
1
2
1
2
1
2
2
2
1
0
0
3
0
1
2
2
0
1
2
2
1
1
0
0
2
1
1
1
1
2
1
1
2
1
1
0
0
0
1
1
1
0
0
2
2
0
1
0
1
0
0
0
1
1
2
0
1
1
1
0
1
0
1
2
0
1
2
1
0
0
0
0
1
0
0
0
0
1
1
2
1
0
1
1
0
0
1
0
1
1
2
1
1
0
1
0
2
1
3
2
1
1
1
1
1
1
0
1
0
1
0
0
3
2
1
1
1
1
1
1
0
1
2
1
0
0
0
2
1
0
0
1
2
0
3
2
2
1
0
1
0
2
1
0
2
0
0
0
0
1
1
0
1
2
0
2
2
2
2
0
2
0
1
0
2
1
0
0
1
1
1
2
0
2
0
1
1
1
2
2
1
1
1
1
1
2
1
1
0
0
0
1
1
1
2
1
0
2
0
1
1
2
1
0
0
1
0
2
0
0
1
1
1
0
0
1
1
1
1
2
0
0
1
0
1
3
1
0
1
1
0
1
0
1
2
1
1
0
0
1
0
1
0
0
2
0
1
2
0
2
0
1
2
0
1
1
1
2
0
0
0
1
0
0
1
1
2
1
1
2
0
2
0
2
2
0
1
1
0
0
1
1
1
1
1
1
0
3
1
1
2
0
1
1
1
1
0
0
1
0
0
1
0
1
1
0
0
1
1
0
0
0
2
2
0
2
1
1
1
2
1
2
1
1
1
2
0
0
1
2
2
2
1
1
2
0
1
1
2
1
0
1
1
0
1
1
2
0
0
1
2
0
1
0
1
0
0
0
3
0
1
2
1
0
1
1
1
3
1
2
2
1
1
2
1
1
1
1
2
2
1
1
2
1
2
2
0
1
0
1
1
0
2
1
1
1
0
0
1
2
1
2
1
0
0
0
0
0
0
0
0
1
2
1
0
1
1
0
2
1
1
1
1
1
1
0
1
0
0
0
1
1
0
1
1
0
1
0
1
9
1
1
3
0
0
0
0
1
1
1
2
0
1
4
1
0
0
2
0
0
0
1
1
0
0
0
2
1
0
0
2
1
0
0
0
2
1
1
2
1
0
0
0
2
1
1
1
1
2
0
1
1
1
1
1
1
0
0
1
0
1
2
0
2
0
0
1
3
1
1
2
0
0
2
0
0
0
1
1
1
2
1
0
0
1
0
2
0
2
1
1
1
3
1
1
1
2
0
2
0
1
2
1
1
1
1
0
0
2
1
0
0
1
0
1
1
2
1
1
0
2
1
0
1
1
0
1
1
0
1
1
1
1
1
1
0
1
2
1
0
1
2
0
1
1
0
1
2
1
1
1
1
1
1
1
0
2
1
1
0
1
0
0
1
0
1
0
0
2
2
0
1
1
1
0
1
2
0
0
1
0
2
1
1
0
1
1
1
2
1
0
1
1
2
1
1
2
1
1
1
1
1
2
3
0
0
1
2
2
0
0
1
2
1
0
3
2
0
2
2
0
1
2
2
1
2
2
1
0
2
1
2
1
2
0
0
0
2
1
1
0
1
1
0
0
2
1
2
0
2
1
0
1
1
1
1
0
1
0
0
1
2
1
0
1
1
1
2
0
1
0
1
1
2
2
1
0
0
1
2
0
1
1
1
1
1
1
0
0
1
1
2
0
2
0
2
2
1
1
0
1
3
0
1
2
0
1
1
0
1
1
2
1
0
0
5
2
2
1
2
1
0
0
2
1
1
0
0
0
2
1
2
0
0
1
0
1
1
0
1
1
1
2
0
1
0
0
0
1
0
2
0
1
1
2
0
2
0
2
2
1
1
0
1
2
0
0
0
1
1
1
1
1
1
1
2
0
1
0
0
0
1
0
1
1
1
2
0
1
1
0
0
0
1
1
2
0
1
2
1
1
2
1
1
2
2
2
1
0
1
1
1
1
0
1
1
2
0
1
1
1
2
0
1
1
1
1
2
1
1
1
0
0
1
0
1
1
0
2
0
2
0
1
2
0
1
0
2
1
0
1
0
1
1
1
0
0
1
2
0
0
1
1
1
1
1
1
1
3
0
0
0
0
1
1
2
0
1
0
1
1
0
1
1
1
1
2
0
0
1
0
3
2
1
1
1
2
0
1
2
0
1
1
1
0
1
0
0
1
1
0
0
0
1
0
2
0
1
1
2
2
1
1
1
1
1
0
1
1
1
2
2
0
0
2
1
1
2
2
1
1
1
0
0
0
2
0
1
0
1
1
1
1
1
1
2
1
1
1
1
0
2
1
1
0
1
1
1
1
1
0
2
1
0
2
0
0
1
1
1
2
1
2
2
1
0
0
2
1
2
0
1
0
2
5
1
1
1
2
1
0
1
0
1
2
1
1
2
0
1
3
0
1
2
2
2
2
2
2
1
0
1
1
1
1
1
2
2
1
1
0
1
1
0
1
0
1
0
2
2
1
1
0
1
0
1
0
0
0
1
1
0
0
0
1
1
1
0
0
1
3
0
1
1
0
1
2
2
2
0
1
1
2
2
0
2
1
1
0
1
1
2
0
0
0
2
0
1
1
2
1
1
1
1
1
1
1
2
2
2
1
1
1
1
1
0
1
1
2
0
2
1
1
1
0
1
0
2
0
0
0
0
2
1
1
0
0
0
1
1
1
1
1
1
2
0
0
1
0
2
1
0
0
1
1
0
2
1
0
2
1
2
1
2
0
1
0
2
1
0
1
6
1
1
0
1
1
1
1
1
1
1
0
0
1
1
0
3
2
1
1
2
0
2
2
1
0
0
1
1
0
1
1
2
2
1
0
2
2
0
2
2
0
2
2
2
2
1
2
1
1
0
0
0
0
2
1
1
1
0
0
2
0
2
1
1
0
1
1
1
1
1
1
1
0
0
1
0
2
1
0
1
1
1
2
1
1
0
1
1
2
1
2
4
1
1
1
1
2
0
1
2
1
2
2
2
2
1
1
0
1
1
2
1
0
1
1
1
2
1
1
0
1
2
0
0
0
2
2
0
1
0
2
0
1
2
1
1
2
0
1
2
2
1
2
2
1
0
2
1
2
1
0
0
1
0
0
1
0
2
0
0
2
1
2
1
0
1
1
0
1
2
1
1
0
0
0
0
0
1
1
0
0
1
2
0
1
2
0
1
0
1
0
1
1
1
1
0
0
1
1
1
1
0
4
1
2
2
1
1
0
0
0
0
2
0
0
1
2
1
1
0
2
2
1
1
1
1
2
0
0
1
1
1
0
1
0
1
1
2
1
1
0
2
0
1
1
0
0
0
0
2
0
1
0
1
1
6
1
2
1
2
1
1
4
0
0
0
1
0
0
1
0
1
1
1
2
1
1
2
1
0
1
2
1
0
1
1
2
0
1
0
0
1
2
1
0
1
0
1
0
1
0
0
1
2
0
0
0
2
0
0
1
1
1
2
0
0
0
0
0
1
0
1
0
1
0
1
0
0
1
1
0
1
0
1
2
0
2
0
2
2
2
1
0
1
1
1
1
1
0
0
1
2
1
1
1
1
2
1
1
1
0
1
0
0
0
2
1
2
1
1
0
1
1
0
2
2
3
1
0
0
1
1
2
1
3
0
0
2
0
1
1
0
1
1
2
1
0
0
0
1
2
2
0
3
0
1
0
0
0
0
2
0
0
1
1
0
0
2
2
0
1
1
0
0
1
0
1
0
1
0
1
2
2
0
1
1
1
2
1
2
1
1
1
0
1
2
2
1
1
1
1
0
0
0
0
1
0
2
1
0
0
1
1
1
2
1
1
0
1
0
1
2
2
1
1
1
0
2
0
2
1
0
1
2
2
0
0
0
0
1
2
1
1
1
1
1
0
0
1
0
1
2
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
0
2
1
1
1
1
1
2
1
1
2
1
1
1
0
1
5
4
0
1
1
2
1
1
1
0
1
2
1
2
0
0
1
1
1
1
1
1
2
2
1
1
2
1
0
2
2
2
2
2
1
1
0
1
0
0
2
0
0
1
4
2
1
0
1
1
1
1
0
1
1
2
2
0
0
0
2
0
1
0
0
1
0
1
2
1
0
1
0
0
1
1
2
0
2
2
2
1
0
1
1
1
2
0
0
2
1
1
0
0
2
3
1
2
0
1
1
2
0
1
1
2
1
2
1
1
0
0
1
0
1
1
1
1
1
0
1
1
2
2
0
1
1
0
1
1
1
1
0
2
0
0
0
2
1
1
1
4
1
0
0
0
0
0
0
2
1
1
1
0
1
1
1
0
2
2
2
0
2
1
2
0
0
1
1
1
0
1
0
0
1
0
1
1
1
0
0
1
2
0
1
1
0
1
0
0
2
2
1
1
1
0
0
2
2
1
1
1
1
1
0
2
0
2
0
0
1
2
1
2
1
0
1
0
1
1
0
0
0
1
2
1
0
1
0
0
1
1
1
1
1
0
0
1
1
3
2
1
0
1
3
1
0
1
1
1
0
1
1
1
0
0
1
1
0
1
1
1
0
0
0
0
0
2
1
1
2
2
0
1
1
0
2
1
1
2
0
0
2
1
1
1
0
1
0
0
0
2
0
2
0
1
0
1
2
0
1
1
2
0
2
1
0
1
2
2
0
0
0
1
0
2
2
2
0
1
1
1
2
1
2
2
2
0
0
1
2
1
2
2
1
1
1
1
0
2
2
0
0
1
1
0
1
0
1
2
1
2
1
0
0
1
2
3
1
1
1
0
1
1
1
1
0
1
1
1
0
0
1
1
2
1
0
2
1
0
1
1
0
1
0
0
1
0
1
1
0
1
0
0
2
2
1
0
0
0
1
0
1
1
0
1
4
2
0
1
1
2
1
2
0
1
0
0
1
1
0
2
1
1
0
0
1
1
1
0
3
0
1
1
0
0
1
0
0
1
0
2
0
0
1
1
2
1
1
0
2
2
2
0
1
0
1
1
1
2
1
1
0
1
1
0
0
1
3
2
0
2
1
2
1
2
0
2
0
1
0
0
2
1
2
1
0
0
1
2
0
0
1
0
0
1
1
2
1
1
2
1
1
0
0
1
2
1
2
1
0
0
1
1
2
0
1
1
1
0
1
2
0
1
0
1
0
1
2
2
2
2
1
0
1
2
0
2
1
0
0
1
0
0
0
1
1
2
0
1
0
1
1
0
2
3
1
2
1
1
1
0
0
1
1
2
1
1
0
2
3
1
1
4
2
1
0
2
2
0
1
1
0
1
2
1
1
1
0
1
1
1
0
0
0
1
0
1
2
0
1
1
1
1
1
0
2
0
1
2
0
1
2
1
2
2
1
2
1
1
0
2
2
2
1
0
1
2
2
3
1
1
0
1
1
1
1
0
0
0
0
2
0
1
1
1
1
0
1
2
2
2
0
1
1
1
0
2
1
2
0
2
2
0
2
2
3
0
0
1
0
0
1
1
1
0
1
1
1
0
2
1
1
1
0
2
0
0
0
1
1
1
0
0
2
1
1
1
1
2
0
2
0
0
0
0
0
1
0
1
2
1
1
1
1
0
1
0
1
2
0
1
1
0
0
2
2
0
0
1
1
0
1
0
2
1
1
1
0
0
0
0
0
1
2
1
2
0
2
0
0
0
1
0
1
0
1
2
1
1
1
0
1
1
1
0
0
2
0
1
0
1
2
1
1
3
1
1
1
1
1
1
0
2
2
1
2
0
1
0
0
1
1
0
1
1
1
1
2
2
2
1
0
2
0
1
1
2
2
0
2
1
2
2
2
0
1
0
1
1
2
0
0
1
1
1
1
1
3
1
1
3
3
2
0
0
1
1
1
2
1
0
1
4
0
2
0
1
2
0
0
1
0
2
2
3
0
1
2
1
2
2
1
1
0
2
1
1
1
2
0
0
2
0
0
2
1
1
1
1
0
1
3
1
1
1
1
2
1
1
1
0
2
1
0
1
0
0
0
1
2
2
3
2
2
0
1
2
0
1
2
2
2
1
1
1
2
1
3
1
0
1
2
1
2
2
0
1
1
1
1
0
1
1
1
0
1
1
1
1
1
0
1
0
1
1
2
3
2
1
3
0
1
0
1
1
0
2
1
1
0
1
1
1
2
0
2
0
1
0
1
2
1
0
1
2
1
1
2
0
2
0
1
2
1
1
1
1
0
1
0
0
1
1
2
1
1
0
2
1
1
1
1
1
0
1
0
1
2
1
0
0
0
0
0
2
2
1
2
0
1
1
0
0
0
0
2
2
2
0
0
1
2
1
1
1
1
1
2
0
1
2
1
1
0
1
2
1
1
1
0
0
1
1
0
2
0
0
2
0
0
0
2
0
2
2
0
0
2
0
0
1
1
1
0
4
1
0
0
0
1
1
2
2
0
2
0
2
1
0
2
1
0
1
2
1
2
1
0
2
1
0
0
0
3
2
0
1
1
2
1
0
0
0
0
3
2
0
2
1
0
0
0
1
0
1
2
0
0
1
2
1
0
0
0
1
2
0
1
1
0
0
1
0
0
1
1
1
1
0
0
1
2
1
0
0
0
1
1
1
2
0
2
0
1
0
2
1
2
1
1
1
1
0
0
0
1
1
1
1
0
1
1
1
1
0
2
1
0
2
1
0
2
2
0
1
1
2
0
1
1
0
2
1
0
1
0
1
0
2
0
0
0
2
0
1
0
1
2
0
0
1
0
2
0
1
0
0
1
0
0
1
0
1
2
0
1
1
1
2
1
1
1
0
2
0
0
2
2
2
0
0
1
0
1
1
1
2
1
0
1
1
2
2
1
0
1
2
0
1
2
2
1
1
2
1
2
1
0
0
0
0
1
0
1
1
1
0
1
2
1
0
1
0
2
1
2
1
1
0
4
2
1
1
1
1
1
0
1
0
0
1
0
1
1
0
1
2
1
3
0
1
1
0
1
2
1
0
2
1
1
1
1
0
1
2
1
1
2
2
1
0
1
1
0
0
1
1
2
0
1
0
0
1
1
2
1
1
0
1
1
1
2
1
1
0
2
1
1
1
2
1
1
0
2
0
1
2
0
1
1
0
0
1
0
2
1
1
2
0
0
0
1
1
1
1
1
0
1
3
0
1
0
0
1
1
2
0
1
0
0
2
2
1
0
2
0
1
0
0
0
1
0
1
1
0
0
2
2
2
1
1
2
1
1
1
0
2
1
2
1
1
0
0
2
0
1
1
1
1
0
1
2
1
1
0
2
1
1
0
1
0
2
0
1
2
0
0
1
1
2
1
0
2
1
0
1
0
0
0
1
2
1
2
0
1
1
1
0
2
1
0
0
2
2
1
1
1
2
1
2
1
1
1
1
0
2
2
1
1
5
1
1
1
0
0
2
0
0
0
1
2
1
0
0
0
0
2
1
2
1
2
1
1
0
0
0
2
1
2
0
1
0
1
1
0
1
0
2
2
1
0
1
1
1
1
0
1
1
6
1
0
1
1
1
1
1
1
2
0
0
1
1
0
1
2
0
1
1
2
1
2
2
1
2
1
1
2
2
0
2
0
2
1
2
2
1
0
2
0
1
2
1
2
0
1
1
1
1
2
1
0
1
0
0
2
1
1
0
1
1
2
2
0
1
0
2
0
2
3
0
0
2
1
1
2
2
1
1
2
1
1
0
1
0
1
0
1
2
0
1
1
2
1
1
0
1
0
1
1
0
1
1
2
0
0
1
1
1
0
1
0
0
0
2
1
2
0
2
1
0
2
1
1
1
1
0
0
0
0
1
2
2
1
2
1
1
1
0
1
1
2
0
0
1
1
1
1
1
0
0
0
1
1
1
1
1
0
1
2
0
0
0
2
1
1
1
1
2
2
0
1
0
0
2
1
2
1
0
3
1
0
1
0
2
2
1
1
1
1
1
2
1
2
0
1
1
0
1
1
2
1
0
0
1
1
2
0
1
1
0
2
0
0
1
1
2
0
1
0
1
2
1
2
2
0
2
1
1
0
0
2
0
0
0
1
2
2
1
1
0
0
1
1
0
2
0
0
1
0
0
1
1
2
0
2
3
2
1
1
1
2
1
0
1
2
0
2
1
1
2
1
2
1
1
0
0
1
1
1
2
1
1
1
2
2
1
1
1
1
0
1
0
0
0
1
1
1
0
0
2
1
1
3
1
0
0
0
1
0
0
2
1
2
0
0
1
1
1
0
0
1
1
2
2
0
1
1
1
0
1
1
2
1
1
2
4
0
1
1
0
2
2
0
1
0
1
0
1
0
2
1
1
1
1
0
1
1
2
2
1
1
0
0
2
1
0
1
0
1
0
0
1
0
1
0
2
1
0
1
3
0
1
2
0
0
0
0
0
0
0
1
0
0
1
1
1
1
0
2
1
1
1
2
0
2
1
0
0
0
1
1
2
0
2
1
1
1
0
1
2
0
2
2
0
0
1
0
1
0
2
0
0
0
0
1
1
0
1
2
1
0
1
2
1
1
0
3
1
1
0
1
0
1
2
1
0
1
0
1
0
1
1
2
0
0
0
2
2
2
1
1
0
0
1
1
2
1
1
1
2
1
0
0
0
1
1
0
0
0
0
1
0
2
1
1
1
2
1
2
0
0
1
1
0
0
0
2
1
0
1
0
0
1
0
1
2
1
0
1
1
0
2
2
1
2
0
0
0
1
1
0
2
1
0
1
0
0
2
0
1
2
1
1
0
1
1
0
1
2
0
2
0
0
0
1
1
2
0
1
1
1
0
1
0
2
2
0
1
1
0
1
1
1
1
0
0
2
2
1
2
0
1
2
0
0
1
1
2
1
1
0
2
0
1
1
0
1
1
2
1
1
2
2
0
0
1
1
0
0
4
1
1
1
0
1
2
2
1
1
1
0
1
1
0
2
1
0
2
0
0
0
0
1
0
1
1
1
0
1
1
0
1
1
1
0
0
1
1
1
0
0
1
1
1
0
0
2
0
0
2
0
2
0
1
0
0
0
0
1
1
1
2
1
1
1
0
2
0
1
0
0
1
1
1
0
1
2
2
1
1
1
1
1
1
0
3
0
0
8
2
2
1
2
1
1
1
1
1
0
1
2
1
0
1
1
1
0
0
0
1
0
1
0
1
0
3
0
1
1
2
1
0
0
2
2
0
1
1
1
1
0
0
0
1
1
1
0
2
1
1
0
1
3
2
2
0
1
0
1
2
0
1
1
0
2
1
2
0
1
2
1
0
0
1
0
0
1
1
1
0
1
1
2
1
1
0
3
0
1
1
2
1
0
1
0
0
1
0
1
1
2
1
1
1
0
1
1
2
2
0
0
1
1
1
0
1
1
1
1
2
1
0
0
0
1
1
0
1
2
0
1
1
1
0
1
1
7
2
0
2
0
1
1
0
1
0
1
0
1
0
1
1
0
0
1
0
0
2
2
2
1
2
1
2
1
1
2
1
1
0
3
1
0
0
2
0
0
1
1
0
2
2
1
0
2
1
0
0
1
1
2
0
2
1
0
0
0
1
2
0
1
0
2
2
1
1
1
0
2
1
1
2
1
1
1
1
0
0
2
2
0
1
1
0
1
0
1
0
4
0
0
1
0
0
1
0
1
0
2
1
2
0
1
0
2
2
1
0
1
1
0
0
1
1
1
1
2
0
1
2
1
0
1
2
1
0
0
2
2
0
2
1
2
0
1
0
2
1
1
1
1
0
1
1
1
1
2
0
1
1
0
0
0
1
2
0
2
1
0
1
0
2
1
1
0
2
0
2
1
1
0
1
0
3
1
1
1
0
2
0
0
0
0
1
2
0
1
0
2
0
2
2
1
2
0
0
1
2
2
2
1
1
1
0
1
1
0
1
1
1
0
1
2
0
1
1
1
2
1
2
0
0
0
2
0
1
2
1
0
2
1
0
2
1
0
1
1
2
1
0
0
0
0
1
3
1
3
1
0
1
1
2
1
0
2
1
0
2
0
1
1
0
2
0
1
0
1
2
0
1
0
0
1
2
1
2
2
1
1
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
2
1
0
1
0
2
2
0
0
0
1
1
1
0
0
1
1
1
0
2
1
2
0
2
1
2
1
0
1
0
0
1
1
0
0
1
2
0
1
0
1
1
1
1
0
0
2
1
2
2
1
3
1
1
2
0
0
0
1
1
0
2
1
1
0
1
0
1
0
0
0
0
0
2
2
0
1
1
0
0
0
1
1
2
0
1
0
1
5
1
1
1
0
1
1
1
1
2
1
1
2
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
2
1
0
2
1
0
1
1
2
0
1
0
1
1
1
0
0
2
2
1
1
4
1
1
0
1
1
1
0
0
0
1
0
1
0
0
0
0
0
1
2
1
1
1
0
0
0
0
1
1
2
0
2
1
1
0
1
2
0
1
0
1
1
1
1
1
1
1
0
2
1
2
1
0
1
1
1
0
2
1
2
1
1
0
1
1
0
2
1
2
1
1
1
0
1
1
1
0
0
0
1
1
1
2
1
0
2
2
0
1
1
2
0
0
1
2
1
1
1
2
1
0
1
2
1
2
1
0
0
0
1
0
0
0
1
1
1
1
0
1
1
0
2
2
0
0
0
2
0
2
1
2
2
0
0
1
1
1
0
1
2
2
1
0
0
1
0
2
0
1
0
1
2
2
0
1
1
2
0
1
0
1
0
1
2
1
0
0
0
0
2
1
2
1
0
1
0
2
1
1
2
2
1
1
1
1
0
2
0
1
1
0
1
0
1
1
2
2
2
1
1
1
0
1
2
2
0
1
0
2
3
0
1
0
1
1
0
2
2
0
0
0
2
1
1
1
1
2
1
0
1
2
1
1
1
2
0
1
1
0
4
1
0
1
1
0
2
0
2
2
0
1
1
1
0
1
1
0
0
2
1
1
0
1
1
4
0
1
2
1
1
1
0
0
1
0
0
2
1
1
1
2
1
0
3
2
3
1
2
2
1
0
0
1
0
10
2
0
0
0
1
2
1
1
0
1
1
0
1
1
0
0
1
0
2
2
1
1
0
1
2
0
0
0
0
2
2
2
0
0
1
0
1
1
1
1
1
2
2
2
0
1
0
0
1
4
1
0
1
1
0
1
0
1
3
1
2
0
1
3
1
1
0
1
2
0
1
0
0
2
1
3
0
1
1
2
2
1
0
0
0
1
0
0
1
1
1
2
1
0
1
1
0
0
0
0
1
3
2
1
1
2
1
1
1
2
2
0
1
1
2
2
1
2
4
0
0
2
0
1
1
0
2
1
0
0
1
0
1
1
1
0
1
0
0
1
3
1
1
0
1
1
1
1
0
2
2
1
0
2
1
0
1
0
2
0
0
2
2
1
0
0
0
0
0
0
0
0
0
3
0
2
0
0
1
0
1
1
1
0
2
0
1
1
1
1
1
2
1
2
1
1
1
0
1
1
2
2
0
0
0
1
0
2
1
1
1
2
1
1
1
0
0
1
0
2
1
0
2
1
1
2
0
2
2
0
1
1
2
1
2
0
1
0
0
1
2
1
1
1
2
2
3
0
2
0
0
1
0
2
0
2
0
0
1
4
2
0
2
0
0
2
0
1
1
1
0
0
1
0
1
1
2
1
2
0
0
1
2
0
0
2
0
0
0
2
1
1
0
0
1
1
0
1
0
1
1
0
2
2
1
1
0
1
0
0
2
0
2
0
1
0
0
1
1
1
1
0
1
1
0
2
2
1
2
0
1
1
0
1
2
1
1
0
1
1
1
2
1
2
2
2
0
2
1
0
2
0
1
1
1
2
2
2
1
1
1
0
1
1
1
0
2
1
0
1
0
1
1
0
1
0
1
2
1
0
1
1
0
0
2
0
1
0
1
1
0
0
1
0
0
2
1
2
2
0
1
0
0
2
2
1
0
1
1
1
1
1
2
1
1
1
1
2
0
1
0
2
0
1
1
1
2
1
1
2
0
2
0
0
0
2
2
0
3
2
1
0
0
1
1
1
2
1
0
1
3
1
2
0
1
2
0
0
1
1
0
1
1
1
1
1
0
1
1
1
0
0
0
0
2
1
2
0
0
1
2
1
2
0
1
1
1
0
1
0
1
1
1
2
0
0
1
1
2
1
0
0
2
1
1
2
2
0
1
0
2
1
1
1
0
2
2
1
0
1
1
1
1
1
1
0
1
1
0
2
2
2
0
1
0
1
1
1
0
2
1
1
2
0
1
1
0
0
0
0
0
1
2
1
1
1
0
2
1
0
0
1
1
1
1
0
0
1
1
2
2
2
3
0
0
0
1
1
0
2
0
2
0
1
1
1
0
0
1
2
2
1
2
2
0
3
0
2
1
1
0
0
1
0
0
2
1
1
2
1
0
1
0
1
0
1
2
1
2
1
2
1
1
1
2
1
1
0
2
1
0
1
1
1
1
1
1
1
1
1
1
0
1
1
1
2
1
0
1
0
1
1
0
0
1
1
1
0
0
1
0
0
2
4
2
1
3
0
0
2
1
1
1
1
0
2
1
1
0
2
0
1
1
1
0
1
2
0
0
1
2
1
0
1
2
0
2
2
1
2
0
2
2
2
1
2
0
1
1
2
2
1
5
0
1
0
0
2
1
1
0
3
0
2
0
0
1
0
0
2
0
1
2
1
1
1
1
2
0
1
0
2
1
0
2
1
1
0
1
0
0
2
1
0
1
1
1
1
2
1
2
2
0
1
1
0
0
1
0
2
0
2
0
1
0
1
0
0
2
1
1
1
1
1
0
0
2
0
0
0
0
2
1
1
0
0
2
1
0
1
0
1
0
1
1
1
0
1
1
0
1
0
2
0
0
0
2
1
1
0
2
1
0
2
1
0
2
0
1
0
0
0
0
0
1
1
0
0
1
1
1
1
1
1
1
1
4
1
2
1
1
2
1
1
0
2
1
1
2
1
0
1
2
0
0
1
0
2
1
1
1
0
1
2
2
2
1
1
2
1
2
0
0
1
0
2
2
1
0
2
3
0
1
0
0
0
3
1
2
1
2
3
0
1
1
1
1
0
1
0
1
1
2
1
0
2
2
1
1
1
1
3
1
0
1
1
1
0
1
1
0
2
2
0
2
0
2
0
1
0
2
2
1
0
2
2
1
1
1
0
1
0
1
0
1
0
0
1
1
1
2
1
1
2
0
1
1
0
0
2
2
1
0
1
0
2
2
2
2
1
1
2
2
2
0
1
1
0
0
1
1
1
0
0
0
2
1
2
0
0
0
0
0
1
0
1
0
1
1
2
1
1
2
1
1
2
1
0
1
1
0
1
1
1
2
0
0
2
0
1
1
0
0
1
2
0
1
1
2
2
0
1
0
2
1
1
0
2
1
0
0
0
1
0
1
1
0
2
4
0
1
0
1
2
0
2
1
1
2
2
1
0
1
2
0
2
1
1
1
1
2
0
1
1
1
1
0
1
1
0
2
1
2
0
1
1
0
2
1
2
1
10
2
1
1
0
1
0
1
1
1
0
1
0
1
1
0
2
0
1
0
0
1
0
1
3
0
1
1
3
1
0
0
1
0
2
2
1
1
0
0
1
2
2
1
1
2
0
1
0
3
0
1
0
0
1
1
2
1
2
0
0
1
1
1
2
0
1
2
1
1
1
0
2
1
0
1
0
1
2
2
2
2
2
1
1
0
0
2
2
2
0
1
0
2
1
0
2
2
2
2
2
1
1
2
1
0
2
1
1
1
2
0
2
1
0
0
0
1
0
1
0
2
0
0
2
2
1
0
1
2
2
0
0
0
1
1
2
1
0
2
0
1
2
0
1
2
0
2
1
1
1
0
1
1
1
1
1
0
2
0
0
2
1
1
1
2
0
0
2
0
0
2
2
1
1
4
0
1
0
0
1
0
1
2
2
1
2
1
0
0
1
0
2
1
1
1
0
0
2
1
1
0
1
2
2
0
0
1
0
1
1
1
1
2
2
2
2
2
2
2
1
1
2
0
1
0
0
0
2
1
1
2
1
2
1
0
2
2
5
1
1
2
1
1
2
0
1
0
0
2
2
0
2
0
2
1
1
0
2
1
0
0
0
0
1
0
0
0
2
1
1
1
0
0
0
2
2
2
0
0
2
1
1
2
1
1
1
0
0
0
0
2
1
1
0
1
0
1
0
1
0
1
1
0
1
2
1
0
2
1
2
1
1
1
2
1
1
2
2
1
1
1
2
1
0
0
1
1
0
1
1
1
1
0
2
1
1
0
1
2
1
0
1
0
2
1
1
1
2
1
2
1
2
0
2
1
0
0
3
1
1
1
1
1
0
1
0
0
2
1
2
1
2
1
0
1
1
1
1
1
1
0
2
1
3
0
0
2
2
0
0
1
0
0
2
0
0
0
1
1
0
1
0
1
0
0
1
1
2
0
1
2
1
1
2
0
1
2
2
1
1
1
1
2
1
0
0
1
0
1
1
0
2
1
1
0
1
2
0
1
2
2
2
1
1
0
1
0
2
1
1
2
0
1
1
1
2
1
0
0
2
2
1
2
0
0
1
1
0
1
2
1
1
1
2
1
2
1
2
0
2
0
2
1
1
0
1
1
1
1
0
0
0
0
1
0
0
2
1
1
2
0
1
0
0
1
2
1
1
1
2
2
1
1
0
1
0
1
1
2
1
1
1
1
1
2
2
1
1
2
1
0
0
0
2
1
2
1
2
1
0
0
1
2
1
0
1
0
1
0
2
1
1
2
0
1
3
1
1
0
1
1
1
0
1
1
1
1
0
0
0
0
0
1
0
0
1
0
1
1
1
0
1
0
2
3
0
0
2
1
0
1
1
2
0
3
0
2
2
2
1
2
2
1
2
1
0
1
1
0
1
1
1
1
2
1
0
0
1
0
2
0
1
2
2
1
0
2
1
2
1
1
2
2
1
1
0
0
1
1
2
0
0
2
1
1
1
2
1
1
1
0
1
2
0
0
1
1
0
0
1
1
1
0
2
1
0
3
0
1
0
1
1
1
0
0
1
1
2
0
0
1
1
1
0
1
1
1
1
1
1
0
1
1
2
2
0
1
0
1
1
1
1
1
1
0
2
2
1
1
0
2
0
3
2
0
1
0
1
1
1
2
1
0
0
1
2
1
0
1
0
2
0
0
0
1
2
0
1
0
1
0
1
1
0
1
2
0
2
2
0
0
1
0
2
2
0
1
1
1
0
1
0
0
2
0
1
1
1
2
2
0
2
2
2
1
1
1
0
1
0
2
1
1
0
1
0
0
2
0
2
2
1
1
1
1
2
1
0
0
0
0
0
1
1
0
1
1
2
1
2
1
1
2
1
1
1
2
0
2
1
0
0
0
2
1
0
0
1
1
0
2
0
2
2
2
1
0
0
2
1
0
0
2
1
0
2
2
1
1
1
1
1
2
1
0
1
1
2
0
2
2
2
2
0
0
2
1
0
1
1
1
1
0
2
0
0
0
0
0
0
2
1
1
1
1
2
2
1
2
2
1
3
0
0
0
1
2
1
2
0
1
0
1
1
0
1
1
0
1
1
0
2
0
0
2
1
0
1
1
1
2
1
1
1
1
1
2
1
0
0
1
1
0
0
0
1
1
1
2
0
0
0
0
0
0
0
0
2
1
0
1
1
1
2
1
0
2
2
0
0
1
1
1
1
1
0
0
0
1
0
1
0
2
1
0
0
1
1
2
1
2
2
2
3
0
0
2
1
1
2
0
2
2
1
1
1
2
0
2
1
1
2
0
1
1
1
1
1
2
1
1
2
1
0
1
2
1
0
0
0
0
1
1
1
0
1
1
1
2
2
2
2
0
0
1
1
2
2
1
0
1
0
1
1
1
1
3
1
0
1
1
0
1
0
2
2
2
0
0
1
2
0
1
1
1
2
0
0
1
0
2
2
0
1
0
0
1
1
2
1
1
1
1
1
0
1
0
1
1
0
2
0
1
0
0
1
1
2
0
0
1
1
0
1
0
1
2
3
0
2
0
2
1
1
0
1
2
0
1
1
1
2
1
0
1
0
1
0
2
1
1
1
1
1
1
0
0
0
0
1
1
0
1
1
2
0
2
1
1
1
1
2
1
1
0
1
0
0
1
1
0
2
0
1
3
0
2
1
2
1
0
2
0
2
0
2
1
0
1
1
2
0
1
1
1
1
0
0
0
2
1
3
1
2
2
2
0
0
1
1
2
0
1
1
1
0
1
1
2
2
1
1
0
1
0
1
0
1
1
2
0
1
0
1
1
0
0
1
1
2
2
1
3
0
1
0
0
0
0
0
0
2
1
1
2
1
2
1
0
1
1
1
2
1
1
1
1
1
0
1
1
2
1
0
1
1
1
2
0
2
0
0
0
2
1
0
1
1
1
0
0
0
0
1
1
1
1
2
0
2
1
0
1
1
1
1
2
0
2
1
0
1
0
1
0
1
0
0
1
1
2
2
0
0
2
1
1
0
1
1
1
1
0
1
1
0
0
0
1
1
1
1
0
1
1
0
0
0
2
0
2
1
1
0
0
1
2
0
1
1
0
1
0
1
0
1
2
1
1
2
2
2
1
2
2
1
1
1
1
1
2
1
2
1
2
1
2
2
0
1
0
1
0
1
3
0
2
2
2
3
2
2
0
0
1
2
0
1
1
1
0
2
0
0
2
0
1
0
1
2
1
0
1
1
1
1
0
1
0
0
1
2
1
1
1
1
1
1
1
1
0
0
1
1
0
1
1
1
1
1
2
1
0
1
1
1
0
1
1
1
1
2
2
2
2
0
1
1
1
1
0
0
0
1
0
1
1
1
0
2
1
1
1
3
2
0
2
1
2
1
0
0
2
1
2
0
2
0
1
1
0
1
2
1
0
1
2
1
2
0
2
1
1
0
0
1
2
0
1
1
1
1
2
1
0
0
1
1
3
2
1
0
2
2
1
1
1
0
1
1
2
0
1
1
2
0
0
0
1
2
1
0
0
1
0
2
1
1
1
2
1
1
0
2
1
1
2
1
0
0
2
0
0
1
1
1
2
1
1
0
1
0
1
1
0
1
1
0
2
1
2
2
1
3
1
1
0
2
2
1
0
0
5
2
1
2
1
1
1
1
2
0
2
1
0
1
0
1
0
2
0
1
0
0
1
0
0
1
2
1
0
0
1
1
0
2
1
1
1
1
1
1
1
1
2
0
1
1
1
2
1
2
0
1
2
1
0
1
1
1
2
0
1
1
0
2
0
1
1
2
0
2
0
0
0
1
2
1
1
2
0
1
0
1
1
1
1
2
1
1
1
1
1
2
3
0
0
0
0
0
1
0
3
2
2
2
3
2
1
2
1
1
1
0
2
1
2
1
1
0
2
1
1
0
2
2
0
0
0
2
1
1
2
2
1
2
1
0
1
1
1
2
1
1
0
1
1
0
2
0
1
1
1
2
0
0
2
2
2
1
1
1
0
0
1
2
1
0
1
1
1
2
0
1
1
1
1
1
0
0
0
0
2
2
2
2
1
1
5
0
0
2
1
2
1
1
1
1
0
2
1
0
2
1
0
2
1
1
0
2
1
1
0
2
1
0
0
0
1
0
0
2
2
2
0
2
1
2
1
0
0
0
1
2
2
2
0
1
2
0
1
1
1
1
1
0
1
2
2
1
1
1
1
1
2
0
0
2
0
2
0
0
1
0
0
1
2
1
0
2
1
1
0
1
0
0
1
2
0
1
1
1
1
1
1
1
1
2
1
2
1
1
0
1
1
1
2
0
1
1
1
1
1
0
1
1
1
0
2
2
1
1
1
2
1
1
0
1
1
1
1
2
0
1
0
1
0
0
2
1
2
0
1
1
1
0
0
1
0
0
0
1
3
0
1
0
1
1
0
1
0
2
0
0
1
1
0
1
1
0
1
0
0
1
1
1
1
1
1
1
1
1
0
0
1
1
1
1
1
1
1
1
1
0
0
1
5
0
0
0
0
0
1
3
2
0
1
0
0
1
1
2
1
1
1
2
1
2
0
0
1
2
2
1
0
0
2
1
2
0
1
1
0
0
2
1
0
0
0
1
1
1
2
1
0
0
1
1
2
1
1
1
0
2
0
1
0
1
1
1
2
0
0
0
0
0
0
3
0
0
0
2
0
2
1
2
2
0
1
0
1
2
1
1
2
0
1
1
1
1
0
0
0
2
2
2
2
0
2
0
2
0
0
1
1
1
1
1
0
2
0
2
1
1
2
2
2
0
2
1
1
2
2
0
1
0
1
2
1
1
0
0
0
1
0
4
1
1
0
2
0
1
0
1
1
2
0
1
1
2
2
1
1
0
0
3
2
0
0
2
1
1
2
1
0
1
1
1
1
1
0
2
1
0
1
0
1
0
1
0
0
0
0
1
0
2
1
2
1
1
1
0
1
0
1
1
1
0
3
2
1
2
1
1
0
0
1
2
1
0
1
1
2
2
0
0
1
0
0
0
1
1
0
0
2
2
0
0
0
1
0
0
1
1
1
2
1
0
0
1
1
5
1
1
0
1
1
1
1
1
1
2
0
1
0
1
2
1
1
0
1
0
1
1
0
1
1
0
1
1
2
0
0
1
0
2
1
1
0
0
1
0
0
2
1
0
1
0
2
1
1
0
0
1
0
0
1
0
2
1
1
2
0
2
2
0
2
0
1
0
0
1
0
2
1
1
1
1
2
0
0
1
2
2
1
2
0
0
1
2
1
1
0
2
0
2
0
0
2
3
2
1
1
1
0
1
0
1
0
0
0
3
0
1
2
0
1
1
2
1
2
2
1
1
1
0
1
1
0
1
1
1
1
0
2
2
1
0
0
2
0
1
0
1
1
3
1
1
1
0
2
4
0
1
2
0
2
2
1
4
1
0
2
1
2
1
1
1
1
1
1
0
0
0
1
1
0
1
2
1
1
1
2
0
0
1
1
1
2
1
0
2
2
0
1
0
1
2
0
2
1
1
1
1
2
1
0
0
0
0
2
0
1
0
1
1
0
2
1
1
1
2
0
0
0
0
0
2
0
2
1
1
0
1
0
1
0
1
1
1
1
0
0
1
2
2
0
0
1
1
2
0
1
1
0
1
2
1
2
1
2
0
0
0
0
1
3
2
1
1
1
0
2
0
1
1
2
1
0
1
1
0
1
1
1
0
0
1
2
1
0
1
2
2
1
1
1
2
2
0
1
0
1
1
0
1
1
1
1
0
0
1
1
2
0
1
0
0
1
1
1
0
1
0
0
1
1
2
0
1
0
1
0
0
0
2
0
1
2
1
1
1
1
0
1
1
1
2
1
1
0
2
1
0
1
2
0
0
1
1
0
1
1
1
0
1
1
2
2
1
1
1
1
2
1
1
2
0
1
2
1
1
1
1
1
1
0
0
0
1
2
0
1
0
2
2
1
1
1
2
1
0
2
0
1
1
3
1
1
1
0
1
1
0
2
0
1
2
1
1
0
0
0
1
1
0
1
2
1
1
0
1
0
2
2
1
0
1
2
0
2
0
0
0
1
1
1
0
1
0
1
0
2
1
1
2
1
0
2
1
1
2
0
2
0
2
1
1
1
2
1
1
3
2
1
0
0
2
2
0
1
1
1
1
1
2
0
0
1
0
2
0
2
1
1
1
0
1
0
1
0
0
1
0
1
0
0
0
1
0
0
0
1
1
0
1
1
1
1
2
1
1
1
1
0
0
1
0
0
0
0
2
0
2
1
1
0
0
1
1
1
0
1
1
0
1
0
2
1
1
1
0
1
3
1
2
1
2
3
2
1
2
1
0
1
1
1
0
0
1
0
1
1
0
2
0
1
1
1
2
1
1
1
0
0
1
1
2
0
1
1
1
2
2
1
1
2
1
1
0
0
1
0
0
1
2
2
0
1
1
2
1
0
1
1
0
1
0
1
1
1
1
2
1
1
2
2
1
1
1
0
0
0
0
1
0
1
1
1
1
2
1
1
1
0
1
2
1
1
1
1
1
1
2
1
0
0
1
1
1
1
1
0
2
1
0
0
2
2
1
1
0
1
0
1
0
0
1
0
1
1
1
0
2
1
1
2
0
2
0
0
1
0
1
0
0
0
1
0
1
0
0
1
2
0
0
1
3
1
1
0
0
0
1
1
1
1
1
0
1
0
1
1
1
2
1
1
1
1
1
0
0
1
1
1
1
0
1
0
1
0
2
1
0
0
1
1
1
3
0
1
1
1
2
2
1
1
1
1
3
1
0
1
0
1
2
0
2
1
0
1
1
1
1
1
1
0
0
0
1
1
1
2
0
2
1
1
1
0
0
0
0
0
0
2
1
1
3
1
1
2
1
0
0
2
1
2
1
1
0
2
0
1
0
2
0
1
1
1
2
2
0
1
1
0
1
2
0
1
2
0
0
2
0
1
1
2
1
0
2
1
0
2
2
0
1
1
0
2
1
2
0
2
0
1
1
1
2
0
0
0
1
2
0
1
0
3
0
1
1
1
2
1
2
2
1
1
0
1
1
2
1
0
2
1
0
1
2
2
1
0
0
2
0
2
0
1
0
2
1
0
0
0
2
0
1
0
0
1
1
0
1
2
2
1
1
1
2
1
0
1
1
1
1
1
1
0
2
0
2
1
2
1
1
2
0
0
1
0
0
2
0
0
0
1
1
2
2
1
0
1
0
0
1
0
4
1
1
1
1
0
1
1
2
2
0
1
0
1
0
1
1
2
0
2
0
2
1
3
0
1
2
0
2
1
0
1
0
2
1
2
2
1
2
1
1
0
2
1
0
0
0
1
1
2
0
1
0
0
0
1
1
2
1
1
1
0
0
1
2
0
1
2
1
0
2
0
1
0
1
0
0
1
0
1
0
1
2
0
2
1
1
0
1
1
2
1
0
0
1
0
2
0
0
2
0
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
0
1
2
1
1
1
1
1
0
2
2
1
2
1
1
1
0
1
1
1
0
1
1
0
0
1
1
1
1
1
0
1
1
1
1
2
0
2
0
1
2
0
1
2
1
0
1
0
0
2
0
0
0
1
1
1
0
2
0
1
1
0
1
0
1
0
1
1
2
1
1
2
0
0
1
0
1
0
0
4
1
2
0
1
0
1
1
0
0
0
1
0
1
0
1
1
1
2
0
1
1
2
2
0
0
1
0
1
0
0
0
0
0
0
1
0
1
2
0
1
0
1
0
1
0
2
1
1
2
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
1
2
1
1
2
0
0
1
2
1
1
2
1
0
1
1
3
1
0
1
0
0
1
2
2
2
1
2
1
0
1
0
0
0
1
1
0
1
1
2
0
0
0
1
1
1
1
1
0
1
1
1
2
1
1
2
1
0
1
0
1
1
0
1
1
1
0
2
2
1
2
0
3
1
1
0
2
2
1
0
2
0
1
1
0
2
1
1
1
1
0
2
1
2
0
1
0
1
1
0
2
0
2
1
2
0
2
2
0
1
0
0
2
1
2
0
0
1
1
0
0
1
1
0
1
0
3
1
1
2
0
1
0
0
3
2
1
2
1
2
1
1
0
3
1
1
1
1
1
0
1
1
1
0
1
2
1
0
1
1
1
1
1
2
0
7
0
2
1
0
1
1
2
0
0
1
2
0
1
0
2
1
1
0
0
1
0
1
0
2
0
1
2
0
2
1
0
1
1
2
1
1
1
0
0
0
1
1
1
1
1
1
1
0
2
0
0
2
2
1
0
4
3
2
1
0
2
1
1
1
1
1
0
1
0
1
1
0
1
0
1
1
0
2
0
2
2
0
1
2
1
2
1
1
2
0
0
1
1
1
3
1
1
0
0
1
1
1
1
1
1
0
1
0
1
1
0
1
0
0
1
0
2
1
0
0
2
1
0
1
1
2
0
1
2
1
2
1
1
2
2
1
0
1
1
0
1
2
1
0
0
0
0
1
1
1
2
0
1
2
2
1
1
1
1
2
1
1
1
0
0
1
1
1
1
1
1
2
2
2
1
1
1
1
0
1
0
1
2
2
1
0
1
2
1
0
2
2
1
2
1
0
1
2
0
2
0
2
1
0
1
2
0
3
0
1
1
1
1
2
0
1
2
1
1
0
0
0
0
0
1
1
1
1
2
2
0
1
1
1
1
1
1
1
1
1
1
1
0
1
1
3
1
2
0
1
2
2
1
1
0
0
0
1
0
0
1
1
1
1
1
0
2
1
1
2
0
2
2
1
1
2
2
0
2
0
1
2
0
0
1
2
1
2
0
0
0
0
0
2
1
0
1
2
1
1
2
0
1
1
2
2
0
0
1
2
1
2
1
2
2
1
2
0
0
0
0
0
0
1
1
1
1
0
1
1
1
0
2
1
1
1
0
1
2
1
1
1
0
2
1
2
1
1
1
2
0
3
2
0
2
1
1
1
2
0
0
2
1
1
0
0
0
1
0
1
1
1
0
0
1
1
0
0
1
0
1
1
1
0
1
1
2
1
2
0
2
2
0
1
3
0
1
0
0
1
1
2
0
1
1
1
1
1
0
1
0
2
1
1
0
0
0
0
2
0
0
2
1
0
2
1
1
0
0
1
1
1
1
0
1
0
1
2
2
2
0
2
2
2
2
0
2
1
2
1
0
2
0
0
1
0
1
1
0
1
1
2
1
2
2
2
0
1
0
2
0
0
0
2
0
1
2
1
0
0
1
1
2
1
2
0
1
1
0
0
1
1
2
1
0
0
1
1
1
2
0
2
1
1
1
0
1
1
1
1
1
2
0
0
0
1
1
1
2
1
1
2
1
2
2
0
1
2
0
0
1
1
1
2
0
1
0
0
1
0
1
2
1
0
2
1
0
1
0
0
1
2
1
1
1
2
1
0
1
2
0
1
0
1
5
2
0
0
2
1
0
1
0
1
1
1
1
1
2
0
2
1
0
1
0
0
2
2
1
0
0
2
0
1
2
1
1
1
0
0
3
1
0
1
1
0
1
1
0
0
0
0
2
0
2
1
1
1
0
1
0
2
0
1
1
0
0
1
1
2
1
0
2
1
2
2
2
1
0
0
2
2
0
1
0
0
0
2
1
2
0
1
1
1
1
1
0
2
1
1
1
0
0
0
0
1
1
1
1
2
1
1
0
0
1
1
1
2
1
1
2
1
1
2
2
2
5
3
0
0
2
1
0
2
1
2
1
2
0
0
1
0
1
1
0
0
2
1
1
0
1
2
1
0
0
0
0
0
2
2
0
0
1
0
0
1
0
2
1
1
2
0
0
0
1
1
2
0
0
1
1
0
1
1
0
0
1
1
0
2
2
1
1
1
1
0
1
0
1
0
1
2
0
6
1
0
0
1
1
2
0
1
0
1
3
2
1
0
2
0
1
0
3
2
1
2
0
1
0
2
1
0
1
0
1
0
1
1
0
1
2
0
1
0
1
2
0
1
1
1
0
1
0
0
2
1
2
0
1
0
1
1
4
0
2
1
2
2
0
2
2
1
1
0
0
1
2
1
1
1
1
1
0
0
1
0
1
1
0
2
0
1
0
0
2
0
2
0
1
1
1
2
1
0
1
0
0
1
1
1
1
0
1
1
1
0
0
0
1
1
2
1
0
1
1
1
0
1
1
0
1
0
1
0
1
1
2
1
0
1
0
1
2
0
0
1
1
1
1
1
1
1
0
1
2
0
0
3
1
0
0
0
2
0
1
1
1
2
1
2
1
2
1
1
0
1
0
1
1
2
1
0
0
1
1
2
0
2
1
1
1
0
1
1
1
1
1
0
1
2
2
1
0
2
0
0
1
2
1
0
2
0
1
0
0
1
0
2
0
1
2
0
0
1
1
1
1
2
0
1
0
2
0
1
0
0
2
1
1
1
0
1
1
2
2
0
1
2
1
3
1
1
0
1
1
1
1
1
2
2
2
0
0
1
3
1
1
1
1
1
1
2
1
1
0
1
2
2
1
1
1
0
1
1
2
1
1
0
1
1
1
1
1
1
0
0
2
0
1
0
0
0
1
1
0
1
1
0
2
2
1
2
1
1
1
1
1
1
1
1
1
1
0
0
0
0
0
1
0
2
0
1
1
1
1
1
0
1
1
1
1
0
2
0
0
1
1
0
2
2
0
1
0
0
2
1
0
0
1
2
1
1
0
2
2
1
1
2
1
1
1
0
2
0
0
2
0
0
1
2
2
0
2
0
0
1
1
0
1
0
1
0
1
0
1
1
1
0
1
2
2
2
0
2
1
2
0
1
0
0
0
2
1
1
1
0
1
0
1
2
0
4
2
1
1
1
2
2
0
1
0
1
0
1
1
0
1
2
0
1
1
1
0
3
1
0
3
0
2
2
2
1
2
0
2
1
1
1
0
0
1
0
0
1
0
1
2
2
0
2
1
0
0
1
1
1
1
2
1
1
1
1
0
2
0
1
0
0
1
2
1
0
0
0
0
0
0
0
1
2
1
0
0
3
0
1
0
2
0
2
1
0
2
0
3
1
0
1
1
0
1
2
2
0
4
0
2
1
0
2
1
1
1
1
0
1
0
1
1
1
1
2
0
1
1
0
2
2
1
1
2
3
1
1
2
1
2
0
1
2
0
1
1
1
0
1
2
2
1
0
1
1
1
2
1
1
1
1
1
2
1
1
1
1
0
0
2
0
1
0
2
0
0
1
1
0
2
3
0
2
0
0
2
0
1
0
1
0
1
0
0
1
0
0
2
1
0
0
2
1
1
2
0
2
1
1
0
1
2
0
0
1
0
0
1
1
0
1
1
1
2
2
1
1
0
1
0
0
1
0
1
1
1
0
1
2
0
0
1
1
2
2
0
2
2
2
0
1
1
0
0
2
1
0
2
2
0
0
2
2
1
0
3
2
1
0
0
1
1
1
1
0
1
0
2
1
0
1
2
2
2
0
3
1
2
0
1
1
0
2
1
1
0
2
1
2
2
1
0
1
0
1
0
2
0
2
1
0
1
0
1
0
0
1
0
2
1
0
1
2
0
1
1
1
1
0
2
2
1
0
2
0
1
0
1
0
0
0
0
2
2
1
2
2
0
2
1
1
1
1
2
0
1
1
0
1
0
1
1
1
1
0
1
1
1
1
1
1
1
0
2
0
1
1
2
0
0
1
0
1
0
1
1
1
1
1
0
1
0
0
1
2
2
1
1
2
2
1
0
1
1
1
1
2
0
1
1
0
0
0
2
2
1
2
1
1
0
2
1
0
0
1
0
2
1
1
1
1
1
0
2
0
1
2
0
1
2
1
2
0
0
0
1
0
1
1
1
0
1
0
0
2
1
1
2
2
0
1
1
1
0
1
2
0
1
0
1
1
1
0
2
1
0
2
0
0
1
1
2
1
1
2
0
0
2
1
2
1
0
1
0
2
0
2
0
0
1
1
0
1
2
1
5
2
0
1
0
0
1
1
2
0
0
1
2
0
1
1
1
2
2
1
1
1
1
1
1
2
0
1
0
0
2
1
0
1
1
1
1
1
0
1
1
0
2
1
0
1
1
3
1
2
0
0
2
0
1
2
2
2
0
0
0
0
2
1
1
1
1
0
1
0
2
0
0
3
0
1
1
0
1
1
0
1
2
1
1
0
2
0
3
2
1
1
0
1
0
0
1
1
2
1
0
1
0
2
1
0
1
2
0
1
1
1
1
2
1
1
2
1
1
1
2
2
0
1
2
2
1
0
0
1
0
0
1
0
1
0
1
0
2
1
1
0
0
1
1
1
1
0
0
2
1
0
0
1
1
2
2
0
2
1
1
1
0
0
0
0
1
0
0
1
2
1
1
1
0
1
1
1
0
2
1
1
2
1
1
1
2
0
1
0
0
2
0
1
1
0
1
1
0
1
2
1
0
1
1
0
2
0
1
0
1
2
6
1
1
0
1
1
1
1
2
1
1
1
1
1
1
1
0
2
2
1
1
2
0
0
0
0
1
0
0
1
0
1
2
0
1
1
0
1
0
0
0
0
1
0
2
0
1
1
0
0
1
0
1
1
0
0
0
0
0
0
1
2
1
1
0
2
1
2
2
0
1
1
0
0
2
0
1
2
0
0
1
2
2
0
0
1
1
2
0
1
1
1
1
0
1
1
1
1
1
0
2
2
1
1
0
1
0
0
0
0
2
1
0
1
1
0
1
0
1
1
1
1
0
0
0
1
2
1
1
1
0
2
1
1
1
0
0
0
0
0
1
2
2
1
0
2
1
2
0
1
1
0
0
0
1
2
0
2
0
1
0
0
1
1
1
1
1
0
0
1
2
1
2
0
1
0
1
1
1
0
0
2
1
0
1
1
1
1
1
0
1
1
1
1
1
2
0
1
2
1
2
0
0
0
0
2
1
1
0
1
0
2
3
2
0
1
1
2
1
0
2
0
1
1
2
0
1
1
1
1
1
2
1
1
1
0
2
3
0
1
1
1
1
0
1
0
0
0
1
1
2
1
1
0
2
1
2
2
1
1
1
2
0
0
1
0
1
1
1
1
3
1
2
1
0
1
1
2
0
1
1
1
2
0
2
1
1
1
1
1
0
0
0
0
0
1
0
2
1
2
0
1
0
0
0
2
1
1
1
1
1
1
2
1
0
0
0
1
1
0
0
1
1
0
2
0
1
1
1
0
0
0
1
0
2
0
1
2
0
2
0
2
1
1
1
2
0
0
0
1
0
2
0
0
1
3
1
2
0
2
1
0
0
1
1
1
1
1
0
0
0
1
1
0
1
0
1
1
0
4
1
1
0
0
2
0
0
0
1
1
1
2
0
2
1
0
1
0
1
0
0
0
1
1
1
0
1
0
0
0
1
2
1
0
1
0
0
0
1
0
1
2
0
1
2
0
1
1
2
2
1
2
1
3
0
1
0
1
0
1
0
0
0
0
2
0
1
0
1
1
2
1
2
1
0
0
0
0
1
1
1
0
2
0
2
1
0
1
1
0
0
2
2
0
0
0
0
1
1
1
1
2
1
0
0
1
1
2
2
1
1
0
1
1
0
0
1
1
1
1
1
0
1
0
0
0
0
0
1
0
2
2
2
1
1
0
0
3
0
2
1
0
0
3
2
0
1
2
1
2
1
1
2
1
2
0
1
0
1
1
2
1
1
2
0
1
1
0
0
2
2
1
0
1
2
1
2
0
1
0
2
1
2
1
2
2
1
0
1
0
1
2
0
2
2
1
1
1
1
1
0
1
1
2
1
1
1
0
0
1
1
1
0
1
1
0
0
2
2
0
0
0
0
1
0
0
1
0
2
0
1
1
1
1
1
0
0
0
2
0
2
0
1
0
1
2
1
1
2
2
2
0
1
0
0
1
2
2
1
0
2
2
1
0
1
1
2
2
1
1
1
1
2
0
1
4
0
1
1
2
2
1
2
1
1
0
2
2
0
1
0
0
2
2
2
1
0
1
1
2
1
1
0
2
1
1
2
2
1
1
0
0
0
1
0
2
0
0
1
1
0
1
1
1
0
0
0
0
1
1
1
1
1
2
0
0
0
2
3
0
2
1
2
2
0
1
1
1
0
1
1
1
1
0
2
1
1
2
1
2
1
0
0
1
0
0
0
1
1
1
2
0
0
0
0
3
1
0
0
0
1
1
0
1
2
0
1
0
1
1
1
1
1
2
1
0
0
0
3
1
0
1
1
2
0
0
1
1
1
1
1
1
1
1
1
1
0
1
0
0
0
1
1
2
1
0
1
2
0
2
1
1
1
0
1
1
1
0
1
1
1
2
0
0
1
2
0
2
0
1
1
0
2
0
1
0
2
0
1
1
1
2
2
2
0
2
1
1
0
0
2
1
2
1
0
0
1
1
1
0
0
1
1
1
1
0
0
0
1
1
1
3
0
1
1
1
1
1
1
0
2
2
0
0
1
1
0
1
1
0
1
2
1
0
2
0
2
0
1
0
0
2
2
1
0
1
1
2
1
3
0
1
3
0
2
2
0
2
0
0
1
0
2
0
1
0
1
0
1
1
1
1
0
1
2
2
0
1
0
1
1
1
0
0
0
0
2
0
2
1
2
2
0
1
0
0
1
2
1
0
2
2
1
2
0
1
1
1
3
0
0
0
2
1
1
0
2
0
1
0
2
1
1
0
0
2
0
2
2
0
1
1
1
0
2
1
3
2
1
1
1
1
0
0
0
1
2
0
1
1
1
1
1
3
1
1
1
0
1
1
1
1
0
0
0
2
1
1
1
0
0
0
2
2
2
1
1
2
2
1
2
1
2
1
1
0
2
1
0
0
1
0
1
1
1
1
1
2
2
0
1
1
1
0
0
0
1
1
1
1
0
0
1
1
2
1
0
2
2
2
0
1
2
0
2
0
0
1
1
1
2
0
0
0
0
1
2
0
0
0
0
0
1
0
2
2
1
0
1
1
1
0
1
2
1
2
1
0
0
1
0
2
1
0
0
3
2
2
1
1
0
1
1
2
1
2
2
1
0
2
1
1
0
0
2
0
2
2
2
2
1
0
0
0
1
1
1
1
1
1
1
1
1
2
1
2
0
2
1
1
1
0
1
1
1
1
1
2
1
2
0
1
1
2
1
2
1
1
2
1
1
0
2
0
1
2
2
1
0
1
0
2
1
0
1
0
2
3
0
2
0
1
1
1
0
0
1
2
2
1
0
1
3
1
2
2
0
0
1
2
2
1
0
2
0
1
1
2
1
2
1
2
1
0
2
0
0
1
1
0
1
2
1
1
0
2
0
1
0
2
1
1
0
2
1
0
0
0
2
0
2
2
2
0
2
1
7
0
2
1
2
1
1
2
0
1
2
1
0
0
0
1
0
0
0
1
1
0
0
2
2
0
2
2
2
1
0
1
3
1
1
1
1
0
1
0
0
0
1
2
0
1
0
1
1
0
1
2
0
1
2
2
0
0
0
0
1
0
1
0
1
1
1
2
1
1
3
0
0
2
0
2
2
0
0
0
1
0
1
1
1
1
1
0
0
0
1
1
2
0
0
0
1
1
1
2
2
0
1
0
1
1
1
2
0
0
3
2
1
1
0
1
0
1
1
2
1
1
1
1
2
2
0
1
1
0
3
0
0
1
1
0
1
0
1
0
1
1
0
0
0
0
0
0
0
1
1
2
0
0
2
1
0
1
0
0
1
2
2
1
1
2
0
0
1
0
0
3
1
2
1
2
1
2
1
1
1
1
0
0
1
2
0
0
0
0
0
2
0
1
1
0
0
1
0
1
1
1
1
0
1
1
0
0
1
1
1
2
2
0
1
1
1
0
2
0
0
1
0
2
0
0
0
0
1
1
2
1
1
1
1
2
2
2
2
1
1
0
1
1
1
1
0
2
2
0
1
0
0
0
0
2
0
2
0
0
1
1
3
1
2
0
0
1
0
1
0
2
1
2
1
0
0
3
2
1
1
1
0
2
0
0
0
0
1
1
0
1
1
1
1
1
1
1
1
0
1
0
0
2
1
0
2
0
2
1
0
0
1
2
1
0
1
0
0
0
1
2
1
1
1
1
3
0
0
1
2
1
1
1
2
0
1
1
1
1
1
1
1
0
1
0
1
1
1
1
0
0
1
1
2
0
0
2
1
3
2
0
0
0
2
2
0
1
1
1
1
1
0
0
1
1
2
1
1
0
1
1
2
1
0
1
1
1
0
2
0
1
2
2
2
1
0
1
1
1
3
1
1
2
1
1
1
0
1
0
0
1
1
1
1
1
2
1
1
1
0
1
2
1
0
1
2
0
1
1
1
0
1
1
1
1
0
2
1
1
0
2
1
1
1
0
1
1
2
1
1
0
0
1
0
1
2
0
1
1
1
0
0
1
1
1
1
0
0
1
1
0
1
0
2
0
0
1
1
0
1
0
1
1
2
0
1
1
1
1
0
1
2
0
0
1
2
0
1
1
0
1
2
0
2
1
0
2
1
0
1
1
1
2
0
1
2
0
1
0
2
0
1
0
0
0
0
1
0
1
0
1
0
1
0
1
2
0
0
1
0
0
2
1
0
1
2
1
2
1
1
1
0
1
0
2
0
0
1
1
1
1
1
1
1
0
2
1
0
1
1
0
1
0
2
0
0
0
0
0
0
2
0
0
1
2
1
0
1
2
3
1
1
1
0
0
0
2
1
1
1
1
0
1
0
0
1
1
2
2
2
1
2
0
2
1
0
2
0
0
2
1
2
0
1
1
2
1
0
1
0
0
0
2
1
2
0
0
2
0
1
0
0
1
2
1
2
2
0
2
1
1
1
0
2
1
1
1
1
1
0
2
0
1
1
2
2
1
3
0
1
1
1
1
3
1
1
1
1
8
0
1
0
1
1
0
0
1
0
1
1
1
1
1
0
2
6
0
2
1
0
1
1
2
1
1
2
0
1
1
1
0
1
0
1
1
2
0
2
1
0
1
0
0
0
0
1
0
1
1
0
2
1
1
1
1
1
2
0
1
0
1
2
0
3
2
1
1
1
0
2
0
2
2
0
1
2
1
0
1
0
1
2
0
1
2
0
0
1
1
0
1
1
0
2
1
5
1
2
0
0
0
1
4
0
0
0
1
1
2
0
1
0
0
0
0
1
2
1
2
0
0
2
2
1
0
1
0
2
0
0
1
1
1
0
1
0
1
0
2
1
1
1
0
1
1
1
0
1
1
2
2
0
1
2
1
1
1
2
1
0
0
1
2
2
1
1
0
1
0
1
0
2
1
0
1
0
1
2
1
2
0
1
0
1
0
1
0
0
1
0
1
1
0
1
3
2
1
2
2
1
1
0
2
0
1
2
2
0
0
1
1
1
2
2
1
2
2
1
1
1
0
1
0
1
1
1
1
1
1
0
1
1
0
1
2
1
1
0
0
1
1
0
0
0
1
0
1
2
1
1
1
1
1
1
1
2
0
1
0
1
2
2
2
2
1
1
2
2
1
0
1
0
1
1
1
1
0
0
0
1
1
4
0
2
1
1
1
2
0
1
0
1
0
0
1
2
0
1
1
0
0
2
1
1
0
1
0
2
1
1
0
1
0
1
1
2
2
1
1
1
2
1
0
0
1
1
2
0
2
0
2
0
0
0
0
0
1
1
1
0
2
0
2
0
2
1
1
1
1
1
1
0
2
0
2
0
2
1
1
1
1
0
3
0
0
2
2
0
0
1
1
2
0
1
1
2
1
2
1
1
1
0
0
1
2
1
1
2
0
1
0
2
2
1
0
0
0
0
2
1
1
1
0
0
2
2
0
1
2
1
0
2
1
3
2
0
0
1
1
1
0
1
3
2
0
0
2
1
0
2
2
1
0
0
1
1
2
0
2
0
1
0
0
1
1
2
1
1
0
0
1
1
1
2
0
2
1
1
1
2
1
0
0
0
0
2
1
1
0
2
1
0
2
1
0
0
1
1
0
0
2
0
1
1
0
1
1
1
0
1
1
0
2
1
1
1
1
0
1
1
1
0
1
0
1
0
0
2
0
0
1
0
1
1
0
0
1
2
2
1
0
1
1
0
0
1
2
1
0
2
0
1
2
0
1
1
1
1
1
1
0
0
1
0
0
2
1
1
0
1
1
1
0
2
0
2
1
0
1
1
2
1
1
0
2
0
1
1
1
1
0
0
1
0
1
1
0
1
1
1
0
1
0
0
0
1
0
1
1
0
0
1
1
1
0
1
1
0
2
0
2
2
0
0
0
1
0
2
2
0
1
0
1
0
2
0
1
3
0
3
1
0
1
1
0
1
3
2
1
1
1
1
1
3
1
1
2
0
1
0
0
1
1
1
0
0
0
1
2
0
2
1
0
1
1
0
2
0
1
1
0
1
2
2
2
1
2
0
1
1
1
1
1
2
2
2
2
1
1
1
0
1
0
1
0
1
2
0
0
0
1
0
1
0
1
1
1
0
1
2
1
2
1
0
1
0
2
2
2
1
0
0
0
0
0
0
1
2
1
0
0
0
1
1
0
0
0
0
0
1
1
1
1
0
1
2
0
0
1
1
0
0
1
1
1
0
0
2
0
2
2
1
1
1
1
1
0
0
1
4
1
1
2
0
0
2
0
1
2
2
2
2
0
1
1
1
2
0
2
0
1
2
1
2
1
2
2
0
0
1
2
2
1
1
0
2
0
0
1
0
2
0
1
2
1
0
0
0
0
1
1
1
2
0
0
1
0
1
1
0
2
2
0
2
0
2
0
2
2
0
0
0
0
1
0
2
1
0
0
0
0
2
1
2
1
0
0
1
1
1
2
0
1
1
1
2
1
1
0
2
1
0
2
0
3
1
2
1
0
1
0
4
1
0
0
0
0
0
0
2
0
2
2
0
0
1
1
0
1
0
2
1
1
2
1
1
1
0
1
1
1
2
0
0
0
1
1
1
1
2
2
2
1
1
0
1
2
1
0
0
0
0
2
1
1
0
1
2
1
1
1
2
0
0
0
1
1
2
0
0
1
0
2
0
1
0
1
0
1
1
2
7
2
2
0
0
0
1
1
2
1
2
1
1
0
1
1
1
2
1
1
1
1
1
0
1
1
0
2
0
0
2
2
1
1
1
0
1
2
1
3
0
0
0
1
3
1
1
0
1
0
0
0
0
0
1
1
1
0
0
1
2
2
1
0
2
1
0
2
1
0
2
1
2
0
0
0
0
0
1
0
0
1
1
0
0
2
3
1
1
1
1
0
1
1
0
1
1
1
0
0
1
0
0
1
0
0
0
0
1
2
1
1
0
0
4
1
0
1
0
1
1
0
2
2
2
1
0
1
2
2
2
2
0
1
2
1
1
1
1
0
0
0
1
0
0
0
0
2
1
1
1
1
1
0
0
0
1
0
1
0
2
2
1
2
1
0
1
1
0
0
0
1
0
2
2
1
1
1
0
2
2
1
3
1
1
0
1
1
2
2
0
0
2
0
0
0
1
1
1
2
1
2
0
0
1
0
0
1
1
0
1
1
1
1
2
0
0
2
1
0
1
0
0
2
1
1
0
1
1
2
1
1
1
0
0
2
1
0
0
1
0
0
1
1
0
1
2
0
0
1
0
2
2
0
1
2
1
1
0
1
1
1
2
0
1
1
2
2
1
2
2
1
1
2
0
1
1
1
1
4
1
1
0
2
1
1
0
1
2
0
2
1
1
1
0
1
0
1
1
1
1
1
1
2
0
2
1
0
1
1
2
2
2
2
2
1
1
2
0
0
0
2
1
0
6
1
1
1
1
0
1
0
2
1
1
2
1
0
2
1
0
0
1
1
1
2
1
1
1
0
1
1
1
1
0
0
1
0
0
0
0
2
2
1
1
1
2
0
2
0
0
0
1
0
1
1
1
0
0
0
1
1
1
2
4
1
1
1
1
1
1
1
1
0
1
2
0
0
1
2
0
0
3
1
1
1
0
0
2
1
0
0
0
1
0
0
1
0
1
0
0
0
1
2
0
2
0
0
0
0
1
2
2
0
0
1
0
1
2
0
0
2
1
0
1
1
1
1
0
2
1
0
0
2
0
1
3
1
1
2
1
0
2
1
1
0
1
0
1
0
1
2
2
1
1
0
0
1
1
0
0
0
1
0
2
0
1
2
0
1
0
0
0
1
2
1
2
0
1
1
2
0
0
0
2
1
0
1
2
2
0
2
0
2
0
1
1
1
1
2
1
2
1
2
2
1
1
0
3
0
1
1
0
2
1
0
2
0
0
0
1
0
1
3
1
0
0
1
1
1
2
0
0
2
2
1
2
2
4
1
2
0
2
2
1
2
0
1
2
0
1
1
1
0
0
1
0
2
0
2
1
1
2
1
2
2
0
0
2
1
0
2
2
1
1
1
2
0
0
2
1
2
0
2
3
1
1
1
3
0
1
3
1
1
0
0
0
2
1
0
0
1
0
0
1
1
0
0
0
1
1
2
1
2
2
0
1
2
0
2
1
0
1
1
1
0
1
1
1
2
0
0
1
3
4
0
0
1
0
2
2
1
1
1
0
1
1
0
1
0
3
0
0
1
2
1
1
1
2
2
0
0
0
2
1
1
0
1
2
1
2
1
1
0
0
1
1
1
0
2
0
1
0
0
0
1
1
0
1
1
1
0
1
0
1
0
0
1
1
1
0
1
2
0
1
1
0
1
1
1
0
0
0
2
2
0
1
1
2
0
2
1
5
0
1
0
0
1
1
0
0
0
0
2
1
2
1
1
0
1
0
1
1
2
1
0
1
1
2
1
1
1
1
0
2
0
0
1
0
0
1
1
2
1
2
1
1
2
1
0
1
1
2
0
1
2
0
1
2
2
1
1
1
1
2
1
1
2
0
1
1
0
2
2
1
1
0
2
0
2
1
1
1
0
1
0
1
1
1
2
1
1
1
0
0
1
1
0
0
1
0
2
1
1
0
2
0
0
2
0
2
1
1
2
2
2
0
0
1
0
2
2
2
3
1
2
1
1
1
0
0
0
1
2
1
1
1
0
1
1
2
1
1
1
1
2
2
3
1
0
0
1
0
0
1
1
0
2
1
1
1
0
1
0
2
1
1
0
1
1
2
2
1
0
0
1
0
1
2
2
1
0
1
0
1
2
1
0
1
2
1
2
0
2
1
1
1
2
2
1
0
2
2
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
1
1
1
1
2
1
0
1
0
1
0
1
0
0
0
0
0
0
1
1
0
0
1
0
2
1
0
2
2
2
1
2
1
1
1
0
1
1
1
1
0
2
1
1
0
0
0
0
0
1
1
0
1
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
2
0
0
2
2
1
1
1
0
0
0
1
0
1
1
1
1
1
1
2
1
0
2
2
0
1
0
1
2
0
1
0
2
1
0
1
1
0
0
1
1
0
1
2
0
0
1
1
1
2
1
2
1
2
0
1
2
1
2
1
2
2
0
3
0
0
1
2
0
2
1
1
0
1
0
1
1
1
0
1
1
0
0
2
1
5
0
0
0
2
1
2
2
1
2
2
0
0
1
2
0
0
0
1
1
0
0
0
1
0
2
1
0
2
0
0
1
0
2
1
2
2
0
1
2
1
0
2
0
1
2
0
1
1
0
1
1
2
1
1
2
0
0
2
1
1
0
1
1
1
1
1
0
0
1
1
1
2
1
1
0
0
0
1
0
2
2
0
1
1
1
1
1
0
1
1
1
2
1
1
0
1
0
2
1
2
0
1
2
0
0
0
0
1
0
2
0
1
0
1
0
2
1
0
1
2
3
0
1
0
0
0
0
0
1
1
2
0
0
0
1
0
1
1
2
2
2
1
2
0
0
0
0
1
0
1
1
2
1
0
1
1
1
2
1
1
1
0
1
1
1
0
2
1
1
1
2
2
0
0
1
1
2
1
2
2
1
2
1
0
2
1
0
0
1
1
2
0
1
0
2
0
0
0
1
2
1
0
0
0
1
2
2
2
1
2
1
0
0
2
1
2
0
1
1
1
0
0
1
1
1
2
0
0
0
2
0
2
1
0
0
0
0
1
0
4
1
0
0
0
1
2
1
0
0
0
0
1
1
1
0
0
1
0
1
1
1
0
1
1
1
0
0
1
0
1
1
0
1
1
0
1
1
1
0
0
0
1
0
1
2
0
1
1
0
1
1
0
1
1
0
2
1
1
1
1
1
2
0
1
1
0
2
0
2
0
1
3
1
2
1
2
1
2
1
0
2
0
1
2
2
1
0
2
1
2
1
1
2
0
1
1
2
2
1
1
1
1
0
1
2
1
0
2
1
0
1
0
0
0
1
0
1
2
1
2
2
2
2
1
1
1
3
0
1
1
1
0
1
0
1
1
0
0
1
0
1
0
1
0
1
1
0
0
0
2
2
2
0
0
1
0
0
1
1
0
1
0
0
0
2
0
1
1
2
2
3
2
1
1
2
1
1
1
11
1
1
1
0
1
1
2
1
1
2
0
0
1
1
2
0
1
1
1
2
2
1
2
1
2
2
1
1
0
1
1
2
2
0
2
1
1
2
0
0
0
1
2
1
2
0
0
1
1
0
2
2
2
0
1
1
0
2
0
0
2
1
1
2
1
0
2
1
2
0
0
2
1
0
1
1
0
2
0
0
1
1
0
1
0
0
0
2
0
1
0
2
0
1
2
1
0
1
0
0
0
1
1
0
1
1
1
1
1
1
0
1
0
0
1
1
1
0
0
0
1
2
1
0
0
0
0
0
1
0
0
2
0
1
2
1
1
0
0
2
2
0
1
1
0
1
3
1
0
0
0
1
1
1
1
0
0
0
2
1
1
1
2
1
1
2
2
1
0
1
1
0
1
2
2
0
2
2
0
1
0
2
1
0
0
0
1
0
0
0
0
0
2
0
1
1
1
0
0
1
2
2
2
2
0
0
2
3
0
1
1
2
2
1
0
4
0
1
0
0
0
1
2
1
2
1
2
1
0
1
0
0
1
1
2
0
1
1
2
0
0
1
0
0
1
1
1
0
2
2
0
1
2
0
1
5
0
1
0
0
2
1
2
0
0
2
0
1
0
1
0
1
1
0
0
2
2
0
0
0
1
0
1
0
0
2
0
1
2
1
0
0
2
2
2
0
0
1
1
1
1
1
0
1
2
0
1
0
0
2
1
0
2
0
1
0
2
2
0
1
1
1
0
0
2
1
0
0
1
0
1
0
1
0
0
1
1
0
1
0
2
0
0
2
1
0
1
0
1
1
1
0
1
0
1
2
1
0
0
2
3
0
0
5
2
0
2
2
0
2
0
0
1
1
0
0
2
2
1
1
0
2
1
1
1
1
1
0
2
0
1
2
1
1
0
2
0
2
0
1
2
0
0
0
1
0
1
1
1
1
1
0
0
1
0
0
2
1
0
2
0
0
1
1
2
1
1
0
1
1
1
2
0
1
1
2
0
2
2
1
1
1
0
0
1
0
0
2
1
0
1
1
0
1
2
1
0
0
2
1
2
2
1
1
1
1
1
2
1
1
0
0
0
1
1
1
1
1
1
1
1
0
2
2
1
0
1
2
2
1
1
1
0
0
1
1
1
1
0
1
2
0
1
1
1
2
0
1
0
1
1
1
1
0
2
1
1
0
1
0
0
1
0
2
1
1
0
1
0
0
1
1
2
2
0
1
2
2
0
1
1
1
0
1
0
0
1
0
1
2
2
2
1
1
0
0
0
2
0
0
1
0
1
0
0
1
1
1
1
1
1
2
1
1
1
0
2
1
1
0
0
2
0
0
1
2
0
0
0
0
2
1
0
2
0
2
0
1
1
0
1
1
0
2
1
1
1
0
0
1
0
0
1
2
0
0
1
1
2
1
2
1
1
0
2
1
0
0
2
1
0
1
1
1
1
1
2
1
1
0
1
2
1
1
1
3
2
0
1
0
1
1
1
2
1
0
3
1
0
0
1
2
2
1
1
0
1
0
0
1
1
2
0
0
1
1
2
0
2
0
1
1
0
1
0
2
2
0
1
1
2
0
1
2
2
1
0
1
0
1
0
1
1
2
0
0
0
1
0
1
1
1
1
2
1
0
1
1
1
1
1
1
1
1
1
0
2
2
1
2
2
1
0
2
1
1
1
0
2
6
0
2
1
1
2
1
0
1
1
1
0
0
1
2
1
0
2
2
2
1
0
0
1
2
2
1
0
0
1
0
0
1
0
2
0
1
1
0
1
1
0
2
1
0
1
1
0
2
0
0
1
2
0
0
0
2
0
1
2
1
2
2
1
2
2
1
2
0
2
0
0
1
1
1
3
0
0
1
1
5
0
0
0
0
2
0
0
0
2
2
2
0
0
1
1
0
1
1
0
1
0
0
0
1
3
1
1
1
0
0
2
0
0
0
1
1
2
2
0
2
2
0
2
1
0
1
2
1
2
0
0
0
0
0
0
1
2
1
2
2
2
1
1
1
1
2
0
1
1
2
1
1
1
1
0
0
0
0
0
2
1
1
1
1
0
1
0
1
1
2
0
1
0
1
2
2
0
3
0
1
1
1
0
2
0
0
1
1
0
2
1
1
2
1
0
1
1
0
2
2
2
0
1
1
1
0
2
1
1
1
0
1
1
1
0
1
1
1
1
2
2
1
1
1
2
1
0
3
0
1
2
1
0
1
0
1
0
1
1
0
0
0
1
0
1
1
3
1
1
1
0
0
1
0
2
2
1
2
1
1
0
1
0
2
0
0
2
0
2
0
0
0
2
0
1
2
0
1
1
2
1
0
1
1
0
0
1
2
0
1
1
1
1
1
1
0
0
1
0
3
1
1
0
1
2
1
0
1
2
2
1
1
1
1
0
2
1
1
1
2
2
1
1
1
1
2
2
0
1
2
1
0
1
2
0
0
0
1
1
0
2
2
1
0
2
0
2
2
1
1
0
0
0
1
1
0
0
1
0
2
0
2
1
1
1
1
1
1
2
1
2
1
2
0
0
0
2
2
2
0
0
2
2
1
1
1
1
0
0
1
0
1
1
0
1
2
1
1
2
1
2
1
1
1
0
1
0
2
2
1
2
2
2
1
2
1
2
0
0
0
2
1
1
1
0
0
1
2
1
1
0
0
1
1
0
0
2
2
1
1
1
1
1
2
1
1
2
2
1
0
0
1
2
1
0
1
0
1
1
0
0
0
0
1
2
2
0
2
0
2
1
0
1
2
2
0
1
1
0
0
0
1
0
0
1
0
2
1
0
1
1
1
1
1
1
2
1
2
0
2
0
2
2
3
1
0
1
1
1
1
0
1
1
0
1
1
2
1
0
2
0
1
1
2
1
0
0
1
0
0
2
0
0
0
1
2
1
2
1
1
1
0
2
2
1
1
1
0
2
1
2
0
0
1
0
1
3
1
1
1
2
2
1
2
1
2
1
1
0
1
1
0
0
1
1
1
1
2
1
1
0
0
0
1
1
0
0
0
2
0
1
2
1
0
2
1
0
2
0
1
1
2
0
1
0
0
0
3
1
1
0
1
2
2
2
1
2
2
2
1
1
0
2
1
0
1
1
1
1
0
1
1
0
1
0
0
1
1
1
1
1
1
0
0
1
0
2
0
0
0
0
2
2
2
2
0
1
2
1
1
1
1
1
1
2
1
0
0
0
1
1
0
1
2
0
2
2
1
1
1
1
1
3
0
1
0
0
1
1
0
0
2
0
2
1
1
1
1
0
0
0
1
0
0
1
0
3
1
1
0
1
1
1
2
1
0
0
1
1
2
1
1
1
0
0
1
1
2
1
1
1
2
1
0
0
1
1
1
1
1
0
1
1
1
1
0
2
1
2
0
5
2
1
3
2
1
0
2
1
2
1
0
1
0
1
0
1
0
2
1
0
0
0
1
2
0
0
0
0
1
0
2
1
1
0
2
2
2
0
1
0
1
0
2
2
0
2
1
1
1
1
3
1
2
2
0
1
2
1
1
0
0
1
0
0
2
0
0
0
3
1
1
0
1
1
1
0
1
0
0
1
0
1
0
0
1
0
0
0
1
1
0
2
0
2
1
0
0
1
0
0
2
0
0
1
0
0
1
2
0
1
1
1
1
1
1
3
0
1
1
1
1
1
0
0
0
1
1
0
1
1
0
1
2
2
1
0
1
1
0
0
2
0
0
0
0
0
2
0
1
1
2
1
0
2
3
0
0
0
2
1
1
0
1
0
2
1
1
1
1
1
1
0
1
0
2
2
1
1
1
1
1
1
1
1
2
1
1
0
1
2
2
1
1
0
0
3
2
1
2
1
0
1
1
0
0
0
0
0
1
2
1
0
0
2
2
0
1
2
1
0
1
0
1
2
2
0
3
0
2
3
1
2
2
0
0
1
0
0
1
1
1
1
0
3
1
1
0
0
1
2
2
0
0
1
1
2
0
1
0
1
1
1
0
1
1
0
0
0
1
0
1
1
2
1
1
1
1
2
0
1
2
0
2
1
1
4
1
0
0
0
0
1
1
3
1
0
0
0
2
1
1
1
1
1
1
0
2
1
0
2
2
2
0
1
1
1
1
0
1
2
2
1
1
1
1
2
1
0
0
0
1
0
2
2
0
0
2
1
2
2
1
0
1
1
0
2
1
0
1
2
1
0
2
1
0
1
1
0
1
0
1
2
1
2
1
0
0
2
0
2
1
1
1
1
0
0
2
2
0
1
1
0
1
0
1
0
0
2
2
2
3
2
2
0
2
1
2
1
1
1
2
1
1
1
1
2
1
2
2
0
1
0
2
1
1
2
0
2
1
1
0
0
1
1
0
1
0
0
1
0
2
1
0
2
1
0
0
0
2
1
1
0
1
0
0
1
0
0
0
1
1
1
0
0
0
1
0
0
0
0
1
2
2
0
1
0
0
0
1
0
0
1
0
1
1
0
0
1
1
1
4
2
0
1
1
2
0
0
2
1
2
1
1
2
0
1
0
1
2
1
2
0
1
2
2
1
2
2
1
0
2
1
2
0
1
1
1
0
2
1
1
2
2
0
0
1
1
0
1
2
2
2
1
0
2
1
1
1
1
2
0
1
1
1
1
1
3
1
1
1
2
1
1
0
0
0
1
1
2
0
2
0
2
1
1
0
0
1
0
2
1
0
1
0
2
1
2
2
2
0
0
2
1
2
0
0
0
1
1
1
1
0
1
0
0
2
2
1
2
1
0
2
1
0
1
1
1
1
0
1
0
2
1
0
1
0
1
2
0
0
4
1
1
1
1
3
1
0
1
1
1
1
2
3
1
2
1
2
2
1
1
0
0
1
0
2
0
0
1
1
1
1
1
0
2
1
0
1
2
0
0
1
2
2
0
0
2
1
0
1
1
1
1
0
1
1
1
2
2
1
1
1
2
1
1
1
0
0
1
1
0
1
2
0
1
0
1
0
1
1
2
4
3
0
2
1
1
0
2
1
2
0
1
2
1
1
1
1
1
0
0
1
2
0
0
1
2
0
0
0
1
1
1
1
1
0
1
1
1
1
0
0
0
1
0
2
1
0
2
1
1
0
1
2
1
2
0
0
1
0
0
2
1
1
2
1
0
2
0
1
0
1
1
2
1
1
1
0
0
0
2
0
1
1
2
1
1
1
2
1
1
0
1
2
2
0
1
2
1
1
2
0
0
1
1
1
0
1
2
0
1
2
0
1
1
3
0
1
1
1
3
2
0
2
1
1
1
0
0
1
0
2
1
1
1
1
2
1
2
0
1
1
1
0
1
1
0
1
0
2
0
0
2
2
2
0
1
2
0
0
2
2
2
1
1
1
3
1
0
0
2
1
2
2
1
2
2
0
1
1
0
1
2
1
6
0
1
2
1
0
0
1
1
1
1
1
2
0
1
2
0
0
1
1
1
2
2
2
1
2
2
0
1
2
2
4
1
1
0
0
2
1
1
0
1
1
1
1
1
1
1
2
1
0
1
1
2
0
0
1
1
1
0
2
0
0
2
2
1
1
1
2
0
2
1
0
2
0
0
1
0
1
0
1
0
0
0
2
0
2
1
0
1
1
1
1
1
1
1
1
0
0
0
1
2
0
1
1
0
0
1
2
1
1
0
2
2
2
0
1
0
3
1
1
1
1
0
0
1
0
0
2
0
1
1
0
0
0
1
1
0
0
1
0
0
0
1
1
2
2
2
2
2
2
2
0
2
1
2
0
1
0
0
0
0
0
1
1
1
0
0
1
2
0
2
1
1
1
0
1
1
2
1
2
1
1
0
0
2
1
2
5
0
1
1
2
0
0
1
1
0
1
0
1
0
0
1
1
1
2
1
2
1
0
0
1
1
0
0
0
1
1
1
2
1
0
1
2
1
1
0
1
1
1
0
1
0
0
1
2
1
1
0
2
1
1
0
0
0
0
1
0
1
1
0
0
1
2
1
2
2
0
1
0
1
1
0
0
2
1
0
1
0
1
1
1
1
1
1
0
0
2
0
1
1
0
1
2
1
1
1
2
0
2
1
1
1
1
2
0
0
2
2
0
1
1
0
1
2
2
0
0
1
2
2
1
0
1
1
0
0
1
0
1
0
0
0
2
1
0
2
1
1
2
0
1
1
1
1
1
0
0
0
0
0
1
1
0
1
2
1
2
1
1
2
1
2
1
1
1
0
1
1
1
1
0
1
1
2
1
1
0
0
0
2
2
1
1
3
1
2
1
1
0
1
0
0
1
2
2
1
1
1
1
1
0
1
2
0
0
0
0
2
0
0
0
2
2
1
1
1
0
2
2
0
3
0
0
2
1
2
0
2
2
1
0
0
1
0
1
2
1
1
2
1
1
0
1
1
1
1
1
1
1
0
1
0
1
0
1
1
1
1
0
0
1
0
1
1
0
1
0
2
1
0
2
1
2
1
1
0
0
1
1
1
0
0
2
1
1
0
1
1
0
2
0
2
1
0
1
1
1
0
0
0
1
2
1
0
1
2
0
1
0
0
0
0
0
0
0
1
1
1
0
2
1
0
1
2
1
0
0
2
2
0
0
1
0
0
2
0
0
2
1
0
2
0
0
1
2
0
0
1
1
2
1
1
1
2
0
0
1
1
1
0
2
1
2
0
1
2
1
1
2
0
2
0
3
1
0
0
2
1
1
0
2
3
1
1
1
1
2
3
1
1
1
0
0
0
1
0
0
0
1
0
1
1
1
2
2
2
0
1
0
1
1
1
2
0
1
0
4
2
1
1
2
0
0
1
1
2
1
1
1
0
2
1
2
0
0
1
2
1
1
2
1
1
1
0
1
0
0
2
2
2
1
1
1
0
0
1
0
0
0
2
0
1
1
1
1
1
0
1
1
0
1
0
1
1
0
1
1
1
1
2
0
1
2
0
0
2
0
0
0
1
1
2
1
1
1
0
2
2
0
1
0
4
0
2
0
1
1
2
1
0
1
1
0
0
1
1
0
0
2
1
1
2
1
1
1
2
2
2
1
2
1
2
0
2
2
0
0
1
0
3
1
2
1
1
1
1
0
1
2
0
2
0
0
0
1
0
0
0
1
0
1
2
1
1
1
0
0
0
0
1
1
0
0
0
1
2
1
1
2
3
0
2
2
1
1
1
0
1
1
3
0
0
0
0
0
1
5
1
2
1
0
0
2
2
1
0
1
0
2
2
1
1
0
1
1
1
0
2
0
1
1
1
1
1
1
1
0
0
2
1
1
0
1
1
1
1
1
1
1
2
1
0
1
0
0
1
1
2
1
1
0
1
1
2
2
0
1
2
1
1
4
0
0
1
1
1
1
0
1
1
0
2
2
0
2
1
1
0
1
1
0
0
1
1
0
1
0
1
1
1
0
1
1
1
2
1
1
1
1
1
1
2
1
2
5
0
0
0
0
0
1
1
2
0
0
2
1
1
1
0
0
1
0
3
0
0
0
0
0
1
1
1
0
0
1
1
0
1
1
1
0
0
0
0
1
1
0
0
0
0
2
0
1
1
0
0
1
1
1
0
2
0
1
1
1
1
2
1
1
1
1
1
2
2
2
1
1
0
0
2
1
2
0
2
1
1
1
1
2
2
0
2
1
1
2
1
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
2
0
1
0
2
1
1
2
0
0
0
0
1
1
2
2
0
0
2
1
1
2
0
0
6
0
1
0
1
1
1
1
2
0
1
2
2
0
1
1
1
1
1
0
1
2
1
1
0
0
0
1
0
1
1
0
2
2
0
1
0
0
0
1
1
1
2
1
1
1
0
2
2
1
0
1
1
1
0
1
0
2
1
1
1
2
0
0
0
1
2
0
0
2
1
1
0
1
1
1
1
1
1
1
1
2
0
1
0
2
2
1
1
0
1
2
0
0
0
2
0
1
1
1
2
1
0
0
1
0
0
1
1
1
0
0
2
1
2
1
1
2
1
0
0
2
2
2
1
2
2
2
0
0
0
0
0
1
2
1
1
1
0
1
1
2
0
2
1
0
0
0
2
0
2
2
0
1
2
2
1
0
1
1
1
2
1
2
0
2
1
1
2
0
0
1
1
1
2
1
2
0
1
1
0
1
1
1
2
1
0
1
1
0
1
2
1
0
0
0
2
1
0
1
1
1
2
0
2
0
2
1
2
1
0
1
1
0
0
1
1
1
1
1
0
1
1
2
1
0
1
0
2
2
2
1
1
2
0
0
0
2
2
1
0
1
1
1
1
1
1
1
1
2
2
0
2
1
1
1
1
1
1
1
1
1
0
0
1
0
1
1
1
2
2
0
1
1
1
1
1
0
1
1
1
0
1
2
1
0
0
1
1
2
2
1
1
0
0
2
2
0
0
2
1
2
1
1
1
1
1
1
2
0
1
0
1
0
1
1
0
1
4
0
1
1
2
0
0
2
2
1
0
1
1
0
1
1
1
0
2
0
2
1
1
1
1
2
0
1
1
1
1
3
0
0
1
2
1
1
2
0
0
1
1
0
1
0
1
1
1
1
0
0
2
0
1
0
0
1
0
1
1
1
0
1
1
1
2
1
1
2
1
1
0
0
0
3
1
0
1
0
1
0
1
1
1
2
1
1
1
1
0
2
1
0
1
1
1
2
0
0
2
0
1
1
2
1
1
0
0
0
1
1
2
0
0
0
1
0
1
1
2
0
1
2
0
0
0
0
1
1
2
2
1
1
1
0
0
0
1
0
2
2
1
1
2
0
1
1
1
1
1
1
4
1
0
1
0
1
1
1
1
1
1
0
0
1
1
0
1
0
1
0
0
0
1
1
1
1
1
1
2
1
1
2
1
1
3
1
0
1
0
2
0
1
1
0
0
3
1
0
1
2
2
1
2
1
0
1
1
0
0
0
1
1
1
0
1
0
1
0
0
0
0
2
1
0
2
1
1
0
1
1
1
0
2
0
0
1
1
0
0
0
0
2
1
2
1
1
2
1
1
1
1
1
0
1
1
1
1
1
0
0
1
0
1
1
2
1
1
0
0
1
0
1
0
3
0
1
0
2
0
0
0
1
2
0
0
1
1
1
0
2
0
2
1
0
2
0
1
2
1
1
0
1
3
0
1
1
1
0
0
1
0
1
0
2
1
1
2
1
0
0
1
1
1
2
1
2
1
2
1
1
2
1
2
2
2
0
1
0
1
2
1
2
0
1
1
1
1
1
1
1
1
0
2
2
0
0
0
1
1
1
0
1
1
1
0
0
1
1
1
0
0
2
0
1
1
0
1
1
2
0
0
0
2
1
0
0
1
1
0
1
1
1
2
1
1
1
1
2
1
1
1
1
0
1
0
2
2
1
2
0
1
0
1
0
0
1
1
1
2
0
0
0
0
2
1
1
0
3
1
1
0
1
1
0
1
0
2
0
0
1
1
1
1
0
1
1
1
0
2
2
1
2
2
0
0
1
1
1
1
1
1
1
0
0
1
2
2
0
0
1
1
0
1
1
0
1
0
0
1
2
0
0
1
0
1
1
1
2
2
1
2
1
1
0
0
1
0
1
1
0
1
2
1
2
1
0
1
2
1
2
1
1
0
0
1
1
0
0
0
3
0
1
0
1
0
1
3
0
1
1
1
0
0
1
1
0
1
0
1
2
1
1
1
1
1
0
2
1
1
2
0
0
0
2
1
1
0
1
1
2
2
2
0
1
1
2
0
2
0
0
1
1
0
2
2
0
1
0
1
1
1
0
1
1
1
1
2
0
1
0
2
0
1
1
1
0
0
2
0
1
2
1
0
1
1
2
1
1
0
1
0
1
1
1
1
2
1
0
0
1
0
2
2
2
2
1
0
0
1
1
2
1
0
2
1
1
1
0
0
0
1
3
0
0
1
2
0
1
1
1
0
0
1
0
1
1
1
1
1
1
1
0
1
2
2
0
0
1
2
2
2
1
0
0
1
1
0
1
2
0
2
0
0
0
0
1
1
1
0
0
1
2
1
0
0
0
0
1
0
2
1
0
0
0
0
0
1
0
1
0
2
2
3
2
0
1
1
0
2
1
2
4
2
1
2
1
0
1
1
1
0
5
1
1
1
0
1
1
0
2
1
1
2
1
1
0
0
2
0
1
0
1
1
0
1
2
1
1
0
2
0
0
1
0
2
0
0
3
1
1
0
0
0
1
0
1
0
0
3
0
1
0
2
0
1
1
1
2
0
1
0
1
0
1
2
1
1
1
2
0
1
0
2
1
2
2
1
1
2
1
0
0
0
3
1
1
2
1
1
0
0
0
1
0
0
0
0
1
0
0
1
0
2
0
0
2
1
0
2
0
2
0
1
1
1
0
0
0
0
0
1
1
1
1
0
2
2
1
1
0
1
1
0
1
1
1
2
2
0
1
2
2
2
2
1
2
0
0
1
0
1
2
1
1
0
1
1
2
1
1
1
1
2
0
1
2
1
1
0
1
1
1
2
1
0
1
1
3
0
3
1
1
1
2
1
1
1
1
0
0
1
0
0
2
1
0
0
1
0
0
0
2
0
1
0
1
1
1
0
0
0
1
0
0
2
0
1
1
2
1
1
0
1
1
0
2
0
1
1
1
0
1
1
1
2
1
0
1
1
0
1
2
1
0
1
1
1
1
0
2
2
2
1
2
1
2
1
0
1
1
2
1
2
1
1
1
3
1
0
0
0
0
1
2
2
1
1
0
1
1
0
0
0
2
1
1
1
1
0
0
2
0
1
0
1
1
1
0
0
2
1
2
0
1
0
2
1
1
1
0
2
1
1
1
4
0
3
0
1
0
1
1
1
1
1
1
1
0
0
1
0
0
1
2
1
1
0
0
2
0
0
0
1
2
0
2
3
0
2
0
1
2
0
0
3
2
2
2
0
1
2
1
1
0
0
0
0
1
1
2
1
0
1
6
0
0
1
1
2
1
1
1
2
1
1
2
1
0
2
1
1
0
1
1
1
2
1
1
2
2
0
0
1
0
1
2
0
2
2
2
1
0
2
0
1
0
1
1
1
1
0
0
1
0
0
1
1
2
2
0
2
1
0
0
1
0
1
3
1
1
1
1
1
0
1
1
1
0
0
1
0
0
0
1
0
1
1
1
2
1
0
0
1
1
0
1
0
1
1
1
0
0
0
1
1
0
1
1
0
1
1
2
1
2
0
1
2
1
1
0
1
0
0
2
0
1
0
1
1
0
1
0
0
0
1
2
1
2
2
2
0
0
0
1
1
2
2
2
2
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
1
1
1
0
1
2
0
2
1
1
0
3
2
1
1
1
1
1
0
1
1
0
1
1
1
0
2
2
1
2
0
2
2
1
0
0
0
1
1
1
1
0
1
1
1
1
1
0
1
1
0
0
1
0
2
1
1
0
1
1
0
1
1
0
1
0
0
1
1
2
2
0
0
1
0
0
1
0
1
0
0
0
2
0
0
0
0
0
1
1
2
1
0
2
1
1
0
1
2
1
1
1
0
0
1
1
0
1
0
1
2
2
0
0
0
0
1
0
1
0
1
0
0
1
0
1
2
0
1
1
2
2
1
1
1
1
2
2
1
1
1
3
1
2
0
0
2
1
3
1
1
1
2
2
0
3
0
1
0
2
1
0
1
2
0
0
0
2
2
1
0
0
2
1
0
0
1
1
0
0
5
1
2
1
0
0
0
0
0
0
1
0
0
1
0
0
2
0
3
0
2
1
1
2
0
1
1
2
0
0
1
1
1
0
1
1
0
1
1
2
2
0
1
1
0
1
1
0
0
1
1
0
1
0
1
1
2
0
1
0
1
1
1
1
1
1
0
0
1
0
1
2
0
2
0
1
1
1
1
1
0
1
1
1
0
0
1
1
4
1
1
0
2
1
2
1
1
1
1
0
1
1
0
1
1
1
1
2
1
1
0
1
0
1
0
0
0
1
0
1
1
0
0
1
0
2
1
0
1
0
0
0
2
1
0
1
1
0
0
1
1
2
2
1
0
0
0
1
2
1
1
2
1
1
2
5
0
2
1
2
1
0
3
0
2
1
1
2
0
1
1
0
1
1
2
1
0
2
1
1
1
1
0
2
2
0
1
1
1
1
0
0
2
1
1
1
0
2
1
1
1
1
0
2
0
1
1
0
1
2
0
1
0
1
1
1
1
0
2
1
0
2
1
0
0
1
0
3
2
2
1
1
3
1
0
1
1
1
2
2
1
0
1
2
0
1
0
0
1
1
2
1
1
1
1
1
0
0
2
1
1
1
1
1
1
1
0
1
2
2
0
0
1
2
1
0
1
1
2
2
0
2
1
2
1
1
0
0
2
0
0
2
1
2
2
1
0
1
1
0
1
1
2
2
1
1
0
0
2
2
1
0
1
1
1
0
0
1
0
1
2
0
0
0
1
0
2
1
1
1
1
0
0
1
1
0
2
2
0
0
1
1
1
0
0
0
1
0
0
1
1
1
0
1
0
1
2
2
1
1
0
1
0
2
0
0
1
1
2
0
0
1
1
0
1
1
0
0
0
0
0
1
0
1
0
1
1
1
2
2
1
0
1
1
1
1
2
1
0
1
1
1
0
0
1
1
1
1
0
2
0
2
0
1
0
0
0
1
0
0
0
0
0
2
1
0
1
0
1
0
0
0
2
2
1
1
0
0
2
1
0
1
2
1
2
0
0
1
0
0
0
0
0
0
2
0
0
1
1
2
1
1
0
1
0
0
0
2
1
3
1
0
0
2
1
0
0
1
0
2
1
1
2
2
1
1
2
2
1
0
1
2
3
0
1
2
1
2
1
0
0
0
0
0
0
0
0
1
1
2
0
0
2
1
2
0
1
2
1
0
1
0
2
2
0
2
1
2
0
1
0
1
2
2
0
1
0
1
1
0
1
1
2
1
1
2
1
2
1
5
2
1
1
2
1
0
1
2
2
0
0
1
1
0
0
0
0
1
0
1
0
1
2
1
1
0
0
2
1
1
1
0
0
0
1
1
0
0
0
1
2
1
0
1
0
2
0
1
2
0
0
0
0
0
2
1
1
1
0
0
1
1
2
0
2
1
1
0
1
11
0
1
1
2
1
1
0
0
1
1
2
1
0
1
1
1
0
1
0
2
1
1
1
0
1
0
1
0
1
1
0
1
2
1
1
0
2
0
2
1
0
1
0
2
0
2
1
2
1
1
0
0
2
1
2
0
0
0
0
2
0
1
1
0
2
0
2
1
2
1
3
1
1
0
1
0
2
0
1
2
2
0
0
0
1
1
0
3
0
0
0
0
2
0
0
1
1
0
2
1
2
1
0
1
2
1
1
2
2
0
1
2
1
1
1
1
3
1
2
1
0
0
1
1
0
1
0
1
1
0
1
0
2
0
3
0
0
1
0
0
0
0
2
2
0
1
1
2
1
1
0
1
0
1
0
0
1
0
1
1
0
1
0
1
2
1
0
0
1
1
0
1
1
2
0
0
1
2
2
0
0
2
1
2
1
0
1
1
0
2
0
1
1
5
1
1
1
2
1
3
1
1
2
0
2
1
1
2
1
1
0
0
1
1
1
0
1
1
1
2
1
1
2
0
2
0
1
2
2
0
1
0
2
0
2
3
1
0
1
2
2
1
2
0
1
0
0
1
2
0
1
1
2
2
0
2
1
2
0
1
2
2
1
1
1
2
1
1
2
1
0
1
0
2
0
1
1
1
3
0
1
1
1
2
1
1
1
0
1
0
0
2
1
1
1
0
1
1
0
1
0
2
0
0
0
0
0
0
1
0
2
0
1
2
2
2
1
0
2
2
2
0
0
0
0
1
1
2
1
1
0
2
0
0
2
0
2
1
1
1
1
1
2
0
1
0
0
0
1
1
2
1
1
0
2
1
0
0
2
1
1
0
2
1
0
2
1
1
1
1
1
2
1
1
1
1
2
1
0
1
2
2
0
1
0
2
1
0
0
1
2
0
0
1
2
2
1
1
2
1
0
0
1
2
1
2
1
0
1
1
1
1
1
0
0
1
1
1
0
1
1
0
1
1
1
1
2
1
0
2
1
0
1
1
1
0
2
0
1
2
2
2
2
1
2
0
1
0
1
0
1
2
1
1
1
2
0
0
1
2
2
2
0
2
2
1
2
1
2
1
1
1
1
2
2
2
1
0
1
1
1
1
1
0
1
0
1
2
1
1
0
0
0
0
2
0
2
2
0
1
1
0
1
0
1
1
1
0
1
1
2
2
1
0
2
0
1
0
1
1
0
1
0
1
0
2
4
0
0
2
1
0
0
1
1
0
0
0
1
1
0
1
2
2
1
0
1
1
0
2
1
1
0
1
1
2
1
0
0
0
3
1
1
1
0
1
1
0
2
0
2
0
0
0
0
0
1
0
1
2
1
1
1
2
0
2
1
1
1
1
2
3
2
1
0
1
2
1
1
0
2
1
0
1
1
0
0
1
0
1
2
2
0
0
1
1
1
1
2
1
2
0
1
1
1
2
1
0
0
0
0
3
1
2
1
1
1
1
0
1
0
0
1
0
1
3
2
1
2
0
0
1
1
1
2
2
1
2
0
1
1
0
1
1
0
2
1
0
0
1
2
0
0
1
1
1
1
0
0
2
1
1
0
0
1
0
2
1
0
1
0
0
1
1
0
0
0
2
2
2
2
1
2
0
0
1
0
0
2
2
0
2
0
2
1
1
3
1
1
2
0
0
0
1
2
2
2
0
1
1
1
1
2
0
1
2
2
1
1
1
1
1
1
1
1
1
0
1
0
1
2
0
1
1
2
1
0
0
1
1
2
1
1
1
2
2
0
4
1
0
1
1
3
1
0
1
2
1
0
1
0
1
4
1
1
2
1
1
1
1
1
1
2
0
1
2
1
0
0
2
1
1
2
1
1
1
1
0
2
1
0
0
1
0
0
0
0
0
0
7
2
1
0
1
0
1
2
2
0
0
1
0
2
0
1
1
1
3
1
0
1
0
2
2
2
0
0
1
1
1
1
1
0
2
1
0
0
1
0
2
1
0
1
0
1
0
1
1
0
0
3
0
1
0
0
2
2
1
1
1
2
1
1
1
0
0
1
2
1
2
0
0
2
0
1
1
1
1
1
0
1
1
0
0
1
1
1
0
2
1
0
0
1
0
1
1
2
0
1
0
2
1
0
1
1
2
1
0
0
2
1
0
0
2
1
2
0
1
1
1
1
1
1
0
0
0
0
0
0
0
0
1
1
0
1
1
2
0
1
2
1
1
2
0
1
0
1
2
0
0
3
2
1
2
0
2
1
1
0
1
0
2
2
0
0
0
1
1
0
2
2
1
2
1
1
1
2
1
2
1
1
0
1
1
3
1
2
1
0
0
1
1
1
0
2
1
1
1
0
1
0
1
1
1
2
0
0
1
1
1
1
2
0
0
1
1
1
2
2
2
0
3
1
1
1
0
1
2
1
1
1
1
1
2
0
1
0
2
0
1
1
2
1
0
1
1
1
1
0
0
1
1
2
2
2
2
2
1
0
1
1
1
0
0
1
2
1
1
1
0
0
2
2
2
1
2
0
2
0
1
1
0
1
0
2
2
0
2
3
0
1
0
1
2
0
1
2
1
0
0
0
2
0
1
0
0
1
1
2
0
0
2
0
0
1
1
1
1
0
1
1
0
2
1
1
3
2
1
1
1
1
1
0
2
0
1
0
0
0
1
0
1
0
1
1
2
0
2
1
2
1
0
0
2
1
1
0
0
0
0
2
0
0
0
1
1
0
1
1
1
1
0
1
1
1
0
2
1
1
0
2
1
0
1
1
1
1
1
2
1
1
1
2
1
2
0
0
0
0
0
1
0
0
1
1
1
2
0
0
0
0
1
2
1
0
0
1
0
1
2
1
2
2
1
1
2
0
2
1
2
2
0
0
1
2
0
1
1
0
1
0
1
0
1
1
1
1
1
1
0
1
1
0
1
1
1
1
0
0
0
1
1
1
2
1
4
0
2
1
1
2
0
0
1
1
1
1
1
2
2
1
2
0
0
0
0
1
1
2
1
0
0
0
2
1
2
1
1
0
1
1
0
2
2
2
1
1
0
2
1
0
0
1
0
1
1
2
0
1
1
2
1
0
1
3
0
0
1
0
2
1
3
0
1
1
1
1
1
1
1
2
1
1
0
1
0
1
3
1
2
2
0
1
0
2
1
2
1
0
1
1
0
1
2
2
1
1
2
2
1
0
0
1
0
2
1
1
2
1
1
2
1
2
2
2
1
2
0
0
1
1
1
1
0
0
1
1
0
0
2
2
1
1
0
0
1
0
1
1
0
0
1
0
0
0
1
0
2
2
0
1
1
0
0
0
0
0
2
0
0
1
0
2
0
0
0
1
0
1
2
0
1
0
2
1
0
0
1
2
0
1
1
2
1
0
1
1
2
0
1
0
0
0
2
0
1
2
2
2
0
2
0
1
1
2
1
2
2
1
1
1
2
2
0
3
1
2
1
1
1
1
0
0
1
0
2
0
0
1
0
1
1
0
1
1
0
0
1
0
1
0
1
0
1
1
2
1
2
1
0
0
2
1
1
2
2
2
1
0
2
1
1
2
1
0
2
0
2
0
3
1
2
1
1
1
1
1
1
1
1
0
2
0
0
2
0
0
0
1
2
1
0
0
1
1
2
0
0
2
0
1
2
2
1
1
1
2
1
0
1
1
1
1
0
0
2
0
2
1
1
0
0
1
1
0
1
2
2
1
1
0
1
0
1
1
2
1
1
0
1
2
1
2
0
1
1
0
1
2
0
2
1
0
1
1
0
0
2
0
2
1
1
1
1
1
1
1
2
2
1
0
0
0
2
1
1
1
1
0
1
2
1
2
2
2
0
2
1
1
0
1
1
1
1
2
1
1
1
0
0
2
1
1
0
2
1
1
1
2
1
1
1
2
1
1
1
4
0
0
1
1
1
1
0
2
2
2
1
1
1
2
2
1
0
0
0
1
0
0
2
0
1
1
0
1
1
0
1
1
1
1
0
0
1
1
1
1
0
0
1
1
0
1
1
1
1
1
2
0
1
0
1
1
0
0
0
2
0
0
1
1
1
1
1
2
1
0
1
0
2
0
0
2
1
0
2
0
0
0
2
0
1
1
0
1
5
0
0
0
1
2
2
2
1
0
0
0
0
0
0
1
0
2
0
0
0
1
2
0
1
1
2
2
1
2
0
2
1
2
1
1
1
1
0
1
1
0
0
1
2
1
2
0
2
0
0
0
1
1
1
1
1
0
1
0
0
1
2
1
1
0
1
1
1
1
1
0
1
1
0
2
1
1
0
1
2
2
1
1
1
1
0
1
1
1
0
1
2
2
1
0
2
2
0
0
1
0
0
2
1
0
1
2
0
0
1
1
0
1
2
0
1
1
0
2
2
2
0
2
0
3
0
2
0
0
1
2
0
0
1
1
0
1
0
0
1
1
1
2
1
2
1
0
1
3
2
0
0
0
0
1
1
0
2
1
0
0
2
0
0
0
2
1
1
1
1
2
1
1
1
1
1
0
0
1
0
0
1
0
0
0
0
1
1
1
1
2
2
0
1
2
0
2
1
1
0
1
2
0
2
0
2
1
1
1
1
2
1
2
2
1
0
1
2
0
0
1
2
1
2
0
1
1
0
2
0
1
2
1
1
0
1
1
0
0
1
1
1
0
0
0
0
2
0
0
1
1
0
1
2
0
2
0
0
0
2
1
2
0
0
1
1
1
2
1
1
0
0
0
2
1
0
0
1
1
1
0
2
1
1
2
1
0
1
2
1
0
0
0
2
1
1
1
0
1
0
0
2
1
0
0
1
1
0
0
0
1
1
0
1
1
1
2
1
1
2
2
0
0
1
0
0
1
1
1
1
1
0
0
1
1
2
1
1
0
1
1
0
2
0
1
1
1
0
1
2
0
0
1
0
1
1
1
1
1
4
1
1
2
2
1
0
1
0
1
2
1
1
0
1
2
1
2
0
0
2
1
0
2
1
5
1
0
0
0
0
1
0
1
0
1
2
3
2
0
2
0
0
1
1
0
0
2
1
3
1
1
2
1
0
2
1
1
1
0
1
1
0
1
1
2
0
1
2
1
2
1
1
0
1
2
1
1
1
1
0
0
1
0
0
0
0
1
1
1
2
1
1
1
0
2
2
2
0
0
2
0
0
0
1
1
1
0
2
0
0
0
1
0
0
1
0
2
0
1
1
2
0
1
1
1
0
0
1
2
2
0
2
2
0
2
1
0
1
1
0
0
0
1
1
2
0
0
0
2
2
0
1
1
0
0
0
1
1
0
1
1
1
1
2
3
1
1
1
2
1
0
1
2
2
2
1
0
2
0
1
2
0
3
0
0
0
2
1
1
0
1
1
2
0
0
0
1
2
1
0
1
2
2
0
0
2
1
2
2
3
1
0
0
0
0
0
2
0
1
1
1
1
2
1
0
1
0
1
0
2
0
1
0
0
1
1
1
0
0
1
2
0
1
0
1
1
0
0
0
0
0
1
0
2
2
1
1
2
2
1
0
1
1
1
2
0
1
2
1
0
1
1
2
1
0
2
1
0
1
2
0
0
1
1
1
0
0
1
1
2
1
1
1
0
1
1
0
0
0
1
1
1
1
1
0
0
0
1
2
2
2
1
1
1
2
1
1
1
0
0
0
1
2
0
0
3
1
1
1
1
2
2
2
2
0
1
2
0
0
1
0
2
0
2
1
0
0
1
2
1
0
0
1
1
0
1
0
1
1
0
0
1
2
2
1
0
1
0
0
0
1
0
2
0
2
1
0
0
2
1
0
1
2
1
0
0
2
1
2
0
0
1
1
0
0
1
0
1
2
1
2
0
1
0
1
2
1
1
1
0
1
2
1
1
2
1
1
2
0
2
1
2
0
0
0
1
2
2
1
1
1
1
1
1
1
1
1
2
2
1
1
2
0
0
0
2
0
1
1
0
1
1
1
0
2
0
0
1
2
0
1
1
0
0
1
0
1
2
1
2
2
0
1
0
0
1
0
0
0
0
1
1
1
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
1
1
1
0
1
1
1
1
1
0
2
1
1
1
1
1
2
1
0
1
1
0
1
1
2
1
0
2
0
1
0
1
2
1
1
1
1
2
1
0
0
0
1
1
2
2
2
2
2
1
2
1
1
1
1
1
1
0
1
0
2
2
1
2
1
2
1
2
1
0
0
0
1
1
2
2
1
2
1
1
1
1
0
0
1
2
1
1
0
0
0
1
0
1
1
2
1
0
0
1
2
1
1
1
0
1
0
0
0
0
1
1
1
2
3
0
0
1
1
1
2
1
0
1
2
1
0
2
1
0
1
2
1
2
1
1
1
1
0
1
0
1
1
1
0
0
1
1
1
1
0
2
1
0
0
1
0
0
0
0
1
1
1
0
1
0
1
1
1
0
2
1
2
5
1
0
1
0
1
1
2
1
0
1
0
1
0
0
2
1
2
0
2
1
0
2
0
1
0
0
0
1
2
0
0
0
0
1
1
1
2
1
1
1
1
1
1
0
1
1
0
2
1
1
1
1
1
1
1
1
1
2
2
2
0
0
1
1
2
2
1
1
1
1
0
0
0
0
2
2
0
2
0
0
0
2
1
2
2
0
1
1
1
1
0
0
1
1
2
1
0
0
1
2
1
1
2
1
1
2
1
1
2
0
0
1
0
1
0
1
0
0
2
2
0
1
2
2
0
1
1
1
0
0
0
1
1
1
1
1
1
0
1
1
0
2
0
0
2
1
0
1
2
1
0
0
0
2
1
2
2
0
1
1
0
1
1
1
0
0
2
2
2
1
1
0
1
2
0
1
1
0
1
0
0
2
1
1
1
2
1
2
1
0
1
2
0
0
1
0
1
1
1
2
0
1
1
2
0
2
1
0
0
0
2
0
2
1
1
1
0
1
1
1
2
2
1
2
0
1
0
2
0
2
1
1
0
2
2
1
1
1
1
1
1
2
0
2
2
1
2
0
1
0
1
0
3
1
0
2
0
1
1
1
2
2
1
1
1
1
0
1
0
2
0
1
0
0
1
0
1
2
2
1
0
1
1
2
1
1
1
2
0
1
0
1
1
1
0
1
0
2
0
1
0
1
0
3
1
0
2
1
2
1
2
1
0
1
1
1
0
1
1
0
0
2
1
1
1
2
2
2
1
1
2
0
1
1
1
0
1
1
0
1
1
2
1
2
0
1
1
0
1
0
1
0
1
0
1
0
1
1
2
1
0
0
1
2
1
1
2
1
3
1
0
1
1
1
2
0
2
1
1
2
0
0
0
1
2
1
1
1
1
1
1
1
0
2
1
0
1
1
2
2
0
0
2
2
0
0
1
1
0
1
1
0
1
1
1
0
1
1
1
0
0
0
2
0
0
0
0
0
1
1
1
1
1
0
2
2
0
0
1
1
2
1
0
1
0
1
1
0
1
1
2
1
2
0
2
1
0
2
1
2
1
0
0
0
2
0
1
0
2
0
1
1
1
2
0
0
0
1
1
2
0
0
1
0
1
2
3
0
1
0
2
2
1
0
1
1
1
2
2
2
1
2
1
1
1
1
0
1
1
0
2
1
2
2
0
3
0
2
0
2
0
2
1
1
1
2
1
2
1
1
1
0
0
1
1
2
1
0
1
2
2
2
1
2
4
0
0
0
0
1
2
0
1
0
0
1
2
1
1
0
0
1
1
2
1
2
1
1
0
1
1
1
1
1
0
1
1
0
0
2
1
1
1
1
2
0
0
2
3
0
0
2
0
1
1
0
1
1
1
1
1
0
0
2
0
1
0
1
2
1
0
0
0
0
0
1
2
1
1
0
4
1
1
1
0
1
0
1
0
2
1
0
1
0
1
1
2
2
1
1
2
2
1
1
3
1
0
1
0
0
3
1
0
2
0
1
1
2
0
0
0
0
1
1
0
0
0
0
0
2
0
1
1
1
4
1
0
0
1
0
1
0
1
1
0
1
1
0
0
0
1
0
0
1
0
2
1
2
2
0
5
1
1
2
1
0
0
0
1
2
1
2
1
0
0
0
1
2
1
1
1
2
1
0
0
0
2
0
0
0
2
1
1
0
0
0
1
1
1
2
0
1
1
1
0
1
0
2
1
0
1
0
2
1
1
0
1
1
0
1
1
2
0
1
1
0
1
1
0
2
0
0
1
0
0
0
1
1
2
1
1
1
0
0
0
1
1
2
1
0
2
0
2
1
1
2
1
1
0
1
2
1
1
1
1
1
1
0
2
2
1
1
0
0
1
0
1
1
2
2
0
2
0
1
2
1
0
1
1
2
2
0
2
2
0
2
2
1
0
2
1
0
2
1
0
1
1
0
0
0
1
0
2
1
0
0
1
1
0
0
1
1
0
1
2
2
1
1
0
1
1
2
1
0
1
2
1
3
2
1
1
2
0
1
1
0
2
1
0
1
1
2
0
0
1
0
2
2
2
2
2
0
2
1
0
1
0
1
1
2
2
0
1
0
0
0
1
1
2
1
0
1
0
0
0
0
2
0
2
1
0
0
1
1
1
0
1
1
0
0
0
0
1
0
1
1
2
1
0
0
0
0
2
2
3
2
1
0
1
2
1
1
0
1
2
1
1
1
0
0
0
1
0
1
0
1
1
0
1
0
1
0
1
0
1
1
0
0
0
1
0
0
0
1
0
1
1
1
2
0
1
0
0
1
1
1
0
0
1
2
2
0
1
2
1
1
2
1
0
2
3
2
1
0
0
2
0
1
0
0
2
1
0
1
0
0
2
1
1
0
1
2
2
0
1
1
0
1
0
0
0
1
0
0
1
2
1
5
1
2
1
2
2
0
1
0
1
0
1
0
1
1
0
2
0
1
2
1
2
2
1
2
2
2
2
1
2
1
0
1
2
0
0
1
0
1
1
1
1
1
1
1
1
1
0
0
1
2
1
1
0
2
2
0
1
1
2
1
1
1
2
1
2
2
0
2
1
0
0
1
1
0
0
0
1
0
1
2
0
1
0
1
0
0
0
2
0
1
2
0
1
2
0
2
1
1
2
0
1
2
1
2
0
2
0
0
1
2
1
1
2
0
1
1
2
1
2
1
1
2
1
1
1
2
1
1
0
2
2
0
1
2
1
1
0
0
0
1
0
1
0
1
3
1
2
1
0
1
0
0
2
1
0
2
1
1
2
1
1
0
0
1
1
0
1
0
1
1
0
0
0
1
2
0
1
2
0
2
1
1
0
1
1
0
2
1
1
2
0
1
1
0
1
1
0
1
3
1
2
0
1
1
1
2
1
0
0
1
1
1
1
1
1
1
1
1
0
0
1
1
2
2
1
0
0
2
0
0
2
1
1
0
1
2
1
1
1
1
1
1
1
1
0
1
2
1
1
2
0
1
1
1
2
1
0
0
1
0
1
1
1
1
0
0
0
1
1
1
0
1
0
1
1
0
2
1
0
0
1
1
1
1
1
2
1
1
1
0
0
0
0
1
1
0
1
2
1
2
2
0
0
1
0
0
1
0
1
1
1
3
2
0
2
0
0
0
0
1
0
2
1
1
1
2
2
2
2
2
2
0
0
1
1
7
2
1
0
0
0
2
0
1
1
0
0
0
1
2
1
1
1
2
1
2
0
0
0
0
1
1
1
1
0
1
1
2
1
0
1
0
1
2
1
0
1
4
1
1
1
1
1
0
1
1
1
1
1
1
1
0
0
1
1
0
1
1
1
0
0
2
2
2
1
0
1
1
1
1
4
0
0
1
2
1
0
2
2
0
1
1
1
1
2
0
0
0
1
1
0
0
2
3
0
0
0
2
0
2
2
2
0
1
2
2
2
1
0
1
1
0
1
0
0
1
1
1
1
1
1
0
1
1
0
2
1
1
0
0
1
0
0
0
1
0
1
1
0
0
1
1
0
1
1
0
1
0
1
0
0
1
1
2
2
0
1
2
0
2
0
0
1
5
0
2
0
0
0
0
2
2
2
0
0
1
1
1
1
2
1
0
2
1
0
0
2
2
1
0
1
1
1
0
0
1
0
1
2
0
0
0
0
1
2
1
2
1
2
0
0
2
1
1
1
0
1
1
0
1
1
1
0
1
1
2
0
1
2
0
1
2
1
1
0
0
1
1
1
2
0
0
0
0
0
2
1
1
1
1
1
1
1
1
0
1
1
1
0
3
1
1
0
0
1
0
0
1
1
1
2
1
1
2
1
0
1
0
1
1
0
0
1
0
1
2
1
2
1
0
2
0
1
1
1
2
1
0
0
1
0
2
1
0
2
1
0
0
1
2
0
1
2
2
0
0
1
1
1
1
2
1
0
2
0
1
2
1
0
1
0
1
1
0
1
0
0
1
0
1
0
0
1
1
0
0
0
2
0
1
1
1
2
1
0
1
1
2
1
1
0
2
1
1
0
2
0
2
2
1
1
0
1
1
2
1
2
2
1
1
1
1
0
0
1
0
2
0
2
1
2
1
0
1
0
0
1
0
2
0
2
2
2
1
1
2
0
1
0
1
2
1
1
0
0
0
1
1
0
2
1
0
1
0
0
0
1
0
0
1
1
1
1
0
1
2
0
0
0
2
1
0
1
0
1
0
1
2
3
0
1
3
1
0
2
1
2
1
2
3
2
1
3
0
1
2
1
0
0
2
2
1
2
1
0
1
1
0
2
1
1
2
0
0
3
1
0
0
1
1
1
1
0
0
0
2
2
1
1
1
1
1
1
2
1
1
1
0
1
1
2
1
1
2
0
0
2
1
1
1
0
0
2
0
2
0
1
0
0
1
1
2
1
1
1
0
0
0
2
0
0
0
0
3
0
0
1
1
0
1
2
1
1
1
1
1
0
1
1
1
0
1
1
1
1
0
0
0
0
1
0
0
0
0
0
2
2
2
1
0
0
1
0
0
0
0
1
0
2
0
1
0
0
1
0
2
0
1
1
2
2
0
0
0
0
0
2
3
1
1
2
1
1
1
1
0
1
0
2
1
1
2
1
1
1
0
1
0
1
0
2
0
1
1
0
2
2
1
2
2
1
1
0
0
0
0
0
0
0
0
0
2
0
1
1
2
1
2
2
0
0
0
0
0
1
2
2
1
1
1
0
0
2
1
1
0
0
1
2
0
1
2
1
0
1
2
1
0
2
1
0
1
3
0
0
2
0
1
1
0
0
1
0
2
1
2
0
1
0
0
2
0
2
2
1
1
1
1
0
0
0
2
1
2
1
2
1
0
1
0
3
1
1
1
1
1
0
0
2
1
0
1
1
0
0
1
2
1
0
1
1
0
1
1
0
1
2
2
2
3
1
1
1
0
1
1
1
0
1
2
0
0
0
0
2
0
2
1
1
0
1
1
2
1
2
1
1
0
1
2
0
0
1
1
0
1
1
1
1
1
1
1
0
0
1
0
0
1
2
1
2
1
0
2
2
0
2
0
1
1
0
1
0
0
0
1
0
2
1
1
2
2
1
1
1
0
1
1
1
0
0
0
2
0
0
1
1
2
0
1
0
1
0
2
0
2
0
1
2
1
1
0
0
1
1
0
0
3
2
0
1
1
2
1
1
2
1
1
1
1
0
2
1
1
0
0
2
2
1
1
2
0
0
1
1
1
2
2
1
2
1
0
1
1
0
0
2
0
0
2
0
2
0
1
1
2
1
0
0
1
0
2
0
1
1
0
2
0
1
1
1
2
0
1
2
2
0
0
1
0
1
2
0
1
1
0
1
0
1
0
0
0
1
2
2
1
2
1
0
0
1
1
1
1
0
1
1
0
0
1
0
1
1
1
0
1
2
1
1
0
0
2
1
1
2
0
2
1
2
0
1
2
0
0
2
1
0
1
1
2
0
0
1
1
0
0
1
0
1
0
0
0
1
2
2
0
1
2
0
1
1
1
2
3
1
1
1
1
2
1
1
1
1
0
2
1
0
2
2
0
0
1
0
1
0
0
1
1
1
1
1
1
2
0
2
0
1
0
0
1
1
1
1
1
0
1
0
2
0
0
0
1
1
2
1
1
1
1
1
1
1
1
0
0
0
1
0
0
0
1
2
0
1
1
0
0
1
0
0
2
1
0
1
1
1
0
0
2
2
1
1
0
2
0
2
0
0
0
2
2
0
1
0
0
0
1
1
2
1
1
0
1
0
1
1
0
1
0
1
1
1
2
2
0
0
2
2
1
2
1
1
1
2
0
0
2
0
1
1
0
0
0
0
2
0
1
2
1
0
0
2
0
1
2
1
1
1
2
1
1
2
1
2
0
0
1
2
1
1
1
1
1
1
1
0
2
2
0
0
1
2
2
1
1
0
1
1
1
2
1
0
0
0
0
1
1
1
1
1
1
0
0
0
0
1
1
0
1
0
2
1
1
0
1
1
1
1
0
1
0
0
0
0
2
1
2
1
1
1
0
2
1
1
0
0
1
3
1
0
0
0
0
1
1
0
0
1
1
0
1
1
1
1
1
1
1
0
1
1
1
2
0
1
0
1
2
0
0
0
0
1
2
2
0
1
2
0
0
2
2
1
3
2
1
1
1
1
0
1
0
1
0
2
0
1
0
1
2
1
0
0
2
0
0
0
1
1
0
1
0
1
1
1
1
1
1
0
1
2
1
0
1
0
1
2
0
2
0
2
1
0
1
0
2
0
2
0
0
1
1
2
0
1
1
1
1
1
1
1
1
2
1
0
2
2
1
1
1
1
0
1
1
0
2
2
1
1
1
1
0
2
1
1
0
2
1
1
1
0
1
0
1
1
0
2
2
2
2
2
1
1
1
0
0
2
1
0
1
2
2
1
1
0
0
0
1
1
0
2
1
0
0
2
0
1
0
1
1
1
0
0
1
0
1
0
2
1
1
1
0
2
1
0
1
2
1
0
1
1
1
1
1
2
0
0
0
0
0
0
1
2
0
1
1
2
1
0
1
1
1
1
1
0
0
1
1
0
0
1
1
1
1
0
1
1
2
1
1
1
0
1
2
0
0
1
0
2
1
1
1
1
0
0
1
1
0
1
1
2
1
2
2
0
2
2
1
0
1
0
2
1
0
0
1
2
0
1
0
1
0
0
1
0
1
1
2
0
1
1
1
1
0
1
0
0
2
1
1
0
0
2
1
1
0
1
1
0
1
0
3
2
0
2
1
0
1
1
0
0
2
0
2
1
0
1
1
0
1
2
0
0
1
0
0
1
0
1
2
0
1
0
0
1
2
0
0
0
0
1
1
0
1
0
1
2
1
1
0
0
1
2
2
0
0
2
1
1
2
1
3
0
1
2
0
0
0
1
0
2
1
0
1
0
2
1
1
1
2
0
1
0
1
0
2
1
2
1
0
1
1
1
1
1
1
0
2
1
2
1
1
1
1
0
2
0
2
0
1
2
1
1
1
2
0
1
1
1
1
1
0
1
1
0
1
7
1
1
1
0
0
1
1
1
1
1
0
0
0
3
1
2
0
2
1
0
2
0
2
2
1
1
1
0
1
0
0
0
0
2
1
1
4
0
2
0
1
1
0
0
2
1
2
0
1
1
1
1
1
1
1
1
1
1
1
1
0
0
1
0
2
1
1
1
2
0
0
0
1
0
1
0
2
1
1
0
0
1
2
0
0
2
2
2
1
1
0
1
2
2
0
0
2
1
0
0
1
1
2
0
1
1
1
1
1
0
0
1
2
2
1
0
3
2
0
0
1
0
2
2
2
1
2
2
2
1
1
1
0
1
1
1
1
0
0
0
1
1
0
2
0
1
2
1
1
1
1
0
2
2
1
0
1
1
1
0
0
1
1
1
0
2
0
2
2
0
1
2
1
1
1
2
1
0
0
1
2
0
1
0
0
0
0
0
1
2
0
0
1
2
1
1
0
0
1
1
1
0
1
1
1
1
1
0
0
1
2
0
0
1
0
0
0
1
0
1
1
0
0
2
0
2
2
0
1
0
1
2
1
1
1
0
1
1
0
1
1
1
1
0
1
2
0
0
2
0
0
2
0
1
1
1
2
0
0
2
0
3
1
0
1
2
1
0
0
2
2
0
1
0
1
1
2
3
0
1
1
1
1
1
1
2
1
0
1
1
0
1
2
1
1
0
2
2
0
0
2
0
2
0
1
1
1
1
1
1
2
0
1
2
2
0
1
1
3
0
0
1
0
0
2
1
0
0
2
1
2
1
1
1
2
0
1
1
1
0
1
0
1
1
0
0
0
0
0
1
1
0
2
0
0
1
1
3
0
0
0
1
0
1
0
2
3
1
1
2
1
1
2
0
1
1
0
2
1
1
0
2
0
2
2
1
1
0
1
1
2
1
0
1
1
0
2
1
2
1
2
1
0
1
0
1
1
1
0
0
0
0
0
1
0
1
1
2
1
0
1
1
1
1
1
0
0
1
1
1
1
2
1
2
1
0
2
1
0
0
0
0
1
1
1
1
1
2
0
3
1
1
0
2
1
0
2
1
2
2
1
2
1
1
2
1
0
0
1
1
1
0
1
2
0
0
0
0
2
1
1
2
1
2
1
0
1
2
1
1
1
1
0
3
0
2
1
0
2
1
1
1
0
1
0
1
0
1
1
1
0
0
2
3
1
0
2
1
1
1
0
0
1
1
1
1
1
0
1
1
2
2
1
1
0
0
0
1
2
0
0
1
3
1
0
2
2
2
0
1
1
1
0
0
1
0
1
2
3
2
1
0
1
2
1
0
2
1
0
0
1
2
1
1
2
2
2
1
0
2
1
2
1
1
1
1
1
1
1
0
1
1
0
1
1
0
1
1
2
1
1
0
0
1
1
1
2
2
0
1
0
1
1
0
1
1
2
2
2
1
2
0
1
2
0
1
1
0
1
1
2
1
2
2
1
1
1
1
0
0
1
0
1
1
1
0
1
0
3
1
1
1
0
0
1
1
1
1
1
0
3
2
1
0
2
0
0
0
2
0
1
1
0
1
1
0
0
2
1
0
0
1
2
0
2
0
2
1
1
1
0
0
0
1
1
0
1
1
1
0
0
1
2
0
0
1
1
2
2
0
1
2
0
1
0
2
0
2
0
1
0
0
1
1
2
0
0
1
1
1
0
1
0
0
2
1
2
1
0
1
1
1
2
1
1
1
0
0
0
1
2
1
0
2
1
0
0
2
0
0
1
2
1
2
1
1
1
2
2
0
0
2
2
1
1
1
0
2
1
0
0
0
1
0
0
0
0
2
0
2
0
0
1
1
1
1
2
1
1
1
1
0
1
1
0
1
0
1
1
1
2
1
0
1
1
3
1
1
0
1
6
0
1
1
0
0
2
0
1
0
1
1
2
1
0
0
2
0
1
0
1
0
2
0
1
1
0
1
1
2
1
0
1
1
0
1
1
0
0
0
2
0
1
0
0
1
1
1
2
1
1
1
1
1
1
1
1
2
1
0
0
0
0
1
1
2
0
1
1
2
0
0
2
0
0
0
0
1
1
0
2
0
0
2
1
1
1
1
1
0
0
1
1
0
0
1
0
1
1
0
1
0
0
2
1
3
0
0
0
0
2
0
1
1
0
1
1
2
1
0
1
0
1
1
1
1
0
2
0
1
2
1
1
0
1
0
2
1
1
2
0
2
1
1
2
1
0
2
1
1
1
2
1
0
0
0
1
0
0
1
1
1
1
2
0
1
0
1
1
0
1
1
1
2
0
1
0
2
0
0
1
1
0
1
1
1
3
1
2
1
2
1
4
0
2
2
1
1
1
2
1
1
0
2
1
0
2
1
1
0
2
2
0
2
1
0
1
0
3
1
2
1
0
1
0
1
2
1
1
2
2
0
0
1
1
2
0
1
2
0
0
0
0
0
1
1
1
0
0
2
1
0
0
1
2
1
0
2
0
0
0
0
1
0
2
0
2
1
1
0
1
1
0
2
1
2
1
2
1
1
0
1
1
0
0
1
0
0
1
1
1
2
1
0
1
1
1
0
0
1
2
2
1
1
1
0
1
1
1
0
1
2
2
1
0
0
0
0
0
1
1
0
1
0
1
1
0
1
1
1
1
1
0
1
1
1
2
2
0
2
0
2
0
0
2
2
2
1
0
1
1
0
1
1
1
0
0
1
1
1
1
1
2
1
1
0
0
1
1
2
0
1
1
0
1
1
0
2
0
1
1
2
2
1
1
2
1
1
0
1
0
1
1
1
1
0
1
0
2
0
1
1
2
1
0
7
2
1
2
1
1
0
1
1
0
0
1
0
1
0
0
1
1
1
0
0
2
0
1
0
1
1
0
1
1
1
1
1
0
1
0
1
1
0
1
1
0
2
2
0
0
1
1
2
1
0
1
0
2
2
1
2
0
2
2
1
2
1
1
1
2
1
1
1
0
1
0
2
1
0
1
0
0
1
0
1
0
0
1
0
0
2
0
1
0
0
0
1
1
2
2
1
2
0
2
1
1
0
0
1
2
0
1
0
0
0
1
1
1
0
1
1
1
0
1
0
0
2
1
0
1
0
2
0
1
2
0
0
0
2
1
0
1
1
2
0
1
0
0
0
1
0
1
1
1
0
1
1
1
1
1
1
2
2
1
1
2
1
0
2
1
0
0
0
0
0
1
2
1
0
1
0
0
1
1
2
1
1
0
0
0
0
1
1
0
1
0
0
2
1
0
0
1
4
1
2
0
1
1
1
2
2
0
2
2
0
1
1
0
1
0
0
2
0
1
0
2
0
1
0
0
1
0
0
0
1
1
0
0
0
2
2
0
0
1
2
1
1
0
1
1
1
0
1
1
0
1
1
2
1
1
2
4
1
2
2
2
0
1
1
1
1
2
1
0
1
2
2
0
1
2
1
2
2
1
0
2
2
0
0
0
1
1
1
1
0
1
0
2
0
0
2
0
0
2
0
2
1
0
0
0
0
1
0
2
1
0
1
0
1
1
2
1
1
0
1
0
1
1
1
1
1
0
1
0
0
1
0
0
0
2
1
0
2
0
0
1
1
0
1
1
2
0
2
0
1
2
1
0
2
0
0
2
1
0
2
1
2
1
1
0
0
2
0
3
1
0
2
1
1
2
2
1
0
0
0
1
2
0
1
0
2
1
0
2
1
1
1
0
2
2
0
1
1
0
0
1
0
1
1
2
2
0
2
1
0
1
0
1
1
0
1
2
0
1
1
0
1
2
1
1
0
0
0
0
1
1
2
0
1
2
0
1
0
0
1
1
0
0
0
1
1
1
0
0
1
1
0
1
1
2
0
1
1
1
0
1
0
0
1
0
1
2
0
1
0
0
2
1
2
2
1
1
0
0
1
0
0
0
2
2
1
1
2
2
2
2
2
1
1
0
1
0
0
1
0
2
1
0
0
1
1
1
0
2
1
0
2
1
0
0
0
1
1
0
1
0
1
0
0
0
1
0
0
1
1
0
2
1
1
0
0
1
2
0
1
1
2
0
1
0
0
2
0
2
1
2
1
1
1
2
0
2
0
1
2
1
1
1
2
1
1
2
1
1
1
1
1
0
0
0
0
0
0
0
2
2
0
2
4
2
1
0
1
1
0
0
2
1
3
1
1
0
1
2
1
1
1
1
2
1
0
1
2
0
1
0
1
1
0
1
0
1
0
1
1
2
1
1
1
2
1
2
1
1
1
0
1
2
1
2
0
2
0
2
1
1
0
0
1
1
1
0
0
1
1
0
1
2
1
0
1
1
1
1
1
1
1
0
0
0
1
1
0
0
1
1
2
1
2
2
1
0
2
1
1
0
1
0
1
0
1
1
0
0
1
0
2
0
2
0
1
1
1
0
1
1
2
0
2
0
0
1
0
2
2
1
1
1
2
0
1
1
1
1
0
1
1
0
1
2
0
0
1
1
0
1
1
0
1
2
0
1
1
1
0
0
0
1
0
1
0
0
1
2
1
2
0
1
1
0
1
1
1
0
1
0
0
0
1
0
1
0
1
0
2
5
1
1
0
0
0
2
0
0
1
0
0
0
1
1
1
1
0
2
1
1
1
0
0
1
1
1
2
1
2
1
0
1
1
1
0
2
1
1
1
0
3
0
1
1
1
1
1
0
2
1
0
0
0
1
2
0
1
1
1
2
0
0
0
1
1
1
2
2
1
2
2
1
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
1
1
1
0
1
1
0
0
1
0
2
2
1
1
1
1
0
0
1
1
0
2
1
1
1
1
1
0
1
0
0
1
1
0
2
1
2
2
2
1
2
3
0
1
2
0
1
2
0
2
2
0
0
0
1
1
0
2
2
0
1
1
1
0
0
1
0
0
3
0
1
1
0
2
0
2
5
2
1
2
2
1
2
0
1
1
1
1
2
1
1
2
1
0
2
1
1
1
1
2
1
0
2
1
0
1
0
1
0
2
2
0
1
1
0
3
1
1
1
0
0
1
1
1
0
0
0
1
1
0
2
0
1
1
1
1
2
1
1
1
1
2
1
1
1
1
1
0
1
1
0
1
0
2
1
0
1
0
1
1
1
1
1
1
1
4
1
0
2
1
0
0
0
1
0
0
0
0
0
1
2
2
1
1
0
2
2
1
0
1
1
0
0
0
2
0
2
0
2
1
2
1
1
2
0
2
1
1
0
2
0
1
1
1
1
0
1
0
2
1
0
2
1
0
0
1
0
0
2
0
1
2
1
0
2
2
0
1
2
0
0
2
1
2
4
2
3
1
2
1
1
1
1
0
1
0
0
0
2
2
1
0
1
1
0
1
1
0
0
0
0
0
0
1
1
1
3
1
1
1
2
1
0
1
1
0
0
0
1
1
1
1
2
1
1
2
0
0
1
0
1
0
2
2
1
2
1
2
1
2
1
1
1
0
1
1
1
2
0
0
0
2
2
0
0
0
0
0
1
0
0
1
2
0
1
1
1
0
1
0
1
1
1
2
0
2
1
1
0
1
0
1
1
1
1
0
1
0
2
1
0
2
1
1
1
0
1
2
1
1
0
0
0
2
1
0
0
0
1
1
0
0
1
0
1
1
0
1
1
2
2
1
0
2
1
0
1
1
2
1
0
0
0
1
2
0
1
0
0
2
0
1
1
1
0
1
1
1
2
1
1
2
0
1
1
0
0
2
1
0
0
1
0
1
2
1
2
2
1
0
1
0
1
0
1
1
1
0
2
1
1
5
1
0
2
1
0
1
0
2
1
1
3
2
2
0
2
0
0
2
0
1
1
0
1
0
2
0
0
2
1
0
3
1
2
0
2
0
0
2
1
0
1
1
1
0
0
0
1
1
1
1
0
0
1
1
0
1
1
2
1
1
1
2
0
1
1
2
0
0
1
0
1
2
2
0
1
0
2
1
1
0
1
2
1
0
1
1
1
2
1
1
1
1
1
2
2
1
1
1
1
2
2
1
2
1
1
0
1
1
0
1
1
0
0
1
1
0
1
1
1
1
2
1
1
1
2
1
1
1
2
0
1
1
1
1
0
0
3
1
0
0
2
0
1
1
2
0
1
1
0
1
1
1
1
2
2
1
1
0
2
0
0
0
1
2
2
2
1
1
0
1
2
0
1
1
1
1
1
2
2
0
2
1
0
0
0
1
1
1
1
0
1
2
0
1
1
1
1
0
1
0
0
2
0
0
0
2
1
0
0
0
1
0
1
0
0
1
1
0
2
1
1
1
1
0
2
1
1
1
1
0
2
1
2
0
0
1
0
0
1
1
1
0
0
2
0
3
1
1
0
2
1
2
0
1
0
0
1
1
0
2
1
0
1
1
2
1
0
2
1
1
1
2
1
1
2
1
0
2
0
2
1
0
1
1
0
2
1
2
2
2
1
1
2
0
0
0
2
2
1
0
2
1
0
1
1
1
1
0
1
1
1
2
1
0
3
0
0
2
2
0
1
2
1
1
0
0
0
2
0
1
0
1
2
1
0
1
0
0
1
1
0
1
1
2
0
0
1
0
1
2
1
1
0
1
0
1
2
0
2
0
0
0
1
0
0
1
0
1
2
0
0
1
1
1
1
0
1
2
0
2
0
0
1
3
2
1
1
2
1
2
2
1
1
0
0
1
1
0
0
1
1
1
0
1
1
0
0
1
2
2
1
0
1
1
1
2
2
1
1
2
1
1
1
0
1
0
2
2
1
1
1
2
0
1
2
1
1
1
1
1
0
2
2
2
2
0
0
2
0
0
0
0
2
1
0
2
0
0
1
1
0
2
1
1
0
0
0
1
1
2
0
2
0
1
1
1
1
1
0
2
1
0
1
1
1
2
1
0
0
1
0
1
1
0
1
1
0
1
0
2
0
1
0
0
2
1
0
1
0
1
1
1
1
1
0
1
0
1
0
0
0
1
1
0
0
0
1
0
1
1
0
1
0
1
0
1
2
0
2
0
2
0
1
0
0
0
0
0
0
2
1
1
1
0
0
0
2
0
0
2
1
2
0
1
1
2
3
0
0
1
1
2
1
1
2
3
1
1
0
0
2
2
1
1
1
1
0
0
2
0
2
0
2
2
1
2
1
2
0
0
0
1
1
2
2
1
1
2
1
2
1
1
1
0
2
0
1
1
0
0
2
0
2
1
2
0
0
1
0
0
1
1
0
2
1
1
2
1
3
0
2
0
2
0
1
1
1
2
0
2
0
0
2
1
1
0
0
1
0
2
0
0
1
2
0
1
1
2
0
2
1
1
2
2
2
1
1
2
1
1
1
2
1
0
1
1
2
0
0
0
0
1
1
0
2
1
2
1
1
0
0
1
1
0
0
2
0
2
2
1
1
0
1
1
0
1
1
0
1
1
0
1
0
2
0
2
2
0
1
0
0
2
0
1
1
1
1
0
0
1
0
2
2
1
0
0
1
1
1
2
1
1
1
2
2
0
0
0
1
1
1
0
1
1
0
2
1
1
0
2
2
1
1
0
2
0
1
0
2
1
2
1
2
0
2
1
1
3
0
1
2
1
1
1
2
2
0
0
1
1
0
2
1
1
0
0
0
2
1
2
0
0
0
0
0
2
0
3
1
1
0
2
2
0
0
1
1
0
0
1
1
0
2
2
0
0
1
2
0
0
0
1
1
1
1
2
1
0
0
1
2
0
1
1
2
0
1
0
1
1
0
1
1
0
0
2
1
2
1
1
1
0
0
1
1
1
1
1
0
0
1
2
1
2
2
0
1
1
0
2
2
2
1
1
0
1
1
2
1
2
0
1
0
2
1
0
1
1
1
1
2
0
2
0
1
1
0
1
0
1
2
1
1
1
2
0
1
1
1
0
0
1
2
2
0
2
1
0
0
0
0
0
1
0
0
0
1
2
0
1
2
0
1
1
1
0
1
4
0
2
2
0
2
0
1
1
1
0
0
1
1
0
1
1
0
2
2
0
1
0
2
0
1
0
2
0
1
0
0
1
4
0
1
1
1
2
0
1
2
2
0
0
0
2
1
0
0
1
0
0
0
5
1
2
0
1
1
1
1
0
0
0
0
2
1
2
1
1
0
2
0
0
1
0
1
1
1
2
2
0
1
1
1
1
1
2
0
0
0
1
2
0
2
0
2
0
1
1
4
1
1
0
0
2
1
2
1
2
1
2
1
2
0
1
0
0
2
1
1
1
2
2
1
0
0
0
0
2
0
2
0
3
1
1
1
0
2
2
1
0
2
1
1
0
0
1
0
1
2
0
1
1
1
1
1
0
1
0
0
1
0
0
0
1
1
0
2
0
2
1
2
1
0
1
1
0
0
0
0
1
0
2
0
0
1
0
0
1
0
2
1
2
0
1
1
0
1
1
2
1
0
1
1
1
1
0
1
1
2
0
0
1
0
1
1
0
1
1
1
1
0
1
2
1
1
0
1
1
0
1
1
1
0
2
2
0
1
2
1
0
1
0
0
1
1
0
1
1
1
1
2
1
1
0
1
1
1
2
0
1
1
1
1
0
0
1
1
0
2
1
2
1
0
1
1
0
0
1
1
1
0
1
1
0
0
1
1
1
0
2
2
1
2
0
1
1
0
2
0
2
1
2
0
0
1
1
0
1
1
1
1
2
2
2
0
2
2
0
0
2
1
1
0
0
1
0
1
1
1
3
2
0
0
1
0
2
0
0
1
2
0
1
0
1
0
0
1
2
1
2
0
1
1
1
1
1
1
0
0
0
1
1
0
1
2
0
2
2
0
0
0
1
1
0
0
1
0
2
0
1
1
0
0
0
1
1
0
1
1
2
1
1
3
0
1
0
2
1
1
0
2
0
1
0
0
1
1
0
1
0
1
1
0
0
1
0
2
2
2
1
2
0
0
0
1
1
1
1
0
1
1
1
0
2
0
1
1
1
1
1
0
1
1
2
1
1
0
2
1
0
2
1
1
1
2
0
0
1
0
2
0
2
0
0
2
0
1
1
1
2
2
0
1
1
1
0
2
0
0
1
3
0
1
1
1
0
1
0
2
0
1
1
2
0
2
0
1
1
0
1
1
1
0
2
2
1
0
2
2
1
0
0
1
2
0
1
2
0
0
1
0
0
0
1
2
1
2
1
2
1
2
2
2
2
1
0
0
0
1
0
1
0
0
0
1
1
1
1
2
1
2
2
0
1
1
0
0
0
1
1
2
1
1
1
2
2
1
3
1
0
0
0
1
0
1
0
1
1
2
0
1
1
1
0
1
1
8
0
2
1
1
1
2
1
0
2
0
1
1
0
0
1
1
1
1
0
1
2
0
1
2
1
0
2
1
0
1
2
0
1
2
2
1
0
1
0
0
1
1
0
2
2
0
1
1
2
1
1
1
2
0
0
1
0
0
1
1
1
0
3
0
0
1
1
0
2
0
1
1
1
2
0
1
2
0
0
1
0
0
1
1
3
1
1
1
2
0
2
5
0
1
2
1
0
1
1
1
1
1
2
0
1
0
1
1
1
0
1
1
0
0
0
0
1
1
0
0
1
2
0
1
0
0
1
2
1
1
0
1
2
0
3
2
0
1
1
2
0
1
1
1
0
2
1
1
1
0
0
1
0
1
1
0
1
1
1
1
1
3
0
1
0
2
2
1
0
1
0
0
1
1
2
0
1
0
0
1
1
1
1
1
0
0
1
2
0
1
5
0
2
1
0
0
1
0
2
0
0
1
2
1
2
1
1
2
1
1
1
0
1
1
2
1
0
0
2
2
2
2
0
0
1
1
1
1
0
2
1
2
0
0
0
2
0
2
0
1
2
1
2
2
1
2
0
1
1
0
1
2
1
1
3
1
1
0
1
1
1
1
1
0
0
1
0
0
1
0
1
1
1
1
0
1
7
1
1
0
0
1
1
1
2
1
2
0
2
1
2
3
0
1
2
2
1
0
0
1
2
1
1
1
2
2
2
0
2
0
2
0
1
0
2
2
0
0
1
1
1
0
1
1
0
0
1
1
1
0
0
1
1
1
0
0
2
1
1
0
0
1
1
1
1
1
1
2
1
0
0
1
1
1
4
1
1
1
1
1
1
2
2
2
1
2
1
2
1
1
0
0
0
1
1
1
1
1
2
1
2
1
0
1
0
1
0
1
0
0
2
1
2
2
1
0
2
2
1
0
1
0
0
1
1
2
0
2
0
2
0
1
1
1
0
2
2
0
2
0
0
1
0
0
1
0
2
1
0
3
2
0
1
0
0
2
0
0
1
1
1
1
2
0
0
2
0
0
1
1
2
2
2
1
2
0
1
1
2
1
2
2
2
1
1
1
1
1
0
0
2
1
0
0
1
1
0
0
1
0
2
1
0
0
1
1
0
0
2
2
1
0
1
2
0
1
1
1
0
1
1
0
0
5
2
0
1
2
1
1
1
2
1
2
0
0
2
1
0
1
0
0
1
0
0
1
2
0
1
1
1
0
1
1
1
0
1
2
2
1
1
1
2
1
1
1
1
1
1
2
2
2
0
0
1
0
0
3
1
1
0
1
0
2
1
0
0
0
0
2
1
4
0
1
1
0
1
1
1
1
0
1
0
0
1
0
1
0
2
0
1
1
0
1
2
0
0
2
1
0
1
3
3
2
1
0
1
0
2
0
1
1
1
1
0
0
2
2
1
0
2
1
1
1
1
1
2
0
2
0
2
1
2
1
4
2
1
2
1
1
1
1
1
0
0
0
1
2
1
0
1
1
1
0
0
1
2
2
1
0
0
1
1
2
2
2
0
0
0
1
2
0
1
1
0
0
1
2
1
2
0
1
2
0
0
1
0
0
1
0
1
1
1
1
2
0
0
0
3
2
2
1
2
0
0
0
0
1
1
1
3
1
0
2
2
1
0
1
2
0
0
1
0
0
1
2
0
4
1
2
0
1
0
0
0
2
0
1
1
0
1
1
1
0
1
1
1
1
0
1
1
1
1
0
0
1
1
1
0
0
3
0
1
1
0
1
0
2
0
0
0
0
0
0
0
1
1
1
0
1
1
1
0
2
0
0
0
1
2
0
0
1
0
2
2
0
0
0
0
0
1
1
2
0
0
0
1
0
1
0
1
1
1
1
2
1
0
2
2
1
2
0
1
2
1
1
2
2
1
0
2
0
1
5
1
0
1
2
1
1
1
2
1
0
2
1
2
1
1
1
1
1
0
0
1
0
1
2
2
2
0
0
1
2
1
1
1
1
1
2
0
1
1
2
1
0
0
2
2
2
1
1
2
1
1
0
1
3
0
0
1
0
0
1
0
1
2
1
0
2
1
1
1
1
0
2
1
0
0
0
2
1
0
0
0
0
2
2
1
1
0
0
2
1
0
1
2
0
2
2
1
0
0
1
0
0
1
0
1
1
0
1
2
1
2
1
1
1
0
2
2
1
0
0
1
1
2
1
1
0
1
2
0
2
1
0
1
0
1
0
1
1
1
1
1
2
1
1
0
2
1
1
1
2
0
1
2
1
2
1
0
0
2
1
1
0
0
2
2
2
1
0
1
0
1
1
2
0
1
0
2
2
1
2
0
1
0
2
0
1
1
2
1
1
1
1
1
10
1
2
1
0
2
0
2
1
2
1
0
2
2
2
0
0
0
2
1
0
1
0
1
0
1
1
1
0
0
1
2
2
2
2
0
1
1
0
1
2
1
0
1
2
0
1
0
0
1
0
0
1
1
0
0
1
1
1
1
1
1
0
1
0
2
1
2
0
1
0
1
1
1
1
0
1
2
2
1
0
1
0
1
0
1
0
2
0
0
1
0
1
2
1
2
1
1
0
0
0
0
1
1
2
1
2
1
0
1
1
1
0
1
2
1
0
0
1
1
0
1
1
0
1
2
2
0
0
2
1
0
0
1
1
0
0
0
0
1
0
0
0
1
0
2
0
0
2
1
0
0
2
2
1
1
0
0
1
0
2
0
0
1
0
0
1
0
0
1
0
1
1
0
2
1
2
1
0
0
1
1
2
2
1
0
0
1
2
0
0
0
1
0
1
2
2
1
1
1
0
0
1
1
0
0
2
2
2
1
3
1
0
1
0
1
2
1
0
0
0
0
1
2
2
1
0
0
0
2
2
0
1
0
0
1
0
1
1
0
0
1
1
0
1
2
0
1
2
0
0
1
1
2
0
0
1
1
2
1
0
0
0
0
0
1
0
1
0
0
2
2
0
1
0
1
1
0
1
2
0
2
2
0
0
2
0
1
0
2
3
0
0
1
0
0
1
1
2
0
1
0
0
1
1
1
1
9
1
2
1
0
1
1
0
0
2
1
1
0
0
0
0
0
2
0
2
1
0
1
1
0
0
0
0
1
0
0
1
0
0
0
1
1
2
1
1
1
0
1
1
2
2
1
1
1
2
0
1
1
1
1
1
1
3
0
1
1
1
0
1
2
2
2
1
0
1
1
0
1
3
2
1
0
1
2
2
1
1
1
1
1
0
1
0
2
0
1
2
0
1
0
0
1
0
1
1
1
1
1
0
1
2
1
1
0
1
1
0
1
1
2
1
2
1
3
0
1
2
1
0
2
2
1
0
1
2
0
1
1
0
2
2
1
0
2
1
1
1
4
1
1
0
1
1
1
1
1
2
1
0
1
1
0
2
2
1
1
0
1
1
1
1
2
0
0
1
2
1
1
2
0
2
1
1
0
2
1
1
1
0
1
0
1
0
0
0
1
2
1
0
2
1
1
1
1
0
0
0
1
1
1
1
0
0
0
1
1
1
2
1
1
2
2
1
0
1
0
0
2
0
2
1
0
1
0
1
0
0
2
2
2
1
0
1
2
1
0
0
1
2
1
0
2
2
1
1
2
1
0
1
0
1
2
1
0
2
1
0
2
2
1
1
1
2
1
1
0
1
2
2
1
1
1
2
2
1
2
2
0
0
0
1
1
1
1
1
1
1
1
0
1
2
0
0
3
0
0
0
0
0
0
0
2
1
1
0
2
2
2
1
1
0
2
0
2
1
0
0
1
1
0
0
1
0
0
2
2
0
0
1
1
0
0
0
2
3
1
0
2
1
0
1
1
2
1
1
2
1
0
0
0
1
2
1
1
2
1
1
2
1
2
2
0
1
0
2
2
0
1
0
0
1
3
1
1
2
0
1
2
0
1
1
1
1
1
1
0
1
1
0
1
2
0
0
0
2
1
1
2
0
1
0
0
1
1
0
1
1
1
0
1
1
2
2
1
1
1
1
0
1
0
0
2
1
1
2
1
2
0
0
1
1
0
2
1
0
0
1
3
1
0
0
0
1
2
1
0
1
0
0
0
1
2
1
1
1
2
1
1
0
2
3
0
1
1
2
1
1
2
1
0
0
1
0
0
1
2
1
2
0
1
2
0
1
0
1
3
2
2
2
1
0
2
2
1
1
1
0
1
0
0
1
2
2
1
1
2
1
0
2
2
0
0
1
2
1
0
1
0
1
0
1
0
0
1
0
1
0
0
0
1
0
0
0
1
0
1
1
1
1
2
1
1
1
2
1
0
1
1
1
0
1
0
1
0
1
2
0
2
1
0
1
0
1
0
0
2
0
2
2
0
1
0
1
1
0
2
1
0
2
2
3
0
1
1
1
1
2
2
0
0
3
0
1
0
0
2
0
1
1
0
1
1
2
1
1
0
0
1
0
1
1
1
0
1
0
4
0
2
1
2
0
2
2
1
1
1
1
2
1
1
0
0
2
1
0
1
0
2
1
1
0
1
2
0
1
1
2
0
0
1
0
0
2
0
2
0
2
1
1
2
1
1
2
0
0
1
1
2
2
1
0
1
1
2
1
1
2
1
1
0
3
1
1
0
2
1
1
4
0
1
0
0
2
0
0
2
1
1
1
1
2
2
1
0
2
1
1
1
0
1
2
0
1
1
1
1
2
2
1
0
0
0
2
1
1
0
1
1
2
1
1
1
2
0
2
1
0
2
1
1
2
2
0
0
1
0
1
1
2
0
1
1
3
2
2
1
0
1
2
0
2
2
3
1
0
1
1
2
0
2
1
1
3
1
1
1
2
1
1
1
0
0
1
0
0
1
3
0
2
1
2
1
1
0
1
1
1
0
2
0
1
0
1
2
0
0
1
1
0
1
0
2
1
1
0
2
1
1
1
0
2
1
2
1
2
1
1
0
0
2
0
1
1
1
1
1
1
0
1
2
1
2
1
1
1
2
1
2
2
1
0
1
0
2
0
0
1
0
0
2
0
0
1
0
0
1
1
0
0
0
2
0
0
0
1
1
2
2
0
1
0
0
2
0
1
1
2
1
1
0
0
0
2
1
1
1
2
1
0
2
0
1
0
1
0
2
2
0
0
1
2
0
1
0
0
1
0
0
1
1
1
1
1
1
0
0
0
0
0
2
0
0
0
1
1
2
0
1
2
1
1
1
2
2
1
0
1
1
1
0
1
2
1
0
1
2
0
1
1
0
1
1
2
0
1
1
0
0
2
5
1
1
1
0
0
2
1
1
1
2
0
0
2
0
2
2
2
1
2
1
1
0
3
1
1
1
0
0
1
2
0
1
2
1
2
0
1
2
1
1
1
1
0
1
1
1
0
1
0
2
0
2
0
2
1
1
0
2
1
1
2
1
2
1
1
0
1
0
0
1
0
2
0
0
2
0
0
0
2
0
1
1
1
1
0
1
1
2
0
2
1
2
1
0
1
0
0
1
1
1
1
0
1
0
1
1
1
2
0
0
2
0
2
0
2
1
1
2
1
2
1
0
1
0
2
0
0
2
1
1
2
1
1
0
0
0
1
2
1
1
2
0
2
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
1
2
2
0
1
0
0
0
3
1
0
1
0
1
1
0
1
1
1
1
1
1
2
2
1
1
2
0
0
2
0
1
2
1
2
1
0
1
1
0
1
0
0
1
1
0
1
2
0
1
1
1
1
2
0
2
2
1
1
1
0
1
0
2
0
1
0
0
1
2
1
3
1
1
1
1
0
1
1
1
1
2
0
0
1
1
0
1
0
1
0
3
2
2
1
2
1
1
1
1
0
1
0
1
2
1
2
1
1
2
1
2
0
0
0
2
2
2
1
0
1
1
2
0
0
2
1
0
1
0
0
1
1
2
1
1
2
2
1
1
2
1
1
0
0
0
0
1
1
1
2
0
2
1
0
1
2
1
1
1
0
2
1
2
1
2
2
2
1
0
0
1
1
1
2
1
1
2
0
1
1
0
0
1
2
0
0
0
1
0
2
2
1
1
1
0
1
0
1
0
0
0
0
0
1
0
0
1
2
2
2
1
0
2
0
1
1
0
1
0
2
0
1
1
2
1
0
1
1
1
25
1
1
1
0
0
1
0
1
0
0
2
2
1
0
1
1
1
0
1
1
1
1
1
0
0
1
0
0
0
1
2
2
2
1
1
0
1
1
0
1
0
0
1
0
0
0
2
2
1
0
1
3
1
1
1
1
0
1
0
0
2
1
1
0
0
1
1
2
2
0
1
0
0
0
0
1
1
0
1
1
1
2
0
0
0
0
1
0
0
1
0
2
2
2
1
2
0
0
1
1
1
1
1
6
1
1
0
2
0
1
0
1
1
1
0
0
1
0
1
2
2
3
1
1
0
2
0
0
1
2
2
0
2
1
1
1
0
0
0
0
1
0
2
1
0
2
0
1
1
1
0
2
0
2
1
1
0
0
0
0
1
0
0
0
0
1
2
1
0
0
1
1
2
1
0
0
2
0
2
1
1
1
1
1
0
2
0
2
1
2
2
1
0
1
1
1
2
2
0
0
2
2
1
1
0
2
0
0
1
1
1
1
2
2
0
2
2
0
1
0
0
2
2
1
1
1
0
1
0
1
0
2
0
1
1
2
1
0
1
0
0
1
2
0
0
1
0
0
0
2
2
1
0
0
2
1
2
1
1
1
1
2
0
2
0
1
1
0
1
1
1
0
1
1
0
0
1
1
2
2
1
0
2
1
0
0
0
0
2
1
1
1
1
0
1
1
2
1
2
0
1
1
1
2
1
0
2
1
1
1
1
0
2
1
1
0
2
1
0
1
2
1
1
0
1
1
0
0
1
1
2
1
0
1
1
1
0
0
2
1
1
0
1
1
1
0
1
1
1
0
0
0
0
2
0
0
1
0
1
1
1
0
1
1
1
1
0
1
1
2
2
0
2
1
1
1
0
2
1
1
1
2
2
1
1
0
2
1
0
1
1
1
1
0
0
2
1
1
1
4
2
0
0
2
1
1
0
0
0
1
0
0
0
1
2
0
1
0
1
1
1
0
0
0
0
1
0
1
1
0
2
0
1
2
0
1
1
1
0
1
2
2
1
0
1
2
1
0
1
0
0
1
0
0
1
1
1
1
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
2
1
2
2
1
1
0
1
1
1
1
1
0
0
1
0
0
1
0
1
0
0
1
1
0
1
2
0
2
0
2
2
0
0
1
0
2
1
0
1
2
2
0
2
0
1
0
0
2
0
1
2
2
1
1
0
1
1
2
2
0
1
0
1
1
1
1
0
1
1
0
0
1
1
2
1
1
1
1
1
1
0
2
0
2
1
2
0
0
1
1
1
0
2
2
1
1
0
1
2
0
1
0
1
1
1
0
1
1
1
0
0
2
0
0
0
0
0
1
1
1
0
0
1
2
2
2
0
0
0
0
2
1
1
2
0
1
1
1
0
1
0
0
1
2
1
0
0
0
1
1
0
1
1
1
1
2
0
0
1
1
0
2
1
1
1
2
0
0
0
0
2
1
1
1
2
0
2
1
0
0
0
2
1
2
0
1
0
2
1
2
1
0
2
1
1
2
0
2
1
1
2
1
1
1
0
0
2
1
0
2
2
2
1
0
1
1
1
0
3
2
1
1
0
0
1
1
1
1
1
0
1
1
2
1
1
0
1
1
1
2
1
0
1
0
1
1
2
1
1
0
1
0
2
0
2
2
0
1
2
1
1
1
1
0
2
1
0
1
0
0
2
0
1
1
2
2
0
1
1
0
0
2
1
0
0
0
0
0
0
1
1
0
0
0
1
1
1
1
2
0
0
2
0
1
1
1
1
1
1
0
3
0
1
1
1
1
2
2
1
2
3
0
1
1
2
0
1
1
0
2
1
0
1
0
1
3
2
2
0
1
1
1
1
0
1
2
2
0
1
1
0
1
4
1
1
2
1
1
1
1
0
1
2
0
2
1
1
1
1
0
2
1
2
1
2
0
0
1
1
1
1
0
2
2
1
0
2
2
2
1
1
2
1
1
2
1
2
0
1
1
0
1
0
2
1
1
0
1
3
1
1
0
2
1
2
1
2
0
1
0
1
1
0
0
0
2
0
1
0
2
0
1
1
1
2
2
0
2
1
2
0
1
1
1
1
1
1
1
0
0
1
1
2
0
1
1
1
2
0
1
2
1
1
2
0
1
0
1
1
0
0
2
1
0
0
1
0
0
0
1
0
1
1
1
1
0
0
1
2
1
2
1
1
2
0
2
0
2
1
2
1
0
1
1
1
1
1
2
0
2
1
0
1
0
2
1
1
1
2
0
1
0
2
1
1
1
1
1
0
0
0
0
1
0
1
1
1
0
0
2
1
2
0
3
1
0
0
0
1
2
2
1
1
1
2
0
0
0
0
0
0
1
2
1
1
1
2
0
1
1
0
1
0
1
1
1
0
1
1
2
0
2
0
1
1
1
0
2
2
1
1
0
2
0
0
2
0
1
1
0
0
0
0
0
2
0
2
2
1
1
1
2
1
0
1
1
2
2
1
2
1
2
0
0
0
1
1
1
0
1
1
2
0
1
1
1
0
2
0
0
0
1
0
0
0
2
0
1
2
2
2
1
2
1
0
2
1
2
0
1
1
1
2
2
0
0
1
2
2
1
0
2
1
2
0
0
1
1
0
0
2
0
1
0
0
2
1
0
0
1
1
0
1
0
2
0
0
0
0
2
1
1
1
0
0
0
0
0
1
2
0
0
2
2
1
0
1
2
2
0
0
2
0
2
1
0
1
2
1
0
2
2
1
1
2
1
2
2
0
0
1
2
2
1
2
0
1
0
1
2
1
0
0
0
0
2
1
3
0
1
1
0
0
0
1
1
1
1
0
1
0
2
2
2
0
1
0
1
0
1
1
0
1
2
1
1
0
0
1
0
0
1
1
1
1
1
0
2
1
1
0
0
1
1
2
1
0
0
1
1
2
2
2
0
0
0
1
1
0
0
1
1
0
2
1
1
0
1
0
0
1
1
0
1
0
1
2
0
1
1
1
0
2
1
1
1
0
1
1
2
2
0
2
1
0
1
1
1
1
2
1
1
1
2
1
0
0
2
1
1
2
0
1
1
0
2
1
1
0
1
2
0
1
1
2
0
0
0
0
2
1
0
1
0
0
0
0
0
1
3
2
1
1
1
1
1
1
2
0
1
0
0
0
2
0
0
2
0
1
1
1
2
1
0
0
0
2
1
1
2
1
2
0
2
1
1
1
1
1
1
1
0
0
0
1
0
1
0
0
1
2
1
0
0
1
1
2
2
1
0
0
2
1
2
2
0
1
1
1
0
0
1
3
1
0
3
1
2
2
1
1
0
1
2
1
0
1
1
1
0
1
1
1
0
2
0
1
1
0
2
0
0
2
3
1
0
1
0
1
0
2
1
2
0
1
1
2
1
1
1
1
0
1
0
0
0
0
2
2
2
1
1
1
1
2
0
1
1
1
0
2
0
2
0
2
2
1
0
2
0
2
0
1
4
1
1
1
0
0
0
1
2
0
0
2
1
0
1
2
1
1
0
1
0
2
0
0
1
1
2
1
2
1
1
1
1
1
0
0
1
0
1
1
3
1
0
1
1
2
1
1
2
1
1
1
0
1
1
2
1
1
2
0
2
0
1
0
0
0
0
0
1
1
1
0
2
1
0
1
1
0
1
0
1
1
1
1
2
0
1
3
2
2
1
0
2
3
0
1
2
2
1
1
0
1
0
1
1
1
0
0
2
0
1
0
1
0
1
0
0
0
0
0
2
2
1
1
1
1
1
1
1
2
1
0
2
1
2
2
0
1
2
0
1
1
1
0
2
1
1
1
0
1
0
1
2
0
0
1
1
0
1
0
0
1
1
2
1
1
1
0
1
1
1
1
1
2
1
1
2
2
1
0
5
0
1
1
1
0
0
1
0
0
1
0
1
1
2
1
0
1
1
0
1
1
1
0
0
1
2
0
2
0
0
2
0
1
0
2
2
1
1
0
0
0
1
0
1
2
2
0
1
0
1
2
0
1
1
0
1
2
2
0
1
1
1
0
0
1
2
2
3
1
1
1
2
0
0
2
1
0
1
2
2
1
1
0
0
1
2
1
1
0
0
1
2
2
0
0
1
1
0
2
0
0
0
1
0
1
1
0
1
1
2
1
0
1
1
1
1
0
0
1
0
1
0
2
1
1
2
1
1
1
0
2
1
1
0
1
1
1
1
2
1
0
2
1
1
2
1
1
0
1
2
1
2
1
1
1
1
1
2
2
0
0
3
0
2
2
0
1
0
2
2
1
1
0
1
1
0
1
1
0
1
0
0
1
2
0
2
0
0
2
2
1
0
2
0
1
0
1
2
2
2
1
0
1
0
1
0
2
1
2
1
1
1
0
2
1
1
2
2
2
1
1
1
0
2
0
2
1
1
1
2
1
2
2
1
1
1
3
1
1
2
1
1
1
0
3
0
2
1
0
0
1
0
1
0
0
0
1
1
2
1
1
0
1
2
0
0
2
2
1
0
1
1
1
2
0
1
1
0
1
2
1
2
0
0
1
1
0
0
1
1
2
0
1
1
1
1
0
0
1
1
0
1
1
1
0
2
2
1
1
2
1
0
1
2
0
2
0
1
0
1
0
1
0
2
1
1
1
0
0
1
0
1
1
1
1
1
1
1
2
1
1
2
1
2
0
2
0
1
1
2
2
0
1
0
0
1
2
0
1
0
2
1
0
1
1
2
0
2
1
1
0
1
1
1
0
2
0
1
0
1
1
1
0
0
0
2
1
1
0
1
1
2
1
2
1
1
0
0
2
2
1
2
1
1
0
1
1
1
1
0
1
1
1
0
1
2
0
1
1
0
2
2
1
0
1
1
0
2
1
2
2
0
1
2
0
3
1
1
1
2
1
0
1
2
0
1
0
1
1
1
2
1
1
2
1
1
0
0
0
2
1
2
0
0
0
2
1
2
1
1
0
1
1
0
1
1
1
1
1
2
0
1
0
2
1
0
0
1
0
1
1
0
2
1
1
2
0
0
1
1
1
1
1
2
0
0
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
1
2
1
2
1
0
2
1
0
2
0
1
1
1
0
0
0
0
0
2
0
1
2
1
1
2
1
0
1
1
2
0
1
0
0
2
0
1
2
0
1
2
0
2
2
1
1
2
1
0
0
1
1
1
2
0
0
1
2
1
1
0
1
1
2
2
1
1
1
3
1
2
2
1
1
1
1
0
0
2
0
0
0
0
1
2
1
1
1
1
1
1
2
2
0
0
0
0
1
1
2
0
0
1
0
0
1
2
1
2
1
0
2
1
1
1
0
1
0
0
2
2
0
1
1
2
1
1
2
1
0
1
0
0
1
1
2
0
1
0
2
0
1
2
1
0
1
2
1
0
0
0
2
0
1
0
2
2
2
0
1
1
0
1
0
1
1
2
1
0
0
0
1
1
1
1
0
2
2
0
2
0
0
0
0
1
0
1
1
1
0
1
1
0
1
1
0
0
2
1
1
1
2
1
1
1
1
0
2
1
2
1
2
1
1
2
0
2
2
2
0
2
0
2
1
0
0
1
2
1
0
2
1
2
0
1
0
2
0
0
0
2
0
1
0
0
2
1
1
2
0
1
0
2
1
2
0
0
1
1
0
0
1
1
1
0
0
2
1
0
1
0
1
0
0
1
1
1
2
2
2
0
1
1
2
2
0
0
0
0
1
0
1
1
1
1
0
0
1
1
0
1
2
0
1
1
2
1
1
0
0
1
1
0
1
0
1
1
0
1
1
0
1
1
3
2
4
0
1
1
0
0
0
1
1
2
2
3
1
1
1
2
0
2
1
1
2
1
1
0
1
2
1
1
2
1
1
1
0
0
1
2
2
1
0
0
0
1
0
0
0
1
2
1
1
0
0
1
2
0
2
0
1
1
1
2
1
1
0
0
2
1
1
0
1
2
0
1
0
1
1
1
1
0
0
2
0
1
0
2
1
0
2
1
0
1
2
1
0
2
2
0
1
0
1
2
1
0
2
1
1
1
2
0
0
1
0
1
1
0
0
2
1
1
2
1
1
1
0
1
1
2
1
0
1
1
2
1
2
1
1
0
0
1
0
0
1
0
0
0
0
2
1
2
2
0
1
1
1
0
0
0
0
2
0
1
1
1
0
2
1
2
1
1
0
1
1
1
0
1
1
1
2
1
1
2
1
0
1
0
1
0
0
3
1
1
0
0
1
0
1
2
1
0
1
2
1
1
1
0
0
0
1
0
0
1
2
2
0
1
2
2
0
2
0
1
0
1
0
0
0
1
0
0
0
1
1
2
0
1
2
0
2
1
0
1
2
0
0
0
0
1
0
1
0
1
2
1
1
1
2
1
1
1
1
0
2
1
2
0
1
0
1
2
3
0
0
1
0
1
1
1
0
0
1
0
2
1
1
0
0
2
2
0
0
2
0
0
1
0
1
2
2
0
0
2
1
0
1
2
1
1
0
0
1
0
0
2
1
0
1
1
1
0
0
0
2
1
2
1
0
3
2
1
1
1
1
1
1
1
1
0
1
1
0
1
1
1
1
3
2
1
2
1
1
2
0
0
0
0
1
1
0
1
2
1
0
0
1
0
0
1
0
0
0
1
1
1
2
0
0
1
0
0
1
0
0
0
2
1
0
1
2
0
0
0
1
0
2
0
2
4
3
1
0
1
1
1
2
1
1
0
1
0
2
0
1
1
2
0
1
0
1
0
1
1
2
1
1
0
1
1
1
1
0
1
1
1
1
1
2
0
2
2
1
1
0
1
1
1
2
0
2
1
1
2
1
1
1
1
0
0
1
1
2
0
2
0
1
2
1
2
0
3
0
0
0
2
0
0
0
0
0
0
1
0
2
1
0
2
1
1
0
2
0
1
1
1
1
1
1
0
1
0
1
0
0
1
0
0
1
1
3
0
0
1
0
0
0
0
1
0
1
1
1
1
0
1
1
1
0
1
1
1
0
2
0
0
0
0
1
1
2
1
0
0
1
1
0
2
1
1
1
0
1
1
0
1
0
0
1
1
1
1
2
5
1
1
0
1
0
1
1
0
2
1
0
1
0
1
2
2
0
0
1
1
1
1
1
0
0
1
1
2
1
1
1
0
2
2
1
0
2
1
2
0
1
0
1
0
1
1
0
2
1
0
0
2
1
1
2
0
0
0
1
2
2
0
0
2
1
1
1
2
2
1
2
1
2
1
0
2
1
1
2
1
0
1
0
1
0
1
1
2
1
0
0
1
1
1
2
1
2
1
1
0
1
1
1
2
1
0
2
0
0
0
2
0
1
2
1
0
2
1
1
0
2
0
1
1
2
1
1
1
9
1
1
1
2
1
0
0
0
0
2
2
1
1
0
1
0
1
1
2
1
2
1
1
0
0
1
1
0
0
1
0
0
1
0
2
0
1
1
1
2
2
0
0
2
2
2
1
0
0
1
1
1
0
2
2
2
1
1
1
1
1
1
0
1
1
1
1
1
3
1
1
1
0
0
0
1
2
0
0
0
2
2
1
0
1
0
0
0
0
1
1
1
1
1
1
0
0
0
0
1
0
0
1
2
1
0
2
1
1
2
0
0
1
2
1
0
1
0
0
0
0
0
0
1
0
0
1
1
0
1
1
2
0
1
1
0
0
0
0
1
2
1
1
2
2
1
1
1
1
1
1
1
0
1
0
1
0
1
0
2
0
1
1
0
2
6
0
2
2
2
0
1
1
1
0
1
1
2
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
1
0
2
2
0
1
2
1
2
2
0
2
2
0
0
1
2
1
1
1
1
1
0
0
2
0
0
0
0
0
1
0
2
1
0
0
1
0
2
1
3
1
1
1
2
1
0
0
2
1
0
1
0
1
1
2
0
1
1
0
2
2
0
0
0
0
1
0
0
1
1
0
1
1
0
1
0
1
2
0
1
0
3
0
0
1
0
2
0
1
1
0
2
1
1
0
0
0
2
2
1
2
2
0
1
1
0
1
0
1
2
1
0
0
1
1
1
1
2
0
2
2
0
2
0
0
0
1
2
2
0
2
0
1
2
0
2
1
0
1
0
0
1
2
0
2
0
2
0
2
1
0
2
1
0
2
1
2
0
0
0
1
0
0
1
1
1
0
0
0
2
0
0
0
2
0
2
1
2
1
0
0
0
2
1
0
1
0
1
2
2
1
0
1
1
0
0
0
1
2
0
2
1
1
1
1
1
0
0
2
1
1
0
0
2
1
1
1
1
1
1
0
2
2
0
1
1
1
0
2
1
2
1
0
0
2
0
0
1
0
1
2
2
2
0
1
0
0
2
1
2
1
1
2
1
1
0
0
1
1
1
1
1
0
0
0
0
2
1
0
2
0
0
1
1
1
0
2
1
2
1
0
1
1
2
2
1
1
2
1
2
1
1
1
1
0
0
2
2
0
0
0
1
0
0
1
2
2
0
2
2
2
2
2
1
3
2
0
1
1
1
2
1
1
2
0
1
0
1
1
0
2
2
2
2
0
1
1
2
1
1
1
0
2
0
0
2
1
1
1
1
0
1
1
1
1
2
2
0
1
1
0
1
1
0
0
1
1
2
1
0
1
0
0
1
1
0
1
1
1
1
0
1
0
1
0
1
0
1
1
0
0
1
2
0
1
2
0
0
2
0
2
1
0
1
2
2
1
1
1
0
1
1
0
1
1
1
0
1
0
2
1
0
1
2
1
0
0
1
0
0
1
1
2
0
1
1
0
1
2
2
0
1
2
0
1
2
2
1
1
1
4
0
1
1
0
2
1
0
1
1
0
3
1
0
2
0
2
2
2
0
1
0
2
1
2
1
0
1
0
2
1
0
1
1
2
2
0
1
0
0
0
1
1
0
0
0
2
0
0
0
1
1
1
1
2
1
0
2
1
1
1
2
0
1
1
1
1
0
1
2
1
1
1
0
0
3
0
1
1
1
1
0
1
2
1
1
1
2
1
1
0
0
2
1
2
0
1
1
1
1
2
2
0
1
1
2
1
1
1
0
2
1
1
3
0
2
0
0
0
1
0
0
1
1
1
1
0
0
2
1
2
0
0
0
0
0
1
1
1
1
0
1
0
1
0
1
0
0
0
0
1
1
1
2
1
1
0
1
2
1
1
1
0
1
1
2
1
0
1
2
1
0
0
1
0
1
2
0
1
1
2
0
1
2
0
1
1
0
1
1
2
1
2
2
1
1
1
1
2
0
1
0
2
0
0
0
0
0
0
1
1
1
1
0
0
2
2
0
1
1
2
1
0
0
1
1
1
1
1
2
2
1
2
2
0
1
1
0
0
3
0
0
1
0
2
2
2
1
1
1
0
0
1
1
2
0
1
1
1
0
0
1
1
1
0
1
1
1
1
1
0
2
1
0
2
1
0
1
0
0
0
0
2
2
1
1
2
2
1
1
2
2
1
0
0
0
0
2
1
1
0
1
2
2
2
1
1
1
1
1
0
1
2
0
1
0
2
1
1
1
1
0
1
0
1
0
2
1
1
0
1
2
1
1
2
1
1
1
1
2
2
2
1
0
2
0
1
1
2
0
0
2
1
0
0
1
0
0
1
2
1
0
0
0
0
0
0
2
1
1
1
1
2
0
2
0
1
1
0
1
1
0
1
1
0
0
2
3
1
1
1
0
1
1
1
0
1
1
1
1
1
0
0
0
0
1
3
1
2
0
0
1
0
1
0
0
1
1
1
1
1
2
1
1
0
2
0
1
0
0
0
1
2
1
1
1
0
0
2
0
1
0
2
1
2
1
0
1
0
1
0
0
1
1
2
0
2
0
2
2
1
1
2
0
0
1
1
1
2
0
1
0
1
1
0
0
0
1
2
2
0
1
0
1
0
1
0
2
0
0
0
1
2
1
0
1
1
0
2
0
0
0
2
0
0
0
0
1
0
0
0
1
1
1
1
1
0
1
1
1
1
0
2
1
1
0
1
0
0
3
4
0
0
2
0
1
0
1
1
1
0
0
1
2
1
0
1
1
0
2
2
1
1
1
1
1
2
1
2
0
1
0
1
0
1
2
1
1
0
1
1
1
1
1
0
0
2
1
1
0
0
1
1
0
0
0
0
2
0
0
2
1
0
2
2
1
0
2
1
1
2
1
0
1
1
0
2
2
3
2
1
0
0
0
2
1
1
1
0
1
0
1
1
2
0
0
1
1
0
1
0
2
1
0
0
0
1
1
0
0
1
2
0
1
2
1
0
0
1
2
2
2
1
1
0
1
1
1
0
0
2
1
0
1
2
1
2
2
1
0
2
1
0
3
2
0
1
0
0
0
1
2
2
0
2
0
0
1
1
1
1
0
0
0
2
1
1
1
0
0
1
1
0
0
3
1
1
1
0
1
1
1
3
1
2
2
0
1
0
1
0
2
1
0
1
1
2
2
2
2
1
1
0
1
2
1
1
1
2
0
0
2
0
0
1
1
1
2
0
0
0
3
0
1
0
0
1
1
1
1
1
0
1
1
0
1
1
1
1
0
0
1
0
1
1
0
2
0
0
0
2
1
1
2
1
1
1
2
2
0
3
1
2
0
0
2
0
1
1
1
1
2
0
1
2
1
1
1
2
1
2
9
1
0
1
0
0
2
1
0
1
2
1
1
2
1
1
1
2
1
0
0
1
0
1
0
2
1
1
2
1
1
2
1
2
2
2
2
0
0
2
2
2
1
1
0
0
3
2
0
1
1
0
1
2
1
0
1
0
1
0
0
1
2
2
1
1
0
1
2
1
1
2
0
0
1
2
1
0
1
1
1
1
4
1
0
1
0
2
0
1
1
1
1
1
2
1
2
0
0
1
0
1
1
1
1
0
1
1
0
0
1
1
2
1
1
2
3
2
2
0
2
1
0
2
1
2
2
1
0
1
0
0
0
2
1
0
1
0
1
1
2
1
0
0
1
0
0
2
0
0
1
2
1
2
0
1
0
2
0
0
2
2
0
0
2
2
1
1
1
1
2
0
2
0
1
1
0
1
0
1
1
0
0
1
0
1
0
1
1
1
0
1
2
1
2
1
0
0
2
2
0
0
1
1
4
2
1
0
0
0
0
1
1
1
1
0
1
1
1
1
0
0
2
1
1
1
0
2
0
2
1
2
2
2
2
0
0
2
0
2
1
2
1
3
2
2
1
0
0
0
0
0
0
1
4
2
0
1
1
2
0
1
2
0
0
1
2
2
1
2
2
1
2
1
1
0
1
1
1
1
0
0
1
1
1
1
0
1
1
2
1
1
0
2
0
0
1
1
0
2
2
0
2
0
0
1
1
2
1
1
1
2
1
1
1
1
1
0
1
0
1
0
2
2
2
2
1
1
2
1
0
0
0
0
2
2
2
2
2
1
1
1
0
1
1
1
1
1
0
1
0
0
1
1
1
0
0
2
3
1
1
2
0
1
2
1
1
0
1
1
1
0
1
2
0
2
0
1
1
2
0
1
1
1
0
1
0
1
1
0
0
1
2
0
1
1
0
2
1
2
1
0
0
1
0
2
2
0
0
0
1
0
1
0
1
1
0
0
1
0
1
1
0
1
1
2
2
0
1
0
1
1
0
0
1
1
1
2
0
1
2
2
0
1
1
1
2
1
1
1
1
3
1
1
1
1
2
1
1
0
1
1
1
2
0
0
2
0
1
0
0
0
0
1
2
1
1
1
0
1
1
1
1
2
1
0
1
1
0
1
0
0
1
2
2
0
0
1
0
1
0
1
1
0
0
1
2
1
1
0
1
0
1
0
1
0
0
0
1
0
2
1
2
0
0
0
1
0
2
1
0
1
1
2
1
0
1
1
0
0
1
1
0
0
1
0
0
1
0
2
0
0
0
0
2
1
0
1
2
0
1
0
1
1
0
0
0
1
0
1
0
2
1
0
1
0
1
0
1
0
1
1
0
2
0
1
0
0
1
1
0
1
0
0
1
0
1
3
0
3
1
2
1
1
2
4
0
1
2
0
2
1
0
1
0
0
1
0
1
1
0
1
1
0
0
1
1
2
2
1
0
1
0
1
1
0
1
0
0
0
1
0
0
1
2
2
1
2
2
1
1
2
0
1
1
1
1
1
2
2
1
1
0
0
0
1
2
2
0
0
2
2
1
0
2
1
2
1
1
0
2
0
1
2
1
2
2
1
0
0
2
3
2
1
0
0
3
2
2
1
1
1
1
0
1
1
0
3
0
1
0
1
1
0
1
0
0
1
0
1
1
0
1
3
1
1
2
0
1
2
0
1
1
1
0
1
1
1
1
2
0
1
1
2
0
2
0
1
0
2
0
0
1
0
1
0
1
1
1
0
1
2
1
1
0
0
2
0
2
1
1
1
0
2
0
1
2
1
0
2
2
2
0
1
0
0
1
1
1
0
0
0
2
0
2
2
0
1
1
0
2
1
0
1
2
0
1
2
0
1
0
1
1
2
1
1
0
1
1
2
1
1
2
2
2
0
2
0
1
0
2
2
0
0
1
1
1
2
2
1
1
0
1
0
0
0
1
2
1
0
1
1
2
2
2
1
1
1
0
1
1
2
1
2
2
1
1
0
2
0
1
1
1
1
1
1
1
1
1
0
1
0
1
2
1
0
1
1
2
2
3
0
1
1
1
0
0
1
2
0
0
2
1
1
2
0
2
0
1
0
1
0
1
1
1
0
1
1
1
1
0
1
0
1
0
2
1
1
1
2
1
0
0
0
1
1
1
1
0
2
2
0
1
1
0
0
0
0
1
2
0
1
1
0
0
1
1
1
2
1
0
1
0
0
2
0
0
0
2
2
0
0
1
1
1
0
0
1
1
2
1
1
1
1
1
2
1
2
1
2
1
2
0
2
2
2
1
2
2
2
2
1
1
1
0
2
0
0
0
2
2
1
0
1
0
2
1
0
2
0
2
1
1
0
0
1
1
2
0
0
3
0
0
1
2
2
1
0
1
0
1
1
0
1
1
0
1
1
0
0
0
1
2
0
2
1
1
0
0
5
2
1
0
1
1
1
1
1
1
0
1
0
1
2
1
1
1
2
0
1
1
0
3
1
1
0
0
1
2
0
2
1
3
0
3
1
1
2
0
2
1
2
0
0
2
1
0
1
2
1
0
1
1
1
1
1
1
1
2
0
0
2
0
1
1
1
0
1
0
0
1
0
1
2
0
1
0
1
1
2
0
2
0
0
1
1
0
0
1
2
0
1
0
1
0
0
0
2
1
1
0
0
2
1
2
0
1
1
1
0
0
1
2
0
0
0
2
1
1
0
1
1
1
2
1
1
1
1
0
0
1
2
1
1
0
1
0
1
1
1
0
1
0
1
1
0
2
1
0
1
2
1
1
0
0
0
0
1
1
2
2
1
0
0
2
0
1
2
0
2
0
0
0
0
2
0
2
1
2
0
0
1
1
2
0
0
2
0
2
0
1
0
1
0
1
1
1
1
1
1
1
1
1
0
2
1
1
0
0
0
1
2
1
1
0
1
2
2
1
2
1
1
0
1
2
2
1
3
2
0
0
0
0
0
1
1
2
0
2
1
1
3
2
0
0
0
1
1
1
2
2
1
1
2
2
1
0
1
0
0
2
0
0
0
0
1
1
0
0
2
2
1
1
1
1
1
2
0
0
2
1
1
0
1
1
1
1
1
1
3
1
0
1
1
1
1
1
0
0
0
0
1
1
0
0
0
0
1
0
2
0
2
1
0
0
1
2
2
2
1
0
2
0
1
2
2
1
1
1
3
1
1
0
0
1
0
2
1
1
0
2
0
1
2
0
2
2
2
0
0
2
0
0
0
1
2
1
2
1
1
1
0
1
2
0
0
1
0
1
1
0
1
0
1
0
0
0
1
1
0
1
1
2
1
1
0
0
0
1
1
2
2
1
0
0
0
1
0
1
0
2
2
0
2
1
1
3
1
0
2
2
1
0
2
0
1
1
2
0
1
0
1
1
1
1
0
1
1
1
0
0
1
0
1
1
0
0
1
0
1
1
1
0
1
1
0
0
1
1
1
1
0
1
1
2
0
2
1
1
0
0
0
1
1
1
2
1
1
1
2
1
2
1
0
2
1
1
0
2
0
0
1
2
1
1
0
1
0
0
1
1
1
1
0
0
0
1
1
1
1
3
1
0
0
0
0
1
2
1
0
1
1
1
1
1
1
1
2
1
3
3
1
1
0
1
2
2
2
2
0
1
0
1
2
2
1
0
0
2
2
1
1
0
3
1
0
1
2
1
1
1
0
1
1
0
5
1
1
1
1
1
1
2
0
0
2
0
0
0
1
1
0
1
1
1
0
1
0
1
0
0
0
0
0
2
1
1
1
1
0
1
0
1
0
0
1
2
2
0
1
1
0
1
0
1
1
1
1
1
0
1
1
2
0
2
1
0
1
0
1
0
1
1
3
1
1
3
0
0
2
1
2
0
1
1
1
2
1
1
0
1
2
2
1
2
0
1
1
0
1
0
1
1
0
0
1
0
1
2
1
1
3
2
0
2
1
1
1
1
0
0
1
0
0
0
0
1
0
3
0
2
2
1
0
2
0
1
0
0
0
1
2
0
2
2
2
0
0
2
1
1
2
0
1
1
1
2
2
0
1
0
0
0
1
1
2
2
0
0
0
0
2
2
2
0
2
1
1
0
1
0
1
0
2
2
1
0
0
1
0
1
1
1
2
2
0
1
0
2
0
0
1
1
2
1
1
1
2
1
1
0
0
1
2
4
1
0
0
1
1
0
0
0
0
0
3
0
0
1
1
1
1
0
1
0
1
1
0
0
2
0
0
0
1
1
0
0
2
1
0
0
0
0
0
0
1
0
0
1
1
1
2
3
0
2
1
0
2
0
1
1
2
2
1
1
0
0
1
0
0
1
2
3
0
2
1
0
1
0
0
0
1
1
0
1
1
0
2
1
1
0
1
2
1
1
1
0
1
1
2
0
1
1
0
1
0
0
1
1
1
1
1
0
1
2
2
1
2
2
2
1
0
0
2
1
0
1
0
3
2
1
2
1
1
2
1
2
1
1
2
1
1
0
1
1
2
1
1
1
0
0
1
0
0
0
2
1
2
2
2
1
2
0
0
1
0
2
1
2
2
1
0
0
0
0
1
0
2
0
1
1
1
0
0
2
1
2
1
1
1
0
1
2
1
3
2
1
1
1
2
0
2
1
0
0
2
0
1
1
2
0
0
2
0
2
1
0
2
1
0
0
0
1
0
0
1
1
0
1
0
0
2
1
3
1
2
2
1
1
1
1
3
1
1
1
1
0
0
2
2
1
1
1
1
2
2
2
0
1
0
0
2
1
1
1
1
1
1
1
1
0
1
2
2
0
0
0
1
1
2
0
1
1
0
1
1
1
0
1
2
1
3
2
1
0
0
2
2
3
1
1
1
0
2
1
0
0
0
0
0
1
0
1
2
1
1
1
1
2
2
0
2
0
2
1
1
1
1
0
1
1
0
1
1
0
1
1
1
1
1
2
2
2
3
2
1
1
2
0
2
0
0
1
0
2
2
3
2
2
1
0
0
1
2
1
0
1
2
1
0
1
0
0
1
1
1
0
2
1
1
1
0
0
1
2
1
2
1
1
0
1
1
1
1
0
2
1
1
1
1
1
1
1
1
1
2
1
0
0
1
2
1
0
0
2
1
1
1
1
2
1
1
1
2
1
1
0
0
1
1
2
2
1
1
1
1
1
0
1
1
0
0
1
0
0
1
0
1
1
0
1
0
0
2
0
1
2
2
0
0
0
0
1
1
2
1
0
1
2
1
1
0
1
1
0
2
0
2
0
0
2
2
1
1
1
1
1
0
1
1
1
2
0
1
2
2
2
1
2
1
1
1
2
0
1
0
1
3
1
0
2
0
0
1
1
1
1
1
1
1
0
0
2
1
1
1
1
1
1
0
0
2
2
1
2
0
1
1
0
1
1
1
1
0
1
2
1
0
1
0
2
0
0
0
0
0
0
0
1
1
1
2
0
1
1
1
1
0
2
0
0
2
0
0
1
1
2
1
1
2
4
0
1
0
0
2
0
1
0
0
1
0
1
0
2
0
0
0
1
1
1
0
2
1
0
0
2
1
0
1
0
2
3
2
0
1
1
3
2
0
1
1
1
1
2
1
2
0
0
0
1
0
2
1
0
0
1
1
1
2
0
0
1
0
0
1
1
0
0
1
0
1
0
0
1
1
2
1
0
0
1
1
1
2
2
1
2
2
0
0
0
2
1
2
4
1
1
0
1
1
1
0
2
1
1
0
1
0
0
2
0
0
1
1
2
0
2
1
1
0
0
0
1
1
2
2
1
1
0
2
0
0
0
0
2
0
1
0
0
2
2
1
1
2
0
0
0
2
2
0
1
0
1
0
1
1
0
0
3
1
5
1
0
0
1
0
0
1
0
0
2
2
1
1
0
2
0
1
1
1
2
1
1
1
0
1
0
1
1
0
0
2
0
1
0
2
2
0
2
3
1
0
2
0
1
1
2
1
1
1
2
1
1
1
1
1
1
2
0
0
1
1
2
1
1
0
2
2
1
0
0
1
0
2
1
0
0
0
0
1
1
1
0
1
1
1
0
0
0
0
1
2
2
2
0
1
0
1
0
2
2
2
1
2
1
1
2
1
1
2
2
0
1
0
1
2
0
1
1
0
0
1
0
0
0
1
3
0
1
2
2
1
1
2
4
0
0
1
1
0
1
2
2
0
2
1
1
0
0
2
1
0
1
2
0
0
1
0
1
0
0
1
2
1
1
1
1
1
0
4
0
0
0
1
0
2
2
1
1
0
0
1
1
0
1
1
0
0
1
1
0
0
0
1
1
0
1
1
1
0
1
0
0
1
1
1
2
0
1
0
0
0
2
0
0
0
1
1
2
1
2
1
1
0
1
1
1
1
1
1
2
1
0
1
2
1
0
1
1
0
0
0
0
0
0
1
0
0
0
1
2
0
0
1
1
1
3
0
1
1
2
1
1
0
1
2
1
1
1
1
0
0
0
2
1
1
0
0
1
1
2
0
1
1
2
0
1
1
1
0
1
1
2
1
2
1
1
0
1
1
1
2
0
1
2
1
1
1
1
1
2
1
1
2
2
2
9
2
2
0
2
1
1
0
2
1
1
0
2
0
1
1
1
1
0
1
1
0
1
3
1
0
1
1
1
0
2
1
2
1
0
2
2
0
0
0
0
0
2
3
1
2
3
1
2
0
2
1
1
0
2
0
0
0
1
2
1
0
2
0
2
1
1
1
0
0
1
1
2
1
2
2
1
1
1
1
2
2
0
0
0
1
0
2
2
2
1
1
3
0
0
5
1
0
0
2
0
0
1
2
0
0
1
1
0
2
0
1
1
0
1
1
1
0
1
0
1
1
2
1
2
0
0
0
1
1
1
1
0
0
0
1
1
2
1
1
1
1
0
0
1
0
1
1
0
1
1
0
1
1
0
0
1
2
0
2
2
1
0
1
1
2
0
0
2
1
2
0
0
2
1
0
2
1
1
0
1
2
0
0
3
1
1
1
4
0
0
0
2
0
0
2
2
2
1
1
1
0
2
1
2
1
1
2
0
1
0
1
2
1
0
1
0
2
0
2
0
1
1
1
2
0
0
2
1
2
0
1
0
1
0
1
0
1
1
2
0
2
1
2
1
1
0
1
1
0
1
1
2
1
0
2
0
1
0
1
1
2
0
2
1
0
2
0
0
2
0
1
2
2
0
1
2
2
1
0
1
2
1
1
2
0
1
0
1
1
2
0
1
0
1
1
0
0
1
2
1
0
0
1
1
1
1
0
0
0
0
1
1
1
1
1
2
1
0
1
1
1
2
0
0
1
1
0
1
1
1
2
0
2
2
1
0
0
1
2
0
1
0
1
0
0
0
0
1
1
1
2
0
0
1
2
2
0
2
0
0
0
1
1
0
1
0
0
1
1
2
1
0
1
0
2
0
1
2
0
2
0
0
1
2
0
2
1
2
1
0
0
1
1
1
2
1
1
2
1
2
1
1
1
1
1
0
0
0
1
0
0
0
0
0
1
0
2
2
0
1
0
0
1
1
1
1
2
0
1
2
1
1
2
1
0
2
1
0
2
1
2
0
2
1
2
1
2
1
3
1
1
1
1
1
2
1
1
1
1
2
1
2
0
2
1
1
1
1
1
1
0
1
2
1
1
1
2
0
1
1
1
0
1
0
1
1
2
1
2
1
0
2
1
2
0
1
1
2
0
0
1
1
0
1
2
1
0
0
0
2
1
1
0
0
1
1
1
1
0
1
0
0
1
0
1
1
0
0
1
1
2
0
1
0
1
0
1
0
2
1
2
1
0
2
0
1
1
1
0
1
2
3
1
3
0
2
2
0
1
1
1
0
0
0
0
3
1
2
1
2
1
1
1
0
0
1
1
1
1
1
0
0
0
2
2
1
2
0
1
1
1
1
1
2
1
1
1
1
2
0
1
0
1
1
2
1
1
0
0
3
1
0
2
1
1
2
0
2
1
1
1
2
1
0
0
1
0
0
1
1
2
1
1
2
1
0
0
0
1
0
1
1
1
0
0
2
0
2
1
1
0
6
2
2
1
0
4
0
1
2
0
1
0
1
1
2
1
2
1
1
1
1
2
0
1
1
1
2
2
1
1
0
0
0
1
2
1
0
2
0
0
1
0
0
1
2
0
2
2
1
1
1
1
0
1
0
2
2
1
1
0
1
1
0
1
0
1
1
2
2
2
1
0
1
2
1
1
0
0
0
0
0
1
0
1
2
1
0
0
1
0
0
0
1
1
1
0
1
2
0
1
1
0
0
2
2
0
2
0
0
0
1
1
0
1
0
0
1
1
0
0
0
0
0
0
2
2
1
1
2
1
1
1
1
0
1
2
3
0
1
0
0
1
2
1
2
0
0
0
0
0
1
2
1
1
2
0
1
2
0
2
2
0
2
0
1
2
2
1
1
2
1
2
0
2
0
0
0
2
4
0
0
0
0
0
1
0
1
1
0
0
2
2
0
1
1
1
0
1
0
2
1
0
1
0
0
0
1
1
2
2
0
1
0
1
1
1
1
0
2
0
1
2
2
1
1
3
2
0
2
0
1
1
0
0
0
2
1
0
0
0
1
2
2
3
1
1
1
0
1
2
1
0
1
0
2
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
1
1
2
2
1
1
2
1
1
0
1
2
1
0
1
1
2
0
1
1
1
0
2
2
0
2
2
0
2
1
3
1
1
1
1
2
0
1
1
2
0
1
0
1
0
0
1
1
0
2
2
0
2
0
0
1
1
1
2
2
1
0
0
0
0
1
0
2
0
1
2
1
2
1
1
1
1
1
2
0
0
1
0
1
1
0
1
0
1
0
0
1
0
1
1
1
0
1
1
1
1
0
0
0
0
0
1
0
1
0
2
2
3
0
0
0
1
0
1
0
1
1
2
0
2
2
1
1
0
1
0
2
0
1
3
1
1
1
1
2
1
0
1
1
1
1
1
0
1
2
1
2
2
2
1
0
1
0
0
0
1
2
0
2
1
1
0
1
1
0
2
1
0
1
2
2
0
0
0
2
0
1
1
1
0
1
2
0
0
2
0
1
2
1
2
2
1
1
2
0
1
0
1
1
2
0
0
2
1
0
2
2
2
2
1
1
2
0
1
2
1
2
0
1
2
1
0
0
1
0
2
1
2
0
1
1
0
0
2
1
1
1
1
0
2
1
1
1
1
2
0
4
0
1
2
1
1
1
0
0
1
1
1
0
2
2
1
2
1
2
0
0
0
1
2
1
1
1
0
0
2
1
1
2
2
0
1
0
0
1
0
1
1
1
0
2
1
0
1
0
1
0
1
1
0
1
1
1
1
0
2
0
1
0
0
0
1
1
1
2
1
1
2
1
1
1
2
1
0
1
1
1
1
0
0
1
1
0
2
0
0
0
1
0
0
2
0
1
1
0
1
0
1
0
1
1
0
2
1
1
0
1
1
0
0
2
0
0
2
0
0
1
2
0
1
0
0
0
1
2
0
3
2
0
2
1
1
0
2
1
1
1
2
2
0
0
0
0
1
2
2
3
1
0
2
1
2
1
2
1
0
0
1
0
4
1
0
0
2
1
2
3
1
0
1
2
0
1
1
2
1
0
1
1
1
0
0
1
0
2
2
1
0
1
1
1
2
2
0
1
1
2
0
1
0
1
0
1
0
6
2
3
1
0
3
1
2
1
1
0
0
2
3
0
2
0
1
1
1
1
1
2
1
2
0
0
0
0
0
1
1
0
2
1
2
2
2
0
0
1
1
1
1
1
1
1
0
1
1
1
2
0
1
0
0
1
2
0
1
1
0
1
2
2
2
2
1
2
1
1
0
2
0
1
2
1
1
2
1
1
2
1
0
0
2
1
0
0
2
2
0
1
1
2
1
0
1
2
0
0
0
1
0
3
3
1
0
2
2
0
0
2
1
1
2
1
0
1
0
1
1
0
1
1
1
2
1
1
0
2
2
2
2
0
2
1
1
1
1
2
1
1
0
2
2
2
0
1
1
1
0
1
1
2
2
1
1
1
0
0
1
1
2
2
1
2
1
1
0
1
2
1
0
2
2
0
1
2
1
2
1
0
0
1
1
2
2
1
1
1
1
1
0
2
1
1
2
1
1
1
1
0
0
3
1
0
2
2
1
1
1
0
0
1
1
1
2
2
1
2
0
1
2
1
1
1
0
0
0
1
0
1
0
1
0
0
1
0
1
2
0
0
0
1
1
0
0
1
1
2
0
1
0
1
2
1
0
1
1
1
0
1
1
0
0
0
0
0
1
1
1
1
2
3
2
2
1
0
0
0
1
2
1
1
1
1
1
2
1
0
1
1
0
1
2
1
0
0
2
1
1
1
0
2
2
0
0
2
1
1
0
0
1
2
2
1
1
1
1
1
0
1
2
2
1
0
0
1
2
1
1
2
2
0
4
0
0
0
1
0
1
1
0
0
2
1
1
0
1
0
2
0
1
0
2
2
0
1
0
2
1
2
2
1
1
0
3
1
2
2
2
1
0
0
1
0
2
2
1
1
2
1
0
0
1
0
2
2
0
0
2
0
1
1
1
2
0
2
2
1
1
1
2
1
0
1
1
2
1
1
1
1
0
0
1
1
1
2
0
2
1
1
0
0
0
1
0
1
1
1
1
3
1
2
1
1
1
2
2
1
1
0
1
1
1
1
0
1
2
1
1
1
0
2
1
1
0
0
0
0
1
0
0
1
1
1
1
1
0
5
3
1
0
1
0
2
2
0
2
1
1
1
2
1
1
0
0
0
1
2
0
2
1
2
1
1
2
0
1
1
2
1
0
1
1
0
2
0
1
2
1
1
0
0
1
2
1
1
0
1
1
1
1
0
1
0
0
2
1
0
1
0
2
2
1
2
0
2
1
0
0
1
2
0
1
1
0
1
0
0
2
1
1
4
0
1
0
1
0
0
2
1
0
2
0
2
0
0
2
1
1
0
1
1
1
0
1
1
1
0
0
0
1
2
1
1
2
1
1
1
1
0
2
1
0
2
2
2
2
1
1
2
1
0
2
2
1
1
2
1
0
1
1
1
1
0
2
2
1
1
1
1
1
3
0
0
0
1
1
0
0
1
0
1
2
2
0
1
0
1
2
1
2
1
1
0
1
0
1
2
1
0
1
0
2
2
1
0
2
1
0
0
1
1
0
1
0
1
1
1
0
0
2
2
0
1
1
2
2
1
2
2
0
2
4
1
1
0
1
2
1
2
1
0
0
0
1
0
0
2
0
0
2
0
1
1
1
1
0
1
1
0
1
1
2
1
1
0
0
2
2
3
0
1
0
1
2
1
1
1
1
0
1
1
0
2
2
1
0
0
0
2
1
0
1
1
1
1
1
1
0
2
2
1
0
1
0
1
0
1
0
1
1
2
0
1
0
2
0
1
1
0
0
0
2
1
0
2
1
1
0
1
1
1
2
0
0
1
1
1
2
0
1
2
0
1
2
0
0
1
0
1
2
1
0
2
1
0
1
2
1
1
0
1
2
2
0
2
2
0
1
0
1
0
2
0
1
1
0
2
2
2
0
1
2
1
2
1
2
1
1
2
1
2
1
1
0
1
0
2
1
0
1
1
1
1
0
1
1
1
1
1
1
1
0
1
1
1
0
0
0
1
0
2
0
1
0
1
1
2
0
1
2
2
1
1
1
0
1
1
0
1
0
2
1
0
0
0
0
2
1
1
1
0
2
0
2
0
1
2
1
0
0
2
2
0
1
1
1
1
2
0
2
0
2
1
1
1
1
1
0
1
0
2
0
1
1
1
1
0
0
0
0
2
1
0
2
1
1
1
0
0
0
1
1
1
0
0
2
0
1
1
2
1
2
1
0
1
1
1
0
2
1
1
1
1
2
1
2
0
0
0
0
2
1
1
1
1
0
1
2
1
0
0
0
2
1
1
0
3
0
1
1
0
2
2
2
0
1
0
1
0
1
0
1
0
0
1
0
0
0
2
2
2
0
2
0
1
1
2
0
1
0
2
1
3
0
1
2
2
0
0
0
2
0
1
0
0
2
1
1
1
2
0
1
1
1
0
2
0
1
1
0
2
1
1
1
0
0
1
1
2
2
1
0
0
1
1
1
1
0
3
2
1
0
0
1
1
0
1
2
2
1
1
0
1
2
0
0
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
2
0
1
1
3
1
2
1
1
1
0
1
1
0
2
1
1
2
2
2
2
2
0
1
0
1
2
1
1
1
1
2
2
0
2
1
0
1
2
1
0
1
1
1
2
2
1
1
1
0
2
2
0
1
1
1
0
1
3
0
3
0
1
0
0
0
1
2
0
1
0
0
0
0
1
1
2
1
1
2
0
0
1
1
0
1
2
2
1
2
1
0
1
0
1
1
1
2
1
2
1
0
2
1
1
2
0
3
0
1
1
1
1
1
2
2
0
2
2
0
1
1
1
0
1
0
1
0
1
1
0
1
0
1
1
1
0
1
0
1
1
2
0
1
2
2
1
0
0
2
1
2
1
2
2
1
1
1
1
1
0
0
2
0
1
0
1
2
1
1
1
2
1
0
0
0
1
0
0
1
0
4
2
0
1
2
1
2
0
1
1
0
1
1
1
1
2
3
2
2
1
0
1
3
1
1
0
2
0
2
2
1
0
1
1
1
2
0
1
1
1
2
2
0
1
1
1
2
2
1
0
1
2
1
1
0
0
1
1
1
1
1
1
1
1
1
0
1
1
0
0
0
2
1
1
0
2
0
1
0
1
2
1
2
1
1
1
1
1
2
1
1
0
1
1
1
0
0
0
0
2
1
2
2
0
1
0
1
2
2
0
1
1
0
1
0
2
1
1
1
2
0
1
1
3
0
2
1
1
2
1
0
0
1
2
1
1
2
1
1
0
1
0
1
1
1
0
1
0
1
0
0
0
2
0
2
2
2
2
1
1
2
2
2
1
2
1
1
1
1
1
0
2
1
1
0
1
0
1
0
2
2
0
0
0
1
2
1
1
2
1
0
2
2
2
1
0
0
1
1
2
2
2
1
0
1
2
0
0
1
1
0
1
1
1
0
0
1
2
1
0
1
1
1
3
2
1
1
1
0
1
1
0
1
2
2
1
0
0
0
0
0
2
1
2
2
1
1
0
1
0
1
0
0
1
0
2
0
0
1
1
2
0
1
0
1
2
1
1
0
0
0
0
3
1
0
1
1
0
2
1
0
0
1
2
1
0
3
2
0
1
0
0
6
1
1
1
0
1
0
2
1
0
0
0
1
1
0
2
1
1
0
0
1
1
2
2
2
1
0
2
2
1
0
0
0
3
2
2
2
2
1
0
2
0
0
1
2
0
2
1
0
0
0
0
1
3
2
0
1
0
0
1
0
1
1
2
1
2
0
1
2
0
2
2
1
2
1
1
2
0
2
0
0
1
0
2
0
0
1
1
0
1
2
0
0
1
1
1
3
1
1
2
0
0
2
0
2
1
0
1
2
1
1
1
2
1
1
2
2
1
1
1
1
1
0
2
2
0
0
2
0
1
0
0
2
0
1
0
0
0
1
0
0
2
1
1
1
1
1
1
1
1
0
2
2
0
2
1
1
2
0
1
0
0
0
1
1
1
1
0
0
1
2
0
0
0
1
1
2
0
0
1
2
3
2
1
1
0
2
0
2
0
0
1
2
1
0
1
1
1
0
2
1
1
0
1
2
0
2
1
1
1
0
1
0
1
1
1
1
0
1
0
2
1
0
0
1
1
1
1
0
0
0
1
1
0
1
1
2
1
2
1
1
0
2
2
0
0
0
1
1
1
1
2
2
0
1
1
0
1
1
0
2
1
0
2
1
1
1
0
1
1
2
2
2
2
1
0
0
0
1
1
2
0
1
1
3
0
2
0
0
0
0
2
1
0
1
2
1
2
0
0
2
0
2
1
1
2
2
1
1
0
3
0
1
0
2
0
1
2
2
1
3
1
1
1
0
0
1
1
0
0
0
3
0
0
1
0
1
0
2
0
0
1
0
1
0
2
0
2
1
0
0
1
1
0
1
2
0
0
1
2
0
0
0
2
0
0
1
1
0
1
2
1
0
1
1
1
0
2
2
0
0
1
0
2
1
2
0
0
2
0
0
0
1
1
3
0
1
1
2
1
1
2
0
1
1
1
0
1
2
0
1
0
0
3
2
0
2
2
1
2
1
0
2
1
1
1
1
0
1
2
1
1
0
2
1
2
0
2
0
0
0
1
2
2
1
1
1
1
0
2
1
1
0
0
2
1
0
0
1
0
1
1
2
0
1
1
0
1
1
1
2
2
1
0
2
1
0
0
0
0
1
1
0
0
1
0
1
1
1
3
0
1
1
0
1
1
0
2
1
1
1
1
0
1
0
2
0
1
0
2
0
1
2
1
1
0
0
1
2
2
0
1
1
1
0
1
2
2
1
2
0
2
2
0
1
0
0
0
0
1
0
1
1
0
2
1
2
0
0
0
0
1
2
2
0
0
1
1
2
1
2
0
1
1
0
1
1
1
2
1
2
2
1
1
0
0
2
1
1
1
0
2
1
0
1
3
1
0
1
1
1
1
2
0
2
2
1
2
1
0
1
1
0
4
2
1
2
1
1
1
2
1
1
2
2
1
1
0
1
2
0
0
0
1
0
1
3
1
1
2
0
1
1
1
1
1
0
0
1
0
1
1
0
1
0
1
1
2
1
2
0
0
0
2
1
0
2
1
0
0
2
2
0
0
1
1
1
1
1
2
1
1
0
1
0
1
1
0
1
0
0
1
1
2
1
0
0
0
1
1
0
1
1
0
1
0
0
0
2
1
0
0
0
0
2
0
0
1
0
2
1
0
1
1
1
1
1
1
2
1
2
2
1
0
0
1
2
1
1
0
2
0
1
1
0
0
0
1
1
1
0
1
1
1
1
0
2
3
2
2
0
0
0
0
1
0
1
0
0
1
1
0
0
1
0
1
0
0
1
2
1
1
0
1
1
1
2
0
2
2
1
2
1
1
2
1
5
1
1
2
0
2
0
1
0
1
1
0
1
0
0
0
0
2
0
1
1
0
2
1
1
1
0
1
1
1
0
1
1
1
0
0
1
1
1
1
0
1
2
2
0
1
1
2
1
1
0
2
1
1
0
0
0
0
1
1
2
1
1
1
2
2
0
1
0
1
0
1
0
0
0
0
1
0
1
0
0
0
2
0
0
1
1
2
3
0
2
1
1
1
0
1
0
1
2
1
1
2
3
1
1
2
0
1
1
1
2
0
1
1
0
2
2
0
1
0
1
2
2
0
0
0
0
1
0
2
1
2
1
1
2
1
2
1
2
0
1
0
2
1
0
0
1
2
0
1
1
1
1
1
0
1
0
0
1
0
0
1
1
1
1
1
2
0
0
1
1
1
2
1
2
2
2
1
0
2
1
2
0
2
0
1
0
1
0
0
2
2
0
1
1
1
1
1
1
1
1
1
2
2
0
1
1
1
0
1
0
1
0
0
0
0
0
2
1
0
1
1
2
1
0
1
1
1
1
1
2
1
1
0
2
2
0
2
1
4
0
1
1
1
0
1
1
1
0
2
1
0
0
2
1
0
1
1
0
1
2
0
2
0
0
2
0
0
1
0
2
1
0
1
1
2
2
0
1
2
0
2
0
0
2
1
0
1
2
2
1
1
2
1
1
2
1
1
1
1
2
0
0
1
2
0
0
0
1
1
1
1
0
2
0
1
2
0
0
1
1
1
0
0
1
1
1
2
0
0
1
1
1
0
2
2
1
1
0
1
0
2
1
1
0
2
1
0
1
2
1
2
1
0
1
0
0
0
1
2
0
1
2
2
1
0
2
1
0
1
2
2
1
0
2
0
0
0
0
1
0
1
2
2
0
0
0
2
1
1
0
2
3
0
1
1
2
0
1
0
0
3
0
0
0
0
0
2
1
1
0
1
1
2
0
2
1
0
0
0
0
1
2
1
0
0
0
1
1
2
1
1
1
2
0
1
0
1
0
0
0
0
1
0
2
0
1
2
1
1
2
1
0
2
0
3
4
1
0
0
3
0
1
1
2
2
0
0
1
0
1
0
2
1
2
2
0
2
1
1
0
1
4
1
0
1
1
0
1
0
2
1
0
1
0
0
0
0
2
2
0
1
0
0
1
2
0
1
1
0
1
1
1
2
2
1
0
0
1
0
0
1
1
0
1
0
2
2
2
1
0
1
0
1
0
1
2
0
0
1
2
2
0
1
2
0
1
2
3
2
4
0
2
2
1
0
2
0
0
0
1
1
0
2
0
2
1
0
3
1
2
1
0
0
1
0
1
1
0
1
1
1
0
1
0
1
2
1
0
1
1
1
0
0
1
1
1
3
1
0
1
1
0
2
2
0
1
0
0
1
1
0
2
1
2
2
1
1
0
0
0
0
1
0
1
0
1
1
0
1
2
0
2
0
0
0
0
1
2
1
0
2
1
1
1
0
0
1
2
0
1
2
1
0
1
1
0
2
2
0
1
1
1
0
2
2
2
1
0
0
2
1
0
0
0
0
1
2
1
2
2
0
0
1
2
1
1
0
0
0
0
0
1
0
0
1
1
2
0
3
2
0
0
1
1
2
2
1
1
1
1
2
0
1
1
3
1
0
1
1
1
1
1
1
1
0
2
1
0
1
2
0
1
1
0
0
1
0
0
1
2
0
1
1
1
1
1
2
2
1
0
0
1
2
3
1
0
1
1
1
0
1
0
0
0
1
1
2
1
1
1
0
1
2
0
2
1
3
2
2
0
2
1
0
0
1
2
1
1
1
1
0
1
1
1
0
1
1
0
0
3
2
1
0
2
0
2
0
0
1
1
1
0
0
1
1
1
1
1
2
1
0
1
0
0
1
2
0
1
1
0
1
2
1
2
0
2
2
1
0
1
2
1
0
2
0
0
1
2
0
2
0
1
1
2
0
2
0
1
1
1
3
0
1
1
2
0
0
1
0
0
1
2
0
0
2
0
1
1
1
2
1
2
1
2
0
1
1
2
0
1
1
2
1
0
2
1
1
0
2
0
1
2
0
1
1
1
1
2
2
0
0
2
1
3
1
1
1
0
0
1
1
1
1
1
0
1
2
0
2
2
1
1
0
0
0
2
0
1
0
0
1
2
2
0
0
2
1
0
2
1
2
2
1
1
0
0
2
1
1
0
1
1
0
2
1
0
1
2
1
2
1
2
0
1
2
0
1
1
1
0
2
1
1
2
0
0
0
1
1
0
2
2
1
2
2
1
1
2
1
1
0
1
0
0
2
2
1
2
1
0
0
0
1
0
2
1
1
1
1
1
1
2
0
0
2
0
0
1
0
1
0
1
1
3
1
0
0
0
1
1
0
1
0
2
0
1
1
0
1
0
1
1
2
1
0
2
2
1
2
2
0
1
1
1
1
0
1
1
2
0
1
1
0
1
1
1
0
1
0
2
2
1
2
2
2
1
1
0
1
2
1
1
0
1
0
1
1
0
0
0
1
0
0
0
2
2
1
1
1
0
0
0
1
0
1
1
1
1
0
1
2
1
2
1
0
0
1
2
1
0
1
0
2
1
1
1
1
0
0
1
1
2
0
2
0
1
1
2
0
0
1
1
1
0
0
0
1
1
1
1
1
1
1
1
0
0
2
2
0
1
1
1
1
1
1
1
2
0
1
2
1
1
3
1
2
1
2
2
1
0
1
1
0
0
1
1
0
1
0
0
0
2
0
0
0
1
2
0
1
1
1
1
1
2
0
1
2
1
0
1
0
2
1
1
1
2
2
1
1
1
1
0
1
0
0
0
2
1
1
1
0
2
1
1
1
0
0
1
0
2
2
1
0
1
0
1
0
1
1
2
2
1
1
1
0
1
1
0
0
3
1
2
1
1
1
1
0
1
0
2
1
2
0
2
0
0
0
1
0
1
1
1
0
2
1
1
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
0
1
1
1
0
1
2
1
2
0
1
1
0
0
0
1
1
1
2
2
0
0
2
2
1
2
1
2
0
2
4
0
2
1
0
1
0
1
1
2
1
1
1
2
1
1
0
1
2
1
1
1
2
2
1
0
1
0
2
1
2
1
3
1
1
0
2
0
3
1
2
2
4
1
0
1
0
1
1
0
1
2
2
1
1
1
0
1
0
0
1
0
0
0
1
1
1
1
1
0
0
0
1
0
1
2
0
1
0
2
1
1
1
3
1
1
1
0
1
1
0
1
1
2
0
1
1
1
5
2
0
1
0
1
1
1
0
0
2
0
0
0
2
1
2
2
0
1
0
2
1
0
2
2
2
0
1
2
0
0
0
0
0
0
1
0
0
2
1
2
0
1
1
0
1
2
1
2
0
1
1
0
0
0
2
0
1
2
1
1
2
0
2
0
1
0
1
2
1
1
0
1
0
2
2
1
0
0
0
1
0
0
0
1
1
2
1
1
2
0
0
1
0
1
1
0
2
1
1
1
1
1
1
1
1
1
0
1
0
1
1
0
0
1
2
0
1
1
1
0
2
1
2
0
1
1
2
0
0
1
1
1
0
1
0
0
0
1
2
1
0
0
0
0
1
0
0
2
0
1
0
1
1
0
1
0
1
0
0
2
0
1
1
0
0
0
1
0
1
0
0
0
2
2
1
0
1
2
0
0
0
0
1
1
1
0
0
1
0
2
0
1
2
0
1
0
0
0
0
0
1
0
1
0
0
1
1
0
0
1
1
0
1
0
0
1
1
1
0
0
1
2
1
1
2
1
1
1
1
1
0
1
0
0
1
1
1
1
0
1
2
0
0
0
1
1
1
1
1
1
2
1
0
2
0
1
1
2
0
1
1
1
0
0
1
1
1
0
0
1
0
2
1
0
1
1
1
1
1
2
2
1
0
1
0
1
1
2
1
0
0
0
1
1
0
1
1
0
2
1
1
0
2
1
1
1
2
0
0
1
1
1
1
1
1
1
1
0
0
0
1
2
0
1
1
0
0
2
1
0
1
1
0
1
1
0
1
1
1
2
0
2
1
1
1
0
1
1
2
0
1
1
2
1
0
1
0
1
0
1
2
1
2
0
0
2
3
1
1
0
0
1
2
1
2
0
1
0
1
0
2
1
1
1
1
1
0
1
2
1
1
1
0
1
3
1
1
2
1
0
0
2
2
2
2
2
2
1
1
0
3
1
1
2
2
1
2
0
1
0
0
0
1
0
1
1
0
2
1
2
0
2
2
1
1
2
1
3
0
1
1
2
2
0
0
1
1
2
1
0
2
3
1
0
2
1
2
0
0
0
1
2
1
1
1
2
2
0
2
1
0
0
2
2
2
2
0
1
0
0
0
1
1
0
0
1
1
1
0
1
0
1
0
1
1
2
0
0
0
0
1
0
1
1
1
1
1
1
2
2
2
1
1
1
0
2
1
0
1
1
2
0
3
1
2
0
0
1
2
1
1
1
1
2
1
1
0
2
0
0
2
1
2
1
2
2
1
0
1
0
2
0
2
1
2
0
2
0
0
0
2
2
3
1
1
0
1
1
2
2
2
1
2
1
1
1
0
0
2
1
1
0
2
2
0
0
0
1
1
0
0
0
1
0
0
0
0
0
3
1
1
1
1
1
1
1
1
1
0
1
0
1
1
0
0
2
0
1
0
2
1
1
2
1
0
1
1
1
2
0
4
0
1
0
1
1
1
0
0
1
1
0
1
1
1
1
2
1
1
1
0
0
1
1
2
0
1
1
1
1
2
1
2
2
1
1
1
3
1
1
2
1
0
1
0
0
0
0
3
1
0
1
2
1
2
2
2
2
1
0
2
0
1
0
1
2
0
1
1
2
2
0
0
1
1
0
2
1
0
1
1
2
2
0
1
0
2
2
2
1
1
1
1
0
1
1
1
0
0
1
1
1
10
2
1
1
0
1
2
1
2
1
0
1
1
0
1
1
0
2
3
2
1
1
2
2
1
0
1
1
0
2
1
2
1
2
1
1
2
0
1
0
1
1
0
0
1
2
1
1
1
1
1
0
1
0
0
0
1
0
1
1
1
0
1
1
0
0
0
1
1
0
0
2
2
1
2
1
1
0
0
1
1
0
1
0
0
1
2
0
0
1
0
1
0
0
0
2
1
1
1
1
0
1
1
1
0
1
1
0
1
1
1
1
1
2
1
1
2
0
2
0
1
1
1
1
2
1
0
2
1
1
2
0
2
1
2
2
0
1
0
2
0
0
1
2
2
0
1
1
1
1
0
0
0
0
0
0
0
2
2
0
3
1
1
2
1
1
2
0
0
1
1
1
1
1
1
0
1
2
2
2
0
0
2
1
0
0
0
1
1
1
0
0
1
0
2
1
0
0
0
0
0
1
1
1
1
1
1
2
2
0
2
0
2
0
2
0
2
0
1
2
1
1
1
0
2
2
1
1
1
0
1
0
1
1
0
1
1
0
2
1
0
1
0
1
1
0
0
0
0
1
1
1
1
1
1
1
1
0
2
2
2
0
0
1
2
0
0
1
0
1
2
2
2
2
0
2
1
0
1
0
0
0
1
0
2
1
1
1
2
1
1
0
0
1
0
1
1
0
1
1
1
0
0
1
0
0
1
0
0
0
0
2
1
2
0
2
2
2
2
1
1
2
2
2
2
2
1
1
2
1
1
0
1
1
1
0
0
1
1
0
2
0
2
2
1
1
2
1
2
0
1
1
1
0
1
1
2
2
1
2
1
2
0
1
0
0
0
2
0
2
2
1
1
0
1
0
1
1
1
2
0
0
0
0
0
2
0
1
1
0
1
0
1
0
1
1
0
2
1
0
1
0
0
0
0
2
2
1
0
1
1
1
2
0
2
1
0
2
1
0
0
2
0
2
0
1
0
0
0
1
0
1
1
2
1
0
1
0
1
2
0
2
0
0
0
0
1
0
1
1
1
2
0
2
0
0
2
0
0
0
0
0
0
1
1
0
1
0
2
0
1
2
2
2
1
2
1
1
0
1
2
2
2
0
2
0
1
0
0
1
2
2
1
2
0
1
1
0
1
0
2
0
1
0
1
0
0
1
2
0
1
0
2
2
1
2
0
0
0
1
1
3
0
0
2
1
2
1
1
2
1
1
2
0
0
0
2
1
1
0
2
0
1
1
0
1
0
0
0
1
1
1
0
1
0
1
1
2
1
0
1
0
1
1
1
1
2
0
0
2
1
3
0
1
0
1
0
1
0
0
2
0
1
1
1
2
2
0
1
1
0
1
1
1
2
2
2
2
2
2
1
1
1
1
1
2
1
1
1
1
2
1
1
1
1
0
1
1
0
0
0
1
0
1
1
1
1
2
1
0
1
1
0
2
1
1
1
2
1
0
0
1
3
2
0
1
0
1
0
2
1
1
2
0
2
1
1
1
1
1
2
0
1
1
0
1
1
1
3
1
2
1
1
1
1
1
1
2
0
1
0
1
1
2
0
1
1
1
2
0
0
0
0
0
1
2
0
1
0
1
2
0
2
1
0
2
0
0
2
0
2
1
0
2
2
0
1
0
1
1
1
1
0
0
0
1
1
1
2
2
0
0
2
2
0
0
1
0
0
2
2
0
0
1
2
2
0
1
1
0
1
0
1
0
2
0
2
1
1
0
2
1
0
1
0
1
1
1
2
2
0
1
1
2
2
0
1
0
1
2
1
1
2
0
1
2
1
0
1
3
1
2
1
0
3
1
2
1
1
1
1
0
0
0
1
4
10
1
1
1
0
2
0
2
1
1
1
2
1
1
1
0
1
1
1
0
1
0
1
2
1
2
2
0
1
0
1
2
0
2
2
0
2
1
1
1
3
0
0
1
1
1
2
1
0
2
0
1
0
1
1
1
1
0
2
2
0
0
2
1
1
1
1
1
1
0
0
0
0
1
0
0
0
1
1
0
1
0
0
2
1
0
1
0
0
1
0
1
2
1
2
0
1
1
1
1
1
2
0
0
2
0
1
1
0
2
1
0
0
1
0
0
1
1
1
2
1
0
2
1
2
1
2
1
0
2
1
0
1
1
2
1
2
2
0
2
2
0
0
2
2
0
2
1
0
2
1
2
1
1
0
1
1
1
2
0
1
1
1
1
0
1
0
0
1
0
0
0
1
0
0
2
3
1
0
1
2
1
1
2
0
0
1
2
2
0
2
1
0
1
1
1
0
0
1
1
1
0
1
1
0
1
1
2
0
1
0
1
0
0
1
1
1
1
1
1
1
0
1
0
0
1
1
1
0
1
0
0
1
1
0
0
1
1
2
0
0
2
1
1
0
2
0
1
2
0
2
1
1
1
2
1
0
1
1
2
1
0
1
2
1
1
1
2
0
1
1
1
1
0
0
0
1
0
1
3
1
1
1
0
1
0
1
1
2
0
1
0
2
1
1
0
1
0
1
2
0
1
1
1
1
2
1
0
1
0
1
2
0
1
2
1
0
1
0
1
1
2
2
2
0
0
0
0
0
0
0
2
2
0
1
0
2
1
0
0
1
1
0
2
1
1
0
1
1
2
1
1
1
0
0
1
1
0
1
1
1
0
2
0
2
1
2
2
1
1
0
0
1
1
0
0
2
1
1
0
1
1
1
0
0
1
0
1
2
2
0
1
1
1
1
0
1
1
1
1
0
1
0
1
1
0
2
1
1
1
0
2
2
1
2
1
0
2
0
0
2
1
2
1
1
0
1
1
2
2
1
1
1
2
1
0
0
0
1
1
1
0
1
1
1
1
1
1
1
0
0
0
1
0
1
2
2
2
0
1
0
1
0
1
2
1
2
0
2
0
0
1
2
1
0
1
2
1
1
2
2
2
0
0
2
0
2
1
1
1
0
1
1
2
1
0
2
0
1
2
1
0
0
1
0
2
2
0
0
1
0
0
1
1
3
1
0
0
2
1
0
1
2
0
1
0
1
0
0
2
2
1
2
1
1
1
0
2
2
0
2
0
0
1
0
1
1
1
0
0
1
2
0
1
1
1
0
0
2
1
0
1
1
1
1
1
2
2
1
0
1
1
2
0
1
2
2
2
3
0
2
0
0
1
1
0
0
1
1
1
0
2
1
0
1
1
2
1
1
1
1
0
2
0
0
0
2
1
1
0
0
1
3
3
1
5
1
0
2
1
0
1
1
2
1
1
1
2
1
0
1
1
0
2
0
1
0
1
1
0
0
0
0
1
2
0
1
1
1
2
1
0
0
0
1
1
0
1
1
1
1
3
0
1
0
1
1
3
1
1
1
1
1
0
1
1
1
2
0
0
0
1
1
2
1
1
0
1
1
2
1
0
2
0
0
1
0
2
2
1
1
2
3
2
1
1
0
3
0
1
1
2
1
1
0
1
1
1
1
0
2
2
1
1
2
0
2
1
0
0
1
1
2
1
2
1
0
0
2
2
1
1
2
0
1
0
0
0
0
3
0
1
0
2
1
1
0
0
2
0
1
1
1
3
1
0
0
2
0
0
1
0
0
0
1
2
1
1
1
2
1
0
3
0
2
2
0
4
0
1
1
0
2
1
1
0
0
2
0
1
1
2
1
1
2
1
2
0
0
0
1
3
0
1
1
2
2
2
1
0
0
0
1
0
0
0
1
2
0
0
1
1
0
2
0
1
1
1
1
1
1
1
0
2
1
1
0
0
0
2
1
0
1
1
1
0
2
1
2
0
2
1
2
1
1
1
1
0
0
0
1
0
1
0
2
2
1
1
1
1
0
1
0
1
2
0
2
1
2
1
0
0
0
2
2
1
0
0
2
0
0
1
1
0
1
1
1
1
0
1
1
3
2
1
0
0
2
1
2
3
1
1
2
0
1
1
0
2
0
1
3
1
2
2
0
0
1
1
1
0
0
1
0
1
2
0
1
1
1
0
2
1
0
0
0
0
0
2
0
0
0
1
1
0
0
2
1
0
0
1
2
0
0
1
1
0
0
0
2
0
2
1
1
2
0
1
2
2
1
1
0
1
0
0
1
1
1
0
0
1
2
0
2
0
0
0
1
1
2
1
1
1
0
1
1
0
1
1
2
1
1
0
2
2
1
2
0
0
0
0
2
1
1
0
1
0
0
1
0
1
1
0
1
0
0
0
2
0
1
0
1
2
1
1
1
1
0
0
0
0
1
0
1
0
0
1
0
4
1
1
1
1
1
1
1
2
2
0
1
1
1
0
1
0
2
1
0
0
1
2
0
0
2
1
0
1
0
0
0
3
2
1
2
2
1
1
1
1
0
0
0
2
1
0
1
1
2
0
0
0
2
2
1
1
1
1
0
1
2
1
0
0
0
0
1
1
1
1
0
1
1
2
1
1
1
4
0
1
2
1
1
2
1
0
1
2
1
0
0
0
2
1
1
1
1
1
0
1
1
0
2
1
0
1
1
1
1
0
1
1
4
0
1
1
1
1
1
1
1
0
1
1
1
0
1
1
1
1
1
2
1
1
1
2
1
2
1
1
0
2
1
1
1
2
2
0
2
1
1
1
1
0
0
1
1
1
0
1
0
1
0
0
2
2
0
1
2
1
1
2
1
0
0
2
1
0
0
1
2
1
2
2
3
2
1
1
1
0
1
0
1
0
1
1
0
1
0
1
0
0
1
1
0
1
2
1
1
2
1
2
0
0
0
1
2
2
0
1
2
2
1
1
2
1
0
0
0
2
0
0
0
2
1
2
0
2
0
0
0
2
2
2
1
1
1
0
1
1
0
1
2
0
2
0
2
1
2
0
1
2
1
1
1
1
0
1
0
1
1
1
1
2
2
1
0
2
2
0
0
2
1
0
0
0
0
0
1
0
0
2
2
1
2
1
1
0
1
1
1
0
4
2
4
0
2
1
1
2
1
0
0
0
0
0
0
0
0
1
1
1
0
3
2
1
1
2
1
0
0
1
2
1
1
1
1
1
2
2
1
0
0
0
0
0
3
0
1
0
0
0
1
0
1
2
0
0
1
2
1
1
0
2
0
2
2
1
0
1
1
1
2
1
2
1
2
1
2
1
2
1
0
0
2
1
1
0
1
1
0
2
1
1
1
1
2
1
2
0
1
1
0
0
0
1
2
1
1
0
1
1
0
2
0
1
1
0
2
1
0
1
0
1
1
2
0
0
1
1
2
1
1
0
2
0
1
1
0
2
1
1
1
0
1
1
2
0
1
1
1
1
1
2
1
1
1
2
1
0
0
1
0
1
1
1
2
1
0
1
1
1
2
1
0
1
1
1
1
1
1
1
0
3
0
1
1
0
0
0
1
0
0
1
1
1
2
2
1
1
0
1
0
2
1
1
1
2
2
1
1
1
2
1
1
0
1
1
0
1
2
0
1
1
1
0
0
0
0
0
2
2
0
0
0
0
0
1
3
1
1
0
0
1
1
0
1
1
0
1
1
1
2
1
1
2
0
0
0
2
0
1
0
0
1
3
2
1
0
2
0
1
0
1
1
0
1
1
1
0
1
1
2
0
0
2
2
0
1
1
1
2
1
2
1
1
1
2
2
1
0
1
2
2
1
0
2
2
0
2
1
1
1
0
1
1
0
3
0
1
1
2
0
1
0
2
0
1
3
1
0
1
1
0
0
1
1
1
1
1
0
2
0
0
0
1
2
2
1
0
1
1
2
0
1
2
0
2
1
0
2
0
0
0
0
1
2
1
1
2
2
1
2
0
0
1
0
2
0
0
0
2
2
1
0
2
0
0
1
0
0
1
1
0
1
1
1
2
2
2
1
1
1
0
1
0
1
1
1
1
1
2
2
1
1
2
1
0
2
0
1
1
2
1
0
1
1
2
0
0
0
0
2
0
0
1
2
1
0
1
0
2
1
0
0
0
0
0
0
1
1
1
1
0
0
1
0
1
0
1
0
0
0
1
2
2
1
0
0
1
1
0
1
1
0
1
2
3
2
0
0
1
1
0
0
1
0
0
1
0
2
1
2
0
0
0
0
0
1
1
1
2
1
2
2
0
0
1
1
1
1
2
0
2
1
2
0
1
0
0
2
1
2
1
1
1
1
2
0
1
1
1
1
0
1
2
0
2
1
0
1
0
0
1
0
2
2
1
2
1
0
0
0
2
0
0
1
1
1
0
0
1
1
0
2
0
0
1
2
0
2
0
1
0
0
0
1
1
1
0
0
1
2
0
1
0
1
0
1
1
0
2
1
1
0
1
2
1
1
0
1
2
0
1
1
2
0
0
1
1
0
0
1
1
1
2
1
0
0
2
1
0
0
2
0
1
0
2
0
0
1
1
1
0
0
0
1
1
1
1
2
2
1
0
2
1
1
1
2
1
0
2
2
1
1
2
1
2
0
2
0
2
1
1
0
1
1
1
1
1
1
2
1
1
1
1
0
2
0
1
0
1
1
1
0
1
2
1
0
0
1
1
0
2
1
0
1
1
2
1
0
2
1
1
1
0
1
0
0
1
2
0
1
4
0
2
2
0
1
0
1
1
1
1
0
1
0
0
2
2
2
2
2
0
1
1
0
1
1
1
0
0
0
0
1
2
1
0
1
0
0
1
2
2
0
1
1
2
2
2
1
1
1
0
0
2
1
2
1
1
0
2
2
0
2
0
1
1
1
0
0
2
1
1
1
0
1
1
0
2
1
1
2
0
1
2
0
2
0
1
1
0
0
1
1
0
1
0
1
1
0
0
0
2
1
2
2
2
1
0
1
2
1
0
1
0
0
1
1
4
1
0
0
1
0
1
2
1
1
1
1
0
1
0
1
0
0
1
0
1
1
1
1
1
1
1
0
0
1
1
1
2
0
0
0
1
0
0
1
1
2
1
0
0
1
3
2
0
1
1
1
2
2
1
1
2
0
2
1
0
0
2
1
2
1
0
1
0
2
1
1
1
1
0
1
1
1
0
0
2
1
0
1
0
0
1
1
1
1
1
1
0
1
2
0
1
0
1
1
2
0
0
1
1
0
1
2
0
1
0
2
1
1
1
0
2
2
1
0
2
2
1
1
2
0
1
1
2
1
0
1
2
2
2
0
2
1
1
2
0
0
1
2
0
1
1
1
1
1
0
2
1
0
1
0
0
1
0
0
2
2
2
2
1
0
2
0
2
1
1
1
1
0
2
2
1
0
1
1
1
0
1
1
1
2
1
1
0
2
2
2
1
1
0
1
1
0
1
1
0
2
2
1
2
1
0
1
1
0
1
1
1
1
2
1
1
1
3
0
3
0
0
0
0
2
0
0
2
2
0
1
1
1
2
1
2
2
1
1
1
1
1
2
1
0
0
1
1
0
1
1
0
2
1
1
1
0
0
0
2
1
0
1
1
2
2
0
1
0
0
2
2
2
0
0
1
2
2
1
1
1
2
1
2
1
2
2
1
1
0
1
0
1
2
1
0
1
1
0
1
1
1
1
0
1
2
1
0
1
2
0
2
2
2
0
1
0
0
1
2
0
1
1
2
0
0
1
0
2
0
2
1
2
1
2
0
1
1
3
2
2
0
0
1
2
0
0
1
1
2
1
0
2
2
2
0
0
0
1
1
0
0
0
1
1
2
0
1
0
2
1
1
0
0
1
1
0
0
1
2
1
2
0
0
2
1
1
1
1
0
1
1
0
2
1
1
0
1
2
2
2
1
1
1
0
0
1
0
1
1
0
2
1
1
1
1
1
2
0
0
2
2
2
1
1
1
1
0
1
1
1
1
1
2
0
2
2
0
1
1
0
1
1
2
0
0
3
1
1
0
1
0
1
0
0
1
1
0
0
1
0
0
1
0
0
1
0
1
1
0
0
0
1
1
1
0
2
1
0
0
0
2
2
2
1
2
1
1
1
1
2
1
2
1
0
0
0
2
1
1
0
1
1
3
2
1
1
1
1
2
0
0
1
2
0
1
0
0
2
1
1
0
2
0
0
1
1
0
1
0
0
2
0
1
0
0
2
0
1
2
0
2
0
1
2
2
0
1
1
2
1
1
0
0
1
0
0
1
0
1
1
1
1
1
0
1
1
2
0
0
1
3
2
2
1
1
0
0
2
1
2
1
1
2
0
1
1
1
0
1
2
0
1
2
0
1
1
2
1
1
0
1
0
0
0
1
2
1
1
1
1
2
1
0
0
0
1
1
0
2
2
0
2
2
1
0
0
2
0
1
1
1
2
2
1
0
1
1
0
0
2
0
1
1
0
1
1
1
1
1
0
1
1
2
2
0
0
1
0
0
0
2
1
0
1
2
0
1
2
2
1
0
1
0
0
1
1
1
2
3
1
2
1
2
1
0
1
0
0
2
1
0
1
2
1
1
0
1
1
1
1
0
0
1
1
1
1
1
0
0
1
1
0
2
0
1
0
0
2
2
1
2
0
1
0
2
1
2
2
1
1
1
1
1
1
0
1
2
1
0
0
1
0
0
0
1
1
0
2
3
0
1
0
1
1
1
1
0
1
1
1
1
0
1
0
0
2
1
0
2
2
1
0
2
2
0
2
1
1
1
1
1
0
1
0
0
2
0
1
0
1
2
0
1
0
2
0
1
0
2
2
2
1
1
2
0
0
2
1
1
1
1
1
1
0
1
1
2
1
1
0
0
2
1
2
1
0
1
0
1
2
2
0
2
0
2
1
2
0
1
1
2
0
0
1
0
1
2
0
0
2
0
0
1
1
2
1
1
1
1
0
0
0
1
2
1
2
0
2
2
1
0
0
1
2
0
1
2
1
1
2
1
1
1
0
0
0
1
0
0
1
1
0
1
0
0
1
1
2
0
2
1
2
1
1
1
0
1
1
2
0
1
1
0
1
1
0
1
0
2
2
0
1
2
1
1
0
1
1
2
0
0
0
1
3
1
0
1
1
1
1
2
2
3
0
1
2
1
2
1
0
0
0
2
2
1
0
0
0
0
2
1
2
2
0
1
1
1
1
1
1
1
0
1
1
0
2
0
0
1
1
1
1
0
2
1
1
0
0
1
0
1
0
1
1
0
1
1
2
0
1
0
0
0
2
0
1
1
1
0
1
2
1
3
1
1
1
1
1
0
1
0
1
1
2
0
1
1
0
0
0
1
0
1
0
0
1
0
0
2
2
1
1
1
0
0
1
2
2
1
0
0
1
2
1
1
1
0
1
0
2
0
0
1
1
0
0
1
1
0
0
1
2
1
2
2
1
1
0
1
1
2
1
1
1
1
1
2
1
1
0
0
2
0
2
2
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
2
3
1
0
1
2
1
2
3
1
0
1
0
0
1
2
1
2
0
1
2
2
0
1
1
2
1
1
1
1
1
0
1
2
1
0
2
0
2
0
0
1
1
1
0
0
1
0
1
2
0
1
2
0
2
1
0
1
1
1
1
2
2
0
2
1
0
1
0
0
1
0
1
2
0
2
1
2
1
2
0
1
0
1
0
2
1
0
0
0
1
0
2
3
0
0
2
0
2
2
0
1
0
0
2
0
2
1
1
2
3
0
0
0
1
0
2
0
0
0
2
2
1
1
1
2
2
1
0
1
1
0
1
3
2
1
0
1
1
1
1
0
0
0
0
0
0
2
0
0
1
1
0
1
1
0
0
1
0
0
1
2
1
1
1
2
0
0
1
1
1
0
0
1
1
1
2
0
0
0
0
1
1
0
1
1
1
2
1
2
2
2
1
1
2
0
1
1
1
1
0
0
1
1
0
0
0
1
2
2
2
1
0
0
1
1
1
0
1
2
1
0
1
1
1
1
1
1
0
1
2
0
1
0
0
1
2
2
1
0
0
1
0
1
1
1
2
1
2
0
1
1
3
1
1
2
0
0
1
0
2
2
2
1
2
2
1
1
1
2
2
2
0
1
0
1
2
0
0
2
2
0
1
0
1
2
0
1
1
0
1
2
0
1
1
1
1
2
0
0
0
2
1
1
1
1
0
0
1
1
1
2
1
1
2
1
0
2
2
0
1
2
2
1
2
0
1
1
0
1
0
0
2
0
1
2
0
1
0
1
0
0
1
2
0
0
0
1
0
0
0
0
1
1
0
1
1
1
2
0
1
1
0
1
1
0
1
1
1
1
1
1
1
0
2
0
2
0
1
1
1
1
1
0
0
0
2
0
1
1
0
0
0
2
1
0
1
2
2
0
1
2
2
1
0
1
0
2
1
0
2
1
1
0
1
1
1
0
0
1
1
3
0
2
1
1
1
0
1
0
2
0
0
1
1
0
0
2
1
1
1
0
0
1
0
2
0
2
2
0
1
1
2
1
2
0
0
2
0
1
2
2
0
1
1
1
1
0
1
0
0
1
1
0
0
1
0
1
1
2
0
1
1
1
0
1
2
0
0
1
0
4
1
1
0
1
1
0
0
1
3
3
2
1
0
0
2
2
1
2
1
0
1
1
2
0
0
1
1
2
1
1
1
0
0
0
1
3
1
0
2
1
1
0
1
1
0
1
0
1
0
1
1
2
1
1
1
0
3
2
0
0
2
1
0
1
0
1
1
1
2
1
0
1
0
1
1
0
1
1
1
1
0
0
0
1
0
0
2
0
1
1
0
1
1
2
1
0
2
1
0
0
1
2
2
2
2
1
2
1
2
0
1
1
0
0
1
0
1
1
0
0
2
0
2
1
0
0
1
2
1
1
0
0
1
1
1
2
1
1
0
1
1
2
1
1
0
0
1
1
1
1
1
0
1
1
1
0
1
1
1
1
1
1
1
1
0
1
0
2
1
0
0
0
1
0
1
2
0
0
1
0
1
1
0
0
2
0
1
1
0
2
0
0
1
1
1
1
0
0
1
1
0
1
0
2
0
1
0
0
0
0
1
1
2
0
0
2
1
1
2
1
1
1
0
2
2
1
2
0
1
1
2
3
1
2
0
2
2
2
1
0
2
0
0
1
1
0
0
0
2
1
2
1
0
1
0
1
2
1
0
1
0
0
1
0
1
0
2
0
1
0
1
0
1
0
2
1
1
1
1
1
3
2
2
0
1
2
1
0
0
1
1
2
1
1
0
1
0
0
0
2
1
2
2
2
2
1
1
1
1
0
1
1
0
1
1
0
1
0
0
1
2
1
0
1
2
1
0
1
1
0
1
1
0
1
2
0
1
1
2
1
1
0
0
0
1
1
2
2
0
2
2
0
1
1
1
1
1
2
0
1
2
0
1
0
0
0
0
0
2
0
0
1
2
0
0
0
0
1
1
1
1
2
1
1
1
1
0
0
1
1
1
0
2
1
1
1
1
2
0
0
2
0
0
1
2
1
1
1
1
0
1
1
2
1
1
1
2
2
2
1
1
1
2
1
1
0
1
2
2
0
0
0
2
0
1
2
0
0
2
1
0
2
0
1
0
1
3
1
1
1
1
1
3
1
1
2
1
1
2
1
2
0
0
1
1
1
1
1
1
2
2
0
1
0
0
0
0
0
0
1
1
1
0
0
3
2
0
0
1
0
0
1
0
1
1
1
1
1
1
0
0
1
1
1
1
1
2
2
1
1
0
2
0
0
2
0
1
0
1
1
0
0
0
2
1
2
0
0
2
1
1
1
0
2
1
2
2
0
1
2
2
0
0
2
2
1
1
0
0
0
2
1
1
1
1
1
0
0
2
2
1
0
1
3
1
0
1
0
2
2
2
2
1
0
0
1
0
0
0
1
2
0
2
0
0
1
1
1
0
0
1
1
0
2
1
0
0
1
0
0
1
3
2
0
0
0
1
2
1
1
0
2
0
0
1
1
1
1
2
2
1
2
2
0
1
0
1
1
1
0
0
1
0
2
0
0
2
1
1
0
0
1
1
2
0
2
2
0
1
1
1
1
1
0
2
1
0
2
1
0
1
1
2
2
2
0
1
1
0
0
0
1
0
0
0
0
1
2
1
1
2
1
1
2
0
1
1
1
2
0
1
2
1
0
1
0
2
0
1
0
0
2
3
1
1
0
1
0
2
0
0
1
0
2
1
1
0
1
1
1
2
1
0
0
0
0
2
1
1
0
0
1
2
0
1
1
0
1
1
1
0
2
0
0
1
1
2
1
0
1
1
1
0
2
1
1
0
1
1
3
2
2
1
0
0
0
0
1
1
0
1
2
2
2
1
2
1
2
1
1
0
0
1
0
2
0
2
1
2
0
1
1
3
2
2
1
0
0
1
1
1
1
1
2
1
0
1
0
1
1
0
1
1
2
1
0
2
1
1
1
2
0
0
0
0
2
2
1
1
2
1
0
1
0
2
0
2
0
0
0
2
1
1
0
1
0
2
1
2
0
1
2
0
1
2
2
0
1
1
0
1
1
0
2
0
0
1
1
0
0
0
0
1
2
1
0
1
1
0
1
0
1
0
2
0
0
2
0
1
0
0
2
1
2
2
1
0
2
1
2
0
1
0
1
3
2
0
2
2
0
1
3
0
2
1
1
1
2
2
1
0
1
1
1
0
1
0
1
0
2
1
2
1
0
2
1
1
0
1
1
2
2
2
1
0
2
1
0
1
2
1
1
2
1
1
1
0
1
0
1
1
0
0
1
1
1
1
0
1
0
2
0
0
1
2
2
2
1
2
1
1
0
0
2
1
2
0
1
0
3
1
0
0
0
1
1
1
2
1
1
2
2
1
1
1
1
1
1
0
0
0
1
2
0
2
0
0
1
2
1
2
1
1
2
1
1
1
1
1
1
0
1
1
2
1
0
0
1
1
0
3
0
2
1
1
1
0
2
0
0
0
0
0
0
2
2
2
1
2
0
1
1
0
2
0
1
0
0
0
1
0
1
2
0
1
1
2
0
0
0
0
1
2
0
0
1
2
2
1
1
0
1
1
1
0
1
0
0
0
1
1
1
2
1
2
1
1
1
1
0
0
1
2
0
0
4
0
1
2
1
1
2
0
1
2
0
0
0
1
0
1
0
0
1
4
0
1
2
1
0
2
0
1
0
1
1
0
1
0
2
0
0
2
1
1
2
0
0
0
0
0
2
2
1
0
2
0
2
2
2
2
2
2
0
2
2
2
1
1
1
0
1
1
1
0
1
2
1
0
1
2
2
2
1
0
2
1
3
0
0
3
1
2
1
1
0
1
1
0
0
1
1
1
1
1
1
2
0
1
2
1
0
1
2
2
0
0
1
1
0
0
1
0
0
2
1
0
1
1
1
2
1
1
1
0
1
1
0
1
1
2
1
1
1
1
2
1
2
0
1
1
0
1
1
2
2
1
1
0
2
1
1
0
1
2
0
0
0
1
2
0
0
1
0
1
1
0
1
0
0
0
0
1
0
1
2
1
2
4
1
1
0
0
2
1
0
0
1
1
2
2
2
1
0
1
0
1
0
0
1
2
1
1
0
2
1
0
0
1
2
0
0
2
1
0
1
0
0
1
1
1
1
1
0
3
1
0
0
2
0
1
2
0
0
1
0
2
0
2
1
2
0
1
1
1
1
0
2
0
1
1
0
0
1
2
0
0
1
0
0
1
2
0
1
3
0
1
1
0
0
2
1
1
1
1
1
1
0
4
1
0
1
1
1
1
1
2
3
2
2
2
0
0
2
2
0
2
0
0
1
1
1
0
1
1
1
1
1
1
1
2
2
3
2
1
2
3
1
1
0
1
1
0
1
1
1
1
0
1
1
0
0
2
1
1
1
1
2
1
0
0
1
1
1
2
0
1
2
2
1
0
2
2
1
1
1
0
1
2
0
1
1
0
1
0
0
1
1
2
1
1
1
1
2
0
0
0
0
1
0
2
3
1
0
1
1
0
2
0
1
0
0
2
1
1
1
0
1
1
2
0
0
1
2
1
1
2
0
2
0
1
0
0
0
0
0
2
1
2
0
0
1
1
0
1
1
0
1
1
0
1
2
1
1
0
2
0
0
0
2
0
1
0
1
1
1
0
1
1
1
2
0
1
2
2
1
2
1
1
1
1
1
2
2
1
1
0
2
0
1
0
0
0
2
2
0
0
0
0
2
1
1
1
0
0
1
0
1
1
1
2
0
0
2
0
1
1
2
0
2
0
0
0
1
1
2
0
2
1
2
1
2
1
1
1
2
1
2
0
0
2
2
1
1
1
1
2
1
1
1
2
1
1
1
1
2
2
2
0
1
2
1
1
1
2
2
1
2
1
0
0
1
1
1
0
0
2
1
1
1
1
0
1
1
2
1
2
0
0
1
0
0
1
1
0
1
1
1
2
1
0
0
1
1
4
0
2
2
0
2
2
1
0
1
0
2
2
0
2
2
1
0
2
1
2
1
2
0
1
1
1
0
1
1
1
2
2
1
0
0
1
1
2
0
1
1
2
1
0
0
0
0
1
1
2
0
0
0
1
2
0
0
1
2
1
0
0
2
1
1
1
3
0
2
2
1
0
1
1
1
2
2
0
0
3
2
1
0
1
1
2
1
0
0
2
2
1
1
1
0
1
2
1
0
0
1
1
2
1
2
1
1
2
2
0
1
0
1
0
1
0
1
0
1
1
0
0
1
0
0
0
1
0
1
2
0
0
0
1
2
2
3
0
2
2
1
1
2
1
1
1
0
0
0
1
1
1
1
1
1
2
1
2
0
1
1
1
1
1
0
1
2
1
2
1
0
1
1
2
2
1
2
1
2
1
2
2
0
1
0
0
0
1
0
2
0
0
0
0
0
1
0
3
1
0
0
0
1
1
0
1
1
0
1
2
1
3
2
1
1
2
2
1
0
1
1
1
0
2
2
2
1
1
1
0
0
1
2
2
1
2
0
1
0
1
1
1
1
1
1
1
2
0
1
1
0
1
1
2
2
1
0
2
2
2
0
3
3
1
2
2
0
0
1
0
0
2
0
1
1
1
1
1
1
1
1
0
0
0
2
1
1
0
0
3
2
0
1
1
2
1
1
0
2
0
0
0
1
0
1
0
1
1
0
1
2
0
1
1
1
0
2
2
0
1
1
0
1
1
2
1
0
0
0
2
2
2
2
0
1
1
0
1
0
1
1
2
2
1
1
2
2
1
1
2
1
2
1
1
1
2
2
0
2
0
0
2
2
1
1
1
1
1
2
2
0
1
1
0
2
2
0
1
0
0
1
1
2
2
0
2
1
1
1
0
0
0
0
1
2
2
1
2
0
1
1
1
1
0
0
2
1
6
0
2
1
0
0
0
1
0
1
0
1
1
0
0
1
0
0
1
2
0
0
1
1
0
1
2
0
1
2
0
1
1
2
1
0
0
1
0
0
0
0
0
1
2
0
2
0
0
2
2
1
0
1
2
2
1
0
2
2
0
2
1
0
0
2
1
1
1
0
0
1
0
2
0
0
2
1
2
1
0
0
2
0
1
2
1
1
0
1
2
1
2
0
0
0
1
2
2
1
1
1
1
0
2
1
1
1
0
0
0
0
1
1
0
1
0
0
2
1
0
2
2
2
2
1
0
2
0
1
1
1
1
2
0
1
0
1
2
2
0
1
2
1
2
1
1
0
0
2
2
0
0
1
0
0
0
1
1
2
2
2
1
1
0
0
1
1
1
0
0
1
0
1
1
1
2
1
1
1
0
0
1
0
0
0
2
1
2
2
0
2
1
0
2
1
1
1
0
0
1
0
0
3
2
0
1
0
0
0
0
0
1
0
1
0
1
0
1
1
2
2
2
3
2
1
1
0
1
0
0
2
0
1
1
2
0
0
0
1
1
1
3
1
2
1
1
1
2
1
1
1
1
0
2
2
2
1
2
1
1
0
1
1
0
2
2
1
0
0
0
2
1
0
1
1
1
1
0
2
2
0
1
1
0
1
2
1
1
0
1
0
1
0
0
1
0
1
3
0
2
1
0
1
0
1
0
1
1
0
2
1
2
1
1
0
0
0
1
2
0
1
0
2
3
0
0
0
0
0
0
0
1
0
1
0
1
2
1
2
1
2
2
2
1
1
2
2
0
1
1
0
1
0
0
1
1
0
1
2
1
0
1
1
0
9
1
0
1
1
0
0
2
2
1
1
1
1
1
1
2
2
2
1
1
1
1
2
1
0
0
1
1
1
1
0
1
1
2
1
1
0
2
1
0
2
1
1
0
0
0
0
0
1
1
1
0
0
0
1
2
1
1
0
1
1
0
3
0
1
2
2
0
0
1
0
2
1
1
0
6
1
1
2
1
1
1
2
2
1
0
1
0
1
0
0
0
2
1
2
3
1
0
1
0
0
1
1
0
2
1
1
1
1
1
1
1
1
0
1
0
0
2
0
1
0
3
0
2
0
2
1
0
0
2
0
2
0
0
2
1
0
1
0
1
2
0
0
1
0
0
1
1
0
2
1
2
2
1
0
0
1
0
0
0
1
1
0
3
0
1
0
0
2
1
2
0
0
1
0
1
0
1
1
1
0
1
1
2
1
2
2
0
1
2
2
1
2
2
1
0
2
0
0
2
2
0
2
0
1
1
0
2
1
0
1
0
1
1
1
1
1
0
2
1
1
0
1
2
0
0
0
1
0
0
1
1
2
0
1
1
1
0
0
1
1
4
0
1
2
3
2
2
1
1
1
0
0
1
1
3
1
1
1
2
3
2
1
1
0
1
0
1
1
0
0
2
0
2
1
2
1
2
2
1
0
1
1
1
1
1
1
1
1
1
0
1
0
1
1
1
0
1
2
0
1
0
1
0
0
1
3
2
1
2
0
0
0
0
1
0
1
2
0
1
2
1
0
0
0
2
0
2
0
0
0
1
2
2
0
2
1
2
2
1
2
0
0
0
0
1
2
0
2
0
1
2
1
0
1
0
0
0
0
1
2
2
2
1
0
0
0
1
1
0
3
2
0
1
1
1
2
1
0
0
0
1
1
0
0
2
0
4
3
2
0
1
0
1
1
0
1
1
2
0
1
2
1
2
2
0
2
0
1
1
0
1
1
1
1
2
2
0
2
1
1
1
0
0
1
0
1
1
0
0
0
0
1
0
1
2
1
0
2
0
0
1
0
0
1
2
2
2
2
1
1
1
2
1
2
1
2
1
1
0
1
1
0
0
2
2
1
1
2
0
1
2
2
0
1
1
2
1
1
4
1
1
1
2
0
1
1
1
1
1
1
1
1
1
1
2
1
1
2
1
1
2
1
1
2
2
0
1
2
0
1
2
2
0
0
0
0
1
2
1
0
2
1
1
0
2
1
1
0
2
1
0
1
1
1
0
1
0
1
0
1
1
0
0
1
1
0
0
1
0
2
1
2
0
1
1
0
1
0
1
0
0
0
1
1
1
0
0
0
2
0
2
1
0
0
0
1
2
0
1
0
2
0
1
1
0
0
1
0
1
0
1
0
1
2
0
1
1
0
0
0
0
1
0
1
2
2
0
0
1
0
1
1
2
1
1
2
0
3
2
1
1
0
0
1
2
2
2
2
1
0
0
2
2
0
1
1
1
0
1
2
1
0
3
1
2
0
1
1
1
1
1
2
0
1
1
0
2
0
1
0
0
1
1
1
1
0
2
4
0
1
0
1
1
0
1
0
0
0
2
1
1
0
0
0
2
0
2
0
0
2
1
2
1
2
2
0
1
1
3
1
1
0
0
1
1
1
1
1
5
1
1
1
0
1
1
1
2
0
2
1
0
1
1
0
0
0
2
0
0
0
1
1
1
2
1
0
2
0
0
0
2
1
1
1
1
1
2
0
1
1
0
0
1
0
2
1
1
1
0
0
2
0
1
1
1
2
0
2
2
2
0
2
0
2
0
1
0
0
1
2
2
1
0
0
1
1
1
1
2
0
2
2
1
1
0
1
1
0
2
0
2
2
1
0
1
1
0
0
1
1
1
2
1
0
1
1
1
1
2
0
0
2
1
1
1
1
2
2
0
1
0
2
0
0
1
2
1
1
1
1
0
1
1
1
2
1
1
2
2
1
0
2
1
1
2
0
1
1
1
1
0
1
0
1
1
1
0
1
0
1
0
0
0
0
2
2
0
3
1
0
0
0
2
2
0
1
0
1
1
1
0
1
0
0
2
0
2
2
1
0
1
2
1
0
1
1
0
0
2
1
0
2
2
2
2
1
0
2
0
1
2
1
1
0
1
0
1
1
1
1
2
0
0
0
2
2
1
1
0
0
1
1
0
2
1
0
2
2
5
0
2
0
0
0
2
1
0
1
2
1
1
2
1
0
1
1
1
1
0
1
0
0
1
2
0
0
0
0
0
0
0
1
1
2
0
1
2
0
0
1
0
1
1
0
1
1
1
0
1
2
1
1
1
2
1
0
0
2
1
1
1
1
1
2
0
2
1
0
1
1
1
1
0
0
2
1
2
1
1
2
1
0
2
1
0
1
1
1
1
1
2
1
1
2
1
0
2
2
1
0
2
2
1
1
1
1
1
1
2
0
1
0
1
0
1
1
0
0
0
1
0
2
2
0
1
0
1
1
1
2
1
2
2
1
1
1
0
2
1
1
0
1
1
2
0
1
1
1
1
0
0
1
0
1
1
1
0
1
1
1
1
1
0
0
0
0
1
2
1
1
2
0
1
1
1
1
0
0
2
1
1
1
0
1
1
0
1
2
1
2
2
1
2
0
0
1
2
0
1
1
2
0
2
0
0
0
1
0
0
0
0
1
0
0
0
1
0
3
2
0
1
1
1
1
0
1
2
1
1
1
2
1
0
1
1
1
1
0
0
1
2
0
0
2
1
0
0
2
1
2
0
0
2
0
1
0
0
0
1
1
0
1
1
1
1
2
2
0
1
0
1
1
3
1
0
1
0
2
2
2
0
1
1
0
2
0
1
0
0
0
1
1
1
0
0
2
1
1
2
0
1
1
1
0
1
0
1
0
0
2
2
0
2
1
0
0
1
1
1
1
1
1
1
1
0
0
0
1
0
1
1
2
2
1
2
0
1
1
1
2
1
0
1
2
2
2
1
1
0
3
1
0
2
2
0
1
2
0
2
0
0
2
1
1
1
2
0
2
1
2
2
1
2
1
1
1
2
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
1
3
1
1
2
1
0
1
0
2
0
1
2
0
2
0
0
1
0
1
1
2
1
2
0
1
2
1
1
2
2
1
1
0
1
4
2
0
1
1
2
1
0
1
1
1
2
2
1
2
2
1
1
2
0
1
1
0
2
1
2
1
0
1
1
3
1
2
0
1
2
1
2
1
1
0
0
2
2
2
0
2
0
2
1
1
1
1
0
0
1
0
1
0
0
1
2
1
0
1
2
2
0
1
0
0
2
0
0
0
0
1
0
0
1
1
1
2
0
0
0
1
2
0
0
1
0
2
1
0
1
0
0
1
0
0
2
0
1
1
1
2
1
1
0
1
0
0
1
1
0
2
0
0
0
1
1
2
2
2
1
2
1
0
1
0
1
1
1
0
1
1
0
1
2
1
1
0
0
1
1
1
2
0
0
0
2
2
2
0
1
2
1
0
0
0
0
0
1
1
1
0
1
1
2
4
1
1
2
1
1
2
1
0
1
1
2
2
0
1
0
2
0
0
0
2
2
1
2
0
0
2
0
0
0
0
2
1
1
1
0
1
1
2
0
1
2
0
0
0
1
2
2
0
2
1
2
1
0
2
1
0
1
0
0
0
0
2
1
2
0
1
1
0
1
1
1
2
1
2
0
2
1
0
1
1
2
0
0
2
1
1
0
1
1
1
2
0
1
0
2
0
1
1
0
2
1
2
2
2
0
1
0
0
0
1
1
2
1
1
2
1
0
1
2
2
2
1
4
2
2
0
1
2
1
3
2
1
1
1
1
0
0
1
0
0
2
1
2
1
1
1
0
0
3
0
0
1
1
2
1
2
1
1
2
0
4
3
2
1
1
1
2
2
1
1
1
0
2
2
1
0
2
1
2
0
1
4
1
0
1
1
0
1
1
2
1
1
0
0
0
1
2
1
2
2
2
2
1
3
1
1
0
1
1
0
0
2
1
0
2
2
0
0
1
1
1
1
1
1
0
2
1
1
0
0
1
1
0
0
0
2
1
1
1
1
0
1
2
1
2
1
1
1
2
0
1
2
0
2
2
0
0
1
1
2
1
0
1
1
1
1
2
1
1
1
1
2
2
0
1
2
1
2
0
2
1
1
2
1
0
1
1
0
2
1
0
2
1
1
1
1
0
1
1
1
1
1
0
1
0
1
1
1
0
0
1
4
2
2
0
0
2
0
1
1
2
1
2
0
0
1
2
1
1
1
2
0
0
1
0
1
1
1
1
2
1
3
0
2
1
2
1
0
0
0
1
1
0
0
0
2
2
0
2
1
0
2
0
3
0
1
2
1
0
1
1
2
2
2
2
1
2
0
0
0
1
0
1
1
1
1
0
1
1
0
1
0
1
2
0
1
0
1
0
0
0
1
1
2
1
1
2
1
0
1
1
1
0
0
1
1
1
2
0
0
1
0
1
2
0
0
1
1
0
2
1
1
1
2
2
2
1
0
1
1
1
1
1
2
0
2
1
1
1
0
2
0
1
1
0
1
1
0
0
2
1
1
1
1
2
2
0
1
1
1
1
1
1
1
2
0
2
1
0
0
0
0
2
1
1
0
1
2
1
0
1
0
1
1
1
0
0
2
2
1
2
2
1
1
1
2
0
1
0
1
0
0
1
0
0
0
1
0
1
1
2
1
0
0
1
0
1
1
1
1
2
0
0
2
1
1
1
1
1
1
1
0
2
2
2
0
0
1
0
1
0
0
0
1
0
1
2
1
1
1
3
1
1
1
0
2
2
1
1
1
0
2
1
2
0
0
1
1
1
0
1
0
0
1
2
1
0
1
2
2
0
2
1
1
2
1
0
2
2
1
1
1
1
0
1
1
1
1
1
2
1
2
1
0
1
0
3
1
1
2
2
1
0
0
1
0
1
1
1
2
0
0
1
0
1
1
2
1
0
0
0
0
0
1
2
1
1
1
1
1
0
1
0
2
1
1
3
1
1
1
1
1
1
1
1
1
0
0
0
1
7
2
0
0
1
2
0
0
1
2
0
1
1
1
2
2
2
2
0
1
0
0
1
0
1
1
0
0
0
2
0
2
0
2
2
1
1
0
2
2
1
2
1
0
1
1
0
1
0
1
1
0
3
2
1
1
0
0
1
1
1
1
2
2
2
1
2
1
0
2
2
1
1
1
1
2
1
1
1
1
1
0
2
0
1
5
0
1
0
2
1
0
1
2
0
1
1
1
0
0
0
1
0
1
0
0
0
2
1
1
1
1
2
1
0
0
0
2
0
2
2
0
2
2
2
3
2
2
1
2
2
1
1
1
2
1
1
1
0
0
1
2
1
1
2
0
1
2
1
1
1
1
1
0
0
0
0
0
0
0
1
1
1
1
1
1
0
1
1
1
1
1
2
0
1
1
0
0
1
0
2
1
1
1
0
1
1
1
0
1
0
2
1
0
1
0
2
0
0
1
1
1
1
2
1
2
1
0
0
1
0
0
0
2
2
1
1
1
1
1
1
2
1
0
0
1
1
0
0
2
1
2
1
1
2
1
1
1
0
0
1
0
0
1
1
2
0
1
3
1
0
0
2
1
1
2
1
1
1
1
1
2
2
1
2
1
2
1
2
0
1
0
0
1
0
2
0
2
2
0
0
0
1
1
2
0
1
1
2
0
0
1
3
1
1
1
1
2
1
0
2
1
1
1
1
2
3
2
1
1
0
2
1
1
0
0
1
2
1
2
0
0
0
1
1
0
1
2
0
1
1
1
1
0
1
1
1
2
1
1
2
1
1
1
2
0
1
1
5
2
1
0
0
1
0
1
2
1
1
1
1
1
1
1
1
2
1
1
2
0
2
1
0
2
2
1
0
1
0
1
1
0
0
0
2
0
1
0
1
1
1
1
2
0
0
0
2
1
2
1
1
2
1
0
0
1
0
0
2
0
0
1
0
0
1
1
2
2
1
1
1
1
2
1
1
2
0
2
2
1
0
2
1
1
0
1
2
0
2
1
0
1
0
1
1
1
1
2
2
1
0
2
2
1
2
1
0
1
1
2
0
0
0
0
0
2
1
0
2
1
0
2
0
2
0
1
1
2
0
0
1
0
1
1
1
0
0
2
0
1
1
1
1
2
0
2
1
1
1
1
1
1
1
1
6
4
2
0
1
1
2
1
0
0
1
1
2
1
1
0
1
1
1
0
1
2
3
1
2
0
1
2
2
1
2
2
0
0
0
1
1
0
0
1
1
1
2
2
1
1
1
0
0
1
0
2
1
0
0
2
1
0
1
1
1
1
1
1
1
1
0
2
1
2
1
0
1
0
1
2
1
1
1
1
1
1
0
2
1
0
2
1
2
0
2
0
2
1
1
0
0
1
1
2
0
2
1
0
2
1
1
2
0
1
3
0
2
2
1
0
2
1
1
1
0
2
1
0
1
0
0
0
0
2
0
0
2
1
0
2
1
2
0
2
0
1
0
1
1
2
0
0
1
2
2
1
0
2
0
1
1
1
0
1
0
0
0
0
2
2
1
1
0
1
0
1
3
1
1
1
0
1
0
0
1
1
1
2
0
1
0
1
1
1
0
1
0
0
0
0
0
0
2
0
1
2
2
1
1
2
1
1
0
2
0
2
2
0
2
2
2
0
1
1
2
1
1
2
0
1
1
2
0
1
1
0
0
1
0
1
0
1
1
2
0
0
0
1
1
0
0
1
0
1
1
3
2
0
0
2
0
0
0
1
2
1
1
2
1
1
0
1
1
0
1
1
1
1
2
1
1
1
0
1
2
1
0
1
2
1
0
1
0
2
1
2
1
1
1
0
2
1
0
2
1
0
0
1
0
0
2
0
1
2
0
0
1
0
1
0
0
0
1
2
1
1
0
1
1
1
1
1
1
1
1
1
2
0
1
0
0
0
1
1
5
2
0
1
1
1
0
0
2
1
2
1
2
1
1
0
0
0
1
1
1
1
1
0
0
1
2
1
1
1
2
1
2
1
2
0
1
0
0
1
1
2
1
0
0
1
1
0
0
1
1
2
1
1
2
0
1
0
3
1
1
2
0
1
2
1
1
1
0
0
2
1
1
1
2
1
2
1
0
2
1
1
1
1
0
1
0
0
1
0
1
1
2
1
1
3
0
0
1
1
2
2
2
2
1
1
1
0
2
2
0
2
1
0
1
2
0
1
1
1
1
0
1
1
0
0
1
1
0
0
0
0
2
0
0
1
0
1
0
0
1
0
0
1
1
0
0
1
0
0
2
2
1
1
0
1
3
0
0
0
0
2
0
1
0
0
0
1
0
1
0
2
1
2
2
1
0
0
1
1
0
1
1
1
2
1
1
1
2
2
1
1
1
1
1
1
0
2
1
2
1
2
0
0
1
0
1
1
0
0
2
1
0
1
2
1
0
0
0
1
2
1
2
1
1
1
0
1
1
1
0
2
1
1
0
0
2
1
2
1
2
0
1
2
0
1
1
1
1
1
0
1
2
1
0
1
1
2
1
1
1
1
1
2
2
1
1
0
1
1
0
1
1
1
1
0
0
1
0
0
0
1
1
1
2
0
1
1
0
1
0
0
2
1
1
1
2
1
0
0
2
1
1
2
2
1
0
1
2
1
1
0
1
1
0
1
1
1
2
1
1
0
1
1
1
2
0
2
1
0
0
1
0
2
1
0
0
0
0
1
2
0
0
1
0
1
1
1
0
0
0
2
1
0
2
1
1
0
0
0
1
2
1
2
1
2
1
0
1
0
1
1
1
2
0
0
2
2
0
2
0
1
2
0
0
1
0
0
0
0
1
1
2
2
2
1
1
1
2
1
1
0
0
2
1
2
0
0
1
0
0
2
2
2
1
2
0
1
1
1
0
1
1
0
1
0
2
0
1
1
1
1
2
1
0
1
1
2
2
1
1
1
0
0
3
0
0
0
0
1
0
0
1
1
2
1
1
0
1
1
2
0
1
0
1
2
1
0
1
1
1
0
0
0
1
1
1
0
2
1
2
0
0
0
1
1
0
1
1
1
0
0
1
1
0
1
0
1
1
2
1
1
1
0
1
2
0
1
1
0
1
0
0
1
0
1
0
2
1
1
0
1
0
2
2
1
0
0
1
0
2
0
0
0
1
0
0
1
1
1
2
1
0
2
1
1
1
2
1
1
0
2
1
1
1
1
1
1
2
0
0
1
1
1
0
1
2
2
1
2
1
1
2
1
2
1
1
0
2
1
2
1
1
0
1
0
1
0
0
2
0
0
1
2
0
2
0
1
1
2
0
4
1
0
2
1
2
1
2
1
1
0
0
2
1
1
1
1
1
0
1
0
0
1
2
0
0
0
0
2
1
0
1
0
1
0
1
0
2
0
0
0
1
1
1
0
0
1
0
1
3
0
1
2
0
0
2
1
2
5
1
0
1
2
2
0
1
2
1
1
2
0
2
0
0
0
1
1
2
0
0
1
0
2
0
0
1
2
2
1
2
0
1
1
1
0
1
0
1
1
0
2
1
1
1
1
4
1
2
0
0
1
3
1
0
1
2
1
1
2
1
2
0
1
1
1
1
1
2
0
1
1
1
0
2
3
0
1
1
2
0
0
1
2
1
1
2
1
1
2
1
0
1
1
0
2
2
2
2
1
1
1
0
2
1
1
0
0
0
2
0
0
0
2
0
2
1
0
0
1
2
0
1
0
2
1
2
2
0
0
2
2
1
1
1
0
1
1
1
1
0
2
2
1
1
1
1
0
0
2
2
2
0
2
2
2
0
1
1
2
1
0
1
2
0
1
2
0
1
2
0
1
1
1
0
0
1
1
3
0
1
1
0
1
1
0
0
0
0
1
1
2
3
1
0
2
1
0
1
0
0
0
1
1
0
1
2
2
0
0
1
2
2
1
1
2
1
0
2
1
2
1
1
0
1
0
2
2
0
3
2
1
1
0
0
2
0
1
0
1
0
2
0
0
1
1
1
1
1
0
1
1
0
1
0
1
1
0
1
2
1
1
2
0
2
0
0
1
2
0
0
1
3
0
1
0
2
1
1
1
1
2
1
1
0
2
2
1
1
0
1
2
1
1
0
2
2
1
0
1
2
1
2
2
1
1
1
2
1
1
1
1
0
1
1
1
1
1
1
1
0
1
1
0
1
2
0
2
1
1
1
1
1
0
0
1
0
2
0
1
2
0
1
0
0
0
1
1
1
0
1
0
2
0
1
0
1
2
1
2
2
0
2
1
2
1
2
1
0
2
1
0
0
2
1
0
0
0
2
0
1
0
0
2
0
1
0
1
3
0
1
1
2
1
0
0
0
1
0
1
1
1
1
1
1
2
1
1
2
0
1
1
0
2
0
0
1
2
0
0
2
1
3
0
1
1
0
1
2
0
1
0
0
1
0
1
2
0
1
2
2
1
1
0
0
3
0
0
0
1
2
2
2
2
0
0
1
0
2
1
2
0
1
1
0
0
1
1
2
1
1
1
1
1
0
1
1
0
1
1
0
1
2
1
1
0
2
1
0
3
2
0
0
2
0
1
1
1
2
0
1
1
1
2
1
0
0
2
1
2
0
1
2
0
0
0
2
1
2
2
1
1
0
1
2
1
0
0
0
1
1
1
1
0
1
1
0
1
1
1
4
1
1
1
0
1
0
0
0
2
1
0
1
2
2
2
0
2
1
1
1
1
1
1
3
1
1
1
0
1
0
1
0
1
0
0
1
0
0
1
0
0
1
1
0
2
0
1
1
0
0
1
0
0
1
0
1
0
0
0
0
2
1
1
0
1
1
2
1
2
1
1
2
1
2
1
1
1
1
1
0
2
1
2
2
1
3
1
1
1
0
0
0
0
1
0
0
1
1
1
2
1
2
2
1
2
2
2
1
0
0
2
0
0
1
1
2
1
0
0
1
0
0
2
1
2
1
1
0
2
1
3
2
1
2
1
0
1
0
1
2
2
1
0
1
1
1
0
1
1
0
4
0
1
1
1
0
1
0
2
1
1
1
2
0
1
1
0
2
1
0
0
0
0
1
1
1
0
0
0
1
0
2
0
2
0
0
1
2
1
2
1
0
1
1
2
1
0
1
0
1
1
2
0
0
1
0
2
1
0
1
1
1
2
1
0
1
1
1
1
1
0
2
1
0
0
1
1
1
0
0
0
1
2
1
0
1
0
1
0
2
0
2
0
0
0
2
0
0
1
1
0
3
2
1
0
0
0
1
0
1
0
0
1
2
1
0
0
0
0
0
2
0
1
1
1
0
0
0
1
0
0
2
1
0
0
0
2
1
2
2
0
1
2
0
1
1
1
0
2
1
1
0
2
2
2
0
1
0
1
1
1
1
1
2
0
0
1
1
1
2
2
1
0
1
1
0
1
2
2
1
0
0
1
0
2
2
1
1
1
0
3
2
1
1
1
1
0
0
0
0
1
2
1
0
0
2
1
2
0
1
1
0
2
1
1
2
2
0
2
0
1
0
1
0
0
1
1
0
2
1
1
1
0
0
2
1
0
0
2
2
0
0
2
0
0
2
1
1
2
2
1
1
2
1
0
0
2
2
0
1
1
0
1
0
1
1
1
1
1
0
0
1
1
2
0
0
1
1
0
2
2
0
0
1
0
1
0
2
1
0
2
1
2
1
1
0
1
1
1
1
2
1
0
1
0
1
1
0
0
0
1
0
1
4
2
2
2
2
1
1
1
0
2
0
1
0
0
0
1
0
1
2
2
1
0
0
1
1
1
0
2
2
0
1
1
1
1
0
0
0
0
1
2
1
2
1
1
0
0
1
2
0
0
2
1
0
0
0
1
1
0
1
2
1
0
0
1
0
1
0
0
2
1
1
1
1
1
2
0
1
1
2
0
0
1
0
1
1
1
1
0
1
5
1
1
1
1
2
1
0
0
0
2
0
2
0
2
0
0
2
1
1
0
1
1
2
0
0
2
2
1
1
1
2
1
1
2
0
0
0
0
0
0
2
0
1
0
1
1
1
0
1
0
2
1
0
2
0
1
0
2
1
1
2
1
1
1
2
0
0
1
1
1
1
2
2
1
0
0
2
0
1
0
1
1
1
1
0
2
1
1
1
1
1
2
1
2
1
1
1
2
1
1
1
1
1
0
2
1
1
0
1
2
1
0
0
1
0
2
1
1
1
1
2
0
1
1
0
0
1
0
1
0
0
1
3
1
1
1
2
0
1
1
1
0
2
1
2
0
0
1
0
1
2
1
1
0
2
0
0
0
2
2
0
1
1
0
2
0
2
0
2
1
0
0
1
1
1
1
1
1
2
2
1
0
2
1
1
0
1
1
1
1
1
1
2
0
1
1
2
1
2
1
0
0
1
1
0
1
0
0
0
1
0
1
1
0
1
0
0
2
1
1
1
1
1
1
0
2
1
1
0
1
1
1
1
1
0
1
0
1
0
0
2
1
2
0
2
0
1
2
1
1
0
0
0
2
0
2
0
3
0
1
0
1
2
1
2
0
2
2
1
2
1
3
1
1
2
2
0
0
0
0
2
0
0
2
0
1
0
1
1
0
1
2
2
1
1
0
1
0
2
1
1
0
0
1
1
1
1
0
0
0
0
1
0
2
1
2
1
0
2
0
1
0
0
0
1
0
2
0
0
0
1
2
0
1
2
0
2
0
2
1
0
2
0
1
2
1
1
1
1
0
0
0
0
0
2
2
0
1
2
0
0
0
2
1
1
2
0
0
0
1
1
1
0
1
1
0
1
1
0
2
1
1
1
1
1
1
0
2
1
0
1
1
1
0
1
1
2
1
0
2
2
1
2
1
0
11
2
1
0
1
0
0
2
2
1
0
0
1
1
1
1
1
0
0
0
1
1
1
2
2
0
0
1
1
2
1
1
2
1
1
0
1
2
2
0
2
2
2
0
0
0
2
2
1
0
1
1
1
1
2
0
1
0
1
2
1
2
1
2
1
1
2
1
0
0
0
2
2
1
1
1
0
0
2
1
1
2
1
2
2
1
1
1
0
2
0
0
1
2
1
0
0
1
1
0
1
0
2
1
1
2
1
1
1
1
0
1
1
1
0
0
2
1
1
2
2
0
2
0
1
1
0
3
0
1
1
3
0
1
3
1
1
1
0
0
1
2
1
2
1
1
1
0
2
1
1
1
0
0
1
0
1
1
2
1
1
1
1
0
2
0
0
1
0
1
0
2
0
0
1
0
2
0
1
2
2
1
2
1
0
1
1
0
2
1
1
2
1
1
1
1
1
2
1
1
2
0
1
1
1
0
1
0
1
2
1
0
0
1
2
0
1
1
1
1
2
1
2
1
0
3
1
0
1
1
4
1
1
0
0
0
2
0
0
1
1
1
1
1
0
1
2
1
2
2
0
2
0
1
2
0
2
0
0
2
2
0
0
1
0
1
0
1
0
2
0
0
0
1
0
1
0
1
1
1
2
1
1
1
1
1
1
1
1
0
0
0
2
1
1
0
0
0
0
1
1
2
3
1
2
1
0
0
2
1
1
2
0
2
2
1
1
1
1
0
1
2
2
1
2
1
2
2
0
1
2
1
1
2
1
2
1
2
0
2
0
1
1
2
0
1
2
2
0
1
2
1
2
0
1
0
0
0
1
0
0
1
0
2
1
0
1
2
1
0
2
0
1
1
1
0
0
0
2
1
1
1
2
2
1
0
2
3
0
2
0
1
2
1
1
1
1
1
0
2
2
1
2
0
1
1
1
2
0
1
1
1
1
1
2
1
2
1
0
2
0
3
0
1
0
0
1
1
1
0
0
1
1
1
2
1
0
1
1
1
1
1
0
1
1
1
1
0
1
0
2
1
0
1
0
1
0
2
1
0
3
1
2
1
0
2
2
1
1
2
1
1
1
0
2
0
0
1
0
1
0
1
1
2
2
1
0
2
1
0
0
1
0
1
2
1
2
0
1
2
1
2
1
1
1
1
0
2
1
1
2
1
1
1
0
0
1
2
2
2
2
1
2
1
0
0
0
0
2
1
1
1
0
0
0
0
2
1
1
4
0
1
0
2
1
0
2
0
1
2
2
1
2
1
0
1
0
0
0
1
1
0
1
0
1
0
0
0
0
1
1
2
1
1
0
0
1
1
1
1
0
0
1
0
1
0
0
1
2
1
1
0
2
0
0
0
1
1
1
0
2
2
1
1
2
1
1
1
1
0
0
1
1
0
0
0
0
0
2
2
1
0
1
0
1
1
1
0
2
0
1
0
0
2
0
2
3
0
0
0
2
2
1
1
2
0
1
1
1
0
1
0
0
0
0
2
1
1
2
2
0
2
2
0
2
1
2
6
0
2
0
0
1
1
2
1
1
1
0
2
1
1
1
1
0
0
0
0
1
0
1
0
2
1
1
0
1
0
2
0
2
0
2
2
1
2
1
0
0
1
1
1
0
1
1
1
1
0
0
1
2
1
0
1
1
1
1
1
0
2
2
1
1
1
0
2
0
1
0
1
0
0
1
0
0
1
0
1
1
1
0
1
1
2
1
0
0
1
0
0
0
2
0
0
1
1
0
0
0
1
0
1
0
3
1
1
1
1
2
1
0
0
1
2
2
1
2
1
2
0
1
0
1
1
1
1
2
1
1
1
0
1
0
0
0
1
0
0
1
0
0
1
0
2
1
1
1
1
1
0
1
1
0
0
1
1
1
0
0
2
1
1
0
1
1
2
1
2
0
2
0
2
0
4
0
1
2
0
1
1
2
0
1
0
0
0
1
1
1
0
0
0
0
0
1
0
2
1
1
1
2
0
1
0
1
0
1
2
1
0
1
0
1
0
2
0
1
1
1
2
1
0
1
1
1
0
1
1
2
1
1
1
0
1
1
0
1
0
0
0
0
0
3
1
1
0
2
1
1
1
1
0
1
1
2
1
1
1
1
1
2
1
0
1
1
1
1
1
0
0
1
1
1
0
1
1
0
1
0
0
1
1
1
1
2
1
2
1
1
1
1
2
0
1
2
0
2
1
0
1
2
1
0
1
2
0
1
1
0
1
0
1
2
2
1
1
2
1
2
1
2
0
3
0
0
0
1
1
0
0
0
0
2
1
1
2
1
0
0
1
1
0
2
1
1
0
1
1
0
2
1
2
0
1
0
1
1
0
1
0
0
1
1
0
0
3
0
2
2
1
0
2
1
0
0
0
1
2
1
1
1
1
0
1
0
0
0
0
0
1
2
0
0
1
1
1
0
1
1
0
0
0
0
0
1
2
0
0
0
2
1
1
0
2
1
2
1
1
1
2
0
1
0
1
2
1
2
1
2
0
1
4
2
1
1
1
1
1
2
1
0
1
2
1
1
2
1
0
1
1
0
1
1
1
2
2
2
2
1
2
1
1
2
1
1
1
1
1
1
2
0
0
1
1
1
2
1
0
2
1
0
2
1
1
0
1
1
2
1
0
0
1
1
1
1
0
1
1
0
1
0
1
2
0
0
1
0
1
1
2
1
1
2
1
0
1
0
0
1
1
0
0
0
1
2
1
1
0
2
2
4
2
0
0
1
2
2
0
1
1
0
2
1
2
0
0
2
1
2
2
1
0
2
1
0
1
2
1
2
2
2
1
1
0
1
1
1
0
1
0
0
2
1
0
2
1
2
1
1
2
0
2
1
1
0
0
0
0
1
1
2
1
1
0
1
1
1
1
0
0
2
1
1
1
0
2
1
1
1
0
0
1
0
1
0
0
2
1
1
1
1
2
1
1
0
0
1
3
1
1
0
0
2
1
2
1
1
0
0
1
1
1
1
1
2
1
0
2
0
0
1
0
0
1
1
0
0
0
1
1
1
1
1
0
0
1
1
2
1
2
1
1
1
1
1
1
2
0
1
0
0
1
0
1
1
0
1
1
0
0
1
1
1
1
0
1
1
1
2
2
0
0
0
1
0
0
1
0
2
2
0
0
2
2
0
1
0
2
1
1
0
0
0
1
1
2
1
2
1
0
2
2
2
0
2
2
2
5
1
1
0
0
1
0
1
2
1
0
1
1
3
0
1
1
0
2
1
1
1
1
2
1
1
1
0
0
2
1
1
2
2
1
0
1
1
1
0
1
1
1
1
1
4
1
0
1
0
2
1
0
0
0
0
1
0
0
1
0
0
0
0
2
1
1
0
1
1
1
0
1
1
0
0
1
0
0
1
1
1
1
1
1
2
2
0
1
1
0
0
1
1
1
1
1
1
1
1
2
1
0
0
1
0
1
1
1
0
1
2
1
0
0
0
0
0
2
1
0
2
1
1
2
2
1
1
0
0
1
2
1
2
0
1
0
2
1
0
1
2
2
1
1
2
1
2
2
1
0
0
0
0
0
0
1
2
0
0
0
1
0
1
1
2
2
1
1
0
1
0
0
1
0
3
1
3
0
0
1
1
1
1
0
2
1
1
1
0
2
0
1
2
1
0
2
0
1
1
0
1
0
0
2
0
0
0
0
1
0
1
1
1
1
0
2
0
0
1
0
1
1
1
0
1
2
0
2
1
1
0
1
0
0
2
1
0
0
0
2
2
1
2
2
0
0
1
0
2
2
2
1
0
2
2
0
2
1
2
1
2
0
1
2
1
1
2
1
0
1
1
2
1
1
1
1
1
1
2
0
1
2
3
1
0
1
0
0
0
2
1
0
1
2
0
2
2
0
1
0
0
1
2
1
1
0
1
0
2
1
1
1
1
1
1
0
1
2
0
1
0
1
1
3
1
1
1
0
2
0
1
1
1
1
2
2
0
1
2
3
2
0
2
0
0
2
1
0
0
0
1
1
0
0
0
1
2
0
0
0
1
1
1
0
1
2
2
1
0
1
0
0
1
1
0
1
0
2
1
0
0
1
0
0
1
1
1
1
1
0
1
1
1
0
1
0
0
1
0
2
1
1
2
0
0
0
2
2
0
1
2
1
0
1
0
1
1
1
1
1
2
1
1
1
0
0
1
0
1
2
0
0
1
0
1
2
1
0
1
2
1
1
0
0
1
1
0
0
2
2
2
0
0
2
0
1
3
0
1
1
1
1
0
0
1
1
1
1
0
0
1
1
0
0
1
1
0
1
0
3
1
2
2
1
0
1
0
0
1
0
1
2
1
1
1
0
0
1
2
0
0
1
1
3
1
0
1
0
1
2
2
3
2
1
0
0
0
0
1
2
0
1
1
1
1
0
2
2
2
0
0
0
0
1
1
1
0
1
2
0
3
1
2
1
0
1
2
0
1
1
0
1
0
0
0
0
0
2
0
1
1
1
1
0
1
0
0
0
0
0
0
1
0
1
1
1
0
1
1
2
0
0
1
0
1
0
2
2
2
0
0
0
0
2
1
2
1
1
0
1
2
2
1
0
1
0
2
0
2
1
0
1
2
1
0
2
1
1
0
1
0
1
1
2
1
1
1
0
1
2
3
2
1
0
2
2
0
0
0
0
0
1
1
1
1
1
1
1
1
2
1
0
0
1
0
1
1
1
0
0
0
0
1
1
0
1
1
0
0
2
0
2
1
2
2
1
1
1
1
0
1
1
1
2
1
1
2
1
0
2
1
1
0
2
2
1
0
1
1
1
1
1
2
2
2
2
1
0
1
2
0
2
1
0
2
0
0
0
2
1
0
1
1
2
1
1
1
0
0
0
0
1
1
1
0
2
0
1
1
1
1
2
1
2
1
0
1
1
3
0
0
1
1
2
0
1
1
2
1
0
1
0
1
2
0
2
0
0
2
1
0
1
0
0
0
0
1
0
2
1
1
2
0
1
0
1
0
1
0
0
0
2
0
0
0
1
1
0
1
3
1
1
0
2
0
0
1
1
1
0
1
0
2
1
0
2
2
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
2
1
0
1
1
1
0
0
2
1
1
0
1
0
0
1
1
2
1
0
1
1
1
1
0
1
1
1
1
2
1
1
1
1
1
1
0
1
2
0
1
1
1
0
1
1
2
2
2
0
2
1
1
5
2
1
2
2
1
1
2
1
1
1
0
2
0
1
2
1
1
1
0
2
0
1
0
0
1
1
1
2
1
1
2
1
2
1
1
0
1
0
0
1
0
1
0
0
0
0
0
2
1
1
2
0
2
2
2
2
0
1
0
1
1
0
1
4
0
1
1
2
0
0
1
0
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
2
1
0
2
1
1
1
1
1
3
1
0
1
0
0
0
0
1
0
0
0
0
1
1
2
0
0
0
1
1
0
1
0
0
1
2
0
1
0
0
0
1
1
1
0
0
0
1
1
1
0
3
0
2
1
1
0
3
1
2
0
0
1
2
1
1
0
2
0
0
1
1
2
1
1
1
1
2
1
0
1
1
1
1
2
0
1
1
0
0
0
0
1
1
2
2
0
1
1
2
1
2
2
1
1
1
0
2
1
2
0
0
0
1
1
1
1
1
1
0
2
2
1
1
1
1
0
1
2
1
0
0
3
2
0
1
0
1
2
1
2
1
1
1
1
1
2
1
2
1
0
0
1
0
1
1
2
2
2
1
1
1
1
0
1
1
0
1
1
1
0
1
1
1
0
1
3
2
0
2
2
1
1
1
1
2
0
1
2
0
1
1
1
2
0
0
1
0
2
0
2
0
0
1
1
0
0
2
1
1
1
4
0
0
0
1
0
0
0
2
1
1
1
0
0
1
0
2
0
2
1
0
0
2
1
1
2
1
1
2
0
1
1
2
2
1
1
2
0
2
1
1
1
1
1
1
2
1
2
0
0
0
2
1
2
0
1
0
1
2
0
0
1
1
1
0
1
1
0
1
1
0
0
2
0
1
1
1
1
1
0
1
0
0
1
0
0
0
1
1
2
0
1
1
0
1
0
0
2
0
1
1
6
2
2
0
0
1
1
1
2
1
1
0
0
0
2
1
2
1
1
1
1
0
0
1
1
1
1
0
0
0
2
2
0
2
2
1
3
1
1
2
1
0
1
1
2
2
0
1
2
0
1
1
1
0
1
1
1
1
0
1
0
2
2
2
2
1
1
2
1
1
0
1
1
1
1
1
2
0
0
2
1
0
0
1
1
1
1
0
4
2
1
1
1
1
2
1
2
2
1
1
0
1
2
0
1
2
0
2
1
2
1
1
0
1
1
2
1
1
2
1
0
1
0
0
2
1
2
1
0
1
1
1
1
1
0
1
2
1
1
0
1
1
2
0
2
2
1
0
0
1
0
1
1
1
2
1
0
2
0
3
0
0
1
0
1
2
1
0
1
1
1
1
1
1
2
0
2
1
2
1
2
0
2
0
1
2
0
2
0
0
0
2
1
1
0
2
0
1
0
1
1
1
1
0
2
1
1
0
1
1
2
0
2
0
1
2
0
1
1
0
0
1
0
0
1
2
2
1
0
1
1
2
2
1
1
1
0
1
1
0
1
0
1
1
0
1
1
2
1
3
1
0
2
1
1
2
1
1
1
0
1
2
0
1
1
0
1
1
0
1
0
2
0
1
0
0
1
1
2
0
1
0
0
0
0
1
1
1
1
2
1
0
2
1
0
0
0
0
0
2
1
2
1
1
1
0
1
0
1
0
2
1
2
1
0
1
1
0
1
1
1
2
1
0
0
2
1
2
2
2
1
0
0
2
1
1
2
0
2
2
0
0
2
0
1
2
0
1
1
1
2
0
1
2
1
1
2
2
1
0
0
0
2
1
1
1
0
0
2
2
2
0
0
0
0
0
1
2
1
0
0
1
1
1
0
2
2
0
0
2
2
1
2
1
1
2
2
1
0
0
1
1
0
1
0
1
2
1
0
1
1
1
1
0
0
2
0
1
0
0
0
0
2
1
1
1
0
0
0
2
2
0
0
2
0
1
4
0
1
1
1
2
1
1
1
2
1
1
1
1
2
0
0
1
1
1
1
2
1
0
0
1
0
2
0
1
1
0
0
2
1
1
0
1
1
2
0
0
2
1
1
2
0
1
1
1
0
1
2
0
1
0
0
2
2
1
2
1
1
0
0
1
1
2
3
2
0
0
2
1
0
1
1
0
1
1
1
1
0
1
2
1
1
0
1
1
1
1
2
1
0
1
1
2
0
1
1
0
1
1
0
0
1
1
0
1
0
2
1
1
0
1
2
1
1
2
1
1
3
2
1
1
0
1
1
0
1
2
0
0
4
2
1
1
2
0
2
2
1
1
0
0
0
2
1
2
2
2
2
0
1
0
2
1
0
0
1
1
2
2
1
1
1
1
0
3
1
2
0
0
2
2
1
1
0
0
0
2
0
2
1
1
2
1
2
2
0
2
1
0
1
1
0
2
1
0
0
0
1
1
2
1
0
1
0
1
1
1
0
2
2
2
1
1
1
3
1
1
2
0
0
1
1
1
1
1
0
1
1
0
1
1
1
1
2
2
1
0
1
1
0
0
1
0
2
2
2
0
2
0
2
1
0
2
1
1
1
0
0
0
2
1
0
0
2
1
1
0
1
0
2
0
1
1
1
0
0
0
0
0
1
1
1
2
0
3
1
1
1
0
2
1
1
1
0
0
1
2
0
1
1
1
0
0
2
2
0
0
1
1
1
0
1
2
1
0
1
1
0
1
1
0
2
0
0
0
1
1
0
1
1
1
1
3
0
1
0
0
1
0
0
1
2
5
1
2
1
0
1
1
1
2
0
0
1
0
2
1
1
0
1
0
0
1
1
2
1
1
1
0
1
1
0
2
2
1
1
1
3
1
1
1
0
1
0
1
1
0
2
1
1
1
1
0
0
0
1
3
1
0
2
0
1
1
0
1
1
0
0
0
1
0
0
1
1
0
1
2
0
1
0
0
2
2
0
0
2
3
2
1
3
0
1
0
1
1
0
2
0
0
0
0
1
1
2
1
1
1
1
0
0
0
4
0
1
1
1
1
1
0
1
1
1
2
0
1
1
1
2
1
1
0
2
1
0
2
1
0
0
1
2
0
0
2
1
2
1
1
2
2
0
2
0
1
1
1
1
6
0
1
2
0
1
0
0
0
0
1
1
1
1
1
1
0
1
2
2
1
0
0
1
2
2
2
1
2
1
0
1
2
0
2
1
1
1
1
1
0
2
0
2
1
0
0
0
2
0
2
1
1
0
2
1
1
1
1
1
1
2
1
1
2
0
2
1
2
0
2
1
1
1
1
0
1
1
1
2
2
0
1
1
1
2
1
0
1
0
0
1
2
0
1
2
0
3
0
1
0
0
0
2
2
0
2
1
1
0
0
0
1
1
2
2
1
1
0
2
1
1
2
0
1
0
2
1
0
1
2
0
0
5
1
2
0
3
0
1
0
1
1
0
2
1
1
1
0
2
1
0
1
0
2
2
1
1
1
2
2
0
1
1
1
2
0
0
1
0
1
2
2
2
1
1
1
1
0
1
0
0
2
0
0
1
1
1
1
2
0
1
0
0
1
2
1
0
1
0
2
0
1
1
1
0
1
1
0
2
3
1
2
1
1
1
2
0
1
0
1
1
2
0
1
1
0
1
1
1
0
2
1
1
0
2
2
1
0
0
1
2
0
1
0
1
1
1
0
2
2
1
0
0
0
0
1
0
1
1
1
2
1
2
2
2
0
1
2
0
1
1
3
2
2
1
0
0
2
0
2
1
1
1
0
1
2
0
0
2
2
0
2
1
1
0
0
0
0
1
2
0
1
2
0
2
1
1
1
0
2
0
2
0
0
0
2
0
2
0
0
1
1
2
2
1
1
2
0
0
0
1
1
0
1
1
1
0
2
1
0
1
0
2
1
1
0
1
1
2
0
0
1
0
1
1
0
1
1
1
1
2
2
1
1
2
0
0
0
0
2
0
1
1
1
1
1
2
2
1
1
0
0
0
0
2
0
0
0
0
1
1
1
1
0
2
0
0
1
1
1
0
0
1
0
1
0
1
2
0
1
1
1
1
1
1
1
2
0
0
0
1
1
1
1
1
0
0
2
0
0
0
1
1
1
0
0
0
0
0
0
1
0
2
1
2
1
2
1
1
1
1
1
1
1
0
1
1
1
0
2
1
1
1
2
2
1
0
0
0
1
2
0
1
1
0
1
1
1
0
0
0
1
0
0
2
1
2
1
2
0
1
1
1
1
2
1
2
1
1
2
2
2
1
0
0
0
1
0
1
2
2
2
1
1
0
0
2
1
0
0
1
1
2
2
1
1
2
1
1
1
1
1
1
2
0
1
2
0
1
1
2
1
0
0
0
1
2
2
2
1
1
1
2
2
1
2
0
1
0
1
0
1
1
1
1
2
0
1
1
0
1
1
0
0
1
1
1
0
1
0
0
2
2
2
1
0
0
1
2
1
1
1
0
2
2
1
2
1
2
1
2
2
2
2
1
1
0
0
1
0
2
4
1
1
2
1
1
1
1
0
1
0
0
2
0
0
1
1
1
0
2
0
0
2
1
1
1
1
0
7
0
2
1
2
0
1
2
2
2
1
2
2
1
0
1
2
1
1
1
2
1
2
2
2
0
0
0
2
1
2
0
2
1
0
2
1
0
2
1
1
1
1
2
0
1
1
1
2
1
1
0
0
1
3
0
1
1
1
2
0
0
1
1
1
0
2
0
1
0
1
2
0
2
1
2
0
1
0
2
2
1
1
1
2
3
2
1
1
0
1
0
0
0
1
1
1
1
0
0
0
1
0
0
0
1
1
1
0
1
1
1
1
2
0
2
1
0
0
0
0
1
1
0
0
0
0
1
1
0
0
1
1
0
1
2
1
2
3
1
2
0
1
0
0
1
1
2
1
2
1
1
1
1
2
2
0
1
0
1
0
0
0
1
1
0
1
0
3
2
0
1
2
0
2
2
2
2
0
1
0
1
0
1
2
1
1
0
0
2
1
1
2
1
1
1
0
0
2
1
0
1
2
2
1
0
1
1
1
0
1
2
1
1
0
0
0
1
0
1
1
0
1
0
1
0
2
0
1
2
1
2
1
2
0
0
1
0
1
2
0
1
2
0
0
1
0
3
0
1
1
0
0
2
1
2
0
2
1
0
0
0
2
3
1
0
2
0
1
1
1
2
1
1
2
1
1
0
1
1
0
1
1
1
0
2
0
1
1
0
2
1
2
2
2
1
2
0
2
1
1
1
1
1
1
2
2
3
1
0
0
1
1
1
0
2
0
1
1
1
1
2
2
0
2
0
0
0
0
0
2
1
2
0
1
1
1
2
2
1
0
1
1
1
1
1
1
2
1
1
2
1
2
0
3
0
0
0
1
2
1
2
0
1
0
1
1
0
2
0
1
1
1
0
1
2
1
2
1
1
0
1
1
1
0
1
1
0
1
0
2
1
0
2
1
0
0
2
2
0
2
0
1
0
2
1
1
2
0
1
2
0
2
3
0
2
2
1
0
1
0
0
0
2
0
2
2
1
1
1
1
2
1
0
2
1
1
2
1
1
1
0
0
1
1
1
1
2
1
2
0
2
1
1
1
1
0
2
0
2
0
0
2
1
0
1
0
1
0
1
1
1
1
1
2
2
2
1
0
0
0
0
1
0
1
0
2
1
0
1
2
1
1
1
0
2
1
0
0
1
0
0
3
0
0
1
0
1
1
2
1
2
2
0
1
0
1
1
2
0
1
0
1
2
1
1
2
0
2
1
0
1
3
1
3
3
1
0
1
1
0
1
1
1
1
2
1
1
1
0
2
1
1
1
1
2
0
2
1
1
2
0
1
1
1
2
0
1
0
2
0
0
1
2
1
1
0
0
1
0
0
1
0
1
1
1
0
2
2
2
2
1
0
2
1
2
1
0
1
1
1
0
0
0
1
2
1
1
0
0
0
0
0
1
0
1
1
4
1
0
2
2
0
0
0
0
1
1
1
4
0
0
0
2
1
0
1
1
0
2
1
0
1
0
2
0
2
1
1
0
2
1
2
0
2
1
3
1
0
2
1
3
1
0
0
0
2
2
1
2
1
1
0
1
0
0
1
2
0
0
2
1
1
1
1
0
0
1
0
1
1
2
0
1
2
1
2
1
1
2
1
1
1
0
1
0
2
3
1
1
0
2
0
1
1
2
1
1
0
2
0
1
1
0
0
1
1
2
0
0
2
1
2
0
1
2
0
0
1
1
0
1
1
1
0
1
0
1
1
2
2
0
0
1
0
1
0
3
2
0
0
1
2
0
1
1
2
1
2
1
0
1
1
0
2
1
2
1
0
1
2
2
1
1
0
1
0
1
1
0
1
2
1
0
1
0
1
1
0
1
0
0
0
0
0
1
1
1
1
0
1
2
0
1
0
0
1
0
0
0
1
0
1
2
1
2
1
1
1
1
2
0
2
1
1
0
1
1
0
0
2
0
1
1
0
1
1
2
1
2
2
0
1
0
0
2
1
1
0
1
2
1
0
1
2
1
0
1
2
1
0
2
1
2
1
0
1
0
0
0
1
2
1
0
0
3
0
0
1
1
1
0
0
0
2
0
1
2
1
1
0
1
2
1
0
0
1
1
0
2
2
1
1
1
0
2
0
1
1
2
1
1
0
0
1
1
0
2
1
1
0
1
0
1
1
1
0
1
1
1
1
1
2
1
0
0
2
4
0
1
2
1
2
1
0
0
2
0
1
1
0
0
0
0
1
2
1
1
2
2
2
0
0
1
2
0
2
2
2
0
2
1
1
1
1
0
0
1
0
1
2
0
1
1
0
0
2
3
1
1
2
2
2
1
1
1
0
0
2
1
0
2
0
0
0
1
2
1
0
0
1
0
1
1
2
2
2
0
0
2
0
1
0
1
3
2
1
1
0
1
0
0
0
2
1
1
0
2
2
2
0
1
0
1
0
0
0
0
0
0
2
1
2
0
1
0
1
2
0
0
0
0
3
1
1
2
0
0
2
1
1
1
1
1
1
1
0
2
2
2
1
1
0
1
2
1
1
2
0
0
0
0
0
1
1
2
1
2
1
0
2
0
2
1
1
0
1
0
0
2
0
0
0
1
0
0
1
0
0
0
1
2
2
1
3
2
1
0
2
1
1
1
0
1
1
2
2
0
2
1
2
0
0
2
6
0
0
3
1
0
2
1
1
1
0
1
2
1
1
1
2
2
0
2
1
1
0
0
0
1
1
0
2
1
1
1
2
2
0
2
1
1
0
2
1
0
1
1
1
0
0
1
1
1
0
1
2
0
0
1
0
1
0
1
0
2
2
0
1
1
0
1
3
0
1
1
0
1
0
1
0
0
0
1
1
0
1
0
1
1
1
0
1
0
0
2
1
0
1
2
2
1
1
0
1
3
2
0
2
1
1
0
0
0
2
2
0
0
1
0
1
1
2
0
1
1
0
2
0
0
1
0
0
1
1
1
0
1
0
1
2
0
0
0
1
1
0
1
0
1
1
1
0
0
1
1
1
0
0
0
2
1
0
0
2
0
1
0
0
0
1
1
1
0
1
1
2
3
0
1
1
1
1
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
1
0
0
2
0
0
1
2
0
3
1
2
1
2
1
1
1
2
1
1
1
0
2
1
1
1
1
2
1
1
0
0
2
1
1
0
2
0
2
1
1
1
2
0
1
0
2
0
0
2
2
0
1
2
0
2
1
2
0
1
1
0
1
0
0
1
1
1
1
1
1
0
1
1
2
2
1
1
0
0
0
1
1
0
1
0
0
1
1
0
1
0
1
1
0
2
2
1
1
2
2
2
0
0
0
0
0
0
1
2
0
0
1
1
0
1
1
1
1
0
2
1
0
0
1
2
2
1
1
0
2
1
0
1
1
1
1
2
1
0
2
0
2
1
0
1
1
2
2
2
1
1
2
0
1
0
2
2
0
0
1
1
0
1
1
1
1
0
1
1
1
2
0
1
0
0
0
2
0
0
1
2
0
0
0
0
1
2
1
0
1
0
0
1
2
1
0
0
0
1
1
1
1
1
2
0
1
0
0
1
1
1
1
1
0
1
5
0
2
1
1
0
0
1
0
0
1
0
2
1
0
1
0
0
2
1
0
1
0
1
1
1
1
2
1
0
0
1
1
2
2
1
1
1
1
2
0
1
0
1
1
1
2
1
2
1
0
1
1
1
1
0
2
1
2
1
1
1
1
1
1
1
1
1
3
2
0
3
1
2
0
0
2
1
0
0
0
1
1
1
1
2
0
0
1
4
1
1
1
0
1
2
0
0
1
5
1
1
0
1
0
2
1
0
0
0
3
1
0
1
0
1
1
2
1
1
1
1
0
2
1
1
0
1
2
0
1
1
0
0
2
0
1
1
1
0
1
0
0
0
1
1
1
2
2
0
1
1
1
0
2
1
1
2
1
1
0
1
0
1
0
1
0
0
0
0
1
0
0
0
2
1
1
0
0
1
2
1
1
1
1
0
0
0
0
0
1
2
0
0
1
1
1
2
2
2
1
0
1
2
1
0
2
1
2
1
1
0
1
0
1
0
1
0
1
1
1
2
1
0
0
0
0
0
1
1
0
0
0
1
0
1
1
0
1
0
1
0
1
1
2
0
0
2
1
0
0
0
0
0
1
1
2
0
0
2
0
1
0
2
3
2
0
1
0
0
2
0
1
0
0
2
1
1
1
0
1
1
1
0
0
0
2
1
2
0
1
2
0
0
2
0
1
1
2
1
1
1
3
0
1
2
0
2
0
2
2
0
2
1
0
1
1
0
0
2
0
1
0
1
1
0
1
1
0
1
1
0
1
0
0
0
1
2
1
0
0
2
2
0
2
1
0
1
0
1
0
0
0
2
2
1
0
0
1
1
0
1
2
1
1
1
0
1
2
0
1
2
0
1
1
1
3
0
2
1
1
2
2
2
0
1
2
2
2
1
2
0
1
0
2
1
1
1
1
2
0
1
1
1
1
1
1
1
0
2
0
0
0
1
1
0
0
0
1
2
0
1
1
1
1
1
1
0
3
0
2
1
1
2
1
2
2
0
0
1
1
0
0
2
0
1
2
1
1
0
2
1
0
0
2
1
1
0
1
1
1
2
1
1
1
0
1
0
0
1
2
2
1
0
0
0
2
1
2
2
1
1
1
1
1
0
1
2
0
0
0
1
0
1
0
0
1
0
1
0
0
0
1
0
0
2
0
1
2
2
0
1
0
0
2
1
1
1
1
2
2
1
1
0
1
1
0
2
0
1
1
0
0
1
0
2
1
1
1
1
1
1
1
1
1
1
0
1
1
1
0
0
0
2
0
0
1
0
2
0
0
0
0
0
1
1
1
1
2
0
2
2
4
0
0
0
0
1
1
0
2
0
2
1
2
2
2
2
0
1
2
1
0
0
2
0
0
1
2
2
1
0
0
1
0
1
0
0
0
1
1
2
0
1
2
2
2
0
0
0
1
1
1
2
1
0
0
2
1
1
0
0
3
0
1
1
2
1
2
2
0
2
2
0
1
1
1
0
1
1
1
0
2
3
2
2
5
1
1
1
1
0
1
1
0
3
1
0
1
0
1
0
0
0
1
1
1
0
1
2
0
1
0
1
2
1
0
0
1
0
2
3
1
2
1
1
0
1
2
2
1
1
0
2
1
0
2
0
0
0
1
1
2
1
2
0
0
0
0
1
1
1
2
0
0
0
2
0
2
2
0
2
0
0
2
0
1
2
1
1
1
0
1
1
0
0
0
0
4
0
2
1
2
1
0
2
2
0
1
2
1
0
1
0
0
1
1
2
2
1
2
1
0
2
1
0
1
1
1
1
0
0
1
1
0
0
0
0
2
1
2
1
0
1
2
1
2
1
0
2
2
0
2
2
2
0
0
0
1
0
1
0
1
1
1
1
1
0
1
0
0
2
0
1
0
1
1
0
0
1
0
1
0
1
1
0
1
2
0
1
1
1
2
1
1
1
0
3
0
3
2
0
0
1
0
1
0
1
3
0
0
2
1
1
0
2
0
1
0
2
1
1
2
0
2
1
0
0
1
0
0
0
1
1
1
2
0
2
0
1
1
2
0
0
2
0
1
0
1
2
0
0
1
3
1
1
0
2
2
1
2
0
0
0
2
1
0
0
1
0
1
1
2
0
1
2
1
2
0
0
2
1
2
1
1
1
1
1
0
2
0
0
0
1
0
0
1
0
1
1
0
0
1
1
1
1
1
0
0
0
0
1
2
0
0
2
0
0
1
1
1
1
1
1
1
2
1
0
2
1
1
2
0
0
1
0
1
1
1
0
1
1
1
0
0
1
1
1
0
0
1
0
2
1
1
0
0
2
0
0
1
1
0
0
1
1
2
1
1
1
2
1
1
2
2
0
0
0
2
0
0
0
1
1
0
1
1
0
2
0
1
2
1
0
1
0
2
2
1
2
2
0
0
2
1
0
1
1
1
0
1
1
0
0
2
0
1
1
0
1
1
1
1
1
2
0
0
1
2
1
0
1
1
1
0
1
1
1
0
0
1
1
1
1
1
1
2
1
1
1
1
0
2
0
0
1
1
1
0
1
1
2
0
2
0
1
0
2
0
1
1
1
0
0
2
2
0
0
1
1
1
1
2
1
1
1
1
1
1
0
0
1
2
0
0
0
1
0
1
1
0
2
0
1
0
2
1
0
0
0
2
0
1
1
1
0
1
2
0
0
1
1
2
2
1
2
1
1
1
0
1
0
0
1
0
2
1
1
0
1
0
2
0
2
1
1
2
0
0
1
2
2
0
2
1
1
1
1
0
1
1
1
1
1
2
1
1
0
1
1
0
1
0
0
1
0
1
1
1
1
1
0
0
0
2
1
1
1
0
1
1
1
2
0
0
2
0
1
0
1
1
1
1
1
2
1
1
1
2
1
1
2
0
0
1
2
2
1
1
0
0
2
1
0
2
0
0
0
2
1
1
2
1
0
1
1
2
1
1
2
0
0
2
2
1
0
1
2
1
1
0
0
0
1
1
0
2
0
2
3
2
0
1
1
2
1
1
2
1
2
0
0
0
1
1
0
0
2
0
1
0
1
0
0
0
0
0
1
1
1
1
1
2
1
2
0
2
1
2
1
0
0
0
1
1
1
0
0
1
1
0
1
0
3
2
1
1
0
1
1
2
0
1
2
2
2
2
1
2
2
2
0
1
1
1
0
0
2
0
0
1
2
0
1
0
0
1
2
0
0
0
0
1
1
2
2
0
1
1
0
1
1
1
1
1
0
1
1
0
2
0
1
0
1
2
1
1
0
2
0
1
1
2
0
1
1
0
0
0
1
2
1
2
0
0
4
1
1
1
0
1
1
1
0
0
1
1
0
1
0
1
2
1
1
1
0
0
0
1
1
1
0
0
0
1
1
2
0
2
0
1
1
1
1
2
1
0
1
1
1
0
0
2
1
1
0
1
2
0
1
0
1
1
1
0
1
2
1
2
2
1
2
3
2
1
1
0
0
1
1
0
0
2
1
1
0
1
0
1
1
0
1
2
2
0
0
2
1
1
2
0
0
1
0
1
2
0
1
0
2
1
0
0
2
1
1
0
2
2
0
1
0
1
1
2
1
0
0
0
1
1
1
0
2
0
1
0
1
2
0
2
1
1
1
1
1
1
0
0
2
1
4
0
0
1
3
0
0
1
2
1
1
1
1
1
1
0
2
1
0
1
1
0
1
0
1
0
0
0
0
1
1
2
2
0
0
0
1
0
0
0
2
1
1
2
0
1
2
1
1
1
1
2
0
1
0
0
1
0
0
0
1
2
2
1
0
5
0
2
1
2
2
1
0
1
0
2
2
1
1
0
0
2
1
2
2
1
2
0
0
1
1
1
0
2
1
1
2
1
2
1
1
2
1
0
1
1
0
1
0
0
1
0
0
2
1
1
0
0
1
0
0
1
0
2
2
1
1
0
0
0
1
0
2
0
1
0
1
0
1
1
0
2
2
0
1
0
1
2
0
2
1
1
1
1
1
1
1
0
2
1
1
1
1
1
0
0
2
1
1
2
1
0
1
1
1
2
1
0
1
1
0
1
0
1
0
1
2
1
1
1
1
0
2
3
0
0
1
0
2
1
1
1
1
1
1
1
1
1
0
1
0
0
1
2
0
1
3
0
1
0
2
0
0
0
0
1
1
1
1
0
1
1
2
0
1
1
2
1
1
0
0
1
1
0
1
1
0
1
0
1
0
1
1
1
2
1
1
1
1
0
2
1
0
1
1
0
1
1
1
0
1
1
1
2
2
1
0
1
1
0
2
1
2
1
0
0
1
1
0
1
1
0
1
1
1
0
0
1
1
1
1
1
0
2
2
0
1
0
2
2
1
2
0
0
1
1
0
1
1
1
0
0
1
1
1
0
1
0
1
1
0
0
1
1
1
1
0
3
0
2
1
1
2
2
1
1
1
1
1
2
1
1
1
1
1
0
1
0
0
1
1
0
0
0
1
2
1
0
1
1
1
1
0
1
0
0
2
2
0
2
0
0
2
0
2
0
1
1
2
1
1
0
2
0
0
1
2
1
0
1
1
2
0
1
0
0
1
1
1
1
1
0
1
0
1
1
0
0
1
2
0
1
0
1
0
1
0
1
0
2
0
1
1
2
0
1
2
1
0
1
0
2
1
3
0
0
0
2
2
1
2
2
2
2
1
1
1
2
0
1
1
1
0
0
0
1
1
1
1
0
2
1
1
1
1
2
1
1
1
1
1
1
0
1
0
0
0
1
1
0
1
1
2
1
0
1
1
1
2
1
1
1
2
1
1
1
1
3
2
1
2
1
0
1
0
0
1
1
3
1
0
1
2
1
1
2
0
1
0
1
0
0
1
0
0
0
1
1
0
1
1
0
1
1
0
1
1
1
0
2
0
3
0
1
0
0
4
1
1
1
1
0
2
0
0
0
0
1
1
0
2
1
1
4
0
2
1
1
2
0
2
1
2
1
1
0
0
1
1
1
0
0
1
2
0
2
0
0
1
0
1
1
0
1
0
1
1
0
0
0
2
1
1
1
1
0
1
2
1
0
0
2
0
2
1
1
1
1
1
2
1
0
2
0
1
1
0
1
1
0
0
2
0
0
1
1
3
1
0
0
1
2
0
3
1
0
1
1
0
2
0
2
2
1
2
0
2
1
1
0
2
2
0
0
2
1
0
2
0
2
1
1
1
1
0
1
0
0
0
0
1
0
0
1
2
2
0
1
2
2
0
0
1
2
1
1
1
0
1
0
1
1
1
0
4
1
1
0
1
1
1
1
2
2
2
1
1
2
1
1
1
0
1
1
2
1
2
1
1
2
2
1
1
2
2
1
0
2
1
2
0
1
1
0
1
2
0
0
0
1
2
1
1
1
0
1
1
0
0
0
1
2
0
0
0
1
1
2
2
2
0
0
0
1
0
1
1
0
2
1
2
0
0
2
0
2
1
2
1
1
1
1
1
1
0
1
2
2
1
0
3
1
1
4
0
1
1
2
1
1
1
1
2
1
1
2
0
1
1
2
2
0
1
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
2
1
1
2
1
1
1
1
2
1
0
1
2
2
2
0
0
3
0
1
0
1
2
1
0
1
0
0
0
2
0
1
2
1
1
2
2
0
3
0
1
0
1
0
0
0
1
1
0
1
2
1
2
0
1
1
1
0
1
2
0
0
0
1
1
0
0
1
2
0
1
1
2
0
3
1
2
0
2
1
1
2
2
1
0
0
0
0
2
2
1
0
1
2
0
1
0
0
0
1
1
2
0
2
1
0
1
0
1
0
2
1
0
0
2
0
2
1
1
1
1
0
0
0
1
1
0
0
1
0
0
1
0
0
1
0
2
1
1
1
0
0
0
1
2
0
1
0
2
0
1
1
1
2
2
1
0
2
1
2
1
0
0
0
1
1
0
0
0
0
1
1
0
1
1
2
0
1
1
1
2
2
1
1
2
1
1
0
1
1
1
1
0
1
0
0
0
2
0
1
1
1
1
2
1
1
1
1
2
3
0
1
2
1
2
1
1
2
2
0
0
1
2
1
1
1
1
0
1
2
1
1
1
2
0
1
2
1
0
1
2
2
1
2
2
1
1
2
2
0
1
0
1
0
1
2
0
0
0
0
2
1
0
2
1
0
0
1
0
2
0
1
1
0
2
1
0
1
0
0
0
1
0
1
0
0
2
1
0
0
1
1
0
1
1
1
1
2
0
2
1
1
1
0
1
1
1
0
0
1
1
1
2
1
1
2
1
1
2
1
1
0
1
1
1
0
0
1
1
1
1
0
1
2
1
1
1
2
0
1
1
1
0
0
1
2
1
0
1
1
2
1
1
1
0
1
0
1
1
1
1
0
1
1
2
1
0
1
1
1
0
0
1
0
0
0
2
2
0
1
0
1
1
1
0
3
1
0
2
1
2
1
0
1
2
3
0
0
2
2
2
0
1
0
2
2
0
1
1
1
0
2
0
1
1
0
0
1
0
1
0
0
1
0
2
2
1
1
0
1
2
0
2
1
0
0
1
1
0
1
2
0
2
1
1
0
2
1
1
1
1
0
1
1
0
2
1
1
2
1
1
0
1
1
0
1
1
0
1
1
1
1
0
2
2
1
2
1
0
0
2
2
1
1
0
0
1
0
0
1
0
0
2
2
1
1
0
0
0
0
0
2
3
0
1
0
0
1
0
0
1
1
0
1
1
0
1
2
1
1
1
1
0
2
0
1
2
1
2
0
1
1
2
0
1
1
0
0
2
0
2
1
1
1
2
0
0
2
0
0
1
1
1
2
1
2
1
2
1
1
1
1
0
0
1
1
2
0
0
1
0
1
1
1
1
0
1
0
0
2
1
1
2
0
6
2
1
2
0
0
0
2
1
2
2
0
1
0
1
0
1
1
2
2
1
1
1
2
1
0
1
1
1
2
0
1
2
0
1
0
2
1
0
2
1
1
0
0
1
1
2
0
1
1
2
0
2
0
0
0
1
0
1
1
1
1
0
0
1
2
4
0
2
1
2
1
0
0
0
0
1
1
1
2
1
1
1
2
1
1
0
1
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
1
0
1
0
1
1
0
1
1
0
1
1
1
1
0
0
0
1
1
1
2
2
0
0
0
2
2
1
1
2
0
1
1
1
2
1
1
1
1
0
1
1
3
0
1
1
0
1
2
1
1
1
2
0
2
0
2
0
1
1
0
0
0
2
0
1
2
1
0
0
0
1
0
1
0
0
2
0
0
1
2
0
0
1
0
1
2
0
1
1
1
0
1
0
0
2
1
1
0
1
2
1
2
0
2
0
2
1
0
0
1
4
0
2
1
2
0
1
1
1
1
0
1
1
0
1
1
2
2
2
1
0
1
2
1
1
0
0
0
1
1
2
1
2
2
1
0
1
1
1
1
1
2
0
1
0
0
1
1
1
1
2
0
0
0
2
1
0
1
2
1
0
1
2
0
0
0
1
1
0
2
0
0
1
1
0
1
0
1
2
0
1
0
0
1
1
2
0
2
1
1
0
1
1
1
2
0
0
0
0
2
2
0
0
0
1
1
0
0
2
3
1
10
2
0
1
1
0
1
0
2
2
1
0
1
2
1
2
1
1
1
0
1
1
1
1
1
0
2
1
1
0
1
0
4
1
2
0
1
1
9
0
0
0
1
1
0
0
0
1
1
1
2
0
1
1
3
0
2
1
1
1
0
2
1
3
0
1
1
1
0
1
0
1
0
0
2
1
2
1
1
0
0
0
2
2
0
1
2
1
0
2
0
0
1
2
0
1
1
2
0
1
0
0
1
1
1
1
1
0
1
0
0
0
0
1
1
1
2
0
2
1
1
0
0
1
1
0
2
1
1
1
1
2
0
0
0
1
0
2
2
0
2
3
0
0
2
2
2
1
0
0
0
2
1
0
2
2
2
1
0
2
1
2
1
0
0
1
1
1
0
2
0
0
0
3
0
1
1
1
1
1
1
0
3
0
1
0
0
0
2
1
0
2
1
1
1
1
1
1
1
1
1
0
1
2
1
2
2
1
1
2
0
1
1
2
1
0
2
1
0
1
1
1
1
1
1
0
2
1
2
1
3
1
1
0
0
1
1
1
1
1
0
1
1
2
1
1
1
1
0
0
0
0
0
2
0
1
5
1
1
0
0
2
1
2
2
1
1
1
2
1
0
1
0
1
1
1
1
1
0
0
1
1
0
0
0
2
1
1
1
0
2
1
2
1
1
1
2
2
0
2
1
1
1
1
1
1
1
1
1
0
0
1
0
0
2
1
0
0
2
2
0
0
1
2
1
1
1
2
1
1
0
2
0
0
0
2
1
1
0
2
1
1
0
0
1
2
1
1
2
1
2
0
0
1
1
2
2
1
0
0
0
0
1
2
1
1
2
1
2
2
0
1
2
0
0
1
4
1
1
2
1
4
1
0
0
1
1
0
1
1
1
2
0
1
0
1
1
1
2
1
0
0
1
1
1
1
1
0
1
1
1
0
1
1
0
1
2
2
1
1
1
1
0
1
1
1
0
0
2
0
1
1
1
2
2
0
2
0
2
1
0
1
2
0
1
1
0
2
2
1
1
0
1
0
0
0
0
2
0
1
1
0
0
2
1
0
0
1
1
0
2
0
0
1
0
2
0
0
1
1
0
0
2
2
1
0
1
0
0
0
0
1
1
0
2
1
1
0
1
2
2
0
0
2
1
1
1
0
1
0
0
1
2
2
0
2
1
1
0
0
1
1
0
0
2
1
1
0
1
1
0
0
0
2
2
0
1
0
0
1
1
0
0
1
0
1
0
1
1
1
1
2
0
0
2
1
1
2
1
1
1
2
1
0
0
0
1
1
2
0
1
2
0
1
0
1
2
0
1
1
1
1
0
0
1
1
0
1
1
1
1
1
2
2
0
0
2
1
0
0
2
2
0
1
1
2
1
0
2
2
0
1
0
1
1
2
1
2
2
0
0
1
1
2
3
2
0
2
2
2
0
0
1
1
0
2
1
0
0
0
1
0
1
1
0
0
0
1
2
1
2
1
2
0
1
1
2
1
0
1
3
1
1
1
1
1
0
2
0
0
1
2
1
1
2
1
0
1
1
2
1
0
2
1
1
2
0
1
1
2
0
1
2
2
2
0
1
1
0
0
1
2
1
0
2
1
1
2
1
0
0
0
2
2
0
1
3
0
1
0
0
2
1
1
1
2
2
0
2
0
0
1
0
1
1
0
0
2
1
0
1
2
1
0
2
0
2
1
0
1
1
2
2
0
0
2
1
0
0
0
1
0
0
0
2
0
0
1
0
1
1
2
0
2
0
1
1
1
1
2
1
1
2
1
1
1
0
1
0
1
0
1
2
2
0
0
1
1
1
0
1
0
0
0
1
0
1
1
1
1
0
1
1
0
0
1
2
1
2
0
1
1
1
0
0
0
2
2
0
2
1
1
0
0
0
0
2
2
0
0
1
0
0
1
1
2
2
1
1
2
0
1
2
0
1
1
2
0
0
0
1
2
3
0
1
0
0
1
2
2
1
1
2
0
2
1
2
0
1
1
1
1
1
1
0
1
2
0
2
1
1
1
1
2
0
2
0
2
0
2
1
1
1
0
9
1
1
2
0
1
0
1
0
0
1
0
1
2
0
2
0
1
1
1
1
1
0
0
1
2
0
1
1
1
0
1
1
0
2
0
2
2
0
1
1
1
1
1
1
0
1
0
0
2
1
2
1
1
2
2
0
1
0
2
2
0
1
2
1
0
0
1
1
0
1
2
0
1
1
1
1
1
0
1
2
0
0
1
0
1
0
0
2
1
2
1
1
1
2
0
4
0
0
0
0
1
0
1
1
2
1
2
1
0
2
0
0
0
1
1
1
0
2
0
1
0
1
1
0
1
0
1
0
1
1
0
0
1
1
0
2
0
1
0
0
2
0
0
1
0
1
1
1
1
0
1
1
1
1
0
0
0
3
2
0
2
2
0
0
1
1
0
1
1
2
0
2
2
1
1
0
0
1
1
2
1
1
0
1
1
1
0
1
0
1
0
2
1
1
1
0
0
1
0
1
2
0
1
0
0
1
2
1
1
1
1
1
0
0
1
2
2
1
2
0
0
5
2
1
1
0
0
1
1
0
1
1
1
2
0
0
0
1
1
1
0
0
2
1
0
2
2
1
2
2
1
1
2
1
0
0
0
0
1
0
1
2
0
2
1
0
1
0
0
0
1
1
0
1
0
0
0
0
0
2
1
1
0
1
1
1
1
1
0
1
1
1
0
1
2
1
1
0
0
0
0
0
0
4
1
2
1
0
1
1
2
1
2
1
2
0
1
2
1
1
2
0
1
1
2
1
2
0
1
1
2
0
2
2
1
1
0
0
1
2
0
1
1
0
0
1
1
1
1
0
0
1
1
1
1
1
0
0
2
0
2
1
2
0
1
1
3
0
1
0
0
0
0
0
0
0
0
1
0
1
1
1
1
1
1
1
2
1
0
2
0
2
0
1
2
1
1
1
1
1
0
0
1
2
1
1
1
2
1
2
0
3
1
1
2
1
2
1
0
1
2
0
2
1
1
1
1
1
1
2
0
2
0
0
1
0
0
1
1
1
1
2
0
1
1
1
2
1
1
1
0
1
0
1
2
2
0
0
0
2
1
1
1
1
0
1
1
1
1
0
2
0
1
2
2
2
0
1
1
2
0
0
0
1
0
1
1
0
0
1
1
1
0
0
1
1
1
1
1
0
1
1
0
2
2
1
2
2
1
0
0
0
2
1
0
2
1
0
1
1
1
1
0
0
2
1
2
0
2
0
1
0
0
2
0
2
1
1
2
2
0
2
1
0
1
0
2
1
0
1
2
2
2
0
0
1
1
1
2
0
1
1
1
0
1
2
2
0
2
0
2
0
2
0
2
1
2
2
1
1
2
0
1
2
2
0
1
2
1
0
1
0
0
0
0
3
2
1
1
0
1
1
2
1
1
0
0
2
1
0
2
0
2
3
0
0
0
1
0
1
1
3
0
2
0
0
0
1
1
0
1
0
1
1
2
1
1
1
0
0
0
2
1
2
0
1
1
0
1
0
1
1
1
1
1
0
0
1
1
0
2
1
0
0
1
0
0
1
2
0
2
0
0
1
2
1
2
1
1
1
0
1
2
1
2
0
1
1
1
0
0
0
1
0
1
1
1
1
1
1
0
0
1
2
0
1
1
0
0
1
2
0
2
1
2
2
0
0
1
1
2
0
1
1
1
2
1
1
2
2
1
0
1
0
0
1
2
0
0
0
2
1
2
0
1
1
1
0
1
1
1
1
2
1
1
0
0
0
0
0
0
2
1
1
1
1
0
0
1
0
0
1
0
2
2
1
1
1
1
1
1
1
2
1
2
1
0
2
0
1
3
0
0
1
0
1
0
1
1
1
0
2
1
1
1
2
2
1
2
1
1
1
1
0
2
1
1
2
2
1
1
1
1
1
1
2
1
2
1
0
1
1
1
3
1
1
0
1
2
0
0
1
1
1
2
0
0
1
2
1
0
2
1
0
1
0
0
0
0
0
1
2
2
1
0
1
0
2
0
1
1
0
1
1
1
0
1
0
2
0
1
0
1
1
1
0
0
0
1
1
0
0
0
1
3
2
1
1
2
1
2
0
2
1
1
0
0
0
0
1
2
2
1
0
0
1
0
1
1
2
0
0
0
1
1
1
1
1
1
0
2
2
0
2
0
1
2
0
1
1
0
0
0
1
1
0
0
1
2
0
1
0
1
0
0
1
0
0
2
3
0
2
1
2
1
1
1
1
2
0
0
1
0
1
0
1
0
1
0
2
2
1
0
1
0
1
2
1
0
0
0
1
0
1
0
1
1
0
0
1
0
1
1
2
1
2
0
1
0
1
2
1
2
3
1
0
1
1
1
0
0
1
0
0
1
1
1
1
1
0
2
1
0
3
0
1
1
1
1
0
1
0
1
2
0
1
2
0
3
0
0
2
2
1
1
0
0
0
1
0
1
0
2
1
0
1
1
1
0
1
0
0
0
1
1
1
1
1
1
0
2
1
1
0
1
0
1
1
0
1
1
1
2
1
2
1
3
0
1
1
0
0
1
1
0
1
0
0
0
1
0
1
1
1
0
1
1
2
2
2
0
1
2
0
2
2
0
0
1
0
1
2
2
1
1
1
1
1
0
1
2
1
0
1
1
1
1
1
0
0
0
0
0
0
1
1
2
1
1
1
1
1
0
1
0
1
1
0
0
2
2
2
1
0
0
2
0
2
1
0
0
2
0
2
1
2
0
1
0
2
0
2
2
1
0
1
1
1
0
0
1
1
1
1
2
2
2
2
0
1
0
1
0
2
1
0
2
2
1
1
0
0
1
0
1
1
1
1
1
2
0
1
1
2
0
1
2
1
2
0
1
0
1
1
2
1
1
1
1
1
0
1
1
1
2
1
0
1
0
0
2
0
1
0
1
2
1
0
2
0
0
0
1
2
2
0
1
0
1
1
1
2
3
0
1
1
2
1
1
1
1
1
2
0
2
1
1
1
0
1
1
0
0
1
2
1
1
1
0
0
1
1
1
1
0
2
0
2
1
0
1
2
0
1
0
2
0
0
2
0
2
1
0
1
0
2
1
0
1
1
1
1
1
1
1
2
2
2
2
0
2
1
0
0
2
2
1
1
0
2
1
3
2
0
0
1
2
1
2
0
0
0
0
1
1
0
1
0
0
2
1
1
2
1
2
0
2
1
2
1
2
1
2
2
3
0
0
0
0
1
1
0
1
1
1
1
1
1
2
1
1
0
0
2
1
1
0
2
2
0
2
1
1
0
0
2
1
1
1
1
1
2
2
2
1
1
0
1
0
0
1
1
1
1
0
1
0
0
0
2
0
2
1
1
0
0
1
0
1
1
1
3
1
1
1
2
0
0
2
1
2
1
1
0
1
2
1
2
1
0
2
0
0
0
0
0
1
1
1
0
1
1
1
0
0
2
0
0
1
2
1
2
2
1
1
2
0
0
1
1
1
0
2
1
0
1
1
0
2
0
1
0
1
2
0
1
0
0
0
1
2
2
2
0
0
0
2
1
0
2
2
0
2
1
0
1
0
0
0
1
2
0
0
2
1
0
0
0
2
1
0
1
1
2
0
1
0
0
1
1
1
1
0
1
0
0
1
2
1
2
1
2
1
1
1
0
0
0
2
1
1
1
5
0
0
0
1
0
1
0
1
0
0
0
1
1
0
1
2
0
1
0
0
0
1
1
0
1
2
0
1
0
1
0
1
1
1
0
1
0
1
1
1
1
1
1
2
0
1
1
1
1
1
1
0
0
0
2
0
1
0
0
1
3
1
1
1
1
0
2
0
1
1
1
2
2
2
1
0
0
2
1
1
1
1
0
2
0
0
1
0
0
2
0
2
0
0
1
1
0
2
0
1
0
0
1
0
0
0
3
1
0
0
1
0
0
0
1
0
2
1
1
1
1
1
1
2
0
1
0
1
1
1
1
2
1
1
0
1
2
1
0
1
2
1
2
1
1
1
0
1
2
0
1
0
0
1
1
0
2
2
1
1
0
1
1
0
1
2
1
2
3
2
3
3
0
0
0
1
0
2
0
0
0
1
1
1
0
2
1
1
1
1
1
1
1
0
2
1
0
1
0
2
0
0
1
1
0
1
1
1
1
2
1
1
0
2
1
1
1
1
2
0
1
1
0
1
1
1
0
1
1
1
2
1
0
1
1
0
1
1
0
1
2
0
2
0
0
3
0
0
0
1
1
1
0
0
0
2
1
0
1
0
1
1
0
2
2
1
1
1
0
1
2
1
1
0
0
0
1
0
2
0
2
0
2
0
0
2
0
1
0
2
0
1
1
1
0
1
2
0
2
1
2
1
1
1
0
1
0
0
0
1
0
1
0
2
0
1
1
0
1
1
3
0
1
0
2
2
1
2
0
1
1
1
1
0
1
0
1
2
2
1
1
0
2
2
1
0
1
1
2
1
2
1
0
0
1
0
1
1
1
3
2
1
2
2
0
2
0
0
1
0
2
2
0
1
2
1
0
1
0
2
2
0
1
2
2
1
1
1
1
2
2
1
1
1
2
2
1
1
0
1
0
0
1
1
1
1
1
1
1
1
1
1
1
2
1
1
3
1
2
2
0
1
2
1
2
1
2
1
1
1
0
1
2
0
1
0
1
1
3
1
0
2
0
2
1
1
2
0
0
2
2
2
0
1
1
0
0
1
0
0
0
0
2
2
2
1
2
2
0
2
0
2
1
1
1
2
0
0
0
2
1
2
1
0
1
0
0
1
0
0
2
1
2
1
0
1
1
1
0
1
2
0
0
1
1
1
2
0
1
1
1
1
1
0
1
1
0
1
1
0
1
1
2
1
1
0
1
1
2
1
1
1
2
1
0
0
1
0
1
0
0
2
0
0
1
0
1
1
1
1
0
0
0
0
1
1
0
2
0
1
1
1
1
1
0
0
1
2
0
2
2
2
1
0
1
1
0
2
0
1
0
0
4
1
0
0
0
1
1
0
1
2
1
2
2
1
0
1
0
1
0
0
1
2
2
1
2
1
2
1
2
0
0
0
1
0
1
0
0
1
0
1
0
2
0
1
1
2
0
1
1
0
0
2
2
0
0
1
1
1
0
1
0
1
1
2
0
1
1
2
2
2
1
1
0
0
1
1
1
1
1
2
0
1
1
1
0
1
1
0
2
0
3
2
1
2
2
1
2
1
1
0
1
0
0
2
2
1
1
2
1
1
2
1
1
1
2
0
0
0
2
2
1
1
1
0
0
0
1
2
1
1
2
1
1
1
0
1
0
2
1
1
1
1
1
0
1
0
2
1
0
2
0
0
1
2
0
2
1
2
1
1
0
1
1
0
1
0
1
0
0
2
0
2
0
2
2
0
1
2
0
2
2
1
2
1
0
0
2
1
2
0
0
1
1
2
1
2
1
0
1
0
0
2
2
2
2
1
0
1
0
0
2
2
1
2
1
2
2
0
0
1
2
1
1
1
1
0
2
1
1
1
0
0
2
1
1
3
0
1
1
1
0
0
1
1
0
0
1
1
1
2
1
0
0
2
1
2
0
1
1
0
0
0
1
0
2
0
2
1
1
0
1
0
0
0
3
0
0
0
1
1
1
1
2
2
1
1
0
1
0
1
2
1
1
1
0
1
1
2
0
0
1
2
2
1
2
0
0
0
1
1
2
0
2
0
1
2
1
0
1
1
1
1
0
1
2
1
2
1
0
0
0
0
2
1
0
0
0
0
1
0
0
1
0
1
2
1
2
1
0
1
1
0
1
2
3
0
1
2
1
0
1
0
1
0
1
0
0
0
1
0
1
0
1
1
3
0
0
0
0
1
0
2
0
1
2
2
2
1
1
1
1
1
1
2
2
2
1
1
1
1
1
1
1
0
1
2
1
1
1
1
1
3
2
1
0
2
1
2
0
1
0
1
0
1
0
0
1
1
1
0
1
0
0
0
1
1
1
1
0
0
1
1
0
0
2
0
1
2
1
1
0
0
2
2
1
1
0
1
2
1
0
1
0
1
1
1
1
0
2
1
2
1
1
1
1
0
1
1
2
0
2
0
1
0
0
1
3
1
1
0
1
2
2
1
1
1
2
0
1
2
1
0
1
1
1
0
1
0
0
2
1
0
1
0
2
1
0
0
1
1
0
1
2
1
1
1
0
1
0
0
1
1
2
1
0
0
1
2
0
1
0
1
2
1
1
1
1
1
1
1
0
0
0
1
1
0
1
1
1
0
3
0
2
0
0
1
1
1
1
3
1
1
1
2
1
1
2
1
0
0
2
2
0
1
0
0
1
2
1
1
1
2
1
2
0
1
0
2
0
0
1
2
3
0
1
1
1
2
1
0
0
0
0
1
2
1
0
1
2
1
2
1
1
1
2
1
1
2
0
2
0
0
1
1
1
0
1
1
1
0
1
1
1
1
1
1
1
0
1
2
1
2
1
1
1
2
1
1
1
1
1
2
2
0
1
1
0
2
1
0
2
0
2
1
1
1
2
0
1
2
0
2
0
1
1
1
2
0
1
2
1
0
1
2
1
2
0
0
2
1
0
1
2
1
2
0
0
1
2
1
0
2
0
1
3
0
1
0
1
0
2
2
2
1
1
1
0
1
0
1
2
0
1
1
2
1
1
2
1
0
2
1
1
0
1
0
2
1
0
1
0
2
0
1
1
0
1
2
1
3
0
2
2
2
1
1
1
1
0
1
0
1
2
0
1
0
0
0
1
1
1
1
1
1
1
2
1
1
0
0
0
2
1
1
1
0
2
1
1
1
2
1
1
0
0
1
0
1
1
0
1
1
0
2
0
1
0
2
2
1
1
2
2
0
1
1
0
2
1
0
2
0
1
1
0
1
0
1
1
1
1
0
1
2
1
0
0
1
2
2
2
1
0
0
1
2
1
2
1
1
1
0
2
1
2
1
1
2
2
0
3
1
1
0
2
0
1
1
1
2
0
1
1
2
1
0
1
1
0
1
0
0
2
2
1
2
0
1
0
1
2
1
0
1
1
2
0
1
0
0
1
2
0
1
0
1
0
2
0
1
0
2
0
0
2
1
1
0
2
1
0
2
2
2
2
1
2
0
0
1
2
1
1
1
1
1
1
1
0
1
0
1
2
1
1
0
1
0
1
1
0
0
0
1
0
1
1
2
1
1
0
1
1
2
0
2
1
0
1
2
2
1
1
1
0
1
1
0
1
0
1
1
0
2
1
0
0
1
1
0
2
1
2
1
0
0
2
2
1
1
1
2
1
1
0
1
0
1
1
0
2
1
2
1
2
1
1
1
1
1
1
0
1
2
1
1
0
0
1
1
1
1
1
0
1
1
1
1
0
0
2
0
1
0
1
1
1
2
0
0
0
2
2
2
2
1
1
2
4
1
2
2
2
0
1
1
1
1
0
0
1
1
0
2
1
1
1
1
1
1
1
1
0
1
1
0
0
0
3
1
2
0
1
1
1
0
2
2
0
1
1
1
2
2
3
1
1
1
1
1
1
1
1
1
2
2
0
1
4
0
0
2
1
2
1
0
1
0
0
2
0
0
1
0
2
0
1
0
2
1
1
2
0
1
0
0
0
0
1
1
2
2
0
3
1
2
2
1
0
1
2
2
1
1
2
1
4
1
1
2
1
1
2
1
0
0
1
1
0
2
2
0
1
2
1
0
1
2
1
0
1
1
0
1
1
0
2
2
1
2
1
1
1
1
0
0
0
2
2
1
1
2
0
1
0
0
2
0
1
2
1
0
1
1
0
2
0
2
1
1
1
0
1
0
0
1
1
1
1
1
0
1
1
0
2
2
1
0
0
2
2
2
1
0
1
1
0
1
2
0
0
0
1
0
1
1
1
0
1
0
2
2
1
0
0
2
2
1
1
0
1
0
0
2
1
2
0
0
2
0
1
0
0
1
1
2
1
0
1
0
0
2
1
3
1
0
1
0
2
0
1
2
0
1
2
3
0
0
0
0
1
0
2
2
0
0
0
0
0
1
0
5
0
0
1
1
1
0
1
1
2
1
1
2
2
0
1
1
2
1
1
2
0
2
2
1
1
1
0
2
2
2
1
1
1
0
4
1
0
1
0
1
1
1
1
2
2
2
1
3
1
1
2
0
1
1
1
1
2
1
2
2
0
1
1
0
2
0
1
1
0
1
2
2
1
0
1
1
0
1
0
2
1
0
0
1
1
0
3
0
1
0
1
2
1
1
0
2
1
0
2
2
1
1
2
0
1
0
1
0
0
2
1
0
2
2
2
1
2
1
0
2
1
1
0
2
0
1
1
2
0
1
1
1
1
0
1
1
2
1
1
1
0
1
1
2
1
2
0
0
0
2
2
2
0
1
2
0
2
1
0
0
1
2
4
1
0
1
1
1
1
0
2
0
0
2
1
1
0
2
1
0
2
1
0
1
0
1
0
1
0
0
0
2
1
0
1
1
0
0
2
2
1
1
1
0
1
1
2
1
0
0
1
1
2
0
2
1
0
1
2
2
1
1
0
1
2
1
1
0
0
1
0
1
0
0
1
0
2
2
1
2
1
0
0
1
0
2
1
1
0
1
0
0
1
0
2
2
1
1
1
0
2
0
1
2
0
1
0
1
2
0
0
0
0
0
0
2
1
2
1
0
0
1
1
1
0
0
0
2
1
2
1
1
0
1
0
0
2
0
1
0
1
0
0
1
1
2
2
2
1
0
2
1
1
1
0
1
0
1
2
2
0
0
2
0
0
2
0
0
1
1
1
0
0
2
0
2
2
1
1
2
1
1
0
2
1
1
0
0
1
0
0
1
0
2
1
1
1
1
0
1
1
1
1
0
0
1
0
0
1
0
0
0
0
0
1
2
1
2
0
1
0
1
4
2
1
0
1
1
1
1
1
0
2
1
1
1
1
1
0
1
0
0
0
1
1
2
2
1
0
0
1
1
1
1
1
0
0
0
0
2
1
2
0
0
0
1
1
0
0
1
1
1
0
2
1
2
1
0
2
0
0
0
2
1
1
2
2
1
2
1
0
0
1
2
2
1
0
1
1
3
0
2
1
1
1
1
2
1
0
1
1
2
1
2
1
2
0
0
0
0
1
0
2
2
1
1
1
2
1
1
0
1
2
2
0
1
2
0
0
0
1
1
2
1
1
0
0
1
0
0
1
0
1
2
0
0
1
1
1
2
1
2
1
1
0
0
0
2
1
0
0
2
1
1
4
1
0
1
2
1
0
1
0
1
0
0
2
0
1
1
1
0
2
0
1
0
1
1
0
1
0
2
0
2
1
0
1
1
2
1
0
1
1
1
1
3
0
0
2
0
2
1
0
2
1
0
0
1
0
1
1
0
1
1
1
2
1
0
1
1
1
2
0
0
0
2
1
1
2
0
1
2
2
1
1
1
2
0
1
0
2
0
1
2
0
0
0
0
1
1
1
1
1
1
1
3
1
2
2
1
1
0
1
1
1
0
1
2
1
0
1
1
1
1
1
2
3
2
1
1
1
1
1
1
1
0
2
2
2
0
0
2
0
2
1
1
0
2
1
0
1
2
0
1
0
1
2
2
1
1
0
1
1
2
0
1
1
1
2
2
0
1
0
0
1
2
0
2
5
0
2
1
1
2
2
1
2
0
1
1
0
1
0
1
1
0
1
2
0
1
1
1
0
1
0
3
2
1
0
1
1
1
1
1
0
1
2
1
1
2
2
2
0
0
0
0
1
0
1
0
1
1
0
0
1
2
0
0
2
2
2
0
1
5
0
0
0
1
1
1
2
1
0
0
0
3
0
2
1
3
0
0
0
2
2
0
1
2
1
0
2
2
0
0
0
0
1
1
1
1
0
2
2
2
1
1
0
3
0
1
0
1
0
1
1
1
0
2
0
0
2
2
0
1
2
0
0
1
0
2
0
1
0
1
0
0
0
0
1
0
0
1
0
2
1
0
1
0
2
0
1
2
0
1
2
0
2
2
0
0
1
1
1
1
3
0
0
1
1
1
0
0
0
1
0
1
2
2
2
1
0
1
1
1
0
1
1
1
2
1
0
1
1
0
1
0
2
2
1
1
0
0
0
0
1
1
0
1
2
1
1
1
0
2
0
0
1
1
1
1
0
2
1
2
0
0
1
2
2
2
2
1
1
2
0
0
1
0
0
1
0
1
2
0
0
2
0
1
2
1
0
1
0
1
1
3
1
0
0
1
2
1
0
1
2
2
2
1
1
0
0
1
1
1
1
3
2
0
0
0
2
2
0
2
1
1
0
1
1
1
2
3
1
2
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
2
2
0
0
1
1
2
1
1
1
0
0
1
0
1
2
0
0
0
0
2
2
1
0
2
2
2
2
1
1
1
2
0
1
2
1
0
0
2
1
1
1
1
1
0
2
1
1
2
1
0
1
2
0
1
0
1
1
2
1
1
0
1
0
0
0
1
0
1
0
2
0
2
1
1
1
0
2
2
0
1
1
1
0
1
1
1
0
1
2
2
2
0
2
2
0
0
1
2
0
1
0
2
2
2
1
1
2
1
1
0
1
1
1
0
0
2
0
2
2
2
1
0
1
0
2
0
1
0
1
1
1
1
0
1
2
5
3
2
2
1
2
1
1
1
2
0
1
1
2
1
1
2
1
0
0
1
0
1
1
0
0
0
1
1
0
1
0
2
0
2
1
0
1
2
0
2
2
1
0
1
1
2
2
0
1
0
1
1
2
0
1
0
1
1
2
1
0
1
1
1
2
1
2
1
0
0
1
0
1
0
2
0
0
2
1
1
0
1
1
0
2
2
1
1
1
1
2
2
1
1
0
1
0
0
0
0
1
0
0
1
2
1
0
0
2
0
0
2
0
2
1
2
1
1
1
1
0
1
1
1
0
2
1
2
1
1
2
2
2
1
1
3
1
0
2
2
2
0
2
1
1
3
1
2
0
0
1
2
0
0
1
1
0
1
1
0
1
1
1
1
0
2
1
2
1
3
1
0
2
2
1
1
0
2
0
1
2
0
0
0
1
0
1
1
1
1
0
0
1
1
0
0
1
1
1
1
2
1
2
1
1
0
1
1
1
2
1
1
2
1
0
1
0
1
0
0
2
1
0
3
0
0
1
1
1
2
2
2
1
0
0
0
0
0
1
2
0
2
0
0
1
0
0
0
2
2
0
1
0
1
1
0
0
1
0
2
1
0
1
1
0
0
0
1
1
1
1
0
1
0
0
0
0
1
0
0
2
1
0
0
1
1
1
1
2
0
1
0
2
1
1
0
1
0
1
1
1
1
0
0
2
0
0
0
1
1
1
0
1
1
2
0
1
2
2
1
0
2
2
1
0
1
0
1
0
0
1
0
2
1
1
2
1
1
1
1
0
1
1
2
1
1
2
1
0
1
1
1
1
0
1
1
1
2
0
0
0
1
0
2
0
0
0
0
3
1
1
0
0
1
1
1
0
0
0
2
2
0
2
2
0
2
0
0
0
1
0
0
0
2
1
0
0
0
1
3
1
2
1
1
2
1
0
1
0
0
0
1
0
3
2
1
2
1
1
1
0
1
1
0
0
1
0
1
1
1
1
1
0
1
1
2
0
1
2
0
1
1
1
1
2
1
1
2
1
1
2
0
2
1
2
1
2
0
0
1
1
1
1
2
1
2
0
2
1
1
1
1
2
0
0
1
0
0
1
3
1
1
0
1
1
0
2
2
1
0
2
0
1
2
0
1
2
1
2
1
2
2
1
0
2
1
0
1
1
1
1
1
0
2
1
1
0
1
1
2
1
1
1
1
1
0
0
1
1
1
2
0
0
1
0
1
2
1
2
1
2
1
0
2
2
2
1
0
0
1
0
1
0
1
0
1
2
1
0
1
0
1
2
0
0
1
1
1
2
1
0
0
1
2
1
1
0
1
1
1
1
0
1
0
0
1
1
1
0
1
2
0
0
0
2
0
2
0
1
2
0
0
1
1
0
2
2
1
1
1
2
1
0
0
2
1
0
2
1
1
2
1
2
1
1
2
2
1
0
3
0
1
1
0
1
0
0
2
0
1
1
1
0
1
2
0
2
3
2
1
1
1
1
1
1
1
1
1
0
1
2
0
1
2
0
0
0
0
1
1
0
1
0
1
1
0
0
1
2
0
0
1
1
0
0
1
1
1
1
0
2
1
1
1
1
1
0
0
1
1
1
1
1
1
1
1
2
2
3
1
0
2
2
1
1
0
0
1
1
1
2
0
2
0
2
1
0
0
1
1
1
0
2
0
0
0
1
1
1
1
2
2
0
2
1
1
1
2
1
1
1
1
0
0
1
1
1
1
1
0
1
2
0
0
2
1
0
2
1
2
1
1
1
3
0
1
2
1
6
2
3
1
1
3
0
0
2
0
0
0
0
1
2
1
1
1
0
1
1
1
0
0
1
0
1
0
0
2
1
1
2
1
0
1
1
0
1
2
1
2
0
0
2
0
0
1
0
2
1
1
0
0
1
1
2
1
0
2
1
1
1
2
0
2
1
1
1
1
1
1
0
2
0
2
0
0
1
1
3
0
0
1
2
2
1
2
2
2
1
1
2
0
1
1
1
1
1
0
1
3
2
3
1
2
1
2
3
1
0
0
2
0
0
2
1
1
0
0
2
1
2
1
1
1
0
0
1
1
0
0
0
0
0
2
0
0
0
1
2
2
2
1
1
0
0
1
1
1
1
1
1
1
0
1
0
1
0
2
0
1
1
0
0
1
1
1
1
1
1
1
0
0
1
1
0
1
2
1
0
1
0
0
0
2
1
1
0
1
1
1
0
1
1
1
1
2
2
1
1
1
0
0
0
0
0
2
2
1
1
2
0
1
0
1
1
0
2
0
1
1
0
1
1
2
1
0
1
1
2
0
0
2
2
2
1
0
0
2
1
1
1
1
1
2
1
1
1
1
0
0
0
1
1
2
1
0
1
0
1
1
0
0
0
1
1
1
1
2
1
1
1
0
1
1
0
1
2
1
2
1
1
2
1
1
0
0
1
3
1
1
1
0
1
1
3
0
1
2
1
2
0
1
0
0
1
1
1
2
1
0
1
0
1
1
2
2
1
0
1
2
0
1
0
1
4
1
1
0
0
0
1
2
0
0
0
2
0
0
2
0
2
1
0
0
1
1
2
2
0
2
1
1
0
0
1
0
2
2
0
0
1
1
1
1
1
1
1
1
1
2
0
2
2
1
0
1
0
1
2
3
0
0
0
1
0
1
1
2
1
1
0
0
2
2
0
2
2
1
0
1
0
1
1
0
1
1
1
3
2
1
0
0
1
0
2
2
0
2
0
2
0
0
0
1
2
2
1
1
1
0
2
1
1
1
0
1
0
1
1
0
0
1
0
0
0
0
0
1
3
1
0
1
1
1
0
1
1
2
1
1
2
1
3
0
2
0
2
1
1
2
0
2
2
1
1
1
2
2
1
0
2
0
1
0
1
0
1
2
0
1
1
2
1
2
1
0
1
2
2
0
0
0
2
1
2
1
0
2
0
0
1
2
1
1
1
2
1
1
1
1
1
2
1
1
0
1
2
1
0
0
1
0
1
1
2
1
2
1
1
0
1
1
1
0
0
0
1
1
0
2
1
1
1
0
1
0
0
0
0
1
1
2
2
0
2
0
1
3
1
0
1
0
1
1
0
1
2
0
1
1
1
1
1
1
1
0
0
1
1
2
1
1
0
0
1
1
2
1
0
0
1
0
1
2
0
1
2
2
0
1
1
1
2
0
1
2
1
1
0
2
1
0
2
3
1
1
0
1
3
0
2
1
1
2
1
1
1
2
0
1
1
0
1
1
1
1
1
2
0
1
0
2
2
1
1
0
1
1
0
2
0
0
1
1
0
0
0
1
0
1
0
1
1
1
1
0
2
1
1
1
0
1
1
1
0
4
2
0
0
1
1
1
1
0
2
2
0
1
1
0
1
0
1
1
6
1
1
1
2
1
1
1
1
1
2
1
1
1
0
2
2
1
2
0
1
1
1
1
1
0
1
1
4
1
1
1
2
0
0
0
0
0
2
1
0
1
1
0
1
2
2
0
2
0
2
0
1
1
1
2
0
1
0
1
0
1
2
3
0
1
0
0
1
0
1
1
2
2
2
1
0
1
2
1
1
2
1
0
1
1
0
1
1
1
2
0
2
1
2
1
0
1
2
1
1
0
1
1
1
1
1
3
1
2
0
0
1
0
1
0
1
2
1
1
2
2
0
1
0
2
1
0
2
0
2
1
0
1
2
1
3
0
2
0
1
0
0
1
1
0
3
2
0
2
0
0
1
0
2
0
2
0
2
0
1
1
1
0
0
1
1
1
1
2
2
1
1
0
0
2
1
1
0
1
0
1
2
1
2
0
0
2
2
1
1
0
2
1
1
2
1
0
0
1
0
0
0
1
0
1
1
0
0
0
1
2
0
0
2
2
0
2
1
1
1
1
0
2
0
1
0
3
1
1
2
1
1
1
1
2
1
1
2
2
1
1
0
2
0
1
1
3
2
1
0
2
1
1
1
1
1
2
0
0
1
0
2
2
1
0
0
1
2
2
1
0
0
0
0
0
0
0
1
0
1
1
1
2
1
2
1
1
2
1
0
0
2
2
0
0
1
1
0
0
0
4
0
2
1
0
3
1
0
0
1
0
1
2
1
1
1
1
1
0
0
2
2
2
1
1
0
1
0
1
2
0
1
1
1
0
0
1
4
1
2
2
2
2
1
1
2
1
1
1
0
1
1
0
1
1
1
1
0
3
0
1
1
1
0
1
0
1
0
1
1
1
2
0
0
2
1
0
0
1
2
1
0
0
2
2
0
1
1
2
0
1
1
1
1
3
1
1
1
1
1
1
0
0
0
0
2
1
1
0
1
1
2
1
1
0
0
1
1
2
2
0
0
0
2
2
0
0
1
1
0
4
1
1
2
1
1
1
2
1
0
1
0
1
1
1
1
0
0
2
1
0
0
1
0
2
2
1
0
2
0
1
0
1
2
0
0
1
1
0
1
2
1
2
2
0
1
0
1
0
2
1
1
1
0
0
0
1
0
2
2
2
1
2
2
1
0
0
0
1
1
4
0
1
1
1
0
2
1
1
1
0
0
0
1
1
2
1
1
1
1
1
0
2
1
0
1
1
2
2
0
1
0
1
2
1
1
0
0
0
0
0
2
1
1
0
0
0
1
1
0
1
2
0
1
1
1
1
1
1
1
1
2
0
1
2
3
0
4
0
0
1
2
1
1
4
0
1
2
0
1
1
2
2
0
1
0
1
0
1
2
2
0
1
1
0
0
0
3
0
2
1
1
1
1
1
0
0
0
0
1
0
1
2
0
1
1
1
1
0
2
0
3
0
2
1
0
1
1
0
1
0
1
0
1
0
2
1
2
1
0
1
1
1
2
1
2
0
0
1
1
0
0
0
0
1
1
2
2
1
1
1
1
1
0
0
1
1
1
1
0
1
1
0
1
0
0
3
0
1
2
0
2
0
2
1
1
0
1
1
1
1
0
0
2
1
1
1
1
1
2
1
2
1
1
0
0
1
0
1
0
0
0
1
1
1
2
0
0
0
3
2
1
1
1
0
1
2
0
0
0
0
0
0
1
0
0
1
1
1
2
1
2
2
0
0
1
1
0
1
1
0
1
0
1
0
0
1
0
0
2
2
0
0
0
0
0
0
0
1
2
0
1
1
2
0
1
0
0
0
1
2
0
0
0
1
1
3
0
1
2
0
1
1
0
1
0
2
0
1
0
1
0
0
0
2
2
1
2
0
2
0
2
1
1
1
1
1
1
0
0
0
1
2
0
0
1
1
0
2
1
1
1
1
0
2
2
1
0
2
1
1
0
0
1
1
0
1
3
1
0
0
1
1
1
0
2
2
2
2
0
2
1
2
0
1
1
2
1
1
1
1
0
1
0
0
0
1
1
1
1
2
1
0
1
1
0
1
0
1
1
1
0
2
1
0
1
2
3
1
1
1
2
0
1
1
1
2
1
0
1
1
1
1
1
0
0
0
1
0
2
1
1
2
0
1
0
1
1
0
1
0
2
1
1
2
1
0
0
2
1
1
0
1
1
1
1
2
2
1
1
1
1
1
0
1
1
0
1
2
0
1
1
0
1
2
1
1
0
0
2
0
1
1
1
3
2
0
0
1
1
0
2
0
1
3
1
1
0
0
1
1
0
0
2
0
4
2
1
2
2
1
1
2
1
1
2
0
1
2
0
2
1
2
1
0
0
2
0
1
2
1
1
0
0
1
2
1
2
2
0
0
1
0
0
1
1
1
0
0
0
1
0
1
1
2
0
2
0
1
2
1
2
0
0
2
1
1
3
0
0
2
1
0
2
0
2
1
0
0
1
1
0
1
0
0
0
1
0
1
2
0
2
0
2
1
0
1
1
2
1
1
2
2
0
1
0
1
6
0
1
1
0
0
2
1
0
2
0
2
1
0
3
2
1
0
0
1
1
1
1
1
0
1
1
3
1
0
0
1
0
0
2
1
0
1
1
2
1
0
1
0
2
1
2
1
1
1
0
0
2
1
2
1
2
0
1
1
1
1
1
0
0
2
0
2
0
1
2
0
1
2
1
6
1
1
0
1
0
2
1
1
0
0
0
1
1
1
0
0
0
2
2
0
1
0
1
1
0
2
2
1
1
1
2
1
0
0
1
1
1
3
1
0
1
2
2
1
0
0
1
0
0
1
1
1
1
1
0
3
0
1
1
0
2
0
1
1
0
0
1
1
2
1
2
0
1
1
1
0
1
1
2
1
0
2
1
2
0
0
2
1
0
1
1
1
0
2
0
1
2
2
2
1
0
1
1
2
1
1
1
0
1
0
1
1
1
2
2
1
0
1
0
3
2
0
1
1
1
1
2
2
0
2
1
1
1
1
0
0
0
0
0
1
0
0
1
1
2
1
1
0
2
1
1
1
0
1
1
1
1
0
0
1
0
1
0
0
2
0
1
1
1
0
1
1
1
1
0
1
1
1
1
1
0
2
1
1
0
3
2
2
0
0
2
0
2
1
0
0
0
1
1
0
1
1
1
1
1
0
1
2
1
1
2
1
2
0
0
1
2
0
0
2
0
0
2
1
1
1
0
0
1
1
0
2
0
0
1
0
0
0
1
0
0
0
2
1
1
1
0
0
0
0
0
0
0
1
1
1
1
0
2
1
0
1
0
1
1
2
0
0
0
0
1
0
0
1
1
0
2
3
0
1
2
0
1
0
2
1
2
2
1
1
2
1
0
0
1
0
2
1
0
0
2
1
2
2
0
1
0
1
1
0
0
0
1
0
0
2
1
1
1
0
0
1
0
1
0
0
0
0
1
0
2
1
1
0
0
0
1
1
2
1
6
0
2
1
0
1
1
1
0
1
2
0
1
0
1
0
0
2
0
1
0
2
0
1
1
0
1
0
0
1
2
2
1
0
1
1
0
1
1
1
1
1
2
2
0
1
2
2
1
1
0
1
1
1
1
2
0
2
2
1
2
2
1
1
1
1
1
1
0
2
0
0
2
1
1
1
0
1
2
0
1
0
1
1
1
1
2
2
0
2
2
1
2
2
1
1
0
1
0
0
1
1
1
2
0
2
0
1
1
1
1
0
0
1
1
1
1
1
1
0
2
0
0
0
1
3
0
0
0
1
2
0
2
2
0
0
0
2
1
2
1
0
1
1
2
1
1
2
2
3
1
1
0
0
1
1
0
2
1
2
2
2
1
0
1
1
0
1
2
2
0
1
1
3
1
2
2
1
0
2
1
0
1
2
2
1
2
1
0
2
0
1
1
1
0
2
0
1
1
1
0
2
0
0
0
0
1
0
1
1
0
1
2
1
0
0
1
2
2
1
1
2
6
2
0
1
0
2
0
1
2
0
1
2
1
1
1
0
0
0
2
0
2
1
1
1
2
0
2
0
1
1
0
0
0
0
1
0
2
1
1
2
1
1
0
1
0
1
0
3
0
2
2
0
0
0
1
1
1
1
1
0
1
3
1
0
0
1
2
2
1
2
1
2
2
1
0
2
0
1
1
2
1
2
0
2
2
1
2
1
0
2
1
0
0
2
0
0
1
0
2
0
1
0
1
1
2
0
1
1
1
0
1
0
0
1
1
1
3
1
0
2
1
0
0
2
1
0
0
2
1
0
0
4
0
1
0
1
2
0
2
2
2
2
0
0
2
1
1
1
0
0
3
1
0
2
0
1
1
2
0
1
1
1
2
2
0
0
2
1
2
0
2
0
1
0
4
0
1
0
1
0
0
2
0
1
2
2
0
1
1
2
0
2
1
0
1
2
1
0
0
3
2
0
0
0
1
1
0
1
2
1
2
1
0
0
2
1
1
0
2
2
1
0
1
1
1
2
0
1
0
1
1
0
0
1
0
2
1
2
1
1
2
1
0
0
1
1
3
1
1
2
0
2
0
2
0
2
1
0
0
0
2
0
2
2
0
0
2
1
1
1
1
0
0
0
3
2
1
0
1
1
0
4
0
0
0
2
1
2
0
1
2
0
1
1
3
3
0
1
1
2
1
1
0
1
0
1
0
0
0
1
0
1
1
1
0
1
2
1
1
1
1
1
1
1
2
0
1
1
2
0
1
1
2
1
0
0
1
0
2
1
2
0
0
1
1
2
0
0
0
0
2
1
2
1
2
0
0
1
0
1
0
2
0
0
1
0
1
1
1
1
1
1
1
0
1
2
1
1
0
1
1
2
1
4
1
1
2
1
2
2
2
0
0
0
1
0
1
1
2
1
2
0
0
0
0
1
1
0
1
1
2
0
1
4
0
0
1
1
2
1
1
1
1
2
1
1
1
0
2
0
1
2
2
5
0
1
1
0
0
0
0
1
1
1
1
1
2
1
2
1
0
1
1
1
1
0
0
2
0
1
1
2
1
0
1
2
0
0
3
2
1
1
2
2
1
0
1
0
2
0
1
1
1
0
1
0
1
0
1
1
1
1
0
2
0
1
0
0
1
1
1
1
1
1
0
1
1
2
0
2
0
2
2
1
0
2
1
1
1
2
0
0
0
3
0
1
0
1
3
1
1
2
2
0
2
1
1
1
0
0
1
0
1
1
1
1
1
0
0
2
2
1
0
0
2
0
1
2
1
1
1
1
0
0
1
2
2
0
1
1
1
1
1
0
0
1
1
0
1
2
0
1
0
2
0
1
2
0
1
1
1
0
0
0
1
0
1
1
2
1
1
2
1
0
0
1
0
1
2
1
1
1
1
0
0
1
1
0
1
1
2
0
1
1
1
1
2
2
0
1
1
4
0
2
0
1
2
1
1
2
0
1
2
0
0
1
2
0
2
2
0
2
1
2
0
2
1
0
1
2
1
1
1
1
2
1
2
2
1
1
1
1
2
0
1
2
2
0
2
1
1
0
1
2
2
0
0
0
1
0
0
1
1
3
1
1
1
1
2
2
0
0
1
0
1
1
2
1
1
1
0
1
2
0
1
1
2
1
1
2
1
0
1
2
2
0
2
1
1
1
0
0
0
1
1
0
0
1
0
2
2
3
2
0
1
0
1
2
0
1
1
1
0
1
0
0
0
2
0
0
2
1
0
0
1
1
0
0
2
2
1
0
1
1
1
2
1
1
1
2
0
0
1
0
2
2
1
5
0
0
1
1
0
1
0
0
2
1
2
0
0
1
0
1
0
2
0
2
1
1
1
1
1
1
0
1
1
1
2
2
0
1
0
1
1
0
1
1
1
0
0
0
0
2
0
0
1
2
1
1
2
0
1
0
1
1
1
1
2
1
2
0
1
3
2
1
1
0
2
2
0
1
1
1
0
1
2
0
1
1
1
0
2
1
0
0
1
1
2
1
1
2
0
1
2
1
0
0
1
1
1
1
0
2
1
2
0
2
2
1
2
1
1
1
1
1
0
0
1
2
2
2
0
3
1
2
0
0
2
1
2
0
0
1
1
0
1
2
0
2
1
0
2
1
0
0
0
1
0
0
0
1
0
1
1
0
0
2
1
2
1
1
1
1
1
1
1
2
0
2
1
0
1
1
0
2
2
0
2
0
0
1
1
0
2
1
0
1
0
0
2
0
0
1
2
1
1
1
1
1
1
0
1
0
1
1
1
2
1
1
1
0
1
1
1
1
2
1
1
2
0
0
2
0
2
0
1
2
2
0
0
0
1
2
0
1
2
0
0
0
1
1
0
1
2
0
0
2
0
1
1
1
1
1
2
1
2
0
0
2
0
0
2
2
1
1
0
1
1
0
1
0
0
0
1
1
1
0
2
0
2
0
2
1
1
0
2
0
0
0
2
0
1
2
0
0
0
2
1
0
2
1
1
1
0
1
1
1
2
0
1
0
1
1
2
0
0
2
0
0
2
0
1
2
0
2
1
1
0
0
1
1
1
1
0
0
2
0
2
0
1
2
2
1
0
0
0
1
2
2
1
2
1
1
0
0
1
1
1
1
0
1
1
1
1
1
1
2
1
1
2
0
2
0
2
0
0
2
2
1
1
0
2
1
0
0
2
0
1
0
1
1
1
1
1
0
1
2
1
1
2
1
0
0
1
1
0
1
1
0
1
1
0
2
0
2
2
1
2
1
1
0
1
1
1
2
1
2
1
2
2
0
2
2
1
2
1
2
1
2
1
1
0
1
1
0
1
1
2
1
1
0
1
2
1
3
0
2
1
1
2
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
1
2
1
1
2
1
0
0
0
1
2
1
1
0
1
0
1
1
0
1
2
2
1
1
0
2
1
0
0
0
0
1
3
2
1
0
1
1
1
2
1
1
2
2
0
1
0
1
2
0
0
0
1
2
0
1
0
0
2
1
1
3
1
1
0
1
1
1
1
0
1
1
2
2
0
2
1
0
1
2
1
1
2
0
1
0
1
0
1
1
1
1
2
1
0
1
1
1
1
1
2
0
2
0
1
1
2
1
0
0
2
0
0
0
1
1
0
0
1
1
1
2
1
1
0
1
0
3
1
2
0
1
0
0
1
1
2
1
1
0
2
1
0
1
0
0
1
0
0
0
0
0
1
2
2
0
1
2
2
1
0
2
0
1
1
1
1
0
1
1
1
1
0
0
1
2
1
0
0
2
0
1
1
1
2
1
2
0
0
1
1
2
2
1
1
1
1
0
0
1
0
0
1
1
0
0
1
1
0
1
2
2
0
0
1
1
0
0
1
1
0
0
0
2
2
1
1
0
0
0
1
1
1
2
0
2
1
1
2
1
1
0
0
2
2
0
2
1
1
0
1
1
0
1
1
0
1
2
1
2
1
0
1
1
2
1
0
1
2
1
0
0
0
0
0
1
0
2
1
2
1
2
1
1
2
0
1
0
0
0
0
1
0
1
1
2
0
0
1
0
0
1
0
0
1
0
0
1
2
2
1
0
1
1
1
2
0
2
1
1
0
0
1
0
1
0
1
4
2
1
2
1
1
1
1
1
0
1
1
1
1
0
0
2
0
0
0
1
1
0
1
0
1
0
0
0
1
0
0
1
0
1
2
1
0
0
1
1
0
1
0
2
1
0
1
1
1
1
0
1
0
0
1
0
1
1
1
1
1
1
1
0
8
1
0
1
0
1
1
0
1
0
1
0
1
0
1
1
1
1
0
0
1
1
0
1
1
2
2
0
3
1
2
0
1
2
0
1
1
0
1
3
1
1
0
2
0
1
1
2
0
0
0
1
1
0
0
0
1
2
2
1
1
2
1
1
0
1
2
0
0
1
1
1
0
0
1
1
2
1
0
0
1
1
0
1
2
2
1
2
0
1
0
1
2
1
0
1
2
2
1
2
2
0
1
1
2
0
2
0
0
1
2
0
2
1
1
0
1
1
2
1
2
1
1
0
2
1
2
0
2
1
0
2
2
0
2
1
2
1
0
2
2
0
0
1
1
1
2
0
1
1
1
1
1
2
1
2
2
0
2
1
1
1
2
0
0
0
1
1
0
0
1
1
1
1
1
1
1
0
2
1
1
2
0
1
1
2
0
2
2
1
1
2
1
1
2
1
3
1
1
0
1
2
3
1
1
1
2
1
0
0
1
1
2
0
0
1
0
0
2
1
1
1
2
0
2
2
2
0
1
1
1
0
2
1
1
1
1
0
1
0
1
1
2
2
2
2
1
0
1
3
1
0
0
1
1
1
0
1
0
1
0
2
0
0
0
0
1
0
1
1
1
1
2
1
1
0
0
1
2
2
0
0
0
1
2
0
1
1
1
1
1
0
0
0
0
1
0
1
1
0
1
1
1
2
1
1
2
1
0
0
0
0
1
0
1
1
0
2
1
1
1
1
1
1
0
1
0
2
1
1
0
0
2
0
1
1
2
0
0
2
2
1
2
1
0
0
2
0
0
0
1
1
1
2
2
1
1
2
0
1
1
1
3
0
2
2
0
2
1
1
0
0
0
1
2
0
0
0
1
2
2
1
1
1
0
1
2
2
1
0
0
1
0
0
1
1
2
1
1
1
1
1
0
1
0
2
1
1
0
1
1
2
1
1
0
0
2
1
2
0
1
1
0
0
0
1
4
0
0
1
2
1
2
0
0
0
1
1
2
1
1
1
0
2
0
1
1
1
1
1
0
1
0
1
1
1
1
1
1
0
0
1
0
0
1
0
1
0
0
1
1
1
0
0
2
0
0
0
1
1
1
0
0
2
1
0
2
0
1
2
1
1
1
2
1
0
2
0
0
0
2
0
1
0
0
2
2
0
0
1
0
1
0
0
1
3
0
1
1
0
0
2
0
2
0
2
0
1
0
1
1
1
1
1
0
0
0
1
1
0
2
2
0
0
2
0
2
2
1
1
1
1
1
2
0
2
0
2
1
1
0
1
1
1
1
0
2
1
1
2
1
0
1
1
1
2
1
1
0
1
2
1
1
2
0
2
1
0
2
1
1
0
1
0
0
0
1
0
1
0
1
2
1
0
1
1
1
0
0
0
0
1
0
2
1
0
2
0
1
0
1
0
2
1
1
1
2
1
0
0
1
2
0
2
0
1
1
0
0
0
1
1
1
0
2
2
1
1
0
0
0
1
1
0
1
2
1
0
1
3
2
1
1
1
0
0
1
1
0
1
1
1
1
1
2
1
0
1
2
2
1
1
2
4
1
1
0
1
0
3
0
1
1
2
2
0
1
1
1
0
1
0
0
0
0
0
2
2
1
0
0
2
1
2
2
2
0
1
1
1
0
1
1
1
0
1
1
2
0
0
0
0
0
2
0
1
1
1
0
1
1
1
0
0
2
1
0
0
1
1
0
0
0
0
1
0
1
1
1
1
1
1
0
0
0
1
2
2
2
0
0
2
0
1
1
0
1
0
2
1
0
1
1
1
3
0
0
0
0
1
2
0
1
0
1
2
1
2
0
1
2
1
0
0
1
0
0
1
0
1
1
0
1
1
0
2
0
2
0
1
0
1
1
2
1
2
0
2
0
0
0
1
2
0
1
2
1
1
1
0
1
1
2
0
2
0
3
0
2
0
2
1
0
2
0
0
0
0
2
1
0
1
1
2
0
1
1
0
1
1
1
0
0
0
2
2
2
2
0
1
0
2
1
0
0
1
1
1
1
1
0
1
0
1
1
0
1
0
0
0
0
1
1
0
0
1
0
5
2
1
1
0
1
2
1
1
0
0
0
1
1
1
0
2
1
1
1
2
0
1
1
1
1
0
0
1
0
0
0
2
2
1
1
0
2
1
2
2
2
0
1
1
0
1
1
0
0
2
1
0
2
0
2
1
0
0
0
5
3
0
0
3
1
1
2
1
2
2
1
0
0
2
0
1
1
2
2
1
1
1
2
2
2
1
1
0
1
2
2
1
1
1
1
2
2
1
1
2
2
1
1
0
1
2
0
2
1
2
1
2
1
1
2
0
1
2
1
0
1
0
1
2
1
2
0
0
0
0
0
1
1
1
1
1
2
1
1
1
0
0
1
2
0
0
0
1
1
0
1
2
1
0
0
0
0
0
2
2
2
1
0
1
0
3
1
1
0
1
2
0
1
1
1
2
1
1
1
1
0
2
1
1
0
0
2
0
0
2
1
1
0
2
0
1
2
0
2
0
1
0
1
0
0
1
0
2
0
2
1
0
2
0
0
0
2
2
1
0
2
1
2
0
1
1
2
2
0
0
2
1
2
1
1
0
2
0
1
0
2
0
2
0
1
0
0
1
0
0
0
1
0
2
1
1
1
2
0
0
1
1
1
0
0
0
1
2
2
1
0
1
1
0
1
2
2
1
1
1
1
1
0
1
0
1
0
1
0
2
1
1
1
1
1
1
2
0
2
1
0
1
1
1
0
0
1
2
1
2
2
2
0
1
2
1
1
1
1
1
2
0
0
1
1
0
1
2
1
2
1
2
2
1
1
0
1
2
0
2
1
1
1
2
2
2
1
1
2
1
1
1
3
0
1
1
1
2
2
2
1
2
0
2
1
1
0
2
0
1
0
1
1
1
1
0
2
0
1
0
1
1
1
1
1
1
2
1
1
0
0
1
0
1
0
1
1
0
1
1
2
2
0
2
0
1
0
1
0
0
3
0
1
2
1
0
2
1
0
1
1
1
0
1
1
0
2
1
1
1
0
0
2
1
0
0
0
0
2
0
1
0
0
1
2
0
1
1
0
2
0
0
0
0
1
2
1
0
1
0
2
1
0
1
0
1
1
1
1
1
1
1
1
0
0
0
1
1
1
1
1
0
0
0
2
1
2
0
1
0
2
1
1
0
0
1
1
0
0
0
2
1
1
2
2
1
0
0
0
2
1
0
0
1
0
2
1
0
2
0
1
2
2
1
1
0
0
2
2
0
1
0
0
0
2
0
2
0
1
2
0
1
0
1
2
0
0
1
1
1
1
1
2
1
0
0
0
2
1
0
3
0
1
1
2
0
0
0
1
1
1
2
0
0
1
1
3
2
0
1
1
2
2
1
0
0
0
0
0
1
0
0
0
0
1
1
0
2
1
1
1
1
1
1
0
1
0
2
2
1
2
2
1
2
0
1
0
2
2
1
1
0
0
1
0
0
1
0
1
1
0
1
2
0
2
2
1
0
1
1
0
1
0
1
0
2
1
0
1
2
2
1
2
1
0
0
1
0
1
1
0
1
0
10
2
2
1
1
1
0
1
0
0
2
2
0
0
2
1
1
2
2
1
0
0
1
2
2
1
2
2
2
1
2
2
1
0
1
0
2
1
1
2
0
1
1
1
1
0
2
1
1
1
1
1
1
1
0
0
0
1
0
2
0
1
1
1
0
0
1
1
1
1
1
2
2
0
1
1
1
1
2
1
0
1
0
1
1
0
0
1
1
0
2
2
0
0
1
0
0
0
0
1
1
1
1
1
0
0
1
2
1
1
1
0
2
0
3
2
0
1
0
1
2
1
2
1
0
1
0
0
2
1
0
1
2
2
1
0
1
1
0
2
0
4
1
1
0
1
1
1
1
2
2
1
2
0
2
0
1
1
0
1
1
2
1
1
6
0
1
0
0
0
0
2
2
0
2
1
1
1
0
0
0
1
1
0
1
1
0
1
1
1
2
2
0
2
0
1
0
1
1
1
2
2
0
2
1
2
1
2
2
0
1
0
0
0
0
2
1
1
0
0
2
0
0
1
1
1
0
0
0
1
1
1
0
0
1
1
2
0
1
0
0
1
1
1
0
2
1
0
3
1
2
1
1
2
1
0
0
2
2
1
0
1
1
0
0
0
0
0
0
1
0
1
1
2
0
0
1
1
0
0
2
1
0
2
0
0
1
2
1
0
1
0
1
5
0
1
0
2
1
1
1
2
0
0
1
1
2
0
0
0
0
0
1
1
1
1
2
2
1
1
2
1
0
1
0
2
0
1
0
1
0
0
0
2
2
1
1
0
2
2
1
0
1
1
2
1
1
0
1
0
1
1
0
1
0
0
2
2
2
1
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
1
1
1
1
0
2
0
0
2
0
1
1
1
1
2
1
0
1
2
2
0
0
2
0
1
1
3
2
0
0
2
2
0
0
1
1
1
1
1
0
2
0
0
1
3
0
1
1
1
0
1
1
0
1
1
2
0
1
2
0
1
1
2
1
0
0
0
0
1
0
0
0
0
1
2
1
1
1
1
2
1
1
2
2
1
0
1
0
0
1
1
0
1
0
0
0
1
1
0
1
0
0
1
1
2
0
2
0
1
0
0
1
0
0
2
1
1
2
1
1
0
0
0
0
0
3
0
2
1
0
0
1
1
2
2
1
0
0
2
1
0
3
1
1
1
3
2
1
2
4
1
1
2
0
2
0
1
1
0
1
1
0
2
3
0
1
0
2
2
2
3
2
1
1
0
1
2
1
1
1
2
1
0
1
1
2
0
1
1
1
0
0
1
1
1
1
0
0
1
1
2
2
1
1
1
0
0
1
1
0
0
1
2
1
3
1
2
2
1
1
2
2
2
2
2
1
0
0
3
0
2
1
1
0
0
1
0
0
1
0
1
0
1
1
2
0
2
1
0
0
0
2
1
0
0
2
1
0
0
0
1
1
2
2
1
2
1
2
2
2
1
0
0
1
0
0
1
1
1
0
1
1
1
0
2
1
0
1
1
0
0
1
1
2
2
2
2
1
1
1
0
2
0
1
1
1
2
1
1
1
0
0
1
0
0
0
2
1
0
2
0
1
1
1
0
1
0
0
0
0
2
1
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
1
0
0
1
2
0
2
2
0
2
2
1
1
1
2
0
2
1
1
0
0
0
0
0
1
0
1
0
1
1
0
1
0
0
1
2
2
0
0
1
1
1
0
1
1
1
1
1
1
0
1
0
2
0
0
2
1
2
1
0
0
1
0
1
1
0
0
1
1
1
0
1
1
1
1
1
2
1
2
0
1
1
1
2
0
3
1
2
1
2
1
1
0
1
0
0
0
2
0
0
1
0
2
1
0
0
1
1
0
1
0
1
1
1
0
0
0
0
0
0
1
1
1
0
0
2
1
1
1
0
0
2
1
0
1
0
0
1
0
2
2
0
1
1
0
1
0
0
1
1
1
1
2
1
1
2
1
2
0
3
1
1
0
1
1
0
2
0
0
0
1
1
1
2
3
0
1
1
2
0
2
1
0
0
2
0
0
1
0
0
0
0
1
1
1
2
0
1
2
0
0
1
1
2
0
1
2
1
4
1
2
0
0
0
1
1
1
0
0
2
0
2
2
1
0
3
2
1
0
1
0
0
2
0
1
2
1
1
0
1
1
1
0
1
1
1
0
0
0
2
0
1
0
0
2
0
1
0
2
0
0
1
0
2
1
1
0
0
2
1
1
0
0
2
1
1
2
2
0
0
0
0
1
0
1
0
1
2
2
0
1
1
2
1
1
1
0
2
1
0
1
0
1
0
3
0
0
1
2
1
3
1
0
1
0
1
1
1
2
0
1
0
1
1
1
1
1
0
1
2
0
2
1
3
2
1
1
2
1
2
2
0
0
1
1
1
1
0
1
2
3
0
0
2
2
2
2
1
1
0
0
1
2
0
0
0
0
1
2
1
1
0
2
2
1
2
0
2
2
1
1
0
1
1
1
0
0
1
0
1
1
0
0
1
2
1
0
0
1
1
0
0
0
0
2
1
1
0
0
0
0
1
1
1
1
0
1
0
1
0
1
2
0
1
0
2
1
1
1
1
0
2
2
0
0
0
1
2
3
0
0
1
0
2
0
1
1
0
0
1
1
3
1
1
0
1
1
1
0
2
1
0
2
0
1
2
2
0
1
1
0
0
0
0
1
2
1
1
2
0
1
0
0
0
0
1
0
2
2
2
0
0
1
1
0
1
1
0
0
1
1
2
1
0
0
0
2
3
1
3
0
0
0
1
2
1
0
0
2
1
1
1
0
1
1
0
1
0
2
0
0
2
0
2
1
0
2
0
1
0
0
1
2
2
0
2
1
0
0
2
0
2
0
0
2
1
1
0
0
0
3
1
0
0
0
1
3
0
1
1
1
1
0
1
0
0
1
0
1
1
0
2
1
0
2
0
1
1
1
1
2
2
1
1
0
0
0
1
0
1
0
2
1
0
0
0
1
1
1
1
0
1
1
1
1
0
0
1
1
2
0
1
1
3
1
1
2
0
1
0
0
1
2
0
0
0
0
1
1
1
1
0
1
2
1
0
2
0
0
2
0
1
1
0
2
0
1
1
1
0
1
0
1
0
1
0
0
0
2
1
1
1
1
0
1
0
1
0
1
1
0
1
1
0
1
1
1
1
0
2
0
1
1
2
2
2
0
0
0
2
1
0
1
1
2
0
2
2
0
3
2
2
1
2
0
0
0
1
2
1
0
0
0
0
2
2
1
0
1
0
1
2
1
1
1
2
2
0
1
3
1
1
1
1
1
0
2
0
3
0
0
1
1
1
2
1
0
1
1
0
0
1
1
0
0
0
0
2
2
0
0
1
1
0
1
2
1
2
0
1
2
1
3
1
0
1
0
1
1
2
1
2
1
1
1
0
2
0
0
1
1
2
0
1
2
0
0
0
0
1
0
1
0
0
1
0
0
1
2
0
2
0
0
1
2
0
2
0
1
0
0
1
1
2
1
0
0
0
0
0
0
1
1
2
1
0
0
1
1
1
0
4
2
1
1
0
0
1
0
0
0
0
0
0
3
1
0
0
0
0
0
1
1
0
0
2
1
2
0
1
2
0
0
0
1
2
2
0
1
2
0
2
2
1
0
1
1
2
0
0
2
1
0
0
2
2
1
1
1
1
1
2
2
1
2
0
0
1
0
0
1
2
2
2
1
1
1
2
1
2
2
1
1
1
2
1
2
1
1
0
0
1
1
1
1
1
0
3
1
0
1
1
1
0
2
0
0
1
1
0
0
2
1
1
2
2
0
0
2
1
2
1
1
1
2
2
2
1
2
0
1
1
1
1
2
0
0
0
1
0
2
1
0
0
1
0
2
1
1
2
1
0
1
1
1
0
2
0
2
2
0
0
1
0
1
1
1
1
0
0
2
1
0
2
1
0
0
0
1
1
0
1
1
0
0
1
0
1
1
1
1
0
2
0
2
0
1
2
0
0
1
1
0
1
2
0
1
1
2
1
1
2
1
1
1
8
2
1
1
1
1
2
1
2
1
0
2
1
0
1
0
1
0
1
1
1
1
3
1
1
0
2
1
2
0
0
0
0
2
0
2
1
0
1
1
1
0
1
2
0
1
0
1
2
1
2
1
0
1
0
1
0
1
0
1
0
2
0
0
2
1
2
0
1
3
0
1
0
1
2
2
1
1
0
1
1
1
1
0
2
2
1
2
2
2
1
0
0
1
0
1
2
2
0
1
1
0
0
0
1
0
1
1
1
0
0
0
1
0
0
2
0
1
2
0
0
1
0
0
1
1
2
0
0
1
1
0
0
1
1
2
1
2
2
1
0
1
0
2
1
1
0
1
0
2
0
1
2
2
1
0
1
2
2
0
0
0
1
0
0
1
0
1
1
2
1
1
2
0
0
2
1
0
2
1
1
0
0
1
1
1
0
0
0
1
1
1
1
2
2
2
2
2
1
2
1
0
1
1
1
0
0
3
1
1
1
0
2
0
1
0
0
1
2
1
0
1
1
0
2
0
1
2
1
1
1
1
1
2
2
1
1
2
1
0
1
0
1
0
1
2
0
1
0
1
1
3
0
0
3
1
1
0
2
1
0
1
0
1
1
0
0
1
0
0
1
1
0
1
2
0
1
1
1
1
1
0
0
3
2
0
0
1
0
0
1
1
2
0
2
1
1
1
0
0
2
1
1
2
1
1
0
1
1
1
1
0
0
2
1
0
2
1
0
0
1
2
2
1
0
1
1
1
1
2
1
0
1
1
0
1
1
0
1
1
0
1
2
0
1
1
0
0
1
2
0
2
1
1
0
1
0
1
1
1
5
0
1
1
1
0
0
1
1
1
0
1
1
0
1
2
0
0
2
0
0
1
0
1
0
1
0
1
1
0
1
1
1
1
1
1
2
1
0
1
0
0
2
1
0
3
1
2
1
2
0
0
0
1
1
1
1
0
1
1
1
1
0
1
1
0
0
0
1
0
1
1
2
1
1
0
0
1
0
1
0
0
0
2
0
0
2
0
1
1
1
0
0
1
0
0
1
0
2
2
1
0
1
1
1
0
0
1
0
1
1
1
3
2
1
0
1
0
0
1
1
1
0
1
0
1
1
0
0
0
1
0
5
0
2
0
0
1
2
0
2
1
1
3
1
1
1
1
1
1
1
1
1
0
0
0
0
1
1
2
1
2
0
1
1
1
0
2
2
0
1
2
0
0
2
2
2
1
2
2
1
1
0
1
1
1
0
1
2
1
0
0
2
1
0
1
0
2
1
0
0
1
1
0
1
1
1
1
2
0
2
1
2
1
0
2
0
1
0
0
1
1
1
0
1
0
1
0
1
2
1
2
1
1
2
0
2
1
0
0
2
1
0
1
1
1
1
0
2
0
0
2
1
1
1
0
3
1
1
0
2
1
0
2
1
0
1
2
0
1
1
1
2
1
0
0
0
1
1
2
2
0
2
1
1
1
0
1
0
0
2
2
1
2
1
0
0
1
1
2
0
1
1
1
1
1
1
1
1
1
0
0
2
2
1
3
1
1
0
1
0
2
1
1
0
1
1
1
1
1
0
1
0
0
0
2
1
1
1
0
2
0
0
0
2
0
2
1
1
0
1
2
1
0
2
2
1
0
0
1
2
2
0
3
4
2
1
0
2
1
0
1
2
2
1
1
0
2
1
1
0
2
1
1
1
1
2
1
1
1
0
2
2
0
1
1
0
1
2
1
0
1
2
2
2
1
1
1
2
1
0
1
2
2
1
1
0
1
0
1
1
1
1
2
1
0
0
1
2
1
2
1
0
2
1
3
0
1
2
2
1
2
1
0
1
1
0
1
1
2
0
2
1
1
0
1
1
1
1
2
2
1
2
2
0
2
1
1
0
0
2
1
1
1
1
1
0
2
2
1
0
2
1
0
1
0
0
1
1
2
1
2
0
1
1
1
1
0
1
1
0
1
1
1
1
0
0
0
0
0
2
2
1
1
0
2
1
2
0
1
0
0
0
2
1
0
0
0
2
0
4
0
1
1
0
1
1
1
1
0
1
0
2
0
1
1
2
2
1
1
0
2
1
2
1
0
1
1
1
1
1
2
1
0
1
0
2
0
2
0
0
1
0
1
1
1
0
0
1
1
1
2
0
2
2
1
1
1
0
1
1
2
1
2
2
0
1
1
1
0
2
1
3
2
1
2
1
0
3
1
0
0
1
0
1
1
0
0
2
0
1
1
0
0
1
1
0
1
1
1
0
1
1
0
0
0
2
1
2
1
2
1
0
2
2
1
1
2
1
1
1
0
2
2
0
0
1
2
1
1
1
0
1
0
1
1
1
1
1
0
0
2
1
0
0
0
0
0
1
2
2
0
0
0
2
1
0
0
0
1
1
1
2
0
1
1
1
2
0
1
1
0
0
1
0
2
2
1
1
2
1
0
1
1
0
2
1
1
0
0
1
0
1
2
0
2
1
1
2
2
1
0
0
1
0
1
1
2
1
2
1
0
0
1
1
2
1
0
1
2
1
1
1
1
2
2
0
1
1
0
1
0
1
1
2
1
1
0
2
0
0
1
1
0
0
1
1
1
1
1
0
1
1
2
3
0
0
1
0
1
2
2
0
2
0
2
1
1
1
1
1
1
2
1
1
1
1
1
0
0
1
0
0
2
1
1
2
0
1
1
1
1
2
0
1
0
1
1
2
0
2
2
1
1
0
0
2
0
0
0
1
0
0
1
1
0
1
2
0
2
1
1
1
2
3
1
0
0
0
0
0
2
0
2
0
0
0
0
0
1
1
1
2
0
0
1
0
1
1
0
2
1
2
0
1
1
1
1
1
2
0
0
0
1
1
0
2
1
2
0
0
0
0
2
1
1
1
1
1
0
1
2
0
0
2
1
1
8
2
2
2
1
0
1
2
1
1
2
0
1
1
1
1
1
1
2
1
2
1
3
1
1
0
0
2
0
0
1
1
1
1
2
0
1
1
2
1
0
1
1
0
1
2
0
0
1
0
1
0
0
2
2
1
2
0
1
1
0
0
1
1
0
2
1
1
0
1
2
0
0
2
2
0
0
2
2
1
0
1
1
0
0
2
1
1
1
0
0
0
0
1
0
0
1
1
1
0
1
0
0
1
2
1
2
0
0
2
1
0
1
2
1
1
3
1
3
1
0
2
2
1
2
1
0
1
2
2
1
1
1
2
1
0
2
0
1
1
2
1
3
1
1
2
1
2
2
0
2
0
3
2
1
2
1
0
1
0
1
2
1
1
1
2
1
1
2
1
2
1
2
1
0
0
1
2
1
0
0
2
0
1
1
0
1
2
2
1
0
0
2
0
0
0
1
2
0
1
0
0
1
0
2
0
0
1
1
0
1
0
1
0
1
3
0
0
0
1
1
1
1
0
1
0
2
2
0
1
1
1
0
0
2
1
0
2
0
1
1
1
1
2
1
1
0
0
2
1
2
1
1
1
0
0
1
0
2
2
2
0
2
0
1
0
2
3
1
0
2
0
1
1
1
2
1
2
2
1
1
0
1
1
1
1
1
0
0
0
0
0
1
1
2
1
2
0
0
2
0
1
0
0
0
1
1
0
1
1
2
2
0
1
0
1
1
1
0
1
0
2
2
0
1
2
0
1
1
1
1
0
0
1
2
2
1
0
0
0
1
1
2
0
0
2
0
2
1
2
1
0
1
1
0
1
0
0
1
1
1
1
1
1
2
2
0
0
2
0
1
2
1
2
1
1
2
0
1
0
2
1
1
1
1
1
0
2
0
1
0
0
1
1
1
2
0
0
2
0
0
1
1
0
0
1
1
1
2
0
1
2
0
0
1
1
2
1
0
2
2
1
2
0
0
2
1
0
0
2
1
1
1
0
0
0
1
0
0
0
1
0
1
1
0
0
1
0
1
2
1
0
2
1
0
1
1
2
0
2
1
0
0
0
2
2
1
2
0
0
0
0
1
2
2
0
1
1
1
0
0
2
1
2
0
1
0
2
1
1
2
1
2
2
0
0
1
3
2
0
0
1
1
1
1
3
1
2
2
0
0
0
2
0
3
1
1
0
0
1
0
1
2
0
1
1
0
0
0
2
1
2
0
1
2
0
0
2
1
1
1
1
2
1
1
0
4
0
0
1
0
1
0
1
1
1
0
2
0
2
0
0
1
0
1
0
3
0
2
1
0
1
2
0
1
1
0
1
1
1
1
1
2
2
2
0
0
1
0
1
0
0
0
2
2
0
1
0
1
1
1
1
0
1
0
0
1
0
0
1
1
2
0
1
2
0
1
2
0
1
2
1
2
0
1
1
2
0
1
0
0
1
2
0
1
1
0
0
1
1
1
1
1
1
2
1
1
0
1
2
1
1
1
1
0
0
1
1
1
2
1
2
1
1
0
1
0
2
0
1
0
0
0
2
0
2
1
1
0
1
0
1
1
2
1
1
1
0
3
2
2
2
1
1
0
0
2
2
1
0
1
1
0
2
1
1
1
0
2
1
1
1
1
1
0
1
0
2
0
2
0
0
0
1
0
0
0
1
0
0
0
1
1
0
1
0
1
1
1
1
1
1
0
0
2
2
2
1
1
1
0
1
1
0
2
0
1
3
0
0
1
0
0
0
1
0
2
0
1
0
0
0
0
1
0
1
1
1
2
1
0
1
1
2
1
0
1
2
1
0
1
1
0
0
2
0
0
1
0
1
0
1
2
2
1
1
1
0
0
2
0
3
3
2
1
0
0
1
1
0
0
2
1
0
0
0
0
1
0
2
0
1
1
1
1
1
1
1
0
1
0
3
2
0
1
2
0
1
1
1
1
0
1
0
0
0
1
0
0
2
0
2
0
1
1
2
1
1
0
0
1
2
1
1
2
0
2
0
0
1
1
1
2
2
1
0
0
1
0
1
2
1
1
1
1
0
2
0
0
0
0
2
1
1
1
0
0
1
2
1
1
1
1
1
0
1
2
1
1
0
1
1
1
0
0
1
0
1
2
1
1
0
2
2
2
2
0
0
0
1
0
1
2
2
1
2
1
0
0
1
2
1
1
0
0
0
0
2
0
0
2
0
1
1
1
0
1
1
0
1
1
1
1
1
1
1
1
1
1
2
0
0
1
0
0
1
0
0
0
2
2
0
1
1
2
2
0
2
0
1
1
1
2
1
1
0
0
1
2
1
1
1
0
0
0
0
3
2
1
1
0
2
2
2
2
2
1
1
0
1
2
0
1
1
1
1
1
1
1
0
0
1
1
1
1
1
1
2
1
1
0
1
1
0
2
2
0
2
0
2
0
1
1
1
2
2
2
0
0
0
0
1
0
1
0
0
2
1
0
0
1
1
1
1
1
0
0
1
1
0
1
0
0
2
1
1
1
0
1
1
0
0
1
1
3
1
1
2
1
1
1
1
2
0
0
1
2
1
1
0
0
0
0
1
1
1
0
0
2
1
1
2
0
0
2
0
1
0
1
0
2
1
2
2
1
2
1
1
1
1
0
0
2
2
1
2
2
0
0
2
1
2
0
0
1
1
2
1
2
2
2
1
0
0
1
0
0
1
2
1
2
1
0
1
1
1
1
1
1
1
0
1
2
0
1
2
1
0
0
0
1
0
2
2
3
0
1
1
0
0
0
1
1
1
1
0
1
1
0
0
0
1
1
0
0
0
0
0
1
2
0
1
1
2
0
1
1
2
0
1
2
1
0
0
1
1
0
2
2
0
0
2
1
2
0
2
1
2
1
1
1
2
2
1
0
0
3
1
1
1
0
0
0
0
1
1
1
1
1
1
1
1
1
0
1
1
0
1
0
0
2
1
1
1
0
3
1
0
2
1
0
1
0
0
1
3
0
0
2
1
0
0
0
1
0
3
1
2
2
0
0
1
2
2
0
1
0
1
0
1
0
1
1
1
0
0
2
1
0
2
1
0
1
0
0
2
2
1
1
2
1
1
0
0
0
1
2
1
0
0
1
1
0
0
3
1
0
1
1
1
0
0
0
1
0
1
0
1
1
1
0
1
0
2
1
1
1
0
0
2
0
0
0
3
1
1
1
1
0
2
2
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
2
1
3
1
1
2
1
1
0
0
1
0
2
2
0
1
0
0
2
0
2
0
1
0
1
1
1
1
1
1
0
0
2
1
0
1
0
1
2
1
0
2
1
0
0
1
2
1
0
1
1
1
1
1
0
1
0
0
2
1
2
1
0
0
0
2
1
0
0
1
1
2
1
2
1
2
1
0
1
0
1
1
0
2
1
1
2
1
1
1
2
1
0
0
2
0
1
1
1
3
1
2
1
0
1
0
0
0
1
2
1
1
0
1
0
0
1
1
0
0
1
2
0
2
1
0
2
1
1
0
2
0
1
1
2
0
1
2
1
0
1
1
2
1
0
0
1
2
2
1
0
2
2
0
2
2
0
0
1
0
2
0
2
1
0
0
1
0
2
2
1
0
0
0
2
1
2
1
0
0
0
1
1
1
2
2
2
1
0
3
2
0
1
0
1
2
1
0
0
2
0
2
2
3
1
1
0
2
1
1
0
1
2
1
2
1
2
1
2
2
2
2
0
1
0
0
1
1
1
2
0
2
0
0
1
0
1
0
0
2
1
0
0
1
1
1
1
0
0
0
0
1
2
1
1
2
0
1
0
0
2
2
0
1
1
1
2
2
0
2
0
1
0
2
2
1
1
1
0
0
1
3
0
1
0
1
1
2
2
0
2
0
0
0
2
2
2
0
1
1
0
0
0
0
1
0
1
1
2
1
0
0
1
5
1
1
2
2
0
1
1
1
0
0
0
1
2
1
0
0
2
0
1
1
0
2
1
1
1
1
3
1
1
1
1
2
0
2
1
2
1
2
1
1
1
1
1
1
1
1
2
1
1
0
1
2
1
1
1
2
1
1
1
0
0
0
0
0
0
1
2
1
0
1
0
0
1
2
1
0
0
1
1
2
1
2
0
0
1
1
1
0
0
1
1
2
0
2
1
1
0
0
0
2
2
1
0
1
0
0
2
0
0
1
0
0
1
0
1
1
2
0
1
0
0
1
0
0
2
1
0
2
0
7
0
2
0
0
0
0
1
0
1
1
0
2
0
0
0
1
1
1
0
1
1
0
0
1
2
1
1
1
1
0
1
0
0
2
0
2
0
1
2
2
2
1
2
1
3
3
2
1
0
1
0
2
2
0
1
0
1
1
0
2
1
0
0
2
0
0
0
1
1
0
0
0
0
1
0
2
0
1
2
2
2
1
1
1
0
1
1
4
0
1
1
2
1
2
0
1
1
0
2
2
0
1
0
1
1
1
1
0
2
0
0
0
1
0
0
1
1
1
2
1
0
1
1
1
1
0
0
0
1
2
0
0
1
2
1
0
0
1
0
1
1
2
2
2
0
2
0
1
0
2
0
0
1
1
2
1
0
1
1
2
1
1
1
0
2
1
2
0
1
0
0
1
0
0
0
2
1
0
1
0
1
1
1
1
0
0
2
2
1
1
1
2
1
0
1
2
1
1
0
0
0
2
2
0
1
0
1
1
1
1
0
1
1
1
0
0
1
1
2
2
0
0
1
2
2
1
1
1
0
1
1
0
1
1
0
2
1
0
0
0
2
2
1
1
1
0
1
0
1
0
2
0
1
0
0
0
1
1
0
1
1
1
1
1
0
1
0
1
1
2
0
0
0
1
1
1
1
0
1
1
1
1
1
2
0
0
1
1
1
0
0
1
1
2
1
1
2
2
2
2
2
1
0
2
1
1
2
1
1
0
2
0
1
1
1
0
0
2
2
0
1
1
1
2
0
0
1
1
1
0
1
2
0
0
1
1
1
1
1
1
1
0
1
0
1
3
1
1
1
0
0
1
1
0
1
1
0
0
2
0
1
0
0
1
2
0
1
1
1
1
1
2
0
2
2
1
1
0
0
2
0
0
2
0
1
1
0
0
1
0
2
0
1
1
0
1
0
1
1
1
0
1
0
1
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
1
3
1
0
2
0
1
1
1
2
0
2
0
1
2
2
0
1
1
0
1
0
2
0
1
0
0
0
1
2
0
2
0
1
2
3
1
1
2
2
2
1
1
4
1
1
0
0
0
1
0
2
0
0
0
0
0
0
0
1
1
0
0
1
0
1
1
1
4
2
1
0
1
1
2
0
0
0
1
2
0
1
3
0
0
0
0
2
0
1
1
2
1
2
1
0
1
1
2
1
0
1
1
0
1
1
2
0
2
1
2
1
0
0
0
1
0
1
2
1
1
0
1
1
1
0
0
1
0
1
0
0
1
1
0
0
1
1
2
1
0
2
1
1
1
0
0
1
1
1
0
1
1
1
2
0
1
1
2
1
1
1
1
2
2
1
2
0
0
2
0
2
0
0
1
1
1
3
1
0
2
1
1
2
1
1
2
1
1
1
2
0
1
0
0
0
1
2
2
2
1
1
3
1
1
0
0
2
1
0
1
1
1
0
0
0
1
0
0
1
2
0
1
1
1
2
1
2
1
1
0
1
1
1
2
2
1
2
2
0
0
0
2
1
2
0
0
2
2
1
0
1
1
1
2
0
1
0
2
1
1
0
1
2
0
2
1
0
1
0
1
1
1
2
1
1
1
1
1
1
6
2
1
3
1
2
0
1
2
1
0
0
0
2
0
1
3
1
0
1
0
1
0
1
1
0
1
1
1
1
0
0
0
1
0
0
0
2
2
0
1
1
0
1
0
1
1
1
2
0
1
2
0
0
1
1
2
0
0
1
1
3
1
1
1
1
1
1
1
1
0
1
0
2
1
2
0
0
1
1
1
0
1
1
0
1
1
0
0
1
2
2
0
0
1
1
1
1
1
2
0
1
2
1
1
1
0
0
0
1
2
4
0
1
1
0
1
1
1
2
2
0
2
1
2
2
1
0
2
1
2
1
0
2
1
1
1
0
2
0
1
1
0
2
1
0
0
0
1
2
2
1
1
2
0
1
1
0
0
1
0
0
2
0
1
1
0
0
2
2
1
0
0
1
2
0
0
1
0
1
1
1
1
0
1
1
1
0
0
2
0
2
0
1
0
2
0
1
1
1
1
2
2
2
3
0
1
1
1
0
2
2
1
2
2
0
1
1
0
0
1
2
1
1
2
3
1
1
1
1
2
1
3
1
1
1
0
0
2
0
1
0
1
2
1
0
0
1
1
1
1
1
1
0
1
1
2
1
1
0
1
0
0
1
1
2
2
1
2
1
2
0
2
0
0
1
0
1
0
1
0
0
2
0
1
0
1
1
1
0
1
1
0
0
2
2
1
2
1
1
1
0
2
1
2
2
2
0
1
0
1
1
0
0
0
0
2
1
1
0
0
2
0
1
1
1
0
0
1
0
2
1
1
1
2
0
1
0
0
1
1
2
0
1
1
1
1
0
1
0
1
0
0
1
0
0
3
1
1
0
1
1
2
0
1
2
1
1
0
3
0
1
0
1
1
0
1
1
3
1
3
1
1
1
0
2
0
0
2
0
1
2
1
0
2
1
0
2
0
1
1
1
1
1
0
1
1
1
1
1
1
1
0
0
2
2
0
1
0
0
2
2
1
2
0
2
1
2
0
0
1
0
1
0
0
0
0
0
1
2
0
1
1
0
1
0
1
0
1
1
2
1
0
0
2
0
1
2
1
1
1
0
0
1
1
1
0
0
1
0
0
0
0
2
0
1
2
2
1
1
0
1
1
0
2
1
1
1
2
1
0
0
1
1
0
1
1
0
0
0
0
1
1
0
1
2
0
0
0
0
0
1
1
1
1
1
1
1
1
0
2
2
0
1
1
0
1
0
1
1
2
1
2
1
1
0
0
1
1
1
1
1
1
2
1
1
0
0
0
0
1
2
1
0
1
1
1
0
0
1
1
1
1
2
0
0
1
1
2
1
0
1
2
2
0
2
0
1
0
1
1
1
1
1
0
1
1
1
0
1
0
0
1
0
1
0
0
2
0
1
1
0
1
1
0
1
4
1
1
1
1
1
1
0
0
2
0
1
0
1
0
0
1
0
1
0
1
1
0
1
1
0
0
3
1
1
0
0
1
2
0
1
0
1
1
2
1
1
1
1
0
0
0
4
3
0
0
1
3
0
1
0
2
1
0
2
1
2
2
3
0
0
0
1
1
1
1
0
0
1
0
0
1
0
0
1
2
2
1
2
0
0
0
1
1
2
0
1
0
2
0
1
0
1
1
1
0
1
1
1
0
1
0
0
2
0
1
2
1
2
1
0
1
2
1
2
1
0
1
0
0
0
1
1
1
1
0
2
0
1
2
2
2
1
0
0
0
2
1
1
1
2
0
0
1
1
0
2
0
1
2
1
0
0
0
1
1
0
1
2
1
0
2
1
0
1
0
2
1
1
0
2
1
0
2
0
1
2
0
1
1
0
0
2
1
1
2
1
1
0
1
1
0
0
0
1
1
0
1
0
2
0
2
1
1
0
1
1
0
1
2
2
1
1
0
1
2
2
1
2
2
2
0
2
3
1
1
1
1
2
1
2
2
1
0
2
1
1
0
0
1
1
1
1
1
1
2
0
1
2
1
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
2
2
1
2
1
0
1
0
2
1
1
1
1
1
0
1
0
1
0
2
1
1
1
1
0
1
1
1
0
2
0
1
0
1
0
2
0
1
1
0
1
1
0
2
3
1
2
1
1
2
1
0
0
1
0
4
0
0
0
0
1
2
1
1
1
0
1
0
1
0
0
2
1
1
0
0
0
0
2
2
1
0
0
0
0
1
0
0
0
1
2
2
2
0
0
0
2
0
0
1
1
0
2
0
2
0
0
1
0
2
0
1
1
0
0
2
0
1
1
1
0
1
1
1
1
2
1
0
1
0
1
1
1
2
0
2
1
2
2
1
0
0
2
0
0
1
2
1
1
0
1
2
1
0
1
0
1
0
1
2
1
1
0
1
2
0
1
2
1
1
0
0
1
2
1
3
2
1
1
2
1
1
0
1
1
2
1
1
0
1
1
2
1
1
0
0
1
1
2
0
0
0
1
0
2
1
0
2
2
0
2
3
0
1
0
1
1
0
1
0
1
1
2
2
0
1
0
1
1
0
1
2
0
0
0
1
1
0
1
3
2
1
1
0
0
2
1
2
0
1
1
1
0
0
1
0
1
2
1
1
2
0
1
5
2
1
1
1
2
1
1
1
2
2
0
1
1
0
0
3
2
1
0
1
2
0
2
1
1
0
0
0
0
1
2
1
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
2
1
0
0
1
1
1
1
0
0
1
0
1
1
1
1
2
0
2
1
0
1
0
2
0
1
1
1
2
1
0
1
0
1
2
1
1
0
0
1
2
0
1
1
1
1
1
2
2
0
0
0
1
0
0
0
2
0
1
2
1
1
2
2
0
2
1
1
1
2
2
2
2
1
0
1
0
0
1
2
0
0
0
3
4
1
0
0
0
0
3
1
0
1
1
1
0
2
1
0
1
1
2
0
1
1
2
2
1
1
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
1
0
1
2
0
0
2
1
1
2
1
0
1
0
0
1
1
0
0
1
0
0
2
1
0
1
0
1
1
1
3
2
1
0
1
2
1
0
0
0
1
2
2
0
0
1
0
2
0
2
1
0
1
1
1
1
1
0
0
2
3
1
2
2
2
1
0
1
1
0
2
2
1
0
0
0
1
1
1
1
2
2
3
1
1
2
1
0
1
0
1
1
1
1
0
0
3
0
0
0
0
1
2
1
1
1
2
0
0
0
0
1
2
1
2
1
1
1
0
0
1
1
0
1
1
1
2
1
0
0
2
2
0
0
0
1
1
0
1
0
1
0
2
0
1
1
0
1
0
2
0
1
1
0
0
1
0
0
1
1
1
0
1
1
1
0
2
1
1
1
4
1
2
1
1
1
2
2
1
2
2
1
0
0
0
2
1
1
0
2
2
0
0
1
1
2
0
1
1
3
0
3
2
1
1
0
1
0
1
0
1
2
1
2
2
1
1
1
0
2
0
0
1
0
2
1
2
1
1
1
1
0
2
2
1
1
2
0
1
4
1
1
1
1
0
0
0
1
0
2
1
1
0
2
2
0
2
1
1
1
0
0
1
1
1
1
1
1
0
1
3
0
2
2
1
1
2
1
1
2
0
1
1
1
1
1
0
2
3
2
3
1
0
2
1
2
0
1
2
0
2
1
1
1
1
1
1
1
2
1
0
0
1
2
0
2
0
1
2
0
0
0
2
0
0
0
1
0
1
1
0
1
2
0
0
0
1
1
2
1
0
2
0
1
0
1
1
1
0
1
1
0
1
1
1
0
0
2
3
0
1
2
1
1
1
1
0
0
0
0
0
1
1
1
3
0
1
0
0
1
2
1
0
1
0
1
1
1
0
2
2
1
1
0
2
1
1
0
1
0
2
0
0
0
1
2
0
1
0
2
0
0
1
1
0
2
2
1
0
1
2
2
1
1
2
1
2
0
1
1
2
0
0
1
2
1
1
1
1
1
0
0
1
2
2
2
1
0
2
2
1
1
0
0
1
1
2
2
1
2
0
1
1
1
0
1
0
0
1
1
0
1
0
1
0
1
0
0
0
1
0
1
1
1
0
0
7
1
1
0
1
1
0
1
2
0
1
2
1
1
1
0
1
1
0
0
2
1
0
0
1
1
1
0
2
0
0
3
2
2
0
2
1
0
1
0
0
0
0
0
0
0
1
1
1
0
1
2
1
0
2
2
2
1
0
2
2
1
1
1
2
1
0
1
2
0
2
0
0
2
2
0
0
1
0
0
0
1
2
0
0
1
0
0
1
0
1
0
1
1
0
1
2
1
0
0
1
1
1
1
0
2
2
0
1
0
2
0
1
3
1
2
1
1
1
1
6
0
0
2
2
1
2
1
0
1
2
2
0
0
0
5
1
0
1
0
0
2
1
0
1
0
0
1
0
0
0
0
1
1
1
1
1
1
1
2
0
1
0
1
1
0
1
2
0
1
0
0
0
1
0
2
1
1
0
2
0
1
2
0
1
1
0
2
2
0
2
2
1
2
2
1
3
2
1
2
2
1
1
1
2
0
1
0
2
1
0
0
0
1
0
1
2
0
1
0
0
2
1
2
0
0
0
2
0
1
0
2
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
2
1
1
0
0
0
0
1
1
2
0
1
0
0
1
1
0
0
0
0
0
2
1
2
2
1
2
1
0
2
1
1
0
0
1
1
1
0
0
1
1
0
2
1
1
0
1
1
0
1
1
0
1
0
1
0
2
1
0
0
1
1
1
0
3
1
1
0
1
1
1
3
0
2
2
2
1
1
0
1
2
1
1
1
2
1
1
1
0
0
1
0
2
0
0
1
1
0
0
0
2
2
1
1
0
0
0
0
2
1
1
1
2
1
0
1
0
2
0
2
2
2
1
2
2
0
1
2
0
1
1
1
0
0
0
1
0
2
1
2
1
0
1
2
2
1
1
0
1
0
0
1
1
2
0
1
0
0
2
1
0
1
2
0
2
1
0
1
2
0
3
0
1
1
0
1
1
0
0
0
2
0
2
1
1
2
1
1
1
0
1
1
1
1
1
0
2
1
0
0
4
1
0
1
2
2
2
1
3
1
1
1
2
0
2
1
0
2
2
1
2
1
1
0
0
2
1
1
1
2
0
0
0
1
2
0
2
0
0
2
1
0
1
1
2
0
1
1
1
2
1
0
1
1
1
0
0
1
1
1
2
1
0
1
2
2
3
0
1
1
1
2
0
0
1
0
0
1
0
0
0
0
1
1
3
1
0
0
0
1
0
1
0
0
1
1
1
1
1
1
2
2
2
1
1
0
2
0
0
3
1
0
0
1
0
0
0
0
1
2
2
0
1
1
2
0
2
1
1
0
1
2
1
1
1
1
1
3
1
0
3
1
2
2
1
1
2
1
1
0
0
2
2
1
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
2
2
2
0
0
0
1
0
0
2
1
0
1
2
1
1
0
2
2
0
0
0
2
0
1
1
1
1
2
1
1
0
1
0
0
1
2
1
0
1
1
0
2
2
0
1
0
1
0
2
2
1
2
0
0
2
1
1
1
1
1
2
0
2
1
3
2
1
1
0
0
0
2
0
1
2
1
0
0
0
0
1
1
1
0
1
1
0
0
2
0
1
0
2
1
0
1
1
1
0
0
1
1
1
2
0
1
0
0
1
2
0
2
1
1
0
2
0
1
1
0
2
2
2
2
1
2
1
0
1
2
2
2
2
1
0
2
1
1
2
0
1
1
1
0
0
1
1
2
1
1
0
0
1
1
0
2
1
2
0
2
1
1
2
1
2
1
1
1
0
0
1
1
1
0
2
1
0
0
0
0
2
2
1
2
2
2
0
1
0
1
0
0
2
0
2
0
1
1
1
0
0
0
1
1
1
0
2
1
0
1
2
2
0
1
2
2
2
1
0
0
0
0
1
1
2
1
2
2
1
1
1
0
0
0
1
1
1
1
1
1
0
0
1
1
0
2
1
0
2
2
0
1
0
0
2
2
2
0
2
1
0
0
0
1
0
1
1
0
1
1
2
0
1
1
2
1
1
1
1
1
2
1
2
1
0
0
1
1
0
0
1
2
2
2
0
2
2
2
0
0
1
2
1
0
1
0
1
1
0
1
2
2
1
3
1
0
1
2
1
0
0
1
1
0
1
1
0
2
1
1
0
1
0
2
0
1
1
0
0
1
1
0
0
2
1
1
1
0
1
0
0
1
1
1
0
0
0
0
1
2
1
0
0
0
1
1
0
2
2
1
0
1
2
0
1
1
0
1
1
2
0
1
2
0
0
1
2
0
0
0
0
0
2
1
0
1
1
0
0
0
0
3
1
0
2
2
0
1
0
0
3
0
1
0
1
2
2
2
2
1
1
0
3
2
1
0
0
0
0
1
1
0
0
1
2
1
0
1
1
1
0
0
0
0
0
0
0
1
0
1
1
2
1
1
0
1
0
1
4
0
1
1
1
1
0
1
1
2
2
0
2
1
0
0
0
1
2
1
1
1
1
2
0
1
2
0
1
0
2
1
1
1
1
2
0
0
0
0
0
0
1
1
0
0
0
1
1
0
1
1
2
0
2
0
1
0
0
1
1
1
0
1
2
0
1
1
1
1
2
0
2
0
0
1
1
1
1
1
0
0
1
0
0
1
2
0
1
0
2
1
0
2
1
1
1
1
0
1
0
1
1
1
0
1
1
2
1
1
2
3
2
1
0
1
1
0
1
1
2
1
0
1
0
1
1
1
0
0
1
0
0
0
2
1
2
2
1
1
0
1
1
1
1
0
1
1
2
1
0
1
2
1
0
0
0
2
0
2
0
0
0
1
3
1
0
0
1
2
1
1
0
2
1
1
2
1
1
1
1
1
1
0
2
0
0
1
0
0
0
2
2
1
0
0
0
1
1
1
0
1
2
2
0
1
2
1
0
0
2
2
0
0
1
2
1
0
0
2
1
0
2
0
1
1
1
1
0
2
0
1
0
1
0
1
0
1
1
0
1
2
1
0
2
1
2
2
1
0
0
1
2
1
1
1
2
0
0
1
1
0
1
1
0
1
1
1
2
2
1
1
2
2
3
2
2
2
1
0
1
1
1
0
1
1
1
2
1
2
1
0
0
0
1
1
0
1
0
1
0
0
0
1
1
1
1
2
2
2
3
1
2
1
0
0
2
1
1
2
2
1
1
0
0
0
0
2
0
2
1
0
0
2
2
0
1
1
0
1
2
1
1
0
0
0
0
0
2
0
1
1
2
0
0
0
1
2
0
0
1
0
1
0
1
0
0
0
1
1
2
0
1
0
3
0
1
0
0
1
2
1
0
1
1
0
1
1
2
1
1
1
0
2
0
0
2
0
2
2
2
2
1
0
2
1
2
1
0
1
2
1
1
0
2
1
1
0
1
2
0
1
2
0
1
1
2
0
2
1
2
1
0
2
1
2
0
1
2
2
0
0
0
3
2
0
0
0
1
1
1
2
0
0
1
1
0
1
0
1
1
1
0
2
1
0
1
0
1
1
1
1
1
2
0
1
0
2
1
0
1
0
4
2
1
1
0
0
2
1
2
2
1
0
1
2
2
2
0
1
1
1
2
1
1
2
2
1
1
0
1
1
2
0
2
0
1
1
0
0
2
0
0
1
1
0
0
2
2
1
1
0
1
1
1
1
1
2
2
0
2
1
2
2
0
2
1
1
0
1
0
1
1
1
1
1
1
1
2
2
1
2
0
0
1
0
2
0
1
2
2
2
0
0
2
1
1
2
1
1
1
1
1
2
2
0
2
0
0
0
2
2
1
0
2
2
1
1
2
1
1
0
1
1
3
2
2
0
1
1
0
0
0
0
1
1
0
0
1
1
0
1
0
1
0
0
1
2
1
0
1
1
1
1
1
0
1
1
1
1
0
1
0
1
1
2
2
0
0
2
0
0
1
1
1
0
0
0
0
1
0
0
1
0
0
0
1
0
1
2
2
0
1
2
0
1
1
2
1
1
2
1
1
1
2
2
0
1
1
1
0
2
0
1
0
2
0
1
0
0
1
0
2
2
2
2
0
2
2
1
2
1
0
1
0
0
1
0
1
0
1
0
1
0
1
1
0
2
0
2
0
0
2
0
2
0
2
1
0
0
0
1
1
1
3
0
0
0
0
1
1
1
3
0
3
2
2
0
0
1
1
0
2
1
1
0
1
3
2
1
0
1
1
1
0
1
2
0
0
0
2
2
2
2
0
1
0
2
1
1
2
1
1
4
2
3
1
1
0
1
0
0
0
0
2
1
2
2
1
2
1
2
1
1
0
0
2
0
0
1
0
0
0
0
2
1
0
0
2
1
2
0
1
1
2
1
1
0
0
2
3
1
2
0
2
2
1
1
0
2
1
1
3
2
0
0
1
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
2
1
1
1
0
0
1
2
2
1
1
1
1
2
1
1
1
2
0
1
1
1
0
1
2
2
1
1
1
1
0
1
1
1
1
1
0
1
2
0
1
2
1
3
0
1
2
1
1
0
3
1
0
2
0
1
0
0
1
0
0
0
3
1
2
1
2
1
1
0
1
1
1
2
0
0
2
1
2
1
2
1
2
1
0
1
1
0
0
1
0
0
1
2
1
0
1
2
1
0
2
1
1
1
1
1
2
1
0
2
0
1
0
1
1
1
2
1
0
0
0
1
2
1
0
2
1
1
1
1
2
1
1
0
1
1
2
2
0
0
1
1
0
0
1
0
2
0
0
0
1
1
0
2
1
1
0
1
1
0
1
1
1
1
0
2
0
2
1
2
1
1
0
1
2
2
1
0
2
2
1
1
1
1
2
1
1
1
1
0
0
0
1
1
3
1
1
1
0
1
0
0
0
2
1
1
0
1
1
1
2
0
1
0
1
0
2
1
0
1
2
2
1
0
1
1
1
2
0
2
1
1
2
1
0
0
1
0
1
1
1
0
1
2
1
0
1
1
0
1
2
2
1
2
1
1
1
0
0
1
0
1
1
1
1
1
2
1
0
1
1
1
1
2
2
2
2
0
1
2
1
2
1
0
2
1
2
1
0
1
1
0
1
2
1
2
1
1
1
2
2
0
1
1
1
0
0
0
0
1
1
1
2
2
2
2
1
1
1
2
0
1
1
2
1
2
1
1
0
0
0
0
1
1
1
1
2
1
1
1
0
0
1
0
2
0
0
1
1
2
0
2
1
0
2
2
1
1
0
1
1
2
1
0
1
1
1
2
1
2
0
1
0
1
1
0
0
1
0
1
1
1
0
2
0
0
0
3
1
1
0
2
1
1
1
0
1
1
2
0
1
1
2
1
1
0
1
2
1
1
0
1
0
2
1
0
2
1
0
0
1
1
3
0
1
0
2
2
2
1
0
1
2
0
2
0
0
0
2
1
1
1
3
0
2
2
1
2
1
2
2
0
1
0
2
1
0
0
1
0
0
0
1
1
1
2
2
1
1
1
1
0
1
2
2
1
0
1
1
2
1
0
0
1
2
0
0
1
2
2
0
0
2
1
1
0
0
2
1
1
2
1
0
1
0
1
1
1
0
1
0
1
0
2
1
1
1
0
0
0
0
1
0
0
2
2
1
1
1
1
6
1
1
1
2
0
0
1
0
0
1
1
1
1
0
0
1
1
0
1
0
2
0
0
0
0
0
2
1
2
0
1
1
2
1
2
1
0
1
1
2
0
1
1
1
2
1
1
0
1
1
2
0
1
0
1
1
0
0
1
0
2
0
2
1
1
2
0
0
1
1
1
1
1
1
1
1
1
0
2
2
0
0
2
1
0
2
1
1
0
2
0
2
1
0
0
1
1
0
1
1
1
2
0
0
2
2
0
1
1
0
1
1
0
1
2
0
0
2
2
0
1
0
2
1
1
1
1
0
0
1
1
0
1
0
2
1
1
1
0
0
1
0
1
1
1
0
1
0
1
2
1
2
2
1
0
1
0
1
0
1
0
1
0
2
0
1
0
0
1
0
2
2
1
1
2
1
1
1
1
1
0
1
2
0
1
2
0
0
2
4
2
0
0
1
0
0
0
1
1
1
1
1
2
1
0
1
0
2
1
1
1
1
2
0
1
1
0
1
0
1
2
0
1
2
0
0
1
0
1
2
3
1
2
0
0
1
1
0
1
2
1
1
3
2
2
1
2
0
0
1
2
2
1
0
1
2
0
1
0
1
2
1
2
1
1
1
1
1
0
1
1
0
1
2
1
4
0
1
1
0
1
1
0
2
0
0
2
0
2
0
1
1
0
2
1
0
2
1
0
1
1
2
1
1
0
1
0
1
0
0
1
1
2
1
0
1
1
0
1
0
1
1
2
0
0
0
1
2
1
2
1
2
1
0
0
0
2
2
1
0
0
0
0
0
0
0
0
1
1
1
1
0
2
1
2
0
1
0
0
0
0
2
0
0
0
0
2
0
0
1
1
0
1
2
0
1
0
0
0
1
1
2
3
1
0
2
1
0
0
0
1
0
0
1
2
1
0
2
0
2
1
0
2
0
0
1
1
0
1
0
1
2
0
2
0
0
1
1
1
0
1
0
1
1
1
0
2
2
0
1
1
2
1
1
1
1
0
0
2
0
2
0
1
1
1
0
1
2
1
1
1
1
0
1
0
1
0
1
0
2
2
0
1
0
1
2
1
1
0
1
0
1
1
0
2
0
1
2
2
2
1
2
0
1
1
1
1
0
1
2
0
2
1
1
0
1
1
0
1
2
0
1
0
0
0
0
1
2
1
1
0
1
0
0
1
1
1
2
0
1
1
1
1
0
1
2
1
1
2
2
2
1
1
6
0
0
2
0
0
1
4
1
0
1
2
1
0
0
2
1
1
0
1
2
0
2
0
2
2
1
0
1
1
1
1
0
2
1
2
1
2
1
0
1
1
1
1
0
1
1
0
0
0
1
1
3
0
2
1
1
1
1
0
2
0
0
0
2
1
1
0
1
0
2
0
2
2
1
0
1
1
2
1
0
1
1
0
2
1
0
1
2
2
0
0
0
0
2
0
1
2
0
1
1
1
1
0
0
1
0
2
2
0
0
1
3
1
2
0
0
2
2
0
1
0
1
0
1
1
0
0
2
1
1
1
2
2
1
1
0
1
0
1
1
1
1
0
1
0
0
2
2
2
2
2
0
0
1
2
1
1
0
0
3
0
0
0
2
2
1
2
0
0
1
2
0
3
1
2
1
1
1
1
0
0
1
1
0
0
2
1
2
0
0
2
1
2
1
0
0
1
1
2
2
0
1
1
1
1
1
1
1
2
0
2
2
2
1
1
0
0
1
1
1
1
2
1
0
0
0
1
0
0
0
0
0
2
1
1
0
0
1
0
0
0
1
0
0
1
0
0
2
0
1
2
0
2
2
2
1
0
0
2
1
1
2
0
1
0
1
2
1
2
0
1
1
1
2
1
1
1
1
1
1
0
0
2
2
1
0
1
1
0
2
1
1
0
0
0
2
0
1
1
1
0
2
1
1
1
2
0
2
0
1
0
0
1
2
1
1
1
1
2
1
1
1
1
1
1
0
0
2
1
1
0
0
1
1
0
1
0
1
1
1
1
1
0
0
2
2
1
0
1
1
0
1
2
2
0
1
2
0
0
1
0
1
1
0
0
1
2
1
1
0
2
0
0
0
0
2
1
1
1
1
0
0
1
0
2
0
0
1
2
1
4
1
1
1
2
1
1
0
1
1
1
0
1
0
0
1
1
0
1
0
1
1
0
0
0
0
1
1
2
0
2
1
0
1
2
1
2
1
2
1
2
1
0
1
1
1
2
3
2
1
2
2
0
0
1
1
0
1
1
0
0
1
0
0
0
1
0
1
1
0
1
2
1
3
1
0
1
1
0
1
1
0
2
0
1
1
1
1
0
1
1
1
2
1
1
2
1
0
1
1
0
0
0
0
2
1
1
2
0
1
2
0
1
2
1
0
1
0
0
1
1
2
1
0
2
1
1
1
0
0
1
1
0
2
2
1
1
1
2
1
2
0
2
2
0
1
0
1
2
1
2
1
1
1
0
0
1
0
0
0
1
0
1
0
0
0
1
1
1
1
1
1
0
2
0
0
1
2
1
2
1
1
1
1
0
2
1
0
1
2
0
0
2
0
1
2
2
2
2
1
0
1
1
0
2
0
2
1
1
1
1
1
0
2
2
1
0
0
1
4
2
1
0
1
0
1
0
0
2
2
2
2
0
1
0
0
2
0
0
1
0
3
1
2
0
1
1
1
1
0
1
0
1
0
2
3
1
1
0
1
0
2
1
0
0
1
0
1
0
2
0
1
0
1
0
2
1
2
0
2
0
0
0
0
2
0
0
1
2
0
1
2
1
1
1
0
0
1
1
2
1
0
0
0
2
3
0
1
1
2
1
2
1
0
0
0
0
0
2
1
1
1
0
1
1
1
0
0
1
2
1
0
1
0
1
1
1
1
2
0
0
1
1
2
1
1
0
1
2
1
0
1
1
0
1
1
1
1
1
2
0
1
3
0
0
1
0
2
2
1
0
1
1
0
1
0
1
1
1
0
0
0
1
1
1
2
0
1
1
1
0
2
2
2
1
0
2
1
0
2
1
2
2
1
2
2
1
1
0
2
1
2
2
1
1
1
2
1
1
1
1
2
2
1
1
1
1
2
0
1
0
2
2
0
1
2
1
2
1
1
2
2
0
1
2
1
1
2
1
2
1
1
2
0
1
0
0
0
1
0
0
0
1
2
0
1
0
0
2
0
1
2
0
0
1
0
0
2
1
0
1
0
1
0
0
2
1
0
1
0
1
1
1
0
2
1
0
1
1
0
2
1
1
2
1
1
1
2
1
0
0
1
0
0
2
2
1
1
1
1
1
2
0
0
1
2
2
0
2
0
1
0
2
0
1
1
2
1
1
0
1
0
2
2
1
1
1
0
1
1
2
1
1
2
1
1
0
1
0
2
0
0
0
0
1
1
2
1
0
1
0
1
1
2
1
0
1
1
0
1
1
1
0
1
2
2
0
1
1
0
2
2
0
1
1
1
0
0
0
0
1
1
0
0
0
2
1
0
0
2
2
1
2
2
0
2
1
0
1
0
2
2
0
1
0
1
1
0
0
2
2
1
2
0
1
1
2
2
0
0
1
0
1
3
0
1
0
1
2
2
2
1
1
1
3
3
1
2
3
2
1
1
0
2
1
1
0
0
0
1
0
2
0
1
1
0
1
1
1
1
0
2
0
1
0
0
2
0
0
1
2
1
2
1
1
0
1
0
1
1
0
2
1
1
2
3
1
1
2
2
1
1
1
2
0
1
1
0
2
1
1
0
2
1
1
0
1
1
0
0
2
0
2
0
1
2
1
0
0
1
2
2
1
1
2
1
0
0
0
1
1
1
0
1
2
1
0
2
1
1
2
1
2
1
1
1
0
0
0
0
1
1
1
1
2
0
1
1
1
0
0
1
1
1
1
2
1
2
0
0
1
1
1
0
1
0
0
0
0
0
0
1
0
2
1
4
2
1
3
2
2
1
0
1
0
0
1
0
2
2
1
1
1
0
1
1
1
1
1
2
2
0
2
0
1
1
0
0
0
1
0
1
2
2
0
1
1
0
2
2
1
1
1
1
0
1
1
0
1
1
0
1
1
1
1
1
1
1
0
1
2
1
0
0
3
0
0
0
0
2
1
0
1
2
0
0
0
1
1
0
1
1
0
1
1
0
1
1
1
0
1
1
2
0
1
0
0
1
1
2
1
1
2
0
0
1
1
0
1
1
0
0
2
2
0
0
0
2
1
0
1
2
0
1
2
1
0
0
0
0
0
0
1
1
1
1
1
1
2
0
1
0
1
1
0
1
1
2
0
1
1
0
1
1
1
2
2
7
0
1
2
2
1
0
1
0
0
0
1
0
0
0
0
1
1
1
1
1
1
1
1
2
0
1
1
2
2
2
1
2
0
1
2
1
2
3
0
2
2
1
0
1
1
2
1
2
1
0
2
1
0
1
1
1
0
0
0
1
1
1
2
1
0
0
0
1
1
2
0
1
0
1
1
1
1
2
1
1
2
3
2
0
1
1
0
1
1
2
1
2
1
1
0
0
0
2
2
1
1
0
1
1
1
1
0
0
2
1
2
2
1
1
0
0
2
0
1
0
1
0
1
0
0
0
0
2
2
1
0
0
2
2
1
1
2
1
1
1
2
0
1
0
1
1
0
1
1
1
1
2
1
1
1
0
1
1
1
0
1
0
1
2
3
0
2
0
2
0
1
0
2
0
2
2
0
1
2
1
0
0
0
1
1
2
0
1
0
1
0
2
1
3
0
1
1
0
1
1
0
1
0
3
0
2
0
0
1
0
2
0
0
3
3
1
1
1
0
1
1
2
2
2
1
1
1
0
0
0
2
2
0
2
0
1
0
0
0
0
2
0
1
1
1
2
0
0
0
1
0
0
1
0
1
0
1
1
0
0
2
2
0
1
1
1
1
2
0
1
1
1
1
0
2
2
1
0
2
0
0
0
2
2
1
2
2
1
1
1
1
0
2
1
0
1
0
2
1
2
1
2
0
1
2
1
3
2
0
2
2
1
1
0
2
1
1
1
2
1
1
1
0
2
1
0
2
1
1
1
0
1
1
1
1
0
0
0
1
1
0
0
2
0
1
2
0
1
0
1
1
0
0
0
1
0
1
1
0
1
1
1
1
0
0
0
0
1
1
1
2
1
0
0
1
2
1
1
2
1
0
1
0
1
1
1
0
2
1
2
0
1
1
1
1
0
1
0
1
0
0
2
1
0
1
0
1
2
2
1
1
0
1
0
2
0
1
1
0
1
2
0
1
0
1
1
1
1
2
1
0
2
1
1
0
1
1
0
2
0
1
1
1
2
0
2
0
1
1
0
1
0
1
1
2
0
1
1
0
1
0
2
2
2
1
0
0
1
0
1
0
1
1
2
0
1
0
1
3
2
0
2
0
0
2
0
0
0
0
0
1
0
1
2
2
1
1
0
1
1
1
1
1
2
2
0
1
0
1
1
1
1
0
1
3
1
2
0
2
0
0
2
1
0
0
1
1
1
1
1
1
0
2
1
2
1
1
0
1
1
0
1
1
1
1
1
0
1
0
1
0
1
1
2
2
1
0
1
1
1
2
3
1
0
2
2
1
1
2
0
0
0
0
2
0
1
0
2
1
0
1
2
1
2
0
1
1
1
1
1
1
1
1
1
0
1
1
2
1
2
0
2
2
1
0
0
1
2
0
1
1
2
1
2
0
1
1
0
0
0
1
0
0
1
0
0
2
0
1
1
1
1
1
0
0
1
1
0
0
1
2
1
1
0
2
1
1
0
0
1
1
2
1
1
2
3
1
2
1
1
1
1
1
0
1
1
1
0
1
1
0
4
2
1
1
1
0
2
1
0
1
1
1
0
1
1
1
0
1
2
2
2
1
0
1
1
1
1
1
0
0
0
2
1
0
2
0
1
1
0
0
2
2
1
2
2
1
0
1
1
1
0
1
1
0
1
1
1
1
0
2
0
2
1
2
2
0
1
0
1
0
2
0
1
0
2
2
0
1
1
1
1
2
1
1
1
1
0
0
1
2
2
1
0
0
1
1
0
2
1
1
0
1
1
0
0
1
1
1
1
1
0
0
2
1
2
2
1
2
0
1
1
1
1
2
1
0
1
1
2
1
0
0
0
1
0
0
1
1
0
1
2
1
0
0
1
1
1
0
1
0
0
1
1
1
1
0
0
1
1
1
1
1
1
0
0
1
1
0
1
1
1
1
1
1
0
2
0
2
1
1
1
2
2
1
0
0
2
0
0
1
0
2
2
0
1
1
1
0
0
1
1
1
1
0
2
1
2
0
2
1
2
1
0
1
1
1
2
2
0
0
1
1
0
1
0
0
0
0
0
0
0
1
2
0
0
1
1
1
1
1
3
1
1
2
1
0
2
2
0
1
2
2
2
1
1
1
2
1
0
0
1
1
0
1
2
2
2
0
0
2
1
1
2
1
2
0
0
1
0
0
1
1
0
0
1
0
2
1
0
1
1
0
1
2
1
1
1
2
1
1
2
1
2
3
2
1
1
1
0
1
1
2
1
0
1
1
1
1
2
1
4
2
1
1
1
1
2
1
0
1
3
1
2
0
2
1
0
1
0
1
0
2
1
1
0
0
0
1
1
1
2
1
0
1
2
1
1
0
1
1
1
1
2
1
1
0
1
2
1
2
1
1
0
2
1
1
1
1
2
1
1
1
0
2
0
2
0
0
2
2
1
2
1
0
1
0
2
1
2
0
1
1
2
0
0
0
0
2
0
2
2
1
1
2
1
1
1
0
1
0
1
0
1
1
1
0
2
1
0
1
2
1
2
4
1
1
0
6
3
0
1
2
0
1
1
1
1
0
0
1
1
1
0
1
1
1
0
0
2
1
1
2
1
0
0
0
1
0
1
1
1
1
1
1
1
1
1
2
2
1
0
1
1
1
1
0
1
2
0
2
1
1
2
0
2
0
2
1
0
1
1
1
0
2
1
0
0
1
0
2
1
0
1
2
3
1
0
0
1
0
0
0
2
0
0
0
0
1
0
2
2
0
0
2
2
1
2
1
2
0
0
1
1
1
0
3
1
1
1
1
1
0
1
0
3
1
1
1
2
2
0
1
1
3
0
0
2
1
1
0
1
0
2
2
1
2
0
0
0
2
2
1
0
2
0
0
0
1
0
0
1
0
0
2
1
0
1
0
1
1
1
2
0
2
1
0
2
2
2
1
1
1
0
1
1
1
1
0
0
1
1
2
1
0
2
1
0
0
0
1
2
0
1
1
0
2
1
1
0
0
1
2
1
1
1
3
1
0
2
0
2
1
2
0
0
1
1
2
0
1
1
2
2
1
1
1
2
1
0
2
0
1
0
1
1
1
0
0
1
0
2
1
1
1
1
1
0
1
0
2
1
2
1
1
0
0
1
0
1
2
0
0
2
0
1
0
1
0
0
0
0
2
1
0
1
1
1
0
2
0
0
0
0
0
2
0
0
2
0
0
1
2
1
0
1
0
0
1
1
1
1
0
2
1
0
0
0
0
0
1
1
0
0
0
1
1
0
0
2
0
0
0
1
2
1
0
0
0
0
1
0
1
1
1
1
1
1
1
1
1
1
0
1
0
0
1
1
1
2
0
2
1
1
2
0
0
1
1
1
1
2
0
1
2
1
0
0
1
0
0
1
0
0
1
0
1
0
0
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
0
1
2
0
1
1
0
0
0
0
1
1
0
0
1
1
0
1
2
2
2
2
2
0
1
2
2
1
0
1
2
1
3
1
1
1
2
2
0
2
1
0
2
0
1
0
2
1
1
1
2
1
2
1
1
1
1
0
0
1
1
0
2
2
1
0
2
0
0
0
0
2
0
1
1
2
2
1
2
2
1
1
2
2
1
2
0
0
0
1
1
0
1
1
0
1
0
1
0
1
2
0
1
2
1
0
2
2
1
1
0
1
1
1
0
1
1
2
1
1
0
1
1
0
0
3
1
1
1
0
2
2
1
1
1
0
0
2
1
2
1
1
2
1
0
2
0
0
0
1
2
1
1
0
0
0
1
2
0
2
1
1
1
0
2
1
2
1
0
0
2
1
1
2
0
0
2
0
0
1
1
0
1
1
2
2
0
1
2
2
1
1
0
0
2
2
1
0
1
1
0
2
1
1
1
2
0
2
0
1
0
0
0
0
1
1
1
1
1
1
0
1
0
1
2
1
0
2
0
1
1
2
1
2
1
0
0
1
2
0
4
1
1
0
1
2
2
2
1
1
0
2
1
0
1
0
0
0
1
0
1
1
0
1
1
2
1
1
2
0
1
2
1
1
1
1
2
0
2
0
2
0
1
1
0
1
1
1
0
2
2
0
0
1
3
1
2
1
1
2
0
2
1
3
2
2
1
0
1
1
0
1
0
0
1
1
2
0
2
0
0
2
2
1
1
0
0
1
1
1
0
0
2
2
2
1
0
1
0
1
1
1
1
1
0
0
0
2
1
1
1
1
1
1
2
1
1
1
0
1
1
0
1
0
2
0
1
2
1
0
1
0
0
2
0
0
2
0
2
0
1
0
0
1
1
1
1
2
1
0
1
1
1
1
1
0
0
0
0
0
0
2
2
2
2
1
1
1
1
0
1
0
2
1
0
2
1
2
0
1
1
0
1
1
1
0
1
1
1
0
2
1
2
1
1
0
1
1
2
1
0
1
2
2
1
3
0
1
1
0
4
0
0
1
3
0
1
2
0
1
2
1
2
0
1
0
1
0
0
1
0
2
3
1
2
0
2
0
1
1
2
1
1
2
0
0
2
1
1
1
2
1
0
1
0
1
1
0
1
0
2
2
2
2
0
1
1
2
1
0
3
0
0
1
1
2
1
1
0
1
1
0
0
2
1
1
1
0
2
1
1
1
1
0
1
0
2
0
0
2
0
0
1
1
1
1
1
1
0
0
1
3
1
0
1
1
2
0
0
0
2
0
1
1
0
0
0
2
1
1
0
1
2
0
1
1
1
2
2
1
1
2
0
0
1
1
1
0
1
1
0
0
0
0
1
2
0
1
0
1
0
2
1
1
1
0
1
0
0
2
1
1
2
1
0
2
0
0
1
2
1
0
2
0
0
0
1
0
0
1
1
2
1
1
1
1
1
2
0
2
2
0
1
1
1
0
2
1
1
1
1
0
1
1
2
1
3
1
1
2
1
1
2
0
2
2
2
0
0
1
1
0
1
1
0
1
1
2
0
1
1
0
1
0
0
1
0
2
0
1
1
1
0
1
1
1
1
2
1
2
1
1
0
2
1
0
1
1
2
1
1
1
0
0
0
2
1
2
1
0
2
1
1
0
2
1
0
3
0
2
2
1
1
0
0
1
1
0
0
1
1
2
0
2
0
0
1
1
2
0
1
1
1
1
1
0
1
1
1
0
0
0
0
1
2
2
2
0
1
1
1
0
1
0
1
1
0
2
2
1
1
1
0
0
2
2
0
1
1
0
1
1
0
0
0
0
2
0
0
2
0
0
0
1
2
0
0
2
0
0
1
1
0
1
1
0
1
1
1
1
0
6
0
1
1
0
1
1
2
2
1
2
1
0
0
0
1
1
1
1
1
0
1
0
1
0
0
0
2
1
1
1
0
2
1
1
1
2
1
0
1
2
1
0
2
1
3
1
0
1
1
0
2
2
2
0
1
0
0
0
1
1
0
0
0
1
2
2
1
2
0
1
0
0
2
0
0
0
1
0
1
2
1
0
1
1
0
0
2
1
0
1
1
1
1
1
1
1
1
0
0
1
1
0
1
0
0
1
1
0
2
0
1
1
1
1
1
6
2
1
2
0
0
0
2
1
2
0
2
1
0
0
0
2
0
0
2
2
1
1
0
2
0
1
2
1
1
1
0
0
1
1
1
2
2
1
1
2
0
1
1
2
2
2
1
1
1
2
1
0
1
0
0
1
1
1
1
1
1
1
2
2
1
2
2
1
2
1
1
1
2
1
2
1
0
1
0
0
1
2
1
0
0
0
0
1
2
1
0
1
1
0
1
1
0
2
1
0
1
6
2
0
0
1
1
1
1
1
1
0
1
0
2
1
0
3
1
1
0
0
0
1
2
0
1
0
0
0
0
1
1
0
0
1
1
0
2
0
3
0
1
0
0
1
1
2
1
2
0
1
0
0
0
1
2
0
0
2
0
2
1
1
0
1
1
2
0
1
2
1
0
1
0
1
1
1
0
1
0
1
1
1
1
1
3
0
0
0
0
2
0
1
2
0
1
0
1
1
0
2
1
1
0
2
2
1
0
0
2
2
2
2
0
2
1
1
0
0
1
1
0
0
0
0
1
1
1
1
0
1
1
1
0
2
2
0
1
1
0
1
2
0
1
1
1
0
1
1
0
0
5
2
3
0
2
2
1
1
0
1
2
1
1
2
0
1
0
0
1
2
2
0
1
2
1
2
0
0
2
0
1
0
1
1
0
0
1
1
2
2
1
1
1
1
2
1
0
2
2
1
0
0
2
0
0
0
0
0
1
2
0
2
1
0
1
0
0
1
1
1
0
2
0
2
1
1
0
1
0
1
0
0
2
1
0
0
0
2
1
2
4
0
0
2
0
1
2
0
2
1
0
2
0
1
0
0
1
2
1
2
1
2
1
0
1
0
2
2
0
1
0
1
1
0
1
1
2
0
2
1
1
2
0
1
2
1
0
1
0
1
2
1
1
0
0
1
1
2
1
1
1
1
1
1
0
1
0
1
0
0
1
2
2
0
0
2
1
2
0
1
0
2
2
1
1
2
0
1
1
1
1
0
0
2
2
0
2
1
2
0
0
0
0
1
1
2
0
0
2
2
1
2
1
1
1
2
0
1
0
0
1
0
1
0
2
1
1
0
1
1
1
1
2
2
2
1
1
1
0
0
2
1
0
2
1
1
4
0
2
1
0
0
1
1
1
1
1
1
0
1
2
0
2
2
2
1
0
2
1
0
0
0
3
0
2
0
0
1
0
1
1
2
0
0
1
1
2
1
0
0
0
1
0
1
0
2
1
0
2
2
1
3
1
1
0
0
1
1
1
1
0
1
1
1
1
0
1
0
1
0
0
1
0
1
0
1
2
1
1
0
1
1
2
2
0
2
0
0
2
1
0
1
1
2
1
2
2
2
0
0
0
1
1
2
0
2
2
1
1
0
1
1
2
2
2
1
0
1
2
1
1
1
0
2
0
1
1
2
1
0
0
2
2
2
1
0
2
1
1
1
2
2
0
2
0
1
1
2
0
1
0
2
1
0
1
1
1
2
2
1
2
0
1
0
2
1
0
2
2
0
1
2
2
0
2
1
0
0
0
1
1
0
0
1
1
1
1
1
0
0
2
1
1
4
2
1
1
1
1
1
0
0
0
1
2
1
1
1
2
1
0
0
1
2
0
0
1
0
2
0
1
2
1
0
2
1
1
2
1
1
0
1
2
2
2
1
1
0
0
0
1
1
1
2
1
1
3
0
2
0
0
0
2
0
1
1
1
1
0
1
0
2
1
1
2
0
1
0
2
0
0
1
1
1
2
0
1
0
1
0
0
0
0
0
0
1
2
2
1
1
0
1
2
2
2
1
0
0
1
2
0
0
0
2
1
2
2
1
1
1
0
1
2
0
1
1
2
0
1
0
0
2
2
1
1
1
1
1
2
0
1
1
1
1
1
1
2
0
1
2
1
2
1
0
1
2
2
0
0
0
1
6
1
1
1
1
1
1
1
0
0
1
2
1
1
2
1
1
1
1
0
2
0
0
1
2
0
1
0
1
1
1
0
2
2
2
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
1
1
2
0
2
0
1
0
1
0
1
1
0
0
0
0
2
2
2
2
0
0
2
0
1
1
2
0
1
0
0
0
0
1
1
1
0
1
1
1
1
1
1
1
2
1
1
2
0
0
2
0
0
1
1
1
1
0
0
2
0
1
2
1
1
1
0
0
1
0
2
1
2
0
1
0
2
1
2
1
0
1
1
1
2
1
1
1
1
1
1
1
1
1
0
0
1
1
1
1
1
1
2
2
1
1
0
1
0
1
1
1
2
0
0
0
2
2
2
1
1
0
1
0
1
1
0
1
1
0
0
1
1
1
0
1
0
2
0
0
0
0
1
2
0
1
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
2
1
2
0
2
1
0
1
2
2
1
1
2
2
1
0
1
1
2
0
0
1
2
0
2
1
0
1
0
3
1
1
0
1
0
0
2
0
1
0
1
1
1
1
1
0
0
0
0
1
2
0
1
0
1
2
2
0
1
1
2
1
1
0
1
4
1
3
0
2
0
0
1
2
1
1
0
3
2
1
1
1
1
1
0
2
1
0
0
1
2
0
1
0
0
1
0
3
1
2
0
1
1
0
1
1
1
2
2
0
3
1
0
1
1
1
2
2
0
0
2
1
1
1
2
0
1
1
0
2
1
1
3
0
0
0
1
1
2
1
2
1
1
1
1
2
1
2
1
1
1
1
1
2
1
2
0
2
2
1
0
2
1
0
0
2
2
1
1
0
3
1
1
1
1
0
1
0
1
1
2
2
0
0
0
0
2
2
1
2
1
0
2
1
2
0
2
2
3
2
0
2
0
2
4
2
1
1
2
0
0
0
0
0
1
1
0
2
0
0
0
1
1
0
1
3
1
1
0
0
1
0
2
0
0
0
0
1
1
0
0
1
0
0
1
1
0
1
0
0
2
0
1
0
6
2
1
2
0
0
0
3
0
2
0
0
0
1
1
1
2
1
0
1
1
0
2
1
0
1
0
2
2
2
1
0
0
2
1
1
2
2
0
2
2
2
0
2
1
1
1
1
2
1
0
1
2
2
2
2
2
0
1
1
1
2
1
1
1
0
2
2
1
0
0
2
1
1
2
1
1
0
0
1
1
0
1
0
1
1
0
1
2
1
0
1
1
0
2
2
1
1
0
1
0
2
0
1
0
0
0
3
1
2
0
1
2
0
1
1
1
1
1
0
1
0
3
0
1
1
1
0
0
3
0
2
2
0
1
2
0
0
1
0
1
0
0
0
1
0
1
1
1
0
1
1
3
1
0
0
0
1
1
2
0
3
2
0
1
0
1
2
1
1
3
1
0
1
1
0
0
0
1
1
1
1
0
2
1
1
1
0
1
1
1
0
2
3
2
1
0
1
1
0
1
0
1
1
1
2
1
2
1
2
1
1
1
2
1
0
1
1
1
0
0
1
0
2
1
2
1
1
1
0
1
1
1
2
1
0
0
2
0
1
0
1
1
0
0
1
0
1
0
1
2
3
1
1
1
2
1
1
1
2
0
0
1
2
2
0
0
2
2
0
1
2
1
1
0
1
0
1
0
1
1
1
1
2
0
2
0
1
1
0
1
0
0
0
0
2
0
0
1
0
1
1
0
1
1
1
1
0
1
2
0
0
1
1
1
1
1
0
2
1
1
1
0
0
0
1
0
1
2
0
1
2
1
1
0
1
0
0
0
1
1
0
0
2
1
1
1
2
1
0
0
1
2
2
0
2
1
2
1
2
0
2
0
1
0
2
1
2
0
1
0
0
1
0
0
1
2
2
2
1
1
1
1
1
1
1
1
0
2
0
0
0
1
0
0
1
1
0
2
1
1
1
0
1
0
0
2
0
1
0
0
2
2
2
1
2
2
0
1
1
0
1
1
0
0
1
2
2
0
1
0
0
2
2
1
1
0
0
1
1
0
1
0
1
1
2
1
1
0
0
0
1
0
0
0
1
0
2
1
0
1
2
1
1
2
1
0
1
2
2
0
0
1
1
0
0
0
1
1
0
2
1
0
2
0
1
0
0
1
0
0
2
1
0
2
1
0
0
1
0
2
2
0
1
0
1
1
2
2
2
1
1
0
0
2
1
0
1
2
0
1
0
0
1
2
0
0
2
1
1
1
1
0
1
1
0
0
0
2
0
2
0
4
1
1
0
3
0
1
0
1
0
0
1
1
1
1
1
2
2
0
1
1
0
1
2
2
0
2
0
0
1
2
1
1
1
1
2
0
1
1
1
1
2
0
0
3
2
0
0
2
1
0
0
1
0
0
1
0
1
2
0
1
1
0
1
1
0
0
1
2
1
0
2
3
1
0
2
1
1
0
0
1
1
0
1
2
1
0
2
0
1
0
0
0
2
1
1
2
2
2
1
0
0
0
1
1
2
0
0
1
1
1
1
1
3
1
1
2
1
0
4
1
2
1
0
1
1
2
1
0
0
0
2
0
1
0
2
0
1
0
0
1
0
0
1
0
2
1
1
1
2
1
2
1
2
0
1
1
2
1
2
0
0
1
0
1
1
1
0
2
1
1
1
2
1
1
1
0
1
2
1
2
0
1
0
0
0
2
2
1
1
0
2
1
1
1
2
1
1
0
0
2
0
2
1
0
1
1
1
0
1
0
1
1
1
1
0
1
2
0
0
0
0
0
1
0
0
1
2
0
2
0
1
1
0
1
0
0
0
1
0
0
2
1
0
0
0
0
2
1
1
1
0
0
0
1
1
0
0
2
0
1
1
0
0
0
0
0
2
1
0
0
0
0
1
1
2
0
0
0
1
1
1
0
0
1
0
2
0
2
2
0
0
5
3
2
1
0
0
2
2
0
0
0
0
0
1
0
1
2
1
1
1
0
0
2
0
1
1
1
2
0
0
1
2
0
3
0
2
1
1
1
2
1
1
0
2
0
0
1
1
1
0
1
1
1
0
1
1
0
1
0
1
0
0
1
0
0
2
1
0
1
2
1
1
1
1
0
0
2
2
2
1
1
1
0
1
3
0
1
1
0
1
1
0
1
2
1
1
1
2
0
1
1
1
0
1
0
1
0
0
1
1
1
1
1
0
2
2
0
2
1
1
1
1
0
1
2
0
2
0
0
1
1
1
2
0
2
2
1
1
1
0
2
0
1
2
1
1
1
1
1
1
2
1
1
0
0
0
2
1
1
1
1
0
2
1
0
0
0
0
0
0
0
2
1
1
1
1
2
2
0
0
2
2
1
0
1
1
1
0
1
0
2
1
1
0
1
0
1
0
1
0
0
1
1
2
2
1
0
0
0
2
0
1
2
0
1
0
1
0
1
1
0
1
2
0
0
0
0
0
2
0
2
2
1
2
1
1
0
1
1
1
0
1
1
0
0
0
0
0
2
0
0
1
3
1
0
2
2
2
0
1
2
2
0
0
1
2
1
1
2
0
2
1
1
0
0
1
1
0
1
0
0
0
1
1
0
1
0
1
0
0
1
1
0
0
1
0
1
1
1
2
0
1
0
0
0
1
1
0
1
1
2
0
1
2
1
1
0
1
1
1
1
0
0
2
1
0
0
0
2
1
2
0
0
1
1
1
1
1
2
1
1
1
2
2
1
0
1
1
0
0
1
2
2
1
0
2
0
0
0
2
0
1
1
1
0
1
1
1
1
0
0
1
0
2
1
3
0
1
1
2
1
0
0
0
0
1
0
1
0
0
1
2
1
1
2
1
0
1
2
1
0
0
1
2
2
1
1
0
1
0
1
1
1
0
0
1
1
1
2
0
2
1
2
0
0
2
1
2
1
2
0
1
2
1
1
1
0
1
1
0
1
2
1
1
1
2
1
0
1
0
1
1
1
1
0
0
1
2
1
0
0
2
1
1
0
1
1
0
2
0
1
1
2
2
0
1
0
1
0
1
1
1
1
1
1
0
1
0
2
1
1
2
1
2
2
0
0
0
0
0
0
1
3
0
1
0
1
0
1
1
1
0
1
2
2
0
1
1
0
2
0
0
1
0
0
0
1
1
2
1
0
1
1
2
0
1
0
1
1
0
0
0
0
1
1
1
0
1
3
2
2
0
1
0
0
0
2
0
1
0
0
1
3
0
0
0
2
2
2
0
2
0
1
0
2
2
2
1
2
1
1
1
1
0
1
1
3
2
0
1
2
1
2
1
0
1
2
0
1
0
0
1
1
1
2
1
2
0
0
1
0
0
2
1
1
1
2
1
2
1
2
1
1
2
1
1
0
2
2
0
1
2
2
1
3
2
0
1
1
1
0
2
1
0
1
2
1
0
1
2
1
0
1
1
0
0
0
2
0
1
0
0
2
2
0
1
1
1
1
1
1
0
0
0
1
1
1
0
1
2
2
2
1
1
1
2
1
1
2
1
1
1
1
2
0
0
1
0
1
0
1
1
1
0
2
1
1
2
2
1
1
1
1
1
0
2
2
1
1
1
1
0
1
0
1
2
1
1
1
1
2
1
1
0
2
2
2
0
1
0
1
1
2
1
2
1
1
0
2
0
1
2
1
0
0
0
1
1
0
0
2
0
1
2
1
1
0
0
2
0
0
1
2
1
0
0
0
2
1
1
0
0
2
1
1
0
1
1
0
2
1
1
1
1
0
1
0
2
0
0
1
0
0
2
1
2
1
2
0
0
0
1
2
1
2
0
1
1
0
1
0
1
0
0
0
1
1
2
1
1
0
1
0
0
0
1
0
2
1
1
2
0
1
1
2
2
2
1
0
2
0
0
1
1
0
2
1
0
2
1
1
1
0
0
0
2
0
0
1
0
2
1
1
0
1
2
1
1
1
2
1
0
1
1
1
0
0
1
1
0
1
2
1
1
2
1
1
2
1
1
0
0
0
0
1
1
1
0
1
0
0
2
1
2
1
2
0
2
1
1
0
0
1
0
0
0
1
0
1
2
3
0
0
2
2
2
1
1
0
2
1
1
2
2
1
1
2
1
0
1
0
2
0
2
1
2
1
1
0
1
1
1
0
2
1
0
1
0
0
1
1
0
1
3
1
0
1
1
1
0
1
0
0
2
0
2
1
0
1
1
2
0
1
0
1
0
1
1
2
0
1
2
1
3
1
1
1
1
0
0
1
2
1
1
0
1
2
1
1
0
0
1
0
3
1
0
0
1
0
3
2
1
1
2
2
2
1
1
1
2
0
1
0
0
0
1
1
1
3
0
0
1
2
1
1
2
0
1
0
2
2
0
2
2
1
0
0
0
2
0
1
2
0
1
1
0
0
2
0
0
2
1
1
0
1
0
0
0
2
1
1
1
2
0
0
2
0
2
1
1
1
0
2
2
0
2
1
1
1
0
1
2
1
0
3
1
2
0
1
1
0
2
1
1
1
1
2
2
2
1
1
1
0
0
1
1
2
0
0
0
1
1
2
2
0
1
0
1
1
2
2
0
1
2
2
1
1
1
0
1
0
2
1
1
2
1
1
0
1
0
1
1
0
0
0
2
0
1
1
2
0
2
2
1
0
0
1
0
1
0
0
1
0
1
1
2
1
1
0
1
1
1
2
1
1
1
1
1
2
1
1
2
1
1
0
0
1
1
0
0
1
1
1
1
0
1
2
2
1
1
1
1
0
1
1
1
0
1
0
1
1
0
1
1
0
0
1
1
1
1
0
1
0
0
1
2
1
1
0
0
0
2
0
1
0
2
1
0
1
2
4
7
1
1
1
0
0
1
0
1
2
0
1
2
1
1
0
1
2
2
1
1
0
1
1
0
1
1
2
0
2
0
2
1
1
1
1
1
0
1
1
1
0
1
1
0
2
1
0
2
0
1
1
0
1
0
0
1
0
1
0
1
0
1
2
1
1
0
1
0
1
0
0
1
2
1
0
2
0
0
1
2
2
1
0
1
1
0
2
0
2
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
2
0
1
1
1
0
2
2
1
0
0
1
2
0
1
0
1
0
1
0
1
1
0
1
1
1
1
1
2
0
0
2
0
0
1
2
0
0
1
1
0
1
2
1
1
2
2
1
1
0
3
2
0
0
1
1
0
0
1
1
0
2
1
1
1
1
1
1
2
1
0
2
1
1
1
0
1
0
0
2
1
2
1
0
0
1
0
0
1
1
2
1
2
0
0
0
1
2
1
0
0
0
0
1
0
2
0
2
2
1
2
2
0
1
2
1
1
2
0
1
0
2
2
0
1
2
0
0
2
1
0
1
1
0
2
1
2
1
1
0
1
0
1
0
1
1
0
1
0
0
2
0
1
1
1
1
0
2
1
2
2
1
4
0
0
0
1
2
0
1
0
1
0
2
1
0
1
0
1
2
0
1
0
0
0
1
2
0
2
0
1
0
1
0
2
1
1
0
1
3
0
0
1
0
0
1
0
0
0
0
1
1
2
0
1
1
1
2
1
1
1
0
1
0
2
1
0
1
1
0
0
1
2
1
0
0
0
1
1
2
0
0
1
0
1
0
1
2
1
0
0
2
0
1
1
1
1
0
1
1
1
2
2
1
1
2
0
0
1
0
0
0
1
1
0
2
0
1
0
1
0
1
2
0
0
1
0
0
0
2
1
2
0
2
0
1
0
1
1
0
2
0
0
0
0
2
0
0
0
0
1
1
2
1
0
2
1
3
2
2
0
0
1
2
0
1
0
0
0
1
3
3
0
3
2
2
1
0
2
1
1
0
1
0
2
1
0
0
0
2
0
1
1
1
0
2
1
1
1
1
2
2
3
1
1
2
0
2
1
1
0
2
1
1
1
0
1
2
0
1
2
1
1
2
0
0
1
0
1
0
1
0
1
1
1
0
0
0
1
0
1
1
0
1
1
1
0
2
2
2
2
2
1
1
2
0
2
2
1
0
1
0
2
1
0
0
1
1
1
0
0
0
0
2
0
1
3
2
0
1
0
0
0
1
0
1
1
1
0
0
0
1
0
2
1
1
0
1
0
0
0
1
2
1
1
1
1
1
2
0
2
0
1
1
1
0
0
1
0
1
0
1
0
1
2
1
0
1
1
2
0
0
2
0
2
1
2
0
1
0
1
1
2
1
2
2
1
1
0
1
1
1
2
1
0
2
1
1
0
2
1
0
2
2
1
1
1
0
0
0
2
1
1
0
1
1
1
2
2
0
2
1
1
0
2
2
0
2
3
0
1
1
1
1
1
1
2
1
0
0
1
0
1
1
1
2
1
1
2
1
2
0
1
1
2
2
0
2
0
2
1
2
1
2
2
1
0
2
1
2
0
0
0
1
1
1
0
1
1
2
0
1
1
0
0
1
0
1
1
0
1
0
0
1
1
1
2
0
2
0
1
1
0
2
1
0
2
1
1
1
2
0
0
1
2
1
2
1
2
1
1
1
2
0
1
1
2
0
2
0
1
1
1
0
0
0
1
0
0
0
1
2
0
1
1
0
0
2
2
2
2
1
1
1
2
1
2
0
1
0
1
0
0
1
1
2
0
0
1
0
2
1
0
2
0
2
0
0
0
1
0
1
2
2
2
1
0
1
1
0
1
2
1
1
1
0
2
2
1
1
2
0
1
0
1
0
0
1
1
2
2
1
0
1
2
1
0
0
2
0
0
2
2
1
2
1
1
0
1
0
0
1
1
0
0
0
0
1
1
1
1
1
1
1
2
0
1
2
1
2
1
1
1
0
0
0
1
1
1
1
1
0
1
1
1
0
1
2
2
1
2
1
1
0
2
0
2
1
1
0
0
0
0
1
0
0
2
0
1
1
1
2
1
2
1
2
2
1
1
0
0
1
2
1
2
1
0
1
1
1
0
0
1
0
2
1
1
2
0
0
0
0
1
0
1
0
0
1
0
0
1
2
2
1
2
1
1
1
1
1
0
1
1
1
1
0
2
1
1
0
1
2
1
2
1
0
2
0
1
1
1
1
0
0
1
1
1
1
2
0
2
1
0
1
1
1
1
2
0
2
0
0
1
1
1
0
0
2
1
2
1
2
1
0
0
0
2
1
1
1
1
1
1
2
0
1
2
1
1
1
1
1
0
2
0
0
0
1
1
0
2
0
1
2
1
2
2
0
1
1
0
2
2
1
1
0
1
0
1
2
0
0
0
1
2
1
0
1
1
1
0
1
1
0
0
1
1
2
2
1
2
1
1
0
1
1
1
1
1
2
1
0
1
2
1
2
1
1
2
1
2
2
2
3
1
0
1
2
1
1
2
2
1
1
2
1
1
0
2
0
1
1
2
1
1
1
1
1
0
1
1
0
1
0
2
1
1
0
1
1
1
0
1
1
0
2
0
1
1
2
1
1
0
0
1
0
0
1
2
0
1
1
1
1
0
1
2
0
1
2
1
2
1
1
1
1
1
1
1
2
0
2
0
0
2
0
1
0
1
0
0
0
1
1
1
1
1
1
3
2
1
1
1
1
0
1
0
1
2
2
1
0
0
2
1
0
0
0
2
1
1
1
0
3
0
0
0
1
0
2
1
1
1
1
0
1
0
1
2
2
1
0
0
1
0
0
1
0
1
2
2
2
2
2
1
1
1
1
0
3
2
1
2
2
0
2
1
1
2
2
1
3
1
1
0
0
1
0
2
1
2
0
1
0
0
0
0
1
1
1
2
1
1
2
2
2
0
1
0
0
2
1
2
0
1
1
1
1
1
2
1
1
2
0
1
0
2
2
0
1
1
1
1
1
1
1
1
1
0
0
2
3
1
0
2
0
2
0
2
1
0
2
0
0
0
1
1
1
0
1
1
0
0
1
0
0
0
0
1
1
1
2
1
1
1
0
0
0
1
1
0
1
1
0
0
0
1
0
1
2
0
0
2
0
1
0
1
1
1
0
2
1
2
0
0
2
1
2
2
0
3
2
0
1
1
0
0
2
1
1
1
1
2
2
0
2
0
2
0
2
2
0
1
1
0
2
1
1
0
1
1
0
3
2
1
3
1
1
1
2
2
2
2
1
1
2
0
2
2
0
0
2
1
0
0
1
0
1
0
0
0
0
1
1
4
1
0
1
1
1
1
2
1
1
2
1
2
0
1
0
0
0
0
1
1
2
0
2
1
1
2
2
2
1
1
1
2
1
1
1
2
0
0
4
1
4
2
1
1
0
1
1
0
1
0
1
1
2
1
0
1
2
1
0
1
1
2
0
1
1
1
1
3
1
1
0
1
0
1
1
1
1
2
1
0
0
1
1
1
2
0
1
1
0
2
2
1
2
0
0
0
2
2
1
1
1
0
1
1
1
1
2
1
1
0
1
1
2
1
0
2
1
1
0
2
0
0
2
1
2
0
1
1
0
1
2
0
1
1
2
0
1
1
1
1
2
2
1
0
0
2
0
0
2
1
2
0
0
0
2
2
1
0
1
0
1
1
2
0
0
0
0
0
2
2
1
0
3
0
1
1
0
2
0
2
0
0
0
1
0
1
1
0
1
1
0
1
0
0
0
2
2
0
2
2
1
1
1
1
0
1
2
1
1
1
2
2
2
1
1
1
2
2
1
1
0
0
1
0
0
1
1
1
0
1
0
1
2
2
1
0
2
1
1
1
4
2
2
0
1
1
2
1
1
1
2
1
2
0
0
0
1
1
1
1
0
2
2
1
2
1
1
1
1
1
2
2
0
1
0
2
0
0
0
1
1
1
2
1
1
0
1
0
1
1
1
2
2
2
0
0
2
1
1
0
2
0
1
1
1
0
2
1
2
2
0
2
0
1
2
1
0
2
0
1
2
0
1
1
1
1
2
0
0
1
1
1
0
2
5
0
0
0
1
0
0
1
2
2
1
1
1
1
2
2
2
0
1
1
0
1
1
1
2
0
1
0
0
1
0
2
0
2
1
1
1
1
1
0
1
0
1
1
1
1
1
1
1
2
1
1
0
1
0
1
1
0
0
0
1
1
1
2
1
0
2
1
1
0
0
1
2
2
1
0
0
1
2
0
0
0
0
0
1
1
2
0
1
0
1
1
2
0
1
2
1
0
2
1
0
1
2
0
1
1
2
0
1
0
0
1
1
1
0
1
1
1
0
0
0
0
1
2
1
1
1
1
0
0
1
1
1
1
2
1
1
1
1
2
1
2
2
0
1
2
1
1
0
1
2
1
1
1
0
0
0
1
2
1
2
2
3
0
0
1
2
2
1
1
1
1
2
1
0
0
1
0
1
0
0
1
1
0
1
0
1
0
1
1
1
0
0
0
1
1
1
2
0
1
0
1
0
0
1
1
0
1
1
0
1
0
2
6
0
0
2
0
2
1
0
0
2
0
1
1
1
1
0
1
1
1
1
2
1
1
0
2
1
0
1
2
1
1
1
2
2
2
1
0
1
0
0
1
1
1
0
0
1
0
0
1
1
1
0
1
1
0
1
1
1
1
2
1
0
2
1
0
2
2
2
0
1
0
0
0
1
2
0
2
2
0
0
1
1
0
4
1
1
1
1
2
0
0
0
1
0
1
1
0
1
1
2
1
0
0
1
1
1
2
1
1
1
1
1
0
2
0
0
0
2
1
2
1
2
1
0
0
2
1
0
0
0
0
0
2
2
2
2
0
2
1
0
0
0
2
1
1
2
2
1
0
1
0
2
1
1
0
1
0
2
2
2
1
1
1
2
1
0
0
2
1
0
0
1
1
2
0
2
0
1
2
1
1
0
1
1
0
0
0
2
0
0
0
1
1
1
1
0
0
0
0
1
2
0
2
0
0
1
2
1
0
0
0
1
1
0
2
1
0
1
1
0
1
2
0
1
2
1
2
2
1
1
0
1
1
1
1
2
1
1
1
0
0
0
1
2
1
0
1
2
1
2
0
2
1
4
0
1
0
1
1
1
0
2
0
1
0
1
0
0
1
2
1
1
0
1
2
0
1
0
1
2
0
1
1
1
0
0
1
1
0
0
1
1
0
0
0
1
0
0
0
2
0
0
1
1
1
2
0
0
2
2
1
0
0
0
0
1
1
1
0
1
0
0
2
1
1
2
2
1
1
0
2
1
1
1
2
0
1
2
1
0
0
0
1
1
0
1
1
0
1
1
1
1
0
1
0
0
1
0
0
0
2
1
0
0
0
1
1
2
1
1
1
0
1
2
1
2
0
1
0
1
2
1
1
1
2
1
0
1
2
3
1
2
1
1
0
0
1
1
1
0
0
2
0
2
0
2
2
1
2
2
1
2
1
1
1
1
1
1
0
0
0
2
1
1
0
2
1
2
0
2
1
2
1
1
1
1
2
1
0
0
1
2
0
0
1
1
0
0
0
1
0
1
0
1
1
2
1
2
1
0
2
1
1
0
1
1
1
0
1
2
1
2
1
1
1
0
1
2
1
1
1
1
0
1
3
2
0
0
1
2
2
0
1
0
0
2
2
1
1
0
1
1
1
3
2
0
1
0
0
1
1
1
0
1
2
1
1
0
0
1
1
1
1
0
1
1
0
0
1
0
0
0
0
0
2
2
1
0
2
1
1
0
0
1
2
0
1
1
1
0
1
0
0
1
1
1
1
1
1
1
2
1
1
1
0
0
1
1
0
1
1
1
2
1
1
0
0
0
0
1
1
2
1
2
1
0
1
1
1
2
1
1
1
0
1
0
1
0
2
0
1
1
1
1
0
0
0
1
1
0
0
0
1
2
1
2
1
1
2
2
0
1
1
1
0
3
0
0
1
1
1
2
0
0
2
2
0
0
0
0
2
1
0
2
1
2
1
0
0
1
1
2
1
0
0
1
2
0
2
0
0
0
1
2
2
2
1
0
0
2
1
2
0
0
0
1
0
1
2
1
1
1
3
1
1
0
1
2
2
0
1
0
0
2
2
1
1
2
0
1
2
0
1
0
1
0
0
1
1
2
0
0
0
1
0
2
1
0
2
2
2
2
2
1
1
0
1
0
1
1
0
2
1
0
2
0
0
1
0
0
2
0
1
0
0
1
1
1
1
1
0
1
1
1
2
0
0
1
1
2
5
0
1
1
1
3
0
2
0
2
1
1
1
1
1
0
1
2
1
1
1
0
3
1
1
0
1
2
1
0
1
1
2
3
0
1
1
1
0
1
2
1
1
2
1
1
2
0
0
1
0
2
2
2
1
0
0
1
0
0
1
0
1
0
1
2
1
0
1
2
0
1
0
1
1
1
1
0
1
0
1
2
1
1
0
1
0
1
2
0
1
1
0
0
0
1
1
0
0
2
1
0
1
0
2
0
1
3
1
2
1
0
0
0
2
1
2
1
0
0
0
0
2
2
0
0
2
1
1
2
1
1
1
1
1
1
1
1
0
3
0
1
2
1
1
0
2
1
0
1
0
2
2
0
1
1
0
2
2
1
0
2
0
2
2
1
1
1
0
1
2
1
1
1
2
0
1
1
0
1
0
0
2
2
2
1
0
2
1
1
0
1
1
3
2
0
1
1
2
1
1
1
0
1
1
0
1
0
1
0
0
1
2
1
2
0
2
0
1
1
0
1
0
0
2
2
0
1
4
0
1
0
1
1
0
1
2
4
1
1
2
1
0
1
1
2
0
2
0
1
1
0
1
0
0
1
0
1
1
1
1
1
4
0
0
2
1
1
2
2
0
0
1
2
1
2
1
1
2
0
0
0
1
1
1
0
0
1
3
0
1
2
1
1
1
2
2
1
1
1
1
2
2
0
0
2
1
1
1
0
1
1
0
2
1
1
1
0
1
1
2
1
0
1
2
1
0
0
1
1
0
0
0
1
1
1
0
2
0
0
0
0
1
0
2
1
1
3
2
2
0
2
1
1
1
1
1
0
1
2
1
1
1
0
0
1
0
2
1
0
1
1
1
1
1
1
1
0
2
1
0
2
1
1
0
1
0
2
0
1
0
1
0
1
2
0
1
0
1
1
0
1
0
0
1
2
1
1
1
1
0
1
1
1
2
1
0
2
0
1
1
1
1
2
0
0
0
1
1
2
1
0
2
1
0
0
0
1
2
0
1
0
0
3
1
1
2
0
1
1
0
2
1
1
1
0
2
1
1
2
1
1
0
1
1
1
0
1
0
1
1
2
2
2
0
1
0
0
0
1
2
1
0
0
1
1
1
0
1
2
0
0
1
0
1
1
2
1
3
1
1
0
1
2
0
0
1
0
1
0
1
0
2
1
1
1
0
0
1
0
1
1
0
2
2
1
0
0
0
0
0
0
2
1
0
1
1
1
2
2
0
0
1
1
0
0
1
1
2
1
1
2
0
2
1
1
0
1
0
0
2
0
0
0
1
2
0
0
2
0
1
1
1
1
1
1
2
1
0
1
0
1
0
1
1
1
1
0
1
1
0
2
1
1
0
1
1
2
0
1
1
1
2
0
0
2
1
1
1
1
0
0
1
1
0
0
0
0
1
2
0
0
2
1
2
1
1
1
1
0
1
1
1
0
0
0
0
1
0
1
0
1
0
2
2
1
0
0
2
1
1
1
0
1
0
0
0
1
1
1
1
1
1
1
5
3
1
2
1
0
1
1
0
1
1
1
0
0
1
0
1
0
1
1
1
1
1
0
0
0
1
2
0
0
1
0
1
0
2
2
1
0
1
1
1
0
1
1
2
1
1
0
1
0
2
0
1
0
0
0
2
0
0
1
0
0
1
2
1
0
0
2
0
0
1
2
1
1
1
1
0
0
1
1
0
0
0
1
2
0
2
0
2
1
1
1
0
0
2
0
0
1
1
1
2
2
0
1
0
2
2
2
1
0
1
2
1
1
0
1
2
2
1
1
1
1
0
1
2
0
2
1
1
0
1
2
0
1
0
0
1
2
1
0
2
1
1
1
0
1
1
2
1
0
1
0
1
0
1
1
1
1
1
1
0
2
1
0
1
1
2
1
0
2
1
2
1
1
1
1
2
1
0
1
1
0
2
1
1
1
3
0
1
0
1
2
0
1
1
1
2
1
0
0
2
0
3
2
1
0
1
1
0
0
2
0
2
1
1
0
1
3
0
2
0
2
1
0
0
0
1
0
2
1
2
0
1
2
1
2
1
1
1
1
2
2
1
0
1
1
2
1
0
1
0
1
0
1
1
0
1
0
0
2
1
1
1
1
1
1
0
1
1
1
1
1
0
1
1
1
1
1
0
1
1
1
2
0
0
0
1
2
0
0
0
0
0
0
1
0
2
0
3
2
0
0
0
2
0
0
0
2
2
0
1
3
2
2
1
0
1
2
2
1
0
1
0
1
1
3
2
0
1
1
1
0
1
1
0
0
2
0
0
2
1
2
2
1
1
1
0
0
0
2
1
2
1
1
1
2
0
0
2
1
1
0
2
2
0
1
0
0
0
1
2
2
0
1
0
1
1
0
0
2
1
1
2
1
0
0
3
2
0
1
1
2
1
2
2
1
0
1
0
0
0
0
0
1
0
0
1
0
0
1
1
0
1
0
2
2
1
2
1
1
0
0
1
1
2
0
2
0
1
1
0
1
1
0
0
2
0
1
2
1
2
1
2
0
0
0
1
1
1
1
0
1
0
1
1
4
1
1
1
1
2
1
1
0
0
0
1
0
2
2
1
0
2
1
1
1
2
0
1
1
1
2
1
2
0
2
1
1
1
0
2
0
2
1
1
1
2
1
2
1
2
1
1
0
0
1
2
1
1
1
1
1
1
2
1
1
0
2
1
1
0
2
1
1
1
1
1
1
1
2
0
1
2
1
3
2
1
1
1
1
2
0
1
1
0
0
1
0
0
1
1
1
1
1
0
2
1
0
1
0
0
2
0
2
0
0
0
0
0
2
0
0
0
1
1
1
2
2
1
1
1
0
2
3
2
1
1
1
1
2
0
0
1
1
0
0
2
1
2
1
1
1
1
0
1
0
1
2
0
2
1
1
0
0
1
1
0
1
0
1
2
1
1
0
0
0
2
1
0
1
1
4
1
2
1
1
1
0
2
1
1
2
2
2
1
1
1
2
0
2
2
2
2
0
1
1
1
0
2
0
0
2
0
2
2
2
0
1
1
1
0
1
0
1
0
0
2
0
0
0
1
1
0
0
1
3
2
0
1
2
0
2
1
1
2
1
1
2
2
2
2
0
1
0
1
2
0
0
1
2
1
1
1
1
0
1
1
1
2
1
2
1
2
2
1
4
1
1
0
1
1
1
1
2
0
1
0
1
0
0
2
0
1
1
1
0
1
1
0
0
1
2
1
2
1
0
1
0
2
2
0
2
1
0
1
2
1
2
2
2
1
1
0
0
2
2
2
2
1
1
1
1
1
1
0
2
1
2
1
1
0
1
2
0
3
2
2
1
0
1
1
1
0
1
0
0
0
1
1
2
2
1
1
1
2
2
0
0
0
2
1
1
1
0
0
0
1
2
1
1
0
0
1
1
2
1
0
0
0
2
1
1
1
2
1
0
0
1
1
1
0
2
1
0
1
1
1
1
2
0
2
1
0
2
2
1
0
0
0
1
0
0
2
0
1
1
0
2
1
0
1
1
1
1
1
2
0
2
1
0
1
1
0
0
1
0
0
0
2
2
0
1
1
1
0
1
0
1
0
0
2
1
1
3
1
1
1
0
0
1
0
2
1
1
0
1
0
0
1
1
1
0
0
1
1
1
0
2
0
1
0
0
1
1
0
1
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
1
2
2
0
1
1
1
0
1
2
0
1
1
0
2
2
1
2
2
1
0
1
0
2
0
1
1
0
1
1
1
0
1
1
0
1
1
2
1
3
0
1
1
1
1
2
1
1
1
1
1
1
1
0
2
1
2
1
1
0
1
2
1
1
0
1
2
2
2
0
1
1
1
0
3
1
0
0
1
1
2
1
0
2
0
0
0
0
0
1
1
0
1
0
1
1
1
0
2
1
0
1
1
0
2
0
1
0
1
1
1
1
2
2
0
2
0
0
2
1
0
1
2
2
0
1
0
0
0
2
1
1
0
0
0
1
2
1
1
2
1
1
2
1
2
1
0
0
2
3
1
2
0
1
1
0
1
2
1
2
0
1
0
2
0
1
1
1
2
1
0
1
2
0
1
1
1
2
0
2
1
5
2
1
0
2
2
1
2
1
1
0
0
1
1
2
2
0
0
2
2
0
2
0
0
0
1
0
2
1
0
1
0
0
1
0
1
0
1
1
1
0
0
0
5
1
0
1
1
1
2
1
0
1
2
0
1
1
0
0
0
0
1
0
1
2
0
1
0
0
0
1
0
1
1
2
2
2
1
2
0
0
0
0
2
1
1
0
2
2
1
1
2
1
1
0
0
1
1
2
1
1
1
2
1
1
2
2
2
0
1
0
3
1
0
1
0
1
1
1
1
0
0
1
0
2
1
2
1
2
1
0
2
1
0
0
1
2
0
1
1
2
2
1
1
1
0
0
0
0
0
2
1
2
1
0
1
1
0
0
1
1
2
1
0
2
2
0
1
2
1
0
0
1
2
1
1
3
2
1
1
1
1
2
2
0
0
1
2
2
1
1
1
0
1
2
1
3
1
1
2
2
1
0
0
1
1
0
1
1
2
2
0
0
1
1
2
0
2
0
1
2
0
1
1
0
1
1
0
2
1
1
0
0
1
2
1
0
1
1
2
1
1
0
3
0
2
1
2
0
2
0
2
1
0
1
1
0
2
1
1
2
1
2
1
1
2
0
0
2
2
1
0
2
0
1
1
1
0
0
0
1
2
0
0
2
2
2
1
1
0
0
1
2
1
1
0
2
1
1
0
2
1
0
2
0
1
0
1
2
0
2
1
1
0
1
0
1
0
1
2
2
2
0
0
2
1
0
2
3
0
0
0
1
1
1
1
2
1
1
1
0
1
0
2
2
1
0
2
1
1
1
0
0
1
2
0
0
1
0
0
0
2
0
1
0
2
1
1
2
2
0
0
0
0
1
1
2
1
1
0
1
1
1
1
1
3
2
0
3
1
1
2
2
1
2
1
0
2
2
0
0
1
0
1
1
2
2
0
1
0
1
2
1
0
0
1
1
1
1
1
0
2
0
1
2
0
0
2
0
0
0
1
0
1
1
1
2
0
0
1
0
1
0
2
1
1
0
1
1
3
0
1
0
0
1
0
0
1
0
0
1
1
0
1
1
1
0
1
2
1
2
4
1
2
2
0
1
0
4
3
1
0
2
1
0
2
2
2
1
0
0
2
1
1
1
0
1
0
1
1
2
1
2
1
1
0
1
0
0
2
1
0
0
1
0
2
1
2
0
0
2
0
0
1
1
0
0
2
0
1
0
1
1
2
0
1
1
1
0
0
0
0
1
1
0
1
0
1
1
1
1
1
2
2
2
1
2
1
1
2
1
2
1
2
2
1
1
1
0
0
2
2
0
2
1
1
2
3
0
4
2
2
1
1
1
0
0
2
1
1
1
1
0
2
1
0
0
1
1
2
0
1
1
1
1
0
1
2
1
1
2
1
1
2
0
1
1
0
2
2
3
1
0
1
1
1
1
2
2
0
0
2
1
1
2
0
0
2
2
1
1
1
2
0
1
1
0
0
1
0
2
1
1
2
0
2
1
0
0
1
0
0
1
0
2
0
2
0
0
1
1
2
0
2
0
0
1
1
2
0
1
1
0
1
2
0
0
1
1
1
1
2
1
0
0
1
0
2
0
0
0
0
0
1
1
1
1
1
1
0
1
1
2
1
0
1
0
0
1
1
1
2
1
2
0
2
1
0
2
0
0
1
1
1
2
0
0
2
1
0
2
2
0
0
1
1
1
1
1
0
1
1
1
0
0
0
2
1
1
1
1
0
2
1
1
1
1
2
2
1
2
0
0
0
0
1
0
1
0
1
0
1
1
0
0
0
1
0
0
1
2
2
2
2
1
1
0
0
1
0
0
2
1
3
2
1
0
1
1
1
2
1
2
2
1
2
0
1
1
0
3
2
0
1
0
1
0
0
1
0
1
1
0
1
0
0
0
1
1
2
1
1
1
0
0
1
1
0
0
1
1
1
2
1
1
2
1
0
1
2
0
1
0
0
1
2
1
1
0
0
1
1
0
0
1
1
1
1
0
1
0
1
0
1
1
1
2
0
1
0
1
1
1
2
2
2
1
0
0
1
0
1
0
1
2
2
0
1
0
2
1
0
2
0
2
1
1
0
0
1
0
1
1
1
1
1
2
0
0
0
2
1
2
0
1
2
1
1
0
0
1
0
1
1
1
2
2
2
1
1
1
0
0
0
1
1
1
0
1
1
1
1
0
1
1
1
2
0
1
1
3
0
1
0
1
1
0
1
0
1
2
1
0
1
1
2
2
2
0
1
0
0
0
0
1
1
2
0
1
1
1
0
1
0
0
2
2
1
1
1
0
1
2
1
0
0
1
1
1
1
2
0
1
1
1
1
2
0
1
2
1
0
0
1
1
0
0
1
0
1
0
1
2
2
2
2
0
0
1
1
1
0
0
0
1
0
0
0
0
1
1
1
2
1
1
2
1
0
2
1
1
1
1
2
2
2
1
1
1
1
2
1
2
0
0
1
1
1
1
0
1
0
0
1
2
1
1
0
3
2
2
1
0
0
1
1
1
1
1
2
0
1
0
0
1
0
0
1
0
2
0
0
0
0
2
0
2
1
0
2
1
0
0
0
1
2
0
0
2
2
0
1
0
0
2
0
1
2
1
1
3
1
1
1
1
2
0
1
0
2
1
0
1
1
1
0
2
0
1
2
1
0
0
2
1
1
2
1
1
1
1
2
0
0
1
0
1
0
1
0
1
2
2
2
0
2
1
1
1
0
2
1
1
0
2
0
1
0
1
1
1
2
0
1
2
1
0
0
0
1
2
1
2
1
1
1
1
1
0
1
1
1
1
2
0
2
2
1
0
1
0
2
0
1
1
1
1
0
2
1
1
1
0
1
1
2
1
1
3
0
1
0
1
1
2
2
1
1
1
0
1
1
1
0
1
2
0
1
1
1
2
1
2
0
3
2
1
1
2
1
1
1
2
2
2
1
0
2
1
2
2
2
0
0
0
1
0
0
0
2
1
0
0
0
2
1
1
1
1
1
1
1
2
2
1
1
0
1
1
2
1
1
1
1
1
2
0
1
0
0
0
0
1
1
1
1
1
0
1
1
2
0
1
2
0
0
2
0
1
1
0
0
1
1
1
1
2
1
1
1
1
1
2
1
1
2
1
2
1
1
1
0
0
1
0
0
1
0
0
1
0
1
1
1
1
2
3
1
0
1
2
1
2
3
2
1
1
0
2
1
0
1
1
1
1
0
0
0
0
0
2
1
0
2
2
1
0
0
2
0
2
0
2
1
1
1
2
1
0
1
1
0
2
1
1
1
2
1
2
1
1
2
1
1
2
1
1
1
1
3
1
1
0
2
1
0
2
0
2
2
1
1
1
1
0
1
2
1
1
0
2
0
1
0
0
1
0
0
0
1
2
2
2
0
0
2
0
0
0
2
2
2
1
0
0
1
1
1
1
2
2
2
0
2
1
0
0
1
0
1
1
0
0
2
1
0
0
0
1
1
1
1
2
1
0
2
1
1
0
1
0
0
1
2
0
1
1
1
0
0
0
2
1
0
0
0
2
0
1
0
2
1
1
3
1
1
2
2
1
0
2
2
0
0
0
0
1
1
1
0
2
0
2
1
0
0
2
1
1
3
0
1
2
2
1
1
1
1
0
0
1
1
2
1
1
1
1
2
2
1
0
1
1
0
3
2
0
3
0
1
1
0
0
1
1
2
0
1
0
0
0
2
1
3
1
1
0
0
0
1
0
1
0
0
2
2
2
1
4
0
1
0
0
0
0
2
1
1
0
1
2
2
0
0
1
1
2
1
0
0
0
1
2
1
0
0
1
3
0
1
2
1
0
2
1
0
1
1
0
1
1
0
2
1
1
1
2
0
0
1
1
1
2
1
1
1
0
1
0
1
2
0
1
1
1
0
3
2
0
1
0
0
1
2
2
0
1
1
0
1
3
1
2
2
1
1
2
0
1
1
1
1
1
1
1
2
1
1
0
1
2
2
1
2
0
0
3
2
0
0
2
1
0
0
1
1
0
2
1
1
2
1
0
0
1
1
0
2
0
1
0
1
1
1
1
1
0
2
1
0
1
1
1
0
1
2
2
1
2
1
2
1
2
0
2
1
1
1
0
0
1
0
0
4
2
0
1
1
1
2
1
1
1
0
1
1
1
0
1
1
2
0
2
0
2
0
1
0
0
0
1
0
1
0
1
0
0
2
0
0
1
1
1
0
0
2
2
1
1
2
1
1
0
2
0
1
1
1
0
1
3
1
2
2
2
1
0
1
0
1
0
0
2
1
1
1
1
1
1
0
1
2
0
1
0
1
1
1
2
1
1
1
0
0
2
2
2
1
2
2
1
1
1
2
2
2
2
0
1
1
0
0
1
0
0
1
2
1
1
1
0
0
3
0
1
0
0
1
0
2
1
1
0
2
2
0
1
2
0
0
2
0
1
0
4
1
1
0
2
2
1
2
1
2
1
2
1
0
2
1
2
2
1
2
1
1
2
0
1
1
1
1
0
2
0
0
1
2
1
1
2
1
1
0
2
0
2
0
0
0
1
1
2
1
2
2
1
2
1
1
1
1
1
0
2
0
1
2
2
1
0
0
1
1
1
1
6
2
1
1
1
1
1
2
2
1
1
0
1
1
2
0
2
1
1
0
1
0
1
1
1
2
1
0
3
2
2
2
1
0
1
1
0
0
0
1
2
0
1
2
0
1
2
1
0
1
2
0
0
1
1
1
0
0
0
1
1
2
1
2
1
1
1
1
2
0
2
0
0
0
1
1
1
1
1
0
0
0
1
1
2
1
0
1
0
0
1
2
0
0
1
1
0
0
0
2
0
0
3
0
1
1
1
2
1
0
1
2
0
2
0
0
2
0
2
0
0
1
1
2
2
2
1
1
1
2
1
2
1
1
1
1
1
0
0
1
2
2
1
1
1
2
0
1
2
2
0
2
0
0
1
1
0
2
2
0
0
1
0
1
1
0
1
0
0
1
1
1
2
1
1
1
1
2
3
2
1
1
0
0
0
0
2
1
1
0
2
2
1
0
1
0
1
0
0
1
2
1
0
1
2
0
0
1
2
2
2
1
0
0
2
0
2
2
0
1
1
2
0
0
0
2
1
1
2
0
2
0
1
0
1
2
1
1
1
0
1
1
1
1
1
0
1
2
1
1
1
0
0
1
0
1
2
1
0
0
0
0
0
1
0
0
1
2
0
0
1
0
0
2
0
1
2
2
0
1
1
0
1
0
2
2
0
0
0
0
1
0
1
0
1
0
1
1
1
0
1
1
2
0
0
1
0
1
0
2
1
1
1
1
1
0
2
0
2
0
1
1
2
2
1
1
2
2
2
1
1
1
1
1
0
2
0
0
2
1
1
1
1
2
2
0
2
2
1
0
1
0
2
1
1
1
0
1
2
1
0
1
1
1
0
0
1
0
1
2
0
0
2
0
0
1
2
0
3
1
1
2
1
2
1
0
2
2
1
2
1
2
1
2
1
1
2
1
1
2
1
1
1
2
0
1
1
2
2
1
0
0
0
0
0
1
0
1
1
0
0
2
0
0
2
0
3
1
1
1
0
1
1
0
1
1
0
2
2
1
0
1
0
2
1
1
0
2
0
2
1
1
2
1
1
1
2
0
0
0
0
2
0
1
1
1
1
1
2
2
1
0
0
0
0
1
0
0
2
0
0
2
1
0
2
1
1
0
1
0
0
0
2
0
2
0
2
1
1
2
2
2
0
0
0
0
1
2
1
2
1
1
0
1
1
1
0
1
1
2
0
0
2
0
0
2
1
0
1
0
1
2
2
1
2
2
2
1
0
0
2
2
0
0
2
2
0
2
2
0
4
2
2
0
1
2
2
0
1
0
1
0
1
2
1
1
0
2
2
0
0
0
1
1
1
1
2
1
1
1
1
0
0
1
1
1
1
1
0
0
1
2
2
0
1
1
1
2
0
1
0
1
0
0
1
2
0
0
1
2
1
0
2
1
1
1
0
0
2
0
7
0
1
1
2
1
0
1
0
2
1
1
0
1
0
1
0
1
1
0
1
1
0
0
0
2
2
1
2
1
0
1
0
2
2
1
0
1
3
0
0
0
1
1
0
0
0
0
1
0
2
2
1
0
1
1
0
2
1
1
1
0
1
1
3
0
1
2
2
2
1
0
2
1
1
2
1
1
2
0
1
2
2
2
2
1
0
1
2
0
1
1
0
1
1
1
0
1
1
1
1
1
1
0
0
1
1
0
1
1
1
1
2
2
1
0
0
1
2
0
1
2
2
2
1
2
1
0
1
1
1
1
1
1
0
1
2
1
1
1
0
1
1
0
2
1
0
0
0
1
2
1
1
0
0
1
1
0
0
1
1
2
1
1
1
2
2
1
1
1
0
1
3
1
0
1
0
1
1
1
2
0
2
2
2
1
2
0
1
2
1
0
1
1
1
0
2
1
1
0
0
0
0
1
1
0
2
0
0
0
0
0
2
1
0
1
2
0
0
0
2
1
1
1
2
1
0
1
2
0
1
2
1
1
1
1
1
1
2
1
1
1
0
0
2
0
1
1
0
0
1
2
1
0
1
1
0
2
1
0
0
0
1
0
1
1
2
0
0
1
1
0
1
1
0
1
0
0
0
2
1
2
2
1
1
1
1
0
2
0
1
2
1
1
1
2
1
2
0
0
1
2
1
2
1
0
2
0
1
0
1
1
1
2
1
2
2
0
1
1
0
2
1
2
0
1
1
1
2
2
0
1
0
0
1
1
0
2
1
1
0
0
1
2
0
1
0
2
0
1
0
1
1
1
0
1
1
1
1
0
0
1
0
0
1
1
2
1
1
0
0
0
1
1
1
0
0
1
1
1
1
2
1
1
1
0
8
2
0
1
0
1
0
2
1
2
1
2
1
1
1
2
1
1
2
0
2
0
2
1
1
0
1
0
1
1
0
1
0
0
1
1
1
1
0
1
1
2
1
2
1
1
0
1
2
0
1
0
1
1
1
1
1
1
2
0
2
2
0
1
2
0
1
1
1
1
1
2
2
1
2
1
1
1
1
0
1
2
1
1
0
0
1
2
1
1
0
0
1
1
0
0
1
2
1
3
2
1
0
1
2
1
2
1
1
2
1
1
2
0
1
1
0
2
2
0
0
0
2
2
1
1
0
2
0
2
1
1
0
0
3
0
1
0
1
1
1
2
0
0
1
0
0
1
0
0
0
2
0
1
2
2
0
0
1
0
1
1
2
0
0
1
1
2
2
0
2
0
1
2
0
2
0
0
1
2
0
0
0
0
1
1
1
1
0
0
1
0
1
1
2
1
0
2
2
3
1
2
1
2
1
0
2
2
0
2
1
1
0
1
2
1
1
0
1
0
2
0
0
1
2
1
0
1
0
0
0
1
0
0
1
1
2
0
0
0
1
2
1
1
2
2
2
2
0
1
0
1
0
1
1
2
1
1
1
2
1
0
1
2
1
0
1
1
1
1
1
1
0
1
2
2
1
0
1
1
1
1
1
1
0
2
2
1
2
0
2
1
1
0
1
1
1
1
1
1
2
1
1
2
1
1
2
1
1
0
0
2
0
1
1
0
1
1
0
2
2
2
2
2
0
2
2
2
2
0
0
2
1
1
0
0
0
1
1
0
0
1
2
1
2
0
2
1
1
1
1
3
1
0
1
0
1
2
1
1
2
0
1
1
6
1
0
1
1
0
0
1
0
1
1
0
1
2
0
0
0
1
0
1
1
1
1
0
0
0
3
1
1
1
0
1
2
2
0
1
1
1
1
0
1
0
1
0
0
1
2
0
0
2
0
0
1
0
1
0
1
2
2
1
0
0
0
0
0
1
0
2
1
2
1
2
0
1
0
0
2
0
0
0
0
1
1
1
0
0
0
0
1
2
2
1
1
2
2
0
0
1
0
2
0
1
2
1
0
0
0
1
1
1
2
0
2
1
0
2
0
2
1
1
1
0
0
1
0
0
2
1
2
0
0
2
1
0
0
1
1
1
0
0
1
1
1
1
0
2
0
1
0
0
1
0
1
1
2
0
1
2
1
1
2
0
0
2
0
0
3
1
2
1
0
2
1
1
0
0
0
2
2
0
1
1
0
1
2
1
1
0
1
0
0
1
3
2
2
0
1
1
1
1
1
1
0
2
2
0
1
2
0
1
1
1
0
1
0
1
1
0
0
0
1
2
1
2
2
1
0
2
1
0
2
1
0
0
2
2
1
3
0
1
1
1
0
1
1
2
2
2
0
2
1
3
0
2
2
0
1
1
1
1
2
1
1
2
2
2
1
0
1
0
2
0
2
1
1
1
2
0
2
0
1
2
1
0
0
2
2
2
2
1
1
1
1
1
1
0
1
2
0
1
0
0
2
1
0
1
1
1
1
2
2
2
2
1
1
0
2
2
0
0
2
2
0
1
1
2
1
1
1
2
1
0
2
2
2
1
1
2
1
1
0
1
1
0
1
1
1
2
0
0
1
2
0
2
1
0
2
1
2
1
2
2
2
1
1
1
2
1
1
0
1
2
0
1
0
1
1
0
1
0
0
1
1
2
1
1
0
1
2
1
2
1
0
1
0
2
2
0
2
1
1
2
1
3
1
2
0
1
1
0
1
0
2
2
0
0
3
1
1
0
2
1
2
0
0
0
2
0
0
0
0
0
0
2
0
3
1
1
1
0
1
2
2
1
2
1
2
2
1
1
1
1
1
0
0
2
1
1
1
2
2
1
0
0
2
1
0
1
0
1
1
0
0
0
1
3
1
1
1
1
2
2
2
1
0
1
0
1
1
0
0
0
2
1
0
1
1
0
1
0
2
2
2
1
2
1
0
0
0
1
1
2
1
2
0
1
1
2
1
1
0
1
2
2
2
0
1
1
0
1
0
1
1
1
0
2
0
0
4
0
1
1
0
0
2
1
2
0
1
1
2
0
1
1
1
2
2
0
1
1
2
2
1
0
1
0
1
1
1
2
1
1
2
0
0
1
1
2
2
1
1
0
1
1
1
2
2
2
1
2
0
1
1
1
1
0
2
2
0
2
1
3
1
1
1
0
0
0
1
0
2
0
0
1
0
0
1
1
1
1
0
1
1
0
2
1
1
0
1
0
0
0
1
4
2
2
1
1
0
1
2
1
2
0
3
0
2
1
1
1
0
1
0
1
0
0
1
2
1
0
1
0
0
0
1
1
0
0
0
2
0
1
0
1
2
3
1
0
0
1
0
1
1
1
0
0
1
1
0
1
1
0
0
0
1
1
0
2
1
1
0
2
2
1
1
0
0
0
2
1
2
1
1
3
1
2
1
2
0
2
1
0
0
2
2
1
2
1
2
0
2
1
1
1
0
2
0
1
1
1
1
1
2
2
0
2
2
0
1
1
1
2
1
0
2
1
0
2
1
1
0
1
1
2
0
1
0
1
2
1
1
0
2
2
1
1
0
1
1
1
1
3
1
2
0
1
0
0
2
0
1
0
6
0
0
1
0
1
2
1
1
0
1
2
0
2
1
2
1
1
0
1
1
1
1
0
1
2
1
1
0
1
0
0
1
2
0
0
2
1
0
1
0
0
2
0
1
2
1
1
1
0
0
1
1
0
0
2
1
1
0
0
2
0
1
1
2
2
2
1
0
0
1
0
0
0
2
0
1
1
0
0
1
0
1
0
0
0
2
0
1
2
2
0
0
2
0
0
1
0
2
2
0
0
1
2
1
0
1
0
1
1
3
1
4
0
1
2
1
0
2
1
1
0
0
1
2
0
0
0
1
0
1
2
0
1
2
0
1
1
0
0
2
1
1
1
1
0
1
0
0
0
2
2
1
1
2
0
2
0
2
1
2
0
3
1
1
4
3
1
0
0
1
0
1
0
1
0
0
1
2
0
0
0
0
1
1
2
1
0
0
2
2
0
1
1
0
1
0
2
2
2
0
2
0
1
0
1
0
0
1
2
0
1
2
0
0
0
1
0
1
1
1
2
0
0
0
0
1
0
2
1
0
0
0
2
2
0
1
0
1
2
1
1
0
1
0
1
1
0
1
0
1
2
1
1
1
1
2
3
0
3
2
0
0
1
1
2
4
0
1
3
2
2
0
0
2
0
5
1
0
2
0
1
3
1
2
0
1
2
1
1
1
0
1
1
2
2
2
1
2
2
1
2
0
2
0
1
2
1
1
1
1
2
2
0
2
2
2
0
1
1
1
0
0
0
0
0
1
0
3
1
0
1
1
1
2
1
2
0
1
0
1
1
0
0
1
1
1
1
2
1
0
0
0
0
1
1
1
0
2
0
2
0
1
2
1
1
1
1
2
1
2
0
0
2
2
1
0
1
1
2
0
0
0
2
0
3
2
3
0
1
2
1
1
1
1
0
1
0
2
1
2
0
1
0
0
1
0
0
2
2
0
0
0
0
1
0
0
1
0
1
1
1
0
0
1
1
1
2
1
1
1
0
0
1
1
0
0
2
0
1
1
0
1
1
0
1
1
2
6
0
1
0
2
1
1
2
1
0
2
1
2
1
0
1
2
1
1
1
1
2
2
0
1
1
1
3
2
1
1
0
0
0
1
1
2
1
0
1
0
1
0
1
0
1
2
1
2
0
2
1
1
0
1
0
0
2
0
0
1
1
1
1
0
0
1
2
1
1
1
1
1
2
0
1
1
1
0
0
2
1
0
0
0
1
1
1
2
1
1
0
1
0
1
0
0
1
1
1
1
0
2
1
1
1
1
2
1
1
0
2
1
0
0
2
2
0
2
1
0
2
1
0
1
2
0
2
1
1
1
1
0
1
0
1
0
1
0
1
0
2
2
1
1
1
0
2
1
1
0
0
5
0
1
1
1
0
1
1
1
0
0
0
3
1
2
2
1
1
0
0
1
2
0
2
1
0
1
2
1
1
1
0
1
0
1
2
1
1
1
2
0
1
0
0
1
2
2
0
2
0
0
1
1
0
2
2
0
2
1
0
1
0
1
1
2
0
0
0
1
0
0
0
1
1
0
0
1
1
1
0
1
1
0
1
0
0
2
1
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
2
1
1
1
1
0
1
1
2
1
0
0
1
1
0
1
1
2
0
2
0
1
1
2
1
1
0
1
0
0
0
2
0
1
1
2
0
1
1
0
1
1
2
1
1
1
2
0
2
2
0
1
1
3
2
2
1
1
2
1
2
0
1
0
1
0
0
0
0
0
1
3
0
1
0
2
0
1
2
1
4
1
0
1
2
0
1
1
1
0
1
2
1
0
2
1
2
1
0
0
2
1
0
0
0
1
0
1
1
0
1
1
0
2
1
0
0
1
0
1
2
2
1
1
1
0
2
1
1
0
1
1
1
0
0
0
0
1
1
2
0
0
0
0
0
1
1
1
1
1
1
1
1
0
1
0
1
0
2
2
1
2
1
1
2
1
2
1
0
2
1
0
1
2
1
1
0
0
0
3
1
1
0
1
2
0
0
0
2
0
2
1
1
0
1
0
1
0
2
1
1
2
1
0
1
0
1
0
0
1
1
2
1
1
0
1
2
2
2
0
1
0
1
1
0
0
0
1
1
0
1
0
0
1
0
1
1
0
2
1
2
1
1
2
1
3
0
0
0
1
1
0
1
0
1
0
0
2
1
1
0
2
1
0
0
1
3
1
1
2
2
0
1
2
0
0
0
1
1
0
4
1
1
1
1
2
1
1
0
1
1
0
1
1
0
1
2
1
1
1
2
1
1
0
0
0
0
0
1
2
1
1
0
0
1
1
1
1
0
0
1
1
0
1
1
2
1
2
0
2
1
1
1
1
0
0
0
1
1
1
0
1
0
1
0
0
1
1
1
0
1
3
0
1
2
1
0
0
1
1
1
1
0
1
2
2
0
1
0
1
1
2
0
1
1
0
2
0
1
1
0
1
1
2
1
1
0
2
0
1
1
2
1
2
0
1
1
1
0
2
0
0
0
1
1
0
1
1
2
1
2
3
1
1
0
0
0
0
0
2
0
2
1
1
1
0
1
1
0
2
1
1
1
0
1
1
0
0
1
1
1
2
1
1
0
1
2
1
0
1
1
0
0
1
1
2
1
1
2
1
0
0
0
1
1
1
0
2
1
0
1
0
0
0
0
0
1
1
1
1
0
2
0
2
4
0
1
0
1
0
1
2
0
1
1
1
0
1
0
1
0
2
1
1
2
0
1
0
1
1
1
1
1
1
1
1
0
1
2
0
1
1
0
2
0
1
1
0
2
0
1
2
1
0
0
2
2
2
1
1
1
1
2
1
2
2
2
1
1
0
0
1
0
0
1
1
1
0
1
0
1
1
1
1
2
0
1
1
0
0
0
0
1
1
0
2
0
0
0
0
1
1
2
0
0
0
1
1
1
0
1
0
1
0
2
1
1
1
0
0
1
0
2
1
2
1
1
1
1
0
0
1
2
1
1
0
2
2
0
2
1
0
0
0
1
1
1
1
0
2
0
1
0
2
1
0
1
0
2
2
2
1
1
1
1
2
0
1
0
2
2
1
0
2
1
2
2
1
1
0
4
1
0
0
1
0
1
1
1
1
1
1
1
0
0
2
1
2
0
0
1
2
0
1
0
0
1
3
1
0
0
1
1
2
1
0
1
0
1
0
2
0
1
1
1
2
1
0
0
1
2
2
1
1
0
2
0
2
1
0
1
1
2
2
0
3
0
2
1
1
1
2
2
2
0
1
1
2
1
1
0
0
1
2
2
0
2
0
1
0
0
0
1
1
2
0
0
0
2
1
1
1
2
1
0
1
1
1
2
0
0
2
0
2
1
1
1
0
0
0
1
1
1
0
1
1
0
1
0
1
0
1
2
0
0
0
1
3
1
1
2
0
1
1
1
1
2
2
0
0
1
1
0
2
2
0
0
1
0
0
1
0
0
2
2
0
1
1
0
0
1
0
1
0
2
0
1
1
2
1
1
1
1
2
2
1
0
1
2
2
1
2
1
0
1
2
1
0
2
1
2
0
2
1
1
1
1
1
1
1
1
1
2
0
1
1
0
1
1
0
0
1
0
1
1
1
2
2
2
1
2
0
0
2
1
1
2
1
2
2
1
0
1
0
1
0
2
0
1
2
0
2
0
2
1
1
1
1
2
0
1
0
0
1
2
1
0
1
0
0
1
0
2
2
0
1
0
0
0
1
3
0
1
1
0
0
0
1
1
0
1
1
0
0
1
0
1
0
1
0
2
0
0
1
0
1
0
1
0
1
0
0
0
1
1
1
0
2
2
0
2
0
0
1
0
2
0
0
1
0
0
0
2
1
2
0
2
1
1
1
0
2
1
0
1
0
0
2
2
3
1
2
2
0
1
0
0
1
0
2
1
2
1
0
1
3
1
0
2
2
0
0
2
0
0
1
0
0
2
2
1
1
0
1
1
0
3
0
1
2
1
0
1
1
1
0
0
2
0
0
0
0
1
0
1
0
1
1
1
0
1
1
2
2
1
1
2
0
1
0
2
1
0
1
1
1
2
0
0
1
1
1
1
0
1
1
1
1
1
0
2
2
0
0
0
1
0
1
2
0
2
1
0
1
0
3
1
2
0
2
0
0
2
0
1
2
1
0
1
1
1
1
0
0
1
2
1
1
2
0
0
0
2
0
1
2
2
0
0
0
5
2
2
0
2
1
2
2
1
2
0
0
3
2
0
0
0
0
0
0
1
1
0
1
1
1
1
2
2
0
7
1
1
1
2
2
1
2
0
1
1
0
1
1
1
2
1
0
2
1
2
0
3
1
1
1
2
1
1
0
1
2
0
1
0
1
1
2
1
0
2
0
2
0
3
2
1
1
2
1
1
1
2
1
1
1
1
0
0
2
0
1
0
2
1
0
0
1
1
1
1
1
0
0
1
1
0
1
1
2
1
2
2
1
0
2
2
1
2
2
1
2
7
0
1
1
0
1
0
2
0
2
2
2
1
1
2
2
0
0
2
1
1
2
1
2
1
1
2
1
0
1
0
1
1
1
2
0
2
1
0
0
1
1
2
1
2
0
2
1
1
1
1
2
1
1
2
2
1
1
1
1
1
0
1
0
1
0
2
1
0
1
0
1
0
1
0
2
2
2
0
0
1
1
1
0
2
2
2
2
2
0
1
0
0
1
2
2
1
2
1
1
0
0
2
1
0
1
1
3
0
0
0
1
0
1
1
0
0
1
1
0
0
0
1
1
1
0
1
0
2
0
2
0
2
1
1
1
2
1
0
1
2
1
0
0
1
1
2
0
1
1
1
1
0
1
1
0
2
0
1
0
1
1
1
3
1
2
0
0
1
1
1
0
1
1
0
0
0
1
0
1
2
1
1
0
2
0
1
1
2
1
1
0
2
0
1
1
0
2
1
0
0
3
0
1
3
1
1
0
1
1
0
2
1
1
0
1
2
1
2
3
0
2
0
0
2
1
0
0
2
2
1
1
0
2
0
1
1
0
1
0
2
0
2
0
1
1
0
1
2
2
0
0
1
1
2
1
2
1
1
0
1
2
0
0
0
2
0
1
2
1
0
0
1
1
1
0
3
1
1
1
1
1
1
1
0
2
0
0
0
1
2
1
0
0
0
2
0
1
2
0
0
0
2
0
0
0
0
0
1
1
0
1
4
0
2
2
1
0
0
1
2
0
0
0
0
2
0
0
0
0
0
2
2
0
0
2
1
1
1
0
1
1
1
0
0
0
1
1
0
2
2
1
1
0
1
1
2
1
0
1
1
1
1
1
1
2
1
1
0
0
2
0
1
1
1
2
1
2
2
0
0
1
2
3
2
1
1
0
0
1
2
1
1
1
0
2
2
2
0
1
1
0
2
1
0
0
2
1
1
1
0
0
1
1
2
0
1
0
1
1
2
1
0
0
0
0
4
1
1
1
1
1
2
1
2
1
0
1
0
0
0
2
0
0
2
2
0
0
2
0
1
1
1
2
2
0
0
2
1
2
0
0
0
2
1
1
1
0
2
1
0
2
1
1
1
0
1
2
0
0
1
1
1
1
2
0
1
1
2
1
2
1
0
1
2
1
0
0
0
1
1
0
1
0
1
0
1
0
1
1
2
2
2
1
2
0
0
1
0
1
1
1
0
1
1
1
2
1
1
2
1
1
1
1
2
2
2
0
1
2
1
1
0
3
0
2
2
0
0
1
0
1
0
1
2
0
2
0
0
2
1
2
0
0
1
2
2
1
1
2
1
1
0
0
2
0
1
1
1
1
2
0
0
1
1
2
1
0
1
2
1
0
2
1
1
2
2
0
0
2
1
1
0
2
2
2
0
0
1
1
1
1
1
0
0
1
0
1
0
0
0
0
1
2
0
2
1
0
1
1
1
1
0
1
1
0
0
0
2
1
3
2
2
1
2
0
0
1
1
2
2
1
2
1
0
2
2
2
1
0
0
0
1
1
1
0
2
1
0
1
2
1
0
2
1
2
2
2
0
1
1
1
1
2
1
2
0
0
2
2
0
0
1
5
1
1
1
0
1
1
2
2
0
2
2
1
1
2
2
0
1
1
1
1
2
0
0
2
1
2
1
1
1
1
0
1
2
2
1
1
1
0
1
1
2
1
1
1
2
2
1
1
3
1
0
3
1
1
2
0
1
1
1
1
0
1
0
1
2
1
0
0
1
1
0
0
4
0
1
0
0
2
2
2
2
0
2
1
0
2
1
2
1
1
1
2
3
1
1
0
2
1
3
0
1
1
1
0
1
1
1
2
1
2
0
1
1
0
1
0
1
1
2
1
1
2
0
1
2
1
2
1
1
2
2
1
1
1
1
1
1
0
0
0
2
2
2
0
0
2
1
0
2
2
1
2
0
0
2
1
0
1
1
1
3
1
0
1
0
0
2
1
2
1
1
2
1
1
2
1
0
1
0
1
0
1
2
2
1
0
0
0
1
2
2
1
3
2
2
1
0
1
1
0
1
1
0
1
1
1
2
0
0
2
1
0
1
1
0
0
2
1
2
2
1
1
1
2
2
2
1
0
1
0
1
0
0
2
1
1
1
0
1
0
0
1
1
0
1
0
0
1
2
1
0
1
0
2
0
1
1
1
1
2
1
2
2
1
2
1
0
1
1
2
2
1
1
3
1
1
1
1
1
2
1
0
1
2
2
0
1
1
3
0
1
0
2
0
2
1
0
1
1
0
1
2
0
1
0
6
2
0
1
2
2
1
1
0
0
2
0
0
0
0
2
2
1
1
1
2
1
2
2
0
2
1
0
2
1
1
0
1
0
1
2
1
2
1
1
1
2
1
1
1
1
1
2
1
0
0
2
1
1
0
0
1
0
1
1
0
0
0
0
1
1
0
1
3
0
0
0
1
2
1
2
2
0
5
1
1
0
0
1
0
1
1
1
2
1
1
2
2
1
1
0
1
0
1
1
0
1
1
0
0
1
0
1
1
1
2
2
1
1
1
2
0
1
1
0
1
1
0
3
1
1
1
0
1
1
1
2
0
1
1
2
0
0
0
0
2
1
0
1
0
2
2
1
0
1
2
1
0
0
2
0
2
1
4
0
1
2
2
0
0
2
1
0
1
0
0
2
0
0
1
1
2
1
2
1
1
2
2
1
1
1
1
2
1
2
0
2
0
2
0
1
0
0
0
1
2
0
2
1
0
2
2
1
1
0
1
1
1
1
2
0
1
0
0
2
0
2
0
0
0
0
0
1
0
0
1
0
1
2
0
2
2
0
0
0
0
2
2
2
0
0
1
0
1
2
2
1
1
1
1
1
2
1
2
0
1
0
1
2
0
0
1
1
1
2
1
0
1
1
1
1
1
0
2
2
0
3
3
0
0
1
1
1
0
0
0
0
3
0
0
1
1
1
1
2
1
0
2
2
2
0
0
2
1
0
0
2
1
1
2
1
1
2
2
1
1
1
3
1
3
0
1
1
1
1
2
0
0
0
0
1
0
1
2
0
1
0
1
1
1
1
2
1
1
0
1
0
1
1
1
1
1
2
0
1
1
0
1
1
2
0
2
0
1
1
2
0
0
2
1
1
0
1
1
1
0
0
2
1
0
1
0
0
2
1
2
2
0
1
2
2
1
0
0
1
1
1
0
2
2
2
1
1
2
2
0
2
0
1
1
2
0
1
2
1
2
1
1
0
2
0
1
1
0
0
2
1
0
1
2
1
0
2
1
0
0
1
1
1
1
2
2
1
0
1
0
1
0
0
1
0
1
2
2
1
1
0
2
1
3
2
1
0
1
2
1
0
1
1
0
1
0
1
1
0
1
0
0
2
1
1
1
0
0
0
1
0
0
1
1
1
0
2
2
1
0
1
1
1
2
0
1
1
1
1
0
0
1
1
0
0
2
0
0
0
0
1
0
1
0
0
1
2
2
2
1
1
2
1
2
0
3
0
2
0
0
0
1
1
0
1
1
1
0
0
2
0
2
0
0
0
2
0
1
1
1
2
0
1
0
2
1
4
1
4
1
2
1
0
1
2
1
1
0
1
1
1
1
3
2
1
0
1
1
0
1
0
1
0
1
0
1
0
1
0
1
1
1
1
1
0
2
1
0
1
0
1
1
0
0
1
0
1
1
2
0
0
1
2
1
1
1
1
2
0
0
1
2
1
2
1
0
1
1
0
0
2
2
0
0
0
2
2
0
0
0
1
0
2
1
2
1
2
1
0
0
1
1
0
0
1
3
2
2
1
0
0
1
1
0
2
2
1
0
1
1
2
0
0
0
1
0
1
2
0
1
1
10
2
1
1
0
0
2
0
3
0
2
2
1
0
0
2
1
0
0
0
0
2
2
1
2
0
1
0
2
2
2
1
2
1
1
2
1
0
0
0
1
2
0
1
1
2
1
2
0
1
1
0
1
2
1
1
0
2
2
2
2
2
1
0
0
1
1
2
0
0
0
1
1
2
2
1
1
1
1
3
1
1
0
2
1
1
3
1
1
1
0
1
1
1
1
0
2
0
0
0
1
1
0
1
1
2
0
1
2
1
1
0
0
0
2
2
0
2
0
1
0
1
1
0
1
0
0
2
2
0
0
1
0
1
1
2
2
0
2
0
2
1
2
2
2
2
0
1
1
0
1
1
0
1
2
0
1
1
1
2
1
1
2
1
1
1
1
0
1
1
1
1
0
2
1
0
1
1
1
1
1
1
0
0
1
2
0
2
2
0
0
0
0
0
0
2
0
1
1
1
0
1
1
1
1
1
0
2
1
1
1
0
2
0
1
0
2
0
1
0
0
2
1
0
0
2
0
1
0
1
1
1
1
2
1
1
0
1
1
2
1
0
1
1
0
1
2
2
0
2
2
2
1
1
2
1
1
2
0
0
1
2
0
2
1
0
1
1
1
0
0
1
1
0
0
1
0
1
0
1
2
1
2
1
1
2
4
1
1
0
1
0
1
2
1
1
1
0
1
1
2
1
2
2
1
1
0
2
1
0
1
1
1
1
1
1
1
1
1
2
1
1
2
0
0
2
1
0
1
2
1
1
1
0
2
1
1
1
0
1
3
2
0
2
1
1
0
1
2
2
2
2
1
1
0
3
0
1
1
1
0
1
2
1
1
0
3
2
2
0
2
0
2
1
1
1
1
0
1
1
0
2
0
0
0
0
1
0
0
1
1
2
2
0
1
1
2
2
1
0
1
1
0
1
0
2
1
0
1
1
0
1
2
0
1
0
1
1
1
0
2
1
2
2
0
0
0
1
0
1
2
1
2
1
2
1
1
0
1
0
0
2
1
1
2
1
0
3
0
2
1
1
1
0
0
1
1
1
0
2
2
0
0
1
2
2
1
2
2
0
1
1
0
3
2
2
1
0
2
2
0
1
0
2
2
0
0
1
1
1
0
1
2
2
1
0
1
2
0
2
2
1
1
1
1
2
0
1
0
1
0
0
0
0
1
1
1
2
3
2
2
1
1
1
0
0
0
3
1
1
1
2
1
0
1
1
1
2
0
1
1
0
2
0
0
0
1
2
2
1
1
0
2
2
1
0
0
2
0
2
0
2
0
1
0
0
1
0
0
0
2
1
1
1
2
2
1
0
0
0
1
0
1
0
1
0
0
1
1
1
2
1
0
1
2
1
4
0
0
0
0
1
0
0
1
0
0
1
0
1
1
2
0
1
0
1
1
2
0
0
2
0
2
1
1
1
0
0
0
2
0
0
0
1
0
1
0
1
2
0
0
1
0
1
0
0
1
2
1
1
1
1
1
1
0
2
1
2
1
0
1
0
1
0
0
1
0
1
2
1
2
1
2
0
1
0
0
1
1
1
0
2
1
2
0
2
0
1
1
2
2
1
0
1
1
2
1
0
0
3
2
0
2
1
2
1
0
0
0
0
0
0
2
0
1
0
0
0
1
0
1
0
0
1
2
2
0
2
0
2
1
0
2
0
1
0
1
0
2
0
1
1
1
0
2
0
1
1
0
2
0
1
2
2
1
1
1
1
0
1
0
2
0
1
1
1
1
0
0
1
1
0
1
0
2
1
0
1
2
1
1
1
1
1
0
1
1
2
0
1
1
0
2
0
0
1
2
2
0
1
1
2
0
1
1
1
1
2
0
1
0
1
1
1
2
1
1
0
1
1
2
1
2
0
4
2
0
1
1
1
1
2
2
1
0
1
0
0
2
0
1
0
1
0
2
1
0
1
0
0
1
1
2
0
0
1
0
0
2
0
2
1
2
1
2
1
1
2
1
2
0
1
0
1
1
0
2
2
2
2
1
1
1
0
0
1
1
2
0
0
1
0
1
0
1
0
0
1
1
0
2
0
1
1
0
3
1
2
2
1
0
0
1
0
2
2
0
0
0
1
2
0
1
2
2
0
1
1
0
2
2
3
1
1
0
2
1
1
2
2
1
2
1
2
0
0
1
0
1
2
0
0
0
1
0
0
1
2
1
0
0
0
1
2
2
1
0
1
2
1
1
1
0
1
1
1
1
0
1
1
1
0
0
0
0
1
2
0
1
0
1
1
1
1
0
1
0
3
2
1
1
2
1
1
1
2
0
3
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
1
1
2
1
1
1
1
1
1
0
2
1
1
1
0
0
2
2
1
1
0
0
0
0
2
0
1
0
2
1
1
2
1
1
0
1
0
1
2
1
0
0
0
2
1
1
0
1
0
1
1
2
0
0
1
0
1
0
1
0
0
1
0
1
1
0
1
2
1
2
1
1
0
2
1
1
0
1
1
1
0
1
1
2
0
3
2
1
0
1
1
1
1
0
1
0
1
1
1
2
1
0
0
1
1
0
2
2
0
0
0
1
1
2
1
2
1
0
2
2
0
0
0
0
1
2
1
0
2
1
2
2
0
1
2
0
1
0
1
0
0
1
1
1
0
0
1
2
1
1
1
1
0
0
1
0
1
1
2
2
0
2
0
2
1
2
1
2
0
1
0
0
2
0
1
0
0
1
2
1
1
0
0
0
0
2
0
1
0
1
1
2
1
0
1
1
2
0
2
0
2
2
0
1
1
1
1
1
1
2
2
0
1
0
2
2
1
1
1
2
1
0
1
1
1
0
1
1
2
0
0
0
1
1
0
1
0
0
1
2
1
1
2
1
1
1
0
2
0
2
0
2
1
0
0
1
2
0
1
0
1
2
1
1
0
1
2
1
1
0
2
2
0
1
1
1
1
2
0
1
2
1
0
0
0
1
1
1
1
2
1
0
2
1
0
1
1
0
1
2
0
1
1
1
0
1
0
1
1
0
0
2
0
0
1
1
2
0
0
0
0
1
0
2
1
2
1
1
0
1
0
0
0
2
1
2
2
1
1
0
1
0
0
0
1
1
1
0
1
1
0
0
0
2
1
1
0
0
1
0
1
1
0
0
1
1
1
1
0
2
0
1
0
0
0
0
1
1
2
0
2
0
2
1
1
1
2
0
2
1
0
0
2
2
0
0
0
1
1
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
1
2
1
1
0
1
2
0
0
2
1
0
1
0
1
1
2
1
1
0
1
1
0
1
1
0
0
0
0
2
2
2
0
0
1
1
1
1
0
0
1
1
1
1
1
1
1
0
2
0
1
1
1
2
0
2
1
0
1
1
3
1
1
2
0
1
0
1
3
1
2
1
1
1
0
0
2
1
1
1
1
1
0
0
1
1
1
0
1
1
0
0
0
1
3
2
1
1
2
1
1
1
0
0
1
0
1
1
1
0
2
0
2
0
2
2
0
0
2
1
1
1
0
1
1
0
2
1
0
1
0
1
0
1
0
0
0
1
2
2
0
0
0
0
2
1
0
0
0
2
1
1
3
1
0
1
1
1
1
2
0
2
6
0
1
1
1
0
0
0
1
2
1
1
2
2
1
3
1
0
1
2
2
1
3
1
1
0
1
1
1
2
1
1
0
2
1
2
1
0
1
1
1
1
0
0
0
2
0
1
0
1
2
0
1
1
1
0
0
0
2
1
0
1
3
1
1
1
0
1
0
2
2
0
1
1
2
1
1
0
0
0
1
0
0
2
0
0
1
2
1
0
1
0
1
1
0
2
0
1
3
3
0
2
0
1
1
0
1
0
1
2
1
1
0
0
0
2
2
2
1
0
0
2
0
1
0
2
0
0
2
1
1
0
0
0
2
0
1
1
2
0
2
2
1
1
1
1
1
1
0
8
1
1
1
0
0
2
0
1
2
1
1
0
1
1
3
0
1
1
1
1
1
0
0
2
1
2
1
1
2
1
1
2
1
1
2
1
2
2
0
1
0
2
2
0
1
1
2
1
1
1
1
1
0
2
0
0
2
1
0
1
1
2
0
1
1
1
1
0
1
1
0
0
1
0
1
1
2
1
0
0
2
1
1
1
3
1
1
0
0
1
0
1
1
0
1
1
1
1
0
2
1
0
0
2
0
0
1
0
1
0
0
0
0
1
2
0
0
2
2
0
1
0
1
1
1
2
2
1
1
2
0
0
2
1
2
2
1
1
1
1
1
0
1
0
0
3
2
1
0
4
0
1
1
1
1
1
1
0
1
0
0
2
2
0
1
0
0
2
0
1
1
1
1
2
0
1
2
0
2
2
1
1
1
0
1
0
0
0
1
1
0
0
1
2
1
1
2
2
1
1
1
2
0
0
0
1
0
0
0
1
2
2
2
1
1
1
2
2
1
0
2
2
2
0
1
0
0
0
1
0
1
1
0
2
0
1
1
1
1
1
2
0
0
1
2
0
0
2
2
3
2
1
0
0
1
1
0
0
0
1
1
1
2
0
1
0
2
1
0
1
2
1
2
1
1
1
0
0
2
1
1
0
1
2
1
1
1
0
1
0
1
1
0
0
2
2
2
1
0
0
0
0
1
1
0
1
2
1
1
1
0
0
1
1
2
1
1
1
1
0
0
1
1
2
1
0
0
1
0
1
2
1
1
0
1
0
1
1
1
1
0
0
1
0
1
1
1
1
1
0
1
1
2
0
0
1
0
0
0
0
1
1
0
1
1
2
1
2
1
0
0
0
1
1
2
1
1
1
1
2
2
2
3
1
1
1
1
1
0
1
0
2
1
0
0
1
1
0
0
1
1
0
2
1
0
2
1
1
2
2
1
0
1
1
0
2
1
2
2
2
0
1
0
1
0
0
2
0
1
0
0
1
1
0
0
1
2
1
1
0
2
1
0
0
1
1
1
1
2
2
1
2
1
0
0
2
1
0
1
1
0
0
2
0
2
0
1
0
0
0
1
0
2
0
0
1
0
0
0
0
2
1
0
1
0
0
1
0
2
0
0
1
2
1
0
1
1
1
0
1
1
2
0
3
2
0
1
2
0
0
1
1
0
1
0
2
1
1
1
0
1
0
0
0
1
1
2
0
1
1
1
1
2
2
1
1
0
0
2
1
1
1
1
1
0
1
1
0
1
1
0
0
1
0
1
0
2
0
1
2
2
2
1
0
0
0
1
0
1
1
2
0
2
0
2
0
1
1
2
2
7
0
2
1
1
0
1
1
0
1
2
0
1
0
1
1
0
0
1
0
1
1
0
0
1
1
1
1
0
2
0
2
2
1
0
2
1
1
1
1
0
0
2
2
1
1
1
1
0
0
3
1
2
0
0
1
0
1
2
1
0
0
1
2
1
0
1
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
2
0
1
0
1
0
1
2
1
0
1
2
2
0
2
3
2
1
1
1
1
1
1
1
1
1
1
0
0
1
3
1
1
1
1
0
0
2
0
2
2
1
1
1
1
1
0
1
0
2
1
2
1
1
0
2
0
2
1
0
1
1
2
2
2
1
1
0
0
1
1
1
0
0
1
1
1
0
2
2
1
0
1
1
1
1
0
2
1
2
0
1
2
2
1
0
2
0
0
0
2
1
0
1
1
1
1
2
1
0
2
1
1
1
0
2
1
1
2
2
0
2
1
0
0
1
0
0
3
0
1
1
1
0
1
1
1
1
1
0
2
2
1
0
1
2
2
1
2
1
1
0
1
2
2
1
0
0
0
1
2
1
2
1
0
2
0
1
1
1
2
0
1
2
0
2
1
2
0
2
1
0
2
1
1
0
1
1
0
1
1
0
2
1
1
0
0
1
1
2
1
1
0
0
0
0
1
2
1
2
0
0
0
0
2
0
1
0
0
0
1
2
0
0
1
2
1
0
1
0
0
1
2
1
0
0
2
1
1
2
0
1
0
1
1
1
0
1
0
2
1
1
0
0
1
1
1
1
1
0
0
1
0
1
0
1
0
1
1
2
2
1
0
1
0
1
2
0
0
2
2
0
1
0
0
0
0
1
0
0
1
0
2
1
2
1
0
1
2
1
0
2
0
0
1
1
0
2
1
0
0
1
1
0
1
1
1
0
2
1
1
1
1
0
2
1
1
0
1
1
2
1
1
1
1
2
0
0
0
1
1
2
2
1
0
2
1
1
2
1
1
1
0
0
2
0
0
2
0
1
1
0
0
1
1
2
1
1
0
0
0
0
0
0
1
2
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
2
2
1
1
1
0
0
0
1
2
1
0
2
0
0
0
1
2
1
0
0
1
2
2
2
1
1
0
1
1
1
1
0
1
1
1
0
2
1
1
0
2
0
1
0
0
0
0
1
0
0
2
0
2
2
1
0
2
0
0
1
0
3
1
0
1
1
2
0
0
1
0
0
0
1
2
3
1
1
1
1
1
2
2
1
0
0
1
1
1
0
1
3
3
1
0
1
2
1
2
3
0
0
0
0
2
1
1
0
2
2
0
0
0
1
2
1
0
2
0
3
0
2
1
2
0
1
2
1
2
1
0
2
2
1
1
0
2
1
1
1
1
2
0
1
0
0
0
0
1
0
0
1
0
1
1
2
0
1
2
2
0
2
0
2
1
2
3
1
2
2
2
0
1
0
2
0
0
3
1
0
2
0
1
0
0
4
2
1
0
0
1
2
1
1
1
0
1
1
2
0
1
2
0
2
2
1
0
0
2
1
1
1
2
1
2
2
2
0
1
1
2
0
0
0
3
1
1
0
4
2
1
1
1
0
0
1
1
1
1
1
2
0
0
1
1
0
2
1
7
2
2
1
0
0
0
1
1
1
1
1
0
2
1
1
1
1
1
2
1
1
0
1
1
1
0
1
2
1
1
0
1
1
1
1
1
1
1
0
0
0
0
1
1
1
4
2
0
0
0
1
2
0
0
2
1
1
0
1
2
2
0
3
1
0
0
0
2
1
0
1
0
0
0
2
1
1
0
0
1
1
2
1
1
1
1
2
0
2
0
0
0
0
0
0
0
2
1
2
1
1
0
2
1
2
0
0
0
0
2
0
0
0
2
2
1
1
1
3
1
0
2
0
1
1
0
0
1
1
1
1
0
1
0
2
0
1
1
0
1
1
0
1
1
2
0
1
0
0
0
2
1
2
1
0
1
1
1
1
2
0
1
1
2
1
1
1
0
1
1
0
3
1
1
0
0
0
0
1
2
0
1
0
0
1
0
0
1
0
0
1
1
0
2
1
2
0
2
1
0
0
2
1
1
2
1
1
0
1
1
1
0
0
0
2
2
1
0
1
0
1
1
0
1
1
1
1
1
0
0
1
1
1
0
0
2
0
2
0
1
0
0
0
0
0
2
2
0
2
1
3
0
0
1
1
1
2
0
0
1
1
2
1
0
1
1
2
0
1
0
2
1
0
1
1
3
1
1
1
1
2
2
1
2
0
0
1
1
1
1
2
1
1
0
0
0
2
1
1
1
2
1
1
1
1
1
2
2
1
0
1
2
1
1
1
1
0
1
0
0
2
0
1
1
0
2
1
1
2
1
1
2
1
0
0
1
0
1
1
1
1
1
0
2
0
1
1
1
1
0
1
1
0
1
0
1
0
1
0
0
0
2
0
1
1
1
2
1
2
3
0
0
0
1
1
2
1
0
0
0
2
2
2
0
0
1
0
0
1
1
0
0
1
0
1
1
1
1
2
1
1
1
1
0
1
1
0
0
1
0
0
1
2
0
1
2
2
0
1
1
1
0
1
0
1
1
1
2
2
2
0
0
0
0
2
1
2
5
1
3
1
0
1
0
2
1
0
1
1
1
2
1
0
0
2
0
1
1
0
0
2
0
1
1
1
2
0
0
2
1
0
0
0
0
0
2
1
2
1
1
2
2
2
1
0
0
1
0
1
1
1
1
1
0
0
2
0
2
1
2
2
2
1
0
1
1
1
1
0
0
0
0
1
1
1
2
1
1
0
0
0
1
1
2
1
1
1
0
2
1
1
0
0
0
2
2
0
1
0
0
1
0
0
2
0
2
2
1
2
1
0
1
0
2
0
2
2
1
1
0
1
1
1
0
1
0
0
0
0
2
1
2
1
1
1
0
2
0
0
2
1
1
0
2
2
0
1
1
2
2
0
1
1
1
1
1
1
2
1
1
0
0
0
0
2
1
1
1
1
2
1
1
0
2
0
0
3
1
0
1
1
1
2
3
0
1
1
0
1
1
0
0
1
1
1
1
2
1
1
0
0
1
2
2
1
1
2
1
0
1
2
0
1
2
2
1
1
1
1
2
1
1
1
1
0
1
0
0
1
1
0
1
0
1
3
1
0
0
2
0
0
1
0
1
0
1
2
2
1
1
2
1
2
1
1
0
1
0
2
0
1
1
1
0
0
2
1
0
1
2
0
2
0
0
2
1
1
2
0
1
1
0
1
2
1
2
1
2
1
2
1
1
1
1
1
0
1
0
2
0
0
1
1
1
1
1
1
0
1
0
1
1
0
0
1
0
0
2
1
1
1
1
2
2
0
2
1
1
0
1
0
0
0
2
1
2
1
0
1
2
0
1
1
1
1
2
0
1
1
2
0
0
2
0
2
0
0
0
1
2
1
0
0
1
0
0
1
1
2
1
0
0
1
1
2
0
0
2
0
0
4
1
1
0
0
2
0
0
0
1
1
1
2
0
1
2
1
0
1
0
2
0
1
0
2
2
2
2
0
1
2
2
1
1
0
2
1
0
0
0
0
1
2
1
2
3
1
0
1
2
1
1
1
2
0
0
1
0
1
1
1
1
1
1
1
1
1
1
1
0
1
2
0
0
1
2
1
1
0
0
0
2
1
1
1
1
1
1
0
0
1
1
2
2
0
1
1
1
1
2
0
0
0
0
1
1
0
2
0
0
0
1
2
2
1
0
1
1
0
1
3
1
0
0
2
0
2
1
1
1
1
2
1
1
0
0
1
2
1
1
0
2
1
0
1
0
2
0
1
2
2
1
1
1
1
2
2
0
0
1
1
0
1
1
2
0
0
1
1
0
1
0
0
0
0
1
1
2
0
2
0
2
0
1
1
1
1
0
2
1
0
0
1
1
2
1
0
0
1
1
1
2
0
1
2
1
0
3
1
1
1
1
1
0
2
0
1
0
0
1
1
0
0
1
0
2
1
2
0
1
2
1
2
1
1
0
0
0
0
1
0
0
1
1
1
0
2
1
2
1
0
1
0
1
1
0
1
0
1
0
1
1
1
1
2
2
0
0
0
0
0
1
1
0
1
2
1
0
2
1
1
1
2
2
1
2
2
0
0
1
0
0
1
0
0
1
0
1
0
0
3
1
2
1
1
0
0
1
2
2
1
2
0
1
1
2
0
2
3
0
1
0
0
0
1
1
1
0
0
0
2
1
0
0
0
0
1
1
0
0
2
1
1
0
1
1
0
1
1
0
0
2
1
1
0
0
1
2
0
0
1
0
2
0
0
2
1
0
0
1
0
1
1
1
1
1
2
1
1
0
0
0
2
2
1
1
1
1
1
1
0
1
1
1
2
2
0
1
1
2
1
1
0
1
1
1
1
0
0
2
1
1
1
2
1
0
0
1
1
1
0
2
1
1
2
0
0
0
2
0
1
1
1
2
1
2
1
1
1
1
0
0
2
2
0
1
2
1
1
0
0
2
2
0
0
0
1
0
1
0
0
2
2
2
1
2
1
1
1
1
0
0
0
2
0
1
0
1
1
1
1
2
0
1
2
1
2
2
0
1
0
1
0
0
1
0
0
1
0
2
0
0
0
2
0
2
1
0
1
1
0
2
1
0
0
1
2
1
1
0
2
2
0
1
1
0
1
1
1
0
0
1
1
0
1
0
1
0
1
2
2
0
0
0
1
2
0
0
0
1
2
1
1
0
1
2
1
0
1
2
1
0
1
0
1
0
2
0
2
1
2
1
1
0
1
2
1
1
0
2
0
1
0
0
0
0
1
1
1
1
1
0
1
1
0
0
2
1
1
1
0
0
2
1
1
0
1
2
0
1
2
0
2
0
0
2
0
1
0
2
0
0
0
0
0
1
1
2
1
1
0
0
1
1
2
0
1
0
0
0
1
1
0
1
0
0
1
1
0
2
0
0
0
0
1
0
1
2
1
5
2
1
1
1
1
1
1
1
2
0
2
1
0
0
1
1
1
1
0
1
2
0
1
0
0
3
1
0
1
0
1
0
0
2
2
0
0
1
0
2
1
2
0
1
1
1
2
0
1
1
0
1
0
1
2
0
1
0
1
3
2
3
1
1
1
0
1
2
1
2
1
2
0
1
1
3
0
0
0
1
0
1
0
0
1
1
1
0
0
1
2
1
1
1
0
2
0
1
1
1
2
1
1
1
0
1
1
1
1
0
0
1
0
1
2
2
2
0
1
1
2
1
1
0
0
0
1
1
2
1
0
0
0
2
1
1
0
1
0
0
2
0
1
3
0
2
2
0
0
1
0
0
1
1
2
2
2
1
1
1
1
2
2
1
0
1
0
1
1
2
1
1
0
1
1
1
1
1
0
1
2
0
1
0
1
1
1
1
0
0
2
1
2
1
1
0
1
0
0
0
2
0
1
1
1
2
1
1
1
0
1
2
0
0
1
1
0
0
1
1
1
2
1
1
2
1
2
0
2
0
0
1
0
1
2
1
2
1
0
1
1
2
1
1
1
0
1
3
0
0
1
1
1
1
0
1
0
1
2
1
2
1
1
1
1
1
2
0
0
2
2
0
1
1
1
0
0
1
0
0
1
0
0
0
2
2
2
1
0
0
1
2
1
0
1
1
0
1
1
1
1
2
2
1
1
0
1
1
2
1
1
1
1
1
0
1
0
1
1
2
1
0
0
0
0
0
0
1
1
0
0
1
2
1
2
1
1
1
0
2
0
1
0
1
0
2
1
0
1
0
0
1
1
2
1
1
0
1
1
2
0
1
2
1
0
1
1
0
1
2
1
1
0
0
3
0
0
0
1
1
0
0
0
1
1
2
1
1
2
0
1
1
0
1
0
2
0
1
0
0
0
1
0
1
1
1
1
1
0
0
0
1
1
1
1
1
1
1
0
2
1
2
0
0
0
1
0
0
1
0
0
1
2
1
0
0
0
1
1
1
0
1
0
0
0
1
0
1
1
1
1
4
0
2
0
0
1
0
0
0
1
0
1
1
1
1
0
0
1
2
0
1
1
0
1
1
0
0
0
1
2
1
1
1
2
2
0
2
1
1
2
1
2
1
1
2
2
2
1
1
1
1
0
0
0
0
1
1
1
3
1
1
1
1
1
2
0
2
1
2
1
2
1
1
1
1
2
1
0
1
1
0
1
1
2
1
0
2
1
0
0
0
1
1
1
1
0
0
0
1
0
0
1
1
2
0
1
2
1
1
0
1
1
1
0
1
1
0
0
1
1
2
1
0
0
2
0
1
1
0
1
0
1
2
0
0
0
1
2
2
1
1
1
0
1
2
0
2
2
1
1
0
1
2
0
1
0
1
1
1
1
0
1
0
1
0
2
2
1
1
1
1
0
2
2
2
1
0
2
0
1
1
1
1
2
0
0
1
2
1
0
0
1
0
0
1
2
2
0
2
3
1
2
1
1
0
0
1
1
2
0
0
0
1
2
0
1
1
1
0
2
0
1
1
1
2
1
1
0
1
0
0
0
0
0
0
1
1
0
1
1
1
1
1
2
1
0
1
0
0
1
1
1
2
0
1
1
0
0
1
0
2
1
2
1
1
1
2
1
0
0
1
2
2
1
0
1
0
1
0
0
1
1
1
0
0
0
0
0
1
1
1
1
1
2
0
1
1
1
2
0
0
1
1
1
1
1
1
0
1
1
1
0
0
0
0
0
2
1
2
2
1
1
3
1
0
1
1
2
0
1
1
1
0
2
1
0
1
1
2
1
1
1
1
0
2
0
1
1
0
0
2
1
2
0
1
1
1
1
1
1
1
1
1
0
0
1
1
0
2
0
0
1
2
0
2
1
0
2
2
1
4
1
0
0
2
0
1
1
0
1
0
0
1
2
1
1
2
1
1
1
0
0
1
1
1
1
1
1
1
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
1
1
1
1
1
1
2
0
0
1
1
0
0
1
2
2
0
1
0
2
2
2
0
0
2
2
1
1
0
0
1
1
2
1
1
1
0
1
2
0
0
2
2
1
1
1
2
1
2
1
0
2
1
2
0
1
1
2
0
2
1
1
0
1
0
1
2
1
1
2
1
0
1
2
2
0
1
0
1
0
2
3
1
1
1
0
1
2
0
2
1
2
1
1
0
1
1
2
1
2
0
0
2
1
1
1
0
3
1
0
0
1
1
1
2
2
1
0
0
1
0
1
2
1
1
0
0
2
0
0
0
2
0
1
1
0
1
1
0
0
0
2
1
2
2
1
1
0
0
1
1
2
0
1
0
1
2
1
1
0
0
0
1
1
1
1
1
1
0
1
2
0
1
1
0
1
0
0
0
1
1
2
1
1
1
1
0
2
0
1
3
0
1
4
2
0
2
1
0
2
1
2
0
0
2
1
0
1
1
0
1
1
1
2
1
0
0
2
2
0
2
1
2
0
2
1
0
1
3
1
0
2
0
0
3
2
1
1
0
1
0
0
0
1
1
0
2
0
2
2
0
0
0
1
1
0
1
2
1
0
1
1
1
0
1
1
0
0
1
2
1
1
2
0
2
0
1
0
0
0
2
1
1
0
1
2
2
1
0
2
1
2
0
0
0
0
0
1
1
0
0
2
0
0
0
1
1
2
1
2
1
2
1
1
1
2
2
1
0
1
2
0
2
0
0
1
1
0
1
2
1
1
2
0
1
1
1
2
1
1
1
0
2
0
0
1
2
1
1
1
1
1
2
3
1
0
2
1
0
0
1
0
1
0
0
1
0
1
1
2
1
1
0
0
1
1
0
0
1
2
0
0
0
0
1
0
0
2
1
0
0
0
1
1
2
0
2
1
1
0
1
1
0
2
0
1
2
2
1
0
1
2
0
0
2
0
1
1
0
1
0
2
1
1
2
2
0
0
2
1
0
0
1
0
4
2
0
1
0
2
2
1
2
1
1
2
2
0
0
2
4
2
2
0
0
2
1
0
1
0
1
0
0
1
1
2
1
1
0
1
0
2
0
2
1
1
0
0
0
1
1
0
0
0
1
0
0
0
0
1
1
0
0
1
1
1
2
1
1
1
2
0
2
1
1
1
0
1
1
1
1
0
0
0
2
0
0
1
1
0
1
0
0
2
1
2
0
1
1
1
1
2
1
2
2
2
1
1
1
1
0
1
1
1
1
1
1
1
0
0
0
0
0
1
0
1
0
0
0
1
0
1
1
2
2
0
0
1
1
1
1
0
3
1
1
1
0
1
2
0
0
2
0
1
1
2
0
1
1
1
1
4
1
2
0
1
1
1
1
2
2
2
1
0
1
1
0
1
1
2
0
0
1
2
2
0
2
0
1
0
1
1
1
1
1
1
1
1
0
0
1
1
1
2
1
1
1
1
1
0
1
0
1
2
1
1
0
2
0
1
0
0
1
0
1
2
1
0
0
1
0
1
0
0
2
0
0
1
0
0
2
0
1
2
2
2
0
1
0
1
2
1
0
1
0
1
1
0
1
0
1
0
2
2
2
0
1
1
0
3
1
2
1
0
2
1
1
0
1
2
1
1
0
1
2
3
1
1
0
0
1
0
0
1
0
2
1
0
1
0
1
0
0
1
0
2
0
1
1
1
0
0
1
0
0
2
1
1
1
0
2
0
0
1
0
1
2
0
0
2
1
1
2
1
0
0
0
1
0
0
0
1
2
1
0
0
0
1
4
0
0
0
2
2
0
0
0
0
0
1
0
0
1
2
1
1
1
2
0
0
0
0
1
0
1
1
1
0
0
1
0
1
1
2
0
0
0
1
0
1
0
0
1
2
1
2
1
1
1
0
3
2
0
1
2
0
0
0
2
0
1
0
0
1
0
1
0
1
2
1
1
1
1
1
1
1
2
2
1
2
0
1
0
0
1
2
0
0
1
1
1
1
2
0
0
0
1
1
0
0
0
2
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
2
0
2
2
0
2
2
1
1
0
1
0
2
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
2
1
0
0
1
2
1
1
1
0
0
2
2
2
0
1
0
1
0
1
1
1
2
1
1
0
1
2
1
0
1
2
0
1
1
1
1
0
0
1
2
1
1
1
2
0
0
1
1
0
1
1
1
1
0
1
1
1
2
1
1
0
2
2
1
1
2
1
3
0
1
0
1
0
1
1
0
1
2
0
0
0
0
1
2
0
0
1
1
0
2
1
3
0
1
1
0
2
2
1
1
1
3
1
0
0
1
0
3
2
0
1
1
2
0
0
2
1
1
1
1
2
0
0
1
1
0
1
1
2
1
2
2
1
0
1
2
1
0
2
2
1
0
1
1
2
1
2
1
1
1
1
0
0
2
0
1
1
2
2
0
2
0
2
0
0
0
2
1
2
1
1
0
1
1
0
1
0
0
2
1
1
1
2
2
0
3
1
1
0
2
0
2
1
1
0
2
1
1
1
1
2
0
0
1
2
1
0
1
2
1
0
1
0
1
0
0
2
1
0
0
1
0
0
1
0
1
0
2
1
1
1
1
1
1
1
1
0
0
0
2
0
1
0
0
1
2
1
1
0
2
1
1
1
0
1
2
2
2
0
1
1
1
1
1
1
0
0
1
2
1
2
0
2
1
1
1
0
1
1
1
1
0
1
1
0
1
0
1
1
1
0
0
1
0
1
1
1
1
1
1
2
1
1
1
0
1
1
1
0
1
0
0
1
2
0
1
1
0
1
1
1
2
2
0
1
0
1
1
1
2
0
1
1
0
1
2
2
1
1
2
1
0
1
1
2
2
1
0
1
1
1
0
1
0
0
1
0
0
1
1
3
1
2
0
1
1
1
0
1
0
1
1
1
2
1
2
1
0
1
1
0
1
0
0
2
1
1
0
0
1
2
1
0
0
0
1
2
0
2
0
2
0
0
1
1
0
0
0
1
2
1
1
1
1
1
0
0
0
1
2
1
2
1
0
1
1
2
1
1
1
2
1
1
0
0
0
1
0
0
2
0
0
1
2
2
4
0
0
0
1
0
1
1
1
1
2
2
2
0
2
1
2
1
1
1
0
1
1
1
1
1
0
1
1
0
1
1
0
0
1
1
0
2
0
1
0
0
1
0
2
1
2
0
1
1
0
2
0
1
1
2
2
1
2
2
0
0
2
2
1
1
1
0
0
0
1
0
1
1
1
2
2
1
0
0
2
1
0
1
1
0
0
2
0
2
0
0
2
1
2
1
1
0
0
1
1
1
1
1
0
0
1
1
2
2
0
1
0
1
0
3
1
1
2
1
1
1
1
0
2
1
0
0
0
0
1
0
3
2
2
1
0
1
0
1
1
0
1
1
1
1
1
1
2
1
2
1
0
0
2
1
2
1
1
0
0
1
1
1
1
1
0
0
0
2
1
0
4
0
1
1
0
2
0
0
2
1
1
2
1
0
1
1
0
1
0
1
0
1
0
1
0
0
2
2
1
1
1
3
1
1
2
2
0
1
1
0
0
1
0
1
1
2
0
0
0
2
2
0
1
0
0
0
2
0
0
0
3
0
1
0
0
0
1
0
1
1
1
1
2
1
2
1
0
2
1
0
0
0
0
1
1
1
1
0
1
0
0
1
1
1
0
2
2
0
0
0
1
1
0
0
1
0
1
0
1
1
0
1
1
2
1
0
0
0
0
0
2
2
1
1
2
0
5
1
0
0
0
1
0
1
1
1
2
1
0
3
1
0
0
0
0
1
0
2
0
2
1
2
2
1
2
1
2
1
2
2
1
0
1
0
2
1
0
2
0
1
2
0
0
0
1
2
1
1
0
1
0
2
2
0
0
2
2
2
0
0
2
1
0
1
1
0
1
0
0
1
1
0
0
2
1
1
1
1
1
1
0
1
0
1
1
2
2
1
0
1
1
0
0
1
1
5
0
1
2
0
1
1
1
1
2
1
0
1
1
1
0
0
0
0
0
1
0
2
1
1
1
1
2
0
1
0
0
1
1
1
0
2
1
1
1
1
1
1
0
0
2
2
1
0
1
1
0
2
1
0
2
1
1
0
1
1
2
1
1
2
2
2
0
0
1
2
0
1
1
1
0
1
0
3
1
2
0
1
1
0
1
2
0
0
2
2
1
1
0
0
0
0
1
1
1
4
1
0
1
0
3
0
0
0
1
1
0
0
0
0
1
1
1
1
2
2
1
1
4
1
0
1
0
1
0
1
0
0
1
1
0
0
2
1
0
1
0
0
2
0
2
1
2
1
2
0
1
1
0
1
1
2
4
2
0
0
1
2
1
1
1
0
0
1
1
2
0
0
0
1
2
0
1
1
1
1
2
0
0
0
1
0
2
1
2
2
2
1
1
2
1
1
0
1
1
1
1
2
0
2
0
2
1
0
2
2
0
1
2
1
1
0
0
2
0
1
2
1
0
0
1
2
0
1
1
0
1
2
1
1
1
0
1
1
2
2
2
0
0
2
2
1
1
1
1
2
0
1
1
0
2
4
1
0
1
0
1
2
0
2
1
0
2
1
0
1
1
2
1
1
0
1
2
1
1
0
2
0
0
1
0
0
2
1
0
2
0
1
0
2
1
0
0
1
0
0
3
0
0
1
2
0
1
0
1
1
0
0
1
0
0
1
2
1
1
1
2
2
1
1
2
4
0
0
1
1
1
0
0
1
1
2
1
1
1
0
0
1
0
1
1
1
0
1
1
0
1
2
2
1
1
1
1
1
1
1
2
1
2
0
2
1
1
1
2
1
1
2
3
0
0
2
1
0
2
0
1
2
1
0
1
1
2
1
2
0
2
1
2
1
0
1
2
1
1
0
0
1
1
0
0
2
0
2
2
1
1
2
0
0
0
1
2
1
2
0
2
0
0
2
0
1
1
0
1
2
2
1
0
2
0
1
1
1
4
2
0
0
2
0
1
0
2
1
0
0
0
0
2
0
1
0
1
1
1
2
1
1
1
0
1
0
0
1
1
2
2
2
0
2
1
0
1
1
0
1
1
2
2
1
0
0
0
0
0
1
2
1
0
0
2
0
0
1
2
1
1
1
0
0
2
1
1
1
0
0
0
1
2
0
2
2
0
1
2
2
1
0
1
1
1
0
1
0
2
1
0
1
1
1
1
0
2
1
1
0
0
1
1
0
1
1
0
2
0
1
0
2
2
2
0
1
0
2
2
1
1
2
1
0
0
0
2
0
1
1
0
2
2
0
0
1
0
1
1
1
0
0
0
0
1
2
0
1
2
1
3
1
2
0
1
0
0
2
0
0
1
0
1
1
0
0
1
1
2
2
2
0
0
1
0
2
0
4
0
1
0
0
0
0
0
0
1
1
3
1
2
1
1
1
1
0
0
1
1
0
2
0
2
2
0
0
1
2
1
1
0
0
0
1
1
0
2
4
1
1
0
1
0
0
1
1
1
0
1
0
2
2
2
1
1
0
0
1
0
1
0
1
1
0
0
1
1
0
2
1
2
1
1
1
1
2
1
1
1
1
2
2
1
0
1
2
2
1
1
0
0
2
0
1
0
1
0
0
2
1
0
2
1
0
0
1
2
0
1
0
1
0
0
1
2
1
1
0
0
0
2
2
0
0
0
1
1
1
0
0
0
0
1
1
1
0
1
0
2
1
1
0
0
0
1
2
1
0
1
0
0
2
0
1
1
1
1
0
0
0
1
1
0
1
1
1
1
2
0
1
1
1
1
0
1
0
1
2
2
0
0
2
1
0
1
1
2
0
2
0
0
2
0
1
2
1
1
0
1
1
0
0
2
1
0
2
1
1
1
1
2
0
1
2
0
2
1
0
2
0
0
1
1
1
1
2
2
2
1
1
1
1
0
1
0
1
1
0
0
1
0
1
1
2
1
1
0
0
0
1
1
0
0
2
1
0
0
1
1
1
2
0
0
1
0
0
1
1
2
0
1
1
1
0
1
0
2
1
1
1
1
2
1
0
1
1
0
0
1
1
2
4
1
0
0
2
1
1
0
1
0
1
1
0
2
2
1
1
0
1
0
0
2
1
1
1
2
0
1
2
1
1
0
1
0
1
1
1
1
1
2
0
0
1
2
0
1
1
1
2
1
2
0
1
1
1
2
0
1
0
1
1
1
2
0
0
3
1
2
0
1
0
1
0
2
1
0
2
2
0
1
0
1
2
1
0
1
1
1
0
1
0
1
2
1
2
0
1
2
3
1
1
1
0
2
1
1
0
0
1
1
2
0
1
0
1
2
0
0
2
1
2
1
0
1
1
1
1
1
0
0
1
1
1
0
1
1
5
1
1
1
2
1
1
3
0
2
1
1
0
3
0
1
2
1
0
1
1
2
0
1
0
0
1
0
1
2
1
0
2
0
1
1
0
2
0
0
0
1
2
1
1
0
0
0
0
0
0
2
2
2
0
0
0
0
1
2
0
1
2
1
2
1
0
2
0
0
0
1
0
1
1
1
2
0
0
4
1
0
1
0
0
1
1
0
0
0
0
1
1
1
2
2
1
0
0
2
2
2
0
2
1
2
1
0
1
1
0
1
2
1
2
1
1
0
1
2
2
1
0
2
1
0
2
1
0
2
2
2
2
2
1
2
0
1
0
1
2
0
1
0
0
2
0
1
2
1
0
2
1
1
1
1
0
2
2
1
1
1
1
1
1
1
1
0
0
0
2
1
2
0
0
0
2
1
1
1
0
0
2
2
2
1
1
2
1
2
0
2
2
1
0
2
0
0
0
0
1
2
0
0
1
2
1
3
1
2
0
1
0
1
2
0
2
2
0
2
1
0
2
1
0
2
1
1
2
2
2
0
1
3
0
1
0
0
0
0
0
0
1
1
2
2
0
0
1
0
1
0
1
1
1
0
0
1
0
1
0
2
0
1
0
2
1
1
0
1
1
2
1
1
0
1
0
3
1
1
2
2
1
1
1
1
1
1
1
5
1
1
1
2
0
0
1
1
1
1
2
0
0
2
1
1
1
2
0
2
0
1
0
0
0
0
2
1
1
2
1
1
1
0
0
0
0
2
0
1
1
2
0
1
1
1
1
0
0
0
2
0
0
1
0
0
1
1
0
1
1
2
1
1
2
1
2
0
0
0
1
1
1
1
0
2
1
1
1
1
0
0
1
1
0
1
0
0
0
1
1
1
0
1
2
2
2
0
0
1
1
1
0
1
0
1
1
0
2
0
1
2
2
0
2
3
0
2
0
0
2
0
1
1
0
0
0
1
2
0
0
1
0
2
2
1
1
0
2
1
1
2
2
1
1
0
0
3
1
1
1
1
1
2
0
1
1
1
0
0
2
0
1
1
0
1
1
2
2
0
1
1
1
0
1
2
0
0
0
1
0
1
1
0
1
2
1
1
1
1
1
1
1
0
0
0
1
2
0
0
0
1
1
1
2
0
0
0
1
1
2
0
1
0
1
0
0
0
2
0
1
0
1
0
1
2
1
1
1
1
1
0
0
1
0
0
1
2
1
1
1
1
2
2
0
0
1
1
0
0
1
1
0
0
1
0
2
1
0
1
1
1
1
2
1
1
0
0
1
0
1
0
1
0
1
1
1
0
2
4
1
1
3
1
1
1
1
1
3
1
2
0
1
0
2
0
0
0
1
1
1
1
1
2
1
1
1
2
1
2
2
1
0
0
1
1
1
0
0
0
0
0
0
2
0
1
1
0
0
1
1
0
1
2
2
0
0
1
1
1
0
1
1
1
3
2
0
2
1
0
2
1
3
2
0
1
1
1
1
2
1
2
1
0
0
0
1
1
1
2
2
1
0
0
0
1
2
2
0
2
1
2
2
1
2
0
1
2
1
2
0
0
1
2
1
1
0
0
5
2
1
1
1
0
0
0
0
1
2
1
2
2
2
2
0
1
0
1
1
1
1
0
1
1
1
1
0
1
1
1
0
3
1
0
0
1
1
1
0
0
0
0
0
1
1
1
0
2
1
2
0
1
0
0
0
2
1
1
3
1
1
1
2
1
1
0
0
0
1
3
1
0
1
0
0
1
0
2
1
1
2
0
1
1
1
0
1
0
2
1
0
1
0
2
0
0
1
2
0
1
0
2
2
2
1
0
2
3
1
0
0
0
1
1
0
0
1
1
1
0
0
1
1
0
1
0
0
0
1
1
0
0
0
1
2
0
2
0
1
2
1
1
1
2
1
1
1
1
0
0
1
1
2
2
3
1
0
1
1
1
1
1
0
2
0
0
1
1
1
1
0
0
0
3
1
1
0
2
0
1
1
1
2
0
1
1
0
0
0
1
1
1
0
2
0
1
1
1
1
1
0
1
2
2
0
1
0
1
0
0
0
0
0
1
0
0
1
2
1
1
0
0
0
1
2
0
2
1
2
1
2
2
1
0
2
1
2
1
1
1
1
2
3
0
0
1
1
1
0
0
1
2
0
1
0
2
1
1
0
0
1
2
2
0
1
0
1
1
0
0
2
0
1
0
0
1
0
1
3
1
1
1
1
1
0
2
0
0
0
0
0
0
1
0
1
2
1
0
1
2
1
0
1
1
1
0
1
0
0
1
2
0
1
2
2
2
0
2
1
0
2
0
2
1
1
1
2
2
1
0
2
1
0
0
0
1
3
0
1
1
0
1
0
0
0
1
1
0
2
2
1
1
2
1
1
1
0
0
1
1
0
1
0
0
0
1
2
2
1
1
2
1
1
0
1
1
0
1
1
0
0
1
0
2
1
2
0
1
1
0
2
0
1
2
0
1
1
1
1
1
2
0
0
0
1
0
1
1
1
1
1
0
1
1
0
0
0
1
1
1
1
0
0
1
0
1
1
1
1
1
0
1
3
1
1
2
1
0
1
1
1
1
0
0
2
0
0
0
0
0
1
2
1
0
0
0
1
1
1
1
0
2
2
1
1
2
0
0
0
1
1
0
1
1
1
1
0
1
1
1
0
1
1
2
0
1
1
1
0
1
1
0
1
4
0
0
1
1
0
2
0
1
0
1
1
1
0
0
2
1
1
0
2
1
0
1
1
0
1
0
1
1
2
5
0
1
3
1
2
1
1
1
0
2
2
0
0
1
1
1
1
2
1
1
0
1
1
0
5
1
1
1
1
0
1
0
2
1
2
0
1
2
0
2
0
0
1
1
0
1
2
0
0
1
0
2
1
1
1
0
0
0
1
1
0
0
1
2
2
0
0
1
2
1
0
0
1
0
2
2
0
0
0
2
2
2
0
0
1
2
1
1
1
0
1
1
1
2
0
1
0
0
1
1
1
1
1
0
2
0
1
2
2
1
3
1
1
1
1
2
0
2
2
1
2
0
0
1
0
0
0
2
1
2
0
2
1
0
0
0
0
0
0
1
0
2
1
0
0
0
1
1
1
1
1
0
0
0
0
1
2
2
1
0
1
2
0
1
0
1
1
2
0
1
1
1
1
1
0
2
1
1
1
1
2
2
0
1
2
0
1
1
1
1
2
1
1
2
0
1
0
0
2
1
1
0
1
0
0
2
0
1
1
1
1
2
1
1
0
0
0
0
1
1
1
2
0
1
0
0
2
3
0
1
2
0
1
1
0
2
2
0
1
2
2
1
1
1
0
2
1
1
0
2
1
1
1
1
2
1
1
0
0
0
0
1
1
1
1
0
2
0
2
1
1
3
1
0
0
0
0
0
0
1
1
1
1
0
0
0
0
2
1
1
1
2
1
0
1
1
1
1
0
1
1
0
1
0
1
0
0
1
1
0
1
1
0
0
1
1
1
1
2
0
2
0
1
1
1
1
1
0
1
1
2
1
1
0
2
1
1
2
0
1
1
0
1
2
0
1
1
0
1
0
0
0
0
0
1
1
0
0
1
0
1
1
1
0
1
1
1
1
0
0
0
1
1
0
0
2
2
1
0
2
2
2
0
0
1
1
1
2
2
1
0
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
0
0
1
0
2
2
1
1
1
1
1
0
0
1
2
2
1
2
0
2
1
0
0
1
2
1
1
0
2
0
1
1
1
1
1
0
1
2
0
1
1
2
2
0
2
0
0
1
1
0
1
3
0
0
0
0
1
1
1
0
0
0
0
1
2
1
1
0
2
2
0
0
0
1
0
0
1
0
1
1
2
1
1
1
3
1
1
1
2
0
1
2
0
0
0
1
1
1
2
2
1
1
0
0
1
1
1
0
2
0
1
1
1
1
1
0
2
2
1
2
0
0
1
0
1
0
0
1
1
1
1
2
1
2
1
1
1
2
2
0
1
2
0
1
2
0
0
2
1
1
1
0
1
0
0
1
1
2
1
0
2
0
0
0
2
2
0
2
1
0
1
0
1
0
0
1
0
2
2
0
2
2
0
2
0
0
1
1
0
1
1
2
0
0
1
1
2
1
0
2
0
0
0
1
0
0
2
0
0
1
1
1
0
1
2
1
1
2
1
0
1
1
2
0
0
1
0
0
0
0
0
2
2
1
2
1
1
2
0
0
0
0
2
0
2
2
1
0
1
1
1
1
0
0
2
1
1
1
2
2
2
0
0
1
0
0
2
0
1
1
1
0
1
2
0
2
1
1
1
0
0
1
0
1
0
1
1
0
2
1
0
2
2
0
2
0
0
1
1
2
2
1
0
1
1
2
1
1
1
0
2
2
1
1
0
0
0
1
0
0
0
0
0
1
1
1
1
0
1
1
1
0
1
1
2
1
0
1
1
0
1
3
0
2
1
2
0
1
2
1
0
1
0
1
1
2
1
0
2
0
0
1
1
1
1
1
0
4
0
0
0
1
1
1
2
0
0
1
1
1
2
1
2
0
1
1
1
0
1
2
0
1
2
2
2
1
2
1
1
1
1
2
1
1
2
0
1
0
0
2
1
3
0
1
1
1
0
0
1
1
0
1
0
0
0
1
0
0
2
1
1
1
0
1
2
1
6
0
1
0
0
0
0
0
3
0
1
2
1
1
2
2
1
1
0
2
0
0
1
0
0
2
1
0
1
0
1
1
1
0
0
0
1
1
0
0
0
0
0
2
1
1
1
1
0
1
2
2
1
0
1
1
1
2
2
1
1
0
2
2
0
1
1
0
2
1
0
2
2
2
1
2
1
2
2
0
0
0
0
2
1
2
0
2
2
0
1
2
0
2
1
0
0
0
0
0
1
1
0
1
0
0
2
1
0
1
0
2
2
1
0
0
1
0
1
0
1
2
2
0
1
2
1
0
1
1
0
0
0
2
1
1
0
0
0
0
0
2
0
1
1
1
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
1
1
2
1
0
1
1
0
1
1
0
0
2
0
1
1
0
2
1
2
2
1
0
0
0
0
2
2
2
0
0
0
1
1
1
0
1
0
1
2
1
1
1
1
1
1
1
0
1
1
1
2
0
2
1
2
2
2
0
1
1
2
1
1
1
1
0
1
1
1
1
1
2
1
2
1
2
0
1
0
0
2
0
2
0
1
2
1
1
2
1
0
1
0
0
2
1
0
1
0
0
2
1
1
0
1
1
0
1
2
1
1
2
0
0
0
0
1
1
1
1
0
1
0
2
1
2
0
1
1
2
0
2
1
0
1
1
0
0
0
0
1
0
0
1
0
0
0
2
0
1
0
2
2
1
1
1
1
1
0
2
0
1
0
1
0
0
0
2
1
1
2
2
0
1
0
1
1
1
3
1
0
0
2
0
2
1
1
1
2
2
1
1
1
1
1
0
1
1
0
1
1
1
0
1
0
1
0
1
0
0
2
1
0
0
0
0
1
0
1
0
1
1
0
2
1
2
1
0
0
1
0
0
0
0
0
1
2
1
1
2
0
3
1
1
1
1
0
0
2
2
1
1
1
2
2
2
0
0
2
0
0
2
1
1
1
1
1
1
0
1
2
0
2
2
0
0
1
1
0
0
1
3
1
1
2
1
2
2
1
1
1
1
1
0
1
1
2
1
2
0
1
0
1
2
2
1
1
1
1
1
1
0
0
0
0
1
1
1
1
0
1
1
2
1
1
1
0
1
1
1
0
1
1
1
2
0
1
0
3
2
1
1
1
2
0
0
2
1
0
3
1
1
1
1
2
2
2
0
0
0
2
0
1
1
0
1
2
2
0
0
0
0
2
2
2
1
0
0
1
1
0
2
1
0
1
1
0
1
2
0
2
0
1
0
1
2
2
1
1
0
1
0
2
1
1
1
2
0
1
0
2
1
1
1
1
0
0
1
1
1
1
2
0
1
0
1
2
2
2
0
2
1
1
0
2
0
2
1
1
1
1
0
3
5
1
0
2
2
0
2
0
0
2
1
0
0
2
2
1
2
2
1
1
0
1
1
0
1
1
0
1
1
2
0
1
2
2
1
1
2
0
1
1
2
1
0
1
1
2
2
1
1
0
0
1
1
2
1
2
0
0
0
2
1
2
2
0
0
2
0
1
0
0
1
1
1
3
1
2
2
2
1
0
0
1
2
0
0
0
1
2
0
2
0
1
1
1
1
0
1
0
0
0
0
0
1
1
0
1
0
0
0
1
2
1
0
2
1
1
2
0
1
1
1
0
1
1
1
0
1
0
1
0
1
0
2
0
2
1
1
0
0
2
1
1
1
2
1
0
2
0
2
0
2
0
1
0
1
1
1
0
2
1
0
2
1
0
1
1
0
1
0
0
0
2
1
1
1
1
1
1
0
0
1
2
1
2
1
0
0
0
0
0
1
1
1
2
1
1
2
1
2
0
0
1
2
0
0
1
0
1
1
2
1
1
1
1
4
0
0
0
2
1
1
2
1
1
0
1
0
1
1
1
2
2
0
0
1
0
1
1
1
0
2
1
1
0
1
1
1
2
1
0
0
1
2
2
1
1
1
0
0
1
1
0
3
1
1
2
1
2
1
1
1
1
1
1
0
1
1
1
0
1
1
0
2
1
2
1
1
1
1
0
1
1
2
0
0
1
1
0
1
2
2
2
0
0
2
0
1
1
1
1
1
1
1
0
2
3
0
2
0
1
1
1
4
1
0
1
1
1
1
1
1
2
0
1
1
2
2
0
0
2
0
0
1
1
0
1
1
1
2
0
0
1
0
1
4
0
0
0
0
0
2
1
2
1
1
2
1
1
0
2
1
0
1
2
1
0
1
0
2
1
0
1
2
1
2
1
1
1
1
1
1
1
2
2
1
0
2
0
1
2
0
1
0
2
1
1
1
1
1
0
0
0
1
1
2
0
2
2
0
0
2
0
0
1
0
2
3
0
1
1
1
0
1
2
2
1
0
0
0
2
1
2
0
2
0
1
0
1
1
1
1
1
0
1
1
0
0
0
2
2
1
0
1
1
0
0
2
1
2
1
1
2
0
0
0
1
2
0
0
0
1
2
1
1
3
2
1
0
2
1
1
1
1
0
0
1
0
1
0
1
2
2
2
1
2
1
0
1
1
0
2
1
2
0
1
0
1
0
1
1
1
1
0
1
1
1
2
0
0
1
1
1
2
0
2
2
1
1
2
0
2
1
2
2
0
0
0
1
1
0
1
2
2
0
2
2
0
0
1
1
1
1
1
0
1
1
0
1
1
2
2
2
0
0
1
2
1
1
2
0
1
0
0
0
0
0
0
1
2
1
0
2
0
0
2
1
2
1
1
1
1
3
1
2
2
1
0
1
2
0
1
0
1
2
1
0
0
0
0
0
0
0
1
4
1
2
0
0
1
0
1
1
1
1
2
0
1
0
2
0
1
2
0
1
0
1
2
0
1
1
1
1
0
0
1
0
0
2
0
0
2
0
1
1
0
0
0
0
1
1
1
0
1
1
0
0
1
1
2
0
0
1
2
1
1
1
1
1
2
1
1
1
2
1
0
1
0
2
0
1
1
1
2
1
0
1
0
2
0
0
1
0
2
2
1
0
1
0
0
1
2
1
0
1
1
2
1
1
2
0
1
0
1
2
1
1
0
2
2
1
0
1
1
0
1
2
1
1
1
2
1
1
0
1
2
1
0
1
1
1
0
0
2
0
1
1
2
1
2
2
2
2
1
0
0
2
0
1
2
1
1
0
1
1
0
2
1
1
2
2
0
2
0
0
2
0
1
1
1
0
0
0
2
0
1
1
0
0
1
0
1
1
1
0
1
1
0
0
1
1
2
1
1
1
0
0
1
0
1
1
0
1
0
1
2
1
2
0
1
2
0
2
0
0
1
2
0
0
0
0
1
0
0
0
1
2
1
0
1
2
0
1
1
1
1
0
1
0
1
2
1
2
1
0
1
2
1
0
1
2
0
2
1
1
0
0
2
0
0
1
0
0
2
0
0
1
1
0
0
3
2
2
1
0
1
1
1
1
0
1
0
0
1
2
0
1
2
0
0
2
0
0
0
1
1
0
0
0
2
0
2
1
2
0
1
1
0
1
1
1
2
0
1
1
2
0
1
1
1
1
0
1
1
2
1
0
3
1
0
0
1
0
1
0
2
0
1
1
2
1
2
1
0
1
1
2
0
0
2
2
0
1
1
0
2
1
0
1
2
0
2
1
4
0
2
0
2
2
0
1
1
2
1
1
2
1
0
0
0
1
2
1
2
1
1
2
1
0
0
1
0
1
1
1
0
1
0
1
0
1
0
0
2
3
0
0
0
1
1
0
1
1
1
0
2
1
0
1
2
0
0
0
2
0
0
2
2
0
1
1
0
0
0
1
0
2
1
2
2
2
1
0
1
3
1
1
0
0
1
1
0
0
2
0
1
1
0
0
0
2
1
0
0
0
1
0
0
0
1
1
2
1
0
0
1
2
2
0
1
0
1
1
1
1
1
0
2
2
0
0
2
0
0
2
1
1
2
2
1
1
1
1
1
1
0
1
1
1
1
1
2
0
0
0
0
1
0
1
1
0
0
0
2
1
2
1
1
0
0
0
2
0
0
0
1
2
2
1
1
2
1
1
1
1
1
1
3
1
1
2
0
1
0
1
1
1
1
2
2
0
2
2
1
1
1
1
0
2
0
2
1
0
3
0
2
1
1
0
0
0
0
2
2
1
1
1
2
1
2
1
0
1
0
1
1
1
1
2
0
2
2
0
1
2
0
2
2
1
1
2
1
1
1
2
0
0
0
1
0
1
0
1
3
1
0
0
1
1
2
2
1
2
0
0
1
2
1
2
1
1
1
1
0
1
0
1
1
2
1
0
0
1
0
0
0
1
0
0
1
1
1
0
2
2
0
0
0
1
2
1
2
2
0
0
1
0
1
2
1
0
1
2
1
2
1
1
1
1
0
0
2
0
1
2
0
0
1
0
2
2
0
0
1
0
0
1
1
1
1
1
0
1
1
0
1
1
2
0
1
1
0
0
0
0
3
1
0
0
1
0
1
0
1
0
2
1
0
1
1
0
0
0
1
1
2
0
1
2
0
2
1
1
1
1
0
1
2
0
1
1
1
1
0
1
0
2
1
0
0
1
1
0
0
1
1
0
1
1
1
0
1
1
0
1
0
2
0
1
2
1
1
1
1
1
1
2
0
1
1
2
0
2
2
1
1
0
1
1
1
0
2
0
1
0
2
1
0
0
1
0
2
0
0
1
1
1
1
1
1
1
2
2
2
2
2
2
1
0
3
0
1
1
1
1
0
2
1
0
1
2
1
2
2
2
1
1
1
1
0
2
1
0
0
1
2
0
1
1
2
1
3
0
1
1
0
1
2
0
2
2
0
0
2
2
1
2
0
0
1
1
0
0
1
0
1
0
1
1
0
0
2
1
1
0
1
1
2
2
0
2
1
2
2
0
0
1
1
1
3
1
1
2
2
1
1
0
1
0
0
1
1
0
0
1
1
2
2
3
1
0
0
1
1
1
1
2
0
2
0
2
0
1
1
0
0
0
2
1
0
1
2
0
0
1
2
1
0
1
0
0
1
2
0
0
1
0
1
0
1
1
1
0
2
1
2
1
1
0
0
0
1
1
0
1
0
1
2
1
1
0
1
0
0
1
0
2
1
1
2
1
1
0
2
2
1
0
0
2
1
3
0
0
0
2
2
2
2
3
0
2
1
0
0
1
0
3
1
0
2
1
0
1
2
2
2
0
1
1
0
1
1
0
2
1
2
1
1
2
0
0
1
1
1
1
1
2
1
2
1
0
1
1
1
3
0
1
1
1
0
0
1
0
0
1
1
0
2
0
0
2
1
2
2
1
0
1
1
0
2
1
2
1
0
0
0
1
2
1
1
2
1
0
1
1
1
0
2
1
0
1
2
0
2
0
0
0
2
1
1
0
1
0
0
2
0
2
1
1
0
1
1
0
0
0
1
1
1
0
1
0
1
1
1
0
1
1
1
2
1
1
1
2
1
1
2
2
1
1
1
2
1
1
2
0
0
3
0
1
1
2
1
1
1
2
2
1
2
1
2
1
1
2
0
0
1
2
0
0
1
1
0
2
0
2
0
0
2
0
0
0
0
0
0
1
2
2
0
1
2
2
2
0
0
0
1
1
0
2
2
1
1
0
2
2
1
1
0
1
0
1
1
4
2
1
0
1
1
2
0
1
1
1
1
1
1
0
2
0
2
0
0
0
2
1
0
0
0
0
1
1
1
1
1
2
1
1
1
1
1
0
0
1
1
1
0
1
1
0
0
2
0
0
1
0
0
0
2
1
1
2
2
0
1
1
1
0
0
0
0
0
2
0
1
1
1
1
0
1
0
2
0
1
0
1
1
2
2
0
1
0
1
1
0
1
1
2
1
2
0
0
1
1
2
1
0
1
2
0
0
1
2
1
0
2
2
1
0
1
2
0
0
0
1
0
0
1
1
0
1
1
2
2
2
1
0
4
2
2
1
1
1
2
2
1
2
0
1
1
1
1
2
1
2
0
1
2
2
1
1
1
1
0
2
0
1
0
1
1
0
1
2
1
0
1
2
0
1
2
0
0
2
0
1
2
1
1
1
0
0
0
1
1
2
1
2
1
0
1
1
0
1
1
2
2
2
1
2
1
0
0
2
0
1
2
2
2
1
1
1
0
0
2
0
0
1
0
1
0
1
2
0
1
2
1
1
1
0
0
2
1
2
2
2
0
0
1
1
0
0
1
0
1
0
0
1
2
1
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
2
1
0
0
2
1
0
2
0
1
2
1
1
1
1
1
0
0
0
2
0
2
1
1
0
1
2
1
0
1
1
0
1
1
1
1
1
0
1
1
0
1
1
1
1
2
0
0
1
0
0
0
0
2
1
2
2
1
1
1
0
1
0
1
1
1
1
0
1
1
0
0
0
2
2
1
1
2
1
0
2
0
2
1
0
1
1
1
0
1
1
0
0
1
2
1
2
1
2
0
1
1
2
2
0
0
1
0
0
0
3
0
1
2
1
1
2
0
2
3
1
1
0
1
0
2
2
0
2
1
0
2
0
2
0
0
0
0
0
1
0
0
2
1
1
0
1
1
0
1
0
0
0
1
0
1
1
2
1
1
1
1
0
1
2
1
1
2
0
1
1
2
1
1
1
1
2
1
1
1
0
0
0
0
1
1
1
1
0
0
0
1
4
1
2
1
1
0
2
2
1
0
2
1
1
0
0
1
1
2
0
0
2
0
2
1
1
0
1
1
1
0
0
0
2
1
0
0
1
0
1
2
0
2
0
1
1
2
0
0
2
1
0
2
0
0
0
1
1
1
0
0
1
1
0
1
1
0
1
1
2
1
1
0
1
1
2
0
1
2
0
1
2
1
2
1
1
2
1
1
1
2
0
1
0
2
1
1
0
0
0
2
0
2
0
0
2
0
0
2
1
0
1
0
2
2
2
0
1
0
1
1
0
0
1
0
0
1
2
2
2
2
0
1
0
0
0
0
0
1
0
1
0
2
3
1
1
1
2
2
3
2
0
0
2
2
1
0
1
3
3
0
1
1
0
1
1
0
1
0
2
1
2
0
1
0
1
0
1
0
0
2
0
0
1
1
0
1
0
2
1
0
0
2
0
1
2
2
0
1
2
1
2
0
2
1
0
0
1
1
1
0
1
0
1
0
1
1
1
1
0
1
0
0
1
0
1
2
1
1
0
0
3
2
1
0
1
3
0
1
1
2
1
1
2
1
2
2
0
0
0
2
0
0
0
0
1
0
1
0
1
2
0
0
2
0
1
2
2
2
2
0
1
1
0
0
1
0
2
1
2
0
2
0
2
1
2
1
1
1
2
1
1
1
1
1
2
0
0
0
1
2
1
0
1
1
0
2
0
0
2
0
2
1
0
1
1
1
0
1
2
0
1
1
1
2
3
7
1
1
1
0
2
0
1
0
0
1
0
1
0
0
2
1
1
1
0
2
2
1
1
0
3
1
0
2
1
1
1
0
0
1
1
1
0
0
1
2
1
2
1
0
2
0
0
0
1
1
0
1
0
0
0
2
2
0
0
1
1
1
1
1
0
0
2
1
2
2
1
2
1
2
2
2
0
1
0
1
1
1
1
1
1
2
0
1
0
2
1
2
1
1
1
0
1
1
2
0
1
0
1
1
0
0
1
1
0
1
1
0
2
0
0
0
1
0
1
2
1
0
1
1
1
4
0
1
0
0
0
0
1
0
0
2
2
1
2
0
2
1
1
1
1
1
1
0
1
2
1
1
0
1
2
2
1
0
0
0
0
0
1
0
1
0
1
1
1
1
1
2
0
3
0
0
0
0
2
2
0
1
1
0
1
0
1
1
1
0
2
2
1
0
1
0
0
0
0
0
1
1
0
0
1
1
1
1
2
2
1
0
0
0
0
1
1
1
0
1
2
1
0
0
1
1
2
0
0
1
1
2
1
0
1
0
2
1
0
1
1
0
1
1
0
1
1
0
1
0
0
1
0
1
1
2
0
1
2
1
1
0
2
2
1
1
1
0
1
2
0
0
0
2
2
0
0
0
0
2
0
1
2
1
0
0
0
2
0
1
1
0
0
1
0
1
2
1
1
1
2
2
1
2
1
1
0
0
0
1
0
0
1
1
1
2
1
0
1
0
2
2
2
0
2
1
2
1
0
1
0
2
0
1
1
2
2
0
0
1
1
0
2
0
0
2
1
1
2
1
1
1
2
0
0
1
0
1
0
1
0
0
2
2
2
0
0
0
1
1
2
0
1
1
2
2
1
2
1
1
0
0
1
1
2
2
1
0
0
1
1
0
0
0
1
1
1
1
1
2
2
1
0
1
2
1
0
0
1
2
1
1
1
1
1
1
0
0
1
1
0
1
1
1
0
2
1
1
2
2
2
1
0
1
1
0
0
2
0
1
1
1
2
1
1
0
1
2
1
0
1
0
1
1
2
2
1
1
1
4
0
2
1
2
0
2
2
1
2
1
1
0
1
0
1
1
0
0
0
1
2
1
2
1
1
1
1
1
2
1
2
1
0
0
1
0
2
0
1
1
0
0
1
0
1
2
0
1
1
1
1
0
1
0
0
0
1
1
1
1
1
0
1
0
1
0
2
2
1
1
2
1
1
0
0
0
0
1
0
0
1
1
1
1
2
1
1
2
0
0
1
1
2
0
1
0
1
0
0
1
1
2
1
1
0
0
1
1
1
0
1
1
0
1
2
2
1
0
1
0
1
1
1
1
1
1
1
0
0
2
1
0
1
0
1
0
1
1
2
1
0
1
2
2
1
0
1
2
0
2
1
1
2
1
2
2
0
0
1
2
0
1
0
2
1
1
0
1
0
0
0
1
2
0
0
1
1
1
1
1
1
0
1
1
2
0
2
1
2
0
2
0
2
0
0
0
2
1
1
1
0
1
1
0
2
0
1
0
2
0
1
1
1
2
0
2
1
0
0
2
2
0
0
0
0
0
1
1
2
1
0
0
0
0
0
2
2
1
0
2
0
0
1
0
2
2
0
2
2
1
0
0
1
0
1
1
0
1
1
0
1
2
0
0
0
1
4
1
0
1
0
1
0
1
0
1
1
0
0
2
0
1
2
1
1
2
1
1
0
2
2
1
1
1
1
1
0
1
1
0
0
1
1
1
0
1
0
0
1
1
1
2
2
0
2
2
1
0
1
2
1
0
0
2
1
1
0
1
1
2
0
0
2
0
0
2
2
2
0
1
2
2
2
2
1
1
1
2
0
1
1
1
1
1
1
1
0
1
0
0
0
1
0
1
1
1
2
2
1
1
1
1
0
1
0
1
2
0
0
0
1
1
1
0
0
0
1
2
0
1
2
2
1
2
1
1
1
1
1
1
1
1
0
1
0
2
1
1
1
1
0
2
1
1
1
0
2
0
1
1
1
2
1
1
2
0
0
1
2
0
1
1
2
1
2
1
0
0
1
0
0
1
2
1
1
0
2
2
1
0
2
1
0
0
1
2
0
1
2
2
2
1
0
1
1
1
1
2
2
2
2
0
0
1
1
2
1
1
1
0
0
1
0
1
2
1
1
0
1
0
0
1
1
2
2
1
0
1
0
3
0
0
1
4
1
1
2
1
2
0
1
0
0
1
2
0
1
0
2
2
0
2
0
2
0
0
1
1
0
2
1
1
1
2
2
0
2
0
1
0
2
1
0
0
0
1
1
2
1
1
1
1
0
1
1
0
1
0
2
3
2
2
1
2
2
2
0
0
0
1
1
1
0
2
1
2
0
1
2
1
2
3
0
1
0
2
2
1
2
0
0
0
1
1
2
0
0
0
1
0
0
0
0
1
1
2
0
1
2
1
1
1
2
0
1
1
1
0
2
2
1
1
1
1
1
1
1
3
1
1
4
1
0
0
1
0
0
0
1
1
2
1
1
2
2
0
1
0
0
1
0
0
2
1
0
0
1
1
1
1
2
1
2
2
2
0
0
2
1
1
0
2
2
1
1
2
1
1
1
1
0
2
1
1
2
0
1
0
1
1
0
2
1
1
0
0
1
1
1
0
1
2
2
2
0
0
1
1
1
0
0
2
1
1
0
2
1
1
1
1
2
0
2
0
1
1
2
1
1
1
1
2
0
1
1
0
0
1
1
0
1
0
2
2
1
1
1
1
1
1
1
1
1
1
0
0
1
1
2
1
0
2
0
0
2
2
0
0
1
2
1
1
2
0
1
1
1
1
1
1
1
1
0
1
1
0
1
2
0
0
0
1
1
1
0
0
0
0
0
0
2
1
2
3
0
1
2
0
1
0
3
0
1
0
0
2
1
0
2
0
1
0
1
1
0
1
2
0
2
1
1
0
1
1
0
1
1
0
1
2
2
1
0
1
1
0
1
2
0
1
1
2
1
0
2
0
2
1
2
2
2
1
1
1
0
1
0
0
1
0
0
0
2
1
1
2
0
0
0
2
0
1
1
2
1
1
1
1
5
0
1
2
2
1
1
1
1
1
2
1
0
2
1
0
2
1
1
7
0
1
2
1
0
1
0
1
2
1
1
0
0
1
1
2
1
0
0
1
2
0
0
0
1
0
1
1
0
1
2
1
1
0
0
1
1
0
1
0
0
1
2
1
0
1
0
1
1
2
0
1
0
1
0
1
0
1
0
1
2
0
1
1
0
0
1
2
1
1
1
1
0
1
0
1
0
1
1
2
2
2
1
0
0
0
2
0
1
0
1
1
0
2
0
2
1
1
1
0
0
3
1
1
1
1
0
0
1
0
1
2
0
1
0
0
1
0
1
0
0
2
2
0
1
0
2
0
1
0
2
2
1
1
0
1
0
0
0
1
1
1
2
1
0
2
3
1
1
2
1
2
0
1
1
1
0
1
1
1
1
1
0
2
0
1
1
1
0
2
0
1
1
1
1
1
2
0
1
2
0
1
1
0
1
0
1
0
2
1
1
2
1
1
2
1
1
0
0
2
2
0
2
0
1
2
0
1
0
4
0
1
0
0
1
2
0
1
0
0
1
2
1
1
1
0
2
0
0
2
0
2
1
1
2
1
1
0
2
0
1
1
1
0
2
1
1
0
0
1
1
0
0
2
1
1
0
0
1
0
2
1
0
1
1
1
2
0
1
1
3
1
2
1
1
0
2
1
1
2
0
0
1
1
2
1
0
1
1
1
4
0
1
0
0
0
2
2
1
1
1
0
1
2
2
1
1
1
2
1
1
0
0
1
1
1
0
1
1
1
2
1
1
1
2
0
0
1
0
0
1
0
2
1
1
2
2
1
1
1
1
0
1
1
1
1
2
1
1
0
0
1
0
1
0
0
0
0
1
2
0
2
1
2
1
0
1
2
0
1
1
1
2
1
1
1
0
2
2
0
1
1
0
0
1
2
2
0
1
1
0
1
0
2
0
1
1
1
0
1
1
1
0
0
0
0
1
2
1
1
0
0
1
0
2
0
0
1
1
0
0
1
1
1
2
0
0
2
2
0
1
1
0
1
1
1
1
0
1
1
1
2
2
1
0
1
1
1
3
2
0
0
0
1
0
1
1
0
1
2
2
0
1
1
2
2
1
1
2
1
1
1
0
0
1
1
1
0
1
0
1
1
1
0
0
0
1
2
1
1
1
0
1
0
1
2
1
1
1
0
1
1
2
0
2
0
1
0
1
1
1
0
1
1
1
1
1
1
1
3
0
2
2
0
1
2
0
0
1
1
1
1
1
1
2
1
0
0
1
2
1
1
0
0
0
1
0
0
1
1
0
0
2
1
1
1
1
0
1
0
0
1
1
1
2
2
1
0
0
1
2
0
1
1
2
0
1
0
0
1
0
0
0
0
0
2
2
1
1
1
1
1
1
2
1
1
0
0
1
0
0
1
1
0
0
1
2
3
2
1
0
2
1
2
1
2
1
2
1
1
2
1
1
2
0
0
2
1
1
0
1
2
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
2
1
1
1
1
1
0
0
0
2
1
0
1
2
0
0
2
2
1
2
1
1
2
1
0
1
1
2
1
3
2
2
0
1
0
1
1
0
0
1
0
0
0
1
1
1
1
0
1
2
0
1
2
0
1
0
1
1
2
2
0
1
0
2
2
0
1
0
1
0
0
1
1
0
1
0
2
1
2
0
0
1
0
1
0
2
1
1
1
1
0
1
0
1
2
2
2
1
1
1
1
0
1
2
0
2
2
1
1
0
2
0
1
1
2
0
1
0
1
0
0
1
0
0
0
2
0
1
1
0
1
2
2
3
0
1
1
0
1
1
1
1
2
0
0
1
1
1
1
1
1
1
0
1
1
1
0
0
2
2
1
1
0
0
1
1
0
2
2
1
2
0
0
1
0
2
2
2
0
0
2
1
0
3
1
1
0
1
0
2
2
1
1
2
0
0
0
1
0
0
0
1
0
0
0
1
1
1
0
1
1
1
0
0
2
1
0
2
1
1
0
1
0
2
1
1
0
0
4
0
0
1
1
1
1
0
1
1
3
1
2
1
0
0
2
1
1
1
0
2
2
1
1
0
0
1
1
0
1
1
0
0
1
1
2
0
2
1
0
1
0
1
2
1
2
1
1
0
0
1
2
1
1
1
1
0
1
0
2
0
0
0
2
1
1
0
1
1
2
0
0
1
1
0
0
0
0
1
3
2
1
1
1
1
1
1
0
0
1
2
2
0
1
3
1
0
0
1
0
0
0
1
0
1
1
0
0
0
2
2
2
0
1
0
1
2
2
0
1
1
1
0
2
0
0
0
1
1
0
1
0
0
2
1
1
1
0
1
2
2
0
2
1
2
2
1
1
1
1
1
0
0
1
0
2
1
1
1
0
2
2
1
1
0
2
1
1
0
0
1
1
1
2
0
2
0
1
1
1
1
1
0
1
0
2
2
1
2
2
1
0
0
1
0
0
0
2
2
2
1
0
0
0
0
2
0
1
1
0
3
1
1
1
1
1
1
2
1
1
1
2
0
2
1
1
1
1
0
1
1
2
1
0
0
0
1
0
2
3
2
1
0
2
1
1
2
0
1
0
2
1
2
1
0
1
0
1
1
0
0
1
2
0
2
2
0
0
1
2
0
0
0
1
1
1
1
1
1
0
0
1
0
2
1
1
1
1
0
0
1
1
0
0
0
0
0
1
1
2
2
1
0
0
2
1
0
1
0
1
1
0
0
1
0
0
1
1
2
1
1
1
0
0
0
1
2
0
1
0
1
0
1
2
0
0
1
1
2
1
1
2
2
1
1
2
0
2
1
2
1
0
0
0
0
0
0
1
1
0
1
0
1
0
1
1
1
0
1
1
2
0
1
0
0
3
1
0
1
1
0
0
2
1
0
1
2
0
0
0
0
0
1
1
0
1
1
1
0
1
1
0
0
1
1
2
0
0
2
1
2
0
3
1
2
1
1
0
1
1
0
1
1
1
2
1
2
0
1
2
2
0
2
0
2
1
0
1
0
0
1
1
1
0
0
1
1
0
0
0
1
1
0
2
0
2
2
1
0
2
2
1
1
1
0
1
0
0
0
0
0
0
2
2
0
1
2
2
1
0
0
1
0
2
1
1
0
1
0
2
0
0
1
2
0
1
0
2
1
1
0
0
2
0
0
1
0
0
0
1
0
1
0
1
0
0
2
1
0
1
1
2
2
2
0
3
2
2
1
1
0
2
1
2
0
1
1
0
0
0
1
1
1
1
0
2
1
2
2
1
2
1
2
2
2
1
0
2
1
1
1
0
2
1
2
0
0
0
1
0
1
1
1
0
0
2
1
1
1
0
2
2
2
1
1
3
0
1
2
2
0
0
2
1
2
1
0
1
0
1
2
2
0
0
1
2
2
1
0
1
0
0
1
1
0
2
0
0
1
1
1
1
0
2
1
1
0
1
1
0
0
0
1
2
1
2
1
0
1
0
0
0
0
1
0
1
1
0
1
1
1
1
1
0
1
1
0
1
2
2
1
1
1
2
0
0
1
0
1
0
1
3
0
1
0
2
0
0
1
0
1
0
0
1
1
1
1
2
0
2
2
2
1
1
1
1
0
0
0
0
0
0
0
2
0
1
0
1
1
0
0
0
2
1
1
2
2
0
2
0
1
2
2
2
2
0
1
1
0
0
0
1
1
2
2
0
1
1
0
0
1
0
1
2
1
1
2
0
1
1
0
0
1
2
0
0
0
2
0
2
1
1
1
0
2
0
1
2
1
1
0
1
1
2
1
1
0
1
1
2
0
1
0
1
1
1
0
1
1
0
0
2
0
2
0
0
1
1
0
1
1
0
0
0
1
1
2
0
0
0
1
0
1
1
1
2
1
2
2
2
1
0
1
1
1
2
1
2
0
0
1
1
0
0
0
3
1
1
0
2
0
0
3
3
1
2
2
0
1
3
0
1
1
1
1
3
0
0
2
1
2
1
0
1
1
1
4
2
1
0
1
1
1
1
1
1
2
1
1
1
0
0
1
1
0
2
1
1
2
1
2
2
0
0
1
1
2
0
2
0
1
1
0
1
1
0
1
1
0
1
2
0
1
2
0
2
0
1
2
2
2
2
1
1
0
0
1
0
1
2
1
1
1
1
1
1
1
0
0
1
0
1
1
1
1
0
2
2
1
0
1
0
1
2
0
1
1
0
0
1
0
1
0
0
0
0
0
1
2
0
1
1
1
0
2
0
1
0
1
0
2
2
0
0
0
2
1
2
2
1
1
0
0
1
0
1
1
2
1
1
1
0
1
0
1
0
4
2
0
2
3
3
2
1
0
1
0
1
0
1
2
0
2
0
2
3
1
0
2
3
0
1
1
0
0
2
2
0
0
2
1
1
1
1
1
2
3
0
0
1
1
1
1
1
2
1
0
2
1
2
2
1
1
2
1
0
2
1
0
0
1
0
2
3
2
2
2
1
0
1
0
1
1
0
2
1
0
0
2
1
1
1
0
1
2
1
2
1
2
2
1
1
1
0
1
1
0
1
0
1
1
0
2
1
0
2
2
1
1
2
1
1
0
1
0
0
0
1
0
2
0
1
1
1
0
1
0
2
2
1
0
1
1
1
1
1
2
1
1
1
1
0
3
1
2
0
2
0
0
0
1
1
2
1
1
2
1
0
1
1
2
1
0
1
2
0
0
1
0
1
2
1
1
1
1
1
2
1
0
0
1
0
0
1
1
1
0
0
1
2
0
1
2
2
0
2
0
1
0
2
0
0
2
1
0
1
0
0
1
1
0
0
1
0
1
0
1
2
1
3
1
1
0
1
0
0
0
0
0
2
1
1
0
0
1
1
1
0
3
0
1
0
0
1
1
2
0
1
1
1
1
1
1
0
2
0
0
1
1
0
1
1
2
0
1
2
1
2
0
2
0
0
2
0
2
1
0
0
0
2
1
1
1
0
0
0
0
0
0
0
0
2
2
1
2
3
1
0
1
1
0
1
1
2
1
1
1
0
0
1
1
0
2
1
1
0
0
0
0
0
1
1
0
0
0
1
1
0
1
0
0
0
0
0
1
0
1
0
1
1
0
1
2
1
0
1
1
1
0
2
1
1
0
0
2
1
2
2
1
2
1
0
0
1
4
1
1
0
1
0
1
0
1
2
2
1
2
2
0
0
1
0
0
0
1
0
0
1
2
0
1
2
0
1
2
2
2
2
0
2
0
0
0
0
0
1
1
0
1
1
1
0
0
0
0
0
1
1
0
1
0
0
1
0
1
0
1
1
0
1
2
1
2
2
1
2
1
2
2
1
0
2
2
2
1
1
2
0
0
2
1
0
0
1
2
0
1
2
0
0
1
0
0
2
0
2
2
1
3
1
1
0
2
2
0
2
1
0
0
2
0
1
0
1
1
1
2
0
2
1
0
1
0
1
0
0
1
1
1
0
0
0
1
1
1
1
1
1
1
1
1
1
0
1
0
2
1
0
2
1
2
2
1
1
1
0
1
1
2
1
1
0
1
0
0
1
0
1
0
0
1
0
1
1
0
0
0
0
0
1
0
0
1
2
0
1
1
3
0
2
2
0
1
0
1
1
0
2
1
0
0
1
0
1
7
1
2
0
1
0
1
0
1
0
0
1
2
0
0
2
0
2
2
1
2
0
2
1
1
1
1
1
0
1
0
1
1
1
0
0
2
1
1
1
0
0
2
0
1
0
0
1
1
2
2
1
0
1
3
0
2
1
0
2
1
2
0
1
0
1
2
1
1
0
2
1
1
1
2
2
1
3
1
0
0
0
0
2
0
0
1
2
0
2
1
2
0
2
0
0
2
1
1
0
0
1
1
2
0
1
0
0
1
1
1
1
0
0
1
0
1
2
0
1
2
2
1
1
0
0
0
1
1
0
1
0
2
1
2
0
1
1
1
2
1
1
1
1
0
0
0
0
1
1
1
0
1
0
1
0
0
0
2
0
1
2
1
0
1
1
1
1
1
1
0
1
0
2
0
2
2
1
1
2
1
2
0
0
2
1
1
1
2
0
1
1
1
2
1
0
2
1
0
0
0
1
2
1
1
1
0
1
2
1
1
0
1
0
2
2
0
0
1
0
0
2
1
2
2
2
2
1
0
0
0
0
0
1
1
2
0
2
0
0
1
0
0
1
2
0
1
1
3
1
1
0
1
0
0
0
0
1
2
1
1
1
2
0
1
1
1
0
1
1
3
0
0
1
2
1
1
0
1
0
1
1
1
0
1
1
0
1
1
1
1
1
0
0
1
1
0
0
0
1
0
2
1
2
0
1
2
1
0
1
0
1
3
2
2
2
1
1
1
2
5
2
1
0
1
1
0
1
0
1
0
0
0
0
0
1
1
2
1
1
1
0
0
2
2
1
1
0
1
1
1
3
0
1
1
2
0
0
0
0
0
0
0
2
1
0
2
0
1
2
1
2
0
1
1
1
1
1
0
1
1
0
0
2
1
1
0
0
0
1
1
1
1
2
1
1
1
0
1
1
1
2
2
1
1
2
0
2
0
1
1
0
1
0
1
2
0
1
0
2
0
1
0
0
0
1
1
1
0
1
1
1
2
0
3
1
1
1
0
0
1
1
2
0
2
2
1
1
1
2
0
2
1
0
0
1
1
0
1
1
0
0
0
0
1
0
0
0
0
1
1
1
1
1
0
0
1
0
1
1
0
0
0
0
1
1
0
0
1
0
1
1
1
2
2
1
0
0
1
0
0
2
1
1
1
1
1
0
1
1
1
1
0
1
1
0
1
1
0
2
0
3
2
2
0
1
2
1
0
1
0
1
0
0
1
2
1
0
1
0
0
0
1
1
1
1
0
1
0
0
1
2
2
1
2
0
0
2
2
2
1
2
2
0
1
0
0
1
2
0
1
1
0
0
0
1
0
1
0
1
1
0
2
1
2
0
0
1
1
1
0
1
1
1
1
0
1
2
2
2
1
2
0
1
2
2
1
0
0
0
1
1
0
0
1
1
2
0
1
0
1
1
1
1
0
2
0
2
1
2
0
0
1
1
0
0
0
1
2
2
0
1
2
0
1
1
1
1
0
0
0
1
1
1
2
0
0
1
1
1
0
0
0
1
1
0
1
1
1
1
2
0
1
0
0
1
2
1
1
1
3
0
2
1
1
2
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
1
1
2
1
0
0
1
1
1
0
1
1
0
0
0
1
1
1
2
1
2
0
2
2
2
2
0
0
1
0
0
2
0
1
0
0
0
0
1
0
0
1
1
0
0
2
0
0
0
2
2
1
1
1
1
1
1
0
1
3
0
0
1
0
1
1
1
1
1
0
2
1
1
1
2
0
1
0
2
0
1
1
0
0
1
1
1
1
1
2
1
2
1
2
0
1
0
1
0
1
0
0
2
0
1
1
1
1
0
1
1
1
1
1
2
1
0
1
2
0
1
1
1
1
1
2
1
2
1
1
2
1
0
1
2
2
2
0
0
4
0
1
1
1
0
1
2
2
0
1
1
0
1
1
2
0
2
1
2
0
0
1
0
1
1
0
2
0
0
0
2
1
0
1
2
1
0
0
1
1
1
0
2
1
2
2
1
0
2
0
2
1
2
1
0
1
1
1
0
2
2
1
1
1
1
1
1
1
1
0
0
0
1
2
2
1
2
1
1
0
1
2
1
2
1
1
1
2
0
0
2
1
0
0
1
1
1
0
2
0
4
1
0
0
1
1
1
0
0
1
2
0
0
0
1
2
0
2
2
0
0
0
1
2
1
1
2
0
0
1
1
0
2
1
2
0
0
2
1
0
1
1
1
0
2
2
0
1
0
0
2
2
1
0
0
1
1
2
1
0
1
0
0
2
1
3
1
1
2
1
2
1
1
1
1
0
2
0
0
1
1
1
0
0
0
2
1
1
0
1
0
1
0
0
1
1
0
2
1
1
0
1
0
1
1
0
0
1
0
1
1
1
2
0
1
1
2
1
1
1
2
1
0
0
1
2
1
1
2
2
1
2
1
1
2
1
1
2
0
2
2
0
1
2
2
4
0
0
1
1
1
1
2
1
1
0
0
1
1
1
0
0
2
1
1
0
2
0
1
1
1
0
0
0
0
2
0
1
0
1
1
0
2
0
2
1
2
0
0
2
0
0
2
2
1
0
2
0
1
2
2
0
0
1
1
1
0
3
0
2
1
2
1
1
2
1
1
2
1
0
1
0
1
1
0
1
1
1
0
1
0
1
0
2
2
1
2
1
1
1
1
2
1
1
0
0
2
0
1
1
2
2
1
0
1
0
1
1
1
1
0
0
1
2
2
0
1
0
0
0
0
1
2
0
0
0
1
2
1
0
1
1
1
0
0
2
1
0
1
1
1
0
1
1
1
0
0
0
1
1
0
2
0
2
2
0
0
0
0
0
2
0
0
1
1
1
2
1
1
0
0
1
1
0
0
2
1
1
1
2
3
2
2
1
2
1
1
1
0
1
1
1
2
0
0
1
1
1
0
2
1
1
1
1
0
1
0
1
0
0
0
1
1
1
0
1
0
1
0
1
1
1
2
1
2
1
1
1
2
1
0
1
1
2
1
0
1
0
0
0
1
0
0
0
2
1
0
1
0
0
0
2
0
2
2
0
1
1
0
1
0
1
2
0
0
0
0
1
2
1
2
1
2
1
1
0
0
0
0
1
0
2
1
0
2
1
0
1
0
0
1
1
2
1
1
1
1
1
1
3
1
1
1
1
1
2
2
2
1
1
1
1
2
0
3
0
0
1
2
0
1
1
1
2
0
0
3
1
0
2
1
2
1
0
0
0
1
0
1
1
0
1
1
1
1
1
1
0
2
1
1
0
0
1
1
0
1
0
0
3
0
1
1
1
1
2
2
2
0
0
1
1
1
0
0
1
0
1
2
1
1
1
3
1
0
1
0
1
1
1
0
0
0
0
0
0
1
1
3
1
1
1
0
0
0
2
1
1
1
1
2
1
2
1
1
2
1
0
1
2
2
2
1
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
1
2
1
1
1
1
0
1
0
1
0
1
1
2
0
2
1
1
0
1
1
2
0
0
2
1
1
2
1
2
0
1
1
2
1
1
2
1
2
0
2
2
6
1
0
3
0
1
1
0
1
1
1
1
1
2
3
1
2
0
2
2
2
1
0
1
0
0
2
0
0
2
0
0
2
1
0
0
0
0
1
2
3
1
1
1
1
1
1
2
1
1
1
0
1
1
0
0
0
0
1
2
1
1
1
0
0
0
2
1
2
1
0
1
1
1
0
0
1
0
2
0
0
0
1
1
1
2
1
2
0
1
1
2
0
0
2
0
2
2
2
0
1
3
1
0
0
1
0
2
1
0
2
1
0
0
1
0
2
1
0
0
0
2
1
0
1
0
1
2
1
2
0
0
1
1
1
0
2
0
0
1
1
0
1
2
1
1
1
0
0
2
1
0
1
1
2
0
1
2
0
2
0
0
2
1
1
1
0
1
0
1
0
1
0
1
1
2
2
0
1
1
1
0
1
0
1
2
0
0
2
0
0
1
1
1
1
0
0
2
0
2
1
1
2
0
0
0
0
0
1
1
1
1
0
2
2
1
0
1
2
2
0
1
2
1
2
0
0
0
1
1
0
0
1
0
2
0
1
0
2
1
0
0
1
2
1
0
1
0
1
2
1
2
1
2
1
1
1
0
0
1
1
1
0
0
0
0
0
0
1
2
1
0
0
1
1
2
0
0
0
1
0
1
2
1
0
1
1
2
0
2
0
1
1
2
2
1
1
2
1
2
1
1
0
2
0
2
2
0
0
0
1
1
2
1
0
4
2
0
2
1
0
1
1
1
2
3
0
1
2
1
1
1
2
2
0
2
1
2
1
2
2
2
0
0
2
1
0
1
2
0
1
1
2
0
0
3
0
1
0
0
0
2
0
0
1
1
1
1
2
0
2
0
0
0
1
0
0
0
1
2
0
0
0
1
1
0
0
2
2
1
1
1
0
2
1
0
2
0
1
2
0
1
0
1
0
2
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
0
0
1
0
0
0
1
0
0
1
2
1
1
1
0
2
3
0
2
1
0
2
0
0
1
1
2
0
2
2
1
0
0
1
1
1
5
0
0
2
2
0
0
0
1
1
0
1
0
0
1
1
2
0
1
1
2
1
0
0
1
0
1
0
1
3
2
2
1
0
2
2
1
0
2
0
1
1
0
1
1
1
1
2
1
0
1
2
0
1
1
1
1
0
0
3
1
0
0
1
1
1
2
0
1
0
1
2
2
0
2
2
1
0
0
1
1
1
1
0
0
0
1
0
1
0
1
0
0
2
2
0
0
2
0
1
2
1
1
2
2
1
0
1
0
2
1
2
0
0
1
0
0
0
0
1
1
2
0
0
2
1
1
0
1
0
1
2
0
0
3
0
2
1
0
0
2
1
1
1
2
1
1
2
0
1
0
1
2
0
1
1
2
0
0
2
2
2
1
0
1
0
1
2
2
0
0
0
1
1
1
1
0
0
1
2
1
1
2
0
1
2
1
1
1
0
3
0
2
2
0
0
1
1
0
0
0
0
1
1
1
1
1
1
0
0
0
0
0
0
1
1
1
0
0
1
1
0
1
0
2
1
1
2
2
1
0
1
1
0
1
0
1
2
0
2
2
0
0
2
0
3
1
1
1
0
2
1
1
1
1
1
1
2
0
1
1
1
0
1
2
3
2
1
0
1
0
1
1
2
0
0
0
2
1
2
1
0
1
1
0
1
1
2
1
1
1
0
1
0
0
2
1
1
1
1
0
0
1
1
1
1
2
0
2
1
2
1
1
1
0
0
0
0
1
1
1
2
2
1
1
0
0
0
2
2
1
1
1
0
2
0
0
0
1
2
0
2
1
0
1
0
0
0
1
1
2
1
1
2
2
0
1
0
2
1
1
1
0
1
2
2
1
1
0
1
1
0
1
2
0
0
1
2
1
1
2
1
0
1
0
1
1
0
0
1
1
0
0
1
0
0
1
1
0
2
1
0
1
1
0
1
0
2
1
2
0
1
2
5
2
1
0
1
1
1
1
1
2
2
0
2
0
1
0
0
2
4
1
2
0
1
1
2
0
2
1
1
1
1
2
2
2
1
0
0
1
0
1
0
0
1
1
1
0
0
0
0
0
1
1
0
2
0
1
1
1
1
0
0
2
1
0
0
1
1
1
1
0
1
0
2
0
2
1
1
1
0
0
0
2
1
0
1
0
2
0
1
2
2
2
1
0
1
1
0
1
2
0
0
0
1
1
0
0
1
0
2
0
1
0
0
1
1
0
2
1
2
2
2
1
0
2
1
3
0
0
2
0
2
2
0
2
1
1
0
1
2
1
1
1
1
0
1
0
1
0
0
1
2
1
1
1
1
1
3
0
0
0
1
1
2
0
2
0
1
2
0
1
1
1
1
1
0
1
0
0
1
2
0
0
1
0
2
1
0
1
1
0
1
2
0
1
1
1
1
0
2
2
0
0
1
1
0
1
1
0
2
1
1
1
2
0
0
1
2
1
2
1
1
1
0
1
0
0
1
0
1
0
1
1
2
1
0
0
1
2
0
0
0
1
1
1
1
1
2
0
1
0
3
1
2
0
1
1
0
2
0
1
1
1
0
1
1
0
2
0
0
0
1
0
2
2
1
1
0
0
1
0
2
1
1
1
0
0
2
0
1
2
1
0
2
2
1
2
0
1
0
1
1
0
0
0
0
0
1
2
0
1
2
0
0
0
0
2
1
2
1
0
0
2
0
0
2
1
1
0
1
1
1
2
0
2
2
2
2
1
2
2
2
1
2
1
0
1
3
1
0
1
1
1
2
2
0
0
0
0
1
2
1
0
1
0
0
1
1
1
2
0
1
1
0
1
1
1
2
0
1
0
0
1
2
2
2
1
0
2
1
0
2
1
0
1
0
1
0
0
1
1
1
1
0
1
1
1
1
1
0
1
0
1
2
2
1
3
2
1
0
0
0
1
2
1
0
0
1
1
2
0
0
1
1
0
2
2
0
1
2
1
0
1
1
2
2
1
1
0
2
3
0
1
2
0
0
2
0
2
0
2
1
1
0
0
0
1
1
0
0
2
1
0
1
2
0
1
2
0
1
1
1
1
0
0
0
2
0
1
2
1
0
0
2
0
1
0
0
0
1
2
1
0
1
1
2
0
1
0
1
2
0
0
0
0
1
0
1
0
1
0
0
2
0
1
3
0
0
1
1
1
2
2
0
1
0
1
0
1
1
2
0
0
1
1
0
2
0
1
0
1
0
0
0
2
1
0
2
2
2
3
1
2
1
1
1
1
1
0
1
1
2
4
2
1
2
1
1
0
1
1
2
1
0
1
1
0
1
0
1
1
2
0
1
2
2
1
1
1
1
0
1
2
0
2
2
1
1
1
1
1
0
0
0
1
2
2
1
1
0
0
0
0
1
2
0
1
1
0
1
0
2
0
1
1
0
1
2
2
1
1
2
1
1
2
1
2
0
1
0
0
0
1
1
1
0
1
2
1
0
0
1
1
0
1
0
2
1
2
1
0
1
1
2
0
1
1
1
1
0
1
1
0
0
2
2
0
0
2
1
2
0
1
0
0
0
0
1
1
0
2
0
1
1
1
1
0
2
1
1
0
0
0
0
1
1
1
2
2
2
0
0
1
0
0
1
1
0
2
1
0
1
1
0
0
1
2
0
1
0
1
2
1
2
2
1
2
1
0
1
1
1
0
1
0
1
1
0
1
1
2
0
1
1
2
1
2
1
0
2
2
1
2
1
1
1
2
0
1
2
0
1
1
1
1
2
0
1
1
1
0
1
1
2
0
1
0
1
0
1
2
0
2
1
1
1
1
0
1
2
1
1
1
4
0
0
3
1
1
0
1
0
1
3
0
0
1
0
1
1
1
0
1
1
1
1
1
1
1
1
2
0
1
0
1
0
1
0
2
1
1
1
1
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
1
2
1
3
0
1
0
1
1
2
1
2
0
2
3
0
1
2
0
2
0
2
0
2
0
1
1
2
0
2
0
2
1
1
2
2
2
2
1
1
0
1
0
2
0
1
1
0
0
1
2
2
1
0
2
1
2
1
1
2
2
1
1
1
2
0
1
0
1
1
2
2
2
0
1
1
0
2
1
0
1
1
1
1
0
3
2
1
0
2
2
1
1
2
1
0
0
1
0
2
2
0
0
0
1
0
1
0
2
1
2
0
2
1
1
2
2
0
0
0
0
0
1
2
0
1
2
1
1
1
0
2
2
4
1
0
1
0
2
0
2
2
1
0
2
1
0
2
1
1
0
2
2
1
1
1
1
0
2
1
0
1
2
0
2
0
2
1
1
1
0
1
2
1
4
1
1
1
2
2
2
1
2
1
0
0
0
0
0
1
2
0
0
1
2
0
0
1
1
1
2
1
1
2
0
0
0
1
1
0
1
1
1
0
1
1
1
1
1
1
1
2
2
1
2
1
2
1
2
0
1
0
2
1
0
1
2
1
0
0
0
0
1
1
2
1
4
1
2
0
0
1
0
0
0
1
1
2
1
1
1
0
2
0
0
1
2
1
1
1
0
2
1
1
1
0
1
1
1
2
1
1
1
1
1
0
0
1
7
0
0
0
1
0
3
0
0
0
1
0
1
0
2
0
2
1
2
0
1
0
0
1
1
0
2
0
2
0
1
2
2
0
1
2
0
1
1
0
0
1
2
0
1
0
0
1
1
0
2
1
1
0
1
2
0
0
1
0
0
1
1
2
1
0
0
1
1
2
1
0
1
0
0
2
0
2
1
1
1
2
1
0
0
2
1
2
0
0
2
1
0
0
0
1
2
0
0
0
1
1
1
0
1
0
1
1
0
1
0
1
2
1
0
1
1
1
2
1
0
0
1
0
1
1
0
2
0
0
0
1
0
1
1
1
1
1
1
1
1
1
0
1
0
0
1
1
0
2
1
0
2
2
1
1
1
2
2
1
1
1
1
0
1
0
2
0
0
1
0
1
2
2
2
2
1
2
0
0
0
1
1
1
0
1
0
2
1
0
2
1
1
1
2
0
2
0
2
1
1
2
0
0
1
2
2
0
0
1
1
2
0
1
1
1
2
1
0
1
0
0
0
1
2
0
1
0
0
1
1
1
1
1
1
1
1
1
0
1
3
0
0
2
0
1
1
2
1
0
2
0
1
1
0
0
1
2
1
0
0
1
1
1
2
0
1
1
0
0
0
0
1
1
0
0
0
1
0
0
1
0
1
1
1
0
0
1
2
2
0
1
2
1
0
2
0
0
1
2
2
0
1
1
2
1
3
0
0
2
1
0
1
1
4
1
0
0
1
2
2
1
1
0
1
0
2
1
0
3
2
0
1
0
1
0
1
2
0
2
1
2
1
1
0
1
0
1
0
0
1
2
1
1
1
0
1
1
3
0
1
1
0
0
2
1
1
2
2
0
0
1
3
3
0
0
0
1
0
1
2
0
1
1
0
0
1
1
1
1
0
1
1
0
1
2
1
1
0
2
0
2
2
1
2
2
0
1
1
0
2
0
1
1
1
1
2
0
1
0
0
2
1
1
1
1
0
1
2
0
2
0
1
2
1
0
1
1
1
0
1
2
0
2
2
1
0
0
0
1
1
1
0
0
1
2
0
0
0
1
0
1
1
1
0
2
2
1
0
2
1
0
0
2
1
0
1
0
0
1
2
0
1
1
0
1
2
1
1
1
0
1
2
0
0
0
1
2
2
2
0
1
0
1
1
2
0
1
0
0
1
2
1
0
0
1
2
0
0
1
2
1
0
1
0
1
1
2
2
1
2
1
2
0
2
2
1
0
1
2
1
0
0
0
1
1
0
1
1
2
0
2
0
1
2
0
0
1
1
0
1
2
0
3
0
1
1
1
2
0
0
1
3
0
2
0
1
3
0
0
2
2
0
0
0
2
1
1
2
0
0
0
1
0
1
0
2
1
2
0
0
0
0
3
0
1
1
2
2
2
1
1
1
2
1
1
1
0
1
2
1
1
0
1
0
2
1
2
2
1
0
1
1
1
1
1
0
1
0
0
0
0
2
1
1
2
1
0
2
0
2
2
0
1
2
1
1
1
1
2
2
1
0
0
1
0
0
0
2
0
1
2
2
2
1
0
0
0
1
1
0
1
2
1
1
0
1
2
2
1
1
1
1
1
1
1
2
1
0
1
1
2
0
2
1
2
1
1
0
0
0
1
1
1
0
0
1
2
0
0
1
1
1
1
0
0
1
1
0
2
0
0
0
0
1
1
2
1
1
0
0
1
0
2
1
1
1
0
1
1
2
2
1
2
1
2
1
0
1
0
1
0
1
0
0
3
2
1
0
2
0
2
1
0
2
0
0
2
1
1
1
0
0
2
0
2
0
1
0
0
0
0
1
0
1
0
1
0
1
1
1
0
0
1
1
1
0
1
2
1
1
2
1
1
0
2
1
1
2
2
2
1
1
0
2
1
1
2
1
1
1
1
2
0
1
2
1
1
2
2
0
2
0
0
2
2
1
0
1
1
2
1
1
1
1
0
2
0
1
1
1
1
2
0
0
0
1
0
1
1
1
2
1
0
0
0
1
0
0
2
0
1
1
1
2
1
1
2
1
0
2
2
0
0
1
0
2
2
2
2
1
2
0
1
1
1
2
1
2
8
2
3
2
1
0
1
1
1
0
1
2
1
0
1
1
1
0
0
2
2
0
1
1
1
1
0
0
2
1
1
1
1
1
1
2
1
1
0
2
1
1
2
1
0
0
0
0
1
1
1
2
0
2
0
1
1
1
0
0
2
1
2
2
2
2
1
0
2
1
1
0
0
1
1
1
1
1
0
2
0
1
1
0
1
0
1
0
0
1
0
2
1
0
0
0
1
0
3
2
1
4
0
2
2
1
0
1
2
1
1
2
0
1
0
0
1
1
2
2
0
1
0
1
0
5
1
2
0
1
0
0
2
1
0
0
1
2
1
0
1
0
0
0
1
0
2
2
3
0
1
0
1
1
1
0
0
1
0
1
2
0
0
0
1
1
1
2
0
1
0
0
2
1
1
1
0
0
0
0
0
2
2
0
0
1
0
0
2
1
1
0
0
0
1
1
0
0
2
0
2
1
1
0
1
2
2
1
1
1
1
1
1
0
1
0
1
2
2
0
0
1
1
1
1
0
1
0
1
2
1
0
0
1
1
0
0
0
0
1
2
1
0
2
0
2
0
1
1
0
2
2
1
1
0
0
1
0
1
0
0
2
2
0
1
1
0
0
1
1
1
1
2
0
2
0
0
1
1
0
2
1
2
1
0
2
2
0
1
0
0
1
2
2
1
1
2
1
1
0
1
0
1
1
0
1
1
2
0
1
0
1
0
0
0
2
1
1
2
1
1
1
2
1
1
0
0
1
1
1
1
0
2
2
0
0
2
3
1
3
4
2
2
0
0
0
1
0
1
1
2
1
1
2
1
0
0
1
1
1
1
2
1
1
1
0
1
2
1
1
2
0
0
0
1
2
1
3
1
0
0
2
1
0
1
0
2
2
2
0
0
0
1
2
1
2
1
1
1
1
1
2
0
0
0
1
0
1
0
0
0
0
2
2
0
2
0
1
1
1
1
1
1
2
1
1
1
1
0
0
0
0
0
1
1
0
0
0
0
0
1
2
1
2
0
0
1
1
1
2
3
1
0
0
1
2
1
2
1
0
2
2
1
1
0
1
0
2
0
0
0
1
2
0
1
1
2
0
2
1
1
1
0
2
0
0
0
1
1
2
0
1
0
0
1
1
1
2
2
0
1
1
1
1
2
1
2
2
0
0
1
2
1
1
0
1
1
0
0
0
0
1
1
0
2
1
2
0
2
0
2
0
2
0
1
1
1
1
0
1
1
0
1
0
0
2
2
1
1
1
0
2
2
2
0
1
1
0
2
1
1
1
1
1
0
1
0
0
1
2
0
1
1
2
2
1
0
1
0
0
1
2
1
0
0
3
0
1
2
1
0
1
1
1
1
1
2
1
0
2
0
2
1
1
2
2
0
1
2
0
1
0
1
0
2
0
2
0
2
0
2
1
1
0
1
0
0
1
1
0
1
0
1
2
0
1
1
1
1
0
2
1
1
0
2
1
1
0
0
0
1
0
1
2
1
0
1
0
2
2
1
1
1
1
1
1
1
2
1
1
1
0
1
1
0
1
4
1
0
0
0
2
1
0
2
0
2
1
0
1
0
1
0
0
0
1
0
1
2
2
1
0
0
0
2
2
1
1
0
1
1
2
0
1
1
0
0
0
1
0
1
2
0
1
1
1
2
0
0
2
2
1
0
0
2
1
1
1
1
1
2
1
1
2
1
0
2
0
1
1
1
5
1
1
1
0
0
0
1
2
0
0
0
0
2
2
2
0
2
0
2
2
1
2
1
2
1
1
0
2
2
1
1
1
1
0
2
2
0
1
0
0
1
1
0
1
0
1
1
1
1
2
0
0
1
0
2
3
2
1
1
0
1
1
2
0
1
0
1
2
0
0
2
1
1
1
2
1
1
1
2
1
0
1
1
1
0
2
0
2
0
0
0
0
0
1
0
1
2
1
0
1
2
2
1
1
1
2
2
1
0
0
0
0
1
1
0
1
1
1
2
0
1
0
2
0
0
2
1
2
1
1
1
0
0
2
1
1
1
1
0
1
2
1
0
0
0
2
0
2
1
0
1
0
1
0
1
0
1
0
0
2
1
0
2
0
2
1
2
2
0
1
0
2
2
2
2
2
2
0
1
1
0
0
0
1
0
1
2
1
0
1
0
2
0
2
2
0
1
0
0
2
1
1
1
1
0
0
0
1
0
2
2
2
1
1
2
0
2
2
1
1
0
2
1
0
0
2
0
1
2
0
1
1
0
1
0
0
0
0
2
0
1
1
1
2
1
1
2
1
1
0
1
1
2
0
0
1
0
0
0
0
5
0
0
0
0
1
0
0
1
1
2
0
2
1
0
2
1
1
2
0
0
1
0
1
2
2
1
1
1
1
2
2
0
1
0
2
1
2
0
1
0
1
2
1
0
1
0
1
2
1
2
0
0
1
1
1
0
1
2
1
1
0
0
0
1
2
0
1
1
0
2
0
3
0
1
2
2
1
1
0
0
1
1
1
1
2
2
1
0
1
1
0
0
0
1
1
2
4
1
1
1
1
1
0
2
1
0
2
0
0
0
0
1
2
1
0
0
1
0
0
0
1
1
2
0
1
2
0
2
1
2
0
1
2
1
0
2
1
1
1
1
2
1
0
0
0
1
2
0
1
2
1
1
0
1
0
0
1
0
1
0
0
0
1
1
1
2
0
0
2
2
1
2
2
1
0
1
2
1
0
1
1
0
2
2
1
1
1
1
2
2
0
1
2
0
1
0
2
1
2
2
1
0
2
0
0
1
2
1
1
0
0
0
1
1
1
1
1
0
0
2
0
2
2
1
1
0
1
0
1
0
2
2
0
1
2
1
0
1
1
0
1
0
0
1
1
0
1
0
0
0
2
2
2
0
1
0
2
1
1
0
0
0
0
0
2
1
1
0
0
1
2
2
1
2
1
2
1
1
1
0
1
1
1
1
0
0
0
0
2
0
2
1
2
0
2
0
0
2
0
2
1
1
1
1
2
1
1
0
2
1
0
0
0
1
1
0
1
0
1
2
0
1
1
0
1
0
1
2
2
2
2
1
2
0
1
0
0
0
1
2
2
1
1
1
1
0
1
2
0
1
0
1
0
1
0
3
0
0
1
1
1
1
2
2
1
0
2
1
0
1
0
1
1
2
0
0
2
0
0
1
0
1
1
0
0
1
0
1
0
0
1
0
1
1
2
0
1
1
1
0
1
2
1
2
1
0
0
2
1
1
0
1
0
1
0
0
0
1
0
1
1
1
1
2
1
1
1
0
1
1
0
0
1
1
2
1
0
0
0
0
1
0
2
2
0
0
0
2
2
0
2
2
1
0
2
0
1
1
1
2
1
0
1
1
1
1
0
1
1
0
1
1
2
1
0
1
1
0
1
1
0
0
0
0
1
2
2
2
1
0
0
1
0
1
2
1
0
0
1
0
1
0
0
1
1
1
1
1
0
2
0
0
1
1
1
1
2
1
2
0
0
0
2
0
1
2
1
0
2
1
0
1
1
1
1
1
0
1
2
1
0
1
2
0
2
2
1
1
0
0
0
2
1
0
0
0
1
2
1
1
0
2
0
1
0
0
3
1
0
0
1
0
1
1
1
1
1
1
1
2
1
1
0
1
2
1
1
1
0
0
1
1
1
1
2
1
0
1
0
1
1
1
1
0
1
1
0
1
1
2
0
0
0
0
0
2
0
2
1
2
1
2
2
1
1
1
1
2
1
0
1
2
2
1
1
1
1
1
1
0
1
3
0
2
2
1
1
1
0
0
2
0
1
2
1
0
1
1
0
0
0
1
1
1
0
2
0
0
2
0
1
1
1
1
2
1
0
0
0
1
1
0
0
1
1
0
0
0
2
0
0
2
2
0
0
1
1
0
2
1
1
1
2
0
0
1
2
0
0
0
1
0
2
0
1
1
3
2
0
2
1
2
0
0
2
0
1
1
1
1
1
2
1
1
1
2
2
1
2
1
2
1
0
2
1
0
1
0
1
1
1
0
1
0
0
0
1
1
1
0
2
1
0
1
1
2
1
2
0
0
0
1
2
1
0
1
1
1
2
0
1
1
1
2
1
0
0
0
1
1
1
0
1
0
0
1
2
1
1
0
2
1
0
2
1
0
2
1
2
2
1
2
1
0
2
0
2
1
0
0
2
0
0
0
1
1
1
0
2
0
1
0
2
2
0
1
0
1
0
0
2
0
1
2
1
1
2
1
0
2
2
1
0
2
2
1
2
1
1
2
1
0
0
1
2
0
0
2
0
2
0
0
1
0
0
0
1
1
0
1
1
1
1
0
1
1
2
0
1
1
2
1
1
0
0
1
1
0
1
1
0
1
0
1
1
1
1
0
3
2
2
1
1
2
0
0
0
0
0
0
1
0
0
2
1
1
2
0
1
1
0
0
0
1
2
1
2
0
0
0
2
0
1
0
0
1
0
1
1
1
1
1
1
0
0
2
1
0
1
0
0
1
0
2
0
1
0
0
2
0
0
2
2
0
0
1
0
0
0
2
2
2
1
0
0
2
1
2
1
0
1
1
1
1
1
1
2
2
2
1
2
0
0
1
1
0
1
1
1
2
0
0
3
2
0
0
0
0
2
1
0
1
2
1
1
1
0
1
1
1
1
1
2
2
0
0
2
0
1
0
2
1
0
2
1
1
2
0
1
2
0
0
0
0
2
1
1
0
0
1
2
1
0
2
1
0
0
1
2
0
0
0
2
1
1
0
0
2
1
1
0
2
0
1
1
0
0
2
1
0
2
0
1
1
0
0
0
1
1
0
1
2
0
0
1
0
0
0
0
2
0
0
1
0
1
0
0
1
1
0
1
2
3
1
2
2
0
0
2
0
1
0
1
1
1
2
1
2
2
0
0
0
1
0
2
1
0
0
1
1
2
0
0
1
2
0
2
0
0
0
2
1
1
1
0
2
0
1
1
1
1
0
1
1
0
0
2
2
1
2
1
1
0
1
3
2
2
1
1
0
1
0
1
2
2
1
1
0
1
2
2
1
2
1
0
0
1
1
1
0
1
2
0
1
1
2
0
1
3
0
0
0
2
0
0
2
2
0
0
1
0
1
1
2
2
0
0
2
0
0
0
2
2
0
1
0
1
0
0
1
1
1
1
2
1
0
0
2
0
0
2
2
2
1
1
2
1
1
1
1
1
2
0
0
1
1
2
1
6
0
2
1
2
0
1
1
1
2
0
1
1
1
0
2
1
1
0
0
2
2
1
0
0
2
1
1
1
1
1
1
1
1
1
1
0
0
1
1
2
0
2
0
2
1
1
0
0
0
2
0
0
1
1
1
0
0
2
2
0
2
1
1
1
2
1
1
1
0
1
1
0
1
0
1
0
1
0
0
2
1
0
0
0
1
1
1
0
1
2
2
2
1
2
0
1
0
1
1
1
0
0
1
0
1
1
0
2
2
1
1
0
1
1
0
0
2
0
0
1
0
1
1
1
1
0
1
0
1
0
1
0
3
1
0
0
1
1
2
2
2
1
2
1
0
0
0
1
0
0
1
1
1
1
1
1
1
1
0
1
0
4
1
1
0
2
2
1
1
0
1
0
0
0
0
1
2
2
2
1
1
0
0
1
0
1
0
0
1
2
1
2
0
0
0
1
1
1
1
0
2
1
1
2
0
1
1
0
1
1
1
1
1
0
0
1
2
1
0
1
2
1
0
2
1
1
0
1
1
1
0
1
1
1
2
1
1
1
2
2
1
0
1
1
2
2
1
1
2
2
1
2
0
1
1
0
1
0
1
1
0
1
1
1
1
0
2
1
1
1
1
0
2
0
2
2
1
0
2
1
1
0
1
2
0
1
1
0
2
1
2
2
1
1
2
1
1
1
0
1
1
1
0
1
0
2
0
1
0
1
1
1
0
1
1
2
0
1
1
0
0
0
1
0
1
1
0
1
0
1
2
2
1
1
0
1
1
1
2
0
1
2
1
1
2
0
2
1
1
1
2
0
1
1
1
1
2
0
2
0
0
0
1
1
1
1
0
1
2
2
2
2
0
1
2
0
0
1
0
0
1
1
0
1
1
0
1
1
0
0
0
1
0
2
1
1
1
3
1
0
1
1
1
2
1
2
1
1
0
0
2
1
1
0
1
1
0
0
2
0
0
2
1
1
2
1
0
2
2
0
1
1
0
2
0
1
1
1
2
1
2
0
1
0
0
1
2
1
0
1
0
1
1
0
0
1
1
2
1
0
1
1
2
0
1
1
1
0
1
2
0
1
1
1
0
1
0
1
1
2
1
2
0
0
0
1
0
0
1
1
1
0
2
1
0
1
0
1
0
0
1
0
0
1
2
0
1
0
1
0
2
0
2
1
0
0
1
1
2
1
1
1
1
2
1
2
1
0
1
1
0
2
0
0
0
1
1
1
1
0
0
0
2
1
1
0
1
1
2
1
1
0
1
0
2
6
1
1
1
2
0
1
0
1
1
0
2
0
0
2
0
0
1
1
0
1
0
1
2
0
3
1
0
1
1
0
0
2
1
0
1
1
1
0
0
1
2
1
0
1
2
2
1
2
2
2
0
0
1
1
1
1
1
0
0
0
1
0
1
1
0
2
2
1
1
0
1
2
1
1
2
1
1
0
1
3
1
0
1
0
2
2
1
0
1
2
1
1
0
1
2
2
0
0
1
2
3
0
1
3
1
0
1
1
0
1
0
1
2
1
1
1
1
1
3
1
1
1
1
1
1
1
1
1
1
0
0
1
0
2
3
0
2
0
1
1
1
2
2
0
1
3
1
0
2
1
0
1
2
1
1
0
2
0
3
2
0
1
0
1
1
2
1
2
0
1
1
0
1
1
1
1
0
0
0
1
0
0
0
1
1
0
1
1
0
0
0
2
1
0
2
2
1
2
0
0
1
1
0
0
1
0
2
0
1
0
2
2
2
2
0
1
2
0
3
0
0
2
1
1
2
1
0
1
2
1
1
1
1
1
0
1
0
2
1
1
2
2
1
1
0
0
2
0
2
0
1
6
2
1
2
0
0
2
0
1
2
1
1
0
2
1
1
1
0
2
1
0
1
1
1
1
0
1
1
1
1
0
0
0
2
2
2
2
0
2
2
0
2
2
1
2
0
1
0
1
0
2
0
1
1
1
1
1
0
0
1
2
1
2
0
2
2
1
1
2
1
1
0
0
0
1
0
1
0
0
1
2
2
1
0
2
1
1
0
1
1
1
0
0
1
1
1
0
1
0
1
1
1
0
0
0
0
0
1
0
0
0
1
0
1
0
2
1
2
0
0
2
1
1
1
1
2
2
1
1
1
0
1
1
1
0
1
1
2
2
0
2
1
1
2
2
0
2
2
0
1
1
1
1
1
2
1
2
1
1
3
0
0
0
1
2
2
1
1
1
0
3
0
0
0
1
0
1
2
0
0
1
0
0
2
0
1
0
2
2
0
0
1
2
0
0
0
0
1
0
1
1
1
2
0
3
1
1
2
0
1
0
9
1
1
1
0
1
1
1
2
2
0
1
1
2
0
0
0
0
1
0
1
0
1
1
2
0
1
1
0
2
0
1
1
0
1
0
1
0
0
0
0
2
0
1
0
1
1
0
2
2
0
0
1
1
2
0
1
1
2
0
2
1
1
2
0
1
2
1
1
0
0
2
2
1
1
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
3
1
0
1
0
0
2
1
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
2
1
1
1
1
0
0
1
1
1
1
0
1
2
1
0
1
2
1
1
1
0
1
1
0
1
0
1
1
0
2
0
1
0
2
0
0
0
0
1
1
0
0
1
0
1
3
0
2
1
1
0
0
1
0
2
0
1
0
0
0
1
0
1
0
2
1
2
1
1
0
2
2
2
2
0
0
3
2
1
2
0
2
1
2
0
0
3
0
1
1
0
0
0
1
1
2
1
0
0
1
1
1
1
2
1
1
0
1
0
2
0
0
0
2
0
2
0
0
2
1
1
1
1
2
2
1
0
1
1
2
0
1
0
0
2
0
1
1
0
0
2
1
2
2
2
2
1
2
1
1
2
1
1
0
0
1
0
0
1
2
0
0
1
2
2
2
2
1
0
2
1
0
1
1
1
0
0
1
0
0
1
1
0
0
0
1
1
1
1
1
2
0
1
1
2
1
1
2
1
0
3
0
2
1
1
1
2
0
0
1
1
1
1
1
0
2
1
1
2
1
2
0
1
2
2
2
0
1
2
2
0
1
0
0
0
0
2
1
2
1
1
2
1
0
0
2
0
1
0
2
0
2
0
0
0
1
1
0
0
2
2
2
1
1
1
0
2
1
1
2
2
0
1
0
1
2
0
0
0
1
1
2
0
2
1
0
1
1
1
0
0
1
1
2
0
1
1
2
0
0
1
2
0
0
2
2
2
1
1
2
0
1
0
1
0
0
0
1
0
1
0
0
2
2
0
1
1
1
0
1
1
0
0
1
0
0
0
1
0
2
0
0
0
2
1
1
0
0
2
0
0
2
1
2
2
1
1
0
2
2
1
2
0
0
1
2
1
1
2
1
1
0
1
2
1
3
0
2
1
0
1
2
2
1
0
0
0
1
2
0
4
1
2
1
0
0
0
2
0
2
1
1
0
1
0
0
1
0
2
1
3
1
2
2
1
2
1
0
2
0
2
1
1
0
1
1
3
2
1
0
0
0
2
1
0
2
1
1
2
1
1
0
0
2
0
1
0
1
1
0
1
0
0
2
0
0
0
1
1
2
1
0
1
1
1
1
0
2
1
0
1
0
2
1
1
0
0
0
1
2
1
1
1
1
2
1
1
0
0
0
1
2
2
1
2
2
1
0
0
0
1
1
0
2
1
1
0
1
1
1
0
2
0
0
2
0
2
2
1
2
0
1
0
1
0
1
0
0
1
0
2
0
1
1
2
2
1
2
2
0
0
1
0
2
1
1
2
0
1
2
2
1
0
0
0
1
1
0
1
0
2
1
0
0
2
0
2
3
1
0
2
1
0
0
2
2
0
0
0
1
2
1
1
2
1
0
1
1
0
2
0
3
1
2
2
1
1
1
2
1
2
1
0
0
1
1
1
1
0
0
2
0
1
2
0
0
0
0
1
2
0
1
1
2
2
1
1
1
1
1
0
0
0
1
3
1
2
0
1
0
1
1
1
1
1
2
1
0
0
0
1
2
1
1
0
1
0
0
0
2
1
2
0
0
1
1
1
0
0
1
2
0
1
1
1
1
0
0
1
0
1
1
2
0
1
3
4
0
1
0
1
0
2
1
1
1
0
0
2
2
0
2
1
1
1
1
0
0
1
1
1
0
2
1
2
2
0
1
2
2
2
1
1
2
1
1
0
2
0
0
0
0
0
1
2
1
0
0
2
1
1
1
1
1
1
2
1
2
2
0
0
1
2
0
1
2
2
2
1
0
1
0
1
1
2
0
1
1
2
1
1
1
1
2
1
0
0
0
1
1
2
0
0
1
0
3
2
1
1
3
2
1
2
1
0
1
2
2
2
0
0
0
2
2
0
2
0
1
1
1
2
1
1
1
1
1
1
1
1
0
2
1
0
2
1
0
1
1
1
1
1
0
1
1
1
1
0
1
0
2
1
2
0
0
2
0
1
1
1
2
2
2
0
2
0
0
0
1
0
1
0
0
2
2
0
1
2
1
1
0
2
1
2
1
1
0
0
2
1
1
0
0
1
1
2
0
0
0
1
1
4
1
1
1
1
1
3
0
0
0
1
1
1
1
1
1
0
0
2
2
1
0
2
1
0
2
0
0
1
1
1
2
0
0
1
0
3
0
1
0
0
0
0
1
0
1
3
1
1
0
0
2
0
2
2
0
1
1
0
0
0
1
0
0
1
2
2
1
1
2
1
0
0
2
0
1
3
2
0
0
1
1
1
1
0
1
2
2
1
1
1
1
1
0
1
0
1
1
0
0
1
0
1
0
0
0
0
0
2
1
1
1
3
3
1
1
1
1
0
1
2
2
1
1
1
1
2
1
1
0
1
1
0
2
1
0
1
2
1
1
1
1
1
2
0
0
1
1
0
0
0
1
1
1
2
1
2
0
1
0
1
3
0
0
0
1
1
1
2
1
0
1
2
1
1
1
0
0
0
0
1
1
1
0
0
1
1
2
0
2
1
1
1
2
0
1
1
2
1
4
0
1
2
0
0
1
0
1
0
2
2
0
0
2
0
0
1
0
0
1
1
0
2
0
1
2
1
2
1
1
1
2
2
0
2
1
0
1
0
1
0
0
1
1
1
0
2
2
1
1
1
1
1
1
1
2
0
2
0
1
1
1
0
0
0
0
0
2
2
3
1
0
0
0
0
2
1
1
1
1
1
1
0
1
2
0
1
0
0
0
0
3
1
0
0
1
2
0
0
1
0
1
0
1
1
1
1
0
0
1
0
1
2
1
1
4
3
3
0
0
1
1
1
1
3
1
0
1
0
1
0
1
0
0
0
2
3
0
1
1
0
1
1
1
2
0
1
0
2
1
1
0
2
1
0
0
1
1
1
0
1
3
0
1
1
2
0
2
1
1
2
2
1
2
1
0
2
1
1
2
0
0
1
2
1
1
1
0
2
1
0
1
0
1
1
2
1
1
0
0
2
2
1
1
2
2
1
1
1
1
0
0
0
1
2
0
0
0
0
2
0
0
2
0
2
0
1
0
0
1
0
0
2
2
3
1
0
1
1
1
0
0
2
2
1
0
1
1
1
1
1
0
3
1
1
1
1
1
1
2
2
0
1
0
1
1
1
1
1
1
1
1
1
1
0
1
2
1
0
1
1
1
0
2
0
1
1
0
1
1
1
0
0
1
0
1
2
1
1
0
0
0
2
2
2
0
0
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
0
2
0
1
1
2
2
1
0
2
2
1
2
0
0
1
0
2
1
0
2
0
2
1
0
0
1
0
2
0
2
2
0
1
1
1
1
1
0
1
2
0
2
2
2
1
0
1
0
0
1
0
2
1
2
1
2
1
1
0
2
1
1
1
0
1
2
0
1
2
1
0
2
0
0
1
1
1
1
1
1
0
1
1
1
1
1
2
0
2
1
2
1
0
0
0
2
1
0
1
1
0
0
1
2
0
1
0
0
2
1
2
2
0
1
1
0
0
0
0
1
3
2
0
0
2
1
1
1
0
1
0
1
1
2
1
1
0
1
1
0
0
2
0
0
1
0
1
1
0
0
1
0
0
2
1
1
0
0
0
1
0
0
1
0
2
1
1
2
1
0
0
2
1
1
2
2
1
2
0
2
0
1
0
1
0
0
0
1
1
1
1
0
0
1
2
0
1
1
1
0
2
4
2
0
1
0
0
0
1
1
0
0
0
1
1
1
2
1
1
2
0
0
1
0
0
1
0
1
2
1
1
2
1
1
2
2
1
0
1
1
1
0
1
1
2
0
1
1
1
1
2
1
0
3
0
0
1
1
0
0
2
1
1
1
0
1
0
2
2
1
0
0
1
0
0
1
0
2
1
2
1
0
0
0
0
1
1
2
2
1
2
1
1
1
1
2
2
1
1
1
1
0
1
1
2
1
0
2
1
1
1
1
1
1
1
1
0
1
1
2
1
1
1
1
0
1
0
0
2
1
2
1
1
0
1
2
0
0
2
0
1
0
2
1
1
0
0
1
1
1
1
2
0
0
0
0
0
0
0
1
0
1
2
1
0
1
1
1
0
0
0
0
0
0
0
0
2
1
2
0
1
0
1
1
1
1
2
2
0
0
0
1
1
1
2
1
2
1
1
0
1
1
0
2
2
1
1
1
0
2
1
0
3
1
0
1
1
1
1
0
2
1
0
2
0
2
2
2
1
1
0
2
1
0
1
1
0
1
1
1
2
0
2
0
2
0
0
1
0
0
1
0
1
1
2
1
1
2
0
0
0
2
2
0
1
0
1
2
0
1
1
0
1
1
1
1
1
1
2
1
1
0
2
0
0
0
0
0
1
1
1
1
1
2
0
0
0
1
0
2
0
2
0
2
0
1
0
1
2
1
2
1
0
2
1
2
1
0
1
0
1
2
2
1
0
2
0
1
1
1
2
0
2
1
3
1
1
1
1
0
0
1
0
0
1
0
0
1
0
0
1
1
1
1
2
2
1
1
0
0
2
1
2
1
2
1
1
0
0
1
1
1
1
0
2
2
3
2
1
0
0
0
0
1
1
1
1
1
1
1
0
2
1
1
0
1
2
0
0
1
1
1
2
0
1
0
1
0
1
1
1
2
0
1
1
1
0
0
2
1
2
1
1
0
1
1
0
0
2
0
0
1
2
0
1
0
2
0
0
1
0
2
0
2
2
1
2
2
0
1
0
1
1
1
1
1
2
0
0
0
0
1
1
1
2
1
2
1
2
0
1
0
2
1
1
2
1
1
0
0
1
2
1
1
1
1
2
3
1
0
1
0
0
1
2
2
0
1
1
1
0
1
1
1
1
0
2
2
2
1
0
2
1
1
2
1
2
1
1
0
1
0
1
0
1
0
1
0
1
2
1
1
1
1
0
2
0
0
0
2
1
1
1
0
1
0
1
2
1
1
2
0
0
0
0
2
1
0
0
0
1
1
2
0
2
0
3
2
0
2
0
2
2
0
1
2
0
1
0
0
0
0
2
0
1
1
1
0
2
1
0
1
2
0
0
2
1
1
2
1
1
1
1
0
1
1
1
1
0
1
0
1
0
0
1
2
0
0
2
0
1
3
0
2
1
0
2
0
1
1
1
0
0
1
1
0
0
0
0
0
1
0
2
1
2
1
2
1
1
1
0
0
1
0
2
1
2
1
2
2
1
2
0
2
2
1
0
2
1
1
1
1
0
1
1
0
1
0
1
2
1
1
2
0
1
0
1
2
2
2
2
0
0
1
1
1
1
2
1
2
0
1
1
1
2
2
2
1
1
1
2
1
0
1
1
1
0
0
0
1
0
0
0
1
2
1
1
1
0
0
1
0
1
1
1
1
0
0
0
1
1
0
0
2
2
1
2
1
1
2
1
2
0
2
1
0
1
1
0
0
2
1
1
0
3
1
1
0
0
0
1
1
2
2
1
0
1
2
0
1
1
0
2
1
0
0
1
0
0
1
1
1
1
1
1
1
2
0
1
1
1
1
0
2
0
2
1
2
2
1
1
1
1
0
0
1
1
2
0
1
1
0
0
1
1
2
2
1
0
1
0
2
1
1
2
0
1
1
1
0
1
2
1
1
0
1
3
1
1
2
2
1
0
2
2
0
0
2
0
1
0
0
1
0
1
0
2
1
0
3
1
1
2
1
1
1
1
0
0
0
1
0
1
2
1
0
3
1
0
0
1
1
0
1
1
1
1
1
2
2
0
1
0
1
0
1
0
0
1
1
1
0
2
0
2
0
2
1
1
0
2
0
1
0
0
1
3
1
2
0
0
1
2
0
1
1
1
2
2
0
3
2
1
1
1
0
0
1
1
0
0
1
0
1
1
2
2
1
0
1
0
1
2
1
1
1
1
1
1
0
1
0
2
1
1
1
1
1
1
1
1
0
1
0
0
0
1
0
2
1
0
1
2
0
0
0
0
1
0
2
2
1
2
0
0
0
2
2
2
1
2
2
0
0
0
1
0
2
1
0
1
0
2
1
1
1
1
1
1
1
0
1
1
3
2
2
2
0
0
1
1
0
0
0
1
1
1
1
1
2
0
1
1
2
1
0
0
0
3
2
0
1
1
1
0
2
1
2
0
1
1
0
2
1
1
2
2
0
1
0
0
0
1
1
2
2
0
2
1
2
0
2
0
0
2
2
1
2
2
1
2
1
2
0
0
0
1
1
1
1
1
0
2
0
0
1
0
1
0
1
0
2
2
1
0
1
1
2
1
2
1
1
2
0
2
0
2
0
1
0
2
0
2
1
1
1
1
2
1
0
0
0
2
1
0
1
0
0
0
1
1
0
1
2
0
2
2
1
1
0
2
0
0
0
1
1
0
1
0
1
4
2
1
1
2
0
0
1
0
1
1
1
0
0
1
1
1
0
1
0
0
1
1
1
0
0
1
2
2
0
1
2
0
0
0
0
1
1
2
1
0
0
0
1
0
2
0
0
0
0
0
0
2
2
1
1
1
1
0
2
1
1
2
2
1
1
2
0
1
1
1
1
2
0
0
0
0
0
0
0
1
1
2
0
1
1
1
0
1
0
0
0
0
1
1
0
1
0
1
0
0
0
2
1
1
1
0
0
2
0
0
1
2
2
1
0
0
0
1
1
1
0
1
0
2
2
1
0
2
0
0
1
0
1
1
1
2
1
2
0
0
1
1
1
1
1
1
2
1
0
1
2
2
1
0
1
2
2
1
0
0
1
0
2
0
1
1
0
0
1
2
0
2
0
2
2
2
0
1
0
1
1
1
1
1
2
0
0
1
0
1
1
1
0
2
1
1
1
2
1
0
2
0
1
0
2
1
0
1
2
1
1
0
1
0
3
0
0
1
0
1
0
0
1
2
1
2
3
0
2
0
2
0
2
0
2
1
2
0
0
1
2
1
2
1
1
0
0
1
1
0
1
1
0
0
1
1
1
2
0
1
0
1
5
1
0
1
0
1
1
1
2
0
0
0
1
2
0
2
0
1
2
0
2
0
1
0
1
1
0
1
1
1
2
0
1
0
1
0
2
1
1
1
1
0
0
0
2
0
1
1
1
2
2
1
0
0
0
1
1
2
1
0
1
0
1
2
0
0
1
1
0
0
2
1
1
0
0
1
2
0
0
1
0
0
1
0
1
1
0
2
1
1
0
1
1
1
0
1
1
0
2
0
0
1
2
1
1
1
0
2
1
1
1
0
1
0
1
1
2
1
2
0
2
1
1
1
1
2
2
1
2
2
0
1
1
0
1
0
2
0
0
1
2
1
0
0
1
0
1
0
0
2
2
1
2
0
1
1
0
1
1
0
1
1
1
1
0
1
0
0
1
1
2
1
1
1
1
2
1
0
1
1
1
8
2
0
0
0
2
0
2
1
0
2
0
0
1
1
2
2
1
2
1
1
1
0
1
1
0
0
2
2
1
1
2
0
1
1
1
1
1
1
3
0
1
0
0
1
2
1
0
1
1
1
1
0
1
0
2
2
1
0
1
1
0
1
1
0
1
1
2
0
0
0
1
2
1
1
0
1
1
0
2
1
0
1
1
2
2
1
2
1
1
0
1
1
0
1
0
0
1
2
1
1
1
1
1
1
0
0
1
1
0
1
0
0
1
1
0
0
0
1
1
1
3
0
1
0
1
2
0
1
2
1
0
1
1
1
0
1
1
2
0
0
2
1
2
1
0
3
0
0
1
2
2
1
2
1
2
1
1
2
1
1
1
0
2
1
1
2
0
1
1
2
1
1
1
0
1
0
1
2
1
3
1
1
2
1
0
0
1
0
1
0
3
0
0
1
0
0
0
1
1
1
0
1
1
0
0
1
1
0
1
1
0
1
2
1
1
0
1
1
1
1
0
1
1
0
0
1
2
1
2
1
2
0
3
2
1
0
1
0
0
2
1
2
0
4
2
1
0
2
2
1
1
2
0
1
2
1
1
1
1
2
2
2
1
1
1
0
2
0
2
1
3
0
0
1
2
1
2
0
1
0
0
1
1
1
1
3
0
0
1
1
1
0
1
2
0
0
1
1
1
0
0
1
1
1
1
0
2
0
1
2
1
0
1
1
1
0
1
1
1
2
1
0
0
0
2
1
0
1
2
2
0
2
1
1
2
2
0
2
1
0
1
1
1
1
1
1
2
2
1
0
1
2
0
0
1
1
0
1
2
1
1
0
0
2
1
2
1
0
1
1
1
1
1
1
1
0
0
0
0
2
0
1
0
2
2
0
2
0
1
0
1
0
1
1
0
1
2
2
1
1
0
0
1
0
1
1
0
2
2
1
1
1
1
1
2
2
0
1
1
1
2
0
2
1
0
0
1
2
2
1
0
1
1
0
1
0
0
2
1
1
0
1
0
1
1
0
1
0
0
0
0
1
2
0
1
0
2
0
1
0
0
1
1
1
1
1
0
1
1
0
1
1
0
1
2
0
2
2
2
0
1
0
2
1
0
0
1
1
1
1
1
1
2
1
0
1
1
0
2
0
0
1
0
1
1
1
2
0
2
0
1
1
0
1
2
0
1
1
0
2
0
1
1
1
0
1
1
1
1
2
1
1
2
0
0
1
0
1
3
1
1
0
0
0
2
1
0
2
2
1
1
1
0
1
1
1
0
3
0
1
2
2
3
1
2
0
0
1
1
1
0
1
0
2
1
2
1
2
1
1
2
1
1
0
0
2
1
0
3
2
0
1
2
1
1
0
1
0
0
0
1
1
2
0
1
0
1
1
1
1
1
2
0
1
1
0
0
0
0
1
0
1
1
1
2
1
1
0
1
0
1
1
1
1
2
1
0
0
1
0
1
0
0
2
0
1
0
1
0
1
0
0
1
2
0
1
2
1
1
1
1
2
1
0
1
0
2
0
2
0
0
1
2
1
0
2
0
1
0
0
0
0
1
0
1
2
1
2
1
0
1
0
3
0
1
1
0
0
2
0
1
3
6
1
0
0
1
0
1
2
1
1
2
2
3
2
1
0
1
1
1
1
1
1
0
0
4
1
0
1
0
0
0
1
0
1
0
1
1
1
2
1
2
2
1
2
1
1
1
0
1
1
0
0
1
2
1
1
0
1
0
4
0
0
1
1
0
0
0
2
2
0
1
1
2
1
0
2
1
2
1
1
0
0
2
0
1
1
1
1
2
1
1
2
0
0
1
0
2
1
1
0
2
1
2
1
1
0
0
1
2
1
2
1
0
1
1
1
2
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
2
2
3
1
1
0
2
0
2
3
1
0
1
1
1
2
1
2
0
1
0
0
1
1
2
1
2
1
1
1
1
2
0
1
1
0
1
2
0
2
0
1
0
0
2
0
2
1
0
2
0
0
0
1
1
1
1
0
1
1
1
0
1
2
0
1
0
1
1
1
0
1
2
1
1
0
0
2
1
1
0
1
1
2
0
0
1
2
0
2
1
1
0
0
1
0
1
1
1
0
0
1
1
1
0
2
2
1
1
3
0
0
1
1
0
1
1
0
0
2
1
1
1
0
2
0
0
0
1
0
0
1
0
2
1
2
1
0
0
0
2
1
2
1
1
1
1
1
2
0
0
2
1
0
0
0
2
2
1
1
1
2
1
0
0
1
0
3
1
1
1
1
0
2
2
0
1
2
0
1
1
2
1
1
0
2
1
0
2
0
0
1
0
2
1
0
0
0
0
2
0
1
1
1
1
1
0
1
0
0
1
1
5
0
0
1
1
1
0
2
1
1
0
0
2
0
1
0
0
1
0
1
1
1
1
2
2
2
2
0
0
0
1
0
0
2
1
1
1
2
1
2
1
0
0
1
1
1
6
2
1
0
1
0
0
3
1
0
0
2
2
3
0
0
0
1
1
1
1
0
1
1
1
0
2
2
0
1
0
2
1
3
0
1
0
1
2
1
0
1
0
1
0
0
1
2
1
1
0
0
0
1
1
0
0
1
0
1
1
0
1
1
0
2
1
1
1
2
2
0
1
1
0
1
0
2
1
2
2
2
0
1
0
1
1
1
2
1
0
2
0
1
2
0
2
2
2
0
1
1
2
1
2
0
0
1
2
1
1
0
1
2
0
0
0
1
0
1
0
0
2
0
1
0
1
0
1
2
1
3
0
2
0
0
0
0
1
1
0
0
0
0
2
1
1
1
0
2
0
2
1
2
1
1
1
1
1
1
0
2
2
0
2
0
1
0
2
0
1
0
1
0
0
0
1
2
1
1
1
0
1
1
1
1
1
0
0
0
1
1
0
2
1
1
0
0
1
1
0
1
2
0
2
2
2
0
1
2
1
0
1
0
1
1
1
1
2
1
0
2
2
0
1
2
1
0
2
1
0
2
1
1
2
1
1
1
0
0
0
0
0
1
0
1
0
1
2
2
0
0
0
0
1
0
1
2
1
1
2
0
2
1
0
0
1
2
1
0
0
1
1
1
1
0
2
0
1
0
1
1
1
2
1
3
0
2
1
0
1
2
1
0
1
0
1
3
1
0
2
1
1
1
0
1
2
2
0
0
0
1
1
1
2
1
1
2
1
1
2
2
1
1
1
2
0
0
1
0
2
1
1
1
0
1
0
1
1
2
0
0
2
1
2
0
1
1
2
1
1
0
1
0
2
1
1
0
2
1
1
1
1
0
1
0
1
2
0
2
0
2
1
1
3
1
1
1
0
2
0
1
1
1
0
1
1
0
1
0
1
1
0
0
1
1
0
1
1
0
0
0
0
0
1
1
1
1
1
2
1
1
1
1
0
2
1
0
2
0
1
1
1
1
2
2
1
0
0
1
2
1
1
0
0
2
1
2
2
0
1
2
0
1
1
0
0
0
0
2
5
1
0
1
0
0
0
1
2
1
1
2
2
1
2
2
0
0
0
1
2
0
0
0
1
0
0
3
2
1
2
1
1
2
2
0
0
2
1
1
2
1
1
0
0
1
1
0
1
2
1
1
0
2
2
2
1
2
2
0
2
2
0
1
1
0
2
2
1
0
1
1
2
1
0
1
0
2
0
1
1
0
3
2
2
1
1
1
2
1
0
2
1
1
0
2
1
0
0
2
2
0
2
2
3
2
1
0
1
1
0
1
0
0
1
2
0
0
0
1
2
0
1
1
0
0
1
3
1
0
1
1
2
1
0
1
0
0
1
1
1
1
1
2
0
0
2
0
2
0
3
0
1
0
0
1
0
2
1
0
1
0
1
1
0
1
2
0
1
0
0
0
2
1
0
2
1
2
1
0
1
1
0
1
1
2
2
2
0
1
0
2
1
1
1
0
2
1
1
0
0
0
2
2
0
1
0
0
2
2
0
1
0
0
1
1
1
1
0
0
0
2
1
0
1
0
0
0
2
0
0
0
1
2
0
2
1
0
0
1
2
0
2
0
1
1
1
1
2
1
0
1
0
1
2
0
0
1
1
2
0
1
1
2
0
1
1
0
1
1
0
1
2
1
0
0
2
1
0
0
0
1
0
0
0
1
2
1
0
1
1
1
1
1
1
1
1
0
1
1
0
0
1
2
0
2
0
2
2
0
1
3
0
2
2
0
1
1
0
0
2
1
0
2
1
0
0
2
2
1
1
0
1
1
1
2
1
1
2
5
0
2
1
1
1
1
1
0
0
2
1
0
0
1
1
3
2
1
0
2
1
1
1
2
2
2
1
1
1
2
2
1
1
0
0
0
3
0
1
0
0
1
0
2
2
1
1
1
0
0
0
0
0
2
0
1
0
1
1
2
0
0
2
1
1
1
0
0
0
0
0
2
2
1
0
0
1
1
0
0
0
1
2
1
1
2
2
1
1
2
0
2
1
2
0
0
1
1
2
3
0
0
0
1
1
0
2
0
1
0
0
1
2
0
1
1
1
1
1
0
1
2
1
0
3
1
2
0
0
0
1
2
2
0
0
1
2
0
1
1
1
1
2
0
2
1
0
2
2
0
1
1
2
0
1
0
2
1
1
1
2
3
0
2
1
0
0
0
2
0
1
0
0
1
1
0
3
0
0
1
1
1
1
1
1
1
0
1
1
2
2
2
2
0
1
2
0
0
1
0
1
1
1
0
1
0
1
1
1
2
2
1
0
1
0
0
2
2
2
0
2
2
1
1
1
1
0
1
1
1
1
2
0
0
0
2
1
2
2
1
1
0
0
1
1
1
0
1
1
2
0
2
0
2
1
1
1
0
0
2
1
1
2
0
2
2
2
0
0
0
1
2
1
2
2
1
0
2
2
0
0
6
2
2
2
1
1
0
2
1
0
0
1
1
3
2
0
0
2
1
1
0
2
2
0
0
1
0
0
2
1
1
1
2
0
0
1
0
2
1
2
1
0
2
0
0
0
1
2
1
1
1
2
0
0
0
1
1
1
2
0
1
0
2
0
0
2
1
0
0
1
1
1
2
0
1
1
0
2
1
1
1
2
0
0
0
1
2
1
1
1
1
2
1
2
1
2
1
1
0
1
0
2
0
1
0
2
1
0
1
1
0
1
1
0
1
2
0
0
1
0
1
2
1
1
0
1
1
1
0
0
2
2
2
1
0
2
1
0
1
0
0
1
1
2
1
2
1
1
0
1
0
0
1
1
2
1
0
1
0
2
2
0
2
2
0
2
1
1
0
2
1
1
2
2
1
1
0
0
0
1
1
0
0
1
1
0
1
1
0
0
0
1
0
1
1
0
5
2
1
0
1
1
0
1
0
0
1
0
1
1
0
3
0
1
1
1
1
0
0
2
2
2
1
1
2
1
2
1
2
1
1
1
1
0
1
1
0
0
0
1
1
0
2
2
0
0
1
0
0
0
1
1
1
1
0
0
2
1
1
0
0
2
2
0
2
2
1
4
2
0
1
1
1
1
0
1
1
1
2
0
1
1
0
1
0
0
1
2
1
2
1
1
0
1
1
1
2
2
1
1
0
2
0
1
1
1
1
1
0
0
0
2
0
1
2
0
0
1
1
1
1
2
3
0
0
0
0
1
2
2
0
0
2
0
2
1
1
1
4
1
2
1
0
2
3
2
2
1
1
0
1
0
1
2
1
1
1
0
0
1
1
0
0
1
1
1
0
1
1
2
1
2
1
2
1
0
0
1
2
2
0
2
0
1
0
0
1
0
1
1
0
0
1
1
0
1
2
2
0
2
2
2
1
1
0
0
0
0
2
2
0
0
1
1
0
1
1
1
0
1
0
1
2
0
1
1
0
2
0
0
0
2
0
2
2
2
0
1
0
0
1
0
0
1
1
2
0
1
2
1
0
1
1
1
0
2
1
1
0
1
1
0
0
2
1
0
0
1
2
1
1
0
1
0
1
2
1
0
2
1
0
1
0
2
1
0
0
0
0
1
0
1
1
1
1
0
0
0
2
3
1
1
2
0
0
1
1
0
2
2
2
1
2
0
0
1
0
0
1
0
0
1
1
1
0
1
2
0
0
1
0
0
0
0
0
0
1
1
0
0
1
3
1
2
0
1
2
2
0
2
0
0
0
1
1
0
1
1
1
1
2
1
2
1
1
1
3
1
0
1
1
2
2
1
0
1
1
2
1
1
1
1
0
1
2
0
0
0
1
0
0
0
1
2
1
1
0
2
2
0
2
0
2
0
1
1
1
0
1
0
0
1
1
0
2
0
0
0
2
0
2
0
0
0
2
0
0
2
0
0
1
2
0
0
1
0
0
1
1
1
1
1
0
2
0
2
0
0
1
1
1
0
1
1
1
0
0
0
1
1
2
2
2
0
0
2
0
1
1
1
0
0
1
2
0
0
0
1
0
1
1
1
0
2
2
1
1
1
0
1
0
1
1
0
0
0
1
2
0
2
0
0
0
1
2
1
2
0
1
0
1
1
1
1
1
1
2
1
0
0
0
1
2
1
0
0
1
1
1
0
0
1
1
2
0
2
1
0
1
1
0
1
1
1
1
2
0
2
1
2
0
0
2
2
1
2
2
0
2
0
2
2
0
2
1
0
0
1
1
0
1
1
0
0
1
1
2
2
1
1
2
1
1
2
1
2
0
1
2
1
2
1
1
2
1
1
0
1
0
2
1
2
1
0
1
1
1
0
2
0
0
3
1
2
2
1
0
0
0
2
2
2
2
2
1
0
0
2
0
2
1
2
2
1
1
1
0
1
0
3
0
1
2
0
2
2
1
1
0
2
1
0
1
0
0
0
0
0
3
1
2
2
0
2
1
1
1
1
2
1
1
1
0
2
2
1
0
0
0
0
2
1
1
0
0
0
1
0
2
0
2
1
0
0
0
2
1
0
2
0
0
1
0
1
0
0
0
1
0
0
2
2
0
2
0
0
2
0
1
0
2
0
0
1
1
2
1
2
0
2
0
1
2
0
0
1
2
1
1
2
1
0
0
1
0
1
0
0
1
0
0
1
0
0
2
0
2
1
2
1
2
2
0
0
1
1
2
2
0
0
1
0
1
0
2
0
2
2
0
4
0
1
1
1
2
1
1
1
1
2
0
1
2
0
1
0
1
2
2
1
1
2
2
0
1
2
2
0
2
1
2
2
1
2
0
1
1
1
0
0
0
2
0
0
1
1
2
2
0
1
1
0
1
1
0
1
2
1
1
0
2
2
0
1
2
1
0
1
0
1
1
0
2
1
0
0
0
2
0
1
1
0
0
1
0
0
0
2
0
1
1
1
0
1
0
2
1
1
2
2
1
0
0
0
0
3
2
2
1
1
1
1
1
0
0
2
0
0
2
1
1
0
2
1
1
0
1
0
2
1
1
1
2
0
1
2
0
0
1
2
2
2
1
0
0
0
0
1
2
1
1
0
0
1
1
1
1
0
2
1
0
0
2
0
2
1
1
0
0
0
0
0
1
2
0
1
4
1
0
1
2
1
2
0
2
1
0
2
1
0
1
2
1
0
0
1
0
0
1
2
1
0
0
2
2
0
0
1
2
2
0
0
10
0
1
1
1
1
1
0
0
0
0
1
2
1
0
0
0
1
0
1
0
0
0
0
2
1
1
2
2
1
2
1
1
0
1
0
1
2
0
2
1
0
1
0
0
0
1
1
1
1
2
0
0
1
1
0
0
0
1
2
1
1
4
1
2
1
2
0
1
2
1
0
0
1
1
2
2
0
0
2
1
1
1
2
0
0
1
1
2
0
2
1
1
0
2
1
0
1
1
1
2
0
2
0
0
2
1
1
0
0
1
1
0
2
0
0
0
0
1
1
1
0
1
1
0
1
2
2
1
1
0
2
2
0
1
0
0
0
2
1
0
0
0
0
1
1
1
1
2
0
0
2
1
1
0
2
2
2
1
1
3
2
2
2
3
1
0
1
2
0
0
0
1
0
0
0
0
0
0
2
1
0
2
1
0
1
0
2
1
1
0
1
0
0
1
1
1
0
2
1
1
0
0
2
2
2
0
0
2
0
0
1
0
1
2
0
2
1
0
0
1
0
2
1
0
1
1
0
1
0
1
0
1
0
2
0
1
0
0
0
0
1
0
1
2
1
1
0
1
1
1
0
2
1
0
2
0
1
0
1
0
1
0
2
0
1
0
1
2
1
3
1
1
0
1
0
1
2
0
3
1
2
1
1
1
1
1
1
1
0
1
2
2
1
1
2
2
1
2
1
1
0
1
1
0
2
0
0
1
0
0
2
1
1
1
1
3
1
0
3
0
0
2
0
0
1
1
1
0
0
0
1
0
1
1
0
2
0
1
0
1
0
1
1
2
1
1
2
0
1
2
2
2
2
0
1
1
2
1
1
2
2
0
0
1
0
2
0
1
0
2
1
0
0
0
1
2
1
2
1
0
2
1
1
1
0
1
0
1
1
1
0
0
1
1
1
2
0
2
0
3
1
1
0
2
1
2
2
1
2
3
2
1
2
1
0
0
1
1
2
1
1
1
2
0
0
1
0
1
2
0
0
1
1
1
0
0
2
0
0
2
2
2
1
1
1
0
1
1
2
1
1
1
2
2
5
3
0
1
2
1
0
0
1
1
1
0
0
0
1
1
2
2
0
0
2
0
1
4
1
1
0
0
0
1
2
1
1
0
1
2
0
0
2
1
1
2
0
2
0
0
1
0
2
1
1
1
0
0
0
0
1
1
1
2
1
1
1
1
2
1
1
3
2
1
0
0
1
1
1
2
1
2
0
0
1
1
0
1
2
1
0
1
0
1
1
1
2
1
0
1
0
2
0
1
1
1
2
1
0
1
1
2
2
2
0
0
0
1
0
1
0
0
1
1
1
1
2
2
1
2
0
1
1
2
1
1
2
0
0
0
0
0
1
2
1
0
1
1
0
0
0
1
1
0
0
0
0
2
1
1
0
0
1
1
1
1
1
0
1
1
1
1
2
0
1
0
3
1
1
1
0
4
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
1
2
2
0
0
0
1
0
1
1
0
1
0
1
1
1
2
1
1
0
0
1
1
2
0
1
1
1
1
2
1
1
1
1
0
2
0
1
1
0
1
2
3
0
2
2
0
1
2
1
1
1
0
1
2
1
1
2
1
1
0
2
0
2
2
0
3
2
2
1
0
0
0
0
0
1
1
1
2
1
1
0
2
1
1
1
0
0
1
0
2
0
1
1
1
1
1
0
2
0
1
2
1
1
1
1
2
1
1
0
2
0
0
0
0
1
1
2
1
0
1
0
1
0
2
1
0
2
2
1
1
1
1
1
1
3
0
0
1
1
0
0
1
2
1
0
0
1
2
1
0
0
1
1
0
2
0
0
1
1
0
0
1
0
1
2
0
0
0
0
2
1
0
2
2
0
1
2
0
1
1
2
1
2
0
2
0
2
1
0
0
1
0
0
0
0
0
2
1
1
0
1
0
2
1
0
2
2
1
0
2
2
2
0
1
0
2
1
0
1
0
1
1
1
2
1
1
0
0
0
1
0
1
2
0
1
0
0
2
2
2
1
3
0
1
1
2
0
1
0
2
2
1
2
1
0
0
1
1
1
1
1
1
1
2
0
0
2
1
2
1
1
0
0
0
1
2
1
3
1
1
2
0
0
2
0
1
2
0
2
2
0
0
2
2
0
0
1
1
0
0
0
2
0
1
1
6
2
2
2
2
2
0
1
0
0
1
0
1
0
1
1
2
1
0
0
0
1
1
1
0
1
1
2
1
2
1
0
1
4
0
0
2
0
2
1
1
1
0
1
1
0
1
1
1
1
1
2
0
0
0
1
1
2
1
1
0
1
1
1
0
0
1
1
1
1
1
0
1
0
1
2
2
1
1
2
2
0
1
0
0
0
1
0
1
1
0
0
0
1
0
0
1
2
1
1
0
2
1
2
0
1
2
0
1
0
1
1
2
1
2
0
1
1
1
1
0
0
0
1
2
2
0
1
1
0
1
0
2
0
1
0
1
1
2
2
0
0
1
2
1
0
1
1
1
0
0
2
1
0
0
1
1
2
0
1
2
1
1
1
1
1
2
0
2
1
1
1
1
0
2
1
1
2
0
0
2
2
1
1
0
2
0
1
1
2
0
1
1
1
2
0
1
1
2
1
1
1
2
1
1
0
1
0
5
0
0
0
0
1
1
1
0
0
1
1
0
0
1
0
0
2
2
2
1
0
2
1
0
1
0
1
1
1
2
2
0
1
0
1
0
2
0
1
0
1
2
1
1
1
1
0
0
2
1
1
2
1
0
1
0
1
1
0
0
0
0
1
1
1
0
0
1
0
2
1
2
1
1
1
0
1
1
0
0
1
0
1
1
0
2
1
1
2
2
0
1
1
1
0
0
1
1
1
1
2
1
0
1
1
0
2
1
2
1
2
1
0
1
0
0
1
0
1
2
1
0
1
2
1
1
0
1
1
2
2
2
0
0
1
0
1
1
1
2
1
1
2
2
0
1
1
1
0
2
2
1
0
0
1
2
0
1
1
0
0
1
0
2
0
1
0
1
1
0
1
1
0
1
1
1
2
0
1
0
1
2
0
1
2
1
2
2
0
2
2
1
2
1
0
0
1
0
2
2
1
2
1
1
1
2
0
1
0
1
1
2
1
0
1
0
0
1
1
0
0
3
2
1
0
1
1
1
0
1
0
2
0
1
2
0
1
1
2
1
1
1
0
0
1
1
0
1
2
2
1
2
0
1
1
1
2
0
0
1
1
1
0
1
1
1
1
1
0
0
1
0
1
1
1
0
1
0
0
1
0
1
0
2
1
2
1
0
1
2
1
1
3
2
1
1
1
1
0
0
1
1
1
2
2
1
0
0
2
3
2
1
2
2
1
0
0
0
2
1
1
1
0
0
0
1
0
2
2
2
0
0
2
1
1
2
0
1
1
1
2
2
1
2
1
1
1
1
1
3
2
0
1
2
3
1
2
0
1
0
1
1
2
1
1
1
0
2
2
0
0
0
1
0
0
2
0
1
1
0
1
1
0
1
1
0
2
1
0
1
2
1
2
0
1
1
1
2
0
0
3
1
1
1
0
2
0
1
1
1
2
2
1
2
1
0
0
1
0
2
0
0
1
1
2
2
1
1
1
1
0
1
1
1
2
1
1
2
0
0
0
1
1
1
1
0
0
0
1
0
0
2
1
1
0
0
1
0
1
1
1
2
2
0
0
0
0
0
1
1
1
1
2
1
2
1
0
2
2
1
0
1
1
1
0
0
0
0
1
1
0
1
1
0
1
0
0
2
1
1
0
1
2
0
1
1
1
0
0
0
1
2
2
0
0
0
0
1
0
1
2
0
0
0
2
0
1
2
0
0
0
0
0
1
0
2
0
1
2
0
1
2
0
1
2
1
0
2
2
1
0
0
1
0
0
0
0
2
0
2
0
1
2
1
0
1
0
1
1
0
1
1
0
1
1
0
1
1
1
0
1
1
1
0
1
2
0
2
2
0
1
1
2
2
2
1
1
1
3
1
4
0
2
0
1
2
1
2
0
1
2
2
0
0
0
1
1
0
0
0
0
0
0
1
0
1
1
2
1
1
1
1
2
2
1
2
0
1
0
1
1
0
2
2
0
0
2
0
2
1
0
1
1
0
1
2
1
1
0
1
1
1
1
1
2
0
2
1
1
0
1
0
1
1
0
2
2
2
3
1
2
1
1
2
2
0
2
0
0
1
0
0
2
1
1
2
0
0
1
0
1
1
1
1
2
1
0
2
0
1
2
1
0
1
0
1
2
1
0
1
1
1
2
0
2
0
1
0
2
1
1
1
0
2
1
0
1
0
0
0
0
1
0
1
1
1
1
0
1
1
0
1
1
1
0
1
1
2
0
2
2
2
0
1
2
1
0
0
1
1
2
1
1
1
1
0
0
1
0
2
0
2
1
0
0
1
0
0
6
0
1
0
2
1
0
1
0
0
1
0
1
2
2
0
1
0
1
0
2
1
1
0
0
0
0
0
0
0
1
1
0
0
2
1
0
0
0
2
1
0
1
2
1
2
2
1
1
1
2
0
0
1
1
0
0
1
0
0
0
0
2
1
1
0
1
1
1
1
0
1
1
2
0
0
2
0
1
0
2
2
1
2
0
0
1
1
0
0
1
2
1
0
1
0
1
2
1
1
2
0
1
1
2
1
1
0
1
2
0
0
1
2
0
0
1
1
2
1
0
1
1
1
1
1
1
1
1
0
1
0
0
1
0
1
1
0
1
1
1
0
1
1
1
2
0
2
2
0
0
1
1
1
2
2
2
0
1
0
0
2
0
0
0
1
2
1
1
2
0
1
0
0
1
2
0
1
0
1
2
1
2
2
1
0
1
1
1
0
2
1
1
2
1
0
0
2
1
1
0
0
2
0
0
1
1
1
1
0
0
0
1
2
2
0
0
2
1
2
0
1
0
1
0
2
0
0
0
0
0
0
1
1
2
1
2
1
2
3
1
1
0
0
2
2
1
0
2
0
1
1
1
2
2
0
0
0
0
0
0
1
2
0
0
3
0
2
0
0
3
2
2
1
1
1
1
2
2
1
1
0
0
0
1
2
0
2
2
0
0
0
1
1
0
1
2
1
1
1
2
1
0
1
1
0
1
1
2
2
3
1
0
3
1
0
1
3
2
1
2
1
1
1
1
0
1
0
0
2
0
1
2
1
0
0
2
1
2
0
0
1
0
0
0
1
0
1
0
2
1
0
1
1
1
1
2
1
1
1
1
0
1
0
1
0
2
1
0
1
1
0
1
0
0
0
2
1
1
2
0
0
1
2
1
1
2
1
1
1
1
0
1
1
1
0
0
1
1
1
1
0
0
1
0
1
0
2
1
1
2
1
1
0
1
1
1
0
0
2
1
1
0
1
0
0
0
0
1
2
2
0
2
1
2
1
0
2
0
1
2
2
0
2
1
0
2
2
0
1
1
0
0
1
0
0
1
1
1
2
1
1
1
1
2
1
0
2
1
1
1
0
0
2
1
1
2
1
2
1
0
1
0
1
0
0
1
0
1
1
0
1
2
1
1
0
1
1
2
1
1
0
0
0
1
0
2
3
0
1
0
0
1
1
1
1
1
2
1
0
0
1
1
2
2
0
2
0
1
0
1
0
0
0
0
2
1
0
1
1
1
1
1
0
1
2
1
0
1
1
1
2
1
0
1
1
1
1
2
1
1
1
2
2
0
0
0
1
0
1
0
0
2
0
0
1
1
0
0
0
1
1
1
2
0
1
1
2
0
1
0
1
1
1
2
2
2
0
2
0
1
1
2
0
0
2
0
1
0
1
1
1
2
2
1
0
2
1
0
2
0
1
0
2
1
0
1
1
3
1
2
1
0
0
1
1
1
1
2
1
0
1
4
0
2
1
2
0
0
1
0
4
1
1
0
1
1
3
0
2
1
1
1
1
1
1
1
0
0
1
0
1
1
1
2
0
1
0
0
0
0
1
1
0
0
1
1
1
0
2
2
1
1
0
1
2
0
1
1
0
1
1
1
0
1
1
1
1
2
1
0
0
1
0
1
0
0
1
2
2
2
1
0
2
0
2
1
2
1
1
1
2
2
1
2
2
0
1
0
0
1
2
1
2
0
1
2
1
0
0
1
1
1
1
1
0
1
1
1
1
1
1
1
0
1
2
1
1
1
1
1
1
0
2
2
0
2
2
0
1
2
1
2
0
1
2
1
1
0
2
1
1
1
0
1
1
2
0
2
2
1
3
2
1
0
1
0
1
2
0
0
0
0
2
0
1
1
1
0
2
1
1
1
1
0
1
0
2
1
0
1
1
0
1
2
1
0
0
0
1
1
0
0
1
0
2
1
1
1
0
1
2
1
0
0
1
2
1
1
1
1
1
1
2
2
1
3
0
0
1
0
0
1
2
1
7
1
1
0
1
1
2
0
0
0
1
0
0
1
0
0
1
0
0
1
2
1
0
1
0
0
2
0
1
2
0
1
1
2
1
0
0
1
1
1
0
0
1
0
0
2
1
1
1
1
0
1
1
1
2
0
0
0
1
0
3
1
1
0
1
1
1
2
1
2
1
1
0
1
0
1
2
1
0
2
1
2
2
0
1
0
0
0
1
1
1
0
1
2
0
1
2
0
1
1
1
1
1
0
0
1
2
0
1
0
1
1
2
1
0
2
1
1
0
1
3
1
0
1
1
2
0
0
1
0
1
3
0
1
1
2
3
1
1
1
2
2
1
2
0
1
1
0
0
1
0
0
2
1
1
0
0
1
0
1
0
1
1
1
0
0
0
0
0
0
1
0
0
2
0
2
1
0
2
0
1
2
0
1
0
0
2
1
1
0
1
2
1
2
1
1
0
2
0
3
1
1
1
1
1
2
1
2
2
1
0
1
0
1
2
0
0
1
0
1
0
1
2
1
0
2
1
2
2
0
2
2
1
1
0
0
0
2
2
2
1
2
0
1
0
2
0
1
1
0
1
2
1
1
2
1
0
1
1
0
1
2
0
2
0
0
1
2
1
1
0
0
2
1
0
0
2
0
0
0
0
1
1
1
1
0
0
2
2
0
1
2
1
0
1
1
0
1
0
0
1
1
2
0
0
1
1
2
0
1
2
0
1
2
0
0
0
1
2
0
0
0
1
1
1
2
1
0
1
1
1
1
1
1
0
1
0
0
1
2
0
0
2
2
2
0
1
2
1
1
1
1
0
0
1
2
2
0
2
2
0
1
2
1
1
1
1
0
2
0
2
2
1
2
0
1
0
1
1
2
1
0
1
0
1
1
0
0
0
1
2
1
1
1
1
1
0
1
1
1
0
0
0
1
1
1
0
0
2
0
1
1
2
1
1
1
2
1
1
1
1
2
1
0
0
1
1
2
2
1
0
1
0
1
2
0
0
1
2
2
1
2
1
1
0
5
0
1
2
1
1
0
3
1
2
3
1
0
2
1
1
1
1
1
1
0
0
1
0
1
0
0
3
2
1
1
0
1
2
2
1
2
1
0
1
1
0
0
2
1
1
1
1
2
0
1
0
0
1
1
1
2
2
1
0
0
0
1
1
1
1
1
1
0
0
1
1
2
0
1
2
0
2
1
0
1
1
1
2
1
0
1
1
1
1
0
1
1
0
0
1
2
0
5
1
0
1
2
0
2
2
5
1
2
1
0
1
1
0
1
1
1
1
1
2
0
0
2
1
1
1
2
2
1
0
0
1
0
0
1
0
1
1
0
2
2
2
1
0
0
1
2
1
2
0
0
1
1
1
0
0
1
0
1
2
1
2
2
1
1
0
0
1
2
2
1
0
1
0
0
1
2
2
0
1
1
0
1
1
2
1
0
1
2
0
1
0
1
0
0
0
1
2
2
1
0
0
1
0
1
0
1
2
2
2
1
1
0
1
2
0
0
1
0
0
2
2
1
0
1
1
1
0
2
1
1
0
1
1
1
0
1
2
1
1
2
1
2
0
1
1
0
1
3
1
2
1
0
0
2
0
0
0
1
1
2
1
0
1
0
1
2
1
0
0
1
0
1
0
0
1
0
0
0
3
1
0
1
1
1
1
1
1
1
2
2
0
0
0
1
0
1
0
2
0
1
1
0
0
1
2
0
0
2
2
0
2
0
0
1
0
1
1
2
1
1
1
0
1
1
3
0
1
1
0
0
0
1
1
1
1
1
1
1
1
0
2
0
1
2
1
0
0
2
0
1
1
0
1
0
1
0
1
0
0
1
2
2
1
1
0
1
0
0
1
1
2
2
1
1
1
0
1
1
0
1
1
1
2
2
0
0
0
1
2
2
0
1
0
2
1
1
0
1
1
0
1
0
1
1
1
0
2
0
0
0
2
1
0
1
0
0
1
1
1
2
1
1
0
0
2
1
2
1
1
0
1
1
1
1
1
0
1
1
2
1
1
0
1
2
1
2
0
0
1
0
1
2
0
1
0
0
2
0
1
0
2
0
1
1
2
0
0
1
0
1
1
2
2
0
1
0
1
1
2
0
2
1
1
1
1
1
1
1
0
1
1
0
1
2
1
1
2
3
1
1
1
1
0
0
1
0
1
1
1
2
1
1
0
0
0
0
0
2
1
0
2
0
0
1
1
1
0
2
2
0
1
1
0
2
1
0
2
1
0
2
0
2
1
2
1
0
2
2
2
0
0
1
1
2
1
1
0
1
0
1
1
1
1
0
2
0
1
1
2
0
1
1
2
2
1
2
0
1
0
2
2
1
1
1
2
1
1
2
0
0
2
0
2
2
1
2
0
2
1
0
0
0
1
1
1
1
2
2
2
1
2
0
0
0
0
1
0
0
1
1
1
1
1
2
2
2
2
2
1
2
2
1
0
0
1
0
2
1
1
2
1
1
1
2
0
1
2
1
0
1
1
0
0
0
1
1
2
2
1
1
1
2
1
1
0
0
0
2
1
1
2
0
1
0
2
0
2
0
1
2
1
1
1
2
0
2
1
2
0
1
0
1
0
0
0
0
1
2
2
1
1
0
0
2
1
2
1
1
0
0
0
1
1
0
2
2
1
0
1
0
1
0
1
2
1
2
1
0
2
1
0
0
1
0
0
0
1
2
3
1
1
1
1
1
1
0
1
2
0
0
0
1
1
0
1
0
2
0
1
1
0
1
1
1
1
2
0
1
2
1
0
2
1
1
0
1
1
1
0
1
0
4
1
1
2
0
0
1
1
3
0
2
1
2
0
0
1
1
0
0
1
2
0
0
0
1
0
0
1
1
1
0
2
1
1
2
1
1
0
1
1
0
0
1
1
1
2
0
0
0
0
1
1
2
2
0
1
0
2
1
2
1
1
0
1
1
1
1
0
2
2
1
2
0
1
0
1
1
0
1
1
1
0
1
0
1
0
0
1
1
1
1
1
1
1
0
2
0
0
1
0
0
1
1
0
1
1
1
0
0
1
1
0
2
0
0
0
1
0
1
1
0
0
1
1
1
0
0
1
2
2
1
2
1
0
0
1
1
1
1
1
2
0
0
1
1
2
0
2
2
0
1
2
0
1
1
1
1
1
1
1
1
1
2
0
3
2
1
1
1
1
2
1
0
1
1
0
2
1
0
2
2
1
0
0
2
2
0
1
1
0
2
1
1
0
2
1
2
1
1
1
0
1
0
1
1
1
0
0
1
1
0
2
2
1
0
2
1
1
2
1
1
1
2
1
2
1
2
3
0
0
1
1
0
1
0
1
1
2
0
0
1
1
1
2
1
0
1
1
1
1
1
1
2
1
0
1
1
0
0
1
0
0
0
0
0
1
1
0
1
0
1
1
0
0
2
2
0
1
2
0
2
0
2
0
1
0
1
0
2
0
2
1
1
1
2
0
0
1
0
0
1
1
2
1
1
1
1
2
1
0
0
0
0
0
1
2
2
4
1
1
1
1
1
1
1
1
1
0
1
0
0
1
1
2
0
2
1
1
2
0
0
1
2
0
1
0
0
0
2
1
0
2
1
0
1
1
1
1
1
1
1
1
0
2
0
2
0
0
0
1
0
0
1
0
1
0
1
0
1
1
2
2
0
1
1
3
4
0
0
1
2
1
1
2
0
2
1
1
1
2
1
0
0
1
1
2
2
0
0
1
6
1
1
1
1
0
2
3
0
4
0
1
0
1
0
1
1
3
0
2
1
1
0
2
1
2
1
1
1
2
1
2
1
2
1
2
0
0
3
0
1
2
0
1
1
1
0
1
1
0
1
1
0
1
1
1
1
0
0
1
0
1
2
0
1
1
3
2
0
2
1
0
2
1
2
1
1
1
0
2
1
1
1
0
1
2
0
0
1
0
1
1
0
0
1
0
1
1
1
0
1
2
1
1
2
0
2
0
1
2
1
0
0
1
0
0
0
1
0
1
2
2
1
2
2
5
1
0
1
1
2
0
1
1
0
0
1
1
1
2
1
0
1
1
0
2
0
1
1
1
1
0
0
1
0
2
0
1
1
1
1
0
0
0
0
0
0
1
1
1
0
0
0
1
1
0
0
1
1
1
1
0
0
1
1
2
1
0
1
1
0
1
0
0
1
0
0
1
1
2
1
0
1
0
2
0
1
2
0
2
1
1
1
0
1
2
0
2
0
2
0
2
0
0
0
1
1
0
1
1
2
1
0
1
2
0
2
1
0
0
1
0
0
1
0
2
0
1
2
1
0
1
2
1
1
1
1
0
1
1
1
2
1
2
0
1
1
3
0
1
0
0
2
0
2
0
2
0
0
1
2
1
0
0
2
0
0
0
1
0
0
1
0
1
1
0
0
1
1
1
1
1
1
1
0
0
1
0
2
3
0
2
0
2
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
2
0
0
1
2
1
1
1
1
1
0
0
1
0
1
1
2
2
1
1
0
1
0
1
2
1
0
2
1
0
1
2
0
2
1
1
0
0
2
1
2
1
1
2
2
1
0
1
1
0
1
1
0
1
2
0
0
1
2
0
0
2
2
0
0
1
1
1
1
1
1
2
1
1
2
2
0
0
2
0
1
2
1
1
2
1
0
0
0
1
2
2
1
1
0
2
1
1
2
3
1
1
2
1
0
1
1
0
0
2
1
0
0
1
0
1
1
1
0
1
0
1
0
0
1
1
0
1
0
0
3
0
1
2
0
2
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
2
2
0
0
1
2
1
0
1
1
2
0
1
0
1
2
0
1
1
1
1
2
2
2
1
0
2
1
0
1
1
2
1
0
1
1
1
1
0
0
0
1
1
0
3
0
1
0
0
1
0
2
2
0
1
1
0
0
1
1
2
1
1
0
0
0
1
2
0
0
2
0
1
1
1
1
1
1
1
0
1
0
1
1
2
0
0
0
1
0
2
1
1
1
0
1
2
2
0
3
1
2
0
1
0
1
0
0
0
2
1
0
1
2
2
1
1
1
1
1
0
1
3
0
0
1
1
0
1
0
1
2
1
0
1
1
0
1
1
0
0
0
0
0
1
1
1
2
1
0
1
2
1
2
2
1
0
1
0
2
2
1
1
2
0
1
2
1
1
0
2
2
1
1
3
0
1
0
2
0
1
1
1
1
1
1
1
0
0
0
1
0
2
0
0
0
1
3
0
0
0
0
0
0
1
0
2
2
1
1
1
0
1
1
1
2
0
2
1
0
0
0
0
1
0
0
0
2
1
0
3
0
2
1
0
1
1
1
0
2
1
0
0
1
2
0
0
1
1
1
0
1
0
1
1
1
0
2
0
2
1
1
1
0
1
0
1
1
1
0
2
0
2
2
1
1
1
0
1
1
2
2
1
0
2
0
0
1
1
0
2
0
2
0
1
1
2
1
1
3
0
1
1
1
1
0
1
1
0
1
1
0
1
0
1
1
0
2
0
0
2
2
1
0
2
1
1
0
0
1
1
0
1
0
1
1
1
1
2
0
1
2
0
1
0
1
1
1
0
2
1
1
2
2
2
0
2
1
1
1
1
0
0
0
1
1
1
0
1
2
0
0
0
1
2
2
0
1
1
1
1
1
2
1
1
0
1
1
0
1
1
2
1
1
2
1
0
2
2
1
1
1
1
2
1
0
4
1
0
2
1
0
1
1
2
1
0
1
1
1
1
0
2
0
1
1
2
1
0
0
0
1
1
0
2
1
1
0
0
1
1
1
0
1
3
0
2
1
2
1
0
0
2
1
0
2
2
0
1
0
0
1
1
0
1
2
1
2
1
2
1
0
1
1
0
1
0
0
0
1
2
1
0
1
0
2
0
2
3
0
2
1
3
0
1
0
1
1
0
1
1
0
1
2
0
0
0
1
1
2
0
1
0
2
1
1
0
1
2
0
1
1
1
2
1
0
1
1
1
1
0
0
0
2
0
0
1
1
2
0
1
0
0
2
1
1
0
0
0
1
1
2
1
0
2
2
1
0
1
1
1
0
0
1
1
1
2
1
1
0
1
0
0
2
0
1
1
2
0
1
0
4
1
1
1
2
1
0
1
1
1
0
1
0
0
1
0
1
2
1
1
1
2
0
3
0
1
0
2
2
1
0
0
0
1
2
0
2
1
0
1
1
1
2
2
2
0
0
0
0
2
0
1
2
0
2
2
1
1
1
0
1
0
0
2
1
0
0
0
0
0
2
2
1
0
2
1
2
1
0
1
1
0
1
1
0
1
2
2
1
1
0
2
0
2
0
0
2
1
0
0
1
0
1
0
0
2
0
1
0
1
0
1
0
0
0
1
0
1
1
0
2
2
1
1
1
2
1
0
1
1
2
1
1
1
3
1
1
0
1
0
5
0
1
1
2
0
0
2
2
1
1
1
1
1
1
1
1
1
1
1
0
2
2
1
1
2
1
0
1
1
1
0
1
0
2
1
1
0
1
2
0
0
1
0
1
0
1
1
2
0
1
2
2
1
1
2
2
0
2
2
2
2
0
1
0
1
1
2
0
0
1
2
2
0
1
0
0
1
2
1
1
2
0
2
0
1
0
0
0
1
2
2
1
0
0
1
1
2
1
1
1
1
1
0
1
0
1
1
0
1
0
0
2
2
1
1
1
1
1
1
0
1
1
1
0
2
0
1
2
1
2
2
2
0
1
1
1
0
1
1
1
2
1
1
1
1
0
1
0
1
1
1
0
1
1
0
0
1
1
1
0
1
0
1
0
1
0
1
2
2
0
1
1
2
1
0
1
0
1
0
1
2
2
0
0
2
2
1
2
1
0
1
0
0
0
2
1
2
0
2
0
0
2
2
1
0
2
0
1
1
2
0
0
2
1
2
2
1
0
2
0
2
0
1
0
1
1
1
1
1
1
0
1
0
0
2
0
0
1
2
0
1
1
1
1
1
0
1
0
1
1
0
2
1
2
0
1
0
0
2
1
2
1
1
1
2
2
0
1
1
1
0
2
1
1
0
0
1
1
1
1
0
1
1
2
1
0
1
1
1
1
1
1
1
2
0
1
0
0
0
1
1
1
0
1
2
1
0
2
1
0
1
1
0
1
1
1
0
0
1
0
1
1
1
0
0
1
1
0
1
2
0
2
0
1
0
0
1
2
1
0
2
0
2
1
2
0
1
1
0
2
2
0
0
0
2
1
1
1
1
2
1
0
2
1
1
1
0
0
1
2
0
1
0
2
1
1
0
2
0
0
0
1
0
1
0
1
2
1
2
1
2
1
1
2
0
2
1
1
1
0
2
1
2
2
1
1
0
3
1
1
1
0
0
1
1
1
0
0
1
0
1
1
0
1
0
1
0
0
1
2
0
2
1
2
2
0
0
2
0
1
1
1
1
0
1
0
0
1
1
0
0
1
2
0
1
2
1
1
1
1
0
1
0
0
1
1
1
0
1
0
0
0
3
2
1
0
2
1
0
0
2
1
2
1
0
1
0
1
0
0
3
1
0
1
2
2
0
0
1
2
1
2
2
0
0
1
0
1
1
1
1
0
0
0
2
0
1
1
1
0
0
1
0
0
1
1
1
2
0
1
2
1
2
1
1
1
0
0
1
0
1
1
1
1
0
0
1
0
1
1
2
2
1
2
0
1
2
0
1
1
1
0
2
1
1
1
1
2
2
0
2
1
0
1
1
2
2
2
0
1
3
1
1
0
0
2
2
0
0
0
0
0
0
1
0
4
1
1
1
1
1
0
1
0
0
1
1
1
0
2
0
1
0
0
1
0
1
1
1
1
3
2
2
1
1
2
0
1
2
1
1
1
0
0
0
0
2
0
0
1
1
1
0
1
1
1
1
2
1
0
1
0
0
1
2
0
2
2
2
0
1
1
1
2
0
0
1
1
0
0
1
1
0
1
1
0
3
2
1
1
0
2
1
1
0
1
1
0
1
1
1
2
0
0
1
1
0
2
1
0
2
0
2
1
1
2
0
0
1
0
0
0
0
1
1
1
0
1
1
1
1
1
2
0
1
0
2
1
0
2
1
0
1
0
1
0
1
1
1
3
1
2
2
2
1
2
0
1
1
1
0
0
1
2
1
0
0
1
0
1
0
1
2
2
1
2
1
1
2
1
2
1
0
1
1
0
2
1
2
2
1
1
2
2
1
1
2
1
1
1
2
2
2
1
3
0
2
1
0
1
2
1
1
0
1
2
0
2
1
1
1
1
2
0
1
1
1
0
1
0
2
0
1
2
0
0
2
0
1
2
2
0
2
0
1
1
1
0
0
1
2
0
0
0
2
0
0
0
1
0
0
0
0
1
2
2
0
2
2
1
1
1
1
1
2
0
0
0
1
0
1
1
0
1
1
2
1
2
0
0
0
0
1
2
2
0
0
1
2
1
3
2
0
2
1
0
2
0
0
1
0
1
1
1
1
1
0
3
2
0
2
2
0
1
1
2
0
0
1
0
2
0
1
0
1
1
0
1
0
0
0
2
0
2
2
1
1
0
4
0
1
1
0
0
1
1
2
2
1
0
1
2
1
1
0
1
1
1
1
2
1
1
1
1
2
1
4
2
1
1
1
1
1
1
1
0
1
1
0
1
2
1
2
2
0
2
0
1
0
1
1
1
1
2
1
0
0
0
1
1
0
1
1
0
2
0
1
0
1
0
2
1
1
1
0
1
0
0
2
0
2
0
1
0
2
1
2
1
1
1
0
0
2
0
1
1
0
1
1
0
2
0
0
2
2
1
1
1
1
2
0
0
2
1
1
0
1
0
0
0
1
1
0
1
2
0
1
2
1
1
2
2
1
0
1
4
0
1
1
0
1
1
0
1
0
2
2
2
0
0
3
2
1
1
0
1
0
1
1
2
1
1
0
1
1
1
0
0
1
1
2
2
1
1
1
2
1
1
1
0
1
2
3
1
1
1
0
0
2
2
1
0
2
1
2
1
1
0
0
1
0
1
0
1
0
0
0
2
1
0
1
2
1
2
3
2
0
0
2
1
1
0
0
1
2
2
0
2
0
0
0
0
2
0
0
2
1
1
2
0
2
0
0
2
3
0
0
1
1
2
0
1
1
1
0
2
0
0
1
2
1
1
1
2
1
0
0
1
1
2
2
1
1
0
1
1
0
0
1
1
1
0
1
0
2
1
1
0
1
0
1
0
2
0
1
0
1
1
1
1
2
0
2
2
1
0
1
1
2
1
1
2
0
0
1
1
1
1
0
0
2
1
1
1
2
1
2
1
0
0
0
1
2
0
0
3
2
0
1
0
0
2
2
0
0
0
2
1
0
2
2
1
2
0
2
2
1
1
0
0
1
0
1
1
0
0
1
2
1
0
0
1
0
1
0
1
0
1
0
1
1
1
1
2
0
1
1
0
1
1
2
0
1
1
2
1
0
0
0
2
1
0
2
3
2
0
2
0
2
1
1
0
0
1
2
1
0
2
0
0
0
0
0
2
0
0
3
0
1
2
0
2
1
2
1
1
1
1
2
1
0
2
1
1
0
2
0
1
3
1
0
0
0
2
1
1
2
1
1
1
0
1
1
2
0
0
1
0
1
2
1
1
0
1
1
1
2
1
0
1
1
0
0
0
1
1
0
2
2
2
1
0
0
0
1
0
2
0
2
1
0
2
1
3
2
2
2
0
0
0
2
0
2
1
1
2
0
0
1
1
2
3
0
1
1
0
1
0
2
1
1
2
1
2
0
1
1
2
1
2
2
1
0
2
2
2
1
2
4
1
2
1
1
0
2
0
0
2
1
2
0
1
0
1
0
0
1
1
3
1
1
0
1
1
0
1
0
2
1
0
1
2
2
0
1
2
1
0
0
2
2
2
1
2
1
1
1
2
2
1
2
0
0
0
1
1
1
1
2
0
1
1
1
2
1
1
2
1
0
1
0
0
0
0
1
1
1
0
1
1
1
2
0
0
2
1
1
0
0
0
1
2
2
0
0
1
1
1
2
2
0
1
0
2
0
0
0
2
2
0
2
2
1
0
0
0
2
0
2
0
0
2
1
1
1
1
1
1
1
2
0
2
0
0
1
0
2
0
1
2
1
0
0
2
1
0
0
2
2
2
1
1
1
0
2
0
2
1
2
1
1
2
1
2
1
2
1
0
0
1
1
0
1
2
1
2
1
0
2
1
0
0
1
1
1
1
0
2
1
1
2
0
0
2
2
0
1
0
0
2
1
2
1
1
1
0
0
0
0
3
2
0
0
0
1
1
2
2
0
1
0
2
0
1
1
1
1
1
2
0
2
0
2
1
1
2
1
0
0
0
2
1
0
0
0
3
1
2
1
1
0
1
1
1
1
2
1
0
2
1
0
1
2
0
1
1
1
1
1
1
0
0
1
1
0
1
0
0
2
0
0
1
2
1
0
0
1
2
4
0
2
0
1
0
1
0
0
0
1
1
2
0
0
0
1
0
1
1
0
0
1
0
2
0
2
0
2
1
0
2
1
2
0
1
1
1
1
1
0
2
1
2
1
1
0
0
2
2
1
1
0
0
1
1
0
0
0
1
0
0
1
1
1
1
1
0
2
2
1
1
1
0
0
1
0
1
4
1
2
1
1
2
2
1
2
1
2
0
1
2
2
1
0
0
2
1
2
0
0
0
1
1
0
1
0
1
1
1
2
1
0
1
2
0
3
2
1
0
2
2
0
0
0
0
1
2
2
3
1
1
0
2
2
1
1
1
2
1
0
0
1
2
0
1
0
0
0
1
0
1
1
2
0
0
2
0
0
0
2
1
1
2
0
1
1
1
0
0
1
1
1
1
0
0
3
2
0
1
1
1
1
1
0
0
1
1
2
0
0
2
0
0
0
3
2
1
1
4
0
1
1
0
0
1
2
2
1
1
0
2
0
2
2
1
1
0
0
0
1
1
0
1
2
0
2
1
0
0
1
2
1
0
0
0
1
1
5
2
1
0
1
2
0
1
1
0
1
0
1
3
1
0
1
0
2
0
0
1
1
1
1
2
0
1
0
1
1
0
2
0
0
1
1
0
1
0
0
2
2
1
2
3
0
0
1
1
0
0
3
1
0
1
1
1
1
1
0
1
1
0
1
1
1
1
1
0
2
1
1
1
1
1
2
0
1
1
2
0
0
1
1
1
0
0
0
2
0
0
1
0
1
0
0
1
0
2
1
0
0
1
0
0
2
1
2
0
1
2
0
2
2
1
2
2
1
0
0
0
2
0
0
0
1
1
1
2
1
0
1
1
0
0
1
1
0
0
0
1
0
2
0
2
0
0
0
2
0
2
1
2
0
2
2
0
1
1
1
1
1
0
1
1
2
0
1
0
1
1
1
2
2
0
0
2
0
0
2
0
2
0
2
1
1
0
2
0
2
1
0
1
1
1
0
1
0
2
2
1
1
0
0
0
1
0
0
1
0
1
0
0
0
1
0
1
1
0
1
0
1
1
2
2
1
1
1
1
1
0
1
1
0
1
1
1
1
0
0
2
3
2
1
0
2
0
0
1
1
2
0
2
1
1
0
0
1
0
1
2
0
2
1
1
2
0
0
0
1
0
1
0
2
1
0
1
1
0
1
1
2
1
1
1
1
2
1
2
0
0
2
1
0
0
1
2
2
1
0
0
1
1
1
2
0
1
0
2
3
1
0
1
1
1
0
2
1
0
1
1
2
1
0
0
0
2
1
1
1
0
0
1
1
0
0
2
0
0
1
1
2
0
2
1
2
1
2
1
0
2
0
0
1
0
0
0
2
1
1
1
2
2
0
0
2
0
0
1
0
1
2
0
0
0
2
0
1
1
1
0
0
0
1
1
1
1
1
0
2
0
2
0
0
1
0
0
0
1
2
2
0
1
0
0
0
2
0
0
1
1
0
1
1
1
0
0
1
0
2
0
0
2
0
0
2
1
2
1
0
1
2
1
3
0
0
1
1
0
1
2
2
0
2
1
2
1
2
1
0
0
2
1
1
0
2
0
1
1
1
2
1
2
1
2
2
1
1
1
1
0
0
0
1
1
1
1
0
2
0
1
0
0
1
3
1
0
0
1
1
2
1
0
0
1
2
1
1
1
0
1
0
2
1
0
1
0
2
2
1
0
0
0
1
0
2
1
1
1
1
0
0
1
3
0
1
1
2
2
1
0
1
1
1
1
2
1
0
2
1
2
1
2
2
1
1
1
1
1
2
2
1
2
0
1
2
2
1
1
1
2
0
0
0
1
0
0
0
2
1
1
1
1
2
2
0
2
0
0
0
0
2
2
3
1
1
0
0
1
1
0
0
1
2
0
2
0
1
0
1
0
0
0
2
2
2
2
0
1
1
1
1
0
1
1
0
1
1
1
1
1
0
1
1
0
1
1
1
1
2
1
0
2
1
0
0
1
0
2
1
0
0
0
1
0
2
1
2
2
0
0
0
1
1
2
0
0
0
1
1
2
0
0
0
1
0
0
1
0
1
1
0
0
2
2
2
0
0
2
0
1
1
0
0
0
2
1
1
1
2
1
1
0
0
0
1
1
1
1
1
0
1
2
1
0
0
1
0
2
0
0
0
2
0
1
0
0
1
1
0
1
2
1
0
1
1
0
2
1
1
0
2
1
2
0
0
1
0
0
0
0
2
2
2
0
2
1
0
0
1
0
1
2
1
0
1
1
0
1
1
0
0
1
0
0
1
0
1
0
0
0
1
1
0
0
2
0
1
1
1
0
1
1
0
2
0
1
0
0
0
0
0
1
1
2
1
0
2
2
1
1
1
0
0
0
1
0
1
1
0
0
0
2
0
1
1
2
2
2
1
1
2
1
2
1
1
1
1
2
3
1
0
1
0
4
1
1
2
1
0
0
1
2
0
2
1
0
1
2
0
0
1
4
1
0
0
0
0
1
1
0
1
4
0
0
2
0
1
0
0
1
0
2
0
0
2
0
1
0
1
1
1
0
0
2
1
0
2
5
2
0
0
0
0
0
1
1
0
2
2
3
2
0
2
1
0
0
0
1
2
0
1
0
1
1
1
1
0
1
0
1
1
2
2
2
0
0
2
2
2
1
0
1
2
1
2
0
0
2
0
1
2
1
2
1
0
2
2
1
1
1
1
3
1
0
0
1
2
1
0
0
2
2
0
2
1
0
2
1
1
0
0
1
1
0
1
1
1
1
0
0
1
0
2
1
0
0
0
1
0
1
1
0
1
0
1
2
2
0
1
0
1
1
0
1
2
0
0
2
0
1
1
1
2
0
1
0
2
2
1
1
2
0
0
9
1
1
1
1
2
2
1
2
2
2
0
1
2
1
2
0
0
0
0
6
1
0
2
1
0
0
1
1
0
1
0
2
2
1
2
1
1
0
1
0
1
2
3
1
0
0
1
2
1
0
0
1
2
2
2
2
0
0
1
0
1
1
0
1
0
1
0
2
1
1
1
1
1
1
1
1
2
0
0
4
2
0
0
2
2
1
2
1
1
0
1
0
0
1
3
1
0
2
1
1
1
1
0
1
2
1
1
0
0
1
0
3
2
1
2
2
0
1
1
2
0
1
2
1
2
0
2
1
1
1
1
1
2
1
0
1
1
1
1
1
0
1
1
1
0
0
0
0
2
1
2
0
2
0
0
1
0
0
0
2
1
0
0
1
1
2
1
0
0
1
1
3
2
1
1
1
1
4
1
1
0
0
0
0
0
0
1
1
2
1
1
1
1
1
1
0
2
0
0
0
1
0
0
1
0
1
2
0
2
1
2
1
2
2
0
1
1
2
0
1
0
0
2
0
0
1
0
1
1
1
0
2
0
1
0
2
1
1
0
0
1
1
1
0
0
1
0
2
1
2
0
1
2
1
1
0
1
1
2
2
0
1
0
2
0
1
1
2
1
2
2
0
2
2
0
2
1
0
1
1
1
1
1
1
0
1
0
1
0
1
2
0
1
0
2
0
1
1
1
2
0
1
1
1
0
1
1
2
1
2
2
0
2
0
1
1
1
0
0
2
0
1
2
1
0
2
0
2
0
1
2
1
0
1
0
1
2
1
0
1
0
1
1
2
1
1
0
2
0
0
1
1
1
0
1
1
0
2
0
1
0
0
0
2
0
2
1
2
2
1
0
0
1
1
0
2
2
0
2
0
0
2
1
0
1
0
2
1
1
0
1
1
1
1
0
2
2
0
2
1
2
1
0
2
2
1
1
0
0
1
2
1
1
1
2
1
3
0
1
2
0
1
1
5
0
2
1
0
0
0
1
1
1
1
1
0
2
1
2
1
0
1
2
0
1
1
0
2
2
1
0
0
1
1
1
1
2
1
2
1
1
0
1
0
1
1
0
0
2
1
0
0
2
0
1
1
1
1
1
1
1
1
0
0
0
0
1
1
1
1
2
2
2
1
1
0
2
1
1
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
1
1
1
1
1
1
1
0
2
0
1
1
0
2
1
1
0
1
2
1
0
0
0
0
2
0
1
1
0
1
1
1
1
1
0
1
1
0
0
2
2
2
1
2
1
0
0
2
2
1
1
2
1
1
2
2
0
0
2
0
0
1
1
0
0
2
1
3
2
1
0
1
1
1
1
3
1
0
0
0
2
4
2
1
1
1
0
0
0
1
1
1
1
2
1
0
0
2
1
2
1
0
1
1
0
0
0
0
0
1
2
1
0
1
1
2
0
2
1
1
0
0
1
1
1
2
0
0
1
0
1
0
2
1
2
0
1
0
1
2
1
0
1
2
2
1
0
1
1
1
2
2
1
1
1
1
1
2
2
1
2
0
1
1
1
0
1
2
1
2
1
1
0
2
1
1
1
2
1
0
0
1
0
1
2
1
2
2
0
2
0
0
1
2
1
1
1
2
2
1
0
1
0
0
1
1
0
2
0
1
0
2
0
2
0
0
0
1
0
1
1
0
0
1
1
2
0
1
2
2
0
0
1
1
0
1
0
1
0
0
1
1
0
0
0
1
0
2
0
1
2
1
2
0
1
1
3
1
1
2
0
0
1
1
0
1
1
1
0
2
1
1
2
0
2
1
0
1
1
1
1
1
1
1
1
1
2
1
0
1
0
0
2
0
0
1
2
2
0
0
1
1
1
2
1
0
1
1
0
1
2
1
2
2
1
1
2
1
1
0
0
0
2
0
1
1
0
2
2
0
1
1
1
1
1
1
2
1
1
0
2
0
1
0
0
0
0
2
0
2
0
1
0
1
2
2
0
1
2
2
2
1
1
0
2
2
0
1
1
0
1
1
1
0
1
1
1
1
2
1
1
2
1
0
0
0
0
0
1
0
1
0
0
0
1
1
1
0
1
0
0
2
1
0
1
1
2
3
0
1
0
1
0
0
2
2
1
1
0
0
0
0
1
1
1
1
0
1
2
1
1
0
0
1
2
1
0
0
0
1
1
1
1
1
0
0
3
0
2
2
2
2
2
0
0
1
2
1
0
0
1
1
1
1
0
1
0
2
0
1
0
1
1
2
0
1
0
1
1
1
2
0
1
0
1
1
1
2
0
1
0
2
0
1
2
0
2
1
0
1
0
2
0
1
2
1
0
1
2
0
2
2
0
0
1
1
2
1
1
0
0
2
1
1
1
1
0
1
4
0
2
1
0
0
1
0
1
0
1
1
1
0
2
1
3
1
0
0
1
1
1
2
1
2
1
0
1
3
1
1
2
1
1
0
2
0
0
2
0
2
1
1
1
1
0
1
1
0
2
0
1
1
4
0
1
2
2
0
1
2
1
1
1
0
1
0
2
1
0
0
1
0
1
1
2
1
2
0
0
0
1
1
4
1
2
1
1
2
1
2
1
0
1
1
0
1
0
2
0
2
2
1
2
1
0
3
2
1
0
0
0
2
0
1
2
0
0
1
1
1
0
0
1
0
1
1
1
1
2
1
0
0
2
0
1
2
1
0
2
0
2
0
1
0
0
0
1
1
0
0
2
2
1
0
0
2
0
1
0
0
1
2
2
1
0
0
1
0
2
1
0
0
1
0
0
0
1
1
1
0
1
2
0
1
1
0
0
0
0
0
1
0
0
2
0
1
1
1
0
0
1
1
1
1
0
1
0
1
1
1
2
1
2
0
1
0
1
0
0
2
0
0
1
0
1
0
1
0
0
1
0
1
1
1
1
0
0
2
1
2
2
1
0
1
2
0
0
1
2
0
0
0
1
0
1
2
2
1
1
8
1
1
1
2
0
0
2
1
1
2
0
2
1
0
0
2
0
1
0
1
1
2
1
1
1
0
1
0
2
1
1
1
0
0
2
1
1
0
1
2
1
1
2
1
1
1
2
1
0
0
2
0
1
1
1
0
0
1
1
1
2
2
2
1
0
2
2
0
1
1
0
1
1
0
1
1
0
2
0
1
1
0
2
0
2
1
2
0
1
0
1
1
2
0
0
0
1
0
2
0
0
0
0
2
0
2
1
1
0
0
0
2
0
1
1
0
1
0
0
1
0
0
1
1
0
1
1
0
1
2
0
1
1
0
1
1
2
0
1
0
1
0
1
0
1
1
0
0
1
1
1
1
2
1
1
1
2
1
1
1
1
1
2
2
0
1
2
1
0
0
0
2
1
2
1
0
2
1
1
1
2
1
0
2
2
2
0
2
0
0
0
1
2
1
1
1
2
0
1
0
0
1
0
0
1
0
2
0
1
1
1
1
1
1
1
0
1
1
1
0
0
1
1
0
1
1
3
1
0
0
0
2
1
0
2
1
1
2
1
2
2
1
1
1
0
2
1
2
0
0
2
1
2
0
2
1
2
1
0
1
2
0
2
0
1
1
2
1
2
3
1
0
1
2
1
0
2
2
0
2
2
1
0
1
1
0
1
0
0
3
0
1
0
1
1
2
2
0
1
0
1
2
0
1
1
2
1
1
0
2
1
0
1
0
1
2
0
0
0
0
1
1
0
0
1
1
0
2
0
0
2
2
0
1
1
2
0
0
4
1
2
1
0
1
2
0
0
0
0
0
2
1
0
0
0
1
0
1
1
0
1
1
1
2
2
2
1
1
1
0
1
1
0
1
1
1
1
0
0
2
1
0
2
2
1
0
1
1
1
1
3
0
1
1
0
0
1
0
2
2
2
2
2
1
2
0
1
1
0
3
1
2
1
1
0
1
1
0
2
1
2
0
3
0
1
0
2
1
0
0
2
0
2
0
1
1
2
1
2
0
1
2
1
0
1
2
1
1
1
0
1
0
0
2
0
0
0
2
2
1
2
0
1
0
1
1
2
1
0
0
4
0
0
0
1
1
2
2
2
2
3
0
1
2
1
0
0
2
0
2
0
2
0
1
0
0
0
1
1
1
0
2
0
1
1
0
1
0
1
1
0
0
2
1
1
1
0
2
1
0
2
0
1
2
1
1
0
1
0
0
0
1
2
0
0
2
0
0
1
0
1
1
0
0
0
1
1
1
0
1
1
0
1
1
1
1
2
0
1
0
2
0
1
1
1
1
3
1
1
2
0
2
2
3
0
2
1
0
0
1
1
1
0
1
1
2
1
2
2
1
0
2
0
1
1
2
0
1
1
0
1
1
2
1
1
0
1
1
2
1
0
1
2
0
0
1
2
1
1
1
2
2
2
0
2
1
0
1
2
0
1
0
1
0
0
0
1
2
1
1
1
0
0
0
0
0
0
2
2
0
0
2
1
1
0
2
1
0
0
0
0
1
0
1
1
1
2
0
2
3
2
1
2
0
1
1
1
0
2
1
0
2
0
1
0
2
1
0
0
0
1
0
1
0
1
1
0
1
2
1
1
1
2
1
1
1
1
1
0
0
2
0
1
2
0
2
2
2
1
0
0
1
2
0
0
0
1
2
1
2
0
2
2
0
0
0
0
1
2
2
0
0
0
2
1
1
0
1
1
1
0
1
0
1
0
1
1
0
2
1
1
1
1
0
2
1
1
1
2
0
0
1
2
0
1
0
1
0
0
1
0
0
2
0
0
0
0
1
0
2
1
0
0
1
2
1
2
0
1
0
2
2
2
2
2
0
1
0
2
1
1
0
1
0
1
1
2
2
1
0
0
0
0
2
2
2
0
1
2
4
1
1
2
0
0
2
3
1
0
1
2
1
0
3
2
0
2
0
2
0
1
0
0
2
1
1
0
0
1
1
0
0
1
2
2
0
2
0
2
1
2
1
0
1
1
0
2
1
2
0
0
1
2
1
1
1
2
1
0
2
2
0
1
1
1
1
3
0
0
1
0
1
1
0
1
1
2
1
1
2
1
1
1
0
1
1
1
2
1
1
1
1
2
1
1
1
2
1
0
0
2
1
1
1
1
3
1
1
1
2
1
0
1
0
0
1
0
1
0
0
1
1
0
1
1
2
1
0
1
2
1
2
1
1
1
0
2
1
1
2
2
0
2
0
1
2
2
0
1
2
2
1
0
0
1
1
2
1
2
1
2
0
2
0
1
1
1
0
1
0
3
1
1
1
0
2
1
1
0
1
1
1
1
0
0
2
2
2
2
1
2
5
1
2
1
1
0
1
2
1
2
1
0
1
1
2
0
1
0
0
2
2
2
2
1
2
2
2
1
2
0
0
1
1
2
1
1
1
2
2
0
0
1
2
1
0
0
0
1
2
0
1
1
1
2
0
1
0
1
0
2
2
0
1
2
0
0
2
0
2
2
1
1
2
2
1
1
0
1
0
1
1
1
0
0
1
2
2
0
1
1
0
0
1
1
2
0
1
1
1
1
0
0
1
0
1
0
0
2
1
0
1
1
1
0
0
0
1
1
2
0
0
2
0
0
0
1
1
1
1
0
1
0
0
1
2
1
0
0
1
2
1
0
0
2
2
2
0
1
0
1
1
0
1
1
1
0
1
2
2
1
0
2
0
0
0
1
0
1
2
2
1
0
1
1
2
1
0
1
2
2
0
0
0
0
2
1
2
0
0
1
0
0
0
0
1
0
1
1
1
1
2
0
1
0
1
0
1
1
1
2
1
2
1
4
1
1
2
1
2
2
1
1
0
1
2
1
1
1
0
1
1
0
1
0
1
1
0
0
0
0
1
1
0
0
1
2
0
1
0
1
1
1
2
1
2
0
1
0
0
0
0
0
0
1
2
1
0
2
2
1
1
1
1
0
1
1
1
1
0
1
1
2
2
2
1
1
1
0
1
0
2
1
1
0
2
0
1
1
0
0
0
0
0
0
1
0
1
1
1
0
0
0
1
1
0
0
2
0
0
1
1
1
1
3
0
1
2
0
0
0
2
0
1
0
0
0
1
0
0
0
2
2
0
1
1
1
0
1
0
0
1
0
2
1
2
0
1
1
2
0
1
2
1
1
0
1
1
0
2
1
0
2
0
1
1
2
1
1
2
1
2
2
0
1
2
0
0
1
0
3
0
2
2
1
0
1
1
0
0
0
1
1
0
1
0
0
1
1
1
8
1
2
1
2
0
2
0
0
0
1
1
1
2
1
1
1
1
1
2
0
1
1
1
0
0
0
1
0
1
2
2
1
2
1
0
1
0
0
1
1
0
1
1
0
0
1
0
0
1
2
0
0
1
0
2
0
2
0
0
2
1
0
1
1
1
1
0
0
1
2
1
0
2
1
2
1
1
0
2
1
2
1
1
0
2
1
2
1
1
1
1
1
1
1
0
2
1
1
0
1
0
2
0
2
2
1
1
1
0
1
1
1
0
2
1
1
0
2
2
1
1
2
1
0
2
1
1
1
2
0
1
0
0
3
0
0
1
1
1
1
1
1
2
2
2
1
1
1
0
1
1
1
1
1
0
1
2
0
0
0
2
1
0
1
2
0
0
0
1
1
1
0
0
2
0
1
0
1
0
2
0
0
1
0
0
0
1
1
1
0
1
1
0
0
2
2
1
2
1
0
0
0
2
2
1
1
2
0
0
0
1
1
1
0
1
2
0
1
1
1
1
0
0
1
2
0
1
1
0
2
1
0
0
1
1
0
1
0
0
1
1
2
1
1
0
1
0
0
0
1
1
1
1
2
0
5
0
1
0
0
1
2
1
1
2
1
2
1
1
2
2
0
0
1
0
1
1
1
1
1
1
1
0
2
0
2
1
1
0
0
0
1
1
2
0
2
1
1
1
0
2
1
1
1
1
1
1
1
0
0
2
0
0
3
1
1
1
2
1
0
0
4
0
1
2
0
2
0
0
2
1
1
0
1
1
0
2
0
0
1
0
1
0
0
1
0
2
0
1
2
2
2
1
1
1
0
2
1
1
2
0
1
2
1
0
3
1
1
0
0
1
2
1
1
2
0
2
1
3
0
1
2
3
2
2
0
2
1
1
0
1
2
2
1
1
1
1
1
1
0
0
0
0
2
1
2
1
1
2
1
0
0
0
1
1
0
1
1
1
1
1
1
0
2
0
1
0
1
3
1
0
0
0
2
0
2
1
1
1
1
0
0
1
0
1
1
1
0
1
2
2
2
1
0
0
0
2
2
1
1
1
1
1
1
1
1
1
0
3
0
2
0
2
0
1
0
1
2
0
1
2
0
1
0
1
1
1
2
0
2
1
0
1
1
1
2
0
1
1
1
2
2
0
0
1
0
1
2
0
1
1
1
1
0
1
2
2
0
1
1
0
0
2
2
1
0
0
2
0
2
1
0
3
1
1
0
2
1
1
0
2
1
1
1
2
1
1
0
1
0
1
2
1
2
0
0
2
0
2
0
2
2
0
1
2
0
1
2
1
0
0
1
1
0
1
1
0
0
1
2
0
0
1
1
2
0
1
2
2
1
1
0
1
2
1
1
0
0
0
1
0
1
0
2
0
0
1
1
0
0
2
1
1
1
0
0
0
1
0
1
2
1
2
1
2
1
0
2
2
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
1
4
2
1
1
2
1
1
0
1
1
1
1
2
1
4
1
1
1
1
0
2
1
1
0
2
2
0
1
2
2
1
2
1
0
1
0
0
1
4
1
1
1
0
0
1
1
0
1
1
0
1
2
0
0
0
0
0
1
3
1
2
1
0
1
1
2
0
1
1
1
1
1
2
1
1
0
0
0
2
0
1
0
1
0
1
1
1
1
0
1
1
1
0
1
2
2
1
3
1
2
1
0
0
0
1
2
1
0
1
0
0
0
1
2
1
0
1
2
1
2
1
1
1
1
0
0
0
1
3
0
1
0
0
0
2
0
1
0
1
0
1
0
0
2
1
1
1
1
0
0
0
1
1
0
1
1
0
1
2
0
2
0
1
1
1
0
0
0
1
2
2
2
0
1
0
1
1
0
1
0
0
1
0
0
1
1
2
1
1
2
1
0
1
1
1
0
2
0
1
1
0
0
1
1
0
0
2
0
0
0
2
0
0
2
2
1
1
0
0
2
0
0
1
2
1
0
1
1
1
0
0
1
2
0
0
2
1
2
0
0
2
1
1
2
0
2
0
0
0
1
0
2
1
2
0
2
1
0
2
1
1
1
1
2
1
2
2
1
0
1
1
0
1
2
0
1
1
0
0
0
0
0
1
1
1
0
1
0
2
1
1
2
0
2
2
0
1
0
0
0
2
1
0
1
0
2
2
0
1
2
1
2
2
1
2
1
1
1
1
0
2
2
0
1
0
2
1
1
2
1
1
1
2
2
0
0
0
1
1
1
1
0
0
0
0
1
1
0
2
1
0
2
2
1
1
2
0
1
2
1
0
2
2
1
2
2
0
0
0
1
0
0
0
0
0
1
0
2
2
1
1
2
2
2
1
1
1
0
1
1
1
1
1
0
1
0
1
0
1
1
2
1
0
0
0
1
1
1
0
1
0
0
1
0
0
0
1
2
2
2
2
2
0
0
2
0
1
0
1
2
0
0
1
0
0
0
1
1
0
1
1
1
1
0
1
0
0
0
0
0
0
1
3
1
1
0
1
1
2
1
1
1
0
2
1
2
2
0
0
1
0
1
0
0
1
0
1
1
1
0
1
0
0
0
2
0
1
1
1
0
0
0
0
0
0
0
0
1
2
0
1
2
1
0
1
0
0
1
0
0
1
2
0
0
0
2
0
0
0
1
1
1
1
1
1
1
1
1
0
1
2
1
2
1
1
0
1
0
1
0
2
1
1
1
1
1
0
1
0
4
1
0
0
0
0
1
1
1
2
0
1
1
1
0
1
1
0
1
1
0
0
1
1
1
1
1
2
1
1
2
0
1
0
0
2
2
0
2
1
0
0
0
0
1
0
1
0
1
2
1
1
0
1
2
1
1
2
1
1
1
0
0
0
0
0
1
1
1
2
1
1
0
2
1
0
0
1
2
1
0
1
1
4
0
1
0
1
0
2
1
2
2
1
0
2
0
2
0
1
1
0
2
0
1
0
2
1
1
2
1
2
2
1
0
0
1
1
1
2
0
0
1
2
1
2
0
2
0
2
1
0
2
2
2
1
2
1
1
1
2
1
0
0
0
2
1
1
2
0
2
1
2
1
4
0
2
1
1
0
1
2
1
1
0
1
1
0
0
1
0
2
0
0
1
0
1
0
2
1
1
2
2
0
1
1
0
1
2
0
0
1
1
1
1
0
0
1
0
2
1
1
1
1
1
1
1
2
0
0
2
2
0
2
1
0
1
0
1
1
0
2
1
1
1
0
0
2
1
2
1
1
1
1
0
1
1
0
1
1
1
0
1
0
0
0
0
1
1
0
0
2
1
2
3
2
0
1
0
2
1
1
0
1
1
0
0
1
1
2
1
0
0
1
0
1
0
0
1
1
0
2
0
1
2
1
0
2
2
1
2
0
1
0
1
1
0
0
2
2
1
1
2
1
0
2
1
1
1
1
1
1
1
0
0
0
2
1
0
0
0
0
1
2
1
0
0
0
0
1
0
2
0
1
2
1
1
1
0
1
2
0
1
0
2
0
2
0
1
1
0
2
2
1
2
3
1
2
2
0
0
1
3
0
0
1
0
2
2
0
1
2
0
0
0
0
1
1
2
0
2
1
1
1
0
1
1
0
0
1
1
1
1
0
1
2
1
1
2
2
1
0
1
0
1
0
1
0
0
1
0
2
1
1
0
2
0
0
1
1
0
0
2
2
1
0
1
1
0
1
1
1
0
0
0
2
0
1
3
1
1
2
0
1
2
1
1
1
0
1
2
1
1
0
1
1
2
0
2
2
1
2
0
1
2
1
1
1
2
1
1
0
0
1
1
2
2
1
1
1
2
1
0
0
0
1
1
1
0
0
0
0
1
0
1
2
0
2
1
1
0
1
1
0
1
2
0
1
1
1
1
0
1
1
0
2
1
0
5
0
1
0
1
0
2
0
1
0
1
2
3
2
1
1
1
2
1
2
1
0
2
0
2
2
2
0
1
1
0
0
1
1
2
0
0
1
2
0
0
2
1
0
0
0
2
3
0
1
0
1
2
1
1
1
0
1
1
0
2
1
2
1
1
0
2
1
1
1
0
3
0
0
1
0
2
2
0
0
1
2
2
1
2
1
1
0
1
1
1
1
1
2
2
1
1
0
2
1
1
0
1
0
1
1
1
1
0
2
0
0
1
0
0
1
0
2
1
1
2
0
1
3
0
2
2
0
2
0
0
1
0
1
0
0
2
1
0
0
1
1
1
2
1
1
2
1
0
2
1
2
1
1
1
1
2
2
0
0
0
0
0
1
1
2
2
1
0
1
0
0
1
0
2
0
2
1
0
1
2
0
2
0
1
1
1
0
1
1
2
1
1
2
2
2
1
0
0
1
0
1
0
2
2
1
1
1
2
1
1
0
1
0
1
0
2
3
2
0
0
0
1
1
2
1
1
0
1
1
0
2
1
0
1
2
0
0
1
0
2
0
1
1
2
2
3
2
1
1
2
0
0
1
0
1
2
0
0
3
0
0
1
0
1
0
0
0
0
1
1
0
1
0
1
1
0
1
0
0
0
2
2
1
2
0
0
0
0
1
1
1
2
1
0
2
2
0
0
0
0
1
1
0
1
0
0
0
2
0
1
2
0
0
0
1
0
0
2
0
2
1
0
1
0
1
2
2
0
0
0
0
0
2
2
1
2
1
1
1
1
0
1
2
1
0
2
1
1
1
1
1
0
2
0
1
1
1
0
2
1
1
2
1
1
0
0
0
0
0
1
2
1
2
0
1
0
1
1
0
1
1
1
3
0
0
1
2
1
0
1
0
1
2
1
0
1
1
1
1
1
0
1
2
1
1
1
1
1
1
1
0
1
0
0
0
0
2
0
0
1
0
0
1
1
1
2
1
1
2
2
0
1
1
0
1
1
0
1
1
1
2
2
1
1
1
0
1
1
1
0
0
1
0
1
2
2
0
0
1
0
0
0
1
2
0
0
1
0
0
2
0
1
1
0
0
1
1
0
2
0
0
1
2
2
2
0
0
1
1
0
2
1
0
1
1
2
1
1
2
0
2
2
0
2
0
0
0
0
0
0
0
1
0
1
1
0
2
1
1
1
0
0
1
1
1
0
1
0
1
0
1
1
0
2
0
1
1
3
1
1
0
2
1
0
1
1
0
1
0
0
0
1
1
0
1
0
1
0
0
1
0
0
2
1
1
0
1
1
1
1
2
2
1
0
3
0
1
1
1
1
1
0
0
0
1
2
2
1
2
1
1
0
2
1
1
0
2
2
2
1
1
0
0
0
1
0
2
0
1
3
0
1
1
0
0
0
1
0
1
1
0
0
0
2
0
2
1
0
0
1
1
1
4
0
1
2
3
1
1
1
0
1
0
1
1
1
1
1
0
0
2
1
1
2
0
2
0
0
0
1
2
0
1
1
2
1
2
1
0
1
0
2
2
2
1
0
2
0
0
1
1
2
0
1
0
1
1
1
1
1
0
2
1
1
2
0
2
1
1
0
1
1
2
1
0
1
1
1
0
0
1
1
1
0
1
2
3
1
1
1
1
1
1
2
1
0
1
1
1
3
2
1
2
0
0
2
0
1
1
0
1
2
0
1
1
1
2
0
0
2
1
0
1
0
2
0
1
1
3
3
2
1
2
2
2
1
0
0
1
1
1
0
0
0
1
0
1
0
0
1
0
1
0
0
1
0
0
1
0
0
1
1
1
0
2
0
0
0
0
2
2
1
0
1
1
1
0
0
1
0
5
1
1
0
2
1
0
1
2
1
2
2
2
1
1
2
1
2
1
0
0
0
2
1
0
1
1
0
1
1
0
0
1
2
2
0
0
1
0
1
0
0
2
0
1
0
1
0
2
1
0
1
0
0
1
1
0
1
0
1
0
0
1
2
1
2
0
0
1
0
1
1
1
2
0
2
0
2
0
2
0
2
0
1
0
2
1
1
1
0
2
0
2
2
2
0
2
1
0
2
1
1
1
2
1
0
1
4
1
1
0
0
0
0
2
0
1
2
1
1
2
1
2
0
0
0
1
0
1
0
1
0
1
0
2
0
1
0
1
1
0
0
2
0
0
0
2
2
0
1
0
1
1
1
2
1
2
1
1
2
1
0
1
1
1
0
1
1
0
0
1
0
0
1
0
1
1
0
1
1
0
0
1
0
1
1
1
0
0
0
2
0
0
0
2
0
0
0
0
0
1
2
1
2
0
0
1
1
0
2
0
0
1
0
1
2
2
2
1
0
1
1
1
1
2
0
1
2
0
1
0
1
0
1
0
2
1
2
1
1
1
0
1
1
0
0
0
1
0
0
2
2
0
0
0
1
2
1
0
0
2
0
1
0
2
0
1
1
1
2
3
0
0
2
1
2
1
0
1
0
1
2
1
1
0
0
0
2
2
2
1
1
2
2
1
1
1
1
0
1
2
0
2
1
1
1
1
1
2
1
1
1
0
2
1
2
0
0
0
1
0
2
1
2
0
0
2
1
1
1
1
1
0
0
1
0
1
1
0
0
0
1
0
1
1
1
1
1
2
2
1
0
0
1
1
0
3
1
1
0
1
1
2
0
1
1
1
0
1
3
2
0
1
2
0
2
1
0
0
1
2
1
1
0
2
0
0
0
1
0
1
1
1
1
0
1
1
0
1
1
1
0
2
1
0
0
0
1
0
0
1
1
2
0
1
1
1
3
0
0
1
2
1
0
2
0
1
0
0
2
0
1
1
1
1
0
1
1
1
0
1
4
1
0
0
1
1
1
1
2
1
3
1
2
1
0
0
0
0
2
0
1
2
1
2
1
0
2
1
2
2
2
0
2
1
2
0
0
2
2
1
0
1
1
1
1
1
1
2
1
2
2
0
0
0
0
1
0
1
2
1
1
1
1
1
0
1
1
1
1
1
1
2
0
1
0
2
1
0
1
1
1
1
0
1
1
0
0
2
1
0
2
0
1
1
1
1
0
1
2
0
1
1
1
2
0
2
3
1
0
2
2
2
2
1
1
1
1
0
0
0
2
1
1
0
0
3
1
1
0
0
0
0
0
2
1
2
2
1
1
0
0
1
1
1
0
1
0
1
0
1
1
2
2
0
0
1
1
0
1
0
2
1
2
2
2
1
2
0
2
0
1
0
1
1
2
2
0
1
0
2
2
2
0
1
0
1
1
0
2
0
1
0
2
1
0
2
0
0
0
0
1
1
2
0
0
1
1
0
2
0
1
1
1
1
0
1
1
0
0
0
0
0
1
2
0
0
0
1
0
2
1
1
0
1
1
1
2
2
1
1
1
2
1
0
1
0
1
1
1
1
0
0
0
1
1
0
1
0
0
0
4
0
1
0
1
1
2
2
1
1
2
1
0
1
1
2
1
2
1
1
2
2
0
2
0
0
1
0
0
0
2
1
1
1
0
2
0
1
1
1
0
1
1
2
0
0
0
1
2
0
0
2
0
1
2
0
2
1
1
0
1
0
1
2
0
0
2
1
1
0
1
0
2
1
1
1
0
2
1
4
1
0
0
0
1
2
0
1
0
3
1
2
2
2
0
0
2
0
0
0
2
1
1
1
1
0
1
1
0
0
3
1
1
0
0
1
0
0
1
0
1
1
1
2
1
0
1
1
1
0
0
1
2
0
1
0
1
1
1
1
1
0
2
2
1
2
0
0
1
1
0
0
2
2
0
2
0
2
0
2
1
1
0
1
1
2
0
1
1
1
1
0
1
1
1
1
1
0
1
0
0
0
0
0
1
1
1
2
2
2
0
0
1
1
2
2
1
1
1
1
2
0
0
2
0
1
0
1
0
1
2
0
0
0
0
0
1
2
2
0
0
1
1
1
1
0
2
1
1
2
1
0
1
0
1
1
1
0
15
2
1
2
1
1
0
0
0
1
1
2
0
0
1
0
0
2
1
1
2
1
1
1
1
0
0
1
0
0
2
2
0
1
1
1
1
1
0
0
1
1
1
2
1
2
2
1
1
1
1
1
0
1
0
0
0
0
2
1
1
0
0
1
1
1
1
2
1
0
2
1
2
0
1
1
2
1
0
0
0
2
1
0
1
6
0
2
0
2
1
1
2
2
0
2
2
1
2
1
2
2
1
2
0
0
0
2
1
0
1
1
2
1
1
1
0
1
2
0
0
1
2
0
0
0
0
2
1
2
2
1
1
1
2
2
1
1
0
1
2
2
0
1
1
1
0
1
1
2
0
2
1
0
0
1
0
0
1
0
1
1
1
1
2
0
1
0
1
1
0
0
1
2
2
1
1
1
2
2
0
0
0
1
0
1
0
0
0
0
0
1
1
2
0
2
2
2
1
2
1
0
0
1
0
1
1
1
0
1
3
0
1
2
2
1
0
2
0
1
0
0
1
1
1
0
1
0
1
0
1
2
0
0
0
2
1
1
0
1
0
2
1
0
0
2
0
2
2
0
1
0
1
1
0
0
3
1
2
1
0
1
0
0
1
1
1
1
1
0
2
1
0
2
0
2
0
0
2
1
0
0
0
0
0
1
2
1
2
0
0
0
0
2
2
2
0
2
1
1
1
2
2
1
0
0
1
0
2
2
1
0
1
1
0
1
0
1
0
1
1
1
2
1
1
2
1
0
1
1
0
2
2
1
0
1
0
2
1
0
1
2
1
2
1
0
1
1
2
0
1
0
1
1
0
1
0
1
1
1
2
0
0
0
1
0
1
1
0
0
1
1
0
0
0
0
0
1
1
1
0
0
1
2
1
0
1
0
0
0
2
1
0
2
2
1
1
0
1
1
1
2
0
1
1
1
2
2
2
1
2
0
2
0
2
1
2
2
2
2
1
1
2
0
0
1
0
1
1
0
0
1
0
2
0
2
1
5
1
2
1
2
1
0
1
0
0
1
2
1
1
0
1
1
1
2
0
2
0
1
1
2
1
2
2
2
2
1
1
0
0
1
1
2
0
2
1
1
1
1
0
2
1
1
1
1
0
1
2
1
1
1
0
0
0
1
2
0
2
1
1
1
0
0
1
1
2
0
0
1
1
0
1
0
2
1
1
0
0
1
0
0
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
0
0
1
2
1
0
1
0
2
1
2
0
1
1
1
1
1
1
1
2
0
1
0
1
1
0
2
1
1
1
2
0
0
2
0
1
2
2
1
1
2
1
1
0
0
0
1
1
2
2
1
0
1
0
1
0
1
0
1
0
1
2
2
0
0
1
1
1
2
1
0
0
0
0
1
2
1
1
0
0
1
1
1
1
2
0
1
1
0
1
0
3
1
1
0
0
1
1
0
0
1
1
2
2
2
1
0
1
0
1
1
1
2
2
0
0
0
0
1
2
2
1
1
2
0
1
0
0
0
0
2
1
1
2
0
2
1
1
0
1
0
1
2
1
0
2
1
0
0
1
2
1
1
2
0
0
1
2
1
0
0
1
1
2
0
1
1
0
0
0
0
1
1
1
0
1
0
0
0
0
1
2
1
0
0
1
1
1
1
1
1
1
1
0
1
1
0
1
0
0
0
1
1
2
0
0
1
3
1
1
1
2
1
3
2
1
0
2
0
2
0
0
1
2
1
1
1
0
0
1
0
2
2
1
0
1
1
1
1
1
1
1
1
2
0
0
2
0
1
1
1
0
2
0
1
0
0
2
0
1
1
0
0
2
1
1
0
0
1
0
2
0
2
1
1
2
2
0
0
2
1
1
2
0
0
1
0
2
2
2
1
1
1
1
2
1
2
1
1
2
0
1
2
0
0
1
2
1
0
1
1
0
1
1
0
1
0
0
2
0
2
0
0
2
1
1
1
2
2
1
2
1
2
0
1
0
1
1
0
0
1
2
1
1
2
0
1
1
0
0
0
2
2
0
0
2
1
1
3
2
2
2
1
1
1
0
1
0
0
1
1
1
0
0
0
0
0
1
0
1
0
0
1
3
1
2
0
0
1
1
2
1
1
1
0
1
2
1
2
2
1
1
1
0
1
2
0
0
1
2
1
0
2
1
1
1
0
0
1
1
1
2
0
2
1
1
1
1
0
1
1
1
1
1
0
1
1
1
0
1
0
0
2
0
2
0
2
0
0
2
1
2
2
0
0
1
0
1
1
0
1
1
1
1
1
0
1
0
0
2
1
2
0
0
2
1
0
0
1
1
0
1
3
0
2
2
0
0
1
1
2
2
1
2
1
0
0
2
0
2
0
1
1
1
2
1
0
1
0
2
1
1
2
0
0
2
1
0
0
0
0
2
1
0
0
1
1
2
1
2
0
1
1
0
0
0
1
2
0
2
1
0
1
0
1
0
0
1
0
0
0
0
0
1
1
1
0
0
2
1
0
1
1
0
2
1
0
0
2
1
0
2
0
1
1
0
2
0
1
1
1
0
0
0
2
2
2
0
1
1
0
2
0
0
1
2
2
2
3
0
1
2
0
1
0
1
2
0
1
1
2
2
0
1
1
0
2
0
2
1
1
1
0
2
1
1
1
0
1
2
2
0
1
1
0
1
0
0
1
0
1
2
2
2
2
2
2
1
1
1
1
1
0
1
1
0
1
0
1
0
0
0
1
1
0
0
1
1
0
0
2
0
2
1
3
0
1
0
1
2
0
0
1
0
1
2
0
1
1
1
1
0
1
1
1
2
2
0
1
1
1
0
2
1
0
0
1
2
2
1
1
2
0
0
0
1
1
0
1
1
0
0
1
2
0
1
0
0
1
2
1
0
0
1
1
1
1
1
1
1
1
1
1
1
0
2
1
2
1
1
0
0
1
1
0
1
0
2
1
0
1
1
1
1
0
0
2
1
2
0
1
2
1
2
1
2
2
0
2
2
1
2
1
0
0
0
0
0
1
0
2
0
1
1
2
1
1
1
0
2
1
0
2
0
1
1
1
0
0
0
1
0
1
0
1
0
1
0
1
1
0
1
0
2
0
2
1
0
0
0
0
0
2
1
0
1
0
0
2
1
0
1
2
2
0
0
0
1
0
2
2
1
0
1
1
2
3
0
1
2
1
0
0
1
0
2
0
1
0
0
1
0
0
1
0
0
2
0
0
0
2
1
0
1
1
0
2
2
1
1
0
0
0
1
0
1
0
0
0
1
0
1
1
0
1
2
0
2
0
0
1
1
1
0
0
2
0
1
0
1
1
1
0
2
1
2
0
0
1
2
1
1
1
0
1
1
1
1
0
0
1
0
7
2
0
0
2
0
1
1
0
1
0
1
1
2
2
2
1
1
0
0
1
2
1
0
1
0
1
1
3
2
0
0
1
0
0
1
0
0
0
2
0
0
1
1
1
1
1
0
2
1
0
0
1
1
0
0
0
1
2
1
0
2
1
0
1
1
1
2
1
0
0
0
2
0
0
0
1
0
3
1
1
1
0
2
0
1
0
1
1
1
2
2
0
0
2
2
0
0
1
0
0
2
1
0
1
0
1
2
0
1
0
1
0
1
1
0
1
0
1
1
1
4
0
0
0
1
1
1
0
1
1
1
2
2
1
2
1
1
0
1
2
1
1
1
1
1
1
0
1
0
1
1
2
2
0
0
1
1
0
3
0
1
2
2
1
1
2
3
1
1
1
1
1
2
3
1
0
0
0
2
1
1
0
1
1
0
0
0
1
1
1
1
1
0
0
2
1
0
0
0
2
0
2
1
1
0
1
2
1
0
0
3
0
1
1
2
1
1
0
1
1
1
1
3
0
0
0
1
2
0
1
0
1
1
1
0
0
2
2
1
0
0
1
0
1
0
1
0
1
2
2
2
1
0
0
1
2
1
1
0
1
2
1
0
1
1
0
1
0
1
0
0
1
1
1
1
1
0
0
1
1
1
1
1
1
0
2
0
2
0
1
0
0
0
1
0
1
0
1
1
1
1
0
1
1
1
1
1
2
0
1
0
0
1
1
0
0
1
2
1
0
1
2
2
0
1
1
3
0
0
1
2
1
1
0
2
1
2
2
2
0
1
0
0
0
1
0
1
1
0
2
0
0
2
1
2
2
3
1
1
2
0
3
1
0
2
1
1
0
1
1
0
0
1
1
1
1
2
0
1
1
1
0
2
1
0
1
0
0
1
0
1
0
1
0
1
1
0
3
1
2
0
0
1
0
0
0
1
1
2
1
1
1
1
1
1
0
1
2
2
1
0
0
1
1
1
1
0
1
0
1
1
1
0
0
1
1
2
0
1
0
1
0
1
1
1
0
2
2
1
1
2
1
1
1
1
1
4
2
2
2
2
1
1
1
0
1
0
2
0
2
0
0
0
0
1
1
1
2
0
2
1
2
1
0
2
2
0
1
0
0
1
0
1
2
2
2
0
3
1
0
1
10
0
1
2
1
0
0
0
1
0
2
2
0
1
2
2
1
0
2
0
2
2
0
0
0
0
1
0
0
1
2
2
2
2
2
1
0
2
0
0
2
1
1
1
1
0
0
1
1
0
2
0
0
0
1
1
1
0
2
1
1
1
1
2
0
1
1
1
4
1
2
0
0
0
1
1
1
1
1
1
3
0
0
2
2
0
0
1
2
1
0
1
2
2
1
1
0
0
0
0
2
1
2
1
1
1
2
1
0
3
2
2
1
1
0
3
0
2
0
3
0
1
0
0
1
1
1
0
0
1
1
1
1
1
0
2
2
0
2
1
3
0
2
1
0
2
1
0
0
0
1
0
0
1
2
1
0
1
2
0
0
1
2
1
0
2
1
0
1
1
1
1
0
0
0
3
1
2
2
1
1
2
2
0
1
1
2
2
0
1
0
2
0
2
0
1
0
1
1
0
1
2
1
2
1
1
0
1
0
1
1
2
0
1
0
1
1
0
1
1
1
0
1
2
0
1
0
0
1
0
1
1
1
2
0
0
1
1
1
1
1
1
2
1
0
0
0
0
1
0
2
1
0
1
0
0
2
1
1
2
1
0
3
1
0
2
2
2
0
0
0
1
3
2
1
1
0
0
1
3
1
0
0
1
1
0
1
1
0
0
1
0
0
0
2
2
0
1
1
1
1
0
1
0
0
0
0
1
2
2
2
1
0
0
1
1
2
2
2
1
2
0
2
1
2
2
2
2
1
0
1
1
1
2
0
0
1
2
2
1
1
2
0
2
0
0
1
1
1
1
1
2
0
1
2
0
1
1
0
1
2
0
1
1
2
1
1
1
1
2
1
1
0
1
1
1
1
1
0
0
0
2
0
0
4
0
0
0
1
2
0
0
0
0
0
1
2
0
0
1
0
1
0
2
1
0
2
2
1
1
1
1
1
0
1
0
1
0
1
1
1
2
0
2
0
1
2
1
1
2
1
2
2
0
1
0
1
2
1
1
4
0
0
1
0
0
2
2
0
1
1
0
0
1
1
2
0
0
1
2
2
2
1
2
0
0
1
0
1
0
0
1
1
0
1
0
1
2
1
1
2
2
0
1
2
1
0
0
0
1
0
1
1
0
2
1
1
1
1
2
0
2
1
1
1
2
1
2
0
5
0
0
1
1
1
2
1
2
1
1
1
0
1
1
1
1
0
0
1
1
0
0
1
2
1
2
1
1
1
1
1
0
1
0
2
0
3
1
0
0
1
1
0
0
0
0
1
1
0
1
0
0
1
1
1
2
2
2
1
0
0
0
1
0
1
0
1
1
2
2
2
0
2
1
0
1
0
0
0
1
1
2
2
0
1
0
1
0
1
1
0
0
0
0
0
2
2
2
0
0
0
0
0
0
2
0
1
1
2
0
1
2
2
3
1
0
1
0
0
0
1
2
2
1
2
0
0
0
1
1
1
1
2
0
0
1
2
2
2
3
0
1
0
0
2
1
1
0
0
0
0
0
0
2
2
0
0
0
1
0
0
1
2
0
1
0
1
0
1
1
1
2
1
1
0
1
1
0
1
0
0
1
0
1
1
2
0
1
1
1
2
0
1
0
1
3
1
3
2
0
1
3
1
1
1
1
1
0
0
0
2
0
2
0
1
1
0
1
1
2
1
1
0
1
1
2
1
1
1
1
2
1
1
1
0
2
0
0
2
1
1
1
1
1
1
1
1
2
2
0
0
1
2
2
1
1
1
2
3
0
1
2
0
1
1
1
1
1
1
1
0
1
2
1
0
1
0
0
2
1
1
2
0
1
2
1
1
2
0
1
1
0
2
0
2
1
2
2
0
0
0
0
1
0
1
0
1
2
1
1
1
0
1
1
0
1
0
0
1
2
2
1
1
0
1
1
1
2
1
1
0
0
2
0
0
0
2
1
0
2
1
0
1
1
0
0
0
1
1
1
0
2
2
0
1
1
2
1
1
2
1
2
1
1
1
2
1
1
0
2
1
0
1
2
1
2
1
0
0
0
1
0
1
1
2
1
0
2
0
2
0
0
1
1
2
0
1
1
1
0
2
1
1
2
0
2
2
0
1
1
2
0
0
1
0
1
1
0
1
2
2
2
0
0
2
1
1
0
2
1
0
1
2
0
1
0
0
2
0
1
0
2
2
2
0
2
1
1
1
1
0
2
1
1
0
0
0
0
0
1
1
2
1
2
1
0
0
0
2
2
2
1
3
1
2
1
0
2
1
2
0
2
2
0
0
1
0
1
0
0
1
1
0
2
1
1
0
1
2
2
0
1
1
1
1
2
0
0
0
2
1
2
0
0
1
2
1
1
2
2
1
2
1
0
0
1
1
1
1
0
1
1
1
1
1
2
0
0
1
0
1
1
0
1
0
0
2
0
2
1
0
1
0
0
1
1
2
1
0
1
0
1
1
1
1
0
0
0
1
1
2
1
2
0
2
0
1
2
1
1
1
2
1
1
0
2
2
1
0
1
1
0
0
1
2
2
1
2
1
1
0
1
1
2
1
0
0
0
2
0
0
0
1
1
2
0
1
2
1
1
0
2
2
1
1
0
0
0
1
1
1
1
2
1
1
1
1
0
1
1
2
0
1
1
1
2
2
2
0
1
1
1
1
0
1
1
1
0
1
0
2
0
2
1
1
1
1
1
0
2
1
1
2
1
0
2
1
1
1
0
1
1
0
1
0
1
1
1
2
0
0
1
2
1
2
1
2
0
1
2
1
1
0
2
0
0
1
2
0
1
1
2
2
1
1
0
0
1
0
1
0
0
0
0
0
1
2
1
2
2
0
0
0
1
3
2
0
1
2
1
0
1
0
1
2
0
1
1
2
0
1
0
1
1
2
1
0
0
0
1
1
2
1
0
0
2
1
1
2
1
0
1
2
0
0
1
0
0
1
1
0
1
2
1
1
0
2
0
1
0
1
1
2
0
1
1
1
1
0
2
1
2
3
2
1
1
1
1
2
1
1
1
2
1
1
1
0
0
1
2
1
1
1
0
1
1
1
1
1
1
0
2
0
1
1
1
1
0
0
2
1
2
0
0
2
1
1
2
0
0
0
1
1
1
2
2
2
0
0
0
1
2
1
0
1
1
0
0
1
1
1
1
0
0
0
0
0
1
2
1
6
1
0
2
1
1
0
1
1
0
3
0
0
0
0
0
1
0
1
1
1
2
2
1
2
0
1
2
1
2
1
1
2
0
1
1
1
2
1
1
2
1
2
1
0
0
1
0
0
1
2
0
1
1
0
1
1
1
1
1
1
0
1
1
0
2
0
0
1
0
1
0
1
1
2
1
0
0
1
0
0
1
1
2
2
0
0
1
1
0
0
0
1
2
3
1
0
0
0
1
0
1
2
0
1
0
1
0
1
1
1
0
2
0
2
1
3
2
1
2
1
2
2
0
1
0
0
1
0
1
2
3
1
0
1
0
1
1
0
1
1
0
1
2
2
1
1
1
2
0
1
0
1
0
0
0
1
2
0
1
1
1
0
0
2
1
2
1
1
2
0
1
0
2
0
1
1
1
0
0
0
0
0
1
1
1
2
2
1
1
0
1
2
2
0
2
1
0
1
1
1
1
0
1
0
1
1
2
1
0
3
3
1
1
0
1
0
2
1
1
0
2
2
1
0
2
1
0
0
0
1
0
0
2
2
0
0
0
2
1
1
1
0
0
1
1
1
1
2
0
1
0
1
1
1
1
0
2
0
0
2
1
0
0
2
0
1
0
0
1
1
0
0
2
1
0
0
1
1
0
0
2
2
2
1
1
1
3
2
0
1
2
1
1
0
2
0
2
0
0
1
1
0
0
1
1
0
1
2
2
2
1
1
1
0
2
2
2
0
0
1
1
1
1
0
0
1
1
1
2
2
1
2
1
1
2
0
1
1
2
1
1
1
1
0
1
0
1
2
0
0
1
2
2
0
1
0
1
0
1
1
1
2
1
0
1
0
2
1
0
0
2
0
0
2
0
1
1
0
1
1
1
1
1
1
0
0
0
0
2
0
0
0
0
0
1
1
1
0
1
1
0
1
3
1
1
1
2
1
0
0
0
2
1
0
0
0
1
1
0
0
2
2
0
0
1
3
1
0
0
0
0
1
1
1
1
1
0
1
0
0
1
0
0
0
0
1
1
0
1
0
1
0
0
1
1
1
0
9
0
1
1
2
0
3
2
2
2
2
1
1
1
1
0
1
1
2
0
2
1
0
2
1
1
0
2
0
0
1
2
2
2
2
1
0
1
0
2
0
1
1
2
1
2
1
2
3
2
0
0
0
1
0
2
0
2
2
2
1
2
1
2
1
0
0
0
0
0
0
0
1
1
0
1
1
1
0
2
0
2
1
0
1
2
1
1
1
1
0
2
0
2
1
2
2
5
0
1
0
1
2
1
0
0
0
2
2
1
1
1
1
0
1
1
0
0
0
1
1
2
1
1
1
1
1
2
2
1
1
1
0
0
2
1
0
4
0
0
0
1
1
2
0
1
0
0
0
0
2
1
0
1
3
0
0
1
2
1
0
0
0
1
2
0
1
1
2
2
1
1
1
1
1
0
1
1
1
0
1
2
0
1
2
1
1
0
1
0
2
1
0
1
1
2
1
0
2
2
2
1
3
0
1
1
0
2
0
1
1
1
2
0
1
3
1
1
1
2
1
0
0
2
2
2
1
2
1
1
1
1
2
1
1
0
1
2
0
1
1
0
1
1
0
0
0
1
1
0
2
1
1
0
1
1
1
0
1
1
1
1
2
1
2
0
6
1
1
0
1
0
0
1
1
1
0
2
1
0
0
1
0
0
2
1
1
3
1
0
1
1
0
2
1
0
1
1
1
0
2
2
1
2
1
0
0
1
1
0
1
1
0
0
1
2
1
2
0
1
1
2
2
1
2
1
0
1
2
2
1
0
0
0
0
1
1
1
0
1
3
1
1
2
2
2
1
0
0
2
0
0
1
0
0
1
0
2
0
1
1
1
1
3
2
0
0
0
0
0
2
2
1
1
0
2
0
1
2
2
2
2
2
0
0
1
1
0
1
1
2
1
1
1
3
1
2
1
0
2
1
1
1
0
2
0
1
0
0
1
1
3
0
0
1
1
2
0
1
0
2
0
0
1
0
1
1
0
0
0
1
2
1
0
2
1
2
2
2
0
1
2
1
0
1
2
2
0
1
1
0
2
0
1
1
2
1
0
1
2
0
0
2
0
2
0
1
1
0
1
0
1
1
1
1
1
1
1
0
1
1
1
1
0
1
2
1
0
1
0
0
2
0
1
0
0
0
1
1
2
0
1
0
1
0
1
0
1
1
1
1
2
0
0
1
2
0
1
2
1
1
1
1
2
1
2
0
0
0
0
1
0
1
1
1
0
1
1
1
1
2
0
0
1
0
1
1
1
1
0
0
1
2
1
1
0
0
0
0
0
0
0
0
0
1
1
0
1
2
0
1
0
0
1
1
1
1
1
0
1
1
1
0
2
0
2
1
0
0
0
1
0
2
1
0
2
0
2
0
2
1
0
1
1
1
1
1
1
1
1
0
0
0
0
2
0
1
1
0
2
2
2
0
2
2
1
1
2
0
0
1
0
1
1
1
1
2
0
1
2
1
0
2
1
1
0
0
1
3
0
0
1
0
1
0
0
1
1
1
2
1
1
2
1
1
1
3
1
1
0
0
0
0
0
0
1
2
0
2
2
1
0
1
2
0
1
2
1
1
0
2
1
1
0
1
2
2
1
2
0
1
2
1
1
0
1
2
2
1
0
0
2
0
0
1
2
0
2
1
0
1
1
2
1
1
1
1
2
1
0
3
2
2
2
0
0
0
1
1
1
1
1
1
0
1
1
0
1
2
2
2
1
0
2
2
0
0
1
1
1
1
1
1
0
0
1
2
1
1
1
1
2
1
0
1
0
0
2
0
0
1
1
2
2
0
1
1
0
1
2
1
0
1
0
1
0
2
0
2
1
0
0
1
0
2
1
1
1
2
2
1
0
2
1
1
0
0
0
2
2
1
1
1
1
1
1
1
0
1
2
2
2
2
0
1
0
0
0
2
1
0
2
1
2
0
1
0
2
2
2
1
0
1
0
2
1
1
1
1
0
2
1
2
2
0
0
1
1
1
2
1
0
1
0
3
1
0
3
1
2
1
1
2
0
0
1
0
1
1
1
1
1
0
1
1
1
1
0
2
2
2
1
1
3
0
2
1
0
1
0
2
0
1
0
1
0
0
0
1
1
1
2
2
1
0
1
1
0
1
1
1
0
1
1
1
0
1
2
0
1
0
2
2
1
1
1
1
1
2
1
2
0
1
0
1
0
0
1
0
1
2
1
1
1
0
0
2
1
2
0
1
0
1
1
0
0
0
1
0
2
2
1
0
1
0
1
1
2
1
1
1
0
1
0
1
0
1
2
0
2
1
1
0
0
1
1
1
0
1
1
1
2
1
1
1
0
0
2
1
1
1
1
1
1
0
0
0
2
0
0
1
1
0
0
2
1
1
1
1
1
1
1
1
0
3
1
1
1
1
0
1
1
2
2
1
0
0
0
2
1
2
1
0
1
1
0
2
0
0
0
2
2
2
0
0
0
1
1
0
0
1
2
1
1
0
0
0
0
1
1
1
0
2
2
2
0
2
0
0
0
1
2
3
1
1
0
2
2
0
0
2
3
0
1
1
0
1
1
2
0
1
1
2
1
2
1
0
1
0
3
1
1
1
2
1
1
2
0
2
0
1
1
0
2
1
0
1
1
0
2
2
2
0
0
1
1
0
1
1
0
0
0
0
1
2
0
1
2
2
1
1
0
0
1
1
1
0
0
0
2
1
1
1
1
2
1
1
0
1
1
0
1
1
1
0
0
2
1
2
0
1
1
2
0
2
1
1
1
2
2
2
2
1
1
1
1
1
1
1
0
0
2
1
0
1
1
0
0
1
1
0
0
0
1
2
1
0
2
2
0
1
0
1
1
2
2
1
0
2
0
2
0
0
1
2
1
4
0
2
2
1
1
2
1
1
1
1
2
0
0
1
1
0
2
1
1
0
1
1
3
2
1
2
0
0
1
1
0
2
2
0
0
2
0
0
0
1
1
2
1
2
2
1
0
2
0
1
2
1
0
2
0
0
3
1
1
1
0
2
0
2
1
0
1
1
0
2
2
1
0
0
1
1
3
3
1
0
1
1
1
2
0
2
0
2
1
1
0
1
2
1
1
2
1
0
1
1
0
2
0
0
1
0
0
1
0
0
1
2
1
2
1
0
1
0
2
1
1
2
2
0
0
1
0
0
1
2
0
0
0
2
2
1
0
1
1
0
2
0
1
0
1
0
1
2
1
2
2
0
2
0
2
2
1
0
1
2
2
1
0
1
1
1
2
1
1
0
0
0
1
2
0
0
1
0
1
2
1
0
1
2
2
0
0
2
1
0
1
2
1
1
1
1
0
2
2
1
1
0
1
1
1
2
1
2
1
1
0
1
0
1
0
1
0
0
2
1
2
2
2
0
3
2
0
1
0
2
0
2
0
1
2
4
2
2
0
2
1
1
1
2
1
2
1
0
1
2
0
1
0
0
0
0
0
1
1
2
0
0
0
0
1
1
1
1
1
2
3
0
0
2
1
2
0
2
3
1
1
1
2
2
2
1
0
0
1
0
1
1
2
0
0
1
0
1
0
1
1
0
1
0
1
0
0
1
0
2
0
1
1
0
1
2
2
1
0
1
0
0
0
1
1
1
1
1
0
1
0
1
2
1
1
1
2
2
1
1
1
1
1
0
1
1
1
1
2
0
2
1
0
1
2
2
0
0
3
0
4
0
1
2
1
1
1
2
1
1
1
0
1
0
1
2
1
1
2
1
0
2
1
1
1
0
2
1
2
1
0
0
0
2
1
0
1
2
1
2
2
0
2
0
0
0
0
0
0
1
1
0
0
2
1
1
2
2
1
0
1
1
1
1
2
1
1
0
2
1
2
0
1
0
0
0
1
0
1
0
2
0
2
2
0
1
1
1
1
0
0
1
0
0
1
1
1
1
2
1
2
1
0
0
1
0
1
1
2
1
1
1
1
0
1
0
0
1
1
2
2
0
0
0
1
1
0
0
3
1
0
0
1
2
1
1
1
0
1
2
0
1
1
1
1
1
1
0
0
0
1
1
1
2
1
0
1
1
2
0
2
0
1
0
0
1
0
0
2
0
1
1
1
1
1
1
1
2
2
2
2
0
0
2
2
1
2
1
0
2
0
1
0
1
0
2
0
1
1
1
0
2
0
0
1
2
0
2
0
1
1
0
0
1
1
2
0
0
0
0
1
2
2
1
1
0
1
1
0
1
2
1
1
0
2
1
1
3
2
1
1
1
0
0
1
0
1
1
0
0
2
2
1
1
1
1
2
0
0
0
1
0
1
1
1
1
1
2
1
2
0
1
2
1
0
0
1
0
1
1
2
0
0
3
2
1
2
2
1
0
2
2
1
2
0
2
1
1
2
0
1
1
1
1
0
2
0
1
1
0
0
0
0
2
2
1
0
0
0
1
1
1
2
1
1
0
1
1
1
1
0
2
1
2
1
1
1
1
0
2
0
2
1
1
1
1
2
0
0
0
0
0
1
1
0
2
1
0
0
0
0
0
0
1
0
0
1
1
2
0
2
1
0
0
0
2
0
2
1
1
0
0
1
0
2
2
1
2
0
1
1
1
1
1
0
1
1
1
1
1
1
1
0
0
0
0
0
0
1
2
1
0
0
1
0
0
1
0
6
0
0
1
0
0
1
0
1
2
1
0
1
1
2
0
1
1
0
1
0
2
1
2
0
0
1
1
1
1
1
1
1
0
1
0
2
1
0
1
1
1
1
1
0
1
2
2
0
1
1
1
1
1
0
1
1
1
2
1
1
2
0
1
0
1
1
1
2
1
1
0
0
0
0
1
0
0
0
1
1
1
1
3
2
0
1
1
0
0
1
1
2
2
0
2
1
2
2
1
0
0
0
0
0
2
2
0
1
0
1
1
2
1
2
1
1
2
1
0
0
1
1
0
0
1
0
0
0
1
1
1
0
1
0
1
1
2
0
1
1
1
0
2
0
1
0
1
0
0
1
0
1
0
2
2
1
1
2
0
2
1
1
1
2
2
1
2
0
1
1
0
0
1
1
1
0
1
0
1
1
0
0
1
1
0
1
1
0
1
0
1
1
0
0
2
1
0
2
1
0
2
0
1
1
1
1
0
1
0
2
1
0
1
0
0
1
1
3
2
1
1
0
1
1
0
0
1
2
1
1
1
0
2
0
0
1
1
1
1
1
2
0
2
2
0
0
2
2
3
2
0
2
0
0
0
0
1
1
2
1
0
0
0
1
2
1
1
0
2
2
1
2
0
1
1
1
0
0
1
3
0
1
1
0
0
1
2
1
1
1
1
1
1
1
1
1
1
1
1
2
0
0
1
0
1
1
1
1
0
1
1
1
2
0
2
2
0
0
1
1
1
0
0
1
0
1
0
0
0
1
1
2
2
0
0
0
0
1
1
2
0
1
0
0
1
1
1
2
1
1
2
0
1
0
2
1
1
1
0
3
1
1
1
1
0
1
1
0
0
1
2
1
0
0
1
1
0
2
1
0
0
1
2
2
0
1
1
2
2
0
1
0
0
1
1
1
0
0
2
0
0
2
0
3
2
1
2
2
1
0
2
1
1
2
0
1
0
1
2
1
0
0
1
0
0
1
2
1
1
3
1
2
0
1
0
1
1
1
1
1
1
1
1
0
1
1
2
1
0
1
2
1
1
0
2
0
1
0
1
1
0
1
0
0
1
2
1
2
2
0
0
1
0
1
1
1
0
2
1
0
1
1
2
2
2
0
0
2
1
1
1
1
0
0
0
1
2
1
1
2
0
0
0
1
1
0
1
0
0
1
0
2
1
1
1
1
1
1
0
2
0
0
2
0
1
0
1
1
0
1
1
1
2
0
1
1
0
1
1
2
0
2
1
0
2
0
1
0
0
1
0
0
0
1
0
1
1
1
1
1
2
1
1
2
1
0
0
1
0
2
0
0
2
1
1
2
1
0
2
0
1
1
2
3
0
0
0
1
1
0
0
1
2
0
1
1
1
2
1
1
0
1
1
1
0
1
0
1
1
0
1
1
2
1
0
1
1
1
0
0
0
1
0
0
2
0
0
1
2
0
0
2
1
1
2
0
1
0
1
2
1
1
1
0
1
2
0
2
0
1
1
0
2
0
0
0
1
0
0
1
2
2
1
0
1
0
1
0
0
1
3
0
2
2
1
2
1
0
1
0
0
0
2
1
0
0
0
2
1
0
1
2
0
0
2
2
1
1
0
1
1
2
2
0
2
1
0
1
0
2
1
1
1
2
0
0
1
0
1
0
0
1
0
2
0
2
0
0
0
1
1
1
1
2
3
2
2
1
1
0
2
0
2
0
0
0
0
0
2
1
1
1
0
0
2
0
1
1
1
0
0
1
2
1
0
0
1
1
3
0
0
1
1
1
1
1
1
1
1
2
0
1
1
0
2
1
0
1
1
1
2
2
0
2
0
2
1
1
1
1
2
1
1
0
2
2
2
0
0
2
1
1
3
2
1
0
0
1
2
2
1
1
1
1
0
2
1
2
0
1
0
0
1
0
1
2
0
1
0
1
0
1
0
1
1
1
0
0
1
1
2
1
2
0
2
1
2
1
0
1
1
0
0
1
1
1
1
1
0
2
2
1
1
1
0
2
1
0
0
0
1
0
1
0
0
1
1
3
1
2
1
2
1
2
3
2
1
2
1
1
1
0
1
2
1
1
1
2
1
1
0
1
2
0
1
0
0
1
0
1
0
2
0
1
2
1
0
2
0
1
1
0
1
2
0
1
4
1
2
2
0
0
0
2
1
0
1
2
2
1
2
0
1
0
0
1
1
0
1
0
1
2
0
2
0
1
1
0
2
1
0
0
3
1
1
0
1
2
2
1
1
1
0
2
1
0
1
1
2
1
1
0
1
0
1
2
0
1
2
1
2
2
1
0
1
2
2
1
2
2
0
1
1
1
1
2
0
1
1
0
2
0
2
1
0
0
2
1
0
2
1
2
0
1
0
0
2
1
1
1
0
1
1
0
1
1
0
1
1
1
2
2
2
0
0
0
1
2
1
0
1
1
2
0
1
1
1
1
2
0
1
0
2
1
1
0
0
1
1
1
1
0
0
1
2
2
1
1
1
2
1
1
1
0
0
1
2
1
0
0
1
1
0
3
2
1
0
0
1
1
2
2
2
1
1
1
0
0
2
0
0
1
1
0
1
0
2
1
1
2
2
0
0
1
1
2
3
0
2
1
0
1
0
2
2
0
0
1
2
0
2
2
1
1
2
0
0
1
1
2
0
1
0
0
0
2
1
1
0
1
1
1
0
0
1
1
0
1
1
2
2
1
0
0
1
2
0
0
2
0
1
0
1
1
1
0
1
0
0
0
0
1
2
0
0
0
0
1
0
1
2
1
1
2
1
2
2
0
1
1
1
0
2
2
0
0
0
1
1
2
0
1
1
1
1
2
2
0
2
1
1
1
1
1
0
2
1
1
0
2
1
0
0
2
3
0
1
1
1
1
3
0
1
1
2
1
2
1
0
0
0
1
0
1
2
1
2
2
2
0
0
2
8
2
1
0
0
0
2
1
0
0
2
0
0
2
1
2
1
0
2
1
2
1
3
0
1
2
1
0
0
0
2
0
1
2
0
2
0
1
0
0
1
2
2
0
1
3
0
2
2
2
0
0
2
0
0
0
1
0
2
0
0
2
0
4
0
0
1
0
0
1
1
0
1
1
1
0
1
0
0
0
1
3
0
2
1
3
1
1
1
2
0
1
1
0
0
1
1
2
0
1
0
1
1
1
1
2
1
2
1
0
0
1
1
1
1
2
1
1
1
0
2
1
1
1
1
0
2
0
1
2
0
1
1
2
0
1
1
0
1
2
0
0
1
1
2
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
2
1
0
0
0
1
2
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
2
0
0
1
1
1
2
2
3
1
0
0
1
0
1
0
1
0
2
1
2
1
3
1
1
1
2
1
0
1
1
1
1
0
2
2
0
0
1
1
2
1
0
1
1
1
2
1
2
0
1
1
1
0
0
0
1
1
2
0
0
1
2
0
0
0
1
2
1
1
2
1
0
1
1
1
1
1
2
0
2
1
1
0
1
2
1
0
1
2
2
0
1
2
1
1
1
0
0
0
0
1
0
0
0
2
2
2
0
0
1
0
2
0
0
0
0
1
1
1
1
1
1
0
1
0
1
0
1
1
2
1
0
2
1
0
2
1
1
1
2
0
0
1
1
1
0
2
2
1
2
0
3
1
2
0
0
0
1
2
1
1
2
1
1
1
2
1
0
1
1
0
1
1
1
1
1
1
1
1
0
0
1
1
0
0
0
0
2
0
1
0
0
1
1
1
0
1
2
0
2
0
1
1
0
2
1
1
1
1
0
1
0
1
2
0
1
1
0
2
1
0
1
1
2
2
2
2
1
1
2
1
1
1
1
1
0
1
1
0
0
1
1
1
1
1
0
0
2
2
2
0
1
1
1
0
1
2
2
1
0
2
2
2
1
1
2
0
2
1
2
1
0
1
0
2
1
0
0
1
0
0
1
0
2
1
1
0
0
1
1
1
1
1
1
1
1
1
1
1
0
2
1
0
0
2
0
0
1
1
1
1
3
1
1
0
1
2
2
1
2
1
1
1
1
1
2
1
1
1
0
1
0
1
2
1
0
1
0
1
0
0
0
2
1
2
2
3
0
1
4
1
0
2
1
0
1
1
0
2
0
1
0
1
1
1
2
0
1
1
1
2
0
0
1
0
0
2
1
2
1
2
2
1
0
0
2
1
0
0
1
0
0
3
2
1
0
1
2
0
1
1
0
2
3
1
0
1
0
1
0
1
1
0
1
2
0
1
0
1
0
2
2
1
2
0
1
2
2
0
1
0
0
1
0
2
1
1
1
1
1
1
0
1
1
2
0
0
2
1
2
0
0
0
0
1
1
0
2
0
1
0
0
2
0
2
2
3
0
0
2
0
0
2
1
3
2
2
1
1
1
1
0
2
0
0
2
1
0
1
1
0
1
2
1
1
0
2
1
2
0
1
1
1
2
1
1
0
1
0
1
0
1
2
0
1
1
2
2
1
1
2
2
0
0
0
1
0
2
0
1
1
2
1
2
3
0
1
1
0
0
0
2
0
1
0
2
1
1
1
0
1
0
0
1
2
1
0
1
1
1
2
1
1
0
0
1
1
2
2
1
1
2
0
1
1
0
1
0
0
3
2
2
1
0
1
2
2
1
1
2
0
0
1
2
1
1
0
2
0
2
2
0
2
0
0
2
1
0
2
2
0
1
6
1
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
2
1
1
2
0
2
0
1
0
1
1
2
2
0
2
1
1
1
1
1
5
2
1
1
0
0
1
3
0
3
0
0
1
1
0
1
1
1
1
0
2
1
1
1
1
0
2
0
1
0
0
2
1
3
2
0
1
1
1
1
1
0
1
0
0
0
0
1
1
2
0
2
1
0
1
1
0
0
0
1
1
1
0
1
0
1
1
2
1
1
0
1
0
0
0
1
0
0
0
1
2
0
0
2
1
0
1
2
0
2
2
1
0
0
2
1
2
0
0
1
0
1
2
1
0
1
2
1
1
1
0
1
2
1
2
1
2
1
1
1
1
0
1
0
2
0
2
2
0
1
2
2
0
1
1
0
0
0
1
1
2
1
1
1
1
1
1
0
0
0
2
0
1
0
0
1
0
1
0
1
0
1
2
1
0
0
2
0
2
0
0
2
0
0
2
0
1
0
0
2
0
1
0
2
1
0
0
0
0
1
1
2
1
2
1
0
0
2
1
0
2
0
0
0
1
1
0
2
2
2
1
1
0
0
0
1
1
0
0
1
0
2
2
1
1
0
1
1
3
0
2
1
0
1
0
1
1
2
1
1
3
0
0
0
0
2
1
1
2
0
2
1
1
2
2
0
2
1
1
0
1
1
1
2
1
0
2
0
0
1
1
1
0
0
2
2
1
2
1
2
1
1
1
1
1
1
0
2
0
2
0
1
2
4
0
1
1
1
1
0
1
1
1
1
0
1
0
2
0
1
0
1
1
0
0
0
1
0
1
2
0
1
0
1
1
2
0
0
1
0
2
1
2
1
2
1
1
1
1
0
1
0
1
0
0
0
1
2
1
2
1
1
1
0
0
0
1
2
1
1
2
0
2
2
0
0
1
1
1
0
1
0
1
1
1
1
0
2
1
2
1
2
1
2
0
0
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
0
0
2
1
0
2
1
2
1
2
0
0
0
1
0
1
0
1
0
0
1
1
1
1
0
3
0
1
0
0
2
1
1
1
1
2
1
0
1
1
0
0
1
0
1
0
1
1
0
2
2
0
2
0
1
2
1
0
0
1
1
1
1
2
2
0
2
2
1
0
1
1
1
0
2
0
1
1
0
1
1
0
2
1
2
2
0
1
1
0
0
2
1
1
0
1
1
1
0
0
1
1
1
2
1
0
0
1
1
1
0
1
1
1
0
0
0
1
0
1
0
1
1
1
0
0
2
2
0
1
2
3
0
0
1
2
2
1
2
1
2
1
0
0
0
2
1
1
0
2
1
2
2
0
0
1
2
1
1
1
0
0
1
0
0
2
1
0
2
0
1
0
1
1
2
1
1
1
0
1
1
0
0
1
1
1
2
1
1
1
0
0
0
0
1
0
0
1
1
0
1
1
1
1
1
0
2
0
0
0
1
1
2
2
0
0
0
2
0
2
0
2
1
1
1
2
0
0
0
0
0
0
0
0
1
2
1
2
1
1
0
2
1
1
2
1
0
2
2
0
1
1
0
0
3
0
2
0
2
1
0
1
0
0
1
1
2
1
0
0
1
1
1
2
2
1
0
1
2
1
0
0
3
2
1
1
0
2
0
0
1
0
2
0
1
0
0
2
1
0
0
1
1
0
0
0
0
1
1
1
0
1
0
1
1
1
0
1
2
0
0
1
2
0
1
1
1
0
0
0
1
0
0
0
0
1
2
1
2
2
1
0
2
1
1
1
0
0
0
1
1
1
0
0
1
2
2
0
2
0
2
1
1
2
1
1
0
0
2
2
1
1
0
0
2
0
2
2
0
1
0
2
1
0
1
1
1
0
1
0
0
1
0
1
0
0
1
2
0
0
1
0
0
2
1
1
0
2
2
1
2
1
1
0
0
0
0
1
0
2
1
1
1
0
1
1
2
0
1
1
2
0
1
3
2
0
0
1
2
0
0
1
1
1
1
0
2
1
1
0
1
1
0
1
0
1
2
0
1
1
1
1
1
0
0
2
0
0
1
0
0
2
2
0
0
1
2
0
1
0
1
1
4
0
0
1
1
0
1
1
0
2
1
0
0
0
1
2
1
2
0
1
0
1
1
0
2
1
1
1
2
2
1
0
1
0
2
0
2
0
7
1
2
1
3
1
2
0
1
1
0
0
0
1
1
2
1
1
0
1
0
1
0
0
0
2
0
0
3
0
2
1
2
1
2
0
2
0
0
1
0
1
2
1
1
1
2
0
2
2
1
0
1
2
0
0
1
1
0
1
1
1
1
1
2
0
1
1
1
1
1
0
0
0
0
1
1
1
0
1
1
0
1
2
2
2
1
2
0
1
2
1
1
1
1
0
0
0
1
1
0
1
1
1
2
1
1
0
1
2
2
2
1
1
1
0
2
0
2
0
1
2
2
1
1
1
1
0
2
1
1
2
2
0
1
1
0
1
2
1
2
1
1
1
1
1
0
0
2
0
1
2
2
1
0
1
4
0
0
1
0
1
0
1
1
0
2
2
2
2
0
1
1
1
1
0
0
1
1
1
1
0
1
2
2
0
1
1
1
0
1
1
2
0
2
1
0
1
1
2
1
0
0
1
2
2
4
1
0
1
1
4
0
1
2
1
0
0
1
0
1
1
1
0
2
1
0
0
1
0
0
0
0
0
1
1
1
1
1
2
1
2
1
0
2
2
0
1
0
0
2
1
1
0
2
1
0
0
1
1
0
0
1
1
2
0
0
0
1
0
1
0
0
1
0
1
2
0
0
1
1
1
0
1
0
1
2
2
2
2
1
1
1
0
1
2
0
0
0
0
1
0
3
2
2
1
1
2
1
1
1
2
2
0
1
2
1
1
1
1
1
0
2
0
1
1
1
1
2
2
0
0
1
2
1
1
1
1
0
0
1
0
2
0
1
0
1
1
0
0
1
2
1
2
0
2
2
0
1
1
0
1
0
2
0
0
0
0
1
0
1
1
1
1
1
0
2
1
0
0
1
0
0
1
0
2
1
1
1
2
2
0
0
0
0
1
0
0
0
1
0
1
2
3
1
1
0
2
0
2
2
0
1
0
1
1
1
1
0
0
0
1
1
1
2
1
1
0
1
0
1
1
1
1
1
1
3
0
1
1
1
1
2
0
0
1
1
2
0
0
1
0
2
1
2
0
1
1
2
2
1
0
0
0
1
0
1
0
2
1
0
0
0
1
1
2
0
1
0
2
1
0
0
1
1
1
0
0
1
0
0
2
1
0
2
0
0
1
1
1
3
2
1
0
2
1
2
0
2
2
0
1
1
1
3
1
1
1
0
1
0
1
1
1
0
2
2
1
1
1
2
1
0
2
0
0
1
0
0
1
1
2
1
2
0
1
1
2
1
0
2
1
2
1
1
0
1
1
0
1
0
2
2
1
2
1
1
0
1
1
1
0
1
0
2
0
1
0
1
1
1
1
1
1
1
0
1
2
0
0
2
1
1
1
0
1
2
0
1
0
1
0
1
0
1
1
2
1
1
1
2
1
0
2
2
1
1
0
2
0
1
1
0
2
0
2
0
1
1
2
1
2
0
1
0
1
1
0
1
0
1
1
1
0
1
4
0
1
0
1
1
2
1
0
1
0
1
1
2
0
0
0
1
1
3
1
0
0
2
0
2
1
0
0
0
2
0
0
0
0
1
0
0
1
1
1
2
1
2
0
1
0
1
0
2
1
0
1
1
1
0
0
2
1
0
1
1
1
0
0
1
1
1
1
1
1
1
1
1
0
2
0
0
1
2
1
0
1
2
1
2
2
1
0
0
1
1
0
1
1
1
0
1
2
0
2
2
2
2
0
1
0
0
1
2
0
2
1
2
1
1
0
1
1
1
1
1
1
2
2
1
2
1
0
1
0
0
0
1
0
2
1
1
1
0
2
0
2
0
1
2
2
0
1
1
1
0
1
0
1
1
0
0
1
0
0
1
1
2
2
0
1
2
0
1
1
0
1
0
1
1
1
0
2
0
0
1
0
2
2
1
0
2
0
1
1
0
0
0
2
3
2
0
0
0
1
0
1
1
0
1
1
0
0
1
2
0
0
1
1
1
1
1
0
1
1
1
2
1
1
0
0
0
1
1
1
1
2
0
1
2
0
0
1
0
1
0
2
1
0
1
0
0
2
1
1
0
0
0
3
0
2
2
0
0
0
2
2
2
1
0
0
1
0
1
1
3
1
2
1
0
0
1
0
0
0
0
1
1
1
1
0
0
1
0
0
2
1
0
1
0
1
2
1
1
1
2
1
1
0
1
0
2
1
0
0
1
2
2
0
1
0
0
2
1
1
2
0
2
2
2
0
1
0
2
1
0
1
0
1
0
0
0
1
1
1
1
1
1
0
2
0
0
2
1
0
1
0
0
0
1
1
2
2
2
1
1
4
0
2
0
0
2
0
0
1
1
0
0
0
1
1
0
1
1
2
0
2
2
0
2
1
0
0
1
2
2
0
2
0
0
1
0
1
0
2
1
1
2
0
0
0
2
1
2
0
1
2
0
2
3
1
0
0
1
1
0
1
0
1
0
0
2
1
0
1
1
2
1
1
2
0
1
1
2
0
0
2
0
1
1
0
1
1
0
1
2
1
1
0
0
0
1
2
0
1
1
0
2
0
1
2
1
2
0
0
1
0
1
1
0
1
1
1
2
1
2
2
1
1
1
0
1
0
1
2
1
0
1
0
2
1
1
2
0
1
0
1
1
2
1
2
1
0
1
1
1
2
1
0
2
1
1
1
0
0
1
1
2
1
1
1
0
2
0
1
3
0
2
0
1
0
2
1
1
1
1
0
0
1
5
2
0
1
2
1
1
2
2
0
1
1
0
1
0
1
0
1
0
1
1
1
2
0
2
1
1
1
0
1
2
1
0
0
0
0
2
2
1
0
1
0
1
2
2
0
1
0
1
1
2
2
1
0
1
2
1
1
0
1
1
1
0
0
0
2
0
1
1
1
2
1
2
2
0
2
0
0
1
1
1
1
0
0
0
0
2
3
0
3
2
1
2
1
1
1
0
2
2
1
1
0
1
0
1
2
1
2
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
1
1
2
1
0
0
0
1
0
0
0
1
0
2
0
3
0
3
1
1
3
1
1
2
1
1
0
0
0
0
1
2
0
1
1
1
1
1
2
1
1
2
1
0
1
1
0
2
1
1
1
1
1
1
1
0
2
2
1
2
0
1
1
0
1
0
2
2
1
1
0
2
1
1
3
1
0
1
0
0
3
0
0
1
2
3
1
0
1
2
2
0
2
0
0
1
0
2
1
0
2
0
1
1
1
1
4
1
2
1
3
0
1
2
2
1
1
1
0
2
1
0
1
2
2
2
0
0
1
0
0
2
0
1
2
1
2
1
1
1
1
0
1
0
0
1
1
0
1
0
0
2
2
1
1
1
1
1
2
0
0
1
2
1
0
1
2
1
2
1
2
1
1
2
1
1
1
0
0
1
2
1
2
0
0
1
0
1
0
1
1
1
0
1
0
1
0
1
1
1
2
1
2
2
0
1
2
2
1
0
0
2
0
1
2
2
1
1
1
1
0
1
1
2
1
1
1
2
1
1
1
1
1
1
1
0
0
1
0
0
1
2
1
0
0
0
1
0
0
1
1
3
1
0
0
2
0
1
2
1
1
1
0
2
1
1
0
1
1
1
0
1
1
1
0
1
1
0
1
2
0
2
1
1
1
0
2
1
0
2
1
2
0
2
0
1
1
1
1
0
0
0
2
1
1
1
1
0
2
1
2
0
2
0
1
2
1
3
2
0
1
1
1
1
0
0
0
1
3
0
1
1
2
1
1
1
0
2
2
1
1
3
2
2
1
2
2
0
2
2
1
0
0
1
1
1
0
2
0
0
1
2
1
1
1
3
2
1
0
1
0
2
1
1
2
2
1
0
1
1
1
0
0
1
0
2
1
2
0
1
1
1
2
0
0
1
2
0
1
1
1
1
2
0
2
2
1
1
2
2
1
2
1
1
0
1
0
1
2
2
0
0
0
2
2
1
1
1
2
0
2
0
1
2
1
1
1
1
2
0
1
0
0
0
0
0
0
1
3
0
1
1
0
0
2
1
2
0
0
0
0
1
0
0
2
2
1
2
1
1
2
2
2
1
1
2
0
2
2
1
0
1
0
0
2
1
2
1
0
0
1
2
2
1
0
2
0
1
0
1
1
0
0
0
1
1
1
0
0
1
2
2
0
0
3
0
1
1
0
0
1
2
2
0
1
0
2
0
0
0
0
0
2
0
0
1
0
1
1
2
1
0
1
1
1
1
2
1
0
0
0
2
2
1
0
0
0
2
1
1
1
0
2
1
1
1
0
0
0
0
1
1
2
1
1
0
0
0
0
1
1
2
1
1
0
0
0
1
2
0
1
0
2
1
0
0
0
0
2
0
1
1
0
4
0
2
0
0
1
0
0
2
0
1
0
0
0
0
1
0
2
3
2
1
2
0
1
2
2
0
1
0
0
1
2
1
2
1
1
0
0
0
0
2
2
2
1
0
1
0
1
0
0
0
2
2
2
0
1
0
0
1
1
2
2
0
1
0
0
1
0
0
1
0
0
0
1
4
1
1
1
0
1
1
1
0
1
0
1
2
3
0
2
2
2
1
0
2
0
0
0
0
1
1
0
2
2
1
1
2
0
1
0
0
0
1
1
1
0
1
2
1
1
0
1
2
0
1
1
1
1
1
0
1
1
2
2
1
2
2
2
0
0
0
1
0
1
1
1
0
2
1
2
0
0
0
2
0
0
1
0
2
0
5
1
1
1
1
1
1
1
0
2
2
1
0
1
0
1
2
0
1
4
0
1
1
1
0
0
1
1
0
1
1
1
1
1
1
2
2
3
0
0
0
2
0
1
0
0
1
2
1
2
1
1
3
0
1
0
0
2
1
2
1
0
0
1
1
1
2
2
0
1
0
1
2
2
0
1
0
0
2
2
0
1
0
2
2
1
0
1
1
1
2
1
4
1
0
0
2
1
1
1
0
0
1
1
1
0
2
0
1
2
0
1
2
1
2
2
1
2
2
0
1
2
0
1
1
0
2
1
0
0
1
0
2
1
1
2
0
0
0
1
2
0
0
1
1
0
1
1
1
1
1
0
1
1
2
0
0
0
1
0
0
1
0
1
1
1
2
0
1
0
2
1
2
1
0
0
0
1
2
0
0
2
1
0
1
0
0
1
1
0
1
2
1
1
0
1
2
1
1
1
0
1
0
1
1
1
1
1
0
0
1
1
0
0
2
1
0
1
0
2
1
1
0
1
1
1
1
0
0
1
0
0
1
1
0
2
0
1
0
1
1
0
0
2
1
0
2
0
0
1
1
1
1
0
1
1
0
1
1
1
0
1
1
0
2
2
1
2
1
1
2
2
1
1
0
0
0
2
1
0
1
0
1
2
0
0
1
1
0
0
1
1
1
0
0
0
1
1
1
1
2
2
0
0
0
0
1
0
0
0
0
2
2
1
0
0
2
1
1
1
1
2
2
1
1
0
1
0
1
1
1
2
0
2
0
1
0
1
2
0
1
0
1
1
1
0
0
0
2
1
2
0
1
1
1
2
0
1
2
0
1
0
0
0
1
1
0
2
2
0
1
0
1
1
1
1
2
0
1
0
1
2
1
0
0
3
0
2
1
2
0
2
1
2
0
1
2
0
0
1
3
2
2
1
2
0
1
0
2
0
1
0
0
1
1
0
2
2
2
1
2
2
1
0
2
1
2
0
3
0
0
1
1
1
0
1
1
1
0
1
1
1
1
2
1
1
1
2
1
2
0
0
0
0
1
4
1
0
1
0
1
0
0
2
2
0
1
1
0
1
0
0
2
0
0
0
1
2
1
1
0
2
1
2
1
1
2
1
1
0
2
2
0
2
0
0
1
2
0
1
1
1
1
2
0
0
2
1
1
0
1
2
1
1
2
0
1
1
0
0
1
2
2
1
2
1
1
0
0
0
1
2
0
3
0
0
1
0
1
2
0
1
1
1
1
1
1
1
2
1
1
1
1
2
2
1
2
1
1
1
0
2
0
1
0
0
2
0
2
1
1
0
2
2
0
0
2
1
1
1
0
1
2
1
0
1
1
0
0
1
2
1
0
0
2
3
0
2
0
1
2
1
0
1
1
1
1
1
1
2
2
1
0
2
0
1
1
2
0
0
2
1
2
1
1
0
0
2
2
0
2
1
1
1
2
2
0
0
2
0
0
0
1
2
2
1
1
0
0
0
2
0
1
1
1
0
2
1
2
3
1
1
0
6
0
1
1
1
1
1
0
3
2
2
1
0
2
0
1
0
0
2
2
1
0
0
0
1
0
0
3
1
1
2
0
1
1
0
1
2
1
2
2
1
2
0
1
2
2
0
1
0
1
1
0
1
1
0
0
1
0
1
2
1
1
1
1
0
1
0
1
0
1
0
0
1
0
2
1
0
1
2
1
0
1
0
1
1
2
1
0
2
1
1
0
0
1
2
0
2
0
1
1
0
1
0
2
1
1
1
0
0
2
1
0
0
1
2
1
1
0
2
1
1
1
2
2
0
0
0
0
0
0
0
1
0
2
1
2
2
1
2
1
2
1
1
1
0
1
1
0
1
1
1
2
1
1
1
0
2
0
0
0
1
1
1
2
1
2
1
1
0
0
0
2
1
2
1
1
1
0
2
0
1
0
3
0
1
2
1
0
2
1
1
0
1
0
0
1
1
2
1
1
2
0
1
0
0
2
1
1
0
2
0
2
0
2
0
0
1
0
1
1
0
0
2
0
2
0
2
0
0
0
2
1
0
0
2
2
2
0
0
1
0
0
0
0
0
1
0
1
2
2
0
1
0
1
0
2
0
1
0
0
1
0
2
0
0
1
0
1
2
2
1
2
0
1
0
0
1
1
1
2
1
1
2
2
0
0
0
2
1
1
1
0
0
2
1
2
1
0
1
2
1
2
1
1
2
0
1
0
0
1
1
1
2
0
1
0
1
0
0
2
1
1
1
1
1
1
0
0
1
1
2
0
1
0
0
2
0
1
1
2
0
2
1
1
3
0
0
0
1
1
1
1
1
1
2
0
1
1
1
1
0
0
0
4
1
1
1
0
2
0
2
0
2
0
0
1
1
1
1
1
1
0
1
0
0
1
1
1
0
0
2
1
1
1
1
1
0
0
1
2
1
0
1
0
1
3
2
1
1
1
1
1
2
1
0
1
2
2
0
1
1
0
1
0
0
2
0
1
1
0
1
0
1
0
0
0
2
0
0
0
0
1
0
2
2
1
0
2
2
0
2
1
0
0
1
0
2
1
0
2
1
1
1
0
0
0
1
2
2
3
1
3
1
1
1
0
0
1
2
2
2
0
0
0
2
2
2
0
0
1
0
1
1
1
1
1
1
1
1
0
1
1
1
1
2
1
1
2
0
1
1
1
2
2
0
1
0
2
0
1
2
1
1
0
0
1
0
2
1
1
2
0
0
0
1
1
1
1
2
1
0
2
0
0
0
2
1
1
0
1
0
0
1
0
0
1
1
1
3
0
0
1
0
2
1
0
0
0
1
0
0
1
0
0
1
2
1
2
1
0
0
2
2
2
2
1
0
1
1
1
2
1
1
2
0
1
1
2
0
1
2
0
1
1
0
1
2
1
0
2
2
2
2
2
0
1
1
1
1
1
0
2
1
0
0
0
0
1
0
0
1
0
1
1
0
0
0
2
1
1
2
1
0
0
1
2
0
1
2
1
2
1
0
1
1
2
1
0
1
0
1
2
2
2
1
2
2
1
1
1
0
0
1
0
0
0
1
2
1
2
1
0
1
0
1
0
0
2
1
2
2
1
2
2
2
1
1
1
0
0
2
2
1
1
2
0
0
0
0
1
0
1
1
0
2
1
0
2
0
0
1
2
0
2
0
0
0
0
0
2
2
0
0
1
2
0
1
0
0
0
1
1
1
1
1
0
1
1
0
1
0
0
2
1
1
1
2
1
1
2
1
1
0
1
1
0
0
0
0
2
1
1
0
0
2
2
1
1
1
1
1
2
1
1
1
1
1
1
1
1
1
0
1
1
1
2
0
0
0
0
2
0
2
0
0
1
1
1
1
0
0
0
0
0
0
1
3
2
0
1
0
0
2
0
0
0
2
1
1
0
1
2
1
0
0
2
2
1
1
0
1
3
1
1
0
0
2
0
1
0
2
0
0
1
0
2
2
0
3
1
1
2
1
3
1
1
1
1
0
2
1
1
0
1
0
2
1
2
2
0
2
1
2
1
1
1
1
0
1
0
1
4
0
1
1
1
3
1
0
0
1
0
2
0
1
2
2
1
0
1
0
0
3
1
0
1
1
1
0
2
1
0
1
1
1
0
0
1
1
0
1
1
1
1
0
1
1
1
1
1
0
1
1
1
1
2
1
1
1
0
1
1
0
0
0
0
0
1
1
1
1
1
1
1
0
0
0
2
3
1
0
0
0
0
2
0
0
1
0
1
0
1
1
1
0
0
1
0
0
0
1
0
2
1
1
0
0
1
1
0
0
1
0
0
0
2
2
1
1
1
1
1
0
0
1
2
1
0
1
1
1
0
2
0
1
1
0
0
0
2
1
1
2
1
0
0
1
1
2
2
0
2
1
1
0
2
0
0
2
0
0
1
0
1
1
1
0
1
0
2
3
2
2
0
1
1
0
1
1
1
2
1
0
0
0
0
1
0
0
1
1
1
2
1
0
0
0
1
0
0
2
1
1
2
1
0
1
1
0
2
0
1
0
1
1
1
0
1
2
1
2
0
0
2
1
0
1
1
0
1
1
1
1
1
2
1
0
2
0
0
1
0
0
1
1
1
1
0
0
1
1
1
0
1
2
1
1
1
0
0
0
1
1
0
2
1
0
2
2
1
0
0
1
2
1
1
0
0
0
1
0
2
1
0
1
0
2
2
1
0
1
2
0
1
0
0
2
0
2
2
2
0
1
0
1
2
1
0
1
0
1
1
0
0
1
0
0
0
1
2
1
1
0
0
1
0
0
0
2
2
2
0
0
0
0
0
1
2
2
2
1
1
0
1
0
0
2
1
1
1
0
0
2
1
1
0
2
0
1
0
0
2
0
2
0
0
1
0
1
1
0
1
1
0
2
1
0
0
2
0
2
1
1
0
1
3
0
0
1
0
0
2
0
0
1
0
2
3
0
0
1
0
2
0
0
0
1
2
0
1
2
2
2
1
0
1
1
0
1
0
2
1
1
2
2
1
2
0
2
2
0
1
1
0
1
1
2
0
2
2
1
1
1
1
2
1
1
1
1
0
1
0
1
1
1
1
2
2
0
0
1
2
0
2
1
0
2
1
0
0
0
2
1
0
1
3
0
0
2
1
1
1
1
2
0
1
2
2
1
3
1
0
0
0
2
2
0
1
0
3
1
1
0
1
1
2
1
0
2
1
1
2
2
2
0
0
0
0
2
1
1
2
0
2
2
0
1
0
2
0
1
2
1
2
0
1
0
0
1
1
2
0
1
2
1
1
0
2
0
1
1
1
1
0
0
1
1
1
0
0
0
1
1
2
2
1
2
0
0
0
2
2
0
1
0
2
1
1
1
1
1
1
1
1
1
1
1
0
2
1
0
1
1
0
1
2
0
0
2
2
1
1
1
2
3
1
2
1
1
1
2
0
1
0
0
0
0
3
1
1
0
1
1
0
1
0
0
0
1
0
1
1
2
0
1
0
0
1
1
1
0
1
1
0
1
1
1
2
1
0
1
1
1
1
1
1
0
0
1
0
0
1
0
0
0
2
1
0
0
1
0
0
2
1
2
0
2
1
3
1
2
0
1
0
2
1
1
1
1
2
0
2
1
1
2
0
1
1
0
0
1
0
1
1
0
0
0
1
1
1
0
1
1
2
0
0
2
0
0
1
0
0
2
2
0
0
0
1
0
0
1
0
2
1
0
2
0
0
1
0
2
1
1
0
2
0
1
1
0
1
2
1
1
1
2
1
1
0
0
1
1
0
1
1
2
0
1
0
1
1
0
0
1
0
1
1
0
1
1
0
0
1
0
2
1
0
2
2
0
2
1
0
1
0
1
1
0
0
0
1
1
1
2
1
2
0
1
3
1
1
0
0
2
1
2
0
0
1
1
0
0
0
1
1
0
0
0
0
3
1
1
0
0
1
2
2
1
1
0
1
2
0
1
1
1
1
0
0
1
2
0
0
1
0
0
2
2
0
1
1
0
0
0
1
1
3
0
3
1
0
0
0
1
1
0
1
0
1
1
1
1
0
1
0
1
1
0
1
1
1
0
0
1
2
0
5
1
1
2
2
2
1
1
0
1
0
1
1
0
1
0
1
1
2
1
2
0
1
1
2
1
0
2
2
0
1
0
1
1
2
0
1
1
1
1
2
0
2
0
1
1
2
1
1
1
1
0
0
1
1
0
0
1
0
0
1
1
1
1
1
0
0
0
1
0
1
1
2
0
0
1
0
0
0
1
1
0
1
1
2
0
1
0
0
0
2
0
1
1
0
1
2
0
0
1
2
1
2
1
1
1
2
2
0
2
2
1
0
1
2
0
1
3
2
0
0
2
1
0
2
1
1
2
1
0
1
1
2
0
2
0
1
2
0
1
0
1
1
2
0
0
1
1
1
1
1
2
0
1
1
0
1
2
1
2
0
0
0
1
2
1
2
0
1
2
0
1
1
1
0
2
1
1
0
0
0
2
2
2
1
1
1
2
2
0
0
1
1
1
2
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
2
1
1
2
2
0
1
1
0
2
0
0
0
2
0
2
1
0
1
1
1
1
0
1
0
0
2
1
1
0
0
1
1
1
3
1
0
1
1
1
2
0
1
2
2
3
2
0
2
1
1
1
0
2
1
0
0
1
1
2
0
0
2
1
1
3
1
1
1
3
0
1
2
1
1
1
1
0
1
0
1
2
2
0
2
1
1
2
0
1
2
2
2
1
1
2
1
1
1
0
1
0
0
1
1
1
1
1
0
2
1
1
1
0
1
0
3
2
1
2
0
2
1
1
1
0
2
0
1
2
2
1
0
0
1
2
1
0
0
1
0
1
1
1
0
0
1
1
1
1
1
2
0
2
1
1
0
2
0
1
0
2
1
1
2
0
1
2
3
0
1
1
0
1
2
1
0
1
1
0
1
0
0
1
1
0
2
1
0
1
2
0
2
0
1
2
1
0
1
0
1
2
0
1
2
1
0
1
1
1
1
2
1
1
1
2
1
1
0
1
1
2
2
1
1
1
0
2
1
1
2
1
0
0
2
0
1
0
2
0
3
0
0
1
1
1
1
1
0
1
1
1
0
0
0
1
0
1
0
2
0
2
0
0
1
2
1
2
0
0
0
1
0
2
1
1
1
2
2
0
0
0
2
0
0
2
1
2
2
2
1
2
2
0
0
0
1
0
1
2
2
2
0
0
0
0
0
0
2
2
0
0
1
0
2
2
1
0
2
0
0
2
0
0
1
1
1
0
2
1
1
1
1
1
2
0
0
1
1
2
0
0
1
0
1
1
1
2
4
1
0
0
1
0
2
1
0
0
0
1
2
2
0
2
0
0
0
2
1
2
1
1
1
1
1
0
0
0
1
0
0
1
1
0
1
0
2
1
1
1
2
1
2
2
1
0
1
0
1
0
0
1
0
2
2
0
0
0
2
0
1
1
1
2
1
0
1
0
0
0
1
2
2
0
0
1
3
2
2
2
2
0
0
1
1
1
1
0
1
0
2
0
1
2
0
0
0
0
1
0
2
0
0
2
2
1
1
0
1
0
1
0
0
1
0
0
0
1
1
2
1
0
0
1
2
2
0
0
2
1
0
1
1
1
1
1
1
0
1
1
2
1
2
1
1
2
0
0
2
1
2
2
1
0
0
1
1
1
0
2
2
0
1
2
2
2
0
1
1
1
1
1
2
2
0
0
1
0
1
2
0
1
3
1
0
1
3
0
0
2
0
0
0
0
4
1
0
1
1
2
1
1
0
1
0
1
2
1
2
1
2
1
1
2
0
2
0
0
1
1
1
2
0
2
2
0
2
2
0
1
1
0
0
0
1
1
1
3
1
0
2
2
3
1
1
1
2
1
2
2
0
2
2
1
2
0
1
0
1
2
0
2
1
1
0
0
0
1
1
0
1
2
0
1
0
2
2
2
1
0
2
0
2
0
1
1
0
2
1
2
0
0
1
1
0
2
1
0
1
1
2
0
0
0
0
0
1
1
0
2
1
0
2
1
0
1
0
0
0
1
1
1
1
1
1
0
1
0
0
3
1
1
2
1
2
1
0
0
1
1
1
0
2
1
1
1
2
0
2
2
1
0
1
1
2
1
2
0
1
0
2
2
1
0
1
2
0
1
1
1
1
2
1
1
1
3
1
1
1
0
2
1
0
1
2
0
1
2
2
0
1
1
2
1
1
0
1
1
1
0
0
2
2
1
1
0
0
1
1
0
0
2
1
2
0
0
1
1
1
1
7
1
1
1
0
0
0
1
2
2
0
1
0
1
0
0
1
1
0
1
1
1
1
1
2
1
1
0
0
1
1
0
0
0
1
1
0
1
0
1
1
2
0
2
1
1
0
2
0
0
2
1
1
1
2
1
0
2
2
1
1
0
2
1
2
2
1
1
0
1
0
1
0
2
1
1
1
2
1
1
0
0
0
1
1
2
2
0
1
0
0
2
1
4
1
1
0
0
2
0
1
2
2
0
1
0
1
1
0
2
0
0
2
1
1
1
0
1
1
1
1
0
1
1
1
1
1
0
1
1
1
2
2
1
1
1
1
1
1
0
2
1
1
0
1
2
0
0
1
0
1
2
1
0
1
1
1
2
2
1
2
2
1
0
1
0
0
1
3
1
1
2
1
2
1
1
2
1
0
2
0
1
1
1
1
0
1
2
1
0
0
3
0
1
0
0
0
0
0
1
1
2
1
0
2
2
0
0
0
1
1
2
2
1
2
0
1
1
0
0
1
1
1
1
0
0
2
0
1
1
0
1
0
0
1
1
1
1
0
0
1
0
1
0
1
0
0
1
1
0
1
1
2
2
0
1
2
1
0
0
1
1
0
2
1
2
0
1
1
2
0
1
1
0
3
1
0
1
0
1
0
1
1
0
0
2
0
0
1
1
0
1
2
2
0
1
1
1
0
0
0
2
0
1
1
0
0
1
1
0
2
1
0
1
1
1
1
1
2
1
1
1
0
1
0
0
2
1
0
1
0
1
1
0
1
1
1
2
0
2
0
2
0
1
0
0
1
1
0
2
1
2
1
1
1
1
1
0
1
1
1
0
1
0
2
1
2
1
1
1
2
0
1
2
0
0
1
0
1
2
0
2
1
4
0
2
1
0
0
0
0
2
1
0
1
1
1
1
3
0
2
1
1
0
1
1
2
0
0
1
0
1
0
1
2
0
2
1
2
3
1
1
0
0
1
3
1
1
1
0
0
1
0
1
2
1
0
1
1
1
0
1
1
1
1
0
1
1
1
1
0
1
1
0
2
0
1
1
0
0
0
0
0
1
0
0
1
1
0
2
0
1
2
2
1
0
2
2
1
0
1
1
1
2
1
0
2
2
0
1
1
1
1
0
0
1
1
1
0
0
0
0
0
0
2
2
1
0
1
1
2
1
0
1
2
1
0
2
2
2
1
0
1
2
2
1
0
0
1
1
0
0
1
2
1
1
2
1
1
2
0
1
1
1
1
2
0
2
0
1
0
2
0
1
1
0
1
0
2
2
0
0
0
1
1
0
2
1
4
2
0
1
2
0
1
1
1
0
0
1
0
1
2
0
1
1
0
0
1
0
0
2
1
0
2
1
2
1
0
2
1
1
0
2
0
1
0
1
0
2
1
0
2
1
2
0
1
0
2
1
1
0
1
0
0
1
1
0
2
1
1
2
1
0
1
0
0
1
1
1
0
0
1
1
3
1
0
0
1
2
1
0
0
0
2
0
0
0
1
0
1
2
0
1
0
2
0
1
0
2
1
2
1
2
2
1
1
1
0
2
1
0
1
1
2
0
1
0
2
1
0
4
0
3
0
1
2
0
0
1
0
1
2
0
0
1
0
0
1
1
0
0
0
2
2
0
0
1
1
2
0
2
0
0
2
1
0
3
0
1
2
0
0
2
0
0
1
1
1
1
1
1
0
0
0
2
2
2
1
2
1
1
0
1
1
0
0
1
2
2
0
1
0
0
0
0
1
2
0
2
1
1
1
1
0
1
1
1
1
1
0
1
0
0
2
0
2
0
1
1
1
1
1
1
1
2
0
0
2
0
0
1
1
1
1
2
1
1
0
1
1
0
0
2
1
1
0
2
0
1
1
0
1
0
0
1
0
1
2
1
0
1
2
0
1
0
2
1
2
0
1
0
2
0
0
1
0
2
1
0
1
0
1
1
1
0
1
0
0
0
2
1
1
2
1
2
1
1
2
1
2
2
2
0
0
1
1
0
1
0
1
2
1
0
1
2
0
0
1
1
2
0
0
1
0
2
0
1
1
1
0
2
1
0
1
2
0
1
2
0
1
1
2
1
2
5
0
0
1
1
1
0
0
0
0
2
0
2
0
0
2
1
3
0
0
1
2
2
0
2
1
1
2
0
0
1
0
2
0
1
1
1
1
1
0
2
2
1
1
0
2
2
0
3
1
0
0
0
1
3
1
1
1
2
2
1
2
1
2
2
1
0
1
1
1
4
2
2
0
2
0
2
1
1
2
0
2
0
2
1
1
0
1
2
2
2
0
0
1
0
2
0
2
1
1
1
1
2
1
0
2
0
1
1
1
2
0
0
2
1
0
0
0
3
1
0
0
1
1
0
0
1
0
1
1
1
1
0
1
2
0
1
0
1
0
2
2
1
1
1
2
1
0
1
0
1
1
0
1
2
0
0
1
0
2
2
1
1
0
0
0
1
1
1
0
1
1
1
1
1
1
0
3
1
0
2
2
0
1
1
0
0
1
2
2
1
0
1
1
1
0
2
1
0
1
0
0
1
1
1
2
2
2
1
0
1
2
1
0
2
1
1
1
1
0
1
1
0
2
1
0
1
1
0
1
1
0
1
3
2
0
0
1
0
1
0
0
0
0
1
1
0
0
0
1
1
1
2
1
2
2
0
0
0
1
2
0
0
3
1
1
0
1
2
0
0
1
0
1
0
0
2
1
1
1
0
1
1
0
1
0
1
0
1
0
0
0
2
1
1
2
1
1
3
2
0
0
0
0
1
1
0
0
1
1
1
0
1
0
4
2
1
2
1
1
2
1
0
2
1
3
1
0
1
2
1
1
2
1
0
1
0
0
1
0
3
1
2
1
1
0
0
2
0
0
1
0
0
2
1
1
0
2
0
1
1
3
1
1
1
2
1
0
0
3
1
1
0
2
1
2
0
2
0
1
1
2
1
2
1
1
1
2
1
2
2
1
1
0
0
2
1
1
5
1
0
1
1
1
1
1
2
1
0
0
0
1
2
0
0
0
1
1
0
0
1
1
2
2
1
0
0
1
2
1
0
0
1
0
2
1
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
1
0
1
2
1
1
0
0
0
1
1
0
2
1
1
1
1
1
1
2
0
0
2
1
1
1
1
0
0
0
0
2
1
0
2
1
1
0
1
1
0
1
1
1
0
1
2
1
1
2
1
1
1
0
0
3
0
1
1
1
1
0
0
1
0
1
0
0
0
2
0
0
0
2
1
0
1
0
0
0
1
2
2
2
0
2
1
1
0
2
0
1
1
1
0
1
1
2
2
0
1
2
0
0
0
0
1
1
0
1
1
1
1
2
1
2
0
2
2
0
1
1
0
1
1
1
3
0
0
1
1
2
1
1
2
1
1
2
0
0
1
1
3
1
0
1
0
1
1
2
1
1
1
1
1
1
1
2
1
4
0
1
1
2
1
1
1
1
1
1
1
1
0
1
0
1
0
0
3
1
2
1
0
0
1
2
1
1
1
1
1
2
1
0
0
0
1
0
2
0
0
1
1
1
2
1
1
0
1
2
0
2
1
0
1
2
1
1
2
1
2
1
1
0
1
1
0
1
1
1
0
1
1
1
1
0
1
1
0
1
1
1
0
1
2
2
0
0
1
2
1
2
1
0
0
1
1
1
1
1
1
2
0
0
2
2
1
0
0
0
1
1
0
2
0
1
4
1
0
1
0
1
1
1
0
1
1
1
1
2
0
1
1
2
0
0
1
1
0
1
2
0
1
0
3
0
2
2
1
1
1
2
2
0
1
0
0
0
2
0
1
1
1
1
0
1
0
1
2
2
0
0
0
2
1
0
0
1
2
2
1
0
1
1
2
0
1
1
2
1
1
0
2
1
1
0
1
1
2
1
0
1
1
0
1
1
1
2
0
1
1
1
1
1
1
1
0
1
1
1
0
1
1
0
0
1
0
0
1
1
1
0
1
0
2
0
0
0
0
1
0
1
1
3
0
1
2
1
2
1
0
2
1
1
4
1
1
1
0
2
0
2
0
2
1
2
0
1
2
1
0
1
1
0
2
2
0
1
1
0
1
2
2
1
1
2
0
2
2
0
1
0
1
0
1
0
0
0
1
1
2
1
0
1
1
1
1
0
0
0
1
2
1
0
1
0
0
1
2
1
1
0
0
1
2
0
1
1
2
0
2
0
2
2
2
1
1
0
2
1
0
0
0
0
2
0
2
1
1
1
1
0
1
1
2
1
1
0
0
2
2
1
1
1
1
2
2
0
1
4
0
0
0
1
0
0
1
1
0
1
0
1
1
0
1
2
0
0
0
1
0
2
0
1
0
1
0
2
1
2
0
2
2
0
0
0
1
1
1
1
0
1
1
0
2
1
0
1
0
0
1
0
1
0
0
1
3
1
2
2
1
0
0
2
0
0
1
2
1
2
3
1
0
0
2
1
1
1
2
2
0
1
1
0
1
0
1
0
1
1
0
1
0
0
2
0
2
1
2
1
0
2
1
0
1
0
0
2
2
0
1
0
2
0
0
1
8
1
1
0
1
1
1
1
1
2
1
2
3
0
1
2
1
2
1
0
1
1
1
0
2
0
0
2
0
2
2
0
2
0
0
0
0
1
1
2
1
0
1
0
2
2
1
1
0
1
0
1
0
0
0
1
0
1
1
0
2
0
1
1
1
0
2
1
1
2
1
2
1
1
1
1
1
1
0
0
1
0
1
1
1
0
1
1
1
0
0
0
3
0
1
1
0
1
2
1
1
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
1
0
1
0
1
0
1
0
0
1
1
0
0
0
1
1
1
2
0
2
1
2
1
0
2
1
1
0
3
0
1
0
0
2
0
0
0
0
2
0
2
0
1
1
1
1
1
1
2
1
2
1
1
0
1
1
1
2
1
0
1
0
1
0
1
0
1
2
0
0
0
0
2
0
2
0
1
0
1
0
2
1
0
1
0
2
1
2
2
1
1
0
1
0
1
0
2
0
1
2
2
2
0
1
1
2
0
2
2
1
1
7
0
1
0
1
6
0
2
0
2
1
1
2
2
2
0
2
0
1
2
1
1
1
0
1
0
0
1
1
1
1
1
2
1
1
2
1
1
2
3
1
0
1
2
0
2
0
1
0
2
0
0
2
1
1
1
2
1
2
2
1
2
2
1
0
2
2
0
1
1
2
1
0
2
2
2
1
1
0
1
1
0
1
0
0
2
0
1
0
0
1
1
0
0
1
0
2
2
0
1
2
0
0
2
1
2
1
1
2
0
1
0
0
1
1
0
1
0
0
1
1
1
1
1
1
2
2
0
1
2
1
1
2
1
1
1
2
1
0
2
1
1
1
0
2
1
1
0
1
1
2
1
0
1
0
0
1
0
0
3
0
1
1
1
1
0
1
1
2
1
2
0
0
0
3
1
1
0
1
2
0
2
0
1
0
2
0
0
2
2
1
0
1
0
0
6
1
1
1
3
1
1
1
0
2
1
2
2
0
0
0
1
2
0
1
0
1
1
1
1
2
2
2
1
0
1
1
0
0
0
1
2
1
0
2
2
1
1
3
0
1
0
1
0
2
1
1
1
1
1
0
0
0
1
1
1
2
1
3
3
0
0
1
0
0
0
1
0
0
1
4
3
2
1
2
0
1
0
2
1
1
1
0
1
2
1
1
1
0
0
0
0
2
1
1
2
1
1
2
0
0
0
0
0
3
0
0
1
2
2
2
2
1
2
1
0
2
1
2
0
2
1
1
1
1
3
2
2
2
0
2
1
0
1
0
0
1
2
2
0
1
0
2
2
1
2
1
0
2
1
1
2
1
1
2
1
1
0
1
1
1
0
1
1
1
1
2
2
0
1
1
1
1
2
1
1
2
2
1
1
1
2
0
0
0
0
0
3
1
1
2
1
1
1
1
2
2
0
1
0
1
1
2
0
2
0
1
2
1
2
1
0
1
0
0
0
0
2
0
2
0
0
0
3
0
0
1
1
1
0
1
0
0
0
1
0
1
1
0
1
0
0
0
1
0
1
1
1
0
0
1
2
0
1
0
0
1
0
1
1
0
0
1
1
0
1
1
1
0
1
1
0
1
1
2
1
1
1
0
0
0
1
1
1
0
1
2
1
1
1
2
2
0
2
2
1
2
1
1
0
2
1
0
0
2
2
0
0
0
1
0
0
0
1
3
1
1
0
0
1
2
0
0
2
0
0
0
1
1
0
0
1
2
1
1
2
1
1
0
2
0
1
0
1
0
2
0
0
1
1
1
2
0
1
3
1
1
2
2
0
1
1
1
1
1
1
0
1
0
1
2
0
2
1
0
1
2
2
0
1
2
0
1
1
0
2
1
0
1
0
1
0
0
1
2
0
0
1
1
2
1
0
2
0
2
0
2
1
0
1
1
2
1
0
1
0
1
0
1
0
1
1
3
1
1
2
0
2
2
2
1
1
2
0
0
1
0
0
1
1
1
2
1
1
0
1
1
1
0
1
1
2
2
1
0
1
1
2
1
2
1
0
2
1
0
1
1
2
1
1
0
2
1
0
2
0
2
1
0
1
1
2
1
0
0
0
1
2
1
0
0
2
2
1
1
3
2
2
0
1
0
1
0
2
1
1
1
0
0
2
2
0
1
0
2
1
2
1
2
3
2
1
1
1
0
0
1
2
0
0
1
1
1
1
0
0
0
3
0
0
1
2
2
1
1
1
1
0
0
1
1
1
1
0
1
2
1
1
0
1
0
0
1
0
0
2
1
2
1
2
0
1
2
1
2
1
0
0
1
2
0
1
1
0
1
1
2
0
1
1
1
1
0
1
1
1
1
1
1
1
0
1
1
0
2
2
0
2
2
0
0
2
1
1
2
1
0
3
0
3
1
0
2
0
1
2
0
2
0
1
2
2
2
0
0
2
0
0
0
0
2
0
3
1
1
0
0
0
2
0
0
1
1
1
2
2
0
1
1
1
1
0
1
0
0
0
0
0
0
1
1
2
1
0
2
2
1
0
1
2
1
1
1
1
1
0
2
1
0
0
0
0
1
1
2
0
0
0
3
2
0
2
1
1
0
1
1
2
2
0
2
0
1
0
1
1
0
0
2
1
1
0
1
1
0
0
1
0
1
0
1
1
1
0
1
1
1
0
1
0
1
1
1
4
1
1
0
1
0
1
1
1
1
0
1
2
1
1
2
0
1
3
1
2
1
0
1
1
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
1
0
0
1
1
0
2
1
0
0
1
2
0
1
0
0
1
1
2
1
2
0
0
0
1
2
1
1
2
2
1
1
0
2
1
0
1
0
1
2
2
1
0
1
1
1
1
1
0
1
1
1
1
2
1
2
0
1
1
1
0
1
1
1
1
2
1
0
0
2
0
0
1
1
0
1
2
2
2
0
1
1
1
0
0
2
1
0
1
0
0
0
1
2
2
0
2
1
1
1
0
0
2
1
0
1
1
2
2
1
1
0
2
2
0
1
1
2
2
1
0
1
2
0
1
1
2
0
2
0
1
2
2
2
0
2
1
0
1
0
2
0
0
2
0
0
1
1
2
0
0
0
1
6
1
1
0
0
1
2
0
0
0
1
1
0
0
4
0
1
2
0
1
2
1
0
2
0
0
2
2
2
2
1
2
0
2
1
1
0
1
2
0
0
0
0
0
1
0
0
1
0
0
0
1
1
1
1
0
0
0
0
1
1
2
1
1
0
0
0
1
0
1
0
0
1
1
0
0
2
0
1
1
0
1
1
1
1
2
0
1
1
2
1
1
0
1
0
0
0
2
1
2
1
0
1
1
1
2
2
2
0
1
0
2
1
0
2
1
3
1
2
1
0
1
1
2
1
1
2
0
1
0
1
0
0
2
2
1
1
1
0
2
1
3
0
1
1
0
1
0
2
0
0
0
0
0
1
1
0
1
1
2
1
1
1
3
2
1
1
1
1
0
3
1
0
1
0
1
0
0
1
1
1
2
2
1
0
2
1
0
1
0
0
0
0
2
1
1
4
2
1
0
0
1
2
0
1
0
2
2
1
0
0
1
0
2
2
1
1
1
0
0
2
1
0
1
1
1
0
0
0
0
2
2
0
1
2
2
0
3
0
2
2
1
0
1
2
0
1
0
1
0
1
1
0
0
0
1
1
2
0
1
1
1
0
3
2
0
0
0
2
1
0
1
2
2
0
1
2
2
0
0
0
3
2
0
0
1
2
0
0
0
1
0
0
1
2
1
1
2
1
1
0
1
0
0
1
1
0
1
1
0
0
1
2
1
0
1
2
2
1
1
2
1
0
0
1
1
0
0
1
2
1
0
0
2
2
1
1
1
0
2
0
1
1
0
2
2
0
0
0
1
1
2
1
0
0
2
1
1
0
0
1
1
1
2
2
1
1
0
1
0
1
1
0
0
1
4
2
0
1
1
1
2
1
0
2
0
1
0
2
1
1
2
0
1
0
2
2
1
0
1
0
0
2
2
1
1
1
0
2
2
0
0
2
0
0
1
0
2
2
1
1
1
0
2
0
2
0
3
0
0
1
0
1
0
0
1
2
2
0
1
1
2
1
0
2
2
1
2
0
0
1
2
2
2
1
2
1
1
2
2
2
1
1
0
2
2
2
0
0
1
1
1
0
1
1
1
0
0
2
0
1
0
0
0
0
1
0
0
2
0
0
2
1
1
0
0
0
1
0
0
2
1
0
2
1
1
1
0
1
0
0
1
1
2
0
1
1
4
1
2
0
1
0
0
3
2
1
0
0
0
1
1
2
1
1
1
1
1
0
0
0
1
0
1
0
2
0
1
1
1
1
0
1
0
0
1
0
2
2
2
2
1
0
0
1
2
1
2
0
1
0
0
0
0
1
2
1
2
2
1
1
1
0
1
0
0
2
2
0
0
1
2
1
0
1
2
6
1
1
0
1
1
0
0
2
2
1
3
1
2
0
0
0
1
4
1
2
0
0
0
0
0
0
1
2
0
0
1
1
0
2
1
0
0
1
1
0
1
1
1
1
0
0
2
1
0
0
1
0
2
1
0
2
0
1
0
1
1
1
0
1
0
1
2
0
1
0
0
0
2
0
1
0
2
1
0
2
2
0
0
1
0
1
1
1
2
2
0
1
0
1
0
2
1
0
0
2
1
1
1
0
0
0
0
0
2
1
2
1
2
2
1
1
1
1
1
2
2
3
1
0
2
1
1
1
2
0
1
1
1
2
0
1
2
2
0
1
2
2
1
1
1
1
1
0
1
1
0
2
1
2
1
2
0
3
1
1
2
0
2
1
2
1
1
1
1
1
2
1
1
1
2
1
2
2
2
1
0
1
1
0
1
1
2
0
2
2
0
0
1
2
1
1
2
0
1
2
1
0
1
1
3
2
2
0
1
1
2
1
2
0
0
1
2
2
1
2
1
2
0
0
1
1
0
0
1
0
1
1
0
1
0
0
1
1
2
1
1
0
2
1
0
2
1
1
1
1
0
0
1
2
1
0
1
1
0
1
1
1
0
3
1
1
4
3
0
1
1
2
1
1
1
1
0
1
1
0
0
0
1
0
2
0
2
1
2
1
1
0
2
1
1
3
1
0
1
1
0
1
2
0
1
2
1
0
2
1
0
0
0
1
2
1
0
1
0
1
0
1
2
1
1
0
1
0
2
0
2
0
2
0
1
2
1
1
3
0
2
0
0
2
0
1
0
2
0
0
1
1
1
2
1
1
2
0
0
0
1
2
0
1
0
0
1
0
1
2
2
2
1
1
0
1
0
1
1
1
2
0
1
1
1
1
1
1
1
1
0
0
1
1
2
0
1
0
1
2
1
0
0
1
1
2
1
1
1
1
0
0
1
3
1
0
1
1
0
2
1
1
2
1
0
0
0
1
1
1
0
1
0
1
2
1
1
1
2
1
2
1
0
2
2
2
1
0
6
1
1
2
1
1
1
1
0
1
0
0
0
1
2
1
1
1
2
2
2
1
0
1
2
1
1
2
0
1
1
1
1
1
0
2
1
1
1
0
1
1
1
1
1
2
1
1
0
1
1
1
2
1
0
0
1
1
1
0
3
2
0
1
1
0
1
0
1
0
0
1
0
1
1
2
0
1
1
1
0
1
0
1
0
1
0
0
1
0
0
2
0
2
2
1
0
0
2
1
1
0
0
0
2
0
1
0
2
0
1
0
1
2
1
1
1
1
2
1
2
1
1
1
1
1
2
1
1
1
2
1
1
0
0
2
2
1
0
0
0
0
0
1
2
1
0
1
2
0
0
0
2
1
2
0
2
1
1
1
2
0
1
1
1
1
1
1
2
2
0
1
0
0
1
0
1
1
0
2
0
1
0
0
2
1
1
1
1
0
2
0
1
0
0
1
1
1
2
0
1
1
0
1
0
2
1
1
1
1
0
0
1
1
1
1
1
0
1
1
0
1
1
0
2
2
2
1
1
1
1
0
1
0
0
1
1
0
2
0
1
1
0
1
1
1
0
2
1
1
1
2
1
3
0
0
0
0
1
0
1
0
1
1
0
0
1
1
0
1
0
0
1
1
2
0
0
1
2
2
5
0
0
0
1
1
1
1
0
1
2
1
1
0
1
0
1
1
1
1
1
1
0
0
0
0
0
0
1
0
1
1
0
0
1
1
1
0
1
1
1
1
2
0
1
1
1
1
0
2
0
0
1
0
3
0
2
0
1
0
0
0
2
0
0
0
0
2
1
1
1
1
1
2
1
1
0
1
1
2
2
1
0
1
0
1
4
0
0
0
0
1
1
0
0
4
0
1
2
0
0
0
2
0
0
0
2
2
1
1
1
0
1
2
1
2
1
2
2
2
1
1
2
0
0
2
1
1
0
0
0
3
0
0
1
2
1
0
1
1
1
1
0
1
1
2
2
1
2
1
2
1
2
1
2
1
1
0
0
1
1
0
0
2
1
1
0
2
0
1
2
1
0
0
1
1
1
1
1
1
1
0
0
1
1
9
0
2
1
2
2
1
0
0
0
0
0
2
0
1
1
2
0
0
0
2
1
6
1
1
0
1
1
1
2
2
1
0
1
1
2
1
0
2
0
1
1
1
0
1
2
1
2
1
2
0
1
0
0
1
1
1
0
1
0
1
0
2
1
1
0
1
1
1
0
1
0
0
0
1
1
1
0
1
0
1
1
1
0
1
0
0
0
1
2
0
1
1
1
0
2
1
0
2
1
0
0
2
0
2
0
1
2
2
0
1
0
2
0
1
2
1
1
1
1
1
1
0
2
1
0
0
0
1
1
1
0
1
2
4
1
1
2
1
2
1
0
1
1
2
0
1
0
0
0
2
0
1
2
0
2
2
2
2
1
2
0
2
2
3
1
0
0
1
0
0
0
1
0
0
1
3
0
2
0
0
2
2
1
0
1
1
0
0
2
2
2
1
0
0
1
2
1
0
0
1
2
0
0
0
1
1
2
1
1
2
1
1
0
2
2
0
1
2
0
1
1
1
1
2
1
0
2
1
0
1
0
1
0
1
1
2
1
0
2
0
1
0
2
3
1
1
1
1
1
0
1
0
0
0
1
0
0
1
1
0
2
0
0
1
2
1
0
0
1
3
1
1
1
1
2
1
1
0
0
1
1
1
2
0
0
0
1
0
2
0
1
1
1
1
2
0
0
1
2
0
1
1
2
1
2
1
1
0
0
0
1
0
0
1
4
0
0
1
2
2
1
0
0
1
2
2
2
1
0
0
1
2
0
1
1
2
0
0
1
0
1
0
1
2
2
1
1
2
1
1
0
1
1
0
1
1
0
2
1
0
2
1
0
1
1
0
2
0
1
2
0
1
1
1
3
2
0
0
0
1
0
1
1
2
0
2
1
2
2
0
0
1
1
0
0
0
2
1
2
2
1
0
1
1
2
1
0
0
1
1
2
1
1
0
1
0
1
1
2
0
1
1
0
0
1
0
0
0
0
0
2
1
0
0
1
3
0
2
0
1
1
1
1
1
1
2
1
2
1
0
2
2
2
1
1
1
0
2
1
1
1
2
1
0
1
1
1
0
1
2
1
2
0
2
0
1
0
0
2
2
1
1
1
1
2
1
0
0
0
0
0
0
0
1
0
2
1
0
0
1
1
1
1
5
1
1
0
0
7
1
1
2
0
2
0
1
0
0
1
2
0
0
0
0
1
0
2
1
1
0
2
2
2
1
0
2
1
1
2
1
0
2
0
2
0
2
1
1
1
0
1
1
1
1
1
1
1
1
1
0
0
2
1
0
0
0
0
2
1
2
1
2
1
2
0
2
0
1
0
0
1
1
0
0
1
0
2
0
0
1
0
1
1
2
2
2
0
1
1
1
2
0
0
0
1
1
0
2
2
2
2
1
0
0
1
0
1
2
1
1
0
1
1
0
1
0
2
0
1
2
1
0
0
0
1
1
0
0
1
2
0
1
2
0
1
0
2
1
1
1
2
2
0
1
1
1
0
1
1
1
0
2
1
2
1
0
1
2
0
1
1
1
0
1
0
2
1
3
2
1
0
1
0
0
0
0
1
1
1
2
1
0
0
1
4
2
1
0
3
2
0
1
1
2
1
0
1
0
1
2
2
0
1
0
1
5
0
2
3
1
2
1
1
1
0
1
2
1
1
1
1
0
0
1
0
0
2
1
0
0
0
1
0
0
2
0
2
1
1
0
1
1
1
1
1
2
2
0
1
0
1
1
1
0
0
1
2
1
0
2
2
2
0
0
1
1
0
0
1
0
2
0
1
0
0
0
1
0
2
1
1
0
1
2
0
1
0
1
1
1
2
0
1
0
1
1
1
1
1
2
2
2
1
1
2
1
3
2
1
0
2
2
2
0
0
1
1
0
1
1
1
1
0
1
2
2
1
1
1
4
0
2
1
2
1
2
0
1
0
1
0
2
1
3
1
0
0
0
0
0
1
2
1
1
1
1
2
1
1
1
0
1
0
0
0
7
0
0
1
0
0
0
0
0
0
1
1
0
1
1
2
2
5
0
1
1
1
1
0
1
1
2
2
0
1
0
1
0
1
0
1
1
1
0
0
1
0
2
0
2
1
1
0
1
2
1
1
2
2
0
1
0
0
0
1
2
1
0
1
1
1
1
1
1
1
2
1
2
2
1
0
0
0
0
1
1
1
1
1
1
0
1
1
2
0
0
1
2
0
1
0
1
1
1
1
2
1
0
1
1
1
1
1
2
0
1
1
1
1
1
0
1
0
1
1
0
0
2
0
0
2
0
0
0
1
1
2
1
2
1
2
2
0
1
1
0
2
2
0
0
1
2
0
0
0
0
1
0
1
1
0
0
0
0
1
1
0
0
0
0
1
1
2
0
3
1
1
0
2
0
1
4
2
0
1
1
1
0
2
3
1
0
1
2
0
2
0
1
3
0
2
1
1
1
0
1
0
2
0
0
2
0
6
1
0
1
1
1
1
0
0
2
0
2
0
1
0
1
2
2
0
1
0
2
1
1
1
1
1
0
0
1
0
2
2
0
0
0
0
0
2
2
1
0
0
1
0
1
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
0
1
0
0
1
0
0
1
0
0
1
1
1
2
1
1
1
0
3
1
0
1
0
1
0
1
0
2
0
0
0
0
0
2
2
1
0
1
1
1
0
0
0
1
0
1
1
2
0
3
2
1
2
1
0
1
2
1
1
1
1
0
0
1
1
2
1
0
0
1
2
0
0
0
1
1
1
2
2
2
0
1
0
0
1
1
2
2
0
0
1
1
1
0
1
0
1
2
0
0
0
1
0
1
1
3
1
1
2
2
1
2
1
1
1
2
2
2
2
0
0
1
0
0
2
0
1
2
0
0
1
1
1
1
0
0
0
0
1
1
0
0
0
0
1
1
2
2
2
0
1
1
1
0
0
0
1
0
1
1
2
1
1
2
2
0
2
0
0
1
2
0
2
0
0
2
1
1
0
1
1
2
0
0
0
0
1
1
1
0
0
2
0
1
2
1
2
1
2
0
0
2
0
1
1
0
0
0
2
0
1
1
1
1
1
1
2
1
2
1
1
2
1
2
1
0
0
0
0
1
2
2
2
0
0
2
1
0
1
1
2
2
1
1
1
1
1
0
0
0
1
1
4
1
0
0
1
2
1
1
0
0
1
2
0
2
0
2
0
1
0
0
2
0
1
1
1
2
0
0
2
0
1
1
0
1
1
0
0
0
1
0
0
1
1
0
0
1
0
0
2
1
2
1
2
1
2
0
0
2
1
1
1
1
0
1
2
1
1
0
0
1
1
1
1
0
2
1
1
1
1
1
1
0
2
2
2
2
2
1
1
2
0
2
0
2
0
1
0
1
0
0
1
1
0
2
0
0
0
1
1
1
2
0
2
0
0
0
0
0
1
1
1
1
0
0
2
1
0
0
1
0
1
1
2
0
0
2
1
0
1
0
2
0
0
0
1
0
1
0
0
2
1
0
1
1
1
2
1
0
1
2
0
1
2
1
2
0
1
0
2
2
1
0
1
0
3
4
0
3
0
0
0
2
0
2
0
0
1
2
1
2
1
1
2
0
1
2
0
3
1
1
0
0
1
1
1
1
1
0
5
1
1
1
1
0
1
1
1
1
0
1
0
0
0
1
0
1
2
1
1
2
1
0
0
1
1
0
0
2
0
0
0
0
1
1
1
0
2
1
1
1
0
2
0
2
1
1
0
1
0
1
1
0
0
1
0
0
0
1
1
1
1
1
1
1
1
0
2
2
0
0
1
0
0
2
1
1
2
0
2
2
1
0
2
0
2
0
2
1
1
0
1
2
1
1
1
2
0
2
2
0
1
1
0
1
1
2
1
1
0
0
2
1
1
1
1
0
0
1
1
1
1
0
1
1
2
2
0
1
1
1
0
1
1
1
1
1
2
1
1
1
2
0
2
1
0
0
0
0
0
2
0
1
0
0
1
0
1
1
2
1
0
1
1
1
1
1
1
0
2
0
1
1
0
0
2
2
1
2
1
1
2
0
0
1
1
1
2
1
2
1
2
1
0
1
2
1
0
0
1
0
2
1
1
1
1
0
0
1
1
2
1
2
2
0
0
1
2
2
0
0
1
1
3
0
1
1
0
2
3
0
2
0
0
1
3
2
1
0
1
0
1
1
1
1
2
0
0
0
0
1
1
1
1
0
1
1
0
2
1
2
0
1
1
0
1
1
1
0
1
0
2
1
1
0
1
1
1
2
2
0
2
1
0
1
0
0
1
1
2
0
2
1
1
1
1
1
0
0
1
2
1
1
2
1
1
1
4
2
1
2
0
4
0
1
2
1
0
0
0
0
0
2
0
2
2
1
2
0
1
0
2
2
1
0
2
1
0
2
1
0
1
0
1
1
2
2
1
0
0
2
2
0
0
0
2
1
0
2
0
2
1
2
1
1
2
0
1
1
2
1
2
0
1
1
2
1
1
1
1
1
0
1
0
2
0
0
0
1
1
1
1
1
1
0
2
0
1
2
1
1
1
2
1
0
1
2
1
1
1
2
0
0
1
1
0
0
1
0
0
0
1
0
1
1
1
0
1
0
3
0
0
1
1
0
1
1
1
1
0
1
1
2
1
1
0
1
0
0
0
0
1
1
1
0
2
2
0
2
0
0
0
3
1
1
1
1
1
1
0
1
1
0
0
2
1
1
0
0
2
1
1
1
0
1
1
1
0
0
1
1
1
1
0
2
0
2
1
2
0
2
2
0
3
0
0
3
2
2
0
2
0
2
2
0
0
1
1
0
2
1
2
1
0
1
0
2
0
0
0
2
0
1
1
0
1
1
1
1
0
1
0
0
0
0
0
1
0
1
2
0
1
1
1
1
0
2
1
0
1
0
1
0
0
0
0
0
0
1
0
1
1
0
0
2
0
1
2
1
2
2
0
2
2
1
1
2
1
1
2
0
1
2
1
1
2
0
2
0
1
2
0
0
1
1
0
1
1
1
1
1
1
3
1
0
1
1
1
1
0
0
1
3
2
0
0
1
1
1
5
1
1
2
2
2
0
0
1
1
2
0
0
1
2
0
1
2
0
1
1
2
0
1
0
1
1
3
1
0
1
1
1
0
2
2
1
1
2
2
1
0
0
0
0
0
0
1
1
1
1
0
2
0
0
0
0
0
0
1
2
0
1
0
2
2
1
1
1
0
0
1
1
2
2
0
2
1
0
1
1
3
0
1
1
0
1
0
0
0
1
0
0
3
2
0
1
2
2
1
0
1
1
1
1
3
1
0
1
1
1
1
2
1
1
0
1
2
1
1
0
2
0
1
1
0
2
0
1
1
1
1
1
1
1
2
1
2
1
1
1
0
4
0
0
1
1
0
0
0
3
1
0
2
0
1
0
0
0
0
0
0
1
0
1
1
1
0
1
1
1
0
2
2
1
1
1
1
0
0
1
0
3
0
0
1
2
2
1
1
0
2
2
1
1
0
0
0
1
2
2
0
1
0
1
2
1
1
2
0
2
1
1
1
2
2
0
0
1
1
1
1
1
1
2
1
1
3
2
1
2
0
3
1
1
1
1
2
0
0
0
0
1
0
0
2
0
1
1
1
2
2
0
1
0
2
0
1
0
2
1
1
0
2
0
1
2
1
1
2
2
1
1
1
1
0
0
1
1
0
0
1
1
0
2
0
0
0
0
0
1
0
2
0
0
0
1
1
1
1
2
1
0
0
1
1
1
0
1
1
0
1
1
1
2
2
2
1
0
2
1
0
1
0
0
1
0
1
2
1
0
1
1
2
2
0
0
3
0
0
1
1
0
2
1
0
0
0
0
2
2
2
0
1
0
2
1
1
1
1
0
0
2
1
1
2
1
1
1
1
1
1
1
2
1
1
1
0
0
2
1
1
1
1
1
1
1
0
0
2
1
0
0
0
1
0
0
1
0
0
0
1
1
1
1
1
1
1
1
0
1
6
1
2
1
1
1
2
0
1
0
1
0
1
1
2
1
1
0
0
0
1
1
0
0
2
1
1
1
2
0
2
1
2
1
1
1
1
0
1
0
0
3
2
1
0
2
2
1
0
2
1
0
1
1
2
1
1
2
0
1
1
1
0
1
1
2
1
1
2
0
0
2
1
2
2
1
2
2
1
1
0
1
1
0
0
1
1
1
1
1
3
0
2
1
1
0
1
1
1
1
0
0
1
1
2
2
0
0
0
2
0
0
1
2
1
0
1
2
0
2
1
1
0
1
2
0
3
2
0
2
0
2
1
1
0
2
1
1
0
1
1
1
2
2
2
2
1
2
3
2
1
0
2
2
1
0
1
2
2
1
2
1
0
1
1
1
1
0
2
1
0
1
0
1
1
1
0
1
0
0
1
0
0
1
0
2
2
1
1
2
1
2
2
0
0
1
2
2
0
1
0
1
2
2
0
0
1
1
1
0
1
0
1
0
1
0
2
0
1
2
2
1
0
2
2
2
2
0
0
1
2
3
1
2
1
1
1
0
2
0
0
0
1
1
2
0
2
1
0
2
1
1
1
1
0
0
1
1
1
0
1
1
1
1
0
2
0
1
1
0
1
2
1
0
2
0
2
1
1
1
1
1
1
1
0
1
3
1
2
0
1
2
2
0
2
0
2
2
1
1
1
0
1
0
1
0
1
1
1
1
2
1
1
0
0
1
0
2
1
2
1
1
1
0
1
1
0
2
2
1
1
1
2
1
1
1
0
1
1
1
2
1
0
2
1
2
0
0
1
1
1
0
1
0
1
1
0
0
2
1
0
1
0
1
2
1
0
0
1
0
1
1
1
1
1
0
2
2
2
1
2
1
1
1
1
1
0
0
2
1
0
0
2
1
0
1
0
0
0
1
2
1
1
0
1
1
1
0
1
0
1
1
0
1
1
1
0
1
2
0
2
2
1
0
1
0
1
1
1
0
0
1
0
0
1
0
0
1
3
0
1
0
1
0
0
3
0
0
1
0
2
1
1
2
0
1
1
2
0
2
0
1
2
0
1
1
0
1
1
1
0
2
1
1
1
1
2
0
1
1
2
0
1
2
1
0
0
1
1
1
2
0
2
0
2
0
2
2
0
0
1
1
0
1
1
1
0
0
0
0
1
1
1
0
2
1
1
0
1
2
0
1
0
1
0
1
1
3
0
1
1
1
0
1
0
0
1
0
1
2
1
1
0
1
2
1
2
1
0
1
2
2
1
2
2
2
0
0
5
1
2
1
2
1
0
2
1
1
0
0
1
1
0
2
1
2
2
1
1
2
1
0
2
2
1
1
1
0
2
0
0
1
0
1
1
1
1
0
1
0
2
1
0
0
0
1
0
1
1
0
0
1
2
0
2
0
1
1
1
1
1
0
0
0
2
1
0
0
1
1
0
0
2
1
2
2
0
0
0
1
0
1
1
0
2
1
1
1
2
2
0
2
1
2
1
0
2
1
0
1
0
0
1
0
0
1
1
0
1
1
1
1
2
0
0
1
2
1
2
1
1
0
0
0
1
0
1
1
1
0
1
0
0
0
0
1
1
1
1
2
2
2
0
0
0
0
1
2
0
0
1
2
1
0
1
0
1
0
0
1
1
0
1
1
0
1
0
1
0
1
0
0
3
0
0
0
2
1
0
1
0
2
1
0
0
1
0
1
2
0
2
2
0
2
2
1
0
1
2
1
2
2
0
0
0
2
1
0
1
0
1
2
1
2
0
1
1
1
1
0
2
2
2
1
0
0
0
0
0
1
1
1
1
0
1
2
0
2
1
0
1
2
2
2
1
2
1
1
2
2
1
0
0
0
3
0
2
1
2
2
2
1
0
1
2
0
0
2
0
1
2
1
1
1
1
2
1
0
0
2
1
2
1
0
1
2
1
1
1
0
1
0
2
1
1
1
1
1
2
1
3
1
2
0
0
1
0
3
1
1
1
2
2
1
2
0
1
1
1
2
0
1
0
1
1
1
0
0
1
1
1
0
1
1
1
0
1
0
0
1
2
1
1
2
1
1
3
2
1
1
0
1
1
1
0
1
1
0
1
1
0
1
0
2
2
2
1
1
1
1
4
1
0
0
1
1
2
1
1
1
1
1
0
1
1
1
0
2
1
1
0
0
2
0
1
0
1
1
0
2
1
1
1
0
2
1
2
1
2
1
2
1
1
0
1
2
2
0
1
1
1
0
1
1
0
1
0
1
1
1
1
1
2
1
0
0
1
0
0
1
1
0
1
0
1
2
0
1
0
1
4
2
2
0
1
1
1
3
2
1
2
1
1
0
2
0
0
1
1
1
1
2
0
0
1
2
1
0
0
0
1
0
2
2
0
1
1
0
2
0
0
1
0
1
0
0
0
1
1
1
1
2
2
0
2
0
1
0
1
2
0
1
0
2
2
0
1
1
0
0
0
2
2
0
0
2
1
0
2
1
0
2
0
1
2
0
1
1
0
2
2
0
2
0
1
0
2
0
0
2
1
2
1
1
1
0
1
2
0
1
0
0
0
1
1
1
1
0
0
1
0
1
1
1
2
0
2
2
2
1
1
2
1
0
2
2
2
1
1
2
0
1
1
0
2
1
2
1
2
1
2
2
0
1
2
2
1
2
1
0
0
1
1
2
0
1
2
1
0
0
1
1
2
0
2
0
1
1
1
0
1
0
1
0
2
1
0
0
0
2
2
0
0
1
1
0
1
0
1
1
0
1
0
2
0
1
2
1
0
2
1
1
2
2
1
0
0
0
1
1
2
2
0
0
0
0
1
2
2
0
1
2
1
0
1
2
1
1
1
2
0
0
0
0
0
1
1
2
0
1
0
1
1
1
2
1
0
0
1
1
0
2
0
0
1
1
1
1
2
1
0
0
1
1
1
2
0
0
1
0
1
2
0
0
2
1
0
1
0
0
2
1
1
0
0
1
1
1
1
0
1
2
0
1
1
0
2
1
1
2
0
2
1
1
3
0
2
2
1
2
0
2
1
1
0
0
0
2
0
0
0
1
1
0
1
0
2
1
2
0
2
1
1
2
0
1
1
2
4
1
1
1
0
0
1
2
1
1
1
1
1
0
1
1
1
1
3
2
0
1
1
0
0
1
0
0
1
0
2
1
1
0
1
0
0
0
0
1
1
1
0
0
1
0
2
1
0
2
1
1
2
0
1
0
1
0
1
2
1
0
0
1
1
2
0
1
1
0
0
1
1
0
2
1
0
1
2
0
1
1
0
1
0
1
1
1
1
0
0
0
0
1
1
0
1
0
1
2
2
1
2
1
0
1
1
2
2
1
2
0
2
0
1
2
3
0
0
0
0
1
0
1
2
0
0
1
2
1
1
1
2
1
1
0
2
2
2
2
0
0
1
1
0
1
2
2
0
1
1
1
1
2
1
1
0
0
0
0
2
1
1
0
2
1
1
0
1
0
2
1
2
0
0
1
1
1
0
1
0
1
1
0
1
0
0
1
1
1
1
0
2
1
1
1
1
1
0
0
1
2
0
1
0
1
0
2
1
2
1
1
1
1
0
0
1
1
0
0
0
1
2
3
1
2
1
1
1
2
1
0
0
0
3
0
1
0
1
1
1
1
2
0
0
1
1
1
1
1
0
0
0
0
1
0
2
1
1
1
2
1
1
2
1
1
1
0
0
2
1
1
2
1
1
2
1
2
0
2
1
0
0
1
0
1
1
1
1
1
1
0
0
1
0
1
1
0
2
1
1
1
1
1
2
1
1
0
1
1
1
1
0
1
1
0
2
2
0
1
0
0
3
0
1
0
0
1
3
0
2
1
0
1
0
0
1
1
0
0
1
1
2
4
0
1
2
1
0
0
2
1
2
1
2
1
1
0
0
0
2
0
0
2
1
1
1
1
0
3
0
0
0
0
2
1
0
1
0
1
1
2
2
1
1
1
0
1
2
0
1
2
1
1
1
1
0
0
0
1
1
0
2
2
0
1
1
1
1
1
1
1
0
2
2
1
0
0
0
1
1
2
0
1
1
1
0
1
2
1
1
1
1
1
1
2
1
0
1
0
2
1
1
5
0
2
2
0
1
0
1
1
1
1
0
0
2
1
2
0
2
1
1
1
0
1
0
0
0
0
2
0
2
0
2
1
1
0
1
0
1
1
1
1
1
1
2
1
0
0
1
1
1
1
0
0
2
1
2
1
0
0
2
1
2
2
1
0
0
2
1
1
1
1
1
1
0
2
1
0
1
2
1
1
1
2
0
1
1
1
1
0
2
1
2
1
2
0
1
2
0
1
1
1
2
0
2
1
0
2
0
1
0
1
0
0
1
0
0
2
1
1
0
1
1
0
2
0
0
1
1
1
1
2
1
0
0
1
2
0
0
1
0
1
0
1
1
1
2
1
1
1
0
2
0
1
1
0
1
2
1
2
0
1
1
1
1
1
0
0
1
0
1
1
0
1
0
1
1
1
0
2
1
1
0
0
1
1
0
1
2
2
2
0
1
0
1
0
0
1
0
0
1
0
1
1
0
1
1
2
1
0
1
0
1
1
3
2
1
0
0
3
1
2
1
0
1
2
1
1
0
2
0
3
0
1
2
2
0
0
2
2
2
1
2
2
2
0
0
0
1
1
2
1
1
1
1
2
1
0
2
0
0
0
1
0
2
0
0
2
5
2
1
0
3
1
1
1
0
0
0
1
0
1
2
1
1
1
0
0
0
1
1
0
1
2
2
2
1
0
1
2
0
0
0
0
1
2
2
1
1
0
0
2
1
2
2
0
0
2
1
1
1
1
1
1
0
1
0
2
2
1
1
1
0
1
1
1
2
0
2
1
0
1
1
2
0
0
1
1
1
2
1
1
0
1
1
0
2
2
1
1
0
1
2
2
0
1
0
1
2
0
1
1
1
0
3
2
0
0
2
0
2
0
1
1
2
1
1
2
1
1
1
1
0
1
1
0
0
2
0
1
0
1
1
2
0
0
1
1
1
1
0
0
1
0
2
0
0
0
1
0
0
1
0
0
1
0
2
2
2
0
2
2
1
1
0
1
2
1
2
1
2
1
1
2
1
0
0
0
1
0
0
2
1
0
1
2
0
1
0
1
0
2
2
1
0
2
1
1
0
1
1
2
1
3
0
2
1
1
0
1
0
2
0
2
0
1
1
1
1
1
0
1
0
1
1
1
1
0
1
2
1
1
2
1
2
1
0
2
0
2
0
2
2
1
0
0
2
2
1
0
2
2
2
0
1
0
0
1
1
1
0
1
0
2
2
1
0
0
1
0
0
1
1
0
0
1
2
2
1
0
0
1
2
0
1
2
1
1
0
0
1
2
0
0
2
0
2
0
1
1
1
1
2
1
0
1
0
2
0
0
1
1
1
0
1
1
0
1
0
1
0
2
1
1
2
0
3
0
0
0
1
2
1
0
2
0
2
2
2
0
1
0
0
1
1
1
0
0
1
2
1
0
1
1
0
0
1
0
1
1
1
2
0
0
1
1
1
1
1
1
1
1
0
2
1
1
2
1
2
0
2
1
1
2
0
0
0
0
1
1
3
0
2
0
1
2
0
1
1
1
1
0
2
1
1
2
2
0
1
1
0
2
2
2
0
1
0
1
0
2
2
1
1
1
1
0
2
0
1
2
0
0
3
1
0
1
1
2
1
2
1
2
0
2
2
2
1
2
3
1
0
1
1
2
0
0
1
1
1
1
1
1
0
2
0
1
0
0
2
0
0
1
0
2
1
0
0
0
2
1
1
1
1
0
0
2
0
0
2
1
0
1
2
0
2
0
0
1
2
1
0
1
2
1
0
1
1
1
1
1
0
1
0
0
1
0
2
1
0
1
2
2
1
2
2
1
2
0
0
1
1
2
0
1
1
1
1
2
0
0
0
1
2
0
1
1
2
1
0
1
0
0
2
1
0
0
0
2
2
1
0
0
0
0
0
2
1
0
1
2
1
0
2
1
0
2
1
0
1
0
2
0
0
0
1
2
0
2
0
2
1
0
0
1
1
2
0
0
0
1
1
1
1
0
1
2
0
2
1
1
1
1
1
0
2
0
0
1
0
1
0
1
2
0
1
1
0
0
0
1
2
2
0
0
0
2
1
1
2
1
3
0
2
2
1
0
0
0
1
1
2
0
2
5
2
1
0
0
2
1
0
0
1
1
1
1
0
1
0
0
1
1
0
1
2
1
1
0
2
2
2
0
0
0
0
1
1
1
1
1
0
2
1
0
0
1
0
0
0
1
1
2
1
0
0
1
1
1
1
1
0
1
0
0
1
1
2
2
1
0
1
1
1
1
2
1
0
2
0
0
1
1
0
2
1
0
1
1
1
2
1
1
0
0
0
1
1
2
0
2
0
0
1
1
0
0
0
1
0
2
2
1
1
0
0
1
0
1
1
1
1
2
1
0
1
2
1
2
2
0
0
0
1
0
0
1
0
1
0
1
1
1
0
1
1
0
2
2
1
1
1
1
1
0
2
1
1
1
2
0
0
1
2
1
1
0
2
2
1
0
1
1
2
2
1
0
2
4
1
3
2
0
1
2
0
0
2
0
1
0
0
2
0
1
1
1
1
0
9
1
1
2
1
1
1
0
1
1
1
0
2
0
1
0
2
0
2
1
1
2
1
1
2
1
1
2
2
2
0
2
1
1
1
0
1
0
0
1
0
0
1
1
2
0
0
0
1
0
0
0
1
1
1
2
2
0
1
1
0
0
1
0
1
1
0
1
0
1
2
0
0
0
1
2
0
0
0
3
2
1
1
1
0
1
1
1
0
1
1
2
0
2
1
1
0
1
1
0
1
2
1
3
1
0
0
1
1
1
0
1
1
1
0
0
2
0
2
1
1
1
0
1
0
0
0
0
1
1
2
1
1
1
1
0
0
1
1
0
0
1
1
1
1
0
2
1
0
1
1
2
0
0
2
2
2
0
0
0
0
0
0
1
1
0
0
0
3
1
1
2
1
1
1
0
0
2
0
1
0
0
1
1
0
2
1
1
0
0
2
0
2
0
1
1
0
1
2
2
0
1
2
0
0
0
0
0
1
0
1
0
1
0
2
0
1
1
1
0
0
1
1
1
2
1
2
0
1
1
1
0
1
1
2
1
1
1
1
0
0
1
1
0
2
0
1
0
1
1
1
0
1
1
0
2
2
0
1
1
0
0
0
0
0
1
2
1
0
0
1
0
1
0
0
1
0
1
0
2
2
0
0
1
1
1
2
2
0
2
1
2
0
0
2
0
0
1
0
1
1
0
1
1
0
1
2
1
0
2
1
0
0
2
0
0
1
1
0
1
2
1
1
0
2
0
1
1
1
1
2
2
1
1
1
0
1
1
2
2
1
0
2
0
2
0
0
0
0
0
1
1
0
1
2
2
1
1
1
0
2
0
2
1
0
2
0
0
0
0
1
1
1
0
2
0
1
1
1
0
1
1
1
1
2
0
0
0
0
0
0
1
0
1
1
1
2
1
0
0
2
0
1
4
1
1
1
1
1
1
0
2
2
1
1
2
0
0
0
1
0
1
1
1
1
3
1
0
0
0
1
1
2
0
1
0
1
0
0
2
0
0
1
0
2
1
1
2
0
1
1
2
0
0
2
1
1
1
1
0
0
0
2
0
0
2
2
1
0
1
1
1
2
1
1
1
1
2
1
2
0
1
1
1
0
1
0
1
0
1
0
1
0
1
0
1
1
0
1
1
0
1
0
2
0
0
2
0
2
0
2
1
1
1
0
1
0
2
0
0
0
2
0
1
0
1
0
0
2
2
2
0
2
2
0
0
0
0
1
2
1
1
1
2
1
0
1
2
1
1
2
2
1
0
0
0
1
0
2
2
2
2
1
0
0
2
1
2
0
0
1
0
1
1
2
1
2
1
1
0
1
2
1
2
0
0
2
0
1
1
0
1
0
2
1
1
1
1
0
0
0
1
0
0
0
2
1
0
1
1
1
2
0
2
0
1
0
0
1
2
1
0
2
1
1
0
1
0
1
2
1
0
2
1
1
1
1
1
2
0
0
2
1
1
1
1
0
1
1
1
1
6
0
1
0
2
2
0
2
0
1
0
1
1
0
0
1
1
0
0
1
3
0
1
1
0
0
1
1
0
1
1
1
2
1
1
0
1
2
0
1
1
0
2
2
1
1
1
2
1
0
1
0
1
0
0
0
1
1
0
0
2
1
2
2
2
0
0
0
1
1
2
2
1
1
0
1
0
0
1
0
0
2
1
1
0
1
0
1
2
2
1
0
0
0
1
1
0
2
0
1
1
1
1
0
1
1
1
1
1
0
1
3
0
1
0
2
0
0
0
1
2
4
0
1
2
1
0
2
0
1
2
1
1
1
2
2
2
0
2
1
0
1
0
2
1
1
0
2
1
1
2
2
1
0
2
0
0
2
0
0
2
0
0
1
1
1
0
0
2
1
1
1
1
0
0
1
1
1
1
1
2
1
0
2
1
2
0
0
2
0
0
1
1
1
1
2
2
0
1
2
0
1
0
1
0
1
1
1
0
1
1
1
1
1
0
1
1
2
1
0
0
0
1
1
1
0
0
1
1
1
1
0
1
0
2
0
1
0
1
0
1
1
1
0
2
1
5
0
2
1
2
1
2
1
1
2
1
0
1
1
1
1
1
0
1
0
1
1
1
0
0
0
1
1
1
2
0
1
2
1
1
1
0
0
2
2
0
1
2
1
3
0
0
2
1
0
2
0
2
1
1
0
2
0
0
1
1
2
1
2
0
1
1
0
0
1
2
0
2
1
2
1
2
1
0
1
1
1
1
1
0
1
2
1
1
1
1
1
1
2
2
2
0
1
1
1
2
1
2
1
0
0
0
1
0
0
0
2
0
0
1
1
2
1
2
1
1
1
1
1
2
1
0
2
2
2
2
0
1
1
2
0
1
1
1
0
1
0
2
0
0
1
1
1
1
1
1
0
1
4
0
0
1
0
0
1
1
0
2
2
0
1
2
0
0
1
0
0
2
3
0
2
1
1
1
1
0
1
0
1
1
0
0
1
1
0
1
0
0
1
0
1
2
1
2
2
1
2
0
1
1
1
3
2
1
1
1
2
0
1
0
2
2
0
1
2
1
2
2
3
2
1
1
1
2
1
0
2
0
2
0
1
1
1
1
2
1
2
1
1
1
0
2
0
1
2
1
1
1
1
0
1
0
0
0
1
1
2
1
2
1
2
2
1
2
0
1
0
2
3
0
0
1
1
0
1
1
1
1
1
0
1
0
2
2
1
0
0
2
2
0
1
0
2
2
0
1
0
0
0
1
1
0
0
0
1
3
0
1
1
1
1
0
1
1
1
0
1
0
1
1
0
1
2
1
2
1
2
1
0
0
1
2
2
2
1
1
0
3
0
2
1
1
1
0
1
1
1
1
1
1
0
2
2
0
1
0
2
0
0
0
0
1
0
0
2
1
0
1
1
0
0
0
1
0
1
1
0
1
1
0
2
2
2
1
1
1
1
1
0
1
0
1
2
1
1
1
0
1
2
1
2
2
1
1
1
2
1
1
2
2
1
1
1
1
2
1
2
2
1
0
0
1
0
0
0
1
0
3
0
1
1
1
1
0
1
1
2
0
0
1
1
1
1
1
0
0
0
0
0
1
1
0
2
1
1
1
1
1
2
1
0
1
1
0
2
1
0
2
1
2
0
0
1
0
0
0
1
1
2
0
1
0
1
0
1
0
1
0
1
2
0
1
0
1
2
2
5
0
1
0
0
1
0
1
1
0
1
0
0
1
0
1
1
0
1
1
0
0
2
1
1
0
0
2
0
0
2
1
0
0
1
2
2
1
1
0
1
2
1
0
0
3
0
0
1
0
0
0
1
0
1
1
0
0
1
1
2
1
2
2
1
1
0
2
0
1
0
1
0
0
0
0
0
0
2
2
1
0
1
2
1
1
2
1
1
2
2
0
0
0
0
0
1
1
2
1
0
0
1
1
2
1
2
1
0
1
2
2
2
0
0
0
1
1
0
3
2
2
2
1
0
0
2
1
1
1
0
0
1
1
0
0
0
0
1
0
0
1
2
1
1
1
2
0
1
1
2
1
0
1
1
2
0
1
3
0
2
3
1
1
0
1
1
0
1
1
1
1
1
0
0
0
2
2
1
0
1
0
0
2
0
0
1
0
1
0
2
0
0
1
1
1
0
1
1
0
2
0
2
2
0
1
2
3
1
1
0
2
1
0
1
1
1
1
2
2
0
0
1
2
1
1
1
1
1
0
0
1
0
1
2
0
1
0
0
0
1
1
0
0
0
1
1
1
0
1
0
1
2
2
1
1
0
0
2
0
1
1
1
1
2
1
2
2
2
1
1
2
1
0
2
0
2
0
1
0
0
1
1
1
1
1
1
0
1
0
3
1
1
1
2
0
2
0
1
2
1
2
1
1
2
2
1
0
0
0
0
1
1
0
1
1
1
1
0
0
0
1
0
0
0
1
0
0
1
0
0
1
1
1
0
1
1
1
0
1
1
2
1
2
1
0
2
1
1
1
0
0
0
0
0
0
0
0
2
0
2
1
2
1
0
2
0
2
1
2
1
1
1
1
1
1
0
1
0
0
1
0
0
1
1
1
2
2
1
0
2
1
2
1
0
1
2
1
1
1
1
0
0
1
2
1
0
0
0
1
1
0
0
1
2
2
1
2
1
0
0
0
1
1
0
1
1
1
0
0
0
0
0
0
1
0
1
1
0
1
0
1
2
1
0
0
0
2
1
0
0
0
2
0
1
0
0
1
0
1
0
0
0
1
0
1
2
0
0
0
0
2
2
0
2
1
0
0
1
1
2
1
2
1
2
1
1
0
0
0
1
0
1
1
1
0
0
0
0
1
1
1
1
1
2
0
0
0
2
1
6
0
1
0
2
2
1
1
1
0
1
1
3
0
2
2
1
2
0
2
1
2
0
2
0
0
1
0
0
0
0
1
2
1
0
0
1
1
0
0
1
0
2
1
2
2
1
1
1
1
1
2
4
1
1
1
1
2
1
1
0
0
2
1
1
1
1
0
0
1
1
1
0
0
0
0
0
2
0
0
2
2
0
2
0
2
0
1
0
2
1
1
2
1
1
0
1
2
0
2
2
0
0
0
1
0
2
1
1
0
2
2
1
0
1
1
2
0
0
0
1
2
2
2
1
0
0
0
1
0
1
0
1
1
1
1
1
0
2
0
1
1
1
0
1
0
0
2
1
0
2
1
1
1
1
1
0
3
1
1
1
0
1
2
1
1
1
2
2
0
0
0
0
1
2
2
2
1
0
2
0
0
1
1
0
1
0
2
1
0
2
1
0
0
1
0
1
1
2
1
2
0
2
1
0
2
0
0
0
0
1
0
2
0
1
2
0
0
1
0
0
1
1
2
1
0
0
1
1
0
1
2
2
1
1
2
0
0
1
1
0
1
1
3
2
2
0
2
2
0
1
2
1
0
2
1
1
1
1
0
2
2
2
1
3
2
1
0
1
1
0
1
1
1
0
1
1
0
0
0
0
1
1
2
1
0
0
0
1
0
1
0
0
0
2
1
2
1
1
3
1
2
1
1
1
1
1
0
2
1
1
0
2
2
1
1
2
2
1
2
1
1
1
1
1
0
2
2
0
1
0
0
1
0
0
0
1
1
1
0
0
0
2
1
0
1
2
0
1
0
0
1
0
3
0
2
2
1
1
1
1
2
0
2
1
0
1
0
1
2
1
2
0
1
0
1
1
0
1
1
1
0
1
0
1
2
1
0
0
1
0
1
1
0
0
1
1
0
2
0
1
0
2
0
0
1
0
2
0
1
1
1
1
2
1
1
1
2
1
2
1
1
0
2
1
2
1
0
1
1
2
1
2
2
0
2
2
1
2
2
1
2
1
0
0
1
2
2
1
1
3
1
1
0
1
2
3
1
1
0
0
1
1
0
0
2
0
0
0
3
1
2
2
1
1
1
0
1
1
2
1
1
1
1
0
1
2
1
1
0
1
1
0
1
0
1
1
0
2
1
1
1
0
2
2
0
0
2
0
1
1
2
1
0
1
1
0
2
1
1
0
0
1
0
2
0
1
1
1
1
0
2
0
2
2
1
0
0
2
1
2
1
1
1
2
1
1
2
2
1
0
1
1
0
0
1
0
2
1
1
1
2
1
2
1
1
1
0
2
0
0
1
2
2
1
0
2
1
2
0
0
1
2
0
1
1
1
0
1
0
1
2
0
1
0
0
0
0
1
1
0
1
0
0
1
0
0
0
1
0
1
0
1
1
1
2
1
0
0
0
1
0
1
0
2
0
2
1
1
2
0
0
0
1
1
2
1
0
2
1
0
1
1
0
2
2
1
2
2
0
2
1
3
1
1
0
0
2
1
1
0
0
1
0
0
0
1
1
0
1
1
1
1
1
1
0
1
1
2
1
1
3
2
0
1
1
2
2
2
1
2
2
0
0
1
1
0
0
2
2
2
6
1
1
0
2
0
1
0
1
0
0
0
3
1
2
1
1
1
0
1
0
0
1
0
1
1
1
1
1
1
0
0
2
1
1
0
0
0
0
1
1
1
0
1
1
1
0
1
3
2
1
1
2
1
1
2
0
2
1
0
1
1
1
1
0
1
0
1
1
1
1
2
0
1
1
1
0
1
1
1
0
0
1
1
0
2
0
1
2
1
1
3
1
2
1
2
0
1
1
0
0
0
0
2
5
1
0
1
1
0
1
1
0
2
0
1
2
2
1
1
2
0
2
1
0
1
1
1
0
1
0
0
0
0
1
1
1
0
0
1
1
2
2
1
1
0
1
0
1
1
1
0
0
1
1
1
1
1
1
1
2
2
0
1
0
0
2
1
1
0
1
1
0
0
2
2
0
1
0
1
0
1
1
2
0
0
1
1
1
0
0
0
1
0
1
0
0
1
1
0
0
0
1
2
1
0
0
2
1
0
1
0
2
0
1
1
0
1
0
0
0
2
1
1
1
0
1
0
1
0
0
1
0
2
1
2
2
1
0
1
1
0
1
0
1
0
1
1
1
0
2
2
0
2
1
1
2
0
0
0
1
0
1
0
1
0
3
2
1
1
2
0
0
0
0
2
0
1
1
1
1
1
1
0
2
2
1
1
2
0
1
1
0
1
1
0
2
1
3
1
2
1
0
2
0
1
1
1
0
1
2
0
0
0
2
0
1
1
2
1
0
1
2
1
2
1
1
2
0
1
0
1
1
1
3
1
2
1
0
1
2
0
1
0
2
1
0
2
1
0
0
1
0
0
0
1
2
0
1
0
0
0
0
0
3
1
1
2
1
1
2
1
1
2
1
2
1
2
2
1
1
1
1
1
2
1
0
1
1
2
0
1
0
0
2
0
1
0
0
1
0
1
0
1
1
1
2
1
0
2
1
0
2
1
0
0
2
0
1
2
1
0
1
1
1
1
0
1
2
1
2
0
1
0
0
2
1
1
1
1
2
1
1
1
2
0
1
1
1
2
1
0
1
1
0
2
0
1
1
1
0
0
1
0
2
1
1
1
2
1
1
1
1
2
1
1
1
0
1
2
1
1
1
0
2
1
0
0
2
2
1
1
2
2
2
2
1
1
1
2
0
0
0
2
2
1
1
0
1
1
0
0
2
1
1
1
1
1
0
1
0
0
0
1
1
1
1
0
2
2
0
1
1
1
2
0
1
1
0
0
0
2
2
0
1
0
1
0
0
1
0
2
2
1
2
0
0
2
1
0
1
0
1
2
1
1
1
1
0
0
0
0
2
1
0
1
1
1
0
2
2
1
2
0
0
1
0
1
1
1
2
1
1
1
1
1
1
1
2
2
1
2
1
2
2
0
1
2
0
1
0
1
1
2
0
0
0
2
1
0
1
0
0
1
1
0
1
2
2
1
1
0
1
1
1
1
1
1
2
0
1
1
1
2
1
0
0
0
0
0
1
1
0
0
1
1
2
3
0
1
1
0
0
1
2
2
2
4
2
1
1
1
1
1
3
1
0
1
0
1
0
0
1
1
2
2
1
0
1
1
0
1
0
1
0
0
2
1
0
0
0
1
1
1
1
0
2
0
1
1
1
2
0
1
1
1
0
2
2
1
0
0
2
1
1
0
0
2
2
0
2
3
0
0
1
0
1
1
1
1
1
1
2
1
1
2
1
1
1
1
0
1
1
1
0
1
1
0
1
1
1
4
0
0
0
2
1
0
1
1
0
2
0
1
1
1
1
1
0
1
1
1
0
2
0
1
0
0
0
2
0
1
1
1
0
2
0
1
1
2
0
2
0
1
2
0
1
1
0
0
1
1
1
0
2
1
0
1
2
1
1
0
0
1
0
1
0
1
1
2
0
1
0
0
0
0
1
1
1
2
1
1
0
1
2
1
2
1
2
1
0
1
1
1
2
1
0
2
0
0
2
2
0
0
1
2
1
1
0
1
1
1
0
1
0
2
1
2
0
0
0
2
1
1
2
2
2
1
4
1
0
0
0
2
2
2
0
2
0
0
1
0
2
1
1
2
0
0
1
0
0
0
1
1
2
1
2
1
2
1
1
1
0
2
0
1
1
2
1
0
1
0
1
1
2
1
1
0
2
2
1
0
1
0
1
0
1
2
0
1
1
0
2
1
2
1
2
0
2
1
0
0
2
1
0
1
0
2
4
0
1
0
0
1
1
1
0
0
2
2
1
0
2
2
2
2
1
2
0
0
2
1
1
0
0
1
1
0
2
1
1
0
0
2
3
3
1
1
0
2
1
0
1
1
1
1
0
0
1
0
1
0
1
0
1
2
0
1
1
2
0
1
0
1
1
1
1
3
1
1
0
0
0
1
3
0
0
1
2
1
0
1
1
0
1
1
2
1
0
1
2
1
0
0
0
1
1
1
2
2
1
0
0
0
0
2
1
2
1
0
0
1
1
0
1
1
1
1
1
0
2
2
1
1
1
2
1
3
2
1
1
0
0
0
1
1
2
1
1
0
1
1
0
0
2
0
1
1
2
0
1
2
1
2
1
1
0
1
1
1
2
1
0
1
1
0
2
1
2
2
0
0
2
1
0
0
0
0
0
1
1
0
2
1
1
1
0
1
1
1
1
1
0
1
0
1
1
0
1
0
3
1
0
1
2
0
0
0
0
2
1
0
0
1
1
1
0
1
3
1
1
1
1
1
2
1
2
2
0
2
2
1
0
1
0
0
1
1
1
0
2
1
0
1
1
0
0
0
1
1
1
1
0
0
0
1
1
0
2
2
1
2
1
0
0
1
0
0
0
1
2
1
1
2
1
0
1
0
1
0
2
1
0
0
0
0
0
2
1
0
0
0
0
1
0
1
1
0
1
0
0
2
0
3
0
0
1
2
2
0
1
2
1
1
0
1
1
2
0
1
2
1
1
1
0
0
0
2
0
0
0
0
0
1
1
1
3
1
0
1
2
1
0
0
0
1
2
1
0
0
1
0
0
1
1
0
0
0
0
1
2
1
1
2
0
0
0
2
2
1
0
2
0
0
0
1
1
0
0
0
0
0
1
2
2
0
1
1
0
1
2
0
1
0
0
0
0
1
0
2
2
2
1
1
1
0
0
0
0
1
2
1
2
0
1
0
1
0
1
3
1
2
1
2
0
2
1
1
1
1
1
2
1
2
0
1
0
0
0
1
1
1
0
0
0
1
1
1
2
1
0
0
0
0
0
1
2
2
0
0
2
1
2
0
2
3
0
0
1
0
1
1
0
1
1
1
1
0
2
2
0
0
1
0
0
0
1
2
1
2
2
0
2
1
2
1
1
0
1
0
1
1
2
0
2
1
1
0
1
2
1
0
1
1
2
2
0
0
0
2
2
2
0
1
1
1
0
0
0
2
2
0
0
1
2
2
2
1
2
2
1
0
0
1
1
1
1
2
1
0
1
2
1
1
1
2
1
2
1
1
2
1
0
2
1
0
1
1
1
1
1
0
0
2
0
2
1
1
1
1
1
0
4
0
0
1
0
0
0
1
0
1
2
0
2
1
1
1
0
0
1
1
1
1
0
0
1
1
2
1
1
1
2
1
1
2
2
2
0
1
1
1
2
1
1
0
0
1
0
0
2
1
2
0
1
0
1
1
1
1
1
1
0
1
3
1
1
1
1
1
1
0
1
0
2
1
2
1
0
1
1
1
2
0
1
0
2
2
1
1
0
1
0
1
2
1
0
0
1
1
0
1
2
2
1
1
1
1
0
1
0
1
1
0
1
2
1
0
2
1
0
0
1
1
0
1
0
1
1
0
0
0
0
2
1
0
2
1
2
0
1
0
1
2
0
1
1
2
1
0
1
0
1
0
2
0
0
1
2
0
0
1
2
0
0
0
0
1
1
1
2
1
1
0
1
1
1
0
0
1
0
2
4
1
2
1
2
0
0
1
2
1
0
0
1
1
1
1
1
2
1
2
1
0
0
2
0
1
1
1
1
1
0
1
0
1
1
1
1
1
1
0
1
1
1
1
2
1
0
2
1
0
1
1
0
0
0
0
0
1
1
0
1
1
1
1
0
0
1
1
2
2
1
2
0
0
0
0
0
2
0
0
1
0
1
0
0
1
0
0
0
1
0
2
0
0
1
1
0
1
1
3
0
1
1
1
0
0
1
1
0
2
2
0
2
1
2
1
0
2
1
0
1
1
0
0
1
0
0
1
1
2
1
2
2
1
2
1
1
1
0
1
2
0
1
1
0
0
0
0
0
0
0
1
1
1
0
2
2
1
1
1
1
1
0
1
0
1
0
1
3
1
1
0
1
0
0
2
2
1
0
0
0
0
0
0
0
1
1
1
0
0
1
0
1
2
2
0
2
0
0
0
1
2
1
1
2
0
0
1
2
1
2
1
2
1
1
0
0
0
1
0
1
1
1
0
1
0
2
1
2
1
0
2
1
1
0
1
0
1
2
2
3
1
0
1
0
1
2
0
1
1
2
0
2
1
1
0
2
1
2
1
1
0
0
2
2
1
1
1
0
1
2
1
0
1
1
1
0
2
1
0
0
1
1
0
2
1
0
0
0
0
0
1
1
0
0
2
1
0
0
0
0
1
1
0
1
1
2
1
0
0
0
0
0
1
0
0
2
5
0
1
1
0
1
0
1
2
2
0
1
1
0
2
0
1
1
1
0
0
1
1
0
0
0
0
0
1
2
1
0
0
0
3
2
2
1
0
1
1
2
1
0
2
1
1
0
1
0
0
2
1
0
0
1
0
3
0
0
0
1
1
1
1
2
1
0
0
0
1
2
2
1
0
1
0
1
1
0
3
0
1
2
1
1
2
1
1
2
0
1
2
0
2
1
1
1
1
1
1
1
2
1
2
2
0
1
0
0
1
1
0
1
2
2
1
2
2
0
1
1
1
0
1
1
2
0
1
0
2
2
2
0
1
1
0
0
0
0
0
0
1
1
0
0
1
2
1
1
0
1
1
1
1
2
1
2
1
2
0
1
0
0
2
0
2
0
1
1
2
2
1
2
0
0
0
1
1
1
0
2
2
1
1
0
2
1
0
0
0
1
1
1
1
2
1
1
0
1
1
2
0
2
1
2
1
1
1
1
0
1
1
0
0
1
2
1
0
1
2
1
0
0
1
1
2
1
1
0
1
1
1
1
2
1
0
2
2
0
1
0
1
1
0
1
1
0
0
2
2
2
0
2
0
1
1
0
0
1
1
1
2
1
1
1
0
1
0
0
1
1
1
0
1
1
1
1
1
2
1
1
1
1
0
1
1
0
1
1
0
1
1
2
2
0
1
1
2
2
1
0
1
1
2
0
2
1
1
2
1
2
2
1
0
0
2
0
0
1
1
2
0
2
1
1
2
1
0
2
0
2
2
2
0
0
1
0
1
3
2
1
2
1
0
0
1
1
1
0
1
1
0
1
1
2
1
0
2
0
1
0
1
1
1
0
0
2
0
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
1
0
0
0
1
1
1
1
1
1
2
2
2
1
0
1
2
2
1
1
0
2
0
1
2
2
1
2
1
2
0
0
0
1
0
2
0
2
1
1
0
2
1
0
1
0
1
0
2
1
1
0
1
1
0
0
1
0
1
0
1
0
0
0
2
1
1
2
1
3
0
1
1
0
0
1
1
1
2
0
0
0
1
2
1
0
1
0
1
1
1
0
0
2
1
1
0
2
1
2
2
0
2
1
1
1
0
2
3
1
2
2
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
2
1
1
1
0
0
0
2
0
3
1
0
1
1
1
0
0
1
1
2
1
1
0
2
1
0
1
0
3
1
1
0
2
0
1
1
0
0
0
2
0
0
0
1
2
1
0
0
1
1
2
1
2
0
2
2
1
0
2
1
0
1
1
0
0
0
2
2
2
1
0
0
0
1
2
1
2
1
2
1
0
1
1
0
1
2
0
0
1
3
0
1
1
1
1
3
0
2
0
0
0
2
2
1
2
0
1
0
0
1
0
1
0
0
2
1
1
1
0
1
3
2
1
2
1
2
3
1
1
0
0
1
1
1
0
1
1
1
1
1
1
2
0
1
2
1
0
2
1
1
1
1
0
1
3
1
0
0
0
1
1
2
0
0
0
1
0
1
0
2
1
1
2
1
0
0
2
3
0
0
1
0
1
0
2
0
2
2
1
2
0
0
1
2
0
1
1
1
2
0
3
0
0
1
1
2
0
0
0
1
1
1
2
2
0
1
0
1
1
2
1
0
0
0
2
0
0
1
2
1
0
2
0
0
0
1
0
0
1
1
1
2
1
1
1
0
0
2
2
2
2
1
2
2
2
1
0
0
1
1
1
0
1
2
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
2
2
2
2
1
0
1
1
2
2
1
1
0
1
2
2
0
0
2
1
0
1
0
2
1
2
2
2
2
2
0
1
1
1
0
2
2
1
2
0
0
1
0
1
1
1
1
2
3
0
1
2
1
1
0
0
0
1
0
1
1
0
2
1
2
0
1
0
0
1
0
2
0
1
1
1
1
0
0
0
0
0
1
0
1
0
2
1
2
1
1
0
1
0
0
2
1
0
1
1
0
1
0
1
0
1
0
2
2
1
1
1
1
0
1
1
2
1
0
0
1
1
1
0
2
0
0
0
0
0
2
2
1
1
1
0
0
0
2
1
1
0
1
1
2
2
0
0
0
1
1
0
1
1
0
0
0
1
1
2
1
1
0
0
2
2
1
1
1
1
0
1
0
1
2
0
1
0
0
0
1
2
0
1
1
1
2
0
0
1
1
0
2
0
2
2
1
1
1
0
1
0
0
1
1
1
0
0
2
1
1
0
1
1
1
1
1
0
0
0
0
0
2
0
0
1
0
1
11
0
1
1
1
1
5
1
1
1
1
3
0
2
0
0
1
2
0
2
0
0
1
0
2
2
1
0
0
0
1
1
2
1
1
1
1
1
0
0
1
0
2
0
1
1
1
1
2
1
1
0
2
4
1
2
2
1
1
0
0
1
0
0
0
0
0
1
2
0
1
0
2
0
1
2
2
1
0
2
1
1
1
1
0
1
2
0
0
1
1
0
2
2
1
0
1
0
1
0
1
1
1
2
2
1
1
0
1
1
1
0
0
1
1
1
1
1
0
2
0
0
1
2
1
1
0
0
2
1
1
0
1
0
0
2
1
0
2
1
0
1
1
1
2
0
1
0
1
1
0
1
1
0
1
1
0
2
0
1
0
1
1
2
1
0
0
0
2
1
1
1
2
0
1
1
2
1
1
2
2
1
1
0
1
1
1
0
1
0
1
1
1
2
0
1
0
0
1
0
1
1
0
1
0
1
0
0
1
1
1
0
0
0
1
1
2
1
2
1
2
1
2
0
0
0
0
0
1
2
1
2
1
1
0
1
2
0
1
1
1
1
0
2
2
2
1
1
2
1
1
2
1
2
1
0
2
2
1
0
2
1
2
0
1
2
2
1
2
1
1
1
2
1
1
0
1
1
0
1
0
0
0
0
0
2
1
0
0
0
1
0
0
4
1
1
2
0
2
1
0
2
0
0
0
0
3
1
1
2
0
0
0
1
2
2
2
2
0
1
0
2
1
1
1
0
1
1
0
1
1
0
0
1
2
1
1
1
2
1
0
0
0
1
2
0
0
0
0
1
0
0
1
0
2
1
0
1
0
1
2
1
1
1
0
0
1
1
1
2
0
2
2
1
2
1
1
2
0
0
0
1
1
0
1
1
1
1
1
1
2
1
1
1
0
2
1
1
2
2
0
1
1
1
0
0
1
1
1
1
0
2
0
1
2
1
0
0
2
2
1
1
1
1
0
1
1
1
1
1
2
2
1
1
0
0
0
1
2
0
1
2
0
0
1
0
0
0
1
2
0
1
0
0
1
1
0
0
0
0
2
1
0
0
0
1
0
2
1
2
0
0
1
2
1
0
2
1
2
1
0
2
0
0
2
0
0
2
0
2
1
1
0
2
0
1
1
0
1
0
1
0
0
1
2
0
1
1
1
0
1
2
2
2
1
1
1
0
1
1
1
2
2
1
2
0
1
2
1
1
1
0
0
2
2
0
1
1
1
1
1
0
1
1
1
1
2
0
0
2
1
0
2
1
0
2
1
1
2
2
1
0
1
0
2
2
0
2
0
1
1
0
0
1
0
1
1
0
0
1
2
1
2
1
1
0
0
2
2
1
1
0
1
1
2
0
0
0
1
1
0
2
1
0
0
1
1
0
2
2
1
0
2
0
1
0
0
4
0
1
2
1
0
0
1
1
2
0
1
0
2
1
0
0
3
3
0
0
1
1
1
1
1
2
0
1
1
2
1
1
1
2
1
2
2
1
2
0
2
1
0
0
1
0
0
1
2
1
2
1
0
2
1
2
1
1
1
1
0
0
2
2
2
1
0
2
1
1
1
0
2
0
1
0
1
1
1
2
0
0
0
0
1
2
1
1
1
1
1
1
2
0
1
0
0
1
1
1
0
0
1
1
1
0
0
1
1
1
5
1
1
1
2
1
1
0
1
1
0
0
0
1
0
1
1
0
0
1
1
2
0
2
1
1
1
0
0
2
0
0
2
0
0
7
2
1
0
2
1
1
2
1
1
0
2
0
1
1
1
2
1
1
2
2
1
1
0
2
0
0
2
0
2
0
1
0
0
1
0
1
0
1
2
2
1
1
0
0
0
0
4
1
1
0
2
2
2
0
2
0
0
0
1
1
0
1
0
1
2
2
0
0
0
1
0
1
2
1
2
0
1
1
1
1
0
2
0
2
0
1
0
1
2
1
1
1
1
2
1
0
1
1
4
0
2
1
2
1
1
0
3
1
0
1
1
1
2
1
2
0
0
0
1
0
2
0
1
0
0
0
0
0
1
2
0
0
3
2
2
0
1
1
1
1
1
1
1
1
3
1
2
2
0
0
0
0
0
0
2
1
1
1
1
1
0
2
0
2
1
1
0
0
1
2
0
1
2
1
2
1
2
1
1
0
0
2
0
2
1
0
0
2
2
0
1
2
2
1
0
1
1
1
0
1
0
1
1
2
0
2
0
0
2
0
0
1
1
1
2
2
1
0
1
1
0
1
1
1
2
2
1
1
1
1
2
1
1
0
0
2
0
2
0
0
2
0
0
2
0
0
0
0
1
1
2
2
3
0
0
3
2
1
1
0
0
1
2
0
1
2
2
1
0
0
2
0
0
0
2
1
1
1
2
1
0
0
2
2
0
0
0
1
2
1
0
1
0
0
0
1
0
0
1
1
3
2
0
2
1
1
1
1
1
1
0
1
1
0
0
0
0
0
1
1
0
0
0
1
0
1
0
1
1
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
2
2
1
2
0
0
2
1
1
1
2
1
1
2
1
2
1
1
2
1
1
0
0
0
2
1
1
1
1
1
3
1
1
0
0
0
0
0
0
2
0
2
1
1
1
2
0
1
0
0
1
0
0
2
1
0
2
2
2
1
1
1
0
2
1
1
1
1
2
1
2
1
2
0
0
1
1
1
2
0
1
1
0
2
1
0
2
2
1
0
1
0
1
0
1
2
2
1
1
1
2
0
2
2
1
1
2
4
0
0
0
2
2
0
0
0
0
1
1
1
2
2
1
1
2
1
0
0
1
1
1
0
3
0
1
1
1
0
0
3
1
2
2
1
0
3
0
0
1
3
2
1
0
1
0
0
2
1
0
0
1
0
1
1
2
1
3
1
0
1
1
1
0
1
1
1
2
0
2
1
0
0
2
1
0
0
2
0
2
1
0
2
0
0
0
1
1
1
0
2
0
0
2
2
1
0
0
1
0
1
1
0
1
2
1
0
0
2
0
0
1
0
1
0
1
1
1
1
1
1
1
0
1
2
2
0
0
1
0
0
0
1
0
2
1
0
1
2
2
2
0
1
0
2
1
2
0
1
1
1
0
1
1
1
0
0
2
2
1
0
1
0
2
1
0
1
1
0
1
2
0
2
1
1
1
0
1
1
2
0
1
1
0
1
2
1
2
1
1
5
0
1
0
1
2
1
2
0
1
1
1
4
1
1
1
0
0
0
1
1
1
1
1
0
0
1
2
1
2
2
2
1
2
1
0
1
2
1
1
2
0
0
2
1
1
0
1
1
0
2
1
1
2
1
1
0
1
0
2
1
0
1
1
0
0
0
1
0
0
1
2
1
1
0
2
0
0
1
1
1
0
0
1
2
0
1
0
1
1
1
2
1
0
1
0
0
0
1
1
0
1
0
0
0
0
1
2
1
0
1
1
1
1
0
2
3
2
1
1
1
2
2
1
0
2
0
1
1
1
0
2
0
0
1
0
0
2
1
0
1
2
0
1
1
0
1
0
1
1
1
1
2
1
0
0
1
0
0
0
1
0
0
0
0
1
2
2
1
0
0
2
1
0
1
0
1
1
0
1
1
1
1
0
2
0
0
0
1
1
1
0
2
0
1
1
1
2
0
1
2
2
1
0
0
1
1
1
0
0
1
1
1
0
1
0
0
0
0
0
2
0
1
2
2
0
1
1
2
0
2
2
2
1
2
0
1
2
1
1
0
0
0
1
2
2
1
1
1
1
0
2
1
0
0
0
1
2
1
1
2
2
1
2
1
0
1
0
2
1
1
1
1
2
2
1
1
1
2
0
0
2
1
1
2
0
2
1
1
1
2
2
1
2
1
0
1
0
2
2
2
0
1
1
2
1
3
1
0
2
1
1
1
1
1
0
1
1
1
1
1
1
0
0
0
0
0
0
2
0
1
0
1
1
1
1
2
0
1
1
1
0
1
2
2
0
0
1
0
0
0
0
0
0
0
2
1
1
0
0
1
1
1
0
1
0
0
0
0
0
1
1
2
1
1
0
2
2
2
1
2
0
2
2
0
0
2
0
1
0
1
0
1
1
2
0
0
2
0
1
2
1
0
3
1
1
0
2
2
2
0
0
2
1
0
0
1
0
1
1
1
1
1
2
1
1
0
0
1
1
0
1
1
0
1
1
0
1
0
0
0
1
1
0
0
0
1
1
0
2
0
1
1
2
1
2
0
2
2
0
1
0
1
0
1
0
1
1
2
0
1
0
0
2
1
1
2
2
0
1
2
1
0
0
1
1
1
1
0
1
1
1
0
0
0
2
2
1
0
1
1
0
0
2
0
0
0
0
1
0
1
2
1
0
0
0
1
0
0
1
0
2
0
1
1
2
2
0
0
0
1
0
0
1
1
1
1
0
2
1
1
1
0
1
2
0
2
1
0
0
2
1
0
0
2
2
2
1
2
2
2
2
1
2
0
0
1
1
0
0
1
0
1
2
0
0
1
1
3
0
0
0
2
1
0
2
0
0
1
2
2
1
1
2
1
2
1
1
2
0
2
2
2
1
0
2
1
1
1
1
1
1
1
1
1
2
0
2
2
1
1
2
0
0
0
3
1
0
0
0
2
1
0
0
2
1
2
1
1
1
1
2
1
1
0
0
1
1
1
1
2
1
0
2
0
0
1
0
1
1
0
1
1
1
1
1
1
1
1
1
1
1
3
2
1
0
0
1
2
1
1
1
1
0
1
0
1
2
0
1
0
0
1
1
0
2
1
1
1
1
1
0
1
0
0
1
1
0
1
0
0
0
2
1
0
2
0
1
1
1
2
1
1
1
1
0
1
1
1
0
0
1
0
2
0
2
1
2
2
0
2
1
1
0
2
0
1
1
1
1
0
1
1
1
0
0
2
3
1
2
2
0
1
1
0
0
1
0
0
2
1
0
2
0
2
0
0
2
1
2
2
1
2
1
1
3
2
0
0
2
1
0
1
0
1
1
1
2
2
1
0
1
1
1
1
1
2
2
1
0
1
0
0
1
2
1
1
0
2
1
1
2
0
1
2
0
2
0
1
0
1
0
1
0
0
1
0
1
1
1
0
1
3
1
1
0
0
2
2
2
0
0
1
1
0
0
1
2
1
1
0
1
1
1
1
1
0
1
2
0
0
0
1
1
0
0
1
0
0
1
1
2
1
3
0
1
2
2
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
2
1
0
0
2
1
1
1
1
0
0
0
1
2
2
1
2
1
2
1
1
1
1
0
0
0
0
2
1
0
1
2
1
1
0
1
1
2
0
0
3
0
1
1
1
1
1
2
1
0
0
1
2
1
1
1
2
1
1
0
1
2
1
1
1
1
1
2
1
1
0
0
1
2
1
2
1
1
1
0
1
0
1
2
1
2
0
0
1
1
1
2
1
0
1
2
2
1
2
2
0
2
1
1
0
2
2
0
0
1
0
1
1
1
2
2
1
1
1
2
1
1
0
2
1
1
1
2
1
0
2
0
1
1
0
0
0
0
2
1
2
1
0
2
1
3
2
1
0
1
1
0
0
1
0
0
1
0
2
2
2
1
1
2
0
1
2
2
1
0
1
2
2
0
1
1
2
2
2
0
1
1
2
2
1
2
0
1
0
1
2
1
1
2
0
0
2
0
1
1
1
0
0
0
1
0
0
1
1
1
0
1
2
0
0
0
0
1
0
2
1
1
1
1
0
0
1
1
0
1
0
0
1
0
1
2
2
1
0
1
0
0
1
1
2
1
2
1
0
1
1
0
0
0
0
2
0
0
0
0
0
1
1
0
2
1
1
0
1
0
1
1
1
2
1
1
1
1
2
2
2
2
0
2
1
0
1
1
1
1
1
0
0
0
0
0
0
1
1
0
1
1
1
2
0
1
2
0
3
2
1
0
1
1
1
4
1
2
2
0
0
0
1
3
1
2
2
1
1
0
1
1
1
2
1
2
0
0
1
2
2
2
2
0
0
0
0
1
0
2
3
2
2
2
2
1
0
0
1
3
1
1
0
2
0
2
1
0
1
2
0
0
1
0
1
2
1
1
0
2
0
0
2
0
1
1
1
2
0
2
1
1
0
1
1
1
2
1
1
0
0
1
2
2
0
2
1
0
0
1
1
1
0
0
1
1
1
0
0
2
2
0
0
1
0
0
1
0
1
0
0
0
2
1
1
1
2
1
1
0
0
1
2
0
0
1
2
0
0
2
1
0
0
0
0
1
0
1
0
1
0
1
1
1
0
2
0
0
2
1
1
1
1
1
0
1
2
0
0
0
1
2
0
2
1
0
0
1
1
0
1
1
2
0
0
2
1
0
1
2
2
1
1
1
2
0
1
1
0
3
1
1
0
0
3
2
1
1
1
0
1
1
0
2
0
2
1
2
0
2
1
1
1
1
0
2
4
0
2
1
0
0
0
2
0
1
1
1
1
0
1
0
1
1
1
0
1
0
0
0
1
2
0
2
0
0
0
0
1
2
1
1
1
1
0
1
0
2
1
0
2
0
2
0
1
4
0
1
0
0
1
0
0
1
1
0
0
1
2
1
2
0
0
2
0
1
0
2
1
0
1
1
1
1
0
1
1
1
0
0
0
1
2
1
0
0
1
1
2
0
1
0
1
0
1
1
1
0
0
0
1
2
0
1
2
0
0
1
0
1
1
0
0
2
0
0
1
0
1
0
2
1
1
0
1
1
2
0
1
1
1
0
1
1
2
1
0
2
2
2
2
1
1
1
2
0
0
1
1
2
0
1
2
1
1
1
0
2
0
1
2
0
0
1
2
2
1
1
0
2
1
2
1
1
1
2
1
0
1
0
0
2
2
1
1
2
1
0
0
2
2
2
0
0
2
0
0
1
1
1
0
0
0
0
1
1
2
1
1
2
1
1
1
0
0
2
0
0
0
0
1
1
1
1
1
0
1
0
1
0
1
0
1
1
0
2
2
1
0
0
2
2
1
1
0
1
2
1
1
0
1
0
2
1
1
1
2
1
0
2
2
2
1
1
1
2
2
1
1
2
0
0
0
2
0
0
1
0
1
0
0
1
0
1
2
1
1
2
0
1
1
1
2
0
0
0
0
1
0
1
0
1
1
2
1
0
1
2
2
2
1
0
1
1
2
2
0
0
0
1
1
1
1
1
2
0
2
0
1
2
1
1
0
0
2
2
1
2
2
1
2
0
0
1
1
2
1
1
2
0
2
1
0
2
1
1
2
0
2
1
1
1
1
0
1
0
2
1
2
1
0
0
1
1
1
0
0
0
0
0
1
1
0
2
1
1
1
1
3
1
1
0
0
2
0
1
0
2
0
1
1
2
0
0
1
1
1
2
0
0
1
1
0
1
2
0
1
0
1
2
4
1
2
1
0
1
0
2
0
0
0
1
1
0
0
0
1
4
0
0
2
0
1
1
2
2
1
0
1
1
0
0
1
1
2
0
1
0
0
1
1
0
0
1
1
1
0
2
0
0
0
0
0
0
1
2
0
2
1
2
0
1
0
0
1
0
1
2
0
1
1
2
1
1
2
0
0
2
0
0
2
0
0
2
1
1
1
1
1
1
0
1
0
1
0
1
1
1
1
2
1
1
0
0
2
1
1
0
0
0
1
1
1
0
0
1
0
0
1
1
0
0
1
1
0
2
1
2
0
1
0
0
0
2
1
1
0
1
1
2
0
1
1
0
0
2
1
1
0
1
1
1
1
1
1
1
0
0
1
0
2
2
0
0
0
1
0
1
1
0
1
1
0
1
2
1
1
1
1
2
0
1
2
0
1
1
2
0
1
1
1
1
0
1
1
1
1
2
4
0
0
1
0
2
0
1
1
1
1
1
2
1
2
1
1
0
1
1
0
0
3
1
2
1
1
0
1
0
0
2
0
2
1
1
1
0
0
1
2
0
1
1
2
2
0
2
2
2
1
1
3
2
1
1
0
0
2
0
1
1
1
1
0
1
1
0
0
0
0
0
1
0
0
2
0
1
0
1
1
1
0
0
1
0
1
0
1
0
0
2
1
0
2
0
0
1
0
2
0
1
0
1
0
1
1
1
0
1
0
1
0
2
2
0
0
1
2
0
0
0
0
1
2
0
0
2
1
1
0
1
1
0
1
2
1
0
0
1
2
0
0
2
1
1
0
0
0
1
0
0
0
2
0
0
1
1
2
2
1
1
1
1
0
0
1
1
0
1
1
0
0
1
1
1
0
0
0
2
1
0
2
0
2
1
3
0
2
1
0
1
2
2
0
2
1
0
1
0
0
0
0
2
1
2
2
1
1
1
1
1
1
1
1
1
1
0
0
2
3
1
2
1
1
2
2
1
1
1
0
2
2
1
1
2
1
2
2
2
2
0
2
1
1
0
1
2
1
0
1
0
2
0
2
1
0
1
1
0
1
2
0
1
2
0
1
1
2
0
1
0
0
1
1
1
1
0
1
3
0
0
1
2
1
1
1
1
1
1
0
0
1
1
0
1
1
2
0
0
2
0
2
2
2
2
0
0
2
1
1
0
0
1
0
1
0
0
1
1
2
0
2
1
2
0
1
1
0
0
0
1
2
0
0
1
1
1
1
1
0
1
1
1
1
2
0
1
2
2
1
1
1
1
1
2
1
1
2
0
0
2
2
3
1
0
1
2
0
2
2
2
1
0
2
2
1
0
1
1
0
0
1
1
1
0
0
0
0
1
1
0
0
0
1
1
1
1
1
1
2
1
0
2
1
0
1
2
1
1
0
0
0
2
1
2
2
1
0
1
1
2
1
0
1
1
1
2
1
1
1
4
0
2
2
0
1
1
2
0
1
1
1
0
2
0
0
0
2
0
0
0
2
0
0
1
1
2
1
1
1
1
2
1
1
0
1
2
1
1
1
1
1
1
1
0
0
0
4
0
2
1
0
0
0
1
3
1
1
0
1
2
1
0
1
1
0
0
1
3
1
0
0
0
1
1
0
0
1
1
0
2
2
1
1
1
2
1
7
1
1
2
0
1
1
1
1
0
1
2
1
1
1
0
1
1
0
2
2
2
1
0
1
0
1
0
1
1
1
0
0
1
2
0
2
0
1
1
1
0
0
0
1
2
1
0
0
0
1
0
1
1
1
1
0
2
1
1
1
1
0
2
1
1
0
1
0
2
0
2
2
1
0
1
1
0
2
1
2
1
1
1
1
0
2
1
2
2
0
1
0
1
2
0
0
0
0
1
0
1
0
1
1
1
0
2
0
0
0
0
1
1
0
1
0
1
1
1
1
2
1
1
3
1
1
1
0
1
0
1
1
0
1
1
0
0
1
1
0
0
1
0
1
0
3
1
2
1
1
1
1
1
1
0
1
1
0
1
2
1
1
3
0
0
0
2
2
1
1
0
1
1
1
1
2
1
2
0
0
2
2
1
0
0
1
1
1
1
0
1
0
2
1
0
1
0
0
1
2
2
0
1
1
1
0
1
1
0
2
2
1
0
0
1
1
1
1
1
1
1
0
0
1
2
1
2
2
6
2
0
1
1
1
0
0
0
1
1
1
1
2
0
1
2
1
0
1
1
0
1
2
1
1
1
2
0
1
0
0
1
4
0
0
2
1
0
2
1
1
1
1
0
0
1
1
1
0
0
2
2
1
0
1
0
2
0
1
2
1
2
1
1
1
1
8
1
2
2
1
1
2
1
1
0
1
2
0
1
2
1
1
1
1
0
0
0
0
1
2
3
1
2
0
1
3
1
0
1
1
2
1
1
2
1
0
1
0
0
1
0
0
2
1
1
0
1
2
1
0
0
0
1
1
1
1
1
0
0
1
1
1
0
1
0
0
3
2
0
1
1
0
0
1
2
2
2
1
0
1
2
0
2
0
1
1
1
0
2
0
0
2
0
1
0
1
2
1
1
2
0
1
1
0
1
2
1
0
0
1
0
2
0
1
1
1
1
2
2
2
0
0
1
0
1
0
0
2
2
0
1
1
1
1
0
1
2
2
0
0
1
1
1
0
0
0
1
0
0
1
0
1
1
1
2
0
1
0
0
1
1
0
1
2
2
0
0
2
2
0
1
0
1
0
0
1
1
2
2
0
1
2
1
2
1
1
0
1
1
0
0
1
1
1
1
2
3
1
1
1
0
0
1
1
1
1
0
0
1
1
2
3
3
2
0
2
1
2
1
1
1
1
1
2
1
0
1
0
0
0
0
1
1
0
1
0
2
0
1
0
2
0
2
0
1
0
0
1
2
0
3
1
1
0
1
1
1
1
1
1
0
1
2
1
1
0
0
2
2
0
1
2
0
2
1
0
0
1
1
0
0
1
1
1
1
0
1
0
0
0
2
0
1
2
1
1
1
1
0
0
1
0
2
1
0
1
1
0
1
2
1
2
0
3
1
1
0
1
1
2
0
1
0
1
1
1
1
1
1
3
1
2
1
2
0
2
1
2
1
0
0
1
1
0
2
1
0
1
0
2
1
0
0
2
1
0
2
0
0
0
0
2
4
0
0
1
1
0
0
1
1
0
1
2
1
2
0
0
2
1
2
1
0
1
1
0
1
1
1
1
1
1
1
1
0
2
1
0
0
1
2
1
1
1
0
2
0
1
1
0
1
2
1
1
2
0
1
0
1
2
2
1
0
2
0
0
1
1
2
1
0
1
1
1
1
1
1
2
1
1
1
2
2
1
0
0
1
1
1
0
0
3
1
1
1
1
2
2
1
1
0
1
0
2
0
1
0
0
1
1
1
0
0
1
2
1
0
2
0
1
1
1
1
2
2
2
2
1
1
2
0
0
1
0
2
1
2
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
1
0
0
3
0
1
2
3
1
1
2
0
1
2
0
1
1
0
1
0
2
1
1
1
3
1
0
1
0
0
1
1
1
0
0
0
0
2
2
0
1
1
0
1
0
0
2
0
0
1
0
1
0
1
1
2
1
2
0
2
1
1
1
1
0
2
0
2
2
0
1
1
2
0
0
1
0
2
1
0
0
2
1
0
1
1
1
0
1
0
0
0
0
1
1
0
0
1
2
2
0
0
0
0
2
1
2
1
2
1
0
0
1
1
1
0
1
0
3
0
2
0
0
0
2
1
0
1
0
2
0
1
1
2
1
1
0
0
2
0
0
1
2
0
2
2
1
0
1
1
2
1
1
1
1
1
1
1
0
1
1
0
1
1
1
1
1
1
0
0
1
1
2
1
2
3
2
1
0
2
0
0
1
2
1
1
2
0
0
1
1
1
2
1
1
0
0
1
1
1
1
2
0
0
1
0
0
0
2
2
1
1
0
1
2
1
0
2
2
2
2
1
0
1
1
0
2
2
1
0
2
0
0
0
0
1
1
1
1
1
1
2
2
3
1
1
1
0
1
1
1
2
1
1
0
2
0
0
1
2
1
1
1
1
1
1
1
0
0
0
2
2
2
0
1
1
0
1
2
1
0
1
1
0
0
0
1
0
1
1
1
2
1
1
1
1
1
0
1
2
2
0
1
1
2
1
0
1
2
2
0
1
0
1
1
1
1
1
0
1
0
0
1
1
1
1
0
0
0
0
1
0
0
2
2
2
0
1
2
2
2
0
2
1
2
1
1
0
0
1
2
0
2
1
0
2
2
1
0
0
0
1
2
0
2
1
1
2
0
0
0
2
1
2
1
0
1
1
0
5
0
1
2
0
1
0
0
0
2
1
1
0
0
1
0
1
0
0
1
2
2
0
2
1
1
0
1
0
1
2
2
2
1
2
1
0
2
0
1
1
2
2
1
0
0
2
1
1
1
1
0
1
2
0
4
0
1
0
2
0
1
1
0
0
0
1
0
1
0
2
1
1
0
0
0
0
1
1
1
1
0
0
1
1
1
0
0
1
2
0
1
1
0
0
1
1
1
0
1
0
0
1
1
0
1
0
1
0
1
1
1
1
2
0
0
2
1
3
1
1
1
0
1
1
2
2
1
2
2
2
1
0
0
1
2
0
1
1
2
1
0
0
0
2
1
2
2
0
0
0
0
3
0
1
1
1
0
1
0
0
0
1
0
1
1
2
1
2
1
0
1
2
1
0
1
0
1
2
1
1
1
1
2
0
2
2
1
2
1
0
0
0
1
1
0
2
1
0
1
0
2
2
1
1
1
1
1
2
2
0
0
1
3
0
0
0
1
2
2
1
0
2
0
1
2
0
1
1
0
0
2
0
0
0
0
0
1
1
0
2
2
2
1
1
0
2
2
2
0
1
1
0
1
1
0
0
1
1
1
1
1
3
1
0
2
1
0
1
1
1
2
2
1
2
0
1
1
1
0
0
0
1
0
0
1
1
1
0
2
0
0
2
0
1
1
1
2
0
0
0
1
1
1
1
2
1
2
1
1
0
1
0
1
2
0
1
2
2
0
0
0
2
1
2
0
1
2
2
0
0
1
2
1
1
2
1
2
1
0
0
0
1
1
2
2
0
0
0
2
3
2
1
2
1
1
0
0
1
1
1
1
1
2
0
2
0
2
1
0
2
0
1
1
0
1
0
3
0
1
2
0
1
1
1
1
1
2
1
1
2
2
0
1
1
1
1
0
2
0
1
2
1
0
1
0
0
1
1
0
3
1
0
1
0
1
2
1
0
1
1
0
2
1
1
1
2
1
1
0
1
0
1
2
1
0
1
1
2
2
0
0
1
1
1
1
1
1
0
0
1
1
0
1
1
0
0
0
1
2
1
1
0
0
1
1
1
0
1
1
1
1
1
1
2
1
1
0
0
1
3
1
0
1
2
0
0
0
1
0
0
0
2
0
1
1
1
1
2
1
1
1
1
0
2
1
4
2
0
0
1
1
0
1
1
1
1
1
1
1
0
0
0
0
2
1
0
1
1
1
2
1
2
0
2
1
1
1
1
3
1
1
1
1
1
1
1
1
3
0
0
2
1
0
0
1
0
1
0
0
1
0
1
0
0
0
2
1
1
1
0
1
2
0
0
0
2
2
0
1
1
1
1
1
0
1
0
0
1
1
1
0
1
2
1
0
0
1
2
0
0
1
1
2
0
0
1
1
1
1
1
0
0
0
1
0
1
2
3
0
0
1
0
1
1
2
1
1
2
0
5
0
0
1
1
1
0
1
2
1
1
2
0
2
2
2
0
1
1
1
1
1
0
1
0
3
2
2
0
0
0
0
2
0
1
0
2
2
0
1
1
2
1
1
0
1
2
1
1
2
1
0
1
1
2
2
1
0
2
2
1
0
1
2
0
0
0
1
0
2
2
1
1
2
2
0
1
2
1
0
2
0
0
1
0
0
0
0
1
1
1
2
1
1
2
2
1
1
1
0
1
1
1
0
1
1
2
3
1
0
1
1
1
1
1
1
1
2
2
2
0
1
0
0
1
0
1
0
0
0
0
0
2
0
1
0
1
1
0
2
2
2
0
2
1
0
1
1
1
0
0
2
2
0
0
2
0
0
0
0
1
1
1
0
1
1
0
1
1
0
2
0
2
1
1
1
1
0
0
1
1
1
1
1
2
0
0
1
1
0
0
0
0
2
0
0
2
2
0
0
1
1
1
0
1
1
2
1
1
0
0
0
2
1
2
0
0
1
3
2
1
1
0
1
1
0
1
1
2
0
0
1
2
0
2
1
1
1
1
2
0
1
1
1
1
1
2
0
1
0
1
2
1
1
0
0
1
1
0
2
4
1
2
3
2
1
1
0
0
0
3
1
2
0
1
1
2
1
1
1
2
0
1
0
0
0
0
0
0
1
1
0
1
1
0
0
1
0
2
1
0
0
0
1
0
1
1
1
1
0
2
0
1
1
0
1
0
1
1
2
0
1
0
0
2
1
1
0
3
1
1
0
0
1
2
1
1
0
1
0
0
2
0
1
1
2
1
2
0
2
0
0
1
1
1
2
2
2
2
0
0
0
0
2
0
2
1
0
2
0
0
1
0
1
1
1
2
0
0
0
1
0
0
2
2
1
0
0
0
1
0
0
0
0
1
1
1
0
0
1
1
2
2
2
1
1
2
1
2
1
0
0
0
2
1
2
0
1
1
0
2
1
1
1
1
0
1
0
1
0
0
1
1
2
0
1
2
0
2
0
2
0
0
1
2
0
1
0
2
0
0
0
1
2
1
2
0
0
0
0
0
1
0
1
2
1
0
1
2
0
2
1
2
1
0
1
1
1
0
1
0
1
1
0
1
1
1
0
1
0
0
1
0
1
0
1
1
1
0
2
0
1
0
2
0
1
1
1
2
0
0
0
1
0
1
1
1
0
2
1
0
0
1
1
1
1
1
2
2
2
2
1
1
0
0
1
1
0
1
1
2
2
0
0
0
0
0
1
0
1
0
2
1
2
2
0
2
0
0
1
1
1
1
1
2
1
2
1
1
1
2
0
1
0
2
1
1
1
3
2
1
0
1
0
0
1
1
0
0
1
0
2
1
2
2
2
1
1
2
0
3
1
0
1
1
2
0
0
1
2
0
0
1
1
0
0
1
1
2
1
0
1
1
2
0
1
2
1
1
0
2
1
2
1
1
1
0
0
1
2
1
0
1
2
1
0
1
1
1
1
1
1
0
0
1
1
1
1
1
1
1
2
1
0
0
1
1
0
1
1
0
0
2
2
1
0
1
1
1
1
2
1
0
0
0
0
2
1
2
2
2
1
1
1
1
1
2
2
2
2
1
1
2
1
1
0
1
1
1
1
0
0
1
0
0
0
2
0
2
0
0
1
0
0
1
0
0
1
1
0
0
2
0
0
0
1
0
2
0
1
0
1
1
0
1
0
1
4
0
1
1
1
0
4
1
1
1
0
1
1
1
2
1
2
1
2
0
0
1
0
1
0
1
1
1
2
1
1
0
2
1
2
1
1
0
2
2
1
0
1
0
2
0
0
1
2
1
1
1
0
0
1
0
1
1
1
0
1
2
0
1
0
1
0
2
1
1
0
0
1
1
1
1
2
0
0
2
1
0
0
1
1
2
2
2
0
0
1
1
2
0
2
1
1
1
1
0
2
1
0
1
1
1
0
0
0
1
2
2
0
1
1
2
2
0
2
0
1
1
1
0
2
2
1
1
0
0
0
1
0
2
1
0
0
1
1
1
2
0
1
0
1
2
2
0
0
1
1
2
2
0
1
2
1
0
1
0
0
1
0
1
1
1
0
2
1
1
2
0
1
0
1
0
1
2
1
1
0
0
0
0
2
1
1
3
1
2
2
0
1
1
1
0
2
1
1
0
0
1
1
1
1
1
0
0
0
3
0
1
1
0
2
1
0
0
2
1
0
1
0
1
1
0
1
1
0
2
0
1
0
1
0
0
0
5
1
0
1
1
0
2
0
0
1
1
0
2
0
0
2
1
1
1
1
0
1
2
2
0
2
1
1
0
2
2
3
1
1
0
0
2
0
1
1
1
1
1
0
0
0
1
1
0
2
2
1
1
1
0
2
2
1
0
1
0
1
1
2
0
3
1
0
1
0
1
1
2
2
1
1
0
0
0
0
0
0
1
3
0
2
2
0
1
1
1
0
1
0
2
1
1
2
1
2
0
2
2
1
2
0
1
2
1
1
0
0
0
2
0
0
1
1
1
1
1
1
3
1
0
0
0
0
0
1
0
2
2
0
0
0
1
1
2
1
0
2
1
2
1
1
1
2
1
1
1
0
2
0
2
0
0
0
0
2
0
1
0
1
1
1
0
0
1
1
2
0
2
0
0
0
2
2
3
0
0
0
1
0
1
0
1
2
0
0
1
2
1
2
1
1
1
1
0
1
0
0
3
2
0
1
2
4
2
1
1
0
1
1
1
0
0
1
0
0
2
1
1
1
0
1
1
0
0
1
1
0
0
1
2
0
1
1
0
0
1
0
2
1
0
4
0
1
0
0
1
2
2
1
0
1
1
1
0
0
2
2
0
0
0
1
2
1
0
2
2
1
0
0
0
2
0
0
2
1
1
0
1
0
0
0
0
0
0
1
1
0
2
1
1
0
2
1
0
1
1
0
1
2
2
0
1
0
0
0
0
1
1
2
0
1
0
1
2
0
0
0
2
1
0
0
1
0
1
1
1
2
2
1
2
2
0
0
1
0
0
0
1
1
1
3
0
0
1
1
1
0
2
1
1
2
2
1
0
0
0
2
0
1
0
1
1
0
0
0
1
1
1
1
1
0
2
2
0
0
0
1
1
1
1
1
2
1
0
2
1
0
2
1
0
1
0
2
1
0
2
0
0
0
1
1
1
1
0
2
1
2
1
1
1
0
1
0
0
0
0
2
1
1
2
0
0
1
0
0
0
2
1
2
2
1
1
1
0
0
1
2
0
2
2
1
2
1
2
1
0
1
1
0
1
1
1
0
0
0
0
0
0
1
1
2
2
2
2
1
1
4
1
2
1
0
1
1
1
1
1
1
0
0
0
0
2
0
1
0
0
0
2
0
0
0
1
0
0
2
0
2
1
2
1
0
0
0
2
2
0
2
2
1
1
1
1
2
1
0
2
1
0
1
0
1
0
1
4
1
0
2
0
0
0
1
1
1
2
0
0
1
0
1
1
0
1
1
1
0
1
1
0
0
1
1
1
1
1
0
0
0
1
2
2
0
1
2
1
0
0
0
0
0
1
1
1
2
0
2
2
1
2
1
0
2
0
2
0
1
0
1
1
0
2
1
0
2
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
3
1
1
0
2
1
1
1
1
1
0
0
1
0
0
1
1
1
0
1
0
0
0
0
1
0
0
1
2
1
2
2
1
0
1
0
0
1
2
2
4
1
1
0
0
2
0
1
0
2
2
0
2
1
0
2
0
0
0
1
0
2
1
1
1
1
1
0
1
0
0
1
1
2
1
0
2
0
1
1
1
1
0
2
1
0
1
0
1
1
1
1
0
1
1
1
1
1
1
0
1
2
1
2
0
1
0
0
1
1
1
1
1
1
1
2
2
2
1
0
0
2
0
2
0
2
1
0
0
1
1
2
1
1
1
0
0
1
1
0
1
0
0
1
0
1
0
0
1
2
0
1
0
0
1
1
1
2
0
2
1
1
1
1
2
2
1
3
1
1
2
2
0
1
0
0
2
0
2
1
0
0
0
1
1
1
0
1
1
0
0
1
0
1
2
1
0
8
1
0
1
1
1
1
1
2
0
1
1
0
2
0
1
1
1
1
0
1
2
1
0
1
0
0
0
1
1
2
1
1
0
0
0
0
0
1
0
2
1
2
1
1
0
2
1
1
0
0
3
0
1
0
2
2
2
1
1
0
1
2
0
1
1
1
0
1
1
1
1
1
2
0
1
1
1
0
0
2
2
2
2
1
1
1
1
1
0
2
2
0
1
1
2
0
1
0
2
0
1
2
1
1
1
1
0
1
1
1
1
1
2
1
1
1
1
2
2
2
0
2
0
0
1
3
2
1
2
1
0
0
0
2
2
1
1
0
0
1
1
1
1
1
1
0
1
2
1
1
1
0
2
0
1
0
0
1
1
0
0
0
1
0
0
1
1
1
2
1
1
1
2
1
2
0
1
0
1
2
2
1
0
1
1
2
0
0
0
1
1
1
0
1
1
1
1
1
1
0
1
1
1
0
2
0
0
0
2
1
1
2
1
0
0
2
1
2
2
2
1
1
0
0
0
2
1
2
1
2
0
0
0
2
2
0
0
2
1
1
1
0
2
2
2
0
1
2
1
2
0
0
0
1
0
2
3
1
0
0
1
2
1
1
0
2
0
1
0
1
1
0
0
2
2
1
1
3
1
0
1
1
0
2
0
0
0
0
0
2
1
1
1
1
1
0
0
0
2
2
1
0
1
0
1
2
2
1
1
0
0
2
1
0
1
1
1
0
1
1
2
1
0
1
1
1
0
2
0
1
0
1
0
2
1
0
2
0
1
0
2
2
0
0
1
1
1
0
4
0
0
2
0
1
0
1
2
0
0
0
1
0
2
0
0
2
0
0
2
2
2
2
0
2
0
2
2
0
0
1
2
1
0
2
1
1
4
1
2
0
0
0
2
0
1
1
2
0
0
2
0
0
1
0
0
0
1
1
1
0
0
0
2
1
0
2
0
2
0
0
0
0
1
2
1
1
0
0
1
2
0
1
3
2
0
1
2
2
1
1
0
1
1
1
0
0
1
2
2
2
2
0
1
1
1
1
1
2
0
0
1
0
3
2
1
0
0
1
1
1
2
0
1
1
1
0
0
1
1
2
0
0
2
2
0
1
1
2
0
3
2
1
0
0
1
2
0
0
1
0
2
1
2
1
1
1
0
1
2
1
0
1
2
0
2
2
2
0
2
2
1
1
2
3
1
1
0
1
5
0
0
1
1
0
0
0
0
1
1
2
0
1
0
0
0
2
1
3
2
0
1
1
0
0
2
1
2
1
1
0
2
0
2
3
2
1
1
0
1
2
1
0
1
2
0
0
0
2
0
1
0
1
0
1
0
1
1
0
0
2
1
0
1
0
2
1
2
0
1
1
2
0
1
4
0
0
0
1
0
0
1
1
1
0
2
0
2
2
0
0
0
1
0
0
0
1
0
0
1
2
1
1
2
1
1
2
0
0
1
0
2
2
2
2
0
1
0
0
2
0
0
1
0
2
1
0
0
2
1
2
2
2
1
2
0
0
0
0
2
0
1
1
0
0
0
1
1
0
1
1
1
2
2
0
2
1
0
0
1
1
1
1
1
1
0
0
2
0
1
0
1
1
2
2
1
1
1
1
1
1
1
2
1
2
2
1
2
0
2
0
1
1
2
1
1
2
1
1
2
1
1
3
2
1
2
1
2
0
1
1
2
0
1
0
0
1
0
0
2
0
1
2
0
2
1
0
1
0
0
1
1
0
2
1
0
0
1
1
0
2
0
0
0
1
1
1
1
1
0
2
0
0
2
1
0
0
2
0
2
2
0
0
1
1
0
0
1
0
1
0
2
1
0
0
2
1
1
0
2
1
1
1
1
1
0
1
2
1
1
0
2
1
2
0
1
1
0
1
2
2
1
0
0
3
0
1
1
0
0
1
1
1
1
0
3
1
0
0
2
1
0
1
1
2
0
3
3
2
2
2
0
0
1
1
1
1
0
1
0
0
2
2
1
0
1
1
1
1
0
2
1
2
1
1
1
2
1
1
2
1
1
1
2
2
1
0
0
1
2
1
1
1
0
0
2
0
3
0
0
1
0
1
1
0
0
1
1
2
0
0
0
2
1
1
2
2
1
0
2
2
0
2
0
2
2
0
3
1
2
1
1
1
2
1
1
2
0
0
1
0
0
1
2
2
2
1
2
1
1
2
1
2
1
7
1
1
1
0
0
1
1
0
2
0
2
2
1
0
0
1
1
2
3
1
1
0
1
2
1
1
2
1
1
1
1
0
2
2
1
2
1
1
1
1
1
1
0
1
0
2
0
1
1
1
1
2
2
0
1
2
0
0
1
1
0
1
0
0
2
1
0
1
1
0
3
1
1
3
0
1
0
1
1
1
2
2
0
0
2
0
1
2
1
1
1
1
1
3
1
0
2
1
1
1
1
0
1
0
1
1
0
0
1
1
2
1
2
0
2
1
1
0
0
1
2
2
1
1
0
1
0
1
2
1
2
1
1
1
1
1
1
1
2
1
1
0
2
0
1
1
0
1
0
1
1
1
1
1
1
2
0
0
1
1
2
2
0
1
2
2
1
0
1
1
1
0
0
1
0
1
0
1
0
0
0
1
1
0
0
2
0
1
2
1
2
0
1
1
0
1
2
0
0
0
1
1
1
1
0
0
2
1
1
3
1
1
1
1
2
1
0
1
0
1
0
1
0
1
2
1
2
0
0
1
0
1
1
0
1
1
1
2
1
3
2
1
2
0
2
1
1
0
1
2
1
2
0
1
2
2
2
0
0
0
0
2
0
0
1
1
0
1
3
0
2
0
1
1
1
2
2
1
2
1
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
1
2
1
0
1
2
2
2
0
2
1
1
1
0
1
1
0
0
0
1
0
1
1
2
0
1
1
1
0
0
1
1
1
0
1
1
1
0
0
2
2
1
1
1
0
1
1
2
1
1
1
0
0
1
2
2
0
2
1
1
1
1
2
1
1
0
0
2
0
1
0
2
0
4
0
1
1
0
0
0
0
1
1
0
1
1
0
1
1
2
2
0
0
0
1
2
0
0
2
0
0
0
2
0
1
0
2
1
1
1
2
1
1
1
1
2
1
0
0
1
1
1
1
0
0
1
2
2
0
0
0
1
0
1
2
2
0
2
0
0
0
0
1
1
1
2
1
1
1
1
0
2
0
0
1
1
0
2
0
0
0
0
1
1
0
2
2
1
1
2
1
0
1
2
1
0
1
0
2
1
3
0
2
0
2
2
0
0
2
0
0
0
1
0
1
2
1
1
1
2
1
1
2
0
1
0
0
1
1
2
1
2
1
7
1
1
0
0
1
0
0
0
2
0
1
0
2
2
1
0
1
0
1
1
0
0
1
2
1
1
0
0
1
1
1
0
1
1
0
1
1
1
2
1
1
0
1
1
1
0
1
0
0
2
2
0
0
0
1
1
1
1
0
1
1
1
0
1
1
2
0
1
4
2
1
1
1
0
2
2
2
1
0
0
0
1
1
2
0
0
1
1
1
2
1
1
1
1
0
2
1
0
1
1
1
1
2
1
0
1
0
3
1
1
2
1
2
0
0
1
2
2
1
2
1
1
0
1
2
2
0
0
1
2
0
1
2
0
0
1
1
1
2
1
1
0
1
1
0
0
2
1
0
0
2
2
1
1
1
0
0
2
0
0
0
2
0
0
0
1
1
0
1
1
1
0
2
1
2
1
2
0
0
0
2
2
1
0
3
1
0
2
0
0
2
2
1
0
2
1
1
1
0
1
2
0
2
0
0
2
1
0
1
0
1
2
0
0
1
0
2
1
1
1
1
1
2
1
0
1
0
1
0
1
1
2
1
1
0
1
2
0
2
1
1
1
1
0
1
1
2
1
1
3
0
1
0
0
0
0
1
0
0
2
2
1
1
2
1
0
0
1
0
1
2
1
0
1
0
3
1
0
0
2
0
1
1
3
0
0
0
0
2
1
0
2
1
0
0
0
0
0
1
1
0
0
2
0
0
0
2
0
0
0
1
1
0
1
1
0
2
2
2
1
1
1
1
1
0
1
2
1
2
1
1
1
1
1
0
1
0
1
0
2
1
2
1
0
1
1
1
1
0
1
0
0
1
1
1
1
1
2
0
0
2
0
2
1
1
0
1
1
2
1
1
1
1
0
1
0
1
1
1
2
1
1
0
2
1
1
0
2
2
1
0
2
1
2
1
0
0
1
0
1
2
1
1
2
2
1
1
2
0
1
0
2
1
2
0
2
0
0
2
0
2
0
2
2
0
0
0
2
1
2
1
2
0
1
0
1
1
2
1
0
0
1
1
1
2
1
1
1
2
1
0
1
1
1
2
1
0
0
1
0
2
2
1
1
2
4
0
1
1
1
1
1
1
0
0
1
1
1
1
2
0
1
2
0
2
0
1
0
2
2
2
0
1
0
2
2
2
0
1
1
1
1
1
3
0
0
3
0
1
1
2
1
1
1
1
0
0
1
0
1
0
0
1
2
0
0
1
1
0
0
1
0
0
1
0
1
2
0
2
1
0
1
0
2
1
0
1
1
1
1
1
1
0
0
1
0
1
2
0
0
2
0
2
2
2
0
0
0
1
0
0
1
0
1
0
2
0
1
0
1
1
1
1
1
1
2
2
0
1
2
2
1
0
2
1
1
1
0
0
2
0
0
0
2
1
1
1
1
2
2
1
0
1
1
0
1
0
0
1
0
1
0
1
0
0
2
1
2
1
0
1
2
1
2
2
0
1
0
2
1
0
0
0
2
1
1
0
1
0
0
1
2
0
0
1
1
1
0
1
1
0
1
1
0
0
0
0
1
1
2
0
2
0
1
2
0
0
0
1
0
1
0
1
1
0
1
1
1
3
1
1
0
0
2
1
1
2
1
0
2
1
0
0
2
1
1
2
1
2
1
1
0
1
0
0
0
0
2
1
2
1
1
2
1
1
1
1
1
1
0
0
0
1
1
0
2
1
1
1
2
0
3
0
1
1
0
2
0
2
0
2
0
2
2
0
1
1
1
0
2
1
0
2
1
0
1
2
0
1
1
1
1
0
0
0
1
2
0
0
2
1
2
0
1
2
0
2
1
1
0
0
1
2
1
0
1
0
1
0
0
1
1
1
1
2
1
0
2
2
2
1
1
1
1
1
2
1
1
0
0
1
2
1
1
0
0
1
1
1
0
0
2
0
1
2
0
2
0
0
2
0
0
2
1
1
0
2
2
1
0
1
1
0
1
1
2
1
1
1
1
1
0
1
0
1
0
4
2
1
2
1
0
0
2
1
1
1
0
1
0
1
0
1
0
1
2
0
0
1
1
0
2
1
1
0
1
0
0
0
1
1
0
1
2
2
1
0
1
1
2
2
0
0
1
10
2
0
2
0
1
1
1
2
1
0
0
2
0
2
1
2
1
2
0
1
1
1
1
0
2
1
1
0
3
1
1
2
2
1
1
1
1
0
0
1
0
0
1
0
0
1
0
1
0
0
1
1
1
2
2
0
0
0
1
1
0
1
2
1
1
1
0
1
1
2
0
1
1
1
0
0
0
4
1
2
0
1
1
0
2
0
0
0
1
1
0
2
2
1
1
1
2
0
1
1
0
0
0
1
1
1
0
0
1
1
0
2
1
2
1
0
1
1
1
2
0
1
1
0
0
0
0
1
1
0
0
2
1
0
2
0
1
0
2
0
1
2
0
1
1
1
0
1
2
2
2
0
1
0
0
0
0
0
1
1
1
0
1
2
2
1
2
0
0
0
0
1
1
1
1
0
1
0
0
1
2
1
2
0
1
1
1
0
1
0
2
1
2
1
1
0
2
0
3
2
1
2
0
1
0
1
1
1
1
2
1
2
0
1
1
2
0
0
0
1
1
1
1
2
0
1
2
1
0
1
2
0
2
0
1
1
1
2
2
2
1
2
0
1
1
2
2
1
0
2
0
0
1
1
0
0
2
0
1
1
0
2
1
1
1
1
2
0
1
2
1
0
1
1
2
1
1
0
1
0
1
1
0
1
1
0
1
1
0
2
2
1
0
2
0
1
0
0
1
2
1
0
2
2
2
1
0
2
0
0
0
1
0
1
0
2
1
2
0
1
1
1
0
0
1
0
1
1
2
2
1
1
0
2
2
1
1
2
2
0
1
2
2
0
2
2
1
1
0
1
0
0
1
0
1
0
1
1
0
1
1
1
1
2
0
2
1
0
0
1
0
0
1
0
1
1
0
1
0
1
2
2
1
1
0
2
0
2
1
0
2
0
2
1
0
1
1
0
2
0
0
1
2
1
1
1
0
1
2
2
1
1
0
0
1
2
0
1
2
2
0
1
0
2
2
1
0
2
2
1
1
1
2
0
1
2
0
1
0
1
2
2
0
1
1
1
0
1
1
1
0
0
1
1
1
1
0
1
2
2
1
1
0
2
4
1
0
1
5
0
0
0
1
0
0
0
1
1
1
1
1
1
1
2
1
2
1
1
2
0
1
0
2
0
1
1
0
1
0
0
1
1
2
1
1
2
2
1
2
0
2
1
0
0
0
0
0
1
0
2
0
0
0
1
0
1
0
1
1
2
1
2
1
1
0
1
0
1
1
1
0
1
0
2
1
1
1
1
1
0
1
0
2
1
0
1
0
1
0
0
1
2
6
0
2
1
1
1
0
2
0
2
0
2
3
1
1
0
1
1
1
0
0
0
1
3
1
0
2
0
1
2
2
0
1
0
0
1
1
1
2
2
1
2
0
1
0
1
0
1
1
2
1
1
1
2
2
0
2
0
2
2
1
1
1
2
1
1
0
1
1
1
0
1
0
3
1
1
0
1
1
0
1
2
0
1
1
1
1
2
1
1
2
1
2
2
0
1
0
1
1
0
2
0
1
2
0
1
1
1
1
0
1
3
1
1
0
2
1
2
1
0
0
1
0
1
1
2
0
2
0
4
0
1
1
0
0
2
1
0
1
0
1
0
0
1
0
2
0
1
0
1
0
2
1
0
1
0
0
3
1
0
2
0
0
0
2
0
1
1
0
2
1
2
2
2
6
0
0
2
2
0
1
0
0
2
1
1
0
0
2
0
1
1
2
1
1
1
1
0
2
0
1
1
1
1
1
0
1
2
1
1
0
0
0
0
1
1
2
0
1
0
1
2
0
1
1
1
0
2
1
2
0
1
1
0
0
1
2
1
0
0
1
1
1
1
1
2
2
1
1
1
1
1
0
1
0
1
1
0
1
0
0
0
2
0
2
1
1
0
1
0
1
1
2
1
1
1
2
0
2
2
1
1
0
1
1
1
0
0
1
3
0
2
1
1
2
1
1
3
0
1
0
0
1
0
1
0
1
1
1
2
1
1
2
1
1
2
0
0
1
1
1
2
1
0
1
0
1
1
1
2
2
0
0
0
2
0
1
1
0
0
1
0
0
1
1
0
2
0
0
0
1
1
0
0
0
2
1
2
1
1
0
1
2
1
1
0
2
2
0
1
1
1
2
2
2
0
1
0
1
1
2
0
1
2
0
2
1
2
0
3
1
2
0
1
2
0
1
2
2
1
1
1
0
0
2
3
1
1
1
0
2
1
0
1
1
1
1
0
2
0
2
0
2
1
1
0
1
0
1
1
0
0
0
0
0
2
2
0
2
1
1
0
1
1
1
0
1
1
0
2
1
1
1
1
2
1
1
1
1
0
3
1
1
1
1
1
2
1
1
1
1
1
0
0
2
2
1
1
1
1
0
0
1
0
0
0
1
1
0
0
1
1
1
1
0
2
1
1
0
2
0
2
2
2
1
2
0
2
1
0
1
1
0
0
1
1
0
1
0
1
2
0
0
0
2
1
0
1
1
1
0
1
0
0
1
1
0
1
1
0
1
1
1
2
1
2
0
3
1
2
0
1
0
1
2
0
1
0
2
0
1
2
1
1
1
1
2
2
0
2
0
2
0
1
2
0
1
2
2
0
0
1
0
0
0
1
0
1
0
1
0
2
2
1
2
1
2
1
0
1
0
2
1
5
2
2
0
0
1
0
0
1
1
0
0
1
2
1
1
1
1
1
0
0
2
1
1
1
1
0
1
0
1
0
0
2
0
1
1
1
0
1
0
0
0
0
1
2
2
0
2
2
1
2
1
1
2
2
1
0
1
2
2
0
2
1
2
1
0
0
0
2
1
1
0
2
1
0
1
1
1
0
1
0
1
1
0
1
0
0
1
2
1
0
0
0
0
0
2
0
0
2
1
1
0
1
1
1
1
0
0
1
1
1
0
1
0
1
1
1
0
1
1
0
2
0
0
2
1
0
1
1
1
0
2
0
2
2
3
1
0
1
1
1
1
1
1
0
2
0
1
2
1
1
1
1
2
1
1
1
1
1
1
0
0
0
2
1
2
0
0
2
1
1
0
1
1
1
2
3
1
0
0
2
0
1
2
1
2
1
2
2
0
0
2
1
1
1
1
0
1
0
0
2
0
1
1
1
0
1
2
0
1
1
2
0
1
0
0
1
1
0
1
1
0
0
2
2
0
0
1
2
0
2
2
0
1
1
2
1
0
2
1
1
2
1
2
2
1
0
2
1
2
2
1
1
0
0
1
1
0
0
1
2
1
1
1
0
0
2
0
1
2
2
1
0
2
1
0
0
0
0
1
1
2
0
2
1
1
0
1
0
0
1
0
0
1
2
1
3
2
1
1
2
0
1
0
1
0
0
0
2
2
1
2
1
1
1
1
1
1
1
1
2
1
2
5
0
2
1
2
2
0
1
1
1
1
1
0
2
3
1
0
0
1
1
1
1
1
0
2
1
0
1
1
0
1
0
1
3
0
2
2
0
1
0
3
1
2
0
1
1
2
1
1
1
0
1
1
1
1
0
0
1
0
0
0
0
1
0
0
0
1
0
1
1
1
2
0
1
0
1
2
0
2
2
1
0
0
0
2
0
1
0
1
1
0
2
0
0
1
1
1
2
0
0
1
0
2
1
2
1
1
1
0
1
2
0
1
0
1
0
0
1
0
2
1
1
2
1
1
2
1
1
0
1
2
1
0
0
1
0
0
2
1
0
1
1
2
1
1
2
1
0
1
0
0
0
2
1
1
1
0
2
1
1
0
1
2
2
2
1
1
1
2
0
0
1
0
0
2
0
1
2
1
1
2
0
0
0
0
1
0
1
1
2
3
3
1
0
3
1
1
0
2
0
2
2
1
1
2
0
0
0
0
0
0
1
1
0
0
0
1
2
1
1
0
1
1
1
0
2
5
1
1
1
1
1
1
1
0
2
0
1
0
0
2
0
1
1
2
2
2
0
2
1
1
0
1
1
1
1
1
1
1
2
0
0
1
1
1
1
1
0
1
1
0
1
0
2
0
3
1
0
2
1
0
3
2
2
2
1
1
0
0
0
0
0
0
1
1
1
1
0
0
2
1
2
2
0
0
0
0
2
0
1
2
1
0
2
0
0
1
1
2
0
1
2
0
1
0
2
1
0
1
1
1
0
2
1
0
0
1
2
0
1
1
1
0
2
1
2
0
0
0
1
0
5
1
1
0
0
0
2
1
0
2
0
1
1
1
0
2
0
2
3
1
0
2
1
0
2
1
1
1
0
0
0
2
3
0
1
2
0
0
2
1
0
0
0
0
0
0
0
1
1
0
0
0
2
1
0
0
1
2
1
1
0
1
1
1
0
1
1
1
1
0
1
2
2
0
0
0
1
1
1
0
0
2
1
0
1
3
1
2
2
2
0
2
2
0
0
1
1
2
1
1
0
1
1
0
1
0
0
1
2
0
0
1
2
1
0
1
0
0
1
1
0
0
2
1
0
1
2
1
0
2
0
0
1
0
0
1
2
0
2
2
1
1
0
1
0
1
2
1
0
0
2
1
0
2
0
2
2
0
1
0
0
1
1
2
2
0
1
1
1
2
0
0
0
1
1
1
0
1
1
2
0
0
2
1
1
2
1
0
1
0
1
0
2
0
0
2
1
3
1
1
1
0
1
2
1
1
0
1
0
0
5
1
2
1
1
1
1
2
1
1
1
3
0
0
0
0
1
0
0
1
1
1
1
0
0
2
1
1
2
1
0
2
0
0
0
0
1
1
1
0
1
1
1
2
2
0
0
0
1
1
0
1
1
1
0
2
1
0
0
0
0
1
0
1
0
0
1
1
1
0
2
0
2
1
2
0
0
1
0
1
1
0
1
0
2
2
1
1
1
2
1
1
1
3
2
0
1
0
1
1
1
1
2
1
0
0
1
1
1
1
1
1
1
1
1
0
0
0
3
1
0
2
1
2
2
2
1
0
2
1
1
0
2
1
1
0
1
2
1
1
1
1
1
0
1
1
1
2
1
0
2
1
1
0
2
1
1
1
0
2
2
2
2
2
0
0
0
0
1
1
1
1
0
1
2
1
0
1
0
0
1
2
1
1
0
1
1
1
2
0
2
1
2
1
1
0
2
0
0
2
0
1
0
3
2
1
1
1
2
1
1
2
1
2
9
1
1
1
1
0
1
1
0
0
1
0
0
1
1
0
1
1
1
2
1
0
0
1
2
1
2
1
0
1
2
1
0
0
2
2
1
0
0
0
0
0
1
0
1
0
1
1
1
1
2
1
0
1
0
1
0
2
0
2
2
0
2
2
2
1
0
0
2
1
1
0
0
1
2
1
0
1
2
2
0
1
1
1
1
0
2
1
0
1
0
2
2
0
1
1
0
0
0
0
1
0
1
0
1
1
2
2
1
1
2
1
2
3
1
3
1
0
1
1
0
0
0
2
1
0
1
2
1
1
0
1
0
0
0
1
0
1
2
1
1
0
1
2
2
1
2
0
1
0
1
1
1
1
2
0
0
0
1
1
1
1
1
1
1
1
2
2
0
0
0
1
0
2
0
0
1
0
1
0
0
2
0
2
0
1
1
0
2
0
2
0
1
2
0
2
2
0
0
1
2
1
1
1
1
2
1
1
1
2
1
1
1
2
0
0
2
1
2
2
1
1
1
2
2
0
2
1
1
1
1
0
0
2
0
1
1
1
1
1
1
0
0
1
0
1
1
0
2
0
0
1
0
2
0
0
1
1
1
0
1
1
3
1
1
1
1
1
1
1
1
0
1
0
0
2
1
2
1
1
1
1
1
1
0
1
0
1
1
2
0
1
1
1
1
0
3
1
1
0
2
1
0
2
2
2
0
1
2
0
0
1
2
3
2
1
1
1
0
0
1
1
1
3
0
1
1
0
1
2
2
2
0
2
1
1
2
0
1
2
4
1
2
0
1
1
0
1
0
1
0
0
1
0
1
1
0
1
3
1
1
1
1
1
0
0
0
1
1
2
1
1
2
1
1
1
0
1
0
0
2
1
1
0
1
0
0
1
1
2
0
0
0
1
0
0
0
0
0
1
1
0
1
4
1
1
1
2
1
1
1
1
1
0
1
1
1
2
1
2
2
2
1
1
1
0
0
1
1
1
0
0
2
2
0
1
2
0
2
2
1
0
1
0
1
0
0
1
0
1
2
1
1
0
2
0
1
2
1
0
1
1
1
1
0
1
0
0
0
2
2
2
1
1
1
1
2
0
0
0
1
1
1
1
2
1
1
2
2
1
1
1
0
0
2
1
0
2
2
0
1
1
0
0
1
1
0
0
1
0
1
0
1
1
2
0
0
0
2
1
0
0
2
1
1
0
0
0
0
3
1
0
1
1
0
1
2
1
1
1
1
1
2
2
2
1
1
0
0
1
2
1
1
1
1
1
2
1
0
0
2
0
2
0
1
1
0
2
0
2
2
1
1
1
0
0
1
1
0
1
1
1
2
2
0
1
1
0
4
2
1
1
1
1
1
1
1
1
0
2
0
1
1
1
1
0
1
1
0
2
0
0
1
1
3
1
0
0
1
1
2
2
0
2
2
1
2
2
1
2
0
0
1
1
1
0
2
1
0
1
0
0
0
2
1
1
0
1
0
1
0
1
0
2
0
0
0
1
1
2
0
1
1
1
1
1
0
2
1
2
2
0
0
0
1
1
1
1
1
2
1
0
1
1
1
0
2
2
1
1
1
1
1
0
0
1
0
1
1
0
1
1
0
1
0
2
0
0
2
1
1
1
1
1
2
1
1
0
0
0
1
1
0
1
1
1
0
1
0
0
2
2
1
0
2
2
2
1
0
0
2
2
1
2
2
0
1
0
2
1
1
1
2
1
0
2
1
1
1
0
1
0
0
1
1
0
2
2
0
2
2
1
1
0
1
0
3
2
1
1
2
2
0
0
6
1
2
1
0
0
0
1
2
1
0
0
1
1
1
0
1
1
0
0
1
1
0
1
0
1
0
1
1
1
0
2
3
2
1
2
0
0
1
1
1
1
0
1
1
1
1
0
0
0
1
0
0
0
0
1
1
2
2
1
1
1
1
1
1
2
1
1
1
2
2
1
1
1
0
2
1
0
1
1
1
1
2
1
1
2
3
1
0
0
1
0
1
2
1
1
1
1
0
2
1
1
3
0
1
0
0
0
0
1
1
1
1
0
0
1
0
0
1
2
1
1
2
2
1
2
2
1
1
1
0
1
2
0
2
2
0
0
1
0
0
1
1
0
0
1
2
0
0
1
0
1
0
0
1
2
3
0
1
0
0
0
1
1
1
0
0
0
0
0
1
3
0
2
0
1
0
1
1
1
2
1
0
1
1
1
0
0
2
1
2
0
1
1
1
2
4
0
1
1
1
1
0
5
2
1
1
1
1
1
0
1
0
2
1
1
2
0
0
1
2
1
1
2
1
0
2
2
0
2
1
1
1
0
1
1
1
2
2
1
1
1
1
1
1
1
0
1
2
2
1
1
1
2
1
1
1
1
2
0
0
1
0
1
0
0
2
1
1
1
2
1
0
1
0
0
2
1
1
1
2
1
1
1
1
1
1
0
1
0
1
0
0
1
0
1
1
0
2
1
1
1
1
0
0
2
2
0
0
2
2
2
2
2
2
0
2
2
1
0
0
1
2
0
1
1
0
1
1
0
1
0
0
1
1
2
0
1
0
0
1
2
0
0
0
1
2
1
1
0
1
1
1
0
1
0
0
0
1
3
2
2
1
1
3
0
0
1
0
0
1
2
2
2
1
1
2
0
0
1
0
0
0
0
0
1
1
0
1
1
0
0
0
1
0
2
0
0
1
1
0
0
1
0
0
0
0
2
0
0
2
1
0
0
1
1
2
0
0
1
0
1
1
0
1
0
1
1
0
1
1
0
0
1
2
0
1
2
0
1
2
0
0
0
0
2
4
2
1
1
0
2
1
1
1
1
2
0
0
2
1
2
1
2
1
1
2
0
0
0
1
0
2
1
0
0
1
2
0
2
1
1
2
1
2
1
2
2
2
2
1
1
0
1
1
1
1
2
1
1
1
0
2
1
0
1
1
1
2
1
0
1
0
0
0
0
2
1
1
0
1
0
1
1
1
2
2
1
1
2
0
0
1
0
0
1
2
1
0
2
0
1
0
1
0
1
1
2
1
0
0
2
1
0
2
2
0
0
1
0
1
0
0
0
1
1
2
2
0
1
1
2
0
1
1
1
2
0
1
1
1
1
0
1
1
1
1
1
0
1
0
1
1
1
0
0
0
1
0
0
1
0
1
2
1
0
2
0
2
0
1
0
2
1
1
2
1
1
2
1
0
0
2
1
1
2
0
2
0
1
0
1
0
1
2
1
0
0
2
0
0
0
1
0
1
0
1
0
0
1
2
0
2
1
1
1
4
3
1
0
0
1
0
0
0
0
2
2
1
1
1
2
0
1
1
2
1
1
2
2
1
0
1
2
0
0
1
1
0
1
0
1
0
0
1
0
0
0
2
2
0
1
1
1
2
2
0
1
0
1
1
0
2
0
1
1
0
2
0
1
1
1
2
1
0
0
1
2
1
1
1
2
2
2
2
0
2
1
0
0
1
1
1
2
2
2
2
1
0
0
1
2
2
0
2
1
1
0
0
2
2
1
1
1
1
2
2
1
1
1
1
0
3
1
1
0
1
2
2
2
1
1
2
1
0
0
1
0
0
0
1
2
1
2
1
2
1
0
0
1
0
0
0
2
0
2
2
2
1
0
0
1
1
2
0
0
1
0
2
0
3
0
2
2
1
1
0
0
2
3
0
1
1
2
1
1
1
1
1
0
3
2
0
0
1
1
0
1
2
0
1
4
1
0
1
1
0
0
1
0
0
0
0
0
0
0
1
2
1
2
0
1
2
1
0
0
0
1
1
2
2
2
0
1
1
1
0
0
1
0
1
0
2
1
0
2
0
0
2
0
1
1
1
2
1
0
2
1
2
1
2
1
0
0
1
1
0
2
1
2
2
0
0
0
1
1
2
2
0
1
1
1
3
2
12
1
1
2
2
1
2
1
2
0
0
1
0
1
1
1
2
2
1
0
1
0
2
1
1
0
1
5
2
1
1
1
1
1
1
1
0
0
1
0
0
2
2
1
1
0
0
2
0
0
0
0
1
0
0
1
0
0
1
2
2
0
1
3
0
1
1
1
2
2
1
0
0
1
1
0
2
1
0
0
2
1
0
1
2
0
7
0
2
1
0
0
1
2
2
1
1
0
2
1
2
0
2
1
2
1
0
0
0
0
0
1
1
0
1
0
1
1
0
1
1
2
2
2
1
1
0
2
0
1
2
1
1
0
2
0
0
0
1
1
1
0
1
0
1
0
0
0
0
1
0
0
1
1
1
1
1
1
2
1
1
0
0
1
1
1
1
1
0
3
0
1
0
1
1
1
1
0
1
1
0
1
1
0
1
1
1
0
0
2
0
0
0
1
1
1
1
0
1
0
1
3
0
0
1
1
1
0
3
1
2
1
2
1
1
1
2
1
1
1
1
0
0
2
2
1
1
2
2
1
1
1
0
1
0
1
1
1
0
1
0
2
1
1
2
1
1
0
2
1
1
0
1
1
1
2
1
0
1
1
2
2
1
1
1
2
1
1
1
0
0
1
0
1
0
1
1
0
2
2
1
1
1
0
0
0
0
1
1
0
0
1
1
1
0
2
1
1
0
0
1
0
1
0
2
2
1
1
0
1
1
1
2
2
1
0
0
0
1
0
0
1
2
1
1
2
1
1
1
1
0
0
2
0
1
0
3
0
0
1
1
1
2
0
2
1
0
0
1
1
1
0
1
1
1
1
1
1
1
1
1
0
0
1
2
1
1
2
2
0
2
1
0
1
0
2
1
2
0
2
1
1
1
2
2
0
1
2
2
1
0
1
1
2
2
2
0
4
2
1
0
1
1
0
0
2
2
0
2
0
2
1
0
2
1
1
0
1
1
0
0
0
0
0
0
3
0
1
3
1
2
1
2
1
1
1
1
2
0
1
0
0
1
0
1
2
0
1
1
3
2
0
1
2
1
1
0
2
2
0
0
2
1
1
1
0
0
0
1
1
2
0
2
0
0
2
1
1
0
1
2
0
1
1
2
2
1
0
0
0
1
1
1
2
1
0
0
0
2
0
1
1
2
2
2
1
2
0
1
2
0
1
1
1
0
2
0
2
1
2
0
1
2
1
0
1
0
0
0
2
0
1
1
0
2
0
1
1
0
2
0
0
2
1
1
2
1
0
0
1
2
1
1
1
1
0
2
0
0
1
2
1
0
2
1
2
0
1
0
2
3
0
0
2
1
0
2
1
1
1
0
0
0
1
2
1
1
1
1
1
1
1
1
0
1
0
3
1
0
1
0
1
1
2
1
2
0
0
0
2
0
0
1
0
0
1
2
1
0
0
0
0
3
0
2
0
1
0
1
1
1
1
0
5
2
1
1
0
0
1
0
1
2
1
1
1
1
0
0
1
2
2
2
1
0
2
2
0
2
0
1
1
1
1
1
1
1
0
0
1
2
1
1
0
0
1
2
0
1
1
1
1
1
0
2
2
1
1
1
1
0
0
1
0
2
1
0
0
1
0
0
1
1
1
2
1
1
0
0
1
1
2
0
1
1
0
1
2
2
1
0
0
0
1
0
1
0
2
3
2
1
1
1
0
1
1
3
1
0
0
1
2
0
0
1
2
1
1
2
2
1
0
0
0
1
1
1
0
2
0
2
1
1
1
1
0
1
1
0
1
0
1
1
0
0
1
0
0
1
1
2
1
2
1
0
0
2
1
1
1
1
1
0
2
1
0
1
2
0
2
2
2
1
2
1
2
1
1
2
1
1
1
1
1
0
0
1
0
0
2
0
1
0
1
0
1
0
0
2
0
2
0
0
0
1
0
1
0
1
2
0
0
0
1
0
1
1
0
2
0
1
2
1
0
0
0
2
0
0
0
0
1
3
0
0
1
0
0
1
1
2
1
1
1
1
0
2
0
1
1
1
1
2
0
1
0
0
0
0
0
0
0
1
0
2
1
0
0
1
0
0
1
0
0
1
2
1
4
2
2
0
0
1
1
1
2
1
1
0
0
1
2
0
1
2
0
1
0
2
1
0
1
2
0
0
1
0
0
1
0
2
0
1
1
0
1
0
0
2
3
1
1
1
1
0
1
0
2
1
3
2
0
0
0
0
0
2
1
1
0
1
1
1
0
1
2
1
1
1
1
1
0
1
1
2
1
0
0
0
0
1
0
1
2
2
1
2
0
1
3
1
1
2
0
1
2
2
1
1
0
1
0
1
2
0
2
0
1
1
0
0
1
0
1
1
0
2
0
0
1
2
1
2
0
0
1
1
2
1
0
2
1
1
1
0
0
1
2
0
2
2
0
1
0
1
0
0
1
1
0
0
2
2
1
1
0
1
2
0
0
0
1
1
0
3
1
0
1
2
1
1
1
2
1
1
1
1
1
1
1
1
2
0
2
2
2
2
0
0
1
0
1
0
1
0
1
0
1
2
1
0
1
1
1
0
0
2
2
9
2
0
0
1
1
0
0
0
0
1
2
0
0
2
0
2
0
0
3
0
0
1
1
1
0
1
2
1
1
2
0
0
1
1
1
1
2
1
1
0
1
1
1
2
2
1
2
0
2
0
0
2
1
0
2
0
0
0
1
1
2
0
0
1
1
0
2
0
0
0
1
0
1
1
0
2
2
2
1
2
1
0
1
0
0
3
0
2
0
2
2
1
1
2
0
0
1
0
1
1
1
0
0
0
0
1
3
0
0
2
0
0
0
1
1
2
0
0
1
2
1
1
0
1
1
0
1
1
0
1
0
1
2
2
1
1
0
1
1
1
1
0
0
1
0
1
0
0
1
1
1
2
2
0
0
1
0
1
1
2
1
1
1
1
2
2
1
1
1
2
2
1
2
1
2
2
1
2
1
0
1
1
1
2
1
0
1
1
0
1
1
2
0
1
2
1
1
1
0
1
2
0
1
0
0
1
1
3
2
0
1
2
0
0
1
1
0
1
1
2
1
1
0
0
1
2
2
2
2
2
0
0
0
2
1
0
0
0
0
2
0
0
1
0
1
0
0
1
1
0
1
0
1
1
0
1
1
0
0
1
1
1
1
0
0
1
1
0
1
0
2
1
2
0
2
0
1
0
1
1
1
1
0
0
0
1
1
1
1
0
2
2
1
0
2
1
1
0
1
1
2
1
1
1
2
1
1
1
0
3
0
0
2
2
2
1
1
1
1
1
0
2
0
1
2
1
0
1
2
1
2
0
1
0
0
2
2
1
2
2
0
2
0
0
0
2
1
2
2
1
1
0
2
0
1
1
0
0
0
2
0
2
2
0
2
1
1
0
0
1
1
2
1
0
1
0
0
0
1
1
2
0
1
0
2
0
0
1
2
1
1
2
1
2
2
0
0
0
0
1
0
1
1
0
2
0
1
4
2
1
1
1
2
1
0
0
1
0
1
1
0
0
0
1
0
1
1
0
0
0
2
1
1
2
2
1
0
0
1
0
0
1
0
0
1
0
1
1
2
0
1
0
0
0
1
1
1
2
0
1
1
0
1
1
2
0
1
1
2
2
0
1
2
4
1
2
0
2
1
1
1
1
1
2
1
1
4
3
1
0
0
1
2
1
1
2
1
2
2
0
2
2
2
1
1
1
2
0
2
1
0
0
0
1
0
1
0
2
2
1
0
2
1
2
1
2
0
1
1
0
1
2
1
0
1
1
0
0
0
0
0
0
1
0
0
1
2
1
2
1
0
1
1
0
0
1
0
1
2
2
1
1
0
0
0
1
1
0
2
1
0
2
2
4
1
0
1
1
1
0
1
1
0
0
1
2
1
2
0
1
0
1
1
1
1
4
0
1
2
1
1
0
0
2
0
1
1
2
1
0
0
2
2
2
1
1
0
1
0
1
1
0
2
1
1
0
0
1
0
1
1
0
1
1
1
0
1
3
0
2
1
0
1
0
0
0
0
0
2
1
1
0
2
0
0
1
0
1
0
1
1
2
1
0
2
1
1
3
1
2
1
1
1
0
2
2
0
0
1
1
1
1
1
1
1
1
1
0
1
2
1
0
1
2
0
2
1
1
2
1
1
2
1
0
1
1
1
1
1
0
1
0
0
0
4
1
0
2
1
0
1
0
0
1
1
0
0
0
0
1
1
1
0
2
0
0
1
2
2
0
2
0
1
1
0
1
1
2
0
2
1
0
1
1
1
2
1
1
2
0
0
1
1
1
0
1
1
1
1
1
1
0
1
2
0
1
0
2
0
1
2
0
1
0
1
0
2
2
0
1
2
2
2
2
0
1
1
1
2
0
0
1
0
1
2
1
1
0
1
1
2
1
1
1
1
1
1
1
2
2
1
0
0
1
1
1
0
1
2
0
1
1
1
0
0
1
1
0
1
1
1
1
2
1
1
1
2
0
2
1
1
0
2
2
1
0
0
1
0
2
1
0
1
2
1
0
2
1
1
0
1
0
0
2
1
2
1
1
2
1
2
0
1
1
2
1
1
2
3
0
1
0
2
1
0
0
0
1
1
2
1
0
1
1
1
1
2
0
2
1
1
2
1
1
1
1
0
1
1
1
0
1
0
1
0
1
1
1
1
0
3
1
0
0
1
0
1
1
0
2
1
0
0
0
0
1
0
1
0
1
2
0
2
1
2
2
2
0
1
1
2
2
0
1
2
1
1
2
1
1
2
2
0
2
1
1
1
0
0
0
2
1
2
0
1
0
2
1
0
2
1
1
0
2
1
2
2
0
1
0
1
0
2
1
1
0
0
3
1
2
0
1
1
1
0
1
1
1
2
1
1
1
0
0
2
2
0
2
2
1
1
0
1
1
1
2
1
0
1
0
1
2
0
1
0
1
0
1
0
0
0
1
0
0
2
1
4
2
0
2
1
0
0
2
2
1
2
0
2
1
0
1
1
1
1
1
0
0
1
0
2
1
1
0
0
0
2
0
2
1
1
2
2
1
0
3
1
0
1
0
3
3
1
0
0
2
0
1
1
1
0
0
0
1
1
1
1
0
1
1
0
1
2
0
0
0
0
2
2
2
1
1
1
0
0
2
0
0
1
1
2
2
0
1
4
0
1
1
1
0
0
2
1
1
0
1
2
2
1
1
2
1
0
1
2
1
1
1
0
2
2
0
1
2
2
1
0
2
2
0
2
0
0
1
0
1
0
1
2
0
1
0
1
0
0
2
1
2
2
1
0
1
1
2
0
0
0
2
0
2
2
2
1
1
1
1
0
0
2
1
1
0
0
1
1
1
0
1
0
1
0
2
0
1
1
2
1
0
0
0
0
2
0
2
2
1
2
1
1
1
0
2
0
0
2
1
1
0
2
1
2
0
2
0
0
1
1
1
1
0
2
1
0
1
1
0
1
0
1
0
0
2
1
0
1
0
1
0
1
0
2
1
1
1
0
0
3
2
0
3
0
0
2
3
2
0
0
2
1
0
0
1
1
0
1
0
2
2
0
1
0
1
2
1
0
2
2
2
1
1
0
2
1
0
2
1
2
0
1
0
2
2
0
0
3
1
0
2
0
1
2
2
0
1
1
0
2
4
0
0
0
2
0
1
0
1
0
1
1
0
0
0
1
1
2
0
0
1
0
0
1
2
1
2
0
1
2
1
2
1
1
2
1
1
2
0
2
2
2
0
0
0
1
2
1
1
2
0
0
1
1
1
0
0
1
0
1
2
2
1
1
0
1
2
0
1
0
1
1
2
0
1
1
1
2
1
0
1
1
1
1
1
1
1
0
2
0
1
2
0
2
1
0
1
1
2
2
1
1
1
0
1
1
1
1
3
1
1
0
0
0
2
1
1
0
1
2
2
2
0
0
1
2
2
2
1
0
2
0
3
0
2
2
1
1
1
1
1
1
0
0
2
1
0
1
1
0
2
0
0
1
1
1
1
2
0
2
2
0
0
1
2
0
1
2
2
1
1
1
1
1
1
2
2
2
2
1
0
1
0
0
1
0
2
1
1
0
1
1
1
2
2
3
1
1
1
1
0
2
2
0
2
2
2
0
1
0
1
1
0
1
2
2
1
1
2
2
0
0
1
2
0
1
1
2
0
1
0
1
1
1
1
1
1
1
1
1
0
1
0
1
1
0
2
1
1
0
0
0
2
0
0
0
1
0
1
2
2
2
0
2
1
2
1
1
0
0
2
2
0
2
0
1
2
0
1
0
0
0
2
0
2
1
1
1
1
0
1
1
2
0
0
0
1
1
0
1
1
0
2
1
2
3
1
1
2
1
0
2
2
0
0
0
1
1
1
0
2
2
0
1
1
1
0
2
2
1
0
2
2
1
1
1
1
1
1
1
1
1
1
2
1
2
0
1
0
2
1
2
0
2
2
2
1
0
1
0
2
0
1
1
1
2
1
0
1
2
2
1
1
1
0
1
2
1
0
1
0
1
2
0
2
1
2
0
0
1
0
1
1
2
1
1
0
1
2
0
0
1
2
1
1
1
1
1
1
1
0
1
0
2
2
1
1
0
0
2
1
2
1
2
0
2
2
2
2
0
0
1
2
0
1
1
2
2
1
0
0
1
4
0
1
0
1
1
1
2
2
0
2
1
1
1
1
0
0
1
0
0
1
0
0
1
1
0
1
0
1
1
0
1
0
0
0
1
0
0
1
2
2
1
1
0
2
0
2
1
0
2
0
1
2
0
1
1
1
0
0
2
1
2
0
2
2
1
1
1
1
0
2
2
2
1
2
1
2
1
0
1
2
2
0
0
0
1
0
0
1
1
2
1
2
0
0
2
2
0
1
1
0
1
1
2
0
0
0
0
0
0
0
0
1
1
1
1
2
1
1
3
0
2
0
0
1
0
2
1
1
1
1
0
3
1
1
2
1
1
1
1
2
1
0
1
2
0
1
0
2
2
1
1
0
2
2
0
1
0
2
1
2
0
1
1
0
1
0
1
2
0
1
1
2
1
2
0
1
2
1
1
1
0
1
1
1
0
0
0
1
1
1
1
0
0
0
0
1
2
0
0
1
1
1
2
0
1
1
0
1
1
1
0
0
1
2
0
1
1
2
0
0
1
1
1
2
2
2
1
0
2
3
1
0
2
2
2
1
2
2
2
1
1
0
1
1
0
1
2
2
2
1
1
0
1
0
0
0
1
0
2
1
0
1
0
1
1
0
2
1
1
0
0
0
1
1
0
2
2
0
0
0
0
2
0
1
1
2
1
1
0
0
2
0
2
0
0
1
0
0
0
2
2
0
0
0
0
0
2
1
2
1
2
0
2
1
0
0
0
0
0
0
2
0
0
0
1
1
2
0
1
1
0
1
1
1
2
1
1
0
0
2
1
0
2
2
1
1
0
1
1
2
0
0
0
0
0
2
1
0
2
1
0
2
1
2
0
1
1
0
0
0
2
0
2
0
0
1
2
1
0
1
1
2
2
1
0
0
2
1
2
2
1
1
1
1
1
0
1
1
1
0
0
1
1
0
2
2
0
1
0
1
2
1
1
3
2
1
2
1
0
1
2
0
0
1
1
1
0
1
2
1
0
0
1
2
1
0
2
1
3
1
0
0
1
1
2
0
0
2
2
0
1
0
1
1
1
1
0
2
2
0
1
1
1
1
3
0
1
0
1
2
0
0
1
0
1
0
0
0
1
0
2
2
2
1
0
0
1
1
2
0
1
1
0
0
1
2
1
2
2
0
0
2
0
4
1
2
0
1
2
0
2
0
0
1
0
2
1
1
0
1
0
0
1
1
1
1
1
0
2
2
1
2
0
2
0
1
2
2
1
0
1
3
1
1
0
2
1
0
1
2
1
1
1
2
0
1
1
2
1
1
0
0
1
0
2
1
2
1
0
2
1
1
0
0
1
2
1
1
0
2
0
0
1
0
0
0
3
1
1
1
0
2
2
1
1
0
0
1
0
2
0
1
0
0
0
1
1
1
1
0
0
0
1
1
0
0
2
0
1
1
2
2
0
1
1
0
0
2
1
1
1
1
1
1
0
0
1
4
1
1
0
1
3
1
1
0
2
0
1
1
1
2
1
1
1
0
0
0
1
1
1
1
2
2
1
0
1
1
2
0
1
1
2
0
0
1
2
1
2
2
1
0
1
1
1
1
0
1
1
2
1
0
1
2
1
2
1
1
1
1
2
1
0
1
2
1
0
0
2
1
0
0
2
0
1
2
0
1
0
1
2
1
1
1
2
2
0
1
0
2
0
2
1
0
1
0
2
0
2
1
0
2
0
2
2
2
1
0
0
0
1
1
0
1
1
1
0
0
1
2
0
1
0
2
1
2
0
0
0
2
0
0
2
0
1
3
1
0
0
1
0
0
1
0
1
2
1
0
0
0
2
1
2
2
1
0
0
1
0
1
2
1
1
1
2
1
1
0
1
2
1
1
1
0
1
0
2
1
0
3
1
1
1
0
2
1
1
2
3
0
2
1
1
0
0
0
1
1
1
1
2
1
0
0
1
1
0
1
1
2
0
1
2
2
1
2
1
2
1
1
0
1
0
2
0
1
1
1
2
1
0
0
0
1
1
2
0
2
2
0
2
0
2
1
2
1
1
2
1
0
0
1
1
1
1
2
3
1
0
0
2
0
0
2
2
2
1
1
0
2
0
1
1
3
1
1
0
1
1
1
0
2
1
0
1
1
0
0
2
2
2
0
2
1
1
1
3
1
1
2
0
1
1
1
1
0
1
2
0
1
1
2
1
1
1
2
0
0
0
0
4
1
1
1
1
0
2
2
1
0
1
1
1
1
1
1
2
1
1
0
1
0
2
1
1
0
1
1
2
0
1
0
3
1
1
1
1
0
2
2
0
0
0
2
2
1
1
1
1
1
2
2
1
1
0
2
0
0
0
1
1
2
2
0
2
1
1
1
1
1
1
0
0
0
0
1
2
0
2
2
0
1
1
1
0
0
1
0
0
0
0
1
2
1
0
1
0
0
1
1
2
2
1
2
0
0
1
0
1
1
1
1
2
0
0
0
1
2
1
2
1
2
0
1
2
1
1
0
2
0
1
2
2
2
0
1
0
1
1
1
1
1
0
0
1
1
1
1
1
2
1
0
0
1
1
0
1
2
2
0
0
1
0
0
0
1
2
0
2
1
1
1
0
0
0
0
0
1
1
0
2
0
2
1
2
0
1
1
0
0
1
2
1
1
1
0
2
1
2
0
2
2
2
1
2
2
0
1
3
1
1
1
1
0
2
0
0
0
2
1
0
0
1
0
0
1
1
1
0
1
0
0
1
0
1
2
0
1
0
1
2
2
0
1
1
1
0
0
1
1
1
2
2
2
0
0
0
2
1
0
2
1
2
1
0
2
0
2
1
1
1
1
0
1
1
1
2
2
0
0
2
1
0
0
2
1
2
1
0
1
0
1
0
0
0
1
2
1
0
0
1
2
1
2
1
2
2
1
1
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
1
0
1
1
1
0
0
1
1
2
2
1
0
1
0
3
2
2
3
1
1
2
0
1
1
1
1
1
2
0
0
2
0
1
1
0
2
0
1
1
2
2
1
1
1
1
1
0
0
1
1
2
0
1
1
1
2
0
0
2
0
0
1
0
2
1
1
1
2
1
1
0
2
1
0
0
1
2
0
1
2
2
1
1
2
2
1
2
0
0
0
0
2
1
1
1
0
1
1
2
0
1
1
0
1
0
0
0
0
1
2
1
2
1
1
0
1
1
0
0
1
1
0
1
2
0
1
2
1
1
0
2
0
1
1
2
1
0
2
0
0
1
0
1
1
0
1
0
2
1
0
0
2
3
2
1
1
3
1
1
0
1
0
1
1
1
0
1
0
0
0
2
1
1
1
2
0
1
2
0
1
2
2
0
0
2
0
0
0
0
2
1
0
1
3
2
1
2
0
0
1
1
2
1
1
0
1
1
1
0
2
1
1
1
1
0
1
1
0
0
0
0
1
2
1
1
0
0
2
0
1
2
1
0
1
0
2
2
0
0
1
0
1
1
0
1
2
1
1
1
0
0
0
0
1
0
2
0
1
1
2
0
2
2
2
1
0
0
2
1
1
2
1
1
2
1
0
0
1
2
1
1
1
2
2
0
0
1
0
0
0
2
1
2
1
1
1
2
2
1
1
0
2
2
0
1
0
0
0
0
1
2
2
2
2
3
0
0
0
1
0
1
0
0
0
1
1
2
2
1
0
1
1
1
1
0
0
0
0
1
1
1
2
0
2
1
2
1
1
1
2
1
0
2
1
6
1
1
1
1
0
0
0
1
0
0
2
1
0
0
0
1
0
0
1
1
1
0
1
2
0
0
1
1
2
2
0
0
2
0
2
1
1
1
1
1
2
1
0
2
0
0
0
0
0
1
2
0
1
0
0
0
2
0
1
4
1
1
0
0
2
1
2
2
1
0
1
1
0
3
1
2
1
1
1
0
0
1
0
2
1
2
2
1
1
1
1
2
0
0
2
1
0
2
1
2
0
1
0
0
2
1
1
2
0
1
0
0
1
1
2
2
1
0
1
0
2
0
1
0
0
2
2
1
3
1
1
1
1
1
1
0
1
0
0
2
0
1
2
2
2
1
1
1
2
0
0
2
1
2
4
1
1
2
0
0
1
0
1
1
0
1
0
1
1
2
1
0
0
1
0
0
1
0
2
0
0
1
1
0
0
1
1
0
0
1
5
0
1
1
1
1
2
1
2
0
0
2
0
2
2
1
0
1
0
1
0
0
0
1
0
2
0
2
2
1
4
0
2
1
0
0
0
2
2
1
1
2
2
1
1
0
1
0
0
3
1
0
1
1
1
0
1
1
0
0
0
2
0
1
1
1
1
0
1
0
0
0
2
2
2
1
1
2
0
1
2
1
2
1
1
0
1
1
2
1
2
2
1
0
2
1
0
0
1
1
1
0
2
0
1
2
0
1
2
2
1
2
0
3
2
0
1
0
0
1
3
2
0
1
1
2
0
2
2
1
2
0
0
0
0
1
0
0
1
1
0
1
2
0
0
0
0
0
1
2
1
0
2
2
1
0
1
1
0
0
1
0
2
0
1
1
1
0
1
0
0
0
0
2
0
1
0
1
1
2
1
2
1
1
0
0
1
1
0
0
0
1
2
1
0
0
0
1
0
1
0
1
0
1
0
1
0
2
1
0
2
1
1
1
0
0
0
0
1
1
1
0
2
1
1
2
1
0
1
0
1
2
0
1
1
2
1
0
0
2
0
1
0
3
0
0
0
2
0
2
0
1
1
0
1
2
0
2
1
0
2
2
0
0
1
0
1
2
1
0
1
1
1
0
0
0
2
2
1
2
1
2
1
1
1
2
1
0
1
2
1
1
0
1
1
0
2
0
0
2
0
1
1
0
1
1
2
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
3
1
0
0
1
1
1
2
0
2
3
3
0
0
1
1
1
1
0
1
0
2
1
0
0
0
0
1
2
3
1
0
0
1
1
1
2
0
0
1
1
1
2
2
0
1
0
1
2
1
0
1
0
2
0
2
1
2
0
2
0
0
2
1
1
0
1
1
0
1
1
2
2
1
1
1
1
0
0
0
2
0
0
1
1
0
1
1
1
0
2
2
0
1
2
1
2
0
3
0
0
1
1
1
0
1
1
1
4
1
2
1
0
2
3
1
1
2
0
2
0
1
2
2
1
0
1
1
0
1
1
1
1
0
1
1
1
2
0
0
0
3
2
0
1
2
1
1
2
0
1
1
0
1
0
0
0
1
1
0
0
0
0
2
2
1
0
0
2
0
1
0
1
1
3
1
0
0
2
1
0
1
0
1
2
1
0
0
0
0
1
1
0
0
0
1
0
1
1
2
1
2
1
0
0
0
1
1
0
0
1
2
1
1
1
0
2
1
2
2
0
0
1
1
0
1
1
1
0
1
1
1
0
2
1
1
2
0
0
1
1
0
2
2
2
2
1
0
1
1
0
0
1
0
0
1
2
0
2
0
0
1
0
0
2
2
1
1
1
2
1
2
0
1
0
2
0
1
0
1
2
2
2
1
0
1
1
1
1
0
1
0
1
1
1
0
1
1
2
1
2
1
1
2
2
0
1
1
1
1
1
1
1
1
2
1
0
1
0
2
2
1
0
2
1
2
1
1
1
0
1
0
0
2
0
1
0
0
2
0
1
1
1
0
0
0
2
1
1
0
1
0
1
0
1
0
1
0
0
0
1
0
1
1
0
0
0
2
1
1
1
0
0
2
0
2
1
0
1
0
0
1
1
1
1
1
1
1
0
1
1
0
0
1
0
1
0
1
0
1
1
2
0
2
0
2
2
0
0
1
0
0
0
1
0
1
0
1
9
1
0
0
1
0
0
1
1
2
1
1
2
1
2
1
1
1
0
2
0
1
1
1
0
0
0
1
0
0
1
1
0
1
1
1
0
2
0
0
1
1
0
0
1
1
1
1
1
0
2
2
0
2
0
0
0
1
0
0
0
1
1
0
1
0
1
2
1
2
1
1
1
0
1
0
0
1
1
1
2
0
2
1
1
1
1
2
1
1
1
1
1
1
0
1
1
1
2
1
1
1
2
0
1
0
2
0
1
1
1
1
1
1
2
2
1
0
0
1
1
2
2
0
1
1
1
1
1
0
1
0
1
0
2
2
2
2
2
1
2
5
1
1
1
1
2
1
1
1
0
1
0
0
1
1
0
0
0
0
1
0
1
1
2
1
1
1
2
1
1
2
1
0
0
2
0
0
0
2
0
0
1
0
1
0
0
0
1
1
1
1
0
1
1
0
1
0
1
2
2
1
2
1
0
1
1
1
2
2
1
3
0
0
1
0
0
1
0
5
0
0
2
1
1
1
2
2
1
1
1
1
1
0
0
1
1
4
3
0
0
2
1
2
1
2
1
2
0
0
1
1
2
2
2
1
0
1
2
1
1
2
0
0
1
2
1
1
1
2
0
0
0
1
1
0
0
0
0
1
0
0
1
1
2
1
0
1
1
0
1
2
1
1
2
1
0
0
0
0
1
1
2
2
2
0
1
0
0
1
2
1
1
1
2
0
0
0
1
0
0
1
1
2
0
0
0
2
1
0
0
1
2
0
0
1
0
0
1
0
4
1
0
1
1
1
2
0
1
0
0
1
1
1
1
1
1
1
2
1
2
1
2
2
1
0
2
0
1
0
0
1
2
2
2
1
2
1
1
1
1
1
1
0
0
2
2
1
1
0
0
2
1
1
0
2
0
0
1
0
1
2
0
1
0
2
1
0
0
0
0
2
1
2
2
2
2
1
1
2
1
0
0
1
1
2
1
1
0
2
2
2
0
1
2
2
1
0
2
1
2
2
1
1
2
0
0
0
1
0
1
0
1
1
1
1
1
1
1
1
2
2
1
0
1
2
1
2
1
1
0
1
0
1
1
2
2
1
2
0
0
1
0
0
0
0
0
1
2
1
0
2
0
1
0
1
4
2
0
1
0
1
0
0
2
0
1
2
0
0
2
0
1
2
0
0
1
1
1
2
2
0
2
0
1
1
0
1
1
1
1
1
3
0
0
2
1
1
0
0
1
1
0
1
0
0
1
0
2
1
0
1
2
2
2
2
0
1
1
1
0
2
1
1
1
1
1
0
0
1
1
0
1
0
0
0
2
1
2
0
1
1
1
1
2
3
0
1
0
0
1
1
1
0
0
2
2
2
0
0
1
0
1
1
2
0
1
0
1
2
1
1
1
0
1
1
0
1
1
0
1
0
1
1
2
1
0
0
1
0
1
2
2
1
0
0
2
0
0
1
1
1
1
0
1
2
1
1
0
0
1
0
1
0
1
1
1
2
0
1
3
1
0
0
1
1
0
1
0
0
0
0
2
1
0
2
0
2
0
1
2
1
0
0
0
1
1
0
2
1
2
2
2
0
0
0
0
1
2
2
1
1
0
2
0
0
1
2
2
1
0
1
1
0
1
1
1
0
0
1
2
2
0
3
2
1
0
1
1
0
2
0
0
1
1
1
0
1
0
1
0
1
2
1
0
2
0
1
1
0
1
1
4
0
2
0
1
0
1
2
2
2
2
0
2
1
1
0
2
1
0
0
2
1
1
0
2
1
0
1
1
0
0
0
0
0
1
0
1
1
2
1
0
0
1
0
1
1
0
1
2
1
1
3
1
0
2
2
1
1
1
0
0
1
1
1
2
1
1
1
1
1
1
0
2
0
2
1
0
0
2
0
1
2
1
2
2
2
1
1
2
1
1
1
0
1
0
1
0
2
1
1
1
2
1
1
0
0
2
0
1
1
0
0
1
0
1
1
1
1
0
1
0
0
1
0
1
0
1
2
0
1
1
2
0
0
1
1
0
0
0
1
1
1
0
0
0
2
2
2
1
0
0
1
2
1
0
1
1
0
0
0
1
1
0
1
2
1
0
2
1
1
0
1
0
1
2
1
1
1
0
0
1
1
1
2
0
1
0
0
1
1
0
2
0
1
0
1
0
1
1
1
1
1
0
0
1
2
1
0
1
2
0
1
2
2
0
1
1
1
1
1
1
0
1
1
1
1
0
1
1
1
1
0
2
1
1
2
1
0
1
1
1
1
0
2
0
0
2
2
1
1
0
1
1
0
1
1
2
1
0
1
1
0
0
0
0
1
1
0
2
2
2
1
1
0
1
2
2
2
2
0
2
0
1
1
1
2
1
2
1
0
1
1
1
1
0
1
2
2
0
2
1
0
1
0
0
1
0
1
1
1
0
2
1
0
0
2
1
2
0
0
2
0
2
1
0
1
0
1
2
1
1
0
1
1
1
1
2
0
1
0
1
2
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
2
1
1
1
1
1
1
2
1
1
0
1
1
1
0
0
2
0
2
1
1
0
0
1
0
1
0
0
2
1
2
1
1
1
1
0
1
0
2
2
0
1
0
1
0
1
2
2
1
2
1
0
0
0
1
1
1
2
0
0
2
1
1
3
0
0
1
2
2
0
0
2
2
2
2
0
1
1
0
1
0
0
2
0
0
1
2
1
2
0
1
0
2
1
0
0
0
0
0
0
1
2
1
1
1
1
0
2
0
0
1
1
1
1
2
1
0
2
0
1
1
1
0
2
1
2
1
3
1
1
0
1
1
1
1
0
1
1
1
0
2
0
2
6
0
1
0
2
0
1
1
1
0
1
4
1
2
1
1
0
0
1
1
1
0
0
2
1
0
0
0
0
1
2
1
2
1
0
2
1
1
0
0
1
0
0
1
1
1
0
1
0
1
0
1
2
0
1
1
1
0
2
1
1
1
2
1
0
2
1
2
0
1
1
0
0
0
0
3
2
0
1
0
1
1
2
0
0
2
0
5
0
0
1
1
1
0
1
0
2
2
1
2
1
1
0
0
0
2
0
1
1
1
1
0
0
0
1
1
3
1
2
1
0
2
1
1
1
0
2
1
2
1
0
1
2
2
0
2
0
1
0
2
1
0
1
1
1
0
2
2
0
0
2
1
1
0
1
0
1
0
1
0
0
2
2
1
2
3
1
2
1
1
2
1
1
0
1
1
0
1
0
1
0
0
2
0
2
1
0
1
1
0
1
1
1
0
0
0
1
0
0
0
1
1
1
0
0
1
1
1
0
0
1
1
2
0
0
0
0
0
0
1
1
0
1
1
1
2
2
0
0
2
1
1
2
2
1
0
0
0
1
1
0
1
0
2
1
0
0
2
1
1
2
1
0
1
0
1
1
1
2
1
3
1
0
2
0
1
1
1
0
2
1
2
1
1
1
0
2
2
1
1
1
0
0
1
2
2
2
0
1
1
2
0
2
1
0
1
0
1
2
2
1
0
0
0
1
1
1
0
1
1
0
2
0
1
1
1
3
1
0
1
1
1
0
0
0
0
1
2
2
0
1
2
0
0
1
0
1
1
0
0
2
2
0
1
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
1
0
2
1
0
1
1
1
1
0
1
0
0
1
1
1
0
0
1
2
1
0
2
0
0
1
1
0
1
1
1
2
1
1
1
0
2
0
1
1
2
2
1
1
0
2
1
0
2
0
1
0
1
1
1
0
2
1
2
1
0
1
0
0
0
0
2
0
1
2
0
1
1
2
0
0
1
0
1
1
1
1
0
0
0
1
0
2
1
1
0
1
0
1
1
0
0
0
0
0
0
1
0
1
1
1
0
1
0
1
0
1
0
1
0
1
1
2
0
0
0
2
0
0
0
1
2
0
1
0
2
0
1
1
6
0
1
2
1
1
1
1
1
0
1
1
1
0
0
2
0
0
1
0
1
1
0
0
0
0
0
1
0
1
0
2
2
1
0
0
0
0
0
1
2
0
2
2
0
1
1
1
1
0
4
1
2
1
0
0
1
2
1
1
0
2
2
1
2
0
1
1
0
2
1
2
1
0
1
1
1
1
1
1
0
1
2
1
0
1
0
1
0
2
1
1
1
1
0
1
1
0
0
0
2
0
0
0
2
1
1
1
1
1
0
1
0
1
0
2
0
1
1
2
2
0
1
1
0
1
0
2
1
1
1
0
1
0
0
1
1
1
1
1
1
2
1
1
1
1
0
1
1
1
1
0
1
0
1
0
1
1
1
0
2
1
1
2
2
1
1
1
2
0
1
2
0
1
1
1
1
0
1
1
0
2
2
0
1
2
0
2
1
1
1
0
0
2
1
1
0
0
0
2
2
0
0
1
1
1
1
0
1
2
2
3
2
0
1
2
1
2
0
1
0
1
0
0
0
0
1
1
1
0
1
1
2
1
1
2
0
2
0
2
1
0
0
0
0
0
0
1
2
1
2
1
3
2
1
0
2
1
2
1
1
0
2
1
1
1
2
2
1
0
0
2
2
0
2
0
2
0
0
1
1
0
1
0
0
2
1
2
3
1
0
1
1
0
1
2
2
0
1
1
1
0
1
0
3
1
2
1
1
1
1
1
1
0
0
1
1
0
2
2
0
2
1
1
0
0
1
0
1
1
1
0
2
2
2
0
0
1
0
0
1
2
2
1
1
1
1
0
1
2
0
2
1
0
1
2
0
3
2
2
1
1
0
1
3
2
0
2
1
1
0
0
2
1
1
0
2
0
2
2
0
2
0
2
1
1
0
1
1
2
1
1
0
2
1
1
2
0
2
1
0
1
2
1
0
2
2
0
0
1
2
2
0
2
0
1
1
1
1
2
2
1
1
1
1
1
1
1
3
0
0
0
1
1
1
0
1
1
2
1
2
1
0
1
1
1
0
0
1
0
2
1
1
0
0
0
0
0
1
0
0
2
1
1
2
1
1
2
1
0
0
2
0
2
2
1
1
1
0
2
0
1
0
1
1
2
2
2
1
0
0
0
1
1
1
2
0
1
1
2
2
0
0
1
1
1
0
0
1
1
1
1
1
0
2
1
1
1
1
1
1
1
0
0
1
0
0
2
0
1
1
1
1
1
2
1
2
1
1
0
0
0
0
0
1
1
0
0
1
2
0
1
0
0
0
1
0
0
0
0
1
2
0
2
0
1
2
2
1
2
0
0
1
1
0
0
0
2
1
1
1
1
1
1
2
1
1
0
2
1
1
0
0
0
1
0
2
1
1
1
1
0
1
3
0
2
2
0
0
1
2
1
2
1
2
1
1
1
0
1
0
1
0
1
0
1
1
2
1
0
1
2
1
2
1
0
1
2
2
0
2
2
1
0
0
2
1
0
0
0
1
1
0
1
0
1
1
2
2
1
0
2
1
1
1
1
1
2
0
1
1
1
3
2
1
1
1
1
1
2
0
0
0
0
1
1
0
1
0
0
0
1
1
2
1
1
2
2
1
0
1
2
1
1
0
1
2
0
0
3
2
1
1
0
0
0
1
1
0
1
1
2
1
2
2
0
0
1
0
0
1
1
1
2
1
0
0
0
1
0
0
1
1
1
1
2
0
0
2
0
2
2
2
2
0
0
2
0
1
1
1
1
0
0
2
0
0
1
0
0
0
1
1
0
1
1
1
0
1
1
1
2
2
1
1
1
1
1
1
2
1
1
0
0
1
0
3
1
2
0
1
1
1
1
1
1
0
0
0
1
1
1
0
1
1
2
0
1
0
1
0
0
0
2
1
0
0
2
2
1
3
0
0
2
2
2
0
1
0
1
0
3
1
0
0
0
1
1
1
1
1
0
0
0
2
2
2
0
1
0
0
0
2
0
1
1
0
0
1
0
1
0
1
0
1
1
1
1
1
0
1
1
0
2
0
0
0
0
1
0
1
1
1
1
2
1
1
2
0
0
1
0
0
0
1
0
2
0
0
0
2
0
1
0
1
1
0
0
1
1
1
2
2
2
0
1
0
1
0
1
1
0
1
0
1
1
1
1
0
1
1
2
0
0
0
1
1
0
0
3
1
1
1
1
1
2
1
1
1
2
1
1
1
0
1
1
0
0
1
1
2
1
1
2
2
1
0
1
1
0
1
2
0
1
0
3
2
1
2
1
1
2
0
1
0
1
1
0
0
1
1
1
1
0
0
2
2
1
0
0
2
2
2
2
1
0
1
0
0
1
1
1
2
0
1
1
2
1
0
3
2
1
2
1
0
0
1
1
1
0
1
0
2
2
1
2
1
2
1
0
2
1
1
0
0
1
2
2
1
1
5
0
1
2
1
1
0
2
1
0
0
2
1
0
1
2
1
0
1
0
1
0
2
1
0
1
3
1
0
1
1
1
1
1
1
0
2
1
0
0
2
1
0
5
1
0
5
1
1
1
0
1
1
1
0
0
1
1
0
2
1
2
1
0
1
1
1
1
2
0
2
0
0
2
2
0
1
0
1
1
1
0
0
0
0
1
0
2
0
0
1
1
0
1
1
2
2
1
0
2
2
1
0
1
1
0
2
2
1
0
1
1
2
1
0
0
1
0
0
1
0
1
1
1
2
2
0
1
2
0
0
1
1
1
1
0
0
0
0
1
1
2
1
2
2
0
1
0
0
1
1
2
0
1
1
1
1
1
1
0
1
1
3
0
1
1
1
0
0
2
2
1
1
1
1
1
1
0
1
0
1
2
1
1
1
1
2
1
1
1
1
1
1
0
2
0
0
1
0
1
0
2
1
1
0
0
2
1
1
2
1
1
0
1
1
0
4
1
1
1
1
0
1
1
1
1
0
0
1
1
1
1
1
2
0
1
0
1
1
1
2
1
2
1
1
2
0
0
2
0
1
1
1
0
1
1
1
1
2
0
1
1
1
1
0
0
1
2
1
2
0
2
2
1
0
0
0
1
1
1
0
1
1
1
0
1
1
1
1
0
1
0
2
1
1
1
0
2
1
0
1
2
2
0
2
1
0
1
1
0
2
0
0
0
1
1
1
1
1
0
2
1
0
1
2
1
2
1
0
1
0
0
1
2
1
1
0
2
0
0
1
1
1
1
1
1
3
2
1
1
0
1
1
0
1
1
2
2
1
0
0
1
1
0
1
0
0
0
1
1
0
1
0
1
1
2
1
1
1
1
0
2
0
1
0
1
2
1
2
0
2
0
1
2
0
2
2
1
0
0
0
0
0
1
0
0
1
1
0
1
1
1
1
1
0
1
2
2
0
1
12
1
1
0
0
1
0
0
1
0
1
2
2
1
1
1
1
2
1
1
2
1
1
1
0
2
2
1
1
1
1
2
2
1
2
2
1
2
1
1
0
0
1
0
2
1
0
1
1
0
0
2
2
0
1
3
1
2
2
3
1
1
1
1
2
1
0
2
2
0
0
2
1
1
1
1
1
1
0
2
1
2
0
2
0
1
0
2
0
2
0
1
0
1
1
0
1
0
1
0
1
0
2
1
0
1
0
2
1
1
2
2
0
1
0
1
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
1
1
0
2
1
1
0
0
1
0
2
2
0
0
1
1
0
0
2
2
1
2
1
1
1
2
0
1
1
1
2
0
0
1
2
0
1
1
2
0
0
1
1
1
1
1
2
1
1
1
0
2
0
1
1
1
0
0
0
2
0
1
2
0
0
0
0
1
1
3
2
0
2
2
0
0
0
0
1
1
0
1
2
1
0
0
1
0
0
0
0
0
0
1
1
1
4
1
2
1
2
0
1
0
1
0
0
2
1
1
2
4
0
1
1
1
0
0
0
1
1
1
1
1
1
1
0
2
0
1
1
1
0
1
1
0
0
2
0
0
0
2
1
1
2
1
2
2
2
0
0
2
1
1
2
2
2
0
1
0
2
2
0
0
1
0
1
0
1
1
0
2
1
2
0
2
0
1
0
1
0
2
1
1
0
1
1
1
1
2
0
0
1
1
1
1
2
1
1
0
2
2
0
2
2
1
0
1
2
0
2
0
1
2
2
1
2
0
1
1
0
0
2
0
1
2
0
1
2
0
0
2
2
0
0
1
0
1
0
2
0
1
1
0
1
1
2
0
2
2
0
2
1
2
1
2
2
2
1
0
2
0
1
2
0
3
3
4
1
1
2
0
1
0
0
0
1
1
2
0
0
0
1
2
1
1
0
1
0
1
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
1
2
1
0
1
1
2
2
0
1
0
0
1
0
2
1
2
1
0
0
0
1
1
1
1
0
1
0
1
0
0
1
1
1
1
1
2
1
2
1
1
2
1
0
1
0
2
2
1
0
0
0
0
2
0
0
0
0
0
0
1
1
0
1
1
1
1
1
2
1
0
2
1
1
2
2
2
1
2
1
1
2
0
1
1
2
2
0
1
2
1
0
2
2
1
2
1
1
2
1
0
0
2
2
1
0
4
2
1
2
1
2
1
0
2
1
1
0
2
0
1
0
1
2
1
0
2
0
1
2
2
1
1
1
2
1
1
1
0
0
0
0
1
3
2
0
1
1
1
1
1
0
3
1
3
2
3
1
1
1
1
0
0
2
0
2
1
2
0
1
2
1
1
1
1
1
1
4
0
1
1
0
1
1
0
1
0
2
3
1
0
0
0
2
0
0
0
1
1
2
1
0
1
1
1
0
1
0
0
2
2
1
1
3
1
1
0
0
0
0
1
1
0
1
1
0
2
0
0
1
1
0
1
2
1
2
0
2
0
2
0
1
0
1
1
0
2
1
2
0
2
2
2
2
1
1
2
1
2
1
1
0
1
0
2
2
2
1
2
2
1
0
1
0
0
0
1
0
0
0
0
0
0
2
1
1
0
1
2
2
1
1
0
0
1
1
0
2
1
0
1
0
1
1
0
2
1
1
1
1
0
1
1
2
2
0
1
1
1
2
1
1
0
1
0
1
0
1
0
2
0
1
1
1
2
1
0
1
1
0
1
1
1
2
0
1
1
1
0
2
1
1
0
0
1
1
1
0
1
1
1
1
1
0
0
1
2
1
1
2
1
0
0
1
0
0
2
0
0
1
1
0
2
1
0
2
2
1
1
1
2
0
2
2
1
2
0
0
0
2
2
1
0
0
0
1
0
1
0
1
0
0
1
0
2
0
1
0
0
1
1
2
0
1
1
0
0
1
1
2
2
2
0
1
1
0
1
1
1
0
1
0
0
2
1
1
2
1
2
1
0
0
0
0
1
1
0
0
2
2
0
1
1
1
1
1
0
1
1
1
2
1
1
2
2
0
1
2
1
0
3
2
0
1
0
2
0
1
1
0
1
2
1
1
1
0
0
1
2
1
0
0
2
2
1
0
1
3
1
1
1
1
4
1
1
1
1
0
1
0
0
1
1
1
0
0
0
0
0
0
2
2
1
1
0
2
1
0
2
1
2
1
0
1
0
1
2
1
1
1
1
0
1
2
1
1
1
1
1
2
1
2
2
0
2
1
1
2
1
0
0
1
0
0
1
1
1
2
1
0
2
0
0
1
1
1
1
0
2
1
0
1
1
0
0
0
0
1
1
0
0
1
3
1
1
1
2
1
2
0
1
1
1
0
0
0
0
1
1
1
0
0
1
1
1
2
0
0
1
1
2
0
2
1
1
0
1
1
1
0
0
1
0
1
0
0
1
1
0
1
2
0
1
0
0
0
0
0
0
2
4
1
0
1
3
1
1
1
0
1
0
2
0
0
0
2
1
0
0
1
1
2
0
1
2
0
1
1
2
1
2
2
0
1
1
0
0
0
0
2
0
0
2
0
1
0
1
0
1
0
1
0
0
2
1
1
0
1
0
0
2
1
2
1
0
1
2
1
1
2
1
2
1
1
2
2
1
2
1
2
1
0
2
2
1
1
0
2
1
1
2
3
0
2
1
0
2
0
0
1
0
0
1
1
2
0
3
0
2
0
3
0
0
0
1
2
0
2
2
1
0
0
1
2
1
0
1
0
2
1
3
1
1
1
0
0
0
1
2
0
1
2
1
0
1
1
0
0
1
1
2
0
0
1
1
1
1
1
1
0
1
0
1
0
2
1
2
0
1
1
0
1
1
0
1
0
1
2
0
1
1
2
1
1
0
1
0
0
0
1
0
2
2
1
2
2
0
0
0
1
1
1
1
1
0
1
0
2
1
0
1
0
0
0
0
0
0
1
1
1
1
0
1
2
2
0
1
1
0
1
2
0
1
0
1
1
2
2
1
1
1
2
2
0
1
1
0
0
0
0
1
1
0
2
1
0
1
1
0
0
0
2
2
2
1
2
1
1
0
2
1
0
1
1
2
0
1
0
0
0
0
1
1
0
1
1
1
0
2
0
2
1
1
2
1
1
2
1
0
1
0
1
1
3
1
1
0
0
0
1
0
0
1
1
1
0
2
2
1
1
0
1
0
1
0
0
0
1
2
0
2
1
2
1
2
0
0
1
1
2
1
1
0
2
2
1
1
1
1
1
0
2
0
0
1
1
0
1
1
2
0
1
2
1
1
1
0
1
0
0
1
1
2
0
2
0
1
0
1
0
2
1
0
0
0
0
1
0
0
0
2
1
1
1
0
0
1
0
1
2
4
2
2
2
1
2
2
1
2
1
0
2
0
0
2
0
0
2
1
1
1
0
1
0
2
0
1
1
0
1
3
2
0
1
1
3
1
1
0
1
0
1
1
1
1
1
1
1
0
0
1
1
2
2
2
0
2
1
2
0
1
1
2
1
1
1
0
0
1
2
1
0
1
0
0
0
1
2
2
1
1
2
2
1
0
1
1
1
2
0
0
1
0
1
0
1
3
2
2
1
0
0
2
1
0
1
0
0
0
1
1
2
2
2
2
1
1
1
1
0
1
2
1
2
1
1
0
0
1
0
0
2
0
0
1
2
3
1
2
1
1
1
1
1
0
1
0
0
1
0
0
1
0
1
1
1
0
0
1
1
0
0
0
0
2
2
2
1
0
1
0
1
0
2
0
1
0
1
0
1
0
1
1
1
1
2
0
0
1
2
1
1
1
4
0
2
0
1
1
0
2
1
1
1
1
0
0
0
1
1
1
1
1
0
1
0
1
0
1
0
0
0
0
0
2
1
1
1
3
1
1
1
1
1
0
0
0
0
1
0
1
1
1
0
1
1
0
0
0
1
1
0
0
2
2
1
0
2
1
1
2
1
0
1
1
2
1
1
0
0
1
1
1
1
1
1
1
0
0
0
0
2
1
2
0
2
0
2
0
0
2
0
1
0
2
2
2
0
1
0
1
0
0
1
1
1
1
1
0
1
0
1
0
1
1
1
0
1
1
0
2
0
1
0
0
2
1
2
1
0
2
2
0
2
1
1
1
1
0
0
1
2
0
1
1
1
1
1
1
2
1
2
2
1
0
2
0
1
2
0
1
1
0
0
0
1
2
0
0
0
0
2
1
1
2
1
1
0
0
1
1
2
1
1
0
0
2
0
2
0
0
1
1
0
1
0
1
1
0
0
1
0
0
2
0
1
0
2
1
1
2
0
2
0
1
1
0
1
0
0
1
0
0
2
0
0
1
1
1
0
0
1
1
1
1
1
1
1
2
1
2
2
2
2
2
1
0
1
2
2
2
2
2
1
2
0
0
1
2
1
0
2
1
0
0
0
1
0
1
0
0
1
2
0
2
1
0
1
0
1
0
0
0
0
2
1
0
0
2
1
0
0
1
0
0
1
0
3
2
1
1
1
0
1
0
2
0
1
0
1
0
0
0
0
0
0
1
1
0
2
2
1
0
0
2
2
1
2
2
2
1
1
1
2
2
0
2
0
0
1
1
0
2
0
0
1
0
1
2
0
0
0
0
1
0
0
1
0
2
1
1
0
1
0
5
1
2
0
2
2
0
1
1
0
0
0
0
2
2
0
1
0
2
1
2
2
1
1
0
1
1
0
0
2
1
0
1
0
1
0
1
1
0
0
1
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
1
1
1
1
1
1
0
2
0
1
1
1
1
0
0
0
2
2
2
1
2
1
1
1
2
0
1
2
0
1
1
2
0
1
0
0
2
2
0
2
1
0
2
1
1
0
0
0
0
1
2
0
1
1
0
1
0
0
1
2
1
1
0
0
2
2
2
1
2
1
1
0
1
1
1
1
0
1
0
1
1
2
1
1
0
1
0
2
2
1
2
0
1
0
0
1
1
2
0
1
0
1
1
1
0
1
1
0
1
2
1
1
2
0
0
0
2
0
1
2
0
0
1
0
0
1
0
1
2
0
1
0
4
2
2
1
1
1
0
0
1
0
1
0
2
0
0
0
0
0
2
1
2
2
1
0
1
0
1
1
1
1
1
0
0
0
1
2
1
2
1
0
2
0
1
0
0
0
1
0
0
1
2
1
0
0
0
2
2
1
0
1
1
0
2
1
1
0
0
0
1
0
2
2
1
0
0
1
2
2
0
2
1
1
1
0
1
2
1
0
1
1
0
1
1
1
1
0
1
2
1
1
1
0
0
1
2
1
0
1
0
0
2
1
0
0
1
1
1
2
1
1
1
0
2
0
1
1
1
0
0
2
1
2
1
0
0
1
1
0
1
1
0
1
1
1
2
1
1
1
0
3
1
1
1
2
1
1
0
0
2
1
0
1
0
1
0
0
0
2
1
2
1
1
0
1
2
1
1
1
2
1
0
2
0
1
2
1
1
1
2
0
1
2
1
0
1
1
2
0
0
0
2
0
0
1
1
2
1
1
0
1
1
1
2
0
1
2
1
0
2
2
2
0
0
2
1
2
1
1
0
1
1
1
2
1
1
0
1
1
0
0
2
1
1
1
1
0
2
1
0
2
0
1
1
0
0
1
0
1
1
2
2
2
1
0
1
1
1
1
0
0
2
2
1
0
0
2
0
0
1
1
1
1
3
1
1
0
1
2
1
0
0
1
1
0
2
0
2
1
0
0
0
1
1
1
1
1
0
0
0
1
1
2
1
0
2
1
2
0
2
1
2
0
0
1
1
1
0
0
0
0
1
0
2
0
1
1
1
1
0
1
1
2
2
3
2
0
1
1
0
0
1
1
1
0
2
0
1
0
1
0
1
2
1
2
0
1
1
1
1
2
2
1
2
1
0
3
1
1
0
1
2
0
2
1
1
1
0
3
0
1
1
1
1
0
0
2
2
1
0
0
0
0
1
1
2
0
1
1
0
0
0
1
1
1
2
2
1
0
0
2
1
1
1
2
0
1
2
1
2
1
0
1
1
2
0
1
1
0
0
2
2
1
0
0
0
0
2
2
1
0
1
0
1
0
1
1
1
1
1
1
2
2
1
2
2
2
1
0
0
1
2
2
1
1
1
1
0
2
2
2
1
2
2
1
2
3
1
1
0
1
1
0
1
0
2
0
0
0
1
2
0
0
0
1
0
1
1
2
1
1
1
0
1
1
1
2
1
2
0
2
1
0
0
1
0
0
1
2
0
3
0
1
1
2
1
0
1
1
0
2
1
1
1
1
0
2
1
1
2
0
1
0
0
2
0
0
1
1
1
1
1
1
1
1
0
2
1
0
1
1
0
2
1
1
2
2
1
0
2
1
2
0
0
1
0
0
2
0
0
0
2
0
0
2
1
2
1
1
1
1
1
1
2
1
1
2
0
1
3
0
2
0
0
1
0
0
1
0
0
0
1
1
0
2
1
0
0
1
2
0
0
0
2
0
0
1
0
0
1
2
2
1
2
0
1
0
2
0
2
0
0
0
0
1
1
0
2
0
0
1
0
1
1
1
0
0
0
0
1
1
1
0
1
1
0
2
0
1
0
0
1
2
2
1
1
0
1
1
1
0
0
2
1
0
1
1
0
1
0
1
2
1
1
1
3
1
2
2
3
1
0
2
2
0
2
1
2
0
2
1
1
0
1
0
1
2
0
1
0
2
0
0
1
0
1
0
2
1
1
1
1
0
1
1
1
0
0
1
0
0
2
1
2
1
2
1
0
1
2
1
2
1
1
0
1
2
1
0
2
2
1
2
0
2
1
2
0
2
1
0
1
0
0
0
2
1
1
2
0
2
0
1
0
2
1
0
0
1
2
1
2
2
0
0
2
1
2
1
0
0
0
1
2
2
0
1
0
1
2
2
0
1
1
1
1
0
0
1
1
1
0
0
1
0
2
2
0
0
0
1
1
1
0
1
1
0
0
5
1
0
1
2
1
1
2
0
1
0
3
0
2
0
1
0
2
1
0
0
1
1
0
1
2
2
1
0
1
0
0
1
2
1
1
0
1
2
1
0
1
0
1
1
2
0
1
1
2
1
1
3
2
2
1
1
2
0
1
0
2
1
2
1
1
2
2
0
1
1
1
0
1
1
1
1
1
1
1
1
2
1
0
1
0
1
1
2
1
1
1
1
0
1
1
0
2
0
1
0
0
2
1
1
0
0
2
1
2
0
1
0
1
0
1
1
1
1
2
1
1
1
1
1
1
2
1
0
0
2
0
0
1
1
0
2
1
1
1
1
0
2
1
1
1
0
1
2
2
1
1
2
0
0
0
0
2
0
0
0
1
2
1
1
1
0
0
1
3
0
1
0
1
0
0
2
2
1
0
1
2
1
0
1
0
1
1
1
0
2
1
2
0
2
0
1
1
1
0
0
0
1
0
2
0
2
1
0
0
1
2
0
1
0
1
1
2
1
1
0
0
0
0
1
0
1
1
2
0
1
1
0
1
0
0
1
1
0
0
1
1
0
1
1
1
0
1
0
0
2
1
2
0
1
2
1
1
1
1
4
1
0
1
1
1
2
0
1
0
1
0
2
2
1
1
2
1
0
1
1
1
0
1
0
1
0
0
1
1
1
1
0
2
0
0
1
3
1
1
0
1
1
1
0
1
1
0
1
2
1
0
2
0
0
0
0
2
2
1
1
2
1
1
1
0
1
0
1
0
1
1
1
1
1
1
0
1
1
1
1
1
1
0
0
0
1
2
0
1
0
1
1
1
1
1
0
2
1
1
2
0
1
0
1
2
0
1
2
0
2
2
0
0
1
1
3
0
1
0
1
1
2
1
1
2
1
1
2
1
1
0
1
0
0
0
2
0
1
1
0
2
0
2
2
2
1
2
2
1
1
1
2
0
1
1
2
1
1
2
1
0
1
1
0
1
1
1
2
0
1
1
1
1
1
4
1
0
2
1
1
2
0
1
2
0
0
0
3
0
1
0
0
1
1
1
1
1
1
2
1
0
2
1
1
0
2
1
1
2
2
0
1
0
1
1
1
2
0
1
0
1
0
1
2
0
1
0
0
0
2
2
2
0
1
2
2
1
0
2
0
2
2
1
1
1
1
2
1
0
1
0
2
0
2
1
0
1
0
1
0
1
0
0
2
1
2
1
1
1
2
1
0
1
0
2
0
0
1
1
1
1
1
0
0
0
1
1
2
2
2
0
1
1
1
0
2
1
1
0
0
0
0
2
0
2
1
1
0
2
0
1
0
1
1
1
1
1
2
1
1
2
0
0
1
2
1
0
0
1
1
3
1
1
1
0
1
2
2
1
2
1
0
0
2
1
2
1
1
2
1
0
1
2
0
2
2
1
1
1
2
0
2
1
1
2
0
1
1
0
1
2
0
1
1
2
1
2
0
1
0
0
1
2
1
0
2
0
0
0
0
1
1
0
0
0
0
2
1
1
2
1
3
0
1
0
0
1
1
0
1
1
1
1
2
0
2
1
1
0
0
1
1
0
2
1
1
0
3
1
1
1
0
2
0
2
0
0
1
1
0
1
0
0
0
1
1
2
2
0
1
1
0
2
1
1
1
0
1
2
1
1
2
2
0
2
0
0
0
1
2
0
0
1
0
1
0
1
1
1
2
1
1
2
0
1
0
1
1
0
1
2
1
2
1
1
1
0
1
1
0
2
1
2
1
2
1
1
1
2
1
2
1
1
0
1
3
0
1
0
1
0
0
1
2
0
1
2
0
1
2
1
0
0
0
0
1
1
0
1
1
0
1
1
1
1
1
1
0
1
1
1
1
0
1
0
0
0
1
0
1
1
1
0
1
0
0
1
1
1
1
1
0
1
1
0
1
1
1
0
2
2
0
2
1
0
0
1
1
0
0
0
0
0
0
1
2
1
0
1
1
0
0
0
2
0
1
2
0
1
0
2
0
2
2
0
1
3
1
2
0
0
1
1
0
1
0
0
1
3
1
1
1
1
1
1
0
1
1
2
1
2
2
1
1
1
1
0
1
1
2
0
2
2
0
0
0
0
1
1
1
1
0
2
0
0
1
0
2
0
1
2
1
1
0
1
0
1
1
3
1
1
1
2
0
2
1
2
1
1
1
1
2
1
0
1
0
2
3
1
0
0
1
1
2
0
0
0
2
1
1
2
1
0
0
1
0
0
1
0
1
1
0
0
2
1
0
0
2
0
1
0
1
0
0
2
0
2
1
0
1
1
2
1
1
2
1
3
0
1
0
0
1
1
3
2
1
0
0
0
2
1
0
0
1
0
2
0
3
0
2
2
0
1
2
1
1
3
0
1
2
0
0
2
1
1
0
1
0
1
2
0
1
1
1
1
5
0
0
1
1
1
1
1
0
0
2
1
1
1
0
1
0
0
3
1
1
0
1
0
1
0
0
1
2
0
1
1
1
1
1
0
0
1
2
0
0
0
1
1
2
0
2
2
1
0
1
1
1
0
0
0
1
1
0
1
2
1
0
1
1
1
0
1
0
0
0
2
0
0
1
1
1
2
2
0
1
2
1
2
0
0
1
1
1
0
0
0
1
2
2
1
0
0
0
1
0
0
0
0
2
2
0
0
1
0
1
0
3
1
1
1
2
1
2
0
1
1
2
1
1
0
0
0
2
0
0
1
2
0
1
2
0
2
1
1
1
2
0
2
1
0
1
0
0
1
0
1
0
1
0
1
2
2
0
1
2
1
2
1
2
1
2
0
1
1
1
1
1
0
0
1
0
0
1
1
2
0
2
1
0
2
2
2
2
2
2
1
0
1
1
1
1
2
1
1
1
2
1
0
0
1
0
0
1
0
1
1
1
2
2
2
0
1
3
2
2
1
0
0
1
1
1
0
1
1
1
2
1
1
3
0
1
1
0
2
2
1
1
0
0
1
2
2
2
0
1
2
1
1
0
0
2
1
2
0
0
1
1
1
2
1
1
1
0
1
0
0
0
0
1
0
3
1
1
2
1
1
1
0
0
0
1
2
1
0
1
2
0
0
1
1
2
1
2
0
1
2
2
1
0
1
2
0
0
1
2
1
0
0
1
0
0
1
0
0
0
2
1
0
0
2
1
0
1
2
0
0
1
1
1
0
2
1
0
0
0
0
0
0
2
2
0
2
1
2
1
1
0
2
0
2
2
1
1
2
0
1
0
0
2
0
1
1
5
1
1
1
1
1
1
0
1
1
2
1
1
0
0
0
2
0
1
1
0
0
1
1
1
1
1
0
0
2
2
1
0
0
2
0
0
1
2
3
0
0
1
1
2
1
2
4
1
1
2
1
0
1
1
1
2
0
2
1
1
1
2
2
0
1
0
2
0
1
1
2
1
0
1
1
1
1
1
1
1
0
0
1
1
1
1
2
2
1
1
2
0
2
0
1
0
0
1
2
4
2
2
1
2
1
2
0
1
1
0
1
1
1
1
1
0
1
0
0
1
1
0
0
2
1
2
1
2
0
0
2
1
1
1
0
0
2
1
1
1
1
1
0
1
1
1
0
1
1
1
3
0
1
1
0
2
2
0
1
0
0
1
2
0
0
0
2
1
0
2
2
0
0
0
0
1
2
1
1
2
1
0
0
0
1
1
0
2
1
0
0
1
1
0
1
1
0
2
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
1
1
1
2
0
0
0
0
2
2
2
1
2
0
2
2
1
1
1
2
1
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
1
1
1
1
1
1
1
2
0
1
0
0
2
1
1
1
3
2
1
0
1
0
2
1
1
2
1
0
0
1
1
2
2
2
1
1
0
1
3
2
0
2
1
2
2
0
1
0
0
0
1
0
0
1
1
1
0
1
0
1
2
0
0
1
2
1
0
1
1
1
0
1
0
2
2
0
1
1
1
2
1
1
1
1
1
2
1
0
2
1
1
3
0
2
1
1
0
2
1
0
2
0
1
1
1
1
0
0
4
1
2
0
0
1
0
0
1
0
1
1
0
1
1
2
1
0
1
0
1
2
0
0
2
0
0
0
0
0
2
1
2
0
0
1
1
1
0
0
2
0
1
2
1
0
1
0
0
1
1
1
2
2
2
0
0
1
1
2
1
2
1
1
2
0
1
1
2
2
0
0
1
0
0
0
1
0
1
0
1
1
0
0
3
1
0
1
1
0
1
0
1
1
1
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
2
2
0
0
2
1
0
1
1
1
1
1
1
2
0
0
1
0
0
0
0
2
1
2
0
0
0
1
2
2
2
1
0
0
0
0
0
2
2
0
1
0
1
3
0
2
1
1
1
0
0
3
1
1
1
2
1
2
2
0
0
0
1
0
1
1
0
1
0
1
2
1
2
1
1
1
0
2
2
1
2
1
1
1
1
1
0
1
2
1
1
2
1
1
1
0
1
0
2
1
1
0
0
1
1
0
1
1
0
2
0
0
0
1
0
1
1
2
1
0
1
0
1
0
0
1
1
0
1
0
1
0
1
0
0
2
0
2
2
1
2
0
1
1
0
1
2
1
1
0
2
1
1
1
1
0
2
0
1
0
1
0
2
0
0
0
1
0
0
2
1
2
0
2
1
1
1
0
1
1
1
2
0
0
1
0
1
0
0
1
0
2
3
2
0
0
0
0
2
2
1
1
1
2
0
0
0
0
1
0
0
2
1
1
1
2
2
1
0
1
0
1
1
2
0
0
1
0
0
2
0
2
1
0
0
1
2
0
0
2
2
1
2
1
2
2
1
2
1
1
0
2
0
1
1
2
2
2
1
0
0
0
0
1
1
1
1
1
1
1
0
0
2
1
2
1
0
1
1
0
2
1
0
2
0
1
1
1
1
0
0
2
0
0
2
3
1
1
0
1
1
1
1
1
2
1
0
1
2
0
1
2
2
0
1
1
1
1
0
2
1
0
2
2
1
1
1
0
0
4
0
1
0
0
1
0
1
1
2
1
1
2
1
1
2
1
1
1
0
2
1
1
1
0
1
2
3
0
1
0
2
1
0
0
2
1
0
1
2
1
0
1
1
1
2
1
1
2
0
0
1
2
1
2
2
1
1
2
0
1
2
1
0
1
2
0
1
1
0
1
1
0
0
1
1
1
1
2
0
0
1
1
1
0
0
1
1
2
2
1
0
1
1
2
1
0
2
1
2
0
2
2
0
1
1
2
2
1
1
0
1
0
0
0
1
1
1
0
0
1
2
1
0
1
1
1
2
2
1
1
1
2
1
0
1
0
1
2
1
1
0
1
0
1
2
0
0
1
2
0
1
0
2
1
1
2
1
3
0
0
1
1
2
1
0
0
1
0
0
0
1
1
1
1
2
1
0
2
0
1
0
2
0
0
1
2
1
2
0
1
0
2
2
1
0
2
0
0
2
0
0
1
1
1
1
0
0
0
2
0
0
1
0
1
1
1
1
2
0
2
1
0
1
0
1
2
1
1
0
2
0
1
1
1
2
2
0
1
1
2
0
0
0
0
3
0
1
2
0
1
2
0
0
1
0
1
0
0
1
2
0
0
2
2
0
1
0
1
1
0
2
1
0
1
1
1
1
0
0
1
0
1
2
1
1
0
1
0
1
1
0
1
0
1
1
1
1
2
2
2
2
0
0
2
0
1
0
2
1
3
0
1
1
1
1
0
1
1
1
1
1
0
2
2
1
1
1
0
1
0
0
1
1
0
2
0
1
0
1
2
0
1
1
0
1
1
1
1
1
0
2
0
0
1
0
2
2
2
1
2
1
0
1
0
0
0
1
1
0
0
1
1
1
0
0
0
0
0
0
2
1
2
0
0
1
0
0
2
1
0
1
1
2
0
2
2
1
0
0
0
1
1
1
1
1
0
0
2
0
1
0
0
1
1
3
1
2
0
2
1
0
1
2
1
1
1
1
0
1
1
1
1
2
0
2
0
1
0
2
0
1
1
0
1
2
1
1
0
1
1
1
0
1
0
1
1
2
2
0
2
1
1
0
1
1
1
3
0
0
0
2
0
1
1
1
2
2
0
0
3
1
1
1
1
1
1
2
2
1
0
0
1
2
1
0
0
0
1
0
1
2
2
0
1
2
2
1
0
2
0
2
2
0
1
2
1
1
2
1
1
2
0
1
2
2
2
0
0
2
0
1
1
2
0
1
0
1
0
1
0
1
1
2
1
1
1
0
1
2
1
1
1
0
0
1
1
1
0
0
2
0
1
1
1
0
1
0
0
1
2
2
0
1
0
1
1
1
0
0
1
1
2
0
1
1
2
0
1
0
2
1
0
1
1
1
0
1
2
1
0
2
1
2
0
1
2
1
2
0
1
0
1
2
1
1
0
1
0
1
1
2
0
1
1
0
1
1
2
3
1
2
1
1
2
1
2
1
2
0
0
1
0
0
2
1
1
0
0
1
1
0
1
2
0
0
0
2
1
0
1
1
1
0
2
1
0
3
1
1
1
1
0
1
2
2
0
0
1
2
0
1
1
1
1
1
1
1
1
0
1
0
2
1
2
0
1
1
1
0
1
2
0
2
1
1
1
2
0
1
0
1
1
1
2
2
0
0
0
1
2
1
0
1
2
1
1
1
0
2
1
1
0
0
1
1
0
1
2
2
2
1
0
2
2
2
2
0
2
0
1
2
0
1
0
0
0
1
1
1
0
1
2
2
0
1
1
1
1
1
0
1
1
1
1
3
1
1
1
0
1
1
2
2
2
1
1
1
1
1
2
2
0
0
1
1
0
0
2
1
0
0
0
0
0
0
2
1
1
1
0
0
2
1
0
1
1
2
2
2
0
1
1
0
1
1
2
1
0
1
0
0
2
2
1
2
1
1
0
0
1
0
2
1
2
0
1
1
1
2
0
0
0
0
0
0
1
0
2
0
2
2
1
0
0
1
2
0
0
2
3
0
0
0
0
2
2
1
1
1
0
0
1
1
1
1
1
1
0
2
1
1
1
2
0
1
1
0
2
0
0
1
1
0
0
0
1
2
2
1
0
1
2
1
1
2
1
0
1
0
1
0
2
1
1
1
0
0
0
1
4
1
1
0
2
0
0
1
2
1
0
0
1
1
0
1
1
1
0
2
0
2
1
4
0
1
0
0
0
2
1
3
1
0
1
0
0
0
1
1
0
1
1
0
1
1
1
0
2
1
1
1
1
0
1
2
0
1
2
2
1
1
0
0
1
1
1
2
3
1
1
2
0
1
2
1
1
0
1
0
0
2
3
2
1
1
2
0
1
0
1
1
1
1
1
2
2
2
0
0
0
2
0
0
2
2
1
0
2
1
1
0
1
1
1
2
0
2
1
1
1
1
2
1
0
2
1
1
1
0
1
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
0
2
1
1
1
1
0
1
0
0
0
2
1
0
1
0
0
0
2
1
1
0
2
2
1
1
3
1
0
0
1
0
1
1
0
0
3
1
0
2
1
2
2
1
1
0
0
2
0
2
1
1
0
0
2
2
1
1
0
0
0
0
1
1
2
0
1
1
0
1
1
0
0
2
0
2
2
1
0
1
1
1
1
0
0
0
0
1
1
1
1
1
1
0
0
0
1
0
0
1
2
0
1
2
0
0
1
1
1
2
1
0
1
0
2
0
1
1
1
2
1
1
1
0
1
1
0
1
2
0
0
0
1
0
1
1
1
0
2
1
2
2
0
1
2
1
1
1
0
0
0
1
1
0
0
1
0
0
1
0
1
1
0
1
0
0
1
0
2
0
2
0
1
0
1
1
0
1
0
2
0
2
0
2
1
1
0
2
1
1
1
1
2
2
0
0
1
2
1
2
2
1
1
2
2
1
1
0
0
0
0
0
0
1
2
0
3
1
1
2
1
1
1
0
1
1
1
0
1
1
2
1
1
1
1
0
0
0
0
1
1
0
0
1
0
1
1
0
1
1
1
0
1
0
0
2
0
2
0
0
1
0
2
2
1
0
1
0
1
3
2
1
2
1
1
1
2
1
2
2
0
0
0
0
1
1
1
1
0
1
0
0
2
0
0
1
1
1
1
0
0
1
1
1
2
1
0
2
2
0
2
1
1
1
0
2
0
0
2
0
2
0
1
1
0
0
1
1
1
1
1
1
0
1
1
0
0
1
1
1
1
1
0
1
1
0
2
0
0
0
0
0
1
1
0
0
2
1
1
1
0
0
1
0
1
1
0
2
2
0
2
2
1
0
0
1
1
1
0
2
0
0
0
0
2
1
1
0
1
1
0
1
0
0
1
0
3
0
1
0
2
1
0
1
0
1
1
1
2
0
0
1
1
1
0
0
2
2
1
0
2
0
1
1
0
2
1
0
1
0
2
2
1
1
0
1
1
0
0
1
2
2
0
1
1
1
2
0
2
1
0
1
2
1
1
0
2
2
1
1
1
1
0
2
0
1
1
0
1
1
1
1
1
1
1
1
1
1
1
2
0
1
1
0
0
2
0
2
0
0
1
1
1
1
0
1
1
0
0
1
1
2
1
2
2
1
1
0
0
0
0
1
0
0
1
0
0
0
1
1
1
0
2
0
2
0
0
1
1
0
0
2
1
0
1
0
1
1
2
0
1
0
0
0
2
0
0
2
2
0
2
2
1
1
1
0
2
0
0
1
2
2
1
0
1
1
0
0
0
0
1
0
0
0
1
2
0
1
2
0
0
2
1
1
0
0
2
1
0
0
0
0
1
2
0
0
1
2
1
1
1
0
0
0
1
1
0
2
1
5
0
1
0
1
2
1
1
0
1
2
2
1
1
0
1
1
1
1
1
1
0
0
1
1
0
2
1
1
0
0
0
1
1
0
1
0
0
0
1
1
0
0
0
0
1
1
0
2
0
1
2
2
1
2
0
1
1
0
1
3
0
0
1
0
0
2
0
0
0
0
0
2
1
2
0
1
1
2
2
0
2
1
0
0
0
2
1
1
0
0
1
0
0
0
0
1
1
0
3
0
5
2
1
0
2
1
1
0
1
0
1
0
2
0
2
1
0
0
1
2
0
1
2
1
0
2
1
1
1
0
1
1
1
1
1
0
0
0
1
0
0
0
0
1
1
2
1
0
2
0
1
1
2
1
1
0
0
1
1
2
1
1
1
1
0
0
0
1
0
0
1
0
2
0
2
1
0
0
2
1
1
2
1
1
0
2
2
2
1
1
2
2
1
2
0
1
1
2
1
0
2
0
0
1
1
1
0
0
1
1
1
1
0
0
2
2
0
1
0
2
1
1
0
2
0
2
0
1
1
2
2
2
1
2
2
1
2
1
2
2
0
1
1
1
2
1
0
0
1
2
1
1
1
1
0
1
0
1
0
1
1
2
0
2
0
0
2
0
1
0
1
2
2
1
1
0
2
1
1
1
0
2
1
2
0
1
0
0
0
0
1
1
1
1
1
2
0
1
1
1
2
4
0
2
2
2
1
2
0
1
0
2
1
2
2
0
2
1
1
1
0
2
2
1
1
0
0
1
0
3
0
0
0
0
0
1
1
3
2
1
2
1
0
2
1
1
0
1
2
1
1
1
2
1
2
1
0
2
2
0
1
1
2
1
1
0
0
1
2
1
0
0
1
1
2
0
1
1
2
1
1
0
1
0
1
2
0
1
0
2
0
1
1
1
1
1
1
0
1
1
0
0
1
0
0
1
1
0
1
0
0
1
0
1
0
1
1
1
0
1
2
0
0
2
1
2
1
1
1
2
0
1
1
2
0
1
0
0
2
1
0
0
1
1
1
3
1
1
2
2
2
2
0
0
3
1
0
1
1
0
0
2
0
0
0
1
2
0
4
0
0
0
1
0
1
1
0
2
0
0
2
1
2
0
0
0
0
2
0
0
0
2
1
0
1
0
0
1
1
1
1
1
1
2
1
2
1
1
0
2
1
2
1
0
2
1
0
0
1
0
1
1
2
1
0
2
1
1
1
0
0
2
1
0
0
0
2
0
1
1
2
2
1
0
2
1
1
0
0
1
0
0
1
2
1
1
0
0
0
1
1
1
2
1
1
1
0
1
2
2
1
1
0
2
2
2
2
1
1
2
1
2
0
0
0
1
0
0
1
1
1
0
0
1
1
1
2
0
2
0
1
1
1
0
1
0
1
1
0
0
1
0
1
0
2
0
1
0
2
1
0
1
0
0
1
1
1
1
0
1
0
0
3
1
0
2
1
0
1
1
0
2
1
1
2
0
1
0
1
1
1
0
1
0
1
1
0
0
2
2
3
0
3
0
1
0
0
0
2
1
0
1
0
2
1
2
1
1
2
2
0
0
1
2
0
0
0
1
1
2
0
1
1
2
0
1
0
0
1
0
1
1
0
1
1
1
2
2
0
1
1
1
0
1
0
2
0
2
2
0
1
1
0
0
0
1
1
2
1
0
2
0
0
1
1
2
0
0
1
0
1
1
1
2
0
0
1
0
2
1
2
0
1
0
0
1
1
2
2
1
1
2
0
2
1
1
0
1
2
1
0
1
0
2
0
0
1
1
1
1
0
1
1
0
2
0
1
0
2
2
1
1
1
2
0
1
2
0
1
0
1
1
1
0
1
2
0
2
0
2
0
1
2
2
0
1
2
2
1
0
1
0
1
1
3
0
1
1
0
1
1
1
0
1
0
1
0
1
0
0
1
0
1
0
0
0
2
0
1
1
1
1
1
1
0
1
2
1
1
0
2
0
0
1
1
2
2
1
1
1
0
2
1
2
2
1
1
2
1
2
1
1
1
1
1
2
1
1
0
0
0
1
0
1
1
2
0
1
2
0
0
0
0
0
0
1
2
1
0
1
2
0
1
1
1
1
1
0
0
2
2
1
1
2
0
3
1
1
0
2
0
1
1
0
1
2
0
2
2
1
0
2
1
3
0
1
1
0
3
2
2
1
0
1
0
0
1
0
0
1
2
0
0
2
0
2
0
1
0
2
1
0
1
1
0
0
1
0
2
0
1
2
1
2
1
0
1
2
1
0
5
0
1
1
0
1
0
1
0
0
0
1
0
0
0
0
0
2
1
0
2
1
1
1
0
0
2
2
1
1
0
0
2
1
0
0
2
0
2
0
0
0
0
2
2
1
1
0
0
1
1
1
2
2
2
1
1
1
1
1
1
1
0
1
1
0
0
0
1
1
1
0
1
0
1
1
1
0
1
0
1
1
1
0
1
1
2
1
1
1
0
1
0
0
0
0
2
0
2
0
1
2
2
1
1
2
2
1
2
0
1
0
1
1
0
1
0
1
1
0
1
0
0
1
0
2
2
1
0
0
1
0
1
0
0
1
1
0
0
0
0
1
0
0
2
1
1
0
0
2
0
0
0
1
0
1
0
1
0
2
2
0
1
0
0
0
1
1
1
1
0
1
1
1
0
0
0
0
2
0
1
0
1
0
0
0
1
2
1
1
0
0
2
2
1
0
0
1
2
0
2
2
0
1
0
2
1
1
1
1
2
0
2
1
1
1
0
0
2
0
0
0
2
0
1
0
1
1
0
1
0
1
1
2
1
0
2
0
0
0
2
2
2
2
1
1
0
1
0
2
2
1
2
1
3
3
2
1
2
1
0
1
1
3
1
1
0
2
2
0
1
2
2
0
0
1
1
1
1
1
2
0
0
1
1
1
1
2
0
1
1
3
0
0
1
1
2
0
2
2
1
1
2
0
2
1
0
1
1
0
1
1
2
1
2
1
2
2
1
1
1
1
1
0
2
0
0
0
1
2
1
0
6
1
1
0
0
1
0
0
1
2
2
2
1
1
1
1
1
2
1
1
0
0
1
1
1
2
1
2
0
0
1
0
1
1
0
2
1
1
2
2
1
0
0
1
2
1
0
2
0
2
2
1
1
1
1
1
2
0
2
0
0
0
0
0
1
1
1
0
0
0
0
1
1
0
1
0
0
0
1
1
1
1
0
2
1
1
1
0
0
1
0
0
1
0
1
2
1
1
2
0
0
1
1
0
2
1
1
1
1
0
1
1
1
2
0
1
0
0
2
0
1
1
2
1
1
2
0
1
1
2
0
1
1
0
0
1
2
1
2
0
2
0
1
6
0
1
1
1
1
1
0
0
2
2
1
1
1
0
1
1
1
1
1
1
3
1
1
1
0
1
1
1
2
1
2
1
1
1
1
1
0
0
2
1
1
0
1
1
1
0
0
0
2
1
2
1
1
1
1
0
1
0
0
0
1
0
0
0
1
1
0
1
2
1
0
1
2
1
0
0
2
0
2
1
1
1
1
1
1
0
2
1
2
2
1
0
1
0
1
0
0
1
1
2
1
2
2
1
1
1
2
1
1
0
1
3
1
0
1
1
0
1
1
1
0
2
0
2
0
2
1
0
2
0
0
2
0
1
1
0
0
1
0
1
0
0
1
0
1
2
0
1
2
2
1
0
0
0
0
0
2
2
0
2
1
1
1
0
1
0
0
1
1
2
2
0
0
1
1
1
2
1
1
1
0
0
1
1
1
1
1
0
1
1
3
1
1
0
1
4
2
0
1
1
1
1
2
1
2
1
2
1
1
1
0
2
1
0
1
1
2
0
1
0
1
0
2
2
0
1
0
0
0
1
1
0
0
2
1
0
0
2
2
2
2
2
1
1
0
0
0
1
1
1
0
2
1
0
1
2
1
1
0
0
1
0
1
2
1
1
1
0
1
2
2
2
1
1
1
0
1
0
1
2
1
2
1
2
0
2
0
5
2
1
1
0
1
2
0
0
0
0
2
1
1
0
2
1
3
1
1
1
0
2
1
1
0
1
0
0
2
1
1
0
0
1
1
2
0
1
1
1
2
0
2
1
1
2
1
0
2
2
0
2
1
1
0
2
0
1
1
0
1
2
1
1
0
0
1
1
1
0
0
2
0
1
2
2
1
1
1
0
0
0
2
1
0
1
0
1
0
1
2
2
2
0
2
1
1
1
1
1
0
0
0
2
0
1
1
0
0
0
1
3
1
1
2
0
1
0
2
0
2
1
0
1
1
0
1
2
1
0
0
1
0
1
2
1
2
2
0
1
0
0
0
1
3
1
0
0
1
0
0
2
0
1
1
1
0
1
2
0
1
2
0
1
2
1
1
3
1
2
0
0
1
2
1
2
1
1
1
1
0
0
0
2
0
2
1
0
1
2
1
0
1
1
0
2
1
1
1
0
0
1
0
0
0
2
0
1
2
1
0
1
1
0
0
0
0
2
0
1
1
0
0
1
2
0
2
1
1
0
1
0
1
2
1
2
0
1
1
1
1
1
1
2
1
1
0
0
0
1
1
2
1
1
1
1
2
0
1
1
0
1
1
1
1
0
1
0
1
1
1
1
2
1
0
0
0
2
1
0
1
0
0
0
2
0
0
0
3
0
0
3
0
0
1
0
0
0
1
3
1
1
1
0
1
1
1
0
0
0
1
1
1
0
1
0
0
2
0
0
0
0
0
1
1
0
1
0
1
0
2
2
1
1
1
2
3
2
1
0
2
0
1
2
0
0
1
0
1
2
2
1
1
2
2
2
1
1
1
0
1
2
2
1
1
0
1
0
2
0
2
1
2
2
1
0
1
1
3
0
1
0
0
1
1
0
2
1
2
2
0
2
1
2
1
1
1
1
0
2
2
1
4
1
0
2
1
0
1
1
0
1
1
2
1
1
2
2
2
2
1
0
1
0
2
0
1
0
2
0
1
0
1
1
2
2
1
0
3
2
1
1
0
2
1
1
2
2
1
1
0
0
1
2
1
0
1
2
0
2
0
1
0
1
1
0
2
1
0
1
1
1
2
1
2
2
0
1
1
0
0
0
0
1
0
2
0
1
2
1
0
0
1
1
1
1
0
2
0
0
0
0
1
2
0
1
0
0
0
2
0
1
2
1
1
0
1
0
1
1
1
0
2
3
1
1
0
3
2
0
1
1
2
1
0
0
1
1
1
1
1
2
1
1
1
1
0
1
0
0
0
1
0
1
1
2
0
1
2
1
1
1
0
0
1
0
0
1
1
0
1
0
0
1
2
0
2
1
1
1
0
1
0
0
1
1
1
0
1
0
1
1
1
2
1
1
1
1
1
2
1
2
0
0
1
2
3
0
1
2
1
1
1
0
2
0
2
2
1
1
0
0
1
2
2
1
0
2
2
1
0
1
2
0
2
2
0
1
0
2
2
1
0
0
2
1
1
0
1
1
1
2
0
1
0
1
2
0
1
3
1
1
0
0
0
2
0
0
1
1
1
1
1
1
2
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
0
2
1
0
0
1
1
2
1
1
0
0
1
0
2
1
0
1
2
0
1
0
1
1
1
1
1
1
0
1
0
0
2
1
0
2
1
2
2
0
2
1
0
1
0
1
0
0
1
1
1
0
1
1
0
0
0
0
1
1
0
1
2
1
0
1
0
0
0
1
2
1
2
0
2
0
1
1
2
0
0
0
2
1
2
0
1
2
2
0
2
2
1
0
2
1
1
1
0
1
1
2
1
1
0
3
1
0
0
1
0
2
0
0
0
2
0
1
0
1
0
1
1
0
1
2
0
1
1
1
1
1
1
1
2
2
0
1
0
0
1
2
1
1
1
0
1
1
1
1
1
0
1
1
1
0
2
0
1
2
1
1
0
1
0
2
0
0
0
2
1
0
1
1
1
1
1
2
0
0
1
1
1
1
1
0
1
0
1
2
0
0
1
2
2
0
0
2
1
1
1
1
2
1
2
2
2
0
2
2
0
1
0
1
2
0
1
0
0
1
1
0
0
2
1
1
2
0
1
1
0
2
2
2
1
0
1
1
1
1
1
1
2
1
1
1
1
1
1
2
0
1
1
0
2
1
2
2
0
0
0
2
0
1
2
0
2
0
1
0
2
1
2
1
0
0
0
2
1
0
0
2
2
2
1
2
0
0
1
1
1
0
0
1
1
1
1
0
0
1
0
1
2
1
0
1
0
0
1
0
2
2
1
1
0
2
1
0
0
0
2
1
1
0
0
1
1
1
1
2
1
1
1
0
1
2
2
2
1
2
1
0
1
2
1
1
0
2
0
2
0
2
0
1
2
1
0
1
2
1
2
1
1
0
1
0
1
0
1
0
2
2
2
0
1
0
1
1
0
0
0
0
1
1
0
2
1
0
2
1
0
2
1
2
0
1
2
0
1
2
1
1
1
1
0
5
0
1
0
4
2
1
0
1
1
1
0
1
0
2
1
0
0
0
2
1
1
1
1
1
0
0
2
1
1
0
2
0
1
2
2
1
2
0
0
0
0
1
1
0
0
2
0
1
1
0
1
0
2
1
1
0
0
2
1
0
1
1
1
0
0
1
1
2
1
0
0
1
1
2
0
0
2
2
0
2
0
0
0
0
1
2
1
0
0
2
0
1
0
1
2
0
1
0
1
2
2
0
0
2
2
1
0
0
1
0
1
2
2
1
0
0
0
0
0
2
2
2
1
2
0
2
1
1
0
1
1
1
0
2
1
1
2
0
0
0
1
2
0
1
1
0
0
1
3
0
2
1
1
1
1
1
1
1
1
1
2
0
0
1
0
0
0
2
2
2
1
0
1
0
1
2
1
1
0
1
2
1
2
1
0
1
2
1
0
2
0
1
1
1
0
3
0
2
3
1
1
2
2
1
2
0
1
1
1
1
2
2
2
0
2
0
1
2
1
1
0
1
1
0
2
1
1
2
0
2
2
2
1
1
2
1
1
2
1
0
1
1
0
1
0
1
1
0
1
1
1
2
0
0
0
2
0
1
0
0
0
1
1
1
2
1
0
0
0
0
1
1
1
2
1
1
1
0
2
1
0
0
0
1
0
0
1
1
0
0
2
0
1
2
1
2
0
3
2
0
1
0
1
0
1
2
1
1
3
0
2
1
0
1
0
2
1
2
1
1
2
0
0
1
2
1
1
1
1
1
2
1
2
0
0
1
1
2
2
1
0
2
1
2
0
1
2
1
1
1
0
0
0
1
1
0
1
0
0
1
0
0
1
0
1
0
1
2
1
0
0
2
1
1
0
0
1
1
0
2
0
0
1
2
2
1
1
0
0
0
0
0
1
1
1
0
0
0
1
0
1
1
0
1
2
1
0
2
0
0
0
1
1
2
1
0
0
0
0
1
1
1
1
0
1
1
2
1
0
2
1
1
2
0
2
0
2
1
0
0
1
0
1
2
1
2
0
0
1
0
0
1
0
0
1
1
1
2
1
0
0
3
1
0
0
0
1
0
1
0
0
1
1
1
0
0
2
2
0
1
2
1
2
1
1
0
0
0
2
1
1
1
0
0
1
2
2
0
1
0
0
1
1
0
1
1
2
1
1
1
1
0
1
1
0
1
0
0
2
0
0
1
0
0
1
0
2
1
2
0
1
1
0
1
2
1
1
1
1
0
2
0
0
1
2
1
0
0
3
2
0
2
1
2
0
1
0
1
2
1
0
1
0
1
1
0
1
2
1
1
1
1
0
1
2
0
1
0
1
0
1
1
1
1
1
0
0
1
1
0
1
0
1
0
1
0
1
1
2
0
1
0
0
2
0
1
2
1
1
0
0
1
0
1
1
0
2
0
1
2
0
1
1
1
1
1
1
2
0
2
1
1
1
1
1
1
0
1
0
2
1
0
1
1
1
1
1
1
0
1
1
0
2
1
1
0
2
0
0
0
1
1
1
1
0
1
1
0
0
1
1
1
1
1
1
1
0
1
1
0
1
1
1
0
1
1
0
0
0
0
0
1
1
1
1
1
2
0
2
0
2
1
1
1
0
1
0
1
1
0
1
2
0
1
2
0
1
1
0
1
1
1
5
0
1
1
0
2
0
0
1
1
2
1
1
1
2
1
2
1
0
0
0
1
1
0
0
1
2
1
1
1
0
2
1
0
1
0
1
1
2
1
2
1
1
1
0
0
2
1
2
1
1
1
1
0
0
2
0
1
1
1
0
2
1
1
1
2
1
2
2
1
0
1
1
1
0
3
0
0
0
1
0
1
1
0
0
1
1
0
2
2
1
0
0
1
1
2
1
2
0
0
2
1
2
0
1
0
0
2
1
1
1
1
2
0
1
3
1
1
0
2
0
0
0
1
2
0
0
2
3
0
1
1
0
1
0
1
1
1
1
2
1
0
2
1
0
1
1
1
0
2
0
1
1
0
0
2
0
0
1
2
1
0
2
2
1
0
0
0
0
1
0
1
1
1
2
1
1
1
0
1
0
1
1
1
1
0
2
1
0
1
1
1
1
2
1
1
2
2
0
1
0
0
1
1
0
1
1
1
2
1
0
2
2
1
1
1
0
1
1
2
1
0
1
0
0
1
1
1
4
1
1
0
0
0
0
0
1
2
2
2
1
0
1
0
0
1
1
1
0
1
2
2
2
0
1
0
0
0
0
1
1
1
2
2
1
0
1
2
2
1
0
0
1
0
1
3
0
2
3
1
2
2
0
1
2
0
1
1
1
1
2
1
1
1
0
2
0
1
2
2
1
2
2
0
1
1
2
0
0
0
0
2
0
1
2
0
1
2
1
2
0
2
0
0
1
0
0
1
2
0
1
1
1
0
0
0
0
0
1
0
0
1
1
1
1
0
2
0
0
2
1
2
1
1
0
2
0
2
1
1
1
0
2
0
1
2
0
1
1
1
0
1
2
2
1
1
0
0
0
1
1
0
1
2
1
1
0
0
0
0
0
0
0
1
1
2
1
0
2
0
2
1
1
1
2
1
0
1
1
0
0
1
0
0
0
2
2
0
0
2
1
2
0
1
2
1
1
1
0
1
0
0
1
0
1
1
1
2
0
2
0
1
0
2
1
2
2
1
0
0
0
0
1
0
0
2
0
1
1
0
2
0
1
1
1
1
1
0
0
1
2
1
0
1
2
0
0
0
1
0
1
2
0
0
2
2
0
0
0
1
2
3
0
0
0
1
2
5
0
1
1
4
1
2
0
1
1
0
1
0
1
1
0
1
0
0
1
0
1
0
1
1
1
1
1
1
0
0
0
1
0
2
1
1
0
0
2
0
0
1
0
0
0
1
2
1
1
1
0
0
2
2
1
0
2
1
0
2
2
0
2
0
1
0
1
1
0
1
2
0
0
2
0
1
2
2
2
0
0
0
2
1
1
1
0
0
1
0
2
1
0
0
1
0
0
0
1
0
0
1
1
0
1
0
0
2
1
1
0
1
1
3
2
0
1
0
0
3
0
2
1
0
0
1
1
3
0
2
0
1
1
1
0
1
1
1
0
1
1
2
0
0
2
0
0
1
3
0
1
0
0
0
0
1
0
0
2
2
0
1
6
1
0
1
0
2
0
0
1
1
0
1
2
2
2
2
1
0
1
2
1
0
1
0
1
1
1
1
0
0
1
1
0
0
0
1
2
2
0
1
1
1
2
0
2
0
2
0
1
2
2
1
0
1
0
1
0
2
0
2
2
1
0
1
0
2
1
1
0
1
0
2
0
1
0
1
1
1
1
1
0
0
0
2
1
1
0
0
2
1
1
1
0
1
1
2
1
1
1
2
0
0
1
0
2
0
2
2
1
2
0
0
0
1
0
0
0
0
1
3
2
0
2
1
2
0
1
0
1
1
1
0
0
2
0
0
1
0
1
1
0
1
1
2
1
1
1
1
0
1
0
1
2
2
0
0
2
1
1
0
1
0
1
1
0
1
2
1
1
0
0
1
2
0
0
1
0
0
1
1
2
0
1
1
1
0
0
1
1
3
2
2
2
0
0
2
2
1
2
0
1
2
2
0
1
1
0
0
0
2
1
2
3
1
2
1
1
1
1
2
2
1
1
0
0
2
3
1
1
0
1
0
1
1
0
1
1
0
0
2
0
1
1
2
0
1
1
0
1
1
0
1
0
3
1
2
1
1
1
0
2
1
2
0
0
2
0
2
0
1
1
1
1
0
1
0
2
1
0
1
0
1
1
1
0
0
1
1
0
0
0
2
1
1
2
0
2
0
1
1
2
1
2
0
0
2
0
0
0
0
1
2
2
0
2
0
2
2
0
2
2
1
2
0
2
0
1
1
0
1
2
1
1
0
2
2
0
1
1
0
0
2
1
0
1
1
0
1
2
1
1
0
1
3
2
1
2
0
2
3
2
1
0
1
2
0
2
0
1
1
2
1
1
1
0
0
1
2
1
0
0
1
0
0
1
2
0
0
2
1
1
1
1
0
1
1
1
0
0
0
0
1
1
1
0
0
0
3
2
0
0
2
2
1
0
0
0
0
0
2
0
1
1
1
1
1
2
1
0
2
1
0
0
2
1
0
0
0
1
1
0
1
0
0
2
1
1
1
2
0
1
1
0
0
1
2
0
1
1
0
1
0
0
0
1
2
1
0
0
0
1
1
0
0
0
1
2
0
1
4
1
2
2
1
1
1
1
4
1
2
0
1
1
1
1
1
2
2
2
0
0
2
1
0
1
1
2
1
0
0
1
1
0
1
1
2
0
1
2
1
2
1
0
0
0
1
1
1
0
0
2
0
1
0
0
1
0
1
2
2
1
0
1
1
1
1
2
0
0
0
2
1
2
2
1
0
1
0
1
0
0
1
0
1
2
0
1
1
1
1
1
1
1
0
1
0
1
0
1
0
1
0
1
0
2
0
0
0
2
1
2
1
1
1
1
3
1
0
1
1
0
0
2
1
1
1
0
1
0
2
1
1
0
1
1
1
1
1
0
1
0
0
0
4
1
2
0
2
0
0
0
0
0
0
0
1
0
0
2
1
1
1
0
0
0
0
0
0
0
1
2
0
1
2
1
2
0
2
2
1
0
0
0
0
1
1
2
2
1
1
1
2
1
1
0
0
1
1
1
1
1
0
2
1
3
0
2
1
2
1
1
2
2
2
0
1
2
2
1
1
2
0
1
0
1
0
1
0
0
1
0
2
2
2
1
1
2
0
0
1
1
0
0
1
2
3
0
2
1
2
0
0
1
1
1
1
1
0
0
0
1
0
1
3
0
1
2
0
3
0
0
0
1
1
1
1
0
1
1
1
2
1
1
1
0
1
0
0
0
1
0
1
1
1
2
2
1
1
1
0
0
1
1
0
1
2
2
2
1
2
0
1
0
1
1
1
1
1
0
1
1
0
0
0
1
1
2
0
2
1
0
2
1
0
1
2
1
0
0
1
2
1
2
1
0
0
2
0
1
2
1
1
0
0
2
0
1
1
2
0
0
2
1
0
1
1
0
1
0
0
1
2
2
0
2
0
2
2
0
1
1
2
1
1
1
0
1
1
2
0
0
1
2
1
1
2
1
0
0
1
0
2
1
2
1
2
1
3
2
0
1
0
2
1
2
0
0
1
2
1
2
0
0
1
0
3
4
1
0
1
0
0
1
2
1
2
2
2
1
1
0
2
1
0
1
0
2
1
0
0
0
2
2
2
1
2
0
2
2
0
0
2
0
1
0
1
1
1
0
1
1
1
2
2
0
2
0
2
1
1
2
1
1
0
0
0
1
2
1
2
1
0
0
0
0
0
2
1
0
1
2
2
0
1
2
0
2
2
0
0
1
1
2
1
1
1
0
1
0
0
0
0
1
0
1
0
0
0
1
1
0
0
1
1
1
0
1
1
1
2
2
1
1
0
0
2
2
1
1
3
0
2
0
1
3
0
0
1
1
0
1
1
2
1
1
0
0
1
1
0
0
0
1
1
2
0
1
2
1
2
0
0
1
0
2
1
0
0
0
1
1
1
0
1
2
0
0
0
1
1
0
0
1
0
0
1
0
2
1
1
0
2
2
0
0
1
1
2
1
2
2
1
1
2
0
1
1
1
1
1
1
0
1
2
1
1
0
0
1
1
0
0
0
1
0
1
1
0
1
2
0
1
0
2
1
1
1
1
0
1
1
0
2
2
1
1
0
2
1
1
1
2
2
0
0
0
1
2
0
3
0
1
2
0
1
0
0
0
0
1
1
0
2
1
1
0
1
1
1
0
0
1
1
0
3
1
0
1
0
0
0
1
1
0
1
0
1
0
2
1
2
1
2
1
1
0
1
1
1
0
0
0
3
2
4
1
0
1
0
1
2
0
1
0
2
0
0
0
0
2
2
0
2
2
0
2
2
1
1
2
0
1
1
1
1
0
1
0
1
0
1
2
1
0
1
2
1
2
1
2
2
0
2
0
1
1
1
2
0
1
1
0
0
1
0
0
1
2
1
0
0
2
0
2
0
1
1
0
2
0
1
0
0
1
0
1
0
6
2
0
0
1
0
0
1
0
2
1
1
2
1
0
2
1
0
0
2
1
1
0
0
1
0
1
2
0
1
0
1
1
2
0
0
1
2
0
1
0
0
0
1
1
2
2
2
2
0
1
0
1
0
1
1
1
1
1
1
0
2
2
1
0
2
1
0
2
2
1
1
2
1
1
0
1
0
0
1
0
1
0
1
0
0
1
0
1
1
2
0
1
1
1
1
1
1
1
1
1
0
0
1
1
0
0
2
1
1
0
2
1
0
1
0
1
0
0
1
1
1
2
2
1
2
0
0
1
2
1
2
0
0
1
0
1
0
1
0
2
1
0
1
1
0
0
0
0
0
1
1
0
2
0
1
0
3
0
1
1
1
2
1
0
0
0
0
0
3
1
0
1
0
1
1
1
0
1
0
1
1
1
2
1
2
1
0
2
2
1
1
2
0
1
1
1
0
2
1
0
2
2
2
0
2
1
2
2
3
2
3
0
2
0
0
1
2
0
0
1
1
1
1
2
0
2
0
2
1
1
1
1
1
0
0
1
1
2
0
0
0
1
1
0
1
1
2
1
1
1
1
2
1
0
0
2
2
1
2
0
2
0
2
0
2
1
1
0
0
0
3
2
2
1
2
2
3
0
1
1
1
0
1
1
0
0
1
1
1
1
1
0
2
1
1
1
1
2
1
1
1
1
2
1
0
1
0
0
1
0
1
1
1
1
0
0
0
0
0
1
0
2
2
1
1
1
1
0
1
1
2
0
0
1
1
1
0
1
2
0
0
0
2
0
0
0
3
1
0
1
1
1
1
1
1
0
1
1
2
2
0
1
2
1
0
0
2
2
1
1
1
0
1
0
1
0
0
2
2
1
1
1
2
1
2
0
0
2
1
2
0
0
0
2
1
1
0
1
1
1
2
2
1
2
0
0
1
1
2
2
1
1
0
0
0
0
2
1
0
0
0
2
0
2
1
1
1
2
0
1
2
0
1
0
0
0
0
1
0
1
1
1
2
2
2
0
1
0
1
3
0
1
2
1
1
0
1
1
1
1
1
1
0
1
6
1
1
1
0
2
2
1
1
2
1
1
1
0
0
1
0
0
1
1
1
2
2
2
1
1
0
1
1
1
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
1
1
2
0
2
1
1
1
1
1
0
0
0
1
1
0
1
0
1
1
0
1
1
1
0
1
1
0
2
1
1
1
1
1
1
2
1
2
0
0
1
0
2
2
1
0
1
2
1
0
1
2
1
0
1
1
0
2
2
2
0
0
1
0
1
0
1
0
0
1
1
0
0
0
3
0
0
1
2
1
0
0
1
2
2
1
0
2
1
0
2
0
0
1
2
0
1
1
2
0
2
1
1
2
2
1
1
0
0
1
1
0
3
2
0
1
0
2
2
1
0
1
1
2
2
0
0
2
0
2
2
1
0
0
0
0
1
2
0
1
2
1
1
0
1
2
1
0
0
0
0
0
2
2
0
0
1
1
1
2
1
1
0
0
1
0
0
1
1
1
2
1
1
1
1
0
1
0
1
0
1
2
2
2
1
0
1
0
0
0
0
1
1
1
1
0
0
1
1
0
1
2
1
1
2
2
0
0
0
1
1
1
1
2
2
1
0
0
1
2
0
2
1
1
0
1
1
1
1
0
1
1
2
0
0
0
0
1
1
1
0
1
1
2
4
1
2
2
1
1
0
1
1
1
1
1
1
3
0
2
1
3
0
2
1
2
1
0
0
1
0
0
1
0
0
0
0
2
0
0
2
2
0
1
1
4
0
1
1
0
1
0
0
0
1
1
0
2
0
0
2
1
1
0
1
1
0
0
2
1
1
1
1
1
0
1
1
0
0
2
1
0
3
1
0
0
1
1
1
2
0
2
1
1
2
1
1
1
0
0
0
2
0
0
1
1
6
0
0
0
1
1
0
2
2
1
0
1
2
0
0
2
2
2
1
1
2
2
1
0
2
1
0
1
1
1
1
1
1
0
1
0
2
1
2
0
0
0
2
2
1
0
1
0
1
2
1
0
0
2
0
2
0
0
0
2
1
2
0
0
1
1
0
1
2
3
2
1
0
2
0
1
1
1
2
1
0
1
3
1
1
2
1
2
0
0
1
0
0
2
0
0
0
1
1
5
1
1
1
1
1
0
1
2
1
0
0
0
0
1
2
1
1
0
0
2
0
0
1
1
1
1
0
1
1
1
1
0
0
0
0
0
1
1
2
0
0
2
1
0
0
1
1
0
0
0
0
1
1
0
0
0
2
1
2
2
0
0
2
1
0
1
1
1
2
0
0
2
1
0
0
1
2
1
2
2
0
1
0
0
2
0
0
2
0
0
1
1
1
1
1
0
0
1
1
1
2
1
2
1
0
0
0
0
1
2
0
0
0
2
0
4
1
1
2
0
0
2
0
2
1
1
1
1
1
1
0
0
1
0
1
1
1
0
2
0
0
2
0
1
2
1
1
1
1
0
3
1
0
1
2
0
2
2
1
1
1
1
0
1
0
0
1
0
2
1
2
0
2
0
2
1
1
0
1
1
1
0
0
0
0
0
1
1
0
0
0
1
1
1
1
1
0
2
0
2
0
0
0
0
0
0
1
0
0
1
2
1
0
0
0
0
0
0
1
0
2
1
1
2
1
0
2
1
2
0
2
2
1
0
0
2
1
1
0
1
0
0
1
0
1
1
1
2
0
1
1
0
0
2
1
1
2
1
2
0
3
1
2
1
1
1
2
2
2
0
0
0
0
1
0
1
1
2
2
2
0
0
2
0
1
2
1
1
2
1
0
2
1
1
2
2
0
1
0
2
1
1
0
0
0
2
1
1
1
2
0
1
1
1
0
1
2
2
2
2
0
1
1
2
1
0
2
0
1
0
2
0
1
1
3
1
0
1
1
1
2
2
0
0
1
1
2
1
1
1
1
0
2
0
2
1
0
0
0
1
1
1
0
1
2
2
2
0
1
1
1
0
1
0
0
1
1
0
1
0
1
2
0
0
1
1
0
0
0
1
2
2
2
0
1
2
2
1
0
1
2
1
1
2
0
0
0
1
1
1
1
2
1
0
1
2
1
0
1
0
1
0
2
0
0
2
1
0
0
0
2
0
0
0
0
1
1
1
1
1
1
1
4
1
1
1
1
0
0
2
0
1
1
1
2
1
1
1
1
0
2
2
1
1
1
2
1
1
0
1
0
2
0
1
0
1
0
1
0
2
2
0
1
1
0
0
0
1
0
1
1
0
1
0
1
0
0
1
1
2
2
1
1
1
1
1
1
1
1
0
2
1
0
2
0
1
3
0
1
0
1
1
2
1
1
0
1
0
1
1
2
1
0
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
0
0
3
1
1
2
2
0
0
2
2
0
0
0
1
2
2
1
2
1
0
1
2
1
0
0
0
2
1
1
1
0
2
0
1
1
1
0
0
2
3
1
1
1
1
0
1
0
1
0
0
1
1
0
0
1
2
1
1
1
1
0
0
1
1
1
0
1
1
1
2
0
1
1
1
1
0
0
0
0
2
0
0
1
1
1
1
1
1
2
0
0
0
2
1
1
0
0
3
2
1
2
1
0
2
0
0
1
1
0
0
0
1
2
0
0
2
1
2
1
0
1
2
1
0
1
0
1
0
1
1
1
0
1
0
1
2
2
2
2
2
0
2
1
1
1
0
1
1
2
1
1
0
0
1
1
0
2
1
0
1
1
0
1
1
1
0
0
1
2
0
3
1
0
1
0
0
1
0
1
0
2
0
0
0
1
0
0
1
0
0
1
2
0
1
1
0
1
0
1
1
0
1
0
1
2
1
2
2
1
1
1
2
0
0
0
0
2
0
1
1
0
0
1
2
0
1
0
2
1
0
1
1
1
2
1
2
2
1
1
1
1
3
0
0
1
0
1
0
0
1
1
0
0
0
0
2
0
0
0
1
0
2
0
1
1
1
1
0
1
0
0
1
2
1
1
1
1
1
0
2
1
1
1
1
0
0
0
2
1
1
0
1
2
1
0
0
0
1
1
1
1
0
1
2
1
1
0
0
1
1
0
2
0
0
3
1
0
1
0
0
0
0
1
1
0
1
1
0
0
0
1
1
1
2
0
1
0
0
1
1
1
0
0
2
0
2
0
2
1
0
2
0
2
0
1
1
1
2
0
0
0
1
0
1
1
1
2
0
0
0
2
0
2
2
2
1
1
1
0
2
1
1
0
1
0
2
1
0
0
2
0
0
1
1
0
2
2
0
1
1
2
2
0
1
1
1
2
2
1
2
1
1
0
2
0
1
2
1
1
0
1
1
0
1
1
2
2
1
0
2
0
0
0
1
2
2
0
0
2
1
1
1
0
1
2
1
0
1
2
1
1
0
2
1
0
1
0
1
2
1
1
1
0
1
2
0
1
2
0
1
1
1
2
1
1
0
0
1
0
0
1
2
2
0
2
0
1
2
1
1
0
1
1
0
2
2
1
1
1
1
1
0
2
1
2
1
2
0
0
0
2
1
0
0
1
0
0
1
0
0
1
1
2
1
1
1
3
2
1
0
1
1
0
1
0
1
0
0
2
2
3
0
0
1
1
0
1
1
1
0
2
1
1
1
0
0
1
0
1
1
2
0
0
2
1
1
1
0
1
1
0
1
0
1
2
2
1
0
1
2
2
1
1
1
1
1
1
1
0
1
2
1
0
0
1
0
1
2
0
0
2
0
1
3
0
0
1
0
1
1
2
0
1
2
0
1
1
1
1
1
0
1
2
2
2
1
1
2
1
2
1
1
1
2
1
2
1
0
1
1
1
1
2
0
1
1
0
0
1
1
3
0
1
0
0
0
0
1
0
1
1
1
1
0
0
1
1
0
1
0
1
1
1
1
2
0
1
0
1
0
0
1
0
1
2
0
0
1
1
1
1
1
0
1
0
2
2
1
2
1
1
0
0
1
1
1
1
1
0
0
1
1
1
2
1
0
1
1
2
2
1
1
0
2
1
1
0
2
2
0
1
1
1
1
0
1
1
0
1
1
2
0
0
2
1
1
0
1
1
1
2
1
1
2
1
0
0
0
1
1
0
0
1
2
0
1
0
2
0
2
1
0
0
1
2
2
0
1
2
0
1
0
1
1
1
2
0
2
1
1
1
0
2
1
1
1
1
1
2
1
1
1
0
3
1
1
0
2
2
1
0
1
1
2
0
2
2
0
0
0
0
1
0
0
1
0
0
1
0
2
0
1
1
0
1
1
0
0
0
1
1
1
0
1
1
1
1
1
1
2
0
0
2
0
0
0
1
0
1
0
0
2
2
0
2
2
0
1
1
2
0
2
2
0
2
1
1
0
1
1
0
1
0
1
2
1
1
0
1
2
0
1
0
2
0
2
1
1
2
1
0
0
1
0
0
1
1
4
2
1
2
1
0
0
1
0
1
1
1
0
0
1
3
0
1
0
0
1
1
2
1
0
1
0
0
1
0
2
2
2
0
1
1
1
1
1
1
2
2
0
1
1
0
1
0
1
1
2
2
1
0
2
1
0
1
1
0
0
0
1
1
0
2
3
0
1
1
2
1
1
1
1
1
2
0
1
1
1
1
1
0
1
0
1
1
1
1
0
1
1
0
0
2
1
1
0
2
0
2
2
2
1
1
0
1
0
1
2
1
1
1
0
2
1
2
0
1
0
0
2
0
1
0
0
1
2
1
1
2
1
1
1
0
2
0
0
1
0
2
1
1
0
1
1
1
0
1
1
1
0
2
0
0
1
1
1
1
0
1
0
1
0
1
2
0
0
0
1
1
1
2
0
1
2
1
1
2
0
1
1
2
1
0
2
2
1
1
1
0
1
1
0
1
1
2
1
0
2
0
1
1
0
0
2
0
1
0
1
1
1
1
0
0
1
1
0
1
0
2
0
2
1
1
1
1
0
0
1
1
2
0
0
0
1
0
1
0
1
1
0
0
1
1
0
1
0
1
0
1
1
0
2
1
2
1
1
0
1
0
0
2
1
0
0
0
1
0
1
0
1
1
1
2
2
1
1
2
1
0
1
0
0
1
1
1
1
0
1
1
0
1
1
1
1
1
1
1
2
0
1
0
0
0
2
2
1
1
1
1
1
0
2
1
1
1
0
2
0
2
1
1
1
1
1
1
0
0
0
0
0
0
1
0
3
1
0
0
1
1
1
0
1
1
0
1
1
1
0
0
1
2
1
0
1
1
0
1
1
0
1
2
0
1
1
2
1
1
1
1
0
1
1
2
1
1
1
1
2
0
1
2
1
0
2
0
0
0
1
0
2
0
0
1
2
2
2
0
0
1
2
1
1
1
1
1
1
0
1
2
0
2
1
1
3
1
2
2
0
1
1
2
2
0
0
1
1
2
0
2
1
1
0
1
1
0
1
1
1
0
0
2
0
2
1
0
2
0
0
1
1
2
2
2
0
1
2
2
0
2
1
0
0
0
1
1
2
0
0
0
1
1
1
0
0
1
2
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
2
1
1
1
1
0
2
1
2
1
1
0
1
0
0
1
2
0
1
1
1
0
0
1
0
1
0
2
1
1
1
2
0
1
2
2
1
2
0
0
2
1
2
2
1
1
1
0
0
2
1
2
1
0
1
0
0
1
3
2
2
1
1
1
0
0
1
1
1
1
1
1
0
1
1
2
3
0
1
1
0
0
1
0
1
3
1
1
0
0
1
1
2
0
1
2
1
4
1
1
0
1
0
0
0
2
0
1
1
0
0
2
0
1
2
0
1
0
1
2
1
1
0
1
2
0
1
0
1
0
1
1
0
2
2
2
2
1
2
0
1
1
1
1
2
0
1
0
1
1
0
1
2
2
1
1
1
1
0
1
0
0
0
0
1
2
1
1
1
0
1
2
0
1
0
0
1
0
0
2
0
1
0
2
1
0
1
1
0
0
1
1
1
0
1
1
0
2
0
2
1
0
0
1
0
3
2
1
0
0
0
1
2
0
0
0
0
1
1
0
1
0
0
1
1
0
1
3
1
1
0
1
1
2
1
0
1
0
0
1
0
1
1
1
0
0
1
2
2
0
1
0
1
1
0
2
1
0
1
1
0
1
1
1
0
2
0
2
1
2
2
2
2
1
0
2
1
1
1
2
0
0
2
1
2
1
1
1
0
0
1
0
1
1
1
0
0
0
2
1
2
0
0
0
0
0
0
1
1
1
2
1
1
1
1
0
0
1
1
1
1
3
2
1
0
1
0
0
1
1
1
1
1
0
2
0
0
0
0
0
1
1
0
2
0
2
0
2
2
2
0
1
0
0
1
0
1
1
1
0
1
0
1
1
2
2
1
0
2
1
0
1
0
0
1
1
0
3
1
0
1
1
2
0
4
2
2
0
2
1
0
1
0
1
0
1
0
1
1
2
1
0
2
1
0
1
1
0
2
1
3
1
1
2
0
1
1
0
1
2
1
0
1
2
2
2
2
0
0
0
1
2
1
1
0
0
1
0
1
1
1
1
1
1
0
1
2
2
2
1
0
1
1
0
1
0
1
0
0
1
1
0
1
0
1
0
0
1
0
2
1
2
0
1
1
2
0
2
0
0
2
1
6
0
0
1
1
2
1
1
0
0
1
2
1
2
0
0
0
0
1
1
1
3
0
0
1
1
0
1
2
0
2
1
2
0
2
1
0
0
0
1
1
1
2
1
0
0
0
0
1
0
0
0
1
1
0
1
1
0
1
0
1
1
1
1
1
0
1
1
0
2
2
0
2
2
1
0
1
1
1
2
2
0
0
0
1
1
2
0
4
2
2
3
0
1
0
1
1
1
1
2
2
0
1
2
0
2
0
1
0
2
1
2
1
2
0
2
0
1
1
0
2
0
1
1
1
1
1
2
0
1
0
1
0
2
1
2
1
2
1
1
2
2
0
2
0
0
1
1
2
1
1
0
1
1
0
1
0
1
1
0
0
1
1
0
0
1
1
0
1
1
0
0
2
1
0
1
2
1
1
2
1
1
2
1
1
1
1
1
1
1
2
0
1
0
0
2
0
1
2
0
2
0
2
1
1
1
1
2
2
0
0
2
0
0
2
1
1
1
1
1
1
1
0
1
0
2
1
0
0
1
2
0
0
2
1
1
0
0
1
1
0
1
1
0
1
2
1
1
2
4
0
0
0
0
1
1
2
1
2
0
2
1
0
2
0
2
0
2
3
0
1
1
1
0
2
0
1
0
0
0
1
2
2
1
1
1
0
1
0
1
1
1
0
0
0
2
0
1
0
0
2
2
0
0
2
2
1
0
0
1
0
2
0
1
0
1
0
0
1
1
0
0
1
0
1
0
2
0
1
2
2
1
1
1
1
1
1
3
1
0
1
0
0
2
2
1
1
0
1
2
1
1
0
2
0
2
2
1
0
0
1
2
3
0
1
1
1
2
1
1
0
0
2
2
0
0
1
0
0
1
1
1
0
1
1
0
3
1
1
1
0
1
1
1
2
1
0
1
2
0
2
2
2
0
2
1
1
0
0
2
2
2
0
1
0
1
1
0
1
1
1
2
2
1
0
1
0
1
2
1
1
1
1
0
0
1
0
0
1
1
1
1
1
0
0
2
3
1
1
1
0
1
1
1
2
0
1
0
1
1
2
0
0
1
2
2
1
0
2
1
1
2
1
1
0
2
0
1
2
1
1
0
1
1
2
1
1
2
1
1
0
1
2
1
1
0
1
1
2
0
1
1
1
0
1
1
1
0
1
2
1
1
0
2
0
1
1
0
1
0
0
2
0
2
1
0
1
0
0
0
2
1
1
0
2
0
0
0
1
0
1
2
1
1
1
2
0
1
0
1
1
1
2
2
1
1
0
1
1
1
1
1
1
2
1
0
2
2
1
2
0
1
1
1
0
1
1
1
2
0
1
0
1
2
3
4
1
0
1
1
0
3
1
0
1
0
0
0
0
1
0
0
2
1
1
0
0
0
2
1
1
2
1
1
1
0
2
0
2
1
0
1
0
1
0
0
1
1
2
0
1
2
1
0
0
1
0
1
0
2
1
0
1
0
1
0
1
2
2
2
0
1
1
2
1
1
0
1
1
1
2
1
0
1
0
0
1
2
1
1
1
2
0
1
1
0
0
0
1
0
1
1
0
5
2
1
1
1
1
0
1
1
0
1
1
0
2
1
0
2
2
1
1
1
2
1
1
0
2
1
0
1
1
2
0
1
0
0
1
0
1
1
0
0
2
1
0
1
2
2
0
0
2
0
1
0
0
4
1
0
0
1
0
0
0
1
1
0
0
2
0
2
1
1
1
2
1
0
1
0
0
0
0
0
1
2
1
1
2
1
1
0
2
1
1
0
0
1
1
2
2
1
1
0
0
1
1
0
0
1
1
1
0
2
1
0
1
1
1
1
0
1
0
0
1
2
1
1
1
1
2
0
1
0
0
1
0
2
1
0
0
2
1
2
1
2
0
2
2
0
2
2
1
1
2
1
0
0
1
0
1
2
0
2
1
0
1
0
1
0
1
4
0
0
1
2
2
2
0
0
0
0
0
1
2
1
0
0
1
0
1
2
0
0
0
0
1
0
0
1
2
1
0
1
2
1
0
0
0
1
1
1
1
2
1
0
1
1
1
1
0
0
1
1
3
1
0
1
0
1
0
2
1
0
0
0
0
0
0
1
1
1
0
0
2
0
1
2
0
3
1
3
1
0
2
2
1
1
0
0
1
2
0
1
3
0
0
1
1
0
0
2
1
2
2
1
1
0
0
2
2
2
1
2
1
1
0
0
1
1
2
2
0
1
1
1
2
3
1
0
1
1
3
0
1
0
2
0
1
2
1
1
1
1
0
1
2
0
2
1
2
0
0
3
1
1
1
0
2
2
2
0
1
2
2
0
0
1
0
2
1
2
1
0
1
0
0
1
0
1
1
2
1
1
1
0
1
0
1
0
0
2
0
0
0
0
2
1
1
2
1
0
0
0
0
0
2
1
2
2
1
0
1
0
2
1
1
0
0
0
1
2
1
0
1
0
2
0
0
0
1
0
1
1
0
1
1
1
0
1
0
0
0
1
1
0
0
2
0
0
0
2
1
0
0
0
0
2
0
0
1
0
1
1
0
0
1
0
2
1
1
0
0
1
1
0
1
0
1
1
1
0
0
1
1
0
1
2
0
1
1
0
0
1
1
0
0
1
1
0
1
0
1
1
0
2
0
1
0
1
1
1
1
2
0
1
0
0
0
1
2
1
2
0
2
2
7
1
0
1
1
0
2
3
3
2
0
0
1
0
0
1
2
1
1
2
0
0
1
0
0
1
0
0
1
1
0
0
1
0
1
2
0
2
1
0
1
1
2
2
2
0
2
1
1
2
2
0
1
2
2
0
2
1
0
1
1
0
2
1
1
1
2
2
1
2
0
1
1
0
0
0
1
0
1
2
1
1
5
1
2
0
1
1
2
2
1
2
1
0
0
2
1
1
1
0
1
0
1
1
0
1
1
1
1
1
1
2
1
0
2
0
3
1
2
0
0
0
0
2
2
2
2
1
1
1
2
2
0
2
2
3
1
1
0
0
2
0
2
1
1
0
0
0
0
2
2
2
0
2
1
0
1
0
1
1
1
0
1
1
1
1
3
0
1
1
1
2
1
0
0
1
2
1
2
2
1
3
0
0
0
1
2
0
1
1
2
2
1
0
1
2
2
2
0
1
1
0
0
0
2
1
0
0
2
2
1
1
1
1
1
0
0
0
1
1
0
1
0
0
2
0
2
0
0
1
0
2
1
1
1
1
2
1
1
2
2
1
0
1
1
0
2
0
1
1
1
0
1
1
2
2
1
1
1
1
1
0
1
1
0
1
1
1
0
1
2
2
2
0
0
1
0
1
0
1
1
1
2
1
2
2
1
0
1
1
2
1
1
2
2
1
2
1
2
2
1
1
2
1
1
0
2
0
1
1
1
0
1
1
1
2
1
1
1
2
1
2
1
2
0
1
0
0
1
1
0
1
1
2
1
0
0
0
2
1
1
1
2
1
1
1
2
2
1
0
1
0
1
1
0
1
1
1
2
1
0
2
1
1
1
0
0
0
0
1
2
0
1
1
0
1
1
2
1
0
0
2
1
2
0
2
2
0
2
1
1
1
2
0
0
1
0
1
0
1
1
4
2
1
0
0
1
0
2
1
0
2
3
1
0
1
0
0
1
0
0
3
1
1
1
0
0
0
1
0
1
0
1
0
0
1
1
2
0
1
1
0
1
1
2
2
2
1
3
1
1
2
0
0
1
1
2
0
0
2
1
1
2
1
1
0
1
1
1
0
3
0
2
1
1
2
0
0
0
0
1
0
0
0
2
0
0
0
0
1
2
0
2
0
1
2
0
1
1
1
0
2
1
1
1
1
1
1
1
0
0
0
0
1
1
1
2
0
1
2
0
2
3
2
0
1
1
2
0
0
0
0
2
1
1
1
1
2
1
2
2
0
0
1
0
0
1
2
2
0
2
0
0
1
1
0
2
1
1
1
2
0
0
1
0
1
0
0
0
1
4
1
1
0
0
0
1
1
0
1
2
1
1
0
2
1
2
0
0
1
2
0
1
2
1
1
0
1
1
1
0
1
0
0
2
2
1
2
2
0
2
0
3
2
1
0
0
2
1
0
1
1
1
0
1
0
1
2
1
2
1
2
1
2
2
1
0
0
2
1
0
2
1
1
0
2
0
1
1
1
1
0
4
2
2
0
2
2
2
1
0
2
1
1
1
0
0
0
1
1
1
1
0
1
1
1
2
0
1
0
2
0
2
1
1
0
2
1
0
0
2
1
1
0
0
0
2
2
0
1
1
2
1
2
0
0
1
0
2
2
1
2
1
2
0
0
0
1
0
1
2
2
2
0
0
1
1
0
0
2
2
1
2
1
1
2
1
0
1
0
1
0
0
0
1
1
2
1
1
0
1
1
1
0
1
0
2
2
0
2
2
2
1
0
1
0
0
1
1
1
0
1
1
2
1
1
1
0
0
2
0
2
1
0
1
1
0
2
0
0
0
0
1
2
2
0
0
2
0
2
1
0
0
1
0
0
1
2
2
0
1
0
2
2
1
2
0
2
0
0
1
1
0
1
1
1
1
1
1
0
2
0
0
1
0
4
2
1
1
1
2
1
2
1
1
0
2
1
2
2
1
1
2
0
2
1
0
2
0
1
0
1
2
0
1
0
1
1
0
1
1
3
0
0
3
1
1
0
2
0
0
0
1
4
0
2
1
2
1
2
0
0
2
1
2
1
0
2
1
2
1
1
1
1
1
1
2
0
1
1
1
1
0
1
0
2
1
1
1
0
1
0
1
1
0
1
0
2
0
1
1
1
2
0
2
0
1
0
1
1
0
0
1
1
2
1
1
0
1
1
0
1
3
2
0
0
0
1
0
1
1
1
1
0
2
2
1
2
0
0
1
1
0
0
3
1
1
0
0
1
3
0
2
1
0
1
0
1
1
0
0
1
2
2
0
2
1
0
1
0
1
0
1
1
2
0
0
0
0
1
1
1
1
2
2
1
1
2
1
2
2
2
1
0
1
2
0
1
2
2
0
1
1
1
1
0
2
1
1
0
2
0
0
0
0
0
0
2
0
0
2
1
1
1
1
0
1
1
2
1
2
2
2
2
2
1
1
0
2
1
1
1
1
1
1
2
0
1
1
1
1
2
1
2
0
0
1
0
0
2
0
2
1
1
0
2
0
2
2
1
2
2
0
0
2
0
2
2
2
2
0
0
0
1
1
1
2
0
0
2
1
1
1
1
1
2
0
1
0
2
1
0
2
1
0
0
1
1
0
0
2
2
2
0
0
1
1
1
1
2
2
1
0
0
1
1
1
0
0
1
1
2
0
0
0
1
2
0
0
1
1
1
0
2
0
1
2
1
0
1
1
2
1
2
0
1
0
3
2
1
1
0
1
0
0
2
0
0
2
0
0
2
2
0
1
1
2
1
0
0
1
0
1
0
2
2
0
1
1
1
2
2
0
1
2
1
0
1
2
0
0
1
1
1
0
2
1
1
0
2
0
1
2
0
1
2
2
1
0
1
2
0
1
0
1
0
1
2
1
0
0
1
2
1
1
1
0
0
0
1
1
1
0
0
0
0
0
0
1
1
2
1
0
1
1
0
1
0
1
2
0
0
2
2
0
1
0
2
1
1
2
0
0
3
2
0
1
1
0
2
0
1
2
0
0
1
1
0
1
0
0
1
1
1
1
0
2
0
0
1
1
0
2
0
0
1
0
2
2
1
0
0
0
1
1
1
1
0
1
1
0
1
0
0
0
0
1
0
1
1
0
0
1
1
0
2
1
0
0
0
0
1
1
0
0
1
0
1
0
0
2
2
1
2
0
1
0
1
0
3
0
3
1
2
2
2
1
0
1
1
1
0
2
1
0
2
1
0
1
1
0
0
2
1
0
2
1
1
1
1
1
2
2
1
1
2
0
0
1
1
0
2
1
1
1
1
1
0
2
1
1
0
1
0
1
1
1
0
1
1
1
0
1
0
1
3
2
1
1
1
0
0
1
2
0
1
2
2
1
2
1
0
1
0
0
1
1
1
0
0
1
0
0
2
1
0
1
1
2
0
2
1
1
1
0
1
1
0
2
2
1
2
0
0
2
1
0
2
2
1
1
0
1
1
1
0
0
0
1
1
4
1
0
1
2
0
2
1
2
1
2
1
0
0
1
1
0
0
1
1
2
1
0
0
0
0
0
2
1
1
2
1
1
0
1
1
1
1
5
0
1
2
0
3
0
1
2
1
2
2
0
1
1
1
1
1
0
1
0
0
0
0
0
10
0
1
0
1
1
2
2
0
2
0
1
1
0
1
1
1
0
0
0
1
0
3
0
0
2
1
2
1
1
2
2
0
1
0
0
1
1
0
1
1
1
1
1
1
0
1
1
2
0
1
0
1
1
2
0
2
0
2
1
2
1
1
1
2
1
2
2
0
0
0
2
0
2
1
2
2
2
0
2
0
1
1
2
2
1
0
0
0
2
0
2
1
0
1
1
0
1
2
1
1
0
0
1
0
0
1
1
2
0
1
2
1
0
0
0
1
1
1
1
1
1
1
0
0
0
2
2
1
0
1
1
1
1
0
1
0
0
1
0
1
1
2
0
0
1
1
0
1
0
2
1
1
0
1
2
1
6
0
1
0
0
3
2
2
1
0
0
1
1
1
0
2
1
1
2
1
2
0
1
0
0
1
1
0
2
0
2
1
1
0
1
0
0
0
1
2
0
0
2
1
1
1
0
0
4
0
1
1
2
1
0
0
1
1
3
1
1
1
1
1
0
2
1
1
0
0
1
1
0
1
6
3
1
1
1
1
1
1
0
0
2
0
1
2
0
1
1
2
1
1
0
2
1
0
0
0
0
1
2
0
2
2
1
1
0
1
0
1
1
2
0
1
1
0
1
1
0
1
1
0
1
2
0
1
1
0
1
0
0
1
1
1
2
1
0
0
1
1
0
0
1
0
0
2
1
1
0
1
0
2
3
0
0
0
0
1
2
0
0
2
1
1
2
2
1
0
1
1
1
1
2
1
0
0
1
0
1
2
1
0
0
1
1
0
1
0
0
0
1
0
1
1
0
2
2
2
0
1
2
2
2
1
0
2
0
1
0
0
1
1
1
2
2
1
1
1
1
0
1
1
0
2
2
2
1
1
0
1
2
1
0
2
1
0
2
2
1
1
1
0
0
2
0
2
0
1
1
0
2
1
1
4
1
1
1
0
1
1
1
0
2
1
2
2
1
0
0
0
0
0
0
2
1
0
2
0
0
1
1
1
1
0
1
1
1
1
2
1
1
0
0
1
1
0
0
1
1
0
1
2
1
0
0
1
1
1
1
0
1
0
2
1
2
1
1
0
2
1
0
2
2
1
1
0
1
2
4
1
0
1
1
2
0
1
1
2
4
1
0
2
1
2
1
1
1
0
2
2
1
0
1
1
2
1
0
0
1
0
0
1
1
0
1
0
0
1
2
1
1
2
2
1
1
0
1
0
1
1
0
1
0
1
2
1
1
0
2
1
0
0
2
1
0
0
0
1
0
1
1
1
0
1
1
1
0
0
1
1
2
1
0
0
1
1
1
1
1
1
1
0
0
0
0
2
1
0
0
1
1
1
1
0
1
1
0
1
0
1
0
3
0
0
2
1
1
1
1
0
1
1
0
0
2
1
1
2
0
1
1
1
1
2
2
0
2
1
2
2
3
2
0
2
2
1
2
1
0
1
2
1
0
1
2
0
1
0
2
0
1
2
1
1
2
1
1
2
0
0
1
1
1
2
0
1
0
0
1
0
2
0
0
1
1
1
0
0
1
1
1
1
2
0
1
0
2
1
0
1
1
2
1
1
2
1
1
0
0
1
0
0
1
1
1
0
1
1
1
1
1
0
1
2
0
0
0
1
0
2
2
2
1
1
2
1
0
1
1
1
1
2
1
0
2
2
1
2
0
1
0
2
1
0
0
0
1
1
1
1
1
0
0
0
0
2
1
1
0
1
1
1
1
1
1
0
1
1
0
2
1
2
0
1
3
1
2
1
0
2
1
1
0
1
0
1
1
2
1
1
2
1
2
1
1
1
1
0
2
1
0
1
1
1
0
1
0
2
1
0
1
1
0
1
0
0
2
2
0
0
0
1
1
2
0
0
0
0
1
0
1
2
6
1
1
1
0
2
1
0
0
0
1
2
1
2
8
0
2
1
1
0
0
2
1
1
0
0
2
2
2
0
0
2
0
2
1
1
1
1
1
1
1
2
2
0
2
1
1
0
2
0
1
1
0
1
1
0
0
1
1
0
1
1
1
1
2
1
2
1
0
0
0
0
1
1
1
0
2
2
2
1
2
2
1
2
2
0
2
1
1
1
0
1
2
0
2
1
1
2
1
1
0
1
2
1
2
2
1
2
2
1
2
1
1
2
2
1
1
1
1
2
0
1
1
0
0
0
1
2
1
0
1
1
1
0
1
2
2
1
1
1
1
1
0
0
0
1
1
2
2
1
0
0
1
1
1
0
0
0
1
1
0
2
0
2
2
1
1
1
2
1
0
0
2
1
0
1
0
0
1
1
1
0
0
2
0
2
2
1
2
1
0
0
1
1
0
1
1
1
2
2
0
1
2
1
1
1
1
1
0
0
0
1
0
1
1
0
1
3
1
1
2
2
1
1
2
0
1
1
0
1
2
1
0
2
0
0
0
1
1
1
2
2
0
1
1
0
0
1
1
1
1
0
0
0
0
1
1
1
0
0
2
1
2
1
0
1
1
0
1
0
1
1
0
0
1
2
1
0
2
1
0
1
0
1
2
0
1
2
2
0
0
0
2
1
0
1
0
1
2
1
1
1
2
1
1
1
0
2
0
1
2
1
1
1
1
0
2
1
2
1
1
1
0
1
1
1
2
0
1
1
2
1
2
0
0
2
1
2
0
0
1
1
0
1
1
2
1
1
2
0
1
0
1
1
0
2
2
0
0
2
0
0
1
1
0
2
0
0
4
1
1
2
1
2
0
0
1
2
2
2
1
0
0
2
1
1
1
0
0
0
1
1
0
1
0
0
1
1
3
0
0
0
0
0
2
0
2
0
0
1
1
1
1
1
2
1
1
0
1
1
1
2
0
1
1
1
1
1
0
1
0
0
1
0
1
1
0
1
1
1
0
1
0
0
1
1
0
2
1
1
1
1
0
1
1
1
1
1
0
1
1
2
2
0
0
0
0
0
1
2
1
0
1
0
1
1
0
2
0
3
1
1
0
0
2
1
1
2
1
0
2
1
1
1
2
2
1
1
1
0
1
1
1
0
0
1
2
1
1
0
2
2
3
1
1
0
1
1
1
1
1
1
0
1
1
1
0
1
0
1
2
0
0
2
2
0
0
0
1
1
1
0
0
0
3
5
0
1
2
0
1
1
0
1
0
0
1
2
1
0
1
0
1
0
2
1
1
2
1
2
0
3
0
1
0
0
2
0
1
1
1
1
1
1
1
1
1
2
0
1
0
1
2
2
2
2
2
2
0
2
1
1
0
1
0
2
2
0
2
0
1
0
1
3
0
1
1
1
1
0
2
1
2
0
1
2
1
0
1
1
2
2
0
1
1
0
1
1
1
1
2
1
1
2
2
1
0
0
1
1
0
2
0
0
1
1
1
1
1
0
0
0
0
0
1
0
3
1
0
1
2
0
1
1
1
1
0
1
1
0
1
2
1
2
1
1
1
0
2
1
0
0
1
1
2
1
0
0
1
2
1
1
2
2
2
1
0
0
0
0
0
2
0
1
0
0
1
1
0
2
2
2
2
1
1
1
1
2
2
0
0
1
0
0
1
0
1
1
0
0
0
1
0
0
1
0
2
0
2
2
1
0
0
1
0
2
2
1
1
1
2
2
1
2
1
0
0
0
0
2
0
1
0
1
1
2
2
2
2
0
1
1
2
0
1
1
2
2
2
0
0
0
1
0
2
0
1
0
1
1
2
2
2
2
0
2
1
1
2
2
0
3
0
0
0
0
0
2
0
1
1
0
1
1
0
1
1
1
0
2
1
0
1
1
1
0
1
1
2
0
0
1
1
2
2
0
0
1
1
0
1
1
2
2
2
2
0
2
1
1
2
0
0
1
2
0
1
0
1
0
1
2
1
1
1
0
0
2
2
0
0
1
0
0
2
1
0
1
2
1
0
2
0
1
1
0
0
1
1
1
2
0
0
1
3
1
1
1
0
0
1
2
4
2
0
1
1
3
2
0
1
1
1
0
0
0
1
1
1
2
1
2
1
0
1
1
1
0
0
1
2
0
2
1
1
1
1
2
1
2
1
2
0
1
1
1
0
1
0
2
0
0
0
2
2
2
1
0
0
1
1
1
0
2
0
1
3
1
1
1
0
2
1
1
1
1
0
2
0
0
1
0
1
2
1
1
1
2
0
1
1
1
1
2
2
2
0
1
0
0
1
0
0
2
1
2
1
2
0
1
2
1
1
1
1
0
2
1
0
1
1
0
0
1
2
2
1
0
0
1
0
2
0
2
1
1
1
1
1
0
0
1
1
1
1
1
0
1
0
0
2
2
1
1
1
0
1
1
1
1
0
1
0
2
1
0
1
0
0
1
0
1
1
0
2
2
1
1
0
2
0
0
1
1
1
1
0
1
2
0
1
0
1
2
0
2
0
2
1
0
1
2
0
1
0
1
0
1
2
1
1
0
0
1
1
0
1
1
1
1
1
1
1
0
0
1
1
0
1
0
1
1
2
2
2
0
1
2
0
1
0
1
1
2
1
0
0
2
2
1
0
1
1
1
1
0
1
1
0
1
1
1
4
0
0
1
0
1
0
1
2
2
0
1
0
0
1
0
0
1
1
0
2
0
1
0
2
1
1
0
0
1
2
2
1
1
0
2
1
2
0
2
0
0
1
2
2
1
0
1
1
0
2
0
1
0
1
0
0
0
1
1
2
1
1
0
1
0
1
0
1
2
0
0
1
0
2
0
1
2
1
1
1
1
1
0
1
0
0
2
1
0
1
2
2
2
1
1
0
1
1
2
0
1
0
0
3
1
0
1
2
0
0
0
1
1
2
1
1
1
2
2
0
1
1
2
1
2
2
1
0
1
1
2
1
2
1
0
2
0
2
2
0
0
0
0
1
0
0
1
1
1
1
2
13
2
0
0
1
0
1
0
0
0
1
1
2
1
3
2
0
0
0
0
1
0
2
0
2
1
1
1
1
1
0
1
1
0
2
1
0
1
1
1
1
1
1
1
1
1
0
0
1
1
2
1
1
3
0
0
0
1
1
2
1
0
0
1
0
2
1
3
2
2
0
1
0
1
1
2
0
2
0
1
1
1
0
1
0
1
2
0
2
1
2
1
0
2
1
0
0
1
1
2
0
2
0
1
1
2
0
0
0
0
0
0
2
0
0
0
2
1
0
1
1
2
2
0
2
0
0
0
0
0
1
0
1
1
1
1
2
0
0
0
2
1
0
0
1
1
1
0
1
2
1
1
0
0
0
1
2
2
2
1
2
1
0
1
0
2
0
1
2
2
1
1
1
0
0
1
1
1
1
1
0
1
0
1
1
1
2
0
0
1
1
0
1
0
1
2
1
0
2
2
2
2
1
1
1
1
1
0
0
0
2
0
0
2
1
1
0
0
0
1
1
1
2
2
2
2
0
1
1
2
2
1
0
0
3
0
2
0
1
2
1
3
1
0
1
2
0
0
1
1
1
0
0
1
1
1
0
0
0
0
2
2
2
1
0
0
1
0
0
0
1
1
2
2
0
0
0
1
0
1
1
2
1
1
1
1
0
0
2
0
0
0
1
0
1
0
2
0
0
1
3
2
1
1
1
2
1
2
1
0
1
0
2
2
0
0
0
0
0
1
2
0
0
0
2
1
0
0
1
0
0
1
0
1
0
3
1
0
0
1
0
1
2
2
2
1
1
0
0
2
1
1
1
0
1
1
0
2
1
1
1
1
2
1
1
0
0
0
2
1
1
1
0
1
0
1
2
1
0
1
2
1
1
0
0
1
0
3
0
0
1
1
0
0
2
0
0
1
1
2
0
1
0
0
1
1
2
1
0
1
2
0
0
0
2
1
1
1
1
2
2
0
0
0
1
0
2
1
0
0
0
1
1
0
2
1
2
2
0
0
1
2
2
2
1
0
0
1
2
0
1
0
1
0
1
1
1
1
1
0
2
0
0
1
0
2
2
1
1
1
2
2
1
1
0
1
0
2
1
0
1
1
1
1
3
1
0
1
0
0
0
0
2
0
1
0
0
1
0
1
0
0
1
0
1
0
0
1
1
2
2
0
2
0
2
2
3
1
2
2
0
1
0
3
0
1
0
1
0
2
1
0
2
1
0
1
2
1
1
1
2
0
0
1
1
1
1
2
2
0
1
2
1
3
1
0
1
1
1
1
0
1
2
1
1
0
2
1
2
3
1
0
1
1
1
1
2
1
1
1
4
0
1
1
0
2
1
2
1
1
0
1
0
0
0
0
0
2
1
2
2
2
1
1
2
2
0
0
2
0
0
1
1
1
0
0
1
1
1
0
0
1
0
1
1
0
0
0
0
2
2
1
1
1
1
2
0
1
0
1
0
0
1
1
1
0
1
0
2
2
3
1
1
1
2
1
2
1
1
0
0
2
1
0
0
2
2
2
2
1
1
1
0
1
2
1
0
0
2
2
1
1
0
1
1
1
1
1
1
2
0
2
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
1
1
0
0
2
2
0
1
0
1
2
2
1
1
2
2
0
0
1
0
1
1
0
1
1
2
1
0
2
2
0
0
2
1
0
0
0
0
2
1
0
1
1
1
1
0
1
1
1
2
1
1
1
1
2
1
1
1
1
0
0
1
2
1
0
2
1
1
1
1
1
0
2
2
0
2
0
1
0
2
2
0
1
1
1
0
0
1
0
1
0
2
1
1
0
1
2
0
0
2
1
1
2
2
0
2
2
2
0
0
1
0
1
1
0
2
1
2
2
1
1
2
1
2
0
0
1
1
0
0
1
1
0
0
0
1
0
2
2
1
0
2
1
2
0
2
0
0
1
1
0
1
1
0
0
0
1
2
0
0
1
1
0
1
1
1
1
1
1
3
1
0
2
0
2
1
0
0
2
1
0
2
0
1
0
1
1
1
0
1
0
1
0
0
2
2
1
0
0
2
2
0
0
1
1
2
1
1
0
2
0
0
1
1
1
1
2
1
0
1
1
1
0
1
0
1
1
0
1
0
0
0
1
1
2
0
1
0
2
2
0
1
2
1
0
1
2
1
1
1
2
1
0
2
0
2
2
0
2
0
1
0
0
1
1
1
1
2
2
2
0
2
2
0
1
1
1
0
1
0
1
1
2
1
2
0
1
2
2
0
0
2
2
2
1
2
1
1
0
1
0
1
2
1
0
1
1
0
0
3
0
0
0
0
1
0
0
1
1
1
1
0
0
0
1
1
0
0
0
0
1
0
2
2
2
0
2
0
0
1
2
1
2
0
1
1
3
0
1
1
2
1
1
0
0
0
0
0
0
2
0
1
0
0
1
0
1
2
2
1
2
2
2
1
0
0
0
0
0
2
1
1
0
0
2
2
0
1
1
0
1
2
0
1
1
0
0
0
1
1
0
1
1
2
1
0
0
0
1
0
1
0
1
1
1
0
0
0
2
1
1
2
0
0
2
0
1
0
0
0
2
0
2
0
1
0
2
2
0
1
0
0
2
1
1
0
0
1
1
0
2
0
0
1
3
1
1
0
0
2
2
0
1
1
3
2
0
0
0
0
0
0
0
1
2
0
1
1
1
1
2
0
1
2
1
2
2
0
2
1
2
1
0
0
1
2
0
1
2
4
1
2
3
1
2
0
0
2
0
2
1
1
2
1
0
1
0
2
0
2
1
1
0
1
1
0
0
0
1
1
2
0
1
0
0
1
1
1
1
2
1
0
0
2
2
0
1
1
2
1
1
0
1
1
1
1
2
0
0
0
1
2
0
0
1
2
1
3
0
0
2
0
0
0
1
1
1
1
1
0
1
0
1
2
1
0
0
1
1
1
1
0
2
1
1
2
1
1
0
1
0
0
2
1
0
1
0
2
0
1
2
2
2
1
4
1
1
0
1
1
0
0
2
0
2
1
1
1
1
0
0
2
1
0
2
2
1
0
1
2
0
0
0
1
0
1
2
2
1
0
0
1
1
2
1
0
1
1
2
0
1
1
1
0
1
1
0
2
2
0
0
0
0
0
1
1
0
0
0
0
1
0
2
0
0
0
0
1
2
1
0
0
1
1
0
1
1
1
2
1
1
1
0
1
0
1
1
0
0
5
1
1
1
1
1
1
1
2
1
0
2
0
2
2
1
0
0
2
1
0
1
1
2
1
1
2
1
2
0
0
1
1
1
0
0
0
0
3
2
2
0
0
1
1
1
0
1
2
1
2
1
0
0
1
0
1
1
4
1
0
1
1
0
0
1
1
1
2
0
1
2
0
0
1
0
1
1
0
1
1
0
0
2
1
0
1
2
1
2
1
2
0
1
1
2
0
0
1
1
0
2
1
0
0
2
1
1
0
1
0
1
0
1
2
1
2
1
1
0
0
1
0
2
0
1
1
0
0
2
0
0
0
0
0
1
0
1
1
2
2
2
2
0
2
2
1
2
1
1
1
1
2
0
1
1
0
3
1
0
1
1
1
1
1
2
1
2
2
1
1
1
1
1
0
1
0
1
2
2
1
0
2
1
3
1
1
1
0
2
1
0
1
2
0
2
1
1
0
1
0
0
0
2
0
1
1
2
1
1
0
0
2
1
2
1
1
0
1
0
5
0
2
0
1
2
0
1
1
1
2
1
0
1
1
0
0
2
1
1
0
2
2
0
0
1
2
1
1
1
1
0
1
1
1
1
1
0
2
0
0
0
2
1
0
1
1
3
2
1
0
2
1
0
2
1
1
0
2
0
1
0
1
1
1
1
0
2
1
3
0
0
1
1
1
2
1
0
0
2
2
0
0
2
0
1
1
2
0
1
0
0
2
1
1
1
0
2
0
2
0
0
2
0
0
0
2
1
0
1
1
0
2
1
1
0
1
1
1
2
0
0
1
2
0
1
0
0
0
1
0
0
1
1
0
2
1
1
0
0
2
1
3
0
1
1
0
0
0
0
1
2
0
2
0
1
1
1
0
0
0
0
2
2
1
1
0
1
1
2
0
0
0
1
1
1
1
1
1
1
0
0
0
1
1
2
1
0
0
1
1
1
2
2
2
0
1
1
3
0
2
1
0
1
2
4
1
1
1
0
1
1
1
2
0
0
0
1
1
1
0
2
2
1
1
1
2
0
0
1
1
2
0
1
0
1
1
0
1
0
1
1
0
1
1
1
0
1
0
2
1
0
1
1
0
0
0
2
0
1
0
2
1
0
0
1
2
2
1
1
0
1
1
0
1
1
0
2
0
0
0
0
1
1
2
0
1
1
1
0
1
1
2
1
0
1
1
2
2
0
0
2
1
1
2
0
0
1
1
0
1
1
0
1
0
1
0
1
1
2
2
1
0
0
1
0
0
1
1
0
1
0
0
1
0
1
1
2
2
0
1
2
0
1
0
0
1
2
0
0
1
1
2
1
1
2
2
0
0
1
0
0
0
0
2
1
1
3
0
0
1
1
1
0
0
0
2
1
1
0
1
0
0
1
0
2
1
0
2
1
3
0
2
0
1
0
0
1
2
0
1
0
1
0
0
1
2
1
2
0
1
1
2
2
2
0
0
1
1
0
1
0
1
2
1
0
0
1
2
1
1
1
1
0
0
1
1
2
1
1
0
1
1
1
1
1
3
1
3
1
2
2
1
1
1
0
0
1
1
1
0
2
1
0
1
0
1
1
0
1
0
1
0
2
0
0
0
1
1
1
1
1
0
1
0
1
0
0
1
2
1
1
1
1
0
1
1
3
0
1
2
0
1
1
1
0
0
1
1
0
0
1
0
0
2
0
1
0
0
1
0
0
0
1
0
1
0
0
1
1
1
0
0
1
1
0
1
1
0
0
0
1
1
0
1
2
2
1
0
0
1
2
0
2
1
0
2
0
1
1
0
1
2
0
1
0
2
1
0
0
2
1
2
1
1
2
0
2
0
1
1
2
2
2
0
0
1
0
1
1
2
0
2
0
1
2
1
1
2
0
1
1
1
0
0
1
1
0
1
1
0
1
0
0
2
0
0
2
1
0
0
0
1
1
0
1
2
0
1
1
1
1
1
1
1
1
2
0
1
2
1
3
1
2
0
1
2
1
1
0
2
0
1
2
2
1
0
1
2
1
2
2
2
0
1
1
0
2
1
1
1
0
1
2
1
1
1
1
0
0
1
0
0
0
1
1
0
2
2
0
2
0
1
1
0
2
0
0
0
0
3
0
1
1
2
2
1
1
2
1
2
2
1
1
0
2
0
2
2
1
2
2
0
1
0
1
2
1
4
0
2
2
1
1
1
1
1
2
2
1
1
0
1
1
1
1
2
1
1
1
0
2
0
0
0
0
2
1
1
1
0
3
2
2
1
2
2
0
2
2
2
2
1
0
1
0
1
1
2
2
0
2
0
1
2
1
0
1
1
1
1
1
0
0
0
1
1
2
1
1
0
1
0
1
1
0
0
2
1
0
0
0
0
1
0
2
1
0
0
1
1
2
1
1
0
0
0
0
1
1
1
1
1
1
0
1
1
1
1
2
1
1
1
2
1
0
0
2
0
2
1
1
1
2
0
1
0
1
0
0
1
1
0
1
0
0
1
1
1
0
0
2
2
1
1
2
2
0
2
1
2
0
2
0
0
1
1
2
2
1
0
2
1
1
1
0
0
1
1
1
2
1
0
1
1
1
0
1
0
1
1
1
1
1
3
0
1
1
2
1
0
0
1
0
2
0
0
0
1
2
0
0
1
1
2
2
1
1
1
0
0
1
1
1
1
3
0
2
1
1
0
0
0
2
1
1
2
0
1
0
2
0
2
2
1
0
1
2
1
2
1
0
2
1
1
1
1
1
1
0
1
2
2
0
1
0
0
1
0
1
0
2
1
0
1
1
1
0
1
1
1
2
0
1
1
2
1
1
0
1
0
0
1
2
1
0
2
0
4
0
1
1
1
1
2
1
0
0
1
0
0
1
0
0
2
2
2
1
1
1
0
0
1
2
1
2
1
2
1
1
1
1
0
0
1
1
2
0
2
0
0
1
1
0
1
0
1
0
1
2
2
2
1
1
1
0
2
1
2
1
0
2
0
1
0
0
0
1
0
1
2
2
0
0
1
1
0
2
1
3
1
0
1
0
0
0
1
1
0
0
1
0
0
0
1
0
1
0
0
0
2
0
2
2
1
1
1
1
1
0
1
0
1
0
1
0
1
0
0
0
1
2
1
1
2
3
0
2
0
1
0
1
1
2
0
0
0
0
0
1
5
2
1
2
1
2
1
0
2
0
1
1
0
0
2
2
1
1
0
2
0
0
1
0
1
1
0
0
0
2
1
1
1
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
1
1
1
0
1
0
1
1
2
2
1
1
1
0
0
2
1
0
1
0
1
0
1
2
1
2
2
1
2
0
1
0
0
1
1
0
0
0
2
2
1
0
1
1
0
1
0
1
1
0
0
1
0
1
0
1
2
1
2
1
1
1
1
0
0
1
0
0
2
2
1
2
1
1
2
2
1
1
0
1
1
2
1
1
0
1
1
1
1
1
0
2
1
0
2
0
1
0
0
0
1
0
0
1
0
1
0
3
1
2
0
2
1
1
1
1
2
0
1
1
0
0
0
0
2
0
1
0
1
0
0
1
1
1
0
1
3
2
0
1
2
2
1
1
1
1
1
0
1
1
1
1
1
0
1
2
0
1
0
1
1
1
1
2
2
0
1
2
1
0
1
1
0
1
1
0
1
0
1
1
1
0
1
2
2
2
2
0
1
0
1
1
0
1
1
1
1
1
0
1
0
0
1
1
0
0
1
1
1
0
0
0
0
2
2
1
1
1
0
2
1
0
1
2
0
1
1
1
1
0
0
0
1
2
1
2
0
2
0
1
1
2
0
2
0
0
1
2
2
0
0
1
1
0
1
1
1
1
0
0
1
1
0
1
1
1
1
2
0
2
2
1
1
2
2
1
1
1
0
1
0
1
1
1
0
1
0
1
1
0
1
0
0
2
0
0
1
1
4
2
1
1
0
2
1
1
1
1
2
1
1
0
0
1
1
2
0
2
0
2
0
1
1
1
1
0
1
0
1
1
0
2
1
1
0
0
1
1
0
1
2
1
0
1
0
1
1
2
1
0
1
2
2
0
1
0
1
0
2
0
2
0
1
1
1
0
2
0
2
1
0
1
0
0
1
2
1
0
1
0
2
1
1
0
1
2
1
1
2
0
1
0
0
1
1
1
0
1
0
1
2
2
2
2
1
2
1
1
2
2
2
1
0
0
0
0
0
2
2
0
0
1
0
0
0
0
1
1
2
2
0
1
0
1
2
0
1
0
0
1
3
0
2
2
0
1
2
0
1
1
0
1
0
1
1
2
1
1
2
0
0
1
0
2
0
2
1
1
0
0
1
1
1
1
2
2
0
0
2
2
1
0
2
1
2
2
3
0
2
1
2
0
2
0
0
1
2
2
0
1
2
0
2
1
2
2
0
2
1
1
0
1
2
0
1
1
0
1
1
1
0
1
0
1
1
0
0
0
2
0
0
0
0
1
0
1
2
0
1
1
2
0
0
0
1
1
0
0
1
5
0
2
2
2
2
1
0
2
0
1
2
0
0
2
2
0
2
0
1
2
1
1
0
1
0
0
1
2
0
2
0
3
1
1
1
0
1
2
1
1
2
2
0
1
2
0
0
1
1
0
0
0
0
1
1
2
0
1
1
0
2
1
1
2
0
0
0
2
0
0
1
2
1
2
1
1
0
1
0
0
0
0
0
2
1
1
1
0
2
0
2
0
0
0
0
1
1
1
0
0
1
1
1
0
1
2
2
1
0
0
0
2
1
2
1
1
1
1
2
1
1
2
0
0
2
1
1
1
0
0
2
0
4
1
2
0
0
0
1
1
1
2
0
0
0
1
2
0
0
0
0
2
2
2
1
0
0
1
0
1
1
1
0
1
1
1
2
1
1
2
0
1
0
2
2
2
2
0
0
1
1
1
2
1
1
0
2
0
0
1
0
0
2
1
1
1
1
0
0
2
0
1
0
0
2
2
0
0
2
2
2
0
1
1
1
0
0
1
2
1
0
1
1
1
1
1
0
2
1
2
0
0
1
0
2
2
1
0
1
2
0
1
1
1
0
1
2
1
1
2
0
0
1
0
2
1
1
1
1
1
1
0
2
1
1
1
3
0
2
0
0
0
0
0
0
0
0
1
1
1
0
1
1
0
0
1
1
0
1
0
2
1
2
0
1
1
0
0
1
2
2
0
2
2
1
1
0
0
1
0
1
1
1
2
0
1
2
1
1
0
1
1
0
0
1
0
0
2
0
1
0
0
2
0
0
2
2
0
0
1
0
1
3
1
0
0
2
0
0
0
0
2
2
1
2
0
1
0
1
2
0
2
0
0
1
0
2
2
2
0
0
1
2
0
0
0
0
1
1
0
0
1
0
0
1
0
0
2
0
3
1
2
1
1
1
0
2
0
1
1
1
1
1
0
1
2
1
0
0
1
1
1
1
1
2
0
1
1
1
1
2
1
2
1
1
1
1
2
1
1
0
1
2
1
0
1
0
3
1
1
1
0
2
2
2
4
1
1
1
0
2
0
0
0
1
2
2
1
0
1
1
1
1
2
2
0
1
2
0
2
1
1
0
1
0
1
0
2
0
1
1
0
1
1
1
2
1
0
1
2
1
1
1
1
1
1
2
0
0
2
0
2
0
0
0
2
0
3
1
2
1
1
0
0
1
2
0
0
1
1
1
1
1
2
0
1
1
2
1
1
0
1
1
1
1
1
0
2
2
1
0
0
0
2
2
2
0
1
2
0
1
0
0
1
3
1
2
1
1
1
1
3
0
2
0
1
1
1
2
1
2
1
1
0
2
1
2
0
1
2
2
1
0
1
1
0
1
1
2
1
1
1
2
1
0
1
1
1
1
2
2
2
1
1
1
0
0
1
1
2
0
1
2
2
0
1
1
0
2
1
1
1
1
2
0
3
1
2
0
1
1
1
3
2
1
0
1
1
0
2
2
1
1
0
0
0
2
1
0
1
1
0
1
2
1
0
1
2
1
1
2
0
0
0
0
1
1
1
3
1
2
0
1
0
1
1
1
1
0
2
1
0
0
1
0
1
2
1
1
1
2
0
1
2
1
1
0
2
0
1
0
1
2
0
2
1
0
0
1
3
2
1
1
0
0
0
2
0
2
0
1
1
1
2
0
1
1
0
0
2
2
1
0
0
0
1
0
0
1
3
2
2
0
1
1
1
1
1
0
1
1
0
0
1
0
1
1
0
1
0
1
2
1
0
2
1
0
0
2
0
2
0
0
1
0
0
1
0
0
2
1
1
1
4
1
2
1
1
1
1
2
0
2
0
1
1
1
1
3
2
1
0
2
2
0
0
1
2
0
2
2
0
1
0
0
2
2
0
0
0
0
1
1
1
1
1
1
0
2
2
0
1
0
1
1
1
2
1
1
1
2
2
1
0
5
1
2
0
0
2
2
0
1
2
1
0
2
1
0
1
3
0
0
1
0
1
1
2
0
1
1
0
0
5
1
0
0
1
2
1
1
1
2
2
2
1
0
0
0
1
2
0
1
1
1
0
1
2
1
0
1
0
0
0
0
1
0
0
2
0
2
1
1
0
2
1
1
2
4
1
2
1
0
1
0
1
0
1
1
2
1
1
1
2
1
0
2
0
1
0
1
1
1
2
0
0
1
1
1
1
1
1
2
1
0
0
1
1
2
1
1
0
1
0
1
2
1
1
2
2
0
1
2
1
0
2
0
0
1
0
1
0
1
2
1
1
2
1
1
2
2
2
0
0
2
0
1
0
1
2
5
2
1
1
1
0
2
1
0
2
2
1
2
0
1
1
2
0
0
1
1
2
0
2
0
0
2
0
1
2
2
0
1
5
1
0
0
1
1
1
1
2
2
1
2
1
0
1
0
1
0
2
1
1
1
2
1
1
1
1
1
1
0
1
1
2
0
0
2
1
2
0
1
1
2
0
1
0
1
1
1
2
0
1
2
0
1
1
1
1
1
1
2
1
1
2
1
1
1
0
2
0
1
1
2
1
3
0
1
1
1
1
0
0
1
1
1
1
0
2
1
1
0
1
2
0
0
0
1
1
1
1
2
0
1
1
1
1
1
0
0
0
1
0
1
0
1
1
1
1
0
0
0
1
1
1
1
0
0
0
2
0
0
0
0
0
2
2
0
1
0
0
1
1
0
2
1
2
0
0
1
1
1
1
1
0
1
1
1
1
1
0
2
1
0
1
1
0
0
0
1
1
1
2
2
1
1
2
0
0
1
1
0
1
2
0
1
1
1
2
1
0
1
1
0
0
2
0
0
0
0
1
1
1
0
0
0
1
0
0
0
2
0
2
0
1
0
0
1
1
1
2
2
1
0
1
5
1
2
2
0
0
1
0
0
2
0
0
0
5
1
0
0
2
1
2
2
1
1
0
2
1
0
0
2
2
1
0
1
0
0
2
1
1
1
0
1
3
0
1
0
2
0
2
0
0
1
2
0
1
1
0
0
0
2
2
0
0
1
2
1
2
1
6
1
1
2
1
1
0
0
1
1
0
3
1
1
1
1
2
1
0
1
2
2
0
3
2
0
2
1
1
1
2
2
2
0
1
2
1
1
1
1
0
1
0
2
1
2
1
1
1
1
0
0
1
0
1
2
0
2
1
1
1
1
0
0
2
0
1
1
0
1
0
2
0
1
0
1
0
1
1
1
0
1
4
1
1
0
1
0
0
1
0
1
0
1
0
0
1
1
0
1
2
1
1
0
1
2
0
2
1
0
0
0
2
1
0
1
1
0
0
2
0
1
0
0
0
1
0
0
1
1
1
1
0
1
2
0
1
2
0
0
1
1
3
0
0
2
1
2
3
2
1
2
2
2
0
1
2
2
2
1
0
1
2
0
1
0
1
1
2
1
2
1
2
0
0
0
2
0
0
0
1
0
2
0
1
1
2
0
1
0
2
1
1
0
1
2
2
1
1
1
2
1
0
0
1
2
1
2
2
0
0
1
2
2
3
0
2
0
1
2
1
0
2
1
0
0
3
1
1
0
0
1
2
0
2
0
1
0
1
1
1
0
1
1
1
1
0
0
0
0
1
1
0
1
0
1
0
0
0
0
1
1
1
1
1
1
1
1
2
0
1
0
0
1
0
1
0
1
0
1
1
0
0
2
0
2
2
1
2
1
0
1
0
2
0
0
0
1
2
1
0
1
0
3
1
0
2
2
0
1
0
1
1
1
0
1
1
1
0
2
1
1
1
0
0
1
2
0
0
0
1
1
2
0
1
2
2
1
0
2
1
0
0
1
0
1
0
0
0
2
0
2
1
0
1
1
1
0
1
2
1
1
1
1
1
1
0
1
1
2
2
0
0
0
1
2
0
0
2
1
1
1
0
0
1
0
1
2
1
1
0
1
1
0
5
2
0
0
2
1
1
2
2
1
1
1
2
2
0
2
1
1
0
1
1
3
1
0
2
2
1
1
0
1
1
0
2
0
1
1
1
1
1
1
2
1
0
2
1
0
2
1
1
0
0
1
0
2
0
1
1
1
0
0
0
0
2
0
2
1
1
1
1
2
1
0
1
2
0
1
0
2
1
0
2
2
0
2
0
0
1
0
1
1
2
2
1
0
0
1
2
2
1
2
1
1
1
2
1
1
0
0
0
1
1
2
1
0
0
4
0
1
0
0
3
1
0
1
0
2
2
2
1
2
0
1
0
2
2
0
1
1
1
1
2
0
2
1
2
2
1
1
1
0
1
0
1
1
3
1
1
0
1
2
1
1
0
0
2
0
0
1
1
0
0
1
1
0
0
0
1
1
2
2
0
0
2
1
2
2
1
2
1
1
0
1
1
1
0
0
0
0
2
2
0
0
1
0
2
1
1
1
2
1
2
1
0
1
3
1
0
0
2
2
1
1
1
0
2
2
0
3
1
2
0
1
1
0
0
0
0
0
1
0
1
1
0
0
2
0
1
0
2
0
2
0
1
1
2
1
1
0
2
1
1
1
1
2
0
3
1
2
0
2
0
0
0
1
1
1
1
1
1
2
0
2
0
2
0
0
1
1
1
0
2
2
1
1
0
0
0
2
1
1
2
1
1
1
1
1
0
2
0
0
2
1
1
0
1
0
1
0
1
0
1
2
1
0
1
0
2
1
1
0
1
2
1
0
2
2
1
0
1
0
1
1
0
1
2
0
1
1
0
1
1
1
0
2
1
1
0
0
1
1
1
0
2
1
1
2
2
1
1
1
0
0
1
0
1
0
2
2
0
0
1
0
2
1
1
1
0
0
0
1
0
1
1
0
1
1
1
2
1
1
0
1
2
1
1
1
1
1
1
0
0
1
1
1
0
0
1
2
0
2
0
1
2
0
0
3
1
0
2
2
2
0
2
2
1
0
1
1
2
2
0
2
0
1
3
1
0
0
2
1
1
1
0
0
2
2
0
1
0
0
2
0
0
2
1
3
0
2
1
2
1
2
1
1
1
1
1
2
1
1
2
0
1
0
0
1
3
0
0
2
1
1
0
0
2
0
0
1
0
0
1
2
1
1
1
3
2
1
1
0
2
2
0
0
2
2
1
1
0
1
0
1
2
1
1
0
2
0
0
1
1
1
1
1
1
1
1
1
1
0
2
1
1
0
2
1
1
2
1
0
2
1
2
0
0
1
0
2
1
0
1
1
0
0
1
1
0
0
1
0
2
0
2
0
1
0
2
0
2
2
1
0
1
0
0
0
1
1
0
1
1
0
0
1
0
2
1
1
1
0
2
0
1
0
0
2
2
1
3
0
0
1
1
1
3
1
0
2
0
0
1
0
1
0
0
0
1
0
1
0
1
0
0
1
0
1
0
2
0
2
0
0
0
0
2
0
1
0
0
0
1
2
0
2
0
0
2
1
2
0
0
1
1
1
1
0
1
1
1
2
0
0
1
2
0
1
0
0
2
0
2
1
1
1
1
0
1
1
0
2
0
2
0
2
2
1
1
1
0
1
2
1
0
0
1
0
1
1
1
2
0
2
0
2
1
3
0
1
3
0
0
0
0
1
1
2
0
1
2
1
2
1
1
2
0
0
1
0
1
0
1
0
1
1
0
0
0
3
1
1
4
1
1
0
1
2
0
2
1
0
2
10
0
2
1
1
1
1
2
0
1
1
2
1
1
1
0
0
1
0
2
1
1
1
2
1
0
2
1
1
2
1
0
0
2
2
1
1
2
1
1
2
1
1
1
0
1
0
1
0
1
1
0
2
0
0
1
1
0
0
6
2
0
1
1
2
0
0
1
2
2
0
2
0
1
1
2
0
1
2
2
1
0
0
1
1
1
0
0
2
0
2
2
1
2
0
0
0
2
0
2
1
0
0
1
0
2
0
0
1
0
1
1
1
0
0
0
2
2
0
0
0
1
1
1
1
0
1
2
0
1
2
1
0
1
1
1
0
1
2
2
0
2
1
2
0
1
1
2
0
2
0
0
0
0
0
1
2
2
1
1
4
1
2
1
1
1
1
1
0
1
2
2
1
2
0
1
0
1
0
0
2
0
1
0
2
2
1
0
0
3
2
1
0
1
2
1
1
0
0
0
1
1
0
0
0
1
3
2
0
1
2
2
1
1
0
2
1
1
0
1
0
1
1
0
0
0
1
1
0
1
1
1
2
1
0
2
1
1
1
2
1
3
2
1
1
0
1
0
1
2
0
0
1
1
0
2
0
0
0
0
0
1
1
2
0
0
0
0
0
1
0
2
2
2
1
2
1
1
1
1
1
2
0
1
1
1
1
0
1
0
0
1
1
0
0
1
2
3
2
1
1
2
0
0
1
2
1
0
2
2
1
1
1
0
1
1
0
1
1
1
0
2
2
1
0
1
1
2
1
2
2
1
0
0
1
2
2
2
0
2
0
2
1
2
3
6
0
1
0
0
0
0
0
2
0
2
0
1
0
0
0
2
0
4
0
1
1
2
0
0
1
0
0
1
0
2
1
0
1
2
0
0
1
0
0
1
1
2
0
0
1
1
1
0
0
1
1
0
1
0
2
1
0
1
1
1
0
1
1
1
1
1
0
1
1
1
0
2
0
0
1
0
2
0
0
0
1
0
2
2
0
0
1
1
1
1
1
0
2
0
0
1
1
1
2
2
0
0
0
0
1
0
1
0
2
0
3
2
1
1
0
0
1
0
0
3
2
0
1
1
0
2
0
1
1
1
0
1
0
1
0
0
0
3
0
2
1
2
0
2
0
1
0
2
0
3
1
2
2
2
1
2
0
1
0
2
0
2
0
0
0
1
0
1
1
0
1
0
4
0
1
2
0
1
0
2
1
2
1
0
0
0
1
1
1
0
0
0
0
1
2
1
1
2
0
1
2
1
0
1
1
1
2
1
1
0
2
1
2
0
2
1
0
2
1
0
1
0
1
1
1
1
2
1
1
0
1
1
1
1
2
0
0
1
2
1
0
0
0
0
0
1
0
0
0
2
1
0
0
1
1
1
1
2
0
1
0
0
0
1
2
1
0
0
0
1
0
1
1
1
2
0
1
0
0
1
0
0
1
2
1
1
0
2
1
1
1
1
0
1
0
0
1
1
0
2
0
1
2
0
2
0
2
0
1
0
2
1
2
0
1
0
1
0
5
1
2
1
1
2
1
2
1
2
2
0
1
1
2
2
0
0
0
0
0
0
2
1
1
0
0
3
1
1
1
0
1
2
2
1
2
0
2
0
2
1
1
1
0
2
1
0
0
1
2
1
2
0
0
2
0
1
0
1
0
0
2
1
0
1
1
2
1
1
2
2
1
2
2
1
1
2
0
1
2
1
1
2
2
0
1
1
1
2
1
2
1
1
0
0
2
2
2
1
1
0
1
0
2
1
2
1
0
1
1
1
1
1
1
1
1
0
0
2
2
1
1
2
2
1
2
1
1
0
1
1
0
1
0
2
1
2
0
2
1
1
1
0
1
2
0
2
0
1
0
1
0
1
0
2
1
0
1
1
0
1
1
2
2
1
1
1
1
1
0
1
0
1
0
0
1
1
1
1
1
2
2
1
1
1
1
2
1
0
0
1
1
2
2
0
2
0
0
0
1
0
1
1
2
0
1
1
0
1
2
0
1
5
1
1
1
0
4
0
2
2
1
1
2
2
2
0
1
1
0
1
1
3
0
0
1
0
1
0
1
0
1
1
1
0
2
2
2
2
2
2
1
2
1
1
1
0
1
0
0
1
0
0
0
1
1
0
0
2
1
2
1
1
2
0
0
0
1
0
2
0
0
0
1
0
1
2
1
2
1
0
1
0
1
0
2
1
2
1
1
2
2
0
2
0
0
0
1
0
1
0
0
2
1
1
2
1
1
0
1
0
2
1
0
0
2
0
1
0
1
1
1
1
1
1
1
2
1
2
0
1
0
2
1
1
0
1
0
0
0
1
1
2
1
1
0
0
1
0
1
1
1
2
1
1
0
1
0
2
0
0
2
0
1
0
1
3
1
1
1
0
2
1
0
1
1
1
1
0
1
2
3
1
1
1
1
1
1
1
0
2
0
0
0
1
2
1
1
1
1
1
0
0
1
0
1
1
1
1
2
2
1
2
0
1
0
1
0
2
0
1
2
1
0
1
0
1
0
0
0
1
2
0
1
0
1
1
0
0
1
1
1
1
1
1
1
1
1
0
1
2
0
0
0
1
1
1
0
1
1
0
1
1
1
0
0
1
0
2
2
0
0
0
0
1
0
3
1
0
0
1
0
1
0
0
0
1
0
1
2
0
1
1
1
1
1
1
1
1
1
0
1
2
1
1
1
0
4
1
1
1
1
1
3
0
0
0
0
0
0
2
2
1
1
1
0
3
2
0
0
2
1
0
2
1
1
0
0
2
2
2
1
1
2
0
0
1
1
0
0
1
1
0
1
0
0
0
2
2
1
0
1
1
1
3
2
2
6
1
1
0
2
0
0
1
0
0
0
0
3
1
2
2
1
0
2
1
1
1
2
1
2
1
0
2
1
2
1
0
0
0
0
0
1
2
1
0
0
1
0
0
1
0
0
1
1
1
2
0
0
0
2
1
1
1
1
2
2
1
0
3
1
1
1
2
1
0
2
0
0
1
2
1
0
0
0
0
0
2
0
1
1
0
1
2
1
1
0
0
1
1
1
1
1
1
1
1
1
0
1
2
0
2
0
1
1
1
1
0
2
2
0
0
2
2
1
0
1
0
0
1
0
2
1
1
2
1
1
0
0
1
0
1
2
2
1
0
1
1
0
2
0
2
2
0
0
1
4
1
1
0
0
2
0
1
0
0
1
0
1
1
2
1
0
0
1
1
0
1
1
1
1
1
1
1
0
1
1
0
1
0
1
0
1
1
2
2
1
0
0
0
2
1
0
1
1
0
0
1
0
2
0
1
0
1
0
0
0
0
2
1
0
0
2
1
0
1
0
1
1
2
2
1
3
1
0
2
1
0
1
1
1
0
1
1
0
0
0
0
1
1
1
1
1
1
0
0
0
0
0
1
1
1
1
2
0
1
1
0
2
2
0
1
1
2
2
1
0
1
0
0
1
0
0
1
2
1
0
1
0
2
1
1
0
0
2
0
1
1
1
1
0
2
1
1
1
1
1
0
2
1
1
1
2
1
0
1
2
1
1
4
2
2
0
0
1
0
2
0
0
1
0
0
2
1
2
1
1
2
1
0
1
1
0
0
0
2
1
2
2
1
2
0
0
1
1
2
1
2
2
0
1
2
0
1
1
1
2
0
0
3
2
1
1
1
1
1
1
3
0
3
0
2
1
2
1
1
1
1
0
1
0
1
1
1
0
1
2
0
0
2
1
1
0
2
1
0
0
1
1
0
1
3
0
0
2
1
1
1
1
1
0
0
0
0
0
1
0
2
2
2
1
1
2
1
0
0
1
0
0
2
1
1
1
1
1
0
1
0
2
1
0
1
2
1
1
2
0
2
1
1
0
0
0
2
1
1
0
2
2
1
1
1
1
2
2
0
0
0
1
2
1
1
0
1
1
0
1
0
1
2
0
2
1
0
0
1
0
2
2
3
0
2
1
0
1
2
0
1
0
1
4
1
2
3
0
0
3
2
0
0
1
0
2
1
1
2
2
0
1
0
2
1
2
2
2
1
1
1
0
0
0
2
2
1
1
1
1
0
0
0
1
1
4
1
3
2
1
1
0
0
2
0
0
2
1
1
1
1
2
1
0
2
1
1
0
0
0
2
1
1
3
1
0
1
1
2
1
3
1
2
1
0
1
0
0
2
0
1
0
1
1
0
0
0
2
0
1
0
1
0
1
1
1
2
0
2
0
1
0
1
0
2
3
1
1
1
1
2
0
1
1
0
1
0
0
0
1
0
0
0
2
0
0
0
1
2
1
2
0
2
1
2
1
1
1
1
2
2
1
0
1
0
2
1
0
2
1
0
2
2
0
1
1
1
1
1
0
0
1
1
0
2
0
2
1
1
2
1
0
1
0
0
0
0
1
0
1
1
3
1
0
1
1
1
2
2
1
1
1
1
2
1
0
0
0
2
1
1
1
0
1
1
2
4
0
0
2
1
1
1
2
2
0
2
0
1
1
0
0
0
1
0
0
1
1
1
0
1
1
0
2
1
1
1
2
1
1
0
0
2
1
1
0
2
1
1
2
1
0
0
1
1
1
1
2
0
1
0
0
0
0
1
2
2
0
2
0
0
0
2
2
2
1
1
0
1
1
0
0
2
2
1
1
1
2
1
1
1
1
2
1
1
2
2
0
1
2
0
2
2
0
2
1
2
0
0
0
1
2
1
1
1
2
2
1
1
0
2
0
1
0
0
1
2
1
0
2
0
1
1
1
3
2
0
1
3
1
2
0
0
1
1
0
1
1
0
1
2
0
2
1
0
1
2
0
0
0
6
0
0
0
0
0
2
1
2
2
2
1
0
1
1
2
2
2
1
2
1
1
0
2
0
2
1
0
0
0
5
0
1
0
2
0
0
2
1
0
0
0
1
2
1
0
1
0
2
0
0
0
2
2
2
0
0
0
1
1
1
1
0
2
1
2
1
2
0
1
2
0
1
1
0
1
1
0
0
1
1
1
0
1
1
1
2
0
1
1
1
1
0
0
1
1
0
3
1
2
1
1
0
0
3
0
1
2
0
1
2
0
2
0
0
2
2
2
2
1
1
1
1
1
1
0
0
1
0
1
0
3
2
2
0
0
0
2
0
2
0
1
1
1
2
1
2
1
1
1
1
1
3
2
0
2
0
0
1
1
1
0
0
1
0
1
2
0
0
0
0
1
2
0
0
1
2
0
1
1
1
0
1
1
1
0
0
1
0
0
1
1
2
0
1
2
2
0
0
2
1
2
1
1
0
0
1
2
2
0
1
0
1
0
1
1
1
0
1
1
2
2
1
1
1
0
1
1
0
1
2
0
0
1
2
0
2
1
1
1
1
1
1
0
2
1
0
1
1
1
0
0
1
1
0
1
0
2
0
0
1
2
1
2
2
1
2
2
2
0
1
1
0
1
2
0
1
1
1
2
1
1
1
2
1
2
2
0
0
2
1
1
0
1
2
2
1
1
1
1
1
0
2
0
2
1
1
0
1
1
1
1
0
0
1
1
1
1
1
2
1
0
0
3
0
2
0
1
1
1
2
0
0
2
1
1
0
1
2
1
0
1
1
0
1
2
0
0
0
2
1
2
2
1
0
0
1
1
2
0
0
0
1
2
1
1
0
0
0
1
1
0
0
3
1
2
0
0
2
0
1
0
2
1
2
2
0
1
1
0
1
2
1
1
3
2
2
1
0
2
2
1
1
0
1
0
0
1
0
1
1
0
1
2
2
0
2
1
1
1
0
2
1
1
0
0
2
0
1
0
0
1
0
1
2
0
1
2
2
1
3
0
1
1
1
2
2
1
0
0
0
1
1
1
1
1
1
1
0
0
2
2
2
0
1
0
2
2
0
0
0
1
1
0
1
2
0
1
1
1
1
2
2
0
0
0
2
1
0
1
1
1
0
1
2
0
0
1
1
2
0
2
0
1
1
1
0
2
1
1
0
0
1
0
1
0
2
1
1
0
1
1
0
0
1
2
1
3
1
0
1
2
0
1
1
0
1
2
1
1
0
1
0
0
0
1
3
2
0
0
0
1
0
1
1
0
0
1
1
2
1
0
2
1
0
2
1
1
2
0
0
1
1
1
2
2
1
0
0
2
0
0
1
1
1
0
1
2
1
1
1
0
1
2
2
2
2
0
2
0
2
1
1
2
2
1
2
1
0
0
0
2
1
1
1
0
0
0
0
1
2
1
1
1
1
1
0
1
1
0
0
2
0
2
2
1
1
2
1
1
1
1
1
2
1
2
0
1
1
0
1
1
2
0
1
0
1
2
0
1
1
0
1
1
2
0
0
1
0
1
0
1
1
0
0
0
0
1
0
1
1
1
0
1
0
0
1
2
0
1
0
2
0
2
0
1
1
2
1
1
0
0
3
4
0
0
2
0
2
1
0
1
0
1
1
1
1
1
2
1
0
1
1
0
0
0
1
0
1
1
1
1
2
0
2
0
0
0
2
1
0
1
2
1
0
0
2
0
1
2
0
2
1
0
1
0
1
1
0
2
0
1
1
1
1
0
1
1
1
1
2
1
0
2
1
1
0
0
0
2
1
2
2
0
2
2
0
1
1
2
0
2
0
0
0
2
0
2
1
1
1
0
0
1
1
1
1
2
1
0
2
1
2
1
2
0
2
1
3
1
1
1
0
2
0
1
0
0
2
1
4
0
2
0
1
1
0
0
1
0
1
0
0
1
0
0
2
1
2
1
2
1
1
1
0
0
1
0
1
1
1
1
2
0
0
1
1
1
0
2
0
0
0
1
0
2
1
1
0
0
0
1
0
0
1
1
2
0
4
2
0
0
1
0
2
1
1
2
1
0
2
0
1
2
0
1
2
0
0
0
1
2
6
1
1
2
0
0
0
0
1
2
1
0
1
1
0
0
1
0
1
1
2
1
2
0
2
0
0
0
2
0
1
0
1
2
0
0
1
0
0
2
0
1
0
1
0
1
2
0
1
0
1
1
1
1
1
1
2
2
1
1
0
0
1
1
1
1
1
0
1
1
1
1
2
1
2
0
0
1
1
1
2
0
2
0
0
0
2
0
1
0
1
1
0
1
0
1
2
0
1
0
2
0
2
2
2
1
2
1
0
0
0
0
1
1
0
1
5
2
0
1
1
0
1
1
1
0
0
1
0
1
0
1
1
0
1
1
0
2
0
2
2
0
1
0
2
1
0
0
0
1
1
0
1
0
1
1
1
1
0
0
0
1
2
0
1
1
1
0
1
2
1
1
1
2
3
1
0
2
1
0
2
1
2
1
0
1
2
1
2
1
1
1
0
0
1
0
2
1
2
0
2
0
0
1
1
1
0
0
1
0
1
0
1
1
1
1
2
2
1
2
1
1
1
0
0
2
1
0
2
0
1
1
1
1
2
1
0
4
0
2
2
0
1
2
2
1
2
2
4
1
1
2
2
1
0
0
1
0
1
0
1
1
0
2
0
1
0
0
1
0
0
3
2
0
1
0
3
1
0
1
2
0
0
1
2
0
0
1
1
0
0
2
1
1
0
2
0
1
0
1
0
0
1
2
2
0
1
1
0
0
1
2
0
2
2
0
2
0
2
0
1
1
0
1
2
0
2
1
1
0
2
1
1
1
0
1
1
0
1
1
0
1
0
2
2
0
0
1
2
0
1
1
0
1
1
0
0
1
2
1
1
1
2
1
2
1
0
0
1
1
0
2
1
0
0
1
3
1
0
1
1
1
1
1
0
1
1
2
2
2
0
1
0
0
0
0
0
1
1
1
0
1
1
0
1
0
1
1
3
0
1
1
1
0
0
1
1
1
0
0
0
1
2
0
2
2
0
2
2
0
0
1
1
0
1
4
1
0
2
0
0
1
0
0
0
1
0
2
2
0
2
0
1
1
1
1
1
1
1
0
2
0
0
1
1
1
2
2
0
1
2
1
0
1
1
1
1
1
1
1
2
1
1
0
0
1
1
0
2
1
1
0
0
1
2
0
0
1
0
1
2
0
1
0
0
1
1
1
2
1
2
2
2
1
0
1
0
2
1
2
1
2
0
0
0
0
0
1
0
0
0
1
1
1
2
0
1
1
1
0
1
1
2
1
2
2
0
1
1
1
1
2
0
0
1
2
0
1
2
2
3
1
2
1
0
1
0
1
0
1
2
0
2
1
1
0
1
1
2
0
0
2
0
1
1
0
0
0
1
1
2
1
1
1
0
0
1
0
2
0
2
0
2
2
0
0
2
2
2
1
2
2
1
2
0
1
2
1
0
2
0
2
2
0
2
0
1
2
2
1
0
2
1
2
0
2
0
0
1
0
1
1
0
1
2
1
2
2
0
1
2
1
0
2
1
0
1
0
1
0
0
0
2
2
1
1
0
2
0
1
0
0
7
2
1
2
2
0
0
0
1
1
0
0
2
0
1
1
1
1
0
2
1
0
0
0
2
1
2
0
1
1
0
2
1
2
1
1
0
0
2
1
0
1
2
1
1
1
2
0
1
2
1
1
0
0
0
1
2
1
1
2
1
1
1
1
2
1
2
0
0
0
0
1
0
1
0
1
1
1
0
1
1
1
0
0
0
1
1
0
0
0
1
2
1
2
0
0
1
1
1
0
2
2
1
2
2
1
2
1
0
2
2
0
1
2
0
1
1
1
0
0
1
1
1
3
1
0
0
0
0
1
0
0
0
1
2
0
1
1
0
0
1
0
1
1
2
1
1
1
1
2
1
2
0
0
0
1
0
1
1
2
1
1
2
1
1
0
2
0
2
1
1
2
1
0
0
1
0
1
1
1
0
2
0
2
0
1
2
0
1
0
1
1
1
2
0
1
0
0
0
2
0
0
1
2
2
0
2
1
2
0
0
1
0
0
1
0
2
0
2
2
0
1
1
1
2
1
1
2
0
1
1
2
0
1
0
1
2
1
1
1
1
2
0
2
1
0
1
0
2
2
1
2
0
1
1
1
0
2
0
0
1
2
1
0
1
0
1
2
0
1
1
0
0
1
0
0
0
0
2
1
0
1
0
1
1
1
0
1
1
1
1
0
1
1
2
2
1
2
0
0
1
1
1
0
1
0
0
1
0
2
0
2
1
0
1
0
1
0
0
0
1
2
1
1
0
2
0
1
0
0
1
1
0
0
0
2
2
1
1
0
2
1
0
0
1
0
0
0
1
2
1
0
1
0
0
0
1
2
2
0
0
0
2
0
2
0
1
1
1
1
1
1
1
0
1
2
1
0
1
0
2
1
1
2
1
1
1
2
1
2
1
1
1
0
1
0
1
1
1
0
1
0
1
1
1
1
1
0
2
2
1
1
0
1
2
1
1
0
1
1
0
1
0
1
0
0
2
1
1
1
1
0
1
1
2
0
0
1
2
1
0
1
0
1
1
2
1
0
0
1
0
0
1
2
2
0
0
1
1
0
1
0
2
1
0
1
1
0
1
2
0
0
1
1
0
1
0
2
2
1
0
0
0
0
1
0
0
2
2
2
1
0
2
0
0
1
0
1
1
2
1
2
1
2
0
1
1
1
2
2
1
1
2
0
0
2
0
1
1
0
1
1
1
0
1
0
1
0
2
0
0
1
1
2
1
1
2
2
1
0
1
1
0
1
0
0
1
2
2
2
2
0
1
1
2
2
2
1
0
0
2
2
0
1
1
1
0
0
1
0
1
0
2
1
1
2
0
1
1
1
2
0
0
1
1
1
2
2
1
3
0
2
1
1
0
1
1
3
3
0
0
1
2
0
0
1
0
4
1
1
3
2
2
1
0
0
0
2
1
0
1
0
1
2
0
1
1
2
1
2
1
0
1
0
1
2
1
1
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
2
1
1
0
2
0
1
0
0
2
0
2
1
0
0
2
1
1
0
0
2
1
1
2
1
1
2
1
1
2
0
0
1
0
0
1
2
1
2
2
2
2
0
1
1
0
1
0
1
2
0
0
0
2
0
0
1
3
0
0
0
1
1
1
1
1
0
2
0
3
1
1
1
2
0
2
1
0
2
1
1
1
2
0
0
1
0
0
3
1
1
1
1
1
0
1
0
0
0
0
1
0
3
2
0
0
1
2
0
1
1
1
1
1
0
1
0
0
2
1
1
2
1
2
2
0
1
0
0
1
0
0
0
1
1
1
2
1
2
0
2
2
0
2
0
2
1
0
2
2
1
2
0
2
0
2
1
1
1
0
2
1
1
1
0
1
2
3
1
2
1
1
2
1
2
1
1
2
0
1
1
0
0
2
2
0
0
2
0
1
0
1
2
1
1
1
1
1
1
0
0
1
1
1
3
0
1
1
0
1
1
1
0
1
0
0
12
0
0
0
1
1
0
0
1
0
2
1
1
1
1
1
0
1
1
1
1
2
0
1
1
1
1
2
1
1
1
0
1
0
0
0
1
0
0
1
0
2
2
1
0
1
1
0
1
0
0
0
1
2
1
0
0
0
1
0
0
0
1
2
0
1
0
1
1
1
1
0
1
1
0
0
1
0
1
0
0
2
0
0
1
1
1
1
1
0
0
0
1
0
1
1
2
1
2
0
1
0
1
1
0
1
0
1
1
1
1
1
1
2
0
1
1
0
1
1
0
1
0
1
1
2
0
2
2
1
2
1
1
1
2
1
1
2
0
0
0
2
1
1
0
1
0
1
2
1
0
0
0
1
0
1
1
1
0
2
0
2
1
1
1
1
0
2
2
1
1
1
1
1
1
1
0
1
0
1
0
1
0
2
1
1
1
1
1
1
1
2
1
2
1
0
0
1
1
1
1
0
1
1
0
2
0
1
0
1
0
1
0
0
2
1
0
0
0
1
0
1
1
1
0
0
1
1
2
1
0
1
2
0
0
1
0
1
1
1
0
0
0
1
2
1
0
1
0
2
0
2
0
0
0
2
1
2
0
0
1
1
0
2
1
0
1
0
1
0
0
1
1
1
1
1
1
0
0
0
1
1
1
2
0
2
1
2
4
2
1
0
1
1
1
1
1
3
1
1
1
0
1
1
0
0
1
2
1
0
2
2
2
0
0
1
0
2
0
2
0
2
0
1
1
0
1
0
0
2
2
1
1
0
1
1
0
1
0
0
0
1
1
1
0
0
0
0
2
1
2
0
1
1
1
2
1
1
1
1
2
0
0
2
1
0
2
1
1
2
1
0
2
2
1
0
1
2
1
2
1
0
3
2
1
0
1
0
1
1
1
0
1
2
1
3
3
0
0
0
1
1
0
1
2
1
0
1
1
1
2
2
0
1
0
1
1
1
2
2
1
1
1
0
2
0
0
1
0
1
1
0
1
1
0
2
1
0
1
2
0
2
0
1
0
1
2
1
1
1
1
0
2
1
1
1
0
2
1
0
0
0
0
0
1
0
0
1
0
2
1
0
0
0
3
1
0
2
0
0
1
1
2
0
2
0
1
2
0
0
1
0
2
0
2
0
2
1
5
1
1
0
1
1
0
1
3
2
2
1
2
1
1
0
2
1
1
0
1
1
1
0
1
1
2
0
0
2
0
1
0
0
1
2
0
0
2
0
1
2
1
1
0
2
1
0
2
1
2
1
2
0
0
0
1
0
2
1
1
0
1
1
2
1
1
0
3
1
1
2
0
0
1
0
2
1
2
2
0
1
0
0
1
0
0
0
0
2
2
1
0
0
1
0
0
1
1
1
0
0
1
2
0
0
1
2
2
2
1
1
1
1
1
2
1
2
0
1
1
1
1
0
0
0
1
0
0
2
2
0
2
2
0
3
0
2
1
1
2
1
1
0
0
2
1
1
1
0
0
0
1
1
1
0
0
1
2
2
1
0
2
1
1
0
1
0
2
2
0
1
0
1
1
1
1
0
1
1
1
0
0
0
2
1
1
1
1
0
1
1
1
1
1
2
1
1
1
1
2
0
1
0
1
2
1
0
1
2
1
1
2
1
0
2
1
2
1
2
2
0
1
1
0
1
1
0
1
1
0
1
0
1
0
2
1
2
1
1
1
2
0
1
0
0
1
1
0
1
0
1
1
1
0
2
2
2
1
1
1
2
0
1
2
0
0
2
0
1
0
0
0
1
0
2
0
0
2
1
2
0
1
1
1
0
2
0
2
1
2
1
3
0
0
0
1
2
3
2
2
0
1
1
2
1
1
0
0
1
1
1
1
0
1
2
0
1
1
0
0
1
1
0
1
0
0
1
4
0
1
2
0
0
1
2
1
1
1
0
0
1
0
1
1
1
1
2
2
0
1
2
0
1
0
0
2
1
0
1
2
1
2
1
2
2
1
0
1
2
1
2
0
0
1
1
0
0
1
2
2
1
1
1
1
0
2
0
2
0
2
1
2
1
2
1
1
0
1
1
1
1
0
2
0
0
1
0
1
1
1
1
2
0
1
0
1
2
2
2
0
1
0
0
2
3
1
2
0
0
0
1
1
1
1
1
1
1
1
0
0
1
2
0
1
0
1
1
1
2
2
1
1
1
2
1
2
2
1
0
0
0
0
1
2
0
1
1
1
2
1
0
2
1
0
0
1
1
0
0
1
0
2
0
1
1
1
0
2
1
2
2
1
1
0
0
1
0
0
1
0
1
0
1
1
1
1
2
2
1
0
1
0
2
1
1
0
1
1
0
1
2
1
0
2
0
2
0
0
1
1
0
2
1
1
2
0
0
2
0
1
1
0
1
0
2
1
0
1
1
2
0
2
0
0
2
1
1
2
1
1
1
1
0
1
0
1
0
2
1
2
1
1
1
1
0
1
1
2
2
2
2
0
1
2
1
1
0
1
2
1
2
0
0
2
1
0
0
0
0
1
2
1
1
1
1
1
1
0
2
0
1
1
0
1
2
2
1
0
1
1
1
2
0
1
1
1
1
0
1
1
1
0
1
3
1
1
1
1
1
0
0
0
1
0
3
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
1
1
1
0
1
0
0
0
0
0
1
1
2
0
1
0
0
2
0
1
1
1
0
1
0
0
3
0
0
0
2
1
0
1
1
1
1
1
1
1
1
2
0
3
0
1
0
0
1
0
2
0
1
0
1
0
1
1
1
2
1
2
0
0
2
2
2
1
2
1
0
0
1
1
2
0
0
1
1
1
1
0
1
1
2
1
0
2
2
1
1
0
2
0
1
1
0
2
2
2
0
1
2
2
1
1
1
0
1
0
1
1
0
1
2
1
0
2
1
0
1
0
0
0
0
1
1
2
2
0
1
1
1
1
1
0
0
1
0
0
1
1
1
2
0
2
1
2
1
1
1
2
1
2
0
0
0
1
0
2
1
1
3
1
0
2
0
0
1
1
0
1
1
1
0
2
2
1
1
2
2
2
0
1
1
1
1
2
2
1
2
1
1
3
0
0
2
2
0
1
1
1
2
2
1
0
0
2
0
2
2
0
1
0
2
0
1
1
0
0
0
2
1
1
0
0
2
0
0
1
0
2
1
1
0
1
2
0
0
3
0
2
1
0
2
1
2
1
0
1
0
2
0
2
1
2
0
0
1
0
0
0
0
0
0
0
2
1
1
1
0
2
2
0
2
0
2
1
1
0
2
0
1
2
0
1
1
0
0
0
1
2
0
1
0
2
0
0
2
2
1
1
1
1
1
1
1
1
0
0
1
7
2
1
0
1
1
1
4
1
0
0
1
0
1
2
1
0
2
0
1
2
1
1
1
1
2
2
0
0
1
0
2
1
1
1
0
1
1
0
1
1
1
0
1
2
1
0
2
2
0
1
0
1
0
2
0
2
2
1
1
1
0
0
1
2
2
0
0
2
0
0
1
0
2
1
0
0
2
0
2
1
0
1
0
1
1
1
0
0
1
1
1
1
2
0
1
2
2
2
0
1
1
1
2
0
2
2
0
0
2
1
2
1
0
2
2
2
0
2
1
0
2
2
0
1
1
0
0
1
1
2
1
0
1
0
0
1
1
1
0
1
0
0
2
2
2
0
0
1
1
2
2
1
2
2
1
2
1
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
2
0
1
1
1
1
0
1
0
0
0
1
0
0
1
0
0
1
0
1
1
1
1
1
0
1
2
1
0
1
2
0
0
0
1
1
2
1
1
1
1
1
1
0
2
2
0
0
0
2
1
1
2
1
1
0
0
0
0
0
0
1
0
1
0
1
0
1
1
0
2
1
2
1
0
0
0
0
0
2
1
1
1
2
2
1
2
1
0
0
1
2
0
1
1
1
1
1
1
0
2
0
2
2
2
1
0
0
0
0
0
1
1
1
2
1
0
1
1
1
0
1
0
0
1
1
0
1
1
1
1
0
1
0
1
0
1
1
1
1
2
1
2
1
0
0
1
0
1
0
1
0
2
2
2
1
1
0
0
2
1
0
1
3
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
2
1
0
1
0
1
0
2
0
0
0
0
0
1
2
1
1
1
1
1
0
1
1
1
0
0
0
2
1
0
2
2
2
1
2
0
1
0
0
2
0
1
1
0
1
0
1
1
2
1
0
0
0
1
2
1
0
1
1
0
1
2
0
0
1
1
0
1
2
1
0
2
0
0
1
2
1
0
0
1
1
0
0
0
1
1
0
0
1
1
1
1
1
1
0
1
0
0
1
1
0
2
1
0
1
0
0
0
0
1
1
0
2
1
0
2
1
1
0
1
0
2
0
0
1
0
0
0
1
1
1
0
1
0
1
1
3
1
0
2
1
1
1
2
0
1
1
1
1
1
1
0
1
0
0
0
0
2
1
0
1
1
1
0
1
1
1
0
2
1
1
0
0
2
1
1
1
0
0
0
1
0
2
1
0
2
0
1
1
0
2
2
2
1
1
0
2
0
1
2
1
1
2
2
2
0
1
1
1
1
1
2
2
0
1
1
0
1
1
1
0
0
1
0
0
1
1
1
1
1
2
2
0
2
0
0
1
1
0
1
1
0
1
1
1
2
0
1
1
0
0
0
1
0
0
2
1
2
1
2
3
0
2
2
0
1
1
1
1
1
1
2
0
0
0
2
2
1
1
1
2
2
1
2
0
1
0
0
1
1
0
1
0
0
0
1
0
1
2
0
1
2
0
0
0
0
0
1
0
1
1
2
2
2
1
0
1
2
1
1
2
0
3
0
0
0
1
2
1
0
1
0
1
2
1
0
1
2
1
0
1
0
0
0
1
0
1
0
0
0
0
2
1
1
1
0
0
2
2
1
1
1
2
1
0
0
0
0
2
1
0
0
2
3
1
2
0
0
0
2
0
2
0
1
1
1
1
1
2
1
1
0
1
0
0
0
0
0
1
0
1
2
2
1
2
1
2
0
1
1
0
1
1
1
5
1
0
0
2
0
2
2
1
0
1
2
0
0
1
1
1
0
0
0
2
1
0
0
1
1
2
1
2
1
0
1
1
0
1
1
1
1
0
1
1
0
0
1
0
1
0
2
2
0
2
1
1
0
2
1
0
1
0
1
0
1
0
0
0
1
0
2
2
2
1
2
1
0
1
2
1
1
1
1
0
0
1
1
0
1
3
2
0
0
0
1
0
2
1
2
0
1
0
0
3
1
0
1
2
0
1
1
1
0
0
1
1
4
1
1
0
0
0
1
0
1
0
0
1
1
1
1
0
1
2
2
2
0
1
2
0
2
0
0
2
2
2
1
1
2
0
1
1
1
2
0
1
0
0
1
0
0
1
1
0
0
0
1
0
1
2
2
1
1
0
1
1
0
1
1
1
2
0
1
2
2
0
3
1
4
1
0
0
1
1
3
0
2
0
0
1
2
1
1
1
1
0
0
1
1
0
1
2
2
0
2
1
1
1
0
0
1
1
0
2
0
0
0
1
2
2
0
1
2
3
1
1
3
1
0
0
3
0
1
1
1
2
0
1
0
0
2
0
1
0
0
1
2
1
1
0
0
0
1
1
1
1
2
1
2
1
0
1
0
1
1
1
2
0
2
1
0
1
1
1
3
0
0
1
1
1
1
0
1
0
1
0
1
1
0
2
0
1
1
1
2
1
0
0
1
2
1
1
0
0
2
0
0
1
1
1
0
1
0
2
1
1
1
1
2
0
1
0
1
2
0
1
0
0
0
0
0
1
1
1
1
2
0
1
0
0
1
3
0
2
1
1
1
0
1
2
1
2
1
1
1
1
2
1
1
0
0
2
1
1
1
1
1
1
1
0
1
1
2
2
1
2
1
1
1
0
1
1
0
2
1
1
1
0
2
1
0
1
1
3
2
1
1
1
0
0
1
0
2
0
0
2
0
0
2
0
0
1
1
1
2
0
0
0
2
2
0
2
0
2
0
0
2
1
1
1
1
0
1
1
0
0
1
1
0
2
0
3
0
0
1
2
3
1
0
0
1
0
18
1
1
1
1
0
1
1
1
2
2
0
2
2
0
1
0
1
0
1
0
3
0
0
1
2
2
1
1
0
1
0
1
2
0
0
0
2
0
0
1
2
0
1
1
2
2
1
0
1
2
1
1
0
0
0
3
1
1
0
1
1
2
1
2
0
4
3
0
1
1
1
2
1
0
0
1
1
1
1
1
2
2
1
1
2
3
1
1
1
1
0
0
0
0
1
1
1
1
1
1
2
1
1
0
1
0
0
1
1
1
0
1
1
0
1
1
1
2
2
2
1
2
2
0
0
1
2
2
0
1
0
1
0
0
0
0
1
1
1
0
2
1
0
1
1
0
1
0
0
1
0
1
0
5
1
2
1
0
1
2
0
2
1
1
1
0
0
1
0
0
1
0
1
2
0
1
1
1
0
1
1
1
1
1
1
0
1
1
2
0
1
0
1
0
1
2
1
1
2
1
0
2
0
0
1
0
1
1
2
2
0
1
1
1
0
1
0
1
0
3
0
1
0
1
1
0
2
0
2
3
0
1
1
0
1
0
0
0
0
1
0
1
0
1
0
1
1
0
0
1
0
1
2
0
0
1
1
0
0
0
0
1
1
1
0
2
0
0
0
2
0
0
0
2
0
1
1
1
1
0
2
0
2
1
0
1
0
1
0
1
1
2
0
1
1
2
2
1
1
0
3
1
2
1
1
0
0
0
0
1
1
2
1
0
1
0
0
2
1
0
1
0
3
0
1
0
0
1
1
0
3
2
0
1
2
2
1
1
0
0
0
2
2
1
1
0
0
1
1
0
1
2
0
1
1
1
1
1
1
1
0
0
1
1
1
0
2
2
2
2
2
1
0
1
2
1
1
0
1
1
0
0
1
2
0
1
1
0
1
1
1
1
1
1
1
2
1
1
0
2
1
0
1
0
1
2
1
1
1
0
0
2
2
1
2
2
0
1
2
0
0
1
1
1
2
2
1
0
1
1
1
1
0
1
1
1
0
1
1
1
0
2
2
1
1
2
0
1
1
2
2
1
0
2
2
2
0
0
1
1
2
0
3
2
1
2
1
1
1
2
1
1
0
0
0
2
1
1
0
1
1
1
0
0
1
1
1
2
2
1
0
2
0
0
1
2
2
1
2
0
0
1
1
1
0
1
2
1
0
1
1
2
1
4
0
1
1
0
0
0
2
1
1
2
1
0
2
2
0
0
1
2
0
1
1
0
0
0
1
0
1
0
2
3
2
2
1
1
2
2
1
1
0
0
0
1
0
1
0
1
3
1
1
0
2
0
0
1
1
0
1
1
1
2
0
2
0
1
2
2
2
2
2
1
0
1
1
1
1
1
0
1
0
1
0
1
0
2
0
2
1
0
0
1
1
1
1
1
0
1
1
0
1
1
2
0
1
2
0
1
1
1
1
1
1
0
1
1
0
2
2
1
1
1
0
1
0
1
0
1
1
1
1
2
1
1
2
0
1
0
1
1
0
1
0
0
2
0
1
0
0
0
0
0
0
1
0
1
2
1
1
1
2
1
1
0
1
0
0
0
0
1
1
2
2
1
0
0
1
0
1
1
1
2
2
0
1
0
1
1
2
1
0
1
2
1
1
1
0
2
0
0
0
0
2
1
0
1
0
1
2
0
0
0
2
1
1
2
2
1
0
0
0
1
0
2
1
1
1
1
1
0
1
2
1
0
1
2
2
1
1
0
0
2
0
1
1
2
2
1
1
1
1
0
2
0
1
1
1
2
0
0
2
0
2
1
1
1
2
2
0
0
1
1
0
1
2
2
1
1
1
1
2
0
2
3
1
1
1
1
2
0
0
1
1
1
0
1
1
1
1
0
3
0
0
0
3
2
0
1
2
1
0
1
0
2
1
1
2
0
0
0
1
0
1
2
1
1
1
0
1
2
1
0
1
1
1
2
2
1
0
1
1
2
2
1
1
1
1
0
0
2
1
0
0
2
1
2
1
1
1
2
0
2
1
0
0
0
0
1
1
2
0
1
1
1
1
1
1
0
2
0
1
0
2
2
2
1
0
0
0
1
0
0
0
0
0
1
0
1
1
2
0
2
0
0
1
0
1
1
1
1
1
2
2
2
0
2
1
0
0
0
0
0
2
0
1
0
0
1
2
1
0
0
1
2
1
1
3
0
0
1
2
2
1
1
1
2
1
0
0
1
0
0
0
1
4
1
1
1
1
0
2
1
0
0
0
1
0
2
1
0
1
0
0
2
2
2
0
1
1
1
0
1
0
0
0
1
0
0
1
2
2
2
1
0
1
2
1
0
1
0
0
4
1
0
0
2
1
1
0
1
1
0
0
1
2
1
2
1
2
1
1
0
2
1
2
1
2
1
0
1
1
0
2
0
2
1
1
0
2
0
1
1
1
1
2
1
1
2
1
1
0
1
1
1
1
2
2
1
2
1
1
0
1
2
1
1
0
2
0
1
0
1
1
0
1
1
1
2
0
1
1
1
2
1
0
0
1
1
0
2
1
1
0
1
0
1
2
3
1
1
1
0
1
1
2
1
1
3
2
0
0
1
0
1
0
2
1
1
1
0
0
2
1
1
1
1
1
0
0
1
1
1
2
1
2
1
2
0
1
1
2
1
2
1
1
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
2
0
1
0
1
1
1
2
1
0
2
1
2
1
2
1
1
2
1
2
1
1
2
0
1
0
2
1
0
0
1
0
1
1
0
1
1
0
1
2
2
1
1
0
1
1
2
2
1
0
2
1
0
1
0
1
1
1
0
2
0
1
2
1
0
0
0
0
2
0
2
2
0
1
2
2
1
2
1
1
1
1
0
1
2
0
0
2
1
1
0
0
1
2
0
0
0
1
1
1
1
2
0
1
0
1
2
1
1
1
2
1
2
0
0
0
2
2
2
2
0
1
1
2
1
1
0
2
1
1
0
1
0
1
2
0
0
0
1
1
2
2
0
2
0
0
2
2
1
1
2
2
1
1
1
0
2
0
1
0
0
0
1
3
1
1
3
1
1
0
0
0
2
2
1
0
1
0
0
0
1
0
1
2
1
1
0
1
1
1
1
2
2
0
1
0
1
0
0
1
0
0
0
1
1
0
1
0
2
1
0
2
1
1
0
1
1
1
1
1
0
1
0
1
0
0
1
2
2
0
1
1
0
0
2
2
1
1
1
1
1
1
2
0
1
0
1
1
1
1
0
0
1
1
0
0
1
7
1
1
2
2
1
2
2
0
2
2
0
0
2
2
1
0
1
1
0
0
1
0
0
1
1
0
1
2
0
2
0
0
0
1
1
1
0
0
0
1
3
2
1
0
0
1
0
1
1
0
1
0
1
0
0
1
1
0
2
0
0
0
2
1
1
2
1
2
0
2
0
1
1
2
0
0
1
2
1
1
2
0
0
2
0
0
1
2
1
0
1
0
1
1
1
1
2
1
1
0
0
1
1
1
2
1
1
2
2
0
1
1
1
4
0
0
1
1
0
0
0
1
2
0
1
1
1
1
1
0
2
0
0
1
1
2
0
1
0
1
1
1
0
0
0
0
0
0
2
0
1
0
1
1
1
2
1
2
1
2
0
2
1
2
0
1
1
0
1
0
1
0
0
0
0
1
1
0
0
2
1
0
2
1
1
0
1
0
0
2
2
2
1
1
0
1
0
2
0
0
1
1
2
2
0
0
0
1
0
0
0
1
1
1
0
0
2
0
1
1
2
1
1
0
2
0
1
1
0
2
0
0
0
2
1
2
1
1
0
0
1
0
2
1
2
1
1
0
1
1
1
0
2
3
2
1
0
0
0
1
0
2
1
0
1
1
1
1
1
0
1
1
1
1
1
1
0
1
0
0
1
1
0
0
1
0
2
1
1
1
2
1
1
2
0
1
1
1
1
0
2
0
1
1
1
0
1
0
1
1
1
2
0
1
5
1
1
0
1
1
2
0
1
0
2
1
1
1
1
1
2
3
1
1
0
0
1
4
2
2
2
0
2
2
2
1
0
1
1
2
2
1
1
1
1
2
1
2
1
2
2
2
1
2
1
0
1
1
1
1
1
1
2
1
1
1
0
2
1
1
2
2
2
1
0
2
2
0
1
0
0
0
2
2
1
0
1
1
1
1
0
1
1
1
1
0
1
0
0
0
2
2
1
1
0
0
2
1
0
1
0
0
1
1
2
0
1
2
2
1
1
1
1
1
0
2
1
2
0
0
1
1
1
0
1
0
2
1
1
0
0
0
2
0
1
1
1
3
1
0
1
1
1
1
1
1
1
0
2
0
0
1
2
0
2
1
0
1
0
1
0
2
1
2
1
2
0
0
0
1
1
1
1
2
1
1
2
0
1
0
0
1
1
2
0
2
6
0
1
0
1
1
5
2
1
1
1
1
0
0
0
4
3
0
1
2
1
1
2
1
2
1
1
1
1
0
1
0
1
1
0
0
0
1
1
1
2
0
1
1
1
2
1
0
1
1
1
2
2
1
1
2
0
1
0
0
2
0
0
2
0
0
1
1
2
1
1
1
0
1
2
1
1
0
1
2
1
2
2
0
1
2
1
1
2
2
0
2
0
2
1
0
1
0
1
1
1
0
2
0
1
0
0
1
0
0
1
1
0
0
2
1
1
0
1
1
0
2
0
0
0
1
1
1
0
0
1
1
0
0
0
1
1
2
2
1
1
0
0
2
1
0
0
2
1
1
2
1
0
3
2
2
2
1
0
1
0
0
0
1
0
1
1
0
1
1
0
0
1
0
0
1
0
0
1
0
1
1
0
1
1
1
2
1
0
1
3
1
0
0
2
1
1
1
1
2
2
0
1
1
1
0
2
0
1
2
0
0
2
1
1
0
0
1
0
1
0
0
2
0
1
0
0
1
1
1
1
0
1
1
2
1
0
0
1
2
0
0
0
0
0
2
0
1
0
3
1
0
1
1
0
0
1
0
1
1
1
0
2
0
0
0
0
1
2
2
0
2
1
0
1
2
2
2
0
0
2
1
0
1
2
1
0
1
0
2
1
2
1
1
1
1
2
0
2
0
2
0
1
0
1
0
1
1
0
1
1
0
1
0
1
1
1
0
1
1
1
0
1
0
0
1
0
2
0
1
2
2
2
2
2
2
0
1
3
2
1
1
0
1
1
1
1
1
0
0
0
0
2
1
0
1
1
1
0
1
0
0
0
2
1
2
1
1
1
0
1
0
0
1
1
1
1
1
1
0
2
2
2
2
3
0
0
1
0
1
0
1
0
0
2
1
1
1
1
2
0
1
0
0
1
2
1
0
1
1
2
0
2
1
2
1
1
0
0
1
1
1
2
1
4
0
2
0
2
1
0
0
0
1
1
1
1
2
1
1
2
0
0
1
1
1
1
0
0
0
1
0
2
0
0
2
0
1
2
1
0
0
2
1
2
0
0
1
0
0
1
0
0
1
1
2
0
2
2
0
0
2
0
1
0
2
1
1
1
0
1
1
0
1
1
2
1
1
0
2
2
1
1
2
2
0
0
1
1
0
0
1
1
2
0
1
0
0
2
1
1
1
1
0
1
1
1
0
2
0
1
1
0
2
1
0
1
1
0
2
1
0
2
1
0
0
0
1
1
2
0
0
2
2
1
1
1
0
0
1
1
2
1
0
2
0
0
0
0
0
2
2
0
1
0
0
7
3
2
1
2
0
1
2
2
0
1
2
1
1
1
2
0
2
2
1
1
0
1
2
2
1
1
1
2
1
2
1
1
1
1
1
1
1
2
0
2
3
2
1
0
0
2
2
0
2
0
2
2
0
0
0
1
1
1
0
0
1
0
1
1
0
1
1
1
0
1
2
1
3
1
0
0
0
0
2
1
1
0
1
0
1
0
1
1
0
0
1
2
1
1
2
0
0
1
2
0
0
0
1
1
0
2
1
1
0
2
1
1
1
2
2
2
0
1
1
1
1
0
1
0
1
0
1
1
1
1
1
1
1
2
1
1
2
0
0
0
0
1
0
1
0
1
2
2
0
2
0
2
0
0
1
2
2
1
1
1
0
1
1
0
1
0
0
0
1
0
1
2
0
1
2
0
1
2
1
1
3
2
0
1
1
2
0
0
2
1
0
1
1
1
0
1
0
0
1
0
1
2
2
1
1
1
0
0
2
0
2
1
1
0
1
0
1
0
2
0
0
1
0
1
1
0
2
0
0
1
1
1
1
0
1
0
2
2
0
1
0
2
0
0
0
1
0
3
2
1
1
1
1
1
0
2
1
2
0
1
2
1
3
0
1
1
1
2
1
1
1
1
2
1
1
0
1
1
1
0
0
1
1
1
1
1
1
2
0
1
1
1
0
1
0
1
1
2
1
0
3
1
0
2
1
2
0
0
1
1
1
1
2
1
1
0
0
1
1
1
0
2
0
0
1
0
2
0
0
2
2
2
1
0
2
0
1
1
1
1
1
1
2
1
2
0
1
0
1
1
0
0
1
2
0
2
1
0
1
1
0
0
0
0
1
1
2
0
1
1
1
1
1
2
0
1
0
0
1
2
1
2
0
1
2
0
0
1
1
0
0
2
2
2
0
3
0
1
0
0
1
1
1
0
2
2
1
1
1
1
1
0
1
1
0
0
0
1
0
2
0
1
1
0
0
2
1
1
1
0
1
1
1
1
1
1
2
2
0
1
2
0
1
0
0
2
1
1
1
0
2
0
1
2
2
1
1
0
1
2
1
0
1
0
2
2
0
0
0
2
1
0
0
1
2
1
2
2
1
0
1
0
1
2
1
1
0
1
0
0
1
0
2
1
1
1
2
1
2
0
2
1
0
2
1
2
0
1
1
0
2
2
1
0
2
0
2
1
2
1
1
0
1
0
2
2
1
0
1
0
1
3
1
0
0
0
2
2
1
2
1
0
2
1
1
1
1
1
1
1
0
0
1
1
1
1
0
1
1
0
0
2
0
1
0
1
2
1
1
0
2
2
1
1
0
0
0
1
2
0
0
1
1
0
0
1
1
2
1
0
0
3
0
1
2
2
2
0
0
1
1
1
2
1
0
0
1
2
5
0
0
1
1
1
1
1
0
1
0
0
2
0
0
0
1
1
1
3
0
0
1
0
2
2
1
0
1
1
1
2
1
2
2
0
1
1
0
1
1
0
1
1
1
1
0
0
1
0
0
1
3
2
0
2
1
1
2
2
1
1
0
1
2
0
0
0
0
2
1
1
0
0
0
0
0
1
1
1
1
0
1
0
2
2
0
1
1
1
1
0
0
1
1
1
2
2
2
1
1
0
0
2
1
0
0
1
1
2
0
2
2
1
3
0
2
1
0
1
1
1
2
0
2
1
1
1
1
2
1
1
2
0
2
0
2
0
2
2
2
2
1
1
0
0
0
1
2
0
1
0
2
1
1
0
0
1
1
2
2
3
0
0
0
2
1
1
0
2
2
0
1
2
1
1
1
2
0
1
1
1
1
1
1
2
0
1
0
0
1
3
1
1
2
5
0
1
2
2
0
0
1
1
0
0
2
1
2
4
0
1
1
2
0
0
0
0
0
1
1
2
1
2
1
1
1
1
2
1
0
1
0
1
2
1
2
1
0
1
0
2
1
2
2
1
2
1
1
1
1
2
1
0
0
0
0
1
1
0
2
1
1
0
2
1
1
0
1
0
0
1
1
0
0
1
1
2
2
2
1
0
0
2
1
2
2
1
1
0
1
0
2
2
2
1
2
0
1
1
1
0
0
0
1
0
2
1
1
2
1
2
0
2
1
1
1
2
1
1
0
1
2
0
0
2
1
1
1
2
1
0
0
1
2
1
2
0
0
1
1
1
0
2
0
1
0
2
1
1
3
1
1
0
2
1
1
1
1
0
1
0
1
1
1
1
1
0
1
2
2
1
1
1
2
1
1
0
0
0
1
2
1
1
2
1
1
1
2
0
1
1
1
1
1
0
1
1
0
2
0
2
0
2
2
1
2
0
1
0
0
0
1
1
0
1
1
0
2
0
2
0
1
1
1
1
2
2
0
1
2
2
0
0
2
2
1
0
0
1
0
1
0
2
0
1
0
1
0
2
1
1
1
0
3
2
1
2
1
0
1
1
0
0
1
0
1
1
0
1
0
1
2
0
1
2
1
1
1
2
0
0
2
0
1
0
0
0
1
1
4
0
1
1
0
2
0
1
3
1
0
5
2
1
0
2
1
1
2
0
1
1
2
1
1
0
1
0
1
1
0
1
1
2
3
1
0
2
0
1
2
1
0
1
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
1
1
1
1
1
1
1
1
1
1
1
1
1
0
2
0
2
2
1
1
2
1
1
2
1
1
2
1
0
1
1
1
0
2
2
1
1
0
2
1
0
0
0
3
0
0
1
0
1
1
2
2
1
1
1
1
2
2
2
2
2
2
1
0
1
1
2
1
1
1
1
2
2
2
1
2
0
1
2
1
1
1
1
2
2
1
0
0
2
1
0
0
1
0
2
2
0
0
1
2
2
1
0
0
0
1
1
1
0
0
1
1
2
1
1
2
2
0
0
1
1
1
1
1
2
2
0
2
1
1
2
1
2
0
1
0
0
1
4
1
0
0
1
1
0
2
1
1
1
1
0
1
0
0
2
1
2
1
0
2
0
0
2
0
1
1
1
3
1
0
1
1
2
1
0
0
1
0
0
2
2
1
0
2
1
1
0
2
0
0
1
2
1
2
1
0
0
1
1
1
0
1
0
2
2
0
1
0
0
0
1
1
0
0
0
0
0
1
0
2
1
2
0
0
0
1
2
1
2
1
0
0
1
1
1
1
1
1
1
1
0
1
1
0
0
0
0
1
0
1
2
0
1
1
1
1
0
0
1
1
1
0
1
1
1
0
2
1
0
0
1
0
0
1
0
1
0
0
0
1
0
1
2
1
0
0
2
1
2
2
0
2
1
1
1
1
1
1
2
1
1
0
1
0
1
1
1
0
0
1
0
1
1
2
2
2
0
2
0
1
2
1
1
2
1
1
2
1
2
2
0
1
1
0
0
1
0
1
0
2
0
0
1
1
2
1
0
1
0
0
1
0
1
0
2
1
0
0
1
0
1
1
0
1
2
1
2
1
0
1
1
1
1
0
0
2
2
1
2
0
2
2
0
1
0
0
2
1
1
1
2
0
2
0
1
1
1
1
1
1
2
1
0
1
2
0
0
1
0
0
0
0
2
1
1
0
0
0
1
2
1
0
1
1
2
0
2
1
1
1
2
2
1
1
1
2
0
5
1
1
1
1
2
2
1
0
1
1
1
1
1
0
1
1
2
0
1
2
1
1
2
2
1
1
0
0
0
1
0
1
2
0
1
1
1
1
1
0
1
1
1
0
0
1
2
1
1
2
3
0
1
2
1
2
0
0
0
2
0
2
0
0
1
0
0
1
0
1
1
0
0
0
0
2
3
0
1
2
1
1
0
0
0
0
0
0
0
0
1
1
2
1
2
0
1
0
1
0
2
1
0
0
1
0
1
1
0
0
1
1
0
2
2
1
1
3
1
0
0
0
1
1
1
2
2
0
2
1
1
1
0
1
0
2
1
0
0
1
2
1
1
1
1
2
2
2
2
0
2
0
1
1
1
0
1
1
1
0
0
0
0
1
1
1
0
1
0
2
1
0
0
1
1
0
0
1
0
2
1
1
1
2
1
0
0
2
1
2
2
1
1
2
0
1
1
2
1
1
1
0
2
1
1
1
2
1
1
2
0
2
1
1
0
0
1
0
0
0
0
0
1
1
1
0
2
1
0
0
1
1
1
0
0
0
0
1
1
2
1
0
1
0
1
0
1
0
0
0
2
1
2
1
0
1
0
0
0
1
0
0
2
1
2
1
0
0
1
1
1
2
2
1
1
2
2
1
0
0
1
1
0
0
1
1
0
2
2
0
0
1
2
0
2
1
0
0
1
1
1
1
9
0
0
0
0
1
1
1
0
0
1
1
1
0
0
1
0
1
1
1
2
2
0
2
1
0
1
0
3
0
1
1
1
0
2
2
0
0
0
1
1
1
1
1
0
1
2
0
1
1
0
1
0
2
1
1
0
0
1
0
1
0
2
1
0
2
0
0
1
0
1
0
0
1
2
1
0
1
0
1
1
1
0
1
0
0
0
0
0
2
1
1
2
2
0
3
0
0
2
1
1
0
2
0
1
0
1
0
0
0
1
0
2
1
1
0
0
1
0
0
1
2
1
0
1
1
2
2
1
0
1
1
0
0
0
2
1
0
2
0
0
1
0
0
1
1
0
1
1
2
2
0
1
2
2
0
1
0
1
1
0
1
1
1
0
2
1
3
1
0
1
2
1
0
0
1
2
2
1
1
1
2
0
1
1
1
0
1
1
1
2
2
2
1
1
2
1
2
0
1
1
2
0
1
1
2
2
2
0
1
0
6
2
1
1
1
1
0
1
1
1
0
0
1
2
0
1
1
2
1
0
0
1
2
1
1
0
1
1
0
2
1
1
0
0
1
0
1
0
3
2
2
1
1
0
0
1
1
2
0
1
3
1
0
0
1
0
3
1
0
0
0
2
0
0
1
0
1
0
2
2
0
0
0
1
0
0
1
1
0
0
1
0
0
1
1
0
0
2
2
2
0
0
2
0
3
0
1
0
1
2
2
0
0
0
2
2
0
0
1
1
2
1
3
0
0
1
2
0
1
0
1
0
1
0
2
2
1
0
1
1
0
3
2
0
2
1
1
2
2
2
1
2
2
1
1
2
2
0
2
2
2
1
0
1
1
0
1
0
0
0
2
1
3
6
0
1
1
0
2
1
1
1
1
2
1
1
1
0
1
0
0
1
0
1
1
2
1
3
1
0
1
2
1
1
0
2
2
2
0
1
0
1
1
1
1
1
2
1
1
1
1
1
1
0
1
1
2
0
2
0
2
1
0
1
3
1
1
0
1
2
0
0
2
1
0
2
2
1
1
1
1
2
1
1
2
2
2
0
1
2
2
2
0
2
2
2
0
0
1
1
1
2
1
0
1
1
0
0
1
2
0
1
1
1
1
1
1
0
1
0
0
2
0
2
0
1
1
1
1
1
0
2
2
1
2
0
2
0
1
1
2
2
2
0
3
1
2
1
1
1
0
2
1
2
1
1
1
1
3
0
0
0
1
1
1
1
1
1
1
0
0
1
1
0
1
3
1
2
6
0
1
2
1
1
0
0
2
4
1
0
0
1
0
0
1
1
1
0
2
2
1
1
1
2
0
0
0
3
0
0
0
0
1
2
2
1
1
1
1
1
0
1
0
1
1
0
1
1
2
1
2
2
1
0
2
2
1
0
0
1
1
1
2
1
0
2
0
0
2
1
2
1
1
1
2
1
0
0
0
2
0
2
1
1
0
0
6
0
1
1
2
0
1
2
1
0
1
1
0
1
0
1
2
2
0
0
0
1
2
1
1
1
1
0
2
0
0
2
0
3
1
0
1
2
0
0
2
0
0
1
1
0
2
2
0
0
0
1
1
1
0
0
0
1
1
1
1
1
0
0
2
1
0
0
0
1
2
2
1
1
1
0
2
0
1
2
0
1
0
0
0
0
1
2
3
1
1
0
1
0
0
0
0
1
0
0
0
2
0
0
2
1
1
2
0
0
0
0
0
0
0
0
2
0
0
1
1
1
0
2
4
1
2
2
1
0
2
1
1
2
0
1
0
0
0
0
2
1
1
0
1
3
1
0
0
0
2
1
0
1
1
0
1
1
0
1
1
1
0
0
1
1
1
0
1
2
2
0
0
1
1
0
1
1
1
0
1
1
1
0
1
1
1
0
2
2
2
2
1
2
0
1
1
0
1
2
0
0
1
0
2
1
2
1
1
1
1
0
1
1
2
1
0
2
0
1
0
1
1
2
1
1
0
0
2
1
1
1
1
2
1
1
0
0
0
2
1
0
2
0
0
1
2
1
1
1
1
2
1
0
1
0
0
1
1
1
0
2
1
1
1
3
1
2
1
1
1
2
1
0
1
2
1
1
1
0
1
1
1
1
0
1
0
0
1
1
1
1
1
0
2
2
2
1
1
2
0
2
1
0
2
1
1
1
1
1
1
1
1
2
0
0
0
1
1
1
0
1
2
0
0
2
1
1
1
0
0
0
2
1
1
2
0
1
1
0
2
0
0
1
1
1
1
1
1
0
2
2
2
2
2
2
0
1
0
0
1
2
1
2
2
1
1
1
1
1
2
1
1
1
1
1
1
1
0
1
1
0
2
1
1
1
1
1
1
2
2
0
0
1
1
2
1
1
0
1
0
2
1
0
1
0
1
0
1
1
1
1
0
0
0
1
1
0
0
0
1
1
2
1
1
1
1
1
1
1
0
0
1
0
0
2
1
2
1
0
1
1
2
2
1
0
2
0
1
2
1
1
2
0
0
2
1
1
2
1
1
1
0
1
2
1
1
0
0
0
0
1
1
1
0
1
0
1
1
0
2
0
0
3
0
2
1
1
1
2
2
1
3
0
1
2
2
0
1
1
1
1
1
1
1
0
1
1
0
0
1
1
0
1
0
1
0
0
0
2
1
0
0
1
1
0
0
0
1
1
0
2
1
1
3
0
1
0
0
1
1
1
0
2
2
1
0
1
0
0
1
1
2
0
1
0
0
1
0
1
2
1
1
0
2
0
3
1
1
0
0
0
1
1
1
0
2
0
2
1
1
1
2
0
0
2
0
1
2
1
0
2
1
1
2
0
1
0
0
0
1
1
1
2
0
0
1
1
0
1
1
2
1
0
2
1
1
2
1
1
1
0
1
2
1
1
1
1
1
0
6
1
0
0
1
0
0
1
1
2
1
0
2
2
0
1
0
1
1
0
0
0
2
0
1
1
0
2
2
1
1
1
1
0
1
0
1
1
1
1
1
0
2
1
0
0
2
2
2
1
1
1
0
0
2
2
1
1
0
2
1
1
1
0
2
0
1
1
1
1
0
0
1
0
4
0
2
0
1
1
2
1
1
3
2
1
1
1
0
2
1
0
1
0
1
1
0
1
0
1
2
1
2
1
0
1
1
0
1
0
1
0
1
0
1
2
1
2
2
1
1
1
2
2
1
1
1
0
2
1
2
1
0
1
1
1
1
2
1
1
0
1
1
1
0
3
0
0
2
1
2
0
0
1
1
0
1
0
0
0
1
0
0
1
0
2
0
2
0
1
1
2
1
0
0
0
1
2
1
0
0
0
0
1
0
1
0
2
2
2
1
0
0
1
1
0
1
1
2
2
0
0
1
1
1
4
1
1
0
0
0
0
1
1
1
2
0
1
1
2
1
2
0
1
0
1
1
0
0
0
1
1
0
1
1
1
2
1
0
1
0
0
1
1
2
0
0
1
1
0
1
1
1
0
0
2
0
2
0
0
1
1
1
0
0
0
0
2
0
2
1
0
2
2
0
1
0
0
1
1
0
0
2
1
0
1
1
1
1
1
0
1
1
0
2
1
2
2
0
1
0
0
2
1
1
0
2
2
1
0
1
0
1
2
2
1
0
0
2
1
1
0
2
0
1
2
1
0
5
1
1
1
1
0
2
1
0
1
1
0
2
0
1
1
1
0
0
1
1
1
1
0
1
2
0
2
0
0
1
6
1
2
1
2
2
1
1
2
1
0
2
1
1
1
1
2
2
0
2
1
1
0
1
0
1
0
0
1
1
1
1
1
2
1
1
1
1
2
1
0
1
0
0
2
0
1
1
0
1
1
1
1
1
2
1
2
0
1
1
1
2
2
1
2
1
2
2
0
1
1
0
2
2
2
0
0
1
2
0
0
0
1
0
0
0
2
1
1
0
2
1
2
1
0
1
1
1
2
2
1
1
0
2
1
2
0
0
2
2
2
0
1
0
0
1
0
0
1
2
1
0
1
1
1
0
1
2
1
0
0
0
0
1
0
1
0
2
0
2
1
0
1
2
1
0
1
1
2
1
2
3
0
1
0
0
1
0
2
1
0
1
1
0
0
1
1
1
0
2
2
1
0
1
1
0
0
1
2
0
0
1
2
0
1
2
0
1
0
0
1
0
0
1
0
1
0
0
1
0
2
0
2
1
2
0
1
2
1
2
2
0
0
0
0
1
1
1
1
1
0
1
1
0
2
1
0
1
0
0
0
2
1
0
0
3
2
0
0
1
1
1
1
0
2
1
2
0
2
1
2
1
1
2
2
0
0
1
2
1
2
2
3
0
1
0
2
0
1
1
2
0
0
2
1
1
1
2
1
1
1
0
0
0
1
1
1
1
1
0
0
1
2
0
1
1
1
2
1
0
1
0
1
0
1
0
0
0
2
0
0
1
1
1
2
2
1
0
0
0
2
1
0
1
0
0
1
0
0
2
0
0
1
0
1
0
1
2
1
1
2
2
2
0
0
1
1
0
0
1
1
0
3
0
2
2
2
0
0
2
2
1
2
0
0
1
1
0
1
1
1
1
0
0
0
0
1
0
1
0
0
2
2
1
1
2
1
1
1
2
1
0
1
1
1
1
0
1
0
1
0
1
0
1
0
1
1
0
1
2
1
1
1
2
1
0
0
1
0
1
1
2
1
0
1
1
2
0
0
2
0
2
0
3
2
0
0
0
2
0
0
1
2
2
0
1
0
2
2
0
2
0
1
1
2
2
0
0
0
1
2
1
0
0
2
1
2
0
2
4
0
1
0
0
1
0
0
1
2
0
0
2
0
1
0
0
1
1
1
2
1
0
1
2
0
1
1
1
2
0
2
1
1
0
0
0
1
1
1
0
2
0
3
0
0
1
0
1
1
1
0
2
1
2
0
2
0
1
0
2
0
1
0
0
1
0
2
1
0
2
1
1
0
1
0
0
0
1
1
1
1
0
1
1
0
0
2
1
1
1
1
0
2
0
1
1
2
2
1
1
1
1
0
0
1
0
0
1
0
1
1
0
2
1
1
0
2
1
1
2
1
0
0
0
1
1
2
2
1
0
0
1
0
2
1
1
3
0
1
1
2
0
2
1
1
2
0
1
1
0
1
2
0
1
0
0
0
2
0
2
2
1
0
2
1
2
2
0
0
0
1
0
1
1
1
1
1
0
0
2
1
1
1
0
2
1
0
0
0
0
1
2
1
1
1
1
1
2
1
1
0
1
2
0
2
1
1
1
0
1
0
0
1
1
1
2
1
2
2
0
1
1
1
0
1
1
1
2
0
0
3
0
2
2
1
1
2
1
1
1
1
1
1
1
0
1
1
1
0
1
1
0
3
1
2
1
1
0
1
1
1
0
0
0
2
2
0
0
0
3
1
1
1
1
0
1
0
2
0
3
0
2
0
1
1
1
1
0
2
0
1
1
1
1
2
0
2
1
1
2
1
2
1
0
1
0
1
1
0
1
1
0
1
0
1
1
1
0
1
0
1
0
1
2
1
2
1
1
0
0
0
2
1
1
1
0
0
0
1
1
1
2
2
2
2
1
1
0
1
1
1
0
0
0
2
1
1
1
0
0
1
2
0
1
2
1
1
0
2
0
0
1
1
2
1
2
2
0
1
0
1
2
0
1
1
0
0
1
0
2
1
1
1
0
2
2
0
0
0
1
0
0
1
0
2
0
1
2
0
2
2
2
1
1
2
1
1
2
1
1
1
0
0
0
1
0
2
0
1
1
1
0
1
1
1
2
1
0
1
1
0
0
1
1
3
1
1
1
1
2
4
1
0
2
1
2
2
2
1
1
1
2
0
0
2
1
1
1
2
1
0
1
3
0
1
0
1
1
2
1
1
0
1
0
2
1
2
0
1
1
0
0
1
1
2
2
1
1
2
1
2
1
2
1
1
2
2
2
1
0
2
1
2
0
1
0
1
1
3
2
1
2
1
1
0
1
1
2
1
2
0
2
2
0
2
1
1
1
0
1
2
2
0
0
1
2
0
1
1
1
0
0
2
1
0
0
1
2
1
0
1
2
0
0
0
2
0
0
1
1
0
0
1
1
1
0
0
0
1
1
1
2
0
0
2
0
1
0
1
1
1
2
0
1
0
2
2
2
1
2
3
2
1
2
0
2
0
2
2
1
1
0
1
1
2
2
1
2
1
1
1
1
1
1
0
1
0
2
0
0
0
1
0
1
0
1
2
1
1
2
1
0
1
4
0
0
1
0
0
1
1
0
0
2
0
1
1
1
1
0
1
1
2
1
0
0
2
0
1
1
0
0
0
0
1
2
2
1
2
1
3
0
1
2
2
2
3
2
2
0
1
2
1
1
2
0
1
2
1
1
2
2
1
0
0
1
1
0
0
0
1
0
0
1
1
0
1
0
0
2
0
0
2
2
1
2
1
2
0
1
2
0
2
0
2
1
0
0
2
1
1
1
1
1
0
0
0
0
1
1
1
0
1
2
2
1
1
0
1
1
0
0
0
1
2
1
2
2
0
1
0
0
0
2
0
1
0
1
1
0
2
0
0
1
1
0
2
0
1
1
0
1
1
1
0
0
0
1
0
1
0
1
1
1
0
1
1
1
0
2
1
1
2
2
0
2
1
2
0
1
3
0
0
0
1
1
0
1
0
1
2
1
1
1
1
0
1
1
1
0
0
1
1
0
0
1
2
1
0
1
1
2
0
2
0
1
1
0
0
1
1
1
2
1
1
1
0
0
1
1
1
1
0
0
0
1
1
0
2
1
0
0
1
2
1
2
0
0
1
1
2
1
0
0
0
2
0
2
0
0
1
0
0
1
0
0
2
1
0
0
1
1
0
2
1
2
2
2
1
0
0
1
1
0
0
1
0
0
0
1
1
1
1
1
1
2
0
1
1
1
1
0
0
1
1
0
1
1
0
1
0
0
1
0
0
2
2
1
1
3
0
1
1
1
1
0
3
0
2
1
1
0
1
2
1
2
1
1
2
1
1
1
1
1
2
3
2
2
1
0
0
0
1
0
1
1
1
0
1
2
0
0
2
0
1
1
1
1
1
1
1
0
1
0
0
1
1
1
1
1
1
0
1
0
1
2
0
2
1
2
0
2
1
0
1
2
1
2
1
1
1
1
2
0
1
1
1
2
0
1
0
0
0
1
1
1
2
1
1
0
1
0
0
3
0
1
0
0
1
0
1
2
1
1
0
1
1
0
0
1
0
0
2
1
2
1
0
1
0
0
1
1
0
0
1
1
1
1
2
1
0
1
2
1
0
0
3
1
0
2
2
2
0
2
0
2
0
0
2
0
1
1
0
1
0
0
1
1
0
1
1
1
0
0
0
1
0
0
2
2
1
1
1
0
0
2
3
2
1
0
0
1
1
1
1
2
1
1
0
1
1
1
1
1
0
1
0
1
0
0
0
1
1
1
1
0
0
0
1
0
1
0
1
1
2
2
1
1
2
1
1
0
1
1
0
0
0
1
1
0
0
1
1
2
2
1
0
0
0
4
2
1
1
1
0
2
2
2
1
0
1
2
0
2
1
0
2
2
1
0
0
1
1
1
1
1
0
0
1
0
1
1
0
2
1
1
1
1
0
0
1
0
0
0
0
1
4
1
1
2
2
0
1
2
1
0
0
0
1
1
1
2
0
1
1
1
1
2
1
1
0
0
1
0
2
0
1
2
0
1
1
0
1
1
1
2
1
2
1
0
1
0
2
2
1
0
0
0
1
1
1
2
1
1
2
0
2
0
1
1
2
1
0
1
1
1
0
1
0
0
0
1
0
2
0
2
1
0
1
0
2
3
1
0
1
2
1
1
0
0
1
1
2
1
0
1
2
2
1
0
2
1
1
1
1
2
0
1
2
1
1
2
0
1
2
0
2
0
0
1
1
0
0
1
1
2
2
1
0
0
2
0
1
1
0
1
0
0
2
1
0
0
1
0
2
0
2
1
1
1
1
2
1
3
2
1
1
0
1
0
1
2
1
1
2
1
2
1
1
0
1
0
0
2
0
0
2
1
1
0
1
1
0
2
1
1
2
0
0
1
0
1
1
0
0
2
2
0
0
2
0
1
0
0
0
1
1
0
0
2
2
0
2
0
1
1
2
0
2
1
0
1
1
0
0
0
0
1
1
1
1
2
1
1
1
3
2
0
0
1
1
1
1
1
1
1
1
1
2
0
2
1
2
1
1
0
1
1
1
0
0
3
0
0
0
1
1
2
1
1
1
1
0
0
0
1
2
2
1
1
1
1
1
0
2
1
1
2
2
3
1
2
1
1
0
1
1
2
0
1
0
0
0
6
1
0
1
2
1
0
2
2
2
1
1
1
1
2
1
1
1
0
1
1
2
0
1
1
0
2
1
0
1
0
1
2
1
2
0
0
0
1
1
0
1
2
0
0
2
1
0
1
1
2
0
1
0
0
1
1
1
1
1
1
0
2
0
0
0
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
0
1
2
1
2
0
0
1
1
1
2
0
2
2
1
0
1
0
2
0
0
0
1
1
1
2
1
0
0
2
0
0
0
2
0
1
0
2
0
1
1
1
1
1
0
1
2
1
2
1
1
1
2
1
0
7
2
1
1
1
1
2
1
1
0
1
1
1
0
2
0
2
1
1
2
0
0
2
0
0
2
0
1
1
1
2
1
1
0
0
1
1
0
1
1
1
0
0
2
0
0
0
1
1
1
0
1
2
2
2
0
2
0
0
1
2
0
0
1
2
0
1
0
1
2
3
0
0
0
0
2
1
0
1
1
3
1
0
1
0
1
2
0
2
1
2
0
0
0
1
1
1
2
0
0
0
1
1
4
0
0
1
1
0
0
1
1
0
1
1
1
0
0
1
1
2
2
0
0
3
1
0
2
1
0
0
0
1
0
2
0
2
1
2
0
0
1
2
1
1
0
0
1
2
1
1
0
1
0
2
1
2
2
0
1
0
2
1
0
0
0
1
1
0
0
0
2
1
0
2
2
0
1
1
1
0
0
0
1
1
1
0
1
0
2
2
0
1
0
0
1
1
2
1
2
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
1
0
2
0
2
1
2
2
1
0
0
1
2
0
1
0
1
1
1
1
2
1
1
1
2
0
1
1
1
0
2
0
0
0
1
0
1
3
1
0
0
0
2
0
2
1
1
0
2
1
2
1
0
2
0
0
1
0
1
0
0
0
1
2
1
1
1
0
0
0
0
0
2
1
2
1
2
0
1
3
1
0
1
2
2
1
0
0
0
1
1
1
2
1
0
1
0
0
0
0
0
1
2
2
0
0
0
0
1
3
1
1
2
1
1
0
1
1
2
0
1
1
2
0
2
1
1
0
1
0
2
1
0
1
0
0
0
2
1
2
1
0
1
0
1
0
1
0
0
0
1
1
1
1
1
0
1
1
0
0
0
3
1
0
1
2
1
0
2
0
0
2
1
0
0
0
2
2
0
0
0
0
1
0
1
0
2
1
1
0
1
1
0
2
0
1
1
1
1
1
2
1
2
1
1
1
2
1
0
0
0
2
1
1
1
1
1
1
2
0
1
0
0
0
2
1
1
0
2
1
2
2
0
0
0
0
0
1
1
1
0
0
0
0
0
0
2
2
3
1
0
0
0
0
1
1
1
2
0
1
0
2
2
2
0
1
2
1
2
0
1
2
1
1
0
1
1
0
0
0
1
2
2
1
1
0
2
0
1
0
1
1
0
1
1
1
0
2
1
1
0
1
1
1
1
1
1
2
1
1
3
0
0
2
2
1
1
0
1
2
4
2
0
1
2
1
1
2
1
1
1
1
1
0
1
1
1
0
0
1
1
0
2
0
0
0
0
2
1
0
1
0
2
1
1
2
1
1
1
1
2
1
2
0
0
1
0
0
2
1
2
2
1
0
2
0
1
0
0
1
1
0
0
1
0
1
0
0
2
2
1
2
2
2
1
3
0
2
2
1
1
1
2
1
0
0
1
1
2
0
3
0
1
1
1
0
1
1
0
0
0
0
3
1
1
1
1
2
0
0
0
2
0
0
2
1
0
0
1
0
1
2
2
0
2
0
1
0
2
1
1
0
2
1
0
1
0
0
1
0
3
2
0
1
0
0
0
1
1
0
0
2
2
0
2
0
0
0
2
1
0
0
0
0
2
1
0
2
1
1
2
2
2
2
1
1
0
7
2
0
0
1
0
0
0
2
2
0
0
0
0
0
1
2
0
1
1
1
1
2
1
1
2
0
1
2
1
1
0
0
0
2
2
1
0
2
0
0
1
0
1
0
1
2
2
2
10
0
2
2
3
0
1
2
2
1
1
0
1
0
1
0
0
1
1
1
0
1
0
1
1
1
2
0
0
1
0
2
2
0
2
1
1
1
0
0
1
1
0
1
0
0
1
1
1
1
1
0
1
0
0
2
2
1
0
0
0
0
1
1
0
2
1
2
1
1
1
1
0
1
2
1
0
1
1
2
1
1
1
1
1
0
0
1
2
1
1
2
0
1
1
1
1
1
0
2
1
1
3
0
0
1
0
1
0
1
0
0
2
0
0
1
0
0
1
1
2
1
1
0
2
1
0
0
1
1
0
1
1
2
1
0
2
2
0
0
1
2
0
0
1
1
1
1
2
0
2
1
1
1
1
0
2
1
2
0
0
3
0
2
2
1
1
0
0
0
0
1
1
0
1
1
1
0
2
2
0
1
2
0
2
1
1
2
3
2
0
2
2
1
1
1
2
0
2
0
0
0
0
2
1
0
1
0
1
1
1
1
0
1
3
2
0
2
1
0
2
0
2
2
1
0
1
1
0
2
1
2
0
1
2
1
1
2
2
2
1
0
0
1
2
0
2
0
0
1
1
0
1
0
1
0
0
0
1
0
1
3
2
2
1
2
1
0
2
1
2
3
1
1
5
1
1
2
2
1
0
1
1
1
2
1
2
2
3
1
1
2
2
0
2
2
2
0
2
1
1
1
2
1
2
2
2
1
0
1
1
0
0
0
1
2
0
0
3
2
1
0
0
2
0
1
2
0
1
0
1
1
2
1
1
0
1
1
2
0
1
2
1
0
2
0
1
1
2
1
0
2
1
1
2
1
0
1
1
1
2
1
0
2
0
1
1
2
1
1
0
1
3
0
2
0
0
1
1
1
0
0
0
0
1
0
0
1
2
0
2
0
1
2
2
1
0
1
0
1
1
0
2
2
0
0
0
1
0
0
1
2
2
0
2
2
1
0
0
0
1
1
1
1
2
2
0
1
1
0
0
1
1
1
0
1
1
1
0
3
1
2
1
2
1
1
0
0
0
1
0
0
1
2
1
0
0
1
0
0
1
1
0
1
0
1
2
0
0
0
0
1
0
1
0
1
1
0
0
1
2
0
0
0
2
1
0
2
1
0
2
0
1
0
1
1
2
0
1
2
0
0
2
2
1
0
1
2
1
1
1
1
1
2
2
0
0
1
1
0
1
0
1
2
2
0
0
0
1
1
0
1
1
2
2
1
2
1
1
2
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
1
2
0
1
2
1
0
1
2
1
1
2
1
1
0
1
0
2
1
2
1
0
1
1
1
1
1
1
0
0
3
1
0
1
2
1
1
1
0
1
1
4
1
0
1
0
0
0
1
0
0
1
2
0
1
2
1
1
1
2
2
0
0
2
0
1
1
0
1
1
0
1
0
1
0
1
2
1
0
1
2
1
0
0
2
0
1
0
0
1
1
1
1
1
1
0
0
0
0
1
0
0
1
2
0
0
2
0
2
0
2
1
2
1
0
1
0
0
2
1
2
0
1
2
1
1
0
1
1
1
2
1
2
1
1
0
1
2
1
0
2
0
1
0
1
0
1
2
0
1
0
1
2
2
1
0
0
1
1
1
0
1
0
1
2
1
2
0
1
1
2
1
2
0
1
2
0
1
2
2
1
1
1
0
0
0
0
1
0
2
2
1
2
1
1
1
0
1
1
0
1
1
0
1
0
1
2
1
0
0
2
1
1
1
0
1
2
1
1
1
2
1
2
0
1
1
0
0
0
1
2
1
1
0
2
2
2
2
1
0
0
2
1
0
2
1
1
1
0
1
1
2
2
2
0
2
0
1
0
2
1
1
1
1
1
0
1
1
0
1
1
1
1
1
0
0
2
2
2
0
1
2
0
1
1
2
0
0
2
0
1
3
0
2
1
0
1
0
2
1
1
1
2
0
2
0
1
3
1
2
2
2
0
2
3
0
1
0
1
0
2
1
0
0
1
0
0
0
1
0
0
0
2
0
1
0
1
1
1
2
0
1
1
1
2
2
1
1
0
0
1
2
1
0
1
2
1
1
0
1
1
1
1
1
0
0
1
1
2
0
1
2
0
2
0
1
1
1
1
2
0
0
2
5
0
0
1
1
2
0
0
1
1
0
1
1
1
0
1
0
1
2
2
2
1
1
0
0
1
2
0
1
0
0
0
1
1
0
1
1
1
0
1
1
1
1
0
0
0
1
1
1
0
0
2
0
1
2
0
0
2
2
2
2
0
1
1
0
0
2
0
1
1
2
1
1
2
1
2
1
1
0
0
2
0
1
0
2
2
0
3
1
1
0
1
0
2
2
0
1
0
1
0
1
2
1
0
1
0
1
1
1
1
0
1
0
0
0
1
0
2
1
0
2
1
1
1
1
1
1
1
1
0
0
1
2
1
1
1
2
0
1
1
1
1
0
1
1
2
0
2
2
0
2
1
0
0
0
2
1
1
0
0
1
0
0
0
1
1
0
1
0
0
1
1
0
1
1
0
2
2
1
2
0
2
0
0
0
2
0
2
0
1
1
1
1
1
0
0
1
1
0
1
0
0
1
1
1
1
0
1
1
2
2
1
2
0
1
1
0
0
1
1
1
0
1
2
1
0
2
1
1
2
2
1
2
1
1
1
1
0
0
2
0
0
3
0
0
2
1
1
3
0
3
0
1
0
1
0
0
0
1
0
0
1
1
1
0
1
3
1
0
1
1
0
0
2
1
3
0
0
2
1
0
0
0
0
3
0
0
2
0
2
2
2
1
0
0
1
1
1
0
1
1
2
1
2
1
1
0
1
1
1
1
1
1
0
2
2
0
1
0
0
1
2
2
1
0
0
0
3
1
0
1
1
2
1
3
1
0
1
1
1
1
2
1
0
0
1
1
1
1
1
2
1
0
3
1
0
2
0
1
0
0
2
1
1
1
1
1
0
2
1
1
1
0
2
0
2
5
1
0
1
1
0
0
1
2
0
0
0
2
2
1
2
1
1
0
1
1
1
1
2
0
1
0
0
1
1
1
0
1
1
2
1
0
2
1
1
1
1
2
3
1
1
2
1
1
2
0
0
0
1
2
2
1
0
0
0
0
1
1
1
0
1
1
0
1
0
1
0
1
0
1
0
0
2
2
1
1
1
1
2
0
0
1
1
1
2
1
3
1
1
0
1
1
0
1
1
1
1
2
1
0
1
1
1
2
0
1
2
1
2
0
1
2
1
1
1
1
0
0
2
1
1
0
1
2
1
0
1
2
1
2
1
1
0
1
0
0
2
1
2
1
2
1
1
1
2
0
0
2
2
0
1
0
1
1
1
1
2
1
1
0
1
2
2
1
2
1
0
1
0
0
0
1
2
0
1
1
0
0
0
0
1
2
0
2
2
0
2
1
1
0
1
1
1
1
0
1
0
1
0
1
2
1
0
0
1
1
1
2
0
0
1
2
2
2
2
0
2
0
2
1
2
0
0
1
1
0
0
1
0
1
1
0
1
1
1
1
0
0
1
1
1
1
0
1
0
0
0
1
1
1
1
2
2
0
2
0
2
0
0
2
0
1
0
0
2
1
2
1
2
2
1
2
1
2
1
1
2
1
0
1
1
2
1
0
2
1
0
0
0
2
1
0
3
1
1
1
1
1
0
2
0
1
0
1
1
0
0
0
2
2
1
2
0
2
1
1
2
4
0
0
1
0
0
1
2
1
1
2
0
1
1
0
1
0
2
1
2
1
0
0
1
1
0
0
2
2
1
1
2
1
1
0
0
1
1
0
1
0
1
0
0
1
0
1
0
0
1
2
1
2
1
0
2
1
0
0
0
0
0
0
2
2
1
2
2
1
1
2
1
1
0
1
1
1
2
3
1
2
3
0
0
0
1
0
0
1
1
0
2
1
1
1
1
1
1
1
0
0
1
1
0
1
0
2
2
1
4
0
1
1
1
1
1
1
2
1
1
0
1
1
1
0
0
1
0
1
1
1
1
1
1
1
0
1
0
0
2
5
1
1
0
1
0
2
0
2
2
0
1
0
0
0
2
0
2
1
0
0
1
2
1
1
0
2
2
3
1
0
2
2
1
0
2
0
1
1
1
0
2
0
1
1
2
1
0
0
1
1
2
1
0
1
0
0
1
0
2
0
2
2
1
1
1
1
0
0
1
1
1
1
0
1
1
2
2
0
1
1
2
0
0
2
1
1
1
1
2
1
1
0
1
0
1
2
2
0
0
0
0
0
0
1
1
2
2
0
0
0
2
1
2
1
1
0
1
2
1
1
1
0
0
1
1
0
2
0
1
1
2
2
1
1
1
1
0
0
1
2
2
2
1
1
1
0
2
0
2
0
1
0
1
1
2
1
1
1
2
1
1
1
2
0
0
1
1
0
0
2
1
0
1
2
2
0
2
1
2
0
1
1
2
2
1
0
2
2
1
1
1
1
1
2
2
5
2
2
1
1
0
1
1
1
2
2
1
1
1
0
1
2
0
2
0
1
0
1
4
0
1
1
1
0
3
2
0
0
1
1
0
0
0
1
1
0
1
0
1
1
0
1
2
2
0
3
2
1
0
2
0
2
1
0
1
1
0
2
0
0
1
1
3
0
0
0
1
2
0
1
0
1
1
1
0
0
1
0
2
0
2
1
2
0
1
0
1
1
1
0
0
2
0
0
2
2
1
2
0
0
2
2
0
1
0
1
0
0
2
1
1
1
1
1
2
0
0
2
2
2
0
0
1
0
2
1
1
1
0
1
0
2
1
0
0
0
0
2
2
1
1
0
1
0
0
0
1
1
2
0
0
1
0
0
1
1
1
1
1
2
0
0
1
0
1
1
1
1
1
2
0
1
0
1
0
1
1
1
1
2
0
2
1
2
2
1
1
2
1
1
0
1
1
0
0
0
2
0
1
1
0
0
1
2
1
1
1
1
0
1
1
1
1
1
0
1
2
0
2
1
0
0
0
2
1
0
1
0
2
0
2
1
0
1
2
2
1
0
0
2
0
2
0
0
1
0
2
2
0
1
1
1
1
0
1
1
0
2
1
0
0
0
0
1
2
1
0
2
0
1
2
1
1
0
1
1
1
1
0
1
1
1
0
1
0
1
1
0
1
0
2
1
1
1
1
1
0
0
0
0
1
1
1
1
1
1
1
0
2
1
1
2
1
0
1
1
2
3
0
2
1
2
0
0
2
0
1
2
3
2
2
1
0
0
1
1
3
2
2
0
2
1
2
0
2
1
1
2
1
0
2
0
0
0
0
1
1
2
1
1
1
1
0
0
2
1
0
1
1
1
0
0
1
2
2
0
1
1
1
0
1
0
1
2
1
1
1
2
0
0
0
1
0
0
2
1
0
1
1
2
1
1
1
1
1
1
0
0
1
1
0
0
0
1
4
1
1
0
1
3
0
1
0
1
1
2
2
0
0
1
0
1
1
0
1
2
0
0
1
0
1
1
2
0
0
1
2
0
1
1
0
2
0
1
1
1
0
1
0
0
1
1
0
1
0
1
2
0
0
3
1
1
0
1
1
0
0
2
2
0
2
0
1
1
1
0
0
2
0
1
1
1
1
0
1
0
1
1
0
0
0
2
2
0
2
2
1
1
1
0
2
1
1
0
0
0
1
0
0
2
3
0
0
2
2
1
2
0
1
0
0
2
1
0
2
1
0
1
1
0
0
0
1
1
0
2
1
2
0
1
0
0
2
2
0
0
1
2
0
0
1
0
0
1
0
0
0
2
1
1
1
1
1
1
1
0
1
2
2
0
1
0
1
3
1
1
1
1
2
0
2
0
1
0
1
1
0
1
1
0
1
1
2
1
0
1
1
2
1
0
1
0
1
1
0
2
0
0
1
1
0
1
1
2
1
1
0
2
1
2
1
1
0
0
1
3
2
2
0
1
0
1
1
0
0
1
0
1
0
0
1
2
1
0
2
1
1
1
2
1
0
0
2
1
2
1
0
0
2
1
0
1
0
0
0
2
0
1
1
1
2
1
0
1
2
0
0
1
0
2
2
1
2
1
1
0
1
0
0
0
2
1
1
1
0
1
0
0
2
1
0
2
2
0
1
1
0
1
1
1
1
1
1
0
0
0
1
1
1
0
0
1
1
0
1
0
2
1
0
2
1
2
1
0
1
0
1
0
0
0
0
0
1
1
0
1
2
0
0
1
2
0
2
0
0
1
1
2
2
0
2
2
2
2
0
0
0
1
1
4
2
0
1
1
0
1
1
2
1
1
0
0
1
1
0
1
2
1
1
0
1
0
1
1
0
2
1
1
1
1
0
0
0
3
0
1
1
2
1
3
2
0
2
0
1
0
1
1
0
2
0
1
0
0
2
1
0
2
2
1
2
2
2
0
1
2
0
1
1
0
0
0
0
0
0
0
1
0
2
1
1
1
1
0
2
2
1
1
1
2
1
0
0
1
2
1
0
1
1
0
2
1
1
1
0
1
0
1
2
1
1
1
1
0
1
2
1
1
1
1
3
1
0
2
0
2
1
0
1
1
0
0
1
1
0
0
0
0
1
2
0
2
0
0
2
2
2
1
1
1
0
0
0
1
1
1
0
0
1
0
1
2
1
1
0
1
0
0
2
1
2
0
2
1
1
2
0
1
0
1
1
2
0
2
1
2
2
2
1
1
1
2
1
1
1
1
0
0
0
1
2
2
0
1
1
1
1
0
2
2
0
0
0
1
2
0
2
1
0
2
1
0
0
0
0
0
0
1
1
0
1
1
2
2
1
1
1
1
0
1
1
2
1
2
1
1
0
1
1
1
0
1
0
0
1
1
0
2
0
2
1
0
1
1
1
1
1
1
0
1
0
1
1
3
1
0
0
0
0
0
1
1
1
1
0
1
0
1
0
2
1
0
1
0
0
0
1
0
0
0
1
0
1
1
0
0
1
0
1
1
1
0
2
0
1
1
1
2
1
1
1
0
2
1
0
1
2
2
2
0
1
1
1
0
1
0
1
1
1
1
1
0
0
1
1
1
2
0
1
0
2
1
0
1
2
0
1
1
0
2
1
0
1
1
0
0
0
1
1
0
1
0
1
1
1
2
2
1
1
1
4
1
1
2
1
1
1
0
2
1
1
1
0
0
1
2
0
1
1
2
1
1
1
1
1
0
1
1
1
1
3
0
0
2
1
1
1
1
0
1
1
0
0
2
2
1
0
1
0
2
1
2
1
2
1
0
1
2
0
1
0
2
1
2
0
1
0
0
0
2
0
1
1
1
1
2
0
2
2
1
0
0
0
0
1
1
0
2
0
1
0
0
1
1
0
0
1
2
1
2
0
1
0
0
1
0
0
1
1
0
1
2
0
2
1
2
0
1
0
1
0
1
2
0
1
0
2
1
1
1
1
2
1
2
0
0
1
2
1
0
0
1
1
0
1
0
2
0
1
1
1
0
2
2
3
1
1
1
0
1
1
1
2
1
0
1
0
2
1
2
2
0
0
0
1
0
1
1
1
1
2
1
1
2
2
0
1
2
0
0
2
1
2
1
2
1
2
1
0
1
0
1
0
2
0
1
0
0
1
2
1
2
1
1
2
0
0
1
2
0
1
2
0
0
2
0
1
2
1
2
1
1
2
0
2
0
2
1
0
1
0
1
1
1
2
0
1
1
0
1
0
3
0
2
0
1
2
1
1
1
1
0
0
1
1
1
1
1
2
1
1
0
2
0
1
0
2
2
1
2
2
0
1
1
2
1
1
0
0
0
2
1
2
0
0
0
1
2
1
0
1
2
2
0
0
1
1
1
0
2
0
2
1
0
1
1
0
3
2
0
0
2
1
3
0
2
0
1
1
0
0
2
1
2
1
1
0
0
2
1
0
0
2
2
2
0
1
1
2
0
0
1
1
0
2
0
1
0
1
1
2
1
1
0
0
0
0
0
1
2
1
0
2
2
1
0
0
0
3
2
2
1
2
0
2
0
1
2
0
0
1
1
1
0
1
0
2
0
0
0
1
1
2
1
3
2
1
1
2
1
0
0
1
1
1
1
1
1
0
0
0
1
1
0
0
2
1
2
0
0
1
2
2
1
0
0
1
1
2
0
1
2
0
1
1
1
0
3
0
0
1
0
0
1
1
2
1
0
0
1
1
1
0
0
0
0
1
1
0
0
0
1
0
1
2
0
1
0
1
1
1
1
1
1
1
1
1
2
2
1
1
2
2
0
1
1
1
1
2
4
1
1
0
0
1
2
0
0
0
0
0
1
1
2
1
2
2
0
2
2
1
1
2
0
1
1
1
1
1
0
0
0
1
0
0
1
1
1
2
1
2
2
0
1
0
1
0
1
0
0
2
1
0
1
2
0
1
0
1
1
2
0
0
2
1
0
1
1
2
1
1
1
1
2
1
0
0
1
1
1
1
0
0
1
0
1
1
2
0
0
2
0
1
1
1
0
1
0
1
2
1
0
1
0
0
0
2
1
1
1
2
0
1
0
1
1
1
1
0
0
0
2
0
0
2
1
0
0
0
1
2
1
2
0
0
2
1
0
0
2
0
1
1
1
0
1
1
1
1
0
0
0
0
1
1
1
0
1
0
1
1
1
1
0
3
2
0
0
1
2
0
1
1
1
2
1
2
2
1
0
0
0
1
1
1
1
1
0
0
0
1
0
0
0
0
2
2
1
0
0
0
1
1
1
2
0
5
2
0
2
1
1
0
1
0
1
2
2
0
1
1
1
1
0
1
1
1
3
1
2
1
2
0
1
1
1
1
0
0
0
1
0
1
2
0
1
1
0
2
1
1
1
0
1
0
1
0
2
0
2
1
1
1
0
1
2
2
2
0
2
1
1
0
2
0
0
0
1
0
0
0
2
1
1
0
1
2
0
1
0
2
1
3
1
0
1
1
1
1
1
1
3
0
1
1
0
3
1
0
0
1
2
1
0
2
0
2
0
2
0
1
2
1
0
0
1
1
2
1
0
2
2
2
1
2
0
1
1
1
0
1
0
0
1
1
1
1
3
2
2
1
2
0
0
0
1
0
1
1
1
1
1
1
0
1
1
0
0
1
2
1
1
1
0
1
0
1
1
0
1
1
1
0
1
1
0
1
0
1
0
2
0
0
1
1
2
0
1
0
1
0
0
2
0
1
1
0
0
1
2
1
0
2
2
1
0
0
0
2
1
0
0
1
0
1
2
1
1
2
0
0
0
2
1
1
1
1
1
0
2
0
1
1
1
0
1
1
1
1
2
1
1
0
0
1
0
1
1
1
1
0
0
0
2
0
1
2
0
0
1
1
0
0
0
2
0
1
2
1
0
1
1
0
3
1
0
2
2
0
1
0
1
1
1
2
0
3
2
2
1
1
0
0
0
0
0
0
1
0
0
2
2
2
1
1
2
1
0
1
1
1
2
1
1
1
1
3
1
2
1
0
0
1
1
1
0
0
1
4
0
1
1
2
1
0
1
0
2
1
1
1
1
0
1
1
0
1
1
2
0
1
0
2
1
0
2
0
1
1
0
2
0
2
1
1
2
1
2
2
1
1
2
2
1
0
1
0
1
0
1
0
1
1
0
0
1
1
0
0
1
0
1
1
2
1
0
1
0
1
0
1
1
2
0
0
2
0
1
1
1
1
1
0
2
2
1
0
1
1
0
0
0
2
2
2
1
1
0
0
2
2
1
0
1
2
1
3
0
2
2
2
2
2
0
1
1
1
1
2
2
1
0
1
0
1
2
1
0
2
1
0
0
2
2
0
2
1
0
1
0
2
1
0
1
0
0
0
1
2
0
1
0
0
2
0
0
0
1
1
2
0
0
1
1
1
1
2
1
2
0
1
1
2
2
2
0
1
0
0
0
1
2
5
2
0
1
1
0
1
1
1
2
1
1
1
0
1
1
1
4
1
0
2
1
0
2
0
2
2
1
1
1
2
0
1
2
0
1
0
0
1
1
1
2
1
0
2
1
2
2
0
1
1
1
0
1
1
0
0
1
1
0
0
1
0
2
0
0
2
1
2
1
0
2
1
1
0
0
2
0
1
1
0
0
1
0
1
1
1
1
0
0
1
1
2
0
1
1
1
1
1
1
0
2
2
0
2
2
0
1
2
2
0
0
1
1
1
0
0
1
1
2
2
0
2
1
1
2
0
2
1
1
1
1
1
0
1
1
1
1
0
0
0
2
0
1
1
1
1
0
2
2
1
1
0
2
0
1
0
0
1
0
1
1
1
0
5
0
1
0
0
2
0
0
1
1
0
0
1
0
1
0
1
1
1
2
1
3
0
2
1
1
1
0
3
0
1
2
0
1
0
0
1
0
0
1
0
1
1
2
1
2
0
1
0
1
1
1
0
2
2
0
0
1
0
2
1
2
0
1
1
1
3
1
0
0
0
2
0
0
1
1
0
0
1
2
2
0
2
0
1
1
0
1
0
0
0
1
1
0
1
0
0
1
1
2
2
0
1
1
2
1
1
1
0
2
1
2
0
2
1
1
0
0
0
0
1
0
0
0
1
1
0
1
0
1
2
1
1
2
1
1
0
1
2
1
1
1
1
0
2
1
0
1
1
1
2
1
2
2
1
1
0
0
1
1
2
2
1
1
2
1
0
1
1
1
1
2
1
2
0
2
2
2
0
0
0
1
1
1
0
1
0
1
0
3
2
1
1
1
0
0
2
2
1
3
2
1
0
1
1
1
0
0
0
1
1
0
1
2
0
0
0
1
1
1
2
1
1
0
0
1
2
0
0
1
0
2
0
2
0
1
2
1
1
2
1
1
0
1
0
0
1
2
1
2
2
0
1
1
1
1
0
2
1
0
2
0
0
0
0
2
1
0
2
1
1
1
0
1
0
1
0
2
1
2
1
1
1
1
0
0
1
1
1
2
1
2
1
2
0
0
1
1
0
0
2
0
1
2
1
0
1
1
2
2
1
0
1
2
0
1
1
2
1
1
1
0
1
1
2
0
1
1
0
1
1
1
1
2
2
1
1
1
1
1
0
2
2
0
1
0
1
1
0
2
1
1
2
1
0
1
2
1
0
0
0
1
3
0
0
2
2
1
2
1
2
0
2
2
0
1
1
0
0
0
1
0
1
0
0
0
1
0
2
0
0
0
1
1
2
1
1
0
0
2
2
0
2
0
1
0
1
0
1
2
2
1
1
0
1
0
0
0
0
1
2
1
1
1
1
2
0
1
0
2
0
0
1
1
1
0
0
1
1
1
1
1
0
0
1
2
0
1
2
2
2
1
2
1
2
1
2
0
1
0
0
0
0
1
1
0
1
2
0
1
0
2
0
0
1
1
1
0
0
1
1
1
0
1
0
0
2
2
2
1
0
1
0
2
0
0
2
0
2
1
0
1
0
1
0
0
0
1
1
2
1
0
1
1
2
0
0
1
0
0
2
2
0
0
0
0
1
2
1
1
1
1
1
0
0
0
1
2
1
2
1
1
0
1
3
1
1
1
0
1
1
1
0
1
0
2
2
1
1
0
0
0
2
1
1
1
1
1
1
1
1
1
1
1
1
0
1
2
0
0
0
1
1
1
1
0
1
1
2
0
1
1
2
2
1
1
0
1
1
0
2
0
1
1
2
0
1
1
0
0
0
0
2
1
0
1
2
0
2
0
0
2
0
1
0
0
1
1
0
0
2
0
0
2
0
2
0
2
0
0
0
1
2
4
1
0
0
2
1
0
0
1
1
1
2
2
1
1
0
0
0
1
1
2
1
0
0
1
1
1
2
1
2
2
1
1
0
2
1
0
0
0
0
1
1
0
2
2
2
2
0
0
0
0
0
2
0
2
0
1
0
0
1
1
1
2
2
1
0
2
1
0
1
0
0
1
1
0
0
0
0
1
1
1
1
1
1
1
2
1
0
2
0
0
0
1
1
1
0
1
2
0
1
0
2
1
0
1
0
1
1
1
0
1
2
2
2
1
0
1
2
1
2
2
0
1
2
2
1
0
1
2
1
1
1
0
1
1
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
1
1
0
1
0
0
2
1
0
2
1
1
0
0
1
1
0
1
1
1
1
1
1
1
1
1
1
1
2
1
2
2
0
1
1
2
1
1
0
1
0
0
1
0
0
2
2
1
2
1
1
0
2
0
2
1
1
0
1
2
0
2
1
1
1
1
1
1
0
0
1
0
2
2
0
2
0
1
0
1
0
1
2
0
1
1
1
2
0
2
1
0
2
1
2
1
1
1
2
0
1
1
1
1
1
1
1
2
0
1
1
1
1
0
0
2
1
1
1
1
1
0
1
2
0
2
1
1
2
1
1
2
2
0
1
1
0
2
1
2
4
2
0
1
0
2
1
2
1
1
0
0
2
0
1
0
1
1
0
0
1
1
1
1
1
0
1
2
0
2
1
2
2
0
2
1
0
2
1
1
0
2
2
1
0
1
1
1
0
1
1
0
1
0
2
2
2
2
0
2
0
0
1
2
1
2
0
2
0
1
1
2
1
1
1
1
0
1
2
0
0
1
2
0
1
1
2
0
0
2
1
1
0
0
0
1
1
1
2
2
1
0
2
0
2
1
0
1
1
0
0
1
2
1
2
0
0
1
2
1
2
6
1
0
2
0
1
1
1
2
2
1
1
1
1
0
0
0
2
2
1
2
0
1
0
1
1
2
1
0
1
1
1
2
1
2
1
0
0
1
1
2
1
1
1
0
1
0
1
2
1
2
2
0
0
2
0
1
2
1
1
1
2
1
1
1
0
1
1
1
2
1
1
1
0
1
0
1
0
0
1
3
1
0
0
2
1
1
2
1
2
1
0
1
1
1
1
1
1
0
4
2
0
0
0
1
2
1
1
2
0
2
1
0
1
1
0
3
2
2
1
0
3
2
1
0
0
0
0
2
1
2
0
2
0
0
0
1
2
1
1
0
1
2
0
1
1
1
1
0
2
0
0
0
0
0
0
0
0
1
2
0
0
2
1
0
1
1
0
1
1
0
0
2
2
1
1
1
1
0
0
0
1
0
2
0
1
0
1
1
1
0
0
1
2
1
2
0
3
2
1
0
0
1
0
0
1
1
1
2
0
0
1
1
3
0
1
2
1
2
0
1
0
2
2
1
1
1
0
2
0
2
1
1
1
0
0
2
0
2
2
0
0
0
1
3
0
0
1
0
1
1
1
1
0
2
0
2
1
1
2
0
0
1
0
1
1
0
0
1
1
1
1
0
0
1
2
0
0
1
1
0
0
0
1
1
0
0
0
0
2
2
0
1
1
2
1
1
1
0
1
0
0
2
4
1
2
1
2
1
0
1
0
1
0
1
0
1
2
1
1
1
2
3
1
1
1
1
2
0
0
2
0
2
0
0
2
1
2
1
2
0
0
2
0
1
0
1
2
1
0
0
1
1
1
1
2
1
1
1
2
1
0
0
2
1
1
1
2
1
1
0
2
2
0
1
1
2
1
0
1
0
0
1
1
1
1
2
0
2
0
0
1
1
0
0
1
1
0
1
1
1
0
1
0
2
2
2
1
0
1
1
2
0
2
0
2
1
2
2
2
1
2
0
0
0
1
1
1
1
1
0
1
2
2
0
2
1
0
1
2
1
1
0
2
1
1
0
0
0
1
2
1
0
1
0
2
0
1
1
0
0
0
1
1
1
1
0
0
1
1
0
0
0
1
0
0
2
0
0
1
1
1
2
0
1
0
1
2
0
0
1
1
0
0
0
1
0
1
0
1
1
2
1
2
2
1
0
2
0
1
0
0
0
1
1
0
1
0
1
1
0
1
1
0
0
1
0
1
1
1
1
1
1
1
2
0
0
2
1
0
2
1
2
1
2
1
0
1
1
2
0
0
0
1
0
2
2
1
2
1
0
4
1
1
0
1
0
1
0
1
2
0
2
2
1
1
0
0
2
2
1
2
2
0
1
1
1
2
1
2
0
1
2
1
0
1
0
1
2
2
1
0
0
0
0
1
0
1
1
0
0
1
0
3
2
1
0
2
1
0
1
2
1
1
0
1
2
1
1
1
1
2
1
1
1
0
1
0
0
1
1
1
0
0
1
0
0
2
0
0
1
2
1
1
1
1
1
2
1
2
0
0
1
2
0
0
0
1
0
1
1
0
1
1
2
1
0
1
0
1
2
1
1
1
1
1
1
0
1
3
0
3
2
0
0
1
1
0
0
1
0
2
0
0
2
1
0
0
2
1
0
0
1
1
1
0
2
0
2
1
0
1
1
0
2
1
1
0
0
1
1
0
1
0
0
1
1
1
1
0
0
0
1
2
1
0
1
0
0
0
2
0
2
0
0
1
2
1
1
1
0
0
2
2
0
0
1
1
1
0
2
2
0
1
0
2
0
0
2
1
1
1
0
1
2
0
2
1
0
0
2
0
0
2
0
1
0
1
1
2
0
0
0
1
0
2
0
2
1
1
3
1
1
3
1
2
0
2
1
0
2
1
1
2
1
0
0
1
1
2
1
0
1
1
0
0
1
1
1
2
0
0
0
2
2
1
1
1
2
1
0
0
2
1
1
2
2
0
0
0
1
0
2
0
0
1
1
2
0
1
2
0
0
1
0
2
0
0
0
1
0
0
1
1
2
1
0
1
2
0
1
2
0
1
1
1
2
0
0
1
1
0
0
2
1
0
0
1
1
2
0
1
1
1
0
0
1
2
1
1
1
1
0
0
2
0
0
0
0
2
2
1
0
2
0
1
0
2
1
2
0
1
1
0
1
0
0
1
0
2
0
2
0
0
2
1
0
0
1
1
0
0
0
2
2
0
1
0
1
1
2
1
0
0
0
1
2
2
1
1
1
2
1
2
1
1
1
2
2
1
2
0
1
0
0
2
1
1
0
2
1
1
0
0
1
1
2
1
1
0
1
1
1
0
0
0
1
0
1
2
1
1
2
1
1
1
1
1
1
1
1
1
0
0
0
2
1
0
0
0
0
1
1
0
0
1
1
1
0
0
0
0
0
1
1
2
0
0
1
2
3
1
3
1
2
1
2
1
1
1
0
0
0
2
2
1
0
2
0
0
0
1
1
1
0
0
0
1
2
1
2
1
0
0
1
0
2
2
0
1
2
1
1
1
1
1
0
1
2
1
0
1
1
0
2
0
0
1
1
2
0
0
1
1
0
1
2
1
2
2
1
0
0
1
1
0
2
1
1
2
0
0
0
2
1
1
2
1
1
1
2
2
2
1
1
2
2
2
3
1
0
1
2
1
1
1
0
1
0
0
1
1
2
2
2
0
1
0
0
2
1
0
0
1
2
2
2
0
1
0
0
1
2
2
1
1
1
0
1
0
2
2
1
2
1
1
2
2
1
0
0
0
1
1
1
1
2
1
1
0
1
1
1
2
2
1
1
1
0
2
0
1
1
1
0
1
1
2
2
2
2
1
2
1
1
2
1
2
1
1
2
1
2
1
1
0
1
1
2
1
0
0
2
0
2
1
0
2
1
0
0
1
0
1
2
0
1
2
0
0
1
0
0
3
0
2
1
2
1
2
2
2
0
1
0
2
0
0
0
0
1
0
1
0
0
1
1
1
0
0
1
0
0
3
1
0
1
1
2
1
0
1
0
0
1
0
1
1
2
0
1
1
1
1
0
1
0
0
0
0
1
2
1
0
1
0
0
0
1
2
0
1
1
2
0
2
1
2
0
1
2
0
1
0
1
0
2
0
0
2
0
0
1
1
2
3
0
1
1
3
2
2
2
1
1
0
1
1
2
1
2
0
1
1
1
0
0
0
1
0
0
1
0
1
0
1
1
1
2
0
1
1
1
2
0
0
2
2
0
3
2
2
1
1
2
1
2
1
0
2
0
2
2
2
1
1
2
0
1
1
1
1
2
0
1
1
0
2
0
1
1
2
0
1
1
2
2
1
0
1
1
2
0
2
2
1
2
0
1
1
1
1
1
1
1
0
0
1
0
2
0
1
0
2
1
0
1
0
0
2
1
2
2
1
2
1
1
1
1
1
1
2
2
0
0
1
2
1
0
1
2
1
2
3
1
2
0
0
0
3
0
1
1
1
2
2
1
2
1
1
1
1
2
1
2
2
0
1
1
0
0
0
0
1
0
1
1
2
0
1
1
2
0
3
1
1
2
1
2
1
1
0
1
1
1
1
0
2
1
2
0
0
1
0
0
0
1
2
0
0
1
1
1
0
2
1
0
2
2
1
1
0
1
0
0
1
0
2
2
2
0
1
1
0
0
1
0
2
0
0
1
2
1
0
1
1
1
0
1
2
2
0
1
0
0
1
0
0
1
1
1
0
2
0
0
0
0
0
1
2
0
0
0
1
1
2
1
1
0
1
1
0
0
0
1
0
2
1
0
1
1
1
1
1
1
2
0
1
0
0
2
2
1
1
1
0
1
1
1
2
1
1
1
1
1
1
1
1
0
1
0
1
2
1
0
2
1
1
0
1
2
1
1
2
1
0
1
0
1
0
2
1
1
1
2
0
1
0
2
1
0
1
2
2
0
0
1
1
0
0
2
0
3
1
1
0
2
1
0
1
0
0
0
1
0
1
0
1
1
1
0
0
1
1
4
1
0
1
1
1
2
0
1
1
1
2
2
1
0
2
1
2
1
2
0
0
0
1
2
0
0
1
1
1
1
1
1
1
2
1
0
1
1
0
2
1
1
0
2
0
1
1
2
2
0
1
1
1
0
2
1
1
2
2
1
0
0
0
1
2
0
2
2
0
2
0
1
0
1
1
2
1
2
0
0
2
0
1
1
0
0
2
0
0
2
2
1
0
1
0
1
0
2
0
0
1
1
0
0
0
0
0
2
1
0
0
0
2
1
0
0
1
1
1
1
1
0
0
0
2
0
0
0
0
0
2
2
0
2
0
3
0
1
1
1
1
1
0
1
2
2
2
0
2
1
2
1
1
0
2
0
0
2
0
0
0
1
2
1
2
1
1
0
1
1
1
0
2
2
1
1
0
0
2
1
1
1
0
2
1
1
1
0
0
1
1
1
2
1
1
2
1
2
2
1
1
1
1
1
1
2
0
1
2
0
2
2
1
2
0
2
1
0
1
2
2
0
1
2
1
0
0
1
0
2
0
2
0
1
1
2
0
1
0
1
1
1
1
1
1
0
1
1
1
0
0
0
1
0
0
1
0
0
1
2
1
1
0
2
1
0
0
1
2
1
1
2
2
1
1
1
1
0
1
2
0
0
1
3
0
3
1
1
0
1
1
1
0
0
2
1
1
2
1
0
1
2
1
1
0
0
1
0
0
1
0
1
1
1
0
1
0
2
1
2
0
0
2
2
1
2
1
1
0
2
0
2
1
1
2
1
1
1
2
1
1
0
1
0
1
1
1
2
1
1
2
0
1
0
0
2
1
0
0
0
2
1
1
0
0
2
1
1
2
1
2
2
1
0
1
6
2
0
1
1
2
2
0
1
1
1
1
0
0
0
0
1
0
1
1
2
0
1
2
1
2
2
2
1
2
0
2
1
1
0
0
1
2
1
1
1
2
1
1
0
2
1
0
1
2
1
1
0
2
0
2
0
0
0
1
2
0
1
2
0
1
1
1
2
0
0
0
0
1
0
1
1
2
1
1
0
1
2
0
1
1
2
1
1
1
1
1
1
1
0
2
0
0
2
1
0
0
1
1
1
0
1
0
2
1
1
0
0
1
1
0
2
1
1
1
1
1
1
1
0
2
1
0
2
0
1
2
0
1
2
3
2
0
1
1
2
1
0
1
3
0
1
1
0
2
1
0
1
0
1
0
1
2
2
0
2
1
0
0
0
1
1
1
1
0
0
0
1
0
2
0
0
0
1
2
0
1
1
1
2
1
2
1
0
0
1
2
1
0
2
0
1
1
1
2
1
0
2
2
1
0
0
1
0
0
2
2
1
2
1
1
1
1
1
1
1
0
0
0
0
1
1
0
0
0
1
1
2
1
1
1
2
1
1
0
0
0
0
0
2
1
0
1
1
2
0
1
2
2
0
0
1
2
0
1
0
1
0
0
1
0
1
2
3
0
3
0
0
0
0
1
1
2
1
1
1
0
2
0
0
2
1
2
1
0
1
0
1
0
1
1
0
2
1
0
2
1
2
2
0
1
1
1
2
1
1
2
0
1
2
0
0
0
1
0
0
1
3
0
2
1
1
1
1
0
1
2
0
1
3
0
0
0
0
0
2
1
1
1
0
0
0
0
1
1
1
2
2
0
0
1
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
0
0
1
0
1
1
2
2
0
1
2
1
1
0
2
1
0
2
1
1
1
0
2
1
1
1
2
0
2
1
0
1
0
2
0
0
1
2
2
0
1
3
2
2
2
0
1
2
2
2
0
0
1
1
1
2
1
0
1
1
1
2
0
2
0
2
0
1
2
0
1
1
0
0
2
0
4
1
1
0
0
0
1
2
1
1
1
1
0
2
0
0
1
0
0
0
0
2
0
0
0
1
2
2
1
2
1
0
1
1
2
1
2
1
0
2
0
2
0
0
1
0
1
1
1
3
0
1
1
2
1
2
2
1
0
2
0
0
1
1
1
0
0
1
1
1
0
0
0
1
0
1
0
1
1
2
1
0
0
1
0
0
1
1
2
0
0
1
1
1
1
2
0
1
1
0
0
0
1
0
0
2
0
3
1
0
1
2
0
1
0
2
1
2
0
2
0
1
1
1
0
1
0
1
0
1
1
0
1
0
2
0
0
0
2
0
1
2
2
0
2
1
0
2
1
2
0
2
0
1
1
1
1
0
2
2
0
0
0
0
0
3
0
1
1
1
1
1
1
1
1
2
1
0
3
0
1
1
1
1
1
1
2
1
0
1
1
2
3
0
1
0
0
1
1
1
1
2
0
1
1
0
1
2
1
1
1
0
0
1
1
0
1
2
1
1
1
0
0
1
1
1
0
2
3
2
0
0
0
0
0
1
0
2
1
0
5
1
1
0
1
0
1
0
2
0
1
1
0
0
2
1
0
0
1
1
2
1
1
0
1
2
1
1
0
0
1
0
0
0
1
0
1
1
1
1
1
0
0
0
1
0
0
2
1
1
1
1
1
1
1
1
0
2
1
1
2
1
1
2
0
1
2
0
1
0
4
0
2
0
2
1
2
0
1
0
1
2
0
0
0
0
1
1
0
2
0
0
2
0
2
0
1
1
1
0
0
0
0
1
1
2
1
0
2
1
1
1
0
1
0
1
1
1
0
0
1
1
1
1
0
1
1
0
0
0
1
1
0
1
0
1
0
1
2
1
1
1
0
0
0
1
0
1
1
2
1
0
0
2
0
2
1
1
1
1
2
0
1
0
0
0
0
1
1
0
0
0
2
1
0
1
1
0
1
0
0
2
1
0
0
2
0
0
1
2
2
1
1
0
1
1
0
1
1
1
1
1
0
2
0
0
1
1
1
1
0
0
2
2
2
1
1
0
1
0
2
1
0
1
1
0
1
1
1
1
0
1
2
1
0
0
0
1
1
1
0
1
1
0
1
1
1
0
0
1
2
1
1
2
0
1
1
2
1
0
2
2
2
0
1
2
1
0
0
1
1
0
0
0
2
1
0
1
1
0
0
0
2
1
0
1
0
1
0
0
0
1
0
1
2
1
1
0
1
5
1
1
0
1
0
2
0
1
2
1
0
2
1
2
1
0
1
0
2
1
2
0
1
1
2
0
0
1
2
0
2
1
1
0
0
1
0
1
0
1
2
1
1
2
2
0
1
0
1
2
1
0
0
0
1
1
0
2
0
1
2
0
1
2
0
0
1
0
1
1
2
1
1
2
1
0
1
0
1
1
1
0
0
1
0
2
1
1
0
1
2
1
2
1
2
0
1
2
1
1
2
0
1
2
0
0
1
2
0
0
1
2
0
1
2
1
1
0
1
1
1
0
0
1
0
2
1
1
1
0
1
0
2
1
0
0
1
0
1
1
0
0
0
1
1
0
1
1
1
2
0
2
1
1
1
1
1
1
0
2
1
1
2
2
1
1
0
1
0
2
2
2
2
0
1
0
1
1
0
1
1
0
2
0
0
0
1
0
0
1
1
1
1
0
1
0
2
1
1
2
2
0
0
0
0
1
2
1
0
2
0
0
2
0
0
0
0
1
0
2
1
2
0
0
0
0
1
0
1
2
2
1
0
0
1
0
0
2
1
1
1
0
2
0
1
0
1
0
2
0
2
1
1
2
2
1
2
0
0
0
2
0
0
1
0
2
1
2
2
0
0
2
2
0
1
0
1
1
2
1
2
1
1
1
0
1
0
1
2
1
1
0
0
2
1
2
2
2
1
1
0
1
0
0
1
0
1
0
2
0
0
1
1
1
0
1
0
1
2
2
0
0
1
1
1
1
2
1
1
0
1
0
1
0
0
1
1
1
1
1
1
1
1
0
0
0
1
2
2
1
1
2
2
1
1
0
1
0
1
1
0
1
0
2
1
1
1
1
1
2
0
1
2
0
0
2
1
1
1
1
1
2
1
1
1
2
1
1
1
1
1
1
0
1
1
1
0
1
1
1
0
1
1
0
1
1
1
2
1
1
1
1
0
0
3
0
1
1
1
3
1
2
2
0
1
0
1
0
1
2
1
2
1
1
2
1
2
0
2
1
1
1
2
0
1
0
2
2
1
2
2
1
1
0
2
0
2
4
0
0
1
1
1
1
1
0
2
0
1
2
1
1
1
2
0
1
2
1
0
1
2
0
2
1
1
0
1
0
0
0
1
1
1
1
1
1
1
2
1
0
0
2
0
0
1
2
1
1
0
0
1
1
0
2
2
1
0
0
1
1
0
1
1
1
1
1
2
0
0
2
1
0
2
1
1
0
2
2
1
2
0
2
1
0
1
2
1
1
0
2
2
0
2
1
1
2
2
0
2
1
1
1
2
1
1
0
1
0
0
1
2
1
1
0
1
0
0
1
1
1
1
0
1
0
1
1
2
1
1
1
1
1
1
2
0
1
1
0
1
1
1
0
0
1
1
1
2
0
2
0
1
2
1
1
0
2
1
2
0
0
2
0
0
0
1
1
2
2
2
2
0
1
0
0
0
0
2
2
2
1
1
1
2
0
1
0
1
1
2
2
0
2
1
1
1
1
2
2
1
2
2
1
1
0
0
1
0
0
2
1
2
0
0
1
0
1
0
1
1
1
0
2
0
0
1
0
0
0
0
1
1
1
0
1
1
1
2
0
1
2
1
1
1
1
0
2
1
1
1
1
2
1
2
1
0
1
1
0
1
0
1
1
1
0
1
1
0
1
1
2
0
0
2
1
1
1
1
1
1
0
1
0
1
1
0
2
2
0
1
0
2
2
0
1
1
1
1
1
1
1
1
1
0
1
1
0
1
1
0
2
0
0
1
0
0
0
2
0
2
0
1
1
0
1
0
1
1
1
1
1
0
1
0
1
2
1
2
2
1
0
1
0
0
0
0
0
0
1
1
2
0
1
0
1
1
1
0
2
0
2
2
1
1
1
1
1
0
1
2
1
0
3
1
0
0
2
2
3
0
0
1
1
1
2
1
1
1
0
0
0
1
1
0
0
1
1
1
1
1
0
1
0
0
2
2
2
1
0
0
0
1
0
0
3
0
1
0
0
3
0
1
2
2
0
0
1
0
0
0
0
3
2
3
0
2
1
2
1
0
1
2
0
1
2
0
1
0
0
0
1
0
2
1
1
2
2
1
1
0
1
0
0
2
1
2
0
1
0
0
0
1
1
0
1
2
1
1
1
2
2
1
1
0
2
2
0
0
1
0
2
1
1
2
2
1
0
1
1
1
0
2
2
1
0
0
3
1
1
1
2
2
2
0
1
1
0
1
1
1
0
0
2
0
1
1
0
1
0
1
3
1
1
0
1
2
2
2
0
0
1
1
0
1
0
0
1
1
0
0
0
0
1
2
2
2
1
2
0
1
0
1
1
1
1
2
0
1
1
2
2
0
0
1
2
2
1
0
1
0
0
0
1
1
0
1
1
1
1
1
1
2
1
2
1
1
0
1
1
0
0
0
1
1
1
1
1
2
1
0
1
2
1
2
1
1
1
2
0
2
3
0
3
1
0
2
2
0
2
1
0
2
1
1
1
3
1
1
1
2
2
0
1
1
2
1
1
2
1
1
2
1
0
2
1
1
1
0
2
2
1
0
0
0
0
0
1
2
1
2
0
1
0
1
2
0
0
2
0
1
1
0
0
1
1
2
1
2
2
0
0
1
1
1
1
1
0
1
0
1
0
2
1
1
0
0
1
0
1
0
1
1
0
2
2
1
1
2
3
1
0
0
0
2
1
2
1
0
1
1
2
2
2
2
0
2
3
0
1
1
1
1
1
1
1
1
1
0
1
0
2
1
2
2
1
1
3
0
2
1
0
1
0
0
1
1
0
2
2
0
1
1
1
1
2
1
1
2
1
0
0
1
0
0
0
1
0
1
1
0
0
1
1
0
1
0
1
1
1
2
0
1
2
3
2
0
1
1
2
1
1
2
1
2
0
2
2
1
0
2
2
0
1
3
0
1
0
0
1
0
1
2
0
1
1
1
2
1
1
0
1
2
2
3
2
1
1
0
1
3
1
1
0
1
0
2
1
1
2
0
1
2
1
2
0
1
2
1
0
0
1
0
0
1
1
1
0
1
0
0
0
0
2
1
2
2
1
2
2
1
1
1
0
1
0
2
1
0
2
1
2
0
0
1
1
1
2
1
1
0
0
0
1
7
2
1
1
0
1
1
0
0
0
1
2
1
0
2
1
2
2
0
1
0
1
1
1
0
1
1
0
0
0
0
2
0
0
0
1
0
0
1
2
2
0
0
2
3
2
0
2
1
1
0
1
1
1
0
1
1
1
1
3
1
1
1
1
1
0
1
1
0
1
0
1
1
0
2
1
1
0
0
1
2
0
1
1
2
0
2
0
1
0
1
2
2
0
2
1
2
2
1
2
0
0
1
2
1
0
1
1
0
1
0
0
1
2
2
2
1
0
0
0
2
1
1
2
1
0
1
2
1
0
1
0
0
2
0
1
1
1
0
0
1
0
1
2
2
1
0
1
0
1
2
1
1
1
0
2
1
1
2
0
2
2
1
1
1
2
1
0
1
2
0
0
1
1
1
1
2
1
1
2
2
0
2
1
1
0
1
2
1
2
2
0
2
0
1
1
1
0
1
2
1
0
1
2
1
1
0
0
1
2
1
1
1
0
1
0
1
1
0
0
0
0
2
1
0
2
0
1
1
2
2
0
1
0
0
0
2
1
1
0
1
1
2
2
0
0
2
1
0
2
1
1
0
1
1
2
1
1
2
0
2
0
1
0
0
0
2
1
1
0
1
2
0
1
1
2
2
0
1
1
0
1
0
0
1
1
1
3
0
1
2
1
0
1
1
2
2
1
1
0
2
0
0
0
1
2
1
1
1
0
0
3
0
0
2
1
1
0
0
1
1
1
1
3
1
0
2
1
0
2
0
1
2
1
0
2
0
0
1
1
1
0
0
0
1
2
0
1
1
3
1
2
0
0
0
0
0
1
0
1
2
0
1
0
1
0
1
1
0
0
2
0
0
0
0
0
1
1
1
0
0
0
1
0
0
2
2
0
0
1
1
1
1
1
0
0
2
0
1
2
2
0
0
2
0
0
1
1
2
1
1
1
2
0
0
1
1
0
0
0
1
0
2
1
1
0
2
0
0
1
0
1
1
8
2
0
0
0
2
1
0
1
1
2
0
0
1
1
1
0
0
1
1
0
2
2
1
3
0
0
1
2
0
0
0
2
1
1
0
1
1
1
0
2
0
1
0
1
2
0
4
2
2
0
1
1
2
1
0
1
1
0
1
1
1
3
0
1
0
2
1
1
0
1
1
1
1
2
1
1
1
2
2
1
1
0
2
2
1
0
0
2
2
0
0
0
2
1
1
0
1
2
2
1
3
1
0
2
1
1
2
0
0
0
0
3
2
1
1
1
0
1
2
2
1
1
1
0
1
1
1
4
1
1
0
0
0
1
2
2
1
2
2
0
2
2
1
0
2
1
1
0
1
1
0
1
1
1
2
0
0
0
0
0
2
1
0
1
1
1
1
1
0
1
1
1
1
1
1
0
0
0
2
0
0
1
1
1
0
2
0
1
2
1
2
0
0
0
1
2
1
0
0
2
2
1
1
0
0
2
1
1
2
1
1
1
0
0
1
0
1
1
1
1
0
0
0
2
1
0
4
0
1
2
1
1
1
1
2
0
1
1
1
0
1
0
0
0
1
0
1
1
0
2
0
1
0
0
0
1
2
1
0
0
0
1
0
1
2
0
1
2
1
6
1
2
1
0
2
1
0
1
1
1
0
1
2
0
2
2
1
0
2
0
0
1
0
0
0
2
2
0
0
2
0
1
1
0
0
1
1
1
1
2
2
0
0
1
0
1
0
0
0
1
0
0
2
1
0
1
2
0
1
2
0
1
1
1
0
0
1
1
2
1
1
1
0
1
1
2
2
2
2
1
0
2
0
0
1
1
0
2
0
1
0
1
1
1
1
1
0
0
0
1
1
2
1
1
2
2
1
1
0
1
2
2
2
2
1
0
1
1
1
2
2
0
0
1
2
1
0
0
0
1
1
0
1
1
1
1
1
0
2
1
1
0
1
0
1
1
0
0
1
1
2
1
1
0
0
0
0
0
1
1
2
1
0
0
0
0
2
2
0
2
0
0
2
0
2
0
2
0
0
1
1
0
1
1
1
1
2
0
1
2
1
0
1
0
2
0
0
1
2
2
1
1
1
1
1
1
1
2
0
0
0
2
0
2
1
0
5
0
1
0
0
2
2
2
0
1
2
1
1
1
1
0
0
0
1
1
0
1
0
1
1
1
1
2
1
0
1
1
0
0
0
2
2
1
1
0
0
1
1
1
2
2
1
2
2
1
2
0
0
2
2
0
1
1
2
0
0
1
1
2
0
1
0
0
1
2
1
0
0
0
2
2
1
0
2
0
1
0
1
3
1
2
0
0
1
2
0
1
1
0
3
1
1
0
0
1
1
0
2
1
0
1
1
2
1
1
1
0
0
1
0
0
1
1
2
1
1
0
0
0
0
0
1
1
1
1
1
1
0
2
1
1
0
1
1
2
2
0
0
2
0
1
2
1
1
2
0
0
1
0
0
0
0
1
1
0
0
0
2
3
2
1
0
1
2
0
0
1
1
2
0
0
0
0
0
1
0
1
1
1
1
1
1
1
1
2
1
0
1
0
0
1
1
0
2
1
2
0
0
1
1
1
1
0
2
0
6
3
0
0
1
1
2
1
1
0
1
1
0
1
0
1
0
1
2
2
1
0
0
1
1
0
2
0
1
0
2
1
2
1
0
1
0
2
0
0
1
0
1
1
1
0
2
2
2
1
1
1
1
0
2
1
0
1
0
1
0
2
0
1
0
2
1
0
3
0
2
1
1
1
0
1
1
0
1
1
1
0
1
2
0
2
0
2
1
1
1
0
2
1
1
3
0
0
0
1
0
1
2
1
1
0
2
1
2
1
0
0
1
1
2
0
2
1
1
1
0
2
0
1
2
2
0
0
0
2
2
0
0
0
2
0
2
2
1
1
0
0
0
1
0
0
1
0
2
0
2
2
1
1
2
1
0
1
1
1
1
1
1
1
0
1
0
1
0
1
1
2
1
2
1
1
1
1
1
0
0
0
0
1
1
1
1
1
1
0
0
1
2
1
2
2
1
0
0
1
1
0
1
2
1
0
0
2
1
2
1
0
1
1
1
0
1
1
2
0
2
0
0
1
0
0
0
1
0
1
1
2
0
0
0
1
0
0
1
0
0
1
2
2
1
1
0
1
0
0
2
0
0
1
2
1
0
1
1
2
1
1
0
2
0
1
0
1
1
1
1
2
1
0
0
2
1
2
0
2
1
0
0
2
0
2
1
0
1
1
0
2
1
0
1
1
2
1
2
2
1
0
0
3
0
2
2
0
0
0
2
1
0
0
2
2
1
1
1
0
0
2
0
1
0
0
1
2
0
0
0
1
1
1
1
0
2
1
0
1
1
2
1
0
2
1
1
0
1
2
1
2
1
1
0
1
2
1
2
0
0
1
0
0
1
0
0
0
0
2
2
1
0
0
2
1
0
0
1
1
1
1
0
0
2
1
0
2
0
2
1
1
2
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
1
1
0
0
1
2
1
2
2
0
2
0
1
0
0
1
0
0
0
2
0
1
2
1
1
0
0
2
1
1
2
1
2
0
0
0
1
2
2
1
1
1
1
0
0
1
0
1
1
2
1
0
0
0
2
1
1
0
1
1
1
1
2
1
0
1
1
1
1
2
1
0
1
0
0
1
1
1
2
0
2
2
0
0
1
2
0
1
1
0
0
2
0
0
2
0
2
0
2
1
4
1
0
2
2
2
2
2
0
0
0
1
0
0
2
3
1
1
2
1
0
0
1
0
0
0
0
2
0
1
2
0
1
0
1
2
0
0
2
0
0
2
1
2
0
1
1
1
1
1
0
0
1
1
1
1
2
0
1
1
1
2
0
2
0
1
1
0
0
2
2
0
1
0
0
1
1
1
0
1
0
1
2
1
1
1
0
1
1
2
2
0
1
0
2
2
1
1
1
0
1
0
1
2
2
0
0
0
0
0
0
0
0
1
0
1
1
0
1
7
0
1
1
0
1
1
0
1
1
0
0
0
2
0
0
0
0
1
0
1
3
0
1
1
1
0
0
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
0
2
0
1
0
1
1
1
1
0
0
1
2
2
1
1
1
1
0
0
0
0
2
0
0
2
0
2
1
0
1
0
1
1
0
2
1
0
0
2
0
1
0
0
2
0
0
0
2
6
1
0
0
0
2
0
0
0
2
2
1
0
0
0
1
0
1
2
1
1
1
0
0
1
1
0
0
0
1
1
0
1
1
2
2
2
1
0
1
2
2
2
0
2
1
2
1
0
1
1
1
1
1
2
0
1
0
1
1
1
0
1
1
1
0
0
0
1
2
1
0
2
1
1
0
2
1
1
0
1
1
1
2
1
1
0
1
0
2
1
0
0
2
0
1
0
0
0
0
1
1
1
0
0
0
1
0
2
1
1
1
0
1
0
0
0
2
1
0
2
0
0
1
0
2
1
0
1
1
2
2
1
1
0
1
1
2
0
0
0
1
1
1
0
0
2
0
1
1
1
2
0
0
0
2
1
1
1
1
0
1
2
0
0
0
0
1
1
1
0
2
1
1
2
2
2
1
0
1
1
1
1
2
1
0
1
0
1
2
0
1
1
2
0
1
0
0
2
0
2
0
1
0
1
0
1
0
2
2
2
1
1
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
3
1
1
0
0
0
0
0
1
1
0
1
1
2
2
0
1
1
1
0
0
1
0
0
1
1
1
1
1
1
0
0
2
4
5
1
1
2
0
1
1
2
0
0
2
0
0
1
0
1
1
2
1
0
1
3
0
0
1
0
0
2
2
2
0
1
1
1
0
1
0
1
2
1
2
0
1
0
0
0
1
1
2
0
1
1
0
0
2
1
1
0
1
0
1
1
0
1
0
0
0
1
1
1
2
1
0
0
0
1
2
1
0
1
2
1
1
1
0
1
2
2
2
2
1
0
0
2
0
1
0
1
1
1
2
1
1
0
0
2
0
1
0
2
0
1
2
0
0
2
1
2
0
1
2
1
1
1
1
1
0
1
2
0
0
0
1
1
0
1
1
1
0
1
1
1
0
0
1
0
0
0
4
0
4
0
1
0
1
0
2
2
1
1
0
0
0
1
1
0
2
1
1
0
2
2
0
1
0
0
1
2
0
0
1
1
0
1
1
0
1
1
0
1
2
0
1
2
1
1
1
1
2
1
2
1
1
0
2
1
1
1
2
1
2
0
0
1
0
1
1
1
2
1
0
2
0
2
1
0
1
0
1
1
0
0
1
1
1
0
1
2
0
0
1
4
2
0
1
1
1
0
1
1
2
0
2
0
0
1
2
1
1
1
1
0
2
2
1
2
2
0
2
1
5
0
1
0
1
2
0
2
2
1
1
1
1
2
1
1
0
0
1
2
0
0
2
0
1
1
1
2
0
0
0
0
1
1
0
2
1
0
0
1
1
1
0
1
1
1
1
1
1
1
0
1
0
0
1
0
1
1
1
0
0
2
0
0
1
0
0
2
2
1
1
0
2
2
0
0
1
1
3
1
1
1
0
1
0
1
2
0
1
1
1
1
0
2
3
1
0
2
0
0
1
1
1
0
1
1
1
0
0
1
2
0
1
1
0
1
0
2
0
1
1
0
1
2
1
1
1
0
1
0
0
0
1
1
1
0
0
1
0
0
2
2
0
1
2
7
1
2
1
1
1
1
2
1
1
2
0
0
2
1
1
2
0
0
0
1
1
2
1
0
0
0
2
1
1
0
0
1
1
1
0
1
2
0
0
1
1
2
0
0
1
0
0
1
1
0
1
0
1
2
1
0
1
2
2
0
1
1
1
0
1
2
1
0
0
1
0
2
1
0
2
1
0
1
2
0
1
1
0
2
1
1
0
1
2
0
0
0
0
0
1
0
1
1
0
1
0
1
1
1
0
1
3
0
1
0
1
2
1
1
1
1
0
1
2
1
0
1
1
1
2
2
1
1
0
0
1
2
2
0
1
0
2
2
2
1
0
0
1
0
0
1
0
0
1
1
2
0
2
0
1
1
1
0
1
0
0
0
0
2
1
0
2
2
0
0
2
1
2
0
2
1
0
2
1
1
0
0
0
0
0
0
1
0
0
2
0
1
1
0
1
1
1
1
0
2
0
0
2
0
0
1
2
1
0
1
2
1
1
0
1
0
0
1
2
1
1
2
1
1
0
2
0
1
1
2
1
0
2
0
1
1
0
1
2
1
0
1
1
0
1
1
0
2
0
1
1
0
0
2
1
2
2
0
1
1
2
0
0
1
1
0
1
0
1
3
0
2
2
1
2
1
1
1
0
1
2
0
0
3
2
2
1
2
0
1
1
1
1
1
1
0
1
2
0
1
0
1
1
1
0
2
1
0
1
1
1
1
1
1
0
1
1
2
0
1
1
1
1
0
0
1
1
1
2
1
1
2
0
1
1
1
0
0
0
2
1
2
0
2
1
2
1
0
2
0
0
1
0
0
1
2
0
2
2
2
1
2
1
2
1
1
1
2
1
1
1
0
0
1
1
1
1
2
1
0
1
2
1
1
1
1
4
2
2
1
2
0
2
0
1
1
2
1
1
0
2
0
2
0
0
0
0
0
1
2
0
0
2
1
1
0
0
1
0
0
2
1
1
0
0
1
0
1
0
1
0
0
1
2
0
2
1
0
1
0
2
1
1
0
1
2
0
1
2
1
0
1
0
2
1
2
1
2
0
0
1
1
0
0
0
1
0
1
0
1
0
1
1
1
0
0
1
0
2
1
1
2
0
1
0
1
1
0
0
1
3
2
2
1
0
1
0
2
1
0
0
0
1
2
1
0
1
0
0
3
1
1
0
2
2
1
1
1
1
1
0
0
0
0
3
0
0
0
1
0
1
2
2
2
0
0
1
1
0
0
0
1
1
1
0
1
1
1
0
2
2
0
2
1
1
1
1
1
0
1
0
0
1
1
1
1
0
1
1
1
1
1
1
1
4
1
1
2
3
1
2
0
0
1
1
2
1
2
0
0
0
2
2
1
1
2
0
1
0
1
0
1
1
1
2
1
1
0
1
2
1
1
0
1
1
1
6
1
1
0
1
0
0
0
1
2
0
2
2
0
0
1
1
2
1
1
2
1
2
0
1
1
0
0
0
0
0
0
1
1
1
1
0
1
1
0
1
2
1
2
1
1
0
0
0
1
1
0
2
0
0
2
0
0
2
0
1
0
2
1
0
0
2
1
0
2
2
1
1
2
1
0
1
1
0
0
1
0
0
0
1
2
1
1
0
0
0
2
1
0
2
0
2
2
1
2
1
2
0
0
0
0
1
1
2
1
1
0
0
1
0
0
1
2
0
2
0
0
1
2
1
0
0
2
1
1
1
1
1
1
1
0
2
1
1
0
2
2
1
0
0
0
1
1
0
1
0
1
3
2
1
1
1
2
0
1
0
1
2
0
2
1
1
0
1
0
1
2
0
0
1
2
1
4
1
2
3
1
2
1
1
0
1
0
1
1
0
0
0
0
1
0
1
0
0
1
1
1
0
1
2
0
1
0
1
1
2
0
0
0
2
1
1
1
0
3
0
1
0
2
2
1
0
2
0
1
2
1
1
0
3
0
1
0
1
2
0
0
2
2
0
1
1
1
1
1
1
1
0
2
2
0
0
1
1
1
1
0
0
2
1
1
2
0
1
2
0
1
1
2
1
1
1
0
0
1
2
0
0
1
1
1
0
1
0
0
1
0
1
1
1
1
2
2
1
0
1
2
2
0
1
2
0
1
2
0
1
0
2
0
1
0
0
1
2
1
1
1
1
1
0
0
1
1
0
0
2
1
1
1
1
0
0
1
1
0
1
0
0
2
1
1
0
1
0
1
2
0
2
1
2
2
1
5
2
1
0
2
0
1
1
1
0
0
0
1
1
1
2
6
0
2
3
0
0
2
0
1
2
0
0
3
2
1
1
1
0
1
0
2
0
1
0
1
1
0
0
0
0
3
1
0
1
0
3
1
0
1
2
2
1
2
1
1
0
0
0
1
1
0
1
1
1
2
0
2
0
1
2
1
1
0
1
1
1
0
1
1
2
0
1
1
0
1
2
1
0
1
1
1
2
1
2
1
1
1
1
0
2
2
0
1
0
2
0
1
0
0
0
1
0
0
1
0
2
0
2
0
2
0
2
1
2
1
1
1
2
0
0
0
1
1
1
0
0
2
0
0
2
2
2
2
0
0
2
1
0
0
1
1
1
1
2
0
2
0
0
1
1
2
1
1
2
2
2
1
1
0
0
2
0
1
1
1
1
1
0
0
2
1
2
1
0
2
1
1
0
1
0
0
1
0
2
1
2
1
2
0
0
0
1
0
1
0
1
0
0
0
0
2
1
0
0
0
0
0
1
2
1
0
0
1
2
2
2
1
1
2
1
2
1
1
1
2
1
0
0
2
1
0
2
1
0
1
1
1
1
1
0
1
1
0
1
0
2
1
1
2
2
0
0
1
0
0
2
1
2
2
0
1
2
0
1
2
2
1
2
0
1
2
1
2
1
1
1
0
2
0
0
1
1
1
1
1
2
0
2
1
0
1
2
1
0
2
2
1
2
1
2
1
1
0
2
0
1
0
0
2
2
0
1
1
0
1
2
1
1
1
1
0
2
1
1
1
0
0
2
0
1
1
1
1
2
1
1
2
1
1
1
0
0
0
0
1
0
0
1
2
0
2
1
1
0
1
2
0
1
2
1
2
1
0
1
2
2
0
0
0
2
1
2
0
2
2
1
1
3
2
0
0
1
0
3
1
0
1
0
1
2
1
1
1
2
2
0
0
1
0
0
2
0
1
1
0
2
0
0
2
0
3
1
0
0
0
2
0
0
1
1
0
1
0
0
0
2
0
2
0
0
2
0
0
1
1
1
3
1
1
1
1
1
1
0
1
0
1
0
0
0
2
0
2
1
0
0
1
3
0
1
0
2
1
0
2
0
0
1
2
1
2
1
0
2
0
2
1
1
0
1
1
0
0
1
0
0
1
1
1
1
0
1
1
0
0
0
3
0
0
1
1
0
1
1
1
1
1
1
2
1
1
1
1
1
2
1
0
1
2
1
0
0
0
1
0
1
1
0
1
1
1
1
1
2
0
0
2
1
0
0
1
0
0
1
1
2
2
0
2
1
1
0
2
0
0
2
2
2
0
1
2
2
0
0
0
2
2
1
1
2
2
1
0
0
0
0
0
1
2
0
1
1
0
1
0
1
0
0
1
1
0
2
1
1
2
2
0
1
1
1
0
1
1
1
1
1
0
1
0
2
0
1
2
1
1
0
0
2
1
2
1
1
1
2
2
1
1
1
0
1
2
1
0
1
0
1
1
1
2
0
0
0
0
0
1
0
1
1
0
2
2
0
2
1
0
1
0
1
0
0
2
0
1
1
0
1
1
0
2
0
0
0
1
2
0
1
1
0
0
0
1
0
1
1
1
1
2
1
1
0
0
1
0
0
0
1
2
2
2
1
1
0
0
0
2
0
0
1
1
1
2
1
0
1
0
1
0
7
2
1
0
1
2
0
2
1
0
0
1
0
0
0
0
1
0
2
1
0
0
2
0
1
1
2
2
1
0
0
0
0
0
0
2
1
1
1
2
2
1
2
7
1
1
1
2
0
0
1
1
1
0
0
0
1
1
1
0
2
1
1
1
1
2
0
1
0
0
0
0
0
1
1
0
2
2
2
0
1
0
0
1
2
1
0
1
2
3
2
2
2
0
0
1
0
1
2
0
0
1
0
1
0
1
1
1
2
2
1
1
0
1
1
1
0
0
0
2
1
2
3
2
2
3
1
0
1
0
0
1
1
0
2
1
2
0
2
1
1
1
0
0
2
2
1
1
1
2
1
0
1
0
0
2
0
1
0
2
0
1
0
1
2
0
0
7
1
1
0
1
0
2
1
0
1
0
2
1
0
1
1
0
1
1
0
1
1
0
1
1
0
2
0
1
2
0
2
1
1
1
1
1
1
1
1
1
1
1
0
1
0
1
1
1
0
1
2
0
0
1
1
2
1
0
1
0
1
0
2
1
1
1
0
0
0
1
1
1
0
1
1
2
0
2
0
2
1
1
0
0
0
1
0
1
0
1
0
0
1
1
0
2
0
0
1
1
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
1
0
0
1
1
0
1
0
1
0
0
0
0
1
2
2
2
2
1
0
1
0
2
1
2
1
0
1
1
1
2
0
1
2
1
0
1
2
1
1
0
0
2
1
0
2
0
1
0
0
0
1
1
1
1
1
1
0
1
2
1
0
1
0
2
1
1
1
1
0
1
1
1
0
1
1
1
1
0
2
1
2
1
2
0
1
1
0
0
1
1
0
2
1
1
1
0
2
2
0
1
0
0
0
0
0
0
1
2
1
4
1
1
2
1
1
0
0
1
2
0
1
1
1
1
0
0
0
2
1
0
2
1
0
0
1
4
1
3
0
1
1
1
2
1
2
0
2
0
1
1
1
0
0
1
0
0
0
1
0
2
0
0
1
1
1
1
0
1
1
2
2
1
1
2
2
0
2
1
0
1
0
0
0
1
1
2
0
0
1
1
2
1
2
2
1
1
2
0
1
1
1
0
1
0
1
1
0
0
1
1
1
0
1
1
2
0
2
2
1
0
0
2
0
1
1
2
0
2
2
0
1
0
0
0
0
0
0
0
2
1
4
1
2
0
0
0
0
1
0
2
1
2
0
2
1
2
1
2
0
0
1
1
1
0
2
0
1
2
0
1
0
0
1
2
1
2
0
1
2
2
0
0
0
0
2
2
1
0
1
2
1
0
1
0
1
0
1
1
0
1
2
0
1
0
1
1
0
0
1
1
0
0
0
1
2
2
1
2
1
1
0
0
0
0
0
2
1
2
0
1
1
1
1
0
0
0
0
2
1
0
2
1
0
1
0
1
1
0
1
1
0
1
0
0
0
2
2
2
0
0
0
1
1
1
1
0
2
1
0
2
0
1
0
0
0
1
1
0
1
1
1
1
2
0
0
1
0
1
1
1
1
1
1
0
0
0
0
0
0
2
0
1
2
2
1
2
2
0
0
1
1
1
0
2
2
2
1
1
1
1
0
1
1
0
0
0
0
2
1
2
2
2
1
1
1
1
1
1
2
2
0
1
1
1
2
2
1
1
1
2
0
2
0
1
0
0
0
1
1
1
2
1
1
2
0
0
0
1
1
0
1
1
2
1
0
1
1
0
1
0
1
2
1
0
2
0
1
1
1
0
0
0
2
0
3
0
1
1
1
2
1
2
1
0
0
1
1
2
0
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
0
2
1
4
0
1
1
1
2
0
0
0
0
0
1
0
2
2
1
1
0
0
1
0
2
0
0
0
0
0
1
2
1
0
0
1
1
1
0
1
2
1
0
0
1
0
1
0
1
0
2
1
1
1
0
2
1
2
0
2
0
0
0
1
1
1
1
0
1
1
0
1
0
2
2
1
1
0
1
0
0
1
2
2
2
2
2
0
0
3
0
1
1
2
0
0
1
0
1
1
0
1
3
0
0
0
0
0
1
0
1
0
2
1
1
1
1
0
2
0
1
2
1
1
0
1
1
1
1
1
0
1
2
1
0
1
1
0
1
0
0
3
0
1
1
0
1
0
0
0
0
1
1
0
1
2
0
0
1
2
3
0
2
0
0
1
1
2
1
1
1
0
1
1
0
2
1
0
0
0
1
1
1
2
0
1
1
0
1
1
0
1
0
2
2
0
1
0
2
1
1
2
1
0
1
0
1
2
1
0
1
0
2
0
1
2
0
1
0
0
0
1
2
0
2
0
1
2
2
0
0
2
1
1
1
0
0
1
1
2
2
1
0
1
2
1
0
0
1
0
1
1
0
2
2
1
1
0
1
0
2
1
0
0
1
0
1
2
1
0
1
0
1
0
0
0
2
1
0
2
1
0
0
2
0
2
1
1
1
1
0
0
0
2
7
1
0
2
2
0
1
2
1
0
0
3
1
2
1
1
1
1
0
1
0
2
1
1
0
2
4
0
0
0
1
1
2
1
2
1
1
2
1
2
1
0
0
3
2
1
1
0
0
1
1
1
1
1
2
0
0
1
1
2
0
1
0
1
1
2
0
1
1
2
0
0
2
1
0
1
0
1
2
1
0
1
1
2
0
0
5
0
1
1
1
1
2
1
3
1
1
1
1
1
1
0
1
1
1
0
1
1
0
2
0
1
1
1
1
0
1
1
2
1
1
0
2
0
2
0
0
2
1
0
2
2
1
1
0
0
0
1
0
2
1
0
1
0
0
0
0
0
1
2
1
0
1
1
1
1
1
2
2
5
2
1
2
0
1
1
1
1
2
1
0
2
0
1
2
1
1
2
1
1
1
0
1
6
0
2
2
1
1
1
1
2
1
1
0
1
1
1
1
2
0
1
0
1
1
1
1
1
0
0
0
1
0
0
1
1
1
1
1
0
3
2
0
1
2
0
1
0
0
2
1
1
1
0
2
1
2
0
2
1
0
2
1
1
0
1
0
1
1
1
2
1
1
1
2
1
0
1
0
2
1
0
1
1
2
0
1
0
2
0
0
0
2
1
1
2
1
1
0
1
0
1
1
0
1
1
1
1
1
0
0
0
1
1
0
0
0
0
0
0
1
2
0
2
1
2
0
2
1
2
0
1
0
0
0
1
0
1
0
1
0
0
1
2
1
1
0
1
2
0
1
0
0
0
2
2
1
1
1
1
2
2
1
0
1
0
0
0
0
1
2
0
2
2
1
0
1
0
1
0
1
1
2
1
1
1
1
2
0
0
1
0
1
1
0
0
2
1
0
0
1
1
2
1
1
2
1
1
2
0
1
1
0
1
2
0
0
3
1
2
0
1
0
0
1
1
1
1
1
0
1
1
1
1
1
2
0
2
0
1
2
0
1
1
0
0
2
1
0
1
0
2
2
1
1
2
0
0
2
1
0
0
0
1
0
0
2
1
1
0
1
1
1
1
1
0
0
1
1
1
1
1
0
2
2
0
1
0
1
1
0
1
2
0
1
0
1
2
1
1
1
1
1
0
0
2
1
1
1
0
0
0
0
1
1
1
2
1
0
1
1
1
0
0
0
1
1
1
1
1
0
1
2
1
0
1
1
1
0
1
0
0
2
0
1
1
0
2
1
0
1
0
0
2
2
1
2
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
1
1
1
1
1
1
1
3
1
1
0
2
1
2
1
0
1
1
2
1
1
1
0
2
0
0
1
1
0
0
1
1
1
0
2
0
0
2
1
1
1
0
0
1
2
1
2
0
0
1
1
1
0
0
0
1
2
2
2
1
1
1
1
2
0
1
0
0
0
0
0
0
2
0
0
1
1
0
0
0
1
1
2
1
3
0
1
1
1
1
3
1
0
1
2
1
1
1
0
2
1
1
1
2
0
2
2
0
1
1
1
2
0
0
2
0
0
0
2
1
2
0
2
1
0
1
0
1
0
0
0
0
1
1
1
2
0
0
1
0
0
2
1
0
1
1
0
1
0
0
1
0
1
1
0
2
2
1
1
1
2
1
2
2
0
0
1
1
1
1
1
0
1
1
1
1
2
0
0
1
0
1
1
1
2
1
2
0
2
2
1
0
0
1
1
0
0
0
0
0
1
1
2
1
1
0
2
2
1
0
3
0
2
0
0
1
1
2
2
0
0
1
4
2
0
1
2
0
0
0
0
0
0
2
0
1
1
2
0
1
1
1
0
1
2
0
0
1
1
0
0
0
3
0
0
0
1
2
1
0
0
2
1
0
2
0
0
0
1
0
1
1
0
0
2
1
0
2
0
0
0
1
0
0
0
0
1
1
2
1
2
2
0
1
1
0
0
1
1
0
1
0
2
1
2
2
1
1
2
1
1
1
0
1
0
2
0
0
0
0
0
0
1
0
1
2
1
1
2
0
0
0
1
0
0
3
0
0
2
1
1
1
2
1
0
1
1
0
0
2
1
1
2
1
1
1
0
0
1
0
2
1
2
1
0
0
1
1
0
0
1
2
0
2
0
0
2
0
0
1
1
0
3
2
2
1
0
0
0
1
1
0
4
0
2
0
2
1
1
1
1
1
1
1
2
2
1
0
0
2
1
2
2
1
1
1
0
0
1
1
0
1
1
1
0
0
1
0
1
1
2
1
1
1
2
2
1
1
2
1
0
0
0
2
0
2
1
1
0
1
1
0
0
1
1
0
0
2
1
0
0
1
1
1
0
2
2
1
1
1
1
2
1
0
1
0
1
2
2
0
1
2
1
1
1
0
3
0
1
1
0
2
1
0
0
2
1
2
1
1
0
1
2
0
1
2
1
0
3
1
2
1
2
1
2
1
0
0
0
4
0
1
1
0
1
1
0
1
0
1
1
0
0
2
1
0
1
0
0
0
0
0
2
2
2
1
1
1
2
1
2
1
1
1
0
1
1
1
1
1
1
1
1
1
2
1
3
2
0
0
0
1
2
1
2
0
2
2
2
1
1
0
1
0
1
0
0
2
1
1
0
0
2
0
1
0
1
4
1
1
1
1
1
1
0
1
0
1
2
0
1
1
1
2
1
0
1
1
1
2
2
2
1
2
1
2
1
0
0
1
0
0
2
1
0
2
0
0
1
1
0
2
2
1
0
1
0
0
0
0
1
1
1
1
1
1
0
2
1
1
1
0
0
3
0
0
0
1
0
0
1
1
1
1
0
0
0
0
1
1
3
0
1
1
0
0
0
2
1
1
1
2
1
1
0
1
3
2
0
2
2
1
0
3
1
2
2
1
1
1
0
1
2
2
0
2
0
0
0
2
2
1
0
1
1
3
1
2
1
0
0
0
1
2
1
1
1
1
0
1
1
0
5
0
0
1
1
1
1
2
0
0
0
2
1
2
2
0
1
1
2
0
2
0
0
1
2
1
1
1
0
1
1
1
0
0
1
0
1
1
0
3
1
1
1
1
1
1
1
1
2
0
1
2
2
1
1
1
0
1
0
0
1
0
0
2
2
1
1
1
1
1
1
1
2
0
1
0
0
1
1
0
1
0
1
1
1
3
1
1
0
0
2
1
1
1
1
0
0
1
1
0
0
1
1
0
0
0
1
1
1
1
1
2
0
0
0
0
1
0
0
1
0
0
1
1
0
1
2
0
1
1
1
2
0
1
1
1
2
0
2
0
0
1
0
0
2
0
0
0
0
0
2
1
1
1
1
0
2
1
2
4
1
1
0
1
2
0
0
0
0
1
1
0
0
1
1
1
1
1
1
1
2
0
2
0
1
0
0
1
0
1
1
0
2
1
1
1
2
2
1
1
2
0
0
2
2
2
2
1
1
1
3
0
1
2
0
2
1
0
2
0
0
2
0
0
0
2
1
1
1
1
0
1
2
0
1
0
0
0
2
2
0
1
1
1
2
1
0
1
0
0
1
0
0
2
2
1
1
2
2
1
2
1
1
0
1
2
0
1
2
1
1
1
1
1
1
2
1
2
1
2
0
0
2
2
0
0
0
0
0
0
3
1
1
1
0
1
2
2
1
1
0
0
0
1
1
2
2
1
0
1
0
1
2
0
1
2
1
1
0
1
1
2
1
2
0
0
2
1
2
2
0
2
1
0
1
1
1
0
1
1
0
2
2
0
1
1
1
0
2
2
1
1
1
0
1
1
0
1
1
0
1
2
1
2
1
1
0
0
1
1
3
0
2
2
1
0
0
1
1
0
1
1
1
1
1
0
2
1
1
1
1
2
0
0
0
1
2
0
1
1
0
1
1
1
1
1
0
1
2
1
2
2
0
2
2
2
2
1
0
0
1
1
1
0
0
0
2
1
2
2
0
1
2
0
0
0
2
1
1
1
2
2
0
1
2
2
1
1
0
1
1
0
1
2
2
0
1
0
2
2
2
2
0
2
0
1
0
1
1
0
0
0
1
0
1
0
2
1
0
1
0
1
1
0
1
3
0
1
1
2
2
1
2
1
1
1
0
1
1
2
1
0
1
1
1
3
0
1
2
1
2
0
1
1
1
2
1
1
0
0
0
1
1
1
0
1
0
0
1
0
2
2
0
2
0
1
2
1
2
0
1
0
1
1
0
0
0
1
1
2
2
1
2
1
0
1
0
0
1
0
0
1
1
1
0
1
2
1
1
1
0
1
0
2
2
2
1
1
1
0
1
0
1
2
1
1
1
3
0
0
0
1
1
1
0
1
3
2
0
0
1
1
1
2
0
7
2
1
0
0
1
0
3
1
2
0
1
1
2
0
1
1
0
1
1
2
1
2
0
2
0
1
1
0
1
0
1
2
0
1
2
1
0
0
1
3
0
0
0
1
1
1
0
1
1
0
2
0
1
1
0
0
0
0
0
0
1
1
1
1
2
3
0
2
1
1
0
1
0
2
0
2
0
1
1
0
1
2
0
0
2
1
1
0
0
1
0
1
1
0
0
0
0
0
1
2
1
1
1
2
0
1
1
2
1
1
0
0
0
0
1
0
1
0
0
1
2
1
0
0
1
1
2
1
0
0
0
0
1
1
1
1
0
2
2
1
2
1
1
1
1
1
1
2
0
1
2
1
3
1
0
0
2
0
2
1
0
0
1
1
2
1
1
0
1
0
1
1
1
2
0
1
1
2
1
2
2
2
2
0
2
1
0
2
1
1
1
1
0
2
5
0
0
1
1
2
2
2
0
1
2
0
0
1
1
1
2
0
1
1
0
1
0
1
8
0
3
0
2
1
1
0
0
1
1
1
1
1
2
1
1
1
2
2
1
2
1
2
1
1
0
2
1
1
0
1
1
0
0
2
0
1
1
2
2
0
0
1
0
1
0
2
0
1
0
0
1
1
0
1
1
2
0
0
2
0
1
0
2
1
1
0
2
1
2
1
1
0
2
2
0
2
1
0
1
0
0
1
2
2
1
1
0
0
0
0
1
1
1
2
2
0
1
0
0
1
1
0
0
0
0
0
0
1
0
1
0
1
3
2
1
1
1
1
2
2
1
2
1
1
1
0
1
2
2
1
1
1
2
1
1
0
0
2
0
0
2
0
0
1
1
2
1
1
2
1
1
1
1
0
0
1
1
1
0
2
1
2
1
0
1
1
1
2
0
1
1
1
0
0
0
2
3
2
1
0
0
0
1
1
1
0
0
1
1
1
0
1
1
0
1
2
0
0
0
1
0
1
1
1
2
2
2
0
1
2
1
0
1
0
1
1
2
1
1
2
0
2
2
1
0
0
0
1
0
1
0
1
1
0
2
0
1
1
1
1
0
2
1
1
0
1
0
0
1
0
1
1
1
1
0
1
0
2
1
0
0
1
1
0
1
1
1
0
2
0
1
0
2
1
1
0
1
0
1
0
0
2
1
2
0
0
1
1
0
0
1
2
1
1
0
1
2
0
1
1
1
0
1
1
0
2
0
1
0
0
0
1
0
1
1
0
1
1
0
0
0
0
0
1
0
0
2
0
1
3
1
6
1
0
0
1
0
1
2
1
2
0
3
1
0
1
1
0
1
0
1
0
1
2
1
1
2
1
1
1
1
0
1
1
0
2
1
1
1
2
1
1
2
1
0
1
1
0
1
1
1
2
1
2
0
0
1
1
0
0
0
0
0
0
0
1
1
1
0
1
2
0
0
1
1
0
0
1
1
3
0
1
1
0
0
0
0
1
1
0
0
1
1
1
1
0
0
1
1
1
2
0
4
1
2
0
2
2
1
1
0
1
1
2
1
1
0
1
2
0
0
2
0
1
1
1
0
2
2
1
0
2
1
0
1
1
0
1
0
2
1
1
0
0
1
0
0
2
0
1
1
1
3
1
0
0
0
1
1
0
1
0
1
0
2
0
1
1
0
1
2
2
0
1
1
2
0
1
0
0
2
0
1
0
1
1
1
0
1
1
1
1
0
1
1
1
0
0
2
1
1
2
1
0
1
0
0
0
1
2
0
2
0
1
0
1
1
1
1
1
1
1
2
0
1
1
1
2
1
0
2
1
1
0
1
1
0
2
2
2
2
2
2
1
0
2
1
0
0
2
2
0
1
1
0
0
1
1
2
1
0
1
1
1
0
1
0
1
0
1
0
2
0
0
1
2
0
1
0
1
1
0
2
0
1
0
1
1
2
2
1
0
1
1
1
0
1
0
1
0
0
0
1
0
1
1
1
1
2
1
1
2
1
2
1
0
0
2
1
1
1
0
0
1
1
0
0
2
1
0
1
2
0
1
1
1
0
0
0
1
2
2
0
1
2
2
0
1
2
0
1
1
0
1
0
0
1
0
0
2
1
0
1
1
1
1
0
1
2
0
0
2
1
1
1
2
2
2
0
2
1
1
0
1
1
2
1
0
0
2
2
0
0
0
0
1
0
1
1
0
0
1
0
0
2
0
2
1
1
0
2
0
0
0
0
0
2
1
1
3
0
2
1
0
1
3
2
1
1
2
1
0
2
1
1
0
2
1
0
0
0
1
0
1
3
1
0
1
1
1
2
0
0
1
0
2
1
5
0
1
2
0
0
0
2
1
1
3
0
1
2
0
1
3
1
1
1
1
1
1
2
0
0
1
0
2
2
1
0
0
0
2
1
1
1
0
1
2
1
0
2
0
0
0
0
2
0
0
0
1
1
0
2
0
0
1
2
0
1
1
0
2
2
0
0
2
1
0
1
1
1
1
1
0
1
0
1
0
2
1
1
2
1
0
1
1
1
0
1
1
0
2
2
0
0
2
2
1
2
2
0
1
0
0
0
2
1
0
0
0
2
1
1
1
1
0
0
1
0
2
0
1
1
0
1
0
2
1
1
1
2
1
1
2
2
1
2
1
2
1
1
0
2
3
0
2
1
0
2
1
1
2
0
0
1
1
1
1
1
0
0
1
0
0
2
3
0
0
0
2
1
0
1
0
1
0
1
1
1
0
1
0
1
2
1
1
0
2
1
1
1
2
0
1
1
2
0
1
2
1
0
0
0
1
0
1
0
0
0
1
1
1
1
2
0
2
0
1
1
0
1
1
2
0
1
1
1
1
2
0
0
0
1
3
0
1
0
2
1
1
0
0
0
1
2
0
2
1
2
1
0
1
2
0
1
1
0
2
1
1
0
2
2
1
1
0
0
2
0
0
0
1
0
0
2
0
1
0
1
0
1
2
0
1
2
0
1
1
1
2
2
0
2
0
2
2
1
1
0
1
0
1
1
1
1
0
1
2
0
1
0
1
1
1
1
0
1
1
1
0
1
0
0
0
1
1
2
1
0
1
1
0
1
1
1
2
1
1
1
2
2
0
2
0
1
2
1
2
0
1
0
0
0
1
0
1
1
0
0
0
3
1
0
2
2
0
1
2
0
2
0
2
1
2
0
2
1
1
0
1
1
1
0
0
0
1
0
2
0
0
0
0
1
1
0
0
2
1
2
0
1
0
0
1
1
1
2
1
2
1
1
0
0
0
2
1
0
1
1
1
0
2
0
0
1
1
2
1
1
1
1
1
1
0
0
0
1
1
0
0
1
2
2
1
0
0
0
0
1
0
1
1
1
1
1
0
1
1
1
1
1
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
2
2
1
0
1
1
0
1
1
1
2
0
1
2
1
0
1
1
2
0
1
1
1
1
2
0
0
1
1
2
2
1
0
0
2
1
1
0
1
0
1
0
1
1
1
1
1
1
1
2
1
1
1
1
1
0
1
1
1
1
0
0
1
1
1
2
1
0
1
0
2
1
2
1
1
1
1
1
1
1
1
0
0
1
0
0
0
0
2
2
1
1
1
1
2
0
0
1
1
2
2
0
2
0
1
0
0
0
2
0
1
0
0
1
0
1
2
1
1
0
1
2
1
0
1
1
0
2
1
1
1
2
1
3
3
0
2
2
2
1
2
1
2
0
1
2
0
0
0
0
3
0
1
1
2
1
0
0
0
0
0
2
1
0
1
0
1
2
1
4
1
1
1
0
1
1
1
1
1
0
1
1
1
0
2
0
0
1
0
1
0
0
1
0
0
1
2
0
2
1
0
1
1
1
1
2
2
2
1
2
1
2
0
1
1
1
1
2
0
1
2
0
1
1
1
0
0
1
1
2
1
1
1
0
0
0
0
2
1
1
0
1
1
2
1
1
1
2
2
1
1
1
0
1
1
1
0
0
1
0
0
2
2
2
1
2
0
1
0
2
2
0
0
1
0
1
1
1
1
1
2
0
2
2
0
1
1
3
2
0
0
0
1
1
1
2
0
2
0
2
0
1
0
0
0
1
0
0
0
1
2
1
1
1
2
2
1
1
0
0
2
2
2
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
2
1
0
1
1
1
0
1
1
0
0
2
0
1
2
0
1
2
0
1
0
2
2
2
2
1
1
2
4
1
0
0
0
1
0
0
1
0
1
1
1
1
2
1
1
0
1
1
0
2
4
1
1
0
4
0
0
2
0
2
1
0
2
0
0
0
0
1
1
1
0
0
2
1
1
2
0
1
1
0
0
0
0
0
0
3
2
1
0
2
1
1
0
1
2
1
0
1
0
1
1
1
1
0
1
0
2
1
1
0
2
1
1
1
0
1
2
0
1
2
2
0
2
1
1
0
1
1
0
0
0
1
0
0
0
0
1
2
2
1
2
1
2
1
1
2
0
2
2
1
2
1
2
1
1
0
1
1
0
0
0
1
0
0
2
0
1
1
1
1
1
2
0
1
0
1
1
2
0
0
0
0
2
0
2
0
1
2
0
0
0
2
0
0
0
0
1
1
0
0
0
2
0
1
1
1
1
1
1
0
0
2
0
1
0
1
1
1
2
0
2
0
1
0
1
2
2
1
0
1
1
0
1
1
1
1
2
0
1
2
1
0
0
2
2
0
2
0
1
2
1
0
2
1
1
2
0
2
1
1
1
1
0
0
0
1
2
0
2
0
2
0
0
1
1
2
1
2
0
1
2
0
1
1
1
0
2
1
0
1
2
0
1
1
0
2
1
0
2
2
2
2
1
2
1
1
1
2
0
1
0
0
1
2
1
2
1
1
1
1
1
1
1
2
1
0
0
1
1
0
0
0
2
0
1
1
1
2
0
4
1
2
1
1
1
1
0
1
0
1
0
0
2
9
2
2
2
0
1
2
1
2
3
0
0
0
1
0
1
0
1
1
3
2
1
0
0
2
1
1
1
1
0
0
1
0
2
1
2
0
0
0
0
1
1
1
0
0
0
0
1
1
1
2
1
0
2
0
1
0
1
1
1
0
1
0
0
2
0
0
1
2
2
0
2
1
1
1
1
1
1
1
2
1
1
1
2
2
3
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
1
1
0
1
1
0
0
0
1
1
2
0
2
1
1
0
0
1
2
0
0
0
1
1
2
1
1
2
1
0
0
1
0
1
2
0
2
1
0
0
1
0
1
0
0
1
1
0
0
2
1
0
1
1
2
0
0
2
2
1
0
1
1
1
1
1
0
1
0
0
1
0
0
0
0
2
0
1
0
1
0
2
0
1
1
1
0
0
1
0
0
1
2
2
2
1
1
1
1
0
0
1
1
0
1
1
0
3
0
1
0
2
2
1
1
0
1
0
2
1
1
2
2
2
1
2
1
2
1
1
0
0
0
2
0
1
1
1
2
0
1
0
0
0
0
1
2
0
0
1
1
0
1
0
1
2
0
1
1
1
1
1
2
0
1
0
0
0
1
2
1
1
2
2
2
2
2
1
1
2
1
2
2
1
0
1
0
1
1
1
2
1
0
0
1
0
1
2
1
1
2
0
0
2
1
0
2
0
1
1
1
0
2
2
2
0
2
1
0
0
0
2
2
1
1
0
2
2
0
1
2
0
1
1
1
0
1
2
1
0
0
5
0
1
1
2
2
0
0
1
1
0
0
0
1
2
1
2
1
2
0
0
0
1
0
0
1
1
0
1
1
1
1
0
1
2
2
1
1
0
1
2
0
1
0
3
1
0
1
1
1
1
2
0
1
1
1
0
0
1
0
1
0
0
1
2
1
0
0
3
1
0
1
0
1
2
1
2
0
0
2
1
2
0
1
1
1
2
0
0
0
1
1
0
0
1
0
2
0
2
2
1
1
0
2
1
0
2
3
2
2
2
0
0
1
0
0
1
1
2
0
2
0
0
1
0
1
1
1
0
0
0
0
1
0
0
1
0
1
1
0
1
1
0
0
0
2
0
1
0
1
0
3
1
0
1
0
0
2
1
2
0
0
0
0
1
0
0
0
0
1
0
2
1
0
0
1
0
0
1
1
2
0
1
2
0
1
1
2
0
2
1
0
0
2
1
2
2
1
1
1
2
4
0
1
1
0
0
2
0
1
1
2
0
0
2
3
0
1
1
0
1
1
1
1
0
2
1
1
1
0
1
0
1
0
6
0
1
2
2
0
1
2
0
2
1
2
0
1
0
0
1
1
1
1
1
0
1
2
0
1
2
1
0
1
0
0
1
1
2
0
0
2
1
1
1
2
0
1
1
1
1
1
0
0
0
1
1
1
0
0
2
0
1
2
0
1
2
2
1
2
0
2
2
1
1
1
1
1
0
1
0
0
1
0
1
0
1
0
2
2
1
1
2
0
1
0
0
1
1
1
0
1
0
2
1
0
0
1
0
1
0
0
2
1
1
1
2
1
2
2
1
1
1
1
0
2
1
1
1
2
2
2
1
1
1
2
0
1
0
2
1
0
1
2
1
2
1
1
1
1
2
0
2
0
0
0
1
1
2
1
1
0
1
1
2
1
1
1
1
1
0
0
1
2
1
1
0
2
1
2
2
0
0
0
1
1
3
2
0
0
1
1
0
0
2
1
2
0
0
1
1
1
1
1
1
0
2
1
1
1
0
0
0
1
2
2
2
0
2
0
0
1
1
1
0
0
2
1
0
0
1
2
2
2
1
0
1
2
1
4
1
1
1
0
1
1
2
0
0
2
2
0
0
2
2
0
1
0
1
0
3
0
0
0
1
1
2
0
1
1
1
1
1
1
0
1
1
1
0
1
1
2
1
0
1
1
0
1
1
1
1
1
0
0
2
1
1
2
0
0
1
0
2
0
2
0
1
1
0
1
1
2
1
1
0
2
0
1
0
1
1
1
0
2
1
0
1
1
1
1
1
2
0
1
1
0
0
0
4
0
0
1
1
1
1
0
1
0
1
1
5
1
3
1
0
2
0
0
0
1
0
1
1
2
1
2
2
0
1
1
0
1
0
1
2
1
0
1
0
0
0
1
0
0
1
0
0
2
2
0
0
0
0
0
1
1
1
1
1
1
4
0
2
1
1
1
1
1
1
0
0
2
0
1
1
1
1
2
1
1
0
2
1
0
0
1
1
1
1
0
0
0
1
2
0
2
2
1
1
0
1
1
1
1
1
2
0
2
0
2
0
2
1
3
0
3
0
1
0
1
2
0
2
1
2
1
1
1
0
2
1
1
1
1
0
1
0
0
2
1
1
1
0
0
1
0
0
0
0
1
1
1
1
2
1
4
2
1
1
2
1
1
0
0
1
1
2
1
0
0
1
2
1
0
0
2
0
0
2
2
0
1
0
1
2
1
0
0
0
0
0
0
1
1
0
0
2
2
2
2
1
1
1
2
1
2
1
2
0
2
1
1
1
0
1
1
0
0
2
2
1
1
0
0
0
0
0
1
1
2
2
0
0
1
0
1
0
0
0
2
1
0
1
2
2
0
1
1
2
1
1
0
2
1
1
2
1
0
1
0
1
0
5
1
1
2
1
0
0
1
0
0
0
0
1
0
1
1
1
1
2
0
2
2
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
1
1
2
2
1
1
0
1
2
1
0
0
1
1
1
3
2
1
2
1
1
0
0
1
1
1
0
0
0
2
1
0
1
0
0
0
1
2
1
2
0
2
1
2
1
1
1
1
1
0
2
1
2
2
0
1
0
2
3
1
1
0
0
1
1
1
1
1
1
2
1
2
1
0
1
1
1
4
1
0
1
0
0
1
0
2
2
1
1
0
0
1
0
0
1
2
1
0
1
1
2
0
1
2
0
0
2
0
1
1
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
1
1
2
1
1
0
2
2
1
0
0
1
0
1
2
1
2
1
1
0
0
2
1
1
0
0
1
0
1
0
0
0
2
2
0
2
1
1
1
1
1
2
3
2
0
0
1
0
0
1
0
0
1
1
1
2
0
0
1
1
1
2
0
2
0
0
1
1
2
2
2
1
1
0
2
0
2
2
1
0
2
3
1
0
1
1
0
1
1
0
0
0
1
0
1
0
2
1
1
1
1
1
2
1
2
1
0
2
1
2
1
0
2
1
1
0
1
1
1
3
0
0
1
1
1
1
2
1
1
0
0
1
1
0
1
0
1
0
2
2
1
1
0
1
1
1
0
2
0
2
0
0
1
1
2
1
1
0
0
1
0
1
1
1
2
1
2
1
1
0
1
0
1
0
1
1
2
0
2
0
0
0
2
0
1
2
6
1
1
3
2
2
0
2
0
1
1
1
0
0
0
1
0
1
1
1
2
0
1
0
0
1
1
1
2
0
2
2
0
0
2
1
0
2
0
2
0
1
0
1
2
0
1
0
1
1
2
0
1
0
1
0
0
1
1
1
0
1
2
2
2
0
0
0
1
1
1
1
1
1
1
0
1
1
1
1
2
0
0
1
1
1
2
1
1
1
0
4
0
0
1
1
1
1
0
0
0
1
1
0
2
1
0
1
2
1
1
2
1
1
1
0
1
5
0
1
0
2
0
0
2
0
2
0
1
2
0
0
0
2
1
1
0
0
0
1
0
1
1
0
1
1
2
2
2
1
1
0
0
1
1
0
1
1
1
2
2
0
1
0
1
1
2
0
0
0
0
1
1
0
1
0
1
2
1
0
1
2
1
1
3
2
0
1
1
0
1
1
2
1
0
1
1
0
1
1
1
0
0
1
2
1
0
0
1
1
0
0
0
3
1
1
1
1
3
0
1
1
1
1
1
0
0
0
2
2
2
1
1
0
1
1
0
3
1
1
1
1
2
1
2
0
0
1
1
1
0
0
1
1
0
0
1
1
0
2
1
0
1
1
1
1
1
1
1
1
1
2
1
1
2
2
2
1
2
0
0
1
1
1
0
0
2
0
0
0
1
0
1
2
0
0
1
2
0
0
2
2
1
0
1
0
0
0
1
1
4
1
0
0
1
1
1
1
0
1
1
0
0
1
2
2
1
1
0
1
2
0
0
0
1
1
0
0
1
1
1
0
1
3
0
2
0
2
1
2
0
0
0
2
2
0
1
1
2
1
0
1
0
2
1
1
0
0
2
0
1
0
2
1
1
2
0
2
0
0
1
0
1
2
1
1
1
2
0
0
1
2
2
2
2
1
0
1
2
1
0
1
0
1
2
0
1
0
0
0
0
0
0
2
1
2
0
0
1
2
1
1
1
0
0
1
2
0
0
2
1
0
0
0
1
1
1
1
1
1
1
1
2
1
3
1
0
0
1
0
3
2
2
1
1
3
2
0
0
2
1
2
2
2
1
1
3
2
1
0
1
0
1
2
1
1
1
2
1
1
1
1
1
0
2
1
1
1
0
1
1
1
2
1
0
1
2
2
1
0
1
0
0
0
0
0
0
0
1
2
1
0
0
2
1
2
0
1
1
1
1
2
0
0
0
2
1
1
1
1
0
0
3
3
1
2
1
0
0
1
1
0
0
1
1
0
2
1
2
2
0
0
2
2
1
2
2
0
1
1
0
1
0
0
0
2
1
1
1
1
1
1
0
1
0
0
2
1
1
0
1
0
3
1
4
0
2
2
2
0
1
1
1
0
1
1
1
0
1
1
1
2
1
1
1
0
1
1
0
0
2
0
2
1
1
0
0
2
2
1
2
2
0
0
1
2
1
1
1
1
2
1
2
1
0
1
0
0
1
1
1
1
2
1
0
2
1
3
1
0
0
2
0
0
0
1
0
0
1
1
2
2
0
1
2
2
0
0
1
1
2
0
1
2
1
2
1
0
1
1
1
1
0
0
0
0
1
2
0
1
0
2
2
2
1
1
1
1
0
2
0
1
1
1
0
0
1
1
0
1
2
1
0
1
2
1
0
1
1
1
1
1
1
0
2
1
0
0
1
1
1
1
1
0
1
1
1
0
0
4
1
1
1
1
1
1
2
0
0
0
1
1
0
2
2
1
1
0
0
1
1
2
0
1
1
1
1
1
0
0
0
1
1
0
0
0
2
2
0
1
0
1
0
0
0
1
0
2
2
1
0
1
0
1
0
2
0
2
2
0
1
0
1
1
0
2
0
0
1
5
2
1
2
0
0
1
1
2
1
2
1
1
0
1
1
2
0
1
0
0
1
1
1
0
1
5
3
2
3
1
0
1
2
1
1
2
1
1
0
0
1
0
1
1
1
1
1
0
1
0
0
0
2
0
2
0
0
1
0
2
1
0
1
2
1
2
5
0
3
2
0
0
0
0
2
2
0
2
1
1
1
0
2
1
1
1
2
1
2
1
0
1
1
1
0
2
1
2
0
0
2
0
0
1
1
1
1
0
1
0
1
1
0
1
0
1
1
0
3
0
1
1
0
1
0
1
0
0
2
1
2
0
0
2
2
0
1
2
1
0
1
1
2
0
0
1
1
1
1
1
1
0
1
1
1
1
2
2
0
2
1
1
0
1
0
1
2
2
0
0
1
2
0
2
0
0
0
1
1
0
2
0
1
1
2
2
2
0
1
0
1
1
1
1
0
1
1
3
1
1
0
1
0
0
1
2
0
1
1
2
3
1
2
3
0
1
2
2
0
2
0
1
1
3
1
2
1
1
2
2
1
0
0
2
1
0
0
0
1
0
0
0
0
1
1
1
0
0
1
1
0
0
0
2
0
0
0
1
0
0
2
2
2
2
0
0
1
0
1
2
0
2
2
0
2
1
0
1
1
1
1
2
1
0
1
2
1
1
1
0
2
1
0
0
0
0
1
0
0
0
0
0
2
0
1
0
1
1
0
1
2
1
1
0
1
0
0
0
3
2
0
2
2
2
2
0
1
1
2
0
0
1
1
0
2
1
0
0
0
1
1
0
0
2
1
0
0
2
1
1
0
2
1
0
0
0
2
0
2
1
1
1
0
1
0
1
0
1
1
0
0
2
0
2
2
0
0
0
0
2
2
1
2
2
1
1
0
2
0
1
0
2
1
2
2
0
0
1
3
0
0
1
0
1
1
0
1
2
1
2
0
1
2
1
1
1
0
2
1
2
0
3
1
2
1
2
0
2
2
0
2
2
1
1
2
2
1
0
1
2
0
0
0
0
1
0
1
2
1
1
1
1
0
2
2
1
1
0
1
1
2
0
1
0
1
0
1
2
0
2
0
0
0
0
1
2
0
2
2
1
0
2
1
2
1
0
1
0
2
2
1
1
0
1
2
1
0
0
1
1
0
0
3
1
1
1
1
0
1
1
0
1
1
1
1
0
1
1
0
1
1
0
2
1
1
2
0
1
2
1
3
2
1
1
0
1
0
1
2
1
1
0
2
2
1
1
1
2
1
1
0
1
0
2
1
0
1
1
2
0
2
0
2
1
1
2
1
1
2
1
2
1
4
0
2
2
1
3
2
1
0
1
0
2
2
1
0
0
0
0
0
0
1
1
2
2
2
1
1
1
2
2
1
2
1
1
1
4
1
2
1
1
1
0
1
0
1
1
1
0
2
1
0
1
0
1
0
1
0
1
1
1
4
1
0
2
0
2
1
2
2
1
1
1
0
1
2
1
0
0
1
0
0
2
1
0
1
0
0
2
2
2
2
0
0
1
0
0
0
2
1
2
0
0
1
0
0
1
0
1
2
0
0
2
2
2
1
1
0
2
1
1
1
1
0
1
0
0
2
2
1
1
1
1
0
1
1
0
1
0
1
1
1
2
0
2
1
2
1
1
0
1
0
1
1
0
1
1
0
1
2
0
0
1
1
1
1
0
1
1
2
1
5
1
2
0
1
1
1
3
2
0
0
0
2
1
1
1
0
2
2
1
0
1
0
1
2
1
0
1
1
1
1
2
0
1
2
1
2
0
2
1
1
1
1
2
1
1
1
0
2
1
0
0
1
0
0
0
2
1
1
1
1
1
1
1
2
1
0
1
1
1
2
2
1
0
0
1
1
2
1
1
1
0
0
1
2
2
0
0
2
1
3
1
1
0
0
1
2
1
1
1
1
1
0
0
1
1
2
3
0
0
1
0
1
1
1
1
2
0
1
0
1
1
0
1
0
0
2
0
1
0
1
1
0
2
1
0
0
1
2
2
0
0
0
1
0
1
0
2
0
0
0
0
1
0
1
1
1
1
0
2
1
1
2
2
0
1
1
1
1
0
1
0
0
1
2
1
1
0
1
0
1
2
1
1
0
1
0
1
1
0
1
2
2
1
2
1
2
2
1
0
1
0
3
3
0
2
1
0
1
0
0
0
0
1
1
1
1
1
2
2
1
1
2
1
1
1
1
1
1
0
0
1
1
1
1
2
0
1
2
1
1
0
0
2
1
1
0
1
1
1
2
1
1
1
0
2
1
1
3
1
1
1
1
1
1
1
0
0
0
0
2
2
2
2
0
2
0
1
0
2
1
1
1
1
1
1
0
1
2
1
0
0
0
1
0
0
1
1
1
1
2
0
1
2
0
0
1
0
1
2
0
2
1
0
1
2
0
1
0
2
2
0
1
1
1
0
1
1
1
1
1
0
0
1
0
1
0
2
1
0
1
1
1
1
0
1
0
2
2
0
0
1
2
0
0
2
2
1
1
1
0
0
2
1
1
1
2
1
0
2
0
2
0
0
1
0
1
2
1
3
1
2
1
1
2
0
0
1
0
2
1
1
1
1
1
2
2
2
1
1
2
1
1
1
1
0
1
1
1
1
0
2
2
1
1
2
1
1
2
2
2
0
2
1
2
0
2
1
1
1
1
1
1
0
0
0
1
0
0
1
1
1
0
0
2
0
1
1
1
0
2
1
2
1
0
1
1
1
2
1
0
1
2
0
2
1
2
2
1
0
0
1
0
2
0
0
4
1
2
1
1
0
3
1
1
1
1
1
0
1
0
0
2
0
1
2
2
0
0
0
1
1
2
0
1
1
0
1
1
1
2
1
1
0
1
3
2
1
0
1
2
0
1
1
0
1
0
0
2
0
0
1
1
1
1
1
1
1
5
0
1
1
0
3
1
1
1
1
2
0
1
2
0
1
1
1
2
1
2
0
1
1
0
2
1
3
0
0
0
0
1
1
0
1
0
2
2
0
2
2
0
0
1
1
1
0
1
2
1
1
1
2
0
2
0
1
1
0
1
1
2
1
1
1
1
1
0
2
0
1
1
1
2
0
0
1
0
0
1
0
0
1
1
0
1
1
2
0
1
1
1
0
1
0
0
0
0
0
2
0
1
0
1
0
1
1
1
1
0
1
1
1
0
1
1
1
1
1
1
1
0
1
0
1
1
2
1
0
2
1
0
2
1
0
1
0
1
0
0
1
2
1
0
1
0
0
2
2
2
0
0
2
1
1
1
2
1
1
1
3
0
1
0
0
1
1
2
2
2
1
2
0
2
1
2
1
1
2
1
1
0
1
0
2
3
1
2
1
2
1
1
1
1
1
0
1
1
2
1
0
1
1
1
2
1
0
1
1
2
1
2
1
2
2
0
2
0
3
0
0
1
2
0
0
0
1
2
0
0
1
0
1
2
1
1
0
1
0
1
2
0
1
0
0
1
0
0
1
2
1
1
2
0
1
0
2
2
2
0
2
0
0
2
1
1
1
1
0
1
0
1
1
1
1
0
0
0
1
1
1
0
1
2
1
1
1
0
2
0
0
2
0
0
2
1
1
2
2
1
2
1
0
3
1
2
0
2
0
1
2
2
2
2
0
0
1
0
1
1
1
1
0
0
0
2
1
0
0
0
2
1
2
1
3
2
1
1
1
1
2
0
1
2
2
0
2
0
1
1
0
1
2
0
2
2
1
0
1
1
1
0
1
3
1
1
0
2
1
1
0
2
2
0
0
0
1
0
1
0
0
1
1
2
1
1
1
2
1
1
2
1
0
3
0
2
0
1
2
0
1
1
1
0
1
0
1
2
1
0
0
1
0
1
0
1
0
2
2
1
2
2
1
0
1
2
2
0
0
2
2
1
1
1
1
0
2
0
2
0
2
1
0
2
0
1
1
0
1
1
2
0
0
1
1
2
1
0
0
1
0
0
1
1
2
1
1
0
0
1
1
0
0
1
0
1
1
1
2
0
0
0
0
0
0
2
1
1
1
0
2
0
0
0
2
0
0
0
0
1
1
3
2
1
1
1
0
1
1
0
0
2
1
0
2
1
2
0
2
1
0
0
1
2
0
1
0
1
1
0
0
1
0
2
0
0
0
1
0
1
0
2
0
1
1
2
2
0
0
0
0
0
1
0
0
1
1
0
2
0
0
2
2
1
0
0
0
0
0
1
1
2
1
1
1
0
0
1
0
0
0
2
1
0
1
0
2
2
2
1
2
1
2
1
2
1
0
0
2
1
2
0
0
1
1
2
1
1
0
0
1
1
2
2
0
0
0
0
1
1
1
1
0
2
1
1
3
1
1
1
2
0
1
2
1
0
0
2
0
1
0
0
1
0
0
0
1
1
0
2
2
0
2
1
0
0
1
0
0
0
0
0
2
0
0
1
1
1
1
0
0
1
2
1
0
0
1
1
0
0
1
2
2
1
2
0
1
1
0
0
1
0
1
2
0
1
1
1
2
2
0
1
0
0
1
2
0
2
0
2
1
1
2
0
0
1
0
0
0
1
0
0
2
0
0
0
2
0
1
1
0
1
0
2
1
1
2
0
2
0
0
1
2
2
2
1
2
1
1
0
2
1
0
1
2
1
0
2
1
1
2
1
1
1
0
2
1
0
0
0
2
0
2
1
0
1
0
2
1
1
2
1
2
0
1
2
0
0
1
0
1
1
1
1
0
0
0
2
1
0
2
0
4
0
1
1
1
0
1
2
0
0
0
1
0
2
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
2
0
0
1
3
1
1
0
2
0
0
0
1
1
0
2
1
0
0
0
1
2
1
0
0
0
1
0
2
1
1
1
1
1
2
1
2
1
1
0
0
2
1
1
1
0
0
0
1
2
2
0
2
2
0
1
1
1
0
1
1
1
2
1
0
1
0
1
1
2
2
1
1
3
2
1
1
1
0
1
0
1
0
0
0
0
1
0
2
0
1
2
0
1
1
0
0
1
1
0
1
2
2
1
0
0
0
1
2
1
1
2
0
1
1
1
1
1
1
1
1
0
2
0
1
2
0
0
1
1
2
2
2
1
0
2
0
1
0
3
0
1
1
1
2
1
0
1
1
0
0
2
0
1
0
2
0
0
2
1
1
0
0
2
0
1
0
0
1
0
1
0
1
1
2
0
2
0
1
2
1
1
1
1
1
1
2
0
1
0
1
0
0
0
0
1
1
1
2
1
0
0
0
2
2
0
0
1
1
1
2
0
1
2
1
1
1
0
1
1
1
1
2
0
4
0
0
0
0
1
2
1
1
2
2
1
1
1
3
0
1
0
2
2
0
0
0
0
1
0
1
2
1
2
0
1
0
0
2
0
2
1
2
1
2
1
0
1
1
2
0
0
2
1
0
1
2
1
1
0
1
2
2
1
0
1
1
1
2
0
2
2
1
0
1
1
0
0
0
1
0
0
1
0
1
1
1
1
1
1
0
1
1
3
1
0
2
0
0
2
2
1
0
1
2
1
1
2
0
2
1
1
0
1
2
0
2
1
1
0
1
1
1
1
0
0
2
2
0
1
1
2
0
1
1
2
3
1
0
2
0
1
0
1
1
1
1
1
0
0
1
0
1
1
1
0
0
1
1
0
1
0
1
0
1
2
1
0
1
1
1
1
3
2
1
0
2
1
0
2
2
0
2
1
1
2
1
2
1
0
0
1
1
1
1
0
2
0
0
3
0
2
2
1
2
1
0
0
2
0
0
1
2
1
0
1
1
2
1
2
2
1
0
0
1
1
1
0
0
0
2
0
1
1
1
2
0
1
1
1
3
1
1
1
1
2
2
2
0
1
0
1
1
1
0
0
1
1
0
2
1
1
0
1
2
1
0
1
1
2
0
1
0
0
0
0
1
1
1
0
1
1
1
1
0
1
0
0
1
2
0
1
2
1
0
0
1
1
0
1
1
0
1
0
1
1
0
0
1
0
1
2
0
2
0
1
1
2
0
2
0
1
2
0
0
1
0
3
2
0
0
0
1
0
1
1
1
0
1
0
0
0
0
2
0
1
2
2
1
1
2
1
1
0
2
0
0
0
0
0
0
2
0
2
1
0
0
2
2
0
1
0
2
1
0
2
2
2
6
1
0
1
3
0
1
1
3
0
2
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
1
1
1
1
1
0
1
1
2
0
0
2
0
2
0
0
1
0
1
1
1
1
1
2
2
2
0
0
2
1
1
1
0
2
1
4
1
1
1
1
1
0
1
0
0
0
0
2
2
1
1
1
1
0
2
3
0
1
0
3
2
1
4
0
2
1
1
0
0
2
2
0
1
0
3
1
2
2
4
2
2
1
0
1
0
1
1
1
1
0
0
2
2
1
0
0
2
0
0
1
0
0
0
2
0
0
2
1
0
1
1
1
2
1
0
2
1
1
1
2
0
1
1
1
1
2
2
1
1
0
1
1
2
1
0
1
1
1
0
0
1
0
1
2
1
1
0
0
1
1
1
0
0
0
1
0
0
0
0
1
1
0
0
1
1
1
2
1
0
2
2
0
2
1
0
2
2
1
0
0
0
2
1
0
0
2
1
1
0
2
1
3
0
0
1
1
2
2
1
1
0
1
0
1
1
0
0
0
2
1
1
2
0
1
1
0
1
2
2
5
0
1
1
0
0
2
1
1
0
0
0
1
0
2
0
2
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
1
1
1
1
2
4
0
1
2
2
0
1
2
0
0
0
0
1
1
0
1
1
0
1
2
1
0
0
0
2
1
1
2
2
0
0
1
0
1
1
1
1
1
2
0
1
0
1
1
1
0
4
0
0
1
0
1
1
2
1
0
1
1
0
1
0
0
1
0
1
0
2
0
1
1
0
0
1
1
1
0
1
1
0
0
0
3
0
2
1
1
1
0
0
1
1
1
0
0
0
1
1
0
2
0
1
1
2
1
0
0
2
0
0
0
0
0
1
2
0
1
2
0
1
2
1
1
1
1
1
2
1
3
1
0
2
1
1
1
1
1
1
0
1
1
2
1
1
1
1
2
2
2
1
0
1
0
2
0
2
0
1
2
0
0
0
1
0
2
1
2
5
1
1
0
1
2
1
0
1
0
2
1
1
1
1
1
0
2
2
0
2
1
1
0
1
0
1
1
1
0
2
2
0
0
0
0
0
0
1
2
1
0
0
1
0
0
0
1
0
1
1
0
2
0
2
0
1
1
0
1
1
1
0
1
1
0
0
0
0
1
1
2
1
1
0
0
1
0
0
2
0
0
2
1
0
1
1
1
1
1
1
0
1
1
0
4
1
1
1
2
0
1
1
1
1
1
1
0
0
1
0
1
3
1
1
1
0
0
0
2
0
2
1
0
0
1
2
1
0
1
0
0
2
1
1
0
1
0
0
0
2
1
0
1
1
0
0
2
2
0
0
0
0
2
2
0
1
1
1
0
0
1
0
1
1
1
2
0
1
2
2
0
0
2
1
1
1
0
2
1
2
0
2
1
0
0
0
1
0
1
0
1
0
2
2
1
0
1
1
2
1
1
2
1
2
1
0
1
1
1
2
0
1
1
1
0
0
1
1
2
2
1
1
0
2
1
1
1
0
1
1
2
0
0
0
1
0
2
2
2
2
1
0
0
2
0
0
1
0
0
0
1
1
1
0
1
1
2
0
1
0
1
0
0
1
1
2
0
0
1
1
1
0
1
2
1
1
0
2
1
1
1
1
1
2
1
2
3
2
0
0
0
0
2
0
1
0
0
1
2
0
1
0
1
0
0
0
1
1
2
1
1
0
1
1
3
0
1
1
0
1
1
0
0
1
0
0
2
2
2
1
0
0
0
2
1
0
0
0
0
2
2
2
1
1
0
0
1
0
0
2
2
0
0
2
0
1
1
2
1
0
0
0
1
1
0
0
1
0
0
2
0
0
1
0
2
0
0
3
2
0
0
0
2
1
1
1
1
0
0
0
2
2
0
1
3
0
1
0
2
0
1
1
0
0
0
1
1
1
2
0
3
0
0
0
1
0
1
0
1
3
0
0
1
1
2
1
1
0
2
2
1
0
0
2
1
1
1
1
1
1
0
1
1
1
0
0
0
1
1
1
1
0
0
0
1
4
1
1
0
1
1
1
1
2
2
0
0
0
1
0
1
0
0
1
1
0
0
0
1
2
2
1
2
1
2
0
2
1
2
1
2
2
1
1
0
2
2
1
0
1
0
2
0
2
0
0
0
1
1
1
1
0
2
1
1
3
1
2
1
2
0
1
1
0
0
1
1
1
0
2
1
1
0
2
0
1
5
0
0
2
1
0
2
1
2
1
0
1
2
0
0
0
1
2
2
1
0
0
2
2
0
1
2
1
1
1
1
1
1
0
2
2
1
0
1
0
0
1
0
2
2
2
1
1
0
0
0
0
0
1
1
0
0
1
0
2
0
1
1
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
4
1
1
0
0
2
5
0
1
0
0
1
1
2
2
2
1
1
2
1
1
1
2
1
0
0
0
2
1
0
0
0
2
2
0
2
1
1
0
1
0
1
2
1
2
2
2
2
2
1
0
0
1
1
0
0
1
1
0
1
1
1
2
2
1
2
1
0
0
1
1
1
1
0
2
2
4
1
0
1
1
0
0
1
2
0
0
0
1
1
1
0
1
0
1
2
1
0
2
0
1
0
1
1
1
1
0
0
2
1
2
1
0
2
0
2
0
1
2
0
0
0
1
1
1
1
1
0
1
1
1
1
2
1
0
2
1
3
1
0
0
1
0
0
0
1
2
0
1
0
1
2
1
1
0
1
0
1
2
0
0
1
2
0
1
2
0
1
1
0
2
1
1
1
2
0
0
2
0
0
0
1
2
1
1
0
0
1
1
3
2
0
0
0
0
1
2
1
1
0
0
0
0
0
2
0
1
0
2
1
1
0
1
2
1
0
2
0
1
1
1
1
2
0
1
0
0
1
0
0
0
0
1
1
1
2
0
2
0
3
1
1
1
0
1
1
0
2
1
1
2
0
1
0
1
1
1
0
0
1
0
0
1
1
1
0
2
0
0
0
1
0
1
2
0
2
0
0
1
0
2
0
0
1
1
2
1
0
1
0
0
1
1
1
0
1
0
1
1
0
1
0
0
1
0
1
1
2
0
2
0
0
0
1
2
1
1
1
1
1
1
2
2
1
0
1
2
1
1
2
0
1
0
1
2
2
0
1
2
1
1
2
1
0
2
2
0
1
1
0
1
1
0
2
0
1
2
0
2
2
0
1
1
0
1
1
0
1
2
1
1
0
1
1
2
1
2
1
1
0
1
1
1
2
1
0
1
0
0
1
1
1
3
2
0
1
2
0
1
1
1
1
0
1
0
0
2
2
3
2
2
1
1
0
0
0
0
0
0
0
2
0
2
0
0
1
1
2
1
1
1
0
0
0
1
2
0
1
1
1
2
1
0
1
2
1
2
1
2
1
1
0
1
1
2
0
1
1
0
0
1
0
1
0
0
2
1
2
0
2
1
0
1
1
5
2
0
2
0
1
2
0
1
1
1
1
1
0
0
1
1
1
1
2
0
1
2
0
1
0
1
1
0
1
2
0
1
0
1
1
0
2
0
1
1
1
1
0
0
1
2
2
0
0
2
1
0
1
0
0
2
1
0
1
1
1
2
0
1
0
1
0
0
0
1
0
1
1
0
1
1
0
1
1
1
0
1
2
2
0
1
1
2
0
0
0
1
1
1
1
0
1
2
1
0
1
1
1
0
0
2
1
1
2
1
0
0
1
1
0
1
2
2
1
0
0
2
1
0
0
1
0
1
2
0
0
1
0
2
1
0
0
1
1
2
1
0
0
1
0
0
0
0
2
0
1
0
1
1
0
0
0
0
1
0
0
2
2
0
1
2
2
1
1
1
0
1
1
1
1
1
1
1
1
1
0
2
1
2
2
1
0
1
1
2
1
0
1
0
1
1
1
1
2
0
0
0
0
1
1
1
0
1
1
1
1
2
0
1
0
1
1
2
2
2
1
0
1
1
0
1
0
1
0
1
0
0
0
1
1
0
2
0
1
1
1
0
1
1
0
3
0
2
0
0
1
2
1
1
1
0
1
0
2
1
0
1
1
0
0
0
2
0
1
0
0
1
0
0
0
2
1
1
0
0
0
1
1
0
0
0
1
2
1
1
1
0
1
1
2
1
1
2
0
1
2
2
2
2
2
2
1
1
1
1
1
1
0
1
1
0
0
0
1
3
1
1
1
1
2
0
1
0
0
1
0
0
0
2
1
0
2
0
3
1
1
1
0
1
1
0
1
1
1
1
2
1
0
0
1
0
2
2
0
2
2
1
1
1
0
0
1
0
0
1
0
1
0
2
0
1
0
1
1
1
1
1
1
0
0
0
1
1
1
1
0
1
0
1
0
0
0
0
1
1
0
1
2
1
1
1
1
2
1
2
2
0
1
0
0
1
1
1
0
0
1
1
0
1
0
1
1
1
0
2
1
1
1
1
0
1
1
0
0
1
1
1
1
0
0
1
1
1
1
0
0
0
0
1
0
2
1
0
0
0
1
1
2
0
1
0
1
1
1
0
0
0
1
1
0
2
0
0
2
0
1
1
2
3
1
1
0
0
2
1
3
0
2
2
1
0
1
2
2
3
1
2
0
1
2
1
0
1
1
0
1
0
1
1
1
1
1
1
1
0
0
2
1
2
1
1
0
2
2
2
4
1
2
0
1
1
1
1
1
0
2
0
1
0
1
2
2
0
0
1
1
2
2
1
1
1
2
2
2
1
2
2
2
1
1
0
0
1
0
0
0
1
0
0
0
1
0
1
1
1
0
0
0
1
2
0
1
1
1
0
0
2
1
0
1
1
0
0
2
2
0
2
2
1
0
1
1
2
1
1
1
0
1
1
1
1
1
0
1
0
1
2
0
1
1
1
0
0
1
1
0
1
1
0
0
0
1
1
0
1
2
1
0
1
0
1
1
2
1
1
2
2
0
2
0
2
2
1
2
0
1
0
4
3
0
1
0
1
2
2
1
0
1
0
0
1
0
0
2
1
2
0
1
0
1
2
2
0
2
1
0
6
0
1
0
1
0
0
0
0
2
1
0
1
0
0
0
1
0
1
2
0
0
1
0
0
0
2
0
1
0
1
0
1
0
1
2
0
2
1
2
1
1
2
2
1
2
1
1
2
2
2
1
1
1
0
2
1
1
2
0
0
0
1
1
2
1
2
0
0
1
2
1
4
1
2
1
0
0
2
1
1
1
0
0
1
1
2
1
0
1
1
1
0
0
0
0
1
1
2
1
0
2
2
2
2
1
0
4
1
1
1
2
1
0
0
2
1
1
0
1
0
1
0
0
2
1
1
0
2
0
1
1
1
0
1
1
1
1
2
1
2
0
2
3
1
2
2
0
1
0
1
1
1
0
0
2
1
0
1
0
0
1
0
1
2
2
0
1
1
1
1
1
2
1
1
1
2
1
1
0
1
1
1
2
2
0
1
1
0
0
1
1
0
2
1
0
0
1
1
1
1
1
1
1
2
2
2
2
2
1
2
1
1
1
1
1
2
1
1
0
1
0
1
0
0
0
1
1
1
1
0
1
0
0
0
2
2
0
0
2
2
1
3
1
1
1
1
1
1
0
1
2
1
0
1
0
1
1
0
2
0
0
0
0
0
2
2
0
2
2
1
1
0
1
1
0
0
1
2
1
1
2
1
1
4
2
1
1
0
2
1
1
0
1
2
1
1
1
0
1
1
1
0
0
0
0
2
1
2
0
0
2
1
0
0
1
1
1
2
1
2
0
0
1
1
0
0
0
1
0
1
1
2
0
4
2
1
2
1
2
0
0
0
1
0
2
0
1
0
1
0
1
1
0
3
1
1
1
0
1
0
0
1
1
2
1
1
1
1
2
2
0
1
1
1
3
1
0
1
0
1
1
0
0
0
2
2
2
1
0
2
0
3
0
2
1
0
0
0
0
0
2
1
0
1
0
1
2
0
0
1
2
0
1
2
0
0
2
1
0
0
1
1
0
0
0
1
1
1
0
0
0
2
0
0
1
2
1
0
1
1
1
0
1
1
0
1
2
0
1
0
1
0
2
0
0
0
0
0
1
1
1
0
1
2
0
2
2
0
1
2
1
1
1
1
0
1
2
2
2
2
0
2
2
1
2
1
1
0
2
0
0
1
0
2
0
2
1
0
1
0
0
0
0
0
1
2
2
1
2
1
0
1
1
1
0
0
1
0
1
1
1
0
1
1
1
1
0
0
2
0
0
1
1
1
2
1
0
0
3
1
0
0
1
1
1
2
0
1
3
1
2
1
1
1
0
0
0
0
0
0
0
0
1
2
0
0
1
1
0
1
1
2
1
1
1
1
2
1
1
0
1
2
1
0
1
0
0
0
1
1
1
0
2
1
3
0
0
0
1
0
2
1
2
1
2
1
1
0
1
2
0
0
1
0
2
1
1
2
1
2
0
3
0
1
0
1
0
1
0
0
2
1
0
1
0
1
1
0
1
0
1
1
1
1
0
1
0
0
1
1
2
0
0
1
1
0
0
0
2
0
1
0
2
0
0
2
2
1
1
0
0
0
2
1
1
1
1
1
1
2
2
2
1
1
2
1
1
1
0
1
0
1
2
1
0
1
1
0
2
0
0
1
0
2
1
1
0
1
1
0
1
0
1
1
1
0
0
0
2
1
0
2
1
1
1
1
1
1
1
0
2
1
2
2
2
2
0
0
1
2
2
1
0
0
1
1
0
0
1
1
0
0
0
2
1
0
1
2
1
2
0
1
0
0
1
1
5
1
1
0
1
1
1
2
1
1
1
0
2
0
2
0
2
0
1
2
1
2
2
1
1
2
0
1
1
0
0
1
1
1
0
0
1
1
0
0
0
1
1
2
2
1
0
2
0
1
1
1
1
0
2
1
0
2
1
0
0
2
1
1
0
1
1
0
1
2
0
1
0
2
1
2
0
0
1
1
1
2
0
2
2
1
2
1
2
0
0
0
1
1
0
2
0
2
1
0
1
0
0
0
0
0
0
1
1
2
2
1
1
1
1
1
1
2
0
0
0
0
0
2
0
2
1
1
1
1
0
2
1
1
1
1
1
2
1
2
1
1
2
1
1
1
1
1
1
0
2
1
0
1
1
2
1
1
2
1
1
1
1
0
2
1
0
2
1
1
1
1
0
0
1
1
4
0
0
1
1
0
0
0
2
1
2
1
2
2
1
0
0
1
1
0
2
2
1
1
0
0
1
0
1
0
0
1
1
1
2
2
0
2
1
0
1
1
0
2
0
2
0
0
1
1
1
1
0
3
1
1
0
1
0
1
2
1
2
2
2
1
0
2
0
1
2
2
0
0
0
1
3
0
2
2
1
2
0
0
1
2
1
1
0
2
0
1
0
1
0
0
0
0
2
2
0
0
1
0
1
0
0
1
1
1
1
1
0
1
1
1
1
1
1
2
0
3
2
1
2
0
1
0
1
1
1
2
0
0
1
2
1
0
0
1
1
1
1
0
1
1
0
0
0
0
2
2
1
1
0
0
1
0
1
1
1
0
0
0
1
0
1
0
0
1
1
1
1
2
1
0
0
2
1
0
0
1
1
1
1
0
1
0
1
1
0
2
0
1
0
1
0
1
0
1
1
0
2
1
1
1
1
1
0
0
0
1
1
0
0
2
2
0
1
1
2
0
2
0
1
0
3
1
0
0
0
2
0
0
1
0
1
0
0
2
2
2
0
1
1
0
1
0
2
0
0
2
1
1
0
0
1
1
1
1
1
2
1
1
2
1
0
0
0
0
1
2
2
1
0
1
0
0
1
0
1
1
1
0
1
2
0
1
0
1
0
1
1
0
1
0
1
1
0
1
1
0
2
0
0
1
2
1
2
0
1
1
0
0
0
0
1
0
0
1
0
2
2
0
3
2
2
1
0
1
2
1
1
2
2
1
0
2
3
0
1
0
0
2
1
1
1
2
1
2
1
0
0
0
1
1
0
1
1
2
2
1
2
0
2
1
1
3
0
0
1
2
1
4
0
0
0
1
0
1
0
2
0
0
0
1
0
1
2
2
0
0
0
1
2
2
1
2
0
1
1
1
1
0
1
1
2
0
1
2
1
1
0
0
1
1
2
1
0
0
1
2
0
2
1
0
0
2
0
1
0
1
2
2
1
2
1
0
2
0
1
3
2
1
2
1
1
0
2
2
2
0
0
0
2
0
1
1
2
1
1
2
0
0
2
0
1
0
0
1
0
0
1
2
0
2
0
1
0
0
1
0
0
1
0
0
2
1
2
2
1
2
0
2
1
0
0
4
2
0
1
2
1
0
0
1
0
0
1
0
2
0
1
1
0
0
2
1
1
1
2
2
1
1
0
1
1
0
1
2
2
0
2
1
2
0
0
0
0
0
2
0
0
1
1
2
0
1
2
0
1
0
1
0
1
0
0
5
2
0
2
0
0
0
0
1
2
2
0
1
1
1
1
0
1
0
2
2
2
2
0
0
1
2
1
0
0
2
1
2
0
1
0
1
2
2
0
0
0
1
1
1
0
1
1
1
1
2
1
0
0
1
0
1
0
0
1
2
1
1
2
0
0
0
1
1
1
2
0
0
0
1
2
1
0
1
0
0
0
2
0
2
1
1
1
2
0
1
1
0
2
1
0
2
1
2
1
1
0
0
2
2
2
1
2
0
2
0
0
0
1
0
0
2
0
0
1
2
1
0
1
0
1
0
0
0
0
0
2
1
1
2
0
0
0
0
0
0
1
0
1
1
1
1
0
1
1
1
2
1
0
1
2
1
2
0
0
1
2
2
1
1
1
1
1
3
0
2
2
1
2
0
2
2
2
1
1
1
0
2
2
2
1
1
0
2
1
1
0
0
0
1
1
1
2
2
1
1
2
2
0
1
0
2
2
1
0
1
1
1
1
0
0
2
1
2
1
1
1
2
1
1
1
1
0
2
0
1
2
1
1
3
2
1
0
1
0
0
1
1
0
0
1
3
1
0
1
0
1
0
1
0
1
2
1
0
0
2
1
1
1
2
1
0
0
0
0
1
0
2
2
1
1
1
1
2
0
0
1
0
1
1
1
2
0
1
0
1
1
2
0
1
1
0
4
0
0
0
1
1
1
1
1
0
0
1
0
0
1
1
0
2
0
2
1
2
0
2
1
1
1
0
1
1
1
1
1
0
1
0
0
1
0
1
1
1
0
0
0
1
1
0
0
1
1
1
1
0
2
0
1
1
0
3
0
0
1
1
1
1
0
0
1
0
2
0
0
2
2
2
1
0
1
1
1
2
1
1
1
1
2
1
0
1
1
1
2
1
1
1
0
1
0
2
1
0
2
1
0
1
4
0
1
1
1
0
0
0
0
0
1
3
1
2
0
0
1
0
1
1
0
1
1
2
1
0
1
0
0
2
1
1
2
1
8
2
2
2
1
0
2
0
0
0
2
2
1
0
0
2
2
1
1
0
0
0
3
0
1
2
1
0
1
0
2
0
2
0
0
1
0
2
0
1
1
1
2
1
2
2
1
0
1
2
1
0
1
0
0
0
1
2
0
0
1
1
1
1
1
2
0
1
0
2
0
0
0
0
1
0
1
1
1
2
1
2
2
2
1
1
1
1
1
0
6
1
1
0
1
0
2
1
0
0
0
2
2
1
1
0
1
1
2
0
2
1
0
0
0
0
0
0
1
1
0
1
2
0
1
1
0
1
1
0
0
1
1
2
1
1
1
0
0
2
0
1
1
0
1
1
0
1
0
1
1
0
1
2
0
1
1
0
2
1
1
1
2
1
2
1
2
1
0
2
1
0
0
1
2
1
0
1
2
2
1
2
1
1
1
1
0
1
0
1
1
1
0
1
1
0
0
0
2
1
1
2
1
0
2
2
1
2
1
1
1
1
1
1
0
2
1
2
2
3
2
1
0
2
1
0
1
1
2
0
0
2
2
1
1
1
1
1
1
0
1
1
1
0
2
2
0
1
1
1
1
1
1
0
0
1
0
1
0
1
1
1
2
0
1
0
0
1
1
1
0
0
1
1
0
1
1
1
1
1
1
1
0
2
1
0
0
1
2
1
1
1
0
1
1
0
1
1
1
2
0
1
1
1
2
2
2
1
2
1
0
0
1
1
2
0
1
2
1
0
2
0
1
2
0
2
0
2
1
2
1
1
1
1
0
0
1
1
2
1
1
0
2
1
1
2
0
2
0
0
1
1
1
0
2
2
1
0
0
2
0
0
0
2
2
1
1
1
0
2
2
2
1
1
1
1
0
1
2
0
4
2
0
0
0
1
0
0
0
1
2
2
0
1
2
1
1
1
0
2
0
0
0
1
2
0
0
1
3
1
1
1
1
0
1
2
0
2
0
0
2
0
2
2
1
0
0
1
1
1
1
1
1
1
1
0
2
2
2
2
0
1
1
1
1
0
2
1
1
1
1
0
0
0
1
1
1
0
2
0
1
0
2
2
1
0
1
0
0
0
1
0
0
4
0
1
1
2
0
1
2
0
0
0
1
1
1
1
1
2
0
1
1
1
0
0
0
2
1
0
1
1
2
1
1
1
1
1
0
1
1
0
1
1
1
1
0
0
0
0
0
0
0
2
1
1
2
1
0
1
1
0
1
1
0
0
1
0
0
0
1
1
0
0
2
2
1
1
0
2
1
0
1
0
0
0
2
1
0
2
1
1
1
0
0
1
1
0
2
1
1
1
2
2
0
1
1
1
1
0
2
2
2
1
1
1
0
0
1
2
2
4
2
0
2
1
1
1
2
2
0
1
0
1
1
1
0
1
4
0
1
1
1
1
1
1
0
2
2
2
1
1
1
0
1
1
1
1
0
0
1
2
1
1
0
2
1
1
1
1
2
0
0
1
2
0
2
1
1
0
0
1
1
0
1
1
0
0
1
0
0
2
2
1
1
3
0
2
0
1
1
2
1
1
0
2
2
0
0
2
1
1
0
1
0
1
1
0
0
0
1
1
0
0
0
0
0
1
0
1
0
1
1
0
0
1
0
0
1
3
1
1
1
1
0
2
1
2
1
0
1
1
0
1
0
1
2
0
2
1
0
1
1
0
1
0
2
1
0
1
0
0
0
1
0
0
1
1
2
0
1
0
1
0
3
0
2
2
2
0
0
1
0
1
1
1
1
2
1
1
0
0
1
0
1
1
1
1
0
1
1
1
0
2
5
1
1
1
1
1
1
0
1
1
2
0
2
0
1
1
0
1
2
1
0
0
0
2
1
1
0
0
0
0
1
0
1
2
2
1
2
2
0
0
2
0
0
1
0
0
2
2
1
1
2
1
1
1
1
2
1
2
2
0
0
1
0
1
2
1
2
1
1
1
1
2
2
1
1
1
1
0
1
0
0
1
1
1
2
3
1
0
1
1
2
1
1
1
0
1
1
0
0
1
0
1
1
2
1
1
1
2
1
1
1
2
1
0
0
1
0
1
2
1
1
1
0
1
0
0
1
2
1
1
0
7
0
2
1
0
1
1
0
0
0
0
0
3
2
0
0
0
0
0
2
1
2
1
1
1
1
0
0
0
0
1
0
0
1
0
0
2
2
0
0
0
0
0
0
2
0
1
1
1
2
3
1
1
2
1
0
1
0
0
1
2
0
0
1
1
2
1
2
1
2
1
1
2
1
1
2
1
2
1
1
2
0
0
2
1
2
0
2
1
1
1
0
0
2
1
2
1
3
3
2
1
2
2
1
1
1
1
0
0
1
0
1
2
3
1
0
1
1
0
1
1
1
0
0
2
1
1
1
1
1
0
0
0
0
2
1
1
0
1
2
1
1
0
1
1
1
0
1
2
1
3
0
2
1
0
1
1
2
1
2
1
1
2
1
2
1
0
1
0
2
0
0
0
1
0
1
0
0
2
2
1
1
1
0
2
2
1
0
1
1
0
1
0
1
0
1
0
0
0
0
2
0
0
1
1
2
2
1
0
0
1
1
2
1
0
1
2
1
0
0
1
1
1
1
0
1
0
2
0
1
0
0
1
2
0
1
1
1
1
2
0
2
0
0
1
1
1
2
1
0
1
0
0
0
0
1
0
1
1
1
1
2
2
1
1
0
2
1
1
0
0
1
0
2
1
0
1
0
0
1
0
2
0
0
1
1
0
3
1
1
0
2
1
1
1
0
1
1
0
1
0
0
2
2
1
3
0
0
1
2
1
0
1
2
0
2
1
0
0
0
2
0
1
1
0
0
2
1
1
0
1
1
2
2
0
0
1
0
2
0
0
2
2
0
2
0
0
2
0
1
2
1
0
1
2
1
2
1
2
1
2
1
0
1
1
1
1
0
1
0
1
3
0
0
1
0
0
2
1
1
0
2
1
0
2
1
0
2
2
0
1
0
1
0
0
1
0
1
0
1
1
0
0
1
1
2
1
1
1
1
1
1
0
2
1
1
2
0
2
0
0
1
2
2
1
1
0
0
0
1
4
1
2
4
1
1
1
1
0
0
2
2
0
2
0
1
0
0
0
0
3
2
0
0
1
0
1
0
0
0
0
2
2
0
2
0
2
1
0
4
0
1
0
1
2
0
1
1
1
1
1
2
0
1
1
1
2
1
3
1
0
1
0
1
0
2
1
1
0
0
0
2
0
0
0
0
2
1
2
1
1
1
1
1
1
2
0
1
2
0
0
1
1
1
2
1
0
1
1
0
2
0
1
2
1
1
1
1
1
1
0
0
1
0
0
1
1
1
1
1
1
0
0
1
1
2
0
0
0
0
2
0
0
1
0
1
1
2
0
1
0
2
0
1
0
1
0
1
0
1
1
1
1
0
2
1
1
0
1
1
0
1
1
2
0
0
2
2
0
2
2
2
0
0
2
0
1
2
1
0
0
0
1
0
1
1
2
0
0
2
2
0
1
0
1
1
2
0
1
0
0
2
0
1
1
1
2
0
0
0
2
1
1
0
1
2
1
2
1
1
0
0
0
0
1
0
1
0
1
1
1
0
0
1
2
0
2
1
0
2
0
1
0
2
0
0
2
1
1
0
1
1
0
1
2
0
1
2
2
2
1
1
2
0
1
0
1
1
0
1
2
2
1
1
2
1
0
1
1
1
1
2
2
1
1
0
0
2
1
1
0
1
0
2
0
0
1
2
2
1
2
1
0
2
2
2
1
1
1
1
0
1
1
2
0
1
2
0
0
1
0
0
1
1
1
1
1
1
3
0
0
2
0
2
1
1
1
0
1
1
0
0
1
1
1
0
0
0
2
2
0
1
1
1
0
2
1
0
0
1
2
1
2
0
2
0
1
0
0
0
0
1
0
2
0
1
0
0
1
2
2
1
1
1
2
2
2
0
0
1
1
0
1
1
2
2
2
0
2
1
2
1
2
1
0
1
0
0
1
0
2
0
1
0
0
4
1
0
1
0
1
2
1
0
0
1
0
1
1
1
2
2
1
2
1
2
2
3
1
1
1
1
1
1
1
0
0
1
0
2
1
1
1
1
2
2
0
0
0
1
1
2
2
1
1
1
2
1
0
0
1
1
0
3
1
0
1
1
0
0
0
0
1
0
5
0
1
2
1
0
0
1
0
0
1
0
1
0
1
1
0
1
1
2
0
0
2
0
0
1
2
2
1
1
0
2
0
1
1
2
0
1
0
2
1
0
1
2
2
1
0
1
2
1
2
1
1
1
0
1
1
1
1
1
2
0
2
1
0
0
0
1
2
2
1
1
2
1
0
1
0
0
0
1
1
0
1
1
1
0
2
2
0
1
0
0
0
1
1
1
3
1
2
1
1
0
0
1
0
2
2
1
0
0
1
0
1
1
0
2
1
1
0
1
1
0
1
1
2
1
2
1
1
0
0
2
1
0
0
0
0
0
0
1
1
0
2
1
1
1
0
0
1
0
0
0
0
1
1
0
0
1
0
1
1
2
0
0
1
2
1
2
1
1
0
1
0
0
2
1
0
0
1
1
1
0
0
0
1
1
1
1
0
2
1
0
0
0
1
1
0
1
1
2
2
0
0
2
0
1
0
1
0
2
2
1
2
1
0
0
0
1
0
0
1
1
2
0
2
1
1
0
1
0
1
0
3
1
0
1
1
2
1
1
0
1
2
0
0
0
0
1
1
0
1
0
2
0
0
0
0
0
1
0
1
2
1
1
0
1
0
1
1
1
1
0
1
1
1
0
0
0
0
2
1
1
1
0
1
0
1
1
0
2
1
2
1
0
0
0
0
2
0
0
1
0
6
1
1
0
1
1
1
0
1
2
0
1
1
2
5
0
0
2
0
2
2
1
1
1
1
1
2
1
1
2
0
2
1
0
0
2
2
1
1
2
2
0
1
0
0
1
1
0
1
0
2
0
0
0
2
1
2
1
0
0
2
0
0
0
0
1
1
1
1
2
1
1
0
0
1
1
1
2
1
0
0
1
1
0
0
1
2
1
2
0
0
2
0
0
0
0
1
1
0
0
0
1
1
1
1
1
1
0
1
1
2
0
2
1
4
0
2
1
0
1
1
2
2
1
2
1
0
0
0
1
1
1
0
0
2
0
0
0
0
1
2
0
2
0
1
1
0
1
1
1
0
0
2
0
0
2
0
0
0
1
0
1
1
2
0
2
1
0
1
0
2
0
0
1
0
1
0
1
2
1
0
1
2
1
1
1
2
1
2
1
0
1
1
0
1
2
0
1
1
2
1
0
1
2
0
1
1
3
1
0
2
1
2
1
1
1
1
2
1
1
0
1
2
2
1
0
0
0
1
1
1
1
1
1
0
1
0
1
0
1
1
1
4
1
2
1
1
1
1
0
2
1
0
2
1
0
1
3
0
1
1
2
0
2
1
0
0
1
0
1
2
1
0
1
0
2
1
0
1
0
2
0
0
2
0
1
1
1
2
1
1
0
0
0
0
0
1
2
0
1
1
1
2
1
1
0
2
1
0
1
0
0
1
0
2
0
0
1
1
2
1
0
0
0
1
0
1
0
1
2
0
0
1
0
0
1
1
1
0
2
2
2
0
1
2
1
0
2
2
1
1
0
0
0
1
2
1
0
2
1
1
0
1
2
1
0
1
0
2
2
1
0
1
0
1
2
1
2
1
1
1
1
0
0
1
0
0
1
0
1
2
0
2
1
1
0
0
1
0
2
1
0
1
1
1
1
0
0
1
1
1
0
0
1
0
1
2
1
0
0
1
0
1
2
2
1
2
1
0
2
1
2
1
2
1
1
0
2
1
0
1
0
1
1
1
1
1
1
1
0
1
0
3
1
0
1
1
0
1
2
3
1
1
0
2
2
0
2
1
1
2
2
1
1
1
1
2
1
2
2
0
0
1
1
1
2
1
2
1
0
3
0
1
0
2
1
0
0
0
0
0
1
1
0
1
1
1
0
0
0
1
1
1
2
0
2
1
1
1
2
2
1
1
0
0
2
1
1
0
2
1
0
1
1
1
1
1
0
0
1
2
1
1
1
1
1
1
1
1
1
2
2
0
1
2
1
0
0
0
0
1
2
2
0
0
0
0
2
0
1
2
0
2
0
0
0
0
0
1
0
2
1
2
1
2
0
1
0
1
0
1
0
2
0
1
1
1
1
1
0
0
0
0
2
0
0
1
0
2
0
0
0
1
1
1
1
0
1
0
0
2
2
1
2
0
0
0
0
2
0
2
1
1
1
2
2
1
1
0
0
0
0
2
0
1
1
0
1
1
1
0
1
2
1
0
1
0
0
0
1
0
0
2
1
2
1
1
1
2
2
1
0
0
0
1
0
0
1
3
1
0
2
0
1
2
0
1
1
0
2
2
2
2
1
1
0
1
0
1
2
1
1
1
1
0
1
1
1
3
1
0
4
0
0
0
1
2
2
2
0
0
0
1
1
1
1
1
0
1
0
2
1
0
0
1
1
1
2
0
1
1
1
2
0
0
0
0
0
1
1
1
2
0
2
2
0
2
0
0
1
0
1
0
2
2
0
1
0
0
1
0
0
2
2
1
1
2
2
0
1
1
2
1
0
0
1
1
0
2
1
1
1
0
0
2
0
1
0
1
1
2
1
2
1
0
1
0
2
1
0
1
0
1
1
2
1
1
1
0
1
2
0
1
1
4
1
1
1
1
0
0
1
1
1
0
1
1
0
0
1
1
1
0
1
1
1
1
1
2
2
1
1
1
1
2
0
0
2
1
1
2
1
0
1
0
1
1
1
3
1
0
0
0
2
2
1
0
1
1
0
1
1
0
0
0
0
1
0
1
1
0
0
1
0
1
2
0
0
2
2
1
0
1
0
0
1
2
0
2
2
2
0
1
2
2
1
2
1
2
1
1
0
1
0
2
2
0
1
2
1
1
0
2
1
3
1
1
3
1
2
0
1
0
0
1
1
0
1
1
1
2
0
0
2
1
2
1
0
0
1
0
2
0
2
1
0
0
0
2
0
0
2
2
0
1
1
1
1
1
1
1
1
1
1
0
0
1
1
0
1
0
0
0
2
1
0
2
0
1
2
1
0
2
0
1
1
0
1
0
1
0
1
2
1
2
1
2
0
0
2
0
0
0
2
1
1
1
0
1
9
0
1
1
0
0
2
1
1
1
0
1
2
4
1
0
2
1
1
0
1
1
0
0
0
3
0
1
0
1
1
0
2
1
2
0
1
2
0
1
1
1
1
0
0
0
2
0
1
0
2
2
1
1
1
2
1
2
1
0
0
1
0
1
2
2
0
0
2
0
1
0
0
0
1
1
0
0
0
2
1
1
0
0
0
0
1
2
2
0
2
0
1
0
1
2
1
1
3
0
1
1
0
1
0
2
0
0
0
2
0
1
0
0
3
1
1
3
2
0
1
0
2
2
1
0
2
1
2
1
0
0
0
1
2
0
0
2
0
0
0
1
0
0
0
1
1
2
0
0
1
1
1
1
0
1
1
1
0
0
2
2
1
0
0
0
1
1
1
1
0
0
0
2
1
0
2
2
1
2
0
1
1
2
1
0
0
1
2
0
0
0
2
0
0
0
1
0
1
0
1
1
2
2
0
1
1
1
1
0
1
1
0
0
0
0
0
0
2
2
1
1
1
1
1
0
2
0
0
1
1
0
2
0
1
0
0
0
2
1
2
0
2
1
0
2
1
1
0
1
1
0
0
3
1
1
1
0
1
2
0
2
0
1
0
3
2
2
1
1
1
0
0
1
0
2
0
0
0
0
0
2
1
1
2
1
1
0
1
1
1
1
0
0
0
0
0
0
0
2
1
1
0
1
1
1
0
0
0
1
1
2
2
2
1
2
0
0
0
2
2
0
0
1
1
0
1
1
1
0
2
1
1
1
1
2
0
2
0
1
0
2
1
2
0
1
0
2
0
1
2
0
2
1
2
0
0
1
1
1
1
2
1
2
2
1
4
0
2
1
1
2
0
0
2
1
0
0
1
2
0
0
3
1
0
1
0
1
0
2
0
1
1
1
2
0
2
1
2
1
2
0
1
0
0
0
0
1
1
1
1
1
1
0
1
0
1
1
1
2
1
1
0
1
1
0
0
2
4
1
1
1
1
0
1
0
2
1
0
1
0
0
1
1
2
0
0
2
1
1
0
1
2
1
1
0
0
1
1
0
0
0
1
1
1
1
1
1
2
0
0
1
1
1
1
1
1
0
0
0
1
4
1
2
2
1
2
2
0
1
0
1
1
2
1
1
1
0
1
0
1
1
0
2
1
1
3
1
2
1
2
1
1
1
2
2
0
0
1
0
0
1
0
1
0
0
2
1
0
0
1
2
0
1
2
2
1
1
2
0
1
1
0
1
2
1
0
0
1
1
1
1
1
0
2
1
0
0
0
1
2
0
1
0
1
0
1
1
0
1
1
1
0
2
0
0
1
1
0
0
0
2
2
0
2
1
2
0
2
1
1
1
1
2
1
0
2
1
0
0
0
1
2
0
2
1
0
5
2
1
0
2
2
2
2
2
1
2
1
1
1
1
1
0
0
0
2
0
1
0
0
1
1
2
1
1
1
1
1
0
2
1
1
2
2
2
0
0
1
0
1
1
1
0
1
2
1
0
2
1
1
0
0
1
0
2
5
2
2
1
2
1
2
1
0
0
2
0
1
1
1
0
1
1
0
0
0
2
1
1
2
1
0
0
1
1
2
1
1
1
0
0
1
0
1
1
2
2
1
1
1
1
1
1
0
2
3
1
2
1
2
0
2
2
1
1
1
2
0
2
0
2
1
1
0
1
2
0
1
0
2
0
1
0
0
2
1
1
0
0
1
1
1
2
2
1
1
0
2
1
1
2
2
1
1
2
1
1
1
1
0
1
1
0
1
1
0
0
1
3
0
1
0
1
0
2
2
0
0
0
2
0
1
0
2
0
1
2
2
0
1
1
2
1
1
0
2
1
0
2
0
1
1
1
0
2
2
2
2
1
1
0
1
0
3
0
2
2
1
0
1
0
2
2
2
1
1
3
1
2
0
0
0
1
1
1
2
0
2
1
1
2
0
0
2
0
2
0
1
1
1
2
0
1
1
4
2
2
1
1
0
1
1
1
2
0
2
1
1
1
1
0
0
2
1
2
1
1
2
2
0
1
1
1
0
2
1
1
0
0
1
0
0
1
2
1
0
1
1
0
0
1
1
2
0
1
1
0
1
1
1
1
0
0
1
1
1
2
0
0
1
1
1
0
0
1
0
2
0
1
0
1
1
1
0
2
0
1
1
0
0
2
1
0
2
2
3
0
0
1
2
0
1
0
2
0
0
3
0
1
0
0
0
0
1
0
2
2
1
0
2
2
0
1
2
0
2
0
1
1
1
0
0
1
0
0
1
1
1
2
1
1
2
1
1
0
2
0
0
2
2
0
1
1
0
1
2
1
1
1
2
1
1
1
2
1
2
2
0
0
1
1
0
0
2
0
1
2
1
0
0
2
1
1
1
1
0
1
1
0
1
2
0
1
0
2
1
0
0
2
1
1
1
0
0
1
0
1
2
0
1
1
1
0
0
1
1
1
1
1
1
1
1
1
1
1
2
2
0
0
1
1
1
1
1
0
0
1
1
2
0
1
1
2
1
0
1
1
1
0
1
1
0
2
2
2
1
0
3
1
0
1
1
0
1
1
1
1
1
1
0
1
0
1
1
1
1
2
1
1
2
4
1
0
0
0
2
0
1
0
2
1
1
1
0
2
1
2
0
0
0
0
3
1
1
1
1
1
2
0
1
1
0
2
5
1
0
1
1
1
1
1
0
0
2
0
2
0
1
0
0
0
0
1
1
2
1
1
2
0
1
0
0
1
1
1
2
1
0
1
1
2
0
1
1
0
2
2
0
0
0
0
2
2
1
0
1
1
1
1
2
1
2
0
1
0
2
1
0
1
1
2
2
0
1
0
1
1
0
1
1
0
2
2
1
1
0
2
0
0
1
2
0
1
1
0
2
1
1
1
1
2
0
0
0
1
1
1
2
2
0
0
0
0
2
1
1
1
0
1
0
0
1
0
1
1
1
2
2
0
2
1
1
2
0
1
1
0
1
0
1
1
2
0
0
1
0
1
2
1
4
1
1
1
2
1
0
2
2
1
0
0
2
2
0
1
2
1
1
1
0
1
0
1
0
0
1
0
1
1
1
1
1
2
2
0
2
1
1
0
1
2
1
1
1
1
0
1
1
2
2
1
0
1
1
0
1
0
1
0
1
2
1
1
2
1
2
0
0
0
1
1
2
1
0
0
0
1
0
0
0
1
0
0
2
1
0
0
2
2
0
1
2
1
0
0
2
0
0
1
2
1
0
1
1
1
2
0
0
2
2
2
1
1
0
3
0
1
1
1
0
1
1
1
2
0
1
1
0
0
0
0
1
1
2
2
1
2
2
1
1
3
1
1
0
2
0
0
1
1
1
1
1
2
1
2
0
1
1
0
1
1
0
2
0
1
2
2
3
1
0
0
0
1
0
0
1
2
0
0
2
0
1
0
1
2
1
1
0
2
0
0
1
1
0
2
1
0
1
1
2
1
3
0
1
2
1
1
0
1
2
0
1
1
2
2
1
0
0
2
1
2
1
0
0
0
1
1
1
0
1
0
1
1
0
2
1
1
0
0
1
1
1
0
2
1
0
1
2
1
1
1
0
2
0
2
0
0
2
1
1
2
2
2
2
2
1
0
2
2
1
1
1
2
2
1
1
1
1
2
2
1
1
1
1
2
1
2
1
1
2
1
0
0
2
1
0
0
1
1
0
0
2
1
0
0
3
0
0
2
0
2
2
0
1
1
1
2
1
1
2
0
0
0
1
2
1
1
1
1
0
1
1
0
1
1
1
0
1
0
1
0
1
0
1
2
2
1
1
1
1
1
0
1
0
0
2
0
0
0
0
1
0
1
1
1
0
0
0
0
0
1
0
0
2
1
1
2
1
0
0
1
2
2
0
1
0
1
0
2
0
1
2
1
1
1
1
0
1
1
1
0
1
1
2
1
2
0
1
0
1
1
0
1
0
1
1
1
0
1
2
1
1
1
1
1
0
2
0
1
1
1
0
1
0
1
2
0
2
0
2
1
1
2
2
1
1
1
0
1
2
0
1
1
2
0
1
0
0
1
1
1
1
3
1
1
0
0
2
1
1
0
1
2
2
0
2
0
1
2
2
0
2
1
2
1
0
1
0
2
1
1
1
1
0
2
1
0
1
0
0
1
1
1
0
0
0
0
0
1
2
1
1
1
0
0
2
2
0
1
1
0
1
2
0
0
1
2
1
2
1
2
1
0
0
2
1
1
1
2
2
0
1
1
0
2
0
2
0
0
1
1
1
1
1
0
1
1
1
1
1
2
1
0
0
0
1
0
2
1
1
0
1
1
2
0
1
2
2
0
1
1
2
1
0
2
2
0
2
0
2
0
1
1
0
1
0
1
0
2
0
2
2
0
0
0
1
1
0
2
2
4
0
0
0
1
2
0
0
2
1
0
0
1
1
1
1
0
0
2
1
0
1
2
1
0
2
0
1
1
1
1
1
0
2
1
1
1
0
1
2
2
0
2
0
2
0
0
2
2
2
1
1
1
1
0
1
1
2
1
0
0
1
1
2
1
0
1
1
1
1
1
1
1
2
1
0
1
1
0
0
0
1
0
1
1
0
0
1
1
0
2
0
2
2
1
2
2
0
0
0
0
0
1
0
0
1
1
1
1
0
0
1
0
0
0
0
1
0
2
0
2
0
1
1
1
1
0
1
0
2
0
1
0
0
1
0
0
0
0
0
0
0
2
2
0
0
1
3
1
0
1
3
0
1
2
0
0
0
2
1
1
1
1
2
2
0
1
1
2
1
1
2
0
0
2
1
1
1
2
1
1
2
0
1
3
0
2
0
0
2
1
2
1
1
0
1
1
2
1
1
0
1
0
1
0
2
0
3
0
0
1
2
0
0
2
1
2
1
1
2
2
1
2
1
0
1
2
1
0
0
0
0
2
2
2
1
0
1
0
1
1
1
1
1
0
0
1
0
2
0
2
1
1
1
2
2
1
1
0
0
2
0
1
1
0
2
0
1
2
1
1
0
0
0
0
2
1
0
0
1
1
0
2
4
0
1
1
2
3
2
1
0
0
1
0
0
0
2
1
2
1
2
1
1
0
0
0
2
0
0
1
1
1
1
2
2
1
1
0
0
0
0
2
0
1
1
0
0
2
1
3
2
1
2
0
0
2
0
0
2
0
0
1
0
1
1
1
1
1
0
1
2
1
0
0
2
1
0
2
1
0
1
0
2
1
2
1
0
2
0
2
0
0
1
2
0
0
1
0
0
0
0
2
0
4
0
1
1
4
1
1
1
1
1
2
1
0
0
0
1
1
0
0
1
1
2
1
0
0
1
1
0
3
1
0
3
1
0
2
0
1
0
1
1
0
0
0
0
2
1
0
1
1
2
2
1
2
0
1
1
0
2
1
2
0
0
1
1
0
2
0
0
0
1
2
1
1
1
1
0
1
1
0
0
1
1
2
1
0
0
0
2
2
2
1
2
0
1
0
2
1
0
0
1
0
1
1
0
0
0
0
1
1
3
1
0
1
2
0
1
1
0
0
0
1
2
1
0
2
0
2
1
5
0
0
1
1
2
0
1
0
1
2
1
1
2
1
0
0
0
0
0
2
0
1
1
2
1
1
0
0
1
1
0
2
2
1
1
1
1
1
1
1
1
1
1
0
1
1
0
0
0
0
1
0
1
1
1
1
1
2
2
1
2
2
1
1
1
0
1
1
1
3
1
0
1
0
2
2
2
2
1
0
0
1
0
2
0
0
0
1
0
2
1
1
1
1
0
1
0
0
1
1
1
0
2
1
1
2
1
1
2
0
0
2
1
1
2
2
1
0
2
1
1
1
1
1
1
2
0
0
2
0
2
0
0
1
0
1
1
1
0
2
2
0
1
2
1
2
1
1
0
2
1
2
0
1
1
0
1
1
1
0
0
1
1
1
0
0
1
0
0
2
1
1
0
3
0
2
0
1
1
0
0
2
1
0
2
3
2
1
1
0
0
1
1
1
1
2
1
0
0
1
2
0
0
2
1
0
1
1
1
2
0
1
0
0
0
2
0
1
1
0
0
1
2
0
1
2
0
0
0
1
1
2
1
0
3
2
1
1
0
1
2
0
2
1
2
2
2
2
0
0
0
2
0
1
0
1
2
1
0
0
2
0
1
0
5
0
0
1
1
1
0
1
1
1
0
0
0
1
0
1
1
1
0
2
0
2
0
1
0
0
1
0
0
3
2
0
5
0
0
1
2
0
1
1
1
0
1
2
2
1
2
2
1
1
1
0
0
1
1
0
1
0
2
1
2
0
0
1
1
1
2
3
0
1
1
2
1
2
1
1
0
2
0
0
2
0
0
0
1
0
0
0
1
1
1
0
1
1
1
1
4
2
2
1
2
1
0
1
2
2
1
0
0
1
1
1
0
2
1
1
0
1
1
0
0
0
0
0
0
1
1
1
2
1
1
0
2
1
2
2
1
1
2
0
2
1
0
0
0
1
1
1
0
0
0
0
0
1
1
0
2
2
0
1
0
0
1
0
0
1
1
1
0
1
1
0
0
2
0
0
0
1
1
0
1
1
2
0
2
1
0
1
3
2
1
1
1
0
1
0
1
1
1
1
0
0
2
0
0
2
1
1
0
0
0
3
2
2
0
2
2
1
1
0
0
0
0
0
0
1
1
0
1
1
2
2
1
1
2
0
1
1
1
1
1
2
1
1
0
0
1
1
3
1
1
2
2
1
0
0
0
1
1
0
1
0
1
1
0
1
1
1
1
2
2
1
0
1
1
2
0
2
0
2
0
0
2
2
0
1
0
1
0
0
2
2
0
2
1
0
0
1
1
1
2
1
1
2
0
0
2
1
1
1
0
1
0
0
2
2
2
1
1
1
1
1
0
3
3
1
0
0
0
0
1
1
0
2
2
0
0
0
1
2
1
0
0
3
2
1
1
2
0
1
2
1
2
2
2
2
1
2
0
0
1
2
1
0
0
0
0
1
2
0
0
2
1
0
1
0
1
0
1
0
1
0
2
1
0
0
0
1
0
1
1
2
0
2
1
1
1
0
2
0
0
1
1
0
0
0
1
2
1
1
1
1
0
1
2
1
1
1
1
2
0
0
3
1
1
1
0
2
0
1
0
1
1
1
0
1
1
2
0
0
1
1
1
2
2
1
0
0
3
1
0
2
1
1
1
0
0
1
0
1
1
0
1
1
0
0
1
1
1
0
2
1
2
0
2
1
1
1
3
1
0
0
1
1
1
0
0
2
1
2
2
1
1
1
0
1
0
1
0
0
1
0
0
1
2
1
2
0
2
0
0
1
2
1
1
0
0
1
0
2
0
1
0
1
1
2
1
1
1
0
1
0
1
1
0
0
0
0
2
0
2
0
0
2
1
1
1
0
0
1
1
1
0
1
2
1
0
1
0
1
0
1
1
3
2
1
2
1
1
0
2
1
1
1
0
0
1
1
1
0
0
0
1
2
1
1
1
0
2
1
1
2
0
0
1
1
1
1
2
1
2
1
0
1
1
1
0
1
0
2
1
2
1
1
2
0
2
0
0
1
0
1
0
1
0
1
1
4
1
1
1
1
1
0
1
1
2
1
1
1
2
0
1
1
1
1
1
0
1
2
1
2
0
1
0
1
1
1
1
1
2
2
0
1
2
2
1
2
0
0
1
0
0
2
2
0
1
0
1
0
1
1
2
1
2
0
1
2
2
0
1
0
0
1
0
1
0
0
2
1
5
0
2
0
0
1
0
0
0
2
1
1
2
0
1
2
0
0
1
0
0
0
0
0
0
0
1
1
1
1
1
2
2
1
1
0
2
2
2
1
0
2
2
0
1
0
0
2
1
1
1
2
0
1
3
0
0
0
2
1
2
2
1
0
0
2
1
2
1
0
0
0
1
2
0
2
1
0
4
1
1
2
0
2
1
0
0
0
1
0
1
0
2
1
0
2
0
0
0
1
2
1
2
1
1
0
0
0
1
1
1
2
0
0
0
1
0
2
1
0
1
0
1
0
0
0
0
0
0
2
0
1
0
0
1
1
0
1
0
1
0
0
1
1
2
1
0
1
2
1
1
0
2
2
1
2
1
2
2
1
1
1
2
1
1
2
1
2
4
1
1
2
0
2
2
0
2
0
0
0
0
1
0
1
2
1
1
1
0
0
2
0
1
2
1
1
2
2
2
1
0
2
0
0
0
1
0
1
2
0
2
1
2
1
2
2
1
5
1
0
0
2
3
2
2
2
1
1
1
1
1
0
3
1
0
0
2
0
0
1
1
0
1
0
1
1
0
2
1
1
2
0
0
1
1
0
1
0
1
1
2
0
1
2
1
0
0
1
6
1
2
1
0
0
2
0
0
2
1
1
0
1
2
1
1
2
2
0
0
1
3
1
1
1
1
1
0
1
2
0
3
2
1
1
1
1
2
3
0
2
0
1
2
0
0
4
2
1
1
0
0
0
2
1
1
1
1
0
0
1
1
2
2
0
1
1
1
1
0
1
1
1
0
1
2
2
2
1
1
1
2
1
1
1
0
2
3
0
1
2
0
0
0
1
0
2
0
0
0
5
1
2
1
2
0
1
0
0
1
2
1
0
2
1
0
0
2
1
1
1
0
1
0
2
0
1
2
1
2
1
0
1
0
1
1
2
0
0
1
0
1
0
1
1
0
2
1
2
0
1
0
1
2
0
1
2
1
1
1
2
1
1
2
1
1
0
0
0
2
0
0
0
0
2
2
2
0
2
0
0
2
3
1
2
2
0
2
1
0
2
0
1
1
0
1
2
1
1
1
1
2
0
2
0
1
2
0
1
1
1
0
2
0
2
1
1
1
0
1
0
0
1
1
1
1
2
1
0
0
1
2
1
1
1
1
1
1
2
1
1
0
1
0
0
1
1
1
1
1
1
0
2
2
1
0
1
0
1
0
0
1
0
1
1
2
2
2
1
0
1
0
2
0
2
1
2
2
1
0
2
0
1
2
0
2
0
0
0
1
1
2
1
0
0
2
1
3
0
1
0
1
0
0
1
1
1
2
1
1
2
1
1
2
1
1
0
1
1
2
1
1
0
2
0
1
2
1
0
2
0
1
1
1
1
1
0
2
1
0
0
1
0
1
0
1
1
1
0
1
1
1
2
1
1
1
3
0
2
0
0
1
2
1
1
2
1
1
0
0
2
2
0
1
0
0
1
0
0
1
0
0
2
1
0
0
1
0
1
2
0
1
0
0
2
1
0
0
2
1
0
1
1
2
0
0
1
1
0
1
1
2
0
0
2
0
1
1
0
2
1
1
1
0
0
0
0
1
1
2
0
0
2
0
0
0
0
1
0
2
0
0
1
2
1
0
0
1
2
0
1
0
0
1
1
0
1
1
0
0
0
1
0
1
1
2
2
1
1
2
0
2
1
0
2
0
2
1
0
0
0
1
0
0
2
0
1
1
0
1
0
2
1
1
1
1
0
0
2
0
2
0
1
2
0
0
0
0
1
0
1
2
0
1
1
1
0
2
0
1
0
2
2
1
1
0
1
1
2
0
2
1
0
1
0
1
2
1
1
1
2
1
2
0
0
1
0
2
0
1
0
0
1
2
1
0
2
0
1
1
0
0
1
0
0
0
0
1
1
1
0
0
1
0
2
0
2
2
0
0
1
1
1
0
0
2
0
1
0
2
1
0
0
2
2
1
1
0
2
0
0
2
1
1
2
2
2
2
2
2
0
0
1
0
1
0
1
1
0
1
1
3
2
0
3
0
1
0
2
1
2
1
2
1
1
1
0
2
0
1
2
0
0
0
1
0
2
0
2
2
1
0
0
0
0
0
2
0
1
2
0
1
0
1
2
1
0
1
1
0
2
1
1
1
1
1
4
0
1
1
0
2
0
1
0
1
0
1
0
2
2
1
2
1
1
2
0
2
0
0
1
0
1
0
0
0
1
0
1
1
1
2
1
0
1
0
2
1
1
2
0
0
2
2
1
1
1
0
1
0
1
0
1
1
0
1
2
1
1
1
0
1
0
1
0
1
1
0
0
0
0
1
2
2
0
1
2
0
0
0
1
2
1
0
0
2
0
0
0
1
1
1
1
1
1
0
2
1
0
1
2
1
0
1
2
0
0
0
0
1
1
2
0
0
0
2
1
0
1
1
2
0
0
1
1
1
0
0
0
0
1
2
1
1
3
0
1
0
0
2
0
1
2
2
0
1
0
0
0
2
2
1
1
2
0
1
0
0
0
2
1
0
0
2
0
2
1
2
0
1
0
2
0
1
1
1
1
1
1
0
2
0
0
1
1
1
2
2
1
1
0
2
2
0
1
0
0
1
1
2
1
0
2
0
2
1
0
2
1
1
1
2
0
1
1
1
2
0
1
1
2
1
1
1
0
0
0
0
0
2
0
1
0
1
0
2
1
2
0
0
0
1
0
4
1
1
2
1
2
1
2
1
0
2
0
0
2
2
0
1
1
1
2
2
0
4
1
1
0
2
0
1
2
1
2
0
0
2
0
1
0
0
1
2
0
1
0
0
1
1
2
1
0
2
2
0
0
0
2
0
0
2
1
2
0
1
0
2
0
0
0
1
1
1
2
1
0
1
1
0
3
2
1
1
0
0
2
0
0
0
1
0
1
1
1
1
0
1
1
0
1
0
2
1
1
1
1
2
1
0
2
0
0
1
0
1
1
0
0
0
0
0
0
0
2
0
1
1
1
1
2
0
1
1
2
2
0
1
0
1
1
2
1
0
2
0
0
0
2
2
0
2
1
1
1
1
0
2
1
0
2
2
3
0
0
0
3
0
0
2
1
1
1
1
2
2
0
2
0
2
1
0
1
1
2
2
2
2
0
1
1
1
0
0
2
0
1
0
2
1
1
1
2
1
1
1
1
2
0
1
2
2
0
0
0
2
1
0
0
1
2
1
1
1
1
1
1
0
1
0
2
6
1
1
0
1
0
0
0
2
1
0
2
2
0
1
2
2
2
2
1
0
0
2
1
0
0
1
1
2
1
1
1
1
1
1
1
2
0
1
1
1
0
0
2
1
0
2
0
2
2
0
1
0
0
0
1
0
1
1
0
1
1
1
0
1
7
1
2
1
0
0
0
2
0
3
0
0
1
0
0
2
2
2
2
2
1
0
1
1
1
1
0
0
2
2
3
2
2
1
1
2
0
1
0
1
2
1
2
2
1
0
2
0
1
1
1
0
0
1
0
2
0
1
1
0
0
2
2
1
0
2
0
0
3
1
1
0
0
0
0
2
0
1
1
0
0
1
1
0
2
1
1
1
0
0
1
2
0
1
1
2
0
0
1
0
1
1
2
1
0
0
1
0
1
0
0
0
1
0
0
1
2
0
0
2
2
0
0
1
1
1
1
2
2
0
1
5
1
1
0
0
0
0
1
2
1
0
1
0
1
0
3
2
1
0
1
0
1
1
1
0
1
1
1
1
0
0
1
1
2
0
2
0
1
2
1
1
0
1
0
1
1
2
2
2
1
0
0
2
2
0
1
2
0
0
0
1
1
0
0
1
2
0
1
1
1
0
1
2
2
2
0
0
1
0
1
1
1
2
1
2
1
2
1
2
2
2
2
2
1
2
2
1
0
2
0
2
2
0
0
1
0
0
0
0
2
2
1
0
1
0
0
1
1
1
0
1
1
0
0
1
2
1
2
2
0
1
0
1
1
1
1
0
2
0
3
0
0
1
0
1
2
1
0
1
2
2
0
0
1
0
0
1
2
0
0
0
1
1
0
2
0
2
1
2
1
0
1
0
1
1
2
1
1
1
0
0
0
1
2
1
0
1
0
0
1
0
1
1
0
1
0
0
1
1
2
1
1
2
2
1
1
1
2
2
0
1
1
0
1
0
1
1
2
2
2
2
1
0
2
2
0
1
1
1
1
0
1
0
0
0
1
0
0
0
0
2
2
0
0
1
1
1
0
1
1
1
2
1
1
0
1
0
0
1
1
2
0
1
0
1
0
1
1
0
0
0
1
0
1
2
2
0
1
0
0
1
1
2
1
2
0
2
1
1
1
2
0
0
0
1
1
0
1
0
0
0
1
0
0
1
1
1
1
0
2
1
0
1
0
0
0
1
1
0
1
2
2
0
0
0
2
1
1
0
0
0
0
0
2
1
0
2
1
0
1
1
0
1
1
0
1
1
1
0
2
0
0
1
2
1
2
1
2
1
1
0
1
1
1
1
2
0
2
2
2
1
2
0
1
1
1
1
1
1
1
1
0
1
1
1
0
1
1
0
0
2
1
1
2
2
1
1
1
1
2
1
1
0
0
0
0
0
0
1
0
1
2
2
0
1
2
2
0
0
0
1
0
1
1
1
1
0
0
1
1
1
0
1
1
1
0
0
1
0
0
0
2
5
1
0
0
2
1
0
1
1
0
0
1
2
2
1
1
0
0
1
1
2
0
0
2
1
2
1
0
2
1
2
0
2
0
1
1
0
0
0
1
0
2
1
0
1
0
2
1
0
1
1
1
1
0
0
1
2
2
0
1
1
2
1
0
0
1
1
2
1
2
0
1
0
0
0
0
1
0
0
0
2
2
1
1
0
1
2
0
1
0
2
2
0
2
1
1
1
1
1
1
1
1
2
0
1
1
0
1
1
0
0
0
2
0
2
0
0
1
0
0
1
2
1
1
3
1
1
1
1
2
0
2
0
1
1
1
1
1
1
2
0
1
0
0
3
0
1
2
0
1
0
0
1
1
1
0
2
1
1
1
0
2
1
1
2
1
1
3
2
0
0
1
1
1
2
1
0
1
0
0
0
1
0
1
0
2
2
2
2
1
1
1
0
2
0
2
2
1
1
0
1
2
1
0
2
1
2
1
2
1
0
0
2
2
1
2
1
0
2
1
1
2
1
0
0
2
2
2
2
2
2
1
1
2
1
0
2
1
1
0
1
1
0
0
0
1
1
2
1
0
2
1
2
0
0
2
2
0
2
1
2
0
0
0
1
1
0
2
2
1
0
0
1
1
1
2
1
1
0
2
2
0
1
1
2
2
0
2
2
2
1
2
1
1
1
2
1
1
2
0
2
0
0
0
0
1
2
2
0
0
0
1
2
2
2
0
2
1
0
1
2
1
1
0
0
2
0
1
1
0
1
4
1
0
0
0
2
1
1
1
0
0
0
0
1
2
0
0
0
1
2
2
1
0
2
0
1
0
1
0
1
0
0
1
0
0
0
2
0
0
1
1
0
0
1
1
2
0
3
1
0
1
1
3
0
1
0
1
0
0
1
0
1
0
0
2
0
1
1
1
1
1
0
1
2
2
1
0
1
0
1
0
2
2
1
1
0
2
1
0
1
0
1
2
1
0
0
2
1
0
2
2
0
0
0
0
0
0
1
0
1
0
1
1
1
1
2
0
0
2
1
1
1
1
1
0
0
0
1
1
2
1
2
1
4
1
1
0
1
2
1
2
0
0
2
1
2
2
0
1
2
0
1
1
1
0
1
0
0
2
0
1
1
0
0
0
1
1
1
0
0
0
0
0
1
1
1
2
1
0
1
1
2
2
1
2
1
2
2
3
1
1
0
1
0
0
1
1
1
2
1
2
1
1
2
2
0
2
2
0
1
2
1
6
2
0
0
0
0
1
0
1
1
1
2
2
2
0
0
0
2
1
1
0
1
1
1
0
1
1
2
2
0
2
2
0
1
0
1
1
3
1
0
0
0
1
1
0
1
2
2
0
0
2
0
0
1
2
1
2
0
1
1
0
0
0
0
0
1
1
2
2
1
0
0
1
0
0
0
0
2
1
0
2
0
0
1
1
1
2
0
1
2
1
1
2
2
1
1
0
0
1
1
2
1
1
1
1
1
2
1
1
1
1
2
1
1
0
0
2
0
1
1
1
0
0
0
1
1
1
0
0
1
0
2
0
2
1
1
2
1
1
0
0
1
0
1
1
1
1
0
0
1
0
1
1
0
2
1
1
0
0
0
0
1
0
0
2
1
1
0
0
1
2
2
1
0
1
5
0
1
0
1
0
2
0
1
1
1
2
1
1
0
2
2
1
1
1
0
1
2
0
0
1
1
1
1
2
0
0
0
1
1
2
1
1
2
0
1
2
1
0
0
1
0
0
1
0
1
1
0
1
1
2
1
1
0
1
2
2
0
2
0
1
1
0
0
1
2
0
2
0
1
0
1
0
0
0
1
1
2
1
2
2
1
0
2
2
1
0
0
1
2
1
1
1
1
1
1
2
1
0
0
0
1
2
1
1
0
0
0
0
1
1
0
2
0
1
0
2
1
0
0
1
0
0
0
1
1
0
1
3
1
2
0
1
1
0
2
0
1
0
1
1
1
0
3
2
0
2
1
1
1
2
1
0
0
1
0
2
2
2
0
0
0
1
1
2
0
2
2
1
0
2
4
2
1
0
1
2
2
1
1
0
2
2
0
1
1
0
1
1
0
2
0
1
2
1
0
1
0
1
1
2
2
2
0
0
0
0
1
1
0
2
0
1
2
1
0
0
2
2
1
1
0
1
1
1
1
0
1
2
1
1
1
1
2
1
2
1
2
4
1
0
2
0
0
0
0
0
2
1
1
2
2
1
1
2
0
1
0
1
1
1
2
0
1
1
2
1
1
1
0
2
1
2
1
1
0
1
0
2
1
0
0
1
2
2
1
2
1
2
2
0
0
0
2
0
1
1
0
1
0
1
0
0
0
0
1
0
1
1
1
1
1
1
2
0
0
1
1
0
1
2
1
0
2
1
1
2
0
1
2
1
1
0
0
1
0
1
0
1
1
0
0
1
1
2
1
0
1
0
2
1
2
1
1
0
0
2
1
2
0
1
0
1
2
1
2
1
1
1
1
1
2
0
1
0
0
2
0
0
2
1
1
1
0
2
1
1
1
3
2
2
0
0
0
1
0
0
0
0
1
0
0
2
0
1
1
0
2
0
0
0
0
2
1
1
1
1
0
0
2
1
1
0
0
0
2
0
2
0
0
0
1
0
0
1
2
1
1
0
0
1
0
1
1
2
2
2
0
1
1
1
0
0
0
1
1
2
1
1
1
1
0
1
0
2
1
0
0
1
1
1
1
0
2
1
1
1
1
1
0
1
0
2
0
2
1
0
2
0
0
0
0
0
0
0
1
1
0
0
2
1
1
1
0
1
0
0
0
2
1
0
0
1
2
1
1
0
2
1
2
1
0
1
2
1
1
0
1
1
1
1
0
2
2
1
0
0
0
2
0
2
0
0
2
2
1
1
0
1
0
2
2
1
1
0
1
1
2
0
1
0
1
0
2
0
1
2
1
1
1
2
0
0
0
0
4
2
2
1
1
0
2
2
0
1
1
1
1
1
2
1
2
0
0
1
2
1
1
0
1
1
2
0
0
0
0
0
0
1
1
1
0
0
0
3
0
1
1
1
1
1
0
0
0
1
1
1
2
1
1
0
1
2
1
2
2
1
0
1
2
2
2
2
2
0
1
1
1
2
0
0
0
2
1
0
2
1
1
1
1
1
1
1
0
1
0
0
1
0
1
2
0
2
0
0
0
1
0
0
1
2
0
1
1
2
1
0
0
1
0
0
1
0
1
1
2
0
0
2
0
1
2
2
1
2
0
1
0
1
1
0
0
0
0
1
1
1
0
2
0
2
0
1
0
1
0
0
2
0
0
0
2
4
1
1
1
2
2
4
1
1
1
1
0
2
1
2
0
0
0
1
1
0
0
2
2
2
1
1
1
1
1
0
1
2
2
0
1
1
1
2
1
2
1
0
1
0
2
2
2
1
0
1
0
0
2
1
2
0
1
0
2
2
0
2
1
1
0
1
2
1
1
2
1
0
1
0
1
1
0
2
0
1
2
0
2
1
1
1
2
0
2
1
0
1
2
1
2
0
0
2
2
2
1
1
0
0
1
1
0
0
2
1
1
0
0
1
0
2
1
2
1
1
0
1
0
1
3
1
1
3
0
2
1
0
0
1
0
1
0
2
2
1
1
2
0
0
1
1
0
1
0
2
0
1
1
1
0
0
1
2
2
1
0
0
4
0
1
0
0
1
2
0
2
1
0
1
2
1
1
1
0
1
1
1
1
0
2
2
0
0
0
1
0
2
0
2
1
1
0
1
2
2
2
1
0
0
1
0
1
0
0
1
0
1
2
0
1
1
1
2
2
1
1
1
2
2
0
1
0
0
1
1
2
1
0
1
1
2
0
1
1
0
1
2
0
1
1
1
0
1
0
1
0
2
0
2
1
1
2
2
0
1
1
1
1
0
0
2
1
0
1
2
0
1
2
1
0
1
1
1
1
2
1
1
1
1
0
0
0
0
1
1
2
0
1
0
1
0
2
0
1
1
2
0
2
0
1
0
1
0
1
2
1
0
1
1
1
1
1
1
2
1
1
2
0
2
2
2
0
1
0
1
1
1
1
0
1
1
0
2
1
2
2
1
0
0
1
1
2
1
1
2
1
1
0
2
0
1
1
0
3
1
0
1
0
0
1
0
2
2
2
1
0
1
2
1
0
1
1
0
1
1
0
1
1
1
2
0
0
0
1
2
0
1
1
3
4
2
0
0
1
0
0
1
1
2
1
2
2
1
0
2
0
3
2
0
1
2
0
1
1
1
2
1
2
1
0
2
0
2
0
2
2
3
2
0
2
1
2
1
2
0
0
0
1
2
1
1
1
0
1
1
0
1
1
2
2
0
2
2
5
1
0
0
2
1
2
0
2
2
0
0
0
1
0
0
1
2
1
0
1
0
0
1
2
0
2
2
1
0
2
1
0
0
1
0
0
1
1
0
2
1
2
0
2
0
0
1
1
0
0
0
1
1
0
1
0
1
0
0
1
1
0
1
2
1
0
0
1
0
1
1
1
2
1
0
0
1
0
3
1
1
2
0
1
1
1
0
2
1
1
0
0
1
1
1
3
2
1
0
0
1
1
0
2
2
0
2
2
0
2
1
2
0
1
0
1
0
1
1
1
1
0
1
1
1
2
2
0
1
1
1
2
1
0
2
0
3
0
1
1
0
0
1
1
0
0
2
0
1
0
1
1
2
2
1
2
0
0
1
1
0
1
1
0
2
2
2
0
1
2
1
1
1
0
1
1
2
2
4
1
0
0
1
1
0
2
1
1
0
1
2
1
1
0
0
0
1
1
1
1
0
1
1
0
2
0
0
1
1
1
1
1
2
0
1
1
1
2
0
1
0
1
2
0
1
1
2
1
2
1
2
0
1
0
1
2
2
1
1
0
1
2
1
0
1
2
2
0
0
1
2
0
1
0
1
0
1
2
1
0
0
1
2
1
0
1
2
1
0
1
0
4
1
1
0
1
2
0
2
0
1
2
1
0
2
1
0
1
0
1
1
2
1
2
2
1
0
1
0
2
1
1
1
0
2
0
0
1
0
1
1
1
0
1
1
1
0
0
2
1
0
0
1
2
3
1
0
0
2
0
2
1
0
0
1
1
2
0
0
2
1
1
1
1
0
1
2
2
1
2
1
0
0
2
2
1
1
2
1
1
1
1
0
2
1
1
0
1
0
1
1
0
1
2
1
0
1
0
1
0
0
1
1
1
2
1
2
0
2
1
0
1
1
2
0
1
1
1
1
2
0
0
1
1
1
2
2
2
1
0
2
0
0
2
1
1
1
1
2
1
1
0
1
0
1
0
1
1
1
1
0
0
1
0
0
0
0
1
1
1
1
1
1
0
1
2
2
0
1
0
0
1
1
1
2
0
1
1
0
1
0
3
2
0
0
1
1
0
2
0
0
0
0
1
2
2
0
0
1
2
0
0
1
2
1
1
2
2
0
0
0
1
1
2
1
0
0
0
2
2
2
2
1
0
0
2
0
0
0
0
1
1
0
1
1
2
2
0
0
2
0
2
1
1
2
0
2
1
1
0
0
1
2
2
1
1
1
2
0
2
1
2
0
0
1
1
2
0
2
0
1
2
0
1
1
1
1
1
1
0
0
0
0
0
1
1
0
2
1
0
3
0
0
1
0
0
0
0
1
1
0
0
0
2
1
0
2
0
1
1
0
1
2
0
0
2
0
2
0
1
0
1
1
0
2
0
1
0
0
2
0
0
0
1
1
2
1
1
1
0
0
2
1
1
0
1
2
2
1
1
0
0
0
2
1
1
2
1
0
0
0
1
0
1
1
0
0
1
0
3
1
1
2
0
0
0
0
0
0
0
1
0
0
0
2
0
2
1
1
1
0
1
0
1
1
0
1
0
0
1
2
1
1
1
1
1
1
1
2
0
0
1
0
0
1
1
2
0
2
0
0
0
0
0
1
0
0
1
1
0
1
1
1
2
0
1
0
0
0
1
2
1
1
1
0
3
2
0
0
0
1
1
0
1
0
2
2
1
0
0
2
1
0
1
1
4
1
1
0
0
2
1
2
2
0
2
1
0
1
0
1
2
0
1
0
0
0
1
1
1
1
0
2
0
0
2
2
0
0
0
0
2
1
2
1
0
0
2
3
1
1
0
1
1
1
1
1
1
1
0
0
0
1
0
0
0
1
0
2
0
1
0
1
2
0
1
0
0
1
1
0
1
1
0
2
1
3
1
0
2
2
1
1
0
0
2
2
0
0
2
0
2
2
2
0
2
0
0
0
2
2
0
2
1
0
0
0
1
2
0
0
0
0
0
1
1
1
0
0
1
1
0
1
1
3
1
0
1
0
0
0
2
2
1
1
1
1
1
1
1
0
2
0
1
2
0
0
1
2
2
1
1
0
1
1
1
0
4
2
0
0
0
1
0
0
0
0
0
1
1
0
0
1
1
0
1
1
1
2
1
0
1
1
0
1
0
0
1
1
0
1
0
0
1
2
0
1
0
0
2
1
1
1
1
4
0
1
1
0
0
2
1
1
1
1
0
0
2
0
0
0
1
1
1
1
0
2
2
0
1
2
2
0
1
0
0
1
2
0
1
0
0
0
0
0
2
1
0
2
0
2
1
1
0
0
2
2
1
1
1
2
0
2
2
3
1
0
2
1
2
2
0
1
1
2
0
1
1
0
2
1
1
0
1
0
1
2
2
1
1
1
1
0
0
1
0
1
1
0
0
0
0
0
2
0
1
1
2
1
4
0
1
0
1
0
2
1
0
0
0
1
0
0
1
1
2
2
2
0
0
2
0
1
1
2
1
0
0
1
1
1
2
0
1
1
1
2
1
1
1
1
1
0
2
1
2
0
1
0
0
1
1
0
1
1
2
1
0
1
1
2
0
2
2
0
0
1
2
6
0
0
0
1
2
0
1
1
0
0
2
4
1
0
1
0
1
0
2
0
2
2
2
2
1
2
0
1
0
0
0
1
0
1
1
1
1
0
2
2
1
1
0
0
0
1
1
0
2
0
3
1
1
0
1
0
2
1
1
1
1
1
1
0
1
0
1
0
2
1
1
3
2
0
1
2
1
2
1
0
0
1
1
1
1
1
0
0
0
1
1
1
1
2
1
2
2
2
1
1
0
1
2
1
1
1
1
0
1
2
1
2
3
1
0
1
2
2
0
1
2
1
0
0
0
0
1
0
1
1
1
2
1
1
1
1
0
1
1
1
1
2
1
1
1
2
0
0
0
1
0
2
1
2
0
1
2
1
1
1
0
1
2
0
0
1
2
0
2
2
2
1
1
0
2
0
0
1
0
2
1
2
0
1
2
1
1
0
2
1
1
0
2
2
1
0
1
1
3
1
2
1
0
0
0
2
4
1
1
0
2
0
1
0
0
0
0
1
0
2
0
1
1
1
1
2
0
1
1
1
0
0
2
0
0
1
0
1
1
0
2
1
2
2
0
1
0
0
0
2
1
1
2
2
0
1
1
1
0
1
1
1
0
0
2
0
0
1
0
2
2
1
3
0
0
1
0
1
0
2
0
1
0
1
1
1
1
2
0
1
0
0
1
0
2
1
0
1
1
2
1
1
0
2
0
0
0
2
1
0
1
1
0
0
2
1
0
1
0
0
0
0
0
1
0
2
1
1
2
0
2
2
1
0
1
0
1
1
0
1
1
2
0
2
2
1
0
0
0
3
0
2
1
0
1
1
2
1
2
0
1
0
2
2
2
1
2
1
1
1
1
0
0
1
0
0
2
1
2
3
0
0
1
2
2
1
1
1
1
1
0
1
0
1
0
1
1
1
2
0
0
0
1
1
1
0
1
1
1
2
2
0
2
1
1
1
0
0
1
1
2
1
1
1
1
1
2
0
0
1
2
2
0
1
1
2
1
0
1
1
2
2
2
0
0
2
5
1
0
2
1
1
2
1
0
2
1
1
0
3
1
1
1
1
1
1
0
1
2
1
3
2
2
0
1
2
1
3
1
2
0
1
1
2
2
0
1
1
0
2
2
2
2
2
1
2
1
1
1
1
3
1
1
0
0
1
0
0
0
0
1
0
2
0
2
0
1
2
0
1
1
2
0
2
0
2
1
1
1
0
0
1
1
0
1
1
2
3
2
1
2
0
1
0
1
2
2
0
0
0
1
2
1
1
1
0
0
0
2
2
2
0
2
1
0
1
0
0
0
1
1
1
0
1
0
1
1
1
0
2
1
2
0
1
1
0
0
1
2
1
1
1
1
2
1
1
2
2
0
2
1
2
1
1
2
1
0
0
1
0
1
0
0
1
0
1
1
2
0
1
1
0
1
1
0
0
1
2
2
0
3
2
1
2
0
0
2
1
0
1
1
0
1
0
2
0
1
2
1
1
0
0
2
0
2
0
2
2
1
0
1
0
1
2
1
0
2
1
0
0
1
1
1
1
0
1
1
1
1
2
1
2
0
1
2
1
2
1
1
0
1
2
0
2
1
2
1
0
1
1
0
0
1
0
1
0
0
1
0
0
1
2
0
1
0
0
0
1
1
2
1
0
0
2
1
1
2
0
0
0
0
1
3
0
0
1
2
0
1
0
1
1
2
1
1
0
1
1
1
2
0
1
1
2
2
1
0
1
1
0
0
1
2
2
2
2
1
3
1
2
0
1
1
1
1
1
0
0
1
1
2
2
0
1
2
1
0
0
1
2
3
0
1
1
0
1
0
1
2
1
0
0
1
0
1
1
0
1
3
0
0
2
0
0
0
2
0
0
2
1
1
2
1
1
0
2
2
1
2
1
2
4
1
1
1
1
1
2
1
1
2
1
1
0
2
0
2
0
1
2
1
1
0
0
0
3
0
2
2
1
1
2
1
1
0
1
2
1
1
2
2
3
1
1
1
0
2
2
1
1
1
0
1
1
3
0
0
0
1
2
1
0
2
0
0
4
0
1
2
1
0
0
1
1
2
1
1
2
2
1
0
1
3
2
2
2
0
1
2
1
1
0
1
0
0
0
0
1
1
0
1
0
3
2
0
1
2
1
2
2
2
0
1
0
1
1
0
2
0
1
1
1
2
2
0
1
0
1
1
0
1
2
2
0
0
0
0
1
0
0
0
2
0
2
1
0
1
2
0
2
0
0
1
1
0
1
2
1
1
5
0
0
0
2
0
1
1
1
1
1
0
2
1
0
1
2
0
1
0
2
1
1
0
0
1
0
2
0
2
0
0
2
2
0
0
0
2
1
0
1
2
0
1
1
2
2
1
1
0
0
0
1
1
1
2
1
1
0
0
1
0
1
0
2
1
1
2
1
0
1
1
1
0
1
2
0
1
1
0
3
1
0
0
1
2
1
1
1
1
1
2
0
0
0
1
0
0
0
1
1
0
1
1
2
1
0
0
1
0
1
1
1
2
1
1
1
1
2
0
0
1
1
1
0
1
0
0
0
1
1
0
0
0
2
0
2
2
2
1
1
1
1
0
0
1
1
0
0
0
0
1
1
2
2
0
1
0
1
1
2
1
0
2
1
1
1
2
0
0
0
2
1
0
0
2
1
1
1
2
2
0
1
0
0
0
1
0
1
0
1
2
0
0
1
0
2
2
1
2
0
1
0
1
2
0
1
0
1
2
0
1
0
1
1
1
1
1
1
1
0
1
2
0
2
0
0
0
1
0
0
0
1
2
2
1
1
1
1
1
1
0
1
2
1
2
2
0
2
0
1
0
1
1
1
1
1
1
1
0
0
1
1
2
1
1
0
0
0
1
0
1
1
0
0
1
1
1
2
1
0
2
1
2
1
1
0
1
0
2
1
1
1
0
0
0
1
2
2
0
1
2
1
1
3
0
1
0
1
1
0
2
0
0
0
2
0
2
1
1
2
0
2
1
2
0
0
2
0
2
0
2
1
1
1
1
1
0
0
0
2
1
1
1
2
1
1
1
2
2
2
1
0
1
0
1
1
1
2
0
0
0
1
2
1
3
0
0
0
1
2
1
1
0
1
0
1
1
0
1
1
1
1
0
1
2
1
1
0
0
0
2
1
1
1
1
2
1
1
1
0
2
1
1
2
0
0
1
0
1
0
1
1
2
0
1
2
1
1
2
0
0
0
1
2
1
1
1
1
2
0
1
1
1
1
0
2
0
1
1
2
0
1
0
1
1
0
2
2
0
0
1
1
0
2
2
1
1
1
2
0
2
0
2
0
2
2
0
0
0
2
2
1
1
3
1
0
1
1
1
0
0
1
3
0
1
0
1
1
2
2
2
2
1
2
1
0
0
0
1
2
0
0
0
0
2
1
2
0
0
0
0
2
0
1
2
1
1
1
0
0
2
2
2
1
2
1
1
0
2
2
1
2
1
1
1
2
1
1
1
1
0
2
1
1
0
0
2
1
0
1
2
1
2
2
0
0
1
0
1
1
0
0
0
1
0
1
1
1
1
1
0
0
1
1
1
1
1
1
2
1
1
1
0
1
1
2
0
2
2
0
1
2
1
0
2
1
2
1
0
1
1
1
0
1
1
1
1
1
0
1
2
1
0
1
0
2
0
0
1
0
0
0
1
2
2
1
0
1
0
0
1
0
1
2
0
0
1
1
0
2
0
0
1
1
0
0
0
0
0
0
1
2
1
0
1
0
0
0
1
0
1
0
1
1
1
0
1
1
1
2
1
1
1
0
1
0
1
2
0
0
1
0
1
1
1
1
1
1
0
0
2
0
1
0
1
1
0
1
0
1
2
1
1
0
1
1
1
2
0
1
0
0
1
1
0
1
1
1
0
2
0
1
0
1
2
1
1
0
0
2
0
1
2
2
2
2
0
3
1
1
0
0
2
0
1
1
2
1
0
1
0
1
1
1
0
2
2
0
2
1
0
2
1
0
1
0
2
0
2
1
2
1
0
0
1
1
0
0
2
1
0
1
1
1
1
0
1
1
0
2
2
2
1
0
1
0
0
1
2
1
0
2
0
2
2
1
1
2
2
1
1
1
1
1
0
0
2
1
0
1
1
0
2
1
0
2
0
0
1
2
0
0
0
0
0
0
2
2
2
1
0
1
2
1
1
0
1
0
2
2
1
0
1
2
1
0
0
2
1
1
1
0
1
1
1
1
0
1
0
0
1
1
2
1
1
0
2
2
0
1
1
0
1
0
2
1
2
0
0
1
1
0
1
1
2
1
1
1
2
1
2
1
0
1
0
1
2
3
0
0
0
1
2
2
0
1
1
1
1
0
1
2
0
0
1
1
1
1
1
2
2
2
2
2
0
2
1
1
1
1
1
0
1
5
1
1
0
1
1
1
1
1
1
2
0
1
0
0
0
2
1
2
1
0
1
0
0
0
0
0
0
1
1
2
1
0
1
1
1
1
1
0
1
0
0
0
2
2
0
1
2
1
0
1
0
1
0
1
0
2
1
1
1
2
0
0
0
2
0
0
1
2
1
2
2
2
2
1
1
0
1
1
1
0
2
1
1
1
1
0
0
2
1
1
0
2
1
0
2
1
1
1
2
0
2
1
0
2
1
1
2
1
0
0
2
0
1
1
1
1
0
1
1
0
2
1
2
2
2
0
1
2
1
1
1
1
0
1
1
2
1
2
1
1
2
1
0
1
2
0
0
2
0
0
1
1
1
1
2
0
1
0
0
1
0
0
0
1
1
2
1
0
1
0
1
2
1
1
1
1
0
0
1
1
1
0
2
0
1
1
3
2
1
0
2
2
0
0
1
0
1
0
0
1
1
1
0
2
0
1
2
0
1
1
1
1
1
1
0
0
1
1
0
0
1
1
0
0
1
1
0
1
0
1
1
0
0
2
0
0
0
1
1
1
1
3
1
1
0
1
0
1
2
0
0
0
1
2
1
0
1
1
3
2
1
2
1
1
2
1
1
1
1
1
0
0
2
0
1
3
2
0
0
0
1
2
0
4
0
1
1
0
0
2
1
0
2
0
0
2
1
1
1
1
1
2
1
2
1
2
2
2
0
0
0
0
0
1
1
1
1
2
0
0
0
1
0
2
2
0
1
1
1
0
0
0
0
2
1
1
1
1
0
0
0
1
0
0
2
0
2
1
1
1
0
2
1
1
0
1
2
1
1
1
1
1
1
1
2
2
0
0
0
0
0
2
1
0
2
1
2
1
0
0
0
0
0
1
0
1
1
0
1
0
1
1
1
0
1
1
0
1
1
3
1
2
1
2
0
0
0
2
1
1
0
0
0
1
2
0
1
2
2
1
0
2
3
1
2
1
1
1
2
1
2
1
1
0
0
0
0
2
0
0
1
0
2
1
0
2
0
0
1
0
0
2
0
0
1
0
1
2
1
1
0
1
1
1
1
2
2
0
2
1
0
2
2
1
1
0
2
0
2
2
2
0
0
0
1
1
0
0
2
3
1
2
0
0
2
1
1
1
1
0
1
1
0
1
2
0
2
2
2
1
0
1
1
1
2
1
2
2
0
2
1
0
1
2
1
0
1
2
1
0
0
2
1
1
2
1
0
2
2
0
0
1
0
0
2
0
1
2
0
2
0
2
0
2
0
2
0
2
0
3
1
2
1
2
1
0
0
0
1
0
1
0
1
2
2
0
2
2
0
0
0
1
1
0
1
2
1
2
1
1
1
1
1
1
1
1
0
2
1
1
0
0
1
1
2
2
1
1
0
2
2
0
1
0
0
1
1
0
0
1
0
0
1
1
1
2
0
1
0
0
1
2
1
0
0
0
1
0
1
1
0
1
1
0
1
1
1
0
1
2
5
3
0
0
2
1
2
1
1
2
1
2
0
1
0
2
0
1
0
1
0
1
0
1
1
1
2
2
1
1
1
1
1
0
2
0
1
0
1
1
1
0
0
1
1
3
0
0
0
1
2
0
1
2
1
0
2
1
0
0
1
1
0
1
0
0
0
1
1
1
0
0
1
1
1
1
2
1
2
1
1
1
2
1
0
0
0
0
1
0
1
2
1
0
0
1
1
2
1
2
1
0
0
1
1
2
0
1
1
0
2
1
0
0
0
1
0
1
0
0
1
0
1
0
1
2
1
2
1
1
0
1
1
1
1
1
0
0
2
2
2
0
1
2
4
2
0
1
1
1
1
1
0
0
4
1
0
1
0
2
2
1
2
0
1
1
2
1
1
0
2
1
2
0
2
2
1
0
1
1
0
3
1
1
2
1
0
0
1
2
2
0
1
1
2
0
1
0
2
0
1
2
2
0
0
2
1
0
1
2
1
2
1
1
1
1
2
0
0
1
1
1
2
1
0
2
0
0
2
2
1
2
1
1
1
0
2
0
2
0
0
1
0
0
2
0
0
1
2
1
2
1
1
1
0
0
0
1
1
1
1
0
1
1
1
3
0
0
1
1
1
0
1
0
0
1
0
1
1
2
1
1
0
0
1
1
2
2
2
1
0
0
1
1
1
2
1
0
1
0
1
1
1
1
1
1
0
1
1
0
1
0
0
1
1
0
2
2
2
1
0
2
3
0
2
0
2
1
2
0
3
1
1
2
1
1
2
1
2
0
0
0
1
1
3
0
1
1
0
0
0
2
0
1
1
1
2
0
0
0
1
1
2
0
1
2
1
2
2
1
2
0
1
0
0
0
1
1
1
1
0
2
0
1
1
0
0
2
1
0
0
0
2
1
1
0
1
1
1
0
0
0
1
2
1
1
2
1
1
2
1
1
1
1
2
1
1
2
1
1
2
1
0
2
2
1
1
0
2
1
2
2
1
1
0
1
1
1
2
0
1
1
2
1
2
0
1
0
0
2
2
1
2
0
0
2
1
1
0
0
1
1
2
0
2
1
1
1
0
1
2
2
1
0
1
0
2
0
1
0
0
1
0
1
1
3
1
0
1
1
1
1
0
1
0
2
1
2
0
1
1
0
1
0
4
1
0
1
0
2
1
1
1
0
0
0
1
0
2
0
1
2
2
1
1
1
2
1
0
1
1
1
2
1
1
2
1
1
0
1
0
0
1
0
2
1
2
1
0
0
2
0
1
1
1
0
2
0
0
1
0
0
0
1
0
0
2
1
2
1
3
2
1
1
1
1
2
0
1
0
2
0
2
1
1
0
2
1
2
2
2
1
1
0
1
0
2
0
0
1
2
1
2
2
0
1
0
1
2
1
0
0
0
2
3
0
1
0
0
2
1
1
2
0
2
2
1
1
1
1
0
0
0
1
1
0
0
0
0
0
1
1
1
0
1
1
0
1
1
0
0
0
1
0
0
1
0
0
2
2
0
0
1
1
0
0
1
0
2
1
1
2
1
1
2
1
2
1
2
1
0
1
0
0
1
1
1
1
2
1
2
0
1
1
2
1
1
0
2
0
2
2
1
1
3
1
1
0
1
1
0
0
1
1
2
2
0
1
1
0
2
0
1
1
0
0
2
0
0
1
5
1
1
1
1
2
1
2
1
1
1
0
0
1
1
0
2
2
0
2
2
2
2
0
1
1
1
1
1
1
1
1
1
0
1
1
2
1
0
0
1
1
0
1
0
2
1
0
0
0
2
2
1
1
0
0
1
1
0
2
0
0
1
2
0
0
0
0
1
2
0
1
1
0
2
0
2
1
0
2
1
1
1
1
0
0
1
1
1
2
0
2
0
0
0
1
1
0
1
1
2
1
0
2
2
1
0
1
0
1
0
1
1
1
0
0
1
0
2
0
0
1
0
1
1
1
1
0
0
1
2
0
1
0
0
0
2
1
1
1
1
0
1
0
1
2
1
1
0
1
1
0
2
1
0
2
1
1
0
1
1
0
1
1
0
2
1
0
1
2
1
2
1
1
2
0
1
1
0
1
2
1
1
0
2
0
1
1
0
1
1
2
1
2
0
0
0
0
1
1
1
1
2
2
1
2
0
0
0
0
0
0
0
1
1
1
0
2
0
1
1
2
1
1
3
1
1
2
1
2
0
2
1
2
0
6
0
1
0
2
0
2
1
2
1
2
2
0
0
0
0
3
0
2
1
1
0
2
1
0
1
1
1
1
2
1
1
1
2
1
2
2
0
1
0
1
2
0
1
1
2
0
4
0
1
0
2
1
2
2
3
1
0
1
0
1
3
1
1
2
2
1
1
2
1
1
2
0
2
1
0
2
0
1
1
1
1
1
2
1
0
0
1
2
2
0
1
1
0
0
2
2
1
0
0
1
1
1
0
1
1
0
0
0
2
1
1
1
0
0
0
1
2
1
0
1
0
1
0
0
0
0
1
2
1
1
1
2
1
1
0
0
2
0
2
1
1
1
0
2
2
1
2
2
1
1
1
0
2
1
1
2
2
0
1
2
0
2
0
1
1
0
2
1
1
1
1
2
0
2
0
1
0
2
1
1
1
1
1
1
1
0
0
0
1
1
0
3
0
2
0
2
2
1
1
0
1
1
1
1
1
1
1
0
1
1
0
2
0
1
1
2
0
2
0
2
0
2
1
2
1
2
0
0
2
0
2
2
1
0
1
2
2
2
2
1
0
1
0
0
0
1
1
0
0
1
1
1
0
1
0
2
0
1
2
1
0
1
1
1
1
0
2
0
0
2
2
1
1
1
1
1
2
1
0
1
1
0
1
0
2
1
1
0
0
0
0
2
0
0
0
1
2
2
0
1
1
2
2
1
2
0
1
0
1
2
0
0
0
0
2
0
0
2
2
2
0
3
0
1
1
1
1
0
1
2
1
2
1
1
1
2
2
1
1
0
0
1
0
1
0
1
1
1
1
0
1
0
1
2
2
1
0
1
1
0
1
1
1
1
2
1
1
0
1
2
0
1
0
1
0
1
0
2
1
2
1
1
1
0
1
2
1
2
1
1
1
0
1
1
0
0
1
1
2
0
2
1
0
0
1
2
0
0
0
0
0
0
0
1
1
1
2
0
0
1
2
0
1
3
2
0
0
2
1
1
2
0
1
2
0
2
1
0
2
1
1
2
2
1
0
1
0
0
2
0
2
1
1
1
0
1
0
0
1
0
2
0
2
1
1
2
1
0
1
0
0
2
0
2
0
1
0
0
2
2
1
0
1
2
2
1
2
1
0
2
2
1
1
0
2
2
2
0
1
1
1
2
1
0
2
1
1
1
2
1
0
1
0
1
1
1
0
1
1
0
2
0
1
2
1
1
1
1
0
2
1
0
0
1
0
1
1
1
1
0
1
1
1
1
1
2
0
1
0
1
2
2
1
0
1
1
0
1
2
1
1
2
1
0
1
1
1
1
0
2
0
2
2
0
2
2
1
0
2
1
1
2
1
0
2
0
0
1
1
3
1
1
0
0
0
0
0
1
2
1
2
1
0
0
1
1
1
1
1
0
2
1
0
1
0
0
1
0
2
1
0
0
1
2
0
1
1
2
0
1
0
1
0
3
1
2
0
1
2
0
1
1
0
0
0
2
0
0
2
1
1
1
1
2
0
0
1
2
0
1
1
0
2
2
2
1
1
2
1
1
2
1
1
1
0
0
1
1
1
0
1
2
0
1
1
0
0
1
1
2
1
1
0
1
0
1
2
0
1
2
2
0
1
2
0
0
0
1
0
0
2
1
2
2
1
1
0
0
1
0
0
0
1
2
1
2
0
2
2
1
1
0
1
0
0
1
0
0
1
1
0
1
1
1
1
0
0
2
1
1
0
2
0
2
0
0
1
3
1
2
1
1
0
1
2
1
1
1
1
1
0
1
2
0
1
1
2
2
0
1
2
1
0
0
1
0
1
1
0
1
2
0
0
1
2
1
1
1
0
0
1
1
0
2
1
2
1
2
0
2
3
1
2
1
1
2
1
0
2
0
1
1
1
1
0
0
2
1
0
2
2
3
1
0
1
1
0
1
3
1
1
2
0
1
2
0
2
0
0
0
1
0
1
0
1
1
0
0
2
2
0
2
0
2
1
2
1
2
1
0
3
1
1
2
0
0
0
0
2
0
1
1
0
1
1
2
1
2
1
0
1
1
0
0
1
1
1
1
2
1
2
1
1
0
1
0
0
0
0
1
0
0
0
1
2
1
1
2
1
1
1
0
0
0
0
2
1
2
2
1
0
0
0
1
2
1
0
2
1
1
2
1
0
2
0
1
0
0
0
1
0
0
1
0
1
0
1
0
1
0
0
0
0
0
1
2
0
1
0
1
0
1
0
1
0
2
0
0
0
0
0
1
0
1
1
1
0
0
0
1
2
1
1
1
0
2
0
0
1
1
0
1
2
1
1
2
1
1
0
3
2
2
2
1
1
0
1
1
0
0
0
0
2
0
0
0
0
1
1
0
1
2
0
0
1
0
1
1
2
1
0
2
1
1
0
0
0
0
1
1
1
0
0
0
2
0
0
1
0
2
1
1
1
1
1
0
2
0
1
1
1
1
0
0
0
2
0
0
0
1
3
1
0
0
0
0
0
0
0
1
0
0
2
2
3
1
1
1
1
1
1
3
1
1
0
0
1
1
1
0
1
0
1
2
0
0
2
1
0
1
0
1
1
1
0
0
1
1
2
2
1
2
2
1
1
1
1
1
1
2
0
1
2
1
0
2
2
0
3
1
1
0
1
1
1
1
0
2
0
0
2
0
1
1
2
0
0
1
0
1
1
0
1
0
2
1
1
2
1
1
1
1
0
0
2
0
2
2
0
0
0
1
1
1
2
2
1
1
0
1
1
0
2
2
1
2
0
3
0
1
2
0
0
1
2
2
2
0
2
0
0
0
0
2
0
1
2
1
2
1
2
2
2
0
1
0
1
0
2
2
0
1
1
0
1
0
1
2
1
1
0
1
1
0
0
0
0
2
0
0
1
1
1
0
3
1
1
0
2
0
2
1
2
1
0
1
1
2
2
0
2
0
2
0
1
0
0
2
1
2
1
1
2
0
2
2
1
0
1
2
0
2
0
2
0
0
0
2
1
2
2
1
0
0
1
0
1
0
1
0
1
1
1
0
1
2
0
1
1
0
0
0
1
1
1
2
0
1
2
1
2
0
1
3
1
0
1
0
2
2
1
0
1
1
0
1
2
0
1
1
2
2
0
0
1
1
2
1
0
1
0
0
0
0
1
2
0
2
2
0
1
0
0
1
3
0
1
2
0
1
0
1
0
4
2
1
2
0
1
2
1
1
0
2
0
3
1
0
2
1
1
1
0
0
1
3
2
1
1
1
1
3
2
0
1
0
1
2
1
2
0
0
2
1
0
2
0
2
0
1
1
1
0
1
1
1
0
1
2
2
0
2
2
2
1
2
1
0
1
1
0
1
2
0
1
2
0
1
0
2
1
1
0
2
2
1
2
1
2
0
1
1
0
1
0
2
0
1
0
0
1
2
1
0
1
1
1
1
1
2
2
1
1
0
0
1
1
2
2
0
0
0
1
0
0
0
3
1
0
1
2
2
1
1
1
2
1
1
2
0
1
1
1
1
1
2
1
1
1
1
0
0
1
2
1
1
0
0
1
2
0
1
1
0
2
0
2
1
0
1
2
1
0
0
2
0
2
2
2
0
0
1
0
0
1
0
0
2
1
0
1
0
1
1
1
2
2
2
1
1
3
0
0
1
0
1
2
0
1
1
0
0
1
0
1
1
0
0
1
0
2
0
0
2
0
0
0
1
0
1
1
2
2
1
0
2
0
2
1
1
2
2
0
0
2
2
2
1
0
2
1
0
1
2
3
0
0
2
2
0
1
1
1
1
2
1
0
1
1
2
2
0
0
0
0
1
2
2
1
1
2
1
1
0
1
2
0
1
1
1
1
1
0
2
1
2
0
0
1
0
2
1
1
0
0
0
1
2
1
1
0
1
0
0
1
0
1
1
2
2
0
0
1
0
1
0
1
0
1
2
0
1
0
1
2
0
0
3
2
0
0
1
2
1
1
0
4
1
1
1
0
1
1
2
2
1
0
0
0
1
0
1
2
1
0
0
1
2
1
0
2
0
0
0
0
2
0
1
0
1
0
1
1
1
2
1
1
2
2
0
2
1
0
0
0
1
2
1
2
0
0
2
0
0
2
1
1
1
1
1
0
0
3
1
1
1
2
0
0
1
1
1
0
1
1
2
0
1
1
2
1
2
1
1
1
1
0
2
1
1
1
1
1
1
3
1
1
0
1
1
0
1
1
0
0
1
2
0
2
0
1
1
0
2
3
2
0
0
1
2
1
1
0
1
0
0
1
1
0
0
0
1
0
6
0
0
0
0
0
2
0
1
1
1
2
2
2
0
1
1
0
0
1
0
1
1
2
1
0
1
1
0
2
1
1
4
1
2
0
0
1
2
0
2
0
1
0
2
0
0
2
0
1
1
1
1
0
1
2
0
0
2
0
0
2
1
2
1
2
0
0
3
1
0
1
2
1
0
0
0
0
1
2
0
1
0
0
0
3
1
1
1
1
2
0
0
1
1
2
1
1
0
0
1
1
0
0
3
0
1
0
1
1
1
1
2
1
0
0
1
0
1
0
0
0
4
0
1
1
2
1
0
2
0
1
1
1
1
1
2
1
1
1
0
0
2
1
2
0
0
2
1
1
1
1
2
0
0
1
1
2
1
1
2
1
1
1
1
1
0
2
2
1
2
0
2
1
2
2
4
1
1
1
1
1
1
1
1
1
1
2
0
1
1
1
0
1
1
1
1
0
2
1
1
0
0
1
0
0
1
2
1
1
0
2
0
1
0
1
1
0
1
1
0
1
1
0
1
1
1
2
1
1
0
1
0
0
1
0
0
1
3
1
0
2
1
1
1
1
1
2
0
0
1
0
0
1
1
2
0
0
1
0
1
1
1
1
1
0
0
1
1
2
0
0
1
1
2
0
0
0
1
1
1
2
1
1
2
0
0
0
0
2
1
1
1
0
2
1
1
0
0
0
0
1
0
0
1
1
2
0
1
0
0
2
0
1
1
1
1
0
0
1
0
2
0
0
1
2
2
1
2
1
0
0
1
2
1
1
1
1
2
1
1
1
1
0
2
0
1
0
1
0
1
1
2
2
0
0
2
2
1
0
1
1
1
0
1
3
1
1
1
1
1
2
0
0
1
1
0
0
1
0
0
1
1
2
1
1
1
2
3
2
0
2
1
0
0
0
0
1
0
0
2
1
1
0
1
0
2
0
1
1
1
0
1
1
1
0
1
0
0
1
2
1
1
2
0
0
0
2
1
0
1
0
2
2
2
1
0
0
1
1
0
1
1
2
2
0
2
1
1
1
2
0
0
0
2
2
2
0
2
0
0
1
1
0
1
1
0
0
1
1
2
3
1
1
1
2
1
0
1
0
1
0
0
0
2
2
0
1
1
0
0
1
1
2
2
0
1
0
1
1
2
1
2
2
0
2
1
2
0
0
1
1
2
2
2
1
0
2
1
2
1
1
1
0
1
1
1
1
0
1
0
0
0
1
0
1
1
1
1
2
1
1
1
0
0
0
1
0
1
1
1
2
2
2
0
1
1
0
2
0
1
0
0
0
1
1
1
0
1
1
1
1
1
1
0
2
2
0
3
1
1
2
3
1
0
0
1
1
1
0
0
1
1
2
1
0
1
0
0
0
2
0
1
1
1
0
1
1
2
0
0
0
0
0
1
0
1
0
0
3
2
0
0
2
1
0
0
2
0
2
1
1
1
1
1
1
0
1
1
1
2
1
0
1
0
2
1
1
2
0
1
0
0
0
2
0
1
1
2
2
2
1
2
0
2
1
1
0
1
1
0
2
0
1
0
1
2
2
2
1
1
1
1
1
0
0
1
0
0
0
2
0
1
0
0
1
1
1
1
1
0
2
1
1
0
2
2
0
1
2
2
2
0
5
1
1
0
1
2
0
1
1
0
1
0
2
0
0
0
1
2
1
0
0
1
1
1
1
2
2
1
1
1
0
1
0
1
2
1
2
0
1
0
0
2
2
1
2
0
6
2
0
0
1
2
1
0
1
1
0
0
1
0
1
1
1
0
1
0
2
2
1
0
0
1
0
0
1
0
1
0
1
1
2
2
2
2
3
1
0
2
1
0
0
0
0
0
3
0
0
1
1
0
2
1
2
1
0
0
2
2
1
1
1
2
0
2
2
2
1
0
2
1
6
1
1
0
1
1
1
1
1
0
0
2
1
1
1
2
2
1
1
1
0
0
0
2
1
1
0
2
1
0
1
1
1
0
0
1
1
1
2
1
0
1
1
0
1
0
1
3
0
1
2
1
0
2
1
2
1
1
2
0
2
0
2
0
1
0
1
1
2
1
1
0
0
1
0
0
0
0
0
2
2
2
2
1
1
2
1
1
0
0
1
1
2
2
1
1
1
1
1
0
0
1
1
2
2
1
0
1
0
0
0
1
2
1
2
0
0
2
0
1
2
2
1
0
2
1
1
2
2
1
1
0
1
0
0
3
0
1
1
1
1
1
1
2
1
1
2
1
2
0
1
0
1
0
1
1
0
0
0
0
0
2
0
2
2
1
0
0
0
2
2
0
0
0
2
2
1
2
0
2
1
0
0
2
2
2
2
1
0
0
2
1
0
0
1
2
1
1
2
0
1
1
0
2
0
0
2
1
2
0
0
0
1
1
0
0
2
1
0
2
1
2
1
1
1
1
0
1
0
0
1
0
0
0
1
0
0
2
2
1
0
1
1
0
2
0
0
1
0
1
1
0
0
2
0
0
0
2
1
0
0
1
1
0
2
0
2
0
2
0
0
0
0
1
3
2
3
1
2
2
1
0
1
1
0
2
2
1
0
0
0
1
0
0
1
0
0
0
2
2
1
2
1
1
2
0
2
1
1
0
1
0
1
1
0
1
0
1
1
0
1
0
0
1
1
1
0
1
1
1
1
1
0
2
3
2
2
0
0
1
1
0
1
0
1
0
0
1
1
0
1
1
0
1
0
0
2
2
1
1
0
1
2
1
0
0
1
0
1
1
1
2
0
1
0
2
1
1
0
1
1
0
0
1
1
1
0
2
2
2
1
1
2
1
2
2
1
1
1
0
0
1
1
1
3
0
1
1
1
2
1
0
1
1
0
1
0
0
0
0
1
2
2
1
2
1
2
0
0
1
0
1
0
1
1
1
1
2
1
0
1
0
0
0
0
0
0
0
2
1
1
1
2
1
1
2
0
1
1
0
0
1
1
0
0
1
0
0
2
1
1
0
1
1
0
1
1
0
0
0
1
0
0
1
0
1
1
2
1
1
2
0
0
2
1
2
0
3
1
1
2
1
3
1
1
0
2
1
1
2
0
0
2
2
1
1
1
0
0
1
2
2
2
0
0
1
2
0
1
2
2
1
0
2
1
1
2
1
0
2
2
0
0
2
2
0
2
0
0
0
0
0
0
2
4
1
0
1
1
0
0
0
2
0
0
2
2
0
1
1
0
1
1
0
1
4
1
1
1
0
3
0
1
1
1
2
1
0
0
0
1
2
1
1
1
0
0
1
0
0
0
2
1
1
1
1
2
0
1
1
2
2
2
1
0
2
2
2
1
0
2
0
2
0
1
1
0
2
1
0
1
3
0
0
0
1
0
1
1
0
3
0
2
2
1
1
0
2
0
0
1
2
0
1
0
1
1
0
2
0
0
1
0
0
0
2
0
1
1
3
0
0
1
1
2
0
1
1
1
0
0
1
2
0
0
1
2
1
1
0
1
1
1
0
1
2
0
1
1
0
0
2
0
1
0
1
0
1
1
0
1
2
1
1
2
2
2
1
1
1
0
1
1
1
1
2
2
1
1
1
1
1
1
0
1
1
0
0
0
2
0
0
1
0
0
2
1
2
0
1
1
1
2
1
1
1
1
1
0
0
1
2
2
1
2
2
0
1
0
1
2
0
0
2
0
1
0
3
0
0
2
0
1
0
0
1
0
1
1
0
1
1
2
1
1
0
1
0
2
1
0
2
0
0
1
2
1
0
1
0
0
2
0
0
2
2
0
2
0
0
0
1
1
1
1
1
2
2
2
2
0
1
0
1
0
0
0
1
1
1
0
1
2
0
1
2
1
1
0
1
0
1
1
0
1
1
0
1
1
1
0
0
0
1
0
2
1
1
1
2
0
1
2
2
0
0
1
1
0
0
1
1
1
0
2
0
1
0
0
0
0
1
0
2
0
0
0
2
2
2
0
1
2
0
1
0
0
0
1
0
1
0
1
0
1
2
1
1
1
2
0
0
0
1
1
2
1
1
1
3
0
1
2
1
1
2
1
1
0
0
1
0
1
2
1
1
1
1
2
1
1
1
0
2
0
3
0
0
0
0
2
0
0
0
1
1
2
0
0
1
1
1
1
0
2
1
1
0
1
0
1
2
0
2
6
0
2
1
0
2
1
1
0
2
2
2
0
2
2
1
0
0
0
0
1
0
1
2
1
1
0
1
2
1
2
0
0
2
1
1
1
1
1
1
1
0
0
0
1
1
0
0
0
0
1
1
1
1
0
2
1
0
0
1
0
1
1
2
1
1
0
0
2
1
0
0
0
1
1
1
2
1
0
1
1
0
2
0
1
2
0
1
2
2
0
0
2
1
0
1
1
1
2
0
2
1
1
0
1
0
1
0
0
0
1
1
1
0
1
1
0
2
2
2
0
1
1
0
0
2
1
1
1
2
0
0
1
3
2
0
1
1
1
0
0
0
2
2
0
2
1
0
1
1
1
2
0
2
1
0
1
2
2
0
0
2
0
1
0
0
0
0
1
1
1
1
1
2
1
2
1
2
0
0
1
0
1
0
0
0
0
1
1
0
1
1
1
0
1
0
1
0
2
0
1
1
2
2
0
0
0
0
1
0
1
0
1
0
1
2
1
0
1
1
1
0
1
1
2
1
2
2
1
1
1
1
1
2
0
1
0
0
0
1
0
0
2
1
1
0
0
2
2
1
1
1
1
1
0
2
2
0
0
2
1
1
1
2
1
3
2
0
1
1
0
0
3
0
2
1
1
0
0
0
0
2
1
1
1
1
1
0
0
1
1
0
1
1
0
1
1
2
1
1
1
3
0
0
1
0
2
1
0
2
0
2
0
0
1
3
1
1
0
1
0
0
1
0
1
0
1
1
0
0
1
1
1
1
1
5
0
1
1
0
0
0
2
3
2
0
1
1
0
1
1
1
1
1
0
0
2
1
1
0
2
0
1
2
2
0
0
1
0
1
0
1
1
1
1
2
0
2
1
0
0
0
2
0
2
0
0
2
1
0
0
1
0
1
0
1
0
1
2
2
1
2
2
1
1
0
1
0
0
0
1
1
1
2
1
1
0
2
1
1
1
1
1
1
1
2
1
1
0
0
1
1
0
1
0
1
0
0
1
1
1
1
2
1
0
1
1
1
2
0
1
1
0
0
2
1
1
1
0
0
2
1
0
1
0
0
0
1
1
1
0
2
2
1
0
0
1
1
1
2
2
1
1
0
1
2
2
3
2
0
2
1
1
2
0
2
0
1
2
2
1
0
4
1
2
1
0
0
2
1
2
0
0
1
0
0
1
1
0
1
1
2
2
0
0
0
2
0
1
0
4
1
1
1
2
0
0
1
1
1
0
1
1
0
0
0
0
3
1
2
0
1
2
0
0
1
0
1
0
2
2
0
0
0
1
1
0
0
0
1
1
1
0
0
1
1
1
0
3
0
0
0
1
1
0
1
0
1
0
1
1
1
1
1
1
1
2
2
0
0
1
1
1
1
2
1
2
2
0
0
0
2
0
1
2
2
1
1
0
1
0
1
1
1
0
2
0
4
0
0
1
1
2
2
0
0
1
1
1
2
1
0
0
2
1
1
1
1
0
1
0
1
0
1
0
2
1
1
2
1
0
3
2
1
2
0
0
2
1
0
1
0
1
1
0
0
1
0
1
1
0
1
1
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
2
0
2
1
1
3
1
0
0
1
1
1
2
2
0
1
1
2
1
2
3
0
0
1
1
1
0
0
2
2
1
3
1
2
0
1
2
0
2
2
2
0
0
0
1
1
3
0
1
2
2
1
0
0
0
2
1
1
1
1
1
1
0
2
0
0
0
0
0
2
0
1
2
1
0
1
0
1
0
0
2
2
1
1
1
2
1
1
2
1
1
1
1
0
2
1
0
1
0
1
1
1
0
0
0
2
2
2
1
2
0
2
0
1
1
0
2
0
1
0
1
0
0
0
0
0
1
1
1
0
2
2
2
2
0
1
4
2
0
1
2
0
2
2
0
0
0
2
1
1
2
0
0
1
0
2
0
0
0
1
0
0
1
2
1
1
2
2
2
1
1
2
1
2
1
0
1
1
2
0
0
2
0
1
1
1
1
1
1
0
0
1
1
2
0
2
3
0
2
2
1
1
1
1
1
0
2
2
0
1
0
2
1
1
1
2
0
1
1
1
1
2
2
0
1
0
1
0
0
2
1
1
0
1
1
1
1
1
3
1
0
1
2
0
0
1
1
0
0
1
2
0
0
1
0
1
0
0
1
1
0
2
2
1
0
1
1
1
0
0
0
1
1
1
1
1
0
1
2
2
2
2
2
1
0
0
0
2
0
0
1
0
1
1
1
0
0
0
1
1
1
2
2
1
2
0
1
0
2
0
2
3
2
0
1
1
1
3
0
2
1
1
2
1
0
1
0
0
2
0
0
1
1
1
0
1
0
0
1
1
0
2
0
0
0
2
2
0
1
0
4
1
1
0
1
1
1
0
1
0
0
0
1
0
2
1
0
1
1
0
1
0
0
0
1
0
1
1
0
1
2
1
1
1
0
1
1
1
2
1
2
1
1
2
0
0
1
1
1
1
1
2
1
1
0
0
0
2
1
1
0
0
1
1
0
1
1
0
0
0
1
1
1
1
1
1
1
0
1
0
2
1
0
1
2
0
0
1
1
1
0
0
0
0
1
1
1
2
1
1
2
0
1
1
0
0
1
1
0
2
2
1
1
3
0
0
0
0
0
2
1
0
1
0
1
0
1
1
1
2
0
1
1
0
1
1
3
1
2
1
2
0
0
1
1
2
1
0
1
2
2
0
1
0
0
0
2
0
1
1
1
1
1
2
1
1
0
2
1
1
1
1
0
2
1
0
0
1
1
3
2
1
1
2
0
2
0
0
2
1
0
1
1
1
1
1
1
0
1
1
1
3
0
0
1
1
1
2
0
0
0
2
0
0
0
1
1
0
1
1
1
0
1
1
1
0
0
0
0
2
2
0
2
1
1
1
1
2
1
1
1
1
1
1
0
1
0
0
1
2
1
1
1
0
0
1
2
0
2
0
2
1
1
1
1
1
2
1
0
2
0
2
0
0
2
0
1
0
2
1
0
2
0
1
1
0
2
1
2
0
1
1
2
0
1
1
2
1
1
1
0
1
1
2
0
2
0
1
1
1
1
0
2
1
1
0
1
0
1
3
2
0
0
1
1
0
2
1
0
0
1
1
1
1
0
2
2
2
2
0
1
0
1
0
0
1
0
1
0
1
1
1
2
2
1
0
0
1
0
0
0
0
2
1
2
0
1
1
0
1
0
1
1
1
1
0
0
1
0
1
0
0
0
1
0
1
1
0
2
1
1
0
0
1
1
2
0
2
1
1
2
1
1
0
0
1
2
2
1
1
0
1
1
1
2
2
1
2
0
0
0
1
1
0
0
5
2
0
0
1
0
2
1
0
2
0
0
1
1
1
0
0
2
3
2
1
1
2
0
1
2
2
0
2
2
1
0
0
1
2
0
1
0
0
1
1
1
1
1
0
1
2
0
1
1
0
1
1
1
1
0
0
1
0
1
1
2
0
0
1
1
0
2
2
1
0
1
2
0
1
1
0
2
0
0
0
1
1
0
2
1
2
0
1
2
2
1
0
1
3
1
1
1
1
1
2
2
1
0
1
1
0
1
0
1
0
0
1
0
0
2
0
1
1
1
0
1
2
0
0
0
2
1
0
1
0
1
0
1
1
2
2
2
1
1
0
0
1
1
1
1
1
1
1
2
1
1
1
1
0
2
0
0
0
0
2
1
1
0
2
1
1
2
1
0
1
2
0
2
2
1
0
0
0
0
1
0
0
1
1
1
2
1
1
1
2
2
2
1
0
1
0
2
2
0
2
1
2
0
2
2
2
2
0
0
1
2
2
0
2
0
2
0
2
0
1
1
1
0
2
1
1
0
2
2
0
0
0
0
2
1
1
2
0
2
2
0
1
0
1
0
0
1
1
2
1
1
2
2
1
0
1
0
1
2
1
1
0
1
1
1
1
2
0
0
1
1
0
0
2
0
0
0
1
0
0
1
1
2
0
0
2
1
0
0
2
2
1
1
0
0
1
1
0
1
0
0
0
0
2
0
0
1
1
1
1
2
2
0
0
1
2
2
1
0
2
0
0
1
1
0
2
1
0
1
1
2
1
1
0
1
1
0
1
0
2
0
2
2
1
1
2
3
0
0
1
1
0
2
0
1
1
0
1
0
1
0
0
1
0
1
2
0
0
1
1
1
1
1
0
0
1
1
1
0
0
0
0
0
1
0
2
2
1
0
1
0
2
0
1
1
0
1
1
0
1
1
0
0
0
0
5
2
1
0
1
2
2
1
0
0
0
2
1
3
2
0
1
1
1
4
1
0
1
2
1
0
1
0
2
2
1
1
1
2
1
0
0
1
1
0
1
1
1
1
1
1
0
2
0
1
1
0
0
0
2
2
2
1
2
1
1
2
1
1
2
1
1
0
1
1
1
2
1
2
0
0
0
0
1
1
2
1
0
0
0
0
0
0
1
0
1
2
1
1
1
1
2
1
1
1
0
2
0
1
1
0
1
1
1
1
2
0
0
0
1
0
1
0
2
2
1
4
2
1
2
1
1
1
1
0
2
2
3
2
1
0
1
2
2
0
0
0
1
1
1
0
1
1
0
0
0
0
2
1
1
1
0
1
1
1
1
0
0
2
1
1
0
0
0
2
0
2
0
1
1
3
2
0
1
1
2
1
2
2
1
1
0
1
0
0
1
1
3
0
1
2
1
0
1
0
1
0
0
1
0
2
0
1
4
0
1
0
1
1
1
2
0
1
2
0
2
1
2
2
1
0
1
1
1
1
2
0
0
1
1
1
1
2
2
0
1
0
1
1
1
0
0
0
2
0
2
2
0
1
1
0
1
0
2
1
2
2
2
0
0
1
1
1
2
1
0
2
0
2
2
1
1
2
0
0
0
0
1
0
2
1
0
2
2
2
2
1
2
1
0
0
2
0
0
0
2
1
0
2
0
1
0
1
0
1
0
1
2
0
0
1
2
1
0
1
0
0
1
0
4
0
2
0
1
0
0
0
1
2
1
1
1
0
2
1
0
2
2
0
0
1
2
1
1
1
0
0
1
2
2
2
0
1
1
1
1
0
1
3
1
0
0
3
1
0
0
0
0
0
1
0
2
0
1
1
0
0
1
0
0
0
3
1
1
0
0
1
1
1
1
0
2
2
2
0
0
2
2
2
2
3
0
0
2
0
1
1
1
1
2
1
0
0
0
0
0
1
0
1
1
1
2
2
0
1
1
1
1
2
2
0
1
1
0
0
1
0
2
2
1
2
0
0
0
1
0
1
2
0
2
0
1
0
0
1
1
0
0
1
1
1
1
2
0
1
1
0
0
1
0
2
2
1
1
0
0
2
1
2
0
1
0
0
0
4
1
0
0
0
0
2
1
1
1
1
2
2
0
1
0
2
0
1
0
0
0
1
1
1
0
2
2
0
2
1
2
1
1
1
0
1
2
1
1
1
1
0
2
0
2
1
0
2
1
1
0
1
3
2
0
1
2
3
1
1
2
2
0
0
0
2
1
0
1
0
1
0
1
0
1
1
1
1
0
0
0
0
1
1
1
1
1
0
2
1
2
1
1
1
2
3
0
2
1
0
2
2
1
1
0
1
0
1
2
0
1
1
1
1
1
1
0
1
0
1
0
0
0
0
0
2
0
1
1
1
0
1
1
2
2
0
0
1
1
0
1
0
1
2
1
0
1
1
1
0
2
2
1
0
4
2
2
1
1
1
1
2
1
0
2
2
1
2
1
3
0
1
1
1
1
0
0
1
2
2
2
2
2
2
1
2
0
1
1
2
1
1
1
1
1
0
1
0
0
0
2
0
2
0
1
0
0
1
0
3
0
1
1
2
0
1
1
1
0
1
0
1
2
1
2
1
1
0
1
0
0
0
1
4
1
2
0
1
0
0
1
1
2
0
1
1
1
0
1
2
2
1
1
0
1
0
1
1
0
1
2
2
1
0
1
0
0
1
2
1
1
1
1
0
1
1
1
2
1
0
0
1
2
2
0
1
1
2
0
1
1
2
1
1
0
0
0
1
0
0
1
1
0
0
1
1
1
1
0
0
1
0
1
1
2
1
0
1
1
1
0
0
0
0
2
2
0
0
0
1
1
0
0
2
1
0
1
1
0
1
0
0
1
2
0
0
1
1
1
1
1
2
2
0
0
0
0
1
2
1
1
0
0
1
0
2
1
2
1
1
0
1
1
1
2
1
0
0
1
1
2
0
2
2
2
1
2
1
1
1
1
0
0
1
1
1
1
0
2
0
1
0
0
1
1
2
2
0
0
2
0
2
0
0
1
0
1
0
1
1
1
0
1
0
0
2
0
1
1
3
1
0
2
1
2
0
0
1
1
0
2
1
0
2
0
1
1
2
3
4
0
1
1
0
0
2
0
0
1
1
0
1
2
1
0
3
0
1
0
1
0
1
1
2
1
0
0
1
1
2
1
1
0
1
0
2
1
1
1
0
2
1
1
1
1
1
3
1
1
2
2
1
0
3
0
0
1
1
0
2
2
0
0
1
2
1
1
4
2
0
2
1
1
2
0
1
0
0
0
0
0
0
1
0
1
0
1
1
0
2
2
2
1
1
1
0
2
0
1
2
1
0
2
0
1
2
1
1
1
0
1
0
2
0
0
1
1
0
2
0
2
1
2
0
1
1
1
0
0
0
0
1
1
2
0
1
2
1
0
0
2
1
2
0
0
2
2
0
1
1
1
1
0
2
2
1
1
1
2
1
1
1
1
3
1
0
1
2
1
0
2
2
1
0
1
2
1
2
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
1
1
1
1
0
0
2
1
0
0
0
0
0
0
0
1
0
0
2
2
2
2
1
2
1
0
0
0
1
0
0
0
1
0
0
1
0
1
0
1
1
1
0
1
0
0
1
2
1
1
1
2
2
2
1
1
2
1
0
0
1
0
1
0
0
1
1
2
1
2
2
0
1
0
2
0
2
2
0
0
1
1
0
0
1
1
1
2
1
1
1
1
1
0
2
2
1
4
1
1
0
0
1
1
1
1
3
0
0
3
2
1
2
2
1
1
1
1
0
1
1
0
1
0
1
0
1
0
1
0
2
0
0
6
1
2
2
1
0
2
0
1
0
1
0
1
1
0
0
1
2
2
0
2
0
0
0
2
2
1
0
1
2
0
1
2
1
1
1
2
1
1
0
1
2
1
1
0
0
1
2
1
0
2
1
2
0
1
2
0
1
2
1
1
0
0
1
2
2
0
1
0
2
2
1
1
2
2
0
1
1
0
1
2
0
1
1
1
2
1
0
2
1
1
1
1
1
1
1
1
0
1
2
1
0
1
1
1
2
1
2
1
3
0
2
0
0
2
2
1
0
0
1
0
0
1
2
1
2
0
0
0
2
0
0
1
2
2
1
0
2
2
1
2
0
1
1
0
0
0
1
0
1
1
1
1
0
0
2
1
2
1
2
1
0
0
1
0
1
0
1
0
0
1
0
0
2
0
1
2
0
0
1
0
1
1
1
1
1
1
1
0
1
0
0
0
0
1
0
0
1
2
2
0
1
1
1
1
1
0
1
0
2
2
0
2
1
0
2
1
1
1
1
0
1
0
0
0
0
0
0
2
2
2
1
1
0
2
1
1
2
0
0
0
1
0
1
2
0
0
1
0
1
1
1
1
0
2
1
1
1
1
1
1
1
1
1
1
2
1
2
1
1
2
0
2
0
3
1
1
0
0
0
3
1
1
1
1
0
2
0
0
1
0
0
0
1
2
0
1
0
2
2
0
0
0
2
1
0
1
2
1
2
1
1
0
0
1
1
2
0
1
1
1
1
0
0
1
1
0
3
1
1
1
1
1
1
0
0
2
0
1
1
0
1
0
1
1
0
2
0
0
0
0
1
1
0
1
1
1
1
1
2
2
0
1
2
0
0
0
0
2
0
1
1
0
1
3
1
0
0
1
2
1
2
2
1
0
2
2
1
0
1
1
0
1
1
1
1
1
0
1
1
0
0
2
3
1
0
1
1
2
1
0
1
1
0
1
1
0
2
2
2
2
1
1
2
0
2
2
0
0
0
1
1
0
1
0
2
1
1
0
1
2
1
2
1
0
0
3
0
0
1
0
0
1
1
1
1
2
0
1
1
1
1
2
0
0
1
2
1
1
0
1
0
1
0
1
2
1
0
2
0
1
0
1
1
1
0
1
1
1
1
2
0
1
1
0
1
0
0
0
0
1
2
1
1
1
0
0
2
4
2
0
1
1
1
1
2
0
0
1
1
0
1
0
0
2
0
2
1
2
1
0
2
2
1
0
0
3
3
1
2
1
2
0
1
1
1
1
0
1
1
2
2
1
0
1
0
0
2
0
2
1
0
0
1
1
1
1
1
2
1
1
0
2
2
0
0
1
1
0
0
1
2
1
2
0
2
1
0
1
2
1
0
2
0
2
0
2
2
1
0
1
1
2
1
1
2
2
1
0
1
0
0
2
1
0
0
2
0
8
2
0
1
1
1
1
1
1
1
0
1
0
0
1
1
1
0
2
0
0
1
1
1
1
2
0
0
1
0
0
2
1
1
1
1
1
1
1
17
1
2
1
1
2
1
2
2
0
2
1
0
0
0
2
1
0
2
1
1
0
1
0
2
0
0
1
2
1
2
1
0
1
0
1
0
1
0
1
0
0
2
1
2
0
1
1
1
0
0
1
0
1
2
2
2
1
1
0
1
1
2
1
2
2
1
0
2
1
2
0
2
2
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
1
0
1
0
1
1
2
1
1
1
1
0
1
2
2
0
0
1
1
1
0
2
1
0
0
2
1
1
0
2
0
1
1
1
2
1
0
0
0
1
1
1
1
1
1
0
1
0
1
0
0
0
2
1
2
0
0
0
0
1
2
1
1
1
1
2
0
1
1
0
1
0
2
0
0
1
0
1
0
0
0
2
2
2
1
1
2
2
1
0
0
1
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
1
2
0
0
0
2
2
2
4
0
1
0
0
2
1
1
1
0
0
1
0
1
1
1
1
2
2
2
1
0
0
0
1
2
0
0
0
1
1
1
0
1
2
0
2
0
1
1
1
1
0
1
1
1
2
0
2
0
1
1
1
2
0
1
2
0
2
1
1
1
1
2
2
0
2
2
0
0
0
1
1
2
1
1
1
1
1
0
0
1
2
1
1
0
0
1
2
1
1
1
0
0
2
1
1
1
2
0
0
0
1
0
0
0
2
0
1
1
1
0
1
2
1
1
2
2
0
0
1
0
1
1
1
2
1
1
0
1
1
1
2
1
1
0
0
1
1
1
0
0
0
0
2
1
2
1
1
1
2
1
0
0
0
1
1
1
1
0
0
1
0
0
1
2
1
1
2
0
2
1
0
2
0
1
2
0
0
3
0
0
1
2
1
1
2
0
0
0
1
1
0
2
0
1
1
1
0
2
0
2
2
0
0
0
0
1
1
1
1
1
2
0
2
1
0
1
1
1
2
0
0
0
1
2
2
1
0
1
0
1
1
2
2
1
0
0
0
1
1
1
1
0
1
0
1
1
0
0
0
2
1
0
1
1
0
2
1
2
0
2
2
1
2
1
1
1
0
1
1
1
0
1
0
0
1
0
1
2
0
1
1
1
1
1
0
0
2
0
0
0
1
0
1
1
1
1
1
1
0
2
0
0
0
2
1
0
1
0
1
0
0
1
0
1
2
2
1
1
2
0
1
0
0
1
1
1
0
1
0
2
0
1
2
1
2
1
1
2
1
2
0
0
1
1
1
0
0
1
2
3
0
1
0
1
1
0
1
0
0
1
1
2
0
2
1
3
0
1
1
1
1
2
0
0
2
2
0
0
1
1
1
1
0
0
2
2
1
1
0
0
2
0
0
0
1
1
0
3
1
0
1
0
2
0
1
1
0
1
2
1
2
2
1
0
2
2
1
0
1
2
1
2
1
0
1
1
2
1
0
0
0
1
4
0
0
0
1
1
2
0
2
0
0
1
1
0
1
0
1
1
0
1
0
1
2
0
2
1
1
1
1
0
0
1
0
0
1
0
0
1
0
1
2
2
2
1
1
2
2
2
1
2
0
1
5
2
1
1
0
0
1
0
1
1
0
2
0
1
0
0
1
3
1
0
2
0
0
1
1
0
2
0
1
0
0
2
1
1
1
1
2
2
1
0
1
0
0
2
2
0
2
0
1
0
1
1
1
2
1
0
1
0
0
2
1
1
1
1
2
1
2
1
2
1
1
1
1
1
2
0
0
1
2
2
1
2
2
1
2
0
0
0
2
0
0
0
1
2
2
1
0
1
1
1
2
1
2
2
0
0
0
0
2
1
0
1
1
0
1
1
0
0
1
0
1
0
1
2
1
0
1
1
1
1
0
0
1
1
0
1
0
2
1
0
0
2
0
1
1
0
0
1
1
1
1
0
0
1
0
1
0
1
1
2
1
1
2
1
0
2
0
2
0
2
1
2
2
0
0
2
1
1
0
1
1
1
1
1
1
2
1
2
1
1
0
1
0
2
0
1
1
0
1
0
0
1
1
2
1
0
0
1
1
0
1
0
1
2
1
2
1
0
2
1
1
0
1
1
1
0
2
1
0
1
1
4
0
0
0
2
0
1
1
1
0
0
1
3
1
0
1
1
0
1
1
1
1
0
1
2
1
2
1
0
3
2
2
1
1
1
1
2
1
2
1
1
3
0
1
1
0
0
2
1
1
0
2
2
2
5
0
1
1
0
1
0
0
1
2
2
1
1
1
1
2
2
1
2
1
1
1
2
1
1
0
1
0
1
1
0
0
1
1
1
0
1
1
0
2
0
0
0
1
0
1
0
2
1
1
1
0
1
1
0
0
0
1
1
0
0
0
2
1
1
2
1
2
1
0
0
1
0
1
2
2
2
2
0
0
1
0
0
1
2
0
2
2
1
1
1
1
2
1
2
1
0
1
1
0
1
2
1
2
0
1
1
1
2
1
1
1
0
1
1
1
0
0
1
1
1
1
1
1
0
1
1
2
1
1
1
1
1
0
0
1
0
1
2
0
2
0
1
1
0
2
1
0
2
0
0
0
2
1
1
1
1
0
1
1
0
0
1
1
2
1
1
1
0
0
0
1
1
2
0
1
0
1
2
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
1
1
0
2
0
1
2
1
1
1
2
1
0
2
1
1
1
0
1
0
1
1
1
0
0
2
1
0
1
1
0
1
1
1
2
0
1
1
2
0
1
1
1
1
3
0
1
1
1
1
0
0
0
2
0
0
0
0
0
1
0
2
1
1
2
0
2
1
2
0
0
3
0
2
1
1
1
1
1
2
1
0
2
1
1
0
0
4
2
1
0
1
2
0
0
1
1
0
0
1
2
0
0
0
0
0
1
0
0
1
3
3
0
1
3
0
1
0
1
0
1
0
2
1
2
1
1
1
1
1
2
1
1
0
1
2
1
0
1
0
2
2
1
1
1
1
0
2
2
1
1
0
1
1
2
0
1
0
1
1
1
1
1
1
1
0
2
1
1
0
1
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
1
0
0
1
0
0
0
0
0
2
0
1
0
1
1
1
2
1
1
0
0
2
1
2
1
1
1
1
1
0
0
0
1
0
3
0
1
0
1
1
1
0
1
0
0
1
2
0
1
0
1
1
2
0
2
1
2
1
0
1
0
2
1
1
0
0
2
1
1
1
0
1
0
2
0
1
0
2
0
1
2
1
1
2
0
0
1
2
0
3
0
2
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
3
1
2
2
1
1
0
1
1
0
1
2
0
1
0
0
1
1
1
1
1
0
2
0
2
1
2
0
2
0
0
0
1
1
1
1
1
0
0
1
1
0
1
2
1
1
2
2
0
0
1
2
0
1
0
0
0
1
0
2
1
2
1
0
0
0
1
2
1
1
0
1
0
2
0
3
1
0
1
2
1
0
0
1
1
0
1
1
1
1
2
2
0
2
0
1
2
1
0
0
1
0
0
1
1
0
2
1
0
0
1
1
0
0
1
2
1
1
0
2
0
1
0
0
0
1
2
0
1
1
0
0
1
1
0
0
0
1
1
2
1
0
1
1
2
1
1
2
1
2
0
1
0
0
1
2
2
2
1
1
2
1
3
1
1
2
1
2
2
1
1
1
1
2
0
2
1
1
0
0
1
1
1
0
2
0
2
1
1
2
1
0
2
1
0
1
0
0
1
1
2
1
2
2
1
1
2
1
1
0
0
0
1
2
0
0
2
0
1
1
2
1
1
2
1
0
2
0
0
1
3
0
0
1
2
1
0
2
0
1
2
0
0
0
1
1
0
1
0
0
1
0
0
2
1
0
1
0
1
0
0
0
0
2
2
1
0
2
5
0
0
0
1
1
0
0
1
0
1
2
1
2
2
2
2
1
2
1
1
1
1
1
1
1
1
1
0
1
0
0
2
0
0
0
2
1
0
1
1
0
1
2
0
1
2
1
1
2
1
0
1
0
1
0
1
1
0
2
1
1
0
1
0
1
2
2
0
0
2
2
0
0
1
0
2
1
1
1
0
1
0
1
1
2
0
0
2
1
2
1
1
1
1
2
2
2
0
0
1
1
0
0
1
2
1
2
1
1
1
2
1
1
1
0
1
1
1
0
1
1
1
0
1
2
2
0
1
0
1
1
0
1
0
0
1
2
1
0
0
0
0
1
2
1
1
1
1
2
0
1
2
2
0
0
1
0
1
1
3
1
0
1
1
1
1
0
1
1
1
1
0
0
0
0
2
1
3
1
0
0
2
0
1
1
1
2
1
0
1
1
2
0
0
2
0
1
2
2
0
2
0
1
2
0
1
2
1
1
1
0
0
0
1
2
0
0
1
0
0
2
1
0
0
1
1
1
1
2
2
0
1
0
1
0
1
1
2
1
0
2
1
0
1
1
1
1
2
2
2
1
2
1
2
1
0
0
3
0
0
0
2
2
1
1
1
1
0
0
0
1
0
1
1
0
0
2
1
1
1
1
0
0
0
2
1
1
2
2
1
2
0
0
0
0
2
0
0
0
1
2
0
2
1
0
1
1
1
0
2
1
0
0
0
1
1
2
1
1
1
1
1
2
0
1
1
1
1
2
1
2
1
0
0
1
1
2
0
0
1
0
0
1
2
1
0
1
1
1
0
0
1
2
1
2
1
0
1
1
3
1
0
1
0
1
2
1
3
1
1
2
0
2
0
2
0
1
0
2
1
0
1
0
1
1
0
1
1
0
0
1
1
2
1
1
0
1
0
0
1
0
0
5
1
2
0
0
1
1
1
2
2
1
0
0
1
1
0
1
0
1
2
0
2
1
0
2
2
2
1
0
1
2
1
2
1
1
1
0
0
2
0
2
0
0
1
1
1
2
1
1
1
0
0
2
0
1
0
1
0
1
2
1
0
1
0
0
1
1
0
1
2
1
2
1
1
1
1
0
0
2
0
0
2
0
2
2
0
1
2
1
1
2
0
1
1
0
1
0
1
1
2
1
2
0
1
1
1
2
2
0
1
0
0
1
0
0
0
2
1
1
1
0
2
2
2
0
0
0
1
0
5
1
0
1
1
0
1
0
1
0
1
0
0
0
1
1
2
1
2
1
1
1
0
0
0
1
1
0
0
0
1
1
1
2
1
0
2
0
1
0
2
1
0
2
1
0
2
0
2
1
0
2
1
2
0
1
0
0
1
2
1
0
1
1
0
1
2
0
1
1
1
1
1
1
1
0
2
2
0
0
0
1
2
2
1
1
0
2
0
2
0
1
0
0
0
2
0
1
1
1
2
1
1
1
0
2
1
1
0
0
0
2
0
0
1
1
1
1
1
0
1
0
1
1
1
2
1
1
0
1
0
0
3
1
1
0
1
0
2
0
0
0
1
1
0
0
2
2
2
1
1
1
1
0
0
0
0
0
2
2
1
3
0
1
2
0
2
0
0
1
0
0
1
0
1
2
2
1
1
1
1
2
1
2
0
2
1
2
2
0
1
1
1
1
2
0
2
0
1
0
1
1
2
0
1
2
1
0
1
1
1
1
1
1
2
1
0
2
1
1
3
1
2
1
0
1
1
0
1
1
0
1
1
0
1
2
0
1
2
0
0
1
1
1
0
1
0
0
1
1
2
1
2
0
1
1
0
0
3
2
2
0
0
1
1
0
0
0
0
2
2
1
2
0
1
0
2
1
2
1
2
0
1
0
0
1
0
0
0
1
1
2
1
0
1
1
0
1
1
0
1
1
1
2
0
1
1
0
0
0
1
0
0
2
1
0
2
1
1
1
0
2
0
2
1
1
1
1
1
0
1
2
1
2
2
2
0
2
1
1
1
0
0
1
2
1
1
0
2
1
1
1
1
1
0
0
2
2
0
0
0
1
1
2
0
1
1
1
0
1
1
1
2
1
0
2
0
2
1
0
1
1
0
0
0
2
1
2
1
2
1
1
1
1
2
0
2
0
0
0
0
0
1
2
1
1
1
2
1
1
1
2
2
0
1
0
1
0
0
1
1
1
0
2
0
1
1
2
1
0
0
1
1
2
2
1
1
2
0
1
2
1
2
1
0
0
1
1
3
0
0
0
2
0
2
1
0
1
1
1
1
2
1
0
0
1
1
2
1
1
2
1
0
3
2
1
0
0
1
1
0
1
1
1
1
0
0
2
1
0
2
2
2
1
1
0
0
1
1
1
1
0
1
0
1
1
1
1
1
0
1
1
0
2
2
1
0
1
3
0
1
0
0
1
2
2
1
0
2
1
2
1
0
0
1
2
0
2
1
0
1
0
0
1
0
1
2
0
1
0
1
1
2
2
1
1
0
0
0
1
3
1
2
0
0
1
1
0
2
0
1
1
2
0
1
0
1
0
1
0
0
1
2
1
1
2
1
1
0
0
2
2
2
2
2
1
0
1
1
1
0
0
1
1
0
2
1
0
2
2
1
0
2
2
1
1
0
1
0
0
2
0
1
0
2
1
1
1
2
1
1
2
2
1
0
0
1
1
1
0
2
1
2
1
1
1
1
0
2
2
0
1
2
1
1
1
1
1
1
2
1
0
2
2
2
0
2
2
0
2
1
0
2
1
1
1
0
1
2
1
1
0
2
2
1
0
0
1
0
1
1
1
1
2
1
0
1
0
0
2
1
2
0
1
2
0
2
0
2
0
1
0
0
0
0
0
0
2
1
0
2
1
1
1
1
0
1
1
0
0
2
0
2
2
1
1
1
2
1
2
1
3
1
1
0
2
1
2
0
1
1
1
0
1
0
2
2
1
1
1
2
1
0
0
1
1
0
0
1
0
1
1
2
1
0
1
1
0
1
1
1
2
1
2
2
1
0
0
0
2
0
2
1
2
1
2
1
1
0
1
1
1
0
0
0
1
2
0
0
1
1
1
1
1
0
2
2
0
4
2
0
2
2
2
2
1
0
1
1
1
3
1
1
0
0
2
0
1
1
2
2
1
2
0
2
2
0
0
0
1
0
0
2
1
1
0
1
1
2
2
1
1
0
1
1
0
1
0
1
0
1
1
1
0
2
2
1
1
0
3
0
2
0
2
2
1
2
1
2
1
1
0
1
1
1
1
1
1
1
1
0
2
0
0
0
0
1
1
0
1
0
1
1
1
1
1
1
0
0
1
1
1
0
1
0
2
2
1
0
0
0
0
0
0
1
1
2
0
2
0
1
1
0
1
0
2
0
0
1
1
0
1
2
1
1
1
0
1
0
2
1
1
2
2
0
1
1
1
1
2
1
1
1
1
1
1
1
2
2
1
0
0
0
0
2
1
1
0
0
1
2
0
0
1
1
0
0
0
1
1
0
0
1
0
0
1
0
1
1
2
0
2
0
1
1
0
1
1
2
2
0
1
1
2
1
0
0
0
1
0
0
2
2
1
1
1
0
1
1
2
1
2
0
2
1
0
1
2
1
1
1
2
1
1
0
1
0
0
1
1
1
1
2
1
1
2
2
1
1
1
1
2
1
2
1
0
1
1
0
0
4
2
0
0
0
1
0
0
1
0
1
1
0
0
1
0
2
1
0
3
1
1
0
0
1
1
0
1
1
0
1
2
0
1
1
1
1
0
1
1
1
2
1
0
1
0
4
0
2
1
1
1
1
0
2
2
2
2
1
1
0
2
2
1
1
2
1
1
2
1
0
0
1
1
1
2
0
2
0
1
1
1
0
1
2
0
1
0
1
1
1
1
0
1
2
2
1
1
1
1
1
0
0
1
0
2
0
2
0
1
0
2
1
0
1
0
1
1
0
1
3
1
2
0
0
1
0
2
1
1
0
2
0
0
1
0
1
0
0
1
1
2
0
1
1
2
0
1
2
0
1
2
1
0
1
1
2
1
0
2
2
2
1
0
1
2
2
0
1
0
0
0
1
0
1
1
0
1
1
1
1
1
1
1
0
1
1
0
1
1
1
0
0
1
0
1
0
1
2
2
0
0
0
1
1
2
1
0
0
0
1
1
3
1
0
1
0
1
2
1
2
2
1
0
0
0
2
0
0
2
0
1
1
0
2
0
2
0
0
1
1
1
0
1
1
2
2
1
0
2
1
0
1
0
1
0
1
2
2
1
1
1
0
0
1
0
0
2
0
1
1
1
1
1
0
1
1
1
1
0
0
2
0
0
2
0
0
0
2
0
2
0
0
2
4
1
1
1
2
1
1
1
0
0
2
2
1
2
1
2
2
1
0
1
3
1
0
0
0
0
1
1
2
1
2
1
0
2
2
1
2
1
2
3
1
0
0
0
0
0
1
2
1
1
1
0
1
1
2
1
1
1
0
1
1
1
1
1
1
0
1
0
2
1
1
1
2
2
2
0
0
2
0
1
1
2
0
1
2
1
0
2
1
0
0
2
0
2
1
0
1
1
1
0
0
2
0
1
0
1
0
0
1
1
0
1
2
1
0
4
2
0
0
0
0
1
0
0
1
2
0
0
1
1
2
0
1
0
2
1
0
1
1
0
0
1
0
0
0
1
1
2
0
2
1
1
0
2
2
2
1
1
0
1
0
1
2
1
2
2
1
2
2
1
0
1
1
2
0
2
0
0
0
1
1
1
2
0
1
0
1
1
0
0
0
1
0
0
0
1
0
2
0
1
1
0
1
0
1
1
1
2
0
1
0
1
1
2
0
1
1
0
1
2
0
1
3
2
2
0
2
0
1
0
0
0
1
1
2
1
2
1
0
1
0
0
0
1
1
0
0
1
0
1
1
1
2
3
2
0
1
1
1
1
1
0
1
1
0
1
2
0
0
0
0
0
2
2
1
1
0
0
0
0
0
0
0
0
0
0
2
3
0
0
1
0
1
1
2
2
1
0
2
0
2
0
0
0
1
1
0
1
1
2
1
1
0
0
2
1
0
0
1
2
1
0
0
2
1
2
1
0
0
3
2
0
0
2
1
1
0
2
2
2
1
1
2
1
1
1
1
2
1
1
1
0
1
1
1
1
1
2
1
1
0
1
1
0
1
0
2
1
2
0
0
1
1
2
0
0
0
1
1
1
1
0
2
1
2
1
0
0
1
1
1
0
0
0
2
1
0
1
2
1
3
1
0
1
1
1
0
2
1
0
1
2
2
0
0
1
0
0
0
0
1
0
0
1
1
1
0
1
1
1
0
1
1
1
0
1
0
0
0
1
0
1
0
0
2
0
1
1
1
2
0
0
1
1
1
1
0
0
1
2
1
1
0
0
0
0
0
2
0
2
1
1
1
0
1
0
1
0
1
1
1
1
0
1
2
0
2
4
1
2
0
0
0
1
1
1
1
2
2
1
2
1
1
1
1
1
1
1
1
1
0
1
0
1
0
0
1
2
1
2
1
0
2
1
0
0
0
0
0
1
2
1
1
1
1
1
2
2
2
1
1
0
1
0
1
0
1
0
2
1
0
0
1
2
0
2
0
2
2
0
2
1
1
0
1
2
0
0
2
0
1
1
0
1
0
0
2
0
0
0
2
0
2
0
1
3
1
0
1
0
1
1
1
0
2
0
1
2
2
1
2
2
0
2
0
1
1
2
2
1
0
1
1
0
0
2
0
2
0
0
0
0
0
2
1
2
2
2
1
1
1
0
0
0
2
3
0
2
2
0
0
1
1
0
1
1
0
2
0
2
1
1
2
2
0
2
2
1
0
1
3
1
0
0
2
0
3
1
1
1
2
1
0
0
1
0
1
2
2
1
1
1
0
0
1
0
0
1
1
0
0
1
1
0
0
0
2
3
0
1
2
2
1
1
2
0
0
1
1
2
0
1
0
0
0
1
0
0
1
1
1
0
0
0
1
1
0
2
0
2
1
1
1
1
0
0
0
1
1
1
1
1
0
1
1
2
2
0
2
2
2
0
1
0
5
2
1
0
2
0
2
0
0
1
0
1
1
1
0
1
0
1
2
1
0
0
2
1
0
2
1
2
1
1
0
1
2
2
2
1
0
1
0
2
1
1
1
0
2
0
1
2
1
0
2
1
2
0
1
0
2
1
1
1
3
0
0
1
1
0
1
1
1
2
2
1
1
0
1
2
2
1
1
2
1
2
1
2
1
1
1
2
2
0
2
2
2
2
1
0
2
1
1
1
0
0
0
3
0
0
1
1
0
1
1
3
0
0
2
0
1
2
1
1
0
1
1
2
1
0
0
0
0
1
0
0
0
1
0
2
1
2
2
2
1
1
1
2
3
1
1
1
1
0
2
0
1
2
1
1
0
2
2
0
1
1
2
2
1
0
1
2
0
1
1
1
1
0
1
2
0
1
0
0
2
2
1
0
2
1
1
0
0
3
1
1
0
2
0
0
2
1
0
2
1
1
1
0
0
0
1
2
0
2
0
0
1
1
1
0
0
1
1
1
0
1
2
1
2
0
1
1
2
1
2
0
1
2
2
0
0
2
1
0
1
0
0
1
2
1
1
1
2
1
0
0
1
2
1
0
0
0
0
1
2
0
0
1
0
0
1
0
1
1
1
1
0
1
0
2
0
1
1
0
1
1
1
2
1
1
1
0
1
0
0
0
1
2
2
0
1
1
1
1
1
0
1
0
1
1
1
1
1
1
0
3
1
0
1
0
0
2
1
1
1
1
2
2
0
0
0
1
2
0
2
2
0
0
1
0
1
2
0
7
2
0
0
1
0
0
1
2
0
0
1
1
1
2
1
1
1
1
0
2
1
0
2
0
2
1
1
0
1
0
1
1
1
1
0
2
1
1
2
1
0
2
0
0
0
0
1
2
1
2
0
0
0
1
0
1
0
2
0
2
2
4
0
0
1
2
2
1
2
1
1
0
1
1
1
1
0
1
1
1
1
1
0
1
1
1
2
0
2
1
1
0
2
1
1
2
1
2
1
2
2
1
1
0
2
2
1
2
2
1
0
1
1
2
0
0
3
0
1
1
2
0
2
1
1
1
1
0
1
2
1
0
1
4
2
0
0
2
0
0
0
0
0
2
0
1
2
1
1
0
1
0
0
0
1
0
0
0
2
2
1
3
1
0
0
1
2
2
1
0
0
0
1
1
1
1
0
0
1
1
0
1
0
2
0
1
0
1
1
1
2
1
2
0
1
0
1
1
1
0
0
3
0
2
0
1
1
0
0
1
0
1
0
1
0
0
1
1
2
1
1
0
0
2
1
1
0
1
2
2
2
1
2
2
0
0
2
1
2
0
0
1
0
0
2
0
2
2
2
3
0
1
1
1
0
0
0
2
1
1
1
0
2
2
0
0
1
1
2
2
1
0
0
0
0
0
2
1
0
0
0
2
2
1
1
2
1
2
3
1
1
1
0
0
0
1
1
0
1
1
0
0
1
2
0
0
0
1
2
1
1
2
0
3
1
1
1
1
0
1
2
0
1
1
1
1
1
0
2
1
0
1
0
1
2
0
1
1
1
0
0
1
0
1
0
1
0
1
0
2
1
1
1
0
1
1
2
1
1
2
1
0
1
2
1
1
0
0
1
0
1
1
0
1
1
1
0
1
0
0
1
2
1
2
2
1
1
1
1
2
0
1
0
0
1
1
1
1
0
1
0
0
1
1
0
2
2
1
1
0
1
1
0
1
2
2
2
1
0
1
1
0
1
0
0
2
1
0
0
0
1
0
2
1
1
2
0
0
2
1
0
2
1
1
1
0
1
1
1
2
1
1
0
1
1
1
0
1
0
1
0
0
0
2
0
0
2
0
1
0
3
0
1
0
0
1
1
0
0
1
0
1
2
1
1
0
3
0
1
1
0
1
1
2
1
2
1
1
0
1
1
0
1
0
1
1
1
0
2
1
2
1
1
0
0
0
1
0
2
2
3
1
0
2
1
1
1
0
2
1
0
1
0
2
2
1
1
1
0
0
0
0
1
1
1
2
2
2
1
1
2
2
1
0
2
0
1
1
2
1
0
2
0
1
1
1
1
1
0
0
0
2
2
0
2
1
2
0
0
0
0
2
2
1
1
1
0
1
1
1
2
0
2
2
1
1
2
1
0
1
1
1
1
1
1
0
0
1
1
0
2
1
1
2
1
2
0
2
1
1
0
1
0
0
0
1
0
1
2
2
0
1
1
0
0
2
1
1
0
0
0
2
0
3
0
2
1
1
0
1
1
2
0
0
1
0
1
1
1
2
2
1
0
1
1
2
0
1
1
1
0
1
0
2
1
0
1
1
0
2
1
0
1
3
2
1
2
2
1
1
1
0
2
0
1
1
1
0
1
2
2
0
1
2
0
2
0
1
1
2
2
1
2
0
2
2
0
0
1
0
2
0
0
2
1
4
1
1
1
2
1
0
1
0
1
1
0
2
2
0
1
1
1
2
2
1
2
0
2
2
0
2
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
1
1
1
0
1
0
0
0
0
0
1
0
1
0
2
1
2
2
1
0
1
1
1
0
1
0
1
1
0
0
1
0
0
1
1
0
0
0
1
2
2
0
0
1
2
0
1
0
0
2
1
1
0
1
1
1
0
1
1
2
0
1
1
1
0
1
1
0
1
0
1
1
0
3
2
2
1
1
0
0
1
2
0
0
2
0
0
2
0
1
1
2
0
1
0
0
1
2
1
2
0
1
1
1
1
4
0
0
2
1
0
1
1
0
2
0
0
1
1
0
0
1
0
2
1
0
1
2
0
0
1
1
0
2
1
1
0
1
0
2
2
1
0
1
0
1
0
0
1
0
1
0
0
1
1
0
2
1
1
2
0
0
1
0
1
2
2
1
0
0
2
1
0
0
1
0
0
0
0
2
0
2
0
1
2
0
1
1
1
0
1
1
1
0
1
0
2
1
1
0
1
1
1
2
1
2
0
2
1
2
0
1
0
0
2
1
1
0
2
0
2
1
0
1
1
2
0
1
1
0
1
1
0
2
0
1
4
1
1
0
0
1
1
0
1
1
2
0
0
2
0
1
0
2
3
0
2
1
1
1
1
2
0
0
1
1
0
1
1
2
0
1
1
0
0
0
0
0
1
2
0
0
0
0
2
1
0
0
1
1
1
0
1
0
1
1
1
0
0
1
1
1
3
1
1
0
1
0
2
0
0
1
1
1
0
0
1
2
0
1
0
1
1
2
1
0
0
0
1
1
0
0
2
1
1
1
2
2
1
1
2
2
2
1
1
1
2
0
1
1
0
2
2
1
0
0
1
1
1
2
2
3
2
0
1
0
2
0
2
1
1
1
0
0
0
1
0
1
1
1
1
2
1
2
2
1
0
0
0
0
1
0
1
0
1
0
2
1
1
2
1
1
0
0
0
1
1
2
1
1
1
1
1
2
2
1
0
0
0
0
1
1
1
0
0
1
1
1
1
2
2
0
1
0
0
2
1
2
3
1
0
2
1
0
1
2
0
1
1
0
2
2
2
1
0
2
1
0
0
1
1
0
1
2
0
1
2
1
0
1
0
0
1
1
2
0
2
0
1
0
2
0
1
2
1
1
2
1
1
1
0
0
2
1
0
1
0
0
0
1
1
0
1
1
0
0
1
1
1
2
2
2
1
0
2
1
1
1
1
0
2
1
1
0
1
1
0
1
2
0
2
1
0
1
2
2
1
1
1
1
1
1
1
0
0
1
0
2
1
0
2
0
2
1
1
2
1
0
1
0
1
0
3
1
0
0
2
2
0
2
0
0
0
0
0
2
0
1
2
2
2
1
0
1
0
1
0
0
0
1
1
1
1
0
2
0
1
0
2
1
1
1
0
0
1
1
2
4
1
1
2
0
0
2
1
0
0
0
0
0
2
2
2
0
1
0
0
2
1
1
0
1
2
1
0
2
0
0
0
1
0
1
2
2
0
0
2
1
2
2
1
0
1
0
0
0
1
1
1
0
1
1
1
1
0
1
0
0
1
1
2
2
2
0
3
1
0
1
0
1
2
0
0
1
0
2
2
2
2
0
1
1
1
0
1
2
0
0
0
2
1
0
1
0
0
1
2
0
0
1
1
1
1
0
1
0
0
1
1
0
1
1
1
1
1
1
1
2
2
0
2
1
3
1
0
2
0
0
1
1
1
0
0
0
0
2
0
1
1
2
0
1
1
1
2
1
1
1
1
0
1
0
0
0
0
0
1
1
1
0
0
1
0
0
0
1
1
1
0
1
1
1
1
0
1
1
0
0
0
1
0
0
1
2
1
0
1
1
2
1
2
1
0
2
1
1
0
1
0
1
1
1
2
0
1
3
2
1
0
2
2
1
0
1
1
1
0
0
2
2
1
1
1
2
0
1
1
0
1
0
0
0
1
1
1
0
0
0
1
2
0
1
0
1
1
1
1
1
1
1
1
1
2
1
2
0
0
4
0
1
1
1
2
1
0
0
1
1
1
1
1
1
1
0
1
1
1
0
1
0
0
1
0
0
1
1
0
2
0
1
2
2
0
0
0
1
0
2
0
0
1
0
1
0
2
0
0
2
1
1
2
1
1
0
1
1
2
2
2
0
1
1
1
1
1
1
1
1
0
0
0
1
0
1
1
1
2
2
1
2
0
3
0
0
2
1
0
4
2
0
1
1
1
0
1
1
0
2
1
1
1
0
1
1
2
1
1
1
1
1
0
0
0
0
2
1
1
2
1
1
1
1
0
0
0
1
2
1
1
0
2
1
2
0
0
1
1
1
0
0
1
1
1
0
1
0
0
1
0
2
0
0
2
0
1
2
1
2
0
2
0
1
0
1
2
2
0
2
2
1
2
1
2
0
1
1
0
1
1
1
1
0
0
2
0
2
2
0
0
1
1
0
0
1
1
1
0
1
2
2
2
1
1
0
1
2
0
1
0
1
2
2
2
1
1
1
1
1
1
2
0
0
1
0
0
1
0
0
2
2
1
1
1
0
1
0
0
0
0
0
1
1
0
0
1
0
1
0
1
1
1
1
3
1
0
1
0
0
0
1
2
0
0
1
1
2
1
1
0
2
0
1
0
0
1
1
0
1
2
0
0
2
0
0
1
2
1
1
0
2
2
0
1
0
2
1
1
2
2
0
1
0
1
0
1
0
0
0
1
0
2
1
1
0
2
1
0
1
1
1
2
0
1
0
1
1
1
1
2
1
0
2
1
2
1
1
1
0
0
0
0
2
0
0
0
2
1
2
1
0
0
1
0
1
1
0
2
1
1
0
1
1
0
1
2
1
0
1
0
1
0
1
1
2
1
0
1
1
2
1
1
3
0
1
0
1
2
1
0
2
1
0
1
0
4
0
1
1
1
1
0
1
1
2
1
0
0
2
2
2
1
1
0
0
1
0
1
0
0
1
0
1
0
0
2
2
1
1
1
1
0
1
1
0
2
1
0
2
1
1
2
0
1
0
0
0
0
1
2
2
1
1
0
0
1
0
2
1
0
0
0
2
0
0
0
1
0
0
0
1
2
2
2
0
2
2
2
0
1
2
0
1
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
1
2
2
1
2
2
1
1
1
2
1
2
1
0
0
0
1
1
1
2
1
0
2
1
1
1
1
0
1
1
1
1
1
1
0
1
1
1
0
1
1
2
0
1
0
0
0
0
2
0
0
1
0
1
1
0
1
1
1
1
0
0
1
0
2
0
1
1
2
4
0
1
1
0
0
2
0
0
1
0
0
1
0
0
0
1
0
0
2
0
2
0
0
0
1
1
0
0
2
1
2
0
1
0
0
2
0
0
1
0
0
1
0
0
1
2
0
2
0
1
1
0
2
0
1
0
0
2
2
1
0
0
1
0
1
0
0
3
1
1
1
1
0
1
2
1
1
1
0
1
1
0
1
2
2
0
2
0
0
2
0
0
1
0
0
1
2
1
2
1
0
1
2
0
1
0
2
1
1
2
0
0
2
0
2
0
0
1
2
2
1
0
2
0
1
2
2
2
0
1
0
1
2
1
0
0
0
0
0
0
0
0
1
1
0
2
2
1
0
1
1
1
2
2
0
1
1
1
2
1
1
1
2
1
1
2
2
0
0
1
1
0
1
2
0
1
1
2
1
0
6
1
0
2
0
2
0
0
0
1
0
0
2
2
1
1
1
2
2
0
0
1
1
1
2
0
0
1
0
1
0
2
0
1
2
1
2
1
1
1
0
1
0
0
1
0
2
0
0
0
0
0
0
0
1
1
1
2
1
2
2
1
0
1
1
2
0
0
1
0
0
0
1
1
1
0
1
2
1
0
1
0
1
2
1
1
1
2
2
2
1
2
1
1
0
2
2
1
1
0
2
0
2
1
1
1
1
1
1
0
0
1
0
0
0
1
2
0
0
2
1
0
1
0
0
1
1
2
1
2
2
1
2
2
1
1
2
0
1
1
0
1
0
1
1
1
0
2
1
1
0
0
2
1
1
0
2
0
1
1
1
1
1
1
1
1
0
0
2
0
1
1
1
0
1
1
1
1
1
0
0
1
2
1
0
0
2
1
1
1
1
0
1
1
2
1
0
0
0
0
1
2
2
2
0
1
1
0
1
0
1
1
1
1
0
0
1
1
1
0
2
0
2
1
2
0
1
0
0
2
1
1
2
1
1
1
1
6
0
2
1
1
0
1
1
1
2
1
1
1
1
0
0
1
1
0
1
0
1
1
0
0
1
1
1
0
1
1
2
1
1
1
1
1
1
1
0
1
0
1
0
0
0
1
1
4
1
1
1
0
2
1
1
0
2
0
0
1
0
2
2
2
0
1
2
1
0
1
1
2
1
1
1
0
1
1
1
1
0
1
3
2
0
1
0
0
1
1
1
1
0
1
1
2
0
1
0
1
0
0
0
2
0
0
1
1
1
1
1
2
1
0
1
1
1
1
1
2
0
1
0
0
1
2
2
2
2
2
1
1
0
0
2
0
1
1
0
0
1
1
2
1
1
1
1
1
1
0
2
1
2
0
0
0
0
0
1
1
1
0
2
1
0
0
1
0
1
2
1
1
1
2
1
2
0
0
1
1
1
0
2
2
0
1
0
1
0
2
0
0
1
1
2
2
0
2
1
1
0
1
0
0
1
3
0
2
0
1
1
1
0
1
2
0
0
1
1
2
1
2
1
0
1
0
0
1
1
0
2
2
0
1
0
1
2
2
0
2
0
1
0
1
0
3
0
1
0
1
0
1
1
0
0
1
2
2
1
1
2
2
2
1
1
2
2
2
1
1
1
1
1
1
1
1
1
2
0
0
0
0
0
1
1
0
2
0
1
0
1
1
2
2
1
1
1
5
0
0
1
2
0
1
2
1
1
0
0
2
1
1
0
1
2
2
1
0
0
1
2
0
2
1
1
2
2
1
0
2
0
0
0
0
0
1
1
1
0
2
0
1
1
0
0
1
1
1
0
0
0
0
1
1
0
2
0
1
0
1
2
2
2
0
1
0
1
0
1
1
1
1
1
1
0
0
1
1
2
1
2
1
1
1
0
1
2
1
2
1
2
1
2
2
1
1
1
0
2
2
1
0
1
2
0
1
1
1
2
1
1
1
0
2
1
0
2
1
1
2
0
1
1
1
1
2
1
2
2
2
1
1
0
0
1
1
1
2
1
0
1
2
1
1
1
1
1
0
2
1
1
0
0
0
0
0
0
2
2
0
0
0
0
2
0
2
1
2
0
0
0
2
1
1
2
1
2
0
1
0
2
1
0
0
1
1
2
0
0
0
3
1
2
2
2
0
0
1
0
1
1
0
0
1
0
0
0
0
1
1
1
0
1
1
2
1
0
1
1
2
6
1
0
2
1
2
0
0
1
2
2
1
0
1
2
0
0
1
0
2
1
2
1
2
1
2
0
1
2
1
0
1
1
0
2
1
2
1
0
0
1
1
1
0
0
2
1
0
1
1
2
2
2
2
0
1
2
1
2
1
0
0
0
0
2
1
1
2
1
1
1
1
1
1
1
1
1
1
0
2
3
1
0
1
3
0
0
0
1
1
0
1
2
1
1
0
2
1
1
1
2
0
0
0
2
0
1
0
2
0
2
1
2
1
1
2
0
0
1
2
2
2
0
0
0
1
0
0
1
1
2
2
2
0
0
1
2
1
0
2
2
0
1
1
2
1
2
0
1
1
1
0
0
0
0
1
1
0
0
1
2
1
2
1
2
2
0
3
1
1
0
1
1
0
1
1
2
1
1
2
1
1
0
0
2
2
1
0
0
2
1
2
3
0
1
1
0
0
1
0
1
1
1
2
1
0
2
0
2
1
0
1
1
2
1
0
0
0
1
1
1
1
1
0
0
1
1
1
1
0
0
0
0
0
0
1
2
1
1
2
1
1
1
2
1
2
0
1
1
0
1
1
0
2
0
1
0
0
0
0
1
0
0
0
1
0
1
0
2
1
1
2
1
0
2
1
1
1
0
0
1
0
0
1
1
0
1
1
1
0
0
2
1
2
2
2
1
2
1
0
1
1
0
2
0
1
1
1
1
0
0
1
2
1
1
0
0
2
2
1
1
0
1
0
0
1
0
1
2
1
1
1
1
2
0
1
1
1
0
1
1
0
0
2
2
0
0
1
1
1
2
1
0
1
2
1
1
1
3
0
1
2
2
0
2
1
1
0
1
2
2
1
0
1
1
1
0
0
0
0
1
0
0
0
0
0
1
1
2
1
0
0
1
0
1
2
0
2
0
1
1
0
0
2
1
2
1
0
1
1
1
0
1
2
1
2
1
0
0
2
1
0
1
0
1
1
0
2
2
2
0
2
2
0
1
2
1
0
1
2
1
2
0
0
1
0
2
1
2
1
0
2
1
1
1
1
1
2
2
2
0
2
1
3
1
0
1
3
2
1
2
0
0
1
2
1
0
1
1
0
1
1
1
1
2
0
1
0
2
0
1
2
2
0
0
1
1
2
2
1
1
0
2
1
1
1
0
0
1
0
1
0
0
1
1
0
2
2
2
2
0
0
0
0
0
0
1
2
1
1
2
1
1
1
0
1
0
1
2
1
0
1
0
1
1
0
0
2
1
1
1
1
2
0
0
1
1
1
2
2
0
0
1
1
0
1
2
1
0
1
1
0
2
0
1
2
2
1
1
2
1
1
1
0
1
0
0
1
2
0
2
0
2
1
0
1
1
0
1
0
3
1
2
0
1
1
0
2
1
1
0
2
0
1
1
1
2
0
0
2
1
0
0
1
0
1
2
0
2
1
2
0
2
1
0
1
2
2
2
1
0
0
0
0
1
0
0
1
3
1
0
1
2
1
0
0
1
0
1
2
1
2
1
2
2
0
0
0
0
1
2
1
1
2
1
0
1
1
1
2
0
0
1
0
1
1
2
0
0
0
0
2
0
1
0
1
0
0
0
0
2
1
0
1
2
0
1
2
0
1
1
2
1
4
0
0
1
1
1
0
1
0
0
1
0
1
0
1
1
1
0
0
1
2
1
2
2
0
1
0
1
1
0
1
1
1
1
1
0
0
1
1
1
0
1
2
0
0
0
1
2
1
0
1
0
0
1
1
1
0
2
0
1
0
1
0
0
0
2
1
1
2
1
2
2
1
1
0
1
0
0
1
0
2
1
1
1
0
1
0
0
0
1
1
0
1
2
1
1
0
1
0
1
1
0
0
0
1
0
0
1
0
1
1
0
0
0
0
1
1
2
2
0
1
1
0
2
0
1
1
0
0
2
1
1
1
1
0
0
2
2
1
2
0
1
0
0
0
2
0
1
0
0
0
1
2
0
1
2
0
0
2
1
0
1
1
1
0
1
1
1
1
0
0
1
0
1
1
0
1
0
0
1
2
1
1
1
0
1
0
2
0
2
0
0
0
1
1
0
1
2
2
0
2
1
2
2
1
0
5
1
0
1
2
2
1
1
1
2
1
1
0
0
0
1
0
1
1
0
1
0
1
1
0
1
2
0
1
0
0
1
2
1
2
0
1
0
1
0
1
1
2
0
1
0
1
2
1
3
1
1
0
1
1
1
0
0
0
1
0
2
1
1
0
1
1
1
0
1
1
0
0
0
1
1
2
0
1
0
2
1
1
2
1
0
0
2
1
2
1
1
2
1
0
2
0
0
1
0
0
0
2
0
1
2
0
0
2
0
1
1
1
3
1
1
0
0
0
1
0
1
1
1
1
1
0
3
2
0
0
1
1
2
2
1
2
1
0
1
2
0
1
0
1
2
1
2
1
0
3
2
2
1
0
0
0
0
1
1
0
1
0
2
0
0
2
1
0
0
1
0
0
0
1
2
2
2
0
2
2
2
2
0
1
1
1
1
0
1
0
1
1
1
0
1
0
0
0
1
0
0
1
0
1
1
1
0
0
1
2
0
1
0
0
1
0
0
1
0
1
1
0
1
1
1
2
0
1
2
0
0
1
1
1
1
0
2
0
1
0
0
0
1
0
1
1
1
1
0
0
0
0
2
2
0
0
1
0
0
1
0
1
1
1
0
2
1
0
2
0
0
0
2
1
1
1
0
0
2
2
1
1
0
0
1
0
1
0
1
0
1
3
1
0
1
0
1
0
4
1
1
1
0
1
2
1
1
1
1
1
0
0
2
0
1
0
0
0
1
1
1
1
0
1
1
2
0
2
0
1
1
1
0
0
1
0
1
1
1
1
2
1
0
1
1
1
1
1
1
1
1
1
2
1
0
1
0
1
1
0
1
1
2
2
0
0
1
2
2
2
0
0
1
0
0
0
0
2
0
2
1
0
0
1
1
0
2
1
0
0
1
1
1
1
1
1
0
0
1
2
6
0
2
1
2
1
0
0
2
1
0
2
2
1
1
1
1
0
1
1
1
0
0
2
1
1
1
2
0
0
2
1
2
0
0
1
2
0
1
2
0
1
2
1
0
2
1
1
0
1
1
1
0
0
1
1
0
0
1
2
2
0
1
1
0
1
1
1
0
1
0
0
1
1
2
0
0
1
0
2
1
0
0
1
1
1
1
0
2
1
1
0
2
0
1
2
1
1
3
2
1
0
0
0
0
1
1
1
1
1
1
0
0
1
1
1
1
0
0
1
2
1
1
1
1
1
1
1
0
0
1
2
1
1
0
0
1
0
1
2
1
1
0
1
1
0
0
0
0
2
2
2
0
0
2
5
1
0
0
0
2
3
1
0
1
1
2
2
1
0
1
2
0
1
1
0
1
1
1
0
3
1
1
0
2
1
0
2
1
1
2
1
1
0
0
1
2
0
0
1
2
0
0
0
0
0
2
1
2
2
1
1
1
1
1
2
0
1
1
1
0
2
1
2
1
0
1
1
1
2
1
1
0
1
0
2
0
0
0
0
1
1
0
1
1
1
1
1
0
0
1
1
1
2
2
0
1
2
1
1
1
2
1
1
0
1
1
0
1
2
2
0
1
0
0
1
1
2
0
0
1
1
1
1
1
1
1
2
2
2
0
1
0
1
0
0
0
2
1
1
2
1
1
1
1
0
0
1
3
1
1
1
2
1
2
1
1
1
1
2
1
1
0
1
2
1
0
1
0
1
1
4
2
0
0
0
1
1
1
1
0
1
1
2
1
2
0
1
1
0
0
0
1
1
1
1
1
1
1
0
0
2
2
0
1
1
1
2
2
1
1
1
1
0
0
0
0
1
1
2
0
1
1
0
1
1
1
1
0
1
1
0
0
2
1
1
1
1
1
0
1
0
2
2
1
0
1
0
0
1
2
1
1
2
0
0
0
2
0
0
0
1
0
2
1
1
1
1
1
1
1
0
0
0
0
2
0
2
2
2
2
2
1
1
1
2
1
1
1
1
0
2
1
1
0
0
2
1
1
1
0
1
1
1
1
8
1
1
2
1
0
1
1
2
0
1
0
1
0
1
1
0
0
2
1
0
0
1
2
0
1
0
0
2
1
1
1
1
0
2
2
0
0
1
1
1
1
1
0
2
2
2
1
0
0
1
2
0
1
2
2
0
0
1
0
1
0
0
1
1
1
1
1
0
2
1
1
1
1
1
1
0
0
2
1
1
1
0
0
2
1
1
2
1
2
2
1
2
1
2
1
0
0
0
2
2
0
0
1
1
1
2
1
1
1
2
1
1
3
0
2
1
0
2
1
1
1
1
3
2
2
1
0
1
1
2
1
1
2
1
0
0
0
1
1
1
2
2
0
1
1
2
1
1
0
0
0
1
0
0
0
1
1
0
2
2
2
2
1
0
2
1
0
1
1
2
1
0
1
2
1
1
0
0
1
1
0
2
1
2
2
0
1
0
2
2
0
0
2
1
0
0
0
1
0
2
1
1
1
0
1
0
2
1
0
1
2
2
2
0
2
2
1
1
2
1
0
1
0
2
2
2
1
2
0
2
1
2
1
2
1
0
2
1
0
1
1
0
0
0
1
1
0
0
1
1
1
0
0
1
1
1
0
1
0
1
1
2
2
1
1
2
0
1
0
1
0
1
1
1
0
2
2
0
1
0
1
0
2
0
1
1
1
1
0
0
0
1
1
1
1
0
0
1
1
1
1
1
1
1
1
0
0
1
2
2
0
3
1
0
0
0
0
2
2
0
0
2
2
1
2
1
0
0
0
0
0
1
1
0
1
1
2
2
1
0
2
1
0
0
1
1
1
1
0
1
2
2
1
1
2
1
0
2
0
1
0
1
2
2
0
2
0
2
2
0
0
0
0
1
1
0
1
0
1
0
1
0
2
2
1
0
1
0
1
1
2
0
1
1
1
0
0
1
2
1
1
1
0
1
1
0
3
2
1
1
0
1
1
1
2
2
1
0
1
1
1
0
1
1
0
0
1
1
2
2
1
1
1
2
0
1
1
1
1
0
1
0
0
2
2
0
1
1
0
0
0
1
0
2
1
1
1
1
0
0
1
0
2
0
0
0
0
2
0
1
0
1
1
0
2
0
2
1
0
0
2
2
2
1
0
1
0
2
2
2
2
1
1
0
0
1
2
1
0
0
1
1
0
1
2
2
0
1
2
0
2
2
1
2
0
0
1
2
2
0
1
0
1
1
0
2
1
0
1
2
1
1
0
2
0
0
0
0
5
0
1
1
1
0
2
0
2
1
1
0
2
1
1
1
1
2
2
1
1
1
2
0
3
1
1
0
0
0
0
2
1
0
1
2
1
0
0
2
1
2
0
2
2
0
1
1
1
2
1
1
0
0
0
1
0
0
0
0
8
0
4
2
1
1
0
2
2
3
1
2
2
1
0
0
1
1
1
1
1
1
0
0
0
1
1
1
0
1
0
0
0
1
0
2
1
0
1
1
1
0
0
0
0
2
2
1
1
0
2
0
1
1
0
1
1
0
1
0
1
2
1
0
0
1
1
2
1
1
2
1
0
1
1
1
0
0
0
1
1
1
0
1
1
0
1
1
0
1
0
1
1
2
0
1
0
2
0
1
0
0
1
0
2
1
1
0
2
2
1
1
0
0
1
3
1
2
1
2
0
0
2
0
0
2
2
2
0
0
1
2
0
0
0
0
2
0
1
1
0
4
2
0
0
2
0
0
1
0
0
1
1
1
2
1
0
0
0
1
2
2
0
1
2
2
1
1
1
1
2
1
0
1
0
0
2
0
1
0
1
1
1
0
1
2
1
1
1
0
0
0
1
1
1
0
0
0
0
1
0
1
1
2
2
0
2
1
0
0
1
1
1
0
0
1
1
0
0
2
1
0
2
1
0
1
1
0
1
1
1
1
1
0
1
2
0
2
2
0
0
0
1
2
1
1
2
1
0
1
1
0
0
0
1
2
1
0
0
2
1
1
0
0
0
2
1
0
2
0
1
2
1
0
0
1
1
2
0
0
1
1
1
0
2
1
1
1
2
1
0
2
1
0
0
1
1
1
1
2
2
1
2
0
0
1
1
1
1
0
2
0
1
1
0
0
0
1
1
1
0
0
1
0
2
0
1
2
0
1
0
0
0
1
0
0
0
1
1
2
2
2
0
2
1
2
1
0
2
1
1
1
0
1
3
2
0
1
0
0
1
1
2
0
0
0
2
0
0
2
0
1
0
1
1
1
1
0
0
1
0
2
0
0
1
2
0
0
1
0
1
0
1
1
2
1
0
2
2
1
1
1
3
1
1
1
1
1
0
1
0
0
2
1
1
0
1
1
2
0
0
2
1
1
1
1
1
1
0
0
0
2
2
1
1
1
1
0
1
0
1
0
1
0
1
0
1
1
0
0
1
2
1
1
2
0
0
0
0
1
1
2
0
0
0
2
0
1
1
0
0
0
2
0
0
0
2
0
0
2
1
2
0
0
1
0
0
2
0
2
0
2
0
1
1
1
3
2
2
0
0
0
1
1
1
0
0
1
0
1
0
1
1
1
2
2
1
2
0
0
2
1
0
0
2
0
1
0
2
1
1
1
0
2
1
1
1
2
2
1
0
1
1
2
2
0
1
2
1
1
1
0
0
0
2
0
1
0
1
1
1
3
2
0
1
1
2
2
1
0
0
1
0
0
1
2
1
2
1
1
0
2
1
0
1
1
2
0
0
0
1
0
2
2
0
2
2
2
1
0
1
1
1
1
0
1
1
2
1
0
0
1
1
2
0
0
2
0
2
0
2
0
2
1
1
0
0
1
0
1
0
0
1
0
1
1
0
1
0
1
0
2
0
1
0
1
1
0
0
2
0
0
1
0
0
1
0
1
1
1
2
2
1
1
5
0
0
1
1
3
1
1
0
0
1
1
1
0
1
1
1
0
1
1
2
0
1
2
0
0
0
0
1
1
0
1
0
0
1
1
1
1
1
2
0
1
0
0
1
1
2
2
1
1
2
1
0
2
0
0
1
0
2
1
2
1
0
0
1
0
1
1
0
1
0
0
2
2
1
2
0
1
1
0
1
1
1
2
0
0
1
2
2
1
0
2
1
0
1
0
0
2
0
1
1
0
2
2
0
0
2
1
1
1
0
0
0
1
0
1
1
2
1
1
1
1
5
1
0
0
0
1
0
0
0
2
1
0
0
0
1
0
0
1
1
0
2
1
2
1
0
2
0
1
0
1
1
0
1
0
0
0
0
1
2
2
2
2
0
1
0
1
0
1
2
1
0
1
1
1
1
0
1
1
1
0
1
0
2
2
0
1
4
1
0
2
1
0
1
1
0
1
1
1
1
1
0
2
0
1
2
1
1
0
2
2
2
2
0
1
0
1
1
2
1
1
2
1
0
0
0
1
1
1
0
0
0
2
0
0
0
0
1
1
2
1
0
1
0
1
0
0
1
2
2
0
2
0
1
2
1
2
0
1
0
1
1
2
3
0
1
1
2
2
2
0
1
1
0
2
2
1
1
1
0
1
0
2
0
0
2
1
1
0
0
1
1
1
0
0
1
0
1
4
1
1
2
0
0
1
2
2
2
1
1
2
0
0
1
1
0
2
1
1
1
2
0
0
2
0
0
0
1
1
2
1
1
2
0
0
2
0
1
0
2
1
0
1
0
1
1
0
1
0
2
1
1
1
2
1
0
0
2
2
2
0
0
0
0
2
0
1
0
0
1
0
0
2
1
0
2
1
0
0
3
2
0
1
1
1
1
1
1
1
1
1
2
2
0
1
1
1
0
1
2
0
0
1
1
0
0
2
1
1
0
1
3
1
0
3
0
1
0
0
0
1
1
1
1
0
1
2
2
0
1
0
1
1
1
1
1
1
0
0
2
0
2
0
1
0
2
1
1
0
0
1
2
0
1
1
1
2
0
1
0
0
1
1
1
2
0
1
0
1
1
0
0
1
2
2
0
1
1
0
2
1
1
1
1
1
1
1
1
0
0
2
0
0
1
1
0
4
0
0
0
1
0
1
1
1
0
0
2
2
1
1
0
1
1
1
0
3
1
0
1
1
1
1
2
0
1
0
0
0
0
0
1
2
0
1
1
2
0
0
1
1
2
0
0
0
0
2
1
1
2
2
1
0
1
1
1
0
1
1
1
1
1
2
0
1
0
0
2
1
0
1
0
1
1
0
2
0
0
2
1
0
2
1
1
0
2
2
1
0
1
0
1
0
0
0
2
0
2
1
1
1
1
2
1
0
1
2
1
0
2
0
1
2
0
0
2
2
0
1
2
0
1
1
0
0
2
1
0
1
0
2
0
2
2
0
0
0
0
0
0
1
1
1
0
1
1
2
1
1
2
0
1
3
2
1
0
1
1
2
0
2
1
0
1
1
0
0
2
1
0
0
1
1
1
1
2
0
1
1
1
1
2
2
0
0
1
0
1
2
0
1
1
1
0
0
1
1
2
2
0
0
2
0
2
1
2
2
2
1
2
2
1
1
2
1
1
1
0
1
1
2
1
0
1
1
0
0
1
0
0
2
0
0
0
1
1
1
1
0
1
0
1
2
1
0
0
1
1
0
1
1
2
1
1
2
1
0
1
0
2
0
1
2
2
0
0
0
0
1
1
1
1
1
2
1
0
0
0
1
1
1
1
1
2
0
0
4
1
1
0
2
0
1
0
1
0
1
1
0
1
1
1
2
1
1
3
0
1
0
1
0
0
1
2
0
2
1
1
1
2
2
0
1
2
1
1
1
0
2
2
0
1
1
0
1
2
1
0
1
2
2
1
0
0
0
1
1
2
0
0
1
1
1
1
0
1
2
1
2
0
1
1
0
1
0
2
2
0
1
1
2
2
1
2
1
2
0
1
1
0
0
0
1
2
2
2
0
0
1
0
2
1
0
2
0
1
1
1
0
0
1
0
1
2
1
1
0
0
1
1
0
0
1
2
0
1
0
2
2
1
1
1
2
0
1
3
2
1
1
2
1
1
1
2
1
2
2
0
1
2
0
2
0
1
1
0
3
2
0
1
1
0
0
1
1
0
1
0
1
1
0
2
1
1
1
2
1
2
1
1
1
3
1
0
2
2
0
1
0
1
2
2
1
1
0
1
1
0
0
0
2
1
0
0
0
0
2
0
0
2
1
0
0
1
0
1
1
1
2
0
1
2
3
1
0
1
1
1
2
1
2
0
3
1
2
2
1
1
1
2
0
0
1
0
0
0
2
1
0
1
1
0
0
2
1
2
1
1
0
0
0
1
2
1
0
1
0
2
0
0
2
2
1
4
1
1
2
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
2
0
0
1
1
1
1
2
0
1
0
2
1
0
1
0
0
2
1
1
0
1
0
1
2
3
0
0
2
1
1
1
0
0
2
2
2
1
2
2
2
2
1
0
0
2
0
1
1
0
1
0
1
1
2
1
0
0
0
1
1
0
1
2
1
1
2
2
1
0
2
3
2
0
2
2
1
0
1
0
0
1
1
0
1
1
1
1
0
1
2
1
1
2
1
1
2
0
2
1
0
0
0
1
1
1
2
2
1
1
1
0
1
1
2
0
1
2
0
0
2
1
1
1
1
0
2
1
0
2
1
0
1
0
1
0
2
1
2
1
2
0
3
1
2
2
1
0
0
1
0
1
0
1
0
1
2
1
1
2
2
1
0
1
1
0
0
1
2
1
1
2
0
0
1
2
2
1
2
2
1
0
1
1
1
0
1
0
1
0
1
2
1
1
0
1
1
0
1
0
0
0
0
1
1
2
0
1
1
0
0
0
1
1
2
0
2
1
1
0
2
0
2
0
0
1
2
2
1
0
0
1
1
1
0
2
1
0
0
3
0
1
1
1
0
2
0
1
1
1
0
1
0
2
2
0
1
0
1
1
1
0
3
1
1
1
1
0
1
0
0
1
2
2
2
2
1
0
1
0
2
2
1
1
0
1
0
0
1
0
1
0
1
1
1
1
1
1
0
1
0
1
2
0
1
0
1
1
0
1
1
0
0
1
2
0
1
1
0
0
0
0
1
1
1
2
1
1
0
1
1
0
0
0
1
1
1
1
0
1
0
1
0
1
1
1
1
0
0
1
1
0
1
2
1
1
0
1
1
1
0
2
0
0
1
1
0
1
0
1
2
0
2
1
0
0
0
0
2
3
0
0
1
2
0
1
0
2
1
0
1
0
1
1
1
2
1
3
0
1
0
2
0
0
1
0
1
1
2
0
1
1
1
2
0
2
1
0
2
0
0
1
2
1
2
1
1
1
1
2
1
1
0
0
2
0
1
1
1
0
1
0
2
0
2
1
1
0
0
1
0
1
0
2
1
1
0
1
1
1
1
1
0
0
1
2
1
0
1
1
1
2
2
1
2
0
0
1
0
0
0
1
2
1
0
1
1
3
0
0
2
2
2
2
1
2
1
1
0
0
1
0
0
0
0
2
1
1
1
2
2
2
2
0
1
1
1
2
0
2
1
1
1
0
0
2
1
0
1
0
2
2
1
0
2
1
1
0
0
2
1
1
2
1
2
2
0
1
1
1
2
1
1
2
1
0
0
2
0
2
0
1
1
1
2
0
2
0
2
2
0
1
0
1
1
2
1
0
1
0
0
0
0
0
0
2
0
1
1
2
1
1
2
1
0
1
2
0
0
1
1
0
2
3
1
0
1
2
1
0
1
1
2
1
0
1
1
1
0
1
2
2
1
2
1
0
0
0
1
2
2
0
0
1
0
1
0
2
1
0
0
2
0
0
0
2
1
1
2
0
1
2
1
1
1
0
1
1
2
1
0
1
1
0
2
0
2
3
1
2
0
1
0
0
2
1
2
1
2
1
1
0
1
2
0
0
1
1
1
2
2
1
1
0
1
0
1
1
0
0
1
1
0
0
0
2
1
0
0
0
1
1
0
1
0
0
1
0
0
0
1
1
1
0
0
2
1
2
0
0
0
2
0
1
0
1
1
1
1
3
1
1
0
2
1
0
1
0
0
1
1
0
1
0
0
3
1
1
1
2
1
2
0
0
1
0
2
0
1
2
0
2
0
1
0
1
2
2
2
1
2
0
1
1
2
4
2
2
0
0
1
1
0
1
0
1
0
1
1
1
1
2
3
1
1
2
1
1
1
1
1
0
0
0
3
0
2
1
0
1
0
0
0
2
1
2
1
1
0
0
0
2
1
1
1
1
1
0
1
1
0
0
0
2
1
1
1
1
2
1
2
1
1
1
0
1
0
1
1
0
1
0
1
1
2
0
0
1
1
0
1
0
1
2
3
0
1
1
1
1
0
2
2
1
2
1
0
2
0
1
0
1
0
1
1
2
0
1
1
0
1
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
1
2
1
0
1
2
1
0
1
1
2
2
1
1
1
2
1
2
1
2
1
1
2
0
2
1
0
2
2
0
0
0
1
2
0
2
0
2
1
1
1
0
1
0
1
2
2
1
1
2
0
2
0
0
0
1
3
0
1
0
1
0
0
2
1
0
2
1
1
0
1
3
0
1
0
0
0
0
2
0
2
0
2
2
0
1
1
0
0
0
5
2
2
1
0
1
0
1
2
1
2
2
1
2
1
0
0
0
0
0
2
3
0
1
2
1
0
0
1
2
1
0
1
1
1
1
1
1
1
1
1
1
0
0
0
1
0
2
1
0
0
0
2
1
0
1
0
0
1
1
1
0
1
1
0
1
1
0
1
1
0
1
0
2
2
2
1
1
2
1
1
1
2
1
1
0
1
0
0
0
2
1
2
0
0
3
1
1
1
2
0
0
1
0
0
1
1
0
0
1
2
1
0
1
0
2
0
1
1
2
1
1
0
2
0
1
0
1
1
0
1
2
1
2
0
1
2
0
0
2
2
2
1
1
1
3
2
1
0
1
1
0
1
0
2
0
0
1
0
0
1
1
0
2
1
0
1
0
1
2
1
1
2
0
0
2
1
1
2
1
1
1
0
1
0
2
0
0
1
1
0
0
1
2
1
1
1
1
1
0
0
2
1
1
2
1
1
1
0
0
1
0
1
1
0
0
0
2
2
2
0
0
1
1
1
1
2
0
0
1
0
1
1
1
1
1
2
1
2
0
1
0
0
2
2
1
1
0
1
0
1
0
1
0
1
0
0
1
0
1
1
0
1
0
0
1
2
2
0
0
0
0
3
0
2
0
1
0
1
0
1
0
2
1
0
0
0
1
1
0
1
2
1
0
1
0
1
1
0
2
2
1
0
0
1
1
1
0
0
1
1
1
2
1
1
2
7
0
2
2
2
1
1
0
1
1
2
1
0
0
1
2
1
2
0
1
2
0
2
0
2
1
1
1
0
2
0
1
1
1
0
1
1
0
0
2
2
0
0
1
1
0
1
1
0
0
2
1
2
0
2
1
1
0
2
5
0
1
1
1
0
0
0
1
0
1
2
1
1
0
2
0
2
0
1
0
1
0
1
0
2
1
0
0
0
0
2
2
1
1
0
1
0
2
0
0
1
1
1
1
0
0
1
0
0
0
2
1
0
0
0
1
0
1
1
1
1
0
1
1
0
3
0
1
0
1
2
2
1
0
2
1
0
0
1
1
2
1
0
0
1
0
0
0
0
0
1
2
1
1
1
0
1
1
1
0
0
1
2
1
0
0
1
0
1
1
1
2
0
1
1
0
1
0
0
1
1
2
2
1
2
2
1
0
2
1
0
0
2
2
2
0
0
1
0
0
0
2
1
1
0
0
1
1
1
0
2
0
0
1
0
1
1
1
2
0
1
2
1
2
1
0
2
2
2
0
0
0
1
0
2
1
0
1
1
1
3
2
1
0
2
0
1
0
1
0
0
1
1
2
2
0
0
1
0
1
0
0
1
0
0
1
0
0
2
2
2
1
0
2
0
2
1
0
0
0
1
0
0
2
1
0
0
1
1
1
2
2
1
2
0
0
1
1
2
1
0
0
0
2
0
1
0
0
0
0
2
1
2
0
1
1
2
0
0
1
0
0
0
0
0
1
3
1
0
1
3
2
0
0
1
0
1
2
2
1
1
0
2
1
1
3
0
1
2
1
1
0
1
1
0
0
1
0
1
0
2
0
1
2
0
2
1
1
0
0
0
1
1
0
1
1
2
1
0
0
0
1
1
2
1
1
1
1
0
1
0
0
0
1
1
1
0
1
2
0
2
2
1
2
2
0
1
1
1
0
1
1
1
0
1
1
1
1
0
0
1
0
1
1
0
0
0
0
0
2
1
0
2
0
0
0
1
1
2
1
0
2
1
1
0
1
1
1
1
2
2
1
1
0
1
1
2
1
0
1
1
1
2
0
1
0
0
2
1
1
2
0
0
0
0
0
2
3
1
1
1
1
2
0
1
2
0
2
0
1
1
1
6
0
2
2
1
1
1
1
1
0
0
3
2
1
1
2
0
0
1
0
0
2
1
1
1
0
0
0
0
0
0
0
2
1
1
1
1
0
0
1
2
0
1
0
1
2
2
1
1
0
2
1
0
1
1
1
2
2
1
1
2
1
1
0
0
0
1
1
0
0
2
1
2
1
1
0
0
0
1
1
1
1
1
0
1
1
2
1
3
0
1
0
2
0
2
3
2
0
1
1
2
2
1
1
1
2
0
0
0
0
2
0
2
1
2
0
2
1
1
0
0
1
1
1
1
1
0
0
2
1
1
2
0
1
0
0
1
1
1
1
1
1
1
0
0
1
2
2
1
2
2
1
2
1
1
0
0
0
0
0
1
0
1
1
2
1
1
2
1
0
1
0
0
1
1
0
2
1
0
0
1
1
1
1
1
1
1
2
2
1
0
1
3
0
1
0
2
2
1
0
1
0
1
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
4
0
1
1
1
0
1
1
0
0
1
1
1
0
0
2
0
0
1
2
0
1
0
0
1
1
7
2
0
2
0
2
1
1
0
0
2
1
1
1
1
1
2
1
2
0
2
0
0
2
0
2
2
1
0
1
1
1
0
0
1
4
1
0
2
1
2
0
2
0
3
0
1
0
0
1
2
0
2
0
0
0
1
2
1
0
1
1
1
1
1
0
2
2
2
0
0
2
2
0
0
0
1
1
1
0
0
0
1
0
1
2
0
0
1
0
1
0
2
1
0
1
2
1
0
0
2
0
1
0
0
0
0
1
0
0
1
1
1
0
1
0
1
2
0
1
0
1
1
2
2
1
0
1
1
0
1
0
0
0
1
2
0
1
1
1
1
0
1
1
0
2
1
1
2
1
2
2
0
0
1
2
1
2
1
0
1
0
1
0
0
1
2
0
2
1
0
0
1
2
2
0
2
1
3
0
1
4
2
0
1
0
0
2
0
1
0
2
1
1
0
2
1
0
2
1
1
1
0
2
1
0
0
1
2
0
0
0
1
0
1
2
1
1
1
1
0
0
2
1
2
1
2
1
1
1
1
1
0
1
0
0
0
4
0
2
1
1
1
1
2
0
1
1
1
1
0
0
1
1
1
1
1
0
1
0
1
1
0
1
1
1
0
0
1
2
0
0
1
1
2
0
2
0
3
2
2
0
2
0
1
0
1
2
2
3
1
0
2
0
0
0
0
1
1
0
1
1
0
3
1
2
1
0
3
0
0
0
3
1
1
1
0
1
2
1
0
1
2
1
1
0
2
0
1
0
1
1
1
2
1
1
1
2
0
0
1
0
2
1
0
2
2
0
2
0
2
0
2
2
1
1
0
1
0
1
1
0
0
1
0
0
0
1
0
0
1
2
0
2
2
0
2
1
1
2
0
1
2
2
1
1
0
0
0
2
1
1
2
0
0
2
0
1
2
2
0
0
1
1
0
0
0
1
2
1
2
2
0
0
2
2
1
0
0
2
0
2
1
0
1
0
1
0
1
0
0
0
2
1
1
2
1
2
1
0
0
2
0
1
0
0
0
2
2
1
0
0
1
0
1
2
0
0
1
1
0
0
1
2
0
1
2
0
4
1
1
1
1
1
2
1
1
2
1
1
2
0
0
0
2
1
1
1
1
0
1
1
0
1
1
1
0
2
1
0
0
1
2
0
1
1
0
1
1
0
1
0
2
1
2
1
1
0
0
1
0
0
0
1
1
1
1
1
0
1
0
0
1
1
2
1
1
1
1
1
0
2
1
1
1
1
1
1
0
1
2
2
0
0
1
1
0
1
1
2
1
1
1
1
1
2
0
1
1
0
1
0
1
0
0
1
1
1
2
1
1
1
1
1
1
2
1
0
1
0
0
1
0
0
1
0
1
0
1
3
0
0
0
2
1
2
2
2
1
1
1
3
1
1
0
2
1
0
2
2
1
2
2
1
2
0
2
2
1
1
1
1
2
2
1
1
1
0
0
1
1
1
0
1
1
1
0
1
0
1
0
1
1
2
0
1
4
2
2
1
0
1
1
1
0
0
0
0
1
2
2
0
1
0
1
2
1
1
2
0
1
0
1
2
1
2
1
2
0
0
1
0
0
2
1
0
1
2
1
1
1
0
0
1
0
1
0
0
1
1
0
1
2
2
0
1
0
1
2
1
0
2
2
1
2
1
0
0
1
2
2
1
1
1
1
0
1
0
0
0
0
0
1
1
2
1
0
0
0
0
2
1
2
0
1
1
1
2
2
0
1
1
1
2
2
2
1
1
2
1
1
1
1
1
0
2
1
0
1
1
0
0
1
0
1
1
0
0
1
1
0
0
0
0
2
2
2
0
0
2
0
2
1
1
0
2
1
1
1
0
0
0
1
0
0
1
1
0
0
1
2
2
0
1
2
0
0
1
0
1
1
1
1
0
2
1
1
0
1
0
2
0
0
1
0
1
0
0
0
0
1
1
1
0
2
1
2
0
0
1
2
1
0
0
2
1
1
1
2
2
1
2
2
1
0
0
1
1
0
0
0
1
1
1
2
1
0
2
0
1
0
1
1
1
1
1
1
0
4
1
0
1
1
2
1
1
0
0
2
0
2
0
1
6
1
2
2
0
0
0
1
1
2
0
1
2
1
1
2
1
0
0
2
1
0
1
0
1
2
1
2
1
1
2
2
1
2
2
2
1
1
1
2
2
0
1
0
1
1
1
0
1
1
1
2
2
1
1
1
0
1
1
0
0
1
1
0
1
0
2
2
1
2
0
1
0
1
1
0
0
0
0
1
1
1
1
2
2
1
2
1
2
1
0
0
2
0
1
2
1
0
0
1
1
1
1
1
1
1
1
2
0
2
0
0
0
0
1
1
0
2
1
1
0
1
1
1
0
1
1
1
0
1
0
0
1
2
2
2
1
0
2
0
1
0
0
0
0
3
1
0
0
0
0
1
0
2
2
0
2
2
1
1
1
2
0
1
1
1
2
0
0
0
1
0
0
2
2
0
0
0
0
0
1
2
1
3
1
0
1
2
1
0
0
2
2
2
2
1
0
0
0
0
1
1
2
2
0
2
0
2
0
0
0
1
2
2
0
2
0
0
1
0
1
0
0
0
1
0
1
1
2
0
2
0
1
1
0
0
1
1
0
2
0
1
0
1
0
1
1
0
0
2
2
1
1
2
1
1
0
1
1
1
0
2
2
0
10
0
1
0
1
2
0
0
0
0
2
2
1
1
1
2
1
1
1
1
2
2
1
1
1
0
2
1
2
1
1
1
1
2
2
1
2
0
0
1
2
2
1
0
2
1
2
1
1
0
0
1
1
1
2
0
1
1
2
1
0
2
1
0
1
2
1
1
2
2
1
1
0
2
2
0
0
0
1
1
0
0
1
0
0
0
2
1
1
1
0
1
0
0
0
0
2
2
0
1
1
1
0
1
2
2
1
0
2
1
0
1
1
1
2
1
1
1
0
1
0
0
1
2
1
2
1
1
1
1
1
1
0
3
2
1
2
1
0
2
1
0
1
1
2
1
1
0
0
1
0
0
1
2
0
0
0
1
1
0
0
0
2
0
0
1
1
1
0
1
1
1
1
2
1
1
1
2
1
0
0
3
0
3
2
2
3
0
1
1
1
1
0
1
2
2
1
0
0
1
1
1
1
1
1
0
0
0
0
0
1
0
0
0
1
0
1
0
2
1
1
0
1
1
1
0
0
3
1
1
1
1
1
0
0
1
0
2
0
1
0
0
1
1
0
1
1
1
1
0
1
0
0
2
2
0
1
1
2
2
2
0
0
2
0
2
0
1
1
0
1
1
1
2
2
1
0
1
0
0
1
1
2
2
0
1
1
1
1
0
1
1
0
0
1
2
0
0
0
2
2
1
1
0
0
1
1
0
0
1
0
1
0
1
2
1
0
0
1
1
1
2
1
1
4
1
0
1
0
1
2
1
2
1
2
0
0
1
2
0
2
2
1
0
2
0
0
0
0
1
1
0
1
1
0
1
0
1
1
2
1
1
0
0
1
0
2
1
1
2
0
1
0
0
1
2
0
1
2
0
0
2
1
1
2
1
0
1
1
0
0
0
1
1
0
0
0
1
2
1
1
0
0
0
1
0
1
0
1
2
2
0
2
0
0
2
1
1
0
2
1
1
2
2
1
0
0
1
2
1
1
1
1
2
1
2
2
3
0
0
1
1
2
0
1
2
1
1
0
1
1
2
0
1
1
0
0
0
1
1
1
2
0
2
0
2
1
0
2
1
1
0
0
0
2
1
2
0
0
1
1
0
0
0
0
1
1
1
1
1
2
1
2
0
1
0
0
0
2
0
0
1
0
1
1
0
0
1
0
1
1
2
0
0
0
0
3
0
2
2
1
2
0
0
1
0
2
1
1
2
0
2
1
0
0
2
2
0
2
2
0
0
1
0
1
2
1
0
2
0
0
0
2
1
1
0
2
1
2
1
1
0
0
0
0
0
0
2
1
0
1
1
2
0
1
1
0
0
0
1
1
0
0
1
2
0
1
0
2
1
3
0
1
0
1
1
1
1
1
1
1
0
2
0
1
1
2
2
1
1
1
0
0
1
1
0
2
1
0
0
1
0
1
0
2
1
2
2
1
2
1
0
2
0
0
3
1
2
1
3
1
1
1
1
2
1
1
0
1
2
0
2
1
1
1
2
0
2
1
2
1
3
1
0
1
2
0
0
0
2
1
1
3
1
1
0
0
0
1
0
0
0
3
0
1
1
0
1
0
0
1
0
1
1
0
0
1
0
2
1
0
1
0
2
0
1
1
0
0
0
1
0
1
1
1
2
1
2
1
1
1
0
0
1
2
0
0
1
1
1
1
0
1
2
0
1
0
2
0
2
0
1
2
0
2
0
0
0
1
1
1
2
2
1
0
1
1
1
0
0
2
1
2
0
1
2
0
1
0
2
0
1
0
0
0
1
0
1
1
2
0
0
2
0
0
0
2
0
0
0
0
2
1
1
1
3
1
1
1
1
1
0
2
2
1
1
1
0
1
1
0
0
0
1
1
1
1
0
0
0
0
1
1
1
0
0
1
2
0
1
1
2
0
1
1
2
1
0
1
1
0
1
1
1
0
0
0
1
0
0
1
2
1
0
0
2
0
1
1
1
0
0
1
1
1
2
1
0
0
2
0
1
1
0
1
1
1
2
1
0
0
0
2
0
2
0
1
2
1
2
1
0
3
1
2
0
0
2
0
2
2
0
0
0
2
2
0
0
1
0
1
1
1
0
1
1
2
0
0
0
0
1
2
0
1
0
2
1
1
1
2
0
1
1
1
4
0
1
0
1
0
1
1
0
2
1
0
1
2
0
1
1
1
0
2
1
0
0
0
2
2
0
2
1
1
0
2
1
0
1
0
0
0
1
1
1
2
1
1
0
2
2
2
0
1
1
0
0
3
0
1
0
2
1
0
1
1
0
1
0
0
0
2
2
0
2
1
0
2
1
2
0
2
1
0
1
1
1
2
0
1
0
1
0
1
1
2
0
1
1
0
2
1
2
0
0
1
0
1
2
8
2
0
1
2
2
1
0
2
1
1
1
2
2
0
0
1
1
2
0
0
3
1
1
0
2
1
0
0
1
1
0
3
2
1
1
0
1
1
1
2
1
1
0
2
1
1
0
1
0
2
1
1
2
1
1
1
0
0
1
2
0
1
0
2
2
0
0
1
0
1
2
3
0
0
1
2
0
2
1
2
1
1
0
2
2
1
1
2
0
0
0
1
0
1
2
0
0
2
0
1
1
1
0
0
1
0
0
1
1
0
1
2
0
1
2
0
0
1
1
0
1
1
1
0
1
0
0
1
1
0
2
0
1
0
0
2
0
2
0
1
1
0
1
2
1
2
1
1
2
0
0
1
1
1
1
2
1
2
0
1
0
0
1
1
1
1
1
1
0
0
2
1
1
1
1
0
2
0
1
0
1
1
1
2
2
0
0
0
0
1
2
1
0
1
1
2
0
1
1
1
0
1
2
2
0
1
0
2
2
0
1
0
1
0
2
0
1
0
1
2
0
1
1
1
0
1
1
0
1
1
0
1
0
1
1
0
1
1
2
0
1
1
1
1
2
0
2
1
0
2
2
0
0
2
1
0
1
1
1
0
1
0
1
1
1
2
1
1
1
1
2
0
2
0
1
2
0
1
2
2
0
2
1
0
0
2
0
0
1
0
0
1
0
0
2
0
1
0
2
2
0
0
2
0
0
1
2
1
0
1
1
0
2
2
1
0
0
1
0
1
1
1
1
2
1
0
1
0
1
1
1
1
3
2
0
1
1
1
0
2
0
1
1
0
1
0
0
0
1
0
0
1
1
1
0
1
0
1
1
0
1
0
1
2
1
1
2
1
1
0
1
2
1
2
0
0
0
1
0
0
0
1
0
1
1
1
0
2
0
1
0
4
1
2
1
1
1
0
1
1
1
1
0
0
2
2
1
1
0
1
0
0
2
0
0
2
2
1
0
1
1
1
2
0
1
1
4
2
0
1
2
2
1
1
2
2
0
1
0
0
0
1
0
1
2
1
0
1
2
1
0
0
0
1
1
1
2
1
2
1
0
0
0
0
0
0
0
1
0
2
1
0
1
2
1
1
0
0
0
1
1
1
0
2
0
2
1
2
1
0
0
0
2
0
0
0
0
0
2
0
0
1
2
1
0
2
1
0
0
1
0
1
1
1
0
2
2
2
1
2
1
0
0
0
0
0
0
5
1
0
1
0
0
0
1
2
0
0
1
0
1
0
1
0
1
1
1
0
1
1
0
2
0
1
3
0
1
2
1
1
0
1
1
1
1
0
1
0
1
1
1
0
0
2
2
1
1
1
1
1
1
0
2
3
1
1
0
1
0
1
0
1
2
1
0
0
2
2
1
1
1
0
0
1
2
0
0
1
0
1
0
1
1
2
0
1
2
1
0
1
1
2
1
0
2
1
1
2
0
0
1
0
1
0
2
2
0
0
1
0
1
2
0
0
1
1
0
2
0
1
1
0
2
0
0
2
0
2
2
0
0
0
1
1
0
1
1
1
0
0
1
0
1
1
0
1
1
2
2
0
2
1
1
2
2
0
2
0
1
2
1
1
1
1
1
1
1
1
2
1
1
2
0
1
0
1
1
0
1
1
1
1
1
9
0
0
2
1
1
1
0
1
1
1
0
1
0
2
1
0
1
0
3
0
0
0
0
0
2
1
2
0
1
2
0
2
2
1
0
0
1
2
1
1
1
0
0
0
0
1
1
1
2
1
1
0
2
2
1
0
0
2
1
2
1
1
0
1
1
0
0
1
2
0
1
0
1
1
0
0
0
1
0
0
1
0
2
0
1
1
1
0
1
1
1
2
1
2
0
0
0
0
1
2
3
1
1
0
1
1
1
2
1
1
1
0
2
0
0
0
0
1
0
0
0
0
2
0
1
2
0
1
2
0
2
1
0
0
1
1
2
0
2
1
0
0
4
1
2
1
1
1
0
2
0
0
0
1
2
0
0
2
0
1
1
2
0
0
1
1
2
1
2
2
2
1
0
1
2
1
0
1
0
2
2
1
0
1
2
0
2
1
0
1
0
0
1
0
1
2
0
3
1
0
0
0
2
1
0
0
1
1
0
1
2
0
0
0
2
2
1
0
0
1
0
1
1
0
1
2
0
0
0
1
1
1
0
1
0
2
1
2
0
2
2
1
1
1
0
0
1
2
1
0
1
2
1
2
1
1
1
0
1
2
1
0
0
0
1
2
1
2
1
1
2
0
2
1
1
1
0
1
2
1
1
1
0
1
1
2
1
0
1
1
0
1
1
0
1
1
0
1
1
2
0
2
3
2
1
1
1
1
0
0
0
1
1
1
2
2
1
1
1
2
0
0
1
0
1
2
1
1
1
0
0
0
1
1
1
1
2
2
0
1
0
2
2
1
0
0
1
0
1
0
1
0
2
1
1
0
0
0
0
1
0
1
0
1
0
1
1
0
1
1
0
1
0
1
0
1
0
3
1
0
1
1
1
1
0
0
1
1
1
1
1
0
0
1
1
2
1
1
1
0
1
0
0
0
1
0
1
0
1
1
1
4
2
1
1
1
1
0
1
2
1
0
2
1
1
2
1
0
0
0
0
1
0
2
0
0
0
0
1
0
1
0
1
1
3
2
1
2
1
0
1
0
1
1
1
1
1
1
1
3
0
1
1
1
1
2
1
2
0
0
1
0
1
0
1
2
0
2
1
2
1
0
2
0
2
0
1
0
0
0
1
0
0
0
2
1
1
1
1
2
2
0
0
1
1
1
1
1
2
0
1
0
0
0
1
2
0
2
1
2
2
1
2
0
0
1
0
0
1
0
1
1
2
0
2
1
0
1
0
0
2
2
1
0
0
0
2
1
0
1
3
2
0
1
1
0
0
1
1
0
0
1
0
2
1
1
1
1
1
1
0
1
1
0
0
2
1
1
2
0
2
1
1
0
1
2
2
0
1
1
2
2
2
1
0
2
1
1
2
1
1
1
1
2
2
0
1
0
1
1
2
0
0
1
1
1
2
1
1
1
1
1
0
0
0
1
1
1
0
1
1
0
1
0
1
3
1
0
2
0
0
0
1
2
0
1
1
0
1
2
1
1
0
0
0
0
0
0
1
1
0
1
1
2
0
1
2
1
1
0
0
1
0
1
0
0
0
1
1
1
1
1
1
1
1
1
2
1
2
1
0
0
2
1
1
2
1
1
1
1
1
1
2
1
0
0
0
0
0
0
2
1
2
1
1
1
1
2
1
2
1
2
0
2
0
0
0
0
1
1
0
2
0
2
1
1
2
1
0
2
0
1
2
2
2
2
1
3
2
2
0
0
2
2
0
2
1
1
2
2
1
1
2
1
0
1
2
0
0
0
0
2
2
1
2
1
0
1
1
1
1
1
2
1
1
0
1
1
0
0
0
0
0
0
3
2
0
0
2
0
1
1
2
1
1
1
2
1
0
1
3
1
1
0
1
0
1
1
0
2
1
1
2
0
1
0
2
1
1
0
4
1
0
2
1
1
0
2
1
0
0
1
0
0
2
0
0
0
2
0
1
1
1
0
1
2
1
1
0
1
2
0
2
0
2
0
1
0
1
0
1
2
0
1
0
2
0
1
0
0
1
0
1
0
1
2
1
1
1
2
1
1
2
0
0
1
0
1
1
0
3
0
1
1
1
1
0
2
0
1
2
2
1
0
0
1
1
1
0
0
1
0
1
0
0
1
1
1
0
1
1
1
1
2
0
2
1
0
2
1
2
1
0
0
0
1
0
0
2
0
0
1
2
1
2
0
0
3
1
0
0
0
1
1
2
1
0
4
2
1
1
0
0
1
1
1
1
1
1
1
2
0
0
1
0
2
0
0
1
1
2
1
1
1
2
0
1
1
1
2
1
1
0
2
2
0
0
1
0
0
0
1
2
0
1
0
0
1
1
1
0
1
0
1
2
0
3
0
6
1
1
1
2
1
2
0
2
0
0
2
1
0
2
1
2
0
0
1
1
0
2
1
1
2
2
0
1
1
0
0
0
2
0
1
1
0
2
1
0
2
1
1
1
2
1
1
0
1
1
0
0
1
1
1
1
0
2
0
2
2
0
2
1
1
0
0
2
0
0
0
1
0
1
1
1
1
1
1
1
1
0
1
0
0
1
1
0
2
0
1
0
1
0
0
1
1
0
1
1
1
1
1
1
1
0
0
0
0
3
2
2
1
1
2
0
1
1
2
1
1
2
1
0
0
2
0
1
0
0
0
0
1
1
0
1
0
0
1
1
2
1
2
1
1
1
1
0
2
1
0
0
1
1
0
1
1
1
0
1
0
1
1
1
0
1
2
1
1
0
1
0
1
2
1
0
1
0
0
1
0
2
1
0
2
0
1
1
2
0
1
2
0
2
1
0
2
1
2
1
0
1
1
1
2
0
1
2
0
1
1
2
2
1
1
1
1
0
1
1
2
0
0
0
0
1
1
1
2
1
1
1
0
3
0
1
1
2
1
0
1
1
1
2
0
0
2
1
2
1
1
0
1
1
1
2
2
0
1
0
1
0
2
0
2
0
0
1
0
0
1
2
1
1
1
2
0
1
0
2
1
1
2
2
1
1
2
2
2
1
2
0
1
1
2
1
1
0
1
1
0
0
1
1
1
0
0
2
0
2
1
1
0
2
0
0
1
0
1
0
1
0
0
1
0
0
1
0
1
1
0
0
2
0
0
1
2
2
0
0
1
0
1
1
0
0
1
0
0
1
2
1
2
2
0
0
0
1
1
0
0
0
0
0
0
1
1
0
1
0
2
2
0
1
0
0
2
0
0
1
1
1
0
1
2
2
3
2
1
0
0
2
1
0
2
0
2
0
1
2
3
1
1
1
2
2
0
0
1
0
0
0
0
2
0
1
1
2
0
1
0
2
2
0
0
1
2
0
1
0
1
1
1
0
0
1
2
2
1
1
0
2
0
1
1
1
1
0
1
0
0
0
0
4
0
0
0
1
0
0
1
1
1
2
2
1
1
1
2
1
0
1
2
0
1
0
0
0
0
0
1
2
2
1
1
2
2
0
1
1
0
1
0
1
0
0
2
0
2
1
1
0
0
1
2
0
0
1
1
0
2
0
0
2
1
0
0
0
0
1
3
1
2
0
1
0
1
2
0
0
1
2
2
1
2
1
1
2
1
1
1
1
0
0
0
0
1
3
0
0
1
0
0
0
0
2
1
2
2
1
0
0
2
2
8
0
0
0
0
1
1
1
1
2
0
0
1
2
1
1
1
1
0
1
0
0
0
0
0
1
0
2
1
0
2
0
1
2
0
0
1
0
2
1
1
1
2
2
1
2
0
1
0
0
1
0
2
2
0
1
1
0
0
2
2
1
1
0
2
2
3
1
0
1
1
0
1
0
2
0
4
0
1
0
5
6
0
2
2
1
0
1
0
0
1
1
0
0
1
1
1
2
1
0
2
0
2
0
1
1
0
0
1
1
1
0
1
3
1
1
0
1
1
1
2
1
0
1
0
0
0
1
1
2
2
1
1
2
2
1
0
2
1
2
1
1
2
1
2
2
0
1
0
0
1
1
0
0
1
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
1
1
2
1
0
1
2
1
1
2
0
0
1
0
0
0
0
0
0
0
0
3
1
2
0
1
0
2
1
1
1
1
0
2
1
2
0
1
2
3
1
1
0
0
1
0
1
1
3
1
1
1
0
0
1
1
1
0
2
2
1
2
1
1
2
1
0
2
0
0
1
0
0
0
1
1
1
2
2
2
2
0
0
1
1
1
1
0
1
3
0
2
1
2
1
8
0
1
0
1
1
0
2
2
0
0
1
1
0
1
1
0
1
1
1
0
1
0
0
3
2
1
1
1
1
1
0
2
2
1
2
1
0
1
1
0
0
1
1
0
1
2
2
0
2
1
0
2
1
0
1
2
2
1
0
0
2
1
0
0
1
1
1
2
1
0
0
0
2
2
0
2
0
1
1
1
0
1
2
1
1
0
0
1
1
0
0
1
1
1
3
2
0
2
0
2
0
1
1
1
0
0
0
1
2
2
0
0
0
1
1
2
0
1
2
2
1
1
0
2
1
1
2
1
1
0
1
1
0
2
0
1
1
1
0
1
1
0
0
0
2
3
1
1
0
3
1
1
1
1
1
1
0
0
0
1
0
0
2
0
1
1
2
2
0
1
1
1
1
1
1
1
2
1
1
1
0
2
0
2
0
1
1
3
1
2
0
1
2
1
1
1
1
1
3
1
1
0
1
0
1
0
2
0
0
1
0
1
2
1
2
1
1
1
1
2
2
2
0
0
2
2
2
1
0
1
0
2
2
1
2
1
1
1
2
0
2
0
3
1
1
2
0
0
1
0
0
2
2
1
0
0
0
1
1
0
1
1
1
0
1
0
2
2
1
0
1
0
1
0
2
2
0
0
1
1
0
2
0
1
0
2
2
0
1
1
1
1
0
0
3
2
0
2
0
1
1
0
1
0
1
1
1
1
1
1
1
1
0
0
2
2
1
1
0
0
0
2
1
0
3
1
0
2
0
1
1
1
1
0
1
0
2
1
2
2
1
1
1
0
2
1
1
1
0
1
1
2
2
1
1
1
1
2
1
0
0
2
1
1
0
1
0
1
1
1
0
1
0
2
3
1
2
1
0
1
0
1
1
2
0
1
1
2
0
1
1
1
1
2
2
0
1
1
0
1
2
0
2
0
2
2
1
2
0
0
0
1
1
0
1
0
0
0
1
1
0
0
1
1
0
0
2
1
1
1
2
2
0
0
0
0
1
1
1
1
1
0
1
2
0
0
1
1
0
1
1
1
1
0
2
2
1
1
1
0
0
0
2
1
2
0
0
0
0
2
1
1
0
0
2
2
1
2
0
1
2
0
1
0
1
1
0
2
1
1
1
0
0
0
1
1
0
2
2
1
1
0
1
1
0
0
0
1
1
1
0
1
1
1
1
1
0
0
1
2
1
1
2
2
2
2
1
1
1
1
1
0
1
1
1
0
0
1
0
1
2
1
1
0
2
2
2
0
0
0
1
2
1
2
0
0
2
1
1
2
1
0
2
1
2
0
0
3
0
0
1
1
1
0
0
2
1
0
0
2
1
1
1
1
1
0
1
1
0
0
2
2
1
0
0
2
1
1
0
1
0
2
2
0
2
2
0
0
0
2
1
2
0
0
0
0
0
2
2
0
0
0
1
1
0
0
1
0
1
1
0
1
1
2
2
1
0
1
2
0
1
1
2
2
2
0
0
0
1
1
2
0
1
0
2
4
1
0
0
1
0
2
2
0
2
0
1
0
1
0
0
2
0
0
1
2
1
1
0
0
1
2
1
1
0
0
0
1
1
1
1
1
1
2
2
0
1
2
0
1
0
0
0
0
0
2
0
1
0
0
1
0
2
0
1
1
1
1
0
2
0
1
1
0
0
1
0
0
0
1
2
1
0
0
0
0
0
1
2
0
0
2
0
1
2
2
0
0
1
0
2
0
0
0
0
0
0
1
0
0
1
0
1
0
1
1
1
1
1
0
1
1
1
1
0
0
1
1
3
1
1
0
2
0
0
2
0
2
0
1
2
1
1
1
2
0
0
1
1
1
1
1
1
0
1
1
1
0
1
0
1
1
1
2
2
1
1
0
0
2
1
1
1
0
1
1
2
1
1
1
2
0
2
1
0
1
2
0
1
2
0
1
0
1
1
2
1
1
1
0
1
2
0
2
1
1
2
0
0
2
0
1
1
1
0
0
1
4
1
1
1
0
1
2
1
1
0
2
0
0
1
1
0
1
0
1
0
1
1
0
1
0
2
1
3
0
1
0
0
0
2
0
2
0
0
1
1
0
1
0
1
0
0
1
7
2
0
0
1
1
0
1
1
2
0
1
0
1
0
2
1
0
0
1
1
1
1
1
2
1
2
1
0
0
1
1
0
1
1
1
0
0
1
2
0
1
2
0
1
1
1
0
0
2
0
1
1
0
0
2
2
1
1
2
2
2
0
0
0
0
1
0
2
0
1
0
0
0
0
1
0
0
1
0
1
0
0
1
1
1
1
0
0
0
1
1
0
0
0
2
1
1
1
0
1
1
0
0
2
0
1
1
1
1
1
0
2
1
0
0
0
1
2
0
2
2
2
1
2
0
0
0
1
1
1
2
1
0
2
1
0
0
1
1
1
1
0
1
0
2
2
1
0
1
2
0
0
1
0
1
1
0
2
1
1
5
2
1
2
1
2
1
1
1
2
0
0
2
0
1
1
0
1
0
1
1
0
1
0
2
1
1
0
0
1
1
1
1
1
0
0
2
1
0
2
2
0
1
2
2
1
1
1
2
1
1
1
2
1
0
0
1
0
0
2
0
0
2
1
1
0
0
1
0
1
0
1
2
1
2
0
0
0
1
0
1
0
1
0
0
1
0
1
0
0
0
1
1
1
1
0
2
0
1
0
0
1
1
0
1
1
2
1
1
0
2
0
1
0
0
3
0
1
1
2
1
1
2
1
0
2
0
1
2
2
0
0
0
1
0
1
0
1
1
2
1
1
0
1
0
0
0
0
1
2
1
1
1
2
1
1
2
0
2
1
1
0
2
0
0
1
1
0
2
0
1
1
0
0
0
1
1
2
0
0
3
1
1
2
2
1
1
1
2
1
0
0
1
2
1
0
0
0
0
1
1
1
1
0
0
2
0
0
0
0
0
2
0
1
1
1
1
1
1
2
1
0
2
0
2
1
1
1
1
0
0
0
1
1
2
0
1
1
1
2
2
1
0
2
3
1
0
0
0
2
1
0
1
2
1
0
1
0
0
0
1
2
2
0
1
0
0
0
2
0
1
0
1
2
2
1
1
0
0
0
0
0
0
1
0
2
0
2
0
2
2
1
1
1
1
2
1
1
2
2
0
0
1
2
1
1
2
0
0
0
1
1
0
1
2
1
0
1
2
0
0
0
1
2
1
0
1
1
1
0
2
0
0
1
0
0
0
0
0
2
1
1
1
1
1
0
1
0
2
1
0
1
2
0
1
1
0
0
1
1
0
0
0
1
0
1
0
2
0
2
1
0
0
1
1
1
0
0
1
0
0
0
1
1
1
0
2
1
1
0
1
1
3
1
0
1
2
1
1
1
0
1
0
2
1
1
1
1
0
1
1
3
1
0
2
2
2
1
2
1
0
1
1
1
2
0
0
0
0
0
0
0
1
2
2
0
2
0
0
2
1
0
0
1
1
1
1
0
1
3
1
0
1
0
1
0
1
0
3
1
1
0
1
1
2
2
2
0
0
0
2
1
2
2
1
0
1
1
0
2
0
0
1
1
1
0
1
2
0
2
2
0
0
1
1
1
1
2
1
0
2
1
1
1
2
3
1
1
1
1
1
1
0
1
1
1
2
1
1
0
2
2
2
1
0
2
0
2
2
1
2
0
2
1
1
1
2
1
1
2
0
0
1
1
0
1
1
1
2
1
1
1
0
1
2
0
2
2
1
1
2
2
2
1
0
2
1
1
0
2
0
0
1
0
2
0
1
2
2
0
3
1
1
1
0
1
1
1
1
2
2
0
0
0
1
1
1
0
0
0
1
2
1
0
2
1
1
1
1
0
0
1
1
0
1
1
0
1
0
2
2
1
2
1
1
1
1
2
2
0
2
0
2
0
0
2
1
0
1
2
5
2
0
0
2
1
1
1
0
0
0
1
2
0
1
0
2
1
2
0
1
2
1
2
1
0
1
1
1
0
2
1
0
0
1
1
2
1
1
1
2
0
2
1
1
0
1
1
1
0
1
2
1
1
2
0
0
0
1
0
0
0
0
0
1
2
1
2
1
1
1
1
0
1
0
1
0
2
2
0
0
0
1
0
1
1
0
2
0
1
1
1
1
0
2
0
0
2
1
2
1
0
2
2
0
2
0
1
2
2
1
1
1
0
1
0
0
0
1
1
0
1
1
1
2
0
1
2
1
1
1
2
2
1
0
0
0
2
1
0
2
0
0
0
2
1
1
1
1
0
1
1
1
3
3
0
0
0
0
1
1
1
1
1
0
2
0
0
1
2
0
1
0
3
1
0
2
1
2
0
1
1
1
0
1
0
2
1
1
1
1
1
1
0
1
1
1
0
1
1
1
0
1
1
1
1
1
2
2
0
0
0
0
0
0
2
1
1
0
0
0
0
0
2
1
0
2
2
2
0
1
1
0
1
1
0
1
1
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
1
1
1
1
0
1
0
2
1
0
1
1
0
1
0
1
2
1
1
0
0
1
2
0
6
1
2
0
0
1
1
1
1
1
1
1
0
1
1
1
1
2
1
1
1
1
0
1
0
1
2
2
2
1
2
1
1
2
0
1
0
0
0
1
0
1
1
0
2
2
0
0
1
0
0
1
0
1
2
1
1
0
0
1
1
0
1
1
2
0
1
2
0
4
2
1
0
1
0
1
1
0
2
1
2
1
2
2
1
4
1
0
2
2
1
0
1
0
2
2
1
0
1
1
3
2
2
1
1
0
0
0
0
0
1
1
2
1
0
1
1
0
0
0
2
0
1
1
1
2
0
1
0
2
0
0
1
1
2
1
0
0
0
3
2
1
2
1
0
1
0
0
0
1
2
0
1
0
0
1
1
1
1
2
1
0
1
0
0
2
1
1
2
1
0
1
0
1
1
0
0
1
1
1
1
1
2
0
2
1
1
1
1
0
0
1
1
1
0
2
0
0
1
2
1
1
0
2
1
1
1
0
1
0
1
0
1
2
1
0
0
1
0
1
0
1
1
0
1
1
0
0
2
0
0
1
2
1
1
0
1
1
1
2
0
0
0
1
2
2
1
1
0
2
1
0
2
1
1
1
1
0
0
0
1
1
1
1
7
2
1
1
2
1
3
1
1
0
1
0
0
0
1
1
0
0
0
1
2
1
2
2
3
1
1
0
1
0
0
1
0
2
1
0
0
0
1
0
1
1
1
0
0
0
0
2
0
0
1
1
0
0
1
2
1
0
1
0
1
0
1
1
1
1
2
2
1
1
0
0
0
1
0
1
0
2
0
0
2
1
1
1
2
0
0
2
2
0
2
1
0
1
2
1
1
0
0
1
1
0
2
1
2
2
1
0
0
0
1
2
1
1
1
0
2
0
1
0
2
0
1
1
1
1
0
0
1
1
0
1
0
0
1
1
1
2
2
0
1
1
0
1
1
2
1
1
1
0
0
0
2
1
1
1
1
1
0
1
0
2
1
1
2
1
1
1
2
1
2
1
1
1
2
2
2
1
2
2
0
2
1
1
1
1
2
1
2
1
1
1
0
1
1
0
2
2
0
0
1
1
2
2
2
1
1
1
1
2
1
1
1
0
1
1
1
0
1
0
2
1
1
1
0
0
2
1
0
2
1
2
0
2
2
0
0
2
0
2
0
2
1
1
0
1
0
2
3
1
2
1
1
1
0
2
0
0
0
2
1
2
1
1
1
0
1
3
0
1
1
1
1
0
1
2
0
1
0
1
0
0
1
0
1
2
1
0
1
0
1
1
0
1
0
1
0
0
1
2
0
1
1
1
0
2
0
0
2
0
1
2
1
0
1
1
0
2
0
3
1
1
1
1
2
2
0
1
1
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
1
0
1
0
1
1
2
2
0
0
0
0
0
1
1
1
0
1
0
1
0
0
1
0
0
1
1
0
0
1
1
0
1
0
0
1
2
1
3
2
0
0
1
0
0
0
2
1
0
1
1
0
0
0
2
1
1
0
1
0
1
0
0
0
0
4
2
0
0
1
1
2
1
1
1
2
2
1
1
1
2
1
0
1
1
1
1
2
0
0
1
0
0
1
1
1
1
1
2
0
0
1
1
0
1
0
0
1
0
0
1
1
0
0
2
0
1
0
0
1
0
2
1
1
1
1
1
2
0
1
2
0
1
2
0
0
1
1
0
2
0
2
2
0
1
1
2
0
0
0
1
1
2
1
4
2
1
2
1
0
2
1
0
1
1
0
1
0
1
1
2
0
2
0
1
1
0
1
0
2
1
1
1
1
2
1
2
0
0
0
1
0
1
2
1
2
1
0
1
1
2
1
1
1
0
1
2
2
1
2
1
1
1
1
2
0
1
0
1
1
0
1
1
0
2
1
0
0
1
2
1
0
1
0
1
1
0
2
1
0
1
1
1
2
1
2
0
1
1
1
0
2
1
1
1
2
1
0
1
0
1
1
2
0
0
0
2
1
0
0
1
1
1
2
1
1
1
1
0
1
1
1
0
0
2
2
2
2
1
1
1
1
2
0
1
1
2
1
2
0
3
1
1
1
1
0
1
0
2
1
0
1
1
1
0
0
0
1
1
1
1
0
1
1
1
2
1
0
1
1
2
0
0
1
1
2
0
0
0
2
8
3
1
0
0
2
0
2
1
0
2
1
1
0
0
1
2
0
1
1
1
1
3
2
0
1
1
0
2
0
1
2
1
1
0
0
0
1
2
0
2
2
0
2
2
2
0
2
1
1
0
0
1
0
2
0
2
1
1
0
1
0
0
0
0
1
0
2
2
1
1
1
1
0
3
2
1
0
1
1
1
1
1
0
0
0
0
2
1
1
1
1
2
0
0
1
0
0
0
2
1
0
0
0
1
2
2
1
0
1
1
3
0
1
1
0
1
2
3
1
1
1
0
1
1
1
0
1
1
1
0
1
1
0
1
0
1
1
1
1
0
3
1
1
0
2
0
2
2
1
1
1
0
1
1
3
1
1
2
1
1
0
2
1
1
1
1
0
1
0
1
2
0
0
0
1
1
2
1
2
0
1
0
2
2
2
1
1
0
1
2
1
2
1
0
2
2
0
2
1
0
0
2
1
1
0
1
1
2
1
2
0
0
3
2
1
1
1
2
2
0
1
1
1
1
1
0
0
1
2
0
0
1
1
1
2
0
2
1
2
1
0
1
0
0
1
0
0
1
0
1
1
0
1
3
0
0
1
2
0
1
2
1
1
1
0
1
4
1
2
1
1
2
0
2
1
2
1
0
2
0
1
0
1
1
0
1
1
1
4
1
0
1
1
0
0
0
1
0
1
1
0
1
0
0
2
1
1
1
0
2
1
1
1
0
1
0
1
0
2
1
0
1
1
1
1
0
0
1
0
0
1
1
0
2
0
0
0
2
1
2
1
2
1
1
2
0
2
0
0
2
0
1
1
1
1
0
1
1
1
0
2
2
2
1
1
0
0
0
1
2
1
0
0
0
0
2
1
1
1
2
1
2
1
1
1
2
2
1
2
1
1
0
0
1
1
0
2
2
1
2
0
1
0
2
1
2
1
1
0
1
0
1
2
2
1
2
1
1
5
2
2
0
2
2
1
1
1
0
0
0
1
0
1
1
0
1
2
1
2
2
1
1
2
2
2
1
0
2
1
0
2
2
1
1
0
0
0
1
2
0
0
2
0
2
1
1
2
1
1
0
0
2
2
1
0
1
0
1
0
2
1
0
1
2
0
1
1
0
0
1
0
2
1
1
0
1
0
0
2
1
0
0
2
1
3
1
0
1
0
0
1
2
1
1
2
0
1
2
1
2
1
1
0
3
0
2
2
0
1
0
2
2
2
0
1
1
0
1
2
1
0
0
2
2
0
1
1
0
1
1
1
1
2
0
2
0
0
0
0
2
0
0
1
1
1
1
0
1
1
1
0
2
1
1
1
1
0
0
1
1
0
1
1
1
2
0
1
1
1
0
1
1
0
2
1
1
0
2
1
3
0
0
1
0
1
0
2
2
1
1
0
2
2
0
1
2
2
2
0
1
0
1
0
1
1
0
1
1
1
2
1
1
1
1
1
2
0
1
2
0
0
1
0
1
1
2
2
4
2
1
1
1
1
0
1
1
1
1
0
1
2
0
0
1
1
1
1
0
1
2
1
2
0
2
1
0
0
1
0
1
0
3
0
1
0
1
2
0
0
2
0
0
2
1
0
0
2
0
0
0
2
1
1
0
1
3
1
0
1
1
1
2
0
0
2
1
1
1
1
1
1
0
1
2
1
2
2
1
1
1
0
1
1
1
1
0
0
1
0
0
0
2
1
2
2
1
0
0
0
1
1
0
0
0
2
0
0
2
1
2
0
0
1
0
0
1
1
0
1
2
1
1
1
1
0
0
1
0
0
1
0
2
2
0
2
0
0
1
0
2
2
2
1
0
0
0
1
0
2
0
1
1
1
1
1
2
1
1
0
0
0
1
1
3
0
2
1
0
0
1
1
0
1
1
0
2
0
2
1
2
0
0
1
1
2
1
1
1
1
0
2
1
0
0
0
0
2
0
1
0
0
0
1
0
2
2
1
1
1
2
0
1
1
1
1
2
3
1
2
0
1
0
0
0
1
0
0
1
0
1
0
0
1
2
0
2
1
2
0
0
0
2
1
2
0
1
0
1
1
0
0
3
2
2
1
1
1
2
0
1
1
0
2
0
2
2
2
1
0
0
2
0
0
1
1
1
0
0
1
1
0
1
1
0
2
1
0
2
1
1
0
1
3
2
0
2
0
1
2
1
2
1
0
1
1
1
1
0
1
2
0
2
0
4
2
0
0
2
0
0
1
0
1
2
0
2
1
2
1
1
0
0
0
0
0
1
2
0
2
1
1
0
1
0
2
0
0
0
0
1
1
0
1
1
0
1
2
0
1
1
0
0
0
1
0
2
1
0
0
2
1
2
0
0
1
0
1
3
0
1
1
0
0
1
2
0
1
1
0
0
1
1
1
2
1
0
2
2
1
0
1
2
0
1
0
1
1
1
0
1
1
1
0
1
2
2
1
2
0
0
3
0
1
1
2
1
2
0
0
2
1
2
1
0
1
1
1
2
0
0
0
2
1
0
0
2
1
0
0
2
1
1
0
0
1
0
0
1
1
1
0
1
1
1
1
0
1
1
1
1
1
0
0
1
1
0
1
2
1
0
1
0
1
1
0
1
0
1
0
2
2
1
0
0
0
1
1
1
0
0
0
1
2
0
1
2
0
0
0
1
0
0
0
0
1
1
1
1
1
0
0
1
1
0
1
0
1
2
0
1
1
0
2
0
1
2
2
0
3
0
1
1
0
1
0
0
1
0
1
1
2
2
1
1
0
0
1
0
1
0
2
1
0
0
0
2
0
1
0
0
2
0
1
1
2
1
2
1
1
1
1
1
1
2
1
1
1
0
0
1
2
1
0
1
1
1
0
0
1
1
2
0
0
0
1
0
0
1
0
1
0
1
2
2
1
2
3
0
2
0
0
0
0
1
0
1
2
0
1
1
2
1
1
0
1
1
1
0
1
2
1
1
1
1
2
0
0
1
2
1
0
1
3
0
0
2
2
1
1
1
1
0
1
0
0
2
0
0
0
2
1
1
1
2
1
0
0
1
1
1
0
0
0
2
1
2
0
0
0
1
1
0
2
0
0
0
1
2
1
1
0
5
1
1
2
0
1
0
0
2
2
1
1
0
1
2
0
1
4
1
1
1
1
1
0
0
0
1
1
0
1
2
0
0
1
2
1
1
1
1
0
1
2
1
2
1
1
2
1
1
1
0
2
2
0
1
1
1
1
1
0
2
0
0
1
0
0
2
1
1
1
0
1
1
1
1
1
2
0
0
0
0
1
0
1
1
1
2
0
1
1
1
0
1
2
1
1
1
2
1
0
0
2
1
1
1
2
0
1
2
1
2
0
1
2
0
1
1
0
1
1
2
2
0
1
0
2
1
0
1
1
1
2
2
1
0
1
1
1
1
1
1
1
1
2
1
1
0
0
0
0
1
4
0
0
1
0
1
1
1
1
0
0
1
1
0
4
1
1
1
0
1
1
1
1
1
1
1
0
1
1
1
1
2
1
0
1
3
3
2
1
1
1
2
2
0
1
1
1
1
0
2
1
0
1
0
1
1
0
1
1
1
2
0
1
2
2
0
2
2
2
2
0
0
0
2
0
1
0
1
0
0
1
1
1
2
1
1
0
2
2
0
1
2
1
1
2
1
0
2
1
1
2
1
1
0
0
2
1
2
0
2
2
3
2
1
0
1
2
1
1
2
1
2
0
1
1
2
2
0
0
1
0
0
1
0
2
1
0
0
0
0
1
2
1
1
1
0
2
1
2
0
1
1
1
0
0
2
0
2
2
2
0
1
1
1
0
0
0
0
1
0
1
0
2
1
1
1
1
0
1
2
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
0
1
2
1
0
0
0
1
1
0
0
1
0
2
0
1
0
1
0
1
1
1
0
1
1
0
1
1
0
0
1
1
0
0
2
1
2
2
2
2
0
0
1
0
0
2
1
0
0
1
1
1
2
1
0
1
2
1
1
0
0
0
1
2
0
2
0
1
1
1
1
0
2
0
1
1
2
1
0
1
1
1
1
2
1
2
0
1
0
1
1
1
0
0
2
0
1
0
1
0
1
0
3
2
1
1
1
2
1
2
1
0
2
1
1
1
2
2
1
1
1
0
2
0
1
1
1
1
2
1
1
0
0
0
0
0
1
0
0
1
2
2
2
0
0
1
2
1
0
1
1
3
1
2
1
1
1
2
1
1
2
1
2
0
0
2
1
1
0
1
0
1
1
1
1
1
0
1
2
0
2
1
1
2
2
0
1
1
2
1
1
1
1
0
0
2
0
0
0
1
2
1
0
2
0
1
1
0
2
1
0
1
1
0
0
0
0
1
2
1
0
2
1
1
2
0
1
1
0
0
1
1
2
2
0
1
0
2
2
0
1
0
0
1
1
1
1
1
2
1
0
0
1
0
1
0
1
1
1
2
1
0
0
1
1
1
2
0
0
0
0
1
1
0
0
2
2
0
0
0
2
1
1
0
1
0
2
3
0
1
2
1
1
1
0
0
1
3
1
1
1
2
0
0
2
2
0
2
0
0
1
1
1
1
1
0
1
0
2
0
2
0
2
0
1
0
3
1
1
2
2
0
2
2
1
1
1
2
0
2
1
0
3
2
1
1
1
1
0
0
1
1
0
4
1
0
1
0
1
2
0
2
2
0
0
0
1
2
0
1
1
1
2
1
0
1
1
1
1
1
1
1
1
2
0
1
0
2
1
1
1
2
0
2
0
1
0
1
0
0
1
1
1
2
1
0
1
1
1
1
1
1
1
1
1
0
0
0
1
1
2
1
1
2
2
0
2
0
0
1
0
0
0
1
2
1
0
1
0
1
0
1
1
2
0
1
0
1
4
1
0
1
1
2
0
2
0
1
1
0
1
1
0
2
2
0
2
0
1
1
1
1
2
1
1
2
1
0
1
1
2
1
2
1
2
1
1
2
0
1
0
1
2
1
1
3
0
2
0
2
1
2
1
1
2
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
2
1
3
1
1
1
1
0
0
0
1
1
0
1
3
1
2
1
0
0
1
0
2
1
1
1
0
1
0
1
1
1
2
1
0
0
0
0
2
2
1
1
0
0
1
1
0
1
2
1
0
0
2
1
1
1
0
0
1
1
2
2
1
0
1
0
0
0
3
1
1
1
1
2
1
1
0
0
2
2
2
0
2
1
1
0
1
2
1
1
1
0
0
1
1
1
2
2
1
1
2
2
2
0
2
0
1
0
1
1
2
0
1
1
0
0
2
0
0
2
1
1
1
1
2
0
1
2
1
1
1
4
3
1
0
1
1
2
0
0
1
0
1
0
0
1
2
0
0
0
1
0
0
0
1
1
1
2
1
2
1
1
0
1
1
1
1
1
0
2
2
0
1
1
1
0
2
2
0
1
2
0
1
0
1
0
2
0
0
1
0
2
0
3
2
1
2
0
0
1
1
1
1
0
2
0
0
2
1
0
2
1
2
0
0
1
1
2
2
1
2
0
0
2
0
2
2
0
0
1
1
2
1
0
1
1
1
2
1
1
1
1
3
1
2
1
1
0
0
0
2
1
0
0
0
1
1
1
0
0
0
1
0
1
1
0
2
1
0
0
1
1
0
2
2
2
1
1
1
0
1
2
0
1
1
1
0
2
0
2
0
0
1
0
1
0
0
0
2
1
1
1
1
0
1
0
1
0
2
1
0
0
1
2
0
0
1
2
0
1
0
0
2
1
1
0
1
2
0
1
2
1
0
2
0
1
0
0
0
1
0
1
1
0
0
2
1
1
2
0
1
2
0
0
1
0
0
1
1
0
0
0
0
0
1
1
1
0
0
1
1
0
0
4
1
2
1
2
1
0
1
0
0
1
0
1
2
2
1
0
0
1
0
2
2
2
1
1
2
1
1
1
0
0
2
2
1
0
2
1
0
0
1
1
2
2
1
0
1
1
2
1
1
1
1
1
1
1
0
0
1
1
1
1
0
0
2
0
0
1
1
1
1
2
1
2
0
2
2
0
0
2
1
1
1
2
2
1
1
2
2
1
1
2
1
1
1
0
1
0
0
0
2
0
1
0
0
2
2
0
2
2
0
0
1
2
0
1
0
3
1
0
1
0
0
1
1
2
1
2
2
1
2
2
0
2
2
1
1
1
1
0
0
1
1
1
0
0
1
1
2
2
2
1
0
1
0
1
2
1
1
2
1
0
2
2
1
1
0
1
0
0
1
0
1
2
1
0
2
1
0
0
0
0
2
1
0
2
0
0
2
1
0
0
1
0
1
0
1
1
0
0
1
2
1
2
1
0
2
2
1
0
1
1
1
1
2
1
3
0
1
0
1
1
2
0
0
0
2
2
0
1
2
2
1
2
1
1
0
1
1
0
2
0
0
3
1
1
1
0
1
3
2
1
0
0
0
2
0
1
1
0
2
1
1
1
3
1
0
1
1
1
0
1
0
0
1
1
0
1
2
2
0
0
1
0
3
1
0
3
0
0
0
0
0
0
1
1
1
2
1
0
1
0
2
1
1
1
1
0
0
1
1
1
1
0
1
2
0
1
0
1
1
1
1
1
2
2
1
0
2
1
2
2
0
1
1
0
0
1
1
1
2
0
0
0
4
1
2
1
1
0
2
1
1
1
0
0
1
1
1
0
2
0
2
1
1
0
2
0
0
0
1
0
0
2
1
0
0
1
0
1
1
0
0
2
1
1
1
0
1
1
1
1
1
0
1
2
0
2
1
1
1
1
0
1
1
1
1
0
0
0
1
1
1
0
1
0
1
1
2
1
0
0
0
1
0
1
1
0
0
1
0
1
2
2
2
0
1
1
0
1
1
2
1
2
1
1
2
0
1
1
1
1
0
1
2
0
0
0
1
0
2
0
1
0
2
2
1
1
1
1
1
1
0
1
1
2
0
1
2
1
1
1
0
0
1
1
1
1
1
0
1
0
0
1
0
1
1
1
1
1
0
0
2
2
0
0
0
0
0
0
0
1
2
0
2
0
0
2
0
1
0
1
1
0
0
0
1
1
0
0
0
2
0
0
0
0
2
2
1
1
1
1
1
0
0
2
1
1
0
1
0
2
1
0
1
0
1
1
1
2
0
1
1
0
1
1
0
1
2
1
0
2
0
0
0
0
1
1
0
1
2
2
0
1
1
2
0
0
2
0
1
0
2
1
0
1
1
2
2
0
0
1
0
1
0
1
2
0
2
0
0
1
0
2
0
1
1
0
1
1
1
0
1
0
2
0
1
2
2
2
0
1
1
0
0
1
1
1
0
1
1
2
1
1
1
1
1
0
1
1
1
1
0
2
2
2
0
0
1
1
0
0
1
1
1
0
1
2
1
1
0
0
1
0
0
2
1
1
0
2
1
2
2
1
1
1
2
2
1
1
2
0
1
2
1
1
1
1
0
1
0
1
1
1
1
2
1
1
1
0
1
0
2
0
1
0
2
0
0
1
1
0
2
2
1
2
1
2
2
1
2
0
2
1
0
1
0
1
0
1
2
1
2
0
0
2
2
1
1
0
1
1
2
2
2
1
0
1
1
1
1
1
0
0
0
0
2
0
1
2
1
1
2
1
2
0
0
2
0
0
2
1
2
1
0
0
1
1
0
1
1
1
1
1
1
0
1
0
0
2
1
2
1
1
0
0
1
1
2
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
1
0
0
2
0
1
1
1
1
0
2
0
0
1
2
2
1
1
0
1
1
1
1
0
0
2
2
2
0
0
2
2
0
1
0
0
1
0
0
2
0
0
1
1
2
0
1
1
1
2
2
1
2
1
1
0
1
3
1
0
1
0
0
0
0
0
0
0
0
1
1
1
0
1
0
1
0
1
2
1
0
0
2
1
0
1
1
1
2
1
1
1
1
1
1
0
1
2
0
2
0
1
2
1
1
0
2
0
0
1
0
5
2
1
1
2
1
0
2
1
1
1
2
2
1
3
0
0
2
2
1
0
0
0
1
2
1
1
2
1
0
1
0
0
2
0
2
0
1
1
1
1
0
1
2
1
2
1
4
2
1
1
1
1
1
2
2
2
1
0
1
2
0
1
0
0
1
0
0
1
1
0
0
1
0
1
0
1
2
3
1
2
0
0
2
2
3
1
1
1
2
2
2
0
1
1
2
1
2
1
1
2
0
2
1
0
2
0
1
0
0
1
0
1
2
0
0
1
0
1
0
1
0
2
0
2
0
1
1
1
1
2
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
2
2
1
1
0
2
2
2
2
0
1
0
0
2
0
0
1
0
1
0
1
0
2
0
1
0
1
0
0
1
2
0
1
0
1
0
0
0
2
0
1
1
2
1
1
0
1
1
1
1
1
1
1
2
1
2
2
0
0
1
1
0
1
1
0
2
1
1
1
1
1
0
0
0
0
1
2
0
1
1
1
0
1
0
1
2
0
0
1
1
0
0
0
2
0
1
0
1
1
1
0
1
1
1
0
0
0
2
2
1
1
2
0
1
0
1
1
0
2
1
1
0
0
1
0
1
1
1
1
1
1
0
1
0
1
1
2
2
1
0
1
2
2
2
2
0
1
2
0
2
1
0
0
1
0
0
0
1
0
1
0
0
0
1
1
0
1
1
1
0
1
1
0
2
0
0
1
2
0
2
1
1
2
0
0
1
1
0
0
1
2
0
2
1
1
0
2
3
0
1
2
1
0
1
3
1
0
1
1
1
0
1
1
1
0
1
2
0
1
1
1
1
0
1
0
1
2
2
0
1
1
1
1
1
1
0
0
1
0
0
1
0
2
1
1
1
1
1
0
1
0
1
0
0
0
0
1
0
3
2
1
2
0
2
0
1
0
0
1
2
2
1
2
0
0
0
0
3
0
0
0
1
1
2
1
0
2
2
1
1
1
1
1
1
1
1
1
1
0
2
0
2
0
2
0
0
0
0
0
1
1
2
2
1
0
1
1
2
0
0
1
1
1
0
1
2
2
1
0
2
1
2
0
0
2
1
1
1
2
0
1
0
1
0
0
2
1
0
1
1
0
1
0
1
0
2
1
1
1
1
1
1
2
2
1
1
1
0
0
2
2
1
0
0
0
0
1
2
1
0
1
2
1
1
0
3
1
2
0
2
1
0
0
0
0
0
2
1
0
0
1
0
1
0
2
2
1
2
0
2
1
2
0
0
0
0
0
1
0
0
1
2
1
2
1
1
1
1
0
1
0
0
2
1
0
1
0
0
0
1
0
0
2
1
1
0
0
0
1
0
1
1
1
2
2
0
2
4
0
1
1
0
0
1
2
2
0
2
1
2
0
2
1
0
0
1
1
2
3
0
0
0
2
1
1
0
3
1
2
2
0
2
1
2
3
1
0
2
8
3
2
1
1
0
0
1
3
0
0
1
1
0
1
2
1
0
0
0
1
0
1
0
2
0
2
0
1
0
0
1
0
0
2
0
0
0
1
2
2
0
1
1
0
0
0
1
0
0
0
0
2
1
1
1
1
0
2
1
2
1
0
1
1
2
1
1
1
1
0
1
2
2
2
1
2
0
1
1
1
0
0
2
0
2
1
0
2
2
1
1
0
0
2
1
1
5
1
1
1
0
1
2
0
0
2
2
0
2
1
2
1
0
0
0
1
3
1
2
0
0
1
0
0
2
2
1
1
2
0
2
1
0
2
2
0
2
0
1
1
2
1
0
1
3
0
1
1
2
2
1
0
0
1
0
1
0
1
2
0
0
0
1
0
2
1
2
0
0
0
1
2
1
1
2
3
0
1
0
0
1
1
2
0
0
2
1
1
1
0
0
1
0
0
1
0
1
1
0
1
2
2
1
0
1
0
0
2
2
1
1
0
0
0
0
2
0
1
1
0
2
1
2
0
1
1
0
2
0
0
0
1
0
2
1
1
0
1
0
2
1
2
1
1
1
0
0
2
2
2
1
2
0
1
1
1
1
2
2
2
0
1
2
0
0
0
1
1
1
1
2
0
0
1
1
0
0
1
2
0
1
0
0
0
1
0
1
0
0
1
2
0
1
1
1
0
0
1
1
2
1
1
1
0
0
0
1
1
0
0
0
2
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
0
1
0
0
1
1
1
0
1
1
0
0
1
2
1
1
2
1
1
1
1
0
0
1
1
2
1
1
1
1
1
0
0
1
0
0
0
1
1
1
1
1
2
1
0
0
1
1
2
2
1
1
0
1
2
1
1
1
1
1
2
1
0
1
1
0
1
2
1
0
0
2
2
0
2
1
0
1
2
1
0
1
2
1
0
0
0
0
1
1
1
0
2
1
1
1
1
0
0
1
2
1
1
0
0
1
1
2
1
1
0
0
1
1
0
0
0
0
1
1
1
0
1
0
3
0
0
1
0
0
1
1
1
2
0
1
1
1
2
2
0
2
0
1
1
0
1
2
0
0
2
2
1
0
0
1
1
1
0
0
1
1
1
1
1
2
0
0
0
1
1
1
1
0
0
2
1
0
2
1
0
0
2
1
0
0
2
1
2
0
1
0
0
0
2
2
0
0
2
2
1
1
1
0
1
2
1
1
0
0
1
1
3
1
1
0
0
1
2
0
0
1
1
0
1
0
1
1
1
0
1
0
0
2
0
2
1
1
1
2
1
0
0
0
2
0
2
1
2
2
2
1
0
1
1
1
0
1
2
2
2
0
2
2
0
1
1
1
1
1
1
0
0
3
1
0
0
0
0
0
1
0
1
1
1
0
1
2
1
2
0
1
2
1
1
0
0
2
0
1
0
1
0
2
0
0
0
0
2
2
1
2
0
2
0
1
2
1
1
0
1
0
0
0
0
0
0
0
0
1
1
1
2
1
0
1
3
2
0
2
1
2
0
1
1
0
0
1
2
1
1
2
0
1
2
0
0
0
1
1
2
0
3
4
0
1
1
2
1
0
0
1
1
1
1
1
0
2
0
1
0
2
1
1
1
1
2
1
1
0
2
0
2
1
0
0
1
0
0
2
1
0
1
0
3
1
1
0
2
1
1
2
1
1
2
0
1
2
2
2
1
1
1
1
1
2
1
2
0
0
2
1
2
2
1
0
3
2
1
0
1
0
3
1
1
0
2
0
2
0
2
1
1
0
0
1
0
2
0
1
0
2
1
1
2
0
1
0
1
1
2
1
1
2
2
2
1
0
2
2
1
1
1
1
1
1
1
1
0
1
1
1
0
2
2
2
1
1
1
0
2
1
1
0
0
0
0
0
0
1
1
1
0
0
1
2
2
0
1
1
2
1
1
0
0
0
2
1
2
0
0
1
0
1
2
0
1
2
2
0
1
0
3
1
0
0
2
0
2
2
2
3
1
0
0
0
0
1
0
1
1
2
0
1
0
0
0
2
1
2
1
0
1
1
1
0
1
1
0
1
1
1
2
0
2
0
0
1
1
0
1
0
0
0
2
1
1
0
0
2
1
0
0
1
1
2
0
2
1
1
1
1
1
2
1
1
0
1
0
1
0
1
1
2
1
1
1
2
0
1
1
1
0
1
0
2
1
0
0
1
1
1
2
0
1
2
1
1
1
0
1
1
1
1
1
2
2
1
2
1
0
1
0
0
1
2
0
0
0
1
1
1
0
1
0
1
1
0
1
0
1
2
2
0
1
2
1
1
0
0
0
1
1
0
1
1
1
1
0
0
2
1
0
2
1
0
0
0
0
0
1
0
1
1
1
1
0
1
0
1
1
0
1
1
2
1
2
1
2
0
1
1
0
1
0
1
0
1
0
2
0
0
1
1
1
0
0
1
0
1
2
1
1
1
1
0
2
1
1
0
1
0
0
0
0
0
0
1
2
1
1
1
2
1
1
1
0
1
1
0
1
1
0
2
1
0
1
1
0
2
1
1
2
2
0
1
1
2
2
1
1
0
3
1
0
1
1
1
1
0
0
0
1
0
1
1
1
1
0
0
0
0
1
1
0
1
2
0
0
1
1
0
1
0
2
1
1
2
0
0
1
0
0
2
2
1
0
2
1
0
1
0
0
0
1
1
2
1
1
1
0
2
2
1
2
0
0
2
2
0
1
2
1
2
1
0
0
0
1
1
1
0
0
2
0
1
0
2
0
5
0
2
0
1
1
2
1
1
2
1
1
0
0
2
1
1
0
2
1
1
2
1
0
1
1
1
0
0
1
2
1
1
2
1
1
2
2
0
0
1
1
1
1
0
1
0
2
2
2
0
1
0
0
0
0
1
2
0
0
0
1
1
0
0
2
2
2
1
2
1
0
0
2
2
0
0
1
2
0
1
0
2
0
1
1
0
0
2
0
0
1
1
0
1
1
0
0
0
1
1
1
0
1
0
0
0
1
0
1
0
0
4
1
0
2
2
2
1
1
0
1
2
0
0
0
1
0
1
0
1
0
1
2
1
0
2
2
1
0
2
0
2
1
0
2
1
0
1
2
0
0
0
0
0
0
2
1
0
1
1
1
1
0
1
0
1
1
3
0
0
1
1
1
2
1
1
1
0
3
1
0
2
1
0
1
0
2
2
2
0
1
2
1
0
0
0
1
1
0
0
1
0
1
1
1
1
1
0
1
1
2
0
1
0
0
0
1
1
1
0
2
0
1
1
2
1
1
1
0
3
1
1
1
2
1
1
0
1
1
2
0
0
2
0
2
2
1
2
2
0
0
1
0
2
2
1
1
0
1
1
1
1
1
2
1
2
0
0
1
0
2
0
0
1
2
1
1
0
1
2
1
2
0
1
1
1
1
2
0
0
1
1
3
0
1
1
0
1
1
0
0
2
1
0
0
1
0
1
0
2
1
0
0
1
2
1
0
0
0
1
0
0
2
0
1
0
1
0
0
1
1
1
1
2
0
2
0
1
0
0
0
0
2
0
0
2
0
1
0
2
0
2
1
2
0
2
1
1
1
2
2
0
2
1
1
1
1
1
1
2
1
0
1
1
1
0
1
1
0
0
0
2
0
0
1
2
0
0
2
0
0
1
1
2
0
1
0
1
1
2
0
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
0
2
2
1
2
0
1
2
0
2
0
2
2
2
1
1
1
0
0
0
2
1
0
2
0
0
0
0
1
1
1
0
1
1
1
2
1
1
0
0
0
0
0
3
1
1
2
1
1
0
1
1
1
1
0
1
2
1
2
2
0
0
1
0
0
1
2
1
1
3
2
0
2
0
1
0
0
1
0
0
0
1
1
1
1
1
0
1
1
2
1
2
1
0
0
2
1
2
1
1
0
1
1
1
1
2
2
2
0
2
1
1
1
0
0
0
0
0
0
1
1
2
0
2
1
1
2
0
1
0
1
2
0
0
1
1
1
1
0
1
0
1
0
1
1
1
2
2
0
1
1
0
2
0
2
1
1
1
1
1
2
1
1
0
1
0
0
0
1
0
1
0
0
0
0
1
1
2
2
1
0
0
1
0
1
0
1
2
1
3
2
1
1
1
1
0
1
0
2
2
0
0
1
1
1
0
1
1
1
1
0
0
2
2
1
1
0
1
4
0
1
0
1
0
0
1
0
1
2
0
0
0
2
1
1
2
2
0
0
0
0
0
2
0
0
2
0
2
2
1
0
0
1
0
0
1
0
0
2
0
1
0
0
0
0
1
1
0
1
1
0
0
1
1
1
0
2
0
1
1
0
2
0
1
1
1
2
1
1
1
2
2
3
0
0
0
1
1
1
2
2
0
2
1
0
1
1
2
0
1
0
1
2
2
1
1
0
2
1
2
0
1
0
1
1
0
0
2
2
1
1
0
2
0
2
1
0
0
2
0
1
0
0
1
1
0
1
1
2
1
1
1
1
1
1
0
0
0
0
1
2
0
1
0
1
0
2
2
1
2
1
2
1
0
0
0
1
4
2
1
0
2
0
1
2
0
1
1
2
0
2
1
0
2
1
1
1
0
1
1
1
0
1
0
2
1
0
1
1
0
2
1
1
0
1
2
0
0
2
1
0
2
0
0
0
2
2
1
2
1
1
2
0
0
0
2
0
1
1
2
0
2
0
1
0
0
2
2
2
1
0
2
1
1
1
0
0
0
0
3
2
2
1
0
0
0
0
1
2
1
1
1
1
1
0
0
0
0
2
1
2
2
0
1
1
1
1
1
1
1
0
0
1
0
2
1
2
1
2
1
1
2
0
1
1
1
1
2
1
0
0
0
1
0
0
1
3
1
1
1
0
0
1
2
1
1
1
0
3
0
1
0
2
1
1
2
2
1
2
1
1
2
2
0
1
2
0
2
2
0
0
2
1
0
0
1
0
1
0
0
0
1
0
2
2
0
1
0
1
2
1
0
0
0
0
0
1
2
1
2
1
0
1
0
0
0
2
0
1
0
0
0
1
1
0
1
0
0
1
1
0
0
3
2
0
2
0
2
3
1
1
0
0
0
2
1
1
0
2
2
1
1
2
0
1
1
1
1
1
1
1
0
1
1
0
2
0
0
0
0
0
0
0
0
1
0
1
2
0
0
1
1
2
1
2
0
1
0
1
1
1
1
1
0
1
1
0
0
0
0
0
0
1
1
0
1
2
1
1
0
0
1
0
0
1
0
1
1
0
1
1
1
2
0
0
4
1
1
1
0
2
2
1
0
2
1
0
0
1
0
1
2
0
0
2
1
3
0
2
0
0
2
1
1
1
0
1
1
0
2
0
0
1
2
1
1
1
1
1
2
0
2
1
1
1
0
1
0
1
1
2
0
2
0
1
0
2
1
1
2
1
2
0
1
0
1
1
1
1
1
1
0
1
1
2
0
1
0
0
0
3
0
0
1
1
0
1
1
0
1
2
2
2
0
2
1
1
0
1
0
2
1
1
2
2
1
1
0
2
2
0
0
0
2
1
0
1
2
1
0
0
2
0
1
0
0
2
1
0
0
1
0
1
1
1
1
0
0
1
0
2
2
1
1
2
1
2
2
1
0
1
2
1
1
0
2
2
1
0
0
1
1
0
1
1
0
0
0
0
2
0
2
1
0
1
1
0
0
2
2
2
0
1
1
1
1
0
1
0
1
0
2
0
2
1
0
1
2
2
1
1
0
0
2
1
1
1
0
1
3
1
2
2
0
2
0
1
2
0
1
2
1
0
2
1
1
2
4
1
1
1
1
1
2
0
0
1
2
1
1
0
0
1
1
1
2
2
2
1
1
0
1
2
1
0
1
0
1
1
1
0
0
1
2
2
1
1
1
0
1
1
1
1
0
1
1
1
0
1
2
1
1
1
2
0
1
1
0
0
0
1
1
1
0
1
0
0
1
0
1
0
0
2
1
1
1
1
0
0
2
0
0
2
1
1
0
2
1
1
0
0
1
1
1
1
2
1
1
1
2
1
0
0
1
2
1
1
1
1
1
1
1
0
0
1
1
0
2
0
0
1
1
0
0
0
0
0
1
0
1
0
1
2
1
1
2
0
2
1
1
1
2
0
0
1
1
0
2
2
2
2
0
2
2
2
1
1
2
0
1
2
0
0
1
1
1
1
1
1
0
2
2
1
0
1
1
0
0
1
2
1
1
0
1
1
1
0
0
1
2
2
0
1
0
0
0
0
0
2
3
1
2
0
1
1
1
1
2
2
0
0
1
0
1
2
1
1
1
1
1
2
0
0
1
1
2
0
1
1
1
1
0
0
1
0
0
1
2
1
0
0
3
0
0
1
0
2
1
2
2
0
2
1
0
2
0
1
1
1
1
0
1
2
0
1
0
2
1
1
2
1
0
0
1
1
3
1
3
0
0
1
0
1
1
0
1
0
1
1
0
0
1
2
0
1
1
2
1
0
0
1
1
2
0
2
1
1
1
2
1
1
0
0
1
2
2
0
2
1
2
1
0
2
1
0
0
0
1
1
0
2
1
1
1
2
0
1
0
1
2
0
0
4
0
1
1
0
2
0
0
0
1
1
2
1
1
1
0
1
2
1
1
0
1
1
0
0
0
1
2
2
0
1
1
1
1
1
1
1
1
1
2
0
0
0
0
0
0
1
1
2
2
0
1
0
1
1
1
2
1
1
1
2
1
2
0
0
1
0
1
0
3
0
0
1
1
1
1
0
0
0
1
0
2
2
1
0
0
0
0
0
2
1
2
0
2
1
1
0
1
3
0
1
1
1
0
1
0
2
0
1
1
0
1
0
2
1
2
1
0
2
0
0
0
0
0
2
2
0
0
1
0
0
2
2
0
1
1
1
0
1
2
0
2
0
1
1
0
1
1
0
1
1
1
0
1
2
0
2
0
2
0
0
1
1
2
3
1
1
0
2
0
0
1
0
1
0
1
0
0
1
1
1
1
1
1
1
1
0
0
0
1
0
1
0
0
0
0
0
1
2
5
0
0
1
1
1
0
3
0
0
2
0
0
2
0
2
1
0
1
0
1
2
1
1
1
1
1
2
3
0
0
0
1
2
1
1
1
1
0
1
1
1
2
0
0
2
1
0
0
0
0
0
2
0
1
1
1
1
2
1
2
1
2
0
1
1
1
1
2
1
1
0
0
0
1
0
1
0
0
2
1
1
1
2
1
0
0
2
0
2
0
1
0
1
1
0
0
0
2
0
1
2
0
0
1
0
2
0
2
1
1
1
0
1
1
1
1
1
0
0
1
0
0
0
1
0
2
2
1
1
2
0
2
2
2
1
2
2
1
1
1
1
2
3
0
1
1
1
2
1
2
1
1
1
1
0
1
1
1
2
1
0
1
0
0
0
0
1
1
1
0
1
1
2
1
0
1
1
0
0
0
1
0
1
1
0
1
0
0
1
1
0
2
1
1
2
1
2
1
0
1
2
2
1
1
2
1
0
2
2
1
0
1
1
1
2
1
0
0
0
0
0
1
1
1
0
1
1
0
0
0
2
1
2
1
0
2
4
0
0
2
0
1
0
0
2
0
1
1
0
1
0
5
2
1
1
1
1
1
0
1
2
2
0
0
2
2
0
2
3
1
2
2
1
1
0
0
0
1
0
1
1
0
1
0
0
0
2
0
0
1
0
2
1
2
2
1
1
0
0
1
1
1
8
0
1
2
1
1
1
1
0
2
2
1
1
1
1
2
0
1
0
0
1
2
0
0
2
2
0
1
1
2
1
1
1
0
0
0
0
0
0
2
0
0
1
1
0
0
1
2
1
1
2
0
2
0
0
0
1
2
1
2
1
1
1
0
0
2
0
1
1
1
0
2
0
1
2
2
2
0
1
0
0
2
0
1
1
0
1
1
1
2
0
0
1
1
0
1
2
0
2
1
1
1
2
1
1
1
0
1
1
2
2
2
1
1
0
0
0
1
2
2
2
1
2
1
0
0
1
1
1
1
1
0
2
3
1
1
0
1
0
1
0
0
0
0
2
0
2
0
1
0
1
1
1
2
2
1
1
2
1
1
0
1
1
1
0
0
2
1
1
1
0
1
0
1
1
0
0
0
2
1
1
1
1
0
0
0
1
2
1
0
2
1
0
2
2
1
1
1
2
2
0
0
1
0
1
0
1
1
2
1
1
1
1
1
1
1
0
2
2
0
1
1
1
2
1
0
1
0
1
1
2
0
0
1
1
0
1
1
0
0
0
1
0
0
0
2
0
1
0
0
1
1
1
1
3
1
0
1
1
0
0
0
1
0
3
1
1
2
0
0
1
1
2
2
0
1
1
2
0
1
2
1
1
2
0
2
1
2
2
1
0
0
1
2
1
1
1
1
0
1
1
2
1
0
2
1
0
1
1
2
1
1
1
0
1
1
0
3
1
0
0
1
0
1
0
2
1
1
0
0
1
0
2
0
0
2
0
0
2
3
0
1
0
2
2
0
1
2
1
0
2
1
2
0
1
2
2
0
1
0
0
0
0
2
0
1
2
1
0
1
1
1
2
2
1
0
1
0
2
1
1
0
1
1
0
1
2
0
1
2
0
2
0
0
6
1
1
0
1
1
1
1
0
1
2
1
1
2
2
2
1
2
0
2
1
2
0
0
0
1
0
1
1
0
1
1
2
0
0
1
0
2
1
1
0
1
0
0
1
1
2
0
1
2
0
1
1
0
1
1
1
0
2
1
2
2
1
2
2
2
0
0
1
2
0
1
1
1
2
2
0
1
6
0
0
0
1
0
1
2
1
0
0
1
0
0
1
0
2
1
0
1
0
0
0
2
2
0
1
0
2
0
1
0
0
2
0
1
2
1
0
0
1
1
1
3
0
0
0
2
2
1
1
2
1
0
2
2
1
1
1
1
0
1
1
1
2
2
1
0
1
0
1
2
0
1
1
2
0
0
1
2
1
0
0
1
0
2
0
1
1
1
1
0
1
0
1
1
2
2
0
1
0
0
0
1
1
0
1
1
0
1
1
0
0
2
1
1
2
1
1
1
1
1
2
0
0
0
2
0
0
0
0
1
3
2
1
1
2
1
1
1
2
1
0
0
0
1
0
2
0
1
2
0
1
1
2
2
1
2
1
1
2
0
1
1
0
1
1
0
1
1
0
0
1
0
0
1
2
1
0
2
1
0
0
0
0
0
2
1
2
2
0
1
0
2
1
0
1
2
0
2
0
1
0
0
1
0
0
1
1
0
1
1
0
0
1
1
0
0
0
0
2
0
1
2
2
0
0
0
1
1
1
0
1
1
0
1
2
1
2
1
1
1
2
0
1
2
2
0
3
1
1
0
0
0
1
0
1
0
1
0
2
1
1
1
2
1
1
0
0
1
1
0
2
1
1
0
0
0
0
1
0
0
1
1
1
4
1
2
1
0
2
0
0
0
1
2
0
2
2
0
2
2
1
1
1
1
1
2
2
1
0
1
1
1
2
0
0
1
0
1
2
2
1
3
1
1
2
2
1
1
1
1
1
1
2
0
1
1
2
2
0
1
0
0
2
0
1
1
0
0
2
0
0
2
0
2
0
2
0
1
1
1
1
1
3
2
1
1
0
1
0
1
0
0
0
0
1
0
1
2
0
1
0
1
2
0
2
0
1
1
0
2
1
1
0
1
0
0
1
2
1
1
1
2
1
0
2
2
1
2
0
1
1
1
0
2
0
1
0
2
0
1
2
1
0
1
2
1
0
2
2
2
1
0
2
1
1
1
1
0
0
2
1
1
2
2
0
2
1
0
1
1
0
1
0
1
1
0
0
2
0
1
0
2
1
0
1
0
0
2
0
1
1
0
1
1
1
0
6
0
1
0
2
1
0
1
1
0
2
0
1
1
0
0
1
2
2
0
0
1
0
0
0
0
1
0
1
1
1
1
1
1
1
1
1
1
1
0
1
2
2
1
0
2
1
1
1
1
1
0
0
2
2
0
0
0
0
0
2
0
1
1
1
2
1
1
1
2
1
2
2
1
0
2
2
1
2
0
1
2
1
1
2
2
1
0
0
2
1
0
1
2
1
1
2
0
0
0
1
0
2
1
0
3
1
0
2
1
0
0
1
1
1
1
1
1
0
1
2
0
1
0
0
2
0
0
2
0
2
1
2
1
1
2
2
1
0
0
1
0
1
2
0
0
2
0
2
1
0
0
0
1
1
2
1
0
0
0
2
1
0
0
1
1
0
0
2
0
2
1
0
2
0
2
1
0
0
1
1
1
1
1
3
2
0
3
0
1
0
0
2
1
0
2
0
0
0
0
2
1
0
1
1
2
0
1
2
0
2
1
1
0
3
0
0
2
1
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
1
1
2
1
1
2
1
2
2
1
0
1
0
0
1
1
0
2
2
2
0
1
3
1
0
2
1
0
2
2
1
2
1
1
0
1
2
1
0
0
1
1
1
2
0
1
1
0
0
2
1
2
1
1
0
1
0
0
1
1
0
2
1
1
2
0
1
1
0
0
2
0
2
2
0
1
2
1
1
0
1
0
1
2
0
1
3
1
2
1
1
2
1
0
1
1
1
0
0
0
1
2
1
0
0
2
1
1
0
1
0
2
0
0
0
2
1
0
1
0
0
0
0
1
0
0
0
1
0
1
2
1
0
2
1
1
2
0
2
2
1
0
2
2
1
1
2
2
1
0
2
1
1
0
1
1
1
1
1
1
0
1
1
1
2
1
1
1
2
1
1
0
1
2
0
0
2
0
0
0
2
0
2
0
1
3
0
1
1
2
1
0
1
0
0
1
1
2
0
1
0
0
0
1
0
1
1
1
2
1
1
0
0
1
0
1
0
2
1
1
1
1
0
0
1
1
1
2
0
1
0
1
1
2
0
2
1
0
2
3
1
1
0
1
1
1
1
2
0
0
1
0
1
0
0
2
0
0
1
0
2
1
0
1
1
0
0
1
1
2
1
2
0
0
1
0
2
1
1
1
2
2
1
1
0
2
0
1
0
2
2
2
2
1
0
1
2
0
1
0
0
1
2
2
1
1
1
1
2
0
1
1
2
1
2
0
1
1
0
2
2
1
1
2
0
0
1
0
1
1
0
2
1
2
0
0
1
1
0
1
0
0
1
1
1
0
0
0
0
1
2
1
1
2
1
1
1
2
0
0
1
1
0
2
0
0
0
2
1
1
2
1
1
2
1
0
1
2
2
1
2
1
0
0
1
1
2
0
2
2
1
1
1
0
2
0
1
0
1
0
2
2
1
0
0
1
0
0
1
0
0
0
1
1
0
1
0
1
0
0
0
3
2
2
0
2
1
1
0
0
1
2
1
1
1
1
1
1
1
3
1
1
1
1
1
1
0
2
2
0
1
0
0
2
0
1
0
2
0
1
2
2
2
0
1
0
2
0
2
1
2
1
1
1
1
2
0
0
1
1
2
1
2
1
1
2
0
0
0
2
1
1
3
0
2
1
1
2
2
1
1
1
1
0
0
1
1
1
1
1
2
0
0
0
1
1
1
1
2
2
1
0
1
1
1
1
0
1
1
0
0
2
2
2
0
0
1
1
1
2
2
3
1
2
1
2
0
2
0
0
0
1
2
0
2
2
0
2
2
0
0
0
1
0
2
0
1
1
1
1
3
1
1
0
0
0
0
2
1
0
2
1
1
2
0
0
2
0
0
1
1
0
1
0
0
1
1
1
1
1
1
0
1
1
0
2
0
2
1
1
0
1
0
1
1
1
0
0
2
1
2
1
1
0
0
1
2
0
1
0
0
0
1
1
1
0
1
0
0
1
1
0
0
1
0
0
2
1
0
1
0
0
1
1
1
1
0
1
1
0
1
1
1
2
1
2
0
1
1
2
1
0
0
1
0
0
1
2
1
0
0
1
1
0
0
0
1
2
1
1
0
1
1
2
0
1
2
2
0
1
2
0
1
2
2
0
0
1
1
1
0
0
2
1
1
1
0
2
1
2
1
1
0
2
2
1
2
2
0
0
0
1
0
1
0
0
1
1
0
1
2
1
2
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
1
1
1
0
0
1
0
2
1
1
1
1
0
0
2
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
1
1
1
1
4
0
1
0
2
2
0
0
2
0
1
0
3
0
2
1
2
1
1
0
0
2
0
2
1
1
0
0
1
0
2
0
1
1
1
1
1
1
2
1
1
0
0
1
0
1
0
1
1
0
0
1
0
2
1
1
2
0
1
1
0
1
0
0
0
0
2
1
0
1
0
2
0
1
2
0
0
1
1
0
0
1
0
2
0
0
0
1
2
1
1
1
1
2
0
1
2
1
0
1
1
5
1
1
2
1
0
0
1
1
0
0
1
0
1
1
0
2
0
0
1
2
2
0
1
1
1
1
1
1
0
1
0
2
0
1
3
2
1
1
0
1
0
1
1
1
2
1
0
1
2
0
1
2
1
1
1
1
2
2
0
1
0
2
1
0
1
1
1
0
1
0
2
0
1
1
2
0
1
1
1
2
0
0
1
1
2
1
0
0
0
1
1
0
1
1
1
2
1
0
0
0
2
1
0
1
0
1
2
1
2
1
0
1
0
2
0
0
1
0
0
0
0
2
0
1
2
0
2
2
0
2
0
1
2
2
1
1
1
1
2
1
0
0
0
0
0
0
1
0
0
0
2
1
0
1
0
0
2
1
0
0
2
1
2
0
0
2
1
2
2
1
1
0
1
0
0
2
3
0
1
0
2
1
1
1
0
1
0
1
1
1
1
1
2
1
2
0
1
1
1
1
0
0
1
1
0
1
0
2
1
1
0
1
2
0
1
2
0
0
2
0
2
1
0
2
1
1
1
1
1
0
0
3
2
1
1
1
2
0
1
0
0
0
1
0
0
1
0
1
1
0
2
1
2
0
0
1
1
2
0
0
0
0
0
0
1
0
0
0
1
1
2
1
1
2
0
1
0
1
2
0
1
2
1
2
3
2
1
0
2
0
1
1
1
1
1
2
1
1
0
1
2
1
0
2
1
2
1
1
0
1
2
0
0
1
0
1
0
2
1
1
0
1
2
1
0
0
1
0
0
1
1
0
1
0
0
2
2
1
0
0
1
1
2
1
1
1
0
2
0
1
0
0
1
0
0
0
1
1
0
2
2
0
1
2
0
1
1
0
1
2
1
1
0
0
2
1
1
0
0
1
1
1
1
1
2
2
2
1
1
0
0
0
0
3
2
4
1
2
0
1
0
0
1
1
1
1
0
1
0
4
1
0
1
2
1
0
1
0
1
0
0
0
1
0
2
0
0
1
0
1
1
1
0
2
1
1
0
3
0
1
0
0
1
1
0
0
1
1
2
0
1
2
1
1
1
1
0
1
0
1
0
2
0
0
2
1
1
2
2
2
1
1
2
0
0
2
1
1
1
0
1
1
2
2
1
0
4
0
0
2
0
1
0
0
1
1
1
0
1
1
1
1
0
2
1
0
1
2
0
1
1
0
0
1
2
0
1
2
1
1
2
1
0
1
0
1
2
1
0
0
1
0
0
1
2
1
2
0
0
0
0
1
1
2
0
0
1
0
2
1
2
1
0
0
0
0
1
0
1
1
1
0
2
0
1
0
0
0
2
1
0
0
1
0
1
0
0
1
2
0
0
1
0
0
0
2
2
0
0
0
1
1
0
1
1
2
1
1
1
0
0
1
1
2
1
0
0
1
2
3
2
1
1
1
1
0
0
2
1
0
1
0
0
2
2
0
2
0
2
1
1
2
2
2
4
0
0
0
0
1
0
1
0
0
1
1
0
2
0
1
1
0
2
0
1
1
1
1
1
0
0
2
1
0
1
0
1
1
1
0
0
0
0
1
0
2
1
1
1
2
2
1
0
1
0
0
1
0
1
0
0
2
0
0
0
0
0
0
2
0
2
0
1
1
2
0
0
0
0
1
1
0
0
2
1
1
1
1
1
1
1
1
1
1
2
1
1
0
0
1
0
2
2
1
2
2
1
1
0
3
0
1
2
0
2
3
3
0
0
0
2
2
2
1
0
1
0
1
0
2
2
0
1
1
2
1
1
0
0
1
0
0
1
2
0
1
1
0
0
1
0
0
0
1
2
1
1
1
1
0
0
0
1
1
0
0
1
1
4
0
2
1
0
1
1
0
0
0
2
1
0
0
1
0
1
0
0
2
1
1
0
0
1
1
2
2
2
1
2
0
1
0
1
2
1
2
0
2
0
1
0
1
1
1
2
1
1
1
0
1
0
1
2
0
0
0
1
0
2
1
0
1
1
1
1
0
1
0
1
1
1
1
0
0
0
2
2
2
3
1
0
2
0
1
2
1
1
0
0
2
2
1
1
0
1
1
0
0
0
2
0
0
1
1
0
0
1
1
1
0
1
0
0
1
1
0
1
2
0
2
0
0
2
0
0
1
2
1
2
1
1
1
0
0
1
1
1
0
0
1
1
1
1
0
1
1
1
1
0
1
0
1
1
1
1
2
1
1
2
1
1
0
0
0
1
0
1
1
1
2
1
1
0
0
0
1
0
1
2
2
2
1
0
1
0
2
1
2
1
1
2
0
1
1
0
1
1
1
1
2
1
1
1
2
2
1
1
1
0
0
1
0
0
1
0
2
1
2
2
1
0
0
2
2
1
1
0
1
1
2
2
2
0
0
2
2
1
1
2
0
1
2
0
0
2
1
1
1
1
0
1
1
2
1
0
0
0
1
1
1
1
2
1
2
2
2
1
1
0
0
0
0
0
1
0
1
2
0
1
3
0
0
0
1
0
1
0
2
1
1
1
1
1
1
1
0
0
1
1
0
1
0
1
0
0
1
0
2
2
1
2
0
2
1
2
0
0
1
1
0
3
0
0
1
2
1
2
0
0
0
0
0
2
1
0
1
1
1
0
1
0
2
2
1
1
0
0
0
1
0
1
1
1
1
0
1
0
2
2
2
1
0
0
1
0
2
0
1
1
0
0
2
2
0
0
0
0
1
1
1
0
0
1
3
2
0
1
0
2
1
1
2
2
0
0
1
0
1
1
0
2
2
1
2
0
1
0
0
0
3
0
0
2
2
1
1
0
2
1
2
0
1
1
0
1
1
1
2
1
1
1
1
1
0
0
0
0
2
2
2
1
2
2
2
1
2
0
1
1
0
1
0
2
0
2
0
0
1
1
1
1
1
2
3
2
2
0
1
1
1
0
0
2
0
1
2
0
1
2
2
1
1
1
1
0
1
1
1
0
2
0
1
2
0
0
0
1
2
0
0
2
2
1
2
0
0
1
2
1
0
0
0
0
0
1
1
1
0
1
0
0
1
1
0
1
0
0
1
1
0
0
1
1
2
1
0
1
2
2
0
0
2
1
2
0
2
0
0
1
0
1
0
1
1
1
0
0
0
2
1
2
1
0
0
1
0
0
1
1
2
1
1
1
1
0
1
0
1
0
1
0
1
0
0
2
0
0
2
2
2
1
0
0
1
1
2
0
2
1
1
2
0
1
1
1
2
1
0
0
0
2
1
0
2
0
1
1
1
2
1
1
0
2
1
1
2
1
1
1
2
0
1
1
0
1
1
2
1
2
1
2
2
0
2
0
1
1
0
2
0
2
1
0
1
2
2
1
0
1
1
2
0
1
1
1
0
1
1
1
4
1
1
1
1
1
1
0
0
2
0
0
2
1
2
2
1
1
1
0
1
0
1
2
1
1
1
1
2
1
2
0
0
1
0
2
1
0
3
1
2
1
1
1
0
1
1
0
1
1
0
2
0
1
0
0
1
0
2
1
0
0
1
1
2
0
1
2
0
1
1
1
2
0
3
0
2
1
2
1
1
1
0
2
0
0
2
1
3
0
0
0
2
1
1
2
0
0
1
1
1
0
1
2
0
1
1
2
0
1
2
0
0
0
1
1
0
0
1
0
1
1
1
0
0
0
1
2
0
0
1
0
2
0
0
2
0
1
0
1
2
1
0
0
0
2
1
2
2
0
2
1
0
2
1
1
0
1
0
0
1
1
0
0
1
2
0
2
1
1
1
1
2
2
0
2
0
1
0
0
2
2
1
0
1
2
2
2
0
0
1
0
1
2
1
1
0
0
2
1
2
0
0
0
0
1
1
1
1
0
2
1
0
1
1
0
1
1
0
1
2
1
0
2
0
0
1
1
0
0
2
1
0
1
0
1
1
1
2
2
0
1
1
2
2
1
2
1
0
0
0
2
1
0
0
2
1
0
2
0
1
2
2
1
1
1
0
1
3
2
1
0
0
0
1
4
0
1
1
1
2
0
1
1
1
1
2
1
1
1
0
0
1
2
0
2
1
1
0
0
1
1
0
2
0
2
1
1
0
1
2
1
0
0
0
0
1
1
0
0
1
0
2
1
0
0
1
1
0
0
1
1
2
0
0
0
2
2
0
0
0
0
1
1
0
0
0
0
0
0
1
1
1
0
1
1
0
0
1
1
0
2
1
1
0
1
0
0
0
0
0
0
1
1
1
2
1
0
1
0
1
1
1
0
0
0
0
1
0
1
1
0
2
1
2
0
1
0
1
1
0
1
2
1
1
0
2
1
0
1
0
1
0
0
2
2
0
0
0
3
1
1
0
0
1
0
0
0
1
1
1
2
1
0
1
0
1
1
1
2
1
0
1
0
0
1
1
2
1
1
1
1
2
1
1
1
0
1
4
1
2
1
1
2
1
0
1
0
2
0
0
2
1
1
1
0
1
0
1
0
0
1
0
1
1
0
1
1
1
2
1
1
0
1
1
1
1
1
0
1
1
0
2
3
1
0
2
1
1
0
0
3
2
0
2
1
1
1
1
0
0
0
1
1
0
2
0
2
1
1
0
2
2
0
2
1
0
0
0
1
2
2
0
1
0
2
2
1
1
1
1
0
2
0
2
0
0
2
0
0
2
1
0
0
1
1
1
1
2
2
1
1
0
1
2
2
0
1
0
2
1
0
2
1
0
2
1
2
1
0
1
0
2
1
0
1
2
1
2
0
0
1
0
1
1
1
0
0
1
1
1
1
2
0
0
1
0
0
2
1
2
1
0
1
1
0
2
1
1
1
2
0
0
1
1
1
0
0
0
1
3
1
1
0
0
1
0
1
0
0
1
1
0
1
1
1
0
1
1
0
2
1
0
1
0
0
1
1
2
0
0
2
2
1
2
2
1
2
1
0
0
1
2
0
2
2
0
1
0
2
1
3
0
1
1
2
0
1
1
0
1
1
0
1
1
1
2
1
0
2
0
2
1
1
1
1
1
0
0
0
1
1
0
0
0
2
0
1
1
1
2
0
0
1
2
0
0
0
1
2
0
2
0
1
0
2
0
0
1
1
1
0
0
2
0
2
1
1
1
0
1
2
1
1
0
2
0
1
2
0
1
1
1
1
0
1
1
2
1
1
0
2
2
1
1
0
0
0
1
1
0
0
2
1
1
0
2
1
0
1
0
0
2
2
1
1
1
2
0
0
1
2
1
0
2
2
0
1
1
2
2
1
1
0
1
2
0
0
1
0
1
0
0
0
1
0
1
1
0
2
1
0
0
0
1
1
0
1
1
0
1
1
0
1
1
1
1
1
0
1
0
1
0
1
0
1
1
0
0
0
0
0
0
0
1
2
0
1
0
2
2
1
2
1
1
1
2
1
1
0
0
1
0
1
2
1
0
0
0
1
1
1
0
1
0
0
1
0
0
0
1
1
0
1
2
2
1
0
0
0
2
2
0
2
1
2
0
1
1
0
1
1
1
2
0
1
2
0
0
1
1
1
1
1
1
1
2
0
2
1
1
1
1
0
1
0
1
2
1
1
1
0
0
0
1
1
0
0
1
2
1
1
0
1
1
0
0
0
0
0
2
2
1
1
0
0
1
1
0
0
0
0
0
1
0
2
1
1
1
0
1
1
1
2
2
1
1
1
0
1
0
1
0
4
0
1
3
0
1
2
0
1
0
2
1
2
0
2
2
2
0
1
1
0
2
0
0
1
1
0
1
1
1
0
2
0
2
0
0
0
0
0
1
2
1
0
2
2
1
2
0
0
0
1
2
2
1
0
1
1
0
0
1
2
0
3
1
2
1
0
1
1
1
1
0
0
0
0
0
1
2
1
1
2
0
1
0
2
1
1
2
1
0
1
2
0
0
0
1
0
0
0
5
2
1
1
0
1
1
1
2
1
0
2
0
0
0
3
2
1
0
0
0
1
1
1
1
1
0
1
0
0
3
0
1
2
2
0
0
0
0
1
1
0
0
1
1
1
1
0
6
2
1
2
1
0
0
1
2
1
2
1
2
0
1
1
0
1
0
0
1
1
1
0
1
0
1
2
2
1
2
2
1
2
1
0
0
2
1
1
1
1
2
2
1
1
0
0
1
1
0
1
0
1
2
1
0
2
1
1
0
0
0
3
0
1
1
0
1
2
1
2
2
1
2
2
0
1
0
0
2
2
1
1
1
1
0
2
1
0
0
0
0
0
1
0
1
0
1
0
0
2
0
1
1
0
1
1
0
1
1
1
1
1
2
2
0
1
1
0
2
1
0
1
0
0
0
1
0
2
1
1
0
2
1
1
1
1
0
2
2
0
0
1
1
1
2
2
0
0
2
1
3
1
0
2
0
0
0
1
1
2
0
1
0
1
1
1
1
0
1
0
0
2
1
2
0
1
1
2
1
1
1
1
2
0
0
0
1
1
1
0
0
2
0
1
1
1
2
0
1
1
0
1
1
0
0
1
2
1
0
0
2
1
0
2
1
0
1
1
2
0
1
2
1
1
1
1
0
1
0
0
1
1
2
0
0
0
2
1
1
1
1
1
0
1
2
1
1
0
1
0
0
0
0
2
1
0
0
1
1
0
0
1
1
1
0
2
0
0
0
1
0
0
1
0
2
0
1
0
1
1
1
0
1
1
0
1
0
2
0
0
0
0
0
1
0
1
1
1
1
2
0
0
1
1
1
1
1
1
1
1
0
1
2
1
1
0
1
1
0
0
2
0
2
0
3
1
1
1
1
0
1
2
0
0
1
1
0
1
2
0
1
2
1
1
1
1
1
4
1
2
0
1
2
2
0
2
2
0
2
0
1
0
0
2
0
1
1
1
1
2
0
0
0
2
0
2
1
0
0
0
0
1
0
2
1
2
0
1
2
0
1
1
1
1
0
1
0
0
0
1
2
1
1
1
1
1
2
2
2
1
1
2
0
0
1
2
1
1
2
2
0
1
2
1
1
3
2
2
0
1
1
1
0
0
1
1
41
0
0
1
0
1
1
2
1
2
0
1
1
2
1
0
2
1
0
0
1
2
0
1
1
0
0
1
2
0
0
2
1
2
2
1
0
1
0
2
0
1
1
0
0
1
0
1
1
1
1
1
1
0
1
1
1
0
1
0
2
0
1
1
0
1
1
1
0
2
0
1
1
1
1
0
2
2
2
1
0
0
0
1
1
1
1
0
1
0
1
2
1
0
0
0
1
0
1
1
0
2
0
1
0
1
1
1
1
0
2
2
1
1
0
1
3
0
1
0
0
0
0
0
2
1
1
0
1
1
2
1
1
2
0
1
1
0
2
1
1
0
1
2
1
2
1
0
0
0
2
0
1
2
2
1
1
1
1
1
1
0
0
1
1
2
0
0
2
1
0
1
0
1
1
2
1
0
1
2
1
0
0
1
0
1
3
0
0
0
1
1
1
1
0
2
1
2
0
2
0
2
0
0
2
2
2
2
0
1
1
0
0
1
0
2
1
1
0
1
1
1
0
1
0
2
2
1
0
0
0
0
0
1
1
2
0
0
0
1
0
0
2
2
0
1
0
0
0
0
1
1
1
1
0
1
0
1
2
0
0
1
1
0
1
2
0
0
2
0
1
1
1
1
0
1
1
0
1
0
2
2
0
1
0
2
1
0
2
2
2
0
1
0
1
1
1
2
2
0
1
1
1
1
1
1
0
1
0
1
2
2
2
1
1
2
1
0
1
1
1
2
1
1
1
1
0
2
2
0
0
2
0
1
1
2
2
0
2
2
2
0
1
0
3
2
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
1
1
1
1
1
1
1
3
1
1
0
0
1
1
1
1
1
1
0
1
1
0
1
2
0
1
0
1
1
1
1
1
1
2
3
1
0
1
1
2
2
0
1
2
2
0
0
2
0
1
1
0
0
2
1
2
0
0
1
0
1
1
1
1
1
0
1
0
2
0
1
0
0
2
1
1
1
0
0
1
0
1
1
1
1
1
1
2
0
0
1
1
0
0
1
1
0
1
1
1
1
1
1
0
0
1
2
2
1
1
1
4
0
2
1
0
1
2
2
0
1
1
1
1
0
1
2
1
0
0
0
2
1
1
1
2
0
0
0
2
0
0
1
1
1
2
0
0
2
1
1
1
0
1
1
1
0
2
2
1
0
1
1
0
2
1
0
0
0
0
1
0
2
1
1
1
1
1
1
3
0
2
1
0
2
2
0
2
0
1
0
0
1
1
1
0
1
0
1
1
2
1
2
0
0
1
0
1
0
2
2
1
3
1
0
1
1
1
0
2
2
1
0
0
1
1
1
0
1
4
1
1
1
2
1
0
1
1
3
1
1
0
0
1
1
1
0
2
1
2
2
1
1
1
1
2
1
1
0
0
0
1
0
1
0
1
0
1
1
2
0
2
2
2
1
0
2
1
1
1
0
0
1
1
1
1
0
1
2
1
0
1
1
0
2
0
0
2
0
1
0
2
1
0
0
0
2
0
1
1
0
2
2
0
0
1
0
1
1
2
1
1
1
0
1
0
2
2
1
0
2
0
2
0
1
1
0
1
2
1
1
0
0
0
0
2
0
1
1
0
0
2
1
0
1
0
2
0
1
0
1
1
1
0
1
1
0
1
0
0
0
1
2
1
0
0
1
2
0
1
1
1
0
1
0
1
0
0
0
1
1
1
1
0
1
0
2
2
2
0
0
2
0
2
2
1
2
0
0
1
1
2
1
0
2
2
1
2
2
0
0
2
0
1
0
1
0
2
0
1
2
2
1
2
0
2
2
1
0
0
1
2
2
0
2
0
2
1
1
0
2
3
0
2
0
0
0
2
0
1
1
1
1
1
1
0
3
0
0
1
2
4
2
1
0
0
1
1
0
0
1
1
1
0
1
2
0
0
2
0
0
1
2
1
0
1
1
2
1
0
0
0
1
0
2
1
1
0
0
1
1
2
0
1
2
1
1
1
2
0
1
1
0
2
2
1
0
1
1
2
2
1
2
1
1
2
1
1
1
1
2
0
0
0
1
2
2
0
0
1
0
0
2
2
1
1
1
0
1
2
0
0
1
0
0
1
1
1
1
0
1
2
0
0
1
1
1
0
1
0
1
2
1
2
2
0
1
2
1
2
0
1
1
0
2
0
1
0
0
0
1
1
2
1
2
2
0
1
1
1
1
1
0
0
1
0
1
0
2
1
2
0
1
1
0
0
2
0
0
0
1
0
1
0
0
1
7
0
0
1
2
0
0
1
1
0
1
4
1
0
2
0
0
0
2
0
1
1
2
0
2
2
0
2
0
0
0
0
0
2
0
1
1
1
0
2
0
2
1
1
0
0
2
2
1
0
2
0
0
3
2
0
0
2
2
0
3
0
1
0
1
1
1
0
2
3
1
0
1
2
0
0
0
1
2
1
0
1
0
1
1
2
2
0
1
0
0
2
2
1
1
0
0
1
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
2
1
1
1
2
2
0
0
0
2
1
0
1
2
0
1
1
2
1
0
2
0
0
0
0
1
0
0
0
1
1
1
0
2
1
1
0
2
0
0
2
1
1
2
2
2
1
0
1
1
0
2
0
0
2
0
1
1
0
1
0
0
1
1
2
0
0
1
1
1
2
0
0
1
0
1
0
1
0
0
0
1
2
0
1
1
1
1
2
1
1
1
1
1
0
1
2
3
2
1
0
0
2
2
2
1
0
0
1
0
1
2
1
4
0
1
0
0
1
0
0
1
1
2
0
2
1
0
2
2
1
0
2
1
2
0
1
1
1
0
3
1
1
1
0
1
2
1
0
0
0
0
0
2
0
2
1
1
1
2
1
0
1
0
2
0
0
1
0
1
1
1
2
1
2
4
0
1
0
0
0
2
2
0
1
2
1
1
1
0
1
2
0
1
2
2
1
2
1
1
0
0
0
1
0
0
2
0
0
0
1
2
0
2
0
0
1
0
1
0
1
0
0
0
1
1
2
2
0
1
0
1
0
1
1
2
2
0
1
2
2
0
1
2
2
1
1
2
1
1
2
0
0
1
1
2
2
0
1
1
1
1
0
2
0
1
3
1
0
0
2
2
0
0
1
1
3
1
1
1
0
2
0
1
1
0
2
0
0
1
1
0
1
2
1
2
2
2
1
1
1
1
0
1
0
0
2
2
0
1
1
3
0
0
1
2
1
0
2
0
2
1
1
2
1
0
0
1
1
1
2
0
1
2
0
2
0
1
2
0
1
1
0
0
0
1
1
2
1
0
2
0
0
2
0
0
1
0
0
1
2
0
2
1
2
1
2
2
1
0
1
1
0
0
2
1
1
1
1
2
1
2
1
2
1
1
2
1
0
0
2
1
0
1
1
1
1
0
1
1
0
2
0
1
0
0
0
2
1
1
1
0
2
0
2
1
1
1
1
1
1
0
1
2
1
2
0
2
1
1
0
1
1
1
0
1
0
0
1
0
0
0
1
1
0
2
1
0
1
0
2
0
1
1
0
0
0
1
1
1
0
1
0
1
1
0
0
1
1
2
0
1
1
1
1
1
2
0
2
2
0
2
1
0
1
1
1
0
1
0
2
0
1
1
0
0
2
2
0
1
0
2
0
0
2
1
1
0
1
0
1
1
0
1
2
0
0
1
1
1
0
1
0
0
0
0
1
0
2
0
0
0
0
1
2
0
1
0
0
1
1
0
0
1
2
0
2
2
2
3
0
2
2
2
1
2
2
0
2
0
1
0
1
1
1
2
0
1
0
2
1
0
3
0
2
0
1
2
0
0
1
1
1
1
1
0
2
2
2
2
0
1
2
0
1
1
1
2
1
2
0
0
1
1
0
2
2
1
2
0
1
2
0
0
0
1
1
1
2
1
0
1
2
1
1
1
1
1
1
1
1
0
0
1
1
0
2
1
2
1
1
0
0
1
0
0
2
2
1
1
1
1
2
2
0
1
1
1
0
0
1
2
1
2
1
2
0
1
1
1
0
1
1
0
1
1
2
0
0
1
1
1
0
1
1
0
1
0
1
2
1
0
2
1
2
0
2
2
0
0
2
1
0
1
0
1
2
1
1
2
2
2
2
1
2
2
0
0
0
1
2
1
1
0
0
2
1
0
2
0
1
1
1
0
1
1
2
2
2
0
0
0
0
2
0
1
1
0
1
1
1
1
1
1
0
0
1
0
1
0
1
1
3
0
1
2
0
2
2
0
0
1
0
0
0
2
2
0
2
0
2
1
1
0
1
1
1
0
2
1
2
2
2
1
1
1
0
1
1
1
0
2
2
0
2
0
0
0
0
0
0
0
1
1
2
2
2
2
0
1
2
1
0
0
1
1
0
1
1
2
1
1
1
2
1
1
0
1
1
0
2
0
0
1
1
1
1
2
1
2
1
1
0
2
1
0
2
1
0
0
2
0
1
2
0
1
0
1
1
1
1
2
1
1
0
0
0
1
1
1
2
0
2
1
1
1
2
2
1
2
1
0
0
1
1
3
2
1
0
1
0
1
1
2
2
0
0
0
1
3
0
1
0
0
1
1
1
1
2
2
1
2
2
0
2
1
1
2
0
0
2
1
1
0
1
0
1
0
0
1
1
0
1
0
1
1
1
1
0
1
1
2
1
0
1
3
0
2
1
1
2
0
1
0
2
1
0
0
1
1
1
1
3
1
0
2
2
0
0
0
0
2
0
1
1
0
0
1
0
1
0
1
1
0
1
0
0
1
0
0
0
0
0
0
2
0
2
0
0
1
2
1
2
0
1
0
2
2
1
2
1
1
1
0
1
1
2
2
1
2
1
1
1
0
0
1
0
1
1
1
1
1
1
1
1
2
0
1
1
1
1
0
1
1
0
0
0
0
0
1
1
0
1
0
1
2
0
1
0
1
0
1
0
3
1
1
2
0
1
0
1
1
0
1
0
0
1
0
1
0
1
2
4
2
1
3
1
1
1
2
1
1
1
0
0
2
0
0
0
0
1
1
0
1
0
2
0
0
0
0
0
1
1
0
0
0
0
2
0
1
1
2
1
1
1
1
1
1
1
0
1
1
0
0
0
1
0
2
0
1
1
0
1
2
0
0
0
1
2
1
1
1
0
1
1
1
0
1
0
0
1
0
1
1
2
1
0
0
1
2
0
1
3
2
1
1
2
0
0
0
0
1
1
0
1
1
1
2
1
1
1
0
0
1
2
0
2
1
0
1
0
0
2
0
2
1
2
0
3
1
0
2
1
2
1
0
1
0
0
1
2
0
1
1
1
2
0
1
0
2
1
2
1
0
0
2
2
0
1
1
1
1
1
0
1
1
1
1
0
1
1
0
1
0
0
2
0
2
1
2
1
1
2
2
1
0
0
1
1
2
0
0
1
1
2
0
0
3
2
1
1
0
1
0
1
1
1
1
1
1
0
0
0
2
0
1
0
2
0
2
2
0
1
1
0
0
3
1
2
2
3
1
1
0
1
2
1
1
1
1
0
1
0
1
1
1
0
2
0
0
1
1
1
1
2
0
2
0
1
3
2
2
2
0
1
1
0
2
1
0
0
2
1
0
1
0
0
0
0
1
0
0
1
0
1
0
1
0
0
1
1
2
0
1
1
0
1
2
2
1
1
2
2
1
1
1
2
1
0
1
0
1
2
0
1
2
1
1
1
2
2
1
0
1
1
2
1
0
1
2
0
1
1
0
1
0
0
0
1
1
0
1
1
1
0
0
1
0
3
2
2
1
1
0
0
2
0
0
1
0
0
0
1
0
0
1
1
2
2
1
1
0
2
0
0
1
0
1
1
0
1
0
0
1
0
3
1
0
2
0
1
1
2
0
2
2
2
0
0
2
0
2
1
1
0
0
1
1
1
2
2
1
1
0
1
0
0
0
2
2
0
1
1
0
1
0
0
1
2
1
1
0
0
1
1
2
1
2
2
1
1
0
1
2
0
1
1
0
0
1
0
0
1
2
2
0
1
1
0
1
0
2
2
2
1
2
1
0
0
1
2
0
1
2
1
0
1
1
1
1
1
2
1
1
0
1
1
0
0
1
1
1
0
1
0
2
1
0
2
1
1
2
0
1
2
2
1
0
2
2
1
2
1
0
1
1
1
0
1
0
0
1
3
0
1
0
1
1
0
0
1
0
2
1
1
2
2
0
1
2
1
0
0
0
1
2
0
1
0
1
0
1
2
2
1
0
0
1
1
0
1
1
1
0
1
1
0
0
2
2
2
0
2
2
2
0
0
2
1
4
2
1
1
0
1
1
1
2
0
0
1
0
0
0
0
1
0
1
2
2
0
1
1
1
1
2
1
1
1
1
0
0
1
1
2
0
1
0
1
0
2
1
2
1
2
1
0
2
0
0
2
2
1
0
1
0
1
1
2
0
1
0
0
0
0
1
2
1
1
0
1
0
2
2
2
0
1
1
0
1
2
0
0
0
1
1
1
1
1
1
0
1
2
0
0
1
1
1
0
2
1
0
1
0
2
1
1
0
2
0
0
2
2
2
1
1
1
0
2
2
1
1
0
0
1
1
0
1
2
1
1
1
1
1
1
1
0
2
1
1
0
1
0
2
1
0
0
1
1
1
0
1
1
0
1
1
1
0
2
0
2
2
2
2
1
2
2
1
1
2
1
0
0
2
1
1
1
1
2
0
2
2
3
0
1
1
1
0
1
2
1
0
1
2
1
1
1
1
0
1
1
2
1
1
0
2
0
0
0
0
1
1
1
1
0
2
1
2
0
2
0
1
0
0
1
1
2
2
1
1
1
2
2
2
0
1
0
1
1
1
0
2
1
1
2
1
0
1
0
0
0
1
1
2
0
1
1
2
1
1
1
0
0
1
3
0
1
1
0
2
1
0
1
2
1
1
1
2
0
1
1
1
1
0
1
2
0
0
1
1
1
2
1
1
6
0
1
1
0
2
0
0
0
1
1
2
1
1
2
1
0
0
2
1
1
1
2
2
2
0
1
1
1
0
3
1
2
0
0
0
1
0
0
2
1
1
1
0
1
2
0
2
0
2
1
1
3
1
0
2
2
1
1
0
1
0
2
1
2
0
1
0
1
1
2
0
0
0
1
0
1
2
0
1
1
1
0
0
2
0
1
1
0
1
1
0
0
2
0
0
1
0
2
1
2
0
0
0
1
1
2
2
0
1
1
0
2
2
1
2
2
1
2
0
1
2
0
1
0
1
1
1
1
2
0
1
1
1
1
2
1
1
2
2
1
1
1
0
0
0
1
2
1
0
2
1
0
2
1
2
1
2
0
1
2
0
0
1
1
2
0
2
1
5
1
0
2
0
1
2
1
1
0
0
1
1
2
0
1
0
4
0
1
0
1
1
0
0
2
0
1
1
1
1
1
0
0
1
4
1
2
1
1
1
0
2
3
1
0
0
1
0
1
1
0
1
1
1
1
0
2
1
3
1
1
2
0
1
0
1
4
2
0
1
0
1
2
0
1
2
0
0
0
1
1
2
0
3
1
0
1
1
0
0
0
1
1
0
2
1
2
1
1
1
1
1
0
1
0
0
0
0
1
1
0
1
1
1
1
2
0
1
2
0
0
2
0
1
0
0
2
2
3
1
2
0
1
2
1
2
0
0
1
1
1
0
2
0
0
1
2
2
1
1
0
0
0
1
2
1
2
0
1
1
0
0
0
2
0
0
1
1
2
1
0
1
2
0
2
1
0
1
1
0
0
0
1
0
2
0
2
1
0
1
0
2
0
0
3
1
0
0
1
1
2
0
1
0
1
1
2
1
1
1
1
0
1
0
0
0
1
2
2
0
1
0
1
2
0
1
2
0
2
1
0
1
1
2
1
2
0
2
1
2
1
2
0
0
1
2
1
0
0
2
0
1
0
2
1
1
2
1
0
1
2
2
1
1
0
0
1
1
0
1
2
0
1
0
0
0
2
0
2
1
1
0
2
2
0
2
2
1
1
2
1
0
1
0
0
0
0
1
1
1
1
0
2
1
0
1
1
1
1
1
1
1
0
2
1
1
2
2
2
2
0
2
1
2
0
1
0
1
0
1
2
2
0
1
4
2
1
1
2
2
0
1
1
2
1
0
0
2
1
0
1
0
0
1
2
0
1
1
2
1
1
1
2
0
2
0
2
2
0
0
1
4
1
0
1
1
1
1
1
0
2
0
2
0
2
0
1
1
1
3
2
0
0
1
0
1
0
1
0
1
1
1
1
1
1
1
0
1
2
0
1
2
2
0
2
1
2
2
0
0
0
0
2
0
1
2
2
2
0
0
1
1
0
2
2
1
0
0
0
0
2
1
2
1
1
2
1
2
2
1
1
0
1
0
1
0
3
2
0
0
1
0
1
0
0
1
1
1
1
0
2
2
3
1
1
1
0
0
0
2
0
0
0
1
1
1
1
0
1
0
0
1
0
0
0
1
1
0
0
0
1
1
2
2
0
1
2
0
0
1
2
1
0
1
1
1
1
1
0
2
0
2
1
1
0
0
0
2
0
2
2
2
2
0
1
1
1
0
0
0
2
2
0
1
2
2
0
1
1
1
2
1
1
1
0
0
1
1
0
0
0
1
0
0
1
2
1
2
0
2
1
0
0
1
1
2
0
0
2
2
0
3
2
0
1
0
1
1
0
0
0
0
0
2
0
1
1
0
1
1
3
0
1
0
0
0
1
0
2
2
2
1
2
1
1
0
1
1
0
0
1
1
0
0
2
2
2
2
1
0
0
2
1
0
0
0
0
1
1
0
1
0
2
1
2
1
1
0
1
2
0
2
2
2
1
0
1
1
0
2
1
2
2
1
1
0
1
0
2
0
0
1
0
2
2
1
0
5
0
0
2
1
2
0
0
0
0
1
2
1
0
0
0
1
1
1
2
2
0
1
0
2
2
1
2
0
1
1
1
1
0
2
0
1
2
0
0
1
0
0
1
1
0
0
0
1
2
0
1
0
0
2
1
0
0
1
1
0
0
0
1
2
0
1
2
0
1
1
1
1
2
2
1
1
1
2
1
0
0
1
1
2
0
0
1
1
2
0
1
1
1
0
0
0
1
2
0
0
0
2
0
2
2
1
0
2
0
1
1
1
0
0
1
0
0
1
2
2
2
2
2
0
2
1
1
0
2
1
0
0
2
0
0
1
0
1
1
0
0
0
0
1
0
1
1
1
0
1
2
2
0
0
0
1
0
0
1
2
0
1
1
0
1
0
2
1
0
0
1
2
1
1
0
0
1
1
1
1
1
1
1
1
1
0
1
1
0
1
2
0
0
0
1
1
0
1
0
1
1
0
0
0
1
1
1
0
1
1
0
2
2
2
2
1
1
1
0
2
0
0
1
0
1
2
1
1
0
1
1
1
1
0
0
0
0
1
1
2
0
0
2
2
1
1
0
0
0
0
1
0
1
0
1
0
1
2
2
1
1
2
1
0
1
1
1
1
1
1
2
2
1
1
2
1
0
2
2
0
0
0
1
2
0
2
0
1
1
1
1
1
0
0
0
0
0
0
1
0
0
0
2
0
0
1
2
2
0
1
0
1
2
1
1
1
0
1
0
0
1
1
1
0
0
0
1
1
2
0
0
1
1
2
1
0
1
0
0
0
0
2
2
0
1
0
1
0
1
1
0
0
0
1
0
1
1
0
1
1
0
1
2
0
2
2
1
1
1
0
2
1
1
2
2
0
1
0
1
0
2
1
1
1
1
2
0
1
0
1
2
2
2
2
0
0
1
2
0
1
0
0
1
1
1
1
0
1
0
2
1
1
0
0
1
0
1
1
0
2
2
2
2
0
2
1
1
0
2
1
1
1
0
1
0
1
1
1
2
1
1
2
1
1
1
2
1
1
0
1
3
1
0
1
1
0
0
2
0
2
1
3
2
1
0
1
0
1
0
2
0
1
0
1
0
0
0
1
0
0
0
1
2
0
0
2
0
1
2
0
1
1
1
1
1
1
1
2
2
1
2
0
0
1
1
1
2
0
0
0
0
0
0
0
0
1
0
0
2
1
2
1
1
2
1
2
0
0
1
2
0
1
1
1
0
1
2
1
1
1
1
1
0
0
2
0
0
0
0
0
0
1
4
0
1
1
2
1
1
0
0
0
2
1
2
0
0
0
1
0
0
1
2
2
0
0
1
1
0
0
0
0
1
2
2
2
2
1
1
1
1
0
2
0
0
0
0
2
2
1
1
1
0
1
0
0
3
0
1
1
0
1
1
1
1
1
1
0
0
0
1
1
1
2
2
0
1
2
1
1
0
4
1
1
0
2
0
0
1
1
2
1
1
2
1
1
1
0
0
1
0
2
2
0
1
1
1
1
0
0
2
1
0
2
2
2
1
1
1
2
0
1
0
1
2
0
2
0
2
1
0
1
1
2
0
0
1
2
1
1
0
0
0
0
2
1
0
1
1
2
0
0
1
4
0
1
1
1
0
0
0
0
1
1
2
1
0
0
2
3
1
1
2
2
1
1
2
2
1
0
2
0
2
1
2
0
1
1
1
1
3
0
2
0
1
0
0
1
0
1
2
0
1
2
2
1
2
1
1
1
0
1
2
0
1
1
1
0
0
0
2
0
1
0
2
1
1
1
1
1
1
0
1
2
0
1
1
1
3
1
2
4
0
1
2
2
2
1
0
1
0
0
1
1
0
0
2
1
1
1
2
1
1
0
1
2
2
2
1
2
2
0
1
0
0
0
0
0
1
2
2
2
1
2
0
2
1
2
1
2
0
0
0
0
0
1
1
3
0
0
4
0
1
0
0
2
1
1
3
1
0
1
0
2
1
0
0
2
2
2
2
1
0
2
0
1
1
0
2
1
2
2
1
0
0
0
0
1
2
1
0
0
0
1
2
0
2
1
1
2
1
1
0
2
2
0
0
1
2
1
1
1
2
1
0
1
1
1
1
0
1
0
2
2
0
2
0
1
0
2
0
0
0
0
0
1
2
3
2
2
0
0
0
1
1
0
1
2
1
0
0
0
1
0
0
1
0
1
0
0
1
0
1
0
0
1
2
1
1
1
1
0
2
0
1
1
1
2
0
1
1
3
1
0
1
2
0
1
1
2
0
0
1
1
0
0
0
1
0
1
2
0
1
0
1
0
1
2
1
1
1
2
1
1
1
1
1
2
0
0
1
1
2
1
0
2
1
1
2
1
0
2
2
1
0
2
1
0
1
0
0
2
0
0
0
0
1
0
1
1
0
0
1
0
1
2
0
1
1
0
1
0
1
2
2
0
1
2
2
0
1
0
2
1
2
1
1
1
2
2
1
0
1
1
0
2
0
0
2
0
0
1
1
1
1
1
0
1
0
0
0
1
1
2
1
2
0
0
2
1
1
2
2
1
0
1
0
1
2
1
0
0
2
1
0
1
1
1
1
1
1
2
0
0
1
2
1
2
0
2
1
2
1
0
1
2
0
1
1
0
0
0
1
0
1
1
1
2
0
1
1
0
2
1
1
4
1
0
1
2
1
1
2
0
0
2
1
2
0
1
2
0
1
1
0
0
1
1
1
0
1
1
1
0
0
1
1
2
1
2
2
0
0
0
1
0
2
0
1
0
2
2
1
2
2
0
0
2
3
1
1
0
2
1
1
2
1
1
1
1
1
0
1
2
0
1
0
0
2
1
1
0
1
1
0
1
2
1
1
2
1
1
2
0
0
2
0
0
2
1
1
1
1
0
0
0
1
0
1
0
0
0
0
1
1
2
0
0
0
0
2
1
2
1
0
0
2
0
1
2
0
1
0
2
1
0
0
2
1
1
0
1
0
2
1
1
2
0
2
1
2
2
1
0
2
0
2
1
0
1
2
0
2
2
1
1
1
0
2
1
1
1
2
1
1
1
0
0
2
1
0
0
2
1
1
0
2
2
1
1
0
0
0
0
2
0
2
1
1
0
0
0
0
0
1
1
0
0
0
2
1
1
1
1
0
0
0
1
1
1
1
1
0
1
4
0
0
0
0
0
0
1
2
2
2
1
2
1
3
0
1
1
0
0
1
0
2
2
0
1
2
1
1
2
3
1
1
0
2
0
1
0
1
1
0
2
0
1
0
1
0
1
0
1
0
1
2
0
0
2
1
1
1
0
0
0
0
1
1
0
0
1
0
0
1
1
0
1
1
2
1
0
1
2
1
2
1
2
2
0
0
0
1
0
2
3
2
2
1
0
1
2
1
0
2
1
2
1
1
2
1
0
1
1
2
0
2
0
1
1
0
1
2
1
2
2
1
0
0
1
2
1
0
0
0
1
0
1
0
0
1
1
1
1
0
0
0
1
2
1
0
2
1
2
1
2
2
1
2
1
0
0
1
1
2
1
0
0
1
1
1
1
1
0
1
2
1
1
1
2
1
1
0
0
2
1
2
0
0
2
0
0
0
2
0
1
2
1
2
1
2
0
1
0
2
2
0
1
1
2
0
1
1
1
1
0
1
2
0
0
1
0
0
1
2
1
0
0
1
1
0
1
0
1
2
1
0
2
0
1
1
0
1
1
1
1
0
1
2
2
1
0
0
0
1
0
1
1
2
1
1
0
0
2
2
0
1
1
2
1
1
0
2
1
1
2
2
1
1
0
1
1
0
1
1
3
0
0
0
1
0
1
0
0
0
1
1
0
1
1
2
0
2
2
0
1
1
0
1
0
1
2
0
2
3
2
0
1
1
1
0
0
1
3
2
1
1
0
2
0
1
2
2
1
1
1
0
2
1
2
0
0
1
2
1
1
0
1
1
2
0
0
0
0
1
1
0
0
2
1
2
1
0
1
1
0
1
1
1
1
1
0
1
1
1
1
2
1
0
0
2
2
1
2
2
1
2
1
2
2
0
0
1
1
0
2
2
0
1
1
0
1
1
2
2
0
2
0
2
2
0
0
0
2
1
1
3
2
1
1
0
0
2
0
1
1
2
1
1
1
1
1
1
1
1
0
2
1
1
1
1
1
1
1
1
0
1
1
1
0
1
2
1
1
1
2
1
1
1
0
1
1
1
0
0
0
0
2
2
1
0
0
1
2
0
1
2
1
0
0
0
2
0
2
0
0
2
1
2
1
2
2
0
0
1
1
1
0
0
2
2
3
1
0
0
0
0
1
0
0
2
1
2
0
2
1
0
1
1
1
0
1
2
2
2
1
0
0
1
1
1
0
2
1
1
1
1
0
2
1
0
0
0
0
1
1
1
1
0
0
0
1
1
1
1
0
2
1
0
2
2
1
2
1
3
2
0
1
0
1
2
0
0
1
0
0
0
0
0
1
1
1
0
2
0
2
0
0
1
2
0
0
1
2
1
1
1
1
1
1
1
2
2
1
2
0
1
1
0
1
1
1
2
1
1
0
0
2
0
0
0
2
1
1
0
2
0
0
0
2
0
1
2
2
1
0
2
2
2
0
1
0
0
0
0
0
1
0
1
1
1
2
0
0
0
1
1
0
0
0
2
0
1
2
3
1
2
1
1
2
2
1
0
2
0
1
1
2
1
2
0
1
1
1
0
2
2
0
2
2
1
1
1
2
1
0
1
2
0
0
0
0
0
1
1
1
0
1
1
0
1
1
0
0
1
1
1
2
2
0
2
0
2
1
1
2
1
0
0
0
1
1
0
2
2
1
2
0
0
0
1
0
2
0
2
0
1
1
1
1
2
3
1
0
1
1
0
0
1
0
2
0
0
2
1
1
0
0
0
2
0
2
2
0
1
2
1
0
0
1
2
1
0
2
0
0
2
1
1
1
2
2
1
1
0
0
1
0
2
0
1
1
1
2
0
2
2
0
1
2
0
0
1
2
2
1
2
0
0
0
0
1
0
1
1
2
2
0
0
1
1
1
1
1
1
0
2
1
0
0
0
0
1
2
1
1
0
1
1
0
1
0
0
0
0
2
1
1
0
0
1
0
0
1
2
1
1
0
1
1
0
0
2
0
0
0
0
1
0
0
1
0
0
1
0
1
0
1
1
1
1
1
2
1
1
1
0
1
2
1
1
1
1
0
0
1
1
1
1
0
0
1
1
1
1
0
0
1
1
1
1
1
0
0
1
1
0
0
2
0
1
0
1
1
0
1
1
0
0
1
2
0
4
1
0
0
2
1
0
1
0
1
0
0
0
1
1
0
2
1
0
1
0
1
0
0
1
2
2
2
2
1
1
1
1
0
1
0
4
1
0
0
1
0
1
2
1
3
1
2
1
1
1
2
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
1
2
0
0
1
0
1
2
0
2
1
1
2
2
0
2
1
1
1
0
0
2
2
1
1
0
2
1
0
1
2
1
1
1
0
1
1
1
1
1
1
1
1
1
2
0
0
1
1
0
1
0
1
1
1
0
1
0
0
0
1
1
0
1
0
0
1
1
0
2
1
0
0
3
1
0
0
0
0
0
0
3
1
0
0
1
1
2
2
2
2
1
0
1
0
2
1
2
0
1
1
2
1
0
3
0
2
0
1
0
1
2
1
0
1
1
0
1
1
0
1
1
1
2
0
1
1
1
3
1
4
1
2
0
1
1
1
1
0
1
0
0
1
0
1
0
1
1
1
1
2
2
2
1
1
1
1
0
0
0
2
0
1
1
0
3
0
2
0
1
1
0
0
0
2
1
1
0
0
0
1
1
1
1
1
1
1
2
1
2
0
0
1
1
0
1
1
1
1
2
0
1
1
2
1
2
0
0
1
2
1
1
0
2
1
1
1
1
1
1
0
0
2
2
2
1
2
1
0
1
1
1
0
0
0
1
1
2
2
2
2
1
1
1
1
1
0
1
1
1
1
1
0
1
4
2
0
1
0
1
2
1
0
0
2
1
1
0
1
1
0
2
1
0
2
2
0
2
2
1
0
2
0
1
0
1
1
2
1
1
2
1
0
0
2
1
2
0
2
1
0
0
1
0
0
0
0
0
2
0
2
1
2
1
2
0
0
0
1
0
2
0
1
1
1
2
1
1
0
1
1
1
0
1
0
1
0
2
0
1
1
1
0
1
1
1
0
0
0
0
2
1
2
1
0
2
2
1
2
0
0
1
1
1
0
1
2
0
2
0
1
2
1
0
1
0
0
0
0
0
1
0
1
1
0
0
0
2
1
2
1
0
0
0
0
1
0
1
2
1
0
0
1
1
1
2
1
1
0
2
0
2
0
1
2
1
2
2
2
1
2
2
1
2
1
2
1
2
2
2
5
2
1
0
0
2
1
0
3
2
2
1
0
1
1
0
2
0
0
0
0
0
1
1
0
1
1
2
0
1
2
1
0
0
0
0
3
1
1
0
1
1
0
0
1
1
1
2
0
0
1
1
0
2
0
1
0
2
2
1
0
1
1
0
0
1
0
0
1
0
2
1
0
0
0
1
1
1
0
0
1
2
0
1
1
1
1
0
2
0
0
0
2
0
2
2
1
2
1
3
2
2
0
0
2
1
1
1
1
1
1
1
2
1
1
2
0
1
1
0
1
1
1
1
1
0
2
0
2
0
1
1
0
2
0
0
0
0
1
1
2
1
1
0
2
0
1
1
1
1
0
1
2
1
1
1
0
1
2
0
1
1
1
1
1
2
1
0
0
1
0
1
1
1
2
2
1
0
0
1
1
0
0
0
1
1
2
0
1
0
2
0
2
1
1
1
2
2
0
1
1
0
1
0
1
0
2
0
0
2
1
2
1
0
0
0
0
0
1
1
0
3
2
2
1
1
0
1
0
1
2
3
0
2
1
0
2
1
2
0
1
0
1
2
1
2
1
0
2
1
1
5
0
0
1
2
2
2
1
2
0
2
1
2
2
2
2
0
0
0
1
0
2
1
1
2
1
0
1
0
2
0
0
1
1
1
0
0
1
2
2
2
2
1
1
1
1
1
1
1
1
0
0
0
0
2
2
2
1
1
1
0
0
0
0
0
2
2
1
1
1
1
1
0
1
0
0
1
2
0
0
0
2
1
2
1
1
3
0
0
2
2
2
1
2
2
2
1
1
0
1
0
0
0
0
2
1
2
1
2
0
0
1
1
1
0
1
0
0
1
0
3
0
0
1
2
2
1
1
1
0
0
1
1
2
0
2
1
2
0
1
1
0
1
0
1
0
1
1
0
0
2
0
1
2
0
2
0
1
0
2
1
1
2
2
0
0
1
1
2
1
0
1
1
1
0
2
0
2
1
1
0
0
0
1
2
3
2
2
0
0
1
1
2
0
0
1
2
1
2
1
1
0
0
2
1
0
1
0
1
1
0
1
2
1
1
2
1
1
1
0
1
0
1
0
0
0
0
1
1
1
4
1
0
2
2
2
1
0
2
1
1
1
1
2
0
1
1
0
0
1
0
2
1
0
1
1
1
0
1
0
2
0
0
0
1
0
1
1
0
2
1
0
1
0
2
3
1
1
2
0
0
0
1
2
1
1
0
1
0
0
1
0
1
0
1
0
1
2
1
1
2
1
3
2
1
0
0
1
0
1
0
2
0
2
0
0
0
1
1
1
1
0
1
1
2
1
0
2
0
1
2
2
1
2
11
1
0
0
0
0
0
0
0
1
0
1
1
1
1
1
1
1
1
0
2
1
0
0
1
0
2
2
2
0
0
1
2
2
2
0
2
0
0
1
2
0
0
0
1
1
2
0
0
0
0
2
0
0
1
1
3
1
1
0
0
1
0
1
0
2
1
1
0
1
1
2
2
2
1
2
0
0
2
0
2
1
1
1
1
0
1
0
0
1
1
1
1
1
0
0
0
2
1
1
0
2
1
1
2
1
1
1
1
1
2
2
2
0
1
0
1
1
0
0
0
1
1
1
1
0
2
1
1
0
1
1
0
0
2
0
1
2
0
1
1
0
1
0
1
0
0
1
2
1
2
1
0
1
1
2
1
1
2
1
1
2
1
0
1
1
1
0
0
0
1
0
2
1
1
1
0
1
0
1
0
0
2
1
2
0
0
2
2
1
2
2
1
0
0
1
1
1
0
1
8
0
0
0
1
0
0
0
1
2
1
0
0
1
1
1
0
0
0
1
0
0
2
1
1
1
2
2
1
0
0
1
1
2
1
1
1
1
0
1
1
2
1
0
0
1
0
1
1
2
1
0
1
2
1
2
1
0
1
0
2
1
1
1
1
1
1
1
1
0
2
0
0
0
2
0
1
3
1
2
0
2
0
1
0
1
1
2
0
2
1
2
0
1
1
1
1
2
0
1
1
1
2
1
1
1
2
1
0
1
2
0
1
0
2
1
1
0
2
1
1
1
1
2
1
1
0
0
1
2
1
2
2
1
0
1
1
1
0
0
1
1
2
0
1
1
2
0
0
2
1
3
1
0
0
2
1
0
1
1
0
2
0
2
2
1
0
0
2
1
0
1
1
2
2
1
1
1
1
0
1
2
1
0
2
1
2
1
2
0
1
1
0
0
2
2
2
1
2
1
1
0
0
1
1
1
2
0
1
1
0
2
0
2
0
2
1
1
1
0
1
3
1
0
2
1
1
1
1
0
1
2
1
1
0
4
0
0
1
1
0
1
2
0
1
1
1
0
1
1
2
1
1
1
1
1
1
1
0
1
0
1
0
2
1
0
0
1
2
2
2
0
1
1
2
2
1
0
1
0
2
1
0
2
1
1
1
3
2
1
2
2
1
1
2
1
3
2
0
3
1
1
0
1
0
2
1
0
1
1
2
1
2
0
2
1
1
0
1
2
0
2
0
2
0
1
1
1
0
0
0
2
1
1
0
2
1
0
1
1
0
2
1
1
0
0
1
2
2
1
0
0
1
1
1
1
1
1
1
0
1
0
1
2
1
0
2
1
1
2
0
1
1
1
0
1
1
0
2
0
0
0
1
2
1
1
2
1
0
1
1
1
1
1
2
0
2
0
2
2
1
0
1
1
0
0
0
1
2
2
1
2
1
2
1
0
1
1
2
0
1
2
0
2
1
1
0
1
1
0
2
2
1
3
2
0
0
1
1
1
0
0
0
0
2
0
0
2
0
2
1
1
1
2
1
0
1
2
2
2
0
0
0
2
1
1
1
0
1
1
1
1
0
2
1
1
1
1
3
1
2
2
1
1
2
2
0
2
0
0
0
1
1
1
1
1
0
0
2
1
1
1
3
1
1
0
1
0
3
1
0
1
0
2
0
0
0
1
0
0
1
2
1
1
1
0
1
2
1
0
0
1
0
0
1
2
0
0
1
2
2
0
2
1
1
1
1
1
1
1
0
1
1
1
2
1
1
2
1
2
0
1
1
2
0
2
1
1
2
1
0
2
1
1
0
0
0
1
2
1
2
1
2
0
0
2
1
0
0
1
2
0
2
1
1
1
0
0
1
1
1
2
2
0
1
2
0
0
1
1
1
2
2
1
0
0
1
0
0
2
1
2
0
1
2
1
2
0
1
1
3
1
2
0
0
2
1
1
0
1
2
1
1
1
0
4
2
1
1
2
1
0
0
1
1
0
0
0
0
0
0
2
2
0
1
2
3
2
1
1
1
1
1
2
0
1
0
0
1
1
0
0
1
3
1
2
1
1
0
1
0
0
1
0
1
0
1
0
2
0
0
0
0
0
2
0
2
2
0
0
2
1
1
2
0
1
2
1
1
1
2
2
1
0
1
0
1
1
2
1
0
0
1
2
1
0
2
1
2
2
0
2
1
1
2
1
1
2
0
0
0
1
1
1
2
2
1
1
1
1
0
1
1
1
1
2
2
1
0
1
0
2
0
2
0
1
1
1
1
0
1
0
0
2
0
1
1
2
2
0
1
2
2
1
2
1
2
1
2
1
0
1
0
2
1
1
1
1
1
1
2
1
2
1
1
0
1
5
1
0
2
0
2
0
0
0
1
2
3
2
1
1
1
1
1
1
0
1
0
0
1
1
0
2
1
1
1
0
1
0
1
1
0
2
1
2
0
2
1
1
0
0
3
1
0
2
1
0
1
1
0
1
0
2
1
1
2
1
2
0
1
0
0
0
2
1
1
0
2
1
0
0
2
0
0
0
1
0
1
1
0
1
0
1
0
1
0
0
1
1
2
0
2
2
2
2
2
0
2
2
2
1
0
1
2
1
0
2
2
1
2
2
1
1
2
0
1
1
1
2
1
0
1
1
1
1
0
1
0
1
2
2
1
1
1
2
0
1
1
2
2
1
2
2
2
1
1
1
0
2
0
2
0
1
0
1
1
1
0
1
1
1
2
0
2
0
2
2
2
1
0
0
1
0
0
1
2
1
0
1
0
0
2
0
1
0
0
1
0
1
0
1
0
1
1
1
0
0
0
2
2
2
1
0
2
1
1
2
0
0
2
2
0
2
2
1
1
0
2
0
0
2
0
1
0
1
0
0
1
0
0
1
1
2
2
1
1
2
1
1
2
0
0
1
2
0
2
1
1
1
1
0
1
2
0
2
2
1
1
0
0
1
0
1
1
1
1
1
0
1
0
1
2
2
1
0
1
1
0
0
2
1
0
1
0
3
0
2
2
1
2
0
1
1
1
2
0
1
1
1
1
0
1
0
1
1
2
0
1
1
1
1
0
2
0
1
0
2
2
1
0
0
1
2
1
1
0
1
0
0
2
0
1
0
2
3
0
0
0
0
1
2
0
1
0
1
0
1
0
0
1
2
0
2
1
0
0
0
0
0
1
0
0
2
2
0
0
2
1
1
1
1
0
1
1
1
2
1
0
1
1
1
1
1
1
1
1
1
1
2
0
0
1
2
0
2
1
0
0
3
0
1
1
0
0
0
2
0
1
1
4
0
1
1
2
2
2
0
1
2
1
0
0
1
0
0
0
0
1
1
1
1
2
3
2
3
1
1
2
2
0
2
1
0
0
1
0
0
1
1
2
1
1
1
0
0
0
0
1
1
0
0
1
2
2
0
1
1
0
2
2
1
1
0
1
2
0
2
0
0
1
1
1
0
1
0
1
1
1
1
2
0
2
1
1
0
1
1
0
2
1
0
0
2
0
1
0
0
2
0
1
2
2
0
2
2
2
2
1
0
1
0
0
0
1
1
1
0
2
1
0
1
0
3
1
1
0
1
1
0
0
0
1
1
1
1
1
0
0
0
0
0
2
2
0
0
1
0
0
1
0
0
1
0
0
1
1
0
0
2
1
0
1
0
1
1
2
0
1
0
2
1
2
0
0
1
0
0
0
2
1
0
0
2
2
0
1
1
1
0
2
0
1
0
1
1
1
1
2
0
0
1
1
2
1
1
1
1
0
0
1
1
1
0
1
5
0
0
1
0
1
0
2
0
1
2
2
1
1
1
1
0
0
1
1
3
1
1
0
1
0
0
1
0
0
1
0
1
1
1
0
2
0
2
2
1
0
0
1
0
1
0
2
1
0
1
1
1
1
1
0
0
0
2
2
1
0
0
1
1
2
1
2
1
1
1
2
1
0
2
1
1
2
2
2
2
0
2
1
1
0
1
1
0
2
1
0
0
1
1
0
1
0
0
0
1
0
1
1
0
1
3
0
1
1
0
1
0
0
0
2
1
1
0
1
2
0
0
2
1
1
4
2
0
2
1
1
1
1
0
1
0
1
3
3
2
1
2
1
2
0
1
2
3
0
0
1
0
1
1
1
0
1
0
1
0
0
1
1
1
0
0
1
1
0
1
2
0
0
1
0
1
1
1
1
0
1
0
0
1
0
1
1
2
3
0
2
2
1
0
2
2
1
0
1
1
2
0
0
1
1
1
2
2
2
1
0
1
2
2
0
2
0
1
1
1
3
3
1
2
1
1
0
1
0
1
1
2
1
1
1
0
0
0
1
2
0
1
0
1
1
1
1
0
2
2
1
0
1
1
0
1
2
1
1
1
0
3
0
0
1
0
3
0
1
0
0
1
0
1
1
0
0
0
1
2
0
1
1
1
0
0
1
1
1
0
0
2
1
0
1
2
2
0
2
0
1
1
0
0
1
1
0
0
0
0
2
2
0
1
2
0
0
2
0
1
0
1
1
0
0
1
1
0
1
0
2
0
1
0
1
0
1
2
2
0
1
1
2
0
3
1
0
2
1
0
0
1
0
0
2
1
0
2
1
1
1
0
1
2
0
1
0
1
1
2
0
0
2
2
0
1
2
1
0
2
1
1
0
0
1
1
0
1
1
2
1
1
0
0
0
0
0
2
0
1
0
3
0
2
0
0
1
1
1
0
1
1
1
1
1
1
2
1
0
1
1
1
2
0
1
0
0
0
0
2
1
1
0
1
0
1
1
0
1
2
1
2
0
0
2
0
1
1
2
1
1
2
0
1
0
1
0
1
2
0
0
0
2
0
0
1
0
1
1
0
0
0
0
1
1
1
1
2
2
2
2
2
2
1
0
2
0
2
0
2
2
1
2
1
0
0
1
2
0
1
0
0
2
2
0
1
1
1
0
1
1
1
1
2
1
0
0
2
1
0
1
2
0
1
2
0
1
1
5
2
0
1
0
0
1
1
1
1
2
1
0
0
2
2
1
1
1
0
1
2
0
0
0
1
1
0
2
1
0
0
1
2
0
1
0
2
0
3
1
1
1
0
2
1
1
1
3
0
0
0
1
2
1
1
2
1
0
1
1
2
1
0
1
2
1
0
1
0
0
2
1
1
1
2
1
2
1
1
0
0
1
0
2
2
1
2
0
2
0
0
0
1
1
1
3
2
0
2
1
0
1
2
0
0
1
1
0
1
0
1
1
0
0
2
0
1
1
1
0
1
2
1
1
0
2
1
0
1
2
2
1
0
1
1
0
2
1
1
0
1
1
2
1
1
1
0
0
2
2
0
1
1
0
0
0
1
1
0
1
1
0
0
0
0
1
0
1
1
1
0
1
1
1
2
0
1
1
0
0
0
1
1
2
0
1
1
2
1
1
1
2
1
2
2
0
0
1
2
2
2
2
0
0
1
1
1
0
0
1
2
1
1
0
1
2
0
1
2
0
2
2
2
2
0
1
0
1
2
2
2
1
2
0
0
3
0
2
1
1
1
2
0
0
1
1
0
1
0
2
1
0
2
0
2
2
0
1
1
1
1
2
0
2
0
0
2
0
2
0
0
1
0
1
2
0
2
2
0
0
1
2
0
1
0
0
0
0
0
0
2
0
0
2
1
0
0
2
0
1
0
0
1
1
2
1
2
1
1
2
0
1
1
2
0
1
1
2
0
0
1
2
0
1
0
0
0
1
1
1
0
1
1
2
0
2
0
1
1
1
0
0
1
0
0
0
2
1
0
4
0
2
1
2
0
2
1
1
2
0
2
2
1
1
0
2
0
0
0
1
1
1
2
1
1
3
0
1
0
0
0
0
0
1
1
1
1
1
2
0
1
2
1
1
2
1
0
1
1
0
0
0
0
1
1
1
1
1
1
0
0
0
1
2
1
1
1
2
2
1
2
0
1
0
0
2
1
1
0
0
0
0
2
1
0
2
1
0
0
2
1
2
1
2
1
0
0
1
1
1
0
1
2
1
0
1
2
0
2
2
0
2
2
2
1
3
1
1
2
1
1
0
2
0
0
1
2
1
2
1
2
0
1
2
1
1
1
0
1
1
0
0
2
0
0
1
0
0
1
0
2
0
0
2
2
0
0
1
2
0
0
0
0
1
0
2
1
0
1
1
1
1
1
0
2
2
0
2
0
2
0
2
1
1
1
2
2
1
2
2
3
1
1
1
1
1
1
0
0
2
1
0
0
0
2
3
1
1
0
1
1
0
0
0
2
1
2
1
2
2
1
2
0
2
1
0
0
2
1
0
1
1
2
5
0
1
1
1
1
0
0
1
2
4
0
0
2
1
1
1
1
0
0
1
1
0
1
1
1
1
1
1
1
1
1
0
2
1
2
1
1
1
0
1
1
1
0
0
1
1
1
1
1
0
2
1
1
0
2
1
1
2
1
1
1
0
0
1
1
1
1
1
0
1
1
1
1
1
2
0
2
0
1
1
0
1
1
0
1
1
0
1
2
0
2
1
1
1
2
2
2
1
2
1
1
1
2
2
3
1
2
1
1
0
1
1
1
1
1
1
0
2
0
2
0
1
1
1
0
0
2
1
0
2
2
0
2
0
0
1
1
0
0
1
1
2
2
1
1
1
1
1
0
2
0
1
2
2
1
0
0
1
0
0
1
0
2
1
1
0
2
2
0
1
0
0
2
1
2
3
0
1
0
2
1
1
0
0
1
0
2
2
1
1
0
0
0
1
1
1
0
0
0
2
0
0
0
2
1
2
1
0
2
1
0
2
1
0
1
1
2
2
2
0
1
1
2
0
2
0
1
0
2
1
1
1
2
1
0
1
1
2
2
0
0
1
1
0
2
0
2
1
0
0
0
1
1
0
3
1
1
1
1
2
3
0
1
3
1
2
2
2
1
1
2
0
0
0
2
1
1
1
2
1
0
1
0
1
1
0
0
0
1
0
2
2
1
1
2
1
2
1
1
1
0
1
2
2
0
1
2
0
0
0
2
0
0
2
2
1
2
2
3
4
0
2
0
1
1
2
1
0
0
2
2
1
0
0
0
0
0
1
1
2
2
2
1
1
0
0
1
0
1
0
2
2
1
1
1
1
1
0
0
0
0
0
1
1
0
0
0
1
2
1
0
1
0
1
1
0
2
0
2
2
0
1
0
2
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
2
1
1
0
1
2
1
1
2
1
2
1
2
0
0
1
0
2
2
0
1
0
1
0
1
0
2
2
0
1
0
1
1
1
1
1
0
0
0
1
0
1
0
1
1
2
1
2
0
0
2
1
1
0
1
1
2
2
1
3
0
1
1
0
1
0
1
0
0
0
2
2
0
1
1
1
2
0
2
0
0
0
0
1
1
1
0
0
1
0
4
0
1
1
0
0
1
0
2
0
2
0
0
2
0
1
2
0
0
1
2
1
1
2
2
0
0
0
1
1
0
1
0
1
2
1
1
0
0
1
0
2
1
1
1
2
1
1
1
0
1
1
2
2
1
2
2
2
1
0
0
1
3
1
2
0
1
2
0
0
1
1
1
0
2
1
0
1
1
1
2
0
0
0
2
2
0
1
1
2
2
2
1
2
2
0
0
2
2
2
1
1
2
1
1
1
1
0
0
0
1
2
2
2
1
0
0
1
1
1
0
3
2
1
0
1
2
1
0
1
2
0
1
1
0
1
2
2
2
1
2
1
1
0
0
0
0
1
0
1
0
1
1
1
0
0
1
0
2
0
1
1
2
1
1
1
1
1
0
1
2
1
0
2
1
1
2
2
1
0
2
1
0
1
1
1
2
2
2
0
3
0
1
2
0
0
1
0
0
0
2
2
1
0
0
0
1
2
0
1
0
1
1
0
1
1
1
0
0
0
0
1
1
2
0
1
1
0
1
0
1
0
0
2
0
1
0
1
1
1
1
1
0
0
2
0
1
1
0
1
0
0
0
2
1
2
2
1
0
1
1
0
1
1
1
1
2
0
1
1
0
0
2
2
0
0
1
1
0
3
2
1
1
1
2
0
1
2
2
2
1
0
3
1
3
1
1
1
0
1
1
0
0
0
2
2
0
0
2
1
1
0
1
0
1
1
0
0
2
0
3
2
2
0
0
0
1
1
2
1
0
2
1
2
0
1
1
0
1
1
1
1
1
2
0
1
1
1
1
1
1
2
1
1
0
1
2
0
2
1
0
0
1
1
1
1
1
0
1
0
2
1
0
1
1
0
2
1
0
0
0
0
0
1
2
1
1
2
0
2
1
1
2
2
0
2
1
2
1
0
0
1
0
1
1
1
1
1
1
1
1
0
3
2
2
0
1
1
1
1
1
0
0
0
2
0
2
2
1
1
1
0
0
0
0
0
0
2
0
0
0
2
1
1
0
2
1
0
0
0
1
1
1
0
1
1
1
2
2
0
1
0
1
1
2
1
1
1
0
2
1
1
0
0
0
1
1
1
1
2
1
1
2
2
1
0
0
0
1
1
0
2
2
2
1
2
1
0
2
2
2
2
0
2
1
2
1
1
2
1
1
1
1
2
1
0
2
1
1
0
1
1
0
1
0
1
0
5
1
1
1
2
0
0
2
0
1
1
0
2
0
1
0
2
0
0
0
0
1
2
1
0
0
1
1
0
0
0
0
1
0
2
2
1
1
1
2
1
2
1
2
2
2
2
0
1
2
2
0
2
2
0
2
1
0
1
0
1
1
0
2
1
0
0
2
2
1
2
0
1
2
1
0
2
1
2
1
1
0
1
1
1
1
1
1
2
2
1
0
0
0
2
0
1
1
1
1
1
1
2
1
1
1
1
2
0
0
0
0
2
1
1
1
0
0
0
2
1
1
1
0
1
0
1
0
1
2
3
0
1
0
1
0
0
1
0
1
0
1
0
1
0
2
1
0
0
0
0
2
2
0
2
2
0
2
1
0
1
2
1
1
0
0
1
1
1
0
2
0
1
2
0
1
2
0
1
0
1
0
1
0
1
0
1
1
1
0
2
2
1
1
1
2
2
0
2
1
0
9
0
2
0
0
0
1
1
1
1
1
0
2
0
1
1
2
0
1
1
1
2
0
2
2
1
2
2
1
2
2
1
2
0
2
2
0
1
1
2
2
0
2
0
2
2
1
2
1
3
2
1
2
0
0
0
1
2
2
1
1
0
0
2
0
1
0
1
1
0
0
1
0
0
2
1
3
2
1
2
2
2
1
0
1
2
1
0
0
1
2
2
1
2
1
2
1
1
2
1
0
1
0
2
0
1
1
0
2
1
2
1
2
1
0
2
2
2
0
2
0
2
1
1
3
0
0
1
1
1
0
1
1
17
0
1
1
0
1
2
1
1
1
1
2
0
1
1
1
2
0
0
2
2
1
2
1
1
2
3
1
1
0
1
1
2
1
1
1
1
1
2
1
0
1
1
0
0
0
2
0
2
2
0
0
2
2
1
2
1
0
1
1
1
0
1
1
1
0
1
2
0
0
1
1
0
1
1
2
0
1
2
1
0
0
1
1
2
1
2
1
0
1
1
0
1
0
2
1
1
0
1
2
2
1
0
0
1
1
2
0
1
1
1
1
2
1
1
2
1
0
3
1
0
2
1
0
1
1
2
0
0
0
0
2
1
2
2
0
2
2
0
2
0
1
1
0
1
1
1
1
1
1
1
0
1
1
0
1
0
0
2
1
0
0
1
0
2
2
2
0
0
2
1
1
1
1
1
1
0
2
1
1
1
2
1
0
1
1
1
2
0
0
1
2
1
1
1
1
0
0
0
1
0
2
2
1
0
1
0
1
0
2
2
0
2
1
0
1
1
1
2
0
0
1
1
1
0
1
0
2
2
0
2
0
1
2
2
1
1
0
1
1
0
1
1
1
1
0
0
0
0
0
1
1
2
2
0
1
0
0
2
1
2
1
0
0
1
2
0
1
2
0
1
1
0
0
0
0
1
0
2
0
0
0
1
0
2
1
0
1
2
1
1
1
1
2
0
0
1
2
0
1
1
0
2
1
1
0
0
1
1
1
1
2
1
2
1
3
1
0
1
1
1
0
2
2
1
1
4
2
1
1
0
4
0
1
1
0
1
2
1
1
2
0
0
1
1
1
0
2
1
1
1
3
0
2
2
0
1
0
0
1
0
3
2
1
1
1
1
0
1
1
3
1
1
1
2
1
0
0
1
1
1
1
0
1
1
0
1
0
1
2
2
1
1
1
1
0
0
0
2
2
0
1
1
0
1
0
2
0
2
2
1
2
1
0
1
0
0
0
1
1
1
1
1
1
1
1
1
1
2
1
1
1
1
1
0
0
2
0
0
0
1
0
1
2
0
0
0
2
1
2
1
1
0
0
0
1
0
0
0
1
1
0
1
0
1
2
0
0
2
0
1
1
1
4
1
2
1
1
1
0
1
2
1
1
1
2
0
0
2
2
0
0
1
1
1
1
0
1
1
2
2
0
0
1
1
0
1
0
0
2
2
0
0
0
2
2
1
1
1
0
0
0
0
1
2
0
1
0
0
1
2
0
1
2
0
1
2
0
1
1
0
1
2
1
1
0
1
2
0
0
1
0
1
0
1
2
1
1
0
0
2
1
2
1
0
1
0
1
2
2
1
1
1
2
0
1
0
1
1
0
2
1
2
1
2
2
0
2
1
1
2
0
1
3
0
0
4
0
0
1
0
1
1
2
2
1
1
1
2
0
2
0
0
1
0
1
3
0
0
2
1
0
1
0
0
2
1
0
1
0
1
1
1
1
0
2
2
0
1
2
2
0
0
2
0
1
1
1
0
0
0
2
1
2
1
0
0
1
0
0
1
1
0
1
3
1
2
0
0
2
0
1
2
0
3
1
2
0
1
2
1
0
0
0
0
0
2
0
1
1
0
2
0
1
2
1
0
1
0
1
1
1
2
0
0
1
0
1
0
2
2
1
2
2
2
0
1
1
1
0
0
0
0
2
2
2
0
2
1
1
0
0
0
0
1
1
0
0
0
1
1
0
1
1
1
2
2
0
3
1
0
0
1
0
13
1
1
2
0
1
2
2
1
2
5
0
0
1
1
1
0
2
0
2
0
0
2
2
0
0
3
2
1
0
0
1
2
1
0
1
1
3
0
2
0
1
0
1
0
1
1
1
2
1
0
0
0
1
0
0
1
1
0
0
1
0
2
0
2
1
2
1
2
1
0
1
2
0
1
1
2
0
1
1
1
1
0
0
2
1
0
0
2
0
2
1
1
1
0
2
1
1
2
2
4
1
2
1
0
1
2
0
1
1
1
0
2
1
3
1
1
1
1
1
1
1
1
0
2
2
2
1
0
2
0
0
2
2
1
1
2
1
1
1
1
1
0
1
1
0
0
2
2
0
1
2
2
0
0
0
1
0
0
0
1
1
1
0
1
0
0
1
1
2
1
1
1
1
1
1
0
1
1
1
0
2
2
1
0
0
1
1
1
1
1
0
0
0
2
1
0
0
0
0
0
1
0
0
1
0
1
0
0
2
1
0
1
0
1
0
1
1
1
2
2
2
0
1
1
2
2
1
2
0
0
1
0
2
1
0
1
2
1
1
0
0
2
1
0
0
1
1
1
1
1
1
2
0
2
0
0
0
0
2
2
0
6
0
1
0
1
1
1
2
0
1
1
1
2
1
3
1
1
2
0
0
0
0
2
1
1
0
1
1
1
2
1
0
2
1
1
0
1
0
2
1
1
1
1
0
1
1
2
1
0
2
1
0
0
3
1
1
0
1
2
1
1
1
1
1
0
1
1
2
1
0
2
0
1
1
0
2
1
0
2
0
1
1
2
1
2
1
1
0
0
0
0
1
2
0
1
1
5
1
0
0
0
2
1
1
0
2
2
1
2
0
0
1
0
2
0
1
2
1
2
0
1
0
1
1
0
0
0
0
2
0
1
0
0
2
0
0
1
1
1
0
1
0
0
0
1
0
0
2
0
2
1
0
1
2
1
1
2
1
0
0
1
0
0
2
2
0
1
0
0
2
0
0
0
1
0
2
2
1
1
2
0
0
0
1
2
0
0
2
0
2
0
1
0
0
0
0
1
2
0
1
2
2
0
0
1
1
1
0
1
0
0
0
2
2
0
0
1
1
0
0
1
2
1
2
2
0
2
2
1
1
1
1
0
0
1
3
1
0
1
1
1
0
2
1
2
0
2
2
2
0
1
0
2
1
1
1
0
2
0
2
0
0
1
1
1
0
1
0
0
0
0
0
1
2
1
2
2
1
1
0
1
0
1
1
1
1
2
1
0
2
2
0
0
1
1
0
1
1
2
0
1
0
2
0
0
0
1
1
1
2
1
0
1
0
1
2
0
0
1
1
1
3
1
1
2
2
1
1
0
1
1
0
2
0
0
0
1
1
2
1
2
0
1
1
2
0
2
0
1
0
0
0
1
0
1
2
1
1
2
3
0
1
2
1
3
1
1
2
0
2
0
0
1
1
0
2
0
0
1
1
1
0
2
2
2
1
0
0
0
1
0
0
0
0
1
1
0
2
1
2
2
0
2
4
2
0
1
1
2
1
0
0
1
0
1
0
0
1
1
1
2
1
0
0
0
0
2
0
0
0
0
0
1
3
0
1
1
0
2
2
1
1
1
1
1
1
0
0
1
1
0
0
1
2
2
2
2
0
2
0
2
1
1
1
2
2
0
2
1
1
2
0
2
0
0
1
1
0
0
0
2
1
0
1
1
1
0
0
2
0
2
1
1
1
0
2
1
0
2
2
0
0
0
1
2
2
0
1
1
2
1
0
1
0
2
1
1
2
0
2
0
0
1
0
0
0
0
1
2
1
1
1
0
1
0
0
0
0
1
0
0
0
1
2
1
0
1
0
0
2
1
1
0
0
0
2
0
2
0
0
0
1
0
1
0
1
2
0
1
1
1
1
1
1
1
1
1
1
1
2
1
0
0
2
1
0
0
0
2
0
1
1
2
2
0
1
1
1
2
0
2
0
0
2
0
0
1
0
1
1
1
0
1
0
0
1
0
1
2
0
1
1
2
1
1
1
2
2
0
0
2
0
2
0
1
1
0
2
0
0
1
1
0
0
1
0
1
0
2
2
0
2
0
1
0
0
2
0
0
2
0
2
2
1
1
0
2
2
0
1
1
0
1
0
1
0
1
1
1
1
2
0
1
0
1
0
0
1
1
0
4
0
0
0
0
2
1
1
2
1
2
1
1
0
0
0
1
0
0
1
2
1
0
1
1
1
1
1
0
1
2
2
1
0
2
2
0
2
2
1
1
2
1
2
1
1
1
1
2
2
1
2
0
0
0
2
0
0
2
1
1
1
1
1
0
2
0
0
0
1
0
1
2
1
0
2
0
0
0
0
0
0
1
2
1
2
4
2
1
1
1
0
1
0
1
1
2
2
2
1
2
1
0
1
2
0
0
1
2
2
1
1
2
0
2
1
0
1
2
0
1
2
2
2
1
1
2
0
0
0
2
2
0
2
0
2
1
1
0
2
0
0
0
1
1
2
1
0
1
1
1
2
0
0
0
2
1
2
0
0
1
0
2
1
0
2
1
2
0
1
0
1
2
1
2
0
2
0
1
1
2
0
1
1
2
1
0
1
1
2
1
0
0
0
0
2
1
1
1
1
1
1
2
1
0
0
2
0
0
1
1
0
0
0
0
3
1
0
1
0
0
0
0
0
0
1
0
0
0
2
0
2
0
2
0
3
2
2
2
2
0
0
0
1
2
0
0
0
2
1
1
1
1
0
1
0
0
0
1
0
2
0
1
2
2
0
1
1
0
0
1
1
1
2
0
1
1
1
0
0
1
0
0
0
1
1
0
0
2
0
2
0
1
1
0
0
2
1
2
0
1
0
1
2
1
1
2
0
1
0
0
0
0
1
2
1
1
0
0
0
1
1
1
0
2
0
1
1
1
2
0
0
2
2
1
1
2
0
0
1
1
0
0
2
0
1
1
1
0
1
0
0
1
0
1
1
1
0
0
1
1
0
0
1
1
2
0
0
2
1
1
1
0
2
0
1
2
1
1
0
1
2
1
0
1
2
1
2
1
1
1
1
0
1
1
2
0
0
1
1
1
2
2
0
1
1
1
1
0
0
2
1
0
1
2
0
1
1
2
0
2
2
2
1
1
1
0
0
2
0
2
0
0
1
0
0
2
1
1
0
0
2
0
2
2
1
1
1
3
0
2
1
1
1
1
1
0
0
0
1
1
1
2
1
2
0
1
0
1
1
1
1
1
0
0
2
0
0
2
1
2
2
1
2
2
1
0
1
2
1
1
1
1
1
1
2
0
2
0
0
2
2
1
1
0
1
1
1
2
2
1
1
0
2
1
2
2
1
2
1
1
0
0
0
2
1
1
1
0
2
1
1
0
2
2
2
2
2
2
1
1
0
0
1
0
1
1
1
1
0
0
1
1
1
0
1
1
0
1
0
1
2
2
0
0
1
2
0
0
1
2
1
1
1
0
0
0
0
1
2
1
1
1
2
1
2
1
2
1
0
0
2
1
0
0
1
1
2
1
2
1
1
2
0
0
0
0
1
1
0
0
2
1
0
1
2
1
1
1
2
1
1
0
1
0
0
1
0
0
1
1
1
1
2
2
0
1
2
2
1
1
1
2
0
1
1
1
0
0
0
0
2
1
2
0
2
5
1
0
0
1
0
1
1
0
1
1
1
1
3
2
0
0
2
0
0
1
1
1
0
0
0
0
4
1
0
0
1
0
1
1
0
0
1
1
1
2
2
0
0
2
1
1
0
2
2
0
3
2
0
1
1
2
1
0
0
2
1
1
0
1
0
0
1
2
2
3
1
0
0
2
1
1
1
2
1
0
1
1
1
1
0
2
1
0
1
0
1
1
1
0
0
0
2
1
1
0
1
0
2
1
1
1
3
2
0
2
0
0
1
1
0
0
0
1
0
2
1
0
0
1
2
0
0
2
2
2
1
1
1
1
1
0
0
2
1
0
1
1
0
0
0
1
0
0
1
1
4
2
2
0
1
0
0
1
1
2
1
0
1
1
1
1
1
0
1
1
2
1
1
2
0
3
0
2
2
0
2
0
0
2
1
0
1
0
2
1
1
1
0
1
2
1
0
1
1
0
0
1
2
0
1
1
1
2
1
2
0
0
0
0
0
2
2
0
2
2
2
0
2
2
2
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
1
0
1
1
1
1
2
1
1
1
0
1
0
1
0
2
0
0
2
1
0
0
1
1
0
0
2
1
1
1
0
0
2
1
1
0
0
0
2
0
2
0
0
2
1
1
1
2
0
1
2
1
0
0
0
1
0
0
1
0
2
1
1
1
7
0
1
2
1
1
2
1
1
0
1
1
3
1
0
1
0
1
1
1
1
2
0
1
2
0
1
0
0
0
2
1
0
1
0
1
0
1
1
0
1
0
1
1
0
1
2
0
0
0
0
1
2
2
2
2
0
0
2
2
1
0
1
1
0
2
0
2
1
1
0
1
2
0
1
1
1
2
1
0
0
2
1
1
2
1
1
1
2
1
2
2
3
1
2
1
0
0
1
0
1
1
0
1
0
2
2
0
1
0
1
2
1
0
2
0
0
1
1
1
0
1
0
1
1
1
1
0
0
1
0
1
0
1
2
1
2
0
2
0
1
1
1
2
0
2
1
2
2
0
0
1
2
2
2
1
2
1
0
2
0
1
2
1
1
2
0
1
0
1
2
0
2
0
1
0
1
1
1
1
3
2
0
2
1
2
0
1
1
2
1
1
0
0
0
0
0
2
2
0
1
0
0
0
0
2
0
2
3
2
0
1
2
0
1
1
0
1
0
0
1
1
2
0
1
0
1
1
2
1
0
0
0
1
1
1
1
2
1
0
0
2
1
1
2
1
1
1
0
0
2
1
2
2
0
0
2
0
1
2
1
2
0
1
0
2
0
2
1
1
1
0
1
0
1
2
2
0
2
1
2
2
2
1
0
1
1
0
2
1
2
1
0
1
0
1
1
0
1
0
2
0
2
1
1
2
1
0
1
0
1
1
1
1
2
1
0
0
0
1
0
0
1
1
0
1
0
1
1
2
1
2
2
2
0
2
1
0
2
1
0
1
1
2
2
2
1
2
0
1
1
1
0
1
3
0
0
0
0
0
3
2
1
1
1
0
0
0
0
0
0
1
1
1
1
1
1
0
2
1
1
0
2
0
1
0
0
0
1
2
3
1
2
0
0
1
0
0
4
1
0
1
0
0
1
1
2
0
1
0
0
1
0
0
2
2
0
1
0
1
1
0
1
1
1
1
0
1
0
1
1
0
2
2
1
1
1
1
1
2
1
1
1
0
1
1
2
3
1
0
1
1
1
1
1
1
2
1
0
1
1
1
1
0
1
2
0
0
0
0
0
1
0
1
2
1
2
1
0
1
0
1
0
0
0
0
1
1
1
1
2
1
1
1
1
0
2
2
0
1
1
1
0
1
0
1
1
0
1
0
1
1
1
1
1
2
1
2
2
0
0
2
0
1
0
1
0
0
2
1
1
2
0
0
2
1
1
0
2
2
2
3
2
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
2
2
1
2
0
0
0
0
8
2
0
0
2
0
0
3
0
0
0
1
0
2
0
0
2
2
0
0
1
0
2
1
0
1
1
0
1
0
1
2
1
1
0
1
1
0
0
1
1
0
0
0
2
1
2
0
0
1
1
1
0
0
1
1
1
0
1
1
0
0
1
1
1
1
0
2
1
0
1
1
0
1
1
1
1
2
0
1
1
0
2
1
2
1
0
2
1
2
1
1
0
0
1
0
0
1
2
1
1
0
0
1
1
0
1
0
2
0
0
1
1
1
1
2
0
2
2
1
2
0
2
0
1
1
0
0
2
1
1
0
1
0
1
2
1
0
1
0
2
0
1
0
1
1
1
2
0
1
2
2
2
1
0
1
1
3
1
2
1
0
1
2
2
2
1
2
1
0
1
0
1
1
2
1
1
1
1
0
1
2
0
1
0
2
1
1
0
1
0
1
0
0
2
1
2
1
0
3
1
1
2
2
1
2
2
2
3
2
1
1
0
2
0
0
1
0
2
0
2
0
1
1
1
0
4
1
1
1
0
1
1
2
1
0
1
2
1
0
0
0
1
1
1
3
1
2
0
2
0
1
0
0
2
1
1
0
0
2
1
1
0
2
0
0
0
0
0
1
1
0
2
0
1
1
1
1
2
2
1
1
1
1
1
2
0
1
1
2
0
1
2
1
1
2
2
1
2
0
0
1
2
1
2
1
2
0
0
0
1
0
1
2
0
0
2
1
3
0
1
1
3
1
1
0
1
2
2
1
1
0
1
0
2
0
1
2
0
0
1
1
2
0
1
0
1
2
1
1
0
1
1
1
0
2
1
1
0
1
0
0
1
0
0
2
2
1
1
0
1
1
1
1
1
2
3
2
1
0
0
0
0
1
1
0
1
1
1
2
0
0
0
2
1
0
2
0
0
1
1
1
1
1
1
2
1
1
2
1
1
2
2
1
2
1
0
0
2
2
2
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
1
0
2
0
1
2
1
1
0
1
1
2
1
1
2
0
1
1
0
4
1
1
1
0
1
2
0
1
2
0
0
1
1
0
2
2
1
1
1
0
2
2
0
0
0
1
1
1
1
3
0
1
1
1
0
1
1
1
0
0
2
1
1
2
2
2
0
1
1
2
2
0
1
0
0
1
0
1
2
1
2
0
2
1
0
2
0
2
0
0
1
1
1
0
2
0
2
1
1
0
1
2
2
0
0
1
0
2
0
1
1
0
1
1
1
0
1
0
0
1
0
1
1
1
2
1
1
1
1
2
2
1
1
1
1
1
1
1
1
2
1
0
0
1
0
0
1
0
1
1
1
1
0
0
0
0
2
0
1
0
1
2
1
0
0
1
2
1
1
1
0
2
0
0
0
2
1
2
1
0
0
2
0
2
1
1
0
1
2
1
2
0
0
1
0
0
1
2
2
2
1
0
0
2
4
1
1
2
0
0
1
1
2
0
1
1
2
3
1
2
0
1
0
2
2
1
1
0
1
1
0
0
2
2
0
0
0
2
0
2
1
0
0
1
1
0
0
0
0
0
1
1
1
0
1
0
1
1
2
2
1
1
2
1
2
1
1
1
0
0
1
1
2
0
1
1
0
0
3
1
0
1
2
1
2
1
1
1
1
0
1
1
3
0
1
0
1
1
0
0
2
1
1
1
2
3
0
1
1
1
0
0
1
2
0
1
2
1
2
2
1
0
1
1
1
2
1
0
1
1
0
2
1
2
2
0
1
2
2
1
0
1
0
1
0
0
1
2
2
0
2
0
0
0
1
0
5
0
0
0
1
1
1
2
1
2
1
2
0
2
2
2
2
1
0
0
0
0
0
1
0
1
1
0
1
1
1
1
0
1
1
1
0
2
3
2
1
1
1
0
0
1
2
2
0
1
2
0
1
1
1
0
1
1
1
1
2
1
1
1
1
1
0
0
1
2
2
0
0
2
0
1
1
1
1
0
2
2
1
0
1
1
3
2
1
0
1
0
2
2
2
1
1
1
1
2
0
0
1
1
0
1
0
1
1
1
2
2
1
0
2
1
2
1
0
0
2
1
2
1
1
1
0
0
0
1
0
1
1
2
2
2
0
1
0
1
1
1
1
3
0
2
0
2
0
1
2
2
1
2
1
2
1
1
1
1
0
0
1
0
0
0
1
2
1
1
0
0
3
0
2
0
1
1
0
1
0
2
2
1
2
2
1
0
0
0
1
0
0
0
1
0
0
1
1
1
4
0
1
1
0
1
0
2
1
0
0
2
1
1
1
1
1
0
0
2
1
1
0
2
0
0
0
0
0
0
1
1
0
1
1
1
0
0
0
0
1
0
0
1
2
2
1
1
1
0
1
2
0
1
1
0
3
2
2
1
2
0
1
1
0
1
1
2
0
0
1
1
1
0
2
0
1
0
2
0
1
0
0
0
0
2
1
0
0
0
0
1
0
1
1
1
0
0
2
1
2
0
0
2
1
0
3
1
1
2
0
1
1
1
1
0
0
0
1
0
2
1
0
1
1
0
1
1
1
1
0
1
1
1
1
1
2
0
0
2
3
0
1
1
1
1
1
0
1
2
0
1
1
0
0
1
0
1
2
2
1
1
1
0
1
0
1
1
2
1
1
1
1
2
1
0
0
2
2
0
0
0
1
0
0
0
0
1
0
0
1
2
1
0
0
2
1
0
1
1
1
0
0
0
0
0
2
1
1
0
1
0
0
2
1
0
1
1
1
1
1
0
0
0
1
2
0
2
0
2
1
2
0
1
1
2
1
2
0
2
0
2
1
0
2
2
0
2
0
0
7
2
0
1
1
1
0
0
1
0
1
2
2
1
1
1
0
1
1
1
1
0
2
1
2
1
2
5
2
0
1
3
2
1
2
1
1
3
1
0
0
2
0
1
1
0
3
1
1
2
1
1
0
0
1
0
0
1
1
1
1
1
1
0
1
2
1
1
1
2
0
2
3
1
1
1
0
0
1
0
2
1
0
1
0
1
3
2
1
0
1
0
1
2
1
1
0
2
2
2
1
1
1
0
1
2
2
1
1
1
1
2
2
1
2
1
2
0
1
1
1
1
1
2
2
1
0
2
1
0
1
1
0
0
0
2
0
1
0
1
2
2
2
2
0
0
1
1
0
1
0
1
1
1
1
1
0
2
2
0
2
1
1
0
1
1
0
1
0
1
1
2
0
0
0
0
2
1
1
1
2
1
0
0
2
0
0
1
1
1
1
0
1
0
1
3
0
1
0
1
0
1
0
1
1
0
1
0
1
2
0
1
1
1
0
0
0
1
2
0
2
1
1
0
1
2
1
0
2
1
0
2
5
2
1
1
0
1
1
2
0
2
0
0
1
1
1
0
0
0
0
1
0
1
0
2
2
0
2
1
1
2
1
1
0
2
1
2
2
1
0
1
0
1
0
1
0
0
0
0
0
1
0
0
2
1
0
1
1
1
2
0
0
2
1
1
1
0
2
2
1
1
1
1
2
0
1
2
1
0
2
2
0
2
0
1
2
1
1
2
0
0
2
0
0
0
1
1
2
2
1
1
1
1
1
1
2
4
1
0
0
4
2
2
2
1
1
0
1
1
1
2
1
1
2
0
1
0
0
0
2
1
0
1
1
1
1
0
2
1
1
0
1
2
1
0
0
0
2
2
0
1
2
0
1
1
2
0
0
0
1
0
0
1
1
0
1
0
1
1
2
0
1
0
1
0
1
3
0
1
0
1
0
0
1
0
5
1
1
0
2
0
0
2
0
2
0
0
1
1
1
1
1
1
0
2
1
1
1
1
0
1
0
1
1
3
0
1
3
1
1
0
1
2
1
1
0
0
1
2
1
0
2
0
2
2
1
1
2
1
1
0
1
0
1
1
1
1
1
0
0
2
0
0
2
1
1
0
1
2
0
0
1
1
0
0
1
2
1
1
1
2
0
2
2
1
2
0
0
1
0
2
1
0
0
0
1
3
2
1
2
1
1
2
2
1
2
1
0
1
0
2
0
2
1
1
1
2
2
0
1
1
0
0
1
1
0
1
1
0
0
2
0
0
0
2
2
1
1
0
2
2
1
1
2
0
0
1
1
2
1
0
1
2
0
1
0
1
0
1
0
2
0
1
1
1
1
1
0
2
1
1
1
1
0
1
1
0
1
0
0
0
0
1
2
0
1
2
0
1
1
0
0
1
2
0
0
0
2
0
1
1
0
0
1
0
2
0
1
1
3
0
2
1
1
1
0
0
0
2
2
2
2
1
1
0
2
1
0
0
3
2
0
1
1
1
1
2
1
2
0
2
2
2
2
1
1
2
0
0
2
1
2
2
2
2
1
0
0
2
2
1
0
2
0
1
1
0
2
1
1
0
1
1
0
1
0
1
1
1
0
0
0
2
2
1
0
0
2
1
0
1
1
0
0
1
1
0
1
2
0
0
1
2
2
1
2
0
0
1
1
0
0
0
0
1
0
1
1
0
0
1
0
3
1
0
3
1
0
2
1
1
2
1
0
1
0
1
0
0
2
1
0
0
1
1
0
1
1
0
0
1
1
1
0
1
0
2
0
1
1
1
0
1
1
2
0
0
0
1
2
0
0
1
0
1
1
0
2
0
3
0
0
0
2
2
2
1
0
2
1
1
0
0
1
0
1
2
1
2
1
2
1
0
1
0
1
2
2
1
1
1
1
2
1
0
1
1
0
1
1
2
1
0
0
1
2
2
1
0
2
1
0
0
0
0
1
1
1
0
1
1
0
1
1
0
1
1
1
0
0
3
0
1
0
2
4
1
1
2
1
2
2
2
2
2
2
2
0
1
0
0
0
1
1
1
1
2
2
0
1
0
2
1
1
1
1
0
1
1
0
2
1
0
2
2
1
1
0
1
0
0
2
2
3
1
0
2
1
2
1
2
1
1
1
0
0
1
2
0
1
1
1
0
1
2
1
0
0
1
1
1
2
2
0
1
2
2
0
1
0
1
0
0
1
2
2
2
1
0
0
0
1
0
0
0
0
1
1
0
2
0
2
0
0
1
0
0
1
0
0
0
1
0
2
0
2
2
0
1
0
1
1
1
0
1
0
1
2
1
0
0
0
1
0
1
2
1
2
1
0
2
1
1
0
1
2
0
1
2
1
1
0
2
1
1
2
1
1
1
1
2
1
0
1
1
2
2
1
1
0
1
0
1
1
0
0
0
1
2
1
0
0
1
0
0
1
2
1
1
0
0
0
2
0
2
1
0
0
1
1
0
0
1
1
2
1
0
0
1
0
1
1
0
1
1
2
2
0
0
0
2
1
1
0
0
0
1
1
1
3
0
0
1
2
0
0
1
1
0
2
2
0
0
1
1
2
1
0
0
2
1
1
0
1
1
0
0
0
0
0
2
2
0
1
1
0
1
1
1
1
1
0
1
1
1
1
0
3
1
0
0
1
0
0
2
1
1
0
2
0
1
2
0
1
0
0
0
1
0
0
1
1
1
0
1
1
1
2
1
0
1
0
0
0
0
2
0
0
1
0
0
0
0
1
0
2
1
0
2
0
1
0
2
0
0
2
1
0
0
0
0
1
0
2
2
0
2
1
1
0
0
1
2
1
2
1
1
1
0
0
1
0
0
0
0
3
2
1
1
1
0
2
1
0
0
1
1
1
1
1
0
1
1
3
0
1
2
1
2
2
2
1
1
2
0
0
0
1
0
1
1
0
2
1
2
0
0
1
2
2
0
0
1
3
1
2
0
2
4
2
1
0
2
2
1
1
2
2
0
1
0
0
1
2
2
1
0
0
0
0
2
1
1
0
1
0
1
1
2
1
0
1
1
0
1
1
1
0
0
0
0
1
2
2
0
0
1
1
2
1
0
0
1
0
2
0
0
2
0
1
1
0
1
2
1
1
2
0
0
1
1
0
0
0
0
0
4
1
2
1
2
1
1
0
0
1
0
2
2
0
1
0
0
1
2
1
0
1
0
1
1
2
1
0
1
2
1
0
2
0
0
1
2
1
1
0
1
1
0
1
2
2
1
2
1
0
1
2
1
0
1
1
1
1
1
1
0
1
2
1
2
0
1
1
0
1
2
2
1
0
1
2
2
1
1
0
1
0
1
0
2
1
0
1
1
1
2
0
0
0
1
2
0
2
1
1
2
1
1
0
1
0
1
0
1
0
2
1
1
1
2
1
0
1
1
0
0
1
1
0
1
2
0
1
1
0
1
1
1
1
0
0
0
1
2
0
0
1
0
1
1
1
1
2
0
0
1
1
0
2
0
0
0
2
0
0
1
0
4
1
1
0
0
2
0
1
2
2
0
0
1
2
0
0
1
1
0
2
2
1
2
1
1
1
0
1
0
1
1
0
0
0
1
0
1
1
1
0
1
2
1
3
1
1
1
0
0
1
0
0
1
1
1
2
1
0
0
2
1
1
0
2
2
1
1
1
0
0
1
1
0
1
0
1
2
1
0
1
0
2
2
2
1
1
2
2
1
1
1
2
1
1
1
1
1
2
2
1
1
0
0
0
3
1
1
2
1
0
1
1
1
1
1
1
2
2
1
0
2
2
1
1
1
0
1
1
0
0
2
2
1
1
1
1
2
2
0
0
1
2
1
0
2
1
0
0
0
0
5
1
0
1
0
1
1
0
1
0
2
0
1
0
0
0
2
0
1
0
0
1
0
0
1
1
2
1
2
0
0
1
2
1
0
1
2
0
3
1
0
0
0
0
1
1
1
0
1
0
0
1
1
0
1
0
1
1
1
2
0
0
1
0
1
0
0
0
0
3
0
1
0
0
2
2
1
1
1
1
1
2
1
0
0
0
3
0
1
1
0
0
1
2
1
1
0
0
0
0
0
2
1
0
1
1
1
2
2
1
1
2
1
1
1
0
2
1
1
0
1
1
0
2
1
0
1
1
0
0
1
1
1
0
0
2
1
0
1
0
1
0
3
1
1
1
1
1
1
1
2
0
0
1
0
0
2
0
1
1
1
2
1
0
1
0
1
0
0
1
1
1
1
2
1
1
2
0
1
2
4
0
1
0
0
0
0
1
2
0
0
3
2
2
1
1
0
1
2
1
1
2
0
0
1
0
1
0
2
1
2
0
0
0
2
1
1
0
1
1
0
0
0
1
0
1
2
2
1
0
2
0
1
1
2
0
0
3
0
1
1
0
1
1
1
0
1
1
2
1
2
1
1
1
0
2
2
2
2
1
0
2
1
1
1
0
0
1
1
2
0
1
2
2
1
1
0
1
1
2
1
0
0
0
1
1
2
1
1
0
0
1
1
1
1
0
1
1
2
0
0
1
1
0
2
0
1
4
0
2
3
0
0
1
0
0
2
0
0
0
1
0
0
0
2
1
0
0
1
1
0
1
1
0
1
1
0
0
2
1
0
1
1
1
1
2
2
2
1
0
2
0
1
2
0
1
1
0
1
1
1
2
1
2
0
1
1
0
0
0
1
1
2
2
1
1
1
1
0
1
2
2
2
0
1
1
1
1
0
1
0
0
2
1
0
0
2
1
2
2
0
1
1
0
1
1
0
0
1
0
1
1
1
1
0
0
0
1
0
1
0
1
0
1
2
0
1
0
0
1
0
0
1
1
0
1
1
1
1
0
1
3
0
2
0
0
1
0
0
1
2
2
5
1
0
0
0
1
1
0
0
1
1
0
1
3
1
2
1
1
2
1
2
1
1
0
0
2
0
1
2
1
1
1
4
0
2
0
1
1
0
0
2
2
1
2
1
1
1
2
1
2
2
1
1
0
2
1
0
1
1
1
0
0
2
0
1
2
1
1
0
0
2
1
1
2
1
1
1
1
1
1
0
2
0
1
0
1
2
0
1
1
1
0
1
1
0
1
2
0
1
1
0
1
0
0
0
1
1
1
2
2
1
0
1
0
1
2
2
0
1
1
1
0
1
0
2
1
1
2
0
2
1
2
1
1
1
0
2
2
1
0
1
2
0
2
1
2
1
0
2
0
1
1
2
0
2
2
2
1
0
2
0
0
1
2
1
1
1
0
0
0
0
0
1
2
1
1
1
0
1
0
1
1
1
0
3
0
1
2
1
0
2
2
0
0
1
2
1
1
0
2
0
2
0
0
3
0
1
0
1
0
0
2
0
0
1
0
1
0
1
1
2
1
1
1
0
0
1
1
2
1
0
2
2
0
1
3
1
2
1
2
1
1
2
0
1
1
0
0
2
1
0
1
0
1
0
2
1
2
0
1
0
1
0
0
0
0
1
1
0
1
0
0
0
0
1
0
3
1
0
2
0
0
0
0
1
1
0
0
1
0
2
0
1
2
1
0
1
1
2
1
0
1
2
2
2
0
1
0
1
0
0
0
0
0
2
0
1
1
0
0
1
0
1
0
1
0
0
2
2
0
0
2
2
1
0
2
0
0
0
1
2
2
0
1
1
1
1
0
0
1
0
0
1
1
1
1
1
1
0
2
0
2
0
1
2
0
1
1
0
0
1
1
1
0
0
1
2
0
1
2
2
1
1
2
1
0
0
2
1
0
1
2
2
0
1
1
2
0
2
1
1
0
1
1
0
1
2
2
0
1
2
1
0
0
1
1
0
1
0
1
0
0
0
1
1
1
1
2
0
1
0
1
1
1
1
1
2
2
1
2
1
0
1
2
0
3
1
0
0
2
0
1
0
1
2
2
2
1
2
1
2
2
1
1
0
0
0
1
0
1
1
2
3
2
0
1
0
0
1
2
1
3
1
0
2
1
0
3
0
0
2
1
0
0
0
0
0
2
1
1
1
2
0
0
1
1
1
1
2
3
2
0
0
0
1
3
1
1
0
2
1
1
1
1
2
0
1
1
0
1
1
2
0
1
1
1
0
1
0
1
1
0
2
0
2
2
1
0
1
1
1
0
0
0
1
1
2
1
1
1
1
1
3
1
1
0
0
0
0
2
0
2
1
1
2
0
0
0
2
1
0
2
1
0
2
1
1
2
0
2
1
2
0
1
2
1
0
2
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
1
1
1
1
2
0
1
1
0
1
1
1
2
1
0
2
1
1
1
1
0
1
2
1
1
1
1
1
2
1
2
0
1
0
0
0
0
0
0
2
0
1
2
1
0
2
0
2
0
2
0
0
0
0
2
0
0
2
2
1
1
2
0
2
1
1
0
1
1
2
0
1
0
0
2
2
0
2
0
1
1
0
2
0
0
2
1
1
0
2
1
2
1
2
0
1
0
1
0
2
1
1
0
2
0
2
0
1
1
2
0
1
0
0
1
2
0
1
0
1
0
1
0
1
0
2
0
0
1
1
1
2
1
0
2
0
0
2
1
1
2
0
1
0
0
0
1
1
0
2
1
2
0
0
0
0
0
1
2
0
0
0
0
1
2
1
0
0
1
3
1
0
1
2
1
2
1
2
0
0
0
1
1
2
1
3
0
0
0
1
1
2
1
1
1
2
1
1
1
1
0
1
0
0
1
1
2
2
0
2
0
1
0
0
0
2
1
1
1
1
2
2
0
0
0
1
1
2
1
1
0
1
0
0
0
1
1
1
1
0
2
1
0
1
1
2
0
1
1
0
1
0
2
2
1
1
0
0
1
1
1
1
0
0
0
0
2
1
0
2
1
0
0
1
0
0
2
1
0
0
1
0
2
2
2
1
2
1
0
1
2
1
2
2
0
0
2
0
1
2
1
0
0
1
0
2
2
1
2
1
1
2
1
0
1
0
0
0
2
0
0
1
1
1
0
1
0
0
2
0
1
0
1
2
0
2
2
1
1
2
0
2
1
1
1
1
1
0
0
2
0
2
2
2
0
0
4
2
1
2
0
0
2
2
1
0
0
1
0
1
1
2
1
1
0
1
3
1
1
1
1
0
0
0
0
0
2
0
2
0
2
0
1
1
0
0
1
1
1
0
0
2
2
2
0
0
0
1
1
0
2
1
2
2
1
2
1
1
1
0
1
0
2
1
1
2
1
0
1
0
1
0
0
1
1
0
1
3
0
0
1
2
1
1
0
1
2
0
2
1
0
0
1
1
1
2
0
1
1
0
2
0
0
2
0
1
3
2
0
0
2
1
1
0
1
5
0
0
2
1
1
1
0
0
0
1
1
1
1
0
0
0
2
2
0
1
1
1
2
0
1
1
2
2
0
2
2
1
2
1
1
1
2
2
1
2
2
1
1
2
1
1
0
0
1
1
1
2
1
0
0
1
0
0
1
0
2
1
0
0
0
2
1
1
0
2
0
0
1
2
1
0
0
0
1
1
1
2
1
0
0
2
1
1
1
0
1
1
1
1
2
1
1
1
1
0
1
2
0
0
0
1
1
0
1
0
1
2
0
2
1
0
1
0
2
1
0
2
2
2
1
0
2
1
1
1
2
2
1
1
1
0
1
1
2
0
1
1
0
2
1
1
1
1
1
1
1
0
2
2
1
2
0
1
1
1
1
2
1
0
1
0
1
1
1
1
1
1
0
3
0
1
0
1
3
2
1
1
2
1
2
0
2
2
0
1
1
3
1
0
0
2
1
1
0
1
1
2
1
1
1
1
0
0
1
0
0
0
1
0
1
0
0
2
2
0
1
1
0
0
0
2
1
0
0
1
0
0
0
0
1
0
1
0
1
0
2
1
1
1
0
0
1
1
0
2
0
1
2
0
1
1
0
1
2
0
1
0
0
1
0
2
1
1
1
1
0
1
0
0
1
0
2
1
1
0
1
1
0
1
0
0
1
1
2
2
0
2
2
1
1
1
1
2
0
0
1
1
0
1
2
2
0
1
1
0
1
1
2
1
0
1
1
2
1
1
1
2
1
1
0
0
0
0
2
0
1
1
2
1
1
1
0
0
1
1
1
0
1
2
1
1
1
1
0
1
0
1
0
2
0
2
1
0
1
0
0
0
1
1
0
0
1
0
1
0
0
0
0
1
1
2
1
0
2
2
1
0
1
0
1
1
2
1
1
1
1
0
2
1
0
1
1
1
0
0
2
1
0
0
1
2
1
1
0
2
2
0
0
1
1
0
1
1
0
2
0
1
2
2
2
0
1
1
0
1
1
0
0
0
1
0
2
3
0
1
0
0
0
1
0
1
1
0
1
0
0
2
2
1
2
1
1
0
0
3
1
2
0
0
1
1
0
1
0
1
0
0
0
1
0
1
0
0
2
0
1
1
0
1
2
1
1
2
3
2
2
2
1
2
1
2
1
2
0
0
1
1
0
2
0
1
1
0
1
1
1
1
0
1
2
2
1
2
0
1
2
1
1
1
1
0
1
0
0
1
0
0
1
2
1
1
1
0
0
4
0
2
1
1
1
2
2
1
1
2
0
1
2
0
1
0
0
1
1
0
0
0
1
0
1
1
1
2
0
1
1
1
2
0
1
1
1
1
2
0
1
0
1
0
1
1
2
0
2
1
1
1
1
1
0
2
0
0
0
1
0
1
2
1
2
0
0
1
0
1
14
1
1
1
1
2
1
0
0
0
0
0
0
1
1
0
1
1
2
1
0
2
2
1
1
2
0
0
0
1
2
2
0
0
0
0
0
1
0
2
1
0
0
1
2
0
1
0
0
1
1
0
1
0
0
2
1
1
1
1
0
1
2
2
0
0
0
2
0
2
1
0
1
2
1
0
0
2
0
0
0
0
2
2
2
2
2
0
1
3
0
0
2
1
2
1
1
2
0
0
2
0
1
1
0
1
0
1
2
1
0
1
1
1
2
2
2
0
1
1
1
1
2
1
0
1
1
0
1
2
1
0
1
1
0
0
0
0
0
0
0
1
2
2
2
2
2
1
1
0
1
1
1
0
1
1
1
1
1
1
3
0
0
2
1
0
2
2
1
0
2
1
0
1
1
1
1
1
1
1
1
1
1
1
2
0
0
1
1
0
1
1
1
1
1
1
1
1
1
3
0
1
0
1
1
1
0
0
2
2
0
2
1
0
2
1
3
0
2
1
1
0
0
2
1
0
2
0
0
1
1
0
1
1
2
0
2
2
1
0
1
1
1
0
2
0
1
0
1
1
0
2
2
0
2
2
2
1
1
0
1
1
0
1
1
1
0
1
0
0
1
0
1
1
1
2
0
1
0
1
1
1
1
0
0
1
2
0
1
2
0
0
1
1
0
1
1
1
1
0
0
1
1
2
2
0
2
1
0
2
1
0
1
0
0
1
0
0
1
1
1
1
0
0
0
0
1
0
0
1
1
0
1
0
0
2
3
2
1
1
2
1
0
0
1
1
1
2
2
0
0
1
1
1
0
0
0
0
1
0
1
2
1
0
1
1
1
1
1
0
1
1
0
0
0
1
1
0
2
1
1
0
1
1
1
1
1
1
1
0
2
1
0
1
0
1
0
2
0
0
2
1
0
0
0
2
0
1
0
1
2
1
1
0
0
2
1
1
0
0
1
0
0
1
0
1
2
1
0
2
0
2
0
1
2
2
0
1
1
0
2
0
1
1
2
1
0
0
1
1
1
2
0
1
3
1
2
2
1
3
2
0
1
2
0
1
1
2
2
1
1
1
0
1
0
0
1
1
1
0
1
1
0
2
1
0
0
1
1
0
2
1
0
1
0
1
1
1
0
2
2
1
2
0
0
3
1
1
2
1
1
1
2
1
1
1
1
1
1
0
1
0
0
0
0
2
0
0
1
1
0
0
1
0
1
2
0
1
2
2
1
1
1
0
1
0
2
1
0
2
2
2
0
1
2
1
1
1
1
1
2
3
1
1
1
0
0
1
0
1
1
2
1
1
1
2
0
2
2
0
1
1
0
0
0
1
0
3
2
2
2
1
1
1
1
0
2
2
1
1
1
0
0
0
1
2
1
0
1
2
2
0
0
0
1
1
1
1
0
2
2
2
1
2
2
1
0
0
2
1
2
0
1
2
2
1
2
2
1
0
0
1
0
0
2
0
2
1
2
0
0
0
1
2
1
0
1
0
0
1
0
0
0
1
0
1
0
1
1
0
1
0
0
0
1
0
0
1
0
2
2
0
0
2
2
1
0
2
2
1
2
0
2
2
2
1
1
1
0
1
1
2
1
0
1
2
1
2
2
1
0
0
2
0
2
0
1
1
1
0
1
2
1
0
1
0
0
0
1
0
0
0
0
2
1
2
3
0
2
0
1
0
0
2
2
1
2
0
0
1
0
0
1
1
0
1
0
0
1
0
0
0
0
1
1
0
0
0
1
2
2
1
0
1
0
1
0
0
0
1
1
2
1
0
0
0
1
1
1
1
1
0
0
1
0
2
0
2
1
2
1
1
0
2
0
1
0
2
0
2
1
1
0
2
1
2
0
0
2
0
0
11
1
0
0
2
0
1
2
0
2
1
1
1
2
2
1
0
1
1
0
2
2
2
2
0
0
2
0
0
1
1
2
1
1
0
1
3
1
1
1
0
1
2
1
1
2
1
2
1
1
2
0
0
0
0
0
0
0
1
1
0
1
0
1
1
5
1
1
0
1
1
0
1
0
0
1
1
1
3
1
1
0
1
0
2
1
0
1
1
1
2
2
1
1
0
2
2
2
1
1
0
0
1
0
0
1
1
2
1
0
2
2
0
0
0
0
1
0
0
0
1
1
0
1
0
1
0
0
1
1
1
1
1
1
1
3
1
1
1
2
0
1
0
1
2
0
1
2
2
2
1
0
1
2
0
1
0
2
1
2
1
1
0
1
0
4
1
2
1
2
1
2
0
1
0
0
0
0
1
2
0
1
2
1
1
1
1
1
2
1
0
0
0
2
0
1
2
0
2
0
0
2
0
1
1
0
1
2
0
0
0
0
0
0
1
1
1
0
2
0
2
1
0
1
2
2
0
1
1
3
1
0
1
1
2
1
1
1
1
1
0
0
0
0
0
1
0
0
1
1
2
2
1
2
2
1
1
0
1
1
0
1
1
1
2
1
1
1
0
1
0
2
0
0
0
3
1
1
3
2
1
2
0
2
1
1
1
0
1
2
2
1
1
0
1
1
1
0
0
0
1
0
0
1
2
1
1
0
1
0
0
0
0
0
1
0
1
1
0
2
1
0
1
0
2
1
0
2
1
2
0
0
1
0
1
2
1
1
0
1
0
2
0
1
1
1
0
2
1
1
2
2
1
0
1
2
1
0
0
1
1
0
0
0
0
1
0
1
0
0
1
1
0
0
0
1
1
0
0
1
2
0
2
0
3
0
1
0
1
1
2
0
2
1
1
1
2
0
1
0
0
1
2
3
0
1
0
1
1
1
1
2
1
2
1
2
0
0
1
1
2
1
1
2
1
2
1
2
0
0
1
1
1
1
1
1
0
0
0
1
1
0
0
2
0
0
1
0
0
1
2
1
2
2
1
0
2
1
2
1
1
2
2
2
0
0
0
1
1
2
0
0
2
1
1
1
0
1
2
0
0
1
1
2
0
0
3
1
1
0
0
0
1
1
2
1
1
1
1
2
1
2
0
2
1
2
0
0
2
1
0
1
2
1
2
0
1
1
0
1
1
2
0
1
1
2
2
1
1
0
0
0
1
0
2
1
1
2
0
0
0
1
1
1
0
1
1
1
2
2
1
2
1
1
2
0
2
3
1
1
1
1
2
2
0
2
0
1
2
1
0
3
1
0
0
0
1
1
1
0
1
2
0
2
2
1
2
1
2
0
2
2
0
0
1
2
2
0
0
1
2
1
1
1
3
2
0
1
2
0
1
0
0
2
1
0
2
2
1
1
1
1
0
1
1
0
0
1
1
1
0
2
0
1
1
1
1
1
2
2
2
1
2
1
0
2
0
0
0
0
2
2
2
0
1
0
2
1
0
1
1
3
2
2
0
2
0
0
2
0
2
0
1
1
2
0
0
1
2
2
2
0
1
2
1
1
0
0
0
2
1
1
2
1
0
2
0
0
0
2
0
0
2
0
1
1
1
0
1
2
1
0
0
2
0
1
1
3
3
0
2
1
0
2
0
0
2
0
2
1
2
0
1
1
1
1
0
1
0
0
2
1
1
0
1
0
1
1
2
0
0
2
0
0
0
1
1
1
1
0
2
0
1
0
1
3
0
1
1
1
1
1
1
1
0
0
1
1
2
0
0
1
1
1
0
1
0
0
1
0
2
3
0
0
2
2
0
2
1
1
2
1
1
1
1
1
1
1
2
1
0
2
1
1
1
0
2
0
0
0
1
0
2
0
2
2
1
0
1
0
0
2
1
0
1
1
1
0
1
0
2
0
1
1
1
0
2
2
1
0
1
1
0
0
1
1
1
0
0
0
1
1
1
0
1
0
1
1
1
0
1
0
1
1
2
0
0
0
2
0
1
1
1
1
0
1
1
1
1
1
3
2
1
0
3
1
0
2
0
0
1
0
0
0
0
1
1
2
0
2
0
0
2
2
0
2
1
2
1
1
1
1
2
2
1
0
0
1
0
0
1
0
0
0
1
1
1
1
1
1
1
2
1
0
0
0
2
0
1
0
0
1
0
0
0
2
2
2
0
2
0
1
1
1
2
1
0
2
4
1
0
1
2
0
0
0
1
2
1
1
0
2
0
0
2
1
1
1
1
2
2
1
1
1
0
1
2
0
0
2
3
1
0
0
0
1
0
1
0
0
0
1
0
0
2
1
2
2
0
0
2
2
1
1
2
1
0
0
1
0
0
1
1
1
0
0
0
1
0
0
0
1
0
1
2
1
0
1
1
0
1
1
1
0
2
0
0
2
1
0
0
0
1
0
1
1
1
1
1
2
1
0
1
1
1
1
0
1
3
1
1
1
1
1
1
0
0
0
1
1
1
0
2
2
2
0
2
1
0
1
0
2
2
1
1
1
0
0
0
0
2
2
2
0
2
3
2
0
0
2
0
1
1
1
0
3
0
0
1
0
0
1
1
0
1
0
1
1
1
1
1
0
1
0
1
2
1
1
1
1
0
1
1
1
0
0
2
0
1
0
0
0
2
1
2
1
0
1
0
2
1
1
0
0
2
0
0
1
1
1
1
0
3
2
0
0
2
2
1
1
0
0
1
0
1
0
3
0
1
1
1
2
2
0
0
1
0
0
2
2
1
1
0
2
0
1
0
0
1
0
0
1
2
0
0
1
1
0
0
0
0
2
2
1
1
1
1
2
1
0
4
0
1
2
2
0
0
1
0
1
0
0
0
3
1
0
2
0
2
0
1
2
0
1
1
2
0
1
1
1
2
0
1
1
0
2
1
2
1
2
2
0
0
2
2
2
0
2
2
1
0
0
0
2
0
2
2
1
2
2
0
1
1
0
1
2
1
0
0
0
0
0
2
1
0
0
0
2
0
1
2
0
1
0
1
0
2
1
1
1
1
1
0
1
0
1
1
0
0
0
2
1
2
1
2
1
2
0
2
1
0
0
2
2
2
0
0
0
0
1
1
1
1
1
1
0
0
1
2
1
0
0
1
2
1
1
1
0
1
0
1
1
0
1
2
0
1
1
2
2
0
0
2
2
0
1
2
1
1
2
0
0
2
1
0
2
2
1
1
1
0
0
0
0
0
0
0
1
1
0
1
1
0
2
2
0
2
1
0
0
1
2
2
0
3
2
0
2
0
2
0
2
1
2
0
2
1
1
1
1
0
0
0
1
1
2
1
0
1
0
2
1
2
0
1
7
1
1
0
4
1
1
1
1
1
0
1
2
3
1
0
2
0
2
1
1
1
1
0
2
2
0
1
0
1
1
0
0
1
2
0
1
1
0
2
1
0
2
0
1
1
0
0
0
1
0
1
1
0
1
2
0
0
1
1
1
1
1
1
0
0
1
2
0
2
0
0
0
2
2
0
2
0
2
1
0
1
1
1
1
2
1
0
0
1
1
2
1
1
0
0
1
0
2
2
0
0
0
1
2
2
2
2
1
0
0
0
1
0
0
0
1
0
1
2
2
1
1
1
1
0
1
0
0
1
1
1
1
1
1
5
1
1
1
1
1
0
1
2
2
0
1
1
2
1
1
2
0
2
1
1
0
2
1
0
1
1
1
0
0
1
1
0
2
2
0
0
2
1
1
2
0
2
0
1
0
1
1
1
0
1
1
0
0
1
0
1
1
0
0
0
0
1
0
1
0
1
2
0
0
2
1
0
1
0
0
1
1
0
1
1
0
0
1
1
2
2
1
0
1
0
2
1
1
1
0
2
0
0
0
1
0
1
1
0
2
2
1
1
2
2
1
0
1
2
2
2
2
1
1
1
0
2
1
0
1
0
1
1
0
2
0
1
1
1
1
1
0
4
1
0
1
1
1
1
1
0
2
2
0
1
0
1
1
2
0
1
0
0
1
1
1
0
1
1
0
2
2
2
0
0
0
2
0
0
1
1
0
2
1
1
1
1
2
1
1
1
1
3
0
1
2
0
1
2
0
2
0
0
3
2
0
1
1
2
1
1
2
2
2
0
1
0
1
0
0
2
0
0
1
0
0
2
1
0
1
0
0
0
0
2
0
1
0
1
0
1
0
1
0
2
2
2
0
1
1
0
0
1
2
1
1
0
1
3
2
1
2
0
2
0
1
0
2
2
1
3
0
2
1
0
2
1
1
1
2
2
0
1
0
0
0
1
0
0
1
1
0
1
2
2
0
1
2
2
2
0
1
1
0
1
0
1
1
1
1
1
1
2
1
2
2
1
1
0
1
0
2
2
1
2
2
0
1
0
0
1
2
0
0
1
1
2
1
1
2
2
0
1
0
0
1
2
0
1
1
0
0
1
1
0
1
1
1
0
0
0
1
0
1
1
1
1
1
1
0
1
1
2
1
0
1
1
2
2
1
0
1
0
1
0
0
0
0
2
1
1
2
0
0
0
1
0
1
2
1
1
0
2
1
1
0
1
1
0
0
1
0
2
0
1
1
1
1
0
0
1
0
1
0
3
1
1
1
2
1
1
1
0
1
1
2
1
0
1
3
0
0
1
1
2
1
1
1
1
1
2
0
2
1
0
1
4
0
1
0
0
0
2
1
2
2
0
1
2
1
0
1
0
1
2
1
0
0
0
0
0
1
1
1
1
1
0
1
2
2
1
0
1
0
0
1
1
0
1
0
0
1
1
1
2
0
0
1
1
1
3
1
0
3
2
1
1
0
0
1
2
1
1
0
1
3
1
1
1
1
2
0
0
0
0
2
1
1
0
0
0
1
0
1
0
2
1
1
2
0
0
1
3
0
1
1
0
0
1
2
0
1
1
2
1
0
2
1
2
0
0
0
1
1
1
2
2
0
1
1
0
2
1
0
0
1
0
1
1
2
1
1
1
1
1
2
1
0
1
2
1
0
1
0
1
0
1
0
0
0
1
1
0
2
1
1
0
1
1
1
2
0
0
2
1
0
0
0
0
2
2
0
2
2
2
0
1
1
1
1
0
0
1
1
0
1
1
0
0
0
0
1
2
1
0
1
1
1
2
1
0
1
1
1
1
0
0
2
2
0
0
0
0
2
2
2
1
1
0
2
1
0
1
1
1
0
0
1
0
1
1
2
2
1
0
1
2
1
1
2
1
1
1
1
0
1
1
0
0
2
3
2
1
0
0
2
4
1
1
0
2
0
1
1
1
2
1
0
1
1
2
2
0
2
0
0
0
2
0
1
2
0
1
1
1
1
0
1
0
1
1
2
1
2
1
2
1
2
1
0
1
2
2
0
1
0
1
1
0
1
2
0
1
1
2
0
0
1
1
1
3
3
2
3
1
0
1
1
1
1
1
1
0
0
2
0
2
1
0
1
1
2
1
1
0
1
1
1
2
1
1
2
1
1
1
1
1
2
0
0
0
0
2
0
0
2
0
2
1
0
0
2
2
1
1
0
1
1
0
2
1
1
2
0
0
2
1
1
1
0
0
1
1
1
0
1
0
0
1
0
1
2
2
1
0
2
1
0
1
2
0
2
0
0
2
0
1
1
1
2
1
2
1
0
3
0
0
1
0
1
0
0
1
0
0
2
1
1
1
2
1
2
1
1
0
1
0
1
1
2
1
1
2
1
0
1
0
0
2
2
1
2
1
2
2
0
0
1
0
1
1
0
1
0
0
1
2
0
0
2
2
1
1
1
0
1
2
0
3
0
1
1
1
1
1
3
2
1
1
0
1
0
1
0
1
1
1
2
1
1
1
0
1
1
2
0
0
0
1
1
0
0
1
1
0
2
1
2
0
0
1
0
1
0
0
0
0
1
1
0
1
1
1
1
0
0
1
1
0
1
1
1
0
1
3
0
0
1
1
0
1
2
2
1
0
1
1
1
2
0
0
1
0
1
2
0
1
0
1
2
2
0
2
0
1
4
1
0
1
2
1
0
1
2
1
0
0
0
1
2
2
2
1
1
0
0
0
1
2
0
1
1
1
2
2
1
1
0
1
0
0
1
0
0
1
1
0
1
0
2
0
1
0
1
1
2
1
0
1
0
1
1
0
0
1
1
0
1
0
1
1
2
1
0
1
1
1
1
2
1
0
1
1
1
1
2
1
1
1
1
0
0
0
0
0
1
1
1
1
2
1
2
0
0
1
0
0
1
1
2
1
1
1
1
0
2
0
0
0
2
1
0
1
2
1
1
1
1
1
0
0
1
1
2
2
0
0
1
1
1
2
0
2
1
1
2
2
1
2
0
0
2
0
2
2
0
1
2
0
0
1
0
1
1
1
0
0
2
0
1
1
2
2
2
1
1
1
1
1
1
1
0
0
1
2
1
1
0
0
2
0
0
4
0
1
0
1
2
2
1
0
0
1
1
1
0
1
2
1
0
0
1
0
0
2
6
1
1
0
0
0
0
0
0
1
1
1
1
2
1
0
0
0
0
0
1
1
3
1
0
2
1
2
2
2
1
0
0
2
1
0
0
0
1
0
0
0
0
2
1
1
1
1
2
2
1
1
2
1
0
1
1
0
0
0
0
0
0
1
1
1
0
1
1
0
2
0
0
0
1
0
1
2
1
1
0
2
2
0
0
1
1
0
1
0
0
0
1
2
2
1
1
1
2
1
1
0
1
1
1
1
0
0
0
0
3
0
1
2
1
0
3
2
2
2
0
1
0
1
0
0
0
1
2
0
0
1
1
1
0
1
0
1
1
0
1
0
0
0
0
0
0
0
1
1
2
0
2
1
1
0
0
0
0
0
0
1
2
2
1
1
0
1
1
2
1
0
2
1
1
0
0
1
1
0
1
2
1
1
1
2
0
0
1
0
1
1
0
0
2
0
1
1
0
1
0
1
0
2
1
1
1
1
0
1
1
1
0
1
0
1
1
1
2
1
1
2
1
1
1
1
0
0
2
1
0
1
2
0
1
2
0
1
0
1
0
0
1
1
1
1
2
0
1
1
1
0
1
1
2
1
1
2
2
0
0
1
0
1
0
2
2
1
0
2
2
2
1
1
0
0
1
1
2
1
2
0
2
0
0
0
2
0
0
0
0
0
1
0
0
1
2
2
0
0
2
0
2
0
1
1
0
1
1
0
1
0
0
1
1
0
0
0
1
2
2
1
1
0
1
0
1
2
2
1
1
1
1
0
0
2
1
1
0
1
0
0
2
3
2
0
1
0
0
0
1
0
1
0
0
1
0
1
0
0
1
0
2
1
0
1
1
1
1
2
0
0
1
1
2
0
0
0
1
0
1
0
1
0
0
2
1
2
0
1
1
2
1
1
1
1
1
0
1
0
1
0
0
1
0
1
1
2
2
2
0
0
2
1
0
1
0
2
0
0
1
2
1
1
2
0
0
2
1
0
1
1
1
0
0
1
0
1
2
0
1
1
1
0
2
1
0
1
0
1
0
2
1
1
0
1
1
0
2
0
0
1
0
1
2
0
1
2
1
1
2
1
2
1
1
2
2
1
1
2
0
1
1
0
1
0
1
2
2
2
1
1
0
0
0
1
1
0
0
0
1
1
0
2
2
0
0
2
0
2
2
0
0
0
1
0
0
0
2
3
1
2
0
0
1
2
1
0
1
0
2
1
1
0
0
0
1
0
0
1
1
1
1
2
0
0
1
1
0
0
1
1
0
0
1
2
1
1
2
1
0
1
0
0
2
0
0
1
1
0
1
1
1
2
0
3
1
1
1
1
1
0
1
3
1
0
1
1
0
2
0
0
1
1
2
2
1
1
0
1
2
0
2
2
0
1
0
2
0
2
1
1
1
1
0
1
1
2
0
2
1
1
0
2
2
1
0
1
0
0
1
3
2
2
0
0
0
1
0
0
1
1
2
1
1
2
2
1
1
1
1
1
2
1
1
1
1
3
1
0
2
1
2
1
0
1
0
2
0
0
2
0
2
1
1
1
1
0
2
0
0
2
0
2
0
0
0
0
0
0
1
3
0
0
1
1
1
1
1
0
2
2
0
1
1
1
1
1
1
0
0
1
0
3
0
1
1
2
3
1
0
0
0
0
1
1
1
1
1
1
1
0
0
1
0
1
0
1
0
2
0
1
1
0
0
0
0
1
0
1
0
1
2
1
2
1
0
1
0
1
1
2
1
1
1
1
1
0
1
2
0
2
1
1
2
1
1
1
1
0
1
2
2
1
1
1
0
0
1
2
1
1
0
1
1
0
1
1
1
0
0
1
1
0
0
1
0
1
0
1
2
1
1
1
0
1
0
0
1
2
1
3
0
1
1
0
1
1
1
2
1
1
1
1
0
2
1
2
1
2
1
0
1
1
1
0
1
0
0
2
2
1
1
1
1
2
0
2
1
0
1
0
0
1
1
2
2
0
0
2
1
0
0
2
1
1
2
0
2
0
3
0
0
2
1
1
0
1
1
2
1
1
1
0
2
2
5
0
1
2
2
0
2
0
2
1
1
1
2
0
1
1
0
1
0
1
0
1
2
0
1
1
0
1
1
0
1
0
1
0
2
1
0
0
0
1
0
2
1
0
1
0
0
0
1
2
2
2
0
2
2
1
0
1
0
0
0
1
1
0
1
0
1
2
1
2
1
2
1
2
1
1
0
0
2
0
0
0
1
1
1
2
1
1
3
1
1
0
2
0
0
0
0
0
1
0
1
1
0
1
0
0
2
0
1
1
1
1
0
2
1
1
0
0
0
2
0
0
1
0
0
1
1
0
0
1
2
0
1
1
1
0
0
0
0
1
1
2
3
0
1
1
1
0
1
1
1
2
2
0
1
1
2
1
1
0
0
0
0
2
0
0
1
1
2
0
1
2
0
1
1
0
1
1
2
2
1
3
1
2
1
0
0
2
0
1
1
0
2
1
1
2
1
2
2
0
0
1
3
0
2
2
0
2
0
0
0
1
1
0
1
2
2
1
1
1
0
0
1
3
2
1
0
0
1
0
1
0
1
1
1
2
2
1
1
1
0
0
0
0
1
2
0
0
1
2
1
2
2
2
1
1
1
1
0
0
1
1
1
1
1
2
1
0
1
1
1
1
1
0
0
1
1
1
0
0
1
0
1
1
2
0
0
0
1
1
1
0
1
1
6
2
2
1
1
2
1
0
0
1
2
0
0
0
0
1
1
1
0
9
1
1
0
1
1
0
1
1
2
1
1
2
2
2
2
1
1
1
1
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
1
1
0
2
1
1
0
0
2
0
1
1
1
1
2
0
0
1
1
2
1
1
2
0
1
2
2
0
1
0
2
1
1
2
1
1
1
0
2
2
0
1
1
0
0
0
1
0
1
0
1
0
1
1
2
1
1
1
0
1
1
1
2
3
1
3
1
2
2
1
1
2
1
0
0
0
1
1
0
2
1
1
0
0
0
1
0
1
1
1
2
2
2
1
1
0
1
1
0
0
0
2
0
0
2
1
1
2
1
2
0
0
2
2
2
2
1
1
1
1
0
0
1
0
0
2
0
1
1
1
0
1
0
1
2
0
1
1
2
1
1
2
1
1
1
1
0
1
1
2
0
1
1
1
1
1
0
1
0
1
1
0
1
2
1
0
1
2
2
1
0
1
2
1
1
1
1
2
0
1
1
0
0
0
0
1
1
0
1
1
2
2
1
0
1
0
0
1
2
1
2
2
1
2
2
1
0
2
1
1
1
0
1
2
0
0
0
1
0
1
0
0
0
0
1
0
1
0
1
0
1
0
1
1
2
2
1
0
2
0
0
1
0
1
2
0
1
2
1
1
1
0
1
1
1
2
1
2
1
1
2
0
2
0
0
0
0
2
2
0
0
2
0
0
1
2
1
2
0
0
1
1
2
0
1
1
1
0
2
1
1
1
2
1
0
0
2
1
0
1
2
2
1
1
1
0
1
1
2
2
1
0
1
0
0
0
0
0
2
2
1
1
0
1
0
1
2
2
0
1
2
1
1
1
0
1
2
1
0
2
2
0
0
0
1
0
0
0
1
1
1
3
0
1
2
1
2
0
1
1
0
0
2
2
0
1
2
0
1
1
2
2
0
2
0
0
0
1
1
2
0
1
1
2
0
1
1
1
0
0
1
1
0
1
1
1
0
1
0
0
0
1
1
2
2
1
0
2
1
1
1
1
0
2
0
2
2
2
1
2
0
0
1
1
3
0
1
0
1
0
0
0
0
0
0
2
0
0
0
1
2
1
1
0
1
2
0
0
0
2
0
1
2
0
1
1
1
0
0
1
2
2
0
1
2
0
1
1
1
2
1
0
2
2
0
1
1
2
0
2
1
1
1
0
1
0
0
1
0
0
0
0
1
2
0
1
0
1
1
0
1
1
1
1
1
2
1
1
1
2
1
0
2
0
0
2
2
1
1
0
1
0
1
2
2
0
2
1
0
2
1
1
0
1
1
0
1
3
0
1
1
1
0
2
0
0
1
1
0
2
1
2
0
2
2
1
0
0
2
1
0
0
1
1
2
1
1
0
1
0
1
1
1
0
2
2
1
0
1
0
1
2
1
0
2
0
2
0
0
2
0
0
1
1
1
0
2
1
0
0
1
1
2
1
0
2
1
1
1
1
1
0
2
1
1
1
0
0
0
0
2
0
1
1
0
1
0
2
2
0
1
0
0
0
1
1
1
1
0
1
1
1
3
0
0
1
2
2
1
2
0
0
1
2
1
1
1
4
0
1
2
0
2
1
1
1
0
1
0
2
1
0
1
1
1
1
1
2
1
2
0
1
2
2
0
0
1
3
1
0
0
0
1
2
1
1
0
0
0
1
0
1
0
0
2
0
1
0
0
2
2
2
2
1
0
2
2
2
0
0
0
0
0
1
0
0
1
1
1
2
1
1
0
1
2
0
1
0
1
1
1
0
0
0
1
1
1
2
0
1
0
1
1
1
0
0
2
0
2
1
0
0
0
1
0
1
1
0
0
2
2
0
0
2
1
1
1
0
2
0
2
2
1
2
2
1
0
2
2
1
0
1
0
1
1
1
0
0
1
2
2
0
0
1
2
1
0
0
0
2
1
2
2
4
1
1
0
2
1
1
0
0
1
0
2
2
1
0
0
2
2
1
1
2
0
0
0
2
0
1
0
2
1
1
1
1
3
0
1
2
2
0
1
0
0
2
2
1
2
1
1
1
0
0
2
1
0
1
0
1
0
1
1
2
1
2
1
0
1
2
1
0
1
1
1
1
0
0
0
1
2
0
0
2
0
0
0
2
1
0
0
1
2
0
0
1
0
1
0
0
1
1
1
1
1
0
1
2
1
2
0
0
1
0
0
0
1
2
0
1
0
0
2
0
2
2
0
1
1
0
2
1
0
1
2
1
1
1
1
1
1
2
1
1
0
1
2
0
1
1
0
2
2
1
1
0
1
1
2
0
0
2
1
1
1
2
2
2
0
0
0
2
0
1
1
2
0
0
0
2
2
2
1
1
0
1
2
2
1
0
1
2
0
1
1
2
2
2
2
1
0
0
0
1
2
1
0
1
0
2
1
1
2
1
1
1
1
2
0
1
1
0
0
1
1
0
2
1
1
3
0
0
1
2
1
1
0
1
0
2
0
1
0
1
1
0
2
0
0
0
0
2
1
0
0
0
2
1
1
1
0
2
2
2
1
1
1
0
1
0
2
1
0
1
0
0
3
1
0
2
0
1
1
0
2
0
2
1
0
1
0
2
0
0
0
2
0
1
0
2
1
2
0
0
1
1
1
0
3
0
0
2
3
0
1
0
0
0
1
0
0
1
0
0
1
2
1
1
0
2
1
1
2
1
2
1
0
1
1
2
0
0
1
0
0
1
1
1
1
0
0
0
0
1
1
0
3
1
1
1
0
0
1
1
0
0
1
1
0
2
1
3
2
1
0
1
0
1
1
0
0
1
1
0
0
2
0
1
0
2
0
0
0
0
1
0
2
1
0
2
1
0
1
0
2
1
2
1
1
1
0
1
0
1
1
0
2
0
1
1
0
1
1
1
0
1
0
0
0
0
0
0
1
0
0
1
1
0
2
0
2
0
0
0
1
1
1
1
1
0
2
1
0
0
1
0
1
1
1
0
0
2
1
1
0
1
2
2
0
0
1
2
0
1
1
2
0
0
2
1
0
0
1
1
3
2
1
1
0
2
0
1
1
1
0
1
1
0
1
2
1
1
1
1
0
1
0
0
0
1
2
2
0
0
2
1
1
2
1
0
2
1
1
1
1
2
0
1
0
1
1
2
1
1
1
1
1
0
2
1
1
1
0
0
1
2
2
0
1
1
0
2
2
1
0
1
0
0
1
1
1
1
1
0
1
1
1
2
0
2
2
0
2
1
0
2
2
1
1
2
1
1
0
0
0
0
1
0
0
0
0
1
2
1
1
1
2
1
0
2
1
1
0
1
1
2
1
0
1
1
1
0
1
1
1
0
1
0
0
2
0
0
0
0
2
0
0
1
1
1
1
1
1
0
1
1
0
1
1
1
0
0
2
0
2
0
0
1
1
1
1
0
0
2
2
0
1
1
0
1
1
1
0
2
2
0
0
2
2
1
2
1
0
2
0
0
0
1
2
1
3
1
1
3
0
0
0
1
1
1
1
1
0
4
0
1
2
0
1
1
1
2
0
1
0
1
2
0
1
0
2
1
0
0
2
0
1
0
1
0
1
1
1
1
2
3
2
0
1
1
3
1
0
2
0
0
0
1
2
1
1
1
1
0
3
1
0
1
2
1
1
0
2
2
1
0
0
2
2
2
1
1
2
1
2
1
1
1
0
2
0
1
2
1
1
1
0
0
0
2
0
0
1
1
1
0
0
1
0
1
1
1
1
1
1
1
1
0
2
1
1
1
2
0
0
2
1
0
1
1
2
2
1
1
1
1
2
1
0
0
0
0
2
0
0
2
1
0
2
1
0
0
1
1
0
1
2
0
0
0
1
1
1
1
1
1
0
2
0
1
0
0
1
1
1
0
1
1
2
1
2
2
2
0
0
1
1
2
1
0
1
0
1
1
0
0
1
1
0
0
0
1
2
2
1
0
0
0
2
0
1
1
0
1
0
0
2
0
2
1
0
0
1
1
1
2
1
2
0
0
0
0
1
0
1
0
0
0
1
1
2
1
0
0
0
1
0
0
1
1
0
1
0
1
0
1
1
1
0
2
1
0
1
2
0
1
0
0
0
0
2
1
1
2
1
2
1
0
1
1
1
0
0
3
1
2
2
1
0
2
2
0
2
0
1
0
0
2
2
2
4
0
2
1
2
1
1
1
1
1
2
1
1
1
0
2
2
1
1
1
0
0
2
0
2
0
1
1
2
1
1
1
0
2
1
2
1
1
1
0
1
0
2
2
1
0
1
1
2
2
1
1
1
1
2
2
1
2
2
1
1
2
1
1
0
1
1
1
2
1
1
1
1
1
0
1
0
0
2
1
0
1
0
0
0
0
1
0
2
2
2
2
2
1
2
1
0
2
0
1
2
1
0
1
1
1
1
1
1
1
1
0
1
1
1
0
1
2
0
1
1
0
1
0
1
2
1
0
0
1
0
1
3
1
2
1
1
0
0
0
0
1
0
0
2
0
1
0
0
0
1
2
0
1
1
0
2
0
0
1
0
1
2
0
0
0
1
1
1
1
0
2
4
1
1
1
0
1
1
3
0
1
1
2
0
0
1
2
0
1
2
1
1
0
0
2
0
1
1
1
1
1
0
1
0
1
1
0
1
1
0
1
0
1
2
1
1
0
0
0
1
1
0
1
4
2
1
1
1
2
2
0
1
1
2
0
0
0
0
0
2
1
3
1
0
2
1
1
1
1
0
2
2
1
1
3
0
0
0
2
0
1
0
1
1
2
0
1
1
1
2
1
2
0
3
1
1
0
1
0
0
0
0
1
2
1
1
1
0
1
2
0
0
1
1
1
1
0
2
1
1
0
2
1
1
0
0
1
0
1
1
1
0
2
0
0
0
1
1
1
0
0
0
0
1
1
1
0
1
0
2
0
0
0
0
2
1
1
2
1
1
0
2
1
1
0
1
0
0
0
0
1
0
2
2
0
1
0
0
1
1
1
1
0
0
0
0
0
1
2
0
0
1
1
1
0
0
1
0
0
2
0
2
1
0
1
2
0
1
0
0
2
0
1
1
0
0
0
0
0
0
1
1
1
1
0
1
0
1
0
1
1
1
3
2
0
1
1
1
0
1
1
1
1
2
1
1
0
0
0
0
1
1
1
1
1
2
0
1
0
0
0
1
0
0
1
2
0
1
1
0
1
1
1
1
2
1
1
0
0
0
1
1
2
1
1
1
1
1
1
1
1
0
0
1
1
0
1
1
0
0
0
2
0
1
1
1
2
1
1
2
0
1
1
0
1
2
2
1
0
1
0
0
0
1
1
1
0
1
2
1
0
2
1
2
1
1
1
1
0
1
1
0
0
0
2
2
1
1
1
0
2
1
0
0
0
1
1
2
0
1
2
0
0
1
1
2
0
1
0
1
2
2
0
2
2
1
3
1
0
1
1
1
0
0
1
2
0
0
4
0
0
2
1
0
0
0
2
1
0
1
0
0
0
3
1
0
0
1
0
1
1
0
0
1
1
1
1
1
0
0
2
1
2
2
2
0
0
1
1
1
1
1
1
1
1
0
1
1
0
1
1
2
2
2
1
1
1
1
0
1
2
1
2
1
0
1
1
1
0
1
2
1
0
0
2
2
1
2
1
2
2
1
0
2
1
0
2
0
0
0
2
1
1
1
0
1
0
0
2
1
2
0
1
0
1
2
1
2
1
2
0
1
2
0
0
1
1
1
0
1
0
0
1
1
0
0
1
2
1
2
1
2
1
2
1
1
2
1
1
0
2
1
2
0
0
0
1
1
1
0
1
1
0
1
1
0
2
1
1
1
2
1
2
0
0
0
0
1
0
1
2
1
1
1
1
0
0
0
0
2
2
2
0
0
1
0
1
0
1
2
1
1
2
1
2
0
2
1
2
0
1
1
1
1
0
1
1
2
0
2
1
1
0
1
1
2
1
1
1
0
0
2
1
1
2
2
2
0
0
0
2
0
2
0
0
1
1
0
0
0
0
0
0
1
2
4
3
0
1
1
0
1
1
2
1
1
0
0
0
1
1
1
2
0
0
1
0
1
0
1
1
1
1
1
1
0
2
1
1
0
0
1
0
1
0
2
0
0
0
0
1
1
2
0
0
1
0
1
1
0
1
2
1
0
1
1
0
2
1
0
2
1
0
0
1
0
0
1
0
0
0
0
2
0
1
0
0
0
1
0
1
1
2
1
0
0
1
1
0
2
1
1
1
2
2
0
1
2
1
2
0
0
0
0
2
0
0
1
1
0
2
1
0
2
0
0
0
1
0
1
2
2
2
1
0
0
0
2
1
1
0
1
1
0
1
1
1
1
0
1
0
0
0
2
1
1
1
1
0
1
1
1
1
1
1
0
1
2
2
2
1
0
1
1
0
2
0
1
2
0
1
1
1
2
0
0
0
1
0
0
1
2
0
2
0
1
0
2
0
2
0
2
0
0
0
0
1
1
1
0
2
0
1
0
2
0
0
0
2
0
0
0
2
1
1
1
1
0
1
2
2
2
2
0
1
1
1
1
1
1
0
0
0
0
2
1
0
0
1
2
2
0
1
0
0
0
1
1
1
1
1
1
1
1
1
1
1
2
1
5
1
0
0
1
0
2
4
1
1
1
1
3
0
1
0
0
1
1
0
2
1
2
0
2
2
1
1
1
0
1
1
1
0
1
1
1
1
1
0
0
2
0
1
1
1
1
0
2
2
2
1
0
1
2
1
2
1
0
1
1
1
1
1
2
1
2
4
2
0
0
0
1
1
0
2
0
3
3
2
0
1
0
1
2
1
1
1
0
2
1
1
1
2
2
1
2
2
2
1
0
2
0
2
1
1
1
2
1
0
0
2
1
1
1
2
1
0
1
1
2
1
1
1
0
1
0
0
1
2
1
0
0
1
0
1
2
1
0
0
0
1
1
1
0
1
2
2
1
0
0
0
2
0
0
1
1
1
0
0
0
1
3
0
0
0
0
2
1
1
0
0
2
1
0
0
2
1
0
1
1
0
2
1
1
1
0
1
1
1
1
0
0
3
1
1
0
1
2
1
0
2
1
1
1
1
1
0
2
2
1
1
0
0
0
2
0
1
1
1
0
2
3
1
1
2
1
1
0
0
1
2
0
0
1
1
0
0
0
1
0
0
2
1
2
1
1
0
0
2
2
0
1
1
1
1
0
0
1
3
1
1
1
0
1
0
1
2
2
0
2
2
0
1
1
2
1
1
1
0
1
1
1
2
0
1
1
0
2
0
1
1
0
1
2
0
0
2
1
0
2
2
0
0
0
1
1
2
0
1
1
0
1
0
1
1
0
1
2
0
1
1
1
1
1
1
1
1
1
1
2
0
0
1
1
0
1
0
0
1
0
0
0
1
2
1
1
1
1
1
0
0
2
1
1
2
2
0
1
1
1
1
2
0
0
0
1
0
1
2
1
1
0
0
1
2
0
0
1
0
0
0
2
1
1
1
0
1
1
1
0
2
0
2
1
0
2
0
0
0
0
1
0
1
1
1
1
0
1
0
0
0
0
1
0
1
1
1
2
2
1
0
3
2
0
0
0
1
1
1
1
0
2
0
2
2
0
0
1
1
1
0
0
2
0
0
1
0
1
2
0
1
1
1
2
1
1
0
0
0
0
0
0
1
1
0
0
0
1
1
1
1
0
1
1
2
1
0
0
1
0
2
0
0
0
2
0
2
0
1
1
1
0
1
0
2
0
1
2
2
1
0
0
0
1
1
1
0
0
0
0
2
2
1
1
1
0
0
1
1
0
2
0
0
3
2
0
3
0
1
2
1
1
0
1
0
0
2
1
2
1
0
1
2
1
1
3
0
1
1
0
0
0
0
1
2
1
5
2
1
0
1
2
2
1
1
1
2
1
2
2
0
1
2
1
1
1
0
1
2
1
2
1
2
1
1
1
0
0
1
1
0
1
0
2
1
0
1
1
0
1
2
0
3
2
1
1
1
2
2
0
0
1
0
1
2
2
0
2
1
0
1
1
1
1
1
0
1
0
0
1
0
2
0
0
1
0
0
0
2
2
0
0
1
2
1
1
1
0
0
1
0
0
1
0
3
1
1
2
1
1
0
1
0
1
0
0
1
10
2
0
1
0
2
0
0
1
1
1
1
0
2
1
0
0
0
0
0
0
1
1
1
0
0
0
1
1
0
2
1
1
0
0
1
1
1
0
2
1
1
0
0
1
1
1
1
0
1
1
0
1
1
0
1
2
2
1
0
0
0
0
0
1
2
0
0
0
1
0
2
1
1
0
2
2
1
0
0
1
1
0
1
1
2
1
0
0
2
2
1
1
0
1
1
1
0
0
1
1
1
1
3
2
1
2
1
0
0
2
1
1
1
2
2
1
0
1
0
0
0
1
1
0
2
0
1
0
1
2
0
1
1
1
0
1
0
1
1
1
0
0
2
2
2
0
1
1
1
0
1
0
1
0
1
0
0
2
1
1
1
2
1
0
2
0
1
2
1
1
0
2
1
1
2
2
0
0
0
0
1
2
0
0
1
2
1
1
1
0
2
0
2
1
0
1
2
0
2
3
1
0
1
0
1
1
0
1
0
1
0
1
2
0
0
1
2
1
0
0
0
0
1
2
1
0
2
0
2
2
2
0
0
0
1
1
1
0
1
0
0
1
0
1
0
1
0
1
2
1
2
0
0
1
0
0
1
1
2
0
1
1
0
1
0
0
1
1
1
1
1
1
2
1
0
2
0
1
1
1
0
1
0
0
1
1
0
0
0
0
0
1
1
2
1
1
0
1
2
2
2
2
2
0
2
2
0
2
0
0
1
1
1
2
1
0
0
2
1
0
2
1
2
1
2
1
1
0
1
2
1
2
1
2
1
1
1
1
1
1
1
2
0
0
1
1
1
2
2
0
0
2
0
1
1
1
0
2
1
2
0
1
0
1
0
2
2
0
1
1
0
0
2
1
2
0
1
0
0
2
0
2
2
2
2
2
0
0
2
1
0
1
1
1
1
1
1
0
1
1
0
1
1
1
1
1
0
0
1
0
0
1
2
2
0
0
0
1
1
0
2
1
2
1
0
1
1
1
1
1
1
1
2
1
1
0
1
1
3
0
0
0
2
0
0
0
0
1
2
2
1
0
1
0
1
2
1
2
1
0
0
0
0
0
5
0
0
1
1
0
2
0
1
1
1
1
1
3
2
2
3
1
0
0
1
0
0
0
1
1
2
2
1
2
1
0
1
2
1
1
1
0
1
2
1
0
0
1
0
2
1
0
1
0
0
1
1
0
1
1
1
0
2
2
1
1
1
3
0
0
2
3
0
0
0
0
0
1
2
0
2
0
2
0
0
0
0
2
0
2
1
2
1
2
0
2
0
1
1
2
1
0
0
0
1
2
0
0
0
2
1
0
2
2
0
0
1
2
1
2
0
2
0
1
0
1
0
0
2
0
1
2
1
0
1
2
0
0
2
0
6
1
0
1
1
0
0
2
1
1
0
2
1
0
1
0
1
0
1
0
0
1
0
1
1
0
1
0
0
0
0
1
0
1
0
1
0
1
0
0
0
1
1
0
2
1
1
0
0
1
0
4
2
0
1
0
0
1
0
0
1
0
2
2
0
2
2
0
0
2
1
2
0
0
1
2
0
0
1
1
2
2
1
2
1
1
2
0
0
0
2
1
0
0
0
0
0
2
2
1
2
1
2
0
1
1
1
0
1
2
1
0
2
2
1
1
0
1
1
0
1
0
2
0
1
1
0
2
1
1
1
1
2
1
1
1
1
2
2
0
1
2
0
1
1
2
0
1
2
1
0
1
0
1
1
3
1
1
0
1
1
0
1
1
2
1
0
1
1
1
2
0
1
2
0
1
1
2
0
1
0
1
2
2
0
1
1
2
1
1
1
1
1
1
2
1
2
1
0
2
0
2
1
1
1
1
2
0
2
1
1
0
0
1
1
1
1
0
1
0
3
2
0
0
1
1
1
2
1
0
1
0
0
0
1
2
3
1
1
0
1
0
2
2
1
1
1
2
1
1
2
1
1
2
1
1
1
0
1
1
0
1
1
2
1
2
2
1
0
0
0
2
0
0
1
1
1
2
0
1
1
3
2
1
1
2
1
1
1
1
0
2
0
0
1
1
0
0
1
0
1
1
0
1
0
0
0
0
1
1
0
2
0
0
2
1
1
1
1
1
0
0
0
0
0
1
1
0
2
1
0
0
0
1
1
0
0
1
1
1
1
0
1
1
2
0
0
0
2
0
2
0
1
1
0
0
0
1
0
1
1
1
1
1
1
0
0
0
0
2
1
2
2
1
2
1
1
0
0
1
0
0
1
1
1
0
1
0
1
1
0
1
0
2
2
1
1
1
0
0
1
2
1
0
0
1
1
1
1
0
0
1
1
0
1
0
1
0
1
1
1
1
2
2
2
1
0
3
0
1
2
0
0
1
1
2
0
1
1
1
1
0
0
2
1
0
0
1
0
3
0
2
1
0
1
2
2
0
0
1
0
0
1
0
0
1
1
1
0
1
1
1
0
1
0
1
1
1
2
0
1
1
1
0
0
1
2
1
2
1
0
0
0
0
1
1
1
0
1
2
1
0
1
1
1
0
1
0
1
0
0
0
0
1
2
1
0
1
0
2
2
2
0
1
1
2
2
0
0
2
0
5
0
0
2
0
0
0
1
2
1
2
1
0
0
1
1
0
1
0
0
0
2
0
0
2
2
1
1
0
0
1
1
2
1
1
0
1
1
0
2
0
1
0
3
1
2
2
2
1
1
1
1
1
2
2
0
3
1
3
1
1
1
1
1
1
2
1
0
2
1
2
2
2
0
0
1
2
2
1
0
1
1
1
0
1
0
0
2
1
1
1
0
1
0
1
1
1
1
1
1
2
0
1
0
0
0
1
1
2
0
0
2
0
1
0
0
1
0
0
0
0
2
1
1
0
2
0
0
1
0
1
2
0
2
0
1
1
0
0
1
1
0
1
1
1
0
1
1
1
0
1
2
1
4
0
2
1
2
0
0
1
0
1
2
2
0
0
1
1
1
1
0
0
1
1
1
1
0
1
2
0
2
2
2
1
0
0
0
1
2
0
1
1
1
0
1
0
1
0
0
1
0
1
2
2
2
1
1
3
2
1
1
1
2
0
1
2
0
0
0
1
1
1
1
2
1
0
1
1
2
2
0
2
0
0
0
2
0
2
0
1
3
2
1
2
2
0
0
2
1
1
1
1
0
1
1
1
0
0
0
1
0
0
1
1
0
1
1
1
1
1
0
0
2
0
1
0
0
0
0
0
1
0
2
1
2
2
2
0
1
2
1
0
0
1
1
2
1
1
1
2
0
1
0
0
0
0
0
2
2
1
1
0
2
1
1
1
1
2
1
2
1
0
2
1
1
0
3
0
1
2
1
2
1
0
1
2
0
1
0
0
1
2
1
0
3
2
1
1
1
1
0
0
2
0
0
1
1
0
1
2
0
2
2
0
2
1
2
1
1
1
0
1
0
2
0
2
0
2
1
0
2
0
0
2
1
1
0
1
1
5
0
0
2
1
2
1
1
2
1
0
1
0
0
2
0
2
2
2
2
0
2
1
2
2
2
2
0
0
1
0
0
2
1
2
2
0
1
1
2
1
0
1
1
0
1
1
0
2
2
1
2
1
1
0
0
0
1
1
0
0
1
1
0
2
0
0
1
0
2
1
2
0
3
2
0
2
1
0
1
0
0
0
0
0
0
1
1
2
0
1
2
0
0
0
0
1
0
1
1
0
1
0
0
1
0
2
0
0
0
2
2
2
1
0
0
3
0
0
1
1
1
0
2
1
0
2
0
2
1
2
1
0
1
0
0
0
1
2
1
1
1
1
1
0
1
3
1
1
1
1
1
2
0
1
0
0
0
1
3
1
0
1
0
2
2
2
2
2
1
2
1
0
2
0
2
1
1
0
0
1
1
0
0
0
0
0
1
2
0
1
1
1
0
2
0
1
0
1
1
0
1
0
1
1
2
2
0
2
2
3
0
0
2
0
1
1
2
0
1
3
1
0
0
2
2
0
1
0
2
1
2
1
1
0
0
0
1
1
1
2
1
0
0
2
0
1
1
0
1
1
0
2
1
2
1
1
1
1
0
0
1
1
1
2
0
1
1
1
2
1
1
1
0
2
1
2
2
3
0
1
0
1
0
1
1
1
1
2
1
2
0
0
0
2
2
0
1
1
1
1
1
2
2
1
2
0
2
0
1
2
0
1
1
1
0
1
1
2
1
1
2
1
1
1
1
1
0
0
1
0
1
0
0
2
2
1
1
0
1
2
1
1
0
0
1
1
2
1
1
0
0
0
1
2
2
0
1
1
0
1
2
1
0
1
0
0
1
2
1
0
1
1
1
1
2
1
0
1
2
0
2
0
1
1
0
0
0
0
1
2
1
1
1
2
0
1
0
2
3
1
1
1
0
1
1
0
1
1
0
0
0
2
0
0
1
0
0
0
0
1
1
1
1
1
0
1
0
1
0
2
1
0
1
0
1
0
1
1
0
0
0
3
2
2
1
0
0
0
1
1
0
2
0
1
2
0
0
0
0
0
2
0
2
1
0
2
0
0
0
2
1
0
0
2
0
1
2
1
0
1
1
0
1
1
0
1
1
0
1
1
0
0
1
0
0
1
1
1
1
0
0
0
0
2
0
1
2
0
2
1
1
0
0
0
1
1
1
0
2
0
1
1
0
0
0
0
3
0
3
1
0
1
2
2
2
0
1
1
0
2
0
2
1
0
2
0
1
2
1
0
4
1
2
2
0
1
2
2
1
0
2
0
0
1
2
2
0
2
2
1
1
1
1
0
1
2
2
2
0
1
2
1
2
0
1
1
1
2
0
1
2
0
1
1
1
1
1
1
1
1
1
1
1
0
1
2
0
1
1
0
2
2
0
0
1
1
2
1
1
1
0
2
0
0
2
0
1
1
0
0
0
1
0
0
2
1
0
1
0
1
0
2
0
1
1
1
3
1
2
1
1
1
0
0
0
1
1
1
0
0
3
0
0
1
0
0
0
1
0
2
0
0
1
0
2
0
0
0
1
1
1
1
2
2
2
1
1
0
1
1
2
1
2
2
1
0
0
2
0
1
1
1
2
2
1
0
1
1
1
2
2
0
1
1
0
1
0
1
0
0
2
1
0
0
1
1
2
0
0
0
0
1
1
2
1
1
2
1
0
0
0
1
2
1
2
7
0
1
1
1
3
2
0
0
1
2
1
0
1
1
0
1
1
0
1
1
0
0
2
1
2
0
3
0
1
2
0
3
2
0
1
0
0
3
1
0
2
1
0
0
0
2
2
0
0
0
1
0
1
1
3
0
2
0
2
1
1
1
0
0
0
2
0
0
0
1
1
0
2
0
1
0
0
1
0
0
2
0
1
1
1
2
0
1
1
2
0
0
2
2
1
1
1
0
1
1
0
0
0
1
1
2
1
2
1
2
1
0
0
1
1
1
2
1
1
0
1
0
1
0
0
1
1
1
2
1
0
0
1
1
1
1
1
2
0
2
0
1
1
1
1
1
6
2
1
1
1
0
0
0
2
1
2
0
2
1
0
1
2
1
1
1
0
1
0
2
2
1
1
1
1
2
0
2
1
0
0
1
0
0
1
0
1
1
1
0
0
1
1
2
1
1
0
2
1
1
2
1
2
1
0
1
0
1
1
1
1
2
1
1
1
0
1
1
1
2
1
1
2
2
2
1
2
1
1
1
1
1
2
2
0
0
2
1
1
0
0
0
1
1
3
0
0
2
0
2
2
0
1
0
0
2
2
2
0
2
2
0
0
1
1
1
0
1
1
0
0
1
2
2
1
1
1
1
0
2
2
0
0
1
0
0
1
2
0
0
1
1
2
2
2
1
3
1
0
0
1
0
0
1
2
1
1
1
1
2
1
3
2
1
1
1
0
1
1
1
2
1
0
0
6
1
2
2
0
2
1
2
0
1
1
0
1
1
2
1
0
0
2
1
2
1
1
1
0
0
1
0
1
2
0
0
0
1
0
1
1
0
0
3
1
1
1
0
1
2
1
0
1
1
2
0
0
0
1
0
1
1
1
1
1
1
1
1
1
2
1
0
0
0
2
1
0
1
1
1
2
2
0
0
1
1
0
1
2
2
0
1
3
0
2
0
1
1
2
1
1
0
0
0
2
2
1
1
0
0
1
2
1
2
1
1
0
2
1
1
1
2
0
1
1
0
2
0
1
0
0
0
0
2
2
0
1
0
1
0
4
2
3
1
3
1
0
2
0
1
0
1
1
0
2
0
0
2
0
1
1
0
0
2
0
0
1
0
1
1
0
2
2
0
1
0
1
1
0
1
2
0
1
0
1
0
0
0
1
1
0
1
1
3
2
0
1
1
1
2
2
1
2
0
2
0
2
1
1
0
1
1
1
1
1
1
1
1
3
1
0
0
1
1
0
1
0
1
2
1
0
0
2
1
0
0
0
0
1
3
1
0
0
2
1
2
2
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
1
0
1
1
2
0
0
0
0
1
0
1
1
0
0
1
2
2
1
1
2
1
0
0
1
0
1
0
1
0
1
1
2
2
1
0
2
0
1
2
1
2
1
1
3
0
1
1
2
0
1
0
0
1
0
1
1
2
0
1
0
0
2
1
1
2
0
1
1
0
0
1
2
2
1
2
0
2
1
1
2
1
4
0
1
0
2
2
1
2
2
2
1
1
0
1
2
0
2
3
0
0
1
1
0
1
1
2
0
1
1
0
3
1
0
0
0
1
0
0
1
2
2
1
2
1
2
1
2
1
3
0
1
1
2
2
1
0
0
1
0
0
0
0
1
0
2
0
0
1
2
0
0
0
1
1
2
1
0
1
2
2
2
0
2
0
0
0
1
0
1
1
2
2
1
1
1
4
2
2
1
1
1
1
1
1
1
1
0
2
1
0
1
2
0
0
1
0
2
0
0
0
0
2
1
1
2
1
0
1
1
1
0
2
2
2
2
0
1
0
0
0
1
1
1
2
0
1
0
0
0
1
1
1
1
1
0
1
1
1
1
1
1
2
1
0
0
0
1
2
1
1
1
0
1
1
1
1
1
0
2
0
3
1
1
1
2
0
0
2
1
2
1
2
2
2
1
0
1
1
0
2
0
2
1
1
2
1
0
1
1
0
2
1
1
2
2
0
1
0
2
0
0
1
1
2
2
1
1
0
0
0
2
0
2
1
1
0
2
2
1
1
1
2
0
4
0
1
2
2
1
0
1
2
1
0
1
2
0
1
0
2
0
1
2
1
0
1
1
2
2
1
0
0
1
1
1
0
1
1
2
1
2
1
2
1
2
0
3
2
1
1
6
1
0
0
1
0
0
1
0
1
1
0
0
0
1
2
0
1
1
0
1
0
3
1
1
0
1
1
1
1
1
1
0
1
1
0
1
1
0
1
1
2
2
1
1
1
1
2
1
1
2
1
1
2
0
0
1
2
1
0
1
0
1
1
1
0
1
0
1
2
0
2
2
0
0
0
2
1
0
0
0
0
1
1
1
2
0
2
0
1
1
0
0
1
0
1
0
0
2
0
1
2
2
0
2
1
1
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
2
0
1
2
1
1
0
2
2
1
1
1
0
1
1
1
1
2
0
1
0
0
0
1
2
2
0
1
1
0
0
2
1
0
1
1
1
0
2
2
1
0
1
0
1
2
1
2
1
1
0
0
0
1
1
1
1
1
1
1
1
0
1
0
1
0
1
0
1
1
1
0
1
0
1
1
1
2
0
1
1
2
2
1
1
0
2
0
1
1
2
2
1
0
0
2
0
2
1
0
0
0
2
0
0
1
0
1
2
0
0
2
2
1
1
2
2
0
1
1
1
0
2
0
1
0
1
2
0
0
0
1
1
0
0
1
0
0
1
1
1
0
1
2
1
1
1
1
0
1
1
0
1
2
1
2
1
0
1
0
1
2
0
0
0
0
2
1
1
3
1
1
1
1
1
2
1
1
0
2
0
1
2
0
1
2
0
1
1
0
0
0
0
0
1
0
1
0
1
1
0
1
1
1
2
0
0
1
0
1
1
1
1
0
0
0
0
0
1
2
0
1
0
1
1
0
0
0
1
0
4
1
1
1
1
1
1
2
1
2
2
2
1
1
0
0
0
1
2
0
1
1
0
0
0
1
1
2
1
2
1
0
0
1
0
1
1
1
1
2
2
0
1
0
1
0
0
2
0
0
0
2
1
2
2
1
1
0
1
0
1
1
0
1
0
1
0
0
0
0
2
1
0
2
1
0
0
0
0
0
1
2
2
1
0
1
1
1
0
2
0
0
0
1
1
2
1
0
1
0
2
2
2
0
1
0
0
2
1
1
0
0
1
0
1
1
1
2
1
0
1
1
0
0
1
2
2
1
1
1
0
2
2
0
0
2
1
0
2
1
0
1
3
0
1
0
0
1
1
1
0
2
1
1
0
1
1
2
2
0
0
2
1
1
2
2
0
0
1
0
0
0
0
1
1
1
0
2
1
0
0
1
0
2
1
1
1
1
0
1
2
2
0
1
0
1
0
1
1
2
0
2
1
1
0
2
1
0
2
0
1
2
1
0
1
1
1
2
0
0
1
1
0
0
0
1
1
2
0
0
1
1
2
0
0
1
1
1
0
1
0
1
0
0
1
0
0
1
0
2
2
0
0
1
1
0
2
0
3
2
0
1
2
1
1
0
0
0
1
0
2
2
0
1
2
2
0
0
0
0
1
1
0
0
1
0
2
2
1
1
1
0
1
2
1
0
1
1
1
1
2
0
2
0
0
2
2
0
1
2
1
2
1
0
1
1
0
1
1
0
1
1
2
1
0
0
1
2
1
1
1
1
1
0
1
0
1
0
2
1
1
4
1
0
1
2
1
1
1
2
1
1
2
1
0
0
2
1
1
4
1
2
2
1
2
1
3
0
2
1
0
1
1
1
1
2
0
1
0
2
2
1
2
1
1
2
1
1
1
1
5
0
1
2
1
0
0
1
1
0
1
1
1
2
1
2
1
1
0
1
1
0
1
0
0
0
1
2
2
2
0
0
2
1
1
0
2
1
1
1
1
1
0
1
1
0
2
2
0
1
1
0
1
1
1
0
0
0
0
0
1
1
0
0
0
0
0
1
1
1
2
0
1
0
0
0
1
1
1
0
0
0
0
1
2
2
1
1
0
1
2
1
0
1
0
0
0
1
0
1
0
2
0
2
0
1
1
1
2
1
1
1
0
0
0
1
0
2
0
2
1
1
0
0
0
0
0
2
0
1
2
1
2
1
0
1
2
2
1
2
1
1
0
2
0
2
0
0
1
2
1
1
2
0
1
2
2
0
2
0
0
1
0
0
2
0
1
1
0
1
0
0
0
0
0
0
0
2
2
1
0
1
1
1
1
2
0
1
0
0
0
0
0
2
0
2
2
1
1
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
1
0
1
2
1
1
0
1
1
1
1
0
0
1
0
1
0
0
1
0
2
2
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
2
1
0
1
1
1
0
1
0
0
0
2
0
0
1
1
2
0
1
0
1
1
1
2
2
2
1
1
0
1
0
1
0
1
1
2
0
0
2
1
1
2
3
3
1
0
0
1
1
0
1
2
0
0
1
0
0
0
2
0
1
0
2
0
1
1
0
0
0
0
1
0
2
3
0
0
1
0
0
0
2
2
1
0
2
2
3
1
2
1
1
1
0
2
1
2
0
1
1
0
0
1
1
1
2
0
1
0
2
1
0
1
0
2
1
1
8
1
1
0
1
1
0
2
1
1
1
1
0
0
2
0
0
1
2
1
2
0
2
1
0
2
0
1
0
2
0
2
1
2
1
0
0
0
0
1
1
0
1
0
1
2
1
2
1
1
2
0
0
1
1
1
2
1
1
1
1
0
0
2
2
0
1
2
2
2
1
1
0
2
2
2
0
0
1
2
1
0
2
0
0
0
0
0
1
2
1
1
1
3
1
1
2
1
2
2
1
1
0
2
2
0
1
1
1
0
2
1
1
2
1
1
2
0
1
1
1
1
0
1
0
0
2
1
2
0
1
1
0
1
0
0
3
1
2
0
1
1
0
0
2
1
2
0
0
0
0
1
1
1
0
1
0
2
2
1
2
1
1
1
2
2
1
1
1
2
0
0
0
0
2
1
2
0
0
1
1
1
2
0
1
1
1
1
0
0
1
1
1
0
1
0
0
0
1
0
0
1
1
1
1
1
2
1
2
1
3
0
1
0
3
1
0
0
1
1
0
2
0
1
1
2
0
0
1
1
0
2
1
1
1
0
2
1
1
0
2
2
0
3
3
2
1
3
0
2
2
2
2
0
1
1
1
2
1
1
1
1
0
1
0
0
1
0
0
3
1
0
5
0
1
0
0
1
4
1
2
3
2
0
1
1
1
0
0
0
2
1
2
1
1
0
1
1
1
0
1
1
1
1
1
0
1
1
0
1
0
0
0
0
2
2
1
4
1
1
2
0
0
1
0
1
0
1
0
1
0
1
1
1
2
2
2
2
0
1
0
2
0
1
1
1
1
1
1
1
0
2
2
2
1
0
1
2
1
1
2
0
0
2
1
0
0
2
1
2
0
2
1
1
1
1
0
0
2
2
1
0
2
1
2
2
1
2
1
0
0
1
1
1
1
1
2
2
1
0
1
1
1
0
0
0
1
1
0
0
0
1
0
1
0
9
1
0
2
1
1
0
0
0
0
0
1
0
1
0
1
1
1
0
1
1
2
1
1
2
1
0
0
2
1
1
1
2
1
1
0
0
1
0
2
1
2
0
1
1
1
0
2
2
1
1
1
2
0
2
1
1
1
0
0
1
0
0
2
1
2
1
0
1
2
0
0
2
0
2
1
1
2
1
0
2
2
2
2
1
0
0
1
1
0
0
1
2
1
1
0
0
2
1
2
1
2
0
1
1
2
0
2
1
2
0
0
2
1
2
1
0
2
2
1
1
1
1
0
0
1
2
0
1
1
1
2
2
1
0
0
1
2
2
2
0
0
0
2
0
0
1
0
1
2
0
2
1
2
1
1
1
0
0
2
1
1
2
2
2
0
1
1
1
2
2
1
0
1
2
1
1
0
1
0
1
1
1
2
1
1
0
2
1
1
1
0
1
2
1
0
0
0
1
1
0
0
2
0
1
0
2
2
2
1
1
0
0
1
2
0
1
0
1
1
0
0
2
2
0
0
1
0
1
1
0
1
0
0
1
0
1
3
0
1
0
0
1
0
0
2
2
2
0
0
1
1
0
1
0
2
0
0
0
1
0
1
1
2
0
0
1
1
1
1
2
0
2
0
1
0
2
1
0
0
0
1
2
0
1
6
0
0
0
0
1
0
0
1
1
0
1
1
2
2
0
1
1
1
1
1
1
0
1
1
0
1
1
1
1
0
0
2
3
0
2
1
1
2
1
0
0
0
1
0
1
1
0
0
1
0
2
1
2
1
1
2
0
2
1
1
0
0
2
2
1
0
1
1
0
1
0
0
1
1
1
0
0
2
1
1
1
0
1
1
0
0
1
2
1
0
0
0
2
1
0
1
2
1
0
0
1
1
1
0
1
0
0
0
1
0
1
1
2
1
0
1
2
1
1
1
1
1
2
1
1
1
0
1
0
2
1
0
0
0
2
0
0
1
1
0
0
1
0
0
2
1
0
1
1
0
1
1
2
1
1
3
1
1
0
1
1
1
1
0
0
2
0
1
1
1
0
1
1
0
0
1
0
1
1
1
1
0
0
1
1
2
2
0
0
1
1
0
1
1
1
0
1
0
1
2
0
2
2
0
1
0
1
1
1
1
1
1
1
0
0
2
0
1
0
1
2
1
0
2
0
1
0
0
0
0
1
0
2
0
1
0
2
1
0
0
1
1
0
0
0
3
0
2
0
0
1
0
0
1
1
2
1
0
2
1
1
0
1
0
1
1
0
1
0
1
2
0
2
0
3
0
0
0
2
1
1
2
1
1
0
0
0
1
1
1
0
1
1
2
1
1
1
1
1
1
1
0
2
0
0
1
0
0
2
2
0
2
2
2
0
1
0
0
0
1
1
1
2
1
1
1
0
1
0
1
2
0
1
0
1
2
2
1
0
1
2
2
1
0
1
1
1
1
2
2
1
2
2
1
1
1
1
2
2
1
1
2
0
1
0
2
2
0
1
1
1
1
1
0
1
0
3
2
1
1
1
1
0
1
0
0
1
1
1
2
1
2
1
0
1
2
2
1
0
1
1
0
1
1
0
0
2
1
1
1
1
1
0
1
2
2
0
0
0
2
1
0
1
1
1
1
1
0
2
0
1
1
2
1
0
2
2
0
2
1
1
1
0
1
2
2
1
1
1
2
1
0
1
1
1
0
0
1
2
2
1
1
0
0
0
0
0
1
1
1
0
0
0
2
0
0
0
0
1
1
1
1
1
1
0
0
1
1
2
0
2
2
1
0
5
2
1
0
0
1
2
2
1
3
1
1
2
0
2
2
0
1
2
2
3
0
0
0
1
1
2
0
2
1
1
1
1
0
2
1
0
0
1
0
0
0
0
1
2
0
1
1
1
2
0
1
1
2
0
1
1
1
0
3
1
1
0
2
2
2
1
1
0
1
2
1
1
1
1
1
0
1
0
1
1
0
0
0
1
0
0
1
1
0
0
0
0
0
1
1
0
0
0
2
2
2
2
1
1
0
1
1
2
0
0
0
1
0
1
1
2
1
0
1
2
0
0
1
0
1
1
3
1
3
0
1
1
2
0
1
1
1
0
0
4
0
1
2
1
1
1
2
0
4
0
2
0
0
0
0
2
2
0
2
0
0
1
1
1
0
0
1
1
0
1
0
0
1
2
0
1
0
0
2
0
0
0
1
1
1
2
0
1
0
0
0
2
1
0
1
1
0
1
0
2
1
0
1
2
0
1
1
1
1
1
1
0
0
1
2
0
0
0
1
0
0
2
1
1
1
1
1
1
0
1
1
1
0
1
2
1
0
1
0
0
0
0
0
1
1
0
1
2
1
1
0
1
1
1
1
2
2
0
1
1
2
0
1
1
1
1
1
1
1
2
1
2
1
2
2
2
0
1
1
1
2
1
0
0
1
2
1
1
2
0
1
1
0
1
1
0
1
2
1
1
3
0
2
1
1
1
1
0
2
2
1
2
0
0
1
0
1
1
0
0
1
1
2
1
1
1
1
0
2
0
2
2
0
0
1
0
1
1
1
1
1
2
0
1
3
0
0
1
0
1
1
2
1
1
0
1
1
1
1
1
1
0
1
2
0
0
1
1
1
1
2
0
0
2
2
2
1
0
0
2
1
0
0
1
1
1
0
0
1
1
0
0
2
1
1
1
1
1
0
0
1
0
1
2
0
1
1
0
1
0
1
2
1
2
0
2
1
0
0
1
1
2
1
1
2
0
1
2
0
1
1
0
2
1
0
1
1
2
1
1
1
0
1
1
0
2
0
1
1
1
2
0
1
0
0
1
2
0
2
1
1
0
0
1
1
1
1
1
2
0
1
0
1
2
1
2
1
1
1
0
0
1
0
0
0
0
1
2
0
1
1
0
1
2
1
0
1
1
1
0
1
2
1
2
1
0
3
1
0
1
1
2
1
1
0
1
0
0
0
0
0
0
0
1
3
1
0
1
0
1
1
1
0
0
2
2
0
2
0
0
0
1
1
2
2
1
0
1
0
0
1
1
1
1
0
0
0
1
0
0
0
0
0
0
2
1
1
0
2
1
2
1
0
2
1
1
0
2
1
2
1
1
2
1
1
1
0
0
2
2
0
0
2
1
1
2
1
0
1
0
1
0
2
1
3
0
1
1
0
0
2
2
2
0
2
1
2
1
2
2
2
2
0
1
0
1
0
1
0
0
2
0
1
1
0
2
1
0
1
0
0
0
1
0
1
1
0
0
1
1
1
1
1
1
1
1
2
1
1
0
0
1
1
2
0
0
1
2
1
1
0
1
2
0
1
1
1
0
2
0
0
1
2
1
1
0
2
1
0
0
1
1
0
2
0
2
0
0
0
1
2
2
1
0
0
1
0
1
1
1
2
0
0
1
0
0
0
0
1
1
1
0
0
1
0
2
0
1
0
0
0
1
1
2
1
1
2
0
0
1
0
0
0
1
2
1
0
2
1
1
0
0
1
0
1
2
1
2
1
1
1
2
1
1
1
1
1
0
1
1
0
0
0
1
2
1
1
1
1
2
0
0
1
0
1
1
2
1
1
0
0
2
1
2
2
1
2
1
0
1
1
0
0
0
1
0
2
1
0
2
0
2
0
0
0
0
2
1
2
1
1
1
3
0
1
0
1
1
1
0
1
0
0
1
1
2
1
0
1
1
1
0
1
2
0
1
1
1
1
0
0
1
0
0
1
2
2
1
1
0
1
2
2
0
1
0
2
0
2
2
0
1
1
0
0
1
1
1
0
1
1
3
2
1
0
2
0
1
2
2
0
0
0
1
0
2
2
0
1
1
1
1
0
0
1
2
1
0
0
1
1
0
1
1
0
0
1
1
1
0
1
0
1
1
2
0
1
1
1
2
1
1
0
3
1
1
1
0
0
1
1
0
2
2
0
0
2
2
1
2
1
1
3
2
1
0
4
1
1
0
1
1
0
0
0
2
0
0
0
0
1
0
1
0
1
1
0
2
0
1
1
0
0
1
0
0
1
1
1
0
1
1
1
0
0
0
2
1
1
0
1
0
0
2
1
0
1
2
2
2
2
1
0
1
1
1
1
0
0
0
0
1
2
0
2
0
2
1
1
0
1
1
0
2
1
2
2
1
1
0
1
0
1
2
1
0
1
1
0
2
2
1
2
0
1
0
1
2
2
0
0
1
0
1
0
0
0
0
0
0
1
1
2
0
0
1
2
2
0
1
1
0
0
0
1
0
1
0
1
0
2
4
1
2
1
1
0
2
1
1
1
1
2
0
2
0
0
3
0
2
1
0
0
0
0
0
1
1
1
2
0
1
2
1
0
2
0
2
1
1
2
1
1
1
2
0
1
0
1
2
2
2
0
0
0
1
0
1
2
0
0
2
2
0
0
0
1
0
2
1
2
1
1
0
2
2
1
2
1
1
1
1
1
2
2
0
2
0
2
0
2
1
0
1
0
2
1
1
0
0
1
1
2
1
1
1
2
2
1
0
1
0
1
0
1
0
0
1
2
1
1
0
0
0
1
0
1
1
1
1
0
0
2
2
1
0
1
2
0
0
1
1
1
1
2
0
0
0
2
1
1
2
0
1
1
1
0
2
0
1
1
0
2
1
1
0
1
0
0
1
0
1
2
2
1
2
0
0
0
1
1
2
2
1
0
1
1
1
0
0
1
0
2
0
1
2
1
2
0
0
1
1
2
0
1
1
3
0
0
1
0
2
1
1
0
0
1
1
1
1
1
2
1
0
0
0
0
1
1
0
1
2
1
1
1
0
0
2
1
0
0
1
1
0
1
0
2
0
2
2
2
0
1
3
0
1
2
1
1
0
2
0
0
2
1
0
0
1
0
1
1
0
1
2
3
2
1
1
0
1
0
1
0
1
1
0
1
0
1
2
1
0
0
1
2
1
1
1
0
2
1
0
0
1
1
1
1
0
1
1
1
1
3
1
2
0
0
2
2
0
0
0
0
0
0
1
1
1
1
0
0
1
1
1
0
0
11
2
1
1
1
2
1
1
2
1
1
1
0
2
1
1
1
2
0
1
2
2
0
2
0
1
1
2
0
1
2
0
2
2
1
0
2
0
2
0
1
1
0
1
1
0
0
1
1
2
1
1
0
1
3
4
2
2
1
1
2
0
0
0
2
1
0
0
0
0
0
1
3
0
1
1
1
1
1
2
1
1
0
1
0
0
1
2
2
0
1
0
1
0
1
0
1
0
0
1
0
0
1
0
1
0
2
2
0
1
1
0
0
0
1
0
0
0
0
1
0
2
0
1
0
1
1
2
0
0
0
1
1
1
0
1
0
1
1
2
1
2
1
0
0
0
1
0
0
1
1
0
0
1
1
1
0
0
1
2
0
1
1
0
1
2
2
2
1
1
2
1
0
1
1
2
2
2
1
1
1
0
3
0
2
0
1
1
0
1
0
0
3
0
1
1
0
1
2
1
1
1
0
1
0
0
1
1
1
1
1
2
2
0
0
1
0
0
1
1
0
0
1
1
1
0
1
0
2
0
1
2
1
0
0
1
0
5
0
2
2
0
1
1
1
0
1
1
1
0
1
1
0
3
1
0
0
2
1
1
1
0
1
1
0
1
1
1
1
0
0
1
0
1
1
1
2
1
1
1
2
2
0
2
1
0
0
2
2
2
8
1
1
0
1
0
1
1
3
1
0
1
1
1
1
0
0
1
1
2
1
0
0
0
0
1
0
1
1
0
0
1
1
2
2
0
1
2
1
0
0
1
3
1
0
2
0
0
0
1
1
2
1
2
2
0
2
0
1
1
1
2
0
2
2
0
1
2
2
0
1
1
0
0
1
0
0
1
1
1
0
0
2
1
0
2
2
1
1
0
1
2
0
1
2
0
1
2
1
1
2
0
1
2
0
1
1
2
0
1
2
1
1
1
1
0
0
1
2
1
1
1
2
2
1
1
2
1
1
2
2
1
1
1
1
2
1
0
0
0
0
2
1
1
1
0
1
0
0
2
0
0
1
0
1
2
3
0
0
0
1
1
1
1
1
1
2
0
0
0
1
0
0
1
1
0
1
1
0
1
1
1
0
0
0
1
2
1
0
0
0
1
3
1
0
1
1
1
0
0
1
2
2
1
2
2
1
0
2
0
1
1
1
0
0
1
0
1
0
0
1
1
1
0
2
1
0
1
3
2
0
0
2
1
1
2
1
2
0
2
0
1
3
1
0
0
0
0
0
1
1
3
2
1
0
1
0
1
1
1
1
1
2
0
0
1
0
1
1
0
0
0
1
2
0
0
0
1
1
2
2
0
2
1
1
2
0
1
0
2
0
3
0
1
1
1
1
1
2
2
2
2
0
2
0
1
1
0
3
1
0
0
1
1
0
0
1
1
1
0
2
0
1
0
0
1
0
0
1
0
0
1
1
2
1
2
0
0
1
0
2
1
0
1
0
2
1
1
1
1
1
0
1
2
1
0
1
3
2
2
3
0
1
1
1
2
2
0
0
2
0
0
0
3
1
1
2
1
0
0
0
2
0
1
2
0
2
2
0
1
1
0
0
0
1
0
2
1
2
1
1
0
1
1
1
2
1
0
0
1
0
0
1
2
2
0
0
1
0
0
1
1
1
0
1
2
1
0
2
1
2
0
1
1
0
2
0
0
1
2
1
0
1
1
1
0
1
2
1
2
0
1
1
1
1
0
0
0
0
2
1
4
1
1
2
2
1
1
0
0
1
2
1
0
1
0
0
0
0
2
1
2
0
1
0
1
2
2
0
0
0
1
1
0
2
1
1
0
1
0
1
1
0
0
1
2
2
0
1
1
0
0
1
0
1
0
0
0
1
2
0
0
1
1
2
1
1
1
2
2
3
2
1
1
0
2
2
1
2
1
0
0
2
0
0
0
1
2
0
2
1
1
1
2
1
0
0
1
0
1
0
1
1
1
2
2
0
1
1
0
1
0
0
0
1
0
1
0
1
0
3
1
1
2
1
0
1
1
1
0
1
2
0
2
0
0
1
0
0
0
2
1
1
1
0
0
0
2
0
1
0
0
0
1
1
0
0
0
1
0
2
0
0
1
1
0
1
1
0
2
1
0
0
1
1
0
1
0
0
0
1
1
2
1
1
1
1
2
0
0
1
1
0
2
1
0
1
0
1
1
1
1
0
0
1
1
1
1
1
3
0
2
0
1
2
2
2
2
2
1
0
2
0
1
0
1
1
1
1
0
0
1
0
2
1
0
2
2
2
1
0
2
0
0
0
1
1
2
2
2
1
2
1
0
1
2
0
1
1
0
0
0
0
1
3
1
1
1
1
0
0
3
1
1
2
1
2
2
0
1
2
1
2
0
0
0
1
0
1
0
1
1
0
1
5
0
1
0
1
0
3
1
0
0
2
2
2
1
3
1
2
2
0
1
2
1
1
1
1
2
3
1
0
1
1
1
0
1
0
1
3
1
2
2
1
2
0
2
1
1
0
1
1
1
0
2
1
2
1
0
0
4
1
1
1
1
1
2
1
0
2
0
2
0
2
1
1
0
2
0
1
1
1
1
1
2
3
2
1
2
1
2
1
0
1
1
1
1
2
2
0
0
1
1
0
1
0
0
2
1
1
0
0
1
0
0
2
0
0
1
2
2
1
0
1
1
1
1
0
1
1
0
2
1
1
0
1
2
0
1
1
1
2
1
2
1
1
1
1
0
0
0
2
1
2
0
0
1
0
2
0
0
1
2
1
1
2
1
1
1
0
1
0
0
0
1
1
0
1
2
1
0
1
0
0
1
2
2
1
2
0
3
1
1
0
1
0
0
2
0
0
1
0
2
0
1
0
1
0
2
0
0
0
2
2
0
0
0
1
1
1
1
1
1
0
1
2
1
0
1
0
1
2
0
1
0
0
0
1
0
2
0
1
1
0
0
1
2
2
1
2
2
0
0
2
1
1
1
0
0
0
2
1
0
1
2
0
1
0
1
1
1
0
0
0
0
0
0
2
1
1
0
1
0
1
0
0
2
0
1
1
1
0
1
1
2
1
1
1
1
1
0
0
1
0
1
1
2
1
0
1
1
2
0
1
1
0
1
2
1
1
2
1
1
2
0
1
0
0
0
1
2
1
2
1
1
2
1
0
1
2
0
1
2
1
1
1
0
1
1
0
1
1
3
2
0
1
1
2
0
0
1
2
2
0
1
0
0
0
0
2
0
1
1
1
1
1
0
3
0
0
0
0
2
2
0
2
1
2
2
1
1
2
0
0
1
1
1
3
2
2
1
0
0
1
1
2
1
2
1
0
2
1
1
0
0
0
2
1
3
0
1
0
1
2
0
2
1
1
0
2
0
2
1
1
1
1
1
1
1
0
1
0
1
0
1
1
1
1
1
1
2
1
1
0
2
2
2
2
0
1
1
1
1
0
1
0
0
2
1
0
0
0
0
3
1
0
0
0
0
1
2
0
1
2
0
0
0
1
0
2
0
1
1
2
2
2
2
2
1
0
0
0
1
1
2
1
1
1
1
2
0
2
0
2
2
0
2
2
0
0
0
2
0
0
2
0
0
1
1
1
1
1
2
1
0
1
1
0
0
1
1
0
1
1
2
0
3
1
1
1
1
0
1
1
2
2
0
0
1
1
1
1
2
1
1
1
2
1
1
0
1
1
1
1
1
1
1
2
0
1
1
1
0
2
1
0
0
0
2
0
0
0
0
1
1
1
1
1
1
2
0
2
0
0
0
0
0
1
2
2
0
1
2
2
1
1
2
2
1
3
2
3
0
1
0
0
0
1
0
1
1
2
1
1
1
2
0
1
1
0
1
2
2
1
1
1
0
0
0
1
1
2
0
0
1
1
1
2
0
0
2
0
0
2
0
1
2
1
2
2
0
0
1
3
1
0
3
0
2
0
1
1
1
1
2
1
1
0
0
0
0
2
1
1
2
0
0
0
1
1
0
1
2
2
0
1
1
2
0
1
2
1
0
0
0
1
1
0
0
0
1
1
1
1
1
1
0
0
1
1
3
0
0
1
0
1
0
1
2
2
0
0
3
0
1
0
0
1
1
0
0
1
1
2
1
0
1
2
1
1
1
3
1
0
0
0
1
2
0
0
1
2
1
0
1
0
0
1
0
1
1
1
1
1
2
1
0
0
0
1
1
0
0
0
1
3
0
2
0
5
1
0
1
2
0
0
0
1
1
0
1
2
2
1
2
2
1
0
0
1
1
0
0
1
1
1
1
2
0
1
1
1
1
1
1
0
2
0
0
0
2
0
1
1
0
1
1
1
1
0
1
1
0
2
2
1
1
2
1
2
1
1
0
0
0
0
1
0
3
1
1
1
2
0
0
1
0
1
2
0
1
1
0
0
2
1
0
1
0
1
0
0
1
1
1
0
0
0
0
1
1
0
3
0
0
2
2
0
0
0
1
1
0
1
3
0
1
1
1
1
1
0
0
1
1
1
1
1
1
1
0
2
1
0
2
0
2
2
1
0
0
2
0
1
1
0
0
0
1
0
1
1
2
1
0
1
0
2
0
2
1
2
1
1
1
0
2
2
1
0
1
0
1
2
0
0
2
0
1
1
1
1
1
2
0
1
0
0
1
0
0
0
0
1
2
0
1
2
2
0
1
3
0
2
1
2
0
0
1
0
1
1
1
1
2
0
1
1
1
1
1
0
1
0
1
1
0
1
2
2
0
1
1
1
1
0
2
0
1
0
0
0
2
1
1
0
0
1
1
1
1
2
1
0
1
0
1
1
2
0
2
1
1
0
1
0
1
0
1
2
0
2
0
2
1
0
1
0
1
1
1
0
0
2
0
1
1
2
0
2
1
1
1
1
1
0
1
0
0
1
0
1
2
1
1
0
0
2
0
2
1
0
2
0
1
1
2
1
2
1
0
1
2
0
1
2
1
0
1
1
0
1
2
2
0
1
1
2
1
1
1
0
2
0
1
2
0
0
2
1
2
0
1
2
1
0
0
1
1
1
2
1
1
0
2
0
1
2
1
0
1
0
1
1
1
2
0
0
1
1
1
1
1
1
0
1
0
2
0
1
1
1
1
0
3
2
0
1
1
0
0
2
1
0
0
1
0
1
1
1
1
0
1
1
1
2
1
1
0
1
0
1
1
1
0
1
0
1
1
1
2
1
0
0
2
1
0
1
0
1
2
1
1
2
0
2
0
2
0
4
1
0
1
0
0
0
1
0
0
2
1
0
0
1
1
1
2
1
2
1
0
1
0
1
0
1
0
1
1
1
2
1
2
1
2
1
1
2
1
2
2
1
0
2
1
1
1
1
0
2
1
1
2
0
1
0
1
1
1
1
1
0
0
2
1
0
0
0
1
2
1
1
2
0
0
0
0
0
2
1
0
0
1
1
1
1
0
1
0
1
0
1
0
1
2
1
2
3
1
2
1
2
0
0
1
2
0
1
2
0
1
2
0
2
1
2
0
1
1
1
0
2
0
1
0
0
1
1
0
16
1
1
1
1
0
2
2
1
0
0
1
1
1
0
1
2
2
0
2
0
1
0
0
0
0
1
1
2
0
0
2
0
0
1
2
0
1
1
2
0
1
1
1
0
2
1
0
1
3
1
2
0
0
1
3
1
0
0
1
1
0
0
0
1
0
0
0
2
1
0
1
0
0
0
1
0
1
1
0
5
1
1
1
0
1
1
2
0
2
0
1
0
0
1
0
2
0
1
0
2
0
0
1
2
2
0
2
1
0
3
0
2
2
2
0
0
0
2
1
2
1
0
1
0
1
0
1
2
1
2
2
2
1
0
2
0
1
1
2
2
0
2
0
2
0
1
0
1
1
2
2
0
0
0
1
1
1
0
0
1
1
1
1
1
1
0
1
0
1
1
0
3
0
0
1
1
0
1
1
0
0
0
1
0
0
1
0
0
1
0
0
1
1
2
2
1
1
2
0
1
1
0
0
1
2
1
0
1
2
1
0
0
1
0
1
0
0
0
1
1
1
2
2
1
0
0
2
2
1
2
0
2
1
0
1
0
0
1
2
0
1
1
2
1
0
1
3
0
0
1
2
1
0
1
1
2
1
1
1
0
0
1
1
1
1
0
2
2
1
0
2
2
0
1
1
0
1
1
1
1
0
1
1
0
1
3
0
1
2
1
0
1
1
2
0
1
1
2
1
1
1
1
1
1
0
1
0
2
1
0
0
1
2
1
2
1
1
2
1
1
0
3
0
0
2
1
1
0
0
1
1
2
0
2
3
2
1
1
1
0
1
0
1
0
1
1
0
1
1
1
1
0
0
0
0
1
1
2
2
0
1
0
2
1
0
1
0
2
1
0
0
1
1
2
1
1
0
2
1
0
1
1
1
1
0
0
0
0
0
2
2
1
0
2
1
0
0
1
0
1
1
0
2
1
2
1
2
1
1
1
1
1
1
0
0
2
2
1
1
2
0
0
1
1
0
0
1
0
2
0
1
1
1
1
1
1
1
1
1
0
1
2
0
1
0
0
1
0
1
1
1
2
2
0
1
2
1
1
1
1
1
1
2
0
1
0
2
1
2
1
1
1
2
1
2
0
2
1
1
2
1
2
1
0
0
1
0
2
2
0
1
1
0
1
1
0
1
2
0
1
1
0
0
2
2
1
1
1
0
0
2
1
1
0
1
0
0
0
0
0
0
2
0
1
2
1
0
1
2
2
1
1
2
2
2
1
1
0
0
1
1
0
1
2
1
1
1
2
2
1
2
0
2
1
1
1
2
1
0
0
0
1
1
0
2
0
0
1
0
1
0
2
0
1
1
1
1
1
2
2
0
1
0
0
1
0
1
0
2
1
0
0
1
1
1
2
0
0
0
0
1
1
1
0
1
1
1
2
1
0
3
0
3
0
2
0
0
1
2
0
0
1
0
2
1
1
1
2
1
2
1
0
2
0
1
1
0
0
3
1
0
1
2
1
2
0
1
0
1
1
1
1
1
0
1
0
1
1
0
0
0
0
1
1
0
1
0
0
1
2
2
1
2
2
1
1
0
1
0
1
1
2
0
0
2
2
0
1
1
1
1
2
1
0
1
0
1
0
0
0
0
1
0
2
0
0
1
1
1
2
0
0
1
2
1
1
1
0
0
1
1
1
2
1
2
0
0
0
2
0
0
0
1
3
1
0
0
0
0
2
0
1
1
1
0
1
0
1
0
1
2
1
1
0
0
1
1
0
0
1
0
1
0
2
0
1
1
2
2
2
1
0
0
1
1
1
1
0
0
1
2
1
1
0
2
2
1
2
1
1
1
0
0
1
0
2
1
1
1
1
0
2
1
0
2
1
1
1
2
1
1
1
0
2
0
2
1
0
0
1
1
1
1
0
1
1
0
0
0
1
2
2
1
1
0
0
0
2
2
1
0
2
0
1
0
1
0
2
0
0
4
0
1
1
0
2
0
1
0
0
1
0
1
1
0
1
1
0
1
2
0
2
1
1
1
1
0
1
1
3
2
1
1
5
2
0
0
0
1
2
1
0
1
1
1
1
0
1
2
1
0
1
1
0
1
0
2
1
0
2
0
1
1
0
0
1
0
1
1
1
1
1
0
2
1
2
2
2
1
1
2
0
2
0
2
1
0
0
1
2
1
1
1
1
0
0
0
0
1
0
2
0
0
0
1
1
2
1
0
0
2
1
1
0
2
0
1
0
1
1
2
2
1
2
2
0
0
1
1
1
1
1
0
0
0
2
1
1
1
2
0
0
2
2
1
1
0
0
0
2
1
0
1
1
0
2
0
0
2
0
4
2
2
1
1
1
0
0
1
2
1
1
1
4
1
0
1
0
1
2
2
0
1
1
3
1
0
0
1
2
1
1
0
1
1
0
1
2
0
2
0
1
0
1
1
1
1
0
1
0
2
1
0
0
1
3
1
2
0
0
0
0
2
0
0
0
0
2
0
2
0
0
1
1
1
1
0
1
2
1
2
0
1
0
0
2
1
1
2
1
1
0
2
1
1
1
1
2
1
1
0
1
0
1
0
2
1
0
2
1
0
1
2
2
2
1
2
0
2
1
1
1
2
0
2
1
2
0
1
0
2
0
1
1
1
1
1
0
2
0
0
2
2
1
1
1
0
1
0
3
1
0
2
1
0
0
1
1
0
2
0
1
1
0
0
1
1
2
2
1
1
1
2
1
0
0
0
1
1
1
0
1
0
1
2
1
2
0
2
2
1
1
1
0
1
1
1
1
0
1
1
1
0
0
2
0
2
2
2
0
0
1
1
1
0
1
1
1
2
2
2
0
0
2
0
2
0
0
0
2
0
0
1
0
2
0
0
1
2
0
1
2
1
2
3
1
0
0
0
1
2
0
0
2
0
1
1
1
2
1
1
1
2
1
2
2
1
0
0
1
0
0
2
2
1
1
0
1
1
0
1
1
1
2
2
0
2
0
0
0
0
1
1
1
0
0
2
1
2
2
0
1
2
0
2
1
1
0
0
1
0
1
2
0
1
2
1
0
1
2
1
0
0
0
0
1
2
0
2
1
1
0
1
1
1
1
0
1
1
0
2
1
2
1
2
1
0
2
1
2
1
2
1
0
0
1
2
1
0
0
2
1
1
2
2
3
2
0
0
0
0
0
0
2
3
0
1
2
0
0
1
1
3
0
1
1
1
1
2
2
0
1
1
0
2
0
2
0
1
1
1
1
0
1
1
0
1
2
1
2
1
0
1
0
2
0
0
1
2
1
2
0
0
0
1
0
0
0
2
1
0
1
0
0
0
1
1
1
2
2
1
1
2
0
0
1
1
0
1
1
1
1
1
2
0
2
2
0
1
0
2
1
1
0
2
1
1
1
2
0
1
1
1
1
1
0
1
0
2
1
0
2
0
0
2
1
0
0
1
2
1
0
1
1
0
1
2
0
0
1
0
1
0
0
1
0
1
0
1
0
1
2
2
2
1
0
2
1
1
0
1
0
1
0
1
0
1
0
2
0
2
0
2
1
2
0
2
0
1
1
2
1
1
2
1
0
0
2
0
1
1
1
0
3
1
0
3
2
1
1
0
1
1
2
2
0
0
3
0
1
1
1
0
0
0
1
1
1
2
1
0
0
0
1
1
1
1
0
2
0
0
0
1
0
1
1
0
1
1
2
1
2
0
1
0
0
1
0
0
0
0
2
1
0
1
1
0
1
0
0
2
0
2
2
0
1
2
0
2
2
1
0
1
1
0
1
1
1
1
0
0
0
2
1
1
1
3
2
1
1
0
2
1
2
1
0
2
1
1
1
1
2
0
0
1
0
0
1
3
1
1
0
2
0
0
0
0
1
1
1
0
1
0
1
1
2
0
2
1
0
2
1
0
0
0
1
0
0
0
0
0
1
0
2
2
1
0
1
1
1
1
1
1
0
0
0
1
1
1
1
0
0
0
0
0
0
2
0
1
0
1
4
2
2
1
1
1
0
2
0
0
2
1
2
1
0
0
2
0
1
0
2
1
1
0
2
2
1
0
1
0
2
0
1
0
1
1
0
0
2
0
1
1
1
1
0
0
1
1
0
0
1
0
0
0
1
1
1
1
2
1
0
1
0
1
0
0
1
1
0
1
2
0
2
0
0
0
2
0
1
0
1
2
1
0
1
1
1
1
1
2
0
1
1
1
1
1
0
0
1
1
2
2
1
0
0
1
1
0
0
1
0
1
1
1
2
2
1
1
1
0
1
0
1
2
0
1
1
2
1
0
0
1
1
0
2
1
1
1
1
1
0
1
2
1
0
0
0
1
1
0
1
2
1
1
2
2
0
1
0
2
1
1
0
0
1
1
1
1
0
0
0
1
1
0
2
1
0
0
2
1
1
1
1
0
0
0
0
1
2
1
0
2
1
1
0
2
2
1
1
2
1
1
1
2
1
2
1
0
0
2
1
0
1
0
1
2
2
1
1
0
1
3
2
1
0
0
1
2
1
0
0
0
2
0
1
1
2
0
1
1
0
1
1
0
1
1
1
2
1
1
1
2
1
2
1
1
2
0
1
2
1
0
0
0
4
0
0
2
0
1
0
1
1
1
2
1
1
0
1
1
2
1
0
1
0
0
1
2
2
2
2
1
0
1
2
0
1
1
3
3
2
0
1
1
2
1
1
2
0
0
2
0
0
2
2
1
2
0
1
1
0
0
0
1
0
0
0
2
0
0
1
0
0
1
2
2
0
0
1
1
2
1
1
0
1
2
1
1
0
0
0
2
1
0
1
0
0
0
0
0
2
0
1
0
1
0
0
2
2
0
1
1
0
0
1
2
0
1
2
1
1
2
0
2
1
0
2
1
2
2
1
0
1
1
0
0
0
0
2
0
0
1
1
1
0
0
2
2
0
1
1
0
1
1
1
1
1
6
1
1
1
1
2
2
0
0
0
1
1
1
0
0
1
2
1
2
2
0
1
1
1
0
0
0
2
1
1
1
0
2
1
1
1
0
1
0
2
0
1
2
1
2
0
2
1
3
0
0
1
0
0
0
0
2
1
1
0
1
1
1
1
1
1
0
1
2
1
1
0
0
0
1
1
1
1
2
0
2
1
0
1
1
1
6
1
1
1
0
2
1
1
0
1
1
1
0
0
3
1
2
0
2
0
1
1
1
0
1
2
2
1
0
2
2
0
0
0
2
2
1
1
1
1
0
0
2
1
0
1
1
1
0
0
2
1
0
2
1
0
1
1
2
1
1
2
0
0
1
2
1
1
2
1
1
1
2
1
1
2
1
2
1
1
1
1
1
2
2
0
1
1
1
1
2
1
0
1
1
1
1
1
0
1
0
0
0
0
8
1
0
0
3
1
1
1
1
0
2
0
0
0
2
1
1
1
0
2
1
1
0
1
1
0
1
0
1
2
1
0
1
2
1
1
1
2
0
2
1
0
0
1
0
0
2
1
0
0
1
1
0
0
1
1
1
2
3
0
1
0
2
0
0
0
0
1
0
1
1
0
0
2
0
1
0
1
1
0
1
1
1
2
1
0
1
2
0
2
2
2
1
1
0
0
0
0
0
0
2
1
1
0
1
0
0
0
0
1
1
0
1
0
1
2
1
1
1
2
0
1
0
0
1
0
1
0
2
0
0
1
0
0
0
0
1
0
2
1
2
1
1
0
1
0
2
0
1
0
1
0
1
0
3
0
2
2
0
0
0
1
0
0
0
1
0
0
2
1
1
0
1
2
0
1
2
0
1
1
0
1
1
2
0
0
0
1
0
0
2
2
2
1
0
1
1
0
2
0
2
1
1
0
2
0
0
0
0
0
1
2
0
2
0
0
1
0
0
1
0
2
2
1
0
1
1
1
2
1
2
2
0
1
2
1
0
1
1
2
0
1
0
1
1
1
2
0
1
1
2
0
1
1
1
1
0
0
1
1
2
2
1
1
0
0
4
2
2
0
2
1
0
1
1
2
0
0
2
1
2
1
1
1
0
1
1
0
2
0
0
0
0
1
1
0
2
0
1
0
1
3
1
3
1
0
2
0
0
0
1
1
2
0
2
1
2
0
1
1
1
2
0
2
0
2
2
2
0
1
1
1
1
1
0
0
1
2
0
1
0
1
0
2
0
1
0
1
2
1
0
0
0
2
2
1
1
1
0
0
1
0
0
1
1
1
1
2
1
0
1
0
3
2
1
0
0
0
1
0
1
1
2
1
1
1
1
2
1
0
1
3
2
1
2
2
0
1
0
1
1
1
1
1
1
0
0
1
2
2
0
2
1
0
0
1
1
1
0
2
1
1
1
1
1
1
0
0
1
1
2
1
2
1
0
0
0
1
1
1
1
0
2
1
0
0
1
1
1
1
2
0
2
1
1
3
1
1
0
0
1
0
1
2
1
0
0
1
1
0
1
1
0
1
1
0
2
1
2
1
0
0
0
0
0
0
2
1
2
0
3
1
1
1
0
0
1
0
0
3
0
3
0
0
2
1
1
1
1
0
2
1
2
1
1
2
0
1
0
1
1
1
2
2
1
2
1
0
1
2
0
1
1
1
0
1
2
0
1
2
2
2
1
1
1
0
1
2
0
0
0
1
0
1
1
0
0
1
1
1
1
1
1
0
1
0
0
1
1
2
1
2
3
1
0
1
0
1
1
1
1
1
1
1
0
1
1
0
1
1
1
0
1
0
0
1
2
1
0
1
2
1
0
0
0
1
2
1
1
1
0
2
0
2
1
2
2
1
0
0
1
1
1
0
1
1
0
1
1
1
1
1
1
2
1
0
2
2
0
2
1
1
0
1
1
1
2
1
1
1
2
1
0
0
0
0
0
2
1
1
1
1
2
2
2
2
0
0
1
2
0
1
0
1
1
0
1
1
0
0
1
0
1
0
0
1
2
1
1
1
0
2
2
1
1
2
0
2
2
1
0
1
1
2
0
0
0
1
1
1
1
1
1
2
1
2
1
0
0
2
0
0
1
2
2
0
1
0
2
0
2
1
2
0
0
2
0
0
0
0
3
2
1
0
1
1
2
1
1
1
2
1
0
0
1
2
2
1
0
0
2
2
0
0
0
2
0
1
0
0
0
1
1
1
0
0
0
1
0
0
2
1
1
0
1
0
0
1
0
1
1
0
1
1
0
1
0
3
1
3
2
2
0
0
1
1
1
1
0
1
1
2
0
0
1
2
0
2
0
0
2
2
0
0
0
1
1
1
2
0
2
2
1
1
0
1
0
2
2
1
0
1
2
1
0
1
2
1
1
1
0
0
0
0
1
1
1
2
0
0
0
2
1
0
0
2
1
1
1
0
2
1
0
0
1
0
2
0
0
0
1
0
1
1
1
0
1
0
0
1
1
1
0
0
1
2
1
1
2
1
1
1
1
0
1
2
0
1
1
1
0
1
2
1
0
2
0
0
0
1
1
0
1
1
0
1
0
0
0
1
1
0
2
0
1
0
1
0
1
0
1
2
2
1
2
0
2
1
0
1
0
1
0
1
1
0
2
0
0
0
0
1
0
1
1
1
0
1
1
0
1
0
0
1
1
1
1
4
2
2
0
1
2
1
0
1
0
1
1
1
1
0
2
0
0
3
0
2
0
2
2
1
1
1
2
1
2
0
0
1
1
0
2
1
2
1
1
0
1
2
1
0
0
2
2
1
0
0
2
1
0
2
0
1
0
1
2
1
1
1
0
0
2
0
1
0
1
0
1
1
0
0
0
0
1
1
1
0
2
0
1
0
1
1
1
0
1
0
1
1
1
1
1
2
0
0
1
1
1
0
0
2
1
0
0
2
0
0
2
2
2
3
0
0
0
2
1
0
1
0
0
1
2
1
1
0
1
1
0
2
0
1
1
2
1
0
1
0
0
0
0
2
0
0
1
0
2
1
1
1
0
1
1
2
1
1
2
1
1
2
1
2
1
0
2
1
0
2
1
1
2
2
2
2
0
0
0
2
1
1
1
0
1
1
2
2
2
1
1
1
2
0
0
0
2
2
2
1
0
0
0
0
1
2
1
0
2
1
2
0
1
1
1
0
1
1
1
0
1
1
1
1
1
0
2
1
1
0
1
0
1
0
1
1
0
0
2
1
1
1
0
0
2
0
1
1
1
0
1
2
1
1
1
0
1
2
0
1
2
1
1
1
0
1
0
2
1
2
1
0
1
1
0
2
0
0
0
1
1
2
0
1
1
1
2
1
1
0
1
1
1
1
2
1
1
2
1
1
0
1
0
1
1
0
0
2
2
2
0
0
0
1
1
1
1
0
0
1
0
1
0
1
2
1
1
0
2
2
1
1
0
2
2
2
0
0
1
1
1
0
0
0
1
0
1
0
0
0
1
1
0
0
2
0
0
0
1
1
1
1
1
2
1
0
0
0
2
2
0
0
1
3
2
2
1
1
0
2
0
0
1
0
1
1
1
2
1
3
1
1
1
0
2
1
0
1
1
0
2
0
1
0
0
0
0
0
5
0
0
0
1
0
1
0
1
0
1
1
2
1
0
0
1
1
2
1
1
1
0
1
0
0
1
2
0
0
0
2
0
1
1
1
1
3
1
1
2
0
0
2
0
1
1
2
1
0
1
0
1
1
1
1
1
0
0
1
1
2
2
1
1
2
0
2
0
1
2
2
1
1
0
0
2
0
0
0
0
0
1
0
2
0
1
0
1
1
1
0
2
3
1
2
1
0
1
1
1
1
1
0
0
0
0
2
1
0
0
0
1
1
0
1
1
1
0
0
2
1
2
0
1
0
0
0
0
0
2
2
0
1
2
1
0
2
0
1
0
0
0
0
0
0
2
2
1
0
1
1
1
0
2
2
0
0
0
1
0
0
0
0
1
0
0
1
1
1
0
1
1
0
0
0
1
1
1
0
0
1
1
2
1
1
1
0
4
2
0
2
2
1
2
0
0
0
1
0
1
0
2
1
0
1
1
0
0
2
2
0
0
1
0
2
0
1
1
0
1
2
1
1
1
0
0
0
1
1
0
1
1
0
1
1
1
1
1
1
2
2
2
5
2
0
0
2
0
2
0
0
0
0
1
0
0
0
1
0
1
1
1
1
0
1
0
0
0
2
2
1
0
0
2
1
0
1
0
1
1
0
0
0
1
1
1
0
1
0
2
1
1
0
1
0
1
1
2
0
0
1
1
1
1
0
1
1
0
0
0
2
1
1
1
0
1
1
1
3
1
0
0
0
2
0
1
1
1
0
0
1
1
1
0
1
1
1
2
0
0
0
0
2
0
1
1
1
2
0
1
1
1
0
0
1
1
2
2
0
0
1
2
1
0
1
1
1
1
2
1
4
0
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
2
0
0
2
2
1
1
2
1
2
1
2
0
2
0
1
1
1
1
1
1
0
2
1
0
0
1
2
0
1
1
2
1
1
0
2
1
0
2
0
1
1
0
0
1
1
2
0
2
1
2
1
1
0
0
1
1
2
1
0
2
2
2
1
0
1
2
1
3
1
0
2
1
0
2
1
0
2
2
1
0
0
2
0
1
8
0
0
1
0
0
2
0
1
0
1
2
2
1
1
0
0
2
0
2
1
1
2
1
1
0
7
1
1
2
0
1
2
2
0
1
1
1
1
0
1
1
1
1
1
1
2
1
0
1
1
0
1
1
1
1
0
4
1
2
1
1
1
0
1
1
2
1
1
0
0
1
1
1
3
1
1
0
0
0
2
1
1
0
1
1
0
1
1
1
0
1
0
0
2
0
1
2
1
1
1
1
1
2
3
2
1
1
0
0
2
3
1
0
3
0
1
2
0
1
1
0
1
2
1
1
0
0
0
0
1
1
1
0
3
0
2
1
2
0
0
0
1
0
1
1
0
1
0
0
2
0
0
1
0
2
0
1
1
0
0
1
1
0
1
0
0
0
0
0
0
1
1
1
1
1
1
1
1
1
2
0
1
2
0
1
1
0
1
0
0
0
1
0
0
0
1
0
1
1
0
1
0
0
2
2
1
0
2
1
1
4
0
0
0
0
2
1
0
1
0
0
0
0
0
2
2
1
0
1
0
0
1
2
0
1
2
0
1
2
0
1
0
2
1
0
0
1
0
0
0
1
1
1
0
0
0
1
1
0
0
1
0
0
2
1
0
1
0
1
2
1
1
2
0
0
0
0
0
1
0
1
2
1
1
1
0
0
1
0
1
0
1
1
2
0
0
2
1
0
1
0
0
1
1
0
2
0
2
0
0
2
1
0
0
1
2
2
2
1
1
1
2
0
0
1
1
0
0
1
1
0
1
1
0
1
0
1
0
1
2
1
1
0
0
1
0
2
0
2
0
2
1
1
1
2
2
2
0
1
1
1
0
0
1
0
0
1
2
2
7
0
0
1
1
0
1
1
1
1
1
0
0
1
0
0
1
0
1
1
1
0
2
1
0
0
0
1
0
2
0
2
2
1
1
0
0
2
1
0
1
0
0
0
1
1
0
0
1
2
1
1
0
1
0
0
2
1
1
1
1
0
1
2
1
1
1
1
1
1
1
2
1
1
0
1
2
1
1
0
0
0
0
1
1
0
2
1
1
0
1
0
2
1
0
0
0
1
0
1
2
0
0
0
0
2
2
0
1
1
2
1
1
0
2
0
2
2
1
0
1
0
1
0
2
1
2
3
1
0
0
2
1
0
0
0
2
0
0
0
1
1
0
0
3
1
1
1
0
0
0
0
1
0
1
0
2
1
2
0
2
2
1
0
1
0
2
1
1
1
0
0
0
0
0
1
0
1
2
2
1
1
1
0
1
1
0
0
1
1
0
0
2
1
0
1
1
1
2
0
0
2
1
0
2
1
0
1
0
2
1
2
2
0
2
0
0
0
2
1
2
2
1
1
0
1
1
2
3
2
0
0
0
1
0
1
0
0
2
1
2
0
1
2
2
2
2
0
1
1
1
0
4
1
0
2
0
0
1
2
1
1
1
1
1
1
0
1
1
1
0
0
1
2
1
1
1
2
0
0
1
0
1
0
2
2
1
0
1
2
1
0
0
0
1
1
2
2
0
1
1
3
0
0
1
1
0
0
2
1
3
0
1
0
0
1
1
2
0
0
1
0
3
1
2
0
1
0
0
2
1
0
0
1
2
1
0
2
1
0
1
0
0
1
1
0
2
1
1
1
1
1
2
1
2
0
2
1
1
1
2
1
2
0
0
0
1
5
0
1
1
0
2
2
0
2
0
0
1
0
1
1
2
1
3
0
0
1
0
2
0
2
1
1
1
0
1
1
1
0
2
1
0
2
1
0
0
0
2
1
1
1
1
1
1
0
3
1
0
1
2
2
0
1
1
1
1
0
1
1
0
2
1
1
1
1
1
2
2
2
1
1
2
0
1
2
1
0
0
1
1
0
2
1
1
0
0
1
2
0
2
1
1
1
1
1
2
0
0
0
0
1
2
0
2
1
0
0
1
2
1
2
1
0
1
1
0
1
2
1
3
1
0
2
2
0
1
0
0
1
0
0
0
0
0
1
2
0
1
2
1
0
1
1
0
0
1
1
0
1
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
1
1
2
1
1
0
0
1
1
1
2
2
2
1
2
1
2
0
1
0
1
0
0
1
1
1
2
1
1
2
1
2
1
0
0
1
1
1
1
1
1
1
0
0
1
2
1
1
1
1
0
0
1
1
1
0
1
4
1
1
0
2
2
1
1
0
0
2
1
1
2
2
0
1
1
0
1
0
1
1
0
0
0
2
2
0
1
1
1
1
0
1
2
1
2
2
1
1
1
0
1
1
1
1
1
1
0
0
0
1
0
1
0
0
2
0
2
2
1
1
2
0
1
0
0
1
2
1
2
2
0
1
1
1
0
1
1
0
1
0
2
0
0
0
2
0
2
2
0
1
0
0
0
0
3
1
1
0
0
1
1
1
1
1
2
0
0
1
2
0
1
0
1
0
0
1
0
2
1
0
1
0
1
1
2
1
0
2
1
1
1
0
1
0
0
0
1
1
1
0
1
0
1
2
0
1
1
1
2
0
1
2
2
1
0
5
0
0
1
0
1
0
0
1
1
1
1
1
1
2
1
1
0
2
2
0
0
0
1
0
0
0
0
0
2
0
2
0
0
1
0
0
1
2
1
1
0
0
2
4
1
0
1
1
2
2
0
2
0
1
0
1
0
0
1
0
0
1
2
0
0
1
2
1
0
0
1
0
0
1
0
1
1
0
0
2
1
1
1
2
0
0
1
1
2
0
0
2
0
0
0
1
0
1
0
2
0
0
0
1
1
0
1
0
4
1
1
0
0
1
2
1
0
0
0
0
0
0
0
0
2
2
1
0
0
1
0
0
0
1
0
0
0
3
0
0
0
0
1
1
0
1
2
2
2
2
1
1
1
0
0
0
0
1
1
1
1
1
0
2
0
3
0
0
1
2
0
1
0
1
0
1
0
0
0
0
0
1
1
1
2
1
0
0
0
1
1
0
0
0
0
2
1
1
0
2
2
1
1
1
0
1
1
2
1
1
1
1
1
0
1
2
0
1
1
1
2
1
0
1
1
2
0
0
0
0
0
0
2
0
2
1
0
0
1
2
0
0
2
1
1
1
1
1
1
1
2
1
0
1
0
2
1
2
0
2
0
2
1
1
0
0
0
0
2
0
0
1
1
0
1
2
0
1
0
1
0
2
1
1
2
0
1
1
1
0
0
2
1
1
0
2
1
0
0
2
2
0
0
0
1
1
1
1
2
2
2
2
2
0
1
1
1
0
0
1
2
1
1
0
1
0
0
1
2
0
1
2
2
1
2
0
1
1
2
2
0
0
1
1
1
0
1
0
1
0
1
3
2
1
1
0
2
1
1
1
2
1
1
1
2
1
2
1
1
1
1
0
2
1
2
0
1
1
0
2
1
1
1
1
1
1
2
0
2
2
2
0
1
1
2
1
2
1
0
1
1
0
1
2
0
1
0
1
0
1
0
0
1
2
0
0
2
0
0
1
0
2
1
0
1
0
0
1
0
1
1
1
0
0
2
1
0
0
1
1
1
1
0
2
0
1
1
1
1
1
1
2
1
2
0
0
0
0
1
2
1
1
2
0
0
1
0
1
0
0
0
3
1
0
2
1
1
0
1
1
0
0
0
0
1
1
2
3
2
0
0
0
1
0
0
0
2
0
2
0
2
1
1
1
1
1
0
0
0
1
1
0
0
0
0
1
2
2
1
1
0
2
2
1
2
1
1
0
2
1
2
0
1
2
0
1
1
2
0
0
3
1
1
0
1
2
1
0
1
1
0
2
2
0
2
2
0
0
1
1
1
2
0
0
0
2
2
1
0
2
1
0
1
2
1
1
1
2
2
0
0
0
1
1
3
2
2
1
2
1
0
1
1
1
0
1
1
0
1
3
0
1
0
0
2
1
0
0
0
0
2
0
0
0
2
1
2
2
0
0
1
0
2
1
2
1
0
2
0
2
0
1
1
1
2
2
2
1
1
0
1
1
1
1
1
1
1
1
0
1
1
2
1
2
2
1
0
3
0
1
1
0
0
2
1
2
1
1
1
1
1
2
0
0
1
2
0
1
1
3
1
1
1
1
1
0
0
0
0
2
0
1
0
0
2
0
0
1
0
2
2
2
0
1
2
2
2
2
1
0
1
0
0
1
0
1
1
1
1
1
3
0
1
2
1
2
2
2
2
1
1
0
0
0
1
1
1
1
2
1
0
0
1
1
1
2
0
0
1
1
1
2
1
2
0
0
2
1
1
0
1
1
0
1
1
0
2
0
0
2
2
1
1
0
0
0
0
0
1
2
1
1
1
0
0
1
1
2
2
0
1
1
0
1
3
1
1
0
2
1
0
2
1
1
0
2
0
0
0
2
2
2
1
1
0
1
0
1
2
2
1
2
1
0
3
0
1
1
1
0
2
0
1
0
2
2
1
1
0
1
1
0
0
2
0
1
2
2
0
2
1
0
2
0
1
1
2
1
0
1
1
2
1
2
0
0
2
2
0
0
0
0
1
0
3
1
0
0
0
1
1
0
1
0
0
1
0
2
2
1
1
1
2
0
1
1
2
0
0
1
2
1
0
2
0
1
1
0
1
1
1
2
0
1
2
1
1
0
3
0
0
1
1
1
2
2
2
0
1
2
0
0
1
0
0
0
1
1
1
0
1
1
0
1
1
0
0
0
0
1
2
1
2
1
0
0
1
0
0
0
2
2
2
1
0
0
2
0
1
1
1
0
2
2
1
0
2
1
2
0
2
0
0
2
0
0
1
0
1
1
2
0
0
1
2
1
2
1
2
0
0
1
1
0
1
0
1
1
1
0
1
1
1
1
2
1
2
1
0
2
1
2
1
6
2
1
0
0
1
2
2
1
3
2
1
1
1
1
1
3
1
2
1
2
0
1
0
1
1
1
1
0
1
1
2
1
2
0
2
0
1
2
1
1
1
1
3
0
0
0
1
1
1
0
1
2
2
2
0
1
1
2
0
0
0
1
2
2
2
0
1
0
2
1
0
0
1
1
0
1
0
2
0
0
0
0
1
2
2
0
2
0
1
1
1
1
2
3
1
2
1
0
1
0
0
0
1
0
0
0
0
0
1
3
1
1
0
0
1
0
1
0
2
1
0
0
1
1
1
1
1
0
1
1
1
1
3
1
2
1
1
1
0
2
0
1
1
0
1
2
1
2
2
0
2
1
2
1
1
0
1
0
1
1
0
1
1
1
1
1
1
0
0
1
1
1
0
1
1
0
0
0
2
2
1
1
0
0
1
1
1
2
1
0
1
1
0
0
1
1
0
0
0
3
0
1
2
1
1
1
2
2
1
2
1
0
1
0
0
1
1
2
1
1
0
2
0
2
0
0
0
1
2
1
1
2
1
0
0
0
2
1
1
1
2
1
3
1
1
1
2
0
1
0
2
0
0
2
0
2
0
1
0
1
3
2
0
1
0
1
0
0
2
1
2
1
1
1
1
0
1
1
0
0
1
0
1
0
2
2
2
0
1
0
1
1
1
0
1
0
1
1
2
0
0
1
1
2
2
1
1
0
0
1
0
3
1
0
0
0
2
0
0
0
2
1
1
1
2
0
0
1
1
0
0
1
1
0
1
2
1
1
0
1
3
1
1
5
2
1
1
1
2
0
1
2
1
1
0
1
2
0
2
1
0
1
0
0
2
2
0
1
3
2
1
1
1
0
1
0
0
1
1
1
0
1
1
2
0
1
1
1
0
1
0
1
0
0
0
0
1
2
0
2
0
0
1
1
1
0
1
2
1
1
1
0
0
0
2
0
2
0
1
0
1
1
1
1
1
2
2
2
2
1
1
1
0
2
0
0
0
2
0
1
1
2
1
0
1
1
0
0
1
0
0
0
2
1
2
1
1
1
0
2
1
1
0
0
2
0
1
2
0
1
2
1
0
0
2
0
0
0
0
1
0
0
1
1
2
0
2
1
2
2
2
0
0
0
2
1
0
1
2
1
0
1
0
0
0
0
1
1
1
2
0
1
1
1
1
1
2
1
1
0
1
0
1
0
1
2
1
2
1
1
1
1
0
1
2
3
1
1
1
1
2
3
2
0
0
0
0
2
1
1
1
1
0
1
2
2
1
1
1
1
1
1
1
1
1
0
0
0
1
2
2
0
0
0
2
2
0
2
1
1
1
1
0
0
1
0
0
0
2
1
2
2
1
0
2
0
1
1
1
1
0
0
0
1
1
0
1
0
1
0
0
1
1
1
0
0
1
0
1
0
0
1
1
1
1
2
1
1
1
2
0
0
1
1
0
1
1
1
1
1
0
1
1
1
1
2
0
1
2
2
1
2
2
1
1
1
1
2
0
1
1
0
1
0
2
0
0
1
0
1
1
0
0
2
1
1
1
2
1
0
1
0
0
0
2
1
1
0
1
1
1
1
1
0
2
0
1
2
2
0
2
1
1
1
2
2
1
1
1
1
0
0
2
1
1
1
1
2
2
0
0
2
1
1
0
0
0
2
0
2
0
1
2
2
2
1
0
2
0
1
0
0
1
2
1
0
0
1
2
2
1
0
0
1
0
0
1
2
2
1
1
0
1
0
0
1
1
0
0
0
1
2
1
0
0
0
1
2
0
1
1
2
2
2
1
1
0
1
1
0
0
0
1
2
2
0
0
2
2
1
2
1
3
0
0
0
2
0
1
3
1
1
2
1
1
2
0
0
1
0
0
1
1
0
0
1
0
0
2
1
0
1
0
0
1
2
1
2
2
2
1
0
0
1
1
1
0
1
0
0
2
1
2
1
0
1
1
1
0
1
0
1
1
1
0
2
2
0
2
0
1
1
0
1
0
2
2
0
0
0
0
1
2
2
0
1
1
7
1
2
0
0
1
0
1
0
1
0
2
2
0
0
0
1
1
0
0
2
1
1
0
2
0
0
1
1
1
1
1
0
2
2
0
0
1
2
0
2
2
0
0
2
2
0
0
2
0
1
2
1
0
1
2
1
1
2
1
1
1
0
0
0
2
2
0
0
1
0
1
1
0
2
2
1
1
2
1
0
0
0
0
0
0
1
2
2
1
1
2
1
1
1
1
2
2
1
1
1
2
1
1
1
2
2
0
1
0
1
1
0
0
1
2
1
0
0
3
0
0
2
2
1
2
2
1
0
0
2
1
1
2
2
0
0
1
1
0
1
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
2
1
1
1
0
1
0
0
1
0
0
0
1
0
2
1
1
2
2
1
2
0
5
1
0
0
0
0
0
2
1
0
1
2
2
1
0
3
1
1
1
1
0
1
2
1
0
1
1
1
1
1
1
1
0
0
1
0
0
1
2
0
0
1
2
1
1
1
2
2
1
2
1
0
0
1
1
0
0
1
1
2
0
1
0
1
2
2
2
1
0
0
1
0
0
0
0
0
2
2
2
0
0
0
0
0
0
1
1
1
1
0
2
1
0
2
2
0
0
1
0
1
2
1
2
1
0
1
0
1
2
1
1
0
0
0
1
1
1
2
0
0
1
1
1
0
1
1
0
2
1
0
1
0
1
2
2
1
0
1
1
0
1
2
2
0
1
0
1
2
1
1
1
1
1
2
0
1
1
0
1
0
1
2
1
0
0
1
1
4
0
1
2
0
1
0
1
1
1
2
3
0
1
0
1
2
1
1
0
2
1
0
0
0
0
0
0
1
0
2
0
1
1
2
2
0
2
0
2
2
0
0
1
1
1
0
0
1
0
2
1
1
1
0
1
1
1
1
0
1
1
1
0
1
1
1
2
1
1
1
2
1
1
1
0
0
0
0
0
2
0
1
0
1
0
1
0
0
1
1
0
1
1
2
2
0
0
1
1
1
2
4
1
0
2
0
0
1
1
2
1
2
2
1
0
2
0
1
0
0
0
0
1
2
1
0
0
0
0
2
1
0
2
0
0
2
0
2
2
1
0
2
0
2
1
2
0
2
2
0
0
2
2
2
2
1
0
1
1
0
3
1
2
0
0
1
1
0
0
2
0
1
2
1
1
1
0
0
2
1
2
1
0
1
0
1
1
0
1
1
1
0
1
0
0
2
0
1
1
0
0
1
0
2
2
1
1
2
1
0
0
2
1
1
1
1
1
0
1
0
1
0
0
1
0
1
1
0
2
0
0
2
2
1
2
1
1
0
2
0
2
1
0
0
0
2
0
1
0
1
0
1
1
2
1
1
2
0
1
2
0
0
2
1
1
0
1
2
0
1
1
2
0
1
0
0
1
0
2
1
0
0
0
2
0
1
0
1
1
0
0
0
2
2
1
2
0
1
1
2
1
1
1
1
2
0
1
2
1
1
0
1
0
0
1
1
2
1
1
0
2
2
1
0
0
1
1
0
1
1
2
1
1
0
1
1
0
1
1
1
1
2
1
1
1
1
1
1
1
1
2
0
2
1
1
1
2
0
1
0
1
0
0
0
1
0
1
2
0
2
1
1
0
2
0
1
1
0
0
2
0
2
1
1
0
2
0
2
1
0
2
2
1
2
1
1
2
0
1
2
1
1
2
1
0
1
1
0
2
1
2
0
0
0
3
1
1
0
1
0
1
0
0
1
1
2
2
0
1
0
1
0
1
2
0
2
2
0
2
2
0
1
1
1
0
1
2
0
1
2
0
1
0
2
1
0
0
1
2
0
1
0
0
1
1
0
0
4
1
1
1
0
0
1
0
1
0
0
1
1
2
2
1
1
2
1
2
0
1
2
0
1
0
2
2
0
1
1
1
2
3
1
2
1
1
0
2
0
1
0
0
0
0
0
2
2
0
1
1
0
0
1
0
2
2
0
0
2
0
2
1
0
2
0
1
1
2
0
0
0
2
1
1
4
1
1
0
0
2
0
1
1
2
0
1
2
1
1
0
1
2
2
2
1
0
0
0
0
1
0
2
1
0
1
1
1
1
1
1
1
0
1
1
1
0
0
1
1
1
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
1
0
1
0
1
0
1
1
0
0
1
2
1
2
0
0
2
2
1
1
3
1
0
0
1
1
0
0
2
1
1
0
1
0
1
2
0
0
0
1
0
2
1
1
1
1
2
2
1
1
2
1
0
2
1
0
0
1
1
1
0
1
1
0
1
1
1
1
1
1
1
0
0
0
0
1
2
1
2
1
1
1
1
2
1
2
0
0
2
1
0
2
1
1
0
1
1
1
1
1
0
1
2
1
1
1
1
0
2
1
2
0
1
0
1
1
0
0
0
0
0
0
3
2
1
2
1
0
1
2
0
1
2
2
1
2
1
1
0
0
0
1
0
0
1
2
1
1
0
2
2
1
0
3
0
0
1
2
1
0
0
1
3
0
0
0
0
2
1
0
1
0
2
0
0
1
0
1
0
2
1
0
1
2
2
1
0
0
1
3
0
2
1
2
1
1
0
2
1
1
0
0
1
2
0
0
0
1
1
1
0
1
0
1
1
1
1
0
1
0
1
1
1
2
2
1
1
2
1
0
0
1
1
2
2
3
1
2
1
1
2
3
0
2
1
1
0
2
1
2
0
2
3
1
0
2
6
0
2
0
2
0
1
0
2
2
1
2
1
0
0
1
0
0
0
1
1
1
1
2
2
0
0
2
0
0
0
1
0
1
0
0
1
0
0
1
0
1
0
0
1
0
0
1
1
0
2
0
0
0
1
0
0
0
1
2
1
0
0
1
1
1
0
1
0
1
2
1
1
0
2
2
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
1
1
0
3
1
2
2
1
1
0
1
1
2
2
2
0
1
0
0
2
0
1
1
0
1
1
0
1
1
2
2
0
0
0
0
0
1
1
2
1
1
1
0
2
0
2
1
0
3
1
0
1
0
0
0
0
2
1
1
0
2
2
1
2
1
0
1
0
2
0
1
1
0
2
1
0
0
0
1
1
2
1
1
2
0
0
1
1
2
1
2
2
1
0
1
2
1
1
1
0
2
0
1
0
0
0
1
0
1
0
1
2
1
1
1
0
1
2
1
0
1
0
1
0
2
2
1
2
2
1
1
2
0
2
1
2
1
0
1
1
2
0
0
2
1
1
1
1
2
0
0
2
0
0
0
0
0
1
0
1
0
0
1
2
0
2
1
1
0
1
1
1
0
0
1
0
1
0
2
0
1
1
0
0
0
1
1
3
2
1
2
1
0
0
1
0
0
2
1
0
2
1
1
2
1
1
0
0
0
1
0
1
0
1
1
0
1
0
0
0
2
2
0
1
2
1
1
0
1
0
0
0
1
1
0
1
2
0
1
1
2
0
1
0
1
1
1
0
0
1
2
1
0
1
0
1
0
0
0
1
0
2
0
0
1
2
0
2
1
1
0
2
2
1
0
1
2
0
0
0
1
1
2
2
0
1
0
1
0
0
0
2
2
0
0
1
0
0
2
2
0
2
1
1
0
1
1
0
0
1
0
2
0
2
1
1
1
0
0
0
2
1
2
0
0
0
1
0
1
1
1
1
0
0
1
1
0
1
1
1
2
1
0
2
0
1
2
1
2
1
1
0
1
2
0
2
2
1
1
1
0
0
1
0
1
0
1
1
2
2
2
1
2
2
3
0
1
1
0
1
0
1
1
0
1
1
1
1
0
1
0
1
1
2
0
0
0
1
1
0
0
0
1
0
2
0
1
1
1
1
0
2
0
2
2
0
0
1
1
2
1
0
1
1
1
1
2
0
0
2
1
0
0
2
0
1
2
2
1
0
2
1
0
5
2
1
2
1
2
0
1
1
1
1
0
2
1
1
2
0
1
1
0
2
1
1
1
2
0
1
1
0
2
2
1
0
0
1
0
0
0
1
1
2
1
2
2
2
0
3
0
0
0
1
0
1
1
1
0
0
2
1
0
0
2
2
2
2
0
0
1
0
0
1
2
1
1
1
0
2
0
2
2
1
1
0
1
7
0
1
0
1
1
0
1
1
2
2
1
1
0
0
1
0
0
0
2
2
2
0
1
1
0
1
1
0
0
2
1
2
1
1
1
0
1
1
1
0
0
1
0
1
0
0
1
1
0
2
0
1
2
2
1
0
2
0
0
1
0
1
1
1
0
1
2
1
1
2
2
1
1
0
2
0
2
1
1
1
1
2
0
1
1
0
1
0
0
1
1
1
0
1
1
1
2
1
2
1
0
0
0
0
1
1
0
1
1
0
6
1
2
0
1
2
0
0
0
2
2
1
1
1
2
1
0
2
2
1
1
0
0
1
1
1
0
1
1
1
1
1
1
1
1
1
1
2
1
0
2
1
1
0
0
1
0
1
2
1
0
0
2
2
0
2
1
2
1
2
0
1
1
2
1
1
1
0
2
1
0
1
0
2
2
0
1
2
2
1
0
0
0
1
0
2
0
2
1
1
0
1
0
1
2
2
0
1
2
1
0
2
1
1
1
2
0
2
2
0
1
1
1
1
0
1
0
1
0
1
2
0
1
2
1
1
1
1
2
0
1
0
1
1
1
1
0
0
0
1
1
0
1
1
1
2
1
1
2
1
1
0
2
1
0
2
1
2
2
0
1
0
2
1
1
2
0
1
0
1
1
0
0
0
0
2
1
2
1
0
0
1
1
1
1
1
0
1
1
0
1
2
0
0
1
1
0
0
0
0
2
1
2
0
2
2
0
1
0
2
0
1
1
1
1
0
1
0
1
2
2
3
1
1
1
2
1
1
1
0
1
1
1
1
0
1
1
2
2
2
0
0
0
2
1
1
1
2
2
0
1
1
0
2
1
1
0
1
0
1
0
0
1
0
1
1
1
2
1
1
2
0
0
1
1
1
1
0
0
0
0
1
3
2
1
1
0
1
1
1
2
0
2
1
1
0
1
1
1
1
1
1
1
2
0
1
0
1
1
1
1
0
0
0
1
2
0
0
0
0
2
0
0
1
1
1
1
1
0
2
0
0
1
1
2
0
1
0
1
1
1
1
2
1
2
2
1
1
0
0
1
1
2
2
0
0
2
0
2
1
1
1
1
1
0
1
0
0
1
1
0
0
0
0
1
1
0
1
1
2
1
1
1
2
1
1
1
0
2
0
0
1
0
1
0
1
1
0
0
1
2
2
2
0
0
1
0
0
0
0
1
1
1
0
2
2
0
1
0
1
1
1
2
1
0
1
0
0
0
1
1
0
0
2
0
1
0
1
1
3
1
0
1
1
1
1
1
0
2
1
0
0
0
1
1
1
0
1
1
1
1
1
1
2
1
2
0
0
1
1
0
1
0
2
1
1
1
1
1
2
1
0
1
0
1
1
0
0
2
1
0
2
1
1
1
0
2
2
1
0
1
2
0
0
2
1
0
0
0
0
0
2
1
0
0
0
0
1
1
1
0
0
0
2
0
1
2
0
0
2
0
2
1
1
1
1
0
0
1
0
1
0
1
1
2
2
2
1
1
2
1
1
1
2
2
2
2
0
1
0
0
2
1
0
1
0
1
0
0
1
0
1
1
1
0
0
0
1
1
0
1
1
1
1
2
0
1
0
1
0
0
1
2
0
2
0
1
2
0
1
0
0
0
0
1
2
0
2
0
1
0
2
2
1
2
1
2
0
1
1
1
1
2
1
1
0
0
1
1
2
1
1
0
1
1
1
2
1
0
2
2
2
1
2
1
1
2
0
0
2
0
1
0
2
1
1
0
1
1
0
1
1
1
0
0
1
1
0
0
1
1
0
0
0
0
1
1
0
2
1
2
0
1
2
1
1
1
1
0
0
1
1
1
1
1
1
0
1
1
0
2
1
0
0
2
2
1
0
1
1
1
0
0
1
2
1
2
0
1
2
1
1
1
1
0
0
0
2
0
1
1
0
2
0
2
0
2
2
0
1
1
0
1
0
0
0
1
0
1
0
1
2
1
0
0
0
1
0
2
1
1
2
0
1
3
0
0
1
0
0
0
0
2
0
0
2
1
1
1
0
2
0
3
0
1
1
2
0
0
0
1
1
0
0
1
1
1
1
1
2
1
1
1
1
0
2
2
3
0
1
1
0
0
2
2
2
2
1
1
2
0
0
2
2
2
1
0
0
2
1
1
1
1
2
0
1
2
1
2
1
1
0
1
2
0
0
2
1
1
1
1
2
0
2
1
1
0
1
0
0
2
0
1
1
2
0
1
2
1
1
1
0
0
0
2
0
1
2
2
1
0
2
0
0
0
1
1
1
1
0
2
0
1
0
0
0
0
1
0
1
1
1
2
0
1
0
1
1
2
2
1
0
2
0
0
1
1
0
1
1
0
0
0
1
1
0
1
2
1
1
0
0
2
2
1
0
1
2
1
2
1
0
0
0
1
2
0
0
1
1
2
2
1
0
1
2
2
2
0
1
1
2
0
1
1
2
0
1
1
0
0
1
1
0
2
1
3
0
2
0
1
1
2
1
1
1
0
1
1
1
0
0
2
1
1
1
1
0
2
2
0
0
0
2
1
2
1
1
1
1
2
0
1
0
1
1
1
1
2
0
2
1
0
0
0
0
1
2
1
0
0
2
0
2
1
1
2
1
0
2
1
1
1
1
1
1
0
2
1
1
0
0
1
0
0
1
0
2
2
2
1
1
1
0
1
1
0
2
1
1
2
2
0
2
0
1
1
0
1
2
2
0
2
1
2
1
1
0
1
2
0
1
2
0
2
1
0
2
1
0
0
0
0
2
0
0
0
2
2
0
2
0
1
2
2
0
1
0
1
0
1
1
2
1
1
1
2
1
1
1
0
0
0
1
0
1
2
0
2
0
0
1
1
1
2
0
2
0
1
0
0
1
1
0
1
0
1
1
0
0
0
0
0
2
1
0
1
0
2
0
1
1
2
0
1
0
0
1
0
1
2
1
1
0
1
2
1
0
2
2
2
0
1
2
0
2
2
1
1
1
1
1
2
1
0
1
1
1
1
0
1
1
0
2
1
1
0
1
1
0
0
1
1
1
1
0
1
2
2
0
0
1
0
0
0
1
1
2
1
1
1
1
1
2
1
0
0
1
1
3
1
0
0
1
0
2
3
0
0
0
2
0
1
1
1
1
1
0
1
1
0
2
2
0
0
1
0
1
0
1
2
0
0
2
1
1
1
2
1
0
2
1
1
1
2
0
0
1
0
1
1
2
1
0
0
0
1
0
1
1
0
0
1
2
0
0
0
1
1
1
1
2
0
2
1
0
1
0
0
1
1
1
2
0
1
0
1
1
1
0
1
1
0
1
1
1
0
0
1
0
1
0
1
0
1
1
0
1
1
1
0
0
2
3
1
1
0
0
1
2
2
1
2
2
1
1
0
2
1
2
1
1
2
1
0
2
0
1
1
1
1
0
1
1
1
1
0
2
0
0
1
1
0
0
0
2
1
2
0
1
0
2
1
1
1
2
0
2
0
2
1
1
1
1
1
0
0
0
0
1
1
0
0
0
1
0
1
1
2
1
0
0
2
2
2
1
0
0
1
1
1
1
0
0
1
1
0
0
0
1
0
2
0
1
0
0
0
1
1
1
1
0
0
1
0
1
0
0
0
0
1
0
1
1
0
1
2
0
0
2
1
0
0
0
1
0
1
1
0
2
0
0
2
1
0
2
0
1
0
2
1
2
2
0
2
1
0
0
2
0
0
1
0
1
1
1
0
1
2
2
1
1
1
0
0
1
1
0
1
2
7
2
0
1
1
1
1
1
2
1
1
1
0
0
1
0
2
0
1
0
0
0
1
1
1
1
0
0
0
1
1
2
2
1
1
1
2
2
0
2
1
1
1
1
2
3
0
1
2
2
0
0
2
1
0
1
0
1
2
0
1
2
0
1
3
0
1
1
0
1
1
1
0
1
0
0
1
2
1
2
3
1
1
0
1
1
2
1
0
1
0
1
1
2
0
2
0
1
0
0
1
0
1
0
0
2
0
1
1
0
1
0
1
1
1
0
1
2
0
1
1
0
0
1
2
1
0
0
1
2
2
1
0
2
1
1
1
0
0
0
0
2
0
2
1
1
2
1
0
0
1
1
0
0
0
2
0
1
0
0
1
1
1
2
0
0
0
2
1
0
1
0
0
2
2
1
1
1
1
1
2
2
1
2
2
0
1
2
2
2
2
0
2
2
0
0
2
0
0
1
1
2
0
1
2
1
2
1
1
0
2
0
0
1
0
0
1
1
1
1
1
1
1
0
1
2
2
1
0
1
1
1
2
1
1
1
0
0
1
1
1
1
2
0
1
1
1
1
1
1
0
1
1
2
1
1
0
2
0
0
0
0
1
0
0
2
0
0
0
0
1
0
1
1
2
1
1
1
0
0
0
1
1
1
0
1
1
2
1
1
1
1
1
0
0
1
1
1
1
0
1
1
1
0
1
0
0
3
2
0
1
1
1
1
3
0
0
0
0
1
0
0
0
0
1
2
1
0
1
0
1
2
0
0
2
0
2
0
0
1
1
2
1
0
0
0
1
1
1
1
1
0
0
0
1
0
1
0
0
2
2
0
0
2
1
0
2
1
1
0
1
0
1
1
2
3
1
1
1
0
1
0
0
1
2
1
0
0
1
0
2
0
1
0
1
1
2
1
2
2
2
2
0
2
0
0
2
1
4
0
2
2
2
0
1
0
0
1
1
0
1
1
0
1
2
0
0
0
1
1
2
0
1
1
0
2
0
0
1
0
0
1
2
0
1
0
1
0
1
0
4
0
1
1
1
1
1
1
1
0
1
1
1
0
0
1
1
1
1
1
0
0
1
1
1
0
0
1
1
1
0
0
2
1
4
1
2
0
0
3
1
0
0
0
0
2
1
1
2
1
2
2
1
2
2
0
1
0
1
1
2
4
1
1
2
1
1
1
0
0
1
1
1
2
0
1
1
0
3
1
0
1
1
2
1
2
0
1
1
1
1
0
1
2
2
1
2
0
1
1
0
0
1
1
1
1
1
2
1
3
2
1
1
1
2
0
2
0
1
1
0
2
1
0
2
1
1
1
0
0
1
0
1
2
1
1
0
1
2
1
1
2
1
2
1
0
2
0
2
1
0
1
1
0
1
1
0
0
2
0
1
1
0
1
0
1
0
1
2
1
0
1
1
3
1
1
0
1
1
2
0
0
0
2
1
2
2
0
1
0
1
1
0
1
0
1
0
1
1
1
2
0
0
1
1
3
1
1
0
1
1
0
0
2
0
1
1
1
1
1
0
1
1
0
0
0
1
0
0
1
1
1
2
1
1
0
0
1
1
1
0
0
2
0
0
2
2
0
0
0
0
0
2
1
0
2
2
2
1
0
1
1
1
1
1
0
1
1
1
0
0
2
1
0
1
2
1
1
1
0
1
2
1
0
0
2
2
1
0
1
1
0
2
2
1
1
2
1
1
0
1
0
0
0
1
2
0
2
1
0
0
1
0
0
1
0
1
2
2
0
1
0
0
0
0
2
2
2
1
1
4
0
1
0
0
1
3
2
0
1
1
0
0
1
2
0
0
1
1
1
1
2
3
0
2
0
1
1
0
0
0
0
1
1
0
1
1
2
1
0
1
0
0
0
1
1
0
1
0
0
0
2
2
0
1
0
0
0
0
2
0
2
1
0
1
0
2
2
0
0
1
0
1
1
1
2
0
1
1
1
0
1
1
1
0
1
1
2
3
0
0
1
2
1
0
2
2
2
2
2
1
1
0
1
0
0
2
1
1
1
2
0
0
2
0
2
0
2
0
0
0
2
2
1
2
0
0
0
0
1
1
1
1
2
1
2
2
2
2
1
1
0
0
2
2
1
0
1
2
0
0
1
1
2
0
1
1
0
1
1
1
0
1
2
2
0
0
1
1
2
1
0
1
2
0
1
2
0
2
2
2
0
0
2
1
1
2
1
1
2
1
2
1
2
2
2
1
1
2
1
0
0
0
1
2
1
2
1
0
1
4
4
1
1
1
2
1
0
0
1
2
9
2
2
1
2
0
0
1
1
1
1
0
1
0
1
0
1
1
2
0
1
0
1
2
1
0
0
1
1
1
1
2
1
1
0
0
0
0
0
1
0
1
0
1
0
0
1
1
1
1
1
0
0
1
0
0
2
1
1
1
1
2
2
2
1
0
1
3
1
2
2
1
0
1
1
1
1
0
0
1
1
1
2
1
1
2
1
0
1
1
1
1
2
0
1
1
0
0
0
2
0
2
1
0
1
2
2
2
0
0
1
0
2
0
2
0
2
0
0
0
0
1
0
2
0
1
0
1
1
1
1
1
2
2
1
5
0
1
0
1
2
0
0
2
1
0
1
1
0
1
1
1
1
4
1
2
0
2
2
0
1
1
1
0
0
1
0
1
1
0
0
1
1
0
2
2
0
2
0
0
1
1
0
1
2
1
0
0
0
0
2
1
0
2
1
1
0
0
1
1
1
0
2
0
1
0
1
2
3
0
1
1
1
1
3
2
2
1
2
0
1
1
2
1
0
2
1
1
0
2
1
1
0
0
0
1
0
1
1
1
2
1
1
0
0
0
1
2
1
0
1
1
0
2
1
1
2
0
0
2
2
2
0
2
1
2
0
2
1
2
1
1
1
0
0
1
1
2
1
2
1
1
0
0
0
1
1
0
0
0
1
1
0
0
2
2
1
1
0
1
0
2
1
2
1
1
0
1
1
1
1
1
1
0
1
1
0
0
1
2
2
2
2
0
0
0
0
1
0
1
1
0
2
0
2
0
1
0
1
1
0
2
2
2
0
0
0
0
0
0
2
0
2
1
2
1
1
0
2
1
1
0
0
0
0
2
2
0
4
0
1
1
1
0
0
2
1
2
2
0
0
1
1
2
0
0
1
1
1
0
0
1
1
2
0
2
1
2
1
0
1
2
0
0
1
1
0
0
1
1
2
1
2
2
0
0
0
1
1
0
0
2
0
1
1
1
1
2
1
3
2
1
1
0
1
2
2
2
1
1
0
0
1
1
1
1
0
1
1
0
2
1
0
1
1
2
0
1
2
1
0
1
1
0
0
1
0
0
0
1
3
2
0
2
0
2
0
1
1
2
0
1
0
2
0
0
2
1
0
0
0
2
1
2
2
0
1
0
0
1
0
0
0
1
0
0
0
0
2
2
2
1
1
0
2
0
0
1
0
0
0
1
2
1
0
1
0
1
1
0
0
1
2
1
0
2
2
2
1
1
1
1
0
1
2
1
1
2
0
1
0
0
1
0
0
1
1
1
0
0
0
1
1
0
2
2
0
2
3
1
1
0
1
0
1
0
0
1
2
1
2
0
1
0
1
2
1
2
1
1
1
2
0
1
0
1
1
0
2
1
1
0
2
2
3
1
2
1
2
0
1
0
0
1
1
0
2
2
1
1
1
0
1
0
2
1
1
1
3
1
1
0
1
1
1
1
0
0
0
0
1
2
0
1
1
1
0
0
1
0
0
2
0
1
2
1
0
1
0
2
0
0
2
0
1
0
1
1
1
1
1
0
1
1
0
0
0
0
0
0
3
1
1
0
1
1
1
0
1
0
1
2
1
0
0
1
0
2
1
0
1
1
0
1
10
1
0
1
0
1
1
1
1
1
1
1
0
1
1
1
1
0
1
0
1
2
2
1
0
1
1
0
1
1
1
2
1
0
2
1
0
0
1
0
1
0
2
0
1
1
1
1
0
1
0
0
1
1
0
2
0
1
0
1
0
1
1
1
0
2
1
0
1
1
3
2
1
0
1
1
2
0
1
0
0
2
2
1
1
1
0
0
0
1
0
2
2
0
0
0
0
1
2
0
0
1
0
1
0
0
1
1
1
1
0
1
0
0
0
0
1
0
0
2
1
0
0
1
1
0
1
1
1
0
4
2
0
0
0
2
0
1
1
1
1
1
2
2
1
1
2
1
0
0
1
1
1
1
1
1
2
0
0
3
0
1
1
1
1
0
1
0
0
0
0
0
0
0
1
1
2
1
2
1
0
2
0
2
2
2
0
1
0
0
0
1
1
2
1
2
0
1
1
0
2
3
1
0
2
1
1
0
0
0
0
2
1
2
1
0
1
2
0
1
1
0
0
1
2
1
1
1
1
0
1
0
0
0
2
2
2
2
2
0
2
0
0
1
0
2
1
1
1
1
0
0
1
0
2
2
1
0
2
2
0
1
2
0
1
1
1
0
1
0
1
2
2
0
2
0
0
2
0
1
1
1
2
1
2
1
1
0
2
1
2
1
0
0
0
0
1
1
1
1
1
1
2
1
1
0
0
0
1
1
0
1
0
0
2
1
1
2
1
1
1
1
1
1
1
0
2
2
0
1
0
0
0
0
0
0
2
0
1
0
1
0
0
1
0
0
1
2
1
1
1
2
0
1
0
0
0
2
1
1
2
1
1
1
2
1
1
0
4
1
0
2
0
0
2
0
0
1
0
2
2
2
0
1
0
0
0
2
1
1
1
3
1
1
1
2
0
1
2
2
4
2
1
1
0
1
0
0
2
1
2
2
0
0
1
1
0
2
2
2
0
0
0
1
2
2
2
1
0
0
1
2
0
1
2
1
1
2
0
2
0
1
1
2
0
1
2
0
1
1
0
0
1
2
0
0
0
3
1
1
1
1
0
1
1
1
2
3
2
0
1
1
0
1
0
1
1
0
1
1
1
0
1
2
1
0
0
0
2
3
0
1
2
0
0
0
0
0
2
2
1
1
0
1
1
1
1
0
0
2
2
0
0
2
1
0
2
0
2
0
0
1
2
1
0
2
2
3
3
2
0
0
1
0
0
3
1
1
1
2
0
0
2
0
0
1
2
0
1
0
1
2
1
0
2
0
1
1
1
1
0
1
1
0
0
1
1
1
0
0
2
0
2
0
1
0
0
1
1
0
1
1
2
2
1
1
0
2
2
1
0
1
1
0
0
1
2
1
1
2
2
2
0
0
1
0
0
0
0
0
1
0
1
1
0
1
1
1
1
2
0
0
1
0
1
0
1
2
0
0
2
1
2
1
2
2
1
2
1
2
1
1
1
0
2
0
1
1
0
0
2
1
1
1
1
0
0
1
1
1
1
0
0
0
1
1
1
0
0
1
0
2
2
2
0
2
1
1
0
1
1
1
0
0
1
1
1
2
0
2
0
0
0
1
0
0
0
1
2
1
0
1
0
1
0
0
0
0
1
1
0
1
2
0
1
2
0
0
1
0
1
2
2
0
0
1
1
1
0
1
1
0
2
1
2
0
2
2
1
0
1
1
1
0
1
0
1
2
0
2
2
0
0
0
0
2
1
0
0
2
1
0
2
2
0
0
1
0
0
1
1
0
1
1
1
0
1
1
2
0
0
1
0
1
0
0
0
1
1
4
2
0
0
1
2
1
0
2
1
1
2
1
2
0
0
0
1
0
2
1
1
0
1
0
0
0
1
2
0
2
1
0
0
1
0
0
2
1
0
1
0
1
2
1
1
1
0
2
0
1
0
0
0
2
0
0
1
2
1
1
2
1
0
2
0
0
1
2
2
2
2
0
1
0
2
1
1
2
0
1
0
2
0
2
1
1
2
0
2
2
1
2
2
1
0
0
0
2
0
1
1
2
1
1
1
2
1
2
1
0
1
1
1
0
1
1
2
1
2
2
0
1
1
1
1
1
1
0
0
2
1
1
2
0
2
0
5
1
0
1
1
1
1
0
0
0
0
0
0
1
0
2
0
1
2
0
1
2
1
1
1
1
2
1
1
2
0
1
1
2
0
1
1
0
1
1
2
2
0
0
2
3
2
2
1
2
1
3
2
2
1
0
1
1
0
1
2
0
1
0
1
1
2
1
2
0
0
0
1
2
1
2
1
0
0
2
2
0
1
1
2
1
0
1
1
2
1
0
0
2
2
1
2
0
1
0
1
1
0
2
1
0
1
0
1
2
0
2
1
0
2
0
0
0
1
0
0
2
0
2
0
2
1
2
0
0
0
1
0
2
1
1
2
0
1
2
0
0
0
1
0
0
1
0
0
1
2
0
2
2
1
1
1
0
0
1
2
0
4
0
1
0
2
2
1
1
0
0
2
2
1
2
1
1
2
1
1
1
2
1
1
0
1
0
0
1
1
2
1
1
0
0
1
2
0
1
0
0
0
0
0
1
0
0
0
0
2
1
1
0
1
0
2
0
1
0
1
0
1
0
1
2
1
2
0
0
3
1
2
2
1
0
2
2
0
1
1
0
1
0
2
0
0
2
2
1
1
1
0
0
0
1
0
0
0
2
2
1
1
2
0
1
0
2
1
2
0
0
2
1
0
0
1
1
1
1
1
1
1
1
2
1
0
0
1
0
1
4
1
0
0
1
0
0
0
0
1
0
2
1
1
1
2
1
0
1
0
1
0
1
1
2
0
0
1
1
1
0
1
2
1
0
1
0
1
0
0
0
1
2
0
0
1
2
1
1
1
1
1
0
0
1
2
1
0
0
1
1
1
1
1
1
0
0
1
1
2
1
1
0
2
1
2
1
0
2
2
0
1
2
1
2
2
0
1
0
2
1
1
1
1
2
0
2
0
0
0
2
1
0
0
0
1
0
2
0
0
1
2
1
1
2
1
0
1
1
0
0
2
2
1
1
1
1
0
1
0
1
0
4
1
0
1
1
0
1
2
2
0
0
1
1
2
0
1
1
1
1
1
2
1
1
1
2
2
1
2
0
0
2
0
0
0
2
1
0
1
0
1
0
1
0
0
2
1
1
1
0
2
2
1
1
0
0
1
2
2
1
1
0
1
1
1
2
2
0
2
1
1
0
5
2
0
0
0
2
1
2
0
1
3
2
3
0
2
1
1
0
1
1
1
2
1
0
1
1
2
0
0
1
1
1
1
0
0
2
0
1
0
2
1
1
0
0
1
1
0
2
1
0
1
2
2
1
2
1
1
1
0
1
0
1
0
0
0
0
1
2
0
0
0
0
2
2
1
2
2
3
1
1
0
0
0
1
1
1
1
1
2
3
1
0
0
1
2
0
0
2
0
1
0
0
2
7
0
0
1
2
0
2
2
1
2
1
1
1
1
1
0
1
0
1
2
1
0
0
0
1
1
0
2
2
0
0
1
1
1
0
1
1
2
0
0
1
1
2
2
1
0
1
1
1
1
1
2
1
1
0
2
0
0
1
1
0
2
1
2
0
0
1
1
1
2
0
1
1
1
0
0
1
0
2
2
0
1
1
1
1
1
2
0
1
1
1
0
0
1
0
0
0
2
2
1
0
0
0
0
2
0
0
2
2
0
2
2
1
1
1
1
1
0
2
1
1
1
0
1
0
0
0
1
1
2
1
2
2
0
0
1
0
0
2
2
1
1
1
0
1
0
0
0
0
1
4
2
1
1
0
2
2
0
1
2
1
0
1
1
0
1
0
1
1
1
0
1
1
0
2
2
1
1
0
1
1
0
2
1
1
0
1
0
0
2
1
2
1
1
0
0
1
2
1
0
1
1
1
2
0
0
1
1
2
0
1
0
1
2
1
2
1
0
0
1
0
1
0
0
0
0
1
1
1
1
1
1
1
0
2
1
2
2
1
2
0
1
0
2
0
2
4
1
1
1
0
2
1
1
0
0
2
0
0
1
1
2
1
0
1
1
1
1
2
1
2
1
2
1
0
3
0
1
0
1
0
2
1
2
0
1
1
2
1
1
2
0
2
0
1
1
2
1
2
2
0
2
0
0
1
1
1
0
0
0
1
0
0
0
0
2
1
0
0
0
1
0
0
0
1
0
2
2
1
0
1
1
1
2
3
1
1
2
0
1
1
1
2
1
1
2
1
1
0
2
0
1
2
1
0
3
2
0
1
0
0
0
0
2
1
0
2
1
2
0
1
0
0
1
2
1
0
2
0
1
0
1
1
0
1
0
1
1
0
0
0
0
0
2
2
1
0
3
1
2
0
2
1
1
0
2
2
1
1
1
2
2
1
2
2
1
1
0
0
1
1
2
0
3
0
1
1
2
0
0
0
1
0
2
0
0
1
1
0
0
2
0
1
0
2
0
0
2
2
2
1
2
2
1
1
1
0
1
1
2
1
1
2
2
0
2
1
1
1
0
1
2
0
0
0
0
1
2
0
1
1
0
1
1
2
0
3
1
2
0
1
1
1
0
2
1
0
0
1
0
0
2
1
0
0
1
0
1
1
0
1
1
2
0
2
2
1
4
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
1
2
0
2
0
1
1
0
1
1
1
0
3
2
1
0
1
2
0
1
0
1
1
1
1
0
1
0
1
0
0
1
0
2
0
0
0
1
2
1
0
2
1
1
2
0
0
1
2
0
1
0
1
2
0
1
1
0
0
0
5
0
0
1
1
2
1
0
0
0
0
1
0
2
2
1
0
2
1
1
0
0
1
2
1
1
1
0
0
0
0
2
1
0
0
1
1
1
0
0
1
2
0
0
0
2
1
0
1
0
0
2
1
2
2
2
1
1
1
0
0
0
0
2
0
1
1
0
1
0
2
0
0
2
2
0
1
0
2
1
1
0
2
2
0
1
0
2
0
0
1
1
2
0
1
1
0
0
1
1
1
2
0
1
1
1
1
0
0
2
2
1
1
0
1
0
2
0
0
2
0
1
1
0
1
0
1
2
1
1
1
0
1
1
1
1
1
1
2
0
2
2
1
1
0
1
1
0
1
0
0
2
0
0
0
1
1
0
1
0
0
0
2
0
1
2
1
2
1
2
1
1
0
1
0
0
2
1
1
0
0
1
2
1
1
1
1
1
2
2
0
2
1
2
1
0
1
1
1
2
0
0
0
2
1
1
1
1
1
2
1
1
1
0
2
0
2
0
0
0
1
1
0
1
1
0
0
3
1
0
1
0
0
1
0
1
2
1
1
1
1
0
2
1
2
0
1
0
2
1
1
2
0
1
1
0
2
2
1
1
0
1
1
1
1
1
0
0
1
1
0
0
0
1
2
0
1
1
0
0
1
1
0
1
1
0
2
1
1
1
0
2
1
2
0
0
1
0
1
0
1
0
0
2
0
0
0
1
0
2
2
1
0
0
0
1
2
1
1
3
1
1
0
0
0
0
2
2
1
1
1
1
0
1
0
0
0
1
2
1
2
0
2
0
1
1
1
0
1
0
1
0
3
0
0
0
0
2
1
2
1
1
0
1
0
0
0
0
1
0
0
2
3
0
2
0
1
0
1
2
0
2
2
1
0
2
2
2
1
0
1
1
0
1
1
1
0
1
4
0
1
1
2
0
1
1
1
0
0
0
0
2
0
1
1
0
1
0
0
0
2
1
0
2
1
0
0
0
1
1
1
1
1
0
0
1
1
0
2
1
1
1
0
0
1
1
2
0
0
2
1
1
1
1
2
2
2
0
0
2
1
1
1
0
2
1
1
2
0
1
1
1
1
0
0
1
0
2
0
0
0
0
1
0
1
2
2
0
2
1
0
1
0
1
0
1
2
1
2
2
2
1
2
2
0
2
0
0
2
0
1
0
1
1
2
1
2
1
0
0
1
0
0
2
0
0
0
9
1
2
2
0
2
1
2
2
0
2
0
0
1
2
1
1
2
2
2
2
2
0
1
0
1
0
1
0
1
0
1
2
1
0
0
0
2
0
3
0
2
1
0
1
2
0
0
0
0
0
1
1
0
2
0
1
0
1
1
0
0
2
0
0
2
0
0
0
2
1
1
2
1
0
2
1
0
1
0
2
0
0
1
1
0
1
0
0
2
0
0
1
1
1
2
1
0
1
0
1
0
0
1
2
0
3
0
0
1
1
0
2
0
3
1
2
1
1
2
2
1
0
0
1
1
1
0
0
1
1
3
1
0
2
0
0
1
1
2
1
1
0
0
1
0
0
2
1
1
0
1
0
1
2
1
0
1
1
0
2
0
2
0
1
1
1
0
0
2
0
1
1
0
1
1
0
0
1
1
1
2
2
0
1
1
1
0
2
0
1
0
0
1
1
1
0
0
1
1
0
23
0
0
1
1
1
0
0
1
1
0
3
2
2
1
1
0
0
2
1
2
1
0
0
2
2
2
1
0
2
0
0
0
1
2
2
0
0
0
2
1
0
2
0
1
1
2
1
2
1
2
0
2
1
0
1
2
2
0
0
2
1
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
1
2
0
0
0
2
1
2
1
2
2
1
2
1
1
1
2
1
1
1
1
1
2
0
1
1
2
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
2
0
1
2
2
1
1
1
1
1
0
1
1
1
1
0
2
0
1
1
1
1
1
1
1
0
1
1
1
0
0
1
1
1
1
0
0
1
2
1
2
0
1
2
1
2
0
2
2
2
2
1
1
1
1
2
0
1
0
0
0
0
1
1
0
1
1
3
0
0
0
1
1
2
0
0
0
1
1
1
0
2
2
1
1
0
1
2
2
0
2
2
2
0
0
1
2
1
0
0
1
2
2
0
0
1
0
0
0
0
5
1
0
1
1
0
1
1
1
0
1
1
0
2
0
1
1
1
0
0
1
2
2
1
1
1
1
0
0
1
2
1
2
2
2
1
1
2
1
0
1
0
0
1
0
1
2
2
0
1
0
2
1
0
0
0
1
2
0
1
1
2
1
0
2
1
2
2
1
0
0
2
1
0
2
1
1
1
0
0
1
0
0
1
2
0
2
0
0
1
1
0
1
1
0
1
0
1
2
1
1
0
2
2
1
0
0
1
1
2
1
1
1
0
2
1
2
1
1
2
1
1
1
2
0
0
1
1
1
2
1
2
2
1
1
1
1
0
0
0
1
1
1
1
1
1
0
0
2
0
0
1
0
1
2
1
1
1
1
2
2
2
1
1
1
1
2
0
0
0
1
1
1
1
2
1
0
0
2
0
1
1
2
1
1
2
1
2
0
0
1
1
1
0
0
2
1
0
0
2
2
2
1
0
1
0
1
1
0
1
1
1
1
0
2
2
0
1
1
0
1
1
2
0
0
1
1
2
2
0
1
1
2
2
1
1
1
1
2
0
1
2
1
1
1
2
1
0
0
0
0
1
0
1
1
2
2
1
1
1
2
0
0
4
0
1
1
1
3
0
0
0
0
1
1
0
1
1
0
2
1
1
1
2
0
1
1
1
0
1
1
1
0
0
1
2
1
1
2
1
0
1
1
1
0
1
1
1
1
1
1
2
2
1
1
0
0
0
0
0
2
1
0
1
1
0
0
1
1
1
3
0
1
1
1
1
1
1
0
1
1
0
1
2
2
0
2
0
0
0
0
0
2
1
1
1
1
0
1
1
1
1
1
1
1
0
0
1
1
1
1
2
2
0
1
1
3
1
2
1
1
1
0
0
1
1
0
1
3
2
1
2
0
1
2
2
1
0
1
0
0
2
0
1
0
1
1
1
1
2
1
1
1
1
2
2
1
1
1
1
1
1
2
1
0
0
1
0
1
0
1
1
1
2
0
2
0
2
0
0
2
1
1
1
1
2
1
0
0
1
0
1
2
1
2
1
0
1
0
1
0
1
1
2
1
1
1
1
0
1
0
0
2
0
1
0
0
0
1
0
1
1
0
0
1
0
1
0
1
1
0
2
1
0
2
1
1
1
0
2
1
1
0
1
0
1
0
1
1
2
0
0
0
1
0
1
0
1
1
4
2
0
2
1
1
1
1
0
0
2
0
0
1
0
1
1
1
1
1
2
1
0
0
6
1
0
0
2
0
0
1
1
0
0
1
1
0
1
1
0
0
1
0
0
2
2
0
1
1
1
0
2
2
0
1
0
1
1
1
1
2
1
0
1
0
1
1
1
2
0
0
0
2
1
1
1
0
1
1
1
1
2
0
1
1
0
0
1
1
1
2
2
2
0
0
1
1
0
1
2
0
2
1
1
1
1
1
2
0
0
0
2
1
2
1
1
2
1
0
1
2
1
1
2
2
3
0
0
0
0
1
3
0
1
0
0
0
1
2
0
0
2
1
1
1
1
0
0
1
2
1
1
0
2
0
0
1
0
0
2
0
0
2
0
0
2
0
2
0
2
0
1
0
2
1
0
2
1
1
1
1
1
0
1
2
1
0
1
1
2
1
1
0
1
0
1
0
2
0
0
0
1
0
1
0
0
0
0
0
1
0
1
2
2
0
2
1
2
0
1
0
1
2
1
0
1
1
1
1
1
1
0
0
2
0
0
2
1
2
2
2
0
1
1
0
1
1
1
0
0
0
1
0
0
1
2
0
1
1
2
0
1
2
0
0
1
0
1
1
1
0
1
2
0
1
2
1
0
0
1
0
1
0
1
0
0
0
1
2
1
1
1
1
1
0
0
1
1
1
2
1
1
0
1
1
1
0
1
1
0
2
1
2
2
2
2
1
0
1
1
1
1
2
0
1
1
1
2
0
2
0
0
0
2
1
1
0
2
1
2
0
2
1
1
0
0
0
1
0
0
0
1
2
0
1
2
2
1
2
1
0
1
1
0
2
1
1
0
2
4
1
1
2
0
0
0
1
0
2
0
1
0
0
0
1
1
2
1
0
0
2
2
2
1
1
2
1
2
0
1
2
1
1
2
2
0
2
0
0
1
0
1
0
1
2
1
2
2
1
2
1
0
0
1
2
0
0
1
1
1
1
0
1
1
0
1
2
1
1
0
2
0
2
0
3
0
0
1
1
0
1
1
3
0
1
1
1
2
1
0
1
0
1
0
1
0
2
3
1
1
2
1
0
2
0
2
1
0
2
2
2
2
1
2
0
1
1
2
1
0
0
1
0
1
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
1
1
0
1
1
1
1
0
0
1
2
1
1
1
0
1
1
1
0
1
0
0
1
1
0
0
1
0
1
1
1
0
1
2
0
2
1
1
0
0
1
2
2
0
1
2
2
2
1
1
1
0
2
1
2
2
1
1
1
1
0
1
1
0
1
1
0
1
1
2
2
2
1
1
2
3
1
1
1
1
1
1
1
2
1
0
2
0
2
1
0
1
1
1
1
1
1
0
1
0
1
0
1
1
1
1
1
0
0
2
0
1
0
0
2
0
0
1
1
1
1
1
2
3
2
2
2
1
2
1
0
1
1
1
0
1
0
1
1
2
2
0
1
0
0
1
0
3
0
0
1
1
0
1
2
0
1
1
1
2
0
0
0
1
2
1
2
2
1
0
1
1
1
1
0
0
2
0
2
0
2
0
1
1
1
1
0
2
1
0
1
0
4
1
0
2
0
0
0
1
1
0
2
0
1
1
1
2
0
1
1
1
1
0
1
0
0
1
1
2
1
2
0
1
1
1
2
2
0
1
1
2
2
2
0
0
1
1
2
1
0
0
1
1
1
1
2
1
2
0
1
0
1
1
1
1
2
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
2
1
2
0
0
0
1
0
1
0
0
0
1
1
0
0
2
2
2
1
0
1
2
1
1
0
1
0
1
2
1
2
0
4
0
1
1
1
3
0
1
2
2
2
0
0
0
0
2
0
0
0
0
1
2
2
1
2
0
1
2
1
0
1
2
0
1
1
1
0
1
1
0
1
0
1
2
1
1
1
2
1
2
2
1
0
2
0
1
0
1
1
1
0
1
0
1
2
1
0
0
0
2
2
0
1
1
0
0
1
0
0
0
0
0
0
2
2
0
0
2
0
1
1
0
0
1
2
1
0
2
0
1
1
1
2
0
1
1
2
1
0
1
2
0
1
1
1
1
1
0
0
2
0
1
1
0
1
0
0
1
0
1
0
1
1
1
2
1
2
0
1
0
2
0
0
1
0
2
1
0
0
2
0
1
1
0
2
2
0
1
0
1
0
2
0
0
1
2
1
2
0
1
0
1
2
2
0
0
0
0
0
1
1
1
1
2
1
0
1
0
1
1
0
1
1
0
2
1
1
0
0
1
1
0
0
0
2
1
1
0
1
1
0
1
0
2
0
2
0
0
0
2
0
0
1
1
1
2
0
0
3
1
0
2
2
0
2
2
1
1
0
0
1
1
1
1
2
0
0
0
1
2
2
0
0
1
1
0
1
1
1
2
1
3
1
1
1
0
1
2
0
0
1
1
1
0
2
0
1
1
0
1
1
1
2
1
0
0
2
1
0
1
1
0
1
1
1
1
0
0
0
0
1
0
2
1
1
2
1
0
0
1
1
2
0
1
1
0
0
2
1
0
1
0
0
0
0
2
1
1
2
1
0
2
2
2
1
1
0
2
0
1
0
0
1
1
1
1
1
1
0
2
0
1
0
1
2
1
1
0
1
1
1
0
1
2
1
0
0
0
1
1
0
2
0
1
1
0
2
0
2
1
2
0
1
0
1
0
1
2
1
0
1
0
2
2
1
2
0
3
1
0
1
0
0
1
1
1
1
0
1
2
1
1
2
2
1
0
0
0
0
2
1
1
3
0
0
0
0
2
0
1
0
0
2
2
1
0
1
1
1
0
0
0
2
2
0
1
1
0
0
2
2
0
0
0
1
0
2
2
2
0
0
1
1
1
2
1
1
2
1
2
1
1
1
2
1
2
0
1
0
0
2
0
0
0
0
0
0
1
2
0
2
1
0
2
1
2
3
2
2
1
0
1
1
2
2
1
1
0
0
1
1
1
1
2
2
0
2
0
2
2
0
4
2
1
0
0
1
0
1
2
1
1
1
0
0
1
1
0
0
1
1
0
1
2
1
1
0
2
3
0
0
0
1
1
1
0
0
1
0
2
0
1
0
0
1
1
1
1
0
3
1
2
1
0
1
1
0
1
2
1
2
0
0
1
0
2
0
1
1
1
1
1
2
2
2
0
1
1
1
0
1
1
0
2
2
2
0
0
10
0
1
0
1
0
2
1
1
1
0
0
1
0
1
1
2
1
0
0
0
0
2
0
1
1
0
0
0
0
1
1
0
2
1
1
1
0
1
1
2
1
2
0
1
1
1
2
2
0
0
1
1
2
0
2
1
3
2
0
0
0
2
1
0
0
0
1
2
1
0
2
1
1
1
1
2
2
1
0
2
0
0
0
1
2
0
0
0
0
1
0
0
2
1
1
0
1
0
0
0
0
2
1
1
0
0
2
3
0
1
1
1
0
1
0
1
2
1
1
1
1
0
1
1
0
0
0
1
1
1
1
0
2
0
1
2
0
1
1
2
1
0
1
0
0
2
1
1
0
0
0
0
0
0
0
1
0
0
1
0
1
1
1
0
1
0
1
1
2
1
0
0
1
1
1
1
1
2
1
0
2
1
1
1
1
0
1
1
1
1
0
1
1
1
0
0
2
0
0
0
1
0
0
0
0
1
2
0
0
0
0
2
0
1
0
0
0
0
2
1
1
2
1
0
1
0
0
0
1
0
1
2
0
1
1
2
2
2
1
2
1
1
0
0
2
0
2
1
1
1
1
0
1
0
2
2
1
2
1
1
1
1
0
1
1
0
0
2
1
1
1
0
0
2
1
0
1
2
1
0
0
2
2
1
1
0
3
0
0
1
1
0
1
0
1
1
1
2
1
0
1
0
2
0
1
1
0
0
1
3
2
3
2
1
2
9
0
0
1
0
0
1
0
1
0
0
1
0
1
2
1
1
0
1
2
1
1
1
0
1
2
1
2
2
1
0
1
0
2
0
0
2
1
1
1
1
0
1
1
2
1
2
1
2
0
1
0
1
1
2
1
1
2
1
0
1
1
0
2
1
1
0
1
0
0
1
1
0
0
0
1
1
1
1
1
2
1
2
0
1
1
1
2
0
0
2
0
2
0
0
0
1
2
1
2
1
3
0
2
2
1
1
1
0
1
1
2
2
1
2
1
2
0
0
1
0
2
0
2
0
1
0
0
1
2
2
0
1
0
0
2
1
1
2
1
0
2
1
1
0
1
0
0
1
0
0
2
1
3
2
0
2
2
1
3
1
2
2
1
1
1
0
2
0
2
0
1
0
0
0
2
1
1
0
2
2
0
2
1
1
1
1
2
1
0
0
0
1
1
1
0
0
0
1
1
0
2
0
2
1
0
1
1
1
0
0
0
1
1
1
2
0
0
1
0
0
1
0
1
2
1
0
0
1
1
1
1
0
0
1
0
0
1
1
0
1
1
0
1
0
3
0
0
1
2
1
0
1
0
0
1
1
1
0
1
0
1
0
2
1
1
2
1
2
1
1
1
2
1
2
1
0
2
0
1
1
0
1
0
2
2
0
2
0
1
0
0
1
2
1
2
2
0
1
0
0
1
2
0
1
2
1
0
2
1
0
2
0
1
1
2
2
0
1
1
0
0
2
2
0
2
0
0
1
2
1
2
1
1
1
1
1
0
1
1
0
0
0
1
1
1
1
1
3
1
2
0
3
0
1
1
1
0
0
0
0
1
0
1
7
1
1
0
2
0
2
1
0
1
2
2
1
1
1
1
0
1
1
1
0
1
1
0
0
2
1
2
0
0
1
0
1
0
0
1
1
2
0
0
1
0
2
1
1
1
1
0
0
0
1
1
0
1
0
2
1
1
0
1
1
1
0
2
1
1
1
0
1
2
1
2
0
2
1
1
0
1
4
1
2
3
0
0
0
0
2
1
0
2
0
1
2
2
0
0
0
1
1
1
1
0
1
1
1
0
0
1
1
0
1
2
1
0
2
0
0
2
2
0
1
0
0
2
0
1
0
0
0
2
1
1
1
1
1
1
0
1
0
0
0
1
1
2
0
1
0
1
1
1
1
0
0
1
2
0
0
1
0
1
2
1
2
1
2
1
0
0
1
1
1
1
1
1
1
1
1
0
0
1
1
1
1
2
0
2
1
1
1
0
0
0
0
0
2
5
0
0
0
1
0
0
1
2
1
0
1
2
1
0
0
2
2
0
2
1
1
2
2
0
0
1
0
0
1
1
0
0
0
1
0
0
0
2
1
1
1
1
0
1
1
2
0
1
0
1
0
2
0
1
1
0
1
0
1
0
3
0
0
0
1
3
0
1
1
1
2
0
1
1
0
1
0
1
1
0
2
1
1
1
2
2
1
1
0
2
1
1
1
1
0
1
0
0
2
1
1
2
0
1
1
0
1
1
0
0
0
2
0
1
0
0
2
0
0
2
0
0
0
1
2
2
0
1
0
3
1
0
1
1
1
0
2
0
2
1
1
1
2
1
0
0
0
1
2
2
0
1
1
0
1
1
2
0
0
0
2
1
1
1
0
1
0
0
2
0
1
0
0
1
0
0
1
1
0
1
1
1
1
2
1
0
2
0
1
2
1
1
1
1
1
1
1
0
1
1
1
0
1
1
0
2
1
1
0
0
1
0
1
2
0
2
0
1
2
2
0
2
0
1
1
2
2
0
2
1
0
1
1
1
1
2
0
0
1
1
1
2
1
2
1
0
0
0
0
0
2
1
0
1
1
2
1
1
1
0
2
2
2
0
0
2
1
0
1
1
1
0
2
0
1
1
1
0
2
1
1
0
0
2
1
0
1
1
0
0
1
0
1
0
0
1
1
1
1
2
0
1
1
1
1
1
2
1
0
2
1
0
2
0
2
1
2
1
1
0
0
0
1
1
1
1
1
1
1
0
0
0
1
0
1
2
0
0
1
0
0
0
2
0
1
1
0
1
0
0
1
1
0
1
0
1
2
0
1
1
0
1
1
2
1
0
1
2
0
0
1
0
2
1
0
0
1
2
0
0
0
0
2
0
0
1
2
2
1
2
1
2
2
1
0
0
1
1
1
3
1
2
2
3
2
0
1
1
0
1
1
2
1
1
0
1
0
2
1
2
1
1
1
2
0
1
2
1
1
1
1
0
0
0
0
2
2
0
1
1
2
0
1
0
0
0
1
0
0
2
1
0
1
1
0
1
0
0
0
1
0
1
1
2
1
1
2
1
1
1
1
1
2
1
1
2
1
1
2
2
2
3
1
2
0
2
1
1
0
0
2
2
0
1
1
0
0
0
1
0
0
0
2
0
2
1
0
1
2
3
1
0
1
0
1
1
2
1
2
0
0
2
1
0
1
1
1
2
1
0
1
0
1
1
2
2
1
0
1
1
2
2
1
2
3
2
0
0
2
0
1
2
1
2
1
1
1
0
1
1
2
2
0
1
0
1
0
1
1
3
1
1
1
1
1
1
0
1
1
0
1
0
0
1
1
0
1
1
0
0
1
1
1
1
1
1
1
0
0
1
1
0
1
0
0
1
1
2
1
0
0
3
0
2
0
0
2
0
1
0
2
2
2
0
1
1
1
1
0
2
0
0
1
0
1
2
0
2
0
0
1
0
0
1
1
1
1
1
0
2
0
1
1
2
0
0
0
1
3
1
1
0
0
0
1
1
1
1
2
0
0
0
0
0
0
1
0
2
2
1
1
2
0
1
2
1
0
0
1
0
1
0
1
0
2
2
2
2
1
0
0
2
2
0
1
0
0
1
2
2
2
0
3
1
0
0
2
1
2
1
0
0
4
0
0
0
0
3
2
1
2
1
2
1
0
1
1
0
1
1
1
1
0
1
1
2
1
3
0
1
1
0
2
1
1
0
1
1
0
0
1
0
1
0
0
2
0
0
0
1
0
1
2
1
2
1
1
2
1
1
1
1
0
2
2
2
0
2
0
2
1
0
0
0
0
2
0
0
0
0
2
1
2
1
0
0
2
0
2
0
2
1
0
1
1
2
1
2
1
2
1
1
2
1
1
1
3
0
1
1
2
2
1
2
0
2
0
1
2
0
0
0
0
2
1
0
1
0
1
1
1
1
1
1
1
2
1
1
2
0
0
1
2
1
0
1
1
0
1
0
1
1
1
0
0
1
1
1
1
2
0
1
0
2
0
0
1
1
0
1
1
1
0
0
2
0
1
1
1
0
1
0
1
1
0
0
2
0
0
1
2
2
0
1
1
1
0
0
1
0
2
2
1
0
0
1
1
1
1
1
0
1
0
1
2
1
0
2
0
2
0
2
0
0
2
0
0
1
2
2
1
1
1
0
2
1
4
2
0
0
0
2
1
1
2
1
0
0
1
3
2
1
2
0
0
1
0
2
0
2
0
3
1
2
0
1
1
1
0
2
1
1
2
2
1
0
2
0
0
1
2
1
0
1
1
0
1
0
0
0
1
1
2
0
0
1
1
0
0
2
0
1
1
1
1
0
1
0
0
0
0
1
0
1
1
1
2
2
2
1
1
2
1
2
1
2
0
0
2
1
1
0
2
2
0
0
0
2
19
1
2
0
0
1
2
1
0
1
2
0
0
3
1
2
1
1
2
0
1
2
2
0
1
2
0
1
1
0
1
0
0
2
1
2
1
3
1
2
0
2
0
0
0
1
1
2
0
0
1
1
0
2
2
1
1
1
0
0
1
3
0
1
1
0
0
0
0
3
1
1
1
0
0
0
1
0
0
1
0
0
0
1
2
0
1
2
0
2
2
1
1
1
0
1
0
2
1
1
1
0
0
1
0
1
2
2
0
1
2
2
2
1
0
0
2
1
2
0
0
1
2
2
1
0
1
0
2
1
0
1
0
0
0
0
2
1
0
0
1
1
2
1
1
1
1
2
0
0
0
2
0
2
3
1
1
2
1
1
0
1
0
0
0
1
1
1
2
1
0
0
1
0
2
0
0
2
1
0
1
0
1
1
1
1
1
1
0
0
2
1
1
2
1
1
0
0
0
0
2
0
2
0
1
1
2
2
2
1
1
1
1
0
2
1
1
1
1
1
1
1
0
0
0
2
1
1
1
1
0
1
1
1
1
1
1
0
2
0
0
1
1
2
1
2
0
1
1
0
0
1
1
2
2
0
2
1
1
1
1
1
1
0
1
0
2
1
0
0
1
2
2
1
1
2
0
0
1
0
0
1
1
0
2
1
0
0
0
1
0
1
0
0
3
1
1
1
0
1
1
0
0
1
2
2
0
1
1
2
1
2
2
0
2
1
1
1
1
0
1
2
2
1
1
2
1
0
2
1
0
1
1
0
0
0
0
0
3
0
1
1
0
1
0
1
1
1
1
1
1
1
1
0
0
2
1
1
0
2
1
1
1
2
0
1
0
1
1
2
0
0
1
1
1
2
0
1
1
1
1
0
1
0
0
2
2
0
0
0
1
0
1
1
1
0
2
1
1
2
0
1
0
1
1
0
0
1
0
1
1
1
2
0
0
1
0
1
1
1
2
1
0
0
3
1
1
2
1
1
1
1
0
0
1
1
0
1
1
2
2
1
1
2
1
2
1
1
1
1
2
2
1
0
1
0
0
0
1
0
1
0
2
0
0
2
1
2
1
2
0
0
0
0
0
0
1
0
0
0
5
2
1
3
2
1
1
0
1
2
2
2
1
2
1
0
2
1
1
0
0
1
2
1
0
2
2
0
2
0
1
0
1
1
2
1
2
0
0
2
1
2
1
2
0
2
2
0
1
0
0
1
1
2
0
2
1
0
0
2
1
0
2
0
0
2
1
2
0
0
0
1
0
3
1
1
1
1
0
0
1
2
1
0
1
1
2
0
2
1
0
1
2
0
2
1
3
2
2
2
0
2
0
1
0
0
0
1
3
1
0
1
1
2
2
4
2
2
2
2
1
0
2
1
1
0
1
0
0
0
0
0
1
1
2
1
1
1
0
1
2
0
1
1
1
2
2
1
1
2
2
1
1
2
0
1
1
1
1
0
0
1
0
1
2
3
1
1
2
1
0
0
0
1
1
0
1
2
1
0
1
1
0
2
0
0
0
1
0
2
1
2
1
2
1
0
0
0
3
2
0
1
1
0
2
2
1
1
0
1
0
0
1
4
1
1
0
1
1
0
1
1
1
0
0
0
0
1
0
1
1
2
1
2
0
1
2
0
0
1
0
0
1
1
0
0
2
1
0
2
1
0
2
1
1
0
1
2
2
1
0
2
1
2
2
2
1
0
0
0
1
1
0
2
1
2
2
1
0
2
1
0
2
1
0
0
2
2
1
0
2
1
0
2
2
2
1
2
2
0
1
0
2
2
1
1
0
2
2
1
1
3
2
2
0
2
0
0
1
1
1
2
0
0
2
0
2
2
1
1
0
0
1
1
0
1
0
0
3
1
0
1
1
1
0
1
0
1
0
0
1
0
1
0
0
2
0
2
2
1
1
1
2
0
0
0
0
0
1
0
0
1
0
1
2
1
2
0
2
0
1
1
0
2
1
0
1
2
0
0
0
2
1
0
1
1
1
0
1
0
2
1
1
0
0
1
2
2
1
2
2
0
1
1
1
1
0
1
0
2
0
0
0
1
2
1
1
1
1
1
1
1
2
2
2
1
0
2
1
0
0
0
2
1
1
2
1
1
1
2
0
0
1
0
1
1
1
2
0
2
1
0
0
0
0
0
1
2
0
0
1
0
2
2
1
1
0
0
0
0
1
2
1
1
0
0
0
0
1
0
1
0
1
1
2
0
2
1
1
0
1
1
1
0
1
2
0
0
0
2
2
0
1
0
1
1
1
1
0
2
2
2
2
0
1
0
0
1
1
2
0
1
1
1
0
0
1
1
0
2
1
0
0
0
0
1
2
1
1
1
2
0
0
0
1
0
1
0
1
1
1
0
1
1
0
1
1
1
1
1
2
0
1
0
1
1
1
0
0
0
2
3
0
0
1
1
2
1
1
0
2
0
2
0
0
1
2
0
2
1
0
2
2
1
0
1
2
1
1
1
1
0
1
1
0
0
1
1
0
1
1
0
1
1
1
1
0
0
1
1
0
2
0
2
0
0
1
1
1
2
0
1
0
1
0
1
1
0
0
1
0
0
2
1
2
2
1
2
0
1
2
1
1
1
2
0
1
0
1
1
0
1
1
1
2
0
1
2
2
2
0
0
2
0
1
1
1
1
2
1
0
0
2
1
0
0
1
1
1
1
1
2
2
3
1
2
0
0
1
1
0
0
2
0
1
0
1
2
3
1
1
1
1
1
0
2
0
0
0
2
1
1
0
0
1
1
1
1
2
1
2
1
0
0
2
0
2
2
0
1
0
1
0
1
2
1
2
1
1
2
0
1
1
1
0
1
1
0
2
0
3
1
1
2
1
2
1
2
0
0
2
0
1
1
0
1
2
2
1
1
1
0
1
2
0
1
0
1
0
1
2
2
1
0
1
1
2
1
0
0
2
1
2
0
1
2
2
2
1
1
1
0
1
1
0
0
1
0
0
1
1
1
1
0
1
0
1
2
0
0
0
0
1
0
1
2
0
1
1
0
2
2
0
0
0
0
0
0
0
1
2
1
0
2
1
0
1
0
1
1
1
0
1
2
0
2
3
0
1
0
0
1
1
1
1
1
0
2
2
2
2
1
2
1
1
1
2
0
1
0
0
1
0
1
2
2
1
1
1
0
2
1
0
0
2
0
1
2
0
0
0
1
0
1
0
1
1
2
3
0
0
0
1
1
1
1
0
2
0
1
1
1
2
0
2
1
2
0
0
2
2
1
1
0
2
1
0
0
0
2
1
1
1
1
0
0
2
2
0
0
0
2
2
2
0
2
2
0
2
0
1
1
0
1
1
0
0
0
0
0
2
1
2
0
1
1
1
1
0
2
0
1
1
1
1
1
0
2
1
2
1
1
1
1
0
2
1
1
2
1
2
1
1
0
0
0
1
0
0
0
1
0
1
1
2
1
0
1
1
2
0
1
0
3
1
1
2
3
1
1
2
2
2
1
1
0
2
0
2
1
1
1
1
0
1
2
0
1
2
0
1
2
2
1
2
2
1
0
2
1
1
1
1
1
1
1
1
1
0
3
2
1
0
1
0
0
1
1
2
0
1
1
2
1
1
1
1
0
2
2
0
1
0
1
0
1
1
1
2
0
1
2
2
2
1
0
1
1
2
1
1
1
1
1
1
2
0
4
2
1
2
0
0
1
1
1
1
0
1
1
1
0
1
0
3
1
0
1
1
0
1
0
3
2
1
2
1
1
0
1
0
1
0
1
0
2
0
0
0
3
1
1
0
2
2
1
1
2
0
0
0
0
2
1
2
1
1
0
1
2
0
0
1
2
2
1
1
0
1
1
1
0
0
1
1
2
2
0
1
0
2
3
0
0
1
1
0
3
1
3
1
1
2
0
1
2
2
0
1
1
1
1
2
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
1
0
1
0
1
1
1
1
0
0
2
2
1
0
0
2
0
1
1
0
2
1
1
1
0
3
1
1
1
1
0
1
0
2
0
0
0
1
7
1
2
1
1
0
0
2
1
1
2
1
2
1
1
0
1
0
2
0
1
1
2
2
1
1
0
0
2
0
0
1
2
1
1
0
1
1
1
1
1
1
0
1
0
0
0
0
0
2
1
1
1
2
3
0
1
1
0
0
0
0
0
1
1
0
2
0
1
1
0
2
2
0
1
0
0
2
0
1
1
0
2
2
1
2
1
1
1
1
2
0
2
1
3
1
1
1
2
2
0
1
0
2
1
2
0
1
1
0
2
1
1
1
0
2
1
1
1
1
0
2
2
1
0
2
2
1
1
0
1
1
1
1
0
1
1
0
1
2
1
0
1
0
0
0
2
1
1
0
1
1
0
0
1
0
0
2
0
1
2
0
1
0
1
2
1
0
0
1
1
0
1
2
12
0
1
2
2
0
1
1
0
0
0
0
1
2
1
0
0
0
0
1
1
2
0
1
1
0
2
1
1
2
2
2
1
1
1
1
2
0
1
0
1
1
1
1
0
1
3
0
2
2
0
0
2
1
1
1
0
2
1
0
1
2
1
2
0
1
0
1
2
0
1
1
2
2
1
1
0
2
1
0
2
1
0
2
0
3
1
0
0
1
0
0
2
0
2
2
2
2
1
1
0
0
0
0
1
1
2
1
1
1
0
0
1
1
2
0
1
2
0
1
0
2
0
1
1
0
1
0
0
1
0
2
1
1
0
1
1
1
0
2
2
1
1
2
1
1
0
0
3
2
0
1
2
2
0
0
0
1
0
0
1
1
1
1
1
0
1
0
1
0
0
1
0
1
1
1
2
2
1
0
0
1
1
1
0
0
0
0
0
1
2
1
1
0
1
0
0
1
0
0
0
2
2
0
1
1
0
1
0
2
1
2
0
2
0
1
1
1
1
2
0
1
0
1
0
1
2
2
1
1
0
0
0
1
1
2
0
1
2
1
1
2
0
0
1
1
1
0
2
0
2
0
1
1
2
1
2
1
1
0
0
1
2
1
1
2
3
1
0
0
1
0
2
1
1
0
1
1
2
2
2
1
2
0
0
1
1
1
1
0
0
1
1
1
2
2
1
0
0
1
0
1
0
0
2
0
1
0
0
0
1
1
2
2
0
1
0
0
1
1
1
2
0
0
1
1
1
0
0
0
2
1
3
0
1
1
2
1
0
0
2
1
0
2
1
3
1
0
0
0
0
1
1
1
1
1
0
0
2
1
0
0
1
2
2
0
1
2
2
1
1
0
0
1
1
1
0
1
3
1
2
2
1
0
2
0
0
0
2
0
1
1
1
0
2
0
2
1
1
1
1
0
0
0
0
1
1
2
1
1
0
1
2
2
1
1
2
1
0
1
2
0
1
1
0
2
2
2
0
0
1
1
0
0
2
1
0
0
1
1
1
2
2
0
1
0
1
2
1
2
1
1
0
0
2
1
0
1
1
0
1
2
2
0
1
0
1
0
0
0
1
0
2
0
1
1
2
0
1
1
0
1
0
1
1
0
0
1
0
0
1
1
1
0
1
1
1
2
2
2
0
0
1
1
2
2
0
0
1
1
2
2
1
0
1
0
0
1
1
0
1
0
1
1
2
1
0
1
0
2
0
0
1
0
0
0
1
1
1
0
0
1
0
2
1
4
1
1
0
2
1
0
1
0
2
0
0
1
0
0
0
1
1
2
1
2
1
0
0
0
1
2
0
0
2
0
2
0
1
0
1
1
2
1
1
1
1
0
0
5
2
3
1
0
1
1
3
0
1
0
1
1
2
1
2
2
1
2
1
0
1
2
1
1
2
2
1
0
0
0
0
1
1
1
1
1
0
0
2
1
1
1
2
0
1
1
1
0
0
0
1
0
1
1
0
1
1
0
1
0
0
0
1
2
0
2
1
1
1
1
1
1
0
1
1
1
0
2
1
0
1
1
1
2
2
1
2
1
1
1
0
2
1
1
0
1
0
0
1
0
1
1
1
1
0
2
1
0
0
1
0
0
1
0
1
1
2
1
1
3
0
1
1
1
2
2
2
0
0
1
1
2
0
0
1
0
1
2
2
2
1
0
1
1
1
2
1
1
1
1
1
0
1
1
1
1
1
1
2
2
0
0
2
1
1
1
1
0
2
0
1
0
3
1
2
1
0
0
0
0
0
2
0
0
1
0
0
0
0
1
1
2
0
1
1
0
1
0
0
1
0
0
1
0
4
1
1
0
0
0
0
2
0
0
0
0
2
0
1
2
2
2
2
2
0
0
1
0
1
0
0
1
0
2
0
0
2
1
1
1
0
1
1
2
1
0
1
0
1
1
2
2
1
0
1
2
1
1
2
1
1
0
0
2
1
0
0
2
0
1
2
2
0
1
1
1
1
1
1
2
1
1
0
0
2
2
2
4
2
0
1
1
0
0
1
1
1
1
0
2
2
2
4
1
1
2
0
0
1
0
0
1
0
1
1
5
0
1
2
0
1
0
2
2
0
2
1
2
1
0
2
2
1
0
1
1
0
2
1
0
1
1
0
0
1
1
1
1
1
1
1
1
0
1
1
1
1
0
1
1
1
0
1
2
1
0
1
0
1
0
1
1
0
1
1
2
0
0
1
1
1
0
4
0
1
1
1
0
1
2
1
1
1
2
0
0
2
2
1
1
0
2
1
1
1
0
2
1
0
2
1
1
2
1
2
0
2
2
2
1
0
0
1
1
1
1
0
1
1
1
1
0
1
2
0
1
2
1
0
0
2
1
1
1
2
1
2
1
1
1
1
1
0
2
1
0
1
1
1
0
0
1
0
1
0
2
0
1
1
0
1
1
0
2
0
0
1
2
1
2
1
0
2
0
0
1
1
1
1
1
1
1
1
1
1
1
1
0
2
1
2
0
2
1
1
2
2
2
0
1
1
0
1
2
1
1
2
1
0
1
1
1
2
2
2
0
0
1
1
0
0
1
0
2
0
0
0
1
0
4
1
0
0
1
1
1
2
2
2
2
0
1
0
0
0
1
2
0
1
1
0
0
1
1
3
0
1
1
0
2
1
1
0
0
2
0
3
1
1
0
1
2
2
1
0
2
1
1
0
2
0
0
2
0
1
2
1
1
0
1
0
1
0
0
0
0
1
1
1
0
0
3
0
2
0
0
0
1
1
0
2
2
1
2
0
2
1
1
0
2
1
0
0
2
0
0
0
2
1
3
1
1
2
0
0
0
2
2
1
0
2
1
0
2
0
0
1
0
0
2
2
0
0
0
2
2
0
1
0
0
1
1
0
0
0
1
2
0
0
0
0
1
1
1
0
1
1
3
3
0
2
2
1
2
1
1
1
2
2
2
2
1
0
0
0
0
2
0
0
1
1
1
2
1
0
2
0
0
2
0
0
0
0
0
1
1
0
2
0
0
1
1
0
1
0
1
0
0
0
1
1
1
1
0
1
1
1
1
1
1
0
1
0
0
0
1
0
2
1
0
1
1
1
3
2
1
1
2
1
2
1
0
1
2
0
0
1
1
0
1
1
1
0
1
1
1
1
1
0
0
1
0
1
0
0
0
0
0
2
1
2
1
2
1
1
1
1
2
0
1
1
1
1
2
1
1
1
1
2
1
0
1
1
2
1
1
0
0
0
0
0
2
2
1
4
1
1
0
1
2
0
1
1
0
0
0
1
2
1
1
0
1
1
2
1
1
1
0
1
0
2
0
0
1
1
1
1
1
0
1
1
1
1
1
0
2
1
1
1
0
1
0
1
0
2
2
0
2
1
0
1
0
2
0
0
0
0
1
1
0
2
0
1
1
1
0
1
1
2
2
1
2
0
2
2
1
1
0
0
1
2
2
0
1
0
1
1
1
1
0
1
0
0
1
0
1
0
2
1
0
1
2
0
1
1
1
0
0
2
1
0
1
1
2
1
0
0
1
1
2
0
2
1
1
0
2
0
1
1
0
1
1
2
0
0
2
1
0
1
0
2
0
2
0
0
2
1
1
1
0
2
5
1
0
0
1
0
1
0
2
1
1
1
0
0
0
1
1
0
0
1
0
4
1
2
0
0
1
2
0
1
1
1
0
1
1
0
1
1
1
1
1
1
0
1
0
1
1
0
0
1
0
1
2
2
0
1
2
1
0
2
1
2
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
2
0
1
2
2
1
0
0
1
1
1
2
0
3
0
0
0
1
1
0
1
1
0
0
1
0
0
1
0
1
2
2
1
1
2
0
1
0
0
1
1
1
2
1
2
0
1
0
0
0
0
2
1
0
2
2
0
1
0
1
1
0
0
2
1
0
1
0
1
0
0
1
1
0
0
1
0
0
0
0
2
0
1
0
2
1
1
0
2
0
1
0
0
1
0
0
2
0
1
0
1
0
0
0
1
1
1
1
1
1
2
0
0
2
0
0
1
0
0
1
0
1
1
2
2
2
0
1
0
0
1
0
1
2
1
0
1
2
0
0
2
0
1
1
2
0
1
0
0
2
0
1
0
1
0
1
0
0
0
0
1
0
0
1
0
1
2
1
3
0
2
0
1
0
0
0
0
1
1
0
2
1
0
1
1
1
1
1
1
1
1
2
0
2
2
1
1
2
0
0
1
1
1
1
0
1
0
3
2
0
0
1
0
0
2
2
2
1
1
1
0
2
1
1
2
0
0
0
2
1
0
1
1
0
0
0
1
0
1
1
1
1
0
2
0
1
0
1
0
1
0
0
0
2
2
1
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
2
1
3
0
0
1
1
0
0
0
2
0
2
1
1
0
2
1
2
2
1
0
1
3
1
1
1
2
0
2
4
1
2
2
0
2
1
0
0
0
1
2
2
0
0
2
1
0
0
1
0
1
2
2
1
1
1
1
2
2
1
1
0
1
2
0
2
1
0
1
1
0
1
1
1
2
2
1
0
2
2
2
1
2
1
0
0
1
1
1
1
0
1
0
1
0
0
2
0
2
0
0
0
1
0
0
0
1
1
0
1
2
2
2
1
0
2
0
2
1
0
0
2
1
1
0
2
1
1
2
2
0
1
1
2
1
2
1
1
1
2
2
0
1
1
0
1
1
0
0
1
2
1
0
1
1
1
1
1
2
1
1
0
0
1
0
0
0
0
2
0
1
0
1
2
2
1
1
0
0
2
1
2
1
0
1
2
1
0
0
1
1
1
0
1
0
0
1
2
0
6
1
1
0
1
0
1
0
1
0
2
0
0
0
2
1
1
1
0
2
0
1
0
1
2
2
1
1
0
1
0
1
1
0
0
0
1
0
1
1
2
1
0
0
1
0
1
0
0
1
1
1
0
0
1
0
0
0
1
1
0
0
2
0
0
1
1
0
0
1
2
1
0
2
1
1
2
0
0
0
0
1
1
2
1
2
2
2
1
1
2
2
1
0
1
1
0
3
0
1
1
3
1
0
0
2
1
0
0
1
2
1
1
1
0
1
2
1
1
0
0
1
1
0
2
0
1
0
0
1
1
1
1
2
1
1
1
0
1
1
0
2
1
0
1
2
1
0
1
4
1
2
1
3
1
0
1
2
1
0
0
1
1
1
1
1
1
0
0
2
0
1
0
1
1
2
1
1
0
0
0
1
0
2
0
1
2
2
0
0
2
1
1
1
2
0
1
2
3
0
2
0
0
1
2
2
2
1
2
1
1
1
1
0
1
0
2
2
1
0
1
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
0
1
0
0
2
0
0
2
1
0
0
0
0
2
1
1
0
1
0
1
1
0
0
2
2
1
1
1
0
1
1
1
0
3
2
0
2
1
0
1
1
1
0
1
2
0
0
1
0
1
2
0
1
0
1
0
0
1
0
2
1
0
2
1
2
0
1
0
1
2
1
2
2
2
0
1
0
1
2
2
1
0
2
1
1
0
0
1
1
1
0
2
1
1
0
0
0
1
2
1
1
2
1
1
0
1
0
1
1
1
0
1
2
1
2
1
1
2
0
1
0
2
0
0
2
2
1
0
2
2
0
0
1
1
1
1
0
0
3
1
1
1
2
1
1
0
0
1
0
1
2
0
1
0
1
2
1
0
0
0
1
0
2
2
2
1
2
0
1
0
0
1
1
1
0
1
0
1
1
0
1
1
1
1
0
1
1
1
0
1
1
1
0
2
1
1
2
0
0
1
1
1
0
1
0
2
1
1
0
0
0
1
1
0
1
0
0
1
0
2
1
1
1
1
1
1
1
1
0
0
0
0
0
1
0
1
0
2
1
1
2
0
1
2
2
0
2
1
1
0
2
2
1
0
1
0
0
0
0
0
1
3
1
0
1
0
1
2
1
0
0
3
2
0
2
1
0
1
2
0
1
0
1
2
3
2
0
1
1
0
2
0
1
0
0
2
0
1
0
2
2
1
2
0
1
0
1
1
2
2
1
1
2
2
0
1
1
2
1
0
1
1
0
0
0
2
0
1
0
1
0
0
0
2
1
2
1
2
1
2
2
2
2
0
0
1
0
1
0
2
2
2
1
2
0
0
0
1
0
1
0
1
1
0
1
1
1
1
2
2
1
1
0
0
1
0
1
1
0
0
0
0
1
1
0
1
1
1
1
1
0
1
2
2
2
2
0
0
2
0
1
0
2
1
1
0
1
0
1
1
1
2
1
0
0
0
2
1
1
0
1
1
1
1
1
0
0
1
1
3
0
1
1
2
1
0
1
0
1
1
1
0
1
1
0
0
0
0
0
1
1
1
1
0
1
1
2
2
0
0
0
1
1
1
1
2
1
0
0
2
1
0
2
0
0
2
1
1
0
0
1
2
2
0
1
1
1
0
2
1
0
1
1
1
1
2
1
0
1
0
1
2
1
1
1
1
1
2
0
1
0
0
1
1
1
0
2
0
1
2
0
0
1
1
0
2
0
1
0
0
1
1
0
1
1
1
1
2
1
1
2
0
1
0
0
1
1
1
0
2
1
2
0
2
1
1
2
1
1
2
1
0
1
1
0
1
0
1
2
2
0
1
0
1
1
0
0
1
2
1
0
2
2
0
1
1
0
0
1
0
2
2
1
2
1
1
1
1
0
1
3
1
1
1
0
0
1
1
0
1
0
0
2
2
1
1
1
0
2
1
0
1
1
0
0
2
2
0
1
1
1
1
1
1
0
0
1
0
1
0
1
4
0
1
0
1
0
0
0
2
1
3
0
0
1
2
2
1
2
2
1
1
1
1
0
2
1
1
0
0
0
0
0
1
1
2
1
1
1
1
1
1
0
1
0
1
1
2
0
0
0
2
1
1
0
1
1
1
2
1
0
1
0
2
2
1
2
2
1
0
0
1
0
0
2
1
0
2
1
2
0
1
0
1
2
0
2
1
1
0
0
1
2
1
1
0
0
1
1
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
1
2
1
0
1
1
2
1
1
1
2
1
1
2
1
0
0
1
2
0
1
1
1
3
0
0
1
0
2
2
1
0
0
1
0
0
1
0
0
0
2
2
2
1
0
0
2
1
0
1
0
0
2
2
1
2
0
0
1
1
2
0
1
1
1
2
3
1
4
2
0
2
1
0
1
0
1
0
2
1
3
1
0
0
2
1
0
1
1
0
1
1
1
1
1
1
0
0
1
1
0
0
1
0
2
1
1
1
1
0
0
0
1
1
1
2
1
1
2
2
1
1
1
1
1
1
0
2
2
1
1
2
1
0
1
1
2
0
2
0
1
1
0
0
0
1
2
1
1
1
1
0
1
1
0
1
2
0
1
2
4
0
0
0
0
2
1
0
1
1
1
2
3
2
1
0
1
1
0
2
2
1
0
2
1
1
0
2
0
2
1
0
1
0
0
0
0
0
0
1
0
0
2
1
0
1
1
2
0
0
0
1
1
1
2
0
0
1
1
0
1
2
0
2
1
1
0
2
2
0
0
0
0
1
0
0
1
1
3
0
0
0
0
0
2
1
2
0
2
1
1
2
1
0
1
1
2
1
1
1
1
0
0
2
2
1
1
0
0
1
2
0
1
0
2
0
2
3
1
1
1
2
1
1
1
0
4
1
0
1
0
0
0
1
1
0
2
1
2
1
2
0
0
0
2
1
2
1
1
1
1
0
1
0
1
1
2
2
2
0
1
1
1
1
1
0
0
0
1
0
1
2
0
0
1
0
1
2
1
2
1
0
0
0
0
2
2
1
1
1
2
1
1
2
1
0
1
1
0
2
1
0
0
2
0
0
1
1
1
1
0
0
1
0
1
1
2
0
0
0
0
1
2
1
0
1
0
0
2
1
2
1
1
1
0
1
2
1
1
1
1
2
0
2
1
2
1
1
2
1
0
1
0
0
1
0
0
1
1
2
1
0
1
1
1
1
0
1
1
0
1
1
1
1
0
0
1
1
0
1
1
1
1
0
0
0
2
2
0
0
2
0
0
2
1
1
0
0
0
0
1
0
1
0
0
2
0
2
0
1
1
2
0
1
1
0
0
2
0
2
2
0
1
0
1
1
0
2
1
1
0
0
1
1
1
1
1
0
1
0
1
0
1
1
1
0
2
1
2
1
2
1
1
0
2
1
2
2
1
0
1
2
4
1
0
1
1
0
2
1
2
1
1
1
1
0
0
1
2
1
2
0
2
1
1
0
1
3
1
1
1
2
0
2
2
2
1
2
1
1
0
0
1
1
1
1
2
2
0
1
1
2
1
0
2
1
2
0
0
1
1
2
0
1
0
0
0
2
2
0
1
1
1
0
2
2
1
2
2
1
1
2
1
2
2
1
1
1
2
1
1
1
0
1
1
0
0
2
1
0
0
1
0
2
0
0
0
1
1
0
2
2
1
2
0
2
2
0
1
0
0
1
1
2
1
0
0
1
1
0
1
1
0
0
1
1
0
1
1
1
1
1
2
2
1
1
1
0
1
1
1
1
0
1
1
2
0
1
1
0
2
1
0
2
2
2
2
1
2
2
1
0
0
1
0
0
0
2
1
2
1
0
0
0
2
1
0
1
1
0
0
0
0
0
1
0
1
1
1
1
1
0
0
0
1
1
2
2
1
1
0
2
0
3
0
1
1
0
0
0
2
1
1
0
2
2
1
1
1
0
2
2
0
1
2
0
0
0
1
2
1
1
1
1
1
0
2
0
2
0
0
2
2
1
1
0
2
2
1
0
0
1
2
1
0
0
0
2
1
0
2
1
0
1
0
0
2
0
0
1
1
0
1
0
1
2
1
0
0
2
1
2
2
2
2
1
1
0
2
0
0
2
1
1
0
0
0
0
1
1
2
1
1
1
1
0
2
1
1
1
0
1
1
2
1
1
0
1
0
0
1
0
1
2
0
0
1
1
1
0
2
0
2
2
2
1
2
1
1
2
0
1
1
1
2
1
1
2
2
1
0
0
0
1
2
1
0
1
0
1
1
1
1
2
1
1
1
1
0
1
0
0
2
1
2
0
1
1
0
1
1
2
2
0
1
2
0
1
1
0
2
0
0
1
0
2
1
1
0
0
0
1
0
0
3
1
0
2
0
0
0
1
2
1
1
1
1
1
2
2
0
1
0
1
0
0
1
0
0
0
1
0
0
1
0
1
2
1
2
0
2
2
2
0
1
1
2
1
0
1
0
2
1
1
1
1
1
0
0
0
1
1
2
1
0
0
1
1
2
0
2
1
0
1
1
0
0
1
0
0
2
0
3
0
0
1
1
2
2
2
0
1
2
1
0
0
2
1
0
2
0
0
1
1
0
1
1
2
2
0
1
1
1
2
0
1
0
1
0
3
1
1
1
1
0
1
1
1
1
1
2
0
1
1
1
0
0
1
0
1
1
0
1
0
1
0
0
1
1
0
1
1
1
2
1
1
0
1
0
0
1
4
2
2
2
0
1
0
0
0
0
1
0
2
0
1
1
1
2
2
0
0
1
1
0
1
0
0
1
0
0
1
0
1
1
0
1
0
2
1
0
0
1
1
2
1
2
0
0
2
0
0
1
1
1
1
2
0
1
1
1
0
2
2
0
2
0
1
0
0
1
2
1
0
1
2
1
1
0
1
1
2
0
2
1
1
1
2
1
1
0
0
0
1
0
1
1
1
0
1
2
0
0
2
1
2
1
1
1
1
0
0
1
1
2
2
0
1
1
0
0
2
0
0
1
2
1
0
0
0
0
1
0
1
0
1
0
0
2
2
0
2
0
2
1
0
2
2
1
2
2
0
0
0
0
0
1
2
0
0
0
2
0
0
1
1
1
2
0
0
1
1
0
1
1
1
0
1
0
0
1
0
1
1
1
0
0
2
0
2
1
2
1
2
1
0
0
2
2
1
1
0
1
0
1
2
2
0
0
2
0
1
0
2
1
0
1
1
2
1
2
0
1
2
2
1
0
1
0
1
2
0
1
0
1
0
2
0
1
0
2
0
4
0
0
0
2
1
0
0
1
0
2
0
0
2
2
2
0
0
0
1
1
1
4
2
1
0
0
2
2
0
2
0
3
1
1
1
3
1
2
1
2
1
1
2
2
1
1
0
2
2
0
1
0
1
2
1
0
0
0
1
0
1
1
1
0
0
1
1
1
1
1
0
0
0
2
1
1
0
0
1
2
5
1
1
1
2
1
0
0
0
1
1
2
1
0
1
1
0
1
3
1
1
0
1
2
0
0
1
0
0
1
2
2
0
1
0
0
1
3
1
0
1
1
0
0
1
0
0
1
1
1
0
1
1
2
1
1
1
1
0
3
2
1
1
2
0
1
1
1
1
1
1
1
0
1
1
1
0
0
1
2
1
0
1
1
0
2
0
2
1
1
3
1
1
0
0
1
1
1
1
1
1
1
0
0
2
1
0
0
0
0
1
2
2
2
0
2
2
0
1
2
0
1
0
0
0
1
1
0
1
2
1
3
0
1
2
0
0
2
2
1
1
1
0
1
1
1
2
1
2
0
1
0
0
1
2
2
0
2
2
2
1
0
0
0
0
1
2
0
1
1
2
0
1
2
2
0
0
1
0
2
2
1
0
0
1
1
0
1
0
2
1
1
1
1
2
0
2
0
1
2
0
0
1
1
0
1
1
0
1
0
0
0
0
1
1
0
1
1
1
1
3
0
2
1
0
1
0
0
2
1
0
1
0
2
1
0
1
0
2
1
0
1
0
2
0
0
1
1
0
1
1
1
2
1
1
1
0
2
0
1
0
0
1
1
1
1
2
0
0
1
0
0
1
0
1
4
0
5
0
1
1
0
0
1
1
2
1
0
0
2
1
0
0
1
0
0
2
1
0
0
0
0
1
1
1
1
0
0
1
1
2
1
1
0
0
1
2
1
0
2
0
0
1
1
1
1
1
2
0
2
2
1
2
0
1
1
0
0
0
0
1
1
2
2
1
2
0
0
0
0
0
1
0
1
1
2
2
1
2
0
1
0
1
2
1
0
1
1
1
1
1
0
2
1
1
1
0
2
0
0
1
2
2
0
2
1
1
1
1
2
0
1
0
1
1
0
1
0
0
1
2
0
1
2
1
1
1
1
0
1
1
0
1
0
1
1
0
1
0
1
0
0
0
1
0
0
3
1
3
2
1
1
0
0
1
2
1
0
0
1
0
0
1
1
1
1
1
1
1
1
1
1
0
1
0
1
1
1
1
2
2
1
1
0
2
0
2
1
1
1
1
2
0
0
0
1
1
1
1
0
1
2
2
2
0
0
2
1
1
0
1
1
1
1
0
0
2
1
0
0
0
1
1
0
1
0
2
0
1
1
1
2
0
1
1
0
2
1
1
2
1
0
2
2
2
2
1
0
0
2
0
0
1
2
0
0
1
1
1
2
1
2
1
1
0
0
1
0
2
0
2
1
0
1
1
2
1
0
1
0
1
2
0
1
2
1
1
1
0
1
1
1
2
1
0
0
3
1
1
0
1
1
1
1
1
1
1
1
1
2
2
2
2
1
1
1
0
1
2
2
2
1
1
0
2
2
0
1
0
0
1
0
0
2
1
1
2
2
0
1
1
2
2
1
1
1
0
0
2
1
0
1
3
1
1
0
0
1
0
1
0
2
1
1
1
1
1
1
1
2
0
1
0
2
3
1
0
2
0
0
2
2
1
1
0
0
1
1
1
1
0
1
0
2
2
1
0
1
0
2
2
0
0
1
1
0
0
1
0
0
1
0
1
0
1
1
2
1
0
1
0
1
0
0
1
0
1
1
1
0
0
1
1
0
1
1
2
1
2
2
2
2
1
1
1
0
0
0
1
1
2
1
1
2
2
1
1
2
2
1
1
1
1
0
0
1
2
1
0
0
0
1
0
1
0
0
0
1
1
0
0
1
1
0
0
1
0
2
0
1
0
2
2
1
0
0
0
0
0
2
1
1
0
1
1
0
1
0
1
0
0
0
0
0
1
1
1
1
0
2
2
0
0
1
1
2
0
0
1
1
0
1
2
1
1
0
2
0
2
0
3
1
2
0
2
1
0
0
1
1
0
1
1
0
1
1
1
1
0
0
1
0
0
1
0
2
0
2
1
1
0
0
0
1
1
1
1
0
1
0
0
1
1
0
1
0
1
1
1
0
2
2
1
1
1
0
0
1
1
1
1
0
0
1
2
2
1
1
2
0
1
0
0
0
0
0
0
2
1
0
1
0
0
2
0
2
1
0
0
0
2
1
0
2
1
3
0
2
1
1
0
2
1
0
0
1
0
1
1
1
0
0
0
1
2
1
1
1
0
2
1
2
0
2
3
2
2
2
1
2
0
1
2
1
1
0
0
1
0
2
1
0
2
0
0
2
1
1
0
1
1
0
0
0
1
0
2
4
2
1
3
2
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
1
1
1
1
2
2
1
0
0
0
0
0
1
0
1
1
1
0
0
0
2
0
0
2
4
1
1
1
1
0
1
0
0
2
1
2
0
1
2
1
1
0
0
1
1
2
0
2
0
1
2
1
2
0
0
1
1
2
1
2
0
1
1
0
3
0
1
0
0
0
1
1
0
1
2
0
0
0
1
1
1
1
0
1
2
1
0
0
0
0
1
1
1
1
0
0
1
0
0
2
1
0
2
0
0
0
1
1
0
0
1
1
0
0
1
1
1
1
0
0
2
1
1
1
1
1
0
0
1
0
1
0
0
3
1
1
0
0
4
1
0
1
1
1
1
1
0
0
0
1
0
1
1
0
2
2
1
2
1
0
0
1
1
2
2
2
0
5
1
2
1
1
0
1
0
2
0
0
0
0
0
0
2
0
0
0
1
1
1
1
0
1
0
2
0
1
1
0
0
1
1
1
0
1
2
1
1
2
2
1
0
1
1
1
0
0
1
0
1
0
1
0
2
0
1
1
2
0
0
1
1
1
0
0
2
0
1
0
0
1
2
1
5
0
1
0
0
0
0
0
1
2
0
1
1
0
1
1
2
1
1
0
1
0
1
1
2
0
2
0
1
1
1
1
0
1
2
0
0
1
2
1
1
2
2
2
1
1
0
0
2
0
1
4
0
0
2
1
2
1
1
2
1
1
1
0
0
1
1
2
1
1
0
1
0
0
2
0
2
2
1
1
0
2
2
2
0
2
1
2
0
1
0
1
0
1
0
0
0
2
0
0
2
0
1
1
0
1
1
0
0
1
1
1
1
0
2
2
0
1
1
0
0
1
0
0
0
1
2
0
2
0
2
0
2
1
1
0
0
2
0
2
0
2
2
0
0
0
1
1
0
0
0
2
0
1
2
1
1
0
0
0
0
3
2
1
1
2
0
2
2
1
2
2
0
2
0
0
0
0
2
2
2
0
2
0
1
1
0
2
2
0
1
0
1
1
1
1
2
1
0
2
2
0
0
0
0
1
0
0
0
1
2
1
2
0
0
2
1
1
0
0
0
2
2
0
1
1
0
1
1
2
1
1
1
0
0
1
0
2
2
0
0
0
2
1
0
1
1
0
1
2
0
0
2
0
2
1
1
1
2
1
1
0
1
1
0
2
2
0
1
1
1
1
0
2
2
0
1
0
0
1
2
2
0
1
1
1
0
0
2
0
0
1
2
0
2
0
1
1
2
0
0
0
1
2
1
0
0
1
0
2
0
0
1
1
2
1
1
1
1
1
0
1
1
2
1
0
1
1
2
0
1
0
2
0
1
2
1
1
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
2
0
2
2
0
1
1
1
0
1
2
1
1
1
1
1
1
1
3
1
0
2
3
1
0
1
0
0
2
0
1
1
1
2
2
2
0
2
0
2
2
0
1
1
2
1
1
0
0
0
2
1
1
0
0
2
1
1
1
2
0
0
1
2
0
2
2
1
1
1
2
1
0
0
2
1
0
1
1
1
0
0
0
2
1
1
1
1
1
1
1
0
2
1
1
1
2
1
2
1
1
2
1
0
0
2
2
1
1
0
1
0
2
0
1
0
0
0
2
2
1
1
2
0
1
2
1
1
0
1
0
0
1
1
1
1
0
1
0
1
2
5
1
0
0
1
1
0
1
0
1
0
1
2
0
0
0
0
1
2
1
1
2
1
1
2
1
0
0
1
1
2
1
1
1
1
2
2
0
1
2
0
2
0
0
1
0
0
1
1
1
1
0
2
3
1
2
1
0
1
1
0
0
1
2
0
0
1
1
0
1
0
2
2
3
1
1
1
0
0
0
2
1
0
2
0
1
1
1
1
1
0
0
0
0
1
0
0
1
0
2
1
2
2
1
2
1
2
0
2
2
0
1
1
1
0
1
1
1
0
2
1
2
1
1
2
2
1
1
1
0
0
1
0
0
0
0
1
1
0
1
0
1
1
1
2
1
2
1
2
1
2
0
2
0
1
0
1
1
2
2
2
2
1
1
1
1
1
0
0
1
1
1
1
1
0
1
1
1
1
1
2
0
1
2
0
0
1
1
1
1
0
0
2
1
0
2
1
1
2
0
0
0
1
1
1
1
2
0
1
1
1
1
2
1
0
1
1
1
0
1
5
2
1
0
1
1
0
0
0
0
1
1
0
0
1
1
1
1
1
1
1
1
2
2
2
1
2
0
2
0
0
1
0
2
0
0
2
2
1
2
0
1
3
1
1
1
1
0
2
1
0
0
1
0
2
2
1
0
2
0
0
0
2
0
1
0
2
3
0
1
1
1
2
1
0
2
1
2
1
1
1
2
0
0
0
1
1
2
0
0
0
1
1
1
1
1
1
0
1
1
2
0
3
1
0
0
2
1
0
2
0
3
1
1
2
0
1
2
1
1
0
0
2
1
5
2
1
1
1
2
0
0
2
2
1
2
2
0
0
2
2
0
1
1
0
1
0
0
4
0
0
0
3
1
0
1
2
0
0
1
2
2
3
2
1
1
1
1
1
0
1
2
2
0
2
0
1
2
2
5
0
0
1
1
2
1
1
2
3
0
1
0
2
1
0
2
1
0
3
1
0
0
0
1
0
0
1
1
0
0
1
1
0
0
0
1
0
1
0
0
0
0
2
1
0
0
0
0
0
0
2
0
2
1
1
0
0
2
1
3
2
1
0
2
1
2
1
0
2
0
1
2
2
0
2
1
0
0
1
1
1
1
1
0
0
0
1
2
1
2
1
2
2
0
3
0
0
0
2
0
0
0
1
1
0
3
0
0
2
1
1
0
0
1
1
1
2
1
0
0
0
1
1
1
1
0
0
1
0
0
0
1
1
2
1
1
1
2
0
0
1
1
1
0
1
0
1
0
1
0
1
1
1
0
0
4
1
2
0
2
1
1
0
1
0
1
0
0
0
0
2
1
1
1
0
2
0
1
1
2
1
0
1
1
0
0
2
0
1
1
1
1
0
3
1
1
0
1
0
1
1
1
1
0
1
0
1
2
1
1
1
1
0
0
1
0
1
2
2
0
0
0
2
2
0
1
0
0
2
1
0
0
1
0
0
1
0
1
0
0
0
2
1
1
0
1
2
2
1
0
1
0
1
1
1
2
0
0
1
0
2
1
1
0
0
2
1
2
0
1
1
2
0
2
2
1
1
1
0
1
1
1
1
1
1
1
0
0
0
2
0
1
1
2
1
2
0
0
0
2
2
1
2
0
1
0
1
1
0
0
0
0
1
1
2
1
0
1
3
1
1
0
1
1
2
0
0
1
0
0
1
1
0
1
1
3
1
0
2
0
2
2
1
2
1
2
0
1
0
2
0
0
0
0
2
0
2
1
0
1
0
2
1
0
2
0
1
1
0
0
0
0
3
0
1
0
1
2
0
1
0
3
0
0
1
1
1
2
1
0
0
1
0
1
1
1
2
1
1
1
1
2
0
1
3
1
2
0
1
1
1
1
2
2
0
0
1
0
4
1
1
2
1
1
1
1
0
1
0
1
2
0
0
0
1
1
0
1
5
0
1
1
1
0
0
3
1
0
1
1
0
1
0
0
0
1
0
1
0
0
1
1
0
0
1
2
1
0
0
0
1
0
0
1
0
2
2
0
0
1
0
2
0
0
1
1
0
0
0
1
1
0
1
0
1
1
1
1
1
1
2
1
0
2
0
1
0
1
2
1
2
2
0
1
0
0
0
1
1
2
0
0
1
1
1
0
1
1
1
0
1
0
2
0
1
2
2
0
1
0
0
2
1
1
0
0
1
0
0
0
1
1
0
0
0
1
2
0
1
2
0
0
0
0
0
1
2
1
2
1
1
1
1
1
1
2
1
0
2
1
0
0
0
1
2
2
0
2
0
2
0
0
0
0
1
1
0
0
1
2
0
0
1
0
1
2
2
1
1
0
0
0
0
0
0
0
2
1
1
0
2
0
0
0
1
1
1
0
0
0
0
0
2
2
1
1
2
0
0
0
1
0
1
2
0
2
2
1
0
0
1
1
1
0
0
0
0
0
2
0
1
0
2
0
0
0
1
0
1
0
0
2
1
1
1
2
2
0
1
2
0
2
1
1
2
2
0
2
0
2
0
1
0
1
1
0
0
1
0
1
0
1
1
1
0
2
0
1
1
2
0
2
2
1
1
0
1
1
1
0
1
2
1
1
1
2
1
2
1
0
1
1
0
1
2
0
1
0
1
0
0
1
0
1
2
0
2
1
0
1
2
1
0
0
2
1
2
2
1
1
1
2
1
1
0
2
1
1
1
0
2
0
1
2
1
2
0
2
0
1
1
1
2
1
0
1
1
1
1
1
1
1
0
1
2
1
2
1
2
1
0
0
1
1
1
0
0
1
1
0
1
1
2
0
1
1
0
0
1
1
1
0
1
0
0
1
0
0
1
0
2
0
0
1
1
1
0
2
0
1
0
0
0
0
0
1
1
0
2
0
1
1
0
0
1
1
2
0
0
1
1
1
1
0
1
0
1
1
2
0
1
1
1
2
1
0
0
0
1
1
2
0
0
0
0
1
0
1
1
0
0
1
2
0
0
0
1
2
2
1
0
1
2
0
2
1
0
2
2
0
1
0
0
1
1
2
0
0
1
0
1
1
1
0
0
0
0
2
1
1
1
0
3
1
1
2
1
1
1
0
2
0
1
0
0
1
1
0
0
1
1
3
0
0
1
1
1
0
1
2
0
1
0
0
0
1
1
1
0
0
2
1
2
2
1
3
1
0
1
1
0
2
1
0
2
0
7
0
1
2
0
0
0
1
0
2
1
1
0
1
1
1
2
0
1
2
2
0
0
2
0
1
2
2
0
0
0
2
1
2
0
0
1
3
1
1
2
2
1
1
1
2
0
2
0
1
0
0
1
0
1
2
2
3
0
1
0
0
2
6
1
1
0
0
0
0
1
2
2
0
0
1
1
0
0
0
2
1
2
0
1
1
2
1
2
2
2
1
0
1
2
0
0
2
0
1
5
0
2
0
2
0
1
0
1
0
2
2
1
1
1
0
0
1
2
0
1
1
1
0
1
0
1
2
0
3
2
2
1
1
1
2
0
1
2
0
1
2
1
2
0
0
0
2
1
0
1
1
0
0
2
1
1
1
0
1
2
0
2
1
0
1
0
4
2
2
1
2
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
2
1
2
0
2
1
0
2
0
1
0
1
1
0
1
0
1
1
0
1
0
2
1
0
0
2
1
2
2
1
1
2
1
1
1
0
2
0
2
0
0
0
1
0
1
0
2
0
0
1
2
1
0
2
1
1
0
1
1
1
1
1
2
0
0
2
1
1
0
2
0
1
0
0
2
0
1
0
1
1
2
2
1
1
2
1
1
2
2
0
1
1
1
1
0
0
2
2
0
1
2
1
1
2
0
0
2
2
0
0
0
0
2
0
1
3
1
1
2
0
1
1
0
2
0
0
1
1
2
2
0
0
2
2
1
1
0
1
0
0
1
1
0
0
1
0
2
1
2
0
1
2
1
1
1
1
1
2
2
1
0
2
1
0
1
0
2
2
1
1
2
1
1
1
1
0
1
1
1
0
1
1
1
0
0
2
0
0
1
1
1
1
2
1
0
0
1
2
0
2
2
1
0
1
1
1
1
0
2
1
0
3
1
2
0
2
0
1
0
1
2
0
2
1
0
2
2
1
1
0
2
1
0
1
2
1
1
2
1
3
0
0
0
2
1
1
1
1
1
1
1
0
1
2
1
2
0
1
0
1
1
2
1
1
0
0
1
3
0
0
1
0
0
0
1
1
0
1
0
3
2
0
0
1
0
1
1
0
1
0
0
2
0
0
1
2
2
0
1
0
1
1
0
0
1
1
1
0
0
0
1
0
0
2
0
1
0
0
2
0
1
1
1
0
1
0
1
0
1
1
1
1
1
0
2
1
1
1
1
1
1
0
0
1
2
0
2
0
1
1
2
1
1
2
0
2
1
2
1
1
1
1
2
2
0
2
0
1
1
1
1
1
2
1
1
2
1
1
0
3
0
1
1
1
0
1
1
1
1
1
0
0
0
1
0
0
2
2
1
1
0
1
1
1
0
2
1
1
0
2
0
2
2
0
1
0
1
1
0
0
2
0
0
0
1
0
0
0
1
0
1
0
2
0
2
0
1
1
1
1
1
0
1
2
0
2
0
1
1
2
1
0
1
1
2
2
0
0
1
2
2
0
1
1
1
2
1
1
0
1
1
2
0
1
0
1
1
2
1
1
2
2
1
0
0
0
1
0
2
0
0
1
1
2
2
0
0
0
2
1
1
1
1
1
0
0
2
2
0
1
2
0
2
0
1
0
0
0
1
1
0
0
0
0
0
0
2
1
0
1
2
1
0
1
1
2
0
1
1
0
2
1
2
1
1
2
2
1
1
0
2
0
0
0
2
1
0
1
0
1
0
1
0
0
1
0
0
0
0
1
2
0
0
2
1
1
1
0
1
2
0
1
0
0
0
1
1
1
0
1
2
0
0
2
0
1
1
1
2
1
0
1
2
2
1
0
1
0
2
2
2
0
0
2
1
0
2
2
0
0
0
1
2
0
0
0
1
0
2
2
2
1
0
2
0
1
0
1
0
2
1
2
0
0
0
1
1
0
0
0
1
1
2
1
2
0
2
2
1
1
1
1
0
1
1
1
0
2
1
1
0
2
1
0
0
1
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
2
2
1
2
2
0
0
1
1
0
1
0
0
1
0
2
0
0
1
0
2
1
0
0
1
0
2
0
0
1
0
2
1
0
1
1
1
1
0
2
1
2
0
0
2
1
2
0
1
2
1
1
0
3
2
0
0
0
0
1
1
1
1
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
3
1
2
1
1
1
0
1
0
0
1
0
2
1
3
1
0
2
1
1
1
0
0
0
2
1
1
1
1
0
2
1
0
0
2
2
1
2
1
0
0
2
2
0
1
0
0
0
1
3
2
0
0
1
2
1
1
1
0
1
0
1
0
2
2
0
2
1
1
1
1
0
0
0
2
0
1
1
2
1
2
1
1
1
0
1
2
1
2
1
0
2
0
1
1
2
1
0
2
0
1
1
0
1
1
2
2
0
1
1
1
1
1
0
0
2
2
2
1
1
1
2
2
1
1
0
0
2
1
1
0
1
0
0
0
0
1
0
1
0
2
1
0
3
1
1
0
2
2
1
0
0
0
0
2
0
1
0
1
1
1
0
2
1
0
1
1
2
0
2
2
1
1
1
1
1
1
2
2
1
2
1
1
2
1
1
1
0
0
2
2
1
1
1
1
1
1
0
0
0
2
1
0
2
0
0
1
2
1
4
1
0
1
1
0
0
2
0
0
0
1
0
0
1
1
0
1
0
1
1
1
2
1
1
0
0
0
1
1
2
0
2
1
1
2
0
0
1
0
0
1
1
0
0
0
1
0
1
1
1
2
2
1
0
1
0
1
1
0
2
1
1
0
0
1
0
0
0
0
0
0
0
2
1
1
2
0
2
2
2
0
2
1
1
2
0
0
2
0
1
1
0
1
1
0
0
2
0
0
0
1
1
1
2
0
1
1
0
1
1
2
0
1
2
1
2
2
0
0
0
1
2
1
2
0
0
1
0
2
0
0
2
0
2
1
2
0
0
1
1
1
0
1
2
0
1
0
1
1
0
2
2
0
1
1
1
0
2
2
1
0
1
0
0
2
1
0
2
0
1
3
0
2
0
2
1
1
0
0
0
0
0
0
1
1
1
1
1
0
1
2
2
0
1
0
1
1
0
1
1
0
0
1
1
0
1
1
0
0
1
1
2
0
2
2
1
1
4
0
3
0
0
0
1
2
1
2
2
1
0
1
2
0
2
1
1
2
0
1
2
0
1
1
1
1
1
1
1
0
2
1
2
0
0
2
1
0
2
1
0
2
0
0
1
1
1
1
1
0
0
1
1
0
1
2
0
0
1
0
0
1
0
1
1
1
1
0
1
0
1
0
1
0
0
1
0
1
2
0
1
1
1
2
2
1
0
0
2
2
2
4
1
2
1
0
1
2
0
0
1
0
0
1
0
1
0
0
1
2
1
2
0
0
2
2
0
0
1
2
0
1
1
0
0
0
2
2
1
1
0
2
1
1
2
1
0
0
1
3
0
0
0
2
1
2
2
2
1
1
2
2
2
1
1
1
0
2
0
2
0
0
0
1
0
1
2
1
2
3
2
0
1
0
3
0
1
0
1
1
0
0
0
1
2
1
1
2
1
2
1
1
0
0
2
3
1
0
1
1
0
2
0
0
2
1
2
1
1
2
1
0
1
0
2
1
1
1
2
0
1
2
0
1
1
0
1
2
0
2
0
0
0
0
1
1
2
0
1
1
0
1
2
1
2
0
1
2
3
2
1
2
0
0
2
2
1
0
1
0
0
1
0
1
1
0
1
0
1
2
1
2
2
0
0
2
0
2
0
0
1
0
0
2
3
2
1
1
0
0
0
1
1
0
0
0
0
2
1
2
2
1
2
1
0
0
0
1
0
0
3
1
2
2
0
0
0
0
0
2
2
1
1
1
1
1
1
2
0
1
1
2
2
0
0
1
1
1
1
1
0
0
2
1
1
1
1
3
2
1
0
0
0
3
1
0
1
1
0
2
0
1
1
1
0
0
0
2
0
1
0
0
1
0
1
1
1
0
2
1
1
2
1
1
1
0
1
0
1
0
1
2
1
2
2
0
2
0
1
1
2
0
1
1
1
1
2
0
1
0
2
1
0
1
1
1
2
1
1
1
0
1
0
1
1
1
1
1
1
1
0
1
1
1
1
0
1
0
2
1
0
0
0
1
1
1
0
0
2
0
2
0
1
1
2
0
2
1
0
0
1
0
1
0
2
0
0
1
1
5
2
1
1
1
0
0
2
0
0
1
1
1
2
0
2
1
0
1
0
2
0
1
2
2
1
2
1
0
1
1
1
0
1
0
1
1
0
0
1
1
2
1
1
2
0
0
1
0
0
0
2
1
2
0
2
1
1
1
2
1
0
1
0
0
0
1
1
1
2
1
2
0
1
1
2
0
0
1
3
1
0
0
1
0
0
1
1
1
1
1
1
1
1
0
0
0
1
1
1
1
2
0
0
1
1
1
2
1
1
0
2
0
2
1
2
0
0
0
0
1
0
2
0
0
1
1
1
1
0
0
0
1
0
1
3
2
0
3
1
0
0
1
0
1
1
1
1
2
1
2
1
1
1
2
2
3
3
2
1
0
1
1
2
0
0
0
1
1
1
0
2
0
0
1
2
0
1
0
0
0
1
1
1
0
1
1
0
0
0
1
1
1
1
1
1
1
1
2
1
0
1
0
0
2
2
1
1
1
1
1
0
1
0
2
1
1
0
0
2
1
1
1
2
1
0
1
0
2
0
0
0
2
1
0
1
1
0
2
0
1
2
0
1
2
0
0
0
2
1
0
2
1
1
0
2
1
0
2
1
2
2
1
0
1
1
0
1
0
2
0
0
0
1
2
1
1
2
1
1
1
1
0
2
2
2
1
1
2
1
1
1
1
1
1
2
4
0
2
0
1
1
1
2
0
0
1
1
0
2
1
1
1
1
1
0
2
1
1
2
2
1
1
1
1
1
0
2
1
2
0
1
0
0
1
0
0
2
0
1
1
0
1
0
1
2
1
0
2
2
1
0
1
0
0
2
1
0
2
1
1
1
1
1
1
1
4
1
2
2
1
3
1
2
1
0
1
0
0
2
0
2
0
1
1
0
1
1
2
1
0
2
1
0
0
1
0
1
2
2
1
1
1
1
1
1
2
0
1
1
1
1
0
0
2
0
0
0
2
1
1
2
1
0
2
2
1
2
1
2
1
1
1
1
0
2
0
0
0
1
2
1
1
0
0
1
0
2
2
1
1
1
0
2
0
2
1
2
0
0
0
2
0
8
0
2
1
0
2
0
1
2
1
2
1
2
1
1
2
1
1
1
2
2
0
0
1
1
1
4
2
2
0
0
2
1
2
1
0
0
1
1
2
1
0
0
0
1
0
0
0
2
0
1
2
1
0
1
0
0
1
3
0
0
0
1
2
0
2
1
0
0
2
1
1
1
1
1
1
1
1
1
0
2
1
2
1
0
1
1
2
2
0
5
0
1
1
0
1
0
1
2
0
0
1
0
1
0
2
1
1
1
1
0
1
0
1
2
1
1
2
1
2
1
1
2
1
3
0
0
0
1
1
0
0
3
0
0
10
0
1
1
3
0
2
0
0
0
0
1
1
1
2
2
0
0
1
0
1
2
2
1
0
1
1
1
1
1
1
0
1
1
1
0
0
1
1
0
2
2
1
1
2
1
2
1
1
0
1
0
1
1
2
0
1
0
0
1
2
2
0
1
2
1
1
1
0
1
0
0
0
0
0
1
1
0
1
1
1
0
0
1
0
2
2
2
0
1
1
1
0
1
0
1
1
2
2
2
1
1
0
1
1
0
1
1
0
2
0
1
1
1
1
1
1
0
0
2
0
0
0
2
1
2
0
1
0
1
0
0
0
0
2
1
0
1
2
1
0
2
1
1
1
1
0
0
1
1
1
2
1
1
0
0
0
0
1
1
0
0
2
2
1
2
2
1
0
1
0
1
3
2
1
0
0
1
0
0
1
1
1
1
1
1
2
1
2
2
1
1
2
0
1
0
0
0
0
0
1
2
1
1
2
1
2
1
0
1
0
0
2
0
1
0
1
0
1
0
0
0
1
1
1
1
0
0
1
1
1
1
2
0
2
0
1
4
1
1
1
1
1
0
1
0
1
1
1
0
1
0
1
0
0
0
1
2
0
0
0
0
0
0
1
1
0
2
1
1
0
1
2
0
0
2
1
0
2
1
1
1
0
2
1
1
2
3
0
0
2
0
1
1
1
1
2
2
2
1
1
0
2
1
0
1
1
1
0
0
1
0
1
1
0
2
1
1
1
1
1
3
1
0
0
1
2
2
1
0
0
0
1
1
1
3
2
0
2
1
0
1
0
1
0
0
0
2
1
0
1
2
0
0
0
2
1
0
1
0
2
0
1
2
1
1
1
0
2
2
1
1
2
1
2
1
2
0
0
0
1
1
1
1
1
1
1
2
0
0
5
2
2
0
1
0
1
0
1
1
1
3
1
0
0
2
1
1
2
2
1
0
0
1
2
1
0
1
0
2
1
0
2
0
2
1
4
0
0
0
0
1
2
0
0
0
0
1
0
1
0
2
1
0
2
3
1
1
1
1
1
2
1
0
0
0
1
2
0
0
1
0
3
1
1
0
0
0
2
1
1
0
2
2
1
1
0
1
2
0
1
1
0
0
1
1
0
0
1
1
1
1
0
1
2
0
0
0
0
2
1
0
0
1
2
0
1
1
0
1
2
0
1
1
0
1
1
1
0
1
2
1
1
0
2
6
0
0
0
2
0
1
1
1
0
1
1
2
1
0
1
0
0
0
2
1
0
0
0
0
2
1
2
0
1
1
0
1
2
1
1
1
1
1
0
0
1
2
0
0
2
1
2
1
3
0
1
1
1
2
0
1
0
0
0
2
1
2
2
0
0
2
0
2
0
0
2
0
1
2
1
1
1
1
2
3
0
1
2
2
2
2
0
0
0
0
2
0
0
1
0
1
1
2
3
1
1
2
0
0
0
1
0
2
1
0
0
1
1
2
1
0
1
1
1
0
1
1
1
0
0
1
0
1
2
1
0
0
0
1
3
0
0
0
1
1
1
1
0
1
1
1
1
0
0
0
2
1
1
2
1
1
0
0
2
2
1
1
2
1
1
2
1
0
0
0
2
1
2
2
1
0
2
1
1
0
1
2
1
3
0
1
1
1
2
0
1
0
3
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
2
1
1
0
0
2
0
1
0
1
1
1
1
0
2
0
1
2
0
0
2
0
0
1
2
0
0
4
1
1
1
1
0
1
0
0
0
1
2
1
2
1
0
1
0
1
0
2
2
2
1
1
1
1
0
2
2
1
0
1
1
1
0
1
0
0
1
1
2
2
1
1
1
0
1
1
0
0
2
0
1
0
1
1
1
2
2
3
1
0
0
1
0
1
1
1
1
1
2
1
0
1
0
1
2
0
1
0
0
2
0
1
1
1
0
1
0
2
1
0
0
0
1
1
0
0
1
1
0
0
3
2
0
1
1
1
0
0
1
1
1
0
1
1
1
1
0
0
1
1
1
2
1
0
0
3
0
0
1
2
2
0
0
0
2
2
1
0
4
1
0
1
0
0
2
1
1
0
2
1
1
2
1
1
1
0
2
0
0
2
0
2
0
1
1
1
0
1
0
0
1
2
1
2
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
2
2
2
2
2
0
1
1
1
1
0
1
1
2
1
0
2
0
1
1
1
1
0
1
2
1
2
0
0
1
0
0
0
3
1
0
2
0
1
1
0
1
1
1
1
1
2
2
1
1
1
1
0
1
2
0
1
2
1
0
2
0
1
1
0
2
0
1
1
1
0
0
2
1
1
1
1
0
1
1
0
1
0
1
0
2
1
1
1
2
1
1
1
2
2
0
1
0
1
1
1
2
0
0
2
2
1
0
1
1
2
2
2
1
5
0
1
0
1
0
0
1
2
1
0
2
2
0
0
1
1
0
2
2
0
2
1
1
1
2
2
1
0
0
2
0
1
1
1
1
2
1
0
0
0
1
1
0
0
0
1
0
1
2
1
0
1
1
0
2
1
1
0
0
1
1
1
0
0
0
0
1
0
2
0
0
0
0
2
0
1
2
0
0
1
0
2
2
2
2
2
0
2
0
1
1
0
1
1
1
1
1
1
1
1
1
3
1
1
1
0
0
1
0
1
0
1
0
0
1
2
2
0
2
1
1
1
1
2
1
0
1
1
1
2
0
1
0
1
1
1
0
0
1
1
1
2
1
1
1
1
1
1
1
0
1
2
0
1
0
0
1
0
1
0
1
1
1
0
1
0
0
1
0
0
2
3
1
1
0
2
1
0
2
2
2
1
2
1
2
2
0
2
1
0
1
1
1
1
0
2
2
1
1
1
0
1
0
0
1
2
1
1
0
1
1
2
0
1
1
1
0
1
1
1
1
0
1
1
0
1
2
0
1
0
0
0
0
1
2
1
1
1
0
3
1
2
1
1
1
1
2
1
1
0
0
1
1
4
0
1
2
0
1
2
0
1
1
1
2
0
2
1
0
1
1
1
2
1
2
2
0
1
1
1
1
2
0
0
2
2
2
1
1
0
1
0
0
1
2
0
2
2
0
1
2
1
2
0
0
0
1
0
1
1
1
0
2
0
0
1
1
2
2
0
2
2
2
0
1
1
0
0
1
1
1
1
2
2
0
1
0
1
1
2
0
0
2
0
0
2
3
2
0
2
2
1
0
1
0
1
1
1
0
2
0
1
2
0
0
0
0
1
2
0
1
1
0
1
1
0
1
1
2
0
1
1
1
0
0
0
1
0
1
0
0
0
1
1
1
0
2
2
2
0
1
2
1
0
0
1
0
1
0
2
0
2
0
2
2
1
1
1
1
1
0
0
1
1
1
2
2
1
0
1
0
2
2
0
0
0
0
0
1
1
0
1
0
1
1
1
1
2
1
0
1
3
1
0
2
2
1
0
2
1
0
2
0
1
0
0
0
0
0
1
0
1
2
1
2
1
1
1
1
2
1
1
1
1
2
0
2
1
0
2
1
0
1
0
2
2
1
0
1
1
2
1
1
1
0
0
0
0
1
1
0
0
0
2
1
1
0
0
2
0
1
1
2
1
1
2
1
1
0
0
0
1
0
1
0
0
1
0
0
0
0
2
1
1
0
0
0
0
1
2
0
0
0
0
0
2
1
0
2
2
0
2
1
0
1
0
1
1
1
0
1
0
0
2
0
1
2
0
0
0
0
2
1
1
1
0
0
0
3
2
0
0
1
1
1
2
1
3
0
1
2
1
1
1
1
0
0
2
1
0
2
0
2
2
1
1
1
2
3
1
0
1
2
2
1
1
0
1
2
0
0
1
1
1
0
0
1
1
0
1
0
0
0
0
0
1
0
1
1
1
1
1
1
2
2
5
1
2
2
1
1
2
2
1
2
1
2
0
2
2
0
1
2
1
2
2
1
1
1
1
0
2
2
0
0
0
0
0
1
1
0
1
0
2
0
0
1
1
0
2
2
0
1
0
1
1
1
1
2
0
2
1
1
1
1
1
2
2
1
2
1
1
2
2
0
0
2
1
0
1
0
1
2
0
0
1
1
1
0
1
1
0
2
0
1
0
0
0
0
2
1
1
0
0
2
1
2
0
1
2
1
0
1
1
2
2
0
0
2
1
1
2
0
1
2
0
1
2
2
0
2
1
1
2
0
1
0
1
0
2
0
2
0
1
1
1
0
0
2
0
1
1
0
2
0
2
1
2
1
2
0
1
1
1
1
2
0
1
1
1
2
0
2
0
0
1
0
1
0
1
0
0
1
0
2
0
1
1
1
1
1
1
1
0
1
0
0
0
0
1
0
2
0
1
3
0
1
2
1
1
1
1
1
0
0
1
0
1
0
0
1
0
2
1
0
1
1
2
2
0
2
1
1
1
0
1
2
0
0
0
0
1
1
1
0
1
1
0
0
1
2
0
1
0
1
2
1
0
1
0
1
2
0
1
1
2
1
0
2
2
0
1
0
1
1
3
2
0
2
1
1
2
0
0
0
1
0
1
2
0
2
1
0
2
2
2
0
0
1
1
2
1
2
0
0
0
1
0
1
0
1
0
2
1
1
1
1
2
2
1
1
1
0
2
1
0
0
2
1
1
0
1
2
0
0
1
0
2
2
1
1
0
0
1
2
0
0
0
1
1
1
2
0
1
2
1
2
1
1
2
0
1
1
2
0
1
0
0
1
0
2
1
2
1
2
0
1
2
1
0
1
1
0
1
0
1
1
0
0
1
0
0
0
1
1
2
0
1
0
1
0
1
0
1
0
2
2
1
1
1
1
1
1
0
1
1
1
2
1
1
0
2
0
0
2
1
2
1
1
0
1
0
0
0
0
0
0
0
1
1
1
0
0
2
2
0
0
0
3
1
0
1
0
1
0
1
2
0
0
1
2
0
0
1
2
1
0
0
2
0
1
1
1
0
0
1
0
1
1
1
0
1
0
0
0
0
1
0
0
0
0
5
0
0
1
3
0
2
2
2
1
0
1
1
2
0
2
0
2
2
2
1
1
1
0
0
0
0
0
1
1
0
1
1
0
0
1
1
2
1
0
2
1
0
0
0
1
2
2
0
0
1
0
1
1
2
0
1
1
1
2
1
0
0
0
1
1
2
0
0
2
1
2
0
2
0
0
0
1
0
2
2
2
0
1
1
1
1
1
5
0
1
1
0
0
1
0
0
0
0
2
1
2
1
2
0
1
2
0
1
2
2
1
1
1
2
1
2
2
1
1
1
1
2
0
0
0
2
0
2
1
2
1
0
2
2
1
2
1
2
0
1
1
2
2
1
0
1
1
1
1
1
1
1
0
1
1
0
1
2
1
4
1
1
1
1
1
0
0
0
2
0
0
0
0
2
0
0
1
0
1
1
1
0
1
0
1
0
0
1
1
1
0
0
1
1
2
1
1
2
0
4
2
0
0
0
2
1
0
2
1
1
0
0
0
1
0
1
1
1
1
1
1
1
1
1
0
1
1
0
1
2
0
1
0
1
1
2
0
3
1
1
2
0
1
1
0
2
0
0
1
1
1
0
1
2
0
0
1
0
2
1
2
2
2
0
1
2
1
0
1
0
1
1
0
1
2
0
1
1
0
1
1
0
1
1
0
1
1
1
5
1
0
0
1
1
2
2
1
1
1
0
1
2
1
0
0
1
1
0
1
0
1
2
2
0
1
2
1
2
1
2
2
1
0
2
2
2
1
0
0
1
0
0
1
0
1
1
0
0
0
1
0
1
0
0
1
1
2
0
1
1
0
0
1
1
1
0
1
1
2
0
0
0
2
2
1
2
2
1
1
0
1
0
0
1
1
1
1
2
0
0
0
2
1
0
0
0
0
0
1
1
2
0
0
0
2
1
1
1
1
1
0
1
0
0
0
0
1
3
1
0
0
0
0
0
1
2
1
1
1
1
1
3
1
2
1
1
0
0
2
0
2
1
2
0
0
1
0
0
1
2
0
1
1
3
0
1
1
3
1
0
2
0
2
1
2
0
0
1
1
1
2
1
1
1
1
0
0
1
2
2
2
0
0
0
1
1
0
1
1
1
1
1
0
0
1
2
1
1
0
1
1
2
1
1
0
0
0
0
2
0
0
0
0
0
1
0
2
0
2
1
1
0
0
1
0
0
0
1
0
0
1
1
0
1
1
2
0
0
1
2
2
2
1
1
3
1
1
1
2
0
2
1
0
0
2
1
0
2
1
0
1
2
1
1
0
1
1
0
1
1
1
1
4
1
0
1
2
1
0
1
0
0
0
1
0
1
0
2
1
0
0
0
1
1
2
1
2
1
2
2
1
1
0
1
1
1
2
0
1
3
0
2
1
0
1
2
1
3
0
1
0
0
2
1
1
1
1
0
1
1
0
1
2
1
1
1
0
0
0
1
1
1
1
2
1
1
1
0
0
1
1
1
2
2
1
1
2
1
2
3
1
1
1
0
2
0
1
0
0
0
2
1
0
2
2
2
0
2
2
1
0
1
1
3
1
0
3
1
1
1
1
0
0
1
1
0
2
2
1
1
1
3
1
1
1
0
1
1
0
0
1
1
1
2
2
2
1
1
1
0
0
1
1
1
0
2
1
1
1
0
0
0
1
0
0
0
1
2
1
1
2
0
2
2
2
1
1
1
2
0
0
2
1
1
1
1
1
2
0
1
1
2
1
0
0
0
0
2
0
2
1
1
2
1
1
0
2
2
1
0
1
0
0
1
1
1
0
2
1
2
1
0
1
0
0
0
1
3
1
2
1
1
1
1
1
2
1
2
2
0
0
0
1
0
2
2
1
1
1
0
2
1
1
0
2
2
1
1
0
1
0
0
2
0
2
1
0
0
1
0
0
0
2
1
1
0
0
0
2
1
1
2
1
0
0
1
0
0
1
0
1
0
1
2
0
0
1
2
1
1
1
1
1
0
0
0
1
2
2
0
1
1
2
1
2
1
1
0
1
0
0
2
1
0
1
0
0
0
1
1
0
1
1
0
0
1
0
0
1
1
0
0
2
0
1
1
2
0
0
0
2
1
0
0
1
0
2
0
0
1
0
1
1
1
0
0
0
0
1
1
1
1
2
0
0
1
1
1
1
0
2
0
2
0
0
1
1
1
0
0
0
0
0
2
0
0
2
1
0
2
0
1
2
0
2
2
1
1
0
3
2
1
0
1
0
2
1
1
1
2
1
1
2
2
1
0
2
1
0
2
1
0
1
2
1
1
0
0
1
2
2
1
0
0
1
1
1
0
1
2
2
1
0
2
2
1
1
0
2
0
1
1
2
1
0
1
1
1
1
1
1
1
1
1
1
1
0
2
1
0
0
2
2
2
2
0
1
1
1
2
2
2
1
0
1
1
1
0
1
0
1
0
1
2
2
1
1
0
2
0
2
1
1
2
0
2
3
0
1
0
0
1
1
0
0
1
0
0
1
2
1
1
1
1
1
2
0
0
0
1
1
1
0
1
0
0
0
0
2
0
1
1
1
1
0
0
0
0
1
1
0
2
0
1
0
1
1
0
0
0
2
0
1
1
0
0
1
2
0
0
2
2
1
1
2
2
0
2
0
1
0
1
1
1
1
0
1
1
0
1
1
1
0
1
2
2
2
2
0
4
0
3
3
2
0
1
0
1
0
0
1
1
0
1
0
1
2
0
1
1
4
1
1
3
1
2
1
1
1
2
0
0
1
1
1
1
1
2
1
2
0
1
1
2
0
0
0
0
2
0
0
0
0
2
0
0
1
2
1
1
2
0
0
2
2
1
0
0
0
1
0
1
1
0
0
1
1
0
1
0
2
0
0
0
0
1
2
1
0
1
1
1
2
1
0
1
1
1
1
1
0
0
1
1
1
1
0
2
0
1
1
0
1
2
1
0
0
2
1
1
0
0
1
1
0
0
1
0
0
0
1
0
1
1
1
2
2
0
2
0
1
1
0
2
1
0
1
1
0
0
2
1
0
1
1
0
0
1
1
2
1
1
0
0
2
2
1
0
2
2
0
1
2
0
2
1
1
2
2
1
1
2
1
1
1
1
1
0
1
0
0
0
1
0
0
3
1
2
0
2
1
7
1
1
0
3
1
1
0
1
1
0
1
0
1
1
1
1
0
2
1
0
0
0
1
0
0
2
0
2
0
0
2
0
1
1
1
1
0
2
0
2
2
0
1
1
1
1
2
0
1
0
0
1
0
2
1
0
1
0
1
0
1
1
0
1
1
2
1
2
1
0
0
2
1
0
0
0
0
0
0
0
1
0
3
0
0
1
0
2
1
1
1
1
1
3
2
2
2
0
0
1
1
0
0
1
1
2
2
0
2
1
0
0
1
0
0
0
1
1
1
3
2
2
1
1
3
3
2
0
1
1
1
1
0
2
1
1
1
3
0
1
2
1
1
1
1
2
2
2
2
2
2
1
1
1
1
0
3
0
2
1
0
2
0
1
1
1
1
1
0
1
1
1
1
2
0
1
0
0
0
1
0
0
2
1
0
0
2
1
1
1
1
1
1
1
1
0
1
2
0
2
2
0
2
0
2
1
2
1
2
0
2
0
0
1
0
1
0
0
1
1
1
1
1
0
1
1
0
0
1
1
2
1
2
0
1
1
1
1
2
1
0
0
0
0
1
1
1
0
1
1
1
1
1
0
0
1
0
0
1
0
1
1
0
1
0
0
2
0
0
0
1
1
1
2
1
0
1
1
2
0
2
0
0
2
2
1
0
0
1
2
1
1
0
2
2
0
2
1
0
1
0
0
2
2
1
0
1
1
0
1
0
0
1
0
0
2
1
1
2
2
2
1
0
1
0
0
0
0
1
1
2
1
0
1
0
1
1
1
1
1
2
1
0
1
0
2
1
1
2
1
0
1
2
0
2
1
0
0
0
1
0
0
0
1
1
0
1
1
2
0
3
2
2
1
1
1
2
1
0
1
2
0
2
0
1
0
0
1
2
2
1
1
0
2
2
1
0
1
1
1
1
1
1
2
1
0
0
3
1
0
2
0
1
0
1
3
0
1
2
2
2
0
0
3
2
0
0
1
1
1
3
0
0
0
0
0
1
2
1
1
2
0
1
1
2
1
1
0
0
0
1
1
1
1
1
2
2
1
0
0
0
2
2
2
2
2
0
1
1
2
2
0
1
1
1
0
1
0
1
0
2
2
1
1
2
0
1
1
2
0
0
1
0
2
0
0
0
1
1
1
0
0
0
2
1
1
0
1
1
1
2
2
0
0
1
0
1
0
0
1
2
0
0
0
2
0
1
0
0
0
2
2
1
1
2
2
0
1
2
1
1
0
1
1
1
0
1
0
1
0
2
2
0
1
1
0
0
1
1
1
0
1
2
0
1
1
2
0
0
1
1
1
1
0
1
0
0
1
1
2
1
1
1
1
0
1
0
1
1
1
1
2
0
1
1
1
1
1
1
1
0
1
1
1
1
0
1
1
0
1
0
0
0
1
2
1
2
0
2
0
0
2
2
1
0
1
1
0
1
1
2
1
0
1
0
1
0
0
0
1
1
0
3
2
1
1
0
0
1
1
1
1
1
1
0
1
0
0
0
0
1
1
1
0
1
2
0
2
1
0
0
3
1
2
2
1
1
0
1
0
1
2
0
1
2
0
0
1
0
1
0
1
0
2
0
2
0
0
0
1
0
1
1
2
1
0
2
1
1
1
2
1
2
2
1
0
1
2
0
1
0
2
0
1
1
2
2
0
0
2
1
2
0
1
0
2
0
0
1
0
1
1
2
0
2
1
0
0
1
2
0
1
2
2
0
3
0
1
1
0
2
0
0
2
0
1
2
1
1
0
2
2
0
1
1
1
2
1
0
2
0
2
0
0
2
1
2
0
0
1
2
1
1
1
0
0
2
1
0
2
2
1
1
0
1
0
0
0
0
1
1
1
0
1
0
1
3
0
2
2
0
0
1
1
1
0
2
1
0
2
1
1
1
1
0
1
1
1
0
0
1
1
2
0
2
2
1
1
0
0
3
0
0
0
1
0
1
0
0
1
2
0
2
0
1
1
1
0
0
1
1
0
0
1
1
0
1
0
3
1
0
1
0
2
0
1
2
1
0
1
2
1
0
1
2
0
1
1
0
1
1
0
1
1
0
2
2
1
2
0
3
1
2
2
1
1
1
2
1
1
0
0
1
0
1
0
0
0
2
1
0
2
1
0
1
1
0
0
0
1
1
2
0
0
1
0
1
2
1
0
1
1
1
1
1
1
1
0
1
0
2
0
0
0
1
1
0
2
0
0
2
0
1
0
2
1
1
0
2
2
1
2
1
0
0
1
1
1
0
1
2
2
1
1
2
2
1
1
1
1
1
2
2
0
1
1
0
1
1
0
1
1
2
1
0
1
1
0
1
2
1
1
2
0
1
0
1
1
0
0
4
1
0
0
0
0
0
1
0
0
0
0
1
1
1
0
1
2
1
1
1
0
2
1
2
2
1
1
1
0
0
1
1
1
2
2
1
0
0
1
1
2
1
2
1
1
1
1
1
0
1
1
2
1
1
2
2
1
0
1
1
0
1
0
3
0
1
2
0
1
0
0
0
2
2
0
1
1
0
0
0
0
1
2
2
0
0
0
1
1
1
2
1
0
0
0
0
1
0
0
0
1
1
3
2
1
1
1
0
0
1
1
0
2
2
1
0
1
1
2
0
0
2
0
0
0
1
1
0
2
0
0
0
0
1
0
2
1
1
1
1
0
0
0
1
0
1
0
1
1
1
1
0
1
0
0
1
0
1
1
0
1
0
1
2
0
1
2
2
2
2
1
1
1
0
0
0
1
1
1
1
0
0
0
2
1
2
1
0
1
0
1
1
0
2
1
1
0
1
1
1
0
2
1
1
2
1
0
1
1
2
0
3
0
0
1
0
3
1
0
2
1
0
1
2
2
0
0
2
1
0
1
0
0
1
0
0
0
0
1
1
1
0
1
1
0
2
1
0
2
2
0
2
0
1
1
1
1
0
1
1
1
0
2
0
0
0
0
2
0
2
0
1
1
1
1
1
1
1
1
1
1
0
1
0
0
2
2
1
0
1
1
2
1
1
0
0
1
0
2
0
0
1
2
1
1
0
2
2
1
1
2
2
0
0
0
1
0
1
2
1
0
1
0
0
0
0
1
1
2
1
1
1
1
2
1
0
1
1
1
1
0
1
0
1
1
1
0
1
0
1
0
1
1
2
2
0
1
1
1
2
2
1
0
1
2
2
2
1
1
3
2
0
1
1
1
0
1
2
2
0
1
2
0
1
1
2
0
0
0
1
1
1
2
0
0
2
2
0
2
0
0
0
1
2
1
1
1
0
1
1
0
0
0
1
2
1
0
0
0
0
0
1
0
2
0
1
2
2
2
0
1
1
0
0
0
1
0
1
2
1
1
0
0
1
2
0
2
0
2
1
2
4
2
0
2
1
3
0
1
1
0
1
0
1
0
2
0
0
2
2
1
1
1
0
1
0
1
1
0
0
4
0
1
2
1
2
0
1
1
1
2
0
0
1
2
1
2
1
0
0
0
2
0
0
1
0
2
0
1
0
0
1
2
1
3
2
0
0
1
2
0
0
1
0
0
0
1
2
1
1
1
0
1
0
2
2
0
1
1
2
1
0
0
3
1
1
2
0
2
0
2
0
1
2
2
2
2
0
1
2
0
0
2
1
0
1
0
0
1
1
0
2
0
1
0
1
0
1
0
2
1
1
2
0
1
0
2
0
0
0
1
2
2
1
1
2
1
1
1
0
2
0
1
0
2
1
0
1
1
1
2
0
0
0
0
3
0
1
0
1
1
2
1
2
1
0
0
2
1
0
1
2
2
2
1
1
1
0
1
2
1
0
1
1
2
0
1
0
1
1
1
1
0
0
0
0
2
0
1
1
0
2
2
0
0
1
0
2
2
2
1
2
1
2
1
1
2
2
1
2
1
1
1
0
1
0
0
2
2
3
0
1
0
2
1
2
0
2
1
0
1
1
0
2
1
0
0
1
0
1
1
1
1
1
2
0
1
0
0
1
0
2
2
1
0
2
0
1
2
1
2
1
1
0
1
0
0
0
0
1
0
1
3
1
1
0
1
0
1
2
0
1
0
0
1
2
0
0
1
0
2
1
1
1
2
1
1
0
3
1
1
1
1
0
0
1
0
0
0
2
1
1
0
2
1
2
1
0
0
1
0
0
1
0
2
0
2
1
2
2
0
2
0
2
1
0
1
1
1
1
0
2
2
1
1
0
0
0
1
1
1
0
1
1
2
2
2
1
1
0
0
1
0
1
0
1
2
0
1
2
0
1
1
1
0
1
1
1
1
1
1
0
0
2
0
0
4
1
2
2
1
0
1
0
1
1
2
0
0
1
2
0
1
0
2
1
1
0
1
1
0
0
2
1
1
1
0
2
2
1
1
0
1
1
1
0
1
2
0
1
0
2
2
1
2
0
0
2
1
1
0
0
1
1
0
1
1
2
1
1
1
1
0
0
1
1
1
1
0
3
2
0
2
1
2
2
1
1
1
0
3
2
2
1
2
0
0
0
2
1
1
1
1
1
2
2
0
1
1
2
1
0
0
0
1
1
1
1
0
2
2
1
0
1
1
0
1
1
0
1
1
1
1
2
1
0
0
0
1
1
1
0
1
1
2
0
0
0
1
1
2
1
0
0
1
1
1
1
1
0
0
1
0
1
0
2
0
0
1
1
2
0
1
1
1
2
2
0
0
2
0
0
1
1
0
2
0
1
1
1
1
0
0
0
1
1
1
0
0
1
0
0
0
2
2
0
0
0
0
1
1
1
0
1
0
0
0
0
0
2
1
1
0
1
0
1
1
2
2
0
1
0
1
2
1
0
0
0
1
2
1
1
1
1
1
1
0
1
0
2
1
1
1
2
1
2
0
0
1
2
0
0
2
1
1
2
2
2
2
1
1
1
0
0
1
2
1
1
0
2
4
1
0
1
1
2
1
0
1
0
3
1
0
1
2
0
1
0
1
1
1
0
1
0
0
1
0
1
1
0
2
0
2
2
0
1
1
0
0
0
1
0
0
1
2
1
2
1
0
1
2
1
1
2
0
0
0
1
0
2
0
1
0
0
1
1
0
1
1
2
1
1
1
2
1
2
1
1
1
1
1
1
1
0
2
1
0
1
2
2
2
0
1
1
1
1
2
2
1
0
1
1
0
0
2
1
2
1
0
1
1
2
1
1
0
0
1
0
2
0
1
0
0
2
0
2
2
1
0
1
0
1
1
1
2
4
2
0
0
1
0
0
1
1
2
1
2
2
0
1
0
0
2
2
2
1
1
0
0
1
0
0
1
1
2
0
1
0
2
1
2
1
1
2
1
2
0
2
2
1
0
4
1
0
1
0
1
0
0
0
2
0
0
2
1
1
1
0
1
2
2
0
0
1
2
0
1
0
0
2
0
0
0
1
0
1
1
1
0
1
2
1
1
1
1
1
1
2
1
1
1
1
0
0
1
0
1
2
1
0
2
2
1
3
1
0
1
1
1
1
0
2
0
1
0
1
1
2
1
2
1
1
2
1
0
0
1
0
0
0
0
1
0
1
4
1
1
1
0
1
1
1
2
2
0
2
1
1
0
1
0
1
1
2
2
1
2
2
2
0
0
1
1
0
1
0
0
2
0
0
2
2
0
1
2
0
1
0
0
0
0
0
0
0
2
0
1
0
0
1
1
0
1
1
1
2
2
0
0
0
1
2
0
0
2
1
0
1
0
2
2
2
2
2
0
1
0
1
1
1
1
0
1
1
1
1
1
4
2
0
1
1
1
0
2
1
1
2
1
1
0
1
1
1
1
1
1
0
1
1
2
1
0
0
1
1
1
1
1
2
2
1
3
2
1
0
1
0
0
1
0
1
0
1
1
0
1
2
1
1
1
0
1
0
0
0
0
0
1
1
1
1
1
0
1
0
1
2
0
0
0
2
0
1
0
0
0
2
0
0
1
0
1
2
1
1
1
1
1
1
2
1
0
0
1
1
0
0
1
1
1
1
1
1
0
1
1
0
1
1
2
1
2
1
2
1
2
1
0
1
1
1
1
0
1
1
1
1
1
0
0
1
1
1
0
0
2
2
1
1
0
1
0
0
0
0
0
3
1
0
2
2
2
0
1
2
0
1
0
0
0
1
0
0
1
0
1
0
1
1
0
0
2
1
1
0
0
1
2
2
0
0
3
2
1
0
1
0
1
1
1
1
1
1
1
3
2
1
0
0
2
1
1
1
0
0
1
0
1
1
1
1
1
2
0
0
1
0
0
0
1
1
0
1
1
2
2
1
0
0
1
0
0
0
0
0
0
1
0
3
2
0
0
1
1
2
1
1
2
1
2
0
0
1
0
0
1
2
2
1
5
1
1
0
0
1
1
1
1
0
0
1
0
1
1
2
1
1
0
0
2
1
1
2
0
0
0
1
1
2
2
0
2
0
1
2
1
2
1
0
1
2
1
2
1
1
0
0
1
0
1
1
1
0
2
1
1
0
0
3
1
0
1
1
2
3
1
1
1
2
0
0
0
0
1
0
1
0
1
1
0
0
1
1
1
0
1
2
2
1
1
1
1
2
2
0
1
0
0
0
0
1
1
1
1
1
1
2
0
0
1
1
1
1
0
1
0
2
1
1
0
1
0
0
1
0
1
0
2
1
1
1
1
0
0
1
1
0
0
1
2
2
0
2
0
1
0
1
0
0
0
0
1
2
0
2
2
1
0
2
0
0
0
0
0
0
0
2
1
1
2
1
2
2
2
1
0
0
2
1
0
1
0
2
1
0
0
0
1
1
2
1
2
1
0
1
2
1
1
1
1
1
0
1
1
1
1
2
1
1
0
1
1
0
2
0
0
1
0
1
0
1
2
1
2
0
2
0
1
0
2
2
2
0
1
1
1
0
1
2
0
2
0
1
0
0
1
1
1
0
1
1
1
2
3
1
1
2
0
0
1
1
1
3
1
2
1
0
1
1
0
2
1
2
4
0
0
0
2
2
1
0
1
0
1
2
0
1
0
3
1
0
0
0
0
0
2
0
1
2
5
2
1
0
1
1
2
0
1
1
1
0
2
1
1
1
1
1
0
1
2
0
1
1
2
1
0
0
0
2
2
0
2
0
0
1
2
0
1
1
2
0
0
1
1
2
2
2
1
0
0
1
0
1
1
1
0
1
0
1
1
1
7
0
0
2
1
1
1
2
1
0
0
1
0
0
1
1
1
1
0
2
2
0
1
1
1
2
0
0
1
1
1
2
1
1
0
0
2
1
1
3
1
0
1
0
2
0
1
1
1
2
1
1
1
1
2
2
0
2
1
1
2
0
0
0
2
1
0
2
1
0
1
2
1
2
0
2
0
0
0
1
0
2
0
0
1
2
1
1
1
2
1
0
2
2
1
0
1
1
0
1
1
1
1
0
0
1
0
2
0
1
1
1
1
1
0
0
0
2
1
1
0
1
0
0
0
1
1
1
0
2
0
2
0
0
1
1
1
1
2
1
2
1
1
0
0
4
1
1
2
2
1
0
1
0
3
1
1
0
1
1
1
2
1
2
1
2
2
2
2
0
2
2
1
0
2
2
3
2
0
1
1
0
0
0
2
1
2
0
2
0
0
1
2
0
2
2
1
2
0
2
2
1
2
0
1
1
1
2
0
2
1
1
1
0
3
1
0
2
1
0
3
1
0
1
0
0
1
1
8
1
1
2
2
1
0
3
0
0
1
1
1
0
1
1
1
0
2
0
2
1
1
0
1
1
0
0
2
0
2
0
0
1
2
0
0
0
1
0
1
0
0
0
0
2
1
0
1
1
0
1
2
2
0
0
0
1
1
1
2
0
3
0
2
1
1
1
1
1
0
2
0
1
1
0
2
1
0
1
0
0
2
1
0
0
1
2
1
0
0
1
0
2
0
1
0
2
1
1
5
2
0
1
0
0
0
2
1
1
1
1
1
2
2
1
0
2
1
0
0
0
1
0
0
1
3
0
0
2
1
0
0
1
1
0
2
1
0
2
0
2
2
0
1
0
0
1
1
1
3
0
1
2
0
1
0
1
1
1
2
0
0
0
0
0
0
1
0
1
2
2
0
1
2
0
0
0
0
1
1
2
2
1
0
2
0
2
1
0
2
1
1
2
2
2
0
2
2
2
2
1
0
0
1
0
1
2
1
0
1
0
1
0
0
1
2
1
0
1
2
0
0
2
2
2
0
1
1
0
2
0
1
1
1
1
1
1
0
0
1
1
3
1
1
1
0
2
0
1
0
1
0
1
0
1
0
2
0
1
1
0
1
1
0
4
1
0
2
3
1
0
1
2
2
1
0
1
1
1
1
1
0
1
1
1
0
1
1
2
1
1
1
1
1
0
0
0
1
1
1
0
1
0
1
2
0
2
1
1
1
2
1
2
0
0
0
4
0
2
0
1
2
1
0
1
0
2
2
1
0
0
1
0
1
0
0
0
2
0
1
2
0
1
1
1
2
1
0
1
0
3
1
1
2
0
1
2
2
1
1
1
2
2
1
1
1
1
2
1
2
2
0
1
0
0
1
1
2
0
0
1
0
1
0
2
1
2
1
1
0
0
1
1
0
1
0
0
3
0
0
1
0
1
1
1
1
0
0
2
1
0
0
1
1
0
3
1
0
1
1
1
3
0
1
0
1
1
1
1
1
0
0
1
1
0
1
0
2
4
3
0
1
2
2
2
0
1
1
2
1
2
1
2
0
2
1
1
1
0
1
0
2
0
0
1
1
1
1
0
1
0
1
2
1
1
1
0
1
0
0
0
2
2
1
1
0
0
1
2
1
0
2
1
0
2
0
0
0
2
0
0
1
0
0
0
1
1
1
2
0
0
2
0
1
0
2
1
2
1
1
0
0
1
1
0
0
1
2
1
0
2
1
0
0
2
1
0
2
2
1
0
1
0
1
1
2
0
2
1
1
2
0
1
2
1
0
2
1
1
0
2
0
2
2
2
2
0
0
1
1
0
2
0
0
2
0
1
1
0
2
1
0
1
1
1
1
1
1
1
0
0
0
2
1
1
1
2
1
0
1
1
0
0
1
2
1
0
2
0
0
1
2
4
1
2
1
1
1
0
1
1
2
0
1
0
1
0
2
1
2
1
1
2
2
0
1
2
1
1
0
0
0
3
1
1
2
1
0
0
3
0
1
0
2
2
1
0
2
1
1
1
3
1
1
0
0
2
0
1
1
0
1
0
1
1
0
1
1
1
1
1
2
3
1
1
1
2
1
0
2
1
2
0
3
1
1
1
2
2
1
1
1
2
1
0
1
0
2
1
0
0
0
2
1
2
1
0
1
0
1
2
1
2
2
0
2
2
1
0
2
1
0
2
2
0
0
2
2
1
1
1
1
1
1
2
0
1
1
0
2
0
0
1
1
1
0
2
0
1
1
0
2
1
2
1
0
1
0
1
2
1
2
1
2
2
2
0
0
0
0
1
0
1
0
1
2
0
0
2
0
1
4
2
2
0
0
1
1
1
1
0
2
1
1
1
0
1
1
3
1
1
2
0
2
0
0
1
2
2
2
2
0
0
2
1
1
0
0
1
1
1
2
1
1
2
2
0
2
1
0
1
2
0
2
2
1
2
0
2
0
2
0
0
2
0
0
2
0
1
0
1
2
2
1
0
1
1
1
0
0
2
1
0
1
0
1
1
1
2
1
1
1
1
1
0
0
2
1
2
0
1
0
0
1
1
0
0
1
1
2
1
1
1
1
2
1
0
0
0
0
0
0
2
2
1
1
1
1
2
1
0
0
0
0
1
0
0
1
0
1
1
1
2
2
1
1
2
1
1
0
1
1
1
0
2
2
3
0
0
0
0
2
2
0
0
0
0
1
1
0
0
0
1
1
2
1
0
2
1
1
2
0
0
0
0
0
1
2
1
1
1
1
2
0
0
1
0
1
0
0
1
1
1
2
1
1
1
1
2
2
1
0
0
1
1
0
0
1
1
0
1
1
2
0
0
0
1
2
2
1
1
1
0
2
1
2
1
1
1
1
0
1
0
0
2
0
1
0
0
1
1
1
1
0
0
0
1
1
4
1
2
1
1
0
1
1
2
0
2
1
2
2
0
1
1
1
2
0
1
0
0
0
0
1
0
1
1
1
2
1
2
0
0
1
1
2
0
1
0
0
0
0
2
1
1
1
1
2
0
0
1
2
0
2
1
2
1
1
2
1
0
0
1
0
1
1
1
0
0
2
0
1
2
1
0
1
1
1
0
1
1
0
1
1
3
1
2
0
1
1
1
0
0
2
0
0
1
3
2
2
0
0
0
1
1
0
1
1
2
1
1
0
0
1
0
1
1
1
1
4
1
0
0
0
1
2
2
0
0
0
1
2
2
1
2
1
0
0
1
0
2
1
1
1
0
0
2
1
0
0
1
0
1
1
1
0
1
0
2
1
1
0
2
1
1
1
1
0
0
0
1
0
2
1
2
0
0
0
2
1
0
0
2
0
0
0
2
0
2
1
0
0
1
0
2
2
2
0
0
0
1
0
0
1
1
0
1
0
1
1
2
2
0
1
2
0
1
1
0
0
0
1
1
0
0
2
1
0
1
2
1
1
1
1
1
1
1
0
2
2
0
2
2
0
1
0
1
1
1
0
3
1
1
2
0
0
1
1
0
2
0
0
1
0
0
1
0
2
1
1
2
0
1
1
0
1
2
0
2
1
2
1
0
0
1
0
0
1
0
0
2
0
2
0
2
1
0
1
0
1
1
1
1
1
0
0
1
2
1
1
0
1
1
0
0
2
0
0
2
1
0
1
1
1
0
1
2
1
1
1
1
1
0
1
0
1
1
2
1
1
2
0
1
2
1
2
2
1
0
1
2
0
3
1
0
1
1
1
1
0
2
1
2
1
2
0
1
1
2
0
1
1
0
1
0
1
2
1
1
0
0
0
0
0
2
1
2
1
0
1
0
1
1
0
0
1
1
1
2
1
1
0
1
1
1
0
0
0
2
1
0
2
1
1
1
1
0
0
2
1
2
1
0
0
1
0
1
1
1
0
2
1
0
0
0
0
2
0
0
0
1
1
0
1
2
0
0
1
2
1
0
1
1
0
1
1
2
0
1
2
1
2
0
0
1
2
1
0
1
0
0
1
0
2
0
0
1
1
1
1
2
0
1
1
0
2
2
1
1
1
2
0
0
1
2
1
1
2
1
2
0
1
1
0
1
2
0
4
0
1
0
1
2
1
2
2
0
1
1
1
0
0
2
1
1
1
2
0
1
0
2
0
1
0
2
1
1
1
1
3
1
0
1
1
1
0
1
0
0
2
1
2
3
1
0
1
1
0
1
2
1
0
2
0
1
1
0
1
2
2
1
1
0
1
0
0
2
1
0
2
2
0
1
1
0
1
1
1
1
2
0
0
2
1
2
1
1
2
2
2
1
0
0
1
1
1
1
2
0
0
2
1
2
0
1
1
0
1
2
1
2
1
2
2
1
1
1
1
0
1
0
1
0
0
0
2
1
2
0
1
1
0
1
1
1
0
2
1
3
1
1
0
0
1
2
1
2
1
0
1
0
1
0
2
2
0
2
1
0
1
1
1
1
0
1
1
1
0
0
0
0
2
1
2
2
2
1
2
1
0
0
1
4
0
0
1
0
0
0
1
0
0
0
0
0
1
2
0
1
0
1
1
1
1
0
0
0
1
1
0
0
1
0
0
1
2
2
2
0
1
0
1
1
1
0
1
0
0
1
1
1
2
0
0
0
1
1
1
1
0
1
0
2
1
0
0
1
2
0
0
0
1
0
1
1
0
1
1
2
1
0
0
2
1
1
0
2
1
0
2
0
1
0
1
1
2
2
0
1
0
0
0
0
0
0
0
2
1
2
0
2
2
1
1
1
0
0
0
2
1
2
0
2
2
0
2
1
1
1
0
1
1
2
2
1
0
2
1
1
1
0
1
1
2
1
0
0
0
2
1
0
2
0
2
2
2
1
2
0
2
0
2
1
1
0
1
1
0
1
0
1
0
0
1
0
1
0
2
0
1
0
0
0
1
1
1
1
1
1
2
1
0
2
2
1
2
1
0
0
1
0
0
1
2
0
1
1
1
0
0
2
0
0
3
1
0
0
1
0
1
1
1
1
0
1
0
0
0
1
0
1
2
2
0
1
0
1
2
1
2
1
2
0
0
0
1
1
1
0
2
1
1
1
1
1
2
0
1
0
1
1
1
1
0
1
2
3
1
0
0
1
1
0
0
0
2
1
1
0
1
1
0
1
2
0
0
0
0
0
0
0
0
1
0
0
1
1
2
1
1
1
1
0
0
0
1
0
0
2
2
0
1
2
0
1
2
1
1
1
1
0
1
3
2
1
1
0
0
0
2
0
1
1
1
1
1
0
3
0
0
0
0
1
1
1
0
1
2
1
0
1
0
0
1
2
1
1
0
0
1
1
1
0
1
2
1
1
1
0
2
1
1
2
2
1
1
0
0
1
1
1
0
0
0
0
1
0
0
0
11
1
1
2
1
0
2
0
1
1
0
0
2
1
2
0
2
0
1
0
1
2
1
0
2
1
1
1
0
0
1
1
0
1
0
3
2
0
2
2
1
1
0
0
2
3
0
1
1
0
0
1
0
0
1
2
1
1
1
1
1
1
0
0
1
2
1
0
2
1
2
1
1
1
2
2
1
0
2
1
0
1
2
2
1
1
1
1
1
2
1
1
0
0
0
1
1
0
1
1
0
0
1
1
1
2
1
1
1
1
0
1
2
0
2
2
0
1
0
1
2
0
0
1
1
1
0
2
1
1
2
2
0
1
1
1
1
0
1
2
1
3
2
0
1
0
0
0
1
2
1
1
0
1
1
1
2
1
2
0
0
2
2
0
1
2
0
4
2
1
2
1
1
0
2
1
2
0
0
1
0
1
1
1
0
2
3
1
0
1
1
0
0
1
0
0
1
2
0
2
0
1
0
0
0
1
2
2
1
0
2
0
0
1
1
0
1
1
0
0
0
2
1
0
0
2
1
1
0
1
0
0
1
0
2
0
1
1
1
1
1
1
1
2
1
1
0
1
1
1
0
0
1
1
0
0
1
1
1
0
0
1
0
1
0
0
1
2
0
1
2
0
2
2
0
0
0
2
2
2
0
0
1
0
1
0
0
4
1
0
1
1
2
0
0
1
1
0
0
0
1
1
2
2
1
1
0
2
1
0
0
0
1
0
1
0
0
0
1
1
1
1
0
0
2
2
2
0
2
1
1
0
0
2
2
1
0
0
0
1
1
1
2
0
1
0
0
1
1
0
1
2
0
1
1
1
0
0
2
1
1
0
1
1
0
2
3
0
3
2
2
0
4
1
2
0
1
2
2
0
0
0
0
0
0
1
0
1
1
2
0
1
2
0
0
0
1
2
1
0
0
0
0
0
1
1
1
2
1
1
0
0
0
0
1
1
1
1
0
0
1
2
1
0
1
0
0
0
2
1
1
1
0
1
0
2
0
0
0
0
0
2
2
0
2
1
0
1
2
1
1
1
1
1
0
0
1
1
1
2
1
0
1
1
1
1
0
1
0
1
2
1
1
0
1
2
0
0
1
0
1
1
0
0
0
0
2
0
1
2
1
0
1
2
1
1
2
2
1
0
1
5
0
0
0
1
0
1
2
1
1
1
0
2
0
1
2
2
1
1
1
1
2
1
0
1
0
1
2
0
2
1
0
0
1
0
2
1
2
0
1
2
0
1
2
1
1
2
1
0
1
2
1
1
0
1
1
2
1
0
1
1
1
2
0
1
1
0
1
1
2
1
2
0
1
1
2
0
1
1
0
2
0
1
1
1
0
0
0
0
2
0
2
0
2
0
2
0
1
1
1
1
0
1
2
0
0
2
1
1
0
1
2
3
1
1
1
0
0
0
0
0
0
0
1
0
2
0
1
0
2
1
0
1
1
3
1
0
1
0
0
1
0
0
0
2
0
1
1
1
1
1
1
1
2
0
2
0
0
0
1
2
1
0
0
1
0
0
0
1
1
0
0
0
1
2
2
0
2
0
1
0
0
0
0
2
2
0
1
2
0
1
0
1
0
0
2
2
2
0
2
0
1
1
1
0
0
0
2
1
1
1
1
1
2
2
1
1
3
0
2
0
1
1
2
0
1
1
1
0
0
2
1
1
1
1
0
1
1
0
0
2
1
2
0
0
0
1
0
1
0
1
1
1
1
1
2
0
2
1
0
1
0
1
1
1
1
2
0
0
0
1
1
1
0
0
0
2
0
1
2
1
2
0
0
1
0
2
2
1
0
1
2
2
0
1
1
2
1
0
1
1
2
1
1
1
2
1
0
0
1
0
1
1
1
1
2
0
1
1
0
2
0
0
1
0
1
1
1
1
1
0
1
1
2
1
2
2
2
0
2
2
1
0
1
1
2
1
1
1
2
1
0
0
0
1
2
0
2
0
1
0
1
0
1
0
1
3
0
1
1
1
0
0
1
1
0
0
1
0
1
1
0
0
0
1
1
1
1
0
0
1
1
0
0
2
0
2
0
0
1
1
1
2
0
2
1
2
0
0
2
0
0
3
1
3
2
0
0
0
0
1
0
0
0
1
1
1
1
2
0
0
2
0
2
2
0
1
1
1
2
1
1
8
4
1
1
0
0
0
1
2
0
1
1
1
2
1
1
0
2
1
0
0
1
0
0
1
2
1
1
0
1
1
0
0
0
1
1
1
1
1
2
1
2
0
1
1
0
2
2
2
2
1
1
0
1
1
2
0
2
0
0
0
1
1
0
2
2
0
0
0
1
1
2
0
0
0
2
1
2
0
0
0
1
1
1
0
0
0
0
1
1
0
1
1
2
2
0
1
1
2
1
0
0
0
2
2
1
1
1
1
1
3
1
2
1
0
0
1
0
2
2
1
0
2
0
1
2
0
2
1
1
2
0
1
2
1
0
1
0
2
1
0
1
1
1
1
1
1
0
2
2
1
2
1
0
1
0
1
1
0
1
0
4
0
0
1
1
0
0
1
2
1
1
0
0
0
2
2
2
0
2
0
0
1
1
1
0
0
1
1
0
1
2
0
2
0
1
0
0
0
1
0
2
0
1
0
1
2
0
1
1
1
0
1
1
0
1
0
0
2
1
0
0
0
0
3
3
1
1
1
0
0
1
0
1
0
2
1
0
2
1
0
1
1
0
1
1
2
1
0
0
2
2
1
0
1
2
2
1
1
0
1
2
1
1
0
1
2
0
2
0
2
1
0
0
1
7
0
2
1
1
0
0
1
0
1
0
1
0
1
2
0
0
2
1
1
0
0
0
1
1
1
0
1
0
0
1
1
2
1
2
0
1
0
1
0
2
1
1
1
0
1
0
0
1
0
1
1
0
2
2
1
1
2
1
0
0
2
1
2
0
0
0
2
0
1
0
0
1
1
0
0
0
0
1
0
3
1
2
1
2
0
1
0
1
1
0
1
2
0
1
1
1
1
1
2
0
0
0
2
1
0
2
2
1
2
0
0
0
2
0
0
1
0
1
0
1
0
1
1
1
1
1
1
1
1
2
2
2
1
1
0
1
1
1
1
0
1
0
0
2
0
0
1
0
1
0
1
1
1
1
2
2
2
1
2
0
2
1
1
0
2
0
1
0
0
0
1
2
1
0
0
0
2
1
1
1
1
0
2
2
1
1
1
1
1
0
0
0
2
1
1
2
0
2
0
1
0
0
0
0
2
0
2
1
0
1
1
1
1
2
1
0
0
0
1
0
0
1
1
0
0
0
1
0
1
1
0
1
1
0
0
1
2
1
1
2
1
1
0
1
0
0
0
2
1
1
2
0
1
3
0
0
1
0
0
0
0
1
1
2
2
0
0
0
1
0
1
0
2
0
1
1
2
0
2
1
0
1
1
1
1
0
1
0
2
0
0
1
0
0
1
0
2
1
0
1
0
2
2
1
1
0
1
0
1
1
1
1
0
2
0
1
1
2
2
1
0
0
0
1
2
0
1
1
1
2
1
1
0
1
0
1
2
1
1
2
1
1
0
2
1
1
1
2
1
1
2
2
1
0
1
1
0
0
2
1
1
1
1
0
1
1
0
0
0
0
2
1
2
0
0
1
0
1
0
1
0
2
3
1
1
1
1
1
1
0
1
2
0
0
2
1
1
0
1
0
2
0
0
2
2
0
1
4
1
0
1
1
0
1
1
2
0
0
2
1
1
1
2
1
0
1
0
0
0
0
1
2
0
1
0
1
2
1
1
0
1
0
0
1
0
0
0
0
2
0
2
0
2
0
0
1
1
2
0
2
2
2
0
0
0
1
0
1
2
0
0
1
2
0
2
1
1
1
1
2
0
1
0
1
0
0
1
0
0
4
1
1
1
1
0
0
0
2
0
0
2
0
0
0
2
1
0
0
1
2
2
2
0
2
0
2
0
0
0
0
1
1
2
2
4
0
0
0
1
0
0
0
0
1
1
1
2
0
0
0
0
0
0
1
1
1
1
1
2
1
0
2
2
0
1
1
1
0
0
2
1
0
3
1
1
1
0
1
1
1
1
2
0
2
0
2
1
1
0
2
1
0
1
1
1
1
2
1
0
0
1
0
1
1
0
0
1
1
1
1
1
1
1
1
0
1
1
1
1
0
1
0
0
0
1
0
1
0
1
2
0
1
2
2
2
2
1
0
2
1
1
0
1
1
0
0
2
1
1
2
1
0
1
0
2
0
0
0
1
1
2
0
1
1
1
0
1
0
1
2
2
2
0
1
0
2
3
0
2
0
1
1
1
1
1
0
3
0
0
0
0
1
1
2
0
1
1
1
1
0
0
2
1
1
1
1
1
0
0
1
0
0
1
1
2
2
1
1
0
1
0
1
0
2
0
0
2
1
2
1
1
1
1
2
1
2
0
0
1
0
1
0
2
1
1
2
1
1
0
1
2
0
0
0
4
1
1
1
1
1
2
0
1
1
0
1
1
1
2
0
0
0
1
1
1
1
1
2
0
1
0
1
1
2
1
1
0
2
0
0
2
2
1
0
1
1
1
2
1
1
1
1
1
1
0
1
0
2
2
1
1
0
1
1
2
1
2
0
1
1
2
0
0
1
0
2
1
3
0
1
2
0
0
2
1
0
0
1
0
2
0
1
1
2
2
0
3
0
0
1
1
0
1
1
2
0
0
1
1
1
1
0
2
0
1
2
1
0
0
2
0
0
1
1
2
1
1
0
2
2
0
0
0
1
1
0
1
2
0
1
2
1
0
0
2
1
2
0
1
1
2
2
1
1
2
2
1
0
0
2
2
0
1
1
1
0
1
1
1
2
2
0
1
3
1
1
1
1
1
2
0
0
0
1
1
0
2
3
1
1
2
0
1
0
0
1
0
2
2
0
2
1
0
1
1
1
0
1
2
0
2
1
1
0
1
2
1
2
0
0
1
1
1
1
0
0
1
0
2
2
2
1
1
0
0
2
1
1
1
1
5
1
2
2
2
2
1
1
1
0
1
1
0
1
2
1
0
1
0
0
1
0
0
0
0
0
1
3
0
1
1
0
0
0
2
0
1
1
0
0
1
2
1
0
1
0
1
0
0
2
1
2
1
1
1
0
1
1
1
0
0
0
1
2
0
1
1
0
0
0
0
1
2
2
2
0
1
0
1
1
0
1
1
1
1
2
0
1
0
1
0
0
1
0
2
0
1
0
0
1
2
1
6
0
0
1
0
1
1
0
1
0
1
1
1
0
1
1
1
4
1
2
0
1
0
1
1
1
1
2
0
1
1
1
1
1
0
1
1
1
1
0
0
0
0
1
2
1
2
0
2
2
0
2
1
2
2
0
1
1
0
0
1
0
1
1
1
2
0
0
2
0
0
1
1
2
0
1
0
2
1
0
1
1
1
0
2
1
1
1
1
0
1
1
1
1
2
0
1
1
1
2
1
1
1
3
0
1
1
2
0
1
2
0
0
1
1
0
1
2
0
1
0
1
0
0
1
0
0
1
1
2
0
1
2
1
1
1
0
2
1
0
0
2
0
2
1
1
1
0
0
0
2
1
0
0
2
0
0
2
2
2
0
0
0
1
2
1
0
1
0
1
1
2
0
0
0
0
1
1
1
1
1
1
0
1
0
0
1
1
2
0
1
1
1
1
2
2
0
2
1
0
2
1
0
2
2
1
1
1
1
1
0
0
1
0
1
1
1
1
1
2
2
0
0
1
2
2
2
0
1
0
1
1
0
2
0
0
1
1
1
1
2
1
2
2
0
1
0
1
0
2
1
1
0
1
0
1
2
0
0
2
0
2
1
2
0
1
1
1
2
1
0
1
1
0
0
1
1
1
1
2
2
1
1
2
0
2
1
0
2
2
1
2
0
0
2
2
2
1
0
2
1
1
0
0
2
0
0
1
1
1
0
1
0
2
0
0
0
0
0
0
1
1
0
0
0
1
1
2
1
1
1
0
1
1
0
1
0
0
2
0
2
0
0
1
1
2
1
1
0
1
1
0
1
1
1
1
0
0
3
0
0
1
1
1
1
0
2
1
0
1
0
0
0
1
2
1
1
0
1
0
0
1
0
2
1
0
0
1
1
0
1
1
1
1
0
2
1
2
0
0
3
0
0
1
0
2
1
0
0
2
2
1
1
0
4
1
1
1
0
0
1
2
2
1
0
0
1
1
1
0
1
1
0
1
2
0
0
0
1
0
0
0
0
0
1
0
2
1
1
2
0
0
0
0
0
0
1
1
1
1
0
1
1
2
0
2
1
2
0
1
2
0
0
0
2
3
0
1
1
1
1
0
0
2
1
1
1
1
1
2
1
0
0
1
2
0
1
1
0
0
2
0
1
2
3
1
2
1
2
1
2
2
0
0
1
0
0
0
1
1
0
1
2
2
0
0
0
1
1
1
1
0
0
3
2
1
0
0
1
1
2
6
0
1
0
0
1
1
1
0
1
0
2
2
0
0
1
1
1
1
1
2
2
1
1
1
0
0
2
1
1
0
1
1
0
0
0
0
0
2
2
2
1
2
1
0
1
1
1
1
0
0
2
1
0
1
0
1
2
1
0
1
1
1
2
1
0
2
2
0
2
1
1
1
2
1
1
2
2
0
0
0
2
1
0
0
2
2
2
2
0
1
1
0
1
2
1
2
1
1
1
1
0
1
1
2
0
0
1
2
2
2
3
2
1
0
1
1
1
1
2
0
0
2
0
0
1
1
2
1
0
1
1
0
0
1
1
1
0
1
1
1
1
0
0
2
0
1
0
2
0
2
0
1
2
0
0
0
1
0
0
2
0
0
2
0
1
1
1
0
1
1
2
0
1
1
2
1
0
1
2
1
3
0
1
1
0
0
1
0
1
0
0
2
0
1
0
2
1
1
2
2
3
1
2
0
1
2
1
1
0
2
0
0
0
0
1
0
2
0
1
2
0
1
1
2
2
0
0
2
0
0
0
2
1
2
1
0
0
1
1
0
1
0
0
1
0
0
2
0
2
1
1
1
1
0
2
1
0
1
0
1
2
0
2
2
1
0
1
0
0
2
0
1
1
1
0
1
0
1
1
1
2
1
0
2
1
1
1
2
1
1
2
2
1
1
0
0
1
0
0
1
2
1
1
1
2
1
4
1
2
2
0
1
1
2
0
2
0
0
2
1
0
1
2
0
1
1
1
1
2
1
1
1
1
1
0
1
0
0
2
1
0
2
1
3
1
1
2
2
1
1
2
2
2
1
2
1
0
1
1
1
2
2
1
1
0
0
1
1
1
1
1
1
1
1
1
0
0
0
2
2
0
1
1
2
1
1
1
3
1
0
1
2
2
0
2
1
2
2
1
0
1
0
1
1
2
0
1
1
2
0
0
2
1
1
1
1
1
0
1
0
0
1
2
1
2
2
1
1
0
1
1
1
0
0
3
1
1
1
0
0
1
2
1
0
0
1
0
0
2
3
2
0
1
2
3
0
0
0
1
0
1
1
1
1
0
2
0
1
1
1
1
1
0
0
2
1
1
0
2
2
2
1
0
0
0
1
1
0
1
1
1
0
2
2
1
0
1
2
0
1
1
1
1
2
0
1
2
0
0
0
1
0
0
0
2
2
0
0
1
0
0
1
1
1
1
1
1
1
1
1
2
1
0
1
2
0
0
0
1
0
1
1
0
1
0
1
0
2
1
1
1
0
2
0
1
1
0
1
1
0
0
1
2
0
1
1
0
1
1
0
0
1
2
1
1
0
2
0
2
1
1
1
0
0
0
0
0
2
2
1
1
0
0
1
1
0
0
1
0
1
1
0
1
0
0
1
2
0
1
1
0
0
0
0
1
1
2
1
0
2
1
1
2
2
2
1
1
0
0
0
1
1
0
0
0
0
0
0
1
2
5
2
0
1
1
1
0
3
1
1
0
1
0
1
1
1
2
0
2
0
0
0
1
2
1
2
1
0
1
0
1
2
2
2
1
1
0
0
1
1
2
0
2
0
0
2
2
1
2
1
1
2
0
1
0
1
0
2
1
2
2
0
1
0
3
1
0
1
3
1
1
1
1
1
2
1
1
1
0
0
1
2
0
2
1
1
0
3
2
0
0
0
0
0
1
1
1
0
1
2
1
2
0
1
2
1
0
1
1
2
0
0
0
1
1
1
1
1
1
0
1
1
1
0
0
1
1
0
1
1
1
2
1
0
1
2
0
0
0
1
0
0
2
2
1
0
3
0
1
1
2
1
0
2
0
1
0
2
1
0
2
1
1
1
0
1
0
0
1
1
2
0
1
2
0
1
0
1
1
0
2
1
1
0
0
1
1
1
1
1
1
2
1
2
2
2
1
0
1
1
0
0
2
1
1
0
2
2
0
1
2
1
1
2
2
2
0
1
0
2
0
0
3
1
1
2
0
0
1
2
0
2
1
0
0
4
0
1
1
1
0
1
1
2
1
0
1
2
1
2
1
0
0
3
1
0
2
0
1
0
0
1
0
1
1
2
0
2
4
1
1
1
2
2
1
0
1
1
0
1
1
0
1
1
2
1
1
0
0
0
1
0
1
4
0
2
0
0
1
1
0
2
0
0
1
1
2
0
1
1
2
2
1
0
2
0
0
1
0
0
1
0
2
0
1
2
0
1
0
1
2
1
0
0
0
1
2
2
1
0
0
1
2
1
0
0
2
2
1
2
0
1
0
0
1
1
0
2
2
1
2
2
3
2
0
0
1
0
0
0
2
0
1
0
0
0
1
0
0
1
2
1
0
0
0
2
0
1
2
0
0
0
1
1
1
1
2
1
0
0
1
1
0
0
1
1
1
0
0
1
2
0
1
0
1
2
0
0
2
1
1
1
0
1
0
0
0
2
1
0
0
1
0
0
1
1
1
1
1
0
2
2
0
1
2
1
1
0
1
1
1
0
1
0
0
2
2
0
1
1
1
1
0
0
1
0
0
0
1
0
0
0
0
0
3
0
0
1
1
0
0
0
0
1
1
1
1
1
0
0
2
1
0
2
1
1
0
0
1
0
0
1
3
0
0
0
1
1
1
0
1
1
1
0
0
2
1
3
1
0
0
2
1
2
1
1
1
0
1
1
1
1
0
0
0
1
0
1
1
0
1
0
2
1
0
1
0
1
1
0
3
4
2
1
0
1
1
4
0
1
1
1
2
1
0
2
1
1
1
0
0
0
1
0
0
1
1
1
1
1
0
2
2
1
0
1
1
0
2
0
0
1
2
1
2
1
2
0
1
0
1
1
0
1
1
0
0
0
1
0
0
1
1
2
2
0
1
0
2
2
0
1
1
1
1
0
2
1
1
1
1
0
0
2
2
0
1
2
0
2
0
1
1
2
1
0
0
0
2
0
2
1
0
0
0
1
1
0
0
1
0
1
1
1
0
1
0
2
0
2
1
2
2
1
1
2
1
1
0
2
0
2
1
3
0
0
0
1
1
1
2
0
1
2
2
0
0
0
0
2
1
0
2
0
1
0
0
2
1
2
1
0
1
0
1
2
1
2
0
1
0
1
1
1
1
1
1
1
0
1
0
2
1
2
1
0
0
0
0
2
2
1
2
1
1
0
2
1
2
0
1
0
1
1
2
0
1
0
2
2
2
1
1
1
1
0
1
1
1
0
0
2
1
1
1
0
0
0
1
1
0
0
2
1
1
0
0
1
0
0
0
0
1
1
0
1
1
2
1
2
0
1
0
0
1
2
2
1
1
1
1
1
1
0
1
1
1
2
2
0
2
0
1
1
0
1
2
0
1
2
1
0
0
2
1
1
0
1
1
0
1
0
5
0
0
2
1
1
1
0
0
1
0
0
1
0
1
0
2
2
0
1
0
1
1
0
0
2
1
1
0
2
1
0
0
0
2
0
1
1
0
1
0
2
0
1
1
0
1
2
2
1
0
1
1
1
1
2
0
0
0
1
1
1
1
2
0
0
1
2
0
2
0
1
1
0
0
2
2
1
1
1
0
2
2
1
1
0
0
1
2
0
1
2
0
2
0
2
1
1
1
1
3
0
1
2
1
1
2
2
1
0
2
0
0
1
0
1
2
0
1
2
0
0
2
0
1
0
1
1
1
1
0
1
1
2
1
2
0
0
2
1
2
1
0
0
2
2
1
0
1
1
1
1
0
0
1
0
0
0
1
0
2
1
1
0
0
0
0
0
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
0
2
1
2
1
1
2
0
0
2
0
1
2
0
1
2
0
1
2
1
2
2
2
1
1
0
0
2
0
1
3
0
1
2
1
0
2
1
0
1
1
1
2
0
0
0
0
0
2
0
0
0
2
1
1
1
0
2
2
1
0
0
1
2
1
1
1
0
2
1
1
1
0
0
2
1
2
1
0
1
0
1
2
1
0
1
2
0
0
1
1
0
0
0
1
1
0
2
0
2
2
1
1
0
0
1
1
2
1
0
0
0
0
1
2
0
1
1
1
0
0
1
1
0
1
1
1
1
1
1
0
0
0
1
1
0
1
0
1
1
1
1
0
1
1
0
1
1
2
1
2
2
1
0
0
1
0
0
1
0
0
0
1
0
0
0
1
1
0
1
1
0
2
0
0
0
1
1
1
1
1
1
0
0
0
1
3
0
0
0
1
1
0
0
1
1
0
2
1
1
1
1
2
1
0
0
1
1
1
0
2
0
1
1
1
1
0
0
1
1
2
1
3
0
1
1
2
1
1
2
1
1
0
2
0
0
1
2
2
1
2
1
0
0
2
1
1
0
2
1
1
2
3
1
1
1
2
1
1
0
0
1
0
2
0
0
0
0
2
0
0
0
1
3
1
1
0
1
1
0
1
1
0
1
4
1
1
0
0
0
1
0
2
1
2
1
0
0
0
0
0
1
3
2
0
2
1
1
1
1
1
0
2
2
2
1
1
0
2
0
2
1
2
1
0
0
0
1
0
0
1
0
1
4
1
1
0
0
2
2
0
2
1
1
1
1
0
0
1
2
0
0
2
2
2
0
0
1
1
0
1
0
2
1
1
2
1
2
1
0
1
0
0
1
2
1
0
1
1
1
0
1
0
0
0
0
0
1
2
1
1
0
2
0
0
2
1
2
1
1
0
0
1
2
0
0
0
2
1
1
1
0
1
1
0
0
0
1
2
0
1
1
0
2
0
1
2
2
0
1
0
0
1
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
1
1
1
2
0
1
0
0
1
0
0
1
1
2
2
1
2
1
2
1
1
2
0
0
1
1
1
1
1
1
2
1
1
1
0
0
0
0
0
1
1
4
0
0
0
0
1
2
1
0
1
2
0
0
1
1
2
1
2
1
0
4
2
0
2
0
0
1
1
0
0
2
0
2
0
1
2
2
4
0
1
1
2
0
1
0
1
7
0
1
0
2
2
1
1
2
2
2
1
2
1
0
0
2
0
0
0
2
1
0
2
2
2
0
0
1
1
0
1
0
2
1
0
1
2
1
0
0
0
0
1
1
1
1
2
0
0
0
2
1
1
0
0
1
0
3
1
0
0
2
1
1
2
0
1
0
1
1
1
2
0
1
0
2
1
1
2
1
0
0
1
0
2
1
1
1
1
1
0
2
1
2
0
1
0
1
0
1
0
1
1
2
2
2
0
0
1
0
0
0
2
0
0
0
1
2
0
2
1
2
1
0
2
2
1
1
0
1
1
1
0
0
0
0
2
1
0
1
0
1
1
2
2
2
2
0
1
0
0
0
1
1
1
0
0
2
1
2
1
1
2
1
1
1
1
1
1
1
1
0
1
0
1
2
1
0
1
0
1
1
2
0
4
1
1
0
2
2
1
0
0
0
1
1
0
1
1
1
0
2
0
0
0
0
1
0
1
1
1
0
1
1
1
2
1
1
0
2
0
2
2
0
1
1
0
2
0
0
2
1
1
3
0
2
0
1
0
1
0
1
1
1
1
1
0
2
1
0
1
2
1
1
2
2
1
0
1
1
1
0
1
0
0
1
0
1
1
2
2
1
2
1
1
1
1
1
1
0
0
0
1
0
0
2
0
2
1
0
1
1
0
0
2
2
1
0
0
1
0
2
0
1
0
1
0
1
0
1
1
0
1
2
1
0
1
1
1
0
1
0
2
0
0
0
0
2
1
0
0
0
1
0
2
2
2
0
1
1
1
1
0
0
1
1
3
1
1
0
0
1
0
1
1
0
0
0
0
0
2
0
0
2
0
0
0
1
1
1
0
1
0
0
0
0
2
2
0
2
1
0
1
1
1
0
1
1
0
0
2
1
0
3
1
0
0
1
0
0
1
0
0
0
2
2
1
1
2
0
1
0
0
1
2
2
1
2
1
1
0
0
1
1
1
1
0
0
0
0
1
2
2
2
1
0
1
2
0
1
2
1
1
0
1
1
1
2
1
1
0
0
0
0
0
0
0
1
1
1
1
0
1
0
2
1
1
1
2
0
0
1
1
2
0
2
0
1
1
0
0
0
0
0
1
0
2
2
2
1
1
1
1
3
2
1
1
1
1
0
1
2
0
1
3
0
2
2
1
2
1
1
2
1
0
1
0
0
0
0
0
1
1
2
0
0
1
1
1
0
1
0
0
0
0
2
0
1
0
1
0
1
2
1
1
2
1
0
0
3
0
0
1
1
1
0
1
2
1
2
1
2
0
2
2
0
1
0
1
1
0
1
2
1
1
1
4
2
0
0
0
0
1
0
2
1
0
1
2
2
0
1
2
0
1
1
0
1
2
0
1
1
1
1
1
1
1
0
0
1
2
0
0
1
2
2
1
0
0
0
1
1
2
2
2
1
1
1
2
2
0
0
1
2
1
0
1
1
2
0
1
0
2
2
0
0
0
2
1
2
1
2
0
1
1
1
2
0
2
1
2
2
1
0
0
1
1
0
2
0
4
2
1
0
1
0
0
0
1
0
2
0
1
1
0
2
2
0
0
1
1
1
1
2
1
2
1
2
1
2
0
0
0
0
2
1
1
2
1
1
0
2
0
0
1
0
2
2
0
0
0
2
0
0
1
1
1
3
0
1
1
0
2
0
0
1
0
0
0
0
1
2
0
0
0
2
0
0
0
2
1
1
2
1
2
1
1
0
1
0
0
2
2
0
0
1
1
1
1
1
2
0
0
0
0
1
2
0
1
2
1
0
1
0
1
1
2
1
0
0
0
1
1
1
0
0
0
2
2
1
2
1
0
2
0
1
0
2
0
0
1
1
0
0
1
0
1
1
2
0
1
1
1
1
1
2
0
1
1
1
0
4
0
0
0
0
1
0
0
1
3
0
1
1
1
1
2
2
2
1
1
1
1
0
2
1
0
0
0
0
2
1
0
0
1
1
0
1
0
1
0
1
1
2
0
1
0
2
3
1
1
2
0
1
1
1
1
0
1
1
0
2
1
1
2
0
1
1
0
2
2
1
1
1
1
1
0
0
2
0
2
0
0
1
1
1
0
1
1
1
0
1
1
0
2
1
2
1
2
2
0
0
1
1
2
0
1
1
1
1
2
1
1
0
1
0
1
0
2
1
1
1
0
0
0
0
1
2
2
1
0
2
1
3
0
1
1
1
0
1
0
0
2
2
2
2
0
0
1
0
1
1
2
1
1
3
1
0
1
0
0
0
1
1
1
2
0
0
1
0
1
0
1
2
2
1
1
0
0
0
0
1
1
1
0
0
1
2
2
2
3
1
0
2
1
1
1
2
1
1
1
0
2
2
1
1
0
1
1
1
2
0
0
0
0
2
1
1
2
2
1
2
0
2
1
1
1
2
0
2
0
1
2
1
1
1
1
1
0
1
2
0
0
1
1
0
1
0
0
0
1
1
0
0
0
1
0
0
0
1
1
1
0
0
0
1
0
2
0
2
0
0
0
0
1
2
1
2
2
2
1
0
0
0
1
0
2
2
1
1
1
0
0
1
1
1
0
1
2
2
1
0
1
0
2
1
0
1
1
1
2
1
1
2
2
1
2
1
1
0
0
2
0
1
0
2
1
2
1
2
1
0
1
0
1
2
1
1
1
1
2
0
1
1
1
1
0
2
2
0
2
1
1
0
0
1
1
0
0
1
0
0
1
0
2
0
0
1
2
0
1
1
2
2
0
1
1
0
0
1
0
0
0
2
2
1
2
1
6
0
1
2
0
1
0
1
1
1
1
0
0
1
1
0
0
1
0
0
0
0
1
2
2
0
2
1
0
0
1
0
0
2
1
0
0
0
1
1
1
1
0
1
0
1
1
1
1
1
1
1
1
0
0
0
1
2
0
1
0
1
0
1
2
0
0
1
2
2
2
0
1
0
1
0
0
0
1
1
0
1
2
1
0
0
2
1
0
0
2
1
1
0
2
2
0
0
0
1
1
1
1
2
2
1
2
1
0
2
1
1
1
1
1
1
2
1
0
0
2
2
1
1
0
0
1
1
1
1
0
2
1
0
0
2
2
0
1
0
0
0
0
2
1
1
0
1
1
2
0
1
1
2
1
0
0
1
1
0
1
2
1
2
1
0
1
1
0
1
0
1
2
0
0
1
0
1
1
1
0
0
0
0
1
0
2
1
0
1
1
0
0
2
1
0
0
1
1
0
1
1
1
2
1
1
2
1
1
1
0
2
0
1
1
1
0
2
0
1
1
1
1
1
0
1
1
0
0
1
1
1
1
0
3
2
0
1
1
1
1
0
2
1
0
0
1
1
1
0
0
1
2
0
1
1
1
1
1
0
0
0
1
2
1
0
1
0
0
1
1
2
0
0
2
0
0
2
0
1
1
1
2
1
1
0
2
2
1
1
1
0
2
1
1
1
1
0
0
0
1
1
1
0
1
0
1
1
0
0
1
0
0
1
1
0
1
1
1
2
2
0
2
1
3
2
1
2
2
0
0
1
2
2
2
0
2
2
0
0
1
1
1
1
1
3
2
0
0
1
1
2
0
1
1
0
1
0
6
1
1
0
1
1
1
0
2
0
1
1
1
1
0
1
1
0
0
2
2
1
1
2
0
1
0
1
1
0
1
1
0
0
1
0
2
0
1
1
1
2
1
0
1
2
2
2
0
2
1
0
0
1
1
2
1
3
0
1
2
1
2
2
2
2
2
2
1
0
0
1
0
2
0
0
1
1
0
0
1
1
1
1
0
2
1
1
1
1
1
1
1
0
1
1
2
0
0
0
1
0
0
0
2
1
2
1
2
0
2
0
2
0
0
1
1
2
0
2
0
0
2
2
1
0
2
3
1
1
0
0
0
1
0
1
1
0
2
1
1
0
2
1
0
2
0
1
1
1
2
2
2
0
0
2
2
0
1
0
0
1
2
1
0
1
1
2
2
2
1
1
0
0
0
2
1
0
0
1
1
0
3
0
2
1
2
2
1
0
0
2
1
2
0
1
0
0
2
2
0
1
2
1
0
2
0
1
0
1
0
1
1
1
0
1
0
0
0
0
3
1
2
0
2
1
2
1
1
1
1
0
1
2
0
0
0
0
1
1
0
1
2
2
0
0
1
1
1
2
1
1
1
1
1
1
1
0
0
1
1
0
0
0
1
0
2
1
1
2
0
1
1
0
0
0
1
1
1
2
2
1
0
0
1
1
1
1
0
0
1
2
1
1
0
1
0
0
1
0
1
0
0
1
2
2
2
1
1
1
2
1
0
1
2
0
1
2
1
1
1
2
1
1
1
0
0
2
0
2
2
0
1
0
1
1
1
1
1
1
1
0
2
1
1
2
1
1
0
0
2
2
0
0
1
1
1
1
1
2
0
0
0
1
1
1
1
0
1
1
1
1
0
0
1
1
1
0
1
1
1
0
2
2
1
1
2
2
0
1
4
0
1
2
0
1
0
0
2
1
2
0
0
2
0
3
1
0
0
1
1
2
0
2
1
0
2
1
2
1
0
0
1
2
2
0
1
1
2
0
0
0
2
1
0
1
0
0
0
1
0
1
0
2
1
1
0
0
0
1
0
1
2
2
1
0
2
1
0
1
1
0
0
0
0
2
0
1
1
0
0
0
2
2
1
0
1
0
1
1
1
2
0
1
0
0
0
1
2
1
0
0
0
1
1
0
1
2
1
1
0
1
1
1
0
1
1
1
5
0
0
1
0
0
1
0
0
0
0
0
0
0
2
1
1
1
0
0
2
0
2
0
0
0
2
1
2
0
1
0
0
2
1
1
1
1
0
2
0
1
2
1
1
0
0
0
1
0
4
1
0
1
2
1
1
1
1
1
0
0
1
2
1
1
1
1
1
1
1
0
0
1
1
1
0
2
0
0
0
1
2
2
1
2
2
1
2
0
1
2
1
0
1
1
1
2
2
0
0
2
1
2
0
0
1
1
2
1
1
3
0
1
0
1
1
1
1
0
1
0
1
1
3
0
1
1
1
1
0
1
2
1
2
1
2
2
1
1
1
2
0
0
1
2
0
0
1
1
2
1
1
0
2
1
0
0
2
2
0
1
1
0
1
1
2
1
0
1
1
1
2
0
0
1
0
2
1
1
1
1
0
1
0
2
0
0
1
1
0
0
1
0
1
1
0
1
1
0
1
2
1
0
0
1
0
2
2
1
2
0
0
0
2
1
1
0
0
1
2
2
1
0
1
1
1
0
1
0
0
1
2
1
1
0
0
1
0
2
1
1
1
0
2
2
1
2
1
1
2
1
1
2
1
2
2
1
0
0
1
0
1
1
1
2
1
1
0
2
2
2
0
0
2
0
0
1
1
1
0
1
0
0
0
0
0
2
1
2
1
0
0
1
1
2
1
1
0
1
0
0
1
1
1
0
0
1
0
1
1
1
0
0
1
3
2
2
0
0
1
1
1
1
2
1
2
1
0
0
1
1
1
2
0
0
0
3
1
1
2
1
1
0
0
1
1
1
2
1
1
1
1
0
0
1
0
1
0
1
2
1
2
0
1
1
0
1
0
0
0
0
0
0
1
1
1
1
1
0
2
1
0
1
0
1
1
2
1
0
0
0
1
0
5
1
1
1
1
1
2
0
0
1
0
2
0
1
1
0
1
0
1
0
1
0
2
1
0
1
0
1
2
0
2
0
0
1
2
2
1
0
1
1
0
1
0
0
0
1
0
2
2
1
1
0
1
0
0
1
1
0
1
1
1
2
1
1
0
0
1
1
0
0
2
2
2
1
1
0
2
2
1
2
1
0
2
2
1
0
1
0
2
2
0
2
0
0
1
1
1
0
0
2
0
0
1
2
1
1
2
0
1
2
0
1
1
1
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
1
2
0
1
2
2
1
1
2
2
1
1
1
0
2
1
2
1
1
0
0
1
2
1
0
1
2
0
2
1
2
0
1
2
0
0
2
2
2
2
0
1
1
0
0
1
1
2
0
2
0
2
0
1
1
0
1
1
1
0
2
2
1
2
2
0
0
2
0
1
1
2
2
0
0
1
2
1
1
0
1
1
1
1
2
0
0
1
1
1
2
0
1
0
1
1
1
0
2
3
2
0
1
0
1
2
2
0
1
0
2
0
1
1
0
1
0
1
1
2
3
1
1
0
2
0
2
1
0
2
0
2
0
0
0
1
2
2
1
1
0
0
0
0
0
1
1
2
2
1
2
1
2
1
1
0
3
1
2
1
0
0
1
0
1
0
0
1
1
0
0
2
1
2
1
1
1
1
0
0
0
0
1
2
0
1
0
2
1
0
1
1
0
1
0
2
1
1
0
2
0
1
0
1
0
1
2
0
1
2
2
2
0
0
0
2
1
2
2
1
1
2
0
0
1
1
2
1
0
2
1
0
2
0
1
0
0
2
0
0
1
2
1
2
0
1
1
1
2
1
1
2
0
0
3
2
0
0
0
2
0
2
0
0
0
1
1
1
0
1
2
1
2
0
2
2
2
0
1
0
0
1
0
2
1
1
1
1
0
1
2
0
1
0
1
4
3
0
1
0
1
1
2
0
1
1
0
0
0
1
0
0
0
0
2
0
0
3
0
2
0
2
1
0
0
0
1
1
2
2
0
1
0
2
1
1
1
1
1
2
1
1
1
2
1
1
0
2
0
0
1
0
1
1
0
0
2
0
0
1
2
0
2
1
2
0
0
0
0
3
0
2
2
0
1
0
1
0
1
0
2
0
1
1
0
1
1
1
1
2
1
1
0
1
7
2
0
0
1
1
2
2
1
0
1
1
1
1
2
2
1
2
1
0
0
0
1
1
1
1
1
1
1
0
0
2
0
2
1
0
2
0
2
1
1
2
1
1
1
1
1
1
1
0
1
0
1
0
1
3
0
2
1
0
1
1
1
0
0
0
2
2
1
2
1
0
1
1
0
1
1
1
1
0
0
1
0
1
1
1
1
0
2
0
1
1
0
5
1
2
2
0
2
1
0
0
0
0
1
1
2
3
1
0
2
2
2
1
1
6
0
0
1
0
1
1
0
1
0
0
1
1
1
1
0
2
0
2
2
0
1
2
0
0
3
0
0
1
0
0
1
1
0
2
0
1
1
1
0
1
2
0
0
1
0
1
0
1
1
1
1
2
0
2
2
2
0
0
1
0
0
1
1
1
0
1
0
1
0
1
1
1
0
2
1
2
1
0
2
0
2
0
1
2
2
1
0
2
0
0
1
1
2
0
2
1
1
1
1
0
2
0
1
1
0
0
2
1
0
0
2
1
1
0
1
0
1
1
1
0
2
1
1
0
1
0
0
2
1
1
1
2
1
0
2
1
0
1
0
1
1
1
2
0
2
1
0
0
1
2
1
0
1
2
1
1
0
1
1
1
1
1
0
0
1
1
1
0
1
1
0
1
0
1
2
2
2
1
1
1
0
1
1
0
3
1
1
1
2
1
1
1
2
2
2
2
2
2
1
1
1
1
1
1
1
0
1
4
2
0
2
2
0
0
1
0
1
0
1
0
0
0
0
2
1
1
1
1
1
2
0
0
0
1
1
2
1
2
0
0
2
1
1
1
0
1
1
0
2
1
1
1
0
0
0
2
1
0
1
1
0
1
2
1
2
1
0
0
2
0
1
1
2
1
1
0
1
0
0
1
1
1
0
0
1
1
0
1
2
1
1
2
2
1
2
0
2
1
2
2
0
1
0
1
1
1
0
0
1
1
0
0
0
1
2
1
1
1
1
0
0
1
3
0
0
2
0
1
1
0
1
1
1
0
1
1
1
0
1
0
1
0
2
1
0
2
0
2
3
0
1
1
0
0
0
3
1
0
1
1
1
1
2
2
1
0
0
1
0
1
0
2
1
0
2
0
0
1
1
2
0
2
1
2
0
1
0
0
0
2
1
1
0
2
1
1
1
0
2
2
0
0
0
2
2
0
1
1
1
1
1
1
2
2
0
1
1
1
2
1
0
1
1
1
1
1
2
1
1
2
2
2
0
2
0
1
2
0
0
1
1
2
1
1
0
0
1
0
2
0
0
0
1
1
1
3
1
0
3
1
0
1
0
0
0
0
1
2
2
0
1
3
1
2
1
1
0
0
0
2
1
0
0
2
2
2
1
2
0
0
1
1
2
0
0
0
2
2
2
0
0
1
0
1
0
1
0
2
2
0
1
1
1
0
1
2
1
1
0
1
2
1
1
2
0
1
0
0
0
0
1
1
2
2
3
0
1
0
1
0
1
1
2
2
0
1
0
2
0
2
0
1
0
1
1
2
1
0
2
1
0
2
1
1
0
1
0
2
2
1
2
1
1
2
0
1
2
0
1
1
0
0
0
0
0
1
2
1
3
1
0
1
1
2
1
1
0
1
3
2
2
1
2
1
1
0
2
4
0
2
1
0
1
0
1
0
0
1
1
1
2
0
1
1
1
0
2
0
0
0
0
0
0
2
0
0
1
2
1
0
1
0
2
1
2
1
1
0
0
2
1
2
1
0
1
1
2
2
0
1
0
1
2
0
1
0
0
0
4
1
0
1
2
0
0
0
1
1
0
1
1
0
1
2
2
1
2
2
2
2
2
1
1
0
2
0
2
2
1
1
2
2
2
1
1
1
2
2
0
1
0
0
2
1
1
1
1
0
1
0
1
0
0
1
0
0
2
2
1
1
1
1
0
1
1
2
2
2
0
0
0
1
1
1
2
1
0
0
1
1
1
0
1
1
0
1
1
1
1
1
0
2
0
0
0
0
0
1
1
1
2
1
2
3
2
0
1
0
0
2
4
1
0
0
0
2
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
1
2
1
1
0
2
2
2
2
0
0
0
1
0
2
1
2
0
0
1
1
0
1
1
1
1
1
2
0
0
2
2
1
1
1
0
1
1
1
2
1
0
2
1
1
1
1
0
2
1
0
1
2
2
1
2
1
1
3
1
2
1
0
1
1
2
2
3
0
3
0
1
2
2
2
0
0
1
1
1
0
0
1
0
1
0
0
1
0
0
0
0
1
1
0
2
1
1
1
1
0
2
0
1
1
1
1
0
2
1
2
1
1
2
1
0
2
3
2
0
1
1
1
0
1
0
0
1
3
2
0
2
0
0
1
1
1
2
1
0
1
1
0
0
0
0
1
2
2
2
1
0
0
0
1
0
1
3
2
2
1
1
0
0
0
0
1
2
1
1
0
0
0
1
0
0
1
2
1
0
1
0
3
1
1
1
1
1
3
1
1
1
1
1
1
1
1
1
1
0
0
1
0
1
1
2
1
2
0
2
1
2
0
1
1
2
0
1
2
0
1
1
1
2
1
0
1
0
2
1
0
2
2
1
2
2
1
0
1
0
0
0
1
0
2
1
1
2
1
1
1
2
2
0
1
0
1
1
2
2
1
2
1
0
2
0
3
2
0
1
0
1
1
1
2
0
1
0
0
1
1
0
1
0
3
1
0
0
1
1
2
1
2
1
0
0
1
1
2
1
0
1
1
1
2
0
1
2
0
2
0
1
2
0
2
1
2
1
2
2
0
2
0
2
0
1
0
3
0
1
2
1
0
0
1
1
1
0
2
0
2
0
1
1
3
2
3
2
2
1
1
1
2
0
1
1
1
1
1
0
0
0
1
2
2
0
1
1
0
4
0
0
2
1
0
2
1
1
0
1
0
1
1
0
1
0
2
1
2
2
1
1
1
2
1
1
0
1
1
1
1
1
1
2
2
1
2
1
1
0
2
0
1
2
2
1
0
6
0
2
0
3
2
0
1
1
1
1
1
1
0
1
5
2
1
1
0
0
0
0
2
3
1
0
1
1
2
1
1
1
2
0
0
1
1
0
1
0
0
0
0
1
0
1
0
2
0
2
1
1
0
2
1
1
0
0
1
0
1
2
0
0
2
1
0
0
1
1
2
0
0
0
1
0
2
0
2
0
1
0
0
1
3
0
0
0
0
2
1
0
1
1
1
2
1
1
2
0
1
1
0
0
0
1
0
1
0
0
2
1
2
1
0
0
0
0
0
0
1
1
1
0
0
2
0
1
0
1
1
0
0
0
0
1
0
1
3
2
1
2
1
0
1
2
1
1
0
3
1
1
1
2
1
1
2
2
1
0
1
0
1
1
1
0
0
1
2
1
1
0
1
0
0
1
0
2
0
1
1
0
2
0
0
2
1
0
0
1
1
1
1
0
0
0
0
2
0
1
2
0
0
1
1
0
0
0
1
0
0
0
1
0
1
1
1
1
1
2
2
2
1
1
0
1
2
3
1
1
0
2
0
0
0
1
0
2
1
1
2
1
0
0
0
2
0
0
1
1
1
0
1
1
2
2
0
2
1
2
1
1
2
2
3
0
2
2
1
0
1
0
1
1
1
0
1
1
1
2
2
1
1
0
1
2
0
2
1
0
2
0
1
0
1
1
1
1
2
0
0
2
1
2
1
1
2
1
0
0
0
0
1
1
1
0
2
1
0
0
2
1
1
0
0
2
2
0
0
0
0
2
1
1
0
0
1
1
3
1
0
0
0
0
0
0
0
2
0
2
1
0
0
1
2
1
1
0
0
2
1
1
2
0
1
0
2
2
1
1
1
2
1
0
1
1
1
0
1
0
0
0
1
1
0
1
2
2
0
1
1
1
1
1
2
1
1
0
0
1
1
0
0
0
1
0
0
2
1
0
0
1
0
1
1
0
0
2
1
3
0
1
1
1
1
0
2
1
2
1
1
2
2
2
0
1
0
0
0
1
0
1
1
1
1
0
1
1
0
0
1
0
1
0
0
1
0
1
2
0
1
2
1
0
2
0
1
1
1
2
1
0
0
2
1
1
1
2
2
0
2
1
1
0
1
3
1
3
0
0
2
0
2
2
1
2
2
0
2
0
2
1
2
2
1
0
1
1
1
0
2
1
1
1
0
1
0
1
0
0
1
0
2
1
2
1
0
0
0
0
0
0
1
1
0
1
0
0
1
0
1
1
0
2
1
1
2
2
0
1
0
0
1
1
1
0
2
1
0
1
0
1
0
0
0
2
1
0
1
1
0
0
1
1
0
0
1
1
0
0
1
3
2
1
1
1
1
1
0
0
0
0
1
1
1
0
0
2
1
2
2
2
2
1
0
0
1
0
1
2
0
0
0
1
1
1
1
0
0
1
1
2
1
1
0
0
0
2
0
1
1
2
0
2
0
1
1
1
3
1
2
0
2
2
1
1
1
0
1
2
0
0
1
0
1
1
0
0
0
0
0
0
1
0
2
1
1
0
1
0
2
0
2
2
0
1
2
2
1
1
1
0
0
0
1
1
3
1
2
1
1
0
1
0
0
2
1
0
1
2
1
0
2
1
0
2
0
1
1
0
2
0
0
2
2
0
1
1
2
1
0
2
2
2
1
1
0
2
2
0
0
2
1
1
0
1
1
2
1
0
2
1
1
1
0
0
2
0
0
0
1
0
1
1
1
0
0
0
2
1
2
1
0
0
2
0
0
1
2
0
0
2
1
0
1
2
0
0
0
1
1
1
0
1
0
1
0
0
2
1
1
2
1
1
0
1
1
0
1
0
0
1
1
4
1
1
1
0
1
1
0
1
0
0
1
0
2
1
0
0
0
0
0
0
1
0
1
2
1
1
0
2
1
2
2
1
1
1
2
0
2
1
2
0
2
0
0
0
1
1
0
0
1
1
1
0
0
0
1
1
1
1
1
0
1
1
0
1
0
0
1
1
1
1
2
2
1
1
0
0
1
0
1
1
1
1
2
1
1
1
0
3
1
2
1
0
0
1
2
0
1
1
0
0
2
1
0
1
2
3
1
2
0
1
2
1
2
0
0
1
0
3
1
2
2
1
1
1
2
2
1
1
0
2
0
1
0
2
1
0
1
0
0
2
0
2
1
1
0
1
2
1
3
1
1
1
1
1
2
2
0
2
2
1
0
1
0
0
1
2
3
0
0
0
0
1
1
1
2
0
2
0
1
1
1
2
1
0
0
1
0
0
2
0
1
1
0
1
2
1
1
2
2
2
1
1
2
1
1
0
1
2
1
0
0
0
1
0
0
2
0
1
1
1
1
1
1
1
0
1
1
0
0
2
2
0
1
2
0
1
0
1
0
1
1
1
2
0
0
1
0
1
1
1
0
1
1
0
0
1
2
1
1
0
2
2
3
0
0
1
2
2
1
0
1
2
2
0
0
2
0
2
1
1
2
2
1
1
0
0
2
1
1
0
0
0
0
0
0
1
0
0
0
2
3
1
2
1
1
1
2
1
0
1
2
2
0
1
2
1
0
1
2
1
1
1
1
1
1
1
1
0
2
0
0
2
0
2
2
2
1
0
1
1
0
2
2
0
1
1
0
2
0
1
1
0
0
0
0
1
1
2
1
0
0
1
0
0
0
1
2
1
1
0
1
1
1
1
0
2
1
1
0
2
0
1
0
1
0
2
0
2
3
1
1
1
0
1
1
2
1
0
0
2
1
0
0
0
1
0
1
0
1
0
1
0
1
0
1
2
1
0
0
2
1
1
2
1
2
1
1
1
1
1
1
2
1
1
0
0
2
0
0
1
0
0
0
5
1
1
2
0
0
0
2
2
0
0
2
2
1
0
0
0
0
0
2
0
0
0
2
0
2
0
2
0
2
1
1
2
1
0
0
2
3
3
0
2
2
2
1
0
1
2
0
0
1
1
0
1
1
2
0
1
0
1
0
1
1
0
1
1
0
2
0
2
1
0
2
2
1
1
1
1
4
2
2
0
1
0
0
0
1
0
0
0
1
1
0
1
1
1
1
1
0
1
0
0
0
0
2
0
0
2
1
1
2
1
0
0
1
2
1
0
1
1
1
1
1
2
1
1
1
0
1
0
0
1
0
0
0
1
1
1
0
1
1
0
2
1
1
0
2
2
1
1
2
1
0
1
2
2
1
0
1
0
1
1
1
0
2
1
0
3
0
2
0
0
0
1
1
0
1
2
0
2
0
1
1
0
1
0
1
2
1
0
2
2
1
0
1
0
0
1
1
0
1
0
1
1
1
2
1
1
1
1
1
2
0
1
0
1
2
1
0
1
1
1
0
0
0
1
0
1
1
0
1
0
1
2
0
1
0
2
0
0
1
0
3
0
1
2
0
1
0
0
2
2
1
2
0
2
1
1
2
1
0
1
2
2
1
2
1
1
1
0
2
1
0
0
1
1
0
1
0
0
2
1
2
1
0
2
1
2
0
2
1
0
1
2
2
0
4
2
2
1
1
2
0
1
1
1
1
1
1
1
2
1
1
1
1
0
1
1
2
1
0
1
2
0
2
0
1
1
1
1
0
1
1
1
1
2
1
2
2
2
0
0
1
0
1
0
1
2
0
2
1
0
0
0
1
1
1
2
2
1
1
1
0
1
1
0
2
1
2
0
2
2
0
0
2
0
0
2
0
1
1
2
0
5
0
2
2
1
0
1
0
2
0
2
1
0
0
0
1
0
0
2
3
1
1
0
2
0
1
0
1
0
1
0
0
0
0
0
1
0
1
2
1
0
2
0
0
1
0
0
2
2
2
1
2
1
0
2
2
2
0
2
1
1
1
0
1
1
1
3
2
2
2
1
2
2
0
1
1
2
0
2
0
1
0
2
1
1
0
0
2
0
1
0
1
0
0
2
1
1
0
0
0
2
1
0
0
2
1
1
0
1
2
0
2
0
0
0
0
1
1
0
1
2
1
1
2
1
0
1
0
1
0
1
2
0
2
2
2
1
2
1
1
2
2
0
0
1
0
0
0
0
1
1
1
0
0
1
0
1
0
0
1
0
0
1
1
0
1
0
0
1
0
0
2
0
2
0
1
1
1
2
1
2
0
1
1
1
0
2
1
2
2
1
1
1
1
1
1
2
1
2
1
1
1
0
0
1
2
0
2
1
2
1
2
1
1
1
0
0
1
1
0
2
0
0
0
1
1
2
2
0
1
1
1
1
1
1
0
2
1
0
2
3
0
0
0
2
1
1
1
1
0
1
0
0
1
1
1
1
0
1
0
2
1
1
1
1
0
0
3
0
0
1
1
1
1
0
0
1
0
2
1
2
2
1
1
2
0
0
1
1
0
1
2
1
2
2
2
1
0
1
0
0
1
0
1
1
0
1
1
0
0
0
0
1
1
2
0
1
1
0
1
0
2
1
0
1
1
1
0
1
0
0
2
4
0
2
1
1
0
1
0
1
2
0
1
0
1
0
2
1
1
1
0
1
1
0
0
2
2
1
0
1
0
0
0
1
0
0
0
1
0
1
1
2
1
0
2
2
2
1
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
2
1
0
2
1
1
0
1
2
1
1
0
1
1
0
1
0
1
0
1
0
0
0
2
0
0
2
1
2
1
0
0
0
1
2
1
1
1
1
0
0
2
2
0
0
1
0
1
2
2
0
1
1
1
1
0
0
0
1
0
1
1
0
1
1
1
1
0
1
2
0
1
2
2
1
1
1
2
1
1
1
2
1
2
1
2
1
0
0
1
1
0
1
0
0
0
1
1
0
1
0
1
2
1
0
0
0
1
1
0
2
0
2
1
0
0
2
1
1
1
0
2
1
2
1
1
0
0
2
1
5
0
1
2
2
0
0
1
0
2
1
0
2
0
0
1
2
0
1
1
1
0
1
0
1
1
2
0
1
1
2
0
0
1
1
1
0
1
1
1
0
0
2
1
1
0
0
2
0
0
0
1
2
0
1
0
1
0
0
0
0
1
2
0
0
1
1
2
0
2
0
1
1
2
2
4
0
2
1
1
0
1
1
0
0
0
1
0
0
0
1
2
1
2
1
0
3
1
2
2
1
1
0
3
1
1
0
0
0
0
0
0
1
1
0
2
2
1
0
1
1
1
0
0
1
0
1
0
2
1
0
1
0
0
2
0
1
0
0
2
0
2
0
1
1
2
2
1
1
1
2
1
0
1
1
0
2
0
1
2
0
0
0
1
0
0
2
0
0
1
0
1
2
0
2
2
0
0
0
1
1
1
1
1
1
1
2
0
1
1
2
1
1
2
1
0
1
1
2
1
1
1
1
0
0
1
0
0
2
2
0
1
1
2
1
0
0
0
2
0
2
0
0
2
0
1
1
0
1
0
1
0
1
0
1
1
1
0
0
2
1
0
0
2
0
1
0
1
2
1
1
2
0
1
1
1
1
2
1
0
2
1
1
2
1
1
0
1
0
1
1
1
0
0
0
1
0
1
0
1
0
2
1
1
3
2
0
5
0
1
1
1
0
0
1
1
1
0
0
0
2
2
0
0
1
0
0
0
1
1
0
0
0
0
0
1
1
1
2
0
1
1
1
0
1
1
0
2
0
0
0
1
0
1
0
1
1
0
0
0
2
2
1
1
3
0
1
2
1
0
1
2
1
1
2
2
1
0
0
2
1
0
0
2
0
0
1
1
0
1
1
0
1
2
1
1
1
0
0
0
1
1
0
2
1
0
2
1
0
0
1
1
2
0
2
2
1
1
1
0
1
0
0
0
2
2
0
0
1
1
0
1
1
1
0
1
2
1
0
1
0
0
0
2
1
0
2
2
1
1
0
1
0
1
0
1
2
2
1
0
1
2
0
1
1
0
0
1
0
0
1
1
1
0
0
2
1
1
1
0
1
0
1
0
0
0
0
1
1
0
2
1
0
0
1
0
0
0
0
0
0
0
1
0
2
1
1
2
0
1
0
1
0
0
1
1
1
0
0
0
2
1
0
0
1
0
0
1
0
1
0
0
4
0
0
2
1
0
1
1
2
0
1
0
2
1
0
0
1
0
1
2
1
0
1
0
1
2
1
0
0
1
1
2
0
1
2
1
2
2
1
1
2
0
0
2
1
1
2
0
3
0
2
1
2
1
3
1
0
0
0
1
2
0
3
2
0
0
1
1
2
2
0
1
1
0
0
1
1
0
0
0
2
2
2
1
2
1
2
1
1
0
1
0
0
1
1
2
1
0
0
1
1
0
0
0
0
2
1
2
1
0
1
1
0
0
0
1
1
0
2
0
1
1
2
1
2
1
0
0
2
2
0
1
2
1
1
0
0
2
0
1
2
1
1
1
0
2
1
2
0
0
1
1
1
1
1
1
1
1
2
1
0
4
0
2
0
1
1
1
1
1
1
2
0
2
1
1
2
0
0
1
1
0
0
1
1
2
1
0
0
2
0
1
0
0
2
0
1
0
1
2
1
1
1
1
1
3
1
2
1
2
0
1
1
2
2
1
0
3
1
1
1
2
1
1
1
1
1
1
0
0
0
0
1
2
0
2
1
2
0
2
1
1
2
0
2
0
0
2
0
0
2
1
1
0
2
0
1
0
1
1
0
2
0
1
1
2
2
1
1
0
0
0
0
0
1
2
1
1
1
0
0
0
1
0
0
0
0
2
1
2
0
0
0
1
2
2
0
2
0
0
0
0
0
0
1
0
1
1
2
0
1
0
2
1
0
1
0
2
0
1
0
0
2
1
1
0
0
0
0
2
0
1
0
0
0
1
0
2
2
0
0
1
1
1
2
1
1
0
1
0
1
0
2
1
1
1
1
3
0
2
1
0
1
0
1
1
1
0
0
0
1
1
2
1
3
1
2
0
1
2
0
0
0
0
0
2
2
1
0
0
1
1
1
4
0
1
2
2
0
0
1
1
0
1
1
0
1
0
2
1
0
0
2
0
0
1
2
1
2
1
2
2
1
0
0
0
2
2
1
0
2
1
0
1
2
1
2
1
1
1
0
0
0
1
0
1
1
0
0
1
0
1
1
1
0
2
1
0
0
1
0
0
0
1
1
2
0
0
2
0
1
0
0
0
1
0
2
2
2
0
0
2
0
0
1
0
0
1
0
0
1
2
1
0
0
1
1
0
0
2
0
1
1
0
1
0
2
0
1
2
2
0
1
1
1
0
1
2
1
1
0
1
0
0
1
1
0
3
0
2
1
0
1
0
0
0
1
1
2
2
0
1
1
1
0
0
0
0
1
1
2
2
0
0
0
1
0
0
1
3
1
2
2
0
1
2
1
1
0
2
1
1
1
1
0
2
0
2
0
0
0
0
0
1
1
1
2
1
0
1
1
1
0
1
0
0
1
2
2
2
2
0
0
1
1
2
2
1
0
1
2
0
0
2
0
0
0
1
0
1
1
1
2
2
1
0
2
2
1
2
0
2
0
0
2
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
1
2
0
0
1
1
0
1
0
1
1
1
1
1
0
1
1
0
0
1
2
1
1
1
3
0
1
1
2
1
1
0
0
2
1
1
0
0
1
1
2
2
0
1
0
0
0
0
1
0
1
1
0
1
2
1
0
0
0
1
1
0
2
0
0
2
0
0
0
1
1
0
0
1
1
1
0
0
0
0
0
1
0
0
2
1
0
1
1
2
0
0
0
1
0
2
0
2
0
0
1
1
0
2
0
0
1
1
1
1
0
1
2
1
0
2
1
2
0
1
0
1
0
1
1
2
1
0
0
0
1
1
0
1
1
0
0
1
1
1
1
1
0
0
0
0
1
2
0
0
0
1
2
1
1
0
2
2
1
1
0
0
1
0
0
1
0
0
2
0
1
1
0
1
1
1
1
2
0
3
1
0
0
2
2
1
0
1
1
0
1
0
2
1
0
2
2
3
1
0
1
1
1
0
1
1
1
4
0
0
1
1
3
2
0
1
0
1
2
0
1
2
0
1
2
1
1
1
1
0
2
2
1
2
0
0
1
0
1
1
0
1
2
2
1
1
3
0
1
1
0
0
1
0
2
0
0
2
1
1
2
0
1
2
1
1
0
3
1
2
2
1
0
0
2
0
1
1
1
1
0
1
2
3
1
2
0
0
2
2
0
0
1
0
1
2
1
2
0
0
1
0
0
1
1
1
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
1
0
1
2
2
2
1
0
1
2
2
2
2
1
1
1
2
0
1
0
1
2
2
1
0
0
1
1
3
1
3
0
0
0
0
0
2
3
0
0
0
2
1
1
2
1
1
0
1
2
1
0
1
2
1
0
3
1
2
0
1
1
1
0
0
1
0
0
0
0
1
1
1
1
1
2
3
0
0
0
1
0
1
0
1
0
1
1
1
1
1
0
0
0
1
1
2
1
1
1
2
0
1
1
2
1
0
0
1
1
1
1
0
0
0
1
1
1
1
3
1
1
2
0
2
3
1
1
1
1
1
1
0
2
2
0
1
2
2
1
0
1
1
1
2
1
1
2
0
1
2
0
2
1
2
1
1
0
1
0
1
0
1
1
0
2
1
0
1
0
0
2
1
1
1
1
1
0
2
1
1
0
2
0
1
0
1
2
1
0
1
2
2
0
2
1
0
2
0
0
1
0
1
0
1
0
1
1
1
1
0
1
1
0
2
0
0
1
1
1
1
2
0
1
0
2
1
1
1
1
2
1
2
1
0
0
2
1
1
1
2
2
1
0
2
0
2
0
0
1
3
0
2
1
1
0
0
1
0
2
3
1
2
1
0
2
2
4
1
2
2
0
1
1
1
1
0
0
2
0
1
0
1
1
0
0
2
1
0
1
1
1
0
1
2
1
1
2
5
1
0
1
2
1
1
0
0
0
1
1
1
0
1
2
2
1
0
1
0
2
0
0
1
1
2
0
0
0
0
1
2
3
0
1
2
0
0
0
1
2
1
2
2
1
0
2
0
3
2
1
2
1
0
1
0
2
1
2
1
1
1
0
1
0
1
1
2
3
2
1
0
1
0
1
2
1
0
1
2
1
0
0
0
1
1
2
0
1
0
2
1
1
2
0
0
0
1
1
0
1
2
0
0
2
0
0
1
0
2
1
1
0
0
1
0
0
2
0
1
0
1
0
2
2
0
0
2
1
2
0
0
2
1
2
2
1
1
1
1
1
1
0
1
0
2
0
1
0
1
1
1
1
2
0
1
1
0
2
1
1
1
0
2
0
0
1
2
1
1
2
1
1
0
1
0
1
2
1
2
0
1
1
1
0
2
1
1
1
2
0
0
0
1
0
0
0
2
1
0
2
1
2
0
1
1
1
0
0
1
2
1
0
0
0
0
0
0
2
0
0
0
2
2
1
1
2
1
1
0
1
0
0
2
5
0
0
2
2
1
0
0
1
1
1
1
1
1
2
1
1
2
1
0
1
0
1
2
0
1
0
2
2
2
0
0
0
0
1
0
1
0
1
2
1
1
0
0
0
0
0
0
0
0
0
2
1
0
1
0
1
0
1
1
1
1
0
0
0
0
1
1
1
1
1
0
2
1
0
1
0
0
0
0
1
1
0
0
1
1
2
0
0
1
2
1
1
2
1
1
0
1
1
1
2
2
0
2
1
2
1
0
1
0
1
0
1
1
2
1
2
1
1
1
0
1
1
1
0
1
1
1
0
0
0
1
0
1
0
1
1
1
2
0
1
1
1
0
0
0
1
1
1
2
0
1
2
1
1
1
2
1
0
2
0
1
1
2
2
2
0
0
0
1
0
2
0
2
1
0
1
1
0
1
1
0
0
1
2
1
2
1
1
1
0
1
0
0
0
1
2
0
1
1
0
3
1
1
1
2
1
2
0
2
2
2
1
1
1
1
0
0
0
1
1
1
2
1
2
1
0
1
1
0
1
1
1
0
1
2
0
1
1
1
0
1
2
1
0
0
1
1
0
0
1
2
0
1
0
0
1
0
1
0
1
0
2
0
0
0
0
1
3
1
2
2
0
1
1
1
1
0
0
2
0
1
1
0
1
1
1
1
0
1
0
0
1
1
0
1
0
1
1
2
1
2
2
2
1
2
1
0
1
1
0
0
2
1
1
0
1
0
1
1
2
1
1
1
2
2
1
0
0
1
0
1
0
2
1
1
1
2
2
2
2
0
1
0
1
1
1
1
2
1
2
1
0
0
1
1
0
1
0
0
2
2
0
2
0
1
2
0
1
1
1
1
1
0
1
1
0
0
2
2
1
0
2
0
0
1
2
0
1
1
1
0
0
1
2
1
2
0
0
1
0
0
0
1
2
1
1
1
1
0
1
2
1
1
1
1
4
0
1
1
3
0
1
1
0
0
1
0
1
2
1
1
2
1
1
0
1
2
1
1
1
1
0
1
0
2
0
0
0
0
2
2
1
2
0
1
0
0
0
0
2
1
0
0
0
1
0
1
1
1
1
1
2
2
1
1
1
1
0
1
2
2
0
0
2
2
1
0
1
1
0
1
0
2
0
2
0
0
2
0
0
2
1
1
1
1
0
1
1
1
1
1
0
0
1
0
1
1
2
1
2
0
3
2
1
0
2
0
0
0
0
0
1
0
2
0
0
1
1
0
1
1
0
1
1
2
0
0
2
2
2
0
2
1
2
0
1
1
0
1
0
1
0
1
0
2
1
1
0
4
2
0
0
2
0
1
1
1
1
0
1
0
0
1
1
0
0
2
2
1
0
1
2
2
0
3
1
1
1
0
0
1
2
0
0
0
0
0
0
1
1
2
1
1
0
0
0
1
2
2
0
0
2
2
1
1
0
0
1
1
0
0
1
1
2
1
2
0
1
1
1
1
0
1
1
0
1
0
0
1
1
2
1
2
1
0
2
4
1
0
0
1
1
0
0
1
1
0
1
0
2
0
0
0
0
0
0
1
0
3
1
1
1
1
0
2
1
2
2
1
2
1
0
0
1
1
1
1
0
2
2
2
1
0
2
1
1
1
0
0
1
1
0
1
0
1
1
1
0
1
1
0
2
1
2
1
1
2
2
0
0
1
2
0
0
2
0
2
1
1
2
0
1
3
2
1
1
0
2
1
1
1
0
1
0
1
1
0
0
2
0
1
0
0
1
0
2
0
0
1
0
2
2
0
1
1
2
0
1
0
2
2
1
1
1
0
0
5
1
2
1
2
1
1
1
1
1
2
2
0
2
0
1
1
0
2
2
1
2
0
2
1
0
1
2
1
0
1
1
1
0
2
1
2
1
1
2
1
0
0
0
2
1
0
1
1
1
2
0
1
0
1
0
2
1
0
0
0
2
0
1
0
1
0
2
0
0
0
2
0
1
1
1
1
2
0
0
0
0
0
1
2
2
1
2
2
1
1
0
1
3
1
1
2
0
0
1
0
0
2
2
2
2
2
0
2
0
1
0
1
1
1
0
0
1
0
0
0
2
1
0
1
1
1
0
1
1
2
0
1
2
0
2
0
0
0
1
1
1
0
2
0
1
0
2
0
0
1
1
1
1
1
0
0
1
1
2
2
1
1
1
1
1
1
0
2
1
1
0
2
0
0
0
0
1
2
3
0
2
1
2
0
1
1
1
1
1
1
1
0
0
1
0
2
1
1
0
1
0
0
0
2
0
1
1
0
0
1
1
2
1
1
1
1
2
1
0
0
2
1
1
1
0
1
0
0
2
1
0
1
0
0
0
0
1
1
2
1
1
0
2
2
2
0
2
1
1
1
1
1
1
1
2
1
1
1
0
0
0
1
0
0
0
1
1
0
1
1
0
0
2
0
0
0
1
0
0
2
1
0
1
0
0
0
0
0
0
2
1
0
2
0
0
1
0
1
1
0
0
0
4
1
2
1
0
2
2
1
1
0
1
0
0
2
1
0
0
0
1
0
1
1
1
2
0
2
0
1
2
1
1
0
0
0
1
2
1
0
0
1
0
1
0
0
0
0
1
1
0
2
0
2
0
2
2
0
1
2
2
0
0
3
0
1
2
0
2
0
0
2
1
1
1
1
0
0
2
2
1
1
1
1
1
0
0
0
1
1
1
1
1
0
1
0
2
0
2
1
2
0
2
2
1
1
1
2
1
0
2
1
1
0
1
0
0
0
0
2
2
2
1
2
1
1
1
0
1
0
1
0
0
2
1
2
1
1
0
2
0
2
0
2
1
1
1
0
0
1
2
1
1
1
1
1
0
1
2
1
1
1
0
1
3
1
2
1
0
2
2
1
0
0
0
0
3
1
2
0
0
1
1
0
1
0
1
0
1
1
2
1
1
2
3
0
1
0
2
1
2
0
0
0
1
0
1
0
1
1
1
0
2
2
1
0
1
1
0
0
1
2
2
1
0
3
0
0
0
2
2
0
2
1
2
1
0
3
2
1
0
1
0
0
1
1
2
0
1
0
1
1
2
0
1
1
1
1
0
2
2
2
1
2
0
2
0
1
1
1
1
0
2
1
1
0
1
0
2
0
2
2
1
1
0
2
1
1
0
0
2
1
0
2
1
0
1
0
2
1
2
1
0
0
1
1
0
0
2
0
0
2
2
1
3
0
1
0
2
1
0
1
1
0
1
1
1
1
2
2
1
2
1
1
2
0
1
0
1
1
0
1
1
0
1
1
1
1
2
2
1
2
0
0
0
1
0
2
0
1
1
1
1
0
0
2
0
1
0
1
0
2
1
1
1
1
2
2
1
1
0
1
2
2
0
0
2
2
1
1
2
1
2
1
1
0
0
0
0
3
2
0
1
2
1
2
2
1
1
1
1
0
1
2
1
0
1
1
0
0
2
0
1
2
2
0
1
1
1
1
1
2
2
1
0
1
1
0
0
0
2
1
0
0
0
1
0
0
0
0
1
1
1
0
0
1
2
1
1
0
0
1
1
0
2
0
1
2
0
1
1
1
2
2
1
1
1
0
1
0
0
4
1
1
1
1
1
0
1
1
1
0
0
2
1
0
0
1
0
0
0
2
0
1
1
0
1
2
2
2
0
0
1
2
1
1
2
1
1
2
1
0
1
0
1
2
1
1
0
0
2
1
1
1
1
2
0
0
0
1
1
0
1
0
0
2
0
2
1
1
0
2
1
1
2
0
2
1
0
1
0
0
1
2
2
2
0
0
2
2
0
2
1
2
0
0
1
0
0
1
0
0
1
1
1
0
0
2
2
1
1
1
0
0
1
1
1
1
2
0
0
2
2
0
0
1
0
0
0
1
0
1
0
1
2
1
1
1
2
1
1
0
2
1
2
1
0
1
2
0
1
0
0
1
1
0
0
2
1
2
1
2
1
1
1
1
1
0
1
0
0
1
0
0
0
2
2
1
2
2
1
1
2
1
2
0
1
1
0
0
1
0
1
1
1
2
1
2
0
1
0
0
1
1
1
3
0
0
1
1
0
2
0
2
0
2
2
0
1
0
1
2
0
1
1
2
1
2
0
0
2
0
1
0
1
2
1
0
0
1
1
0
1
2
0
0
0
1
1
0
1
0
1
2
0
0
0
0
0
0
3
1
0
2
0
1
2
0
1
0
3
0
0
1
1
1
0
2
0
0
0
0
1
0
1
0
0
2
2
1
1
1
0
1
1
0
3
0
0
2
1
0
0
1
1
0
1
2
0
1
0
3
1
0
2
0
0
0
0
1
1
1
1
0
0
0
0
2
2
2
0
0
2
2
0
2
1
1
0
1
1
1
1
1
0
0
1
0
7
2
0
0
2
2
1
0
2
1
2
1
0
1
2
1
1
3
1
0
2
3
1
0
1
0
0
1
2
0
0
1
1
1
1
1
1
1
1
1
0
1
0
0
1
1
2
1
0
2
0
1
0
1
1
2
1
2
0
2
0
0
2
1
0
1
0
1
0
0
1
1
2
2
0
2
2
2
2
0
2
0
1
1
1
1
2
2
0
2
0
1
1
1
1
0
0
0
1
0
1
1
1
1
1
2
1
0
2
1
3
1
1
1
2
0
2
0
2
0
0
1
1
1
0
1
1
2
2
1
0
0
1
2
3
0
0
1
2
1
1
3
1
3
2
3
2
1
2
1
1
1
1
1
1
2
1
2
1
2
3
1
0
0
0
0
1
0
2
0
1
1
1
2
0
0
1
0
3
1
1
2
2
1
2
1
1
2
0
1
0
2
1
1
2
0
0
1
1
1
0
0
0
1
1
0
2
1
2
1
2
0
0
2
1
2
2
1
0
1
2
0
2
1
1
0
0
1
1
2
0
0
2
3
1
1
1
1
0
0
0
0
2
2
0
0
0
0
1
1
2
1
0
2
1
1
1
0
1
1
2
0
1
2
1
0
0
1
1
1
1
0
0
1
1
1
2
0
0
0
1
1
0
0
0
0
2
1
1
0
1
0
1
1
0
1
2
1
0
1
1
1
1
2
0
0
2
2
0
0
2
1
2
1
0
1
2
0
2
2
0
0
1
0
3
2
1
1
2
0
1
2
1
0
1
1
1
1
1
2
2
2
0
0
2
0
1
1
1
2
0
2
0
2
1
3
1
1
1
3
1
3
1
1
1
2
2
1
2
1
1
1
1
0
2
0
2
2
0
0
2
1
2
1
2
2
0
1
1
1
1
0
0
2
1
0
0
1
0
2
1
1
1
2
2
2
1
1
2
0
0
0
0
0
2
1
2
1
1
0
1
1
2
2
1
0
0
0
0
0
2
1
0
0
2
2
1
1
0
1
1
1
2
2
2
1
0
1
2
1
0
2
0
2
0
1
2
0
0
0
0
2
0
0
0
1
1
1
1
2
0
2
2
2
0
1
0
1
0
0
0
2
2
0
1
2
0
1
1
2
0
2
0
1
0
1
2
2
1
0
1
2
2
0
0
1
0
1
0
1
0
2
2
1
0
0
0
0
2
2
1
1
2
0
2
1
1
0
0
1
2
1
2
1
2
1
1
0
1
3
0
2
0
0
0
0
1
1
1
0
1
0
0
2
2
0
1
1
1
2
1
1
2
2
3
1
0
1
1
1
1
1
1
0
0
1
0
0
3
2
1
1
2
0
0
1
1
0
1
0
1
2
0
2
0
0
0
0
2
1
0
2
1
1
0
0
0
1
1
2
0
2
1
1
1
1
0
1
1
1
1
2
1
1
1
2
1
0
1
0
0
2
1
1
0
0
1
2
1
0
1
2
1
0
0
0
0
0
0
0
2
1
1
2
1
1
1
1
1
2
1
1
0
2
1
1
1
0
0
1
2
1
1
0
1
1
0
2
0
0
0
1
2
1
1
1
1
2
0
0
2
1
0
0
2
1
1
1
2
0
1
1
0
0
1
1
1
1
0
1
2
1
1
1
0
1
2
1
0
1
2
2
1
0
1
0
2
0
1
2
1
0
1
1
1
0
0
1
2
1
1
0
0
2
0
0
2
1
0
1
1
0
1
0
1
2
0
0
1
1
0
2
1
2
1
0
2
1
0
2
2
1
0
1
2
1
0
0
0
1
0
1
0
0
1
0
1
1
1
1
1
0
0
2
1
0
0
0
2
1
2
0
1
1
0
0
1
1
2
1
0
1
1
1
0
1
1
1
1
0
1
1
0
0
0
0
2
2
1
1
1
2
0
0
0
1
0
0
1
0
1
1
0
1
2
2
0
0
0
0
1
0
1
1
1
2
0
1
0
1
1
4
2
0
1
0
1
1
0
0
1
2
0
2
2
0
1
0
0
1
2
0
0
0
1
1
1
1
1
1
2
0
0
2
0
1
0
1
2
2
0
0
1
0
0
3
0
0
2
1
2
0
1
2
0
1
1
0
0
1
1
1
1
0
0
0
2
0
2
1
1
2
2
1
1
0
1
0
2
1
1
2
1
4
0
0
0
1
0
0
0
2
1
0
1
1
0
2
1
1
1
2
1
2
2
0
0
2
1
1
2
0
1
1
1
1
0
1
2
1
1
0
1
1
2
0
0
0
2
1
1
0
1
1
2
1
0
4
1
1
0
1
2
0
0
1
0
1
0
0
1
0
0
1
1
2
1
1
1
0
0
0
2
2
0
2
0
1
1
0
1
0
1
0
0
1
1
0
2
0
1
1
1
2
1
1
2
2
0
1
0
2
1
0
1
0
0
0
0
0
1
1
0
0
1
1
2
1
2
2
2
1
1
1
0
0
1
1
0
1
1
2
3
1
1
1
1
0
2
2
1
1
0
1
0
2
0
0
2
1
0
0
1
0
1
0
0
1
0
0
0
1
1
1
0
1
0
1
1
0
0
0
4
2
1
0
1
0
0
2
1
3
0
0
1
1
2
0
1
0
1
1
2
2
0
1
0
0
1
1
0
0
0
2
0
1
1
0
0
0
1
1
1
1
0
0
0
1
0
2
1
0
2
0
2
2
1
0
0
0
2
0
2
0
0
0
1
2
2
2
1
2
1
0
1
1
0
1
1
1
0
1
3
2
1
1
0
1
1
1
3
0
1
1
0
2
2
2
1
0
2
1
2
1
2
2
0
2
2
0
0
0
0
1
0
0
1
1
2
1
2
0
1
1
1
2
1
2
1
1
0
0
2
2
3
1
0
1
1
2
1
1
2
1
0
2
1
2
1
3
1
1
1
0
2
0
1
0
0
4
0
0
3
0
2
0
0
0
0
0
2
0
1
1
0
0
0
0
1
2
1
0
1
1
0
1
1
0
3
2
1
0
0
0
0
0
0
1
0
0
1
0
2
1
1
2
1
1
1
2
0
1
1
0
1
1
0
2
2
1
1
0
0
2
0
0
1
0
1
1
1
1
0
1
1
2
1
0
1
2
1
0
1
0
0
2
2
2
1
1
1
0
1
2
1
1
2
0
1
1
0
2
2
1
0
1
1
0
2
1
1
0
0
2
1
2
0
1
0
1
0
0
0
1
0
1
2
2
1
1
0
0
1
0
0
1
1
2
1
0
1
1
0
2
1
1
0
1
2
1
2
2
1
2
1
1
2
1
0
1
0
1
0
1
0
2
2
1
1
2
1
0
0
1
1
0
0
1
0
0
0
1
1
2
1
2
0
2
1
2
1
2
0
1
2
0
1
0
2
1
2
1
1
1
0
0
2
1
1
1
1
1
1
1
3
1
0
2
1
3
1
2
2
0
1
1
2
0
0
2
1
0
2
0
1
1
1
2
0
1
1
0
2
1
0
1
1
0
0
0
2
1
1
2
1
1
1
0
1
0
0
1
1
1
2
1
2
1
1
2
0
0
2
2
1
0
0
0
0
2
2
1
1
0
0
0
1
0
2
1
1
2
0
1
0
0
0
1
1
1
0
1
0
0
0
1
0
1
0
0
2
0
0
0
2
1
0
1
1
2
1
1
1
2
0
1
0
0
1
1
2
1
0
0
2
1
0
2
0
1
2
1
1
1
0
1
0
2
0
1
2
3
0
0
0
1
1
2
1
0
1
1
0
1
0
0
2
2
2
6
1
2
2
0
1
1
2
1
0
2
2
1
2
1
2
1
1
0
1
0
1
1
1
1
0
0
2
1
2
1
0
2
0
1
0
2
2
1
0
1
2
1
1
0
1
1
1
2
2
0
1
0
0
0
1
1
1
0
1
2
1
2
0
0
0
1
2
2
2
1
1
0
2
0
2
1
0
1
1
2
2
2
1
1
1
1
0
1
2
1
1
2
1
0
0
1
1
1
1
1
1
0
0
0
0
0
0
2
0
1
1
0
1
0
0
1
0
0
1
0
2
1
1
2
1
1
0
1
1
1
0
2
1
0
1
2
1
0
0
1
1
1
1
1
1
0
2
0
1
1
2
1
0
1
0
1
0
1
2
1
1
0
1
1
1
1
0
0
0
2
1
0
0
1
0
1
2
2
1
2
0
1
0
2
1
2
0
1
2
1
1
1
2
1
0
2
0
0
0
2
1
1
2
0
0
0
0
1
2
0
0
0
0
0
0
1
2
0
1
2
1
0
1
1
0
0
1
1
0
0
1
0
1
0
0
1
1
2
0
0
0
0
1
2
1
1
1
1
1
0
0
1
2
0
0
1
0
1
1
2
1
0
1
1
0
0
1
0
1
1
0
1
2
1
2
1
0
1
0
1
2
1
2
1
0
0
0
1
0
0
1
0
0
1
1
1
1
1
1
2
0
0
1
1
0
0
2
0
1
2
2
1
1
1
1
0
1
1
1
0
1
1
1
1
0
0
2
0
1
2
2
2
0
0
0
2
2
1
2
1
1
0
0
0
0
1
0
0
0
0
2
2
1
1
0
0
0
1
0
0
0
2
0
1
0
1
1
1
0
2
2
0
1
0
1
0
0
1
1
2
1
0
0
0
0
1
1
1
2
2
1
0
0
0
0
0
1
0
0
0
1
2
1
2
2
0
1
0
2
0
1
1
1
0
1
0
1
0
0
0
0
1
1
0
1
0
2
1
1
1
1
2
3
1
0
1
1
0
1
0
2
1
1
1
1
1
0
0
2
0
0
0
1
0
1
0
0
2
0
2
0
1
1
1
2
1
2
2
2
2
1
0
0
1
1
0
1
0
0
1
1
2
2
1
0
1
1
1
2
1
0
3
2
1
0
2
0
0
0
3
1
0
1
1
1
0
1
0
0
2
0
0
0
0
1
0
2
0
1
1
0
0
2
1
2
1
0
0
1
1
1
1
1
2
1
0
1
0
0
1
0
0
1
1
2
1
1
1
0
1
1
0
1
0
1
1
0
1
1
1
1
0
2
0
6
1
2
0
0
1
1
0
1
1
1
1
1
0
1
0
0
0
1
2
1
1
1
0
2
1
1
1
1
1
0
1
0
1
0
1
1
1
1
0
1
0
1
1
1
1
1
1
0
0
0
1
2
2
3
1
0
1
0
2
2
0
2
0
2
1
0
2
0
0
2
0
1
1
2
1
1
0
1
1
1
1
0
1
2
1
1
0
1
1
4
1
0
2
1
0
2
0
1
0
1
2
0
0
0
1
0
2
0
0
2
1
2
0
2
0
0
1
0
2
0
0
1
1
0
2
2
1
2
2
0
1
2
0
0
1
0
2
1
0
0
2
0
2
1
0
0
1
1
0
3
1
2
1
0
1
0
1
1
1
3
1
1
1
0
0
1
0
1
2
1
0
0
2
0
0
2
0
0
1
1
2
1
1
2
1
2
0
1
1
0
1
2
1
1
1
1
2
2
0
1
0
1
1
0
2
2
2
1
0
0
2
1
0
0
2
1
2
1
2
2
1
2
1
0
1
1
0
0
1
3
1
1
0
1
1
0
1
1
2
1
2
1
2
0
0
0
1
0
1
2
1
0
1
1
1
1
0
0
1
1
2
2
0
0
3
2
2
1
0
1
2
1
2
1
1
0
0
0
0
1
2
0
0
0
2
2
2
3
0
2
1
1
0
1
2
1
1
1
1
1
1
2
0
0
0
3
1
0
2
1
0
0
2
1
2
2
2
1
2
0
2
1
1
0
1
1
0
2
1
2
1
2
2
1
0
0
1
0
0
2
1
2
2
0
1
0
0
0
1
0
1
1
1
1
0
2
0
0
1
0
0
0
0
1
0
1
0
0
0
2
0
1
1
1
1
1
2
1
1
1
0
0
2
1
1
1
1
1
2
0
1
1
0
0
1
1
2
0
1
2
0
2
0
0
1
0
1
1
0
1
0
1
1
2
1
2
1
1
2
1
1
1
1
0
1
0
0
2
0
2
1
1
1
1
2
2
1
0
3
0
3
0
1
1
0
2
0
0
2
0
1
1
1
1
1
1
1
0
0
0
0
1
2
1
0
0
2
1
0
0
0
1
2
0
1
2
1
1
2
1
1
2
2
0
0
0
0
1
0
1
0
1
1
0
2
0
0
1
3
1
0
1
1
1
1
2
2
2
1
3
0
2
2
1
0
1
1
0
1
2
0
1
0
0
1
2
1
1
1
0
2
0
2
1
2
1
0
1
2
0
1
1
0
1
1
0
1
0
1
1
1
1
0
1
0
0
1
0
1
0
1
0
1
1
0
1
2
2
1
1
1
1
2
1
1
1
2
2
0
0
1
0
1
2
2
1
0
1
0
1
1
1
0
1
2
1
2
0
0
1
1
0
0
1
0
0
1
0
1
0
1
0
3
0
0
1
2
1
1
0
1
1
1
2
0
0
0
0
0
0
0
1
0
1
1
1
1
2
1
0
0
1
1
1
0
1
0
1
1
0
0
0
1
2
1
1
0
0
0
2
0
1
2
2
0
1
1
1
1
0
1
1
2
0
0
1
2
2
0
2
1
1
1
0
0
1
1
0
2
1
2
0
0
1
1
1
1
1
2
0
0
0
2
2
1
0
0
1
0
2
0
2
1
0
2
0
2
1
0
1
2
0
1
1
3
0
2
1
2
0
0
2
1
1
2
0
0
1
1
2
1
0
1
2
1
2
1
1
1
2
1
1
3
2
1
2
0
1
1
1
2
0
2
1
2
0
2
0
1
0
0
1
0
2
1
0
1
0
1
0
0
0
2
0
1
0
2
1
0
1
1
1
1
1
1
0
2
1
0
1
0
0
1
1
0
1
1
2
0
0
0
1
1
0
0
2
1
1
0
0
2
0
0
1
2
2
0
0
2
3
0
0
1
1
0
1
1
1
0
1
1
1
0
0
1
1
0
0
0
2
1
1
0
0
3
1
0
1
1
0
3
1
2
1
0
1
1
1
2
0
0
1
0
1
0
1
2
0
0
1
1
1
1
1
1
2
1
1
0
1
1
1
1
2
1
1
1
0
0
1
0
1
1
0
0
2
0
0
2
1
1
1
1
0
1
2
0
0
1
0
0
2
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
2
0
1
1
2
2
0
2
1
0
2
1
1
0
0
1
0
1
0
0
0
0
1
2
1
1
0
0
2
2
0
0
0
2
0
1
1
1
0
1
2
2
1
2
2
3
0
1
1
1
1
0
0
2
1
0
1
2
0
2
0
0
0
1
0
1
0
2
0
0
0
1
2
2
2
0
0
1
0
0
1
0
1
0
2
0
1
1
3
1
0
1
0
1
4
1
1
0
0
1
0
0
0
0
0
0
1
2
2
1
0
1
1
2
0
2
1
0
0
1
0
1
0
0
1
1
2
1
0
1
0
0
2
0
0
1
2
0
2
0
2
1
1
0
0
0
0
1
1
0
2
1
1
1
1
1
2
2
1
0
0
1
0
2
1
2
1
2
0
1
1
0
0
0
1
0
1
0
1
2
2
2
0
2
1
0
0
0
0
0
3
1
0
1
1
0
2
1
0
0
2
1
0
0
1
1
0
1
1
2
1
0
2
0
0
1
0
0
2
0
0
2
2
1
1
0
1
1
1
2
1
0
0
1
0
1
0
2
0
0
1
0
1
0
1
0
0
0
2
0
0
3
1
0
1
1
0
2
0
1
0
2
2
1
1
1
0
1
1
0
1
1
1
0
1
1
0
1
2
1
0
2
0
1
1
0
1
2
0
1
0
0
1
2
0
1
1
0
0
1
2
0
1
0
3
0
1
0
1
0
0
0
2
2
1
0
0
1
2
1
1
0
1
2
1
2
0
0
1
0
1
0
1
0
1
1
0
1
0
1
1
0
1
2
1
1
1
1
0
2
2
1
2
2
2
1
1
0
1
2
1
1
0
0
2
1
0
2
1
1
0
2
2
1
0
2
1
2
2
2
2
1
3
1
0
3
1
1
1
0
1
2
2
2
2
1
2
0
1
2
0
2
0
2
0
2
0
0
0
0
2
1
1
1
0
1
1
1
0
2
1
1
1
0
0
2
1
4
2
2
0
0
2
0
2
0
1
0
2
2
2
2
2
0
2
1
1
0
0
2
0
0
0
1
1
1
0
2
1
1
0
0
1
1
1
1
1
0
1
0
1
0
0
0
0
1
0
1
2
1
1
1
0
0
2
0
0
2
0
0
1
2
0
1
0
1
1
2
0
2
1
1
0
0
2
2
1
0
1
0
2
1
0
2
1
2
2
0
1
0
2
0
2
0
2
2
2
1
2
0
1
1
1
0
0
0
2
0
0
0
2
1
2
2
1
2
1
0
2
1
2
0
1
1
0
1
2
0
1
0
0
0
1
1
0
0
0
1
1
1
0
1
0
1
2
1
0
0
1
1
1
0
1
0
0
1
1
2
2
0
1
2
1
1
0
1
1
2
0
0
1
2
0
2
1
0
1
1
3
0
1
5
2
2
0
0
0
0
0
0
0
1
2
0
1
0
1
2
1
2
0
2
1
1
2
1
2
1
2
1
1
0
2
2
0
0
1
0
1
1
1
0
0
0
1
2
0
0
0
0
1
0
0
2
1
1
1
0
3
1
2
3
1
2
0
1
2
1
0
0
0
0
1
1
1
1
1
1
0
1
0
0
0
2
1
2
2
1
2
0
1
0
0
0
0
2
0
2
1
2
2
0
1
2
0
0
1
2
3
1
0
0
2
0
2
2
0
1
2
2
0
1
1
1
0
0
1
2
1
0
0
1
1
2
0
2
0
2
1
2
1
1
2
0
0
1
1
0
1
2
1
0
0
2
1
1
0
0
0
2
1
0
0
0
1
0
0
1
1
0
2
0
1
1
0
1
0
0
0
0
1
2
1
1
1
0
2
0
1
0
1
1
0
1
2
1
0
0
2
2
1
1
1
1
3
0
0
0
1
1
1
1
2
0
0
1
0
1
0
1
2
0
0
1
0
1
1
1
2
0
1
1
0
1
1
1
2
2
2
0
1
1
0
2
1
0
0
2
1
2
0
1
1
2
1
2
0
2
1
1
2
1
0
1
1
0
0
0
1
2
1
1
2
0
1
0
1
1
1
1
1
2
1
1
1
1
0
1
0
1
1
0
1
0
0
0
2
0
0
1
1
1
1
0
1
1
2
1
2
0
2
0
0
0
1
0
1
2
0
1
0
1
1
1
1
0
1
1
1
3
0
2
0
1
1
1
1
0
1
2
1
2
2
1
1
2
2
1
1
6
0
1
2
0
1
1
2
1
1
1
0
1
0
2
1
2
0
1
1
1
3
1
2
1
1
0
2
2
0
1
2
2
0
0
0
2
1
1
0
0
2
1
0
1
1
1
0
1
1
1
2
1
2
2
1
2
1
2
2
1
0
2
1
0
1
1
2
1
1
0
0
1
1
0
0
0
1
1
2
1
2
0
2
1
1
0
0
2
2
0
2
0
1
2
0
0
2
1
1
0
0
1
1
1
1
1
1
0
1
0
0
1
1
0
1
2
1
0
1
2
0
1
0
1
0
1
1
1
1
1
2
2
0
2
0
0
1
0
0
0
2
1
0
0
2
0
1
0
1
0
0
0
0
2
0
2
1
1
2
1
2
2
2
1
2
2
1
0
0
0
0
1
1
2
1
1
0
1
2
0
0
2
1
2
2
0
0
0
0
2
1
0
1
0
1
1
1
2
0
2
2
1
2
1
0
0
0
0
1
2
1
0
2
2
0
2
0
1
1
2
2
0
1
0
0
0
0
0
2
2
2
1
2
2
0
1
1
6
0
1
1
0
0
2
0
1
1
1
2
2
2
1
0
2
0
2
2
0
2
1
1
0
1
1
0
0
0
0
0
1
1
0
0
1
1
0
1
2
1
0
1
1
4
1
1
0
0
0
1
1
1
2
0
0
1
2
0
1
0
1
1
1
1
0
1
0
2
1
0
1
2
1
0
0
0
1
2
2
1
3
1
2
6
1
4
1
1
0
1
1
0
2
0
1
1
1
0
2
2
0
2
1
1
2
1
2
1
1
1
2
0
1
1
1
1
0
2
0
1
0
6
1
1
0
1
1
1
1
1
0
0
0
1
0
2
4
1
2
1
0
1
1
2
0
1
1
1
1
2
0
1
1
2
0
2
1
1
1
0
2
1
2
1
2
2
0
0
0
1
2
0
1
1
1
0
2
0
0
1
0
2
3
2
1
0
1
1
0
1
1
0
0
1
1
0
1
0
1
2
0
1
0
1
1
1
1
2
2
2
0
1
1
0
1
0
1
0
2
0
0
1
1
0
2
1
0
1
0
1
2
0
1
1
1
1
1
0
0
0
1
0
2
0
0
1
1
1
2
2
0
1
1
0
2
1
2
1
0
1
2
0
1
2
0
2
0
1
1
2
1
0
0
0
2
1
0
0
0
0
2
2
2
1
1
2
1
0
0
1
1
2
0
2
1
1
3
0
0
8
1
1
1
0
1
4
2
0
1
0
0
0
1
2
1
0
0
1
2
2
0
1
1
2
1
0
0
1
2
0
0
1
1
1
0
2
0
2
2
0
3
0
0
0
0
2
1
1
1
2
2
0
0
1
2
0
1
0
0
2
1
2
2
1
2
2
2
0
0
2
1
1
0
2
0
1
1
1
0
2
1
1
2
1
0
1
0
3
2
0
1
1
1
1
0
1
1
1
1
2
1
0
0
0
1
1
1
1
0
1
1
2
0
2
1
1
0
1
0
1
0
1
1
2
1
0
2
0
0
1
0
1
3
0
0
1
0
1
0
2
0
1
1
0
0
0
2
0
1
0
1
1
0
1
2
1
0
1
2
3
1
1
1
1
1
0
2
2
1
1
2
0
2
0
1
1
1
0
0
1
2
1
0
0
2
0
2
1
1
2
0
2
1
0
1
0
2
1
1
2
0
1
1
1
0
1
0
0
2
1
2
1
2
0
1
1
0
0
0
2
2
0
0
0
0
1
0
0
1
1
1
1
1
1
0
2
0
1
1
0
2
0
1
2
1
1
0
0
1
0
1
0
1
0
1
2
0
1
0
1
1
0
3
0
0
0
0
1
2
0
0
4
0
2
1
1
1
0
0
1
1
0
0
1
1
1
0
1
1
1
2
2
1
1
0
1
1
1
0
1
2
0
3
2
1
2
0
1
1
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
2
1
0
0
0
0
2
0
1
2
2
1
1
1
0
0
0
0
2
1
0
1
0
1
2
2
1
1
1
1
2
1
1
1
1
0
0
0
1
1
1
1
0
1
1
1
1
2
2
0
2
0
0
1
2
0
1
1
1
1
1
0
0
0
1
1
1
0
0
2
0
1
2
1
1
1
1
0
1
2
0
1
2
0
0
2
2
2
2
1
0
2
0
0
1
2
0
1
0
1
1
2
0
2
2
0
1
2
1
1
1
1
1
1
1
1
1
1
0
0
1
1
1
1
0
2
2
1
0
2
1
1
3
1
2
1
1
0
0
0
2
0
2
1
0
0
1
0
0
2
0
0
0
0
2
0
1
1
1
2
2
1
1
1
1
2
1
0
1
0
1
2
2
0
1
0
0
2
1
0
2
0
2
0
0
0
1
1
1
0
1
1
1
2
0
0
2
0
1
0
1
0
1
1
0
1
4
1
1
0
0
1
0
1
0
1
1
2
1
0
1
2
0
2
0
1
2
0
1
1
0
0
1
2
0
1
0
0
0
1
0
1
0
2
2
1
1
0
1
1
0
1
1
1
1
0
2
1
2
0
1
0
1
1
0
2
0
1
0
2
1
1
0
1
0
0
1
1
1
1
0
0
1
1
1
0
0
3
1
1
0
1
1
0
1
1
1
2
0
0
2
1
2
1
1
4
2
0
1
0
1
2
1
1
2
0
1
2
4
1
2
2
0
0
0
1
0
2
2
1
1
1
1
0
2
1
0
0
0
0
2
2
2
1
1
2
1
0
0
1
0
1
0
0
1
1
2
1
2
1
1
1
1
0
0
1
0
2
0
1
1
1
2
1
1
1
0
2
1
1
0
0
1
2
0
1
1
1
2
1
2
1
2
0
1
1
0
1
1
1
0
1
1
0
0
0
0
0
0
1
3
1
1
1
2
1
1
0
2
1
2
0
0
2
0
0
0
1
1
0
2
1
1
0
2
2
1
0
0
1
0
0
2
0
0
0
0
0
0
1
1
1
0
0
1
1
1
0
1
0
1
0
2
1
1
0
1
2
1
0
1
0
1
0
0
2
0
2
0
1
0
0
0
2
0
2
0
1
1
1
0
2
2
2
1
2
3
1
1
1
1
2
2
0
0
0
1
1
1
2
2
0
1
1
1
0
1
0
0
0
2
1
1
1
1
1
0
2
1
0
0
1
0
1
1
0
1
0
2
0
1
2
0
0
0
0
2
0
2
0
1
0
0
0
2
0
0
1
1
0
1
0
2
1
0
2
2
1
0
0
0
2
0
1
0
0
2
1
0
1
1
1
2
0
0
1
2
1
1
2
0
0
1
1
0
0
1
0
1
0
2
2
2
2
1
0
1
1
1
1
0
0
0
0
1
2
2
1
1
1
1
1
1
0
0
1
0
1
0
0
0
0
1
0
1
0
0
1
2
0
1
0
2
1
1
1
1
2
1
1
2
0
1
0
0
0
0
3
0
1
1
1
1
0
1
1
0
0
0
0
1
0
2
0
2
1
1
1
0
0
0
1
1
0
1
2
2
1
0
1
2
0
1
0
0
0
0
1
1
0
0
0
1
0
2
2
2
1
0
1
1
2
2
0
2
2
1
0
2
2
0
1
0
0
1
1
0
0
1
1
3
1
0
2
1
0
0
0
2
1
2
0
0
1
0
1
0
2
1
2
0
1
1
1
0
2
1
2
0
2
2
1
1
0
1
2
0
0
1
1
0
1
0
0
1
1
1
0
1
1
2
1
0
2
0
1
2
1
0
1
2
0
1
0
0
1
1
0
0
0
2
0
0
0
2
0
1
1
4
1
1
0
1
0
1
2
1
1
0
1
0
0
0
2
0
1
2
1
2
0
1
0
2
0
0
2
2
2
0
0
0
0
1
2
0
0
1
1
1
2
1
1
2
0
0
4
1
2
2
1
1
2
1
1
1
0
1
0
1
0
1
0
0
1
1
1
1
2
1
0
1
2
0
0
1
1
2
2
2
1
2
2
2
1
1
0
1
2
0
1
2
0
1
1
1
1
0
0
0
0
0
1
1
2
1
2
1
0
0
2
1
0
0
2
1
1
0
0
0
2
2
0
1
1
1
2
1
2
0
0
0
0
0
1
2
2
1
2
2
1
1
1
1
1
1
1
1
0
0
2
0
0
0
1
2
1
1
2
0
2
1
0
1
1
0
1
2
0
0
1
1
1
2
1
1
2
1
0
0
0
1
2
0
1
0
0
2
0
1
0
1
1
1
1
0
0
0
1
1
1
0
1
2
0
2
1
0
2
0
1
0
2
2
0
1
0
1
1
1
0
1
1
1
0
1
2
1
1
1
1
1
1
1
1
1
1
2
2
1
0
1
0
1
2
2
1
0
1
2
0
0
1
0
0
1
1
1
2
0
2
1
1
1
0
0
2
2
1
1
1
1
3
1
1
0
1
0
1
1
0
1
1
2
0
1
1
1
1
0
2
0
2
0
2
1
0
1
0
0
2
2
1
1
1
2
1
0
0
0
0
0
2
1
0
0
0
2
2
0
1
0
0
0
0
0
1
0
0
1
0
2
2
1
0
1
2
1
1
0
0
0
2
1
2
1
2
2
0
0
0
1
2
1
1
0
2
1
1
4
2
1
0
1
2
1
2
1
2
0
2
2
0
1
0
2
2
0
1
2
1
0
1
1
1
3
0
2
1
2
0
2
2
2
1
2
0
1
2
0
0
1
1
2
0
1
0
1
1
0
1
0
1
2
2
1
1
0
1
2
1
1
0
0
1
3
0
2
1
0
0
1
1
1
0
0
2
1
0
0
1
1
0
2
0
1
2
2
0
1
2
1
1
0
1
0
0
0
1
1
0
2
1
1
1
1
2
2
0
0
1
1
1
0
1
0
0
1
1
1
0
0
0
0
0
0
1
0
2
0
2
1
2
0
1
0
1
2
1
0
2
1
2
0
0
1
2
0
1
0
1
0
0
0
1
1
0
1
0
1
2
1
1
2
1
1
1
2
1
1
0
0
0
1
0
1
1
0
1
0
1
1
2
1
1
0
2
1
2
1
2
0
0
0
0
1
1
0
0
0
1
0
0
0
2
1
0
2
1
1
0
1
1
0
1
2
1
0
0
0
0
1
0
1
1
1
0
1
2
1
1
1
0
2
2
0
1
2
1
0
0
2
1
0
0
0
2
1
2
0
3
1
0
1
1
0
0
0
0
0
1
1
2
0
0
1
1
2
0
1
2
0
0
1
1
1
0
1
2
3
1
1
2
0
2
1
1
0
1
0
0
0
0
1
2
1
0
1
0
0
0
0
0
2
2
2
2
0
1
0
0
2
1
1
1
1
0
1
1
0
0
2
2
2
1
2
0
1
1
1
0
1
1
2
1
0
0
1
2
1
0
0
2
0
0
1
2
1
1
1
0
1
0
2
0
0
2
1
1
1
2
0
1
1
2
1
2
1
1
0
1
1
1
0
2
2
1
0
1
1
0
0
1
0
1
2
0
1
2
1
1
1
0
0
0
1
1
2
0
1
0
0
2
1
1
0
1
0
1
1
1
0
0
0
0
2
2
2
2
2
1
2
0
2
0
1
2
1
1
2
1
1
1
2
1
0
2
0
1
1
2
0
0
1
0
1
1
0
1
0
1
0
1
1
0
0
2
0
1
0
1
0
2
0
2
1
0
1
0
3
1
0
1
2
0
1
0
3
2
1
2
2
1
0
0
1
1
0
2
1
0
1
0
2
1
1
1
1
0
1
1
1
0
1
0
1
0
1
0
2
0
0
2
0
1
2
0
1
0
0
1
1
1
1
0
2
1
2
0
1
0
1
1
2
0
0
1
0
1
0
1
2
1
2
1
2
0
2
1
0
1
1
1
1
1
2
1
1
1
2
3
1
2
1
1
2
1
2
0
2
1
2
1
2
1
1
2
1
0
1
1
0
2
1
1
0
0
2
1
0
1
1
2
0
3
0
3
0
0
1
1
2
1
1
1
1
2
0
1
0
2
1
0
1
1
1
1
1
0
1
0
1
0
1
0
1
1
1
1
0
0
1
3
1
1
0
1
2
1
2
0
2
1
1
0
0
1
0
0
0
0
1
0
1
2
2
2
0
2
3
1
2
1
5
2
0
0
1
1
2
0
5
2
0
1
0
1
1
0
0
1
0
0
1
0
2
0
1
1
1
2
1
0
0
1
0
0
3
1
1
1
1
0
1
0
0
0
0
0
2
0
2
0
0
0
2
1
2
1
2
1
1
1
1
0
0
0
0
2
0
0
2
1
0
2
1
1
0
2
1
2
2
1
2
1
11
2
0
0
1
1
0
2
1
1
0
1
1
2
0
1
1
0
0
0
2
0
1
0
2
1
1
3
1
2
2
0
2
1
1
0
0
2
2
0
1
0
2
0
0
1
0
1
1
1
1
1
1
2
0
1
2
1
0
0
3
1
1
0
1
1
1
2
1
1
0
2
0
1
0
1
0
2
1
1
0
0
3
2
0
4
2
2
0
0
0
5
1
0
0
0
0
0
1
1
1
3
1
1
1
2
0
1
2
2
9
1
1
1
1
0
1
6
2
0
0
2
2
2
1
0
0
0
2
0
0
3
0
0
0
1
0
1
0
1
2
0
1
0
1
1
1
1
1
1
1
2
0
1
0
2
2
2
0
0
1
1
1
1
2
1
0
0
1
0
2
1
0
1
2
0
2
1
0
1
1
1
0
1
0
2
1
0
1
1
2
1
1
0
2
1
0
0
2
1
0
1
0
2
0
1
1
0
1
1
2
2
1
0
2
0
0
2
1
0
0
2
1
0
0
2
2
1
3
1
2
1
0
2
1
2
0
0
1
2
0
0
2
0
0
1
2
0
1
2
1
0
1
0
1
1
1
1
0
1
0
1
1
1
0
0
2
0
0
1
1
1
2
2
2
0
1
0
1
0
1
0
2
1
1
1
0
0
0
1
0
1
0
1
4
2
1
0
0
0
0
2
1
0
1
1
0
0
1
1
0
0
1
0
1
2
1
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
1
1
2
2
1
1
2
2
0
2
0
0
2
2
0
1
0
1
2
5
1
0
2
0
2
0
0
1
1
0
1
1
0
1
1
2
0
1
2
2
0
1
0
2
0
1
1
1
1
1
0
0
0
0
1
2
1
1
1
0
2
0
0
1
1
4
0
2
0
1
0
0
2
1
1
1
1
1
2
2
0
1
1
2
1
2
0
1
1
1
0
1
1
0
2
1
0
0
0
2
1
0
2
0
1
1
1
1
0
2
1
0
1
1
1
0
2
0
1
0
0
1
0
1
2
0
0
0
1
0
2
1
2
2
1
1
0
1
0
2
2
2
2
1
2
2
1
1
0
1
1
1
4
0
0
2
1
2
0
0
1
2
2
1
0
0
2
0
0
1
1
1
1
1
0
1
1
1
1
1
1
0
2
0
2
2
0
0
0
1
2
1
2
0
1
0
1
0
0
1
0
2
2
2
1
0
2
1
1
0
1
2
0
2
0
0
1
0
1
1
0
0
1
3
1
1
0
3
2
1
1
0
0
1
0
1
1
2
0
2
1
0
2
1
1
1
0
2
0
1
2
0
1
1
1
1
2
2
0
2
1
0
2
0
0
0
0
2
0
0
2
3
4
0
0
0
1
0
0
0
2
0
3
0
1
2
1
2
1
0
2
1
2
1
1
2
1
1
1
0
0
1
1
1
0
0
2
1
1
2
0
0
1
0
0
1
0
1
0
2
2
1
1
1
2
0
0
0
1
0
1
1
2
0
1
0
1
0
1
0
1
0
2
1
2
2
1
1
2
1
1
0
1
0
2
0
1
1
0
1
0
1
0
2
2
0
1
2
3
2
1
0
1
1
1
1
1
1
1
2
1
1
1
1
1
1
1
2
1
0
1
1
1
1
1
0
1
1
0
1
1
0
1
1
1
0
1
0
2
1
0
1
0
0
0
0
0
1
0
2
1
0
0
1
1
1
2
2
2
2
1
2
0
0
0
0
0
0
0
1
1
1
1
1
2
2
1
0
1
0
1
2
1
0
2
2
0
2
1
2
0
0
0
0
1
0
0
1
1
1
1
2
1
2
1
1
1
0
2
1
2
1
0
2
2
1
1
0
1
1
1
1
0
0
2
2
1
0
2
0
1
2
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
1
1
1
0
0
1
0
1
1
0
1
0
1
1
0
1
1
2
0
0
2
1
0
1
1
1
2
0
0
1
0
0
1
1
0
0
1
2
1
2
2
0
1
2
1
4
2
2
3
1
1
0
0
1
0
1
0
1
0
1
0
0
1
1
2
1
2
0
0
2
0
2
0
0
2
1
2
0
1
2
1
1
0
2
0
1
0
0
1
0
1
1
0
2
0
0
2
1
1
1
1
2
1
0
1
0
0
0
0
1
1
0
0
1
1
1
1
1
0
0
0
1
2
0
1
1
0
0
1
2
0
1
2
1
1
1
0
0
1
2
0
5
2
0
2
0
1
1
0
0
0
2
2
1
1
2
3
2
0
1
2
2
1
2
2
0
0
1
1
2
1
0
0
0
0
1
1
0
1
1
1
2
0
0
1
1
1
1
1
0
1
0
0
1
1
1
0
1
0
1
0
2
1
0
0
0
0
1
2
1
2
0
1
0
2
0
3
1
0
1
1
1
2
2
1
1
0
2
1
0
0
2
1
0
0
1
0
1
0
2
0
2
1
1
0
1
0
0
2
0
0
0
0
2
1
2
2
0
0
0
1
2
0
2
2
1
2
2
0
1
0
1
1
0
2
2
1
1
1
0
2
0
2
0
0
2
1
1
0
1
1
2
1
0
0
1
1
0
2
0
1
0
1
0
2
0
1
0
1
1
0
1
0
1
1
1
0
2
1
1
1
2
1
0
2
1
1
1
1
2
1
0
1
2
2
1
1
1
0
2
0
0
0
1
0
2
2
0
1
0
1
1
0
1
1
2
1
1
1
1
0
0
0
2
2
0
2
1
1
0
2
2
1
1
1
0
1
2
1
0
0
1
1
1
1
0
2
1
2
1
1
0
0
2
2
0
1
0
3
1
1
0
1
1
1
0
1
0
0
1
2
2
0
2
2
1
1
2
1
0
0
1
1
0
1
1
1
1
1
2
1
1
3
1
1
3
1
1
2
1
1
1
1
1
2
1
0
0
2
1
2
2
2
1
2
1
1
1
0
0
1
0
1
1
1
3
1
0
0
0
0
0
1
0
2
0
2
1
0
1
2
2
1
2
3
1
0
3
1
1
1
0
0
1
1
0
0
1
0
2
1
0
1
1
0
1
1
1
1
0
0
2
1
0
1
1
1
1
1
1
0
0
1
1
2
0
2
1
1
0
0
2
0
0
1
0
2
0
0
0
0
2
0
1
2
0
1
0
2
1
2
2
0
2
1
1
1
1
2
1
1
0
0
0
0
1
1
0
2
1
1
0
1
1
0
0
1
0
2
0
0
0
2
1
0
0
0
0
0
1
2
1
1
1
2
1
0
2
1
1
1
2
2
0
0
2
0
0
1
1
1
1
0
2
2
0
2
0
0
1
2
0
0
2
2
1
0
1
0
0
0
1
0
2
0
1
1
0
0
0
1
1
0
2
1
1
0
1
2
1
1
1
0
1
0
1
0
2
0
2
2
0
2
1
0
1
1
3
1
0
2
0
0
1
0
2
0
1
2
0
1
2
0
1
0
2
2
0
0
0
0
1
0
2
0
1
2
1
1
1
0
2
1
3
1
4
1
1
2
0
1
0
0
0
1
1
1
1
4
1
0
0
1
0
0
3
0
1
1
1
1
1
0
0
1
0
1
1
1
1
0
2
1
0
1
0
1
3
1
2
2
1
1
0
1
0
0
2
2
0
1
0
0
1
1
1
0
2
0
2
0
0
0
2
0
2
2
1
2
0
2
0
0
2
1
3
2
0
0
0
2
2
1
1
1
0
0
1
1
0
2
1
1
0
0
1
2
2
1
1
1
1
1
2
1
1
2
0
1
1
1
1
1
0
2
1
1
1
1
1
1
2
1
1
0
0
0
1
1
0
0
0
1
0
1
1
1
1
0
1
3
0
1
2
0
0
0
2
3
1
1
5
1
1
1
2
1
0
1
2
1
1
0
1
2
2
2
1
0
0
0
2
1
1
0
2
0
0
0
0
2
1
0
1
2
2
3
0
2
0
0
0
2
0
1
0
1
1
1
0
0
0
1
2
1
1
1
0
1
2
1
0
0
0
2
2
0
1
0
2
0
1
1
1
2
0
2
2
2
1
2
2
1
0
1
1
0
0
1
0
0
0
1
1
1
1
0
0
1
2
1
1
0
1
0
1
0
0
0
1
0
2
1
1
1
1
0
1
1
0
0
0
1
1
1
0
2
0
0
0
1
2
1
3
1
1
2
2
0
0
1
1
1
1
1
1
1
0
1
3
1
0
0
2
1
0
1
0
0
0
1
0
0
0
1
0
2
1
1
2
1
0
1
1
0
0
0
1
1
1
1
1
0
2
2
0
2
1
1
0
1
1
0
2
2
1
2
0
0
1
2
2
2
1
0
2
1
1
1
0
1
0
0
0
1
1
1
0
0
1
1
2
1
1
0
0
2
2
0
1
1
1
2
2
1
1
0
1
0
1
0
0
1
0
0
0
2
0
2
1
0
1
1
2
0
1
2
2
0
1
0
1
2
1
2
0
2
0
0
0
2
0
1
1
3
2
1
2
1
1
1
1
0
0
2
0
0
1
2
1
1
1
2
0
2
3
0
1
0
1
1
1
2
1
1
0
1
2
1
2
1
1
1
2
2
0
0
1
2
0
3
0
0
0
0
1
1
1
0
2
2
0
0
1
0
1
0
1
0
2
0
0
1
0
0
0
1
1
0
1
1
2
1
2
2
2
1
1
0
1
0
1
1
2
1
1
1
0
1
1
1
1
0
1
2
0
2
1
0
2
1
1
2
2
0
1
2
1
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
1
1
1
0
1
0
2
0
1
2
2
0
0
0
0
1
0
0
0
2
1
1
1
0
1
1
2
1
2
2
2
0
2
1
1
2
1
1
3
2
2
1
0
2
1
2
2
0
1
1
0
0
2
0
1
0
0
0
0
2
1
2
1
0
1
0
0
1
0
1
1
0
0
1
0
0
2
0
1
0
0
1
0
0
1
0
2
1
1
2
1
1
0
2
0
2
0
1
2
1
1
0
2
1
1
0
0
0
2
0
1
0
1
1
1
0
1
1
0
1
1
1
1
0
0
1
0
0
2
1
1
1
0
2
1
1
0
1
1
1
2
1
2
1
0
1
0
2
1
4
0
1
1
2
3
1
2
3
1
1
2
0
1
0
2
0
0
0
0
0
0
1
1
1
2
0
3
1
1
2
0
0
0
0
1
0
0
0
0
1
2
0
0
1
1
2
2
2
2
1
2
1
1
2
1
0
1
1
0
2
1
0
1
0
0
2
1
1
0
0
1
0
0
3
1
0
1
1
1
1
1
0
1
2
0
2
0
1
1
2
1
1
0
1
2
0
0
2
1
0
0
0
2
1
1
1
1
1
1
1
0
1
0
1
0
1
0
0
2
0
1
0
3
0
0
2
0
1
1
2
1
1
0
0
1
2
1
0
2
2
2
0
0
1
0
0
1
0
1
1
2
1
1
0
1
2
1
0
2
1
4
1
2
1
0
1
1
1
0
2
0
0
0
1
0
1
2
0
0
1
1
0
0
0
1
1
3
0
2
2
0
1
1
1
0
1
0
1
1
1
0
2
1
1
8
2
0
1
1
3
0
0
1
0
2
0
0
1
2
2
1
1
1
1
2
3
0
1
2
1
2
1
0
0
1
1
1
1
0
1
0
2
0
1
2
0
1
0
2
1
1
0
0
1
2
0
2
1
1
0
1
1
0
2
1
1
0
0
1
1
2
1
1
1
0
0
0
0
1
0
2
0
0
0
1
1
0
0
1
1
2
1
1
1
0
0
2
2
1
1
1
2
0
0
1
2
2
1
1
2
1
1
0
1
3
4
0
1
0
1
0
0
0
1
0
1
1
1
1
0
0
0
2
0
1
0
2
0
1
1
1
1
0
1
0
1
0
1
1
0
0
0
0
0
0
0
1
1
0
2
1
0
1
1
2
2
1
1
0
1
2
0
0
1
0
2
0
1
0
0
0
1
1
0
0
0
2
0
0
0
0
1
1
1
1
2
1
0
1
1
1
0
2
1
0
1
0
1
1
3
2
1
2
0
2
0
2
1
1
0
1
1
1
1
0
1
0
0
1
1
1
0
1
0
0
2
1
1
2
1
1
1
0
1
0
0
0
0
1
1
0
1
2
0
2
1
1
0
0
1
2
0
1
1
0
0
1
1
0
0
0
0
1
0
2
1
0
0
0
2
0
2
1
0
0
2
1
1
1
1
1
0
1
1
1
2
0
0
0
3
1
1
1
1
0
0
0
1
0
1
0
0
1
1
0
1
2
1
1
1
1
1
0
2
2
1
2
1
1
0
0
0
0
2
2
2
1
1
0
0
2
0
1
2
2
1
1
0
0
0
2
2
0
0
2
1
1
0
2
1
1
1
2
2
1
0
0
2
1
3
1
1
1
0
1
0
1
2
1
1
1
1
2
1
1
2
1
0
2
0
2
1
0
1
0
0
1
1
2
1
1
0
0
2
2
0
0
1
2
0
2
1
1
1
0
2
0
1
1
1
0
0
1
1
1
0
2
1
1
1
1
0
2
2
2
2
0
0
1
1
0
0
1
1
2
2
1
1
1
1
0
0
0
1
1
1
0
0
1
0
0
2
0
0
0
0
1
1
2
0
1
2
1
1
0
1
2
0
2
0
1
1
1
2
1
0
1
1
1
1
0
1
0
2
0
1
1
1
2
1
1
2
1
0
0
2
2
2
1
1
2
2
0
1
0
1
1
1
1
2
2
0
0
0
2
0
1
2
0
1
1
2
0
1
1
0
2
1
1
0
0
0
0
0
0
1
1
0
1
2
0
1
1
0
2
1
1
0
1
0
2
0
1
2
2
2
1
0
1
0
0
2
1
0
0
1
0
2
0
1
1
0
0
0
3
2
0
1
1
1
0
0
0
0
0
2
1
0
0
1
2
0
0
1
1
2
0
0
2
1
2
1
1
1
3
0
0
1
2
0
2
1
1
0
1
0
1
2
2
0
0
0
0
1
1
1
0
1
0
0
1
1
2
0
1
1
1
0
2
1
0
2
3
1
1
1
0
2
0
1
0
0
0
0
2
2
1
1
2
1
0
1
1
1
2
2
1
3
0
1
0
1
0
2
1
0
2
2
0
0
0
1
2
1
1
1
2
1
0
1
1
2
1
0
1
0
1
1
2
0
2
0
1
1
1
0
2
0
1
1
0
2
1
2
1
0
0
2
1
0
2
2
2
2
1
0
1
0
0
2
2
1
0
1
0
0
1
2
0
1
2
1
1
0
0
0
0
0
2
2
1
0
1
0
2
0
2
0
2
1
2
0
2
2
1
1
2
1
1
0
2
1
1
1
0
2
0
1
0
0
0
1
0
2
2
2
1
2
2
2
1
2
1
2
1
1
0
1
0
1
1
1
2
0
2
0
1
0
1
2
1
0
0
0
1
1
2
2
1
1
1
2
1
1
1
2
0
2
1
1
0
0
2
1
2
1
0
0
0
1
2
2
2
0
0
0
0
0
0
0
2
1
0
1
0
0
2
0
2
1
1
1
1
2
0
1
1
2
1
2
0
0
2
1
3
2
0
1
2
2
0
2
1
2
1
2
1
1
0
2
1
0
2
1
2
2
0
1
1
0
0
0
0
2
2
2
0
1
2
1
0
0
2
1
2
1
1
0
2
2
1
1
2
0
2
0
0
0
2
2
3
1
1
0
1
1
1
0
0
0
2
0
1
2
4
0
2
1
0
0
0
0
1
2
1
1
1
1
1
2
1
1
1
1
0
2
0
1
0
0
0
1
1
2
1
1
1
2
0
1
2
0
1
1
2
0
2
1
0
0
0
1
0
1
1
2
1
0
0
0
0
1
0
1
1
2
0
1
1
0
0
2
1
0
1
1
2
1
1
1
2
1
0
2
0
4
2
0
0
1
2
2
1
0
2
0
2
1
0
0
0
1
0
0
1
2
2
1
0
2
1
1
0
1
0
0
2
0
0
2
1
1
1
2
1
1
1
2
2
1
0
0
0
0
1
0
1
1
0
0
2
1
0
1
0
0
2
1
1
2
2
2
0
1
0
1
1
1
0
0
3
1
2
1
0
1
2
1
2
0
2
1
1
1
1
2
0
1
1
1
1
0
0
1
1
1
0
1
1
1
0
1
1
1
2
1
0
2
1
0
0
0
2
1
3
1
4
1
2
2
0
2
2
1
0
1
1
1
1
2
2
1
1
1
2
0
1
0
1
1
0
0
1
1
1
0
0
0
0
2
2
1
1
1
1
0
1
1
0
0
0
0
1
1
1
1
1
2
2
1
1
1
1
0
0
2
1
1
0
4
0
1
0
0
2
0
0
0
1
0
0
1
1
0
1
2
0
1
0
1
1
0
1
0
1
1
2
1
0
2
1
1
1
0
0
1
1
1
1
2
0
1
1
1
0
1
0
1
1
2
0
2
1
1
0
1
2
2
0
0
0
0
2
0
1
2
1
0
2
2
0
0
2
1
2
1
0
2
2
0
2
1
1
2
1
0
1
0
2
1
1
1
1
2
1
2
0
0
2
2
0
0
1
1
1
0
0
0
0
2
1
2
0
1
1
0
0
1
2
1
2
0
1
1
2
1
3
0
0
2
1
0
2
2
2
2
0
2
0
2
0
1
1
0
0
1
0
0
0
1
2
1
0
1
1
2
0
0
2
0
1
0
1
0
0
2
7
1
1
2
0
1
0
0
2
0
0
0
0
0
0
2
0
3
2
1
1
0
1
0
0
2
2
1
0
0
0
2
0
0
0
1
0
1
0
0
0
1
1
0
1
1
1
0
0
2
1
1
1
0
1
0
1
1
1
2
1
1
1
2
1
2
1
2
0
0
0
2
2
1
0
0
0
0
0
1
0
1
2
2
0
1
1
0
2
0
1
1
1
2
2
0
1
1
1
1
1
2
0
1
0
1
1
2
0
1
0
0
0
0
1
1
1
0
0
0
1
0
1
0
1
1
1
0
2
0
1
2
2
1
1
0
2
1
2
1
3
1
1
1
2
0
1
0
2
2
3
0
1
0
1
0
0
0
2
2
2
2
0
0
2
1
1
1
0
2
1
2
2
1
1
1
2
1
1
0
0
1
2
1
1
2
1
2
1
0
0
1
0
0
0
0
1
1
0
1
1
1
2
1
1
1
1
1
1
0
1
1
0
2
1
2
0
1
1
1
0
0
0
1
1
1
1
1
2
0
0
1
0
2
0
0
2
1
2
1
1
0
0
2
2
1
0
0
1
0
2
1
1
0
0
1
1
0
0
0
2
0
2
2
1
1
1
1
3
2
1
1
1
0
2
1
1
2
0
1
0
2
0
0
2
2
1
0
1
0
0
0
2
0
0
1
1
1
1
1
2
1
0
0
2
0
0
2
0
0
1
1
1
0
2
1
0
1
1
1
2
0
2
0
2
1
1
2
0
0
1
1
2
0
0
0
1
2
0
1
1
1
2
1
1
2
1
1
0
1
1
1
1
0
0
0
1
0
1
1
2
0
0
0
2
0
2
0
0
0
0
2
1
0
0
0
0
0
1
1
1
2
1
0
1
1
0
1
2
2
1
2
2
0
2
2
1
1
2
1
1
1
1
1
2
1
1
1
0
1
0
1
2
2
1
1
4
0
1
2
2
0
2
2
0
0
1
1
0
1
1
0
1
1
0
0
1
0
1
0
1
0
1
0
1
2
0
2
2
0
2
0
2
1
2
2
1
2
2
1
2
0
2
0
0
1
0
0
2
2
3
0
0
0
0
2
0
0
1
0
1
0
0
0
1
2
2
2
0
1
0
1
1
0
0
0
1
2
2
2
0
0
2
0
1
2
0
1
1
0
0
2
1
0
0
1
0
0
2
1
1
0
2
0
0
1
1
1
0
0
1
2
2
1
0
1
0
1
2
0
2
1
0
1
1
1
0
2
1
0
0
2
2
0
1
0
0
1
1
1
2
1
0
1
1
1
1
0
2
1
1
1
0
2
0
1
0
0
5
2
2
0
1
1
1
0
1
2
0
0
2
1
2
0
0
0
0
0
2
0
1
1
2
0
1
0
1
2
1
0
0
3
2
0
0
1
1
0
1
0
1
1
0
2
1
1
0
1
1
0
1
1
0
2
0
2
0
3
0
0
0
0
1
2
3
1
1
1
1
0
0
2
2
1
0
0
0
1
1
1
3
1
1
1
0
3
1
3
1
1
1
2
0
0
1
1
0
0
1
1
1
1
0
1
1
2
2
1
1
0
2
0
0
0
0
0
1
2
2
0
1
2
0
2
0
1
2
0
1
1
0
1
0
2
2
2
1
2
2
1
0
0
1
1
1
0
1
1
0
1
0
1
1
0
2
0
0
0
1
1
1
0
0
2
1
1
1
2
0
2
0
2
2
1
2
1
5
0
1
0
0
1
0
0
2
2
2
1
0
1
1
0
0
2
2
1
1
1
0
1
0
0
2
0
0
1
0
2
0
1
1
0
0
2
2
0
1
0
1
1
0
1
1
1
0
1
1
1
2
1
2
1
0
2
1
1
0
1
1
2
2
0
1
2
0
0
1
0
1
1
1
0
1
1
1
1
0
0
2
0
1
0
1
1
1
2
2
1
1
0
1
0
1
1
1
0
0
1
0
1
0
1
0
0
0
0
2
1
2
0
0
0
2
1
1
1
0
1
1
0
1
1
1
0
0
2
1
1
0
0
2
2
0
2
1
2
0
0
0
2
2
1
0
1
1
2
0
0
0
1
0
0
0
1
1
1
1
2
0
2
0
2
0
1
1
1
0
0
0
1
0
1
1
0
0
2
1
0
0
0
0
1
2
1
2
1
1
1
1
2
0
0
1
0
2
0
2
1
1
0
1
1
0
1
0
1
0
0
0
0
2
0
1
0
1
0
0
1
0
0
0
2
2
1
1
0
0
0
0
2
0
2
1
1
1
1
0
1
0
0
0
2
1
0
0
2
2
0
2
2
0
2
0
0
1
1
1
0
2
0
2
1
0
2
1
0
0
0
2
2
1
2
1
1
2
1
2
2
0
0
2
0
2
0
0
2
0
2
0
2
2
2
1
1
0
1
0
1
1
0
1
0
0
2
2
1
1
1
1
0
2
1
2
1
0
0
1
0
1
0
2
0
0
1
0
3
2
0
2
1
1
0
2
2
1
2
1
1
1
1
2
1
1
0
0
0
0
0
0
1
1
1
1
1
0
2
1
0
1
1
0
1
0
2
2
1
0
1
1
2
0
0
0
0
0
2
1
0
1
2
0
1
2
0
1
0
2
1
0
2
2
1
1
1
0
2
1
2
2
1
2
2
1
0
1
2
1
2
1
0
0
0
1
1
0
1
1
0
1
0
1
1
0
2
0
1
0
1
1
0
1
0
0
2
0
0
1
2
1
1
1
0
1
0
1
0
1
0
0
1
1
2
0
0
1
2
0
0
1
1
0
0
0
2
1
2
2
0
1
0
2
2
0
1
1
1
2
1
2
0
2
0
0
2
1
2
0
1
1
0
0
0
1
1
1
1
0
0
0
1
1
0
1
2
1
1
1
1
0
0
2
1
0
0
1
1
0
1
1
0
0
1
0
1
0
1
2
1
2
2
0
1
2
0
2
0
1
2
0
2
0
1
3
1
0
0
1
0
0
0
1
2
2
2
1
2
2
0
0
2
0
1
1
0
0
2
1
2
1
1
1
4
1
0
1
1
0
2
0
0
2
0
2
0
0
3
1
1
1
2
0
2
1
2
2
0
1
1
0
1
1
1
1
2
2
0
0
4
0
2
2
1
0
1
2
0
1
0
1
2
1
1
1
2
0
1
0
1
2
2
0
1
2
1
1
1
0
1
0
0
1
0
2
1
0
0
0
2
0
1
2
1
1
3
2
2
1
0
1
1
1
0
0
0
2
0
0
0
1
1
1
1
2
1
1
0
2
0
6
1
1
0
1
2
1
2
1
2
1
2
1
1
2
1
2
0
2
0
1
0
0
1
2
2
0
1
1
1
1
1
1
0
1
1
0
1
1
0
0
2
0
1
2
0
1
2
1
0
1
0
2
2
1
0
1
0
2
0
3
1
1
0
0
2
1
1
0
2
1
0
1
1
0
3
1
1
1
1
1
0
2
0
1
1
1
0
3
1
1
2
1
1
1
2
1
1
1
0
1
2
1
2
1
1
1
2
0
1
0
2
1
0
2
1
0
0
1
0
0
0
1
0
1
2
0
2
2
1
0
1
1
0
0
0
0
1
1
1
1
0
1
0
0
1
0
0
0
1
1
0
0
1
0
1
1
0
0
1
1
0
0
0
0
2
1
0
0
0
2
1
0
1
1
2
2
0
1
0
2
0
0
2
2
1
2
2
1
1
2
1
1
1
0
2
2
1
2
0
1
1
1
1
0
0
1
2
2
1
1
1
2
1
0
0
1
1
2
1
1
1
3
0
1
1
1
0
1
0
0
0
2
2
1
0
1
1
1
1
2
2
1
0
1
0
1
2
1
1
0
2
1
1
1
2
0
0
0
1
1
1
0
0
1
1
3
0
1
1
1
2
1
1
1
0
0
2
0
1
1
0
2
0
0
1
1
1
2
2
1
1
0
0
0
2
2
0
1
0
2
0
1
1
2
1
1
6
2
2
2
2
0
4
0
1
0
1
2
1
1
0
0
1
1
1
1
2
0
0
0
1
1
0
2
2
1
1
0
1
1
1
1
2
1
0
0
1
0
1
2
1
1
1
0
1
1
1
0
1
1
1
1
1
1
2
1
2
0
1
2
0
1
1
3
1
0
2
0
1
0
1
1
1
1
1
2
1
2
1
1
0
2
1
0
0
2
0
1
0
3
2
0
2
0
2
1
2
1
1
0
0
0
1
1
2
1
1
1
1
2
1
0
2
1
2
0
1
0
0
1
0
1
1
1
0
2
0
1
2
1
0
1
0
3
1
0
2
1
0
0
1
1
0
1
2
1
2
0
1
2
1
1
1
1
0
1
2
1
1
2
2
0
0
2
0
1
1
0
0
2
1
0
1
1
1
1
2
0
1
1
2
2
3
2
1
1
0
1
2
1
1
0
2
0
2
2
0
0
1
1
0
3
0
0
2
0
0
1
2
0
2
0
0
1
2
0
0
0
0
0
1
1
1
0
2
1
1
0
0
0
2
2
0
1
1
0
0
2
1
1
0
1
2
0
1
0
0
0
2
2
0
2
0
2
0
0
1
1
2
0
2
0
2
0
0
0
0
0
1
1
1
1
0
0
0
0
1
0
0
2
1
0
0
5
1
1
0
0
1
2
0
1
1
1
1
0
0
1
2
1
1
2
0
1
2
1
0
1
1
0
2
1
0
0
0
1
1
0
2
0
0
2
0
0
0
2
0
2
3
2
0
1
2
1
0
1
0
0
2
4
0
0
2
1
2
1
1
0
0
1
2
1
1
2
1
1
0
0
1
1
1
1
0
1
0
2
2
1
1
0
0
1
1
1
1
2
0
0
1
2
1
0
0
0
1
1
2
1
2
2
0
0
1
0
0
1
1
1
2
2
1
1
2
0
0
0
1
0
1
0
2
1
2
0
0
0
0
2
0
0
0
1
0
1
0
2
1
0
1
1
1
1
1
0
3
1
1
2
1
0
1
2
0
0
1
1
2
3
0
0
1
0
0
0
0
1
1
0
0
0
3
0
1
0
1
1
1
2
0
0
1
0
1
0
1
1
2
2
1
1
1
0
2
0
0
3
2
2
1
0
2
0
1
0
0
1
1
0
1
0
0
1
0
0
0
1
2
2
1
2
0
1
1
0
1
1
1
2
0
1
0
0
1
2
2
1
0
2
3
2
2
0
1
0
2
0
2
0
0
1
3
2
0
1
0
2
2
1
0
1
0
1
0
1
1
0
0
1
2
1
1
2
0
2
0
2
1
1
1
2
0
2
0
0
1
1
2
1
1
0
0
3
0
2
2
3
2
1
0
2
1
0
0
1
2
0
0
0
0
1
1
0
2
1
1
0
1
1
0
2
1
2
0
0
1
0
0
0
1
0
2
1
1
1
0
2
1
0
1
0
0
2
2
0
1
1
0
0
1
1
0
0
1
2
1
3
2
0
0
1
1
2
0
0
1
1
1
0
0
1
1
0
2
0
0
0
1
1
0
1
1
2
2
0
1
0
1
1
3
2
1
0
1
0
1
0
0
2
1
0
1
0
1
0
0
1
2
0
1
1
0
1
1
0
1
1
0
1
1
2
1
0
1
1
1
1
1
1
1
1
1
0
0
1
1
0
0
2
0
0
2
1
2
1
0
1
0
0
1
1
0
2
1
2
0
1
2
0
2
1
2
0
1
0
2
0
2
1
1
1
1
1
1
1
1
1
0
2
1
1
1
1
0
0
2
2
1
1
2
2
2
0
1
1
2
0
0
2
0
1
1
1
1
3
2
2
0
0
2
2
2
0
0
1
0
2
1
7
0
0
2
0
1
0
1
1
1
1
0
1
1
2
2
1
1
1
2
1
1
2
0
1
2
2
0
0
0
1
1
1
0
0
2
1
1
2
1
1
0
0
0
1
0
1
2
1
0
1
0
2
2
0
1
1
1
1
1
2
2
2
0
1
1
0
1
0
1
0
2
0
0
2
2
2
1
2
0
0
0
1
0
2
0
2
2
0
0
1
0
0
0
1
1
1
0
0
0
2
2
0
0
1
2
1
1
0
1
0
1
2
1
1
1
1
2
0
0
0
1
2
1
2
3
0
1
1
3
1
1
0
1
0
1
1
1
0
2
1
2
0
1
1
0
1
2
1
2
0
0
1
2
0
0
1
2
0
0
1
0
0
1
1
4
1
0
2
1
2
0
2
1
0
1
1
1
0
1
2
1
1
0
2
0
0
0
2
1
0
0
1
1
2
0
1
1
1
1
1
1
0
1
0
1
1
1
1
2
1
0
0
2
1
2
1
0
2
0
1
1
0
0
1
0
0
1
1
1
2
0
0
0
0
1
1
1
0
0
2
1
1
3
0
0
1
0
1
1
0
0
1
1
1
1
1
1
0
0
2
1
1
1
1
0
2
0
0
1
2
1
1
1
1
2
2
2
0
2
2
2
0
1
1
0
1
1
1
1
1
1
1
1
1
1
1
0
1
0
0
0
2
1
1
0
0
0
1
0
0
1
2
0
0
1
2
4
0
2
1
1
0
1
1
2
0
1
1
0
2
0
2
0
1
1
0
0
0
1
0
1
1
1
0
1
1
1
1
2
2
2
1
1
2
1
1
1
1
0
0
0
2
1
1
0
1
0
0
1
0
0
1
0
1
2
1
0
2
0
2
0
1
1
1
1
2
0
1
1
1
1
0
0
1
1
2
1
1
2
0
1
0
1
1
1
5
0
0
3
1
1
2
1
1
1
1
0
1
2
0
1
1
0
0
1
0
0
1
0
1
1
0
2
1
1
1
1
0
0
0
1
1
0
1
1
0
2
1
2
1
1
2
0
2
1
1
1
1
0
0
0
1
1
0
0
1
3
2
0
0
1
2
0
1
1
0
0
0
0
3
0
0
0
0
1
1
0
0
0
0
2
1
1
0
1
2
0
0
0
0
1
1
0
2
1
1
0
2
1
0
0
0
1
1
0
2
2
0
2
0
2
2
0
1
0
1
2
2
2
1
0
0
2
0
0
3
2
2
1
0
1
0
2
1
1
0
0
0
0
0
0
1
2
0
1
1
0
0
2
2
2
0
1
1
1
0
2
0
2
2
1
1
0
0
1
1
0
2
1
1
2
1
0
0
1
1
0
2
1
2
1
0
1
0
0
1
1
0
0
2
1
2
0
1
0
2
1
1
2
0
0
1
0
1
0
2
0
0
0
0
1
1
1
2
1
1
1
0
2
1
0
2
1
1
0
0
2
1
2
2
2
0
2
0
0
1
2
0
0
1
0
2
0
0
0
1
0
0
2
1
0
1
1
2
0
1
0
1
1
1
2
1
1
1
0
0
2
1
1
1
0
2
2
2
0
0
0
0
0
0
1
2
0
0
1
1
2
1
0
1
0
1
1
2
1
1
0
2
0
0
0
0
1
1
0
0
2
0
1
0
1
0
2
0
2
0
1
1
2
2
2
0
2
0
0
0
0
0
1
1
0
1
1
0
0
2
2
1
2
0
1
1
0
2
2
0
1
0
1
2
0
0
0
2
1
0
1
1
1
2
1
1
0
1
0
0
1
3
0
0
2
0
1
1
2
0
0
1
0
1
2
0
0
2
1
1
1
2
0
1
0
0
1
1
1
0
1
1
1
1
2
2
0
0
0
0
1
1
0
0
2
0
0
2
2
0
3
0
0
2
1
0
2
1
0
2
1
0
1
1
2
0
1
1
0
1
1
1
0
1
2
2
1
2
0
1
1
0
2
2
1
1
0
0
1
0
1
0
1
1
2
1
0
1
0
0
1
1
2
1
0
0
0
1
2
0
2
1
0
0
0
0
0
0
2
1
1
1
1
1
0
1
0
2
1
1
1
2
0
0
0
0
0
1
0
3
1
0
1
1
1
1
1
0
4
0
0
1
2
0
3
1
1
1
1
1
1
0
1
1
1
0
0
1
4
1
1
1
0
1
2
1
1
1
0
2
1
1
2
2
1
1
2
0
0
0
1
0
1
1
2
2
1
2
0
0
2
4
2
1
0
1
1
1
1
1
1
0
1
1
1
2
2
0
1
2
1
1
0
3
0
1
1
0
0
1
0
2
2
0
2
1
2
0
0
2
1
1
1
2
0
2
4
2
0
2
2
0
0
1
0
0
1
1
1
0
1
0
2
2
1
1
1
3
0
0
1
2
2
1
1
2
1
0
0
1
1
2
0
3
1
1
1
0
1
0
0
1
0
2
1
1
0
6
0
1
0
1
0
2
1
0
0
2
0
0
1
0
0
1
0
0
1
0
1
1
1
2
1
1
1
1
1
2
1
0
0
1
1
1
2
1
1
1
0
2
2
1
1
2
2
0
2
2
2
0
0
1
1
2
2
1
0
0
1
2
1
0
0
1
1
0
0
1
0
1
1
2
0
2
0
1
0
0
0
0
2
1
2
0
1
1
0
0
1
1
2
0
1
0
1
1
0
1
1
0
0
1
2
2
1
1
2
2
1
0
0
1
1
0
1
2
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
2
0
0
1
0
2
0
1
0
2
1
2
2
1
0
1
1
1
1
0
2
2
1
0
2
2
0
0
1
1
1
1
0
1
0
1
1
0
2
2
1
0
0
1
0
1
1
0
3
0
0
2
1
6
1
1
0
2
0
0
2
1
1
0
2
1
1
0
0
2
0
1
2
0
0
0
0
1
2
2
1
0
2
1
2
1
1
1
2
0
1
2
1
1
0
0
0
1
0
0
1
0
1
0
1
1
3
1
0
0
2
1
2
0
1
0
0
0
0
0
1
1
1
1
1
2
0
0
1
1
2
0
1
0
1
0
0
1
1
1
1
1
1
1
1
0
0
2
0
1
0
3
0
1
0
1
2
2
0
1
0
1
0
2
1
1
1
1
0
1
1
1
3
0
1
1
0
2
2
0
1
0
1
1
1
2
0
2
0
1
0
1
1
0
0
1
0
1
1
1
0
1
0
1
0
2
1
0
2
0
2
0
2
2
1
0
1
2
1
0
0
1
1
0
1
2
1
0
1
2
1
0
0
1
2
1
1
0
1
0
1
0
0
1
0
1
2
0
1
2
0
1
4
1
0
1
2
2
1
0
0
0
1
0
0
1
1
2
1
1
1
1
2
0
1
0
0
0
1
1
0
0
2
0
2
1
0
0
1
1
2
0
0
2
0
0
0
0
2
1
1
1
1
2
0
1
0
1
0
2
3
0
1
1
1
0
1
2
2
1
0
2
1
1
1
0
0
0
1
0
1
1
3
2
0
1
1
1
1
0
2
0
1
1
0
1
1
1
1
0
0
2
1
1
0
2
0
0
1
2
1
1
1
2
1
0
0
1
0
2
0
0
2
1
0
0
2
0
1
0
1
0
0
1
1
2
2
1
0
0
1
1
1
1
0
1
1
2
2
1
2
1
1
1
1
0
0
2
2
1
1
1
0
1
1
0
1
1
1
1
0
0
2
1
1
1
0
1
0
0
2
1
1
1
1
2
0
1
1
1
1
0
0
2
0
2
0
3
2
0
0
0
1
2
2
0
0
0
1
0
0
0
1
2
0
2
0
1
1
1
1
2
0
1
0
3
1
0
2
0
0
2
0
1
0
1
1
2
1
1
1
0
2
0
1
0
1
0
1
1
1
1
0
1
2
1
2
1
1
1
0
1
1
0
2
2
2
0
1
0
1
2
1
1
2
1
1
0
0
1
1
0
0
2
1
2
2
1
1
1
1
2
2
1
0
1
1
1
1
0
0
0
1
1
1
2
0
1
1
1
0
2
3
0
0
0
0
1
1
1
2
1
0
2
0
1
2
1
0
1
1
2
1
0
1
2
2
0
1
2
0
1
2
2
2
1
1
0
2
1
0
1
0
0
1
1
0
1
1
0
0
2
0
1
1
0
0
1
1
2
0
2
1
2
1
2
0
1
1
0
1
2
0
0
1
0
1
1
2
1
0
1
2
0
0
0
0
1
1
0
0
0
0
1
1
0
0
1
1
1
1
1
0
3
1
2
0
0
0
0
1
0
1
1
1
1
0
2
1
1
0
1
0
0
1
2
1
1
2
0
0
2
0
1
0
1
0
1
2
1
0
0
0
3
2
0
1
1
1
0
2
1
1
0
1
1
2
2
2
2
0
0
2
2
1
0
1
1
1
4
0
1
0
0
1
0
0
0
0
1
1
0
2
1
1
2
2
1
2
2
1
0
1
0
1
2
1
1
1
1
2
1
2
1
2
0
2
1
2
1
0
0
1
1
1
2
0
0
0
0
1
2
2
0
0
1
0
0
0
0
2
0
2
2
0
2
2
0
1
0
2
1
1
1
1
0
2
1
1
1
1
1
0
1
0
2
0
0
2
1
1
0
0
1
0
2
0
0
0
0
1
1
1
0
0
0
1
0
1
2
0
1
2
2
1
1
0
2
1
2
2
1
1
1
1
0
1
0
0
3
1
0
0
1
1
0
0
1
1
2
1
2
2
1
1
0
0
1
1
2
0
1
0
2
0
1
1
2
0
0
0
1
1
0
0
0
1
2
0
1
2
2
1
2
2
1
2
1
1
0
0
0
1
0
0
0
0
1
1
1
2
1
0
2
2
0
2
1
1
0
1
1
0
0
1
2
1
1
0
2
1
3
1
2
1
1
1
1
2
2
2
0
1
0
1
2
2
2
1
2
0
1
2
1
1
0
0
2
0
0
0
1
2
0
1
0
1
3
1
2
1
2
0
1
2
2
1
0
1
1
2
0
2
0
1
0
0
1
1
0
1
1
2
0
2
2
1
1
1
1
2
0
0
2
0
0
1
2
1
1
2
1
1
0
0
2
0
1
1
1
2
1
2
1
2
0
1
0
0
0
0
1
0
1
2
0
0
0
1
1
1
1
1
1
1
0
1
2
0
1
1
2
2
1
0
0
2
2
0
1
1
1
0
0
1
1
0
2
2
1
1
1
2
1
1
0
1
0
0
0
0
0
2
1
0
2
1
2
2
2
0
1
1
2
1
0
1
1
2
1
0
1
0
0
2
1
2
0
1
2
1
1
1
0
0
2
0
1
2
1
0
2
1
2
1
2
1
2
1
0
2
2
1
0
1
1
1
0
2
2
2
1
0
0
0
0
0
0
2
1
1
1
2
1
1
0
2
0
2
1
1
2
0
0
0
2
1
2
0
1
1
4
2
1
2
1
0
0
0
2
0
2
1
0
2
2
0
0
1
1
2
2
0
0
1
1
2
1
2
0
2
2
1
1
1
1
2
1
1
0
1
2
1
2
0
2
2
2
2
2
0
0
1
1
2
1
1
1
2
0
0
2
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
2
2
1
2
2
0
0
0
0
2
1
1
1
0
1
0
0
1
0
0
1
2
1
2
2
2
0
1
1
2
1
1
1
1
1
2
0
2
0
1
2
1
0
2
0
0
0
0
0
1
0
1
2
1
1
1
1
0
2
1
2
0
1
1
1
2
0
1
0
1
1
1
1
1
1
2
0
0
3
1
1
0
0
1
0
1
1
0
1
0
0
2
1
2
0
0
1
2
0
0
1
0
0
1
1
1
2
1
1
0
0
0
2
0
0
1
0
0
1
0
0
0
3
0
0
2
0
1
1
0
0
0
0
0
2
1
1
0
1
2
2
2
1
1
1
2
0
2
1
2
2
1
0
3
1
1
1
1
2
0
1
0
0
1
2
0
0
2
2
1
1
1
1
0
1
2
1
0
0
0
2
0
0
0
0
2
1
2
0
1
4
1
1
2
0
1
1
0
1
1
1
0
1
0
1
0
1
1
2
2
3
0
0
1
0
1
2
2
1
0
2
1
3
0
1
1
2
2
2
2
0
2
1
1
3
0
2
1
1
0
1
1
1
0
1
1
1
0
2
0
0
0
0
3
1
1
1
1
1
0
1
2
1
1
1
1
0
2
2
0
0
2
0
1
0
1
1
0
1
1
2
1
2
1
2
2
0
2
1
3
1
0
0
2
1
0
0
0
0
0
1
2
1
0
0
0
1
0
1
2
0
0
1
2
2
0
2
0
0
1
1
1
1
2
1
1
1
3
1
0
1
0
0
1
1
0
1
0
2
0
0
2
0
1
1
0
0
1
1
1
0
1
0
1
0
2
0
1
0
0
2
1
0
0
0
2
0
2
0
1
1
2
2
0
2
1
1
1
1
1
1
0
0
2
1
1
0
0
1
1
0
0
1
2
2
0
1
1
2
0
0
1
1
0
1
1
1
0
0
1
3
0
0
1
1
0
1
0
1
2
0
0
0
3
1
2
0
2
0
0
1
2
0
1
1
1
0
1
0
1
0
1
0
0
2
2
2
1
0
1
2
1
2
1
1
1
1
0
1
0
2
2
0
2
1
1
2
0
0
1
0
1
0
2
1
1
1
1
1
2
3
2
1
1
2
2
2
1
0
1
0
0
0
2
0
1
0
1
2
1
2
1
1
2
1
1
0
2
0
2
2
2
1
1
0
0
1
0
1
2
2
1
2
2
1
1
1
1
1
2
2
0
0
0
1
0
0
1
1
3
1
2
2
2
2
0
1
1
0
2
1
0
1
1
2
1
2
2
1
1
1
0
0
1
1
1
0
1
1
1
1
1
1
0
0
1
2
0
1
2
1
2
0
0
1
0
2
0
1
0
0
0
1
0
1
0
0
1
1
2
2
2
1
0
1
0
3
3
0
2
2
0
1
0
2
1
0
0
0
0
1
1
2
2
1
1
2
1
1
2
0
0
1
1
0
1
2
2
1
1
0
1
1
0
0
2
0
0
1
0
1
1
0
0
1
2
1
0
1
0
1
1
1
1
0
1
0
1
1
1
1
1
0
1
0
0
2
1
2
1
0
0
1
0
0
0
1
0
0
1
1
1
1
2
0
0
1
0
0
1
0
0
0
2
1
2
0
1
0
0
0
0
0
3
1
0
1
2
0
1
2
0
2
0
0
1
1
2
1
1
0
1
1
0
0
3
1
0
0
1
1
1
1
1
0
1
0
1
0
0
0
1
0
1
0
2
1
0
0
1
2
2
0
2
0
2
4
0
1
1
0
1
1
0
1
2
0
2
3
0
1
0
0
1
0
1
0
1
0
1
1
0
2
0
0
0
1
0
2
1
1
0
0
1
1
1
1
0
1
1
1
1
0
2
0
1
2
0
1
1
0
2
1
0
2
0
1
1
0
1
0
0
2
2
0
2
1
1
1
1
1
0
1
2
0
1
1
2
1
2
1
2
0
1
1
2
2
1
3
1
1
2
0
1
1
1
0
0
1
1
2
0
0
0
0
0
0
0
2
0
1
2
0
0
1
0
1
1
4
1
1
2
0
1
1
2
1
0
1
0
0
1
0
1
0
1
1
2
1
0
1
0
0
2
0
0
1
2
0
0
0
2
0
0
3
0
1
0
1
1
1
1
0
2
1
3
2
0
2
1
1
0
1
2
1
0
1
0
1
2
1
1
1
0
2
1
2
2
1
1
2
1
1
0
1
1
1
2
1
1
1
0
1
2
1
0
0
1
0
1
1
2
2
2
1
0
0
0
3
2
1
1
0
2
0
1
0
0
0
1
0
2
1
2
0
2
1
1
0
1
1
0
2
1
2
1
0
1
1
0
0
2
1
2
2
1
0
1
1
1
1
0
1
0
2
2
1
2
1
1
2
3
1
1
2
2
1
0
0
0
0
2
0
0
1
0
1
0
1
1
0
1
1
2
0
2
1
1
1
1
0
2
1
0
0
0
2
1
1
0
0
0
0
1
2
0
3
1
1
1
0
0
0
0
0
2
1
1
1
2
0
0
1
2
0
1
1
0
2
1
1
0
0
2
1
2
1
2
0
0
2
0
0
1
0
2
2
2
0
0
0
4
2
1
2
1
0
1
2
1
1
1
1
0
1
2
1
0
1
2
1
0
2
2
0
0
2
0
0
1
1
2
0
2
2
1
0
0
1
0
2
0
0
1
0
1
2
2
1
2
0
1
1
1
1
2
0
0
1
1
1
3
1
2
1
2
2
1
1
0
0
0
0
1
2
1
0
1
1
0
1
0
1
1
2
0
1
0
0
0
0
1
0
0
2
0
0
2
0
1
2
1
1
2
0
1
1
3
1
1
1
0
0
0
1
1
4
0
2
0
0
0
1
0
2
1
1
1
1
2
1
1
2
1
1
2
2
0
1
0
0
1
2
1
0
0
2
1
1
2
2
0
2
2
0
1
0
1
1
1
0
2
1
0
1
1
0
0
0
0
2
0
1
1
1
0
2
1
2
0
1
0
1
0
0
1
0
1
2
0
1
1
0
0
0
1
1
0
1
1
0
2
1
0
0
1
1
1
1
2
2
0
0
0
1
1
1
1
1
2
2
2
2
0
0
2
0
1
1
1
2
1
0
0
1
1
0
1
2
1
0
2
0
1
0
2
1
2
0
1
1
2
0
1
1
1
1
1
1
0
2
1
2
0
2
0
2
1
1
0
0
2
0
1
0
1
2
0
0
2
1
0
1
1
0
0
1
2
1
1
1
1
1
1
2
0
1
0
0
2
2
1
1
1
0
1
2
0
1
1
1
0
0
1
0
0
1
1
0
1
2
1
0
0
1
0
2
0
0
1
1
0
1
1
1
2
0
2
1
1
0
0
2
1
0
1
0
1
1
0
0
1
1
0
1
2
1
2
0
2
1
0
0
1
0
1
1
1
0
2
1
2
0
1
0
1
1
1
1
1
1
0
1
0
2
0
2
1
0
1
1
0
1
1
1
0
0
0
1
0
2
2
1
2
1
1
0
0
0
1
2
1
1
1
0
0
0
0
0
0
1
1
2
2
2
0
0
1
0
1
1
2
1
0
1
2
1
2
2
1
1
1
2
1
0
1
0
1
1
2
0
1
2
1
1
2
2
1
1
1
0
1
0
0
0
1
0
1
1
1
0
1
0
1
3
0
0
1
1
0
0
0
1
2
1
1
1
3
1
1
0
2
1
1
1
1
2
1
2
1
0
2
0
0
1
1
1
0
1
1
5
0
2
1
0
1
2
1
0
1
1
1
0
1
2
0
2
1
1
2
1
1
0
2
1
2
1
1
0
1
2
0
2
1
1
1
0
2
1
0
1
0
0
1
0
2
1
2
2
1
1
0
1
1
0
1
1
1
1
0
1
2
0
0
1
2
0
0
2
0
0
0
0
0
1
0
0
0
1
1
1
0
2
2
0
1
1
1
0
0
1
0
1
0
0
2
1
1
0
2
0
0
2
0
2
0
0
1
2
1
0
2
2
0
1
0
1
1
2
1
0
1
1
0
0
3
1
1
1
1
2
2
0
2
1
1
2
1
0
0
0
2
1
2
0
1
2
1
1
1
2
0
3
1
1
2
1
1
1
2
0
1
1
3
1
2
2
0
0
1
0
0
1
1
1
2
1
1
0
2
2
0
1
0
0
1
1
0
1
1
0
0
2
0
2
1
0
0
0
0
1
1
1
1
1
1
2
2
1
2
3
1
1
1
1
0
1
1
0
0
1
0
1
0
2
1
1
1
1
0
2
1
1
1
0
2
1
2
1
0
2
0
0
0
2
2
0
0
0
1
1
0
2
1
0
0
1
1
0
0
3
1
0
1
1
1
2
0
1
1
1
2
1
1
1
0
0
1
1
2
1
0
0
2
1
1
0
1
0
1
1
1
0
0
1
1
0
1
1
2
0
1
1
0
1
2
1
1
1
0
0
2
1
1
1
0
1
0
1
1
1
1
1
2
0
2
2
0
2
0
1
0
2
4
0
0
1
1
0
0
0
0
0
1
0
1
0
1
1
1
1
2
0
0
1
1
0
2
1
1
1
1
0
1
0
0
0
1
1
1
1
2
0
2
0
0
2
0
0
1
1
2
0
1
1
0
2
3
0
0
2
0
2
2
3
1
1
1
2
0
2
0
1
2
1
1
2
2
1
1
0
0
0
1
0
1
1
1
1
1
1
0
0
0
2
1
1
0
1
2
0
1
2
1
1
1
0
1
2
0
1
1
1
2
0
0
1
0
2
2
2
1
0
0
2
2
0
1
1
2
0
3
0
2
0
1
0
0
2
1
0
1
1
2
2
1
0
1
1
2
1
1
0
2
1
0
0
1
2
1
3
2
1
1
0
0
0
0
2
2
1
0
0
0
0
1
0
0
0
2
1
1
2
1
0
0
1
0
2
1
1
2
2
2
1
1
1
0
3
1
0
1
1
1
2
1
0
2
2
2
1
1
0
0
1
0
2
0
2
1
2
0
2
1
2
1
0
2
1
0
1
2
2
0
0
2
1
0
2
1
0
0
1
0
1
1
0
0
1
1
2
2
0
1
0
2
1
1
1
1
1
0
0
1
1
0
1
0
1
1
0
0
0
1
1
1
1
0
0
2
1
2
1
1
1
1
0
0
1
1
1
1
0
1
1
0
1
2
0
2
0
0
2
0
0
0
1
2
0
0
0
1
1
2
1
0
1
1
2
2
0
0
0
0
1
2
1
0
0
0
2
1
1
0
0
2
1
0
1
0
1
1
1
1
0
1
0
2
2
2
2
1
0
0
1
0
3
1
1
2
0
0
2
0
1
1
2
0
1
0
1
1
0
1
1
2
0
0
1
1
0
0
3
0
2
2
1
2
1
1
1
0
2
3
1
0
0
0
0
0
1
2
1
2
1
0
0
2
0
0
2
0
2
1
1
1
0
0
2
0
0
1
0
2
0
1
1
0
0
1
1
0
1
1
1
1
1
1
0
1
1
1
1
0
2
1
1
2
0
1
1
1
2
0
0
1
1
1
0
1
0
0
2
2
0
2
1
1
2
1
1
1
1
0
1
0
1
1
2
1
1
1
0
1
1
1
1
2
0
0
1
0
0
0
0
2
2
2
3
1
1
1
0
2
1
1
0
0
2
1
1
0
0
2
2
2
0
0
3
1
1
1
2
1
2
1
2
1
1
0
1
1
2
2
1
0
2
0
1
0
1
1
2
0
1
1
1
0
0
0
0
1
1
0
0
1
1
0
0
1
1
1
0
2
0
0
0
1
0
0
1
0
1
1
2
0
1
0
0
1
2
1
1
0
0
1
1
1
1
0
2
2
2
2
0
2
1
0
0
2
1
1
2
2
1
1
0
0
0
2
1
1
0
0
0
2
0
1
2
1
0
0
0
1
0
1
5
2
0
0
2
1
1
0
2
0
0
0
2
0
2
0
0
2
0
1
2
1
1
0
1
0
2
0
1
2
0
1
1
1
0
1
1
1
1
0
0
1
1
0
2
0
1
2
1
1
1
4
1
1
1
2
1
2
0
0
0
0
1
2
0
2
0
1
1
1
1
1
0
2
0
1
1
1
0
1
1
2
0
1
0
1
1
2
2
1
1
2
1
0
1
0
1
1
1
2
1
1
2
0
3
2
1
0
2
0
1
0
1
1
2
1
1
0
0
1
0
1
0
0
0
1
0
2
0
1
1
3
0
0
0
1
1
0
0
0
0
0
2
2
1
1
1
0
2
0
0
1
2
4
2
0
2
1
2
0
1
0
0
2
0
0
1
1
1
1
1
1
3
2
1
0
0
2
1
0
0
0
2
1
2
1
1
1
1
1
1
1
1
0
0
1
3
1
0
0
1
0
1
0
2
0
1
1
0
2
1
2
0
2
2
1
1
2
1
2
1
0
1
1
0
2
0
0
0
0
0
1
1
1
0
2
1
0
1
1
0
0
3
2
0
1
0
0
1
0
1
0
0
2
2
1
2
2
1
2
0
0
0
0
1
1
1
0
2
0
1
0
2
2
2
1
1
4
0
0
0
0
0
2
0
1
1
1
2
1
1
2
1
1
2
0
1
0
1
1
1
2
2
0
0
1
1
1
0
1
0
0
0
0
1
0
1
0
0
1
0
1
2
1
1
1
1
0
2
1
1
4
0
2
1
0
1
1
1
1
1
1
1
1
0
0
1
2
2
1
0
1
0
1
1
0
2
1
2
0
1
1
1
1
1
0
0
0
2
0
1
1
0
0
0
0
0
0
2
1
1
2
1
1
2
1
0
2
2
1
2
2
1
2
0
1
0
0
2
0
0
1
0
1
0
0
0
2
2
1
1
1
0
0
1
0
2
2
0
2
1
0
0
0
1
0
1
1
0
0
2
0
0
1
0
1
1
0
1
1
0
1
0
1
1
0
2
1
1
1
0
2
0
1
2
0
1
0
1
0
0
2
1
1
1
1
1
0
1
0
1
0
0
0
1
1
1
2
1
1
2
2
1
0
2
0
1
1
1
1
0
1
0
0
1
1
0
1
2
0
1
0
1
0
0
2
1
0
1
2
2
0
0
2
1
2
1
0
2
2
1
1
0
2
1
1
0
0
1
0
0
1
1
0
2
0
1
2
1
0
2
0
0
2
2
1
1
2
1
0
0
0
0
1
2
1
0
1
0
0
0
1
2
1
2
3
1
0
2
2
0
0
2
0
0
2
1
1
1
1
1
0
1
1
0
1
0
1
0
2
1
0
0
0
0
1
0
0
0
1
4
0
1
2
0
0
1
0
0
1
0
1
2
2
0
2
1
2
1
0
2
2
1
1
1
1
1
1
0
2
5
2
2
1
2
2
0
0
1
0
0
1
0
0
0
0
1
0
1
2
1
0
1
0
1
0
0
0
1
5
0
1
0
1
1
0
0
0
0
2
0
1
1
0
0
2
2
1
0
0
1
2
2
1
1
1
0
1
1
0
2
2
1
0
1
0
1
0
1
1
2
0
1
1
0
1
0
1
3
1
1
2
0
2
0
2
1
1
0
2
1
1
0
0
2
1
1
2
0
1
2
0
2
0
0
1
0
1
1
2
0
0
0
0
2
1
1
0
0
0
2
0
2
0
0
2
0
1
0
1
1
1
1
0
1
1
3
0
0
1
0
1
1
1
1
1
2
2
2
0
0
1
0
1
0
1
0
0
1
1
2
1
1
2
1
1
1
2
0
0
0
0
0
1
0
1
0
1
2
0
1
2
2
1
1
0
1
0
2
2
1
2
0
0
1
0
1
1
1
1
0
2
1
2
2
1
1
1
1
1
1
0
0
1
0
1
1
1
1
1
1
1
2
0
2
1
2
2
0
1
0
0
1
1
1
2
1
0
1
1
1
2
0
0
2
0
2
2
1
1
0
0
1
0
0
2
0
1
0
0
0
0
1
0
2
0
0
0
0
2
0
0
2
0
0
4
1
0
0
1
1
0
2
0
1
0
2
1
1
1
0
1
1
2
1
2
1
1
2
1
1
2
0
1
2
0
0
0
2
1
0
1
2
0
1
2
1
1
1
1
0
2
0
0
1
1
2
1
2
0
1
1
2
0
0
1
2
1
2
1
1
0
1
1
1
2
0
1
1
1
1
1
0
2
0
1
2
2
0
0
1
1
1
3
1
1
2
1
1
2
1
1
0
1
1
0
0
1
1
1
1
0
1
1
1
0
0
1
1
1
0
0
1
0
1
0
0
0
0
0
2
1
2
2
1
2
0
1
0
0
2
0
0
0
2
2
0
2
1
0
1
1
2
0
1
1
0
0
1
0
0
0
1
1
0
0
1
2
2
1
0
2
2
1
2
0
0
1
1
3
2
0
1
1
0
0
1
1
1
1
0
1
2
0
1
0
2
1
1
0
0
2
0
1
1
1
2
1
0
1
1
1
1
0
1
1
1
2
0
2
0
0
1
1
1
2
2
0
1
1
0
0
1
1
0
0
0
2
1
1
2
0
1
0
1
4
0
1
1
1
1
1
2
1
1
1
0
2
1
0
0
1
2
0
0
1
1
1
0
1
1
1
1
1
2
1
0
0
0
1
1
1
0
1
1
0
1
2
1
0
1
0
1
2
0
1
1
0
1
1
1
0
1
1
0
0
1
0
2
0
0
1
2
2
2
1
1
0
1
0
1
0
0
0
1
1
0
0
0
2
1
0
2
2
2
1
0
0
0
1
1
1
1
1
1
1
0
0
1
0
0
1
0
1
0
1
0
4
0
2
1
0
0
1
1
1
1
0
3
0
3
0
1
0
1
1
1
0
1
0
2
0
0
1
2
1
1
2
1
1
1
1
0
1
0
0
2
1
1
1
2
1
1
0
1
0
1
1
1
3
1
2
0
1
1
0
0
1
0
2
1
1
1
1
1
2
1
1
0
1
1
1
2
1
0
0
1
0
2
0
2
1
0
1
1
0
0
0
1
1
2
2
2
1
0
0
1
0
1
2
0
2
2
1
1
0
2
1
2
0
1
1
0
0
1
1
0
1
2
1
1
0
1
2
0
0
1
3
2
2
1
1
2
0
0
0
1
1
0
0
1
2
0
1
0
2
1
0
2
0
2
2
1
0
1
1
1
2
0
0
0
1
0
1
1
1
0
2
0
2
0
1
0
0
3
2
0
1
1
1
0
2
2
0
0
1
1
0
2
4
0
1
1
1
0
1
0
1
0
0
2
2
2
0
1
0
2
2
1
2
0
2
1
1
2
2
1
0
1
1
0
0
3
1
0
0
2
0
2
1
2
0
2
1
2
2
2
1
0
1
2
1
1
1
0
1
1
1
4
0
1
1
0
2
2
1
0
1
0
1
1
0
2
1
2
0
0
1
2
2
0
2
0
2
1
1
1
0
2
2
1
2
0
0
1
5
1
0
1
1
1
0
1
1
1
0
1
1
1
0
0
1
2
1
2
0
1
1
1
1
1
1
2
1
1
2
2
0
0
1
1
0
0
1
1
0
4
1
2
1
1
2
2
2
1
0
2
0
0
2
1
1
1
1
2
2
2
0
2
2
0
1
1
0
1
2
1
0
0
1
2
0
0
1
1
2
1
2
2
1
2
1
1
0
1
0
0
1
2
1
1
1
0
1
0
1
1
2
1
1
0
0
1
1
2
1
1
1
0
2
2
2
0
2
1
2
2
2
0
2
0
0
0
1
0
1
2
0
2
2
1
1
1
0
2
0
0
0
1
1
1
1
1
0
0
1
2
0
2
0
1
0
0
0
0
0
1
0
0
0
2
1
1
2
1
0
2
0
2
1
2
0
0
2
0
1
0
0
0
2
0
0
1
0
2
1
3
2
1
0
1
2
1
0
0
2
0
1
1
1
1
1
0
1
0
0
0
0
1
0
1
0
0
2
0
0
1
0
2
1
0
0
2
2
1
1
2
0
1
1
0
1
0
3
1
1
0
1
0
1
2
1
1
1
1
1
2
0
1
0
4
0
2
0
1
1
2
0
1
1
0
0
2
1
1
1
1
1
1
1
1
3
1
0
1
1
1
0
2
0
0
0
1
1
1
0
0
0
0
1
2
0
1
1
1
0
0
0
1
2
1
0
0
0
1
2
0
0
1
1
2
0
0
2
1
1
0
1
0
0
0
0
2
0
1
0
1
1
1
0
1
1
2
0
1
1
1
0
1
0
1
0
2
1
0
1
0
0
0
0
0
0
1
1
0
1
0
1
1
1
0
1
1
0
1
2
0
0
0
0
1
1
0
0
2
2
3
0
0
1
1
1
0
1
0
0
2
2
0
2
1
1
0
2
1
1
2
2
0
2
2
2
0
2
1
3
0
0
0
2
1
0
2
1
1
0
1
0
1
1
2
2
1
1
0
0
0
1
1
0
1
1
0
1
0
2
1
0
1
1
1
2
1
2
0
1
1
0
0
1
0
1
1
1
1
1
4
0
2
1
0
1
2
1
2
0
1
1
1
1
0
2
1
1
1
0
1
1
1
1
1
0
1
2
2
0
0
2
3
0
0
1
1
2
1
1
2
0
1
1
0
0
0
1
2
0
2
1
0
1
0
0
1
0
0
2
0
2
0
2
0
0
2
0
2
0
0
0
2
0
1
0
1
0
0
0
1
0
0
2
0
0
0
1
1
1
1
2
1
1
0
2
0
1
2
1
1
1
1
1
2
0
1
2
2
1
1
1
0
1
1
1
1
1
2
0
1
0
2
1
0
2
2
1
1
1
0
0
0
2
0
2
0
1
0
0
0
1
0
2
2
1
0
1
1
0
1
2
1
1
2
1
1
2
0
2
0
1
1
0
1
0
2
1
2
1
0
4
1
2
0
0
1
0
0
0
1
0
0
1
2
1
2
1
1
0
1
1
2
1
0
1
1
1
1
1
2
0
1
0
0
0
1
1
0
2
0
1
1
1
2
1
0
0
0
2
1
1
1
1
0
2
2
1
0
1
0
1
0
1
2
1
1
1
0
2
2
0
1
1
1
1
1
0
0
1
2
0
1
0
2
1
0
0
2
2
0
1
0
1
0
1
0
1
0
0
1
0
1
1
0
2
1
0
1
0
0
1
0
1
2
2
0
0
2
1
1
0
0
0
2
1
0
0
1
1
1
1
0
1
0
1
0
2
0
1
3
2
1
1
0
1
0
0
1
0
1
1
0
0
1
2
0
0
1
1
1
0
0
0
2
0
2
1
1
1
1
0
0
1
0
1
1
1
2
1
1
0
2
1
0
2
1
1
1
0
5
1
2
1
3
2
1
3
1
2
1
1
2
1
1
1
0
1
1
1
0
1
1
1
0
2
2
2
0
0
2
1
2
2
1
3
1
2
1
1
2
2
0
0
0
2
1
2
0
1
0
2
2
1
2
1
1
0
0
2
1
1
4
0
1
2
2
2
0
1
3
2
2
0
1
2
1
0
0
0
1
1
2
1
0
1
2
1
1
1
0
0
0
1
0
0
1
1
0
1
0
2
1
1
1
2
1
1
1
1
1
0
2
1
0
0
1
0
0
1
1
2
2
2
0
1
1
1
1
1
1
1
1
1
0
2
0
1
1
1
1
1
2
1
2
1
2
2
0
1
0
1
0
1
2
0
0
0
1
0
2
2
0
2
1
0
1
1
0
2
0
1
2
0
0
0
1
1
0
1
0
2
0
1
0
1
1
1
2
0
1
0
3
2
1
5
0
2
0
0
1
1
0
0
1
1
1
1
0
1
2
0
2
1
1
2
1
1
0
1
2
1
1
2
1
1
0
0
1
1
1
1
1
0
2
1
1
2
0
2
0
0
2
0
1
1
0
0
1
0
0
2
1
0
1
0
1
0
2
1
0
1
2
1
0
0
0
0
1
2
2
2
1
0
2
2
2
1
0
2
2
1
1
1
0
0
0
1
0
1
1
1
1
1
3
0
0
0
0
0
0
2
1
1
0
1
0
0
0
1
2
0
0
1
2
1
0
0
0
0
3
2
1
0
0
2
2
1
1
1
0
3
0
2
1
1
1
1
1
2
2
0
0
2
0
1
2
1
1
1
0
1
1
1
0
2
1
1
2
1
0
2
2
0
0
2
1
0
2
0
1
1
1
0
1
0
0
1
0
1
2
1
1
0
1
0
1
0
1
1
1
1
3
0
0
1
1
1
0
0
1
1
1
0
1
1
2
1
2
1
0
1
0
2
0
1
0
1
1
1
2
1
0
2
1
1
0
0
0
1
0
2
0
2
0
2
2
2
0
0
1
1
2
3
1
0
1
2
0
1
1
0
2
1
2
0
0
1
0
0
1
2
2
2
0
1
0
0
0
1
1
0
2
0
0
0
0
2
1
2
1
0
1
1
0
1
0
0
1
2
1
0
2
0
0
1
0
1
1
1
1
2
1
2
0
1
1
0
1
3
0
2
3
2
0
1
2
0
0
2
2
0
1
2
1
0
0
1
0
0
1
3
0
1
1
1
0
2
1
0
2
1
1
2
1
1
0
0
1
1
1
0
1
1
0
0
0
1
0
0
2
0
1
0
1
1
0
0
1
0
1
0
1
0
0
0
0
0
1
1
0
2
2
2
1
0
0
2
2
1
0
0
0
2
2
1
1
3
1
1
0
1
1
2
1
0
1
1
1
1
1
0
1
0
2
0
1
1
0
0
1
1
1
1
1
1
2
0
0
1
1
0
1
1
0
0
2
0
1
2
1
1
0
1
1
1
1
0
0
1
1
1
1
3
1
3
0
2
1
1
1
0
2
1
1
1
1
2
0
1
0
0
2
0
0
2
2
1
0
1
1
0
2
2
2
0
1
0
1
1
1
0
0
1
2
2
1
1
2
6
1
2
2
2
2
2
1
0
0
1
1
1
1
1
1
0
0
0
1
2
2
0
0
2
1
2
1
0
2
0
0
1
1
0
2
2
0
1
1
2
0
0
3
1
0
0
0
1
2
0
0
0
0
0
0
0
0
2
1
1
2
1
1
2
0
1
0
2
0
0
0
2
1
1
0
1
0
1
2
4
2
1
2
1
1
1
0
0
2
1
1
2
0
1
2
2
0
0
0
0
3
2
2
1
2
0
2
1
0
1
2
0
1
0
1
1
0
1
0
0
1
2
3
1
1
1
2
2
1
1
2
0
1
1
1
2
1
1
0
1
0
2
1
1
1
1
1
1
1
0
0
1
1
2
0
1
0
0
2
1
0
1
0
0
1
0
0
1
0
1
0
2
1
1
3
2
0
1
2
2
0
1
0
1
0
1
2
0
0
1
0
2
1
0
1
1
1
1
1
2
0
2
1
0
4
1
0
1
1
1
1
2
1
2
1
2
1
1
1
0
2
0
2
0
2
2
2
1
2
2
1
0
1
2
1
0
0
1
0
0
0
0
0
1
1
1
1
2
1
2
0
1
0
1
2
2
2
7
2
1
1
2
1
2
1
1
1
2
1
2
0
0
2
1
1
2
1
0
0
0
1
0
2
2
2
2
0
4
1
0
1
2
2
2
0
1
2
1
1
1
2
1
2
0
0
0
0
2
2
1
0
0
0
1
2
2
0
2
0
2
0
0
2
1
1
1
1
2
2
1
0
0
0
2
2
0
1
3
1
4
2
0
1
0
1
0
3
0
0
1
2
0
1
1
1
0
1
1
0
1
2
0
0
1
1
2
2
0
1
1
1
2
0
1
2
0
1
2
2
2
1
0
1
1
1
1
2
1
0
1
0
0
1
2
0
0
2
2
1
0
1
2
2
1
1
0
1
0
2
0
5
2
0
1
1
1
0
2
0
0
2
2
2
0
1
2
1
1
1
1
0
1
1
1
0
0
2
0
0
0
0
1
2
0
2
1
2
1
1
0
2
0
0
0
0
3
2
1
1
0
0
0
1
1
0
0
0
1
1
0
2
2
2
1
1
2
1
2
1
1
2
10
1
1
1
2
1
1
1
1
0
3
1
2
2
2
2
1
2
0
1
0
1
0
0
1
2
1
0
2
1
0
2
2
1
2
0
1
1
0
0
2
0
2
0
1
2
2
2
1
0
0
1
1
2
1
1
2
1
1
1
1
1
2
2
0
1
0
2
2
1
1
1
0
2
1
1
0
1
1
1
0
1
0
2
1
1
1
0
0
1
0
1
0
1
1
2
1
1
0
0
1
2
1
2
0
0
2
0
0
1
1
0
0
1
0
0
1
1
0
1
1
0
0
0
0
1
2
1
2
2
1
0
2
1
1
1
0
2
0
1
1
0
1
1
0
3
0
2
0
2
1
1
2
0
1
2
1
1
2
1
1
0
1
1
0
2
0
0
1
2
1
2
2
0
2
3
2
0
2
0
0
0
0
2
0
0
0
1
1
1
1
2
2
1
2
1
0
1
1
1
0
1
1
1
1
1
2
1
0
1
0
0
1
0
0
2
1
2
0
2
1
1
1
1
1
1
1
1
1
0
0
1
0
1
2
1
0
0
1
2
1
1
2
1
1
0
1
1
0
1
0
0
0
0
2
1
0
1
0
1
0
1
2
1
1
1
0
1
0
1
2
1
1
1
2
0
2
0
2
2
2
2
0
0
1
1
1
2
2
1
2
1
2
1
1
2
1
1
1
1
0
1
0
2
1
2
1
1
1
0
0
1
2
1
1
1
1
2
1
1
1
1
1
1
0
0
1
2
0
1
2
2
1
0
1
1
2
1
2
1
0
1
0
3
2
1
0
2
2
1
0
0
0
1
1
0
1
1
2
0
0
1
0
1
1
3
1
2
1
2
1
2
1
0
1
0
1
0
1
0
1
1
1
2
2
2
1
1
0
1
2
0
1
1
0
1
1
1
1
2
1
0
0
3
1
0
0
1
0
1
2
0
0
2
1
0
2
1
0
1
0
0
1
0
0
1
0
2
0
2
0
1
0
1
0
1
0
2
1
1
1
2
0
0
0
3
2
0
0
2
1
2
2
1
1
0
1
1
0
0
1
1
1
2
0
1
0
1
1
0
2
0
1
1
0
0
0
2
1
0
1
1
1
0
0
1
1
2
1
2
1
1
0
0
0
0
0
2
1
1
1
0
1
2
0
2
0
0
0
0
1
1
1
0
1
2
2
2
2
1
0
1
2
1
0
1
0
1
2
0
1
1
0
0
1
2
1
2
0
1
1
0
1
2
0
2
2
0
1
0
1
0
0
1
1
1
2
0
1
0
1
1
1
2
0
1
1
1
0
0
2
0
2
2
2
0
1
2
1
0
1
1
2
0
0
0
1
1
0
1
1
1
0
1
2
1
1
1
1
0
1
1
0
0
0
0
0
1
1
0
0
1
2
0
0
1
1
0
0
0
1
1
2
2
1
1
2
0
1
1
2
2
2
3
1
2
1
2
1
1
1
1
1
2
2
0
1
0
2
0
1
1
1
2
1
0
1
1
0
1
3
1
2
0
0
2
1
1
2
1
1
2
1
2
0
2
2
1
0
0
2
2
0
0
2
1
1
0
2
1
1
0
0
2
5
0
1
1
1
1
1
1
2
1
0
1
2
1
1
2
1
1
1
1
1
2
0
1
0
1
1
3
1
1
0
1
2
0
1
0
0
1
1
0
2
1
1
2
0
2
2
0
0
0
2
1
0
1
0
0
1
2
1
1
0
2
1
0
2
1
0
1
2
0
1
0
2
2
1
2
1
2
2
2
0
1
1
1
1
1
0
1
0
0
1
0
0
2
1
1
1
1
2
1
3
1
1
1
1
2
0
0
3
0
2
0
0
0
1
1
1
0
2
1
0
1
0
2
1
1
0
0
1
1
0
1
0
0
2
1
0
1
0
1
1
0
0
1
0
1
2
1
0
1
0
0
0
1
0
0
1
1
0
0
1
1
0
1
1
1
2
2
1
0
0
0
2
2
2
1
0
0
1
0
2
0
1
2
2
0
2
1
0
0
1
0
0
0
1
1
2
2
1
2
0
1
1
0
0
1
0
0
2
1
1
1
0
1
2
1
1
1
1
0
0
1
1
0
3
2
0
1
1
0
0
0
1
2
0
0
1
1
2
1
1
1
1
0
0
2
1
1
2
1
1
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
1
2
1
0
1
0
1
1
1
1
1
0
1
2
1
0
1
2
0
3
0
1
0
2
1
1
1
2
0
1
2
2
0
1
1
1
2
0
1
0
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
1
1
0
1
1
0
2
1
1
1
1
1
0
0
1
1
1
1
1
0
1
0
2
2
0
1
2
1
2
0
1
1
0
1
2
2
1
1
1
0
0
0
0
0
0
2
2
0
1
0
1
0
1
2
0
0
1
0
0
1
0
0
0
1
1
1
1
2
0
1
0
1
2
0
1
2
0
0
2
2
0
3
2
0
2
1
2
2
1
1
0
1
1
0
1
0
2
2
1
0
0
1
2
1
2
0
1
1
1
0
0
2
1
1
0
2
2
2
1
1
1
0
1
2
1
0
1
2
0
0
1
0
1
1
1
1
0
2
1
0
0
0
1
1
1
1
2
0
1
0
1
1
0
0
1
0
2
0
2
2
1
0
0
1
0
1
1
1
0
2
0
0
0
2
0
1
0
1
1
0
0
2
1
1
0
2
2
0
0
1
1
1
2
0
1
0
2
0
2
1
1
1
0
1
0
0
0
1
1
1
0
1
2
0
0
1
2
0
0
1
2
1
1
3
2
1
2
1
1
3
1
1
1
0
1
2
1
1
1
0
2
1
1
1
0
0
0
0
0
2
0
1
1
1
0
1
2
1
0
1
2
1
1
0
0
1
1
0
2
1
0
0
1
2
0
1
2
1
1
0
1
1
1
0
1
2
1
0
0
0
1
2
0
0
0
0
2
0
0
7
1
0
0
0
1
0
2
2
0
0
0
1
0
1
0
0
2
0
0
1
1
1
1
1
2
2
0
0
2
1
0
2
1
1
0
1
1
2
0
0
1
0
1
2
0
0
1
1
2
2
1
0
1
0
1
1
1
2
2
1
1
2
2
1
1
0
1
1
0
0
2
0
1
0
1
2
0
0
1
1
0
0
2
1
1
1
6
0
1
1
1
1
0
2
0
2
0
0
1
2
1
3
0
1
1
0
0
1
1
2
2
0
0
1
0
0
1
1
1
0
1
1
1
1
2
0
1
0
0
1
0
2
0
0
1
1
2
0
2
0
0
1
2
2
0
1
0
1
1
1
2
0
2
1
0
0
0
1
1
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
2
1
2
1
2
0
0
1
1
1
0
0
1
1
1
0
1
1
2
1
2
0
0
2
2
1
0
2
0
0
0
2
0
0
2
1
0
1
1
1
0
0
1
1
0
0
1
0
0
1
1
0
0
1
0
1
1
1
1
1
0
1
0
1
1
0
3
0
0
0
1
0
0
0
0
0
0
0
0
1
1
2
0
0
0
1
0
1
2
2
0
0
0
1
0
2
0
2
0
1
0
1
0
2
0
1
0
0
0
1
0
1
1
1
1
0
0
1
0
1
0
3
0
1
3
1
2
2
0
0
2
1
0
0
2
1
1
0
1
0
1
1
1
2
0
1
1
1
0
1
0
2
0
0
1
1
0
0
1
1
0
0
2
1
0
0
1
0
2
1
0
2
1
0
1
0
2
1
0
1
1
2
0
0
1
1
1
0
1
2
0
0
0
0
0
0
2
2
1
0
1
0
1
2
1
0
1
1
1
0
0
1
1
1
1
0
1
0
2
1
0
1
2
2
0
2
0
2
0
1
0
1
0
0
0
1
1
2
1
2
2
1
1
1
1
1
0
1
2
0
1
1
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
1
0
2
1
1
0
1
1
0
2
0
1
1
2
1
2
1
1
1
1
1
1
1
1
2
1
2
2
0
1
1
0
0
1
2
1
0
1
1
2
2
0
2
2
2
0
0
1
0
2
1
1
1
2
2
0
2
0
1
1
0
1
2
0
3
0
0
1
1
2
2
1
1
0
2
2
0
1
2
1
2
1
1
2
4
1
0
2
0
1
2
1
0
0
2
2
1
1
1
1
0
0
2
1
0
1
0
1
1
2
1
1
1
1
0
0
1
1
0
1
1
1
1
0
1
1
0
1
0
1
0
1
0
1
1
1
2
0
1
2
0
0
0
0
1
3
0
0
1
1
1
1
0
1
2
1
2
1
0
2
0
1
0
1
0
0
1
1
1
0
1
1
2
0
1
0
3
1
1
1
0
1
0
0
0
1
0
1
1
1
2
2
2
1
1
2
1
0
0
1
1
0
2
0
0
0
1
2
2
0
1
0
0
0
1
0
0
2
1
2
2
0
2
2
2
3
3
1
2
0
0
0
2
1
1
1
1
0
2
1
0
1
2
1
2
2
2
1
0
1
1
1
1
1
0
2
0
1
0
2
1
1
1
1
0
0
1
0
0
1
1
1
2
1
1
1
2
1
1
1
1
1
2
0
2
0
0
2
1
2
0
0
2
1
2
0
1
2
1
0
3
0
0
1
1
0
1
0
0
2
0
3
1
0
1
1
1
1
1
1
0
0
0
0
1
1
2
2
2
1
1
0
1
2
2
1
1
2
1
1
1
1
2
0
2
1
1
0
0
2
0
1
1
1
0
1
1
1
2
1
2
2
1
2
0
1
2
0
1
1
1
2
1
0
0
0
0
1
2
1
2
2
1
2
2
1
1
1
2
1
2
1
0
0
1
1
1
0
0
0
0
0
2
1
0
0
0
1
0
0
0
2
3
2
2
0
1
0
0
2
0
2
2
1
0
2
0
1
2
0
1
2
0
0
1
0
1
2
1
0
0
1
0
1
2
1
0
1
1
2
1
0
0
1
1
1
0
1
0
2
1
1
1
2
0
0
1
2
0
0
0
1
0
0
1
1
1
1
1
2
0
2
0
1
1
0
1
1
0
1
1
2
1
0
1
0
1
2
1
0
0
1
1
2
1
0
2
0
1
2
2
1
1
1
0
2
2
0
2
2
2
2
0
1
2
1
1
2
2
0
1
0
1
1
1
1
1
2
1
2
0
0
0
2
0
1
1
1
1
0
1
1
0
2
1
0
0
2
0
1
1
1
0
1
1
2
1
1
2
0
2
0
2
2
0
1
2
1
1
0
0
1
0
0
0
1
3
1
0
1
1
3
0
1
1
1
1
1
2
0
1
2
1
1
0
1
1
2
2
1
2
0
2
1
0
1
1
3
0
0
1
2
1
0
1
0
0
2
1
1
2
1
1
0
2
1
2
2
0
2
2
1
0
0
0
0
1
2
0
2
1
0
0
1
0
0
1
0
0
0
2
2
0
1
2
2
2
1
1
1
0
1
2
0
1
1
0
1
0
2
1
1
0
1
0
1
2
1
2
1
0
1
0
1
1
2
0
2
2
1
0
1
1
2
1
1
3
1
2
2
2
1
1
0
1
0
1
0
1
0
0
0
1
0
1
0
0
1
0
1
1
0
1
0
2
1
0
0
1
2
2
1
0
2
0
1
0
0
2
1
3
0
1
0
0
1
1
0
0
2
2
1
1
2
2
2
2
0
1
0
0
0
0
1
2
1
0
2
1
0
0
1
0
1
0
1
1
0
0
2
2
2
1
0
1
2
0
1
1
2
1
1
2
2
0
3
1
1
2
1
1
1
0
2
0
1
1
1
1
2
0
2
2
1
0
0
0
0
2
2
1
0
0
1
0
2
0
1
0
1
1
1
0
2
0
2
1
0
2
1
0
0
0
1
1
0
1
1
0
0
2
1
0
0
1
1
0
2
2
1
1
1
1
1
1
2
0
0
1
2
0
0
0
0
1
2
0
0
0
1
0
1
0
0
0
0
2
2
1
1
2
0
2
4
0
1
1
0
0
0
0
1
1
1
0
2
0
1
0
1
0
1
1
1
1
1
0
1
1
2
2
1
2
0
0
1
0
2
2
1
1
1
1
0
0
2
1
2
1
1
0
1
0
1
0
1
1
1
0
0
1
0
2
2
1
1
2
1
0
2
1
1
2
1
0
0
1
0
0
2
1
2
4
0
1
1
1
0
3
2
1
1
1
0
0
1
1
2
1
0
0
0
1
1
1
1
1
0
1
1
0
1
0
2
0
1
0
1
0
1
1
2
1
1
2
1
0
1
0
0
1
0
1
0
2
1
2
1
0
0
0
1
1
0
1
1
1
1
1
0
2
0
2
0
0
0
1
1
0
1
0
0
1
2
0
0
1
2
0
0
0
0
1
0
2
0
0
1
1
0
1
0
2
0
0
0
1
1
2
1
1
0
0
0
2
0
0
0
1
2
2
2
1
0
0
0
3
0
1
1
1
0
1
0
0
0
1
1
0
1
2
0
1
1
1
1
2
0
2
1
0
0
1
1
1
1
1
1
2
1
2
0
2
1
1
2
0
1
0
2
2
1
0
1
0
1
2
0
0
2
1
1
1
3
1
2
0
1
1
0
1
0
0
0
1
2
1
2
1
0
0
1
1
0
0
1
2
2
2
2
1
0
1
0
0
1
1
1
0
1
2
1
1
1
1
1
1
2
0
0
2
0
2
0
1
0
0
0
2
1
0
2
1
0
0
2
1
0
1
0
1
2
1
0
1
0
0
0
1
1
0
2
2
0
0
0
0
0
1
1
2
0
1
1
1
0
1
2
1
1
1
1
0
2
2
0
1
1
1
2
0
1
1
0
1
1
4
0
1
0
0
0
1
0
0
0
1
2
1
2
2
1
1
0
1
1
0
0
0
1
1
4
1
1
0
1
1
0
1
0
1
2
1
0
2
1
0
2
1
1
2
0
2
1
1
0
0
1
1
0
2
0
0
1
1
0
0
0
2
1
0
1
0
1
1
0
0
2
2
1
1
0
2
2
3
0
1
2
0
2
0
1
1
3
2
1
0
2
1
1
0
0
2
0
1
0
2
0
2
2
0
1
1
2
0
0
1
0
0
1
0
2
1
2
1
2
1
1
0
2
1
2
0
1
3
1
1
1
2
0
1
0
0
1
0
0
1
2
1
1
1
1
0
0
0
1
1
0
2
1
1
1
1
1
0
2
1
0
1
0
0
1
0
0
1
1
0
1
1
0
0
1
1
2
1
1
0
1
0
2
0
3
1
1
0
0
0
0
2
0
1
1
1
0
0
1
0
2
1
2
1
1
1
1
2
1
0
1
2
2
0
1
0
2
2
2
0
1
1
1
1
2
2
1
0
0
1
1
1
1
1
0
1
0
1
0
2
1
2
2
0
1
1
1
2
0
0
1
0
0
1
1
1
2
0
1
1
0
0
2
1
1
1
0
1
0
1
0
2
0
0
0
1
0
2
0
1
1
2
0
1
2
1
2
2
1
1
0
2
2
1
0
2
2
2
0
1
0
1
4
2
0
2
0
1
1
1
1
1
0
0
0
2
1
1
1
0
0
0
0
0
2
1
0
1
1
0
1
1
0
1
2
3
2
1
0
1
0
2
0
0
1
0
0
1
1
2
1
1
0
1
0
2
0
1
2
0
1
1
0
0
2
1
2
1
0
1
0
0
0
1
1
1
0
0
0
1
2
0
1
0
1
2
0
2
0
0
1
1
1
4
1
0
0
0
0
2
1
2
2
2
0
1
0
2
0
0
2
0
0
1
0
2
1
0
2
0
0
1
0
1
1
1
1
0
1
1
1
2
1
1
3
0
1
1
0
1
1
0
1
0
2
0
1
0
1
1
2
1
1
0
0
1
2
2
1
0
1
0
0
1
1
0
0
1
1
1
0
0
1
2
0
1
2
1
0
1
1
0
0
1
1
0
2
1
0
0
1
1
0
0
2
1
0
1
0
1
2
0
1
2
0
1
2
1
1
3
0
2
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
2
2
0
1
2
1
1
0
0
1
2
2
2
1
0
0
0
1
1
0
0
1
0
1
1
0
2
1
2
0
2
1
0
1
1
0
0
1
2
0
2
2
2
0
1
0
0
1
1
0
1
1
0
2
2
0
1
1
2
0
0
2
0
0
0
1
0
1
0
0
2
0
2
2
1
2
1
1
1
0
2
1
1
0
1
0
2
1
1
0
2
0
0
2
2
2
0
2
1
1
2
1
1
1
1
1
2
1
0
0
1
0
0
1
2
1
1
1
0
1
1
1
2
0
0
0
1
0
1
2
1
1
1
1
0
1
1
2
0
2
1
1
0
1
1
1
0
0
0
0
1
1
1
1
0
1
2
1
2
1
1
0
0
0
3
2
1
1
1
1
0
0
2
2
2
0
1
0
0
1
0
0
0
2
2
3
1
0
0
0
1
0
0
1
0
1
1
0
2
2
1
1
0
1
0
1
2
0
1
0
1
1
1
2
1
0
0
1
0
0
0
0
2
1
2
1
1
0
0
2
1
0
0
1
0
1
1
2
1
2
1
2
1
1
1
1
1
0
0
1
2
2
1
1
2
0
1
2
0
0
2
0
0
1
0
2
1
1
2
0
2
0
0
2
0
0
1
2
1
0
1
2
2
2
2
1
0
1
0
0
0
0
1
0
1
2
0
0
1
1
1
1
2
0
1
1
2
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
2
0
1
1
1
0
0
2
0
2
0
1
1
1
2
1
1
0
2
1
0
3
2
1
1
1
2
1
1
2
0
1
1
1
1
1
0
2
1
1
1
0
1
0
0
1
2
0
2
2
1
1
0
1
1
2
2
2
1
1
11
1
0
0
1
2
1
1
2
1
2
2
1
1
1
0
1
1
1
0
2
1
0
0
1
1
1
2
2
1
2
0
2
2
0
1
2
0
2
1
1
1
1
0
0
0
0
2
0
1
1
1
2
0
0
1
1
1
2
1
1
0
1
2
1
0
1
1
0
0
2
1
2
0
1
1
0
0
1
0
1
1
2
0
0
4
1
2
2
0
1
2
1
0
1
0
0
2
2
0
2
0
0
1
0
1
1
1
2
1
2
1
1
2
0
0
1
2
1
0
2
0
2
2
0
2
0
1
1
0
1
1
0
1
2
0
1
1
0
1
1
1
0
0
0
2
2
1
3
2
1
1
1
2
2
0
2
1
0
1
0
2
2
1
1
2
2
0
1
1
0
1
0
1
1
1
3
1
1
3
0
1
0
2
1
1
2
1
2
0
1
2
4
1
0
2
0
1
1
2
0
0
1
1
0
1
0
1
1
2
1
1
2
1
0
0
2
1
0
1
1
1
2
0
0
2
1
1
2
1
1
1
2
1
2
0
1
0
2
0
2
2
1
2
0
0
0
0
2
2
0
1
2
0
8
1
0
2
2
2
1
0
0
1
0
2
1
0
1
1
1
0
1
2
2
1
1
1
1
0
2
0
0
3
0
2
1
2
0
1
1
2
1
1
1
2
0
1
1
1
1
0
0
2
1
0
0
1
0
2
0
1
0
1
2
0
0
0
0
4
1
3
0
1
0
0
0
1
2
0
2
0
1
1
0
1
1
2
0
1
2
0
1
1
0
0
1
0
1
0
0
1
1
1
2
0
1
1
1
2
1
1
1
1
0
1
1
2
0
0
1
0
1
1
2
1
0
0
1
3
0
0
1
0
1
1
1
0
0
2
2
1
0
1
1
1
3
1
1
1
0
1
0
2
0
1
1
0
1
2
1
1
2
2
1
0
1
2
0
0
0
2
0
0
0
0
0
0
2
2
0
0
2
2
1
2
2
0
0
1
1
0
0
0
1
0
0
1
1
0
1
1
0
3
0
0
1
2
0
1
0
0
2
1
1
0
1
0
2
0
1
0
2
1
1
1
1
0
0
2
0
2
0
1
1
2
2
1
1
2
0
2
0
0
1
0
2
0
0
2
0
1
2
1
1
1
1
2
1
1
0
1
0
0
2
0
2
2
1
2
1
0
2
0
1
2
3
2
0
0
0
0
2
1
1
0
2
2
1
0
0
1
0
3
0
0
2
0
0
0
0
2
2
1
1
0
1
2
1
1
2
2
2
1
1
1
2
2
2
1
0
0
0
0
1
0
0
0
0
0
1
0
0
2
2
1
2
0
2
2
0
2
0
1
0
0
0
1
0
0
0
0
0
2
1
1
0
0
2
1
0
0
1
0
0
2
1
1
1
0
0
1
1
0
0
1
1
2
1
0
0
0
1
2
1
2
0
1
0
0
1
1
0
2
0
1
1
1
1
1
1
1
1
0
1
0
0
1
1
0
1
1
0
1
0
2
1
0
1
1
1
1
2
0
3
2
1
2
1
1
0
1
0
0
2
2
0
0
0
1
2
0
0
1
0
1
0
1
1
1
0
1
1
3
1
0
2
2
0
0
0
1
0
1
1
1
0
1
2
0
1
1
3
0
0
1
0
2
3
0
1
1
0
0
0
0
0
2
1
2
2
1
1
3
2
1
1
1
1
1
0
0
0
1
0
1
1
0
1
1
1
1
1
2
0
1
2
2
1
0
1
1
1
0
2
1
1
0
2
1
2
1
0
0
2
0
0
0
2
2
0
2
2
0
1
2
2
2
1
0
1
1
1
1
0
2
0
0
1
0
1
2
2
1
1
0
0
1
2
0
2
1
0
0
3
2
0
1
0
2
0
2
1
0
2
1
3
1
0
1
0
1
2
0
2
0
1
1
0
2
1
0
2
1
1
1
0
0
0
0
0
1
0
0
2
0
1
0
0
1
0
1
1
1
1
1
0
1
1
1
1
1
2
0
0
0
0
2
0
1
0
0
0
4
0
0
2
2
1
1
1
1
0
1
0
2
2
1
1
1
0
1
1
0
2
1
1
1
1
2
1
2
2
0
2
2
1
2
0
2
0
0
1
0
2
1
1
1
2
1
0
1
2
1
1
0
1
0
0
0
1
0
0
1
1
0
1
2
0
1
0
0
1
1
0
2
2
0
2
1
0
0
0
1
0
2
1
0
0
1
1
2
1
2
1
2
1
0
0
1
0
2
2
1
1
1
0
1
0
0
2
0
0
0
2
0
0
1
0
1
0
1
1
1
1
0
0
2
0
0
0
2
2
1
1
1
1
0
0
0
0
1
1
1
0
1
0
2
2
0
2
1
2
0
2
1
1
0
2
2
1
2
1
0
0
0
2
1
1
1
2
2
0
0
1
0
2
0
1
0
1
0
0
0
2
0
1
3
2
2
0
1
1
0
1
1
1
1
1
2
0
0
1
0
0
1
1
2
2
1
0
1
1
0
0
2
4
0
2
1
1
1
0
0
1
1
2
0
1
0
1
1
2
0
2
0
1
3
0
2
0
0
2
1
0
2
0
2
2
2
0
0
1
0
0
1
1
1
1
1
0
1
2
2
0
1
1
2
1
0
2
1
0
1
1
1
0
0
0
2
1
0
0
2
1
2
0
2
0
0
2
1
1
0
2
1
0
1
1
0
4
0
0
2
2
0
1
2
2
2
1
1
1
0
0
1
1
1
2
2
0
0
2
1
1
0
1
1
0
0
1
0
1
2
0
1
1
1
0
0
2
2
1
2
0
1
0
1
0
0
1
2
1
0
3
1
0
0
2
0
2
1
2
1
1
0
2
3
0
1
1
0
1
1
0
0
0
1
1
1
1
2
0
0
0
1
0
0
0
0
0
2
0
0
0
1
2
0
0
2
0
2
0
1
2
0
0
1
0
0
1
0
2
0
0
0
0
1
1
0
0
0
0
0
1
0
2
0
0
0
0
1
1
2
1
0
0
1
1
0
1
0
0
3
0
1
1
1
0
0
1
1
2
0
0
0
1
1
0
0
0
2
1
1
2
2
0
1
2
0
0
2
1
1
2
0
1
0
1
0
0
2
1
1
1
0
1
0
2
0
1
1
0
1
2
0
1
0
1
1
0
0
2
2
0
0
1
1
0
2
0
2
0
1
2
1
0
1
1
2
2
0
2
1
0
3
3
0
0
2
2
2
0
1
2
1
1
2
0
0
1
0
2
1
2
0
0
1
1
2
0
1
2
2
4
2
3
1
1
0
1
0
2
0
2
1
3
2
1
0
1
1
0
0
0
1
0
1
4
0
2
1
0
1
3
0
2
1
0
2
2
1
2
1
2
1
1
0
1
0
2
2
0
1
2
0
1
2
1
1
0
2
1
1
1
0
1
0
2
0
0
0
2
1
1
1
2
2
0
1
3
1
2
2
2
2
1
2
0
1
2
0
2
2
1
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
1
2
1
0
2
1
0
1
0
0
2
1
0
0
2
1
1
2
0
0
0
3
0
1
2
0
2
1
1
2
0
0
0
2
0
0
1
0
0
1
0
2
1
1
0
1
1
1
0
0
2
0
0
0
2
0
1
0
0
0
1
1
2
1
0
1
0
0
0
0
0
2
0
2
2
1
1
2
1
0
1
2
2
1
1
1
0
2
0
1
0
0
1
1
1
2
1
0
2
0
1
0
1
0
1
2
2
2
0
0
1
0
0
2
1
1
0
2
1
2
0
1
1
1
1
1
0
1
2
1
0
2
1
1
1
2
1
1
0
2
1
1
2
0
2
0
1
1
0
2
1
1
1
2
1
2
1
2
2
0
2
0
1
2
2
1
0
1
1
0
2
2
0
0
1
1
2
0
1
3
1
2
1
2
1
0
1
1
2
2
0
2
0
2
1
0
1
0
0
0
1
0
2
2
2
2
2
1
0
2
2
0
2
0
2
2
0
2
0
1
2
1
0
1
1
1
0
0
1
1
0
3
1
0
0
1
0
1
1
1
2
2
0
1
1
1
1
2
1
1
1
1
0
2
2
1
1
2
1
1
1
2
2
1
0
0
1
1
1
0
1
2
0
1
2
0
0
1
1
1
1
1
1
1
0
2
0
0
1
0
0
1
1
1
0
1
0
0
0
1
0
2
1
2
1
0
1
2
2
1
0
1
1
0
2
0
1
0
1
1
1
1
1
1
2
2
0
0
2
0
0
1
0
2
0
1
0
0
0
2
0
0
2
1
0
2
2
0
2
1
1
0
1
1
1
0
1
1
2
0
1
1
0
1
1
0
2
0
0
2
1
0
1
1
0
0
1
2
2
1
3
0
1
1
2
2
2
0
0
2
2
1
0
0
2
1
0
1
1
1
0
0
4
0
2
0
0
2
1
1
2
1
1
2
1
0
1
0
0
2
0
0
1
0
0
2
4
0
1
1
2
0
1
2
0
1
1
1
1
0
2
2
0
0
0
3
0
1
2
0
1
0
1
0
1
0
1
2
2
2
0
1
2
2
1
0
2
1
2
2
2
0
2
1
1
0
1
1
1
1
0
1
0
2
0
1
1
2
2
1
2
0
0
1
1
0
0
2
2
0
1
1
0
1
1
1
1
0
1
0
7
1
2
1
1
0
2
0
1
1
0
2
2
0
0
2
0
1
1
3
0
0
0
1
1
1
1
0
2
2
2
0
1
1
1
2
1
1
1
0
2
1
1
1
1
1
1
1
0
1
3
0
0
0
0
1
1
2
1
1
1
1
2
2
2
0
2
1
1
1
0
0
1
1
0
0
1
2
2
1
0
0
0
1
0
1
1
0
1
0
1
2
0
1
1
1
1
1
2
0
1
1
0
1
0
0
2
0
0
1
0
0
0
2
1
1
0
1
1
2
1
1
1
2
2
0
1
1
0
0
1
2
2
0
1
0
1
1
1
1
2
1
0
0
2
0
1
2
2
1
2
0
1
1
2
1
1
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
2
0
0
1
2
1
1
1
1
0
0
0
0
0
0
0
1
0
0
1
0
2
1
1
1
1
2
1
1
2
0
0
0
1
0
1
1
2
2
3
0
0
1
1
2
0
1
2
1
1
1
0
1
1
2
1
1
0
0
1
1
0
1
1
1
0
1
1
4
1
0
2
0
2
0
1
0
2
0
1
1
1
2
2
1
0
0
0
1
0
2
1
0
1
1
1
2
1
0
2
1
2
2
1
1
1
1
0
1
1
1
0
2
1
0
2
0
0
0
1
1
1
0
1
0
0
0
0
1
2
1
1
1
1
1
0
1
1
1
1
0
0
1
1
0
2
1
1
1
2
1
1
1
0
1
1
1
2
2
1
0
0
1
2
0
0
0
2
2
1
0
1
1
2
0
1
2
2
0
3
2
0
0
0
2
1
1
1
0
2
2
0
1
1
0
2
1
2
1
2
0
2
1
2
1
0
1
1
1
1
2
2
0
1
0
1
0
0
1
0
0
1
1
0
2
1
0
1
0
1
1
2
0
1
2
1
1
1
1
0
3
2
0
1
0
1
1
0
2
2
1
1
1
1
1
1
0
1
1
0
0
0
1
1
0
0
2
0
2
2
1
2
2
2
0
1
0
2
0
1
0
1
0
1
0
2
0
0
1
0
1
0
1
1
0
2
1
1
2
2
1
0
1
3
0
1
0
0
0
0
0
1
1
1
1
2
0
1
1
1
1
2
1
1
1
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
2
1
0
2
0
1
1
0
1
1
1
0
1
0
0
0
1
1
2
2
1
0
2
0
2
1
2
0
2
1
1
1
2
2
2
2
2
0
2
2
3
0
0
2
1
1
0
1
2
1
0
0
0
2
0
2
0
1
2
2
2
1
1
2
1
1
1
2
0
1
1
1
1
1
0
1
1
2
1
1
0
1
0
2
1
0
0
1
0
0
2
1
1
1
1
1
0
1
2
0
1
1
1
0
1
1
0
0
0
0
0
2
0
1
0
0
0
2
0
2
0
0
0
1
0
0
1
0
1
0
2
1
0
3
1
0
0
1
2
0
0
2
0
2
1
1
1
0
1
0
0
2
1
1
1
2
1
0
1
2
1
1
2
0
2
1
2
1
0
1
0
0
0
1
0
1
1
0
0
0
0
2
1
0
0
1
2
1
2
0
2
2
2
1
0
0
0
1
1
1
1
0
0
1
1
0
0
1
0
1
1
1
1
1
1
0
1
2
0
0
2
3
0
1
1
2
2
0
2
0
1
1
0
1
0
2
0
1
0
1
2
3
2
1
0
1
2
2
1
0
1
2
1
0
1
0
2
1
0
1
2
2
1
2
1
0
1
1
1
2
2
1
1
1
1
2
1
1
0
1
1
0
2
1
2
1
0
2
0
0
0
2
0
2
1
1
2
1
2
2
0
0
2
1
0
0
0
4
1
1
1
2
1
1
0
1
0
1
1
0
0
1
0
0
0
0
0
0
1
1
1
0
1
1
2
0
1
1
0
1
2
0
0
1
1
1
0
1
2
0
0
2
1
0
0
1
1
0
1
1
0
1
1
2
1
1
6
2
0
1
0
0
1
0
1
1
1
0
1
0
1
0
1
0
1
3
1
2
0
2
1
2
0
2
2
0
0
1
1
0
2
2
1
0
0
1
0
2
2
1
1
4
1
0
0
2
0
1
1
0
2
1
1
0
0
2
0
0
2
0
1
0
0
0
1
2
1
1
0
2
1
1
3
2
1
1
2
1
0
2
0
2
2
2
1
2
1
1
1
0
0
0
2
0
2
2
1
0
0
1
0
2
2
2
1
0
1
2
1
2
3
1
1
2
0
2
2
1
1
0
1
1
2
0
1
1
4
0
2
1
1
1
2
0
0
0
1
0
0
1
0
0
2
0
1
0
0
1
1
1
1
1
1
2
1
2
1
0
1
0
0
0
1
2
1
0
1
0
1
1
0
0
1
2
1
0
0
1
1
2
1
1
1
1
1
1
0
0
1
0
0
0
1
2
1
0
2
2
0
1
2
1
1
1
1
0
0
0
1
0
1
1
2
2
0
1
2
1
2
1
0
0
2
2
1
0
1
1
1
1
0
0
1
0
1
2
1
2
1
0
0
1
1
0
1
0
1
0
0
0
1
3
1
0
1
1
2
0
1
1
1
0
0
0
0
0
1
0
1
1
0
0
0
2
2
2
0
0
3
2
0
0
1
2
0
0
1
1
1
1
0
0
0
1
0
0
2
0
1
0
1
1
1
0
1
1
2
1
1
0
0
0
2
2
1
2
0
0
1
0
0
1
1
1
1
0
1
0
0
1
0
0
0
0
1
1
0
1
1
1
2
0
2
2
1
2
0
1
1
2
2
2
1
0
1
2
2
1
0
0
0
2
0
1
2
0
2
2
1
1
2
1
1
1
1
0
3
0
1
1
1
0
1
1
0
1
2
0
0
2
1
1
1
1
2
1
2
0
1
1
0
0
1
0
0
1
1
1
2
2
2
1
0
0
2
2
1
1
2
1
2
1
0
0
0
0
1
1
1
1
2
1
2
0
0
2
2
1
0
0
1
1
1
1
0
2
1
1
0
1
0
1
0
2
1
2
1
0
1
1
1
0
0
1
2
2
2
1
2
1
0
3
1
0
1
1
2
0
1
1
0
0
1
1
0
0
0
0
1
2
2
2
2
1
1
1
0
0
2
0
1
0
2
1
1
1
1
1
0
1
0
1
0
2
0
2
1
2
0
1
1
3
1
1
1
1
1
1
0
0
1
1
0
0
1
1
1
0
2
1
1
2
1
0
1
0
1
1
1
0
2
1
2
2
1
0
1
1
1
0
0
2
2
0
1
2
1
0
2
4
1
1
0
0
0
1
2
0
0
0
0
0
1
2
0
1
2
1
0
0
1
1
1
2
1
1
0
0
1
0
1
1
0
3
1
1
0
0
2
2
0
0
1
1
0
1
1
2
2
2
1
1
1
3
2
0
1
2
0
1
1
0
1
0
2
0
1
1
2
2
2
1
6
1
2
1
0
0
1
1
2
1
1
1
0
2
2
1
0
2
1
0
3
0
1
1
0
2
1
1
2
2
1
2
2
1
3
2
1
1
0
2
1
1
1
1
1
1
1
0
1
0
2
0
1
1
2
1
1
0
1
0
1
0
0
1
0
0
3
1
1
0
0
1
0
0
0
1
0
1
1
1
0
2
2
0
1
2
1
1
1
1
0
2
0
2
2
0
1
2
1
0
0
0
2
0
2
1
1
2
2
0
1
0
1
0
0
2
3
1
1
1
0
1
2
0
1
0
1
0
0
2
0
0
1
2
1
2
1
0
1
1
1
0
1
0
1
2
1
1
1
1
1
1
1
2
0
0
2
2
0
2
4
0
0
2
1
2
1
0
0
0
1
1
1
0
0
2
1
0
0
0
0
1
0
1
0
1
1
1
0
0
1
0
0
0
1
0
2
2
0
2
1
1
1
0
2
1
1
0
1
0
0
2
2
1
2
1
0
1
2
2
0
2
2
2
0
0
1
2
0
0
1
1
2
1
1
1
2
0
0
1
1
2
0
0
1
2
0
1
2
1
1
0
0
0
2
1
1
2
1
1
1
2
1
2
1
1
0
1
1
0
2
1
1
1
1
1
1
2
0
2
1
0
0
1
2
1
1
0
2
0
0
2
1
1
1
0
1
0
1
1
1
1
0
1
1
2
0
0
0
2
0
0
1
1
1
0
2
2
0
0
1
1
2
1
2
1
0
1
1
1
0
4
0
0
0
2
1
1
1
1
0
0
0
0
0
2
2
1
0
2
0
2
1
0
2
1
1
0
2
0
0
2
0
1
1
0
1
1
1
2
1
0
1
0
0
0
1
0
1
2
0
0
1
2
1
2
2
0
0
1
1
2
0
1
1
1
1
1
1
0
1
0
1
0
1
1
0
1
0
0
1
0
0
1
1
0
0
0
1
0
1
2
0
1
0
0
0
0
0
0
2
1
0
2
0
0
0
2
1
1
0
1
2
2
1
1
0
0
1
1
1
1
0
1
2
1
1
1
2
0
2
0
2
1
0
0
2
0
1
2
2
0
1
0
1
2
0
2
0
1
1
2
1
0
0
1
1
1
1
1
0
0
2
2
1
1
1
1
1
1
0
2
1
2
1
1
1
0
0
1
1
0
1
1
0
1
0
1
0
2
2
0
0
0
2
2
1
0
1
2
1
0
0
2
2
1
1
0
2
0
0
1
2
1
0
0
1
1
1
1
1
1
2
1
0
1
1
0
0
1
0
1
0
3
1
0
1
1
1
1
0
0
0
0
0
0
1
1
2
0
1
2
1
2
0
0
2
0
1
1
0
0
3
1
1
1
1
0
1
0
2
1
1
0
1
6
0
2
0
2
0
1
1
0
0
0
1
2
2
0
0
1
0
0
2
1
0
1
0
2
0
1
1
1
0
0
1
2
0
1
2
0
0
1
1
1
1
2
1
1
1
0
1
1
0
1
0
1
0
1
0
2
0
2
2
2
0
2
0
0
0
0
1
2
2
1
0
0
1
0
1
2
0
1
0
0
2
0
1
1
0
0
1
1
2
0
1
0
1
1
1
0
0
1
1
1
1
1
1
0
1
0
1
0
2
1
1
1
2
0
0
0
1
1
1
1
3
1
1
0
2
0
2
1
1
0
1
0
0
1
1
1
2
0
2
2
1
2
1
1
2
0
2
2
1
1
2
1
2
2
2
2
1
0
0
1
1
0
2
0
2
1
0
1
1
0
1
0
1
1
1
1
2
2
2
1
2
3
0
1
1
0
1
2
0
1
1
0
1
1
2
1
1
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
1
1
2
1
1
0
1
0
2
0
1
1
1
0
0
2
0
0
1
0
0
0
1
1
2
0
1
1
1
2
1
0
1
1
0
1
1
1
2
1
0
0
0
2
2
1
1
1
1
1
1
1
1
2
1
0
2
2
2
1
1
1
2
1
0
2
0
2
1
1
1
1
1
1
1
1
1
0
0
2
0
1
1
1
2
1
0
2
0
1
0
2
0
0
1
0
1
1
0
1
2
0
1
1
1
2
0
1
0
0
1
1
2
2
2
1
2
1
0
0
1
1
0
0
2
1
0
2
1
2
1
1
1
0
1
1
2
0
2
2
0
1
1
0
0
1
0
1
0
2
0
1
2
1
1
1
1
2
1
0
2
1
2
1
2
1
0
1
1
2
1
1
3
0
0
2
1
1
1
1
0
1
1
1
1
1
1
2
1
0
1
0
0
0
1
0
3
2
1
1
1
1
2
0
0
2
0
0
0
1
1
1
1
0
1
1
1
0
1
1
2
1
0
1
1
0
1
1
1
1
0
1
1
0
0
1
0
0
1
2
1
2
1
1
2
1
0
1
1
1
0
2
0
2
0
0
0
1
0
1
2
0
2
0
0
1
1
0
0
0
2
2
1
0
0
1
2
0
1
2
2
0
0
1
0
1
1
0
1
1
2
2
1
0
2
0
1
0
0
0
0
0
1
0
2
1
2
0
1
1
0
1
2
0
0
0
0
1
2
1
2
0
0
0
2
2
1
0
1
2
0
0
0
1
2
1
1
1
1
0
2
1
0
0
0
1
2
0
2
0
1
2
1
1
2
1
0
1
1
1
0
1
0
1
1
1
2
1
1
1
0
1
0
0
1
1
0
0
1
2
2
0
1
0
2
0
0
1
0
1
0
1
0
1
2
1
2
0
2
1
1
0
0
1
1
0
1
0
1
0
0
0
1
2
2
1
2
0
1
0
2
0
0
0
1
1
1
0
1
0
0
1
2
1
1
0
2
0
2
2
2
1
1
0
0
0
2
1
1
1
0
1
1
1
2
0
1
1
1
0
0
1
2
0
0
2
2
1
1
2
1
0
1
1
2
0
1
0
1
1
1
0
2
0
1
0
1
1
1
0
0
0
2
1
0
2
2
3
2
2
1
0
1
2
2
1
2
0
1
1
1
2
1
1
0
2
0
2
0
1
1
1
1
0
2
2
1
2
0
0
1
0
1
0
1
0
0
1
1
3
1
2
0
1
1
1
0
1
0
4
0
0
0
1
2
1
1
1
2
0
2
2
0
1
1
0
1
0
0
1
2
1
1
2
0
1
2
2
1
0
1
2
1
0
2
2
1
2
2
1
0
1
2
0
0
0
1
0
0
1
0
1
1
1
0
2
0
1
1
0
2
0
1
1
2
0
1
0
1
1
0
0
1
1
2
0
1
0
0
1
1
1
1
0
1
1
2
0
0
0
1
1
1
1
1
0
1
1
0
0
1
1
0
1
0
1
0
1
2
0
1
0
1
2
0
2
1
1
2
2
2
2
2
0
1
0
0
1
0
1
1
0
0
1
0
1
3
1
0
1
0
0
2
0
2
0
1
0
0
1
1
1
1
0
2
1
0
1
0
2
1
0
1
1
0
0
1
2
1
0
0
2
0
0
0
1
0
0
1
1
1
3
2
1
1
2
0
0
2
2
0
2
1
0
1
2
1
2
0
0
0
0
2
2
1
1
1
1
2
0
0
1
2
2
0
1
2
1
1
2
2
1
2
0
0
2
1
1
0
2
2
2
0
0
0
2
1
0
0
2
2
2
0
1
0
0
0
1
0
1
0
0
0
1
0
1
1
1
2
0
0
0
1
0
0
0
0
0
0
0
1
1
1
2
0
1
1
1
2
1
2
1
1
2
0
0
1
2
0
1
0
0
0
1
0
0
1
0
1
0
2
0
2
1
0
1
1
1
2
0
1
0
2
0
0
1
2
0
0
1
2
2
0
2
2
2
1
2
2
0
2
1
1
1
1
0
2
1
0
0
2
1
0
3
2
0
0
1
2
0
0
2
0
2
2
3
1
1
1
1
1
1
1
2
1
0
1
2
1
2
1
2
0
0
0
0
1
1
1
2
2
1
2
1
2
0
1
1
2
0
2
0
2
0
1
1
1
1
0
1
0
1
0
0
1
1
1
0
0
1
0
1
1
0
2
1
1
1
2
1
3
0
2
0
1
1
0
1
0
2
0
2
0
2
1
1
0
1
1
2
1
0
2
0
1
0
1
0
2
0
1
0
0
0
0
0
0
0
1
2
0
1
2
1
1
2
0
1
2
1
1
2
1
2
0
0
0
0
1
1
0
1
0
1
2
2
1
2
1
1
0
0
0
0
1
2
1
0
1
0
0
1
0
2
0
0
0
0
1
1
1
0
1
1
0
2
0
0
2
0
0
2
0
1
1
0
1
0
1
1
1
0
1
1
1
1
0
2
1
2
1
1
0
1
2
1
0
0
1
0
2
1
1
1
1
0
1
2
1
0
0
0
2
2
1
0
2
1
1
2
0
2
1
1
1
1
0
2
0
0
1
2
0
1
0
1
1
1
0
2
2
1
0
1
0
0
1
1
1
1
0
0
1
0
2
0
0
2
1
1
1
2
1
1
1
1
0
0
0
2
1
0
0
2
0
0
1
1
0
2
4
0
0
1
1
1
0
1
0
2
1
1
1
1
0
1
1
2
2
1
3
0
0
1
1
1
0
0
1
1
0
1
1
1
1
1
1
2
0
1
2
1
0
0
0
2
1
0
0
1
1
0
0
0
0
1
2
1
0
1
2
0
1
2
0
0
0
1
0
1
2
1
1
0
0
0
0
1
2
0
0
1
0
1
0
1
0
0
1
1
1
0
0
1
1
0
1
0
0
0
1
0
0
1
2
1
0
0
0
1
0
1
1
2
1
0
1
1
3
1
1
1
0
0
2
0
1
2
0
1
1
1
0
1
2
1
1
1
2
1
2
2
2
1
1
2
1
1
2
1
2
0
1
2
2
2
0
1
1
0
2
0
0
1
0
1
2
1
1
2
1
0
0
1
1
1
1
0
3
1
0
0
1
0
1
2
2
1
2
1
0
1
1
2
1
1
0
2
0
0
0
1
0
1
0
0
1
1
0
1
0
1
0
1
1
0
1
0
1
0
1
1
0
2
0
0
1
0
1
0
2
2
1
1
0
0
1
1
0
1
1
1
2
0
0
1
1
1
1
0
1
1
1
1
2
1
1
3
1
1
1
0
0
2
2
1
0
1
1
1
0
1
1
2
2
2
0
0
0
0
0
0
2
1
0
1
2
0
1
0
2
1
0
0
1
1
1
1
1
2
2
1
2
1
0
2
0
1
2
0
2
0
1
1
0
0
1
3
0
2
1
0
0
0
2
1
1
1
0
1
1
2
0
2
0
1
1
2
1
0
1
0
1
2
2
1
1
2
6
0
0
0
1
2
0
1
0
0
1
0
0
1
2
0
2
0
2
1
2
1
0
0
2
0
1
0
0
1
1
0
1
0
0
1
1
2
1
0
1
2
1
0
2
0
0
1
1
2
0
1
0
2
1
0
2
0
0
1
0
0
3
1
1
1
0
2
2
2
0
1
1
2
1
0
0
1
1
2
0
1
1
1
1
0
0
0
0
1
0
0
1
0
1
1
1
0
0
0
1
1
0
2
1
0
0
0
4
0
1
1
2
0
0
1
0
2
1
0
2
2
0
2
0
1
1
0
0
0
0
0
1
1
2
1
2
0
0
0
2
2
0
2
2
0
1
1
1
1
1
2
0
0
1
0
3
1
0
1
1
1
1
0
0
1
0
1
0
0
2
0
0
0
0
0
1
0
1
1
1
1
1
1
1
2
0
1
0
1
1
2
2
1
2
2
1
1
2
0
0
0
0
2
0
1
3
1
3
1
1
2
0
1
1
0
1
1
1
2
1
0
0
1
1
2
0
1
1
1
0
2
3
0
0
2
2
2
1
0
0
0
1
0
0
2
1
1
0
0
0
0
1
0
1
1
1
0
0
1
1
1
0
2
0
0
0
1
2
2
1
0
1
1
0
0
0
0
0
0
2
0
2
0
1
0
0
2
0
0
2
1
2
2
0
1
3
2
1
1
0
1
2
2
1
0
1
1
0
1
0
2
2
1
2
2
0
2
1
0
1
1
0
0
0
0
1
1
1
0
1
0
1
1
0
1
1
2
2
2
1
2
0
0
1
1
0
2
2
1
0
1
2
1
0
0
1
1
1
0
0
2
1
2
1
2
1
1
0
1
2
2
1
1
0
0
2
1
1
0
2
2
2
1
1
2
1
2
2
1
0
2
1
2
0
0
1
2
2
0
2
0
1
0
1
2
0
0
1
2
2
0
0
0
1
2
2
1
3
1
0
2
1
1
1
0
2
0
1
0
1
1
1
2
1
0
1
1
1
0
0
1
0
0
0
0
0
0
1
2
1
2
2
0
2
0
0
1
1
1
2
1
0
1
1
2
0
0
1
3
0
1
2
1
0
0
0
2
1
0
2
0
1
0
0
2
0
2
1
2
1
1
1
1
1
0
1
2
0
2
1
1
0
1
2
2
0
0
1
1
0
1
2
2
2
1
2
0
0
0
0
1
0
0
2
1
1
1
0
0
2
0
0
2
0
0
1
2
2
0
2
0
0
2
0
0
0
1
0
1
0
1
1
1
2
1
0
1
0
1
0
0
1
2
1
0
1
0
1
2
1
0
2
0
0
2
1
1
0
2
1
2
2
0
1
0
0
1
1
1
1
2
1
2
1
1
3
1
2
0
1
0
1
0
0
0
0
0
0
0
1
1
1
0
1
2
2
0
0
0
0
1
1
2
0
0
2
1
1
1
1
1
2
0
1
1
1
0
0
0
1
2
1
1
0
1
1
0
1
1
0
1
0
2
0
1
0
0
3
2
1
0
0
0
2
0
1
1
1
1
1
0
1
1
1
2
2
2
0
1
0
1
0
1
1
2
0
1
2
2
0
1
0
0
0
2
0
1
1
2
1
2
1
3
2
0
1
1
1
0
1
0
2
1
2
0
2
0
2
1
0
1
2
1
1
0
1
0
1
1
2
0
2
0
2
1
2
2
1
0
2
0
0
1
2
1
0
0
1
1
1
1
1
1
1
2
1
1
1
0
0
1
1
2
1
1
0
2
1
2
1
0
1
1
1
1
2
0
0
1
0
1
0
1
0
1
1
2
1
1
1
1
0
1
0
1
2
1
1
1
0
0
1
0
1
5
0
0
1
1
0
1
0
1
1
0
1
1
2
1
0
0
2
0
0
1
1
1
1
0
1
1
0
3
2
1
3
1
1
0
2
2
2
2
0
1
11
2
1
2
1
2
0
3
1
1
0
0
2
2
1
2
1
2
2
1
1
0
1
1
2
1
1
1
1
2
1
0
0
0
0
0
2
0
0
0
0
1
0
0
1
1
1
1
1
2
2
0
1
2
2
0
1
1
1
0
2
2
0
0
0
2
2
0
1
1
0
1
0
1
2
1
1
2
0
0
1
1
1
1
0
0
0
1
1
0
0
0
1
0
2
1
0
0
0
2
2
1
1
1
2
1
0
0
1
1
1
2
1
2
1
0
1
1
0
0
0
1
2
1
1
0
2
0
1
1
1
1
0
0
0
0
1
1
0
0
2
2
0
1
1
0
0
1
2
0
1
2
0
2
0
1
1
1
0
2
0
2
0
1
2
0
0
0
1
2
0
0
1
1
2
0
2
1
0
1
0
1
0
0
0
1
1
1
1
1
1
0
2
1
0
1
0
0
1
0
0
0
2
1
0
1
0
3
1
2
2
2
2
0
2
0
0
0
1
0
1
0
1
1
2
1
0
5
2
1
0
1
0
2
1
1
0
2
1
1
1
1
0
1
1
2
0
2
2
1
1
0
0
1
0
2
1
1
1
1
0
2
2
0
0
1
1
1
0
2
2
1
0
0
0
0
2
1
1
0
1
1
0
0
0
1
2
0
1
2
0
1
0
2
1
1
0
1
1
1
1
1
1
0
1
0
1
1
1
2
1
1
0
2
1
1
0
0
2
1
1
2
0
2
0
2
1
2
1
0
2
0
0
2
0
0
3
1
2
2
0
0
1
2
2
2
0
0
3
0
0
2
0
0
2
0
1
0
2
1
1
2
1
0
0
1
1
1
0
2
1
2
0
1
1
1
1
1
1
0
2
0
0
0
2
0
3
2
1
0
0
0
2
1
1
2
0
1
2
0
2
1
1
0
1
1
1
2
0
1
2
2
1
1
0
6
0
0
2
0
1
0
0
0
0
0
1
2
0
1
0
1
2
2
1
1
0
2
0
1
0
2
0
0
1
0
0
1
1
0
3
1
1
0
1
2
1
1
1
0
1
2
0
1
1
0
2
0
1
0
2
0
1
0
0
1
1
0
1
1
2
0
1
1
2
2
0
0
0
2
3
2
1
1
0
1
1
2
0
0
0
0
0
1
0
2
0
0
2
1
1
1
0
1
1
0
0
1
1
0
1
0
0
1
2
2
2
0
0
2
1
2
2
1
2
1
0
1
0
1
0
1
1
1
1
1
0
0
0
0
1
0
1
0
0
1
0
1
1
1
1
0
2
1
2
2
2
2
3
1
0
1
1
0
0
0
1
2
0
1
1
1
2
0
1
1
0
0
0
2
1
0
2
1
1
1
1
1
1
2
0
1
1
0
2
0
0
1
0
0
1
1
0
0
2
0
1
0
0
2
0
2
1
2
1
0
1
0
1
0
2
0
1
1
0
1
2
2
2
0
2
1
1
0
1
2
0
1
1
1
0
1
2
0
2
0
1
0
1
1
1
1
1
2
2
1
2
0
1
1
2
0
1
2
2
1
1
1
1
0
0
1
0
0
1
0
1
1
0
0
1
0
1
1
1
1
1
0
1
2
1
0
1
1
0
1
0
1
0
1
0
0
1
0
0
5
0
0
1
0
2
1
2
1
1
2
2
0
2
1
0
0
3
0
1
0
0
1
2
1
0
0
2
1
1
2
0
0
2
1
2
0
1
1
1
1
1
2
2
0
0
2
0
0
2
1
1
0
1
1
1
0
0
1
0
0
2
2
0
0
2
2
2
1
2
2
2
1
0
1
0
0
2
1
0
0
0
1
0
1
2
2
1
0
1
1
2
0
1
0
2
1
0
1
1
0
1
1
0
1
2
2
0
1
1
0
2
2
1
0
1
2
0
1
0
1
1
0
0
2
0
1
0
1
0
2
2
1
1
0
3
1
0
0
2
1
2
1
0
1
0
1
0
1
1
1
3
2
0
0
0
2
1
0
1
1
0
2
0
1
0
0
1
3
1
0
2
1
1
0
0
1
1
0
2
2
1
0
1
0
2
0
2
1
1
2
0
1
0
0
0
2
1
0
2
2
1
2
1
2
1
1
0
2
1
1
0
0
0
1
0
1
0
0
1
1
1
0
0
2
2
2
0
1
2
1
2
1
1
0
1
1
1
2
1
1
0
2
0
1
1
0
2
2
0
1
1
0
0
0
0
0
1
1
2
1
0
0
0
2
1
1
1
1
0
1
0
2
0
2
0
2
1
2
2
1
3
1
0
2
0
2
2
1
0
0
2
0
2
0
1
1
1
0
3
1
1
1
0
1
2
1
0
2
2
1
0
1
0
0
1
2
1
0
1
1
1
0
2
1
2
2
2
2
0
0
3
1
2
1
1
0
2
1
2
0
1
1
2
1
0
0
0
2
0
0
1
0
1
1
2
0
2
1
1
1
2
0
1
0
2
0
2
2
1
1
1
0
3
1
1
1
0
2
1
0
0
1
2
1
2
0
0
1
3
0
1
1
1
1
0
1
2
1
0
1
2
0
2
1
1
1
1
1
0
0
1
0
2
1
1
1
1
1
2
0
0
1
0
1
2
1
0
1
1
2
1
0
0
2
1
0
0
2
2
0
1
0
2
1
1
2
1
0
0
1
2
2
0
3
1
0
1
1
0
2
1
1
1
2
2
8
0
1
1
1
1
1
2
1
2
0
1
1
0
0
1
2
1
0
2
1
0
0
2
0
0
1
1
2
1
0
1
1
0
0
0
1
1
0
0
1
0
0
0
1
1
0
0
2
1
1
0
0
1
1
1
1
2
1
0
2
0
1
1
2
0
0
1
1
2
0
1
2
1
1
2
1
2
2
2
0
0
0
1
1
1
1
2
1
1
0
1
0
1
1
0
1
1
0
0
1
1
1
0
1
0
2
0
0
0
1
0
0
1
2
1
1
1
2
1
2
1
0
0
1
0
1
0
2
1
2
1
0
1
2
0
0
0
1
2
2
1
0
1
0
1
2
2
1
0
1
2
0
1
1
1
1
0
1
0
0
0
0
0
0
0
1
1
0
2
1
0
2
1
1
2
0
0
0
1
2
1
1
1
1
1
1
1
1
0
0
2
1
1
1
1
2
1
0
2
0
0
1
0
1
0
0
2
0
1
1
2
0
2
2
1
2
2
2
0
0
0
1
0
1
2
0
3
2
1
0
1
2
0
0
1
2
2
1
1
1
2
0
0
1
2
1
1
1
1
1
1
2
1
2
0
1
1
1
2
0
0
0
1
0
1
1
1
0
0
1
0
1
1
0
2
2
2
1
1
2
1
0
2
1
2
1
0
0
2
0
0
1
0
2
2
0
1
2
2
1
1
0
1
1
2
0
4
1
1
1
2
0
0
1
0
1
2
1
1
0
1
0
0
0
2
0
1
0
0
2
1
2
0
0
0
1
1
0
1
0
1
0
2
1
1
0
1
0
0
2
0
0
1
0
0
1
2
1
2
2
0
0
2
1
1
0
2
1
0
0
0
0
0
2
7
0
1
1
0
1
1
2
3
0
1
2
0
2
1
1
2
1
2
1
1
0
0
1
2
1
1
1
1
0
1
1
0
2
1
2
2
1
3
0
0
0
1
1
1
0
2
0
2
2
2
1
2
2
2
1
1
1
1
2
0
0
0
0
2
1
1
1
1
1
0
2
2
0
0
3
0
1
0
2
1
0
1
2
0
0
0
0
1
0
0
0
2
1
0
0
1
1
0
1
2
2
1
0
2
0
0
2
1
2
1
0
0
2
1
0
1
2
1
1
2
0
1
1
2
1
2
0
1
2
1
0
0
1
1
2
1
2
1
1
0
1
2
1
1
0
2
0
2
1
2
0
1
0
0
1
0
2
1
0
1
0
0
2
0
2
1
2
1
0
2
0
0
0
0
0
1
2
2
1
1
3
1
2
2
1
1
0
0
0
1
1
0
1
1
1
1
1
2
1
0
0
0
1
1
2
0
0
1
1
2
1
1
1
0
1
0
0
1
0
2
0
0
1
0
1
0
2
0
0
0
1
1
1
0
1
1
1
1
1
0
0
1
2
1
2
2
1
1
1
2
1
0
2
3
0
2
1
0
2
0
1
1
1
0
2
1
1
2
0
1
2
1
0
0
0
0
0
1
1
0
1
2
0
0
0
1
0
1
1
1
1
1
0
2
1
2
0
1
1
1
2
1
0
0
1
0
1
2
1
1
2
1
2
0
2
1
0
1
1
2
1
1
2
2
1
0
1
1
1
1
1
1
2
1
0
0
2
0
2
1
1
1
1
1
4
1
1
1
0
2
0
2
0
0
2
0
1
0
2
0
2
0
1
1
2
0
1
1
0
1
1
2
0
2
1
0
1
0
0
1
2
0
1
1
1
0
1
1
2
2
0
2
1
0
2
1
2
1
0
0
0
0
0
1
1
2
0
1
1
0
1
1
1
1
0
2
2
1
0
1
2
0
0
0
0
1
0
2
0
2
2
2
1
0
1
1
0
2
0
1
0
1
1
1
0
0
1
1
2
1
1
1
2
1
2
0
2
2
2
1
1
2
0
0
1
0
0
2
2
1
1
1
1
2
1
2
1
2
1
0
1
2
1
0
0
2
0
0
2
1
0
1
1
0
0
1
0
0
1
3
0
2
1
0
2
1
0
0
1
7
1
2
0
1
2
2
1
0
2
2
1
0
1
0
0
0
0
1
0
1
2
1
0
0
0
2
1
0
0
0
0
2
1
1
2
1
0
0
0
2
2
0
0
0
2
1
0
0
0
2
0
1
2
0
1
0
1
1
0
0
1
0
1
1
1
1
0
0
2
1
2
0
1
0
2
1
2
2
1
2
1
2
1
2
1
1
2
0
0
0
0
2
0
0
1
1
2
0
1
0
1
0
2
2
1
1
0
0
2
0
2
1
0
1
0
0
1
2
1
0
1
0
0
0
0
3
0
0
0
0
1
1
1
1
1
1
2
1
2
2
2
1
2
2
1
0
0
0
0
0
1
0
3
1
2
1
0
2
0
1
2
0
1
1
1
1
1
2
1
0
1
2
1
0
0
0
0
1
1
1
0
1
2
1
0
2
0
0
1
0
2
1
0
1
0
0
0
2
1
0
2
0
0
1
1
0
1
1
1
1
2
1
2
1
2
1
1
1
2
0
2
1
0
2
2
0
1
1
1
1
2
1
0
0
2
2
1
1
2
0
0
1
1
0
1
2
2
1
1
2
2
0
1
1
1
2
0
0
5
1
1
0
0
1
1
2
0
1
2
1
2
1
2
2
1
3
0
0
1
1
1
0
1
2
1
2
0
0
1
0
0
0
0
2
2
2
1
1
0
0
1
1
2
0
1
1
1
1
0
0
0
1
0
2
1
0
1
1
0
0
1
1
0
1
1
2
1
0
1
1
0
0
2
1
0
1
0
1
0
3
0
0
1
1
2
2
1
0
1
2
3
1
1
1
1
1
0
1
0
2
0
0
2
0
0
2
1
1
2
1
0
2
1
0
0
0
0
2
1
2
1
1
0
0
1
0
1
1
0
2
0
0
1
2
1
0
2
1
0
0
0
0
2
1
1
1
0
1
1
2
0
0
1
2
3
1
1
2
2
1
1
2
0
1
2
1
2
1
0
0
0
0
1
1
0
2
1
1
0
1
1
1
1
1
0
0
2
1
2
0
1
1
1
1
0
0
1
0
0
1
0
1
4
2
0
0
0
1
1
0
1
1
1
1
1
3
2
1
2
1
1
4
0
1
1
3
1
1
0
0
1
0
1
1
0
2
0
1
1
0
1
1
2
2
1
1
0
2
1
2
1
0
1
1
1
1
0
9
0
0
0
1
0
0
0
0
1
0
2
0
1
2
0
0
1
0
2
6
1
0
1
2
1
3
2
0
0
1
2
1
2
6
2
5
2
1
0
1
1
1
0
1
1
4
0
2
1
0
2
0
0
1
0
0
1
2
2
1
0
0
2
0
0
0
1
2
1
1
2
0
1
1
2
1
0
2
1
0
1
1
1
2
2
1
1
2
1
0
2
0
1
2
1
0
2
0
2
1
2
1
0
0
2
1
1
1
1
2
1
2
2
1
1
1
1
2
1
0
0
2
1
1
2
0
0
0
0
1
1
1
1
0
1
0
0
2
0
0
0
1
0
2
2
0
2
1
1
1
0
2
2
0
1
1
1
0
0
2
1
2
0
0
0
2
1
1
0
1
0
1
1
2
0
1
0
1
0
0
1
2
0
0
2
1
0
0
0
2
0
0
2
2
0
1
2
1
0
0
2
1
0
0
1
1
1
0
0
0
1
2
0
0
1
0
1
1
0
0
2
1
3
2
1
2
1
2
1
2
0
0
1
1
3
2
1
2
2
1
0
1
1
3
1
2
2
0
2
1
1
1
2
2
2
1
0
0
0
2
0
1
0
0
1
0
5
1
1
2
1
1
0
1
0
1
1
1
0
2
1
2
0
1
1
2
0
2
1
0
1
2
0
0
2
0
2
1
2
0
0
1
0
1
1
1
0
2
2
1
2
0
2
1
0
1
2
0
0
1
2
2
1
1
0
2
0
1
0
2
1
0
1
1
0
0
0
2
1
1
0
0
0
0
2
0
1
2
0
3
0
1
2
0
1
1
1
0
2
1
0
0
1
2
1
1
2
3
1
0
1
0
1
1
1
1
0
1
0
1
1
4
1
0
1
0
1
2
0
0
1
1
0
0
1
0
2
0
1
3
2
1
0
1
1
0
1
2
1
1
2
0
1
2
1
2
2
1
1
0
2
2
2
0
0
1
1
0
1
2
0
0
1
0
1
1
0
2
1
2
1
2
1
0
0
1
1
2
1
1
1
0
1
1
0
1
0
0
0
1
0
0
1
0
0
3
2
1
0
1
0
1
1
1
2
0
1
1
1
0
1
2
1
2
0
0
1
1
0
0
0
0
0
2
0
1
5
0
1
1
2
1
0
1
0
0
0
0
0
2
1
0
2
1
2
1
1
1
1
0
0
0
1
2
0
1
2
2
1
1
0
1
0
1
1
1
1
1
2
1
3
1
1
2
0
2
1
3
1
0
0
1
2
1
0
0
0
1
0
0
1
0
1
1
1
1
0
1
2
1
0
1
0
0
0
0
1
1
1
1
3
1
2
2
2
1
1
0
0
2
2
1
1
1
4
0
0
1
2
0
2
0
2
2
1
1
0
0
0
0
0
1
1
0
1
1
0
2
2
1
0
2
1
0
2
1
1
1
0
0
0
1
0
1
2
0
1
0
1
2
1
1
1
1
1
2
1
1
0
2
2
1
2
0
1
2
1
2
1
0
2
0
0
0
0
1
0
2
1
1
0
2
1
1
1
0
1
1
2
2
0
1
2
1
0
1
2
1
4
0
0
1
0
1
2
1
1
1
1
2
2
2
0
1
2
1
2
2
0
0
1
2
1
1
0
1
1
0
1
0
2
0
2
1
0
0
2
1
2
2
2
1
1
1
0
0
0
2
0
0
0
1
1
1
0
1
0
0
0
1
3
0
0
1
0
1
0
0
0
2
1
0
2
1
2
0
1
1
0
0
1
2
0
0
0
2
1
0
1
1
0
1
1
1
0
1
1
2
2
0
1
0
0
1
0
1
1
0
2
1
1
0
1
2
1
1
1
1
2
2
0
1
0
1
2
2
1
2
3
0
1
2
0
2
0
0
2
1
0
1
1
2
0
1
1
1
1
0
1
1
1
0
0
0
1
0
1
1
1
2
1
1
0
1
0
1
1
2
2
1
0
1
2
1
1
6
0
4
1
2
2
2
0
0
0
0
0
0
1
1
0
0
2
0
1
1
1
1
2
1
1
2
0
1
0
0
1
0
1
1
0
0
0
1
0
2
2
0
1
1
1
0
0
1
2
1
1
1
1
1
2
0
0
1
1
1
0
0
1
0
0
0
0
1
1
2
1
1
2
1
2
0
2
0
2
1
1
0
0
1
0
1
0
1
0
1
2
0
1
1
0
1
0
0
2
1
2
2
4
0
1
0
2
1
1
1
1
2
2
2
0
2
2
0
1
0
0
0
2
1
0
1
0
1
2
2
0
2
2
1
0
0
0
0
2
1
1
0
0
0
1
1
0
2
2
1
0
1
2
1
1
2
2
1
1
0
1
2
2
0
0
2
2
2
0
1
0
0
0
0
0
2
1
2
1
1
0
1
0
0
1
2
2
1
2
0
0
2
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
1
0
0
1
1
1
0
1
0
1
0
2
1
2
1
0
2
0
0
0
2
0
0
0
1
0
1
0
2
2
1
1
0
0
0
1
0
2
2
1
1
2
1
1
1
2
2
1
0
1
1
0
1
1
1
2
1
1
0
1
1
2
2
2
1
0
2
2
2
1
0
1
2
2
0
2
1
0
2
1
1
1
0
1
0
1
2
1
2
0
2
1
2
2
0
0
4
0
0
0
1
1
0
1
0
2
1
2
1
0
0
1
0
2
1
2
3
2
1
1
1
0
1
2
2
0
1
0
0
1
1
0
0
1
2
0
1
1
1
1
0
1
1
0
0
0
1
0
1
1
1
1
1
0
1
1
1
2
1
1
1
2
2
2
0
2
0
2
2
2
1
1
1
1
1
1
1
2
0
1
0
0
1
0
1
1
0
2
2
0
0
0
0
0
0
2
0
2
0
1
0
1
0
2
0
2
0
0
1
1
1
0
0
2
0
1
1
0
3
1
0
0
2
0
1
2
0
1
1
1
1
2
0
0
2
0
1
1
0
0
1
2
2
1
1
2
2
1
0
1
1
1
2
1
2
1
0
1
2
1
0
2
0
1
2
1
0
0
0
2
0
1
0
2
2
2
0
0
0
0
1
0
0
1
2
1
2
1
0
2
2
0
1
1
0
0
0
0
0
0
2
4
0
0
0
0
0
2
0
0
0
0
1
1
2
0
3
0
0
0
0
1
1
1
1
1
1
1
1
0
1
0
0
1
1
0
4
1
0
1
0
2
0
1
2
3
1
1
1
0
1
1
0
1
1
1
0
1
1
0
1
1
0
2
1
0
2
0
0
2
2
0
1
1
0
0
1
0
0
1
0
0
1
2
1
0
1
1
1
0
0
2
1
0
1
1
2
0
1
0
0
2
0
0
2
1
1
1
1
1
1
2
1
1
1
0
0
0
2
1
0
2
0
2
2
2
1
0
2
1
0
2
1
1
1
0
3
1
2
0
0
2
2
0
0
2
1
1
1
1
1
1
0
1
0
0
1
2
2
1
0
2
2
1
2
1
0
1
2
1
2
2
1
0
2
1
2
0
2
0
1
0
2
1
0
0
1
1
1
0
0
0
0
2
2
1
0
1
1
0
1
1
7
1
1
2
1
1
0
0
1
2
1
0
0
2
1
2
2
2
2
0
1
1
0
2
1
1
2
0
1
1
0
0
1
1
1
1
0
0
0
1
1
1
0
1
1
1
0
2
0
1
1
2
1
0
0
1
1
0
0
1
3
2
0
1
1
0
2
1
1
2
1
1
1
0
2
1
0
0
0
1
2
0
0
0
1
0
1
2
1
0
1
0
0
0
1
0
0
0
0
0
0
2
1
1
2
0
2
1
1
1
0
1
1
0
2
1
1
1
0
1
2
1
2
0
0
0
0
1
3
1
2
1
2
1
0
2
1
0
1
0
1
2
1
0
1
2
0
0
0
0
0
1
1
0
1
1
2
1
0
0
1
0
1
2
1
1
0
2
2
1
1
1
0
1
2
2
2
1
2
1
1
0
0
0
1
0
1
2
0
2
0
1
0
0
1
1
0
1
0
1
2
2
0
1
0
1
3
1
1
2
1
0
0
1
1
0
2
0
1
1
1
1
1
0
1
1
0
1
1
1
2
0
0
1
0
1
2
1
1
2
0
0
1
0
0
1
0
1
0
0
0
0
1
0
1
1
2
1
0
0
2
0
2
0
3
2
1
1
1
0
1
1
2
0
2
0
1
0
2
1
2
1
2
2
1
2
2
1
1
0
1
0
2
0
1
0
2
0
0
0
1
0
0
0
2
3
0
1
1
0
1
2
2
2
0
1
1
1
1
0
2
1
0
1
0
0
2
1
1
1
1
1
1
2
1
0
0
1
0
2
1
0
0
1
0
0
1
1
0
1
1
0
2
2
0
2
0
0
1
1
2
1
1
1
0
1
0
1
0
0
0
0
1
1
0
1
0
1
2
3
1
1
0
0
0
1
0
0
1
1
2
2
1
1
1
1
0
0
1
1
2
2
0
1
1
0
1
1
4
1
0
1
1
2
0
1
2
0
2
2
1
2
2
2
0
0
1
4
2
1
1
2
1
1
1
2
2
0
1
2
0
0
0
1
1
2
2
1
1
0
0
1
2
1
0
2
2
1
2
0
2
1
1
1
1
1
0
0
2
0
1
2
2
1
2
2
1
2
1
0
0
2
1
1
1
0
1
1
0
0
2
2
1
1
2
0
1
1
0
2
1
0
2
2
1
0
0
1
0
0
1
1
2
1
0
1
3
0
2
0
2
1
1
1
0
1
1
2
1
0
1
0
2
2
1
2
0
2
1
0
0
2
2
0
2
0
1
2
1
1
2
0
1
1
0
1
0
2
2
0
2
1
2
1
0
1
2
0
1
0
0
0
2
0
2
0
0
1
1
1
2
1
2
1
2
0
0
2
1
2
1
1
1
1
0
0
1
1
1
1
1
0
0
1
1
0
2
1
1
3
2
1
2
1
0
1
2
2
1
0
0
2
3
0
1
2
2
2
1
0
0
0
0
0
1
1
0
2
2
0
0
0
0
0
2
1
2
0
0
2
1
1
1
2
1
1
2
1
1
0
2
0
1
1
0
2
1
0
0
2
2
1
1
1
0
2
0
0
0
1
1
2
0
1
2
0
2
0
0
1
2
3
1
2
2
1
1
0
1
0
2
1
1
1
1
0
0
0
2
0
0
0
2
1
1
1
1
2
1
1
0
1
1
1
0
0
1
1
1
1
1
1
0
0
0
1
2
0
1
1
1
2
2
1
0
0
2
1
0
1
2
1
1
0
1
1
0
0
1
1
1
2
1
0
1
1
0
2
1
0
1
0
2
1
0
1
1
2
0
0
0
1
0
0
1
1
0
0
1
1
0
2
1
0
1
0
1
2
1
1
0
0
0
1
2
2
2
1
2
1
2
0
1
2
0
2
0
0
0
0
1
1
0
2
1
1
1
1
1
2
2
0
1
1
0
2
1
1
1
0
1
1
0
1
1
1
2
0
1
1
0
0
0
1
2
0
1
1
2
2
1
0
1
0
0
0
1
0
1
0
0
1
0
1
1
0
2
2
2
2
0
1
2
0
0
0
1
2
0
2
0
1
1
0
1
2
0
2
2
2
2
0
0
2
0
1
0
1
2
0
1
0
0
1
2
1
2
1
1
0
2
0
0
1
0
1
0
0
0
2
2
0
0
0
0
2
0
1
5
1
2
2
1
2
2
1
0
0
1
0
1
0
0
1
0
0
1
0
1
0
2
1
1
0
0
2
0
1
0
1
1
1
1
2
0
1
0
0
1
2
1
0
0
1
0
2
2
0
0
1
0
2
1
2
1
0
1
1
1
0
1
1
0
2
1
1
0
0
2
1
0
1
1
0
1
0
0
2
1
1
3
2
2
1
1
1
0
1
1
2
0
0
2
0
0
0
1
0
1
0
2
1
2
2
1
0
0
0
1
0
1
2
0
0
1
0
0
0
0
0
2
0
1
1
0
0
2
0
0
2
0
2
1
2
2
0
1
0
1
2
2
2
2
1
0
0
2
0
1
2
1
0
2
1
2
0
1
0
1
1
2
0
2
1
1
0
1
0
1
3
0
1
2
0
1
2
1
1
0
1
0
1
1
1
1
1
1
1
1
0
1
1
2
0
1
0
2
2
1
0
1
2
1
1
1
1
1
1
1
0
1
2
1
1
0
1
2
1
2
1
1
1
1
1
0
0
0
1
1
4
2
1
1
1
0
2
0
1
2
2
1
1
1
2
2
1
1
2
0
1
2
0
1
1
1
2
2
3
1
1
0
0
2
3
1
1
0
0
1
2
0
1
1
1
2
1
0
1
0
1
1
2
2
0
1
1
1
0
0
1
2
0
1
2
1
0
0
1
0
1
1
2
1
1
1
1
1
0
1
0
1
1
2
2
2
0
1
1
2
1
1
1
1
0
1
2
2
1
1
1
0
1
1
1
1
0
1
2
2
1
1
0
1
1
0
0
2
2
0
1
1
1
1
0
0
1
1
2
0
0
1
2
1
0
0
2
4
2
0
1
0
0
0
1
2
0
0
0
2
1
0
0
0
0
1
0
1
1
1
0
2
2
1
1
1
1
0
1
0
1
0
1
0
0
0
2
1
2
0
0
1
0
1
0
0
0
1
1
1
1
0
2
3
1
1
2
0
1
1
1
2
3
1
2
1
0
0
1
1
2
1
0
2
0
0
0
0
0
2
1
1
2
2
2
2
2
0
2
2
0
0
0
0
0
2
1
2
1
0
2
0
0
1
1
1
0
1
1
2
2
0
2
0
2
0
1
2
2
0
1
1
2
1
0
2
2
1
1
1
2
0
2
0
2
0
1
0
2
2
2
3
0
2
2
1
1
2
0
2
2
0
1
0
0
2
2
0
1
1
1
0
0
1
2
1
2
0
1
1
1
0
2
1
1
2
1
0
1
1
0
0
0
1
2
0
0
1
0
1
0
0
0
1
1
2
0
1
0
0
1
1
0
2
0
1
0
2
2
1
0
2
1
1
0
2
0
1
2
2
1
1
1
1
1
2
2
0
2
1
1
3
2
1
2
0
0
0
2
1
0
1
2
0
2
2
0
0
2
0
1
0
2
1
1
0
2
2
1
1
2
0
1
2
0
1
0
0
1
2
1
0
2
0
2
0
1
1
1
0
0
2
1
1
0
1
2
1
0
1
0
2
2
1
0
1
2
2
2
2
1
1
1
1
0
1
0
2
1
1
1
0
0
1
0
1
2
1
1
0
1
2
0
1
2
0
0
0
1
0
1
0
2
2
1
0
1
1
3
1
0
1
0
0
0
0
1
1
1
2
2
1
0
0
1
1
2
2
2
0
0
1
1
1
1
0
1
0
2
2
1
2
0
1
0
1
2
1
1
0
1
0
1
0
2
2
1
0
1
1
1
1
2
0
1
1
1
1
1
0
1
0
1
2
1
1
0
1
2
2
1
2
0
1
0
2
0
0
0
1
0
2
2
2
0
1
0
0
1
2
1
1
0
1
0
1
1
1
2
1
0
0
1
0
2
1
1
1
1
1
1
1
1
0
2
2
1
1
0
1
0
1
0
2
0
1
0
1
0
0
0
0
1
0
2
2
2
1
2
1
0
1
1
0
1
2
2
1
1
0
0
2
1
1
2
0
2
2
1
1
2
0
3
0
0
2
3
2
2
3
2
2
2
4
2
1
1
1
1
0
1
0
1
2
1
0
0
0
1
1
1
0
3
1
0
0
1
1
2
0
0
1
2
1
1
0
1
1
1
1
1
2
2
0
0
2
1
2
1
2
0
3
1
2
3
0
1
1
0
1
2
1
0
1
2
0
1
0
1
0
0
2
2
1
0
0
1
1
1
1
0
1
1
1
1
0
2
1
0
1
0
1
2
0
1
1
0
1
2
2
0
2
1
2
1
2
1
0
2
2
0
3
2
1
0
1
0
1
2
2
0
0
1
2
0
2
1
2
1
1
2
1
0
2
1
0
0
2
2
1
0
2
0
1
0
1
0
1
1
1
1
0
1
1
2
0
1
0
1
2
0
1
1
0
2
1
2
2
2
0
0
0
2
1
1
2
1
2
1
2
0
0
1
3
0
2
2
1
0
0
1
0
1
1
1
0
2
1
1
2
1
2
0
1
0
0
1
0
0
0
1
1
0
1
1
1
1
1
1
0
1
0
1
2
1
2
1
1
0
1
0
0
0
2
1
1
0
1
1
1
0
1
0
1
1
1
2
1
1
1
0
1
1
1
1
0
0
1
1
1
1
0
2
0
0
1
1
0
1
1
0
0
1
0
0
0
0
1
2
0
1
2
1
2
1
0
2
0
2
2
1
0
2
0
1
1
1
1
2
2
0
1
1
2
0
0
0
1
0
1
1
1
2
1
0
1
0
2
1
1
2
1
2
1
1
0
0
1
1
0
0
0
0
1
2
2
1
2
1
1
0
0
0
2
1
0
2
1
0
2
0
1
0
0
2
2
0
1
0
1
0
2
1
1
1
1
2
1
1
1
0
0
1
2
1
0
0
1
1
2
1
1
0
1
0
2
2
1
1
2
2
1
1
0
0
1
1
2
1
0
2
2
1
2
1
0
1
1
1
1
2
0
0
2
0
1
1
0
0
0
1
1
1
1
1
0
1
0
0
2
1
2
1
0
0
2
2
0
2
1
2
0
0
2
2
1
1
2
1
1
0
1
1
1
1
0
0
1
1
0
0
1
2
2
1
1
1
0
0
1
1
2
1
2
0
2
0
2
1
2
0
1
2
1
0
0
1
2
0
0
2
0
2
1
0
1
2
3
0
0
1
1
1
1
1
1
0
0
0
2
1
0
0
0
1
1
2
0
1
2
0
2
1
2
1
1
0
1
2
1
1
0
1
1
2
2
0
1
0
0
4
2
0
0
0
0
1
2
0
0
0
1
0
1
2
1
0
1
2
1
0
1
0
1
1
1
0
0
2
0
2
0
0
0
2
2
1
2
0
0
2
0
1
1
1
2
0
1
1
2
2
1
0
0
2
0
0
1
1
2
2
1
1
1
0
0
0
0
0
1
2
0
1
1
2
1
1
1
2
2
2
0
1
0
1
1
1
1
2
1
1
0
1
1
1
1
1
1
1
1
1
1
1
0
1
1
0
0
2
0
0
1
2
2
1
1
1
0
2
2
2
3
2
1
2
0
2
0
1
1
2
1
1
1
0
1
2
0
3
1
1
1
1
0
1
0
2
0
0
0
0
0
0
1
1
0
2
0
1
1
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
2
1
1
1
1
2
1
1
2
1
1
2
1
1
1
1
1
0
2
2
0
2
1
2
2
1
1
1
1
1
3
1
1
2
0
2
0
2
1
1
0
1
1
0
0
2
2
1
1
0
1
2
1
0
1
0
1
0
2
0
0
1
1
2
0
0
2
1
1
1
0
0
1
1
0
0
1
2
0
0
0
2
1
0
1
1
1
1
1
1
1
0
1
1
1
0
2
1
1
0
0
0
0
1
1
1
0
1
1
1
2
0
1
1
1
1
1
1
0
0
2
0
1
0
0
1
2
1
1
3
1
0
2
2
0
1
1
0
2
1
0
1
2
1
0
1
1
1
0
0
2
0
1
0
2
2
1
1
0
1
1
1
1
1
2
0
1
2
2
1
2
1
1
0
1
0
1
1
0
0
0
0
0
0
1
1
1
1
2
0
1
0
1
1
0
0
0
0
0
2
0
0
0
1
0
0
1
2
2
0
2
0
0
1
2
1
0
0
0
2
0
1
2
1
1
1
0
1
2
0
2
1
1
1
2
1
1
1
0
1
0
1
1
1
2
0
2
0
1
0
0
1
1
0
1
0
0
1
1
0
2
2
0
0
2
0
1
0
2
1
1
2
3
3
2
0
0
1
0
2
1
0
0
0
2
1
0
1
1
0
1
0
0
1
1
1
2
1
1
2
1
3
1
0
3
2
1
0
1
0
1
0
0
2
1
2
1
0
1
0
2
0
0
2
1
1
1
0
1
2
0
2
1
2
0
1
1
1
2
0
1
1
1
0
1
1
0
1
2
0
1
1
1
0
1
1
2
1
1
1
0
1
2
1
0
2
2
0
0
0
0
0
1
1
0
1
2
2
2
0
2
2
1
1
1
0
0
0
1
1
0
0
1
1
0
1
1
2
1
2
1
0
0
0
1
1
2
0
0
0
2
1
0
2
1
0
0
0
1
0
2
1
1
1
0
0
2
1
2
1
2
0
0
1
2
1
0
0
1
0
0
1
0
2
0
1
0
1
0
0
0
0
0
2
0
0
0
2
1
2
3
2
2
1
2
5
0
0
1
2
1
0
2
1
1
0
0
0
0
1
0
0
0
2
0
2
1
0
1
0
1
1
0
1
1
0
1
0
1
1
0
1
1
0
0
2
0
2
1
1
0
3
1
0
1
0
2
0
1
1
1
0
0
2
2
1
1
2
2
0
0
2
1
2
0
1
2
2
1
1
2
2
0
1
1
2
0
0
1
0
0
2
1
0
2
1
1
0
0
2
1
1
2
2
1
1
1
1
0
1
1
2
0
1
2
2
0
0
0
0
2
1
0
2
1
1
1
1
0
0
4
1
0
0
1
2
2
2
0
1
1
3
0
1
2
1
1
2
0
0
1
0
1
1
2
1
2
0
1
1
2
2
0
1
0
0
2
1
0
1
1
1
0
1
1
1
2
1
0
1
2
1
0
0
1
1
0
1
1
1
1
2
0
0
1
1
1
0
0
0
1
0
1
0
1
1
0
1
0
0
0
1
1
1
2
1
2
1
1
0
0
1
0
0
1
2
2
0
0
0
0
1
1
0
1
1
2
0
1
1
1
1
1
0
1
0
0
1
1
2
1
1
0
1
2
2
0
1
1
0
0
2
0
1
1
0
1
1
1
0
0
1
2
1
0
0
1
1
0
0
0
0
2
1
0
1
0
0
1
1
0
1
0
1
2
1
1
2
2
1
0
0
0
0
1
0
2
1
1
1
1
0
0
1
1
0
2
1
0
0
0
2
0
2
1
0
1
1
1
1
2
1
2
0
1
1
0
0
1
2
0
2
0
1
0
0
2
1
1
1
1
0
2
0
1
1
0
2
0
0
0
2
1
1
0
1
1
0
0
0
0
0
0
1
1
1
1
0
0
2
0
0
0
0
1
0
1
1
1
0
1
2
1
0
2
0
0
0
0
1
2
0
1
0
1
1
1
1
1
2
0
2
2
1
0
1
0
1
1
1
1
0
0
3
1
1
1
1
1
1
2
2
0
0
0
1
1
0
0
2
1
0
2
1
1
1
0
1
1
0
1
0
1
0
1
0
0
1
1
1
1
2
1
0
1
1
1
0
1
2
0
0
1
1
0
1
1
0
0
0
1
2
1
0
0
1
0
2
1
0
2
0
1
0
1
2
1
0
1
2
1
0
1
1
1
1
1
1
0
1
0
3
0
1
0
0
1
1
1
2
1
1
1
1
0
2
1
1
0
2
0
1
0
1
0
2
1
0
1
0
1
1
1
0
1
0
0
0
0
1
1
0
1
0
1
1
1
0
1
0
1
0
2
1
2
1
1
1
0
1
2
0
1
1
0
1
1
1
2
0
1
2
0
1
0
1
0
1
1
0
2
0
1
0
1
2
2
0
0
1
0
0
1
1
1
0
0
1
0
2
0
2
2
0
0
1
0
1
0
1
3
2
1
2
0
0
1
0
0
1
1
3
1
1
1
0
2
1
1
2
0
2
0
1
1
1
1
1
2
2
1
4
1
1
0
0
1
2
0
0
1
0
0
1
0
1
1
2
1
0
0
0
0
0
0
0
0
1
1
0
1
2
1
0
2
1
2
2
1
1
1
0
2
1
0
1
2
1
1
0
1
0
0
0
0
2
1
0
1
0
2
1
2
1
0
0
1
1
1
0
0
2
1
1
1
1
0
1
1
0
1
0
2
1
2
0
4
2
1
0
1
0
1
0
0
0
1
4
1
1
1
2
0
0
2
0
0
0
2
0
0
0
0
1
1
2
1
2
0
0
1
0
2
0
1
0
1
1
1
1
0
1
1
1
2
0
2
1
1
0
1
1
0
0
1
1
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
2
0
0
2
2
0
0
1
0
1
0
0
0
0
2
1
0
2
0
0
0
2
0
0
1
1
1
1
0
1
0
2
1
2
0
1
0
0
2
0
2
1
1
1
0
0
1
0
1
1
1
1
1
1
1
2
1
2
1
0
1
2
0
0
1
0
0
0
0
2
1
0
1
2
3
1
0
2
2
0
1
1
2
2
1
0
0
2
2
1
1
1
2
2
2
0
2
2
1
0
0
0
1
2
0
1
0
1
0
0
0
0
1
2
0
2
3
1
0
0
0
1
2
1
0
1
1
2
0
1
0
1
1
2
1
0
1
0
2
2
1
1
0
1
0
0
2
1
1
1
0
3
0
2
0
0
2
1
0
1
0
0
1
2
1
0
0
0
1
0
1
2
0
0
1
1
0
2
2
4
2
1
2
0
0
1
0
1
2
2
1
1
0
2
2
0
0
2
0
1
1
1
1
2
2
0
0
0
1
1
2
1
1
6
1
0
1
0
0
1
1
1
2
0
1
0
0
2
2
0
0
1
2
1
2
1
1
1
1
0
2
1
1
2
3
1
0
2
0
1
0
1
1
0
0
1
1
0
2
0
0
0
2
2
1
0
0
0
0
0
2
1
1
1
0
1
0
0
1
0
1
2
3
0
1
2
0
1
1
2
0
1
0
2
1
0
1
1
1
1
2
0
0
0
1
0
2
2
0
1
1
1
1
2
1
0
1
1
1
1
2
1
1
3
0
1
2
1
1
0
2
0
1
0
0
0
1
1
1
0
2
2
1
0
3
0
0
1
1
0
1
1
2
1
1
1
1
2
0
2
0
0
1
2
1
0
1
1
0
2
1
0
0
2
0
1
2
2
1
2
1
1
2
1
1
0
1
2
0
0
0
0
1
2
1
2
2
2
2
2
0
1
0
1
0
1
1
0
1
2
1
2
0
2
1
0
0
0
1
2
1
0
1
3
0
0
0
0
2
0
0
1
1
1
1
0
0
0
2
0
1
1
0
1
4
1
0
1
1
1
0
0
0
1
0
1
0
2
0
1
1
2
2
1
1
0
0
2
0
2
2
1
1
2
0
0
0
0
1
2
1
1
0
2
0
1
0
1
1
1
1
0
1
1
0
1
1
0
0
0
1
1
1
0
1
0
2
0
1
0
1
0
0
1
1
1
1
1
1
2
1
0
1
0
1
1
0
0
2
1
0
1
0
1
0
1
2
1
1
0
0
0
2
1
0
1
1
1
0
0
1
0
0
2
2
1
0
1
0
1
0
0
0
1
1
1
1
0
0
1
1
2
0
2
1
1
1
2
0
1
0
0
1
1
0
1
1
1
2
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
2
0
0
2
2
2
0
1
0
0
3
0
0
1
0
0
1
0
0
0
1
1
1
0
1
2
2
1
1
1
2
1
2
1
0
1
1
1
0
0
1
1
1
2
0
0
0
1
3
1
0
2
0
1
2
2
1
2
0
1
0
2
2
1
1
1
0
1
1
2
1
1
2
0
1
0
1
1
3
1
0
0
0
2
1
1
0
1
2
0
0
1
2
2
1
2
0
2
1
1
0
1
1
1
0
1
1
1
1
1
1
2
1
0
0
1
0
1
1
2
1
1
1
1
1
0
1
1
1
0
2
0
1
2
1
1
1
2
1
1
0
1
2
7
1
0
1
0
1
1
0
1
0
1
1
2
2
0
0
1
2
1
1
1
1
2
0
1
0
1
1
0
1
2
1
2
2
2
2
1
2
1
2
1
0
0
0
0
0
2
1
0
0
3
0
2
0
0
2
0
2
1
1
2
2
2
1
1
2
1
0
0
0
1
1
2
0
1
2
1
0
2
1
2
2
0
0
2
0
0
1
0
1
2
1
1
2
2
1
2
2
0
1
0
1
1
2
0
1
0
1
0
1
0
1
0
1
2
2
0
0
0
2
1
1
1
0
0
1
0
2
0
1
0
5
2
0
0
2
2
0
0
1
2
3
0
1
2
2
0
1
0
1
1
2
1
1
1
0
0
0
1
0
0
0
1
0
1
1
1
1
1
0
2
0
0
0
2
1
1
0
2
2
2
1
1
2
2
0
0
0
2
0
0
2
1
0
2
2
2
1
0
2
0
0
1
1
0
2
2
1
2
0
0
0
0
1
1
2
1
1
0
1
1
1
0
0
1
0
0
1
1
2
2
2
1
2
1
0
2
0
1
0
1
2
0
0
0
0
1
0
2
1
1
1
0
2
2
2
0
1
1
1
1
0
1
1
1
0
1
1
1
0
1
2
0
1
0
0
0
1
1
0
2
0
2
1
0
2
1
0
2
1
1
0
1
0
1
1
0
0
2
1
0
2
0
1
0
2
1
1
1
2
1
1
1
1
1
1
2
0
2
1
0
0
2
2
1
1
1
1
1
0
0
2
1
1
1
1
1
1
2
1
0
1
0
0
0
0
1
0
0
1
0
1
0
1
0
1
0
1
0
1
0
2
1
1
2
0
1
2
1
1
1
0
1
1
1
1
1
0
1
1
0
0
1
1
1
0
0
1
1
0
2
2
1
1
1
0
1
1
1
1
0
1
0
1
0
2
0
0
1
1
1
2
1
1
1
0
0
0
0
2
1
1
0
1
1
0
2
1
1
2
1
0
2
1
1
0
1
1
1
1
0
2
0
0
2
1
1
1
1
0
0
1
2
0
0
3
1
1
1
2
0
2
0
1
0
2
0
1
2
1
0
1
1
2
0
1
1
1
2
0
1
0
2
1
2
0
2
0
1
1
1
1
0
0
1
0
1
0
2
0
0
2
0
0
1
0
1
1
0
1
0
1
0
1
0
0
2
1
0
1
1
1
1
1
1
1
0
2
1
1
1
0
0
0
0
1
0
1
1
1
0
0
0
1
1
1
1
2
0
0
1
0
1
1
2
1
0
2
2
0
0
1
0
1
0
2
1
2
1
0
0
0
2
1
0
1
0
2
2
1
0
1
1
1
0
0
0
2
0
0
2
1
1
0
0
1
2
1
2
2
1
0
0
0
2
0
0
1
0
1
3
1
0
0
2
1
0
1
0
2
0
1
0
1
1
1
1
0
2
2
1
1
0
2
1
0
1
2
2
1
0
1
0
1
1
0
0
0
0
1
0
2
1
0
1
1
1
2
0
2
1
2
1
0
0
2
2
1
1
2
2
2
0
1
2
0
0
1
0
1
2
1
0
0
0
1
2
2
0
1
1
1
2
2
1
0
1
2
0
1
0
0
2
2
0
0
2
2
1
1
2
0
0
0
1
1
2
1
2
1
0
2
0
0
1
0
0
2
1
2
2
2
0
2
0
1
1
0
1
0
0
1
4
0
0
2
0
1
1
1
1
0
1
0
1
0
0
0
0
1
1
0
1
1
2
0
1
1
0
2
1
1
1
3
1
1
1
0
0
1
0
1
1
2
0
0
1
2
1
1
0
0
1
0
1
2
1
1
1
0
1
1
1
1
4
2
2
1
2
0
0
0
0
2
0
1
2
0
2
2
2
1
0
2
1
0
2
0
0
1
1
0
2
1
0
1
1
1
2
2
2
1
1
1
1
0
0
2
1
0
0
0
1
1
0
0
2
2
2
2
2
0
0
1
0
1
0
2
0
1
2
3
2
0
1
0
0
1
1
1
1
0
1
0
0
2
1
0
1
1
1
1
2
2
2
0
0
1
1
1
1
1
0
1
0
1
0
0
1
0
0
0
0
1
2
1
1
6
1
3
0
2
0
1
1
0
0
1
1
1
0
1
0
1
0
0
0
1
2
0
1
1
0
1
0
2
3
1
1
0
0
0
1
1
0
1
1
0
2
0
0
1
2
0
1
1
0
0
2
2
0
1
0
3
0
2
2
0
3
0
0
0
1
2
2
0
1
0
2
1
0
2
1
1
2
0
1
1
0
1
0
1
0
0
1
0
1
1
0
1
1
1
1
2
0
1
1
2
1
1
0
1
3
1
2
0
2
1
2
1
0
0
0
1
2
1
0
2
1
0
1
0
1
2
1
2
2
0
1
0
1
1
0
1
0
1
1
2
2
0
2
0
0
0
0
1
2
1
1
0
1
1
1
2
0
1
0
1
1
1
1
0
0
0
2
2
2
1
1
2
1
1
1
1
1
2
1
1
0
0
0
1
2
1
0
1
4
0
1
2
1
0
1
2
0
1
1
0
1
1
1
1
0
1
0
1
1
1
1
1
1
0
0
0
0
1
0
1
0
0
0
2
0
0
2
0
0
0
1
1
1
2
1
2
1
1
1
1
1
0
1
0
1
3
2
0
2
2
0
0
1
0
2
0
0
2
0
1
1
0
0
3
0
1
1
2
1
0
1
0
0
0
0
0
0
2
1
0
1
1
0
2
0
1
3
0
1
2
0
1
1
1
0
1
0
0
2
0
2
1
1
1
1
1
1
2
1
2
0
1
2
0
2
0
1
0
0
1
0
1
2
0
0
0
1
0
1
1
0
1
0
0
0
1
1
2
2
1
1
2
2
2
0
1
2
0
1
1
1
2
0
0
0
1
0
1
1
2
1
0
1
1
1
1
1
0
1
2
1
1
2
2
1
1
2
0
1
0
0
0
1
1
1
0
0
0
1
1
1
1
2
0
0
0
1
3
1
2
2
0
0
1
0
0
0
0
0
0
1
0
0
1
1
1
0
1
0
1
2
0
1
0
0
0
1
1
0
0
0
1
0
2
0
0
2
0
2
0
0
0
0
1
0
0
2
0
0
2
0
1
0
3
0
1
3
0
1
2
1
2
0
2
1
0
3
2
1
3
0
4
3
1
1
2
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
2
0
1
1
2
1
2
1
1
1
1
1
2
1
2
0
1
2
0
2
0
1
0
1
0
1
2
1
1
1
0
1
1
2
1
2
1
1
0
1
2
0
1
0
1
0
1
1
2
1
1
1
0
1
0
0
0
1
1
1
2
2
1
2
0
0
0
0
2
1
1
1
0
1
1
0
1
0
1
2
1
0
1
0
1
3
1
1
1
1
1
1
1
0
1
1
1
0
2
0
1
1
0
0
2
1
0
2
0
0
0
2
1
0
1
1
1
1
2
0
0
0
1
0
0
1
0
2
0
1
1
2
1
1
1
1
1
2
1
0
1
2
0
0
2
0
0
0
1
1
1
1
1
0
0
1
1
1
0
0
1
0
0
0
1
2
0
1
0
0
0
0
0
1
2
1
2
0
0
1
0
1
1
0
1
2
1
1
1
1
1
0
2
0
0
0
1
1
1
1
0
1
0
1
0
1
0
1
1
0
1
0
0
1
1
1
1
0
0
1
1
1
1
0
0
0
1
2
0
0
2
1
2
1
1
0
0
2
1
0
1
0
2
1
1
0
1
0
1
1
1
0
1
0
1
1
1
2
0
2
2
0
1
0
2
0
0
1
1
2
0
3
0
1
1
1
0
0
1
1
0
0
1
0
1
1
2
0
2
0
2
2
0
1
1
2
0
1
2
2
1
1
1
3
0
0
0
1
1
1
2
1
0
1
1
2
1
0
1
1
0
2
2
0
1
0
0
0
2
2
1
0
1
0
1
1
2
0
1
1
0
1
0
0
0
1
1
0
1
1
0
1
0
0
3
0
2
2
1
2
0
0
1
1
1
1
1
0
2
0
0
1
1
0
1
2
1
1
1
1
1
1
1
1
1
1
2
1
0
1
1
0
1
2
2
0
0
1
1
1
1
4
2
0
2
0
1
0
0
0
2
2
1
0
1
1
2
2
2
1
1
2
0
1
2
1
1
1
0
0
1
1
0
1
1
2
3
1
1
0
1
1
2
1
0
0
0
2
0
1
2
0
1
2
0
2
1
1
3
1
1
1
0
2
2
1
0
0
0
0
0
1
1
2
2
0
2
0
2
1
0
1
0
1
1
1
0
1
0
0
2
1
1
0
2
1
1
2
2
0
0
2
2
1
0
3
2
1
0
0
0
2
0
1
1
1
1
1
1
1
0
0
2
0
0
2
1
2
1
1
1
1
2
0
0
1
0
1
0
2
2
2
0
4
2
1
0
1
1
1
1
0
1
0
2
2
2
2
0
0
0
1
1
1
2
1
1
1
1
0
0
2
0
2
1
1
0
1
1
2
1
0
0
1
0
2
0
1
1
1
1
1
0
0
1
0
2
2
0
1
1
0
1
1
2
1
0
1
0
1
1
1
1
1
1
2
0
2
1
0
0
0
1
1
1
0
1
0
0
1
0
0
1
2
1
0
1
2
0
1
0
1
0
0
0
2
1
0
2
2
1
1
1
0
1
2
2
0
0
1
2
0
2
1
0
1
1
1
2
1
1
1
0
0
1
0
3
1
0
2
1
1
2
1
1
1
0
1
2
1
1
1
1
1
1
1
1
0
0
1
0
0
1
1
1
2
1
1
1
1
0
1
0
0
1
0
1
1
0
1
2
0
0
1
2
3
1
1
0
2
2
0
2
2
2
1
0
0
1
1
1
1
2
2
1
1
0
1
1
1
0
1
0
0
1
0
0
1
0
0
1
0
0
2
0
0
1
0
0
1
2
2
0
0
0
0
0
1
1
2
1
1
1
1
1
0
0
0
1
1
0
0
0
2
0
2
0
0
1
0
1
0
0
1
1
1
0
6
0
0
1
1
1
1
1
1
1
0
0
1
1
1
3
1
0
2
0
0
0
1
0
0
0
0
2
2
0
1
0
1
2
1
1
1
0
2
1
1
1
0
0
0
0
0
2
1
1
2
2
2
1
1
0
1
0
0
2
1
1
0
2
0
1
1
1
1
0
2
1
0
0
1
2
0
0
2
0
1
1
0
0
2
2
1
2
1
0
0
0
0
0
1
0
1
1
2
0
1
2
0
1
0
1
2
0
0
0
1
0
0
1
1
1
0
1
3
2
2
1
0
1
0
0
0
1
1
1
0
0
0
2
0
1
2
0
0
1
0
0
0
0
1
1
2
1
0
0
2
2
2
0
1
7
0
0
1
0
0
1
0
2
1
0
1
1
1
0
0
1
1
1
2
0
0
0
0
0
0
0
1
2
1
0
1
1
2
1
0
1
1
1
1
1
0
1
0
2
1
1
1
1
2
1
1
2
2
2
0
2
0
2
2
1
0
0
1
1
1
1
2
0
1
1
1
1
2
1
1
2
0
0
1
1
1
0
2
2
2
1
0
0
1
0
1
0
1
0
0
0
0
1
2
0
1
1
0
1
1
2
0
0
0
0
2
1
1
2
1
1
0
0
2
2
1
0
2
2
1
0
0
2
1
1
2
0
1
1
1
0
0
1
1
0
1
1
1
0
2
1
2
0
1
0
0
0
0
1
1
0
0
2
1
1
1
1
1
2
2
2
1
1
0
0
1
1
1
0
0
1
0
2
1
3
0
1
4
0
1
0
0
1
0
0
0
1
2
1
1
1
1
1
1
1
0
1
1
0
2
1
2
0
1
1
1
2
1
1
0
1
1
2
1
1
1
0
2
0
0
0
2
0
1
1
2
1
1
1
1
2
1
1
1
2
0
0
2
1
0
0
2
0
1
1
1
0
1
0
2
2
1
0
1
0
0
1
1
1
2
1
1
0
1
0
0
1
0
1
0
2
0
1
0
1
1
3
2
3
0
1
1
2
1
0
0
1
2
0
3
1
1
1
2
1
1
2
1
0
1
1
2
0
0
1
0
1
0
1
2
0
0
1
1
0
2
2
2
2
2
1
0
0
1
0
1
2
0
1
1
2
1
1
1
0
1
0
0
0
0
1
2
0
1
0
1
0
2
1
0
2
1
0
1
1
1
1
0
0
0
0
0
1
1
2
1
0
2
1
0
1
1
0
0
1
1
0
1
0
1
0
1
1
1
0
1
0
2
1
2
1
1
2
1
0
1
1
2
2
2
2
1
1
1
0
1
1
0
1
2
0
0
1
0
0
2
1
1
1
1
2
0
1
2
0
1
0
1
2
1
1
1
0
1
1
0
0
0
1
0
0
2
1
1
2
1
0
1
0
1
5
2
0
2
1
1
1
1
0
0
0
1
0
0
0
0
1
0
1
1
0
2
1
1
0
0
1
2
1
1
1
2
1
3
2
1
1
2
2
0
2
0
1
2
1
1
1
1
2
0
1
0
1
0
0
0
2
0
1
2
1
0
0
0
0
0
1
0
1
1
0
0
0
0
1
2
0
0
2
1
1
0
1
0
1
1
1
1
4
1
2
0
1
1
1
0
1
2
0
2
1
0
2
2
0
1
1
2
2
0
0
2
1
0
0
1
0
3
1
1
1
2
0
1
2
2
1
2
0
0
1
1
1
1
1
0
0
1
0
0
2
1
1
0
1
0
1
1
2
0
1
4
1
0
1
2
1
0
1
0
0
1
1
2
0
1
2
0
1
2
0
1
0
1
0
1
2
1
2
1
2
1
1
2
1
2
1
0
0
1
2
1
0
1
1
1
0
2
0
0
2
0
0
0
0
0
1
0
0
1
1
0
1
0
0
1
0
2
2
1
2
0
1
2
1
0
1
1
1
1
1
1
1
2
1
0
0
2
2
1
0
1
2
1
2
1
2
0
1
0
1
2
1
0
1
1
2
0
0
0
1
2
1
0
1
0
1
1
0
0
1
0
1
2
1
0
0
0
2
1
1
0
0
1
1
2
2
1
2
2
1
1
1
1
3
0
1
2
1
2
1
1
2
2
1
2
1
0
1
1
0
1
0
2
0
1
1
0
1
2
1
2
2
1
0
0
2
2
0
2
1
0
0
1
0
0
0
0
1
0
2
1
1
1
0
0
2
2
1
1
1
0
2
1
0
0
0
0
0
1
1
1
1
0
2
1
1
1
0
0
0
0
2
0
1
2
2
0
1
0
0
1
1
1
0
1
0
0
0
2
1
1
0
2
2
2
2
2
1
2
1
1
0
0
1
2
1
0
2
0
2
2
0
0
1
3
0
1
1
1
1
1
1
2
0
1
0
2
2
1
1
1
3
2
0
2
2
0
1
1
0
1
1
1
1
2
1
1
2
0
0
2
0
1
0
0
0
1
1
2
1
1
0
1
0
1
1
1
2
1
0
2
2
2
0
0
1
0
0
2
2
0
0
1
2
1
0
1
1
1
1
0
1
1
2
1
0
2
1
1
1
1
0
1
0
2
1
1
2
1
0
1
1
1
2
1
0
1
0
0
0
1
2
0
1
1
0
1
0
0
0
0
2
0
2
0
1
1
0
1
0
0
0
1
0
1
0
1
0
2
0
1
1
1
2
1
1
0
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
0
1
1
2
0
0
0
1
0
1
0
0
0
1
1
1
0
2
0
0
1
1
0
1
0
2
1
2
0
1
1
2
1
0
0
1
0
0
1
1
1
0
1
0
3
0
0
0
0
1
2
0
1
2
0
1
0
1
0
2
1
2
1
1
1
1
1
1
0
1
1
2
0
0
0
0
2
2
1
1
0
0
0
1
1
0
2
0
1
0
1
2
1
1
0
3
0
2
0
2
1
1
1
2
1
0
1
1
1
1
1
0
1
1
2
1
0
0
1
2
0
1
2
2
0
0
5
0
1
0
1
0
0
0
0
1
1
2
2
2
1
1
1
0
0
1
1
2
0
0
0
2
0
0
3
0
1
1
0
0
0
0
2
0
0
0
0
1
1
0
1
1
1
0
1
1
1
1
1
1
2
2
0
2
1
0
1
2
1
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
1
0
0
1
1
0
1
1
1
0
0
1
1
0
1
0
0
2
0
2
0
0
0
0
0
1
1
0
0
3
1
0
2
0
0
0
2
1
0
1
0
0
2
0
1
1
0
0
0
1
0
1
0
0
1
1
1
0
2
1
1
2
2
0
0
2
1
1
1
0
1
2
1
0
2
0
0
1
0
1
2
1
2
1
1
1
0
1
1
2
1
1
0
0
2
1
2
2
0
1
0
1
1
1
1
1
1
1
1
0
2
1
2
0
2
1
1
2
2
1
0
1
1
0
1
1
2
1
1
1
3
1
3
2
1
2
2
1
0
2
2
0
0
2
1
0
2
1
1
0
0
1
0
1
0
0
1
0
0
1
0
0
0
1
1
1
1
0
1
2
1
0
0
1
0
0
2
1
0
1
1
2
0
0
0
2
1
2
1
2
1
1
1
1
2
0
1
1
2
0
1
0
2
0
2
1
0
1
1
0
1
1
0
0
1
1
1
1
1
0
1
2
1
1
0
2
2
1
2
1
0
1
1
1
0
1
0
0
2
2
0
1
1
2
1
0
2
1
1
0
2
1
0
0
1
1
2
0
2
2
0
2
0
0
1
2
1
1
1
1
0
0
0
0
1
1
2
0
1
1
0
2
2
2
2
0
0
1
1
1
0
0
0
1
1
0
2
0
0
0
1
1
0
1
0
1
0
1
1
1
0
1
0
0
1
2
0
1
2
1
1
0
0
1
1
2
0
0
2
0
1
2
1
0
2
1
1
2
0
1
2
0
2
0
1
1
0
0
1
3
0
1
2
0
0
2
0
1
0
1
0
1
2
1
1
0
1
2
1
0
1
2
0
1
2
0
1
0
2
1
1
1
1
0
1
1
0
0
2
0
1
1
0
0
2
2
1
2
0
1
2
0
1
1
1
0
2
0
1
1
1
1
0
1
1
0
0
0
1
2
2
1
0
2
0
0
2
1
2
2
1
2
0
0
1
0
0
0
1
2
0
1
0
2
1
2
0
2
2
2
0
0
0
0
2
1
0
0
0
0
1
0
1
1
1
1
0
0
0
1
0
0
0
0
2
1
0
1
2
1
0
2
2
0
0
1
2
0
1
1
1
0
0
2
2
1
2
0
0
0
0
0
0
2
1
2
2
1
3
1
0
1
0
0
1
1
1
1
0
1
2
2
2
0
0
1
0
0
1
0
1
1
0
1
5
2
0
1
0
0
0
0
0
0
1
1
1
0
1
2
2
1
0
2
1
1
2
1
2
0
0
0
1
1
1
0
2
0
1
2
0
0
0
0
0
0
2
1
0
0
0
1
1
1
0
0
1
1
0
1
1
0
2
0
0
0
2
2
0
0
1
1
1
0
1
4
1
0
0
0
0
2
1
0
0
2
1
0
2
0
0
1
1
0
0
1
1
0
2
0
1
0
2
0
0
1
0
0
2
2
0
2
2
2
1
2
1
1
3
2
0
0
1
0
0
1
0
3
0
0
1
0
0
0
2
0
1
0
0
0
1
0
0
1
0
0
1
2
0
1
0
0
2
0
2
2
2
0
0
0
1
0
1
0
0
1
1
1
1
1
0
0
1
1
1
1
1
2
2
1
0
2
2
0
0
1
0
1
0
1
2
1
2
1
1
1
1
0
1
1
1
0
1
0
1
1
1
1
1
0
1
0
1
1
0
1
2
1
1
2
1
2
1
2
0
0
2
1
2
1
2
0
2
1
1
2
1
0
0
0
0
0
0
1
2
1
0
2
1
0
2
2
1
1
0
1
1
0
1
1
0
1
1
0
1
1
1
1
0
1
0
1
0
2
0
0
1
1
0
1
0
1
2
0
1
1
1
0
0
0
0
0
2
1
1
1
1
0
2
1
2
0
0
2
1
0
1
1
1
1
0
1
0
0
1
2
0
0
0
1
0
1
0
1
1
1
2
1
2
0
1
1
0
1
2
0
2
1
1
2
0
0
0
0
0
1
1
1
1
1
0
2
1
1
0
0
0
0
0
1
0
0
1
1
1
0
2
2
1
2
1
0
1
1
2
2
0
3
1
0
1
2
2
1
2
1
1
1
1
2
1
2
1
0
1
1
2
2
1
0
0
0
1
0
2
0
1
1
0
2
1
0
0
1
0
2
1
0
0
2
2
1
1
0
0
2
0
2
0
1
2
1
1
0
2
1
0
1
0
0
0
1
1
2
1
1
0
2
2
1
0
0
1
1
1
1
2
0
0
0
0
1
1
0
1
1
1
1
2
0
0
0
1
1
2
0
0
0
0
1
2
0
2
0
1
1
1
2
0
2
0
1
1
1
1
0
1
0
1
1
2
0
2
1
0
0
2
0
1
0
1
1
1
4
2
1
2
2
1
0
2
2
0
1
0
1
0
0
0
1
2
2
1
1
0
1
1
1
2
0
1
2
2
2
2
1
0
1
1
2
0
0
0
0
1
2
1
0
0
2
1
1
2
2
1
0
0
2
1
0
2
1
1
0
1
2
0
2
0
1
1
1
0
1
1
1
0
0
0
1
0
1
2
2
1
0
2
0
0
2
1
2
1
2
3
2
1
1
2
0
1
2
1
1
2
1
0
1
1
1
0
2
1
0
1
1
1
1
0
0
0
1
1
1
1
0
2
2
0
0
0
2
2
1
1
0
1
2
1
0
0
0
1
0
1
1
0
0
1
1
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
1
0
1
2
2
1
0
1
2
2
0
1
0
0
2
1
1
1
0
2
2
0
2
1
1
0
0
2
1
2
1
2
0
1
0
2
0
0
0
1
0
1
2
0
0
0
2
0
2
2
0
0
2
1
0
0
1
2
0
1
1
1
1
0
2
2
0
1
2
2
1
1
1
1
2
0
1
0
1
0
1
1
2
1
1
2
1
0
2
1
1
1
0
1
0
2
0
1
2
1
2
0
0
2
1
2
0
1
1
0
1
1
1
1
0
2
1
2
1
2
0
2
1
1
1
1
0
1
1
0
2
1
3
1
0
1
1
1
1
2
0
2
0
1
0
1
3
1
1
1
1
0
1
1
1
0
1
1
2
1
1
1
1
1
0
2
1
0
2
1
0
0
1
0
2
3
0
0
1
0
1
0
1
1
2
0
0
4
1
0
1
1
0
0
2
2
0
1
1
2
0
0
2
3
1
1
0
1
1
1
2
1
2
1
1
1
1
0
0
0
0
0
1
2
1
0
0
1
0
0
1
0
1
1
1
1
2
2
1
1
1
1
2
2
2
1
0
1
2
1
2
0
2
0
2
0
1
0
0
1
0
0
0
2
1
1
1
0
2
1
0
1
0
2
0
1
0
0
0
1
1
1
2
0
1
0
0
1
1
2
1
2
1
0
2
2
2
1
1
0
1
2
2
0
1
2
1
0
0
0
1
0
0
0
1
2
0
1
1
1
0
1
1
0
0
0
1
1
0
1
0
0
0
1
1
2
2
2
0
2
0
2
0
0
2
1
1
2
0
2
1
1
1
3
1
0
1
2
0
2
1
2
0
0
1
0
1
0
1
0
1
1
0
0
1
0
1
1
0
1
0
1
2
1
2
0
0
2
0
0
1
2
3
2
1
1
2
0
2
0
2
0
2
0
1
0
0
1
1
0
0
1
1
1
0
1
2
2
0
1
1
1
1
1
1
0
1
1
1
1
1
0
0
2
0
1
0
2
2
1
1
0
1
2
1
6
1
0
1
0
1
1
0
0
0
2
1
2
0
1
0
1
2
0
0
1
3
0
2
1
2
0
0
1
2
1
1
2
1
1
0
0
2
1
0
0
2
0
1
1
0
1
1
1
0
1
1
2
1
0
0
3
1
1
1
0
1
2
2
1
1
2
1
0
2
0
1
2
1
0
2
4
1
2
0
0
2
2
0
1
0
1
2
1
1
0
2
1
2
0
0
2
1
0
1
1
0
2
0
0
0
1
0
0
0
2
2
2
2
1
1
1
2
1
1
1
1
2
0
1
2
0
0
1
0
2
1
1
0
0
2
0
1
1
2
1
1
0
2
2
1
0
0
2
1
1
1
0
1
1
0
1
2
0
1
0
1
0
0
0
1
0
0
1
1
1
0
1
0
0
0
1
1
0
2
0
1
0
0
1
0
1
1
1
0
2
2
0
2
1
0
0
1
2
1
0
2
1
0
0
1
1
2
2
1
0
2
0
0
2
0
0
2
2
1
1
1
0
0
2
1
0
1
0
1
1
1
1
0
1
0
0
2
2
0
0
0
0
2
0
0
0
1
2
2
2
1
1
2
3
1
1
1
1
1
0
0
2
0
2
0
0
0
3
2
0
0
2
1
4
0
1
1
2
1
0
2
1
2
2
1
1
0
1
1
1
0
1
1
0
1
0
0
0
1
1
0
2
0
0
0
1
1
1
2
2
1
2
0
0
1
1
2
1
2
0
1
0
1
1
1
0
1
0
0
0
2
0
2
4
0
1
2
0
2
0
1
1
1
2
1
0
0
1
1
1
2
2
1
2
2
0
1
0
0
1
0
1
1
0
0
1
1
0
0
3
1
0
1
1
1
1
0
0
1
0
0
1
1
1
1
2
1
0
1
0
0
0
2
1
1
1
2
0
1
1
1
1
0
2
2
1
0
0
1
2
1
2
0
0
0
0
0
1
1
2
1
2
2
1
1
1
2
1
0
0
0
2
2
1
1
0
1
2
0
1
1
1
1
2
1
1
1
2
0
2
0
1
0
1
2
2
1
1
1
0
0
1
1
0
1
0
1
0
1
1
2
0
0
0
1
0
2
2
0
2
3
1
1
0
1
1
1
0
0
1
2
2
1
0
2
1
2
1
0
0
1
2
2
0
1
1
1
1
1
0
2
2
1
1
0
2
1
1
1
0
1
0
0
2
0
1
1
0
1
0
1
0
2
0
0
1
3
0
0
1
1
1
0
1
1
1
0
1
1
1
1
1
2
2
0
2
2
2
0
1
1
0
0
0
1
0
1
0
2
0
0
0
1
0
2
0
2
0
1
0
0
0
1
1
0
1
0
0
0
1
1
2
2
3
0
1
1
0
0
0
1
0
1
0
3
2
0
3
0
0
0
0
2
1
0
0
1
1
1
1
1
1
0
2
0
1
2
1
1
0
0
0
0
2
1
0
1
0
2
1
0
0
1
1
1
1
1
1
1
1
1
3
0
1
1
1
1
1
0
1
1
1
2
2
1
2
1
0
1
1
0
1
1
0
1
0
1
0
0
3
2
0
1
0
0
1
2
1
1
2
2
0
2
0
1
1
2
1
0
2
1
0
2
1
0
0
0
1
1
0
1
1
1
0
0
1
0
2
1
0
1
0
0
0
0
1
0
0
0
0
0
1
2
1
0
0
1
0
0
2
2
2
2
1
2
1
2
0
1
0
1
1
2
0
1
0
1
1
1
0
2
2
0
0
2
1
1
1
1
1
2
1
1
0
1
0
1
2
2
0
1
0
1
0
1
1
2
1
2
0
1
1
1
1
2
1
3
2
0
0
0
1
1
0
0
0
1
0
1
1
2
2
2
2
0
0
2
2
1
1
1
0
1
1
2
0
1
1
2
0
1
1
1
0
1
2
2
2
1
0
1
3
0
2
2
1
0
1
2
1
1
2
2
2
0
1
2
0
1
2
1
2
2
2
3
1
1
0
0
2
0
1
0
1
3
2
0
2
1
2
2
2
1
0
1
0
2
1
2
1
0
2
1
0
0
1
1
1
1
0
1
2
1
0
1
1
1
1
0
0
0
1
0
1
0
2
2
2
1
1
1
1
1
2
0
1
0
1
2
0
0
1
1
1
0
0
1
1
2
0
1
1
1
1
1
1
2
1
1
2
0
2
0
0
2
0
2
1
0
0
0
0
1
0
0
0
1
1
0
0
2
0
2
2
0
1
0
5
0
0
2
1
2
0
0
0
0
1
1
0
1
0
0
0
1
1
2
0
0
0
0
1
1
0
1
1
1
1
1
1
0
2
1
1
0
1
0
0
1
1
1
1
0
1
1
0
1
2
0
2
1
2
1
1
1
0
1
1
0
0
1
3
1
1
0
2
1
2
1
0
1
2
1
1
0
1
1
0
1
2
1
1
1
2
0
2
1
0
1
2
2
2
0
1
0
1
1
1
3
1
1
0
0
1
1
1
1
2
0
1
1
2
2
0
0
1
1
1
0
0
2
1
0
1
4
1
0
1
0
0
0
0
0
1
2
1
0
0
0
2
0
0
2
1
0
0
1
2
1
0
1
0
2
1
1
1
1
2
2
2
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
4
6
2
1
0
0
1
2
0
1
1
2
1
1
0
0
2
2
0
0
1
1
0
2
0
1
0
1
0
2
2
2
0
1
0
1
2
2
2
0
2
1
1
0
2
0
0
0
0
0
1
0
1
0
1
2
1
1
0
0
1
0
1
1
1
0
2
0
0
1
1
1
0
1
1
0
1
0
0
2
1
2
1
1
1
1
1
0
4
2
1
2
2
0
0
1
0
3
1
1
2
2
1
1
2
2
2
2
2
0
1
0
2
1
0
2
0
1
0
2
1
0
1
0
1
1
0
0
0
0
1
0
1
2
0
1
2
1
0
0
2
2
1
0
1
1
1
1
1
1
1
2
0
1
0
1
0
2
2
0
2
0
2
0
1
2
1
0
0
0
0
2
1
2
1
1
2
0
0
0
2
2
1
1
0
0
0
1
0
1
2
2
2
1
2
0
0
1
1
1
0
1
0
1
0
2
2
0
2
1
1
0
0
2
1
1
0
1
1
1
1
0
1
1
1
0
0
1
0
0
1
2
0
1
2
3
1
0
0
2
2
1
2
0
0
0
0
2
0
1
1
0
1
2
0
2
0
0
1
2
0
1
2
1
0
2
0
1
1
1
0
2
0
0
0
0
0
0
2
0
0
1
0
1
3
1
0
1
0
1
0
1
2
2
0
0
1
3
1
1
0
1
2
0
0
0
0
0
1
1
1
0
1
1
1
1
0
2
2
2
1
1
0
1
1
1
1
2
1
1
0
0
1
1
2
0
1
0
2
0
3
2
1
1
2
1
1
1
0
0
2
1
2
1
2
0
0
0
0
1
0
1
1
3
2
1
1
1
1
1
0
1
1
2
2
3
0
2
0
1
0
1
0
4
1
1
1
0
2
0
0
1
0
0
3
1
2
0
1
0
0
1
1
0
1
1
1
2
0
3
2
0
2
3
2
2
2
1
1
0
0
1
0
0
0
0
1
0
1
0
1
1
0
1
0
4
1
1
0
1
2
2
1
1
0
1
1
2
1
1
1
0
0
0
2
0
1
1
0
3
1
0
0
0
1
1
0
1
1
0
0
1
1
2
0
0
2
0
1
2
0
1
0
0
1
1
1
0
1
0
0
1
1
1
1
2
1
1
1
1
1
0
1
0
1
0
2
0
0
0
1
0
1
0
2
0
1
1
0
0
0
1
0
0
1
1
0
2
0
2
1
2
1
1
0
1
0
1
1
1
1
1
0
1
1
2
2
2
1
0
2
1
2
1
2
0
1
1
0
2
1
1
1
2
1
1
2
0
0
2
1
1
1
0
1
1
0
2
0
0
1
1
3
2
1
0
2
1
1
0
1
1
1
1
1
2
0
2
1
2
2
1
1
0
0
0
1
1
1
1
0
1
0
2
0
0
0
2
1
1
0
0
0
2
0
0
1
0
2
2
0
1
0
0
0
2
0
1
2
2
1
0
1
2
1
1
0
0
2
1
2
0
1
0
0
0
2
0
1
0
0
0
1
1
0
0
1
0
2
1
0
2
1
1
2
0
0
1
2
1
1
1
1
1
0
2
2
0
0
1
0
1
0
1
0
0
1
1
0
1
0
0
1
0
2
1
1
2
0
2
1
1
2
0
2
1
1
1
0
1
1
1
1
1
0
1
2
0
1
0
0
0
1
0
1
0
0
2
0
0
0
1
2
0
1
0
1
2
1
1
1
1
1
2
1
0
0
0
0
0
1
0
1
2
2
0
0
1
0
1
1
2
2
1
1
1
1
0
1
1
0
1
0
1
2
0
1
1
2
0
2
1
1
0
1
1
0
0
0
0
2
2
0
2
2
1
0
0
2
1
2
2
3
1
0
1
0
1
2
1
2
1
3
0
3
2
0
1
0
0
1
0
1
1
0
1
0
0
1
0
0
1
1
0
1
1
0
0
0
0
0
2
1
2
1
0
1
1
1
2
2
2
2
0
0
2
1
1
1
1
0
1
2
0
0
1
2
1
1
1
1
1
1
1
2
2
0
0
1
1
0
2
0
1
2
2
1
0
1
1
0
2
0
1
1
0
0
0
2
3
0
1
2
0
1
0
2
1
0
0
2
0
2
2
0
2
2
0
1
0
2
1
2
1
0
2
1
0
1
0
2
1
1
0
1
1
2
2
0
0
2
1
1
0
1
1
2
0
0
1
1
0
0
0
1
1
1
1
1
2
1
1
0
0
1
2
2
0
1
0
0
0
1
1
1
0
0
1
0
2
0
2
1
2
0
1
2
1
2
1
1
1
1
0
2
1
0
0
1
1
2
0
0
1
0
0
1
1
2
0
1
0
1
1
1
1
0
1
0
1
2
0
1
0
2
0
1
0
1
0
0
1
0
1
1
1
1
0
2
1
2
1
1
2
0
0
0
0
1
1
1
1
1
0
0
0
1
0
1
0
0
1
1
2
0
0
1
1
1
2
3
2
1
2
1
0
0
1
1
2
2
2
2
0
0
2
1
4
1
1
2
0
0
0
2
0
1
0
2
0
1
2
1
0
0
1
3
1
0
1
2
1
0
2
2
1
1
0
1
2
1
2
2
0
2
0
0
1
0
2
2
3
0
0
1
2
1
1
4
0
1
1
2
0
1
2
0
2
0
1
0
1
0
1
0
1
2
0
2
1
2
0
0
1
1
0
0
2
0
0
1
2
0
0
1
0
0
0
1
1
2
1
1
1
1
3
0
0
2
0
0
1
1
0
1
1
0
1
3
2
3
1
2
3
0
0
1
2
1
2
1
0
2
1
1
1
0
1
1
1
0
0
0
1
0
0
1
1
0
1
2
2
0
1
0
2
1
2
1
0
2
3
1
0
1
0
1
0
0
0
0
0
2
1
2
1
1
0
0
0
0
2
0
1
0
2
0
0
2
2
0
2
1
0
1
1
0
1
0
2
1
0
1
1
1
0
1
1
1
0
2
0
0
2
2
0
1
2
1
1
2
2
1
0
0
0
0
1
0
2
1
2
1
0
1
0
1
0
1
0
0
2
0
0
1
1
1
1
1
1
0
2
1
0
1
1
0
1
0
2
0
2
1
2
2
0
1
2
0
1
1
1
0
2
0
2
1
2
0
1
0
1
1
2
0
3
1
2
1
0
0
1
1
1
0
0
1
1
1
1
1
1
2
0
1
0
1
0
2
1
2
0
1
0
0
0
0
1
2
1
0
2
0
2
1
3
0
2
1
0
2
1
0
1
2
1
0
0
2
0
1
2
1
2
1
2
1
0
0
2
1
0
2
2
1
1
2
0
2
3
1
2
1
1
2
0
1
0
0
1
1
0
2
0
1
2
1
1
1
0
2
1
0
0
1
0
0
0
1
1
1
0
2
0
0
1
2
1
0
0
1
0
1
0
0
0
1
0
0
0
2
0
2
2
0
0
0
0
0
1
2
2
1
1
1
1
0
0
0
1
0
1
2
0
1
1
2
1
0
0
1
2
0
2
2
0
1
0
1
0
0
1
0
2
1
2
1
1
0
2
0
0
2
2
2
2
0
0
1
0
1
0
1
3
1
1
2
0
2
1
2
1
1
1
0
0
0
1
1
2
0
1
0
2
1
0
0
1
1
2
0
2
2
0
1
0
0
1
1
0
2
0
0
1
0
2
1
1
0
0
0
1
2
2
0
1
0
1
2
1
1
3
1
2
1
0
0
2
0
2
1
2
0
1
1
1
1
2
0
0
2
0
1
1
0
2
1
1
2
1
2
1
1
1
2
1
0
2
1
1
2
0
1
0
2
2
2
1
1
2
1
2
2
0
0
0
0
0
0
2
0
1
1
1
0
0
1
1
0
1
0
1
1
1
1
0
1
0
1
2
0
1
1
2
1
1
2
0
1
2
1
0
0
0
2
1
2
0
0
1
2
0
0
2
2
0
0
1
0
1
2
1
1
1
0
0
2
0
0
0
2
0
1
2
1
1
1
2
0
1
2
1
1
1
2
1
1
0
1
0
0
1
2
3
0
1
1
0
1
0
1
0
2
1
1
0
1
1
1
0
2
1
1
0
1
1
0
0
1
1
2
2
1
2
1
0
2
0
1
1
1
1
0
1
3
1
1
0
1
1
1
0
2
1
0
2
0
1
0
0
1
1
0
1
1
2
2
1
0
0
0
0
0
1
1
1
1
1
1
2
2
1
1
2
0
0
2
4
1
2
0
0
2
0
1
0
1
1
1
1
0
1
1
1
0
0
0
1
2
0
0
0
2
3
0
1
2
1
2
1
2
1
0
0
1
1
2
1
1
2
2
0
1
0
1
1
1
1
0
0
0
1
2
2
1
2
2
1
1
1
1
1
0
2
1
1
0
0
0
1
1
1
2
0
0
1
0
1
2
4
3
2
1
0
2
1
0
1
0
0
1
0
1
1
1
0
0
1
1
1
1
0
1
1
1
1
1
2
0
0
2
2
0
1
1
1
1
1
0
2
0
1
1
1
0
0
0
0
2
1
1
1
2
0
0
0
0
1
0
0
2
1
0
1
0
1
0
1
0
0
1
0
0
2
0
1
0
1
5
1
0
0
1
2
0
1
0
1
2
0
0
0
0
1
1
0
1
1
0
1
0
0
1
0
0
0
1
0
0
1
1
2
2
1
1
2
2
1
1
2
1
1
1
1
0
0
0
1
0
1
0
1
1
0
1
0
1
1
0
1
1
1
1
0
1
1
1
3
0
0
0
0
0
0
2
0
2
2
1
1
0
1
0
2
0
0
1
1
0
1
0
1
1
0
1
2
1
0
2
1
0
1
2
0
1
1
0
1
2
3
1
2
2
0
1
1
0
1
2
1
0
1
0
0
2
1
1
1
2
1
1
1
0
2
0
1
1
1
2
1
1
2
3
2
2
2
1
0
1
0
5
2
1
1
0
1
1
0
1
1
2
2
0
2
1
2
1
0
2
2
2
0
2
1
0
1
2
0
0
2
2
1
0
0
0
0
0
2
1
2
1
1
0
1
2
2
1
1
0
1
2
0
0
0
2
2
0
3
2
2
1
1
1
0
1
1
1
1
1
1
0
1
0
0
0
2
1
1
1
0
1
1
0
1
1
0
0
2
1
1
0
0
1
0
2
0
0
3
1
1
1
2
0
0
2
1
1
0
1
2
0
0
0
2
0
1
1
1
2
1
1
1
0
1
2
0
1
2
0
0
0
0
0
0
2
1
0
0
1
2
0
0
1
2
0
0
0
1
1
0
0
0
1
1
2
1
0
3
2
0
0
1
1
0
0
1
0
0
2
2
1
2
1
0
2
2
0
1
0
2
1
2
1
1
1
1
0
0
0
0
1
1
0
2
1
1
1
2
1
0
0
1
0
0
1
2
2
0
0
1
0
1
2
0
0
1
2
1
2
0
1
1
1
2
0
0
4
2
0
1
0
1
2
1
1
2
1
1
0
1
0
1
0
1
1
0
1
1
0
2
0
0
1
2
1
0
0
1
1
0
1
2
1
1
2
2
1
1
2
2
1
1
0
0
1
1
2
2
0
0
1
1
0
1
0
2
1
1
1
1
2
1
0
1
1
1
0
1
1
1
1
0
1
1
1
2
0
1
1
1
2
2
0
2
2
2
5
2
0
0
0
2
0
0
0
1
1
0
1
0
2
0
0
1
1
1
1
0
0
0
1
2
0
2
0
1
0
1
1
1
1
1
2
0
2
0
0
1
1
1
1
2
1
0
0
2
0
1
1
1
2
1
2
0
1
0
0
4
2
1
0
1
0
1
2
0
0
1
2
1
1
0
2
1
1
0
0
1
2
1
1
0
1
1
1
1
0
1
1
2
1
1
1
0
1
0
0
1
2
0
1
1
1
0
2
2
1
1
1
2
1
0
0
0
1
0
2
1
0
1
0
1
1
1
1
2
2
2
1
0
0
1
0
1
1
2
0
1
1
2
0
1
1
0
0
1
1
2
1
0
1
0
0
2
0
0
1
0
1
2
1
0
1
0
0
1
0
1
0
1
0
2
0
0
0
1
4
0
1
0
1
0
0
1
1
0
1
1
2
1
0
2
0
0
0
0
2
1
1
0
1
2
1
0
0
0
0
2
1
0
2
1
1
1
1
0
2
0
1
0
1
1
1
1
1
0
1
1
1
2
0
2
2
1
2
0
1
2
0
0
1
0
1
1
2
0
1
0
1
1
2
1
1
1
0
0
1
1
0
2
1
1
0
0
0
0
2
1
1
1
1
1
1
1
0
4
1
0
0
0
2
1
2
1
1
2
1
0
1
1
0
2
2
1
2
1
1
0
0
1
1
1
2
1
2
1
1
1
2
0
2
2
0
2
0
1
1
1
1
1
1
1
1
1
2
0
0
0
0
0
1
0
0
2
0
0
1
1
0
1
1
0
0
1
1
0
1
1
2
1
2
1
2
1
1
1
0
2
2
0
3
0
0
2
2
2
1
1
0
1
0
4
0
2
0
1
0
1
1
1
1
0
1
0
1
0
1
2
1
2
2
2
1
1
2
0
1
0
0
2
0
0
0
2
2
0
0
0
1
7
0
1
4
1
1
0
0
2
0
2
1
0
1
1
0
1
3
1
2
2
1
2
1
1
1
1
0
1
1
0
1
2
1
1
0
0
0
1
0
2
0
1
0
1
2
4
2
2
1
2
0
1
1
0
2
0
1
1
0
0
2
1
1
1
1
1
1
0
1
1
0
0
1
0
1
1
1
0
1
1
1
0
2
1
1
1
0
0
2
0
2
1
1
1
1
1
1
2
0
1
1
1
0
0
1
2
0
2
0
0
0
0
0
0
1
1
1
1
2
0
1
0
3
1
1
0
2
0
1
1
0
1
0
1
1
1
2
1
0
1
2
1
1
3
0
2
0
1
1
0
1
1
2
0
2
0
1
0
0
1
0
1
0
1
0
1
0
0
0
0
0
1
0
0
2
0
2
0
0
0
1
1
1
2
1
0
1
1
1
0
1
0
0
0
1
1
0
0
1
1
2
0
0
1
1
2
1
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
1
1
1
0
0
1
1
0
0
1
1
0
2
0
0
2
2
0
1
0
0
2
1
1
0
2
0
1
0
0
0
1
0
2
1
1
0
2
1
2
0
0
1
3
0
3
0
0
2
2
3
1
1
1
0
1
0
0
1
1
0
1
1
2
2
0
2
2
1
1
1
1
0
2
0
1
1
2
0
1
2
0
0
0
1
0
2
0
0
2
1
2
1
1
0
2
1
0
1
1
2
1
3
0
1
2
0
1
1
1
1
0
0
1
1
2
0
0
2
0
1
0
0
1
0
1
1
2
2
1
2
0
2
2
2
1
1
0
1
0
0
2
0
1
1
0
1
2
0
0
0
1
0
0
2
2
1
1
1
0
1
1
1
2
1
1
1
0
2
1
1
1
1
1
2
1
3
1
0
0
1
1
2
1
0
1
1
2
1
1
1
0
0
2
1
1
2
0
1
2
1
0
1
0
2
1
2
0
1
0
0
2
1
1
1
1
1
2
1
0
0
2
0
1
0
0
1
0
1
1
0
0
0
1
1
1
0
0
1
0
2
0
0
1
1
2
1
2
1
1
1
1
2
1
0
1
2
1
0
1
1
0
0
2
0
1
1
1
4
1
2
1
0
1
1
0
1
1
1
1
1
2
2
1
0
0
1
1
1
0
1
0
1
1
2
2
0
2
2
1
2
0
0
0
1
2
1
1
1
1
1
1
0
0
2
0
1
1
1
1
0
0
1
1
0
1
1
0
0
0
0
1
0
0
2
0
1
0
1
0
0
1
0
2
2
1
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
2
1
1
2
0
1
7
0
0
0
1
1
1
2
1
0
1
0
1
0
1
2
1
0
0
1
2
1
0
2
1
1
1
1
1
1
1
0
1
0
0
0
2
2
1
1
2
0
1
0
1
1
1
1
1
0
1
0
0
1
0
1
2
1
0
1
0
0
2
1
0
1
1
1
0
0
0
1
1
2
0
0
2
1
1
1
1
1
0
1
2
1
0
2
0
1
1
2
1
1
0
1
1
0
4
2
1
0
0
1
1
1
0
1
0
1
1
1
1
0
1
0
1
1
1
2
2
1
2
1
1
0
1
1
1
1
0
1
0
2
0
1
0
0
0
2
1
0
0
0
1
1
0
0
1
0
2
1
1
2
1
0
1
2
2
1
5
1
2
1
1
0
0
1
0
1
2
0
1
1
2
1
2
0
0
0
3
2
0
1
1
2
1
1
1
0
1
1
1
2
0
1
2
0
0
1
0
1
4
0
1
0
0
0
1
0
0
0
1
1
1
0
2
0
2
1
2
1
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
2
0
0
1
2
1
0
0
1
1
1
2
2
2
1
1
1
0
1
1
1
1
2
2
0
1
1
1
2
0
1
2
0
1
1
2
0
1
1
2
3
1
0
1
1
1
5
1
0
1
1
1
0
0
1
1
0
1
1
0
1
0
1
0
0
1
2
1
0
1
3
0
1
0
0
1
0
0
1
1
0
0
2
1
0
2
1
1
2
0
0
1
2
2
2
1
2
0
1
1
0
1
2
0
1
1
1
2
1
0
2
1
1
1
1
0
1
0
1
0
2
0
1
0
2
1
2
0
0
1
1
0
0
1
1
1
1
0
0
1
0
0
2
0
1
1
0
0
1
0
0
2
0
2
1
2
1
2
1
1
0
1
1
1
0
1
0
1
2
1
1
1
1
1
0
0
1
2
0
2
0
2
0
2
2
4
1
2
1
1
1
0
1
0
1
1
1
1
1
1
1
1
0
0
0
0
0
3
2
1
0
1
0
2
0
0
1
2
1
2
2
0
0
2
2
1
1
1
1
1
1
0
0
1
1
2
1
2
5
0
1
2
2
1
1
1
1
1
1
0
1
0
1
1
0
0
1
2
0
1
1
1
0
1
2
1
1
0
1
1
0
1
0
0
2
1
2
1
2
2
1
1
2
1
0
3
1
0
0
1
1
1
1
1
1
0
0
0
0
0
0
1
0
0
0
0
2
1
1
1
1
0
2
0
0
0
2
1
1
1
1
1
0
0
2
1
0
1
0
1
2
0
0
2
0
1
0
0
1
1
1
2
0
0
1
1
0
0
2
1
1
1
0
2
1
1
0
1
1
1
0
0
0
1
1
1
0
1
0
0
0
1
1
1
1
0
0
0
1
1
1
1
1
0
0
1
0
0
2
2
0
1
1
1
1
0
0
2
1
1
1
2
1
1
1
0
1
1
2
0
1
1
1
0
1
2
2
1
0
0
0
0
1
1
0
0
1
0
1
0
1
1
0
0
0
1
2
0
0
1
1
1
0
0
0
1
1
0
1
0
0
0
0
1
0
1
0
1
1
1
1
0
0
1
2
2
0
2
0
2
0
1
0
0
0
1
1
0
0
1
1
1
0
1
1
2
1
2
1
0
1
0
0
1
1
1
2
1
1
0
0
1
1
2
1
2
0
0
1
0
0
0
0
0
3
1
1
1
1
0
0
0
1
1
1
1
0
1
1
2
1
1
1
2
0
2
1
1
2
1
0
2
0
1
1
2
0
2
2
1
2
1
1
2
2
1
2
0
1
0
2
2
1
1
0
0
2
0
0
0
2
2
0
1
0
2
2
2
1
1
1
1
1
2
1
1
1
0
1
1
0
0
1
2
2
0
1
2
1
2
2
1
1
1
0
19
0
0
0
1
0
1
0
1
3
0
1
1
1
1
1
0
2
1
0
1
2
2
1
0
0
2
2
1
1
1
1
1
1
2
1
0
2
2
0
2
1
1
0
1
3
1
0
0
0
2
1
2
0
1
1
0
1
2
0
1
1
2
0
1
1
2
1
1
2
1
1
1
0
1
0
0
1
1
1
0
0
1
6
2
0
1
1
0
2
0
1
0
1
0
1
1
1
1
0
1
1
0
1
0
0
0
1
2
1
1
1
2
0
1
1
1
0
0
1
1
2
2
1
0
1
1
0
2
0
2
1
2
1
0
1
0
0
0
0
0
2
1
0
0
0
1
0
2
1
1
2
0
2
0
1
1
0
0
1
2
0
2
1
2
1
2
1
3
0
0
1
0
1
0
0
2
1
0
1
1
1
0
0
1
2
2
0
1
0
0
0
1
2
1
1
2
0
1
0
1
2
1
0
0
1
2
2
0
2
1
1
0
2
0
0
1
2
1
1
0
0
0
1
0
0
0
2
1
2
1
0
0
1
0
1
1
1
0
0
0
0
0
1
1
2
2
0
1
1
1
2
1
0
1
0
0
2
1
1
2
2
1
2
0
0
0
0
2
2
2
1
1
0
1
1
0
2
0
2
0
1
0
2
0
0
3
2
1
0
1
2
1
0
1
0
0
1
0
1
1
0
0
0
4
0
1
0
1
1
1
2
2
1
1
1
2
2
0
1
1
2
1
0
2
0
2
0
1
1
1
0
2
1
1
0
2
1
1
1
1
2
1
2
0
1
0
1
0
0
1
1
1
0
0
0
0
1
1
1
1
2
0
1
2
2
1
2
0
1
1
1
0
1
1
1
0
2
0
2
2
3
0
0
2
0
1
1
0
1
1
2
1
0
1
1
1
1
1
0
1
0
2
2
0
1
0
0
0
0
0
2
1
2
0
2
1
1
1
0
1
1
1
2
1
0
0
1
1
2
1
0
1
2
2
0
1
2
1
0
0
1
1
1
0
1
0
1
1
0
0
2
1
1
2
0
1
2
1
1
1
0
0
1
0
2
1
0
1
1
0
0
1
0
0
0
1
1
1
2
2
3
0
1
1
0
0
2
1
0
1
1
1
1
0
0
1
1
2
0
1
2
2
1
0
1
1
1
0
1
3
0
0
1
0
2
0
1
1
1
2
0
5
2
0
2
0
2
0
1
0
1
2
7
1
1
1
2
2
2
2
1
1
2
0
0
0
1
0
1
0
2
0
2
0
1
0
2
2
0
0
1
2
2
2
0
2
1
0
1
2
1
0
1
1
0
1
1
0
2
2
1
0
1
1
0
0
1
0
1
0
0
0
0
0
2
0
0
3
0
0
1
2
0
2
2
1
2
1
0
1
1
2
1
1
1
1
2
0
1
1
1
2
1
2
1
2
1
0
1
2
1
0
0
1
2
0
0
1
0
1
0
2
0
0
1
1
2
1
1
0
2
0
2
1
0
1
1
1
1
1
1
3
1
0
1
0
0
1
1
1
1
0
0
4
1
0
0
2
1
2
2
2
1
1
2
0
0
2
2
0
1
0
1
2
0
2
1
1
1
1
0
1
2
0
1
1
1
1
1
0
0
0
0
1
0
1
1
0
0
2
0
0
1
1
2
1
0
0
1
0
0
1
2
1
1
1
1
0
2
1
2
1
0
1
0
0
0
0
2
2
0
0
1
2
1
0
0
1
1
2
1
0
0
0
1
0
0
1
0
2
1
0
0
0
1
0
0
1
1
1
1
3
1
1
0
1
2
0
0
0
2
1
1
1
0
0
0
0
1
2
2
1
1
0
1
0
0
1
2
1
0
1
1
3
0
2
1
0
1
0
1
1
1
1
0
0
2
0
1
1
0
1
1
2
1
1
3
0
0
0
2
2
2
0
1
0
1
1
1
1
0
0
2
1
1
0
2
1
0
1
0
1
2
1
1
1
1
0
0
0
0
1
1
1
0
0
1
0
1
2
0
1
0
0
0
1
1
0
1
1
2
1
2
0
2
0
1
1
0
1
2
2
0
0
1
3
2
0
1
0
1
0
1
1
0
0
1
1
1
0
0
5
2
0
1
1
1
2
2
1
1
6
0
1
2
2
0
1
0
1
1
0
1
0
2
0
1
1
1
0
1
0
1
1
0
1
2
0
0
2
1
1
0
0
0
2
1
1
1
2
1
2
0
1
2
0
1
0
1
1
2
0
1
1
1
0
2
2
0
0
1
1
0
4
1
1
2
2
0
0
1
2
0
0
0
1
0
2
1
1
1
0
0
0
1
0
0
1
1
0
1
0
0
0
1
2
1
0
0
1
0
1
2
0
2
1
0
0
0
1
0
0
2
0
1
2
2
2
0
2
0
2
2
2
0
1
1
1
1
0
1
0
1
2
2
2
1
1
1
1
1
0
0
0
1
1
0
2
1
1
2
0
0
0
0
2
1
0
1
1
1
0
0
1
0
1
0
0
0
0
0
1
2
0
0
0
0
2
1
1
3
1
1
0
2
0
0
2
1
0
2
0
1
1
1
0
2
1
2
1
0
2
1
1
0
0
0
1
0
2
0
1
2
0
0
0
3
0
2
0
1
0
0
1
2
2
0
0
2
1
1
2
1
2
1
0
2
1
2
0
1
0
2
3
1
0
1
0
1
2
0
1
1
0
1
1
2
2
1
0
0
1
0
1
1
2
0
1
1
2
1
0
1
1
1
2
1
0
1
2
1
2
0
2
1
1
1
1
1
1
2
1
1
1
0
1
1
0
2
0
1
1
0
1
1
2
0
1
0
0
1
1
0
2
1
0
1
1
2
1
0
1
1
1
0
0
1
2
0
1
1
1
2
1
1
0
2
0
2
1
2
2
2
2
0
2
2
0
0
1
0
0
1
2
1
1
2
1
1
1
1
1
1
1
1
0
0
0
2
2
2
0
1
0
1
0
2
1
1
2
0
1
0
0
1
0
1
0
1
0
1
0
0
1
2
1
1
1
0
0
0
1
1
0
1
0
0
1
0
2
0
0
1
2
1
2
0
0
3
1
1
1
2
2
0
2
2
0
2
0
0
2
0
3
1
2
1
0
2
0
0
0
0
0
1
2
1
0
1
1
3
2
0
0
2
0
1
1
0
0
1
0
1
2
0
1
1
1
0
1
1
0
2
1
1
1
2
0
2
2
3
0
1
1
2
1
2
1
0
2
0
0
0
1
1
2
0
0
2
1
1
0
1
2
2
0
1
1
0
1
1
1
1
1
3
0
2
2
1
1
1
0
0
1
1
1
1
1
0
0
2
2
1
2
0
0
2
0
1
0
2
1
0
2
1
0
1
0
1
0
1
1
2
1
1
2
1
0
0
1
0
0
1
2
0
1
0
2
0
0
3
1
0
3
1
0
0
0
2
1
0
1
1
0
1
2
1
1
3
0
2
0
2
1
0
0
1
2
1
0
0
2
1
1
1
2
1
0
1
2
2
1
2
0
1
1
0
1
1
0
1
1
2
1
1
1
1
0
1
0
1
0
1
3
1
0
1
1
1
0
1
1
1
1
1
1
0
0
1
1
2
2
1
1
1
2
1
2
0
1
0
2
2
1
1
0
2
0
1
0
0
2
0
1
1
0
1
1
0
2
0
0
1
1
1
1
2
1
0
4
0
1
1
0
0
0
2
1
0
0
0
0
1
1
0
1
2
1
0
1
2
0
1
1
1
2
0
0
1
0
1
0
1
1
2
0
0
1
1
1
1
0
0
1
1
1
1
1
1
1
1
1
2
0
1
2
1
2
0
1
0
0
1
1
1
0
1
0
1
1
2
2
1
0
2
1
0
1
0
1
0
2
2
0
0
0
2
2
1
1
1
1
3
0
1
1
1
0
0
1
0
1
1
0
0
1
2
1
1
1
0
2
3
0
0
1
1
2
0
1
1
1
0
0
0
0
1
2
1
2
1
2
2
0
0
2
0
1
3
0
0
0
2
2
1
1
2
0
1
1
0
0
0
3
2
2
1
1
0
0
0
3
1
1
1
2
0
2
2
2
1
1
0
0
1
1
0
0
2
0
0
1
0
1
1
0
1
1
1
0
0
0
1
0
2
1
1
0
1
1
0
2
2
0
0
1
1
1
0
0
2
1
1
1
0
2
1
2
0
1
3
0
1
3
2
1
1
2
5
1
1
1
1
1
0
1
1
1
1
3
1
2
0
2
0
2
2
0
1
1
1
2
2
0
2
1
1
2
0
1
0
2
0
1
0
0
0
1
0
1
1
0
0
1
2
0
0
2
1
1
0
0
0
2
2
0
1
1
2
0
0
0
1
0
2
3
0
1
1
2
1
3
0
0
1
1
1
1
2
0
1
1
1
2
2
0
0
1
1
5
0
1
1
1
4
1
2
2
0
1
0
3
1
1
1
2
2
1
1
0
0
1
1
1
1
0
2
1
1
1
1
1
1
1
2
0
0
0
1
1
0
1
2
1
0
1
0
1
0
0
0
0
1
0
0
2
2
0
1
0
1
1
2
0
2
1
0
0
1
1
1
0
1
0
1
0
1
0
1
2
0
0
1
1
2
4
1
0
1
0
3
0
1
1
0
0
3
2
0
2
0
0
1
1
0
2
1
2
2
2
0
0
1
1
2
2
1
0
1
2
1
1
2
1
0
1
1
0
1
1
0
1
1
1
2
0
2
0
1
2
1
1
0
1
0
2
1
1
0
2
1
0
0
0
1
1
2
1
0
1
1
1
1
1
0
0
2
0
1
0
0
2
1
0
1
0
0
0
1
0
0
0
1
2
1
2
0
1
2
1
0
2
1
0
0
1
1
1
0
1
0
0
2
0
1
1
0
2
1
2
1
1
1
0
0
1
1
1
1
1
0
2
1
2
1
1
0
1
2
2
1
0
2
0
0
1
1
1
1
1
1
0
1
0
0
0
0
1
1
0
1
0
0
2
1
2
1
1
1
0
1
2
1
1
0
0
2
1
0
0
2
3
1
0
1
1
0
1
0
2
3
0
1
0
2
0
1
0
1
1
0
1
1
0
2
1
0
1
1
1
1
0
1
1
2
1
0
0
2
1
2
1
0
1
0
1
1
1
0
2
2
1
2
0
1
0
2
0
0
1
1
1
1
0
1
1
0
1
1
1
1
1
1
1
3
1
1
2
2
0
1
1
0
0
1
1
2
1
2
2
2
0
2
1
0
0
0
0
1
3
0
1
1
1
1
0
0
1
2
1
0
1
3
0
0
1
2
2
0
2
0
1
2
1
0
1
1
2
1
0
0
1
1
1
2
0
1
1
0
1
1
2
1
1
2
1
1
1
0
2
0
1
1
1
2
0
0
2
0
0
1
1
1
2
1
1
1
2
0
2
0
1
0
0
1
1
2
1
0
0
0
0
0
2
1
0
2
2
0
0
0
0
2
1
3
2
0
2
1
3
2
1
0
2
1
0
1
0
2
0
7
1
0
0
1
1
0
0
2
2
2
0
1
0
0
1
1
0
2
1
0
1
2
1
1
1
1
1
2
2
0
0
1
0
0
2
1
2
1
0
2
1
1
0
2
0
0
1
1
1
1
2
0
3
0
1
2
1
0
0
2
2
5
1
1
2
1
0
3
1
1
1
2
0
0
0
2
2
2
1
1
1
2
2
0
1
0
1
2
0
0
1
0
2
2
1
2
1
1
0
0
1
1
1
1
1
2
0
1
1
2
0
0
1
0
0
2
2
0
1
2
0
0
0
1
2
1
1
0
1
1
2
1
1
1
0
1
1
1
1
2
0
0
1
2
2
0
0
2
1
2
0
0
2
2
0
1
0
0
1
0
2
1
1
1
2
0
1
0
1
1
2
2
0
1
1
2
1
1
1
0
2
1
0
1
1
1
1
1
0
0
2
0
0
1
1
3
0
2
0
1
0
0
1
1
1
2
0
2
1
1
1
1
1
0
1
3
2
0
1
0
0
2
0
1
1
1
1
1
1
1
2
1
0
2
0
1
0
1
1
0
2
1
1
1
0
1
0
2
1
2
0
1
1
2
2
2
0
1
1
0
1
0
1
1
0
1
1
1
1
0
2
0
1
0
1
0
1
1
5
2
0
3
0
1
1
0
0
0
1
0
1
1
2
0
0
1
1
1
0
4
2
2
0
1
0
0
1
0
0
1
2
1
0
2
2
0
0
5
2
1
2
2
3
1
1
0
0
0
1
2
1
1
0
1
2
1
1
1
1
0
1
0
2
1
0
0
1
1
0
1
1
1
1
1
2
1
2
0
0
1
2
0
2
1
2
2
2
1
0
1
1
0
2
0
1
2
1
0
0
2
0
2
0
1
1
1
0
1
2
2
1
1
1
2
2
1
1
0
0
2
1
0
0
1
1
0
1
0
2
1
1
1
0
2
1
1
2
2
1
0
1
0
1
0
1
1
1
0
2
2
1
3
1
1
2
1
1
1
0
0
0
1
1
1
1
1
1
1
2
1
0
0
0
2
1
2
0
2
0
0
1
0
0
1
0
1
1
0
1
1
0
0
1
1
1
0
1
2
0
1
2
0
1
0
1
1
0
1
2
0
2
0
1
1
0
1
0
1
1
1
0
1
2
2
0
2
2
2
1
1
2
0
2
0
1
2
0
0
1
0
0
0
1
1
2
0
1
1
0
2
0
0
2
1
0
0
1
2
0
2
1
0
0
0
1
1
2
0
1
4
2
0
1
1
0
0
2
0
1
0
2
2
0
1
2
2
2
1
1
0
0
2
0
1
0
0
0
0
1
1
1
2
3
1
2
1
2
3
2
1
0
0
0
0
1
2
2
1
1
1
2
2
0
2
0
0
1
1
1
0
2
0
1
0
0
0
2
1
0
1
0
2
1
2
1
0
1
1
1
0
1
1
1
2
1
1
1
1
0
2
2
2
0
2
1
1
1
2
1
0
1
2
1
1
1
0
0
1
2
1
2
0
2
0
1
1
0
2
2
0
0
0
2
0
0
1
2
0
0
0
1
1
1
2
1
0
2
1
2
1
0
2
1
0
1
1
0
1
2
1
0
1
2
2
1
1
1
1
0
2
1
0
0
0
0
2
1
0
1
1
0
1
2
2
1
2
1
0
1
0
1
1
0
1
0
0
0
1
0
0
1
1
1
0
1
1
0
0
1
1
2
0
0
0
1
1
1
1
1
2
1
0
1
0
0
0
0
0
1
0
1
1
1
1
2
0
2
0
1
2
0
1
1
2
1
1
2
1
1
0
2
1
0
1
2
0
0
1
1
1
2
1
2
1
0
1
1
1
0
2
0
0
0
0
2
1
1
1
0
0
2
0
0
0
1
1
4
2
2
0
0
1
0
0
1
0
1
1
0
2
0
2
0
2
1
1
2
0
1
1
0
1
1
0
0
2
0
2
1
0
1
0
2
2
2
2
0
0
1
1
1
2
2
1
0
0
1
1
1
0
0
2
1
2
3
2
1
0
1
1
0
0
2
1
1
2
1
1
0
1
0
0
2
0
0
0
2
0
0
1
0
0
2
1
1
1
0
0
1
0
0
0
2
0
0
0
1
3
0
0
2
0
2
0
3
1
1
1
1
1
1
1
0
2
1
0
0
0
1
1
1
0
1
0
0
1
2
2
3
0
1
1
1
0
2
1
1
1
1
0
0
1
1
0
1
0
0
1
1
2
0
1
1
2
1
1
3
1
1
2
1
0
2
0
1
1
2
1
1
2
1
1
0
1
0
0
0
1
0
1
1
2
1
1
0
0
2
2
1
0
1
1
1
2
0
1
1
0
0
0
2
0
0
0
1
2
0
1
0
1
0
1
0
2
0
1
0
1
4
1
1
2
1
1
2
1
2
0
1
0
0
1
0
2
0
0
2
1
1
0
2
0
0
1
2
2
2
1
1
0
0
1
2
2
1
2
1
0
1
0
1
1
1
1
0
1
1
0
1
2
0
1
2
1
0
1
0
2
1
0
1
0
1
0
0
1
0
1
2
1
0
1
1
0
2
1
0
1
1
0
0
2
0
2
1
1
1
1
0
0
1
2
0
0
0
1
0
0
0
0
0
0
1
0
1
3
0
1
1
1
1
2
0
0
1
1
0
0
2
2
0
0
0
2
1
0
2
0
2
2
0
0
0
1
0
2
1
0
2
1
0
1
2
1
0
2
1
0
1
1
1
1
2
0
0
1
1
1
2
1
1
2
2
1
2
0
3
2
0
2
0
1
3
1
2
0
1
1
0
0
1
1
0
0
2
1
0
1
0
2
0
2
1
1
0
0
1
2
0
2
1
1
1
0
0
0
2
2
1
0
1
1
0
1
1
0
2
0
0
0
1
0
2
2
1
1
0
2
1
2
1
1
2
1
0
0
0
2
2
1
0
1
0
1
2
0
0
1
0
0
2
1
2
1
0
2
0
1
0
0
1
0
1
1
2
2
1
1
1
2
2
1
0
0
1
1
0
0
1
2
0
0
0
1
1
1
1
0
0
2
0
2
2
0
0
1
2
0
1
1
1
1
1
1
1
2
2
1
1
0
1
1
1
0
2
1
2
0
2
1
1
0
0
0
3
2
1
3
2
0
2
1
2
1
2
0
2
1
2
2
1
0
1
2
2
0
0
1
0
0
2
0
0
1
1
1
0
0
1
2
1
1
0
2
1
1
0
2
2
1
0
0
0
0
0
2
2
0
0
1
2
1
0
1
0
1
2
1
1
0
2
1
0
2
0
1
0
0
1
2
1
0
1
2
3
1
1
2
0
4
1
1
0
2
1
1
1
2
1
2
0
2
0
2
2
1
1
0
0
0
0
1
0
1
2
0
2
1
0
2
1
2
0
2
0
2
1
2
2
1
2
1
0
2
3
1
0
0
2
1
0
1
1
1
1
2
1
1
1
1
2
2
1
1
2
1
0
0
2
1
1
0
2
0
2
1
0
1
1
1
0
2
1
0
1
0
0
0
0
2
0
2
2
2
1
1
1
1
2
1
0
0
1
1
2
3
2
2
1
2
2
1
1
0
2
1
1
2
0
1
1
0
0
1
0
0
2
2
2
3
1
0
2
1
0
0
1
1
0
0
2
1
0
0
0
2
0
1
0
1
1
2
2
2
0
0
2
1
1
0
0
0
0
2
1
0
0
1
2
1
0
2
0
2
2
1
1
0
1
1
1
1
1
0
0
2
2
0
1
0
1
1
1
2
1
1
2
2
1
2
1
0
1
1
0
2
0
0
1
0
1
0
2
1
2
2
1
1
0
2
1
2
1
2
1
0
2
1
0
0
0
1
1
2
0
1
1
0
0
1
0
1
1
1
1
2
0
0
1
1
2
1
0
2
0
1
2
0
0
1
1
0
2
0
0
1
3
3
0
2
0
1
0
1
1
2
1
1
0
2
1
1
1
1
0
0
2
0
1
0
0
0
2
2
1
1
1
2
2
1
1
1
1
1
1
2
0
1
1
1
0
1
1
1
2
0
0
0
0
0
1
0
1
1
1
2
2
1
1
0
1
0
1
0
1
2
0
1
1
0
0
0
1
2
0
0
2
0
0
1
2
2
1
0
1
2
0
1
2
1
1
0
1
0
1
0
0
1
0
2
1
1
0
2
2
2
2
0
2
1
1
0
1
0
2
2
1
1
0
0
1
0
1
2
2
1
1
0
0
1
2
0
0
0
1
0
0
0
1
0
1
0
0
2
2
0
1
0
0
0
1
2
1
1
2
2
1
0
1
2
0
1
1
0
0
1
2
0
2
2
2
1
1
1
1
2
1
0
1
2
1
0
2
0
2
1
0
2
3
2
1
2
0
1
1
1
1
2
1
1
0
2
1
2
0
1
0
1
0
0
1
0
0
1
2
1
0
1
2
1
2
0
2
1
1
1
2
1
0
0
2
0
2
1
2
1
2
1
1
1
0
0
1
1
1
1
1
0
2
2
1
1
2
0
1
0
1
2
0
1
0
0
1
1
0
0
1
0
0
1
1
0
1
0
0
1
2
0
1
1
0
0
1
1
0
0
1
2
1
0
0
1
0
0
0
0
0
0
1
0
1
1
0
1
1
1
1
0
0
1
1
1
0
2
1
0
1
1
1
2
1
1
2
0
0
1
0
0
1
2
0
0
2
2
0
0
1
2
2
0
0
1
0
1
2
1
1
2
0
2
2
1
1
1
0
2
0
0
0
1
0
0
1
1
1
2
0
0
1
2
0
0
0
1
0
1
1
1
1
0
0
0
1
0
1
1
1
1
1
2
0
1
2
1
1
1
2
1
0
0
1
1
1
2
1
1
2
0
1
1
0
0
1
2
2
0
0
0
1
1
1
1
0
1
2
0
1
1
1
0
2
2
0
1
1
1
1
1
1
1
2
2
1
1
1
1
1
1
0
1
0
0
0
0
1
1
1
1
0
1
0
1
1
1
1
0
1
0
1
1
2
0
1
1
1
1
1
2
0
3
2
1
0
0
0
2
0
0
2
1
2
1
2
2
0
1
0
3
1
1
0
0
2
1
1
0
1
0
0
0
1
2
0
1
0
0
2
2
0
0
2
0
1
0
0
1
1
1
1
1
0
1
2
1
0
0
1
0
3
1
2
2
2
1
1
1
0
1
1
1
1
2
2
0
0
2
0
0
0
0
2
1
2
0
0
1
1
1
0
1
0
1
0
1
0
1
0
1
0
0
0
1
0
1
4
0
1
1
2
0
0
1
0
1
2
0
1
2
1
0
0
0
0
0
0
3
0
0
0
0
0
1
2
0
2
2
1
1
1
2
2
0
2
0
2
1
0
1
0
1
0
2
1
0
1
0
2
0
2
0
2
0
2
1
1
0
0
1
1
2
1
5
2
0
3
1
1
1
2
1
1
3
2
0
2
0
1
2
2
0
0
1
1
0
3
2
2
1
0
1
2
1
2
0
2
1
0
1
1
2
0
0
1
1
0
0
1
1
1
1
2
2
2
2
2
0
1
0
1
1
0
0
1
1
1
0
1
0
0
1
2
2
1
0
0
1
1
1
0
0
0
1
0
1
2
1
1
4
1
0
2
3
2
2
0
0
0
1
0
1
1
0
0
2
0
0
0
0
2
0
1
2
2
1
1
0
1
0
0
1
0
1
0
1
2
0
0
1
1
1
2
0
0
0
1
0
0
1
1
0
0
1
1
0
1
0
1
1
0
1
0
0
0
2
1
1
1
0
1
0
1
0
2
1
2
2
1
1
0
1
1
0
0
2
1
1
1
2
0
2
2
0
0
0
0
2
0
1
2
1
2
0
1
1
0
0
1
2
2
1
0
1
2
3
0
2
0
2
0
1
1
1
1
1
1
0
0
1
0
2
1
1
1
0
1
2
1
0
1
1
1
0
0
0
1
0
2
1
1
1
0
1
0
1
2
2
0
2
0
1
2
0
0
0
1
2
1
0
0
0
2
1
2
2
1
1
0
1
1
1
0
1
0
1
0
2
1
0
0
0
1
2
2
2
1
0
2
2
2
2
1
1
0
0
0
1
1
1
0
1
0
2
2
0
1
0
0
1
2
0
0
0
1
1
0
1
0
5
0
0
2
4
0
1
1
1
0
1
0
1
0
2
1
2
1
0
0
2
1
1
0
0
1
1
2
0
1
1
2
1
2
1
0
0
1
0
1
0
1
0
1
0
1
2
0
0
2
1
1
2
0
0
2
0
0
1
0
1
1
2
0
1
2
0
0
0
2
0
0
0
2
2
1
1
1
0
0
1
0
0
1
2
1
1
2
1
0
0
0
1
0
0
1
1
1
0
1
1
1
1
0
1
0
0
0
0
0
1
1
2
1
2
2
2
0
0
0
1
1
0
0
0
0
1
0
0
1
1
1
1
2
2
0
2
1
1
2
1
1
1
0
0
2
1
0
0
0
2
0
1
1
0
0
2
2
1
1
0
0
1
0
0
1
2
1
1
2
1
1
0
0
0
0
1
1
0
1
1
2
0
2
2
1
0
1
1
0
1
1
1
2
0
0
2
1
0
1
1
2
1
0
0
2
0
0
1
0
2
0
2
2
1
0
1
2
1
0
1
2
0
0
2
0
2
1
0
1
1
1
1
1
0
2
0
0
1
0
1
0
1
1
0
1
0
1
1
1
1
0
3
2
1
0
2
0
1
1
1
0
1
1
1
1
1
1
1
1
1
2
2
2
0
1
1
0
0
2
1
0
1
1
1
0
0
0
0
0
1
0
0
0
2
0
1
2
2
2
2
0
2
1
1
0
0
1
1
2
2
1
1
0
1
0
1
0
1
0
1
2
2
1
2
1
1
1
1
1
2
0
0
2
0
2
1
1
0
1
2
0
2
0
2
1
0
0
1
1
1
1
1
1
1
1
0
2
1
1
1
0
0
0
0
2
1
0
1
2
1
1
0
2
1
1
1
3
1
2
0
2
2
2
1
1
0
2
0
2
0
2
2
1
1
1
2
1
0
2
2
1
0
2
1
0
0
1
1
1
0
1
0
1
0
1
1
1
0
2
2
0
6
0
0
0
0
0
2
1
1
0
0
0
2
1
1
1
1
0
0
0
1
1
0
2
2
1
0
2
1
2
1
1
1
1
0
1
0
0
0
1
1
1
1
0
1
0
0
1
1
2
0
0
2
0
1
0
0
1
2
0
0
2
2
1
0
2
1
2
2
1
1
0
1
1
1
0
1
1
2
2
0
0
0
1
1
0
0
0
1
1
2
0
1
0
0
2
0
2
1
0
1
0
2
0
3
0
0
1
2
0
1
2
1
1
3
0
2
1
2
0
2
1
1
0
1
1
1
2
1
1
1
2
1
2
2
1
0
0
0
2
0
0
1
0
1
0
1
2
2
1
0
1
0
2
1
1
2
1
1
1
0
1
1
0
2
1
1
2
0
2
2
1
1
1
0
2
1
0
0
2
2
4
1
2
0
0
1
0
2
0
0
0
1
0
1
1
1
1
1
1
0
0
0
1
2
1
0
2
1
1
1
3
0
1
1
1
1
1
0
1
0
0
2
0
1
1
0
2
1
1
0
0
0
0
0
1
2
1
1
0
0
1
2
1
0
2
2
2
2
2
2
1
1
2
2
1
2
1
2
0
2
0
1
1
1
1
2
0
0
1
0
1
2
2
1
0
1
5
1
1
2
0
0
4
1
1
0
1
1
1
0
1
1
0
0
1
0
1
0
0
1
2
1
0
0
1
0
0
1
1
1
2
2
0
0
0
0
2
2
1
1
1
1
1
0
2
2
0
1
2
2
2
0
0
2
0
2
0
1
0
2
1
0
2
2
1
0
0
1
1
1
0
1
1
0
0
1
1
0
0
1
0
1
1
1
1
1
2
2
0
1
2
1
0
0
2
0
0
0
0
2
0
1
1
0
1
2
1
1
0
0
0
1
2
2
2
1
0
0
0
1
1
2
0
2
0
0
0
1
0
1
1
0
0
2
0
0
1
1
2
2
1
1
2
2
2
2
0
1
0
1
0
1
0
1
1
0
2
0
1
0
0
1
0
0
1
1
2
1
1
2
0
1
1
2
1
1
2
2
0
1
2
0
0
2
1
2
2
1
1
2
1
2
1
2
2
0
1
2
3
0
1
0
1
2
1
2
2
0
0
1
2
1
2
1
1
1
1
1
1
1
0
1
1
1
0
1
2
1
3
1
1
0
1
1
0
1
0
0
2
2
0
1
1
0
2
2
1
0
1
1
0
2
1
7
0
1
1
0
1
2
0
2
1
0
1
1
1
1
0
2
1
1
1
1
2
0
0
1
0
0
2
2
0
1
1
1
0
1
2
2
0
1
2
0
2
1
1
1
1
0
0
2
0
0
0
1
1
1
1
1
0
0
1
0
1
2
1
0
1
0
0
2
1
1
1
1
2
0
1
0
1
0
2
0
0
2
0
1
2
1
2
2
2
1
0
0
0
0
1
1
1
1
1
0
1
0
1
1
1
0
1
1
0
0
1
2
0
1
0
1
0
0
0
2
0
2
1
2
0
0
1
2
2
1
2
2
0
0
0
0
0
0
1
2
0
1
0
1
1
1
1
1
1
2
1
1
1
4
1
2
0
1
0
2
2
1
1
0
0
1
1
0
1
1
1
1
1
1
1
2
0
2
1
1
1
1
1
1
0
1
1
1
0
2
0
0
2
0
2
1
1
2
0
0
0
0
2
1
0
1
0
2
2
2
1
2
0
1
1
1
0
1
1
0
0
0
1
2
2
0
1
1
0
2
0
0
0
2
1
0
1
1
0
2
0
2
0
1
1
1
0
1
2
1
1
0
1
1
1
1
1
1
1
0
1
1
1
1
0
1
1
1
0
1
1
0
2
2
2
1
0
1
1
2
0
1
1
1
1
1
3
0
1
2
2
0
0
2
0
1
2
1
0
0
2
0
1
0
2
0
2
2
0
0
0
0
0
0
1
1
2
1
0
0
1
0
0
1
2
0
2
0
0
1
1
0
2
1
2
0
1
0
2
0
0
1
1
0
1
1
2
1
1
1
1
0
1
0
0
1
0
0
2
0
1
1
2
1
2
2
1
0
0
1
0
0
1
0
2
0
2
2
0
1
0
1
0
0
0
0
0
0
1
2
1
1
1
0
2
1
1
3
1
0
1
2
0
1
1
0
1
0
1
1
1
0
1
1
0
0
3
0
0
1
0
1
0
0
0
1
0
2
1
0
2
1
0
0
2
2
1
0
0
1
0
0
0
1
1
1
0
0
0
2
1
1
0
1
1
1
0
2
0
2
2
0
1
0
2
2
1
1
2
1
1
0
1
1
1
2
1
1
1
1
0
1
0
1
1
3
2
1
1
1
0
1
0
0
0
2
1
1
0
1
1
0
1
1
0
0
2
0
2
1
1
1
0
1
2
1
1
0
0
2
1
1
0
2
0
0
1
1
0
1
0
1
0
2
0
0
2
0
0
0
0
0
1
1
2
1
1
1
0
0
1
1
1
2
0
0
1
1
0
2
2
0
1
0
2
1
1
1
2
0
1
1
1
0
1
0
1
2
0
0
1
1
0
2
1
1
1
2
2
0
2
2
1
1
0
0
1
1
1
2
2
2
1
2
0
1
0
2
0
1
1
0
1
1
0
0
2
2
2
1
1
0
0
1
0
0
0
2
0
1
1
0
1
0
0
0
1
0
1
1
0
0
1
0
1
2
1
0
0
1
1
0
1
2
1
2
1
0
0
2
1
2
2
1
0
0
1
0
2
1
1
1
0
0
2
0
0
0
1
0
0
0
2
3
2
1
2
2
0
1
1
2
2
1
2
1
1
1
2
0
2
2
2
1
0
1
1
0
5
0
0
2
1
1
2
1
1
1
1
1
1
0
1
1
1
1
1
2
1
1
1
1
0
1
0
1
0
0
0
1
1
1
2
1
1
1
0
0
0
1
0
0
1
0
0
0
1
1
2
0
1
2
2
0
0
1
1
0
0
1
1
1
1
2
0
0
1
1
2
2
1
1
1
0
0
0
1
0
1
1
0
2
1
4
2
2
2
1
1
0
1
2
0
1
1
1
1
1
1
1
1
2
0
1
0
1
0
0
0
1
0
0
2
2
0
1
0
2
2
1
1
1
2
2
0
1
2
0
1
0
1
2
1
1
1
1
1
0
0
2
1
1
0
1
0
1
1
0
0
1
1
2
2
0
2
2
1
1
0
1
1
0
1
1
1
2
1
0
0
0
0
1
0
0
1
2
1
0
0
0
2
2
0
0
0
3
0
1
1
0
2
2
1
0
0
2
1
0
1
0
1
1
0
0
0
1
2
1
2
1
0
1
2
1
2
1
0
0
2
2
0
1
1
0
2
0
0
0
2
1
1
0
2
1
0
1
0
1
1
0
0
1
1
1
0
3
0
0
1
1
0
1
0
0
0
1
2
1
1
0
1
0
0
2
1
0
0
0
1
0
1
1
1
2
0
2
1
0
0
2
1
2
1
1
1
0
3
0
0
0
1
0
1
0
2
1
1
0
2
0
0
1
0
2
0
4
0
1
0
1
1
0
2
0
1
0
2
0
1
1
2
1
0
1
2
0
0
0
2
1
2
1
1
0
1
0
0
2
1
0
1
1
2
2
1
1
0
1
0
0
2
1
1
2
1
2
0
0
0
1
0
0
1
1
1
2
2
1
1
1
0
1
1
2
1
1
1
0
0
0
1
0
0
2
2
0
1
2
1
0
2
0
1
2
1
1
0
2
0
0
2
0
1
0
0
1
1
1
1
1
1
2
1
2
0
1
0
1
1
1
1
0
2
0
2
1
1
0
1
0
1
0
0
0
1
0
1
1
2
2
1
1
0
0
2
3
1
0
0
0
0
1
0
1
0
1
2
0
1
2
0
0
1
1
0
0
1
1
1
1
2
2
0
1
2
1
1
0
0
2
0
1
1
0
1
0
0
0
2
1
0
1
1
0
1
1
0
0
0
0
2
0
2
2
1
1
1
1
2
1
2
1
0
1
2
1
0
2
0
0
0
0
1
0
2
1
2
1
1
0
0
0
2
1
0
2
0
2
1
2
0
1
2
1
0
0
0
0
2
1
2
0
0
0
1
1
0
1
2
1
1
1
1
1
1
2
1
1
1
1
1
1
2
1
1
0
1
1
3
0
0
2
1
1
1
1
0
1
1
2
1
0
0
0
1
0
1
1
1
2
1
0
1
2
1
1
0
0
1
1
1
1
2
1
1
1
2
1
2
1
1
0
2
2
1
1
0
2
1
0
2
0
0
0
2
0
1
1
1
2
0
1
0
0
1
2
1
1
0
1
1
0
1
0
0
2
1
0
1
1
2
1
1
0
1
0
0
1
1
0
2
1
1
2
1
0
0
1
0
2
1
0
1
0
1
0
1
0
1
1
2
1
1
1
0
2
0
1
1
0
2
0
1
2
1
1
0
0
0
2
2
2
2
1
0
1
1
2
1
0
0
0
2
0
1
1
1
0
0
0
1
1
1
1
2
2
1
1
0
2
2
1
0
0
1
1
0
3
1
1
2
1
1
1
0
1
0
0
0
0
2
0
1
1
1
1
3
1
0
1
2
0
0
0
0
0
0
1
2
1
1
0
1
0
2
2
0
0
2
2
1
2
0
1
1
1
2
2
0
0
0
0
1
0
0
0
1
0
2
0
1
1
2
0
0
2
1
0
0
0
2
0
2
0
2
0
1
0
1
0
1
1
1
1
2
0
1
0
0
1
2
1
1
2
0
1
2
1
1
1
0
1
2
1
0
1
1
1
0
1
1
0
2
2
0
2
1
1
1
1
1
1
0
0
0
1
0
1
1
1
2
1
2
1
2
0
1
0
1
0
0
0
1
2
1
2
2
0
2
1
1
1
0
2
1
0
1
1
2
1
2
2
0
0
1
0
0
1
0
3
1
2
1
1
1
0
1
0
2
0
1
2
0
1
0
1
2
0
1
2
2
1
0
1
1
1
0
1
0
1
1
1
1
0
1
0
1
2
0
1
0
1
1
1
2
1
1
1
1
2
0
2
1
2
0
1
2
0
0
1
1
0
0
0
2
1
0
1
0
0
2
1
2
2
0
2
0
1
1
0
2
2
0
0
1
1
0
0
1
0
1
2
2
0
2
1
1
2
1
1
1
1
2
2
1
1
0
1
0
0
0
1
1
1
1
1
0
0
1
0
1
0
0
2
1
2
1
0
1
3
2
2
2
0
1
0
1
1
2
0
2
0
0
1
0
2
1
1
1
0
1
0
2
1
0
2
0
1
1
1
0
1
1
0
2
4
0
2
2
1
1
0
2
2
0
0
1
0
2
1
2
1
1
1
0
1
1
1
0
1
0
1
3
1
1
0
0
1
1
2
1
0
1
2
2
0
1
2
1
0
0
0
2
1
1
2
0
0
0
2
1
1
2
1
1
0
1
0
1
1
1
0
2
0
2
1
0
0
0
0
0
0
1
1
1
1
2
2
2
2
2
1
1
0
0
2
0
1
1
0
1
2
0
1
0
0
0
1
2
2
0
1
0
1
2
1
1
0
0
1
2
0
1
3
1
0
0
1
0
1
1
0
1
1
1
0
2
3
2
1
1
1
0
2
1
2
2
1
1
2
0
1
1
1
1
1
1
1
1
0
0
1
2
2
0
1
1
1
1
0
1
0
1
0
1
2
1
0
1
1
2
3
1
1
0
0
1
0
0
1
0
0
2
1
0
1
1
0
0
2
0
1
0
1
2
0
1
2
5
2
0
2
1
1
1
2
1
1
0
0
2
0
1
1
0
2
1
0
1
2
1
2
1
0
1
1
2
1
1
0
2
0
2
0
1
1
2
0
0
0
1
1
1
0
2
2
0
1
2
2
1
1
0
2
0
2
1
1
1
1
1
0
0
2
0
0
2
0
2
1
1
2
2
1
1
0
1
2
1
0
1
0
1
0
1
2
2
1
1
0
0
1
2
1
0
1
0
0
1
1
1
1
1
2
0
0
0
1
3
1
1
0
2
1
0
0
1
0
1
0
1
0
1
0
1
1
1
0
0
1
2
0
0
0
1
1
1
1
2
0
0
1
2
1
1
1
0
0
1
0
1
0
0
2
1
0
2
0
0
1
2
0
2
0
1
0
1
0
1
2
2
1
0
0
1
1
2
1
0
2
0
2
0
1
1
1
2
1
1
0
1
2
0
0
1
2
2
1
2
1
0
0
1
0
0
2
0
0
2
1
0
1
0
1
1
2
1
0
3
1
1
2
2
0
1
1
5
1
1
0
0
2
0
0
1
0
0
0
0
0
1
2
1
0
2
0
2
1
1
0
1
2
2
2
0
1
0
2
2
1
0
0
1
1
0
1
2
1
0
1
0
0
1
1
0
0
1
1
0
0
1
1
1
1
0
0
0
0
1
0
2
1
0
0
0
2
2
1
2
1
1
1
1
1
1
2
0
1
0
2
1
0
0
1
0
1
0
1
0
0
3
0
2
2
2
1
1
1
1
0
1
0
2
0
2
1
1
2
1
2
2
2
2
0
4
2
2
0
2
2
1
1
1
1
0
1
1
0
1
1
1
1
0
0
1
0
0
0
1
2
0
0
1
1
2
1
0
1
0
0
2
2
0
1
0
0
0
0
2
1
0
2
1
0
1
1
1
1
1
2
1
2
0
0
1
0
1
1
1
1
0
1
0
1
1
1
0
1
1
1
2
2
1
1
0
2
1
0
1
2
0
4
1
0
2
0
0
2
1
1
1
2
0
1
0
0
0
0
0
2
0
1
1
1
1
1
1
1
1
0
1
1
1
0
1
1
0
0
2
0
1
0
2
0
0
1
0
2
2
0
2
0
1
1
1
0
2
1
2
1
2
2
1
1
2
2
1
1
0
1
2
1
1
0
1
2
2
2
1
1
1
2
2
2
1
0
1
1
0
0
2
1
2
2
0
1
1
0
1
0
2
1
1
1
1
1
0
1
1
2
0
0
1
0
1
1
0
1
0
2
1
0
1
1
0
0
0
0
1
2
0
2
1
0
1
0
1
0
2
1
2
0
0
0
2
1
0
4
1
2
1
0
1
0
1
0
1
2
0
2
0
0
1
0
0
1
0
1
0
1
0
2
0
1
0
0
1
1
1
1
1
1
0
1
1
0
0
0
1
1
0
0
2
0
0
1
0
1
0
2
2
0
1
0
1
2
2
0
1
1
3
1
1
0
1
2
1
1
1
1
2
1
0
1
1
1
0
0
0
1
0
0
1
0
1
0
1
0
0
1
1
1
2
1
2
1
1
2
0
0
1
1
2
0
1
1
1
0
1
2
0
2
2
2
1
1
0
0
0
3
0
1
0
1
0
0
0
1
1
1
2
2
2
0
1
1
0
2
2
0
0
0
1
1
0
0
2
2
1
1
0
1
2
1
1
1
1
1
1
1
2
0
0
2
2
1
1
1
0
2
2
0
0
1
1
1
1
0
1
1
2
3
0
1
1
2
0
1
1
0
2
1
1
0
0
1
1
1
2
1
1
0
1
1
2
2
0
0
2
1
1
2
0
2
1
2
2
0
0
0
1
0
0
0
2
1
2
0
2
1
1
0
0
0
0
0
1
0
2
2
1
0
1
0
1
1
0
1
1
2
0
2
1
2
0
2
0
1
1
1
1
1
0
1
1
0
0
1
0
1
0
3
0
1
2
2
1
0
2
3
1
1
2
0
2
2
0
2
1
0
0
1
0
0
0
2
1
1
0
1
1
0
1
1
2
0
1
1
2
0
1
0
1
1
2
0
0
2
1
1
2
1
3
0
1
1
1
1
1
0
0
2
2
0
1
1
1
1
0
1
0
1
0
2
1
0
0
1
2
2
2
1
1
1
2
0
0
0
1
0
1
1
1
0
0
1
1
0
1
1
1
1
1
0
2
1
0
2
1
0
2
0
0
0
1
0
1
2
0
1
1
0
1
1
3
1
1
1
1
1
0
1
2
2
0
1
0
2
1
0
0
2
1
2
1
1
0
1
1
1
2
0
0
2
0
1
0
1
1
1
0
0
0
3
1
0
2
1
2
2
2
0
2
2
1
1
0
1
2
1
1
1
1
1
1
1
0
3
2
2
0
1
2
1
1
1
0
1
0
1
1
1
0
1
1
1
1
0
0
1
0
0
0
0
1
0
2
1
1
1
2
0
2
1
0
1
1
0
1
0
0
0
2
0
1
2
2
2
0
1
1
0
0
1
2
2
0
1
2
0
3
1
1
0
1
1
0
2
0
1
1
1
1
2
1
0
1
1
1
1
1
0
2
1
0
1
0
0
2
0
0
2
0
1
0
0
0
1
1
0
0
1
1
1
0
0
0
1
2
2
0
3
1
2
0
2
1
2
0
0
0
2
2
2
0
0
0
0
0
1
1
0
1
0
1
2
2
2
1
2
1
1
0
1
1
1
1
2
1
1
1
0
0
0
3
0
1
0
1
0
0
2
2
2
0
2
1
1
1
0
1
1
2
0
0
2
0
0
0
0
1
0
1
1
1
1
0
2
0
1
0
1
1
1
0
1
2
0
1
0
0
0
0
1
0
1
1
1
2
1
1
0
0
1
2
2
2
1
1
0
0
1
0
0
2
1
1
0
1
1
0
0
0
0
1
1
1
1
1
2
0
0
1
0
1
0
1
2
1
0
2
1
0
1
1
5
1
1
1
1
1
2
1
1
0
0
1
3
2
0
0
1
1
1
0
0
1
0
2
1
0
1
2
0
1
0
0
1
0
2
0
1
0
0
0
0
1
1
0
1
0
0
0
0
1
2
1
0
1
1
0
1
0
0
0
2
1
1
0
2
1
2
1
2
2
0
1
1
2
0
1
0
0
1
0
1
0
1
1
0
1
0
2
0
0
1
0
1
1
0
2
0
0
1
2
1
2
2
0
0
2
1
1
1
0
1
0
0
0
2
2
1
0
0
2
2
0
1
0
2
2
1
1
2
0
1
1
0
0
1
1
0
2
2
1
1
1
2
1
1
1
2
0
0
0
0
0
0
1
2
2
0
0
0
0
1
0
1
1
2
2
0
2
2
2
1
1
0
2
1
0
0
2
0
0
0
2
1
2
0
1
2
0
0
0
2
1
2
1
1
0
2
1
0
1
1
0
1
1
2
0
0
1
1
1
0
1
0
0
0
2
2
1
0
2
0
1
1
1
1
1
2
1
0
0
1
0
1
1
1
0
0
1
0
0
0
0
1
1
0
1
1
1
0
0
0
0
1
0
0
1
2
0
1
1
1
1
0
2
1
1
2
0
0
1
2
0
1
1
1
1
1
1
0
0
0
0
0
0
1
2
2
0
2
0
2
0
2
1
1
1
0
0
1
1
1
1
2
0
2
1
1
2
2
0
1
1
0
2
1
1
0
1
1
1
2
2
0
1
1
0
1
0
0
0
1
1
2
2
2
2
0
2
2
0
1
0
1
2
0
1
2
1
0
1
1
2
0
0
1
0
2
1
0
1
1
2
0
2
2
1
0
0
0
0
1
0
0
1
0
1
0
1
1
2
0
1
1
0
0
0
1
0
2
0
2
1
0
1
2
0
0
1
1
1
2
0
0
0
1
1
2
1
0
0
0
0
1
0
1
1
2
0
1
1
1
0
1
0
1
1
2
0
0
4
1
0
0
0
1
1
0
1
1
3
2
1
2
2
0
2
1
1
0
1
0
0
2
0
1
0
1
0
2
1
2
2
1
1
2
2
1
2
0
0
1
2
2
1
1
0
1
1
1
0
1
0
2
1
1
1
1
0
1
2
1
0
0
1
1
1
1
1
0
1
1
1
2
1
0
1
0
1
1
1
1
0
0
0
0
1
3
1
0
1
0
2
0
1
0
1
1
1
1
2
2
0
1
1
2
0
0
1
1
1
0
1
1
2
1
1
1
1
0
0
0
0
2
3
0
0
2
2
0
0
0
1
0
0
0
1
1
1
1
3
2
2
1
2
1
1
0
0
0
0
0
0
2
0
1
0
1
0
0
0
2
2
1
1
1
0
0
0
3
1
1
2
1
1
1
1
1
0
0
0
2
1
0
2
1
1
0
0
2
1
0
0
0
0
0
1
1
1
0
1
2
1
0
1
0
1
0
0
1
0
0
0
0
0
0
1
2
1
0
1
0
0
1
0
1
0
2
2
0
0
1
1
1
2
2
0
1
1
1
0
1
0
2
2
1
0
1
1
0
1
0
2
0
2
1
1
1
1
3
1
3
1
1
1
2
2
0
1
2
1
2
1
0
2
2
2
2
0
0
0
1
1
2
0
0
1
1
1
0
0
1
0
0
0
2
1
0
1
1
1
0
1
1
2
1
1
1
1
0
0
0
1
0
1
1
0
2
1
0
0
1
1
1
1
0
0
1
1
0
1
1
2
1
1
2
0
1
2
1
2
1
0
1
1
2
1
1
1
0
1
0
0
0
1
0
0
0
1
0
0
1
0
1
2
1
1
0
0
1
1
0
1
1
2
0
2
0
2
2
2
0
0
1
0
2
2
2
1
1
1
0
1
1
0
1
2
0
1
1
2
1
1
2
2
2
2
1
1
1
0
0
0
1
1
0
1
1
1
1
2
1
0
2
0
0
0
1
0
2
1
1
2
0
1
0
1
0
1
2
1
1
2
0
1
0
1
2
1
1
0
0
1
1
0
0
2
2
0
0
2
1
0
1
1
2
0
1
0
0
2
0
1
1
1
0
1
1
0
2
0
1
0
2
1
0
1
0
1
1
0
0
1
1
0
1
1
0
1
2
1
2
2
0
2
1
2
2
1
0
1
2
2
0
1
1
0
0
1
2
1
0
0
1
1
1
0
1
1
0
0
0
0
1
0
2
1
0
0
1
2
1
1
1
1
0
0
2
0
1
1
1
1
0
1
2
2
1
0
1
0
1
0
2
0
1
1
0
1
0
0
1
0
0
0
0
1
1
0
2
1
2
0
1
1
2
2
1
0
0
0
2
1
1
1
0
1
1
0
0
1
2
0
2
0
1
2
1
1
1
0
2
1
2
0
2
1
0
0
1
0
1
0
0
2
2
2
1
0
0
1
1
0
1
3
1
2
2
1
0
0
1
0
1
2
0
1
0
0
2
0
1
0
4
1
2
2
0
2
1
1
3
2
1
1
0
1
0
0
2
0
2
1
0
0
1
0
1
0
0
0
2
1
0
0
0
0
2
2
1
1
1
1
0
0
2
0
1
0
1
0
0
2
2
0
2
0
1
0
0
1
0
1
0
0
0
2
1
1
1
0
0
0
1
1
1
1
2
0
1
1
1
0
1
1
0
0
4
2
3
0
0
2
1
1
0
2
1
1
1
2
2
1
2
2
2
1
0
1
1
2
1
3
1
0
2
1
0
1
2
1
1
2
0
1
0
0
2
0
1
2
1
0
2
0
1
0
2
2
0
1
0
1
0
2
0
0
1
1
1
2
2
1
0
1
0
0
1
2
2
2
0
1
1
2
1
1
1
1
1
1
0
2
1
2
2
0
1
2
0
0
0
0
1
1
0
0
0
0
1
0
2
1
1
0
2
0
0
1
1
0
0
0
2
2
0
1
0
1
2
0
2
2
0
1
1
0
1
0
1
1
1
1
0
1
2
1
2
0
0
2
0
0
2
1
2
1
1
2
1
0
1
1
1
1
0
0
0
0
2
1
2
1
3
0
0
0
2
0
0
2
1
0
2
0
1
0
2
1
1
0
2
0
3
2
0
0
1
0
1
1
0
0
0
1
1
1
1
0
1
1
0
0
0
1
0
1
0
0
1
1
1
1
1
1
1
0
1
0
0
0
2
1
0
0
1
1
0
0
2
0
0
1
0
1
2
2
0
0
2
1
1
0
0
1
1
0
2
1
1
1
1
1
1
0
1
1
0
0
2
1
1
1
1
2
0
0
1
0
0
2
0
1
1
1
2
3
0
0
1
0
1
1
0
2
1
2
1
1
1
1
1
0
0
0
0
2
1
1
1
2
1
0
0
1
0
0
1
1
0
1
1
1
1
1
4
0
0
2
0
0
0
2
2
0
2
0
3
0
2
1
0
1
1
0
0
1
0
0
1
2
0
2
1
0
2
2
0
0
1
0
1
0
2
1
1
0
1
1
0
0
1
1
2
0
1
1
1
1
1
0
2
0
0
0
1
2
1
1
2
1
2
1
2
1
1
0
1
0
1
2
2
2
1
2
0
0
1
0
1
2
1
1
0
1
1
1
0
0
0
2
1
0
2
1
1
2
1
0
2
2
2
1
0
2
0
1
1
0
2
2
0
2
0
1
0
2
0
0
2
1
1
1
2
2
2
1
0
2
2
1
2
1
0
2
0
0
0
0
1
2
0
1
0
1
1
1
2
1
1
1
2
0
1
1
0
1
1
0
1
1
2
0
2
1
2
0
2
1
1
0
1
1
0
1
1
0
1
0
1
1
1
0
0
0
1
0
0
1
1
0
0
1
2
1
0
0
2
2
2
2
0
0
0
1
0
1
0
0
0
0
1
0
1
4
1
2
0
0
2
0
1
0
2
0
1
1
0
1
1
0
3
2
1
0
1
1
1
1
0
0
0
0
1
0
0
2
1
2
1
1
0
1
0
1
1
2
1
0
2
2
1
0
2
0
2
2
1
1
0
3
0
2
0
0
1
0
1
1
1
1
2
2
1
1
0
1
2
2
1
1
2
0
2
1
0
2
1
0
1
1
2
1
2
0
0
1
2
1
0
0
1
1
1
1
1
1
1
2
0
2
1
0
0
0
2
1
1
1
1
2
1
0
0
1
0
1
2
0
2
1
0
1
1
0
0
2
1
0
1
0
1
2
2
0
1
2
1
0
0
3
0
0
0
1
0
2
2
0
5
0
0
0
0
1
0
1
2
1
1
1
2
2
1
2
0
1
0
0
2
1
1
1
2
1
2
0
0
1
1
0
2
1
1
1
2
0
1
0
0
1
1
1
2
2
1
1
0
2
0
0
1
1
0
1
1
1
0
0
0
1
1
1
2
0
0
1
0
1
2
1
0
0
0
1
0
2
0
2
1
0
0
1
1
1
1
0
1
1
2
2
0
1
0
1
0
2
1
1
2
2
1
1
0
1
1
6
2
1
0
1
2
2
2
1
1
0
1
0
1
1
1
2
3
0
0
1
2
1
1
2
3
0
0
1
1
0
1
0
2
1
1
0
2
1
0
2
1
0
1
1
0
0
1
0
1
0
0
2
1
0
1
2
1
1
2
1
1
1
1
3
0
1
0
0
1
1
0
0
3
1
1
3
0
1
0
0
2
3
1
0
1
0
0
0
2
3
0
0
1
1
1
1
0
0
0
0
0
1
1
2
0
1
0
0
1
0
0
2
1
0
1
0
1
2
0
1
2
1
0
2
2
1
2
0
2
0
1
0
0
1
0
0
1
0
1
2
2
1
1
2
1
1
0
2
0
1
0
1
0
1
0
2
1
2
0
0
2
1
1
1
1
0
1
0
1
1
1
4
1
2
0
2
2
2
1
1
0
1
1
2
0
1
2
1
1
0
1
0
0
0
2
0
1
0
2
2
1
0
2
0
0
2
0
2
2
3
0
0
0
1
2
1
2
0
1
1
0
1
1
2
1
1
1
1
2
0
0
2
1
0
1
1
1
1
1
0
2
1
2
0
0
1
2
0
1
3
1
2
1
2
2
0
2
0
0
1
3
1
1
0
1
1
1
1
0
1
2
2
0
1
1
0
1
1
0
0
2
1
0
0
0
0
1
2
1
1
2
1
1
0
1
2
2
1
0
0
1
2
0
0
1
1
1
2
0
0
1
0
0
1
1
0
1
1
2
1
1
1
1
0
2
2
0
1
0
2
2
1
1
1
1
0
1
0
0
0
1
2
1
0
1
1
2
0
0
2
1
1
2
1
0
0
1
2
2
0
0
1
3
1
2
0
0
1
2
1
1
1
1
1
2
1
1
1
1
2
1
1
3
1
2
1
0
0
0
0
2
0
1
1
0
1
3
1
2
1
1
1
2
1
2
0
2
1
1
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
2
2
0
1
2
0
4
2
1
2
1
0
2
1
2
1
1
1
0
0
1
0
0
2
1
1
1
0
0
1
1
1
2
1
0
5
0
0
0
1
0
0
0
0
0
1
0
0
1
3
1
0
0
0
2
0
0
0
0
1
1
0
1
0
1
1
2
1
1
0
2
0
0
1
0
1
2
3
2
2
0
1
2
0
0
0
0
0
2
1
1
1
0
1
2
0
0
1
2
0
1
1
0
2
1
2
1
1
1
1
0
2
1
0
1
0
2
1
1
0
0
0
2
2
1
1
0
2
0
0
1
0
2
0
0
1
1
1
1
1
1
2
1
0
0
1
2
0
0
1
0
1
6
0
1
1
1
0
0
1
1
1
1
2
1
1
0
0
0
1
1
0
1
2
0
2
0
1
2
0
0
1
1
1
0
1
1
0
1
1
2
1
1
0
0
0
2
0
0
2
2
0
1
0
0
0
0
2
0
2
2
2
1
1
1
2
0
1
0
2
2
2
0
1
1
0
0
0
2
2
0
0
0
0
1
0
0
0
3
1
0
2
0
2
2
2
1
1
1
1
1
1
1
0
0
1
0
0
1
2
2
1
1
0
1
0
0
0
0
0
1
1
1
1
2
3
1
1
0
1
2
0
0
1
1
2
2
1
1
0
1
0
0
0
0
1
1
2
0
2
2
0
1
2
0
1
0
0
1
1
1
1
0
2
0
1
0
1
1
4
1
1
0
0
0
1
1
1
0
2
1
1
1
2
1
0
1
7
0
0
2
1
1
1
0
2
2
1
0
0
2
0
2
0
1
0
1
2
1
3
1
1
1
0
2
0
1
1
2
1
0
1
0
0
1
1
1
0
2
2
2
0
1
1
2
1
1
1
0
0
0
0
0
3
1
0
0
1
0
0
2
0
2
0
0
1
0
0
0
0
1
1
0
1
2
1
0
1
2
1
2
1
0
1
1
1
1
1
0
1
0
1
0
2
1
1
0
0
1
0
0
1
2
1
1
1
0
1
2
0
0
0
1
1
0
0
2
1
0
2
0
0
0
1
0
2
1
0
2
0
0
1
0
0
2
1
4
1
1
0
0
1
2
2
1
1
1
0
0
2
0
0
1
2
0
0
0
0
2
0
2
1
1
1
2
1
2
2
1
2
1
0
1
2
2
1
1
2
0
0
0
1
0
1
0
1
0
1
1
1
1
2
2
0
0
2
1
0
0
2
0
0
1
1
0
0
2
0
0
2
1
0
0
0
0
0
2
2
1
2
1
0
2
1
1
0
0
1
2
1
2
0
0
1
2
0
0
0
1
0
2
1
1
2
0
1
2
0
0
0
1
2
0
0
2
2
0
0
1
2
0
0
0
0
2
1
2
0
0
0
2
2
2
1
0
0
1
1
2
2
0
1
1
0
1
2
0
0
2
1
0
1
0
2
0
0
1
0
1
1
1
1
2
1
1
0
1
1
1
1
0
0
0
2
1
0
0
1
2
2
3
0
0
1
2
1
0
0
1
0
1
0
0
1
0
1
0
2
1
3
0
2
1
1
1
0
0
1
0
2
0
1
0
1
0
2
0
0
1
1
2
0
0
2
0
1
0
0
0
0
1
0
0
1
2
0
2
2
2
1
2
0
1
0
3
2
3
2
2
0
1
2
1
1
0
2
2
1
1
1
0
0
0
0
1
0
1
0
1
2
0
0
2
1
0
1
1
1
0
1
2
1
0
2
1
0
1
0
0
1
2
0
2
1
0
0
3
1
1
0
0
2
1
0
1
1
0
1
0
1
2
1
2
0
2
1
0
0
1
3
0
1
1
1
2
1
0
0
2
2
0
2
1
1
0
0
2
2
2
2
0
2
0
0
0
2
0
1
1
1
1
1
1
0
2
2
0
2
1
0
2
0
0
1
2
1
0
2
0
0
1
2
0
1
1
2
2
0
1
1
1
1
1
2
1
0
0
1
2
1
1
1
1
0
1
0
0
0
0
1
0
1
2
1
0
2
2
0
0
0
2
0
1
1
2
2
0
1
1
1
1
2
1
3
2
0
1
0
1
2
0
1
0
1
2
0
1
1
1
0
1
0
0
0
0
1
1
1
0
2
2
0
1
0
1
0
1
0
0
0
1
1
0
2
2
0
1
0
1
0
0
1
2
0
1
1
0
1
1
1
2
1
1
0
2
1
1
1
0
1
0
1
1
0
2
2
2
1
0
0
2
1
1
1
1
1
1
1
1
0
1
1
0
1
0
1
0
1
1
1
1
1
3
0
1
1
1
0
0
0
0
0
0
1
0
1
0
1
1
2
0
1
0
0
0
0
1
1
1
0
0
2
2
2
2
1
0
2
2
1
0
0
2
0
0
1
2
1
0
2
0
1
1
0
2
0
3
1
0
1
0
0
1
2
1
1
1
0
2
1
1
2
1
1
2
1
2
1
0
2
0
1
1
0
1
0
2
1
1
1
0
2
0
1
0
1
1
0
0
0
0
0
0
2
0
2
2
2
0
0
1
2
0
0
0
0
1
1
0
2
2
0
2
1
2
1
0
2
2
1
1
2
0
2
0
0
2
0
2
1
2
0
1
0
1
0
1
0
1
1
1
2
0
3
1
1
0
1
0
2
1
0
2
0
0
0
1
0
2
1
2
0
1
1
1
0
2
0
0
1
0
1
0
2
1
2
1
1
1
1
1
0
1
0
1
1
2
1
0
1
1
0
1
1
2
0
1
1
1
0
0
0
2
0
3
2
1
2
0
2
0
2
0
2
1
0
1
2
0
1
1
1
0
1
2
1
1
1
1
1
1
1
0
2
1
0
1
1
0
0
0
2
2
1
2
1
1
1
0
0
1
0
0
2
1
2
1
1
0
1
0
1
0
2
2
1
0
1
2
0
1
1
2
0
0
0
1
0
3
1
1
0
0
0
1
0
2
0
0
1
0
0
1
3
0
2
0
0
1
1
1
1
0
2
1
1
2
2
0
2
0
1
1
0
0
1
1
1
0
0
0
1
2
0
0
1
2
1
1
1
1
0
2
2
1
0
1
0
2
1
1
3
0
2
1
0
1
0
2
1
2
0
0
3
1
1
0
2
1
2
1
0
0
2
1
1
1
1
1
1
0
1
1
0
1
2
2
0
0
2
0
0
2
1
0
1
0
0
3
0
1
2
0
1
1
0
0
0
0
2
1
1
1
2
0
2
0
1
0
1
0
2
1
1
4
1
2
1
2
1
0
1
2
1
2
0
2
1
2
0
2
1
1
0
2
0
1
1
1
0
1
3
0
0
0
1
0
1
2
2
1
2
1
1
1
0
2
2
0
2
0
2
1
2
1
1
0
0
1
2
1
1
0
1
1
1
1
1
0
1
2
3
1
2
0
1
1
1
0
0
0
1
1
1
1
0
1
0
2
2
1
0
1
0
0
0
0
1
1
0
2
0
1
1
1
0
0
2
0
0
2
0
0
2
1
1
1
0
0
0
2
1
1
1
2
1
2
1
2
0
1
3
1
1
0
2
0
0
2
0
0
1
1
0
2
1
1
1
0
1
1
1
0
1
2
2
2
2
0
1
1
2
1
2
0
1
0
1
2
0
0
2
1
1
1
2
1
0
0
1
3
0
1
2
0
0
2
1
0
1
2
0
1
0
1
0
2
0
3
1
2
0
1
1
1
0
1
2
2
1
0
2
1
0
1
1
1
1
0
3
1
1
1
1
1
1
0
1
2
1
1
1
0
1
1
0
0
1
1
1
2
1
0
1
1
0
1
0
1
1
0
2
0
2
0
1
1
1
1
1
1
1
0
2
0
0
0
1
0
0
1
0
0
1
0
1
1
0
0
1
1
1
1
1
1
0
0
0
0
1
1
1
1
2
1
1
1
0
1
1
0
2
1
1
1
0
0
0
1
1
2
0
2
0
0
1
1
0
1
1
0
0
1
0
0
1
1
1
1
0
0
0
0
0
1
2
1
2
3
1
0
1
1
1
2
1
1
2
2
1
0
1
1
2
0
1
0
0
2
0
0
1
0
1
0
0
2
0
2
0
2
0
0
1
2
1
0
1
0
2
1
1
0
0
1
1
2
0
0
0
1
1
0
1
0
1
1
2
0
0
0
0
0
1
0
1
1
1
2
2
1
2
0
2
3
0
2
0
0
1
4
2
0
1
0
0
1
1
1
1
2
1
2
0
0
2
1
1
1
0
0
0
1
2
1
1
0
2
1
1
1
1
2
0
1
1
2
1
0
1
0
1
1
2
2
0
1
1
0
1
0
1
2
1
2
1
0
0
1
2
1
1
0
1
2
0
1
2
1
0
0
1
0
3
1
2
0
1
2
0
0
1
1
1
5
2
0
1
1
1
0
0
0
0
2
1
1
1
0
0
0
2
0
1
1
0
2
1
2
2
2
1
2
1
0
0
2
1
2
2
0
2
1
2
0
0
1
0
0
0
2
1
3
1
0
1
1
1
0
2
0
0
0
0
0
2
0
1
2
1
2
1
0
0
1
1
1
1
1
0
2
1
0
2
2
1
0
0
1
0
2
0
2
0
1
1
1
2
1
1
1
0
0
1
1
1
0
0
0
0
0
2
2
1
2
1
1
1
1
2
0
1
1
1
0
1
0
2
2
1
1
0
2
0
1
0
1
1
1
0
1
2
0
1
0
0
0
1
0
0
1
2
1
0
1
2
0
0
3
1
0
1
2
1
1
0
2
1
2
1
1
1
0
1
1
1
3
1
2
1
2
2
3
2
1
0
2
1
0
1
1
1
0
0
1
1
0
1
1
1
1
0
1
1
0
2
1
2
2
2
1
1
2
1
0
0
1
1
1
2
0
1
1
0
0
2
0
1
1
1
0
1
1
1
1
1
1
0
0
0
1
2
1
1
1
0
0
0
2
1
0
2
0
0
2
1
0
0
0
1
2
0
0
3
1
0
1
0
0
0
0
1
0
1
2
0
0
1
0
0
1
1
1
0
0
1
0
0
0
1
2
0
0
0
1
2
0
0
2
1
2
2
0
1
2
2
0
1
0
1
0
0
0
0
0
1
2
0
1
1
1
0
1
1
1
0
1
0
0
0
1
1
0
2
1
1
0
2
1
2
1
0
0
2
1
0
0
1
0
0
0
0
1
2
3
0
0
2
0
1
1
1
0
1
0
0
1
0
2
1
1
3
0
0
1
1
0
2
2
0
0
0
0
0
2
1
0
0
0
1
0
0
1
2
1
1
0
0
0
1
0
0
1
1
1
1
0
1
1
1
0
2
0
2
1
1
1
1
0
0
0
1
1
2
1
0
2
1
0
2
1
2
2
0
0
1
2
2
1
0
2
1
0
2
1
1
0
0
1
0
0
1
0
2
0
3
2
2
0
0
0
0
0
1
1
1
1
0
1
0
0
0
1
1
1
1
0
0
0
0
0
0
0
1
1
0
1
2
0
1
2
1
2
0
0
1
1
1
0
1
2
0
0
1
0
0
0
2
1
0
0
0
0
1
1
1
1
1
0
0
1
1
1
1
1
2
2
0
0
1
0
1
0
2
1
2
1
2
2
1
0
1
1
2
0
1
1
1
1
2
2
1
2
0
0
0
1
1
0
2
1
0
2
0
0
2
0
0
1
1
0
0
1
2
1
2
1
1
0
1
1
0
1
1
2
2
2
0
0
1
1
1
0
1
0
1
0
1
0
1
1
0
1
2
2
0
1
1
0
0
0
1
2
1
1
1
2
2
1
1
2
0
2
0
2
1
0
0
0
0
2
0
1
1
0
2
1
1
2
1
1
1
1
0
1
1
0
2
2
1
2
0
0
1
0
0
2
1
0
0
0
1
0
0
0
1
0
1
1
1
1
1
2
2
0
0
3
1
0
1
0
3
2
2
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
2
1
0
2
2
1
1
1
2
1
1
0
1
1
2
0
2
2
2
2
1
1
1
0
1
0
1
1
0
0
0
1
0
2
2
0
1
2
0
1
1
0
1
1
1
2
2
0
1
1
0
1
1
1
1
1
0
1
1
1
1
2
1
1
2
1
1
1
0
1
3
2
1
2
1
0
1
1
1
1
0
0
1
0
1
1
1
1
0
0
2
0
0
1
0
1
1
1
0
1
1
1
1
0
1
1
2
2
1
1
1
1
0
0
2
2
1
0
0
2
2
2
1
1
0
2
1
0
1
0
0
0
1
0
0
0
0
0
5
1
1
1
1
0
2
1
0
2
0
0
0
0
1
1
0
1
0
2
2
0
2
1
0
1
1
0
0
0
0
2
1
0
0
0
1
3
2
0
1
0
1
1
0
1
0
0
2
1
2
0
0
1
2
2
0
0
1
1
1
1
0
2
1
1
0
1
1
1
1
0
2
2
1
1
2
2
0
2
1
1
2
2
1
0
0
1
1
2
0
1
1
0
1
1
0
0
1
0
1
0
2
1
2
2
1
1
1
1
1
1
2
1
1
1
2
2
1
1
1
2
1
1
0
0
2
0
0
1
1
1
1
0
0
1
1
1
1
2
2
0
0
2
1
1
0
3
1
2
0
1
1
0
0
3
1
1
2
1
0
1
1
0
1
1
0
1
1
2
0
0
0
0
1
0
1
2
1
0
2
0
0
1
1
1
4
1
1
0
2
2
0
0
0
0
1
0
1
1
1
1
0
2
1
1
2
1
1
0
0
2
2
2
1
0
1
0
2
0
2
0
2
1
0
1
1
2
1
0
1
0
2
2
0
1
1
0
0
2
1
1
2
1
2
1
2
2
0
1
0
0
1
1
2
0
1
0
1
2
0
1
0
2
1
1
0
0
0
0
0
2
2
1
2
0
2
0
0
1
1
1
1
0
0
0
1
0
0
1
2
0
0
2
0
1
2
1
2
2
0
1
1
1
1
0
2
1
1
2
1
2
0
0
1
0
1
2
0
0
0
2
0
1
1
0
0
1
0
0
0
1
1
1
0
1
1
0
0
1
0
0
1
0
0
1
2
0
0
0
0
1
1
0
1
0
0
0
1
1
2
2
2
1
1
1
0
0
0
1
2
0
0
1
1
1
0
1
1
0
0
1
1
1
1
2
1
1
0
1
1
1
1
0
1
0
0
2
2
1
1
1
1
0
1
0
0
2
0
2
1
2
0
0
1
1
1
0
1
1
2
1
0
1
1
1
0
4
0
1
2
0
5
0
2
0
0
1
0
1
1
0
2
2
2
0
0
0
1
1
0
0
1
1
1
0
1
1
2
0
1
1
0
2
1
0
0
1
1
0
0
2
1
2
1
0
1
0
1
0
0
2
0
0
2
0
1
2
1
0
1
0
2
0
1
0
1
1
1
1
1
2
1
3
1
0
2
1
2
3
1
1
1
2
1
0
0
0
1
0
1
2
1
1
1
0
0
1
2
1
0
2
0
0
1
0
1
0
1
1
1
1
0
1
0
1
1
0
1
0
0
1
1
0
1
2
1
1
1
1
1
3
0
0
1
1
0
1
2
1
0
1
1
0
1
0
0
0
1
2
2
2
1
0
2
0
2
0
0
1
1
1
1
1
1
0
0
1
0
0
2
1
1
2
0
0
0
1
0
0
1
4
0
1
2
1
0
3
0
2
0
0
0
0
1
1
0
1
2
1
2
2
1
2
0
2
1
2
2
2
1
1
0
0
1
0
1
1
2
0
1
1
1
0
1
1
1
1
0
1
1
0
2
0
2
2
1
2
0
1
2
2
0
1
1
0
0
1
1
0
0
2
3
1
1
0
1
2
1
1
1
1
0
3
0
2
0
1
0
1
0
1
2
1
1
2
0
0
2
0
2
1
2
0
1
0
2
2
2
1
0
0
1
1
1
0
1
0
0
1
0
1
0
1
2
1
2
2
2
1
0
1
0
1
1
0
1
2
0
1
3
2
0
1
0
2
1
5
1
0
2
0
1
1
0
0
2
2
2
0
1
1
1
0
2
0
0
2
0
1
0
3
0
1
2
1
2
1
1
1
0
2
2
2
0
1
0
0
2
2
2
0
1
1
1
2
1
0
2
0
2
0
0
1
1
1
1
0
1
1
1
0
0
0
0
0
1
2
0
0
1
2
3
1
1
0
0
1
1
1
2
0
0
0
1
1
0
2
1
2
0
1
1
1
1
0
0
1
2
1
0
2
1
0
0
1
0
0
0
0
0
1
0
0
2
0
0
2
1
1
1
1
1
0
1
1
2
1
2
0
0
0
0
1
0
1
0
0
0
1
1
2
2
1
0
1
1
1
1
1
1
2
2
1
0
0
2
1
0
1
0
2
0
1
1
0
1
1
2
2
2
1
2
2
2
1
0
1
0
1
0
0
0
0
1
1
0
0
1
1
0
0
0
1
1
1
1
1
0
0
0
2
0
1
2
1
1
2
0
0
0
2
0
0
0
0
1
0
1
0
2
0
2
0
2
2
0
0
2
1
2
1
2
1
1
1
1
1
1
0
2
0
1
0
0
0
1
0
0
1
0
0
0
0
2
0
0
2
1
0
1
1
2
0
0
2
1
2
2
2
1
0
0
0
0
1
1
1
1
0
1
2
0
1
1
1
1
1
2
3
0
1
0
1
2
2
2
1
0
1
0
1
0
0
1
2
1
2
1
2
2
0
2
2
1
2
1
0
2
0
1
1
2
1
1
3
2
2
0
2
1
2
1
1
1
0
1
1
1
0
1
0
2
0
2
0
0
1
0
1
0
1
0
0
2
0
0
0
1
0
0
0
0
1
2
2
1
0
1
0
2
0
0
1
2
0
0
1
1
0
0
0
0
1
2
2
0
1
1
0
0
2
1
1
0
2
0
2
1
1
0
1
0
1
0
1
2
0
0
1
0
0
0
1
1
0
2
0
0
1
1
0
0
1
2
0
1
0
0
3
1
0
0
0
2
0
1
0
0
1
2
1
1
1
1
0
1
1
1
8
0
2
0
0
1
1
0
1
2
1
0
1
0
1
2
0
0
2
2
0
1
2
0
0
1
0
1
0
1
0
5
2
1
0
0
1
1
1
1
0
1
3
2
0
1
0
0
0
1
1
0
2
1
0
1
1
4
0
1
1
0
0
0
0
1
1
2
0
1
1
2
1
0
0
1
1
1
2
2
1
2
0
0
1
1
0
0
1
1
0
1
0
2
2
1
2
0
0
2
1
2
0
0
0
1
2
1
2
1
0
0
1
1
1
2
1
2
0
0
0
0
0
1
0
3
1
1
0
0
0
1
0
0
0
2
2
2
1
1
2
0
0
0
1
2
2
0
0
0
0
1
1
1
1
1
1
0
1
1
0
1
2
0
0
0
0
1
1
1
0
0
1
2
2
0
1
0
1
1
1
2
1
0
0
1
2
2
0
0
1
0
1
0
1
0
1
0
2
1
1
1
0
0
1
0
2
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
2
0
0
0
1
2
1
0
0
2
0
1
1
2
1
4
0
0
1
1
0
0
0
1
0
0
0
1
1
1
1
1
1
1
1
0
0
1
2
0
3
0
1
0
2
1
1
0
1
2
0
2
1
3
0
1
1
0
1
0
0
1
1
1
3
2
2
0
0
1
1
1
1
2
0
1
1
1
0
1
0
2
2
1
0
2
2
0
0
1
0
2
2
2
0
0
0
2
0
1
0
1
2
0
1
1
1
2
2
2
0
1
1
1
1
0
2
1
0
2
1
0
1
1
1
0
2
1
2
1
1
2
1
2
0
0
1
1
1
1
1
0
2
0
1
1
0
2
0
2
0
0
0
1
1
0
1
1
1
1
1
1
2
2
1
1
2
2
2
0
0
0
1
1
0
0
0
0
0
1
0
2
0
0
1
1
0
0
2
1
0
2
1
0
1
2
1
0
0
2
1
1
1
3
3
0
1
0
1
1
1
1
0
0
1
2
1
2
0
1
2
0
0
1
1
0
1
0
0
1
1
2
1
0
1
1
1
1
1
1
1
2
0
0
2
2
0
1
2
2
2
1
1
0
1
2
2
2
0
0
2
0
1
0
1
1
0
2
0
0
2
2
1
1
0
1
1
0
0
4
1
0
2
1
1
1
2
1
1
2
0
0
0
0
3
1
1
0
0
0
1
1
1
2
2
2
1
3
1
0
0
0
3
0
1
1
1
2
1
0
2
1
1
0
2
1
0
0
2
0
2
2
3
0
1
0
1
1
2
2
0
0
0
0
1
1
0
0
2
2
0
2
2
1
0
1
1
1
1
1
1
1
0
0
0
2
1
1
0
1
1
3
1
0
1
0
0
2
1
1
1
2
1
2
2
2
2
0
0
1
0
1
0
1
0
1
0
2
0
0
0
2
1
2
0
1
0
0
2
2
2
1
2
2
0
0
1
2
0
0
0
0
0
1
1
0
1
2
0
2
0
1
2
0
0
2
2
1
1
1
1
1
0
2
2
0
1
0
1
1
2
0
1
1
2
2
4
2
0
1
0
1
1
1
0
0
1
1
0
1
0
0
1
2
0
2
1
0
0
2
1
0
1
0
1
2
1
0
1
0
1
2
2
3
1
2
1
0
2
0
2
2
1
1
2
0
1
1
2
0
2
0
1
3
1
1
2
0
1
2
0
2
0
1
5
0
1
2
2
1
1
0
2
2
0
0
0
2
0
2
0
1
1
0
2
1
1
0
0
1
0
1
1
0
1
1
0
2
1
3
1
0
1
1
1
1
1
1
0
1
0
2
2
1
2
2
1
1
1
2
0
1
0
2
0
1
1
1
2
1
0
1
1
0
0
1
0
0
1
1
1
1
0
1
0
2
2
1
2
0
1
1
0
0
0
0
0
1
0
0
1
0
1
2
2
1
1
0
0
1
1
1
2
1
1
0
4
1
0
0
1
2
1
1
0
0
0
1
0
1
1
0
1
1
2
1
0
2
1
1
2
0
0
3
0
1
0
0
0
2
1
0
1
1
1
1
1
1
1
2
0
1
0
1
0
1
3
0
1
1
2
2
2
2
0
0
0
0
1
0
2
0
1
1
1
2
0
2
2
0
1
1
0
1
1
1
1
0
1
0
1
1
1
0
2
1
2
1
1
2
0
2
0
0
2
1
2
1
0
1
1
0
2
1
1
2
2
1
2
1
0
0
2
0
2
0
0
1
1
2
0
2
0
1
1
1
2
1
1
1
0
1
1
0
0
1
2
1
2
1
1
1
2
0
1
0
0
1
0
2
1
1
0
0
0
2
2
0
1
1
2
1
0
1
1
1
2
1
0
2
0
0
0
1
1
1
1
1
1
0
0
0
0
1
1
2
0
0
0
1
2
1
1
1
1
0
2
1
1
1
2
1
1
0
0
0
1
0
0
1
1
0
2
2
0
1
0
1
1
2
1
1
0
1
1
3
0
0
0
0
0
0
1
1
1
1
1
0
1
1
1
1
1
0
2
0
2
1
2
1
0
1
0
2
0
1
1
0
1
2
0
0
0
1
1
1
0
1
0
0
1
1
1
1
0
2
0
0
1
0
1
2
0
2
2
1
1
1
1
0
1
1
0
1
0
1
0
2
0
2
2
2
0
0
1
0
0
0
0
2
2
1
1
0
1
0
0
1
2
1
1
2
2
1
1
2
1
0
0
0
2
0
1
0
0
1
0
2
1
1
0
1
0
1
2
1
0
0
1
1
1
2
0
1
1
0
0
0
2
1
0
1
1
0
2
1
0
1
0
2
1
1
2
1
2
0
1
0
0
2
1
1
1
1
2
0
1
2
1
0
2
2
2
0
1
0
1
1
2
2
0
0
1
2
2
0
2
1
1
0
0
1
2
1
1
0
0
1
0
1
1
0
1
0
0
2
0
1
0
0
1
0
1
2
2
0
0
2
0
0
1
0
0
0
0
3
1
2
1
0
1
1
1
0
0
1
2
2
2
1
2
1
0
2
2
2
0
0
0
1
1
1
0
0
0
0
0
2
1
2
1
0
1
1
1
0
1
2
1
0
0
0
2
0
0
1
1
1
0
1
1
1
2
0
1
1
0
1
1
0
2
1
0
1
2
0
0
0
0
2
2
1
2
2
2
1
1
0
1
1
0
1
1
0
2
1
1
1
1
1
0
1
1
0
0
0
0
2
1
2
2
39
1
1
1
1
0
1
1
1
0
2
1
0
0
0
1
1
1
1
2
2
2
1
2
2
2
1
0
0
0
0
0
1
0
3
0
1
1
1
0
0
1
1
2
2
1
1
0
2
0
1
1
0
1
0
0
2
0
0
4
2
0
1
2
0
1
0
2
1
0
2
2
0
1
0
1
1
1
0
1
1
0
2
0
0
1
0
0
0
1
0
0
2
0
1
1
0
1
0
1
2
2
2
1
3
2
1
1
1
1
1
0
2
1
1
1
0
1
1
2
1
1
0
1
0
1
0
1
0
1
2
1
1
0
1
2
0
0
2
3
0
2
0
0
0
0
0
1
1
2
2
2
2
0
2
1
0
2
0
1
0
1
1
2
0
1
1
1
1
1
0
1
1
1
2
1
0
0
0
0
2
1
0
0
1
2
1
0
1
2
0
1
1
0
0
0
1
0
0
1
2
0
1
1
2
1
0
1
1
0
2
1
2
1
1
1
1
1
0
1
0
1
2
2
2
0
0
0
1
1
0
2
0
1
0
1
2
2
0
0
1
1
1
1
1
1
1
1
0
1
1
2
0
1
1
2
0
2
1
1
5
0
2
1
0
2
1
0
1
2
0
2
1
0
0
2
2
0
1
1
1
1
2
2
0
1
1
0
0
2
0
0
0
1
0
0
1
1
2
2
1
1
1
0
1
1
1
1
2
0
0
0
1
1
1
1
0
1
0
2
1
0
1
1
1
2
0
0
0
2
1
0
2
0
0
0
1
1
0
0
0
0
0
0
0
2
0
1
1
2
1
2
0
0
0
2
2
0
0
1
1
1
0
0
2
1
2
2
2
0
1
0
0
2
1
1
1
2
0
1
0
2
1
1
1
1
1
0
1
1
0
1
0
1
1
2
1
2
1
2
1
0
1
1
1
1
0
2
1
1
2
1
0
1
2
0
2
0
1
1
1
1
0
1
1
0
0
0
0
2
1
1
0
2
2
2
2
0
2
1
0
0
1
1
1
1
1
1
1
2
0
0
0
0
0
0
1
1
2
0
0
0
2
2
1
2
2
0
1
1
1
1
1
1
1
1
2
2
1
2
0
0
1
1
0
0
1
0
1
2
0
2
1
1
0
1
1
1
0
0
1
2
0
0
2
0
0
0
1
1
2
1
1
0
0
0
0
0
1
2
0
1
1
2
2
1
2
0
0
1
1
1
1
2
1
1
1
2
1
1
0
1
0
0
0
2
0
1
0
0
0
2
2
2
2
2
1
2
2
1
1
0
0
2
0
2
1
2
0
1
0
0
1
0
1
1
1
1
0
1
0
0
1
0
1
2
1
2
0
1
1
1
0
1
1
1
1
0
2
1
1
0
0
2
0
1
0
0
2
0
1
1
2
2
2
1
3
1
2
0
1
0
0
1
1
0
0
0
0
1
0
1
2
0
0
0
2
1
0
1
1
2
1
0
0
0
0
1
0
0
1
0
1
2
0
1
0
1
3
2
1
2
0
1
0
0
1
0
1
1
0
1
1
1
1
0
0
1
2
4
0
0
2
1
0
1
1
1
0
0
1
1
2
1
0
0
2
2
2
0
0
2
1
1
1
1
0
2
0
1
0
2
1
1
0
0
2
2
2
1
2
1
1
0
1
0
2
0
1
2
1
1
1
2
1
1
1
0
1
1
2
2
1
2
0
0
1
2
1
1
0
2
0
0
0
3
1
2
1
1
0
1
1
0
1
1
0
1
0
1
1
0
0
1
0
1
1
1
2
1
1
1
1
0
2
2
1
0
0
1
1
0
1
1
1
1
1
2
0
0
1
0
2
1
1
1
0
1
1
0
1
1
0
1
0
3
0
1
0
0
0
1
1
1
2
2
4
1
2
0
1
0
0
1
0
1
1
1
1
0
0
2
1
2
1
1
0
0
0
1
1
1
2
1
1
1
1
0
1
2
1
0
1
1
0
0
0
1
2
0
1
3
2
0
0
1
0
1
4
1
0
0
0
0
1
4
2
1
0
2
2
2
2
1
1
2
0
1
1
1
0
1
1
2
1
1
1
1
0
0
1
0
0
0
1
0
2
1
1
1
1
2
1
1
3
0
0
1
0
0
2
0
0
0
1
0
2
0
2
3
0
2
0
2
1
0
1
2
2
0
0
0
1
0
1
2
0
2
2
2
1
2
2
2
0
2
2
1
1
0
1
0
1
0
1
2
6
1
1
2
1
1
2
0
1
2
3
1
2
2
2
0
2
0
2
1
0
1
0
1
1
3
0
1
2
0
1
2
1
1
1
1
1
0
1
0
2
2
0
0
2
1
1
1
2
1
1
1
2
2
0
1
0
1
1
0
1
1
1
1
1
2
1
2
2
1
1
1
0
1
1
0
0
1
1
1
2
1
1
0
1
2
2
0
0
1
0
1
0
3
1
1
0
1
1
1
2
1
0
1
0
1
3
0
2
1
1
1
2
1
2
0
1
0
1
0
2
1
0
1
2
1
2
1
0
0
1
1
1
1
1
1
3
1
2
2
1
1
1
1
1
0
2
0
1
1
2
0
2
1
0
0
1
1
0
0
1
0
1
1
0
2
1
0
4
0
0
5
0
1
1
1
0
0
2
0
1
2
1
1
1
4
0
0
1
0
0
1
0
0
1
2
0
1
1
1
1
2
1
0
2
1
0
1
1
1
2
1
1
0
0
0
0
0
0
1
1
1
0
0
2
0
0
1
0
1
0
0
2
1
1
1
0
0
2
1
0
1
0
1
1
0
0
1
1
0
2
2
0
0
2
3
1
1
2
1
1
1
1
1
2
1
1
0
0
2
2
1
2
0
0
0
1
1
5
0
2
0
2
0
2
2
2
1
0
0
1
0
1
0
1
3
0
0
1
2
0
0
1
0
1
1
0
1
1
1
2
1
0
1
2
1
0
2
2
0
1
2
1
0
0
0
2
1
1
1
0
0
4
0
0
1
1
0
0
1
2
0
0
1
1
2
1
0
0
2
2
0
2
2
0
2
1
0
1
0
2
2
1
0
2
2
0
1
1
1
1
1
0
3
0
1
1
1
1
2
2
0
0
1
0
2
0
0
0
1
0
1
1
0
1
2
1
1
0
1
1
2
1
2
1
1
1
1
1
2
1
1
0
1
2
1
1
0
2
1
0
1
1
2
1
2
0
2
0
2
0
0
0
1
2
0
2
1
1
1
0
0
2
1
2
0
0
2
0
1
2
1
0
1
1
0
0
2
0
4
0
0
1
1
1
0
1
2
0
1
1
1
0
1
0
0
2
2
2
0
1
1
2
1
2
0
0
2
2
0
1
0
1
2
1
1
1
0
0
1
2
0
1
0
2
1
1
1
0
1
7
1
2
1
1
0
0
1
1
1
0
1
0
1
1
0
1
0
0
1
2
1
2
1
0
0
2
1
1
1
1
2
1
1
2
0
1
0
1
0
1
1
0
2
2
1
3
1
0
1
1
0
1
0
1
0
1
1
2
1
0
1
0
0
2
1
2
1
1
1
1
1
2
0
2
1
1
1
1
0
0
2
1
1
0
2
1
0
1
1
0
1
0
1
2
3
0
1
0
1
1
1
0
0
0
2
1
0
1
0
1
1
1
1
0
0
0
3
1
1
2
0
1
0
1
0
1
0
1
2
1
0
1
0
2
1
1
0
0
1
0
1
0
0
0
0
2
1
0
3
0
0
0
0
1
2
0
2
0
3
0
0
2
0
2
1
1
1
0
0
0
1
1
1
2
0
0
1
0
0
2
1
1
1
0
1
1
0
0
1
1
0
1
1
0
0
0
0
0
2
0
1
2
0
2
1
0
1
1
2
0
1
0
1
1
0
1
2
1
1
0
2
0
1
0
0
0
2
1
0
1
1
1
1
1
2
1
0
1
2
1
2
1
0
1
2
1
0
2
1
2
2
1
1
0
2
1
0
2
0
1
0
1
2
1
1
1
1
0
1
1
1
2
1
1
0
2
1
2
1
1
2
1
1
0
1
1
2
1
2
1
0
1
1
1
1
0
1
1
1
1
1
2
1
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
2
0
1
1
1
1
2
0
2
0
2
1
0
1
1
1
1
1
0
1
1
1
1
1
2
1
1
1
2
0
0
1
0
0
0
0
1
2
0
0
2
1
0
2
2
0
1
1
1
2
1
2
2
1
1
0
1
0
1
0
1
1
1
0
1
1
1
0
2
1
0
1
0
0
0
1
1
0
0
3
0
2
1
1
0
0
2
1
1
1
1
0
0
1
0
0
0
0
1
0
1
0
0
2
2
0
0
0
0
1
0
1
0
0
0
0
1
1
0
1
0
1
1
1
2
1
1
0
0
0
0
2
2
1
1
1
0
1
0
0
2
2
1
0
1
1
0
1
0
1
0
1
0
1
0
0
0
1
0
0
0
0
2
1
2
0
1
0
0
0
2
2
0
1
0
0
0
0
2
2
0
0
0
2
2
1
1
0
1
2
1
0
1
1
0
2
2
0
2
0
1
0
0
2
2
2
1
1
1
0
0
2
0
1
0
1
2
2
1
0
0
0
1
1
1
1
0
1
0
1
1
2
1
1
0
0
1
1
1
1
1
2
1
0
2
0
0
0
0
0
2
1
0
2
2
2
0
1
1
0
0
0
1
1
2
0
1
1
2
0
2
0
1
0
0
1
1
1
3
0
1
1
2
0
0
0
1
1
0
2
0
0
1
0
0
1
0
0
1
1
2
1
1
2
2
0
2
0
1
0
0
1
1
1
0
1
1
2
1
0
0
2
0
0
1
1
0
1
0
1
0
2
1
0
1
2
3
0
1
3
0
0
1
1
1
0
0
2
1
1
0
1
0
2
2
1
0
1
2
2
0
0
2
0
1
1
0
1
0
1
1
0
1
2
2
1
2
0
0
1
1
0
1
1
2
1
2
2
1
1
1
0
0
1
1
0
2
1
2
0
1
1
0
1
2
0
0
0
0
1
1
0
1
1
1
1
1
1
1
1
0
2
2
0
1
0
0
1
1
1
2
1
1
2
1
1
1
1
0
1
0
1
1
1
1
0
1
0
0
0
0
0
1
2
2
0
1
1
0
0
1
1
2
0
2
0
1
0
3
0
1
1
1
1
1
0
0
1
0
1
1
2
2
2
0
0
1
2
1
2
1
1
2
2
1
0
2
0
1
1
1
2
0
0
1
0
0
0
2
1
1
1
1
0
2
1
2
2
1
1
2
1
1
1
1
3
1
0
0
2
3
0
1
1
2
2
1
1
1
1
1
0
1
1
0
0
1
1
1
1
1
2
1
1
0
2
2
2
0
2
0
2
2
2
1
1
1
1
1
1
0
1
2
3
1
0
1
1
0
0
0
0
1
2
1
2
2
0
0
1
1
2
3
1
2
0
2
2
2
0
1
0
2
0
2
2
0
0
0
1
0
1
1
0
1
0
1
2
1
1
2
1
0
2
0
1
0
1
0
1
0
1
0
0
1
1
0
1
1
1
0
0
1
0
0
1
2
2
1
2
1
0
0
0
0
0
1
0
0
0
1
1
1
1
0
0
1
1
2
2
1
3
0
1
1
2
2
2
1
0
1
2
1
1
0
1
0
0
0
0
0
1
2
1
1
0
0
2
2
1
1
0
1
1
1
0
0
0
0
1
1
0
1
1
2
0
0
0
0
1
0
0
1
0
2
1
2
0
1
0
2
1
3
2
1
1
1
2
0
0
0
1
4
0
2
1
2
1
2
2
1
0
1
1
0
2
2
0
2
0
1
0
0
1
1
1
1
1
0
3
1
0
0
1
0
1
1
2
2
0
1
1
1
1
2
0
1
1
1
1
1
0
0
0
2
1
1
0
2
2
1
1
0
0
1
0
0
1
0
0
1
1
1
0
0
0
0
2
0
0
1
2
1
1
2
1
0
1
1
1
0
1
1
1
1
0
2
1
1
0
1
1
1
2
1
0
1
3
0
0
2
1
2
0
0
2
1
0
1
0
2
0
0
0
1
0
0
1
0
1
1
1
0
0
0
0
0
1
1
3
1
1
0
1
1
0
1
1
0
2
2
1
0
1
2
0
2
1
1
2
0
1
0
1
0
1
0
1
0
0
2
0
1
1
1
2
3
2
1
2
1
1
0
1
0
0
1
0
0
1
1
0
0
0
1
2
2
1
1
1
2
2
1
1
0
1
0
3
0
2
2
0
1
1
1
1
0
1
2
2
0
0
2
0
1
1
1
0
2
0
3
1
1
0
1
0
1
1
1
1
2
2
1
1
0
2
2
0
2
0
1
1
1
0
1
1
0
2
0
1
0
1
2
1
0
2
1
2
1
0
0
1
0
0
1
1
1
1
2
2
2
1
1
0
1
0
1
0
0
0
1
0
2
1
2
1
0
0
1
1
1
0
1
2
0
2
1
1
0
1
1
1
0
0
0
1
2
0
1
0
2
0
0
0
1
1
0
0
1
1
1
0
0
0
2
0
1
0
1
0
1
2
1
0
0
1
1
0
2
2
0
1
2
1
0
1
0
2
0
1
1
2
1
1
1
1
1
0
1
2
1
0
1
0
0
0
1
2
0
1
0
2
0
1
1
2
1
0
2
1
1
2
1
2
0
2
1
1
0
0
1
1
1
0
2
1
0
1
1
2
1
4
1
1
7
1
2
0
1
0
2
0
2
1
2
0
2
1
1
0
1
2
1
1
0
0
1
0
1
2
0
0
0
0
0
1
0
1
0
2
0
1
0
0
0
1
1
0
0
2
2
2
0
1
0
1
0
2
1
1
1
1
2
2
2
1
0
0
0
1
1
0
0
0
0
1
1
1
1
1
0
1
1
2
1
0
1
0
1
1
1
3
1
2
0
1
2
1
0
1
0
2
2
2
1
1
0
0
0
2
0
0
2
1
1
0
1
0
0
0
0
1
1
0
6
0
1
1
0
2
0
1
1
1
1
2
0
1
0
0
2
0
1
0
2
0
0
1
1
2
1
0
0
0
1
1
1
0
2
2
1
0
2
1
2
0
1
1
0
0
2
3
2
0
0
1
1
1
0
0
1
0
2
1
1
2
8
0
1
0
1
0
3
0
0
1
1
1
1
1
1
0
1
1
0
0
1
1
1
2
2
1
0
2
1
0
2
0
1
1
1
2
0
0
0
1
1
1
1
2
0
0
1
0
1
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
2
0
1
1
1
1
1
1
0
0
0
0
1
1
0
2
1
0
1
1
0
2
1
1
2
1
1
0
0
1
1
2
0
0
1
1
0
0
1
0
0
0
1
1
0
2
0
1
1
0
1
1
1
0
0
0
1
0
1
0
0
1
2
0
2
1
2
4
1
1
0
0
1
1
1
0
1
2
1
0
0
2
1
1
0
2
0
1
1
0
0
0
1
0
1
1
0
1
0
2
0
2
1
1
1
3
2
3
1
2
1
3
0
0
1
0
1
1
0
1
1
2
1
0
0
0
1
2
2
1
2
1
0
0
2
2
0
2
1
1
1
1
2
0
1
0
1
2
1
0
0
0
1
0
1
0
1
2
1
0
1
1
1
2
1
1
0
1
0
2
1
0
0
2
1
0
0
2
1
1
1
2
1
1
0
0
0
0
1
2
2
1
0
2
0
1
1
3
0
1
0
1
1
2
0
1
0
2
1
2
0
2
0
2
0
0
1
0
1
0
1
1
0
1
0
2
0
1
0
0
1
0
1
0
0
0
0
1
2
0
1
0
1
0
0
0
0
1
0
0
2
0
1
2
2
1
1
2
1
1
1
1
2
2
0
0
1
0
0
2
0
2
1
1
1
0
3
0
1
0
1
1
1
0
1
2
1
0
0
1
0
2
2
1
0
0
1
2
1
1
0
2
0
0
0
2
2
0
0
0
1
1
1
0
0
1
1
0
2
1
0
0
1
1
1
0
2
0
0
2
0
1
2
0
0
0
2
1
2
0
2
0
1
0
1
1
1
1
2
1
0
1
0
0
1
1
2
0
0
2
0
2
1
0
1
1
2
1
1
2
2
2
0
2
1
1
2
0
1
2
0
3
1
1
1
1
1
0
2
1
0
2
0
3
0
1
0
1
1
0
0
0
1
2
1
1
0
0
1
0
2
0
0
0
1
1
1
2
0
1
0
1
1
0
0
1
0
1
0
0
2
0
1
2
1
1
1
0
1
1
0
0
1
1
1
0
0
2
0
1
1
1
0
0
2
2
1
1
1
0
0
2
1
0
2
1
2
1
0
2
2
1
2
0
1
0
1
1
0
2
0
0
0
1
2
2
1
2
2
0
2
1
0
1
1
0
2
2
1
1
1
0
0
1
1
0
1
2
3
1
1
0
1
2
0
1
2
1
2
2
3
6
1
1
2
1
0
0
2
1
1
1
1
1
1
3
2
1
0
0
1
1
1
1
0
1
1
1
1
0
0
0
2
0
0
0
2
2
1
0
0
0
1
0
1
0
2
0
1
1
0
1
1
1
1
2
1
0
2
2
0
0
1
2
1
1
0
1
0
0
2
0
1
2
2
5
2
0
0
0
0
1
0
0
1
0
1
1
1
1
1
0
0
2
2
2
1
0
2
1
1
0
0
0
1
1
1
0
2
1
2
1
1
2
2
1
0
1
1
1
1
1
1
1
2
0
1
1
1
1
1
0
1
0
1
2
2
0
0
1
1
1
1
2
0
2
2
1
1
1
0
1
1
1
0
0
1
1
1
1
2
0
1
1
1
0
1
1
2
2
1
0
0
1
1
0
0
2
1
0
2
0
2
0
2
1
0
0
1
0
1
1
2
2
2
2
0
0
1
0
1
0
2
0
1
2
0
0
0
2
0
0
2
2
1
2
0
2
1
1
1
0
1
1
2
0
0
2
2
1
1
0
1
2
1
1
0
0
1
1
0
2
0
1
0
2
1
1
1
1
1
2
1
1
2
1
0
0
1
1
1
1
1
3
2
1
2
1
1
1
1
1
0
2
1
1
2
1
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
6
2
0
0
0
1
2
1
1
3
1
1
2
2
1
1
0
3
2
1
1
1
2
1
0
1
2
2
1
0
0
2
0
1
0
2
1
1
1
2
1
0
2
0
1
0
1
0
2
0
1
1
0
0
0
1
0
0
2
1
2
1
1
0
1
1
1
1
2
0
0
1
1
1
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
1
0
0
1
3
2
1
1
0
0
1
0
1
1
1
2
1
2
0
3
2
0
0
1
2
2
2
1
3
2
0
1
0
0
1
1
1
0
0
2
1
1
0
1
2
1
1
0
1
0
1
0
1
0
1
0
0
2
0
1
2
2
1
2
2
1
0
0
1
2
1
0
1
0
2
1
2
0
0
1
1
0
1
1
0
0
0
0
1
2
0
0
0
0
1
2
1
2
1
0
2
1
0
1
0
2
1
2
2
1
1
1
1
2
2
0
2
1
1
1
2
0
0
1
2
1
0
0
1
2
1
1
0
2
0
2
1
1
2
1
2
0
2
0
1
0
1
2
1
1
0
0
0
1
1
2
1
1
2
1
0
0
1
0
1
1
1
1
0
0
2
2
1
1
1
0
0
1
1
2
0
1
2
2
2
1
0
1
2
0
1
2
1
0
1
1
0
2
0
2
2
2
0
0
1
1
0
1
1
0
1
1
0
0
1
0
0
0
2
0
0
2
1
2
1
0
0
0
1
1
0
0
1
0
2
0
2
0
0
1
2
0
1
0
0
3
1
0
2
2
0
0
2
1
1
0
0
1
2
0
2
1
1
1
1
0
0
1
0
0
0
0
1
1
2
2
1
1
1
1
1
0
0
1
2
0
1
0
2
2
0
0
2
1
2
1
1
0
1
0
2
1
1
1
2
1
1
1
1
1
1
1
0
2
1
1
2
0
2
1
1
3
1
0
1
1
1
0
0
1
1
0
2
1
1
1
0
0
2
2
0
0
1
0
0
0
2
0
1
1
3
2
0
1
2
0
2
0
0
1
0
0
1
1
2
1
1
0
1
1
2
0
0
0
1
1
0
0
2
1
1
0
3
2
0
2
2
0
2
1
1
1
1
0
1
1
2
1
1
2
2
0
1
1
0
1
1
0
1
1
2
1
0
0
2
0
1
1
1
2
2
1
2
0
0
0
0
1
0
0
1
0
1
0
1
2
1
2
0
1
0
1
0
1
0
1
2
2
1
2
1
3
0
1
1
2
1
0
2
1
0
1
4
0
0
0
1
1
1
1
1
0
0
1
0
0
2
1
0
1
0
2
2
3
2
1
1
0
0
2
0
0
2
0
2
1
1
1
0
1
0
2
0
1
0
1
0
1
1
0
1
0
2
1
1
2
0
0
1
2
2
1
2
2
1
0
0
0
1
2
1
1
0
0
1
0
0
0
0
1
0
1
1
1
1
1
1
0
2
2
1
2
2
0
1
1
0
0
1
0
1
2
1
0
2
2
2
0
2
2
0
0
2
0
3
0
0
1
2
0
0
1
1
0
1
1
2
0
1
1
2
1
0
0
0
2
0
2
2
1
1
1
2
1
2
1
2
1
1
1
0
1
1
1
1
1
0
0
1
0
0
0
0
2
1
1
0
1
1
1
4
1
2
1
0
1
1
2
0
2
1
0
2
0
1
0
0
0
0
0
1
1
1
1
2
0
1
0
0
1
0
0
1
1
2
2
0
1
0
1
0
0
0
1
0
0
1
2
2
1
0
0
1
1
1
0
0
2
0
1
2
2
0
1
0
0
1
2
0
1
2
1
2
1
0
1
0
0
0
1
1
0
1
0
0
0
1
2
2
0
0
0
2
0
2
3
2
2
1
0
1
1
1
1
0
1
1
0
1
1
1
1
0
1
2
1
0
1
1
1
1
0
2
0
2
1
2
2
0
1
5
1
1
0
0
2
2
0
0
0
0
1
1
0
0
0
2
1
1
1
0
2
2
0
0
1
0
1
0
3
2
1
1
1
1
0
1
0
1
1
0
1
2
0
1
1
0
1
2
1
0
2
0
0
1
1
1
1
1
1
1
1
3
0
2
1
0
1
0
1
1
1
0
1
2
1
1
3
1
1
0
1
1
1
1
0
1
0
3
2
0
2
2
0
0
2
0
1
0
1
1
0
2
1
1
0
2
1
2
2
0
1
0
1
0
1
0
0
0
0
0
1
1
2
0
0
2
1
1
1
2
1
2
2
0
0
2
1
1
1
0
0
0
0
0
1
1
1
1
2
1
0
0
1
0
1
1
1
0
1
1
2
2
1
0
1
0
1
1
1
1
0
1
0
3
1
1
1
1
0
1
2
2
1
0
0
1
2
0
0
0
3
0
0
1
2
1
0
0
0
1
1
1
0
2
1
1
0
2
0
2
1
0
1
0
0
0
0
1
2
1
0
1
1
1
0
1
0
1
0
1
0
0
1
1
1
1
0
0
1
2
1
2
0
1
1
1
1
0
0
1
0
1
1
1
1
0
1
0
0
2
0
0
1
1
0
2
0
0
0
0
0
1
0
3
1
2
1
1
2
0
0
0
0
0
1
0
1
1
1
0
2
0
0
0
2
0
0
0
0
0
2
2
2
0
1
0
0
0
1
1
1
1
1
0
2
2
2
0
0
1
2
0
1
0
1
0
1
1
1
1
1
1
1
0
1
1
0
0
1
0
0
1
1
2
1
1
1
0
1
1
1
0
0
0
1
0
0
2
1
0
0
0
0
1
1
1
1
2
0
0
0
1
1
1
2
0
1
1
3
0
1
0
0
1
1
1
0
0
0
0
2
0
1
0
1
1
2
2
1
1
1
1
0
0
1
1
2
1
2
0
1
1
1
0
1
0
2
1
2
0
2
1
2
1
1
1
2
0
2
0
1
1
0
2
2
1
1
2
1
0
1
3
1
1
1
2
0
0
2
2
2
3
1
1
0
2
1
1
2
1
2
0
3
0
0
1
2
0
2
1
0
0
1
0
1
1
0
1
2
1
1
0
5
1
2
2
0
0
1
2
1
0
2
1
2
0
1
1
0
1
0
1
2
1
0
1
1
0
0
0
0
0
1
0
0
0
1
1
0
1
0
2
1
1
0
3
1
1
0
1
0
0
0
1
1
0
1
1
1
2
0
2
1
0
1
2
1
1
1
1
2
1
1
1
2
2
2
1
2
2
1
2
0
0
1
0
1
0
3
1
1
2
1
1
3
1
1
0
1
1
1
0
0
2
1
0
1
1
2
2
1
0
0
2
1
1
0
1
2
1
0
0
2
1
0
2
0
0
1
1
0
1
0
2
1
2
2
1
1
2
0
1
0
1
0
0
1
1
1
0
0
1
1
2
1
1
0
1
2
1
1
2
0
1
1
1
1
0
1
2
2
1
1
0
1
1
2
0
0
1
0
2
1
0
1
2
2
0
1
1
1
2
1
2
1
1
0
1
1
1
0
0
2
1
2
2
0
0
0
1
0
1
1
0
1
1
1
1
1
1
1
0
1
1
1
1
0
1
1
1
0
1
0
1
2
0
0
0
0
0
1
2
1
1
3
1
0
2
1
2
2
0
0
0
0
1
1
1
0
1
1
1
2
2
1
0
1
1
3
1
1
0
2
1
1
0
0
2
1
1
2
0
2
1
1
1
2
2
2
1
0
2
2
0
2
0
0
0
1
1
0
3
1
2
0
0
1
0
1
1
0
2
0
0
1
1
0
0
1
0
1
2
1
2
2
0
1
0
1
1
2
1
2
1
1
0
1
1
0
1
1
1
1
2
2
0
1
0
2
1
3
1
2
1
1
1
0
0
1
1
0
1
1
2
0
2
0
1
0
1
1
2
1
1
2
0
1
2
1
2
0
2
1
1
1
2
1
0
2
0
2
0
1
1
0
1
0
2
1
2
2
1
0
1
0
2
0
1
1
1
1
1
0
1
2
0
1
1
1
1
2
1
1
1
1
0
1
0
1
0
2
2
2
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
2
2
0
0
1
2
1
1
2
1
1
2
0
1
2
1
0
0
0
2
2
0
1
0
0
2
2
0
2
0
2
2
2
1
0
1
2
0
1
0
0
0
0
1
0
1
0
1
1
0
1
1
0
0
1
0
1
0
1
0
1
2
0
2
2
2
0
0
1
0
1
0
1
1
0
2
1
0
1
0
1
1
1
0
1
0
2
0
1
0
1
1
2
2
1
1
1
1
1
0
1
0
1
1
1
1
2
0
1
1
0
2
0
1
1
0
2
1
1
1
1
1
1
2
1
1
0
1
1
1
1
1
1
2
2
1
2
1
1
1
0
1
0
1
1
1
0
2
1
1
1
1
0
0
1
0
1
0
0
0
2
2
0
0
2
1
2
1
2
1
0
1
2
0
0
0
0
1
2
1
1
0
1
1
2
2
2
0
0
0
2
0
1
1
0
1
1
1
0
2
1
0
1
2
1
1
1
1
0
1
1
2
3
1
2
1
1
0
0
0
0
0
2
2
0
1
2
1
1
1
0
2
1
0
1
1
1
2
1
1
0
2
1
2
2
3
2
1
0
1
0
1
1
2
1
1
1
0
1
1
1
0
2
1
0
1
0
1
1
1
1
0
0
0
0
1
2
1
2
1
1
0
1
1
1
1
2
0
0
0
0
0
0
1
0
0
1
0
1
0
1
2
1
0
0
1
1
1
1
1
0
1
1
2
0
1
3
2
1
1
0
1
1
1
0
0
0
0
1
1
2
1
0
2
1
2
1
0
2
0
0
1
0
3
1
0
1
2
0
1
0
0
1
1
0
1
1
1
1
0
0
1
0
0
1
0
1
0
0
0
0
2
0
3
0
1
1
0
0
1
1
0
0
1
0
2
1
0
1
0
1
1
0
1
2
1
1
1
0
4
2
0
0
1
0
0
1
2
2
0
3
2
1
1
3
2
1
1
0
1
1
0
0
1
0
1
2
2
1
1
1
1
2
2
0
0
0
0
0
1
0
2
1
1
2
1
2
0
2
0
1
1
0
1
0
1
0
2
0
0
2
1
1
0
1
0
2
1
2
0
2
2
0
0
1
2
1
1
0
0
2
1
0
0
0
1
1
0
0
1
0
1
1
1
2
0
1
1
1
2
0
1
1
0
0
1
1
0
0
1
2
1
1
2
0
0
2
2
1
1
0
0
2
1
1
1
2
1
1
0
1
0
1
1
0
0
0
1
2
2
1
1
1
2
1
0
3
1
0
2
3
0
1
0
0
0
1
1
0
3
3
0
0
1
2
0
0
0
0
0
2
0
1
2
1
1
0
2
0
1
1
0
0
2
2
1
0
0
0
1
2
0
0
0
0
1
1
2
1
0
2
1
1
0
1
1
2
2
1
0
1
0
0
2
1
2
1
1
1
1
0
1
0
1
1
1
0
2
1
0
1
0
1
1
1
1
0
1
2
0
2
1
1
1
0
1
0
1
2
1
2
1
1
0
1
0
1
0
1
2
0
0
0
2
0
2
0
2
2
2
0
1
0
0
0
1
1
1
2
1
2
2
2
0
1
1
1
0
2
2
0
1
1
2
2
1
1
2
0
2
2
3
0
0
1
1
3
1
0
1
1
1
0
1
0
0
1
1
0
1
0
0
1
2
0
1
1
1
0
1
2
3
1
0
1
2
2
1
2
0
0
1
1
0
0
2
1
1
2
0
0
1
1
0
1
0
0
0
1
1
0
1
1
0
1
2
2
0
0
0
1
1
1
0
1
0
0
2
0
2
2
2
1
0
1
1
0
1
1
2
0
0
1
0
2
0
0
1
0
1
1
1
1
1
0
1
1
1
2
2
0
2
0
1
1
1
2
1
2
2
1
2
2
0
0
1
0
0
3
0
1
0
1
1
0
1
1
2
1
2
2
1
1
1
1
1
1
0
1
1
2
1
1
0
0
0
2
2
1
1
0
0
2
1
1
0
1
2
0
1
0
0
2
0
1
1
0
0
0
0
0
0
0
2
0
0
1
1
2
1
0
2
0
2
0
1
0
0
0
2
1
1
0
2
0
1
2
0
1
2
1
0
2
1
2
0
1
1
2
2
0
1
1
0
1
3
0
1
2
0
2
0
2
2
2
2
1
1
1
0
2
1
2
1
2
1
2
2
0
0
1
0
1
2
1
1
1
0
1
0
1
1
1
0
0
0
0
1
1
1
1
2
0
2
1
1
1
1
0
3
1
1
0
1
1
0
1
1
0
1
1
0
0
1
2
3
1
0
1
1
0
1
1
0
1
1
2
0
0
0
1
1
1
0
2
1
1
0
2
0
1
1
1
0
2
2
1
1
1
0
0
1
0
3
2
0
0
1
0
0
2
1
0
0
1
0
2
0
0
0
2
1
0
2
3
0
0
0
2
1
1
2
1
1
0
1
0
1
1
1
1
2
2
0
1
0
0
0
1
0
1
0
1
1
1
1
1
2
2
1
2
0
2
0
0
1
2
2
1
1
1
1
0
2
1
1
0
2
1
0
0
2
1
0
1
1
1
1
1
1
1
0
0
1
0
2
0
0
1
1
1
1
0
1
2
1
1
1
0
1
1
1
0
0
1
1
0
0
1
1
1
0
1
0
1
2
1
1
0
0
0
1
1
1
0
2
0
1
0
0
1
1
0
1
1
0
2
0
2
0
1
0
2
0
1
0
2
0
0
2
1
1
1
1
1
1
0
0
0
0
1
1
1
0
0
0
0
2
1
1
1
1
0
0
0
2
2
1
1
3
0
2
2
1
1
2
1
1
0
2
1
1
1
0
2
2
1
1
0
0
1
1
2
0
1
0
0
0
0
1
1
1
1
1
0
0
1
1
2
0
1
2
0
0
1
0
0
0
1
1
0
1
0
0
0
2
0
1
1
1
1
0
0
1
1
1
0
1
2
2
0
0
1
2
1
1
2
1
2
0
1
0
2
0
1
1
0
0
0
0
0
0
1
3
0
2
1
0
0
0
0
2
2
0
1
1
1
1
0
0
0
1
2
2
1
1
0
1
2
0
2
1
1
0
0
2
0
0
2
0
0
1
1
1
1
1
1
0
1
1
0
0
1
2
0
0
2
1
2
1
1
2
0
1
1
1
2
1
0
2
0
2
2
1
1
1
0
0
0
0
0
1
1
0
0
1
1
2
2
0
0
0
1
2
2
2
1
2
3
1
1
1
2
2
1
1
0
1
1
1
1
2
2
2
2
0
2
0
1
1
1
0
1
2
1
1
1
1
0
0
0
2
1
0
3
0
1
0
0
0
0
2
1
1
0
1
2
1
1
0
0
1
1
2
2
1
2
0
0
1
0
1
2
0
0
0
1
1
0
1
1
1
3
3
2
0
1
1
2
1
1
1
0
1
2
1
0
0
0
2
1
2
1
2
2
1
1
0
0
2
2
1
1
1
0
2
1
0
1
2
1
2
0
0
2
1
2
2
3
1
0
0
0
2
1
0
0
2
1
0
1
2
1
0
0
1
2
1
2
2
1
1
1
0
0
1
2
1
1
0
2
0
0
0
0
0
1
1
1
2
0
1
1
0
1
1
0
1
1
2
1
1
2
1
1
0
0
1
1
0
2
0
0
0
0
1
1
1
0
0
0
1
0
0
0
1
0
2
0
0
1
1
1
0
0
1
1
0
0
0
1
0
1
2
0
0
1
0
1
1
0
0
0
0
1
2
1
1
1
2
0
0
1
1
2
1
0
2
1
1
2
0
0
0
1
1
0
0
1
0
1
0
2
1
0
0
1
2
1
1
0
1
2
0
1
0
1
1
0
0
2
2
1
2
2
1
1
0
1
0
1
1
2
1
0
2
1
1
2
0
1
1
1
0
0
0
1
1
1
1
0
1
0
2
1
0
0
0
1
0
0
1
0
1
1
2
1
1
1
1
1
0
1
0
1
2
0
1
1
1
1
1
2
1
1
1
2
0
1
2
1
1
2
0
1
1
0
1
1
0
0
2
0
0
0
0
0
1
0
0
0
2
1
0
1
2
0
0
1
1
1
1
0
0
1
1
1
1
0
0
1
1
2
1
0
1
0
0
0
1
1
1
1
1
1
1
2
1
2
1
1
1
1
1
0
1
0
2
2
1
0
0
1
0
1
0
0
0
0
1
2
0
1
1
2
0
1
1
1
0
1
2
0
0
1
0
1
2
0
1
0
1
0
1
0
1
0
1
1
1
3
1
0
2
1
0
1
0
0
1
0
1
2
1
2
1
0
2
2
0
2
2
0
0
0
1
0
0
2
3
1
1
1
2
1
3
0
2
1
0
2
0
4
1
0
0
0
1
0
0
1
2
0
0
1
2
1
0
1
0
1
1
1
2
0
1
0
0
0
0
1
1
1
1
2
0
0
0
0
1
1
0
1
2
2
0
1
1
0
1
0
1
1
0
2
2
0
0
2
1
0
2
2
1
2
2
1
0
1
0
1
1
0
1
2
1
0
2
1
1
1
2
1
1
0
1
2
0
1
1
2
1
0
1
1
1
0
0
0
0
2
1
1
2
0
1
0
0
0
2
1
2
1
1
1
1
1
1
1
0
1
1
1
0
1
1
2
0
2
0
0
2
1
2
2
0
0
2
1
1
1
0
1
1
1
1
0
1
0
0
0
1
1
2
2
1
0
0
1
1
0
0
0
1
1
0
1
1
0
1
1
0
2
2
0
1
0
1
1
2
0
1
0
0
1
0
1
1
2
1
2
1
1
1
1
2
1
1
0
0
0
1
0
0
1
1
0
1
1
1
0
2
1
1
6
1
0
1
1
1
0
2
2
2
0
1
1
0
0
2
0
2
0
0
1
0
1
1
1
1
0
1
1
0
0
1
1
1
1
3
0
0
1
2
0
2
0
1
2
2
0
0
1
2
1
1
0
1
2
3
0
0
1
1
1
1
1
1
1
1
1
1
0
0
0
1
1
0
0
1
1
0
0
0
1
1
0
1
1
1
0
4
1
1
0
1
1
2
1
2
1
1
1
1
1
1
1
1
2
2
0
1
0
1
1
0
3
1
0
1
1
1
2
1
1
1
0
0
0
0
0
0
1
0
1
0
2
1
2
2
0
3
0
1
2
0
1
0
1
0
0
0
1
2
2
0
1
0
1
0
1
1
1
0
2
0
1
1
1
2
1
1
1
1
1
1
1
1
1
0
1
1
2
2
0
0
2
0
1
0
0
1
0
1
1
1
0
2
1
1
2
1
2
2
1
2
1
2
1
1
1
0
0
1
0
4
3
1
1
1
3
0
1
0
1
1
1
0
2
0
1
0
2
1
0
1
2
0
1
1
0
1
2
0
0
0
0
1
1
0
0
2
0
0
1
0
0
1
0
0
1
1
1
1
0
1
0
2
2
1
1
1
0
1
3
0
0
1
2
1
1
1
1
0
0
0
2
2
2
1
1
0
2
1
0
1
0
2
1
2
1
0
2
1
1
0
0
0
2
0
1
1
0
0
1
0
0
0
1
1
1
1
0
0
0
0
1
0
0
0
2
0
1
1
1
1
1
2
2
2
1
2
2
2
1
2
1
0
0
0
0
1
1
2
3
0
2
1
0
1
0
0
0
0
0
0
0
1
0
3
0
0
1
0
2
1
1
1
1
2
1
2
0
3
1
1
0
2
0
1
1
2
0
2
1
1
1
1
0
0
0
0
0
0
1
1
2
0
1
1
2
2
1
1
2
2
1
0
1
0
0
1
1
0
1
0
0
2
0
1
0
1
1
0
2
1
0
0
0
4
0
1
1
1
4
1
1
1
1
0
0
1
2
1
0
2
1
1
2
2
0
1
1
2
0
0
3
1
0
0
0
2
0
1
0
0
1
1
0
3
1
1
1
1
1
0
1
2
1
2
2
2
1
0
0
0
1
1
1
1
2
1
2
1
0
1
0
1
2
0
0
1
0
0
1
0
1
0
2
0
1
2
1
1
2
1
0
1
0
0
1
0
2
2
0
1
1
0
2
0
1
1
1
1
0
0
1
1
1
0
1
2
1
2
1
0
2
0
1
0
0
0
0
2
1
1
0
0
1
1
2
0
1
0
0
0
0
1
2
0
2
1
1
0
1
1
0
2
0
1
1
0
1
0
2
2
1
1
1
2
1
1
1
0
2
0
0
1
2
0
1
2
0
1
2
1
2
2
2
0
0
0
1
1
1
1
1
0
0
0
0
2
2
1
1
1
1
1
2
0
1
1
0
1
1
0
0
2
0
1
0
0
0
0
2
1
1
0
2
1
0
1
0
2
1
1
2
3
4
0
0
0
1
0
0
0
2
1
1
2
1
2
2
1
0
0
1
0
1
1
1
0
0
0
1
1
2
1
4
2
2
1
1
0
1
1
0
2
2
1
1
0
0
0
0
2
0
2
2
1
0
2
1
2
1
0
1
0
0
0
1
0
2
1
2
0
1
0
2
1
1
0
1
1
2
1
2
0
2
1
2
0
2
1
2
2
0
1
0
4
0
0
1
1
1
2
1
1
1
1
0
1
1
0
0
1
0
2
1
1
0
1
1
1
1
0
1
2
1
0
1
1
1
1
1
10
3
1
1
0
0
2
0
1
0
2
1
0
1
1
1
1
0
0
0
0
1
0
1
0
1
0
1
1
0
0
0
1
1
0
0
0
0
2
0
1
0
2
1
1
0
1
1
0
2
1
1
0
1
0
1
0
1
0
1
1
0
1
2
0
2
0
0
0
2
0
0
1
1
1
2
0
0
2
0
1
0
0
0
2
3
1
2
0
1
1
1
0
1
0
1
0
1
0
0
1
1
1
1
0
0
1
0
1
1
2
1
0
0
1
1
0
0
1
0
1
1
0
1
1
1
1
0
2
0
0
0
1
2
0
2
1
1
2
1
2
1
0
1
1
2
0
1
2
0
1
0
0
1
1
0
1
1
1
0
0
0
1
1
2
0
1
0
0
1
1
2
0
1
1
2
0
2
2
0
0
2
1
2
0
2
2
1
1
1
1
0
0
1
1
1
2
0
1
1
0
1
0
0
2
2
1
1
2
1
2
0
0
1
0
2
1
0
0
2
2
2
0
1
1
1
1
2
1
1
0
2
1
1
0
0
0
0
0
1
0
0
1
0
1
0
2
0
1
2
0
0
1
0
1
0
0
0
0
0
1
1
1
0
1
2
0
1
0
1
2
1
1
1
1
0
2
1
1
0
1
2
0
1
1
1
1
1
1
2
0
0
1
1
0
0
1
1
0
1
1
2
2
2
1
1
2
1
1
0
2
3
0
1
0
1
3
1
2
2
0
2
2
0
0
0
0
0
0
2
0
1
2
1
0
0
0
1
1
2
2
1
1
1
2
0
1
1
1
0
0
0
1
1
1
0
1
1
2
2
2
1
0
0
0
0
1
0
2
2
2
1
0
0
2
1
1
1
0
0
2
3
1
3
0
0
2
2
2
1
1
1
1
1
0
1
2
2
2
0
3
1
0
1
1
2
0
2
1
1
0
1
1
1
1
1
1
1
0
2
0
2
2
1
0
1
1
1
0
1
0
2
0
1
1
1
1
1
0
0
1
0
0
0
1
2
1
0
1
2
1
1
1
2
2
1
1
0
1
1
1
0
1
1
0
0
1
1
1
2
1
2
1
0
0
2
1
1
1
1
0
2
0
0
0
2
1
2
0
2
0
2
0
1
1
0
0
1
1
1
0
1
1
1
1
1
2
0
0
0
0
2
2
2
0
1
1
0
1
2
0
0
0
1
0
2
1
0
1
0
1
1
1
1
0
1
0
0
1
1
0
0
0
0
0
2
2
0
0
1
1
1
1
0
1
1
0
1
2
2
2
0
1
1
0
0
1
0
2
2
2
1
2
0
0
2
1
0
2
0
0
2
0
0
1
0
1
0
0
0
1
0
1
1
2
0
0
0
1
0
2
0
2
2
2
1
2
1
1
1
1
1
0
0
1
1
0
2
1
1
1
1
1
1
1
0
1
0
2
1
0
0
1
2
2
2
0
1
2
0
1
0
1
2
0
1
0
0
0
0
1
0
2
0
0
1
2
1
2
0
1
0
0
1
2
2
1
0
0
2
1
1
2
1
1
0
2
1
1
1
1
0
1
1
1
0
1
0
1
2
0
1
0
1
1
2
0
0
0
1
0
1
2
1
0
2
2
2
0
0
0
2
0
0
1
2
2
2
0
0
3
2
2
0
1
1
0
1
1
0
0
0
0
2
1
2
0
0
2
3
3
0
1
3
1
1
0
1
0
1
0
0
0
1
2
0
2
0
0
1
1
1
0
0
1
1
2
0
2
2
2
0
0
1
1
1
2
1
0
2
0
0
1
0
1
2
0
1
0
1
0
2
0
0
1
0
0
1
0
1
2
0
2
2
2
2
0
1
1
2
1
1
1
2
1
1
2
1
0
0
0
0
0
1
1
0
1
0
2
1
0
2
1
4
0
0
2
0
1
1
1
2
1
2
2
0
1
1
1
4
2
1
1
0
0
2
0
0
1
1
3
1
1
2
0
0
0
1
2
1
2
0
1
0
1
1
1
2
3
0
1
0
2
1
1
1
2
0
1
1
0
1
1
0
1
1
1
1
0
2
2
1
0
0
0
1
0
0
1
1
2
1
0
1
1
1
1
0
1
2
2
1
1
0
2
1
1
1
2
1
0
1
0
1
1
2
1
2
1
0
0
0
0
1
0
2
2
1
1
0
1
0
0
1
1
2
0
0
1
1
0
0
1
2
0
1
1
0
0
1
1
0
0
1
0
1
0
0
0
2
0
1
1
0
1
0
2
1
1
1
0
0
2
0
1
0
1
0
1
1
0
1
1
1
1
0
1
0
0
1
1
0
0
1
1
0
1
1
0
0
2
1
1
1
1
2
1
0
0
1
0
2
1
2
2
1
0
0
0
0
0
0
2
2
2
0
2
2
1
0
0
2
1
1
1
1
1
0
0
1
2
1
0
1
0
2
2
1
1
0
3
2
1
0
2
1
1
1
1
1
0
2
1
2
1
0
0
0
1
0
2
0
2
1
2
1
1
2
0
1
2
0
1
2
1
0
1
1
1
0
0
1
2
0
1
0
1
1
0
2
0
1
1
0
1
2
2
0
1
0
0
0
2
1
1
0
2
2
1
1
0
1
2
1
1
1
1
1
0
1
1
1
1
2
0
0
0
2
0
3
2
1
1
0
0
0
0
1
0
1
1
0
2
0
0
0
1
0
0
0
1
1
2
2
1
2
2
0
1
0
0
1
1
0
2
1
0
0
0
1
1
2
0
1
1
0
0
0
1
0
0
0
1
0
1
1
2
1
2
0
1
0
2
2
0
1
2
1
1
2
0
0
0
2
11
1
0
1
1
1
1
0
1
1
0
2
2
1
1
0
2
1
0
0
2
0
1
0
1
1
0
1
0
1
1
0
1
0
2
0
2
1
1
2
1
0
2
0
1
6
0
2
0
0
1
2
2
3
0
1
2
3
1
0
0
1
1
0
1
1
2
1
1
0
1
0
0
2
1
0
1
0
0
2
1
1
0
0
1
1
0
0
0
1
1
1
2
2
0
0
0
1
1
1
0
0
2
1
1
1
1
1
1
1
2
2
1
1
2
0
0
0
0
1
0
1
2
1
0
1
1
0
2
1
1
0
0
3
0
0
2
1
1
0
2
1
0
1
1
1
2
1
2
2
1
0
1
0
2
1
0
1
0
2
1
1
0
1
1
0
2
2
0
0
0
1
0
1
1
0
0
0
0
1
1
2
1
1
0
0
1
1
1
1
1
1
1
0
0
4
1
0
1
0
0
1
0
0
1
1
1
1
0
2
0
0
1
8
1
1
1
1
1
1
0
1
1
1
0
1
0
1
1
0
1
1
1
1
0
1
1
0
1
1
1
0
2
2
0
0
1
1
0
2
0
0
1
2
1
0
1
1
0
1
0
2
1
2
0
0
0
1
1
1
1
1
2
0
2
0
1
1
1
1
1
1
2
1
1
0
0
1
1
1
0
1
1
0
1
0
0
1
0
1
1
2
1
1
0
0
2
0
0
1
0
1
1
1
1
2
2
1
0
1
0
2
2
1
0
2
2
2
1
0
2
1
1
0
1
0
0
2
1
1
2
2
2
1
0
0
2
0
0
1
2
0
0
0
1
0
1
1
1
1
3
1
0
1
1
0
2
0
0
1
1
1
3
2
1
1
1
1
2
1
2
0
0
0
0
0
1
1
0
1
0
0
0
0
1
1
1
1
1
0
0
1
0
0
1
0
1
1
0
0
1
1
1
2
1
1
1
1
2
1
2
0
0
0
1
2
2
1
1
1
0
0
1
1
1
1
0
1
0
0
2
0
0
1
1
0
0
0
0
5
0
1
2
0
1
1
1
0
1
2
1
1
1
0
1
2
2
2
0
2
1
1
1
0
1
0
2
1
2
0
0
1
2
2
0
3
0
1
0
2
1
2
0
0
0
2
1
0
1
2
0
0
1
0
0
0
3
0
0
0
1
1
0
2
1
1
2
2
0
1
0
1
1
1
0
1
0
2
1
1
1
1
1
1
1
2
0
1
1
1
0
1
0
1
1
0
1
2
1
2
0
1
0
1
2
0
2
0
0
1
1
0
1
0
0
2
0
0
0
0
2
1
2
1
0
1
0
1
1
0
1
0
1
2
1
1
0
1
1
2
2
1
0
2
2
1
0
1
1
0
1
1
1
6
0
2
1
1
0
1
2
0
1
1
1
1
1
1
1
0
1
1
0
0
1
0
1
2
1
1
0
0
0
1
0
1
1
8
1
1
2
0
2
1
0
1
1
0
1
1
1
2
1
0
1
1
0
1
1
1
2
1
1
1
0
1
1
0
1
1
1
0
0
1
2
1
0
0
1
0
0
2
2
1
2
3
1
0
2
0
0
2
1
0
1
1
2
0
3
0
1
0
2
0
2
0
2
0
1
2
1
1
0
0
1
0
0
2
2
1
2
1
3
2
1
1
1
0
2
1
0
0
2
0
2
2
1
1
1
1
1
1
1
0
2
0
1
2
1
1
2
0
0
1
2
0
2
1
1
1
0
0
0
1
0
0
0
2
1
2
1
0
0
1
1
0
1
0
0
2
2
1
0
1
1
1
2
2
0
2
1
0
2
1
0
1
2
0
1
1
1
1
2
2
1
2
0
1
3
1
1
1
1
1
1
0
0
0
1
1
1
1
1
2
0
1
0
1
0
0
1
1
2
1
0
2
2
0
1
1
1
1
1
2
0
1
0
2
5
0
1
1
1
1
1
0
0
0
2
1
1
2
0
0
1
1
1
2
0
1
1
1
1
2
1
0
1
1
0
1
0
2
0
0
2
2
0
1
1
0
2
0
1
2
1
1
2
1
2
0
0
0
3
1
1
1
1
1
1
0
1
0
0
1
1
0
0
2
0
0
1
1
0
0
1
0
0
1
1
1
1
1
1
0
2
2
1
1
2
1
1
0
2
0
1
0
2
0
1
0
1
0
2
1
0
1
2
2
5
2
1
2
0
1
0
0
1
1
2
0
0
1
0
2
2
0
1
1
2
1
2
0
1
1
1
1
2
1
1
0
0
0
2
2
1
2
1
1
1
0
1
2
1
0
0
0
2
1
2
0
2
1
2
1
0
2
1
1
0
1
2
1
0
0
1
2
0
1
1
0
1
0
1
0
1
1
1
0
0
0
2
4
2
0
1
2
0
1
0
0
1
1
1
1
1
2
0
3
3
1
0
1
1
1
2
0
2
0
1
0
2
0
0
1
1
1
1
1
1
1
1
2
1
1
1
0
0
1
0
0
0
1
0
2
2
0
1
1
0
1
1
0
1
1
0
0
1
0
1
0
1
3
1
1
0
2
0
0
2
2
0
0
2
0
1
2
2
1
2
1
0
1
1
0
0
1
2
0
1
1
0
1
1
2
1
1
1
0
0
0
0
0
2
2
2
1
1
1
1
2
2
1
1
0
0
1
2
0
3
1
1
0
1
2
2
0
1
2
1
1
2
1
3
2
0
0
2
1
1
2
2
1
2
2
0
1
1
1
1
2
1
1
2
0
2
1
0
1
0
2
1
0
1
1
1
1
2
0
1
1
0
1
1
2
0
1
0
0
1
0
1
2
1
1
0
1
1
1
1
1
2
0
1
2
0
0
1
0
0
0
2
1
1
1
1
1
0
3
0
1
1
0
0
1
0
1
2
1
1
1
0
0
0
1
0
2
3
1
1
1
2
1
1
1
0
1
0
0
1
2
0
2
2
1
2
0
1
2
2
2
0
0
2
4
2
0
1
1
1
1
1
0
0
1
0
1
2
0
0
2
0
0
0
1
1
2
1
1
1
2
1
0
1
4
1
1
2
2
0
1
1
1
0
1
2
1
0
1
3
1
1
1
1
3
0
1
1
2
2
0
0
2
1
0
0
1
2
1
0
2
2
0
1
0
0
1
0
0
0
1
2
2
0
1
0
0
2
1
0
1
0
1
1
0
0
0
1
1
0
1
1
1
2
1
1
0
0
1
1
1
0
0
1
1
0
1
1
2
0
2
0
2
0
0
0
0
0
1
0
1
0
2
1
0
1
0
0
0
1
0
0
0
1
0
1
0
0
1
1
2
0
0
2
2
2
3
1
0
0
0
1
0
2
5
1
2
3
0
1
0
1
0
2
1
1
2
2
1
1
0
2
0
0
1
1
5
1
0
0
0
0
1
2
1
1
0
1
0
1
1
1
1
1
0
1
1
2
0
2
2
1
1
1
1
1
0
2
1
1
1
0
0
1
0
1
1
1
1
0
0
2
1
0
0
1
1
2
0
2
2
0
1
1
0
1
2
0
1
2
0
1
0
0
0
0
0
2
0
0
1
0
0
3
1
1
1
1
1
0
2
1
1
4
0
0
1
0
1
0
0
0
1
0
0
2
0
1
1
1
1
0
0
2
2
2
0
2
0
0
2
2
0
0
0
2
2
1
2
0
0
1
1
0
0
1
1
2
2
1
2
1
2
1
0
2
3
1
1
1
1
2
0
1
1
2
0
0
0
0
0
1
1
0
1
1
0
1
1
1
1
0
0
0
2
0
1
2
3
0
1
1
0
1
0
1
1
2
2
2
0
2
2
0
1
2
0
0
1
1
0
1
2
0
2
2
1
1
1
0
0
1
1
1
1
1
1
1
0
1
1
0
1
0
1
0
0
1
0
0
0
1
1
0
1
0
1
2
0
2
2
1
1
1
0
1
0
0
0
1
1
1
1
2
1
2
2
0
1
0
2
0
2
1
2
2
1
1
0
0
1
1
1
2
0
1
0
1
2
2
0
2
0
0
0
1
2
1
1
1
2
1
1
1
1
0
0
1
1
1
0
1
1
1
0
2
2
0
0
0
1
2
0
1
2
1
0
2
0
1
0
2
1
2
0
0
1
0
1
0
1
1
2
1
0
0
0
2
2
0
0
2
0
0
2
1
1
1
3
0
2
0
1
1
1
2
1
0
1
0
3
3
0
2
1
1
1
0
1
1
0
0
0
0
0
0
1
2
0
1
1
0
2
2
2
0
1
0
0
0
1
2
2
1
1
1
0
1
0
1
2
2
1
2
1
0
0
3
0
0
2
2
1
1
2
2
1
2
0
2
1
1
0
0
0
2
2
1
0
1
1
1
1
0
6
2
0
2
1
5
1
1
2
0
1
1
1
0
1
1
0
0
2
0
0
1
1
1
1
1
1
1
1
1
2
0
0
1
0
1
1
1
1
1
0
1
0
0
1
1
1
0
0
1
0
0
1
0
1
2
0
1
0
1
1
0
1
0
0
1
0
2
1
2
1
2
2
0
0
0
2
2
0
2
0
1
1
0
1
1
1
2
1
0
1
0
1
0
2
0
2
3
1
0
2
1
0
1
0
1
1
0
1
0
1
1
1
3
1
0
2
1
1
2
0
0
1
2
0
2
0
1
2
2
1
0
1
0
0
0
1
2
0
2
1
3
2
0
0
1
0
1
1
0
0
0
1
2
1
0
2
1
1
2
1
1
0
1
0
2
1
1
0
2
0
0
1
1
2
2
0
0
1
0
0
1
0
0
0
1
0
1
0
1
2
4
1
0
0
0
1
0
1
0
0
1
1
0
0
1
1
1
1
2
1
2
0
1
1
1
1
0
2
1
1
1
0
1
0
1
2
2
0
0
0
1
1
0
0
2
1
2
2
0
0
1
0
1
2
2
1
0
2
2
1
0
2
1
2
1
0
1
2
0
0
0
1
1
1
1
0
1
1
0
1
1
0
1
2
1
2
0
0
1
1
1
0
0
2
3
1
1
0
0
1
2
1
0
0
1
1
2
0
0
2
0
1
1
2
1
0
2
2
0
2
0
1
1
0
1
2
0
0
3
2
2
0
1
1
1
0
0
1
1
2
1
3
2
0
0
2
1
1
0
2
1
0
1
1
0
1
1
1
2
2
1
1
1
1
2
1
1
0
2
1
1
1
0
2
1
2
1
0
2
1
3
1
2
0
1
2
0
1
0
0
1
2
2
1
0
1
0
1
1
1
1
1
1
2
2
2
2
1
0
2
1
1
2
0
0
1
0
1
2
1
2
1
0
2
0
2
1
1
0
1
1
0
1
1
0
2
2
1
0
1
1
1
3
1
2
0
1
2
2
0
0
1
1
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
1
0
2
1
1
1
0
0
1
2
0
0
0
0
1
1
0
0
2
0
1
1
2
0
1
2
2
1
0
1
0
0
1
1
0
1
0
1
0
0
2
2
1
2
1
0
1
2
1
0
1
2
0
0
0
2
1
0
0
0
2
1
0
1
2
1
1
2
1
0
0
1
1
0
0
2
0
1
1
1
0
1
0
2
0
2
0
1
0
0
1
1
0
1
1
2
2
1
0
0
2
0
1
0
0
1
1
0
0
1
2
0
2
1
1
0
0
1
0
1
2
1
2
0
0
2
2
1
2
0
0
2
1
1
1
1
1
2
1
0
0
1
1
0
1
1
0
1
2
1
2
2
0
0
1
1
0
1
0
1
1
1
1
0
1
0
2
1
1
0
0
0
1
0
0
0
1
1
2
0
2
2
1
0
0
0
1
0
1
2
1
0
0
0
1
0
0
1
0
1
0
1
0
2
0
1
1
1
1
1
0
0
3
1
2
1
1
0
1
1
1
1
2
0
0
2
0
0
0
1
1
2
0
0
1
0
2
0
0
1
1
0
1
1
1
0
2
2
1
1
1
0
1
1
0
2
1
1
2
0
1
2
2
1
0
0
0
1
2
0
1
0
1
1
1
0
0
1
1
0
0
0
1
0
2
3
2
1
0
0
2
0
0
1
2
1
1
1
0
1
0
3
0
2
0
0
0
0
2
1
1
2
0
0
0
1
1
1
0
2
1
0
1
1
0
2
0
1
0
2
1
1
1
0
0
2
0
1
1
2
0
0
0
1
0
0
1
1
0
0
1
1
1
0
1
1
1
1
2
2
0
0
0
1
1
1
0
2
1
1
1
1
0
1
0
0
0
0
0
0
1
0
2
3
0
0
1
0
0
1
1
2
1
1
1
2
1
0
0
1
1
1
1
1
1
0
1
0
2
2
1
1
1
1
1
1
2
1
0
0
1
1
3
1
1
0
0
0
1
1
0
1
1
2
1
1
2
1
2
0
2
0
1
2
1
1
1
1
0
1
1
3
2
1
0
2
0
0
1
2
2
1
2
0
1
1
1
1
0
1
1
2
2
1
0
1
1
1
0
1
0
2
0
0
0
1
0
0
1
1
1
1
2
2
0
1
1
2
1
1
0
2
2
2
0
2
1
1
1
2
0
1
1
0
1
1
1
4
0
0
1
0
1
1
0
1
1
1
2
0
1
1
1
1
0
2
0
2
1
1
1
2
0
0
1
0
1
3
0
0
2
1
1
0
0
0
0
0
2
1
0
1
2
0
1
1
1
1
0
2
1
1
0
1
1
0
0
1
1
0
0
0
0
1
2
0
2
2
0
2
0
0
0
0
2
0
1
0
2
2
1
1
1
2
0
1
1
0
0
1
1
1
1
1
0
2
0
1
0
1
0
2
2
2
0
0
0
0
1
2
1
2
0
1
2
2
0
2
0
2
1
2
2
1
0
0
1
0
2
1
2
0
0
1
0
0
1
1
0
1
1
0
1
1
1
2
1
1
0
4
0
2
1
1
2
1
1
2
0
0
2
2
2
0
1
1
0
0
0
1
1
1
0
2
0
1
1
1
1
0
0
2
0
0
1
7
3
2
1
2
0
0
2
2
1
0
1
2
1
1
2
5
2
2
2
0
1
0
1
1
2
1
2
1
1
1
1
0
2
2
2
1
2
1
0
2
2
1
2
0
0
0
1
0
1
0
2
0
1
1
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
2
0
1
1
0
1
2
2
2
0
1
0
1
1
2
3
1
2
0
1
2
1
1
1
1
1
2
0
0
1
2
0
0
1
0
1
0
1
1
1
0
1
1
1
0
1
2
2
1
0
0
1
1
1
0
1
0
0
1
0
1
1
0
1
0
0
1
0
3
0
0
2
2
1
0
0
2
0
1
2
1
1
0
2
1
1
0
1
2
1
0
1
2
0
0
0
0
0
0
0
1
1
0
2
0
0
1
2
1
0
1
0
2
1
1
1
2
1
1
2
3
2
1
0
0
1
1
1
2
0
2
0
0
1
2
0
1
1
1
0
2
1
2
0
2
0
2
1
0
0
1
0
2
2
0
1
1
1
0
0
1
1
2
0
2
0
0
2
1
2
0
1
1
1
2
1
2
0
0
2
2
0
2
1
0
1
1
0
0
2
0
0
1
1
0
1
0
0
0
2
0
1
1
1
2
0
0
2
0
0
1
2
0
2
3
0
1
1
2
1
0
1
1
2
1
1
1
0
0
2
0
0
1
0
1
1
0
2
1
1
1
1
2
2
1
0
0
0
1
1
0
1
1
0
0
1
0
0
1
1
1
1
1
1
2
1
4
0
1
2
1
2
1
1
1
0
1
0
1
2
1
3
2
1
2
2
1
2
1
2
1
0
1
0
2
1
0
1
1
1
2
2
0
2
0
2
1
0
0
2
2
0
1
0
0
1
1
0
0
0
0
1
1
0
1
1
1
1
1
2
1
0
1
1
2
0
2
2
2
0
2
2
0
0
1
3
0
0
2
1
0
1
0
0
2
2
0
1
2
0
2
1
0
1
3
0
1
1
0
0
1
0
1
2
2
2
2
0
0
0
0
0
2
0
0
0
2
1
0
0
2
3
1
1
3
0
2
2
1
1
1
3
1
1
2
2
1
2
1
0
0
0
0
0
1
1
2
0
2
0
0
2
1
0
1
1
0
3
0
0
0
0
1
1
2
2
2
2
2
0
0
2
1
1
1
2
2
1
2
3
0
2
1
1
1
1
0
2
1
1
0
0
1
0
2
0
0
0
1
1
1
1
2
2
2
2
2
1
0
0
0
1
1
0
0
1
0
1
0
0
2
1
1
0
0
0
1
2
4
1
1
1
0
0
1
1
1
1
2
1
1
0
0
0
0
0
1
0
0
2
0
1
1
2
1
1
2
1
1
1
0
2
1
0
0
0
0
1
1
2
0
2
0
0
1
1
1
0
1
3
0
0
2
1
1
0
0
0
1
2
2
0
1
1
2
2
1
1
0
0
1
1
1
1
0
0
2
0
0
0
1
0
0
1
2
0
0
1
1
0
1
1
0
2
1
1
2
0
0
1
0
0
2
0
2
0
2
0
1
1
1
2
2
1
2
1
1
1
1
2
2
2
0
1
0
4
1
0
2
2
1
0
2
2
0
1
0
3
0
1
0
1
1
1
1
1
1
1
2
2
0
1
1
2
1
1
2
1
1
1
0
0
1
0
0
2
2
1
0
1
1
0
0
2
1
2
0
0
2
0
3
1
1
1
0
0
1
1
1
0
1
1
0
2
1
1
0
1
2
1
1
0
0
0
2
1
1
0
0
2
1
1
1
0
1
2
1
0
1
1
1
0
0
1
1
2
1
0
0
0
0
1
0
1
1
0
1
6
2
2
0
1
1
2
2
0
0
0
1
2
1
0
1
2
1
1
0
2
0
0
0
1
1
1
1
1
2
0
2
1
1
0
0
1
0
0
1
1
0
2
1
1
0
0
0
0
2
0
2
0
1
2
1
0
1
1
0
1
0
1
0
0
1
2
1
1
1
1
2
1
0
1
1
0
0
0
1
0
2
0
0
1
2
0
0
2
0
1
1
0
1
0
1
2
1
1
1
2
2
1
1
0
2
1
1
0
1
2
1
0
1
1
1
2
0
1
2
0
1
0
1
1
0
1
0
0
0
1
1
1
1
2
1
1
1
1
0
1
0
1
3
0
1
0
1
2
0
0
1
1
0
1
2
2
1
1
1
1
0
1
2
2
2
1
1
1
2
2
1
0
1
2
1
1
0
1
0
1
1
0
2
1
0
0
2
3
2
0
1
1
0
1
0
2
1
1
1
1
0
1
1
2
1
1
1
1
1
0
2
2
1
1
0
2
1
0
0
0
0
2
0
0
0
1
1
0
1
1
1
1
1
0
1
0
0
1
0
1
0
0
1
0
2
2
2
0
1
1
3
0
2
2
0
0
3
0
1
1
1
0
2
2
1
0
2
2
1
1
0
0
0
1
1
0
2
0
1
0
1
2
0
0
1
0
1
1
2
0
0
1
2
1
0
1
0
1
1
0
1
0
0
2
2
0
2
0
1
2
1
0
2
2
0
4
5
0
1
1
1
0
1
0
1
1
0
1
1
1
1
1
0
1
1
1
0
1
2
0
1
0
2
2
1
1
1
0
2
3
0
0
2
0
2
0
1
1
0
1
1
0
1
1
0
1
1
1
1
2
1
1
1
1
0
0
1
1
0
2
1
1
2
0
0
0
1
0
2
1
1
0
0
1
1
1
0
1
2
0
1
0
2
0
2
1
2
0
2
1
1
1
2
1
1
0
1
1
1
0
1
0
1
0
0
0
1
0
1
0
0
1
1
1
2
2
0
0
1
0
1
1
1
1
1
1
0
2
0
2
0
2
0
1
1
2
0
0
2
1
2
1
1
1
2
1
0
1
0
0
1
0
1
1
0
1
0
1
1
1
0
2
0
1
1
0
0
2
1
1
3
1
2
0
1
2
0
1
1
0
0
0
0
2
2
0
0
2
1
0
0
1
0
1
0
0
2
0
0
1
2
2
0
2
0
2
0
2
1
1
2
1
2
1
2
1
0
0
1
1
2
1
1
1
0
0
1
0
2
1
0
2
3
1
2
0
2
2
1
1
0
0
1
2
1
1
1
1
2
2
1
2
0
1
0
0
2
2
0
1
2
1
1
0
2
1
1
1
0
2
1
2
5
0
2
1
0
2
2
2
1
2
1
1
1
2
1
0
0
1
0
1
0
0
0
1
0
0
1
0
1
1
2
0
1
2
1
0
1
0
1
1
1
1
1
1
0
0
1
0
0
0
1
1
2
1
1
1
1
1
0
1
1
0
1
2
0
1
1
0
0
0
2
1
1
1
1
1
0
0
2
1
0
0
1
0
2
0
0
2
2
0
1
1
1
0
1
1
0
1
1
2
1
0
1
3
1
1
1
0
0
2
1
1
1
1
0
1
0
2
2
2
2
3
2
2
3
1
0
1
1
1
0
0
0
2
1
1
1
1
0
1
2
1
0
1
2
2
2
2
2
0
1
2
1
1
0
1
1
1
1
1
1
0
0
1
1
0
1
1
2
1
0
1
2
1
1
1
0
1
0
1
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
1
2
0
3
0
0
1
0
0
0
1
1
0
0
1
1
1
0
0
0
2
1
2
1
1
1
0
1
0
2
2
0
1
0
1
1
1
1
1
0
0
2
2
2
1
0
1
1
1
1
0
0
1
1
0
1
2
0
0
1
0
0
2
2
0
1
1
1
2
1
1
0
1
0
0
2
0
1
2
1
1
1
1
1
1
1
0
1
2
0
0
1
0
0
2
0
1
0
1
0
1
1
1
2
0
0
0
1
0
0
1
1
0
0
1
0
1
0
1
1
2
0
2
0
2
0
4
1
0
1
0
0
0
1
0
1
1
1
1
1
1
0
1
2
1
2
2
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
1
1
0
1
1
2
1
1
1
0
1
0
1
2
1
2
1
1
2
1
1
2
0
1
0
2
0
2
1
1
0
1
1
0
0
1
0
1
1
1
2
2
1
0
1
1
0
0
0
3
1
1
2
2
1
1
2
1
2
2
1
1
1
2
0
1
1
1
2
0
0
2
1
2
1
0
2
0
2
1
2
1
0
1
0
1
1
1
1
1
2
0
2
2
0
1
2
1
2
1
0
0
1
0
1
3
0
1
1
0
0
2
2
1
1
1
2
0
1
0
1
1
0
0
0
1
1
2
1
2
2
1
0
2
1
2
2
0
0
1
0
0
1
2
1
1
1
0
1
2
0
2
1
1
1
0
1
1
1
1
2
0
1
0
1
0
1
1
1
1
1
0
1
2
0
2
1
2
2
1
0
2
2
0
0
1
1
2
1
0
1
4
0
0
2
2
1
1
2
1
1
2
0
1
1
0
1
0
1
2
2
2
2
1
1
1
3
0
1
1
0
0
0
0
1
0
0
1
0
2
0
1
1
0
1
1
2
0
1
2
0
0
2
1
1
1
0
0
0
0
2
0
1
1
0
1
2
0
1
0
1
0
0
0
1
1
1
1
1
2
1
0
0
0
1
2
0
1
2
2
0
4
1
1
0
0
2
1
0
2
1
1
2
1
0
0
1
2
1
1
2
2
0
1
1
2
2
2
0
1
1
2
0
0
2
1
0
2
1
0
2
0
0
0
0
0
1
0
2
2
0
2
1
2
2
1
1
1
2
1
1
1
2
2
1
1
2
1
0
1
2
0
1
1
2
0
1
0
0
2
0
1
0
0
0
2
1
1
1
2
1
1
1
1
0
1
1
1
2
0
0
0
2
0
1
1
1
1
0
1
1
1
1
1
1
2
2
0
0
1
1
1
1
1
2
2
1
0
0
2
0
1
1
0
0
1
2
0
0
1
0
1
0
2
0
1
1
0
3
2
1
2
1
0
0
0
1
1
2
1
0
1
1
0
1
0
0
1
0
2
1
0
0
1
1
1
1
1
4
1
1
0
1
1
1
0
2
0
2
2
0
2
2
1
1
1
2
0
1
1
2
0
0
1
1
0
2
1
0
1
2
2
1
0
2
1
0
0
1
0
1
1
2
0
0
2
1
0
1
1
1
1
1
0
1
2
1
2
1
1
1
1
0
0
2
0
0
1
1
1
0
1
1
1
0
1
0
1
1
0
0
1
1
0
1
1
1
1
0
1
1
0
1
1
0
1
1
0
1
0
1
0
0
1
2
1
1
0
1
1
2
0
1
1
0
2
0
1
2
1
1
0
0
0
0
0
1
0
3
1
2
1
1
1
0
0
1
2
2
1
1
2
0
1
1
0
2
2
0
0
2
0
2
1
1
1
4
0
1
0
1
1
1
1
1
2
1
0
1
2
1
0
2
1
2
0
0
0
2
1
0
1
1
1
2
0
2
0
1
0
2
1
1
1
1
1
0
1
0
1
1
0
0
0
1
1
2
1
0
0
1
1
0
0
1
1
0
0
0
0
1
1
2
0
1
2
1
0
1
0
1
1
0
0
1
0
0
0
1
1
2
1
0
0
1
1
0
0
0
1
0
0
0
2
0
0
2
0
1
0
0
2
1
1
1
0
1
0
2
1
1
2
2
0
1
2
1
1
1
1
0
1
1
1
2
1
2
0
2
2
1
1
1
1
1
0
1
0
2
0
0
1
1
1
2
0
0
1
2
0
0
2
1
1
1
2
0
0
2
1
0
1
1
0
1
1
2
0
1
0
0
1
0
1
2
0
1
1
1
3
1
1
0
2
0
0
0
1
0
0
0
2
0
0
0
1
3
1
1
0
1
1
1
1
0
1
2
0
1
0
0
2
2
0
1
0
0
1
0
0
2
2
0
2
0
0
2
0
2
1
1
0
1
1
0
1
0
1
1
0
2
0
0
1
2
1
0
0
2
0
1
0
2
1
1
1
2
0
1
1
1
0
1
1
0
1
1
1
1
0
1
1
0
1
1
1
1
0
6
2
0
0
0
1
1
0
0
0
1
2
0
2
0
0
0
0
0
1
0
2
2
0
0
1
2
0
3
0
1
0
2
0
1
0
1
0
1
1
2
0
0
1
0
1
0
1
1
1
1
0
1
2
1
1
0
2
1
1
2
2
0
1
2
0
0
1
2
0
1
1
1
0
1
0
1
0
2
1
0
2
2
1
2
0
0
0
1
2
1
1
1
1
1
2
1
2
1
0
1
2
0
2
0
1
0
1
1
0
1
1
1
1
1
0
2
2
1
1
1
0
1
1
2
1
1
1
0
0
0
0
1
1
1
1
1
0
0
0
1
2
0
1
1
1
1
3
0
2
0
1
1
0
1
1
2
0
2
0
1
2
1
0
0
1
1
0
2
1
2
2
0
1
1
0
1
1
2
2
2
1
0
1
1
2
1
2
1
1
2
2
1
1
1
2
0
2
2
0
0
1
2
1
1
1
2
1
2
0
2
2
1
1
2
1
0
0
0
2
1
1
2
2
2
0
1
1
1
2
1
0
1
2
0
2
2
2
1
2
1
1
1
1
1
0
1
0
0
1
0
1
1
1
1
2
2
0
0
0
0
1
2
1
1
0
1
0
2
1
2
0
0
2
2
1
0
1
1
1
0
0
0
2
1
1
0
0
0
1
1
0
0
2
2
1
1
1
0
0
0
0
2
1
1
1
1
2
2
0
0
1
1
0
2
1
1
1
1
1
1
1
0
0
1
1
0
0
0
0
0
2
0
0
1
0
1
1
1
0
1
1
0
1
1
1
1
0
0
0
0
0
2
1
0
0
2
1
3
0
2
0
2
1
2
0
0
0
0
1
1
2
0
1
1
2
2
0
1
1
0
2
1
2
0
1
1
0
2
0
0
1
0
0
0
0
0
1
1
1
0
1
1
1
0
2
0
0
0
0
0
0
3
0
1
1
1
0
1
0
1
1
2
0
3
0
1
1
0
0
2
1
2
0
0
1
1
1
2
1
1
1
1
2
2
2
1
0
1
1
1
0
1
0
1
0
0
2
1
1
1
1
1
0
1
1
0
2
1
1
0
1
2
2
2
1
0
0
0
0
1
1
1
1
2
2
2
2
1
0
0
1
1
3
2
1
0
0
1
2
0
1
1
0
2
2
1
0
1
0
2
0
1
1
0
2
0
2
1
0
2
0
3
1
1
2
1
2
1
1
1
2
8
1
2
2
0
2
0
1
0
1
1
1
2
1
0
2
2
3
1
1
1
1
1
1
1
0
0
0
2
1
0
2
1
1
1
1
1
1
2
1
1
2
2
0
1
2
1
1
1
1
0
1
2
2
1
1
1
1
0
0
3
1
0
0
1
0
0
2
1
1
1
2
0
1
2
0
0
2
1
0
1
1
1
0
1
1
0
1
0
1
0
1
0
0
0
2
0
0
2
2
0
0
2
0
1
2
1
0
1
0
0
0
0
0
1
2
0
1
0
0
1
0
1
3
1
1
1
0
1
1
7
1
0
0
1
1
0
0
2
2
0
1
0
0
1
1
3
2
1
0
1
0
2
1
0
1
0
2
1
0
1
1
1
0
1
2
0
2
1
1
0
1
1
0
0
0
1
2
0
0
1
0
2
2
1
0
1
1
1
0
0
1
0
0
0
0
1
0
0
2
0
0
0
1
0
3
0
0
0
1
2
0
2
1
1
1
2
1
2
2
0
1
1
1
1
0
2
1
0
0
1
2
1
2
2
0
1
1
1
0
2
1
0
3
0
1
2
1
0
1
1
0
1
2
1
2
3
0
0
0
2
0
1
0
1
0
0
1
0
0
1
0
0
0
1
1
1
2
2
1
3
0
3
1
2
2
1
1
0
1
1
0
0
1
0
0
1
1
1
1
2
1
0
0
0
1
1
1
0
0
1
1
1
0
1
0
1
1
1
2
0
1
0
1
1
1
1
1
2
1
0
0
1
1
1
0
0
1
1
1
0
3
0
1
0
1
0
1
0
0
2
1
1
1
1
1
0
1
0
0
0
2
1
0
0
2
1
1
1
0
2
1
3
0
2
0
1
1
2
1
1
1
0
1
2
4
0
1
1
0
1
1
1
0
0
1
1
0
2
0
0
0
2
0
0
1
1
3
2
2
0
2
0
2
2
1
1
0
2
0
0
0
0
1
0
1
1
1
2
2
2
1
1
0
1
1
1
2
2
0
0
2
1
1
1
1
1
2
1
2
1
0
1
2
0
2
2
2
1
1
0
1
1
2
1
0
1
0
1
0
0
0
3
0
0
2
0
2
0
1
0
1
1
0
2
1
2
0
1
2
1
0
1
2
2
2
0
0
1
0
0
1
1
1
0
1
1
0
0
0
0
0
2
2
0
0
0
1
2
1
0
2
0
1
0
2
0
1
2
2
2
0
1
1
2
0
0
2
0
0
1
2
0
1
1
0
1
1
0
1
1
0
0
2
1
1
1
1
1
0
0
1
1
0
2
1
2
1
1
1
1
0
1
1
1
0
1
1
0
1
2
0
0
0
2
2
0
1
1
0
1
2
1
0
0
0
1
2
0
1
1
4
0
2
1
1
2
0
1
2
1
0
2
1
1
1
1
0
2
0
0
0
0
0
2
2
0
1
1
1
0
2
1
1
1
1
0
2
0
1
1
1
1
1
1
0
0
1
1
0
0
0
0
1
0
0
2
0
0
2
2
0
1
1
2
1
0
0
2
2
1
0
1
0
1
1
0
0
1
0
0
1
1
1
2
1
1
1
1
2
0
8
1
2
2
2
0
1
1
1
2
3
1
0
1
0
1
0
1
0
2
2
2
1
2
1
1
0
0
0
2
1
2
0
1
1
2
0
0
1
0
1
0
0
1
1
0
0
1
0
0
2
0
1
0
0
0
1
1
3
0
1
0
0
0
0
0
1
0
1
1
1
1
1
1
1
0
0
1
2
2
1
2
0
2
0
1
0
0
1
1
1
1
2
0
1
1
1
1
2
1
0
1
2
0
3
1
0
0
0
2
0
2
1
1
1
2
0
2
1
1
0
1
0
1
1
1
0
0
1
3
1
1
1
0
1
1
1
1
0
0
2
0
0
2
1
1
2
0
0
0
1
0
1
1
2
0
0
1
1
1
1
0
1
1
1
1
1
1
0
0
0
1
2
0
0
0
0
0
2
1
1
1
0
0
1
1
0
1
2
3
1
1
1
0
2
2
0
0
1
0
1
1
1
1
1
2
0
1
0
0
1
2
1
2
1
2
2
2
1
1
1
1
1
0
1
1
1
2
0
2
1
0
0
1
2
0
0
2
0
1
1
1
1
0
1
0
1
2
2
1
1
2
1
2
2
1
0
0
0
2
1
0
1
0
1
0
0
3
2
1
2
2
0
1
2
0
0
1
0
1
0
2
2
0
1
1
1
0
0
1
2
1
0
0
2
1
2
0
1
2
1
2
0
0
2
0
0
0
2
1
0
3
1
1
0
0
0
0
2
0
1
0
2
2
0
2
0
1
0
2
3
1
0
0
1
0
1
1
0
0
0
1
1
0
1
2
0
0
1
0
1
0
0
1
2
0
1
2
0
2
1
0
1
2
1
1
1
1
2
1
2
1
2
2
0
0
1
1
1
0
1
2
1
1
0
0
0
1
0
1
0
0
1
2
2
1
0
0
2
0
0
2
1
2
2
1
1
2
1
0
2
1
0
0
1
0
1
1
2
2
0
1
1
1
1
1
0
0
1
0
0
1
2
0
0
0
1
2
2
1
2
1
1
2
1
2
2
1
1
2
0
0
1
1
1
0
0
0
0
1
2
1
1
1
0
1
2
0
1
1
0
2
1
2
0
1
0
0
2
2
1
0
3
1
0
1
1
0
1
0
1
0
0
1
1
1
1
0
0
2
0
0
0
0
2
1
0
2
1
2
2
1
1
1
1
1
0
1
0
0
1
0
1
0
0
2
2
1
2
0
2
0
1
1
1
1
0
0
2
1
1
0
1
1
2
1
0
2
0
0
0
2
2
0
1
2
1
1
1
0
0
0
2
2
0
1
0
1
1
0
1
0
0
1
1
2
2
0
1
2
1
1
2
1
0
0
1
1
0
0
2
3
1
0
1
1
1
0
4
1
2
0
0
0
1
0
1
2
2
0
1
2
1
1
1
1
1
1
2
0
1
0
0
2
2
0
1
0
2
0
0
0
1
2
2
1
1
1
2
1
1
2
1
2
0
1
1
0
2
0
0
1
0
1
1
0
0
0
2
2
1
0
2
1
0
0
0
1
4
0
1
2
1
0
1
2
0
11
2
0
0
1
0
2
1
0
1
0
1
0
0
3
1
1
3
1
2
1
1
0
0
1
0
1
0
2
0
1
1
1
2
0
0
1
0
0
1
1
2
2
1
1
1
1
1
0
1
1
0
2
1
1
1
1
2
2
0
0
3
1
0
0
0
0
0
1
0
0
0
1
1
1
1
2
1
1
0
0
0
0
0
0
2
1
0
1
1
1
1
2
1
0
1
0
1
0
1
0
0
0
1
1
0
2
1
0
0
1
2
0
1
1
1
0
1
0
3
2
1
2
0
1
0
0
2
2
1
1
0
2
0
0
3
2
0
2
2
1
1
0
1
0
1
0
0
0
0
1
0
0
1
1
0
2
0
0
5
1
1
1
2
1
1
1
1
0
1
2
0
0
0
2
1
1
0
2
1
1
0
0
1
1
0
1
0
2
2
2
1
0
1
0
1
0
1
0
1
1
2
2
0
1
1
2
2
1
0
3
2
0
0
1
0
1
0
1
1
2
0
0
1
0
1
0
2
2
1
0
1
1
1
2
1
0
0
1
0
0
1
0
1
1
1
0
1
1
1
1
2
3
1
2
0
1
0
2
1
0
0
0
2
1
0
5
2
0
0
1
1
2
0
0
2
4
1
1
1
0
0
2
0
0
2
1
0
1
0
1
1
2
0
0
1
0
0
2
1
0
1
0
0
0
1
0
1
2
2
1
0
0
0
0
2
0
1
2
2
2
1
0
0
2
0
2
1
2
0
1
1
1
1
1
1
1
1
1
1
2
0
2
1
0
2
1
3
1
0
0
2
0
1
1
2
0
0
0
1
2
0
2
2
0
0
0
2
0
1
1
1
0
1
1
1
2
1
0
1
1
0
0
1
0
2
1
1
1
2
1
2
0
1
1
1
0
1
1
0
1
0
0
1
1
2
1
2
1
0
0
1
3
2
1
2
1
0
2
4
1
2
1
2
0
2
0
0
1
1
0
1
1
1
1
0
2
1
0
1
0
2
1
2
1
0
0
2
0
2
2
0
0
2
0
1
0
1
1
1
1
0
1
1
0
0
1
0
0
1
0
1
0
0
1
1
1
1
0
2
0
0
2
2
0
0
1
1
0
1
0
1
1
0
0
0
1
0
2
0
1
1
1
1
2
1
0
2
0
1
2
2
2
1
1
1
1
1
1
0
0
1
1
3
0
1
1
2
1
1
2
1
1
0
0
2
1
2
2
0
1
0
0
1
0
1
0
3
1
1
1
0
1
2
1
0
0
0
1
0
0
0
1
2
1
1
0
1
1
2
0
1
0
1
1
2
0
2
0
2
0
1
0
2
0
0
0
2
0
1
2
2
1
2
1
0
0
0
0
1
2
1
1
1
1
0
2
2
1
0
0
1
0
0
1
0
1
2
2
0
1
2
0
2
0
0
2
1
2
0
1
0
0
0
2
0
1
0
0
0
0
0
0
1
3
3
1
1
1
0
1
0
1
1
2
1
1
0
1
1
0
0
0
0
1
2
0
1
0
2
2
0
1
1
2
0
1
2
0
0
1
2
0
0
1
1
1
0
0
1
0
0
2
1
0
0
0
1
0
0
1
0
1
0
0
1
1
1
2
0
1
1
1
0
2
1
2
2
2
1
0
0
1
1
1
0
1
1
0
2
1
2
2
1
2
1
1
0
1
1
1
1
0
2
1
4
2
1
0
1
2
1
1
0
0
0
0
0
0
0
1
0
0
1
1
2
0
1
2
0
0
0
1
1
1
1
1
0
2
1
2
1
0
1
0
1
1
1
1
1
0
0
2
1
2
1
0
1
1
1
0
1
1
1
0
5
0
2
1
0
1
2
2
1
2
1
0
1
2
1
1
2
1
0
2
1
1
1
0
1
0
0
3
1
0
0
0
1
2
1
1
2
1
1
0
0
1
1
1
1
1
1
0
1
1
1
1
1
2
0
1
2
1
0
0
0
2
0
2
2
2
1
2
1
1
1
0
1
1
1
0
2
2
0
1
1
0
1
0
0
0
2
1
0
3
0
0
2
1
0
0
2
2
1
1
2
1
0
0
0
2
1
0
0
1
0
2
0
1
1
1
1
2
1
0
2
2
0
1
0
0
1
2
2
1
2
0
3
1
0
2
0
0
1
1
1
2
1
1
2
2
2
0
0
2
0
0
1
0
2
1
0
0
2
0
0
2
0
1
1
0
0
0
0
2
1
1
2
0
1
0
1
1
1
0
0
1
0
1
1
0
0
0
1
2
0
2
2
2
1
0
2
0
0
0
2
0
2
2
0
0
0
0
0
1
0
0
1
6
1
1
2
0
0
1
1
1
1
1
1
2
1
2
1
0
1
2
0
0
0
1
2
1
0
1
0
1
2
1
1
0
1
0
0
1
2
0
1
1
1
1
2
2
0
1
1
0
1
0
0
1
1
0
2
1
1
1
0
1
0
2
0
1
1
1
1
2
0
1
3
0
0
1
0
0
1
0
1
1
0
0
0
2
3
1
1
0
1
0
1
1
1
0
1
3
1
0
2
1
0
1
1
3
1
0
0
1
0
2
0
0
1
2
2
2
1
0
0
0
1
0
2
1
0
0
0
13
1
0
1
0
1
1
1
0
2
0
0
0
2
0
0
0
1
0
0
0
0
1
1
1
0
1
1
2
2
1
0
1
0
1
1
2
0
2
0
0
2
2
0
1
0
0
1
0
2
1
2
0
1
0
1
0
2
1
2
2
0
1
0
1
0
0
0
0
0
1
1
1
1
0
2
2
0
1
0
0
0
0
0
2
2
1
1
0
2
1
0
2
1
0
0
2
1
1
1
2
0
1
4
1
2
0
2
1
0
1
1
2
1
0
1
2
1
2
1
1
2
0
1
0
1
2
0
0
2
1
0
1
1
1
2
0
2
0
0
0
1
1
0
2
0
2
0
1
0
2
1
1
1
0
2
0
0
2
1
1
1
0
1
1
2
2
1
1
1
0
1
1
1
1
0
0
0
2
2
2
1
2
0
2
0
0
1
0
0
0
0
0
0
1
0
2
2
0
1
0
1
2
1
1
0
0
0
0
0
2
0
0
1
0
0
1
2
2
0
0
0
1
1
1
1
1
2
1
0
1
0
2
0
0
0
0
0
0
0
2
1
2
0
0
0
1
0
1
1
1
2
1
2
1
0
1
0
0
1
2
0
1
1
0
0
0
1
1
2
2
0
1
0
2
0
1
1
2
1
2
0
1
1
2
0
0
0
1
1
1
2
0
1
1
2
0
0
1
0
0
1
1
1
1
1
3
0
0
2
1
0
2
2
1
1
1
1
1
1
2
1
1
2
1
0
3
2
0
0
2
2
1
1
1
0
2
0
0
2
1
2
1
1
3
1
2
1
1
1
1
0
0
1
0
1
1
1
0
0
1
2
0
1
2
1
1
0
0
1
0
2
2
2
1
1
1
1
1
1
1
2
1
2
0
0
1
2
1
0
2
0
2
1
2
0
0
2
2
1
1
0
2
0
1
0
1
0
2
1
2
2
0
0
1
1
0
2
1
1
1
2
1
1
1
1
2
0
0
1
1
1
2
2
0
1
1
1
0
0
1
1
1
0
1
0
1
1
1
1
1
0
1
0
2
0
1
0
0
0
1
0
1
2
1
0
1
0
1
0
2
0
1
1
1
1
2
1
1
2
2
1
1
1
1
0
1
1
1
1
2
1
2
1
1
1
1
0
1
2
0
1
1
2
0
2
0
1
0
0
0
0
1
1
0
0
2
2
2
0
0
1
0
0
1
2
1
1
1
0
0
0
0
5
0
0
1
0
0
1
1
0
1
1
0
0
0
0
2
1
0
2
2
2
1
1
0
0
2
1
1
0
0
1
0
0
1
1
1
1
1
1
1
1
1
1
0
0
1
1
0
2
1
0
0
1
1
0
2
1
2
1
1
1
1
2
1
1
1
0
1
0
2
1
0
1
1
1
1
0
0
1
2
2
0
1
2
1
2
1
0
0
1
1
0
2
1
0
2
2
1
0
1
1
0
1
1
2
2
1
0
0
1
0
2
1
0
2
1
1
1
0
2
2
1
0
0
1
1
2
0
1
0
1
0
2
1
1
1
1
1
0
1
1
0
1
1
2
0
2
0
2
1
0
0
0
1
0
1
1
0
0
0
1
1
1
2
0
0
0
1
2
1
0
1
1
0
2
1
1
1
1
1
2
1
0
1
0
2
1
1
0
2
0
0
2
0
0
0
2
0
2
1
0
2
0
0
0
2
1
3
1
0
0
0
2
1
2
1
0
1
0
0
0
0
0
0
0
1
1
3
1
1
1
1
1
2
2
3
1
2
2
2
2
2
2
0
1
1
1
0
2
1
1
2
0
1
1
1
1
0
1
1
2
2
0
1
1
1
2
0
1
0
1
1
0
0
2
2
2
1
1
1
0
1
1
1
0
2
0
1
1
2
0
2
0
1
1
2
2
2
2
0
0
1
1
0
1
1
2
1
0
2
1
2
0
1
2
0
0
1
0
1
0
0
1
1
2
0
0
1
0
0
0
0
0
1
1
1
1
3
0
2
1
1
2
1
2
0
1
2
2
1
0
0
0
2
1
1
2
0
2
0
0
0
1
1
0
0
1
1
1
1
1
0
0
2
1
1
0
2
2
0
0
1
1
1
1
0
0
1
0
1
2
1
0
2
0
2
1
2
1
0
0
1
1
0
1
2
1
2
0
1
1
1
1
0
2
0
1
0
2
2
0
1
1
0
1
2
2
1
1
1
1
0
2
1
2
1
0
0
1
1
1
1
2
0
0
1
2
1
0
0
2
1
0
0
1
0
1
2
0
0
1
1
0
1
0
0
0
1
1
0
1
2
2
0
1
2
3
0
1
1
0
1
2
2
0
2
0
0
0
0
0
0
0
1
1
0
2
0
2
2
0
1
0
0
1
2
0
1
0
1
2
1
0
0
0
1
2
2
2
2
0
1
1
1
1
1
0
2
0
1
0
1
1
0
1
1
1
2
0
0
1
1
2
1
2
1
1
1
2
0
0
1
0
1
2
1
0
2
0
1
0
2
2
1
0
1
1
0
2
1
2
1
1
1
1
0
0
1
0
0
2
0
1
1
2
0
0
0
0
0
0
1
1
1
2
2
0
0
2
0
1
2
0
0
0
2
0
1
2
0
1
2
1
1
0
1
0
0
0
0
1
0
2
0
1
2
1
1
2
0
1
2
1
1
1
1
2
1
1
1
0
2
1
1
0
2
1
2
1
1
0
0
1
1
0
1
0
0
0
1
2
1
1
1
1
1
0
2
1
2
1
2
0
0
1
0
1
1
2
1
1
0
1
1
1
0
0
1
1
1
1
0
0
0
0
1
0
2
2
1
2
0
0
0
2
1
2
0
1
0
1
0
1
0
0
0
1
0
1
2
1
0
0
2
2
0
1
2
2
1
2
1
1
2
0
1
3
2
1
0
1
0
1
1
0
1
0
1
0
2
1
0
2
2
1
0
1
1
1
1
2
0
2
2
0
2
2
0
0
0
2
0
3
2
2
1
1
1
1
0
2
2
0
1
1
0
2
1
2
2
0
0
1
1
0
1
1
1
1
2
0
0
1
1
0
1
1
2
2
0
1
2
0
0
0
0
2
1
0
0
0
1
1
1
1
0
1
0
1
1
2
1
2
0
1
0
0
0
1
1
1
1
0
1
0
1
1
0
1
1
1
0
1
0
1
0
0
0
1
1
0
0
0
0
1
1
2
2
1
0
0
0
0
1
0
1
0
0
2
2
0
0
1
2
2
2
1
0
1
1
0
2
1
0
0
2
0
2
3
0
0
2
2
2
0
1
1
1
1
1
1
1
3
1
0
1
2
1
2
6
1
0
0
2
2
1
1
2
1
0
2
2
1
0
0
1
0
1
0
2
2
1
1
1
2
1
0
2
1
1
2
0
2
0
2
0
0
2
1
0
2
0
0
1
1
0
2
0
1
0
2
0
0
0
1
0
2
1
0
1
1
2
2
0
0
2
2
2
1
0
0
0
1
0
1
1
2
1
0
0
0
0
1
1
1
2
1
1
1
1
0
1
2
1
1
2
2
0
1
0
1
0
0
1
2
1
1
1
1
1
0
0
0
1
1
1
2
2
1
0
0
1
0
0
3
1
0
1
2
1
0
2
0
3
2
0
2
1
0
1
1
0
1
1
1
0
1
0
1
1
2
0
1
0
0
1
1
0
1
5
0
1
0
1
1
1
1
2
1
1
0
1
0
1
1
0
1
1
2
0
1
1
0
1
2
0
1
0
0
0
0
1
2
0
0
1
1
1
1
0
0
0
1
0
1
0
2
1
0
0
0
0
0
2
1
1
2
2
1
1
1
1
0
0
0
0
2
2
1
0
1
1
0
1
1
0
0
1
1
2
1
0
1
1
0
0
1
2
0
0
2
1
2
0
1
1
1
0
1
2
1
1
1
3
0
1
1
2
0
1
0
0
1
1
0
0
1
0
0
0
0
1
1
1
1
1
0
2
2
0
0
2
2
0
0
0
1
0
1
2
2
2
0
0
0
1
2
1
1
2
1
0
0
1
1
0
1
1
1
0
1
2
0
0
0
2
0
0
0
0
2
1
1
0
0
1
1
0
0
2
1
0
1
1
1
0
0
1
1
1
0
0
2
2
2
1
1
1
3
1
1
1
0
4
0
0
0
3
2
0
3
1
0
1
1
0
0
1
1
1
0
1
1
0
0
1
2
1
1
1
0
5
0
0
0
1
2
0
1
2
2
1
1
0
1
0
0
0
0
0
1
0
0
1
0
0
1
2
0
1
0
0
1
1
0
0
1
1
0
2
1
0
2
1
2
2
0
0
0
1
2
0
2
2
2
1
0
1
1
1
1
2
1
1
1
0
1
0
0
1
0
2
0
1
1
0
0
0
0
0
1
2
1
1
2
0
0
1
1
2
0
2
2
1
1
0
0
2
1
1
0
0
1
2
1
2
0
2
0
1
3
1
2
0
1
1
0
2
1
0
1
0
2
1
0
1
1
2
0
1
1
1
1
1
1
0
1
1
0
2
0
2
0
2
1
2
2
1
0
1
0
1
1
0
1
2
0
1
1
2
2
3
1
0
1
1
1
1
2
1
1
0
2
1
0
0
2
0
0
1
3
1
1
1
0
1
2
0
1
2
0
1
1
2
0
0
0
2
1
0
1
1
1
1
2
1
0
1
0
2
1
2
1
0
1
0
3
0
2
1
0
1
2
1
0
2
0
0
1
3
1
0
2
0
0
1
0
2
0
0
2
2
1
2
1
1
2
1
1
0
1
2
0
0
1
2
2
1
0
0
1
1
2
1
1
1
0
2
0
1
2
2
0
2
1
2
1
0
0
2
0
1
0
2
0
1
2
1
0
1
2
1
1
1
1
1
0
1
3
2
1
1
0
1
2
0
1
1
1
2
2
1
1
2
2
1
0
2
0
2
0
1
1
3
2
1
0
0
2
2
1
0
1
0
2
1
1
0
1
0
1
0
1
0
0
2
2
1
1
2
0
2
1
2
2
1
1
1
1
0
1
1
1
1
0
2
1
2
0
0
0
1
0
1
1
0
0
2
1
2
2
1
0
0
1
1
1
0
0
0
0
0
1
2
2
0
2
0
0
0
0
1
0
1
3
1
0
1
0
0
1
1
0
0
1
1
0
1
2
1
0
1
0
1
0
1
2
0
1
1
1
1
2
2
0
2
1
0
0
1
1
1
0
1
1
1
0
2
2
0
1
1
2
0
0
1
1
0
1
1
0
2
1
0
1
0
1
1
1
1
1
1
2
1
2
1
0
1
2
3
0
0
1
0
0
1
0
0
2
0
1
0
0
0
2
0
0
0
2
1
2
1
1
2
1
0
0
2
0
2
0
1
0
1
0
1
2
1
2
2
0
0
1
2
1
1
1
1
0
2
1
1
1
0
2
1
2
0
0
0
0
2
2
1
1
1
2
1
0
1
3
0
0
1
1
2
1
0
0
1
1
0
1
0
1
0
1
1
1
1
1
2
1
1
0
0
1
2
1
1
0
2
0
0
2
0
0
1
1
0
0
0
0
0
1
1
2
1
0
0
0
1
0
1
1
1
2
1
0
2
1
0
0
2
1
1
1
1
0
0
0
1
0
0
1
1
2
1
0
0
1
1
0
0
1
2
0
0
1
0
0
1
1
0
1
1
0
0
0
1
1
1
1
1
0
1
0
0
1
1
0
0
2
1
2
2
1
0
2
1
1
1
1
0
1
0
0
1
0
1
1
0
1
0
1
2
2
0
1
1
1
0
0
2
2
1
2
2
0
2
1
0
2
2
3
0
2
0
0
1
0
2
1
1
1
2
0
1
1
0
0
0
2
0
2
2
1
1
2
2
0
1
1
0
2
1
0
2
0
0
0
2
2
0
1
1
2
1
1
0
0
0
0
1
1
2
2
1
0
1
1
0
0
1
0
0
2
1
0
1
1
1
1
2
0
1
0
0
0
1
0
1
1
1
1
1
0
0
1
2
0
1
0
0
2
1
1
0
0
1
0
2
0
0
1
2
0
0
2
1
2
1
1
1
1
1
2
1
1
1
1
1
0
0
1
2
0
0
1
2
1
1
0
0
0
2
1
2
2
0
1
0
0
2
0
0
1
2
2
2
1
1
1
2
1
1
2
1
0
0
2
2
1
2
0
0
4
0
1
2
0
2
1
0
0
2
1
1
2
1
0
1
1
1
1
2
2
2
2
1
1
1
0
0
0
0
1
0
2
0
0
0
1
2
2
1
1
1
1
0
0
0
1
1
0
1
1
1
1
1
1
0
2
2
2
2
1
0
2
0
0
2
2
0
0
0
1
0
1
0
2
1
2
1
1
1
0
1
1
1
0
0
3
0
1
0
2
1
1
1
0
0
2
1
0
0
2
0
0
1
0
1
0
0
1
1
1
0
2
0
1
2
1
2
2
1
0
0
0
0
0
1
0
1
4
2
0
0
0
0
0
0
1
2
0
1
0
2
0
1
0
1
1
0
2
0
0
2
2
1
1
1
0
2
0
1
1
2
0
0
2
0
1
0
2
0
2
0
3
1
0
0
0
2
0
1
2
0
2
1
0
0
2
0
1
0
0
1
2
1
1
1
1
0
1
0
1
0
1
2
0
2
0
5
2
0
0
0
0
0
1
1
1
1
1
2
1
1
1
0
1
0
0
1
0
2
1
1
0
2
1
1
2
1
2
0
1
0
2
1
0
2
2
0
0
1
1
1
0
1
2
2
0
1
1
0
0
2
0
0
1
1
2
0
2
0
0
0
0
0
2
0
0
0
1
1
1
0
1
1
1
1
0
1
1
1
1
1
0
1
2
1
0
2
0
1
1
2
2
1
1
2
1
0
2
1
0
2
2
0
0
0
0
0
2
1
1
0
1
0
2
0
0
1
0
1
1
0
2
1
1
0
0
2
0
0
0
1
2
2
1
0
0
0
2
1
0
2
2
0
1
1
1
1
1
1
1
1
2
1
2
2
2
0
1
1
0
1
2
2
1
0
1
2
1
0
1
2
1
1
0
0
2
1
0
1
1
0
2
0
1
1
1
0
0
1
0
0
1
1
1
1
2
0
1
1
0
0
1
2
0
0
2
2
0
0
1
1
1
1
1
1
1
1
0
0
5
1
0
1
1
1
1
2
0
1
1
2
0
2
1
2
1
2
2
1
0
2
1
1
1
1
0
2
0
1
1
1
1
1
1
0
2
1
0
1
1
1
1
1
0
2
0
0
1
2
0
1
1
0
1
0
2
2
1
1
0
0
1
1
1
0
1
1
1
2
1
0
1
2
2
0
1
1
0
1
0
2
1
1
0
3
0
1
1
1
0
1
1
1
0
0
0
0
1
1
0
1
1
0
3
1
3
2
1
1
2
1
0
1
3
1
2
2
0
1
0
0
2
0
1
3
0
2
1
1
1
1
0
1
1
1
0
1
0
0
2
2
0
2
2
0
1
0
0
1
2
0
0
1
1
0
0
1
0
0
0
0
0
2
1
2
0
0
1
1
0
1
1
1
0
0
1
0
0
0
1
1
0
1
1
2
0
2
2
1
0
1
1
0
1
1
0
3
1
2
0
0
1
1
2
2
1
0
1
2
1
4
2
0
2
0
1
0
1
1
1
1
0
1
0
1
0
1
2
0
0
0
1
0
2
1
1
0
2
2
1
2
0
0
0
1
1
1
0
0
1
1
0
0
1
1
2
0
0
1
0
1
1
1
1
1
0
2
0
1
1
0
0
1
1
1
1
1
2
0
0
0
1
1
0
1
1
0
1
1
2
0
0
1
0
1
1
2
2
2
0
1
2
1
1
0
1
1
0
1
1
2
0
1
0
1
1
1
1
2
1
1
1
0
2
1
1
0
1
1
1
1
1
0
2
0
0
0
2
1
0
0
0
0
1
1
0
2
0
0
1
0
0
0
0
2
1
0
1
1
0
1
1
0
1
1
1
0
0
1
2
1
2
0
1
1
0
0
0
0
2
0
0
2
2
0
0
2
0
1
0
1
1
0
1
1
1
0
1
2
1
0
2
1
2
1
2
1
2
2
2
0
0
1
0
1
0
1
1
1
0
0
1
1
0
1
0
0
0
0
0
0
1
1
2
1
1
2
1
0
2
1
0
1
1
0
2
0
0
0
0
2
1
1
0
1
1
1
2
0
1
1
0
2
1
0
0
0
0
1
2
2
0
0
2
0
2
0
0
0
1
1
1
2
0
1
1
0
2
1
0
1
2
1
2
0
0
0
1
1
1
2
1
2
1
0
1
2
1
0
1
1
0
1
0
2
0
2
1
0
2
0
0
2
2
1
0
0
2
1
0
0
1
1
2
2
0
1
1
0
0
1
1
1
0
1
2
1
0
1
0
2
1
1
0
2
2
2
0
2
1
0
0
2
3
2
1
0
2
1
1
0
1
2
0
2
1
2
0
2
1
0
0
0
1
1
0
1
0
0
1
0
0
1
0
0
2
0
1
1
1
0
2
1
2
1
1
1
0
2
0
1
2
0
1
1
2
1
1
1
2
1
1
2
0
0
3
0
1
1
0
2
0
1
0
1
1
0
2
1
0
1
2
1
0
2
1
1
2
1
2
0
0
0
0
1
0
2
2
0
0
1
2
0
2
1
1
1
2
2
2
1
1
1
1
1
0
1
1
1
1
1
0
1
1
2
1
0
1
2
2
0
2
1
0
1
0
1
1
2
0
0
2
2
3
0
2
0
2
0
0
0
1
2
0
1
1
0
1
2
2
2
0
2
1
1
1
2
1
0
2
1
0
1
0
3
2
0
0
2
1
1
2
0
0
1
1
0
0
0
1
1
1
1
2
0
1
1
1
2
1
1
1
0
0
0
2
0
1
1
2
2
2
2
2
1
2
1
1
0
1
1
0
4
0
2
2
0
0
1
1
1
0
1
0
1
1
2
2
2
1
1
2
0
2
1
1
0
1
2
0
1
0
0
1
2
0
0
0
1
2
1
1
2
1
0
1
0
1
1
2
0
1
0
0
1
0
0
0
2
0
2
0
1
1
0
1
1
0
0
1
0
1
1
0
1
2
1
0
0
0
1
0
2
2
1
2
2
1
0
1
1
0
1
1
0
0
0
0
1
2
2
1
1
1
0
1
2
0
0
1
2
1
0
1
0
2
0
1
1
3
2
1
2
1
2
0
2
2
1
0
2
1
0
0
1
0
0
1
1
1
0
1
2
4
0
1
2
0
1
1
1
1
1
2
0
2
2
0
2
2
1
0
0
2
1
0
1
0
0
1
1
1
0
0
1
2
1
0
0
1
2
1
0
1
0
0
2
1
1
1
0
1
0
0
0
0
0
0
1
1
0
0
1
0
3
2
1
1
0
1
0
0
0
0
0
0
1
0
0
1
1
1
0
0
2
1
1
1
0
2
1
1
0
1
1
1
2
0
0
0
0
2
0
1
1
1
1
1
0
0
1
2
0
0
1
1
0
1
2
2
2
1
0
2
1
2
1
1
1
1
1
2
1
0
2
2
1
0
0
0
1
1
1
0
1
1
0
2
0
0
1
0
0
0
1
1
2
2
0
1
1
2
1
1
0
0
1
0
0
1
2
0
1
0
0
2
2
0
0
1
2
0
1
2
2
3
0
0
0
2
1
2
1
0
1
0
0
0
0
1
1
2
2
1
0
1
0
2
0
0
1
1
2
1
0
1
0
1
0
0
0
0
1
2
0
0
1
0
0
0
0
2
2
1
1
0
0
1
0
1
0
2
2
0
0
2
2
1
2
1
0
1
2
1
0
1
1
1
1
0
0
1
1
1
1
0
2
2
2
1
0
1
2
0
0
2
2
1
2
1
1
2
2
2
2
2
0
0
0
0
2
2
2
1
0
1
2
0
1
1
2
0
1
1
0
1
2
0
2
2
2
0
0
1
1
2
1
2
0
2
0
2
1
1
0
0
2
0
2
3
1
1
0
0
1
1
1
1
1
0
2
1
1
0
0
0
1
0
1
1
1
1
2
1
2
1
0
1
1
2
1
1
0
1
0
1
2
2
0
1
1
1
2
1
1
1
1
0
0
0
1
1
1
1
0
0
1
1
0
0
1
1
1
0
0
1
2
4
1
2
0
0
2
0
0
2
1
1
1
1
3
0
0
0
1
0
1
1
2
2
1
0
0
0
0
0
0
2
0
2
0
1
0
2
1
2
1
2
2
2
3
2
1
0
0
1
1
0
0
0
1
0
0
1
1
2
1
1
0
1
0
0
0
0
4
1
0
1
1
1
1
1
1
0
0
1
0
2
1
0
2
1
0
1
1
1
2
1
2
1
0
1
0
1
0
0
0
1
1
2
1
0
0
2
1
0
0
0
1
0
2
1
3
1
1
0
0
1
2
2
1
1
1
0
0
1
0
1
0
1
1
1
1
1
1
1
0
0
1
0
1
1
0
0
2
0
0
1
2
2
2
1
0
1
2
1
1
0
0
0
1
1
1
1
1
0
0
0
0
0
1
1
1
1
0
0
2
1
1
1
2
1
2
1
1
0
1
1
2
1
1
0
0
1
1
2
0
0
0
0
0
1
2
1
1
1
1
2
1
1
1
1
0
0
3
0
2
1
1
0
0
0
1
1
1
1
0
2
0
2
1
0
2
7
1
1
2
0
0
0
1
0
1
2
2
2
0
1
0
0
0
2
1
2
1
2
1
1
1
0
1
1
0
0
2
1
2
3
1
0
2
0
1
1
1
0
1
1
2
2
2
0
0
2
1
1
0
1
0
1
0
1
1
1
1
1
0
1
1
1
2
1
0
1
1
1
0
1
1
0
0
1
1
2
1
1
0
1
2
0
0
2
2
1
1
0
2
1
1
1
0
1
0
1
1
2
1
1
0
0
1
0
1
0
2
1
1
2
0
0
1
0
0
0
2
1
1
0
1
1
2
1
1
0
0
2
2
1
1
0
0
0
0
0
3
2
2
1
1
1
2
1
0
1
0
1
1
0
0
1
1
0
1
1
1
1
1
2
1
0
0
2
2
2
1
0
1
1
0
2
1
1
1
2
1
1
1
0
0
0
0
2
1
0
0
0
1
1
1
1
2
2
0
1
2
1
1
0
2
1
2
0
2
0
1
1
0
1
2
0
2
0
0
1
0
0
1
0
1
0
1
1
2
2
0
0
1
1
0
0
0
1
0
1
1
1
1
0
1
1
2
0
2
0
0
1
0
2
1
0
2
2
0
1
3
1
2
1
2
1
0
0
1
1
1
0
1
1
0
0
1
1
1
1
1
0
0
1
0
0
2
2
1
1
0
1
0
0
2
1
0
1
0
2
0
2
1
2
2
1
0
2
1
0
1
0
1
1
0
1
1
3
0
0
1
2
2
1
1
0
1
0
2
1
0
0
1
0
0
0
0
1
1
1
1
1
0
2
2
0
2
1
2
0
0
1
1
0
0
2
1
1
0
0
2
1
1
1
3
0
0
1
0
1
2
2
0
1
1
1
1
0
3
0
1
2
0
1
1
0
1
0
1
1
0
1
1
1
0
0
1
0
1
2
1
1
1
4
2
1
1
0
2
2
0
1
0
1
1
0
3
0
1
0
0
0
0
1
0
0
0
1
1
2
1
1
1
1
0
0
1
1
0
1
1
2
2
2
0
1
2
1
1
2
0
1
1
1
1
1
1
1
1
1
1
1
2
1
2
1
0
0
2
1
2
1
0
2
1
1
1
2
1
0
1
0
1
0
2
1
2
0
1
1
0
1
0
0
2
2
0
2
2
0
0
0
0
1
1
1
2
2
0
0
1
0
0
1
1
0
2
0
2
1
1
0
2
1
2
0
1
2
0
1
1
2
1
1
0
0
1
0
1
0
1
1
2
1
2
1
0
0
1
1
1
2
2
0
1
2
1
0
0
1
1
2
1
0
1
1
1
1
0
1
2
4
0
0
0
1
0
1
1
0
0
1
1
0
0
2
1
2
1
1
0
0
1
0
2
1
2
0
1
1
0
0
1
0
1
0
0
1
0
1
3
0
1
2
0
1
1
0
1
1
0
1
0
2
1
1
1
0
0
2
1
0
0
1
0
0
1
1
0
1
0
1
0
1
1
1
0
2
0
2
1
2
1
2
0
1
0
0
2
0
2
1
1
0
2
1
1
1
2
2
0
1
1
2
0
0
0
1
1
1
0
1
1
0
1
2
3
0
0
0
1
0
2
3
1
0
2
1
1
1
1
0
1
1
0
3
0
1
1
1
1
0
1
2
2
0
2
0
0
0
0
1
0
2
0
1
1
1
1
0
1
1
1
1
0
3
1
0
1
1
1
1
0
0
1
1
1
1
0
1
1
1
0
1
1
0
1
0
0
0
0
1
1
0
0
2
0
0
0
3
1
1
1
0
1
0
0
1
1
0
1
0
2
1
0
0
1
0
2
1
1
0
0
1
0
3
1
1
3
2
0
1
1
1
0
0
1
0
2
0
1
0
1
1
0
2
0
0
0
1
1
1
1
1
2
1
1
0
1
1
2
0
0
0
0
0
1
2
1
0
0
1
2
3
0
1
0
1
0
0
0
0
1
1
2
1
1
0
1
0
1
1
1
0
0
0
2
1
0
3
1
1
0
0
0
1
0
0
2
1
1
1
1
1
1
0
0
1
2
1
1
2
0
1
1
0
0
1
1
0
1
0
0
2
0
0
0
1
0
1
2
0
0
1
2
1
2
2
1
1
2
1
0
1
1
0
0
0
1
0
0
2
0
1
3
1
1
1
0
1
1
1
1
0
0
1
1
0
1
2
0
1
2
2
0
0
1
1
0
2
1
1
1
2
1
0
0
1
0
0
0
1
2
1
1
1
1
0
1
2
0
1
0
0
1
3
1
2
1
0
1
0
0
0
0
0
0
1
2
0
1
0
2
1
1
1
2
0
1
0
0
0
0
1
0
1
2
1
1
2
0
2
3
0
0
1
2
1
0
0
1
2
1
0
1
1
2
1
2
0
2
2
1
0
0
2
0
0
0
0
2
0
1
2
1
0
2
0
0
1
1
2
0
2
1
0
1
2
0
0
0
1
1
1
2
2
0
0
1
1
2
2
2
0
0
1
1
2
0
2
1
1
0
1
1
3
1
0
1
0
0
1
2
1
0
1
0
1
1
0
1
1
0
1
2
1
1
1
0
1
0
2
0
1
0
1
1
1
2
1
0
1
1
0
2
1
0
1
1
1
1
1
2
3
2
1
1
0
1
1
0
1
1
0
0
1
1
0
3
2
1
1
0
0
1
0
0
0
0
0
0
0
1
1
0
1
1
2
1
1
0
0
1
1
2
0
0
2
0
1
3
0
0
2
0
1
0
1
0
1
1
2
0
0
1
1
2
0
1
0
0
1
2
0
0
1
0
0
0
1
0
0
1
2
1
1
1
1
1
2
3
0
0
1
0
0
0
1
2
0
1
1
0
0
1
1
1
2
0
0
2
2
2
1
1
0
0
2
1
1
2
1
0
2
1
0
0
2
0
0
1
2
2
0
0
1
1
2
0
1
1
0
2
1
1
1
1
0
0
0
0
2
2
1
0
0
0
2
0
1
2
0
0
0
1
1
1
1
1
1
1
1
1
0
1
1
1
0
1
0
0
1
1
1
1
1
1
1
0
2
0
0
1
0
1
2
2
0
0
1
0
0
1
0
0
0
1
0
2
0
1
0
1
1
2
3
1
1
2
2
1
0
2
3
1
1
2
0
2
1
1
0
0
1
0
2
2
0
0
2
1
2
2
1
0
2
1
0
1
1
1
1
1
1
0
1
0
0
0
0
1
0
0
0
1
1
1
1
0
1
2
0
1
1
1
1
2
0
1
1
1
2
2
0
1
1
1
2
2
1
1
1
0
0
0
0
1
1
2
1
0
2
0
0
2
1
1
2
2
1
1
4
0
2
1
1
2
1
0
1
0
0
2
0
0
1
2
0
0
1
1
2
1
3
2
1
2
0
2
1
1
1
2
2
0
1
0
1
2
1
1
2
1
1
2
0
1
1
0
0
1
1
1
1
1
0
0
3
0
0
0
1
0
1
0
0
0
0
2
2
2
0
1
0
1
2
1
0
1
0
0
1
2
2
1
1
1
0
0
1
0
1
0
0
1
1
0
1
0
2
1
1
1
0
1
2
0
0
1
2
1
2
1
0
1
1
0
0
1
1
1
2
2
1
1
2
2
2
0
1
1
1
2
1
0
0
1
2
0
1
1
0
0
0
2
1
1
1
1
0
2
0
1
0
1
0
2
0
0
1
1
1
3
1
2
1
1
0
0
0
1
1
1
1
0
1
1
1
1
1
0
1
1
0
0
0
0
1
0
2
0
1
1
1
0
1
0
0
1
0
2
0
0
1
0
1
1
1
2
0
0
1
1
1
1
1
1
1
1
2
1
1
0
2
0
1
0
0
1
1
1
1
0
1
2
1
0
1
0
1
1
1
0
1
0
2
0
0
5
2
1
0
0
1
0
2
0
1
1
2
2
1
1
1
2
0
0
0
1
0
0
0
2
0
1
0
2
1
2
0
1
1
0
2
1
1
1
1
1
3
0
0
1
0
1
0
2
1
0
2
2
1
0
1
1
0
0
0
3
1
1
0
2
1
0
0
0
2
1
0
2
1
2
2
2
1
2
0
1
0
1
2
2
0
2
1
0
1
0
1
2
0
0
0
0
1
2
1
2
1
1
0
1
0
1
0
1
1
0
0
1
0
2
2
2
1
2
2
1
1
0
1
1
1
0
0
0
0
0
1
1
1
0
1
1
0
1
1
2
1
1
2
1
1
2
0
0
1
2
2
0
1
0
2
0
1
1
0
2
1
1
0
2
1
1
2
2
0
2
1
1
1
1
1
0
1
1
2
1
0
0
2
0
0
0
1
0
1
2
0
1
0
0
2
0
1
1
1
1
1
0
0
2
2
1
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
2
0
3
0
2
1
1
0
0
1
1
0
1
0
1
1
1
1
2
0
1
0
3
2
1
0
0
0
0
2
1
0
1
0
2
0
0
0
1
1
1
1
2
2
1
1
0
1
0
0
1
2
1
1
1
0
3
0
1
0
1
0
0
1
2
2
1
0
1
0
2
1
1
1
0
1
0
3
0
2
1
0
1
0
1
0
0
0
0
1
1
1
2
0
2
0
0
1
0
1
1
1
2
2
1
1
1
0
0
3
2
0
2
2
1
1
1
1
0
0
1
1
0
2
0
1
0
1
1
0
0
0
1
2
1
1
1
1
2
0
2
1
1
0
2
0
0
0
2
1
0
1
0
0
0
0
0
0
2
1
0
1
2
0
0
0
1
1
1
2
1
1
0
1
0
1
0
0
1
2
0
1
1
0
2
1
1
0
0
1
2
0
2
2
0
0
0
1
1
1
1
0
1
2
1
1
1
0
1
0
0
1
2
0
0
1
1
0
2
1
0
0
1
1
1
0
1
0
2
1
0
0
0
0
0
2
1
1
1
1
2
0
2
0
1
1
0
1
1
0
1
2
1
0
1
2
2
1
1
1
0
1
0
0
2
2
1
1
0
0
0
0
2
0
2
0
1
0
2
1
2
1
0
1
0
0
1
0
0
0
0
0
1
2
0
1
1
2
0
1
0
2
1
1
2
3
1
0
1
2
1
0
1
3
2
0
1
0
1
0
1
2
1
0
0
1
2
2
2
1
1
0
0
1
0
1
2
1
2
0
2
0
1
1
1
0
2
0
0
1
2
0
0
1
1
2
0
0
2
2
1
1
0
1
1
0
0
0
0
1
0
5
0
1
0
0
1
1
1
0
2
0
0
1
0
1
1
0
0
1
0
0
0
1
1
0
1
1
2
1
0
1
1
2
2
0
1
0
0
1
1
1
1
1
0
0
0
0
1
1
1
5
1
2
0
1
1
1
1
1
2
0
1
1
0
0
1
1
0
0
0
1
0
0
1
0
0
2
0
2
1
0
0
0
3
2
0
1
0
1
1
1
2
3
2
1
2
0
1
1
0
2
0
1
2
5
1
0
1
2
1
0
1
1
0
0
0
2
2
1
0
0
2
1
2
2
2
1
0
0
1
1
0
1
0
1
0
0
1
1
0
2
0
2
2
0
2
1
1
2
2
1
2
0
2
2
3
1
0
0
1
2
0
0
1
1
0
1
1
1
1
1
0
1
1
1
1
1
0
0
0
0
0
2
1
1
1
0
1
1
1
0
2
2
0
1
1
0
1
1
0
1
1
1
2
1
0
0
0
1
0
0
0
0
1
0
0
0
2
2
1
2
2
2
1
1
0
0
2
1
2
1
1
1
1
1
1
1
2
0
1
1
0
0
0
0
0
1
1
0
1
1
0
0
1
1
1
0
1
2
0
1
0
0
2
0
0
0
0
1
2
1
0
1
1
0
2
2
0
2
3
0
1
1
1
1
1
0
1
0
0
1
1
2
0
0
0
0
1
0
1
1
1
2
0
1
0
1
0
1
1
0
1
1
0
0
0
1
1
2
2
1
0
3
0
0
0
0
2
2
1
1
1
0
1
1
0
1
0
0
2
0
0
0
1
2
1
0
2
2
2
1
2
1
0
1
2
1
0
1
1
2
0
1
0
2
1
2
0
0
0
1
0
1
2
0
1
2
1
0
1
0
1
2
3
2
1
0
0
1
0
0
0
1
0
1
0
1
0
0
0
2
0
0
2
1
0
0
0
2
0
1
2
1
2
0
0
1
0
2
1
0
2
2
1
1
2
2
1
1
1
1
1
1
1
1
0
0
0
0
1
2
1
1
1
1
0
0
2
2
1
0
0
2
0
1
0
1
0
2
0
2
2
0
2
3
2
0
1
1
0
0
2
2
2
0
1
1
2
1
2
2
2
1
0
1
1
1
0
1
0
2
0
0
1
0
0
1
1
2
0
1
0
1
1
1
1
0
1
0
1
1
2
2
1
2
0
2
1
0
0
2
0
0
0
2
0
0
0
1
0
1
2
0
1
1
0
4
1
1
1
2
0
1
1
2
1
1
0
1
1
1
1
2
2
0
0
0
0
2
0
0
2
2
0
1
2
0
0
0
0
1
1
1
1
0
0
1
2
1
1
1
2
3
2
0
1
1
1
1
2
1
1
2
2
1
1
1
1
1
0
1
0
1
1
0
1
0
1
0
1
0
1
0
0
0
0
2
0
0
2
0
2
3
2
2
1
2
0
0
0
0
2
0
2
0
0
1
0
0
1
1
1
0
0
1
1
0
0
0
0
0
0
1
2
2
1
1
0
1
0
2
2
0
0
0
1
0
0
1
1
0
2
1
0
0
0
1
1
1
0
0
0
0
1
0
1
2
0
1
0
1
1
1
1
1
0
0
1
0
2
0
0
0
1
1
1
1
0
2
0
1
0
0
1
1
1
2
2
2
1
1
0
1
2
2
1
0
0
1
1
1
0
0
1
2
1
0
1
0
2
1
0
1
2
1
0
1
1
1
2
2
1
1
0
1
1
1
0
1
2
1
0
2
1
1
1
0
1
0
0
1
0
0
1
2
2
0
1
0
2
0
1
1
0
1
1
3
1
1
1
0
2
1
2
0
1
0
0
1
1
0
0
2
1
2
2
0
1
0
0
2
0
1
1
1
2
0
1
0
3
1
0
2
2
0
2
0
2
0
2
1
2
0
0
1
0
0
2
1
0
1
0
0
0
0
2
0
1
2
1
1
0
2
1
1
2
1
2
0
1
0
1
1
1
1
2
1
1
1
2
2
0
1
0
1
1
1
1
0
1
1
1
1
2
0
1
0
2
0
0
3
1
1
1
1
0
0
0
1
0
1
1
3
2
1
2
0
2
2
1
1
0
2
0
0
0
1
0
0
1
2
0
1
1
1
0
2
2
0
1
0
1
1
1
1
1
1
0
0
2
3
1
1
0
0
1
1
2
1
0
0
0
1
1
1
0
2
2
1
2
1
0
2
0
1
1
1
0
1
1
1
1
2
2
0
1
1
1
0
1
0
3
1
1
1
2
1
1
0
1
2
2
0
0
0
1
2
1
1
0
2
2
1
1
0
1
1
0
1
0
0
1
2
0
0
1
2
0
2
1
0
2
0
0
1
1
0
1
1
2
0
0
0
1
0
1
0
0
1
1
2
1
1
0
1
2
1
1
2
0
0
1
1
2
0
1
1
1
0
2
0
1
0
2
2
1
0
1
0
1
0
0
0
0
0
2
0
0
1
1
1
0
2
0
1
0
2
2
1
1
1
0
1
0
1
1
1
4
2
0
2
0
2
2
2
1
0
0
1
1
0
2
1
0
0
2
0
0
2
0
1
1
1
1
0
2
1
0
1
0
1
1
1
0
0
0
1
0
2
0
2
1
1
2
0
1
2
2
0
1
1
0
2
0
1
0
1
0
1
0
1
0
0
0
2
0
2
2
2
2
2
1
0
1
1
1
2
1
0
0
2
0
2
2
2
2
1
2
1
1
1
1
1
2
1
0
2
1
2
1
3
1
1
0
0
0
1
0
2
1
1
1
3
1
1
1
0
2
1
1
2
2
1
2
1
0
2
1
0
1
2
1
0
0
1
2
2
0
1
1
0
0
1
0
1
2
0
0
1
1
1
2
1
0
0
2
0
0
1
0
2
1
0
0
0
1
2
0
0
1
0
0
0
1
1
1
1
2
0
0
1
1
1
1
0
0
2
1
0
1
1
1
1
1
2
0
1
0
2
2
0
1
0
1
0
1
1
1
1
1
1
0
0
1
1
0
0
2
1
0
2
0
6
1
1
1
2
1
1
0
0
2
2
3
0
0
1
0
2
1
1
2
2
1
2
0
1
1
2
0
1
1
1
1
1
1
1
1
0
0
1
0
1
1
0
2
2
0
0
2
0
2
1
0
1
1
1
1
0
0
2
1
1
2
0
2
0
0
2
1
1
1
0
0
2
0
2
1
2
2
1
2
2
2
0
2
2
1
0
0
1
2
3
1
1
3
1
1
1
0
2
2
1
1
1
2
2
2
1
0
0
1
0
1
1
0
1
0
1
2
2
1
0
0
2
2
1
1
4
1
1
1
0
0
0
1
1
0
2
1
1
2
1
2
0
2
1
0
1
1
2
6
2
2
2
1
0
0
1
2
2
0
2
0
1
0
0
2
1
0
1
0
2
0
1
1
1
2
3
2
2
2
0
1
2
1
2
0
1
0
0
0
1
1
0
0
1
1
0
0
1
1
1
1
1
1
1
1
1
1
0
0
2
0
1
0
1
0
2
1
1
0
1
2
1
0
2
0
0
1
2
2
2
2
0
0
1
0
1
2
1
0
1
0
0
1
1
0
0
2
1
1
1
0
1
2
1
1
0
0
2
0
0
1
2
2
2
0
1
0
1
3
1
1
3
2
1
0
1
0
1
1
1
1
0
1
2
1
0
1
2
1
1
1
1
0
1
1
1
0
1
0
1
2
2
0
1
1
0
1
2
1
1
0
2
2
1
0
0
0
2
0
0
1
0
1
1
1
0
2
1
0
2
0
0
1
0
1
2
0
1
1
1
0
1
2
1
2
2
1
0
1
0
1
0
0
2
1
2
0
2
0
1
0
1
0
1
0
1
1
0
0
1
0
2
0
0
2
1
3
0
0
1
1
2
0
1
1
1
1
1
0
1
3
1
1
0
1
1
1
0
2
1
0
0
1
1
0
0
1
1
3
2
2
1
1
0
2
1
1
0
2
0
1
2
0
0
1
1
1
1
0
2
0
0
2
1
1
1
1
0
0
0
1
2
0
1
1
0
1
0
1
2
2
1
0
1
1
2
0
0
0
2
0
0
1
1
0
2
1
1
2
0
2
1
0
0
1
2
1
1
1
2
1
1
0
0
2
1
0
0
1
1
2
0
0
0
0
1
1
0
1
1
1
0
1
0
1
0
2
1
0
1
1
2
1
0
0
1
1
1
0
0
0
1
1
0
0
0
2
0
0
1
0
2
1
1
0
1
2
2
0
0
1
1
1
0
2
2
2
0
2
1
1
1
1
1
1
1
0
2
1
0
1
0
1
0
1
1
2
1
1
0
0
1
2
2
2
0
0
1
0
2
2
2
0
1
1
1
0
0
0
0
2
2
2
0
2
0
1
0
2
1
1
0
1
2
0
0
1
1
2
0
1
1
1
0
2
1
0
2
0
0
1
1
0
1
0
2
0
1
1
2
1
0
1
0
0
0
1
1
2
1
2
0
1
1
1
2
1
1
0
1
1
0
1
0
2
3
1
1
1
2
1
1
1
2
1
1
1
1
0
1
1
1
1
1
1
1
0
1
2
1
1
2
1
2
1
0
2
1
1
1
0
2
1
0
1
1
0
3
1
0
2
0
1
1
1
1
0
1
0
2
2
0
1
1
0
2
0
2
3
0
2
1
0
0
0
2
0
2
0
1
1
0
2
0
2
1
1
0
2
1
0
2
1
0
1
1
1
0
2
1
1
1
1
1
1
1
0
1
0
1
1
0
0
0
1
1
0
1
0
0
1
2
1
0
1
1
2
1
0
1
1
2
0
1
1
1
1
2
1
2
2
0
1
1
1
0
0
2
1
1
0
0
0
1
0
1
2
2
1
2
2
0
2
0
2
1
0
1
0
0
1
0
2
2
1
2
1
2
1
1
0
2
1
0
1
1
1
0
1
0
2
1
1
1
0
1
0
1
2
1
1
2
2
0
1
1
0
2
1
1
0
1
1
2
1
2
1
1
1
1
1
1
1
1
1
2
1
1
0
0
2
2
1
0
0
1
0
0
1
0
1
0
1
1
1
1
2
0
2
0
2
0
0
1
1
0
1
1
0
1
1
1
2
0
2
0
1
0
1
0
0
2
1
1
2
1
1
3
2
0
1
0
1
2
1
1
1
1
0
1
1
2
0
1
2
0
1
0
0
2
1
1
2
2
1
2
1
0
1
1
1
1
0
0
1
1
0
2
2
2
1
1
1
1
0
0
1
1
0
1
1
1
2
0
0
0
1
1
0
2
1
1
2
1
2
1
0
2
0
0
0
1
0
1
0
2
0
2
1
2
2
0
0
2
0
0
2
0
0
1
0
0
3
1
2
0
1
0
2
1
4
0
1
1
0
1
0
0
1
1
2
2
0
0
2
0
0
0
1
1
1
1
1
1
1
1
2
2
1
1
0
1
2
0
1
0
1
1
1
0
0
1
2
2
0
2
2
3
0
2
2
1
1
1
1
1
0
1
0
1
1
0
2
1
1
1
0
0
0
1
1
2
1
1
1
0
0
2
2
2
1
0
1
0
1
2
0
2
1
0
1
0
2
0
1
0
1
0
1
1
1
1
0
1
1
2
0
2
2
1
0
1
0
1
0
1
0
1
1
1
0
2
0
0
1
1
0
0
0
0
1
0
2
0
0
3
2
0
0
2
0
1
2
1
0
0
2
2
0
1
2
2
2
1
1
0
0
1
0
1
1
0
1
0
2
1
1
1
3
0
2
1
0
1
1
0
1
0
0
0
1
1
2
1
0
0
2
0
1
2
2
1
0
0
0
0
1
0
1
1
1
2
1
1
2
0
0
2
1
1
0
1
1
2
3
3
2
1
0
2
1
1
2
1
1
1
2
2
1
1
2
1
0
1
1
0
2
2
2
1
1
0
0
0
3
0
0
0
0
2
2
0
0
2
0
2
0
0
3
1
0
0
0
2
2
2
1
3
0
2
1
1
0
1
1
1
2
1
0
1
0
1
0
1
0
1
1
1
2
1
1
0
0
2
1
1
0
0
1
0
2
0
0
0
0
2
1
3
1
1
0
0
0
0
2
2
1
0
1
2
1
1
1
1
0
0
1
0
1
2
0
0
2
0
0
1
5
1
1
2
1
1
0
0
1
1
1
1
2
0
2
0
0
2
0
0
1
1
1
1
2
0
1
1
1
0
2
2
1
0
1
0
0
0
0
1
1
1
1
2
1
0
0
1
2
0
0
2
1
2
1
0
1
0
1
1
0
1
0
0
1
1
1
1
0
1
3
1
1
1
2
0
0
1
0
2
1
1
2
1
0
2
0
2
0
2
0
1
1
0
0
0
0
1
2
0
2
2
2
0
2
1
1
1
0
0
0
1
1
0
1
1
1
0
0
0
1
1
2
1
0
1
2
1
2
1
0
0
0
0
1
2
1
2
0
2
0
1
0
1
1
2
1
0
4
2
0
1
1
2
1
1
0
2
1
0
2
2
2
2
1
1
1
0
3
2
0
0
1
0
0
1
1
1
2
0
0
1
0
2
0
3
0
2
1
1
0
1
0
1
2
2
0
1
0
2
1
0
2
1
1
1
1
1
2
0
0
1
0
2
0
1
0
0
0
1
1
0
0
1
0
4
0
2
1
0
1
2
0
1
0
1
1
2
2
0
2
1
1
0
1
2
1
0
1
1
2
1
1
0
1
0
0
1
2
2
0
1
0
0
1
0
1
1
2
0
1
0
0
1
1
0
0
1
0
1
3
0
1
0
0
1
3
1
1
1
2
0
1
0
0
1
0
0
0
2
1
0
1
1
1
1
0
2
0
0
1
1
1
1
1
1
0
1
1
2
0
2
2
0
2
1
1
0
2
1
2
1
0
0
0
0
0
1
1
1
1
1
1
0
0
2
2
0
1
1
1
1
1
2
0
0
2
1
1
2
0
1
0
1
0
1
1
1
2
0
2
1
1
1
0
1
1
0
2
3
3
0
2
1
1
2
1
0
1
0
0
2
1
2
1
0
0
1
0
0
2
1
2
2
0
0
2
2
0
2
1
1
1
0
2
2
1
1
1
0
0
0
1
1
1
1
1
1
1
2
0
1
0
1
1
0
0
0
3
1
1
1
0
1
1
1
0
2
0
1
1
0
2
1
1
0
0
1
1
1
1
1
1
1
2
0
1
1
1
0
1
0
1
2
1
0
1
0
1
0
1
2
0
0
1
0
0
2
0
1
0
2
1
0
2
0
1
0
1
1
0
0
1
1
0
0
1
0
2
1
0
0
0
1
1
1
1
2
0
1
0
1
0
1
0
0
2
1
0
1
0
2
1
3
0
1
1
0
1
1
1
1
2
0
0
2
1
0
2
0
2
1
0
0
1
1
0
0
1
1
1
1
1
1
1
2
0
1
1
2
1
0
0
1
0
0
0
2
0
1
1
2
2
0
0
1
1
2
2
2
1
2
0
0
1
0
1
1
1
0
2
1
1
0
1
2
0
0
0
2
1
1
1
0
1
1
3
1
0
1
0
3
0
0
2
0
0
0
1
1
1
1
2
0
2
0
0
2
1
0
1
1
0
2
2
1
2
2
1
2
1
1
0
1
1
1
2
2
2
2
1
0
1
1
0
1
2
0
0
0
4
1
0
0
1
1
0
1
0
0
1
2
2
1
1
2
1
1
1
1
4
1
0
2
0
2
0
3
1
1
0
1
0
1
2
2
0
2
0
2
2
1
1
1
1
0
0
2
1
1
0
1
1
0
1
1
2
1
0
1
1
2
1
1
0
1
5
1
0
0
1
0
0
2
0
0
2
1
0
1
0
0
1
1
1
2
2
1
0
2
1
1
1
0
0
1
2
2
1
1
1
0
1
1
0
0
0
1
0
0
1
1
0
1
2
2
0
1
0
1
0
0
1
1
0
2
1
0
1
2
1
2
2
0
1
2
1
1
1
0
0
2
0
1
0
1
1
2
2
0
0
2
2
0
0
1
1
1
1
0
2
2
0
2
0
0
1
1
0
0
2
2
0
2
1
1
1
1
0
2
0
0
1
1
0
1
0
2
1
1
2
1
2
0
0
1
1
0
0
0
1
0
1
0
0
0
2
3
1
1
1
1
1
0
0
3
0
1
2
0
0
2
0
2
0
0
1
1
1
0
1
2
2
1
2
0
1
2
0
0
1
0
0
0
1
1
1
1
2
2
1
2
1
0
0
1
0
1
1
7
1
0
0
0
2
0
1
0
1
2
0
1
1
1
1
1
3
0
2
2
0
0
1
1
2
2
0
0
1
1
1
0
0
1
1
1
1
1
0
0
0
1
0
1
0
1
2
1
0
0
0
0
2
1
1
1
0
2
0
1
1
0
2
2
1
0
1
1
1
1
0
2
1
1
0
2
1
0
0
2
1
1
0
1
2
0
1
2
1
2
1
1
0
0
1
0
2
2
0
1
0
2
0
1
1
0
0
2
0
1
1
0
0
0
2
1
1
0
1
2
1
3
1
0
1
2
1
1
1
0
0
0
2
1
1
1
0
0
0
2
1
2
1
1
1
0
0
0
1
2
0
1
3
1
0
1
1
1
0
2
1
2
1
2
0
1
2
1
1
1
0
1
1
1
0
2
0
1
0
1
1
0
0
2
1
1
1
0
2
0
0
2
0
0
0
0
0
2
0
0
1
2
0
0
2
1
1
0
0
1
1
2
0
1
0
0
0
0
0
1
0
0
1
2
0
1
0
1
0
0
0
0
0
0
1
2
0
1
0
2
0
0
2
2
0
2
1
2
2
2
0
1
0
2
0
0
1
0
0
1
0
3
1
2
0
1
0
2
1
2
0
1
2
0
0
1
1
0
1
1
1
1
1
2
0
1
0
0
0
2
1
0
0
0
3
1
2
0
2
0
0
0
1
1
0
2
2
0
2
0
1
2
1
0
0
0
0
2
1
1
0
0
1
1
1
0
1
0
2
2
1
0
1
0
1
2
0
0
0
1
0
3
0
0
2
1
0
2
1
1
2
1
1
0
1
0
0
0
0
0
1
1
2
0
2
0
1
2
1
0
0
2
0
0
0
0
0
2
0
0
1
0
2
1
0
0
1
0
1
0
1
2
1
1
1
2
1
0
2
0
0
0
1
0
1
1
0
1
2
0
2
0
1
2
1
1
0
0
2
0
0
1
0
1
1
2
2
3
0
0
0
1
0
0
1
0
1
2
1
1
2
2
1
1
0
2
1
2
0
0
1
0
2
1
1
1
1
1
0
0
0
2
1
1
0
0
2
0
2
1
0
1
0
2
1
2
1
0
2
1
1
2
1
2
2
0
2
1
1
0
1
2
1
0
1
0
0
0
0
2
1
1
0
2
3
0
3
0
1
0
1
1
0
1
0
1
0
2
1
1
0
0
1
1
0
0
1
0
0
2
0
2
0
0
1
0
1
1
1
0
1
1
2
1
0
0
0
0
1
0
2
1
0
0
2
2
0
0
1
1
1
0
0
2
1
0
1
1
1
1
1
2
0
1
1
1
0
5
1
1
2
2
1
2
0
1
0
1
0
0
1
1
1
1
1
1
0
1
1
0
2
2
0
1
1
1
1
1
2
0
2
1
1
1
0
0
1
0
2
2
1
1
2
1
1
0
1
1
1
0
0
1
0
1
1
0
1
0
0
2
0
2
0
1
1
1
0
0
1
1
1
0
1
0
1
0
1
4
1
0
0
2
1
0
0
2
1
1
1
2
1
0
0
1
1
1
0
1
1
1
4
0
3
1
1
1
1
1
1
1
0
2
1
2
1
2
1
1
0
2
0
0
1
0
0
1
1
2
1
1
0
1
0
2
0
1
2
3
1
1
2
1
2
1
1
2
3
0
2
0
2
0
1
0
1
2
1
0
0
1
0
3
1
0
2
1
2
3
1
0
2
8
2
1
2
1
2
2
2
0
2
0
2
1
1
2
0
1
0
1
1
0
0
2
0
2
1
0
1
1
2
1
1
1
2
0
2
1
0
0
1
1
0
1
2
1
0
0
2
1
2
1
0
1
1
2
1
2
0
1
1
0
0
1
0
0
1
0
2
0
0
1
0
1
0
1
1
0
1
0
0
0
1
1
2
0
0
2
0
0
0
1
0
2
1
0
1
0
1
2
0
2
1
1
0
0
1
1
0
0
0
1
1
2
0
0
1
1
2
0
1
1
0
1
1
1
0
2
2
2
1
0
0
2
1
0
1
2
0
2
2
1
1
1
2
0
1
0
1
2
2
0
2
1
1
2
1
1
1
2
2
1
1
1
0
0
0
1
1
0
0
0
0
0
0
3
1
2
2
1
1
1
1
0
0
0
0
0
0
1
2
1
1
3
8
2
1
1
2
0
0
6
1
2
1
0
1
2
1
1
1
0
1
0
1
3
0
1
0
1
1
1
2
1
1
2
0
0
0
2
1
2
1
1
1
0
0
2
2
1
1
0
1
1
1
2
1
0
0
1
1
1
0
0
1
0
1
0
0
0
1
2
0
2
0
0
3
2
2
2
1
2
0
0
0
0
1
1
1
0
1
1
2
1
0
0
0
0
1
0
1
0
2
1
0
1
1
1
0
0
1
0
1
0
1
0
0
1
3
0
1
1
0
0
0
0
0
1
2
1
0
0
0
1
1
1
1
2
2
0
1
0
1
1
0
2
1
0
0
0
0
0
1
2
1
2
1
1
0
0
0
0
1
1
0
0
0
1
2
0
1
1
1
1
2
1
0
0
1
0
1
1
0
1
2
1
1
0
2
1
1
1
2
2
2
0
0
0
1
1
0
0
1
1
0
1
0
0
1
2
0
2
1
1
0
0
0
2
0
0
0
0
1
2
1
1
0
2
1
1
0
2
0
0
1
1
0
1
1
2
0
0
0
2
2
0
1
0
1
1
1
1
0
0
1
0
2
0
0
1
2
1
1
1
1
1
0
1
1
1
0
1
0
2
1
1
2
1
2
0
1
0
2
1
0
1
1
0
1
1
1
1
1
1
2
2
2
0
2
0
2
2
1
1
0
0
0
1
1
1
1
0
2
1
0
1
2
1
1
2
2
0
1
1
2
1
2
2
1
2
0
0
0
1
1
2
0
0
1
1
2
0
1
0
1
0
2
1
2
0
0
2
0
0
1
0
1
2
0
1
1
1
0
1
2
1
0
0
0
0
0
1
1
1
0
1
2
1
2
1
0
1
0
0
1
2
1
1
1
2
1
1
0
1
2
0
0
2
2
1
1
1
1
1
1
1
0
0
0
2
0
3
0
2
0
2
1
1
1
1
1
0
1
0
0
2
1
1
2
0
1
0
0
1
1
2
1
1
0
0
3
1
0
2
0
1
1
1
0
1
0
1
2
1
1
2
0
1
1
0
0
1
0
1
0
0
2
1
2
2
1
1
1
0
1
1
0
0
0
2
1
1
0
0
2
3
1
2
2
1
1
0
1
1
1
2
1
0
0
1
1
1
2
1
0
1
1
0
0
1
1
2
0
1
0
0
1
1
0
2
2
4
1
1
1
1
0
0
0
2
2
2
1
0
1
1
0
0
0
0
2
1
0
2
2
1
0
0
1
1
1
0
1
1
1
1
1
1
1
1
1
1
0
1
0
0
1
2
0
2
2
0
2
2
1
0
1
2
0
0
0
2
0
1
2
0
0
0
2
0
1
0
1
1
1
1
0
1
2
1
1
1
2
0
1
1
0
1
1
0
1
2
1
1
0
1
1
1
0
0
1
1
1
0
1
0
1
1
0
1
2
2
2
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
2
0
1
1
1
0
0
0
0
0
1
2
4
2
0
1
1
1
1
2
1
1
0
2
1
1
2
2
1
0
0
2
2
1
4
2
0
1
0
0
1
2
1
0
0
1
2
0
1
2
1
1
1
0
2
1
2
1
0
0
1
0
0
1
1
1
0
1
2
2
1
0
0
0
2
2
1
2
0
1
2
2
2
1
2
2
2
0
0
0
1
0
1
0
1
2
0
0
2
2
0
5
2
0
2
0
2
0
2
1
1
2
0
1
0
0
1
2
0
1
2
2
0
2
1
1
0
0
0
0
1
0
1
0
1
0
1
0
1
1
2
0
2
0
0
1
1
2
0
0
2
0
1
1
2
0
0
1
1
2
1
0
0
0
1
1
1
1
1
0
0
0
2
1
1
2
0
0
0
1
2
0
0
0
1
0
0
2
1
1
2
0
0
0
2
1
0
1
2
0
0
1
0
0
1
2
1
1
0
1
2
4
0
2
1
0
0
0
2
0
1
1
0
1
1
1
0
1
2
0
2
1
1
0
1
1
0
0
1
1
0
1
1
2
2
1
0
0
0
1
1
1
0
0
2
1
2
1
1
2
0
0
0
0
0
0
2
1
0
2
1
2
1
1
2
1
2
0
2
0
0
1
0
1
0
1
0
1
1
1
1
2
1
1
2
2
1
1
1
1
2
2
1
0
1
1
2
2
2
0
2
1
0
3
0
1
2
1
1
1
0
1
0
0
1
1
0
0
1
2
1
0
0
2
0
0
2
1
2
1
0
2
0
1
2
0
0
1
0
1
2
0
1
1
0
0
2
2
0
2
0
0
0
2
2
1
0
2
0
0
0
1
0
2
0
0
2
1
2
0
1
1
0
0
2
0
1
2
0
0
1
2
0
0
1
2
1
1
2
0
1
2
2
1
0
1
0
1
1
1
0
2
0
0
1
2
1
1
1
1
1
0
1
0
1
0
2
0
1
1
1
0
1
0
0
0
1
2
2
2
1
0
0
0
1
1
1
2
0
1
2
0
0
1
0
2
0
1
0
0
0
1
0
2
2
0
0
2
2
1
0
0
1
1
0
1
0
0
0
1
2
1
0
0
1
1
2
1
1
0
1
0
1
0
2
0
0
0
1
1
0
0
1
0
1
2
1
0
0
1
1
0
0
1
3
1
1
0
0
2
1
0
0
1
2
1
0
1
1
0
1
2
1
1
2
0
1
0
0
1
0
0
0
1
1
1
2
1
2
2
0
1
1
2
2
0
0
0
0
0
2
2
1
2
1
0
1
1
1
0
0
2
2
0
0
0
1
1
0
1
4
0
2
2
1
1
0
2
0
0
2
1
0
0
1
1
1
2
0
0
3
1
1
0
1
2
2
0
2
1
1
0
1
2
0
1
1
0
1
1
0
0
1
1
1
0
0
0
1
0
0
0
1
1
1
0
2
0
0
0
1
0
1
0
1
1
1
1
2
1
0
1
2
1
0
0
0
2
0
0
0
1
0
0
2
1
1
1
0
2
0
0
1
1
2
0
0
0
1
1
0
1
1
0
2
1
1
0
2
1
1
0
2
0
1
0
0
1
0
1
1
1
1
1
0
1
1
1
1
2
0
1
1
0
0
0
0
0
1
1
1
1
0
1
0
0
1
0
1
0
1
1
0
1
0
1
0
0
2
0
1
0
1
2
1
1
2
0
1
0
0
1
0
1
3
2
1
1
0
1
2
3
1
2
2
1
1
1
2
1
0
1
0
0
0
2
2
0
2
3
0
0
0
1
2
1
2
1
2
0
0
0
2
1
2
1
1
1
0
0
0
0
0
0
1
0
1
1
2
1
0
0
1
1
1
1
0
1
0
1
0
0
0
0
1
2
0
1
2
1
0
0
2
0
0
0
2
1
0
0
2
2
2
0
1
1
2
1
1
2
0
1
1
1
0
0
0
1
0
1
0
1
0
2
2
2
2
1
2
0
1
0
1
2
1
2
0
1
0
2
0
0
0
1
0
1
1
1
1
1
2
0
0
0
1
1
1
1
0
1
1
1
0
2
1
0
0
1
1
0
1
0
0
1
0
1
3
1
1
2
0
0
2
1
2
1
2
0
2
0
0
1
1
1
2
2
2
0
1
0
0
1
2
3
0
0
1
0
2
0
0
0
1
1
2
1
0
0
1
1
2
0
2
2
0
1
2
1
0
2
2
1
0
1
0
2
0
1
0
3
2
0
1
1
2
1
0
0
2
1
1
1
0
0
1
1
2
0
0
1
1
0
1
1
0
0
0
1
2
0
1
1
1
1
0
1
0
1
1
2
1
0
4
2
2
1
0
1
3
2
0
1
1
2
2
0
1
1
2
2
1
0
0
0
1
1
2
1
0
0
2
0
0
2
0
0
1
1
0
1
0
1
1
1
1
0
1
0
2
0
2
0
0
1
0
1
2
0
1
1
1
1
3
1
0
1
1
1
0
0
0
1
0
0
0
0
2
0
0
2
1
2
0
2
0
2
1
1
1
1
1
2
1
0
1
1
2
0
0
0
0
2
2
1
0
2
0
1
0
2
1
0
1
2
1
2
1
0
1
2
0
1
2
2
2
1
1
2
1
2
1
0
1
1
0
0
2
1
0
0
0
2
0
2
1
1
0
1
0
0
2
1
2
0
1
0
0
1
1
2
3
1
1
2
2
1
1
1
0
1
1
0
2
1
0
2
1
0
0
1
1
0
0
0
1
1
2
1
0
0
0
0
1
0
0
0
1
1
0
1
1
0
2
1
0
1
2
3
2
1
3
2
2
2
1
0
1
2
2
0
1
1
1
0
0
1
0
2
1
1
1
1
2
1
0
1
0
1
1
2
0
0
1
1
0
2
1
0
1
1
0
1
0
2
0
2
0
1
1
1
1
0
0
1
2
0
1
1
0
1
0
2
2
2
1
2
0
2
0
1
2
0
0
2
2
0
1
1
2
0
0
2
0
2
2
2
0
2
1
1
0
1
1
2
1
2
1
2
0
1
0
2
2
1
1
0
1
2
1
0
1
0
0
0
0
2
1
0
1
1
1
0
0
1
0
1
0
1
2
1
2
1
1
1
2
0
1
1
0
0
0
1
2
0
1
2
1
2
0
1
2
0
1
0
0
1
1
0
1
1
2
2
0
1
1
1
1
0
0
1
1
0
1
0
0
2
0
0
2
1
1
1
0
1
1
0
0
2
1
0
2
1
0
1
2
0
0
0
1
2
1
1
0
2
1
0
1
0
2
0
0
1
1
0
1
0
1
0
1
2
0
0
3
1
1
1
1
0
1
0
0
1
1
2
0
0
0
0
1
1
1
1
2
1
1
2
2
1
2
1
0
0
1
0
2
1
1
1
1
2
1
1
0
2
0
0
0
0
0
1
1
0
2
2
2
1
2
1
1
0
1
0
0
2
0
2
0
0
2
1
2
1
1
1
1
0
1
1
2
1
1
1
1
2
0
1
0
1
0
1
0
1
0
1
1
0
0
0
0
0
1
3
1
0
1
0
1
0
1
1
2
1
0
1
0
0
2
1
2
1
0
1
2
0
0
1
1
1
0
1
0
0
1
1
0
2
0
1
2
8
1
2
0
0
2
0
2
0
5
0
1
2
0
1
0
0
1
0
1
0
0
1
2
2
2
0
1
0
1
0
2
2
0
2
0
0
0
1
2
0
1
0
1
2
1
1
1
1
1
0
0
1
2
2
1
0
0
1
2
2
2
0
1
1
1
2
1
1
2
1
0
2
0
0
0
0
0
2
1
1
1
1
1
0
0
2
1
1
0
1
0
1
1
1
0
0
2
0
1
1
1
0
0
0
0
0
2
1
2
1
1
2
0
2
5
0
0
1
0
0
1
1
1
1
4
1
1
1
0
2
0
1
0
0
2
1
1
0
0
1
0
0
0
1
1
2
0
0
0
2
0
2
0
1
2
2
2
1
0
0
0
1
0
2
1
1
1
1
3
0
4
2
1
1
2
0
1
2
2
0
2
1
1
0
0
0
0
1
0
0
0
2
2
1
2
0
1
0
2
1
0
0
0
2
1
1
2
0
0
2
0
2
1
0
0
0
2
0
2
0
1
1
0
1
0
1
0
1
2
0
2
0
2
0
0
2
0
0
2
0
1
1
0
2
1
1
2
2
1
0
0
1
1
2
0
1
1
0
1
1
1
0
0
1
2
2
1
1
2
1
1
2
2
4
1
1
2
1
1
0
0
1
1
0
1
0
1
0
1
0
0
0
2
1
1
2
1
2
1
1
0
1
1
2
2
0
0
1
1
2
1
1
2
1
0
1
0
1
0
0
1
2
1
0
2
1
0
1
0
2
0
2
1
1
1
1
1
1
1
1
2
3
0
0
4
0
2
1
1
0
0
1
0
1
2
2
0
0
0
2
2
1
0
0
1
1
2
1
0
2
0
2
0
0
0
1
1
3
1
1
0
1
1
0
3
0
3
2
3
0
1
0
0
0
1
0
0
1
1
1
1
2
0
2
0
2
1
2
0
1
1
0
1
2
1
0
2
0
1
1
0
2
0
0
0
1
1
1
0
2
1
0
1
2
2
1
2
1
1
0
2
1
1
2
2
2
0
2
1
0
2
0
2
0
1
1
1
1
1
2
0
1
1
1
1
1
2
0
1
2
2
2
0
2
0
0
1
1
2
1
0
0
0
1
2
2
1
0
1
1
0
3
1
0
1
1
1
2
1
1
1
1
0
1
1
3
2
1
1
0
0
0
0
0
0
1
2
3
1
2
2
1
1
2
0
2
1
0
2
1
0
1
1
0
2
2
0
1
1
0
1
0
0
0
1
2
0
1
1
1
2
1
0
1
0
1
1
1
2
2
2
0
1
0
2
1
0
0
1
0
0
2
1
0
2
1
0
1
2
1
1
1
1
2
2
0
0
1
1
1
0
0
0
1
0
1
1
2
0
0
1
3
0
0
0
0
1
1
2
1
0
1
0
1
0
0
0
0
2
2
2
2
0
0
0
1
2
1
1
1
0
1
1
2
0
2
1
1
1
1
0
0
1
0
1
2
1
1
0
1
2
1
1
0
1
2
0
2
0
2
1
1
1
2
1
1
1
1
2
1
1
0
0
0
1
0
2
1
0
1
2
1
1
0
1
1
1
1
0
2
1
0
0
2
1
2
1
0
2
0
2
2
1
1
2
0
1
1
0
5
0
2
1
0
1
0
1
1
1
1
0
2
1
0
1
1
1
0
0
1
0
2
2
1
1
0
0
1
0
1
0
1
1
1
2
2
3
1
0
0
0
1
1
0
1
0
0
1
2
0
1
1
3
2
2
1
0
1
2
2
2
1
1
1
1
1
0
0
1
0
1
2
2
0
0
1
0
1
1
1
2
1
1
1
1
7
0
1
0
0
1
1
0
1
1
0
1
1
0
0
1
1
0
1
0
2
0
2
0
2
1
0
0
2
0
2
0
2
0
2
1
1
2
1
2
0
2
2
2
0
1
0
2
1
0
0
1
0
0
1
1
0
0
1
0
0
0
0
2
0
1
0
1
2
1
2
1
1
2
0
0
1
0
1
1
2
0
0
3
1
0
1
2
2
1
0
1
2
2
1
0
2
0
4
0
0
0
2
1
1
0
1
0
1
0
1
5
1
1
2
1
1
0
2
0
1
1
0
2
1
2
1
0
1
0
1
0
0
0
0
0
1
0
0
1
1
1
0
0
0
1
1
0
1
0
2
1
0
2
0
0
2
0
1
1
1
2
0
2
2
1
1
1
1
2
0
1
0
0
2
2
1
0
0
0
1
1
1
1
1
2
0
0
4
1
3
2
1
0
2
0
0
1
2
3
0
1
1
0
1
0
0
0
1
1
1
0
1
2
1
1
1
0
0
2
2
0
0
0
0
1
0
0
0
0
1
1
1
1
0
2
2
2
0
1
2
1
0
1
2
1
1
1
1
0
1
0
2
0
1
0
3
0
0
0
1
2
1
2
1
1
0
1
1
1
2
1
1
0
0
0
1
0
2
1
1
1
0
2
1
0
2
2
1
0
2
2
1
1
1
2
0
0
1
1
0
1
2
0
0
1
0
1
0
1
0
1
0
0
1
1
0
1
1
1
1
0
2
1
2
2
0
2
1
1
0
0
0
2
2
5
0
0
0
1
2
0
1
1
0
1
1
0
2
0
1
0
0
0
1
0
1
2
2
1
0
0
2
2
1
2
0
1
0
0
0
2
2
2
0
0
0
2
1
1
1
2
2
0
1
0
1
2
1
1
2
2
0
1
0
0
1
2
0
1
0
1
1
2
1
2
1
1
2
2
1
0
0
1
0
1
1
1
0
0
2
0
1
1
1
0
0
1
0
0
1
0
1
0
2
0
0
1
0
1
0
0
1
1
2
1
2
1
1
0
0
0
1
1
2
2
0
1
0
2
2
2
0
2
2
0
1
1
0
1
2
0
1
0
1
2
2
0
1
1
1
1
0
0
0
2
2
1
0
1
1
2
0
2
0
1
0
2
1
0
1
1
2
1
1
2
0
0
0
1
2
0
0
0
2
2
1
2
0
1
2
0
1
0
0
2
0
1
1
0
1
1
1
2
2
1
1
2
0
2
2
2
0
1
0
1
1
0
1
0
1
0
1
0
0
0
1
1
0
1
1
1
0
1
0
2
1
1
1
1
2
2
1
0
1
1
0
0
1
1
0
2
1
0
1
1
1
2
0
2
1
1
1
1
1
1
0
0
0
2
0
0
2
2
0
1
2
0
1
1
1
2
2
1
0
1
0
2
1
1
2
1
0
2
0
1
0
0
1
2
1
1
0
0
1
2
1
1
1
0
0
1
0
4
0
1
1
1
2
0
0
1
1
2
0
1
3
3
1
1
1
2
1
1
1
2
0
2
1
1
1
1
1
0
1
0
1
0
2
0
1
1
2
1
2
0
0
1
1
0
0
1
1
0
0
1
1
0
2
0
0
0
1
2
0
1
1
2
1
1
1
1
0
0
1
1
0
1
0
1
1
1
2
1
2
1
1
3
1
1
0
3
0
2
1
1
0
0
1
1
1
2
0
1
0
1
0
0
1
2
1
1
0
1
1
1
1
2
0
1
1
1
0
0
0
0
0
0
1
2
1
1
2
0
3
1
2
0
0
1
1
2
1
3
0
1
0
1
3
2
2
2
1
0
2
1
0
0
0
0
1
1
1
1
1
1
0
0
0
1
0
1
1
1
2
2
1
2
1
1
2
0
2
1
2
1
1
2
1
2
0
2
1
1
1
1
1
0
0
0
1
0
1
1
0
0
0
3
0
2
1
5
0
1
3
1
1
1
0
0
1
0
0
2
1
0
0
2
0
0
1
0
0
1
0
2
1
1
2
2
1
0
0
0
1
1
1
0
1
1
1
0
1
1
1
1
2
1
1
2
1
1
1
0
1
1
1
1
1
0
1
3
2
0
0
1
0
0
0
0
1
2
0
0
1
1
2
0
2
1
1
2
0
2
1
2
2
1
2
0
0
1
2
1
0
2
0
1
0
1
1
0
1
1
1
2
1
2
2
0
1
1
0
1
1
1
2
1
1
2
1
2
1
1
2
1
1
0
0
0
2
2
0
1
1
0
0
1
1
1
1
2
0
0
0
0
1
1
0
1
0
0
1
0
1
0
1
2
1
2
2
1
1
0
1
0
1
1
0
2
1
0
0
2
2
3
3
2
1
1
0
1
1
2
2
2
2
1
2
1
1
1
0
1
3
1
1
1
2
2
0
0
1
1
1
1
2
1
1
1
2
1
0
1
1
1
1
0
2
1
1
2
0
0
1
1
1
0
2
2
0
0
0
1
1
0
0
1
1
1
2
2
2
1
2
1
0
0
0
0
1
0
2
2
1
1
0
2
1
2
0
1
1
1
0
0
1
1
1
2
0
0
1
0
1
1
1
0
1
2
0
1
0
1
1
2
0
0
2
0
2
1
0
1
1
0
4
1
1
2
1
1
1
0
0
0
1
0
2
0
1
1
0
0
0
1
2
0
1
1
2
1
2
1
0
2
1
1
0
2
0
0
1
1
1
0
1
1
1
0
1
2
1
1
2
1
2
0
0
0
2
1
1
0
0
2
2
1
0
1
0
1
0
0
1
1
1
2
0
1
2
1
4
0
2
1
1
0
1
1
0
0
2
2
0
0
0
2
1
1
0
0
1
1
2
2
0
1
1
1
0
1
2
1
2
0
2
0
0
1
1
0
2
1
0
0
2
1
0
1
1
1
1
2
0
0
0
0
0
1
2
0
0
0
0
1
2
0
0
0
1
1
0
2
0
0
0
0
0
2
0
1
2
1
0
1
2
0
0
1
0
0
0
2
0
1
0
2
1
1
0
1
1
1
2
0
0
0
1
2
1
0
2
2
0
1
2
1
1
1
0
2
1
0
0
1
1
2
1
1
0
2
1
0
0
1
0
0
2
1
2
0
2
1
1
0
1
1
0
1
1
1
1
0
1
1
1
1
1
2
2
2
2
2
0
1
2
1
2
0
1
1
1
0
2
1
0
2
1
1
3
0
1
2
0
1
1
1
0
1
1
0
1
0
1
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
2
2
0
2
0
2
2
0
0
0
0
0
2
0
2
2
2
2
2
1
0
0
0
1
0
1
1
0
1
0
2
1
2
1
0
1
0
0
1
2
1
1
2
0
2
1
1
1
1
0
1
0
2
0
0
0
2
0
2
0
2
0
2
2
2
2
1
0
0
1
0
0
0
1
1
1
0
1
0
0
1
0
0
0
0
2
2
1
2
2
0
0
0
1
0
1
1
4
0
0
1
0
0
2
1
2
1
1
1
2
1
0
1
2
2
1
1
1
2
0
2
2
1
1
0
1
0
0
2
1
1
0
2
1
0
0
2
2
1
1
0
1
2
0
2
1
1
0
1
0
1
1
2
1
1
0
0
0
0
2
0
1
2
0
1
0
2
1
0
1
0
0
2
1
0
1
1
1
3
1
1
2
1
1
0
1
1
2
1
0
1
2
0
1
0
2
1
1
0
2
1
2
1
0
2
1
1
1
3
1
0
2
2
1
0
2
1
0
2
1
0
1
0
1
2
3
1
1
2
1
2
0
1
0
2
1
1
1
2
2
1
1
1
1
1
0
1
1
0
2
1
2
2
1
0
2
0
2
0
0
0
1
1
2
0
2
0
0
0
1
2
0
0
1
0
1
1
1
1
0
1
0
3
0
0
0
2
1
1
3
0
0
1
0
1
2
2
2
1
1
1
2
1
1
2
1
1
1
0
0
1
2
0
1
0
2
0
0
1
0
0
3
0
0
0
1
0
2
1
1
1
1
1
0
0
2
2
0
1
1
2
3
0
0
0
2
1
1
2
1
0
1
1
1
0
0
2
1
1
2
2
2
1
2
2
1
1
1
2
0
0
2
0
0
1
0
1
1
1
0
0
2
1
3
2
1
1
2
0
1
0
2
1
2
2
1
0
0
0
2
0
0
0
1
2
0
1
1
1
1
0
2
0
1
2
1
1
2
0
0
0
1
3
2
0
0
1
0
1
1
2
0
1
0
1
1
0
0
1
0
1
2
1
0
0
2
0
2
1
0
1
2
0
0
1
0
0
2
3
0
1
2
0
1
2
2
0
1
0
0
1
0
0
1
0
0
2
0
1
1
1
0
1
1
0
0
1
0
2
0
1
2
1
0
0
0
1
2
1
0
1
1
1
0
2
1
0
1
0
0
0
1
0
1
0
1
1
1
0
2
1
0
2
1
0
2
1
1
1
1
0
2
1
0
0
0
1
2
0
0
2
1
1
1
1
1
2
0
1
0
0
1
2
2
2
1
1
0
0
0
0
0
1
2
1
1
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
1
1
0
1
2
1
1
0
1
1
1
2
2
1
2
1
0
2
0
1
1
1
1
0
2
1
0
0
0
0
1
5
1
1
1
0
1
1
0
1
1
1
1
2
2
0
0
1
2
1
0
0
0
0
1
2
0
2
1
2
1
1
1
2
1
0
1
0
1
1
1
2
0
0
0
0
1
1
1
1
0
1
1
0
2
1
0
1
2
1
2
0
1
2
0
1
1
2
0
1
1
0
0
1
0
1
3
1
0
1
0
1
0
1
1
0
2
1
4
1
2
0
2
1
2
1
1
1
0
1
2
1
0
2
2
3
1
2
0
1
1
1
1
2
1
2
0
3
1
0
2
2
0
0
0
0
1
2
2
1
1
1
0
0
1
2
0
1
0
0
1
2
0
2
1
1
1
0
0
3
0
1
0
1
2
1
1
2
1
0
0
1
1
3
1
1
1
0
0
1
8
1
0
0
2
1
1
0
0
0
1
1
2
0
1
1
1
0
1
0
1
1
1
2
0
4
0
0
0
1
0
0
0
1
0
1
0
0
1
0
1
2
1
1
0
1
1
1
0
1
2
0
2
1
1
0
0
1
3
0
2
0
0
1
1
1
0
2
0
0
1
1
1
0
1
1
1
0
1
1
2
0
2
0
2
0
3
1
1
0
1
2
1
0
1
0
0
2
1
0
0
2
1
2
0
0
1
0
0
0
0
2
0
1
2
0
2
2
0
1
2
2
2
0
0
1
2
1
0
0
0
0
1
2
0
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
2
1
0
1
1
2
0
1
1
2
1
1
0
1
6
2
1
1
0
1
1
0
1
0
2
0
2
2
0
1
0
1
1
0
2
0
2
2
0
1
0
1
0
1
1
1
1
1
0
1
0
0
0
2
0
1
0
2
2
0
1
1
1
2
2
0
0
0
0
1
1
0
0
1
2
1
2
1
1
2
0
0
4
1
0
1
0
1
0
3
1
0
0
0
1
1
0
0
0
2
1
1
1
1
0
1
2
1
2
1
0
1
2
1
0
1
0
2
0
0
1
1
2
1
0
0
0
1
1
1
0
2
0
1
1
1
0
1
0
1
2
1
2
1
1
1
2
0
1
1
0
1
1
0
2
2
2
1
1
3
3
1
0
1
2
0
1
0
0
0
0
2
1
1
2
2
0
1
1
1
1
0
2
1
1
0
1
1
0
1
2
1
1
0
1
1
1
0
1
1
1
1
2
0
1
0
1
1
2
1
0
1
1
0
1
1
1
0
1
1
0
1
0
0
1
1
0
1
3
1
1
1
2
1
1
1
1
1
1
1
2
1
1
2
1
2
0
1
0
2
0
1
2
0
0
0
1
0
1
2
2
0
1
0
1
1
2
0
0
2
1
1
1
2
0
1
0
2
1
1
1
2
1
0
1
0
0
0
0
1
2
1
0
0
1
1
1
2
1
0
1
1
0
1
0
2
0
2
0
0
1
1
2
1
0
1
1
2
2
0
2
1
1
0
0
0
1
0
0
1
1
2
1
0
1
1
0
1
1
1
1
1
2
2
0
0
0
1
2
2
1
1
1
1
0
0
0
0
1
2
1
3
0
0
0
1
1
1
1
2
1
1
2
0
2
1
3
0
1
0
1
2
2
1
1
1
1
2
1
2
1
1
2
0
0
1
0
0
0
1
0
1
1
0
1
0
2
0
0
1
1
0
0
3
1
1
2
0
0
1
2
0
0
1
0
0
1
2
0
1
2
0
1
0
0
1
0
1
0
0
2
1
1
0
1
0
1
1
0
2
1
1
0
0
1
0
2
0
0
1
2
0
0
0
1
0
0
1
0
2
0
1
0
2
0
0
0
0
1
3
0
1
1
2
0
2
1
1
2
1
1
0
0
1
1
2
0
1
1
0
0
0
1
2
2
1
1
0
2
0
0
5
0
2
2
2
1
1
2
2
1
0
1
2
0
1
1
0
0
0
0
1
1
0
1
0
1
2
1
0
0
1
0
0
0
2
1
2
2
0
1
0
2
1
1
1
0
1
2
0
1
5
1
1
2
1
1
1
3
0
0
1
0
0
1
0
1
0
0
0
2
0
0
0
2
2
1
2
1
0
1
2
1
2
1
0
2
2
0
1
1
0
0
0
2
1
2
0
0
1
0
1
1
2
2
1
0
1
0
1
2
2
4
2
1
2
1
2
0
0
0
1
2
0
1
2
1
1
0
2
2
1
2
1
0
0
1
1
0
1
0
0
1
0
2
0
0
0
2
2
2
2
1
1
2
1
0
1
0
1
0
2
2
1
2
1
1
0
1
0
0
1
0
0
0
1
1
0
0
2
2
2
2
1
2
0
0
3
0
1
1
0
0
0
1
2
0
0
0
2
0
0
0
2
2
0
1
1
1
1
1
1
1
2
1
0
1
1
1
1
0
0
2
0
0
1
1
1
0
0
1
0
2
0
1
0
0
1
0
2
3
0
1
1
1
0
2
1
1
1
1
1
1
0
2
1
1
1
1
1
0
2
1
0
1
0
1
2
1
1
2
2
2
1
0
1
0
1
0
3
2
1
2
1
2
2
2
0
1
0
0
0
2
0
1
0
1
0
1
0
0
2
1
1
1
1
0
1
2
2
3
1
0
0
0
1
0
1
0
1
1
1
0
1
1
1
0
0
0
1
1
1
0
1
1
1
1
1
5
2
1
2
0
1
1
1
1
0
2
1
2
1
0
1
2
0
0
1
1
0
0
1
0
1
1
1
0
2
2
1
1
2
0
1
0
1
0
1
0
2
1
0
2
1
1
0
1
0
1
1
1
0
3
2
0
0
0
1
1
0
1
1
1
0
0
0
2
0
1
0
1
1
1
1
1
2
0
1
1
2
3
0
1
1
0
2
1
0
1
1
2
2
2
1
2
1
1
1
1
0
1
1
1
0
3
1
2
2
2
1
0
2
0
1
0
1
0
1
2
0
1
2
1
1
2
2
1
0
1
2
0
1
2
0
0
1
1
1
1
0
5
1
2
1
0
1
1
1
1
0
0
1
1
1
2
0
2
1
1
1
0
0
0
0
0
0
0
1
0
2
1
0
1
1
1
0
2
1
0
1
2
1
1
1
1
1
1
1
1
2
1
1
1
0
0
2
2
0
0
0
1
2
0
1
1
2
1
0
1
1
2
1
1
1
2
1
2
2
1
0
1
0
2
3
1
1
1
2
2
0
0
1
0
2
0
0
1
2
1
0
2
0
1
1
1
2
2
1
3
0
0
1
1
1
0
1
1
0
1
0
2
1
0
0
0
1
1
0
0
0
1
1
1
1
1
0
1
1
0
2
0
2
1
2
1
2
3
1
0
1
1
2
0
1
1
1
1
0
0
0
2
0
2
0
0
0
1
0
0
0
1
0
2
1
0
3
1
0
1
2
2
0
1
2
2
0
0
0
1
0
1
2
0
1
2
0
0
0
2
0
1
1
2
1
0
2
1
0
1
1
1
1
0
0
1
2
0
2
1
1
1
1
1
1
1
1
2
1
2
1
1
1
1
2
1
0
1
1
0
2
0
0
1
1
0
1
1
2
1
0
2
0
0
1
0
0
0
1
2
1
2
1
1
1
0
2
0
2
0
0
1
2
1
0
2
1
0
0
2
2
2
2
0
1
0
1
2
3
0
1
2
1
0
1
2
1
2
0
1
2
2
1
1
2
0
0
1
0
1
0
1
2
1
0
0
1
2
1
0
2
0
1
1
0
1
0
1
1
0
0
2
3
2
1
0
0
0
2
2
0
5
1
2
1
1
1
0
0
1
1
1
0
0
1
0
1
1
0
2
1
0
0
1
0
0
2
0
1
1
0
1
2
2
0
1
0
0
0
0
0
0
0
0
1
1
0
2
1
0
1
0
0
0
2
0
1
0
0
2
1
0
2
0
1
2
2
0
1
1
2
1
1
1
0
2
1
0
2
2
1
3
1
1
0
2
0
1
2
0
1
0
1
0
1
1
1
1
1
1
0
1
1
1
1
3
1
2
1
0
0
0
1
1
0
1
1
1
1
0
0
0
0
2
0
0
1
1
0
1
2
2
0
1
1
1
0
1
0
1
0
1
1
1
2
0
1
1
2
1
2
3
1
1
0
0
1
1
0
0
0
0
1
0
1
2
0
2
0
1
2
1
1
2
3
0
2
1
2
1
0
1
1
1
2
0
1
2
0
1
0
1
1
0
2
0
0
2
1
1
1
0
0
2
1
2
0
1
1
1
0
0
0
1
1
2
1
1
1
1
1
1
0
2
1
0
2
0
0
1
0
0
2
1
3
2
0
1
0
1
2
1
1
0
0
2
2
1
2
1
1
0
1
1
1
2
1
1
0
1
1
1
1
1
0
0
1
0
2
2
0
1
0
0
2
0
0
0
0
0
1
2
1
1
1
1
1
2
1
0
0
1
1
0
0
2
1
0
0
1
0
2
1
1
0
1
0
1
0
0
0
0
1
1
2
1
1
1
1
2
0
1
1
1
2
0
1
0
1
2
1
1
0
1
1
2
1
1
0
1
0
0
1
1
1
1
1
0
0
2
2
1
1
0
1
1
5
0
1
0
0
2
1
1
2
2
1
1
0
0
1
2
2
0
0
2
0
0
1
0
1
3
0
0
1
0
0
2
2
0
1
1
2
2
1
1
0
0
1
1
0
0
1
0
1
1
1
1
1
1
0
1
2
0
2
2
1
0
0
0
2
2
2
2
2
1
1
0
2
0
0
0
1
2
2
0
1
0
2
1
1
2
0
1
0
2
0
1
2
1
2
2
0
1
2
2
2
0
1
1
0
0
0
1
1
1
0
1
0
1
2
0
1
1
0
2
1
2
1
0
2
0
0
1
2
0
1
2
1
0
2
1
1
0
2
2
1
0
1
0
1
0
1
0
1
0
1
0
0
1
0
1
1
0
2
0
0
1
2
0
0
1
0
0
0
0
0
0
1
1
0
1
1
0
0
2
0
1
0
1
1
1
0
1
1
2
0
1
1
1
0
1
1
1
1
1
2
2
0
1
0
0
0
1
2
1
1
0
1
2
1
1
1
1
1
2
0
1
2
2
0
1
2
1
1
1
0
0
2
0
2
0
0
0
1
0
1
1
1
2
1
0
1
1
1
0
0
0
1
2
0
2
1
0
1
1
0
1
1
1
1
1
0
0
1
2
0
0
1
1
0
0
2
0
1
1
0
3
2
1
0
1
2
0
1
1
1
1
2
0
2
2
1
2
2
1
0
1
1
2
0
0
2
0
1
1
0
0
0
1
0
2
2
0
1
0
0
1
1
1
1
1
0
0
3
2
0
3
0
1
1
1
0
0
2
0
0
0
1
0
0
0
0
1
1
1
1
1
1
1
1
0
1
1
1
2
0
1
0
1
1
0
2
0
0
0
2
1
1
2
1
1
1
0
1
1
1
0
1
0
2
2
1
0
1
0
0
2
0
0
1
2
2
0
0
1
1
0
1
1
2
0
0
2
1
0
0
1
1
2
0
0
1
1
0
1
0
1
1
1
1
0
2
1
0
4
1
3
2
0
1
0
1
2
0
2
2
0
0
0
2
0
2
1
1
0
0
1
2
1
1
2
1
0
2
4
1
0
1
1
1
2
1
0
1
0
0
1
1
0
2
1
2
0
2
2
2
1
2
2
1
0
1
0
1
2
1
0
2
0
0
2
1
1
1
2
0
1
1
2
1
2
2
0
1
1
0
1
1
1
1
0
1
1
1
1
0
2
0
0
1
1
2
1
2
1
2
2
0
1
1
2
1
0
1
0
1
1
1
2
1
0
1
1
0
0
0
1
1
1
2
2
0
2
0
1
0
2
0
0
0
2
2
0
1
2
0
0
1
1
0
2
2
2
1
2
1
0
1
2
0
0
1
2
1
0
2
0
1
1
1
2
2
1
2
1
0
2
0
0
1
1
2
2
1
1
1
0
2
1
0
0
2
0
0
1
1
1
1
1
2
2
1
0
2
1
0
2
1
0
0
0
0
1
2
0
0
1
0
2
1
2
1
0
0
0
0
0
0
0
1
0
1
1
0
1
1
0
1
2
0
0
0
1
2
1
1
0
2
2
1
1
2
1
0
0
1
0
1
0
0
1
2
0
0
0
1
0
2
1
0
0
1
1
0
0
1
2
4
2
1
0
2
0
0
2
0
2
1
0
2
1
0
1
4
2
0
0
1
2
0
0
0
0
2
0
2
0
0
0
1
0
0
0
2
3
1
1
0
0
0
1
1
1
1
1
0
1
2
1
1
0
0
1
0
0
1
2
0
1
1
1
0
3
1
1
1
1
0
0
2
0
0
1
2
1
1
2
0
2
0
1
1
0
0
0
2
1
1
0
0
2
14
1
0
1
2
1
0
0
0
0
2
0
0
1
2
1
2
1
0
2
1
0
1
2
1
0
1
1
0
0
2
2
0
0
2
1
0
2
1
0
1
1
0
1
1
1
1
2
1
2
1
2
0
2
0
0
9
2
0
0
0
1
1
0
0
2
2
1
1
1
0
0
1
1
2
1
3
3
1
2
1
1
1
2
1
1
2
0
1
2
0
1
2
2
1
0
2
2
1
2
0
2
0
0
2
2
1
0
0
1
0
1
2
0
2
0
1
0
1
0
1
0
0
1
0
0
2
0
0
1
0
2
1
0
0
0
1
1
1
1
0
1
0
1
2
0
0
1
1
0
0
1
0
1
1
2
1
1
2
0
1
1
1
2
0
1
1
0
1
0
1
2
1
0
0
1
0
1
0
1
1
0
1
1
1
2
2
1
0
0
1
1
0
0
0
1
0
1
0
0
0
1
1
0
1
0
2
0
2
0
0
2
0
1
2
0
1
0
1
1
1
1
2
1
1
2
1
1
1
2
1
1
1
0
0
2
0
1
1
2
1
0
0
2
2
0
1
0
0
1
0
2
1
2
0
0
0
2
0
1
0
0
2
1
1
1
1
1
1
0
0
0
2
2
2
0
0
0
1
2
1
1
1
1
1
1
0
2
0
1
0
2
0
1
1
1
0
0
2
0
1
1
1
2
2
1
1
2
1
0
1
0
1
2
1
2
1
1
2
1
0
1
2
2
1
1
0
1
0
0
1
2
1
1
1
1
1
0
2
2
0
1
0
0
1
1
0
2
1
0
0
2
0
2
2
0
0
2
0
2
0
2
1
0
0
0
1
2
1
2
2
0
1
1
0
2
1
0
0
1
2
1
0
0
0
1
0
2
0
0
1
1
0
1
1
1
0
0
4
0
3
1
1
2
1
1
1
2
1
2
0
0
2
0
0
1
1
0
0
0
1
0
0
0
0
1
2
2
0
2
2
0
1
0
1
1
2
1
2
2
2
1
0
1
2
2
0
0
2
1
0
1
1
1
0
2
2
4
1
2
1
2
1
0
2
1
1
2
1
1
0
0
0
0
1
0
0
0
1
1
2
2
0
2
0
1
1
0
0
1
1
0
1
1
0
1
0
0
1
0
1
2
0
2
0
0
0
1
2
0
0
0
1
1
0
0
1
0
0
2
1
1
0
0
0
0
2
1
2
0
0
1
1
1
1
2
3
1
1
1
1
1
0
0
2
0
0
0
2
1
1
0
2
0
2
1
2
2
0
1
1
0
1
2
0
0
0
0
0
1
1
0
2
1
3
0
0
1
0
0
1
1
1
2
2
1
2
2
1
1
1
1
1
1
1
0
2
1
2
2
0
3
0
0
2
1
0
1
2
0
0
1
1
1
0
2
1
0
0
1
0
1
1
0
2
0
0
0
0
2
1
2
0
0
2
2
1
1
0
0
2
1
0
1
1
1
1
1
1
0
2
2
1
2
0
1
0
1
3
1
0
1
0
1
0
1
1
0
1
0
0
1
1
1
0
2
1
1
0
0
2
0
1
0
0
2
1
1
0
2
0
0
1
0
1
1
2
0
1
0
2
0
1
1
1
1
1
2
0
1
0
1
2
0
1
0
1
1
1
0
1
0
0
0
0
2
1
1
1
0
1
2
0
0
1
1
3
2
0
0
1
0
2
2
1
1
0
2
1
1
2
0
1
0
0
2
2
1
1
6
0
2
1
2
1
1
1
1
3
2
0
1
0
1
0
1
0
2
1
2
0
0
0
0
1
1
0
0
0
1
1
0
1
3
0
0
0
0
2
1
2
2
3
0
0
3
1
0
0
2
2
1
1
1
1
1
0
1
2
0
0
2
2
2
1
1
2
1
1
2
0
1
2
1
0
1
0
0
2
1
1
1
1
1
1
1
1
2
1
0
0
0
2
0
1
0
0
1
0
1
1
0
2
1
0
1
1
1
1
0
0
1
0
0
1
1
2
0
0
1
3
0
1
0
0
0
1
0
0
1
2
2
1
0
0
1
0
0
0
0
1
1
1
0
2
0
0
0
1
1
2
2
1
1
2
0
0
0
1
0
1
2
1
1
2
0
1
1
1
0
2
0
0
0
1
3
0
1
1
0
0
0
2
1
2
0
0
0
0
0
1
1
1
1
1
0
1
0
1
0
1
1
0
1
1
1
2
2
1
0
1
1
0
1
1
1
3
0
2
0
1
0
1
2
1
0
0
0
2
1
0
1
1
1
2
1
0
0
2
0
1
1
1
2
1
2
1
0
1
0
0
1
1
1
0
1
1
1
1
0
2
1
0
0
1
1
1
0
1
1
2
0
1
2
1
1
0
0
2
0
1
0
1
1
1
1
0
1
0
2
0
1
0
0
2
1
1
0
1
2
0
1
1
2
0
0
1
1
2
0
1
1
0
0
1
0
3
0
1
0
0
0
0
0
0
2
2
0
1
0
1
0
1
0
0
0
0
1
2
1
2
1
1
0
0
2
1
2
1
1
1
1
1
1
1
0
1
0
0
1
1
0
1
2
0
1
1
0
2
2
0
2
1
0
0
1
2
2
2
1
0
1
2
1
1
1
2
1
0
2
0
2
2
2
0
2
1
2
0
0
1
0
0
1
0
2
0
1
0
1
1
0
0
2
0
3
0
0
0
1
2
2
3
1
2
1
1
0
3
2
1
0
1
1
2
2
0
0
1
2
2
1
0
2
1
0
0
5
1
0
0
1
1
0
2
0
1
1
0
0
2
0
2
2
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
2
0
2
2
0
0
2
1
1
2
0
1
1
2
1
0
0
1
2
1
0
1
0
0
0
0
1
1
0
1
0
0
3
2
1
1
1
1
0
1
0
2
0
1
1
1
1
2
2
1
1
2
1
2
1
1
0
0
1
2
1
2
1
0
1
1
0
0
0
0
0
0
1
0
0
1
1
1
0
1
1
0
0
0
0
1
2
0
1
1
0
1
2
2
2
1
0
0
1
1
0
1
0
0
1
1
1
0
2
0
1
1
1
1
0
1
2
1
1
2
2
0
0
2
0
0
1
1
0
1
1
1
1
1
1
2
0
1
1
1
1
2
0
0
2
1
0
2
2
0
0
0
2
2
0
1
1
5
2
0
0
1
1
0
2
1
2
1
2
1
2
2
0
1
1
1
1
1
1
1
0
1
0
1
1
0
0
1
2
1
0
0
1
0
1
1
0
1
1
2
0
0
1
0
2
1
0
1
2
2
1
1
2
1
1
2
1
0
2
1
1
0
1
0
1
0
1
1
0
0
0
0
1
1
0
3
1
1
0
1
1
0
0
0
0
1
1
0
0
0
0
1
1
1
2
0
2
2
2
1
2
0
1
1
0
0
0
0
1
1
1
2
0
1
2
0
2
1
2
0
2
1
1
2
2
0
1
0
1
1
1
5
1
0
1
1
0
0
1
1
0
1
1
2
0
1
0
0
0
0
1
0
0
1
1
1
0
0
0
0
2
1
2
0
2
0
0
1
2
2
2
0
0
0
2
0
1
2
0
0
2
1
2
0
1
2
1
0
1
5
0
1
1
0
0
1
1
3
1
2
1
1
0
2
1
1
2
0
1
2
1
1
2
0
0
1
0
2
1
0
1
1
3
1
1
2
0
0
1
0
2
0
0
1
1
2
2
0
1
1
0
1
1
2
1
1
0
1
0
1
2
1
2
1
1
2
1
2
1
1
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
2
1
0
2
2
0
0
0
1
4
0
0
0
1
2
2
2
2
0
1
2
0
1
1
2
2
2
2
1
1
2
0
0
1
0
2
1
0
2
0
1
0
2
1
1
1
2
1
1
0
1
0
2
3
1
0
0
0
0
1
1
2
0
1
0
1
0
1
0
2
1
1
0
0
1
2
0
2
1
1
1
1
0
1
1
3
0
0
2
2
1
0
0
1
2
2
1
2
1
2
1
1
1
1
0
2
1
1
2
1
2
0
0
1
0
1
2
0
0
1
1
2
0
1
0
0
1
0
1
0
0
1
0
1
1
0
1
0
0
0
2
1
1
1
2
1
1
1
1
1
1
0
2
0
0
1
1
1
0
1
2
1
0
1
0
0
0
1
2
0
1
0
1
0
2
0
0
1
0
3
1
1
2
0
0
1
1
1
1
2
1
1
0
3
1
0
0
2
2
0
0
0
2
2
0
2
2
1
1
0
0
0
1
0
2
0
3
2
2
1
1
1
0
0
0
2
1
0
0
0
0
1
1
0
2
1
0
1
0
0
0
1
0
2
1
4
2
0
1
1
0
1
4
2
0
0
1
2
0
0
0
1
1
1
2
1
0
1
1
1
0
0
0
1
2
2
2
0
1
1
1
0
1
1
1
0
0
1
2
0
2
2
2
1
2
1
0
1
0
2
0
0
0
1
1
1
1
1
1
0
0
0
0
2
1
1
0
1
0
0
1
1
0
0
0
0
1
0
1
1
0
0
0
1
0
2
1
1
1
1
1
1
0
0
1
0
1
1
2
1
1
2
2
1
0
0
1
1
0
1
0
1
1
1
0
0
1
0
0
2
1
1
1
0
0
1
0
0
2
2
0
0
2
1
1
0
2
1
2
1
1
1
1
2
2
1
1
2
0
1
1
1
0
1
0
1
1
1
2
1
1
1
2
2
1
0
1
3
1
0
1
1
1
2
1
1
0
2
1
0
1
0
1
1
1
0
3
0
1
1
1
0
0
2
1
2
3
0
0
1
0
1
0
0
0
1
2
1
0
1
1
2
1
1
0
0
2
3
1
0
2
0
1
1
1
1
0
0
1
1
1
2
1
0
1
1
0
1
0
1
0
2
1
2
0
1
0
0
0
2
1
2
0
1
2
0
0
1
1
1
1
2
0
0
1
2
1
0
0
1
1
0
0
1
2
2
1
0
0
2
1
0
2
0
0
1
0
2
1
1
0
2
0
0
0
2
0
1
2
1
1
0
0
1
1
1
0
2
1
1
0
0
1
0
0
0
2
0
1
0
1
0
2
0
3
1
1
2
1
2
1
2
2
1
1
1
0
0
0
1
0
1
1
0
2
2
0
0
2
2
0
2
1
0
0
2
0
2
1
1
0
1
1
0
0
1
1
0
1
0
0
0
2
1
2
0
2
1
1
2
1
2
0
2
0
1
1
1
2
1
0
0
1
0
2
1
1
1
0
1
0
0
2
0
0
0
2
1
1
2
2
2
1
0
1
0
0
1
2
1
0
0
0
1
0
1
0
2
2
2
0
2
2
2
0
0
1
1
1
0
5
0
1
0
0
1
1
1
0
0
1
0
1
0
1
1
0
0
0
1
0
1
0
2
0
0
0
1
2
2
0
1
1
0
1
1
1
0
1
1
0
0
2
2
2
1
1
0
2
1
1
2
1
2
1
0
1
0
1
0
1
1
1
1
0
2
1
1
2
2
1
0
1
0
1
1
1
1
1
0
1
0
1
0
0
0
1
0
2
0
2
0
2
1
2
0
2
1
2
0
0
0
0
0
2
3
1
1
1
0
0
0
0
1
0
0
2
1
1
2
2
0
2
0
1
2
1
2
1
1
1
0
1
1
0
1
0
0
1
2
1
1
2
3
1
5
0
2
3
1
1
1
1
0
1
0
1
1
0
2
0
2
0
0
1
1
2
0
1
1
0
0
2
1
2
1
2
0
0
1
0
2
1
1
0
1
0
2
1
1
0
1
0
0
1
0
1
1
1
1
1
3
1
2
0
1
1
0
1
0
1
0
0
1
2
2
1
1
0
0
0
1
1
1
1
1
1
2
0
0
1
0
1
2
1
0
0
1
2
2
1
1
0
1
1
1
1
1
0
2
0
1
1
2
1
0
1
0
0
2
0
0
0
1
1
1
2
0
1
2
2
1
2
1
2
1
1
1
1
2
1
0
1
1
1
0
1
0
0
0
0
1
1
1
0
0
1
0
2
2
2
1
1
1
0
1
0
1
0
0
2
1
2
1
0
1
2
0
2
1
0
2
0
1
2
1
0
0
2
1
2
0
1
0
1
1
2
0
0
2
1
1
2
0
2
1
3
1
2
0
1
0
1
1
1
1
0
1
1
0
0
1
0
2
2
1
1
1
0
1
0
0
1
1
2
1
1
0
1
1
0
0
2
1
1
1
0
1
1
1
1
0
1
0
1
0
0
0
2
1
1
1
2
0
2
1
0
0
1
1
0
2
2
1
2
0
0
1
1
1
0
1
1
0
1
1
2
1
1
2
1
1
1
0
1
1
1
1
1
1
2
2
0
1
0
1
1
0
2
1
2
0
0
1
2
1
1
0
0
1
2
0
0
0
1
2
0
1
1
1
1
0
1
0
1
1
0
1
1
1
0
0
1
1
2
0
0
0
0
2
2
1
1
1
1
1
0
1
2
1
1
0
1
0
1
0
1
0
0
0
1
1
0
0
0
2
2
1
2
0
0
1
0
1
1
2
2
2
1
1
1
0
0
1
0
1
0
1
1
1
2
1
0
1
1
0
0
0
0
2
1
2
1
0
1
2
0
1
0
0
1
0
1
1
1
1
2
1
1
0
1
1
1
2
0
1
0
0
2
1
0
0
1
0
2
2
3
1
2
1
0
1
0
1
1
2
2
2
1
1
1
1
2
0
1
1
0
3
2
1
1
1
2
0
3
0
0
2
0
1
2
1
1
0
1
1
1
0
1
1
1
0
0
0
2
1
1
2
0
1
2
0
1
0
1
1
0
1
2
1
1
1
1
0
1
1
0
2
0
1
0
0
0
1
0
1
0
2
0
2
1
1
1
2
1
2
1
1
1
0
2
0
2
0
2
2
1
2
1
1
0
0
2
1
1
2
1
1
0
2
1
1
2
1
0
0
0
0
0
2
3
1
0
1
0
0
1
1
0
4
0
0
0
0
0
1
2
2
1
0
0
0
1
3
1
0
1
0
2
1
1
0
0
0
1
4
1
0
2
2
0
1
0
1
1
0
1
2
1
0
0
1
0
1
1
0
2
0
2
1
4
0
0
1
1
1
1
1
2
1
2
1
0
1
2
2
1
2
1
2
1
1
0
1
1
0
0
0
0
1
3
1
0
1
1
1
2
0
0
7
2
1
0
1
1
2
0
1
2
1
0
0
0
1
0
1
0
1
0
1
1
0
0
1
1
2
0
1
1
0
2
2
0
1
0
0
1
1
1
2
0
1
1
1
2
1
0
1
2
2
0
0
2
2
0
0
1
0
2
0
0
0
0
0
2
0
1
0
1
0
1
1
0
2
0
1
1
0
2
1
1
1
2
0
1
2
1
0
0
1
1
2
0
1
1
1
0
1
2
0
1
0
0
0
0
2
0
1
0
1
0
2
2
2
0
1
1
3
0
1
1
1
1
1
2
1
0
0
1
0
0
1
2
2
0
2
2
2
1
1
0
1
0
1
2
0
0
1
1
1
4
0
2
0
1
0
1
1
1
0
0
0
1
1
0
1
0
0
1
1
1
1
1
1
0
2
1
2
0
2
1
2
2
1
1
0
2
1
2
0
0
0
1
0
2
2
1
0
0
1
0
1
0
1
1
1
1
0
2
1
1
0
0
2
1
2
0
1
0
2
1
1
2
1
0
0
0
2
2
0
0
1
1
1
1
1
2
0
1
2
0
1
0
1
0
0
2
0
0
0
1
0
1
1
0
1
1
2
0
1
1
0
2
2
1
1
0
1
1
1
2
1
2
2
1
3
0
0
0
1
1
1
1
2
0
1
1
0
0
1
0
1
1
1
1
2
1
3
1
0
2
2
0
1
0
1
2
1
0
1
1
1
0
2
1
0
0
1
2
0
1
2
1
0
0
1
0
1
1
0
0
1
2
2
1
1
2
0
2
1
0
0
1
2
0
1
2
1
2
0
0
0
2
1
1
1
0
1
2
1
0
1
2
3
1
1
1
2
0
0
0
1
2
0
0
0
0
1
1
1
2
0
1
2
1
0
1
1
1
0
1
0
2
1
2
1
0
2
1
0
2
0
1
1
0
1
0
1
2
0
1
2
0
1
1
1
1
1
1
2
2
0
2
0
2
1
0
2
1
1
0
1
2
0
2
2
1
1
1
0
1
1
0
0
0
2
1
0
2
0
1
0
2
1
1
1
1
0
0
0
2
1
1
0
2
0
2
0
2
0
1
1
2
2
2
1
2
1
1
0
0
2
1
2
1
0
0
1
2
0
2
1
2
2
0
1
1
2
0
2
1
0
0
0
0
0
1
1
0
0
1
1
1
0
0
0
1
2
1
2
0
0
2
0
2
0
0
0
1
1
0
2
2
2
1
0
1
0
0
1
0
1
1
2
0
1
0
1
0
2
2
0
1
1
0
1
1
1
0
1
1
1
1
2
1
1
0
2
1
0
1
0
0
0
1
0
0
0
0
0
1
2
1
1
0
2
1
2
0
1
0
1
1
0
1
1
0
0
1
1
2
2
0
1
1
1
0
0
1
0
2
2
0
1
1
0
0
0
0
0
0
0
0
3
1
2
2
2
1
1
0
0
1
1
0
0
0
1
0
1
1
1
0
2
1
1
1
1
1
0
1
1
0
1
0
0
0
1
1
0
0
1
2
0
0
0
1
0
2
2
1
0
2
0
2
1
2
2
2
1
3
0
1
0
1
1
1
1
0
1
1
1
1
0
2
1
1
0
1
0
2
1
2
1
0
2
1
2
0
2
0
4
0
1
1
1
1
1
1
2
2
1
0
0
1
0
0
2
2
1
2
0
1
0
1
0
2
1
1
2
1
1
1
0
0
2
2
2
2
1
1
1
2
0
2
2
1
1
2
1
0
0
2
1
0
1
1
1
0
0
0
0
2
1
1
1
1
2
1
0
2
0
0
0
1
1
0
1
0
0
1
0
1
1
1
1
1
1
0
0
0
2
0
1
2
0
2
2
1
1
0
2
1
0
1
0
0
1
2
0
0
1
1
1
0
1
2
1
1
1
1
1
2
1
0
0
1
1
0
0
2
1
1
0
0
1
3
2
4
0
0
1
2
0
1
0
0
2
3
2
1
1
0
0
1
1
1
1
1
1
0
0
1
1
0
1
1
0
1
0
1
0
1
2
0
1
1
0
0
1
0
1
1
2
2
2
2
1
0
0
1
1
0
1
1
3
1
2
0
0
0
0
0
0
1
1
2
0
1
2
1
2
0
1
1
0
1
1
0
1
0
1
1
0
1
2
0
1
0
1
1
2
1
1
0
1
3
1
2
1
2
1
1
2
2
1
1
1
0
4
0
2
1
2
0
1
1
1
1
0
1
1
2
1
1
0
0
0
1
1
1
1
0
0
0
1
2
0
0
1
0
1
1
1
1
1
0
2
0
1
0
1
0
2
1
0
0
0
1
2
0
0
0
1
0
1
1
1
1
1
1
1
1
2
0
0
1
2
1
1
0
2
0
1
1
1
0
0
1
0
1
1
1
2
1
0
0
0
1
2
2
2
1
0
1
0
0
0
2
0
0
0
0
1
1
0
1
0
1
1
1
1
0
2
1
0
0
1
3
2
0
0
0
2
0
1
1
0
2
1
0
0
1
1
0
2
3
1
1
1
2
0
1
1
2
0
2
1
0
1
0
0
0
1
0
2
1
1
1
1
1
1
2
1
0
0
1
2
0
0
0
0
0
2
2
1
1
2
1
1
0
1
0
2
1
1
1
0
1
2
1
2
1
2
1
0
1
0
1
0
0
1
2
1
0
1
1
1
2
1
1
1
2
1
0
2
1
0
0
2
0
0
0
0
1
1
1
0
1
0
0
1
2
0
2
1
1
0
1
1
2
0
1
1
1
1
0
1
1
0
0
1
1
0
1
0
0
1
1
0
0
0
1
1
2
2
0
2
0
1
1
1
0
0
2
0
0
1
1
1
2
0
1
2
0
1
1
0
1
1
0
2
0
1
1
1
0
0
1
1
1
0
0
2
1
0
1
2
1
1
0
2
1
3
2
1
2
2
0
0
0
2
1
0
1
0
2
0
0
2
1
0
0
0
2
1
0
0
1
1
1
0
1
3
2
1
0
0
1
0
1
1
3
2
0
1
0
1
1
1
1
2
0
2
1
1
0
0
1
1
0
3
1
0
0
1
0
1
4
1
0
0
0
1
1
0
2
1
1
2
0
2
1
2
1
1
2
0
2
1
1
2
1
0
0
0
2
2
1
0
0
0
1
1
0
1
1
2
2
0
0
1
1
0
1
1
2
1
0
2
1
1
1
1
1
2
1
0
1
1
2
2
2
2
0
1
0
2
0
1
0
1
1
1
2
0
0
0
1
0
0
0
2
0
1
1
0
1
1
0
1
0
2
1
1
2
0
1
1
2
0
4
0
1
2
0
1
0
2
3
0
1
0
1
1
1
0
2
0
1
0
2
1
2
1
0
0
1
2
0
1
0
2
1
1
1
2
1
1
0
0
2
0
0
1
1
2
2
0
0
1
0
1
1
0
0
2
1
0
1
2
2
1
2
0
2
1
2
0
0
0
1
0
1
1
0
0
2
1
1
2
1
2
3
1
1
1
0
2
0
2
1
1
1
1
1
1
1
1
0
0
1
0
1
1
1
2
1
2
0
0
1
1
1
1
0
1
2
1
0
0
1
1
1
0
0
0
1
2
2
1
1
0
1
2
0
0
2
1
0
1
0
0
0
3
2
1
1
1
1
0
0
0
1
0
1
0
0
0
1
2
0
0
1
0
0
0
2
2
1
1
0
0
0
1
1
1
0
0
2
2
0
1
1
1
1
0
0
2
1
0
1
1
0
0
0
0
0
1
1
1
1
0
1
1
0
0
2
0
0
0
0
1
0
1
1
0
0
1
2
1
0
3
0
2
1
0
0
2
1
1
2
0
1
3
2
0
1
2
1
1
1
1
2
1
1
1
2
0
1
1
1
1
0
1
0
2
1
2
2
1
1
1
1
2
2
1
0
1
1
2
2
0
1
2
1
2
2
0
2
2
1
2
2
1
1
1
0
2
2
1
2
2
1
1
2
2
0
1
1
0
0
0
1
2
1
1
3
0
1
1
0
0
0
0
2
1
1
2
1
1
0
1
0
2
1
0
1
2
0
0
1
0
1
4
2
0
1
0
1
1
0
1
0
0
0
0
1
2
2
1
0
1
0
0
1
0
1
0
1
0
1
1
0
0
2
0
1
0
2
1
1
1
1
1
0
0
1
0
0
0
0
0
0
1
2
2
1
0
1
1
0
1
2
0
1
1
0
2
1
1
1
1
2
1
0
0
2
1
1
1
0
0
3
6
1
0
2
0
0
0
1
0
1
0
0
1
0
0
2
0
0
0
0
1
1
1
0
0
2
2
0
1
1
2
2
0
0
2
0
1
0
1
1
2
1
0
1
0
1
1
2
2
2
0
0
0
2
2
1
1
2
0
0
1
2
0
0
2
2
0
2
1
0
2
0
1
1
0
1
2
0
1
0
2
3
1
1
2
2
1
1
1
0
1
0
1
1
1
0
1
0
1
1
1
1
1
1
1
1
0
2
4
1
2
0
2
1
1
0
2
0
2
1
1
2
1
0
0
2
1
1
0
1
0
1
3
1
2
1
0
2
1
3
1
0
1
2
1
1
1
2
1
2
1
0
1
0
1
1
0
0
0
0
2
0
0
0
0
1
2
0
1
2
0
2
1
1
2
0
0
1
1
2
2
0
1
0
1
1
0
1
0
1
0
2
1
1
1
0
2
1
1
1
1
1
1
0
2
1
1
1
0
0
1
1
0
1
1
1
1
1
1
1
0
1
1
1
2
3
1
1
3
0
2
0
2
0
1
1
1
0
0
0
0
2
1
2
1
1
2
0
2
2
1
2
1
0
1
0
1
0
1
0
2
1
1
4
1
1
0
0
0
1
1
1
0
0
0
1
0
1
1
1
0
1
0
1
1
0
2
1
2
1
1
0
0
0
0
0
2
1
0
0
1
0
1
0
0
0
0
1
0
2
2
1
2
1
0
0
0
2
1
2
0
0
1
0
2
1
1
0
0
1
0
2
2
1
1
0
1
1
1
1
1
2
1
1
2
0
0
0
1
0
0
1
0
2
2
2
1
0
1
0
1
1
1
0
0
1
1
0
0
2
1
0
0
0
1
3
0
1
1
3
2
1
1
1
1
0
1
2
0
1
1
0
1
1
2
0
1
1
0
1
1
1
1
0
1
2
1
0
0
0
0
0
0
1
1
0
1
2
1
1
0
1
2
1
0
0
0
0
1
0
1
1
1
0
0
0
0
1
1
1
1
1
1
2
1
2
0
1
1
0
2
1
1
0
2
0
2
2
0
2
0
0
2
1
0
0
2
0
0
0
1
1
1
0
0
2
1
1
1
2
2
2
2
0
1
1
1
1
1
2
0
1
1
0
2
0
0
0
0
2
0
0
1
0
0
1
0
2
1
2
1
2
2
1
2
1
0
0
1
2
1
0
0
0
2
1
0
1
1
1
1
0
1
0
2
1
1
1
0
0
1
0
0
2
1
1
0
2
1
0
0
1
1
2
3
1
0
0
1
1
1
2
2
0
2
0
0
1
0
1
0
2
1
0
1
1
1
1
1
0
1
0
2
1
1
0
1
0
1
1
0
2
0
1
1
0
1
0
2
0
0
1
1
1
0
0
1
0
0
0
2
1
1
1
0
1
0
1
2
0
1
1
1
0
2
2
2
1
0
0
1
0
0
0
0
1
0
1
1
0
1
1
1
0
0
1
0
1
0
0
1
0
1
0
1
1
2
1
1
2
1
0
4
0
2
1
0
1
1
2
1
1
0
0
2
1
0
1
0
0
1
1
1
1
1
0
0
1
1
1
0
1
1
1
0
1
1
2
0
1
1
1
1
1
2
2
0
0
0
0
1
2
0
1
1
2
0
1
2
1
0
1
2
0
1
1
1
0
0
1
1
0
0
0
2
1
1
0
0
0
2
0
0
0
0
0
1
0
0
2
1
0
0
2
1
1
0
2
1
1
0
1
1
1
0
1
1
0
0
0
1
1
0
1
1
1
1
0
0
0
1
1
1
0
1
1
0
4
0
0
1
1
1
1
1
1
2
0
0
0
0
1
0
1
4
2
2
1
0
0
0
1
1
2
1
0
0
1
1
1
2
0
0
0
1
1
1
1
2
1
1
2
1
2
0
0
1
0
2
2
1
2
2
0
0
0
1
1
1
0
0
2
1
2
2
1
2
1
0
0
1
0
2
0
1
1
0
0
0
2
2
0
1
1
2
1
0
2
0
0
0
1
2
1
2
0
0
1
1
0
2
0
1
0
1
1
1
0
1
1
1
2
1
0
1
1
1
0
0
0
2
2
2
0
1
1
0
0
1
0
1
1
0
0
1
2
0
1
0
1
0
2
1
0
0
4
1
1
1
1
0
0
0
0
0
2
1
0
2
1
1
1
1
0
1
3
2
1
1
0
0
1
1
1
2
1
2
0
2
1
0
0
1
2
0
2
2
0
1
2
1
1
0
2
2
1
1
1
0
1
0
0
0
0
0
1
1
2
1
1
2
1
1
0
0
0
1
0
1
0
0
1
0
1
0
1
2
1
4
2
1
0
1
0
0
1
0
0
1
1
0
1
1
1
0
0
3
2
2
0
0
1
1
2
1
1
1
0
0
2
0
0
0
2
2
0
0
2
0
2
1
2
0
0
0
0
2
0
1
1
1
4
2
2
0
0
0
0
0
1
0
1
1
1
0
0
2
2
0
2
0
2
0
0
0
1
1
2
0
1
1
0
2
0
2
1
1
1
1
1
0
1
0
1
0
0
0
0
1
2
1
1
1
1
0
1
2
0
1
2
0
1
0
2
2
2
0
1
2
1
0
0
0
2
0
1
2
1
2
2
0
0
2
2
0
1
1
1
1
0
1
1
0
1
0
0
0
0
1
1
1
1
1
1
1
1
2
0
1
0
0
0
1
1
1
0
1
0
1
2
1
2
1
2
0
0
1
1
0
2
1
1
2
1
2
0
1
0
1
1
1
0
0
1
1
0
1
2
1
1
1
0
1
0
0
2
1
1
1
2
1
1
0
1
1
2
1
1
1
1
0
1
0
2
0
2
2
1
0
0
0
0
1
1
0
0
1
1
0
0
0
2
1
1
2
1
0
1
1
1
2
0
2
1
0
1
0
1
0
3
1
0
1
1
1
2
3
1
2
0
1
1
0
1
0
0
1
0
0
1
1
1
0
2
0
1
1
2
0
1
1
0
1
1
2
0
2
0
1
2
1
1
2
1
0
2
0
1
2
1
1
1
1
2
2
0
2
1
2
0
1
1
1
1
0
1
0
1
2
2
2
1
0
1
2
1
2
2
1
0
2
2
2
2
1
1
0
1
0
0
2
1
1
0
1
1
1
2
0
2
1
0
0
0
2
1
0
0
2
4
0
0
2
0
1
0
0
2
0
0
1
1
2
2
1
0
0
2
2
2
1
0
1
2
3
0
0
0
0
0
0
0
0
2
0
2
1
1
0
0
1
1
1
0
1
1
1
2
4
1
1
0
1
0
2
1
1
2
1
0
1
1
1
1
1
0
0
1
0
1
0
2
1
0
1
1
0
3
0
0
1
2
1
1
0
1
0
1
0
0
1
0
0
0
1
2
0
0
1
1
2
0
0
1
0
2
0
1
0
0
0
1
1
1
1
2
2
1
1
0
0
1
0
1
0
1
2
1
1
1
0
1
1
0
0
2
2
1
0
0
0
0
1
2
1
1
1
1
0
1
0
1
0
3
0
1
1
1
3
0
1
1
1
1
1
0
0
0
0
1
2
0
1
1
1
0
1
2
2
2
1
2
2
2
0
0
0
1
2
1
2
2
1
1
0
1
1
0
1
1
0
1
0
1
2
1
0
1
1
0
1
0
1
2
2
2
1
0
1
1
0
2
0
0
1
0
1
1
0
1
0
0
0
2
1
1
0
2
1
1
1
1
1
0
2
2
2
2
1
1
1
1
1
0
1
0
1
1
1
0
0
0
0
1
0
2
2
0
2
0
0
0
0
1
0
1
2
1
1
2
1
0
1
0
0
0
2
1
2
0
0
0
3
0
1
0
0
0
2
1
1
0
1
2
2
2
0
0
0
0
1
1
1
1
0
3
1
2
1
1
1
1
1
1
1
2
0
0
1
1
1
1
0
2
0
1
0
1
2
1
2
0
0
2
0
1
0
2
0
0
1
2
1
0
0
1
0
0
1
0
0
1
1
1
0
1
1
2
0
2
1
0
1
1
0
0
2
2
0
1
1
0
1
1
1
0
1
0
2
1
0
0
0
1
1
1
1
1
0
0
3
1
1
2
1
1
1
1
2
0
1
1
0
1
1
0
1
0
0
1
1
1
0
1
1
2
1
2
1
1
1
0
1
1
1
0
2
2
0
1
2
1
0
0
2
0
1
1
0
1
1
0
1
2
0
2
2
0
0
1
2
0
2
2
0
2
0
2
0
1
0
1
0
1
2
0
0
0
0
3
0
0
1
1
1
0
1
0
0
2
1
2
0
0
0
0
1
1
0
0
1
0
0
1
2
3
0
1
2
2
1
2
0
0
1
0
1
0
1
1
0
0
1
0
2
1
1
2
1
1
0
2
1
2
2
2
0
1
2
2
1
0
1
1
1
2
1
2
0
1
0
1
0
1
2
0
1
2
0
0
1
0
0
0
1
0
1
0
1
1
0
2
0
1
1
2
0
2
0
1
0
2
2
0
0
0
1
0
2
1
3
0
2
0
2
1
0
1
1
0
1
1
0
2
0
1
0
1
2
0
0
1
0
2
1
0
0
0
0
0
1
1
1
1
1
1
2
0
1
1
2
13
1
1
1
2
2
1
2
2
1
1
1
0
0
0
0
2
2
1
0
0
3
0
1
1
2
1
1
0
1
1
1
2
2
2
1
0
2
0
2
1
1
1
1
0
1
2
2
1
1
1
1
0
0
1
0
0
1
1
1
1
1
3
1
2
0
0
1
0
3
1
1
0
1
0
1
2
0
0
1
1
2
2
0
2
2
1
2
2
0
0
1
0
1
1
1
2
0
1
2
1
1
1
1
0
0
1
0
0
0
0
1
2
1
1
1
2
2
1
2
0
1
0
0
1
2
1
2
1
0
0
0
1
1
0
2
1
0
2
1
2
0
1
0
1
0
0
0
1
0
0
0
1
0
0
2
2
3
1
0
3
1
1
0
0
1
0
0
0
2
2
0
1
1
0
0
1
0
1
2
1
0
1
0
1
0
1
0
4
1
0
1
1
1
1
0
1
1
1
0
0
0
0
1
0
2
1
0
0
0
2
1
1
2
0
0
2
2
2
2
1
1
1
2
0
1
2
1
0
2
1
1
1
0
0
0
2
1
0
2
2
1
1
0
0
1
1
0
1
0
0
0
0
0
2
0
0
1
2
0
1
1
1
0
2
0
1
1
1
0
1
1
1
0
1
0
0
0
1
1
1
2
1
1
2
2
1
1
0
1
2
0
0
0
0
0
1
1
2
2
2
1
0
1
0
1
0
2
0
2
0
1
2
0
0
1
2
0
1
1
1
1
1
2
1
0
1
0
1
1
1
1
0
0
0
2
1
1
1
0
1
2
0
0
1
1
1
0
1
1
1
1
2
1
0
1
1
1
1
1
0
1
1
1
0
0
2
0
0
1
2
1
0
1
0
0
1
2
0
0
1
0
2
0
0
0
2
1
1
1
2
0
1
1
0
2
1
2
1
0
1
0
1
0
0
0
0
1
0
0
3
0
1
1
0
0
2
0
0
0
1
1
0
1
2
1
1
0
1
0
1
1
0
1
1
2
1
0
1
1
2
1
1
2
1
1
0
0
2
0
0
1
1
3
1
0
0
1
0
1
1
1
0
1
0
1
1
1
2
2
2
2
2
1
0
1
1
1
0
0
1
0
0
2
2
2
1
0
2
0
1
1
3
2
1
2
1
1
0
0
2
2
0
0
0
0
1
0
1
1
0
1
0
2
2
0
0
1
0
0
2
0
1
0
1
0
0
1
1
1
1
1
1
1
1
2
0
2
2
0
0
1
2
1
1
2
1
1
1
2
1
1
1
0
2
0
0
3
1
1
1
0
1
0
0
1
0
1
0
0
0
1
0
1
1
0
1
0
1
1
0
2
3
1
0
2
1
1
2
1
0
0
1
2
1
1
1
1
1
0
2
0
2
1
1
0
1
1
1
2
1
0
1
0
2
1
1
2
1
1
0
1
1
2
0
0
0
1
1
0
2
1
0
1
2
1
1
2
1
2
1
0
1
2
1
1
0
1
0
0
1
1
1
2
1
0
1
1
0
1
1
2
0
0
0
2
1
2
1
1
1
0
1
1
2
0
1
1
1
1
0
0
0
1
3
2
0
0
1
1
2
0
1
1
0
0
0
0
0
0
2
1
1
1
1
2
1
1
0
0
0
2
0
1
1
0
0
1
2
0
0
0
2
2
1
1
0
0
3
0
0
1
1
1
0
1
1
2
1
1
2
1
1
0
2
1
2
1
1
2
0
1
0
1
0
2
1
2
1
1
0
1
0
2
1
0
2
0
0
1
2
2
0
0
1
0
1
2
1
1
1
0
0
0
1
0
1
1
0
1
1
1
1
2
1
1
1
1
0
2
0
2
1
1
2
0
1
0
1
0
0
1
0
2
0
1
0
1
0
0
1
1
2
1
0
0
0
1
0
0
1
1
2
2
1
1
0
1
1
1
0
1
3
2
0
2
2
0
2
1
0
0
1
2
2
0
2
1
1
2
1
1
1
0
2
1
1
1
0
0
2
2
1
1
0
1
0
0
0
0
1
1
0
2
1
2
0
1
0
1
1
1
0
2
0
1
1
1
2
3
1
0
0
0
2
2
1
0
1
1
2
1
0
1
1
1
1
1
0
1
0
1
0
0
0
0
0
1
0
0
3
0
1
1
2
1
1
1
1
0
2
2
0
2
1
1
2
2
2
1
1
1
0
0
1
0
2
1
0
1
1
0
1
1
1
2
0
2
0
0
1
3
0
1
3
0
1
2
0
1
0
0
1
1
1
0
1
1
0
1
1
1
0
1
2
3
0
1
1
1
1
0
2
2
1
1
2
1
1
1
1
2
2
1
0
1
2
1
1
2
0
3
0
1
1
0
1
2
0
0
1
1
1
0
1
0
1
1
0
2
1
1
1
2
2
1
0
0
1
2
0
0
2
1
1
1
1
0
2
1
0
1
2
1
2
0
0
0
2
1
1
0
0
1
2
1
1
1
0
1
0
2
1
1
0
1
1
3
0
0
1
1
0
2
0
1
0
1
1
1
0
0
1
0
0
0
2
1
1
1
0
0
0
0
2
0
2
1
4
2
2
1
1
0
2
2
0
1
2
1
0
0
0
1
0
0
0
2
0
1
2
1
1
0
2
1
1
1
1
0
1
1
0
1
0
6
0
0
1
0
1
2
2
0
1
1
1
0
0
0
3
0
0
1
2
2
1
1
1
0
1
1
1
2
1
0
0
1
2
1
0
1
0
1
0
1
0
0
1
0
2
1
0
1
1
2
0
2
0
1
1
1
1
0
1
0
1
1
0
0
1
1
1
2
0
1
0
1
0
0
1
1
1
1
0
1
1
0
2
1
0
1
0
0
0
1
1
2
0
1
0
0
1
2
0
2
1
1
3
0
0
0
1
1
1
0
1
3
0
0
1
1
0
2
1
1
1
1
1
0
1
0
0
0
0
0
2
1
1
4
1
0
1
0
1
0
1
0
0
0
1
1
1
1
2
2
1
2
0
0
0
1
1
2
1
1
0
1
1
3
1
0
1
1
1
0
1
0
0
0
0
2
0
1
0
2
2
1
2
2
1
0
0
1
1
2
2
2
1
1
0
0
0
1
1
1
0
1
1
1
1
3
1
1
0
0
1
2
2
0
2
2
1
2
1
0
0
1
0
0
0
1
1
1
1
0
1
0
2
1
1
0
1
2
0
1
0
3
1
1
2
1
0
0
0
1
0
0
2
0
0
0
1
2
2
1
0
1
2
1
0
1
1
1
1
1
0
0
2
1
0
1
1
1
0
1
2
2
0
1
2
0
1
2
1
1
1
2
1
1
0
1
1
2
1
0
2
2
1
0
1
1
0
1
0
2
1
1
1
2
1
0
0
0
2
1
2
2
0
1
2
2
1
1
2
1
2
1
5
2
1
2
2
1
0
0
1
0
1
1
1
0
1
0
0
0
1
0
1
1
1
3
2
2
1
1
0
2
0
1
0
1
2
2
1
1
1
0
2
1
1
0
0
2
1
2
0
1
2
1
1
0
2
0
0
0
1
2
0
3
0
2
1
1
1
0
2
1
2
0
1
0
2
2
1
2
2
0
0
1
1
0
1
0
1
1
2
2
0
1
1
0
3
2
0
0
2
0
1
0
0
1
3
4
0
0
0
1
0
2
0
1
0
0
0
2
1
1
0
0
1
1
1
0
2
1
1
1
1
0
2
0
1
2
1
0
1
0
0
1
2
0
1
1
2
0
0
0
1
1
1
2
0
3
1
1
2
1
1
1
0
1
1
0
0
0
0
1
2
1
0
1
0
2
2
2
1
0
0
1
2
1
2
2
2
1
1
2
0
2
0
1
1
0
1
1
0
0
0
0
0
1
0
0
0
1
2
1
0
0
0
1
0
1
1
1
1
0
1
1
1
0
2
1
1
1
1
2
1
0
1
0
1
0
2
0
2
1
1
0
1
1
1
1
2
0
0
1
2
1
0
0
0
1
1
2
1
1
1
1
0
0
0
0
1
1
1
2
1
1
0
2
2
1
1
0
1
1
3
2
0
1
1
0
0
2
1
0
0
1
0
1
1
1
0
2
0
0
0
0
0
2
1
1
0
0
1
0
1
1
0
1
0
0
1
1
1
1
1
1
2
0
1
0
1
1
1
1
1
2
2
0
0
0
0
1
0
1
2
1
0
0
1
0
2
1
1
1
2
0
2
0
0
0
0
2
1
1
1
1
0
2
0
2
1
0
1
1
1
1
0
0
1
0
0
2
2
1
1
1
0
1
1
1
1
1
1
0
1
1
2
1
0
2
1
1
0
1
1
1
1
0
0
2
1
1
0
0
1
1
0
1
2
1
0
1
0
2
2
1
2
0
1
1
1
2
2
1
1
0
1
0
2
0
1
3
1
0
2
2
1
1
2
2
0
1
0
0
1
1
1
0
3
1
2
1
1
0
0
0
1
1
1
2
0
1
1
1
1
0
2
2
2
1
0
1
1
0
0
1
2
0
1
1
0
1
1
1
1
0
1
0
1
2
0
0
0
0
2
0
2
0
1
1
0
2
2
1
2
0
0
1
0
2
1
1
2
2
2
0
0
2
1
2
1
0
1
1
2
0
1
3
1
1
1
0
1
0
1
1
1
1
2
2
1
1
0
0
0
1
0
0
1
1
0
2
1
1
0
2
2
0
1
1
2
2
1
0
1
1
0
1
0
3
0
0
1
1
1
3
0
0
1
0
1
0
1
0
1
1
0
1
1
1
2
0
1
0
0
0
0
3
3
0
1
0
0
1
2
2
0
0
2
1
2
1
1
1
0
2
2
1
1
1
0
0
1
0
2
2
0
2
1
1
0
2
1
0
0
0
2
0
1
3
2
1
0
2
0
1
0
2
1
0
1
1
1
2
1
2
1
1
1
2
1
1
0
1
0
1
0
1
2
2
2
0
0
0
1
0
2
1
2
0
2
2
0
2
1
1
0
0
3
0
2
2
1
0
1
0
1
1
2
0
1
0
1
1
0
2
2
0
0
0
0
0
0
1
0
1
0
1
1
0
2
0
0
0
1
0
0
2
1
0
2
1
1
3
0
1
1
1
1
1
1
1
0
0
2
2
1
1
0
1
1
1
1
2
0
0
0
0
0
0
0
2
1
1
0
2
2
0
2
1
2
1
0
1
2
2
1
0
1
1
2
0
1
1
4
1
1
1
0
0
1
1
1
2
2
0
2
0
1
3
1
2
2
0
1
2
0
1
2
1
1
2
0
1
0
0
1
1
2
1
1
0
1
1
1
1
1
0
0
1
1
1
0
2
1
1
1
2
0
1
1
2
0
1
0
0
0
0
2
2
1
2
1
0
0
1
2
0
0
0
3
2
1
0
1
1
1
1
0
1
0
1
0
1
2
1
0
1
0
1
2
2
1
1
0
1
1
0
0
1
0
0
1
1
1
0
2
1
2
1
1
0
1
1
1
1
0
1
1
1
2
2
0
0
1
0
2
1
0
1
0
0
0
1
0
1
1
1
0
1
1
2
1
1
1
1
1
1
2
0
2
1
1
1
3
0
1
1
0
2
1
0
1
1
0
1
1
1
0
1
0
1
0
1
2
2
1
1
1
0
0
1
1
1
0
2
1
1
1
2
2
3
0
1
1
1
0
2
0
1
1
1
0
1
2
0
0
2
2
0
0
0
0
0
1
2
0
0
1
1
1
0
0
1
1
0
2
0
1
1
2
2
0
1
1
3
0
1
2
0
0
0
2
1
0
1
2
0
1
2
1
0
1
1
2
1
1
0
2
1
0
0
3
1
1
1
0
1
0
0
1
1
1
1
2
1
2
0
1
0
0
9
0
1
1
0
0
1
2
2
2
0
2
2
1
1
1
1
1
1
0
1
0
1
2
2
0
0
1
2
2
1
0
0
2
0
2
1
1
2
0
0
1
1
1
1
0
1
2
1
1
1
1
1
1
1
1
2
3
0
1
0
1
1
0
0
1
0
1
0
1
4
1
1
1
1
2
0
1
2
1
1
0
1
0
0
2
0
1
2
1
1
0
1
2
1
1
1
0
1
0
2
2
1
1
3
2
2
2
1
1
2
0
0
1
1
2
1
0
0
2
1
1
1
1
1
2
1
2
0
0
2
2
0
0
2
1
2
2
2
2
0
2
0
0
0
0
1
0
2
1
1
0
2
1
1
2
0
0
0
1
1
0
0
2
0
0
2
1
1
0
1
2
1
2
0
1
0
0
1
2
1
0
1
0
0
1
0
1
0
0
1
1
2
1
1
1
0
0
0
2
0
0
2
1
0
1
0
0
1
1
1
1
1
1
1
0
1
0
0
1
1
1
0
1
0
2
1
1
2
0
1
2
1
1
4
0
2
1
1
0
2
1
0
2
2
1
2
1
3
0
0
0
2
2
0
1
1
2
1
0
2
2
1
1
0
2
1
1
2
0
1
1
0
0
1
1
0
0
2
2
1
1
0
0
0
0
1
1
1
0
1
1
1
0
2
0
1
0
1
2
2
1
0
1
1
2
1
1
1
2
1
0
3
0
1
1
1
2
2
1
0
1
2
0
0
0
0
1
0
1
0
0
1
0
2
0
1
0
1
1
0
0
0
1
0
1
2
1
0
2
2
1
2
1
1
0
1
1
0
1
1
1
2
0
0
0
1
0
1
1
1
0
0
1
1
1
0
1
1
0
0
1
2
2
1
1
1
1
1
2
0
1
1
1
0
1
0
1
1
0
1
2
2
2
2
0
0
0
0
0
1
1
1
1
2
1
0
2
1
2
0
0
2
1
1
1
0
0
2
1
0
2
2
1
1
0
2
1
1
1
1
1
2
1
1
0
1
0
2
2
1
0
0
2
1
0
0
1
0
1
2
0
1
0
2
2
1
2
0
0
0
0
0
1
2
1
0
0
1
0
1
1
2
1
0
1
1
0
0
1
0
0
0
2
0
1
1
2
1
1
0
1
1
2
5
1
2
2
1
1
2
1
1
2
0
0
0
2
1
0
1
0
0
1
1
0
2
0
0
2
3
0
1
0
1
2
1
0
1
0
2
1
1
0
0
0
0
1
0
3
0
0
1
0
2
0
1
0
1
0
0
2
3
1
1
0
2
1
1
1
0
1
0
1
1
1
1
1
1
2
1
2
1
0
0
0
0
1
2
0
1
0
0
0
1
1
2
0
1
1
0
1
0
2
0
1
0
0
1
1
0
0
1
2
2
0
1
1
3
0
1
2
0
0
2
1
1
0
1
1
1
1
1
0
1
3
0
0
0
0
0
1
0
0
0
0
0
1
1
1
1
0
0
1
1
0
2
0
1
0
0
0
2
1
0
2
0
0
1
0
1
1
1
1
1
2
1
1
1
2
0
1
3
0
2
1
1
1
1
0
0
1
1
1
0
0
0
2
1
0
0
0
1
0
1
0
2
2
1
0
1
1
1
1
1
0
1
0
2
2
1
1
1
1
2
0
1
2
0
2
0
2
1
0
1
1
0
0
0
1
0
1
2
0
1
1
0
0
2
0
1
2
2
1
0
2
0
1
1
3
1
0
0
0
1
0
0
1
0
1
1
0
1
2
0
1
1
1
0
0
0
0
0
2
0
0
0
1
0
1
0
1
1
1
1
0
1
0
1
2
1
0
0
2
1
1
0
3
1
2
0
2
0
1
0
1
0
2
2
2
1
1
1
1
0
0
2
1
0
2
0
1
0
2
0
2
1
1
2
2
3
0
1
0
1
1
1
0
1
0
1
0
2
0
0
0
1
0
2
1
0
2
0
2
0
1
1
1
1
0
1
0
1
2
0
1
9
1
3
1
0
0
1
1
1
0
0
0
1
1
1
1
0
2
3
0
2
1
2
2
0
1
1
0
1
0
1
0
1
4
0
1
0
1
2
2
1
2
0
0
0
1
0
1
0
2
0
1
0
0
1
1
3
2
1
1
1
2
1
0
3
1
0
0
0
2
0
0
2
1
1
2
1
0
0
1
2
1
2
2
1
0
1
0
1
0
0
1
0
1
0
1
1
1
0
2
0
0
0
1
1
0
0
1
0
0
0
1
0
0
1
2
0
1
0
2
2
0
1
0
1
1
2
1
2
1
1
2
0
2
0
1
1
0
1
1
0
0
2
0
1
0
2
1
1
0
0
2
1
0
0
3
2
0
2
1
1
0
1
0
0
0
0
1
0
0
0
1
0
0
2
1
2
0
0
1
3
2
0
2
1
0
1
0
2
2
1
0
0
2
1
1
0
1
2
1
1
2
1
0
0
0
0
1
2
0
0
2
3
1
2
1
0
1
2
1
1
0
2
2
1
1
1
2
0
1
1
1
2
2
1
2
1
1
0
0
2
2
1
0
2
2
1
2
2
2
0
1
2
1
2
1
1
2
2
0
2
1
0
0
1
0
0
0
2
0
0
0
0
2
2
1
1
1
0
0
0
0
1
0
0
1
1
0
1
1
0
1
0
1
1
2
1
0
1
0
1
0
2
2
2
0
2
2
0
0
3
2
1
0
0
0
1
0
0
2
2
0
0
2
0
2
0
1
0
1
0
1
2
1
1
0
1
1
2
1
1
2
1
0
0
1
1
0
1
0
0
2
1
1
0
2
1
0
2
1
0
0
0
0
1
1
0
0
0
0
1
0
0
5
1
0
2
0
0
0
0
0
1
0
2
1
2
1
2
2
2
1
2
0
1
1
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
1
1
1
0
1
1
2
1
0
0
1
0
1
1
0
1
3
0
3
2
2
2
2
2
0
0
0
1
0
1
0
1
1
1
2
0
0
1
2
1
1
1
2
3
1
2
0
0
0
1
1
1
0
1
2
2
1
2
1
2
2
1
1
2
0
1
1
1
1
0
0
2
0
1
0
2
0
0
1
1
0
1
1
0
0
1
2
0
2
1
0
0
0
1
1
0
0
2
2
1
0
2
0
0
1
0
1
1
0
2
0
0
1
2
0
0
0
0
0
0
1
1
1
2
1
1
1
1
0
1
1
1
2
1
2
2
1
2
1
1
0
0
0
2
0
1
3
0
0
0
0
0
2
0
2
0
2
0
0
2
0
2
0
0
0
2
1
1
0
0
0
2
2
0
1
1
1
0
0
2
2
1
0
1
0
1
0
0
0
2
1
2
2
0
2
0
2
2
0
2
0
0
0
1
0
0
0
1
0
1
1
1
1
1
1
0
0
1
1
1
1
0
0
0
1
0
3
0
0
0
1
1
2
1
0
1
2
2
1
0
1
0
0
1
2
2
1
0
1
0
0
3
1
0
0
1
0
0
0
0
0
1
2
0
0
2
0
0
1
1
1
1
1
0
0
1
1
1
1
0
1
1
0
1
0
2
0
1
2
0
0
1
2
0
0
1
0
0
1
1
0
1
0
1
1
2
1
0
0
0
2
0
1
1
0
2
1
0
1
1
0
1
0
1
1
1
2
1
0
1
0
1
0
0
1
0
1
1
0
2
2
2
0
0
3
1
1
1
0
0
2
0
0
1
1
2
2
1
2
1
2
0
0
1
1
0
0
2
1
2
1
2
1
1
3
2
2
1
1
0
1
1
0
1
0
1
0
2
1
1
2
0
1
2
0
2
2
1
0
0
0
1
0
0
2
0
0
1
0
1
2
0
1
1
1
1
1
2
2
1
2
1
1
0
1
2
2
0
2
2
2
1
0
2
2
0
1
0
1
2
2
0
0
2
1
2
0
1
1
0
0
0
1
1
0
1
1
2
1
2
2
0
1
1
4
1
0
3
0
0
2
0
2
1
2
1
1
0
1
1
2
1
2
0
1
0
1
0
1
0
1
2
0
2
0
0
0
1
2
2
1
0
0
1
0
1
1
1
3
1
1
0
0
0
0
1
1
1
1
0
1
0
2
2
2
1
1
0
0
2
1
1
1
1
1
2
1
1
0
0
0
1
2
0
1
1
0
2
2
1
1
0
0
0
0
0
1
1
3
0
2
1
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
1
1
0
3
0
0
2
1
2
2
1
2
0
2
1
1
1
1
2
1
1
2
1
1
0
2
0
2
1
1
1
2
2
1
0
1
2
1
2
1
0
1
1
0
1
1
1
0
1
1
0
2
2
0
0
1
2
0
0
1
1
0
1
0
0
0
2
0
3
2
0
1
2
1
0
2
1
1
1
1
0
1
1
0
1
3
0
0
0
0
2
1
2
0
0
0
1
1
1
2
1
1
0
2
1
2
2
2
1
1
0
2
1
1
0
1
1
2
0
2
1
1
0
1
1
0
2
1
2
0
2
1
2
0
1
0
3
0
1
0
0
1
2
1
1
0
2
1
1
0
1
1
2
0
0
0
0
0
1
0
0
1
0
1
1
1
0
1
2
1
0
1
1
2
2
0
1
1
2
1
1
2
2
1
2
0
0
2
0
0
1
1
1
1
1
1
1
1
1
0
0
1
1
1
1
2
0
0
1
0
0
0
1
1
1
2
0
2
2
0
0
0
2
0
1
1
1
2
1
1
0
0
0
1
2
1
0
1
1
1
1
1
1
0
0
1
1
1
1
1
0
1
0
0
1
1
2
2
1
1
0
0
1
1
1
0
1
0
2
1
1
1
2
1
1
1
0
1
1
1
0
0
1
2
1
2
2
0
0
2
1
0
1
1
1
1
0
1
0
2
2
2
1
2
1
0
0
1
3
1
2
0
0
0
1
1
0
0
1
0
1
0
2
2
1
1
2
2
1
0
1
1
1
1
1
1
1
1
0
2
1
0
1
2
0
2
0
1
2
2
1
1
0
0
0
0
2
2
0
0
1
0
0
1
0
1
0
1
1
0
1
0
0
1
0
2
2
1
1
1
0
2
1
2
2
0
2
2
1
5
1
2
1
1
1
2
1
2
0
0
0
0
1
1
1
1
0
1
1
0
1
0
1
1
0
2
0
1
0
2
2
0
1
2
2
1
1
2
2
1
2
1
0
1
2
0
1
1
2
0
1
0
0
0
1
1
1
0
1
0
1
2
1
2
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
2
1
1
0
0
1
1
0
0
0
2
2
0
1
1
1
1
1
1
1
0
1
1
1
1
0
1
0
0
1
2
0
2
1
0
1
0
2
2
3
2
0
2
1
0
1
0
0
0
0
0
2
1
1
1
1
1
3
2
0
1
2
1
0
0
1
2
1
1
1
0
0
1
1
0
2
1
0
0
0
1
2
1
1
2
1
2
1
1
2
0
1
0
0
0
0
1
1
3
2
2
0
0
1
0
2
1
0
2
0
0
2
0
2
2
1
1
0
0
1
2
0
2
2
1
0
2
1
2
0
1
0
1
0
0
1
0
1
1
1
2
1
0
1
1
1
1
1
1
2
0
2
2
1
1
1
2
1
2
0
2
0
1
2
1
1
1
1
0
0
0
1
1
1
0
1
2
1
1
1
0
2
2
0
0
1
1
1
2
4
1
0
0
0
2
1
0
2
1
1
1
1
2
1
1
1
2
2
1
1
1
1
2
2
1
1
1
2
0
0
2
2
1
2
0
0
0
2
2
0
1
0
0
2
1
1
2
0
0
1
0
2
1
0
0
2
2
2
2
0
2
0
1
0
0
2
1
3
1
1
1
1
1
2
2
2
0
1
1
0
1
0
0
2
2
0
0
0
0
1
0
1
2
3
1
1
1
0
2
0
0
2
0
1
2
3
1
1
1
0
1
0
0
0
1
1
1
0
2
0
1
0
1
0
4
1
0
0
2
1
2
0
0
1
1
3
2
0
1
2
1
1
1
1
1
2
2
0
2
1
2
1
0
1
2
0
2
2
1
1
2
0
2
1
1
1
1
1
2
2
0
0
1
0
0
0
0
0
0
1
0
0
2
2
3
0
0
0
0
0
0
2
0
2
1
1
4
1
0
2
1
0
0
1
2
1
1
2
1
2
1
1
1
1
0
1
2
1
2
2
0
0
2
0
3
0
2
1
1
1
2
1
3
2
2
2
0
1
1
1
1
1
1
0
0
0
1
2
1
0
1
0
1
1
0
0
2
0
1
1
2
1
1
0
1
2
1
2
2
2
0
0
0
1
2
1
2
1
2
0
1
1
1
2
0
1
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
0
0
2
1
0
1
0
0
2
1
0
0
3
2
1
0
0
1
1
1
1
0
2
1
0
0
1
1
1
0
2
1
0
2
1
0
0
0
2
1
0
0
1
1
1
1
3
0
1
1
0
0
2
1
1
0
0
0
1
0
0
1
1
0
0
2
1
2
0
0
0
1
0
0
2
0
0
0
1
3
0
0
0
0
2
1
0
1
2
1
1
1
2
2
1
2
1
0
0
2
2
0
3
0
0
1
0
0
0
0
1
0
1
2
1
2
0
1
1
1
1
1
0
2
0
2
1
0
0
0
1
1
1
1
1
1
1
0
0
1
2
2
1
0
2
2
1
0
0
0
1
2
2
0
0
1
1
0
1
1
0
0
0
1
3
1
1
0
1
2
1
1
0
1
0
0
2
1
0
2
2
1
1
1
1
1
1
0
1
1
0
0
1
1
1
1
0
1
1
0
1
1
1
0
1
1
0
1
0
0
2
0
0
2
3
0
1
2
0
2
0
1
0
0
1
0
1
0
1
1
1
1
0
1
2
1
0
0
1
2
2
2
1
1
2
0
1
0
3
2
1
0
0
2
0
1
1
2
1
1
0
0
1
0
0
1
0
1
0
1
0
1
0
1
0
1
1
0
1
1
0
1
2
1
0
1
2
0
1
2
2
1
2
3
1
0
0
2
1
1
0
0
1
1
1
1
2
0
2
1
1
1
1
1
1
1
0
0
1
0
1
1
1
1
0
2
1
1
1
1
0
0
1
3
1
1
0
0
2
0
0
0
1
1
1
1
2
1
1
1
0
1
1
0
2
1
1
0
0
1
0
1
2
0
1
0
1
1
4
1
0
0
0
0
0
0
0
0
1
0
1
2
1
2
1
1
1
0
1
2
2
1
0
0
1
0
0
1
2
2
0
1
0
1
1
0
0
0
2
1
1
1
2
1
1
1
0
1
0
1
0
1
1
1
2
1
1
1
0
1
2
2
2
0
2
0
0
1
1
2
0
0
1
1
0
1
2
0
1
1
0
0
2
0
1
1
0
2
0
0
1
1
1
1
1
1
0
1
0
2
1
1
0
1
0
0
2
0
1
1
2
1
1
0
2
2
2
0
0
2
1
0
1
0
0
1
2
1
1
1
2
0
2
1
1
2
0
1
0
1
0
0
1
1
1
2
0
0
2
0
0
1
3
1
1
0
1
0
0
2
2
0
2
1
1
2
0
0
0
2
2
1
0
0
2
2
0
2
0
1
1
1
0
1
1
1
0
0
2
0
1
0
0
1
0
1
0
0
1
1
0
1
0
2
2
0
0
1
0
1
1
1
1
1
4
1
2
0
0
4
1
0
1
0
0
1
0
1
0
2
1
1
0
0
2
0
2
0
1
2
2
0
0
1
2
2
0
0
1
1
0
1
0
0
0
2
1
1
0
2
1
0
2
0
1
1
2
1
2
1
1
1
1
1
2
1
2
0
1
2
2
0
1
1
2
1
1
0
2
1
2
1
2
1
2
1
1
1
2
2
1
1
0
0
1
1
0
0
0
0
0
1
0
2
1
1
2
1
2
0
1
2
1
0
1
2
1
1
0
0
0
1
1
0
0
0
0
1
1
2
1
0
1
0
1
0
0
1
1
1
0
2
1
0
0
0
2
2
2
1
1
0
1
1
0
1
2
1
1
0
1
1
1
1
0
2
1
1
0
0
0
1
0
1
0
0
1
1
0
0
1
2
1
1
1
0
2
0
0
2
1
1
0
1
2
1
1
0
1
0
0
0
0
0
2
1
1
2
1
2
4
0
1
2
1
0
1
0
2
1
0
1
2
0
2
0
1
1
1
2
2
0
0
1
0
1
2
1
1
0
2
1
0
0
2
0
1
0
1
2
1
2
1
0
1
1
0
1
1
1
1
1
1
1
1
1
0
0
0
2
2
0
0
1
1
1
2
0
1
0
1
0
3
1
1
1
1
2
1
1
0
1
0
0
2
0
1
2
0
0
1
2
2
0
0
1
1
0
1
2
2
0
0
1
2
1
1
1
1
1
2
2
0
0
1
0
1
0
1
0
1
1
0
1
2
1
0
0
0
0
4
1
1
1
2
1
2
2
1
1
1
0
1
1
1
1
1
1
1
0
0
0
1
1
0
2
2
1
0
1
1
1
1
2
2
1
2
1
2
0
0
1
2
1
1
0
1
0
0
2
0
0
1
0
0
1
1
2
1
1
1
1
3
1
1
2
2
2
0
1
0
1
2
2
1
1
1
1
0
1
1
2
0
1
1
1
0
2
0
2
0
2
0
1
0
1
0
1
0
1
1
1
1
0
0
0
2
0
0
1
2
0
1
0
1
2
1
1
0
0
1
1
1
0
0
1
0
0
0
1
1
0
0
1
0
1
1
0
0
0
2
1
2
1
0
0
0
0
1
0
1
1
1
0
1
1
2
0
1
0
2
2
2
1
2
0
1
1
2
1
0
1
1
1
2
1
2
0
0
0
0
2
0
0
1
1
2
2
1
1
1
1
0
0
2
0
2
0
1
1
2
1
0
1
1
0
1
1
0
2
0
1
2
2
1
2
2
0
3
2
2
2
0
0
2
0
0
1
0
2
1
0
1
1
2
2
2
1
2
1
0
1
2
0
1
1
0
2
1
0
0
1
1
0
0
1
0
0
1
2
2
1
1
2
1
0
0
2
1
2
2
2
1
1
2
0
0
1
1
0
2
1
0
1
2
0
2
1
1
0
1
1
2
2
1
2
1
0
1
1
0
0
2
1
1
0
1
0
2
2
0
1
2
1
0
0
0
0
1
0
1
1
0
1
1
0
0
0
1
1
1
1
0
0
1
2
1
1
2
0
0
1
0
2
0
0
2
1
1
1
0
1
0
1
1
1
0
2
0
1
0
1
2
1
0
1
1
2
0
0
0
0
1
0
1
1
0
0
0
1
0
2
3
1
1
1
1
0
0
0
0
0
2
1
0
0
1
1
0
2
0
1
2
1
0
1
1
2
0
1
1
2
0
0
2
1
1
1
2
0
1
1
1
0
1
0
1
0
0
0
3
0
1
0
2
2
1
1
1
0
0
0
1
1
0
0
1
0
0
1
1
1
1
1
0
2
1
1
0
1
1
0
1
1
2
1
1
1
2
2
2
2
1
0
2
1
0
1
1
1
1
0
1
1
1
0
1
0
0
1
1
2
0
1
1
2
1
2
0
2
2
0
1
1
1
0
0
0
1
1
2
1
1
0
2
1
2
2
0
0
1
1
1
0
2
1
1
1
0
1
1
1
1
1
0
2
0
1
1
2
0
0
2
1
0
2
0
1
0
1
1
0
1
0
1
1
2
1
1
1
1
2
2
1
2
0
1
0
2
0
6
0
1
0
2
2
2
0
1
0
2
0
0
1
1
1
2
0
1
2
2
0
1
1
0
1
0
0
0
1
1
0
0
1
1
1
1
1
0
1
0
0
0
0
2
0
2
0
2
2
1
0
1
1
0
2
0
1
0
1
1
1
2
1
0
1
0
0
1
2
1
0
0
2
0
1
1
2
1
1
0
2
1
3
1
2
1
0
0
0
1
2
0
0
2
0
0
0
0
2
2
2
0
0
1
1
0
0
1
1
1
2
0
1
1
0
1
1
1
2
0
1
1
1
0
2
0
1
2
0
0
2
2
2
1
1
0
1
2
1
1
3
2
2
0
0
1
1
2
0
1
0
2
2
1
1
0
1
0
0
2
1
0
1
2
1
0
1
1
0
1
0
0
0
1
0
1
0
1
0
0
2
0
0
0
1
0
2
1
0
1
2
1
0
0
1
1
2
1
1
1
2
2
1
1
2
0
2
1
1
2
0
0
1
1
2
1
1
1
2
2
1
0
1
1
1
1
0
0
1
0
0
2
1
1
0
1
2
1
0
2
1
0
2
2
1
1
0
4
1
1
3
0
2
1
0
0
1
0
2
0
2
2
0
0
1
0
1
2
2
0
0
0
2
0
0
0
2
0
0
1
0
0
1
1
1
0
0
2
0
2
0
1
1
2
1
1
1
0
1
2
0
2
1
2
1
0
0
0
1
1
0
2
2
1
1
0
1
1
1
2
1
1
0
1
1
0
1
2
2
0
1
0
1
1
1
0
0
1
1
0
0
2
0
2
0
2
1
2
2
3
0
1
2
1
0
1
0
1
0
1
0
1
1
0
1
1
0
1
1
0
0
0
0
2
1
1
0
1
0
2
2
1
1
0
1
1
2
0
0
1
1
2
0
2
0
0
0
1
0
0
1
0
0
0
1
0
0
0
2
0
1
0
1
2
1
0
1
1
1
0
1
1
0
1
2
1
0
0
0
1
1
1
1
1
1
1
0
2
0
0
0
0
0
0
1
1
1
1
1
1
1
0
0
1
0
0
1
0
0
0
1
1
2
1
1
2
1
2
2
1
0
0
0
1
1
2
1
1
0
0
1
1
0
2
0
1
1
2
2
1
0
1
1
1
0
0
1
2
1
0
0
1
2
1
0
1
2
2
1
2
2
1
0
1
1
1
0
1
1
1
0
2
2
1
1
0
1
0
1
1
1
0
1
0
2
0
1
1
1
2
1
0
1
2
1
1
2
1
1
2
0
0
0
0
1
2
0
0
1
2
0
1
0
0
1
1
1
5
1
2
1
0
1
1
1
1
0
1
1
1
2
1
0
2
1
2
1
1
0
1
0
0
2
1
0
0
1
1
1
2
1
2
0
0
1
0
2
0
2
2
0
0
2
1
0
1
2
2
1
1
0
1
2
2
5
2
0
1
1
1
2
1
1
1
0
1
1
1
1
0
0
1
2
1
2
1
2
0
0
1
0
1
0
0
0
1
0
0
2
1
2
1
0
1
1
0
1
1
2
1
0
1
1
1
1
3
1
0
1
1
0
0
0
0
0
0
2
0
0
2
0
1
1
1
1
0
2
1
1
2
0
1
0
1
0
1
1
2
1
0
0
0
1
1
1
1
1
1
0
2
1
1
1
2
1
1
2
0
2
1
2
1
2
0
0
0
1
2
1
0
0
0
1
1
1
1
2
0
0
1
2
0
2
2
1
1
1
0
1
2
1
2
1
0
0
1
0
1
0
0
0
2
1
0
2
1
1
0
0
0
2
1
0
1
0
0
1
2
1
1
0
2
0
1
0
0
2
1
1
1
0
0
2
1
0
0
2
0
0
2
1
1
0
0
1
0
1
1
2
0
1
0
0
1
1
1
1
1
2
0
2
1
1
1
0
0
1
0
1
1
1
0
1
3
1
0
0
0
1
2
0
2
0
4
0
5
1
2
1
0
2
1
0
1
2
2
0
0
0
3
2
1
1
2
2
3
0
0
0
1
0
2
1
1
0
1
1
0
2
2
2
0
1
0
0
1
2
0
1
0
0
0
1
2
2
3
3
0
2
2
0
0
1
0
1
0
2
0
2
1
1
1
0
0
0
0
0
0
1
0
1
1
1
1
3
1
2
2
0
1
2
1
2
1
2
1
0
2
0
0
2
0
0
2
1
1
0
2
0
0
1
1
1
0
0
1
0
1
0
1
0
0
2
1
2
1
1
1
2
0
0
1
1
0
1
1
1
0
1
0
1
0
1
1
0
2
2
1
0
0
1
0
0
0
2
2
2
1
2
1
0
1
0
1
1
0
1
2
1
0
0
0
2
2
0
0
2
1
0
2
1
1
0
0
1
1
1
1
0
1
0
1
2
2
0
0
1
0
0
1
1
1
1
0
1
1
2
0
2
1
0
2
1
2
0
2
0
0
0
0
0
1
1
0
4
1
0
0
2
1
0
1
2
1
0
1
1
1
1
1
1
1
0
2
1
2
1
1
0
1
1
2
0
1
1
3
1
2
0
0
2
2
2
1
1
0
0
1
2
0
1
2
0
1
0
1
2
1
1
0
0
1
2
2
1
0
1
2
0
0
0
1
0
2
0
1
1
2
0
1
1
0
2
0
1
1
0
0
2
0
2
1
1
1
0
1
3
0
0
0
0
2
1
1
2
2
0
2
2
2
0
0
1
0
1
1
2
1
2
1
1
2
1
1
1
1
0
1
1
0
0
0
0
1
0
2
0
1
1
1
0
1
0
1
2
0
0
1
0
0
0
1
0
1
3
1
0
1
0
0
2
0
1
1
0
0
2
1
0
1
0
1
1
2
2
0
2
0
1
0
0
0
1
1
0
2
0
0
2
2
2
0
1
0
0
1
1
0
0
1
1
2
0
0
0
1
0
2
2
1
2
1
2
2
1
2
1
1
0
1
0
1
1
0
0
2
2
2
0
0
2
1
0
2
1
0
1
2
1
1
1
2
2
1
1
0
2
1
1
0
2
1
2
1
2
1
0
0
2
0
0
0
0
1
0
1
1
0
2
2
2
2
0
0
1
0
2
0
2
2
1
0
1
1
2
0
1
0
1
2
1
0
0
1
1
1
1
1
0
1
0
0
2
0
1
0
0
0
2
2
0
0
1
0
1
1
1
2
1
1
0
1
0
0
1
1
1
0
1
1
0
2
0
1
1
0
2
1
0
2
0
1
0
2
1
0
2
1
1
2
0
0
1
2
0
2
1
3
2
1
1
0
0
2
2
1
0
1
2
0
1
1
0
1
1
1
1
1
1
1
1
1
2
2
0
1
2
2
1
2
0
1
1
0
0
2
1
0
1
3
1
1
0
1
1
2
0
0
2
2
2
2
1
1
0
1
0
1
2
0
2
0
1
0
1
0
2
1
0
1
2
0
1
1
2
0
2
0
1
2
0
2
2
2
0
2
1
1
1
1
2
1
1
0
2
1
1
0
0
0
1
1
1
0
1
1
1
1
2
0
1
2
0
1
2
2
0
1
2
1
1
0
2
0
2
1
0
1
2
1
0
1
2
2
1
1
0
2
1
1
1
1
0
0
0
0
1
2
0
2
1
1
0
0
1
2
1
0
1
3
0
0
1
0
1
0
0
1
0
1
0
1
2
1
0
0
0
0
1
1
1
2
1
0
1
1
1
1
1
1
2
1
0
1
1
0
1
2
2
0
1
1
2
2
0
0
1
2
2
1
2
1
0
1
1
1
3
0
1
1
1
0
0
2
0
0
0
1
1
2
2
2
1
0
1
1
1
1
0
2
1
0
0
2
0
1
1
1
2
2
0
2
1
0
2
0
0
1
1
0
1
1
2
1
2
1
1
0
2
2
0
2
1
1
1
1
1
2
1
2
2
2
0
1
0
2
3
2
1
1
0
2
0
0
0
0
0
2
0
0
1
2
1
0
0
2
1
1
1
1
1
1
0
0
0
3
0
2
0
2
2
1
3
0
2
0
2
1
0
1
0
1
0
0
1
1
1
0
0
2
0
2
0
1
1
2
2
1
1
2
0
1
2
1
1
1
1
2
1
0
2
2
0
2
2
2
0
1
1
0
1
2
1
0
1
1
0
0
1
2
1
2
0
1
0
1
1
0
1
0
1
1
2
0
3
1
2
1
1
0
0
1
1
2
1
3
1
1
0
1
0
1
2
1
0
1
1
1
2
0
0
1
0
2
1
2
0
1
0
2
1
1
0
0
0
2
1
0
3
1
0
2
1
0
0
2
1
2
0
0
1
1
1
0
0
0
0
0
0
1
0
1
1
1
0
2
0
0
2
1
0
0
1
2
2
2
0
3
2
1
1
1
1
0
1
1
1
2
2
2
2
1
0
0
1
0
1
2
4
0
2
0
1
0
1
1
1
0
0
2
0
2
2
1
2
2
2
1
0
1
2
1
0
1
1
0
0
1
2
0
1
1
0
1
1
3
1
1
1
2
2
1
1
1
1
1
1
1
1
0
2
2
0
0
1
1
1
0
2
2
0
0
2
0
2
0
2
2
0
2
1
1
1
2
2
0
1
2
1
0
0
0
0
4
1
1
1
1
0
2
1
2
0
0
2
2
2
2
0
1
1
2
1
1
1
1
1
0
1
1
1
0
0
1
0
2
0
1
0
2
1
1
2
1
1
0
1
0
2
0
1
1
1
2
2
1
2
1
1
1
0
1
1
2
1
2
0
1
0
2
2
1
0
2
4
0
0
2
0
2
1
2
2
2
2
0
2
0
0
1
2
0
0
2
0
1
0
2
1
1
1
0
1
0
0
1
1
0
0
0
4
1
1
1
0
0
1
2
0
2
4
1
0
0
2
0
2
1
0
1
0
1
2
1
1
1
0
0
2
2
1
0
0
1
2
0
0
1
1
0
1
1
1
1
0
1
0
2
1
1
2
1
1
0
0
2
0
0
3
1
2
0
0
0
3
1
2
0
4
1
1
1
0
0
0
1
0
0
1
1
0
1
1
0
2
2
3
1
1
0
0
2
1
2
2
0
3
1
1
0
0
1
1
1
0
2
2
1
0
0
1
1
0
0
0
1
0
2
1
1
2
0
1
2
0
0
0
1
0
1
1
0
0
1
2
0
0
1
0
2
1
1
1
0
1
0
1
2
0
2
1
2
2
2
1
2
1
1
1
6
0
1
0
0
0
2
0
1
1
0
1
1
0
0
1
2
1
0
2
0
1
0
1
1
2
0
0
0
1
1
0
0
0
1
0
2
0
0
4
0
0
1
0
0
1
1
1
0
2
0
2
0
1
0
1
1
2
1
1
0
1
2
1
1
1
1
0
0
1
1
1
2
2
1
1
0
2
0
0
0
1
0
0
2
2
0
0
0
0
0
1
1
2
0
1
2
0
2
0
0
0
0
2
2
1
0
0
1
1
0
1
0
0
1
1
1
2
1
1
2
1
1
0
0
0
2
0
1
1
1
1
1
1
1
1
0
1
0
0
0
0
0
1
1
2
1
0
0
0
0
2
2
1
1
2
1
1
0
0
0
0
1
0
1
0
2
0
1
1
1
1
0
0
1
0
0
1
1
0
2
2
2
1
3
0
2
0
0
1
1
1
2
1
0
0
0
0
1
1
2
2
1
1
1
0
2
2
0
1
1
1
1
1
1
1
2
0
1
0
0
0
0
1
1
0
1
1
1
0
1
1
1
0
0
2
3
1
1
0
0
1
2
1
0
1
0
1
0
0
0
2
1
0
0
1
0
0
2
0
3
2
1
0
2
2
3
1
0
0
1
2
1
2
3
1
2
1
1
0
2
1
0
0
2
2
1
0
0
0
1
1
0
0
1
1
0
1
1
1
0
1
1
0
1
0
1
2
3
1
1
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
1
2
1
0
0
1
0
0
0
0
0
0
0
2
0
1
2
1
1
0
1
1
0
0
0
0
0
1
1
1
1
0
0
0
0
1
0
1
2
2
1
0
1
1
1
1
1
1
1
0
0
0
0
0
2
1
1
1
0
3
2
0
1
0
0
0
0
1
2
0
0
1
0
2
1
1
0
1
2
1
1
0
1
0
2
1
1
0
1
2
1
0
1
1
0
1
1
1
1
1
2
2
2
0
1
1
2
0
1
0
2
1
1
2
1
0
0
0
0
1
0
1
1
0
0
2
0
0
1
1
1
0
1
1
0
2
0
0
0
0
2
2
0
0
1
1
0
1
2
0
1
2
0
1
1
0
0
0
0
0
1
1
1
2
0
2
1
0
0
0
1
0
0
1
0
1
0
0
2
0
0
1
1
1
1
1
1
0
0
1
0
0
1
0
2
1
1
1
2
0
2
0
0
3
2
1
1
1
1
1
0
1
0
1
1
0
0
1
0
0
1
0
2
0
0
0
3
0
1
1
1
1
1
2
2
1
0
2
0
1
1
0
1
1
1
0
1
0
1
0
0
1
1
1
1
0
1
1
2
1
1
1
1
1
1
0
1
1
0
1
1
1
1
2
0
0
0
1
0
0
1
0
3
1
0
1
2
2
2
2
1
0
0
0
0
0
0
0
2
2
1
2
0
0
3
1
1
2
2
1
0
1
2
1
1
0
0
0
3
2
1
0
1
2
0
1
2
1
2
0
2
2
0
0
0
0
1
1
0
1
1
1
2
1
0
0
0
1
1
2
1
1
2
1
2
1
0
1
2
1
1
1
2
0
1
0
3
1
1
0
2
0
0
1
1
0
1
1
1
1
1
0
1
0
0
0
1
2
0
1
0
1
1
2
1
1
0
1
0
0
1
0
0
0
1
1
0
1
0
2
1
2
1
0
0
2
1
0
0
0
2
2
1
0
1
1
0
0
0
0
0
3
0
2
0
1
2
1
0
2
1
0
1
2
1
0
2
1
0
1
0
2
2
1
1
0
0
0
1
0
0
2
0
0
1
1
0
0
1
1
2
0
1
2
0
2
1
0
1
1
0
2
0
1
2
2
1
2
0
0
1
2
0
2
2
1
1
1
0
1
0
2
0
1
1
1
1
1
0
1
2
0
0
1
0
1
1
2
2
1
1
1
2
0
0
0
0
0
1
1
1
0
0
1
0
0
1
0
0
2
2
0
0
1
0
1
1
2
2
1
2
1
1
0
1
2
0
0
2
2
1
2
1
0
0
1
0
2
1
2
1
1
1
1
0
2
0
1
0
2
2
2
2
1
2
2
2
1
0
1
0
0
1
2
2
1
1
3
1
0
0
2
1
1
1
2
1
1
1
0
2
1
1
2
2
0
0
2
0
1
0
2
2
0
0
2
1
1
2
0
1
0
6
2
1
2
0
0
1
1
1
2
2
1
0
0
1
0
2
0
0
0
2
1
1
1
1
2
1
0
0
1
1
0
2
1
1
2
2
0
2
1
2
0
0
2
1
1
1
0
0
1
2
1
2
1
2
1
1
3
0
1
1
0
1
1
1
0
0
1
0
1
0
1
8
2
1
2
0
1
3
1
0
2
0
0
1
1
1
2
2
1
2
2
1
1
1
1
0
1
0
0
1
2
0
0
2
2
0
2
1
2
1
1
1
0
1
0
2
0
1
1
1
2
1
1
2
0
2
2
0
2
1
1
0
2
0
1
2
2
0
0
0
0
2
2
1
1
0
3
1
1
1
4
2
0
2
1
1
0
1
0
0
2
2
2
0
1
2
2
2
0
1
0
0
0
1
0
1
0
1
0
0
0
1
1
1
0
1
1
3
0
2
1
2
0
1
0
1
1
1
0
1
2
0
1
0
2
0
1
1
0
2
1
0
0
2
0
2
0
0
0
1
1
1
1
1
1
2
2
0
0
2
2
2
0
3
2
0
1
1
2
2
1
2
0
2
2
0
1
2
0
1
1
0
1
1
2
1
1
1
3
2
1
0
1
1
1
0
0
0
0
1
1
1
0
1
0
1
2
0
0
0
1
1
2
2
2
1
1
2
2
1
0
0
1
1
1
0
1
1
2
1
0
1
1
1
1
0
1
2
2
1
2
1
1
0
1
1
2
1
1
1
2
0
1
1
4
1
1
1
0
1
0
1
1
1
1
1
2
2
2
2
0
0
2
1
1
0
2
1
1
0
2
1
1
1
0
1
1
1
2
1
1
1
4
2
0
0
0
2
0
2
0
0
2
1
0
1
0
1
2
1
0
0
1
1
2
2
0
1
1
0
0
0
1
0
2
1
0
0
1
0
0
2
2
1
0
0
2
1
1
1
1
1
1
2
1
0
0
0
0
1
0
0
1
1
2
0
0
0
1
2
1
0
1
0
2
1
0
1
1
2
2
0
1
0
2
2
1
4
1
1
1
2
1
0
1
2
0
1
1
0
0
0
1
1
1
0
0
0
1
1
2
0
5
2
1
1
2
1
1
1
0
0
0
0
3
1
0
1
1
1
1
0
0
1
1
1
2
0
0
1
1
2
1
1
0
0
1
1
0
1
1
1
1
1
3
0
1
2
1
1
0
1
1
1
1
0
2
1
1
2
2
0
1
1
4
0
1
0
0
1
0
0
0
1
2
0
2
0
0
0
1
1
0
0
1
0
1
0
0
1
1
1
0
1
0
2
1
1
1
1
0
0
0
0
0
0
1
1
1
1
2
2
2
2
1
0
1
1
2
0
0
0
2
2
2
0
1
0
1
2
2
1
1
2
1
2
0
2
2
1
2
1
0
1
2
0
2
1
1
1
1
2
1
2
1
2
1
1
1
0
2
1
2
2
1
0
1
2
0
2
1
0
1
1
2
2
0
1
2
2
1
1
0
2
1
1
1
2
1
0
2
0
1
1
0
2
0
0
1
0
1
1
1
0
1
2
1
0
0
0
1
1
0
2
1
1
0
1
0
1
2
0
2
0
1
0
0
2
2
1
0
2
1
2
0
2
1
2
0
1
1
1
1
1
0
1
0
2
2
1
0
0
1
0
2
1
2
1
0
1
0
1
0
0
1
1
1
1
2
0
1
0
2
0
1
0
0
0
1
2
2
0
1
0
1
2
1
2
2
1
1
3
0
1
1
0
1
1
0
1
2
0
2
0
0
1
1
0
0
0
1
0
0
2
2
0
1
0
1
0
1
0
1
0
2
2
2
1
0
0
0
1
2
0
0
0
0
1
2
0
2
1
1
2
1
1
0
0
1
2
0
0
3
0
0
1
1
0
1
1
2
2
1
0
1
0
1
1
1
2
2
1
0
1
1
2
2
1
1
1
0
1
1
2
1
0
0
0
0
1
0
1
2
1
0
1
0
0
0
1
3
0
0
0
1
1
0
1
2
2
1
0
1
3
0
1
1
0
0
0
1
1
1
1
2
1
1
0
1
1
1
0
0
1
2
0
0
1
1
1
1
2
1
0
1
1
1
0
0
0
2
2
0
1
0
1
2
0
2
1
1
2
2
2
1
2
2
0
0
0
0
0
1
1
0
1
2
0
0
1
1
1
0
1
1
1
1
1
1
1
0
0
1
2
1
2
3
1
1
2
0
1
0
0
1
1
2
2
2
1
1
0
0
2
0
1
0
1
3
1
0
0
1
2
1
0
0
3
1
1
2
0
0
1
0
1
0
2
1
1
1
2
0
2
3
1
1
1
1
2
0
1
2
0
1
2
0
1
0
0
1
1
0
1
0
1
0
2
0
1
1
1
2
1
1
1
0
0
0
0
1
1
0
1
2
0
2
0
1
1
1
1
0
2
0
2
1
1
1
0
1
0
1
0
1
1
1
1
1
0
0
0
1
0
1
2
0
2
1
0
3
0
2
0
0
1
1
1
1
2
2
1
1
1
2
2
0
1
0
1
2
0
1
0
1
1
1
0
1
1
2
0
2
2
0
0
0
0
2
2
2
0
1
0
1
0
2
0
0
0
0
0
2
0
1
1
2
0
2
1
2
0
0
1
3
0
1
1
1
1
0
0
0
0
0
2
1
1
1
1
2
0
0
0
2
1
1
1
0
1
0
0
0
2
1
1
2
1
1
0
2
1
1
0
2
1
1
2
1
0
2
0
0
2
1
0
0
1
1
0
0
1
1
1
1
1
0
2
0
1
1
0
2
1
2
0
1
2
2
0
0
3
2
1
0
0
1
0
0
1
2
0
0
0
1
0
1
2
1
2
1
0
0
0
2
1
0
1
1
0
1
0
1
1
0
0
1
1
1
1
2
1
0
0
1
1
1
1
2
0
1
1
0
2
1
0
0
2
0
1
1
1
1
2
0
1
1
0
1
0
1
1
1
2
1
0
1
1
0
1
2
1
2
0
0
1
2
1
0
1
1
0
1
0
0
1
1
1
0
0
0
2
2
0
1
1
1
2
2
1
1
1
2
1
1
1
1
0
0
0
1
1
0
0
2
1
2
1
1
0
1
2
0
1
0
2
1
1
1
0
0
0
0
1
1
1
1
2
2
0
2
2
0
2
0
1
0
2
2
0
0
2
1
1
0
0
0
1
2
0
1
2
2
2
0
2
0
1
1
2
0
0
0
0
3
1
2
1
2
1
1
2
2
1
2
2
2
1
1
0
0
1
1
1
1
1
1
0
1
1
0
0
2
0
1
0
1
0
1
1
1
1
2
4
1
1
0
0
2
0
2
0
2
1
2
0
0
0
2
1
1
1
1
0
1
1
0
0
2
2
0
0
0
1
1
2
0
0
0
1
2
1
1
0
2
0
0
1
1
4
1
1
1
2
1
0
2
1
1
0
0
0
1
2
0
1
0
1
1
0
1
1
2
1
0
2
2
1
1
2
0
1
2
0
2
1
0
1
2
0
0
1
1
0
0
0
1
0
1
0
1
1
1
0
0
1
3
1
0
2
1
1
0
0
1
0
1
2
1
0
0
1
2
0
0
1
0
1
1
0
0
1
0
0
1
0
1
2
1
2
1
0
2
0
2
0
1
0
0
0
1
0
0
0
1
0
1
1
0
0
0
1
1
1
1
0
0
0
1
1
0
1
0
1
1
2
1
1
1
2
1
1
2
2
2
0
1
1
0
1
1
1
1
2
0
1
1
0
0
1
0
2
1
1
0
2
1
1
2
1
1
1
0
1
1
0
2
1
0
1
0
1
2
1
1
2
0
1
1
2
0
1
0
2
1
1
1
1
0
1
0
1
1
2
1
1
1
1
0
0
1
2
1
2
1
2
1
4
1
0
2
0
0
2
1
3
1
1
0
1
2
0
1
0
0
2
1
0
1
1
1
0
0
1
3
1
1
2
2
0
1
1
0
0
1
1
1
2
3
0
2
1
0
0
1
1
0
1
0
2
2
1
0
0
0
0
2
1
0
1
2
3
0
0
1
1
1
1
2
1
2
0
1
1
0
1
0
1
0
2
0
1
1
1
2
0
0
0
0
0
0
1
1
0
0
0
1
0
2
1
2
1
0
1
0
0
2
6
1
2
0
1
0
1
0
0
0
0
0
0
1
0
1
0
1
1
1
0
1
2
1
2
1
1
1
1
2
2
2
1
1
0
3
1
2
1
2
0
0
0
2
0
1
1
0
1
2
0
1
1
2
1
0
1
0
2
2
1
0
2
1
1
4
2
2
2
1
0
1
1
0
2
1
2
1
1
0
2
1
1
2
3
2
2
0
0
1
1
0
2
0
0
1
2
2
2
1
0
1
0
0
2
0
1
2
2
1
0
0
0
0
2
0
2
0
1
1
2
0
0
0
0
1
2
2
0
1
0
1
0
0
1
2
0
2
0
1
0
2
0
0
0
2
1
0
0
3
0
1
0
1
1
0
0
0
1
0
1
0
0
2
2
0
1
0
0
0
1
1
2
1
0
0
4
2
1
2
1
1
1
1
0
1
0
0
2
2
0
2
1
1
1
2
1
2
1
0
0
0
0
0
1
1
2
0
0
0
0
1
1
0
1
1
0
1
1
2
1
1
1
0
0
0
1
3
1
0
1
1
1
0
0
1
1
2
2
1
3
1
0
0
0
0
1
0
0
0
1
0
1
1
1
3
1
1
1
1
1
2
0
0
1
1
1
0
1
1
0
1
0
1
2
1
1
1
0
0
1
1
2
1
1
0
1
1
2
2
1
1
2
1
1
1
1
1
4
1
1
3
0
0
1
0
0
1
0
0
1
1
0
1
0
2
1
0
1
1
0
1
2
1
1
0
2
0
0
1
1
1
1
1
0
1
0
1
0
0
1
1
1
0
1
0
0
0
1
0
2
0
1
2
2
0
2
1
0
0
2
1
1
0
1
1
0
1
0
1
1
1
0
1
2
0
1
1
1
1
3
2
0
1
1
2
1
1
2
0
0
0
0
2
1
1
2
2
1
0
2
0
1
1
0
1
1
2
0
2
0
2
2
1
1
0
1
1
2
0
2
2
0
0
1
0
0
3
2
0
1
0
2
0
0
2
1
0
0
2
1
2
2
1
2
0
0
0
1
1
0
0
0
2
1
1
1
1
1
0
2
1
1
0
0
0
2
1
1
1
0
0
1
1
0
1
2
2
0
1
2
2
0
2
2
2
0
1
0
1
1
0
0
0
1
0
1
1
1
2
1
1
0
1
2
0
0
0
0
1
0
0
2
0
0
1
0
0
1
1
2
1
2
0
2
0
0
1
2
0
2
0
2
1
0
0
1
0
0
0
1
0
1
1
0
1
1
0
0
0
0
1
1
1
1
1
1
1
3
1
1
0
0
0
2
1
2
2
0
0
1
1
2
0
0
0
0
0
1
0
1
0
0
2
1
0
1
1
0
1
0
2
1
0
0
0
1
0
0
0
1
0
0
1
1
2
1
1
2
0
1
1
1
0
0
2
1
1
1
0
3
2
1
1
2
0
0
0
0
1
2
0
2
1
0
1
2
1
0
1
0
2
2
0
2
0
2
1
0
1
0
0
0
2
2
0
1
2
1
1
0
1
2
1
0
0
1
1
0
2
0
0
1
1
0
2
0
1
0
1
2
4
2
2
2
1
1
2
0
0
2
1
1
2
0
0
1
0
2
1
0
0
0
2
1
2
1
1
0
0
0
2
2
0
0
3
1
2
0
1
2
1
0
0
0
1
1
0
1
1
2
0
2
2
2
1
0
0
1
0
0
1
2
0
2
1
1
2
1
0
2
0
0
1
5
0
2
1
0
1
0
0
0
0
1
0
2
0
1
1
2
2
1
1
1
1
1
0
2
2
1
1
0
0
2
1
0
0
2
1
0
0
2
2
0
2
0
2
0
0
1
1
1
1
0
1
0
2
1
2
1
0
0
0
0
1
0
0
1
1
4
1
0
1
0
1
0
1
1
0
1
1
0
2
2
2
2
2
1
1
1
0
1
1
0
1
1
1
2
0
1
0
1
1
0
1
1
1
0
2
1
1
1
2
0
1
0
1
0
1
1
0
1
2
1
1
0
1
0
0
0
1
1
2
1
1
0
0
0
2
0
2
2
0
2
4
0
2
0
1
0
0
1
2
0
1
0
0
1
0
1
2
2
2
0
1
2
0
0
0
0
2
1
0
1
1
0
2
0
0
0
0
2
2
0
2
0
1
0
2
0
2
2
0
1
1
2
1
1
0
2
2
1
2
1
1
2
0
0
0
0
4
1
1
1
2
1
0
0
2
1
1
0
1
0
1
1
0
1
1
0
0
0
0
2
0
1
0
0
3
2
0
0
0
1
1
1
1
0
0
1
0
0
1
1
1
0
2
0
1
2
1
2
0
0
0
2
1
1
0
0
1
1
0
1
1
0
2
1
2
0
2
2
3
1
2
2
2
0
2
1
0
0
4
0
1
3
0
1
2
1
0
0
1
1
2
0
0
2
1
2
3
1
1
1
1
2
0
2
2
0
1
1
0
1
0
2
1
1
1
0
1
1
2
1
1
1
2
0
1
1
2
1
0
0
2
0
2
0
1
0
0
0
0
1
0
1
1
2
1
0
0
0
0
1
0
2
1
0
1
1
0
2
1
2
1
0
0
2
1
1
1
1
0
1
1
0
1
0
2
0
1
2
1
1
2
2
2
1
2
0
0
0
0
1
2
1
3
1
1
0
1
1
2
1
1
1
2
2
1
1
0
0
1
0
0
0
1
2
1
0
2
1
2
2
1
1
1
1
2
0
1
2
0
0
0
1
1
1
1
0
2
1
2
0
3
0
2
0
0
0
2
0
2
1
1
1
1
0
1
2
1
1
0
1
1
2
2
2
1
1
1
0
1
0
1
1
1
1
1
1
0
0
2
0
1
2
1
0
0
2
2
1
1
1
1
0
2
1
0
0
1
1
1
0
2
2
0
2
1
1
0
0
0
1
1
1
1
0
1
1
2
0
1
0
1
1
2
0
0
2
1
1
0
2
0
1
0
0
2
0
1
1
2
1
1
0
2
0
1
0
4
0
0
1
2
1
1
0
1
1
1
1
1
1
2
1
0
1
4
1
1
2
1
1
2
1
1
1
1
3
1
1
0
0
2
1
0
0
2
1
1
1
1
1
1
0
0
1
1
2
1
0
2
2
0
1
0
1
1
2
0
1
2
2
0
0
2
0
0
1
1
1
1
1
0
1
2
2
2
1
2
0
1
0
1
0
2
0
0
0
1
1
1
1
0
1
2
0
1
2
2
0
1
0
2
0
0
2
2
0
1
1
1
0
2
2
2
1
1
0
1
0
1
2
1
0
0
1
1
2
0
0
1
1
1
1
1
0
2
0
2
2
2
1
0
0
0
1
1
1
2
1
2
0
0
9
2
2
2
0
0
0
1
1
2
2
0
2
0
1
0
2
0
1
1
1
1
1
1
0
2
1
2
0
2
1
0
0
0
0
2
2
1
1
0
1
1
0
1
1
1
2
0
0
0
1
3
1
0
0
1
0
0
0
0
2
1
0
1
0
2
2
0
0
1
1
0
1
0
2
2
2
1
0
0
1
0
1
0
0
1
1
0
2
1
2
1
1
0
1
1
1
2
1
4
0
3
2
1
0
1
0
2
1
0
0
1
1
1
0
0
1
0
2
0
0
0
1
2
1
0
0
1
2
0
1
0
1
2
0
1
0
1
1
0
2
1
0
1
1
1
1
0
1
0
0
1
1
1
0
1
2
0
1
2
1
2
1
1
0
0
0
0
0
1
1
1
1
2
0
0
1
0
1
1
0
0
0
0
0
0
2
2
0
0
2
2
1
1
2
2
2
1
1
3
2
2
1
2
0
1
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
2
0
1
1
0
3
1
2
0
1
1
0
0
2
1
2
0
0
1
1
0
1
0
1
1
0
1
0
2
2
1
2
2
0
0
1
0
1
1
1
2
1
0
1
0
0
2
2
0
0
1
2
2
1
1
0
1
1
3
2
1
1
2
0
2
2
1
2
0
1
1
1
1
1
2
2
2
2
0
1
0
1
1
0
0
1
2
2
2
2
0
2
0
0
1
0
1
1
1
1
1
2
1
1
1
1
0
1
0
1
1
1
2
1
1
2
1
1
1
0
0
1
1
0
0
0
0
2
1
1
0
1
1
1
2
0
0
1
2
3
0
0
3
0
1
2
2
2
0
1
0
1
1
1
0
1
1
0
0
1
1
2
0
1
2
0
1
0
2
3
2
0
0
0
1
1
0
1
1
1
1
2
1
1
0
1
2
0
1
0
0
2
2
1
0
0
1
1
2
1
0
0
0
3
2
0
2
1
1
2
1
2
0
0
0
0
0
1
0
1
1
1
1
2
1
0
1
0
1
2
1
2
1
1
1
0
1
0
1
1
0
1
1
0
1
0
2
2
1
0
2
1
2
1
1
0
0
1
2
2
1
1
2
0
0
1
0
1
2
0
0
0
0
0
0
2
3
1
1
1
0
1
0
1
1
0
1
0
1
1
1
0
1
1
2
1
1
0
2
1
1
0
1
1
1
0
0
0
1
1
0
0
1
2
1
1
0
0
0
1
2
1
1
1
1
0
2
2
2
2
2
2
2
2
2
0
2
1
2
1
1
2
1
1
1
2
2
2
2
1
1
2
1
1
1
4
1
0
1
1
0
3
1
2
0
0
1
1
1
3
0
0
1
0
0
2
1
1
1
2
1
0
0
0
1
1
2
1
1
0
1
1
1
1
1
2
0
2
0
2
2
2
0
2
0
0
0
0
0
1
1
2
1
0
1
1
1
0
0
2
1
1
0
1
1
0
0
1
1
1
1
0
0
1
2
0
1
0
0
1
2
1
2
0
1
0
0
2
1
0
1
0
0
0
1
0
1
2
1
1
0
1
2
1
1
1
1
0
1
2
0
1
2
1
2
1
1
0
2
0
2
0
1
1
0
1
1
0
0
0
2
0
1
0
2
1
1
1
0
2
0
1
1
0
2
1
2
0
0
0
2
3
1
0
2
1
3
1
1
1
2
0
1
1
1
0
2
0
1
2
0
1
0
1
1
2
0
0
2
1
1
1
1
1
1
4
1
0
1
1
0
1
2
0
1
0
2
1
1
0
1
0
2
0
2
2
1
3
0
1
1
1
0
1
2
0
0
0
1
0
0
1
1
2
1
1
0
2
1
0
0
0
1
0
0
2
2
0
1
2
3
1
1
1
0
2
2
0
0
1
0
1
2
2
1
1
1
0
0
1
2
1
0
0
0
1
1
0
1
0
0
1
1
2
0
0
0
0
1
1
1
1
0
0
0
0
1
0
0
1
1
0
1
1
0
1
1
2
0
0
1
1
0
1
1
0
1
0
0
1
2
0
1
0
0
0
2
0
1
1
0
2
0
1
0
2
1
1
2
1
1
0
0
1
0
0
1
0
2
0
0
0
1
1
1
1
1
1
2
1
1
2
2
1
1
0
2
0
1
1
1
0
2
1
1
1
1
0
2
1
3
0
1
0
2
0
0
2
0
1
1
2
0
1
0
1
1
2
2
1
2
1
1
1
1
1
1
0
1
0
1
1
1
0
2
0
0
0
1
1
1
0
0
0
0
0
6
0
1
2
1
2
1
0
0
0
0
1
1
0
1
0
0
6
0
1
1
1
1
2
0
1
1
1
0
0
1
2
1
0
2
2
0
1
1
0
0
0
1
0
0
1
1
0
0
2
2
1
0
1
0
0
0
1
1
1
2
0
2
1
0
0
0
2
0
0
2
1
0
1
1
2
0
0
2
1
2
1
2
1
0
0
2
0
1
0
2
0
1
1
0
0
1
0
1
0
1
1
1
1
0
0
1
1
2
1
2
0
1
1
2
0
1
0
1
1
1
1
2
0
0
2
0
1
0
1
1
1
0
1
0
1
1
2
1
0
0
0
2
1
1
1
1
2
0
1
0
1
0
0
1
1
1
1
2
2
1
1
1
2
1
0
1
1
2
2
1
0
0
1
0
1
0
2
2
2
0
0
1
2
0
0
1
0
2
2
3
0
0
1
1
1
2
2
2
0
2
1
1
0
1
0
1
1
1
4
1
2
1
1
1
1
1
2
1
2
2
0
0
0
0
0
1
0
1
1
2
1
1
1
2
1
0
1
0
0
1
2
1
1
1
0
0
2
3
2
0
1
0
2
2
1
1
1
0
0
0
0
0
2
2
1
0
1
0
0
1
0
2
1
1
1
1
1
1
2
1
1
2
2
1
1
1
4
2
1
0
0
1
0
2
2
2
1
0
2
0
2
2
2
0
2
1
2
1
1
0
0
1
1
1
0
1
1
1
2
0
0
1
2
1
1
1
4
0
1
0
1
1
1
1
4
1
2
1
2
1
2
0
7
0
0
1
0
0
1
1
3
1
1
2
1
0
1
0
1
2
2
0
1
0
2
3
1
0
1
1
1
0
1
0
0
0
2
0
0
0
2
0
1
2
2
1
0
1
0
1
1
2
1
0
1
2
1
1
1
1
1
2
1
0
0
0
0
0
1
0
1
1
1
0
0
2
2
1
1
2
0
0
0
2
0
1
0
1
1
0
1
1
2
1
1
0
0
1
1
1
0
0
1
2
0
0
3
2
0
1
0
2
1
1
2
1
2
1
2
1
0
2
0
1
2
0
0
1
1
0
2
1
0
0
2
2
1
0
2
1
0
6
1
1
1
1
0
2
0
1
0
0
0
2
2
2
2
1
1
0
1
1
0
2
1
1
1
1
1
0
1
0
2
1
0
0
0
0
1
1
0
0
0
3
2
1
0
0
1
0
0
0
0
1
1
1
2
0
1
2
1
0
1
1
1
3
1
0
1
1
2
0
0
1
1
0
1
1
1
0
1
0
1
2
2
0
1
3
1
0
2
3
1
0
1
1
1
1
0
2
0
1
1
1
1
0
2
0
2
0
1
2
0
0
0
1
1
0
2
0
1
1
1
0
1
2
1
2
0
0
0
2
0
2
0
1
2
2
1
2
1
0
1
0
1
1
1
0
1
1
0
1
2
2
0
2
1
1
1
0
1
1
0
2
2
1
1
1
0
1
0
0
1
0
2
2
0
1
1
1
2
0
1
3
0
0
1
3
2
1
0
0
0
0
1
1
1
2
0
2
1
2
0
1
0
0
2
0
2
0
1
1
0
1
2
1
0
0
1
0
2
0
1
0
1
1
0
1
2
1
0
1
0
1
0
2
0
1
1
2
0
1
1
0
1
1
1
0
0
1
2
0
1
1
0
0
1
3
0
1
0
0
1
0
2
1
1
1
1
1
2
0
0
0
1
2
1
0
2
1
2
1
2
1
0
1
1
1
1
1
0
0
1
0
2
0
1
1
0
0
2
0
0
1
1
1
2
1
2
1
2
2
0
0
2
0
1
1
1
1
1
2
2
0
2
0
1
2
0
2
1
1
0
0
0
0
1
0
1
0
0
2
0
0
0
1
2
0
1
1
1
0
0
0
0
0
1
1
1
2
0
1
0
2
1
2
1
2
0
0
1
1
1
1
2
1
1
0
2
0
2
0
0
1
0
1
1
0
2
0
2
0
0
0
0
1
0
0
1
1
0
1
0
0
1
2
1
2
1
1
2
1
1
0
2
1
1
0
0
0
1
0
2
1
1
1
0
1
1
2
2
0
1
0
1
0
1
1
2
1
2
2
0
0
1
1
2
2
1
0
1
2
1
2
1
2
1
2
2
1
1
1
1
0
1
3
0
1
1
1
1
3
1
1
1
2
0
3
2
1
1
1
2
1
0
1
0
0
3
1
1
1
0
0
2
1
0
2
0
1
1
0
1
0
1
0
2
1
0
0
2
1
1
2
1
1
2
1
3
1
1
0
1
0
0
2
1
1
0
0
0
1
0
0
0
3
2
2
0
2
1
1
0
2
2
1
1
0
1
1
2
1
0
1
0
0
2
1
1
0
0
0
1
1
0
1
1
1
1
1
2
0
2
1
0
0
5
2
0
2
1
1
2
2
1
0
1
1
2
0
1
1
1
1
1
0
0
1
2
1
1
1
0
1
2
1
0
0
1
0
0
0
0
0
2
1
1
1
0
0
1
2
1
2
1
1
1
0
0
1
0
2
0
1
0
1
0
0
2
1
1
2
0
1
2
1
0
0
1
1
0
0
3
0
0
0
0
0
1
1
1
0
0
1
0
2
1
0
2
0
0
2
1
1
2
0
1
1
2
0
1
0
1
2
0
1
1
1
2
2
1
1
3
1
0
0
1
0
1
2
1
0
1
2
0
1
1
2
0
1
0
1
1
0
1
1
0
1
1
6
0
1
0
1
0
0
1
2
2
1
1
1
0
2
1
0
0
2
1
0
2
0
0
1
1
0
2
2
2
0
0
2
2
1
0
1
2
1
1
2
0
0
2
0
1
1
1
0
3
1
1
0
0
1
2
2
1
0
0
1
1
2
0
1
0
2
2
1
0
1
0
0
1
2
1
0
1
1
1
1
2
2
2
2
2
0
1
2
1
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
2
1
2
1
2
1
1
1
1
0
0
0
0
1
1
0
0
1
1
1
0
2
1
0
0
0
2
1
1
0
1
1
2
0
1
1
1
2
1
0
1
2
1
0
1
1
2
3
1
2
2
0
1
0
0
0
0
1
0
2
0
0
0
0
1
0
2
0
1
2
0
2
4
1
7
1
1
1
1
0
2
1
1
1
0
1
4
2
0
2
0
1
2
3
0
1
2
0
0
0
1
0
0
0
2
0
0
1
1
0
2
1
1
1
1
2
0
0
1
1
0
1
1
1
1
1
0
1
2
2
1
1
1
0
0
0
0
1
3
0
2
1
0
0
0
0
2
1
2
1
2
1
3
2
1
3
0
0
0
1
0
1
6
1
2
2
0
1
0
2
0
0
1
2
0
0
1
1
2
1
0
1
1
1
2
1
1
1
2
1
0
0
1
1
2
1
1
2
2
1
1
0
0
2
0
0
0
0
0
1
1
2
1
2
1
1
1
2
2
1
0
1
0
1
2
0
0
1
0
1
0
0
0
0
0
1
0
1
2
1
0
1
2
1
0
1
1
1
1
1
1
2
1
3
1
1
2
1
1
0
0
1
0
1
1
2
2
2
0
0
1
2
1
1
1
0
1
0
1
1
2
1
0
1
2
1
1
1
2
2
1
0
2
1
1
1
1
2
0
1
2
3
0
2
2
2
1
0
0
0
0
1
0
3
1
1
2
0
1
1
2
1
0
8
0
2
1
0
1
0
1
2
1
1
2
1
0
0
0
1
1
1
0
2
1
1
1
1
2
1
0
0
1
0
0
0
0
0
2
1
1
1
0
1
1
2
1
2
2
1
1
0
1
1
0
0
1
0
2
0
0
0
0
0
1
1
2
1
1
2
1
0
2
2
2
2
0
0
0
1
1
1
2
0
1
0
1
1
0
1
1
1
2
1
0
0
0
0
1
2
0
1
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
2
1
0
0
2
2
0
0
1
2
1
1
1
1
1
1
2
0
1
1
0
0
0
0
0
1
1
1
0
2
1
0
1
0
1
0
1
0
0
0
1
1
2
1
0
1
1
1
0
0
1
1
1
0
1
1
0
0
2
2
1
0
2
0
1
1
1
0
2
0
1
1
0
0
0
1
1
0
0
0
0
1
2
0
2
3
1
2
0
0
2
1
1
1
1
1
0
0
1
1
1
1
0
1
1
1
0
1
0
1
3
0
0
2
0
0
0
1
1
2
1
0
1
2
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
1
2
1
1
1
0
2
2
1
1
1
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
1
0
2
0
1
1
1
1
0
1
1
2
1
0
1
1
1
0
0
1
1
0
0
1
2
1
0
1
0
2
0
1
0
0
1
1
0
1
1
0
2
1
2
0
1
1
2
1
0
1
0
1
1
1
0
1
1
3
2
1
1
0
0
1
1
0
1
0
1
2
1
0
1
2
2
2
1
0
2
0
1
0
2
1
0
0
0
0
2
1
0
0
2
1
2
0
1
0
1
0
0
1
1
2
0
1
0
1
0
0
1
1
1
1
1
2
2
1
1
2
0
1
2
2
1
0
0
1
1
0
2
1
2
2
1
1
1
2
1
1
1
2
2
1
1
2
1
2
1
2
1
2
1
0
2
1
2
1
0
1
1
1
1
1
1
0
1
2
1
0
1
1
1
2
1
0
4
0
0
3
2
1
0
1
2
1
1
0
1
1
1
1
2
1
0
2
1
0
1
1
4
0
0
0
1
2
2
1
1
0
2
1
1
1
0
0
0
1
0
2
1
0
0
0
2
0
0
1
2
1
1
1
2
1
0
1
0
2
0
1
1
2
0
1
0
1
0
1
1
1
2
2
1
2
1
0
0
2
1
0
0
2
1
2
2
2
0
1
2
0
1
2
1
2
0
2
3
1
0
1
0
1
1
1
2
1
2
0
1
0
1
1
0
0
0
1
1
1
0
2
1
1
1
2
1
0
1
2
1
1
1
0
0
0
0
1
1
0
0
1
0
2
1
0
1
0
3
0
2
1
1
0
0
1
2
1
0
0
0
0
0
0
1
0
2
1
0
0
1
0
0
0
1
1
1
1
1
0
1
0
2
2
2
0
2
2
1
1
1
1
0
0
1
2
1
1
1
1
1
1
1
0
1
2
2
1
2
1
0
1
2
2
2
0
1
0
1
0
1
0
1
1
0
0
1
0
1
0
2
0
4
3
2
1
1
1
1
0
2
2
2
2
2
1
1
1
2
0
2
1
0
1
0
2
1
1
1
0
1
1
0
1
1
0
2
0
2
1
2
2
2
2
1
2
0
0
2
0
2
1
0
0
2
0
2
1
2
0
2
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
1
1
0
0
2
2
0
1
1
2
0
0
0
1
1
2
1
0
0
2
0
1
1
2
2
1
0
1
1
2
1
1
0
1
0
2
1
1
1
1
1
3
2
1
1
0
1
1
1
2
1
0
1
0
1
1
0
1
1
1
1
2
1
2
1
1
0
1
0
0
0
0
1
1
1
2
1
1
2
0
1
1
1
0
1
2
0
0
1
1
0
0
1
0
1
2
1
2
0
3
1
2
1
1
1
2
0
0
2
0
1
2
1
0
1
1
0
1
0
1
1
0
1
2
1
2
0
0
1
0
1
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
2
2
1
0
0
2
1
0
2
1
0
1
2
0
1
1
1
2
1
1
0
2
1
0
0
0
0
0
1
0
1
0
0
1
1
2
4
1
1
0
0
0
2
1
1
1
1
0
1
2
1
1
0
0
0
2
0
1
1
1
2
1
0
1
1
1
0
1
1
1
1
1
2
1
2
1
1
0
3
0
1
1
0
0
1
2
4
1
1
0
2
0
2
2
0
1
0
1
2
0
1
1
1
0
1
0
2
0
0
2
0
1
1
0
2
1
0
1
1
1
0
2
1
1
9
0
1
1
1
0
2
1
2
1
0
0
0
1
1
1
1
1
2
1
2
0
1
0
2
0
0
1
1
1
1
1
0
1
1
1
0
1
2
1
2
1
1
0
0
2
0
0
1
1
1
2
0
2
1
1
1
0
1
1
1
1
1
0
0
0
2
0
1
1
0
2
1
1
0
0
0
3
1
0
1
2
2
2
1
0
1
2
2
2
2
2
1
1
2
0
1
0
1
1
2
3
0
0
1
2
0
0
2
1
0
0
0
0
0
1
1
1
0
0
1
1
1
1
1
2
0
1
0
0
1
0
1
2
1
0
1
2
0
2
1
1
1
0
1
2
0
1
0
2
1
2
1
0
2
1
2
1
0
1
1
1
1
1
1
0
0
0
1
1
0
1
1
0
0
0
2
1
2
1
0
1
0
2
0
2
1
1
1
2
0
1
1
1
2
1
1
2
2
2
0
3
0
1
2
0
0
0
0
1
0
0
1
1
1
1
1
0
2
1
1
1
1
1
0
0
0
0
1
1
1
2
1
1
1
1
2
0
0
1
0
0
1
0
1
1
2
1
0
0
2
2
2
0
1
1
2
0
1
1
1
1
1
2
2
0
0
1
0
1
1
0
0
8
1
1
0
1
1
0
3
2
2
1
0
0
2
1
1
2
0
3
0
0
2
0
1
2
1
1
1
1
1
0
1
2
0
0
2
1
2
0
0
1
1
1
1
1
1
0
2
1
2
0
1
1
2
1
0
0
2
1
0
1
0
0
0
1
1
0
2
1
1
0
1
0
1
1
1
0
1
0
2
1
1
1
1
2
1
0
1
1
2
1
0
1
2
0
1
0
0
1
2
1
1
2
2
0
1
3
2
1
1
1
0
1
1
0
0
0
0
1
1
0
1
2
1
1
0
1
0
0
1
0
0
3
1
1
0
1
0
2
1
1
1
0
2
0
2
2
2
0
0
0
0
1
0
2
0
1
2
2
0
0
1
2
0
0
1
1
1
1
4
1
1
1
0
1
2
1
1
1
1
1
0
0
0
0
0
2
0
0
1
1
1
0
0
0
0
0
1
2
0
0
1
1
1
0
1
0
1
0
0
0
1
1
1
1
1
1
0
1
0
1
1
1
2
1
2
0
1
1
0
0
2
1
0
0
2
0
1
2
0
1
1
1
0
0
0
1
2
1
1
1
0
0
0
1
1
1
0
1
2
2
1
1
1
0
2
0
0
0
1
1
0
0
2
0
0
2
1
2
3
0
1
1
2
2
1
1
2
1
1
1
2
0
1
1
1
3
2
0
1
2
1
0
0
0
2
0
0
1
2
0
1
2
2
1
3
2
3
0
2
1
2
0
1
2
1
2
2
1
0
1
1
1
1
0
1
1
0
2
0
1
2
2
2
0
2
1
2
1
1
1
0
2
2
1
1
2
0
2
0
0
0
0
0
2
1
1
1
1
2
1
0
0
1
2
1
1
0
0
0
1
1
0
1
2
1
0
3
0
1
0
2
1
0
1
1
2
0
2
1
2
2
2
0
2
1
2
1
0
1
2
0
1
2
2
4
1
2
0
0
2
2
1
0
0
0
1
1
1
1
0
0
0
0
0
2
0
0
0
0
1
0
1
2
0
1
2
1
2
0
2
2
0
0
1
1
1
0
1
1
0
1
0
0
0
0
1
1
0
1
1
0
2
0
0
0
0
2
1
0
1
0
1
1
1
0
1
2
1
1
2
0
1
0
1
1
1
2
0
0
0
2
1
2
1
2
2
1
2
0
1
2
1
0
2
2
2
2
1
1
2
1
0
0
0
0
1
2
0
0
0
1
0
1
1
0
1
1
0
1
2
1
1
1
1
0
1
0
2
1
2
0
0
2
1
0
1
1
2
2
0
1
1
2
0
2
2
1
0
1
0
1
1
0
1
2
0
3
2
0
2
2
2
0
1
0
1
1
0
0
2
2
0
0
2
1
1
0
0
1
0
2
2
0
2
2
1
0
2
0
2
1
1
1
0
0
1
1
0
1
2
1
2
1
1
0
2
2
2
0
1
0
2
0
2
1
0
1
2
1
2
0
2
2
2
0
0
1
2
1
2
1
2
2
0
1
1
1
2
2
1
1
0
2
1
0
2
0
2
0
1
0
2
0
1
1
1
1
0
0
1
0
0
2
2
2
0
1
1
0
0
0
0
1
1
1
0
2
0
1
3
0
0
1
1
2
1
1
2
0
1
1
0
1
0
0
1
1
1
1
1
0
1
1
1
2
0
1
1
2
1
2
1
0
1
2
0
2
2
0
0
1
0
1
1
1
2
1
1
1
0
1
0
1
2
2
0
1
2
0
0
0
1
1
0
1
1
1
0
1
2
1
1
1
1
1
1
2
1
0
0
0
1
2
1
0
0
0
0
0
0
0
1
2
1
1
3
2
1
0
1
3
0
1
0
1
2
1
2
0
0
2
0
0
1
1
0
1
3
0
1
0
0
1
1
1
2
0
1
1
2
0
0
2
2
0
1
0
2
0
0
1
1
1
0
1
1
1
0
1
1
2
1
1
2
0
0
0
0
1
1
2
2
1
2
2
0
1
0
2
2
1
0
2
1
1
2
1
1
1
0
0
1
1
2
1
1
1
0
2
2
0
2
0
1
2
2
0
0
0
0
1
2
0
1
1
1
0
0
2
0
0
0
1
1
2
1
2
0
1
0
0
0
1
1
1
1
3
0
0
2
1
2
2
1
2
1
0
0
0
1
0
0
1
2
1
1
0
1
2
0
0
0
2
1
1
1
0
0
0
0
0
1
0
0
4
2
0
2
0
1
0
0
0
2
1
2
1
0
0
0
0
1
1
0
1
1
1
1
0
1
1
0
0
2
1
1
0
1
1
1
2
1
0
0
0
1
2
0
1
0
0
2
0
1
0
1
0
0
1
0
0
2
1
0
0
0
1
1
0
1
2
0
0
0
1
1
2
2
1
1
0
2
1
0
0
0
2
1
2
1
0
0
2
0
2
1
0
0
0
2
1
1
2
0
1
2
0
1
2
0
2
0
0
2
2
3
0
0
4
2
1
0
0
0
1
0
2
2
0
0
2
0
2
0
2
2
0
1
0
2
1
2
1
1
1
0
0
0
0
1
1
0
0
0
1
1
1
0
2
1
2
1
1
2
1
1
0
1
1
1
0
1
2
0
1
0
0
0
0
1
2
0
0
1
1
0
1
1
0
0
2
1
1
2
0
0
1
1
0
1
0
1
1
1
3
1
2
1
1
1
1
1
1
0
1
0
0
0
0
2
2
0
1
0
1
1
2
0
2
0
2
2
0
0
1
1
0
1
1
2
2
2
1
2
0
1
1
1
1
0
3
0
1
0
0
1
0
1
2
1
0
1
0
1
0
0
1
0
1
1
1
0
1
1
2
2
1
2
0
0
0
1
1
0
1
1
1
2
1
0
0
1
0
1
0
2
2
1
0
0
0
0
0
1
1
1
0
2
2
0
1
2
0
1
2
1
0
4
0
0
0
1
3
1
2
0
1
0
0
1
3
1
0
1
1
1
1
1
1
1
0
1
2
0
0
0
2
0
0
2
4
2
0
2
1
1
1
0
1
0
1
0
1
1
1
1
2
0
0
1
2
1
0
1
0
2
1
0
2
2
0
1
0
0
0
1
0
0
0
2
1
1
1
1
2
3
0
2
0
1
1
4
1
0
1
0
1
1
2
0
1
2
0
1
1
0
0
1
2
2
1
0
1
1
2
1
0
1
0
0
0
2
0
1
0
1
1
2
1
2
1
1
1
0
0
0
2
1
0
2
2
1
1
2
0
1
0
1
0
1
0
1
1
1
0
2
0
2
0
0
0
2
2
0
1
1
1
0
1
1
1
1
1
0
1
0
0
1
0
1
1
0
0
1
1
0
0
3
1
1
1
0
1
2
1
2
1
1
1
2
0
1
0
1
1
1
1
1
1
1
1
1
0
2
2
0
0
2
2
0
1
2
0
1
1
2
2
0
0
1
1
0
2
0
1
0
1
1
1
0
0
2
0
0
1
1
0
0
3
0
0
0
0
0
1
1
1
0
0
1
2
0
1
2
0
2
0
1
2
0
1
0
0
0
0
2
2
1
1
2
0
0
0
0
0
1
1
2
1
1
0
0
1
1
0
2
1
0
2
0
2
0
2
1
1
2
0
1
2
1
0
1
2
1
1
0
1
1
0
1
5
0
1
2
1
1
1
1
1
2
1
2
1
0
1
1
0
1
2
0
0
0
2
0
1
0
2
2
1
1
0
0
2
1
1
0
1
0
1
0
1
1
2
0
0
2
0
0
0
1
1
0
2
1
1
1
0
0
0
1
1
1
2
1
0
0
1
1
1
1
1
0
0
0
2
0
0
2
0
1
0
0
0
1
1
2
1
1
2
3
1
1
0
1
2
0
1
1
1
2
0
1
1
2
0
1
1
2
1
1
0
0
1
2
0
1
1
1
0
2
0
2
1
0
1
1
1
1
1
2
2
2
1
2
0
1
1
1
1
2
2
0
2
2
1
1
0
1
0
0
2
1
1
0
0
1
1
1
1
0
3
1
2
1
0
2
0
0
1
1
0
0
2
2
1
0
1
4
1
1
0
0
1
0
0
1
2
1
0
1
2
1
0
0
0
0
0
0
0
2
1
1
1
0
2
1
0
0
2
2
1
1
2
0
1
0
0
0
0
0
2
0
2
1
2
1
1
1
1
0
2
2
2
1
1
1
2
1
1
1
2
2
2
2
1
1
0
1
2
1
2
1
0
0
1
1
1
0
2
0
1
2
0
1
0
1
1
0
0
0
0
2
0
0
0
1
1
2
1
1
1
2
1
0
1
0
0
0
1
2
0
1
1
1
1
2
1
0
1
0
1
1
1
2
0
0
3
1
0
1
0
1
2
1
0
0
1
0
1
1
2
0
1
0
2
1
1
0
1
1
2
0
0
2
2
1
1
1
1
0
1
0
1
1
1
1
1
0
1
0
1
0
1
2
1
0
2
0
2
2
0
1
1
0
0
1
1
1
0
1
0
0
0
1
0
1
1
2
1
0
0
1
1
2
1
1
1
3
1
1
0
0
0
0
1
1
0
1
1
1
1
2
0
2
1
0
2
2
2
2
1
0
5
2
1
1
1
2
1
0
1
1
1
2
1
1
1
1
2
2
1
0
3
2
0
2
1
1
1
0
0
0
0
1
2
2
1
2
2
0
1
1
1
1
0
0
1
0
2
1
0
1
1
2
2
2
0
2
0
0
0
1
0
1
6
2
0
1
1
1
1
2
1
0
1
0
2
0
1
1
0
1
0
2
2
1
1
1
0
0
1
1
1
2
0
0
0
1
2
1
0
1
1
1
1
1
1
2
0
1
0
1
3
0
1
1
0
2
1
2
0
1
1
2
1
1
0
2
0
0
1
2
0
2
1
0
0
0
2
1
1
0
0
1
2
0
1
2
3
0
1
1
0
0
1
0
0
0
1
2
1
0
2
0
2
0
1
0
2
0
2
2
3
1
2
2
2
1
1
1
3
1
0
1
0
1
2
2
1
2
0
2
0
1
1
0
0
0
0
2
2
0
2
1
1
2
0
0
0
0
0
0
2
1
1
1
1
0
1
1
1
1
0
2
2
0
1
0
1
0
1
0
1
1
0
0
1
1
1
1
1
1
0
0
0
0
1
0
2
0
0
1
0
2
1
0
0
1
2
1
0
1
1
1
0
1
0
0
2
1
2
0
1
1
0
1
0
2
1
1
1
1
1
2
1
2
2
2
1
2
1
0
1
1
3
0
0
0
1
2
0
1
0
2
1
2
0
1
0
0
0
2
0
2
2
1
2
0
1
2
0
0
1
0
1
0
1
0
1
2
1
2
0
2
1
1
1
1
0
1
1
1
2
1
2
0
3
2
0
2
2
0
1
1
1
1
0
1
0
0
1
1
0
0
3
0
1
0
2
1
0
0
0
1
0
2
0
1
1
0
0
1
0
1
2
0
1
1
1
1
1
1
1
0
1
1
1
2
0
1
2
0
1
1
0
2
0
1
1
1
0
1
1
0
1
2
0
2
2
1
0
0
0
0
2
1
1
1
1
1
0
2
0
0
1
0
2
2
1
2
0
0
0
0
0
0
0
1
1
0
1
2
1
2
2
1
0
2
2
1
0
2
1
0
1
0
1
0
0
1
1
0
0
1
1
0
0
1
1
0
1
1
0
2
2
2
0
1
1
1
1
2
1
3
0
2
0
2
0
2
1
0
2
1
0
1
0
1
0
0
1
1
0
1
0
0
2
2
2
1
0
1
0
1
1
1
2
1
0
2
1
1
0
0
2
0
2
1
0
0
1
1
1
0
2
1
2
2
1
3
1
0
1
1
1
1
0
0
0
2
1
1
2
2
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
2
2
2
1
2
0
2
1
1
0
1
0
2
0
0
2
0
2
2
0
0
0
2
2
1
1
0
0
1
1
0
1
0
0
0
1
2
0
2
2
0
0
2
2
0
0
1
0
0
1
0
1
2
1
1
2
2
1
1
1
1
1
0
2
1
0
0
2
1
2
0
0
0
1
1
1
0
0
0
0
2
1
1
2
0
1
0
0
1
1
1
0
1
0
2
1
2
1
1
0
1
1
1
1
0
1
1
2
0
2
0
0
1
0
1
2
2
0
0
0
0
1
2
0
1
2
2
3
2
1
0
0
2
0
1
0
2
0
1
0
0
1
1
1
1
2
1
2
0
0
1
1
2
1
0
0
1
0
0
0
1
2
1
1
0
1
0
1
1
0
2
1
0
1
2
0
1
0
0
0
1
0
1
5
1
0
1
0
0
1
1
2
2
1
1
1
1
1
3
0
0
1
0
0
2
1
1
0
0
0
0
1
0
1
1
2
2
2
1
1
1
2
0
0
2
0
1
2
1
0
2
1
0
0
2
1
0
1
2
0
1
2
0
0
2
1
0
0
2
0
0
1
0
2
1
1
1
2
1
0
1
1
0
2
1
0
2
1
1
3
0
0
0
1
0
2
1
0
0
1
0
2
1
0
0
0
1
2
1
1
0
1
0
1
1
1
0
2
2
1
1
1
1
0
2
0
2
1
1
2
0
2
0
1
1
1
0
2
2
0
0
0
1
0
1
2
1
1
0
0
0
0
0
1
0
0
1
0
2
1
1
0
0
1
0
1
4
1
1
1
4
1
1
0
0
0
2
1
2
2
0
1
2
1
0
1
0
1
1
2
0
2
1
0
0
1
1
0
0
0
2
0
0
1
1
0
0
1
0
1
0
2
0
2
1
2
2
0
1
0
0
0
1
2
0
1
1
0
0
0
1
0
1
0
0
2
0
1
2
0
1
0
0
0
0
0
1
1
1
0
0
1
0
1
0
1
1
4
2
0
2
0
1
1
1
1
1
2
1
1
0
1
1
2
2
1
8
0
0
1
1
1
0
0
0
1
1
0
0
1
0
1
0
1
2
1
0
1
1
1
0
1
3
0
1
1
0
1
0
0
1
2
1
1
2
1
2
3
2
0
1
0
1
0
1
0
0
1
1
0
1
0
2
1
0
1
1
2
1
1
1
1
2
1
1
1
1
0
1
2
2
1
2
0
0
2
1
2
0
0
1
1
1
1
1
1
1
1
0
1
0
0
0
1
0
1
0
0
1
1
0
2
0
1
1
0
0
0
1
2
1
1
1
0
1
1
1
0
0
1
1
0
0
1
0
0
2
4
0
0
0
2
2
1
2
1
2
0
1
1
0
0
0
2
0
1
1
1
2
0
2
2
2
1
1
2
2
0
0
1
2
1
0
1
1
0
1
1
1
0
2
1
0
0
0
1
1
0
0
0
1
1
0
0
0
1
1
0
0
0
0
1
2
1
1
2
0
0
0
1
2
1
1
0
1
0
0
0
0
2
2
0
0
0
1
0
2
1
2
1
1
0
2
0
2
1
0
2
1
0
1
3
0
1
0
1
0
2
2
0
0
3
0
0
1
0
1
0
1
2
0
0
0
0
0
0
2
0
1
0
2
1
0
1
1
1
2
1
1
1
0
0
0
3
1
2
1
0
2
1
1
0
0
1
0
3
0
1
1
1
1
1
2
0
1
1
1
1
0
0
0
0
2
2
0
1
1
0
2
2
2
1
2
0
0
2
1
0
1
1
1
1
1
0
0
0
1
1
1
1
1
3
0
1
0
2
0
0
2
0
0
2
1
0
0
0
1
2
0
0
1
1
2
0
1
0
0
1
0
2
2
2
1
0
0
0
0
1
0
1
0
2
0
0
2
1
1
1
1
0
1
2
2
0
2
1
2
0
1
2
1
0
0
1
1
2
1
1
1
0
1
0
1
2
1
2
1
2
1
1
0
2
2
0
0
2
1
1
2
0
0
1
2
1
1
3
1
1
1
1
0
2
2
1
2
1
0
1
1
0
1
2
2
1
0
3
2
0
1
1
0
2
2
0
2
1
0
0
2
0
1
0
1
0
0
0
0
2
1
0
0
1
2
1
1
2
1
1
2
1
0
0
0
0
1
2
0
1
0
0
1
1
0
0
0
0
1
0
0
2
0
1
0
1
0
1
0
0
0
2
0
1
1
2
0
0
0
1
2
1
1
0
1
0
1
0
2
1
2
1
1
1
1
1
0
0
1
2
1
2
1
2
0
0
2
2
0
0
1
1
0
0
0
1
0
0
0
1
2
0
0
2
2
1
0
1
0
2
0
0
1
0
2
1
1
0
1
2
1
0
1
1
1
1
1
0
1
0
1
1
1
3
0
1
2
1
0
0
1
1
1
1
0
2
0
2
1
1
0
1
0
2
1
0
1
0
2
0
5
1
1
1
1
1
1
0
2
1
1
0
1
0
1
0
2
0
0
2
2
1
0
1
0
1
1
1
1
0
0
0
1
0
1
2
1
1
2
0
1
1
2
0
1
0
1
1
0
1
0
2
1
2
0
1
1
2
1
1
1
1
1
2
1
2
1
1
1
1
1
1
0
2
0
1
0
0
1
2
0
1
1
1
0
0
1
2
0
1
1
2
2
0
2
0
1
0
1
1
0
1
0
1
1
1
0
1
1
1
0
1
0
0
2
0
0
0
1
1
2
0
1
1
0
2
0
0
2
1
1
0
1
0
0
0
0
1
1
1
1
1
2
1
1
2
2
1
0
1
1
0
0
2
2
2
2
0
0
2
2
1
1
0
1
1
2
2
0
1
0
3
1
2
0
1
2
0
1
1
0
0
2
0
1
2
0
0
1
1
1
2
1
1
1
1
0
0
0
0
1
2
2
2
1
0
1
2
0
2
2
1
0
0
0
0
1
0
1
2
0
1
1
1
1
0
0
0
2
1
0
0
0
2
2
2
1
1
0
0
1
0
1
0
2
1
0
0
0
2
0
1
1
0
2
1
2
1
2
0
1
0
0
0
0
1
2
0
2
1
0
1
0
1
2
0
2
0
0
1
0
2
1
2
2
2
0
1
2
2
1
1
1
0
2
1
1
1
0
1
2
1
0
0
2
0
1
1
2
1
2
1
0
0
0
1
0
1
2
1
1
0
0
0
2
2
0
1
0
0
2
0
1
0
0
1
1
0
0
1
2
0
1
1
0
1
0
0
2
1
1
1
0
0
1
0
1
1
0
0
1
1
0
0
1
1
1
0
1
1
1
0
1
0
1
3
0
1
0
2
2
1
1
1
2
0
1
2
2
1
0
0
0
0
0
2
3
0
1
2
2
0
2
2
0
1
0
1
1
0
0
0
1
0
1
2
2
1
0
1
2
1
1
1
0
1
1
2
0
2
0
0
1
0
1
0
0
2
2
1
1
0
0
0
0
0
1
1
0
0
1
2
2
1
2
2
0
0
2
0
2
0
0
0
0
2
0
0
1
1
2
0
3
0
1
1
1
0
2
1
1
1
1
1
2
1
0
1
1
1
1
3
0
0
2
1
2
1
0
2
0
2
2
2
1
2
1
1
1
1
0
1
2
2
0
0
2
0
1
1
1
0
0
1
1
0
2
1
1
2
1
1
1
1
2
0
0
2
1
1
0
2
1
2
0
2
2
2
2
0
2
1
1
1
2
0
1
1
0
2
2
1
1
0
0
2
0
2
2
0
1
1
2
6
2
1
1
3
0
0
3
0
2
1
0
1
1
0
0
2
1
0
0
1
2
2
1
1
0
1
0
1
2
0
1
1
1
0
2
1
0
1
0
1
0
1
1
1
0
1
1
1
2
1
3
3
2
1
0
2
1
0
1
1
1
1
1
2
1
0
2
1
0
0
1
1
0
1
0
2
1
0
0
1
0
1
1
1
1
0
1
0
0
1
1
2
1
1
1
1
1
1
2
2
0
0
0
1
1
0
2
1
0
0
2
1
2
1
2
1
1
0
1
1
1
1
1
0
1
0
1
1
1
0
0
1
0
0
1
1
0
1
1
1
0
1
2
1
2
2
0
1
2
2
0
1
2
1
0
0
1
0
0
0
2
0
1
0
0
1
0
0
1
0
1
2
1
0
1
0
1
0
1
1
2
1
2
0
2
0
0
1
0
2
1
1
1
2
2
0
2
2
2
0
1
2
0
0
1
1
1
2
1
1
1
1
2
3
1
1
1
1
1
1
0
0
1
0
1
1
0
0
0
0
1
1
0
1
0
2
0
0
1
1
0
0
0
1
0
2
1
0
1
0
0
1
1
2
0
0
0
2
1
1
0
1
0
1
0
1
1
0
2
2
1
0
1
1
1
2
3
0
0
1
1
0
1
0
2
2
1
1
2
0
0
2
3
0
0
1
1
1
1
1
2
0
2
1
1
1
0
1
1
1
0
2
0
1
2
0
2
2
0
1
2
0
1
1
1
1
2
0
3
0
0
0
1
2
0
0
2
1
0
1
1
1
0
2
2
0
1
2
1
2
0
0
0
0
1
1
2
1
2
0
2
0
0
2
0
2
2
0
2
2
0
1
0
0
0
2
1
1
0
0
1
2
0
2
0
2
1
3
0
1
1
0
1
0
0
0
1
0
1
0
1
0
1
0
0
2
1
1
1
0
0
1
1
2
1
0
1
1
0
1
1
2
1
2
1
0
1
1
1
2
0
1
0
1
1
1
0
0
1
1
2
0
2
1
1
0
2
1
2
1
0
0
1
1
1
2
1
0
1
2
1
0
1
0
1
1
1
1
2
1
0
2
2
4
1
2
0
2
1
1
1
1
1
0
0
1
0
0
0
2
1
2
1
2
2
1
1
0
1
0
1
0
1
1
1
1
1
0
1
1
0
1
2
0
1
2
1
1
1
1
0
2
2
1
2
1
0
2
0
1
2
1
2
0
1
0
0
2
1
0
0
1
0
1
1
2
3
1
0
2
2
0
2
1
0
0
1
1
1
1
2
1
0
0
3
1
1
2
2
1
1
1
2
1
3
2
0
2
0
1
2
1
0
2
2
0
1
2
1
0
0
1
0
2
0
0
0
1
1
2
0
0
1
1
0
3
0
1
0
1
0
1
1
0
0
2
2
2
0
1
0
0
1
2
2
1
0
0
2
0
1
1
2
0
1
0
1
1
1
1
0
2
0
0
0
0
0
2
1
0
1
0
1
1
2
0
0
1
0
2
1
0
2
0
1
0
2
1
2
2
1
1
2
2
1
1
2
0
0
0
1
2
1
0
0
2
0
1
2
1
2
0
1
1
2
2
1
0
2
0
0
1
0
2
0
1
2
0
0
0
0
1
0
1
0
0
1
1
2
1
2
8
1
0
1
1
0
0
1
1
0
1
1
0
2
0
2
0
0
0
0
1
1
2
2
1
0
0
2
0
1
2
1
0
2
0
0
2
2
1
2
1
2
1
1
0
1
0
0
1
0
0
0
0
1
0
0
5
1
2
2
1
0
1
0
0
2
0
0
0
2
1
2
1
1
2
0
0
0
0
0
1
0
1
0
1
1
2
2
2
1
3
0
3
2
2
1
1
0
1
0
0
0
0
0
0
1
2
1
0
0
1
1
2
0
0
1
0
0
1
2
1
1
2
0
1
1
1
0
0
0
1
0
2
1
0
1
0
0
1
1
2
2
1
1
2
0
2
0
0
0
0
1
0
1
1
2
1
1
2
1
1
0
0
1
1
1
1
1
2
1
0
0
0
1
2
0
1
0
0
1
2
1
2
1
2
0
1
0
0
0
2
0
0
1
2
0
0
1
0
2
2
0
1
0
0
1
1
1
1
1
2
0
0
2
1
2
1
1
1
0
2
1
1
0
1
1
2
0
0
0
1
2
1
2
0
1
2
2
2
1
1
1
2
1
0
2
1
0
0
0
0
1
1
1
2
1
0
0
0
0
2
1
2
2
0
1
3
1
2
0
1
2
1
1
1
1
0
0
1
0
0
0
1
2
1
0
1
0
1
0
1
1
1
0
1
0
1
0
1
0
1
1
1
0
1
0
1
1
0
0
1
1
2
1
0
0
0
0
1
2
1
2
0
0
1
1
2
1
1
0
1
1
0
2
1
1
2
1
2
2
1
1
0
2
2
1
0
0
2
1
2
2
2
0
0
0
2
1
1
0
0
0
0
0
0
2
1
1
0
0
1
1
1
1
0
0
0
1
2
1
0
0
1
0
2
1
1
0
1
1
0
0
2
2
0
1
1
1
1
1
2
0
0
1
0
1
1
2
1
2
1
1
0
1
0
1
1
1
1
1
2
1
0
0
0
2
0
1
0
1
1
2
1
1
1
0
2
1
1
2
0
0
1
2
0
2
1
1
0
0
0
0
1
0
0
1
0
0
1
0
1
2
1
1
0
0
1
1
0
3
1
2
1
0
1
2
1
0
1
1
1
0
0
2
1
1
1
1
0
1
2
1
1
2
1
1
1
2
2
2
1
0
1
1
1
1
2
0
0
1
0
1
0
0
2
1
1
2
1
1
1
1
2
0
1
1
2
2
2
1
1
2
2
2
1
2
0
2
1
1
2
1
0
2
1
1
0
2
2
0
0
1
2
2
3
0
0
0
1
1
0
0
1
2
1
2
1
1
1
0
0
2
0
0
0
0
1
1
0
2
2
0
1
1
2
1
1
1
1
0
0
3
0
1
1
0
1
2
2
2
1
0
2
2
1
0
2
2
1
2
2
1
1
1
1
3
0
0
1
1
2
1
0
1
0
1
1
0
1
0
0
0
0
0
1
2
7
1
0
0
1
0
2
0
0
0
0
1
0
2
1
2
0
0
0
1
0
2
2
2
2
3
0
2
0
2
0
3
0
0
0
1
0
2
1
1
0
1
1
1
2
1
0
2
1
0
1
0
1
1
2
0
2
0
2
1
1
2
1
1
1
1
2
1
1
0
1
2
0
0
1
0
2
1
0
0
2
0
0
0
1
1
1
0
1
2
2
1
1
1
2
1
0
1
1
1
1
0
0
1
4
0
2
1
1
0
2
0
0
1
1
1
0
1
1
1
0
0
1
1
1
3
1
1
0
0
1
0
0
2
0
2
0
0
1
1
1
0
1
1
2
0
1
1
1
0
1
1
0
1
1
2
1
1
2
1
0
1
1
1
0
2
1
1
2
0
0
1
0
0
1
1
2
1
0
2
0
1
1
2
1
1
0
0
2
2
1
1
2
1
1
1
1
1
1
0
0
2
1
2
1
1
0
0
2
1
2
0
1
0
1
0
2
0
2
2
2
1
2
2
0
1
0
2
2
1
1
0
0
0
0
1
0
2
1
1
2
0
1
0
2
0
0
2
2
1
1
1
0
1
0
0
2
1
2
0
0
0
1
5
1
1
2
1
2
0
0
1
1
0
1
0
1
1
1
0
0
0
1
1
0
1
1
2
0
0
1
0
0
0
1
1
2
1
2
0
1
2
1
0
0
2
0
1
1
1
2
0
2
0
1
0
1
1
1
2
1
0
1
0
1
0
2
1
0
0
2
1
0
1
0
0
0
0
2
1
0
0
2
1
1
0
0
3
1
2
1
0
1
1
0
0
1
0
1
1
1
1
1
1
0
2
1
1
1
1
1
2
1
1
0
0
2
0
1
1
1
1
1
1
1
1
0
1
2
1
0
0
0
1
0
0
1
2
1
1
0
2
2
1
0
1
1
0
0
1
0
1
0
1
2
0
1
0
0
0
2
1
1
0
1
0
0
1
0
1
0
1
2
1
1
1
1
0
0
1
0
0
2
0
0
1
2
2
0
1
1
1
2
2
1
0
3
0
2
2
2
0
0
1
1
2
1
2
1
0
0
1
1
1
1
0
1
1
1
1
0
0
2
2
0
2
1
1
1
1
1
1
2
3
0
0
1
1
2
0
3
1
1
2
1
2
1
1
1
2
0
0
0
2
2
1
2
1
0
1
0
1
1
0
0
1
1
1
1
2
1
0
1
0
1
0
1
0
2
1
1
1
1
0
1
1
0
0
2
0
0
1
0
0
0
0
2
0
2
1
0
1
0
0
0
2
0
1
0
0
1
1
0
0
2
0
1
1
1
2
0
1
0
1
2
0
0
2
0
2
1
1
1
0
2
0
1
0
2
1
1
1
2
1
2
1
1
0
1
1
2
1
1
0
0
1
1
1
1
0
2
0
2
0
1
1
0
0
2
1
2
1
1
0
0
1
2
2
0
2
0
2
0
1
2
0
1
1
0
1
1
1
1
1
0
1
1
1
0
1
1
0
0
1
2
0
2
0
1
0
2
2
1
1
1
3
0
0
1
1
0
1
1
1
3
1
0
2
2
0
2
2
0
2
0
1
0
2
1
1
0
2
0
1
0
0
2
2
1
2
0
1
1
1
0
2
1
1
2
1
1
0
1
1
2
3
2
0
1
0
2
0
4
1
1
0
1
0
2
2
2
1
1
2
1
0
1
2
1
1
1
0
0
1
1
1
1
2
1
1
1
1
0
1
2
1
2
0
2
1
0
1
0
1
0
0
0
0
1
1
1
1
2
1
0
1
2
0
0
0
1
2
2
2
2
1
1
2
0
2
0
2
1
1
0
1
0
0
0
2
1
1
1
0
1
1
2
1
1
1
1
2
1
1
1
1
1
2
2
2
0
1
2
1
0
0
1
2
0
1
1
2
0
1
1
1
2
2
2
2
0
0
1
1
1
1
1
1
1
1
2
0
0
0
1
1
2
0
1
2
1
2
0
1
0
1
0
1
1
1
0
1
1
0
0
0
1
2
0
1
0
1
1
2
2
1
0
0
0
1
0
0
1
1
2
1
1
0
1
1
1
2
1
1
0
0
1
0
0
2
0
1
0
1
0
1
0
2
0
2
2
0
2
1
2
0
1
1
1
2
0
2
1
1
0
0
0
1
0
1
1
0
1
1
0
2
1
1
0
0
2
2
2
2
0
0
1
2
1
2
0
2
1
0
0
1
1
1
1
1
0
1
1
1
1
1
1
2
0
2
0
2
4
2
2
1
2
1
1
0
1
0
1
0
0
2
0
1
0
0
0
2
1
0
2
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
2
1
2
0
1
1
0
0
0
2
1
1
0
0
1
0
2
0
1
2
1
2
1
1
2
1
0
1
2
1
2
0
1
1
0
0
2
2
1
1
0
1
0
1
0
1
0
1
1
2
0
1
2
1
0
0
1
1
2
1
2
0
0
0
0
0
1
2
0
2
0
3
2
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
1
2
1
1
2
1
3
2
1
1
1
5
0
1
0
2
1
1
0
0
2
0
0
2
0
2
2
0
1
2
2
1
1
0
3
1
1
0
0
0
1
1
1
0
1
1
1
0
1
1
1
1
0
0
2
1
0
1
1
1
1
0
2
0
2
0
1
0
1
0
1
1
0
0
2
1
0
1
2
0
2
2
1
1
1
0
0
2
1
1
0
1
0
1
1
0
2
1
1
0
0
1
1
2
2
0
0
0
0
2
0
0
0
0
1
0
1
0
1
1
1
1
1
1
2
0
1
2
0
1
0
0
0
1
0
1
1
0
1
0
2
1
1
2
2
1
2
1
1
0
1
0
0
0
2
0
2
0
3
1
1
2
1
1
0
0
2
1
0
1
0
2
3
2
1
1
1
0
0
1
0
0
1
0
2
1
2
1
0
1
1
1
1
1
1
1
0
1
1
2
0
0
2
2
0
0
0
0
0
1
0
1
0
1
1
2
2
2
1
2
1
1
3
2
0
1
2
0
0
1
1
2
2
1
1
1
0
2
0
0
0
0
0
0
1
0
0
1
2
1
1
1
0
1
1
0
1
0
1
0
1
0
1
1
3
2
0
1
1
2
2
2
0
1
0
1
1
2
1
1
2
2
1
2
1
0
1
2
0
2
2
0
0
1
2
1
1
0
1
1
0
2
0
1
1
0
1
0
0
0
2
2
1
1
0
1
0
2
0
2
2
1
2
1
1
2
1
1
1
0
0
2
2
1
0
1
0
1
1
2
1
0
0
0
0
1
0
1
0
1
1
1
1
1
2
2
1
1
0
1
2
0
0
2
1
1
1
2
1
2
1
2
0
2
0
1
2
1
2
0
1
0
1
1
0
0
1
2
1
0
0
1
0
0
0
1
2
2
1
0
0
2
1
0
0
2
0
1
2
1
0
1
2
2
1
0
1
1
1
2
0
1
1
2
2
0
2
0
0
2
0
1
1
1
1
0
1
2
1
2
1
0
1
0
0
1
1
0
2
0
2
1
2
2
0
0
2
0
2
2
1
1
0
1
1
1
1
0
1
2
2
0
2
0
2
1
1
1
2
1
2
1
0
2
0
1
0
1
1
2
1
2
1
0
0
1
0
1
0
2
1
0
1
1
2
1
0
0
1
0
0
1
2
0
0
4
0
2
1
1
1
2
2
1
2
0
0
1
0
1
0
1
1
2
1
0
0
2
1
2
0
0
1
1
0
0
1
2
1
0
0
1
1
0
0
0
1
1
1
2
0
1
1
1
1
0
0
1
2
1
1
1
0
0
2
2
2
1
2
1
1
1
2
1
0
0
3
2
0
0
0
2
0
1
0
1
1
0
1
1
2
0
1
1
0
1
1
1
0
0
0
2
1
2
2
0
1
2
2
2
0
0
0
0
0
0
2
1
0
1
1
2
1
2
1
0
1
2
0
0
0
0
2
2
1
2
1
0
1
1
1
1
0
2
1
1
1
2
1
1
1
1
0
1
1
1
1
1
1
2
0
1
2
2
1
0
1
0
1
1
0
0
1
0
1
1
1
1
1
1
0
2
1
0
2
0
0
1
2
0
1
1
2
0
2
1
1
1
2
0
1
1
1
1
2
0
2
1
1
1
1
2
0
1
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
1
1
1
2
1
0
1
0
1
0
0
0
0
1
0
0
0
1
2
0
0
0
1
1
1
2
1
0
1
0
1
1
1
2
0
0
0
2
2
2
0
1
1
2
2
0
2
0
2
2
2
1
0
0
1
1
1
1
1
1
0
0
5
1
1
0
1
0
2
1
0
1
0
1
2
1
1
1
1
1
1
0
0
2
2
0
2
1
0
0
0
1
0
1
2
1
0
0
1
0
1
0
2
0
0
2
2
0
1
0
2
1
2
2
1
2
0
0
2
1
0
0
1
0
1
0
0
1
1
0
0
1
1
0
0
1
1
2
0
1
2
2
1
1
2
0
0
1
1
1
0
0
0
1
2
1
0
2
1
2
1
1
0
1
0
0
1
1
0
0
0
1
2
0
1
2
1
0
1
1
2
0
2
2
0
0
1
1
0
0
1
2
0
1
2
1
1
1
1
0
2
1
0
1
1
2
2
1
0
0
1
0
2
0
0
1
0
1
0
2
1
2
1
0
1
0
1
1
0
0
2
1
2
2
1
0
1
0
0
1
1
0
1
0
2
1
1
1
1
1
2
0
2
0
1
0
1
1
0
1
0
0
1
1
0
2
1
1
0
3
0
0
0
0
0
1
0
0
1
0
1
1
1
0
1
0
1
2
1
2
1
0
0
2
0
0
1
2
1
2
7
1
0
1
1
1
0
1
0
0
2
1
1
1
2
1
1
1
0
0
2
1
0
2
1
0
1
1
0
1
1
0
1
2
0
2
0
1
2
1
0
0
1
1
2
0
1
2
1
1
0
1
1
2
0
1
0
0
1
2
0
0
2
0
1
2
0
2
1
0
0
0
1
0
1
0
1
1
0
0
1
2
0
0
1
1
1
2
0
0
1
2
0
0
0
1
1
1
1
0
2
0
1
0
1
0
1
1
1
1
0
0
1
1
1
0
0
1
1
1
2
0
1
2
0
0
1
0
0
1
1
0
1
0
0
0
1
0
1
0
0
0
1
1
0
1
0
2
1
0
1
3
2
1
2
2
2
1
0
4
1
1
0
1
2
0
2
2
1
1
0
0
1
1
2
1
2
0
1
0
1
1
1
0
1
1
1
1
1
0
1
1
0
0
2
1
0
0
0
0
2
2
3
2
3
1
1
1
1
2
1
0
0
1
2
1
1
1
1
0
2
0
0
1
1
0
1
0
1
1
0
0
2
2
1
1
2
0
1
1
2
1
1
2
1
2
3
0
0
2
1
0
0
1
2
1
1
0
2
0
1
2
1
1
2
2
2
1
2
0
2
2
1
1
1
0
1
2
1
0
1
1
1
1
1
0
2
1
1
0
1
0
1
0
1
0
1
0
0
0
0
2
1
2
0
2
1
1
0
1
1
1
0
3
0
1
0
1
1
2
0
1
0
2
0
1
1
2
1
0
1
1
1
0
1
1
0
0
0
6
1
2
2
1
1
0
0
2
1
1
2
0
0
1
2
0
1
1
0
2
0
1
1
1
0
2
0
2
1
0
0
1
1
1
1
0
2
0
1
1
1
2
0
0
1
1
1
1
1
3
1
0
0
0
0
0
0
2
1
0
1
1
0
1
0
2
0
1
1
1
0
0
1
1
0
2
0
1
1
1
0
0
2
0
2
1
0
1
0
0
1
0
0
2
1
0
3
1
2
1
1
2
0
1
2
1
0
1
1
0
0
2
0
0
2
2
0
2
1
0
1
1
1
0
0
1
1
0
0
2
1
0
1
1
0
0
1
1
1
1
2
1
1
0
0
0
1
2
0
2
1
0
0
0
0
1
1
1
0
1
1
0
1
0
2
2
0
1
1
2
2
1
2
2
0
3
1
1
2
2
2
2
2
1
0
1
2
0
1
0
0
1
0
0
2
0
2
0
1
0
1
0
0
3
2
2
2
1
1
2
1
0
0
1
2
2
1
1
1
1
0
3
0
1
1
1
0
1
2
2
2
1
0
1
1
1
0
2
1
0
0
2
0
1
0
2
0
0
1
2
2
1
1
1
0
0
0
2
1
2
1
0
0
1
1
0
2
1
2
2
0
1
1
0
2
1
0
0
0
2
1
1
2
0
1
1
1
1
1
2
0
1
0
2
1
1
0
1
2
0
1
1
0
0
1
1
1
2
0
3
2
2
0
1
1
1
1
0
0
0
1
2
1
0
1
0
1
0
1
1
1
1
1
1
0
0
0
2
1
0
0
1
0
0
1
0
0
2
1
2
1
1
0
0
1
2
1
1
1
2
1
1
0
2
0
2
0
0
0
1
1
0
3
1
1
0
0
0
4
2
0
0
1
1
1
1
0
1
2
3
0
2
2
0
0
0
0
1
1
1
0
0
2
0
1
1
0
1
2
1
1
1
1
2
2
0
1
4
0
1
1
0
0
1
1
1
0
2
0
1
1
1
0
1
0
1
0
1
2
0
0
2
1
0
1
2
0
3
1
0
0
1
2
2
1
3
0
1
1
1
1
1
0
0
1
1
1
1
0
1
2
1
1
0
1
1
0
1
2
1
1
1
1
2
0
1
2
1
0
2
0
0
1
1
0
0
1
2
0
1
2
2
0
1
1
4
2
1
1
0
2
1
0
0
2
1
2
0
2
0
1
2
2
1
1
0
2
0
1
0
3
0
0
0
1
0
0
0
1
2
1
0
1
1
2
1
1
2
0
0
1
0
1
0
0
1
0
2
0
0
1
2
1
1
1
1
0
2
1
1
2
1
0
0
2
1
1
0
0
1
1
1
0
1
0
2
0
1
1
2
0
1
0
2
1
1
0
1
1
2
2
1
2
1
1
0
1
2
1
1
0
0
0
0
2
1
2
0
2
1
2
0
0
1
1
1
0
2
2
2
2
0
1
2
0
1
1
0
0
1
0
0
1
2
0
2
2
2
1
1
1
2
0
1
1
2
1
1
2
0
1
2
2
2
2
0
0
1
1
2
1
1
2
2
0
2
0
1
0
1
2
1
1
0
0
1
0
0
1
1
0
1
1
2
1
0
0
1
1
3
2
1
1
2
0
1
2
1
1
1
0
2
0
0
2
4
2
0
1
0
4
0
3
1
1
1
1
1
1
3
0
2
2
2
1
1
1
0
0
2
2
1
2
3
0
1
3
0
1
0
1
2
2
2
0
2
2
2
1
0
1
0
0
1
0
0
0
0
1
1
2
1
1
0
0
0
1
0
1
2
2
0
1
1
0
1
1
0
0
1
0
0
0
1
1
0
1
0
1
2
1
1
0
1
0
2
0
2
2
0
2
1
1
1
0
1
1
1
1
0
5
0
0
3
1
0
0
2
0
0
0
0
1
1
0
0
2
1
2
0
1
1
0
0
1
1
2
4
0
1
2
1
1
0
1
0
0
1
0
0
0
1
0
0
0
2
1
0
2
1
1
0
2
2
1
0
0
0
0
0
1
1
2
1
0
1
2
0
1
1
1
1
1
2
0
1
2
1
1
0
1
0
0
1
1
0
1
2
0
1
2
1
0
2
5
1
0
2
1
1
1
0
2
2
0
0
1
1
1
0
1
0
1
2
0
2
0
1
2
1
2
0
2
1
1
1
3
0
0
0
0
1
3
1
0
2
2
2
2
1
0
0
1
0
0
1
0
1
2
2
1
1
1
0
1
1
0
0
0
1
2
2
1
2
1
0
1
0
0
3
0
0
2
2
0
1
0
2
1
1
1
0
1
0
1
1
2
0
0
1
2
0
2
1
1
1
0
0
2
0
0
0
0
1
0
2
0
0
0
1
1
1
0
0
2
1
0
0
2
1
1
1
2
0
1
1
1
0
1
1
1
0
0
1
0
1
1
1
0
0
2
0
0
1
2
0
0
0
0
3
0
1
1
1
1
0
1
0
1
1
1
0
2
0
0
2
1
0
1
1
1
2
2
1
1
0
1
1
1
1
4
2
1
1
1
2
0
1
2
2
2
1
1
1
2
2
1
1
1
1
1
1
1
0
3
0
0
1
0
1
2
2
1
1
1
1
0
1
0
1
2
1
1
0
1
1
1
1
0
1
1
1
1
1
1
1
2
1
2
1
0
0
0
1
2
2
2
0
1
1
1
1
2
0
1
2
0
1
2
1
1
1
2
0
2
1
0
0
1
2
0
1
0
0
1
0
0
0
0
0
0
0
2
0
1
0
2
2
1
0
2
1
1
2
1
1
2
0
0
0
0
0
1
1
1
1
0
0
0
1
1
0
2
2
0
1
1
1
1
1
2
0
0
0
2
2
2
0
1
0
2
1
0
0
0
0
0
0
2
2
1
0
1
2
1
0
0
0
2
2
3
2
2
1
1
0
2
0
0
0
2
2
1
1
0
2
0
1
1
1
0
1
0
2
2
0
1
0
0
2
1
1
1
0
0
2
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
2
1
0
2
1
0
1
0
2
1
1
0
1
2
0
1
1
1
1
1
2
0
2
0
0
0
2
0
1
1
2
1
1
1
1
1
0
2
0
2
1
0
1
2
0
2
0
0
0
1
1
1
2
0
0
1
2
0
1
1
0
3
2
1
1
0
0
0
1
0
0
1
1
0
1
1
1
1
2
0
1
0
1
2
2
1
0
1
1
1
2
2
1
2
1
1
3
0
0
1
0
2
1
0
2
1
1
2
1
1
0
1
2
1
1
1
0
0
1
0
1
1
2
0
2
3
1
2
1
1
2
2
2
2
1
1
1
0
0
0
1
0
0
2
1
1
1
0
0
1
1
1
0
1
1
1
1
0
0
0
1
1
0
0
0
1
0
1
0
1
0
0
1
2
2
3
0
2
2
0
1
0
0
0
2
1
2
0
0
2
2
0
1
2
2
1
0
1
1
0
1
1
1
0
1
2
2
1
1
0
2
0
1
1
0
0
0
0
2
1
1
2
1
2
2
1
1
2
0
1
2
0
0
1
0
2
0
0
1
2
1
2
0
0
0
2
1
1
0
1
1
2
1
2
0
1
2
0
1
1
1
0
1
0
1
0
0
1
0
0
0
2
2
1
0
1
0
0
0
1
0
0
1
0
1
3
0
2
0
1
0
2
1
1
1
1
0
1
0
2
1
0
2
0
1
1
2
1
1
1
1
1
1
1
1
1
0
1
2
1
1
1
1
2
0
2
1
0
2
2
0
1
0
1
1
0
0
0
0
1
1
1
2
0
2
2
1
1
1
1
2
1
0
1
1
1
1
1
0
2
1
1
2
1
1
1
1
1
2
2
1
0
1
4
0
1
0
1
1
1
1
1
1
1
0
0
0
0
1
1
0
1
1
1
4
1
2
2
1
1
0
2
0
1
1
2
1
1
1
0
1
1
0
0
0
1
0
0
1
0
1
0
1
0
0
2
0
2
0
1
1
0
1
2
2
2
1
1
1
0
0
1
1
0
0
1
1
1
1
2
0
3
1
0
0
1
2
1
1
1
0
1
0
2
1
0
1
2
1
1
1
2
1
0
2
1
0
1
1
1
0
0
0
1
1
2
1
0
2
2
1
1
0
2
1
1
2
1
0
1
0
1
0
3
0
1
1
1
2
1
1
0
1
1
1
0
1
1
3
2
1
3
0
0
1
0
0
1
0
0
1
2
2
0
0
0
1
1
2
1
1
1
2
1
0
2
0
2
2
2
1
1
1
0
1
0
2
1
3
1
0
0
3
1
2
0
0
0
1
1
1
2
0
0
1
1
0
0
2
1
3
1
2
1
0
2
0
0
0
0
2
2
0
1
1
1
0
2
1
0
0
1
2
1
1
0
1
1
0
1
2
0
0
1
0
0
1
2
1
0
0
0
3
0
0
1
1
1
1
0
1
0
2
0
1
1
0
2
1
1
2
1
0
0
1
0
1
1
0
0
0
0
1
2
0
0
1
1
2
0
0
2
1
2
0
0
0
0
1
2
1
1
0
0
1
0
2
1
2
0
1
1
1
0
2
0
1
2
1
1
1
0
0
2
0
1
1
0
0
1
0
2
1
3
1
0
3
2
1
0
2
1
2
1
2
2
1
0
1
0
0
0
1
1
0
2
1
0
0
0
0
2
1
2
1
1
1
1
1
0
1
0
1
0
2
1
0
1
2
1
1
1
2
0
2
0
3
0
0
2
1
2
2
0
0
2
1
0
1
1
0
2
1
0
2
0
0
0
1
0
1
2
1
1
0
1
2
0
2
0
0
1
1
0
0
1
1
1
2
0
0
0
1
2
0
2
1
1
2
0
0
0
0
0
1
0
1
1
0
1
1
1
0
1
2
1
1
1
0
0
1
1
1
1
0
2
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
1
0
1
1
0
1
1
0
1
0
2
1
0
0
2
1
0
1
0
0
1
2
0
0
1
0
1
2
0
1
0
1
1
1
1
0
2
2
0
0
0
1
0
1
0
1
0
1
1
2
0
1
2
2
1
2
1
5
2
1
0
0
1
0
0
0
1
1
0
0
1
1
1
1
0
0
1
2
2
0
2
0
1
1
1
2
2
2
1
0
0
1
0
1
2
2
1
0
1
2
2
0
6
1
2
1
2
1
2
0
1
1
1
0
1
1
2
0
0
0
1
1
1
0
0
1
1
1
0
2
2
0
2
0
0
0
2
0
2
2
1
0
0
1
2
1
1
0
1
1
1
1
1
1
0
1
2
0
1
2
1
1
1
1
0
1
1
1
1
0
1
2
0
0
1
2
2
1
2
1
0
1
1
2
2
2
2
2
2
0
2
0
1
0
2
0
2
1
5
2
0
0
0
0
2
1
2
1
1
1
1
1
1
0
0
0
0
1
0
1
0
0
2
1
0
1
2
2
0
0
2
0
0
0
1
0
1
1
0
0
1
2
4
1
2
1
0
1
1
1
0
0
0
0
1
1
2
2
1
2
1
2
1
1
1
1
1
2
1
1
0
0
0
0
0
1
0
0
1
1
1
2
0
0
1
1
2
2
1
2
1
0
0
2
0
1
1
1
1
0
1
1
2
0
0
0
1
0
1
0
1
1
0
1
0
1
2
1
0
1
0
0
2
0
1
3
1
2
1
1
0
0
1
2
1
2
0
2
1
0
1
0
1
1
0
1
0
2
0
2
0
1
2
2
1
1
0
0
1
0
1
2
1
0
1
1
1
0
2
0
1
1
0
0
0
1
0
0
1
1
1
0
0
1
0
1
1
2
2
0
2
1
2
1
1
1
2
2
2
0
0
0
0
0
0
1
2
2
0
0
0
2
1
0
0
1
0
0
0
2
1
1
1
0
0
1
0
0
0
1
0
0
1
1
2
1
1
1
1
2
1
1
0
1
2
2
0
0
1
3
0
1
2
0
2
0
0
2
0
2
0
1
1
2
2
0
2
1
1
2
1
1
1
2
0
2
0
0
0
1
1
0
2
0
2
0
0
0
1
1
2
1
0
2
0
0
1
0
1
0
0
0
0
1
1
0
1
1
2
0
2
2
1
0
1
0
0
2
0
1
0
0
2
2
0
1
2
1
1
0
1
1
0
0
2
0
1
1
1
0
1
1
1
2
2
1
0
2
0
0
1
0
0
0
2
0
0
0
1
1
1
1
1
1
1
1
1
2
0
1
1
0
2
0
2
2
0
1
1
0
2
2
1
1
1
1
1
1
1
0
1
1
1
1
0
2
3
0
0
0
1
1
2
2
1
0
0
1
2
2
0
1
1
0
2
1
1
0
2
0
2
0
2
1
0
2
0
1
0
1
1
1
0
0
1
1
2
2
1
0
2
2
0
1
0
1
2
1
1
1
0
1
1
0
1
0
1
2
0
2
0
1
0
0
1
1
1
0
2
2
0
1
0
0
2
2
1
1
1
2
1
1
0
0
0
1
1
0
0
2
1
2
0
0
0
1
2
0
2
0
1
1
0
1
0
0
1
1
1
0
2
0
0
1
0
0
1
0
1
1
2
1
0
1
2
2
2
1
2
0
7
1
0
1
2
0
2
1
1
2
2
2
0
0
0
1
1
1
1
1
1
0
1
1
1
2
0
0
1
1
2
0
2
1
1
2
1
0
0
2
1
1
1
2
0
0
0
0
1
2
1
2
2
1
1
0
0
1
0
1
2
1
2
1
2
2
0
0
1
2
0
2
2
2
0
0
0
0
0
1
1
0
0
0
2
1
0
1
2
0
1
1
1
1
1
2
0
2
1
1
2
1
0
1
0
0
1
2
0
0
2
2
0
1
0
0
0
0
0
2
1
1
0
1
3
0
0
1
0
1
1
2
2
1
0
2
1
0
1
1
0
0
1
2
2
1
1
3
1
1
2
0
2
1
1
0
1
1
0
1
0
1
0
0
2
0
1
0
1
0
0
0
1
2
0
1
1
1
0
1
0
2
0
0
2
0
1
1
0
1
1
2
2
2
0
2
3
0
1
2
1
0
0
2
5
2
1
1
0
1
2
1
1
1
2
0
1
1
1
1
1
0
2
0
1
0
0
1
0
2
1
0
2
2
1
1
1
1
2
0
1
1
0
1
0
0
2
1
0
1
0
0
2
2
0
1
1
2
0
1
1
0
2
0
1
1
0
1
6
1
0
1
1
1
2
1
1
1
1
1
2
0
2
2
2
0
2
0
0
1
1
2
0
0
2
1
0
1
0
1
1
1
1
2
1
1
1
0
1
1
1
3
0
1
1
1
0
0
2
1
0
2
1
0
1
1
0
2
2
1
1
0
2
1
0
0
1
1
0
1
1
1
0
2
0
0
2
1
1
1
2
0
1
2
1
0
0
1
1
1
1
2
0
1
2
1
1
0
2
1
1
0
1
0
0
2
2
1
0
0
1
1
0
2
2
1
2
0
0
0
1
0
0
1
1
0
1
2
1
1
1
1
1
2
0
1
1
0
0
2
0
2
1
2
0
1
0
1
1
1
0
0
1
2
1
0
1
0
1
0
1
1
1
1
0
0
2
0
1
1
0
1
1
1
3
2
0
1
1
2
1
1
0
2
1
1
1
1
1
6
2
1
3
2
1
0
3
3
1
0
1
0
2
0
3
0
0
1
0
2
1
1
2
0
1
1
0
1
1
0
1
1
1
0
1
1
0
1
1
0
1
2
0
0
1
1
0
2
1
1
1
1
0
0
0
0
1
2
1
0
1
1
0
0
1
1
1
1
2
4
2
2
0
2
0
0
2
1
0
2
2
2
0
0
1
1
1
0
0
0
2
1
1
0
2
0
2
1
0
2
1
2
0
2
0
0
5
0
0
2
1
0
0
1
1
0
1
0
0
2
1
1
0
1
0
0
1
0
0
1
1
1
1
0
2
0
0
1
0
1
1
2
0
2
0
1
1
1
0
0
1
0
1
1
2
1
1
0
2
0
1
2
0
1
2
2
1
1
0
0
0
2
0
0
1
1
2
1
1
2
0
0
0
2
0
0
2
2
0
1
2
0
1
1
0
1
2
1
0
1
2
2
0
0
0
1
0
0
0
0
0
1
1
0
2
1
1
0
0
0
2
1
2
2
1
3
0
0
0
1
2
1
0
0
1
1
1
2
0
2
0
1
0
1
0
0
2
1
0
2
2
0
0
2
1
1
0
1
1
0
2
2
1
1
1
1
1
1
2
0
1
1
2
0
1
2
2
2
1
0
0
2
0
2
0
1
2
1
1
1
1
0
0
2
1
1
0
2
1
0
0
1
1
1
1
0
0
0
0
1
2
1
2
0
1
1
1
1
2
1
0
0
2
1
2
0
2
0
0
1
1
2
1
2
2
2
1
1
1
2
2
0
0
0
2
0
1
1
2
1
1
1
1
1
2
1
1
0
1
1
0
1
1
1
1
0
2
2
1
0
0
0
0
0
1
1
0
1
0
2
1
2
0
0
0
1
0
0
0
2
0
0
2
1
0
0
0
0
1
0
2
1
0
0
2
0
2
1
3
1
0
1
0
0
1
1
0
0
2
0
0
0
0
2
1
1
1
1
1
2
0
0
1
2
2
2
0
1
0
0
3
1
1
1
1
1
2
2
1
0
0
2
0
0
1
0
1
1
1
0
0
0
0
0
0
2
2
1
1
1
1
1
1
1
2
1
2
1
1
2
1
1
2
0
0
1
0
2
1
2
0
0
2
0
1
1
1
0
0
1
2
1
0
4
1
1
2
1
0
1
0
0
1
0
0
0
1
0
1
0
1
1
0
1
1
1
1
1
1
2
1
4
2
1
1
2
1
0
1
1
2
1
0
2
0
0
1
2
0
0
2
1
1
1
2
1
0
0
0
1
3
2
1
1
1
0
0
1
1
1
1
4
1
2
1
0
0
0
1
1
1
1
1
0
0
1
2
0
1
1
0
0
3
1
0
1
0
0
0
2
0
1
0
1
0
2
2
0
1
0
1
1
1
0
1
1
1
2
1
1
1
1
1
1
2
0
2
2
1
1
0
1
1
0
1
0
1
3
1
2
1
0
0
2
1
1
0
0
0
0
1
1
0
0
0
3
1
0
0
1
0
1
0
0
1
0
4
1
0
1
2
1
0
1
0
1
1
0
0
1
0
0
1
0
2
0
1
3
1
0
0
1
0
3
0
2
0
3
1
1
0
1
0
0
1
1
1
1
0
0
2
0
1
1
1
2
2
0
1
0
0
1
0
0
1
2
0
1
0
0
1
1
2
1
0
2
0
2
2
1
1
0
2
0
1
0
2
1
1
0
0
0
1
1
2
1
0
0
2
0
1
1
0
2
1
1
1
1
0
2
1
0
1
2
1
1
1
0
0
2
1
0
3
1
0
0
1
1
0
0
0
0
1
1
1
1
0
1
0
0
2
0
4
1
2
0
2
1
0
0
3
0
0
0
0
0
0
2
2
2
0
0
0
2
3
0
2
0
2
0
2
2
1
0
1
1
0
0
1
0
2
0
0
0
0
2
1
2
1
1
0
0
2
1
0
1
0
1
0
0
1
1
2
2
0
1
0
0
0
1
0
1
0
0
0
2
1
0
0
3
2
1
0
0
1
0
1
1
1
1
0
0
1
0
0
3
1
1
0
0
2
0
0
1
1
1
0
1
0
1
0
1
0
2
0
1
0
2
2
0
2
0
0
1
1
1
1
0
0
1
0
2
1
0
1
1
0
2
0
1
1
2
0
0
1
2
1
2
0
1
2
0
0
3
1
0
1
1
1
1
1
1
1
1
1
0
2
0
1
2
1
1
1
0
0
1
1
1
0
2
1
5
0
2
1
1
2
1
0
0
1
1
2
3
1
0
0
0
0
1
0
2
1
0
1
0
0
0
0
2
0
1
0
1
1
1
1
0
2
0
0
1
1
2
0
1
2
1
0
0
0
1
2
1
1
0
1
2
1
1
1
1
1
1
1
1
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
1
1
2
1
2
0
1
1
1
1
1
0
2
1
1
1
1
1
2
1
1
2
0
0
0
2
1
1
2
2
0
1
1
1
1
0
0
1
2
3
2
2
1
0
0
1
0
0
1
1
0
1
1
0
1
2
1
1
1
1
2
3
1
0
2
2
0
1
1
0
0
2
1
1
1
1
2
1
0
1
2
0
0
1
1
1
1
1
1
0
1
1
1
1
0
1
2
2
0
1
2
2
1
0
2
1
1
1
0
0
0
0
0
1
0
2
1
0
0
0
0
1
0
0
1
0
3
0
0
3
2
0
0
0
0
1
0
1
2
2
2
0
2
1
0
1
1
2
0
0
1
0
1
0
1
4
0
2
0
0
1
1
1
1
2
2
0
1
0
0
1
1
0
0
1
1
1
2
3
0
1
3
2
0
1
0
1
1
2
1
1
1
1
0
0
2
1
0
1
0
2
1
1
1
1
0
0
1
2
1
1
0
1
0
1
1
1
0
0
2
2
1
1
2
2
1
0
0
0
0
1
2
2
1
1
1
0
2
1
0
0
2
0
2
7
1
0
0
1
0
2
1
0
0
0
0
2
0
0
1
0
2
1
2
0
1
0
1
1
2
1
2
2
0
0
0
0
0
0
0
0
1
2
1
1
1
1
1
2
2
1
1
2
2
2
1
1
0
0
0
1
0
1
0
0
0
0
3
1
0
2
0
1
0
0
2
1
0
2
0
2
1
1
0
1
2
0
0
0
0
0
0
1
1
2
1
0
2
1
0
0
1
2
1
0
0
1
0
0
2
1
1
1
0
1
1
2
1
1
0
0
1
0
2
1
2
0
2
0
0
0
0
1
1
0
2
0
0
1
2
2
1
0
1
2
0
1
1
2
2
0
2
1
1
0
1
1
0
0
2
1
0
0
1
1
1
1
0
0
2
0
0
1
1
0
0
2
1
2
2
0
0
0
1
2
1
1
0
1
2
0
1
0
0
2
1
0
1
0
1
1
1
1
1
3
0
1
2
1
1
1
0
2
1
0
1
1
1
0
2
2
0
2
2
1
0
1
0
1
1
1
1
0
2
2
0
1
1
1
0
0
2
1
1
1
1
0
0
3
2
1
0
0
1
1
0
0
0
2
0
1
0
0
0
0
2
0
3
1
0
2
2
1
1
1
0
3
0
4
0
0
1
1
1
0
1
1
0
1
0
2
0
0
2
0
0
0
2
0
0
1
1
0
1
1
0
0
1
1
0
1
1
2
2
0
1
2
0
1
2
1
2
0
2
0
0
1
1
1
1
1
1
1
1
0
1
0
0
2
2
0
1
1
1
1
1
1
5
1
2
1
0
2
0
2
2
2
0
0
3
2
1
0
0
1
2
0
0
0
1
0
0
1
0
0
2
0
0
2
2
1
1
0
2
1
2
0
1
1
1
1
0
2
2
0
1
0
1
0
1
0
0
1
1
1
1
0
1
0
1
0
0
2
0
1
1
1
0
0
1
0
0
0
2
2
0
1
1
0
1
0
0
1
1
1
2
0
2
0
5
0
0
1
1
0
1
2
0
0
0
1
1
0
0
2
2
0
1
0
0
2
0
0
1
0
1
0
0
2
1
1
0
0
2
0
1
2
2
1
1
1
2
0
1
0
2
1
2
1
2
1
2
2
2
1
0
2
1
2
0
2
0
0
2
1
0
1
1
1
0
1
0
1
1
2
0
0
1
1
2
0
1
1
0
0
1
0
0
1
1
2
1
0
2
0
1
0
0
0
2
0
1
1
0
0
0
0
1
0
1
0
0
2
2
1
2
1
2
0
0
0
1
2
1
0
0
2
2
0
1
1
0
0
1
1
1
1
1
2
0
2
1
1
1
1
0
2
0
1
1
1
1
1
1
1
2
1
1
0
0
2
0
1
1
0
4
0
2
0
1
0
2
1
0
1
0
2
5
0
1
1
0
1
1
2
0
1
0
1
2
2
2
1
0
2
2
1
2
2
1
0
0
0
1
0
0
0
2
1
0
2
0
1
1
1
0
2
2
2
0
0
0
2
1
1
0
2
1
2
2
0
0
2
1
1
0
1
1
0
0
1
0
1
1
0
0
2
0
0
1
0
1
1
1
2
0
0
2
1
1
0
2
0
2
0
1
1
1
1
1
2
1
1
0
2
0
2
2
0
0
0
2
0
1
1
0
1
2
0
0
1
0
1
1
2
1
1
0
1
0
0
1
2
1
1
1
1
0
0
2
1
1
1
1
1
1
0
0
1
2
2
1
0
1
2
2
0
2
2
1
1
2
1
2
0
0
1
0
1
2
0
1
1
0
1
1
0
2
0
1
2
0
2
1
2
1
1
1
0
1
1
1
0
0
1
2
2
1
1
1
0
0
0
1
2
1
1
0
2
0
1
2
0
1
1
0
0
2
0
0
0
0
1
0
3
0
0
2
2
0
1
0
1
2
2
1
2
2
1
0
2
2
2
1
1
1
2
1
0
2
0
2
1
2
0
1
0
2
1
2
0
1
0
2
0
1
0
0
2
0
0
1
2
1
0
1
5
2
0
0
1
1
1
1
2
2
2
1
0
0
0
0
2
1
0
0
0
2
1
0
0
2
1
0
3
0
2
0
0
1
1
1
0
0
1
2
2
0
0
1
0
1
0
1
2
0
0
1
1
0
2
0
0
0
0
0
0
1
1
1
2
0
0
0
1
0
1
1
2
1
1
0
0
2
1
1
1
1
1
1
2
1
1
2
0
1
1
1
0
2
0
1
1
3
1
0
0
0
1
0
0
1
0
1
0
2
1
0
2
2
1
1
1
0
0
0
2
1
0
0
1
0
1
0
1
1
0
1
0
1
0
0
0
0
1
2
1
2
1
1
0
2
1
0
1
1
1
1
1
1
1
1
1
0
1
2
0
1
2
3
1
0
0
2
0
1
0
1
0
1
1
0
1
0
0
2
0
1
1
1
0
0
1
0
1
2
1
1
1
2
2
1
2
2
2
0
1
1
1
2
2
2
0
2
0
1
1
1
2
0
2
1
1
2
2
1
1
2
1
1
1
0
1
0
1
1
0
0
5
0
1
0
1
1
0
1
2
1
1
3
1
1
2
0
1
0
0
1
1
0
1
0
0
0
2
2
1
0
1
0
2
2
2
0
1
0
0
0
1
1
2
1
0
2
0
0
0
0
2
0
0
0
1
1
2
2
1
0
0
0
2
0
2
0
2
0
1
0
1
1
0
1
1
2
1
2
0
2
0
1
1
1
2
2
1
2
0
1
0
1
0
1
1
0
0
1
0
0
1
0
0
0
1
1
1
2
2
2
0
0
2
2
2
1
1
1
2
1
0
2
0
0
0
2
1
1
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
2
0
0
1
2
1
0
1
2
0
0
0
0
0
1
1
0
1
1
1
1
1
0
1
0
1
1
1
0
1
1
0
0
0
2
1
2
0
0
1
2
0
1
0
1
1
2
0
0
1
0
2
2
0
0
2
0
1
1
1
2
0
1
0
1
0
2
1
1
0
1
0
1
1
2
1
1
2
1
0
2
1
2
2
1
0
1
2
2
2
1
1
2
1
1
0
0
0
1
0
2
2
1
1
0
2
0
0
2
1
1
1
0
1
0
1
0
0
0
2
3
0
0
1
0
0
2
2
1
2
0
1
3
1
0
1
0
1
0
0
1
1
1
0
1
1
1
1
2
2
1
1
0
1
2
2
1
1
0
2
0
1
0
0
0
2
0
1
1
0
1
1
0
0
2
0
1
2
0
0
1
1
0
1
2
1
1
1
1
1
0
0
2
2
1
0
0
1
2
1
1
1
2
2
2
2
2
1
0
0
0
2
2
1
1
0
1
1
1
1
1
2
2
0
0
2
1
1
0
1
1
1
0
1
0
0
0
1
2
0
1
0
1
1
1
1
0
1
2
1
1
1
0
1
1
1
0
1
2
2
1
1
1
1
1
0
0
0
1
1
0
0
1
2
0
0
2
1
2
0
0
0
0
0
0
1
1
2
2
0
1
0
0
1
0
0
1
2
1
1
2
1
1
0
2
2
1
1
2
2
1
1
0
0
1
0
2
1
2
1
2
1
2
0
0
1
1
1
0
2
0
1
1
1
2
2
0
0
1
0
0
2
0
0
0
0
0
2
1
1
0
1
2
1
2
1
1
0
1
1
1
2
1
2
1
0
1
1
0
2
0
1
1
1
1
2
2
2
0
1
0
1
0
0
0
2
2
0
0
3
2
1
1
1
2
1
0
1
2
2
1
2
1
0
0
0
2
0
0
1
0
1
2
1
1
1
1
1
1
1
2
1
2
0
0
2
0
2
2
1
0
1
1
1
2
0
0
1
1
2
0
1
2
1
2
0
0
0
0
1
2
1
1
2
2
1
0
0
2
1
0
0
0
1
0
1
0
1
0
2
1
0
1
0
0
0
0
2
0
2
0
1
1
0
0
0
2
0
0
0
2
2
2
2
1
0
1
0
1
2
1
0
1
0
0
1
2
0
1
0
0
0
1
0
1
0
0
1
0
2
1
1
1
0
0
1
0
2
1
2
1
1
0
1
1
1
1
0
2
1
2
0
2
1
2
0
0
2
1
0
1
2
0
2
0
1
0
2
1
1
1
0
5
2
0
2
1
1
0
1
2
0
2
2
0
0
1
1
1
1
0
1
0
1
1
1
1
0
1
0
0
0
1
1
1
2
2
0
1
2
1
1
0
0
0
1
2
0
0
1
1
1
1
1
0
0
2
2
1
1
1
0
1
2
1
2
0
2
1
1
1
1
0
2
0
0
0
1
0
2
0
1
0
1
1
1
1
2
1
1
1
1
1
0
2
2
2
2
2
1
0
0
1
1
1
1
1
0
0
0
0
1
2
2
1
0
1
0
0
2
0
0
1
1
1
0
2
1
0
1
1
1
2
1
1
1
1
0
2
0
0
2
0
0
1
1
2
0
1
0
1
0
1
0
0
2
2
0
0
1
1
1
0
1
1
0
0
0
2
1
1
0
1
0
1
1
1
2
1
2
3
1
2
1
1
0
2
0
0
2
0
0
1
0
0
1
0
1
0
0
2
0
2
1
1
1
1
1
2
1
1
1
0
0
1
1
1
1
2
2
1
1
2
1
1
1
1
0
0
2
1
0
2
1
2
1
1
1
2
1
0
1
2
0
0
1
0
2
0
1
0
1
1
1
1
0
2
1
1
0
0
0
0
1
1
1
0
1
1
2
1
1
2
0
0
1
1
1
1
1
0
0
0
0
1
0
2
0
0
0
1
0
0
1
0
2
1
0
1
1
0
1
0
1
0
2
0
2
0
3
1
1
2
1
1
1
0
1
1
0
0
0
1
0
0
1
1
1
1
0
0
1
0
0
0
2
1
0
1
2
1
1
2
2
1
0
2
2
1
1
2
1
0
1
1
0
1
1
1
1
2
1
1
0
0
1
1
2
1
2
1
0
1
1
0
0
1
0
1
2
1
0
1
2
1
1
2
0
3
1
1
1
2
1
0
0
1
1
2
1
2
0
0
1
1
2
1
1
1
1
0
1
1
1
0
1
2
0
1
2
2
1
0
2
0
1
1
1
2
1
1
0
2
1
2
0
1
0
0
0
2
0
2
1
1
1
1
1
3
0
2
1
2
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
1
2
2
2
0
0
1
1
0
1
0
1
1
0
0
1
1
1
1
1
1
2
2
0
1
1
1
1
0
1
1
0
2
2
1
1
1
0
1
2
2
1
1
2
0
1
1
0
1
1
1
1
1
0
0
0
2
2
1
2
1
0
0
1
0
1
1
1
2
1
2
1
1
0
0
0
1
1
2
1
1
1
2
0
0
3
0
1
1
1
1
1
1
0
1
0
0
1
1
1
0
0
1
1
1
1
2
2
1
0
2
0
0
0
1
1
1
1
2
1
0
2
0
1
0
3
1
2
2
1
0
0
0
1
0
2
0
1
1
1
0
0
1
0
0
0
0
2
1
0
0
1
0
3
2
1
2
1
1
0
2
0
1
1
0
1
1
0
1
0
0
0
2
1
1
1
1
1
2
2
0
0
1
1
1
1
2
1
2
0
0
0
0
1
1
1
1
1
1
2
0
4
1
1
1
2
1
1
2
1
2
1
1
1
1
1
0
2
0
0
1
1
1
0
1
2
1
1
0
1
1
0
0
2
1
1
2
1
1
1
0
1
3
2
0
0
1
2
0
0
1
1
0
1
1
1
1
2
0
1
0
2
1
2
0
2
1
0
2
1
1
2
2
1
1
0
1
1
2
1
1
1
2
1
2
0
1
1
0
0
2
0
2
0
1
0
1
0
1
0
0
1
1
0
0
0
1
0
0
1
0
0
1
0
2
2
2
0
0
1
0
2
0
1
1
0
0
1
0
0
0
0
1
1
2
0
1
1
1
0
1
2
1
0
2
2
0
6
1
0
2
1
1
1
0
0
1
1
1
1
1
1
1
0
1
0
2
0
2
0
0
1
1
0
1
2
0
1
0
1
2
2
1
0
0
0
0
1
1
1
1
0
1
2
1
1
0
0
1
2
2
0
1
2
0
2
0
1
0
1
0
2
2
0
1
1
1
1
0
0
0
0
1
0
0
1
1
0
1
2
0
1
1
0
0
0
0
1
1
0
1
1
0
1
1
2
2
0
1
2
2
0
1
0
1
1
0
0
2
2
0
0
1
1
2
1
0
1
2
1
1
2
2
2
0
1
0
0
1
2
1
2
1
2
0
0
2
2
2
2
0
0
1
1
2
1
2
1
0
0
1
2
2
2
1
0
1
1
1
1
1
2
1
1
0
0
0
0
0
1
3
1
0
0
1
1
1
2
1
0
0
1
3
0
2
0
0
0
1
0
2
1
0
0
1
0
0
0
1
2
0
0
2
2
0
2
1
0
2
2
2
0
0
0
1
1
0
0
1
1
2
0
1
0
2
0
1
1
0
0
0
0
1
1
2
0
0
0
1
1
0
1
0
2
2
1
0
0
1
2
0
2
0
0
2
0
1
1
0
1
2
1
2
2
1
0
0
2
0
2
0
0
1
0
0
0
1
1
0
0
1
1
1
0
0
1
2
1
0
0
0
2
2
1
2
2
2
2
0
0
1
2
1
2
1
0
0
0
2
0
0
1
2
1
2
1
0
0
1
0
0
0
0
0
1
1
1
0
1
0
2
0
1
0
0
1
1
0
2
0
1
1
0
1
2
1
0
2
1
1
1
0
0
1
2
0
2
1
0
0
1
0
2
2
1
0
1
0
2
0
1
1
0
0
1
1
1
1
2
1
1
0
1
1
1
1
0
1
0
0
0
1
2
0
0
0
0
1
2
1
0
4
1
1
0
0
3
0
1
0
0
1
1
0
1
0
1
1
0
1
1
2
2
0
0
0
0
1
2
0
0
1
1
1
1
1
0
4
1
2
0
2
0
2
0
1
2
1
1
1
0
2
1
1
0
1
0
0
1
1
1
3
2
1
1
1
0
2
0
0
0
1
1
0
0
1
1
2
1
1
0
2
2
1
2
2
2
1
1
2
2
2
0
2
1
1
0
0
0
2
1
2
2
1
0
1
1
1
0
1
0
1
2
2
1
1
1
0
1
0
0
2
1
2
1
2
0
1
1
1
1
1
1
0
2
1
1
0
0
1
0
2
0
2
2
1
0
1
0
1
2
1
0
1
1
0
1
2
2
1
1
0
1
3
0
2
1
0
2
2
1
0
1
1
1
0
1
0
1
0
0
1
2
1
1
1
0
1
0
0
2
0
0
0
2
0
0
1
0
0
0
1
0
1
0
0
1
1
0
1
0
2
2
2
0
0
1
1
0
2
0
2
2
0
0
1
1
1
2
1
2
0
0
0
1
0
2
0
2
1
1
2
2
1
1
2
0
1
1
2
0
0
1
2
0
1
1
0
1
1
1
1
2
1
2
2
2
0
0
1
0
10
1
1
0
1
4
1
2
0
0
0
1
2
0
2
1
0
0
1
1
0
1
1
2
1
1
0
1
2
1
2
1
2
0
1
0
0
0
1
3
1
1
1
1
2
1
0
1
1
0
2
1
0
1
2
2
0
3
1
0
1
2
2
1
0
2
2
0
0
0
2
2
0
2
1
0
2
0
1
1
0
1
0
2
1
0
1
1
0
0
1
0
1
2
1
1
2
1
1
0
0
0
1
2
0
0
1
1
1
0
0
2
0
2
1
0
0
2
2
0
1
2
1
1
2
1
1
1
2
1
2
1
1
1
1
2
1
0
0
2
0
1
1
0
2
1
1
0
1
1
1
0
1
1
2
1
2
1
0
1
0
2
2
1
1
1
1
1
1
1
1
2
0
0
2
2
0
1
0
0
1
1
1
1
0
0
1
1
0
1
1
1
2
1
1
2
0
0
0
1
0
1
2
1
1
1
0
1
1
0
0
2
1
1
0
1
1
1
2
1
1
1
0
1
1
0
1
2
1
0
1
0
2
1
1
1
0
1
0
1
1
0
2
1
2
1
0
2
0
1
0
0
1
1
1
1
0
1
1
0
0
1
1
1
1
0
1
1
2
1
2
1
2
1
1
0
0
2
1
1
2
0
0
2
0
0
1
1
1
1
0
0
0
0
1
1
0
0
0
1
1
1
1
0
1
2
1
2
2
1
1
1
1
1
1
0
1
1
1
1
1
1
2
0
0
0
2
0
2
0
4
2
0
0
1
0
2
0
0
2
1
0
0
1
0
2
0
1
0
2
0
0
1
0
2
2
2
0
1
0
1
1
0
2
0
1
0
0
0
0
2
0
0
2
2
2
0
1
1
0
1
0
1
2
1
1
0
2
0
1
4
2
1
0
1
0
1
1
1
1
1
0
1
1
2
2
1
1
1
2
0
1
0
0
0
2
1
1
2
2
0
1
1
1
2
0
0
0
0
1
0
2
1
0
0
2
1
2
0
1
1
1
1
2
1
1
1
0
1
1
0
0
0
1
0
0
2
0
2
2
1
0
1
1
0
0
2
1
0
1
0
0
1
1
1
3
1
3
1
1
1
1
1
0
0
0
1
1
1
2
0
0
0
0
1
0
2
1
0
1
1
1
1
1
2
2
1
1
0
1
1
1
0
0
1
0
2
5
1
0
1
1
1
0
1
0
1
0
0
0
1
1
2
2
0
2
1
1
2
1
4
1
1
2
1
2
2
0
1
1
2
1
1
1
1
1
0
2
0
1
0
1
0
0
0
1
1
1
0
0
2
1
0
0
0
1
1
1
0
1
0
0
0
1
1
1
2
1
0
1
1
0
0
1
2
0
0
1
0
0
2
1
1
2
2
0
0
1
0
1
1
1
1
2
2
4
0
0
1
1
0
2
1
0
0
1
1
1
0
0
1
0
0
1
1
1
1
1
1
1
1
1
1
0
0
0
1
0
1
1
1
0
0
0
2
0
0
0
0
1
1
0
0
0
1
1
0
0
1
2
1
2
1
0
1
1
2
0
1
1
1
1
1
1
1
1
2
0
0
0
1
1
1
2
1
0
1
2
1
0
2
1
2
1
2
0
0
0
0
1
1
2
2
0
0
0
0
0
0
1
0
1
1
1
0
2
1
1
1
0
0
2
0
1
1
1
0
0
1
0
2
0
1
0
1
1
0
2
2
0
1
2
0
1
0
2
1
2
2
2
1
2
0
0
1
0
1
2
0
1
1
3
1
2
2
3
1
0
1
0
0
1
0
0
0
1
1
0
1
0
1
0
2
0
1
1
1
2
1
1
1
1
0
1
1
2
0
1
1
1
0
0
1
2
0
1
1
1
0
2
2
0
1
2
0
0
0
1
0
1
2
2
0
2
1
1
0
0
1
1
0
1
0
0
1
0
1
1
0
1
0
1
1
0
0
0
1
2
2
1
1
1
1
1
0
1
0
1
0
1
1
0
2
0
2
1
1
1
1
2
2
1
2
0
1
0
3
0
1
1
0
1
0
1
0
0
0
2
0
1
0
1
0
1
1
1
0
0
2
0
2
0
0
0
0
0
0
1
1
1
1
0
2
1
0
0
2
2
1
2
1
2
4
0
1
1
0
2
1
1
1
1
0
1
0
1
2
2
0
1
1
2
2
1
0
1
1
2
0
1
0
0
0
2
0
2
1
1
2
2
0
0
1
0
1
1
0
1
1
0
1
1
0
0
1
1
1
0
1
0
2
0
1
0
0
2
2
1
1
1
1
3
1
1
0
1
0
1
1
1
1
2
1
1
1
0
0
1
0
2
0
0
1
2
1
2
1
1
4
2
1
0
2
1
0
0
0
2
1
1
1
1
0
2
1
0
1
0
0
1
2
1
1
0
0
1
1
2
0
1
0
1
1
1
1
0
1
0
2
2
1
1
1
0
2
1
1
0
1
1
0
2
1
0
1
1
1
0
2
1
2
0
2
1
0
0
2
0
1
0
0
1
1
1
2
0
2
2
0
0
0
1
2
1
0
1
1
1
0
1
1
1
2
0
0
0
0
1
0
2
0
2
0
0
2
0
1
1
1
1
1
0
0
2
2
2
0
0
0
3
1
1
1
1
2
0
0
0
0
3
0
1
2
0
2
0
0
0
2
2
1
0
2
1
1
1
1
0
0
0
0
2
1
0
1
2
1
0
0
0
1
0
2
1
0
1
1
1
0
1
1
0
1
1
0
1
0
1
0
0
0
2
2
0
0
1
0
2
0
0
1
2
2
2
1
0
0
2
0
0
0
2
2
1
0
1
1
2
1
0
1
2
2
0
1
1
1
0
2
1
2
2
2
1
0
1
0
2
0
1
1
0
1
1
0
1
0
1
2
1
2
2
2
0
1
0
0
1
0
1
1
0
0
0
1
2
0
2
2
2
1
1
0
0
1
2
0
1
1
1
0
2
2
1
1
1
0
1
0
2
0
1
1
0
2
0
1
0
2
0
2
1
2
1
2
1
1
0
0
1
2
0
1
0
1
1
1
2
2
1
2
0
1
0
1
2
1
0
1
1
1
1
1
1
1
1
2
1
1
2
1
0
2
0
0
0
1
0
0
0
1
1
0
0
2
3
2
2
2
1
0
0
1
1
0
2
0
1
0
1
0
1
2
0
3
1
0
2
0
5
1
2
1
2
1
2
0
2
2
2
0
1
1
2
1
0
0
0
2
1
0
0
1
2
0
1
1
1
0
1
1
0
0
0
0
1
1
1
0
2
1
3
1
0
1
0
0
0
1
0
2
1
0
1
0
0
0
2
0
0
2
1
1
0
1
1
0
2
2
0
2
1
1
1
0
1
1
2
0
1
2
0
0
2
1
0
1
0
0
2
1
2
0
1
1
0
0
0
2
1
2
0
1
1
1
1
1
1
0
2
2
0
0
2
0
0
1
0
1
1
2
1
2
2
1
0
0
0
0
1
1
1
2
2
5
1
0
0
2
0
0
2
2
1
0
1
1
0
0
1
1
1
1
0
2
0
0
0
0
1
2
1
0
0
1
2
0
0
0
1
1
0
0
0
1
0
1
1
1
1
1
1
1
1
1
1
0
2
1
0
1
0
1
2
1
1
2
0
2
1
1
1
0
0
1
1
1
2
0
1
0
1
0
2
0
1
0
2
4
0
1
0
1
1
0
1
0
1
1
1
1
0
1
1
1
1
1
1
0
1
1
0
1
1
0
1
1
1
2
1
1
2
0
2
0
1
0
0
2
2
2
2
1
0
1
1
2
1
2
1
2
1
1
1
1
1
1
1
0
1
0
0
0
2
1
1
1
1
1
1
0
2
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
1
2
2
0
0
0
1
1
1
2
1
1
0
2
2
1
1
0
0
1
0
0
1
1
2
0
1
1
1
0
0
1
0
1
0
1
0
0
1
4
0
2
1
0
0
2
2
1
2
0
1
1
0
1
2
0
0
1
0
1
2
1
1
0
0
0
2
1
2
0
2
1
2
2
3
1
1
0
0
1
1
1
2
0
1
0
0
1
2
0
0
0
0
1
1
0
0
0
0
0
1
2
0
1
2
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
1
1
0
1
0
0
0
0
1
2
1
1
1
0
1
0
0
0
1
2
0
0
0
1
2
1
0
1
2
1
0
1
0
0
2
1
1
1
2
0
0
1
0
1
1
0
1
1
0
2
1
1
1
1
1
2
0
0
1
0
0
2
1
2
2
1
1
0
0
2
2
2
1
0
0
0
2
2
0
1
0
1
0
1
2
1
2
0
1
1
1
0
2
1
1
0
0
1
1
2
0
1
0
0
2
2
0
1
2
1
4
1
1
0
1
0
0
0
0
2
1
0
1
1
1
0
2
4
1
0
0
0
2
0
0
1
1
1
0
2
1
0
2
0
0
2
1
6
2
0
0
0
0
0
2
0
1
1
0
0
1
2
0
0
2
1
0
0
0
2
1
0
1
0
1
1
0
2
0
1
1
1
0
1
0
1
1
0
2
0
1
1
1
1
2
1
0
2
2
1
4
1
0
0
0
2
2
1
1
0
0
0
0
1
2
1
0
0
0
0
1
2
1
2
0
1
1
0
0
1
0
0
2
2
1
0
0
1
0
0
0
0
3
0
1
1
0
1
1
0
2
0
1
0
1
1
1
0
0
1
2
0
1
0
0
1
1
0
0
0
1
2
2
2
1
0
1
1
1
2
2
1
0
2
0
2
0
0
2
0
1
2
2
1
0
1
2
0
1
1
0
1
1
1
2
2
0
1
1
0
0
1
0
0
0
2
1
0
0
2
2
0
1
0
2
0
0
1
1
1
2
0
0
1
0
2
1
0
2
1
0
1
2
0
1
0
0
1
2
1
1
2
3
1
1
2
0
2
0
0
1
1
2
0
1
0
0
2
3
2
1
0
0
0
1
2
1
0
1
0
1
0
0
2
2
1
1
1
0
0
0
2
1
1
1
0
1
1
2
1
0
2
1
2
1
0
1
2
2
2
2
1
1
2
1
1
0
0
0
1
0
3
0
1
1
1
1
1
1
1
2
1
0
1
0
0
0
2
0
1
0
1
0
1
1
1
0
2
1
2
0
1
0
1
1
0
3
0
1
0
0
1
1
0
2
2
2
0
2
1
2
0
1
2
1
0
0
1
0
1
2
0
1
1
1
0
0
1
2
0
0
1
1
0
0
2
0
0
1
0
0
0
2
1
1
1
0
0
1
2
0
1
1
2
0
1
0
1
1
1
0
1
1
0
1
1
2
2
1
0
0
0
0
0
1
0
1
2
1
2
1
2
1
1
0
0
1
1
0
1
1
1
2
3
0
0
2
0
0
0
1
1
0
1
0
0
1
1
0
1
1
0
0
0
0
2
0
0
2
1
1
0
0
1
0
1
2
1
2
0
0
1
0
2
2
0
1
1
1
3
1
1
0
2
1
2
1
2
2
2
2
2
1
0
1
1
0
0
2
0
2
2
1
0
1
0
1
1
0
0
2
0
0
0
1
2
2
1
0
0
0
1
1
0
1
1
1
0
1
1
0
0
1
0
1
2
0
2
0
2
0
1
1
1
0
0
0
2
2
2
2
1
1
0
1
1
1
2
1
1
0
0
0
0
2
1
1
3
1
0
3
1
0
0
1
1
1
0
1
0
0
0
0
1
0
0
1
2
2
1
1
0
2
1
1
1
1
1
0
0
0
1
1
2
0
0
1
1
1
0
0
0
1
1
2
0
0
0
2
0
2
2
2
0
1
2
0
0
1
0
0
1
1
2
0
1
1
2
0
2
1
0
1
0
1
1
0
0
1
1
1
1
0
2
1
1
1
2
1
1
1
1
2
0
2
0
2
1
0
1
2
0
0
0
0
0
1
1
0
2
1
5
0
2
2
0
0
0
1
1
0
2
1
2
3
1
0
1
1
1
0
2
0
1
0
0
1
1
1
1
1
1
0
1
0
1
2
1
1
0
1
1
2
1
1
1
1
2
1
1
1
0
1
0
1
2
4
1
0
2
1
1
0
0
1
2
1
0
1
2
1
1
1
0
1
1
1
0
1
0
1
2
0
1
1
1
0
1
1
1
0
1
0
2
1
1
1
2
1
0
1
1
0
1
0
1
0
0
3
0
1
1
1
1
2
2
0
1
0
0
2
2
0
1
1
2
1
2
0
1
1
0
1
0
0
2
1
0
2
4
1
0
0
2
1
0
2
0
1
2
0
0
1
1
0
2
1
1
1
0
1
2
1
0
2
0
1
2
0
1
2
0
1
1
0
1
1
2
2
0
1
0
0
1
2
1
1
0
1
0
0
2
2
1
1
1
0
0
0
0
0
1
2
0
0
1
2
1
0
2
1
0
0
1
2
1
1
1
0
0
0
0
0
0
0
0
0
2
0
0
1
2
1
1
0
2
1
1
2
0
2
0
1
0
1
1
0
1
0
1
1
0
3
1
2
1
1
0
2
0
0
1
1
2
0
1
1
1
0
0
2
0
1
0
0
0
1
0
4
0
0
2
0
1
1
1
2
1
0
2
1
0
1
1
1
1
3
2
0
2
0
2
0
0
0
0
1
0
1
1
1
1
1
2
0
0
1
1
1
1
1
0
0
0
0
0
1
1
0
0
0
1
1
1
1
0
2
1
0
0
0
2
4
1
0
1
1
0
1
1
1
1
1
1
0
0
0
1
2
2
2
1
2
1
1
1
0
2
1
1
2
0
0
3
0
0
2
1
2
2
2
2
0
2
1
0
0
1
1
2
0
1
0
2
2
1
0
0
2
0
1
4
1
1
1
1
1
1
1
1
1
2
1
2
2
0
0
1
0
2
1
0
2
0
2
1
1
1
2
0
2
1
0
0
1
2
1
0
1
1
0
1
0
0
0
1
0
2
1
2
1
1
2
1
1
1
0
1
2
0
1
1
1
0
0
1
1
1
0
1
1
2
0
1
1
0
1
1
1
0
0
1
0
1
0
2
2
0
1
1
1
1
1
1
2
0
0
2
2
2
2
0
1
3
1
0
3
0
2
1
1
2
1
0
1
0
0
0
2
1
0
0
2
0
2
0
0
0
2
0
2
1
0
0
0
0
2
0
0
1
0
1
0
0
0
1
2
2
2
1
2
1
0
0
1
1
2
0
0
1
0
2
0
1
1
0
2
0
2
1
1
0
2
2
2
0
0
1
1
1
0
2
0
1
1
3
0
1
2
1
0
2
0
1
1
1
2
1
1
2
0
2
2
1
1
1
1
2
1
1
2
0
0
2
1
0
1
1
0
2
2
0
1
4
1
1
1
0
2
1
1
1
0
1
1
1
0
2
1
1
1
0
2
2
1
1
1
1
2
0
1
1
1
1
2
1
2
0
0
1
0
0
0
0
1
1
1
0
0
1
1
1
0
2
1
0
1
1
0
0
0
1
0
1
0
2
0
1
0
2
0
2
1
1
2
2
0
0
1
1
3
0
1
1
1
0
1
1
1
0
2
1
2
1
0
0
1
1
2
1
2
0
1
0
0
0
0
2
0
1
0
1
1
1
1
0
2
1
1
1
0
2
0
1
1
0
1
1
1
2
2
2
2
0
0
0
1
0
1
0
0
1
2
0
0
0
2
1
2
2
1
0
1
1
1
1
0
1
0
2
2
1
0
2
1
0
2
0
1
1
0
2
0
2
0
0
0
2
0
1
0
1
2
0
0
1
0
1
1
1
2
1
0
1
2
2
2
1
2
2
0
0
0
2
0
0
2
1
1
2
1
2
1
0
0
1
2
1
1
0
1
1
2
0
1
2
0
2
0
1
1
1
1
1
1
2
1
0
1
0
0
1
1
1
2
1
0
1
0
1
1
0
1
2
2
1
2
0
2
3
3
0
1
3
2
1
1
1
1
0
2
0
0
1
0
0
0
1
0
0
0
1
2
2
1
2
1
0
0
1
0
3
0
0
2
3
0
2
1
0
1
1
1
1
1
1
2
3
2
0
1
1
0
1
1
1
1
2
1
0
0
2
0
1
1
0
0
2
1
0
1
2
1
1
1
2
2
0
0
1
1
1
0
0
2
1
1
1
1
2
0
1
1
0
1
2
2
2
1
1
0
1
2
2
0
1
1
0
1
2
2
1
0
0
0
0
2
1
0
0
0
0
0
2
2
0
2
1
2
2
0
1
0
0
0
1
0
0
0
0
1
0
1
2
0
0
0
0
2
1
0
1
1
1
0
0
3
1
0
2
1
0
0
2
2
1
0
0
2
1
0
2
0
0
2
1
1
1
1
0
0
0
0
0
1
1
0
0
2
1
0
2
1
0
1
0
0
0
1
2
1
0
1
2
0
2
1
1
1
0
1
1
1
1
1
1
2
2
1
1
0
0
0
1
1
2
1
0
2
0
1
2
1
0
1
2
2
1
0
3
2
2
2
0
0
1
1
1
2
1
1
0
1
0
1
0
2
1
1
2
1
1
1
2
0
0
2
0
1
0
1
1
1
1
1
2
1
0
1
0
2
2
0
0
1
1
0
2
2
1
0
2
1
1
1
0
2
1
2
1
1
0
0
1
2
1
1
0
0
1
0
1
0
1
1
0
0
1
1
1
0
1
2
2
0
2
2
2
2
0
1
0
2
1
1
0
2
3
1
1
0
1
1
0
0
1
1
1
0
2
0
2
1
0
3
0
0
0
1
2
2
1
1
1
1
0
1
2
0
1
1
1
1
2
0
1
2
0
0
0
0
0
0
2
1
0
2
1
1
1
0
0
2
0
0
0
2
1
2
1
1
0
2
0
0
2
0
1
0
1
2
0
1
0
1
1
1
0
2
1
1
0
0
0
1
2
3
2
1
0
2
0
1
2
2
0
0
1
0
1
1
0
1
0
0
2
0
1
0
2
0
0
2
1
0
1
1
0
2
1
1
0
2
0
1
1
0
0
2
1
1
1
1
0
1
2
0
1
0
2
2
2
1
1
1
1
0
3
1
2
0
1
1
0
1
2
0
1
1
1
1
1
0
1
0
1
2
0
0
0
0
2
1
1
1
1
0
1
2
0
2
1
0
1
2
1
0
0
0
1
0
2
0
1
0
1
7
0
0
1
0
2
0
0
3
0
1
0
1
0
0
1
0
1
0
2
1
2
1
0
2
2
1
0
1
1
0
1
2
0
1
2
0
2
1
1
1
2
1
1
1
0
1
1
2
0
0
0
0
1
2
1
1
1
0
2
1
3
1
1
1
0
1
2
0
1
1
1
0
1
1
2
1
1
1
2
0
2
1
1
2
0
2
2
1
0
0
0
1
1
1
1
1
0
0
2
0
1
0
1
0
0
1
1
0
0
1
0
0
0
0
2
2
0
1
1
1
0
0
2
1
0
0
0
0
1
0
0
0
1
2
3
1
2
2
1
2
2
0
0
1
2
1
1
0
2
1
1
0
2
0
2
1
1
2
0
1
2
1
0
2
2
0
1
2
0
2
1
0
2
0
1
2
2
0
1
0
1
3
1
0
0
1
0
1
2
0
2
1
2
0
0
2
0
2
0
2
1
2
1
2
0
0
0
0
0
1
1
2
0
1
1
0
0
1
1
0
1
1
1
0
0
2
2
0
1
1
1
0
1
2
1
2
0
1
1
2
0
3
0
0
1
2
2
0
1
1
4
0
1
1
2
1
1
1
0
2
1
0
0
1
1
1
0
2
0
1
0
0
0
0
0
1
2
0
1
1
0
1
2
0
1
1
0
0
0
1
0
0
0
1
1
0
0
2
0
2
0
0
0
2
1
1
1
1
2
0
0
0
1
1
0
0
1
0
1
0
1
0
2
2
0
0
0
0
1
1
0
0
1
1
1
0
1
0
1
1
0
1
2
0
0
3
1
2
1
0
2
2
1
0
0
1
0
1
0
2
0
1
2
0
1
0
1
0
0
0
1
1
0
2
0
0
1
0
0
0
2
0
1
1
2
1
1
1
2
2
1
2
1
1
1
1
0
1
1
1
2
0
1
2
1
2
0
2
1
1
0
1
2
0
0
0
0
0
1
2
2
1
0
1
0
0
0
2
0
0
0
1
2
0
1
0
1
1
1
1
1
1
0
1
0
1
1
1
1
2
0
0
2
1
1
0
0
0
0
2
0
0
2
2
1
2
0
1
1
2
2
1
1
1
2
1
1
0
0
2
1
0
0
1
0
1
2
0
0
2
1
0
1
0
1
0
1
4
1
2
1
0
0
1
0
0
0
2
0
2
1
0
1
1
1
1
0
0
1
1
2
0
2
1
0
2
0
1
1
1
3
2
0
0
2
1
1
0
0
3
1
1
2
0
2
1
1
0
1
1
0
0
0
0
2
0
1
1
2
2
0
0
1
1
1
0
1
1
2
2
2
1
0
2
0
0
0
1
0
1
0
1
1
2
1
0
1
2
0
2
1
0
0
2
2
2
7
0
1
1
1
2
2
0
0
1
1
2
2
1
1
0
2
1
1
1
1
1
0
1
0
1
0
0
2
2
4
1
1
0
1
2
1
1
1
0
0
2
3
0
1
1
1
0
1
1
2
1
0
1
0
2
0
1
0
1
2
1
0
0
2
3
0
2
1
0
0
1
0
1
0
1
2
1
1
0
1
2
1
1
2
2
2
1
1
2
0
1
1
1
1
0
1
1
1
0
1
1
1
2
1
2
2
1
1
1
1
0
0
2
0
0
2
2
2
1
1
1
0
0
0
1
1
1
2
0
0
1
2
2
2
1
0
2
1
1
2
0
0
2
2
0
1
1
0
0
1
1
1
2
0
0
2
0
0
1
1
2
1
0
0
2
2
0
0
0
2
0
2
1
1
1
2
2
2
0
1
1
0
1
3
2
2
1
0
1
1
1
2
0
1
1
1
1
1
2
0
0
1
0
1
1
2
1
1
0
2
2
1
0
1
1
0
3
2
2
0
0
0
1
0
2
1
0
1
2
0
2
1
0
1
1
0
1
1
0
1
0
2
0
0
1
1
0
1
0
0
1
0
1
1
0
0
0
1
1
0
0
3
1
0
0
1
0
1
0
2
0
0
1
2
1
0
0
1
1
1
1
1
1
2
2
3
1
0
1
1
2
1
2
2
1
0
0
1
0
1
1
1
1
1
0
1
0
1
0
0
1
0
0
2
1
1
2
0
1
2
0
0
0
0
1
1
0
0
1
1
0
0
0
2
0
1
0
0
2
1
2
0
1
0
1
2
2
0
0
0
0
1
1
1
0
1
0
1
1
1
0
0
1
1
0
1
2
0
1
0
0
0
2
0
0
2
0
1
1
1
1
1
0
1
1
0
0
1
0
2
1
0
1
0
1
0
1
0
3
1
2
1
2
0
2
1
0
2
0
1
1
1
0
1
2
0
2
0
1
1
2
2
1
1
1
1
0
0
1
1
1
1
0
1
0
2
1
0
2
2
1
1
0
2
0
1
1
1
1
2
2
2
0
0
1
1
2
2
0
0
2
0
1
1
0
2
0
1
0
0
2
2
1
2
1
0
0
2
2
0
0
2
0
0
1
0
4
2
0
7
0
2
1
1
0
0
0
1
1
1
2
1
1
1
1
1
1
0
1
1
1
0
2
1
1
0
1
0
1
0
1
2
2
3
0
2
1
0
1
1
0
2
1
2
1
1
3
1
0
2
1
1
2
2
0
1
0
2
0
2
1
1
0
0
2
0
1
2
1
2
1
2
2
1
0
2
0
2
2
1
2
0
0
2
0
0
1
1
1
1
0
1
2
3
2
0
0
1
0
0
1
0
0
2
2
1
2
1
1
0
1
0
2
1
1
2
2
2
1
1
2
1
0
1
2
2
1
2
1
0
0
0
2
0
0
2
1
0
0
1
1
0
1
2
0
1
1
1
0
0
2
2
2
0
0
0
0
0
1
1
1
1
1
0
0
0
1
0
1
0
0
0
1
0
1
0
1
1
1
0
0
3
0
0
0
1
1
0
0
1
0
0
3
1
0
1
1
2
0
1
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
1
2
1
1
1
0
1
2
1
1
1
2
1
1
1
2
2
0
0
0
1
0
2
2
1
0
0
1
1
0
1
1
2
0
0
1
1
1
1
0
1
0
0
0
1
0
1
0
2
1
0
0
0
2
0
2
0
1
1
1
0
1
0
1
1
2
1
1
2
0
1
0
2
2
1
0
1
1
2
0
1
0
1
2
1
1
0
2
1
1
1
1
0
0
0
2
0
6
0
2
1
0
1
1
0
0
1
1
1
1
2
1
1
1
0
1
1
1
0
0
1
0
0
0
1
2
1
1
0
2
2
0
0
0
1
1
1
1
2
2
3
0
2
1
1
1
0
2
2
0
0
1
1
0
2
0
2
1
2
1
1
2
1
0
2
2
1
0
0
1
0
1
1
0
3
2
1
1
0
1
1
0
2
1
1
1
1
2
2
1
1
1
0
3
0
1
0
0
0
1
1
1
0
1
2
1
0
1
1
2
1
1
0
2
1
0
1
0
0
0
1
1
3
0
0
1
2
1
1
2
2
1
1
2
0
0
1
1
1
0
0
1
0
1
0
2
1
1
0
0
0
0
1
0
1
1
0
0
1
1
2
0
1
0
0
1
1
2
1
0
1
1
0
0
2
2
2
1
3
1
0
0
0
1
2
0
1
0
1
1
1
0
0
0
1
0
1
2
0
0
0
1
0
1
0
1
0
1
0
0
1
2
1
1
0
0
2
0
2
1
0
1
1
1
1
0
0
1
1
0
2
0
0
1
1
1
1
1
0
1
0
2
1
0
0
1
1
1
1
0
1
0
1
2
0
2
2
1
1
1
1
1
2
1
1
1
1
2
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
1
1
1
0
1
0
1
1
0
1
1
0
0
1
0
0
1
1
0
1
1
0
0
1
2
0
1
1
0
0
1
2
0
1
0
1
0
0
1
0
0
1
2
1
0
0
1
1
0
2
1
0
0
0
1
1
0
0
1
0
0
0
0
1
2
1
1
0
1
0
1
1
0
1
1
1
1
1
1
0
2
0
2
1
0
0
0
0
1
1
1
3
0
0
2
1
1
1
0
2
1
1
0
0
1
2
2
1
0
2
2
1
1
0
0
0
1
0
2
1
1
1
2
1
1
1
1
1
0
1
0
1
2
0
0
0
2
2
0
0
1
0
1
1
1
1
0
0
0
0
0
1
0
0
2
0
1
2
0
0
1
0
1
2
2
0
0
0
1
2
0
2
0
1
0
1
1
0
0
2
2
2
1
0
0
0
1
0
2
2
1
0
0
1
2
1
1
2
2
1
2
1
1
0
1
0
2
1
0
1
1
0
1
0
2
0
0
0
0
0
0
0
2
2
2
0
1
2
0
2
1
0
1
1
0
1
2
1
2
0
2
0
0
2
0
1
2
1
0
1
0
1
1
2
1
1
2
0
1
1
0
0
1
0
1
1
1
1
1
1
2
2
1
2
0
0
1
1
1
2
1
0
2
0
1
2
0
1
1
1
2
2
0
0
0
2
1
0
1
0
1
1
1
2
0
3
1
1
2
2
0
1
0
0
1
0
0
0
1
1
1
2
0
1
0
1
0
0
0
1
0
0
0
0
0
1
2
1
0
1
1
1
1
1
1
0
0
0
0
2
0
1
0
0
0
1
2
1
1
1
1
2
2
1
1
3
0
2
2
0
0
1
1
0
1
0
1
3
2
2
0
1
0
2
0
1
0
0
1
2
0
0
0
1
0
0
0
2
0
2
2
1
1
2
2
0
1
2
1
1
0
1
1
2
0
1
1
0
0
0
2
3
1
2
1
0
2
1
1
1
2
1
0
2
1
0
1
0
1
0
0
0
1
0
1
1
1
1
0
1
1
1
1
1
0
1
2
2
0
1
1
2
1
0
2
1
1
1
0
1
1
1
1
1
1
1
3
0
0
1
1
0
0
0
2
1
0
1
0
2
2
1
2
3
2
0
1
0
0
1
1
1
1
0
0
1
1
0
1
1
1
0
2
1
2
1
0
0
0
0
0
1
0
0
1
5
1
0
0
0
1
1
1
1
0
1
1
2
1
2
2
2
1
1
0
2
0
0
0
1
1
0
1
2
1
1
1
1
0
1
1
2
0
1
1
0
0
0
0
0
0
1
0
1
1
0
2
1
0
1
1
2
2
1
1
2
2
1
0
0
2
1
1
1
0
0
1
1
1
0
1
0
0
1
2
2
2
1
0
0
1
1
2
2
1
0
1
2
1
2
1
0
0
2
2
2
0
0
1
1
1
0
0
1
2
1
0
2
1
1
0
0
0
1
2
1
0
2
1
1
1
1
1
0
0
0
1
0
1
2
1
1
2
0
2
0
1
0
1
1
1
1
1
0
1
1
1
1
1
2
0
1
1
2
0
0
0
0
2
0
1
2
1
1
0
0
1
0
1
0
0
0
1
1
1
1
1
1
1
0
2
1
2
0
1
1
0
0
1
0
1
0
2
0
0
1
0
1
2
1
1
1
2
0
2
1
2
0
1
1
2
1
2
1
1
1
0
1
2
1
0
2
1
0
1
0
1
0
1
2
1
0
1
0
1
1
2
0
1
0
1
0
1
2
0
1
1
0
0
2
0
0
1
1
1
1
0
1
2
1
1
1
1
2
1
1
0
0
1
2
1
2
1
0
2
0
0
1
1
0
2
2
1
0
2
1
1
0
2
1
2
1
0
1
1
1
1
1
1
1
2
0
1
1
0
0
2
1
0
0
2
2
2
1
1
0
2
0
1
1
1
1
1
0
1
1
0
0
0
1
1
0
0
2
0
0
0
1
0
1
1
1
1
0
2
1
1
1
1
1
0
2
0
1
1
2
0
2
0
0
0
1
1
1
0
1
1
0
1
0
1
2
0
2
1
1
1
0
2
0
2
0
1
1
2
2
2
1
1
1
1
0
1
0
1
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
1
0
0
0
1
2
0
1
2
0
0
2
0
1
1
0
0
1
2
0
2
1
1
1
2
0
1
1
1
0
2
0
2
1
0
0
1
2
1
0
1
1
0
1
1
1
2
2
2
2
0
1
0
0
1
0
1
2
3
1
2
2
0
0
1
0
1
2
0
0
2
2
2
1
1
0
0
2
1
1
0
1
2
0
0
0
2
3
1
0
0
1
2
0
2
1
0
2
1
0
0
0
1
0
1
1
0
1
1
0
1
0
1
0
0
2
2
1
0
0
2
2
1
2
1
0
1
2
0
0
1
1
2
2
0
0
2
1
1
2
1
0
2
2
0
0
1
0
1
1
1
1
1
0
0
1
0
2
1
2
2
0
1
1
0
2
1
2
0
3
0
2
1
1
0
1
2
1
1
0
0
0
2
0
2
0
1
1
0
0
1
1
1
0
0
1
1
1
2
2
1
0
2
0
0
1
1
1
1
2
0
1
1
0
0
1
2
1
1
0
2
3
2
2
1
2
1
0
1
0
0
1
1
2
0
0
1
1
0
0
1
0
2
1
1
0
0
0
2
1
1
0
1
0
1
1
1
0
1
2
1
1
1
2
1
0
1
2
1
2
1
0
0
0
2
1
1
1
1
2
1
0
1
2
2
1
2
0
0
1
0
0
0
2
0
0
0
1
2
1
1
1
1
0
2
0
1
1
1
0
0
0
2
2
1
0
1
1
0
1
2
0
0
0
1
1
1
2
1
2
2
0
2
1
0
2
0
0
2
1
0
0
0
0
1
0
1
2
2
0
1
1
1
1
0
0
1
1
2
0
1
0
0
1
0
0
0
0
1
3
2
2
0
0
2
0
2
2
0
0
1
1
0
0
1
2
2
2
0
1
0
0
1
0
2
2
1
0
0
1
1
1
0
2
2
2
1
2
0
1
0
0
0
1
0
1
2
1
0
0
1
1
2
1
0
0
0
1
2
2
0
1
0
0
0
2
1
2
1
0
1
0
0
0
2
2
1
2
1
1
2
0
0
1
1
1
1
0
2
1
12
1
0
1
0
2
0
2
1
2
1
1
2
1
1
1
1
0
1
0
2
0
0
2
0
0
1
0
0
1
2
0
0
0
1
1
1
1
1
1
1
1
1
1
1
2
1
1
0
2
1
0
1
0
0
0
2
2
0
2
0
1
0
1
1
0
1
0
1
1
2
1
0
2
1
1
1
2
3
0
2
0
1
1
0
1
1
0
1
1
1
2
1
1
0
2
1
1
0
0
0
0
0
1
4
2
2
1
0
2
1
1
2
2
1
2
2
2
2
1
0
0
2
2
0
0
2
0
1
0
0
1
2
0
2
1
0
1
0
2
1
1
1
0
0
2
1
2
2
0
1
1
1
0
0
2
0
0
1
0
1
2
1
0
2
0
2
2
1
2
0
1
1
2
2
0
0
0
2
1
2
0
0
1
0
1
0
1
0
0
0
1
2
1
0
1
0
1
1
0
1
1
2
0
0
2
1
1
0
0
0
1
0
0
1
1
0
0
0
1
1
1
1
1
1
1
0
1
0
1
1
1
2
0
1
0
1
1
1
0
2
1
1
5
0
2
1
2
1
1
0
1
1
0
0
1
0
0
1
0
1
2
1
0
1
2
2
0
2
1
1
0
2
0
0
1
1
1
1
5
1
1
0
1
0
0
3
1
0
1
0
2
2
0
0
2
1
2
1
0
1
2
1
1
1
1
0
1
1
2
1
1
2
2
1
2
0
2
1
0
0
0
1
1
0
0
2
0
0
2
1
1
2
1
2
1
0
1
0
0
1
1
0
0
0
0
0
1
1
1
0
0
2
1
1
0
0
0
1
1
1
0
0
0
1
1
0
0
1
1
0
0
1
0
0
0
0
1
2
1
1
0
1
1
0
0
0
0
2
1
2
0
0
1
1
0
0
1
0
0
3
2
1
0
1
0
1
1
1
2
2
0
2
2
1
0
0
1
0
0
0
0
1
0
0
1
0
1
0
1
1
1
1
0
0
1
1
1
2
2
0
2
1
0
2
1
0
2
1
2
0
0
1
0
1
0
1
0
1
1
1
2
1
0
1
0
1
1
0
0
0
0
0
1
1
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
1
1
0
2
2
0
1
0
1
0
1
1
1
2
1
1
1
1
0
2
0
1
1
2
1
2
0
1
1
0
2
1
1
0
0
0
1
2
1
0
0
4
0
1
1
0
2
1
0
0
2
1
1
1
0
0
1
2
0
0
2
3
3
2
1
0
1
2
2
2
2
2
0
1
2
0
0
1
1
1
0
0
1
0
0
0
1
0
1
0
1
3
2
2
2
2
0
1
2
0
2
0
1
2
0
0
0
2
1
0
2
0
0
1
0
1
1
2
1
0
0
2
2
0
0
1
1
0
0
0
0
1
1
2
2
0
0
2
2
2
1
0
2
1
1
0
1
0
1
1
1
2
2
1
1
0
2
0
0
0
1
0
1
2
0
0
0
2
0
2
1
0
1
1
0
1
1
1
0
1
2
2
0
0
1
0
3
1
2
2
2
1
1
1
0
1
1
0
0
1
1
2
0
4
0
1
1
1
2
2
2
0
1
1
1
1
2
1
1
0
1
2
2
2
0
2
0
2
1
2
2
0
1
1
1
2
1
1
3
1
1
1
0
1
2
0
1
0
0
1
0
0
1
1
2
2
1
2
0
1
0
0
2
1
2
1
0
1
0
2
0
1
2
2
0
1
1
0
0
0
0
0
1
0
1
1
0
0
1
2
2
0
2
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
3
1
1
0
0
0
1
1
0
2
2
1
0
0
1
0
1
1
1
1
1
0
2
1
0
1
0
0
2
2
2
1
1
2
2
1
0
0
0
1
1
0
0
0
1
1
1
1
1
2
1
0
2
0
0
2
1
1
0
1
0
2
2
2
2
1
1
1
2
3
2
1
1
0
2
2
3
0
0
2
0
1
1
0
2
2
1
1
1
2
0
1
1
2
2
0
0
0
0
0
1
1
1
0
0
1
1
2
0
2
1
0
0
0
0
0
2
1
2
1
1
2
1
0
1
0
1
1
0
1
2
1
1
1
0
2
1
2
2
1
2
4
0
2
0
0
1
0
1
2
1
0
0
0
1
2
1
0
0
0
2
1
0
0
1
2
1
1
2
1
1
1
1
2
1
1
0
2
1
1
2
2
1
1
2
1
1
6
0
0
2
2
0
0
2
0
2
1
2
0
0
0
1
1
1
2
0
1
1
1
2
0
0
0
2
1
2
4
1
2
0
2
1
2
1
1
2
0
1
0
0
0
1
2
1
0
2
2
0
2
2
1
1
0
0
0
0
1
0
0
1
1
0
1
1
2
1
2
2
2
0
1
0
0
2
1
1
1
1
0
0
2
2
2
2
2
1
0
2
1
1
2
0
0
0
0
2
0
1
0
0
2
2
1
1
0
2
1
0
2
0
0
1
0
1
0
1
1
2
1
1
0
2
2
1
0
1
0
0
1
0
1
0
1
0
1
2
1
0
1
2
0
2
4
0
0
0
2
0
1
0
0
1
3
0
1
0
2
1
2
0
1
0
1
2
1
0
1
1
0
1
1
0
1
1
2
1
2
2
1
2
1
2
0
1
1
1
1
2
1
1
0
2
1
1
1
0
3
0
0
1
2
1
0
2
1
1
1
1
0
0
1
0
0
0
0
0
1
2
1
1
1
1
1
0
0
0
1
0
1
0
2
1
0
0
2
0
1
1
2
0
0
0
1
2
1
3
1
0
2
0
1
0
2
1
1
1
0
1
0
2
0
0
1
0
1
2
1
1
1
0
1
1
0
0
1
1
0
2
0
0
1
1
1
1
0
1
0
0
0
1
1
1
3
2
0
1
1
0
0
1
2
1
0
2
0
2
0
0
1
0
2
2
0
1
1
0
3
0
2
0
1
0
1
0
1
1
2
1
1
2
1
0
0
0
0
1
0
1
2
1
1
2
1
1
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
1
2
1
1
0
2
0
0
2
2
2
0
2
0
2
1
0
0
2
2
0
3
0
1
1
0
4
0
0
1
2
1
1
2
1
1
2
0
1
2
2
0
2
2
1
0
0
1
1
0
0
0
0
1
2
0
0
1
1
1
1
2
2
1
1
0
0
1
1
2
1
0
2
0
1
1
0
1
0
2
0
0
1
0
0
1
1
1
1
1
1
0
1
1
1
0
0
1
1
2
1
2
0
1
1
1
1
0
1
1
1
2
0
1
1
2
1
4
1
0
0
0
1
2
2
1
0
2
0
2
0
0
1
0
2
1
0
2
0
1
1
1
1
2
0
0
0
1
1
0
0
1
1
1
1
0
0
2
0
0
0
2
2
0
1
2
1
1
2
2
2
1
0
0
2
0
2
1
2
0
1
0
2
2
0
0
1
0
0
0
2
1
2
0
2
3
2
0
1
1
1
2
0
1
1
2
0
2
1
1
1
2
0
0
1
0
2
1
1
0
0
2
1
2
2
1
1
1
1
1
1
1
1
1
2
0
0
0
1
0
0
1
1
1
5
1
1
0
1
0
2
1
1
1
0
2
1
1
1
0
1
1
1
0
1
1
0
1
0
0
2
0
0
1
0
1
0
1
1
2
1
1
1
2
3
0
2
0
2
2
0
2
0
1
2
0
1
0
1
1
0
2
1
1
0
2
1
2
1
2
2
2
0
0
0
2
1
0
0
1
1
0
0
2
1
2
2
1
0
0
0
1
0
2
0
1
1
2
2
2
1
1
0
2
2
0
1
0
0
0
1
1
1
2
1
1
0
0
1
1
2
2
2
0
0
2
0
1
0
0
1
1
2
2
0
0
1
1
1
0
1
1
1
1
1
0
0
1
1
1
1
1
1
1
2
0
0
1
0
0
0
0
1
1
1
1
2
1
0
1
1
1
0
2
2
1
0
2
0
0
0
2
1
1
0
0
1
2
0
1
2
0
1
2
2
2
0
0
1
0
1
2
1
1
2
0
0
0
1
1
3
0
0
0
1
0
1
0
0
1
0
1
1
3
1
0
2
0
1
2
1
0
0
1
1
1
1
1
0
2
0
2
2
1
0
0
0
0
1
1
0
1
1
0
0
0
0
1
1
1
1
0
2
1
3
1
2
0
1
0
2
1
1
1
0
2
0
1
0
0
2
1
4
1
2
2
1
0
0
0
1
1
0
0
2
0
2
4
0
2
1
0
0
1
1
1
2
0
1
0
0
0
2
1
2
0
1
2
0
0
0
1
0
1
1
0
1
1
1
1
0
0
0
0
1
0
1
1
1
1
0
1
1
1
0
1
1
2
1
1
0
1
2
0
1
1
0
0
1
1
1
2
1
1
0
1
0
0
1
1
1
1
0
0
1
1
2
0
1
1
0
0
1
0
0
1
2
0
1
0
1
0
1
1
0
0
1
1
0
1
2
0
2
1
1
2
2
1
1
0
0
1
1
1
0
2
1
1
1
1
1
2
1
0
1
0
1
1
2
0
2
0
1
2
0
1
1
1
2
0
0
1
0
0
1
2
2
1
1
0
2
1
0
2
0
2
0
1
0
0
0
0
0
0
1
0
1
1
0
2
1
1
1
2
0
2
1
0
2
1
1
2
1
1
2
2
0
0
1
0
1
1
0
4
1
0
2
1
1
1
2
0
2
0
0
1
0
0
0
2
1
1
0
1
1
1
1
0
2
0
2
1
0
1
0
2
0
0
3
0
0
0
2
2
1
0
1
2
1
1
0
0
0
1
0
0
0
2
2
0
1
0
1
0
1
2
0
1
1
1
1
3
1
0
0
2
2
0
0
0
2
1
1
2
1
1
1
0
0
1
1
2
0
1
0
2
0
1
1
2
1
1
0
1
1
2
1
0
3
1
0
1
0
1
2
1
0
2
2
1
2
1
0
1
2
2
0
1
0
0
2
1
1
1
1
1
0
1
0
0
2
0
1
1
0
2
0
1
0
1
2
2
0
2
0
1
0
1
1
1
1
1
1
1
0
1
1
1
1
2
0
2
0
1
2
1
1
4
1
0
2
2
1
0
2
2
0
0
0
0
0
1
0
2
1
0
3
2
1
0
1
1
0
1
0
2
1
0
0
2
1
0
0
1
1
1
0
3
1
2
2
1
2
0
0
2
0
1
0
1
0
0
1
0
0
1
1
1
1
1
1
0
1
1
1
2
0
2
0
1
0
0
1
0
0
0
1
2
2
0
1
0
1
1
2
1
0
2
1
0
1
1
0
2
0
1
0
2
1
0
2
1
1
0
1
1
1
0
0
1
0
1
1
0
0
1
1
0
0
2
2
2
1
0
1
1
1
3
1
2
2
1
1
1
1
0
1
1
0
0
0
1
0
1
1
0
0
1
0
1
2
1
2
1
0
0
2
1
1
1
0
0
1
0
2
2
1
2
0
0
2
0
1
1
1
1
1
0
2
1
1
0
2
2
2
1
2
0
0
1
1
2
0
3
2
0
0
1
0
1
1
2
1
0
0
0
0
0
1
1
0
0
1
2
2
0
0
0
2
0
0
2
2
0
0
1
1
0
1
1
1
1
1
1
1
0
1
1
2
1
1
0
0
0
1
1
0
2
2
1
1
1
0
1
1
2
1
3
1
1
0
0
0
0
3
1
1
1
0
2
1
1
1
1
2
0
2
0
2
1
2
1
0
1
0
1
0
2
0
1
1
1
0
1
2
0
1
2
1
2
2
1
1
1
1
0
1
0
2
0
0
0
1
0
1
1
1
0
2
1
1
1
2
2
0
1
0
0
2
1
1
0
0
1
0
1
0
2
1
2
0
2
1
1
1
1
0
1
0
0
0
1
1
2
1
2
1
0
1
1
1
2
0
1
0
0
2
1
1
2
1
0
1
2
1
1
1
2
3
1
1
1
1
1
1
1
0
1
1
1
0
2
0
1
3
1
0
0
0
2
0
1
0
2
1
1
2
0
0
0
0
0
1
0
1
0
1
1
1
0
1
1
1
1
0
2
4
1
2
0
1
0
1
0
0
1
1
1
0
0
0
1
1
0
0
0
1
0
2
1
0
1
0
1
2
0
1
0
2
1
0
1
1
1
0
1
0
1
0
1
2
0
2
1
0
2
1
0
2
2
2
1
1
1
2
0
0
0
1
0
1
1
0
0
1
0
1
1
0
1
2
2
0
1
2
0
0
0
2
0
1
0
0
2
1
0
1
1
0
2
1
0
1
1
0
2
0
1
0
0
1
0
2
0
1
1
1
1
0
1
1
2
1
1
1
1
2
0
1
1
0
0
1
1
1
1
0
2
0
0
1
1
0
2
1
1
1
0
1
0
0
1
1
0
0
1
0
1
0
1
2
2
0
1
1
0
1
2
0
4
1
1
2
0
2
1
2
0
0
2
2
1
0
1
1
0
1
10
1
1
0
0
2
2
0
0
0
1
2
2
2
1
2
0
0
0
1
0
0
0
1
1
0
3
0
1
2
0
2
0
1
0
2
0
0
2
1
0
2
1
1
1
1
1
0
0
1
0
0
0
0
0
2
0
1
0
1
2
0
1
2
0
0
1
0
0
0
1
2
0
2
0
0
1
1
1
1
1
1
1
2
0
0
1
1
2
1
1
1
1
0
1
0
3
1
1
0
1
1
1
0
1
0
0
0
1
1
1
1
3
0
1
0
1
0
1
1
1
0
0
0
0
1
1
2
1
0
2
1
1
1
0
1
2
1
1
0
0
0
1
1
1
0
1
1
0
1
1
0
0
1
0
0
2
1
2
0
2
0
0
2
2
2
2
1
2
0
2
0
2
1
1
1
2
1
1
1
1
1
1
1
0
1
1
2
1
0
2
0
0
1
2
1
1
1
2
1
0
1
0
0
1
1
1
0
1
0
1
1
1
1
1
0
2
3
2
2
1
2
1
0
2
0
0
0
2
0
0
0
2
1
0
1
0
1
1
2
0
0
1
1
2
0
0
1
1
1
0
2
2
0
0
2
0
2
0
0
1
0
0
1
0
0
0
2
2
2
1
1
0
1
1
0
2
1
1
2
1
1
2
1
1
0
2
0
2
0
1
2
2
0
1
1
0
0
0
2
1
2
1
2
1
1
1
1
1
0
1
2
1
2
8
0
0
1
0
0
0
0
1
0
2
1
1
1
1
1
2
2
2
2
1
2
1
1
0
4
1
1
3
2
1
0
1
1
1
0
2
1
0
2
0
0
1
0
0
0
2
1
1
0
2
0
1
1
2
1
0
0
1
0
0
2
0
0
1
0
0
1
0
2
3
1
0
1
2
0
0
2
2
1
0
0
1
1
1
2
1
1
2
0
2
0
2
1
1
2
1
3
1
2
1
3
0
2
2
1
0
1
1
0
1
0
1
1
1
2
1
1
1
0
0
0
0
0
0
1
1
1
2
1
0
1
1
2
1
2
2
1
0
0
0
0
1
1
0
1
1
1
1
1
0
0
2
0
1
0
1
1
1
0
1
0
1
2
1
1
2
0
0
2
0
1
1
0
1
4
2
1
0
1
1
1
1
1
1
2
0
2
9
0
1
1
1
1
0
0
0
2
1
0
2
0
1
1
1
1
0
0
2
2
1
2
1
1
1
0
0
0
1
1
1
2
2
2
0
4
1
1
1
0
1
1
2
1
0
1
0
2
1
0
2
1
1
1
1
0
0
1
0
0
1
1
1
0
0
1
1
0
0
1
2
0
1
1
1
1
1
0
1
1
2
0
0
0
1
1
1
1
1
1
0
0
0
0
0
1
1
0
1
2
1
0
1
1
0
1
1
0
2
1
0
1
1
1
1
2
1
1
1
0
1
0
0
0
1
0
1
0
0
2
1
1
1
0
1
2
0
1
1
1
1
1
1
1
0
1
0
2
0
1
1
1
2
0
1
0
1
0
0
1
1
1
1
1
2
1
2
1
1
1
0
1
0
1
0
1
0
1
0
0
2
0
1
1
0
0
2
1
0
2
0
0
0
1
0
0
0
1
0
1
1
0
2
0
0
0
1
2
1
2
1
1
1
0
0
2
0
2
2
0
0
0
2
1
1
0
1
1
1
0
1
2
2
1
1
2
1
2
0
1
1
0
0
2
2
1
1
0
2
1
0
1
2
0
2
1
2
2
2
0
1
1
0
0
1
2
1
0
2
1
0
0
0
1
0
0
0
0
2
0
1
1
0
1
1
1
1
0
1
0
1
0
2
1
3
0
2
2
2
1
0
0
2
0
1
1
1
0
1
0
1
1
0
0
2
2
0
0
2
0
2
1
1
0
2
1
2
0
1
1
1
1
0
0
2
0
0
0
1
0
1
0
1
0
0
1
1
1
1
0
0
1
4
0
1
2
2
1
2
0
1
1
2
2
0
1
1
0
1
1
1
1
0
2
0
0
1
1
0
2
2
0
2
0
1
1
1
1
1
1
1
2
2
1
1
2
2
2
1
2
1
0
1
3
0
0
1
1
3
1
0
2
1
1
1
1
1
1
0
1
1
1
1
3
2
1
1
1
1
0
2
0
2
1
1
0
1
1
1
0
2
0
2
2
2
2
0
1
0
1
0
1
0
0
0
1
1
1
0
1
2
0
2
0
1
2
0
1
1
0
2
1
2
0
0
0
2
0
1
0
2
1
2
0
0
1
1
0
1
0
0
1
1
0
0
0
0
1
1
1
0
1
0
1
0
2
1
1
0
2
0
0
1
0
1
0
0
1
1
2
0
2
3
0
1
0
1
1
1
1
0
2
2
1
0
1
1
0
0
1
2
0
0
1
0
0
0
0
0
1
1
2
1
0
3
2
1
2
2
0
0
0
1
1
0
0
0
0
2
1
2
0
0
3
1
1
0
2
0
0
1
2
0
0
1
2
0
1
2
2
1
1
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
2
0
1
0
1
0
0
2
1
0
0
1
1
0
1
0
0
1
1
2
1
0
1
1
1
0
2
1
0
0
0
1
0
2
1
0
0
0
1
2
2
0
1
1
1
0
1
0
1
2
1
2
1
1
1
1
1
1
0
2
1
0
1
0
1
0
2
1
1
2
0
1
0
2
0
1
1
0
1
1
2
2
1
1
2
1
2
1
1
0
1
2
1
1
2
2
0
1
0
1
1
1
0
1
1
1
1
1
1
1
0
0
1
1
1
1
1
1
0
1
2
2
0
1
0
1
0
1
0
0
0
1
1
0
1
2
1
0
1
1
4
0
1
1
1
1
0
1
0
1
0
2
1
1
0
0
1
2
0
2
0
0
1
1
0
0
1
1
2
2
1
2
0
1
1
2
1
1
0
0
2
0
1
2
0
1
2
2
0
1
0
0
1
0
1
1
2
2
1
0
1
1
1
0
0
2
0
0
0
3
2
2
1
2
1
1
0
1
0
0
1
2
2
0
1
1
2
1
1
1
1
2
2
0
1
0
0
1
3
1
1
1
2
1
2
1
1
2
1
0
0
1
1
0
2
0
2
0
3
0
1
1
1
0
0
0
2
1
1
0
1
0
0
1
1
1
1
1
0
2
0
2
2
0
0
1
1
1
1
0
0
1
2
2
0
2
1
1
1
1
1
2
2
0
0
0
1
1
1
1
0
1
0
1
0
0
0
0
2
0
0
2
0
0
2
1
2
1
1
2
1
1
0
0
1
0
1
1
0
2
1
0
2
1
1
0
2
0
2
0
0
0
0
0
1
0
0
1
1
1
0
0
1
1
1
1
1
2
0
2
0
2
0
0
1
1
1
2
0
0
2
0
1
0
1
3
0
2
0
1
2
1
2
1
1
0
1
1
2
2
4
0
2
1
2
1
1
1
1
0
2
2
1
0
1
7
1
1
2
1
0
0
1
1
2
2
1
1
2
1
4
1
2
1
1
0
0
1
1
2
0
1
0
1
1
1
1
1
1
1
0
2
1
2
1
1
1
1
0
0
2
0
1
0
1
1
1
1
1
1
1
0
0
0
0
1
1
0
2
1
0
0
2
2
1
0
1
3
1
1
0
1
1
1
0
1
0
1
1
1
2
2
2
1
0
1
1
1
1
2
2
0
0
1
0
0
0
1
2
0
1
1
2
2
2
1
2
1
1
0
2
0
2
0
0
0
2
1
1
0
0
1
0
0
1
2
2
0
3
1
0
0
0
0
1
2
0
0
0
1
1
0
1
1
0
0
2
0
2
1
0
2
0
1
2
1
2
1
0
1
0
0
2
0
0
0
0
1
0
2
1
0
0
0
2
0
2
1
2
1
1
1
0
0
1
0
0
0
4
2
1
2
1
0
2
1
2
1
1
1
0
1
2
0
2
1
0
1
2
0
1
1
2
1
1
1
1
0
0
0
1
1
1
0
2
1
2
1
0
1
2
1
1
1
0
0
2
6
0
1
0
1
0
0
2
1
1
1
0
0
1
0
2
1
2
0
1
1
0
0
0
1
0
1
1
2
0
1
2
1
0
1
2
2
0
1
1
1
1
0
1
0
1
2
0
1
0
0
1
0
0
1
0
1
0
0
1
2
1
1
0
0
2
0
1
1
0
2
1
1
0
2
1
0
0
1
1
0
2
1
1
0
1
1
0
0
0
2
0
2
2
1
2
2
0
0
1
0
0
2
0
0
2
1
0
1
2
2
2
0
1
2
1
0
0
2
0
0
0
1
1
1
2
0
0
1
0
1
0
2
1
0
1
2
1
0
1
0
1
0
1
1
0
0
0
1
2
1
0
0
0
0
2
0
2
2
2
2
0
0
1
1
0
1
0
0
2
0
0
1
0
0
1
1
1
1
2
1
2
1
0
0
1
0
1
2
0
2
1
2
0
2
0
1
0
0
2
0
2
0
0
1
0
2
2
0
2
2
0
0
2
0
1
2
1
1
0
2
1
2
0
1
1
2
2
2
4
1
0
1
0
1
0
1
2
0
0
1
1
0
2
1
0
0
0
0
0
1
0
1
2
0
0
0
2
0
1
0
2
1
0
2
2
2
1
1
0
0
1
2
2
1
1
1
0
0
0
1
2
1
2
1
0
1
2
2
0
2
1
1
1
2
1
2
0
1
0
0
1
0
2
0
0
0
1
0
0
2
2
0
0
2
2
0
1
0
1
0
1
1
1
0
1
0
1
1
2
2
1
1
0
1
1
2
0
1
2
1
1
1
2
2
2
2
0
1
0
1
0
0
2
1
0
1
0
1
1
0
1
2
0
2
1
1
0
0
1
1
2
2
2
0
1
1
1
1
0
1
0
2
2
1
1
2
1
1
0
0
0
1
1
0
0
0
2
1
1
2
3
2
2
1
2
2
1
1
1
2
0
0
0
2
0
2
0
0
1
0
1
1
1
0
1
2
1
0
0
0
0
1
2
0
0
2
0
1
0
2
0
0
2
0
1
2
1
0
2
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
0
0
2
1
0
3
0
1
1
0
0
0
0
2
1
0
1
1
1
2
1
0
2
1
2
1
2
0
1
1
1
0
2
2
2
1
0
0
0
1
0
1
0
1
2
0
2
1
0
0
1
1
1
2
1
1
0
1
1
0
0
2
2
1
0
1
2
1
0
1
3
0
0
1
1
0
1
0
0
1
2
0
1
0
0
2
0
0
1
1
1
1
1
3
0
0
2
0
0
0
1
2
2
1
1
0
1
0
0
1
1
1
3
2
1
2
1
1
2
0
2
2
1
0
0
0
1
1
1
1
0
1
1
0
1
0
1
0
0
0
0
0
1
1
2
0
1
1
1
1
0
1
0
0
0
0
1
1
2
0
2
0
1
0
1
1
2
1
2
0
1
1
1
0
1
0
1
0
1
1
0
2
2
2
0
2
0
0
1
0
1
0
0
0
1
1
1
1
0
1
0
0
2
0
2
0
2
1
0
1
2
2
0
2
1
3
3
1
0
2
0
0
1
0
0
3
1
2
1
0
0
1
1
2
1
1
0
2
0
1
1
0
0
1
1
1
0
1
1
1
1
0
2
2
0
0
0
1
0
1
0
0
0
1
1
0
0
1
1
1
1
2
0
2
2
2
0
1
1
2
1
1
1
2
0
1
0
0
0
0
2
0
1
0
1
0
1
1
0
2
1
0
2
1
1
1
1
1
1
2
0
1
1
1
1
0
0
1
1
2
1
1
0
1
1
1
0
0
2
1
2
1
0
0
0
0
0
2
0
1
0
1
2
0
0
0
1
0
1
0
2
0
0
1
2
0
0
0
2
2
2
1
0
2
2
1
1
1
0
1
0
1
0
1
1
1
2
1
0
2
1
0
1
1
0
1
2
2
2
1
1
0
0
1
2
0
0
0
1
1
1
1
1
0
0
0
2
2
2
2
1
0
0
2
0
1
1
1
1
1
0
1
2
2
0
1
0
3
1
2
0
0
0
2
0
1
1
2
0
1
0
2
1
2
2
0
1
0
2
2
1
0
1
1
2
2
1
0
0
0
1
0
1
1
0
0
1
2
0
0
0
1
1
0
0
0
0
0
1
1
1
1
1
0
0
0
2
0
1
0
1
2
0
0
0
0
0
0
0
2
1
1
0
1
1
2
0
1
1
0
1
0
2
0
0
1
0
2
2
0
1
0
2
1
1
1
2
0
1
0
1
0
2
1
1
1
1
0
1
2
2
1
0
1
2
1
0
1
1
2
1
1
1
1
0
1
2
0
1
1
1
0
0
1
0
0
1
0
1
1
2
0
0
0
1
0
1
1
1
1
1
1
0
0
2
1
0
2
1
2
0
0
1
0
0
2
0
1
0
0
1
0
0
2
0
1
1
0
0
0
0
1
1
1
2
2
0
1
0
0
2
1
1
1
1
5
0
0
3
0
1
1
1
2
0
0
0
2
1
0
1
1
1
2
0
1
0
0
1
0
1
2
0
1
1
0
1
0
2
0
1
1
1
0
1
2
0
2
1
0
1
1
3
1
2
1
0
2
1
2
1
1
0
0
1
0
1
2
1
0
1
0
1
0
1
3
2
0
1
0
1
0
0
0
1
2
0
0
1
0
0
3
1
2
1
1
0
1
1
0
1
0
0
1
1
1
1
0
1
2
1
2
2
2
0
0
8
1
2
1
1
0
1
1
2
0
1
0
1
0
0
0
2
0
0
2
1
3
2
0
1
0
3
2
1
0
1
0
2
0
1
1
1
1
0
1
0
1
3
2
1
2
0
0
2
0
1
1
0
2
0
1
1
2
2
0
2
0
0
0
2
2
1
1
2
1
0
2
0
0
1
0
1
1
1
2
1
2
1
1
0
0
0
1
1
2
0
0
2
1
1
2
0
1
2
2
0
1
2
1
0
0
0
0
0
0
1
1
1
0
1
0
0
1
0
0
0
0
0
1
1
0
0
1
1
2
1
1
1
0
1
0
0
0
2
0
1
0
1
2
1
0
2
1
2
1
0
1
3
0
1
0
2
2
2
0
1
0
0
2
0
1
0
2
1
0
0
1
2
1
0
0
2
0
0
1
1
0
0
1
1
1
0
0
1
0
0
0
1
1
0
0
1
1
2
0
0
0
1
0
2
1
2
1
0
0
1
0
4
0
1
0
1
1
1
1
1
1
0
0
1
1
2
1
1
2
2
0
0
0
1
1
1
0
1
1
1
0
0
1
1
0
0
1
1
0
1
1
2
0
0
2
1
0
0
1
0
0
0
1
1
1
1
2
0
1
1
2
1
1
2
1
1
1
1
0
1
0
1
1
2
0
2
1
2
2
0
0
0
0
0
1
0
1
2
1
1
0
0
1
0
0
1
2
1
1
2
0
1
0
1
1
0
1
2
2
1
1
0
0
1
1
0
1
0
2
2
0
0
0
2
0
1
1
1
1
2
1
1
2
1
0
2
2
1
2
1
0
2
0
1
1
0
0
1
1
1
1
0
0
2
2
0
1
2
0
1
1
2
2
2
1
2
3
2
0
1
0
2
1
1
2
1
0
1
0
0
1
0
1
1
0
2
1
1
0
2
1
1
3
1
1
0
2
3
1
2
0
1
1
2
1
0
1
1
1
1
1
1
2
0
0
0
0
2
2
0
0
0
1
0
1
0
2
0
0
0
0
0
1
3
2
0
1
2
1
1
1
1
1
2
1
2
0
1
1
1
1
1
1
1
2
0
1
1
1
1
1
1
0
0
1
1
1
1
1
1
1
0
1
1
2
2
1
2
1
1
0
2
1
0
0
1
0
1
3
2
1
1
1
1
1
0
5
1
1
0
1
0
1
2
1
1
0
0
1
2
2
0
3
1
0
1
1
2
1
1
0
1
2
5
1
2
1
0
1
0
0
1
1
1
0
1
0
0
0
1
2
0
0
1
1
0
1
0
2
1
1
1
0
0
0
2
0
2
1
0
1
2
2
0
2
2
0
1
2
0
1
2
1
1
0
0
0
1
0
2
1
1
0
1
1
0
0
0
0
1
1
1
1
1
0
1
1
0
1
1
0
1
2
0
2
0
1
1
1
1
1
1
0
2
2
0
1
0
1
2
1
1
2
0
0
1
1
1
0
2
0
1
2
2
1
1
1
1
1
0
2
2
1
1
0
1
1
0
1
0
1
2
1
1
1
0
1
0
0
0
0
2
2
1
0
0
0
2
4
1
0
1
4
0
0
0
1
1
2
1
0
0
1
0
0
1
0
2
1
0
0
0
0
0
1
0
1
2
0
2
1
2
1
0
1
2
0
1
0
2
1
2
2
0
1
1
2
1
1
2
1
0
0
0
0
2
0
1
1
1
1
1
1
2
1
0
1
2
1
0
1
2
1
1
0
0
2
0
0
1
2
1
1
1
0
1
0
1
2
1
1
1
0
4
2
4
1
0
0
0
0
1
0
1
0
0
0
1
1
1
0
1
1
1
2
1
2
0
0
0
2
0
0
1
0
0
1
1
1
1
1
1
1
1
0
1
0
2
1
0
1
1
0
0
2
0
1
2
0
1
0
3
0
2
2
2
1
1
0
1
2
0
0
2
1
1
1
2
1
3
1
1
2
0
2
0
0
1
1
1
0
1
2
1
2
2
1
1
1
0
0
1
1
1
0
0
0
1
1
0
2
1
2
1
2
1
1
0
1
0
0
2
0
1
0
0
1
0
1
0
2
1
1
0
1
1
2
1
2
1
1
1
1
0
1
0
1
0
0
0
0
1
2
0
0
0
1
2
1
1
2
0
1
0
1
2
0
1
1
2
1
1
2
1
0
1
0
1
0
0
2
2
0
2
1
2
1
0
2
2
0
0
3
0
2
0
1
0
2
1
0
1
1
1
2
1
1
2
2
0
0
0
1
0
1
1
2
0
1
0
0
1
1
0
7
1
1
2
1
0
2
1
0
2
0
1
2
1
0
0
1
1
1
0
2
1
0
1
1
1
2
1
0
1
0
1
0
0
0
1
2
1
0
0
0
0
0
2
0
1
0
0
2
0
1
1
1
1
1
2
0
0
1
1
2
2
1
2
1
1
0
2
1
0
2
0
0
1
0
2
0
0
2
2
0
2
2
0
1
1
2
1
0
1
1
1
1
0
0
1
2
2
0
0
2
1
0
2
2
2
1
1
0
0
2
0
0
0
1
0
0
1
1
0
1
0
0
0
0
2
1
0
1
0
2
0
2
1
1
1
0
0
0
0
0
2
2
1
0
1
0
0
0
0
0
0
1
0
2
0
1
1
1
1
0
1
1
0
1
0
1
2
2
1
0
1
0
0
2
1
2
2
0
1
1
1
1
1
1
1
1
1
1
0
0
2
1
1
0
2
0
1
2
1
0
1
2
1
1
0
2
1
1
1
1
1
0
1
0
0
1
0
0
1
2
1
1
1
0
1
0
1
1
1
2
0
1
0
0
0
0
0
2
0
1
2
0
0
1
0
0
0
0
1
1
3
1
0
0
2
2
2
1
0
1
0
1
1
1
2
0
0
0
1
2
1
1
1
1
1
2
1
1
2
3
2
1
1
1
0
1
1
2
0
0
0
2
1
0
2
0
2
1
2
1
0
0
1
2
2
1
1
1
0
1
0
1
1
2
2
0
1
1
1
2
0
1
1
0
1
2
1
2
2
1
1
0
1
1
1
0
1
1
1
2
2
1
1
2
1
0
0
0
1
1
2
1
0
1
0
1
1
0
2
0
1
2
1
0
0
1
2
0
0
2
1
1
1
0
0
0
0
0
1
1
0
2
2
0
1
0
2
1
0
1
4
2
1
2
0
0
0
1
2
0
0
2
0
0
2
1
1
1
1
2
1
0
2
1
1
0
1
3
0
1
1
1
1
2
0
0
2
2
1
2
0
2
0
1
1
0
0
2
1
1
1
1
2
2
3
1
1
0
0
0
1
2
2
0
2
2
2
1
1
1
1
1
0
0
0
0
1
1
2
2
0
0
1
0
1
2
0
0
1
2
1
1
2
0
1
0
0
0
2
0
1
2
1
2
3
1
1
1
1
2
0
0
0
2
0
1
0
0
0
0
2
0
2
2
0
1
1
1
1
1
1
0
2
0
1
2
1
0
0
0
2
1
0
1
1
0
0
1
0
2
1
1
1
0
1
2
1
0
1
1
1
1
0
0
1
0
2
1
1
1
0
0
1
2
2
0
0
0
1
0
0
2
1
2
1
1
0
0
0
0
3
1
0
1
0
1
1
1
1
2
1
2
1
0
0
0
1
1
1
2
1
5
2
0
2
0
1
2
1
2
0
0
2
0
0
0
0
1
2
1
1
1
0
2
0
2
0
1
0
2
1
2
1
0
1
0
0
1
1
1
1
3
0
0
2
1
0
0
0
2
0
1
0
0
2
0
2
2
0
0
1
0
0
2
1
0
2
0
1
1
2
1
1
1
1
0
1
2
1
1
1
1
1
1
2
1
1
1
0
0
1
0
2
0
2
2
0
1
1
1
1
0
0
4
0
1
0
0
0
0
0
1
0
2
0
1
2
1
2
2
1
1
1
1
0
2
0
1
0
0
0
0
0
0
1
1
1
0
1
1
0
1
2
2
0
1
2
2
0
1
0
1
0
1
0
1
1
1
0
0
0
0
2
1
1
2
1
1
0
1
2
0
0
1
0
0
2
1
2
1
0
1
1
1
1
0
1
0
1
0
1
1
1
0
1
0
1
2
0
1
2
0
1
1
1
2
2
1
1
1
0
0
0
2
2
2
0
2
1
2
0
0
0
1
1
0
1
1
2
1
0
2
2
0
0
0
1
1
1
1
2
0
1
0
1
1
0
0
0
4
1
2
0
2
0
1
0
0
0
0
1
0
1
1
1
1
0
2
2
2
1
2
0
0
1
3
1
1
2
2
1
1
2
0
1
0
1
2
0
0
0
1
1
1
0
1
0
1
1
1
0
0
1
2
0
2
2
0
0
0
2
0
1
0
0
4
1
0
1
0
0
1
0
2
1
0
2
2
1
2
1
1
1
1
2
0
2
0
1
1
0
2
1
0
0
2
0
1
0
1
1
2
2
1
0
1
1
2
1
1
2
3
1
1
0
0
0
0
0
1
1
0
2
1
2
1
1
0
0
1
3
1
1
1
1
1
3
1
2
0
2
0
0
1
1
0
0
2
2
2
0
2
0
0
0
1
2
1
1
2
1
1
1
1
3
2
2
1
1
1
0
2
2
3
2
0
2
1
0
2
1
1
2
1
2
1
1
0
1
2
2
2
0
0
1
0
1
0
0
2
1
2
2
1
2
0
1
1
0
0
1
0
1
2
1
1
1
2
1
0
1
1
2
0
0
1
0
0
1
2
1
0
1
1
2
0
2
1
0
1
0
0
1
1
0
2
0
1
1
1
1
0
0
1
1
0
2
1
1
1
0
0
2
2
2
1
1
2
1
1
0
2
1
0
2
2
0
2
2
1
2
1
2
0
0
0
1
0
2
1
1
3
1
0
1
1
2
1
0
1
2
0
2
0
1
0
1
1
1
1
0
2
0
0
1
1
1
2
0
2
2
1
2
2
1
1
1
1
0
0
0
0
1
0
1
1
1
0
1
2
1
0
2
2
2
1
1
1
3
0
1
1
1
0
1
1
0
0
0
1
2
1
1
1
2
0
1
1
0
1
2
3
1
0
2
0
1
0
2
2
0
1
0
0
2
0
1
0
0
2
0
1
1
1
1
1
1
1
0
0
1
2
0
1
0
0
1
0
2
2
0
2
0
2
1
1
0
2
0
1
2
0
0
1
0
2
1
0
1
0
0
0
0
1
0
0
1
1
0
2
1
2
1
0
1
0
0
1
0
0
1
1
2
0
2
1
2
0
2
3
0
2
2
1
1
0
0
2
0
1
1
0
1
2
1
0
2
1
1
1
0
0
1
2
2
0
1
1
0
1
0
1
0
1
0
1
1
1
1
1
0
0
0
1
2
0
2
2
0
0
1
2
2
1
2
2
0
1
0
1
0
0
0
1
0
0
0
1
0
2
1
1
0
1
0
1
2
1
0
1
0
1
1
2
0
0
2
0
1
2
1
0
0
1
2
0
0
2
0
0
2
1
0
0
0
2
0
3
2
1
1
2
1
1
2
1
1
2
0
0
2
2
2
1
1
1
2
1
2
1
0
0
1
1
0
0
1
1
1
0
1
0
1
1
0
1
0
0
3
1
1
0
2
0
1
1
1
1
1
2
2
1
1
1
2
1
0
1
1
2
2
2
1
0
1
1
0
0
0
2
0
1
1
0
1
0
2
2
2
2
0
2
1
0
1
1
0
0
1
1
0
0
2
1
0
0
1
2
0
0
0
1
3
0
0
2
1
0
2
2
1
2
1
0
1
1
0
0
4
0
1
0
0
2
2
0
0
2
1
0
2
2
0
0
0
1
0
2
1
0
2
1
1
2
1
1
0
1
0
0
1
2
0
1
0
1
0
1
0
1
2
1
2
1
2
1
1
0
2
1
1
1
1
2
1
1
2
2
2
2
0
1
1
0
0
2
2
1
0
0
1
1
2
2
0
0
1
2
2
1
1
1
2
1
1
1
1
1
1
2
1
0
0
1
0
0
2
1
1
3
2
2
2
1
0
1
1
1
1
0
0
0
2
1
0
1
1
0
1
1
1
1
0
2
0
2
1
0
0
0
0
2
2
1
1
1
1
2
1
2
2
0
2
1
1
0
2
2
0
0
1
0
2
1
1
1
1
1
0
1
1
1
1
2
0
0
1
1
0
0
0
1
0
2
2
1
1
0
1
0
2
1
2
1
1
1
1
3
0
1
1
1
0
1
0
1
0
1
1
0
4
1
0
1
1
0
0
1
1
1
0
1
0
1
1
0
0
0
1
1
2
0
0
3
1
0
1
2
0
0
0
0
2
1
1
0
1
0
0
2
0
1
1
0
1
1
0
1
0
1
1
0
2
2
2
1
0
0
0
1
1
2
0
0
2
0
0
1
2
2
0
0
0
2
0
0
2
0
1
1
3
0
1
0
1
1
0
1
0
2
0
0
0
1
2
2
1
0
0
1
1
2
0
0
0
1
0
0
1
0
1
2
1
0
0
2
1
3
2
1
1
1
1
1
0
1
1
0
1
1
2
1
2
1
1
2
0
2
0
0
2
1
1
2
0
0
2
1
0
2
0
0
1
0
1
0
1
2
3
1
0
0
0
2
1
2
1
0
0
2
2
0
1
2
0
1
1
1
1
1
0
1
0
0
1
2
1
1
1
1
2
0
1
1
0
0
0
1
1
1
1
1
1
1
2
1
1
2
0
0
1
0
1
1
1
0
1
0
0
0
0
1
0
0
1
1
2
0
0
1
1
1
1
1
0
0
1
0
2
0
0
0
1
2
1
0
0
2
2
1
0
0
1
0
0
1
1
0
0
0
1
0
2
0
1
1
0
3
2
0
3
1
1
0
1
0
1
0
1
2
0
1
1
0
1
1
1
1
0
0
0
2
1
0
0
0
1
0
0
2
0
2
0
1
1
0
0
1
1
2
1
0
1
0
2
2
2
1
1
0
2
0
1
1
1
1
3
0
0
2
2
0
1
1
0
1
1
0
1
1
1
1
0
2
2
1
3
1
0
1
1
0
1
1
2
2
0
1
1
1
0
0
1
1
0
2
0
0
1
0
0
3
2
0
0
2
0
2
1
0
1
2
1
2
0
1
1
1
0
2
1
0
1
1
0
2
1
1
1
2
0
1
0
2
1
2
1
0
2
2
0
0
2
0
2
1
2
1
0
2
1
2
1
0
1
1
2
1
1
1
1
1
1
1
0
0
1
1
2
1
1
1
3
0
0
1
1
2
1
1
0
0
0
0
1
1
1
1
1
0
0
0
0
0
0
0
1
0
1
1
0
1
0
1
1
0
1
0
0
1
1
1
0
2
1
0
1
0
2
2
0
1
0
2
1
0
2
2
0
2
2
0
1
2
1
0
0
0
1
1
0
2
1
1
2
0
1
1
2
0
2
1
2
0
0
2
2
0
1
0
2
3
0
1
0
1
1
0
2
2
2
0
1
0
1
1
2
2
1
2
1
1
1
0
1
0
0
1
1
0
1
0
1
2
1
1
2
1
1
0
1
1
2
1
1
0
0
1
1
1
0
0
0
1
0
2
1
1
0
1
1
1
1
2
2
0
2
0
1
0
2
0
0
0
1
2
2
3
1
0
0
0
4
0
1
2
0
2
2
1
1
1
2
0
1
0
1
1
0
2
2
0
2
1
1
0
0
7
1
2
1
0
0
1
1
1
0
2
1
1
1
2
1
1
1
1
0
0
1
1
0
0
1
1
2
1
2
1
1
0
2
4
1
2
0
2
0
0
1
0
0
1
1
1
1
0
1
1
1
0
0
1
0
1
1
0
0
0
1
0
1
0
2
1
1
0
1
1
1
3
0
1
2
2
0
0
0
1
1
1
5
1
0
2
0
0
2
0
1
1
0
0
1
3
0
2
1
1
0
1
0
0
1
0
0
1
0
1
0
0
3
0
0
2
1
1
1
2
2
1
1
0
1
1
1
0
1
1
2
1
2
1
1
0
0
1
1
1
1
1
1
1
0
2
2
0
0
1
2
1
1
1
1
0
1
1
1
3
1
2
1
0
0
2
1
1
2
0
0
0
2
0
1
2
2
1
1
1
0
0
0
1
2
1
1
1
1
0
0
0
1
2
0
1
0
1
2
1
0
0
0
2
1
0
1
1
1
1
0
2
2
2
1
1
0
0
0
0
0
1
1
2
1
1
0
0
0
2
1
0
1
0
0
0
1
0
1
2
1
0
3
2
0
0
1
1
1
3
0
3
1
1
1
2
1
2
1
0
2
2
2
1
1
2
1
2
1
1
0
1
2
1
3
1
1
2
0
0
0
2
0
1
1
0
3
1
1
0
0
1
2
0
2
1
1
0
2
1
1
2
0
0
1
1
0
1
1
1
1
1
1
0
0
1
1
0
0
1
1
0
1
1
0
0
0
0
1
1
0
2
0
1
2
1
1
0
2
1
2
1
2
0
0
2
0
0
0
0
0
1
1
0
0
0
2
1
0
0
2
1
0
0
2
1
0
0
1
1
1
3
2
2
2
2
0
0
2
1
0
2
0
0
0
1
1
0
0
2
0
1
1
0
0
1
1
1
1
0
1
1
1
1
1
0
0
0
1
2
0
1
0
0
2
0
1
1
0
1
1
0
1
0
7
1
1
2
4
0
0
2
1
0
2
1
1
1
0
0
2
1
1
1
1
2
1
0
0
1
0
0
1
2
2
1
0
1
1
2
1
1
1
1
1
3
0
1
1
1
1
2
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
1
2
0
1
2
0
0
1
0
0
2
2
1
0
1
1
1
0
1
1
1
2
2
0
2
0
0
4
2
2
0
1
0
2
2
2
0
0
1
0
1
2
1
1
0
2
0
2
4
1
0
0
1
1
0
0
0
1
2
1
0
1
1
0
1
0
0
0
0
1
1
1
0
2
1
1
0
0
1
2
0
1
1
0
1
2
2
1
1
2
1
0
0
2
1
0
1
2
1
1
1
1
0
0
2
1
0
0
2
0
1
0
1
2
1
0
1
1
1
1
1
1
0
2
0
0
0
0
6
0
0
1
0
0
1
2
2
1
3
2
1
0
0
0
0
1
1
0
2
0
1
0
2
2
0
1
2
2
0
0
2
1
0
2
1
0
2
1
0
1
0
1
0
1
0
2
0
2
0
1
1
1
1
1
1
2
1
1
2
2
2
0
0
1
1
0
1
0
0
1
1
1
1
1
1
0
2
1
1
0
0
1
0
1
1
1
0
1
1
0
0
1
1
1
2
0
0
2
2
0
0
2
0
0
1
1
1
0
1
2
1
1
0
1
3
0
2
1
0
2
1
0
0
1
1
2
1
0
0
1
2
0
0
0
1
0
0
1
0
1
0
2
1
0
0
0
1
1
0
0
2
1
0
0
0
1
1
1
0
1
0
1
0
0
1
1
0
1
0
2
0
2
1
0
2
1
1
0
0
1
1
0
2
1
1
1
1
0
2
0
1
0
0
0
2
0
2
0
1
0
3
1
0
0
2
0
0
1
1
0
1
2
1
1
1
1
3
0
0
2
0
2
0
0
2
1
1
0
1
0
1
2
1
0
0
1
1
1
1
2
0
2
0
2
0
2
1
3
0
2
1
1
0
1
1
0
0
1
2
1
2
0
1
0
1
1
1
0
3
1
1
0
1
1
2
1
0
0
1
2
1
2
1
1
1
0
1
1
1
0
2
0
1
1
1
2
1
1
1
0
2
1
1
3
0
1
0
0
0
0
2
0
2
1
1
3
2
1
0
1
1
0
1
1
1
2
0
1
0
1
0
2
0
2
2
0
1
0
0
1
1
1
0
0
0
1
0
0
0
2
1
1
1
1
2
0
0
0
2
0
1
1
2
0
1
0
1
0
0
0
0
2
0
1
2
0
0
2
0
1
0
2
1
0
1
1
0
0
1
0
2
1
0
2
1
1
1
0
1
1
1
2
1
2
1
0
1
0
1
2
2
0
1
2
2
1
0
1
0
1
0
1
2
1
0
3
2
1
3
3
1
0
1
2
0
1
1
1
2
1
0
1
1
1
1
1
0
0
0
1
0
2
0
1
1
2
1
0
1
0
0
1
1
2
2
2
1
3
1
2
1
1
0
1
0
0
0
2
2
0
2
2
1
0
3
0
2
0
2
3
1
1
0
0
1
1
0
2
2
1
1
2
1
1
1
0
0
2
0
0
1
0
2
1
1
1
0
3
2
0
2
1
2
0
0
0
0
0
0
0
2
3
1
0
1
2
0
1
2
1
1
0
2
2
0
0
0
1
1
1
0
1
2
1
0
2
2
0
2
0
1
0
1
2
0
1
1
1
1
1
1
2
2
2
2
2
1
0
0
0
1
0
1
2
0
0
0
2
0
0
1
0
0
1
0
2
0
2
1
0
1
2
0
0
0
1
1
1
2
1
1
1
1
0
1
2
0
0
2
1
1
0
1
0
0
0
2
2
1
0
1
2
0
1
1
1
2
0
2
0
2
1
0
0
0
0
0
0
2
1
1
2
1
0
0
1
0
1
0
0
0
2
1
2
0
1
2
0
0
1
0
0
1
1
1
1
1
0
1
1
1
2
2
1
1
2
2
1
0
1
1
0
0
1
1
1
2
2
1
1
1
2
1
0
0
1
1
2
1
0
1
1
0
1
2
2
1
0
1
1
0
0
2
2
0
2
1
3
0
1
0
0
0
1
1
1
0
4
3
3
0
0
0
0
0
1
2
0
0
2
1
1
1
4
0
0
0
1
1
0
1
1
0
1
2
2
0
2
1
0
2
0
0
2
1
1
0
0
0
1
0
0
0
1
1
2
2
1
1
0
0
0
0
0
1
1
2
1
1
1
2
1
1
2
2
1
2
1
0
0
2
1
1
0
1
0
1
1
0
0
0
1
1
2
0
1
2
0
1
1
1
0
0
0
1
0
0
1
0
1
1
2
2
2
2
1
0
0
0
0
1
0
0
0
2
1
0
2
2
2
0
0
1
0
2
1
0
2
1
0
0
1
0
2
1
1
0
2
1
0
2
1
0
0
1
0
2
0
0
0
2
1
0
1
1
0
3
1
2
0
0
0
1
1
1
0
2
2
3
0
0
1
1
0
0
1
0
1
2
1
1
1
1
1
1
0
1
1
0
0
1
0
1
1
1
0
0
1
2
1
0
2
1
0
2
0
0
1
1
0
1
0
0
1
2
1
0
1
2
0
3
0
2
1
2
2
0
1
2
0
1
0
2
1
0
0
1
0
0
1
0
1
1
2
0
1
1
1
0
1
3
0
1
0
0
0
1
1
1
1
1
2
1
0
1
0
0
1
0
2
3
1
0
2
0
2
1
0
2
1
1
0
1
1
1
1
1
1
1
0
0
0
1
0
2
0
0
1
0
2
2
0
1
2
0
0
1
1
2
1
0
1
2
1
1
0
2
2
1
2
0
1
1
1
1
0
1
0
1
1
1
2
1
0
1
2
2
1
0
1
1
0
2
1
1
1
2
2
1
3
0
1
1
2
1
2
0
0
1
1
1
1
1
0
1
2
1
0
0
2
1
0
2
0
1
1
0
1
1
1
1
2
2
1
0
0
1
0
1
1
0
2
0
0
0
2
3
0
1
0
1
1
1
2
0
0
1
0
1
0
0
0
1
0
1
0
0
1
1
1
2
1
0
1
1
0
1
2
1
0
1
0
1
1
1
1
1
0
1
2
0
3
0
0
2
1
1
2
2
0
1
1
0
0
0
1
1
1
0
1
0
1
1
0
1
2
1
2
0
2
0
0
2
2
1
2
2
1
0
0
0
0
2
1
2
1
1
1
1
2
0
0
1
0
1
1
2
0
1
0
1
5
1
1
1
2
0
1
2
0
0
0
0
1
1
1
1
1
1
1
0
1
2
1
0
3
1
0
1
0
0
0
0
0
0
2
0
0
1
1
0
2
1
0
1
1
1
1
2
1
0
1
3
0
2
1
0
1
0
2
1
1
0
1
0
1
1
1
0
1
0
0
1
0
1
0
2
3
1
1
0
2
1
1
0
0
1
0
0
3
0
1
0
0
1
1
0
0
1
1
2
0
2
0
1
0
1
1
2
0
2
0
1
0
0
0
1
3
2
0
1
0
2
0
1
0
0
1
1
2
0
0
2
1
1
1
1
1
1
1
0
0
2
1
0
0
1
0
0
1
0
2
1
1
1
0
4
1
1
2
0
1
1
1
1
1
0
1
2
0
1
0
2
0
0
0
1
2
1
0
1
0
1
0
1
0
3
2
1
1
2
2
1
2
0
2
0
1
1
3
2
1
2
0
2
1
0
1
0
1
1
1
0
1
0
1
1
0
2
0
0
2
1
0
0
0
5
2
1
0
2
1
1
0
0
1
1
0
1
0
1
2
2
1
1
1
0
1
0
0
2
1
0
1
1
1
2
0
2
2
0
1
0
1
1
0
1
0
0
2
0
0
0
1
0
0
2
2
0
2
0
2
1
1
2
2
2
0
0
1
1
1
0
2
0
1
0
2
0
1
2
0
1
0
1
0
0
2
4
1
2
1
2
1
2
1
1
0
1
0
1
1
0
1
2
1
0
0
2
0
1
1
0
2
1
1
1
0
2
1
1
2
1
1
0
1
1
1
1
2
0
0
1
2
2
1
1
0
0
2
1
0
1
1
0
0
0
0
0
0
1
0
1
1
2
2
1
1
0
2
1
1
0
1
2
0
0
1
0
0
1
0
0
0
0
0
1
2
1
2
1
0
2
0
1
0
0
1
0
0
2
2
1
0
0
2
1
2
1
1
0
2
2
1
1
1
1
2
2
0
2
2
2
0
0
1
0
2
2
1
1
1
0
1
1
2
2
1
0
2
1
1
1
0
0
1
2
0
0
2
0
1
2
0
1
1
2
5
0
0
1
1
1
0
2
1
0
2
1
1
1
0
2
0
2
1
0
1
1
1
2
1
1
0
2
1
0
0
0
1
1
0
0
0
2
1
2
0
2
2
1
1
2
0
0
0
2
1
2
1
1
1
1
1
1
1
0
2
1
2
1
0
0
1
2
0
1
1
0
2
2
0
1
0
0
1
2
0
1
1
1
0
0
3
2
2
0
0
0
1
0
0
2
1
1
0
1
1
1
0
1
1
1
1
0
2
0
0
1
1
1
0
0
3
0
1
0
1
2
2
1
1
2
0
1
2
2
0
2
0
1
0
1
1
2
0
0
0
1
1
1
2
0
2
1
0
0
1
1
1
1
1
1
1
0
1
1
1
0
1
0
0
0
0
1
2
0
1
1
2
0
1
1
0
0
0
0
1
1
0
0
0
2
0
1
1
2
1
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
2
0
2
2
2
0
1
2
2
2
0
1
0
0
0
1
0
2
0
1
1
0
0
1
1
1
1
1
2
0
0
1
0
2
1
1
0
0
0
2
1
0
1
0
2
1
0
1
0
1
1
1
1
0
1
0
0
0
0
2
1
1
1
2
0
1
0
0
1
1
1
0
0
2
0
0
0
1
0
1
2
0
0
0
0
1
1
0
1
2
2
0
0
0
1
1
1
1
1
1
1
0
0
0
1
1
0
0
0
0
1
1
0
1
1
1
0
2
1
1
2
0
0
1
1
0
1
1
3
2
2
0
1
2
0
2
3
0
0
1
1
0
1
0
0
1
1
2
0
0
2
2
0
0
0
2
0
0
1
0
0
0
2
1
1
1
0
0
2
1
2
1
0
0
0
1
1
2
0
3
1
1
2
1
0
1
1
1
0
1
0
2
2
0
1
1
0
2
1
0
2
2
1
0
0
1
0
0
0
2
1
1
1
2
1
0
1
1
0
1
1
1
1
2
0
1
3
0
0
0
0
2
1
1
1
1
2
1
0
0
2
2
0
0
1
1
1
1
1
1
0
1
2
1
0
2
0
0
2
1
0
1
1
1
0
1
0
1
1
0
2
0
0
1
1
1
1
0
1
2
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
2
0
1
1
2
1
1
0
1
1
0
2
1
1
0
0
2
1
1
0
2
1
0
1
0
1
1
0
2
0
0
0
0
1
0
0
1
1
0
1
0
1
0
0
2
1
0
0
0
1
1
0
1
0
0
0
2
1
1
1
0
0
0
0
1
0
0
0
1
1
0
2
2
0
2
2
1
1
0
0
0
2
2
0
0
1
2
1
0
2
2
0
1
1
2
2
2
0
0
0
0
2
1
0
3
0
1
1
0
1
3
1
0
0
1
0
1
1
1
0
2
0
1
2
1
0
1
1
1
0
1
2
1
0
0
0
2
2
0
2
1
2
0
1
2
0
3
0
1
1
1
1
0
1
2
0
0
0
0
0
1
0
0
2
0
1
0
0
1
1
1
1
1
1
0
0
2
0
0
0
1
2
2
2
1
2
1
1
2
1
1
1
0
0
1
0
1
1
1
1
1
0
0
0
2
2
1
0
0
0
1
0
0
2
1
0
0
1
0
1
0
1
1
2
0
1
1
1
1
0
1
0
1
1
2
0
1
1
1
2
0
1
1
0
1
0
1
2
0
2
1
0
2
0
0
1
1
0
1
0
0
1
0
1
1
1
0
2
1
2
1
2
1
0
1
0
0
1
1
1
0
1
2
0
0
1
2
1
2
0
1
1
0
0
0
2
1
1
1
0
1
2
1
1
1
1
2
1
1
2
2
0
0
1
0
0
2
1
2
2
2
0
2
0
0
1
2
0
0
1
1
2
0
1
1
1
2
0
1
1
2
1
2
0
0
0
0
0
2
1
0
1
1
2
2
0
1
2
0
1
0
0
1
0
1
1
0
0
2
1
2
2
1
1
0
1
1
0
1
1
1
1
0
1
2
0
1
0
4
3
1
2
0
0
0
2
1
0
0
0
1
0
4
0
0
1
2
1
2
1
2
1
1
2
2
0
0
2
0
0
1
0
2
1
1
0
0
2
2
2
2
1
0
1
0
0
2
0
1
1
0
0
1
0
1
1
2
1
2
0
1
1
2
0
1
3
0
1
1
1
2
0
0
2
0
2
2
0
2
1
2
0
0
1
0
1
3
1
1
2
1
1
0
2
1
1
1
1
0
0
0
0
1
2
1
1
2
1
2
1
0
1
1
0
1
1
0
1
1
1
0
0
2
2
0
1
0
0
0
1
2
0
1
2
0
1
1
1
1
0
0
2
1
0
1
0
0
3
1
0
0
1
2
0
0
1
2
1
1
0
0
1
0
0
1
1
2
4
2
1
1
1
0
0
1
2
0
0
1
1
0
2
0
1
0
0
2
1
2
1
0
1
1
1
1
1
2
0
0
1
2
1
0
1
1
1
1
0
1
1
2
1
3
2
2
1
2
0
1
1
0
1
2
0
0
1
2
0
1
1
1
1
0
0
2
1
1
2
1
0
1
1
1
0
0
0
1
0
0
1
1
1
1
0
0
2
2
3
0
1
2
1
0
2
2
2
0
0
1
1
0
0
1
2
0
0
1
1
1
1
0
0
3
1
0
1
0
1
1
0
2
1
1
0
0
1
2
2
0
1
0
1
0
0
2
0
1
0
1
0
1
1
0
1
1
0
2
1
1
2
0
0
2
0
0
0
1
1
1
0
1
0
2
2
2
0
2
1
0
1
1
2
0
1
2
1
2
0
0
0
2
0
2
1
0
1
1
1
1
1
0
2
0
1
0
1
1
1
1
1
0
1
0
0
1
2
1
0
2
1
0
1
0
1
0
0
0
2
0
1
0
0
1
0
0
0
2
1
0
1
1
1
2
2
1
1
1
0
1
0
0
1
0
1
2
0
1
1
1
1
1
0
1
2
1
1
0
1
1
1
0
1
1
0
1
1
0
0
2
1
2
2
1
0
1
0
0
2
2
1
2
1
0
0
0
1
1
2
0
2
0
1
0
1
0
1
0
1
2
1
1
1
2
1
0
1
1
2
1
2
0
2
1
0
1
0
0
0
0
2
0
1
1
1
0
0
1
0
1
1
1
2
2
0
1
2
0
1
1
2
1
1
0
2
2
0
1
2
0
0
0
1
1
0
1
1
4
0
2
1
0
0
0
0
1
2
1
1
1
2
0
2
0
1
0
2
2
2
1
0
1
1
0
1
1
0
0
0
2
2
2
2
2
1
0
1
2
1
1
2
3
1
2
1
0
1
1
1
0
2
1
1
2
0
2
0
1
1
1
1
0
1
1
1
0
0
1
1
1
0
1
4
1
0
1
1
0
0
2
0
2
0
0
0
2
0
0
0
1
0
0
2
1
1
1
0
1
1
0
1
2
1
1
2
0
0
0
0
1
1
0
0
1
1
1
1
0
1
1
1
0
1
1
2
0
1
0
1
2
1
0
0
0
1
1
0
1
0
0
1
2
2
1
1
2
2
0
1
1
2
1
1
0
2
0
0
2
1
1
0
1
2
2
1
2
0
1
0
2
2
1
4
0
0
1
1
1
1
0
1
0
1
0
1
0
0
1
2
2
1
1
0
1
2
2
2
0
0
0
0
1
0
1
0
0
1
0
0
2
4
0
1
0
0
1
0
0
0
0
3
0
0
0
2
0
0
1
2
0
1
0
1
0
2
0
1
0
0
1
0
1
2
1
0
1
0
0
2
2
0
1
0
1
0
0
1
1
1
1
0
2
1
0
0
0
2
1
1
1
0
0
1
1
2
2
1
1
0
1
2
1
1
1
1
1
2
2
0
2
1
2
1
2
0
0
1
1
0
1
0
0
0
2
2
3
1
1
1
1
0
0
2
1
0
2
0
0
1
2
1
1
0
1
1
1
1
0
1
1
0
1
2
0
1
2
1
2
2
1
0
1
0
2
1
0
0
0
1
1
2
0
1
2
0
2
0
1
0
1
2
1
0
0
2
0
1
1
2
2
1
1
1
0
1
1
2
1
0
2
1
1
0
0
1
0
1
0
0
0
0
0
1
1
1
0
1
0
1
0
1
0
0
1
1
1
1
2
2
1
2
0
0
2
0
2
2
1
1
0
0
2
0
0
1
1
2
0
1
0
1
3
0
0
2
3
1
0
2
0
0
2
0
2
0
1
0
0
0
2
2
0
1
2
1
0
2
4
0
1
2
0
1
0
0
1
0
1
2
2
1
1
1
0
0
0
0
1
0
0
2
2
1
2
1
1
2
1
0
2
2
0
1
3
0
1
1
0
2
0
1
0
0
1
1
1
1
0
1
1
1
0
0
2
0
2
2
0
1
0
0
0
0
2
0
1
0
1
1
0
1
1
0
1
1
0
0
1
0
1
2
0
0
0
2
0
1
0
1
1
0
5
1
0
1
1
0
0
1
0
0
1
0
0
2
1
2
1
1
2
0
1
0
0
0
1
1
0
1
1
1
1
0
2
0
1
0
0
1
1
2
0
0
1
0
3
1
2
0
0
1
1
2
2
2
0
2
0
1
1
1
2
0
1
0
3
1
1
2
1
0
2
0
1
1
0
2
1
1
2
2
1
0
0
1
1
0
0
3
1
0
1
0
1
0
0
2
0
2
0
2
1
1
1
1
0
1
1
0
0
0
0
1
2
2
1
1
1
1
2
2
0
1
0
1
1
0
1
1
3
1
1
1
0
1
0
2
1
0
0
1
0
0
2
0
2
1
2
1
2
0
0
0
0
0
0
2
0
1
1
0
0
1
0
1
0
1
0
0
2
1
1
2
3
1
2
2
1
0
1
0
2
1
0
1
1
0
1
1
1
0
1
2
0
1
0
1
0
0
2
1
1
0
0
1
4
1
1
0
1
1
1
1
3
0
2
1
0
1
1
0
1
2
2
2
0
1
0
1
0
1
1
0
1
2
0
2
0
1
1
1
0
0
0
2
0
1
0
1
1
0
0
0
2
0
2
0
0
0
0
4
1
2
0
0
0
0
1
1
1
1
2
2
1
1
2
2
0
1
0
1
0
0
1
0
0
0
2
1
1
1
1
1
2
2
1
2
1
2
1
2
1
1
1
2
0
1
1
1
0
0
1
2
1
2
0
1
1
1
1
0
0
1
2
1
1
0
2
1
1
1
1
1
2
0
1
0
0
1
1
0
2
1
0
0
0
2
1
1
0
2
1
2
2
1
2
0
1
1
1
1
0
1
0
1
1
0
1
2
1
2
1
0
1
4
2
1
1
1
0
1
0
1
1
0
0
0
2
0
1
2
1
1
2
2
0
1
1
1
2
1
0
0
2
1
1
1
1
1
2
1
1
0
1
0
1
0
2
1
1
0
1
1
2
2
0
0
1
0
0
0
1
1
0
0
1
0
1
2
2
1
2
2
1
0
0
2
4
3
0
2
1
1
1
0
1
0
0
2
1
0
1
1
0
0
0
0
0
0
1
1
0
2
1
0
2
1
2
1
1
1
2
0
1
1
0
1
1
0
1
0
0
1
1
1
0
1
0
1
1
0
1
1
0
2
1
2
1
1
1
1
1
1
1
2
0
1
1
0
1
0
0
1
4
1
1
2
3
0
1
1
1
1
0
0
1
0
1
2
0
1
1
1
0
1
1
2
1
0
0
1
2
1
1
0
2
2
1
1
1
0
1
1
1
1
0
1
0
1
1
1
0
1
1
1
0
0
2
1
1
1
1
1
1
1
0
0
0
0
1
1
0
1
0
1
1
1
2
1
2
0
2
2
1
1
1
0
0
1
1
0
0
0
2
1
0
0
1
1
2
1
1
1
2
1
0
1
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
2
1
0
0
3
1
1
0
0
1
0
0
1
0
0
1
1
0
1
1
1
1
1
1
1
2
0
2
1
0
1
1
2
1
1
0
0
1
1
0
2
1
0
3
1
2
1
0
1
0
1
1
0
0
1
0
0
0
1
1
1
1
1
1
0
0
0
0
1
0
1
1
2
1
1
0
1
2
0
1
1
1
1
2
0
0
2
2
0
1
0
0
2
1
1
1
1
2
1
1
1
0
1
1
1
1
0
0
2
2
2
2
1
0
2
0
1
1
1
1
0
2
0
0
1
0
0
2
2
1
0
1
2
1
0
1
0
1
0
0
1
0
0
3
2
1
0
1
1
0
0
2
0
2
0
2
2
2
1
2
0
1
0
2
1
0
0
3
1
1
1
2
2
1
1
1
1
0
1
1
2
2
1
1
1
0
1
0
0
3
0
2
0
1
1
1
0
0
0
2
0
0
1
1
0
1
0
2
0
1
0
1
1
0
0
1
2
1
0
0
2
1
1
1
2
0
0
1
1
2
1
0
1
1
1
2
0
1
0
1
0
0
1
2
0
0
0
0
1
0
0
0
0
1
0
1
1
1
1
0
2
2
0
3
2
1
0
0
2
0
1
2
1
1
2
1
0
2
2
1
2
1
0
0
0
1
0
0
1
2
0
0
0
2
1
1
0
0
2
0
2
2
1
1
0
1
0
1
1
1
0
1
0
0
1
1
1
1
1
0
1
1
1
1
0
0
1
0
2
1
0
0
0
1
0
2
1
0
2
1
1
3
1
0
0
2
0
0
0
0
1
3
3
0
1
0
1
2
1
1
1
1
0
1
1
1
2
2
2
0
1
1
0
0
1
2
1
1
1
2
1
1
0
1
2
0
2
0
1
2
1
1
1
1
1
2
1
2
0
1
1
1
0
1
1
2
2
1
2
0
0
1
1
0
0
1
1
2
1
1
0
0
1
2
0
0
1
1
0
0
2
1
3
3
0
1
1
0
2
1
0
0
0
1
1
0
2
1
1
0
0
1
1
2
0
0
2
2
1
0
2
0
1
0
0
2
0
0
1
0
1
2
2
0
2
2
0
1
0
2
0
1
0
1
3
1
1
2
1
1
0
2
0
2
1
1
0
1
3
0
1
1
1
2
1
2
2
1
3
1
2
3
0
1
0
1
5
6
1
1
1
1
1
1
1
1
1
0
2
0
1
0
0
2
1
3
1
0
2
1
2
0
1
0
1
2
0
0
0
0
0
0
0
2
1
0
1
2
2
2
0
2
2
1
2
1
1
0
0
1
1
2
1
0
1
1
0
1
2
1
0
1
0
1
0
1
2
0
1
2
2
1
1
1
1
2
0
0
2
2
2
1
2
0
0
0
1
2
1
1
1
4
1
0
0
1
3
1
0
2
2
0
2
1
1
1
0
1
1
0
2
0
2
2
0
0
1
2
1
1
1
2
1
1
0
1
2
1
1
1
1
2
1
2
1
0
1
2
2
0
3
1
1
0
1
1
1
2
1
1
0
1
0
0
2
1
1
2
2
1
2
1
0
3
2
0
0
1
1
1
1
2
2
0
1
1
0
2
1
2
1
1
0
1
0
0
0
1
0
1
0
1
1
0
1
1
2
0
0
1
2
1
1
1
1
1
0
1
2
1
0
1
1
1
1
1
0
2
1
1
1
1
0
1
1
2
1
1
2
1
2
1
1
1
2
1
1
4
0
0
1
1
0
0
1
1
2
1
2
0
1
2
5
2
0
1
0
0
2
1
0
2
2
1
2
1
1
1
1
0
1
2
1
0
2
0
1
1
1
1
0
2
1
1
2
1
1
1
1
0
3
1
0
0
1
0
1
0
1
3
1
2
1
1
1
0
0
0
2
0
2
1
0
2
0
0
0
1
0
1
3
0
1
1
1
0
0
0
0
1
1
0
2
1
0
0
1
0
1
0
0
1
0
1
2
0
0
1
2
2
2
1
1
3
2
1
2
1
1
0
1
2
0
3
1
0
1
2
0
1
1
1
1
1
1
1
1
0
1
1
2
1
0
0
0
2
1
0
2
0
1
1
0
2
0
0
2
2
0
1
2
1
1
1
1
1
2
0
1
2
2
0
2
1
0
1
0
1
1
1
1
1
1
1
1
2
0
2
1
1
2
0
2
0
1
0
2
2
2
2
1
2
0
3
1
1
0
0
1
2
0
1
1
0
2
0
1
0
0
0
0
0
1
0
1
1
0
2
1
1
1
1
0
1
1
0
0
2
1
0
1
1
2
0
2
1
1
1
2
0
2
0
1
0
0
2
0
0
3
1
2
1
1
1
2
1
1
1
2
0
1
1
2
2
1
0
1
0
0
0
1
1
0
0
0
2
0
1
2
1
2
0
1
1
1
1
1
1
1
2
0
2
1
0
1
0
0
1
0
0
1
2
2
1
0
1
0
2
1
1
1
1
2
0
1
1
1
1
2
0
0
2
1
1
1
1
0
1
1
1
1
0
1
2
1
2
0
2
0
2
0
0
2
3
1
2
1
2
0
0
0
1
2
1
1
2
2
1
1
1
0
2
1
0
1
1
2
1
2
1
0
1
0
0
0
0
0
2
1
1
1
1
1
0
2
1
1
2
1
0
0
2
1
1
2
0
0
3
1
0
1
2
0
2
1
2
2
1
0
0
0
0
0
1
1
4
2
1
0
0
2
0
0
0
1
2
0
1
2
2
0
1
1
1
2
1
0
2
0
0
1
1
1
1
0
3
0
1
0
2
0
0
2
0
1
2
0
0
1
1
2
1
2
1
0
0
1
1
1
1
1
2
0
3
0
0
2
1
0
1
1
0
2
1
1
0
0
0
0
1
1
1
1
1
1
1
1
1
5
2
1
0
0
0
1
1
1
0
2
1
2
3
2
2
1
2
2
1
1
0
1
2
0
0
0
2
0
0
2
1
0
0
0
2
0
1
2
2
1
2
2
0
2
0
0
1
1
0
0
1
1
0
0
0
2
1
4
0
1
1
0
0
3
0
1
0
1
0
2
0
1
2
0
1
1
0
1
0
0
1
0
1
1
0
1
0
0
2
2
0
1
0
0
0
2
2
0
1
2
1
1
1
0
1
0
1
1
0
2
1
1
2
0
0
0
1
0
1
0
1
1
0
1
2
0
1
2
0
0
0
0
0
1
1
1
1
2
1
1
2
1
1
1
2
1
1
1
0
2
0
0
0
1
1
2
1
1
1
1
0
1
0
1
0
1
0
2
2
0
0
3
1
0
3
2
0
1
1
1
0
0
1
1
2
2
0
2
0
0
0
0
0
1
0
0
0
1
1
1
2
1
1
2
3
0
2
0
2
1
0
2
1
2
1
1
1
1
0
1
0
2
0
0
2
1
0
2
0
0
0
2
1
1
0
0
0
0
1
0
2
0
1
0
1
1
2
0
1
2
0
0
0
1
1
2
2
1
1
2
1
1
2
1
0
2
1
0
1
1
0
2
1
2
2
0
1
1
1
1
1
0
0
0
0
1
1
1
0
1
0
2
1
1
0
0
2
1
2
0
0
0
0
0
2
0
0
1
2
0
0
2
0
0
1
0
1
2
1
0
1
2
0
1
2
0
1
1
2
2
2
1
0
2
2
1
1
1
2
2
1
2
0
0
1
1
1
0
0
1
0
0
0
2
0
0
0
0
2
0
2
0
1
0
1
2
0
0
0
0
1
1
1
0
1
0
2
1
1
0
1
1
0
2
1
0
1
0
0
1
2
0
1
2
0
1
2
1
0
1
1
0
1
1
0
2
2
2
1
1
2
1
2
2
1
0
0
0
0
2
1
0
0
2
0
2
1
2
0
1
1
1
0
0
2
2
1
1
1
1
2
1
2
0
2
2
1
1
0
1
2
1
1
1
1
1
2
0
1
2
1
1
0
0
4
0
0
6
1
0
2
0
0
1
0
0
2
1
1
1
1
1
2
1
1
0
1
0
2
1
0
0
2
0
0
0
0
0
1
2
2
1
0
0
0
1
1
0
2
0
0
2
1
0
0
1
0
0
1
2
0
1
0
1
2
0
1
1
3
0
0
2
0
1
0
1
1
1
1
0
1
1
0
0
0
2
2
1
2
1
1
1
0
0
0
1
1
2
0
2
0
0
1
0
0
0
1
0
0
0
1
1
1
2
1
1
0
0
0
0
0
1
0
0
1
2
2
1
0
2
2
1
0
0
1
0
2
2
0
1
1
2
0
1
1
1
2
1
0
0
1
0
1
1
1
1
2
0
1
1
0
2
0
0
1
1
1
0
0
1
1
0
0
1
1
0
2
2
0
2
2
1
1
0
0
0
1
0
0
1
2
0
0
1
0
1
0
0
2
0
1
2
1
0
1
0
1
1
1
0
1
2
1
2
2
1
0
0
1
1
1
1
1
0
1
1
1
4
1
1
2
0
1
0
0
0
2
1
1
1
1
0
1
1
2
2
1
0
0
1
0
1
2
1
0
1
0
1
1
1
0
1
0
1
1
2
2
2
1
0
1
1
1
2
2
1
2
1
1
0
2
1
0
0
0
0
2
1
1
2
0
0
1
0
1
2
0
2
2
0
0
1
2
1
1
3
1
0
0
1
1
0
0
0
0
2
0
1
1
0
1
0
0
0
1
0
1
0
2
0
1
1
0
1
0
2
1
1
1
2
0
0
2
0
1
2
2
0
1
1
1
4
2
1
2
0
2
2
1
0
1
1
2
3
0
1
2
0
1
1
0
1
2
0
0
2
0
0
4
1
1
0
1
1
1
1
0
1
1
1
2
0
2
1
0
0
2
0
1
0
1
0
0
2
0
0
1
1
1
1
1
1
0
1
1
2
1
2
1
0
0
1
2
2
1
2
0
1
1
1
1
1
0
2
3
0
2
1
1
0
0
1
2
2
2
1
0
2
1
1
2
1
0
1
0
0
1
0
0
2
1
1
0
0
1
1
0
2
0
1
0
1
0
0
0
0
1
1
1
0
2
1
0
0
0
3
0
0
1
2
1
0
0
0
0
0
1
5
2
0
0
2
2
2
0
2
1
0
1
0
2
1
2
1
1
0
0
0
0
0
1
2
2
0
2
1
0
0
1
0
0
0
2
0
3
1
2
2
1
0
1
1
1
0
1
2
0
2
0
1
0
0
2
0
1
1
1
1
2
1
1
1
2
1
2
0
4
1
0
1
2
0
4
2
0
1
1
1
2
1
2
2
1
1
1
1
0
1
0
1
2
1
0
1
0
0
0
1
1
1
1
0
0
2
2
1
2
1
2
2
2
2
2
1
0
1
1
0
2
0
2
1
0
1
1
0
0
1
1
1
0
2
1
2
0
0
0
1
0
1
1
1
1
0
1
1
0
2
1
0
0
2
1
0
1
1
2
0
4
1
1
0
2
2
1
0
1
0
1
0
0
1
0
2
2
0
1
1
1
1
2
1
1
2
1
1
0
0
0
1
0
1
2
0
1
0
1
4
2
2
1
1
0
0
1
2
1
1
0
0
3
0
4
2
1
2
0
0
0
2
1
1
1
1
1
3
0
2
0
1
1
1
1
1
1
2
0
0
1
1
1
2
0
1
2
1
0
0
1
1
2
1
0
1
0
0
1
2
1
1
0
1
1
0
2
1
0
1
0
1
1
0
2
0
1
0
0
1
0
1
0
1
0
2
1
0
2
0
0
3
1
1
2
1
1
1
1
0
1
1
0
1
1
1
2
1
0
2
0
1
2
0
2
1
1
1
0
4
2
0
0
1
0
0
0
0
0
1
0
2
1
2
1
1
1
1
1
2
0
1
0
1
2
1
3
2
0
0
0
1
2
0
0
1
1
2
3
1
0
1
1
1
0
1
2
2
1
1
2
0
1
1
1
0
0
0
1
2
1
2
1
1
1
1
1
1
2
2
1
1
2
2
2
2
1
1
1
0
0
2
1
0
0
2
2
0
0
0
1
2
1
2
0
0
2
1
2
1
1
1
2
1
0
0
0
1
0
0
0
2
1
0
1
1
1
0
1
1
1
1
2
1
1
0
2
2
0
0
1
1
1
2
1
1
0
2
0
0
1
2
0
2
0
3
1
0
1
0
2
1
2
1
1
1
2
2
0
1
1
1
0
0
0
0
0
1
0
0
1
1
2
3
0
1
0
1
0
1
1
2
1
0
1
0
0
0
2
2
1
0
0
1
0
1
1
0
0
1
0
0
1
1
1
1
1
2
2
1
1
0
1
1
0
1
0
0
3
0
1
1
0
0
2
2
0
1
1
0
1
0
1
0
0
0
1
2
0
1
1
0
2
3
0
1
1
1
0
1
0
0
3
0
0
0
1
2
2
1
0
0
0
0
0
0
1
1
1
0
1
0
1
0
2
0
0
1
0
2
0
2
2
2
0
0
2
1
1
0
1
0
2
0
0
0
2
0
2
0
0
4
2
1
1
2
0
2
1
1
1
0
0
0
0
2
2
2
1
1
1
0
1
1
1
2
0
1
1
0
1
0
0
0
1
1
1
0
2
1
1
0
1
0
2
0
0
0
1
1
2
0
1
1
1
1
0
1
1
1
1
1
2
1
2
1
0
2
2
1
1
0
1
2
0
2
1
1
0
0
0
1
1
1
0
1
0
1
1
0
1
1
1
2
1
1
1
1
0
2
2
1
0
2
1
2
2
1
0
0
1
0
0
1
0
0
0
2
2
0
1
2
0
0
2
2
1
1
0
0
1
1
0
0
1
1
1
1
0
2
1
2
1
0
1
2
0
0
1
1
2
0
1
1
2
1
0
2
0
1
1
1
1
2
0
2
1
1
0
0
0
0
0
1
1
0
1
2
1
2
1
0
1
0
0
1
1
0
0
0
1
1
0
1
0
2
2
0
0
0
2
0
1
2
2
1
0
0
0
1
2
1
2
1
0
3
2
0
1
0
1
0
0
0
1
1
2
0
0
2
2
1
0
0
2
0
0
2
2
0
0
0
1
2
3
2
1
2
2
0
3
2
0
1
0
0
1
2
1
2
2
2
1
1
2
1
2
0
1
1
1
1
0
0
2
0
2
0
0
1
0
2
0
1
1
2
1
2
0
0
1
1
2
0
0
1
1
2
0
1
1
1
0
1
2
1
0
1
2
1
1
2
1
0
1
1
0
0
2
0
0
1
1
1
2
1
1
1
1
2
2
1
2
0
1
0
0
0
1
2
2
0
1
1
2
2
0
0
1
0
1
0
0
2
0
0
2
0
1
0
0
2
1
1
1
0
2
0
2
1
1
1
1
2
2
1
0
2
1
0
1
0
0
0
2
2
1
1
0
0
1
1
0
1
1
2
1
0
1
1
1
1
0
0
3
0
2
1
1
1
4
0
1
1
0
1
1
0
2
0
1
1
1
1
0
1
1
1
0
0
1
0
2
2
0
0
0
3
0
2
1
1
1
0
2
2
0
2
1
0
0
0
0
2
2
0
0
0
1
0
0
1
0
4
0
0
2
2
1
1
0
1
1
0
1
2
0
1
1
2
2
0
1
0
0
0
5
1
2
0
0
0
1
0
1
0
0
0
0
2
1
0
0
2
1
1
1
0
2
0
0
0
2
1
0
1
0
0
0
2
1
0
0
1
2
1
1
0
1
0
0
2
1
0
1
1
0
1
0
0
1
2
1
1
0
0
0
1
0
0
0
1
2
1
2
1
2
1
1
0
1
2
0
0
0
1
1
1
1
0
0
2
1
1
1
1
0
0
0
1
2
1
0
1
0
2
2
0
0
1
1
0
1
2
0
1
2
0
1
2
1
1
0
0
0
1
1
1
1
0
1
0
1
0
0
0
1
0
1
1
2
1
0
1
0
0
1
0
0
2
0
1
1
1
0
0
3
0
0
2
0
1
0
0
1
2
1
1
1
1
1
0
2
2
2
1
0
2
1
0
0
1
2
0
2
0
2
1
0
1
0
2
1
2
1
2
0
2
1
6
0
2
1
1
1
1
1
1
1
0
0
1
1
1
0
0
1
1
0
1
2
2
0
2
1
2
2
0
2
2
1
2
1
0
1
1
0
1
1
1
1
2
1
0
0
0
1
2
0
2
0
0
1
0
0
0
0
2
2
2
0
1
2
0
0
0
1
2
1
0
0
1
1
0
0
1
2
1
0
0
1
1
0
0
1
1
0
2
1
2
0
2
0
1
2
0
1
0
0
0
1
1
2
0
0
0
2
3
2
1
0
1
1
0
0
2
1
1
1
2
0
1
0
0
1
2
1
0
0
1
1
2
1
2
2
1
1
0
0
0
1
0
0
0
0
0
0
0
2
1
1
0
1
1
0
2
0
0
1
0
0
1
1
0
0
0
1
1
1
1
1
0
2
2
1
1
0
2
1
2
1
1
2
1
0
1
2
1
2
1
1
0
0
1
1
2
2
0
0
0
1
2
0
1
1
0
2
1
1
1
1
0
1
1
1
1
0
2
2
1
1
0
1
1
1
0
1
0
1
1
0
1
9
1
0
1
0
2
1
0
0
2
2
2
0
0
1
1
2
1
1
0
2
0
3
1
2
4
1
0
0
1
2
1
0
0
1
0
1
1
1
1
1
0
1
1
1
0
0
0
3
1
0
1
0
1
0
1
1
0
1
2
1
1
0
1
1
1
1
1
0
2
0
1
1
0
1
1
1
1
0
1
0
1
2
1
2
2
1
0
1
0
2
0
1
1
0
2
1
0
1
0
0
1
1
2
1
1
0
2
1
1
0
0
1
2
1
0
0
2
0
0
0
1
0
0
2
0
1
1
0
2
2
0
0
1
1
1
3
1
0
1
1
1
0
2
0
1
1
0
2
1
0
1
2
2
3
0
0
1
3
1
1
2
1
1
1
1
0
1
1
2
0
2
3
0
2
0
1
1
1
2
1
1
1
1
0
2
0
3
0
1
1
0
1
0
1
1
0
0
0
1
0
1
1
0
1
1
2
1
1
0
2
2
0
1
1
2
1
1
0
1
0
0
2
2
1
0
0
0
1
0
1
0
1
0
0
2
2
0
2
1
1
1
1
2
1
2
0
1
2
0
0
2
1
2
0
1
2
1
1
1
2
2
1
1
0
1
0
1
1
1
2
1
2
1
2
2
1
2
1
2
2
0
2
1
1
0
2
1
0
1
0
1
1
1
0
0
0
1
2
2
1
1
0
0
0
0
0
1
2
1
2
1
2
1
1
1
1
1
0
0
0
0
1
1
0
2
0
0
0
3
0
2
2
1
1
0
0
1
0
1
0
1
1
1
0
0
1
2
2
2
2
2
1
0
1
3
1
0
1
1
0
1
2
1
1
1
0
0
2
0
0
0
1
1
0
1
0
2
2
1
1
1
0
1
1
0
1
1
0
1
2
1
1
1
1
2
1
0
1
1
1
2
0
0
1
0
0
2
1
2
2
0
0
2
1
0
1
1
0
1
2
0
0
2
1
0
1
1
2
0
2
0
1
1
0
1
0
0
0
0
1
0
1
1
0
1
2
2
2
0
1
1
0
2
1
0
2
1
0
2
2
2
1
1
0
2
1
1
0
2
1
0
1
1
1
0
2
1
0
1
2
0
3
2
0
1
1
1
1
0
1
0
1
1
1
1
0
1
1
0
1
2
1
1
1
1
1
0
0
1
2
1
2
2
0
0
0
1
1
0
0
3
0
1
0
1
0
0
1
3
0
1
0
1
0
0
0
1
0
1
0
0
2
2
1
1
1
2
0
0
0
1
2
0
2
0
1
2
2
1
0
1
1
2
2
1
0
0
1
1
0
1
1
1
1
1
0
0
1
2
1
0
0
0
1
1
1
0
0
2
1
0
1
1
1
2
2
0
0
2
1
0
2
2
0
0
1
2
1
0
0
1
3
1
0
0
0
1
0
1
1
0
0
1
0
1
1
1
1
0
1
0
1
2
0
1
1
0
0
0
2
0
2
1
3
1
1
0
2
0
1
0
0
1
1
1
2
0
1
0
2
1
2
1
1
1
0
1
1
1
1
4
0
2
1
1
0
2
1
1
1
1
1
0
2
1
1
2
2
0
0
1
1
0
0
2
2
2
0
1
2
0
1
1
1
1
1
1
2
0
0
0
0
1
1
2
0
0
0
1
0
0
0
1
1
2
1
1
2
0
1
0
0
1
0
1
2
1
0
2
2
0
1
0
0
1
0
1
0
1
3
1
2
0
2
1
1
0
1
2
1
1
2
2
1
0
1
0
0
0
1
1
1
0
0
1
2
0
0
0
1
0
2
1
2
1
2
0
1
1
1
0
2
0
1
2
0
2
2
2
2
0
1
2
1
0
1
0
0
0
0
2
2
0
1
0
2
0
2
1
1
2
0
1
0
1
0
0
0
1
1
1
1
1
1
1
0
0
1
0
0
0
1
0
0
0
1
1
1
2
4
0
1
1
0
1
0
1
0
1
1
1
0
2
0
1
1
0
0
0
1
2
0
0
0
1
2
0
1
1
0
2
1
1
1
2
1
2
2
0
1
1
0
0
1
1
0
0
1
1
1
2
3
1
0
2
0
1
0
1
0
0
1
1
2
0
1
0
1
0
1
0
1
1
0
0
2
0
1
4
1
1
0
1
0
1
1
0
1
0
0
1
0
0
3
0
1
1
1
1
0
1
2
2
0
1
1
1
1
1
0
0
0
2
1
1
1
1
0
2
1
2
2
1
0
2
1
0
0
0
1
0
1
1
2
1
1
0
1
3
1
1
2
0
1
2
0
1
1
1
0
2
2
2
1
1
0
1
1
1
0
1
2
1
0
0
0
0
1
1
2
0
0
2
0
0
1
0
0
2
2
1
2
1
2
0
0
0
0
0
1
2
0
1
1
1
1
2
1
1
0
0
1
0
0
0
2
0
1
0
1
1
2
1
1
2
1
2
1
3
3
2
0
0
0
0
1
1
2
1
1
0
1
1
0
1
0
2
1
1
2
1
0
0
1
1
3
2
2
1
1
1
0
2
1
0
0
1
0
0
0
1
0
1
1
1
3
1
0
2
0
1
0
1
1
0
1
0
1
1
0
1
0
2
1
1
0
1
0
1
1
0
1
2
2
1
0
1
1
2
2
1
2
1
2
1
1
0
2
2
1
1
2
0
0
2
2
1
3
1
1
2
1
1
0
2
1
1
0
0
0
1
2
0
0
1
1
0
1
2
2
0
1
2
1
1
0
1
0
2
1
2
2
1
0
2
2
1
0
1
2
1
2
0
0
1
0
1
0
2
2
1
0
2
0
0
0
0
0
0
0
0
2
2
1
0
1
2
0
1
1
1
1
0
1
2
1
2
0
1
1
0
1
1
0
3
1
1
2
1
1
1
2
0
0
2
1
2
2
1
2
1
2
2
1
1
2
0
2
0
1
1
1
1
0
1
1
0
0
2
0
1
2
0
1
0
0
0
2
0
0
0
0
1
1
0
1
0
1
1
1
0
1
1
0
1
2
1
1
1
0
0
1
1
1
0
0
0
1
0
1
0
1
0
4
2
2
0
0
1
0
0
1
1
1
1
0
0
1
2
1
0
1
1
1
1
1
0
1
0
1
1
0
1
1
0
0
0
0
1
1
0
1
2
0
1
1
0
0
1
1
0
2
1
2
2
1
1
0
2
1
2
1
0
0
2
3
1
2
1
1
0
0
1
1
1
0
1
1
1
0
0
1
0
0
0
1
2
1
1
0
1
2
4
1
0
1
0
2
1
0
0
0
1
0
0
2
1
0
0
1
1
1
2
2
1
1
1
0
2
2
1
2
0
2
0
1
0
2
2
0
1
1
1
1
1
0
2
1
0
0
0
2
1
0
0
1
0
3
2
0
1
1
1
0
0
0
1
2
1
1
2
0
2
2
1
0
1
0
0
0
0
1
1
1
0
1
2
0
0
2
1
1
1
1
0
2
1
1
0
0
1
0
0
0
1
0
1
1
2
1
0
1
2
0
0
0
1
2
1
0
0
2
2
1
3
0
1
0
1
2
2
0
1
0
0
0
0
1
13
0
2
1
0
0
2
0
2
0
2
1
0
2
0
0
1
0
2
0
0
2
1
1
1
0
0
1
1
1
1
1
2
1
0
0
2
0
0
1
0
0
1
0
1
2
2
0
0
1
2
1
2
0
2
1
1
1
0
2
0
0
0
1
1
0
0
2
2
2
0
3
0
1
0
0
0
0
0
1
1
0
2
0
2
2
2
0
1
0
0
2
0
1
0
0
0
1
2
2
0
0
1
1
0
1
0
2
2
2
1
0
2
0
0
0
0
0
1
0
0
2
0
1
1
0
0
1
0
2
0
2
2
0
0
1
2
0
2
1
1
0
0
1
1
1
1
0
0
2
3
1
0
0
0
1
1
1
2
0
0
1
0
1
2
3
1
1
0
0
0
0
2
0
1
1
2
1
1
0
2
0
0
1
0
1
1
1
1
0
0
1
1
1
0
1
0
1
1
2
0
1
1
1
0
2
1
0
1
1
2
1
0
2
1
1
1
1
2
0
2
2
1
1
2
0
2
0
2
1
1
0
2
2
2
0
2
2
1
1
2
1
0
0
2
1
1
0
2
1
0
1
0
1
0
1
1
0
1
0
1
0
1
0
2
0
2
0
1
1
0
0
1
1
1
1
1
1
2
0
0
0
2
0
1
2
1
2
0
0
0
0
1
2
1
1
0
0
2
0
1
1
0
1
0
0
2
4
1
2
0
0
1
0
1
0
2
1
2
2
0
0
2
1
0
1
1
0
0
0
0
1
1
3
1
2
1
0
2
1
2
0
0
2
2
1
0
0
0
1
1
1
1
2
0
0
1
0
0
1
1
1
1
2
2
2
0
0
2
0
0
2
0
0
1
1
1
1
1
1
1
2
0
2
2
1
1
1
0
1
0
0
0
1
1
2
0
1
1
1
0
0
0
1
0
2
1
2
1
0
1
2
2
0
0
1
0
1
1
0
0
1
2
0
1
1
2
0
0
2
0
0
2
0
2
2
1
0
2
1
0
1
2
1
1
0
0
2
2
0
1
2
0
1
1
1
0
0
1
1
1
0
2
0
1
1
1
2
1
0
1
2
1
2
2
0
0
1
0
2
1
2
0
1
0
0
1
0
0
1
1
1
0
0
1
0
0
7
1
1
1
2
1
1
0
0
0
1
0
1
1
0
0
1
0
1
1
2
1
1
0
2
1
2
0
2
2
1
0
0
0
1
0
1
1
1
1
3
0
2
1
1
1
0
1
2
2
2
0
0
0
2
1
1
1
1
2
1
0
1
2
1
1
2
0
2
0
1
0
0
1
0
0
2
1
0
2
1
1
0
0
1
1
0
2
1
0
1
1
0
1
0
2
0
1
0
1
1
2
0
0
0
1
0
1
0
2
1
0
2
0
0
1
1
0
2
1
4
1
1
0
1
2
0
2
2
1
0
0
0
3
0
2
0
1
0
1
0
0
0
2
1
1
1
1
0
0
0
1
1
1
2
1
2
0
2
1
1
1
1
0
1
0
2
0
1
0
1
2
2
0
1
0
0
1
1
0
2
1
1
1
1
0
2
1
0
0
2
1
1
0
0
2
0
1
1
1
0
0
0
2
1
1
1
0
0
1
1
1
1
1
0
0
2
1
0
1
2
2
0
1
1
1
0
0
1
1
0
2
1
1
2
1
1
1
0
1
2
1
0
1
2
2
2
1
0
2
4
1
2
0
0
1
1
1
2
0
1
1
1
0
2
0
1
0
2
1
0
1
1
1
0
1
0
2
0
1
2
1
1
1
1
0
1
2
0
0
4
1
0
1
1
0
0
0
2
1
2
0
3
1
1
1
1
0
1
1
0
2
2
1
1
1
1
2
0
0
2
1
1
2
2
0
0
1
1
0
0
1
2
1
0
0
1
0
0
1
0
0
2
1
2
0
0
2
0
2
0
0
1
0
2
2
0
2
1
2
2
5
0
1
0
0
1
1
1
1
2
2
3
1
1
2
2
2
1
0
1
0
2
2
0
1
2
2
1
2
2
1
0
1
2
0
0
1
1
1
1
1
1
0
0
0
0
2
0
0
4
2
1
1
2
1
1
1
0
0
1
1
1
1
1
1
1
2
0
0
0
2
1
2
4
1
1
2
0
1
1
0
2
2
2
1
0
2
1
1
0
0
2
0
0
1
4
1
2
0
2
2
2
2
1
0
1
2
0
1
1
0
0
1
0
1
1
0
1
0
1
0
1
1
1
0
0
2
0
0
1
1
0
0
1
2
1
0
3
0
0
1
1
0
1
2
0
0
1
0
0
1
0
0
0
0
2
2
1
2
1
0
0
2
1
2
0
1
2
1
2
0
4
0
0
0
1
1
1
0
0
0
0
1
2
1
1
0
1
1
0
0
0
1
1
2
2
0
1
2
0
1
2
2
2
1
1
0
1
2
1
1
1
0
1
0
1
1
0
1
0
0
1
0
0
1
1
2
2
2
1
1
0
2
2
2
1
2
0
0
2
0
1
2
1
0
0
0
1
2
1
1
1
0
0
1
1
1
1
1
0
1
1
1
0
2
1
0
1
0
1
1
2
0
2
1
1
1
2
0
2
1
2
0
2
1
0
1
0
0
1
1
2
2
0
1
1
2
0
2
1
0
0
0
3
0
2
1
2
2
1
0
2
2
1
1
0
1
2
2
1
2
2
0
0
2
1
2
1
1
2
0
0
1
0
0
1
0
1
0
0
2
0
2
0
1
1
1
1
0
1
1
1
1
1
1
0
1
0
0
1
1
0
0
1
1
1
0
1
3
0
1
1
0
1
2
0
0
2
1
1
0
2
2
2
1
0
0
1
2
2
0
1
2
2
0
1
0
0
0
1
2
0
0
0
1
2
0
1
1
2
0
1
0
2
0
1
1
0
0
1
2
1
0
1
1
2
1
0
0
1
1
0
0
1
2
1
0
1
2
0
1
2
1
1
1
1
2
1
1
1
1
1
0
1
0
1
2
1
1
1
0
1
1
0
1
0
0
1
0
1
0
0
1
1
1
0
1
0
1
2
0
0
1
0
1
1
0
2
1
1
0
1
0
0
2
2
2
0
2
1
2
2
2
1
1
1
1
0
0
1
1
1
2
0
0
2
0
1
1
0
1
2
1
0
1
0
2
1
1
2
1
1
0
1
2
2
2
0
0
1
0
2
1
2
1
0
1
1
1
1
1
0
1
2
2
1
1
1
1
0
0
0
2
1
0
0
0
0
1
1
1
1
2
1
1
2
1
0
2
1
2
1
0
1
1
0
2
2
0
2
2
3
1
0
0
2
1
1
4
0
1
2
0
0
1
0
1
2
1
1
2
1
1
0
0
1
2
1
2
1
1
1
0
0
1
2
0
0
1
1
2
1
1
1
1
1
0
0
0
0
1
0
1
1
1
3
1
1
1
1
0
0
0
0
1
1
0
0
1
1
0
1
0
1
0
0
1
1
1
0
3
1
2
1
2
1
3
1
0
1
0
1
0
1
0
2
0
1
2
2
2
1
2
0
0
1
0
0
0
0
1
0
1
1
1
0
1
1
1
2
0
2
2
0
1
1
2
0
1
0
1
1
0
2
2
1
1
1
1
1
1
0
0
0
2
0
1
2
2
1
1
0
1
1
1
0
1
1
1
1
1
1
2
1
1
4
2
2
1
0
3
1
1
2
1
1
1
2
2
0
0
0
0
2
1
1
2
0
2
1
2
1
0
1
1
1
2
1
0
2
1
1
2
0
0
1
0
1
1
1
1
1
1
2
0
2
1
0
2
1
1
1
0
2
1
0
1
2
2
0
2
1
1
0
2
1
1
0
0
2
2
1
2
1
0
0
0
0
2
2
0
0
2
1
0
0
1
2
2
1
2
1
0
0
0
1
2
1
0
1
0
0
1
1
0
0
1
1
2
0
0
1
1
0
0
1
2
1
1
0
2
0
1
1
0
0
1
2
0
2
1
2
2
1
1
2
2
1
2
1
2
0
1
2
1
0
1
1
0
0
2
2
2
0
0
1
2
0
0
0
0
1
1
2
1
0
0
1
1
1
1
2
0
0
1
0
1
1
0
0
2
0
1
2
0
0
0
0
0
1
1
1
0
1
3
1
0
1
2
0
0
0
1
0
1
0
0
0
0
1
1
2
1
2
0
1
1
0
0
1
1
0
0
0
1
0
2
1
1
1
2
1
2
0
1
0
1
1
0
0
2
0
2
0
0
2
1
1
0
0
0
2
2
0
0
1
0
0
0
1
1
2
1
0
0
0
1
6
2
1
1
0
1
0
2
0
1
1
1
2
1
0
0
1
0
1
0
0
1
1
0
0
0
2
2
2
2
0
1
1
1
1
1
2
2
0
1
1
2
0
1
0
0
0
2
0
0
1
0
1
0
2
1
1
0
1
1
0
0
2
3
1
1
0
0
1
2
1
0
1
0
1
0
1
2
1
0
2
0
0
1
1
0
0
4
1
2
0
0
0
0
1
0
1
0
1
1
2
2
2
1
2
1
1
2
1
0
1
1
2
2
0
1
1
1
0
1
2
1
0
2
1
1
0
0
1
0
1
1
2
1
1
0
0
1
0
1
2
2
1
1
0
2
2
1
2
2
2
1
0
1
0
1
2
1
0
0
1
1
3
2
2
1
2
0
0
1
1
1
0
1
2
1
0
0
0
1
0
0
0
1
0
0
2
0
0
1
0
2
0
1
0
0
1
0
0
2
1
2
0
0
0
1
0
2
0
0
1
0
1
1
0
0
0
0
1
1
1
2
0
1
1
1
0
1
1
0
2
2
0
0
1
1
1
1
0
0
1
0
0
1
1
1
1
1
2
1
0
1
1
1
0
0
1
1
0
0
0
1
0
1
0
2
0
2
0
1
0
2
2
1
1
1
2
0
1
2
1
1
2
0
0
0
1
0
1
2
0
2
0
1
0
1
0
0
0
0
0
1
1
2
1
2
0
2
0
0
0
1
1
0
2
1
3
0
1
1
1
6
0
2
0
1
0
0
0
1
0
0
2
0
1
2
0
0
1
2
1
1
1
0
2
2
0
1
0
1
0
0
1
0
1
1
1
2
2
1
2
2
0
1
0
0
1
2
0
1
2
1
2
1
1
1
1
1
2
0
3
1
1
2
1
4
2
0
1
0
1
0
2
2
3
1
1
1
1
1
0
1
2
0
0
2
0
0
2
1
1
1
2
1
1
1
0
0
1
0
1
2
1
0
0
0
0
0
0
0
1
1
0
0
2
1
1
1
0
0
1
0
2
2
0
1
2
0
1
1
1
0
0
1
0
0
0
0
0
0
2
0
1
1
0
0
0
0
1
1
0
2
1
2
0
1
2
1
0
0
0
1
2
1
1
1
2
1
1
0
1
0
1
2
2
1
0
2
2
0
1
1
2
0
0
2
1
2
1
0
0
0
2
1
0
0
1
1
0
2
0
0
0
0
1
0
0
0
0
3
1
2
2
1
0
0
0
1
1
1
1
1
1
1
2
1
2
2
1
0
2
0
1
1
1
1
1
0
2
1
1
1
1
1
2
0
0
1
1
1
3
2
1
3
0
2
0
1
0
2
0
0
0
1
0
2
3
2
0
0
1
0
1
2
2
1
0
0
2
0
0
0
0
1
1
1
0
1
0
1
2
2
0
1
1
1
1
1
0
1
0
0
1
0
0
0
1
2
0
1
2
2
2
1
0
2
1
0
2
1
2
2
1
1
1
1
1
1
1
0
0
1
1
2
0
0
0
0
0
0
1
0
1
1
1
0
1
1
2
1
0
1
0
0
2
0
1
1
0
1
1
1
1
2
0
0
1
6
1
1
2
1
2
0
1
1
1
1
2
2
0
1
2
0
1
1
1
4
1
0
0
3
0
1
1
0
0
1
1
1
1
2
2
1
0
0
2
2
1
1
3
2
0
0
0
2
0
2
1
1
0
2
0
2
1
1
0
0
1
2
0
1
1
1
2
1
1
2
0
1
1
0
2
1
2
1
1
2
1
2
0
0
2
0
0
1
1
2
1
1
0
1
2
1
1
2
0
0
1
0
2
2
0
1
0
1
2
1
1
1
1
2
1
0
1
0
1
1
0
0
2
2
1
1
0
1
2
0
1
0
1
0
1
0
1
0
0
2
1
2
2
0
1
1
1
0
1
1
2
2
1
0
0
1
0
0
0
1
0
2
2
0
1
1
1
1
0
0
1
1
0
1
0
1
2
2
0
1
1
0
0
1
2
2
1
0
1
1
2
1
1
0
1
0
0
2
2
2
2
1
2
2
1
0
1
0
1
2
0
1
5
0
1
0
1
0
1
1
0
1
0
2
1
0
1
2
2
1
1
1
0
0
1
1
0
1
0
1
1
1
9
2
0
1
1
1
0
0
1
0
2
1
1
0
2
0
2
0
1
2
0
0
2
0
1
0
1
0
1
0
0
1
1
2
0
1
1
1
1
0
1
1
1
2
0
0
1
2
1
2
1
0
1
0
0
1
1
0
0
2
1
1
1
0
1
1
0
1
2
1
0
1
1
0
0
0
0
2
1
1
0
0
1
2
1
0
0
1
1
3
0
2
2
3
0
1
0
1
1
1
1
0
2
1
0
1
2
1
1
1
1
0
0
0
0
0
2
0
0
0
0
2
3
1
1
0
2
1
0
0
2
0
0
1
0
1
0
1
0
2
1
0
1
0
1
1
0
0
1
2
0
1
0
1
1
0
0
1
2
0
0
1
0
2
1
1
2
0
2
2
1
5
1
0
1
2
4
1
0
2
0
1
0
0
1
1
2
0
0
2
1
3
0
1
2
0
2
1
1
0
0
0
2
0
2
1
1
0
2
0
2
0
0
0
2
0
0
0
1
2
2
0
1
2
1
1
1
0
0
2
2
2
1
1
0
0
1
1
1
1
1
1
1
1
0
2
2
1
1
1
1
2
0
1
1
0
0
0
2
2
2
2
0
1
1
2
0
0
2
1
1
2
0
1
1
1
2
2
1
1
1
1
0
1
2
0
1
2
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
1
0
0
0
0
0
2
1
1
0
0
0
3
0
1
1
2
1
4
0
0
1
0
0
0
0
2
0
0
1
1
0
2
1
1
1
1
0
2
2
1
1
1
1
0
0
2
2
0
2
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
0
0
2
2
1
3
1
1
1
2
0
1
0
1
0
0
2
1
2
1
0
1
1
1
1
2
1
0
0
1
1
0
0
0
1
2
1
0
1
0
0
2
1
1
0
1
0
1
1
1
1
1
1
0
0
1
1
0
0
0
2
0
0
0
0
0
0
1
0
1
0
1
1
2
1
0
0
0
0
1
1
0
0
1
0
0
1
2
0
0
0
2
2
0
0
1
0
0
0
1
1
1
1
0
0
1
0
0
1
0
0
2
0
1
2
0
0
0
0
0
0
1
1
0
2
1
0
1
0
1
1
1
0
1
2
2
0
0
1
1
0
0
0
1
0
1
2
0
0
1
1
1
0
0
0
1
1
0
1
0
1
2
1
1
0
0
0
0
1
2
0
0
2
1
1
2
0
2
0
2
0
2
0
2
1
2
0
1
2
1
0
2
2
1
1
1
0
1
1
2
1
0
0
1
1
1
2
0
1
1
0
1
1
1
3
2
2
1
0
1
1
1
2
1
1
1
0
0
1
2
0
1
0
0
1
3
1
2
1
1
0
0
1
1
1
1
0
0
0
1
1
2
1
0
1
1
1
0
1
0
3
2
1
0
2
1
2
0
0
0
2
0
2
1
1
2
1
0
0
2
0
0
0
2
0
1
2
2
2
1
0
0
0
2
0
1
1
1
0
1
0
0
0
0
1
2
1
1
0
2
1
2
2
0
2
1
1
1
0
1
1
1
0
2
1
2
4
0
1
0
1
1
1
1
1
1
2
0
0
2
1
0
0
0
2
1
2
1
1
2
0
1
0
2
0
0
1
4
0
1
0
1
1
1
1
2
0
1
1
1
1
2
1
1
0
2
2
2
1
1
1
0
0
0
0
1
1
1
2
0
1
0
1
1
1
1
1
1
1
0
2
1
1
2
2
1
1
1
1
0
0
1
2
0
2
1
1
0
1
1
0
1
1
2
0
0
1
1
1
1
0
0
1
1
1
0
0
0
0
1
1
2
2
1
1
1
2
1
0
2
1
0
1
2
1
1
1
2
1
0
1
0
1
1
0
1
1
0
0
0
1
1
0
0
1
0
0
2
0
0
0
0
1
0
1
0
2
1
1
1
1
1
0
1
1
1
0
1
2
1
0
0
0
1
1
1
0
0
1
1
1
1
0
0
1
2
2
1
1
1
1
0
1
0
2
0
2
0
1
1
1
1
0
0
1
0
0
1
1
2
1
1
4
2
1
1
1
0
1
0
0
2
1
0
2
2
0
1
2
2
1
2
1
1
0
2
1
1
0
2
1
1
0
2
3
0
1
2
1
0
1
2
1
1
0
2
0
0
1
0
0
1
1
1
0
2
0
2
0
0
1
0
1
1
1
1
0
0
2
0
3
2
1
1
2
1
1
0
0
1
2
1
2
2
0
1
0
2
1
0
0
2
1
1
2
0
1
0
1
1
0
0
0
1
0
0
0
1
0
0
1
0
0
1
1
0
0
2
1
3
0
0
1
1
0
1
0
0
1
1
2
1
2
1
1
0
1
0
0
1
1
1
2
2
0
1
0
0
1
2
1
0
1
1
0
1
1
0
1
1
1
0
2
2
1
2
2
1
0
1
0
1
0
2
1
0
0
0
0
0
0
1
2
0
1
1
1
1
2
1
1
1
1
2
0
0
1
0
0
1
0
2
1
0
0
1
0
1
1
0
0
1
0
2
2
1
0
0
2
1
0
1
0
0
1
0
2
1
1
1
1
2
1
1
1
0
1
2
0
0
2
0
0
0
2
0
1
0
0
0
1
1
1
1
1
0
0
1
2
0
2
0
0
1
2
2
2
4
0
2
2
2
1
0
0
0
2
0
3
1
1
1
0
1
1
0
1
0
1
2
0
1
1
1
1
0
2
0
0
0
2
1
0
1
0
0
1
0
1
0
0
0
0
1
0
0
1
1
1
0
1
1
1
0
1
1
1
2
1
1
1
2
2
0
1
1
7
1
1
2
0
1
0
2
1
0
1
2
0
1
2
0
1
1
1
0
0
1
2
2
1
0
0
0
2
0
0
2
0
1
2
1
1
0
4
0
2
2
1
0
0
1
1
0
1
1
0
1
1
1
1
1
2
1
1
2
0
0
2
0
2
0
2
2
0
1
0
1
2
1
1
0
2
1
1
1
0
0
1
0
1
1
0
1
0
0
2
0
0
0
0
0
0
2
0
0
2
0
1
1
1
1
2
0
1
0
1
1
0
1
1
1
1
2
1
0
0
2
1
0
1
2
2
2
1
1
1
1
1
0
1
1
2
1
2
1
0
1
2
2
0
1
2
1
2
0
0
1
0
1
0
1
2
1
1
1
1
1
0
1
1
2
1
1
1
1
0
2
1
0
0
1
2
1
0
0
1
1
1
1
0
1
2
0
0
0
1
0
0
2
0
0
4
1
1
2
2
1
0
1
1
0
1
0
0
0
1
1
1
0
1
1
1
1
2
2
1
0
2
1
1
0
1
2
2
0
0
1
1
0
2
0
1
1
1
0
0
2
1
0
0
0
1
0
2
0
2
1
1
0
1
1
0
1
0
3
1
1
2
2
0
0
0
2
1
1
1
1
0
1
1
0
1
0
1
1
2
1
0
1
0
1
2
1
0
2
0
0
2
2
0
1
5
0
1
1
1
0
0
2
0
1
0
0
0
2
2
1
1
1
0
0
0
1
1
1
0
2
0
2
0
2
1
1
2
2
1
0
1
2
1
0
2
0
2
2
0
1
2
1
1
1
0
1
0
2
0
0
2
2
3
0
2
1
0
2
2
1
1
1
1
2
1
0
2
0
0
1
1
1
0
0
1
0
0
0
1
1
0
0
1
2
2
1
1
0
0
1
0
2
1
1
1
2
1
1
0
1
2
0
1
1
1
1
0
0
1
0
2
1
1
0
1
0
1
2
0
1
2
0
1
1
2
0
1
1
1
2
2
0
1
0
2
0
0
0
1
2
2
0
1
0
3
0
2
1
1
2
0
0
1
0
1
0
0
0
1
0
1
1
0
2
1
0
1
0
2
1
1
0
2
0
2
1
0
1
2
0
0
0
0
1
1
0
1
1
0
2
1
0
2
2
0
1
1
1
2
2
1
3
2
1
0
1
2
0
0
1
2
1
0
0
1
2
0
0
1
1
1
1
0
0
1
2
0
0
1
1
2
0
1
0
3
1
0
1
1
0
1
0
1
0
1
0
0
1
0
0
2
2
1
1
1
1
1
1
0
2
0
2
0
1
1
2
1
1
1
2
1
0
1
2
2
1
0
1
0
1
2
1
1
1
0
1
1
2
1
1
0
0
0
2
1
2
2
1
2
1
2
2
1
1
2
0
0
1
1
1
2
1
1
1
1
0
0
1
0
0
0
2
0
1
1
1
1
2
1
3
0
1
0
2
3
1
1
0
4
1
1
0
0
0
1
1
1
2
1
2
1
0
0
1
2
1
0
0
1
0
1
1
1
2
0
3
2
1
0
1
2
2
1
0
2
0
1
0
0
0
2
0
2
1
0
1
0
0
1
0
0
1
2
0
2
2
1
1
2
0
1
3
1
2
2
0
0
2
1
2
0
2
2
2
0
3
0
2
0
1
0
2
1
1
1
0
0
1
1
2
0
0
1
0
0
2
0
0
2
0
1
0
2
1
2
2
1
1
3
0
1
2
1
1
0
0
0
0
2
0
1
0
0
1
0
0
0
0
1
0
1
1
0
1
0
1
2
1
2
1
1
0
0
1
1
0
0
2
1
2
1
2
1
1
1
0
0
0
2
1
0
1
1
0
1
1
0
0
0
0
1
2
1
2
0
2
2
0
1
0
2
0
0
2
0
0
1
0
1
1
2
0
2
0
0
0
0
1
1
1
1
2
0
1
1
2
1
1
0
1
0
1
0
1
1
0
2
0
0
0
0
0
0
2
0
0
2
0
1
1
0
0
0
1
0
1
1
1
0
2
0
1
2
0
0
0
1
0
0
1
0
0
2
3
1
0
2
0
0
1
1
1
0
2
1
2
1
1
0
1
1
0
0
1
1
1
1
0
1
2
0
1
1
0
1
0
1
2
1
1
1
1
2
0
1
2
1
2
0
2
2
2
3
1
0
1
0
0
0
1
1
0
1
0
2
1
2
1
2
2
1
0
2
0
0
1
2
1
0
1
1
1
1
1
0
4
1
2
2
1
1
1
0
0
0
0
0
3
0
0
2
0
1
1
0
2
1
1
0
0
0
0
2
1
1
1
0
2
0
1
0
0
2
0
1
1
0
0
1
1
2
1
1
1
3
2
0
1
0
0
1
0
0
0
1
1
2
1
0
0
1
1
1
0
0
2
1
0
1
0
0
0
0
1
0
1
1
2
0
1
0
0
0
1
1
1
1
0
1
2
0
2
0
2
0
0
0
0
0
0
0
1
1
1
2
0
0
1
2
1
3
1
1
1
0
2
1
2
1
1
0
0
2
2
2
1
0
0
0
1
2
1
0
2
1
2
0
1
0
1
2
0
2
0
0
0
0
1
1
3
1
1
1
2
0
0
0
0
1
1
1
1
1
2
0
2
2
0
1
0
0
2
4
0
1
1
1
0
1
3
0
0
0
1
0
1
1
3
1
0
1
0
1
1
0
1
1
0
1
0
0
0
2
0
2
2
1
1
0
2
1
1
1
2
1
1
0
0
1
0
0
1
3
1
0
0
1
0
0
2
1
2
0
1
0
1
0
2
1
1
1
1
0
2
2
2
1
0
1
1
0
1
0
0
2
1
2
2
0
0
0
1
1
0
0
0
2
2
2
1
1
0
2
0
2
0
1
1
0
1
2
1
1
1
1
1
1
2
1
1
0
1
1
1
1
0
1
0
1
2
1
0
1
0
1
0
1
2
0
0
1
1
3
1
0
0
1
0
0
0
1
1
2
0
0
1
2
1
1
1
1
0
2
0
1
0
0
1
0
0
0
1
0
1
0
2
0
2
0
0
0
1
1
1
0
0
2
1
1
1
0
1
1
1
1
0
0
2
0
2
0
0
2
2
1
0
0
0
0
1
0
1
2
1
1
3
2
1
1
0
1
0
1
1
0
1
0
1
1
1
0
0
1
1
0
0
1
1
1
1
2
1
0
1
1
0
1
0
2
1
0
0
0
2
1
1
0
0
0
2
1
2
1
1
3
1
0
1
2
1
1
0
2
1
0
1
2
1
0
0
2
1
1
0
2
2
0
0
0
0
0
2
1
1
0
0
1
0
2
0
0
2
1
1
2
2
0
0
1
0
0
1
2
1
2
2
0
0
1
1
0
1
0
0
0
1
2
2
1
1
1
1
1
1
1
0
1
1
2
0
3
2
2
2
2
1
0
2
1
2
0
1
2
2
1
1
2
0
0
1
0
0
1
2
1
1
0
1
0
2
1
1
0
1
0
0
1
0
1
1
0
1
0
1
1
0
1
1
0
2
1
0
1
2
1
0
2
2
0
1
1
1
0
1
0
0
1
1
0
1
2
2
0
0
1
2
1
1
0
3
2
1
0
1
2
2
1
1
2
1
1
2
0
2
2
0
0
1
0
0
2
1
0
0
0
1
2
0
0
2
1
0
2
0
1
2
1
0
0
0
2
0
1
1
2
0
2
0
1
1
0
2
1
1
2
3
1
1
0
1
1
1
1
0
1
2
2
2
0
2
1
2
1
0
3
1
0
0
2
1
2
1
1
2
2
1
1
1
1
0
1
1
0
1
2
2
3
0
1
0
0
1
0
0
0
1
1
2
3
1
1
0
1
2
0
0
1
0
0
2
0
2
1
1
0
0
0
2
0
0
0
1
2
1
1
1
1
2
1
3
2
1
1
1
0
2
2
0
1
0
1
1
0
1
0
1
1
0
0
1
1
0
0
2
1
1
2
1
2
1
1
0
2
1
2
0
0
1
2
1
2
2
2
0
1
1
2
0
0
2
2
0
0
2
1
0
1
2
2
1
0
0
1
1
0
1
0
1
0
1
2
1
2
1
0
1
1
0
0
2
2
2
0
1
3
0
1
1
1
0
1
0
2
1
1
2
1
1
1
1
1
1
2
1
4
2
1
0
0
0
1
2
0
1
2
0
1
1
1
0
0
0
1
1
1
1
0
0
1
0
2
1
1
1
2
1
1
1
2
0
1
0
1
0
0
2
1
0
1
1
1
2
2
0
2
0
1
2
2
2
2
1
2
2
0
0
0
0
0
0
0
1
0
3
0
0
2
1
0
1
0
0
1
0
1
7
0
1
0
0
1
0
1
1
1
1
1
2
0
1
3
2
0
2
0
1
3
3
1
2
1
0
1
1
1
1
0
2
0
2
1
1
0
0
1
1
1
0
1
2
2
0
1
2
2
2
1
1
1
1
0
0
1
0
0
0
0
2
1
2
1
1
0
0
1
2
1
0
1
0
1
1
1
1
0
0
0
1
1
1
1
0
1
2
1
1
0
1
2
0
1
2
0
0
0
0
1
1
0
2
1
0
0
1
1
2
2
1
0
2
0
1
0
0
1
1
1
0
0
1
1
0
1
1
0
1
2
0
0
0
2
2
0
0
2
0
3
0
0
2
0
0
1
0
2
0
2
1
1
0
1
1
1
0
1
0
1
2
1
0
2
1
0
1
2
0
1
0
1
1
0
2
1
1
0
1
0
1
0
0
0
1
0
0
2
1
2
0
1
0
1
1
2
2
1
0
2
3
1
1
3
1
2
0
1
1
1
0
1
0
1
0
1
0
1
2
10
1
2
1
1
1
1
2
2
1
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
2
2
0
1
0
1
0
1
0
0
1
1
1
0
0
0
2
0
1
1
1
0
0
0
1
1
1
1
0
2
0
1
2
1
1
2
1
1
0
1
1
2
1
1
0
1
1
2
0
1
1
0
2
0
0
1
0
0
5
1
1
1
0
2
0
0
2
1
0
1
0
0
1
2
0
2
1
0
1
2
1
0
1
0
2
1
0
1
0
1
0
0
0
0
0
0
2
1
2
1
0
2
2
0
1
1
2
0
0
0
0
1
1
2
0
0
1
2
2
0
0
1
0
1
2
2
1
1
2
0
1
0
1
1
1
2
2
0
0
0
0
1
0
1
1
1
0
1
2
2
0
0
2
0
2
1
2
1
1
1
0
0
2
0
1
1
2
0
2
0
1
1
0
2
2
0
0
1
0
2
1
1
1
1
0
0
0
1
1
1
0
1
1
2
0
1
0
1
2
0
2
2
0
0
0
2
1
1
1
0
1
1
0
1
2
2
0
1
0
2
1
3
1
1
2
0
1
0
0
0
0
0
1
2
0
0
1
1
1
1
1
1
1
2
0
0
1
1
1
0
0
1
0
1
2
1
0
0
2
2
0
1
0
2
0
1
2
0
0
2
1
2
1
1
1
1
1
1
2
0
0
0
0
1
1
0
2
0
0
1
1
1
1
1
1
2
1
2
1
0
0
1
1
0
0
0
0
0
1
2
0
1
1
1
2
0
0
1
0
0
1
0
0
1
0
2
0
0
2
0
1
0
1
0
0
0
1
0
0
0
0
2
0
1
1
1
3
2
1
1
2
0
1
1
1
2
0
0
2
1
1
1
1
0
1
2
0
1
1
1
0
2
1
0
1
2
0
1
2
1
0
5
1
2
1
2
1
0
2
0
2
0
0
1
2
2
2
0
1
0
2
1
2
0
1
2
0
1
0
1
0
1
1
1
2
1
1
0
2
2
1
1
0
1
1
1
1
0
0
2
1
0
0
2
3
0
1
0
3
0
0
1
1
0
0
2
0
0
1
1
0
2
1
1
1
0
1
0
1
0
3
1
1
0
1
0
1
0
1
2
1
1
2
1
0
2
1
2
1
1
1
0
0
2
2
1
1
0
0
0
0
1
0
1
1
0
0
0
0
2
0
1
0
2
0
0
1
0
0
0
0
1
1
5
0
2
2
1
2
0
1
0
0
1
2
1
0
1
0
1
0
0
1
1
0
0
1
2
1
1
1
1
0
1
0
0
1
1
1
0
1
0
0
1
1
1
0
0
0
1
0
1
1
2
0
6
2
2
0
1
1
1
0
0
1
1
1
2
0
1
1
1
0
1
1
3
0
0
1
2
1
1
0
2
1
1
2
0
4
2
1
1
0
2
0
0
1
0
0
2
0
1
4
1
2
1
0
1
1
0
0
0
2
0
0
0
1
1
1
2
1
0
1
1
0
1
0
2
0
0
0
0
1
1
1
2
0
0
0
3
1
1
1
1
1
1
0
1
0
0
2
2
1
1
3
2
0
2
1
0
1
1
0
0
1
1
1
0
0
1
2
1
0
2
1
1
1
1
2
1
2
1
2
2
0
1
1
3
2
0
1
1
1
0
2
0
2
3
1
1
1
0
2
0
1
0
0
0
2
1
1
2
1
2
1
1
1
1
1
2
0
2
2
2
0
0
0
1
2
2
1
2
0
0
1
0
1
0
1
2
1
2
1
1
0
5
0
2
0
2
0
2
1
0
0
0
0
0
2
0
1
0
2
0
1
1
2
0
2
0
2
1
1
2
0
0
0
0
1
0
0
1
1
0
0
1
2
1
1
1
1
0
0
1
2
0
2
0
1
0
1
3
2
0
0
0
0
0
1
0
0
2
1
0
1
0
2
0
0
2
1
0
2
0
1
0
1
1
0
2
2
2
1
1
0
0
1
1
1
1
0
2
0
0
1
1
1
2
1
0
1
1
1
1
1
2
0
2
1
1
2
2
2
1
2
1
1
0
0
0
0
1
2
1
0
0
1
0
0
0
1
0
0
1
0
0
2
4
0
0
0
0
0
1
0
0
0
2
0
1
1
0
1
1
1
0
1
0
1
0
1
0
1
1
2
2
2
0
2
1
1
1
2
1
1
1
0
1
0
0
2
1
2
1
0
2
1
2
1
1
1
1
0
1
0
0
1
1
1
0
1
1
0
2
0
1
0
1
0
0
1
1
0
1
0
2
0
1
1
1
0
1
1
0
0
1
0
0
1
2
2
0
1
1
1
2
0
1
2
1
2
1
1
1
0
1
0
0
0
2
0
2
2
0
0
0
1
1
1
1
0
0
1
1
1
0
1
1
0
1
0
0
0
0
0
2
0
1
1
0
0
1
0
1
1
1
0
1
0
0
0
0
0
2
1
2
2
2
1
0
1
1
0
1
1
2
1
0
0
1
0
1
0
0
0
2
2
0
2
1
1
0
0
0
0
1
0
0
0
0
0
1
2
0
1
1
0
1
1
2
1
2
0
1
0
2
1
2
0
2
0
1
1
1
0
2
1
1
2
2
0
0
1
0
1
1
1
2
0
1
0
0
1
0
2
1
1
0
0
0
2
0
0
2
0
1
1
0
2
0
0
0
2
0
2
1
0
1
1
0
1
0
1
1
0
2
1
2
1
0
0
2
0
1
1
1
2
2
1
1
1
2
0
2
1
2
0
2
2
1
0
0
0
1
0
1
1
1
0
1
2
1
1
2
2
0
2
1
0
0
0
2
1
2
1
0
1
2
2
0
1
1
0
0
1
1
1
2
1
0
0
0
1
1
0
0
2
1
1
0
0
0
0
2
0
0
1
1
1
2
0
2
1
1
0
1
0
2
1
0
0
0
1
0
0
1
0
1
0
1
1
0
0
2
2
1
1
0
1
1
1
1
2
3
0
1
0
1
1
2
2
1
0
2
0
0
2
2
0
1
1
1
0
0
1
0
2
1
0
0
0
0
0
2
2
2
0
1
0
0
2
0
1
1
1
2
0
0
0
0
2
1
0
1
0
0
1
2
3
0
1
1
1
0
1
0
1
1
0
1
2
1
2
0
2
2
1
1
2
0
2
2
0
2
1
0
1
0
0
1
0
1
1
1
1
1
0
1
0
0
0
0
1
2
2
1
0
0
2
1
2
1
0
1
1
2
0
2
2
1
0
1
0
1
2
2
1
0
0
1
0
0
0
1
1
2
0
0
2
1
2
1
1
0
0
0
0
2
0
2
0
0
2
1
0
0
0
0
0
1
0
0
1
0
0
2
0
0
2
0
1
1
1
1
1
0
1
2
1
0
2
1
0
0
2
2
1
1
2
1
0
0
1
1
2
0
2
7
1
1
1
1
1
1
1
1
0
1
2
2
1
3
1
0
0
0
0
1
1
0
1
2
0
0
0
1
0
1
0
1
2
1
2
1
1
2
1
1
1
0
0
0
1
2
0
1
0
2
2
5
1
0
1
0
0
2
0
1
0
1
0
0
0
1
0
1
0
0
2
2
0
1
2
0
1
2
0
1
0
0
1
1
1
0
1
1
1
0
0
0
0
1
2
2
1
0
1
3
0
1
0
1
1
1
0
3
3
0
2
2
0
2
0
0
1
2
1
0
0
1
0
0
1
0
0
1
2
0
0
1
0
1
4
1
2
2
0
1
10
2
1
2
0
1
1
1
1
1
1
1
1
1
1
0
0
2
1
1
0
2
2
0
2
1
0
0
1
0
0
0
0
1
2
1
0
2
1
1
0
2
1
0
0
0
0
1
0
1
2
0
0
2
0
0
0
1
1
1
3
1
0
0
0
1
1
2
0
1
1
2
0
1
0
1
2
1
1
0
1
0
1
0
0
0
1
1
0
0
1
1
1
0
0
2
1
2
0
1
1
1
1
0
1
0
0
1
2
0
1
1
0
2
1
0
0
0
1
0
1
1
0
2
1
2
0
1
1
0
0
0
0
0
1
1
0
1
1
1
1
1
0
1
0
1
0
0
1
0
1
0
0
1
0
2
0
0
1
0
0
0
0
2
1
1
1
1
1
1
1
0
0
0
1
1
2
0
1
2
1
0
0
1
1
1
2
2
1
0
1
2
1
1
2
2
2
0
0
0
0
2
0
0
0
1
1
1
0
0
1
0
0
1
0
2
2
1
0
1
2
2
1
2
0
1
1
0
0
2
0
1
1
0
0
2
1
0
0
1
0
0
1
0
0
2
0
2
2
0
1
1
0
1
2
0
0
1
1
1
1
1
2
1
0
2
2
0
1
1
2
2
0
1
2
1
1
1
1
2
1
0
0
2
2
1
1
0
3
2
0
1
0
1
2
2
2
1
0
2
0
1
2
2
1
0
2
1
1
1
1
0
2
1
0
2
2
1
2
0
1
2
0
0
1
0
0
0
1
2
0
1
2
0
1
2
1
0
0
0
1
0
1
0
1
2
1
1
1
0
0
2
1
1
2
1
1
1
0
0
0
0
0
0
1
1
1
1
2
1
0
1
2
0
0
0
1
2
0
0
1
1
1
0
1
1
0
1
0
0
1
0
0
1
0
1
2
0
1
1
1
3
0
1
0
1
1
3
1
0
0
2
0
1
0
0
0
1
1
0
0
1
0
0
0
0
2
2
1
4
0
1
0
1
1
1
0
2
2
0
0
0
1
0
2
2
0
1
0
0
1
2
1
2
0
2
1
1
0
0
1
0
1
1
0
0
1
1
2
0
0
0
2
1
0
2
1
2
0
2
0
0
0
0
0
2
0
3
1
0
0
1
0
3
0
1
0
1
2
4
0
1
2
0
0
1
2
1
0
0
0
0
1
0
1
1
1
1
0
1
0
1
0
1
1
1
2
0
1
1
1
0
1
1
1
0
1
2
1
2
3
2
3
2
1
1
0
1
1
2
1
2
2
3
0
1
2
0
2
0
2
1
1
2
1
1
0
1
0
0
0
1
1
0
0
0
1
0
1
0
0
1
2
1
0
1
1
0
2
0
1
1
1
2
1
0
2
0
0
2
1
1
1
1
1
2
1
2
2
0
1
0
2
1
0
1
0
1
1
2
1
1
1
1
0
1
0
0
2
1
1
2
1
0
2
1
1
2
0
1
2
1
2
0
2
0
1
0
1
0
0
2
2
2
1
2
1
1
0
1
1
0
0
1
0
1
2
2
0
1
1
0
1
1
1
0
0
2
1
1
2
2
1
0
0
1
1
2
0
1
2
1
0
1
0
1
0
2
1
0
2
1
0
2
0
0
1
0
3
0
2
2
1
1
0
1
2
2
0
0
1
2
0
0
0
0
1
0
1
0
0
1
2
1
2
0
0
0
0
1
2
1
0
2
1
0
1
1
0
0
2
0
1
0
0
1
0
0
2
1
2
2
2
1
2
2
0
1
1
0
0
0
1
1
1
1
1
2
1
2
1
0
1
0
2
0
1
1
1
0
1
2
2
1
2
1
2
0
0
1
1
1
2
0
2
0
1
1
1
0
0
0
1
0
1
0
1
1
0
2
1
1
0
0
1
2
1
2
2
1
0
0
1
0
1
2
0
1
0
0
1
2
1
1
0
0
2
1
0
2
1
1
3
2
0
2
1
2
1
2
0
1
1
0
1
1
1
1
0
0
1
0
2
1
1
0
1
0
0
1
0
1
0
0
1
1
2
1
1
2
0
0
3
0
0
2
2
2
2
1
0
1
0
2
1
0
0
1
0
0
2
0
0
0
0
2
1
1
0
0
0
1
0
1
1
1
0
0
2
1
1
2
0
1
0
1
0
1
0
0
1
0
0
1
2
3
1
0
2
1
0
2
2
0
0
0
1
0
0
0
2
1
0
0
1
2
1
1
0
1
0
1
2
0
2
1
0
1
1
0
2
2
0
1
0
0
1
2
1
1
2
0
0
0
0
1
0
2
0
1
0
1
1
1
1
2
0
1
2
2
0
1
2
0
1
0
1
0
2
0
2
1
2
1
1
0
1
1
1
1
0
1
0
1
0
2
1
1
1
0
2
1
1
1
1
1
1
2
1
1
1
1
1
2
1
1
2
0
0
2
0
0
2
0
0
2
1
1
1
1
1
0
2
1
2
0
3
1
0
1
0
0
2
1
1
0
0
0
0
1
1
1
0
0
1
2
4
1
0
0
2
1
0
1
1
0
3
0
1
0
2
1
0
0
0
2
0
0
0
0
1
2
2
0
2
2
0
1
1
2
2
1
0
0
0
0
0
1
0
2
0
1
2
0
0
1
2
2
0
2
1
2
0
0
1
1
0
1
0
1
0
1
1
1
1
0
1
2
2
2
0
1
2
0
3
1
0
1
2
0
2
1
1
2
0
1
2
1
2
0
1
0
0
1
1
2
0
2
0
1
1
0
0
0
0
0
2
1
1
0
0
1
1
0
1
2
0
0
0
0
2
2
0
0
0
0
0
0
0
1
1
1
2
0
1
0
2
1
0
0
2
0
0
0
0
0
1
1
0
0
1
1
1
1
2
2
1
0
0
0
1
0
1
0
3
1
0
1
0
0
1
2
0
1
0
1
0
1
0
2
9
1
2
2
2
1
0
1
2
2
1
2
1
0
2
0
0
0
0
1
1
1
1
1
1
1
1
1
0
0
2
1
0
0
1
0
2
1
2
0
0
0
1
0
1
1
0
1
1
1
0
0
1
1
0
1
2
1
0
0
1
0
1
0
1
1
0
0
0
1
2
0
0
1
0
2
2
1
1
2
1
1
1
1
1
1
1
1
0
2
1
1
2
0
0
1
0
0
2
2
0
0
1
0
0
0
2
1
2
2
2
1
1
1
1
1
1
1
0
0
0
1
1
0
2
1
2
0
1
1
1
2
1
3
1
1
1
1
2
2
1
0
1
2
2
1
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
1
2
2
1
2
0
2
0
0
1
0
0
2
5
2
2
1
0
1
0
2
3
0
1
1
2
1
0
2
1
0
0
2
1
1
1
2
2
0
2
1
1
1
1
1
0
1
2
2
0
2
2
2
1
1
1
0
0
1
1
1
2
1
0
0
1
1
1
0
0
2
1
0
2
2
0
1
1
2
1
0
2
0
0
2
0
0
0
2
0
1
2
1
1
0
0
2
0
2
1
0
1
1
0
0
0
1
2
2
2
1
2
0
1
1
1
2
2
1
0
0
0
0
0
0
0
2
0
0
1
0
1
0
1
1
1
0
0
1
1
0
1
2
1
1
1
0
2
2
1
1
0
0
1
2
1
1
1
0
1
1
0
0
0
2
1
0
0
0
2
0
1
2
1
2
0
2
2
0
1
0
0
2
1
1
0
0
1
0
1
1
0
1
1
2
1
1
0
0
1
2
0
1
0
1
1
1
2
0
1
2
0
1
2
1
0
1
2
2
2
1
0
1
0
1
2
1
2
0
1
1
1
2
0
1
1
0
1
2
0
1
2
0
1
1
2
0
0
0
1
2
1
1
1
2
1
1
2
1
0
1
2
2
0
1
1
2
2
2
0
2
0
2
1
0
0
0
1
0
1
0
0
1
0
1
1
0
0
0
2
3
0
0
1
1
0
0
1
2
0
2
0
1
2
3
1
0
0
1
0
2
1
0
1
1
2
1
1
0
0
1
1
1
1
2
0
0
0
1
0
2
1
2
0
1
2
2
2
2
0
0
1
0
2
1
0
0
0
2
1
0
1
0
0
0
2
1
0
0
1
0
1
0
1
1
0
2
1
1
1
1
0
0
1
0
0
1
2
0
1
0
0
0
0
0
1
0
0
1
1
1
1
1
2
1
1
1
2
2
1
1
0
1
0
1
0
1
2
0
1
0
1
0
2
1
1
1
0
0
0
1
1
0
0
1
2
1
1
0
1
1
1
1
0
0
0
0
0
2
1
0
2
1
0
0
1
0
1
3
1
0
0
0
0
2
1
1
0
0
0
0
1
2
0
0
0
2
1
1
0
0
0
0
1
1
0
0
0
1
0
1
0
1
0
0
1
2
2
2
0
1
1
1
1
1
0
2
1
1
1
3
1
0
1
1
1
0
0
2
1
1
0
1
2
0
2
0
0
0
1
0
1
1
1
1
1
1
1
1
0
0
2
2
1
1
0
1
2
1
0
1
2
0
1
2
0
1
1
1
1
1
1
1
1
0
1
1
1
1
0
1
2
2
1
2
0
0
1
0
1
1
0
0
0
2
0
2
1
1
0
0
3
1
0
0
1
1
4
2
0
2
0
1
1
2
1
0
0
1
1
0
3
0
1
3
0
1
1
1
1
0
1
0
0
2
1
1
1
0
2
0
1
0
1
0
0
2
1
2
1
2
1
1
2
1
1
3
2
0
1
0
2
0
0
1
0
1
1
2
0
1
0
1
0
1
2
1
1
2
0
0
1
1
0
1
1
0
1
1
1
1
1
2
0
0
0
1
0
0
1
1
1
0
2
1
1
1
1
1
1
0
2
0
2
2
1
1
1
2
0
1
1
0
0
0
1
2
0
0
1
2
1
2
0
2
1
0
0
2
1
2
0
0
0
0
1
1
1
1
2
0
0
1
1
1
1
3
1
0
2
1
0
0
1
1
0
0
2
1
0
2
0
1
0
2
2
0
0
2
0
1
1
1
0
0
2
0
1
1
1
1
1
1
0
1
1
1
0
1
1
2
1
0
2
1
0
0
0
2
2
2
0
0
0
1
1
1
1
0
1
0
1
2
2
1
1
1
1
1
1
1
2
2
1
1
0
0
2
1
1
1
0
0
0
0
1
0
1
0
0
2
2
0
1
1
0
1
1
2
0
2
0
0
1
0
0
0
2
1
2
0
2
1
0
0
1
1
1
1
0
1
1
1
1
0
0
1
1
1
1
1
1
1
0
2
2
1
1
1
0
1
2
1
2
2
1
1
2
0
0
0
1
2
0
1
1
1
2
0
0
1
2
1
1
1
2
1
0
2
1
2
0
1
0
0
0
0
0
0
2
1
0
0
1
0
1
1
0
1
0
0
0
1
2
1
1
1
2
1
0
2
1
1
2
0
0
0
1
2
1
0
1
2
1
0
2
1
1
2
2
0
2
0
2
1
1
0
3
0
0
0
3
0
1
0
2
1
1
0
0
3
0
1
1
0
1
2
0
0
1
1
0
0
0
0
0
1
2
0
0
1
2
1
1
1
1
2
1
2
2
0
2
1
0
0
0
0
0
0
2
0
1
1
1
1
1
1
0
1
1
2
0
1
1
0
1
1
1
1
2
2
1
1
2
0
0
0
2
2
1
1
0
0
3
2
0
1
1
1
0
1
1
1
1
1
4
1
0
1
1
0
0
0
2
0
2
1
2
1
1
0
2
0
0
0
2
2
2
1
1
1
0
1
0
1
3
3
2
1
0
2
0
0
0
0
2
0
0
0
1
1
0
0
0
0
1
0
0
2
2
0
1
0
0
1
0
2
0
1
0
0
0
1
0
2
0
1
1
1
0
1
3
0
1
1
1
0
2
0
1
2
1
1
2
1
0
1
0
0
3
0
1
0
3
0
0
2
2
1
2
2
1
0
2
0
0
1
1
0
1
1
1
0
1
1
0
1
0
0
2
0
0
1
2
0
0
0
1
1
0
1
0
2
2
1
0
2
2
1
1
2
1
1
1
2
2
3
0
1
1
1
0
0
0
1
1
0
1
0
0
1
0
1
1
0
1
1
0
1
0
2
0
1
0
1
1
0
0
2
1
0
1
0
1
1
1
0
1
1
1
1
2
1
1
0
2
0
1
2
1
0
0
1
2
1
1
0
1
2
0
2
0
2
1
0
0
2
1
1
2
1
2
0
1
1
2
0
1
1
0
0
1
2
1
0
0
1
0
2
1
1
1
0
2
2
0
2
0
1
1
2
1
1
0
2
0
0
0
1
1
0
1
1
2
0
0
0
0
0
3
0
1
1
1
2
1
1
1
1
0
1
0
2
0
0
0
0
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
2
1
1
1
0
1
2
0
2
1
1
1
0
1
0
1
2
5
1
0
2
0
1
1
0
1
1
1
1
1
0
1
0
1
0
2
0
2
1
2
0
0
0
1
1
2
1
0
2
2
1
1
0
1
1
0
0
0
0
1
0
0
0
2
0
0
0
1
1
0
1
0
1
0
0
1
1
0
0
0
1
0
1
0
0
2
0
0
1
1
2
1
1
2
0
1
0
0
1
2
1
2
2
0
0
2
2
2
1
1
1
1
1
0
1
0
2
0
1
0
0
0
1
1
1
1
1
1
0
0
0
1
2
1
0
3
0
0
1
2
0
2
1
1
0
0
0
1
2
1
1
2
0
0
2
0
1
1
0
1
1
0
2
3
1
1
1
4
2
0
0
0
1
1
1
1
0
1
0
0
1
1
0
0
1
1
0
0
2
1
1
1
1
2
0
1
2
0
0
3
1
0
3
0
1
2
0
2
1
2
1
2
1
2
1
0
0
0
1
1
1
1
2
2
1
1
2
2
1
1
0
1
1
1
1
0
2
1
0
0
0
2
1
1
1
1
1
1
1
0
1
0
1
1
0
2
1
2
1
1
0
2
1
1
2
1
1
1
0
0
0
1
0
0
1
0
1
1
1
0
2
0
1
0
1
1
1
0
0
0
0
1
0
1
1
2
1
1
1
0
0
1
1
1
1
0
2
2
6
0
1
1
0
2
0
2
0
1
3
2
1
0
0
0
0
0
2
0
1
1
2
2
1
2
0
1
2
1
0
1
1
1
2
1
2
0
1
1
2
0
1
1
1
0
1
0
1
0
2
1
0
0
1
1
1
0
1
0
0
1
0
0
1
0
1
1
1
1
0
0
1
0
2
1
0
0
2
0
0
2
2
0
2
2
0
0
0
0
2
1
1
0
1
0
2
0
1
1
2
0
1
0
1
0
2
0
2
2
0
0
0
0
2
0
1
1
1
1
0
1
2
1
0
1
1
0
0
0
1
1
1
1
2
1
2
0
1
3
0
2
1
1
2
1
0
2
0
2
2
2
1
1
2
1
2
1
2
1
0
1
2
1
0
0
0
1
2
1
2
2
1
2
0
0
2
1
1
1
0
2
1
1
2
0
1
0
2
1
0
0
1
2
1
0
1
1
1
2
0
2
1
2
1
0
1
0
2
1
0
2
1
1
1
2
1
1
0
0
1
0
1
1
1
1
1
1
1
0
0
0
0
0
1
1
1
0
2
0
2
2
1
0
1
1
1
0
2
0
1
0
1
0
1
0
0
1
1
2
0
0
2
0
1
0
0
0
1
1
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
1
1
0
1
1
0
2
16
0
1
0
2
0
0
1
1
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
2
1
1
0
2
0
0
0
1
1
1
1
0
2
2
0
0
1
2
0
2
0
0
0
1
1
2
0
1
1
0
1
2
1
1
2
2
1
0
0
0
0
0
2
0
1
2
2
0
0
1
0
0
0
1
1
1
1
0
2
2
0
0
0
1
0
0
1
2
2
2
0
1
1
0
0
1
1
0
3
2
0
1
0
1
0
0
1
2
1
0
1
0
0
1
0
1
1
1
2
1
1
1
2
2
0
2
0
0
0
0
1
0
2
0
0
0
1
0
0
0
2
1
0
2
0
1
1
2
0
0
0
0
2
1
1
2
0
0
2
1
1
0
2
1
0
0
2
1
1
0
0
1
0
1
0
0
0
1
1
2
2
0
1
1
1
0
2
1
1
1
1
0
1
1
2
0
0
2
2
3
0
2
2
2
0
0
1
1
0
1
1
2
0
2
1
0
2
1
2
0
2
1
0
1
2
2
1
2
2
1
2
1
1
1
1
0
1
0
1
1
2
1
1
3
0
0
1
0
0
0
0
1
1
2
2
1
0
2
1
1
1
0
0
0
2
0
1
1
1
1
1
0
1
2
0
2
0
1
1
1
1
1
0
1
1
2
1
1
3
2
0
0
1
1
1
0
2
1
1
1
1
0
1
1
1
0
0
2
1
0
1
0
0
1
0
0
1
1
0
1
1
1
1
0
0
0
0
0
2
0
2
1
1
1
2
2
1
1
0
1
1
1
0
0
0
0
0
0
0
2
2
2
0
2
1
1
0
1
1
1
1
1
1
2
0
1
1
1
0
0
0
1
1
2
1
1
0
1
0
1
2
0
1
1
1
1
1
0
0
1
0
1
0
2
2
0
1
1
1
0
1
1
0
1
1
0
0
2
0
1
1
2
0
2
0
2
0
1
1
2
1
0
0
1
1
1
1
1
1
0
0
2
1
0
0
1
0
2
2
1
0
0
0
0
0
1
1
0
1
0
1
1
0
1
4
1
0
1
0
1
2
0
0
2
1
2
1
2
2
1
0
1
1
0
1
2
0
0
1
1
1
0
0
0
3
1
0
1
1
1
3
0
2
2
1
1
0
0
1
2
0
2
1
2
1
2
2
1
1
0
1
0
0
2
0
0
1
1
0
0
0
1
1
1
0
0
1
0
1
2
2
1
1
0
1
3
0
0
0
2
1
1
0
0
0
2
0
1
1
0
2
0
0
1
1
2
0
0
1
0
1
1
2
1
1
1
0
1
2
0
1
1
1
1
0
1
0
0
1
1
2
0
1
0
1
2
0
1
1
1
1
0
0
1
1
0
0
2
2
1
2
3
0
0
1
1
2
1
1
1
1
2
0
0
1
0
0
0
1
0
2
2
1
0
1
1
1
0
0
0
0
1
1
0
1
2
0
1
1
2
1
1
0
1
2
1
1
0
1
2
2
2
1
0
0
1
2
2
0
1
0
0
0
1
2
0
1
1
0
1
1
1
0
1
1
1
0
2
1
0
2
2
2
1
1
1
1
1
0
0
0
2
2
0
2
0
0
2
1
0
2
1
2
0
1
0
1
0
1
0
2
1
0
0
1
0
2
0
1
1
0
0
1
1
0
2
0
1
1
1
1
0
0
0
0
1
1
0
1
0
2
1
0
1
1
0
0
1
2
1
1
2
1
5
1
1
1
1
1
16
0
1
2
1
1
0
0
0
0
0
0
2
2
1
1
0
2
6
1
0
2
1
0
2
2
2
2
0
1
1
1
1
0
1
2
0
1
0
2
2
2
0
2
0
1
1
0
1
0
2
0
2
2
1
0
1
2
1
1
0
1
2
1
0
1
1
1
0
2
0
1
1
2
1
0
1
1
1
1
1
1
0
1
0
0
1
0
1
0
1
3
1
2
1
0
0
1
1
2
1
0
0
1
1
1
1
2
2
3
0
1
0
1
2
0
0
0
1
2
2
1
0
1
1
0
2
0
2
1
1
0
1
1
1
2
2
1
0
0
2
2
0
0
2
0
1
0
1
2
0
0
2
2
1
0
2
0
1
0
0
0
0
0
2
2
0
1
0
0
2
0
1
1
0
0
0
1
0
2
2
1
1
2
2
1
1
1
1
2
1
2
1
2
1
1
1
1
1
0
0
0
1
1
0
0
2
0
0
0
1
1
1
1
2
0
0
0
1
1
1
0
1
1
1
0
0
2
0
1
1
1
1
1
1
0
1
2
0
2
0
1
1
1
1
1
1
0
2
1
1
1
1
1
1
0
0
1
1
0
1
0
0
1
2
0
2
2
0
0
2
0
0
1
1
1
1
0
1
2
1
1
0
2
0
0
4
1
2
0
2
0
2
2
0
0
1
0
0
0
2
0
2
2
2
2
0
2
2
0
1
1
0
1
0
1
2
2
0
0
0
2
2
2
0
0
1
0
1
1
1
1
1
1
1
1
1
1
0
1
0
0
2
0
1
1
2
0
0
2
2
0
0
0
1
2
0
2
2
1
1
1
1
1
1
1
1
2
1
2
0
1
1
1
0
3
0
1
0
1
0
1
2
0
0
2
1
2
1
0
0
0
0
1
2
1
2
0
3
2
0
0
0
1
2
1
0
1
1
2
1
0
0
0
0
1
0
0
0
1
0
1
1
1
1
2
1
1
2
2
1
0
2
1
0
1
2
1
0
2
1
2
2
1
1
0
1
2
0
0
2
1
0
1
0
0
2
1
1
0
0
0
0
0
4
0
0
3
2
2
1
0
0
1
2
2
1
1
0
1
2
1
1
0
0
1
0
2
1
1
2
1
1
1
0
0
0
2
0
1
0
1
0
1
0
3
0
1
2
1
0
0
0
0
2
0
2
1
2
2
2
1
1
0
2
1
1
1
0
1
1
0
1
1
2
0
2
0
2
1
0
1
0
2
2
1
1
2
2
2
2
1
2
1
0
0
1
2
1
1
2
1
2
1
2
0
0
0
1
1
0
1
1
2
2
0
1
1
1
1
1
1
0
1
2
1
0
0
2
0
2
1
1
1
1
0
0
1
0
1
0
0
1
0
0
1
2
2
1
1
0
1
1
1
1
0
0
0
0
2
0
1
3
0
2
1
0
2
3
1
1
1
0
2
1
1
1
0
2
0
1
0
0
2
0
2
2
2
2
1
1
1
1
0
0
2
0
1
1
3
0
1
1
0
0
0
2
1
1
1
1
1
0
0
1
0
2
2
0
0
0
1
1
1
0
0
2
3
0
2
0
2
1
2
2
1
2
0
0
1
1
0
1
1
1
0
1
1
1
1
1
0
2
2
2
1
1
2
1
2
0
0
0
0
0
1
1
1
1
1
2
1
1
1
1
1
2
1
1
1
0
1
0
1
2
0
0
1
0
0
1
2
0
1
0
1
0
0
2
0
1
1
2
1
2
0
0
1
1
1
2
0
0
1
1
0
1
1
1
0
0
1
1
2
0
0
2
1
0
0
2
0
1
1
2
1
0
1
0
2
0
1
1
0
1
1
0
2
1
1
1
1
1
2
0
2
0
1
1
2
0
0
2
1
1
2
2
2
1
1
0
2
0
0
2
0
1
1
0
1
0
1
1
1
1
0
0
2
2
2
1
2
1
1
0
5
2
0
2
0
0
2
0
0
0
0
2
2
0
2
1
1
1
1
1
2
1
2
1
2
0
1
2
1
0
1
1
3
2
0
0
1
2
0
1
2
1
0
2
0
1
1
2
1
0
2
1
1
0
0
0
1
2
1
2
0
1
0
1
2
0
0
0
0
0
2
0
0
0
0
0
1
2
0
1
1
0
2
0
2
1
1
1
1
1
0
1
1
1
1
0
0
0
1
1
1
2
1
0
0
0
1
0
1
1
1
1
0
1
0
1
1
2
0
2
2
0
2
1
1
2
1
0
2
2
2
1
0
0
2
1
0
1
1
0
0
0
1
0
1
2
0
0
0
2
1
1
0
1
0
0
0
1
0
2
2
1
1
0
1
1
1
0
1
0
1
2
0
1
1
0
0
2
1
0
2
1
0
2
1
0
2
1
0
2
0
0
1
0
2
0
2
2
2
0
0
1
0
0
0
2
2
0
0
1
1
0
0
1
2
0
2
0
0
0
0
2
0
1
2
1
1
0
0
0
2
0
1
0
0
1
1
1
1
1
1
0
1
0
0
0
0
0
1
2
1
2
1
1
2
0
0
1
0
1
2
1
3
0
1
0
1
1
0
1
1
0
2
1
2
2
1
1
0
1
0
1
0
0
2
1
1
0
0
0
0
0
2
1
0
1
0
0
1
1
2
0
2
2
0
1
1
1
2
1
0
2
1
1
1
0
0
2
1
3
0
2
1
0
1
0
1
0
1
0
2
0
2
2
2
0
0
1
0
1
2
1
2
2
2
1
2
1
2
2
1
2
1
0
1
0
2
0
1
2
0
1
0
1
2
0
0
1
0
1
0
1
0
2
0
2
1
0
1
0
1
1
2
0
1
0
2
1
2
2
1
1
1
1
1
0
2
0
1
1
0
0
1
1
1
2
0
0
0
1
1
1
1
0
1
3
1
1
0
1
0
1
2
0
2
2
1
2
0
3
1
1
2
0
1
1
2
0
0
0
1
2
0
1
1
0
2
0
0
1
0
1
1
2
2
0
2
1
3
0
0
0
0
0
1
1
2
1
2
1
1
1
0
2
1
0
0
1
0
2
0
0
2
1
0
2
0
0
0
0
0
1
0
0
2
2
1
1
0
1
1
2
3
1
0
2
1
1
0
0
2
1
0
1
1
2
2
1
0
0
1
1
0
2
0
1
2
0
1
0
2
0
2
0
0
0
2
2
1
1
1
0
0
0
1
0
0
0
1
0
2
1
1
2
2
1
0
1
1
0
0
1
0
1
0
0
3
3
1
1
1
2
0
2
1
0
1
2
1
2
0
0
3
1
1
0
0
0
1
2
0
0
0
0
1
0
0
1
2
1
1
1
1
2
0
0
4
1
0
1
2
1
0
0
1
1
0
1
0
1
2
1
0
2
0
1
0
0
1
2
2
1
1
2
1
1
2
1
2
0
2
2
0
0
1
0
1
0
1
1
1
1
0
1
1
0
0
2
0
1
1
0
3
2
0
2
2
2
2
1
1
1
1
1
1
2
1
0
3
1
1
2
1
1
0
0
1
0
0
1
1
0
1
1
2
0
1
0
2
0
2
0
1
1
1
2
1
0
1
2
0
1
2
1
0
2
0
1
1
1
1
2
2
4
1
0
1
0
1
1
0
2
1
0
2
1
0
0
1
1
1
0
0
1
1
1
1
0
0
0
1
0
2
1
2
0
0
0
1
1
0
1
0
1
3
0
0
2
1
1
1
0
1
1
0
0
2
0
0
0
1
0
1
0
1
0
1
1
0
1
2
1
1
2
2
2
1
0
2
0
1
1
1
2
2
0
0
1
2
0
3
1
1
1
0
0
1
1
2
2
0
2
0
0
0
1
0
1
2
0
1
0
2
0
2
1
0
0
3
0
1
1
2
1
1
0
0
0
2
1
4
1
1
1
1
2
1
2
0
1
1
1
1
2
1
0
2
1
0
0
1
0
1
0
2
0
0
0
0
1
0
1
1
0
2
0
1
1
0
1
0
0
0
1
1
1
2
0
0
1
0
0
1
1
1
0
1
0
0
2
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
2
1
1
0
0
1
0
2
2
0
0
1
2
2
0
2
0
1
0
0
2
0
1
1
1
0
1
2
1
2
0
1
1
1
1
1
2
0
0
2
2
1
0
2
1
2
2
1
0
1
0
1
0
1
1
0
1
2
0
2
2
1
1
1
0
0
2
1
1
2
1
0
0
1
1
2
2
0
0
1
2
0
1
2
1
1
0
0
0
1
0
1
2
1
2
1
0
1
0
0
0
0
2
1
0
1
2
0
1
0
2
0
1
1
0
1
2
2
2
1
1
2
2
4
0
1
2
0
1
2
1
1
2
2
0
0
1
0
0
1
1
0
2
2
1
2
2
1
0
2
1
2
0
1
0
1
1
1
1
2
0
2
1
1
2
1
1
0
0
1
0
1
2
1
0
2
1
0
1
1
0
0
0
0
1
1
0
2
1
0
1
2
0
2
1
0
1
2
0
0
0
2
0
0
1
1
0
2
5
1
1
2
1
1
1
0
1
2
1
0
2
1
3
1
0
0
2
0
1
1
0
1
2
1
1
2
1
1
0
1
1
0
1
1
1
0
0
0
2
1
0
1
2
1
1
2
2
1
1
0
0
2
0
2
0
0
0
0
0
2
1
1
1
0
1
0
1
0
2
0
1
0
1
2
0
0
2
0
0
0
1
0
1
0
0
2
1
0
2
0
2
0
1
1
1
1
1
0
2
0
0
2
1
0
0
0
0
0
0
1
1
1
1
1
0
2
2
0
0
3
0
3
0
0
1
0
1
0
1
1
2
1
2
0
1
2
2
0
3
1
0
0
0
3
0
2
1
0
1
1
1
1
1
1
1
1
0
1
0
1
1
0
2
0
1
1
1
1
0
1
1
1
0
2
1
0
0
2
2
1
1
1
2
2
1
1
2
0
2
0
0
2
2
0
1
0
2
1
1
0
2
1
3
1
0
2
1
0
0
1
1
0
0
1
0
1
0
0
0
0
1
0
1
3
1
2
1
0
1
0
0
1
1
0
1
1
0
2
2
1
1
1
2
1
1
1
1
1
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
2
2
1
1
0
0
0
1
0
1
2
2
1
1
1
1
2
1
1
1
2
1
0
1
2
0
2
1
2
1
2
1
0
0
0
4
1
1
0
1
0
1
1
2
1
1
2
1
1
0
0
1
0
4
0
1
0
0
2
1
0
0
0
1
1
0
0
2
2
0
1
0
0
2
0
2
1
0
1
0
1
1
0
1
0
0
1
0
1
2
2
1
0
0
1
2
1
1
1
0
2
2
1
2
0
1
0
1
2
1
0
1
0
1
0
2
0
1
1
0
0
0
1
0
1
1
0
2
2
1
0
1
1
1
0
0
0
0
1
0
0
0
1
1
0
2
1
0
2
1
0
2
1
0
0
2
2
0
0
1
2
1
0
0
2
1
0
0
1
0
0
3
2
0
1
1
1
0
1
0
2
0
0
0
2
2
0
1
2
0
0
0
0
1
1
1
1
1
0
0
2
1
1
2
1
0
1
2
0
2
2
1
1
2
0
2
1
0
0
1
2
0
1
0
0
0
2
1
1
1
1
0
0
0
0
1
1
0
1
2
0
1
0
2
1
1
0
2
2
0
0
2
0
1
2
0
0
0
1
1
0
0
0
1
1
0
1
2
0
0
0
2
0
0
0
0
1
1
2
0
0
2
2
0
0
0
2
0
1
0
2
0
2
0
1
0
1
0
0
0
2
1
2
2
0
0
1
0
1
2
0
1
0
2
2
0
1
0
0
0
0
1
2
0
1
0
0
1
2
2
0
0
2
2
0
1
2
2
1
0
0
1
3
1
0
0
1
0
0
0
0
0
1
2
2
0
1
1
3
0
1
1
1
0
0
0
3
1
0
1
1
1
1
1
1
0
10
1
0
1
0
0
1
1
0
0
1
1
2
1
1
1
0
2
1
1
0
1
1
2
1
2
0
2
2
1
2
1
1
0
0
0
1
0
1
1
0
0
1
0
1
0
1
1
1
1
1
1
2
1
0
0
1
1
0
1
1
1
2
1
2
1
1
0
0
1
2
1
0
1
1
0
1
2
0
0
1
0
0
2
1
0
0
1
1
2
1
1
0
0
0
1
1
0
0
0
0
1
2
0
0
1
2
2
1
1
1
2
2
2
1
0
1
2
1
2
0
0
0
1
0
1
1
0
1
1
0
2
0
1
0
0
1
1
1
1
0
1
1
1
1
0
1
1
1
2
2
1
2
1
0
1
0
3
1
0
1
0
2
2
0
1
1
2
2
2
0
0
2
1
0
0
0
1
0
1
2
1
1
0
0
0
1
2
0
0
2
1
2
1
2
1
1
2
1
1
2
0
1
2
0
1
1
0
0
2
0
2
1
1
3
1
0
0
2
2
1
0
1
1
2
1
0
2
1
1
2
1
0
1
1
0
0
2
2
1
1
0
1
0
2
2
1
1
1
1
2
0
0
2
0
2
0
2
0
0
1
2
0
2
1
2
1
2
1
1
2
0
0
0
2
0
1
2
0
2
0
2
2
0
1
2
0
0
0
2
0
0
0
0
1
2
0
2
1
2
0
2
0
2
0
0
1
1
0
4
2
0
2
0
4
0
9
1
2
1
1
0
1
1
2
1
1
1
2
0
0
2
1
2
1
2
1
2
0
2
0
0
0
0
1
1
1
1
0
2
1
1
1
1
0
1
0
4
0
2
2
1
5
0
1
1
0
1
0
0
2
1
0
1
1
1
2
1
2
2
0
1
2
0
0
1
2
1
1
2
1
0
1
2
0
1
0
2
0
0
1
1
2
0
0
0
2
0
0
0
0
1
1
1
4
0
1
0
0
0
0
1
1
2
0
0
2
2
0
1
1
2
1
0
0
1
0
2
0
0
1
1
1
1
0
1
0
0
0
0
0
2
2
1
1
0
1
1
2
2
0
1
2
0
1
0
2
1
1
2
0
0
0
1
1
0
2
1
0
2
1
0
1
0
1
1
0
2
1
0
1
1
2
0
0
1
1
0
0
0
1
1
1
0
0
0
1
1
2
1
2
1
1
1
0
2
0
3
1
1
3
0
0
2
0
0
2
2
2
1
1
1
1
0
1
1
1
0
1
1
1
1
1
1
1
0
1
1
2
1
1
1
1
1
0
2
0
0
0
0
0
1
1
0
0
0
3
0
1
1
2
1
0
2
1
0
2
1
0
2
1
2
0
1
1
0
0
1
0
1
1
0
0
1
4
1
0
0
0
1
0
1
1
1
2
0
1
1
1
1
1
1
1
0
1
1
1
1
0
1
1
1
0
1
0
1
0
1
2
2
2
0
1
0
0
1
0
0
2
1
0
0
0
2
2
0
0
1
2
0
1
1
1
1
1
1
2
1
1
2
1
1
0
1
1
2
0
1
0
2
1
0
0
0
2
1
4
1
2
1
1
1
2
0
1
1
1
0
1
0
2
2
1
0
0
0
0
2
1
1
1
0
0
0
1
0
2
1
0
1
0
2
1
2
1
0
1
1
1
2
0
0
1
1
0
2
2
1
3
0
0
0
0
2
2
1
2
0
0
0
1
2
1
2
2
0
0
1
0
2
1
0
1
1
1
1
1
2
1
2
1
0
1
2
1
0
0
1
1
2
0
0
0
0
2
1
3
0
1
1
0
1
1
0
0
1
2
1
2
0
2
1
0
1
1
1
1
1
0
1
1
0
1
0
1
0
1
0
1
0
2
2
0
2
0
1
2
0
2
0
2
1
0
0
0
1
1
1
0
1
2
0
1
0
1
2
0
1
1
1
1
1
1
1
1
1
2
2
1
1
1
1
2
0
1
2
2
1
0
1
0
0
0
1
0
1
1
0
2
1
1
2
1
0
1
0
0
1
1
2
0
2
0
1
2
1
0
1
0
0
1
0
1
1
2
0
1
2
1
0
0
0
0
0
1
1
0
0
1
2
0
0
1
2
1
0
2
0
0
1
1
1
0
3
2
0
0
0
1
1
1
0
2
2
0
1
0
0
1
0
1
0
0
0
1
2
0
1
0
1
0
3
1
2
2
1
1
1
2
1
1
2
1
1
1
0
0
1
1
1
4
0
1
1
1
0
0
1
2
1
1
0
0
1
0
1
2
2
0
1
1
1
0
1
1
2
1
1
0
0
0
0
0
2
2
0
1
1
0
1
0
0
2
1
0
2
1
2
1
2
1
0
1
1
0
0
2
1
1
0
1
2
1
0
1
1
2
2
1
2
1
2
2
2
2
0
0
1
0
1
2
0
1
1
0
1
2
2
2
0
3
2
0
2
1
0
1
2
2
2
1
2
1
1
1
1
1
1
0
0
0
0
0
1
2
0
2
0
2
1
1
2
0
1
1
2
2
2
0
0
1
0
0
1
2
1
2
3
0
1
1
0
0
1
1
1
0
0
2
1
1
0
0
2
0
1
0
2
1
0
1
0
1
0
0
0
1
2
2
1
1
2
1
0
1
2
1
0
2
0
0
0
1
0
2
0
0
0
0
1
1
1
2
2
0
0
0
0
1
1
1
1
1
1
0
1
0
2
0
1
1
0
1
0
1
0
0
0
0
2
0
4
2
1
2
1
2
1
0
1
2
1
0
1
2
2
2
1
1
1
0
1
1
1
0
1
0
1
1
2
0
1
2
3
0
1
0
0
1
1
2
0
0
1
0
0
1
0
0
2
1
1
1
1
1
2
1
2
2
2
0
1
0
1
0
0
1
2
2
0
2
2
2
2
0
0
3
0
2
0
2
0
0
0
0
1
1
1
0
1
2
2
2
1
1
1
0
0
0
1
1
1
2
0
1
1
1
1
0
1
2
1
1
0
0
2
0
2
2
2
1
1
2
2
2
0
1
1
0
0
0
0
0
0
1
2
2
0
0
1
1
0
3
1
0
0
2
2
0
1
1
1
0
0
0
0
1
1
2
1
0
2
2
3
1
1
2
1
0
1
2
2
5
0
1
1
1
0
2
0
2
1
0
0
2
1
0
2
2
2
2
2
0
1
1
1
0
2
1
1
0
0
1
1
0
1
1
1
1
4
2
0
0
1
0
1
1
0
0
1
0
0
1
0
1
1
0
1
2
2
0
0
2
1
1
0
0
1
1
0
1
1
0
1
1
0
2
0
1
0
1
1
1
1
1
0
1
0
0
2
0
1
1
1
0
1
1
0
1
0
1
0
1
1
0
0
1
1
1
2
2
2
1
1
1
0
1
0
2
2
0
1
1
1
1
1
1
1
5
1
1
6
0
1
1
0
0
0
0
2
2
0
2
0
0
0
1
1
2
1
1
0
0
2
1
1
7
2
1
1
0
1
1
1
1
0
1
0
1
1
0
2
1
0
2
1
0
1
1
0
1
1
0
0
1
1
0
1
0
2
1
1
1
2
0
1
0
1
2
2
2
0
1
1
1
1
1
0
1
1
2
2
2
1
2
1
1
1
0
2
0
1
1
1
0
1
0
1
2
0
1
1
1
0
1
1
0
0
1
0
1
0
1
0
0
2
1
1
1
0
1
1
1
1
1
0
0
2
0
1
1
0
0
4
1
2
0
1
2
0
1
1
1
1
1
2
2
1
1
0
2
0
1
0
0
2
0
1
0
1
0
0
0
4
1
0
2
1
0
1
2
1
0
1
0
2
2
0
0
1
0
0
2
0
0
0
0
0
2
2
2
1
0
0
2
0
0
2
0
1
0
0
2
1
0
0
2
1
0
0
0
1
1
0
2
4
0
0
0
1
0
3
1
1
0
1
0
0
1
0
0
0
2
0
2
0
1
0
1
1
1
0
1
1
1
2
0
1
2
1
1
1
1
2
2
1
3
0
0
0
2
1
0
0
2
0
1
0
1
0
1
0
0
0
2
1
1
0
1
2
0
0
1
2
0
2
1
0
0
0
2
2
0
1
2
1
0
0
1
2
1
3
1
2
1
0
0
1
0
0
2
1
1
1
0
1
0
1
2
0
1
0
1
1
1
1
2
1
1
2
1
0
1
3
3
1
0
0
2
0
3
2
1
2
2
1
0
2
0
1
0
0
0
0
0
1
0
1
2
0
0
1
1
2
2
0
1
1
1
2
2
1
0
2
1
1
0
1
1
1
1
0
0
1
1
1
0
1
1
1
0
1
1
1
0
0
0
1
0
3
0
1
0
2
0
2
1
0
1
0
2
2
0
1
0
1
0
1
0
1
0
0
1
2
1
1
0
0
1
1
1
0
2
2
1
1
1
0
1
0
1
1
1
2
2
1
1
1
2
0
1
2
1
2
1
2
1
2
1
0
1
2
0
0
1
1
2
2
1
1
0
0
1
1
1
1
1
0
1
2
0
1
1
0
0
1
0
1
0
1
0
0
0
2
0
1
0
1
0
1
1
2
1
2
0
0
1
1
0
3
1
1
0
0
1
0
0
2
1
1
0
1
0
1
0
0
1
2
0
1
2
1
1
1
1
1
0
0
2
0
2
0
1
1
2
0
1
0
1
1
2
0
0
1
1
1
1
1
0
0
0
1
1
1
0
1
0
2
2
0
1
1
1
1
0
1
0
1
2
2
1
1
0
1
4
0
0
1
2
1
0
1
1
1
2
2
1
0
1
1
2
3
0
0
1
0
0
0
1
2
0
1
2
0
1
0
1
0
0
1
2
0
0
2
1
0
2
1
1
0
1
1
1
2
0
1
1
1
2
1
0
1
0
2
0
0
0
2
2
1
2
1
1
1
1
0
1
2
0
0
0
1
1
0
1
1
2
2
0
2
1
1
1
0
1
1
0
0
2
1
1
1
2
1
1
1
1
1
1
2
0
0
2
0
2
3
1
2
2
1
2
0
2
0
1
0
1
0
1
0
0
2
1
3
0
1
0
2
0
0
2
0
0
0
1
1
2
1
0
0
1
1
1
4
0
2
0
2
2
0
0
0
0
1
1
1
2
0
0
0
0
0
1
0
1
0
1
0
2
1
2
1
1
1
0
0
2
0
2
1
0
1
0
1
1
0
1
0
1
1
1
1
1
1
1
1
2
0
1
0
2
1
0
0
1
1
0
2
0
1
1
0
0
0
2
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
0
0
0
0
0
1
2
1
1
1
0
2
2
2
1
0
1
0
1
1
0
1
1
1
0
1
1
0
1
5
0
0
1
1
1
0
1
1
0
0
2
1
3
1
2
0
1
1
0
0
3
0
1
0
0
0
1
2
2
0
2
1
0
0
1
1
2
1
2
1
0
1
0
0
0
1
2
1
0
0
1
2
1
1
1
0
0
0
1
1
0
0
0
0
0
2
2
0
2
0
2
1
1
1
0
1
1
2
2
1
0
2
0
0
1
0
1
2
1
0
1
2
0
1
2
0
0
0
2
0
0
0
2
2
0
0
1
1
1
2
1
1
3
1
1
1
2
1
0
1
1
0
0
0
1
0
2
2
0
0
0
2
0
0
2
1
0
1
0
1
1
5
2
2
0
0
1
1
1
0
0
2
0
1
2
1
1
1
1
1
1
1
1
1
1
2
1
1
0
0
1
1
1
0
2
2
3
2
1
0
1
0
2
0
1
1
0
0
1
0
1
0
1
0
0
0
1
1
0
0
2
1
0
2
1
0
0
0
2
1
0
0
1
1
2
0
3
2
2
2
0
2
0
2
2
2
1
1
0
1
1
2
0
2
0
1
1
2
0
2
0
2
2
0
0
0
0
0
2
0
1
3
1
0
0
1
2
1
0
1
2
0
1
1
1
1
1
1
2
1
3
0
0
1
1
1
1
0
1
0
1
1
1
1
1
0
0
2
1
0
1
0
2
2
2
2
0
0
0
1
1
1
1
1
1
1
1
2
1
0
0
1
1
1
0
1
1
0
1
2
0
1
0
0
0
2
0
0
0
2
2
0
1
2
1
0
1
0
1
0
1
0
0
1
0
1
0
1
1
2
0
2
1
2
0
2
1
0
1
1
1
0
1
0
0
1
0
2
1
2
2
2
1
1
0
1
1
0
1
1
2
1
0
1
1
1
0
2
1
1
1
1
0
2
1
0
0
2
2
0
0
0
0
1
0
1
2
0
1
2
1
0
0
0
1
0
1
0
1
1
1
0
1
0
0
0
2
0
1
0
1
3
0
1
2
2
0
0
2
1
1
2
0
0
0
1
1
0
0
1
1
0
2
0
0
2
0
1
1
0
2
1
2
2
1
0
0
1
2
1
1
1
1
1
1
0
1
2
2
1
1
0
1
2
2
0
1
3
0
0
1
2
1
2
1
0
2
1
2
1
2
1
0
1
1
1
0
1
1
0
0
1
0
1
0
2
1
0
1
0
1
1
1
1
1
2
2
2
2
0
1
1
0
2
1
1
0
2
0
1
0
0
1
2
2
0
0
1
0
1
0
1
1
2
1
2
1
1
1
1
2
2
1
1
1
2
0
0
0
1
1
1
0
0
1
0
0
2
0
0
0
2
1
1
1
1
1
1
0
1
1
0
1
2
1
0
0
1
1
1
2
2
1
0
1
2
1
1
0
2
2
1
0
1
1
2
1
2
0
0
0
0
1
1
0
1
0
0
2
1
1
0
2
2
1
1
2
0
0
1
1
2
3
1
0
1
0
1
1
2
2
1
2
1
2
1
0
1
1
1
2
0
2
1
1
0
1
3
1
2
1
0
1
1
2
0
1
1
1
0
1
1
2
1
1
0
2
1
1
1
0
0
0
1
2
0
1
1
2
0
2
2
1
1
0
2
0
1
2
0
2
0
1
0
1
1
1
0
1
0
2
0
3
1
0
1
1
1
1
1
1
0
0
0
1
1
0
0
2
1
0
0
0
1
1
2
1
1
2
1
0
2
2
1
1
1
0
0
0
1
0
0
0
1
0
0
2
1
1
1
2
1
0
1
1
2
0
0
2
1
1
0
1
2
1
1
1
1
0
2
0
0
1
1
0
1
1
0
1
1
1
3
1
0
0
0
2
1
0
1
0
2
0
1
1
1
0
0
1
1
0
1
2
0
0
1
2
1
1
0
0
2
0
1
1
0
0
1
2
1
0
1
0
1
2
1
0
2
1
0
2
1
1
0
0
1
0
0
0
1
1
1
1
0
1
0
1
1
1
0
1
2
0
0
1
2
1
0
1
0
1
1
3
0
0
0
2
0
2
1
0
0
0
1
0
2
0
1
1
0
2
0
2
2
0
0
0
0
2
1
1
0
1
1
1
1
1
0
0
1
1
1
0
1
1
1
0
0
1
1
0
1
0
2
1
0
0
0
1
1
0
0
1
1
1
2
2
1
1
0
0
0
2
0
2
0
2
0
1
0
0
3
0
2
0
2
1
1
0
2
1
0
2
1
2
0
1
1
1
0
2
0
1
2
0
2
1
0
0
0
1
2
0
2
1
2
1
1
1
2
0
2
2
0
2
1
2
2
1
2
0
0
2
0
1
0
1
0
0
2
0
0
1
0
0
2
2
0
1
1
0
1
1
1
0
1
0
2
0
1
1
1
1
0
1
1
1
2
1
1
0
1
0
2
1
2
2
2
1
1
0
1
2
1
2
1
3
0
1
0
1
1
2
1
0
2
1
0
1
0
0
3
1
2
2
2
1
1
0
2
2
0
1
1
1
1
0
0
2
0
1
1
2
2
1
2
1
1
1
1
1
1
0
2
0
1
2
2
1
2
0
1
1
0
0
1
1
0
0
2
2
1
1
2
0
1
0
2
1
1
2
0
0
1
1
1
0
0
1
1
1
0
1
0
1
2
1
0
0
1
0
3
0
0
0
1
1
1
0
2
1
2
2
1
1
2
0
2
1
2
1
0
1
0
0
0
2
2
0
0
0
1
0
0
0
1
1
2
1
0
2
0
1
0
0
1
1
1
1
1
0
0
3
0
0
0
1
1
0
1
2
0
2
0
0
1
2
0
1
0
0
0
1
2
1
1
0
3
0
0
1
2
1
1
1
1
1
0
2
1
1
2
1
0
2
0
0
1
0
0
0
1
0
1
1
0
0
1
0
0
1
1
1
2
0
1
2
1
1
1
0
0
0
1
2
2
2
0
0
0
0
1
2
0
2
2
0
4
0
1
1
0
2
1
1
1
1
0
1
0
1
2
3
0
0
1
3
2
1
2
1
0
2
1
1
1
1
0
0
2
1
0
1
2
3
1
2
2
0
0
2
1
1
0
2
1
1
1
2
1
2
0
1
0
0
0
1
2
2
1
1
0
0
2
0
1
0
1
1
1
1
0
1
0
0
1
1
1
0
0
1
1
0
0
1
2
2
0
1
1
1
0
2
0
1
1
2
2
1
1
1
0
2
0
1
2
1
2
2
0
0
2
0
0
1
1
0
1
0
2
1
1
1
0
1
0
0
1
0
0
0
1
2
2
0
0
1
0
1
1
1
0
0
1
0
0
2
0
0
0
2
3
1
5
1
2
1
0
0
1
0
1
1
0
1
0
0
1
0
2
1
0
1
2
1
0
0
0
1
1
0
0
0
1
1
0
2
0
2
2
1
1
2
0
0
1
0
2
0
0
1
2
1
0
1
2
1
2
0
0
0
2
2
0
0
0
2
1
1
1
1
0
1
2
2
0
2
0
2
0
2
0
2
2
0
1
2
1
0
0
0
2
2
0
1
1
0
0
0
0
2
0
2
1
0
2
0
0
1
1
2
1
0
1
1
0
2
2
0
1
1
1
0
0
1
0
0
0
0
0
2
1
1
1
0
2
1
1
0
1
0
0
1
0
2
0
0
1
0
1
1
0
1
0
1
1
1
1
0
2
1
0
2
1
1
1
1
1
1
0
0
0
2
1
2
2
1
1
1
2
0
2
1
0
0
2
1
0
0
2
1
0
2
4
0
1
0
1
1
0
1
1
1
1
2
0
0
0
0
0
0
2
1
1
1
0
1
1
1
1
0
1
0
2
0
0
0
2
1
1
0
0
1
1
0
2
1
2
1
0
0
0
1
1
0
1
0
1
1
0
0
2
3
1
1
0
0
2
2
1
1
0
1
0
1
0
0
1
0
1
1
1
1
0
1
0
1
1
1
1
0
0
2
0
0
1
0
0
2
1
2
1
2
1
2
2
2
3
0
1
0
0
1
3
2
0
2
0
0
0
1
0
1
1
2
1
2
0
1
0
0
2
1
1
1
2
0
1
0
0
0
0
2
2
0
1
0
0
1
2
0
2
1
0
2
0
0
1
1
0
1
1
1
1
1
0
1
0
1
0
0
0
0
0
1
2
2
1
1
1
1
1
0
2
1
0
0
2
1
1
0
2
2
1
2
0
2
0
0
0
0
0
0
2
1
1
1
0
1
2
1
1
0
0
1
0
1
0
0
1
1
0
2
1
2
2
1
0
0
1
1
0
0
0
0
2
0
1
1
0
2
1
1
0
1
0
0
1
0
1
0
1
1
1
1
0
0
0
2
0
0
1
0
0
1
0
1
0
2
1
2
1
0
1
0
0
1
1
1
2
1
1
0
2
0
2
0
2
0
0
0
1
0
2
2
1
1
1
1
2
1
1
2
2
0
0
0
2
1
2
0
0
0
2
2
0
1
1
0
0
0
2
1
1
2
2
0
1
1
1
2
0
1
0
0
2
2
2
1
2
1
2
1
0
0
1
0
0
1
1
2
0
0
0
2
0
0
1
1
0
1
0
1
0
1
2
0
1
1
1
0
1
1
0
2
1
1
0
1
0
1
1
2
1
1
0
2
0
4
1
2
1
1
1
0
0
0
1
1
0
2
1
1
0
0
2
2
1
1
0
2
1
1
2
2
1
0
2
2
0
2
0
0
2
1
0
1
1
1
2
2
2
2
1
2
1
1
1
1
2
0
0
1
1
2
0
1
1
1
2
2
2
0
0
0
0
2
2
1
1
2
0
1
1
1
0
1
2
1
0
1
2
0
0
0
2
1
1
0
2
1
1
1
2
0
2
1
0
0
3
2
1
1
1
1
0
1
0
1
1
1
1
2
2
0
0
0
1
1
2
0
1
1
2
2
1
0
1
1
3
2
0
2
1
1
1
1
1
0
1
1
1
0
2
1
1
0
0
2
0
0
1
1
0
1
0
0
1
1
1
0
1
0
2
1
0
1
1
0
0
0
1
2
1
0
1
1
0
0
1
0
2
2
1
2
0
0
0
0
1
1
0
2
0
0
1
1
1
0
0
0
1
1
0
0
0
1
2
0
0
3
0
0
5
1
0
0
2
0
0
0
2
1
0
0
0
1
0
0
1
2
1
0
1
0
1
2
2
0
1
1
0
0
0
0
1
0
2
0
1
0
1
2
2
2
1
1
1
0
1
0
2
0
2
0
1
0
0
1
1
0
1
2
0
1
0
0
0
0
0
0
1
0
1
0
2
8
1
0
0
0
0
0
1
1
1
1
1
1
0
1
1
1
1
1
1
0
2
1
0
0
3
0
1
1
2
1
2
2
1
1
0
2
2
1
0
0
0
1
1
0
1
1
0
0
1
2
2
0
2
0
1
1
1
1
1
0
0
0
0
0
1
2
1
1
2
0
0
2
2
0
0
1
0
1
0
0
1
1
0
1
0
1
1
0
2
0
1
1
0
1
0
2
1
1
0
0
0
0
2
1
1
1
0
0
0
0
1
1
0
0
0
2
1
1
0
1
1
1
1
0
1
1
1
3
1
0
0
0
0
0
0
1
1
1
0
1
0
1
1
1
2
1
1
2
0
1
2
1
0
1
0
1
2
0
0
1
0
1
0
1
2
1
1
0
2
1
0
0
1
2
1
1
1
1
0
0
2
1
2
2
1
0
1
1
0
1
0
0
0
0
1
0
1
0
0
2
2
2
0
0
0
0
1
1
2
1
1
1
1
0
0
0
1
1
1
0
0
1
1
2
1
1
1
1
0
1
2
0
1
2
1
1
0
1
0
2
0
1
1
1
1
0
1
2
0
0
0
1
0
2
1
1
1
2
1
3
0
0
1
2
0
0
1
0
2
1
2
2
1
0
1
2
0
1
0
3
1
1
0
1
0
1
0
2
0
1
0
2
1
2
1
0
1
0
1
0
0
1
0
0
0
0
0
1
2
1
0
0
0
1
0
1
0
0
0
0
2
1
2
2
2
0
2
1
2
1
0
1
2
1
3
2
1
1
1
0
2
2
1
1
1
2
0
2
2
0
1
0
0
0
1
0
1
1
1
1
0
1
0
2
3
0
1
1
0
1
1
1
0
1
1
1
1
1
1
1
0
0
1
0
2
0
0
0
0
1
1
0
0
0
1
1
1
0
2
1
1
1
1
0
1
1
2
0
0
1
2
2
0
2
0
2
2
2
0
0
1
0
1
1
2
1
0
2
0
0
0
1
1
2
0
0
1
1
1
1
1
0
2
0
1
1
3
1
1
0
0
0
0
1
0
0
0
2
0
0
0
0
1
1
1
1
0
1
0
0
0
1
1
0
0
0
2
1
1
1
1
2
1
2
0
0
1
1
2
1
1
1
1
1
0
2
0
1
1
1
1
1
2
2
1
1
1
2
1
2
1
0
1
0
1
1
0
0
1
1
1
1
0
2
0
0
1
2
0
2
1
2
1
0
1
1
1
1
0
0
2
2
1
0
0
0
2
1
1
1
0
2
2
0
1
0
2
1
1
1
1
0
2
2
1
1
1
1
2
2
1
1
1
0
0
2
0
1
0
2
1
2
0
1
1
1
2
2
2
1
0
0
1
1
0
0
0
2
2
0
0
1
1
1
0
0
2
0
0
1
1
2
1
1
1
0
2
1
0
0
2
2
1
1
2
2
0
0
0
0
0
2
1
2
1
1
1
1
0
0
2
2
1
1
1
2
1
1
0
1
0
1
0
0
0
2
2
1
0
1
2
1
2
0
2
1
0
1
0
1
1
1
0
0
1
0
0
0
0
2
2
0
0
0
1
2
2
1
1
2
1
1
1
1
1
1
1
1
0
1
1
1
1
0
0
1
2
2
1
1
1
2
1
3
2
1
1
1
1
2
1
1
0
2
1
1
0
1
0
0
4
1
2
1
1
2
0
1
0
1
1
2
1
0
2
0
0
2
0
0
1
0
1
1
2
1
1
1
1
0
0
1
0
1
0
0
0
1
1
1
0
0
1
3
0
1
2
2
1
1
1
1
1
1
2
2
0
1
0
0
1
2
2
0
0
2
0
1
2
1
1
2
1
2
1
0
0
0
1
0
2
0
1
2
0
0
0
1
2
1
1
2
1
2
0
1
0
2
0
2
2
0
1
0
4
2
0
1
0
2
1
2
1
3
1
0
1
1
1
1
2
1
1
2
0
0
1
0
1
0
0
0
0
0
2
2
1
0
2
2
2
1
1
1
0
1
0
1
1
1
0
1
2
1
0
2
0
1
2
0
2
1
1
1
1
0
0
1
1
0
1
2
0
1
1
0
2
0
0
2
0
0
1
0
1
1
1
2
0
0
1
2
1
0
0
2
1
1
1
2
1
2
0
0
0
1
2
2
0
0
0
0
0
0
0
0
1
0
1
2
1
1
1
1
2
0
0
2
1
1
1
2
1
0
1
1
2
1
0
1
0
1
1
0
1
0
1
0
0
2
1
1
0
2
1
0
2
0
1
2
0
0
2
1
2
0
1
1
2
0
0
1
0
2
0
1
0
1
2
1
1
1
1
0
2
0
0
0
1
0
1
1
1
0
1
0
1
3
1
0
0
1
2
1
1
0
1
0
0
0
1
1
0
1
1
0
2
2
0
0
1
0
2
1
1
0
1
2
2
2
2
0
2
1
3
1
0
2
1
0
0
1
1
1
0
2
1
2
1
1
1
0
0
1
0
1
2
2
0
1
1
2
1
1
0
2
0
1
0
1
0
1
2
0
2
1
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
1
1
1
0
2
0
0
1
1
2
2
1
2
1
2
1
2
3
1
0
1
2
0
0
1
1
0
1
1
0
1
0
2
1
2
0
0
1
1
0
1
1
0
1
1
1
2
0
2
1
1
1
1
0
2
0
1
1
0
0
0
2
2
2
0
0
2
1
1
1
1
1
0
1
1
0
1
1
1
0
0
2
1
0
1
0
2
0
2
0
1
0
1
1
0
0
0
2
1
2
1
0
1
1
1
2
1
1
1
1
0
0
2
1
2
1
2
1
0
0
1
2
1
2
1
1
1
1
1
2
0
1
1
0
2
0
0
1
2
0
0
1
0
1
1
0
1
0
2
0
1
0
1
1
1
0
0
1
2
1
2
2
3
0
0
1
2
0
1
1
1
1
1
0
1
1
1
2
1
0
1
2
1
0
2
0
2
1
2
1
2
1
1
0
0
0
2
1
1
2
1
1
1
1
0
2
1
0
1
1
0
1
1
0
0
0
0
2
1
2
1
1
2
0
2
2
0
2
0
2
1
0
0
1
0
0
0
1
0
1
1
0
0
1
0
1
1
1
0
0
1
0
2
0
0
1
0
2
0
0
0
0
2
0
1
1
2
1
0
0
2
1
2
2
1
0
0
2
2
0
1
0
4
1
1
1
2
1
0
0
0
2
2
1
2
2
1
1
1
1
0
1
2
2
1
2
1
2
1
2
1
2
1
2
0
1
2
0
3
2
2
1
2
1
1
1
1
1
1
0
0
2
0
2
0
2
1
0
2
0
0
1
2
1
0
0
1
1
1
6
0
1
1
0
0
0
1
0
0
2
2
0
0
0
1
0
0
1
0
0
2
1
1
1
2
1
0
0
2
0
1
2
1
2
2
1
0
2
1
3
1
1
2
2
0
1
1
2
0
2
0
0
0
1
1
1
0
0
0
1
0
0
0
0
1
1
2
2
1
3
0
0
0
0
1
0
2
0
2
0
1
0
1
1
1
1
1
0
1
2
1
0
1
0
0
2
1
1
0
1
2
0
1
1
1
1
1
1
0
1
0
1
0
0
0
0
1
2
0
1
1
0
2
0
1
1
0
2
0
2
1
3
2
1
2
3
1
1
0
0
1
0
1
2
0
2
1
0
1
0
1
0
0
1
1
2
0
0
0
1
2
0
0
1
4
0
1
2
0
0
0
0
2
0
1
1
1
1
1
0
1
0
2
0
1
0
0
1
1
0
1
1
1
0
0
1
1
0
0
1
1
2
3
0
1
1
2
3
2
0
1
0
2
2
2
1
1
1
1
0
1
0
0
1
2
0
0
1
1
0
0
1
1
2
2
2
1
1
1
1
0
1
1
0
1
1
1
1
1
1
0
1
1
2
1
1
1
0
1
1
0
0
0
0
0
1
2
0
2
2
2
0
0
2
0
1
0
1
0
1
0
1
0
0
1
0
0
0
1
0
1
0
0
1
1
1
0
2
0
0
0
1
0
0
1
1
0
3
1
1
0
0
0
0
0
1
2
1
2
1
2
0
1
1
1
1
1
1
2
1
1
0
2
2
1
0
1
0
1
0
0
2
0
1
0
0
1
2
1
0
0
1
0
0
1
0
0
2
0
0
2
1
0
2
2
2
0
1
1
1
0
1
1
2
0
1
1
2
0
0
1
2
3
2
1
2
0
0
2
0
1
0
0
2
2
1
0
1
1
2
0
0
2
2
1
0
0
0
2
2
1
1
1
0
1
0
1
2
0
0
1
0
1
0
2
2
1
1
0
2
0
0
2
1
1
2
0
0
2
0
1
2
0
2
0
2
2
1
1
2
0
1
1
1
1
0
0
1
0
1
0
1
2
2
2
2
0
1
4
2
2
2
2
2
0
0
0
0
1
1
1
1
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
2
2
1
1
0
0
0
2
1
1
2
0
0
1
0
1
1
1
0
2
1
1
1
2
0
1
1
3
1
2
0
0
2
1
0
0
0
1
2
1
0
1
0
2
1
0
0
0
1
1
0
2
1
0
0
1
0
2
0
0
2
0
2
1
0
0
0
2
0
0
0
2
1
0
0
0
1
0
1
0
1
0
1
0
0
2
0
1
1
0
0
1
1
1
1
2
0
2
1
1
1
0
1
0
3
2
1
0
0
2
0
1
0
0
1
2
1
3
1
0
1
1
2
2
0
0
0
0
1
0
1
2
0
0
0
0
1
0
1
3
0
2
1
2
2
1
2
1
0
1
1
1
0
0
0
1
0
1
1
1
1
1
0
2
2
1
1
1
1
1
1
1
1
1
1
1
1
0
2
2
1
0
1
0
1
1
2
2
2
1
2
1
0
1
0
1
1
1
1
1
2
2
0
1
0
1
2
1
1
1
0
1
2
2
1
3
2
2
1
0
1
1
1
2
0
1
0
1
0
2
0
2
1
0
0
1
1
2
0
0
3
1
0
1
1
1
0
0
0
2
2
0
0
2
1
1
0
1
3
0
2
0
1
0
1
0
1
1
0
1
0
0
1
2
0
1
1
2
1
2
1
1
1
1
2
1
0
0
2
2
0
0
0
0
1
2
1
0
2
0
2
0
0
1
2
0
1
1
0
0
1
1
1
1
0
1
1
1
1
0
1
1
2
1
0
0
3
1
1
0
1
1
1
2
3
0
2
2
2
2
2
0
1
1
0
1
1
2
1
0
0
1
0
1
1
2
1
0
0
2
1
1
0
2
0
1
2
1
0
0
0
0
0
0
1
1
1
1
2
2
0
0
1
2
1
2
0
2
2
1
1
1
0
2
0
1
0
1
1
0
0
0
0
0
0
1
0
2
2
0
0
0
0
1
1
1
3
2
1
1
0
1
0
0
2
0
2
2
0
2
2
1
0
0
1
0
2
0
1
0
2
2
1
0
0
1
0
2
1
2
0
2
2
2
1
1
2
0
1
2
0
1
1
0
1
0
1
1
0
2
1
3
1
1
1
0
0
2
3
0
0
2
0
0
0
1
2
2
1
2
2
1
0
1
2
0
2
1
2
0
2
1
2
0
0
0
1
1
3
0
1
0
2
1
0
1
0
0
0
1
2
1
0
0
0
2
2
3
2
1
0
1
2
1
0
1
1
0
0
1
0
2
2
1
1
2
0
1
2
1
1
1
1
0
1
2
1
2
1
1
1
0
1
1
1
1
1
2
0
0
1
0
0
1
1
0
1
0
0
0
1
0
0
1
0
2
1
1
1
0
0
2
0
0
0
1
0
1
2
0
2
0
0
2
1
1
2
0
0
2
0
2
2
2
2
2
0
2
2
2
0
1
1
3
1
2
0
0
0
2
1
0
0
0
2
0
1
0
2
0
0
1
1
2
0
1
1
1
1
2
2
0
0
1
0
1
2
1
0
1
1
2
1
5
1
1
1
0
0
0
0
0
2
0
1
0
1
1
0
1
1
1
2
0
0
1
1
1
0
1
1
0
0
1
1
0
1
0
0
1
2
0
1
2
1
2
0
5
1
2
1
0
2
0
2
1
2
0
2
2
0
1
0
1
1
1
2
1
0
0
1
0
0
0
0
0
1
2
1
1
1
2
1
2
1
0
1
1
2
1
0
1
0
2
0
1
0
0
1
0
0
0
1
0
1
0
0
1
1
1
2
2
1
2
1
0
1
0
0
1
1
1
0
0
1
0
1
1
0
1
0
0
1
2
0
0
2
0
1
1
2
0
0
0
1
1
2
2
2
1
2
2
0
0
2
2
2
1
1
1
1
2
1
2
1
1
2
1
1
1
1
1
0
0
2
1
0
2
2
2
0
0
1
0
2
1
2
1
1
1
0
2
0
1
2
0
1
0
1
1
0
1
1
0
0
1
0
1
1
0
2
0
2
2
2
1
0
2
0
1
1
1
1
1
1
2
2
1
0
2
2
1
1
2
0
2
0
1
2
1
1
1
1
2
0
0
1
1
2
1
0
1
0
2
1
2
2
0
1
0
1
1
1
2
1
2
0
2
0
1
0
1
2
2
1
1
0
0
1
1
1
1
2
2
1
0
0
2
0
0
1
2
1
1
1
0
1
0
0
1
1
0
2
1
0
2
0
0
0
2
1
0
2
0
0
1
0
0
2
2
0
0
1
2
0
1
1
0
1
0
0
1
0
2
0
1
2
1
0
0
0
0
1
0
1
2
0
0
0
0
2
0
1
1
1
0
1
0
0
1
0
1
1
0
0
1
2
0
0
0
1
1
0
2
1
1
2
1
1
1
0
1
1
1
1
2
1
1
0
0
0
2
1
2
0
1
2
2
0
1
2
1
1
0
1
1
1
0
2
1
1
0
1
0
1
1
1
0
1
0
1
0
2
2
1
1
1
2
2
2
1
0
1
2
0
0
1
2
1
3
1
1
0
1
1
1
1
1
2
0
0
1
2
1
2
2
2
1
1
2
1
1
2
0
1
1
1
2
1
1
1
1
0
1
0
2
2
1
2
1
1
0
1
0
2
2
1
0
2
2
0
1
0
0
2
0
0
0
1
1
1
2
2
1
1
1
1
0
2
1
0
1
1
2
2
2
2
0
0
0
1
1
1
0
4
1
1
0
1
2
2
0
0
2
0
0
1
1
1
0
1
1
2
0
1
0
0
2
1
1
1
0
0
0
1
2
1
1
0
1
1
2
0
1
2
1
1
2
0
1
0
0
0
1
0
0
2
0
2
1
0
1
1
1
1
1
0
1
0
1
0
1
0
1
3
1
2
0
0
1
0
1
1
0
2
1
0
1
1
2
0
2
0
1
2
1
0
1
1
2
0
2
1
0
1
0
0
1
1
2
1
0
1
1
0
0
2
1
2
0
1
0
1
0
0
1
1
1
0
1
1
1
1
1
1
1
2
1
1
1
1
0
4
1
2
0
1
1
0
1
0
2
1
2
1
1
3
1
0
0
1
1
1
0
0
0
3
0
1
0
0
1
0
2
0
0
1
2
2
1
2
0
3
0
1
0
1
2
0
1
0
1
1
0
0
1
1
3
1
2
0
0
2
0
2
0
0
0
0
1
2
1
1
1
2
2
1
1
1
1
2
2
1
1
1
2
1
0
0
1
0
1
1
0
1
0
1
1
1
2
0
0
0
1
1
2
0
1
2
0
2
1
2
0
0
1
0
1
0
2
3
1
0
1
2
0
2
1
1
1
2
0
0
0
0
1
1
0
2
0
2
1
2
1
2
2
0
1
2
1
2
2
0
1
0
0
1
2
1
0
2
3
2
6
0
1
1
2
2
2
1
0
1
1
1
0
0
1
1
0
0
0
0
0
0
0
1
1
2
1
0
0
2
2
0
1
0
0
2
1
0
2
0
2
0
0
0
2
1
0
1
0
0
0
0
1
0
1
0
1
2
2
2
0
2
3
1
1
1
3
1
1
1
0
1
2
1
1
2
0
0
1
1
1
1
1
1
1
0
1
0
1
1
1
0
0
1
1
0
2
2
1
1
2
0
2
1
2
0
1
0
1
1
0
1
1
0
0
0
0
0
2
1
0
1
0
0
2
1
1
0
0
0
1
2
1
2
1
0
1
2
0
0
0
0
0
2
0
1
2
1
0
0
1
1
1
0
2
1
2
1
0
1
0
0
0
1
2
0
2
0
2
1
2
2
1
1
1
0
2
0
0
1
2
1
0
1
2
1
1
1
1
1
0
1
1
2
2
1
0
2
0
1
2
0
0
1
1
2
0
2
2
1
1
0
0
1
1
1
1
2
1
0
0
1
2
1
1
0
0
0
1
0
0
1
0
1
1
1
0
0
2
1
1
1
2
1
0
0
1
2
1
0
2
1
1
0
0
0
0
2
1
2
1
1
0
2
0
0
0
1
2
1
0
1
0
0
1
1
0
2
1
2
1
1
0
1
1
0
1
0
0
0
1
0
1
2
2
1
1
0
1
0
0
1
1
1
2
1
1
1
0
3
0
0
2
2
1
0
1
0
0
1
0
1
2
1
0
0
1
1
1
1
1
0
1
0
1
1
0
0
0
0
1
1
1
1
1
1
1
0
2
0
0
0
1
1
1
2
2
0
0
2
1
0
0
1
1
0
0
1
0
2
2
1
2
1
0
0
0
0
2
1
0
1
0
1
1
1
1
2
2
1
2
1
2
1
0
1
1
0
2
2
1
2
1
0
1
1
2
0
0
0
2
1
0
2
1
1
0
0
1
1
1
2
0
2
0
0
1
0
2
1
0
0
2
0
2
2
0
1
1
0
0
0
0
2
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
1
1
1
0
1
1
2
1
0
1
0
2
1
1
1
0
1
1
1
0
2
1
0
0
1
1
0
0
2
2
0
2
1
2
0
2
0
2
0
1
2
0
0
2
0
1
2
0
1
0
3
2
1
0
0
0
0
1
1
1
0
2
0
1
0
1
1
1
1
0
1
1
0
0
0
0
2
0
1
0
1
0
1
1
1
1
0
1
1
1
1
0
2
0
1
0
0
0
2
1
1
2
1
2
1
2
0
1
0
0
0
1
0
1
1
1
0
1
2
3
0
2
1
2
0
1
1
0
1
0
0
0
1
0
1
0
0
2
1
0
0
1
1
0
1
0
2
2
0
1
1
0
1
1
1
1
0
1
1
0
1
0
1
1
1
2
1
2
1
1
0
0
0
1
1
0
1
1
1
1
1
4
1
1
2
1
2
1
1
1
0
1
0
1
1
2
0
1
0
0
0
1
0
0
1
1
3
2
3
1
2
2
5
2
1
0
1
1
2
0
2
1
2
5
2
0
1
0
2
2
0
2
2
0
0
0
2
2
1
2
1
1
1
0
2
1
0
1
2
1
1
0
0
1
1
1
0
1
2
0
4
1
0
0
1
1
1
2
0
0
1
0
1
1
0
0
0
1
1
0
1
1
1
2
2
2
0
1
0
1
1
1
1
1
1
2
1
1
2
1
0
2
1
0
0
0
1
1
1
0
2
1
0
0
0
0
1
1
0
1
2
2
0
0
0
0
0
1
2
1
2
0
1
1
1
1
3
0
0
0
1
0
2
0
1
2
0
2
1
1
0
0
2
1
1
1
1
0
0
1
1
0
1
1
1
1
0
0
0
2
1
0
0
0
1
0
2
0
1
2
0
2
2
1
1
1
2
0
1
2
1
0
0
1
2
2
1
0
1
1
1
1
1
1
1
1
0
0
0
2
1
1
1
1
0
0
1
0
0
1
1
1
2
1
1
5
1
1
1
1
1
0
2
1
2
2
2
0
0
0
1
1
0
0
0
1
1
1
2
0
1
0
1
1
0
1
1
0
0
2
1
1
2
1
1
1
2
0
0
2
1
1
0
0
0
1
1
1
2
1
0
0
1
2
0
1
0
2
0
0
1
0
1
0
1
0
2
1
0
1
0
0
0
1
1
1
0
0
1
1
1
0
2
1
1
0
1
0
1
1
2
1
1
1
0
1
2
0
1
1
1
0
0
0
1
0
1
1
0
2
1
0
1
0
0
0
2
0
1
0
3
0
2
1
0
2
1
0
0
1
0
0
0
2
0
1
1
0
2
0
1
0
1
2
0
2
1
0
1
0
0
1
0
0
0
1
2
1
0
0
2
1
2
1
2
0
1
1
1
2
1
0
1
1
2
1
2
1
1
2
0
0
4
2
1
0
4
1
1
1
2
1
1
1
2
1
1
1
1
1
2
1
1
1
2
2
1
0
0
0
1
2
1
0
0
1
2
1
1
2
1
1
1
1
0
0
2
1
0
2
0
1
3
0
0
0
1
0
1
2
1
2
1
0
0
2
1
1
0
0
1
1
1
2
2
0
1
1
2
1
0
1
1
0
1
1
0
2
0
0
0
1
0
0
0
0
1
0
1
1
1
0
2
0
1
0
1
2
0
1
1
1
1
2
1
1
0
1
2
0
0
1
2
0
1
1
0
3
0
0
2
0
2
0
0
0
0
0
1
1
1
1
2
1
0
1
1
0
2
0
0
0
0
0
1
1
1
2
0
1
0
0
1
1
1
1
2
1
2
1
1
1
0
1
0
0
1
0
0
1
1
2
1
2
2
0
0
3
1
1
1
0
2
2
0
2
0
1
1
1
2
2
0
1
0
2
0
0
2
0
0
2
0
1
0
0
1
0
0
1
2
2
0
0
0
1
0
1
0
2
1
2
0
2
1
1
0
2
1
1
0
1
1
0
2
1
0
1
1
0
1
0
2
1
2
1
1
5
1
0
1
1
3
1
2
0
0
0
1
2
2
2
1
1
2
3
2
2
2
1
0
1
1
3
0
1
1
0
1
1
1
2
0
0
1
0
1
1
1
0
0
2
2
1
2
0
2
0
1
1
1
0
2
0
0
0
1
2
0
1
2
0
1
1
0
0
1
1
1
2
1
1
1
1
2
0
0
1
2
0
1
0
1
0
0
2
0
1
1
2
2
0
0
2
1
0
0
1
1
0
2
1
1
1
0
0
1
1
0
0
0
0
1
2
0
1
0
1
0
1
1
1
1
0
1
0
1
0
0
2
1
0
1
0
2
0
1
1
1
0
1
2
0
1
2
2
1
1
0
2
2
4
2
1
2
0
0
0
1
0
1
1
2
1
0
1
1
2
0
1
1
1
1
2
2
1
0
1
0
0
0
1
1
1
2
1
2
0
2
0
1
1
2
2
1
1
2
2
2
2
2
2
2
2
0
1
3
2
1
1
1
0
2
1
0
2
2
0
2
0
1
1
1
1
1
3
1
0
0
0
2
0
1
0
1
1
0
0
1
2
1
1
0
1
0
1
1
0
1
0
0
0
3
0
0
1
0
2
1
1
1
0
0
1
1
1
2
2
2
0
0
0
2
0
2
0
0
1
0
0
2
2
1
1
0
1
1
1
1
0
2
0
1
2
2
0
1
2
1
0
0
0
1
0
0
0
0
0
0
0
0
1
2
1
1
2
1
0
0
0
1
1
1
1
2
2
0
1
0
0
0
0
2
1
0
1
0
1
1
2
2
2
1
1
1
1
2
2
2
2
0
3
1
1
0
1
0
1
6
0
1
0
0
1
1
0
1
1
1
2
0
2
0
0
6
1
0
0
1
1
0
0
0
0
1
0
1
0
1
1
1
2
1
1
0
2
0
2
1
0
2
0
2
0
0
1
0
0
1
1
1
1
0
1
3
0
0
1
1
0
0
1
0
0
2
4
1
1
1
0
0
0
1
2
1
3
1
0
1
0
0
0
0
1
1
0
2
1
1
1
1
1
1
0
1
1
1
1
0
0
2
1
0
1
1
0
2
0
1
1
1
1
1
1
0
2
2
1
0
0
2
0
1
2
1
1
1
2
0
0
0
2
0
0
2
2
1
0
0
2
1
1
0
1
2
0
2
1
1
1
1
1
0
0
1
1
1
1
1
1
1
1
0
2
2
1
3
1
1
1
0
0
0
2
1
0
2
0
0
1
1
2
1
1
2
0
2
2
2
0
1
0
0
2
1
2
1
1
0
1
0
0
1
0
0
1
0
3
1
3
1
0
2
1
1
1
1
1
2
1
1
1
2
1
0
1
2
0
0
2
1
1
1
0
0
0
0
2
0
1
0
0
2
0
0
0
1
0
1
1
0
0
0
2
1
1
1
0
1
0
0
1
1
1
1
1
1
1
0
1
1
1
2
1
0
1
2
0
1
1
0
0
0
0
2
0
1
1
1
1
0
0
0
1
0
2
0
1
0
2
0
2
2
0
2
1
0
0
0
1
1
1
0
0
0
2
0
1
7
2
1
2
1
0
0
0
2
0
0
0
0
2
1
1
0
2
0
2
1
0
2
2
1
0
0
1
0
0
1
1
0
1
0
2
0
2
0
1
1
0
1
1
1
0
1
2
2
0
1
1
0
1
1
1
0
2
0
0
0
0
2
1
0
2
0
0
0
2
1
1
1
1
0
1
0
0
1
2
0
0
0
0
0
1
1
1
2
1
0
2
1
0
0
2
2
1
1
1
1
1
1
1
1
1
1
1
2
1
0
0
1
0
0
2
2
1
1
0
0
1
0
1
2
1
0
0
0
1
1
0
1
2
1
1
1
0
1
1
1
2
0
2
0
1
1
2
1
1
0
1
2
1
1
2
0
0
1
1
1
1
1
1
2
1
2
0
0
1
0
0
4
1
1
1
0
2
0
1
0
1
1
1
1
1
1
0
2
1
0
1
1
0
1
1
0
0
1
0
2
1
0
0
1
2
1
1
2
1
1
1
1
1
2
2
0
1
0
0
0
1
0
1
0
2
0
0
3
1
0
2
1
2
1
1
0
0
0
0
0
1
2
2
0
0
1
1
1
1
1
0
1
1
0
0
1
0
0
0
0
1
1
2
1
2
0
2
0
2
0
2
2
0
1
1
0
1
2
0
0
1
1
1
1
1
0
1
0
0
1
1
2
0
0
1
2
3
0
0
2
1
1
2
0
0
0
0
0
1
2
2
0
1
0
2
1
0
0
1
1
1
1
1
2
1
2
0
1
1
0
0
1
7
1
0
0
1
0
1
4
0
0
1
2
0
0
1
3
1
0
0
1
2
0
0
1
2
0
0
0
0
3
1
3
0
1
2
1
0
2
1
0
0
0
1
2
0
2
2
1
2
1
2
2
0
1
1
0
0
1
1
1
0
1
0
1
0
0
0
1
2
1
0
1
1
0
1
1
1
1
0
2
0
1
1
0
1
1
0
1
1
0
1
1
0
2
0
1
2
1
0
1
1
1
1
2
2
0
1
1
1
1
1
0
1
0
1
2
1
0
0
0
2
2
1
1
0
2
0
1
0
0
0
1
1
0
2
0
2
1
0
1
1
1
1
1
0
0
1
0
1
2
1
1
1
1
1
1
1
0
0
2
0
1
0
1
2
1
1
1
0
0
1
2
1
0
3
0
0
0
0
2
0
1
1
1
0
1
1
1
1
2
1
1
1
0
0
1
2
1
0
0
1
1
1
1
0
0
1
2
2
0
1
1
2
0
0
1
1
1
2
0
1
1
1
0
2
2
1
0
0
2
3
2
1
2
2
1
0
2
0
1
2
1
1
1
1
1
2
0
0
0
1
1
1
2
1
1
1
2
2
0
0
2
0
1
0
1
0
0
0
0
0
1
0
2
1
1
0
0
0
2
1
1
1
1
0
2
1
0
1
1
1
1
1
2
0
1
1
2
1
2
1
2
1
1
1
1
2
1
2
0
2
0
0
0
1
2
1
0
0
2
0
1
1
0
0
0
1
0
2
0
2
1
0
4
1
2
0
0
1
2
0
1
1
1
0
2
0
1
0
2
0
1
1
1
0
2
2
1
0
2
0
1
1
2
1
1
0
1
0
0
1
0
1
0
0
1
0
1
2
0
0
1
1
0
0
2
1
1
0
0
1
2
1
0
2
0
0
1
0
2
0
1
5
0
2
0
1
2
0
1
0
3
0
1
2
0
1
0
1
2
2
1
1
1
2
2
0
1
0
3
0
1
0
1
0
1
1
1
2
0
0
1
1
2
0
0
0
0
2
2
1
0
0
2
2
0
1
2
2
1
2
2
1
1
2
1
1
1
1
0
1
2
0
1
0
0
0
1
1
0
2
0
2
2
1
1
1
0
2
0
0
2
1
2
1
1
1
0
2
0
1
2
2
1
2
0
1
1
0
1
0
1
0
0
1
1
2
1
0
1
2
0
0
0
0
1
1
1
2
1
1
1
3
0
1
2
2
1
0
1
2
0
1
2
0
2
0
1
0
1
1
2
1
2
2
1
1
0
1
1
0
0
0
1
0
1
1
0
1
0
0
1
2
1
3
0
0
2
1
1
0
0
0
1
3
0
1
0
1
1
1
0
0
1
0
0
0
1
2
2
2
1
1
1
1
1
0
1
0
2
0
1
1
1
1
2
0
1
1
1
0
2
1
1
2
1
2
1
0
0
2
2
1
0
1
0
0
0
0
2
0
2
0
1
1
1
0
1
0
1
1
1
1
0
1
0
0
2
2
1
1
2
1
2
0
0
1
1
1
1
1
0
1
0
1
1
1
3
0
0
1
2
2
2
0
1
0
2
1
1
1
0
1
2
1
0
1
1
2
0
1
0
3
2
1
0
0
3
2
1
1
0
1
2
0
1
0
0
1
1
2
1
1
0
0
0
2
1
0
0
0
0
1
1
1
2
2
2
1
0
0
2
0
1
1
1
1
0
2
0
0
0
2
0
2
2
0
0
1
0
0
2
0
1
2
0
2
1
0
2
0
2
0
0
1
1
2
0
1
1
1
1
2
1
0
2
1
0
0
2
2
0
1
0
0
1
0
2
1
0
1
1
0
1
1
0
0
0
0
1
1
0
1
1
2
1
1
1
0
0
2
1
1
0
0
1
0
2
1
1
1
0
0
2
1
2
1
1
0
2
1
1
0
0
0
1
2
1
1
1
1
0
2
1
0
1
0
1
1
4
1
1
2
1
0
2
1
0
1
1
2
0
1
1
2
2
0
0
1
2
0
0
0
0
0
2
1
0
2
1
1
1
1
0
1
2
2
1
1
0
0
2
0
1
2
1
0
1
1
1
0
2
1
0
0
2
0
0
0
1
1
2
1
1
0
0
1
2
0
0
1
0
0
2
1
1
0
1
2
1
0
0
0
2
2
1
2
2
0
2
1
2
2
1
0
0
0
1
0
1
2
1
1
0
0
0
1
0
1
2
0
1
2
0
1
1
1
1
2
1
0
1
1
0
0
0
2
1
1
1
2
0
1
0
1
2
3
1
1
1
0
1
1
1
0
0
0
2
1
2
0
3
2
0
1
2
2
1
0
0
1
1
0
0
1
2
1
1
0
1
2
0
2
0
1
1
2
0
1
1
0
1
0
1
0
0
1
0
2
1
0
1
1
0
1
1
0
0
0
1
2
2
1
1
0
1
2
0
1
0
0
1
2
2
0
0
2
1
0
0
0
1
0
1
2
2
2
0
0
2
1
0
0
1
1
0
0
1
2
2
1
2
2
0
1
0
2
0
1
1
1
1
0
1
0
2
0
0
2
0
1
1
2
1
0
1
0
1
2
1
1
1
0
2
2
1
2
0
2
1
0
0
0
1
2
3
1
0
1
1
1
2
0
1
0
1
1
0
0
0
0
2
1
0
2
0
1
0
1
2
1
1
1
0
2
1
0
2
1
1
0
2
0
1
1
1
2
1
1
1
1
1
1
1
1
0
0
0
1
1
0
0
1
0
1
1
0
1
2
1
1
0
1
2
2
1
0
1
0
1
1
1
0
2
1
0
1
1
0
1
0
0
1
1
1
1
2
1
1
1
2
0
1
1
0
0
1
0
2
0
0
0
2
1
1
1
1
0
0
1
0
1
0
1
0
2
2
1
1
0
0
0
2
2
1
0
1
0
2
0
2
0
1
0
0
0
2
0
1
0
2
2
3
0
2
1
1
2
0
1
1
0
1
0
1
1
0
0
1
2
0
0
0
1
1
1
0
2
0
0
1
1
1
1
2
1
0
0
2
0
2
0
2
0
0
2
2
2
2
1
0
0
2
1
2
1
1
1
1
2
3
0
1
0
0
1
1
2
1
2
2
0
0
1
1
1
0
0
0
2
0
0
1
0
0
4
0
1
1
1
1
1
0
0
0
0
0
1
1
0
2
0
1
0
0
0
1
2
0
2
0
0
1
0
2
1
2
1
1
1
1
1
2
1
2
0
0
2
0
0
1
2
0
1
1
2
2
1
5
1
1
1
1
1
2
0
1
4
3
0
1
0
1
0
0
0
1
0
0
0
1
0
1
1
2
0
0
0
1
1
0
2
2
2
0
0
1
0
0
1
0
0
2
2
2
0
1
1
1
2
1
0
1
1
0
0
2
0
1
0
2
1
2
0
1
1
1
1
1
2
1
1
1
1
0
0
1
1
0
1
1
0
0
1
1
1
1
0
2
1
0
2
1
1
0
2
0
1
1
1
0
1
1
2
0
1
2
0
1
1
0
1
1
1
0
1
0
1
1
1
0
0
1
1
1
1
0
0
0
1
1
0
1
0
0
2
0
1
0
1
0
0
0
1
3
1
1
0
0
2
0
1
0
0
1
0
1
0
4
0
1
0
1
1
1
0
1
1
1
1
0
0
1
2
1
0
0
1
2
1
0
0
0
0
0
0
2
1
0
0
2
1
0
1
2
0
1
0
2
0
1
1
1
1
1
0
0
0
0
2
0
1
1
0
1
2
0
2
1
1
1
0
1
1
0
2
2
1
1
1
1
0
2
1
2
1
1
1
2
2
0
1
2
0
0
0
0
2
1
0
0
2
1
1
0
0
0
1
0
1
0
1
0
0
1
1
3
1
0
1
2
1
1
1
0
0
2
0
1
0
2
2
0
1
2
1
2
0
0
2
0
0
0
0
1
1
2
0
2
1
0
1
1
2
1
2
0
1
0
2
1
1
0
0
1
1
1
0
1
0
1
2
1
0
1
2
1
0
2
6
1
1
1
0
1
1
1
0
1
0
2
2
0
0
1
0
2
1
0
1
0
0
2
1
3
2
1
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
3
0
1
1
1
0
2
1
1
2
1
0
0
0
0
2
0
1
2
2
1
2
2
1
2
0
0
1
2
1
1
0
0
1
1
2
1
2
2
0
1
1
1
0
1
1
1
0
1
0
2
0
1
0
0
0
1
1
1
0
1
2
0
1
1
0
1
2
0
1
1
2
1
2
1
0
1
1
0
0
0
1
2
2
2
3
0
2
1
0
0
1
1
1
0
1
1
2
0
0
1
1
1
0
1
1
2
0
0
1
1
1
2
0
0
2
1
0
0
1
0
0
0
1
1
1
1
1
1
1
1
0
0
1
1
1
1
1
0
1
0
3
0
2
1
3
1
2
2
1
2
1
0
0
2
1
0
1
0
1
2
0
1
3
2
0
0
4
1
0
2
0
2
2
1
2
0
1
1
1
3
2
0
1
0
0
2
1
0
2
2
1
0
1
1
0
1
0
0
0
0
2
2
0
2
1
1
0
2
1
1
1
0
1
2
1
1
0
0
2
1
2
1
1
2
0
0
2
0
0
1
1
1
1
2
0
1
2
1
1
0
0
1
3
2
1
1
3
0
1
1
1
1
2
0
1
1
0
0
0
1
1
2
1
2
0
2
1
2
1
1
2
1
2
1
0
1
1
1
1
2
1
1
0
1
1
1
1
0
1
2
0
0
2
1
1
0
1
1
1
1
0
0
0
1
1
0
2
5
1
1
0
1
1
1
0
2
2
0
0
1
1
1
2
0
1
2
1
2
2
0
1
0
1
2
1
0
0
0
2
0
1
0
1
1
1
1
0
3
0
1
0
0
0
2
0
0
1
2
0
1
1
1
1
1
1
1
3
0
1
0
0
1
0
0
1
2
2
1
0
0
2
0
0
0
1
0
0
1
2
2
0
0
1
2
1
2
0
2
0
1
1
0
1
1
1
2
0
2
3
0
0
1
1
2
0
1
1
3
0
0
2
0
0
0
1
0
1
0
1
0
1
0
2
0
1
0
1
0
2
0
2
1
0
0
4
1
4
0
1
0
2
1
2
0
2
1
0
1
1
1
2
1
0
0
2
2
1
1
1
1
0
2
1
0
0
1
0
0
0
0
0
1
1
0
2
0
2
0
2
1
0
0
0
0
1
2
1
1
0
1
1
2
2
2
0
1
0
1
2
0
0
1
1
0
0
1
0
2
1
1
1
0
0
0
1
0
1
0
2
2
0
1
0
1
1
0
2
1
2
2
0
1
0
0
0
0
0
2
2
2
0
1
0
1
2
1
0
1
2
0
1
0
1
1
1
0
1
1
1
0
1
1
1
0
2
1
0
0
1
3
2
2
2
0
2
0
0
0
2
2
1
1
1
1
1
0
0
0
0
2
1
2
2
2
1
1
2
1
1
1
1
2
1
1
0
1
0
0
2
1
1
1
1
0
2
1
1
1
0
1
1
0
1
0
1
1
2
0
2
0
1
2
1
0
2
1
1
1
2
2
1
1
0
1
0
0
2
1
1
1
0
0
1
1
2
1
1
2
0
2
0
0
1
0
1
0
1
1
0
2
0
2
0
0
1
0
0
0
2
1
1
0
0
1
0
0
1
2
2
1
1
0
1
2
1
1
0
0
0
1
0
0
1
0
2
1
1
1
0
0
1
1
0
0
0
1
0
0
0
1
0
1
0
1
1
1
2
0
0
1
0
1
1
2
2
1
2
1
0
1
0
1
1
1
2
1
2
1
0
0
1
0
0
0
1
1
0
2
1
1
1
0
0
0
2
1
1
0
0
0
0
1
0
2
0
1
1
2
0
0
2
0
0
1
0
1
1
2
0
0
1
1
0
1
0
2
3
2
2
0
2
0
2
1
1
1
0
1
1
0
0
0
1
1
1
1
0
2
0
2
1
2
2
1
0
0
0
2
2
1
2
0
2
1
2
1
0
1
0
1
1
1
0
0
1
2
0
2
2
1
0
2
0
2
1
0
0
2
2
1
1
2
1
0
0
0
1
3
1
2
2
1
1
0
1
2
0
1
0
0
0
1
1
0
1
2
1
1
0
2
3
2
0
0
0
0
0
0
0
2
1
1
1
0
0
1
1
1
1
0
2
1
1
0
1
1
0
2
1
0
1
2
0
0
1
2
2
1
0
3
0
2
1
0
2
1
1
1
1
0
2
2
1
1
0
1
0
2
1
1
2
0
0
0
2
0
1
1
1
1
1
0
2
1
0
0
0
2
0
0
0
2
1
0
0
0
1
1
1
1
0
0
0
0
1
1
0
1
1
1
1
0
1
2
2
1
1
1
0
3
0
0
2
0
1
1
1
1
1
1
1
1
0
1
2
1
0
1
2
1
1
0
3
1
1
1
2
3
0
1
0
1
1
2
2
1
2
1
1
2
2
0
0
1
1
1
0
0
1
0
1
1
1
1
0
0
0
1
0
0
1
0
1
2
1
1
0
0
1
1
0
0
0
2
2
2
0
1
0
2
1
0
0
1
2
1
2
2
0
2
1
0
0
1
0
2
1
0
0
1
0
0
2
0
0
0
1
1
0
0
0
0
1
0
1
1
2
2
1
1
1
0
0
1
2
1
0
1
1
2
1
0
2
1
2
1
0
0
1
2
0
1
0
1
0
0
0
0
0
1
2
0
2
1
2
1
1
0
0
0
2
1
2
0
2
1
0
1
1
1
1
1
0
1
1
2
0
1
1
0
1
2
2
1
0
1
1
2
2
1
0
0
1
0
1
1
1
1
1
1
2
1
2
0
3
1
0
0
2
0
0
2
1
1
2
0
1
1
1
1
0
0
1
0
2
1
2
1
0
1
0
1
1
2
1
1
1
1
1
2
1
0
1
2
0
0
0
1
1
1
1
0
0
2
1
2
1
1
1
0
1
1
1
0
2
1
2
0
1
1
0
0
0
1
1
1
1
1
1
2
2
2
2
0
2
1
1
1
0
1
1
1
1
0
2
0
0
1
1
2
2
1
0
1
0
0
1
1
0
0
2
0
0
1
1
1
0
1
1
1
1
0
2
0
0
1
1
1
2
0
2
0
1
0
1
0
0
0
0
1
1
2
2
2
1
0
0
0
1
0
2
0
0
0
1
0
1
1
0
1
3
0
0
0
1
1
0
1
1
1
1
0
2
2
0
0
1
1
0
2
0
0
1
2
0
2
0
0
0
0
1
1
0
1
0
3
2
1
0
1
0
2
1
0
0
0
0
0
2
2
0
0
0
0
0
1
1
1
0
1
0
1
2
0
0
1
0
0
0
1
1
1
2
1
2
0
1
1
1
1
0
0
0
1
0
1
1
0
0
0
0
1
0
0
2
1
1
0
2
0
2
1
1
0
0
0
1
0
0
1
2
1
2
0
1
0
0
1
1
2
2
2
1
1
0
0
1
2
1
1
1
1
2
1
1
0
1
0
1
3
2
0
0
0
1
0
2
1
1
0
2
1
1
1
0
0
0
2
1
2
1
1
0
0
0
2
2
1
0
1
0
0
1
0
1
0
1
1
1
0
2
1
1
0
0
0
1
1
1
1
2
1
2
2
0
0
2
0
0
0
0
0
0
0
1
1
3
0
0
1
0
1
0
0
0
0
2
2
1
0
0
1
0
0
1
0
0
1
0
1
1
1
2
2
1
2
0
2
0
0
2
0
0
2
0
0
0
1
1
0
0
1
0
1
0
1
0
0
0
1
2
0
2
1
1
1
0
0
0
1
1
0
1
1
1
2
2
1
2
2
0
1
1
2
1
0
1
2
0
0
0
0
1
0
0
0
0
0
2
0
1
0
1
3
1
1
2
0
0
2
0
0
0
1
0
0
1
1
2
1
2
1
0
2
2
1
1
2
0
0
0
1
0
2
2
1
1
0
2
1
2
1
0
0
1
1
0
0
1
1
0
1
1
1
0
2
2
2
0
1
0
0
0
1
2
1
0
0
1
0
1
1
1
0
0
1
0
2
1
1
2
2
2
1
1
2
0
2
1
0
0
2
1
0
0
0
0
1
1
0
1
1
0
2
0
1
2
0
1
0
1
1
2
0
1
0
1
2
0
1
1
2
1
0
1
1
1
1
1
1
0
2
0
2
1
0
0
0
1
0
0
2
0
0
1
0
2
1
0
1
0
1
0
1
1
2
0
0
1
1
0
2
0
1
0
0
2
0
2
0
0
0
0
0
0
2
0
3
0
0
1
2
1
0
3
1
1
1
0
0
0
2
0
1
1
0
2
1
2
0
1
1
1
0
2
1
0
0
0
2
2
0
2
1
0
0
2
0
0
1
0
0
0
2
1
0
1
1
2
1
1
1
0
1
0
0
2
1
1
1
1
1
1
0
0
1
2
1
1
0
1
2
0
0
1
0
0
0
0
0
2
1
0
1
1
2
0
0
0
0
1
2
1
2
1
2
2
1
1
1
1
1
1
0
3
2
1
0
0
1
0
1
0
1
0
1
2
1
0
1
1
0
2
1
1
1
0
0
0
1
2
1
0
2
1
1
0
2
4
2
1
1
1
0
0
0
1
1
0
1
0
0
0
1
2
0
1
0
2
2
1
0
1
1
1
0
0
1
0
0
2
0
0
1
1
1
0
0
2
0
2
1
0
2
1
0
1
2
0
0
2
0
2
1
0
1
0
0
1
0
0
0
1
1
1
2
2
0
0
1
2
2
0
2
1
0
1
0
1
1
2
2
1
1
2
0
2
3
0
1
1
0
1
0
1
0
0
1
0
0
0
0
0
2
1
0
1
1
0
2
0
1
2
1
0
1
0
0
2
1
1
0
1
0
0
2
1
2
2
1
1
1
2
1
4
1
0
1
0
0
2
0
1
1
0
1
2
0
1
1
0
0
1
0
1
1
1
1
3
1
1
1
0
1
0
1
1
1
1
1
1
1
1
0
2
1
1
0
0
2
2
0
2
0
0
0
1
1
2
1
1
0
1
0
0
2
1
1
0
0
0
1
2
1
1
1
1
0
2
1
1
1
2
4
0
0
0
1
1
2
1
1
0
2
1
2
0
1
0
2
2
0
1
1
7
0
1
0
2
2
0
0
2
2
1
0
0
0
1
2
2
1
0
1
2
1
2
0
1
0
1
2
2
0
2
1
2
2
1
1
1
0
0
0
3
1
1
1
0
1
0
2
1
0
1
0
2
0
1
2
0
1
0
2
3
1
2
1
1
0
1
0
1
0
1
1
2
1
0
2
1
0
1
1
1
2
2
1
1
1
0
1
0
0
0
0
2
0
1
2
0
2
0
1
2
2
0
0
2
1
2
1
2
1
1
2
2
2
1
1
0
2
4
2
1
1
1
1
1
0
0
0
0
1
1
2
1
0
1
1
0
0
0
1
1
2
1
1
1
0
1
1
0
1
2
1
1
0
0
3
0
1
2
1
2
2
1
0
0
2
1
0
1
0
0
0
2
0
1
1
0
1
0
1
2
1
2
0
1
0
2
2
0
0
2
0
1
1
1
1
1
0
0
1
5
0
1
0
2
1
1
0
0
2
0
0
0
0
2
2
2
0
1
1
0
2
0
2
0
2
2
2
0
0
1
1
1
0
0
1
1
0
0
1
0
2
1
2
1
1
1
1
1
1
0
0
1
1
2
1
2
2
1
1
0
1
1
0
1
1
1
1
1
0
0
1
1
1
0
1
2
0
1
1
2
1
0
0
2
1
0
0
2
0
1
0
1
0
1
1
2
0
1
2
1
0
0
0
0
1
0
1
2
1
1
0
1
1
2
0
1
0
3
2
2
1
0
0
0
1
1
0
1
1
1
0
2
0
1
0
0
1
2
1
1
1
1
0
1
1
0
1
0
0
1
2
1
0
0
2
0
1
0
1
0
1
2
2
1
0
0
1
1
2
0
1
2
1
1
2
1
1
0
2
2
1
0
2
0
1
1
0
2
1
0
0
0
1
1
0
1
2
0
0
1
0
0
1
1
0
1
0
1
2
2
1
2
0
1
2
1
2
2
1
2
0
0
2
2
1
1
1
0
0
0
1
1
0
2
2
0
0
0
2
0
0
1
5
1
0
0
1
1
1
1
2
1
1
1
1
0
1
1
1
1
0
1
1
2
2
1
1
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
1
0
2
1
0
0
0
1
2
0
0
0
1
0
1
2
0
1
1
2
1
2
2
2
0
2
2
0
0
1
0
0
1
0
1
0
0
1
1
0
0
1
0
0
2
0
1
0
2
0
0
2
1
1
2
1
0
1
2
0
0
0
2
0
0
1
1
2
1
0
1
1
1
0
1
2
1
1
0
1
1
2
1
1
2
1
0
0
0
1
1
1
2
0
0
1
0
2
1
1
1
0
1
1
0
1
2
0
1
0
0
0
1
0
1
1
2
0
0
1
1
3
1
0
2
0
0
1
0
0
7
0
1
0
1
0
0
0
0
2
1
1
1
2
1
0
0
2
1
0
0
0
1
0
0
2
0
1
1
2
2
0
0
1
1
1
1
0
1
0
1
1
2
1
1
0
0
0
0
1
2
0
1
1
2
0
0
1
1
1
1
1
0
2
0
1
0
0
0
1
1
0
1
1
1
1
0
0
0
1
6
0
2
1
1
1
1
1
1
2
2
1
0
0
3
1
1
0
1
0
0
1
1
1
1
1
1
1
2
0
1
1
2
1
1
2
1
0
0
1
0
0
1
0
2
0
1
0
2
0
2
2
1
1
0
1
2
1
1
1
2
1
0
0
2
1
1
1
0
0
1
0
0
2
1
2
1
2
1
0
1
2
1
0
0
1
1
1
1
2
1
0
1
0
1
1
1
1
0
0
3
0
1
0
1
2
0
1
2
1
1
2
0
0
1
0
0
1
1
1
1
2
1
0
0
1
2
1
2
0
2
0
1
2
1
2
1
0
1
0
1
2
2
0
0
2
1
0
2
1
1
1
0
1
0
0
0
1
1
0
0
2
1
0
2
1
0
1
1
0
0
1
2
0
0
0
1
0
1
2
0
0
0
0
2
0
2
0
3
0
1
1
0
2
1
0
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
0
1
1
2
1
0
2
0
2
2
0
0
0
0
1
2
0
2
1
1
0
0
1
1
0
0
1
1
0
1
0
1
2
0
0
0
0
2
0
2
0
0
3
1
0
0
1
2
1
0
0
0
1
0
1
3
0
0
1
1
1
1
0
1
2
2
1
2
1
0
2
2
0
0
0
2
1
1
0
2
0
0
1
2
0
2
0
3
2
0
0
1
1
1
3
1
1
1
1
1
2
2
1
1
2
2
1
0
0
2
0
1
1
0
1
2
2
1
1
2
1
0
2
2
0
1
0
1
2
1
1
2
1
0
1
1
0
1
0
1
0
0
0
2
1
1
1
0
1
1
1
1
0
1
1
1
1
0
0
1
1
0
1
1
1
1
1
0
0
1
0
1
0
0
1
1
1
0
0
1
2
1
1
0
2
2
0
0
1
0
0
2
2
0
0
1
1
1
1
0
2
1
1
1
2
1
1
1
2
1
1
1
1
1
0
1
1
2
1
0
1
1
0
2
0
0
1
0
0
0
0
0
1
1
1
0
1
1
0
0
0
0
0
0
2
2
1
1
2
0
1
0
1
0
1
1
1
2
0
2
2
1
0
1
0
0
0
1
1
1
0
0
2
1
0
1
1
1
0
1
0
1
1
2
0
1
1
1
2
0
0
0
2
1
1
1
2
0
0
0
1
1
0
0
1
0
0
1
2
1
2
1
0
2
1
1
0
1
2
0
1
0
0
1
0
0
1
0
2
0
0
0
1
1
0
1
3
1
2
1
1
1
1
2
2
2
0
2
0
0
1
0
1
2
1
2
1
2
0
1
1
0
1
1
2
1
0
0
0
2
0
1
1
0
1
1
0
3
0
0
2
1
1
2
1
2
1
1
1
1
1
1
0
0
2
2
0
1
2
1
1
0
1
0
1
2
0
2
2
0
2
2
0
2
1
2
1
1
0
0
2
1
1
0
2
1
1
0
1
1
0
0
0
1
2
1
0
0
1
1
0
2
0
0
1
2
0
0
0
0
1
2
0
1
2
0
1
2
1
0
1
1
1
2
1
0
1
1
1
1
1
0
3
1
0
0
1
1
2
0
0
1
0
0
2
1
1
0
1
1
1
2
2
1
1
1
1
1
0
2
1
2
1
2
0
0
0
1
1
0
1
0
1
0
1
1
0
1
3
0
2
0
1
2
2
1
2
1
1
0
2
1
0
0
0
1
0
1
0
2
0
1
1
1
1
1
0
0
2
2
1
3
2
5
1
2
1
1
1
0
0
0
2
1
1
1
0
1
1
2
0
1
0
0
2
0
0
2
2
0
2
1
0
0
1
1
0
1
1
1
0
1
1
2
0
2
1
2
3
2
2
2
1
1
1
0
0
1
0
2
3
0
1
0
0
0
0
1
1
0
0
0
1
1
0
2
1
0
1
0
0
1
1
1
0
2
0
1
0
0
1
0
1
0
0
1
0
2
0
1
1
1
1
1
1
1
1
2
0
0
1
1
0
1
2
0
1
1
0
2
0
4
0
0
2
1
3
0
0
0
2
0
1
2
1
2
2
1
1
1
0
2
1
2
2
0
0
2
1
2
0
2
0
1
0
2
1
1
0
2
0
0
0
0
1
1
1
2
1
0
1
2
1
1
1
1
0
1
1
2
0
2
1
1
0
1
0
0
0
2
2
0
0
1
0
0
1
1
2
0
3
2
1
0
1
2
1
0
1
1
0
1
1
0
0
0
1
0
3
2
2
0
0
0
1
0
1
1
1
0
2
1
1
0
1
1
1
4
0
1
1
1
2
1
1
3
1
0
0
0
2
0
3
1
1
0
0
2
1
1
0
0
1
2
0
0
2
0
0
1
1
1
2
1
1
1
0
1
1
1
2
2
0
2
1
0
2
0
0
1
2
1
1
0
1
1
0
1
2
2
2
0
1
1
0
0
2
1
2
0
0
0
1
0
0
1
2
2
2
0
2
2
2
0
0
0
0
0
1
1
0
0
0
0
2
0
0
1
2
2
0
0
2
1
2
0
2
0
1
1
0
1
0
1
0
0
2
2
1
0
2
1
0
1
1
0
2
2
1
1
0
0
0
1
0
3
1
2
1
2
1
0
0
1
1
1
1
2
0
0
0
2
1
0
0
0
2
1
0
0
1
1
2
1
0
1
1
0
1
1
1
1
1
0
0
2
1
2
0
0
1
2
0
2
2
1
0
1
2
2
0
0
0
1
1
3
0
0
1
1
0
1
1
0
1
1
2
0
0
1
1
1
2
0
0
2
2
2
1
1
1
1
0
1
0
2
2
1
0
1
3
0
2
0
0
0
1
0
0
0
2
1
0
1
0
1
0
0
0
2
0
0
2
2
1
0
0
0
1
0
2
1
0
0
2
1
0
2
2
0
0
0
0
1
1
1
2
1
0
1
2
1
0
1
1
1
0
1
0
1
1
1
0
2
2
1
3
1
1
2
1
0
0
1
2
1
0
1
0
1
1
1
1
0
1
0
0
2
1
1
0
0
0
1
0
1
2
0
0
0
0
0
1
1
4
2
2
1
2
2
1
0
2
1
1
1
0
1
2
1
2
0
0
1
1
1
3
0
1
2
2
0
2
1
2
0
1
2
1
0
1
0
0
2
2
1
0
2
1
1
0
2
0
2
0
0
2
0
1
1
1
2
1
1
2
2
0
0
0
1
1
1
2
2
1
0
1
0
1
1
0
0
0
2
0
0
0
0
0
0
2
1
0
2
0
2
1
1
0
1
1
2
0
2
0
1
2
1
1
0
0
0
2
1
1
0
0
2
0
1
1
1
2
2
1
0
0
2
1
1
0
0
1
2
1
1
1
0
1
1
1
1
1
0
0
1
1
1
1
1
0
1
0
1
0
0
2
2
0
1
0
1
2
1
0
1
0
0
2
1
1
2
1
1
2
1
1
1
2
2
3
1
1
0
0
2
0
2
1
0
0
2
0
1
2
2
2
1
2
0
1
2
0
0
2
1
1
1
1
3
1
1
1
0
1
1
1
1
1
2
1
1
1
2
1
1
1
0
1
0
1
0
2
1
1
1
1
0
1
0
1
0
1
0
0
0
2
1
0
2
4
1
2
1
0
0
1
1
0
1
2
1
0
1
1
1
0
1
1
2
2
1
1
2
1
2
2
0
2
1
0
1
1
0
0
1
0
1
0
1
0
2
1
0
0
0
0
0
0
1
2
1
0
0
1
2
1
0
0
3
2
0
2
1
2
1
0
1
1
2
0
2
0
0
1
0
0
0
0
2
0
1
0
1
0
0
0
0
1
1
0
1
2
0
1
0
2
0
1
2
0
1
0
1
1
2
1
1
2
2
1
0
1
1
0
1
1
1
0
2
0
1
1
0
1
1
1
2
1
1
1
2
2
0
2
1
0
1
1
1
1
2
2
0
1
0
0
0
0
1
0
1
2
0
0
1
0
1
0
2
1
0
2
1
2
0
1
0
0
0
0
2
0
0
2
1
0
0
0
1
1
0
2
0
2
1
1
0
0
2
2
0
1
1
0
1
2
1
1
0
2
1
0
1
1
0
1
2
3
2
1
1
0
2
0
1
0
1
1
0
0
1
1
2
2
1
0
0
0
0
1
1
0
2
2
2
0
2
0
2
0
1
2
0
1
0
0
0
1
2
0
1
1
1
1
1
2
0
1
0
0
1
0
2
1
2
1
0
0
0
2
1
1
0
0
2
1
2
1
1
0
1
2
0
0
2
1
0
0
2
0
1
1
1
2
1
1
2
1
0
2
0
1
2
1
2
1
2
2
2
1
1
2
1
0
1
0
0
3
0
1
0
0
1
1
2
1
1
0
0
1
0
1
2
1
2
2
0
0
0
0
1
1
2
0
0
1
2
0
2
1
1
2
2
2
2
1
0
1
0
0
3
1
1
0
2
1
1
2
0
1
1
2
1
6
2
0
1
1
1
1
1
0
1
1
1
1
0
0
0
0
0
0
0
0
1
0
2
2
1
1
1
0
1
1
0
0
0
1
1
2
0
1
1
2
0
1
2
0
1
0
1
1
0
0
1
1
0
2
1
2
1
1
1
1
0
0
2
1
2
1
1
2
0
0
0
0
1
1
1
0
0
1
0
1
1
0
0
1
0
0
1
2
0
2
0
2
1
0
1
0
0
2
0
0
2
0
0
0
1
0
1
2
1
2
3
1
0
2
1
2
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
1
1
1
2
0
2
1
0
0
0
0
1
0
0
0
2
0
1
0
1
2
0
0
0
3
0
1
1
1
2
1
0
1
0
1
1
0
2
0
0
2
0
0
0
0
1
2
1
1
2
2
2
0
0
1
1
0
2
1
2
1
1
1
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
2
0
1
1
1
0
1
0
0
1
0
0
0
0
1
1
0
1
0
2
1
1
0
2
0
1
0
0
0
1
1
2
1
0
2
0
2
2
1
0
2
2
1
2
1
0
2
1
1
1
0
2
0
0
1
0
0
2
0
0
2
2
1
2
1
2
1
0
2
1
2
2
2
0
0
0
0
2
1
1
0
1
0
1
0
2
0
1
2
1
1
1
1
0
2
1
1
2
2
1
1
1
1
0
0
0
1
1
1
1
2
1
5
0
0
0
2
2
1
0
1
1
0
0
1
0
0
0
0
1
1
1
1
3
0
0
1
1
1
1
1
0
1
1
1
1
1
0
1
0
0
2
0
2
3
2
1
2
0
1
1
0
3
1
2
2
0
1
2
1
0
1
1
0
0
2
1
0
2
0
1
2
1
0
1
0
1
0
0
1
0
1
1
0
3
1
0
0
1
1
0
0
2
0
1
1
0
0
2
1
2
2
2
3
0
1
1
0
1
1
0
2
1
1
1
0
0
0
0
2
0
0
0
2
0
0
0
0
2
2
1
2
0
0
2
1
0
1
0
0
1
0
1
1
1
0
2
0
2
1
1
1
1
1
0
1
1
2
0
0
0
0
1
2
1
1
2
1
1
2
2
1
2
0
1
2
1
0
0
0
1
0
0
0
1
1
0
1
1
1
2
2
2
1
1
2
1
1
0
2
0
0
1
0
2
2
0
1
2
1
1
1
2
1
1
2
1
0
1
1
0
2
2
0
0
1
0
0
1
1
1
0
2
0
1
2
0
1
2
0
0
0
1
1
1
2
1
2
0
0
0
2
0
2
0
1
1
2
0
1
1
0
0
1
0
1
2
1
0
2
2
0
2
2
0
2
2
0
1
0
0
1
1
0
0
1
1
0
2
2
1
1
2
0
1
2
0
1
1
0
0
0
1
1
2
0
1
2
1
0
1
1
0
1
1
0
0
0
1
2
0
1
0
0
0
1
0
0
0
0
0
2
2
0
1
1
0
1
1
0
2
2
0
0
1
2
2
2
0
0
1
0
1
1
1
0
1
1
1
2
0
1
1
1
1
1
2
1
2
1
0
2
1
0
0
2
1
0
1
1
1
1
0
0
0
1
0
0
2
1
2
1
0
1
0
2
1
1
1
0
1
0
0
0
0
1
1
0
0
2
0
1
1
2
1
2
2
0
2
0
2
1
0
0
1
0
1
2
1
0
1
0
1
2
1
0
1
2
0
1
1
2
0
0
1
0
0
1
2
2
0
0
1
2
0
0
2
0
2
2
0
1
1
2
0
1
2
0
2
0
1
2
1
0
1
0
1
1
0
0
2
2
0
2
0
0
3
0
0
1
1
0
0
2
2
1
0
1
1
0
2
2
0
1
1
1
1
0
2
1
0
2
1
1
1
2
0
2
0
1
1
2
0
1
2
0
0
1
1
2
0
0
1
0
0
0
1
0
1
1
0
0
1
0
1
0
1
2
0
0
2
0
0
0
1
2
2
1
0
0
1
0
2
0
0
1
1
1
0
2
1
1
0
1
0
0
0
0
1
2
1
1
0
1
1
1
0
0
1
2
1
2
1
1
0
1
2
2
0
1
0
0
2
1
2
1
0
2
0
1
2
0
2
0
1
0
0
0
0
1
0
0
0
2
0
1
1
1
2
0
1
1
0
1
0
2
1
1
1
0
1
1
3
2
1
2
0
1
0
0
0
2
1
0
1
1
1
1
0
1
1
1
0
1
1
0
2
3
1
1
1
2
2
1
1
2
0
2
1
2
0
1
0
2
2
1
1
0
1
0
1
0
2
1
2
2
2
1
1
1
2
2
2
1
0
1
0
2
0
1
2
2
3
0
0
0
1
1
0
1
1
2
1
0
1
1
1
0
1
1
1
0
0
0
2
2
1
0
0
0
1
0
1
1
1
1
2
0
2
2
1
0
2
2
2
3
0
0
0
0
0
1
0
1
1
1
0
2
0
0
2
2
1
1
2
0
1
0
2
1
0
0
1
2
2
0
2
1
0
2
0
0
0
1
1
1
2
1
2
2
1
1
0
1
0
1
1
0
1
1
1
0
1
1
0
3
1
1
1
1
0
1
0
1
0
1
1
2
1
0
0
0
0
0
1
2
0
0
0
1
1
2
1
1
2
1
2
2
2
1
1
1
2
1
0
1
0
0
1
0
2
4
0
2
2
0
2
0
0
2
3
2
1
2
2
1
3
0
1
0
1
2
1
0
2
0
3
1
0
1
1
1
0
1
0
0
1
0
0
0
1
0
2
0
1
1
1
0
1
1
0
1
0
0
1
1
1
0
0
1
1
1
0
0
1
1
1
1
3
1
2
2
0
0
0
0
2
0
2
0
2
2
2
1
0
1
0
0
1
0
2
1
0
1
1
0
0
1
0
1
1
1
1
0
0
1
0
0
1
2
1
1
1
2
0
2
3
0
0
1
2
0
1
2
1
1
0
0
0
2
2
1
0
0
2
2
2
2
1
0
2
0
1
1
0
1
0
0
0
0
1
2
2
0
0
0
2
0
1
0
1
1
2
1
2
2
0
2
1
1
1
2
0
1
2
2
2
2
0
1
0
0
2
2
0
0
3
0
1
1
0
0
0
0
2
0
2
1
1
0
0
1
0
0
0
0
0
0
1
2
2
3
1
0
0
0
1
2
2
0
1
1
3
1
2
1
1
2
0
6
0
1
1
1
1
0
1
0
0
1
1
0
0
0
0
0
1
0
1
1
0
0
0
1
1
3
0
0
1
1
1
1
1
0
1
1
0
1
1
2
1
1
1
1
2
2
1
0
2
0
1
2
0
1
1
2
2
2
1
1
0
1
1
1
1
1
0
1
1
2
0
4
0
2
1
0
1
0
1
1
0
1
2
0
2
2
0
0
0
0
1
0
2
1
2
1
1
1
1
0
1
0
0
1
5
2
1
0
1
1
0
1
1
1
1
0
1
2
1
1
1
0
0
1
0
2
1
1
1
0
1
1
0
2
0
1
2
2
0
1
1
1
0
2
1
2
1
1
1
0
2
0
0
1
1
1
0
1
1
1
2
0
1
1
1
0
0
1
2
1
0
0
0
1
0
2
0
1
1
1
0
2
0
1
2
1
1
0
1
1
0
0
1
2
2
4
1
1
0
2
1
0
2
1
1
1
1
2
0
0
0
0
0
0
1
2
2
0
2
1
0
0
1
3
1
1
0
0
0
0
2
2
0
0
1
1
1
1
0
0
1
2
0
0
0
0
1
4
0
0
2
2
1
0
1
1
0
1
1
0
0
1
1
2
0
1
1
1
0
1
2
2
1
0
0
0
0
2
0
2
2
1
0
2
1
1
1
0
2
2
0
1
2
6
0
0
1
2
1
1
1
1
0
0
0
0
0
0
2
2
1
2
0
2
3
0
0
0
0
1
0
2
2
2
2
0
1
1
0
2
1
0
2
2
0
1
1
0
1
1
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
2
1
2
0
0
0
0
1
0
2
0
2
0
2
1
0
0
0
0
0
0
1
0
0
1
1
0
0
1
1
1
3
0
1
0
1
1
1
2
2
0
0
2
1
1
1
1
0
1
0
1
1
2
1
0
0
0
3
1
1
1
0
0
1
1
0
0
1
1
1
0
0
2
2
1
0
2
0
1
1
0
2
0
1
0
1
0
2
1
1
0
2
1
1
1
2
1
0
1
1
1
1
0
0
1
1
2
0
1
2
1
1
1
0
0
0
1
0
1
1
1
0
2
0
1
1
2
0
0
0
2
0
1
1
1
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
1
2
0
1
1
2
1
0
0
0
1
0
2
1
0
1
1
0
1
1
0
0
2
0
0
2
1
1
1
1
0
1
0
0
0
2
0
0
2
1
0
1
2
2
0
0
1
0
0
2
1
0
1
0
2
2
0
1
0
0
1
0
2
1
0
0
0
1
0
2
2
0
1
0
1
2
1
1
0
2
2
2
1
1
2
0
0
0
1
2
0
1
0
1
1
1
1
1
0
1
1
0
0
1
0
0
1
1
4
0
2
2
0
0
0
2
1
2
1
2
1
0
0
0
0
0
1
0
1
1
1
0
0
2
2
0
2
1
0
1
0
2
1
1
0
0
1
2
3
0
2
1
1
0
0
2
1
3
0
1
0
0
1
0
1
1
1
2
0
1
1
1
0
1
0
1
1
1
1
0
0
1
1
0
1
0
1
0
2
1
1
1
1
1
0
0
0
1
1
0
2
1
1
1
0
0
1
2
0
2
0
0
1
0
0
0
2
2
2
1
0
0
0
0
0
0
2
1
1
0
0
1
0
0
2
1
2
0
1
0
2
1
0
1
0
1
1
0
0
1
2
2
0
1
2
1
0
0
1
0
1
0
0
1
1
0
1
0
3
0
1
0
1
1
1
1
0
0
1
1
1
1
2
1
2
0
0
1
1
0
0
0
0
1
2
1
0
1
1
1
1
0
0
1
1
0
0
0
3
1
0
0
1
1
0
1
1
1
0
1
0
0
1
1
0
1
0
2
0
0
0
1
1
0
3
1
2
0
1
0
0
1
1
0
0
2
1
2
0
0
1
0
1
0
1
0
0
0
0
0
1
1
1
1
0
2
2
1
1
1
1
0
1
1
2
1
1
1
2
2
2
0
0
0
0
2
1
0
0
1
2
2
1
1
0
1
0
2
0
0
1
2
2
0
1
0
0
1
1
1
1
1
0
2
1
1
1
1
0
0
1
0
2
1
0
2
0
0
1
0
3
0
2
1
0
1
1
1
0
2
0
0
2
2
1
0
1
1
3
0
2
0
1
2
2
0
1
1
0
2
0
2
2
1
0
0
0
0
1
0
0
1
2
2
0
2
2
0
3
0
1
1
1
1
0
1
2
0
1
0
0
1
0
1
0
1
1
0
1
1
1
2
0
1
0
0
1
1
1
0
0
0
3
0
1
2
1
1
0
1
2
2
1
1
2
2
2
0
0
0
0
2
1
1
1
1
0
1
0
0
1
2
1
0
1
0
0
2
0
1
2
1
0
1
0
2
1
1
1
2
1
0
1
0
1
1
1
0
1
0
0
0
1
1
2
0
1
0
2
0
1
1
1
1
1
2
0
2
1
1
3
0
2
0
0
0
1
0
1
1
1
1
0
3
0
0
2
0
0
0
2
0
2
1
1
0
2
0
0
5
0
0
1
0
0
2
0
0
0
1
0
1
0
2
0
1
0
1
2
2
1
1
0
0
0
1
1
0
0
2
2
1
0
2
1
0
0
0
1
2
1
1
1
0
1
1
0
2
0
0
1
1
0
0
0
0
0
2
1
1
0
0
1
1
0
1
1
2
2
1
0
0
2
1
2
2
0
1
0
0
1
0
0
0
1
1
0
1
1
1
2
2
0
2
1
0
2
1
0
2
1
1
0
1
2
1
1
1
1
2
1
0
1
1
1
0
1
1
1
1
0
0
2
2
0
2
1
2
0
0
1
0
1
0
0
2
2
1
0
0
1
2
1
0
0
1
2
1
1
1
0
0
0
2
1
0
0
1
0
0
2
0
1
1
0
2
1
1
2
1
0
0
1
2
0
2
0
0
2
1
0
2
1
2
0
0
1
0
1
0
2
0
1
2
1
2
1
0
1
1
0
1
2
1
0
1
0
1
2
1
1
0
2
2
1
2
1
0
0
0
0
2
0
0
1
2
1
3
0
1
2
1
2
2
2
0
1
1
1
5
1
0
1
2
1
2
1
1
0
0
1
1
0
2
2
1
0
1
1
0
2
1
0
0
1
0
0
1
2
0
0
0
1
2
1
0
0
0
0
0
2
2
3
0
1
1
1
0
2
1
1
2
2
2
0
1
1
1
1
1
0
1
1
1
1
1
1
1
2
0
1
0
0
0
2
0
0
1
2
2
1
1
0
0
2
0
1
1
0
2
1
2
0
2
2
1
1
2
1
1
0
1
0
2
1
0
1
1
1
1
2
2
0
0
2
3
0
2
1
1
2
0
1
0
1
0
1
1
1
0
1
1
1
1
1
3
1
0
1
2
2
1
1
1
1
1
2
0
1
0
1
0
2
2
2
0
1
0
0
0
0
1
0
1
2
1
0
1
0
1
2
1
1
1
0
1
1
1
1
0
0
2
1
0
0
0
2
2
1
1
0
0
1
2
2
2
0
0
1
0
2
0
2
0
1
1
0
0
0
0
0
0
1
1
0
1
0
0
1
2
0
0
1
1
1
0
0
2
0
1
0
1
0
2
0
0
2
0
0
1
0
1
0
0
2
1
2
0
2
0
0
1
1
0
0
0
0
0
0
1
0
2
1
2
1
2
0
1
2
0
1
2
1
0
2
1
0
0
0
1
2
2
0
0
0
1
0
0
0
1
1
0
0
2
0
0
0
0
2
1
2
0
1
0
0
1
2
0
0
0
3
0
1
0
0
1
2
1
1
0
1
0
2
1
2
0
1
1
2
2
1
1
2
1
2
2
1
0
1
1
0
0
0
1
1
2
0
0
0
0
1
0
1
1
0
1
1
2
0
1
0
2
1
1
0
0
2
1
1
1
2
1
0
2
1
3
1
0
1
1
1
0
1
1
0
2
1
1
1
1
0
1
1
1
0
1
0
0
0
1
0
0
0
2
1
1
0
2
1
0
1
0
1
1
0
1
1
1
1
0
3
0
2
0
0
0
0
0
2
0
1
1
0
0
2
2
0
2
2
2
1
1
0
1
0
2
2
0
2
0
1
1
1
1
2
2
2
2
1
0
2
0
0
0
1
1
0
2
0
2
1
0
1
2
2
0
0
0
0
0
2
1
1
0
0
2
2
0
1
0
0
0
1
0
1
1
2
0
1
1
0
0
0
1
1
0
2
0
3
2
0
0
0
0
1
0
1
0
1
0
2
0
1
2
0
1
1
0
2
0
1
1
1
1
1
2
0
0
0
1
1
1
2
2
0
1
1
2
0
0
1
1
0
1
0
1
1
1
0
1
1
0
0
0
1
1
1
1
1
1
1
2
0
0
3
1
0
3
1
0
0
0
1
0
2
2
0
1
1
2
0
0
0
1
1
1
1
2
1
0
2
1
1
0
1
0
0
1
2
0
2
0
1
1
0
2
0
2
0
2
0
1
2
2
0
2
2
1
0
0
0
1
0
0
2
2
0
1
1
1
0
1
0
0
1
2
1
0
1
0
2
0
1
0
0
0
0
1
1
1
0
0
1
1
0
1
2
1
1
0
0
1
1
0
2
1
0
1
0
3
1
1
1
2
1
2
1
2
0
1
1
0
1
1
2
2
2
1
1
0
0
2
1
2
0
1
2
0
2
2
2
1
0
1
0
0
1
2
1
0
1
0
1
1
1
1
2
2
1
1
1
0
1
0
1
2
0
1
0
3
0
1
1
1
0
1
0
1
1
0
1
0
1
1
0
0
6
1
1
0
2
1
1
2
1
2
2
0
1
0
2
2
2
0
1
1
0
1
1
2
1
1
2
1
0
1
0
0
1
1
2
1
1
0
0
1
1
1
2
1
0
0
0
0
1
1
1
0
2
2
1
0
0
1
0
2
0
0
0
0
2
1
2
0
1
0
1
2
2
2
0
0
1
2
1
0
1
0
2
1
1
0
1
0
0
0
1
0
1
1
0
1
2
1
0
1
1
2
1
1
0
0
1
0
1
1
2
2
1
0
1
0
1
0
0
2
1
2
1
0
1
0
2
0
0
2
0
2
1
1
0
0
0
2
1
1
1
2
1
1
1
2
1
2
0
1
2
1
2
0
0
1
2
0
1
1
1
1
2
2
0
0
1
0
1
0
1
0
0
0
0
2
1
0
1
1
1
0
0
1
1
1
0
0
1
1
2
0
1
1
0
2
1
1
0
1
1
1
1
0
0
1
0
2
0
0
0
1
2
2
1
2
3
2
1
0
0
1
1
1
1
0
0
0
1
1
2
1
2
1
0
2
0
1
1
1
1
0
1
0
0
2
1
1
0
2
2
2
0
1
0
0
0
2
0
1
1
1
2
1
1
1
0
1
0
0
2
0
1
2
1
1
2
1
0
1
0
0
1
1
0
1
1
1
2
1
2
2
0
0
1
1
1
1
1
1
1
1
1
1
0
0
1
1
3
1
1
1
1
0
1
2
2
1
0
0
2
2
0
2
0
1
0
2
0
0
1
1
0
1
1
2
1
1
0
2
1
1
2
0
0
0
0
1
1
1
3
1
2
1
1
1
2
0
0
1
0
1
1
2
1
1
1
1
0
2
2
1
1
2
0
0
1
2
0
1
0
2
1
2
3
2
1
1
2
1
0
1
1
1
2
0
2
1
0
2
0
1
3
3
2
1
1
0
1
0
1
1
1
2
1
2
1
0
1
1
2
0
0
1
1
0
1
1
0
2
0
1
1
1
0
1
2
2
0
1
0
2
0
1
2
0
2
1
1
0
2
2
0
1
2
2
1
1
1
1
2
0
2
0
2
0
0
1
2
2
0
0
2
1
1
1
2
2
2
1
2
0
1
0
0
1
0
3
0
3
0
1
0
2
1
1
1
0
1
2
2
1
1
2
0
0
2
1
0
0
2
0
0
2
0
1
0
0
1
2
1
2
2
0
1
0
2
1
1
2
0
1
2
0
1
2
0
2
0
1
0
2
2
0
1
3
2
1
0
1
1
0
1
2
0
0
1
1
2
0
1
1
1
0
2
2
0
0
0
1
0
2
1
1
1
1
2
1
2
1
0
2
2
0
2
2
0
0
0
0
2
1
1
0
0
1
1
0
0
0
1
2
0
2
0
0
0
0
1
0
2
2
1
0
0
1
0
1
2
1
1
0
1
2
0
1
0
1
1
0
0
1
0
1
0
0
1
1
0
0
1
0
1
0
0
0
2
0
0
1
2
0
1
0
1
1
2
1
1
2
0
0
1
0
1
1
0
0
0
2
0
0
2
2
1
2
1
0
0
1
1
0
1
1
0
1
0
1
1
1
1
1
1
0
0
0
1
0
1
0
0
2
1
2
1
0
0
2
2
1
0
0
2
1
1
1
0
0
1
2
1
0
1
0
0
2
1
2
2
0
1
0
1
2
1
2
2
1
0
2
0
0
0
1
1
0
1
1
0
1
1
2
1
2
1
1
0
1
1
1
0
1
2
0
1
0
2
1
0
1
0
0
1
0
0
1
1
0
1
1
1
2
1
2
0
1
0
0
3
0
1
1
1
0
1
0
2
1
2
2
1
1
0
0
1
1
3
0
0
1
2
1
1
2
2
2
1
2
1
0
2
1
2
0
2
1
1
1
0
0
1
1
0
0
1
1
1
2
1
0
0
0
2
1
2
0
1
2
2
0
2
1
1
0
0
1
0
1
2
1
1
2
0
1
1
2
1
0
1
0
2
1
1
2
2
1
1
3
0
1
2
1
1
0
2
1
0
1
2
1
0
0
2
0
0
2
0
1
0
1
1
0
0
2
0
1
0
1
0
1
1
1
2
0
6
1
1
2
1
2
2
0
1
0
0
2
0
0
1
0
0
1
0
2
0
3
2
1
1
2
2
1
1
1
2
0
0
1
1
2
2
1
1
0
1
1
1
0
2
1
0
1
0
1
0
0
0
0
3
1
1
1
1
1
0
1
1
0
1
0
1
0
2
0
0
0
2
0
0
1
1
2
2
0
0
1
0
1
1
0
0
0
1
1
0
1
2
2
0
1
1
0
1
1
1
2
4
0
1
2
2
2
1
2
0
2
1
1
1
0
0
2
1
1
1
1
0
1
2
1
0
1
2
1
0
0
1
1
2
0
1
2
3
0
2
0
1
2
0
1
1
1
2
0
0
1
1
1
1
0
1
1
1
1
1
1
1
1
1
0
0
2
1
2
1
2
1
1
0
0
1
0
1
1
0
2
1
2
0
1
1
0
1
2
1
0
2
1
2
0
2
2
0
1
0
1
1
2
0
2
1
0
1
1
1
0
0
1
1
2
2
3
0
0
2
1
0
2
1
1
2
0
0
1
0
1
1
1
1
1
2
2
2
1
2
1
1
3
0
2
0
0
0
1
0
2
0
1
0
0
1
0
2
1
2
0
1
0
0
0
3
1
0
3
1
2
1
0
1
1
0
1
1
2
2
1
0
0
1
0
1
0
1
0
1
1
0
1
2
1
0
0
0
0
1
1
0
2
0
0
2
0
1
0
0
1
0
2
0
0
1
0
1
1
1
1
1
0
1
0
2
1
1
0
2
0
2
2
0
1
1
2
0
1
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
2
2
1
2
0
1
1
0
1
1
0
1
0
1
1
0
0
1
1
1
1
0
1
0
0
0
1
1
0
0
2
0
1
2
2
2
0
2
2
1
1
0
0
1
0
1
1
1
1
1
1
1
3
2
1
0
0
0
0
0
0
0
1
0
1
1
1
1
3
0
1
0
1
2
0
2
1
1
0
1
0
2
1
0
0
2
0
0
1
0
3
1
0
0
2
0
1
2
2
0
3
0
0
1
1
0
0
1
2
0
0
0
0
0
1
2
0
2
0
0
1
0
0
2
2
1
0
0
0
2
2
1
0
1
2
1
0
1
1
0
0
1
0
2
1
2
1
1
0
0
2
1
1
1
1
1
0
1
1
2
1
0
1
1
1
2
2
1
0
0
1
2
0
1
1
1
1
1
0
1
0
0
0
0
1
1
1
0
1
2
0
1
3
1
0
2
2
0
2
0
0
0
0
1
0
1
1
1
2
0
0
0
1
0
2
0
0
1
0
1
0
0
1
2
0
3
1
2
1
1
2
1
0
0
1
1
0
1
1
2
0
0
1
1
2
2
1
1
0
1
0
1
1
0
1
0
0
0
2
1
0
1
2
1
1
1
1
2
2
1
2
0
0
0
2
1
1
1
1
0
1
0
2
1
0
1
1
2
1
0
0
0
1
0
2
1
1
1
0
2
1
1
1
0
1
2
1
0
0
2
1
0
0
0
2
1
0
0
2
0
1
1
0
1
0
1
2
1
1
0
0
0
0
1
1
0
2
1
1
1
2
0
0
2
1
0
1
0
2
1
1
1
2
0
0
0
0
0
2
1
0
0
0
0
0
1
0
1
2
0
1
2
1
2
0
1
0
0
1
1
1
1
0
2
1
1
1
1
1
0
2
1
1
1
0
1
0
0
2
1
1
1
0
1
1
1
2
1
2
0
0
1
0
0
1
1
2
1
1
1
1
0
1
1
2
1
0
3
2
2
1
1
0
0
0
1
0
1
0
1
1
0
1
1
0
1
0
1
1
2
1
0
1
2
1
1
0
0
1
0
1
2
1
1
0
2
2
0
1
1
1
1
0
2
2
0
1
0
0
0
1
1
2
1
2
2
0
1
0
0
0
1
1
1
1
2
1
1
0
2
1
2
0
0
2
1
0
1
1
1
0
2
1
0
0
1
0
0
1
2
1
0
0
0
2
1
0
1
0
1
2
1
2
2
1
0
0
1
2
1
1
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
1
1
0
1
1
1
2
1
0
2
0
1
1
2
0
0
0
1
2
0
0
2
2
1
1
2
1
2
0
1
2
0
1
1
0
0
1
2
1
1
0
2
1
0
0
2
0
2
0
1
1
1
2
0
1
1
0
0
2
2
1
1
1
0
2
2
0
1
0
1
1
0
1
2
2
1
1
1
0
0
0
1
2
1
0
2
1
1
0
1
1
0
0
1
1
2
2
1
0
0
0
1
1
0
0
0
1
0
2
0
3
0
1
0
1
2
1
0
0
1
0
1
0
1
1
0
2
0
1
1
2
0
1
0
2
2
1
1
0
0
0
2
1
2
1
1
0
1
1
1
2
1
1
1
1
1
0
0
1
4
2
1
0
1
2
2
0
0
2
2
0
0
2
0
0
1
2
1
0
1
2
0
0
0
0
1
0
0
0
1
0
1
3
1
0
1
0
0
0
0
1
4
2
2
2
0
0
1
0
0
2
2
2
0
2
0
2
1
1
1
2
1
0
1
0
0
0
1
0
1
1
2
0
0
1
2
2
2
2
0
2
2
1
1
1
1
1
1
2
1
0
1
3
2
0
1
1
2
2
1
0
1
1
0
0
2
1
1
1
1
1
1
1
1
0
1
1
2
1
1
1
1
0
1
0
2
1
2
0
0
0
1
1
2
1
2
1
1
1
2
1
2
2
1
1
0
0
0
0
0
0
2
0
1
2
0
1
0
0
1
1
2
2
2
2
1
0
1
2
1
1
1
2
1
0
0
2
1
1
0
1
0
1
1
1
2
1
1
0
1
0
2
1
2
1
1
1
1
1
1
0
2
1
1
0
1
0
0
0
1
1
1
3
1
2
0
2
1
1
3
2
0
0
2
2
2
0
2
1
2
1
0
1
1
1
0
5
1
1
2
1
0
1
1
1
0
0
1
1
0
0
0
1
1
0
0
0
2
0
0
0
0
1
2
0
0
1
1
1
1
0
0
0
0
1
0
0
1
1
1
0
2
2
1
1
1
2
2
1
1
0
0
2
1
2
1
0
1
3
1
2
1
2
1
2
1
2
1
1
0
0
1
0
2
1
1
0
0
1
1
0
1
1
2
1
1
0
1
0
0
1
0
1
1
1
1
2
1
1
3
0
0
0
2
1
2
0
2
2
3
0
1
2
2
0
0
0
0
1
0
1
2
2
2
0
1
0
2
1
0
1
0
0
1
0
1
1
2
1
2
1
2
1
0
2
1
0
0
1
1
0
1
1
2
1
0
1
0
0
1
0
2
0
1
1
0
2
1
0
0
2
0
1
0
0
0
1
0
1
2
2
1
2
0
0
1
0
1
1
1
3
0
0
2
1
0
6
0
1
1
0
2
1
1
0
1
0
0
1
0
0
0
2
1
0
1
0
1
0
0
2
0
2
3
0
2
2
0
2
1
2
2
1
1
0
2
1
1
1
0
0
1
2
2
1
1
2
1
1
0
2
0
2
0
1
2
1
2
0
1
0
1
0
0
1
2
0
2
0
1
0
0
1
2
0
1
2
0
1
0
1
1
0
0
1
1
0
2
1
0
1
1
0
1
0
1
2
1
2
1
0
0
1
0
1
0
2
1
1
2
2
2
2
1
1
0
2
1
1
0
0
0
2
1
1
1
0
0
1
1
1
0
0
0
1
1
0
1
0
2
1
1
2
0
2
1
1
0
1
1
0
0
1
1
0
0
0
0
2
1
0
0
0
1
1
1
1
2
1
0
1
2
1
2
0
0
0
0
2
0
2
1
2
0
0
1
1
2
0
0
0
2
2
1
2
0
0
1
1
2
1
1
0
1
2
2
2
1
1
0
0
1
0
1
2
2
0
1
0
1
1
0
0
1
2
0
0
2
2
0
1
1
0
2
0
0
0
2
1
2
0
0
0
2
0
0
2
2
0
2
0
2
0
2
1
1
2
1
2
1
0
1
2
0
0
0
0
0
1
0
2
0
1
1
1
1
2
0
0
1
0
0
1
1
2
1
2
2
1
2
1
1
1
2
2
0
2
0
1
0
0
0
0
2
1
1
1
0
0
0
1
0
1
1
2
0
0
1
1
0
1
0
0
0
0
2
0
1
2
2
0
1
2
1
2
2
1
1
1
0
2
1
2
0
2
1
1
1
1
0
1
1
1
0
1
1
0
0
2
2
0
2
1
2
0
0
2
2
0
2
1
2
1
1
1
0
1
0
1
2
1
1
1
1
1
0
0
0
0
0
2
1
1
1
0
1
2
0
0
0
1
1
0
1
1
2
2
1
2
1
0
1
0
0
1
2
1
1
1
1
1
1
0
1
0
1
1
1
0
1
2
2
0
0
2
2
0
1
0
1
2
1
0
2
2
0
1
0
0
2
2
1
1
1
2
2
1
1
2
0
1
2
1
1
0
0
0
1
0
2
0
2
1
1
1
1
0
1
0
0
2
0
1
1
1
0
1
1
2
0
1
0
2
0
1
0
0
1
1
1
1
0
0
1
1
1
2
0
0
2
2
1
1
0
2
1
2
1
1
1
1
2
2
1
2
0
1
1
0
1
2
1
1
1
0
1
1
1
1
0
2
0
1
1
1
1
1
1
0
0
1
1
0
1
1
1
0
1
1
0
1
1
1
0
0
1
0
0
0
0
1
2
1
1
0
0
0
1
0
0
2
0
2
2
2
2
1
0
2
1
0
1
2
1
1
1
1
0
0
5
0
3
0
1
1
1
1
1
1
1
1
0
0
2
1
1
3
1
1
1
2
2
3
2
0
0
0
0
2
1
0
1
1
1
1
0
0
1
1
1
1
1
1
1
1
2
1
0
2
1
0
1
0
2
1
2
0
0
0
0
0
2
2
0
1
0
1
2
1
2
0
1
1
0
2
1
2
2
1
2
1
1
0
4
1
2
1
2
1
1
1
1
0
0
0
2
0
1
0
0
0
0
1
0
1
2
2
1
1
1
1
0
2
1
1
1
0
2
1
2
1
1
2
2
1
2
1
1
3
1
1
1
0
0
0
1
1
1
1
1
0
0
1
0
0
0
3
2
2
0
0
1
1
1
0
1
1
1
1
0
1
1
1
1
1
0
1
0
0
1
1
1
0
0
1
0
2
2
1
0
1
1
1
0
0
1
0
1
2
0
1
2
2
0
1
1
0
1
0
1
1
1
1
0
0
1
0
0
0
2
0
2
1
0
1
2
1
0
1
1
0
1
0
2
2
1
2
2
2
0
0
0
2
1
0
2
2
1
1
4
2
1
2
0
1
0
1
1
1
0
3
1
1
0
0
2
2
2
1
1
0
2
2
1
0
1
0
2
1
1
2
1
1
1
1
2
1
0
1
1
1
0
1
1
1
2
0
1
2
0
2
0
0
0
0
1
1
0
2
0
2
1
1
0
1
1
0
0
2
1
0
2
0
0
1
2
2
0
2
2
0
2
1
1
1
0
0
1
1
1
0
2
0
2
0
0
3
1
0
0
0
0
0
0
0
2
1
1
2
0
2
0
2
1
2
0
1
1
1
0
2
1
1
0
1
1
0
0
2
1
0
1
1
0
1
4
2
1
0
1
0
1
0
1
1
0
1
0
0
0
0
0
1
0
1
0
1
1
0
0
0
2
3
0
1
0
1
1
1
0
1
1
0
2
1
2
1
0
1
2
0
2
0
0
1
2
1
0
0
1
2
2
1
1
1
2
1
1
1
1
1
2
1
1
0
0
1
0
1
1
1
0
3
1
2
0
0
1
2
0
1
1
1
0
1
1
2
0
0
1
0
2
0
0
2
2
1
0
1
2
2
2
2
0
2
1
1
2
3
1
1
0
2
0
1
0
2
1
0
1
1
1
0
0
1
2
1
2
0
1
3
0
1
0
1
2
1
2
1
0
0
0
0
0
1
0
2
1
1
1
0
2
0
2
2
0
2
1
0
2
1
2
1
1
1
2
2
0
0
1
1
1
1
1
2
2
2
2
1
0
1
0
1
2
1
0
0
1
2
2
1
1
1
2
0
0
0
1
0
0
0
1
1
1
1
1
1
1
1
1
0
1
0
1
0
0
2
0
2
1
1
1
0
1
1
0
0
2
1
1
1
0
1
1
1
1
0
0
2
0
0
1
2
1
1
0
1
1
0
2
0
2
0
2
2
1
1
2
2
2
1
0
2
1
0
0
1
0
0
0
1
0
0
0
0
1
1
1
0
0
2
2
1
0
0
2
0
2
0
1
1
2
1
0
1
2
0
2
1
1
0
0
2
0
2
2
0
2
2
1
2
1
2
0
2
0
1
2
0
1
1
1
0
0
1
2
1
1
0
1
1
0
0
2
1
0
0
2
0
0
1
0
2
2
1
2
1
0
2
1
0
2
1
1
1
1
2
1
0
0
1
1
0
1
0
0
2
0
2
0
0
0
1
1
2
0
2
1
1
1
0
1
1
1
0
1
0
0
1
1
1
2
0
0
1
1
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
2
0
0
1
2
1
1
0
1
1
2
2
0
0
1
1
0
0
1
0
1
1
0
0
1
2
0
0
2
0
0
1
0
2
3
2
0
2
2
2
0
1
1
1
0
2
1
2
0
2
1
1
2
0
2
1
0
1
0
1
1
1
1
1
2
2
2
0
1
0
2
0
1
0
2
2
0
1
1
1
2
2
0
1
2
1
1
1
1
2
1
1
1
0
1
0
0
0
1
0
1
1
1
1
1
1
2
2
1
1
1
0
1
1
0
1
0
0
0
1
1
1
1
0
2
2
1
1
0
0
0
2
1
0
1
0
1
0
1
0
1
1
2
1
2
0
0
2
0
1
2
1
2
0
2
0
0
1
1
0
0
1
1
0
0
2
1
1
2
1
1
0
2
2
0
0
1
0
0
2
3
2
2
1
1
0
1
2
2
0
2
1
0
1
2
2
0
2
1
0
0
0
1
2
0
2
1
0
1
1
2
0
0
1
1
1
1
2
0
1
0
0
2
0
1
1
0
1
1
1
2
1
2
0
1
0
1
0
1
1
0
2
0
0
2
2
1
1
0
1
1
1
0
1
1
1
0
1
0
1
1
1
1
0
1
1
1
0
0
1
1
1
0
0
2
2
0
0
1
0
1
0
0
0
1
1
1
0
0
0
0
0
2
1
0
1
0
1
2
3
0
2
0
2
0
1
0
0
0
0
0
1
0
2
2
0
0
2
1
5
3
2
0
2
0
1
2
2
2
1
2
1
2
1
1
1
1
0
2
2
2
0
0
0
1
2
0
1
1
0
1
1
1
0
0
0
2
1
0
1
1
1
1
3
0
0
2
0
2
1
3
1
0
2
0
1
0
2
2
0
1
1
2
1
0
0
0
0
0
1
0
1
2
0
0
1
0
3
1
1
0
0
1
0
0
1
1
1
0
1
1
1
1
0
1
1
2
1
1
1
1
1
1
2
1
0
0
2
1
0
1
1
0
1
1
2
0
2
1
1
1
2
2
1
0
0
2
2
0
0
1
0
1
0
2
0
0
3
0
0
1
2
0
1
0
0
2
0
0
1
2
2
0
1
0
2
0
2
0
1
2
2
2
1
5
1
1
1
1
0
0
2
1
0
0
1
2
1
2
0
1
1
3
1
2
0
1
0
1
0
2
0
0
1
2
1
0
1
1
0
1
0
0
0
0
2
2
1
0
0
1
2
2
1
0
1
0
0
2
0
0
0
2
0
0
0
0
0
1
2
0
1
1
1
0
2
0
0
0
0
1
1
1
0
0
0
2
0
1
1
1
0
0
0
0
2
1
0
0
1
1
0
2
2
0
0
1
1
0
1
1
0
1
2
1
1
4
1
0
1
1
2
2
1
1
1
1
0
0
0
1
0
0
0
0
1
0
0
1
1
0
2
0
1
1
0
1
0
3
1
0
1
1
0
1
2
0
0
1
0
1
0
2
1
1
0
2
2
0
0
1
1
0
0
0
1
2
2
1
0
0
0
0
0
1
1
0
1
1
0
1
0
1
2
1
1
0
2
2
0
2
0
1
0
1
1
2
1
0
0
1
2
3
0
2
1
0
3
0
1
1
3
2
2
0
2
2
2
0
1
1
0
1
1
1
2
0
1
0
1
0
1
0
1
0
1
1
0
3
0
1
0
0
0
2
1
2
1
1
1
2
0
0
0
0
0
2
2
2
1
1
1
1
2
1
1
0
0
1
0
1
1
1
2
1
0
1
0
2
1
1
0
1
0
1
1
2
1
2
0
1
1
1
0
1
1
1
1
0
0
0
1
0
0
0
2
0
1
2
0
1
2
1
1
2
0
3
0
0
0
2
1
0
1
1
0
1
1
0
1
2
2
1
2
2
1
1
1
2
1
1
1
1
1
0
0
1
2
2
2
1
1
0
0
2
2
1
0
1
0
0
0
1
1
0
1
0
2
1
3
0
1
1
2
1
0
1
0
0
0
1
0
2
0
1
1
2
1
1
0
0
2
0
1
1
2
0
1
2
1
1
0
2
0
2
0
1
0
1
2
2
2
2
1
0
0
2
1
2
1
1
1
0
0
1
0
0
2
1
1
0
1
1
1
2
2
2
2
1
2
1
2
1
0
3
1
0
0
0
0
0
1
1
0
0
1
1
2
1
1
2
2
2
1
0
0
1
0
0
0
1
1
2
0
0
1
0
1
0
1
2
0
1
1
1
1
1
1
2
2
1
1
2
0
0
0
1
1
1
1
0
1
1
1
1
0
0
0
1
0
1
0
1
0
2
2
1
0
1
1
1
2
0
0
1
1
1
0
1
1
1
2
1
0
1
1
1
1
0
0
1
0
0
1
1
0
0
2
1
0
1
1
0
1
1
2
2
0
2
2
2
2
0
1
1
2
1
0
1
0
0
1
1
0
0
1
0
1
1
1
1
2
1
0
2
0
1
2
2
2
1
0
2
0
1
1
1
1
0
0
1
1
0
2
1
1
2
1
2
1
1
1
1
0
2
1
1
0
1
1
2
1
1
0
1
0
0
1
1
0
2
1
1
1
1
0
1
1
2
0
0
1
1
0
0
1
0
0
1
0
1
1
1
2
0
2
2
0
1
2
1
2
2
1
2
0
2
0
2
0
1
1
2
1
1
1
1
1
1
1
0
0
0
1
2
1
0
1
3
0
0
0
2
1
1
0
1
0
0
1
0
0
0
0
2
0
1
0
0
1
2
0
2
2
0
0
0
2
0
1
0
1
0
0
1
1
2
0
0
2
1
2
1
1
0
0
2
0
1
1
2
1
1
0
1
0
2
0
1
1
0
1
2
2
1
0
0
0
7
2
2
2
1
1
0
0
0
1
1
0
0
1
2
0
1
1
2
0
0
0
1
0
2
0
2
0
1
1
0
2
1
1
1
0
2
2
0
1
1
1
1
2
0
0
2
2
2
1
1
1
0
0
1
0
1
2
0
2
1
1
0
1
1
1
1
0
0
0
0
1
0
0
2
2
0
0
1
0
2
0
1
0
1
2
1
1
1
0
1
1
3
1
2
2
0
2
0
2
1
1
2
2
1
0
2
1
1
0
2
1
1
1
2
0
1
0
4
1
1
1
2
2
0
1
0
1
1
1
1
0
2
1
0
1
1
1
0
0
0
1
0
0
1
1
0
1
0
1
0
1
0
0
4
2
2
1
1
0
0
0
0
0
0
1
1
1
0
0
0
0
1
1
1
0
0
1
2
1
0
1
1
0
1
2
0
1
0
2
1
1
0
0
5
1
1
2
0
1
1
2
2
1
0
2
0
0
1
0
0
0
1
1
1
0
0
0
2
1
2
0
0
0
1
0
0
2
0
0
2
1
0
1
1
1
0
0
1
3
0
0
1
0
2
1
0
0
0
0
1
1
1
1
3
1
1
1
1
0
0
2
0
6
2
1
0
1
1
1
1
1
0
3
1
0
0
1
1
0
1
0
2
1
0
2
0
1
1
0
1
0
2
0
1
2
1
1
1
0
0
2
2
1
2
2
0
2
1
0
1
0
2
2
1
1
1
1
1
1
2
1
1
1
0
0
0
0
0
0
1
1
0
0
2
2
0
0
0
0
1
0
2
2
1
2
0
1
0
1
0
1
1
1
0
1
0
2
1
0
0
0
0
0
0
0
1
0
1
1
0
0
1
2
0
1
2
1
0
0
1
1
0
1
0
0
0
1
0
2
1
1
1
1
2
2
2
0
2
0
2
0
1
1
0
1
2
2
2
0
3
1
0
2
0
0
1
1
1
2
0
2
0
0
2
0
0
1
1
2
1
1
0
2
2
1
2
0
1
1
1
2
1
1
0
1
0
0
0
1
1
2
1
2
1
1
0
1
1
2
0
0
1
0
0
1
0
1
2
1
1
1
0
2
1
1
1
2
0
2
1
1
2
0
1
1
1
1
1
1
1
0
1
2
1
1
0
0
2
3
1
2
0
0
0
2
0
1
1
1
2
1
2
1
0
0
2
2
0
1
0
1
0
0
1
1
1
2
1
2
0
2
2
1
0
1
0
2
1
1
0
1
2
1
0
0
1
1
1
1
1
0
1
2
0
2
6
0
1
1
1
2
2
2
0
0
2
0
0
1
1
1
1
0
2
1
2
2
1
1
1
0
0
2
0
0
2
1
3
0
2
0
1
1
2
2
1
0
0
2
1
1
2
2
1
1
1
0
1
1
1
2
1
1
1
1
1
1
1
0
1
2
3
0
0
0
0
0
3
0
1
2
0
2
1
1
1
2
1
1
1
0
1
0
1
1
0
1
2
2
0
0
0
2
0
1
1
2
1
2
3
0
1
1
1
1
0
0
0
1
2
0
0
1
0
2
1
1
0
1
0
1
0
0
0
2
0
2
1
3
2
1
1
0
1
0
2
2
2
1
0
1
1
1
0
2
2
2
2
0
1
1
2
2
0
2
2
1
2
0
0
2
0
0
0
1
0
1
0
1
0
1
1
0
0
2
2
1
2
0
0
1
0
0
3
2
0
0
1
0
1
0
0
2
0
2
2
0
0
0
1
3
1
0
0
0
2
0
0
1
1
0
0
2
0
0
0
0
0
0
0
1
0
1
1
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
1
1
1
0
1
0
1
1
0
1
0
1
3
1
0
0
0
1
0
2
1
0
0
2
2
1
2
2
1
1
0
2
0
0
0
1
2
0
1
1
0
0
0
0
0
0
0
1
2
0
2
1
1
1
0
1
0
1
0
1
0
0
1
3
1
1
1
0
1
0
1
2
1
2
1
0
2
0
2
0
1
2
1
2
0
1
1
0
0
1
1
1
1
0
3
1
2
0
2
1
0
0
0
0
1
2
2
2
1
1
1
1
0
1
0
2
0
0
0
0
0
0
1
1
0
1
0
1
1
1
2
1
1
0
0
0
0
1
0
1
2
1
0
0
1
0
0
0
1
1
1
0
2
0
0
1
2
2
1
0
1
0
1
0
0
2
0
1
1
0
1
0
0
2
1
1
1
0
1
1
0
1
0
1
0
1
2
0
1
0
2
0
2
1
1
1
2
1
1
2
0
0
0
2
2
0
3
2
3
2
0
0
1
0
2
1
1
1
1
1
2
1
0
1
0
1
1
0
0
0
1
0
0
1
1
2
0
2
2
0
1
1
2
1
1
2
0
1
0
0
1
0
2
1
0
1
0
2
1
0
1
1
1
0
2
0
0
1
2
2
0
1
1
0
2
1
1
1
2
2
0
1
0
2
1
1
0
0
1
1
1
0
2
0
0
0
0
1
0
2
1
1
1
1
1
0
0
1
2
1
1
1
0
0
1
1
1
0
0
0
1
2
1
1
1
2
1
0
3
1
0
0
1
1
1
1
1
0
1
1
1
0
2
0
2
0
0
2
0
1
1
1
1
1
2
2
1
1
0
0
2
2
1
0
0
2
0
1
1
1
0
1
0
0
0
0
0
0
1
0
0
2
1
2
2
2
2
2
0
0
0
1
2
2
2
1
0
0
0
1
0
1
0
1
0
0
1
1
0
1
2
1
1
2
1
1
1
2
0
1
0
0
1
3
0
2
0
2
1
1
0
0
1
0
1
1
3
1
0
0
1
0
1
1
0
2
2
0
0
1
0
1
0
0
1
2
2
1
1
0
1
2
2
1
0
1
0
2
1
0
0
0
2
0
1
2
1
1
0
1
0
0
0
1
1
0
1
1
0
1
0
1
2
0
4
0
0
0
1
2
2
0
0
2
1
1
2
0
0
0
2
0
1
1
1
0
1
1
0
2
1
0
1
1
1
2
1
1
2
1
1
0
0
0
1
0
0
0
1
1
1
1
0
1
0
2
1
2
0
2
1
1
1
0
1
0
2
0
1
1
0
1
0
1
0
0
0
2
1
2
2
0
2
2
1
1
1
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
1
1
1
0
1
0
2
0
0
0
1
1
1
0
1
2
0
0
2
0
0
1
0
0
1
0
1
1
0
1
0
1
1
2
2
1
0
0
1
1
1
1
0
1
3
1
2
0
1
1
1
1
0
2
1
0
0
2
1
1
1
1
0
0
1
2
0
1
2
0
0
1
1
0
2
0
2
2
1
1
0
1
1
0
1
1
0
1
1
1
0
2
0
1
2
2
0
1
0
2
1
0
1
0
1
1
0
0
1
0
1
0
2
0
0
1
2
0
0
0
1
1
0
1
1
2
0
0
1
1
2
0
2
1
1
0
2
1
1
1
0
2
1
1
2
0
2
0
1
1
1
0
1
1
0
1
2
0
1
3
2
0
1
0
2
0
1
1
1
0
1
0
0
1
1
2
1
2
2
2
2
0
1
1
0
1
0
0
2
2
1
1
2
1
1
1
1
2
1
0
1
2
1
0
1
0
2
2
0
0
0
2
1
1
0
1
0
0
0
1
0
0
1
1
0
0
2
2
1
0
0
0
1
2
1
1
0
1
0
1
0
1
2
1
2
1
0
1
1
2
2
0
0
2
1
2
1
0
1
1
0
0
0
1
0
2
1
3
2
1
1
0
2
2
1
1
0
1
0
0
1
0
1
1
1
1
0
1
1
0
0
1
1
1
3
0
1
0
0
0
1
1
1
1
1
2
1
1
0
0
2
0
0
1
1
2
1
1
1
2
1
2
0
1
2
0
1
0
0
0
0
0
1
1
0
0
1
0
0
2
1
0
2
0
0
1
2
1
1
0
1
1
0
1
2
1
1
0
0
1
1
0
2
2
1
2
1
0
1
0
0
2
2
1
2
3
0
0
1
2
1
2
2
0
1
0
1
1
2
1
2
2
2
1
2
0
0
1
2
1
0
1
0
1
0
0
1
0
1
1
0
0
1
1
2
0
0
1
0
1
1
1
2
0
2
0
0
1
2
0
1
2
0
1
1
2
1
2
2
1
0
2
1
0
0
0
0
1
2
1
1
0
2
2
1
0
1
1
2
1
2
1
2
1
1
2
1
1
1
0
0
1
1
1
2
3
0
0
1
0
0
1
1
2
2
2
0
2
0
0
1
1
0
1
1
0
2
0
2
2
1
1
2
1
1
0
1
2
2
2
1
0
1
0
0
1
1
0
1
1
0
2
2
1
0
0
0
1
2
0
1
1
0
0
0
1
2
1
0
1
0
2
0
0
1
2
0
0
1
0
1
2
1
2
2
0
2
0
2
0
1
1
1
0
2
0
2
1
0
0
1
2
0
0
1
0
0
1
0
2
0
0
2
0
2
1
1
1
2
0
0
2
0
1
1
1
1
1
2
0
0
0
0
0
1
0
1
1
0
1
1
2
1
0
0
2
2
1
1
1
5
0
1
2
0
0
0
0
1
2
1
0
0
2
2
0
1
2
2
2
1
1
0
1
1
1
1
0
0
1
1
0
1
1
2
2
2
3
0
1
1
0
1
2
1
0
0
1
1
1
2
1
0
1
0
2
1
0
1
1
1
1
1
1
1
0
2
1
0
3
0
1
1
1
0
0
2
0
1
0
1
1
0
0
1
1
0
0
0
0
4
1
1
0
2
1
1
0
2
0
0
2
1
2
1
1
0
1
2
0
1
1
1
1
2
2
0
1
1
1
0
0
0
1
1
1
1
2
1
2
1
2
0
0
0
0
0
1
1
0
2
0
0
0
0
1
2
1
2
0
2
2
0
1
1
0
2
1
0
1
2
0
2
0
1
1
2
1
1
1
2
1
2
0
0
1
1
0
1
1
2
1
0
1
0
1
1
0
0
2
2
0
1
1
1
0
2
0
1
1
1
0
0
1
1
2
2
2
1
0
0
1
1
1
1
1
0
2
0
1
0
2
0
0
1
2
0
0
0
0
0
0
0
2
1
0
0
2
1
1
0
0
1
0
0
1
0
1
1
0
1
1
0
0
1
2
1
0
1
1
0
1
1
1
1
0
1
1
2
1
0
0
1
0
0
2
0
1
1
0
1
0
2
1
0
0
0
2
1
0
1
2
2
0
2
0
1
0
0
1
1
0
1
0
1
2
1
1
1
2
0
2
1
2
1
1
1
0
0
0
0
0
1
0
1
1
0
0
1
1
0
0
2
1
0
1
0
1
0
1
0
1
1
1
1
1
0
1
0
0
1
0
0
2
0
1
0
2
1
1
1
1
0
0
2
1
2
0
1
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
1
1
1
2
2
1
1
1
0
0
1
2
1
0
2
1
1
1
0
1
2
0
2
2
1
0
0
0
0
2
0
2
2
0
1
0
0
1
0
0
0
0
0
1
0
1
1
1
0
2
1
2
0
1
1
2
1
1
1
1
1
6
1
0
1
1
1
0
0
2
1
1
1
0
2
0
0
2
2
3
0
1
0
1
0
2
0
0
1
0
1
1
1
0
0
1
2
2
1
0
1
0
0
2
2
1
0
0
1
0
1
2
0
1
1
0
1
0
2
1
0
0
0
0
2
1
2
2
1
1
1
1
1
1
1
1
0
2
0
2
1
1
1
1
0
2
1
2
1
1
1
0
1
0
1
0
1
1
1
2
1
2
1
1
1
1
0
0
0
2
0
1
1
2
0
1
1
1
1
0
0
2
1
0
2
1
0
0
1
0
3
0
0
1
0
1
1
1
1
0
1
1
0
0
2
1
1
1
2
0
1
0
2
1
0
0
1
0
0
1
0
1
0
1
0
1
1
1
3
0
0
2
0
1
2
3
2
1
1
0
1
1
2
1
2
1
1
1
1
1
1
1
1
0
1
1
2
0
1
2
1
2
1
1
1
0
1
2
2
0
2
1
1
1
1
0
1
1
0
1
2
0
1
2
2
2
1
2
0
1
1
0
0
1
1
1
1
0
1
0
0
0
0
0
0
0
1
2
1
0
0
1
2
1
1
0
0
1
2
1
1
2
2
1
0
1
1
1
2
2
1
1
2
0
1
0
2
2
1
0
0
0
0
1
1
0
0
1
0
0
0
0
2
2
1
0
2
1
2
1
1
0
1
0
2
0
2
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
1
1
2
0
2
1
0
0
0
1
1
0
1
1
1
0
1
0
0
0
1
1
1
2
2
0
0
0
0
1
1
1
1
2
0
3
0
1
2
0
0
1
2
0
1
0
1
1
1
2
0
0
1
0
1
0
0
2
1
1
1
1
3
0
0
1
0
1
0
1
0
2
0
0
1
1
1
0
1
1
2
1
2
0
0
0
1
1
0
1
2
0
0
2
0
0
1
1
1
2
2
1
0
1
0
1
2
2
0
0
1
0
0
0
1
0
1
0
1
2
1
0
0
0
2
0
0
0
0
0
2
0
0
0
1
1
2
0
2
1
0
0
1
1
0
1
0
1
0
0
0
0
1
0
0
0
0
2
0
2
1
0
0
0
1
2
1
1
0
2
1
2
1
1
0
1
1
1
0
0
0
2
0
0
1
1
0
0
3
1
0
2
1
0
0
1
0
0
1
2
0
1
2
2
0
1
1
1
1
2
0
1
1
2
0
0
2
1
1
0
1
0
1
1
1
2
0
0
1
1
0
2
1
1
0
2
2
2
0
1
1
1
2
1
1
0
2
0
1
2
1
1
2
0
2
0
1
1
2
1
0
0
2
1
0
1
2
2
0
1
1
1
1
0
1
1
0
2
2
2
1
0
1
2
1
0
0
1
1
0
0
0
1
2
0
1
0
0
0
0
1
1
2
1
1
1
1
1
2
1
1
0
0
2
0
1
1
1
0
2
0
1
1
2
1
0
0
0
0
1
1
1
0
2
0
0
1
1
0
1
0
0
2
0
2
2
1
1
0
0
2
0
2
0
2
0
1
1
0
0
1
1
0
0
0
1
0
0
1
0
1
1
1
1
1
1
1
1
0
1
2
1
2
1
0
1
1
1
1
2
3
0
1
1
0
0
1
1
0
0
0
0
2
1
2
0
0
0
1
1
1
0
0
1
0
2
1
1
2
1
3
1
2
2
2
0
1
1
1
2
0
1
0
2
1
0
0
0
1
1
1
2
2
2
1
0
2
1
1
0
2
0
1
0
1
2
1
1
2
2
1
0
1
1
1
0
1
1
0
1
1
2
0
2
0
1
0
0
0
1
2
2
1
1
1
1
1
1
1
1
0
1
0
1
0
1
0
0
1
2
1
1
1
1
1
2
0
1
1
1
1
1
1
1
2
4
0
1
0
2
0
0
1
1
1
0
0
2
2
1
1
1
0
2
1
1
2
1
0
2
1
2
1
1
1
2
0
1
3
0
1
1
0
0
2
0
1
1
0
0
1
0
1
2
1
0
0
2
1
1
2
0
0
0
0
1
0
1
2
0
1
1
1
2
1
1
1
0
0
2
2
2
0
1
1
1
2
1
1
2
1
1
2
1
0
0
1
1
0
1
2
0
0
1
2
0
0
1
0
3
2
1
1
1
1
1
2
1
1
1
1
0
2
2
2
0
2
0
0
0
1
0
1
6
0
1
2
1
0
1
0
1
1
0
1
3
0
0
1
0
0
0
2
2
0
0
0
1
0
0
0
0
1
0
1
0
1
3
0
2
1
2
2
2
2
1
1
1
1
0
0
1
2
0
1
1
1
1
0
1
2
1
1
1
0
1
1
1
2
0
1
1
0
1
0
1
0
0
2
0
0
3
0
2
2
0
1
0
1
0
1
1
2
2
1
1
0
1
1
1
1
1
1
2
1
2
1
0
0
0
1
0
1
0
0
1
0
2
1
0
0
1
0
0
1
1
1
1
1
1
2
0
0
1
0
0
2
1
0
1
0
1
2
1
2
0
0
2
1
1
0
0
1
0
1
0
3
2
1
0
1
2
1
2
0
2
2
1
1
1
1
1
2
0
0
2
0
0
2
2
1
1
2
1
0
1
1
1
2
1
0
2
0
0
1
0
0
1
1
0
1
1
1
2
2
0
1
0
0
2
1
1
0
0
3
0
0
1
0
1
0
1
0
1
2
2
1
1
1
1
0
1
1
0
1
0
2
4
0
0
0
1
2
1
1
0
1
1
0
1
2
0
1
1
1
1
1
2
0
2
0
2
1
2
1
1
0
1
1
0
1
2
1
2
2
0
1
2
1
0
2
1
1
0
0
1
0
0
2
2
0
2
0
0
1
1
2
1
1
1
1
0
0
1
0
2
1
2
1
2
0
1
2
2
0
1
0
0
0
2
1
1
0
0
2
2
0
1
1
0
1
0
1
1
1
0
0
0
1
1
1
1
0
0
1
1
2
0
0
0
2
0
0
0
0
1
1
1
1
2
1
1
1
0
0
1
0
1
2
2
2
0
1
0
0
1
2
0
1
0
0
2
1
0
2
0
0
1
1
1
1
1
0
2
1
0
1
0
1
1
1
3
2
0
1
0
0
2
0
1
0
1
2
0
0
2
1
0
1
1
2
1
2
6
0
2
1
0
1
0
2
1
1
0
2
1
1
2
0
1
1
1
0
2
1
1
0
1
1
2
1
1
2
0
1
1
1
1
1
2
2
1
1
0
0
2
2
0
1
0
2
1
0
2
0
2
1
2
2
2
2
0
1
1
2
2
1
1
1
0
2
0
1
0
0
0
0
1
1
0
0
0
2
1
1
1
1
0
0
1
1
1
0
1
2
1
2
0
0
0
5
1
2
1
0
2
1
1
1
0
1
0
2
1
0
2
0
0
0
1
1
2
0
4
2
1
2
1
1
0
1
0
0
0
1
0
1
0
0
1
2
2
1
1
2
2
2
2
1
2
1
1
1
1
1
0
1
1
1
0
0
0
1
0
2
0
2
1
1
1
0
2
0
1
1
0
1
2
0
1
1
0
2
2
2
1
1
1
0
1
2
0
1
1
0
2
0
0
0
0
1
0
1
0
2
0
0
2
0
0
2
1
1
1
1
0
2
1
1
1
2
2
0
2
1
1
0
2
0
0
1
1
2
0
0
2
1
1
1
2
0
1
1
0
0
2
1
1
1
2
0
1
1
2
1
1
1
1
2
0
1
1
0
0
2
1
1
2
2
1
0
1
2
0
1
1
2
0
2
0
0
0
1
0
1
1
1
2
1
0
0
1
1
1
1
0
0
2
0
1
0
1
1
2
2
2
1
1
1
0
1
0
0
2
0
1
1
1
1
2
1
2
0
0
0
2
1
1
2
1
1
0
0
0
1
1
1
1
0
2
1
1
0
0
1
1
1
0
0
0
2
1
0
1
1
0
0
1
2
0
1
1
0
1
1
1
0
1
1
2
0
0
2
1
1
0
1
2
0
1
1
0
0
1
2
1
0
2
0
2
2
2
0
0
0
1
0
1
1
1
2
1
1
1
1
1
0
0
2
1
1
0
1
1
1
1
0
1
1
0
1
2
0
1
1
0
0
2
0
0
1
2
2
1
1
1
1
2
2
0
1
1
1
0
1
0
4
2
1
2
1
1
1
0
2
1
2
2
1
2
1
1
1
1
1
2
0
1
0
2
1
1
1
0
2
1
0
1
1
0
2
1
0
1
2
1
1
2
1
0
2
0
0
0
1
0
0
1
1
2
1
1
2
0
2
0
1
0
2
2
0
1
3
1
0
0
0
1
1
0
2
0
0
1
1
0
1
0
0
1
0
0
5
2
1
1
0
1
1
5
1
1
1
0
0
2
2
0
2
1
0
2
2
0
0
2
1
2
1
1
1
0
0
0
0
0
0
1
1
2
1
2
1
1
0
0
0
2
1
1
0
1
2
0
2
1
0
0
0
1
2
0
3
0
2
0
1
1
1
1
2
0
2
2
0
0
0
3
0
0
2
0
2
1
1
0
2
0
1
1
0
1
0
0
0
1
1
1
0
0
1
1
1
0
1
1
2
0
2
2
0
0
1
0
1
1
1
2
1
2
0
0
0
0
1
0
1
1
2
1
1
1
0
1
1
0
1
1
1
2
2
0
2
0
1
0
0
0
0
0
2
1
1
1
0
0
2
0
1
1
0
0
1
0
0
0
1
1
0
3
0
2
1
0
1
0
1
2
0
0
0
2
0
0
0
1
1
2
2
1
0
1
1
2
0
1
1
2
0
0
1
2
1
1
0
1
0
0
2
0
2
1
2
1
1
0
2
0
0
0
2
2
2
1
0
1
1
1
0
1
1
0
0
1
1
1
2
1
0
0
0
1
0
1
0
0
1
1
1
0
1
2
2
1
0
2
0
0
1
1
2
2
1
0
2
2
0
0
0
1
2
2
1
1
1
0
0
0
2
0
1
1
2
0
0
0
2
1
0
0
1
2
0
1
0
1
1
0
1
0
0
1
2
1
2
0
1
1
2
2
0
0
0
0
1
1
0
1
1
0
0
0
1
3
0
0
1
1
0
0
0
0
1
0
1
2
0
0
1
1
0
2
1
0
0
2
1
2
2
2
1
1
0
1
1
1
1
1
1
0
2
1
1
0
2
0
1
0
0
2
0
0
0
1
1
0
0
2
1
0
2
1
1
0
0
2
1
1
1
0
0
0
0
1
0
0
2
2
1
0
0
0
0
1
0
2
0
0
0
2
0
0
1
1
0
2
0
0
0
0
0
1
2
0
1
1
1
1
1
2
1
0
1
2
1
1
0
0
1
1
2
0
1
1
1
2
0
1
2
0
0
0
0
1
1
0
2
0
0
3
0
0
1
1
1
1
0
0
1
0
1
2
1
1
6
1
2
0
1
1
2
1
1
1
0
1
1
1
0
2
1
0
1
1
1
2
0
0
2
1
0
2
1
1
1
1
2
1
0
2
1
2
1
4
1
0
1
1
2
1
0
0
0
2
0
2
0
0
2
0
2
0
0
1
1
2
1
1
1
1
0
1
0
1
0
1
0
2
0
2
1
1
0
1
1
0
0
1
0
0
1
1
0
1
1
2
1
0
0
0
1
0
1
0
1
1
2
1
1
0
0
0
1
3
1
3
0
0
1
0
0
2
2
1
0
2
1
2
2
2
1
0
2
0
2
2
1
1
1
0
1
2
2
0
2
1
1
1
1
0
2
1
0
1
1
2
1
0
1
1
1
0
1
1
2
2
1
1
2
1
1
0
2
1
1
1
2
0
0
1
1
1
0
0
2
2
1
2
0
1
1
1
0
0
1
1
0
1
0
0
1
0
0
0
0
0
1
1
0
2
1
1
1
2
2
0
0
0
1
1
1
1
2
0
0
0
1
0
0
1
1
2
0
1
0
2
2
0
1
1
1
1
1
1
0
0
0
1
1
2
1
0
1
0
2
0
1
4
1
1
0
0
0
1
0
1
0
0
2
0
0
0
0
1
1
0
1
1
2
0
2
2
1
0
2
2
2
2
1
0
2
1
2
2
3
1
2
0
0
1
1
2
1
2
0
2
1
0
1
1
0
2
0
2
1
2
2
1
1
0
1
1
0
1
2
1
1
1
0
0
0
0
1
2
0
2
0
1
1
0
2
1
2
1
2
0
2
0
1
0
1
1
1
2
0
2
1
0
0
2
0
2
2
0
0
0
1
2
0
1
1
1
1
0
2
1
1
1
0
2
1
1
0
1
0
0
1
0
0
0
2
0
2
1
0
0
0
1
1
0
0
1
0
1
0
1
0
2
5
1
1
0
1
2
0
1
0
0
2
2
2
0
1
0
2
1
1
1
3
1
0
1
2
1
1
2
0
1
0
1
0
2
0
1
1
1
1
2
0
0
1
0
2
0
2
0
1
1
1
1
0
1
1
0
1
0
0
1
0
2
2
1
0
0
1
2
0
2
0
1
1
1
1
1
2
0
0
1
0
1
1
1
1
2
0
2
2
0
1
1
1
1
2
0
0
0
0
1
0
1
0
0
3
2
2
0
1
2
1
2
2
0
1
0
1
1
0
2
2
1
0
0
2
1
2
0
1
2
0
2
0
0
0
2
1
2
1
2
0
2
0
1
1
0
1
0
1
0
1
0
0
3
2
1
1
2
0
2
2
1
1
0
1
5
1
1
2
1
0
1
0
2
0
2
0
1
2
0
0
0
0
0
1
0
1
1
0
0
2
1
1
1
0
2
0
2
1
0
0
0
0
0
0
0
0
0
2
1
2
1
0
2
2
1
2
1
2
1
2
1
0
0
0
2
1
0
0
1
1
3
0
0
2
0
1
0
1
0
1
0
0
0
0
1
0
0
1
1
0
2
0
1
1
2
0
0
2
1
1
2
0
2
0
0
1
1
0
0
0
1
2
2
3
1
0
0
2
0
1
0
0
1
1
0
0
1
1
1
0
0
0
1
2
2
0
1
1
3
1
2
1
1
0
1
1
1
2
0
0
1
1
1
1
2
1
2
1
1
2
1
1
1
1
1
0
1
0
0
1
0
0
1
2
0
1
4
0
1
0
1
1
1
0
0
0
0
0
1
1
0
2
1
1
0
1
0
0
0
1
2
2
0
1
1
1
0
1
0
2
3
1
3
0
1
1
0
1
2
1
0
1
1
2
2
0
1
2
1
0
0
1
2
2
1
1
1
2
0
0
2
1
0
0
1
0
0
1
2
0
2
2
1
1
0
1
2
0
0
0
1
1
0
1
2
0
0
1
1
1
2
1
0
0
0
1
0
1
0
0
0
1
0
1
1
1
1
0
1
1
1
1
1
0
2
1
1
0
0
1
0
2
1
2
1
1
0
2
0
1
2
2
2
1
2
1
1
1
2
4
1
2
0
2
1
2
1
2
1
0
0
2
2
0
0
0
0
2
1
1
1
0
0
0
0
1
1
0
0
2
2
0
3
2
1
1
0
1
2
1
1
1
0
1
2
0
2
2
2
0
0
0
1
1
2
2
0
1
2
1
1
2
1
0
1
2
0
2
1
1
2
0
1
0
0
1
1
1
0
2
2
0
2
0
1
1
0
2
2
1
0
1
2
2
0
0
0
1
0
2
1
0
0
1
0
0
0
0
2
1
0
1
1
1
1
0
1
1
0
0
1
1
1
0
2
1
0
2
0
2
1
0
2
1
1
1
0
1
1
1
1
0
0
1
1
2
2
1
2
0
1
2
1
0
2
0
1
2
1
0
1
1
2
2
0
1
2
0
1
2
1
1
2
2
1
0
0
1
2
0
1
0
0
1
2
0
1
1
0
0
1
2
1
1
1
2
2
2
0
1
1
1
1
1
1
0
2
1
0
0
2
1
2
1
0
0
1
1
0
0
0
0
0
1
1
2
4
1
1
1
1
1
0
0
0
1
1
0
1
1
1
0
2
2
0
2
1
1
0
1
0
1
1
0
0
0
2
1
0
0
0
2
1
1
2
4
2
2
1
1
2
1
3
2
2
2
2
2
0
0
2
0
1
1
0
1
1
0
1
1
3
2
1
1
2
1
1
0
2
1
0
0
1
0
2
7
0
1
0
1
2
1
0
1
1
2
2
0
0
1
0
1
2
0
1
1
2
2
0
1
2
0
1
2
1
1
2
2
3
2
0
2
0
2
2
0
0
2
0
1
1
1
0
0
2
2
0
0
2
0
1
0
1
1
0
1
2
1
2
0
0
1
2
1
1
0
0
1
0
0
0
1
0
2
0
0
2
0
0
0
1
1
0
1
1
2
2
1
1
1
1
1
1
1
1
0
2
1
1
1
2
0
2
0
0
1
1
2
1
0
0
1
1
1
0
0
1
1
0
2
2
2
1
2
2
0
1
1
1
0
1
1
1
1
1
0
0
3
1
1
0
2
1
1
2
2
1
1
0
0
2
0
0
0
2
1
1
0
0
2
1
1
0
1
1
1
0
0
0
4
0
1
0
0
2
1
1
1
2
2
0
2
2
1
1
1
1
1
1
0
1
0
1
0
0
1
2
0
1
2
2
2
0
2
0
1
1
1
1
1
2
0
0
1
0
1
2
1
2
1
0
1
0
0
2
1
1
2
1
0
0
1
2
0
2
1
2
0
2
2
1
0
1
2
1
1
2
0
1
1
0
2
0
2
1
1
0
0
1
0
0
2
0
2
1
3
1
0
0
0
2
1
0
0
1
2
1
0
1
0
2
0
2
1
1
0
0
1
0
1
1
0
1
2
1
0
1
1
2
0
2
2
1
2
1
1
2
2
0
1
0
0
0
1
0
0
0
1
1
1
2
1
1
1
0
2
2
2
1
1
1
1
0
0
2
1
1
0
1
2
1
1
0
1
0
2
1
0
1
0
1
0
1
0
1
1
1
1
0
0
1
1
0
1
0
0
1
0
0
0
0
1
0
1
0
2
0
0
2
0
0
2
0
1
0
0
0
2
1
1
2
1
0
0
1
0
0
1
1
6
1
1
0
2
2
2
0
0
1
0
1
0
0
1
1
1
0
0
0
2
0
2
0
0
1
0
1
2
2
1
1
0
1
1
2
0
1
0
0
1
1
0
0
2
0
2
2
1
1
2
0
0
1
0
0
1
1
2
2
1
1
1
2
0
1
0
0
1
0
1
0
2
0
2
1
0
1
0
2
0
2
1
1
0
0
2
0
0
1
1
2
0
0
0
1
0
0
1
2
1
2
0
0
0
0
2
1
0
2
2
1
2
0
1
0
1
1
0
1
0
1
2
0
0
2
2
0
1
1
1
1
0
0
1
2
2
2
0
1
2
0
1
0
0
0
1
1
0
1
0
1
1
1
0
0
3
0
1
0
1
2
0
0
1
1
1
1
1
1
0
2
1
1
1
2
0
1
1
0
0
1
1
2
0
0
1
2
1
0
1
2
1
2
1
1
0
0
1
0
0
0
1
1
0
2
2
2
1
1
1
0
1
0
2
1
0
2
0
1
2
0
1
1
0
2
2
0
1
0
1
2
1
0
1
0
0
2
1
3
1
1
0
2
0
0
1
1
2
0
0
2
0
0
2
0
1
3
3
1
1
0
1
0
1
2
1
1
1
0
1
0
1
0
1
0
1
0
0
2
3
1
1
1
1
0
1
0
1
0
1
1
2
1
2
2
1
1
2
1
1
1
0
0
1
1
0
1
0
0
0
0
1
1
1
1
2
0
0
1
1
0
0
1
1
1
0
0
1
0
1
0
0
0
1
1
0
2
2
1
2
2
0
5
1
1
1
0
2
2
0
1
4
1
2
2
0
1
1
1
1
0
1
0
0
1
0
1
1
0
1
1
2
0
2
0
0
1
1
1
0
0
1
1
2
1
2
2
1
0
0
1
1
1
1
1
0
0
0
0
2
0
0
0
0
0
1
1
1
0
0
1
1
1
0
1
0
1
1
1
2
0
1
1
0
1
1
0
2
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
1
1
2
0
1
0
0
0
0
2
0
0
0
0
0
1
2
2
1
1
1
1
1
0
2
1
3
2
0
0
0
0
2
0
0
0
1
2
1
2
1
0
1
0
1
0
0
1
1
0
2
1
1
1
2
0
0
2
0
0
0
2
1
0
0
0
1
1
2
0
1
1
1
0
0
2
1
2
0
0
1
0
2
2
1
1
2
0
2
2
1
0
0
1
1
2
0
1
2
2
0
0
0
1
0
1
1
2
2
1
1
1
1
0
3
1
0
1
1
0
0
0
0
1
2
1
1
1
2
0
2
0
1
0
2
0
0
1
0
0
0
2
0
0
1
2
1
2
1
2
1
6
2
1
0
0
1
2
0
0
1
0
1
1
0
1
1
0
2
0
1
0
1
2
0
1
0
1
5
2
0
0
0
0
1
0
2
1
0
0
1
0
1
2
0
0
0
2
1
0
2
0
1
1
2
2
1
2
1
0
1
1
1
1
1
1
1
1
1
0
1
1
0
1
0
0
1
1
0
1
2
0
1
0
1
0
0
0
2
2
1
1
2
1
0
1
1
0
0
2
0
1
2
1
1
0
1
0
1
1
2
2
2
0
0
0
2
0
0
1
0
1
2
0
2
1
1
3
2
1
0
0
0
1
1
2
1
1
2
1
0
1
0
2
1
0
1
0
0
2
0
0
1
1
1
1
2
1
0
0
0
1
2
1
1
2
2
1
1
1
1
0
0
1
1
1
1
1
1
0
0
0
1
1
0
1
0
1
0
0
1
2
2
0
0
0
1
1
1
1
2
1
1
1
0
0
0
0
1
1
1
1
1
2
0
1
2
0
1
2
0
0
0
0
2
0
0
1
1
0
1
0
2
1
0
1
1
1
0
1
1
0
1
0
1
3
1
0
2
0
1
0
0
2
2
2
1
1
1
1
1
1
0
1
0
0
1
0
1
1
1
0
0
0
0
0
4
2
1
1
0
2
1
2
1
2
0
0
1
0
0
1
1
1
1
0
0
1
0
2
1
0
0
2
1
0
2
2
2
1
1
2
0
1
1
3
0
1
2
0
1
0
1
0
0
1
0
1
0
0
2
1
0
1
1
1
1
0
2
0
0
1
0
1
0
0
2
1
1
0
1
2
1
0
1
0
2
0
0
2
0
1
1
0
0
1
2
0
1
0
1
1
0
0
0
2
1
1
1
1
2
2
0
1
0
0
1
1
1
0
0
2
0
1
0
2
0
2
2
0
2
0
2
2
0
1
1
0
1
0
2
2
0
1
1
2
1
0
0
2
1
1
1
0
0
1
1
0
0
0
0
0
0
0
1
1
0
2
1
0
0
2
0
0
1
0
0
0
2
0
2
2
0
0
1
1
2
2
1
0
0
1
1
0
1
0
1
1
0
1
2
0
0
1
0
0
2
2
1
0
1
2
0
0
2
0
1
1
0
0
0
0
1
1
0
0
1
1
1
0
1
0
0
1
2
1
1
1
0
1
0
1
1
2
1
2
1
0
2
0
1
0
1
2
1
2
0
2
0
0
2
1
1
1
2
0
1
0
2
1
1
0
1
1
2
0
0
2
0
4
0
1
0
1
1
0
0
1
1
0
2
2
2
0
0
1
1
1
1
1
0
2
2
1
0
0
1
1
1
1
3
0
1
0
0
1
0
0
0
1
0
0
1
2
1
2
1
1
0
1
1
0
0
0
2
1
1
1
3
0
1
0
1
1
1
1
0
0
1
1
0
0
1
0
1
1
2
0
0
1
0
1
2
0
1
1
2
2
1
1
2
0
0
0
1
1
0
0
1
2
0
1
2
1
1
0
1
0
0
0
2
2
1
1
1
0
1
0
1
0
2
1
2
0
1
1
0
1
2
2
1
1
2
2
1
2
2
0
2
0
1
0
2
0
2
0
1
1
1
1
0
1
0
1
2
0
0
1
1
1
1
0
0
0
0
1
2
0
2
0
0
0
1
1
0
1
2
1
1
0
0
2
2
0
1
2
2
0
1
1
2
1
1
0
2
0
2
2
0
0
0
2
1
8
1
1
1
0
0
2
0
1
1
2
1
0
2
2
0
0
0
0
0
0
0
1
1
3
1
1
1
0
0
1
0
1
1
0
1
1
1
7
2
0
2
1
1
0
1
2
1
1
1
1
1
2
0
0
0
0
0
1
1
1
1
1
1
2
2
1
1
1
0
0
0
1
1
1
2
1
1
2
2
3
1
2
0
1
1
0
1
2
2
3
1
1
0
1
0
2
3
0
2
1
1
1
1
1
0
1
0
1
1
2
0
1
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
2
2
2
1
1
0
0
0
0
0
2
0
2
1
0
0
0
1
1
1
2
1
0
1
1
0
1
0
0
2
1
1
1
2
2
0
1
0
0
1
0
2
1
3
2
0
0
2
1
2
0
0
1
1
1
2
2
2
2
0
0
1
4
2
1
1
1
0
0
1
1
0
1
1
1
0
1
0
0
0
1
1
2
1
0
1
0
1
2
1
1
2
1
1
4
1
1
1
1
1
2
1
0
1
0
2
0
0
0
0
0
1
1
1
2
1
1
3
1
0
2
0
3
0
1
0
0
1
0
0
2
1
0
0
1
1
1
4
0
1
2
1
1
2
1
0
0
1
1
0
0
0
0
0
1
0
1
0
1
1
0
1
0
1
0
1
1
2
1
0
2
1
1
1
2
2
2
0
0
0
1
0
0
1
1
0
1
1
1
1
0
1
1
1
0
1
0
1
0
2
0
1
1
2
1
1
0
2
1
1
0
0
0
0
1
1
2
2
1
2
1
1
1
2
1
3
2
2
1
2
2
1
0
2
0
0
2
0
1
0
1
0
0
0
1
1
1
0
1
1
1
1
0
2
1
1
1
1
3
2
0
0
2
0
0
1
1
1
1
0
0
2
0
1
1
1
1
0
0
1
0
3
1
0
1
1
1
0
1
2
0
2
1
1
0
1
2
0
1
3
8
2
1
0
0
1
2
0
0
1
1
1
0
1
0
0
2
2
1
1
2
0
1
0
0
2
2
0
1
3
1
2
2
0
1
1
2
2
2
0
2
0
2
0
1
0
1
0
1
1
1
4
0
2
1
1
1
1
1
1
2
0
1
0
2
2
0
0
2
2
0
0
1
2
1
1
1
1
1
0
1
2
1
1
1
1
2
1
1
1
2
0
1
2
1
2
0
1
0
1
0
0
0
0
1
2
1
0
1
2
1
0
1
0
1
0
1
0
0
1
0
0
0
0
2
0
0
0
0
1
2
1
1
2
0
0
0
0
1
5
0
1
2
2
0
1
1
0
1
2
1
1
1
0
0
2
0
0
0
1
1
1
2
2
1
0
2
1
1
0
2
0
2
1
0
3
0
0
2
2
1
0
0
0
3
1
0
1
0
0
1
0
0
0
2
0
2
1
1
1
0
2
9
0
2
1
1
0
2
2
0
1
0
0
2
2
2
2
0
2
1
1
1
0
1
2
1
1
1
1
0
1
0
2
1
0
0
1
1
1
0
2
2
0
0
0
2
0
2
0
0
1
0
2
0
0
0
0
1
1
0
1
1
0
0
1
1
2
2
2
1
0
0
1
1
2
1
0
1
0
0
2
2
0
1
1
1
0
0
1
1
0
1
1
0
0
2
1
2
1
1
2
4
1
1
2
0
0
1
2
0
0
2
1
1
0
0
1
0
1
1
1
0
2
2
0
0
1
2
0
0
0
0
0
1
2
0
0
3
0
1
0
0
2
0
0
2
1
1
1
1
2
1
1
0
0
2
1
1
0
0
2
1
2
1
2
2
2
0
1
0
1
0
1
1
1
1
2
1
1
2
2
1
0
1
1
1
2
1
2
1
2
1
0
1
0
1
0
0
2
0
1
0
1
1
1
2
1
0
1
2
2
1
0
0
0
0
1
0
1
1
2
0
0
0
1
1
1
2
0
0
1
1
1
1
1
0
0
1
1
2
0
3
1
0
1
1
0
1
2
1
0
2
1
1
0
1
0
2
1
2
1
1
1
1
0
2
0
0
0
0
2
1
2
0
0
1
0
1
2
0
1
0
1
0
0
1
2
0
2
0
0
0
1
2
2
1
2
0
3
2
2
2
0
0
0
0
1
0
0
0
0
1
1
1
1
0
0
2
2
1
1
2
2
0
1
1
0
0
1
1
0
1
0
1
1
0
2
0
0
1
0
1
1
0
1
0
1
2
1
3
2
2
1
2
1
1
0
0
1
0
0
1
1
0
2
1
0
1
1
0
1
0
1
1
2
1
0
1
0
1
2
1
0
1
2
0
1
1
1
3
2
2
2
0
2
1
1
1
2
0
1
1
1
0
0
1
0
2
1
1
2
0
2
0
2
3
1
0
2
2
0
1
2
2
0
1
1
1
2
1
1
0
2
1
1
1
2
1
2
1
2
0
1
1
1
2
2
0
0
0
1
0
0
1
0
0
1
1
1
1
2
2
0
1
1
0
1
1
0
2
0
0
1
0
0
0
1
1
1
1
1
0
1
0
1
0
2
1
0
0
1
0
1
1
1
0
2
1
1
1
1
0
0
1
1
2
0
1
1
2
2
0
1
1
1
2
1
1
0
0
1
2
0
0
1
1
0
2
1
2
1
1
1
1
1
0
1
1
2
1
0
0
0
0
2
1
0
0
0
2
1
1
1
1
2
1
1
2
0
0
1
1
1
0
0
3
0
1
0
0
0
2
2
0
2
0
1
1
0
0
2
2
1
2
0
2
0
0
1
2
0
1
1
0
1
0
1
1
2
0
1
2
2
2
1
1
1
0
2
2
0
2
1
1
1
0
0
1
2
1
0
1
0
1
1
0
1
0
1
3
0
1
0
0
2
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
0
0
2
0
0
1
0
1
2
0
1
1
1
1
1
1
2
0
1
0
1
2
0
1
1
1
1
0
2
2
2
0
2
0
0
1
1
0
1
0
1
0
1
3
0
1
1
0
1
1
1
1
0
1
2
2
0
0
2
1
2
1
0
2
1
0
0
1
1
1
1
2
0
1
1
0
0
1
1
0
0
0
2
0
1
0
1
1
0
0
1
1
0
1
2
1
0
1
2
1
1
1
0
0
2
2
1
0
0
1
1
2
0
1
1
2
0
0
0
0
1
2
2
0
1
1
0
1
2
0
2
1
2
0
0
0
1
0
1
1
1
0
1
0
1
0
2
2
2
1
1
1
1
1
1
0
1
2
1
0
1
2
1
1
0
1
1
1
1
0
1
0
1
1
0
1
0
1
1
1
0
0
2
0
0
2
2
1
1
0
0
0
0
1
1
0
1
2
0
0
2
2
0
0
1
4
3
1
1
1
2
0
0
0
0
1
0
0
1
2
1
2
0
2
0
2
1
0
1
0
2
0
1
0
0
1
0
1
0
1
0
0
1
1
1
0
0
1
1
0
0
1
1
1
1
1
1
1
4
1
2
1
0
2
0
1
1
0
1
2
2
0
0
2
1
0
0
1
1
1
0
0
1
0
2
1
0
2
0
1
0
1
0
2
2
2
2
0
0
0
1
0
1
2
2
0
2
2
0
2
1
0
1
2
1
1
1
1
1
0
2
1
0
1
1
1
1
0
0
0
0
0
0
0
0
1
0
2
2
0
1
0
1
1
1
0
1
3
0
1
1
0
0
0
1
2
2
2
2
2
0
2
1
1
1
0
1
1
1
0
1
0
1
0
1
0
0
0
1
1
1
0
2
1
0
2
0
0
1
0
0
1
2
3
0
1
0
0
0
2
0
1
0
1
2
1
2
1
1
1
0
2
2
1
1
0
0
1
0
0
2
1
2
1
2
0
1
2
0
1
0
0
1
2
0
0
1
1
0
1
0
2
0
0
2
1
1
0
0
1
1
0
0
1
0
1
0
1
1
1
1
0
0
2
0
2
2
1
0
0
0
1
1
2
1
0
0
2
1
0
1
1
1
2
2
0
1
1
0
2
1
2
0
0
1
0
0
0
1
2
0
2
2
0
1
2
0
2
0
2
0
0
0
2
1
1
0
1
1
0
1
1
1
1
1
1
0
0
0
2
2
0
1
0
0
0
1
2
2
0
0
2
0
1
0
0
1
1
1
0
1
1
0
1
1
0
1
0
1
0
0
0
2
3
2
0
2
0
2
0
1
0
0
0
0
1
0
1
0
1
0
2
1
0
0
0
1
1
0
2
0
0
2
1
0
1
2
0
1
1
0
1
1
1
0
1
1
1
1
0
2
1
0
1
0
1
1
1
0
1
1
0
0
2
2
0
0
1
2
0
0
1
0
1
3
1
1
1
0
1
2
1
0
1
0
0
1
0
1
2
2
1
1
3
1
2
1
0
1
1
1
1
2
1
0
1
0
1
1
3
1
2
2
0
2
1
1
1
0
0
0
0
2
1
2
1
1
0
1
2
2
1
0
1
2
1
1
1
1
0
0
0
1
2
1
2
1
0
1
0
0
0
0
0
0
2
1
0
0
1
1
0
1
2
1
0
1
2
2
0
2
1
0
1
0
1
1
1
2
0
0
1
0
1
0
0
0
0
1
0
0
1
0
2
1
1
0
1
0
1
0
2
1
1
2
0
1
0
0
2
0
1
1
0
0
2
1
0
2
0
0
0
2
1
0
1
0
0
2
2
0
1
1
0
1
0
1
1
1
0
0
0
2
2
0
1
0
1
2
1
1
0
2
1
1
1
1
0
2
2
2
0
1
2
0
1
0
2
0
2
1
1
2
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
2
1
0
0
2
2
0
1
1
2
1
2
0
0
0
2
0
0
0
1
1
0
1
0
2
1
2
1
1
1
2
0
2
1
1
0
0
0
0
0
1
0
1
1
1
1
2
3
2
0
1
0
1
1
1
1
1
0
1
2
2
0
1
0
2
0
0
0
2
0
1
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
1
1
2
1
1
0
1
3
0
0
2
2
1
1
1
1
0
2
1
0
0
0
1
2
1
2
2
0
0
0
0
1
0
1
2
0
0
3
1
1
1
1
2
1
0
3
1
2
0
1
2
1
0
0
0
0
1
2
0
1
2
1
2
1
1
0
0
2
0
1
1
1
1
1
0
3
1
1
0
3
0
0
2
2
1
0
1
1
1
0
0
1
1
0
1
0
1
1
1
1
0
2
2
0
1
0
0
1
0
2
0
1
1
0
0
1
2
0
0
0
1
0
1
0
1
0
1
1
1
1
1
1
0
1
1
2
2
2
2
2
1
0
1
1
0
1
0
2
1
2
2
0
2
0
2
1
0
0
1
2
1
1
1
2
0
0
1
0
0
0
0
1
2
1
2
2
0
3
0
1
2
1
2
0
0
2
0
2
2
1
2
1
1
2
1
2
2
0
0
1
0
6
2
3
1
0
1
0
2
2
1
0
1
1
2
2
2
1
1
0
2
1
2
1
2
0
0
1
0
0
2
2
2
1
1
2
0
1
2
2
0
0
1
0
2
0
1
2
1
2
2
1
1
1
1
1
0
0
1
0
2
0
2
1
1
1
2
0
1
2
0
1
1
0
0
2
1
1
2
2
1
0
2
0
0
1
0
0
0
1
1
3
1
0
1
0
0
1
1
0
0
0
1
1
1
0
1
0
2
1
1
1
0
0
1
2
2
0
1
0
1
1
1
2
1
2
1
1
0
0
2
1
1
1
0
1
2
1
1
0
1
1
2
0
0
0
1
1
0
0
0
0
1
2
0
0
1
0
0
1
0
0
0
1
0
2
1
1
1
0
1
0
1
1
0
0
2
0
1
1
1
0
1
1
1
2
1
2
1
0
1
1
1
1
1
1
2
2
1
1
0
0
0
1
1
1
0
1
2
0
0
0
1
0
2
1
0
1
0
2
2
0
0
2
1
0
2
0
2
1
0
0
2
1
2
0
1
1
1
3
1
0
0
1
2
0
1
0
1
1
2
1
1
1
1
0
1
1
2
1
0
1
2
0
1
0
0
1
1
1
0
0
0
0
1
2
0
1
0
1
0
0
1
1
2
2
2
1
2
1
1
1
0
1
0
0
1
0
0
0
1
1
0
1
2
1
2
1
0
0
1
0
2
0
1
0
1
0
1
0
0
1
0
1
1
0
1
1
0
0
1
0
1
0
2
0
1
0
2
2
0
2
2
1
1
2
2
2
2
1
1
1
1
1
2
1
2
1
1
2
0
0
1
2
0
1
0
1
0
1
0
3
2
1
0
0
1
1
0
1
0
0
1
0
1
1
0
1
0
0
0
0
0
2
3
2
1
0
0
2
1
1
1
0
0
0
0
0
2
1
1
0
1
2
2
2
0
3
1
0
1
1
2
0
1
1
1
1
1
1
1
0
1
2
2
1
1
1
1
0
2
3
2
0
0
1
0
1
0
2
1
0
1
2
0
0
2
0
1
2
0
1
0
1
1
1
1
1
1
2
1
1
1
0
1
1
1
2
0
2
0
1
1
0
3
1
2
0
2
0
1
0
1
1
0
0
0
0
2
0
2
0
0
0
0
2
0
1
0
2
1
2
1
1
0
0
2
0
2
2
0
0
1
1
0
2
1
1
0
0
1
1
0
2
0
2
0
1
1
1
2
0
0
2
2
1
1
2
1
1
0
1
0
1
0
0
0
1
1
3
0
2
2
0
1
0
1
0
3
0
0
2
0
0
0
0
1
0
1
0
1
1
1
2
1
0
2
2
2
0
0
1
1
3
1
1
1
1
1
2
0
0
1
2
0
1
2
0
1
0
2
1
1
0
2
0
1
1
2
0
1
1
1
1
1
1
0
1
0
0
1
0
2
1
0
0
0
1
1
2
2
1
0
1
0
1
0
1
2
0
2
0
0
1
1
1
0
1
1
1
1
2
1
1
0
5
2
1
1
0
2
2
0
2
1
1
1
1
0
0
0
2
1
0
1
0
0
2
2
1
1
2
2
2
0
0
0
1
2
1
1
1
1
0
0
1
1
0
2
0
1
1
1
1
1
1
1
1
1
5
2
2
1
2
1
0
2
3
2
1
1
2
1
0
0
2
2
0
2
1
1
0
1
1
1
0
1
2
1
1
1
0
0
1
2
2
1
0
3
0
1
1
2
4
0
0
0
0
1
3
2
2
1
0
1
0
0
2
0
1
0
2
0
0
1
1
1
4
0
2
0
0
1
0
0
0
2
0
1
1
1
0
0
0
1
2
1
0
2
0
2
1
1
1
1
0
0
1
2
0
1
1
0
0
1
2
1
1
2
1
1
1
1
1
1
0
1
0
0
2
2
1
2
0
0
1
2
0
1
1
0
2
1
1
0
2
1
0
0
2
1
1
0
0
2
0
2
1
3
2
1
0
1
1
1
0
1
2
1
0
2
1
1
0
2
1
1
1
0
1
2
1
2
0
2
1
0
1
2
2
1
0
2
2
1
1
0
2
1
2
0
2
2
1
1
0
0
2
1
0
0
1
0
1
2
1
0
1
1
1
0
1
1
1
2
1
1
1
1
0
0
0
0
2
0
0
2
1
1
0
0
1
1
2
2
0
0
0
0
0
2
2
0
2
0
1
0
2
1
0
1
0
1
0
0
0
2
2
1
0
1
2
2
0
0
0
1
1
3
1
0
1
1
0
0
0
0
2
0
1
1
1
1
0
2
1
0
2
1
1
0
2
2
0
2
0
2
0
2
1
0
2
0
0
1
3
2
0
1
1
0
1
1
1
2
0
1
1
1
1
1
1
1
1
1
1
1
0
1
0
2
0
0
1
2
1
2
1
1
1
0
2
0
1
3
1
2
2
1
2
1
0
0
1
1
1
0
2
0
1
2
1
0
1
1
1
2
2
1
2
1
1
1
0
0
1
1
3
0
1
2
2
1
1
1
0
1
1
2
3
1
1
2
0
1
2
0
1
0
2
1
0
1
0
2
1
2
1
0
0
3
1
1
2
2
2
2
1
0
1
1
1
2
0
1
0
1
1
0
1
1
2
1
1
0
2
0
0
2
1
0
0
2
2
0
0
2
0
1
0
0
1
0
1
0
0
1
0
1
1
2
0
1
1
2
1
1
0
2
0
1
1
0
1
1
1
1
1
2
0
2
2
0
0
0
1
0
2
0
2
2
1
1
1
1
1
1
0
1
2
1
2
1
0
1
0
2
2
2
1
1
2
0
1
0
2
0
1
2
0
0
0
1
2
2
0
0
1
0
1
1
1
0
0
0
2
1
0
1
2
1
0
1
0
1
1
1
2
1
2
0
2
0
0
1
1
1
2
1
1
0
0
0
1
2
1
1
0
2
2
0
1
2
0
0
1
0
0
2
1
1
2
1
0
1
1
0
2
1
2
1
0
0
0
1
0
1
1
2
0
1
1
0
1
0
0
1
0
1
2
0
2
1
0
0
1
0
1
2
1
1
2
1
1
0
1
0
0
3
0
0
0
2
2
0
0
2
1
1
1
2
0
1
2
0
0
1
0
1
2
2
1
2
1
1
2
1
0
2
1
1
0
1
0
2
2
1
1
2
1
1
2
0
0
2
1
2
2
1
0
1
2
0
0
2
1
1
2
0
1
1
0
1
1
0
1
1
0
1
1
0
1
0
0
1
2
0
0
0
1
2
0
1
2
0
1
0
1
0
2
1
1
1
1
0
1
2
0
1
2
2
1
1
1
0
1
1
0
2
1
0
0
0
0
1
1
1
0
0
1
1
0
1
1
1
1
0
0
1
1
0
1
2
2
0
1
1
1
1
2
0
1
2
1
0
0
1
2
0
2
0
2
0
0
0
0
1
1
0
0
1
1
0
0
0
2
0
1
3
1
1
0
1
1
1
2
0
1
1
1
1
0
1
0
0
0
1
1
2
2
1
0
1
0
0
0
0
1
1
2
1
1
0
0
1
1
1
1
0
1
2
0
1
2
0
1
0
1
1
1
1
0
2
1
2
1
1
1
0
1
1
0
0
0
2
2
1
2
1
2
1
0
2
2
0
2
2
1
1
2
0
1
0
2
0
0
1
1
0
1
0
0
1
1
0
2
0
1
1
2
0
1
1
2
1
0
2
0
2
1
0
1
0
1
1
0
0
1
2
1
1
0
1
0
1
1
1
1
0
1
1
0
2
4
1
0
2
1
0
1
2
0
0
0
0
0
1
1
1
1
1
1
1
0
1
1
0
1
0
0
1
1
0
0
1
0
0
1
0
2
0
1
0
0
0
1
1
1
0
1
1
1
0
1
0
0
0
0
2
0
2
0
1
1
2
2
0
0
2
0
2
0
1
2
1
1
0
0
0
1
1
1
0
1
1
0
0
0
2
0
1
0
1
0
1
1
2
2
0
0
1
1
1
1
0
1
1
0
1
1
0
1
1
0
2
0
1
0
2
2
1
2
1
2
2
0
0
0
2
0
2
2
1
1
1
2
2
0
0
1
0
1
2
1
0
0
0
0
1
1
1
1
1
0
2
1
2
1
1
2
1
0
0
0
0
0
0
2
0
0
1
1
2
1
1
2
0
0
1
1
0
1
0
1
2
2
0
1
0
2
2
0
1
1
1
1
1
0
1
1
0
2
2
0
0
1
1
1
2
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
1
0
1
1
3
1
1
2
0
2
1
1
0
2
0
1
1
1
1
1
0
0
0
0
1
1
0
1
0
1
0
1
2
1
1
0
1
2
2
1
1
0
1
0
0
2
1
1
1
0
0
1
2
1
1
0
0
1
1
1
1
1
1
2
0
1
1
1
2
2
0
0
0
1
0
2
1
0
0
1
0
0
3
0
1
1
2
1
1
0
1
1
1
0
0
0
0
1
1
2
0
2
0
2
1
1
1
0
0
1
0
1
0
0
1
0
0
2
2
1
2
2
0
1
1
2
0
1
1
0
0
1
2
0
0
0
1
0
1
1
1
1
1
0
1
0
0
0
0
2
0
0
2
2
1
0
0
2
0
0
2
1
1
0
2
1
0
1
0
0
1
1
1
0
0
0
1
2
0
1
0
1
1
2
2
1
0
0
2
1
1
0
1
0
0
1
2
1
1
0
1
0
2
1
2
1
0
1
1
1
0
1
2
1
2
2
1
0
2
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
2
1
1
1
0
1
2
0
1
0
0
1
2
0
3
1
1
2
1
1
1
0
0
0
0
3
1
4
1
0
0
2
1
0
3
0
1
2
1
0
2
0
3
1
2
1
0
2
1
0
1
1
1
2
1
0
0
2
0
1
0
1
2
0
0
1
2
2
1
0
1
0
2
2
1
2
1
2
1
2
1
2
0
0
1
0
1
1
3
1
1
0
2
2
2
1
2
0
1
0
2
0
0
2
0
1
0
1
1
2
1
1
0
0
0
2
0
2
1
0
2
1
3
1
0
1
0
2
1
1
0
0
0
0
3
1
1
2
1
2
2
1
2
1
1
0
1
0
2
1
0
1
2
0
1
0
2
0
2
0
1
2
0
2
0
1
1
3
1
2
0
0
1
0
0
0
1
1
0
0
2
1
1
0
2
2
0
1
0
1
1
2
3
2
0
1
1
2
0
0
2
0
2
1
1
0
2
0
0
1
0
0
0
1
0
0
1
1
1
1
0
1
1
1
1
1
1
1
2
0
2
2
0
0
0
1
1
1
2
0
1
0
2
2
0
0
1
3
1
1
3
1
2
0
1
0
2
0
1
1
0
1
1
1
1
2
0
0
1
2
1
1
0
2
1
0
6
1
2
2
1
0
1
0
2
2
0
1
0
0
1
0
1
1
2
0
1
0
2
1
1
0
0
1
1
1
1
0
2
1
0
1
1
2
2
0
2
1
1
0
2
0
0
0
1
1
1
1
1
2
0
2
0
3
1
1
1
1
1
0
0
0
0
2
1
0
1
1
2
1
1
2
2
1
1
2
2
3
1
0
1
1
1
1
2
0
1
0
1
2
1
0
1
0
0
0
1
2
1
2
1
1
0
1
2
2
0
1
1
1
1
3
2
1
1
0
0
1
0
2
1
0
0
2
2
0
1
1
2
0
1
2
1
2
2
0
1
1
0
0
0
2
0
0
0
2
1
0
1
1
4
1
0
1
3
2
1
1
0
1
1
1
2
1
0
0
1
1
1
0
1
1
2
0
0
1
0
0
0
1
1
2
0
1
0
1
0
0
2
3
1
2
1
0
1
0
0
2
0
2
2
2
1
0
0
2
1
2
1
1
1
2
1
2
1
0
2
1
0
1
1
2
2
2
1
1
1
1
1
0
2
2
1
0
1
2
1
2
1
0
1
1
1
0
0
2
2
0
0
1
1
0
2
1
0
0
1
2
1
0
1
0
1
1
1
0
2
2
1
1
0
1
1
1
0
2
0
1
0
1
1
1
0
0
0
1
1
1
0
0
2
1
1
0
1
0
0
0
2
0
2
0
3
2
2
0
0
2
0
1
1
0
0
1
2
1
0
0
0
0
1
1
0
0
1
2
1
1
1
0
1
1
2
2
1
0
0
1
1
1
0
2
2
1
1
0
0
0
1
0
0
0
1
2
0
0
0
1
2
1
1
1
0
2
1
0
0
1
0
2
2
5
2
0
1
2
0
1
0
10
1
1
2
1
3
0
1
0
1
0
1
1
2
1
1
0
1
0
0
1
2
1
0
0
0
0
0
2
1
1
1
0
3
1
2
0
0
1
1
0
0
2
1
1
3
1
1
0
0
1
1
1
1
1
0
2
0
1
0
1
1
0
0
0
0
0
2
2
0
1
0
1
0
0
2
1
1
2
0
0
1
0
2
0
0
0
1
1
2
0
0
0
2
0
1
1
1
1
0
1
1
0
0
1
0
3
0
0
1
2
1
0
1
2
2
0
1
1
2
0
0
0
2
0
0
0
2
0
0
0
0
1
2
0
0
1
1
0
2
1
0
0
1
0
2
1
1
1
1
1
0
0
0
2
0
0
0
1
0
1
1
0
0
1
0
0
1
1
1
0
1
0
0
1
2
1
0
1
1
2
3
0
2
2
1
1
0
4
2
2
1
1
1
2
2
0
1
2
0
0
0
2
0
1
2
0
0
3
1
1
0
2
0
3
0
2
0
1
2
1
1
1
1
0
2
1
1
1
0
1
1
2
1
0
1
1
0
2
2
1
1
0
1
2
0
1
2
1
2
1
0
1
2
1
0
1
1
1
1
0
0
2
1
2
2
2
2
0
2
1
0
1
1
2
1
0
1
2
0
1
0
1
1
1
1
2
2
1
0
0
0
1
1
0
2
1
2
2
1
1
0
1
0
1
1
2
1
1
0
0
1
1
0
0
1
1
0
2
1
0
2
0
0
1
2
1
0
1
2
2
1
1
2
0
1
0
1
0
0
0
1
2
1
0
0
2
1
1
0
0
3
2
1
1
0
1
1
0
0
2
0
2
0
2
1
1
0
3
1
1
1
0
1
2
1
1
1
2
1
1
1
1
1
1
2
1
0
1
2
3
0
0
1
1
1
1
1
1
1
1
0
2
0
1
2
0
1
2
1
1
2
2
0
1
1
2
1
1
1
1
1
0
0
1
2
0
0
1
0
1
2
0
0
1
1
0
2
1
2
2
0
0
2
0
3
1
0
2
1
2
1
1
1
0
0
2
0
0
0
1
1
0
0
1
1
1
0
1
1
0
1
1
2
1
1
1
1
0
2
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
1
2
0
1
0
2
2
2
0
2
2
1
2
1
1
0
0
1
1
1
1
0
1
0
0
0
0
2
0
0
0
0
2
1
0
1
0
1
2
1
0
1
0
0
0
1
2
1
1
1
0
0
1
0
1
1
0
0
2
2
0
3
2
1
0
0
0
0
1
0
0
1
2
1
1
2
1
2
0
0
0
1
0
0
2
1
0
1
3
2
2
0
2
0
3
1
0
0
2
0
2
0
0
0
0
3
1
0
0
1
2
1
0
1
1
2
1
1
1
0
1
2
0
1
1
1
2
0
0
0
2
2
1
1
1
0
1
0
1
2
0
3
0
0
2
0
0
0
0
0
0
3
2
0
2
1
2
1
0
1
2
0
2
2
1
0
0
0
0
0
0
1
2
1
1
1
0
1
2
2
2
1
1
1
0
1
2
1
0
1
0
1
1
2
1
2
2
0
0
1
1
0
0
1
1
1
0
1
1
1
1
1
0
1
0
2
2
0
0
1
1
1
1
1
0
1
2
0
0
1
1
2
1
2
0
2
2
2
0
2
0
0
0
0
2
0
0
3
0
0
1
0
0
1
1
1
2
2
1
2
2
1
1
0
2
1
1
1
1
2
0
0
0
0
1
0
2
1
0
0
1
0
0
0
0
1
2
1
2
2
0
1
0
1
0
0
0
1
1
1
1
1
1
0
0
3
0
2
2
2
0
0
1
2
1
0
1
0
2
0
2
0
2
2
3
1
1
0
0
1
0
1
0
2
0
0
2
0
1
3
1
1
1
2
0
1
0
3
2
0
0
0
1
0
2
1
0
2
0
1
0
1
2
1
1
1
1
1
1
1
2
1
1
0
0
2
0
1
0
1
1
0
0
1
0
4
2
1
0
2
2
1
1
1
0
1
1
1
0
1
0
1
0
1
1
0
0
1
1
0
1
1
0
1
0
2
1
0
1
1
1
1
1
0
2
1
2
2
2
0
0
1
1
0
1
2
0
0
1
2
0
1
1
1
1
0
0
1
1
2
1
0
0
1
1
0
1
0
0
1
0
0
2
0
1
1
1
1
1
1
2
0
0
0
0
1
1
1
0
1
0
1
0
0
0
0
1
2
0
0
1
2
0
0
2
0
1
0
0
1
1
2
0
0
2
0
1
2
0
0
0
0
0
1
0
0
1
1
0
0
1
1
2
2
1
0
1
0
2
1
2
0
1
1
2
1
0
1
0
0
1
2
1
0
2
0
0
0
1
1
2
1
1
0
1
1
0
1
2
0
1
1
1
2
1
2
0
1
1
2
2
0
1
0
1
0
0
1
0
0
0
1
1
1
1
2
1
1
0
0
1
2
2
1
2
2
1
1
0
1
1
0
0
1
1
0
1
2
0
1
1
0
1
1
2
2
3
1
0
1
0
1
1
0
0
1
2
1
0
2
0
2
0
0
1
1
1
2
1
1
1
0
1
1
0
2
1
0
0
2
1
2
2
2
1
1
1
2
2
0
0
2
1
1
0
1
2
1
0
0
1
2
1
1
1
0
1
2
0
0
1
0
1
0
0
1
1
1
0
0
1
0
1
0
0
0
1
1
1
0
0
2
2
1
1
2
2
0
0
0
1
0
0
1
1
1
2
0
0
2
1
1
2
2
0
1
2
1
2
0
2
0
1
0
1
0
2
0
0
2
1
2
0
1
0
1
1
1
0
0
0
1
2
0
1
1
0
1
0
1
0
1
0
1
2
0
2
2
0
1
1
1
1
1
1
1
2
1
0
0
1
1
0
0
1
0
1
1
2
0
0
2
0
1
2
1
1
2
1
1
2
0
1
3
1
2
1
0
0
0
1
1
0
1
2
0
3
1
0
0
2
1
2
2
1
1
1
0
0
1
1
1
2
0
2
1
2
1
0
2
0
0
1
2
0
1
0
2
1
1
0
2
1
1
1
1
0
0
1
2
1
0
0
0
0
1
1
0
0
1
0
1
2
2
2
1
2
1
2
0
1
0
1
1
2
1
1
0
2
0
2
0
0
2
0
1
3
1
2
1
1
1
1
0
0
1
0
1
1
1
1
2
1
1
0
1
1
2
2
2
1
2
0
0
1
0
2
0
0
2
1
1
0
2
0
2
2
1
1
2
0
1
1
2
2
2
0
0
1
0
2
0
0
1
2
1
2
1
2
1
0
1
1
0
0
2
1
0
1
1
1
1
1
0
1
2
0
0
0
0
1
0
0
0
0
1
1
1
2
0
1
1
0
1
1
0
2
0
1
2
0
1
0
1
0
1
0
0
1
0
2
2
0
0
1
1
1
1
0
1
2
0
1
2
1
1
1
0
1
0
2
2
0
1
0
1
0
1
0
0
1
0
2
1
1
1
1
0
1
0
0
2
0
1
0
1
1
1
1
1
2
0
0
1
2
0
1
1
2
1
1
1
1
1
1
0
2
2
0
1
1
0
0
0
1
0
1
2
0
1
1
2
0
2
0
0
2
0
0
2
1
1
1
0
0
2
1
1
2
2
2
0
1
2
0
0
1
0
1
2
0
1
2
1
2
2
1
0
1
1
1
1
1
0
1
0
1
2
0
1
0
0
0
2
0
1
1
1
1
1
1
1
1
1
1
0
0
3
1
0
0
1
2
2
0
2
2
0
1
1
0
1
2
0
1
1
0
0
0
0
0
1
1
1
0
1
0
1
0
1
1
0
1
1
1
0
0
1
2
0
2
0
1
2
0
1
1
0
0
1
2
1
0
1
0
2
1
1
2
0
0
0
1
0
0
1
0
0
1
0
2
1
4
0
0
1
2
1
1
1
0
0
1
1
0
1
1
2
0
1
3
0
0
2
2
1
1
0
0
0
2
1
0
0
1
0
2
1
0
0
0
0
0
0
2
2
0
1
1
0
0
1
1
2
0
0
0
1
0
0
1
1
1
0
0
2
1
0
1
0
0
0
0
0
2
0
0
0
0
2
1
0
1
0
1
2
0
2
0
2
3
0
2
1
1
1
0
1
1
1
0
1
1
2
1
1
1
0
2
0
0
0
2
0
1
1
1
0
1
0
1
0
1
2
1
2
1
0
1
0
1
1
0
2
1
3
2
2
1
0
2
1
1
1
0
0
2
0
1
1
0
1
0
0
1
1
1
3
1
0
2
0
0
0
1
2
1
2
0
2
1
2
2
0
1
1
0
0
1
0
2
1
1
1
0
1
2
2
0
1
0
0
2
1
1
0
0
0
0
1
0
3
0
1
1
1
1
1
1
0
1
2
1
0
0
0
0
1
2
2
1
1
2
1
2
1
0
0
0
1
0
0
2
0
1
0
1
1
0
1
1
2
1
2
0
0
1
0
1
1
1
1
0
0
0
0
2
1
0
1
0
0
1
2
1
1
0
2
1
0
1
1
1
0
2
0
1
0
1
1
1
1
0
0
1
1
0
2
1
0
1
1
0
1
1
0
0
0
0
1
1
0
0
0
0
1
1
0
1
0
1
0
0
0
1
2
0
0
1
1
0
3
1
0
1
0
2
1
0
0
0
1
2
1
0
0
0
1
2
0
0
0
0
1
2
1
2
2
2
2
1
2
4
1
0
1
1
3
1
1
1
1
1
0
0
1
2
2
2
0
0
1
1
2
0
0
1
1
2
1
1
0
1
1
1
1
0
2
1
2
0
1
1
0
1
2
2
0
0
0
0
1
1
1
2
0
1
1
0
2
1
0
0
2
2
1
1
0
1
1
0
0
0
1
1
2
0
2
1
0
0
1
1
2
1
3
2
2
1
0
3
1
1
0
0
1
1
1
0
2
1
1
1
1
1
2
0
1
0
1
0
1
0
1
1
1
0
0
1
1
2
1
1
1
2
2
2
2
2
1
0
1
0
0
0
1
0
0
2
1
0
2
0
0
1
1
0
0
2
0
2
0
0
4
1
1
0
1
1
1
0
0
0
0
0
2
1
1
0
2
0
0
1
2
1
1
1
2
2
0
1
2
0
0
0
0
2
1
2
0
1
1
1
2
5
1
0
0
1
1
0
0
1
2
1
2
1
2
2
1
0
0
0
0
1
2
1
0
0
2
0
2
2
1
1
0
1
2
2
1
1
1
1
0
1
0
0
0
1
0
1
2
0
1
1
2
1
1
2
0
1
0
0
2
1
2
1
0
2
0
1
1
0
1
1
2
0
0
1
1
2
0
2
1
1
2
0
2
2
1
2
2
0
1
1
1
1
2
1
2
1
2
0
1
0
1
1
0
2
0
0
0
1
0
2
3
1
1
0
1
0
2
1
0
0
0
1
0
1
2
0
1
1
1
1
1
1
1
2
0
2
2
0
0
2
2
0
2
0
0
1
0
1
0
1
2
0
0
1
0
1
1
1
0
2
1
0
1
3
0
0
0
1
1
1
0
1
0
1
1
0
0
2
1
1
0
2
2
2
1
0
0
0
1
0
1
0
1
0
1
2
1
1
2
0
0
2
0
2
1
0
1
0
0
1
0
2
0
0
1
2
0
1
0
0
1
3
1
0
0
0
0
2
1
2
2
0
1
1
0
0
1
1
2
1
1
1
0
2
0
2
2
1
1
0
1
1
0
0
1
1
0
1
0
2
0
2
1
1
1
0
1
2
2
3
1
1
1
2
0
1
2
0
0
1
1
0
0
1
2
2
1
0
0
1
0
0
0
0
2
1
1
0
1
1
1
0
0
2
2
0
0
2
0
1
0
0
0
1
1
0
1
0
1
1
2
1
0
0
2
2
0
0
1
0
1
0
1
0
0
2
0
1
0
2
1
1
0
0
1
1
0
1
2
0
1
1
1
1
1
2
1
0
2
0
1
0
2
0
0
1
0
1
1
2
1
0
1
0
1
0
0
1
0
0
1
0
0
0
3
1
2
2
0
0
2
1
1
2
1
1
1
0
0
0
1
2
2
1
0
0
0
2
1
0
0
1
2
0
2
1
3
0
0
1
1
1
2
2
0
3
0
1
1
0
0
2
1
1
0
1
1
0
1
2
1
0
2
1
2
1
1
2
2
2
2
2
1
1
0
2
2
3
1
0
0
1
0
0
1
0
0
2
1
0
0
0
2
1
2
2
2
1
1
2
1
0
1
0
0
1
1
1
0
1
0
1
1
2
1
0
2
2
0
1
1
1
0
0
0
1
0
0
0
2
1
0
1
0
2
1
0
0
0
0
1
2
2
0
0
0
1
0
1
0
0
2
0
0
1
0
1
2
0
0
2
2
1
0
2
0
1
1
0
0
1
0
2
1
0
1
0
0
1
1
1
1
2
1
1
0
1
1
2
0
0
1
1
2
1
0
0
2
0
0
0
2
1
2
1
2
0
0
2
1
0
0
1
2
1
1
0
0
1
1
1
1
1
0
0
1
0
2
1
1
3
1
2
0
0
2
1
2
1
1
0
1
0
1
0
0
1
0
1
0
1
1
0
0
0
1
0
0
1
1
1
0
0
0
1
1
1
0
0
2
1
1
1
0
1
1
1
1
1
1
1
1
1
1
2
0
2
0
0
0
2
2
3
0
1
1
1
0
3
1
2
1
1
1
1
2
0
1
1
0
1
0
1
2
0
2
0
2
1
0
1
2
0
0
1
0
1
1
1
1
0
2
1
0
0
1
1
1
1
1
0
0
1
0
1
2
2
1
0
0
0
1
2
2
1
0
1
1
0
2
2
1
1
1
0
1
2
1
0
1
0
2
2
2
0
3
0
1
1
1
0
2
1
1
1
1
1
1
0
1
2
3
2
1
0
1
0
1
0
2
4
2
1
0
1
0
1
2
0
1
1
0
1
0
2
0
0
2
1
0
0
0
2
1
1
1
1
2
2
0
1
2
1
2
0
2
3
0
0
1
2
0
1
1
0
0
1
1
1
0
0
1
0
2
1
2
0
1
1
0
0
0
1
1
0
0
2
0
0
2
1
2
1
2
0
2
0
0
0
0
2
2
1
3
1
0
1
0
1
1
2
1
1
2
1
1
0
1
1
1
0
0
2
2
0
1
1
1
3
2
1
2
0
2
1
1
0
1
1
2
1
1
2
1
2
2
0
2
2
1
0
1
1
2
0
0
2
1
3
2
0
0
1
0
2
2
0
1
1
0
1
0
1
2
2
0
0
1
1
1
2
0
2
2
0
1
1
0
1
0
1
1
1
0
1
0
2
0
1
1
1
0
0
1
2
2
2
1
2
2
0
0
1
1
0
1
2
0
1
1
2
0
1
0
1
0
0
0
1
0
0
2
0
0
3
3
0
3
0
1
1
1
1
1
0
1
1
0
1
1
2
2
0
1
1
1
2
2
1
1
1
0
0
0
0
1
0
0
1
1
4
0
1
2
2
0
0
2
0
1
0
1
0
1
1
1
1
0
0
0
0
0
2
2
2
0
1
1
0
1
1
1
1
2
0
1
1
1
1
0
2
1
2
1
2
1
0
1
0
1
2
1
0
1
0
0
0
2
1
2
1
1
0
2
1
0
1
0
1
0
0
2
1
1
2
1
1
0
0
2
2
0
1
1
0
2
1
2
2
1
0
0
0
1
1
2
1
1
0
0
0
1
2
1
2
0
0
1
0
0
1
0
1
0
2
0
0
2
1
0
1
2
1
1
3
2
0
0
0
0
1
0
0
2
0
0
1
1
0
1
0
1
2
0
1
0
1
1
2
0
0
0
2
2
0
1
0
0
1
2
0
0
1
2
1
0
0
0
0
1
0
2
0
2
1
1
1
0
1
0
0
0
0
0
1
1
1
0
2
1
1
2
0
0
1
1
0
0
0
2
1
0
1
0
0
0
1
0
1
1
0
1
0
0
1
2
2
0
0
1
0
2
0
0
2
1
0
1
1
2
1
0
1
2
0
1
0
1
2
0
0
0
0
0
0
2
0
0
2
1
2
1
0
2
0
0
1
1
0
2
0
2
1
0
1
0
0
0
1
0
0
0
1
0
0
2
1
2
0
1
0
0
2
0
1
0
1
2
1
0
2
0
1
1
0
2
1
0
1
1
1
1
1
1
1
0
0
0
2
0
0
1
1
0
1
2
1
1
0
0
0
2
2
2
0
1
2
1
1
1
3
2
4
3
0
0
1
1
1
2
1
1
1
0
1
1
0
0
0
1
2
2
0
1
2
2
1
1
0
2
1
1
0
1
1
0
1
1
1
0
0
0
0
1
0
1
2
0
0
2
1
0
1
1
0
0
0
0
1
0
0
1
1
2
1
1
2
0
1
0
1
1
2
0
2
0
1
1
2
0
0
0
1
0
0
2
0
1
0
0
0
1
0
1
1
0
2
1
1
0
0
3
1
1
2
2
2
2
1
0
2
1
0
2
1
1
0
2
0
0
0
0
0
2
1
2
1
0
2
1
2
1
1
0
0
1
1
0
3
0
2
0
0
0
1
0
0
2
1
1
1
0
1
0
2
2
1
1
2
0
0
1
0
1
1
0
1
1
1
0
0
1
1
2
1
0
0
0
1
1
0
0
1
2
1
0
0
0
2
2
1
1
1
0
1
0
1
1
0
1
0
2
0
1
0
0
1
1
2
2
2
1
0
1
1
2
1
2
0
1
2
1
2
0
2
2
0
1
1
1
1
0
1
2
0
0
2
1
1
0
1
1
2
2
1
2
0
1
1
0
1
1
0
2
0
0
0
1
1
1
2
0
1
0
1
2
1
0
2
0
0
2
1
1
2
1
1
1
1
1
2
1
0
2
0
0
1
1
1
2
1
1
1
0
2
2
1
2
1
0
1
1
1
1
1
0
0
2
2
0
0
2
0
1
1
1
1
0
2
1
1
0
1
1
0
1
0
1
2
0
1
2
2
0
1
2
1
2
2
1
1
2
1
1
0
1
0
0
0
0
0
2
1
1
1
1
0
1
1
0
0
0
0
0
0
1
2
0
1
0
0
0
1
1
0
0
1
1
1
0
1
1
0
1
1
2
2
0
1
0
0
0
1
0
1
1
2
0
1
0
1
1
1
0
0
1
0
1
2
1
1
1
1
1
0
0
2
0
0
0
0
0
1
1
2
2
1
0
1
0
1
0
1
1
0
1
1
1
0
1
0
0
1
0
1
0
0
0
1
2
1
2
1
1
1
2
2
1
1
2
2
1
1
1
0
1
0
0
0
2
0
1
2
2
3
1
1
1
1
1
2
1
1
0
0
0
0
1
0
0
1
0
2
1
0
0
1
1
0
1
2
1
1
1
4
0
3
0
0
1
1
2
1
1
2
2
2
0
0
0
1
2
0
0
2
1
0
0
2
0
0
1
0
1
2
0
2
1
1
1
1
0
0
0
0
0
1
0
0
0
1
1
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
1
1
0
2
1
0
1
0
0
2
1
2
2
1
0
1
2
0
1
1
1
2
0
0
1
1
1
0
2
0
0
0
0
1
2
1
0
1
1
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
0
0
1
0
1
2
1
1
2
1
1
2
0
1
2
1
0
1
1
0
1
1
0
0
0
1
0
0
0
3
0
2
1
2
1
0
1
0
1
1
1
1
0
0
1
1
0
1
0
1
1
1
1
1
0
0
1
0
1
1
3
0
0
0
1
1
1
1
1
0
0
1
0
1
0
1
2
2
1
0
0
1
0
0
0
1
1
1
1
1
0
1
0
0
0
2
1
0
0
1
1
1
1
2
1
1
1
1
1
0
1
0
1
0
0
0
0
1
1
1
1
2
1
1
2
2
0
0
0
1
1
1
2
1
0
0
0
0
0
1
1
1
1
1
1
0
0
1
2
1
1
0
1
0
1
1
2
1
0
2
1
1
3
0
2
0
1
0
2
1
2
1
2
1
0
3
2
0
1
3
2
1
0
1
0
1
0
0
2
0
0
2
1
0
2
0
0
0
2
1
0
1
1
0
2
2
1
1
1
2
0
2
2
1
2
2
0
1
1
0
1
0
2
0
0
2
0
0
2
1
0
1
2
2
2
0
2
0
0
0
2
0
1
2
1
2
1
1
0
0
1
1
1
2
2
0
2
1
1
1
1
2
1
0
0
1
2
1
0
1
0
1
2
0
1
1
1
0
1
0
2
1
2
0
1
0
0
0
0
2
0
1
1
1
1
1
0
1
3
2
2
2
1
1
0
0
0
0
1
0
1
1
2
1
2
0
2
1
0
0
1
2
0
2
1
1
1
1
0
2
1
1
0
0
1
1
0
1
0
1
2
1
1
0
1
1
0
1
0
2
1
0
0
1
1
2
2
2
0
0
1
0
1
1
2
2
0
1
0
1
2
0
1
2
0
0
0
1
0
1
2
2
0
1
1
2
1
0
1
0
1
2
0
1
1
2
2
1
0
2
0
2
1
0
0
1
1
0
0
1
1
1
0
0
0
0
4
0
2
1
0
1
1
2
0
0
1
0
0
1
2
1
1
0
0
1
0
1
1
1
2
0
2
1
2
1
0
0
0
1
1
0
0
2
4
1
0
1
0
2
1
1
1
0
2
0
0
0
0
0
0
1
0
1
0
0
3
0
0
2
4
2
0
2
0
1
2
1
1
2
0
1
2
0
0
1
0
0
0
1
3
1
0
1
0
1
0
1
1
2
0
2
2
1
0
1
2
1
2
2
1
0
1
0
1
0
2
0
2
0
1
1
0
0
2
0
2
0
2
4
1
1
2
0
2
1
0
1
1
0
0
1
1
0
1
0
2
1
0
0
0
0
0
2
1
1
1
0
1
1
0
2
0
2
0
1
2
1
2
1
0
1
0
1
0
1
2
0
1
3
2
1
1
0
2
1
1
0
1
0
2
2
1
0
0
1
0
2
1
0
1
0
0
2
1
2
2
3
1
0
1
1
0
1
0
2
1
1
0
0
0
0
0
0
1
3
1
0
1
1
0
2
1
0
0
0
1
2
0
1
0
1
1
1
0
3
0
1
1
1
0
0
2
1
0
1
1
1
0
1
0
0
1
1
0
1
2
0
0
1
0
0
1
1
2
1
2
1
5
2
0
0
1
2
1
0
0
2
0
0
1
0
1
1
0
1
2
0
1
0
0
0
0
0
1
1
1
1
2
1
0
0
0
1
1
1
0
1
2
1
0
0
0
1
2
0
0
1
1
1
0
0
0
2
1
2
0
0
1
0
1
0
0
0
0
1
1
1
2
1
0
0
2
0
0
1
0
1
0
0
0
0
1
0
1
1
1
0
0
2
1
1
2
2
1
0
1
1
2
1
1
2
1
1
1
0
1
1
1
1
0
0
2
2
0
2
1
1
2
2
0
0
1
0
1
1
2
1
2
1
2
0
0
1
0
2
2
0
1
1
2
2
0
1
1
1
0
2
2
1
0
1
2
1
1
2
1
1
1
0
1
1
0
0
1
1
0
1
0
0
1
2
1
2
1
0
1
0
0
1
0
2
1
0
0
2
1
1
1
0
1
1
0
1
1
1
0
0
2
0
0
1
0
1
1
1
1
0
1
1
1
0
0
0
0
2
0
2
0
0
2
0
0
1
3
2
1
1
1
1
1
2
0
1
0
2
0
2
1
2
2
1
0
2
0
1
1
0
0
1
1
0
0
2
1
2
1
0
0
1
0
1
1
0
1
0
2
2
3
2
0
1
0
1
0
1
1
2
0
0
3
1
1
1
0
0
0
0
0
0
2
1
0
0
0
2
1
2
1
2
0
2
2
3
2
0
1
0
1
2
0
0
0
0
1
2
2
1
1
1
0
0
0
0
0
0
1
1
4
2
1
0
0
0
0
1
1
1
0
1
0
1
1
2
0
0
0
2
0
2
0
2
1
0
1
0
0
0
0
0
0
1
2
2
0
2
0
0
0
0
1
2
2
0
2
0
0
2
2
2
0
1
0
1
2
1
2
1
2
2
0
1
0
2
0
0
0
0
1
1
2
1
2
1
2
0
5
0
0
0
0
1
2
2
1
1
0
0
1
2
0
2
1
1
0
0
1
1
1
1
1
1
0
2
1
1
1
2
0
1
0
0
1
0
1
1
2
0
0
1
2
0
0
2
1
0
1
1
0
0
0
0
0
2
1
0
1
1
1
0
2
2
1
2
1
2
2
2
1
2
1
0
1
0
1
0
5
0
0
2
0
1
2
1
2
1
2
0
2
1
0
2
1
2
2
0
1
2
0
1
1
2
1
0
1
1
0
1
2
0
0
0
1
2
0
2
1
2
2
2
0
0
1
0
1
1
1
1
0
1
0
1
1
1
1
1
2
1
1
0
1
1
2
1
1
1
1
2
0
2
1
0
0
0
2
1
0
0
0
1
1
1
2
0
1
2
0
0
1
1
1
0
1
1
0
2
0
0
0
1
1
0
1
0
2
1
2
1
0
2
1
0
2
0
0
0
0
2
0
1
1
0
2
2
1
1
2
2
0
1
2
0
1
0
0
0
1
0
0
1
0
1
0
1
1
0
0
1
1
0
0
0
1
0
0
2
0
2
1
0
1
0
0
0
0
1
1
0
1
2
2
1
0
0
0
1
1
1
2
1
0
2
1
1
0
1
1
1
2
0
3
0
1
0
2
0
0
0
2
0
0
0
0
1
0
2
1
2
1
1
1
1
0
2
2
0
1
1
2
1
2
0
1
1
1
0
0
1
1
1
1
0
0
1
0
1
1
3
2
0
1
2
3
0
0
1
0
0
0
0
0
2
1
1
0
1
1
0
1
0
2
0
1
2
1
1
2
1
2
1
2
0
0
1
0
1
4
1
0
2
2
1
1
2
1
1
0
1
1
2
0
2
0
2
1
0
1
1
0
2
1
0
1
2
0
0
1
1
1
1
0
1
2
2
1
2
1
0
2
0
2
1
0
1
2
1
0
2
1
2
0
3
0
0
1
2
2
0
0
2
2
1
0
1
2
1
0
1
1
0
1
1
1
1
1
2
0
1
2
1
0
2
0
1
1
1
2
1
1
0
0
1
3
2
1
1
1
2
0
2
0
9
0
1
0
1
1
0
0
2
0
2
0
1
0
1
0
1
1
2
3
0
0
1
1
1
2
1
1
1
2
1
1
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
1
2
2
2
0
2
0
0
1
1
1
0
0
2
1
1
1
0
1
2
0
0
1
0
1
2
1
1
0
1
0
2
2
2
1
2
1
1
0
0
1
1
1
1
0
1
0
2
1
1
2
0
0
3
0
1
1
0
0
0
1
0
1
0
0
2
0
1
1
0
1
0
1
1
0
1
0
1
2
0
0
2
1
0
1
0
0
0
1
0
0
1
0
0
1
1
0
1
0
1
2
0
0
1
2
1
0
1
0
1
1
1
1
1
2
0
1
2
1
1
0
2
0
1
1
5
2
0
1
0
1
1
1
0
0
1
2
0
0
0
0
2
0
1
0
0
2
1
1
1
1
0
1
0
0
0
0
0
1
1
0
0
0
2
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
1
1
1
0
2
1
1
0
2
1
0
1
1
2
0
1
2
1
2
0
2
1
0
2
1
1
1
2
1
0
0
1
0
0
0
1
0
1
0
1
1
1
1
2
2
0
1
2
2
0
2
2
1
1
2
1
0
1
0
0
1
0
0
1
0
2
1
2
0
0
0
1
2
0
2
2
1
6
0
1
1
2
1
2
0
0
1
1
0
1
2
1
1
1
1
2
1
0
1
1
1
1
0
0
1
0
0
1
2
0
2
2
0
1
2
0
0
2
2
1
0
0
0
2
0
1
0
0
1
0
2
10
2
1
0
1
0
0
1
2
0
2
1
1
1
1
0
0
1
2
0
0
0
1
0
0
1
1
1
4
1
0
0
0
1
0
0
1
1
2
0
1
0
2
1
0
1
1
0
1
2
2
1
0
1
1
2
0
2
0
0
0
2
0
1
1
0
0
0
1
0
0
2
1
1
0
1
0
1
1
0
2
0
1
1
1
1
0
2
2
0
2
2
2
1
1
0
0
0
0
0
2
0
1
1
2
0
1
2
0
2
0
1
2
2
0
1
0
0
1
2
0
1
1
0
1
0
0
1
1
2
0
0
0
1
0
1
0
2
1
1
1
0
0
0
1
1
1
2
1
0
0
0
0
1
0
2
0
1
0
1
0
1
1
0
2
1
0
0
1
2
0
1
3
2
0
0
0
1
0
1
0
0
0
0
1
0
2
1
0
0
0
2
1
1
2
2
1
2
0
0
1
0
1
1
0
0
0
1
1
1
1
0
1
1
0
0
1
1
2
1
1
2
1
0
0
0
1
1
0
0
1
0
2
0
2
6
2
0
1
2
1
0
0
0
0
0
1
1
1
1
1
0
1
1
0
2
1
1
1
0
0
2
1
0
2
1
0
0
1
0
1
1
0
2
0
2
1
2
0
0
0
2
1
1
1
1
1
0
1
1
2
0
1
2
2
1
1
0
1
1
0
1
0
0
0
0
2
1
0
1
0
0
0
1
2
1
1
1
1
1
1
0
1
2
2
0
1
1
2
0
1
3
0
1
2
2
2
0
0
0
0
1
1
2
0
0
1
2
1
0
0
0
2
1
0
3
2
1
1
2
0
1
0
2
1
1
1
0
0
0
2
0
2
1
2
2
4
1
1
2
1
0
3
2
0
2
0
1
1
0
1
0
0
2
1
0
2
1
1
0
2
2
1
0
1
1
0
2
0
1
0
1
1
0
1
0
2
0
0
0
0
1
0
1
1
0
0
1
0
0
2
0
1
2
3
2
0
3
1
0
0
1
1
2
1
0
1
0
1
1
2
1
0
0
1
2
2
4
0
1
2
1
0
1
1
0
1
2
2
1
2
0
0
1
1
0
0
0
0
0
2
2
1
2
1
1
0
1
0
0
0
1
0
1
1
1
2
0
1
0
2
1
0
2
0
2
2
0
2
0
1
0
1
2
2
0
2
2
1
2
1
1
3
3
2
0
1
1
1
1
0
0
2
8
0
1
1
2
2
1
0
0
0
1
0
1
2
0
1
0
1
1
1
2
1
1
0
1
1
0
1
1
0
1
1
0
2
0
2
1
2
1
1
1
1
0
2
1
0
1
0
0
1
0
2
1
0
0
2
0
1
2
1
0
1
0
1
2
0
1
0
1
1
2
1
0
1
1
0
0
2
0
0
1
0
1
1
1
1
1
1
0
4
2
0
2
2
0
2
0
2
0
1
2
1
2
1
2
2
0
0
0
2
0
0
1
1
0
1
0
2
1
1
1
1
0
1
0
2
2
0
1
2
1
2
0
0
1
2
2
1
1
0
0
0
0
2
1
0
0
1
0
1
0
1
1
1
2
1
0
1
0
0
1
1
1
2
0
1
1
2
0
0
2
1
0
2
1
1
1
1
0
0
1
2
2
1
0
0
0
0
2
2
0
1
2
2
0
2
2
1
0
0
1
1
2
2
1
0
0
1
1
2
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
2
0
2
0
1
2
0
0
0
2
0
0
1
1
1
0
0
2
2
1
0
1
1
0
0
1
1
0
1
1
1
0
1
1
1
0
1
0
1
0
1
0
0
1
0
0
1
0
0
0
2
0
2
1
2
2
1
0
0
0
1
0
2
1
1
0
0
0
1
2
1
1
0
1
2
1
2
2
0
0
0
2
2
2
2
0
1
0
0
2
0
1
0
1
1
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
1
2
0
1
0
1
2
1
2
2
0
1
1
0
0
0
1
0
1
1
1
0
2
0
1
2
2
2
2
1
1
2
1
1
0
0
0
1
1
1
2
0
0
1
1
1
2
2
0
0
1
1
1
1
2
1
1
0
1
0
1
0
0
1
0
0
0
1
0
1
0
1
1
2
0
0
0
0
1
1
1
0
1
0
2
0
2
2
0
0
0
0
0
2
1
0
1
2
1
1
1
1
1
1
0
1
0
0
1
2
0
2
1
1
1
0
1
0
11
0
1
1
1
2
1
0
1
0
0
0
1
1
0
1
1
1
0
1
1
1
0
1
0
1
1
0
2
0
1
0
0
2
0
1
0
1
0
0
2
1
1
0
0
0
0
2
1
0
1
2
0
0
1
1
1
2
0
2
1
1
4
1
2
0
1
1
1
1
2
2
0
1
1
0
1
1
0
1
0
1
0
2
1
0
1
2
0
1
1
2
1
1
2
0
1
1
1
1
0
0
1
1
2
1
2
1
0
0
2
1
1
1
0
1
0
2
1
1
1
1
0
1
1
1
0
1
2
0
0
0
0
1
1
1
2
1
0
0
0
1
1
0
1
1
2
0
1
2
1
0
1
2
2
1
0
0
2
1
0
3
2
0
1
0
0
0
1
2
0
2
1
1
0
2
1
0
2
0
0
1
1
2
0
2
2
0
1
1
0
0
0
1
0
0
1
0
1
2
0
0
1
0
1
2
1
2
0
0
2
0
2
0
0
1
0
0
2
1
0
1
1
3
1
0
2
0
0
1
0
1
1
1
1
0
0
1
2
0
1
0
2
1
0
0
1
0
0
0
1
1
1
0
2
0
1
2
1
0
0
2
1
0
1
0
0
0
2
2
0
2
2
1
0
0
2
1
1
1
0
2
1
0
0
0
1
0
1
2
1
0
2
2
0
0
1
2
0
1
0
0
1
1
1
0
1
1
1
1
1
1
2
1
1
0
1
0
1
0
1
0
0
0
1
1
1
1
0
2
2
1
2
1
0
1
1
1
1
0
0
0
0
0
1
1
0
1
2
0
4
2
1
2
2
0
0
1
1
2
1
0
3
1
0
1
0
1
2
2
1
1
1
1
1
1
0
0
2
0
2
1
1
0
2
1
1
1
2
0
0
0
0
0
2
0
1
2
2
1
1
0
2
0
0
0
0
1
1
0
2
1
0
1
1
2
0
1
0
1
1
1
0
1
0
0
0
0
1
0
1
0
2
1
0
0
0
1
1
0
2
1
0
0
1
0
0
0
1
1
1
0
1
0
1
0
0
2
0
1
0
0
1
1
2
0
2
0
1
0
0
0
1
1
1
1
0
1
1
1
0
1
1
1
2
0
1
1
0
2
0
1
2
1
0
2
0
0
0
1
2
0
1
2
1
2
1
1
1
1
1
1
0
0
2
2
2
1
0
2
3
2
1
1
0
0
0
1
0
1
0
1
3
1
2
2
2
0
1
1
0
2
0
1
2
1
1
1
0
0
1
0
0
0
0
0
2
1
0
2
2
2
2
0
1
1
0
1
0
1
2
0
1
1
1
1
0
2
1
1
1
0
1
0
0
1
0
0
1
0
1
2
0
1
2
2
1
1
1
1
1
0
1
0
1
0
0
1
0
0
0
3
0
0
0
0
1
0
1
0
0
0
3
0
1
1
1
0
2
1
0
0
0
0
0
2
0
1
1
0
3
0
0
0
0
2
0
1
1
2
0
2
1
2
2
2
1
0
2
1
3
2
2
0
1
1
0
0
1
3
0
1
1
2
1
1
0
2
1
0
0
0
1
2
1
0
2
2
2
0
0
1
1
1
3
0
0
0
3
2
1
0
0
2
0
0
2
2
0
1
0
0
2
0
1
2
1
1
1
0
2
0
1
0
0
1
1
1
1
0
1
1
1
1
1
0
1
1
2
1
0
0
0
2
0
1
1
1
2
0
0
0
0
1
2
0
0
0
0
1
2
0
1
1
0
1
1
2
2
1
0
0
1
2
0
2
1
0
3
0
2
0
2
0
1
0
0
1
0
0
0
0
1
0
0
0
1
3
0
0
1
0
0
0
1
2
0
3
0
2
0
1
0
1
0
0
2
6
1
0
1
0
1
1
0
0
1
0
0
2
2
1
2
2
1
1
0
3
0
2
2
1
2
0
1
1
0
0
1
1
1
0
1
1
2
2
0
1
0
1
1
0
1
0
0
0
1
0
2
0
0
1
1
2
0
0
1
0
1
1
0
1
0
1
1
0
0
0
1
0
1
0
0
1
0
2
0
0
2
0
0
1
1
0
1
2
1
1
1
0
1
1
1
1
1
1
1
1
1
1
2
1
1
1
0
1
0
1
1
2
1
0
0
0
3
1
1
0
1
1
1
0
2
0
2
2
2
0
1
1
1
1
1
0
0
0
1
2
2
0
1
0
0
2
1
0
0
1
1
0
0
2
0
0
0
0
1
2
1
0
0
0
0
0
2
0
2
1
0
0
0
1
1
0
1
1
1
0
0
0
1
1
0
2
3
0
2
2
1
1
0
1
2
0
1
1
2
0
2
0
0
1
0
0
1
0
0
0
0
0
1
0
2
3
0
0
1
0
1
0
1
1
0
1
0
2
1
0
1
1
0
1
1
2
1
0
1
1
0
0
0
0
2
0
2
1
0
1
1
1
0
0
0
1
2
0
1
0
0
0
1
1
0
0
1
1
2
2
1
1
0
2
1
1
0
0
1
0
2
1
1
0
1
1
1
0
2
2
1
0
0
0
2
0
1
2
0
1
0
1
2
1
2
1
1
0
0
1
1
0
2
1
0
0
2
0
0
1
0
1
2
5
0
1
1
1
1
0
1
0
0
1
0
0
0
2
0
1
1
0
0
0
2
1
1
1
1
2
0
2
2
2
0
0
2
2
1
2
0
0
1
1
1
1
1
1
1
1
1
2
0
1
1
2
1
0
1
1
2
1
0
2
0
0
2
0
2
0
0
0
3
1
1
1
1
0
2
1
1
1
0
0
1
2
0
2
1
0
3
1
0
0
2
1
0
0
1
0
1
1
1
1
2
1
1
1
0
2
2
0
2
1
1
1
2
1
1
1
0
1
1
2
2
1
1
2
2
2
2
0
1
0
2
0
1
0
0
1
0
1
0
0
0
1
2
0
2
1
0
0
1
2
0
2
0
3
2
1
0
0
2
0
0
0
1
1
1
1
1
1
3
3
2
1
0
2
0
1
0
0
1
2
0
1
2
1
1
0
0
1
0
1
1
1
0
3
0
0
0
0
2
1
1
1
1
1
2
2
2
0
1
0
0
2
1
1
0
1
1
1
2
0
0
0
0
2
1
0
0
5
1
0
0
0
2
0
0
1
1
0
1
1
1
0
1
0
0
2
1
1
1
3
0
0
1
1
0
2
0
0
1
0
1
1
1
0
3
0
0
1
0
2
1
0
1
0
1
1
0
2
2
1
0
1
2
2
0
1
0
1
2
2
1
0
1
1
2
0
2
0
1
0
1
1
2
0
0
1
0
1
0
0
2
1
1
2
1
1
0
1
1
1
0
0
1
0
1
0
0
1
1
2
1
0
1
0
1
1
1
0
2
0
1
0
1
1
1
1
1
1
0
1
0
0
1
3
2
2
1
1
0
0
0
2
2
0
0
0
0
2
0
0
0
1
0
2
0
1
2
1
1
1
0
0
2
0
0
0
0
1
2
0
1
0
1
1
2
0
1
1
1
2
0
2
1
0
0
0
0
0
1
1
0
0
1
2
2
1
2
1
0
2
0
1
1
0
2
0
0
1
2
1
1
1
2
3
1
1
0
0
1
2
2
2
1
2
0
2
2
1
1
2
1
1
0
2
2
1
1
0
1
0
0
1
1
0
1
1
1
1
2
0
1
2
1
1
0
1
1
0
0
1
0
0
2
0
1
1
1
1
1
0
1
1
1
1
1
1
2
1
0
2
1
0
1
2
1
2
1
0
2
1
2
1
1
0
0
0
1
0
2
0
0
0
1
1
1
1
1
1
0
0
1
1
1
1
4
2
2
1
0
0
2
4
0
0
0
2
1
1
1
2
0
0
1
1
1
1
1
0
2
0
1
1
2
0
1
0
0
0
2
0
0
1
2
2
1
0
1
0
0
2
0
0
1
0
0
0
0
0
3
1
1
1
0
0
0
1
2
1
2
2
0
2
1
0
1
2
0
0
2
1
1
1
2
0
0
0
0
1
1
2
0
2
1
0
1
1
0
0
0
0
3
1
0
2
2
0
2
0
0
1
1
0
0
2
1
0
2
1
1
0
0
2
1
1
1
2
0
0
2
1
0
0
1
1
1
2
0
0
0
0
1
0
0
1
0
0
1
0
1
0
2
1
1
2
2
1
1
2
2
2
0
1
1
2
2
2
0
0
0
1
0
1
0
1
2
0
0
0
2
2
1
1
1
2
2
2
0
1
0
0
1
0
0
0
2
1
3
1
0
1
0
1
0
0
1
0
2
1
2
2
2
1
2
1
2
1
2
1
0
1
1
2
1
1
2
1
2
1
1
0
0
1
1
0
0
0
2
2
0
1
0
1
2
2
0
1
2
0
1
2
0
0
0
2
3
1
1
2
1
2
0
1
1
0
2
1
1
0
2
1
1
0
3
0
1
0
0
0
0
0
0
1
0
0
3
0
0
2
1
1
1
0
2
0
0
0
1
0
0
0
1
2
0
1
2
3
1
5
0
1
2
0
1
0
0
1
0
2
0
1
1
1
1
0
1
0
0
0
1
0
2
0
1
0
2
1
1
0
0
2
0
1
2
1
1
1
1
0
1
2
1
0
1
1
0
2
2
2
2
0
0
2
1
0
0
1
2
0
0
2
0
0
1
1
2
1
2
3
1
0
0
0
0
0
1
2
1
1
1
2
0
1
2
2
2
1
1
1
0
0
1
0
0
1
0
0
2
1
0
0
2
1
0
2
0
1
1
2
1
1
2
2
1
0
2
0
1
0
0
0
1
0
1
0
2
1
2
1
0
0
0
1
0
1
1
1
0
2
2
1
1
0
1
0
0
1
0
2
2
0
0
0
1
2
4
1
0
0
0
2
1
0
2
2
1
4
1
1
1
1
1
2
0
2
0
0
2
1
1
1
2
1
2
1
1
1
1
2
1
0
2
1
1
0
1
0
1
1
1
2
0
1
1
0
1
2
2
1
1
2
1
1
1
1
3
2
0
0
0
2
0
1
0
1
0
1
2
1
2
2
1
1
0
1
1
1
0
0
2
0
2
0
2
1
0
2
1
0
1
2
0
1
1
0
0
0
1
3
2
0
2
1
0
0
1
0
2
0
1
1
0
1
2
1
1
0
2
2
1
0
0
0
1
0
2
0
0
1
1
0
1
0
1
1
0
1
0
2
2
0
0
1
1
0
1
1
0
1
0
0
3
1
0
2
2
1
1
0
0
0
2
1
0
0
1
1
2
0
0
2
1
0
1
0
0
0
1
1
2
1
2
0
0
1
2
1
0
0
0
1
1
0
3
1
2
0
0
2
0
1
3
0
1
1
0
1
2
1
1
2
1
1
1
0
1
2
1
1
1
1
1
0
1
2
1
2
0
1
0
1
0
0
0
1
2
0
1
1
0
2
1
2
0
2
3
0
2
1
0
0
0
2
1
0
1
2
1
0
1
1
1
0
1
1
3
1
0
2
0
0
1
0
0
0
1
1
1
1
1
1
1
0
0
1
1
3
1
0
0
1
0
2
0
0
1
2
1
1
1
0
0
1
0
0
1
2
1
2
1
0
2
0
0
2
0
1
2
1
0
1
0
2
1
1
1
1
1
0
2
1
4
1
2
0
1
2
0
2
0
1
2
1
1
1
4
0
1
2
1
0
1
1
2
0
1
0
0
0
0
2
2
0
0
0
2
1
3
1
1
1
0
1
1
0
1
1
1
1
0
1
0
1
1
2
1
2
3
1
1
2
1
1
1
0
0
5
1
0
0
2
0
0
1
0
0
1
1
1
0
2
0
1
1
0
1
0
0
0
2
1
2
3
1
1
1
0
0
1
2
1
2
2
1
2
1
0
2
1
1
0
1
0
1
0
1
2
0
1
1
1
1
0
0
2
1
1
1
1
1
2
2
1
0
1
1
0
1
1
0
0
1
2
1
0
2
1
1
0
1
2
1
2
1
0
0
0
1
0
0
1
1
1
1
1
1
0
1
2
0
0
1
0
2
1
0
2
0
1
2
0
0
0
0
2
2
1
0
1
0
3
2
0
1
1
1
1
1
0
1
1
1
0
2
0
2
1
0
2
0
2
1
0
1
1
0
1
0
1
2
1
1
0
2
1
2
1
0
1
0
0
1
0
0
2
2
2
1
1
0
2
1
0
0
0
0
0
0
1
0
2
2
0
1
1
2
0
1
1
1
2
1
0
1
1
1
0
2
0
0
2
1
6
2
0
1
2
1
2
0
1
0
0
1
1
0
1
1
0
1
0
1
0
0
0
0
0
1
2
0
1
0
0
0
0
1
1
1
2
0
1
1
1
0
0
2
0
1
0
0
0
0
1
0
2
3
0
2
1
2
0
2
2
2
1
0
1
2
0
1
0
1
0
1
0
0
1
1
1
0
0
0
1
1
2
1
2
1
2
1
0
1
2
1
1
2
1
2
1
0
2
2
1
0
1
0
0
0
1
0
1
1
1
1
0
0
1
0
1
1
1
1
2
1
2
1
1
0
1
0
0
1
1
1
0
0
2
0
0
1
0
1
1
0
3
1
0
2
0
2
0
1
1
1
1
1
0
0
0
0
1
0
1
0
0
1
1
0
1
0
0
2
2
1
1
2
1
1
0
1
2
1
1
1
3
2
0
0
2
1
0
2
1
0
0
2
1
2
0
0
2
2
1
0
0
0
0
1
2
1
0
2
1
0
0
2
1
2
3
0
0
1
3
0
1
0
0
0
0
0
2
0
2
2
1
0
2
1
0
1
1
0
1
0
2
2
0
1
1
1
1
1
0
0
0
1
0
2
0
0
0
1
0
1
2
0
1
1
0
0
0
1
1
1
1
0
1
1
0
0
1
0
2
2
1
0
2
0
0
0
1
0
1
2
1
2
2
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
3
0
0
0
1
0
2
1
2
1
0
1
0
0
0
1
1
2
0
1
2
1
0
0
1
1
1
0
0
1
2
1
0
0
0
1
1
1
2
0
1
1
0
1
1
1
0
2
1
2
1
2
0
2
0
1
0
1
1
0
1
1
0
2
2
0
0
1
1
0
2
1
0
0
0
1
1
0
1
2
2
1
1
0
2
3
0
0
1
1
2
2
0
1
0
2
0
2
0
1
0
2
1
0
1
2
1
2
2
1
1
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
3
2
0
0
0
1
0
0
0
0
0
0
2
2
0
1
0
1
2
0
0
1
2
1
0
1
1
2
2
1
0
0
1
1
0
1
0
0
0
0
2
0
3
0
2
0
1
1
2
1
1
0
1
2
1
0
1
0
0
1
0
5
1
1
0
0
1
0
0
1
1
1
0
1
1
2
0
2
1
2
2
0
0
2
0
0
2
1
0
0
1
1
1
0
1
1
0
1
1
0
0
0
1
0
0
1
1
0
0
0
1
2
2
2
2
2
0
0
1
2
1
2
1
0
0
0
0
2
2
0
2
0
0
1
2
3
1
0
1
0
0
1
0
1
1
0
1
1
1
1
1
1
2
3
1
1
0
0
2
1
0
1
1
1
1
3
1
0
1
2
0
1
2
1
0
2
1
1
0
2
2
1
1
0
1
0
0
0
2
2
1
1
0
0
0
1
1
1
0
2
0
1
0
1
0
2
1
0
2
1
0
1
3
2
1
1
1
2
2
1
1
0
1
1
1
2
0
1
1
2
1
2
0
1
1
1
1
0
0
1
1
0
2
2
1
0
2
0
0
0
3
1
1
2
1
1
1
2
2
0
2
0
2
0
1
0
0
1
1
1
0
1
1
0
1
0
1
0
0
1
0
1
2
1
0
1
0
1
1
2
0
1
0
1
0
1
1
2
1
1
0
2
1
1
1
1
0
0
2
0
2
1
1
2
1
3
1
0
1
0
0
1
0
1
2
1
1
0
0
1
0
1
1
1
1
1
1
2
0
2
2
1
1
0
2
0
0
2
1
0
0
2
1
0
1
2
2
1
1
1
0
2
1
1
1
0
0
1
2
0
0
0
1
2
2
2
0
1
0
0
2
1
1
0
2
0
0
1
1
1
1
2
0
2
1
2
1
2
1
0
2
0
0
1
1
0
1
2
0
1
1
2
2
0
2
0
1
0
1
0
1
2
2
1
1
1
1
0
1
2
0
1
1
0
2
1
1
1
1
1
1
2
2
1
0
1
2
1
1
0
1
2
2
0
2
0
1
2
1
1
2
0
0
1
2
1
2
0
0
2
2
1
1
0
1
0
1
1
0
1
2
1
0
2
1
0
1
0
0
1
3
1
1
0
2
0
1
0
1
0
0
0
1
1
1
1
2
1
0
2
0
1
1
1
2
1
0
0
2
1
0
0
1
0
0
3
3
0
0
1
2
0
0
1
2
0
1
0
1
0
1
0
1
1
1
3
1
0
0
0
2
0
0
0
0
2
0
1
0
0
2
1
0
0
1
1
0
1
1
1
2
1
0
0
1
0
1
2
2
4
1
1
1
1
0
1
1
1
1
1
1
0
1
1
2
1
1
2
2
0
0
1
2
2
0
1
1
0
2
0
0
0
0
2
2
0
0
1
1
2
0
1
1
0
1
2
0
2
1
0
1
0
0
2
0
0
2
0
1
0
2
0
1
0
2
2
0
1
1
1
2
1
1
3
1
2
1
0
3
0
0
1
0
1
2
0
1
0
1
1
1
2
1
1
2
1
0
0
1
2
0
1
1
1
2
2
2
0
0
0
1
1
1
1
1
1
1
0
0
1
1
0
1
2
1
1
0
1
0
1
0
0
0
1
0
2
1
0
2
0
1
0
0
1
1
0
1
1
1
1
2
0
1
2
2
0
2
0
0
1
1
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
1
3
1
2
1
1
1
0
2
1
1
0
0
0
1
0
2
0
2
2
2
0
0
1
2
1
1
0
0
2
2
1
0
0
1
1
1
1
0
2
2
2
2
2
1
0
1
1
1
2
0
1
0
0
0
0
1
0
1
0
1
1
1
1
1
0
1
1
2
0
1
0
1
1
0
1
1
0
1
2
0
1
1
2
1
1
1
1
2
0
2
2
2
2
2
2
1
1
1
0
1
0
2
2
2
0
0
0
6
1
2
2
1
0
1
2
1
2
1
0
2
0
0
2
2
1
0
0
2
0
0
1
1
1
0
1
1
2
0
0
1
2
1
2
0
0
2
1
3
1
1
2
0
1
1
2
1
0
2
1
0
1
1
1
0
0
1
1
0
1
0
2
2
1
1
0
2
0
4
1
1
0
0
1
3
1
1
0
1
0
0
1
1
1
0
2
0
1
2
1
2
1
1
0
1
1
1
2
1
3
0
1
2
2
0
1
2
2
0
1
0
1
0
2
1
1
1
0
0
1
2
0
0
0
0
0
1
1
2
0
1
0
1
1
0
2
0
1
1
0
1
1
0
1
2
1
2
1
0
2
1
0
0
2
0
1
1
2
0
1
1
0
2
2
2
0
0
0
1
1
2
0
2
0
2
2
1
0
0
1
1
1
2
0
1
2
1
2
2
1
0
2
2
0
1
0
1
2
1
1
1
0
1
1
1
0
2
1
0
2
0
1
0
1
1
2
1
0
0
0
0
1
1
3
1
1
1
0
0
2
1
1
1
1
1
1
1
0
0
2
3
1
1
0
1
2
0
1
1
0
0
0
2
1
1
2
1
0
2
1
1
2
2
1
0
2
0
1
0
0
1
0
1
2
0
0
1
2
1
0
0
0
1
1
1
1
1
2
1
2
2
1
0
0
1
1
0
0
2
1
0
0
0
1
0
2
1
0
1
0
0
0
1
2
1
2
3
1
2
1
0
1
0
2
1
1
1
0
0
2
0
1
1
0
2
1
1
1
1
2
1
2
0
2
1
0
0
0
2
0
0
1
0
1
1
0
0
1
0
0
2
1
1
1
1
1
0
2
1
0
0
0
1
2
3
2
1
2
1
1
2
2
2
1
0
1
1
2
0
2
1
1
2
1
0
0
1
2
1
0
0
0
0
1
2
0
2
2
2
0
1
0
1
0
1
2
1
0
2
2
2
1
2
0
0
0
1
1
1
1
1
0
1
0
2
0
1
2
2
2
2
1
1
0
2
0
0
1
0
0
2
1
2
1
0
0
1
0
3
1
1
1
0
0
0
1
0
1
1
0
1
0
1
0
1
0
1
2
0
0
0
0
0
0
0
1
0
1
2
1
0
1
1
2
0
1
1
0
1
0
0
0
1
1
1
0
0
1
1
0
1
1
2
2
3
0
1
1
0
1
2
2
0
0
1
0
2
0
0
0
1
2
1
2
1
2
0
0
2
1
0
0
2
0
2
1
1
2
0
1
1
2
1
2
0
0
1
2
2
2
1
1
2
1
1
0
1
1
1
0
1
2
2
2
1
0
2
1
0
2
1
1
1
1
2
1
0
1
1
0
0
2
1
0
0
0
1
1
1
0
1
1
0
0
0
1
1
1
2
0
2
0
1
2
1
1
0
1
2
0
0
0
0
2
1
0
0
0
1
1
1
1
2
0
1
0
0
1
1
1
0
1
0
0
1
2
0
1
1
0
1
2
2
1
0
1
1
0
0
2
1
2
2
0
2
0
0
3
1
1
0
2
1
0
2
0
1
1
1
2
1
1
0
0
1
1
2
0
2
1
0
2
0
0
1
2
1
0
4
0
0
0
0
1
2
1
1
1
1
5
1
1
1
0
0
0
1
1
1
0
2
1
0
0
0
1
0
2
1
0
2
0
1
0
1
1
1
0
1
1
0
1
0
1
2
0
1
2
0
1
1
3
0
0
0
0
1
0
1
2
0
2
0
0
1
2
0
0
3
1
1
2
2
2
1
0
1
1
2
1
1
2
1
0
2
2
1
2
0
1
0
1
0
1
0
1
1
1
2
1
1
0
2
1
0
0
1
0
0
0
1
2
2
2
1
1
0
1
0
0
0
1
0
2
0
3
0
1
0
1
2
1
1
0
0
0
0
0
0
1
1
1
1
1
1
0
1
2
2
0
0
0
0
1
2
1
1
1
2
0
1
1
1
0
3
2
2
0
1
1
2
0
1
1
1
0
2
1
1
0
1
1
0
2
0
0
0
2
1
0
1
2
0
1
1
2
1
0
1
1
1
1
1
4
1
0
0
2
0
0
2
2
1
1
2
1
1
1
0
0
0
1
1
0
1
2
1
0
0
1
0
2
1
0
1
0
2
0
1
0
0
1
1
1
2
1
2
0
0
0
1
0
0
0
1
1
2
0
0
2
0
1
0
0
0
1
1
1
0
0
0
1
1
0
1
3
1
0
0
0
1
0
1
0
0
1
0
2
0
2
1
0
0
0
0
4
0
1
1
2
2
0
0
0
0
2
2
1
0
2
1
0
1
1
1
1
0
0
1
1
2
1
0
2
1
0
0
0
1
1
2
1
1
2
2
0
1
0
2
1
1
2
1
0
0
1
0
1
1
1
2
4
2
1
2
1
2
0
0
1
1
1
2
3
0
0
0
1
1
1
2
0
0
1
1
2
0
1
0
0
1
1
1
0
0
1
0
0
1
0
2
0
1
1
1
1
2
1
1
1
0
1
1
0
0
0
0
2
1
2
1
0
1
0
1
1
2
0
1
2
1
1
2
2
2
0
2
0
0
1
0
2
1
2
0
2
1
2
1
1
1
0
0
2
4
1
0
1
0
0
0
0
1
1
0
0
1
2
1
1
2
1
0
2
3
1
2
1
0
0
1
2
2
2
0
1
0
0
0
1
0
0
2
3
0
1
0
0
0
2
0
1
3
1
2
5
1
2
1
0
0
0
0
1
1
1
2
1
1
1
2
0
2
1
2
1
0
2
1
1
2
1
1
2
1
0
1
1
1
0
0
0
0
1
1
1
1
2
0
2
2
2
1
0
2
2
1
1
1
1
0
1
1
1
1
0
1
0
0
0
2
0
2
1
1
0
1
2
0
2
0
1
1
0
0
2
1
0
0
1
0
0
0
1
1
1
0
0
3
1
1
1
1
0
0
1
2
2
2
1
0
0
1
2
2
1
0
1
1
2
1
2
3
2
0
0
1
2
1
1
1
0
2
3
2
0
2
1
1
1
0
1
2
2
1
0
0
1
1
1
0
0
1
2
0
2
0
0
1
0
1
1
0
1
1
1
0
1
1
0
3
1
1
2
2
0
1
0
0
0
2
1
2
0
1
0
1
0
1
2
0
1
1
1
0
0
1
1
0
1
1
2
0
1
1
1
1
0
0
0
2
0
2
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
1
1
2
1
2
1
0
0
2
0
0
1
0
1
0
1
0
1
0
1
0
2
2
1
1
0
0
1
0
2
0
0
3
0
0
1
1
1
0
0
1
2
2
0
0
2
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
2
1
1
1
1
0
0
2
0
1
2
1
0
0
0
1
1
2
1
0
0
1
0
2
0
2
1
2
2
2
0
0
2
1
1
0
0
0
1
0
1
1
1
0
1
0
0
1
1
2
0
2
0
1
0
2
0
1
0
2
2
1
1
1
0
1
1
1
0
0
0
1
0
2
1
0
2
0
0
0
0
0
1
1
2
1
1
3
0
2
0
1
2
1
1
0
1
1
2
0
1
1
0
0
2
0
0
0
1
0
2
2
2
1
1
1
0
0
1
2
0
1
0
2
2
2
1
1
1
2
1
0
2
1
1
1
1
1
1
1
0
0
2
1
1
0
0
1
1
1
0
0
1
2
0
0
1
0
0
2
1
0
2
1
1
0
2
1
1
0
0
0
1
0
0
1
2
2
1
0
3
1
2
0
1
2
1
2
1
0
2
2
0
2
3
1
2
2
2
2
1
2
1
2
1
1
0
0
1
1
0
0
2
1
2
0
2
1
1
2
2
0
0
1
3
1
2
1
0
0
1
1
2
1
2
2
1
0
0
2
0
3
2
1
2
2
1
1
1
0
1
2
1
1
1
1
2
1
1
0
2
0
0
1
2
0
2
2
0
2
1
0
0
0
2
1
1
0
1
0
1
0
2
2
1
1
1
0
1
0
0
1
1
2
2
1
0
0
1
1
0
0
0
1
2
1
1
2
0
0
0
0
0
1
1
1
1
0
1
1
2
1
2
2
1
1
0
1
1
1
2
2
1
0
0
1
1
0
1
2
1
2
1
0
1
1
2
0
2
0
0
0
1
0
2
1
1
1
0
1
0
1
0
1
1
0
0
2
1
1
2
1
1
1
0
0
1
2
1
1
1
0
2
1
2
0
1
0
0
0
0
0
2
1
0
3
2
1
0
1
0
1
2
0
1
2
2
1
0
0
0
1
1
0
1
0
2
1
1
1
0
1
0
1
2
2
2
2
0
1
0
1
3
1
0
1
1
1
1
1
0
2
1
1
2
0
1
2
0
1
2
0
1
1
2
0
2
0
1
2
3
2
2
1
1
0
1
2
5
2
1
0
0
2
0
0
0
1
1
1
1
2
0
1
1
0
0
1
2
2
1
0
2
1
1
0
0
2
0
1
1
2
2
2
1
1
0
2
0
2
1
1
2
2
5
2
0
2
1
0
0
0
2
2
0
2
3
1
2
1
0
2
1
2
2
0
0
0
1
2
0
0
0
1
1
0
1
1
1
1
1
1
1
1
2
2
0
0
0
1
0
1
1
1
1
1
2
0
0
2
1
0
0
0
1
1
0
0
2
1
2
1
0
1
0
0
0
0
1
0
0
1
0
1
0
0
2
2
1
1
1
0
2
0
1
0
0
0
1
0
1
1
2
1
2
1
0
1
2
2
0
0
0
0
0
1
0
1
1
3
2
1
0
2
1
0
0
2
0
0
0
1
1
4
1
2
0
1
0
0
1
2
0
1
1
1
1
0
1
1
1
4
0
0
1
0
0
1
1
1
1
0
1
1
0
0
2
1
2
0
2
0
1
1
1
1
0
1
2
1
0
1
2
2
0
2
1
1
2
1
1
2
1
1
2
1
0
0
0
2
1
1
0
1
1
2
1
0
0
2
1
2
1
1
2
1
1
2
2
2
0
1
1
0
2
0
2
1
0
1
0
1
0
0
1
1
2
2
1
0
1
2
0
0
0
3
1
2
3
1
0
0
1
0
1
1
2
2
1
0
1
0
1
0
1
1
2
2
2
0
2
0
1
1
0
0
1
1
2
2
0
0
0
1
2
1
0
0
1
0
1
0
2
4
1
0
0
2
1
0
0
1
0
1
0
1
1
0
1
0
0
2
1
1
1
0
0
0
1
0
1
2
0
1
1
0
0
1
2
0
0
0
0
1
0
2
0
1
1
0
1
1
1
0
1
1
0
1
3
2
1
1
1
0
2
2
2
0
0
2
1
0
1
1
2
1
0
1
1
1
1
0
0
0
2
2
0
0
1
0
0
1
1
1
1
0
0
2
1
0
0
1
1
1
1
0
1
2
2
0
2
3
2
0
3
2
0
2
1
1
0
0
0
2
0
1
1
1
0
0
2
1
1
2
0
0
0
0
1
2
1
0
1
0
1
1
1
1
2
2
2
2
0
0
1
0
2
1
0
1
1
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
1
1
3
1
2
0
0
0
2
2
1
2
0
1
2
2
0
4
1
0
1
1
1
0
0
1
0
0
0
1
2
1
3
1
1
0
2
1
1
0
1
0
1
1
1
3
1
1
1
1
1
1
2
1
1
0
0
0
2
2
0
0
1
2
1
0
0
0
0
2
0
0
1
0
1
2
0
2
2
0
0
0
0
2
2
0
0
1
0
0
1
1
0
1
0
1
2
2
0
2
1
2
2
0
1
0
1
0
0
0
1
0
1
0
1
0
0
0
1
0
0
1
0
1
1
1
1
1
2
2
1
2
1
1
1
2
0
0
1
0
1
1
1
0
1
0
0
2
1
1
0
1
0
0
1
0
1
0
0
1
0
0
1
2
0
0
1
0
0
0
0
0
1
2
2
0
1
2
0
2
2
1
1
1
1
0
1
1
2
0
1
2
2
1
0
1
2
2
0
0
0
0
0
0
1
0
1
0
1
2
1
0
1
1
1
0
1
0
0
1
1
1
0
1
1
0
2
0
0
0
0
1
0
2
2
1
0
1
1
1
2
1
0
0
0
2
0
2
1
3
1
2
1
2
0
1
1
2
0
2
0
1
1
0
1
2
1
1
1
2
1
1
1
1
0
0
2
1
0
1
1
0
0
2
0
1
0
1
0
3
2
1
2
2
1
1
1
1
1
1
1
1
0
1
0
0
0
1
1
1
0
0
1
1
0
2
1
0
2
1
1
2
2
1
2
1
2
1
1
2
1
1
0
0
1
1
1
1
2
1
1
2
0
1
2
1
0
1
1
1
1
0
0
0
0
1
2
1
1
2
1
0
1
2
0
2
2
0
1
0
0
1
1
0
1
1
1
2
0
2
1
0
0
0
1
1
1
0
1
1
1
0
0
0
1
1
2
1
1
0
2
1
1
1
2
1
2
0
1
1
2
0
2
0
1
1
1
0
4
1
1
1
1
2
1
2
1
0
2
0
2
0
1
1
3
0
1
1
0
1
1
0
1
0
1
0
1
0
1
2
1
2
1
1
0
1
1
0
2
1
3
2
2
1
1
2
1
0
0
1
2
0
0
0
0
1
0
2
1
1
1
7
1
2
0
2
2
0
1
0
1
1
2
1
0
1
2
0
1
2
2
0
1
2
2
0
2
1
1
1
0
0
1
0
2
1
0
0
0
2
0
2
1
2
0
0
1
2
0
1
1
0
1
1
1
0
0
0
0
1
0
2
1
0
0
0
0
0
1
1
0
1
1
2
1
0
2
0
0
1
0
0
1
0
2
1
0
1
1
2
1
1
0
0
1
1
1
2
0
1
1
0
1
3
0
1
2
1
0
1
2
0
1
1
1
2
0
0
0
2
0
2
0
0
1
0
2
1
2
0
1
1
1
1
1
2
2
0
1
1
1
1
1
0
2
0
1
2
0
0
1
1
1
0
1
1
1
1
2
2
2
0
0
2
1
2
2
1
1
0
0
0
0
1
3
2
0
1
0
0
0
0
0
1
1
2
1
0
0
0
1
1
0
0
0
1
0
2
2
1
0
0
1
1
0
1
0
0
0
1
1
0
1
2
1
0
0
2
1
2
2
0
1
0
1
2
2
0
1
2
2
0
0
1
1
2
0
0
0
0
0
0
2
0
0
1
1
3
2
1
1
0
1
0
0
2
0
1
2
1
2
1
1
0
0
1
1
1
0
1
1
0
0
2
1
1
1
0
0
0
0
3
2
2
1
0
0
0
2
0
0
1
2
0
0
1
1
1
0
1
1
0
1
0
2
0
1
2
1
0
1
0
0
1
1
2
1
1
1
2
0
1
1
1
2
1
2
2
0
0
0
2
0
1
0
2
1
1
1
0
2
2
0
4
2
2
1
2
2
3
1
1
2
0
0
1
1
1
1
1
0
1
1
1
1
0
1
2
0
1
1
1
0
0
0
0
1
2
0
0
1
1
2
1
0
1
0
2
0
2
1
1
1
3
0
1
2
0
1
1
0
2
0
0
0
0
1
0
1
0
2
1
1
1
1
2
1
2
1
0
2
0
2
1
1
1
2
2
0
0
0
2
0
0
1
1
0
2
1
1
1
2
0
1
0
1
1
0
0
2
1
1
0
0
1
2
1
0
1
2
1
0
2
1
1
0
1
2
1
0
1
1
1
2
0
1
1
0
0
1
1
0
1
0
1
1
1
1
2
0
1
0
0
2
0
1
1
2
1
2
0
0
2
1
2
0
1
1
0
1
1
1
0
0
0
1
0
1
2
2
2
0
1
1
2
0
2
0
1
2
0
0
0
1
0
2
0
1
0
1
2
1
0
2
1
4
0
3
2
1
1
0
2
1
3
0
0
0
0
2
1
1
0
1
1
1
1
0
1
0
4
1
0
1
0
0
0
0
2
1
1
1
1
2
0
0
0
0
1
1
2
0
1
0
1
1
0
2
0
1
1
0
2
0
1
1
1
0
0
2
0
1
2
0
0
1
0
0
0
0
2
2
0
1
1
2
1
1
1
1
1
0
3
2
1
1
1
0
2
0
2
2
0
0
1
0
1
1
0
1
0
4
1
1
1
0
1
1
1
0
0
1
1
1
1
2
1
1
1
2
0
1
2
1
1
0
0
0
1
2
1
1
0
2
0
0
1
2
1
2
0
1
0
0
0
0
1
1
1
1
2
0
2
0
2
0
2
1
1
0
0
1
2
0
0
1
1
1
0
1
1
0
0
0
1
0
0
1
0
0
1
0
0
1
1
0
1
0
1
1
0
1
2
1
0
1
0
0
1
0
1
0
1
0
2
1
0
2
2
2
1
0
1
0
0
2
1
2
0
1
1
0
0
0
0
1
1
5
1
1
3
0
1
0
0
0
1
1
0
2
0
1
0
1
0
1
2
1
1
2
1
1
1
0
0
0
1
2
1
2
4
1
0
2
1
0
0
1
2
0
2
1
0
1
0
1
0
1
0
0
0
2
1
1
1
1
1
0
2
2
0
2
0
1
1
0
0
0
0
0
1
0
1
1
1
1
0
2
2
0
2
1
2
1
1
1
0
1
1
1
0
0
2
0
0
1
0
2
1
0
1
1
1
1
1
2
0
2
1
1
2
0
1
1
2
1
1
2
2
1
0
1
1
0
0
2
2
1
1
1
1
0
1
1
1
1
2
2
2
2
1
0
1
1
0
1
1
0
0
1
1
1
0
0
0
0
1
1
0
1
0
2
2
2
1
1
1
0
2
1
1
0
2
0
1
0
1
1
0
1
0
0
2
1
1
2
0
1
0
2
1
0
0
1
1
0
1
2
2
1
1
1
0
1
1
1
2
1
1
0
2
1
1
2
2
2
1
3
1
0
0
0
1
1
1
0
0
0
0
2
1
3
0
2
1
1
1
2
2
2
2
1
1
0
1
0
1
1
1
0
1
2
2
1
1
0
0
0
1
1
2
1
2
0
1
1
0
0
1
0
1
0
1
1
0
0
1
0
0
1
1
1
0
0
1
1
0
2
1
0
1
6
2
1
0
2
3
0
2
2
2
2
0
1
0
2
2
0
1
0
1
1
0
1
0
1
0
0
1
1
0
1
1
0
0
1
1
1
1
2
1
0
2
0
2
1
1
0
0
0
1
1
1
0
2
0
2
3
2
1
1
1
1
0
1
1
0
0
2
1
2
2
0
1
1
0
0
1
0
2
0
2
1
1
1
0
2
1
1
0
1
1
0
0
1
3
1
2
1
0
1
2
2
2
1
2
0
1
0
2
4
2
1
0
0
1
0
0
1
1
2
0
1
1
1
0
2
1
0
2
1
1
0
0
1
2
2
0
2
3
1
0
0
1
1
0
1
1
0
0
0
1
2
2
1
2
2
0
1
2
0
1
2
2
1
2
0
1
1
1
1
1
1
0
0
2
1
1
1
1
2
2
0
0
1
0
1
1
1
2
2
0
0
1
1
1
1
1
2
1
1
1
1
1
2
0
1
0
1
0
0
2
2
0
0
2
0
0
1
0
2
2
1
1
1
1
0
0
0
1
1
1
1
2
0
0
0
0
1
3
0
0
1
0
2
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
1
1
1
0
0
1
1
2
0
2
2
1
0
2
2
1
0
0
0
0
2
0
1
1
0
1
2
0
1
0
1
2
1
0
1
1
1
1
0
0
1
0
1
1
0
0
2
0
0
0
0
2
1
0
2
0
2
0
0
1
1
1
1
1
0
1
1
0
1
2
0
0
2
2
0
0
0
1
1
1
0
0
1
0
2
1
2
0
0
1
2
1
2
0
0
1
1
2
0
1
1
0
0
1
1
0
1
0
1
5
1
1
1
2
1
0
0
1
0
1
0
2
2
2
1
0
0
1
0
2
1
2
0
0
0
1
0
0
0
1
1
2
0
3
1
0
1
1
2
0
0
1
1
2
1
2
0
0
1
0
0
0
0
0
1
1
0
2
1
0
1
2
1
0
0
0
0
0
1
2
1
1
2
1
2
2
2
0
3
1
1
1
0
1
0
0
0
1
0
1
1
1
1
1
1
0
2
0
0
2
1
0
2
0
0
1
1
0
1
1
0
0
2
1
1
1
2
1
0
1
2
0
0
1
1
1
1
2
1
1
1
1
0
0
2
0
1
0
2
1
2
0
1
2
0
0
0
0
0
2
1
0
0
0
0
1
1
1
0
1
0
2
1
0
1
0
1
1
1
0
0
1
2
0
0
2
0
1
2
0
1
0
1
2
1
1
1
0
1
1
0
1
0
2
1
1
2
2
0
1
1
1
1
1
0
1
1
1
0
2
1
1
2
2
1
1
1
0
2
0
2
1
0
1
3
1
2
0
0
1
0
3
0
1
1
1
0
0
2
1
2
0
1
0
1
1
2
2
1
0
1
1
0
0
0
0
1
1
2
1
0
0
0
0
1
2
0
0
0
1
2
0
1
0
2
1
1
1
1
0
1
1
1
1
2
2
0
0
1
1
0
2
0
1
0
1
2
2
1
0
1
1
0
1
0
0
1
1
1
2
1
0
0
1
0
1
2
0
0
1
0
1
2
1
2
1
0
0
1
0
0
0
2
1
2
1
1
1
1
2
0
0
2
1
0
0
2
1
0
0
1
0
2
0
1
3
1
0
3
1
1
0
1
1
1
0
0
0
1
0
0
0
1
1
1
0
0
0
1
1
0
1
0
0
1
0
0
1
2
2
1
1
1
2
2
1
0
1
0
1
1
2
1
1
2
1
0
0
1
0
0
0
1
1
1
2
0
0
1
2
1
1
1
1
2
1
1
0
0
2
1
1
0
1
1
2
2
2
0
2
0
1
1
2
3
0
1
2
0
2
1
0
1
2
0
2
1
1
1
0
1
1
1
0
0
0
0
1
1
1
1
2
0
2
0
0
0
1
1
1
2
1
1
3
0
2
1
1
1
2
0
1
1
0
2
0
0
2
1
2
0
1
0
1
0
1
0
0
1
2
1
1
2
0
1
0
1
1
1
2
2
1
0
0
2
2
3
3
0
0
1
1
0
1
0
1
0
1
0
1
0
0
1
3
1
1
0
0
0
0
2
1
2
0
0
1
2
1
0
1
1
0
0
0
1
0
1
0
0
0
2
1
0
1
0
2
2
2
0
0
1
0
0
1
2
2
0
0
0
0
0
0
1
2
2
1
1
2
0
0
0
1
0
1
3
0
0
1
1
1
1
1
2
1
0
0
1
0
3
0
0
1
0
1
2
3
0
1
0
2
0
2
0
0
2
0
1
2
3
2
0
2
2
2
2
2
1
0
0
2
0
0
0
3
0
0
0
0
1
0
0
1
1
2
2
2
1
1
0
2
0
0
0
0
0
1
0
1
1
0
3
1
0
1
1
2
0
1
1
0
0
1
1
1
0
0
0
2
0
2
2
2
2
1
0
2
0
0
0
0
0
1
0
1
1
1
0
0
1
1
0
2
1
0
0
1
0
1
1
1
1
1
0
1
0
1
7
1
1
1
0
1
0
1
1
0
1
1
1
0
2
0
2
1
0
1
0
0
1
1
0
2
0
0
2
0
2
2
1
1
2
0
0
2
1
1
2
1
0
1
0
0
0
1
2
0
1
0
0
1
0
0
1
1
0
0
1
1
0
1
0
0
2
1
0
0
2
0
1
2
1
0
1
0
1
1
1
0
0
0
1
0
2
2
2
0
1
1
0
0
2
1
0
2
0
2
2
0
1
1
2
0
1
4
0
0
1
0
0
1
1
2
1
1
1
2
0
0
2
0
2
2
0
2
1
2
0
1
1
2
1
1
2
2
1
2
1
1
1
2
1
1
3
1
1
1
2
0
1
0
2
2
1
0
0
0
0
1
1
2
2
1
1
0
0
2
1
1
3
0
0
1
1
0
2
0
0
0
0
2
0
2
1
2
2
1
0
2
1
1
2
2
0
0
1
1
1
2
1
1
0
1
1
1
2
1
1
0
1
0
2
1
0
2
1
0
1
0
1
0
1
1
2
1
0
0
1
0
0
2
0
1
0
1
0
1
1
1
3
0
2
1
1
1
1
1
0
1
1
0
1
1
1
3
0
0
0
2
0
0
1
0
1
0
0
1
0
1
0
1
3
0
0
0
2
2
1
2
0
0
0
0
2
1
1
1
0
0
2
0
0
0
1
1
1
1
0
1
1
1
1
1
1
0
0
1
1
2
0
1
0
0
0
1
0
0
2
1
0
2
0
0
1
0
0
1
0
0
0
1
0
2
2
0
1
0
0
1
1
0
0
0
1
2
1
2
1
2
0
2
2
1
2
2
1
1
1
1
0
0
2
0
1
0
0
0
1
1
1
1
0
0
2
0
2
0
0
0
2
1
1
1
0
0
1
1
2
1
3
1
0
0
2
1
1
1
1
0
2
1
0
2
0
2
1
0
1
0
1
0
0
0
0
0
1
1
1
1
1
0
0
0
2
0
2
2
1
2
0
1
0
0
0
0
3
2
1
1
0
2
1
2
0
1
1
1
1
1
0
2
1
1
0
0
1
0
0
1
2
0
0
2
1
0
0
0
1
2
1
0
0
2
2
0
2
2
1
1
0
2
0
0
0
0
2
2
0
1
1
0
0
1
2
0
2
0
2
0
0
0
1
0
0
1
0
1
0
2
2
0
2
1
1
0
1
1
0
1
1
0
0
1
0
2
2
2
2
1
0
1
2
0
2
2
2
0
1
1
2
1
1
2
1
1
0
1
0
0
1
0
2
0
0
0
1
2
1
1
1
1
2
2
1
0
0
1
2
0
1
1
0
0
0
1
1
3
0
0
1
0
2
1
0
0
0
1
0
0
1
2
0
1
4
2
1
0
1
1
0
2
1
2
2
1
2
2
1
0
0
0
2
0
0
1
1
1
1
0
2
0
1
0
2
0
1
0
0
2
2
2
2
0
2
2
1
0
1
1
2
1
1
1
1
1
2
0
1
0
0
0
0
0
2
1
2
0
0
0
0
0
1
1
1
2
0
1
2
0
1
0
0
0
1
1
1
0
1
0
0
1
1
0
1
1
1
0
1
1
1
2
1
0
2
0
0
1
0
3
1
0
1
2
1
1
1
1
1
1
2
1
1
2
0
1
0
1
1
0
0
1
0
1
0
2
0
2
0
0
0
1
1
1
1
1
1
1
0
1
0
0
0
1
0
1
2
0
1
1
2
0
0
2
1
1
2
1
0
0
0
0
0
1
0
1
2
1
2
0
1
1
2
1
2
1
1
2
0
2
1
1
2
1
2
1
0
1
2
4
1
1
0
1
0
0
2
0
0
1
1
0
1
2
2
1
2
1
1
1
1
2
2
0
1
1
0
0
0
1
1
1
0
0
1
0
0
2
0
7
2
1
0
2
0
1
0
1
2
2
1
1
1
0
0
0
1
0
0
1
0
1
1
2
1
1
1
2
1
1
0
2
0
1
0
0
0
2
0
2
0
0
0
1
0
1
1
0
0
1
2
1
1
1
0
1
1
2
0
0
2
0
0
2
1
0
0
0
2
1
0
0
0
1
0
1
1
1
1
1
2
1
0
1
1
2
2
0
0
2
1
3
1
0
1
1
0
0
0
1
1
1
2
0
1
1
1
1
0
2
0
1
2
1
1
1
2
1
1
0
3
0
0
2
0
0
0
0
1
1
1
0
2
0
0
3
2
1
0
0
0
1
1
2
2
2
1
0
2
1
1
0
0
1
0
1
0
0
0
4
0
1
2
1
1
1
0
1
1
1
0
0
0
1
0
2
1
0
0
1
1
0
2
0
1
2
2
1
2
0
1
2
2
1
1
0
1
1
1
0
0
1
1
0
1
0
1
0
0
2
0
1
0
0
0
1
0
0
1
2
0
1
0
1
0
0
0
2
2
0
0
0
1
1
1
1
1
0
0
1
1
0
1
2
1
1
2
2
1
0
2
2
2
1
1
1
0
0
1
1
1
1
1
1
1
1
0
0
0
0
2
0
2
1
0
1
0
1
2
2
0
1
2
0
1
0
2
1
1
0
0
2
0
1
1
0
0
0
2
1
2
0
0
1
1
2
1
0
1
0
1
1
1
1
1
2
1
1
1
1
0
0
1
1
2
0
1
0
0
0
1
0
2
0
0
1
2
0
0
0
1
1
2
1
1
0
0
1
1
0
1
1
2
2
1
1
1
0
1
3
2
2
0
1
1
1
1
0
0
1
0
0
0
0
2
1
1
0
1
1
4
2
2
1
0
0
1
0
1
0
0
1
1
2
1
1
1
0
1
3
2
0
1
1
1
1
2
0
1
0
1
1
0
1
2
0
2
0
0
1
0
2
2
0
0
0
0
0
1
0
0
1
1
1
1
0
1
2
1
1
1
0
2
1
0
0
1
2
1
2
1
1
2
1
0
0
0
0
0
1
1
2
0
0
0
1
0
1
0
1
0
2
0
0
1
1
1
2
0
1
1
1
0
0
0
4
1
0
1
1
1
1
0
1
2
0
2
2
1
2
2
1
1
1
1
1
2
1
1
0
1
2
2
0
1
0
1
2
1
0
0
1
1
1
1
0
0
2
1
2
0
0
0
1
2
0
1
1
1
0
0
1
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
3
0
0
1
1
2
1
1
0
0
0
0
2
0
1
0
0
2
1
1
2
1
1
0
0
0
1
1
2
2
0
1
0
0
0
2
1
0
1
2
1
1
0
1
1
1
0
1
1
0
1
1
0
0
1
1
0
1
2
2
2
0
0
1
2
1
1
1
0
2
1
2
2
0
1
1
2
0
0
1
2
1
1
1
1
2
0
1
0
2
0
0
0
1
1
2
1
1
1
1
0
2
1
1
2
1
2
2
0
0
1
0
0
0
2
0
0
1
0
1
2
0
0
2
0
1
1
0
1
0
2
1
2
1
1
0
0
1
1
0
0
0
1
2
0
1
1
2
2
2
1
0
1
1
1
1
0
1
0
0
1
0
1
2
1
1
1
1
1
1
1
1
2
1
1
1
1
0
0
2
1
1
2
0
1
2
2
1
2
2
1
0
1
0
1
1
0
1
1
0
1
0
1
0
0
1
2
1
0
0
1
2
2
3
2
0
1
0
2
0
1
0
3
0
1
1
1
1
0
1
2
1
0
0
0
1
2
2
0
2
1
1
0
1
1
1
1
0
0
2
1
1
2
0
1
1
1
1
0
1
0
0
1
1
0
0
1
0
0
0
0
0
1
2
2
1
0
1
1
2
0
1
2
0
2
1
0
2
1
1
1
2
1
2
1
0
1
1
1
0
1
0
0
1
1
0
1
0
1
0
1
2
1
0
2
1
3
0
2
0
0
0
2
1
1
2
0
0
0
2
2
0
0
1
0
2
1
2
2
2
2
1
2
1
0
1
0
0
1
1
1
1
2
2
1
2
2
2
2
1
1
0
1
2
1
1
0
2
1
1
1
3
2
0
0
1
0
0
1
1
0
2
0
0
1
1
2
2
1
0
1
1
1
0
0
1
0
1
0
1
1
2
1
0
0
0
1
1
0
2
1
0
0
1
2
1
2
0
0
0
0
0
1
1
1
1
0
2
1
1
0
0
1
1
0
0
2
1
2
0
0
0
0
2
1
0
1
1
0
2
0
1
1
0
0
4
0
0
2
0
1
0
0
1
1
0
1
0
0
0
2
1
0
4
1
1
0
0
1
2
0
1
1
1
1
0
2
1
1
0
0
0
0
0
0
0
1
1
1
1
3
1
0
0
0
1
1
2
4
0
1
2
1
1
0
0
0
0
0
1
1
0
2
0
2
1
0
1
1
0
0
0
0
2
0
2
2
1
1
2
1
0
2
0
1
1
1
2
2
2
0
1
1
0
1
1
0
1
2
1
2
0
0
1
1
2
2
1
2
0
5
1
0
3
2
0
1
2
0
0
0
0
0
2
1
1
0
1
1
0
0
1
1
1
1
1
0
0
2
0
0
2
1
0
2
0
0
0
1
0
0
1
1
1
1
0
0
2
1
0
2
1
1
0
0
2
1
1
0
0
0
1
0
0
0
1
1
0
0
0
0
1
2
0
1
0
1
0
1
0
0
1
0
0
0
0
2
1
0
1
1
1
0
2
0
0
2
0
0
0
0
1
0
1
2
1
1
0
0
1
2
2
0
0
1
0
0
1
0
1
1
0
1
1
1
1
2
0
1
0
1
0
1
1
1
1
0
0
2
0
2
0
0
1
1
1
2
0
1
2
1
2
2
1
1
1
1
1
0
1
1
1
1
2
0
0
1
0
2
3
2
1
0
0
1
0
2
1
0
1
2
1
1
1
0
1
2
2
2
1
0
2
1
0
0
0
1
2
1
1
1
0
1
2
0
0
0
2
1
1
1
1
1
1
1
1
2
2
0
1
2
0
3
1
1
2
1
1
1
0
2
0
2
0
1
1
1
1
0
2
2
2
1
1
1
0
0
0
1
1
1
1
2
1
0
0
2
2
1
0
2
0
2
1
0
0
1
0
0
1
0
1
2
0
0
1
0
2
1
1
0
2
2
1
0
1
1
2
2
0
0
1
1
1
0
0
1
1
2
1
0
2
0
1
1
2
1
1
2
1
0
3
0
1
1
1
1
0
1
0
0
2
0
2
0
1
1
0
1
1
1
2
2
2
1
0
2
1
3
0
1
2
0
0
1
1
1
1
1
1
0
1
2
1
0
0
3
1
1
1
0
1
1
0
0
2
2
2
1
0
2
0
2
1
3
1
0
1
2
2
1
1
2
1
0
2
1
2
1
0
0
1
1
2
1
1
2
2
2
0
1
2
1
1
0
0
0
2
1
1
1
1
1
2
1
1
1
0
0
0
1
0
4
0
1
0
0
0
2
1
0
1
1
1
1
0
0
0
1
1
0
1
2
1
2
1
0
0
0
1
1
1
1
0
0
0
2
2
0
0
2
0
1
1
1
0
1
1
0
2
0
0
2
1
3
1
1
1
0
0
2
0
0
1
1
1
0
1
0
1
0
1
2
1
1
0
0
1
0
1
1
0
1
0
2
1
0
0
1
0
2
0
0
0
1
1
2
3
0
0
1
2
1
2
2
2
2
1
0
1
1
2
1
2
1
1
2
0
0
1
1
1
1
1
1
1
1
0
1
0
1
0
0
1
0
1
0
1
0
0
1
0
1
0
1
2
0
1
0
1
1
2
1
0
0
2
2
1
2
1
1
2
1
0
0
1
1
2
2
0
2
2
1
2
1
0
3
0
0
0
0
0
2
1
2
0
0
1
1
1
0
1
2
1
2
1
1
1
0
1
0
0
0
1
4
2
1
1
1
1
1
1
0
1
0
1
0
2
1
2
0
1
1
0
1
1
0
0
1
0
2
0
0
1
1
0
2
1
1
0
2
1
0
0
2
2
0
0
1
2
0
1
1
1
1
0
1
1
2
0
1
0
0
2
0
1
0
1
0
2
0
0
0
0
1
0
2
0
2
1
0
1
0
0
1
1
0
2
2
1
1
2
1
0
2
0
0
1
2
1
0
2
0
1
0
1
0
1
1
0
0
0
1
0
0
1
0
0
0
1
1
2
2
0
0
0
0
0
0
2
1
2
1
1
1
0
1
1
2
1
2
0
1
0
1
2
1
2
0
0
2
0
1
1
1
2
1
0
2
3
0
0
1
0
0
1
1
0
0
1
0
3
1
2
0
0
1
1
0
1
0
2
1
2
0
0
2
2
0
0
0
0
1
2
0
2
1
0
0
0
0
1
1
2
0
2
0
0
2
0
1
0
1
3
2
2
2
1
1
2
4
1
2
1
2
2
1
0
1
2
2
1
0
0
1
2
0
2
1
3
1
0
3
2
0
1
1
0
0
1
0
1
1
2
1
1
0
0
1
1
0
2
1
2
2
2
2
1
1
0
3
1
2
1
1
0
1
0
2
0
1
1
1
0
1
0
0
1
0
1
1
0
0
2
1
1
2
1
1
2
0
0
0
1
0
0
2
0
1
1
0
0
1
1
0
0
1
0
0
0
1
0
2
0
1
0
1
0
0
1
1
1
1
1
0
1
1
0
1
2
1
1
0
1
1
0
1
0
1
1
2
1
2
1
2
1
1
0
1
2
1
1
2
0
2
5
1
0
1
2
2
0
1
1
0
0
2
0
2
0
1
0
0
1
1
2
2
1
0
0
0
0
1
1
1
0
1
1
0
0
1
2
3
2
3
2
1
0
2
1
0
2
2
3
1
0
1
2
0
2
2
1
2
1
0
1
1
1
0
0
1
2
0
1
1
0
1
1
1
0
0
1
0
2
0
1
2
1
0
1
0
0
1
0
2
0
1
0
2
1
1
0
0
2
2
2
0
1
2
1
0
1
0
0
2
1
0
0
2
1
1
0
0
2
2
1
0
1
0
0
2
0
0
0
1
0
1
0
0
1
2
2
1
1
1
1
2
1
1
1
1
2
1
1
0
1
0
0
1
1
1
2
1
1
1
0
0
0
2
0
0
1
0
1
0
1
0
1
0
1
1
1
0
2
1
0
0
0
1
0
2
2
1
1
0
2
2
0
1
2
2
1
0
0
1
2
1
2
1
2
0
1
1
1
0
0
2
1
0
1
2
2
2
1
2
2
1
1
2
0
0
0
1
0
3
0
0
0
0
1
1
2
1
0
1
1
1
1
1
2
1
1
4
1
2
2
0
0
0
0
2
0
0
2
2
0
1
0
2
1
1
0
1
0
0
0
1
2
1
0
1
2
1
0
2
1
1
2
0
1
0
0
1
0
1
1
1
0
1
0
0
0
0
2
0
1
0
1
2
1
1
1
1
2
0
0
1
0
0
0
1
1
0
2
2
1
0
1
1
4
1
1
2
1
0
0
1
1
2
1
0
1
2
0
2
1
0
1
2
1
3
1
0
2
1
1
2
1
0
1
2
2
1
0
1
0
1
1
2
1
1
2
0
0
2
1
1
0
1
1
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
2
0
0
0
0
1
0
2
2
0
1
1
0
0
1
2
1
0
1
0
2
1
1
2
0
1
0
0
1
0
0
2
1
1
0
2
1
0
2
2
0
0
2
0
1
3
0
0
1
1
1
1
0
0
0
2
0
1
0
0
0
1
0
2
2
2
0
0
1
2
0
1
0
2
2
1
0
0
1
0
1
0
1
0
1
0
3
0
0
0
2
2
1
0
2
2
2
1
2
1
1
1
1
1
0
2
0
0
1
0
2
0
0
1
0
2
1
2
0
0
0
0
1
0
3
1
2
1
1
0
0
0
0
0
1
1
2
1
1
1
1
0
1
2
1
2
2
1
2
0
1
1
1
1
1
1
0
0
0
0
0
2
0
0
0
0
1
0
0
1
3
1
1
2
0
1
0
1
0
3
1
2
2
1
3
2
0
1
1
2
1
0
1
0
1
1
2
1
0
0
0
1
2
0
0
2
1
0
2
1
0
1
1
0
1
0
1
1
2
0
1
0
0
0
0
1
1
1
0
1
2
2
1
0
0
0
0
0
2
0
1
2
0
1
1
2
1
1
0
0
1
0
0
1
3
0
2
0
0
2
1
2
0
1
1
2
1
1
1
1
0
1
1
0
1
2
0
2
1
1
0
2
2
1
1
2
0
1
1
0
0
0
2
1
0
1
1
0
2
0
0
0
0
2
0
1
0
0
1
0
1
1
0
2
1
2
2
1
1
0
1
0
0
2
2
2
0
0
2
0
1
2
1
1
2
0
2
0
1
1
0
0
1
0
1
0
1
1
1
1
1
0
2
2
2
1
2
1
0
1
0
1
0
1
1
1
1
1
0
0
1
3
0
1
0
0
2
0
1
0
2
1
1
1
2
1
1
1
0
0
1
0
2
1
0
2
1
1
0
1
0
1
0
0
1
2
0
0
0
2
1
0
0
0
2
3
0
1
0
2
2
0
1
2
2
0
1
2
1
0
1
1
2
2
2
0
1
0
1
1
2
2
0
0
2
2
0
1
1
0
0
1
0
1
1
1
2
1
2
1
1
1
0
2
1
0
0
1
0
0
1
1
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
1
1
2
2
2
1
0
0
0
0
0
0
0
2
1
1
0
1
1
2
0
0
3
0
0
1
1
0
1
0
2
1
1
0
1
0
0
1
1
1
0
0
1
1
1
0
2
2
2
2
2
2
0
1
0
2
1
1
0
1
0
1
1
1
0
0
0
0
1
1
2
2
0
0
2
1
1
0
2
0
0
0
1
2
0
1
2
0
1
0
1
2
0
1
0
1
2
2
1
1
2
2
2
1
1
1
0
2
0
1
2
0
0
1
0
0
1
1
1
0
0
1
1
0
2
2
0
1
2
0
1
0
0
0
1
0
1
1
0
2
0
1
1
1
0
1
0
1
0
1
0
1
3
1
0
0
0
2
2
1
1
1
0
2
0
1
1
2
2
0
0
1
2
0
0
0
0
0
2
2
0
1
1
2
1
0
0
1
2
1
2
1
0
0
2
2
1
1
1
0
0
0
0
1
2
1
1
1
1
0
0
1
1
3
0
0
2
1
0
1
0
1
1
0
2
2
2
1
0
1
1
0
0
0
1
1
0
2
2
0
0
2
2
1
2
2
1
1
0
1
4
0
0
1
1
1
1
0
2
1
0
0
0
2
2
1
0
1
0
1
0
0
1
1
1
0
1
0
1
0
1
2
1
1
1
2
2
1
0
2
1
3
0
1
1
2
1
2
2
0
1
0
0
1
0
2
2
0
0
0
0
1
1
2
0
1
1
0
3
2
1
1
2
1
1
1
1
2
0
2
1
0
0
2
1
1
1
2
0
1
1
0
2
1
2
1
0
3
0
0
3
1
1
1
0
1
1
2
0
1
2
0
0
0
1
2
1
0
1
2
1
2
2
1
1
1
2
2
2
0
2
1
1
0
0
2
0
1
0
2
0
2
0
0
2
0
0
0
0
0
1
0
2
0
1
1
1
0
1
1
1
2
0
0
1
1
1
0
0
1
0
1
1
0
0
0
0
0
0
3
1
1
1
0
0
1
1
1
1
0
1
1
1
2
1
0
1
0
1
0
0
1
3
1
1
0
1
1
0
1
0
2
1
2
0
1
1
0
0
2
0
1
0
2
1
3
1
1
1
1
0
2
0
1
0
1
0
0
1
0
1
1
1
0
2
2
2
1
1
0
2
1
0
0
1
2
2
1
1
0
0
2
0
2
1
2
2
0
1
1
1
1
0
1
0
0
4
1
0
0
0
0
1
1
1
0
1
1
1
0
0
2
1
1
2
2
2
1
0
2
1
0
1
0
2
0
2
2
2
1
0
1
0
2
2
2
2
2
0
2
1
1
0
1
0
2
0
1
2
0
1
0
1
1
1
1
1
1
0
1
0
0
0
2
1
1
2
1
0
1
1
2
1
2
2
0
1
1
0
1
0
0
0
0
1
2
1
0
0
1
0
0
1
0
1
1
1
2
1
2
0
0
1
0
2
0
1
0
1
0
1
1
2
0
1
1
1
1
1
1
0
0
0
2
1
1
0
2
1
1
1
0
0
2
1
1
0
2
0
2
1
0
1
2
1
2
1
0
0
0
2
1
0
1
2
1
2
2
1
0
2
1
0
1
0
0
1
1
0
0
0
1
2
0
1
1
0
0
1
2
0
0
1
0
1
1
0
1
0
1
2
1
0
0
1
1
1
0
1
0
0
1
1
0
2
1
0
1
2
0
1
0
1
0
0
1
2
1
1
1
1
2
2
0
0
1
1
0
0
0
0
0
2
1
2
0
1
1
1
1
1
1
0
1
1
2
1
2
1
0
2
0
1
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
1
2
0
0
1
2
1
2
0
2
0
1
1
0
0
0
2
0
1
1
0
1
1
0
1
1
1
2
1
1
0
2
0
0
1
1
2
2
2
3
0
0
2
5
1
0
2
1
1
0
1
1
1
0
2
0
0
1
0
2
0
1
1
0
0
1
1
1
1
0
0
0
1
0
2
0
1
0
1
0
2
0
0
1
1
2
0
0
1
0
1
0
0
1
2
2
2
1
1
2
2
0
0
1
0
2
0
2
1
0
0
1
1
1
0
2
0
1
1
1
0
1
0
1
1
0
0
0
0
1
0
2
1
0
0
2
1
1
1
1
1
1
1
1
0
1
1
2
1
2
0
1
1
1
1
1
0
2
1
0
1
2
2
1
1
0
1
1
0
1
1
1
0
2
1
2
1
1
0
1
0
1
1
1
0
2
2
1
0
2
1
1
2
1
0
1
0
2
1
2
0
0
1
1
1
2
2
0
0
2
1
0
1
2
2
2
2
0
2
1
1
0
2
2
2
1
0
1
1
1
1
0
0
1
0
4
1
2
2
0
2
1
1
0
1
1
0
0
0
1
3
2
0
1
0
0
0
1
1
1
2
0
1
0
2
1
1
1
1
1
1
0
1
0
0
0
0
1
1
2
1
2
1
0
0
0
1
0
0
2
1
2
1
1
1
2
0
2
0
1
1
1
1
1
2
0
0
1
2
1
0
0
0
1
5
1
0
0
2
1
1
1
1
2
1
0
1
4
1
1
2
0
3
0
1
2
1
1
2
1
0
0
0
0
2
0
1
1
0
1
1
0
1
0
1
2
1
1
1
2
0
0
0
0
1
1
1
0
1
0
2
1
1
0
0
0
1
1
1
0
1
1
0
0
1
0
1
1
1
1
1
0
1
0
0
1
0
0
1
0
0
2
0
1
2
0
1
0
1
0
0
1
2
0
1
1
0
0
0
2
0
0
2
1
2
1
2
0
2
2
2
1
2
1
2
2
1
1
1
1
1
1
1
0
2
0
1
0
2
1
1
1
1
1
0
1
0
1
1
2
0
0
0
2
1
0
0
1
0
0
2
2
0
1
1
1
0
0
2
0
1
0
1
1
0
0
1
0
0
2
0
1
1
0
1
0
1
0
0
2
0
1
1
0
1
1
0
1
2
1
0
1
2
0
2
1
1
1
0
0
1
2
1
0
2
0
0
0
0
1
0
1
0
2
1
0
1
1
2
2
0
1
0
0
2
1
1
2
1
1
0
1
1
1
1
1
1
1
0
2
0
1
1
0
0
0
0
1
1
0
1
2
1
1
0
1
1
1
0
0
1
1
0
0
2
0
0
0
1
1
1
2
0
1
1
1
0
2
1
2
0
1
0
1
0
2
1
1
2
0
0
1
2
1
2
1
0
0
0
0
0
0
0
1
0
1
1
1
2
1
0
0
0
0
1
1
1
1
1
1
2
0
0
2
2
1
1
0
1
3
2
1
1
0
1
1
1
1
2
2
1
0
0
0
2
1
1
1
1
0
0
0
1
2
1
0
0
1
1
1
1
0
2
1
1
3
0
1
2
1
1
0
0
2
0
0
1
1
1
1
1
1
1
1
0
0
1
0
0
1
1
1
1
1
0
0
2
0
1
2
1
2
1
2
2
0
1
2
0
2
2
0
1
1
0
1
2
0
1
2
1
2
1
0
1
0
2
1
0
0
0
1
1
1
1
1
0
3
0
3
2
0
0
1
2
1
1
1
1
1
0
1
1
2
1
2
2
1
2
0
2
1
0
1
0
1
0
1
1
0
0
1
1
0
0
1
1
0
2
0
1
0
1
2
1
2
1
1
2
0
0
2
1
1
1
0
1
1
0
1
1
1
0
1
0
2
1
0
0
1
1
1
1
1
0
0
0
0
2
0
1
1
0
0
2
0
0
0
2
0
0
0
0
1
2
0
2
0
0
0
1
1
1
2
3
2
2
0
1
0
0
0
0
1
1
1
2
2
2
0
1
2
1
1
2
0
2
2
0
2
1
1
1
0
1
0
1
2
2
2
1
1
1
1
1
0
0
0
1
0
0
2
0
2
2
1
1
0
0
1
0
2
2
1
1
2
0
0
1
1
2
0
1
0
1
0
2
0
0
1
0
1
2
1
1
1
1
0
0
1
1
0
1
2
1
1
0
1
0
2
2
1
1
2
0
1
0
1
2
1
0
0
1
1
1
2
1
0
1
1
2
2
0
3
0
0
2
2
0
2
0
3
0
0
2
0
0
1
2
0
1
1
1
0
0
0
0
1
0
0
1
0
2
1
1
3
0
0
2
1
0
1
1
2
1
1
0
0
1
1
1
1
2
1
2
0
0
2
2
0
2
0
2
2
0
1
0
1
2
0
1
2
2
0
2
0
1
2
0
2
2
2
1
1
1
1
2
2
0
1
1
1
1
1
0
0
2
1
1
0
1
0
0
1
2
2
2
0
0
1
1
2
1
0
2
0
1
1
2
2
0
1
0
1
2
0
1
0
1
1
1
1
0
0
2
0
1
2
2
1
0
1
0
2
1
1
0
0
0
2
2
1
1
1
0
1
2
2
2
1
1
1
1
1
1
1
1
1
1
2
0
0
0
0
0
1
0
0
0
0
2
1
0
0
1
4
1
1
2
0
1
2
1
0
0
1
2
1
0
0
1
0
0
1
0
0
0
1
1
0
0
0
1
2
2
1
2
1
1
1
0
1
0
1
0
1
1
0
1
1
2
2
1
0
0
0
1
3
0
1
0
1
1
1
2
2
0
1
1
2
3
1
0
0
1
2
2
0
1
1
1
2
1
2
0
1
0
1
1
0
2
2
1
0
2
1
1
1
1
1
2
1
2
1
0
2
1
0
2
1
0
1
2
1
1
1
0
0
0
1
1
1
1
0
1
1
0
2
0
0
1
0
1
0
0
0
1
0
1
1
0
1
2
2
0
0
1
0
1
1
0
0
0
2
2
2
1
1
1
1
0
0
0
1
2
0
0
1
1
1
0
0
1
0
1
0
0
1
1
2
1
0
2
1
2
1
2
0
1
1
3
2
1
2
1
1
2
0
2
2
1
0
0
1
0
1
0
1
0
1
1
1
0
0
1
0
0
0
0
0
0
1
2
2
0
1
1
2
1
1
0
0
1
0
0
0
1
2
0
0
2
0
0
1
0
0
0
0
2
0
1
1
1
0
3
1
1
1
2
2
0
2
1
2
1
1
1
2
0
0
1
0
2
0
1
0
0
0
1
2
1
1
0
1
0
1
0
2
0
0
1
3
1
2
0
0
1
2
1
0
0
0
0
1
0
0
1
1
0
1
1
0
0
1
0
2
1
0
1
0
0
2
0
1
1
1
0
0
2
1
2
1
1
0
0
2
0
1
0
0
1
2
1
2
0
0
0
0
2
1
1
0
0
2
1
2
1
0
0
2
1
0
0
1
0
1
1
0
0
0
1
1
0
1
1
1
0
1
1
2
2
0
0
1
1
1
1
1
1
1
0
2
2
0
1
2
2
0
2
1
2
2
2
0
2
0
0
0
0
0
2
2
0
0
0
0
0
1
1
2
0
1
1
0
2
1
1
1
1
0
2
0
0
0
1
1
0
0
2
2
0
2
1
1
2
0
1
1
0
0
2
1
3
0
0
1
2
2
1
0
1
2
0
0
3
1
0
1
1
0
0
0
0
1
1
0
0
2
0
1
1
2
0
2
0
0
1
1
1
0
1
1
1
0
0
1
1
2
1
2
0
0
1
1
1
0
0
0
2
0
2
0
0
0
1
1
1
2
1
1
2
1
0
1
0
0
1
0
2
2
0
2
0
1
1
0
2
2
0
1
0
1
1
0
1
0
1
1
2
1
0
0
0
1
1
0
1
2
0
1
1
1
1
0
2
2
2
3
1
2
0
0
0
1
1
1
0
1
2
1
0
2
1
0
1
0
1
0
2
2
1
2
2
0
1
4
1
0
0
1
0
1
1
2
1
0
2
1
1
0
2
0
1
0
0
2
2
0
0
0
0
0
1
1
0
0
1
1
1
1
1
0
1
0
0
1
1
1
1
0
1
2
0
1
0
0
0
2
0
1
1
1
0
0
2
0
1
1
0
0
0
1
1
1
1
0
1
1
2
0
2
2
2
1
1
1
1
1
0
0
0
3
0
1
0
2
0
2
2
1
0
1
1
2
0
1
0
2
1
0
0
1
1
0
0
0
0
1
0
0
1
1
2
1
1
2
1
0
0
2
0
0
1
2
1
2
0
1
2
0
1
1
0
1
0
3
0
1
1
1
1
2
3
1
1
1
0
1
0
1
0
0
1
2
1
1
1
0
2
0
2
1
0
0
2
1
0
1
1
0
0
1
1
1
1
0
0
1
2
1
1
1
0
2
3
0
1
0
2
1
0
0
1
1
1
1
2
0
1
0
0
1
1
0
0
1
1
1
0
0
1
2
1
1
1
2
0
0
1
0
3
0
2
0
0
1
1
0
1
2
1
0
1
0
1
2
1
2
0
1
0
1
1
0
1
1
2
1
1
0
0
0
1
1
1
0
0
0
1
0
1
1
0
0
1
0
0
0
1
0
1
1
1
2
0
2
1
0
0
0
0
0
0
1
0
2
0
1
1
1
1
0
1
0
1
1
1
0
1
3
1
1
1
0
0
2
1
2
0
1
0
1
0
2
0
1
0
0
1
1
1
1
1
3
1
2
1
0
2
0
1
1
0
0
0
2
0
2
0
0
1
1
0
1
0
1
0
2
0
0
1
0
0
1
2
1
1
0
0
2
2
2
0
1
1
0
0
2
1
1
0
1
1
2
0
2
1
2
0
0
0
1
0
1
1
1
1
0
1
0
2
2
1
1
1
0
3
2
0
0
0
1
1
0
0
1
0
1
2
1
0
0
1
0
1
2
0
0
1
1
1
0
0
1
1
1
0
1
0
0
1
1
1
1
0
1
1
0
1
1
1
1
1
1
0
0
2
1
2
2
2
0
0
0
1
0
0
0
2
2
0
3
1
0
2
2
2
1
2
2
1
1
1
1
0
2
1
0
1
0
1
0
1
1
0
0
2
0
0
0
2
2
1
2
2
1
1
2
3
2
1
1
1
2
2
1
2
0
2
0
2
0
1
0
2
0
1
2
1
0
3
1
2
0
1
1
1
1
0
1
0
1
2
0
2
1
0
2
0
1
0
2
2
0
2
1
2
2
2
0
1
0
0
0
2
0
1
1
2
1
1
2
2
0
0
0
2
0
0
0
0
1
2
1
2
2
1
2
1
0
1
0
1
3
0
1
0
0
1
1
1
0
1
0
2
2
1
1
1
1
1
0
0
1
1
2
1
2
0
1
1
1
0
0
3
1
0
0
0
2
1
0
2
1
0
0
1
2
1
2
0
0
0
1
0
2
0
1
0
1
2
1
0
1
1
2
1
0
2
0
0
1
2
0
1
0
1
0
1
1
0
1
0
0
1
0
2
1
2
1
0
0
2
2
0
1
1
0
2
1
0
0
0
2
4
0
1
2
0
0
3
0
1
1
0
2
2
0
1
0
1
1
1
1
1
0
1
1
1
2
1
1
2
1
1
0
1
1
0
1
1
0
1
0
0
2
1
2
0
0
1
0
1
1
1
2
0
0
1
2
1
1
1
0
2
2
2
0
0
1
3
1
0
0
0
0
2
0
0
1
0
2
0
0
0
1
0
0
1
4
0
2
1
1
1
0
1
1
0
2
1
0
2
1
1
1
0
1
0
1
0
0
0
1
1
1
0
2
1
0
0
2
2
0
0
0
0
1
1
2
2
0
0
0
0
0
1
0
0
2
0
1
0
1
0
0
0
1
0
0
0
0
1
1
1
0
2
2
0
0
0
0
1
1
2
2
2
2
1
1
1
0
1
1
0
0
2
1
1
0
1
1
1
0
2
2
1
2
1
1
0
0
0
1
1
0
1
0
1
0
0
0
1
2
1
0
1
1
2
0
1
0
0
0
1
2
0
0
0
1
1
1
1
0
0
1
2
1
2
1
1
0
0
0
0
1
1
2
2
1
0
2
1
1
0
2
0
1
1
0
2
0
2
0
0
1
0
2
2
1
0
2
0
0
0
0
1
2
2
1
1
0
1
0
2
2
0
0
0
0
2
0
0
1
0
2
1
2
1
1
0
1
0
1
2
2
1
0
1
1
1
1
1
0
0
0
0
2
0
0
1
2
1
2
2
1
0
2
2
1
1
1
0
1
3
0
0
1
0
2
2
1
0
0
2
1
0
0
0
2
1
0
0
0
1
2
1
0
1
1
1
1
1
0
2
1
1
0
0
1
1
1
0
1
0
1
0
0
1
2
0
1
2
1
0
2
1
1
1
2
0
1
1
2
0
4
1
0
0
0
2
1
0
0
0
1
0
2
1
2
0
0
1
0
2
1
1
1
1
0
0
2
2
1
0
1
1
0
3
0
0
1
1
1
0
0
3
1
1
0
2
0
1
1
1
0
1
1
0
0
1
1
0
2
2
2
0
2
2
1
0
2
0
1
0
1
0
4
0
1
0
1
1
2
2
1
1
0
0
0
1
1
0
2
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
1
1
1
1
0
2
1
1
0
1
1
0
0
1
0
1
2
1
0
2
0
0
0
1
0
0
0
2
0
0
1
1
0
1
0
1
1
0
3
2
2
0
2
0
0
0
0
1
1
1
0
1
2
1
0
0
0
0
2
2
0
1
1
1
0
1
0
1
0
0
2
1
1
2
0
0
1
0
0
2
2
2
1
0
1
0
2
2
1
2
1
2
1
2
0
1
1
2
2
0
2
1
0
0
2
0
0
2
0
0
1
0
2
1
1
1
1
2
2
0
0
1
5
1
2
0
3
1
1
0
1
1
1
1
1
2
1
1
1
1
1
1
0
1
0
1
2
1
0
0
1
0
0
1
1
2
0
2
1
0
2
1
0
2
0
0
1
0
1
0
1
0
1
0
2
1
0
2
1
1
1
2
4
0
1
0
0
0
1
1
0
0
0
2
1
1
0
1
0
0
1
2
1
0
2
1
0
1
1
0
0
0
1
0
0
1
1
1
2
1
0
0
0
2
0
0
0
1
1
1
0
1
2
2
0
1
2
1
1
1
1
0
0
2
0
0
0
0
1
0
0
1
1
1
0
1
1
0
1
1
2
1
0
0
0
2
0
1
0
1
1
1
0
2
1
0
0
2
0
1
1
1
2
1
1
0
2
1
0
1
0
2
1
0
0
1
2
0
2
1
2
1
0
2
2
0
2
1
2
2
1
1
1
2
1
0
1
1
1
0
1
2
0
1
1
1
2
1
0
1
0
2
1
1
0
0
1
1
1
2
1
1
1
1
0
0
0
0
0
2
0
0
1
0
0
2
0
2
1
0
0
1
2
1
1
1
0
1
2
0
1
1
1
0
0
0
0
1
1
1
0
0
1
2
1
0
1
2
0
1
1
1
0
2
0
0
0
2
0
2
0
0
2
1
0
1
1
2
0
0
0
1
1
1
0
1
0
1
1
1
0
1
1
1
1
2
2
0
1
2
0
1
0
0
1
2
1
0
1
1
1
0
2
2
1
1
0
0
0
1
0
2
1
0
1
1
0
1
1
0
0
0
0
0
2
1
0
1
1
0
1
1
0
0
0
0
2
0
0
2
0
1
1
2
2
0
2
1
1
3
0
0
0
1
0
1
1
0
1
1
3
1
0
1
1
1
1
2
1
0
2
0
2
1
1
0
1
1
2
0
0
0
1
1
0
1
2
1
1
1
1
0
0
1
0
2
1
1
1
0
1
1
1
1
0
1
2
1
0
0
0
1
2
1
1
0
1
1
1
0
1
2
0
2
1
2
0
0
1
0
2
1
2
1
0
1
1
0
1
0
2
1
2
1
1
1
0
3
0
0
0
2
1
1
2
0
0
0
0
1
2
0
0
0
1
0
1
0
1
0
1
1
2
2
1
1
1
1
4
2
1
1
1
0
1
2
0
1
1
1
0
1
1
0
1
2
1
1
2
1
2
1
1
0
1
1
1
2
0
0
1
2
0
2
3
0
2
0
2
0
1
0
0
0
1
0
1
1
0
0
0
1
2
0
1
0
0
2
1
2
0
0
1
0
1
1
0
3
2
1
1
0
0
2
2
2
0
1
0
1
0
2
1
2
1
0
1
2
0
1
0
2
2
1
2
0
0
0
0
1
1
0
1
2
1
1
1
1
1
2
0
0
1
1
1
1
0
1
0
0
0
0
1
0
1
1
2
2
0
1
2
1
1
1
0
1
1
0
1
0
1
0
1
0
0
0
0
1
1
1
1
2
1
2
1
2
2
1
1
1
1
1
0
2
2
0
0
1
1
0
1
0
1
1
1
1
1
1
2
2
0
6
0
1
0
2
2
2
1
0
1
1
0
1
0
0
2
0
1
2
1
0
0
1
1
0
1
1
2
0
1
0
1
1
2
0
1
0
1
1
2
2
0
1
1
1
1
2
0
2
1
2
1
2
1
0
0
0
1
1
2
0
2
1
1
0
0
1
0
0
1
0
0
2
0
1
1
2
1
0
1
0
0
0
0
2
0
0
2
0
0
1
0
1
1
2
1
0
1
1
1
1
2
2
1
1
1
2
0
1
1
1
0
1
0
1
1
1
0
0
1
0
0
1
0
1
0
1
1
2
1
1
1
1
0
0
0
0
2
0
1
0
1
1
1
0
0
0
2
1
1
2
0
0
0
0
2
1
0
1
0
2
0
2
1
1
2
0
0
1
0
1
1
1
1
0
0
1
0
0
1
0
0
0
1
2
1
0
2
2
1
1
2
1
0
2
0
1
1
0
2
1
1
0
1
1
1
2
2
2
0
0
2
1
0
1
0
1
1
2
0
0
3
1
0
0
0
2
0
1
1
0
0
0
1
1
0
2
0
0
1
1
0
1
1
0
1
3
1
1
1
1
2
1
0
0
0
1
0
1
0
2
0
0
1
1
1
0
1
1
0
1
2
1
1
1
1
3
1
1
2
1
2
0
1
1
1
2
1
1
1
1
1
0
0
1
1
0
0
2
1
2
1
2
0
0
0
2
0
2
0
2
2
0
1
2
1
3
3
1
1
2
0
0
0
1
0
1
0
2
0
1
2
2
0
1
0
1
0
0
2
1
0
0
1
0
1
1
1
1
0
1
0
1
0
1
0
0
0
0
1
0
1
1
0
1
1
1
1
1
0
1
0
1
1
0
2
2
1
0
2
1
2
0
1
1
1
0
0
0
0
2
1
0
2
1
0
1
1
1
2
0
1
2
0
0
0
1
0
1
0
0
1
2
0
0
0
2
1
1
1
1
0
1
2
2
1
2
1
0
2
2
0
1
1
0
1
0
1
0
0
1
1
1
2
1
0
1
1
0
0
1
0
0
2
0
1
0
3
2
1
0
1
0
1
1
0
1
1
0
1
1
0
1
1
0
2
2
0
0
2
0
0
1
1
0
0
0
1
1
2
1
2
1
1
0
1
1
1
0
0
2
2
0
0
1
0
2
2
2
2
0
0
0
1
1
1
1
0
1
1
0
1
0
0
2
0
1
1
2
0
1
1
1
1
1
1
0
1
0
2
2
1
0
0
0
0
0
1
0
0
0
1
0
1
2
1
0
1
1
0
1
0
1
0
0
1
2
1
0
1
2
1
3
0
1
1
1
1
1
1
1
1
0
2
1
1
0
0
1
0
1
0
1
2
1
0
0
0
0
2
2
1
0
1
1
0
1
2
0
0
2
2
1
0
2
1
1
1
1
2
2
0
0
2
0
0
0
2
0
1
1
2
0
1
1
1
0
2
1
0
2
1
3
1
3
0
0
2
3
1
0
0
1
0
0
2
1
0
1
2
1
2
0
0
1
1
0
1
1
2
1
1
1
1
1
0
0
0
1
1
2
0
2
1
1
1
0
1
1
2
0
2
0
0
1
0
1
1
0
0
1
0
0
1
0
0
2
1
2
2
2
0
0
1
0
1
1
2
2
2
1
0
2
0
2
1
2
0
1
0
0
2
0
2
1
0
1
0
1
0
0
1
0
1
1
0
2
2
1
0
1
1
1
0
2
1
1
0
0
0
1
1
1
1
0
0
1
0
2
2
0
2
1
2
1
2
1
0
0
2
0
2
1
0
3
1
1
1
0
0
1
0
0
0
1
0
1
1
2
1
0
0
0
0
1
0
2
1
1
1
1
2
1
1
1
1
1
1
1
2
1
0
2
1
1
1
0
0
0
1
1
0
0
2
1
1
0
0
1
0
2
0
0
1
0
0
1
0
1
1
0
1
1
2
2
1
1
0
2
0
2
0
0
1
1
1
1
1
1
3
1
2
0
1
2
1
1
2
0
1
2
1
1
3
0
0
1
0
0
1
2
0
0
1
0
1
1
0
0
0
1
0
2
0
0
0
1
1
1
0
2
0
0
1
0
1
0
0
2
1
2
0
0
1
0
2
1
1
1
2
1
0
1
2
0
1
2
1
0
1
1
0
1
1
0
1
2
1
0
0
0
0
1
1
1
2
0
1
0
2
2
0
1
2
0
2
1
0
0
0
1
1
1
2
1
0
2
2
0
1
2
2
0
2
2
0
0
3
2
0
0
1
1
0
0
0
0
1
0
1
1
0
2
4
0
0
0
1
1
1
0
1
1
0
0
0
1
0
1
1
0
2
1
2
0
0
0
1
0
1
1
1
1
0
1
1
0
2
2
1
0
2
0
0
1
1
0
1
0
1
1
1
1
0
1
2
0
2
2
0
0
2
0
1
0
0
1
0
1
3
1
1
2
2
0
1
0
1
2
1
0
1
1
1
0
0
2
0
1
1
0
1
1
2
1
0
1
1
1
1
2
2
1
0
2
0
1
0
2
1
3
1
1
1
2
0
0
0
2
0
0
1
1
1
0
2
0
1
0
1
0
1
1
1
0
2
2
0
1
1
1
1
2
0
0
1
2
0
0
2
1
1
0
2
0
1
1
1
1
0
1
2
0
2
0
0
2
0
2
2
1
2
0
2
2
2
0
1
1
1
0
0
1
0
1
1
0
1
0
1
0
1
4
0
2
0
1
1
0
3
1
0
1
2
1
1
0
1
1
2
3
2
0
0
0
2
2
1
1
3
1
0
1
0
2
0
1
0
0
1
4
2
1
0
0
0
0
2
2
1
1
0
0
1
1
1
0
1
2
2
0
1
0
0
2
0
1
0
0
0
1
1
1
1
1
1
0
1
1
1
1
0
0
0
0
2
2
0
1
0
0
0
0
1
0
2
1
0
1
1
1
1
1
2
1
2
2
0
2
1
0
0
2
3
1
1
0
2
1
0
1
2
0
1
1
0
2
1
2
3
1
0
2
1
1
1
0
1
1
0
1
1
0
0
1
1
0
1
0
1
0
0
0
0
3
0
0
0
0
1
2
1
2
1
1
1
0
1
3
0
0
1
0
1
1
2
0
2
1
0
1
0
2
2
0
2
0
1
1
0
1
0
0
0
0
0
2
2
0
2
1
1
0
0
2
0
2
0
1
0
0
0
2
1
2
0
1
1
0
2
0
0
1
1
1
2
2
1
1
1
0
1
2
1
1
1
1
1
2
2
1
0
1
1
2
2
1
0
0
0
0
2
0
2
1
2
2
1
1
1
3
2
1
1
0
0
1
2
1
1
1
0
0
2
0
0
1
1
1
1
0
1
0
0
1
0
1
0
2
2
1
1
0
1
1
0
0
0
1
0
0
0
0
1
1
1
0
1
1
0
1
1
1
0
1
1
1
0
0
1
2
1
0
1
2
2
0
2
0
0
0
3
0
0
2
2
0
2
1
0
0
0
1
1
2
1
1
1
1
1
0
0
1
1
0
1
1
1
0
1
1
1
0
1
1
1
0
0
1
1
1
2
1
0
2
1
1
2
0
1
2
2
0
2
2
2
0
0
1
2
0
0
1
1
2
2
0
3
1
1
2
0
0
0
1
2
0
0
0
1
1
2
0
2
0
1
1
1
1
1
1
2
1
1
0
1
1
1
1
2
1
1
0
0
1
0
0
1
2
1
1
0
2
2
1
0
3
1
1
2
0
1
0
1
0
1
2
0
0
1
2
0
0
1
1
0
2
2
0
1
0
1
2
0
2
1
2
0
0
1
1
0
2
1
1
1
2
0
0
2
1
0
0
0
2
2
2
1
0
2
2
1
0
1
0
1
1
2
1
0
1
1
1
0
1
0
1
2
1
1
2
1
0
1
0
0
0
1
1
2
1
1
2
1
2
0
1
0
1
2
0
1
0
1
1
1
3
2
1
4
0
0
1
0
1
2
3
2
1
0
2
0
2
2
0
1
1
0
0
1
1
2
2
2
1
1
1
1
0
2
0
2
2
0
0
1
1
0
1
1
1
2
0
0
2
0
0
2
2
0
0
0
1
1
1
0
0
2
0
1
1
2
1
1
0
1
0
0
0
2
1
1
2
0
0
2
1
0
1
0
0
0
1
0
1
0
0
2
0
0
0
2
0
2
1
0
0
2
0
0
0
0
1
1
1
2
1
1
2
1
1
0
1
0
1
1
0
2
0
0
1
2
0
1
2
1
2
0
1
1
1
0
0
8
1
1
0
1
2
0
1
0
0
0
1
2
1
0
2
0
2
1
0
3
1
2
1
0
1
3
2
1
1
2
1
0
0
4
2
1
0
0
2
2
1
0
2
0
0
1
1
0
2
0
2
2
1
3
0
1
1
1
0
0
1
0
2
1
0
1
2
2
1
1
1
1
0
0
2
1
1
2
2
0
1
1
2
1
0
2
0
1
1
1
0
0
0
1
1
1
1
0
0
2
0
3
0
2
0
0
1
2
0
1
1
1
0
0
0
1
1
2
0
1
0
1
0
2
1
1
2
2
0
1
1
1
0
1
1
4
0
0
2
1
0
2
0
1
0
2
1
1
2
0
0
0
1
0
2
0
2
0
1
1
1
1
2
1
2
1
0
2
0
1
0
1
1
2
2
1
1
0
1
2
1
0
1
0
1
1
2
2
2
1
1
0
1
2
0
1
1
0
1
1
1
0
0
0
2
2
2
1
1
0
1
0
1
0
2
0
2
2
1
2
1
2
1
3
0
1
2
1
0
4
1
0
0
1
1
2
2
2
2
2
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
1
1
1
0
1
0
1
1
1
0
1
0
2
1
1
0
0
0
1
0
1
1
0
0
2
1
1
0
1
1
1
2
1
2
1
1
0
1
1
1
1
1
1
0
2
1
2
1
0
1
2
0
1
2
2
3
0
2
1
1
2
1
2
2
1
1
1
2
0
0
1
0
0
1
0
0
2
0
1
1
1
1
1
1
1
0
0
0
0
1
0
1
0
2
0
0
1
1
0
0
0
1
1
2
1
0
0
2
0
1
1
1
2
0
1
0
2
1
2
2
1
1
1
0
1
1
0
1
1
2
0
0
2
1
0
1
0
1
1
0
2
0
2
1
0
1
2
0
1
0
1
2
0
1
1
1
1
0
2
2
1
1
0
0
0
2
1
2
0
0
0
2
1
1
1
1
1
2
0
1
1
2
0
1
1
0
2
2
0
1
1
2
2
0
2
1
1
1
2
1
1
1
2
1
0
1
0
2
0
1
1
1
0
0
0
0
0
0
0
0
2
1
2
1
2
0
1
2
0
0
1
2
1
0
2
0
2
0
0
2
1
1
1
1
2
1
1
2
0
1
1
1
2
1
1
2
1
0
1
1
1
0
2
0
0
1
0
2
2
0
0
0
1
1
0
2
1
0
1
2
2
0
2
0
1
0
2
0
1
1
1
2
1
2
0
0
1
0
0
2
1
0
0
0
1
2
2
2
0
1
1
1
0
1
0
1
0
1
1
0
0
2
1
3
1
0
0
2
2
1
0
1
1
1
0
0
0
2
1
0
1
1
0
0
1
0
0
1
1
14
1
1
1
1
1
2
0
1
0
1
1
1
1
2
1
1
0
1
0
5
0
0
2
2
1
2
0
0
0
1
2
1
2
0
1
1
1
1
1
1
0
0
1
0
1
2
2
2
1
0
1
1
0
0
0
0
2
2
1
0
1
0
1
2
0
2
2
1
1
1
1
0
1
1
2
2
0
1
0
1
1
2
1
1
2
1
2
0
0
0
0
1
0
1
0
1
1
2
1
0
0
0
2
2
1
1
0
0
2
2
1
5
1
2
1
1
2
1
1
1
1
1
0
1
1
1
1
2
2
1
0
2
0
0
1
0
1
2
1
0
1
2
1
0
3
3
1
2
1
2
2
0
2
2
1
2
1
0
0
0
1
1
6
3
0
1
0
0
2
1
0
0
1
1
1
3
2
0
1
0
0
2
2
3
0
1
2
1
2
1
1
1
2
3
2
2
1
0
0
2
1
1
0
5
0
1
0
2
0
0
0
1
0
2
1
0
1
0
1
1
1
0
2
2
0
1
0
1
1
2
2
1
0
1
1
8
2
2
1
1
3
0
0
1
1
1
0
1
0
1
1
0
2
1
0
2
1
2
0
1
0
1
1
1
1
2
0
2
1
0
0
2
1
2
2
0
0
4
2
0
1
0
0
0
2
0
2
0
0
2
0
1
0
0
0
2
0
1
0
0
0
0
0
0
1
1
1
0
0
2
1
1
2
1
1
0
5
0
0
1
0
1
1
0
1
2
0
0
3
0
0
0
1
2
1
0
2
2
0
2
1
0
0
1
1
0
1
2
0
2
0
1
0
0
0
1
1
1
0
0
1
1
1
0
0
2
0
2
0
1
1
1
0
1
1
0
1
2
1
0
0
1
0
1
1
0
0
1
1
0
0
0
0
0
2
1
0
1
1
1
1
0
0
1
1
0
2
2
0
1
2
1
0
1
0
0
1
0
1
1
0
1
0
2
1
0
1
2
1
2
2
0
0
2
1
1
2
2
0
0
1
0
0
1
0
1
0
2
3
2
0
1
2
0
2
0
0
0
0
0
1
1
2
1
0
0
1
1
0
1
0
2
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
1
3
0
1
2
0
1
0
0
0
1
2
1
1
1
1
1
0
0
0
1
2
2
0
2
2
1
0
1
1
1
1
2
4
2
1
0
0
2
1
1
2
1
1
1
1
1
2
1
0
1
0
0
0
1
0
0
1
1
0
2
0
0
1
0
1
1
0
1
1
1
0
2
1
0
1
1
2
0
1
1
2
2
0
1
0
1
0
0
1
1
1
0
0
1
3
1
1
3
2
1
2
1
2
0
1
1
0
0
1
0
1
1
0
1
1
0
2
0
1
1
2
2
0
0
0
2
0
1
1
0
0
1
3
3
0
0
1
2
2
2
1
1
1
0
1
2
1
1
0
2
0
2
0
0
0
2
2
0
2
1
1
1
0
2
1
0
0
2
1
0
1
2
0
1
3
0
0
0
1
2
0
0
3
0
0
0
1
0
0
0
1
0
2
2
2
0
0
1
1
0
1
1
2
0
1
1
1
0
0
2
2
1
1
1
2
1
0
2
0
0
1
1
0
1
1
0
0
0
0
1
1
1
1
1
1
1
1
0
2
2
0
2
0
1
1
2
1
2
0
0
0
1
3
1
1
0
2
1
2
0
0
1
0
1
0
1
2
0
0
1
2
2
0
0
0
0
2
0
2
1
0
0
1
0
2
1
2
1
1
1
1
1
1
1
1
2
0
0
0
1
0
1
2
0
2
0
1
2
1
1
1
1
1
2
1
1
0
1
0
1
2
0
0
1
0
2
1
1
0
0
1
2
1
0
2
2
0
1
1
1
2
1
1
0
0
0
2
1
0
1
1
1
1
0
2
1
0
1
2
2
0
1
1
3
2
0
0
1
0
0
0
2
0
1
0
2
2
2
1
0
1
3
2
1
0
1
1
0
1
0
0
0
1
2
0
1
2
1
1
0
1
2
1
0
0
1
0
1
0
2
1
0
2
0
1
2
0
0
1
1
1
1
1
0
1
1
1
0
0
1
0
0
1
1
1
2
1
2
0
1
1
1
2
0
2
0
1
1
2
0
1
0
1
2
1
1
1
2
0
2
1
0
0
1
0
0
1
2
0
0
0
0
0
1
0
1
0
0
2
2
0
1
1
2
1
0
0
0
0
1
0
1
1
1
2
2
0
0
0
1
0
1
1
2
1
1
1
1
1
2
0
1
1
2
0
0
2
0
0
1
1
1
1
0
1
2
0
0
1
2
1
1
2
2
2
1
1
2
2
1
1
0
1
0
0
0
0
2
1
0
1
2
5
2
0
1
0
0
0
0
0
1
0
1
2
1
1
0
2
2
1
1
0
1
0
1
1
2
1
0
0
1
1
0
0
0
0
2
1
2
1
2
2
2
2
2
1
1
0
1
0
1
1
1
1
1
1
1
0
0
0
0
1
2
1
1
1
1
0
0
1
1
2
0
1
1
1
1
1
1
1
1
1
0
1
0
1
1
0
0
0
2
0
1
2
5
2
1
2
0
2
1
1
0
1
2
0
1
0
0
1
1
1
2
1
1
2
1
1
1
1
0
2
0
1
0
0
1
3
0
0
1
1
1
2
0
1
1
1
1
1
2
2
1
1
0
0
1
0
1
0
0
1
1
1
1
2
1
0
1
1
2
3
1
0
1
1
1
0
1
0
0
0
1
0
0
1
1
2
2
2
0
1
2
1
1
1
2
0
0
0
1
1
1
0
0
0
1
0
0
1
0
0
2
0
0
1
1
1
0
0
0
0
1
0
2
0
2
2
0
0
2
1
1
0
2
1
0
1
2
0
1
2
1
2
2
1
1
0
4
1
0
0
3
1
1
1
1
0
1
0
2
0
0
0
1
1
0
1
0
2
0
1
2
0
0
1
1
0
0
2
1
0
0
0
1
2
2
0
2
0
1
0
1
0
0
1
1
0
0
1
1
1
1
0
0
2
0
2
1
0
1
0
1
0
1
1
0
0
0
0
1
1
1
1
1
0
0
2
1
0
1
2
1
1
1
1
2
0
1
1
0
1
0
1
1
1
2
2
0
2
0
0
0
1
1
1
0
2
1
1
1
1
0
0
1
0
0
2
0
2
1
1
2
0
0
2
0
1
0
0
1
0
1
0
0
0
1
0
2
2
1
0
2
1
1
0
1
0
1
2
1
0
0
2
1
0
2
2
0
0
0
1
1
1
2
1
0
0
0
2
1
0
1
1
1
0
1
3
0
2
0
0
0
0
0
1
0
2
1
0
0
0
0
0
1
2
2
0
1
4
1
1
2
1
0
2
0
1
1
1
0
1
2
0
0
2
2
2
0
2
1
1
1
1
1
0
1
1
0
0
2
1
1
1
1
2
0
1
0
1
0
2
1
2
0
0
1
2
2
1
1
0
1
1
1
1
1
1
2
1
1
1
1
0
0
2
1
1
1
1
0
2
0
1
0
1
1
2
1
0
0
0
0
0
1
1
1
0
0
2
2
2
0
0
1
0
0
1
1
3
2
1
2
2
1
1
1
2
1
1
2
1
2
0
1
2
2
1
1
1
1
1
1
2
2
0
0
1
0
1
1
1
1
2
0
0
0
3
0
0
1
0
0
2
1
0
2
2
2
1
2
2
2
0
0
2
1
0
1
0
0
0
0
2
2
1
0
1
2
1
1
1
1
0
0
0
0
0
0
0
0
0
0
2
0
1
1
1
1
0
0
2
1
0
1
1
2
0
0
0
1
1
0
1
0
0
0
0
1
2
2
1
1
1
0
2
0
2
1
0
1
0
0
1
2
1
1
0
1
1
0
0
2
0
0
0
1
0
1
0
2
0
0
0
1
0
1
2
1
0
1
1
1
0
1
0
0
2
0
0
2
1
2
2
0
1
1
1
1
0
1
0
0
2
2
1
1
1
2
0
1
1
1
2
0
0
1
2
1
0
1
0
1
0
2
2
1
2
0
2
2
0
0
0
2
1
1
0
1
0
2
1
0
2
1
1
1
0
0
1
1
1
0
0
2
1
0
2
0
1
1
2
1
2
1
0
0
1
2
1
1
2
1
1
0
0
2
0
2
0
0
0
1
1
0
1
2
2
2
0
0
1
1
1
0
2
1
0
0
1
2
0
1
1
2
1
1
2
2
2
2
0
3
1
1
2
0
2
2
0
1
1
2
1
3
0
0
3
1
2
0
2
0
1
1
1
1
1
2
2
0
1
1
1
1
0
1
0
0
1
2
1
1
1
0
1
1
1
1
0
0
1
2
0
0
1
2
0
1
1
2
2
0
1
2
0
0
2
1
1
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
2
1
1
1
1
2
2
0
1
0
0
2
1
1
0
0
1
0
0
2
2
2
2
0
1
0
1
1
1
1
2
2
1
0
0
1
0
2
1
1
0
1
2
1
1
2
1
1
0
1
2
0
2
0
0
1
1
1
0
1
1
1
0
0
0
1
0
2
1
0
1
1
2
0
1
1
2
1
0
0
0
2
2
1
2
0
1
2
1
0
2
0
2
2
1
0
0
0
1
1
0
0
2
1
1
2
2
3
1
2
1
0
1
1
1
2
0
0
0
0
1
2
2
1
0
1
1
1
1
2
1
1
1
1
1
0
0
1
1
0
2
0
1
1
0
1
0
1
2
0
0
0
2
1
1
2
0
1
0
0
2
2
1
0
1
0
2
1
1
0
1
1
0
0
0
2
1
0
0
2
1
0
0
1
1
0
1
0
0
2
1
1
2
1
0
0
1
1
1
1
1
2
1
2
1
0
1
1
1
2
1
1
0
1
0
0
1
2
0
1
0
1
1
1
0
2
1
2
0
1
0
1
0
2
2
0
0
1
0
0
0
1
0
0
2
1
2
1
2
1
1
2
0
1
1
2
0
0
0
2
1
1
2
1
0
1
1
1
2
1
0
1
2
0
1
1
2
0
1
1
1
1
0
0
2
0
1
1
1
0
2
0
2
0
0
1
0
1
1
1
4
1
2
1
2
1
0
1
2
1
1
0
1
0
2
0
0
1
3
2
0
1
0
2
0
0
1
1
1
0
0
0
1
0
1
0
1
1
1
1
1
2
1
2
1
1
3
2
0
1
0
1
0
0
1
2
1
1
0
4
0
3
1
2
0
1
0
0
0
1
1
0
0
2
2
1
1
1
0
0
1
2
0
0
1
1
1
2
1
1
1
1
2
2
2
0
1
1
1
0
0
0
2
1
1
1
0
0
0
0
0
1
0
2
1
0
2
1
0
0
0
2
1
0
1
2
0
0
0
0
0
1
1
0
1
0
0
0
2
2
0
1
0
2
1
1
1
2
0
2
1
2
1
1
2
2
0
2
1
1
0
1
0
0
0
0
0
1
2
1
1
0
0
0
0
0
1
2
10
2
1
0
2
0
1
0
1
0
2
1
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
8
0
1
1
0
0
0
2
0
0
1
1
0
1
0
0
1
2
3
0
1
0
1
0
0
2
0
1
0
0
2
0
0
2
0
1
0
1
1
2
1
3
1
0
1
0
1
0
0
2
2
0
1
2
1
1
1
2
1
1
1
0
2
1
0
0
0
0
2
0
2
0
2
2
1
2
2
0
1
0
0
1
1
2
1
1
1
1
1
0
2
0
0
0
2
1
0
1
1
0
2
0
0
2
0
2
1
0
2
0
1
2
1
1
2
0
0
0
2
2
0
2
0
1
0
1
2
2
0
0
1
0
5
1
1
1
2
1
0
0
1
0
0
1
0
2
0
0
2
1
1
0
0
2
1
0
2
0
0
2
0
0
0
0
0
0
3
2
0
0
1
0
0
0
2
0
0
1
0
2
1
0
0
2
1
0
1
0
0
1
2
2
1
0
0
2
2
2
1
0
2
3
0
1
0
2
2
0
1
1
0
0
1
2
0
0
1
3
1
2
1
2
1
1
1
1
0
1
2
1
1
0
1
0
0
0
2
1
0
1
1
1
0
0
1
1
0
2
2
2
1
2
2
1
1
0
2
1
1
1
2
1
0
0
1
1
0
1
3
0
2
0
0
1
2
1
2
1
1
2
1
2
0
1
1
1
1
2
1
1
1
0
2
0
3
0
1
0
2
0
0
2
1
1
1
1
1
1
0
1
1
0
1
0
3
1
1
1
1
1
1
0
1
0
0
1
0
0
2
0
1
0
1
6
0
1
2
0
1
1
1
1
2
0
0
2
2
1
1
0
1
0
0
0
1
0
1
1
1
0
2
1
0
2
0
1
0
0
0
0
1
1
1
0
2
2
1
1
1
2
0
2
0
1
1
2
1
0
1
1
0
1
0
0
0
1
1
1
0
1
1
1
0
0
1
0
1
0
1
0
1
0
2
0
2
1
0
2
2
1
1
0
1
1
0
1
1
1
0
0
0
2
1
1
2
1
1
0
0
0
1
2
0
1
0
1
0
1
1
1
2
0
0
0
1
2
1
1
1
2
0
2
1
0
1
1
1
1
1
1
1
2
2
2
1
2
2
0
1
1
0
0
1
1
1
0
1
2
0
0
1
0
1
1
1
2
1
0
1
1
1
2
0
2
0
2
0
2
0
0
1
0
2
2
0
1
0
1
1
4
1
0
0
2
1
1
0
0
0
0
0
1
1
0
1
1
0
0
1
1
1
1
1
2
2
0
2
0
1
1
0
0
0
2
2
2
3
2
0
1
1
2
1
1
1
2
0
2
1
1
1
0
1
2
3
0
0
3
3
1
2
2
2
1
2
0
1
1
1
2
0
2
0
0
1
1
0
2
1
1
0
1
1
1
1
1
1
0
1
2
2
0
1
1
2
0
1
0
0
0
1
0
0
0
1
1
1
1
1
0
1
0
0
2
1
2
0
2
1
2
0
0
0
1
1
1
1
1
1
0
1
1
0
1
2
2
2
2
1
3
0
1
1
2
0
2
2
2
1
1
1
1
2
1
1
1
0
1
1
0
0
0
1
0
1
1
1
1
2
0
2
2
1
0
2
0
2
2
0
0
1
2
1
0
1
1
0
1
1
0
1
2
2
0
0
2
1
1
0
0
2
0
0
0
0
0
1
0
1
1
0
1
0
1
2
0
0
1
2
2
2
2
0
0
1
2
1
0
2
1
2
2
1
2
2
0
1
2
1
1
1
0
0
2
1
0
1
2
1
1
1
1
0
0
0
1
0
1
2
1
1
1
1
0
0
1
1
1
2
0
2
0
0
1
1
2
2
0
0
2
1
1
0
0
1
1
1
1
0
1
0
0
0
0
0
0
1
1
1
1
1
0
0
1
1
1
1
0
1
2
1
2
0
0
2
2
1
1
1
1
0
1
0
1
0
2
0
2
1
0
0
1
0
1
2
2
1
1
3
0
0
1
0
1
2
0
1
1
2
1
0
1
1
1
0
1
0
0
0
1
0
1
1
1
0
0
1
1
2
1
2
0
0
0
0
0
0
0
1
0
2
2
1
1
1
1
1
0
1
2
1
2
0
2
0
0
2
0
1
1
2
1
1
0
0
0
1
0
2
1
0
0
0
2
1
0
1
0
1
1
0
1
0
0
2
1
1
1
1
0
1
1
0
1
1
0
1
2
2
1
0
1
2
0
0
1
1
0
1
2
2
1
1
0
1
0
0
1
1
1
2
1
1
1
1
0
1
1
1
0
0
0
0
0
0
0
0
2
1
1
1
0
0
0
0
1
0
1
2
1
2
2
0
3
1
0
1
1
0
1
0
1
0
0
0
0
2
1
2
2
1
1
1
1
1
1
0
1
0
0
1
0
1
1
1
1
2
1
1
0
1
1
1
1
3
2
1
1
1
1
0
0
1
2
1
1
2
2
1
1
1
0
2
1
1
1
0
0
0
0
0
0
2
1
1
0
0
0
0
0
1
2
0
1
1
0
1
0
0
0
2
2
0
1
0
1
1
1
2
2
0
2
3
1
1
0
0
1
0
1
0
1
1
0
1
1
1
1
1
1
1
0
1
1
1
0
0
1
1
1
1
1
1
1
2
1
2
0
2
1
1
1
0
1
2
1
0
0
2
0
0
0
0
4
1
1
0
2
0
0
2
0
0
0
1
0
0
1
1
0
1
2
0
0
0
1
1
2
2
1
0
0
2
2
0
1
0
2
0
0
1
1
0
0
0
0
0
2
1
2
1
0
0
1
1
1
1
1
1
0
1
2
1
1
0
1
1
2
0
2
1
2
1
1
0
0
1
1
2
4
3
2
1
1
1
0
0
1
1
2
0
1
2
0
1
1
0
0
0
2
0
2
1
0
0
0
1
0
2
2
1
2
0
0
2
1
0
2
1
0
0
1
2
1
2
2
1
0
0
2
1
1
0
0
0
0
0
1
0
0
0
3
1
0
1
0
1
0
1
1
0
0
2
1
2
0
0
0
2
2
1
1
2
1
0
0
1
0
0
1
1
2
1
1
1
1
0
0
2
1
0
2
0
9
1
0
2
0
2
1
1
1
1
1
1
1
2
0
0
0
2
0
1
1
1
0
1
1
0
1
1
2
2
1
1
1
0
1
1
3
1
0
3
2
1
0
1
0
1
1
1
0
1
0
3
1
0
2
0
0
0
1
0
2
0
1
0
1
1
2
0
0
2
1
1
0
0
2
1
0
1
0
0
0
1
0
2
0
1
2
0
0
1
0
0
2
0
0
1
1
0
0
1
0
2
0
1
2
0
1
1
2
0
1
1
1
0
1
0
2
1
0
0
1
1
2
1
2
0
2
0
0
2
1
1
1
2
1
0
2
2
0
0
1
0
0
1
0
1
1
0
1
0
1
0
2
2
1
0
2
1
1
1
2
0
1
0
1
0
2
1
1
2
2
0
1
1
1
1
2
0
2
1
0
1
0
1
3
0
2
1
2
0
2
1
1
0
0
1
1
1
1
1
0
1
1
1
2
1
0
2
1
0
1
0
1
0
1
0
1
2
0
0
0
2
2
0
0
2
1
1
1
2
1
0
0
1
1
1
2
1
0
1
3
0
2
0
0
2
0
1
2
1
0
0
0
2
0
1
1
0
0
5
0
1
1
0
1
1
1
1
2
0
1
0
0
0
2
0
2
0
2
2
2
0
0
0
1
2
2
2
0
1
1
2
1
1
0
1
0
0
1
2
0
1
1
0
0
0
1
1
1
1
2
0
0
1
1
1
1
1
2
1
1
2
0
0
0
0
1
1
0
1
2
1
0
0
2
1
2
1
0
0
1
0
0
1
1
1
2
1
0
1
1
1
2
2
1
2
1
2
1
1
0
0
2
1
2
1
1
1
1
1
0
1
2
1
2
0
1
1
2
1
1
1
0
0
0
2
0
1
2
3
1
0
2
0
0
1
3
1
1
1
1
1
2
2
1
0
0
1
1
0
1
1
1
2
0
1
1
1
0
3
1
1
0
1
1
1
2
0
0
0
2
0
2
1
0
0
0
1
0
0
1
0
0
1
1
2
0
1
2
1
1
1
1
0
1
1
2
0
0
1
2
0
1
0
0
0
1
2
1
1
0
1
0
1
0
0
2
1
2
2
1
1
0
0
1
1
0
1
2
1
1
0
2
2
1
1
1
0
1
2
1
1
1
2
0
0
2
1
0
1
0
0
0
1
2
0
1
1
2
2
1
2
1
0
0
0
0
3
2
1
0
2
1
0
2
1
1
2
1
2
0
0
1
1
0
1
1
2
0
1
1
1
3
1
0
0
1
1
0
1
0
1
1
1
0
0
2
2
0
0
0
3
1
1
1
2
1
1
0
0
2
1
1
1
2
0
1
1
3
2
1
1
1
0
1
1
1
1
2
0
1
1
0
1
2
1
1
2
1
1
0
2
1
0
0
0
1
1
1
1
1
0
0
1
1
1
1
1
2
1
0
2
2
0
0
0
1
2
1
2
2
2
3
0
0
4
2
1
0
1
0
1
0
2
0
0
1
1
0
1
1
0
1
1
0
1
0
1
1
2
1
0
1
0
0
2
2
1
1
1
1
1
0
0
1
1
0
1
0
1
1
0
2
2
1
1
0
1
1
0
2
0
1
1
1
0
1
1
1
2
2
1
1
0
0
1
1
2
0
1
2
1
0
0
1
0
0
1
0
0
1
0
0
0
2
1
1
3
1
1
2
0
0
2
2
0
1
1
0
0
1
0
0
0
0
0
0
1
1
2
0
0
1
2
0
2
0
0
1
1
0
1
0
3
2
0
1
0
1
2
1
0
2
1
1
1
1
2
0
0
0
0
1
1
0
0
0
1
1
2
2
2
1
1
2
1
1
1
0
0
1
1
0
2
1
0
0
1
1
1
0
3
0
1
1
1
0
0
2
0
0
0
1
0
1
0
0
1
0
0
0
2
1
1
1
0
1
0
1
2
2
3
2
0
1
2
2
1
0
1
2
1
1
1
0
0
0
1
0
2
1
1
0
1
0
2
2
0
1
0
1
0
2
0
0
0
1
0
2
2
1
1
0
0
0
0
0
2
0
0
0
1
1
2
2
2
1
1
0
1
0
2
1
1
1
1
0
2
1
0
0
0
1
0
2
1
0
1
2
1
0
1
1
1
0
0
1
2
0
1
0
1
2
0
0
0
1
0
2
2
2
1
0
1
1
1
1
1
0
1
0
3
0
1
1
1
0
0
1
2
1
0
0
1
1
1
1
0
2
0
0
0
0
1
0
2
2
1
0
1
0
0
0
0
1
1
1
2
2
1
1
0
1
1
2
1
0
1
0
2
2
1
0
2
0
0
2
0
1
0
0
1
2
0
1
0
1
0
1
1
2
1
1
0
0
1
0
1
1
2
2
0
0
1
0
1
0
2
1
1
1
1
2
2
0
2
2
0
1
0
1
1
0
1
0
2
1
2
0
0
2
0
0
0
0
2
0
3
0
1
1
2
1
1
1
0
1
1
1
1
1
0
0
2
0
1
2
2
1
3
1
2
1
0
0
1
1
2
0
0
1
1
1
1
1
2
0
2
1
2
0
1
0
1
0
2
2
0
0
0
0
2
0
2
0
1
0
1
0
0
0
2
1
0
1
0
0
3
0
0
1
0
0
1
0
1
0
0
2
0
2
1
1
1
1
2
1
0
1
1
2
0
1
1
2
3
2
0
0
1
0
1
0
0
0
1
0
2
1
0
2
2
1
2
1
2
1
3
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
1
1
1
1
0
1
0
1
0
1
1
0
1
0
2
1
0
0
2
1
2
0
0
1
0
2
1
1
0
0
1
0
0
0
2
0
1
0
1
1
2
0
1
2
0
0
2
0
1
2
0
1
0
4
1
2
1
1
1
1
0
0
1
2
0
1
1
2
0
1
1
1
0
0
2
0
1
1
0
1
1
0
2
0
2
2
1
1
1
2
2
2
0
0
1
1
1
1
0
0
0
0
2
1
0
1
1
0
1
1
2
2
1
2
0
2
1
1
0
0
1
2
2
1
0
0
1
0
0
0
0
0
2
1
0
1
0
1
1
2
1
0
1
2
2
2
0
2
1
1
0
0
0
0
2
1
1
2
1
1
0
0
1
2
0
0
0
1
1
2
2
1
2
2
1
0
0
1
1
1
0
0
0
0
2
0
1
2
1
1
0
3
0
0
2
2
0
0
0
0
0
2
1
0
2
0
0
0
1
1
0
0
1
0
0
2
0
1
0
0
1
1
0
0
1
1
1
1
1
0
1
2
1
0
1
2
1
1
0
2
0
1
0
1
1
1
0
1
2
1
2
2
0
1
2
0
0
1
0
1
0
0
1
0
1
1
0
1
0
0
1
3
0
0
2
1
2
0
1
0
2
0
0
0
1
0
2
1
1
0
0
2
2
0
1
2
2
0
1
1
1
0
2
0
0
0
2
1
0
2
0
1
2
1
1
1
2
1
0
1
1
1
0
2
1
0
1
1
0
0
0
0
0
1
0
1
1
0
2
1
1
0
0
1
4
1
0
0
0
3
0
1
2
0
1
0
1
1
2
1
2
0
2
1
1
1
1
0
0
0
2
0
2
0
0
0
1
1
1
1
0
1
1
1
1
1
1
1
0
0
2
1
0
3
0
2
1
1
1
0
0
1
0
2
1
2
0
0
1
0
1
1
0
2
1
0
1
2
0
0
3
1
2
0
2
0
1
1
2
1
0
0
1
1
1
1
2
1
2
2
1
0
1
1
1
1
2
2
2
1
0
0
2
0
2
1
2
0
0
1
0
1
1
0
0
0
0
2
0
2
1
0
1
0
2
2
0
0
0
1
0
1
1
0
4
0
0
2
1
1
0
1
0
0
0
0
2
1
1
2
1
0
2
1
1
2
4
1
1
0
0
2
1
3
0
1
0
1
1
1
2
1
0
2
1
1
1
1
0
1
1
1
1
2
0
2
1
0
1
1
0
0
1
1
1
0
2
0
1
1
1
2
0
0
1
0
2
0
2
2
1
0
1
1
2
0
1
1
0
0
1
2
2
1
1
1
0
0
1
1
0
0
0
2
1
2
0
1
2
1
1
1
0
0
2
2
1
2
2
0
1
2
1
0
1
1
1
1
2
0
0
2
1
2
1
1
0
0
0
1
1
0
2
0
1
2
1
1
2
0
1
0
1
0
2
0
2
1
1
1
1
1
0
2
1
2
2
0
0
0
0
0
0
0
1
0
1
2
0
1
2
2
1
1
2
0
2
0
0
3
1
1
0
1
0
0
2
1
1
1
1
1
1
4
1
1
2
2
1
1
0
0
1
0
1
1
1
1
2
1
1
1
2
1
2
3
0
0
2
1
0
2
2
1
1
2
2
0
0
1
1
1
0
1
2
1
0
1
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
2
1
1
0
0
0
2
0
2
1
2
0
2
2
1
1
2
0
0
0
1
0
0
0
0
3
1
0
0
0
0
1
1
1
1
1
2
1
1
0
1
0
0
0
1
0
0
1
0
0
7
1
1
1
0
0
1
2
2
2
0
2
0
0
0
1
0
0
2
2
1
0
2
0
0
0
2
1
2
0
0
0
1
0
1
4
1
0
0
2
0
0
0
1
1
1
0
0
1
1
1
1
1
1
1
1
0
1
2
1
2
0
2
2
1
1
1
1
1
2
1
1
0
2
2
2
0
0
1
0
1
1
2
1
0
1
0
1
2
1
2
2
1
0
0
2
1
0
2
0
2
4
2
0
0
0
3
0
1
1
1
2
1
0
1
0
0
2
0
0
1
4
1
0
0
1
0
1
1
0
1
2
1
2
1
0
1
0
1
0
1
2
1
0
0
2
0
1
2
2
2
0
0
1
0
1
1
0
1
1
1
1
1
0
1
0
0
2
2
0
1
0
0
0
2
1
0
0
2
1
1
1
0
0
2
2
0
1
1
0
0
1
0
0
1
0
2
1
1
0
0
0
0
2
0
1
0
0
2
1
0
0
0
0
2
1
1
1
2
1
1
0
1
1
1
1
0
0
0
2
0
0
1
0
0
1
0
1
0
0
1
1
0
1
1
0
2
1
1
2
0
1
1
6
1
0
1
0
1
0
1
1
2
0
2
1
2
1
1
2
2
0
1
0
1
1
2
5
2
0
1
1
0
1
0
1
0
1
1
2
2
1
2
0
1
1
1
0
0
0
3
1
0
1
0
0
1
2
1
1
2
0
1
1
0
0
1
0
1
0
1
0
1
0
1
0
1
2
1
0
1
1
2
2
0
1
0
2
1
2
2
0
7
0
0
0
2
2
1
1
0
0
1
0
2
1
0
1
1
0
0
1
2
0
1
1
2
0
2
0
1
0
1
1
1
1
1
0
1
1
2
1
0
1
0
0
1
2
0
1
1
0
1
2
3
0
1
0
1
0
0
1
1
1
0
0
2
1
0
0
0
0
0
1
1
0
0
0
0
1
1
0
2
1
0
2
0
1
0
0
0
1
0
2
1
1
1
0
0
1
2
1
1
2
0
0
2
1
1
0
1
1
0
0
3
1
0
1
0
1
0
0
2
2
0
0
0
0
1
1
1
1
2
1
2
0
0
0
1
2
0
1
0
1
1
0
1
0
1
0
0
0
2
1
1
2
1
1
0
1
1
2
2
0
0
1
1
0
2
1
2
1
0
0
2
0
0
0
0
2
2
1
0
1
2
2
0
1
2
4
0
3
0
2
2
2
0
1
0
0
1
1
1
0
1
0
0
1
0
0
2
2
1
0
1
1
1
0
1
0
0
2
1
0
1
2
1
1
1
1
1
0
1
1
0
0
0
1
1
1
1
1
2
0
0
2
1
0
1
1
0
2
0
1
1
0
2
2
1
0
1
1
5
1
1
1
0
0
2
0
1
0
1
1
1
1
1
1
1
1
1
0
1
2
1
1
1
2
1
1
2
1
0
1
1
0
0
0
1
1
1
0
2
3
0
0
0
0
1
3
0
1
1
1
0
2
2
1
0
2
0
0
0
2
0
1
1
1
0
0
1
0
2
1
0
2
0
0
1
0
0
1
0
1
1
1
1
0
2
1
1
0
0
0
0
1
0
2
0
2
1
0
2
1
1
1
2
0
7
1
0
1
1
2
0
0
2
2
0
1
2
2
1
1
1
1
1
0
2
0
2
1
0
0
2
2
0
0
1
0
0
0
3
1
0
1
1
1
0
1
1
2
0
0
1
2
0
0
0
1
1
0
1
0
1
0
2
0
0
1
1
1
0
1
0
1
0
2
1
2
1
0
0
0
1
3
2
0
2
1
0
0
1
1
2
2
1
1
1
0
1
0
1
1
2
1
1
1
2
1
2
1
1
1
2
1
0
1
1
2
1
2
1
0
2
0
0
1
0
1
1
0
1
1
2
0
1
0
2
2
1
0
3
1
1
0
0
1
0
0
2
2
1
1
1
0
1
1
2
1
0
1
1
0
1
0
0
2
1
1
2
1
0
0
0
0
2
2
2
0
1
0
1
0
1
1
0
1
0
0
0
0
1
2
0
0
2
1
0
1
1
0
1
0
1
0
2
1
1
2
1
0
1
0
0
0
1
0
1
0
0
0
1
1
0
2
2
1
1
1
0
2
0
0
1
1
1
0
0
0
1
1
2
0
1
2
1
1
0
2
0
0
0
1
0
0
1
2
1
0
0
2
0
0
2
0
0
1
0
0
0
1
2
1
1
0
2
1
1
1
0
0
2
0
0
1
1
0
0
2
0
1
0
2
1
2
0
1
0
0
1
2
0
2
0
1
0
4
0
0
2
1
1
2
1
0
0
1
2
1
1
0
1
1
0
0
1
4
2
0
0
2
0
0
0
1
1
0
1
1
1
0
1
0
3
2
0
0
1
1
1
2
0
1
0
0
0
1
0
0
1
1
1
0
0
1
1
0
0
0
0
0
1
0
3
1
2
2
2
1
0
0
1
1
1
1
0
0
1
0
1
0
1
0
3
0
0
0
1
0
1
1
0
0
2
1
0
1
2
2
2
3
1
1
0
0
0
0
1
1
0
0
1
2
2
1
1
0
0
2
2
0
0
2
1
0
1
2
0
0
1
1
1
1
2
2
1
1
0
0
1
2
1
1
0
1
1
1
0
2
0
1
1
0
2
1
0
0
0
1
1
2
2
1
1
1
1
0
1
2
1
0
0
1
2
1
2
2
1
0
0
0
2
1
0
1
1
2
0
0
0
1
0
1
1
1
1
2
1
0
1
1
0
0
2
2
1
1
2
0
1
1
0
2
1
1
0
1
0
2
2
0
3
0
1
1
2
0
0
1
2
2
0
1
1
0
0
0
1
0
0
0
2
1
0
0
1
0
1
1
0
2
1
2
0
0
1
1
0
2
0
0
2
0
2
1
0
1
3
1
2
0
1
0
1
2
1
3
0
0
0
1
0
0
2
1
1
1
0
2
2
0
2
1
1
1
2
1
0
0
0
0
1
1
2
1
2
3
1
1
1
1
2
1
1
0
2
1
1
1
0
0
1
3
0
1
0
1
1
1
1
0
0
1
0
2
1
2
1
1
1
1
1
2
2
0
0
0
2
1
1
0
0
1
1
2
2
1
0
2
0
2
1
2
1
0
3
1
2
0
0
1
0
1
1
1
1
2
0
1
0
1
0
0
0
0
1
1
1
1
0
1
0
1
0
1
0
1
0
2
0
0
0
2
1
0
1
0
0
1
1
2
0
0
1
0
1
0
1
0
0
1
1
1
1
1
2
0
1
0
0
0
0
2
1
0
2
2
2
3
1
1
1
1
1
2
0
1
2
1
1
1
2
0
1
1
1
2
2
0
0
0
0
2
0
0
0
1
1
0
2
1
2
1
2
1
0
2
2
0
0
2
1
0
0
1
0
1
1
0
0
0
2
0
2
2
1
0
1
0
2
0
0
0
1
1
0
0
0
0
1
0
0
1
2
0
0
0
0
0
1
0
1
1
1
1
2
0
0
0
0
0
0
1
2
0
0
1
1
1
1
2
1
0
0
1
1
0
2
2
0
1
0
0
0
1
0
1
1
2
2
1
0
1
1
1
2
1
1
0
1
0
2
0
0
3
2
0
0
2
1
0
2
1
1
1
1
0
1
2
1
1
1
1
1
2
0
1
1
0
1
0
1
0
3
1
2
1
2
1
2
1
2
0
0
1
1
0
0
2
1
2
2
2
1
2
0
0
0
2
0
1
0
3
0
1
1
2
1
1
2
0
1
1
0
0
1
0
2
0
0
1
1
0
2
0
2
1
0
1
1
2
0
0
0
1
1
1
2
1
0
2
2
1
2
1
0
2
1
2
0
2
1
0
2
1
1
1
3
0
0
0
0
0
0
0
1
0
1
1
1
0
2
0
1
0
0
1
2
1
2
0
0
0
2
0
0
2
0
0
1
0
0
1
0
1
2
1
1
1
0
1
1
1
1
1
0
2
1
0
0
0
0
0
2
2
0
0
1
1
2
3
0
2
0
2
0
1
1
2
1
0
0
0
1
1
1
0
0
1
0
2
0
0
1
0
1
1
1
2
0
2
2
0
1
2
2
1
1
1
2
2
1
0
0
1
0
0
0
1
0
1
1
1
2
1
2
1
1
2
1
0
2
1
2
1
0
0
0
1
1
1
1
1
4
1
2
2
1
0
2
2
0
2
0
0
1
2
1
1
2
1
1
0
2
2
2
1
0
1
3
1
0
1
0
0
2
0
0
2
1
1
0
2
0
1
0
1
2
1
0
0
0
2
0
2
2
1
0
1
1
2
0
0
1
1
2
2
1
0
0
1
1
1
1
0
1
1
2
1
0
0
2
0
1
0
1
1
0
0
1
0
0
0
0
0
1
2
0
2
2
0
1
1
1
0
1
0
0
2
1
1
2
1
1
1
0
0
1
1
2
2
1
1
0
0
0
1
1
0
0
1
0
0
0
2
1
2
0
1
1
2
1
1
1
0
1
1
2
1
0
0
2
1
0
1
4
1
0
0
2
2
1
0
2
1
0
2
3
2
0
1
0
0
1
0
2
2
1
2
1
0
1
2
1
1
0
0
1
1
2
2
0
0
0
1
0
0
1
2
1
2
0
1
0
0
0
1
1
1
0
0
0
0
2
0
1
2
0
1
1
3
1
1
0
0
1
0
1
1
0
1
1
2
0
0
1
2
1
0
0
1
0
0
1
2
1
0
1
1
0
0
1
1
1
0
1
0
0
1
1
0
2
1
0
0
1
2
1
0
1
1
2
1
1
1
1
0
2
0
1
1
1
0
2
2
1
2
0
2
2
0
1
2
1
1
0
1
1
1
1
1
2
1
1
0
0
2
0
1
1
0
1
0
1
0
2
1
1
0
0
1
1
1
2
1
1
1
1
2
1
1
0
1
2
0
0
1
2
2
0
1
0
1
1
2
2
1
2
2
1
1
0
1
0
1
0
2
1
0
2
1
1
0
1
0
0
2
0
0
1
0
2
1
0
1
1
0
0
0
0
0
2
1
0
0
0
1
0
0
0
1
1
0
1
0
1
1
0
2
2
0
0
2
0
1
1
1
0
0
1
0
1
2
0
1
0
2
0
1
0
1
1
0
0
2
1
1
0
1
2
0
2
0
0
1
1
1
0
2
0
1
1
0
0
1
0
0
0
0
2
0
0
2
1
0
1
1
1
2
0
1
1
2
0
2
2
0
2
0
1
1
2
0
1
0
0
0
2
1
0
1
0
0
1
0
0
1
0
0
0
1
0
0
1
1
2
1
0
0
2
1
0
0
0
0
2
0
1
2
1
1
0
0
1
1
0
1
1
1
0
1
1
0
0
0
1
0
0
2
1
1
2
0
0
2
0
1
1
0
0
1
0
0
0
1
6
1
0
2
1
1
2
1
0
2
2
0
3
2
0
0
2
1
1
1
0
0
1
2
0
1
1
0
0
1
0
1
1
1
0
0
1
1
1
0
2
1
2
1
1
1
0
4
1
0
2
2
2
1
0
0
0
0
2
2
1
2
0
1
1
2
0
2
2
0
0
1
0
1
2
0
1
1
0
0
0
0
2
1
1
1
1
1
2
2
2
0
0
1
0
0
1
1
1
1
0
2
1
1
2
2
1
1
2
1
1
0
1
1
1
1
0
0
2
2
0
1
2
0
2
0
1
1
2
0
0
0
0
1
2
0
2
2
1
2
2
1
2
1
0
1
1
1
0
1
0
1
0
2
2
1
1
0
0
0
1
1
1
0
1
0
1
1
2
0
0
0
1
0
0
0
1
1
0
2
1
1
0
0
0
0
0
1
2
1
0
1
0
1
2
0
0
1
3
1
1
0
3
1
1
1
0
1
1
0
1
0
0
2
0
0
0
0
1
0
1
2
2
2
1
0
2
1
1
0
1
0
1
0
3
0
1
0
0
0
1
0
1
2
1
2
2
1
1
2
1
2
0
0
0
2
1
3
0
0
4
1
1
0
2
0
0
0
0
0
0
1
0
0
1
2
1
2
0
1
1
6
1
2
2
2
0
0
0
2
1
1
0
2
0
0
0
2
2
0
0
0
1
1
1
0
2
1
1
1
0
0
0
0
1
0
1
0
2
2
0
1
0
1
2
1
1
0
2
0
0
0
2
1
4
0
0
1
2
2
0
1
1
2
0
1
1
0
1
1
0
1
1
2
2
0
1
2
1
2
0
4
0
1
3
1
1
1
2
1
1
1
1
0
0
1
0
2
1
1
1
1
2
0
2
1
2
1
1
0
1
1
2
1
0
0
0
1
0
1
0
0
2
0
1
1
0
1
0
2
2
2
1
0
1
1
0
1
0
2
1
1
0
0
1
1
1
2
0
0
1
1
1
3
0
1
2
0
0
2
0
0
1
2
1
0
1
2
1
1
0
2
0
0
1
0
1
3
0
1
1
2
0
1
2
0
0
2
0
1
1
0
1
1
3
0
0
1
1
1
2
2
2
2
1
0
1
0
0
1
1
1
0
1
0
1
1
1
2
0
1
0
2
2
2
0
1
1
1
1
2
0
1
1
1
0
1
2
0
1
0
2
1
2
1
5
1
1
0
1
0
1
1
2
0
2
1
1
0
1
1
2
1
2
0
1
1
1
1
1
0
0
2
1
1
0
1
0
1
1
2
0
2
0
1
2
1
2
1
2
3
1
0
1
1
2
0
1
1
0
1
0
0
1
3
0
1
1
1
2
2
1
1
0
2
2
2
1
0
0
1
1
0
0
1
2
1
2
2
0
1
2
1
0
0
1
1
0
0
1
2
2
1
2
2
1
0
0
1
0
0
1
0
1
1
1
0
1
0
1
0
2
0
1
1
0
1
0
2
2
1
2
0
1
1
1
2
1
1
2
1
2
0
1
1
2
2
0
0
0
0
1
1
0
2
0
2
0
2
0
1
1
3
2
1
1
2
1
2
1
0
1
1
3
0
0
0
0
0
1
1
0
1
0
1
0
2
0
0
0
0
0
1
1
0
0
0
2
1
0
0
1
1
2
0
1
0
1
0
2
1
1
2
2
0
1
2
0
1
0
1
1
1
0
1
0
2
2
0
3
1
1
2
2
0
1
0
0
0
0
1
1
2
0
1
0
1
1
0
0
2
1
1
0
1
0
2
1
0
1
2
1
1
0
2
1
2
0
0
0
0
0
0
1
0
1
1
2
1
2
0
1
1
0
2
0
0
0
0
2
0
1
1
0
1
1
1
0
1
0
0
1
1
0
1
1
0
0
2
0
2
1
1
3
0
0
1
1
1
0
0
1
1
1
1
1
0
2
0
0
2
2
1
0
0
2
0
0
0
0
1
2
1
1
2
1
2
1
1
0
0
0
0
1
1
0
0
2
1
0
1
0
0
2
1
1
1
1
1
1
4
0
0
1
2
2
1
1
1
2
0
2
1
1
0
1
1
1
0
0
0
0
1
1
0
1
0
1
2
0
0
1
0
2
0
0
2
0
0
0
0
0
1
0
1
1
0
0
3
0
1
0
0
1
0
3
2
0
1
1
0
1
0
2
1
0
0
0
1
1
1
1
1
0
1
3
1
1
1
1
2
0
1
2
0
1
0
1
0
0
1
0
6
2
0
1
0
1
0
1
0
1
0
2
2
1
1
1
1
0
1
2
2
1
1
2
2
1
0
1
1
2
2
1
1
2
0
0
0
1
2
0
0
1
2
1
2
0
1
0
0
0
1
0
2
0
0
2
2
5
1
2
1
1
0
0
1
1
0
1
2
0
0
1
1
1
0
1
2
0
0
0
1
0
1
1
0
0
1
0
0
1
0
2
1
2
0
0
2
0
0
1
2
1
0
0
0
0
3
0
0
0
1
2
0
1
0
0
0
2
0
0
1
2
0
1
0
0
2
0
0
0
0
1
2
1
1
2
1
1
0
1
1
2
1
2
1
0
1
0
1
0
2
1
2
1
1
0
1
1
0
0
0
0
2
1
1
1
0
1
1
0
0
0
0
0
0
0
1
1
2
0
1
0
0
0
1
1
2
0
1
2
2
1
1
1
2
1
0
0
0
0
0
1
4
1
0
1
0
1
1
0
1
1
1
1
0
0
0
1
1
1
0
0
0
2
1
1
1
0
2
1
1
1
0
1
2
0
1
0
1
2
1
1
1
1
0
0
1
1
1
2
1
1
0
0
2
0
1
2
0
0
2
2
1
1
1
1
1
0
0
1
1
0
2
1
2
2
1
1
1
0
0
1
0
2
1
2
1
2
2
1
1
1
1
2
0
1
1
1
0
2
1
0
4
1
2
1
0
0
0
0
1
8
0
1
0
0
2
1
0
2
2
1
0
0
1
0
1
1
1
0
0
0
0
1
0
0
1
1
0
1
1
0
2
1
1
0
2
1
1
2
2
0
1
2
1
1
0
1
1
1
2
0
2
0
0
1
1
1
2
0
1
1
1
1
0
1
2
0
0
1
1
0
1
1
1
0
2
1
1
0
0
0
4
1
1
0
1
1
2
0
1
1
1
0
1
0
1
1
0
0
0
2
1
1
1
1
1
0
0
0
1
0
0
0
0
2
1
1
1
0
1
0
1
0
2
1
1
1
0
1
1
0
2
2
0
2
2
1
2
0
1
0
0
1
0
0
1
2
1
0
2
2
1
0
1
0
2
2
2
1
0
0
0
1
1
0
2
2
0
1
2
0
1
0
0
1
0
0
1
0
0
1
2
1
0
0
0
1
0
0
0
0
1
0
1
0
1
0
1
1
0
0
1
1
1
2
0
0
0
0
2
2
1
1
0
3
1
0
1
3
1
0
1
1
1
0
1
0
1
2
1
2
1
3
1
2
0
2
1
1
1
0
1
1
1
2
1
2
0
0
0
0
2
2
0
2
1
0
0
0
0
2
1
1
0
0
2
0
1
1
1
1
1
0
2
1
0
1
1
2
2
1
0
2
0
1
0
0
2
2
0
0
2
1
2
2
2
1
2
2
0
0
0
0
1
0
0
1
1
1
1
2
1
1
1
3
1
1
1
2
0
1
1
0
1
1
1
0
0
1
0
2
1
1
0
0
1
0
1
1
1
0
0
2
1
1
0
1
2
0
0
0
2
2
1
1
0
1
0
0
0
1
0
1
2
0
2
1
2
0
1
0
0
1
2
0
0
0
0
2
0
0
0
2
1
1
2
1
2
1
1
1
2
0
0
1
0
0
0
1
0
1
1
2
0
3
0
2
0
3
0
1
1
2
0
0
0
1
1
0
1
1
3
1
1
1
1
1
1
1
0
0
0
2
2
1
1
2
1
1
1
1
2
1
2
1
1
2
0
0
0
2
0
1
0
0
2
1
0
2
1
1
0
2
2
0
1
0
2
2
0
2
0
1
1
2
2
4
2
0
2
0
2
0
2
0
0
1
1
0
0
0
1
1
0
2
0
2
0
0
2
1
1
1
2
0
1
1
2
2
4
0
1
1
1
0
1
1
0
1
1
0
2
1
0
2
1
2
1
0
1
1
1
1
1
0
2
1
0
0
2
0
2
2
0
0
1
1
1
1
0
0
1
1
0
1
1
0
1
1
0
2
1
2
2
0
2
0
2
2
1
1
2
0
1
1
2
0
1
0
2
0
0
1
0
0
0
1
1
0
1
1
1
1
1
0
2
1
1
1
0
0
1
1
0
1
3
1
0
1
0
1
0
1
2
2
2
0
0
2
0
1
0
0
2
2
1
0
1
1
2
0
1
0
0
1
0
1
0
2
1
1
2
1
4
0
1
1
1
1
1
2
1
0
1
2
0
1
1
1
0
1
1
2
2
0
0
1
2
2
1
1
2
1
0
0
2
0
0
0
1
1
1
2
0
1
0
0
0
1
0
2
0
1
0
1
1
1
0
0
1
1
0
0
1
1
2
1
2
1
1
2
1
1
2
3
1
1
1
0
1
0
1
2
2
1
2
0
1
2
0
0
1
0
2
0
2
1
1
0
1
0
1
1
1
0
2
1
0
1
1
2
1
2
0
0
1
0
2
0
0
0
0
1
0
0
1
0
0
1
2
0
0
2
0
0
0
2
1
0
1
2
1
2
0
2
1
0
1
2
1
0
1
1
0
1
1
0
0
2
1
1
0
2
1
0
1
1
0
1
1
1
0
1
0
0
2
1
1
1
1
0
1
2
2
1
1
1
2
0
1
0
0
0
2
1
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
1
0
1
0
0
0
1
1
0
0
1
2
0
1
1
1
0
2
1
1
1
0
1
0
0
0
2
0
2
1
1
1
1
1
1
1
0
0
1
2
0
2
2
1
2
1
2
1
0
1
3
2
1
1
0
1
1
0
0
1
0
2
1
0
1
1
2
0
1
2
0
1
2
0
1
2
1
1
0
1
1
0
0
0
2
1
1
2
1
1
0
1
0
1
1
2
1
0
1
0
2
1
1
1
2
1
0
0
0
1
0
1
1
1
1
2
0
1
0
2
2
0
1
0
0
1
1
1
0
2
2
1
1
1
1
0
2
1
1
2
2
1
0
1
0
1
1
0
0
2
0
2
1
1
0
1
1
2
1
0
0
0
0
2
0
0
1
2
1
1
1
1
1
2
2
0
0
1
1
1
0
2
1
1
2
0
1
1
2
1
2
2
0
0
0
2
1
0
1
0
1
2
0
2
0
0
2
0
0
0
1
1
1
0
0
1
2
2
1
1
0
1
1
2
0
2
1
0
1
1
1
0
0
1
1
1
1
1
2
0
2
2
1
1
2
1
1
0
1
1
0
0
1
0
1
1
2
1
2
2
1
1
1
0
2
0
0
0
2
1
2
2
1
0
1
0
1
1
1
1
1
0
1
1
2
1
1
0
1
1
1
0
1
2
1
0
0
1
2
1
0
0
2
0
2
1
1
1
2
2
1
1
1
0
0
2
1
0
1
1
1
1
1
1
0
0
1
0
0
0
0
1
1
1
0
0
2
1
1
1
2
0
1
1
0
0
1
2
1
0
2
1
1
0
1
1
1
0
1
2
0
1
0
0
0
0
0
0
2
1
1
2
1
2
0
0
1
2
1
0
0
1
1
0
0
2
2
2
0
0
0
1
0
1
2
0
1
1
2
2
2
0
3
0
1
1
2
0
0
2
2
2
1
1
0
2
2
1
1
0
0
2
0
1
1
1
0
0
0
0
1
1
2
0
0
0
1
1
1
2
1
1
1
0
1
1
2
0
0
1
1
1
1
1
1
0
1
1
0
1
1
0
1
1
1
0
2
2
1
2
0
1
0
1
2
2
2
0
0
0
1
0
0
1
1
1
0
1
2
2
1
0
2
1
2
1
0
0
0
1
2
0
1
2
1
1
0
1
0
1
0
3
0
0
1
0
1
1
2
1
0
2
1
0
2
0
1
0
1
2
0
1
1
0
2
0
1
1
1
0
2
0
1
2
1
0
0
2
2
0
1
2
0
1
1
0
2
0
2
1
1
1
0
0
2
0
2
0
2
1
3
2
1
1
0
0
1
0
2
1
1
0
2
1
1
1
0
2
2
1
3
1
2
0
0
1
1
1
1
2
1
2
1
0
0
0
0
1
1
1
1
0
1
4
0
0
0
2
1
1
2
0
0
1
0
1
0
0
1
0
1
2
0
2
1
2
1
2
2
0
1
1
1
0
0
1
1
2
1
1
2
1
0
2
0
0
1
2
0
1
1
0
0
2
2
1
0
1
2
1
1
2
0
2
1
1
0
1
1
0
1
1
1
1
0
2
4
1
0
2
1
1
0
2
1
1
1
1
1
0
0
1
2
0
0
0
1
0
1
11
0
0
0
0
0
0
2
1
0
2
1
0
2
0
1
1
1
2
1
1
3
2
1
2
1
1
1
2
0
1
1
0
1
2
1
1
0
1
1
4
0
1
1
0
0
0
2
0
2
0
0
0
1
1
2
1
1
1
1
0
0
0
2
1
0
0
1
0
1
2
0
1
2
2
2
0
0
0
2
0
1
0
1
3
1
1
1
0
1
0
1
1
0
0
1
0
1
2
1
2
0
2
2
2
1
0
0
2
1
1
1
2
0
2
2
0
1
1
2
2
2
0
1
0
0
0
0
1
2
0
1
1
2
0
1
2
1
1
1
1
2
1
1
1
0
2
0
0
1
0
1
1
1
1
1
1
1
0
1
2
1
1
1
0
2
1
1
2
1
2
1
1
3
0
1
0
0
1
0
2
1
2
2
1
0
1
2
2
1
1
0
2
0
1
2
1
0
2
1
0
2
1
0
0
0
0
0
1
0
1
1
0
0
0
1
0
1
0
1
1
1
1
0
1
1
0
0
0
1
1
1
0
2
2
0
1
2
2
6
1
1
0
2
0
3
1
0
1
0
2
1
1
2
0
1
1
0
0
6
0
0
1
0
0
1
1
2
1
0
1
1
0
1
1
1
1
1
0
1
2
1
1
1
0
4
1
2
1
2
0
0
1
2
1
0
1
0
0
2
1
1
2
1
2
0
2
1
2
1
0
0
2
0
0
0
0
1
1
0
1
1
1
0
0
2
2
0
1
0
1
1
1
0
0
0
2
0
1
0
1
0
1
0
0
0
0
0
1
1
0
2
1
0
0
1
0
2
2
2
0
1
0
1
0
0
0
2
1
1
0
1
1
1
1
1
1
0
0
2
0
0
0
2
1
0
0
1
1
0
0
1
0
2
0
2
2
1
1
1
1
0
0
1
0
2
0
0
0
2
0
0
1
0
0
0
2
2
1
2
1
1
1
1
1
1
0
1
1
1
1
2
1
1
0
1
0
1
2
1
1
0
0
0
1
0
0
1
1
0
1
0
0
1
1
1
0
0
0
2
0
0
1
1
2
0
1
1
0
1
1
0
0
1
0
0
2
2
0
2
1
1
1
1
1
1
1
2
1
1
1
1
1
2
0
1
1
2
3
2
0
0
1
0
2
0
0
0
0
1
2
1
0
1
0
0
1
0
3
1
2
1
1
0
0
2
1
0
1
1
1
2
1
0
0
2
1
2
1
0
2
1
2
1
1
1
1
0
0
2
4
1
0
0
0
2
1
1
2
1
2
1
1
1
1
0
2
1
1
1
2
0
1
0
1
2
0
1
1
1
0
1
0
1
2
0
0
0
1
0
2
1
1
2
0
2
0
0
1
2
0
1
0
1
1
2
1
1
0
0
0
1
1
2
0
1
2
1
0
0
1
0
1
0
1
0
0
0
1
0
0
0
2
1
1
0
0
1
0
0
2
1
2
2
2
0
2
1
0
0
1
0
1
0
2
1
1
1
1
0
1
1
0
0
0
1
1
1
0
0
0
1
1
0
1
1
1
0
0
0
1
0
1
0
1
3
0
1
0
0
1
2
1
0
0
1
0
1
2
2
0
3
0
1
1
1
1
2
0
1
0
2
1
2
2
2
0
1
3
2
2
0
1
0
0
1
1
0
0
1
2
0
2
1
1
2
1
1
2
2
0
0
0
2
1
0
1
1
0
1
2
1
1
1
0
0
1
1
2
2
1
0
0
1
2
1
0
1
0
0
0
1
1
1
1
2
1
1
1
1
0
0
1
0
1
1
1
1
1
0
0
1
1
2
1
2
2
0
1
1
1
2
1
0
2
2
0
0
1
1
0
2
0
1
0
0
1
1
2
1
1
0
1
1
1
2
2
1
0
0
1
1
0
0
1
1
1
1
0
2
0
1
1
0
2
2
1
1
1
0
0
0
1
0
2
1
0
0
4
1
1
1
1
0
0
0
1
0
1
1
1
0
1
2
0
2
1
0
2
0
1
2
1
2
2
1
1
1
1
3
0
0
1
2
0
0
1
2
1
0
1
0
2
1
2
0
1
1
2
1
0
0
0
0
1
0
1
0
1
1
0
2
1
1
0
1
0
1
0
2
0
0
1
0
0
1
0
1
1
0
1
1
1
2
2
1
1
1
0
1
1
1
0
1
0
1
2
2
2
0
1
0
1
0
2
1
0
1
2
1
1
1
0
0
1
0
2
1
2
1
2
0
0
2
0
0
1
0
0
1
0
2
1
1
0
0
1
0
2
1
0
2
0
1
0
0
0
0
2
2
1
1
1
2
0
2
2
1
1
2
2
1
1
1
2
2
0
1
0
1
0
0
0
2
0
1
1
0
0
0
0
0
0
1
1
2
2
1
0
1
0
1
0
1
2
0
0
1
2
0
3
2
0
1
1
1
1
3
0
2
2
0
1
0
0
0
0
2
6
2
4
1
0
2
2
0
2
0
1
0
0
2
2
0
0
0
0
0
1
0
1
0
0
1
1
1
1
2
1
1
0
1
1
2
0
1
0
0
1
2
0
0
2
0
0
1
1
0
2
0
1
2
0
1
0
0
0
1
0
0
1
1
0
0
0
1
1
0
2
1
1
0
0
0
2
1
0
2
1
0
0
1
2
0
0
0
2
1
1
0
0
1
1
1
2
1
0
0
1
1
2
0
0
2
1
1
0
1
2
1
1
1
1
1
1
1
1
2
1
2
2
1
1
0
1
0
2
1
2
1
1
0
0
0
1
0
2
0
1
1
1
2
0
0
1
0
1
1
1
2
0
1
1
1
1
1
1
1
0
1
2
2
0
0
1
2
1
2
1
0
0
1
1
1
2
0
2
2
1
0
1
0
1
2
0
2
1
0
1
1
1
1
2
1
2
2
0
1
0
1
1
2
1
2
2
0
1
0
2
1
0
2
1
0
1
1
2
2
1
0
0
1
1
0
1
1
1
1
1
1
2
1
2
1
0
1
0
2
0
2
0
0
0
0
1
0
2
3
0
0
1
1
0
1
0
2
1
1
0
1
1
2
1
2
2
2
1
1
0
1
2
1
2
2
0
1
1
1
2
2
1
1
0
1
1
1
2
1
0
0
0
0
1
0
0
2
3
1
0
2
2
1
1
1
0
0
1
0
1
1
0
0
1
1
1
0
0
1
2
0
2
1
1
2
0
1
0
0
1
1
2
0
1
1
2
2
2
0
0
0
0
2
2
1
2
1
1
1
1
1
0
1
1
0
1
1
1
0
0
1
2
1
0
1
0
1
1
0
0
1
2
0
1
2
1
0
1
1
0
1
1
0
2
2
1
0
0
0
1
2
1
2
0
0
2
1
1
1
0
0
1
1
1
1
0
1
0
1
1
0
0
1
1
1
2
0
0
2
0
1
1
1
2
2
2
1
0
2
1
2
2
0
1
1
0
0
0
0
1
0
1
1
2
1
1
1
0
1
0
1
0
1
1
1
1
1
0
0
2
1
1
1
0
0
0
1
3
1
0
0
0
1
0
1
2
0
2
1
1
0
0
1
0
2
0
0
0
2
2
1
2
1
2
1
0
0
0
3
0
0
1
2
0
1
0
2
2
2
0
0
1
0
0
0
0
1
2
1
0
0
1
0
1
0
0
1
0
1
1
2
0
1
0
2
1
0
1
0
2
0
0
0
1
2
1
1
2
0
2
1
2
0
2
0
2
0
2
1
1
2
0
0
2
1
2
0
0
1
0
1
1
2
0
0
0
1
3
1
1
1
0
0
2
1
1
0
1
0
1
1
0
1
2
1
0
1
1
0
1
2
1
1
0
1
0
0
1
4
0
1
0
0
2
1
1
0
1
1
0
0
0
1
3
1
3
1
0
1
0
0
1
2
0
0
1
0
0
1
0
1
0
1
1
0
0
0
1
0
1
0
1
0
1
2
2
1
0
0
2
1
2
1
2
1
1
0
1
0
0
1
1
0
1
0
0
1
2
2
0
1
0
1
1
0
0
0
1
1
2
0
1
2
0
2
1
0
1
0
1
1
0
0
1
2
0
2
0
0
1
1
0
1
1
1
1
0
1
0
1
2
1
2
0
0
1
1
1
0
0
1
0
0
0
1
1
0
0
0
2
0
2
0
1
0
0
1
2
3
2
2
1
1
0
1
2
1
1
1
1
1
1
2
1
1
0
1
2
1
2
0
1
0
0
0
1
0
2
1
1
1
0
0
1
1
1
1
2
0
1
0
2
1
0
0
1
2
1
2
1
0
0
0
0
0
0
1
1
2
2
2
0
0
2
0
0
1
0
2
0
1
2
1
2
1
2
1
1
0
1
0
2
1
1
0
1
1
2
2
0
2
0
0
0
0
1
0
0
0
1
1
0
2
0
2
2
2
0
1
1
2
2
0
1
1
2
1
1
2
2
0
2
2
1
1
1
0
1
0
1
0
1
2
1
1
1
2
2
0
1
0
0
0
1
1
0
1
1
0
0
1
0
0
1
1
0
0
2
2
1
1
2
1
1
0
0
1
0
1
1
0
2
0
1
0
1
0
0
0
1
1
0
1
0
1
1
1
0
1
1
2
2
2
0
1
0
0
0
1
0
3
0
0
1
0
0
2
1
2
0
2
1
2
2
0
0
0
1
2
1
1
0
1
2
1
1
2
1
1
2
0
2
0
0
0
0
1
0
0
1
0
1
1
0
1
1
1
1
0
0
0
1
1
2
1
1
2
0
1
1
2
1
0
0
0
0
0
0
0
0
1
0
1
1
1
0
2
1
1
1
0
0
1
1
1
1
0
0
0
2
0
2
2
1
0
1
0
0
1
2
0
0
1
1
0
2
2
1
2
0
1
2
2
2
1
3
2
0
1
0
2
0
1
0
0
0
0
0
0
1
1
0
1
2
0
1
0
1
0
0
1
1
0
1
2
0
1
0
2
2
1
0
0
2
0
1
2
2
1
0
1
0
0
0
0
2
2
0
0
1
1
2
2
1
1
1
1
1
2
1
2
1
1
2
0
0
1
2
0
0
1
1
1
0
0
1
0
1
1
0
1
2
1
1
0
2
2
1
2
0
0
2
1
0
5
1
5
3
0
2
0
0
0
0
1
0
1
2
1
1
2
2
1
0
0
0
1
1
3
1
1
1
1
0
0
2
0
1
1
0
0
1
1
0
2
0
0
1
0
1
1
0
1
0
1
2
0
1
1
2
0
0
1
1
0
1
3
1
1
0
2
1
0
1
1
2
1
0
1
0
0
0
1
0
0
1
1
0
1
0
0
1
1
1
0
1
0
0
3
2
0
0
2
0
0
1
2
2
0
1
0
0
0
1
2
1
1
1
0
0
2
0
1
0
0
1
1
0
2
1
0
1
1
1
1
1
0
1
1
0
2
3
1
1
0
1
1
0
1
0
0
1
1
1
0
2
2
1
1
2
1
2
1
1
0
1
0
0
1
0
1
2
1
0
2
0
0
1
1
2
2
1
1
0
1
0
2
0
0
1
3
1
1
1
1
1
0
0
1
1
0
7
2
2
1
0
2
1
0
1
1
0
1
0
2
2
0
2
2
2
2
2
1
0
1
2
1
1
2
2
0
0
0
0
0
1
0
2
0
1
0
0
2
0
1
0
1
0
1
0
2
1
0
1
2
0
1
1
2
0
1
0
1
1
0
1
0
1
0
1
0
0
1
2
0
1
0
0
2
2
1
1
0
1
2
0
0
1
0
2
2
0
1
1
0
1
2
0
0
2
2
0
1
2
0
1
1
1
0
2
2
0
0
1
2
0
1
0
2
3
2
3
0
2
2
1
0
0
0
1
1
0
0
0
0
1
0
0
1
2
1
0
0
1
0
1
0
0
0
2
2
1
0
1
1
2
0
2
0
1
0
1
1
0
0
2
1
2
0
0
1
2
0
2
0
0
3
0
1
0
1
0
1
0
3
0
1
0
0
1
1
1
1
1
1
0
1
1
1
0
1
2
2
0
2
1
1
1
1
0
0
0
1
2
1
0
1
2
0
1
0
2
1
2
1
2
0
0
0
2
1
1
2
0
0
1
1
0
1
1
1
0
2
0
1
1
2
1
0
0
2
1
1
2
4
2
0
1
1
1
2
0
0
0
0
2
0
1
0
0
2
2
2
1
0
0
2
2
0
0
2
1
0
2
1
2
2
2
3
1
1
2
0
1
0
1
2
2
1
1
1
0
1
0
1
2
1
0
1
1
0
0
2
0
0
2
2
1
1
2
1
0
0
1
1
0
0
0
0
0
0
1
1
2
1
0
2
0
2
0
0
0
1
1
0
2
0
2
1
2
2
2
1
2
0
0
1
2
0
1
1
0
1
0
1
1
2
2
0
1
0
1
0
1
1
0
2
2
1
1
0
0
1
0
0
0
2
0
2
1
2
0
2
0
0
1
0
0
2
1
0
0
0
0
0
2
1
1
1
1
0
0
0
0
2
1
0
0
2
1
1
2
0
1
1
0
1
1
2
1
0
0
2
0
0
0
2
0
1
1
1
2
1
1
0
1
0
2
1
0
2
1
0
1
0
1
1
0
1
0
2
1
0
1
1
1
0
0
0
0
0
1
3
1
0
0
2
0
2
1
1
1
1
1
1
0
2
0
2
0
1
0
0
0
2
1
0
1
1
1
1
1
1
0
1
0
1
0
0
0
1
1
2
0
0
0
0
1
0
2
2
1
1
1
0
1
0
1
1
0
0
2
1
1
2
1
1
1
3
1
0
2
1
0
0
1
1
1
2
1
2
1
2
1
1
0
2
0
1
1
1
1
0
1
1
0
1
1
2
1
0
0
1
0
0
0
0
1
1
1
0
2
1
2
3
0
2
1
1
0
1
2
0
2
1
0
2
1
1
0
2
1
0
2
0
2
0
1
0
0
1
0
1
1
2
2
0
2
1
2
2
0
0
0
0
1
1
1
1
2
0
1
0
2
2
2
0
1
1
1
0
0
2
1
0
0
1
0
0
1
2
2
1
1
0
1
2
0
2
0
1
0
0
1
1
0
0
0
2
0
2
1
1
0
1
1
0
0
1
1
0
0
0
3
1
3
0
1
0
0
2
2
2
2
1
1
1
0
0
2
1
2
1
0
1
0
0
0
0
0
0
1
1
0
0
1
3
1
1
1
2
1
2
0
0
2
1
0
1
1
2
1
2
1
1
1
0
0
2
2
1
2
2
1
2
2
0
0
0
1
0
2
1
0
0
2
2
1
1
2
1
1
2
1
0
1
1
2
1
0
0
0
0
1
0
0
1
0
2
0
2
1
0
1
0
0
2
2
1
1
2
2
0
1
0
0
2
0
0
0
0
2
1
2
0
1
1
0
2
2
1
0
1
1
1
1
0
0
1
0
2
0
0
2
0
0
1
0
1
1
1
0
1
0
1
1
1
1
0
1
1
0
1
1
1
1
2
2
1
0
1
1
1
2
1
2
1
1
2
1
1
1
3
2
1
1
0
1
1
1
1
1
0
2
1
2
0
1
0
0
0
1
2
0
0
1
1
1
2
0
0
1
1
2
0
1
0
1
1
0
1
0
0
0
1
2
3
0
1
1
2
0
1
0
2
2
1
1
1
0
1
0
2
1
2
0
0
1
1
0
0
0
2
1
1
1
2
0
0
0
4
1
0
3
2
1
0
2
0
1
0
1
1
1
1
1
2
0
1
2
1
0
1
0
1
1
2
1
2
2
1
1
1
0
2
0
1
1
0
1
1
1
1
1
1
0
0
1
0
1
0
0
1
1
2
2
1
0
1
0
2
0
1
0
1
1
1
1
1
1
1
0
1
0
1
2
2
2
2
2
1
0
1
0
1
0
1
1
1
0
2
0
1
1
0
1
1
1
0
1
0
0
2
2
0
0
1
1
0
2
0
0
1
3
1
1
1
1
1
1
0
1
1
1
2
0
0
1
0
1
1
0
1
1
0
2
3
0
0
0
1
0
1
0
0
1
0
1
0
1
0
1
2
0
0
0
0
0
2
1
0
0
0
2
0
2
2
0
2
1
1
0
1
1
0
1
2
1
0
1
1
5
2
1
0
1
1
0
0
1
2
0
2
0
0
1
1
0
0
0
0
1
2
1
0
0
1
1
1
0
0
1
0
0
1
1
0
1
0
1
0
1
1
1
0
1
2
1
1
2
0
2
0
2
1
2
0
1
0
0
1
1
0
1
0
1
1
1
1
0
1
2
0
1
2
0
1
1
1
1
1
0
2
1
2
1
1
2
1
1
2
1
2
2
0
4
1
0
2
1
1
0
0
0
2
1
0
2
0
1
1
0
1
0
1
0
1
0
1
1
2
2
0
0
0
2
1
0
2
1
0
0
0
1
1
1
1
2
0
1
2
1
0
0
0
2
2
2
0
1
0
0
0
1
0
1
1
1
0
2
0
0
2
0
0
0
2
0
0
1
2
1
4
1
1
0
0
1
1
1
2
0
0
0
3
2
2
0
0
2
1
2
1
0
0
3
1
2
1
0
2
1
2
2
1
2
1
1
1
2
0
0
0
0
0
1
0
2
3
1
0
1
1
2
1
2
0
1
1
0
1
1
0
2
2
0
0
0
1
1
1
1
1
0
0
1
1
1
0
1
0
1
1
2
1
1
1
0
1
2
1
1
1
1
1
0
1
2
1
0
1
0
5
2
2
1
2
2
1
0
0
2
1
0
1
1
0
0
0
1
0
2
0
1
2
0
2
1
0
1
2
1
2
0
0
0
0
1
1
2
1
1
2
1
0
0
1
0
1
2
1
1
1
0
0
1
0
0
0
0
0
1
1
1
0
1
2
2
2
1
0
0
0
2
1
0
0
2
2
1
0
0
1
1
2
0
3
3
1
1
1
1
1
0
0
0
0
1
0
1
1
0
0
1
0
2
0
0
1
0
2
0
0
0
2
2
1
1
1
1
0
1
1
0
1
0
1
0
0
0
1
4
1
0
1
1
1
1
2
0
1
1
0
0
1
1
1
0
0
2
1
2
0
1
1
0
1
2
1
1
1
2
0
2
1
1
0
1
0
1
0
4
2
0
0
1
0
2
1
2
2
1
2
2
1
1
0
2
1
0
0
0
1
1
1
2
1
1
0
1
1
0
0
1
0
2
2
0
1
1
2
2
0
1
2
1
2
1
0
1
2
0
2
2
0
1
1
1
0
0
1
1
1
0
1
0
1
1
0
0
1
0
0
1
0
3
0
1
0
1
0
0
0
0
1
2
1
2
0
1
0
0
0
2
2
0
0
1
2
1
1
0
1
2
0
1
0
2
1
2
2
0
2
1
1
1
0
1
1
0
1
2
2
0
0
2
1
0
1
0
1
2
2
2
0
3
1
2
0
0
1
1
0
1
1
1
1
2
1
1
0
2
2
1
1
1
2
1
1
1
0
2
1
2
0
1
0
1
0
0
1
2
2
0
1
1
1
1
1
1
1
1
2
1
1
0
1
1
0
2
0
1
0
2
1
1
2
0
0
0
2
2
0
0
2
2
2
0
0
0
1
1
0
0
1
1
1
0
2
2
1
0
1
0
0
2
1
0
2
2
1
0
1
2
0
2
0
2
1
1
1
0
0
0
0
1
2
4
1
2
1
0
0
1
1
1
1
2
1
2
1
1
0
0
1
0
0
2
2
0
1
2
1
1
0
1
2
2
0
2
1
2
1
1
2
0
1
0
0
1
1
0
0
2
2
1
1
3
2
0
1
1
1
1
1
2
0
0
0
1
0
0
1
1
0
0
1
1
0
1
0
0
1
0
1
2
2
1
1
0
1
0
2
0
1
1
0
0
0
1
0
1
1
2
0
0
1
0
2
1
1
1
2
1
1
1
0
1
2
0
0
0
2
1
0
1
0
0
0
1
1
1
1
0
1
0
0
2
2
2
0
0
2
2
1
2
1
0
0
2
0
0
1
1
0
1
1
2
1
0
0
1
2
0
0
2
1
2
1
0
0
1
0
0
2
2
0
0
2
0
0
1
0
0
0
0
2
1
2
1
0
2
1
1
2
2
2
0
0
1
2
1
0
1
0
2
0
1
0
1
2
2
1
0
0
0
1
1
0
1
2
1
2
0
0
0
2
0
0
0
0
2
1
0
1
0
1
0
2
0
2
2
0
0
2
2
1
0
0
1
1
1
0
1
1
2
0
1
0
2
1
0
1
0
0
1
2
2
0
0
1
1
1
0
2
1
0
2
1
1
0
0
2
0
0
0
1
1
0
1
0
1
1
2
1
2
1
0
0
0
2
1
1
2
1
0
2
1
0
1
2
0
1
0
0
1
1
1
2
0
2
0
2
1
0
1
2
0
0
0
1
1
2
0
1
1
2
2
2
1
1
0
1
0
2
1
0
1
0
2
1
0
2
4
0
1
3
0
0
1
1
0
0
1
0
0
1
1
1
0
2
1
2
4
1
0
0
1
1
1
2
0
2
0
1
3
1
0
0
0
1
0
0
1
2
0
0
1
1
2
1
0
1
0
1
0
0
2
0
1
1
1
1
0
0
1
2
1
0
1
0
1
0
1
0
1
0
0
1
1
1
1
2
1
0
2
0
2
0
1
1
2
1
0
0
0
1
1
1
1
0
2
1
2
0
2
2
0
1
0
1
1
0
0
0
1
1
2
0
1
1
2
1
1
0
1
0
0
0
2
0
2
1
4
1
0
1
0
2
0
0
3
1
2
2
0
1
0
0
2
0
2
2
2
1
0
2
0
0
0
2
1
2
0
1
0
0
0
1
0
1
0
0
0
2
2
0
1
1
0
0
1
1
0
1
0
0
0
1
1
0
1
2
1
0
0
0
0
2
2
2
0
0
1
2
0
0
0
0
2
1
1
0
1
1
3
0
1
1
1
1
1
1
1
1
1
0
0
0
1
2
2
0
2
1
2
1
1
0
1
0
0
1
0
1
1
0
1
0
1
2
0
1
0
2
1
1
0
0
0
1
2
1
1
0
0
1
0
0
0
1
1
0
2
2
2
0
0
0
0
2
1
0
1
0
2
1
2
0
0
1
1
1
1
0
2
1
2
1
0
1
1
1
0
2
0
1
1
1
1
1
1
2
0
1
0
1
1
1
0
1
3
0
0
0
1
1
0
1
1
1
0
1
0
1
1
2
0
1
0
1
1
0
4
0
2
1
2
1
0
0
1
0
1
0
0
1
2
0
1
1
0
1
0
2
0
1
1
2
0
1
0
1
0
0
2
1
1
2
0
0
0
1
0
1
2
2
2
1
0
0
1
0
0
1
0
2
1
1
1
1
1
0
0
1
0
1
0
1
0
0
1
0
1
0
1
1
0
1
1
2
1
1
0
0
3
0
1
1
0
2
1
0
1
2
1
0
1
0
1
0
1
1
0
0
2
0
1
1
1
0
2
0
0
2
1
1
0
1
1
2
1
1
0
0
1
0
1
1
1
1
0
0
2
1
1
1
1
2
2
1
1
1
1
0
1
2
1
0
1
1
1
0
0
0
2
0
1
2
1
0
1
1
0
1
2
1
0
0
0
1
2
0
1
0
1
1
1
2
2
1
1
0
1
0
1
2
0
2
0
0
1
0
0
0
1
2
1
1
1
1
2
1
0
2
2
0
0
2
0
0
1
1
0
2
1
2
1
0
0
1
1
0
1
0
1
2
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
2
2
2
2
0
0
1
1
0
1
0
1
1
1
2
2
0
0
1
1
0
1
2
0
0
2
0
0
1
1
4
0
1
1
1
2
1
3
0
0
0
1
0
0
0
1
1
1
0
1
1
2
0
1
0
2
0
0
0
2
1
1
0
1
1
1
1
0
0
1
0
2
2
1
1
2
2
1
2
1
1
2
1
2
2
0
0
1
0
2
0
1
2
1
1
2
1
0
1
0
1
1
1
0
2
0
0
2
1
1
0
1
0
2
2
2
1
1
0
0
1
0
2
1
0
1
0
2
0
1
0
2
1
0
0
0
2
0
1
2
1
0
0
2
0
0
0
1
2
1
0
2
0
2
0
1
1
0
1
1
0
0
1
2
1
0
2
0
0
1
2
0
0
2
0
2
1
1
0
1
2
2
1
1
1
0
1
1
1
1
1
1
1
0
0
1
2
1
1
2
1
1
1
1
1
1
0
0
1
1
1
1
3
1
1
1
0
1
0
0
2
1
1
2
1
0
1
2
2
0
0
0
2
1
0
0
1
0
1
1
2
0
1
0
0
3
1
0
1
0
2
1
0
0
0
0
1
0
0
2
0
1
0
1
0
1
2
1
1
1
2
0
0
0
0
2
1
0
2
0
0
1
0
0
2
1
0
2
0
0
0
2
0
1
0
0
1
1
1
1
0
0
2
0
0
1
1
1
0
0
1
1
1
1
0
1
1
0
1
0
1
0
1
1
1
1
1
4
1
0
0
2
0
0
0
0
0
2
1
0
1
1
1
1
1
0
2
2
1
2
0
1
1
0
0
0
0
0
1
0
1
0
1
1
1
1
1
2
0
2
2
0
1
2
0
2
1
0
1
2
0
3
1
2
2
1
1
0
1
2
1
1
1
1
1
1
1
1
1
1
1
2
0
1
0
0
1
1
1
1
0
2
3
0
2
0
1
2
0
0
0
1
2
0
0
1
1
1
1
1
0
2
0
0
0
0
2
1
1
2
0
0
0
2
1
2
1
2
2
0
2
1
0
1
1
2
0
1
2
1
2
1
0
0
0
0
0
0
1
1
0
2
1
2
1
1
1
1
1
3
0
0
1
1
0
0
2
1
2
0
2
2
0
1
0
1
0
0
0
2
0
0
0
4
2
0
2
2
1
0
1
1
2
0
1
0
0
0
1
0
0
2
1
2
2
0
1
0
0
0
0
0
1
1
0
2
1
2
2
0
0
2
2
0
1
1
1
1
0
0
1
0
1
2
1
1
0
2
2
2
2
2
0
1
2
0
1
1
2
1
1
1
1
1
0
2
1
2
0
0
0
1
1
1
0
1
0
0
0
0
1
1
0
2
0
2
0
0
0
0
2
0
0
1
1
0
2
1
1
1
0
2
0
0
0
0
1
0
2
0
0
0
0
1
3
0
2
1
2
3
2
1
0
0
0
0
1
0
2
2
1
0
1
2
0
0
1
1
1
2
2
0
1
0
0
0
3
1
0
0
1
2
0
1
0
1
1
0
1
2
1
0
1
1
0
0
0
0
1
1
1
0
0
0
0
1
0
2
0
1
1
2
2
0
2
2
2
1
1
1
1
0
0
2
1
1
1
1
2
2
2
0
1
1
0
1
1
0
0
0
1
0
0
1
1
0
0
0
1
1
2
2
0
1
2
1
0
0
2
0
2
0
1
1
0
2
0
0
1
1
0
1
2
1
1
2
1
2
1
0
0
0
1
1
1
1
1
2
0
2
1
0
0
0
1
1
1
0
2
2
0
0
0
1
0
2
1
0
0
1
2
1
2
1
1
0
1
1
0
0
2
0
0
0
2
2
2
1
1
1
1
0
0
1
1
1
1
1
1
2
0
0
1
0
2
1
0
1
1
0
0
0
0
1
0
1
0
1
0
0
1
1
0
1
2
0
4
1
0
1
1
2
0
1
0
2
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
2
1
0
2
0
0
1
2
0
1
1
0
1
0
1
2
0
0
0
0
0
0
0
0
0
1
1
3
0
0
0
1
2
1
2
1
2
1
1
2
1
0
0
0
2
1
1
2
1
1
2
0
1
2
0
2
0
0
0
2
1
2
2
2
2
0
0
0
1
2
1
5
0
0
1
0
0
2
0
1
1
1
0
1
2
2
0
0
1
0
1
1
0
0
0
1
2
0
1
0
2
1
0
1
0
0
1
0
0
0
3
0
2
0
1
0
0
2
1
0
1
0
1
0
1
2
0
0
2
1
0
0
1
2
1
1
0
1
1
2
1
2
0
0
1
1
0
2
0
1
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
3
2
2
1
1
1
0
2
1
2
1
2
1
2
2
2
1
0
2
0
1
0
1
1
1
1
2
0
0
1
0
1
0
1
0
0
3
0
1
1
1
2
2
1
0
1
1
0
0
1
0
1
2
0
2
1
1
1
1
0
1
0
0
2
0
1
1
1
0
1
3
0
0
0
1
0
0
1
0
1
0
1
1
0
0
1
0
0
2
0
0
1
1
1
0
0
0
0
0
1
1
0
2
1
2
2
0
1
1
1
1
1
1
1
1
0
0
2
1
3
0
1
1
1
1
0
2
1
1
2
0
2
1
0
1
0
0
1
0
2
1
1
1
0
2
1
0
2
0
2
1
1
0
1
1
4
0
0
0
1
0
1
1
1
2
1
2
0
0
1
0
1
1
2
2
2
0
1
0
2
0
2
0
1
1
1
1
1
0
0
1
0
2
0
1
1
0
0
1
1
1
1
1
0
0
0
0
2
0
2
0
1
2
0
2
0
0
0
0
0
2
1
1
0
0
0
2
0
2
1
2
1
1
1
0
0
0
2
1
1
0
0
0
2
0
0
0
0
1
1
0
1
1
2
0
3
0
0
2
2
1
0
2
2
0
0
0
1
1
2
1
2
2
1
1
1
0
0
2
2
0
0
2
0
1
0
2
2
1
2
1
2
1
3
1
0
1
1
0
2
2
1
0
0
0
1
2
0
1
1
2
1
2
0
0
1
0
2
1
1
0
0
5
0
1
1
1
0
0
0
0
2
1
1
0
0
0
1
0
1
0
1
1
0
1
2
2
1
1
0
0
0
2
0
3
1
1
2
1
0
1
0
0
1
1
0
0
1
0
0
2
1
1
1
1
1
0
0
2
1
1
2
0
1
0
1
1
0
2
2
0
0
0
0
1
2
0
0
1
0
2
0
2
0
0
0
0
2
2
0
1
1
0
2
2
0
1
0
1
1
0
1
1
2
1
1
1
0
1
1
0
1
2
1
2
1
1
2
1
2
1
1
0
2
1
2
2
1
2
1
2
1
1
1
0
0
1
2
0
0
1
1
0
1
0
2
1
0
0
3
0
2
1
0
0
1
0
0
0
1
1
0
2
0
0
0
0
1
1
1
0
0
1
0
1
0
2
0
0
0
1
1
1
0
0
0
1
1
3
0
1
1
2
2
0
1
1
1
0
1
1
0
0
0
1
2
2
2
3
1
0
0
1
0
1
1
1
1
0
2
1
0
2
2
0
2
0
0
3
1
0
2
1
2
0
1
1
0
0
3
0
0
2
1
1
0
0
1
1
0
0
0
1
1
0
1
0
2
1
0
2
2
1
0
0
0
1
1
1
1
1
0
2
1
1
1
1
2
1
0
2
0
2
1
0
2
1
1
1
0
1
0
0
1
0
2
2
2
1
3
1
0
2
1
1
0
0
1
1
0
0
0
2
0
1
0
1
1
2
0
1
1
0
1
2
0
1
1
0
0
0
0
0
0
1
0
0
1
0
1
3
0
0
0
2
2
2
0
2
1
1
0
0
0
2
0
1
1
2
0
2
1
1
1
2
0
2
1
0
0
1
1
1
0
1
0
2
2
2
1
0
1
1
1
1
2
2
0
1
0
2
0
1
1
2
0
2
2
0
1
0
0
0
0
1
1
2
0
1
0
0
0
2
2
0
2
3
2
1
2
0
1
1
1
1
2
1
1
1
0
1
1
0
1
0
1
0
1
2
0
0
0
0
2
1
1
2
0
0
3
2
1
0
0
0
0
2
1
0
1
0
1
2
2
1
1
0
1
0
1
1
1
1
0
2
1
2
1
1
0
1
1
0
2
1
0
2
1
1
0
1
1
2
0
1
1
1
1
2
1
1
1
1
2
1
1
0
1
2
1
1
2
1
2
1
1
1
0
1
0
1
0
0
1
2
0
0
1
1
2
2
0
1
1
1
1
1
1
2
2
2
0
0
1
2
2
1
0
1
0
0
1
1
1
0
1
1
2
0
1
0
1
0
0
1
2
1
1
0
2
0
1
1
0
0
1
1
0
2
1
2
2
0
0
2
0
0
0
1
1
2
2
0
3
1
1
1
0
1
0
2
0
0
0
0
0
1
1
0
0
0
1
1
1
2
1
1
1
1
0
1
1
2
1
1
1
1
0
1
1
0
0
2
0
2
1
0
1
1
0
1
1
0
0
2
0
2
0
1
1
0
2
3
1
2
0
1
2
1
1
0
1
1
2
0
1
0
2
0
2
3
0
0
1
1
3
1
0
1
2
1
2
0
1
1
0
0
0
0
0
1
2
0
1
1
1
1
0
1
1
1
1
1
1
0
0
1
1
2
2
1
2
1
1
0
0
1
0
3
1
0
1
0
2
2
2
1
1
2
2
1
1
0
0
0
1
2
1
1
1
0
1
1
1
0
0
1
2
2
1
1
2
1
1
1
0
0
0
2
2
1
0
1
1
1
1
2
2
0
0
2
2
1
0
0
1
1
2
0
0
2
1
1
1
2
0
1
0
0
0
1
2
1
2
1
0
0
2
1
1
0
0
0
2
1
0
2
2
1
3
2
0
2
0
0
1
2
1
1
2
3
2
1
0
0
1
1
1
1
2
0
2
0
2
1
1
1
1
1
0
1
2
1
1
1
1
1
0
1
1
0
1
3
1
2
0
2
0
1
1
0
1
0
0
0
0
2
0
2
0
1
2
0
2
1
1
0
0
1
0
0
1
0
0
2
2
0
1
2
2
1
0
2
2
1
0
0
1
2
1
2
2
2
2
0
0
0
2
1
1
0
0
2
3
0
0
1
2
1
0
2
0
1
2
0
1
1
1
1
1
1
2
2
1
2
1
1
1
0
0
2
1
0
1
1
2
1
0
0
0
0
2
2
1
2
1
1
0
2
2
1
0
0
1
1
1
1
0
0
1
0
2
1
0
0
0
1
2
1
0
0
0
1
0
2
0
0
1
0
2
0
0
1
1
1
1
1
2
0
2
1
0
5
1
1
1
0
1
0
0
1
0
2
1
1
1
0
0
0
1
1
0
1
1
2
2
1
2
2
1
0
0
1
0
2
1
1
2
0
0
0
3
0
1
1
2
1
0
2
1
4
1
2
1
2
0
1
0
0
2
2
0
0
2
2
0
1
0
2
2
2
1
2
2
0
3
3
1
1
0
0
2
1
0
0
0
2
1
1
2
1
2
1
1
1
1
2
1
0
1
0
1
1
0
3
0
1
1
2
1
0
1
1
2
0
2
2
1
4
4
1
3
1
0
1
0
2
2
0
1
0
2
1
2
1
1
0
2
0
0
0
1
0
0
0
1
0
1
1
1
1
1
1
0
0
3
1
1
1
0
2
1
1
1
0
0
2
2
1
1
0
2
1
1
2
1
0
0
2
1
0
3
1
2
0
1
0
2
0
2
1
2
2
2
0
1
0
1
0
0
0
1
0
1
1
0
1
2
0
1
1
1
0
1
0
1
1
2
0
1
2
1
0
1
2
0
1
1
1
1
2
1
0
3
0
2
1
2
1
2
0
1
1
2
0
1
2
1
0
2
1
1
1
1
1
0
2
1
1
1
1
1
0
2
2
1
1
0
1
2
0
0
1
1
1
1
2
0
2
2
2
1
1
0
1
2
2
1
1
0
0
1
1
0
1
1
0
1
1
0
2
0
0
2
2
2
2
1
1
0
1
1
1
1
1
0
0
1
2
1
0
1
0
0
1
2
1
2
1
1
1
1
2
1
0
2
2
0
2
1
1
0
1
0
0
2
2
0
1
1
0
1
0
1
1
0
1
0
1
0
1
1
1
1
1
2
0
2
1
0
2
1
0
1
1
2
1
0
0
1
2
1
1
0
1
1
2
2
0
1
0
1
1
2
1
0
1
0
1
0
1
2
0
1
0
0
0
2
1
0
1
1
0
0
1
1
2
2
1
1
0
0
0
1
0
0
0
0
0
0
0
4
1
1
1
1
1
1
1
1
0
0
0
0
0
1
0
3
1
2
1
1
2
1
2
0
0
0
2
0
1
1
2
2
2
0
0
2
0
3
0
2
0
0
0
1
0
2
1
0
0
2
0
1
1
1
1
0
1
1
1
0
2
2
2
0
2
2
2
1
1
3
0
2
1
0
0
1
2
0
0
0
1
1
0
2
0
1
1
0
0
0
2
0
0
0
0
0
0
0
1
1
0
2
1
1
1
0
1
2
1
1
0
0
0
0
0
0
1
0
1
1
0
1
2
0
1
1
1
2
1
2
1
1
0
0
1
2
2
0
2
1
0
1
2
0
2
0
0
2
2
0
0
2
1
0
2
1
0
2
0
0
0
1
2
1
1
1
0
0
1
0
1
1
1
1
1
0
0
2
2
0
0
1
1
0
2
2
0
0
0
2
1
2
1
2
1
1
1
0
1
0
0
1
2
1
0
1
2
2
1
1
2
0
1
1
2
2
0
1
2
1
2
1
0
1
0
2
2
0
1
0
2
1
2
1
0
2
0
1
2
1
0
1
2
2
0
1
0
1
1
0
2
0
2
1
2
1
1
0
0
0
1
0
0
0
2
1
2
1
2
1
1
0
2
0
0
2
2
0
0
0
1
0
0
2
0
0
0
1
0
0
1
0
2
3
2
0
1
0
1
1
2
0
0
1
0
2
1
0
1
0
0
1
2
1
1
0
1
0
2
0
0
1
0
0
0
0
1
0
2
1
0
0
0
2
0
1
2
0
1
3
2
1
0
1
1
1
0
1
0
1
1
0
1
0
1
0
2
0
1
1
1
0
2
0
2
2
0
1
2
0
0
0
0
1
2
0
0
0
1
1
0
1
0
0
1
1
0
1
0
1
1
0
2
1
0
0
2
0
2
1
1
1
2
0
1
0
1
1
1
2
1
0
1
1
1
2
1
1
1
1
2
1
0
2
1
0
1
2
1
2
1
0
2
0
1
1
2
3
1
0
0
0
2
0
1
1
0
1
0
2
1
1
1
0
2
1
1
1
0
1
1
2
0
0
1
0
2
0
1
1
0
0
4
0
1
0
2
1
0
2
1
1
1
0
2
0
1
1
1
2
2
1
0
0
0
0
1
1
1
0
0
2
0
2
1
2
0
2
1
1
1
0
1
0
1
1
1
1
2
0
1
0
2
0
2
0
0
1
1
2
0
2
0
0
0
2
1
2
1
1
1
0
0
1
1
0
1
1
0
0
0
1
0
1
0
1
1
1
0
0
0
0
0
2
0
1
1
1
2
1
2
1
0
2
2
1
3
0
0
0
0
1
0
0
1
1
1
2
0
0
1
0
0
1
1
1
0
2
0
0
1
2
2
1
1
0
0
0
1
0
0
0
2
1
0
1
1
1
1
1
2
0
2
0
1
1
1
1
2
1
1
0
2
0
0
0
2
0
1
1
2
1
2
4
0
1
1
1
1
0
0
1
1
0
0
1
1
2
1
0
1
3
1
2
1
0
1
1
1
0
1
1
0
1
1
1
0
1
1
2
0
1
1
1
2
0
1
0
0
1
1
1
0
0
1
1
0
3
2
0
0
1
1
0
1
0
1
2
0
1
1
0
0
1
0
3
0
0
2
1
1
1
2
1
1
0
4
1
2
2
1
1
0
0
0
2
0
0
1
2
2
1
1
2
0
2
1
0
0
2
1
1
0
0
4
1
1
2
1
1
0
2
2
0
1
0
0
2
0
1
0
1
1
1
1
1
0
2
0
1
1
1
1
2
1
0
1
1
1
0
0
2
2
1
0
0
2
1
0
1
1
2
2
0
1
1
1
2
1
0
0
2
2
1
1
1
0
1
0
1
1
1
0
0
1
0
1
1
1
1
1
1
0
0
1
1
1
1
1
2
1
0
2
0
1
3
1
2
0
1
1
0
0
0
1
1
2
0
0
1
2
2
0
1
2
0
1
1
1
0
1
0
0
1
2
1
0
0
1
1
0
1
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
3
1
3
1
1
1
0
2
0
1
0
1
2
0
1
1
0
1
0
1
0
1
0
1
1
0
2
2
0
0
0
2
1
1
0
1
0
1
1
1
1
1
0
0
1
1
0
1
0
1
1
1
0
0
2
0
1
2
0
0
2
1
1
2
1
0
0
0
1
2
1
1
1
1
1
1
1
0
0
1
1
1
1
1
0
0
0
1
0
1
1
0
0
0
2
1
1
0
2
1
3
1
2
0
0
0
2
2
3
0
0
2
1
1
0
2
0
1
0
0
0
0
2
0
2
0
0
1
1
3
0
0
0
2
0
0
1
1
1
0
0
1
1
0
0
1
1
2
0
1
1
0
0
0
1
1
1
0
0
1
0
0
1
3
1
1
0
0
1
0
2
1
1
1
0
1
0
1
1
1
0
1
2
0
2
1
0
0
0
0
0
1
0
0
3
0
0
1
0
1
1
2
1
0
2
1
0
2
0
1
0
0
0
1
1
2
0
1
0
0
0
0
1
2
0
0
2
1
1
0
2
1
0
1
1
1
0
2
0
2
1
0
1
1
0
1
1
2
2
1
0
0
2
1
0
2
1
1
0
1
0
2
0
1
0
0
2
2
2
1
1
0
1
2
2
0
1
0
0
0
1
1
1
1
0
2
1
0
1
1
2
2
0
0
0
0
0
0
0
0
1
0
0
0
2
1
1
0
2
0
0
0
3
1
2
1
1
2
0
0
2
1
1
2
1
2
2
2
1
0
2
1
0
1
0
1
0
1
0
1
0
0
1
2
0
2
1
2
2
1
2
2
0
2
0
0
0
3
1
1
0
2
2
1
2
0
1
0
1
1
0
1
1
2
1
1
1
0
0
1
2
1
2
1
0
1
2
1
0
2
1
1
2
0
0
1
2
0
1
0
0
2
2
0
1
1
2
1
1
0
1
2
2
0
2
1
2
0
0
0
1
1
1
1
2
1
0
1
1
2
1
0
1
1
0
0
2
2
0
1
1
0
1
7
0
2
0
1
0
2
0
1
0
0
1
2
2
1
1
0
1
1
1
1
0
0
0
2
1
2
2
0
1
0
1
0
3
2
1
0
3
2
1
1
1
0
2
0
0
2
1
3
1
1
2
0
1
1
1
0
0
1
1
0
0
0
1
0
1
2
0
1
0
0
0
0
2
0
2
0
1
1
1
0
0
2
2
1
2
0
1
1
0
1
2
1
1
0
1
2
0
0
1
1
1
2
1
2
1
1
2
0
2
1
0
2
2
1
1
1
0
1
1
2
1
1
2
0
0
0
1
1
2
0
1
1
1
1
1
0
2
2
1
1
3
0
0
2
0
1
1
2
1
2
4
0
2
0
1
1
2
0
1
0
1
2
0
0
1
0
0
0
1
1
1
0
2
1
2
1
2
0
0
0
1
2
1
2
0
1
1
2
0
1
1
2
1
1
0
1
1
0
2
4
0
1
2
1
0
1
1
2
1
1
1
1
1
2
1
1
3
0
1
2
2
1
2
2
1
1
0
1
1
1
0
1
1
0
2
0
1
0
2
1
0
1
1
1
1
2
1
1
0
0
1
1
1
2
0
1
1
0
0
1
0
0
0
2
1
2
0
0
1
0
1
0
0
0
2
0
2
1
1
3
2
0
2
2
1
2
0
2
2
1
0
1
4
1
0
1
0
1
1
0
1
0
2
2
2
0
1
1
1
1
0
1
0
0
0
0
0
1
1
1
0
1
1
1
1
0
0
2
1
0
0
2
1
5
1
1
0
0
1
2
1
2
1
2
0
1
0
3
1
0
1
0
1
0
1
1
0
1
0
0
1
0
1
1
1
2
1
0
0
0
1
0
1
1
0
1
2
1
0
0
1
1
0
1
1
1
0
0
0
1
0
0
0
0
2
1
1
0
2
1
2
1
2
0
2
3
2
1
0
1
0
0
1
0
1
0
0
1
1
2
0
0
2
1
1
2
1
1
1
1
0
0
2
2
1
1
2
1
1
1
2
1
0
0
1
0
1
2
1
1
1
1
0
0
0
0
1
1
2
0
1
1
0
0
2
1
2
1
1
0
0
2
2
2
1
1
0
1
0
1
0
1
1
0
0
0
0
1
0
0
0
0
1
1
0
1
1
2
2
2
1
1
0
1
0
0
1
0
1
2
2
1
0
1
0
1
2
1
1
1
1
0
1
1
2
1
1
1
1
1
0
0
2
0
0
0
0
2
0
1
1
1
0
2
1
1
2
1
0
1
1
0
1
1
1
2
1
0
0
2
0
1
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
2
0
1
2
1
1
0
1
1
1
2
1
1
1
0
0
1
1
0
0
2
1
1
0
0
2
2
0
1
2
2
1
0
1
2
0
0
1
2
0
1
1
2
2
1
1
1
0
1
0
1
1
1
0
2
1
1
1
2
0
2
2
2
0
2
1
1
1
2
1
3
0
1
2
0
1
1
0
1
2
1
1
2
0
1
1
1
2
1
0
1
1
0
2
1
2
2
1
1
2
1
0
0
2
2
1
1
1
3
0
1
1
0
2
1
0
1
2
1
2
1
1
1
3
2
2
1
2
0
2
1
2
1
1
1
2
1
4
0
1
1
0
0
0
2
0
0
1
0
0
2
1
0
0
0
1
1
2
1
0
0
1
1
0
0
1
0
0
0
2
0
1
0
2
0
1
1
1
2
0
0
0
1
1
2
2
0
1
1
2
0
0
1
2
1
0
2
0
1
0
0
0
0
1
0
2
1
2
1
1
0
1
1
2
2
2
1
1
1
1
2
0
0
0
2
1
1
0
1
0
1
2
0
1
2
1
1
1
2
1
1
0
0
0
0
1
2
1
1
2
1
1
0
2
1
1
0
0
1
1
1
0
0
0
1
0
1
0
3
1
1
2
2
0
0
1
1
2
1
1
0
2
0
2
1
2
0
0
0
0
1
0
1
1
1
2
0
2
0
0
0
1
1
0
1
1
1
2
0
0
1
2
0
1
2
0
1
0
2
0
2
0
0
2
0
1
0
2
0
1
0
1
1
2
0
2
1
1
2
1
1
0
4
1
0
3
1
1
2
2
1
2
1
1
0
2
1
0
2
1
1
1
2
1
1
1
2
1
0
1
1
2
0
2
1
0
0
1
2
3
0
0
1
2
0
1
1
2
3
0
1
2
2
2
1
0
2
1
0
0
0
2
0
1
0
0
0
0
2
0
1
0
1
0
1
2
1
1
0
2
1
2
1
1
1
1
1
0
1
0
1
0
0
3
2
1
2
0
1
0
1
1
1
2
1
0
0
0
1
1
1
1
1
1
1
0
0
2
0
0
1
0
0
1
2
1
1
1
1
0
2
0
0
1
0
2
2
1
0
2
1
2
2
1
1
2
1
2
1
1
2
1
1
0
0
0
1
0
2
0
0
2
1
0
1
2
1
1
2
0
0
1
0
1
2
0
1
0
1
0
1
1
1
2
2
0
2
0
1
1
1
0
1
2
0
1
1
2
2
0
2
0
1
0
1
1
0
0
2
1
1
1
0
1
2
1
2
0
1
0
2
1
1
1
0
0
0
1
1
1
0
1
1
0
2
1
1
2
0
0
0
1
2
0
1
1
1
2
0
1
1
1
0
1
2
0
0
1
1
1
1
1
1
1
1
1
1
4
1
0
2
0
0
1
2
1
1
2
2
2
1
0
0
1
0
0
1
1
0
0
2
1
2
1
0
0
1
1
0
2
1
1
1
2
0
1
0
0
0
0
1
1
1
1
1
1
0
1
1
2
1
0
0
2
1
0
1
1
0
2
1
1
2
0
0
0
1
2
0
0
1
1
1
1
0
1
1
1
1
1
0
0
0
2
1
1
1
2
0
0
1
0
0
2
1
2
0
2
0
2
2
0
2
2
1
2
1
1
2
0
1
1
1
2
0
1
0
0
0
2
0
3
0
0
0
2
2
1
0
1
1
0
2
2
0
1
2
1
0
1
2
2
1
2
0
1
0
1
1
2
0
2
1
1
1
0
2
1
1
1
2
1
1
1
1
1
1
1
0
1
1
1
0
2
3
1
1
1
1
1
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
1
1
1
2
2
0
1
0
0
0
0
1
0
1
4
2
0
1
1
0
2
2
0
2
0
0
2
2
0
0
0
1
1
1
0
0
0
0
2
1
0
1
1
0
1
2
2
2
0
1
0
1
0
1
0
1
2
0
0
0
1
0
0
1
0
2
1
1
3
0
1
0
1
0
0
0
1
1
1
2
0
2
1
1
0
1
2
0
1
1
1
3
0
0
0
1
1
2
2
2
0
1
0
2
0
0
0
1
1
1
0
1
2
2
0
0
0
0
0
1
1
0
0
1
1
1
1
1
1
1
0
2
1
2
0
1
1
0
0
3
0
0
0
0
0
2
1
2
1
1
0
1
1
1
2
0
1
1
0
0
2
0
1
0
0
2
0
2
6
0
0
1
2
1
1
2
0
1
0
0
2
2
1
1
0
2
0
2
2
0
2
1
1
1
1
1
2
2
0
0
0
0
1
1
0
1
0
1
0
2
1
0
1
0
2
0
1
0
7
0
1
2
0
1
0
1
3
2
1
1
3
1
3
0
2
1
2
1
0
1
2
1
0
0
1
1
1
0
2
1
0
2
1
0
0
2
2
1
1
1
1
1
1
1
1
2
2
1
1
1
0
2
1
2
0
1
0
1
1
0
1
2
1
0
1
1
1
0
0
1
1
0
0
0
1
2
7
1
1
0
1
0
1
0
1
1
0
1
0
1
2
2
0
0
2
0
1
0
1
0
2
1
0
0
1
2
2
0
0
0
0
0
1
1
2
0
2
1
1
2
0
1
0
0
0
4
0
0
2
1
1
0
2
1
0
1
2
0
0
1
1
0
1
1
1
0
2
0
1
0
0
1
2
1
2
0
1
1
2
1
1
1
1
2
2
0
1
0
2
1
2
1
1
1
1
0
1
2
1
1
0
1
1
2
0
1
1
1
2
1
0
1
1
1
0
2
1
2
1
1
1
0
1
2
1
0
1
2
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
1
1
0
0
2
0
0
2
0
2
1
1
1
0
1
1
0
1
0
2
1
1
1
1
1
1
0
1
2
2
0
1
1
0
1
0
2
1
0
1
0
2
2
0
1
1
1
1
1
2
0
0
0
1
1
2
1
2
0
0
1
0
1
2
2
2
2
1
2
1
0
1
2
0
1
2
2
0
0
0
0
2
1
1
2
0
1
0
1
1
0
1
0
2
0
2
0
1
0
1
2
0
2
1
0
0
0
2
0
1
1
1
1
1
2
0
2
0
0
2
1
1
1
0
0
1
2
0
2
0
2
3
1
1
1
2
1
1
1
1
1
0
2
1
0
2
1
2
0
0
1
0
0
0
0
1
0
1
0
1
0
1
0
0
0
1
1
0
2
1
1
1
0
1
0
1
0
1
1
1
0
2
1
0
0
1
0
1
2
0
0
0
2
1
1
2
0
2
2
1
1
0
2
1
0
1
0
0
0
0
2
1
1
0
2
1
1
0
2
2
1
1
0
0
1
1
2
1
2
1
2
2
1
1
2
0
1
2
1
1
1
2
1
1
1
2
1
0
1
1
0
0
1
1
2
2
2
2
1
1
1
0
0
1
0
0
0
0
1
0
0
0
1
0
2
0
2
1
1
1
1
0
0
2
0
2
1
0
1
0
1
1
0
0
2
1
1
0
0
1
1
2
1
2
0
0
1
1
1
0
1
0
1
1
1
1
1
2
0
0
0
1
2
2
0
0
2
0
0
2
0
2
1
1
1
2
3
0
1
2
0
0
1
1
2
1
1
2
1
2
1
0
1
0
1
1
0
1
0
1
1
0
0
0
1
1
1
0
3
2
2
1
0
0
2
0
1
1
0
0
0
2
0
2
0
0
0
0
1
0
1
0
1
1
2
2
2
0
1
0
1
0
0
0
1
1
0
2
0
1
1
0
1
3
1
1
1
1
1
1
1
0
1
0
0
1
0
1
0
1
2
2
1
2
2
0
1
1
0
0
2
2
1
1
2
0
1
2
1
1
0
0
0
1
0
0
2
1
0
1
1
3
0
0
0
1
1
0
1
1
2
0
0
2
0
1
1
2
1
0
2
1
2
0
3
1
2
1
1
1
1
0
2
2
2
1
1
0
2
0
2
0
0
0
2
2
0
1
0
1
1
0
0
1
1
1
1
1
1
0
0
1
0
3
1
1
0
1
0
0
2
1
0
0
0
6
0
1
1
0
2
3
2
2
0
0
1
1
0
1
2
1
1
1
2
1
2
0
1
0
1
0
0
1
0
2
0
2
2
1
0
1
2
2
1
2
0
2
0
2
2
0
1
0
0
0
1
1
1
2
0
1
0
2
2
2
2
1
0
2
0
0
0
1
0
1
2
0
0
1
1
2
1
1
0
2
1
0
2
1
2
1
0
1
1
0
0
1
1
0
2
1
1
1
1
1
0
0
1
1
1
0
1
2
0
1
4
2
0
3
1
1
0
1
0
2
1
0
0
1
0
2
0
2
1
2
0
0
0
0
1
0
1
0
1
0
1
2
1
1
1
1
0
0
0
2
1
0
1
2
0
2
0
1
1
2
0
1
0
1
0
1
2
2
1
1
1
0
1
1
2
1
1
1
0
2
0
0
0
1
0
2
0
1
2
1
0
0
1
1
1
0
1
1
1
0
1
2
2
2
0
2
0
0
2
1
0
0
0
2
1
1
0
2
0
2
2
0
0
0
0
2
1
2
1
2
1
0
0
1
0
2
2
1
2
1
1
1
0
1
1
1
1
1
1
2
2
2
3
1
1
1
3
0
2
1
0
2
1
1
1
1
0
0
1
0
0
1
0
1
1
1
2
2
0
0
0
0
1
2
1
1
1
2
0
1
1
1
1
1
2
0
1
1
0
1
0
0
1
0
1
1
2
0
0
0
2
1
1
3
2
0
2
1
1
1
1
0
4
0
1
0
2
0
1
0
1
1
2
0
4
2
1
1
0
3
0
0
2
2
1
0
0
1
0
1
0
2
2
1
1
0
1
0
2
1
1
1
1
1
2
2
0
0
0
2
1
2
0
1
2
2
1
0
0
3
2
2
0
1
0
1
1
2
0
1
0
2
2
0
1
2
4
1
2
1
1
0
0
1
2
0
1
1
2
1
0
0
0
2
2
0
1
0
1
0
0
2
0
0
0
0
0
1
1
1
1
0
0
1
1
0
1
2
1
0
1
1
1
0
1
2
1
1
2
0
1
2
2
1
2
0
2
0
1
0
2
1
1
1
2
1
1
1
1
1
1
0
1
2
1
0
1
1
4
1
0
2
1
1
1
1
0
1
1
0
1
0
2
1
1
1
0
0
1
1
0
1
1
0
1
1
1
0
0
1
1
0
2
1
0
1
0
2
1
0
0
1
0
2
1
2
2
0
0
1
1
3
0
1
0
1
0
0
0
0
1
1
0
2
0
1
2
0
0
0
0
1
1
2
2
0
1
2
2
0
1
1
1
0
1
1
1
2
1
1
0
2
2
1
0
1
1
1
2
2
0
0
1
1
1
0
1
0
1
1
0
1
1
2
3
1
0
2
1
1
0
0
1
0
1
0
0
0
1
2
1
1
1
1
2
1
1
0
1
0
2
0
1
1
0
2
0
0
2
1
2
2
1
1
2
0
0
0
2
2
2
2
1
2
0
1
1
0
1
1
1
0
1
2
0
0
1
0
1
0
2
1
2
0
0
1
0
1
1
1
0
1
0
0
0
0
1
1
1
0
0
1
2
1
0
1
0
1
2
1
1
2
1
1
1
0
1
0
0
0
0
0
2
2
0
0
1
2
2
2
2
0
0
1
1
1
1
2
0
0
1
1
0
3
1
0
1
1
2
0
1
1
1
1
0
2
1
2
0
2
0
4
1
1
1
0
2
1
2
0
0
1
2
1
0
1
1
1
0
2
1
1
0
0
0
0
1
1
2
1
2
2
0
0
0
1
0
1
1
0
0
1
0
1
1
1
1
0
0
2
1
2
0
1
0
1
1
0
0
1
1
1
2
1
0
1
1
0
1
1
0
0
1
1
1
0
0
2
0
0
1
0
1
1
0
1
1
0
0
2
2
0
0
2
0
2
2
0
0
0
2
1
0
3
0
1
1
0
0
0
2
0
0
0
0
1
1
2
2
1
0
0
2
0
0
1
0
1
0
3
1
0
0
0
2
0
0
3
1
1
0
1
1
2
2
1
1
0
1
0
0
1
1
1
1
1
0
0
1
0
1
1
0
0
1
0
1
0
2
1
3
1
2
0
0
0
1
2
1
0
1
2
0
1
0
1
2
0
3
2
0
1
0
1
0
1
0
2
1
2
0
0
0
2
0
0
1
4
0
1
0
2
3
1
1
1
2
2
0
1
0
0
1
2
0
0
0
0
2
1
2
1
0
1
1
2
0
1
0
1
0
1
2
1
1
2
1
1
2
0
2
0
0
0
2
0
1
0
0
1
0
1
2
0
2
1
0
2
1
2
0
0
2
0
2
1
1
1
1
1
1
0
1
1
1
2
0
0
1
0
2
0
0
1
2
1
0
1
1
1
1
0
0
0
2
2
1
2
1
0
0
1
1
0
0
0
0
0
0
1
2
1
2
2
2
1
1
0
1
0
2
1
1
1
1
1
0
2
2
1
0
1
1
1
2
2
2
1
1
1
2
0
1
1
1
1
2
3
0
0
1
1
0
0
1
2
1
1
0
1
1
0
1
2
0
0
0
0
1
1
0
1
0
1
2
0
1
2
0
2
1
0
0
2
2
1
1
1
0
1
2
0
0
0
0
1
2
0
2
1
0
2
0
2
0
0
1
1
0
1
0
1
1
0
0
1
0
1
1
0
1
2
0
0
1
2
1
0
0
0
1
1
0
1
1
1
0
1
1
0
1
1
0
1
2
0
2
1
2
0
1
1
0
0
1
1
2
0
2
2
0
0
2
0
0
1
2
0
1
0
1
0
2
2
2
2
1
1
0
1
1
1
1
1
1
4
0
1
1
0
0
1
1
0
0
0
0
4
0
0
1
1
1
1
1
1
0
2
1
0
1
0
0
0
1
0
1
0
0
2
1
2
0
0
2
0
1
0
1
0
1
2
1
1
2
2
2
1
0
0
0
2
1
0
0
0
1
1
2
0
0
1
0
1
1
0
1
2
0
2
1
3
0
8
1
2
0
0
0
2
1
0
0
0
0
1
1
1
1
2
1
1
2
0
1
0
1
1
2
0
0
1
1
0
1
1
0
0
1
1
0
1
2
1
1
0
2
1
1
0
2
5
2
1
2
1
1
2
1
0
2
0
0
2
0
2
1
0
0
2
1
1
0
1
1
1
1
2
1
0
1
0
0
0
1
0
1
0
0
1
2
4
1
0
2
2
1
0
0
1
1
1
0
1
0
0
0
1
0
0
2
2
0
2
0
0
1
0
0
1
1
0
2
0
1
1
1
0
1
2
2
0
1
1
0
0
1
1
4
1
0
0
0
1
0
0
1
2
2
1
2
0
2
2
0
0
1
1
1
1
1
0
0
2
0
2
0
0
0
2
1
0
2
0
1
2
2
1
1
2
1
2
1
0
2
0
1
1
1
1
2
0
2
1
1
1
1
1
0
1
0
1
1
1
1
1
1
0
2
0
1
1
1
1
1
1
1
2
4
0
0
0
1
1
1
1
0
0
1
2
1
0
0
0
2
2
1
2
2
1
0
2
1
2
0
2
0
1
2
1
1
1
1
0
1
0
1
0
1
2
0
0
2
0
1
0
2
0
1
2
1
0
0
1
1
0
0
0
0
2
2
1
1
1
2
1
2
0
0
1
0
0
0
1
1
0
2
0
1
1
1
0
1
1
0
1
2
1
0
1
0
2
0
1
1
0
0
1
1
3
0
1
2
1
1
0
2
0
1
2
0
2
1
2
1
1
0
1
0
2
1
0
0
1
2
0
1
2
0
1
2
0
0
2
1
1
0
2
2
0
1
1
1
0
2
2
2
1
1
1
2
0
0
0
0
1
2
2
0
3
1
1
2
2
2
2
0
0
0
0
1
0
1
0
0
1
1
1
3
1
1
0
0
1
3
1
1
1
1
1
2
1
1
1
0
0
2
0
0
1
1
1
0
1
0
1
2
0
1
1
0
1
0
0
0
0
0
1
1
1
1
1
0
1
0
1
0
3
0
8
0
1
0
1
2
0
0
2
1
0
1
1
1
1
0
1
2
0
2
2
0
0
0
1
0
1
2
1
0
0
2
0
0
0
1
1
1
1
1
1
0
1
2
1
2
1
0
1
1
0
0
2
0
0
1
2
0
2
1
0
1
1
1
0
2
0
0
1
2
0
0
2
0
2
0
1
3
2
1
0
0
1
2
0
1
1
1
1
3
0
1
1
0
1
0
1
1
0
0
1
1
2
0
1
1
0
0
1
1
3
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
2
1
0
1
0
1
1
1
1
1
1
1
0
2
1
1
1
0
0
1
0
1
1
0
2
2
0
2
1
1
1
1
2
1
1
1
2
0
0
0
2
0
0
0
2
0
1
2
2
1
1
1
2
1
1
1
0
0
2
1
1
0
0
0
1
1
1
2
0
0
1
0
1
1
2
1
2
0
1
1
0
1
2
0
1
2
1
0
0
0
2
0
1
1
0
0
0
0
0
1
1
1
1
2
2
0
1
2
1
0
3
1
0
1
0
0
0
1
1
2
0
2
0
0
2
0
0
0
1
0
3
1
1
0
2
1
0
2
1
2
0
0
1
0
1
2
0
1
0
1
0
0
0
0
1
0
1
2
2
0
2
0
0
0
0
2
1
2
0
2
1
1
2
2
1
1
1
1
0
2
0
1
0
1
0
0
1
0
1
1
1
1
2
0
0
2
0
1
0
1
0
1
0
1
0
1
1
0
0
1
2
0
1
2
0
0
0
0
0
0
0
1
1
1
0
1
1
0
2
0
2
1
0
2
0
2
2
1
1
0
1
1
1
3
1
2
1
0
2
1
0
0
1
0
1
1
1
0
2
1
2
2
0
2
1
0
1
0
1
1
5
1
1
0
0
0
0
1
1
2
0
0
0
1
2
0
1
1
1
1
0
2
0
2
1
2
1
1
0
1
0
1
1
1
2
0
0
1
3
1
1
0
0
1
0
1
0
1
0
1
1
2
1
0
0
0
0
2
2
0
1
0
1
2
0
0
0
0
1
0
1
2
1
0
0
1
0
2
1
0
1
1
0
2
1
2
1
1
1
0
1
0
2
1
2
1
2
0
1
0
2
1
1
0
0
0
1
0
0
0
0
0
0
0
0
2
2
2
2
2
0
0
1
1
1
2
1
1
0
1
0
1
2
0
0
1
0
2
1
0
2
0
2
0
2
0
1
2
1
0
2
0
1
1
0
0
0
0
0
1
4
1
2
1
0
1
1
1
1
2
1
1
1
0
0
2
3
3
1
2
2
2
2
0
3
0
1
0
0
1
1
1
2
1
1
1
0
0
0
0
1
1
0
0
0
0
0
1
2
1
3
1
1
0
1
1
1
1
2
1
1
0
1
1
1
0
1
1
1
0
1
1
1
2
0
0
1
0
0
1
0
2
0
2
0
2
0
1
1
1
1
0
1
1
0
0
1
1
0
3
1
1
0
0
1
1
2
1
0
1
0
2
1
2
1
1
0
0
1
2
2
1
2
0
1
1
0
2
0
2
0
1
1
1
1
1
0
0
1
0
0
0
0
0
0
1
0
1
0
5
0
2
1
1
1
2
1
0
1
0
8
0
1
2
1
2
0
0
1
1
0
0
2
0
1
1
0
1
2
2
0
1
2
1
1
0
0
0
2
0
0
2
2
1
1
0
0
1
0
1
2
1
1
1
0
0
0
2
1
0
2
1
0
0
0
0
0
0
2
0
1
0
2
0
1
0
0
0
0
0
0
2
0
0
1
2
2
0
1
1
0
1
1
0
0
1
2
2
2
1
2
0
2
0
1
1
0
1
2
0
1
1
2
0
0
1
2
2
1
2
1
1
0
0
3
0
2
1
2
1
0
0
1
1
2
3
0
2
1
1
2
1
1
0
0
1
2
0
1
0
0
2
1
1
1
1
0
0
1
0
3
0
0
1
1
0
2
2
2
0
1
2
2
0
1
2
2
1
2
0
2
0
1
1
0
2
0
1
0
2
0
2
0
2
0
1
0
0
2
0
0
0
0
1
0
0
1
2
1
0
1
2
1
0
1
0
1
1
1
0
1
1
2
1
0
0
2
1
1
0
1
0
1
1
1
2
2
2
2
1
0
1
0
1
2
0
2
0
0
2
2
0
1
0
2
1
1
0
0
0
0
2
0
0
0
2
0
2
1
0
0
2
1
1
1
2
0
0
1
1
0
0
0
0
0
1
0
0
2
2
1
1
1
0
1
1
1
1
1
0
1
0
1
1
3
0
0
2
1
1
2
1
2
0
0
1
1
0
2
0
2
0
1
1
0
0
1
0
1
0
1
0
0
1
0
2
2
2
1
0
1
1
1
1
1
1
1
2
1
1
0
2
0
2
1
1
2
2
2
0
1
2
1
0
0
1
0
0
1
1
1
2
0
1
2
0
1
1
2
1
1
0
2
1
0
1
2
1
1
1
2
1
1
1
1
1
0
1
2
1
1
1
0
2
0
1
3
0
1
0
1
1
0
1
1
0
2
2
1
0
0
1
2
1
0
0
1
2
1
0
1
1
0
0
1
2
1
1
2
1
0
1
0
1
0
2
2
2
0
0
1
0
0
1
2
1
1
1
1
0
1
1
1
0
1
1
1
1
1
2
1
1
0
0
0
1
1
2
0
2
2
1
1
1
1
2
2
0
0
1
0
0
1
1
1
0
1
0
1
0
2
0
1
0
0
0
0
0
1
0
1
2
2
0
1
0
1
2
0
0
0
0
1
0
0
2
2
1
0
1
1
0
1
2
0
0
1
0
0
0
0
0
1
0
0
0
1
1
1
2
0
2
0
2
0
0
0
1
0
1
1
1
1
1
1
1
2
1
1
1
1
2
2
0
1
1
0
1
0
2
2
1
3
0
2
3
0
1
1
1
2
2
1
1
1
0
1
1
0
2
1
1
0
0
1
1
1
0
1
1
1
1
1
0
1
1
2
0
1
0
2
1
0
2
1
0
0
1
0
2
1
3
0
1
1
2
1
0
1
0
0
1
1
0
1
1
1
2
1
0
2
1
0
0
2
0
1
2
0
0
1
0
1
2
1
2
0
1
1
1
4
0
1
0
1
2
2
0
2
0
0
1
1
1
0
0
2
0
1
2
0
0
0
1
0
2
0
2
0
2
4
0
0
0
1
0
1
1
1
2
0
1
2
0
0
1
1
2
1
2
0
1
1
0
1
0
0
1
2
1
1
0
2
0
0
3
2
0
1
1
1
0
1
1
1
2
1
2
2
3
2
2
1
2
1
2
1
0
0
0
2
0
1
0
1
0
1
1
1
2
1
2
2
2
2
2
1
2
0
1
1
2
1
1
0
2
1
1
0
2
0
1
2
0
1
0
0
0
0
0
1
1
0
0
2
0
2
2
1
1
0
1
2
0
0
1
0
0
2
1
1
0
1
0
2
1
0
0
0
0
1
0
0
0
1
0
1
0
1
1
0
1
0
2
2
3
0
2
2
1
0
1
0
1
2
2
0
0
0
1
2
0
0
1
1
1
2
2
0
1
1
1
0
0
2
1
0
1
1
2
2
2
2
0
1
1
0
1
0
1
2
2
1
1
2
1
1
0
1
0
1
0
0
2
1
0
0
1
2
0
0
1
0
1
1
1
1
1
0
0
0
0
1
1
1
2
1
2
1
0
0
2
1
1
0
0
0
0
0
0
2
0
2
1
2
3
1
2
0
2
1
1
1
1
0
1
1
2
1
1
1
0
0
2
1
0
2
1
1
1
1
2
2
1
0
2
3
0
0
1
1
1
1
1
1
1
2
1
1
2
1
1
1
1
1
1
2
1
0
2
2
1
1
2
1
0
0
1
0
1
1
1
0
0
1
2
0
0
1
0
2
1
0
1
1
1
0
1
0
0
1
0
2
0
0
1
1
0
0
1
2
1
1
1
0
1
1
2
0
1
1
2
0
0
2
2
2
1
0
2
2
2
2
1
0
1
1
1
2
0
0
1
2
1
0
2
1
2
1
1
0
1
1
2
1
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
2
1
0
2
1
0
0
1
1
1
2
0
1
3
0
0
1
2
2
1
2
1
1
0
1
0
0
1
1
0
0
0
2
2
1
1
1
0
0
1
0
2
1
1
2
0
0
2
1
2
1
0
1
1
1
0
4
2
0
1
0
1
0
0
0
1
0
2
1
2
0
0
1
0
2
0
0
0
0
0
1
1
3
1
1
1
2
1
1
2
2
1
0
0
1
1
2
2
1
0
0
2
1
0
1
1
0
0
0
0
0
1
0
1
0
1
0
0
1
0
3
0
1
2
1
0
1
0
1
0
1
0
1
2
0
0
1
0
1
0
0
1
1
2
2
1
0
1
0
2
2
1
1
0
2
0
0
0
1
0
1
1
1
1
1
2
2
2
0
2
2
0
1
0
2
1
2
1
1
0
1
0
2
0
1
2
0
1
1
2
2
1
0
1
0
1
2
0
2
2
0
1
2
0
1
2
1
1
1
0
0
1
1
0
2
0
1
1
2
2
0
0
0
1
0
0
1
1
0
0
0
0
1
2
2
2
1
1
2
0
2
1
0
0
1
0
2
0
0
1
0
1
2
0
1
2
0
0
2
1
3
0
1
1
1
1
0
0
1
0
2
1
1
0
1
0
1
0
1
0
1
0
0
0
0
0
0
1
0
1
2
0
0
2
1
1
2
1
3
0
1
1
0
2
2
0
1
2
1
2
0
2
2
1
0
1
2
0
1
1
1
1
0
0
0
1
0
0
1
0
1
0
2
0
1
1
1
0
1
1
2
1
1
1
2
0
0
1
0
2
1
0
2
2
1
1
0
0
1
0
1
0
1
0
1
0
1
1
1
0
1
0
1
2
0
2
1
2
1
0
0
1
15
1
0
0
1
0
1
3
0
2
0
1
0
0
0
0
1
0
2
0
1
0
1
2
0
1
1
0
0
1
2
1
1
3
1
1
1
2
2
0
0
1
1
1
0
2
2
2
1
0
1
1
1
0
1
1
1
1
1
1
1
0
2
2
0
1
1
2
0
1
1
0
1
2
1
1
0
0
0
1
0
1
2
1
1
0
1
2
1
0
1
0
1
1
1
1
2
0
2
1
0
0
1
1
0
2
1
0
1
0
0
2
1
2
1
2
1
1
2
2
0
2
0
0
1
1
1
1
2
1
0
1
0
1
0
0
1
0
1
2
0
0
0
0
0
0
1
1
0
1
1
0
2
0
1
1
1
0
1
0
2
2
1
1
0
0
2
0
1
0
2
0
0
0
1
2
2
0
1
1
0
0
1
1
1
1
1
1
1
1
2
1
0
0
1
0
0
2
2
0
1
0
2
1
0
1
0
1
1
2
1
1
1
3
0
0
1
1
0
2
0
2
2
1
0
2
2
0
0
0
1
0
1
1
2
0
1
0
1
1
0
2
1
1
0
2
0
1
2
2
4
0
2
1
1
1
0
0
2
1
0
1
1
0
0
0
2
0
1
0
1
0
0
1
1
0
1
2
2
0
0
1
1
0
0
0
2
0
0
1
1
2
1
2
1
0
2
0
0
1
2
1
2
2
4
2
0
1
1
1
2
0
0
2
1
0
1
1
0
1
1
0
1
2
2
1
0
0
1
2
0
0
1
1
0
1
1
0
1
1
3
0
1
0
2
1
0
2
2
1
0
1
0
0
0
1
0
0
1
1
1
1
0
0
0
1
2
2
0
0
0
2
2
2
1
1
1
0
2
2
1
1
1
1
0
1
0
0
2
0
1
1
0
1
1
2
1
0
1
3
0
0
1
0
1
1
0
1
0
0
0
1
1
1
1
0
0
2
0
0
0
1
0
1
2
0
1
1
1
1
2
0
0
1
3
0
1
1
2
0
2
0
1
1
0
1
1
1
0
0
1
2
0
1
1
2
0
0
1
1
0
2
0
1
1
0
0
0
1
0
0
3
0
0
0
2
1
2
1
1
1
1
1
2
1
2
0
0
1
1
0
4
1
0
1
1
0
1
0
0
2
1
1
0
0
1
0
1
0
2
1
1
0
1
1
0
2
0
1
0
0
1
0
0
0
2
1
2
0
2
1
2
2
1
1
2
0
1
0
0
2
1
0
2
0
1
1
2
0
0
1
1
0
0
0
2
0
1
2
1
1
1
0
1
0
0
0
0
1
0
2
2
1
1
2
2
0
2
1
0
0
1
2
2
0
0
1
1
1
1
1
0
1
1
0
2
0
0
0
2
1
0
3
1
0
0
3
0
0
2
0
1
0
0
1
0
0
2
0
1
2
0
1
1
1
1
2
1
1
1
0
1
2
2
2
2
1
0
0
0
1
0
0
1
0
0
2
2
3
0
1
0
2
2
2
2
1
0
2
0
1
2
3
1
1
1
1
1
1
2
1
1
0
0
0
0
0
1
2
0
1
0
0
2
1
1
0
1
1
0
1
0
1
1
1
1
2
0
0
2
0
1
2
0
2
2
0
2
0
1
0
0
1
1
0
0
3
0
1
0
2
0
2
1
0
1
1
0
0
0
0
2
0
2
1
2
1
1
0
0
1
2
1
1
1
1
0
0
0
1
1
0
2
0
2
0
1
0
0
0
1
0
2
0
1
2
0
1
3
0
0
0
0
0
2
1
0
2
1
0
1
2
1
0
1
0
1
1
0
1
0
0
0
2
1
1
1
0
1
0
2
1
0
2
1
0
0
1
2
0
2
0
1
1
0
0
1
0
2
2
1
0
1
1
2
1
1
0
1
1
1
2
1
1
1
0
2
0
1
1
2
1
2
1
2
2
0
0
2
1
1
0
1
0
0
1
1
1
0
1
0
2
0
0
1
1
1
2
0
1
0
2
0
0
1
1
1
1
1
1
2
1
0
0
2
0
1
0
0
1
1
2
1
1
2
1
1
0
1
0
1
1
0
1
0
1
1
0
0
0
1
0
1
1
2
1
1
1
0
2
2
1
0
1
1
2
0
0
1
0
2
1
0
1
2
0
0
1
0
0
2
0
1
2
0
2
1
1
1
0
0
1
0
2
0
0
0
1
1
1
0
0
1
0
2
0
0
0
0
1
0
1
0
2
2
1
0
1
1
1
2
0
1
0
0
1
0
0
2
2
1
0
1
1
1
0
1
2
1
2
2
1
2
0
1
0
1
0
1
1
1
0
3
1
2
0
0
1
1
1
2
1
0
0
0
0
1
0
0
0
0
0
0
1
1
2
2
0
0
1
2
2
2
0
2
2
0
2
2
0
2
1
0
0
0
1
1
1
0
0
1
0
2
1
1
1
0
1
0
0
2
2
1
2
2
1
1
2
0
0
0
0
1
1
0
1
2
3
0
2
0
1
2
2
1
0
1
0
0
1
1
1
0
0
1
0
0
1
2
1
0
0
0
1
1
0
1
1
1
1
0
0
2
1
2
2
2
1
2
1
2
1
1
2
1
2
1
0
1
0
1
0
0
0
1
1
0
1
1
0
0
2
2
0
1
2
1
2
1
1
2
1
2
1
2
1
1
1
1
1
1
0
2
0
0
1
2
1
1
1
1
1
2
0
1
3
1
2
0
0
2
2
1
1
1
1
0
1
1
1
0
2
2
1
1
1
1
0
1
0
2
3
1
3
1
1
0
0
1
0
1
1
0
2
0
1
0
2
0
2
1
2
2
0
2
0
1
0
1
0
0
1
1
1
0
0
1
2
2
0
0
2
1
2
1
3
1
0
2
2
0
0
2
1
0
0
0
1
1
1
1
1
0
0
2
2
1
0
1
0
1
1
1
1
1
0
0
2
1
0
1
1
2
0
1
2
1
2
2
1
0
1
1
2
1
1
0
0
1
0
0
0
1
1
1
2
0
1
2
0
1
0
2
0
0
2
2
0
2
2
0
1
0
0
1
0
1
0
1
1
1
2
1
1
1
0
1
1
1
0
1
1
2
1
1
0
0
1
2
1
0
1
1
0
1
1
2
0
0
0
3
0
0
2
1
1
1
1
1
2
0
0
2
2
1
0
1
1
0
0
2
1
2
1
2
1
2
1
1
2
0
0
1
0
2
0
2
1
1
0
1
2
1
0
1
2
0
1
1
2
0
0
2
0
0
2
1
1
1
1
1
2
1
2
2
0
1
0
2
0
1
2
1
1
2
2
0
1
3
2
0
2
2
1
2
2
1
1
0
0
0
2
1
1
1
1
2
0
2
1
2
0
0
1
0
1
1
1
1
0
1
0
2
0
2
1
0
0
2
2
1
2
0
1
1
1
1
0
0
2
0
0
1
0
2
2
1
0
1
0
2
1
2
0
1
2
1
1
1
3
0
0
1
0
2
2
2
2
2
1
1
1
2
1
1
1
2
1
1
1
1
2
2
0
1
1
0
0
0
0
2
2
1
2
1
0
1
1
1
1
1
1
1
2
2
0
0
2
1
1
0
0
2
0
1
1
0
1
1
1
0
2
1
2
0
2
0
1
2
1
1
1
2
1
0
1
1
0
0
0
1
0
2
0
0
0
0
1
1
1
1
0
2
1
0
2
3
2
2
1
2
0
2
1
1
1
1
1
1
0
1
1
2
1
0
2
2
0
1
2
1
0
2
2
0
1
0
1
1
1
2
0
1
0
1
1
2
1
0
1
0
0
0
0
1
1
1
1
3
0
2
1
2
1
0
0
2
0
1
0
1
1
2
0
0
0
0
0
1
2
0
0
1
0
1
0
0
1
1
0
1
0
0
0
1
1
1
2
0
0
1
1
0
1
0
0
1
1
1
0
1
2
0
2
2
3
1
0
1
2
0
0
0
2
2
1
0
1
0
0
1
2
0
1
0
2
1
1
0
2
0
1
0
0
1
0
0
0
1
1
0
0
0
2
1
0
2
1
1
2
0
0
0
1
1
1
0
1
0
0
1
0
0
1
2
0
2
2
0
0
2
0
1
1
1
1
1
1
1
0
1
0
1
1
1
1
1
0
1
0
2
0
0
0
2
1
0
1
1
2
4
1
0
7
1
1
0
1
1
1
1
0
0
1
0
1
1
1
3
2
0
2
2
1
0
1
4
1
1
1
0
0
0
0
2
1
1
1
0
1
0
0
0
1
2
0
2
2
1
2
0
1
1
2
1
0
1
1
0
1
2
0
4
0
0
1
1
0
1
1
1
1
2
0
2
2
0
1
2
2
3
2
2
2
1
2
1
0
0
0
1
0
0
0
1
1
1
1
0
1
2
0
0
0
0
2
1
0
1
0
0
1
0
1
2
0
2
1
2
1
0
2
2
0
1
0
2
2
2
0
0
0
0
1
0
1
0
0
1
1
1
1
0
0
0
3
1
2
0
1
2
1
0
2
0
1
0
0
0
0
0
0
1
0
1
1
2
1
0
0
2
2
3
1
3
0
0
0
0
2
1
0
0
1
0
1
1
0
1
1
1
4
0
0
1
2
1
0
2
1
2
1
2
0
1
0
2
1
1
0
2
1
2
1
0
1
1
0
0
1
2
0
0
0
0
0
2
0
0
1
0
1
2
1
1
1
0
0
1
1
2
3
2
2
1
0
1
2
0
1
1
0
0
2
2
1
0
1
1
0
1
1
2
1
1
0
2
0
0
1
0
0
1
0
1
1
0
1
1
2
0
2
1
1
1
2
0
0
1
1
0
1
1
0
1
0
1
2
0
1
0
0
2
0
2
3
0
0
1
1
1
2
1
1
1
1
1
1
0
0
1
2
2
0
1
0
2
0
2
0
2
1
1
0
1
1
1
1
0
2
1
0
1
2
2
0
1
0
1
2
1
0
2
2
4
1
0
1
2
1
1
2
0
1
2
1
0
1
1
2
2
0
1
2
2
0
0
0
0
1
0
1
1
0
1
1
1
2
0
3
0
0
2
0
2
0
1
0
0
1
2
2
0
0
1
1
2
0
1
0
0
2
2
0
1
1
2
1
1
0
0
0
2
2
1
2
0
2
2
0
2
0
1
1
0
0
0
0
0
2
1
0
0
1
1
0
1
1
0
0
1
3
0
2
1
1
1
0
1
2
1
1
0
0
1
1
0
1
2
0
1
0
2
0
1
1
0
1
0
1
1
1
1
0
2
0
1
0
1
0
2
2
0
1
1
1
1
0
0
1
0
0
0
0
0
1
1
1
0
0
0
1
1
1
0
2
1
6
1
2
0
1
1
1
1
0
1
2
2
2
1
0
0
1
6
1
1
2
1
1
2
1
1
0
1
0
2
1
2
1
1
2
0
1
0
4
0
0
1
2
2
2
0
1
2
2
0
1
0
1
1
0
2
0
0
0
1
1
1
2
2
1
1
0
0
1
0
0
1
0
0
0
0
2
2
3
0
1
1
1
0
1
1
1
1
2
0
1
0
0
0
1
0
1
1
1
0
0
0
1
1
2
1
1
2
0
2
1
2
2
1
1
1
1
0
0
1
2
1
2
1
2
1
3
1
0
1
1
1
1
2
2
1
1
2
1
1
1
1
1
2
1
0
1
2
2
1
1
0
1
1
2
1
1
1
1
2
1
2
0
0
1
0
0
1
0
0
0
0
0
1
0
0
2
0
1
0
2
1
2
2
0
2
0
0
0
1
1
3
2
1
0
0
0
1
0
0
1
0
0
2
0
0
0
0
1
2
0
2
1
1
1
1
2
0
1
0
1
0
0
0
1
1
1
0
0
0
2
2
1
1
1
1
1
1
1
1
1
0
1
0
2
2
0
0
1
1
1
1
1
1
1
2
0
0
2
1
1
1
1
0
1
0
0
1
1
2
2
0
0
1
0
0
1
0
2
1
2
1
0
1
2
2
0
1
1
0
1
2
2
0
1
2
2
0
2
0
0
0
0
2
2
2
2
0
1
0
2
1
2
1
1
0
0
0
1
2
0
1
0
0
2
0
0
1
2
0
2
1
1
0
0
0
0
2
1
1
0
0
0
2
0
1
0
1
2
1
2
0
0
2
2
1
0
2
0
1
1
1
1
1
1
0
1
1
0
2
2
1
3
0
2
0
0
1
3
1
2
0
2
1
1
0
1
2
1
0
1
1
1
1
2
0
1
1
1
2
1
1
1
1
0
0
1
1
0
1
0
0
2
0
1
1
1
1
1
4
0
1
1
0
1
0
1
1
0
0
0
1
2
0
0
0
0
2
0
1
1
1
1
1
2
0
2
1
2
2
0
1
2
0
2
1
1
1
1
2
0
0
0
0
0
0
0
1
0
0
1
0
1
0
2
1
5
0
2
0
0
1
0
0
0
0
2
1
0
1
1
0
2
0
1
0
0
0
0
1
1
2
1
2
0
1
1
0
0
0
1
0
2
0
0
0
1
1
1
0
0
1
0
0
1
1
0
1
0
2
1
0
0
0
0
0
1
1
1
1
0
1
1
0
2
0
0
1
1
1
1
2
0
1
0
1
0
1
1
0
1
0
1
0
1
0
2
2
0
1
0
0
1
0
0
1
1
0
1
1
2
2
0
2
1
1
0
2
1
0
2
2
0
2
1
1
2
0
0
1
1
0
2
2
0
0
2
0
0
0
0
1
0
0
0
2
1
2
2
1
0
7
1
2
0
0
1
2
2
0
0
1
0
1
1
0
1
1
2
0
0
0
0
1
1
2
0
2
1
2
0
1
1
1
1
1
2
1
0
0
2
0
1
1
2
2
1
1
0
0
0
1
2
0
1
1
2
2
0
0
0
2
2
1
0
0
1
1
1
2
1
2
1
0
1
1
0
0
1
0
0
2
0
0
0
0
1
0
1
0
0
0
1
1
0
0
1
0
1
1
1
1
2
3
2
0
1
0
0
2
2
1
2
0
2
1
1
0
2
0
1
1
2
4
1
1
2
0
1
0
0
1
0
1
0
2
1
0
0
1
1
0
1
1
2
1
1
0
1
0
0
1
0
1
2
1
0
2
2
1
2
1
0
0
0
2
1
0
0
0
0
2
1
0
4
2
1
0
0
2
2
1
0
0
1
0
1
0
0
0
1
0
0
1
1
1
0
1
0
1
0
0
2
0
0
0
0
2
2
1
0
0
2
1
1
1
0
2
0
2
1
0
2
2
0
2
1
0
2
1
0
0
0
1
0
0
2
0
0
1
1
1
0
1
0
1
0
0
0
1
1
2
1
2
1
1
1
1
1
3
1
2
2
1
0
0
2
2
1
0
1
2
0
1
0
0
1
3
1
0
1
0
2
1
0
1
2
2
0
1
0
0
1
1
1
0
1
1
2
1
1
0
1
1
0
1
1
1
1
0
0
0
1
1
0
0
2
1
1
3
0
0
2
0
0
0
0
0
2
1
1
2
0
0
2
1
0
1
0
1
0
1
1
1
1
0
1
0
1
2
0
1
1
0
1
0
1
2
1
0
1
2
0
1
1
0
3
1
1
0
1
2
1
1
1
0
1
1
1
1
2
0
0
2
0
0
1
1
1
0
1
0
2
1
1
0
0
2
1
0
2
0
0
1
4
1
0
1
2
0
0
1
1
2
1
2
0
0
1
2
2
1
1
2
0
1
0
0
1
2
1
1
1
1
1
0
0
2
1
2
1
0
0
1
0
0
0
0
0
3
1
1
2
0
0
0
1
0
1
2
1
0
1
0
1
2
2
1
1
1
2
1
0
1
2
0
1
1
1
1
2
2
1
2
0
0
0
0
1
1
2
1
1
0
1
1
0
2
1
3
0
1
0
2
0
0
1
2
0
2
2
2
1
0
0
1
1
2
0
0
2
0
1
0
0
0
2
0
1
0
3
1
2
0
1
1
2
2
2
0
0
1
1
1
0
1
0
1
1
2
0
0
2
0
1
0
1
1
1
1
1
0
2
0
1
0
0
1
1
2
1
3
1
1
3
0
1
0
1
0
2
0
2
0
2
1
1
1
1
2
1
0
1
2
2
1
0
1
1
0
1
1
1
0
1
2
0
1
0
1
0
1
0
1
1
0
2
0
1
1
1
1
1
1
0
1
2
0
1
1
1
1
2
0
0
0
0
1
2
2
0
0
0
0
0
2
0
0
2
2
1
0
1
0
0
2
1
0
0
1
0
0
1
1
2
0
0
0
0
0
1
1
2
0
1
0
2
1
1
0
0
1
1
0
1
2
1
1
1
1
0
1
0
1
2
0
2
1
1
1
1
2
2
2
1
0
0
2
0
1
1
1
1
2
2
0
1
2
0
1
1
2
0
0
0
0
1
1
1
0
1
1
2
0
1
1
1
1
1
1
0
1
2
0
0
2
0
1
1
0
1
1
0
1
2
1
2
0
0
1
3
2
3
2
0
1
1
1
0
0
0
2
0
2
2
1
0
1
0
0
0
0
0
1
0
1
2
0
1
2
1
1
1
1
0
1
0
0
1
1
0
1
0
1
2
0
0
1
2
1
0
1
0
1
0
3
1
1
1
0
0
1
0
0
1
1
1
1
0
0
0
0
2
1
2
1
1
0
0
2
1
0
1
1
2
2
1
1
0
0
0
0
1
0
0
1
1
0
2
1
1
1
0
2
1
0
0
2
0
2
2
1
1
2
2
1
1
0
2
1
2
1
2
0
0
1
1
1
1
2
0
0
0
0
1
0
0
1
1
1
2
2
0
0
2
1
1
1
0
2
0
2
1
0
0
1
1
1
0
2
0
1
0
1
0
0
0
2
0
2
0
1
0
1
1
0
2
2
0
3
1
1
1
2
0
1
0
0
3
0
1
0
1
0
1
1
0
3
2
1
2
1
0
2
2
0
0
2
1
1
2
1
1
0
2
2
0
1
1
1
1
0
2
1
0
0
1
2
0
1
1
0
2
0
1
1
1
1
2
1
1
1
1
1
1
1
0
0
0
1
2
1
0
1
1
0
1
1
2
1
2
1
1
0
0
1
0
2
2
2
1
1
0
2
1
1
0
0
0
1
1
0
0
1
0
1
0
1
3
1
0
1
2
0
2
3
1
0
0
2
0
0
0
0
0
2
2
1
1
2
1
1
0
0
0
0
1
2
1
0
1
1
0
1
1
1
0
1
0
1
0
1
1
1
0
0
0
1
2
0
0
2
1
0
0
1
2
0
1
0
1
1
0
2
1
1
0
0
0
1
1
1
2
2
2
2
0
1
1
2
0
2
1
0
1
1
0
0
2
0
1
1
1
0
1
1
1
2
0
2
0
1
0
0
1
1
0
0
1
0
1
1
2
0
1
1
0
2
0
1
0
1
1
1
1
0
1
2
2
0
0
0
0
0
1
2
3
2
0
1
0
0
1
1
1
1
2
0
0
1
1
1
0
0
1
1
2
0
1
0
2
0
2
1
2
0
0
1
2
1
1
1
1
2
0
1
0
0
0
0
1
1
1
0
1
1
0
1
1
0
0
1
2
2
0
1
2
0
1
2
0
2
0
1
2
1
0
0
0
2
0
2
1
0
0
0
2
1
2
1
2
0
0
0
0
1
1
2
1
2
0
3
1
1
1
2
0
0
0
1
1
0
3
1
1
0
1
0
2
0
2
1
0
1
1
2
0
2
0
0
1
1
1
1
1
2
1
0
0
0
1
1
0
1
2
1
1
1
2
0
0
0
1
2
1
0
0
3
0
1
2
1
1
1
1
1
0
0
0
0
0
0
0
1
2
1
0
0
2
0
1
0
1
0
0
2
1
2
3
2
0
2
1
0
0
0
0
1
1
2
1
1
2
2
0
1
0
2
1
0
0
2
1
0
1
2
0
1
1
2
1
0
1
1
1
0
0
0
2
0
1
0
1
0
1
1
0
2
2
0
1
0
1
0
1
0
2
1
0
1
0
2
3
0
2
2
2
2
0
1
3
3
1
2
0
1
0
0
0
1
0
0
0
1
1
1
2
1
2
0
0
0
0
0
0
6
0
0
2
0
0
1
1
0
1
1
5
2
0
1
1
0
1
3
2
1
1
1
0
2
1
1
0
0
2
1
2
1
1
1
1
0
1
1
0
0
0
0
1
0
2
1
1
1
0
2
0
2
2
0
1
1
1
0
2
1
1
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
1
0
1
0
1
0
1
2
2
1
2
1
0
0
0
0
1
0
1
4
1
1
1
1
2
0
0
0
1
1
0
2
1
1
1
2
0
1
1
2
1
1
1
0
1
0
2
1
0
1
1
1
1
1
0
0
1
0
2
0
0
0
1
0
1
1
1
1
2
0
0
0
1
1
1
1
2
0
2
2
2
1
1
2
2
1
1
0
1
1
2
1
0
1
1
1
1
1
1
2
2
1
0
2
2
0
1
1
2
2
0
2
1
6
1
2
0
0
2
0
0
1
1
2
1
0
0
0
1
1
1
2
1
1
0
1
2
2
1
0
2
4
0
2
2
1
2
1
2
1
0
1
0
2
0
1
1
0
1
4
0
0
0
1
0
1
2
0
2
2
2
3
1
0
1
2
0
2
0
0
0
0
2
1
1
2
0
0
2
2
0
2
1
1
1
2
1
0
1
2
1
1
1
0
1
2
1
2
2
2
2
2
0
0
0
0
2
0
1
0
1
0
0
1
1
1
1
1
2
0
0
1
2
0
2
0
2
2
2
0
5
2
2
1
0
0
1
0
1
0
1
1
1
1
1
1
1
0
2
0
0
0
0
0
1
0
2
1
1
3
2
1
1
0
1
0
1
1
2
1
2
2
1
0
1
0
1
1
1
1
0
1
1
1
1
1
0
0
1
1
1
1
1
1
2
5
1
1
2
1
0
1
1
0
0
0
0
1
1
2
0
0
0
2
0
0
0
0
1
2
1
1
1
2
0
0
0
1
2
0
1
0
0
0
4
0
1
2
2
0
2
1
1
3
1
0
2
0
3
2
1
1
0
0
3
1
1
1
1
1
0
1
1
0
1
1
0
0
2
1
1
0
1
1
0
0
0
1
2
0
0
1
0
1
2
2
1
2
1
1
0
2
1
0
2
1
0
3
0
2
0
2
1
0
1
0
2
1
1
2
1
0
0
2
1
1
2
0
1
2
1
1
3
4
0
1
1
1
1
1
0
1
0
2
1
2
1
0
1
1
0
0
0
2
0
0
0
1
1
0
2
1
0
0
0
0
1
1
1
0
3
2
2
2
1
0
0
1
0
0
2
0
0
1
1
1
0
0
1
1
1
0
0
1
1
0
0
0
0
0
1
2
0
2
0
0
1
2
1
0
1
0
2
0
0
0
1
1
1
1
0
2
1
1
2
2
1
1
1
1
2
0
1
2
0
1
2
1
0
0
1
2
2
0
1
2
1
2
1
0
0
1
1
1
0
1
0
1
2
1
0
0
1
0
0
1
1
1
1
0
2
2
0
1
1
1
0
0
0
1
2
1
1
1
1
0
1
0
2
0
0
0
1
5
1
0
2
2
2
1
1
2
0
3
1
1
2
2
2
2
0
0
0
0
0
2
2
1
0
0
3
0
1
0
0
1
2
0
0
0
2
1
0
2
1
2
0
0
0
1
2
0
2
1
2
1
0
1
0
1
0
0
1
1
0
2
0
1
1
1
0
0
1
1
1
0
0
1
1
1
1
2
1
1
1
1
1
0
0
1
2
2
0
1
1
0
0
1
0
2
0
2
2
2
1
1
0
1
1
1
1
0
1
0
0
2
1
1
0
5
0
1
2
0
0
0
0
1
1
2
0
0
0
2
2
0
2
1
0
0
0
0
1
0
0
2
0
0
1
0
1
0
1
0
1
0
1
0
0
0
0
2
0
1
0
1
1
1
1
2
1
1
2
2
1
0
0
0
0
0
2
1
0
0
1
1
2
3
0
1
2
1
1
0
3
2
0
2
0
0
1
1
0
1
1
1
2
2
2
1
0
0
1
0
1
2
0
1
1
2
0
1
1
1
1
1
0
0
2
1
0
1
2
2
0
1
0
1
4
0
1
2
2
0
1
0
0
1
2
0
1
1
0
0
0
1
3
1
0
0
2
1
1
0
0
1
1
2
0
2
1
1
1
2
1
0
1
1
2
1
0
0
2
1
1
2
2
0
1
1
1
1
1
0
0
2
1
1
0
1
2
0
0
1
0
2
2
1
1
1
1
1
1
1
0
1
2
0
1
1
2
1
0
0
0
2
1
0
1
2
2
0
0
0
0
2
2
2
2
1
0
0
2
0
0
1
1
1
1
0
0
0
1
0
0
1
1
0
0
0
2
3
1
0
3
0
2
1
0
2
2
0
1
0
2
1
2
0
0
1
2
2
1
1
1
1
3
2
2
1
2
0
1
1
1
1
1
2
1
1
0
0
1
0
1
1
1
2
0
1
1
1
1
1
0
0
1
2
2
2
1
1
0
2
1
1
0
1
1
2
1
0
2
2
1
0
1
1
0
1
0
0
1
1
2
2
2
0
0
1
0
1
0
0
1
0
1
2
0
1
2
0
0
0
1
0
0
1
1
1
0
1
1
0
1
1
0
1
2
0
1
0
0
0
1
2
2
1
0
0
2
1
0
1
1
2
0
1
0
2
0
0
1
0
0
2
2
2
0
0
1
2
0
1
1
2
0
0
0
2
3
0
1
1
0
2
0
2
1
2
2
0
0
1
2
0
1
4
1
2
0
2
0
1
0
1
1
1
2
1
0
0
0
0
1
0
1
1
1
1
0
1
2
0
1
2
2
0
0
0
1
1
0
0
1
1
1
1
2
1
1
0
0
0
2
1
1
1
0
1
0
0
0
1
0
3
0
0
2
1
1
1
1
2
0
1
1
2
1
0
2
1
2
1
1
1
0
1
2
0
0
1
1
0
0
1
1
0
2
1
1
1
1
2
1
2
0
1
0
1
1
0
2
2
1
2
1
1
1
0
2
1
1
1
0
2
1
1
2
1
0
0
0
1
0
1
0
0
0
0
1
1
1
1
1
1
1
5
2
0
1
2
1
2
2
1
1
2
1
0
0
2
1
1
1
0
1
2
2
1
1
1
0
0
1
3
0
0
1
2
2
0
0
0
2
1
0
0
1
0
1
2
1
1
1
0
2
0
1
2
0
1
0
0
0
0
1
1
0
1
0
2
0
3
0
0
1
2
1
0
0
0
1
1
2
2
1
0
1
1
1
0
1
0
3
1
0
2
2
2
1
1
1
1
2
0
1
0
1
0
0
0
1
1
0
2
0
0
0
0
0
1
1
1
0
1
1
2
0
0
1
0
0
1
2
1
1
1
1
2
0
1
2
0
1
1
2
0
2
1
0
0
0
2
0
0
0
1
0
2
2
1
0
1
0
0
0
0
2
0
0
1
1
0
2
1
0
0
1
2
2
1
1
1
2
1
0
1
2
0
2
2
2
1
1
0
1
2
2
1
0
1
0
1
2
1
1
0
1
2
0
2
2
0
0
2
1
1
2
1
0
1
1
1
1
2
0
0
1
0
0
0
1
1
0
2
0
0
2
1
2
2
1
1
1
1
0
0
1
2
2
1
1
1
1
1
1
0
1
0
2
0
0
1
1
1
0
1
1
1
0
0
1
0
0
2
1
2
0
1
1
1
1
2
1
0
1
0
1
0
2
0
2
0
0
1
1
1
1
1
2
1
1
1
1
1
1
0
1
2
1
0
1
2
2
0
0
0
2
2
2
1
2
1
0
0
2
0
0
2
3
0
1
1
0
0
2
2
1
1
1
1
0
1
1
0
0
1
1
1
0
1
2
2
1
1
1
0
0
1
0
1
1
1
1
0
1
2
1
0
0
1
0
1
0
1
0
0
0
1
2
2
2
0
0
1
0
2
1
2
2
1
2
0
1
1
2
1
0
1
0
0
0
1
1
0
2
0
1
2
1
1
1
0
1
1
0
5
0
0
2
0
1
1
1
1
0
1
0
0
1
0
0
1
0
1
0
2
2
2
0
1
1
1
1
0
1
0
1
1
0
2
1
0
1
2
1
2
2
0
1
0
0
0
1
0
1
0
0
1
2
1
2
2
1
1
1
3
1
3
2
2
0
3
3
0
0
1
0
0
0
0
0
0
0
1
1
1
1
1
0
1
0
0
1
0
1
1
1
2
1
1
2
0
1
1
1
1
1
0
0
0
0
1
2
0
1
1
1
1
2
1
1
2
1
0
0
0
1
0
0
0
1
1
0
2
0
2
2
0
0
1
1
1
1
1
3
2
0
1
1
2
2
1
1
1
0
2
1
1
1
2
1
2
0
2
0
0
0
1
0
2
0
1
2
2
0
0
0
0
1
1
0
2
0
1
0
1
1
0
2
1
1
1
1
2
3
1
2
1
1
1
0
3
1
2
2
1
2
1
2
1
1
2
0
1
1
0
1
0
1
2
0
0
3
0
2
1
1
2
2
1
0
1
0
0
0
0
4
2
0
1
0
1
1
2
1
0
2
2
1
2
1
1
1
0
2
0
0
0
1
2
1
0
0
2
0
0
0
0
0
2
0
1
1
1
0
0
1
2
0
0
1
1
0
0
1
0
1
1
1
0
1
2
0
0
1
0
0
1
1
1
1
0
1
1
0
1
2
1
1
1
2
0
2
0
2
1
1
1
0
0
0
0
1
1
1
0
0
0
1
1
1
0
1
1
1
0
2
1
1
1
2
1
1
0
0
2
1
1
0
0
1
1
1
0
1
2
2
0
0
2
1
0
2
2
1
1
1
0
1
2
1
1
1
0
0
2
2
0
0
1
0
0
0
1
0
0
1
1
1
2
1
2
1
1
1
2
0
2
0
0
1
0
2
1
1
2
2
2
2
0
0
0
1
0
0
1
2
2
0
1
0
0
2
1
1
1
2
2
1
2
2
1
1
0
1
0
2
2
0
1
0
0
1
2
2
2
2
1
0
2
0
0
0
0
0
0
1
1
1
2
0
1
1
1
2
1
0
0
0
0
1
1
1
2
1
2
0
2
0
0
0
1
2
1
1
2
0
2
0
1
1
1
0
0
1
1
0
1
2
1
1
1
0
1
0
0
0
1
1
1
0
0
1
1
1
0
1
0
1
1
2
2
2
0
0
1
0
0
0
1
1
2
1
0
1
1
0
1
0
0
1
1
1
2
1
0
1
0
0
1
0
1
0
0
0
1
0
1
0
0
0
2
1
1
1
0
1
0
1
0
2
0
2
0
0
0
1
0
0
2
1
1
1
2
1
1
1
0
0
1
1
0
1
1
0
0
1
2
1
2
1
1
2
0
2
0
1
1
2
1
0
2
1
1
0
1
1
0
2
0
0
0
0
0
2
0
1
1
2
2
1
1
1
0
1
0
1
2
0
2
0
0
0
1
1
1
1
1
1
0
0
1
1
1
0
2
2
0
0
0
2
1
0
5
0
0
0
0
0
0
2
1
1
1
0
22
2
2
0
1
0
0
0
1
1
1
1
1
1
0
2
1
1
0
1
0
0
2
1
1
2
1
2
1
0
0
2
1
2
0
0
0
0
1
1
1
2
0
0
0
0
0
2
0
0
2
2
0
2
2
2
1
0
2
1
1
0
1
0
1
1
2
2
0
0
0
1
1
0
2
1
0
1
0
2
0
0
1
0
0
1
0
2
1
0
1
1
1
1
0
1
1
1
2
0
2
1
0
1
0
2
1
1
2
0
0
1
2
1
2
0
2
0
1
1
0
1
2
1
1
1
1
1
2
1
0
2
1
1
0
1
0
1
0
0
1
1
2
1
1
1
0
1
2
0
1
0
1
1
0
1
0
0
1
1
0
2
0
1
1
2
0
1
0
1
1
0
2
0
0
2
0
0
1
1
1
1
2
1
0
0
1
1
1
2
2
1
1
1
0
2
1
0
1
0
0
2
2
0
2
1
2
1
1
2
1
1
1
1
1
0
1
1
1
1
0
1
0
1
1
0
1
0
0
1
1
1
1
1
1
1
2
0
1
0
1
1
2
1
2
1
0
1
0
3
2
1
1
0
3
1
1
0
1
0
1
2
0
0
1
0
2
2
2
0
1
2
0
0
1
1
2
1
1
0
0
0
1
0
1
0
0
1
0
1
1
0
0
1
1
0
0
1
1
1
1
2
1
0
2
0
0
0
1
3
0
1
0
1
1
1
1
0
2
2
1
1
2
2
1
2
0
1
2
1
1
1
1
0
1
0
1
4
0
1
2
1
1
0
0
1
3
0
0
1
1
2
1
0
3
0
1
1
0
0
1
1
1
0
0
1
2
2
0
0
2
0
2
0
0
2
0
2
2
1
1
2
3
2
0
1
0
2
1
1
1
1
2
2
2
1
0
1
1
1
2
0
0
0
0
1
0
2
1
1
0
0
2
1
0
0
1
1
2
1
1
0
1
2
2
2
1
2
1
1
0
1
0
2
2
0
2
0
1
0
2
0
0
0
1
3
1
0
1
2
0
0
0
1
0
1
1
3
2
2
0
1
1
1
1
2
0
1
0
1
1
0
1
2
0
1
1
2
2
2
2
0
1
2
0
2
1
1
0
0
1
0
1
0
1
2
0
0
0
1
2
0
2
0
1
0
2
1
1
1
0
1
1
1
0
1
1
0
0
1
1
1
1
0
0
0
1
1
1
0
0
2
1
2
2
0
1
2
2
0
2
0
0
0
1
1
0
1
1
0
1
1
0
2
1
2
1
1
1
1
0
2
0
0
0
0
0
1
2
1
0
1
0
0
0
0
1
0
1
0
1
0
0
0
2
1
0
0
1
0
2
1
2
2
0
1
2
1
2
1
1
0
2
0
1
2
1
2
2
0
0
2
2
2
1
1
1
1
0
3
1
1
0
1
1
1
1
0
0
0
0
2
2
0
1
1
0
1
1
2
0
0
0
1
0
1
1
0
0
0
2
1
0
0
2
1
1
1
1
0
2
0
1
1
0
1
0
0
1
1
0
1
2
1
2
0
1
1
1
1
0
0
2
0
2
0
2
1
0
0
1
0
0
0
2
1
0
2
0
1
1
1
2
1
1
1
0
3
1
0
2
0
0
2
0
1
1
2
2
0
1
0
2
1
2
2
2
0
1
2
2
1
0
1
1
1
1
0
0
1
0
1
0
0
1
0
1
0
1
2
0
2
1
1
1
2
1
1
0
0
0
1
0
1
0
2
2
1
1
1
1
0
0
2
2
0
0
1
0
1
0
0
1
0
2
1
0
1
1
1
1
1
2
1
1
1
0
0
0
0
0
1
1
0
2
2
2
0
1
1
1
1
2
2
1
0
1
2
2
1
1
1
2
2
0
2
1
1
2
1
0
1
1
1
0
0
2
0
1
0
1
1
0
0
2
1
2
0
1
2
0
1
0
1
1
2
0
2
0
2
1
0
2
0
2
0
0
0
1
1
0
1
1
0
1
0
1
0
1
2
0
1
2
1
1
0
1
1
1
2
0
0
0
1
0
2
2
1
0
0
2
1
1
0
1
2
1
1
1
0
0
0
0
2
0
0
0
8
2
0
0
0
0
1
2
0
1
2
0
0
1
0
0
2
0
1
1
1
1
1
1
0
1
0
1
1
0
2
0
0
2
2
0
0
0
3
2
1
1
0
1
2
2
1
1
0
0
1
1
1
0
1
1
1
1
0
2
1
1
2
0
0
2
2
2
0
2
1
0
1
2
2
0
1
3
1
0
0
0
1
0
1
2
1
2
1
0
0
0
0
1
0
2
0
1
1
0
0
2
1
1
1
0
1
0
0
1
2
1
0
1
2
0
1
2
1
1
1
1
1
1
0
1
1
2
3
0
2
0
1
0
2
0
1
1
1
0
1
2
0
1
0
1
0
1
1
1
2
1
1
0
2
2
1
1
2
1
0
0
0
2
1
2
2
1
0
0
1
1
1
1
0
2
1
1
1
2
2
2
1
1
1
0
2
1
2
1
2
0
2
2
0
7
0
2
0
2
0
1
1
1
0
2
0
1
1
2
0
1
0
0
1
1
1
0
1
0
2
1
0
2
0
1
2
1
1
1
0
2
1
1
0
2
1
1
1
1
2
2
0
1
1
1
0
5
2
0
1
0
1
0
0
0
1
2
2
3
1
0
1
1
1
0
0
1
0
1
2
0
1
0
2
0
1
1
1
0
1
0
1
1
1
5
0
2
1
1
1
1
0
0
2
1
1
0
1
0
2
0
1
0
1
2
0
6
1
2
1
0
0
2
1
0
0
2
1
0
0
2
0
1
0
1
0
1
0
0
0
0
0
2
0
1
0
2
1
1
0
1
1
2
1
0
1
2
1
0
0
2
0
1
0
1
0
1
1
0
1
1
1
2
0
1
0
1
0
1
0
0
1
1
0
0
0
1
1
0
1
0
0
1
0
3
2
0
1
1
2
1
0
1
0
1
1
0
0
0
2
0
1
1
1
1
0
2
1
1
0
2
0
0
1
2
0
1
0
0
0
1
0
0
0
1
3
0
1
0
1
1
0
2
1
0
2
2
2
2
0
1
1
1
1
1
0
2
1
0
0
1
3
2
2
2
0
0
1
3
1
0
1
0
0
1
1
1
1
0
1
1
1
0
1
2
1
1
1
1
1
1
0
2
2
1
1
1
1
2
0
1
1
0
1
0
0
2
1
0
1
1
0
1
0
1
0
1
2
2
0
1
1
1
1
0
1
1
0
0
2
1
0
1
1
1
0
0
0
1
0
1
2
1
0
2
0
3
0
0
0
1
0
0
2
1
2
1
1
0
1
0
0
0
0
2
0
1
1
1
0
0
1
0
0
0
1
0
0
3
1
1
0
1
1
2
0
0
2
0
1
0
0
0
2
1
1
0
0
0
1
1
1
0
1
1
2
2
2
0
1
1
0
0
1
2
0
3
1
1
0
2
1
1
1
2
0
1
2
0
1
2
0
0
2
0
0
3
1
1
1
2
0
1
1
1
2
2
1
0
2
1
1
0
2
0
0
0
1
0
1
2
2
1
1
1
1
0
1
2
1
0
1
1
2
1
0
1
2
1
1
2
0
2
1
2
1
1
0
0
0
2
0
1
1
1
2
1
2
0
1
0
2
1
1
1
1
1
0
0
1
0
2
0
1
1
0
1
0
2
1
1
2
1
2
0
0
0
0
1
3
4
0
0
1
1
0
1
1
0
1
1
1
1
0
2
0
0
2
0
2
0
0
1
1
1
0
2
2
0
1
2
0
0
0
2
2
1
0
2
1
1
0
0
0
1
0
0
2
1
1
0
0
2
0
0
0
1
0
1
1
1
1
0
1
1
1
0
1
1
1
0
0
0
2
1
1
0
0
1
2
2
1
2
6
1
0
0
0
0
0
2
2
2
2
0
6
2
0
0
0
2
2
0
1
1
0
0
1
1
0
2
0
1
0
1
1
1
0
0
1
0
1
0
0
1
0
1
0
1
0
0
1
1
1
1
0
1
0
1
0
0
1
0
0
2
1
2
1
0
1
0
1
2
1
1
0
0
0
1
0
2
1
2
2
2
1
2
2
0
0
1
1
2
0
0
1
1
2
1
1
0
0
0
2
0
1
1
0
2
0
0
1
2
0
0
1
1
1
1
0
1
1
2
1
1
1
0
1
2
1
0
0
0
2
1
2
1
0
0
1
2
2
0
0
1
1
0
0
1
1
0
0
1
0
1
0
2
0
2
1
2
1
1
0
1
1
2
1
1
2
0
1
1
1
0
3
1
2
1
2
0
1
1
0
0
1
0
1
1
2
0
2
2
0
1
1
2
1
1
2
1
1
2
0
2
0
2
2
0
2
0
0
2
0
0
0
0
2
1
1
1
1
2
1
1
1
2
0
0
1
1
2
0
0
1
1
1
1
2
0
1
0
0
0
0
2
0
0
1
1
2
0
0
0
2
0
1
2
1
2
1
2
2
1
0
1
2
2
2
1
0
1
1
2
1
0
2
0
0
1
1
0
1
2
2
0
0
0
1
2
0
2
0
1
0
2
2
0
1
0
2
0
2
1
0
1
1
0
1
0
1
1
0
1
0
2
0
0
2
0
1
1
0
1
0
0
0
0
0
0
2
0
5
2
2
1
0
0
0
0
1
2
2
1
0
1
1
0
1
2
1
0
1
0
1
1
2
1
1
1
3
1
0
2
0
0
1
1
1
2
1
2
2
1
0
2
2
1
2
0
1
1
0
1
2
0
2
0
1
2
0
2
0
1
2
0
2
0
0
2
0
0
0
2
0
1
2
1
2
1
1
1
2
1
1
1
0
2
2
1
1
1
1
1
0
1
0
0
2
0
3
0
0
2
0
2
2
1
0
0
2
0
2
1
1
1
1
1
1
0
2
1
0
0
1
1
1
1
0
2
1
1
0
2
2
0
1
2
0
1
1
1
1
1
1
0
1
1
1
2
1
1
2
0
1
2
1
1
1
1
0
1
1
1
2
0
1
0
1
0
0
1
0
0
2
2
1
0
2
0
1
0
0
1
0
2
0
0
1
2
2
0
0
2
2
0
1
1
1
1
0
0
1
0
2
1
1
0
0
0
0
2
0
0
1
2
0
1
1
0
1
1
0
1
1
2
1
1
1
1
1
0
2
1
1
0
0
1
1
2
1
0
0
1
1
1
2
2
0
2
1
0
2
2
1
0
0
1
1
1
2
1
2
2
2
0
1
1
0
2
1
0
1
1
1
1
1
2
0
0
0
1
0
2
1
2
1
1
1
1
2
0
1
1
2
1
0
1
0
2
0
2
1
2
0
0
1
0
0
2
1
0
1
0
1
2
0
2
1
0
1
1
0
1
1
0
1
1
3
0
0
0
1
0
0
1
2
2
1
1
0
0
0
1
1
0
0
0
1
1
0
1
1
0
2
1
1
1
3
2
0
2
2
0
1
2
1
0
0
0
1
2
0
2
1
1
1
3
0
0
1
0
0
0
2
2
1
1
0
1
0
1
1
0
3
1
2
1
0
0
1
0
2
0
0
1
2
0
1
0
2
0
1
0
0
0
1
2
1
1
1
1
2
0
2
1
0
0
3
1
0
1
0
1
0
0
1
0
0
0
1
0
0
1
0
0
1
1
1
2
2
2
0
0
1
0
0
1
0
3
2
0
1
2
2
1
0
1
0
2
2
2
1
0
1
2
2
0
0
1
0
0
3
2
2
0
1
1
0
1
1
2
2
0
0
1
1
0
0
1
2
2
0
1
0
0
2
3
2
0
0
1
0
2
1
0
2
0
1
0
2
2
1
1
1
1
3
1
0
2
0
0
0
0
0
1
1
0
0
2
0
0
0
1
1
0
1
0
1
1
2
2
0
0
1
0
1
3
1
2
2
1
1
0
2
1
0
0
1
2
1
1
3
1
1
1
3
3
2
0
2
2
0
1
1
0
1
1
2
1
0
0
1
2
0
1
1
0
1
0
1
0
0
1
2
0
2
1
1
2
0
2
2
0
2
1
0
0
0
1
0
1
1
1
0
2
1
2
0
2
4
1
0
1
2
0
0
0
1
1
0
1
1
0
0
0
0
0
0
2
2
1
1
2
0
1
1
2
1
0
1
0
2
2
0
1
2
0
1
0
0
0
1
1
1
2
0
0
2
2
0
0
2
1
1
0
0
2
0
2
1
1
0
5
1
1
0
0
2
1
1
2
0
0
0
2
1
0
1
0
0
1
2
1
0
1
1
0
0
0
2
1
2
1
0
0
1
0
0
0
1
0
0
1
1
1
1
1
1
0
2
0
2
0
0
0
0
6
0
1
1
0
1
1
2
1
1
0
1
1
2
0
1
1
0
0
0
0
2
1
1
2
1
0
1
1
2
0
0
2
0
2
2
0
1
2
0
0
2
2
1
0
0
0
1
1
1
1
1
1
2
1
1
0
1
0
1
2
1
2
0
2
1
1
0
0
1
0
1
2
0
1
1
0
1
1
1
1
1
1
1
0
0
0
2
0
1
0
0
0
0
2
1
2
2
0
1
1
0
1
1
1
0
2
2
1
2
2
0
0
1
0
1
2
1
1
0
2
0
1
1
1
0
0
1
3
0
3
1
2
0
1
2
1
0
3
0
0
0
1
2
0
0
1
0
0
0
1
0
1
0
1
2
0
0
0
2
1
3
0
2
1
0
0
1
2
0
0
1
1
0
1
3
1
0
0
1
0
0
1
0
1
1
1
0
0
1
0
0
0
1
2
0
2
1
0
0
1
1
0
0
0
1
0
0
2
1
0
2
1
1
1
1
1
0
1
1
0
0
2
1
1
0
0
3
2
2
1
1
2
0
0
2
2
2
2
1
0
1
0
1
1
0
2
1
0
0
2
2
1
0
2
0
1
0
2
1
2
1
1
0
2
1
1
0
0
2
2
1
1
0
2
1
2
1
2
0
0
1
2
1
2
1
1
2
2
1
0
0
1
1
2
0
1
0
0
2
1
0
0
2
0
2
3
0
1
0
1
1
0
1
2
2
1
0
1
2
1
1
0
1
2
0
1
0
1
0
2
0
0
1
0
3
0
0
0
1
1
0
1
0
1
1
2
1
0
2
1
1
1
1
0
1
0
0
0
0
1
1
2
1
0
2
0
0
1
2
2
2
2
2
0
1
0
2
2
0
1
1
2
1
1
1
1
1
1
2
0
0
2
1
0
1
0
1
1
0
1
2
1
1
0
1
0
1
1
2
1
0
1
0
0
0
2
1
1
1
2
2
0
0
1
0
2
1
1
1
1
1
2
0
0
1
1
1
0
0
0
1
0
2
1
0
1
1
1
1
1
0
1
0
3
1
0
0
0
0
1
1
0
0
0
2
0
2
0
0
1
0
1
0
2
1
1
2
0
0
2
1
2
0
2
0
1
2
0
0
0
1
1
1
0
1
0
0
1
0
2
0
0
1
2
1
1
0
0
0
1
1
1
0
0
0
0
1
0
1
1
0
0
2
0
1
2
1
0
1
1
0
1
0
1
1
1
1
0
1
0
1
0
0
1
0
1
1
1
1
2
1
0
1
0
1
0
2
2
1
1
1
1
1
2
1
0
1
0
0
0
0
2
1
1
2
1
2
1
0
0
1
2
0
1
1
1
1
0
1
0
0
1
2
1
1
1
1
2
0
0
1
0
1
2
0
0
2
0
0
0
1
0
1
2
0
0
2
2
0
0
0
0
2
0
2
0
1
0
2
0
0
1
1
2
1
2
0
0
0
1
1
1
0
1
2
1
1
1
1
0
1
0
1
0
0
1
0
2
2
1
0
0
0
2
1
2
0
1
2
0
0
0
0
1
1
0
1
1
2
1
1
2
2
0
0
2
2
0
0
0
2
0
0
0
1
2
1
0
2
1
0
0
1
2
1
2
2
0
0
2
2
1
1
1
0
0
1
3
2
0
0
2
1
1
1
2
2
0
0
0
0
1
2
2
1
2
1
2
0
0
1
2
1
0
0
0
0
0
0
1
0
2
3
2
1
1
2
2
1
0
1
1
1
1
0
0
0
2
2
2
2
1
0
0
1
1
0
0
1
1
0
1
2
1
2
2
1
2
0
1
0
1
0
1
1
1
2
0
0
1
1
0
0
0
0
0
4
1
1
1
1
3
1
1
1
0
1
2
1
0
0
2
1
0
1
1
2
2
1
1
2
2
0
1
1
1
1
2
0
1
2
0
0
0
0
1
1
0
0
0
0
1
0
1
1
2
1
0
1
1
0
1
0
1
0
2
0
1
0
1
1
1
0
1
0
2
2
0
0
1
2
1
0
1
0
1
0
1
1
1
1
0
1
3
0
2
0
2
1
2
2
0
0
1
2
0
0
1
2
1
1
0
1
0
1
1
0
1
1
1
1
0
0
2
0
0
1
0
0
2
1
1
2
0
0
0
0
1
1
0
2
0
0
0
1
1
0
1
2
1
0
1
3
1
1
0
1
0
1
1
0
2
0
1
0
0
0
0
0
1
0
1
1
2
3
0
2
1
2
0
1
0
1
2
1
0
0
2
0
1
1
0
2
1
1
1
1
1
1
0
0
1
2
0
0
0
2
2
0
1
0
1
2
1
0
0
0
1
0
1
2
1
2
0
0
0
1
0
1
1
1
0
1
1
2
0
0
2
0
1
1
0
2
2
1
2
1
1
0
0
0
1
2
0
2
0
1
0
0
1
0
1
1
1
1
1
2
2
1
0
1
1
1
1
1
0
0
1
2
0
1
0
1
1
1
0
1
2
1
2
2
1
1
0
0
0
0
1
0
2
1
1
1
0
0
1
1
1
1
1
1
1
2
1
0
1
1
4
1
0
3
0
2
1
2
2
1
0
1
0
0
2
0
1
1
1
1
0
1
0
0
1
2
1
0
0
0
1
0
0
0
1
2
0
0
1
0
0
2
0
1
1
1
0
2
1
1
1
1
2
0
0
1
2
1
1
2
0
0
1
1
0
2
0
2
1
1
1
2
1
0
1
0
1
2
0
0
0
2
0
2
1
0
0
4
0
0
2
0
1
1
1
0
1
2
0
2
0
0
1
1
2
2
1
2
1
0
0
0
0
1
2
0
1
0
0
0
1
1
2
0
0
1
1
2
1
0
0
2
2
3
1
2
1
2
0
0
1
2
2
0
1
0
0
1
0
2
4
2
1
0
0
1
1
1
1
1
0
1
1
0
0
0
2
2
0
0
1
2
0
1
1
1
0
1
1
0
0
1
1
2
0
1
1
0
0
0
1
0
0
0
0
1
0
1
1
0
2
2
1
1
1
2
3
2
1
0
1
1
2
0
1
0
1
2
0
0
0
0
2
1
0
1
1
1
0
2
0
0
3
1
1
1
2
0
0
0
2
1
1
1
0
0
2
1
0
3
0
1
1
0
1
0
2
0
0
0
0
2
2
1
1
0
2
1
2
0
2
1
0
0
1
1
1
1
1
0
1
2
1
0
2
1
0
2
1
0
1
2
0
1
0
0
3
2
2
1
0
2
0
0
2
0
0
2
0
1
2
1
1
1
2
1
2
1
3
0
2
0
0
1
0
0
0
0
1
0
2
2
1
2
1
1
2
1
1
1
1
1
1
0
0
1
1
1
0
1
1
0
1
0
1
1
1
2
0
0
0
1
0
0
1
0
1
0
0
1
1
1
2
1
0
2
1
1
1
0
0
1
0
1
0
1
1
0
1
0
0
1
1
1
0
2
1
2
1
0
1
1
0
0
1
0
0
0
1
2
1
1
1
0
0
1
0
2
1
1
0
1
1
1
2
1
1
2
1
1
1
0
1
1
1
0
2
2
1
0
1
0
2
1
1
1
0
1
1
1
2
1
1
2
0
1
1
0
0
0
1
1
2
0
2
2
0
2
2
1
2
0
2
1
0
0
2
0
1
0
0
2
0
0
0
2
1
2
2
1
1
1
0
1
2
0
0
1
0
2
0
2
1
0
2
1
0
3
1
1
0
1
0
1
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
1
1
2
0
2
2
0
0
0
2
2
2
0
1
1
0
0
2
2
2
0
0
0
0
2
0
0
1
0
1
2
1
0
0
0
0
0
2
0
2
0
1
0
0
0
1
2
2
2
0
1
1
1
1
4
0
1
0
0
0
1
0
1
0
1
0
1
3
2
1
2
1
0
1
1
1
0
1
2
2
1
0
0
2
2
1
0
0
1
0
0
1
1
2
0
1
0
0
1
1
1
1
1
1
1
2
2
0
0
1
0
1
1
0
3
0
2
0
2
0
0
0
2
1
1
1
2
0
0
2
1
1
2
2
1
0
1
1
1
1
2
2
2
0
2
2
0
1
1
3
1
0
1
1
2
2
1
1
1
1
1
3
2
1
0
2
2
1
1
1
2
0
2
0
3
1
0
1
1
1
2
0
1
0
1
2
0
0
0
1
2
1
0
1
2
0
1
0
0
2
1
2
0
1
2
1
0
0
1
2
1
1
0
1
2
0
0
0
1
1
2
2
3
0
0
1
2
0
1
0
2
1
1
2
1
0
2
0
0
1
0
1
1
1
1
1
1
0
0
0
1
1
0
0
2
0
2
2
2
1
0
2
1
2
0
1
0
0
1
0
2
0
1
0
1
4
0
0
2
1
0
0
1
1
0
1
1
2
0
0
2
1
2
2
1
0
1
0
2
0
2
2
2
0
1
1
1
0
2
0
0
0
2
0
2
6
1
1
2
0
0
1
1
1
2
0
1
1
1
0
2
2
2
2
1
1
1
1
0
1
0
2
2
0
1
0
0
1
1
0
0
1
0
1
0
1
1
1
1
0
1
0
0
0
0
1
1
1
1
2
0
2
1
2
0
1
1
1
1
2
1
0
1
1
0
0
1
1
1
2
1
0
0
0
2
0
4
1
1
2
1
0
1
0
0
0
2
1
0
1
2
1
2
2
1
0
0
1
2
1
1
1
0
1
0
1
2
1
0
0
1
1
1
2
2
1
2
0
2
1
3
2
2
1
1
1
0
1
1
2
0
0
0
2
1
1
2
1
0
0
2
2
0
0
1
2
1
0
0
1
2
0
1
1
0
1
1
1
0
0
1
2
2
1
0
0
1
0
0
1
3
0
0
0
2
0
0
1
1
1
1
1
1
0
2
0
0
0
2
2
1
2
1
2
0
1
0
1
0
2
2
2
1
1
3
0
1
1
0
2
0
0
0
0
0
0
2
1
2
0
0
1
0
0
0
0
0
2
0
1
0
0
1
0
0
1
1
0
1
0
1
0
1
1
0
1
1
1
1
1
1
1
0
3
2
2
2
1
0
1
1
1
0
0
0
0
1
1
1
0
2
0
1
2
1
0
1
0
2
1
1
0
0
1
0
1
0
2
1
0
2
1
2
1
0
0
0
2
2
1
1
0
1
2
0
0
1
1
0
2
0
2
2
1
0
1
2
0
1
0
0
0
2
1
2
0
2
2
1
1
0
1
2
1
1
1
0
1
0
1
2
1
1
0
0
2
2
0
1
1
2
0
0
1
1
1
1
0
1
2
0
1
0
1
0
1
0
2
0
1
1
2
0
1
1
1
1
0
1
2
0
1
0
1
1
1
1
1
0
0
1
2
1
1
0
1
0
2
1
0
0
0
1
0
1
2
0
1
6
0
0
0
2
0
0
0
0
1
1
1
1
1
1
0
1
1
2
1
1
1
0
0
0
1
2
1
0
2
2
2
2
2
2
1
1
2
2
1
0
2
0
2
0
1
0
1
0
2
1
1
0
1
0
0
2
0
0
0
0
1
2
1
2
1
1
1
2
1
0
0
0
1
1
2
1
1
0
1
1
0
1
0
1
2
1
0
0
2
0
0
0
1
1
2
0
3
0
2
1
1
0
0
0
1
0
0
0
2
1
1
1
0
0
0
0
0
0
1
1
1
1
0
2
0
2
0
1
0
0
0
1
0
2
1
2
0
0
2
0
1
1
3
1
2
1
0
0
1
2
1
2
2
1
1
1
0
3
0
1
0
0
1
1
0
0
0
0
0
0
0
2
0
1
0
1
2
2
0
1
1
1
0
2
0
1
0
0
0
3
1
1
1
0
1
2
1
0
1
0
1
0
0
1
0
0
2
2
2
0
1
0
5
1
1
1
1
1
1
1
1
0
0
2
1
1
0
2
2
0
2
6
1
2
2
0
1
1
2
1
2
13
2
1
0
2
1
1
0
2
0
0
0
1
1
1
1
3
1
1
2
1
0
0
1
0
0
2
1
1
1
0
1
0
2
0
1
1
0
1
0
1
0
1
1
1
1
0
1
2
0
0
1
2
1
0
1
0
2
1
1
1
2
2
1
1
0
0
0
0
0
1
0
2
0
1
2
1
1
2
1
1
1
2
1
1
1
3
2
0
1
0
0
0
0
2
0
0
1
0
2
1
2
0
2
0
1
1
0
1
0
1
1
1
0
1
1
0
1
2
0
0
2
1
0
0
4
1
2
0
1
0
0
1
0
2
1
0
0
2
0
0
2
1
0
2
0
1
0
0
0
1
0
1
2
0
2
0
1
0
0
4
1
0
2
1
1
2
1
0
2
1
1
1
0
2
2
2
1
2
1
2
1
2
2
0
2
0
2
2
0
0
0
0
2
1
1
0
2
1
2
1
0
1
0
2
0
1
1
2
0
2
0
2
2
1
2
0
1
0
0
0
1
1
0
1
2
1
1
2
1
2
0
1
1
0
1
0
1
0
2
1
2
0
0
2
2
0
0
2
2
1
0
0
0
0
1
1
1
1
2
1
1
0
0
2
2
1
1
1
0
1
0
2
1
1
2
1
1
2
1
1
0
0
2
1
1
0
1
0
0
1
1
1
1
0
1
0
1
0
2
1
0
1
1
0
0
2
1
1
1
1
2
0
2
0
1
2
0
1
1
0
0
0
0
1
2
0
2
2
0
1
0
0
0
0
1
0
0
1
1
0
1
2
0
1
0
1
1
0
3
0
0
2
2
1
2
0
2
1
1
0
1
1
0
1
1
1
2
0
1
1
1
0
2
2
2
1
1
1
1
1
0
2
0
0
1
1
0
0
0
2
0
1
1
2
2
0
0
2
0
0
0
2
1
2
0
0
1
2
1
2
1
2
1
1
0
0
1
0
2
0
0
0
0
2
1
0
1
1
0
2
1
0
0
1
1
0
2
0
1
1
0
0
1
2
1
2
0
1
1
2
3
0
0
1
0
1
3
0
0
0
1
2
1
2
0
1
1
1
0
2
2
1
1
2
2
1
1
0
0
0
1
1
1
2
0
0
2
2
1
0
0
0
0
1
0
0
0
0
0
0
1
2
1
1
1
0
1
2
0
1
1
1
1
2
1
0
0
2
2
0
0
0
1
2
0
1
1
1
0
1
0
0
1
0
0
0
0
2
2
0
1
1
1
2
0
0
2
0
0
1
2
0
1
2
2
0
0
0
2
1
1
1
1
0
1
1
1
0
0
0
2
1
1
1
1
0
0
0
2
2
1
1
2
0
0
0
0
1
0
0
1
1
1
0
0
2
0
2
2
1
1
1
1
0
2
0
2
1
0
0
1
1
1
0
0
1
0
0
0
0
1
1
0
2
1
1
0
0
0
0
1
0
2
1
0
2
0
1
1
1
1
0
1
1
2
1
0
1
1
0
1
1
0
0
1
0
1
1
1
0
2
0
1
1
0
1
2
0
1
2
0
0
1
0
0
0
1
2
0
0
2
0
1
0
1
2
1
1
1
0
0
2
1
0
2
2
1
1
0
1
1
0
1
1
2
0
1
1
2
1
2
0
1
0
0
1
2
0
0
1
0
2
0
0
0
1
1
0
0
1
2
1
2
0
1
1
2
2
0
0
0
0
0
1
0
1
2
1
0
1
0
0
0
0
1
0
1
2
1
1
1
0
0
0
1
0
2
0
2
2
2
0
0
1
2
1
1
0
0
0
0
2
2
1
0
1
2
2
1
0
2
0
1
0
1
0
0
2
2
0
1
1
0
2
0
2
2
0
2
1
1
0
0
2
0
2
2
2
1
2
1
0
0
1
2
1
0
0
0
1
1
0
0
0
1
2
1
1
2
0
1
2
1
0
0
1
1
0
0
0
5
0
0
0
1
1
0
1
0
2
1
1
1
2
0
0
0
0
2
1
1
1
0
1
0
2
1
0
0
1
0
1
2
0
1
0
8
1
1
2
2
0
1
2
1
0
1
1
0
2
1
0
0
1
2
0
1
1
0
2
1
1
0
1
2
1
0
2
1
1
0
1
1
1
0
1
0
0
1
1
1
2
2
0
1
0
0
1
0
2
1
1
1
2
1
1
0
0
1
1
1
2
1
1
0
1
2
0
2
2
2
1
0
0
4
2
0
1
0
0
1
1
0
1
0
0
0
0
2
2
0
1
0
0
1
2
0
1
0
1
1
1
1
0
2
1
0
1
1
0
0
0
0
1
0
1
0
2
1
1
0
0
0
2
2
1
2
0
1
0
2
0
1
1
0
1
1
1
2
2
1
2
1
0
2
1
0
2
2
1
0
1
1
1
1
0
1
1
0
2
1
0
0
2
1
2
2
0
2
2
0
1
2
2
2
0
1
1
0
0
0
1
3
1
2
0
1
0
1
2
0
1
0
0
0
0
2
2
2
0
0
1
2
1
2
1
0
1
1
0
1
0
0
0
2
0
0
0
0
1
1
0
2
1
2
1
0
0
1
1
1
0
0
0
1
1
1
0
2
2
1
0
1
0
0
1
0
2
1
2
2
0
0
0
0
0
0
0
2
1
0
2
0
1
2
2
0
0
1
1
0
1
2
0
0
1
0
0
1
2
1
0
2
1
2
0
0
1
1
3
1
1
1
1
2
0
2
2
0
1
1
3
0
2
2
0
0
1
0
1
1
0
2
1
0
1
1
2
0
2
2
1
1
2
0
0
0
0
1
1
1
0
1
1
1
1
0
2
0
0
1
2
0
0
1
1
1
2
1
3
0
0
0
0
1
4
1
1
2
0
0
0
2
1
1
0
1
1
1
2
0
0
2
1
0
2
0
0
2
0
2
2
0
1
1
1
0
2
0
0
2
0
0
3
1
1
2
1
0
0
0
0
1
0
4
0
0
0
1
0
0
1
0
0
2
0
1
2
2
1
2
0
1
1
1
0
1
2
0
0
1
1
1
1
0
0
1
1
0
1
1
2
2
0
0
2
0
0
1
1
2
0
2
1
0
0
4
0
1
1
0
1
2
2
1
2
1
0
0
1
0
1
0
1
0
0
1
0
1
1
1
1
0
1
1
1
0
1
1
1
2
1
0
2
0
1
1
0
0
2
1
1
1
0
1
0
2
1
1
2
0
1
0
2
0
0
1
0
0
0
0
1
0
2
1
1
0
1
0
0
0
0
0
0
0
0
1
0
1
2
2
0
0
0
1
1
0
1
6
0
0
0
0
0
2
2
0
0
2
0
1
0
1
0
1
0
0
0
0
0
2
2
0
0
0
0
0
1
1
0
1
1
0
2
1
2
0
0
1
0
1
1
2
0
1
0
0
0
1
2
0
1
1
1
1
1
0
1
0
1
2
1
1
1
1
1
0
1
0
1
2
0
1
2
0
0
0
0
1
1
1
2
1
1
2
2
1
2
2
2
1
0
0
0
0
3
0
0
2
1
2
0
2
0
4
0
2
2
1
1
1
1
1
1
1
1
0
0
1
0
0
0
0
0
2
1
0
2
2
0
0
2
0
1
1
0
2
0
1
1
0
2
1
2
1
1
1
2
1
2
0
2
0
1
0
1
1
1
2
0
0
1
0
1
2
1
1
0
1
0
1
1
1
1
0
2
0
1
1
0
1
0
1
0
0
0
0
2
1
1
0
2
1
0
0
2
0
0
2
0
0
1
0
2
3
1
0
1
0
2
0
0
0
0
1
0
1
2
0
0
3
2
1
1
1
1
1
2
0
0
0
0
0
0
1
1
1
1
0
0
1
0
2
0
2
1
0
0
0
1
0
1
1
1
0
2
0
0
0
0
0
0
0
1
0
1
0
1
1
2
0
2
1
2
2
0
1
0
2
1
0
2
0
0
1
0
1
3
1
1
0
2
1
1
0
0
0
0
1
0
0
1
2
0
0
2
0
1
1
0
2
2
0
1
2
1
0
2
0
1
1
1
0
0
0
2
2
2
1
0
1
1
0
0
0
1
0
1
0
2
1
2
0
1
0
0
1
0
0
0
1
1
0
2
2
2
1
0
2
1
2
0
2
1
1
0
0
1
0
1
1
1
0
1
1
1
2
0
2
0
0
1
0
1
0
0
0
1
2
1
1
0
2
0
2
1
1
0
1
1
2
0
0
2
0
2
3
1
0
1
2
1
1
2
1
1
2
1
1
1
0
1
1
1
2
1
0
1
0
2
0
1
0
0
0
2
0
2
1
1
2
1
1
0
1
2
2
1
0
1
0
0
2
1
0
0
2
0
2
0
2
1
1
1
0
2
0
2
2
0
7
2
1
1
0
1
2
2
0
1
0
1
1
0
1
0
1
1
1
2
0
1
2
1
0
2
0
1
0
1
1
1
0
2
2
0
2
0
0
0
2
1
2
1
1
0
2
0
1
2
0
0
2
1
0
1
0
0
0
0
0
2
1
0
2
0
1
2
2
1
0
1
2
0
1
0
2
1
1
1
0
2
1
0
1
1
1
2
0
2
1
0
2
1
1
1
0
2
2
1
2
1
1
0
0
1
1
2
2
1
1
2
1
0
0
0
1
2
1
0
1
0
2
0
1
1
2
1
0
3
0
1
1
1
1
1
0
1
0
2
0
0
1
1
1
2
2
0
2
0
1
2
1
0
2
1
1
0
1
2
1
1
0
0
1
0
0
2
0
0
1
0
2
1
0
0
1
1
0
1
0
2
1
2
0
1
0
2
1
2
0
2
0
0
1
0
2
2
1
2
0
0
1
1
1
2
1
0
1
2
1
2
1
0
2
0
2
1
0
1
1
1
0
0
1
0
1
2
1
0
1
0
1
2
2
1
0
1
1
0
0
1
1
2
0
0
0
2
2
1
0
2
2
7
0
1
0
1
0
0
1
1
0
1
1
5
0
1
0
1
0
0
0
0
1
1
3
0
0
2
0
0
1
1
1
1
0
0
1
1
1
1
1
3
1
1
0
1
0
1
1
2
1
0
0
1
2
0
1
1
0
5
0
0
0
1
1
2
2
2
1
1
1
1
1
1
2
0
1
2
3
2
0
1
2
2
1
1
0
1
1
0
2
1
0
0
1
0
0
1
1
0
2
0
0
1
2
1
1
0
2
1
1
3
1
0
2
0
0
2
1
2
0
2
2
0
1
0
1
0
0
2
0
2
1
1
0
2
1
0
1
2
0
2
2
0
1
1
0
0
1
0
2
1
0
0
1
0
0
0
2
1
0
0
2
0
0
0
1
0
0
0
0
1
1
0
1
0
1
2
1
2
2
0
1
1
1
1
0
1
1
1
1
3
0
1
2
1
1
1
2
1
0
2
2
2
2
1
2
1
2
1
2
1
1
1
2
0
2
0
2
1
1
0
0
0
2
2
0
1
0
0
0
2
2
1
0
0
0
1
1
2
0
2
0
0
2
0
1
1
0
0
0
2
0
2
1
2
1
2
1
1
0
1
1
1
0
0
0
1
0
1
0
2
2
1
0
2
1
0
2
0
1
0
1
0
0
2
2
2
2
1
2
0
0
0
0
1
1
0
1
1
2
1
1
1
1
2
2
1
1
0
1
2
1
1
2
0
1
2
2
1
1
0
0
2
0
4
1
0
0
1
1
0
1
0
0
1
2
1
1
1
3
0
0
1
2
1
1
1
2
1
1
0
0
1
2
1
1
2
2
2
0
1
2
2
2
2
2
0
2
2
2
1
1
2
1
3
1
2
5
1
0
1
0
2
1
1
1
1
1
0
1
1
0
1
1
0
1
0
0
1
1
1
1
1
2
2
1
1
0
0
1
1
1
1
1
0
1
0
1
1
3
2
1
0
2
0
1
1
2
0
4
2
0
0
1
1
1
1
2
2
0
0
2
0
4
1
0
2
1
1
1
1
1
0
0
1
1
1
2
1
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
1
0
0
1
1
0
1
0
0
1
1
0
2
1
1
2
0
2
2
1
0
2
1
2
0
0
2
1
1
1
0
1
0
1
0
1
0
1
2
0
0
2
0
0
0
0
1
1
0
1
1
1
2
1
2
0
1
2
1
1
0
0
0
0
1
1
1
1
0
1
1
2
1
1
0
1
0
1
0
1
1
0
0
1
2
1
0
1
0
0
1
1
0
1
1
0
3
1
0
0
1
0
0
1
1
2
0
0
1
1
1
2
2
1
2
2
1
1
0
0
2
0
1
2
2
1
2
1
1
2
1
0
0
1
0
1
1
1
3
2
0
2
2
1
1
2
1
1
1
1
1
2
2
1
0
0
1
1
1
2
6
2
0
1
0
0
0
0
1
0
1
0
1
0
2
1
2
1
1
0
1
1
0
1
0
0
0
1
0
1
2
0
1
0
1
1
1
0
1
1
1
0
1
0
0
0
1
0
1
3
0
0
1
0
1
1
1
2
2
1
0
2
0
0
0
3
0
1
1
0
2
1
1
0
0
0
2
0
1
1
1
1
0
0
1
1
0
1
1
0
1
0
1
2
1
1
0
2
1
1
1
0
0
1
1
1
0
0
1
1
1
0
2
0
0
1
0
0
1
0
0
0
1
2
0
0
0
2
0
2
2
0
2
0
2
2
0
1
0
0
1
1
4
1
0
1
1
0
0
1
0
0
0
1
1
2
0
2
2
1
0
1
1
1
2
2
1
2
0
0
0
0
0
2
0
2
2
1
1
2
0
1
0
2
1
1
1
2
0
1
0
0
2
0
2
1
0
2
1
1
1
2
0
2
1
1
1
2
1
2
1
0
1
0
0
2
0
0
0
0
1
2
1
0
0
1
1
2
0
1
1
1
0
1
0
2
1
2
0
0
2
2
0
1
0
1
2
1
0
1
1
1
1
2
0
1
1
0
0
1
0
2
1
1
1
0
2
1
0
1
1
0
1
1
1
2
0
1
0
1
0
1
0
3
2
1
1
1
2
0
0
2
1
0
0
1
0
0
3
1
1
2
1
3
0
2
1
2
1
2
0
1
0
0
1
2
1
1
0
2
2
1
3
2
1
2
1
0
2
3
1
0
0
3
2
2
0
2
0
2
0
1
2
1
1
1
1
1
0
2
2
0
1
0
2
0
1
2
1
1
1
2
1
1
1
1
2
2
0
0
0
0
0
0
0
0
0
1
0
2
1
1
2
1
1
1
1
1
0
1
0
1
0
0
0
2
1
2
0
2
0
2
1
0
2
1
2
1
2
2
1
0
1
0
2
2
0
1
2
1
1
2
2
2
2
2
1
1
1
1
0
2
0
0
0
0
1
1
0
2
2
0
1
1
2
0
1
0
1
1
1
0
1
1
0
1
2
0
5
1
0
0
0
1
0
0
1
3
1
0
2
0
0
1
1
0
1
2
2
1
1
0
0
0
0
1
2
0
1
2
2
0
1
1
1
0
0
1
1
0
0
0
0
0
0
1
0
2
2
1
0
1
0
1
2
1
2
1
2
0
1
1
1
1
2
1
1
4
1
2
0
1
0
0
2
1
0
0
1
1
2
1
0
0
2
1
1
1
0
1
2
0
2
1
0
2
0
0
1
1
0
1
1
0
0
1
1
1
0
2
2
2
1
2
1
1
1
2
0
2
0
1
2
1
3
1
1
0
2
0
0
0
1
0
1
2
0
1
1
0
3
1
2
0
1
4
2
0
0
1
0
1
2
2
0
0
1
0
0
1
1
0
0
0
0
2
2
0
1
1
1
0
1
0
0
1
1
0
2
0
2
2
2
1
0
0
1
1
2
2
0
1
0
2
0
0
1
2
0
1
1
2
1
1
2
0
0
0
0
0
2
2
1
1
1
1
1
1
1
1
0
1
0
0
1
0
0
1
1
1
1
0
2
0
0
1
1
2
0
1
0
1
1
0
2
2
1
0
0
0
2
1
1
2
0
0
1
1
0
0
2
2
2
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
2
1
1
1
1
1
0
0
0
0
1
1
1
0
0
1
1
1
1
0
1
0
2
1
1
0
0
1
1
1
1
1
0
0
1
0
1
2
1
1
0
1
1
1
0
1
2
1
2
0
0
2
1
0
1
1
0
0
2
0
0
0
0
2
2
1
2
1
1
0
1
0
0
0
1
0
2
1
0
0
0
1
0
1
0
1
2
2
1
0
1
0
0
0
2
2
1
0
2
1
0
0
0
0
1
2
1
0
0
0
1
0
0
0
1
1
1
1
0
0
2
2
1
1
0
2
2
0
0
0
1
1
1
1
1
2
3
1
0
1
1
0
1
1
1
1
1
0
1
1
3
2
0
1
1
2
2
1
2
0
1
1
0
1
1
2
0
0
1
2
1
0
0
0
1
1
1
2
1
0
0
1
1
0
1
0
1
2
0
2
1
2
2
0
1
1
1
0
1
0
1
0
0
0
0
1
2
0
0
0
0
1
1
2
2
0
1
0
1
1
0
2
2
2
0
0
2
1
1
0
1
0
0
0
0
1
2
0
1
0
1
1
2
1
0
0
2
2
0
2
2
0
2
0
2
0
0
0
1
1
1
0
0
1
0
0
1
2
2
0
1
0
0
0
3
0
0
1
0
1
2
0
2
0
0
1
0
2
0
2
0
2
1
0
2
1
0
0
1
1
0
0
0
0
3
0
1
1
0
0
0
0
0
0
1
1
0
1
2
0
0
2
0
2
1
2
2
1
2
1
1
1
1
0
0
1
0
0
1
1
2
2
0
0
0
0
2
2
2
1
2
0
1
1
1
2
1
0
0
2
1
0
0
2
0
1
0
1
1
1
2
2
1
2
2
0
2
2
0
1
2
0
1
2
1
0
1
2
2
3
1
0
3
1
0
1
0
1
1
1
0
0
1
1
0
0
0
0
1
1
2
2
1
1
2
0
0
0
0
0
1
1
1
0
1
2
1
1
1
0
1
1
1
2
0
1
1
0
0
0
3
0
0
0
1
0
0
0
1
0
1
0
2
0
0
0
1
1
1
0
0
1
0
0
1
0
1
2
2
2
1
1
1
1
2
1
0
0
1
0
1
0
1
0
1
0
0
2
1
1
0
1
0
1
1
2
0
0
0
1
2
2
0
0
1
1
0
2
1
1
0
0
0
1
1
0
1
1
0
2
2
0
0
1
1
1
1
0
1
1
0
1
1
2
1
0
1
0
2
1
1
0
0
3
0
2
0
1
2
2
1
1
1
1
0
3
0
0
1
1
1
2
1
1
1
1
1
0
1
1
0
0
2
1
1
2
0
0
1
2
0
1
0
2
0
2
0
1
1
1
1
1
1
0
1
1
1
0
1
1
2
0
2
0
1
0
1
1
1
2
1
2
1
0
0
2
0
0
0
1
2
1
0
1
1
1
1
2
0
1
1
0
0
2
0
0
0
1
0
1
0
3
0
0
2
1
2
0
0
0
0
1
1
1
1
1
3
0
1
0
0
1
0
0
2
0
0
1
0
1
1
0
0
1
0
0
2
1
2
2
0
0
1
0
1
1
1
0
2
1
1
2
0
2
0
0
0
1
0
0
2
1
1
1
0
1
1
0
1
0
0
1
2
1
0
1
2
2
2
0
1
2
2
0
0
0
1
0
1
1
0
0
3
1
0
1
0
2
0
0
0
1
2
2
2
0
1
1
2
1
0
0
0
1
0
3
1
0
0
0
0
0
0
0
1
1
0
1
0
0
2
1
0
1
2
2
0
0
1
1
2
2
0
0
2
2
1
2
2
2
0
1
1
0
2
1
0
2
0
2
2
1
0
0
2
1
2
1
1
1
1
0
0
2
0
2
1
2
0
0
1
2
0
0
2
0
2
2
0
1
0
1
1
2
1
0
1
1
1
0
0
0
0
1
1
1
1
0
0
1
1
1
0
2
1
1
0
2
2
0
0
1
0
1
1
0
1
0
0
1
1
1
0
0
2
1
1
0
0
1
1
0
0
0
1
1
1
2
0
0
0
1
1
2
1
0
1
1
1
2
1
2
0
1
1
1
2
0
2
0
2
0
1
0
2
1
1
1
3
3
2
1
1
0
0
1
1
2
0
2
1
0
0
2
1
2
0
0
2
2
0
1
2
0
1
0
1
1
1
0
0
0
1
2
2
1
1
1
1
1
0
1
1
1
0
2
2
1
1
0
2
0
0
0
2
2
1
0
2
2
1
2
1
1
1
2
0
1
2
1
2
2
2
1
2
2
2
1
2
0
0
0
5
0
0
1
0
0
2
1
2
1
0
1
0
0
2
0
0
0
0
2
0
1
2
0
0
0
0
1
0
0
1
2
0
2
2
0
0
1
0
2
0
0
0
1
1
2
2
0
0
0
0
1
0
1
1
0
1
2
0
0
1
1
2
1
1
1
0
0
0
1
0
1
2
2
2
0
2
0
1
0
1
1
1
0
1
1
0
1
2
0
1
2
2
1
0
0
0
0
0
0
1
0
0
2
1
0
1
0
1
0
0
1
1
0
1
1
1
2
1
1
1
1
1
0
1
2
1
1
1
0
0
1
1
0
1
0
0
1
1
0
2
1
0
1
2
1
0
2
0
2
0
0
1
0
2
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
1
2
2
2
0
1
1
2
0
0
1
1
2
2
2
0
2
0
0
0
0
2
1
1
1
1
0
1
0
1
1
1
1
1
0
1
1
3
0
0
1
1
0
0
2
0
0
0
1
0
3
2
1
0
0
0
1
4
2
0
1
2
1
3
0
0
1
2
0
1
0
1
1
2
2
1
3
2
1
1
2
0
0
1
0
0
1
2
1
0
1
1
2
1
1
0
1
0
0
2
0
2
1
0
0
0
0
0
0
2
0
1
2
1
0
0
2
1
1
1
0
1
1
2
2
1
2
1
0
1
2
2
1
0
1
1
2
1
1
0
0
1
2
0
1
2
2
0
0
1
1
0
0
2
1
0
2
1
0
2
1
2
1
0
0
1
2
1
2
1
1
1
2
0
0
1
1
0
1
1
0
0
1
0
1
0
0
0
1
0
1
2
1
1
0
2
0
1
1
0
0
2
2
0
2
0
2
2
3
1
0
0
0
0
1
2
0
0
1
1
2
1
1
1
1
3
2
0
1
1
1
2
2
0
0
0
1
0
1
1
1
1
0
0
3
0
1
0
0
1
2
1
2
1
2
0
3
0
0
0
0
0
0
2
0
1
0
0
1
0
2
1
0
0
0
0
1
0
1
2
1
1
1
1
0
0
2
0
1
0
0
0
2
1
0
2
1
1
1
1
1
1
0
0
1
0
1
1
0
2
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
1
1
3
0
2
0
1
1
0
2
1
0
0
0
0
1
2
0
1
0
0
1
2
2
0
1
1
0
1
1
0
1
1
2
2
2
2
1
1
1
1
1
2
0
2
0
2
1
0
0
0
0
1
2
2
0
1
0
2
1
1
2
1
0
2
0
0
1
0
1
2
0
1
0
1
2
0
1
1
1
1
2
0
0
0
1
0
1
0
1
0
1
0
0
2
1
2
0
0
1
1
1
0
2
2
1
1
0
0
0
1
1
0
1
2
0
2
1
0
1
1
0
2
0
1
2
1
2
2
1
0
1
0
1
0
1
1
1
0
0
2
0
0
2
1
1
2
1
1
1
1
1
0
2
2
1
0
0
2
0
1
1
0
0
0
0
0
1
0
2
0
2
2
0
0
2
0
3
0
0
1
2
2
0
1
3
2
1
0
1
0
2
0
0
0
1
0
2
1
0
1
1
2
1
1
1
0
0
1
0
1
0
1
0
0
2
2
0
1
1
1
1
1
0
0
2
1
0
1
2
1
0
2
1
0
0
0
1
0
0
1
2
2
2
2
0
1
0
3
0
2
1
2
1
1
1
2
1
1
1
2
2
2
0
1
0
0
2
0
0
3
1
2
0
1
1
1
1
2
2
2
1
1
0
2
0
1
1
1
1
0
0
1
1
1
1
1
1
0
0
3
0
1
2
1
2
0
2
2
0
1
0
2
1
2
1
1
0
1
0
0
1
0
1
0
2
0
1
0
0
0
1
1
0
2
0
1
1
0
2
0
2
0
1
1
2
2
2
0
1
0
2
0
1
2
1
0
1
1
1
0
1
1
1
0
2
0
1
0
0
0
1
0
0
1
0
1
1
2
0
0
1
1
0
1
1
0
0
2
1
0
0
2
1
0
0
1
0
1
1
1
2
1
0
1
2
0
1
1
0
0
1
2
0
0
0
2
0
1
1
2
2
0
0
0
0
0
2
0
0
2
1
6
0
1
1
1
0
0
1
1
1
1
1
1
1
1
0
1
0
0
2
0
0
3
0
0
2
0
1
1
0
1
0
0
0
2
0
0
1
2
0
0
0
1
1
0
2
0
0
0
1
0
0
2
3
0
1
0
1
1
0
2
0
1
1
2
2
1
1
0
0
1
0
0
1
1
0
0
0
2
1
1
1
1
0
2
1
1
1
1
2
0
1
1
1
1
1
2
2
0
0
0
0
1
3
1
1
1
1
1
1
0
0
2
0
1
0
1
1
2
2
2
0
2
0
1
2
1
0
0
2
0
0
0
0
1
1
0
0
1
0
0
2
1
1
1
1
0
1
0
2
2
0
0
1
0
0
1
0
1
0
0
1
2
0
1
0
1
0
1
0
1
1
0
0
1
0
2
2
2
1
2
1
1
0
1
2
1
1
0
1
1
0
1
2
2
0
2
2
2
0
1
2
1
1
2
2
0
2
0
0
1
0
1
1
0
1
2
0
1
0
0
1
1
2
0
1
0
0
0
0
0
1
0
1
1
1
1
1
0
0
1
0
0
2
0
0
0
0
2
0
1
1
0
0
2
2
0
1
0
0
1
2
1
0
0
1
2
0
1
0
0
0
0
0
1
1
2
1
1
1
1
0
1
1
1
1
1
1
0
0
1
1
0
2
0
0
0
2
2
0
0
1
1
1
0
0
1
2
0
0
1
0
0
1
0
0
2
0
2
0
1
0
0
1
1
1
1
1
0
1
0
1
1
2
0
0
1
1
1
1
2
0
1
0
0
0
1
2
1
2
0
0
1
1
2
2
0
1
1
0
0
0
0
1
1
0
0
1
0
0
0
1
0
1
0
1
1
1
0
2
1
1
1
0
0
2
1
1
1
1
0
1
0
1
0
0
0
0
1
1
1
1
1
2
0
1
1
1
2
2
1
0
2
0
1
1
1
2
0
1
1
0
1
1
1
2
2
1
0
0
2
1
0
0
1
0
0
0
0
1
0
0
2
1
0
0
0
2
1
0
1
2
0
1
0
1
1
1
0
1
0
0
0
1
2
1
0
0
0
0
1
1
1
0
0
1
2
0
1
0
1
0
0
1
1
0
1
2
1
0
1
1
0
1
1
0
0
2
2
3
2
1
1
1
1
2
1
0
1
1
2
1
1
1
0
0
1
1
1
1
2
1
1
1
1
0
2
2
2
1
0
0
1
0
2
2
2
1
0
1
1
0
0
4
2
2
2
1
1
1
1
1
1
0
2
2
0
2
3
0
0
1
0
1
2
1
1
1
0
1
1
1
0
1
0
2
1
1
0
1
1
2
1
0
1
0
2
0
2
1
2
2
1
1
0
1
1
0
0
2
0
0
1
3
1
1
1
1
1
2
0
0
1
1
1
1
1
1
0
0
0
1
2
0
1
0
2
0
1
1
2
0
0
0
0
1
0
1
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
1
0
2
1
1
0
0
2
0
3
0
0
0
3
0
2
0
2
1
2
1
0
2
1
0
1
0
0
0
1
0
1
2
1
2
3
0
1
1
0
1
1
0
0
1
0
0
0
1
1
2
1
3
1
1
1
0
1
0
2
0
0
3
0
2
1
1
2
2
0
1
2
0
0
1
1
0
1
1
1
3
0
1
1
1
1
0
1
0
1
2
0
1
1
1
2
1
1
0
1
0
2
1
0
1
2
2
1
1
1
0
0
0
0
1
0
1
1
0
1
1
2
0
1
2
1
1
1
1
0
2
1
0
1
2
1
0
0
0
0
1
1
1
1
2
0
3
2
1
0
1
1
2
0
1
0
1
2
0
1
0
0
0
1
1
0
0
1
0
1
0
1
1
0
0
2
1
0
1
2
1
0
0
0
0
0
2
1
1
0
0
2
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
1
1
2
1
2
1
2
1
3
0
2
0
1
1
2
2
1
1
0
1
1
0
0
0
2
0
0
0
1
2
0
1
3
2
2
0
0
0
0
0
0
0
0
1
1
1
2
0
0
0
0
0
1
0
1
0
0
0
1
2
1
1
2
2
1
1
1
2
0
2
0
2
0
1
1
1
1
0
2
0
0
1
1
1
1
0
0
0
1
0
2
1
0
1
2
0
1
0
2
0
0
1
2
1
1
1
1
2
0
1
2
0
1
0
1
1
2
1
0
0
2
1
0
1
0
0
1
0
0
1
1
0
2
0
0
1
1
1
1
1
0
0
1
2
2
0
0
0
1
0
0
1
0
0
1
0
0
0
0
3
1
1
1
0
1
1
2
0
2
1
1
0
2
0
0
0
1
0
0
2
0
0
1
0
0
1
0
2
0
1
1
2
0
1
0
0
2
1
4
0
2
1
1
2
1
0
0
2
1
1
1
1
2
4
0
2
2
0
0
1
1
1
0
1
0
1
2
1
1
3
2
0
0
0
2
1
0
0
0
1
0
0
0
2
0
2
1
1
1
0
0
0
0
1
0
1
0
1
0
1
1
1
1
1
1
1
2
1
1
2
0
0
3
1
1
0
1
5
4
1
2
1
0
2
2
0
0
1
0
1
1
1
2
1
0
0
1
0
2
0
1
1
0
1
1
0
1
2
0
2
0
2
0
0
0
1
2
1
0
0
1
1
0
0
5
0
1
0
1
1
2
0
0
3
0
0
1
0
1
0
1
0
0
0
1
2
0
0
0
1
2
0
2
1
2
1
1
2
2
1
0
1
1
1
0
0
0
0
1
2
1
2
2
1
2
0
0
1
1
1
1
2
0
2
1
1
0
2
1
0
0
2
1
0
1
0
0
0
1
0
1
2
0
1
1
1
0
2
0
1
0
0
0
2
0
1
1
1
1
1
1
2
1
2
0
0
0
0
1
1
0
1
2
2
0
0
1
0
0
1
0
0
1
1
0
0
2
1
2
0
1
1
1
0
0
1
2
1
1
0
0
0
0
1
1
2
0
0
1
2
3
1
0
1
1
0
2
1
1
0
1
1
0
0
2
0
0
2
0
0
2
1
0
2
0
0
0
1
0
0
0
2
0
1
1
0
1
0
1
0
0
0
0
1
1
1
1
2
0
2
1
1
0
0
2
2
2
0
1
1
1
2
1
0
1
0
1
0
0
1
0
0
0
1
1
1
0
1
2
1
1
1
0
2
1
0
1
1
1
1
1
0
0
1
1
0
0
1
0
0
1
1
0
0
0
0
0
1
0
1
2
1
2
2
0
1
1
0
1
0
0
1
2
2
0
0
2
0
1
1
2
1
2
1
2
1
1
0
0
2
2
1
0
0
2
0
2
1
1
1
2
1
1
1
0
1
1
1
1
1
2
0
0
1
3
0
0
0
0
3
2
0
1
0
2
1
1
1
0
2
1
1
1
0
1
2
2
1
2
1
0
0
0
11
0
1
1
0
1
1
1
1
2
1
0
2
0
1
2
0
2
1
1
0
1
2
0
2
1
0
2
1
0
0
0
1
1
1
1
2
1
0
1
0
0
0
0
1
1
0
0
2
1
2
1
1
0
1
1
0
1
1
0
0
0
1
0
1
0
1
0
0
0
2
0
0
0
0
1
0
2
2
0
1
0
0
0
2
2
1
0
0
1
1
2
1
2
1
1
1
0
2
2
1
1
0
1
1
2
0
0
2
0
0
1
1
2
1
3
0
1
2
0
1
1
1
1
0
2
3
1
1
1
2
1
0
1
0
0
1
1
0
2
1
1
1
2
0
0
4
0
1
1
1
2
1
1
0
2
0
1
2
0
1
1
2
2
0
2
2
1
2
2
1
0
2
1
0
1
0
1
0
2
4
2
1
0
2
2
1
1
0
2
1
0
0
1
1
1
1
2
0
2
0
0
2
0
0
1
0
1
2
1
0
1
2
2
1
0
1
1
1
1
1
0
2
2
1
1
0
0
0
2
0
0
2
2
1
0
0
1
0
2
1
0
2
0
1
2
1
2
0
2
0
0
1
1
0
2
2
0
2
1
2
1
0
1
0
1
1
0
0
2
1
1
0
0
0
0
0
2
0
0
0
2
0
1
0
2
2
0
0
2
0
0
0
1
0
0
1
1
0
0
0
2
0
0
1
0
0
0
2
0
0
1
1
2
1
2
2
1
0
1
2
0
1
1
2
2
1
1
1
0
1
0
0
1
0
1
0
1
0
0
0
1
1
2
2
2
1
2
2
0
1
1
1
0
1
1
1
2
1
0
0
1
0
0
1
2
2
1
0
1
0
0
0
1
0
3
2
0
1
0
1
2
0
0
2
0
1
2
0
1
0
2
2
2
1
1
0
0
2
1
2
1
0
1
2
0
0
1
2
2
1
1
2
7
1
2
0
2
2
1
1
0
2
0
1
2
1
1
0
1
0
0
0
2
1
0
0
1
1
0
0
2
0
1
1
1
0
2
1
2
1
1
0
0
0
1
0
1
1
0
1
0
0
1
2
1
1
0
1
1
0
0
2
0
0
2
0
5
1
0
1
1
0
1
1
0
0
1
0
2
0
1
0
1
0
1
0
1
0
1
0
2
2
1
1
2
1
1
2
1
0
2
2
3
0
0
2
0
1
1
2
1
1
2
3
0
0
0
1
0
2
2
2
0
0
1
1
1
1
1
2
0
1
2
1
2
1
2
1
0
1
0
1
1
1
3
0
1
1
0
1
1
2
0
1
0
2
0
1
0
0
1
1
1
0
2
2
2
0
0
2
1
1
1
1
1
1
1
1
1
0
1
1
1
0
0
0
0
0
1
0
0
1
0
2
1
2
2
1
1
2
0
1
2
1
0
1
1
0
2
0
3
1
0
0
0
2
1
0
2
1
1
2
0
1
1
1
1
2
0
0
1
1
2
1
1
0
0
1
0
1
2
1
1
2
2
2
1
2
1
0
2
1
0
0
0
2
0
2
2
0
0
1
2
5
0
2
2
2
0
1
2
0
1
0
0
0
1
2
1
1
0
0
2
5
1
1
2
2
1
0
1
1
0
0
1
0
1
0
1
1
0
2
1
0
1
1
2
2
1
2
0
1
2
1
1
1
1
0
0
0
1
0
2
0
2
2
2
1
0
2
0
1
1
0
0
1
2
0
0
0
1
1
2
1
2
0
1
1
1
2
2
0
0
2
0
0
2
0
0
1
1
1
0
2
2
2
0
0
1
1
2
1
1
1
1
2
2
2
0
0
1
0
2
0
0
1
1
0
0
1
2
2
2
1
1
1
1
0
0
0
1
1
0
1
1
0
1
0
1
1
0
0
1
6
1
0
2
0
0
2
2
0
2
1
1
0
1
2
0
1
2
2
1
0
0
1
0
0
0
0
1
2
1
2
1
1
3
1
0
1
1
1
1
1
1
0
1
1
1
0
0
1
0
0
2
3
2
0
0
0
0
1
3
0
0
2
1
3
1
0
1
0
0
1
0
1
2
1
1
1
1
1
1
2
1
0
0
0
2
2
2
3
1
1
0
1
3
0
1
0
0
1
1
1
0
2
0
1
1
1
1
0
1
1
0
1
0
0
2
1
1
1
2
0
1
0
0
1
2
1
0
1
1
0
1
2
2
1
0
0
1
0
1
1
1
0
1
2
1
1
1
3
1
0
2
0
1
0
0
2
0
0
1
0
1
3
1
2
2
1
0
2
1
1
1
2
2
2
1
1
0
1
0
0
2
0
1
0
0
1
3
1
0
0
1
3
2
1
1
0
1
0
0
0
1
1
1
3
1
0
1
1
1
0
0
0
0
2
0
2
1
2
1
0
1
1
0
3
1
1
0
1
1
1
1
0
1
1
2
0
0
0
1
0
1
0
0
0
1
1
0
1
0
0
0
1
0
2
0
0
2
4
1
3
2
0
1
0
0
2
1
1
1
1
1
0
0
1
0
2
2
0
2
1
0
0
1
0
1
0
0
1
0
0
2
2
3
2
2
0
1
1
0
1
1
0
1
1
0
2
0
0
0
0
0
2
0
1
1
2
0
0
0
1
1
2
1
0
0
2
1
0
0
0
1
1
1
2
1
1
1
1
1
4
2
1
1
1
0
1
1
1
1
1
1
2
0
0
1
0
1
0
1
0
0
2
0
2
2
2
0
0
0
0
1
3
0
0
2
2
3
0
1
0
0
3
2
1
2
2
1
1
1
1
0
1
1
1
2
1
1
1
2
2
3
1
1
0
1
0
0
1
1
0
1
0
0
1
0
0
1
1
1
2
2
0
0
0
1
1
0
2
1
1
1
0
1
2
0
2
1
1
0
1
1
2
0
0
1
1
2
0
0
1
0
2
1
3
1
0
0
0
2
0
0
0
2
2
0
2
0
0
2
1
1
0
1
0
1
1
0
4
1
0
0
2
5
1
2
0
0
0
1
1
1
0
1
2
0
0
0
2
0
0
2
0
1
1
1
0
0
2
1
2
2
1
0
0
0
0
2
1
1
2
0
2
1
1
1
1
0
0
0
0
0
0
0
1
1
0
2
1
0
0
1
0
0
2
1
1
0
1
1
1
1
0
1
0
1
1
1
2
1
1
0
0
1
1
1
0
1
1
2
3
2
0
1
1
0
0
2
1
1
0
1
0
2
1
1
1
0
0
1
1
1
1
1
0
0
2
0
2
0
2
1
1
0
2
0
0
0
1
0
2
0
0
0
2
0
1
0
1
1
1
0
1
0
1
1
1
0
2
1
0
1
1
1
1
1
2
2
0
1
2
0
1
0
0
3
0
0
0
1
0
0
4
1
0
2
0
0
1
2
2
0
1
1
1
0
1
1
1
0
1
2
0
1
2
2
1
2
1
0
2
0
2
1
0
2
0
2
0
2
1
0
0
1
1
1
0
0
0
0
1
0
6
2
2
1
0
1
1
1
1
1
2
1
2
1
0
1
1
1
2
1
2
0
2
1
1
1
0
1
0
2
0
1
3
1
1
0
0
1
1
1
0
1
2
0
0
1
2
0
0
0
0
1
0
1
2
0
2
0
0
0
2
1
0
1
1
0
1
0
0
0
2
0
1
0
1
0
1
0
1
0
0
0
0
1
2
1
1
1
0
0
1
1
2
0
0
1
2
2
1
1
1
1
0
1
0
2
2
0
0
2
0
1
2
0
2
1
0
2
0
2
1
1
2
0
0
0
1
1
0
1
1
1
1
1
2
0
1
1
1
2
1
0
1
1
0
0
0
3
0
1
1
0
2
1
0
2
1
1
0
1
0
3
1
1
0
1
2
1
1
0
0
2
1
2
1
1
1
0
1
0
0
0
1
0
2
1
2
2
0
0
1
2
0
0
0
0
1
1
1
1
2
1
1
2
0
0
0
0
0
0
0
2
0
0
0
1
2
0
1
1
1
2
2
1
2
0
1
0
0
0
2
2
3
1
0
1
0
1
1
0
1
0
0
1
0
1
2
2
2
2
1
1
0
1
1
0
0
1
0
0
1
1
0
2
1
2
0
1
1
1
0
1
2
1
0
2
0
2
1
1
0
0
0
0
0
0
1
0
1
1
1
1
1
0
0
1
0
0
2
1
0
1
0
2
1
1
2
1
1
1
0
1
1
1
0
0
1
1
2
1
2
0
1
1
1
0
1
2
1
2
1
2
0
0
2
0
1
1
0
1
1
0
1
2
0
0
3
1
0
1
2
1
2
0
1
0
0
1
1
0
1
1
0
2
2
1
0
0
0
1
2
1
0
1
1
0
1
0
2
1
1
2
1
1
2
0
0
0
0
1
0
0
0
0
1
1
1
2
0
1
1
2
0
2
2
1
1
2
3
1
1
0
0
1
2
1
1
2
1
1
0
2
0
0
1
2
1
2
1
2
0
2
1
1
0
1
0
1
1
2
1
1
1
1
0
0
1
0
1
0
1
1
0
0
1
1
1
2
0
0
0
0
0
0
0
1
3
2
1
0
1
1
1
2
1
2
2
1
1
1
1
0
0
0
0
1
1
1
1
1
1
2
0
0
0
1
0
1
0
0
2
1
1
2
0
1
1
0
1
1
0
0
1
1
2
1
0
1
0
1
0
0
1
1
0
0
0
0
0
1
0
2
0
0
1
0
3
1
1
1
0
1
2
0
0
1
0
2
1
1
1
1
1
1
2
0
1
0
1
3
2
0
0
0
2
2
0
1
0
1
0
2
0
0
0
2
1
1
0
2
0
0
2
1
2
1
2
1
0
1
0
2
0
1
1
1
1
1
1
2
2
0
0
2
1
1
0
1
0
1
2
2
2
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
1
0
1
0
0
1
0
0
2
0
1
2
2
1
2
1
1
0
2
1
1
1
1
0
1
0
2
1
1
1
0
0
1
0
0
0
0
0
2
2
0
0
1
0
0
1
1
0
0
1
0
0
1
2
1
0
1
0
1
2
0
2
1
0
1
0
1
0
2
1
0
2
4
0
1
0
1
0
0
1
0
0
2
3
0
1
1
0
0
2
0
2
0
1
0
2
1
1
0
1
1
0
0
0
2
0
0
1
1
1
0
2
2
2
0
1
0
1
1
1
0
1
2
0
0
1
1
2
2
1
2
1
1
1
1
0
2
0
0
2
4
0
2
1
0
2
0
0
0
1
1
0
0
0
0
1
1
2
1
1
1
1
0
1
1
1
0
1
0
0
1
2
0
2
0
0
1
0
0
1
1
3
2
1
2
0
1
2
0
1
0
0
2
0
1
0
0
2
1
1
1
1
1
2
0
0
2
1
1
0
0
1
0
0
0
1
1
0
0
1
0
2
2
0
1
0
1
1
2
2
0
0
1
0
2
0
0
1
1
2
2
1
0
1
0
1
2
0
1
0
1
1
0
1
1
2
2
2
0
1
1
2
1
1
0
1
0
2
1
0
0
1
0
0
0
0
1
1
1
1
2
1
0
0
1
0
1
1
0
1
1
2
1
1
0
1
2
0
0
0
1
0
0
0
1
2
1
1
0
0
1
1
1
0
0
1
3
0
2
0
0
0
1
0
0
0
2
1
1
2
2
3
1
1
2
0
1
2
0
1
1
1
0
2
1
2
1
1
0
0
1
0
0
1
0
0
1
0
0
0
1
0
1
2
1
2
0
1
1
0
1
2
1
0
0
2
2
2
1
2
1
0
2
0
1
1
1
1
0
1
0
0
2
1
1
0
0
1
1
1
1
1
0
0
0
0
0
2
0
0
0
1
1
0
1
2
0
0
1
1
0
1
0
0
1
0
0
0
2
2
1
1
1
1
0
0
1
1
2
1
0
2
0
1
1
1
0
1
0
2
1
2
0
0
1
2
1
0
0
1
1
0
1
1
2
0
1
0
2
0
1
0
1
1
0
1
0
0
2
0
0
0
2
0
1
0
1
2
1
2
0
2
0
1
1
1
0
0
0
0
0
1
2
1
0
2
0
0
1
2
1
0
1
2
2
1
0
2
0
1
2
0
1
1
1
1
2
2
1
0
0
2
0
1
0
0
1
1
3
0
1
1
0
1
1
0
0
1
0
0
1
0
1
1
0
1
2
2
1
1
0
0
1
0
0
2
2
1
2
1
3
0
2
0
1
0
0
1
2
1
1
1
1
2
0
1
2
2
1
0
0
2
0
1
2
0
1
2
1
0
1
2
2
2
1
0
1
1
2
1
1
0
2
1
0
1
1
0
0
1
2
2
1
2
0
1
2
0
1
2
2
1
0
1
0
0
0
2
1
2
1
2
0
1
3
1
1
0
1
0
2
1
1
3
0
1
1
1
2
1
1
0
0
1
0
1
2
1
1
1
1
1
1
2
1
0
2
0
0
0
0
0
1
1
3
2
2
0
0
1
2
0
2
2
2
0
2
1
0
0
2
2
2
0
0
0
0
1
0
1
0
1
0
2
1
0
1
1
0
1
0
2
0
2
0
1
1
1
1
1
1
0
1
0
1
1
1
2
1
2
2
1
2
1
1
0
0
1
0
1
1
1
0
2
0
1
2
2
0
1
0
2
2
1
0
0
0
1
0
1
0
1
2
0
0
1
0
1
2
1
0
1
1
0
0
0
0
1
1
1
1
1
1
0
0
3
1
0
1
2
1
0
1
2
1
1
0
0
0
1
0
1
1
1
2
1
4
1
0
0
1
3
1
0
0
0
0
0
0
2
1
1
2
1
1
1
1
1
4
1
2
2
2
2
1
2
1
1
0
0
2
1
3
0
0
0
0
0
3
2
0
0
1
1
0
2
0
1
0
1
0
2
0
1
1
0
0
1
2
1
2
0
2
2
2
1
1
0
1
1
1
0
0
2
1
2
0
1
0
2
0
0
2
1
0
2
1
1
0
1
1
2
0
0
1
2
2
0
2
0
1
0
0
1
0
1
2
1
0
2
0
2
0
1
1
0
1
1
2
0
0
2
1
0
0
1
0
0
1
2
1
2
0
2
1
1
0
0
0
1
1
1
0
1
1
1
2
0
1
2
0
0
1
2
1
0
1
1
2
1
1
2
2
1
1
1
2
2
0
0
2
0
1
2
0
1
0
0
1
0
1
2
1
1
1
0
2
0
2
1
1
1
1
0
1
2
2
0
0
2
2
0
2
1
2
0
1
1
1
2
1
1
1
2
1
1
0
0
1
1
0
1
0
2
0
1
1
1
1
1
0
0
0
0
1
0
0
0
2
1
1
0
1
0
1
1
2
1
0
0
1
1
0
0
1
1
0
1
0
0
0
1
1
0
0
1
2
1
1
0
1
0
0
2
1
0
0
1
0
2
1
1
1
2
1
1
1
0
1
1
1
1
2
0
0
1
2
4
1
1
2
0
1
2
0
1
1
0
1
1
0
1
0
1
1
2
1
0
1
2
2
1
2
1
0
0
0
1
0
0
2
0
1
0
1
0
0
1
1
0
1
1
1
1
2
2
2
1
1
2
1
4
0
0
0
0
0
1
2
1
0
1
1
1
0
2
0
1
2
0
2
1
0
0
2
2
1
1
1
1
3
1
1
1
1
0
2
1
0
1
1
0
0
1
1
0
1
1
2
1
0
1
2
1
1
0
2
2
0
1
1
1
0
2
2
0
0
1
0
1
0
1
1
1
0
1
2
2
1
2
0
0
1
1
0
1
1
2
0
0
1
0
0
0
2
0
1
3
0
2
1
0
1
3
1
0
0
2
2
0
1
1
1
0
0
0
1
1
1
0
1
1
1
1
1
1
0
1
1
0
0
0
0
1
0
0
0
1
0
1
2
0
1
0
1
2
0
0
2
2
0
0
2
1
2
1
0
0
0
2
0
0
1
1
0
2
0
2
1
0
1
0
0
0
1
0
2
1
0
1
2
2
1
0
0
0
0
2
1
1
0
2
2
2
0
2
0
1
1
0
0
1
0
2
1
2
2
1
0
0
2
0
0
1
1
1
1
0
0
0
0
0
1
1
1
1
0
2
3
1
0
0
2
0
0
2
0
2
1
0
1
2
1
0
0
0
2
0
2
1
2
1
1
1
1
0
0
0
0
1
1
1
0
0
1
0
1
0
3
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
2
1
2
0
1
1
1
0
1
0
1
1
0
0
2
1
1
0
1
1
0
1
1
1
0
1
0
0
0
0
0
2
1
1
1
1
1
0
3
1
1
2
1
1
1
0
1
2
0
0
2
1
0
2
2
1
1
1
0
0
2
2
0
0
1
1
0
1
0
2
1
1
2
2
1
1
2
2
0
2
0
1
1
1
2
1
1
1
0
1
0
1
0
2
1
0
2
0
0
1
0
0
1
0
0
1
0
0
1
3
0
2
2
1
1
1
2
2
0
2
0
0
0
1
0
2
1
1
2
1
0
0
0
1
1
0
1
1
1
1
0
2
2
1
1
1
0
0
1
1
1
1
1
1
1
0
1
2
2
0
0
2
1
2
1
0
0
2
2
0
1
1
1
0
2
1
1
1
0
0
1
2
1
0
1
1
2
1
0
0
2
1
1
0
1
1
0
0
0
0
0
2
1
0
0
1
1
0
1
1
1
0
0
1
0
1
1
2
2
1
1
0
1
1
2
2
1
2
0
2
2
0
1
2
2
0
0
0
0
1
1
0
1
2
1
0
1
1
1
2
1
1
0
1
0
1
2
1
0
1
1
0
1
0
1
0
0
1
1
2
1
1
1
1
0
2
1
2
0
2
0
0
0
1
0
1
2
0
1
2
0
0
0
0
0
0
0
0
1
2
0
0
1
0
1
1
2
0
0
0
2
0
2
1
1
0
1
1
1
0
0
1
1
2
2
1
0
1
1
0
0
2
1
2
1
1
0
0
1
0
1
0
0
0
0
1
1
0
2
0
1
1
1
1
0
1
1
1
1
1
0
1
0
1
1
2
0
0
0
1
1
1
2
0
1
1
1
1
2
0
1
2
1
1
0
0
0
1
1
2
0
1
0
1
2
0
0
2
1
1
1
1
1
0
0
2
5
2
0
1
0
0
0
2
1
0
1
2
1
0
0
0
0
1
2
1
1
0
1
0
2
1
0
0
4
1
0
1
0
0
1
1
1
0
2
0
0
0
1
2
2
1
1
1
2
1
0
0
0
0
0
1
0
1
1
1
1
2
1
1
1
1
1
0
1
1
1
0
2
2
1
1
1
0
2
0
2
1
2
2
0
1
2
0
0
1
2
2
1
1
1
1
1
1
2
0
2
0
1
2
1
0
0
0
1
2
0
0
1
1
1
0
0
0
1
1
0
2
0
1
3
0
0
1
0
1
1
0
1
0
0
0
0
0
0
1
2
2
2
1
0
1
0
1
0
0
0
2
1
1
1
1
0
0
0
2
2
1
0
1
1
1
1
0
0
3
2
0
1
1
2
0
0
0
1
1
0
2
3
0
1
0
0
0
1
0
0
1
0
2
0
1
1
1
0
0
1
2
0
3
0
1
0
2
2
0
1
1
0
1
0
2
2
0
1
1
2
1
0
1
0
1
1
0
0
1
1
1
2
1
1
0
1
2
3
0
1
1
1
1
1
1
0
0
1
0
1
0
1
0
1
1
1
0
0
1
0
2
1
0
1
1
2
0
1
1
1
1
2
1
2
1
0
2
1
1
1
2
1
0
1
1
1
2
0
0
1
1
1
2
1
3
0
1
1
2
4
1
0
1
2
0
2
1
1
2
2
0
1
0
2
2
2
1
0
0
1
1
0
0
1
1
0
0
1
2
0
2
0
2
1
0
1
0
0
1
1
0
0
1
1
2
0
1
2
1
1
1
0
1
1
1
0
0
0
0
1
0
2
1
2
2
2
1
1
2
1
1
2
0
0
1
0
0
1
1
1
2
2
0
1
2
0
1
1
0
0
0
1
0
1
0
1
1
0
0
0
2
0
0
0
0
0
2
0
1
2
1
0
0
0
2
0
0
2
1
1
1
0
0
1
1
1
0
2
0
0
1
0
1
2
0
1
1
2
0
1
0
1
2
1
3
2
3
1
1
2
2
2
2
1
0
0
0
0
1
0
1
1
2
0
0
1
1
1
0
2
1
1
2
0
1
0
1
2
0
1
1
1
2
1
1
2
0
0
1
1
1
2
0
1
1
0
2
1
2
1
2
0
1
1
0
2
1
1
1
2
1
1
0
2
0
2
2
1
1
0
2
0
1
0
1
1
0
1
1
1
1
1
0
1
0
0
0
1
1
2
1
0
1
0
2
1
1
2
0
1
1
1
2
1
0
0
1
1
1
2
1
2
1
2
1
0
0
0
0
0
0
1
0
0
0
1
1
0
2
1
2
1
1
1
2
2
2
2
2
1
2
1
2
2
1
2
0
2
2
2
0
1
2
1
2
1
0
1
1
1
0
1
2
1
2
6
1
1
1
0
0
2
0
1
0
1
0
2
1
1
2
0
0
0
2
1
2
2
1
2
1
0
1
0
0
1
2
2
2
1
0
3
0
0
1
0
1
1
1
1
1
0
0
1
1
1
0
1
1
0
2
1
0
1
0
0
1
1
1
0
1
1
0
1
3
0
1
1
2
1
0
1
2
0
1
0
2
0
1
2
1
1
0
1
1
1
0
2
0
2
0
1
1
1
0
2
1
2
0
0
0
0
1
3
2
1
2
0
0
2
0
1
0
1
1
1
0
0
2
1
2
1
0
2
0
1
0
2
0
0
2
2
2
0
1
1
1
0
1
0
1
0
1
0
2
1
1
1
2
1
0
2
0
0
0
0
0
1
0
1
0
1
1
1
0
0
1
0
0
0
2
0
2
1
0
0
1
1
0
0
2
2
0
0
4
1
0
1
1
0
0
1
0
1
2
0
1
0
0
1
1
0
0
1
0
0
1
1
0
1
0
2
0
1
0
2
0
0
1
2
0
1
1
2
2
0
1
1
1
1
0
1
1
3
0
2
1
0
0
1
1
2
0
1
2
0
1
1
0
3
0
0
2
1
1
1
0
0
0
0
0
0
1
1
0
0
2
2
0
0
0
1
2
2
1
0
2
1
2
1
1
1
0
1
1
2
0
2
1
1
1
1
1
2
0
1
1
1
0
1
1
2
0
2
2
0
1
2
2
1
2
2
2
2
0
2
2
1
2
1
2
1
0
1
0
1
2
0
0
0
0
0
0
0
2
1
1
1
1
0
1
3
1
1
2
1
0
0
1
1
0
1
0
0
0
0
0
1
0
1
0
1
1
2
0
1
1
0
2
0
1
1
1
1
0
0
2
0
2
2
0
1
0
1
0
1
1
0
0
1
1
0
0
0
1
1
1
2
1
1
4
0
2
0
0
1
1
1
1
0
2
2
0
1
2
2
0
0
0
0
1
0
0
0
1
1
2
1
1
1
0
0
0
1
0
2
0
2
0
1
1
1
0
1
0
0
1
2
1
2
1
1
0
1
1
0
2
1
1
1
2
0
0
0
1
2
2
2
2
1
2
0
0
0
0
2
2
0
0
0
0
1
2
0
1
1
2
0
2
2
1
2
1
0
0
2
0
2
2
1
1
0
0
0
0
1
0
0
0
1
1
1
0
1
1
2
1
3
1
0
0
1
0
2
0
0
0
1
0
0
2
1
1
1
1
1
0
1
2
1
0
3
0
3
1
0
1
1
2
0
0
1
0
0
0
0
1
0
1
0
2
0
2
0
0
2
2
0
0
0
2
0
0
1
0
0
0
2
0
1
0
0
1
0
1
0
1
0
1
0
1
1
0
0
1
0
0
1
0
1
1
0
0
2
2
1
0
1
1
0
2
0
0
0
1
0
0
0
2
0
2
1
0
1
1
2
0
2
0
0
0
1
0
2
0
2
0
1
0
2
0
1
1
2
1
2
0
1
0
1
0
1
2
0
1
1
1
1
0
2
2
1
2
2
2
1
0
1
2
0
0
0
1
0
0
2
2
1
0
1
1
2
1
0
2
0
0
0
1
0
2
1
0
1
0
2
0
1
2
1
2
2
1
2
0
1
1
0
1
2
1
1
1
0
0
2
1
0
0
1
1
1
1
1
0
1
2
4
0
1
1
1
0
2
0
1
1
2
1
2
1
0
1
1
1
1
2
1
2
2
0
1
1
0
0
1
1
2
0
2
0
1
0
1
2
0
3
1
1
1
2
1
1
0
0
2
0
1
1
2
2
0
1
1
2
2
0
2
1
2
1
0
0
2
1
0
1
1
2
1
1
0
1
0
2
1
0
1
1
0
1
1
1
2
2
0
1
2
1
7
2
2
1
2
0
2
0
0
0
0
0
1
0
0
0
1
4
0
2
1
1
1
0
0
1
2
0
1
1
0
2
0
1
0
0
1
0
2
1
2
1
0
0
1
0
1
0
1
1
1
2
0
2
2
1
1
2
0
1
0
0
0
1
1
0
1
1
1
0
0
1
0
0
0
2
0
1
1
0
2
0
1
1
0
1
1
1
2
0
0
0
0
0
1
1
1
1
0
2
1
1
1
0
1
0
2
0
0
0
0
1
0
2
0
2
2
0
0
1
0
0
0
2
0
0
1
1
1
0
1
0
2
0
1
0
0
0
1
2
0
0
1
1
3
1
1
1
2
1
1
2
0
0
0
1
2
0
0
0
1
1
1
1
1
1
0
1
0
3
1
0
0
1
0
0
0
1
1
2
0
1
2
1
0
2
1
1
1
1
1
0
1
0
0
1
0
1
0
2
0
1
1
0
2
1
2
1
0
0
2
2
0
2
1
1
1
1
2
1
2
0
2
0
0
0
2
0
2
4
2
2
2
0
2
0
0
1
0
1
0
1
0
1
0
2
0
1
0
0
1
1
1
1
1
0
2
2
0
1
1
1
0
0
1
1
1
0
0
1
0
1
1
2
0
0
1
0
1
0
2
0
1
0
1
1
1
1
1
0
2
2
2
1
1
1
2
1
2
0
0
0
1
0
1
1
0
0
1
1
0
2
1
0
0
0
1
3
1
0
0
0
0
1
0
0
2
0
1
2
1
1
2
0
0
2
0
1
1
1
0
0
0
1
0
0
1
1
1
2
0
0
0
1
0
1
0
1
1
1
0
0
1
1
0
0
1
1
1
1
1
0
1
0
0
1
0
1
1
0
1
0
0
1
0
1
1
2
0
0
1
0
1
3
1
1
2
1
0
0
0
0
0
2
0
1
0
1
1
3
0
2
2
0
0
1
0
1
1
0
1
1
3
0
2
2
2
1
2
1
0
2
1
1
0
2
1
1
1
2
0
2
1
0
2
2
1
2
0
0
1
2
1
0
2
2
0
1
0
1
2
2
1
1
1
2
1
0
1
1
0
2
1
1
2
1
0
1
0
1
2
0
0
1
1
0
2
1
2
2
2
1
0
1
1
1
1
2
0
2
1
1
2
1
0
2
1
2
2
1
2
0
0
1
0
1
1
0
0
1
0
0
2
1
1
1
1
2
1
0
0
0
0
0
0
0
0
1
1
1
3
1
0
0
1
2
1
2
1
1
0
0
0
2
1
0
1
2
2
2
1
0
0
1
2
1
2
0
1
2
1
2
0
1
0
1
0
1
0
1
1
1
2
1
1
1
0
0
1
0
0
0
1
1
1
2
2
1
0
1
1
1
3
1
1
2
0
1
1
0
1
0
2
2
0
1
0
1
3
1
1
0
1
1
0
0
1
1
1
0
0
1
0
0
1
0
0
1
1
0
0
1
1
1
0
1
2
0
1
1
1
0
1
0
1
0
2
0
0
0
0
1
3
0
2
1
1
2
0
1
2
0
0
1
0
1
0
1
1
1
0
1
0
0
1
1
1
1
2
0
0
0
2
0
1
2
2
0
0
1
2
1
2
2
1
1
0
1
0
0
1
1
0
0
1
2
2
2
0
1
0
1
1
2
2
2
1
0
1
1
1
2
0
1
2
2
1
0
1
2
1
0
0
1
0
1
1
1
1
1
4
2
0
1
1
2
0
0
0
2
2
0
0
0
1
2
0
0
1
0
1
0
1
0
2
0
0
0
2
1
1
1
1
1
1
0
0
2
1
1
1
1
1
1
1
0
2
0
0
0
0
0
2
2
1
2
0
1
0
2
1
1
0
2
0
1
1
1
2
1
0
0
0
2
1
1
1
1
2
1
1
0
1
1
2
1
1
0
1
2
1
2
0
1
0
1
0
0
1
0
0
1
0
1
0
3
0
1
1
1
1
2
1
0
1
0
1
1
1
1
2
1
1
2
2
0
1
0
1
0
0
0
0
1
0
2
2
1
1
1
1
0
1
2
1
0
3
0
1
0
0
0
0
1
2
1
1
0
2
1
0
1
2
0
1
1
0
0
0
2
0
2
0
1
1
2
1
2
1
2
2
1
1
0
1
0
0
2
1
1
0
1
1
0
0
2
1
0
0
1
1
0
1
0
0
1
0
0
0
1
1
2
1
0
1
2
1
0
1
0
0
0
0
1
0
1
1
2
0
1
0
1
0
0
2
1
0
0
0
0
0
0
0
2
1
1
1
0
1
1
2
1
1
0
2
2
2
1
1
0
0
1
1
0
0
1
1
0
1
1
0
2
1
0
0
0
1
0
1
1
1
3
0
1
0
1
1
1
1
2
0
1
1
2
2
1
0
1
1
1
2
1
2
1
2
1
0
1
0
1
2
0
0
1
0
1
0
0
1
1
1
1
0
2
0
1
1
2
0
1
1
0
0
0
0
1
0
1
2
0
0
0
1
0
1
0
2
2
1
0
1
2
1
1
0
0
1
2
0
1
1
1
1
0
2
0
1
0
0
0
0
1
1
0
2
1
1
0
1
1
0
0
1
0
0
2
2
2
0
0
0
1
1
0
0
0
0
1
1
1
1
3
1
0
1
0
0
1
0
1
0
1
0
1
1
0
0
1
0
2
0
1
1
0
2
1
0
2
1
0
1
0
0
0
1
2
0
0
1
1
0
2
1
1
0
1
1
1
0
1
0
1
2
2
2
0
0
2
1
1
0
0
1
1
0
1
2
0
1
2
1
1
1
0
2
0
0
0
7
0
1
1
1
2
0
1
1
1
0
1
0
1
0
0
1
2
0
1
1
1
0
1
2
0
1
0
1
2
1
1
1
1
0
1
1
1
0
3
0
1
2
2
1
0
1
0
0
1
1
1
1
0
0
0
0
1
1
1
2
1
0
1
0
2
2
5
1
2
1
0
2
1
1
2
2
1
1
0
0
1
1
2
1
0
0
2
0
0
2
1
0
0
2
1
0
1
0
2
0
0
2
1
0
0
0
2
1
0
1
0
1
1
1
1
2
2
1
2
2
0
1
0
1
2
0
0
2
0
2
2
0
0
2
1
0
1
1
0
1
2
0
2
1
1
0
0
1
0
3
0
0
0
0
2
0
2
1
1
1
1
4
2
2
1
2
0
2
5
1
0
0
0
0
2
1
1
2
1
0
0
0
0
0
2
0
0
1
0
1
0
0
0
1
1
2
2
2
1
0
1
1
0
0
0
1
0
1
0
2
2
0
0
1
2
1
0
0
1
1
0
0
1
0
0
1
0
0
3
0
1
0
1
2
2
2
0
0
2
1
2
1
2
0
2
1
2
1
1
0
0
2
1
0
1
0
1
1
1
1
2
2
1
1
0
0
1
1
0
0
0
1
1
0
0
1
2
1
0
0
2
1
1
2
1
0
1
0
1
1
0
2
0
1
2
1
1
1
0
0
0
0
1
0
2
1
1
0
2
2
2
0
1
1
0
2
3
0
2
1
0
1
0
1
0
1
1
2
2
1
1
0
1
1
1
2
1
0
2
0
0
2
2
0
1
0
0
1
1
0
0
1
1
0
1
0
0
2
3
2
0
0
1
1
1
1
0
1
1
0
0
2
1
1
2
0
0
1
0
0
1
2
0
0
1
0
2
0
1
2
0
1
0
1
1
2
1
1
1
8
1
0
2
1
0
2
2
1
1
2
2
1
1
0
3
1
0
0
1
1
0
1
2
2
3
2
0
1
0
1
0
0
0
1
0
0
0
0
1
1
0
1
1
1
0
1
1
2
2
0
1
0
1
2
0
0
0
2
2
0
0
2
1
2
1
1
0
1
1
0
1
1
0
1
2
1
1
1
2
1
0
2
1
2
0
1
0
2
0
1
1
0
1
1
1
0
0
1
0
2
0
0
1
2
0
2
0
0
0
0
1
0
1
1
1
1
1
0
3
1
1
0
0
1
1
0
1
2
2
2
1
2
0
1
1
2
2
2
1
1
2
2
2
3
1
1
0
2
2
2
0
2
2
1
1
1
1
0
2
0
2
1
0
2
1
1
0
0
1
0
0
1
1
1
0
1
2
1
0
0
1
1
2
1
2
0
2
3
2
1
0
0
1
1
2
0
1
0
0
2
1
1
1
0
0
2
2
2
2
0
1
2
4
0
0
2
2
1
2
2
0
0
0
1
1
2
1
0
1
0
0
1
0
1
0
0
1
2
1
1
0
1
1
1
0
1
1
0
0
0
1
0
0
0
0
0
1
2
0
0
1
0
2
0
0
1
0
0
0
0
1
2
1
1
1
1
1
0
1
0
1
2
0
2
1
0
0
1
0
1
2
1
0
2
1
1
2
1
0
0
1
2
1
0
2
1
0
0
3
0
2
1
0
1
2
2
0
1
1
1
2
0
1
0
0
1
2
2
1
1
0
1
0
1
2
0
1
1
1
2
0
1
1
2
1
0
1
2
2
0
0
2
1
1
1
0
0
1
0
0
1
0
0
0
2
2
2
1
2
0
2
0
1
0
3
2
0
1
2
1
1
0
1
1
1
1
1
2
3
0
1
1
2
1
0
0
0
0
2
0
1
0
0
2
1
2
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
1
0
1
0
1
0
0
2
0
2
2
0
1
1
2
0
1
0
1
1
0
0
1
0
2
3
0
1
0
0
1
2
1
0
2
1
1
0
0
1
0
2
0
1
1
0
1
0
2
2
0
2
0
2
1
2
1
2
1
2
2
2
2
0
1
1
1
0
2
1
0
2
2
1
0
1
1
0
1
2
1
0
0
0
2
1
2
0
1
2
0
0
0
2
1
1
2
1
2
1
1
1
0
0
1
0
3
0
1
0
1
0
1
1
1
1
0
1
0
0
0
2
1
2
1
1
2
2
1
0
0
1
1
0
1
1
0
0
1
2
0
0
0
0
0
0
1
0
0
1
2
1
0
1
0
1
0
0
0
2
2
0
0
1
1
0
1
1
2
2
1
1
1
0
0
1
1
2
0
0
0
1
1
1
2
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
2
1
1
0
0
1
1
0
0
1
1
0
2
0
2
2
1
2
1
1
2
2
1
0
0
0
1
0
2
1
1
0
0
1
0
1
1
1
1
2
0
1
0
0
0
1
0
0
0
1
1
1
2
1
0
0
0
1
1
0
2
1
1
1
2
1
0
1
0
1
3
2
1
2
2
2
1
0
1
2
0
1
2
2
1
2
1
1
1
1
0
0
3
0
1
1
1
1
0
1
0
1
1
1
2
0
0
1
3
1
2
0
1
0
1
1
1
0
2
0
0
1
2
2
1
1
1
1
0
0
0
1
0
1
0
1
1
2
1
1
1
1
1
1
2
0
1
0
0
0
1
2
2
1
0
0
1
1
0
0
0
3
1
2
1
0
1
0
0
0
5
6
0
0
1
0
1
0
2
1
1
0
1
1
0
0
1
1
0
0
1
1
1
1
0
2
0
3
2
1
1
1
0
0
0
1
0
0
0
0
2
4
0
1
1
1
1
1
1
1
1
0
1
1
2
2
0
1
0
3
0
0
0
0
1
2
2
0
0
0
0
1
1
0
1
1
1
0
1
0
1
0
0
0
0
3
2
0
0
2
1
0
2
1
0
0
0
2
2
2
1
1
0
2
0
0
2
1
2
0
0
1
0
1
0
1
2
0
3
0
2
0
0
1
0
1
1
1
0
0
2
2
1
1
1
0
1
0
2
2
0
0
0
0
0
1
0
3
1
2
1
0
2
1
0
1
1
0
0
1
2
1
1
1
1
2
0
0
1
1
2
1
1
0
2
0
1
2
1
0
0
1
2
0
1
2
2
2
2
2
1
1
0
1
2
1
2
1
1
1
2
1
1
2
0
0
1
1
0
1
0
1
3
2
1
0
2
0
1
0
0
0
2
0
1
1
1
1
0
2
2
0
1
2
0
1
2
0
2
0
1
0
1
1
1
0
1
1
2
1
1
0
2
0
1
0
1
1
0
0
0
1
0
1
2
1
0
0
1
1
0
0
0
1
0
2
1
0
0
1
1
2
0
1
1
1
1
1
1
0
0
2
0
2
0
1
0
2
0
0
2
1
1
0
0
0
1
0
0
2
0
0
1
0
0
1
2
1
0
0
1
1
2
1
0
0
0
0
0
1
0
1
1
1
0
1
2
0
0
0
1
2
1
0
2
1
2
1
0
2
2
1
1
0
2
0
0
1
0
1
1
1
0
0
0
1
0
0
0
1
2
0
0
1
0
0
0
1
0
1
1
0
1
2
0
1
2
1
2
2
1
0
1
0
0
0
1
1
1
0
1
1
1
1
1
0
2
0
2
2
1
2
1
1
0
0
1
2
2
2
1
0
1
2
2
2
1
4
1
0
1
0
0
0
1
1
0
2
0
1
0
0
0
0
2
0
1
0
2
2
2
2
1
2
0
0
2
0
1
2
1
1
0
1
1
2
1
0
1
1
1
2
1
1
1
0
1
0
2
0
0
1
1
1
1
1
0
1
0
0
0
1
1
0
0
2
1
2
1
2
1
1
1
1
0
1
2
2
1
1
1
1
0
0
1
2
1
2
2
2
0
2
1
0
0
2
1
2
1
2
0
1
2
1
1
0
1
2
1
0
1
1
1
0
0
1
2
0
1
0
1
0
0
1
2
1
0
1
1
1
1
2
1
0
2
1
0
2
0
0
0
1
1
0
1
1
1
1
1
0
2
1
1
1
2
1
0
2
2
1
1
1
2
2
1
0
1
1
1
1
1
2
0
1
2
1
0
1
0
2
1
1
1
0
1
1
1
1
0
2
1
1
1
2
2
1
0
0
0
2
2
0
2
1
0
0
1
1
1
1
1
0
1
1
1
1
1
0
1
1
0
0
1
0
1
2
2
1
2
2
1
1
3
2
1
1
0
0
2
0
1
1
0
0
0
1
1
0
1
0
2
0
2
1
2
1
1
2
0
0
0
1
0
1
2
1
1
1
2
0
1
1
2
0
0
0
0
1
1
0
0
1
1
2
2
1
0
0
0
0
1
2
1
2
2
1
0
0
0
1
0
0
2
0
1
0
0
0
1
0
0
0
2
1
0
0
0
1
0
0
0
2
0
2
0
1
2
1
1
1
0
2
0
2
1
0
1
2
5
0
0
0
1
1
1
2
1
1
1
0
1
2
1
1
2
0
0
2
0
2
0
1
0
0
1
0
0
1
1
1
0
0
1
2
0
2
0
1
0
0
0
1
0
2
1
1
1
1
1
0
0
1
0
1
0
0
0
0
2
1
0
1
2
1
2
2
2
2
2
2
3
1
1
1
0
1
0
1
0
1
1
0
1
1
0
1
1
2
0
2
1
2
0
0
0
1
2
0
1
1
1
4
2
1
1
0
1
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
1
0
2
1
0
0
0
0
0
2
2
1
2
1
1
1
1
0
0
1
2
2
0
2
2
2
0
2
3
0
0
0
1
1
1
0
2
1
0
0
1
2
0
1
0
1
0
1
0
0
0
2
2
1
2
0
2
0
3
0
1
1
0
1
1
0
1
1
0
0
1
0
0
1
0
1
1
2
0
1
1
0
2
0
1
0
0
0
0
1
0
0
2
0
1
1
1
0
2
1
1
1
2
1
0
0
0
2
0
1
1
0
1
2
0
1
1
1
0
2
2
3
2
0
1
1
0
1
0
0
1
0
1
1
0
0
0
0
1
1
1
0
0
1
1
2
2
1
2
1
1
1
0
1
1
2
0
1
0
1
0
2
0
1
2
1
1
1
2
0
2
0
0
0
3
0
0
1
3
1
2
0
1
0
2
0
1
0
0
0
2
1
1
1
2
5
0
2
1
1
1
0
0
0
2
1
0
2
0
0
0
2
2
1
0
0
0
0
2
0
0
0
0
1
1
1
1
1
0
1
0
1
3
0
0
2
2
1
1
1
2
1
0
1
1
0
2
0
0
1
0
3
0
0
1
0
1
2
0
0
1
0
1
0
2
0
1
0
0
2
1
1
2
0
0
0
0
1
0
1
1
2
0
1
0
1
0
0
1
2
0
1
0
0
0
0
2
2
0
2
1
0
2
0
1
0
0
0
1
1
2
1
0
0
1
1
0
2
1
2
0
1
0
1
1
1
0
0
1
1
3
0
1
0
0
0
3
2
2
0
0
1
1
2
2
2
1
0
0
2
3
2
1
0
1
0
1
0
1
1
2
1
1
0
0
2
2
2
1
0
1
2
2
2
0
2
1
0
0
1
0
0
0
1
0
1
0
0
0
1
0
2
1
1
0
1
1
1
3
2
1
2
3
2
0
1
2
2
0
2
0
1
2
0
1
0
1
0
0
0
2
0
2
0
0
1
0
0
1
0
1
1
2
0
0
0
1
0
2
0
1
1
2
2
2
2
1
0
0
0
0
1
1
2
1
0
2
0
2
0
1
0
1
1
0
0
2
2
1
1
2
2
1
1
2
0
0
0
0
0
0
2
1
0
1
0
0
1
1
1
0
0
0
0
1
0
1
1
1
1
1
2
1
1
2
0
0
0
0
2
1
1
2
1
1
1
1
2
0
1
0
1
1
0
2
1
0
2
1
1
1
0
0
0
0
1
1
1
1
1
0
1
1
1
0
1
1
1
0
0
2
0
2
0
1
0
2
0
1
1
0
2
2
1
1
1
1
0
2
0
2
0
2
0
2
1
0
0
0
1
2
1
1
1
2
1
0
2
1
0
2
1
1
0
0
0
2
2
2
0
2
1
1
1
0
1
0
0
0
3
1
0
2
2
2
1
0
1
1
1
1
0
2
0
2
1
1
2
2
2
0
0
1
2
0
1
1
2
0
1
2
0
1
1
2
2
1
0
0
2
1
0
0
1
0
0
1
1
2
1
0
2
3
1
0
1
0
2
1
1
0
0
1
1
1
0
1
2
1
1
0
0
1
0
0
0
1
0
1
1
2
0
0
0
1
1
1
0
2
1
1
1
2
1
1
1
2
1
0
0
0
0
0
1
1
1
0
1
1
3
1
0
0
0
0
2
0
0
0
0
1
1
1
0
1
0
2
0
2
0
0
1
2
1
0
2
0
2
0
0
0
0
0
0
2
2
3
1
1
0
3
1
0
0
1
1
1
2
0
0
0
2
2
2
1
1
2
1
0
0
1
2
1
0
1
0
1
0
0
1
1
2
1
2
0
0
1
0
1
2
2
1
0
2
0
1
1
1
1
1
0
1
1
1
1
1
0
0
1
1
2
0
1
0
0
0
2
1
1
2
0
1
0
0
2
1
1
1
0
0
0
1
2
2
1
2
1
1
0
1
0
0
0
0
0
0
2
1
1
2
2
1
1
1
0
2
0
0
0
1
1
1
0
1
1
1
1
1
1
1
1
2
2
0
1
2
1
2
0
3
0
1
2
0
0
2
0
0
1
1
0
0
1
0
2
0
0
1
1
1
1
1
0
1
0
0
1
2
0
2
1
1
1
1
1
3
0
0
1
1
1
2
1
1
0
0
1
2
1
1
8
1
0
1
3
1
1
1
0
1
0
1
2
1
0
2
4
0
1
2
2
2
1
0
0
0
0
1
1
1
0
0
0
1
0
0
1
0
1
1
1
1
1
1
1
2
2
0
1
0
0
1
0
1
1
0
0
0
1
1
0
2
2
1
2
0
0
2
0
2
1
1
0
0
0
0
1
1
2
1
2
0
2
0
0
0
0
0
1
2
1
1
2
0
8
1
1
0
2
0
1
4
0
0
1
1
2
1
0
0
1
1
1
0
0
1
0
0
2
1
0
1
1
2
1
0
2
1
0
1
2
2
2
0
0
3
0
1
3
0
2
0
1
0
0
0
1
2
1
3
1
1
1
2
1
1
0
0
0
0
1
1
0
1
2
0
1
0
1
0
1
0
2
0
1
0
2
0
0
0
1
0
1
0
2
1
2
2
3
0
0
0
0
1
0
0
0
2
1
1
1
1
0
1
1
2
0
1
0
2
0
0
2
1
2
1
2
1
0
1
2
0
3
1
1
0
1
2
0
0
1
1
1
2
0
1
2
1
0
1
2
0
1
1
2
0
1
1
0
0
1
0
0
0
0
2
1
1
2
0
1
2
0
1
0
0
1
3
2
1
3
0
1
1
0
0
0
1
0
1
1
1
0
1
2
0
1
1
1
0
1
1
3
2
1
1
1
0
2
0
1
1
1
1
0
2
0
1
2
1
2
0
1
2
0
2
2
1
0
1
2
0
2
1
1
0
0
2
0
2
0
0
0
1
1
2
1
0
0
2
2
1
0
0
1
1
2
0
1
1
1
0
0
0
1
0
0
0
0
2
0
1
0
1
0
1
1
2
0
0
1
0
0
1
0
1
1
2
1
1
0
1
1
1
0
0
2
2
1
1
0
0
0
1
2
0
1
1
0
2
1
0
1
2
0
1
1
0
1
2
1
2
1
1
1
0
1
1
1
0
0
1
1
1
1
2
1
2
2
2
0
1
0
1
0
0
0
0
2
0
1
2
0
2
1
1
2
0
0
0
1
0
2
2
1
1
0
0
1
1
1
0
1
2
0
1
2
1
1
0
2
1
2
2
2
0
0
2
0
0
0
2
1
2
1
1
0
0
1
1
0
0
0
1
0
1
0
3
2
2
2
1
1
0
1
0
1
1
0
0
1
2
1
1
0
1
1
0
2
1
1
0
2
1
1
0
1
1
2
0
2
0
0
0
0
2
0
1
1
0
0
0
2
2
0
2
1
1
1
0
0
1
0
1
1
1
1
1
0
1
1
1
1
0
0
0
2
1
0
2
0
1
2
1
0
0
1
2
1
1
0
1
0
2
0
0
2
0
0
1
2
1
0
2
0
0
3
0
1
1
1
0
1
0
1
4
0
1
2
2
0
0
2
1
1
1
0
0
0
0
1
1
2
1
1
0
2
1
0
1
0
1
1
0
2
0
0
1
1
0
1
1
1
1
0
0
0
1
1
0
0
4
0
2
0
1
0
1
0
1
0
0
1
2
2
2
2
1
1
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
2
2
0
1
0
1
0
2
1
2
2
0
1
0
2
0
1
3
0
0
0
2
2
0
0
2
2
1
1
2
0
0
2
2
4
1
1
1
1
0
1
0
2
1
0
0
2
2
1
1
0
1
1
0
0
2
1
0
0
1
0
1
1
0
1
2
2
1
1
1
2
0
1
0
1
0
0
1
0
0
2
1
1
1
1
2
0
0
0
1
0
2
0
1
1
1
0
0
1
1
0
1
1
2
1
1
1
3
0
0
2
1
2
2
0
0
1
1
0
0
0
1
0
0
1
0
1
1
0
0
0
2
1
2
0
0
0
1
0
1
0
0
2
1
0
1
1
1
0
0
2
0
1
0
1
0
1
2
1
0
1
2
2
1
2
1
0
1
2
1
2
0
0
0
1
0
1
2
0
0
2
1
1
1
0
0
0
2
0
1
0
0
3
1
1
0
1
0
1
2
0
1
2
1
0
1
1
1
2
1
1
0
0
0
0
0
0
0
0
1
0
0
1
2
0
1
0
2
0
0
0
2
0
2
1
2
0
2
0
1
2
2
1
1
0
0
1
1
1
0
2
0
0
0
2
0
2
1
0
1
2
0
1
1
2
0
0
1
1
1
1
0
1
1
1
2
1
0
0
1
0
0
0
0
2
1
1
0
0
0
2
3
2
0
0
1
0
1
0
3
1
2
1
2
2
0
1
2
0
1
1
1
0
1
1
0
2
1
2
0
3
0
1
0
2
0
0
2
0
1
1
0
1
1
1
1
1
0
1
0
0
1
1
0
0
2
1
1
2
1
2
2
1
0
1
0
1
0
0
0
1
3
0
2
1
1
2
1
2
1
2
3
1
3
1
1
2
1
0
0
0
0
0
2
2
0
1
0
1
2
0
2
0
1
2
1
2
1
1
2
2
3
2
0
2
2
0
0
2
0
2
0
1
0
1
1
0
0
0
1
1
0
1
0
0
1
2
0
2
1
1
0
2
0
1
1
2
0
0
1
0
1
1
0
1
0
0
0
0
0
0
1
1
0
1
1
1
2
1
2
1
1
0
0
1
2
1
1
0
1
1
1
0
1
1
0
1
0
0
2
2
0
3
0
1
1
0
2
1
1
2
0
0
2
0
2
1
2
1
2
2
0
0
1
1
1
0
0
0
0
1
1
0
1
1
1
1
1
1
1
1
2
2
1
2
1
0
0
1
0
1
1
0
1
1
2
1
1
2
0
1
1
2
2
0
0
1
1
0
2
0
0
0
1
1
0
2
1
0
1
0
1
0
1
0
2
1
1
0
3
0
1
0
0
1
0
0
1
1
2
0
2
0
0
0
1
0
0
1
0
0
1
1
1
1
0
2
0
1
1
2
2
0
0
1
0
2
0
0
0
0
1
1
2
1
2
0
0
0
0
0
1
2
0
1
1
0
1
2
2
1
1
2
0
1
0
2
2
0
0
2
1
1
0
0
1
0
0
0
1
3
0
1
1
1
0
0
0
0
1
2
0
0
1
1
1
1
0
2
1
0
1
0
1
0
1
0
0
1
1
0
0
2
0
2
0
1
1
1
1
1
1
1
1
0
0
1
0
1
0
0
0
1
0
1
1
1
1
1
0
1
0
2
0
0
1
1
1
0
2
1
0
2
1
1
1
0
0
0
0
0
0
0
0
0
2
2
0
1
0
2
1
1
1
0
0
0
0
0
1
0
1
0
1
0
0
0
2
1
0
1
0
1
0
2
3
2
0
1
0
0
0
1
1
1
1
2
2
0
2
1
1
1
0
0
1
0
0
0
0
3
0
2
1
0
1
0
2
2
1
2
0
0
2
2
0
1
1
1
2
0
1
1
1
0
1
2
0
2
2
0
1
0
0
2
0
2
0
2
1
1
0
0
0
1
1
1
0
1
2
1
1
1
1
1
0
1
2
1
1
1
1
1
0
1
1
2
2
0
0
0
0
0
2
2
0
0
1
1
0
0
0
0
1
1
0
1
0
2
1
1
0
1
2
0
1
1
0
2
2
0
1
2
0
2
1
2
1
1
2
0
1
2
0
2
1
0
0
1
1
0
1
1
0
1
0
0
2
1
0
0
0
0
0
1
2
0
1
1
1
0
2
2
0
1
0
1
1
1
1
1
1
1
1
0
2
1
2
2
1
1
2
3
0
1
1
1
0
2
1
1
2
2
1
0
0
2
1
1
1
0
0
1
1
0
1
2
0
1
0
3
1
2
1
0
2
0
0
1
1
0
0
1
1
1
2
1
1
0
1
2
0
0
1
5
1
1
0
1
1
1
2
0
0
2
0
0
0
1
1
1
0
1
2
1
2
0
0
2
1
2
2
2
2
1
1
0
2
0
1
1
1
0
2
0
1
1
2
0
0
0
2
1
1
2
1
1
0
0
1
0
2
0
0
0
2
0
1
1
1
2
0
1
2
1
0
1
1
1
0
1
3
1
1
2
0
0
0
0
2
2
0
0
0
0
2
2
1
0
2
0
0
0
2
1
0
1
2
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
1
1
1
1
1
3
1
1
0
1
1
2
1
2
1
1
0
1
0
1
1
1
1
1
0
1
1
1
0
1
1
2
0
1
0
2
0
1
1
0
0
1
1
0
1
1
0
2
1
2
0
0
2
2
0
0
1
1
0
2
1
2
2
1
0
2
1
1
1
0
1
2
1
3
1
2
1
0
1
1
1
4
1
0
1
1
0
1
1
2
2
0
2
0
1
2
0
1
0
2
0
2
0
1
0
1
1
1
1
2
1
1
2
0
2
1
1
1
0
1
1
0
1
2
2
1
0
0
1
1
2
2
2
0
1
1
2
0
0
1
1
2
1
0
0
0
0
0
1
2
1
1
1
0
1
1
1
0
2
2
2
2
1
2
0
1
1
2
1
1
0
1
0
0
0
1
1
0
0
1
1
1
1
1
1
1
2
0
2
2
2
0
1
2
0
1
2
2
0
1
1
2
1
1
1
0
1
1
0
1
2
1
0
2
2
2
0
0
2
1
2
0
0
2
1
1
2
1
1
4
0
2
0
2
1
0
2
1
2
1
2
2
1
1
0
0
2
0
1
1
0
0
2
0
1
1
0
0
0
1
1
1
1
2
0
1
2
2
1
0
1
1
0
0
0
1
1
0
1
2
1
1
2
1
1
1
0
1
0
1
2
1
1
0
0
0
2
1
2
2
0
1
0
1
2
3
1
2
1
1
2
1
1
0
1
2
2
1
1
2
2
1
1
0
2
0
1
0
0
0
1
2
1
0
1
1
0
2
2
1
0
1
2
0
0
0
0
1
0
2
0
0
2
1
2
2
1
0
0
2
0
2
2
2
1
2
1
0
1
1
2
0
2
1
0
0
1
1
0
0
0
0
1
0
1
1
0
0
0
1
1
0
0
1
1
0
1
2
2
1
1
1
1
2
2
0
0
0
0
1
1
1
0
2
0
1
2
1
0
1
2
1
1
1
0
1
1
1
1
1
1
1
1
0
0
1
1
2
0
0
0
1
0
1
1
1
2
1
2
1
1
0
0
0
0
1
1
0
0
1
2
2
0
0
1
0
0
2
1
2
1
1
0
0
2
0
0
0
2
1
2
1
0
0
0
0
0
1
0
2
1
0
0
0
1
0
0
1
0
2
2
2
0
1
2
2
2
0
2
2
1
1
1
2
2
0
1
0
1
0
2
1
0
0
2
0
5
0
0
0
1
2
1
2
2
0
1
0
1
0
0
2
0
1
1
0
2
1
1
0
1
0
0
0
0
0
0
0
0
0
2
1
0
1
2
3
2
2
0
1
2
0
0
2
0
1
0
0
2
1
1
1
0
0
1
0
0
1
1
0
1
0
2
2
0
1
0
0
0
0
0
2
1
1
0
2
1
1
2
0
1
0
0
0
1
1
1
2
2
2
1
0
2
0
0
1
2
1
2
1
1
0
2
1
1
2
1
2
0
1
1
0
0
0
0
0
1
2
1
0
0
1
2
2
0
2
1
0
2
0
1
0
0
2
2
0
1
2
1
0
1
1
0
0
2
1
2
1
0
0
0
0
1
2
1
0
1
1
3
0
0
1
2
0
1
1
1
1
2
0
1
2
0
2
4
1
2
0
2
2
1
1
2
1
0
0
0
1
0
1
1
1
1
0
1
1
2
0
1
3
2
2
0
0
0
1
1
2
1
1
0
0
1
0
0
1
1
0
0
1
0
1
1
1
1
0
1
0
0
0
2
0
0
0
0
1
0
0
1
1
0
1
2
2
0
0
2
1
2
2
0
2
5
0
0
0
1
1
2
0
1
1
2
1
1
0
0
0
2
2
1
1
1
2
0
0
0
2
2
0
1
0
0
1
1
1
1
1
1
2
2
1
1
1
1
2
0
1
0
2
2
2
0
1
0
0
2
0
1
2
0
2
2
0
1
2
0
1
0
0
2
1
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
2
0
0
0
1
1
1
2
3
1
1
2
2
0
2
0
0
0
0
2
0
0
2
1
1
0
1
2
2
0
0
1
1
0
1
1
1
1
0
1
0
1
0
1
0
1
1
3
1
1
0
2
0
1
2
1
1
0
0
2
0
2
0
2
0
0
1
2
0
2
0
1
1
2
1
1
1
1
1
0
1
1
0
1
0
0
1
2
0
0
0
1
0
2
0
0
0
0
0
2
1
2
1
0
0
1
0
2
1
0
0
0
1
1
1
0
2
0
2
0
1
1
1
1
1
1
1
1
1
0
1
0
2
0
1
0
1
1
1
1
0
2
1
1
0
0
2
1
0
1
1
2
1
2
1
2
1
2
0
0
0
2
1
1
1
2
2
1
2
1
1
1
0
0
0
0
0
1
1
0
2
0
2
1
2
0
0
0
0
0
2
0
1
1
1
2
1
2
1
1
0
0
0
1
0
0
2
2
1
1
0
2
1
1
1
0
2
1
0
2
2
1
1
1
0
3
0
1
2
0
2
0
2
1
1
0
2
2
0
2
1
1
0
1
1
1
1
0
0
1
1
1
3
2
2
0
1
1
1
0
1
1
0
0
0
1
1
0
0
2
1
0
0
1
1
0
0
1
0
1
0
1
1
1
1
2
0
0
2
1
0
1
0
1
1
0
2
0
2
0
1
2
1
1
0
2
1
0
1
0
1
1
1
0
0
0
0
1
2
1
2
2
4
2
1
0
2
0
0
1
2
0
1
1
1
1
1
2
0
1
1
1
1
2
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
2
0
1
0
0
1
1
1
1
0
0
1
0
0
2
2
2
1
1
1
3
1
1
0
1
0
2
0
0
1
1
1
1
1
2
1
1
0
2
0
0
1
0
0
3
2
0
1
2
0
1
1
2
0
2
0
2
1
1
0
1
0
2
0
2
2
1
0
1
0
1
0
0
1
0
0
0
1
1
1
1
1
2
0
2
0
1
1
1
0
1
0
1
1
1
0
1
1
0
1
0
2
0
1
0
0
1
0
2
2
1
1
2
2
2
0
2
0
0
0
0
0
1
1
1
2
1
0
1
1
2
2
0
1
2
1
1
1
4
1
2
0
1
2
1
1
2
2
1
2
0
1
1
2
1
0
0
0
2
2
1
0
1
2
1
2
0
0
0
0
2
1
0
1
0
0
1
1
0
2
0
2
1
1
1
1
0
2
2
2
1
0
0
2
1
0
0
0
1
2
1
1
0
1
0
1
0
1
0
1
1
2
1
1
0
0
0
2
0
0
1
0
1
1
1
0
2
1
1
0
2
0
1
0
0
1
1
1
0
1
0
2
2
2
0
2
1
1
2
1
0
1
0
1
0
1
0
0
0
1
3
1
0
0
2
1
1
3
2
0
1
2
2
1
1
2
2
0
1
1
2
0
1
2
1
0
2
2
0
0
0
2
0
1
0
1
2
0
1
0
1
1
1
1
1
1
1
0
0
0
2
1
0
1
1
2
1
1
3
1
2
1
2
1
0
0
1
0
0
0
0
1
0
0
1
0
0
2
1
1
2
1
0
1
1
1
1
1
1
0
1
2
0
0
1
0
1
1
2
1
2
1
1
0
2
2
1
0
0
0
2
0
2
2
1
0
2
1
1
0
1
1
1
0
1
1
1
1
2
1
1
1
1
0
0
1
0
1
0
1
0
2
0
2
0
0
2
1
2
0
0
1
0
1
0
0
1
2
2
0
2
2
2
1
1
2
1
2
2
1
2
0
0
1
1
2
1
2
1
0
0
1
0
0
1
0
0
1
1
1
0
0
0
0
2
0
0
1
1
1
0
0
1
2
1
0
3
1
0
0
1
0
1
0
2
2
1
1
0
2
1
1
0
1
1
1
0
2
0
0
0
0
1
2
0
2
0
1
2
3
1
1
0
2
0
1
1
0
0
0
2
1
2
1
2
1
0
1
1
2
0
1
0
1
2
2
1
0
1
1
1
1
2
1
2
0
1
1
1
0
2
2
0
1
1
1
1
1
0
2
0
0
1
0
1
1
1
2
0
0
0
0
0
0
2
1
1
1
1
0
1
0
2
2
0
3
1
0
2
0
0
0
1
2
0
1
2
0
2
1
0
0
1
2
0
1
0
1
0
1
0
1
1
0
2
3
0
2
1
1
0
1
1
2
0
0
1
0
2
1
2
2
1
1
1
0
0
1
0
0
2
1
1
1
0
1
3
1
1
0
0
1
1
1
1
0
0
2
0
1
1
1
1
0
2
0
1
1
1
1
0
0
1
1
0
0
0
1
1
0
0
1
0
1
1
1
0
0
0
0
1
2
2
0
2
2
0
2
0
1
0
0
0
2
1
2
1
1
1
1
1
1
1
0
0
0
2
1
0
0
0
2
1
1
0
0
1
0
0
1
2
2
0
1
0
1
2
1
0
1
1
2
0
1
1
1
2
0
4
1
2
0
0
0
2
1
1
1
0
2
1
0
0
2
0
1
0
0
0
2
0
1
1
1
0
1
1
0
2
0
0
2
0
1
2
1
1
2
0
0
0
1
1
1
1
0
1
3
2
1
2
2
2
0
0
1
1
1
2
0
1
0
1
0
1
2
0
1
1
0
2
0
0
1
3
1
0
2
1
1
2
0
2
1
3
1
2
1
0
0
0
0
1
0
2
0
0
0
0
0
0
3
1
0
2
0
1
1
2
1
0
1
0
0
1
1
0
2
0
0
1
0
1
0
1
1
1
1
0
1
0
1
1
2
1
1
0
1
1
2
0
1
1
2
2
2
2
1
0
0
1
0
1
2
0
0
1
0
1
1
0
0
0
1
2
0
0
0
2
1
2
0
0
2
0
2
0
1
1
0
2
1
1
1
0
0
0
0
0
0
0
2
2
1
0
1
1
1
2
2
1
1
1
0
1
1
0
1
0
1
0
1
1
1
2
2
0
1
0
1
1
1
2
1
2
2
1
0
1
0
2
1
1
2
2
1
0
2
0
2
0
1
0
2
2
1
0
0
2
0
1
2
1
0
1
0
0
1
2
2
1
1
0
2
1
1
1
1
1
0
0
0
2
0
2
1
1
2
2
1
1
0
0
1
1
0
1
2
2
0
1
0
1
0
0
0
1
1
1
0
1
2
1
0
0
2
0
0
1
0
2
1
1
1
1
0
2
0
2
1
1
1
0
2
0
0
1
0
0
0
0
0
0
2
1
1
1
2
0
1
0
1
2
0
1
0
0
0
1
1
1
1
10
1
2
2
2
1
1
1
2
1
1
3
1
0
1
0
1
0
1
1
1
2
1
0
1
1
2
0
2
2
1
1
1
0
1
0
0
0
1
0
2
1
0
1
1
2
0
1
2
2
0
1
0
0
1
0
1
1
2
0
1
0
0
0
2
0
0
2
1
2
1
0
0
2
0
0
2
1
1
1
0
1
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
1
1
0
2
2
2
2
1
0
1
2
1
0
2
0
1
1
2
0
0
0
0
0
2
2
1
1
2
0
0
1
1
2
1
1
0
1
0
2
0
2
1
0
1
3
1
0
1
0
2
1
0
1
1
0
2
2
1
0
0
2
2
1
1
0
1
1
1
1
1
1
0
2
3
1
1
2
2
1
1
1
1
1
1
0
0
0
0
0
1
1
0
2
2
1
2
1
2
0
1
1
0
1
0
0
0
2
1
0
1
0
1
0
0
1
2
1
0
1
0
0
1
0
0
1
2
1
2
1
0
0
1
0
1
1
1
1
1
2
2
1
1
2
0
1
1
1
2
0
1
1
2
0
2
2
0
2
2
1
0
0
2
0
0
2
0
4
0
1
0
0
1
0
2
0
1
0
1
2
0
1
0
0
1
0
0
0
0
2
3
0
1
0
1
1
1
1
1
0
0
1
2
2
0
1
2
1
1
0
1
2
0
1
0
0
1
1
0
1
1
0
1
1
2
1
1
2
2
1
0
2
0
0
1
2
1
0
1
2
0
1
1
0
2
0
1
0
1
0
1
1
1
1
1
2
2
0
1
1
2
0
0
2
0
0
0
1
1
1
1
0
1
2
1
1
0
2
1
1
1
1
0
0
2
2
0
2
0
0
2
1
1
0
0
0
1
1
1
1
0
1
0
2
0
0
1
0
1
0
1
2
1
2
0
2
0
0
2
2
1
1
2
0
2
0
0
1
0
0
1
1
1
2
1
1
1
1
1
0
1
0
1
1
2
1
0
1
1
1
1
1
1
2
2
2
1
0
0
0
1
2
0
2
0
0
2
1
1
0
1
0
1
1
1
1
0
2
1
1
1
0
0
1
1
1
0
1
1
0
1
2
1
0
1
0
0
1
2
2
1
2
0
2
2
1
1
3
1
1
0
0
1
0
0
1
1
2
1
1
1
1
1
1
0
0
1
1
2
2
2
0
2
1
2
0
1
1
0
1
1
0
0
1
2
2
2
2
0
1
1
0
0
0
1
1
0
2
1
1
0
1
3
0
0
0
2
1
1
1
0
2
0
0
0
2
0
0
0
1
1
0
1
1
1
0
1
2
0
0
0
0
2
2
1
0
1
0
0
3
1
0
2
3
1
1
1
1
1
1
0
0
0
2
0
0
1
0
0
0
2
0
1
2
1
2
0
0
1
0
1
2
2
0
2
0
2
1
0
1
1
2
1
1
1
0
1
3
2
0
1
0
1
2
1
2
0
1
0
0
1
0
1
1
2
1
1
0
0
0
2
0
1
1
0
1
2
0
2
2
1
1
0
0
1
1
4
1
0
1
0
0
1
1
2
1
0
0
0
2
1
0
0
1
2
0
1
0
1
0
1
2
0
2
1
0
0
0
2
2
1
1
0
2
1
1
1
2
0
0
0
0
1
2
4
0
0
2
0
0
0
1
1
1
0
2
0
2
1
1
0
2
3
1
2
2
0
1
0
0
2
0
2
1
1
2
0
0
1
1
1
0
2
2
2
0
0
1
1
2
2
1
1
0
0
0
0
2
0
0
2
1
1
2
1
1
2
1
0
1
0
0
0
1
2
1
1
1
1
2
0
1
1
1
0
1
1
2
2
0
2
2
0
2
0
2
1
2
0
1
1
2
2
1
0
0
2
1
1
2
2
1
0
0
0
1
1
2
0
1
1
1
1
1
0
2
1
1
1
1
0
0
0
0
1
1
0
0
0
2
0
0
1
1
0
1
1
1
0
2
1
0
0
1
1
0
2
0
1
0
1
0
1
0
0
0
0
2
1
0
0
1
1
2
1
2
2
0
1
1
1
1
2
0
2
1
1
1
2
2
1
2
2
1
0
2
2
1
1
0
1
1
0
1
0
0
0
1
1
0
2
0
0
1
1
2
1
0
0
0
2
3
0
0
0
0
0
0
3
2
0
1
2
0
2
1
0
0
1
1
0
1
0
2
0
1
1
0
0
4
0
2
0
2
0
1
5
1
2
2
0
1
0
1
1
1
0
0
2
0
0
2
1
1
2
1
0
0
0
1
2
1
1
2
0
2
2
0
1
0
2
2
0
1
1
0
2
2
2
0
1
0
0
1
1
1
1
1
1
0
1
0
2
0
0
1
0
0
0
2
1
0
0
1
0
2
1
0
2
2
2
0
2
1
0
2
0
2
0
0
1
2
1
0
0
0
2
1
0
0
2
2
2
1
1
2
2
0
1
2
1
0
2
1
1
0
0
1
1
2
1
2
1
0
1
1
0
0
0
0
2
1
0
1
2
1
0
1
0
0
2
1
2
2
2
0
1
2
0
2
1
0
1
0
1
2
1
1
2
1
2
0
1
2
0
1
2
1
0
1
0
2
0
1
1
2
3
2
1
1
2
2
1
0
0
2
1
1
1
1
0
1
2
0
2
1
0
1
1
1
1
1
1
1
1
1
1
1
0
1
0
2
1
1
0
0
2
2
1
1
0
0
1
0
2
0
1
1
1
1
1
1
0
2
2
1
1
1
0
0
0
0
0
1
2
1
2
2
1
1
0
1
1
2
1
1
2
0
1
0
0
0
0
0
1
2
0
1
0
1
0
1
1
0
1
3
2
2
0
0
1
1
1
1
1
0
2
2
0
1
0
2
2
0
1
0
1
0
0
2
0
0
0
1
1
0
1
1
0
1
1
2
1
3
0
2
1
1
0
0
1
0
2
1
1
1
0
0
1
1
0
2
2
1
0
1
1
0
0
1
1
1
2
0
1
1
1
0
0
0
0
1
2
1
2
1
2
1
0
1
1
0
1
1
1
0
0
1
3
1
0
1
2
0
1
0
2
1
0
1
0
1
0
0
0
2
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
1
1
1
0
2
0
1
2
1
1
0
1
2
1
1
0
0
0
0
0
0
1
1
1
2
1
2
0
0
0
2
1
1
0
1
2
1
1
1
2
1
0
2
0
1
1
1
1
1
1
2
0
1
1
2
1
1
1
1
0
0
2
0
1
1
1
1
1
0
2
1
2
0
0
2
0
0
3
0
1
1
0
0
1
1
1
0
2
1
1
1
0
2
2
0
1
1
0
0
2
1
2
0
1
1
1
2
2
1
2
0
0
1
1
0
1
1
2
1
2
1
0
0
1
1
0
2
0
0
0
1
1
2
1
0
3
2
1
0
1
0
0
2
1
2
1
2
0
1
0
1
0
0
0
1
1
0
1
0
1
1
1
0
1
3
2
0
0
1
1
0
0
2
2
1
2
2
0
2
1
1
0
1
1
2
1
1
0
0
1
1
1
0
2
1
1
2
1
1
1
1
0
0
1
1
2
3
0
0
0
0
1
2
0
0
1
1
0
1
0
0
1
0
1
2
2
1
1
1
0
2
0
0
0
2
2
2
0
2
0
1
0
0
0
0
1
0
2
1
1
1
0
0
0
3
2
2
1
1
1
1
2
1
0
1
2
0
0
2
0
0
0
0
0
1
0
1
0
2
1
1
1
2
1
0
0
2
0
2
2
0
1
2
0
1
0
1
1
1
0
1
2
1
1
2
1
2
1
0
2
2
0
0
2
0
2
1
0
0
1
1
1
1
1
2
0
1
1
0
0
2
1
0
0
0
0
3
2
1
2
1
1
0
1
3
1
0
1
2
0
1
0
0
1
2
1
1
0
0
0
1
2
1
0
2
0
1
3
1
0
0
0
1
2
1
2
1
1
1
1
0
1
0
1
1
1
1
0
0
0
0
3
1
0
2
1
2
1
2
1
2
2
0
2
2
0
0
1
0
1
1
0
2
1
0
1
0
0
1
1
0
1
0
2
2
1
0
1
0
2
1
0
0
1
2
0
1
0
0
1
1
2
1
1
0
2
2
2
0
1
1
0
0
0
2
1
0
0
2
1
0
1
1
0
1
1
0
1
0
1
1
0
1
0
1
5
1
0
0
1
2
0
1
0
2
0
1
1
2
2
0
1
1
1
0
2
0
2
0
0
0
1
2
0
0
1
0
2
0
1
0
1
1
0
0
1
1
0
0
2
1
1
0
2
0
2
2
2
1
0
1
0
1
2
1
2
0
2
2
1
2
0
1
0
0
1
1
0
0
1
0
0
0
2
2
1
1
0
0
0
1
0
0
1
2
0
0
0
1
0
0
2
0
1
0
2
0
1
2
1
2
1
1
1
0
1
2
0
1
0
2
2
2
1
2
2
1
1
1
1
1
0
2
2
0
0
1
0
2
0
0
1
0
1
0
0
0
2
0
1
2
1
0
0
1
1
1
2
2
0
1
1
2
0
0
2
1
0
1
3
0
1
0
1
0
2
2
0
1
0
1
1
1
1
0
1
0
0
1
1
0
1
1
2
1
0
1
2
1
2
1
0
2
2
1
0
0
1
1
1
1
0
1
1
0
2
1
0
0
5
1
1
0
0
1
0
0
1
1
2
0
2
2
0
0
1
1
1
1
1
0
1
2
2
2
2
0
0
1
2
1
0
0
0
1
0
1
0
1
2
1
1
1
1
0
0
1
1
0
1
0
1
1
1
1
0
1
2
2
0
0
1
0
2
1
0
0
1
0
1
0
1
1
1
1
0
1
1
2
0
0
2
0
1
2
1
1
2
1
1
1
1
0
1
0
0
1
2
1
1
2
1
1
1
0
2
1
0
0
0
0
1
0
2
2
2
1
0
2
0
0
0
1
2
1
0
1
0
0
2
0
0
1
0
0
2
1
1
0
0
1
1
1
0
2
0
2
0
1
1
0
0
2
1
2
0
0
1
2
1
0
0
0
2
1
2
2
2
1
2
1
0
2
1
1
1
0
1
0
1
2
1
1
1
0
0
0
1
1
0
1
1
1
1
0
1
0
1
1
3
0
0
1
2
0
2
1
0
0
1
1
0
0
0
1
2
1
0
1
2
0
0
0
0
2
1
0
0
1
2
1
2
1
0
0
0
0
1
1
1
0
1
0
0
4
1
2
1
1
1
0
1
1
1
1
2
1
2
0
2
0
0
1
2
1
1
1
0
2
0
2
1
0
0
0
0
1
1
1
0
1
0
3
2
1
0
0
1
1
0
1
1
1
1
2
0
1
1
0
2
1
1
1
1
0
1
1
0
1
1
1
2
0
3
0
1
0
0
0
2
0
0
0
2
1
1
1
0
2
1
2
1
3
0
1
1
2
1
0
2
1
0
1
1
0
2
1
0
0
1
0
0
1
1
2
1
7
1
0
1
0
2
0
1
1
0
0
1
2
1
2
1
1
2
1
1
1
1
0
2
0
0
0
0
1
2
1
1
1
2
1
1
1
0
0
2
2
1
2
0
1
2
2
1
1
0
1
0
4
0
0
1
2
0
2
2
2
0
0
1
1
2
0
0
2
1
0
1
2
1
0
0
1
2
1
0
1
2
0
0
2
1
0
2
1
2
1
1
1
0
2
1
1
1
0
2
0
1
0
0
2
1
0
0
0
0
1
1
1
0
0
3
2
0
2
1
0
2
1
2
1
0
0
0
0
0
2
2
2
1
1
0
0
0
2
1
0
2
1
1
1
1
2
0
2
1
2
2
0
2
0
0
1
1
1
0
0
2
4
1
1
2
1
0
2
0
0
2
0
0
1
0
0
1
3
1
0
1
0
1
2
1
2
0
1
1
0
0
0
1
1
1
1
2
2
0
2
0
1
0
2
1
0
3
0
0
1
2
2
2
1
2
1
1
0
1
0
1
0
0
0
0
1
1
1
1
1
0
1
1
1
1
2
1
2
0
0
0
1
0
2
0
0
1
1
3
0
1
1
1
1
0
1
1
1
0
0
0
2
1
0
2
0
1
0
0
1
0
0
1
1
1
2
1
2
2
0
1
0
2
0
1
1
1
2
1
0
2
0
2
2
0
0
0
1
0
0
0
2
1
1
2
1
1
2
0
1
0
2
2
0
1
1
1
1
1
0
2
1
1
1
1
1
2
1
1
1
0
2
2
1
1
2
1
1
2
0
0
1
1
1
0
0
0
0
1
0
2
0
0
0
0
1
1
0
1
1
0
0
1
2
2
0
1
2
0
0
1
1
0
1
0
2
0
1
2
0
0
1
1
1
1
3
0
3
0
0
0
1
0
0
1
0
0
2
0
1
2
2
1
2
1
0
1
2
2
0
1
0
2
0
0
1
1
0
1
2
0
2
1
1
2
0
1
0
0
1
2
0
0
2
1
0
1
0
0
1
2
2
1
1
1
0
2
2
2
1
1
1
2
2
0
1
0
0
1
1
2
1
1
0
1
1
1
1
2
0
2
0
1
1
0
0
1
2
1
2
0
0
1
0
2
0
1
0
3
1
1
1
0
1
2
0
0
1
0
0
2
0
0
1
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
2
1
0
1
1
2
0
0
1
1
0
2
1
1
2
0
1
1
2
1
1
0
1
2
0
0
2
2
1
1
0
1
1
2
5
2
0
1
1
1
2
1
0
2
1
1
0
0
0
1
1
0
2
0
1
1
1
1
2
0
2
1
0
1
1
1
0
1
1
1
1
1
1
1
0
0
1
1
0
1
1
2
1
1
0
0
1
0
0
0
1
0
0
1
0
1
1
1
0
1
0
0
1
1
0
1
1
1
1
1
0
1
1
1
2
1
1
1
1
2
1
1
1
1
1
2
0
0
2
0
1
0
0
1
1
0
0
2
2
5
0
1
0
0
1
2
0
2
1
1
0
2
3
1
1
3
2
1
2
1
0
1
0
1
2
1
0
0
0
1
1
0
0
0
0
0
2
1
0
0
1
0
0
1
0
1
1
2
1
1
1
0
0
1
3
0
2
0
2
1
1
0
2
4
0
1
0
2
0
2
0
1
2
1
0
0
1
0
0
2
1
0
2
0
0
2
0
1
2
2
0
2
0
0
0
0
0
0
0
2
2
2
2
0
1
1
1
1
1
1
1
1
2
0
1
0
1
0
1
1
1
1
1
0
2
0
1
0
0
0
0
2
2
0
0
1
0
2
0
2
1
0
1
1
0
1
0
2
2
0
0
1
2
1
1
0
2
1
1
0
0
1
1
1
0
0
1
1
2
1
1
1
3
1
0
0
3
0
1
1
0
0
2
1
0
1
1
1
0
1
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
2
0
1
2
1
1
1
1
0
2
1
2
0
1
0
1
2
0
1
1
0
0
0
0
0
1
1
1
1
1
1
1
1
1
0
1
1
2
2
0
0
1
3
1
0
1
2
0
1
1
0
1
0
0
1
0
2
1
2
1
0
0
2
1
2
2
0
2
1
2
0
1
1
1
2
0
1
1
0
1
1
1
0
1
1
0
2
0
1
1
0
0
2
0
0
1
1
0
2
1
0
2
1
0
0
0
3
2
0
1
0
2
0
0
1
2
0
1
1
2
2
0
2
1
0
1
1
1
0
0
1
0
3
1
1
1
0
0
0
2
0
0
0
1
1
1
0
0
1
2
3
1
1
1
2
0
0
2
2
1
1
1
1
2
0
0
1
2
1
0
2
0
0
0
1
0
0
2
2
0
2
1
0
0
2
1
1
1
1
1
1
1
0
2
1
0
1
1
0
0
2
2
0
2
1
0
0
1
0
2
1
1
0
2
2
2
1
0
0
0
1
0
1
2
1
0
0
1
1
0
1
1
1
0
0
2
1
0
1
0
0
1
1
0
0
1
1
1
2
0
0
2
2
1
2
0
1
1
0
1
0
0
1
0
1
1
1
3
1
1
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
1
2
1
1
0
2
2
0
2
0
1
1
1
2
0
1
1
1
2
1
1
1
0
2
1
0
0
1
0
0
3
1
1
0
1
1
2
1
1
2
1
1
2
0
0
1
1
0
0
1
3
2
1
0
1
2
0
0
2
2
0
1
1
2
1
2
0
1
1
1
1
0
0
0
0
0
0
6
0
2
0
0
2
1
1
1
1
1
0
2
1
0
1
2
0
2
2
0
1
0
2
2
1
0
2
1
1
3
1
0
2
0
1
0
1
2
1
1
1
0
1
1
0
1
2
1
0
0
0
1
0
2
1
0
1
0
0
0
0
1
1
1
0
0
1
0
0
0
2
0
2
0
0
2
1
0
2
0
0
0
2
0
0
0
0
2
0
0
1
0
1
0
0
2
1
2
0
0
1
1
1
1
0
1
2
1
1
1
1
1
0
0
0
1
1
1
0
2
0
0
2
0
1
2
1
0
1
1
0
1
0
1
1
2
1
2
2
2
1
2
1
0
1
0
1
0
1
0
0
0
2
1
2
1
1
1
1
2
1
1
2
0
1
2
1
2
0
1
1
1
0
1
1
0
2
1
2
2
0
1
0
1
0
1
2
1
1
2
2
0
0
0
1
0
1
0
1
2
0
0
2
1
1
1
1
1
2
1
1
0
1
0
0
2
1
0
1
0
1
2
2
2
0
2
0
0
0
2
1
1
0
0
0
0
0
0
3
0
0
1
2
0
2
1
1
0
2
1
1
1
1
0
1
1
0
0
3
1
1
1
0
1
1
1
0
1
0
0
3
0
1
1
0
0
0
1
2
1
0
1
0
0
2
2
2
1
1
0
0
0
0
1
0
1
2
1
0
2
1
1
1
1
1
1
1
0
0
1
1
0
2
0
1
2
0
1
1
2
0
0
2
0
2
1
1
2
1
0
1
1
0
1
1
1
1
0
1
0
0
2
1
2
1
0
0
0
1
0
0
0
0
1
1
0
0
1
1
1
0
1
2
0
1
0
0
2
0
1
0
0
1
1
2
2
0
1
0
0
1
0
2
2
1
2
2
1
0
0
2
1
0
1
0
0
0
1
1
0
0
0
0
3
1
0
2
1
2
0
1
1
2
0
0
1
2
1
0
1
0
0
2
0
1
0
1
2
1
2
1
1
1
0
1
0
0
2
0
1
0
2
1
1
0
2
2
0
0
2
0
2
0
0
3
0
2
1
1
2
0
2
0
2
1
1
2
0
0
2
1
1
1
0
1
2
0
1
1
1
1
2
1
2
1
0
1
2
0
0
1
1
2
1
1
1
1
0
0
1
2
0
1
1
1
0
2
2
0
0
1
2
2
1
1
3
1
0
0
2
1
0
1
2
2
0
1
0
0
2
0
1
1
0
0
0
0
1
2
0
1
1
0
1
1
1
0
2
1
1
1
3
0
0
2
1
1
1
1
2
1
1
1
0
0
0
1
1
1
1
2
0
0
0
0
0
2
3
1
1
0
0
0
0
2
2
0
1
0
2
1
0
1
1
0
0
0
2
0
0
0
2
1
0
2
0
2
2
2
0
2
1
0
0
2
0
0
1
0
1
1
0
0
1
0
1
0
0
1
1
0
2
1
2
2
1
0
2
1
2
0
1
1
0
1
1
0
0
2
0
1
1
0
0
0
0
2
0
0
1
0
1
1
1
1
4
0
1
2
2
2
0
1
2
0
1
2
1
0
1
3
0
1
0
0
1
2
1
1
1
0
2
1
1
0
2
0
1
1
1
1
0
0
1
1
2
0
1
1
0
2
3
0
1
2
0
0
1
0
0
1
0
1
2
1
2
1
0
1
0
2
1
1
0
1
0
1
1
0
1
1
0
0
1
2
0
0
0
1
2
1
0
1
0
0
2
0
1
0
2
1
0
2
2
2
2
1
2
0
1
0
1
2
2
0
1
0
1
2
2
0
1
2
1
1
2
3
2
2
2
1
2
1
1
0
1
0
2
1
0
2
2
0
1
1
0
2
1
1
2
1
4
0
1
0
1
0
0
0
2
1
1
1
2
0
2
1
2
1
2
1
1
1
0
2
0
0
0
0
1
0
0
2
3
1
2
0
1
1
0
2
0
0
1
1
1
0
1
0
1
0
0
1
0
1
2
2
0
0
1
1
2
3
1
2
2
1
2
1
0
0
1
0
1
2
0
0
1
1
0
0
1
1
1
1
1
0
2
1
0
2
0
0
2
1
1
0
1
1
0
1
2
0
1
0
2
0
0
0
0
1
0
2
1
1
1
1
2
2
1
0
2
1
0
1
0
1
1
1
1
1
1
1
0
0
2
0
2
1
1
2
2
1
1
0
0
1
1
1
4
1
0
0
1
0
2
2
1
0
1
1
1
0
1
0
1
1
0
1
1
0
0
0
2
1
1
0
1
1
2
0
2
1
0
5
2
1
0
0
1
0
1
0
1
2
0
0
0
0
0
1
1
1
0
2
0
0
0
0
0
0
1
0
2
0
2
1
1
0
1
2
2
3
1
2
0
1
0
0
2
2
0
0
2
1
2
1
0
2
1
1
0
2
0
0
1
1
1
0
1
1
0
1
0
1
0
1
1
0
0
0
2
1
0
0
1
0
2
0
0
3
1
0
1
0
0
1
0
1
1
0
1
0
2
1
1
1
0
0
1
0
1
0
0
0
2
1
0
3
1
0
1
0
1
2
0
2
0
0
0
0
0
0
2
1
1
1
2
2
2
1
1
2
0
2
2
1
1
0
2
0
0
0
0
1
0
0
1
1
2
0
1
0
1
0
0
1
1
0
0
1
2
0
2
0
0
1
0
1
0
1
0
1
1
0
0
0
0
2
0
0
0
1
2
1
0
1
1
1
0
2
0
0
1
2
0
0
2
0
0
2
1
0
0
1
1
0
0
0
0
0
1
2
3
2
1
2
2
0
1
2
1
1
0
0
1
0
1
0
2
0
1
0
0
2
0
0
1
1
0
0
0
0
0
0
1
2
1
3
0
0
1
0
1
0
0
1
1
0
2
1
0
2
1
1
2
1
1
1
1
2
0
1
0
0
0
1
1
0
1
2
0
2
0
2
1
1
1
0
2
0
1
0
0
1
1
0
1
0
2
2
1
1
0
1
1
1
1
2
1
0
1
1
1
1
0
1
1
1
0
1
0
1
0
0
0
1
1
0
2
0
1
2
1
2
2
0
2
1
2
0
2
1
0
0
1
1
0
1
0
0
1
1
0
2
1
1
0
0
0
1
0
0
1
1
0
2
0
1
2
2
2
1
1
2
0
1
2
0
0
1
0
1
0
2
1
0
2
0
1
1
1
0
1
2
1
0
2
2
1
2
3
0
2
1
1
1
1
2
0
1
1
1
0
2
0
2
1
1
0
1
1
1
2
1
0
2
2
2
1
1
0
0
2
1
2
2
1
0
1
1
0
1
1
1
1
1
1
1
1
0
1
1
1
2
2
0
0
1
2
2
0
1
1
1
0
0
1
1
1
1
2
2
1
0
0
1
2
1
1
0
0
3
1
1
1
1
1
1
1
1
0
0
0
1
0
0
0
1
2
2
2
2
1
0
1
2
1
0
1
1
1
0
2
1
2
1
1
1
1
2
0
0
1
0
1
0
1
0
2
1
2
0
2
1
0
0
1
1
1
0
0
2
2
1
2
1
1
0
1
0
1
1
2
0
0
2
2
1
1
2
1
0
0
1
0
1
0
0
0
0
0
1
0
1
1
0
1
1
0
3
0
1
1
1
2
0
1
2
2
1
0
2
2
0
0
1
1
0
0
1
0
1
1
0
1
2
0
1
1
2
0
1
0
0
0
1
1
2
0
1
0
1
1
1
1
0
2
0
1
2
1
2
1
1
1
0
0
0
1
1
1
0
2
0
1
1
5
2
0
1
2
0
1
1
1
0
2
0
1
1
1
1
1
0
1
1
2
0
2
0
0
1
0
1
2
3
1
0
1
2
1
2
0
0
1
1
2
2
1
1
1
0
0
1
1
0
1
0
1
1
1
1
1
1
2
1
0
0
2
0
1
1
0
1
0
0
0
2
0
0
2
2
1
1
2
0
1
1
0
2
0
1
1
2
0
2
2
2
1
0
1
0
1
2
0
2
1
1
1
1
1
0
0
1
2
0
1
0
1
1
0
1
2
1
1
1
1
0
2
1
2
1
0
1
0
0
0
2
0
2
2
0
1
1
1
1
1
1
2
2
0
0
0
2
0
1
0
1
1
1
1
1
0
1
1
0
1
1
0
0
0
1
2
0
0
2
1
1
0
4
1
2
0
1
0
0
2
1
0
1
0
1
2
1
1
1
0
0
0
1
1
0
0
0
0
2
2
0
1
1
1
1
0
2
1
0
1
0
0
0
1
2
0
1
0
1
0
4
2
1
1
1
1
2
2
1
1
1
0
1
1
0
0
1
1
2
1
2
1
1
2
0
1
1
1
1
1
1
0
0
1
0
2
1
0
1
2
1
1
1
2
1
1
2
0
1
1
2
0
1
0
1
0
1
0
0
0
1
1
4
2
1
1
0
0
0
2
1
1
0
1
1
0
1
0
1
1
1
1
1
0
2
1
1
1
0
1
0
0
1
1
2
1
1
0
0
0
1
1
2
0
0
0
0
0
0
1
0
1
2
1
1
2
1
1
1
1
0
1
1
0
0
1
0
1
1
1
1
0
0
1
2
1
1
1
0
1
0
1
0
2
1
1
0
1
1
0
0
1
0
1
0
2
0
1
1
2
1
1
1
1
1
2
0
1
1
0
0
1
0
0
2
1
1
2
0
1
0
2
1
0
0
2
1
1
0
1
2
1
0
1
0
0
0
2
2
0
0
1
0
0
1
2
2
3
0
0
1
1
0
2
1
0
1
0
1
2
1
2
1
0
1
1
1
1
0
0
1
0
0
1
1
1
0
2
1
0
0
1
1
0
0
2
2
0
1
1
2
1
1
1
1
1
1
0
0
0
1
0
0
0
1
1
1
1
1
2
2
1
1
1
1
1
2
2
0
1
0
0
2
0
0
0
1
0
0
2
2
0
1
0
0
0
0
2
1
2
1
1
0
2
0
2
0
0
0
0
2
1
2
1
0
2
1
1
0
0
0
1
1
1
0
3
2
1
1
0
1
0
0
1
0
1
2
0
1
2
1
0
1
0
2
1
0
2
2
1
2
1
2
0
1
0
1
2
1
0
1
1
3
2
0
1
2
0
0
1
0
2
1
1
1
0
0
0
1
2
0
0
1
0
0
0
2
1
0
1
1
2
2
1
0
0
0
2
1
2
0
1
0
0
1
1
2
0
0
1
0
0
1
0
1
0
1
2
1
1
2
1
1
0
0
2
2
0
0
1
1
2
1
1
1
2
1
2
1
2
0
2
2
1
0
0
1
1
2
1
0
0
1
1
1
1
0
2
1
1
1
1
2
1
2
0
0
0
3
0
2
1
0
1
0
2
1
1
0
0
1
0
1
0
0
1
1
2
0
0
2
0
2
1
2
1
1
1
0
5
1
2
1
2
1
1
0
1
1
0
0
2
0
2
1
0
2
2
1
1
1
1
1
1
0
2
0
2
1
1
1
1
1
1
0
0
1
2
1
2
1
0
2
0
6
1
1
0
1
1
1
0
1
0
2
1
2
1
1
0
0
0
1
1
1
0
2
0
0
1
0
1
2
1
0
1
1
0
1
1
2
2
2
1
1
2
0
0
1
1
1
1
1
1
1
2
1
0
0
1
1
0
1
0
0
1
0
1
1
0
2
2
0
1
1
2
0
1
1
1
1
1
0
0
1
0
1
0
0
1
1
0
0
1
3
2
1
0
0
2
0
2
2
0
0
2
1
0
1
1
0
0
2
0
0
2
1
0
2
2
0
1
0
1
2
1
1
1
2
1
1
1
2
0
1
1
1
1
1
0
1
0
1
0
1
0
2
0
1
2
2
2
1
2
2
2
0
1
0
0
1
0
2
0
1
0
0
0
0
0
2
1
1
1
0
2
1
2
2
1
1
1
2
0
0
1
2
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
2
1
1
1
2
0
1
2
0
2
1
0
0
1
1
0
2
0
1
0
3
0
2
1
1
0
0
1
0
0
1
1
2
1
1
0
0
0
2
1
0
0
1
0
0
2
0
1
0
2
0
1
2
0
1
2
1
1
0
0
1
0
1
2
2
0
2
0
1
1
1
2
0
2
0
1
2
2
1
1
0
0
0
1
0
1
1
1
0
1
2
2
1
0
0
0
2
2
0
1
0
0
2
0
0
2
0
1
2
0
1
0
1
0
0
1
2
0
1
1
1
2
0
0
1
2
2
2
2
1
0
0
1
1
1
0
1
2
0
1
0
4
1
1
0
0
0
0
1
0
0
2
1
0
1
1
0
0
2
0
0
3
1
1
0
1
0
1
0
1
0
1
1
2
1
0
0
1
0
0
1
2
1
1
0
2
1
1
0
0
2
1
0
0
0
1
1
1
2
0
0
0
0
0
1
0
1
0
1
0
1
0
1
2
1
1
2
0
1
1
0
1
1
2
2
0
1
0
1
2
0
1
0
2
0
0
2
1
0
0
1
0
1
0
4
1
1
1
0
1
2
0
2
0
0
0
1
2
1
0
1
2
1
0
1
1
2
2
2
1
0
2
1
1
2
1
1
0
1
0
2
1
0
2
0
1
0
1
2
1
0
2
2
1
0
1
2
0
2
0
0
2
2
1
0
1
1
2
1
1
1
1
0
0
0
1
0
2
1
2
0
2
0
0
1
2
0
0
2
0
0
0
2
1
1
1
2
1
0
0
0
1
1
2
2
1
2
1
2
0
2
0
0
2
1
1
0
0
1
1
2
1
2
1
0
0
1
2
0
2
1
2
2
1
1
1
0
0
2
0
0
0
0
2
0
0
1
2
1
0
0
1
2
1
0
2
1
1
2
1
0
1
0
1
0
1
1
1
1
0
1
0
0
3
1
1
1
0
0
2
0
1
0
1
2
0
2
0
0
1
0
1
2
1
0
1
2
0
2
2
0
1
1
0
1
1
1
1
0
1
0
1
0
1
0
1
0
0
1
1
1
2
0
2
0
1
0
1
1
1
0
0
1
2
2
2
1
0
2
0
1
0
0
2
0
2
1
0
0
0
0
1
0
1
2
1
1
1
0
0
0
1
0
0
1
1
0
2
0
1
1
2
0
2
1
0
0
1
1
1
0
2
1
1
2
2
0
1
1
2
0
0
1
2
1
1
0
1
1
1
1
0
1
1
0
1
0
1
0
0
2
2
2
0
1
0
1
1
1
0
0
0
0
2
0
1
1
0
2
1
1
1
0
2
2
1
2
2
0
1
0
0
1
1
0
0
0
0
1
0
2
1
1
1
1
0
1
0
0
0
1
0
1
1
0
2
0
1
0
2
1
0
1
1
1
0
2
0
0
0
0
0
2
1
1
1
0
0
1
0
0
0
1
0
2
0
1
0
2
2
0
2
0
1
0
1
1
0
2
1
2
1
2
1
1
1
0
1
3
2
1
1
2
0
1
2
0
0
0
0
1
0
1
0
1
2
1
2
1
0
0
2
1
1
0
1
0
1
3
1
1
1
3
1
2
2
2
1
1
2
0
2
2
0
0
0
0
1
1
0
0
1
0
2
1
1
1
2
1
2
0
0
2
1
2
1
0
0
0
1
2
1
1
2
1
0
1
1
1
0
0
2
1
1
2
1
1
1
1
1
2
0
0
0
2
2
0
2
1
0
1
0
1
1
1
2
2
2
0
1
2
0
1
1
1
0
2
0
1
1
0
1
1
1
1
0
0
0
1
1
2
0
1
2
2
0
6
1
2
0
2
0
0
0
2
1
2
1
1
0
0
0
2
0
1
1
0
1
0
1
1
0
1
0
1
0
1
2
2
0
2
0
0
2
2
1
0
1
2
1
1
1
0
2
2
2
1
1
1
1
1
1
0
0
0
1
1
0
2
1
1
0
2
2
1
0
1
0
1
0
0
0
0
0
1
0
1
1
1
0
1
0
2
0
0
0
1
1
1
1
0
2
2
2
1
0
2
1
1
2
0
0
0
0
0
1
0
1
0
1
0
0
2
1
1
1
0
2
0
0
1
1
1
0
1
0
2
0
1
0
0
2
0
1
2
1
0
2
0
1
1
0
0
0
2
0
0
0
0
0
1
1
1
1
1
1
1
1
1
2
1
1
0
2
1
1
1
1
0
0
1
1
1
0
1
2
1
0
3
0
1
1
0
1
1
0
1
2
2
0
1
0
1
1
1
0
1
0
1
0
0
0
2
0
1
2
1
2
1
1
1
1
1
0
2
0
1
1
0
1
1
1
1
1
0
1
0
0
0
1
0
1
0
1
0
0
1
1
1
2
0
1
1
1
1
3
0
2
1
1
0
0
2
1
2
1
2
2
1
0
0
0
2
2
0
1
2
0
0
0
2
1
1
0
0
1
2
2
1
2
3
0
1
1
2
1
0
1
1
2
0
0
2
0
1
0
2
1
2
0
1
0
0
1
0
1
1
0
0
1
2
1
2
2
0
0
1
2
2
2
2
2
0
2
0
1
0
0
1
1
0
2
1
0
0
1
0
2
2
1
1
0
1
1
0
2
0
1
2
0
0
0
1
0
0
1
3
1
1
1
1
1
0
0
1
1
1
2
1
3
0
0
0
0
1
3
2
0
0
1
1
2
1
0
2
0
2
1
0
0
1
0
2
0
0
1
0
2
1
0
1
3
2
1
2
1
1
0
0
2
0
0
0
2
0
1
0
1
2
0
1
1
0
0
1
1
1
1
1
3
0
1
2
0
0
2
0
0
1
1
0
0
0
1
2
0
1
4
1
0
0
1
0
2
0
1
0
2
1
2
1
1
2
0
1
0
1
1
0
0
0
0
0
4
2
2
1
1
1
3
0
0
0
1
0
1
2
2
1
1
1
1
1
0
0
1
0
0
0
2
2
0
2
1
2
0
1
1
1
2
1
1
1
2
0
1
1
0
0
1
1
0
0
0
1
1
0
0
1
1
1
1
2
1
2
2
2
1
0
1
1
0
0
2
0
1
0
2
0
0
1
0
2
2
1
1
0
0
1
2
0
0
2
1
0
0
0
0
1
0
0
1
2
2
0
1
0
0
0
3
0
2
1
0
0
1
1
2
0
1
2
2
0
2
1
1
1
0
1
1
3
1
1
2
2
0
1
1
0
0
0
2
0
0
2
0
0
0
2
1
2
0
0
0
0
1
2
1
0
1
0
1
0
2
2
0
2
2
2
2
1
2
0
1
2
1
0
1
0
1
1
2
1
2
1
1
2
1
1
1
1
0
3
0
0
2
1
1
0
1
0
2
1
1
2
1
0
0
1
2
2
1
0
0
1
1
0
2
1
0
0
2
0
0
0
0
2
0
2
3
1
0
2
1
1
0
2
1
1
1
1
1
2
0
0
0
2
1
0
0
0
2
2
0
0
0
0
1
2
2
0
2
1
2
2
1
0
0
0
1
2
0
0
1
2
1
0
2
0
1
1
1
1
2
1
1
0
1
0
1
1
1
1
1
0
0
1
1
1
0
1
2
0
0
1
1
1
1
1
1
1
0
1
1
1
0
2
2
0
0
0
1
1
0
1
1
0
0
1
2
1
0
2
0
1
0
0
1
0
1
2
0
0
1
0
2
0
1
0
1
0
1
2
0
1
1
1
2
1
1
0
2
0
1
0
0
1
1
0
2
1
1
0
0
1
1
2
1
0
2
0
2
0
1
1
0
0
2
0
0
2
1
1
1
0
1
0
1
1
1
1
0
2
0
1
2
0
1
0
3
0
2
2
2
1
1
0
2
2
1
1
2
2
2
0
2
2
0
2
0
0
2
1
1
1
1
1
0
1
0
3
0
0
2
0
0
0
0
0
0
0
2
0
1
1
1
0
1
1
0
1
0
1
1
2
1
0
0
2
0
2
1
0
1
1
1
0
0
1
0
1
1
0
1
2
1
1
1
1
1
2
3
1
1
2
2
0
1
0
0
1
0
1
0
1
2
0
1
0
0
3
2
1
1
0
1
1
0
1
0
1
1
1
1
0
2
1
1
0
0
1
0
2
1
2
1
2
2
1
1
1
0
1
0
0
0
2
0
0
1
1
0
0
1
1
0
0
0
2
0
1
1
0
0
1
1
0
4
0
1
1
0
0
1
1
1
1
1
1
0
1
1
2
1
1
1
1
1
1
0
1
0
1
0
1
0
2
2
2
1
0
2
1
1
1
0
2
0
1
2
0
1
3
2
2
2
1
1
0
0
2
2
2
0
0
0
1
0
0
1
1
2
0
0
1
2
0
2
0
1
2
0
0
1
1
0
1
1
0
2
1
2
2
1
1
0
1
1
0
2
2
0
0
1
0
0
0
1
0
0
2
0
0
1
2
0
1
0
0
2
0
0
2
2
2
1
1
0
0
2
0
0
0
0
2
1
1
0
0
0
0
0
2
1
1
4
0
2
2
1
0
1
0
2
0
2
1
1
0
0
1
0
2
0
0
0
0
1
1
1
0
2
1
2
0
2
1
1
0
0
1
1
0
0
2
1
0
0
0
2
2
1
0
1
2
1
2
3
1
2
2
1
2
0
1
1
0
2
2
0
0
1
1
3
1
0
1
1
1
1
0
0
0
0
2
2
0
1
2
2
0
1
1
0
1
1
1
0
0
1
1
2
1
0
1
0
0
1
0
1
0
1
0
1
3
0
0
1
1
2
0
2
1
1
0
2
1
1
0
1
0
2
0
1
0
0
1
1
1
2
0
2
1
1
2
1
1
1
1
0
1
0
0
1
0
2
2
0
2
1
1
0
1
0
2
0
2
2
0
1
0
1
1
1
0
1
0
2
0
1
0
0
0
1
1
0
0
0
1
0
2
2
2
2
1
1
1
0
1
0
1
1
1
2
1
0
0
1
0
1
1
2
0
2
1
1
0
1
2
1
1
0
0
1
0
0
0
2
0
0
0
1
0
2
1
0
0
1
2
2
1
0
0
2
1
0
1
0
1
0
0
1
0
2
0
2
2
1
0
1
0
1
1
1
1
0
1
0
0
0
1
0
0
1
2
0
1
1
1
2
1
1
0
1
0
1
2
0
1
0
0
0
3
1
0
2
0
0
0
0
2
1
1
5
1
1
2
0
1
0
0
1
1
1
0
1
2
1
1
1
2
0
1
2
1
0
1
0
1
1
0
1
0
0
1
2
0
0
0
0
0
1
2
1
1
0
2
1
1
1
1
0
2
1
0
2
0
1
0
0
0
0
2
1
1
0
0
0
0
1
2
1
1
2
0
1
1
1
1
1
1
0
1
1
0
0
2
1
1
0
1
0
0
1
2
0
2
1
0
2
1
0
0
2
0
1
2
1
0
2
0
0
0
3
1
0
0
1
0
0
0
0
0
1
0
2
0
2
2
1
0
2
2
0
1
0
0
2
2
0
2
2
2
1
1
0
1
2
0
1
2
1
1
0
1
1
0
0
2
5
1
1
1
1
0
0
2
1
2
1
0
0
1
0
2
1
2
5
0
1
1
0
1
2
0
0
3
1
0
1
0
1
1
0
1
0
2
2
1
2
1
2
3
2
2
1
2
0
0
0
1
0
0
1
1
1
2
2
2
1
1
0
1
1
1
0
3
1
1
1
2
2
1
0
0
0
1
1
0
1
1
2
0
1
0
1
1
1
0
1
1
2
1
1
1
1
0
1
1
2
0
1
0
2
1
0
1
0
0
2
0
1
3
1
0
0
1
1
0
1
0
1
0
1
4
1
0
3
1
0
0
0
1
0
1
2
2
1
2
1
2
1
1
1
0
1
1
2
1
2
1
1
2
1
1
1
0
1
1
1
1
1
0
0
0
1
2
1
1
0
1
2
0
1
2
0
0
2
1
0
0
2
1
1
1
1
1
2
2
0
0
0
1
0
2
1
0
2
0
2
0
2
1
0
1
0
1
0
2
0
2
0
2
1
0
1
2
2
2
2
0
3
0
1
2
1
1
2
1
1
1
1
1
0
2
1
1
1
1
2
1
2
0
1
1
0
0
1
1
2
1
0
1
0
1
1
2
0
2
0
2
0
2
0
2
0
2
1
0
0
1
0
1
1
1
1
1
1
1
0
2
1
2
1
2
1
1
1
0
0
0
0
1
2
2
1
1
1
2
0
2
1
0
2
2
2
1
1
0
1
2
2
1
0
0
1
0
0
0
0
1
1
1
3
0
1
1
2
2
0
0
0
1
2
0
2
0
1
0
0
0
1
1
1
2
2
1
0
1
1
1
0
0
2
1
1
2
0
0
0
1
0
1
0
2
2
1
1
2
0
0
0
0
1
0
0
4
1
1
0
0
0
0
1
2
0
0
1
1
1
2
2
1
2
1
1
0
0
0
0
2
1
2
1
0
0
0
0
0
2
2
2
1
0
1
2
2
0
1
0
1
0
2
2
0
0
1
1
0
0
1
2
0
2
1
1
1
0
1
1
1
0
1
1
1
0
0
1
1
1
1
1
1
0
1
0
0
1
0
1
0
2
2
1
0
1
0
0
1
1
1
0
1
2
2
2
1
0
2
1
1
2
1
1
1
1
0
2
0
0
2
5
1
0
1
1
0
0
1
1
0
1
0
0
0
1
0
1
0
0
1
0
0
1
0
1
0
1
1
1
2
0
1
1
0
2
2
1
0
1
0
0
1
0
0
1
0
1
0
0
2
1
0
1
2
0
0
0
0
1
2
2
1
0
0
1
0
0
2
1
0
1
0
1
1
0
2
0
2
2
1
0
0
0
0
1
2
1
1
0
0
1
0
1
1
0
0
1
2
0
2
0
1
0
2
0
2
1
1
1
0
0
1
2
1
0
0
0
1
0
0
0
2
0
0
0
0
1
0
1
1
1
0
0
0
0
2
1
1
0
0
2
0
0
2
0
0
0
1
0
2
0
2
1
1
0
0
0
0
2
0
1
2
2
1
0
1
3
0
2
1
2
2
1
0
1
1
2
2
0
0
2
1
2
1
1
0
2
1
1
0
1
2
0
0
1
0
0
0
1
0
2
1
2
0
0
0
1
0
1
2
0
2
1
0
1
1
1
1
1
2
0
1
0
1
1
1
2
2
3
0
1
2
0
2
1
2
1
2
1
0
0
1
1
1
0
0
0
1
2
0
0
0
2
1
1
1
1
1
0
2
2
0
3
0
0
1
1
1
0
0
0
0
0
1
0
1
0
1
0
2
2
1
0
0
0
0
1
1
2
2
1
2
2
0
1
1
0
2
1
2
0
2
1
1
2
0
1
1
2
0
1
0
1
1
1
0
0
1
0
1
0
1
1
0
2
2
1
0
0
1
1
1
1
2
1
0
0
1
1
0
1
1
1
1
1
0
0
0
0
0
0
0
2
1
0
1
1
2
2
1
2
0
0
1
0
0
2
2
1
1
0
2
1
2
1
1
0
1
1
0
0
6
1
1
1
1
2
1
0
1
1
1
2
1
2
0
1
2
1
0
0
2
0
1
0
2
0
2
0
2
0
0
1
1
1
1
1
1
0
1
0
1
1
1
2
1
2
1
2
0
1
1
1
2
1
1
0
0
1
1
0
0
1
0
0
0
0
3
0
2
0
2
1
1
2
0
0
1
1
2
1
0
0
0
2
1
0
0
1
1
1
0
0
2
1
2
0
3
3
0
1
1
0
2
0
0
1
1
2
0
1
2
1
2
1
0
2
1
2
0
1
1
2
0
2
1
0
2
1
0
0
2
0
1
1
1
0
0
1
1
1
0
1
1
1
2
0
0
0
0
1
2
2
2
2
0
1
2
0
1
0
1
1
3
2
1
2
1
0
2
2
1
1
2
0
3
0
2
1
1
0
0
2
1
2
1
0
0
1
1
0
0
0
0
1
1
1
1
0
1
0
2
2
0
0
0
1
1
0
2
1
2
0
1
1
1
0
1
1
2
0
0
0
1
1
2
1
0
1
2
1
2
0
2
0
3
0
1
1
0
0
2
1
0
1
0
1
2
2
1
1
0
1
1
0
1
1
0
1
1
2
1
2
2
0
2
1
0
1
1
1
2
1
1
1
0
2
1
0
2
0
0
0
2
1
0
2
1
1
0
2
0
1
1
1
0
1
2
0
1
0
1
2
0
0
2
0
0
1
2
1
1
0
1
1
1
1
0
1
0
2
2
0
1
2
1
1
0
1
1
3
3
1
0
0
0
0
1
2
1
1
2
1
0
2
1
1
1
1
1
0
1
1
2
0
0
3
1
2
1
2
1
1
0
2
0
2
0
0
1
1
0
0
1
0
0
2
0
1
2
2
2
0
1
1
1
2
2
1
0
1
0
0
1
2
0
0
0
2
2
1
0
2
1
0
1
1
2
2
2
1
0
1
1
1
1
0
1
0
1
1
0
1
0
0
1
1
0
1
0
1
2
1
1
2
0
0
0
0
0
0
1
1
0
0
0
0
1
2
1
2
0
1
2
0
1
0
2
2
2
0
1
1
1
1
0
2
3
1
2
1
1
0
1
0
2
0
1
1
1
2
2
1
2
0
0
2
0
0
0
2
0
2
0
0
2
0
0
1
1
2
2
0
2
2
1
0
1
2
0
2
1
0
2
1
1
1
2
2
0
0
0
0
0
1
2
1
2
2
1
2
1
0
0
2
1
2
2
1
1
2
0
1
2
2
1
0
1
1
0
1
1
0
1
1
0
0
1
2
1
0
0
0
1
0
1
1
0
3
0
0
0
2
2
0
1
1
0
0
0
2
0
0
0
1
1
2
0
1
1
1
1
1
0
1
0
2
0
0
0
2
1
0
0
1
2
2
1
1
1
2
1
2
1
1
2
0
2
1
2
0
0
1
0
0
0
0
0
0
1
2
1
0
2
2
2
1
1
0
0
1
1
1
0
0
0
2
0
0
0
0
4
0
1
0
1
1
2
0
2
1
3
0
1
1
0
0
1
1
1
1
1
2
0
1
1
0
1
2
1
0
1
0
2
1
2
1
0
1
2
1
2
1
0
0
1
0
0
2
0
1
1
1
1
2
0
0
2
2
2
1
2
0
0
1
0
0
2
0
1
0
1
1
2
0
2
2
0
0
0
2
0
0
2
0
1
2
1
1
2
2
0
0
0
0
0
0
1
1
1
1
1
1
0
0
3
0
2
1
1
2
0
1
1
0
0
2
2
2
0
1
0
2
1
1
1
2
1
0
1
0
1
0
1
1
0
2
2
1
0
0
3
1
0
0
1
1
1
2
1
1
0
0
2
1
0
2
2
0
2
1
1
0
1
0
0
1
2
1
0
0
1
0
1
0
2
0
2
0
1
0
2
1
0
1
1
0
0
1
1
0
3
0
0
1
1
1
0
0
1
2
0
0
1
0
2
0
1
1
1
1
1
0
1
2
2
0
0
1
0
0
2
2
0
1
1
2
1
1
1
0
1
2
0
1
1
0
0
0
1
1
1
0
2
1
0
0
1
1
2
2
2
1
0
1
1
0
1
2
2
0
0
0
1
0
1
0
1
2
0
1
1
0
0
2
2
2
1
2
0
0
0
0
0
0
1
1
1
1
1
0
1
0
1
0
1
1
1
2
2
0
0
1
0
0
2
0
1
1
1
1
2
1
0
3
1
1
0
1
1
1
1
2
2
0
1
2
1
1
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
1
1
0
2
1
1
0
3
1
2
0
0
1
1
2
0
0
0
0
0
0
1
0
1
0
2
0
2
1
1
0
2
3
2
1
0
2
2
0
0
1
2
1
1
1
1
0
2
0
0
0
0
0
1
0
0
1
2
2
0
0
0
1
1
1
0
0
0
1
1
1
1
0
2
0
0
5
0
0
0
0
0
1
1
0
0
1
0
1
2
1
1
0
0
1
1
1
1
0
1
0
0
0
1
2
2
1
0
0
0
1
0
2
1
1
0
3
0
1
0
1
1
0
1
0
2
0
0
1
0
0
0
3
1
1
2
1
0
0
2
0
1
0
0
0
1
1
0
0
2
0
1
2
2
4
2
1
3
1
1
0
0
1
1
1
0
1
2
1
0
0
1
1
1
0
1
2
1
3
1
1
2
1
1
0
1
1
0
0
1
0
3
1
2
1
0
1
1
1
1
1
0
1
0
2
1
1
0
0
2
1
1
0
1
1
1
0
1
1
2
2
1
2
1
1
2
0
1
0
1
0
1
0
0
3
1
1
0
0
1
2
1
0
1
0
3
1
0
0
1
1
1
2
2
2
0
0
0
2
0
1
0
1
2
0
1
0
0
1
0
1
0
0
1
1
1
0
2
2
0
0
3
1
0
0
2
2
1
2
0
0
3
1
1
1
1
0
1
1
1
2
0
0
2
2
0
0
2
0
0
0
2
2
0
1
0
1
1
0
0
1
0
0
1
0
0
1
2
1
1
2
0
1
1
0
2
1
1
5
0
0
1
1
0
2
1
1
0
1
1
1
1
0
1
2
0
0
0
0
1
1
2
0
0
1
0
2
2
1
1
0
2
1
1
1
0
1
0
1
1
1
0
2
0
2
2
0
0
1
2
1
0
2
1
2
0
0
2
2
0
0
1
1
1
2
2
0
1
0
1
0
1
0
0
1
0
1
0
1
0
1
2
1
1
1
0
2
0
0
1
2
1
1
0
1
0
2
1
1
0
1
0
0
0
0
1
0
1
1
0
2
0
1
1
1
0
0
0
0
1
0
1
1
0
1
2
0
0
1
0
1
0
1
1
1
1
2
0
0
2
1
0
1
2
1
1
1
0
1
1
1
2
2
1
1
0
1
2
0
0
0
2
2
0
0
0
0
2
1
0
2
0
2
0
1
1
1
2
0
2
1
1
2
1
1
3
0
2
0
1
1
2
0
0
1
0
0
0
0
2
0
0
2
1
1
0
1
0
0
2
1
2
0
0
2
2
1
1
1
1
1
0
1
1
0
0
2
1
0
1
0
2
0
1
1
1
2
0
2
6
0
0
1
1
2
2
0
1
0
1
2
1
3
1
0
2
1
0
0
2
1
1
2
0
2
1
0
0
0
1
0
2
1
2
1
1
2
4
2
1
3
1
2
0
2
2
0
1
1
0
1
2
2
1
1
1
1
1
1
1
0
1
1
0
0
0
0
2
0
1
2
1
1
1
1
1
0
1
0
0
1
0
1
1
2
1
1
1
1
2
0
1
0
0
1
1
2
1
1
0
1
0
0
0
1
1
1
2
1
0
2
0
2
2
1
1
1
1
0
2
0
1
2
0
0
2
0
2
2
1
0
1
1
0
1
1
3
1
0
0
1
1
1
2
0
2
1
1
1
0
0
1
1
1
2
0
1
2
2
0
2
2
0
0
1
1
0
1
0
0
0
1
0
0
1
2
2
0
2
1
2
2
1
1
0
2
1
0
2
1
0
1
2
0
1
1
0
0
1
0
0
1
2
0
2
0
2
1
0
1
1
1
0
0
0
0
0
2
1
1
1
0
0
0
1
1
1
1
2
0
1
3
1
0
0
2
2
1
0
0
2
1
0
1
0
0
1
0
2
0
1
1
2
1
0
0
1
1
0
2
0
1
1
1
2
0
1
1
0
0
0
1
0
1
0
0
1
1
0
2
1
0
1
0
0
0
0
0
1
0
1
1
0
1
1
2
1
1
0
1
1
2
1
1
0
1
1
0
0
2
1
0
0
0
0
0
1
1
1
1
0
1
1
1
2
1
0
0
1
0
0
2
1
1
2
0
1
0
0
1
0
2
1
1
0
1
1
2
0
1
1
0
2
0
1
0
1
1
0
1
0
0
0
1
1
1
1
0
0
0
1
1
3
0
1
1
1
0
1
0
0
2
2
2
1
2
2
2
2
2
0
1
0
1
1
0
1
0
0
1
0
0
1
1
2
1
2
1
3
0
1
0
1
0
1
1
1
2
2
0
0
2
1
0
1
2
2
0
0
1
1
0
0
1
0
0
2
0
0
1
2
2
0
1
0
1
1
0
1
0
2
1
1
1
0
1
0
0
0
2
2
0
0
0
0
1
0
1
1
2
1
2
0
2
1
1
0
2
3
0
1
4
2
1
1
0
1
1
1
0
1
1
0
2
1
1
0
1
1
0
1
1
2
2
1
2
0
0
1
0
2
1
2
1
0
2
1
2
1
0
2
0
0
0
2
0
2
1
0
1
1
3
1
1
1
0
0
0
2
1
1
0
0
2
1
2
1
2
2
1
0
2
2
2
0
2
3
2
1
2
1
1
0
0
1
2
1
0
3
0
2
1
1
2
2
2
0
0
2
0
0
1
0
0
0
2
1
0
2
1
1
1
1
1
0
2
1
1
1
0
4
0
0
1
0
1
2
0
1
2
2
1
2
0
0
0
1
2
0
1
2
1
2
0
0
1
1
1
2
2
1
1
0
1
0
1
1
2
1
0
2
0
2
1
0
0
2
1
2
2
1
1
1
1
0
0
0
0
1
0
2
0
0
0
0
1
2
0
0
0
3
0
2
0
0
1
2
1
1
1
1
1
2
0
1
1
1
2
1
2
2
2
1
2
1
1
1
0
2
0
1
1
0
0
1
2
0
0
0
0
3
1
0
0
1
2
0
0
0
1
0
0
0
1
4
0
1
1
1
1
1
0
2
1
2
1
1
1
1
0
1
1
1
3
1
0
1
0
1
1
2
0
0
1
1
3
1
0
0
1
1
0
2
0
2
2
1
0
0
1
1
2
0
0
1
1
1
0
0
1
1
0
3
2
0
1
0
1
1
0
0
2
0
0
1
0
2
0
0
2
1
0
0
0
0
0
1
1
1
2
0
1
0
0
2
1
0
0
2
1
2
0
0
0
1
2
0
0
0
0
0
1
0
0
2
1
0
0
1
1
0
0
1
0
2
1
2
0
2
0
1
1
1
0
0
1
0
2
0
0
2
1
1
2
0
0
1
2
0
4
0
1
2
0
0
1
1
0
1
1
1
0
1
1
1
0
2
1
1
0
2
0
1
0
2
1
2
1
0
1
0
1
2
1
2
1
0
1
0
0
1
1
2
0
1
0
2
2
0
2
1
1
2
1
0
0
1
0
1
0
2
0
0
1
0
2
0
1
0
1
1
0
0
1
1
2
1
1
2
0
2
1
0
0
0
1
0
0
0
2
1
2
1
0
1
0
0
1
1
0
1
0
1
1
2
1
2
0
2
0
0
1
0
0
0
0
0
1
0
1
0
2
1
1
0
0
0
0
1
0
1
1
2
1
1
2
0
2
2
1
0
1
2
1
1
2
1
1
1
2
0
2
1
1
0
0
1
1
0
1
1
1
0
2
0
0
1
1
2
2
1
0
2
2
1
2
0
1
2
0
1
0
1
0
0
1
1
1
0
1
2
0
1
2
2
0
0
0
2
1
1
0
2
0
0
1
1
1
1
2
2
1
1
1
2
2
1
0
0
0
1
1
2
0
1
2
1
2
2
1
1
2
0
0
0
1
1
0
1
1
1
0
1
0
1
0
0
1
0
3
0
1
0
0
2
0
0
1
2
0
2
0
1
0
0
0
0
0
2
3
2
2
0
2
1
0
1
1
0
1
0
2
2
2
1
0
0
1
0
1
0
0
1
0
2
0
1
1
2
1
1
2
2
2
3
1
0
0
0
0
1
0
0
1
1
1
1
1
2
2
1
2
1
0
1
0
1
0
2
0
2
0
2
2
1
2
1
1
1
1
1
0
0
0
2
1
1
0
3
1
0
0
1
1
0
1
1
0
1
0
2
0
1
0
0
2
0
1
0
1
2
2
1
2
1
0
0
1
1
1
0
2
1
1
0
0
1
0
0
1
0
2
1
2
1
0
1
0
1
1
0
1
0
2
0
1
0
0
2
1
0
1
2
1
2
2
1
0
0
0
2
1
1
1
1
2
0
0
1
0
0
0
1
0
0
1
2
0
2
0
0
1
0
1
1
2
0
1
2
2
0
4
0
0
1
1
0
1
2
1
0
0
1
0
1
2
1
1
1
1
2
1
2
1
1
2
0
0
1
1
3
0
1
0
2
0
1
1
1
1
4
1
1
1
1
0
0
2
0
2
2
1
2
1
1
1
0
2
0
0
1
0
0
1
1
0
1
1
0
2
0
2
2
1
0
1
2
1
4
1
1
0
2
2
0
0
0
1
1
2
0
1
1
2
1
0
1
2
2
0
1
1
0
0
1
2
0
0
2
0
0
0
0
1
0
1
0
1
1
1
1
2
2
2
0
0
1
0
0
2
0
0
2
0
0
1
0
0
1
0
3
0
0
1
1
0
0
1
1
1
0
1
0
0
3
0
0
3
0
0
0
0
0
0
2
1
0
2
1
0
2
0
0
0
1
0
1
0
1
1
0
2
2
0
0
0
0
1
0
4
2
0
0
0
2
2
1
0
2
0
0
0
0
0
1
1
1
1
0
1
2
0
0
2
0
0
0
2
0
0
1
1
0
2
2
2
1
0
0
3
0
0
1
0
1
1
0
2
0
2
0
1
1
2
1
0
1
1
0
0
1
0
1
1
1
2
0
1
1
1
0
0
1
0
1
2
1
2
0
0
2
0
0
0
1
2
1
0
1
0
1
0
1
2
1
0
1
0
1
2
3
1
1
1
0
0
0
2
1
1
0
0
0
0
1
0
1
1
0
0
1
2
1
1
1
2
2
1
1
1
0
1
1
1
2
0
0
1
1
0
0
1
0
0
1
0
1
0
0
0
2
1
0
0
1
0
2
2
1
1
0
0
2
2
0
1
1
1
0
2
0
0
1
1
0
2
2
1
0
0
1
0
1
1
0
0
1
1
2
3
1
0
1
0
0
1
1
0
2
1
2
1
1
1
1
1
1
0
2
0
0
0
0
0
2
1
0
0
1
1
2
2
1
0
2
0
1
0
2
1
1
1
0
0
2
1
1
0
1
0
0
0
1
1
0
2
1
1
0
0
2
0
1
0
0
0
0
1
2
2
0
0
2
1
1
0
0
0
1
1
0
1
2
0
3
2
2
1
0
0
0
0
1
0
2
2
0
1
0
1
1
0
1
1
0
0
1
0
1
0
0
0
0
1
1
2
0
2
0
0
2
2
1
2
0
0
2
0
2
1
0
2
1
0
2
1
1
2
1
1
1
1
0
1
1
0
0
0
1
1
2
0
0
0
1
0
1
0
1
0
1
1
3
2
1
1
1
0
0
2
1
2
0
2
1
0
1
1
1
0
0
1
0
1
1
1
1
1
2
1
2
1
0
1
2
1
1
0
2
0
1
0
1
0
1
1
1
1
2
2
1
0
0
0
1
0
0
0
1
2
1
2
0
0
2
0
2
1
0
1
1
1
1
0
1
1
1
2
0
1
1
0
1
0
1
2
1
1
2
0
0
1
0
0
0
1
2
1
0
0
0
0
0
0
3
0
0
0
0
1
1
1
1
1
2
2
0
0
0
1
0
1
2
0
0
1
2
1
0
2
0
1
2
0
0
0
0
0
0
0
1
1
2
1
1
1
2
0
0
3
1
1
2
0
1
1
1
2
1
0
0
1
1
1
0
2
2
1
2
1
1
2
0
1
0
0
1
0
0
0
0
1
1
2
1
0
2
2
0
1
1
0
1
2
0
1
2
1
1
0
1
1
0
0
0
1
2
2
1
1
1
0
2
2
1
1
2
0
0
1
0
2
2
0
1
1
0
2
1
0
2
2
0
2
0
2
1
0
1
2
0
1
1
0
1
0
0
0
1
0
1
0
1
0
2
0
2
1
0
1
2
0
1
1
0
0
2
0
1
2
2
0
0
1
1
1
1
1
1
0
1
2
0
2
1
2
1
1
1
1
0
2
2
0
1
1
0
1
0
2
0
0
0
1
0
1
0
1
0
0
1
1
2
1
1
2
2
0
2
0
0
1
1
1
0
0
0
1
0
2
0
1
1
1
1
1
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
1
1
0
1
0
2
2
1
1
2
0
0
0
0
1
2
1
1
0
0
1
1
0
3
0
0
0
0
2
0
2
2
2
1
0
1
1
2
2
0
1
1
0
0
0
1
1
0
0
0
0
0
2
2
1
0
2
2
0
1
0
2
2
1
1
2
1
1
0
1
0
2
1
1
1
1
2
2
1
1
2
0
2
2
0
1
2
1
1
0
0
1
1
1
2
1
0
1
0
0
0
0
0
2
0
0
1
0
1
1
1
0
0
1
2
0
0
0
0
0
0
2
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
2
5
0
2
0
1
2
0
1
1
3
0
2
1
1
1
2
1
1
1
1
1
3
1
0
1
1
0
2
2
0
1
1
1
0
2
1
1
0
1
0
3
0
1
2
1
1
0
2
2
1
1
1
2
1
3
1
1
2
2
0
1
0
0
2
1
0
2
2
1
2
0
2
1
1
1
1
1
1
2
0
1
1
1
1
2
0
1
2
1
1
0
0
2
1
1
1
2
0
1
1
0
0
1
1
0
1
0
1
1
1
1
1
0
0
1
0
2
0
1
1
1
0
2
2
0
1
0
1
1
2
1
1
2
1
0
0
2
2
2
1
2
2
1
0
0
2
0
2
0
0
1
1
1
2
1
0
1
0
0
0
0
1
2
0
1
2
0
0
1
1
0
0
0
0
1
2
1
0
0
1
0
1
1
2
1
0
1
1
1
1
0
0
0
1
0
1
2
1
0
1
1
1
1
2
0
2
0
2
0
1
1
1
0
2
0
1
1
0
1
0
1
0
2
1
0
2
0
0
0
1
2
0
2
1
0
2
1
2
1
1
0
0
0
2
2
1
1
2
0
0
1
0
2
0
0
0
1
2
0
1
2
0
1
2
0
0
0
0
0
1
0
0
1
0
2
3
0
2
1
0
0
0
0
2
1
1
0
2
0
0
1
1
1
0
0
0
0
0
1
0
1
0
1
0
1
1
2
0
1
0
0
1
2
1
2
2
1
0
0
1
2
2
1
2
1
2
0
0
2
1
1
0
0
1
0
0
1
1
1
0
1
0
1
0
1
2
0
1
1
0
1
2
2
1
0
1
1
4
0
0
0
0
2
0
1
1
0
2
1
1
1
1
0
1
1
1
1
1
2
2
0
0
0
0
0
1
1
1
0
0
1
2
2
1
0
0
1
2
0
1
1
2
0
0
0
1
1
6
1
0
1
1
0
0
1
2
1
1
1
1
0
2
1
0
1
0
0
0
0
1
1
0
1
0
0
0
0
1
1
0
0
0
1
0
2
0
1
0
2
0
2
1
1
1
2
1
0
2
0
1
0
1
0
0
1
1
2
1
0
0
0
0
2
1
2
0
1
1
0
2
2
1
0
1
0
0
3
0
1
1
0
1
1
0
1
2
0
1
1
1
1
1
2
1
0
0
1
0
0
1
0
0
2
1
2
0
1
1
0
2
1
0
1
2
0
0
0
0
0
2
0
0
1
0
0
1
0
3
1
2
1
0
2
1
2
0
2
1
2
0
1
0
1
1
2
0
1
1
0
0
2
0
0
0
1
0
0
1
2
0
1
2
0
0
1
0
2
1
1
0
0
3
1
1
0
3
1
2
1
1
0
1
2
0
2
0
0
1
1
0
1
2
0
1
2
0
1
0
0
0
0
0
0
0
1
2
1
0
0
1
1
0
0
1
1
1
1
0
1
2
1
0
2
1
1
0
1
0
2
1
1
1
0
2
0
1
1
1
1
1
1
0
0
1
1
1
1
1
0
0
0
2
1
2
1
0
0
1
1
0
2
1
1
0
1
0
1
1
1
0
0
1
1
1
1
2
1
0
2
1
0
2
0
1
1
1
0
2
1
0
0
0
1
2
2
0
0
2
0
0
2
0
0
1
0
1
0
0
0
1
2
1
1
0
1
1
0
1
1
1
1
1
0
2
1
0
0
1
0
1
0
0
1
0
3
2
2
1
1
1
1
1
0
3
0
1
1
0
0
0
0
1
0
1
2
0
0
2
1
2
2
0
1
1
1
0
2
2
2
1
0
0
0
1
1
2
1
2
1
1
0
1
2
1
0
0
2
3
1
2
1
2
0
0
0
0
2
1
1
1
0
2
1
0
2
1
0
2
1
1
1
1
0
0
1
0
2
1
0
1
2
1
2
2
1
1
0
2
1
2
2
1
1
0
0
0
0
1
2
2
0
0
1
2
1
0
0
1
0
1
0
2
1
1
0
1
1
2
1
1
1
1
2
0
0
0
1
0
1
1
1
3
1
2
3
2
1
0
0
2
2
0
1
2
0
1
0
1
1
1
0
2
1
0
1
0
0
1
0
2
1
0
1
2
2
0
1
1
1
1
2
1
1
0
0
0
1
1
0
0
0
0
0
1
0
1
2
1
0
2
2
0
2
0
2
1
1
0
0
0
1
1
0
1
1
0
0
0
1
1
2
1
1
1
0
1
2
0
2
1
1
0
0
0
1
1
1
1
0
0
1
0
0
1
1
2
1
1
1
1
1
1
1
2
2
1
1
2
0
0
0
1
0
1
0
1
2
1
1
0
1
1
2
1
1
1
1
1
1
1
1
1
0
1
0
0
2
2
0
1
0
2
1
1
2
0
1
0
0
1
1
1
1
1
1
2
1
1
1
0
1
1
2
1
2
1
0
2
2
1
3
1
1
1
0
0
0
2
2
1
1
1
1
0
1
0
0
0
2
3
1
2
1
2
1
0
1
1
0
1
1
2
1
1
0
0
0
0
0
0
0
2
1
1
0
2
1
0
1
1
2
0
1
1
1
2
1
1
0
1
0
0
0
2
1
0
2
3
1
2
3
0
0
0
0
1
1
1
0
2
1
1
0
1
2
1
2
1
2
0
0
2
1
0
0
0
1
2
1
1
1
0
0
1
0
1
1
0
1
2
0
1
1
0
1
2
0
2
0
1
2
0
1
1
1
0
2
0
0
2
3
2
0
1
1
0
0
1
0
0
1
2
0
0
0
1
0
1
1
1
0
2
0
0
0
1
2
1
1
0
0
1
0
1
0
1
1
1
1
1
1
1
2
1
2
0
0
0
0
2
1
1
1
0
1
0
1
2
0
2
0
0
0
1
1
2
1
1
0
0
2
1
0
2
2
0
0
0
2
2
3
1
1
0
1
0
0
0
1
2
0
2
2
0
0
2
0
2
1
0
1
2
0
0
0
1
1
0
2
0
1
2
0
0
2
1
0
1
1
1
0
0
1
1
1
1
1
2
2
0
1
1
0
1
0
0
2
0
1
1
2
2
1
1
1
0
1
1
0
1
1
0
1
1
1
1
0
1
0
1
1
1
1
2
0
0
1
0
1
1
0
1
0
0
1
0
1
1
1
1
2
0
0
2
0
1
0
1
0
2
0
0
0
0
0
0
1
0
1
2
1
1
0
0
0
1
1
1
0
1
0
0
1
3
1
0
2
0
1
0
0
0
0
1
0
1
0
1
0
2
1
1
0
1
2
2
0
2
2
1
1
2
1
2
0
2
0
2
0
0
0
0
1
2
1
1
1
0
0
0
0
1
1
1
2
0
0
1
2
1
1
2
0
2
1
1
0
0
1
1
2
1
1
1
0
1
1
1
1
1
2
2
3
2
2
2
1
1
1
2
2
2
1
1
1
0
1
2
1
1
1
1
1
0
0
2
0
0
0
0
1
1
0
1
2
1
2
2
1
2
1
1
1
1
0
0
2
1
0
1
0
2
0
1
0
1
0
2
1
1
1
0
1
0
1
2
1
1
2
1
0
1
0
1
0
0
1
1
0
0
0
1
1
1
0
2
1
0
0
2
1
1
1
1
2
1
0
1
0
0
1
1
1
2
1
1
1
2
0
0
0
1
0
1
1
2
1
1
1
1
0
1
2
2
1
1
2
1
1
1
0
0
1
0
1
1
1
1
1
2
2
0
0
0
0
1
0
1
2
1
0
2
0
1
0
0
1
2
2
0
1
1
0
1
1
0
1
0
1
0
0
0
2
0
0
0
1
1
3
1
0
2
0
0
1
2
1
0
0
1
1
2
2
0
1
2
1
1
1
0
1
2
0
1
0
1
1
0
1
2
1
1
2
1
2
1
1
0
0
2
1
1
1
1
2
2
1
2
0
0
0
0
1
2
0
2
0
1
1
1
3
0
2
1
0
1
2
1
1
1
0
2
1
0
1
1
0
1
1
1
2
0
1
0
0
0
2
10
1
0
1
2
0
1
1
1
3
1
1
1
0
1
2
1
2
0
0
1
0
0
3
1
0
0
0
0
1
2
1
1
1
2
1
0
2
1
0
0
0
2
0
0
2
2
0
1
1
1
0
2
1
1
1
0
1
2
0
0
0
2
1
0
2
0
1
0
2
1
0
1
2
1
0
2
1
10
0
2
1
1
1
0
1
1
0
0
1
0
0
1
1
0
1
1
2
1
2
1
0
1
1
1
2
0
2
0
1
2
0
2
0
1
0
1
1
1
1
1
1
0
1
0
2
1
1
1
0
0
0
1
0
1
1
0
2
2
1
0
0
1
0
0
2
0
1
0
0
1
1
1
1
1
0
2
1
0
0
2
2
0
1
3
1
1
0
1
0
0
2
0
0
2
0
0
1
0
1
1
1
0
1
0
0
1
0
0
1
2
1
1
1
2
1
2
1
2
0
1
2
1
1
0
2
1
2
2
1
2
0
2
0
1
1
1
2
1
0
3
1
0
0
0
1
0
2
0
1
1
1
1
0
1
1
1
0
0
0
1
2
2
0
1
2
1
1
2
1
0
1
1
1
1
3
0
1
1
2
1
1
2
1
1
1
1
0
1
1
0
0
0
1
0
1
0
1
1
1
0
1
0
0
0
1
2
1
1
1
0
0
1
1
1
1
0
2
1
0
0
1
2
1
1
1
0
3
1
2
0
0
1
1
1
2
2
0
0
0
2
1
2
1
1
1
1
3
2
1
0
4
0
1
0
2
1
0
2
0
1
1
0
1
1
2
1
0
2
0
0
1
1
1
1
1
1
1
1
0
1
0
0
0
0
1
2
1
1
2
1
1
2
1
1
0
1
0
2
2
0
2
1
2
2
1
2
1
2
3
2
1
0
2
1
1
0
0
2
1
1
4
2
0
0
2
1
2
1
0
1
0
0
0
0
0
1
1
0
0
0
2
0
2
1
0
1
2
1
2
3
1
2
0
0
2
1
1
2
2
2
1
0
2
1
3
0
0
1
2
0
2
1
1
1
0
0
1
0
0
1
0
1
0
2
0
1
0
0
1
0
2
2
1
1
1
1
1
0
1
0
1
0
0
1
0
1
0
1
1
1
2
1
0
0
0
1
0
3
2
0
1
0
0
2
2
1
1
0
2
0
0
2
0
0
1
1
2
0
1
4
2
0
0
0
0
2
0
3
0
1
1
1
1
2
1
0
1
0
1
1
1
0
0
3
1
2
2
0
2
0
1
2
1
1
1
0
0
2
0
0
2
1
0
0
0
1
1
2
2
2
0
2
2
0
2
1
0
0
2
0
2
0
0
0
0
2
1
1
2
1
2
2
1
0
0
1
1
0
0
0
0
0
0
0
2
1
0
2
2
0
2
1
1
0
0
2
1
0
0
0
0
2
2
0
1
0
2
1
1
1
0
0
0
0
0
2
1
2
2
0
0
2
2
5
1
2
1
0
1
2
2
3
2
0
0
1
1
1
0
1
0
1
2
0
1
0
1
0
1
0
0
1
1
0
1
1
1
1
2
0
0
2
4
2
0
1
1
0
1
1
0
2
2
1
3
1
0
1
1
1
2
2
1
0
1
1
1
0
0
1
2
0
1
1
1
0
2
2
0
2
0
2
0
1
0
0
1
1
1
1
2
2
0
2
0
2
0
1
1
2
1
0
1
0
1
0
1
0
1
0
1
0
2
2
1
2
1
2
0
2
1
0
3
1
2
0
0
1
0
2
0
1
2
0
1
1
1
2
1
2
0
1
1
1
0
1
1
0
0
0
1
0
1
1
1
0
0
2
0
1
2
1
2
0
0
1
1
2
1
0
0
2
0
2
1
0
0
2
0
0
0
1
1
0
2
1
1
2
2
2
1
1
0
1
1
0
1
0
1
1
1
1
1
2
2
0
0
2
1
0
2
0
0
1
2
0
1
0
1
2
0
0
0
2
1
2
1
0
1
1
2
0
0
1
1
0
1
3
1
0
2
2
2
1
1
2
0
1
2
0
1
2
1
2
0
2
2
0
1
0
3
0
2
0
1
2
0
2
0
0
2
3
1
1
1
2
1
0
1
1
0
1
1
2
1
0
0
1
0
1
1
1
0
2
1
3
2
1
0
2
2
2
1
0
0
1
2
2
2
2
1
0
1
2
1
2
1
1
1
1
2
1
2
1
1
0
0
0
0
1
2
0
0
0
2
1
2
2
3
1
2
0
0
2
2
0
0
2
1
0
3
0
0
0
1
1
1
2
1
0
0
1
1
0
2
0
1
1
0
0
1
1
1
1
0
0
0
1
0
2
1
1
1
2
1
1
1
0
2
1
1
2
2
3
1
1
1
1
2
1
2
0
0
0
0
0
0
2
2
0
0
1
1
2
1
0
1
0
2
1
0
2
0
0
0
0
1
1
1
1
2
2
0
1
0
0
1
1
1
1
1
2
0
0
0
1
1
1
0
2
2
2
2
1
1
1
0
0
1
0
1
2
0
0
2
0
1
2
0
1
1
0
1
1
1
0
0
2
2
0
1
2
1
0
1
0
0
1
0
2
1
1
1
2
2
1
0
0
2
2
0
0
2
1
1
1
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
1
0
0
0
0
2
1
0
2
1
0
1
2
0
1
1
1
2
0
1
0
0
1
0
1
1
0
2
1
1
1
0
1
0
1
3
1
2
1
1
2
0
0
1
0
0
1
0
0
0
1
1
0
0
3
2
0
0
0
1
0
2
0
0
0
2
0
2
1
1
0
2
1
0
0
2
2
2
3
1
1
2
1
0
0
2
0
1
1
1
0
1
1
1
2
1
1
1
0
1
2
0
2
0
2
2
1
3
1
1
1
0
0
1
0
1
0
1
1
0
2
0
0
0
0
0
2
1
0
1
1
0
0
1
2
2
1
0
2
0
0
0
0
1
0
0
1
0
0
0
1
1
0
1
1
0
0
0
1
2
0
2
1
0
1
0
1
2
3
2
1
2
0
0
0
2
1
2
0
0
1
0
2
1
0
0
1
0
1
1
2
2
1
1
0
1
1
0
1
2
0
0
2
2
1
3
0
0
0
1
1
2
1
0
1
0
0
1
1
2
0
2
2
0
0
0
0
0
2
0
1
1
0
2
0
0
1
1
1
2
1
0
0
1
2
1
0
0
2
0
1
0
0
3
1
1
0
0
0
1
1
1
1
1
0
0
2
1
2
0
0
0
0
0
1
0
0
0
0
0
2
2
2
1
0
2
2
2
2
1
0
0
1
1
2
1
1
2
0
0
2
2
1
1
1
2
0
1
1
2
1
1
1
2
0
0
1
0
0
0
2
1
0
2
0
0
0
1
1
1
2
2
1
1
0
1
1
2
0
1
1
1
2
1
2
1
1
1
0
0
2
1
0
1
1
1
1
0
1
0
2
1
1
0
0
2
2
0
3
0
3
0
1
0
2
0
1
1
0
0
0
1
0
2
1
1
1
1
0
1
1
0
0
1
1
0
1
0
2
0
0
0
1
0
0
2
1
1
1
2
0
2
2
1
1
0
2
0
1
0
2
0
0
0
0
1
1
1
2
0
2
1
1
0
0
0
2
2
0
2
1
1
0
0
0
0
1
1
2
2
0
0
2
1
1
1
0
2
2
1
0
0
0
1
2
1
0
1
1
2
0
1
2
1
2
0
0
2
2
1
2
0
2
1
1
1
0
2
2
1
2
2
0
0
2
1
0
1
0
1
0
2
1
2
2
2
0
1
2
0
0
2
0
0
0
1
1
0
1
2
0
0
1
1
2
2
0
0
1
1
1
1
1
1
1
4
1
1
2
0
1
1
0
0
2
0
2
2
0
1
0
0
1
2
1
0
0
0
1
0
0
1
2
2
0
0
1
1
1
1
0
1
0
0
0
0
0
0
1
0
1
1
2
2
1
2
0
0
0
1
1
0
2
2
1
0
0
0
2
2
2
2
1
0
2
1
0
0
2
0
0
1
2
0
1
1
0
0
1
0
0
2
1
0
0
1
0
1
0
0
0
0
0
0
0
2
3
2
2
1
1
1
1
0
0
2
0
2
1
1
1
1
1
2
1
1
1
1
0
0
2
0
1
0
3
0
0
1
0
2
0
1
0
0
0
0
2
0
2
0
0
1
0
2
1
2
1
0
1
0
2
0
1
0
0
2
1
2
1
2
0
1
1
1
1
1
0
2
0
0
1
2
1
2
2
1
0
0
1
0
0
0
1
2
2
2
1
0
3
0
0
1
0
2
2
0
2
1
0
2
1
0
1
1
1
1
2
2
1
1
1
0
0
2
2
0
0
0
1
0
1
0
2
0
1
1
1
1
1
0
1
1
1
1
1
1
1
1
0
2
0
2
0
1
0
1
1
0
0
1
0
2
0
1
1
1
0
1
0
1
0
0
2
0
0
1
2
1
0
0
1
0
1
1
3
0
0
0
1
1
0
1
1
0
0
2
1
3
0
1
1
0
1
1
0
1
0
1
1
1
1
2
0
2
1
1
2
2
1
1
0
0
1
0
2
2
1
1
2
0
1
0
2
1
0
0
1
1
0
0
2
0
1
1
1
1
2
0
2
1
1
0
0
0
1
0
2
1
1
1
0
0
1
1
0
0
1
0
2
1
1
1
2
1
2
0
1
1
1
0
0
2
0
0
1
1
1
1
1
2
0
1
1
2
0
0
0
2
2
1
0
1
0
0
1
0
1
2
1
0
1
0
0
0
1
1
3
0
1
1
0
1
1
1
0
0
1
1
1
1
2
0
1
1
2
2
0
1
1
2
1
1
1
2
0
0
1
0
1
2
1
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
2
0
2
2
1
1
1
0
2
2
2
0
1
2
0
1
0
0
1
1
2
0
1
0
1
1
3
0
2
1
2
0
0
0
1
0
1
0
0
2
1
1
0
0
0
1
2
0
0
0
0
1
2
1
1
2
2
2
0
2
2
2
1
2
0
2
1
0
1
2
0
0
1
3
2
1
0
1
1
1
2
2
2
0
1
0
2
0
1
0
3
1
1
2
0
0
0
1
1
1
1
1
1
1
2
0
1
1
0
0
1
1
1
0
0
1
1
1
1
1
0
0
1
0
0
1
0
1
1
2
1
1
0
0
0
1
0
2
0
0
0
0
1
0
0
2
0
0
0
1
2
0
0
0
0
0
0
1
1
0
0
1
0
1
1
0
1
0
0
2
0
1
0
0
1
1
1
0
1
0
0
1
2
1
2
2
0
2
2
1
2
1
0
1
1
1
1
1
2
2
0
1
0
1
1
1
1
1
0
2
1
1
0
2
0
0
1
1
0
1
2
0
2
1
0
2
0
1
2
4
0
1
1
1
0
2
1
0
1
0
0
0
1
2
2
1
0
1
1
0
1
1
2
2
1
0
1
1
0
0
2
1
1
1
1
1
0
1
2
3
1
1
2
1
0
2
2
0
2
2
2
1
1
2
0
2
0
1
0
0
1
2
0
1
0
1
0
2
3
1
1
0
2
0
1
1
0
0
1
1
1
1
2
1
0
1
0
0
1
1
1
2
1
0
1
2
0
1
1
2
1
2
0
0
1
2
0
1
2
2
0
1
0
1
1
1
0
0
1
3
0
1
0
2
0
1
0
0
1
0
1
0
1
1
0
0
0
1
1
2
2
0
2
0
2
1
1
0
2
2
1
1
0
1
1
2
0
0
3
0
0
1
0
1
0
1
1
0
1
1
1
1
1
1
1
1
1
2
2
2
0
0
1
1
1
2
0
2
2
1
1
2
1
0
2
1
1
1
0
1
1
1
1
2
0
1
1
1
2
1
0
0
0
2
2
0
1
0
1
2
0
1
2
0
0
0
2
1
2
1
1
1
2
2
2
1
0
1
1
0
0
0
0
2
0
0
0
2
1
1
1
2
0
2
0
2
1
0
2
0
1
2
1
1
1
1
1
1
0
0
1
0
0
1
2
0
0
2
0
0
0
2
1
1
1
0
0
2
2
1
0
0
1
0
0
1
0
1
0
2
1
1
0
1
1
1
1
1
1
1
2
2
1
0
1
0
1
2
0
1
2
1
0
1
2
3
1
2
2
0
0
2
0
0
0
2
1
1
1
1
3
0
1
1
1
0
1
0
2
0
0
1
1
0
1
1
1
0
0
1
0
2
1
1
2
0
1
2
2
0
2
0
0
2
2
0
1
0
2
1
1
1
1
0
1
2
0
0
0
1
0
1
1
0
0
1
1
2
0
0
0
2
1
0
2
1
1
2
3
0
1
1
1
0
2
2
0
0
1
1
0
0
2
2
1
0
1
1
1
0
0
2
0
1
2
0
0
1
2
1
1
2
2
1
1
1
2
1
0
1
1
0
0
0
1
0
3
1
1
0
0
1
1
1
2
1
1
0
1
1
0
1
0
1
0
0
0
5
1
0
0
0
1
0
0
0
0
1
1
0
1
1
2
1
1
2
0
0
0
1
2
0
0
1
1
2
1
1
1
1
1
0
1
2
1
1
1
0
0
3
0
0
2
1
0
1
0
1
1
1
2
1
1
1
1
1
1
0
1
0
1
0
0
1
2
1
2
1
0
0
0
0
2
0
1
0
1
0
0
2
1
2
0
0
2
3
1
0
1
0
0
1
0
2
0
1
0
1
0
1
1
1
0
1
2
1
0
0
0
0
1
3
0
1
1
0
0
0
1
2
0
1
1
1
1
0
1
2
1
1
1
0
1
1
0
0
1
0
1
1
1
0
1
0
1
1
1
0
1
1
1
2
1
1
1
1
0
1
1
1
0
2
1
2
2
2
0
0
0
1
1
2
1
1
1
0
3
1
1
1
2
1
1
0
0
0
0
1
1
1
0
1
0
1
2
2
2
1
1
2
1
2
2
0
1
0
1
1
1
1
1
0
0
2
1
1
0
0
1
1
0
1
0
1
1
0
0
0
1
2
0
0
0
1
0
0
0
0
0
1
2
1
0
0
1
0
2
2
1
2
0
2
0
1
1
2
0
1
0
0
0
1
2
0
2
0
2
1
1
3
0
1
2
1
1
0
0
1
0
0
0
0
0
1
0
1
2
0
0
1
0
1
2
1
1
1
0
1
2
1
1
1
1
1
2
1
1
2
2
1
0
1
1
1
0
1
1
2
2
1
0
1
1
0
0
0
3
1
1
1
1
1
2
1
0
0
2
1
1
1
1
2
3
1
0
1
2
0
1
0
0
0
1
0
0
1
1
2
1
0
1
0
2
2
0
1
2
1
0
2
0
0
0
2
0
0
0
0
0
0
2
2
5
1
1
1
0
1
1
1
1
1
0
1
2
1
1
0
0
2
1
0
0
1
2
1
0
0
1
1
1
0
1
1
0
2
1
0
2
1
1
1
1
2
1
1
1
1
1
1
1
3
1
1
1
0
1
1
1
0
2
1
0
0
0
0
2
1
2
1
1
1
1
0
0
1
0
1
0
2
1
1
2
1
2
0
0
0
0
1
1
4
0
0
2
2
1
1
1
2
0
1
0
3
0
1
2
1
0
0
1
0
1
1
1
1
0
0
0
0
0
1
2
2
0
0
1
0
2
0
0
0
1
2
1
0
1
0
1
0
0
0
1
0
0
0
0
1
2
0
0
1
1
2
2
1
0
1
1
1
2
0
1
0
1
0
1
3
0
2
1
1
0
2
0
1
0
1
0
9
1
1
0
1
1
1
2
1
2
0
1
2
3
0
2
0
1
0
0
1
1
2
1
1
0
0
0
0
0
2
0
0
2
1
1
0
1
0
0
0
1
0
1
1
0
0
0
0
1
1
0
0
2
1
0
1
2
1
1
2
0
1
1
0
0
1
1
0
0
0
1
1
2
1
0
2
0
0
1
2
2
1
0
0
1
1
1
0
0
1
1
2
2
0
1
2
2
0
1
0
0
2
1
1
1
2
0
0
2
1
0
1
1
2
1
0
0
2
2
1
0
1
5
0
1
0
1
1
0
1
1
1
2
1
1
1
2
0
2
1
1
2
2
1
0
1
0
1
2
0
2
0
2
0
0
2
1
0
2
0
0
1
1
0
1
0
0
1
0
0
0
0
2
1
1
0
1
1
2
0
2
1
1
0
2
0
1
0
0
1
2
0
1
1
2
2
0
0
1
1
1
1
0
0
0
2
2
2
1
0
0
2
1
1
0
0
1
0
1
2
0
1
0
1
0
2
1
1
3
0
0
2
0
0
0
0
1
0
0
0
1
1
1
0
1
1
0
1
1
0
1
0
1
1
0
2
2
0
0
2
2
1
0
0
0
2
2
0
1
1
2
2
1
1
0
2
1
1
1
0
0
1
0
1
1
2
2
2
1
1
1
1
1
0
0
0
1
1
2
0
9
0
1
2
1
0
2
2
1
0
0
1
1
1
0
0
0
1
1
0
1
0
1
1
0
0
0
0
1
0
0
1
1
2
0
0
1
1
1
0
1
0
0
1
1
0
1
0
2
1
1
0
1
1
4
1
0
0
1
2
1
0
2
0
0
0
2
1
0
0
0
2
0
0
2
1
1
0
0
0
1
1
2
0
0
2
1
0
0
1
0
1
0
0
2
0
1
1
1
0
0
1
1
0
0
0
2
1
2
1
2
1
1
2
0
1
1
0
1
1
1
0
1
1
2
0
1
0
1
1
0
1
1
1
1
0
3
2
0
2
2
0
1
1
1
1
0
1
0
2
3
1
2
0
1
2
0
2
0
2
1
0
0
0
0
1
1
2
0
0
1
2
2
1
1
1
2
1
0
1
1
2
1
0
0
0
0
1
0
1
1
2
1
2
1
1
1
1
1
1
0
1
1
0
1
2
0
1
1
2
1
1
1
0
2
0
2
0
1
2
2
0
1
0
1
1
0
2
1
1
1
1
1
1
0
0
0
1
0
1
1
1
0
1
1
1
0
1
2
1
2
0
2
1
0
1
1
3
1
1
2
2
2
0
0
2
2
0
1
0
1
0
0
1
0
1
0
2
2
2
2
0
2
0
0
1
1
2
0
1
2
1
1
2
2
0
2
0
1
0
1
1
2
0
2
1
2
0
2
1
1
0
1
1
0
2
0
0
0
0
1
0
1
1
2
2
0
1
0
1
1
1
1
1
2
0
1
0
1
0
2
0
1
3
1
0
2
1
2
0
0
0
1
1
2
0
1
2
0
1
0
2
2
0
0
1
1
1
2
1
2
1
2
1
0
0
1
2
2
1
0
1
1
2
1
0
2
1
1
1
2
2
1
1
2
1
1
1
0
0
1
0
0
0
0
1
2
2
1
0
2
2
1
0
1
3
0
0
0
1
0
0
1
0
0
0
0
2
0
1
1
1
0
2
0
0
0
0
2
0
2
0
1
1
0
0
0
0
2
1
0
1
1
3
1
0
1
1
1
1
1
1
0
1
1
1
0
1
0
1
0
1
3
2
1
3
3
0
0
1
2
0
2
1
1
0
1
0
2
1
0
0
1
1
0
0
1
1
1
2
1
2
1
0
1
0
2
2
0
2
0
4
2
2
0
1
1
1
2
1
2
3
0
1
1
2
1
1
1
0
2
1
0
1
1
0
0
0
2
1
3
2
2
0
1
0
0
2
0
0
0
0
2
1
0
2
1
0
2
0
0
2
0
0
1
1
1
0
1
2
2
1
0
1
1
1
0
1
2
1
2
1
3
1
0
1
2
1
1
1
2
0
3
1
0
0
2
1
1
2
1
2
1
2
2
0
1
1
1
2
2
0
1
1
1
1
1
0
1
1
0
1
1
1
1
2
2
1
1
1
1
3
1
1
0
1
0
0
1
1
0
1
2
1
0
1
1
1
1
1
1
1
1
1
0
0
2
1
0
0
0
1
1
2
2
0
1
0
1
0
1
2
1
2
0
1
1
0
1
2
0
0
2
0
1
0
0
1
0
1
1
1
0
2
1
1
2
0
2
0
0
2
2
0
1
2
1
0
1
1
0
1
2
0
2
1
0
1
2
2
2
1
1
1
1
1
2
2
2
0
2
1
0
0
2
0
2
2
1
2
1
1
1
1
1
2
0
0
0
1
1
0
2
1
0
1
1
1
1
1
0
0
1
0
1
1
1
2
1
1
1
0
0
2
2
1
0
1
0
1
1
1
1
1
1
0
1
1
2
1
2
0
1
0
0
0
1
1
0
1
0
0
0
0
2
1
0
2
0
1
1
1
0
2
1
0
1
0
1
1
0
1
1
1
2
2
1
1
0
0
0
2
0
0
0
0
1
0
0
1
1
1
1
1
0
0
2
2
2
2
1
2
0
1
0
0
0
1
0
0
1
0
1
2
1
0
1
0
0
1
0
1
1
1
1
1
0
2
0
1
2
0
1
0
1
1
2
1
1
1
0
2
1
2
0
1
0
1
1
1
2
0
0
0
8
1
1
1
0
1
1
0
1
0
1
2
0
0
0
2
1
0
0
1
0
1
1
1
3
2
2
1
1
2
1
1
0
3
2
0
2
0
0
0
2
0
1
0
2
0
1
0
0
2
0
2
0
1
1
2
2
1
1
1
0
2
1
1
2
1
2
2
0
1
1
0
1
1
1
0
0
0
0
1
1
0
1
1
1
1
1
0
2
0
2
1
1
0
1
0
0
2
2
0
1
0
0
3
0
0
1
0
0
0
0
0
0
1
1
0
2
1
1
2
2
2
2
2
1
0
0
1
0
1
1
2
1
1
0
3
2
1
2
2
1
1
0
1
1
0
0
2
1
0
2
1
0
0
1
0
0
1
2
1
2
2
3
1
1
0
2
1
0
1
2
0
1
1
2
2
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
2
2
1
0
2
0
2
1
0
2
1
1
0
0
0
1
0
0
2
2
1
1
0
0
0
3
1
0
0
0
1
0
1
0
1
2
1
1
0
0
0
0
2
1
1
0
1
1
2
2
1
1
1
2
1
0
1
2
1
2
0
1
0
2
1
0
0
0
2
1
1
1
1
1
1
0
2
2
0
0
1
1
1
1
1
1
0
0
1
0
1
0
2
1
0
2
0
1
1
1
2
1
0
0
0
3
1
2
1
0
0
2
0
1
2
1
2
0
2
0
0
2
0
0
2
1
0
0
1
0
1
1
2
0
1
0
0
1
1
1
1
2
1
2
0
2
1
0
0
1
0
1
1
1
0
0
0
1
1
1
2
1
0
2
1
0
0
0
1
2
0
2
1
1
2
0
2
1
1
1
1
0
0
2
1
1
0
3
1
2
0
0
0
0
1
0
2
1
1
1
2
0
1
1
0
1
2
1
1
3
0
1
2
1
1
1
2
2
1
1
0
3
2
0
0
1
6
1
1
2
1
1
1
1
0
1
1
0
1
1
1
2
0
3
2
0
0
1
2
1
2
0
0
0
1
0
2
1
2
0
0
0
0
1
1
2
0
0
1
1
1
2
0
0
1
0
0
0
2
2
3
0
1
1
2
2
0
2
1
0
2
1
2
0
1
1
0
0
1
0
0
0
0
0
0
2
1
1
0
0
1
1
1
1
2
1
1
0
1
1
2
1
2
1
1
1
0
0
2
0
0
1
0
0
2
1
0
2
2
0
1
1
1
1
0
0
2
1
2
2
2
1
0
1
0
1
0
1
1
1
2
1
1
0
1
0
1
0
1
1
1
1
2
1
0
1
1
2
2
1
2
2
1
1
1
0
0
1
1
0
0
0
2
0
0
0
1
1
0
0
0
4
1
1
2
2
1
2
1
1
2
1
0
1
1
2
1
1
1
2
1
0
1
1
1
1
0
0
0
0
0
2
1
1
2
1
1
1
0
2
2
2
1
1
1
2
1
0
1
1
0
0
1
2
2
1
2
2
1
2
0
0
1
1
0
0
0
1
1
2
2
2
1
1
1
1
1
1
2
2
3
0
1
2
2
0
1
0
1
0
1
0
2
0
1
0
1
0
2
0
0
0
1
0
1
1
0
0
0
1
0
1
1
1
1
1
2
1
0
0
2
0
1
4
0
1
0
1
3
0
0
1
0
1
1
0
1
1
1
1
1
1
2
1
1
1
0
0
1
0
1
1
1
0
1
0
0
1
1
0
0
1
1
1
1
1
0
1
1
2
0
1
1
1
0
2
1
1
2
0
1
1
0
1
1
4
1
0
0
2
0
2
0
0
1
2
0
0
1
1
0
1
0
0
1
0
0
0
2
1
1
1
0
1
1
1
1
2
1
2
0
0
0
2
1
0
0
1
1
2
0
2
0
2
1
1
2
1
0
1
1
1
0
0
0
3
0
1
1
6
0
1
0
1
3
2
0
1
1
2
0
0
1
2
2
1
1
2
0
0
0
0
2
1
1
0
1
2
0
1
0
1
2
0
0
0
1
0
0
1
2
0
2
2
1
0
1
0
1
3
0
0
1
1
1
1
0
1
2
1
1
0
0
1
0
2
1
1
0
1
2
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
1
2
0
0
0
1
0
1
2
0
1
2
1
1
0
0
1
2
0
2
1
2
1
2
1
0
2
2
0
0
1
1
0
1
0
2
0
2
2
1
2
2
1
1
2
3
0
2
2
1
1
1
0
1
1
2
0
0
2
1
1
1
2
1
0
1
0
1
2
1
1
2
1
1
1
0
2
1
1
1
0
1
1
1
0
0
0
1
2
1
1
1
1
1
1
0
0
1
1
2
0
2
0
2
1
1
0
2
0
1
1
2
2
1
2
0
1
2
1
1
2
2
0
1
2
0
0
1
0
1
1
1
0
0
1
0
1
0
0
2
0
0
0
0
1
2
0
0
0
0
1
0
0
1
1
1
0
0
0
0
1
2
0
2
1
1
0
0
1
0
0
0
1
0
0
2
1
0
0
0
1
0
1
0
3
1
2
0
1
1
1
1
0
2
0
0
0
0
1
1
1
2
1
1
1
2
1
0
2
0
1
1
0
0
1
0
1
0
1
1
1
0
0
2
2
0
0
0
1
2
0
1
1
1
1
1
2
0
0
0
1
2
1
1
1
0
1
2
1
0
0
1
1
0
0
2
1
2
2
0
0
4
1
2
1
2
0
1
1
1
1
3
1
0
0
2
1
0
1
1
0
1
0
1
2
2
2
1
0
0
0
0
0
0
0
1
0
1
2
2
0
1
0
0
1
0
1
0
2
1
1
0
1
0
1
1
0
1
0
1
1
1
1
0
2
1
1
0
0
1
1
1
0
0
2
0
2
1
1
1
1
1
1
2
0
1
1
0
2
0
2
2
2
2
1
1
1
1
1
2
0
0
2
1
1
0
0
2
0
0
0
0
2
1
2
1
3
0
2
1
1
0
1
0
2
1
0
0
0
1
2
2
1
1
2
1
1
1
1
2
0
1
0
0
0
0
1
2
0
1
0
1
2
0
1
1
0
0
0
1
0
0
0
1
1
0
2
0
0
1
1
1
1
2
1
2
0
0
2
1
0
5
0
1
1
0
1
0
1
0
0
2
2
0
0
0
0
2
0
2
1
2
0
2
1
2
2
1
2
2
0
0
0
1
0
1
1
0
2
0
1
0
0
0
0
0
1
1
1
2
2
1
1
1
0
0
0
1
2
1
0
1
2
1
0
2
1
1
0
0
0
2
0
0
1
1
0
2
1
1
0
1
0
0
1
0
2
2
1
2
0
2
1
0
1
1
1
1
1
0
1
1
1
0
0
1
2
0
4
0
0
1
2
0
0
0
0
1
1
1
1
1
2
1
1
1
1
0
1
1
1
1
1
0
0
1
2
2
0
1
0
1
1
2
2
2
0
1
2
1
0
1
0
0
1
1
1
1
0
0
1
1
1
0
2
1
1
0
0
0
0
1
1
1
2
2
0
1
1
1
1
1
1
1
0
2
0
1
0
2
0
0
0
1
1
0
2
1
1
1
0
0
0
1
1
1
0
1
1
1
1
0
0
2
1
1
1
0
0
0
2
2
2
0
1
0
2
1
1
1
0
2
2
0
1
1
2
1
1
1
0
2
0
1
0
0
0
1
2
1
2
1
1
0
2
2
0
0
0
1
2
1
1
0
0
0
1
1
2
0
2
1
0
2
0
0
0
0
2
0
1
2
2
0
0
2
0
1
2
1
1
2
1
1
0
1
2
1
1
0
1
1
1
1
0
0
2
1
2
1
0
0
2
1
0
0
1
1
1
2
1
1
1
1
0
0
0
1
0
0
0
1
1
0
1
0
0
2
0
7
1
0
0
2
1
1
0
1
1
2
1
1
0
1
0
0
1
1
2
1
0
0
0
1
1
0
2
2
2
2
0
1
1
1
1
2
1
2
0
1
2
0
0
0
1
1
2
1
1
0
1
0
1
0
0
0
0
0
0
0
1
3
2
0
2
1
2
0
0
1
0
1
0
1
3
1
1
1
0
2
2
0
1
1
1
0
0
0
1
0
1
1
2
1
1
1
0
0
1
1
0
1
1
1
1
1
1
1
0
1
0
0
0
2
1
1
0
0
2
0
0
1
1
1
0
0
1
1
0
1
1
0
1
2
2
0
1
2
1
0
0
1
1
2
1
0
0
1
1
0
1
2
0
1
2
0
0
0
0
0
0
1
1
0
0
1
2
0
1
0
2
0
0
0
1
0
1
0
1
1
1
1
0
2
2
2
1
2
1
2
0
1
1
0
1
0
0
0
1
2
1
2
0
2
1
1
1
0
0
1
2
2
1
1
1
1
1
2
0
2
0
1
2
1
2
2
0
1
0
1
1
2
0
0
1
1
1
1
0
0
2
0
1
0
1
0
0
1
0
1
0
1
0
3
0
1
1
1
0
2
1
2
1
0
1
0
2
0
0
0
0
0
0
0
2
1
1
1
0
1
1
0
1
1
0
0
1
1
0
2
0
1
1
1
0
2
1
0
2
0
0
0
0
0
1
2
2
0
2
2
0
0
1
1
2
2
1
0
1
2
0
2
1
0
1
0
3
1
1
0
0
1
0
1
1
0
0
0
1
0
1
0
0
0
2
1
0
0
1
0
3
0
1
2
2
1
1
1
1
0
0
2
1
1
1
0
2
0
2
1
2
1
1
2
1
0
0
1
2
0
0
2
0
0
1
1
0
0
1
0
2
2
1
2
0
0
0
0
0
1
0
1
2
1
0
1
1
1
1
1
0
1
0
0
1
1
1
2
2
2
0
1
1
1
1
1
1
2
0
1
1
1
2
0
1
1
0
1
1
2
1
2
0
0
1
1
1
0
2
0
2
0
1
0
1
1
2
1
1
1
0
0
1
0
1
2
0
0
1
0
1
1
1
1
0
0
0
1
1
0
0
0
1
2
0
1
1
0
2
0
1
1
0
0
1
2
0
0
0
0
0
0
1
0
2
2
0
2
4
0
0
1
2
1
1
1
0
0
1
0
0
2
0
2
0
1
2
0
2
0
2
2
1
0
1
0
2
0
2
0
1
1
1
2
0
0
0
1
2
1
0
0
2
1
0
0
1
2
2
0
0
1
1
0
1
0
0
1
2
1
1
0
0
0
1
1
0
2
0
0
0
1
2
0
3
0
2
1
1
0
0
1
0
1
2
2
1
1
2
1
1
0
2
1
1
1
0
0
2
1
1
1
2
0
0
1
0
1
1
0
0
0
2
0
2
2
0
3
1
1
1
0
0
1
0
1
1
1
1
0
1
0
1
0
1
1
2
2
1
0
1
2
0
0
1
1
1
0
1
0
0
1
1
2
0
2
1
0
0
0
2
0
1
0
2
1
0
1
1
1
1
0
1
2
0
1
2
2
1
1
0
0
2
0
2
2
1
1
1
0
2
1
0
2
0
1
1
1
2
3
0
0
0
0
0
1
1
1
0
1
0
0
1
2
2
1
2
1
1
1
1
2
3
2
1
2
1
0
2
2
0
0
2
0
1
1
0
0
1
5
1
2
0
0
0
0
3
1
1
2
1
1
1
2
4
0
0
0
1
0
0
1
0
0
1
0
2
0
1
0
0
1
0
0
2
0
2
0
0
2
1
1
1
1
1
1
1
1
2
1
1
1
0
3
1
2
1
3
2
1
1
0
1
0
1
0
0
0
1
1
1
1
2
0
4
1
5
2
2
2
0
1
1
0
1
2
1
1
1
1
2
0
0
0
0
0
0
1
1
1
0
0
1
1
0
1
0
2
1
0
0
1
0
1
1
2
0
2
2
2
1
0
1
0
0
0
1
0
2
1
1
2
0
1
1
0
1
1
1
2
1
2
2
0
1
2
1
2
1
2
1
0
0
1
0
2
2
2
0
0
0
1
1
1
0
1
1
0
0
0
0
2
3
0
2
1
2
0
0
1
0
0
0
2
0
1
1
1
1
1
0
1
0
0
0
1
1
0
0
0
0
2
0
1
0
0
2
0
0
0
1
3
1
2
1
1
0
1
0
2
0
1
2
1
2
0
0
1
1
0
1
1
0
2
2
1
1
1
1
1
1
1
2
1
0
1
0
2
0
2
0
2
0
1
1
0
2
2
0
2
2
0
1
0
1
0
0
1
1
1
0
1
0
1
0
0
1
2
2
2
2
0
0
1
2
1
0
1
0
1
1
0
0
0
1
2
1
2
0
0
1
1
0
1
0
0
0
2
2
2
0
0
2
0
0
2
1
4
1
2
1
2
1
2
2
1
1
0
1
0
1
2
2
2
0
1
0
0
1
0
1
1
0
1
0
1
0
0
1
1
2
3
1
1
0
1
1
2
2
1
1
0
1
0
1
1
1
0
0
1
1
2
1
0
0
0
0
0
1
1
1
0
0
2
0
1
2
1
1
2
0
2
0
0
0
0
0
0
0
1
2
1
0
1
1
1
1
1
0
0
1
0
0
2
2
2
1
1
1
0
2
0
0
0
1
2
0
0
1
0
0
1
1
0
0
1
0
0
0
1
1
2
0
1
2
1
2
0
0
0
1
1
0
0
0
2
5
2
0
0
0
1
0
0
1
2
0
0
1
0
0
1
1
2
0
1
1
2
0
2
2
1
0
0
0
0
2
1
1
0
1
1
2
1
1
0
1
0
2
1
0
0
1
0
1
1
0
1
0
0
1
1
2
3
1
1
1
1
2
0
2
1
1
0
1
1
1
1
2
3
1
0
0
1
2
2
1
1
1
1
0
0
0
2
0
0
2
1
1
1
1
0
1
2
0
1
1
1
0
1
0
0
0
0
1
0
1
1
1
0
0
0
1
1
1
0
1
1
1
1
0
0
2
1
2
1
0
0
0
1
0
1
0
2
1
1
1
0
0
1
1
2
2
0
0
0
2
2
1
0
1
0
1
0
2
0
1
2
1
1
0
1
0
2
2
2
0
0
0
2
0
2
0
3
1
0
1
0
0
0
2
0
1
0
2
0
4
2
1
2
2
1
2
1
1
2
0
0
1
0
0
0
0
0
0
2
0
2
1
2
1
0
0
0
0
1
1
3
1
2
1
1
2
2
2
2
0
2
2
2
1
1
0
1
1
0
1
1
1
2
2
2
0
1
0
2
0
0
6
0
1
2
0
1
0
1
1
2
2
0
2
0
1
1
1
1
0
1
2
0
2
1
0
0
1
1
1
0
1
0
2
1
2
1
0
1
1
1
0
2
0
0
0
1
0
1
0
0
2
0
1
0
3
0
1
1
0
1
1
1
2
1
3
0
0
1
1
0
0
1
2
0
2
1
0
2
0
0
0
0
0
1
1
0
2
1
2
2
2
2
0
0
2
2
0
0
1
0
1
4
1
0
0
1
1
2
1
2
2
0
0
1
0
0
1
2
0
0
1
1
2
2
0
2
0
1
1
2
1
4
1
1
2
1
0
2
2
0
0
0
0
2
1
1
2
1
1
1
1
2
2
2
2
0
2
1
1
2
0
3
0
2
1
2
12
0
1
2
0
1
1
0
1
1
1
1
1
0
1
0
0
1
0
0
2
1
0
0
1
2
1
1
0
0
0
0
0
0
2
1
0
2
1
2
0
2
2
0
1
0
1
1
1
0
0
1
1
1
0
3
1
0
1
1
2
1
1
1
0
0
1
0
0
1
1
0
0
2
0
2
2
0
2
1
1
0
1
0
2
1
1
0
3
0
0
1
1
1
1
0
2
1
1
1
1
0
1
1
1
0
1
1
1
1
1
1
0
0
2
1
1
1
0
0
3
1
1
1
1
1
0
2
0
1
0
0
1
1
1
0
0
2
1
1
2
0
2
1
1
0
0
1
1
1
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
2
1
1
2
2
1
0
0
0
0
1
0
0
2
2
0
0
2
0
1
0
2
2
1
1
0
1
2
1
2
0
1
0
0
1
0
0
0
3
2
0
0
0
1
0
0
1
1
1
2
0
0
1
0
1
1
1
0
1
1
0
0
2
1
0
1
1
1
1
0
0
0
2
1
1
0
0
1
0
0
2
1
1
0
0
1
1
2
2
0
0
2
2
1
0
2
1
2
0
1
1
1
1
0
1
0
2
1
1
0
1
1
0
2
1
0
1
0
1
0
0
2
0
1
0
2
0
1
0
1
0
0
0
0
1
0
1
1
0
1
1
2
2
1
1
1
2
0
1
1
0
2
1
0
1
2
2
2
0
0
1
0
0
0
1
1
1
1
2
1
2
0
2
1
1
1
1
1
2
1
0
2
1
1
1
1
2
1
1
0
0
2
2
2
1
2
2
1
0
2
2
0
2
0
1
0
1
0
1
0
1
2
3
2
1
0
1
1
1
0
2
0
0
1
1
1
0
1
1
0
1
0
6
1
2
1
1
1
1
1
0
0
1
0
0
1
1
2
1
0
1
1
0
1
0
0
1
2
1
2
2
0
0
1
2
1
1
0
0
2
2
1
0
1
1
1
0
0
0
1
1
1
0
1
1
0
1
2
2
0
2
0
2
0
2
0
2
0
1
2
0
2
0
2
1
0
1
1
1
2
0
1
1
2
0
1
0
1
1
0
1
0
0
1
1
2
2
0
1
1
0
1
1
1
1
2
1
0
1
1
1
0
1
1
0
2
0
0
2
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
1
1
0
1
0
1
1
0
2
1
1
1
1
1
2
1
1
0
2
1
0
0
0
2
0
1
1
2
0
1
2
1
2
0
1
0
0
2
1
1
0
2
0
2
0
0
0
1
0
2
0
0
1
2
1
1
1
1
0
2
0
1
0
0
0
2
2
1
0
1
2
1
0
1
0
1
0
1
1
1
1
0
0
1
2
2
0
1
1
2
1
1
0
0
1
2
1
1
0
2
2
0
1
2
2
2
0
2
0
1
1
0
2
0
1
0
2
2
0
0
1
1
1
1
1
2
1
1
2
0
1
0
1
1
1
0
1
1
0
1
1
0
1
0
0
1
2
2
0
1
0
2
0
1
0
3
1
1
1
0
0
0
1
1
1
2
0
0
0
1
2
0
2
0
2
0
2
1
1
1
1
0
2
0
0
0
1
0
0
1
1
1
0
2
1
0
2
0
1
2
0
2
0
0
0
0
1
0
0
1
2
0
0
0
0
2
1
1
0
2
1
1
1
1
0
1
1
0
2
1
2
1
2
2
1
0
1
0
0
0
0
0
0
0
1
1
2
1
3
1
0
0
2
2
0
1
1
0
1
0
0
1
1
0
1
1
0
2
1
0
2
0
2
2
1
2
0
0
1
1
2
0
2
1
1
0
1
0
1
1
1
2
1
2
2
1
0
1
2
2
0
1
2
1
2
0
0
0
0
0
0
0
0
1
1
1
0
0
2
1
0
1
1
2
1
1
0
2
0
2
0
2
1
1
1
0
1
2
1
1
0
2
2
0
0
0
1
2
2
0
1
2
0
0
2
0
0
1
0
0
2
1
1
0
0
0
0
0
2
0
1
2
2
0
2
3
0
2
1
1
1
1
1
1
1
0
0
0
1
1
0
0
1
1
0
2
0
1
2
1
2
2
1
2
0
0
1
0
2
2
1
0
0
1
0
2
0
1
0
1
0
1
1
2
3
1
1
0
0
1
0
1
0
2
0
2
1
0
1
1
2
1
0
2
0
0
1
1
2
1
1
1
2
1
2
1
0
1
0
0
0
2
2
2
0
0
0
2
1
0
0
1
0
1
4
2
1
0
0
2
0
1
1
1
2
0
2
1
1
0
1
1
0
0
0
2
1
0
1
1
0
2
0
1
0
2
0
0
0
1
1
0
0
0
1
1
1
1
1
1
0
2
2
0
0
0
2
2
0
0
1
0
2
0
2
0
2
1
0
1
2
3
1
0
2
1
2
0
0
2
2
1
1
0
1
2
0
1
1
2
0
1
0
1
1
2
1
0
2
1
1
1
0
1
1
1
1
1
1
1
0
1
1
1
0
1
0
1
1
0
0
0
0
0
1
2
0
0
0
1
1
0
1
1
0
1
0
0
1
1
1
2
0
1
0
1
0
0
1
1
0
1
2
2
1
1
1
1
0
0
1
1
2
2
1
1
2
2
0
1
2
0
0
1
2
1
1
0
0
0
1
2
1
2
1
1
0
2
0
1
1
1
0
1
2
0
0
1
0
2
0
1
1
2
1
0
1
1
2
0
2
1
0
0
0
1
1
2
1
1
1
1
1
1
1
2
0
2
0
0
0
0
0
2
1
2
2
1
1
2
1
1
0
0
0
2
1
0
0
1
2
0
1
0
1
2
1
2
1
1
0
0
0
2
1
0
0
0
2
1
1
2
1
1
2
2
0
0
2
1
2
1
2
1
1
0
2
2
2
0
1
2
2
2
0
1
0
2
0
0
0
1
1
0
0
1
2
1
1
1
0
1
0
1
0
1
0
0
0
0
2
0
1
0
0
0
1
0
1
2
0
1
1
2
0
2
1
1
1
2
3
3
0
0
0
1
3
1
1
1
1
3
0
1
2
0
2
1
0
1
0
0
0
0
1
0
0
2
0
2
1
0
1
1
0
1
1
2
0
1
1
0
2
1
2
0
0
2
1
1
1
1
2
1
0
0
0
1
1
2
1
2
0
1
2
1
0
1
2
2
0
0
0
1
0
0
2
0
0
1
0
2
0
2
0
1
0
1
1
0
2
0
2
2
2
0
1
0
1
1
0
1
0
0
0
0
0
0
0
2
1
1
1
0
1
0
1
0
0
0
0
0
1
1
0
0
0
2
0
1
0
0
0
0
1
0
1
2
1
0
0
1
2
1
2
1
1
2
1
1
0
2
0
0
1
2
0
2
1
1
0
1
1
0
0
1
0
1
1
1
1
1
0
1
0
1
0
0
0
2
2
0
1
2
0
2
0
0
2
1
0
0
1
1
0
1
1
0
1
1
0
2
0
1
1
0
0
1
0
0
2
0
1
2
0
0
1
0
1
0
0
0
2
1
1
2
1
0
2
1
0
0
0
0
0
2
0
0
0
0
0
2
2
0
1
2
0
1
1
1
0
1
1
1
2
1
1
1
0
1
1
1
1
0
0
1
1
1
1
0
1
1
2
0
0
1
0
2
0
1
1
0
1
0
0
0
2
0
0
2
1
2
1
0
1
2
0
1
1
2
0
3
1
0
1
2
1
0
1
1
3
1
1
1
0
1
1
0
1
1
0
1
0
1
2
0
2
2
0
0
0
0
0
2
1
0
0
2
1
2
0
1
0
1
2
1
1
0
1
1
1
1
0
0
1
1
1
1
0
0
0
0
0
0
2
0
1
0
0
2
2
1
0
1
0
1
0
0
0
0
1
2
0
0
0
1
0
1
0
2
0
1
0
1
0
1
0
0
1
1
1
2
2
1
0
1
1
2
1
1
1
2
2
1
2
1
1
0
2
1
2
0
2
1
0
1
2
1
2
2
1
0
1
1
1
1
0
2
1
1
2
1
2
1
1
0
0
1
5
0
0
2
0
0
1
0
1
2
0
0
1
2
1
2
2
0
2
0
0
1
1
1
0
1
1
1
2
0
1
1
1
0
1
1
2
0
1
1
0
2
0
1
0
1
0
0
0
1
0
0
1
1
2
1
2
1
2
1
0
0
0
0
0
0
1
1
1
0
0
0
0
1
1
2
2
1
0
1
0
0
0
1
1
0
2
1
2
1
1
1
1
1
0
1
1
0
1
0
1
1
1
0
0
0
0
0
2
0
1
0
0
1
1
1
1
1
0
1
2
0
2
1
2
1
1
1
2
1
1
1
1
1
1
2
2
1
1
0
2
1
0
1
0
1
0
0
1
2
1
0
2
1
1
1
1
0
1
1
1
1
0
0
0
2
1
0
0
1
0
1
0
1
1
2
0
3
1
1
0
0
2
0
1
0
2
0
2
0
1
1
0
2
1
0
0
3
2
1
1
1
2
0
1
1
0
0
1
0
0
1
2
0
0
2
0
1
0
0
1
1
1
0
0
2
1
0
1
1
0
0
1
1
2
2
2
1
0
1
3
1
1
0
0
2
2
2
3
2
2
0
0
2
0
2
1
1
1
1
1
2
0
0
1
0
0
1
0
1
0
1
1
2
0
1
1
2
2
1
0
2
2
1
2
1
1
2
1
0
0
1
0
0
2
2
0
0
0
1
2
1
0
0
1
0
2
3
2
0
1
2
0
0
1
1
1
1
1
2
0
2
2
2
0
2
3
0
2
1
0
0
2
1
0
0
1
1
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
3
1
1
1
1
1
1
1
2
1
1
0
1
2
2
1
2
1
1
2
1
0
1
0
1
2
0
2
1
1
1
0
0
0
2
1
2
1
0
0
1
0
0
2
0
0
1
1
1
1
1
1
1
1
1
0
0
3
0
1
0
0
0
1
1
2
2
1
1
2
0
1
0
0
1
1
1
0
1
1
1
2
0
1
1
0
0
0
2
2
0
1
1
1
0
2
2
0
2
2
0
0
1
1
0
1
1
0
2
1
2
2
2
0
1
1
1
1
2
1
1
1
0
2
1
1
0
1
0
2
0
1
2
2
0
1
0
1
1
1
1
1
0
1
0
1
0
0
1
1
2
1
1
2
0
0
2
1
1
3
1
1
1
4
0
1
2
2
2
1
2
1
1
1
0
1
1
2
0
0
1
1
1
0
0
2
2
2
2
1
1
0
2
1
1
0
2
0
1
0
1
2
1
2
1
1
2
1
2
0
0
1
1
1
1
0
1
0
0
0
3
1
0
2
1
1
0
2
1
2
2
0
1
1
0
1
0
2
1
1
0
1
1
2
1
1
0
0
1
0
0
2
0
1
2
0
0
3
1
2
1
1
1
1
1
2
0
1
0
0
2
1
1
5
1
0
1
0
0
1
1
1
1
1
1
1
0
1
1
1
1
0
1
1
0
0
2
0
0
1
2
1
0
0
2
0
2
2
0
2
1
2
1
0
6
2
1
0
1
2
2
2
0
0
0
1
1
1
0
0
1
0
1
0
1
0
2
1
1
1
0
2
1
1
1
2
2
0
1
2
1
0
2
1
2
1
0
0
1
0
1
1
0
1
0
1
1
1
1
0
0
1
1
1
1
1
3
1
0
0
2
2
2
2
0
1
0
1
1
1
1
1
2
0
0
1
0
0
0
0
2
2
2
1
1
2
2
0
0
0
2
0
1
1
1
1
1
2
0
1
0
2
0
0
0
1
0
0
1
2
2
1
1
1
2
1
1
0
0
1
0
0
0
1
1
0
0
1
0
1
2
0
2
3
1
0
0
1
1
0
2
3
2
2
0
0
2
1
0
1
0
1
0
0
1
0
1
2
0
1
1
0
2
0
1
0
0
2
1
0
2
1
0
1
2
0
1
2
0
0
0
1
1
1
2
1
1
1
1
2
0
1
2
0
0
1
0
1
0
0
1
1
0
1
0
1
1
2
0
1
0
1
0
1
2
0
2
1
0
0
1
1
0
1
3
2
0
0
1
0
1
1
0
1
0
2
0
1
1
2
2
2
1
2
0
0
1
0
0
0
1
1
2
4
0
0
0
0
0
1
0
2
1
0
1
1
2
2
1
1
1
0
0
2
0
2
0
1
0
0
0
0
0
0
2
2
2
0
0
1
1
0
2
1
1
0
0
1
0
1
0
1
0
1
0
0
0
0
1
0
1
3
0
0
0
1
0
2
1
1
0
2
1
1
1
1
1
2
1
0
0
1
1
1
0
1
0
0
1
1
0
1
0
0
1
1
0
2
0
3
1
1
0
2
1
1
1
1
1
0
5
0
0
0
0
1
0
0
1
1
1
3
2
0
1
0
1
1
0
1
2
0
1
2
2
1
1
0
0
0
0
0
1
2
1
1
1
2
1
2
0
2
1
1
1
0
3
2
1
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
2
0
0
1
1
0
0
1
1
0
1
1
1
1
2
1
0
0
0
1
2
2
1
0
0
0
1
2
2
0
0
0
2
0
1
1
0
1
0
2
0
1
0
2
2
1
1
1
0
1
2
1
1
0
2
0
0
1
2
1
1
0
0
1
1
2
1
2
0
1
0
1
0
0
3
0
2
0
2
2
1
2
1
4
4
1
0
1
1
1
0
1
0
0
1
1
1
2
1
2
0
1
1
1
1
2
2
0
1
0
1
1
0
1
2
0
1
0
0
1
0
1
0
1
0
1
1
0
0
2
1
1
1
1
3
0
2
0
1
1
1
2
0
1
2
1
0
2
1
2
0
2
2
2
2
0
1
2
0
1
2
0
1
1
0
1
1
2
0
1
0
1
2
1
2
0
1
2
2
2
0
1
1
1
1
1
0
0
0
3
0
0
2
1
2
2
3
0
1
1
1
0
0
1
1
0
1
2
1
1
1
0
1
2
0
1
1
1
1
2
1
0
1
1
2
1
0
0
2
1
1
0
2
1
1
0
1
0
1
2
1
0
1
0
1
1
2
2
0
1
0
2
0
2
0
1
1
2
1
2
2
0
1
1
1
2
1
2
0
2
2
1
0
1
2
0
0
1
2
0
0
1
1
0
1
0
2
2
2
0
0
1
2
1
0
2
1
2
2
2
1
0
0
0
0
0
2
0
1
2
0
1
0
1
1
2
1
1
2
1
1
0
2
1
1
1
1
1
0
0
1
0
0
2
2
1
0
0
2
1
0
0
1
1
1
3
2
1
2
1
1
1
1
0
1
1
0
1
1
2
1
0
1
1
2
1
2
1
1
0
1
2
1
0
2
0
0
1
0
0
1
1
1
2
1
2
1
2
1
1
0
1
0
0
1
1
0
1
0
0
0
1
0
0
0
2
0
2
0
0
2
2
1
0
1
0
1
2
1
1
1
3
0
2
0
0
1
2
0
1
1
1
0
2
2
2
1
1
1
1
2
1
0
1
0
0
1
1
1
0
1
0
1
2
0
1
4
0
1
2
0
1
2
1
1
0
1
1
1
0
1
0
2
1
0
0
1
1
0
0
1
0
1
3
0
1
0
0
2
2
2
0
2
0
0
1
0
0
0
0
0
2
1
1
1
0
1
0
0
1
1
0
2
1
1
1
1
1
0
2
2
1
0
1
1
1
0
1
1
1
0
1
0
0
2
1
0
1
0
0
0
1
0
1
0
0
1
1
2
2
2
2
1
2
1
1
0
1
1
1
1
1
2
2
2
2
2
1
0
1
1
1
0
2
1
2
2
2
1
2
2
1
2
2
1
0
1
0
1
1
2
0
0
1
1
1
2
1
0
1
2
0
1
1
1
1
0
0
2
1
1
0
1
1
1
0
1
0
0
1
2
1
0
1
2
3
0
1
2
0
1
0
1
2
1
1
0
0
1
0
1
1
0
2
1
1
0
1
1
0
0
0
2
0
0
0
0
1
0
2
1
0
1
0
2
2
0
4
0
2
1
1
0
1
0
1
1
0
0
2
1
0
1
0
0
1
0
0
2
1
0
0
1
1
2
0
2
0
2
1
1
2
1
1
1
1
1
1
1
0
1
0
1
1
1
1
1
1
0
0
1
0
0
1
0
2
1
1
0
1
2
0
0
0
1
1
1
0
0
0
1
1
0
0
0
0
0
0
1
0
3
2
1
2
1
2
1
2
0
3
1
1
0
2
1
1
0
1
3
2
1
1
1
1
1
0
2
1
0
0
2
0
0
2
1
1
0
0
2
1
1
0
0
0
1
1
2
1
0
0
1
0
1
0
1
2
0
1
2
0
1
1
0
1
0
2
0
2
1
0
0
1
0
0
1
0
0
0
1
2
1
2
1
0
3
4
0
1
0
0
2
2
1
2
2
1
1
2
1
0
0
1
1
1
0
0
0
1
1
0
0
2
1
2
1
1
1
1
1
1
1
3
2
1
1
3
1
2
2
2
1
1
2
2
0
1
0
1
0
2
0
1
1
0
1
2
0
1
1
2
0
0
1
0
1
0
0
0
2
1
3
1
1
1
2
1
1
1
2
0
1
0
1
1
1
1
0
2
1
0
0
0
0
1
0
2
2
0
2
1
2
2
1
2
0
0
1
1
0
0
0
0
2
0
1
2
1
1
1
0
0
0
0
0
0
0
4
2
1
1
2
1
1
0
4
1
0
1
2
1
1
2
1
0
2
2
2
1
1
1
1
1
2
1
1
1
1
2
0
2
0
1
0
0
1
0
1
2
0
1
0
0
2
0
0
0
1
0
1
1
2
0
1
0
1
1
2
2
1
0
2
0
1
2
1
1
2
0
0
2
2
2
0
1
1
0
1
1
1
1
2
0
0
1
2
1
1
0
0
0
1
0
0
2
0
0
0
2
0
1
1
0
0
2
0
0
0
2
1
2
1
1
2
1
3
0
0
0
2
1
0
1
0
4
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
2
1
2
2
1
0
0
1
0
0
0
1
0
1
0
1
2
0
1
2
1
0
0
2
0
0
1
0
2
1
1
0
2
1
0
1
1
0
1
2
1
1
1
0
0
0
0
2
2
1
2
1
1
1
2
1
1
0
1
1
1
0
0
2
1
0
1
0
1
1
0
1
0
1
1
0
1
2
0
0
0
1
2
1
2
1
1
1
1
0
2
1
1
0
2
0
1
0
1
0
0
1
1
1
1
1
0
1
0
1
1
1
2
2
0
1
0
1
1
2
1
1
1
1
1
1
2
1
0
0
2
0
0
0
0
1
2
1
0
1
1
1
0
0
0
0
1
1
0
0
1
1
1
2
0
2
1
2
0
2
1
2
0
1
2
1
1
0
1
1
1
0
0
0
2
0
0
3
1
1
3
0
1
2
1
0
0
0
1
1
1
0
1
2
2
0
1
0
0
1
2
1
0
2
0
0
0
2
2
1
1
1
2
1
2
1
1
1
2
0
1
1
1
2
1
1
0
0
1
0
1
1
1
0
0
0
1
0
0
0
0
1
0
4
2
1
2
2
0
0
1
0
1
1
1
1
0
2
1
1
0
1
2
2
1
0
2
1
1
1
2
0
0
0
3
1
2
0
1
1
0
1
1
1
1
2
0
1
1
0
2
2
2
1
0
0
1
0
0
2
1
1
0
1
1
0
0
1
1
0
0
0
0
1
0
2
0
1
4
1
1
0
0
2
1
2
0
1
1
2
2
0
1
1
2
0
1
0
1
2
2
0
0
1
0
0
2
2
0
0
0
1
0
1
1
1
1
0
0
0
2
0
2
1
2
1
2
0
1
0
1
1
2
0
2
0
1
2
1
2
0
0
1
1
0
0
1
1
0
0
2
0
0
1
1
2
1
0
0
1
2
0
1
2
1
1
0
0
0
5
1
1
0
1
0
0
1
1
1
0
1
2
2
1
2
2
1
0
1
1
1
2
1
0
1
2
2
0
1
0
1
0
2
2
1
1
0
0
1
1
1
0
0
0
1
1
2
1
2
0
1
0
1
0
1
0
1
1
0
1
1
1
0
2
0
1
2
0
1
1
0
1
1
1
0
0
2
0
1
2
1
1
0
2
0
1
0
1
1
1
1
2
2
0
2
2
0
0
0
1
0
1
1
0
1
1
1
0
1
1
1
1
1
1
0
1
1
1
1
2
1
2
1
1
0
0
0
0
0
0
0
0
0
2
0
1
2
1
2
1
0
1
0
0
0
0
1
1
0
1
1
1
1
1
1
2
2
1
1
0
1
0
2
0
0
1
0
1
1
0
1
2
2
0
2
0
1
0
0
1
2
1
2
1
0
1
0
1
2
0
0
0
0
1
1
0
0
0
2
1
1
1
1
2
2
0
1
0
2
0
1
0
0
0
1
1
0
2
0
2
2
2
1
0
2
0
0
2
0
0
1
1
1
1
1
1
1
2
1
0
1
0
0
1
2
1
2
0
1
2
2
0
0
1
3
1
2
0
0
1
0
0
1
0
2
1
0
1
2
0
0
0
0
2
1
1
0
0
1
0
1
1
0
2
1
0
0
1
0
0
1
1
2
2
1
1
1
1
0
2
0
0
1
0
1
0
1
0
1
1
1
0
1
2
0
0
1
0
1
1
2
1
0
1
0
3
1
2
1
0
2
1
0
0
1
2
0
1
2
0
1
1
0
1
2
1
1
3
1
2
1
0
2
0
1
2
2
0
0
1
2
1
0
1
1
0
0
0
0
1
1
1
1
0
1
2
0
1
1
1
0
1
0
0
0
0
0
2
0
1
0
2
0
0
1
1
1
0
0
1
0
2
0
0
1
0
1
0
0
0
2
0
2
1
1
1
1
0
0
0
0
0
2
2
1
0
0
1
1
2
1
0
0
2
1
0
0
1
0
0
2
1
0
1
0
0
1
1
1
2
2
1
1
0
2
1
1
1
1
0
0
0
0
1
1
0
1
0
1
0
1
0
0
1
1
0
0
0
1
0
2
2
2
1
1
0
0
1
0
1
0
2
1
0
0
0
0
1
0
1
1
2
2
0
2
2
4
1
2
0
1
1
0
1
0
1
0
2
2
2
1
1
3
1
1
0
0
2
1
0
1
2
0
1
1
1
1
1
2
1
2
0
1
1
0
1
0
0
1
1
2
0
2
2
1
0
0
1
0
2
0
2
0
2
2
0
2
1
1
0
0
1
0
0
0
1
1
0
1
2
0
0
2
0
1
1
1
2
2
1
1
1
1
2
0
0
0
1
2
1
0
0
1
0
1
0
0
3
1
1
1
0
2
1
2
2
0
0
2
2
0
1
0
2
2
0
0
0
2
1
1
0
1
1
2
1
0
1
1
1
0
1
2
1
2
0
0
2
1
1
0
2
1
1
0
0
1
1
0
0
1
0
0
2
0
2
2
1
0
0
0
1
1
5
0
2
0
0
1
2
1
2
1
1
2
2
1
1
1
0
1
0
1
1
0
1
0
0
1
1
1
1
2
1
0
0
0
1
0
0
2
2
2
0
2
2
1
1
1
1
0
1
0
1
1
0
0
0
0
0
0
1
0
1
1
1
0
1
0
0
1
1
1
2
1
2
2
1
1
0
1
0
1
1
1
2
2
7
1
1
0
1
2
1
1
0
1
1
0
2
0
0
1
1
2
0
0
1
1
1
0
1
0
1
1
0
1
0
0
1
2
2
1
1
1
0
1
2
3
1
1
1
2
0
2
1
1
0
0
1
1
1
1
0
1
1
2
1
0
1
1
1
0
1
2
2
0
0
1
1
2
1
2
0
1
0
0
1
1
2
0
0
1
1
3
0
0
1
1
0
0
1
2
2
0
1
0
1
2
0
1
0
0
1
0
0
2
0
2
2
1
1
1
2
0
1
1
2
2
2
0
0
2
0
0
0
0
0
0
0
0
1
0
1
2
1
1
2
2
0
0
0
0
0
0
2
1
1
0
0
1
0
0
2
1
1
0
1
0
0
0
3
1
1
1
0
0
1
0
1
1
0
1
2
0
0
2
0
1
0
2
0
0
0
1
2
0
1
2
2
1
0
1
0
2
1
0
0
1
1
0
0
0
0
0
0
0
1
0
1
2
1
0
0
0
1
0
2
1
0
0
2
0
4
2
0
2
0
0
0
0
4
1
1
0
1
0
1
1
1
0
0
0
1
0
0
1
2
0
2
1
2
1
2
1
1
0
0
2
1
0
1
0
0
1
0
2
0
1
2
1
0
1
0
0
0
1
1
1
2
1
1
1
2
2
0
1
3
1
0
0
1
0
0
0
0
1
1
2
2
1
2
2
1
0
0
3
1
0
1
0
1
0
1
0
2
1
0
1
2
2
2
1
1
2
0
1
0
1
1
1
0
1
2
1
1
2
1
1
0
1
1
0
2
2
2
0
1
1
0
1
1
0
1
1
0
1
1
1
0
1
0
0
2
2
1
2
1
0
0
0
0
1
0
2
2
1
1
0
2
0
2
1
1
2
0
1
2
2
2
0
1
0
0
0
1
0
1
3
2
1
1
2
0
0
1
0
0
0
2
0
1
0
0
1
3
0
0
0
1
0
2
2
0
1
2
0
2
0
0
2
4
1
0
1
0
1
1
1
0
1
1
1
0
2
1
0
0
2
1
2
1
1
1
0
1
0
0
2
1
0
1
1
0
0
1
1
2
3
0
0
1
1
1
1
1
0
0
0
0
1
1
0
1
1
0
1
0
0
0
0
3
0
0
2
0
1
0
2
2
1
3
1
2
0
0
0
2
0
2
0
0
0
1
0
1
1
1
1
1
1
1
1
0
0
1
0
0
0
1
1
3
0
2
0
0
1
0
0
0
0
1
1
2
0
0
1
0
1
2
0
0
0
0
2
2
1
1
0
1
0
2
0
1
0
1
2
2
0
2
1
1
1
2
0
2
1
1
0
0
1
1
0
0
1
1
2
1
1
1
0
2
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
2
2
1
0
2
1
0
1
1
0
3
1
0
1
0
0
0
3
0
1
2
0
1
2
0
2
1
2
1
2
0
0
3
2
0
1
1
2
1
2
0
1
2
0
2
0
1
3
1
0
2
2
0
1
0
0
1
0
0
1
2
0
1
0
2
1
2
1
2
1
1
2
1
1
1
2
0
0
0
0
2
0
1
1
0
0
0
0
1
1
1
2
1
2
1
0
2
2
0
1
0
2
0
1
2
0
1
0
1
0
1
2
1
1
1
0
0
0
1
0
1
0
0
1
2
1
0
0
1
1
1
0
2
0
2
2
1
1
0
2
0
2
7
0
0
1
0
1
1
1
1
0
2
1
1
1
0
0
1
0
0
1
2
1
0
0
4
1
0
1
1
0
1
1
0
2
0
0
0
1
1
2
1
1
1
2
1
0
1
2
2
1
1
0
1
1
0
0
2
1
1
0
1
0
1
1
0
2
1
1
0
0
2
1
1
1
1
1
0
0
1
1
0
1
1
2
1
0
0
1
0
1
1
0
2
2
0
1
1
0
1
0
0
2
0
1
0
2
1
1
2
2
1
3
2
1
1
2
0
0
1
1
0
0
2
1
1
1
1
0
2
1
1
1
1
1
1
2
1
2
1
1
0
1
0
0
2
1
0
0
1
0
2
2
2
1
0
1
1
0
2
1
2
1
1
0
1
1
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
2
1
0
1
0
2
1
2
1
0
1
1
2
0
1
1
0
2
0
1
1
2
0
2
1
2
0
1
2
0
1
1
2
2
2
0
2
1
1
2
0
2
1
1
2
1
0
1
0
1
0
2
1
1
2
1
1
0
0
2
1
1
1
2
2
0
1
0
1
1
2
0
0
1
0
1
0
0
2
1
1
1
0
1
2
0
0
0
1
0
1
2
1
1
0
1
0
1
1
1
0
2
1
0
0
1
2
0
1
1
1
1
2
1
0
1
0
2
0
0
1
1
1
1
0
1
0
2
0
1
1
1
1
1
0
2
0
2
1
1
0
2
0
2
2
1
0
2
0
1
0
2
0
1
0
1
0
0
2
2
1
0
1
2
1
1
3
2
3
1
1
2
1
0
2
2
2
0
1
0
2
0
1
2
0
0
1
1
0
1
0
0
0
4
2
1
1
2
1
1
0
0
0
1
1
2
1
0
1
2
0
2
0
2
0
2
0
1
2
2
1
0
0
2
0
0
0
1
1
0
0
0
0
1
1
0
0
1
1
1
0
1
1
0
0
3
0
2
2
1
1
0
1
0
0
1
0
0
1
1
1
1
0
0
1
1
1
1
1
1
1
1
1
1
3
0
0
0
0
2
0
0
0
1
1
0
1
1
0
0
1
0
1
0
1
0
0
0
1
1
4
2
2
0
0
0
2
2
1
0
0
1
1
1
1
1
1
1
1
1
0
1
1
2
2
2
1
0
0
2
0
0
1
1
1
0
3
1
1
1
0
0
0
2
1
1
1
1
2
0
0
1
0
1
0
1
0
1
0
0
2
3
2
1
1
1
1
0
2
0
1
0
1
1
1
1
0
0
1
1
0
1
0
1
2
1
0
1
0
2
1
1
0
0
0
0
1
2
0
0
2
3
0
0
0
1
0
1
0
1
0
1
1
2
0
1
2
0
2
1
2
1
0
1
0
1
1
1
0
0
0
1
1
0
0
0
1
2
0
0
0
0
0
0
2
1
0
0
0
2
0
0
1
2
1
1
1
0
2
1
0
1
0
0
0
1
1
0
1
1
0
2
0
0
3
1
1
1
2
0
1
0
0
0
2
0
2
1
2
0
1
1
2
2
0
2
0
0
1
1
1
1
0
1
1
2
0
0
3
0
0
2
1
1
1
0
1
1
1
1
1
0
2
1
0
2
2
1
1
2
1
1
0
2
1
0
0
1
0
0
1
1
1
0
1
2
0
1
2
1
5
2
0
2
0
0
2
0
0
0
1
2
2
1
4
1
1
2
0
2
1
1
2
1
0
2
0
0
0
1
1
0
1
1
0
0
0
1
0
1
0
2
0
1
0
1
0
0
1
0
1
0
1
0
0
1
0
1
1
3
0
2
1
1
2
2
1
0
1
2
0
0
0
0
0
2
1
2
1
1
1
1
0
2
0
0
1
0
1
0
0
1
1
0
2
2
1
1
2
0
2
2
1
0
0
1
1
0
0
1
2
0
0
0
1
1
2
0
0
0
1
1
1
1
0
0
2
0
2
1
0
2
0
0
2
0
1
0
0
2
2
1
1
2
2
2
1
0
2
1
0
1
1
1
0
0
1
0
0
0
1
1
1
2
1
0
2
0
1
0
2
0
2
0
0
1
0
1
1
0
1
2
1
2
0
0
1
1
0
2
2
0
2
3
2
2
2
1
1
2
0
2
0
0
1
1
0
0
0
1
1
0
0
1
0
2
2
0
0
0
2
0
1
2
0
1
1
1
0
0
1
1
1
1
1
0
1
1
2
0
1
0
0
2
0
0
1
1
0
0
0
1
1
1
1
5
2
0
1
0
0
2
0
0
1
1
1
0
1
2
2
0
2
1
1
2
2
2
1
0
1
2
0
1
0
1
2
0
0
2
0
0
2
0
1
1
1
0
1
0
1
0
3
0
0
2
0
0
1
1
1
1
0
0
0
1
1
2
1
2
1
1
2
3
0
2
1
1
3
0
0
0
0
0
2
0
0
1
1
0
0
1
0
0
1
0
2
1
1
2
2
1
0
1
1
1
2
1
0
1
1
0
1
1
1
1
0
0
2
1
1
1
0
0
0
2
1
1
0
1
1
0
0
1
1
2
0
1
2
0
1
1
2
2
3
2
1
1
2
0
1
1
1
1
1
0
1
1
2
1
0
0
2
2
0
1
1
1
0
0
3
0
1
0
0
1
2
1
1
2
1
0
2
0
0
1
0
2
0
1
0
1
0
1
2
0
0
1
0
1
1
2
2
1
0
0
1
2
0
2
1
3
2
2
1
0
0
2
4
2
0
0
1
1
1
3
0
0
0
2
0
2
1
1
2
1
1
1
1
0
0
1
1
1
0
0
2
0
0
0
1
1
1
0
0
1
1
1
3
0
2
4
1
0
1
0
1
1
1
2
1
0
0
2
1
0
2
1
1
1
1
1
1
2
2
2
2
0
2
0
2
0
2
2
1
1
1
2
0
0
2
1
0
0
0
0
1
1
2
1
1
0
2
0
1
0
2
0
1
0
1
2
1
0
2
2
2
1
0
0
2
1
0
0
0
0
0
0
1
2
1
1
0
0
0
1
1
0
1
2
0
1
1
2
1
1
0
1
1
1
1
1
0
2
1
1
0
0
1
0
2
1
1
0
0
1
1
0
0
0
2
0
1
2
0
0
1
0
1
0
0
1
1
2
0
0
2
0
2
1
1
0
2
0
2
2
0
1
0
0
2
0
0
2
0
0
2
0
0
0
1
2
0
2
1
2
1
0
2
2
2
1
1
1
0
2
2
0
1
0
1
1
0
0
1
2
1
2
1
0
0
1
1
1
1
1
1
1
1
1
1
0
2
0
2
2
1
0
1
0
1
0
0
2
2
1
1
1
0
0
1
1
0
0
0
0
1
1
1
0
1
1
1
2
0
1
2
0
0
1
1
1
1
0
1
2
0
1
2
2
0
0
1
2
0
0
0
1
1
0
1
1
1
1
1
1
0
0
1
0
2
1
1
1
1
1
2
1
2
0
0
1
0
0
0
1
1
0
0
1
1
2
0
0
2
1
0
1
0
1
1
0
1
0
0
1
1
0
0
2
1
1
0
0
0
2
1
1
0
1
2
7
0
0
0
2
1
1
1
0
1
2
0
1
1
1
2
1
1
0
0
0
2
0
1
0
1
0
2
0
1
0
0
1
2
2
2
1
0
0
1
2
1
2
1
2
1
0
2
1
2
0
2
0
2
0
1
0
0
0
0
3
1
1
1
1
0
0
1
0
0
0
0
1
0
2
1
0
1
0
0
1
1
0
0
1
1
2
1
1
1
2
2
2
0
2
0
1
0
0
0
1
2
0
2
2
2
1
0
0
1
1
2
1
0
2
1
1
0
0
1
1
0
2
0
1
1
2
2
1
0
0
1
1
1
0
1
0
1
2
1
0
0
1
1
1
2
2
1
8
0
1
1
1
1
1
2
2
2
0
0
2
1
1
1
1
1
1
1
1
1
2
1
2
1
2
0
2
1
2
1
1
0
0
3
2
0
1
0
0
1
1
1
0
1
0
1
2
1
0
0
2
1
1
2
2
0
0
2
1
2
1
1
2
0
2
1
1
2
2
0
1
1
1
0
0
1
1
1
1
0
0
0
1
1
1
2
0
1
1
0
2
1
1
0
2
1
1
1
2
1
0
1
1
2
1
0
0
2
0
0
1
0
2
2
1
1
1
0
1
2
0
1
2
0
0
1
0
0
0
1
1
2
0
2
0
2
0
1
2
0
0
1
2
2
0
1
0
2
1
1
0
0
1
1
1
2
0
0
0
1
1
1
1
1
1
2
2
1
0
2
0
1
2
0
1
1
1
1
1
0
2
1
0
1
1
2
0
0
0
2
0
0
1
0
1
1
1
0
1
1
0
0
0
0
0
0
2
0
1
2
2
1
0
1
1
1
1
1
1
1
1
2
0
0
0
1
1
1
0
1
1
1
1
0
1
0
2
2
0
1
0
1
1
1
2
0
1
2
1
1
0
1
0
0
0
1
0
2
1
2
0
2
1
2
1
0
0
0
1
1
0
2
1
1
1
1
0
0
1
3
1
2
0
1
0
0
1
2
1
0
0
0
0
0
1
0
2
0
0
0
0
4
0
0
1
1
2
1
0
2
0
0
0
2
0
0
1
0
0
0
1
0
2
1
2
0
2
0
0
1
0
1
0
0
1
0
0
0
1
2
1
0
0
1
1
1
1
2
1
0
4
1
1
2
0
0
1
3
1
1
2
1
1
2
1
0
0
1
0
2
1
0
1
0
1
1
1
1
1
2
0
2
0
1
0
1
0
0
0
0
3
0
0
1
1
0
0
0
0
1
0
4
1
1
0
0
0
2
2
0
1
2
0
0
2
2
1
1
1
0
0
1
0
1
1
1
3
1
0
1
0
0
2
0
2
1
1
0
1
2
0
1
0
0
2
1
1
0
0
1
1
2
1
1
1
0
2
1
0
0
1
1
2
0
2
0
2
1
1
0
2
0
1
0
0
1
0
1
0
2
1
1
0
2
0
2
2
1
0
1
1
1
1
1
1
3
1
0
2
1
1
1
1
0
0
0
0
0
2
2
2
0
0
0
1
2
0
1
0
0
0
2
1
0
2
1
0
2
1
2
0
0
1
1
0
0
0
1
0
2
1
2
1
2
0
0
0
1
1
0
2
2
0
0
1
1
1
2
1
2
1
1
0
0
1
0
2
1
0
2
1
1
0
1
2
1
0
1
0
0
1
1
0
1
1
1
1
0
0
0
2
2
0
2
2
0
0
1
1
0
0
0
0
1
2
0
2
0
1
2
0
1
0
1
2
1
1
0
0
0
0
1
0
1
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
1
1
2
0
1
0
0
1
2
2
1
2
1
0
1
0
0
0
1
1
1
1
0
0
0
0
0
0
0
2
0
0
0
1
0
2
2
1
1
2
2
2
2
0
1
2
2
1
0
2
2
2
2
2
0
1
0
1
0
1
0
1
2
0
0
2
2
0
1
1
0
1
0
0
2
2
1
0
1
0
2
0
1
0
0
1
2
2
1
0
0
1
2
2
0
0
1
1
2
0
1
0
1
1
0
1
1
2
0
0
1
1
0
2
0
0
1
3
0
2
2
0
2
1
0
0
0
1
0
0
0
1
1
1
1
1
1
1
0
2
2
2
1
0
2
0
0
2
0
0
0
0
0
2
0
1
1
1
1
1
0
0
0
2
1
0
3
0
2
1
1
1
0
0
1
2
0
0
0
0
2
1
2
1
3
0
0
2
1
2
0
1
0
1
0
1
2
0
1
0
0
1
0
2
0
0
0
0
1
0
1
2
0
0
1
0
2
0
2
0
0
2
1
0
0
0
1
2
0
5
2
1
0
0
2
1
1
0
1
2
1
1
0
2
1
2
0
0
0
0
2
0
1
0
1
1
1
1
1
1
0
2
0
1
0
2
1
1
0
2
0
1
0
2
1
0
0
2
1
1
0
2
1
1
1
1
0
1
0
1
1
1
2
1
0
1
0
0
0
0
2
2
2
0
0
0
1
0
0
2
1
1
0
1
1
1
1
0
1
1
0
2
1
1
0
0
1
0
0
0
0
0
0
1
1
1
1
1
0
1
1
0
1
1
2
0
2
0
0
1
0
4
2
1
0
2
2
1
2
0
0
2
0
0
1
1
1
1
2
2
0
1
0
0
1
1
0
1
2
0
1
1
1
2
1
1
0
0
1
0
0
1
0
1
0
1
1
0
2
1
1
2
2
1
2
1
2
0
1
0
0
1
2
1
2
1
1
1
1
0
2
0
2
2
0
2
0
2
1
0
1
0
2
1
0
1
0
1
1
0
1
2
2
0
1
9
2
1
0
0
0
1
2
2
2
0
1
0
0
1
2
1
0
0
1
2
0
0
0
2
1
0
2
1
2
2
1
0
0
3
1
0
2
2
0
2
1
0
0
2
0
0
1
1
0
0
1
1
0
1
0
0
1
2
3
2
0
1
1
2
0
1
0
2
1
1
1
0
1
2
0
0
0
2
0
2
1
2
1
1
0
1
1
0
1
0
0
2
2
1
2
1
0
0
1
0
0
2
1
2
1
0
1
1
1
1
1
0
1
2
1
2
1
1
1
1
1
1
2
1
1
1
0
0
2
0
1
1
1
2
0
0
2
0
0
1
0
1
1
1
1
1
0
0
1
1
1
2
0
0
2
0
0
0
3
1
1
1
1
2
0
1
1
1
1
1
2
1
2
1
0
1
2
0
1
3
1
0
1
1
0
0
0
0
0
2
2
2
1
2
0
1
0
1
1
1
1
0
1
2
0
1
1
0
0
1
0
1
0
0
0
1
2
1
1
0
0
1
0
2
1
0
0
0
1
2
1
1
1
2
2
0
0
1
0
2
0
0
0
0
1
1
0
1
1
0
2
1
2
1
1
1
0
1
2
3
0
1
0
1
2
0
1
1
1
1
0
0
1
1
1
1
1
0
0
2
2
0
0
0
1
1
0
0
1
0
1
2
2
2
2
0
0
1
1
0
2
1
1
0
2
1
1
1
1
0
2
1
1
2
2
2
0
1
2
0
1
2
0
1
0
1
0
1
0
0
2
0
2
0
0
1
1
1
1
0
0
0
0
0
1
0
0
0
1
0
2
0
1
1
1
2
0
1
2
1
1
1
0
0
1
1
0
0
1
0
0
2
1
1
1
1
0
0
1
0
1
1
1
1
1
0
1
0
1
0
3
1
2
0
0
1
0
0
1
1
4
0
1
0
0
0
0
0
0
2
0
1
1
1
0
0
1
1
1
1
0
0
1
1
1
1
0
1
2
1
0
0
1
1
0
1
1
1
1
2
1
1
1
0
0
0
2
1
1
1
1
1
1
0
0
1
2
0
1
0
0
1
1
2
1
0
0
0
0
1
1
0
1
0
1
2
2
0
2
1
1
0
1
0
0
1
0
0
2
2
0
2
0
0
0
2
0
2
0
2
1
1
3
1
2
1
0
2
2
0
2
0
0
0
1
0
1
0
0
0
0
1
0
2
0
2
2
1
0
0
2
1
1
1
0
1
0
0
1
1
0
2
0
0
0
2
1
1
1
0
0
0
0
4
1
2
1
2
1
0
2
0
1
1
0
1
1
1
1
1
0
1
2
1
0
2
0
1
0
0
1
0
0
1
1
1
0
0
0
1
1
2
1
1
1
0
0
2
0
2
0
0
0
1
2
2
1
0
1
2
2
2
1
0
1
0
0
0
1
0
1
2
2
0
1
0
0
0
2
0
0
0
2
0
1
0
1
0
1
2
1
2
0
0
0
0
1
1
0
2
0
0
0
1
1
0
1
1
2
1
1
2
1
0
1
0
2
0
2
1
1
1
0
1
1
0
3
2
0
1
0
0
2
1
1
3
0
1
0
0
0
0
0
1
2
1
2
2
0
0
0
1
0
2
1
2
1
2
0
0
1
2
2
0
2
1
0
1
0
1
1
0
0
1
2
1
2
1
1
2
2
0
0
1
0
1
1
1
0
2
0
1
0
0
1
2
1
0
0
0
1
1
1
0
1
2
1
1
1
1
2
2
1
0
1
2
1
1
1
1
0
0
1
1
0
2
0
2
2
0
1
0
0
2
1
1
0
0
1
0
0
0
2
1
2
1
1
1
2
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
1
1
2
2
2
2
0
1
2
0
0
0
1
0
2
2
1
2
1
0
1
0
0
0
1
0
1
2
0
1
0
0
2
1
1
1
2
2
0
1
1
2
1
0
1
2
1
0
4
0
0
2
0
0
0
2
0
1
0
0
0
1
0
0
1
1
1
0
0
0
1
0
2
0
0
1
1
1
4
1
1
2
1
1
0
0
1
1
1
1
2
0
0
0
1
2
1
2
1
0
1
0
1
1
6
1
0
1
1
0
0
1
0
1
2
1
1
0
2
2
0
2
0
1
3
0
2
1
0
0
2
2
2
1
1
2
1
2
1
1
0
1
1
1
2
1
0
0
1
0
1
2
1
0
0
1
1
1
2
0
1
1
1
1
0
1
1
1
1
1
1
0
0
0
0
2
0
2
1
0
1
1
0
1
1
2
0
1
1
0
1
0
1
1
1
1
1
0
1
2
2
1
1
2
1
0
1
0
1
0
1
0
2
1
0
1
0
1
1
0
2
0
1
1
2
0
0
1
1
2
0
2
1
1
2
0
2
1
0
1
2
0
0
3
2
1
0
4
0
0
1
0
0
2
1
2
0
0
1
0
2
0
0
2
0
1
1
0
1
1
1
1
1
0
1
0
2
2
1
0
2
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
3
0
1
0
0
2
2
0
1
1
2
1
1
2
2
2
0
0
2
0
0
2
2
1
1
1
0
0
1
3
1
0
0
1
2
0
0
1
2
0
4
2
0
2
2
1
1
0
2
4
2
0
1
1
2
0
0
0
0
0
0
2
2
1
2
1
3
3
1
0
0
0
0
0
2
1
2
0
2
1
2
1
0
1
1
2
1
1
0
1
1
2
0
2
1
0
0
2
0
1
2
3
1
1
1
2
1
0
1
0
0
0
2
1
1
0
2
1
2
1
2
0
1
2
0
1
0
1
1
1
1
0
0
1
1
0
1
0
1
2
2
1
0
1
0
0
0
1
0
2
1
0
5
0
1
0
1
1
0
2
0
0
0
1
1
0
0
3
0
2
2
3
1
1
0
1
0
0
1
1
2
0
1
1
0
0
1
1
2
1
0
1
0
2
1
2
0
2
0
2
0
0
1
1
0
0
1
3
0
1
2
0
2
0
1
2
0
1
1
2
0
2
1
2
1
1
1
2
1
1
1
0
1
1
1
0
0
1
1
1
1
0
1
0
1
1
1
0
2
1
1
1
0
1
2
2
1
0
2
3
1
0
1
0
0
1
0
1
2
0
0
0
1
1
2
1
0
0
2
1
1
0
1
0
2
1
0
0
0
1
1
1
0
0
1
1
1
0
1
1
1
1
2
1
2
1
2
1
0
1
1
2
0
2
2
0
0
0
1
1
1
0
1
1
0
0
1
0
0
0
1
2
1
0
2
1
1
2
1
1
1
1
1
0
0
2
3
0
3
1
1
3
0
1
1
1
1
2
2
0
0
1
1
2
2
1
1
2
2
1
0
1
1
0
2
0
2
0
0
2
1
0
1
1
1
2
1
0
0
1
2
1
0
2
1
1
0
2
2
0
0
1
1
0
0
0
1
0
0
2
0
1
0
0
1
0
2
0
0
2
0
1
2
1
1
0
0
1
1
1
1
0
1
1
2
0
1
2
0
2
3
1
1
1
0
1
0
1
2
0
1
1
0
0
3
0
0
1
1
2
2
1
0
1
1
0
1
1
1
1
1
0
1
1
0
0
1
0
1
0
0
2
0
1
0
2
1
0
2
2
1
0
0
2
2
0
0
1
2
1
1
0
1
1
0
1
0
1
1
2
0
0
2
0
2
1
1
2
0
1
0
0
1
1
1
1
1
1
1
2
2
0
1
0
0
2
0
0
1
0
1
2
0
1
1
1
2
0
1
1
0
0
0
2
2
1
0
1
2
2
1
1
0
0
1
1
2
1
1
1
0
1
1
1
1
1
1
1
1
0
1
0
1
0
1
2
2
2
1
0
2
0
1
0
1
0
2
0
1
1
0
0
0
1
0
1
0
0
1
1
1
0
1
2
0
1
1
1
0
1
2
0
0
0
1
0
2
0
1
1
2
2
1
1
2
0
2
1
0
0
0
1
1
0
0
2
2
2
2
0
2
0
2
1
1
0
0
1
1
0
2
1
2
1
2
2
0
1
1
0
1
1
2
1
1
4
1
1
0
1
0
2
0
2
1
0
2
0
0
1
1
0
1
1
1
0
1
1
2
1
1
0
0
1
1
1
1
2
1
0
0
1
2
0
1
0
0
1
1
0
0
0
0
0
1
1
0
1
0
1
2
1
1
0
2
2
2
1
2
2
0
0
1
1
1
2
2
1
1
1
2
2
0
1
1
1
0
1
2
1
0
0
2
1
0
1
0
2
1
0
0
0
0
1
1
0
2
1
1
2
1
0
3
0
1
1
2
1
1
1
2
1
1
0
0
3
1
0
0
1
1
0
1
0
1
0
2
1
1
1
0
0
1
0
0
2
0
0
1
1
1
1
1
1
0
1
0
1
1
1
0
0
1
1
2
0
1
2
1
1
1
1
1
0
1
1
2
1
2
1
1
1
0
2
0
0
0
0
0
2
1
0
0
0
1
0
1
1
0
0
1
2
2
1
2
0
0
2
0
0
1
1
2
0
1
0
2
1
2
2
0
1
1
1
0
0
3
0
1
1
0
0
0
1
1
0
1
2
1
0
2
2
0
1
2
0
1
2
2
1
1
1
0
1
1
3
2
0
0
0
0
2
0
0
0
2
0
0
1
0
1
0
1
0
1
2
0
0
2
1
1
0
2
1
1
0
1
0
1
0
0
0
1
0
0
1
2
1
1
0
1
0
1
2
0
1
0
0
3
0
0
0
1
1
0
1
0
1
2
0
1
0
1
0
0
0
0
0
0
0
0
1
2
0
2
0
1
2
1
1
1
0
0
1
0
0
0
0
1
2
1
0
1
2
0
2
0
2
1
1
1
0
0
1
1
1
1
0
1
1
2
0
0
2
2
1
0
1
2
2
1
1
1
1
0
1
1
0
2
0
2
2
1
0
1
1
1
0
0
2
2
2
0
1
5
1
2
2
0
1
1
1
2
0
0
1
2
2
0
1
1
0
0
0
0
0
1
2
2
0
2
1
2
2
0
2
0
1
2
0
2
1
1
2
0
0
0
2
1
1
2
1
0
0
1
0
1
0
0
1
0
0
1
0
2
1
2
0
0
2
0
2
2
0
1
2
1
1
1
1
1
2
0
0
0
0
0
0
1
0
2
2
0
2
1
2
1
0
1
0
0
0
1
1
0
0
2
0
0
0
0
0
2
2
1
1
2
0
1
1
1
0
2
2
1
1
2
2
1
1
1
0
0
0
2
0
0
1
2
0
2
2
0
1
1
2
0
2
0
1
1
0
0
1
2
0
0
2
1
1
1
2
1
1
1
2
1
2
2
0
2
0
1
0
1
0
1
1
0
1
1
1
0
0
1
1
1
1
2
0
1
0
0
1
0
0
0
3
2
1
2
1
1
0
1
0
1
0
1
0
0
1
0
0
1
0
1
0
0
1
0
1
2
1
0
2
2
0
0
1
1
1
1
0
2
1
1
1
1
1
2
1
1
0
1
2
1
0
1
2
2
0
1
0
0
0
1
1
0
0
2
1
1
2
0
1
1
0
2
1
0
1
2
0
0
1
1
0
1
0
0
1
0
1
2
2
1
2
1
0
2
0
1
1
0
0
2
2
0
1
2
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
2
0
1
1
0
1
1
0
0
0
0
2
0
0
1
0
0
1
0
0
1
2
1
1
0
0
0
0
0
0
1
1
1
1
1
1
3
0
0
0
1
1
0
0
1
2
1
2
1
0
1
1
3
1
1
2
1
0
0
1
1
0
1
2
1
1
1
1
2
2
1
1
1
2
1
1
0
0
1
2
0
0
0
1
1
0
2
0
0
2
2
0
1
0
0
1
0
1
1
1
3
0
1
0
1
1
0
1
0
0
2
0
0
0
2
2
1
1
2
1
1
2
0
0
2
0
1
1
2
1
0
0
0
2
3
2
0
0
1
1
1
1
0
1
1
0
1
2
1
0
1
2
2
1
0
1
0
2
0
2
1
2
0
1
0
1
0
1
0
1
0
2
0
1
0
0
0
1
1
2
0
1
0
1
1
0
1
1
1
1
1
1
0
0
2
0
0
1
0
0
0
2
1
1
0
1
0
1
2
1
2
0
1
1
2
1
1
0
1
0
0
1
1
1
2
0
1
0
0
0
0
0
0
1
1
0
2
1
0
1
1
0
1
1
0
2
1
2
2
1
2
1
2
1
1
2
8
0
1
0
1
1
0
1
1
1
2
1
1
2
1
0
0
0
2
2
0
1
3
0
1
0
1
2
1
0
0
1
0
0
1
1
1
2
0
1
1
1
2
1
2
1
0
0
2
1
2
0
1
2
0
0
0
0
0
1
2
1
1
2
1
0
2
1
1
0
0
1
1
1
1
0
0
0
0
1
1
0
0
0
2
2
2
1
1
1
1
1
1
0
1
0
0
1
1
2
1
2
0
0
1
0
1
1
1
0
1
1
0
0
0
2
1
2
2
0
3
1
0
0
1
2
3
1
2
1
0
2
1
1
0
1
0
2
0
0
1
0
1
1
0
1
1
1
1
0
1
0
1
2
1
4
2
0
2
1
0
1
1
1
0
2
1
1
2
2
0
0
2
0
1
1
1
1
2
1
0
0
0
1
0
1
1
0
0
0
1
0
1
1
1
0
2
1
0
1
0
2
0
0
0
1
1
2
1
2
2
1
1
0
1
0
1
1
1
2
0
0
1
2
1
1
1
1
1
0
0
0
1
1
0
0
1
1
1
1
2
2
2
1
0
0
0
0
0
0
2
0
2
0
1
1
0
0
1
2
1
0
0
0
2
1
2
0
1
1
0
1
0
1
2
0
0
1
0
2
1
0
1
0
1
0
1
0
0
0
0
1
1
1
0
2
2
0
0
2
2
2
1
1
0
0
2
1
1
0
0
2
0
1
1
2
0
1
2
1
0
0
1
1
2
1
2
1
0
2
1
0
2
1
0
0
1
1
0
2
1
2
0
0
2
2
1
1
2
0
0
1
2
1
1
1
2
0
1
0
0
1
0
2
0
2
1
0
1
1
1
2
0
2
0
2
0
0
1
0
2
0
2
1
0
0
1
0
0
0
1
0
0
0
1
1
0
1
2
1
0
2
2
0
0
1
0
0
2
0
1
1
0
2
2
0
0
1
2
0
1
0
0
0
2
0
1
0
0
0
0
1
2
0
0
1
1
0
2
0
1
0
2
1
1
0
0
1
2
0
1
0
1
1
1
0
1
1
0
1
0
1
0
0
1
0
1
1
0
1
0
2
0
0
2
1
1
2
2
1
0
0
1
1
2
2
1
1
1
0
3
2
2
1
2
1
1
0
2
0
0
1
0
1
0
0
0
1
2
1
1
1
0
2
1
1
0
1
1
0
0
0
0
1
0
1
1
2
1
1
0
2
1
0
1
0
0
2
0
2
0
0
0
1
1
0
0
1
0
0
0
1
2
0
1
1
0
2
2
0
2
0
2
1
1
1
1
0
1
0
0
1
0
1
2
1
2
2
1
1
1
0
1
0
1
2
1
1
1
2
1
0
2
2
2
0
1
0
2
1
0
0
1
2
0
2
0
1
2
0
1
0
1
1
0
0
0
1
0
0
0
0
0
1
1
1
0
1
0
0
1
2
0
1
1
1
1
2
1
1
3
0
1
1
1
0
0
1
2
0
1
1
0
1
1
2
1
1
1
0
0
2
1
1
1
0
0
1
1
0
1
2
0
1
1
1
0
1
0
0
0
1
0
1
1
2
1
0
2
1
2
1
0
0
2
1
0
0
0
2
0
0
1
1
0
2
2
0
0
2
1
0
1
0
1
0
2
1
0
1
1
0
1
0
0
1
1
0
0
0
1
1
1
1
1
1
1
0
1
2
0
0
1
2
1
0
2
1
0
0
0
2
0
0
2
1
1
0
0
1
0
1
1
0
1
0
0
0
0
1
1
2
2
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
2
1
1
1
0
2
2
1
0
2
1
2
2
2
3
1
1
2
0
1
1
0
1
0
0
1
1
1
2
1
1
0
0
2
0
1
1
1
2
1
1
1
1
1
1
1
2
1
0
2
2
0
1
0
1
2
1
1
1
1
1
0
1
1
0
0
2
1
1
0
1
1
1
2
3
1
2
0
0
1
2
1
0
1
2
1
1
1
1
1
1
2
2
0
1
0
1
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
2
2
2
0
1
1
2
0
2
0
1
0
1
0
1
1
2
2
0
1
1
1
1
0
0
2
0
2
0
1
2
1
0
2
1
2
1
0
0
0
1
1
1
1
1
0
0
0
0
1
2
0
0
0
1
0
0
1
0
0
0
1
0
0
1
1
2
2
0
0
1
0
0
0
0
1
1
1
2
0
0
0
1
1
0
1
2
1
1
2
1
0
0
0
0
0
0
1
3
1
2
1
1
2
0
1
0
0
0
2
0
0
0
0
2
2
2
0
1
0
1
0
0
2
0
0
0
1
0
0
0
2
0
0
2
0
1
3
1
0
1
1
0
0
0
0
0
1
2
1
3
1
0
1
3
0
2
2
0
0
0
0
2
0
1
0
0
2
0
0
0
0
1
0
1
1
2
2
0
0
0
0
0
0
2
0
1
1
1
0
0
2
0
0
1
1
0
0
1
1
0
2
0
1
0
1
1
0
1
1
1
1
0
1
1
0
0
1
1
1
0
2
2
1
1
1
1
0
1
1
0
0
1
0
2
0
0
2
0
0
1
1
1
1
1
1
1
2
1
1
0
0
3
1
0
0
1
0
1
0
3
0
2
1
1
0
1
0
0
2
1
1
0
1
0
1
1
1
0
2
0
0
0
0
1
1
1
2
1
2
1
0
0
0
2
2
1
0
1
1
1
1
0
1
1
1
1
3
0
1
0
2
1
0
1
1
1
2
1
1
2
1
2
2
0
0
0
0
0
2
0
2
2
3
0
1
1
1
0
1
0
1
1
2
1
0
1
1
0
0
1
2
2
0
0
0
1
2
2
1
1
0
1
1
1
1
2
0
0
1
1
1
0
2
1
1
0
0
0
1
1
1
2
0
1
2
0
0
1
0
0
2
2
0
4
0
1
0
2
1
2
1
1
1
0
0
0
1
1
1
1
0
2
1
0
1
2
0
1
1
0
2
2
1
2
0
1
1
1
0
1
2
0
1
0
1
2
1
2
1
1
2
1
0
2
0
2
0
1
0
0
1
1
1
0
0
1
0
2
1
0
1
1
3
1
0
1
0
1
1
0
2
1
1
0
1
0
1
2
0
2
1
1
0
2
2
2
1
1
0
0
0
2
1
1
0
0
0
0
0
2
1
0
0
1
0
0
0
1
0
1
2
0
1
0
1
0
1
1
1
0
0
0
0
0
0
2
1
1
0
0
0
1
1
1
1
1
0
0
2
1
1
0
2
0
2
2
0
1
0
2
2
3
1
0
0
1
2
1
0
2
2
0
2
0
1
0
0
1
0
0
1
1
1
1
1
1
0
0
1
1
0
1
1
2
1
1
1
2
0
0
0
0
1
0
2
1
0
0
3
1
0
1
1
2
1
0
0
0
0
1
1
1
0
0
2
1
0
1
1
0
0
0
1
0
0
0
0
1
2
0
1
0
1
0
1
1
0
2
2
0
0
0
1
0
1
1
1
0
1
1
1
1
0
1
0
2
2
1
1
2
0
0
1
0
0
2
1
0
0
1
0
1
0
1
0
0
0
1
0
1
1
2
0
2
0
0
2
1
1
1
0
0
0
1
0
2
0
2
1
0
0
1
2
0
2
0
0
2
1
2
2
1
2
1
0
1
0
1
1
2
0
0
0
0
2
1
1
2
2
1
2
2
1
2
0
2
2
0
2
0
0
1
0
1
2
0
1
1
1
1
0
1
0
2
1
0
1
0
1
1
0
0
0
1
1
1
1
2
1
1
2
0
1
2
1
0
2
3
0
0
2
1
1
1
1
0
2
1
0
1
1
0
1
0
1
1
1
2
2
1
0
1
2
0
1
0
0
1
4
0
0
2
0
0
2
2
1
2
2
1
1
1
0
4
3
0
0
0
1
1
2
1
1
2
0
2
2
0
2
0
2
1
0
2
2
1
1
1
2
0
1
1
1
0
1
1
0
0
0
1
1
1
1
0
1
3
0
1
2
1
2
0
3
1
0
1
2
2
2
1
1
2
0
2
2
1
1
1
0
0
2
2
0
1
2
0
1
1
1
0
0
1
0
0
1
2
0
1
1
1
0
0
1
2
2
0
0
2
1
2
1
0
2
0
0
1
1
1
2
1
0
1
3
2
1
0
0
1
1
1
2
0
0
2
1
0
2
1
1
2
0
1
1
2
0
2
1
1
0
2
0
1
1
0
0
0
1
2
3
1
2
0
0
0
2
0
2
1
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
1
0
0
2
0
0
1
1
1
1
2
2
1
0
1
1
0
0
1
0
2
1
2
1
2
1
0
0
0
0
1
1
1
0
1
0
1
0
1
0
1
0
1
0
0
0
3
1
2
1
2
0
1
0
0
0
1
1
2
0
0
0
2
0
1
2
2
1
0
0
1
2
0
0
1
3
0
0
0
0
0
0
0
2
0
0
1
0
1
1
3
2
1
1
0
2
0
1
0
1
0
1
2
1
0
0
0
1
1
1
1
1
0
1
2
0
0
0
0
1
2
2
0
0
0
0
2
1
7
1
1
0
0
2
1
0
0
1
2
1
1
0
2
1
1
2
1
2
0
0
2
2
1
2
0
2
0
1
1
1
2
1
0
2
0
0
2
1
1
0
2
1
2
1
1
2
0
1
1
0
1
1
1
0
1
2
1
0
2
1
2
1
2
1
1
2
0
1
0
0
2
0
2
1
2
1
2
2
0
0
0
2
2
0
2
2
0
2
2
2
0
2
2
0
2
2
2
0
1
1
1
1
0
0
2
1
0
1
0
0
0
1
1
1
1
1
1
0
2
1
0
2
0
2
0
1
1
0
1
1
0
0
1
1
1
2
0
1
2
0
1
1
1
1
1
0
1
0
0
0
1
1
1
1
1
2
0
1
0
0
2
0
2
1
2
0
3
1
1
0
1
1
1
0
1
1
2
2
1
2
0
2
2
0
1
2
0
1
1
0
0
1
1
1
1
1
0
1
1
0
1
1
0
1
1
1
1
0
1
0
1
1
0
2
0
1
1
1
0
0
1
0
1
0
0
1
1
1
2
1
0
0
1
1
2
2
1
0
0
1
0
1
1
0
1
0
0
2
0
2
2
1
1
1
0
0
1
1
1
0
1
0
0
1
1
1
1
2
2
1
0
1
1
1
1
2
1
2
0
1
1
0
0
2
0
0
2
1
1
2
0
0
0
1
0
1
2
0
1
3
1
0
1
0
1
2
1
1
0
3
0
0
2
1
1
0
2
0
1
1
0
1
0
1
0
0
0
1
2
1
1
2
0
2
2
0
0
1
2
0
0
0
0
2
1
0
1
1
0
0
1
2
2
3
0
2
1
0
2
0
2
0
1
2
0
0
0
2
2
1
2
2
1
0
2
1
0
1
2
1
1
1
1
0
1
2
1
2
0
2
1
1
2
2
0
0
1
1
1
1
1
1
1
0
0
2
2
0
1
0
0
2
1
1
0
1
1
1
2
1
1
2
0
0
2
1
2
0
1
1
0
0
2
1
1
1
0
1
1
0
0
2
0
1
0
0
0
0
0
0
1
2
0
0
2
1
0
1
2
0
1
0
0
1
0
1
0
1
1
1
1
1
0
0
0
1
2
2
2
0
1
1
2
0
0
0
2
1
1
0
0
1
1
0
1
1
2
3
2
2
0
0
0
0
0
1
0
0
2
2
2
2
1
0
1
1
0
0
1
0
0
1
1
0
0
1
2
0
4
1
1
1
1
0
0
2
1
0
0
2
0
2
0
1
2
2
0
0
2
3
0
0
4
1
0
0
2
0
1
1
2
1
1
1
2
0
1
0
0
1
1
1
1
1
2
1
0
2
1
1
2
0
1
2
0
2
0
0
0
1
2
2
3
0
1
3
0
0
0
1
0
1
0
0
1
1
1
1
1
0
1
0
1
1
2
1
2
0
0
1
0
0
2
1
1
1
1
1
2
1
1
1
0
1
0
1
1
1
1
2
1
1
0
1
2
1
1
0
1
1
1
1
1
2
2
0
2
0
0
1
2
0
2
2
2
0
1
1
1
0
2
1
0
0
1
1
1
0
1
0
2
2
2
1
1
1
2
1
2
1
0
0
3
2
2
2
1
0
1
1
0
1
1
1
1
0
0
2
1
0
2
0
0
0
1
1
0
1
1
1
1
2
0
0
0
2
1
1
0
1
1
1
1
0
1
1
0
2
1
1
2
0
0
0
1
1
1
1
0
1
1
0
1
1
2
1
0
2
0
0
0
0
0
0
1
1
0
2
0
3
1
0
2
0
0
0
1
3
0
0
1
2
1
1
0
1
1
0
1
1
1
1
0
0
2
0
2
1
2
0
0
0
0
1
2
2
0
0
0
1
0
0
1
1
1
0
0
0
2
1
0
0
0
0
0
1
2
0
0
2
2
0
1
1
2
1
0
1
0
0
2
1
1
0
1
0
0
0
8
1
2
0
3
1
0
1
1
0
0
1
0
0
1
1
1
0
1
0
0
1
1
0
1
1
2
1
0
1
1
0
0
2
1
2
0
0
2
1
0
1
1
0
1
1
0
1
2
0
2
0
1
0
2
1
1
2
2
2
2
1
1
0
1
1
1
1
1
0
0
1
0
1
0
0
3
1
0
1
0
0
3
2
0
1
1
1
1
1
0
2
1
2
1
1
0
1
1
0
2
0
0
1
2
1
2
0
0
0
0
2
0
2
2
0
1
0
1
1
0
0
2
2
2
1
1
1
1
0
1
2
0
1
1
0
0
1
2
2
2
2
1
0
0
0
0
0
1
2
2
2
3
0
1
2
2
2
1
1
2
1
0
2
0
2
1
0
0
1
1
1
1
1
0
1
0
0
1
0
1
0
1
2
0
2
0
1
0
0
1
1
0
0
1
1
0
1
0
0
1
1
1
1
1
0
1
0
0
2
1
1
1
0
2
2
0
1
0
1
1
0
1
1
0
0
2
2
1
1
1
1
1
1
0
0
0
0
1
0
1
1
0
1
0
0
2
2
2
2
1
1
0
1
2
1
0
2
1
0
0
1
2
1
1
1
1
1
0
1
1
0
2
2
0
1
0
0
1
1
1
2
0
1
2
0
0
0
1
1
1
2
0
0
0
2
0
2
1
2
1
0
1
1
1
2
1
1
0
0
1
2
0
0
0
0
1
1
1
1
2
1
2
0
0
0
0
0
0
0
0
1
1
0
1
1
1
0
0
1
1
0
0
1
0
2
0
0
1
2
0
0
1
0
1
1
2
1
0
1
1
1
1
2
0
1
2
0
0
1
0
0
0
2
2
0
1
0
0
0
0
2
1
2
2
2
0
0
0
0
2
1
2
3
0
2
1
0
8
0
1
0
1
0
1
0
2
1
2
0
1
1
2
0
2
2
2
2
1
0
1
0
1
2
0
2
0
0
0
1
0
0
0
1
2
2
0
1
0
2
1
0
1
2
2
1
1
0
1
0
2
1
2
1
0
0
0
1
0
0
1
2
1
0
2
2
0
2
0
1
2
0
0
2
0
0
0
2
2
1
0
0
0
2
0
0
0
0
2
0
0
1
1
0
1
0
1
2
1
0
0
2
1
2
0
2
1
1
2
2
0
1
4
0
1
0
1
2
0
0
1
2
0
0
0
0
1
2
1
0
1
2
2
1
2
0
0
1
1
0
1
1
0
0
0
1
1
1
0
2
1
3
2
0
2
0
1
0
1
0
0
1
0
1
1
2
1
1
2
2
3
0
1
2
1
0
0
0
1
1
1
1
2
2
2
0
0
0
1
0
1
0
2
1
1
0
0
1
2
1
1
2
0
0
0
0
2
0
0
2
1
1
1
2
1
0
1
1
1
1
1
1
2
0
0
0
0
1
1
0
0
1
0
1
0
2
1
0
1
2
0
0
2
1
2
0
1
1
2
0
0
2
2
1
1
0
0
2
0
1
4
0
1
1
0
0
1
1
4
0
1
0
0
2
2
2
2
2
0
1
1
1
1
0
2
0
0
1
2
1
1
2
1
2
0
0
1
1
1
1
1
2
2
0
1
1
0
0
2
0
0
0
1
1
1
1
2
0
0
0
0
2
1
1
1
1
3
2
1
2
0
0
1
1
1
0
1
1
0
0
2
2
2
1
1
0
1
1
1
1
2
0
2
0
1
0
0
1
2
1
0
0
0
0
1
1
1
0
1
0
2
1
1
0
1
0
0
0
0
2
0
0
1
2
0
0
3
1
1
0
1
0
0
1
0
2
2
2
0
0
1
0
1
0
1
1
1
1
0
0
1
1
2
0
0
1
1
1
1
1
1
0
0
1
2
1
0
1
2
0
1
0
0
0
1
2
2
1
2
1
0
0
0
2
0
1
0
1
2
2
0
1
2
1
1
1
1
1
1
1
1
1
0
1
0
1
0
0
1
0
1
0
1
2
2
1
1
1
0
0
2
2
0
1
1
0
1
1
0
1
0
0
0
0
2
1
1
1
2
0
2
2
0
2
1
0
0
2
0
0
1
2
1
1
0
0
1
1
1
0
2
2
1
1
1
0
0
0
2
0
1
1
0
0
0
0
0
2
0
0
1
0
0
1
0
2
1
2
0
2
1
1
0
0
0
0
0
1
1
2
2
0
0
0
0
1
2
1
2
0
0
1
2
2
1
0
0
1
0
0
3
1
0
2
2
1
0
1
0
0
1
0
1
2
1
0
1
0
0
2
0
0
1
0
0
1
0
0
2
0
0
0
0
1
1
0
1
0
1
0
1
1
1
0
1
2
0
1
0
1
1
2
2
1
0
1
2
0
2
0
1
1
1
1
1
1
2
1
0
1
0
0
1
1
1
2
1
2
1
0
1
1
1
2
2
0
2
1
1
0
1
1
0
1
1
1
1
0
0
1
1
0
1
0
0
1
2
1
1
1
0
0
2
1
1
1
1
0
1
0
1
1
1
0
0
1
0
0
0
1
1
0
1
0
1
0
1
1
0
2
1
1
1
0
1
0
1
2
1
1
1
0
1
1
1
1
2
1
0
0
1
0
1
1
1
0
1
1
0
1
0
1
1
0
2
2
0
0
1
1
2
0
1
0
1
1
1
2
1
0
2
1
2
2
1
1
0
1
0
2
0
0
2
0
1
1
0
0
0
1
1
1
2
2
0
0
2
2
1
0
2
1
0
0
2
0
1
0
1
1
2
2
1
0
1
0
2
0
1
0
0
1
1
0
0
1
2
1
2
1
1
1
2
2
1
0
2
2
0
0
1
1
0
2
2
0
1
1
1
1
0
0
1
2
0
2
4
0
1
1
0
1
1
2
0
1
0
1
1
1
1
1
1
0
0
0
1
0
1
1
2
1
1
0
0
0
1
0
1
1
6
0
1
1
2
1
2
0
1
1
1
1
1
2
0
1
2
0
0
2
1
1
0
1
2
0
1
1
1
0
0
0
0
1
0
2
2
0
2
2
4
1
1
0
2
1
0
1
0
2
3
2
1
3
0
1
0
3
1
1
2
2
2
2
1
1
0
0
1
1
1
1
2
1
1
0
1
1
0
0
2
0
0
1
0
1
2
1
1
1
0
2
0
2
0
2
2
2
4
0
2
1
2
1
2
0
1
0
0
0
0
1
0
1
2
0
1
0
0
0
2
3
1
1
2
1
0
0
1
1
2
1
0
1
0
1
2
1
1
1
1
0
0
0
1
0
1
1
0
0
1
2
2
0
0
2
1
1
1
0
0
1
2
0
1
1
2
2
1
1
1
2
1
1
0
1
0
2
2
0
0
0
2
2
1
1
0
0
1
0
0
0
2
0
1
0
0
0
1
2
0
1
2
0
1
1
0
2
1
1
0
1
2
1
1
0
0
0
0
2
2
1
2
0
1
1
1
1
1
1
0
2
0
0
1
0
1
0
0
0
1
1
1
1
2
1
1
1
1
2
2
2
2
0
1
0
1
2
0
0
2
1
1
0
2
4
0
1
0
0
1
0
2
1
0
2
2
1
2
0
1
0
2
1
1
1
1
2
2
0
1
1
0
0
0
1
0
2
1
0
0
1
1
1
3
2
1
1
1
4
0
0
0
0
0
0
0
0
2
1
1
0
0
1
0
0
2
0
1
1
0
1
1
0
0
1
0
2
1
1
2
1
1
3
2
2
2
1
0
1
0
1
1
0
2
1
1
3
2
1
1
2
2
0
2
0
1
1
1
0
2
1
0
1
0
0
1
1
0
1
1
1
0
2
0
1
2
1
2
2
2
0
1
1
1
2
1
0
1
2
0
0
1
0
0
1
1
1
0
1
1
0
1
0
0
0
1
1
0
0
0
1
2
0
3
1
0
1
2
0
1
1
1
2
1
0
1
0
2
0
2
0
0
1
8
0
0
1
0
2
1
0
2
1
1
1
2
1
1
0
0
0
0
1
1
0
2
2
2
1
1
0
2
1
0
1
2
1
1
2
0
0
0
0
1
1
1
0
0
1
3
1
0
0
2
1
0
2
1
2
1
2
0
0
1
2
2
1
0
1
0
2
1
1
1
0
2
0
1
2
1
0
2
0
0
0
2
1
1
0
3
1
0
0
1
1
3
1
0
1
1
1
0
0
2
1
1
2
0
1
0
0
0
2
0
3
1
1
1
0
4
0
1
0
1
1
3
1
0
1
2
0
0
1
2
0
0
2
0
1
2
0
0
2
1
0
1
0
1
0
0
1
4
1
2
2
1
0
0
0
1
0
2
0
1
1
0
0
1
2
1
3
1
0
0
0
2
1
1
1
0
2
0
2
1
2
2
2
0
2
0
1
0
2
0
1
1
0
1
0
1
0
1
2
2
0
1
1
1
0
2
0
1
0
0
0
2
0
2
0
1
1
1
1
0
0
1
1
1
0
0
0
0
0
0
1
0
1
0
0
2
0
1
0
2
0
1
1
1
1
2
0
0
1
4
0
1
0
2
1
1
0
0
2
0
2
0
0
0
0
1
2
0
1
0
0
1
1
0
0
2
1
0
0
2
1
1
1
0
2
0
0
1
1
1
0
2
0
0
1
1
2
1
0
1
0
1
1
1
2
1
1
2
1
2
0
2
0
1
2
0
1
1
2
0
1
2
3
1
0
0
1
2
0
1
0
0
2
2
0
3
0
2
1
1
3
2
2
1
1
0
1
1
0
1
2
2
2
0
1
1
1
2
0
1
1
3
2
2
1
0
0
0
0
1
1
0
0
1
1
0
2
0
0
1
0
0
1
2
2
1
2
0
2
2
0
2
2
1
1
0
0
0
0
0
0
2
0
2
1
0
1
1
0
0
1
0
0
1
3
0
0
0
1
0
1
0
0
1
1
0
1
2
1
1
3
1
1
1
0
0
1
0
1
3
1
2
1
2
0
1
2
0
1
1
0
2
0
1
2
0
1
2
1
0
2
2
2
0
0
1
0
2
0
0
2
0
0
2
1
1
1
2
1
2
1
0
0
1
1
0
0
0
2
0
2
3
0
0
0
0
0
0
1
1
2
1
0
1
0
0
1
2
1
2
2
2
1
1
0
2
0
1
0
2
1
2
0
1
1
1
0
0
1
0
1
0
1
1
2
0
1
2
1
1
1
1
1
1
0
0
1
2
1
0
1
2
1
3
1
2
1
1
1
1
0
2
0
1
1
1
1
2
0
0
1
2
0
2
1
2
1
0
1
0
1
1
1
2
2
2
2
1
1
1
1
0
1
0
1
0
2
1
0
0
0
3
0
2
2
0
1
1
0
0
2
1
1
0
0
1
2
0
2
1
5
2
0
0
0
0
2
1
0
0
3
2
2
1
1
2
1
2
1
2
1
2
1
2
1
1
0
1
1
0
1
1
1
1
1
2
1
0
0
0
0
1
0
1
0
1
2
1
1
1
0
0
1
0
0
2
2
1
2
3
2
0
0
0
2
1
2
1
1
2
1
1
0
2
2
1
1
2
1
2
2
1
0
1
1
0
2
1
1
2
0
0
0
0
1
1
0
1
2
0
0
0
0
1
0
0
0
1
0
0
1
6
1
0
2
1
1
2
1
0
2
0
2
0
3
0
0
0
0
1
1
0
0
2
0
1
0
1
1
1
0
2
2
0
0
1
1
0
0
0
1
1
1
1
0
0
0
2
0
1
0
0
1
1
1
1
1
1
1
0
1
2
1
0
1
1
2
0
0
1
2
0
1
1
1
0
1
1
2
0
0
0
1
1
0
6
0
2
1
0
2
2
0
2
1
2
1
0
2
4
1
1
1
0
0
0
1
0
2
2
0
0
0
1
2
2
1
0
2
0
1
0
1
1
0
2
2
1
1
0
0
1
0
1
1
0
1
0
1
0
1
1
2
0
0
0
1
1
1
1
0
2
0
0
0
0
1
1
2
0
1
1
0
1
0
1
0
2
0
1
1
0
0
1
1
1
1
2
0
0
1
0
0
2
1
2
0
1
2
2
2
0
1
0
1
0
0
2
1
0
0
1
0
1
0
1
2
1
0
0
1
0
1
0
3
2
1
2
1
1
1
1
0
2
1
1
1
0
1
1
1
1
1
0
2
1
1
2
0
2
2
0
0
1
1
0
0
1
2
1
2
1
2
2
1
0
0
2
0
1
2
2
0
1
1
0
1
0
0
0
0
2
0
1
1
0
0
1
1
2
2
0
0
1
1
2
1
1
0
1
1
0
0
2
1
0
3
1
1
1
1
1
0
0
2
2
1
2
1
0
0
0
0
1
0
1
1
2
1
0
1
0
0
1
1
0
0
0
1
0
0
1
1
0
0
0
2
2
1
0
0
1
1
0
0
3
2
1
1
0
1
1
0
2
2
0
0
0
0
1
0
2
0
0
1
2
0
1
2
1
0
0
0
1
1
0
2
1
0
0
0
2
0
1
1
1
1
0
2
0
1
0
2
0
1
0
1
0
2
1
0
0
0
0
2
2
0
0
1
2
2
3
1
0
0
1
0
1
0
2
0
1
1
0
2
0
2
2
0
1
0
1
0
1
0
0
0
0
1
1
0
2
1
0
0
0
1
1
1
1
1
1
1
1
0
1
2
0
2
1
1
1
1
1
0
0
1
1
1
0
1
0
1
2
1
2
1
2
0
0
2
1
0
0
4
2
1
1
1
0
0
0
0
1
3
1
1
2
0
1
1
0
0
2
1
0
0
2
1
0
1
2
0
1
1
2
1
1
1
0
1
1
0
0
1
1
1
1
2
1
1
0
0
1
2
1
0
0
0
0
1
0
1
1
2
2
1
1
2
0
0
1
0
0
1
1
1
2
1
2
0
1
1
0
0
0
0
1
2
2
2
1
0
0
2
4
1
0
1
0
0
2
1
0
0
1
2
1
1
0
2
0
1
2
2
0
0
0
2
2
0
0
2
1
2
2
2
0
1
1
0
0
2
0
1
0
1
1
0
0
2
2
0
0
2
1
1
1
2
1
2
2
1
1
2
1
0
2
7
0
1
0
1
2
1
0
1
1
0
0
1
1
2
0
0
0
1
1
2
1
1
0
0
1
0
1
1
1
1
0
1
1
2
1
1
1
2
1
0
1
1
1
1
2
2
0
1
1
0
1
0
1
1
1
1
2
1
0
1
1
1
2
0
1
1
2
1
1
2
1
1
1
0
1
1
0
2
1
2
1
0
2
3
2
2
1
0
0
0
0
0
0
1
2
0
2
1
2
2
0
1
0
0
1
2
0
0
1
1
1
1
2
2
1
0
1
0
1
1
0
2
1
2
0
2
1
1
2
0
0
2
0
0
2
1
2
1
1
0
2
1
2
1
1
2
0
1
0
0
2
0
0
0
0
0
0
1
1
2
1
2
2
2
1
1
1
2
2
0
0
0
0
1
2
1
0
1
1
3
0
0
2
1
0
0
2
1
0
2
2
0
2
1
0
2
1
0
1
1
1
0
1
0
2
2
0
2
2
1
2
2
1
2
0
2
0
1
4
2
0
2
0
0
2
1
2
0
1
1
0
1
0
2
0
0
1
1
1
2
1
2
1
1
0
1
0
0
1
1
1
0
3
1
1
1
1
1
1
0
0
0
1
1
1
0
2
1
2
0
0
2
1
0
2
1
2
1
0
0
0
1
0
1
0
2
1
1
0
2
1
2
1
0
0
2
0
0
1
1
0
1
1
2
0
0
1
2
1
0
1
0
3
2
1
1
1
0
1
0
1
1
0
1
2
1
2
1
0
1
1
0
2
2
2
1
1
0
1
0
0
1
2
2
1
1
1
1
0
2
2
1
1
0
0
2
1
1
1
1
2
1
0
0
0
0
0
0
2
0
2
3
2
0
1
1
1
0
1
1
1
2
1
1
0
0
0
1
0
1
1
0
2
2
1
0
2
1
0
1
0
1
1
1
2
0
1
2
1
0
1
0
2
0
0
0
2
2
1
2
2
1
1
0
0
0
0
0
0
1
1
1
0
2
1
2
0
2
2
2
0
1
0
1
0
0
1
1
1
3
0
2
1
2
0
1
2
0
0
2
1
2
1
0
1
0
0
2
1
2
1
1
0
0
1
1
0
1
0
2
3
5
1
0
1
1
1
0
0
3
0
1
1
1
1
1
2
0
2
2
1
0
1
2
1
2
0
0
0
0
1
0
1
1
1
4
1
0
1
0
1
0
2
0
1
0
1
2
2
1
1
1
2
1
1
0
2
2
0
0
1
1
1
2
0
0
0
2
1
0
2
1
0
0
0
1
0
1
0
1
2
2
1
0
0
2
1
0
1
2
1
1
2
1
1
1
1
0
0
2
2
0
1
0
1
0
1
0
3
0
2
1
0
1
0
2
0
0
2
1
0
1
0
1
1
0
1
1
0
0
2
0
2
1
0
1
1
0
1
1
1
2
1
0
1
0
1
1
0
1
0
2
2
1
1
1
1
2
0
0
3
1
0
2
0
2
0
3
2
0
1
2
2
1
1
1
0
0
1
0
0
0
0
1
1
2
0
0
1
1
1
0
1
1
0
1
2
2
3
1
0
2
1
0
0
0
1
1
0
0
0
2
2
2
2
0
1
2
1
1
2
0
1
1
1
2
2
1
1
0
1
0
0
2
1
0
2
1
1
0
1
2
1
1
0
0
0
1
0
1
2
1
0
2
2
0
0
1
0
1
1
0
1
2
2
2
0
0
1
1
0
0
0
2
1
3
0
1
1
2
0
2
0
2
2
0
1
1
0
2
2
0
0
1
2
0
3
0
1
2
1
0
2
0
1
0
0
0
2
1
0
2
1
1
0
1
2
2
3
0
0
0
1
1
2
0
1
1
1
1
2
2
2
1
1
1
1
2
0
1
0
1
2
1
0
2
0
2
0
0
1
2
1
2
2
0
1
2
2
1
0
1
1
2
0
3
1
0
1
1
0
1
2
2
0
1
1
1
0
3
0
0
0
3
2
0
0
0
1
1
1
2
1
1
1
0
2
1
0
0
1
1
1
2
1
0
1
0
0
0
1
4
1
1
3
1
0
0
1
1
1
2
0
2
1
0
2
0
0
1
1
2
0
0
0
1
1
0
1
1
1
2
2
2
1
0
1
3
1
1
0
0
2
2
1
0
1
2
1
1
0
2
1
1
2
1
1
1
1
0
1
1
1
3
0
0
2
1
0
1
1
0
0
0
0
0
1
1
2
0
1
0
0
0
2
0
2
0
1
0
0
1
1
2
1
0
0
0
2
1
2
1
1
0
0
0
1
1
0
0
0
2
1
1
1
1
1
2
2
0
2
0
0
2
1
1
1
1
0
2
2
2
1
0
1
0
1
1
2
0
0
2
1
2
0
2
2
1
1
0
1
0
0
0
1
1
2
1
0
1
0
1
0
0
1
2
1
1
1
0
1
0
1
2
1
1
1
2
0
0
1
2
0
0
0
2
1
2
1
1
0
0
2
2
1
0
0
2
1
0
1
1
0
2
1
2
1
0
1
0
2
1
1
2
1
1
2
0
0
0
0
0
0
1
0
1
0
2
0
1
1
0
2
2
1
0
1
0
0
1
2
2
1
2
0
0
0
1
0
0
1
0
0
0
2
1
2
1
0
2
0
0
0
0
1
0
0
0
2
1
1
1
0
0
1
0
0
0
1
2
1
1
1
1
0
1
1
1
0
0
1
0
2
1
1
0
2
1
1
2
0
0
0
0
1
0
0
1
1
2
1
0
0
0
2
1
0
0
1
1
2
1
1
1
0
2
0
2
2
2
0
1
0
0
0
1
1
1
1
3
2
1
1
1
1
1
0
1
0
1
1
1
0
1
0
0
0
1
2
0
0
2
0
0
1
1
0
0
1
1
1
0
0
2
0
1
2
2
1
1
1
1
1
1
0
1
2
0
0
1
0
2
0
0
1
2
2
1
1
2
1
1
1
0
2
0
0
1
2
1
0
1
1
1
2
0
1
0
0
1
0
0
2
1
0
1
1
1
1
2
1
0
0
1
1
1
1
0
1
1
0
1
0
0
2
0
2
1
0
0
1
1
1
0
1
2
1
2
1
1
0
2
0
2
2
1
1
2
0
0
0
0
2
1
1
1
0
0
0
0
0
0
2
2
2
1
2
1
2
1
1
0
0
1
0
0
1
1
1
1
2
2
1
0
2
0
1
1
0
0
0
0
0
2
1
1
1
1
2
1
0
1
2
1
2
1
0
1
1
2
1
2
0
0
0
1
0
2
0
0
0
2
1
2
1
2
1
1
0
1
0
2
1
3
2
0
2
0
0
1
1
1
1
1
1
0
0
2
0
1
0
0
1
0
0
1
2
2
1
1
0
1
2
1
0
0
2
0
2
1
0
1
2
1
1
0
1
1
1
2
2
2
1
0
1
2
2
1
1
0
0
2
1
1
1
0
0
0
0
1
0
0
1
1
1
0
1
0
1
1
0
1
0
1
0
1
1
1
0
0
5
1
2
0
1
1
1
3
1
2
1
0
1
1
1
0
0
2
0
2
1
2
2
0
1
2
1
1
2
2
1
1
1
1
0
0
0
2
2
1
1
1
2
2
0
0
0
2
2
0
0
2
2
1
0
1
0
1
0
0
1
0
1
2
1
0
2
2
0
0
0
0
2
1
2
1
1
0
1
2
1
1
0
2
0
2
4
0
1
1
1
3
0
0
1
1
1
2
1
2
2
1
0
1
2
0
1
1
1
1
2
2
1
1
1
2
0
0
0
1
2
0
1
0
0
2
1
1
1
0
1
0
0
2
1
1
0
0
0
2
0
1
0
0
1
0
0
0
2
2
1
2
2
2
1
0
1
3
1
1
2
2
3
2
0
1
1
0
0
1
0
1
2
2
1
0
1
2
0
1
1
2
2
0
2
0
0
1
0
0
1
2
0
0
1
0
1
1
2
1
1
1
1
2
2
1
1
1
1
2
1
1
1
0
0
0
0
2
0
0
1
1
1
1
1
1
0
2
1
1
1
1
1
1
1
0
1
0
2
2
1
1
0
1
0
2
1
0
0
1
0
0
0
3
1
1
1
0
0
1
2
0
0
2
0
0
0
0
2
1
0
2
2
0
1
0
0
0
1
2
1
0
1
2
1
1
2
0
0
0
0
2
2
0
0
0
1
3
0
1
2
2
0
0
0
1
2
1
1
1
0
0
1
1
0
1
0
2
2
1
1
1
2
1
0
2
3
1
2
2
1
0
0
0
0
1
1
1
0
0
0
2
2
0
0
1
1
1
1
1
1
1
1
1
0
2
2
1
1
2
1
1
0
1
2
0
0
0
2
0
0
0
1
0
2
0
0
1
1
0
0
2
0
1
1
1
0
0
1
2
2
0
1
1
1
0
0
1
0
0
1
1
0
0
1
1
0
1
1
2
1
0
2
2
2
1
0
0
0
0
2
0
1
1
0
1
0
1
1
1
0
1
0
0
0
1
0
2
2
1
1
1
2
1
0
2
1
1
0
0
0
1
9
0
2
0
1
0
1
1
0
2
0
1
1
0
2
1
0
0
0
1
2
0
1
0
2
1
2
1
1
2
1
1
0
0
1
1
1
0
1
0
1
0
0
0
1
0
1
1
1
1
1
1
1
1
0
2
0
1
1
1
1
1
1
0
0
0
0
0
2
2
0
2
0
1
0
1
2
2
0
0
0
0
0
2
1
2
1
1
1
1
0
2
1
1
0
2
1
0
2
1
2
3
2
1
0
1
0
0
0
0
2
1
2
1
1
1
0
1
2
1
0
0
2
2
1
1
0
0
1
0
1
0
0
0
1
1
1
1
0
0
2
1
1
1
0
0
0
0
2
1
2
0
0
1
0
1
1
0
0
1
0
1
0
2
2
1
2
2
1
1
1
0
2
2
1
0
0
2
2
0
1
2
1
5
0
2
0
1
0
1
2
1
0
2
0
1
1
1
2
1
1
1
0
1
0
0
2
0
1
0
1
1
0
1
0
1
2
1
2
1
1
1
2
0
0
0
1
1
1
2
1
0
0
1
1
2
0
0
1
1
1
1
1
2
1
1
1
0
0
3
0
0
0
1
2
1
2
0
0
0
1
1
0
0
1
4
1
2
1
0
0
1
2
0
1
0
3
1
1
0
1
1
0
0
0
1
0
1
1
2
0
2
2
1
1
0
2
0
0
0
0
1
0
1
1
1
0
0
0
0
2
0
2
1
1
2
1
0
1
2
1
2
1
2
0
2
2
2
1
1
0
1
1
1
1
0
2
1
1
1
1
1
1
0
1
0
0
0
1
1
0
0
2
1
1
0
1
2
1
1
0
2
0
0
2
1
2
1
0
0
0
1
0
1
1
0
1
1
0
1
0
1
0
1
1
1
0
3
1
2
2
0
0
2
1
0
0
0
1
1
0
1
2
0
1
0
1
0
1
0
0
1
0
2
0
0
0
0
2
2
0
0
2
2
0
1
1
2
0
1
1
0
0
0
0
1
0
1
1
0
0
1
0
0
1
1
2
1
0
1
1
1
0
2
0
0
2
1
0
1
0
0
1
1
1
1
1
1
1
1
0
1
1
0
3
0
0
1
0
2
0
1
0
2
1
1
2
1
0
2
1
1
1
1
1
1
0
2
1
0
0
1
0
0
0
1
1
1
2
0
0
0
1
0
2
0
0
1
0
0
2
2
2
1
1
0
1
0
2
1
2
1
1
0
1
0
1
2
1
1
0
1
0
1
1
2
1
1
1
0
2
0
2
1
0
0
4
0
0
1
1
1
0
2
0
0
0
1
1
1
0
2
1
3
1
0
0
1
1
0
0
0
0
0
0
1
0
1
1
2
1
1
2
2
2
1
2
1
1
2
2
0
0
1
0
1
0
0
2
1
0
1
0
1
0
1
1
3
1
1
3
0
0
2
1
2
2
0
1
1
1
0
0
1
2
1
1
1
0
0
0
1
0
0
2
1
2
1
0
0
0
0
1
1
1
1
2
1
0
0
1
2
2
2
0
1
0
1
0
1
2
1
0
4
1
1
3
0
1
2
1
2
0
2
1
0
2
0
1
1
0
1
1
2
0
0
1
1
0
2
1
1
0
2
2
0
2
1
1
1
0
0
1
2
0
1
0
0
1
1
1
0
0
0
0
1
1
2
1
0
2
2
0
0
1
0
0
2
0
0
1
0
0
2
1
0
0
2
0
0
0
0
0
0
1
1
1
0
2
0
0
1
2
2
0
1
0
1
0
1
1
1
2
0
1
0
0
2
0
0
0
2
1
0
1
0
0
1
0
1
0
0
1
1
0
1
1
0
1
1
1
0
0
1
1
1
0
3
0
0
2
1
0
2
0
1
0
2
1
0
0
1
1
2
1
1
2
2
0
0
1
0
0
0
2
2
0
1
0
2
1
2
0
0
2
2
0
1
3
1
2
0
0
1
1
0
1
1
1
0
1
1
0
0
1
0
1
2
2
1
2
1
1
1
0
1
0
1
2
1
1
0
1
1
1
1
0
1
0
0
2
1
2
2
1
2
2
1
1
1
1
1
1
2
1
1
1
0
1
1
1
3
0
1
1
1
2
2
2
2
0
0
0
2
1
0
0
0
1
1
0
0
1
1
0
0
2
2
0
1
0
0
1
0
1
0
1
1
2
2
0
0
0
1
0
2
1
1
0
0
1
0
2
1
1
0
1
1
2
2
1
0
1
1
1
1
2
1
2
0
1
0
0
2
1
1
1
1
0
0
1
0
0
0
1
2
0
2
2
0
2
1
1
2
0
0
0
1
1
0
0
1
2
0
0
3
0
2
0
0
2
1
1
0
1
2
1
2
0
0
0
1
1
1
0
0
0
0
0
2
0
3
1
1
0
0
0
0
0
0
0
2
2
0
0
2
1
1
0
1
1
0
0
1
1
1
0
1
1
2
1
0
2
1
2
0
0
0
1
0
0
0
1
1
1
0
1
2
0
0
3
2
1
0
2
0
1
2
0
0
0
0
1
1
1
1
0
0
2
1
0
0
1
2
0
0
2
2
0
2
0
2
0
2
0
2
0
0
1
0
0
1
2
0
0
0
1
1
1
1
1
1
2
1
0
1
0
0
0
2
0
1
1
0
1
1
0
2
1
0
1
0
2
1
1
0
0
1
1
0
1
2
2
0
1
0
0
1
2
0
2
0
2
0
1
2
1
1
1
0
0
1
0
1
1
0
1
1
0
1
1
2
1
1
1
0
1
0
0
0
1
2
0
0
2
1
1
1
2
0
2
0
0
1
0
1
2
2
1
2
0
1
2
1
2
2
0
2
0
0
0
0
2
1
1
1
0
2
0
0
0
1
1
0
0
0
1
1
1
1
2
1
0
1
1
1
0
1
0
1
2
2
0
1
2
0
0
0
0
0
0
2
0
1
1
1
1
1
1
0
0
1
0
0
1
1
1
1
0
2
0
2
2
1
0
0
2
1
0
2
2
0
0
0
1
1
0
1
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
1
1
1
0
1
0
2
2
0
1
0
0
0
3
0
2
1
0
2
1
0
4
0
0
2
0
2
0
1
0
0
0
1
0
0
1
2
0
1
2
2
2
0
0
2
0
1
0
0
0
0
1
1
0
1
0
0
0
1
2
1
0
2
2
1
1
0
1
1
1
0
1
2
1
1
2
0
0
0
1
0
2
1
1
2
2
2
0
0
0
1
1
1
0
2
1
0
1
1
2
1
2
0
0
0
1
0
1
2
0
2
2
1
1
1
0
1
1
0
2
1
2
2
1
0
2
1
1
0
0
1
1
1
0
2
2
0
1
0
1
1
0
1
1
1
2
2
1
1
2
1
1
2
0
2
0
0
2
0
1
1
0
0
1
1
0
1
0
1
0
0
0
2
1
2
2
0
0
1
2
1
1
0
1
1
2
2
0
1
2
0
0
1
1
1
2
2
2
1
1
1
1
2
1
0
2
1
2
2
3
2
0
1
2
2
1
1
0
1
0
1
1
1
0
1
0
0
0
0
1
1
2
2
1
0
0
2
1
0
2
1
1
0
1
0
0
0
0
1
0
1
1
1
1
1
0
0
2
0
1
1
0
2
0
1
1
0
1
2
0
0
1
0
1
1
1
2
2
0
1
2
1
2
0
0
0
1
0
2
1
1
1
0
0
1
2
1
0
1
1
0
1
0
1
1
1
0
2
0
1
1
1
0
0
1
1
2
1
2
1
0
2
0
1
0
2
1
1
0
1
0
1
1
0
1
1
2
2
1
1
0
1
2
2
1
2
1
2
1
0
2
0
1
0
0
1
0
3
1
1
0
1
0
0
2
1
2
1
0
0
0
0
0
1
0
1
1
0
1
2
1
1
2
1
0
1
2
0
0
0
0
0
2
0
1
2
0
1
0
0
0
0
0
1
1
1
0
2
1
0
1
0
0
2
0
1
0
0
0
0
1
0
0
0
0
2
0
1
0
1
1
0
1
2
2
0
0
0
1
1
0
1
2
0
0
1
0
1
0
1
1
2
0
0
2
1
1
2
2
1
0
1
0
1
1
1
0
2
2
1
2
0
1
1
1
1
0
1
0
1
0
0
1
0
0
2
0
2
0
1
2
0
0
0
1
0
2
0
0
0
2
0
0
2
0
1
1
0
1
1
0
1
2
2
1
3
1
1
2
0
3
1
0
1
2
1
1
0
0
1
1
1
1
0
0
1
1
0
1
1
0
1
1
0
1
2
2
1
0
0
1
1
0
0
1
0
0
2
1
1
2
2
0
4
1
0
2
1
2
1
1
0
1
0
1
0
1
0
0
2
0
1
0
1
1
1
1
1
1
0
1
2
1
1
2
1
2
0
0
1
2
0
0
2
2
1
0
0
2
2
2
1
1
0
2
0
0
0
0
2
1
1
1
0
2
1
0
1
3
2
1
1
1
1
0
1
1
1
0
0
1
0
1
0
1
2
0
0
2
0
3
1
0
0
0
0
1
1
0
0
2
0
1
1
0
0
2
1
1
3
1
0
1
1
0
0
0
0
2
1
0
0
0
0
1
1
2
1
0
1
1
2
0
0
1
1
0
0
0
2
1
2
1
0
0
2
0
0
0
2
2
0
1
2
1
3
0
0
3
1
2
1
0
1
1
0
0
1
1
0
0
1
0
1
1
0
2
1
1
0
0
1
0
0
1
0
0
0
2
1
1
1
0
1
2
1
1
1
0
0
0
2
0
2
0
1
2
1
1
0
0
2
1
1
1
1
1
1
2
2
1
0
0
1
1
1
2
1
0
1
1
0
0
1
3
1
1
2
1
3
2
2
1
0
2
2
0
1
1
1
0
1
0
0
1
1
2
2
0
1
1
0
0
1
2
2
0
1
1
0
0
0
1
1
0
1
1
0
3
2
0
1
2
2
1
1
0
1
1
2
1
1
0
1
1
1
2
3
0
1
1
1
1
1
0
1
0
0
1
2
1
0
2
1
2
1
1
0
1
0
0
2
1
1
0
1
0
0
2
0
0
2
1
2
1
0
0
2
2
1
0
1
0
0
1
2
2
2
2
2
0
0
1
1
0
1
1
1
1
1
1
2
0
0
2
1
2
0
1
0
2
0
1
1
1
1
2
2
1
1
2
1
0
1
1
0
1
0
1
2
1
1
1
2
0
0
1
0
2
0
1
0
0
0
2
1
1
0
1
1
1
2
1
0
1
1
2
0
1
2
2
1
0
1
0
0
2
0
1
1
0
1
2
0
1
0
2
1
2
0
1
1
1
1
2
0
1
1
1
2
0
0
1
2
0
1
0
2
1
1
1
0
0
1
1
1
0
0
2
0
1
1
1
2
2
2
1
1
2
1
2
1
1
1
1
0
1
1
0
1
0
1
1
0
1
1
1
0
0
1
2
1
1
1
0
1
2
1
1
3
1
0
1
0
1
1
1
0
1
1
0
0
0
2
1
0
0
0
1
1
2
0
0
0
0
2
1
1
1
1
0
1
0
2
1
0
0
1
0
2
1
1
0
1
2
1
1
0
2
0
2
0
1
1
1
0
2
1
2
2
1
3
1
1
0
2
2
2
2
1
0
1
1
1
1
1
0
1
1
1
1
1
1
1
0
1
0
0
3
3
0
0
0
1
0
0
0
1
1
1
1
0
1
0
1
0
0
0
1
2
1
1
0
1
1
1
1
1
1
0
0
1
2
0
0
1
1
2
0
1
1
0
2
0
0
0
1
2
0
1
1
0
1
5
2
1
1
1
2
0
0
1
0
1
1
1
1
1
1
0
0
1
0
1
0
0
2
1
1
2
1
0
0
2
1
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
1
0
1
2
1
1
0
1
1
2
0
1
2
1
1
0
2
0
0
1
2
2
0
2
1
0
2
1
1
2
0
1
1
1
0
0
1
2
2
1
1
2
2
2
1
1
1
1
0
3
1
0
0
1
1
1
0
0
2
0
1
0
0
1
1
1
2
1
0
2
1
0
1
0
2
2
1
0
1
0
1
0
0
0
2
1
0
0
1
1
0
0
0
1
2
4
1
1
2
1
1
0
0
0
0
2
2
1
0
1
1
1
1
1
0
1
2
2
3
1
0
2
1
2
0
2
0
1
0
0
1
1
0
0
1
1
1
0
1
3
0
1
0
0
0
1
1
0
1
1
1
1
2
2
1
0
0
1
0
1
0
0
0
1
2
1
1
1
0
1
0
1
0
0
2
1
1
1
1
0
0
1
0
2
0
0
2
1
1
1
2
1
0
2
0
1
1
0
1
1
0
0
1
0
1
2
2
0
0
3
2
1
0
0
0
1
1
1
2
0
2
2
1
3
0
0
1
2
0
1
0
1
0
2
0
3
2
2
1
1
1
1
0
1
1
2
0
0
1
2
1
1
0
1
0
2
1
0
3
3
1
1
1
2
0
1
1
2
1
0
1
1
2
2
2
1
0
0
1
2
2
1
0
1
0
1
0
1
0
0
0
2
2
0
2
1
1
2
0
1
2
2
0
2
1
1
2
1
0
1
0
1
0
1
1
0
0
0
1
4
1
1
2
2
0
0
0
1
1
1
1
0
1
2
0
1
1
1
1
0
0
0
0
2
1
2
0
2
0
2
1
0
0
0
0
1
1
1
1
2
1
2
0
1
1
0
0
0
6
2
2
0
1
0
1
2
1
1
0
0
1
1
2
0
1
0
1
0
2
2
0
3
0
0
1
1
1
1
0
1
1
2
0
2
2
1
2
1
2
1
2
0
1
2
1
1
0
1
1
2
2
1
0
1
0
1
1
1
0
0
0
0
0
2
1
1
1
1
0
2
1
1
1
1
4
1
0
1
0
2
0
1
0
1
0
1
1
1
0
1
0
1
2
2
1
1
1
0
1
1
0
1
1
0
0
0
1
0
1
2
0
0
0
1
1
0
2
0
2
0
0
1
1
0
2
0
1
0
1
0
0
0
0
2
2
0
2
2
0
1
1
1
1
0
1
1
2
1
0
1
0
1
0
0
0
1
1
0
1
2
0
2
0
2
0
0
2
0
2
2
0
1
2
1
0
1
0
0
2
0
1
1
1
1
2
2
0
1
1
1
0
1
1
1
2
3
2
1
1
1
2
1
2
1
1
1
2
1
0
1
0
2
0
2
2
0
0
1
0
0
1
1
0
1
1
0
0
1
2
0
0
0
2
1
0
1
1
1
1
2
1
0
0
0
0
1
0
0
0
0
1
1
0
1
3
1
0
0
0
2
1
1
1
0
0
1
0
1
2
2
2
0
2
1
0
2
1
1
1
0
0
1
1
1
0
0
0
0
1
0
1
2
0
0
0
1
2
2
0
0
2
1
2
1
2
2
1
1
0
0
1
1
1
1
1
1
0
2
1
0
0
0
2
0
1
1
0
1
0
0
1
2
0
2
2
0
1
1
2
1
0
2
0
2
1
0
1
3
1
0
2
1
1
2
0
1
2
2
0
1
2
1
1
1
0
0
2
2
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
1
1
0
0
0
0
0
0
2
1
1
0
0
1
1
0
0
1
0
1
1
1
1
1
1
1
0
1
2
0
1
2
2
1
0
1
1
2
0
0
1
0
0
0
0
1
0
2
0
0
0
1
1
3
2
1
2
2
0
1
2
1
1
1
0
0
0
0
0
0
2
0
1
1
1
0
1
1
1
0
2
2
2
1
0
1
0
0
0
2
0
0
0
1
0
1
2
0
0
0
2
0
2
0
1
0
1
2
0
2
0
0
1
0
1
1
1
1
1
1
0
1
0
1
2
2
0
1
0
0
0
1
0
0
0
2
1
0
0
0
1
2
2
1
0
1
0
1
2
0
1
1
0
1
2
0
1
1
1
1
2
0
0
1
2
2
2
1
1
0
1
2
2
0
0
1
0
0
1
0
1
1
0
0
1
1
0
2
0
1
0
2
1
0
0
2
1
1
0
0
0
0
2
1
2
1
0
1
1
0
2
1
0
0
0
0
1
2
0
1
1
2
0
1
1
2
1
1
1
2
1
1
1
1
1
1
1
2
1
1
1
1
2
1
1
0
1
2
2
0
0
2
0
1
1
0
1
1
2
1
2
1
1
1
0
0
0
1
1
2
1
1
0
1
0
2
0
3
0
1
0
1
2
1
0
3
0
0
0
0
0
0
0
1
0
2
1
2
0
0
0
2
3
1
3
1
2
2
0
1
0
0
2
0
0
0
1
1
0
1
1
1
0
0
0
0
1
2
1
1
1
0
1
1
1
0
1
2
0
3
2
1
1
1
0
1
1
2
1
2
1
3
0
2
0
0
1
0
1
1
1
1
1
2
0
0
2
2
3
0
0
0
0
0
2
0
1
0
2
2
0
0
2
1
1
1
0
0
0
1
0
2
0
2
0
1
2
1
1
1
3
0
0
0
1
1
0
1
0
2
1
2
0
0
2
2
0
2
2
2
0
0
1
0
0
2
1
1
0
0
1
0
1
1
4
1
0
1
2
1
1
1
1
1
1
1
0
1
1
1
0
1
1
2
0
2
1
0
0
2
0
0
1
0
0
1
0
1
2
2
2
1
0
1
0
0
2
2
0
0
0
2
1
1
1
2
0
1
0
1
1
1
2
1
0
1
1
0
3
1
1
1
2
1
1
1
1
0
1
1
1
2
1
0
0
2
1
2
2
0
1
2
0
0
0
1
1
0
2
1
0
2
0
0
0
0
0
1
0
0
0
1
4
1
1
0
1
0
0
1
0
1
1
2
1
2
0
1
2
1
1
1
2
0
2
0
1
1
0
2
1
1
0
1
1
0
1
2
0
2
0
1
1
2
2
2
1
0
0
0
1
0
0
1
1
2
1
0
2
1
0
0
1
1
1
1
1
1
1
1
0
1
1
0
0
2
3
0
0
2
1
1
0
1
2
2
0
0
1
0
2
0
1
0
1
0
1
2
1
1
0
1
0
0
0
2
3
1
1
0
2
0
0
0
2
2
0
1
1
0
1
0
0
1
0
0
0
1
1
1
2
1
0
0
0
0
1
0
2
0
1
1
0
0
1
1
2
1
2
1
2
2
1
0
0
0
0
0
1
2
1
0
0
1
1
2
1
0
1
2
0
2
2
1
0
0
0
1
1
5
1
2
1
2
0
0
0
0
2
1
0
0
1
1
1
1
1
1
2
0
0
2
2
0
2
0
2
1
0
2
0
2
1
0
1
0
0
0
0
1
1
1
0
0
2
0
1
2
0
0
1
0
1
0
3
2
1
0
1
0
2
0
1
1
0
1
2
2
0
0
2
0
2
2
1
0
1
1
1
0
2
0
5
0
1
2
0
2
2
1
2
0
0
0
1
0
1
0
0
1
1
0
1
1
0
1
0
0
0
1
0
3
0
1
2
0
0
1
1
1
1
0
1
2
2
1
0
1
1
2
1
0
0
2
0
0
1
0
1
0
1
0
2
0
2
1
1
0
1
0
1
1
1
0
0
0
0
1
0
1
0
2
1
1
2
0
1
0
0
2
1
1
0
0
1
1
0
0
0
2
1
1
2
1
0
0
1
0
1
1
0
2
1
2
2
0
1
0
0
0
2
2
4
1
0
1
1
2
2
1
2
2
0
1
2
1
0
0
1
2
1
0
0
2
2
0
2
0
1
0
1
1
1
1
0
0
0
2
2
0
1
0
1
0
0
1
1
1
0
2
1
0
0
2
2
2
0
0
1
0
2
1
2
0
0
1
0
1
2
1
0
1
0
2
1
1
0
1
2
2
1
1
0
2
2
1
0
1
2
0
0
1
1
0
2
0
2
0
1
1
2
1
1
0
1
1
0
1
0
0
1
2
1
0
1
1
2
2
0
0
1
0
11
0
0
0
2
1
2
0
1
1
0
0
0
0
1
0
0
1
0
0
2
2
1
0
1
0
0
2
2
1
0
0
0
2
3
0
2
1
1
0
0
1
1
0
3
0
0
0
2
0
0
1
1
0
1
2
0
1
0
1
2
0
2
0
0
1
2
1
2
0
1
2
2
1
1
1
1
0
1
2
2
1
0
1
2
1
0
2
3
0
1
1
1
0
1
2
1
0
1
1
0
0
1
1
0
2
1
0
1
2
1
0
0
0
1
1
1
1
1
0
0
1
2
0
0
1
1
0
0
2
0
1
2
0
1
1
0
0
1
0
1
0
1
0
1
1
0
2
0
1
1
0
0
0
2
1
1
0
0
1
2
0
1
2
0
2
0
1
1
1
0
1
1
0
1
1
0
0
2
0
2
0
1
1
0
0
0
2
0
1
0
0
0
1
0
0
1
1
2
0
0
1
2
2
1
1
0
0
1
2
0
0
0
1
0
0
1
0
0
2
1
1
2
2
1
2
0
0
0
2
2
1
2
1
1
1
0
2
0
1
2
2
0
1
2
1
0
1
0
1
1
1
1
1
2
0
1
1
1
0
1
1
1
1
1
2
0
1
2
0
1
1
2
2
1
0
1
1
2
1
1
2
2
2
1
1
1
1
0
1
1
1
0
1
0
0
2
0
0
2
0
0
1
0
0
0
0
0
2
0
2
2
1
0
1
2
0
0
2
0
0
0
0
0
4
1
1
1
1
1
0
0
1
0
0
0
1
4
1
1
2
2
0
0
1
0
0
1
0
0
0
0
0
1
2
0
2
1
0
1
1
0
0
1
0
2
2
0
0
1
0
1
1
0
2
2
0
2
1
0
0
0
0
1
2
2
1
2
0
2
0
1
4
2
2
2
2
0
2
1
0
0
0
0
0
0
1
0
1
0
2
0
0
2
1
2
2
0
2
2
1
0
2
1
0
1
2
2
1
2
1
0
1
1
2
0
1
0
1
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
1
1
1
1
3
0
1
1
1
1
1
1
1
3
2
1
1
2
2
2
1
0
1
2
1
2
1
1
0
1
0
1
2
1
2
1
3
0
2
2
0
1
2
1
1
2
1
0
2
2
1
0
2
1
0
2
1
0
0
0
1
1
2
0
1
1
0
2
0
2
2
1
2
2
1
1
0
0
1
1
0
2
1
1
2
1
1
0
1
0
0
2
1
1
1
0
1
0
0
0
1
0
1
0
2
2
2
1
1
0
1
1
0
0
0
0
0
0
1
2
1
2
0
1
0
0
2
0
0
0
1
2
0
2
0
0
1
1
1
0
1
2
0
0
1
1
1
0
2
1
0
2
0
0
0
0
3
1
1
1
1
0
0
1
0
2
0
0
0
0
2
0
1
1
0
1
3
0
0
1
0
0
0
0
2
2
1
0
1
0
1
0
0
0
1
0
2
0
1
1
1
0
1
0
0
1
0
1
0
1
0
1
2
1
2
1
1
0
2
1
1
2
0
0
1
1
0
2
2
1
1
1
2
1
2
1
1
0
1
1
0
1
0
0
1
2
0
1
0
1
0
2
0
1
0
2
1
0
0
1
1
0
1
2
1
2
2
0
1
1
0
2
1
0
1
2
1
1
0
1
1
0
2
1
0
1
1
1
0
2
1
0
1
0
2
0
0
2
1
1
0
0
2
1
0
0
0
2
2
1
0
1
1
0
1
0
1
1
1
1
2
0
0
1
2
1
2
1
0
0
1
1
2
0
0
0
1
0
0
1
1
0
0
2
0
0
1
1
0
0
1
0
1
2
1
1
8
1
1
1
0
2
1
0
0
2
2
2
1
2
0
1
1
2
2
1
1
1
1
1
0
0
2
1
1
0
0
2
1
2
2
4
0
1
0
0
1
0
2
1
2
1
1
2
0
2
3
0
1
1
2
0
1
0
2
0
0
0
1
0
2
0
1
2
0
0
0
1
0
0
0
0
0
0
1
2
2
1
0
2
1
0
0
0
0
1
1
1
1
0
0
0
1
1
2
1
2
0
0
0
0
1
0
1
0
1
1
0
1
1
0
1
1
1
2
2
2
0
2
2
1
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
1
1
1
2
1
0
0
1
0
2
0
1
1
1
0
2
0
2
2
2
2
1
1
1
0
3
2
0
1
0
1
0
1
0
1
2
1
0
1
0
0
0
0
0
1
1
1
0
0
2
1
2
1
0
1
2
2
1
0
1
2
1
0
0
2
1
1
0
0
2
3
1
0
1
2
1
1
0
1
1
1
2
2
0
1
2
0
0
0
0
2
0
1
4
0
2
0
1
2
2
1
2
2
2
1
0
1
0
1
0
0
1
1
1
0
0
2
0
0
2
1
0
1
0
0
0
2
0
1
0
0
1
1
1
2
0
1
2
2
1
2
0
0
2
2
2
1
0
2
1
1
1
1
1
0
1
0
1
1
0
1
1
1
0
0
2
1
1
0
0
0
0
0
2
0
3
2
0
2
1
2
0
1
2
1
1
0
1
2
2
0
1
1
1
0
0
0
0
2
1
1
0
2
0
0
2
1
0
2
0
0
0
2
0
0
0
1
0
0
1
1
1
0
2
2
1
1
0
1
2
0
1
1
1
0
0
1
0
1
0
1
1
0
0
2
2
0
0
2
0
2
0
1
2
0
0
0
0
1
0
2
1
2
2
2
0
0
0
1
0
2
1
2
2
2
1
0
0
1
1
1
0
1
0
0
2
0
0
2
4
0
2
1
0
1
0
1
2
2
1
0
0
1
0
1
0
0
2
0
1
0
1
0
0
2
1
2
1
2
2
2
1
2
0
2
0
0
1
0
2
3
1
1
2
0
0
1
0
2
0
2
1
1
1
2
2
1
2
0
0
0
1
1
2
1
0
1
1
2
1
2
1
1
1
1
2
1
0
1
2
0
1
2
0
1
0
1
0
1
1
1
0
0
1
1
2
1
0
0
2
2
0
1
3
1
1
0
1
0
2
0
0
1
0
2
1
0
2
2
1
0
1
0
2
0
1
2
1
1
0
0
2
0
0
1
1
0
0
0
1
2
1
0
1
1
0
1
1
0
1
1
2
4
1
0
1
0
2
0
0
0
1
1
0
1
1
1
1
3
0
2
0
1
0
1
0
0
0
2
2
0
0
0
0
1
1
0
1
1
1
0
0
0
1
0
0
0
0
1
1
1
1
0
1
0
0
1
1
0
2
0
0
2
1
1
1
2
0
0
1
0
0
0
0
1
1
0
0
2
0
1
1
1
0
0
3
0
1
1
1
1
1
0
0
1
0
0
0
2
1
0
0
0
2
1
1
0
0
0
2
1
0
1
0
0
1
2
1
2
1
0
4
0
1
1
0
0
1
1
0
0
1
1
0
1
2
0
2
1
1
1
1
1
1
1
0
0
1
1
0
0
2
0
1
2
2
1
1
0
1
0
1
0
1
1
0
2
1
0
0
2
1
0
0
0
0
0
1
0
0
2
1
1
0
1
0
0
1
1
0
2
1
0
1
0
2
1
1
0
1
2
0
2
1
0
1
0
2
1
1
1
2
1
1
0
1
1
0
2
2
0
1
0
1
1
1
2
2
1
2
0
1
2
0
0
1
0
0
1
0
0
0
1
1
1
0
0
1
0
1
1
1
1
1
0
2
0
1
2
1
2
1
1
2
1
1
0
0
1
1
0
1
0
1
1
1
1
1
1
1
0
1
1
1
1
0
0
2
2
1
0
0
1
1
1
1
1
1
0
1
0
0
2
2
1
0
1
0
1
2
0
2
0
1
0
1
0
1
1
2
2
1
0
1
1
0
2
0
0
1
1
1
1
1
1
2
2
2
0
2
1
1
0
1
1
2
1
1
2
1
1
1
0
0
1
1
1
2
1
0
2
2
2
0
0
0
1
1
1
2
2
1
0
2
0
0
0
1
1
0
2
0
0
0
1
1
0
2
1
1
1
1
2
1
2
0
2
2
1
1
0
2
1
1
1
0
2
1
1
1
2
0
0
2
1
0
0
2
0
0
1
1
0
1
1
2
1
1
3
2
1
1
1
2
1
0
1
1
0
0
0
1
2
0
0
1
0
0
1
0
0
1
0
0
0
1
1
0
2
0
1
1
2
0
1
2
0
1
1
1
1
0
2
0
0
2
1
1
2
2
0
1
2
2
1
1
0
0
1
0
0
1
2
0
2
0
0
1
1
1
1
0
1
1
2
1
6
3
1
0
1
0
1
1
0
0
0
2
1
0
0
0
0
1
1
2
1
0
2
1
0
1
1
0
0
1
1
0
1
1
1
1
1
1
0
0
0
0
2
1
0
2
2
1
0
2
0
1
1
0
1
2
1
0
0
1
0
0
0
2
1
2
0
1
2
3
2
0
0
1
1
0
0
0
2
2
1
0
0
0
1
0
1
2
2
1
0
1
2
2
1
2
1
3
2
0
1
1
1
0
1
1
1
2
1
2
1
0
1
0
1
0
1
1
1
0
1
1
0
0
3
1
1
2
1
1
0
0
2
1
0
0
0
1
0
1
1
2
2
0
0
1
2
2
0
1
1
0
1
2
0
0
0
0
2
0
3
0
0
1
3
0
1
1
1
1
0
0
1
0
2
2
2
1
1
0
0
0
2
2
1
0
0
1
1
2
0
1
2
1
0
0
1
1
0
1
1
0
2
2
2
1
0
0
0
1
4
0
1
1
0
0
0
1
2
2
0
0
1
1
0
2
1
1
1
1
0
1
0
0
1
1
2
0
1
2
0
0
1
1
0
0
1
1
0
1
1
0
1
0
2
0
1
1
1
0
0
1
2
1
1
0
2
2
0
1
1
1
1
1
0
1
2
1
1
2
0
1
0
1
0
1
0
1
1
0
1
3
0
2
0
2
0
1
0
1
2
1
0
2
1
0
1
1
1
1
2
0
0
1
0
0
1
1
1
4
0
2
2
2
2
1
2
2
0
2
1
1
1
2
1
1
1
3
1
2
0
0
1
2
1
2
1
1
1
1
2
1
1
1
1
0
2
1
1
0
0
2
1
1
1
1
2
1
1
1
0
1
0
1
2
2
0
1
2
0
2
1
4
1
0
1
1
0
1
0
0
1
2
0
1
0
1
0
1
0
1
2
0
0
0
1
0
2
1
4
1
0
0
0
0
2
3
0
0
0
0
2
0
1
1
1
1
2
1
1
2
1
2
0
1
0
1
1
1
1
0
2
0
0
1
0
1
1
2
2
1
0
2
1
0
0
1
1
1
1
0
2
1
0
1
1
2
1
2
0
1
0
2
0
0
0
2
1
1
0
1
1
1
0
0
1
2
1
1
1
2
1
0
1
0
2
0
1
1
0
1
1
1
0
1
1
0
2
1
1
0
1
1
1
0
1
1
0
2
2
1
1
0
3
0
0
2
2
1
0
0
1
0
2
1
0
1
1
2
2
0
0
2
2
1
1
1
0
1
1
1
1
2
0
2
1
1
4
1
1
1
1
1
2
2
0
1
2
0
2
0
0
1
1
1
0
0
1
1
0
1
1
0
0
2
1
0
0
0
1
0
2
1
2
1
1
0
2
2
1
1
1
0
1
1
0
2
0
1
0
2
0
1
1
1
1
0
2
2
2
0
1
1
1
1
0
1
0
2
1
2
2
1
2
0
0
1
2
0
1
2
0
0
0
2
1
1
0
2
2
0
1
0
1
2
1
1
1
0
2
2
0
0
0
2
1
0
0
0
1
1
0
0
0
0
0
1
1
2
0
0
6
1
2
1
1
1
2
1
1
0
1
2
0
0
0
0
1
0
0
2
0
0
1
2
1
1
1
0
1
2
0
2
2
1
0
0
0
2
2
1
1
1
1
1
1
1
2
0
1
0
0
0
0
1
1
1
1
0
0
0
1
1
2
2
1
0
0
0
1
1
1
1
1
0
0
0
0
2
0
1
0
0
1
0
1
0
0
1
1
0
0
2
2
2
3
0
0
1
2
0
0
1
1
2
1
2
0
2
0
1
2
1
5
1
1
1
2
0
1
1
1
1
0
1
2
2
0
2
0
2
1
1
0
1
2
0
0
0
0
1
0
1
0
1
1
0
2
0
1
3
2
0
1
1
1
0
0
1
1
0
1
1
2
1
0
0
2
0
2
2
0
1
0
0
0
1
1
0
2
0
1
0
0
2
2
1
0
0
0
2
2
0
1
1
1
2
1
0
1
1
1
1
2
2
0
1
2
1
2
0
1
1
1
0
1
2
2
1
1
2
1
2
2
0
1
1
0
1
1
0
1
2
1
1
1
0
1
1
0
1
1
2
1
1
2
0
0
1
1
0
1
4
2
1
2
0
1
1
1
0
2
1
0
2
2
2
2
2
0
1
2
1
1
0
2
0
0
1
1
0
0
0
0
1
1
0
2
1
1
1
1
1
1
0
0
1
2
1
0
1
1
2
1
0
0
1
0
2
1
0
0
1
2
2
2
1
1
0
0
1
2
1
0
0
1
1
2
1
1
1
0
1
0
0
1
1
2
1
1
1
2
1
2
1
2
0
2
1
0
1
2
0
1
1
1
2
2
2
0
0
0
2
0
1
2
2
1
0
0
2
0
6
0
1
1
2
2
1
1
1
2
0
0
2
1
1
1
0
1
1
0
1
2
0
0
2
0
0
1
1
1
1
1
0
2
0
1
1
1
1
0
1
0
0
2
1
0
1
0
0
0
0
1
1
1
1
0
2
2
0
2
1
1
1
1
2
0
1
2
1
5
1
0
1
2
1
3
1
0
1
0
1
2
1
1
0
1
0
0
0
1
1
1
1
1
0
1
1
0
0
1
0
1
2
0
2
1
1
2
0
0
2
0
0
0
1
2
0
4
2
1
0
0
0
2
0
2
2
1
2
0
0
2
1
1
2
0
0
1
1
1
2
2
2
1
1
2
0
1
1
0
0
1
1
2
2
2
1
2
2
0
2
2
4
2
1
1
1
0
2
2
0
2
0
0
3
1
1
0
2
1
0
1
0
1
3
2
0
0
0
0
2
1
2
1
1
1
1
0
0
2
4
0
0
0
0
0
0
2
2
1
0
0
2
0
1
1
1
1
1
1
1
2
0
0
3
0
0
1
0
2
0
0
1
1
1
2
1
1
0
0
1
0
0
1
1
0
1
5
1
2
1
2
1
1
1
0
1
0
2
1
1
1
1
1
0
0
0
0
2
2
2
1
1
2
1
1
2
2
1
2
2
2
1
2
0
2
0
2
1
0
2
2
0
1
1
0
1
1
1
0
1
2
0
1
2
1
0
0
0
1
1
0
1
2
1
2
0
0
2
2
1
1
2
0
0
2
0
0
1
2
0
2
4
1
0
1
0
1
1
0
0
0
2
0
0
0
2
0
1
0
1
0
1
1
1
0
0
1
2
1
1
2
1
0
0
0
0
2
2
1
1
0
2
0
2
0
0
0
0
0
1
1
2
0
2
0
0
1
0
2
2
0
0
2
1
1
1
0
0
2
1
3
2
2
0
2
2
1
2
2
3
0
0
1
1
0
1
2
0
0
1
0
2
1
1
0
1
1
1
0
0
0
1
2
0
1
2
1
0
0
2
1
1
0
0
0
2
0
3
0
2
0
3
0
2
2
0
2
0
0
0
0
0
0
2
0
1
1
0
2
1
0
2
0
2
0
1
1
0
0
1
2
0
1
1
1
2
1
1
2
2
0
1
1
0
2
1
1
2
1
1
0
1
1
1
0
2
0
0
0
1
0
1
0
1
1
2
1
0
0
2
0
0
0
1
1
1
2
2
2
1
1
0
1
1
0
2
2
1
0
0
0
2
2
0
2
2
1
1
2
1
2
0
0
0
1
1
2
2
1
1
0
0
1
3
0
1
2
1
1
1
1
1
2
0
0
1
0
0
1
0
0
1
1
0
0
1
1
1
1
2
1
2
0
1
0
1
1
1
1
0
2
0
3
1
1
1
1
1
0
1
1
0
1
1
1
0
0
1
1
2
0
0
0
1
2
1
0
1
1
1
1
1
3
0
0
3
0
0
0
1
0
0
0
1
2
0
1
1
0
2
0
0
1
0
2
1
2
1
0
1
2
1
1
1
2
0
1
0
0
0
1
0
2
1
2
1
1
3
1
0
2
1
0
2
2
0
2
0
1
2
0
0
0
0
0
2
0
2
0
0
1
2
0
1
1
2
2
1
2
0
1
0
0
0
0
1
2
1
0
1
1
0
1
2
1
1
1
1
1
0
1
0
0
1
0
0
3
0
0
2
1
1
0
0
0
0
0
0
1
1
1
2
0
2
2
1
0
1
2
0
1
1
0
1
2
0
1
2
2
2
1
1
1
1
2
2
0
0
1
1
0
0
0
0
0
1
2
2
1
0
1
1
0
0
1
1
1
0
0
1
1
0
1
1
1
1
0
2
3
1
0
0
1
1
1
1
0
0
2
1
0
1
0
0
0
1
0
1
1
1
0
2
1
1
0
0
1
2
1
1
0
0
0
1
1
1
0
2
1
0
1
0
1
0
2
0
1
2
1
1
2
0
1
2
1
0
2
1
1
0
1
1
1
2
2
0
2
1
1
1
2
2
1
1
0
2
0
2
2
1
0
1
1
1
1
0
1
1
0
2
0
0
1
1
0
0
0
1
1
2
1
1
0
2
1
0
0
0
0
2
1
0
1
0
1
1
1
0
1
1
0
2
1
0
1
2
0
1
2
2
1
1
1
1
2
1
1
1
4
2
0
2
1
1
0
1
0
2
0
0
3
2
2
2
2
0
2
1
0
1
1
1
1
1
0
1
0
1
1
1
0
2
2
0
1
1
1
1
1
0
0
1
0
2
2
1
1
0
0
0
0
1
0
0
0
0
0
2
1
0
2
2
0
1
0
2
1
2
2
1
0
0
1
0
2
1
1
1
0
0
0
1
1
0
1
2
2
1
2
1
1
1
0
2
0
2
0
0
0
0
2
2
2
1
0
1
0
1
0
0
1
1
1
1
1
1
0
0
0
1
1
0
0
1
0
1
0
1
0
1
0
0
0
1
1
2
3
1
1
1
4
0
0
0
0
2
0
0
1
1
2
0
1
0
1
1
1
0
3
2
0
1
0
2
1
0
2
0
0
1
0
2
1
1
0
2
2
1
1
0
2
2
1
2
1
1
1
1
1
1
0
1
0
2
1
0
0
1
1
0
0
0
1
1
4
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
2
3
1
2
2
2
1
2
0
1
2
1
1
0
2
0
0
0
1
0
2
0
0
2
2
0
1
0
1
1
1
1
0
0
2
1
2
2
0
2
0
1
2
1
0
1
1
1
0
1
2
1
1
2
1
0
1
2
0
0
2
1
1
0
0
0
2
1
0
0
0
1
2
2
0
0
2
2
2
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
0
2
2
1
1
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
2
0
0
2
1
0
2
1
0
1
2
1
0
1
1
1
1
1
2
0
0
1
2
2
0
0
0
0
0
0
1
0
1
0
0
0
2
1
1
2
0
1
0
1
1
2
1
1
2
2
0
1
2
1
1
2
1
1
2
0
0
0
0
0
1
2
2
1
1
1
1
1
0
1
1
1
0
1
0
2
1
1
0
1
1
2
1
0
1
1
2
1
0
1
1
0
1
2
1
1
2
1
2
2
1
1
1
1
2
0
0
0
0
0
1
1
1
2
2
1
1
2
0
2
0
0
0
1
1
0
0
1
2
1
1
0
2
0
1
0
0
1
2
2
0
0
1
0
1
1
2
0
0
1
1
1
0
1
1
0
1
0
2
1
0
1
2
2
1
0
2
1
1
0
0
2
2
1
0
2
0
2
1
0
0
2
2
1
1
0
0
0
1
1
1
0
0
1
2
2
2
0
1
0
0
0
0
1
1
2
0
0
2
1
0
0
1
0
1
1
0
2
1
1
1
0
0
0
1
0
1
0
2
0
0
1
1
2
1
2
1
2
1
0
1
0
2
1
0
0
1
0
1
0
0
0
2
0
1
2
0
2
3
2
2
0
2
0
1
1
1
0
2
1
1
0
1
1
0
1
1
1
2
1
2
3
0
2
1
1
1
0
1
1
1
1
1
0
2
1
2
0
0
1
0
1
1
1
0
0
2
1
0
1
0
0
0
2
0
1
2
1
1
0
0
0
1
0
1
0
0
1
1
1
0
1
2
1
0
2
0
0
1
0
1
1
2
2
0
2
0
1
0
1
1
1
0
0
1
0
0
0
1
1
1
1
0
0
0
0
1
1
2
0
0
2
0
0
0
2
1
1
1
0
0
0
0
0
1
1
2
0
2
1
0
1
0
0
2
2
0
1
2
0
0
0
0
1
1
2
1
1
1
1
1
0
0
1
0
0
2
0
1
0
3
0
2
1
1
1
0
1
0
1
0
0
0
0
1
1
0
1
0
0
0
1
1
0
1
2
0
2
1
0
1
2
1
2
0
2
2
2
1
2
0
1
5
5
0
2
0
0
0
1
0
0
2
1
1
1
2
1
1
0
0
2
0
0
1
2
1
1
1
0
0
2
0
1
2
1
1
1
1
0
0
3
0
1
0
0
0
0
0
0
0
1
1
3
2
2
1
0
2
1
1
1
2
0
2
1
0
0
2
1
0
2
1
2
1
2
1
1
1
2
0
2
0
0
0
1
1
0
1
1
0
2
1
1
1
0
0
0
1
0
1
1
2
1
1
1
0
1
0
2
4
5
1
0
0
2
1
1
1
2
1
1
2
2
0
1
1
2
1
0
1
0
3
1
1
2
1
2
2
1
0
1
0
2
0
0
1
0
1
2
1
1
0
1
1
0
0
1
1
2
0
0
1
2
2
0
1
2
4
2
1
1
2
1
0
0
1
0
0
2
1
1
1
0
0
1
1
2
2
0
1
1
1
2
0
0
0
0
0
0
2
1
2
0
2
0
1
1
0
3
1
1
1
1
2
1
0
1
1
1
1
1
1
2
0
1
2
0
2
2
2
2
2
0
2
0
2
0
2
1
1
2
1
1
0
1
1
1
2
0
2
0
2
0
1
0
0
1
0
0
1
0
2
1
2
1
2
0
1
0
1
1
0
1
1
1
1
0
1
2
0
2
0
1
0
1
1
1
1
0
1
2
0
1
1
0
0
0
2
1
1
0
0
1
1
1
0
0
2
1
1
2
1
1
0
1
0
1
1
1
1
2
1
2
2
1
0
0
2
1
1
1
2
1
1
1
1
1
0
1
0
0
4
1
1
2
2
1
1
1
2
1
0
0
1
1
3
1
0
0
0
2
1
1
2
0
1
2
1
0
0
1
2
2
0
0
0
0
1
0
1
0
1
1
1
0
1
1
0
0
1
0
0
0
0
1
1
1
1
0
2
1
2
2
0
0
0
2
1
1
1
0
0
1
0
1
2
2
2
0
2
1
2
2
0
1
0
1
2
0
0
0
0
0
0
1
0
1
0
0
0
2
0
2
2
1
0
1
1
0
0
1
0
1
0
0
2
1
2
1
1
0
1
0
1
0
0
1
1
0
0
1
1
0
1
1
1
1
1
2
1
1
2
0
0
0
1
1
0
1
0
1
1
0
2
2
2
2
2
0
1
1
1
0
2
1
0
0
1
1
0
0
1
1
0
1
1
1
1
2
0
0
2
0
2
1
1
0
0
0
0
0
0
2
2
0
1
1
0
1
2
0
0
2
0
1
2
1
0
0
1
2
1
0
0
0
2
0
2
1
0
2
1
1
1
1
1
1
1
0
0
2
2
2
2
2
1
1
0
0
0
2
3
1
2
1
2
0
0
1
1
1
0
0
2
2
2
2
0
2
1
1
1
0
2
0
1
0
1
2
1
0
0
1
0
0
1
1
2
1
2
2
0
2
2
1
0
1
0
0
0
0
1
1
1
0
2
0
1
2
0
1
1
0
0
0
1
1
0
2
0
0
0
1
0
2
2
1
0
1
1
0
2
0
2
2
1
0
2
1
0
0
2
1
2
1
2
2
1
1
1
4
1
0
2
2
0
0
0
0
0
0
2
0
1
2
1
1
1
0
1
0
1
0
0
2
2
1
0
1
2
1
1
1
1
2
0
0
0
0
0
0
1
0
0
1
2
0
1
0
2
0
2
2
0
1
0
1
0
2
2
2
0
0
1
2
0
1
0
2
0
1
2
1
2
0
1
0
0
0
1
1
0
4
0
0
0
2
2
0
1
0
3
0
1
1
0
0
0
1
1
2
0
2
1
1
0
0
2
1
1
1
0
0
1
1
0
2
2
1
1
1
0
1
0
1
1
0
2
1
0
1
1
1
1
0
1
1
0
1
1
1
1
2
0
2
2
0
2
1
1
1
0
0
1
2
1
0
1
1
1
1
2
0
0
2
1
2
0
0
0
0
1
1
2
1
1
2
2
2
1
0
0
1
1
0
1
0
1
2
0
0
1
0
0
1
0
0
1
1
0
0
2
0
0
0
1
1
1
1
1
1
0
0
0
1
1
1
0
2
1
2
1
1
1
1
1
1
1
0
1
0
2
2
0
0
0
1
0
0
1
2
2
3
1
0
1
2
1
1
0
1
1
1
1
0
1
1
0
0
0
1
0
0
2
0
1
1
1
1
1
2
0
1
0
1
0
2
1
0
2
0
2
0
0
1
2
1
1
1
2
1
2
2
1
0
1
0
2
0
0
0
0
0
0
1
0
0
1
1
1
0
0
2
0
1
1
0
1
2
1
0
0
2
1
0
1
1
0
0
1
1
0
2
2
1
2
1
2
0
1
0
0
0
0
2
1
0
0
0
2
0
0
1
0
0
1
1
0
0
1
0
0
1
1
2
0
0
1
0
0
1
0
0
0
2
2
0
1
1
0
2
0
2
0
0
0
1
2
0
0
1
0
2
2
2
2
0
2
0
0
0
2
0
1
0
1
0
1
1
1
0
0
1
0
0
1
1
1
0
0
1
0
1
1
0
0
0
1
0
0
2
1
1
2
1
0
2
1
2
1
2
0
1
1
1
1
2
0
1
1
2
2
0
1
0
2
0
1
0
1
1
3
0
0
0
0
1
0
0
1
0
0
0
1
1
3
0
0
0
0
1
1
0
2
2
1
0
0
1
2
1
0
1
0
1
1
0
0
0
1
1
0
0
0
1
0
0
2
0
2
1
1
0
2
2
0
2
2
2
0
1
1
0
0
1
1
4
1
2
0
2
0
1
0
1
0
2
1
0
0
1
0
1
1
0
0
2
2
0
2
0
0
1
0
2
0
1
0
2
0
1
0
2
0
1
1
1
1
1
0
0
0
3
2
1
2
2
1
0
0
0
1
1
1
1
2
0
1
2
0
0
2
1
0
1
1
3
1
3
0
1
1
0
0
0
1
1
1
1
1
1
1
0
1
1
0
2
2
1
1
1
2
0
1
1
2
2
1
2
0
2
0
1
1
1
1
0
1
0
3
1
2
2
1
0
1
0
1
2
0
0
1
2
1
0
1
0
0
0
2
0
1
1
0
0
1
0
1
0
0
1
1
1
0
1
0
1
0
2
1
0
0
2
0
2
0
1
1
2
2
1
1
0
0
1
1
2
1
1
1
1
0
0
2
4
2
0
1
1
0
0
2
0
0
2
1
0
0
0
1
0
2
1
2
0
0
2
1
0
0
1
0
1
1
1
1
0
1
2
2
1
1
2
2
0
1
2
0
0
1
1
0
1
0
2
1
0
2
1
1
1
0
0
0
0
0
1
0
0
0
2
1
0
1
0
1
2
0
1
1
0
0
0
0
0
1
1
0
1
0
0
1
1
0
1
2
1
0
2
1
2
0
1
2
1
2
0
0
1
1
1
0
1
1
1
1
1
1
1
3
0
1
0
0
0
2
2
1
0
0
0
0
0
1
1
0
0
1
1
1
0
0
1
2
0
2
0
1
0
2
1
0
1
1
2
0
0
1
0
1
0
1
2
0
0
0
0
1
0
2
1
0
1
0
0
0
2
0
0
1
1
1
0
0
0
1
1
2
0
2
0
1
2
1
1
1
1
2
0
0
0
0
0
1
0
1
1
1
1
0
1
3
1
1
0
1
2
1
1
1
0
0
1
1
2
2
1
1
2
0
0
1
0
2
0
1
2
0
0
1
0
0
2
0
0
2
5
1
2
0
1
2
1
1
2
0
2
1
2
1
0
0
2
2
1
1
0
0
1
2
0
2
1
2
1
2
1
0
0
2
0
0
0
2
0
0
1
0
0
0
0
1
0
1
0
1
2
0
0
2
0
1
2
1
1
0
1
0
1
5
0
1
2
1
2
1
1
0
1
2
0
0
2
0
1
1
0
0
0
0
2
1
2
0
0
0
2
2
2
0
1
1
2
1
2
2
1
2
1
0
0
0
2
2
2
0
0
1
1
2
0
1
1
0
2
1
0
0
0
0
1
0
1
0
2
0
1
0
1
1
1
1
1
1
0
0
2
2
0
0
0
1
0
0
0
1
0
2
1
0
3
1
1
2
2
2
0
2
1
1
3
2
1
1
0
0
3
1
0
1
1
1
1
0
2
0
1
1
0
2
0
0
0
1
1
2
0
2
1
1
1
1
0
0
2
0
1
0
0
0
2
1
0
1
1
1
1
0
1
2
2
1
0
1
0
0
0
2
1
2
0
1
0
1
0
2
2
2
1
1
0
1
2
1
0
1
2
2
0
1
0
1
0
0
1
0
2
1
1
1
1
0
1
1
1
2
1
0
0
2
1
0
2
1
2
1
2
0
1
0
0
1
1
3
1
2
0
0
1
1
0
1
2
0
1
0
1
1
1
0
2
0
2
1
1
0
1
0
2
0
0
0
0
0
1
0
0
1
1
0
0
0
1
2
0
0
1
1
2
2
0
2
1
1
1
2
0
1
1
1
0
1
1
2
0
0
1
0
1
1
0
1
2
1
2
0
2
2
1
1
0
1
1
0
1
1
0
1
1
0
1
0
1
0
2
0
0
2
1
1
0
2
2
2
0
2
2
0
1
0
1
1
1
1
1
1
0
0
1
0
2
0
1
0
0
1
1
3
0
0
0
0
1
1
2
0
2
1
2
0
2
1
0
1
0
0
1
0
1
1
0
1
0
0
0
1
2
1
0
2
9
0
0
1
2
1
0
0
0
2
0
0
1
0
0
1
0
0
1
1
2
0
2
1
1
0
0
2
2
1
2
2
1
1
0
1
1
0
1
1
0
2
2
2
1
2
0
0
0
0
2
0
1
1
1
0
1
1
1
2
2
0
0
2
2
0
2
1
1
1
1
2
0
0
0
1
1
1
0
1
2
0
1
1
0
1
0
2
1
1
0
0
1
2
2
2
0
2
0
0
0
2
1
2
1
0
1
1
0
0
2
1
0
1
4
1
1
0
1
0
2
2
0
1
1
1
2
0
1
1
2
2
1
1
2
2
1
0
1
2
0
0
2
2
2
2
1
0
3
0
0
2
2
2
2
1
0
0
2
2
0
1
0
2
0
1
1
0
0
2
1
0
1
0
1
0
0
1
1
2
1
2
0
0
2
0
1
2
1
0
1
1
0
1
2
2
2
2
2
2
2
1
2
1
0
2
2
0
0
1
1
0
1
0
0
0
1
1
0
1
1
1
0
2
1
0
1
1
1
2
1
0
0
1
1
0
0
2
0
2
1
1
0
2
0
0
1
1
1
0
2
1
1
1
1
3
1
0
2
0
2
1
2
0
1
0
1
1
0
1
0
1
1
1
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
1
2
1
1
2
0
1
1
0
0
0
1
0
1
1
0
1
1
0
1
0
0
1
0
0
1
1
1
1
1
3
2
1
1
1
1
0
0
2
0
1
0
2
1
0
2
1
2
2
1
1
1
0
0
2
0
1
2
1
1
1
0
0
1
0
2
0
1
2
3
0
1
1
0
0
0
0
0
2
2
0
3
1
1
0
0
2
0
3
1
0
0
1
2
0
0
2
2
1
1
1
2
2
0
0
1
1
1
2
1
1
1
1
0
0
0
1
1
2
1
1
0
2
0
1
0
0
1
0
0
1
0
2
1
1
1
2
2
0
0
0
0
1
2
1
2
0
0
1
1
0
0
3
0
0
1
2
0
1
1
1
0
1
0
0
0
1
2
1
0
0
2
0
1
0
0
0
0
1
0
1
2
0
1
1
2
1
0
2
1
2
2
0
0
0
1
0
2
1
1
0
2
1
0
2
0
2
1
2
1
1
0
0
1
0
0
1
1
1
1
2
1
1
0
0
0
2
0
1
2
0
1
2
0
1
0
1
0
2
2
0
1
0
0
1
2
1
1
2
0
0
0
1
2
0
1
0
2
1
1
1
2
0
0
0
1
1
2
2
0
1
2
1
0
1
2
0
1
1
0
0
2
1
1
0
0
1
0
1
2
1
0
0
2
2
2
0
1
0
1
0
2
2
2
1
1
1
2
0
1
1
2
0
1
1
1
1
0
2
2
2
3
0
0
1
1
0
1
1
0
0
0
0
1
0
1
0
0
2
2
1
1
1
1
0
0
0
0
1
0
2
1
0
0
1
1
1
2
0
0
1
2
1
0
1
1
0
1
1
0
0
2
1
2
0
1
1
1
2
0
0
1
1
2
1
2
0
0
1
0
1
2
2
2
1
0
0
0
1
2
1
1
0
0
1
1
0
0
2
0
1
0
1
1
1
1
1
0
2
0
1
0
0
1
1
1
2
1
1
1
1
1
1
1
1
0
1
0
1
1
0
2
2
1
2
1
0
1
0
1
2
1
0
0
0
2
1
0
1
0
1
0
2
2
1
2
1
2
2
1
2
0
0
2
0
0
2
1
1
0
1
1
1
0
1
0
0
0
2
1
2
0
2
2
0
0
1
1
2
1
0
1
0
1
1
1
1
0
0
0
1
1
0
1
1
0
2
0
2
1
1
1
0
0
1
1
1
0
0
0
1
0
0
2
0
0
1
1
0
1
1
1
1
1
1
0
1
1
2
1
0
0
0
1
1
2
2
1
1
1
3
2
3
1
2
1
1
2
1
2
1
0
1
2
1
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
1
0
0
2
1
1
2
0
2
2
1
0
2
0
1
0
2
2
2
0
0
2
1
2
1
0
0
1
1
2
0
2
1
0
0
0
0
0
0
0
0
1
2
1
2
0
1
1
0
2
2
0
2
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
1
1
0
1
1
0
0
2
2
1
0
2
0
1
0
2
3
1
0
1
2
1
2
1
3
0
2
2
0
1
0
0
1
2
0
1
1
0
1
1
2
0
2
1
1
1
1
0
1
2
0
2
1
1
1
1
2
1
0
3
1
0
0
0
1
0
0
1
0
1
0
0
1
2
1
1
1
0
2
0
0
0
0
1
0
1
1
1
0
2
1
0
0
3
1
0
0
2
0
1
2
1
1
1
0
1
1
1
1
0
1
1
1
1
0
0
1
0
0
0
0
1
1
1
1
0
1
2
0
2
1
2
0
1
2
2
0
1
2
2
0
1
1
2
3
0
1
1
2
0
0
1
0
1
0
2
0
2
4
0
1
1
0
1
2
2
1
0
0
1
0
0
0
0
2
0
4
1
2
0
1
1
0
0
0
0
0
0
1
1
2
2
1
1
1
1
1
1
0
1
1
0
2
0
1
3
1
3
0
2
0
2
2
1
0
0
0
1
1
2
0
0
0
2
1
1
0
2
3
0
0
0
1
1
1
2
1
0
1
0
1
1
0
1
1
0
3
2
0
1
0
2
2
2
1
1
1
0
1
1
0
1
1
0
0
1
1
2
1
1
0
1
1
1
1
1
1
2
2
0
0
0
0
1
1
1
1
1
2
2
1
1
0
0
1
2
0
0
0
2
0
2
1
0
1
2
1
1
1
0
1
1
1
0
0
0
2
0
0
0
2
1
0
0
1
0
0
0
1
2
0
1
1
1
0
1
2
2
2
1
4
0
0
0
0
0
1
1
1
0
0
0
0
1
2
2
1
1
1
0
2
0
1
1
1
0
2
0
2
1
1
0
0
0
1
2
0
0
0
1
2
1
0
0
2
1
0
0
1
1
1
1
1
0
0
0
0
1
1
2
1
1
0
2
2
2
1
1
1
0
0
1
0
1
0
0
2
1
3
1
1
0
2
0
1
1
0
0
0
0
0
1
3
1
1
1
2
0
0
2
0
0
1
0
1
4
1
0
0
0
2
0
0
1
1
0
1
0
0
2
1
1
1
2
1
2
1
2
1
0
2
0
1
1
1
1
1
0
2
2
2
1
1
2
1
1
0
0
0
1
0
0
2
1
0
0
2
1
1
0
0
1
1
2
0
1
1
1
2
0
3
0
2
2
3
2
0
1
2
1
2
2
1
0
0
0
0
1
1
2
1
3
0
0
2
1
0
1
0
1
0
2
0
3
0
0
0
1
0
0
1
0
0
0
2
1
1
1
2
1
1
1
2
2
0
1
1
1
1
0
1
0
0
1
1
1
0
0
0
0
0
1
0
0
1
0
0
1
0
1
1
0
0
2
2
1
1
1
1
2
1
2
2
2
2
0
1
1
0
1
1
0
0
0
0
1
2
0
0
0
1
2
1
0
1
1
1
0
1
0
0
0
0
1
2
0
2
1
1
1
0
2
0
0
1
0
0
0
0
1
2
0
0
0
2
0
2
0
2
1
0
0
0
0
1
2
0
0
0
1
0
0
0
1
1
2
1
2
0
1
2
1
1
1
1
1
1
2
1
1
0
0
1
1
1
1
1
1
1
0
1
1
1
1
0
1
1
2
1
2
2
0
0
2
1
2
0
1
0
2
2
1
0
0
0
0
1
1
1
0
1
2
2
1
1
1
0
1
0
2
2
1
1
0
1
0
0
0
1
2
0
0
0
1
0
2
1
2
0
1
1
1
1
2
1
0
1
0
2
0
0
0
2
2
1
0
1
2
0
0
0
1
1
2
1
0
0
0
1
0
1
1
1
1
0
0
1
0
3
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
1
0
2
1
3
0
0
2
0
1
2
2
2
2
2
0
1
1
1
2
0
1
0
1
2
2
0
0
1
2
2
0
3
1
0
1
0
1
1
1
0
1
0
0
0
0
0
0
2
0
0
2
2
0
0
1
1
1
1
1
0
0
1
1
0
0
0
1
0
2
0
1
2
1
2
1
1
0
1
1
0
0
1
0
1
0
0
0
0
1
1
0
0
2
2
2
0
1
0
1
2
0
1
1
0
2
1
0
2
1
2
1
1
0
1
2
1
1
1
1
1
0
0
1
1
1
1
1
2
2
0
1
0
0
0
0
4
2
1
3
1
1
1
2
1
0
0
1
0
1
1
1
2
1
0
1
0
2
1
0
1
1
2
0
2
2
0
2
2
0
1
0
2
1
0
0
6
1
1
0
1
0
2
0
2
2
0
2
0
1
1
0
2
0
1
2
0
2
2
1
0
2
1
1
2
1
0
0
2
0
1
1
0
1
0
0
1
0
1
1
1
1
0
0
0
2
0
0
1
1
0
2
0
4
0
1
2
0
0
1
1
2
0
0
0
2
0
0
0
0
3
0
0
2
1
0
1
1
2
1
0
0
1
2
1
1
0
2
0
2
0
0
2
0
0
1
0
2
0
0
0
0
2
0
0
1
2
0
2
1
0
0
0
1
3
2
1
0
1
2
1
1
0
0
1
0
1
2
1
0
0
0
1
0
1
1
2
1
0
2
0
1
1
0
2
0
0
1
0
2
1
1
0
0
1
1
1
1
0
1
0
1
0
1
0
1
0
1
2
2
2
1
0
2
1
1
1
0
1
1
1
0
1
0
0
0
1
0
2
0
1
2
1
1
1
1
0
1
1
1
2
1
1
0
1
2
1
1
1
1
2
1
1
0
0
2
1
2
0
1
2
1
2
1
0
2
0
0
3
0
2
1
0
1
0
1
1
0
2
1
0
2
1
0
2
1
1
4
1
1
1
2
1
0
1
0
1
2
0
2
2
1
0
0
0
0
0
0
0
2
4
0
3
1
2
1
2
2
1
1
1
0
0
2
0
1
0
0
1
2
1
2
2
1
1
1
1
1
1
1
2
2
0
0
2
0
1
0
0
0
2
1
0
0
1
1
0
2
0
0
0
1
1
2
2
0
0
0
1
1
0
1
0
0
1
0
1
0
1
2
1
2
1
0
2
2
1
1
0
1
0
1
0
0
2
1
0
0
0
1
2
0
1
1
2
2
2
0
1
0
2
0
1
3
1
0
1
0
2
0
0
2
1
0
1
0
1
1
1
0
2
0
1
0
0
1
2
2
1
0
2
0
0
0
0
2
2
3
1
0
2
0
2
1
1
2
2
2
0
2
1
1
1
2
2
0
2
3
1
0
1
2
0
0
1
2
0
2
0
0
0
0
2
0
1
1
1
1
2
1
2
1
2
1
0
2
1
2
1
1
2
0
2
0
0
1
0
2
0
1
1
0
0
0
0
0
1
1
1
2
1
0
1
1
0
1
0
2
1
0
2
0
0
1
2
0
0
0
0
0
1
0
1
2
1
0
1
1
1
0
1
1
1
1
2
0
0
1
1
2
1
1
1
3
0
2
0
2
0
0
0
1
1
3
0
2
1
0
1
1
0
1
0
2
2
1
1
1
1
1
0
1
0
1
2
1
0
0
2
2
1
1
1
0
2
0
1
2
1
1
1
1
0
1
2
0
1
1
0
1
1
0
2
0
0
2
1
1
0
0
0
2
1
1
0
1
1
0
1
0
1
0
1
2
0
2
0
1
1
0
0
0
2
1
1
0
1
1
1
2
0
1
1
1
0
2
0
0
1
0
1
0
0
0
0
1
1
0
1
2
0
2
1
0
3
0
2
0
1
2
1
1
1
0
1
0
1
2
1
0
2
1
1
1
2
1
0
2
1
2
1
1
1
0
2
1
0
1
1
1
0
2
0
2
2
0
1
2
1
0
0
1
0
1
0
0
0
1
1
2
1
1
0
1
2
0
2
1
2
1
0
2
2
0
2
1
0
1
1
1
0
2
2
6
2
0
0
0
2
0
1
1
2
1
1
1
1
1
1
2
0
2
2
1
0
1
0
1
1
1
1
0
1
0
0
1
1
1
0
2
1
1
0
0
0
2
1
3
0
2
0
0
1
0
1
2
1
1
0
1
1
1
0
1
0
1
0
1
1
2
1
2
1
1
0
1
1
2
1
1
0
2
2
1
2
0
1
1
0
1
2
0
2
1
1
0
0
0
0
0
1
2
1
0
0
2
2
0
1
2
1
0
2
1
0
2
2
2
0
1
1
0
1
0
2
1
1
0
0
1
0
1
1
2
0
1
2
0
1
0
2
0
2
1
1
0
1
1
0
1
2
0
1
2
1
1
1
0
2
1
1
2
1
1
0
1
2
2
2
1
0
0
1
2
0
1
1
1
1
1
1
2
1
2
0
1
2
0
2
1
0
1
1
0
1
1
2
0
1
1
1
1
1
2
0
1
0
0
1
0
1
0
2
2
1
2
1
0
0
2
1
0
1
0
2
1
0
1
2
1
0
3
2
1
1
1
1
0
1
1
1
0
0
2
2
0
0
1
1
1
0
1
0
0
1
0
1
1
0
0
1
1
2
2
0
1
1
1
0
1
1
0
2
2
2
0
2
1
1
0
2
1
1
0
2
0
2
2
0
1
0
2
1
2
0
0
1
0
0
2
0
0
1
0
0
1
1
1
1
0
2
1
2
2
0
2
1
2
0
2
0
2
0
0
0
2
0
2
2
1
1
2
1
1
1
2
0
2
1
1
1
2
0
1
0
1
2
1
1
0
0
1
1
1
0
2
2
1
1
1
1
0
2
0
0
0
0
1
3
0
0
0
0
0
0
2
0
1
2
0
1
3
1
1
2
0
0
1
1
2
1
1
0
1
0
2
0
1
2
0
1
0
0
1
1
3
2
0
1
0
2
1
3
2
0
0
1
0
4
1
1
0
1
1
2
1
0
2
1
1
2
2
2
1
1
0
1
2
0
2
1
1
0
0
2
1
0
2
1
0
0
2
2
1
0
1
2
0
1
1
0
2
1
0
2
1
0
0
2
0
0
3
0
0
0
1
0
2
1
1
2
2
1
0
2
1
2
0
2
0
0
1
0
0
1
1
2
0
1
0
1
0
1
2
2
3
0
1
1
2
1
2
1
0
1
0
0
0
2
2
0
2
1
1
0
1
2
1
0
0
1
0
2
0
1
1
2
0
1
1
1
0
0
1
1
1
0
0
0
2
0
0
2
3
1
1
1
1
0
1
2
1
1
0
1
1
1
1
0
2
0
1
1
0
0
1
1
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
1
2
1
1
0
1
1
1
0
1
0
0
1
1
0
1
1
0
0
1
0
0
2
0
1
0
2
2
1
2
1
1
1
2
2
0
0
0
1
0
2
1
2
1
1
1
2
0
1
2
0
2
1
1
1
1
2
1
2
1
1
2
1
0
0
1
0
1
1
0
2
0
0
0
0
0
2
0
2
1
0
0
0
0
1
2
2
2
2
1
0
0
1
3
1
2
1
0
1
1
1
0
2
2
1
2
0
2
1
1
3
0
2
2
1
2
2
0
0
2
1
1
1
1
2
0
2
1
0
2
0
1
1
2
2
1
0
1
2
2
0
0
0
0
1
0
0
2
0
0
2
0
2
0
1
0
2
0
0
1
0
0
2
1
1
1
0
1
1
0
1
0
2
0
1
0
1
2
1
1
1
1
2
1
0
1
2
1
1
0
1
1
2
0
1
0
1
0
2
1
2
2
0
1
0
1
0
2
1
0
2
0
1
2
1
0
0
2
2
2
0
1
1
0
0
1
0
2
1
0
0
0
0
1
0
4
0
1
0
1
1
0
0
0
1
0
2
2
0
1
1
2
0
0
1
0
1
2
1
0
1
1
0
2
1
1
2
1
0
0
0
2
2
0
2
1
0
0
1
0
0
1
1
1
1
1
0
1
2
2
2
1
1
0
2
0
1
0
0
1
0
1
0
0
1
1
1
0
2
2
0
0
0
1
1
1
0
0
1
1
0
0
0
0
0
1
0
0
0
6
0
2
0
1
1
1
1
1
1
0
2
0
0
1
0
0
1
1
0
0
0
0
1
1
1
1
0
1
0
3
0
1
0
2
0
1
3
0
3
0
2
0
1
1
0
1
1
1
1
0
2
2
1
1
2
0
1
0
1
1
0
1
1
0
0
1
2
1
2
2
1
1
1
1
0
1
0
1
0
2
1
1
0
0
1
1
2
0
1
1
0
2
2
0
1
0
1
0
0
0
2
1
1
2
0
2
0
0
0
0
1
2
2
0
1
1
0
0
0
2
1
2
1
0
1
0
2
1
1
0
0
1
2
1
0
0
1
1
1
0
1
1
2
0
0
1
1
0
0
2
2
2
1
2
0
0
1
1
1
1
0
1
1
1
4
0
1
2
2
1
2
1
0
0
1
1
1
0
0
1
1
1
1
1
0
1
0
1
1
0
0
2
0
0
1
1
1
0
0
1
1
1
0
0
0
1
2
1
0
0
2
3
2
1
1
2
1
1
0
2
2
0
1
1
0
0
1
2
2
2
0
1
1
1
0
2
0
0
0
0
0
1
0
1
1
0
0
1
1
0
3
0
1
0
0
1
1
0
0
0
3
2
0
1
1
1
0
1
2
0
1
2
2
4
1
1
1
0
1
2
0
0
1
1
0
0
1
2
1
1
2
1
1
1
1
1
2
0
1
0
2
0
0
1
0
1
0
0
0
0
1
2
1
0
0
0
0
2
0
1
0
2
1
1
1
2
0
1
0
2
1
1
1
1
1
2
0
0
2
1
2
2
1
0
1
1
0
1
1
0
1
1
2
0
1
1
0
0
0
2
1
1
0
2
0
1
2
0
1
2
0
0
1
0
0
2
2
0
0
0
0
0
1
0
1
0
1
2
0
2
1
1
0
0
1
1
0
1
1
1
1
2
0
1
1
3
2
2
1
1
1
1
0
1
0
2
0
0
2
3
1
1
0
2
0
1
0
0
0
2
2
0
0
0
0
0
1
1
2
2
1
0
1
2
1
0
1
1
1
1
2
2
1
2
0
1
2
2
1
2
0
0
0
1
0
0
1
1
1
2
0
1
1
4
0
1
0
1
2
0
1
1
0
1
0
1
0
1
0
0
0
2
1
1
0
0
2
1
0
0
1
1
2
0
0
0
1
2
0
2
1
0
1
0
0
1
1
1
1
0
1
0
2
2
0
1
1
1
1
0
1
1
2
1
2
0
1
1
1
1
1
0
1
0
1
2
2
0
1
0
1
2
1
1
0
3
3
0
1
0
1
2
1
1
2
0
2
2
1
0
2
1
1
0
1
0
0
1
0
1
0
1
3
0
0
2
2
0
0
1
2
0
0
2
1
0
1
0
1
1
3
1
1
1
2
0
0
1
0
1
0
0
1
2
2
1
2
1
1
1
1
1
1
2
1
1
2
1
1
2
1
0
2
0
1
0
0
1
1
2
0
1
2
2
1
0
0
0
0
0
3
0
1
1
1
1
0
2
1
1
0
2
0
1
0
0
2
1
3
2
0
0
0
0
1
0
2
0
2
0
0
1
2
0
0
2
0
1
0
0
2
2
0
2
0
0
0
1
1
1
0
1
0
0
0
0
1
1
1
1
1
1
0
0
2
1
2
1
1
0
2
2
1
1
1
1
0
0
1
0
0
1
1
2
0
1
2
1
1
0
0
0
0
1
1
1
1
0
1
1
0
0
1
1
2
0
1
2
0
0
0
2
2
0
0
0
3
1
2
0
0
1
0
1
2
1
1
1
1
2
1
0
0
1
1
2
1
1
1
1
0
2
2
1
2
0
2
2
1
2
1
1
0
0
2
1
2
1
1
2
0
1
0
2
0
0
2
0
2
0
1
0
0
2
1
1
1
1
0
0
0
2
2
1
1
1
1
3
3
0
0
1
1
1
2
1
1
1
0
2
1
1
3
1
1
1
0
0
2
2
1
1
2
2
0
0
1
1
2
1
0
1
0
2
1
0
0
1
2
0
1
0
0
2
1
1
0
2
2
1
0
2
1
1
1
2
1
2
1
1
0
1
0
1
0
0
0
0
1
2
0
0
0
1
1
0
1
0
0
1
1
1
1
0
1
1
0
3
0
0
2
1
0
1
0
0
1
1
0
1
1
0
0
0
2
1
0
2
0
2
0
0
1
0
0
2
2
2
0
1
0
0
1
2
1
0
4
0
1
1
2
1
0
0
1
1
0
1
2
0
2
1
1
0
2
1
1
1
2
0
1
1
2
0
0
0
1
0
0
1
1
1
1
0
0
1
0
1
1
0
0
0
1
1
1
0
2
0
1
2
0
0
1
1
0
1
2
0
2
0
1
0
3
0
1
2
0
1
0
2
0
1
1
1
0
1
0
1
2
1
0
0
2
0
0
1
0
1
0
1
1
1
1
1
0
2
0
0
1
1
0
2
2
2
0
0
1
2
2
1
1
1
2
1
1
2
0
0
1
2
3
1
1
0
3
1
0
0
2
0
0
0
2
1
0
0
1
1
2
0
0
2
1
2
1
0
1
2
0
2
1
1
0
1
2
0
0
0
2
1
0
2
2
0
0
2
1
0
2
0
0
0
0
0
0
1
1
2
2
1
1
2
0
0
1
2
1
1
2
1
1
1
0
1
0
1
1
0
0
1
1
0
0
0
1
2
1
0
0
1
0
1
2
1
0
1
1
1
0
0
1
1
1
1
0
2
2
0
0
2
1
0
1
0
0
2
1
1
0
1
0
0
0
1
1
2
2
1
2
1
0
1
1
1
1
0
1
2
1
1
1
1
1
1
0
1
1
1
0
1
1
1
1
1
2
1
2
2
1
1
1
0
1
1
1
0
0
1
1
2
1
2
0
2
1
1
0
2
0
0
2
1
3
0
0
0
0
1
1
1
1
0
1
1
2
0
2
0
0
1
1
2
1
2
2
0
1
2
0
0
0
1
0
2
0
1
1
0
1
1
1
1
2
1
1
1
2
0
0
1
1
2
1
2
2
1
1
1
0
1
0
1
1
0
1
0
1
0
0
2
0
1
1
1
1
0
1
2
0
1
1
0
1
2
1
0
1
2
0
0
0
1
2
5
2
1
2
2
1
1
1
1
0
0
0
3
2
1
0
0
2
2
1
1
0
2
0
2
0
0
1
1
0
0
2
1
1
1
0
0
1
2
2
1
3
2
1
1
2
1
1
1
0
0
1
3
1
0
1
1
2
1
0
3
1
1
0
1
0
1
1
1
2
0
0
0
1
2
1
0
1
0
0
1
1
0
1
2
2
1
1
0
1
1
0
1
1
2
1
0
1
0
1
1
0
0
1
1
0
1
0
0
2
1
2
1
2
1
2
1
2
2
0
0
0
1
0
0
1
0
0
0
2
1
0
1
0
1
1
0
0
1
0
1
0
0
1
1
1
0
0
0
2
0
2
1
0
2
0
1
0
1
2
2
0
0
1
0
2
1
1
1
1
1
3
1
1
0
2
1
1
2
0
0
0
0
1
1
0
2
2
0
1
1
2
0
2
0
0
2
1
1
0
1
2
2
2
0
1
0
0
1
1
1
2
0
1
1
1
0
0
1
0
2
1
2
0
1
0
0
1
1
2
0
1
0
2
1
2
0
1
1
2
0
1
1
1
1
0
0
1
2
1
2
1
0
1
1
0
0
2
0
0
1
0
1
2
1
1
0
0
0
1
0
1
2
0
0
1
1
0
0
1
1
0
1
0
1
0
2
1
0
1
1
1
0
1
2
1
1
2
0
1
3
0
0
2
0
1
1
2
1
0
2
0
0
2
2
2
2
2
2
0
1
0
2
1
1
2
0
0
0
0
2
0
0
2
3
3
1
0
1
1
0
1
0
0
2
2
0
2
1
0
1
1
1
0
1
1
0
1
0
1
2
2
2
2
0
1
2
1
1
0
0
2
2
1
1
1
1
2
1
1
1
1
0
1
1
1
3
1
1
1
1
1
0
1
2
0
0
1
1
1
1
2
1
0
1
0
0
1
2
1
1
0
2
2
2
1
2
2
0
1
0
2
0
1
0
1
0
2
2
1
1
0
0
0
1
0
2
2
2
0
1
1
1
2
2
2
2
1
2
1
2
1
2
0
1
1
1
2
3
1
0
0
1
2
2
0
1
2
0
1
0
0
0
2
0
1
2
2
0
0
1
1
0
2
1
0
1
1
3
0
1
1
1
2
0
2
0
2
2
2
0
2
0
2
1
2
1
0
1
0
0
0
1
1
0
1
1
1
0
1
1
1
0
0
0
1
1
0
2
0
2
2
1
1
1
1
0
0
0
1
1
0
1
0
1
1
2
0
0
2
0
2
2
1
1
2
0
2
2
1
1
1
1
0
2
0
1
2
1
0
2
1
1
1
1
1
0
2
0
0
1
2
1
2
1
2
0
1
1
0
0
1
0
0
0
2
0
1
1
0
0
0
1
2
2
1
2
2
1
0
1
2
1
1
1
0
2
0
1
1
1
1
0
1
1
2
1
0
1
2
2
0
2
0
2
1
1
0
2
1
1
1
1
0
1
1
3
0
1
0
0
0
0
1
0
1
2
1
1
1
2
2
1
1
0
1
0
2
0
1
2
2
0
0
0
1
2
0
2
1
0
0
2
1
0
0
1
0
3
0
0
1
0
0
1
0
1
2
1
0
0
1
2
1
0
2
2
6
2
1
0
0
2
0
0
1
0
2
1
1
0
2
0
0
1
0
1
1
1
2
2
1
1
1
2
2
2
1
2
2
0
1
1
0
1
1
1
2
0
1
2
2
0
0
0
1
1
0
1
1
0
0
2
1
0
0
2
0
0
1
2
0
1
0
1
1
1
1
2
1
1
1
1
0
0
1
1
1
1
0
6
0
1
2
0
1
0
2
2
0
1
0
2
1
0
2
1
1
0
1
1
2
1
0
2
1
1
0
1
1
2
0
1
1
2
0
1
1
0
0
1
0
1
1
2
0
1
1
0
2
1
1
1
1
2
2
0
0
2
1
0
0
2
0
1
2
1
1
1
1
1
2
1
2
0
0
1
1
2
2
2
2
0
1
2
3
1
0
2
2
0
1
1
2
1
0
0
1
1
0
1
0
0
0
1
3
1
2
2
1
1
0
0
0
0
1
0
1
1
0
1
1
1
0
1
1
2
0
1
0
0
2
0
1
1
3
0
0
1
1
0
1
0
2
0
1
1
1
0
0
0
2
1
1
0
2
2
1
1
0
0
0
0
2
2
2
1
2
0
1
1
0
2
2
1
1
1
0
3
0
0
2
2
2
0
0
1
1
0
1
0
2
0
1
1
1
0
0
2
2
0
1
1
1
0
1
2
1
1
0
0
0
1
2
0
2
0
3
0
2
0
1
0
1
1
0
0
0
0
2
0
1
0
1
1
0
0
1
1
2
0
2
1
1
2
1
2
0
0
1
1
2
1
0
0
0
1
1
0
1
2
0
1
0
0
1
0
0
0
2
0
0
1
0
2
0
2
1
1
2
1
0
1
2
2
3
0
1
1
0
0
0
1
2
0
2
0
0
0
2
0
1
0
2
2
0
1
1
1
1
1
0
0
0
2
0
2
0
0
2
1
1
2
0
2
2
1
2
1
1
0
0
0
2
1
1
1
1
1
0
0
0
1
1
2
1
0
2
1
1
1
0
1
2
2
1
2
2
1
0
0
0
3
2
1
2
1
1
0
1
2
2
1
1
0
0
1
0
1
2
0
2
1
0
1
0
0
1
0
0
0
0
1
2
0
1
0
2
0
1
2
1
0
0
2
0
0
2
0
0
1
0
2
2
2
1
1
0
1
2
0
2
1
1
0
1
1
0
1
1
0
0
0
2
0
2
0
0
1
1
1
1
2
0
1
1
1
0
1
1
1
0
1
1
0
0
2
1
0
2
2
0
5
1
1
0
0
0
2
0
2
2
0
1
0
1
2
0
1
0
0
0
1
1
0
0
2
2
0
1
1
2
2
2
1
0
0
2
0
1
2
1
0
0
0
2
2
0
1
0
0
2
0
2
0
0
0
1
2
2
2
0
0
2
1
0
1
1
3
0
0
0
3
2
0
1
1
1
0
1
3
0
1
0
1
1
2
0
2
0
0
0
2
0
1
0
2
2
3
1
4
0
2
1
1
3
1
1
1
0
2
1
0
2
0
1
1
2
1
1
0
1
1
1
1
1
0
0
0
1
2
0
1
0
0
0
1
0
3
0
1
0
1
2
2
0
1
0
2
2
0
0
1
1
2
0
1
0
2
0
1
2
0
0
1
1
1
1
1
2
2
2
0
2
1
0
2
0
1
2
1
0
1
1
0
0
2
2
2
1
0
2
0
0
2
0
3
0
0
1
0
1
0
3
2
1
1
1
0
1
1
1
2
1
3
0
0
1
0
0
1
1
1
1
1
1
0
2
1
1
1
1
1
0
1
1
1
1
1
0
0
1
2
1
2
1
2
0
2
1
0
0
0
0
0
1
2
1
2
1
0
1
1
1
1
1
1
0
1
1
1
1
1
1
0
1
1
0
1
0
1
1
2
1
1
0
1
2
1
1
1
2
0
1
2
1
0
0
1
1
2
1
0
1
0
1
3
1
2
1
1
0
1
2
2
0
1
0
0
0
1
0
1
0
0
0
1
1
2
1
2
0
0
2
2
0
2
2
1
1
2
0
2
1
2
1
0
0
0
1
2
0
0
2
1
1
0
1
0
1
2
1
2
0
0
1
1
2
2
0
0
0
0
4
0
2
1
1
0
1
1
2
0
1
1
1
1
2
0
1
1
1
0
0
1
1
1
1
1
1
0
0
1
2
1
0
0
0
1
0
0
1
1
2
1
1
0
0
0
1
1
2
1
0
1
1
1
2
2
0
1
1
1
0
2
0
0
0
0
1
0
2
1
1
0
0
0
0
0
0
1
0
1
0
0
0
2
1
2
1
1
0
0
2
1
1
1
0
1
2
2
1
1
4
0
0
0
1
2
2
1
0
0
2
0
0
2
0
2
0
0
1
2
1
0
1
0
2
1
1
0
1
1
2
1
0
0
0
1
1
2
1
0
1
1
1
0
2
0
0
0
2
2
1
0
1
0
0
1
1
0
1
3
2
1
0
0
2
0
0
0
0
2
1
0
1
0
1
1
1
2
1
1
3
1
2
1
1
1
1
0
0
2
1
2
2
2
0
0
2
1
1
1
0
1
1
1
2
2
0
0
1
1
1
1
1
2
1
1
0
2
0
1
0
0
1
1
1
0
0
0
0
1
2
1
1
1
2
2
0
0
1
1
2
0
1
1
0
1
0
0
1
0
1
0
2
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
1
0
1
2
0
1
1
1
1
0
0
0
1
1
0
0
0
0
2
3
1
2
2
0
0
2
1
1
1
2
0
0
2
2
0
1
0
0
0
0
2
2
2
0
0
1
0
2
1
1
1
1
0
1
0
1
1
2
0
1
0
0
1
1
1
0
0
0
0
1
1
0
1
2
1
1
0
1
0
1
0
1
2
1
0
1
0
1
1
1
2
0
1
1
1
0
0
1
1
2
2
0
0
0
0
0
2
0
0
0
0
1
2
0
1
1
1
2
1
0
1
1
0
1
2
1
1
0
1
0
2
0
2
0
1
0
2
2
1
1
0
2
0
2
1
1
0
2
1
0
3
0
0
1
1
2
0
0
0
0
0
2
0
1
0
2
3
2
1
2
2
2
1
0
0
2
1
2
2
1
1
1
1
1
0
0
1
0
1
2
0
0
1
1
1
1
1
1
1
2
1
1
2
1
0
0
2
0
1
0
1
0
2
2
0
2
1
1
1
0
0
0
1
2
0
0
2
1
2
2
0
2
1
1
2
1
0
2
1
0
4
1
0
1
1
1
1
0
0
1
2
0
4
0
0
3
2
0
0
1
2
1
0
1
1
1
1
0
0
0
0
0
1
2
1
1
0
1
1
2
1
1
1
0
0
1
1
0
1
0
1
1
0
0
1
2
0
0
1
2
1
2
2
2
2
4
1
1
1
0
0
1
1
1
1
0
0
2
1
0
2
1
1
1
0
1
0
1
1
0
2
2
0
2
1
1
2
2
1
2
0
2
1
0
1
1
2
0
2
1
0
0
0
1
0
1
0
1
0
1
1
0
0
0
0
1
1
0
1
1
1
2
0
0
1
2
2
2
0
2
1
0
0
1
0
1
0
1
2
1
1
2
0
2
0
1
0
2
1
1
2
0
1
1
1
1
1
0
2
3
2
0
0
2
1
1
1
2
1
2
0
1
0
0
2
2
0
1
3
1
1
1
2
2
0
0
1
2
3
1
1
2
0
1
1
1
1
1
1
1
1
1
2
0
0
2
1
0
1
0
0
1
0
0
1
1
1
2
1
0
0
1
0
0
2
1
0
2
0
1
2
1
2
1
0
1
1
0
0
0
0
0
1
1
1
0
2
0
0
0
1
2
0
0
0
2
3
0
2
1
1
0
0
1
3
1
1
1
0
1
1
0
1
0
2
0
2
0
1
1
1
0
1
2
1
1
2
0
1
0
0
0
1
1
0
0
2
2
0
1
1
1
1
1
2
0
1
0
0
2
1
0
0
2
2
1
1
3
1
2
1
0
1
0
2
2
1
1
1
1
0
1
2
1
2
0
2
1
0
3
1
0
0
0
1
2
0
0
1
2
1
2
1
0
1
1
0
0
0
1
1
0
0
0
0
0
0
1
2
1
0
1
2
1
0
0
0
1
1
1
2
1
1
0
0
2
0
0
1
1
0
0
0
1
2
0
1
0
0
0
0
1
1
2
1
2
1
0
1
0
0
1
0
1
1
0
0
0
0
0
2
2
0
1
0
1
0
1
0
1
2
0
0
0
1
1
1
1
0
0
1
1
1
1
1
1
1
2
0
1
1
2
1
0
2
0
1
0
0
0
1
2
1
0
0
0
0
1
0
2
1
2
2
0
0
0
0
0
1
1
1
1
0
1
1
0
0
2
2
1
1
1
1
2
1
0
0
0
0
1
2
0
1
1
0
0
0
2
0
0
0
1
0
0
2
2
1
2
1
1
0
0
1
1
1
0
3
0
2
0
1
0
1
1
2
0
2
1
0
1
0
1
1
2
1
0
0
1
1
0
0
1
3
0
1
1
2
0
2
1
1
0
0
0
1
1
0
0
1
2
1
0
1
1
2
1
1
0
1
1
2
1
1
2
1
1
0
0
0
1
2
0
1
1
0
0
3
0
1
1
1
0
0
1
0
1
0
0
0
2
0
1
2
0
0
1
3
0
1
0
0
2
3
1
0
2
0
0
1
0
2
1
1
1
1
1
1
1
0
2
1
1
0
1
0
1
0
0
1
0
3
2
1
1
1
1
3
0
1
0
1
0
2
0
1
0
2
1
1
0
2
0
1
0
0
1
1
1
0
2
1
0
0
2
0
1
1
1
1
2
0
0
0
0
2
2
3
0
3
0
1
2
0
2
1
1
1
1
2
0
0
1
0
2
0
1
0
2
1
2
1
0
0
0
0
1
1
1
1
2
1
0
1
1
0
0
1
3
1
1
0
0
0
1
1
1
1
1
2
1
1
2
1
2
0
1
1
2
1
1
0
0
1
1
0
0
2
0
0
1
1
2
1
1
0
0
2
1
2
1
1
0
1
1
0
1
0
0
2
2
1
0
0
2
0
1
1
1
1
2
1
1
1
1
0
0
0
2
2
1
0
2
2
1
0
2
0
2
0
1
2
0
1
1
2
1
1
2
1
0
2
1
1
0
3
1
1
1
2
0
1
2
2
0
0
0
1
0
0
1
1
0
0
0
1
1
4
2
2
0
3
3
0
0
2
1
1
0
1
1
1
1
1
0
1
0
2
1
1
1
0
1
1
1
0
0
2
0
0
2
0
1
1
1
1
1
2
0
0
1
1
2
0
1
0
1
2
1
0
2
1
1
1
0
2
2
1
0
1
0
0
0
0
2
2
0
1
1
2
1
1
2
2
2
0
0
0
0
1
1
0
1
0
0
2
0
1
1
2
2
1
2
0
1
1
1
2
1
0
1
2
0
2
0
1
0
0
1
1
0
2
1
1
1
0
1
1
0
1
1
1
1
1
0
2
1
0
1
2
1
1
0
0
2
2
0
1
1
0
4
2
0
1
0
0
1
0
2
1
1
1
0
1
1
0
2
1
1
0
0
1
1
0
2
1
1
2
1
1
3
0
0
0
0
0
2
1
1
1
1
1
1
0
2
1
1
2
0
1
1
1
0
1
1
1
1
1
1
1
0
2
1
0
0
1
7
2
1
2
0
1
2
2
0
0
1
0
0
2
2
0
0
0
0
2
0
1
0
0
1
1
1
0
0
2
5
2
0
0
0
2
0
0
0
0
1
2
1
1
1
0
2
1
1
0
2
1
1
1
1
0
0
2
2
1
0
0
2
0
0
3
2
3
2
2
0
1
0
1
1
0
1
0
0
2
0
1
1
1
0
2
0
0
1
1
0
1
2
0
1
0
1
0
0
0
1
1
1
1
0
0
1
0
1
3
2
2
0
2
1
1
0
0
0
0
3
0
1
2
2
0
2
1
0
2
2
0
0
1
1
0
1
1
0
1
0
0
0
0
0
1
1
1
1
2
2
0
0
0
1
1
0
2
0
2
3
1
2
1
2
1
1
0
2
0
2
1
1
0
0
0
0
0
0
0
0
0
0
2
0
1
1
1
1
2
1
1
0
0
1
0
2
0
3
2
1
1
0
2
1
1
0
2
0
1
0
0
3
1
1
1
2
1
0
0
0
0
0
1
0
0
2
0
1
4
2
0
1
1
0
0
0
0
0
1
1
2
1
2
2
1
0
0
0
1
1
1
4
0
2
2
1
1
0
1
1
1
0
0
1
2
1
1
0
0
1
2
0
0
0
2
1
2
2
0
2
2
1
1
0
2
2
0
2
0
2
0
0
0
2
1
0
1
0
2
1
1
0
1
1
1
0
0
2
2
1
1
1
6
0
1
0
0
2
0
1
1
2
0
1
2
1
1
0
1
0
2
1
1
1
0
0
1
0
1
0
1
0
0
1
2
1
0
2
2
1
1
0
1
1
0
2
0
1
0
1
1
1
2
0
1
0
2
1
1
1
0
1
2
0
2
2
1
1
1
0
2
1
1
0
0
2
0
0
0
2
1
0
0
0
2
1
0
0
0
1
1
1
1
1
1
1
2
1
1
2
0
1
1
2
1
1
2
1
1
0
0
0
1
2
0
1
1
1
2
0
1
2
1
0
0
1
0
2
3
0
0
1
2
0
1
2
1
1
1
2
2
1
1
0
1
2
1
1
1
0
1
2
2
1
1
0
1
2
1
0
1
2
0
0
0
1
1
0
0
0
1
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
2
1
1
0
1
1
1
1
1
1
0
1
2
0
1
1
1
1
2
0
1
1
0
0
2
1
2
1
2
1
0
0
0
1
2
1
0
0
0
0
0
2
0
1
2
2
1
1
0
1
0
1
0
2
1
0
0
1
2
1
0
1
0
0
1
1
0
0
0
0
0
4
0
2
0
2
2
0
2
0
2
1
0
0
0
0
1
0
0
2
2
0
2
2
2
0
1
1
0
2
2
1
3
1
0
2
1
0
1
1
1
0
0
2
2
1
0
0
0
1
0
2
0
0
2
0
0
0
0
2
0
0
2
1
1
0
1
0
1
0
0
0
1
1
0
0
1
1
1
0
0
1
2
0
0
1
2
2
2
2
0
0
1
0
0
1
2
2
1
1
1
0
2
0
1
0
1
3
1
1
1
1
2
0
0
0
2
1
1
1
0
1
1
1
0
0
0
0
0
0
0
2
1
0
1
1
1
1
1
1
1
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
1
1
2
2
1
0
1
1
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
2
2
2
1
1
1
1
0
1
1
1
1
1
1
2
0
0
1
1
0
1
1
0
1
2
1
0
3
1
2
1
0
1
1
0
1
2
0
0
0
1
2
0
1
2
1
1
0
0
2
2
2
0
1
0
0
0
1
0
0
1
0
2
2
0
1
0
1
1
2
0
3
0
0
0
0
1
0
0
0
1
1
0
1
2
1
1
3
4
0
1
1
1
1
1
0
1
0
1
0
1
0
2
0
2
1
0
1
0
1
1
2
0
1
1
1
1
0
2
1
0
0
0
1
0
1
0
0
0
1
0
2
3
0
1
1
0
0
1
0
0
2
1
2
2
1
2
1
2
0
0
0
2
2
1
1
0
0
1
1
1
0
0
0
2
0
0
1
0
1
2
1
2
1
2
0
1
2
1
0
1
0
1
1
2
1
1
1
0
0
1
0
0
0
1
1
0
0
2
2
0
1
2
1
2
0
0
2
1
0
0
1
1
1
1
1
1
1
1
1
1
1
0
0
0
1
2
0
0
2
2
0
2
1
1
0
0
0
1
2
2
1
1
0
1
1
1
0
1
1
1
1
2
0
1
0
0
0
2
1
0
0
0
0
1
0
1
0
2
1
1
0
0
0
1
2
0
2
1
0
1
1
0
4
2
0
1
2
0
1
2
2
1
0
2
1
1
0
1
0
0
0
2
1
1
1
1
2
1
1
0
1
0
0
1
2
0
1
0
1
1
2
1
1
1
0
2
0
0
0
0
2
2
2
1
0
0
0
0
2
0
2
1
1
2
0
0
0
0
0
1
0
1
1
1
1
0
0
1
0
2
2
3
0
0
1
2
1
2
1
1
0
0
3
1
1
0
0
2
2
0
1
2
1
0
0
2
0
2
0
1
0
1
1
1
1
1
2
0
0
1
1
0
2
1
1
1
0
0
0
2
1
0
0
1
0
1
1
1
1
0
0
3
1
0
2
1
1
1
0
0
1
1
1
2
1
1
1
0
2
1
1
0
0
0
1
2
1
0
0
1
1
1
0
0
1
0
1
0
2
1
1
2
0
1
1
2
2
0
1
2
0
0
2
0
1
0
1
1
0
0
0
2
0
2
0
2
1
0
1
2
2
2
1
1
1
2
2
2
1
1
1
1
0
1
0
0
1
1
0
1
1
1
0
2
0
2
0
1
1
2
2
1
0
2
3
0
0
1
0
1
2
1
1
1
1
1
2
1
1
3
1
0
0
1
1
2
1
2
1
0
0
0
0
0
0
0
1
1
1
0
2
0
1
0
0
0
1
0
0
1
0
1
1
2
2
0
0
0
0
1
2
1
1
0
4
0
0
1
1
1
2
0
2
1
0
1
0
1
0
1
0
2
1
0
1
0
1
2
1
0
2
2
0
0
1
0
1
0
0
1
2
0
0
1
2
2
0
0
1
1
2
1
0
1
1
0
0
1
0
1
1
1
1
1
1
1
0
2
0
0
0
1
2
1
0
2
2
1
0
0
0
0
0
0
1
2
2
2
1
2
0
1
0
0
1
2
1
0
2
0
0
1
1
0
0
1
1
0
2
1
1
1
1
0
0
1
0
1
0
0
2
0
1
1
1
1
0
1
0
0
0
1
0
0
1
0
0
1
0
0
2
2
0
2
0
1
1
0
2
2
1
2
0
1
0
3
1
1
0
2
0
1
1
0
2
1
0
1
0
0
1
0
1
0
1
1
1
2
0
1
0
1
1
1
1
0
1
0
0
1
0
1
2
1
1
1
0
1
1
1
1
1
1
2
0
1
0
1
1
0
0
0
0
0
1
0
1
0
0
1
2
1
1
2
1
1
0
2
2
1
0
0
2
0
0
2
1
2
2
1
2
3
3
1
2
2
0
1
0
1
2
0
0
1
2
2
1
1
1
3
0
2
1
1
2
3
2
2
0
0
1
0
2
2
1
1
1
1
0
1
1
1
0
0
1
0
0
0
1
1
2
0
1
1
1
1
1
1
1
1
1
1
0
2
1
0
0
0
1
0
2
1
0
2
2
3
2
0
2
1
0
1
1
1
1
1
3
2
2
1
1
1
0
0
0
1
1
2
2
0
1
0
0
1
1
0
2
0
1
2
0
1
2
0
0
1
1
0
0
2
1
0
1
1
0
1
1
0
0
2
2
1
0
2
0
0
0
3
1
2
1
1
1
0
2
0
1
0
0
2
1
0
0
2
1
2
1
0
0
0
0
1
0
1
2
0
0
2
1
1
0
1
0
1
0
0
2
1
0
2
1
1
2
1
1
6
0
0
1
1
3
2
2
0
1
2
1
1
0
1
0
2
1
0
1
2
0
2
1
0
1
0
0
2
2
0
1
1
1
2
1
1
2
1
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
2
2
1
0
0
0
0
0
1
1
0
2
2
0
0
1
0
0
2
0
0
1
0
1
1
0
1
1
1
0
2
1
3
1
1
0
0
0
1
0
0
0
1
2
1
0
1
1
1
2
0
1
0
2
1
0
3
2
0
1
1
0
1
1
1
2
0
1
1
1
1
1
2
1
0
0
2
2
0
1
0
1
1
1
2
0
1
0
1
1
2
1
1
1
1
2
0
1
2
1
2
1
1
2
1
1
1
0
1
0
1
0
0
1
0
1
1
0
2
0
2
2
1
1
1
0
0
0
0
0
1
1
0
2
0
1
0
0
2
1
0
0
3
1
0
2
0
0
2
0
1
1
2
1
2
1
0
0
0
1
2
3
0
1
2
2
0
1
2
0
0
1
2
0
1
1
1
1
0
1
1
1
2
1
0
0
1
1
1
1
0
1
0
1
1
0
1
0
1
2
0
0
0
0
1
0
1
0
1
1
0
0
1
0
0
1
1
0
2
1
2
0
1
1
0
1
0
1
2
1
1
2
0
1
1
1
0
1
0
1
0
0
1
2
2
1
2
0
3
1
1
2
0
1
1
2
1
1
1
1
0
2
2
0
0
0
0
0
2
1
5
1
1
2
0
1
1
1
0
0
1
0
1
2
1
0
0
0
1
1
0
4
1
0
2
1
2
2
0
1
0
2
2
0
0
2
1
1
2
2
1
0
2
1
0
0
1
2
1
1
1
1
1
1
2
1
1
0
3
1
2
1
1
1
1
0
0
0
1
0
0
3
1
0
0
2
0
2
1
1
1
2
1
1
1
1
1
1
2
1
1
1
0
1
1
0
2
1
1
1
0
1
0
0
2
2
0
0
0
1
1
0
1
0
2
0
2
1
1
2
2
2
0
1
1
1
1
2
1
1
0
0
0
1
0
0
1
1
2
0
0
1
0
1
2
0
1
1
0
0
1
0
1
0
1
0
0
0
1
0
1
2
1
2
1
1
0
0
2
2
1
0
0
2
2
1
1
1
0
1
0
1
0
2
2
2
1
0
2
1
1
0
2
0
0
0
1
0
0
2
1
0
2
0
0
0
0
0
0
2
2
2
2
2
0
0
1
2
2
1
2
0
1
0
1
1
2
1
1
0
0
1
1
2
0
0
1
2
2
1
2
1
1
0
0
0
1
2
1
2
0
1
0
1
0
2
0
2
1
0
2
1
0
1
1
0
1
1
1
0
1
1
1
1
1
0
1
0
2
1
1
2
0
0
1
1
0
0
0
0
1
1
0
0
0
1
1
1
0
2
1
2
0
1
3
1
1
0
2
0
0
2
0
2
1
1
2
0
0
0
1
0
0
0
2
1
0
0
0
2
0
1
0
0
0
1
0
0
2
1
0
1
2
1
0
1
2
1
0
3
0
1
0
1
0
1
1
0
1
2
0
0
0
2
0
1
1
2
0
1
1
6
2
1
2
2
0
0
0
0
1
1
1
0
1
2
1
0
0
0
2
2
2
1
0
1
0
1
0
0
1
1
1
1
0
1
1
0
0
2
0
1
0
0
1
0
2
0
0
1
0
1
2
1
0
1
1
1
2
1
0
2
1
2
1
1
1
1
0
0
0
0
2
1
0
0
0
2
0
2
1
1
0
0
0
1
1
2
1
1
1
0
1
0
1
2
0
1
1
1
1
0
0
0
1
1
0
1
0
1
1
2
0
2
0
1
2
2
0
2
2
0
1
1
1
1
1
3
1
1
0
2
0
0
0
0
1
1
0
1
1
3
2
1
2
2
0
1
1
1
2
2
1
1
0
1
1
0
1
1
0
1
1
1
0
0
2
1
0
3
1
0
0
0
2
0
0
2
1
1
1
2
1
3
10
0
0
1
0
2
1
1
0
0
0
0
0
0
0
1
0
1
2
1
1
2
0
0
0
1
0
1
3
1
0
2
0
0
1
2
2
1
0
1
2
1
2
2
2
0
1
1
0
0
0
0
1
1
1
1
1
0
1
0
2
1
2
1
1
2
1
0
0
0
1
0
2
0
2
1
2
1
0
1
1
1
2
2
0
1
2
1
0
1
0
1
1
1
2
0
0
1
0
2
2
1
3
2
1
1
2
0
0
2
2
0
0
1
1
2
1
0
1
2
2
0
1
1
0
1
1
0
1
1
1
1
1
0
1
0
0
2
0
1
1
0
2
1
1
0
0
2
1
0
2
0
0
0
0
1
0
1
1
1
1
0
0
0
1
2
0
1
1
1
1
2
0
0
0
1
0
0
0
1
0
1
2
2
0
1
0
0
0
2
2
0
0
1
2
1
0
2
1
1
0
1
0
1
0
1
0
2
0
0
0
1
1
0
0
0
1
0
1
0
1
3
0
0
2
0
0
0
1
1
1
0
1
0
1
2
0
1
2
0
0
0
1
0
0
2
1
2
0
0
1
1
1
2
2
2
0
1
0
1
0
0
3
2
2
0
2
1
0
1
1
0
0
0
0
1
1
0
2
1
0
1
1
2
0
0
0
1
0
2
2
0
1
1
1
0
1
0
1
1
2
1
1
0
1
1
1
1
0
1
1
0
1
0
0
2
2
1
0
0
1
1
0
1
2
1
1
1
2
0
0
1
1
0
2
2
1
1
0
2
1
2
0
0
1
2
0
1
0
0
1
1
1
2
2
0
0
0
1
0
0
0
0
1
0
1
0
0
2
0
2
1
0
0
1
2
0
2
2
0
2
2
1
0
0
3
1
1
0
1
2
2
2
0
1
1
1
0
2
0
0
1
0
1
0
2
1
1
1
1
2
1
0
1
0
1
1
1
0
2
0
0
1
0
0
1
0
5
0
0
0
0
1
2
3
1
2
1
1
0
1
1
3
2
1
0
0
0
0
2
0
0
0
0
1
2
2
2
2
0
1
0
0
0
0
2
0
0
0
0
2
0
2
0
0
2
0
2
0
1
2
1
1
1
1
0
2
2
2
0
0
1
0
0
1
2
1
0
0
1
1
0
1
2
1
2
1
2
2
0
0
0
1
3
0
0
0
0
2
0
2
1
1
0
1
1
2
2
0
2
1
2
1
1
0
0
2
0
2
1
2
0
2
1
2
2
0
1
2
0
1
1
0
0
3
2
0
2
0
5
1
1
0
2
1
1
0
2
0
0
0
1
1
0
0
2
0
1
1
0
2
0
1
0
1
2
0
1
2
1
2
2
0
0
2
0
0
2
2
0
0
1
0
1
1
0
1
0
1
3
0
1
1
0
0
0
0
0
2
1
0
1
0
1
2
1
1
3
2
0
0
0
0
2
1
1
1
1
2
2
0
0
1
0
1
1
1
2
1
0
1
0
2
0
1
2
0
0
0
2
1
1
2
0
1
0
1
1
1
2
0
0
1
0
2
0
0
2
0
2
0
0
0
0
0
0
1
1
1
0
0
1
1
5
1
1
0
2
0
3
2
2
4
2
0
0
2
2
2
0
2
0
0
0
1
0
1
1
3
0
0
1
1
0
0
0
0
0
1
1
1
1
2
0
1
2
1
1
1
1
2
1
2
0
1
1
1
0
0
0
1
0
2
0
1
0
2
2
1
1
1
1
4
0
2
1
1
1
0
0
2
0
2
1
0
1
1
0
4
2
1
0
0
0
1
0
2
2
1
1
2
1
0
1
2
2
0
1
0
1
0
2
0
1
2
1
1
1
1
1
1
1
1
1
1
0
1
2
2
0
0
0
1
0
1
1
2
0
1
3
2
2
0
1
1
1
0
1
2
1
0
1
1
1
1
1
2
1
1
1
1
1
0
0
0
1
1
2
0
0
1
2
2
0
1
1
2
1
1
1
0
0
1
1
2
0
0
2
2
0
2
1
1
0
0
0
2
1
2
0
0
0
1
1
1
1
1
0
2
0
1
2
1
1
1
0
1
0
0
1
2
0
0
1
2
0
0
1
0
1
0
1
1
1
1
3
1
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
1
2
1
0
1
5
2
0
1
0
0
2
1
0
2
1
0
1
1
1
2
2
1
0
2
0
0
1
0
0
1
2
0
1
0
0
1
2
0
1
1
0
1
1
1
0
0
1
2
0
2
1
3
2
1
0
0
2
1
0
1
2
1
2
1
1
1
1
0
0
0
1
0
0
2
1
2
1
1
1
2
2
0
1
0
1
0
0
1
0
1
0
1
1
0
1
2
1
2
1
2
0
0
1
0
1
2
1
2
1
2
1
2
2
0
2
0
2
0
1
1
1
1
2
2
1
1
0
1
1
1
1
1
2
0
0
0
1
1
0
0
0
2
2
1
2
0
2
2
0
1
1
2
2
0
1
2
1
2
0
2
1
0
0
0
1
2
1
2
0
0
1
0
1
2
2
0
1
2
1
1
1
1
1
0
2
1
0
1
1
2
0
0
1
0
0
2
1
1
1
2
1
0
1
1
0
1
0
0
1
0
1
1
1
1
0
0
1
0
2
1
0
0
0
2
2
0
0
2
0
0
2
0
0
1
0
1
1
2
1
1
1
0
0
2
2
1
2
0
1
0
0
0
0
0
1
0
0
1
2
1
2
1
2
2
2
1
2
1
0
1
1
0
0
1
1
0
0
1
0
2
0
2
1
2
1
0
1
1
2
2
0
1
1
1
2
0
1
1
1
2
1
1
1
2
0
0
0
1
1
1
1
1
1
2
0
0
1
2
2
1
1
1
1
2
1
1
0
1
3
2
0
1
2
0
2
1
0
1
0
1
2
1
0
1
2
1
2
2
0
2
1
1
0
1
2
1
2
1
0
0
2
2
2
0
1
1
0
1
0
1
1
0
2
0
1
2
2
0
2
0
2
0
1
1
1
1
0
1
0
0
2
0
1
0
1
0
1
1
1
1
1
1
0
2
1
0
0
2
0
0
1
1
0
2
2
0
0
2
0
1
1
1
0
2
1
1
0
2
0
1
2
1
0
1
2
0
0
1
0
0
1
1
3
0
0
1
1
0
0
0
1
1
2
0
1
0
2
0
1
0
2
0
0
2
1
1
1
2
0
2
0
1
0
1
2
1
0
0
1
2
1
0
1
0
2
0
0
0
0
3
2
0
1
1
0
0
1
0
2
0
0
1
1
2
2
0
2
1
0
0
1
0
0
0
0
0
1
2
0
0
0
1
1
1
1
0
1
1
0
1
0
1
1
1
0
1
1
2
2
2
0
1
2
0
1
0
0
1
1
0
0
1
0
0
0
1
1
0
2
0
0
0
0
2
0
1
0
1
2
0
1
1
2
0
1
1
1
0
0
0
1
0
2
0
0
1
2
0
2
2
1
1
0
2
0
0
0
0
1
1
2
0
1
2
0
0
0
0
2
2
2
1
0
1
1
1
1
2
1
0
0
0
0
2
0
0
1
0
1
1
1
1
0
1
1
1
2
2
1
1
1
2
1
2
0
0
1
2
0
2
1
1
1
0
1
1
0
1
1
2
0
1
0
1
1
0
2
0
1
1
0
1
0
1
2
1
0
1
1
1
1
1
1
0
0
1
1
1
0
2
1
2
4
1
0
1
1
2
2
1
0
1
1
0
2
0
1
0
0
0
0
2
0
1
2
0
2
2
1
0
1
1
1
2
0
1
1
2
1
1
1
1
1
0
0
1
1
1
1
0
0
1
0
1
2
1
1
0
1
1
0
0
1
1
0
2
0
0
2
1
1
0
2
2
0
1
0
1
0
0
0
1
0
0
0
1
1
2
0
1
2
1
2
0
2
1
2
2
0
1
0
0
0
2
2
3
1
0
2
1
1
1
1
0
0
0
2
0
1
0
2
1
0
1
2
0
2
0
1
1
1
2
0
0
1
2
4
1
1
1
0
1
1
0
1
1
0
2
2
1
1
0
1
0
0
0
2
1
2
1
1
2
1
1
0
2
2
1
1
1
0
0
2
1
2
1
1
0
0
1
2
1
1
1
0
1
0
0
2
0
0
0
0
1
1
1
0
2
5
1
2
2
1
2
0
0
1
2
1
0
0
0
1
0
0
2
0
0
2
0
1
0
2
1
1
1
1
0
0
1
3
2
1
2
0
0
1
0
0
0
1
2
1
1
0
2
0
0
1
1
1
1
1
0
0
0
0
2
1
0
1
0
0
1
1
1
0
1
0
1
1
1
0
1
0
2
0
2
2
0
0
2
2
0
1
0
0
1
0
1
0
3
1
3
0
0
2
1
0
0
0
2
1
1
1
1
0
1
1
2
0
1
2
1
1
1
0
1
2
2
1
0
0
1
0
1
0
1
1
1
2
1
0
2
0
0
0
1
0
1
1
1
0
1
0
0
2
1
1
1
1
2
1
0
0
1
1
1
1
2
1
2
0
1
2
1
1
1
0
0
0
0
1
0
1
0
0
0
2
1
2
1
1
1
0
0
1
2
1
0
1
1
1
0
0
2
2
4
1
0
1
0
0
1
1
2
1
1
2
0
2
2
2
1
0
0
1
2
1
0
2
0
2
1
0
2
1
2
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
1
1
0
1
2
0
0
0
0
2
0
0
0
0
1
2
0
0
1
2
0
0
2
1
1
0
1
2
1
0
2
1
2
0
1
1
0
2
2
1
0
0
1
1
1
1
1
1
0
0
2
0
0
2
1
0
0
0
0
1
1
1
3
2
2
0
1
0
1
1
0
1
1
0
2
2
2
1
0
1
0
1
1
1
0
1
1
0
2
0
0
2
1
1
2
0
1
0
1
1
0
1
1
1
1
0
0
2
0
1
0
2
1
0
0
0
1
0
2
0
1
1
0
2
1
0
0
0
4
1
1
2
0
2
0
0
0
2
3
1
0
1
1
0
0
2
0
1
1
0
2
1
1
2
1
0
1
0
1
1
0
0
1
1
1
2
0
0
3
1
1
2
2
1
2
1
1
0
0
1
3
1
2
1
0
1
0
2
0
1
0
0
1
1
1
0
3
2
0
2
1
1
2
1
1
0
0
1
1
1
2
0
2
0
1
2
0
2
0
1
1
0
2
1
0
1
2
2
1
1
2
0
1
2
2
1
0
1
2
0
0
1
1
1
1
2
1
0
1
1
0
1
1
2
1
0
0
2
0
0
0
0
0
1
0
0
0
1
1
0
2
1
0
0
1
1
0
0
1
1
2
0
4
0
1
0
2
1
0
1
0
1
0
0
1
2
1
0
2
0
0
2
1
2
0
1
0
2
1
1
2
0
0
1
1
2
1
0
0
1
1
2
1
0
0
3
2
1
1
0
1
1
1
3
0
1
1
2
1
0
2
2
2
1
0
1
0
0
0
0
0
0
2
1
0
1
0
0
3
0
0
0
1
1
1
2
0
2
0
1
0
0
1
0
1
0
2
0
1
0
2
0
1
0
1
1
0
1
1
1
0
2
1
2
1
2
0
1
0
2
1
1
0
0
1
0
1
1
0
2
2
2
0
1
1
1
0
0
0
2
0
1
0
2
0
0
1
1
2
0
0
0
2
2
0
0
2
1
0
1
0
1
0
0
1
2
1
0
1
0
1
0
2
2
0
1
0
2
1
1
1
0
1
1
1
1
1
1
1
0
1
1
0
1
0
1
1
0
1
0
0
0
0
2
0
1
1
2
5
0
0
0
0
1
2
1
1
1
1
1
2
2
1
1
2
2
0
1
0
1
1
1
1
0
1
0
1
0
0
1
2
1
1
1
2
1
1
0
0
1
3
0
2
1
1
0
2
3
0
2
0
1
3
0
0
3
2
0
1
0
2
1
2
0
2
1
1
1
1
0
2
1
0
1
2
1
1
1
1
2
1
1
1
2
2
1
1
1
1
0
1
1
0
0
1
0
0
1
1
2
1
1
1
0
1
2
1
0
0
0
1
1
1
0
1
1
0
0
2
0
0
1
0
2
1
0
1
0
1
1
1
1
1
1
4
0
1
0
2
0
2
0
0
0
2
1
0
2
0
0
1
1
0
0
1
1
1
0
2
1
2
0
1
1
0
0
0
0
1
1
1
1
0
0
1
0
1
3
2
1
0
1
1
2
1
1
2
3
2
1
2
1
1
1
0
1
2
1
1
3
1
1
1
0
0
3
2
2
2
1
0
1
0
0
1
2
2
1
1
1
2
0
1
1
2
1
2
1
0
2
1
2
2
1
1
1
0
1
0
0
2
3
2
1
0
2
0
0
1
1
0
2
1
0
0
2
0
2
2
0
0
0
2
0
0
2
1
1
0
1
1
0
2
0
2
0
1
0
0
1
2
0
2
2
0
0
2
0
1
0
2
1
1
0
2
0
1
0
0
1
1
0
0
2
1
0
1
1
2
0
1
2
1
2
1
1
1
1
0
2
1
1
0
1
2
1
0
0
2
1
0
1
2
2
0
0
0
1
1
1
2
0
1
0
0
0
1
1
2
0
1
1
2
0
2
1
0
1
0
1
1
1
1
2
1
2
0
2
0
0
2
5
0
0
0
1
1
1
0
1
2
0
1
0
0
0
1
0
0
0
1
0
2
2
0
1
0
2
1
1
0
1
0
1
2
1
0
2
1
1
0
1
2
0
0
0
1
0
1
1
2
0
1
1
0
0
0
2
1
0
1
0
1
2
0
1
0
1
1
0
1
1
1
2
0
2
0
0
0
0
0
0
1
0
1
2
1
1
1
1
0
0
1
1
2
1
0
2
0
1
0
0
0
0
1
0
0
1
0
0
1
1
1
2
0
1
2
1
2
0
1
1
0
0
0
2
1
0
0
1
0
0
0
2
2
0
3
1
0
0
0
0
1
0
2
2
1
1
0
2
1
0
0
0
2
1
0
1
0
2
2
1
1
2
0
2
2
0
0
0
0
0
1
1
3
2
2
1
1
1
0
1
0
0
1
1
1
0
2
1
1
1
2
0
0
0
2
1
0
1
2
1
0
0
0
1
1
2
0
0
2
1
2
2
0
1
2
2
0
1
2
0
0
1
1
2
0
2
2
0
0
2
0
3
0
0
0
1
1
0
3
1
0
0
0
2
1
1
1
2
1
0
2
1
0
0
1
0
2
2
1
0
2
2
0
0
1
2
1
2
1
2
0
0
2
0
0
1
1
1
1
2
0
2
1
1
1
3
1
0
0
0
1
0
0
1
2
0
2
1
0
2
1
0
2
1
1
1
1
1
0
2
2
0
1
0
0
2
0
2
0
0
1
0
1
0
0
1
1
2
1
0
2
1
0
1
1
1
0
0
0
0
2
0
1
0
1
1
1
0
0
1
1
2
0
0
2
0
1
1
2
0
1
1
0
0
0
0
0
0
0
1
2
0
2
2
2
1
1
0
2
1
1
1
4
0
0
1
0
1
1
0
2
3
1
0
1
1
0
2
2
0
1
2
2
2
2
0
0
0
2
0
2
1
2
1
2
2
0
0
1
2
1
0
1
0
0
1
1
0
2
1
1
0
1
0
1
1
1
1
2
0
1
1
1
0
2
1
1
2
0
2
1
2
1
2
0
2
0
0
1
0
0
1
0
0
1
1
0
2
1
0
2
0
0
0
0
0
1
0
0
0
2
3
1
1
1
0
1
2
0
1
0
2
1
0
1
0
1
1
0
2
0
1
2
1
1
1
2
0
1
1
1
2
1
0
1
2
1
2
2
1
1
0
0
3
1
0
2
0
1
1
1
0
2
0
0
1
1
2
0
4
2
1
2
1
2
0
1
0
2
0
0
1
1
1
1
0
0
0
2
1
0
0
1
2
2
1
1
1
0
1
0
1
0
1
2
0
2
0
0
1
1
1
1
0
1
1
0
0
2
1
0
2
2
1
1
0
1
1
0
0
2
0
1
1
1
0
1
0
0
2
0
2
1
1
1
1
1
0
0
2
0
2
1
1
2
2
2
0
1
1
0
1
2
0
1
2
1
1
1
0
0
1
0
0
5
2
0
0
1
1
2
1
1
1
1
1
0
1
2
2
4
1
1
1
1
1
0
1
1
2
1
1
1
1
0
1
1
0
1
0
1
1
0
2
0
0
0
1
1
0
1
1
1
1
2
1
2
1
1
1
1
0
1
1
2
0
1
1
2
1
0
0
0
1
1
1
0
2
0
0
1
1
0
1
0
0
0
3
0
1
0
1
0
0
2
0
0
0
2
1
1
0
1
0
1
0
0
1
1
1
3
2
1
0
2
1
2
2
0
1
0
1
1
0
1
1
2
2
0
0
1
0
3
1
0
1
2
0
0
0
1
0
0
1
0
1
1
0
2
1
0
2
0
1
1
1
1
1
2
1
0
0
0
0
0
2
0
1
1
2
1
1
1
0
0
0
2
1
1
2
2
0
2
1
0
0
2
3
0
1
0
0
2
0
0
0
1
2
0
2
1
1
0
1
3
2
1
0
2
2
1
0
1
0
1
0
1
0
1
2
2
1
0
3
2
0
1
0
3
0
1
0
1
2
1
1
1
1
1
1
2
1
0
0
0
1
1
0
1
1
1
0
0
0
1
1
2
0
0
2
2
0
1
0
0
1
0
2
1
0
2
1
0
1
0
3
1
1
0
1
0
0
1
2
1
1
1
2
0
1
0
2
0
1
1
2
1
0
2
2
1
0
3
1
1
0
0
3
2
1
2
0
2
0
0
2
1
0
3
1
2
2
1
2
1
2
2
1
0
1
2
2
0
0
2
2
0
0
0
1
1
0
0
1
2
3
0
2
2
0
1
0
0
2
1
2
1
0
1
0
1
0
0
1
1
0
1
0
1
0
2
0
0
2
2
1
2
0
0
2
2
1
2
1
1
1
0
2
0
1
0
1
2
1
1
1
0
2
0
0
0
2
0
1
0
0
1
1
0
1
1
2
2
0
1
1
0
0
1
1
1
0
0
2
2
2
1
1
1
1
1
1
2
1
1
2
1
0
2
0
0
0
2
0
0
1
2
1
0
0
0
1
2
2
3
0
0
1
0
2
0
1
1
1
1
0
0
1
0
1
2
1
2
1
1
1
1
1
0
1
0
0
0
2
1
1
2
1
1
0
1
1
2
1
0
2
1
0
1
1
2
1
1
6
2
1
2
0
4
0
4
2
0
1
0
2
3
2
1
1
1
1
0
1
1
1
1
2
0
1
2
1
1
1
0
0
1
1
0
0
2
2
0
0
0
1
2
1
0
1
1
0
2
0
0
1
1
1
0
1
3
1
0
1
1
0
0
1
1
0
0
0
0
1
1
0
0
0
1
0
2
2
0
2
0
1
1
1
1
1
0
2
1
0
1
1
0
3
0
1
0
1
2
1
2
2
2
1
1
1
0
0
0
2
2
1
2
1
2
0
1
1
0
1
2
1
2
0
1
0
0
2
0
1
0
1
1
2
1
2
1
0
1
1
0
1
0
2
0
1
0
0
1
1
0
1
2
1
2
2
1
1
1
0
0
1
1
0
1
1
1
1
0
1
1
2
0
1
2
2
1
0
2
0
1
2
0
2
0
0
3
0
0
1
1
1
0
1
1
0
3
1
1
0
0
1
0
0
1
1
2
0
1
1
1
3
1
0
0
0
2
1
2
1
2
0
0
3
1
1
1
0
0
2
1
0
0
0
2
1
0
1
0
1
0
0
1
0
0
1
0
1
0
1
0
0
1
1
1
1
1
0
2
1
1
2
1
0
0
1
1
1
2
0
1
0
1
2
2
2
1
0
1
2
1
2
1
0
0
1
0
1
0
5
2
0
1
1
0
1
2
1
1
0
1
1
1
0
1
0
2
5
1
2
1
0
0
1
1
0
2
2
0
2
1
2
1
0
2
0
1
2
1
2
0
1
2
1
0
1
2
1
0
1
1
0
0
0
1
0
1
0
1
2
2
0
1
1
2
2
0
2
2
1
0
2
0
0
1
0
1
2
1
1
2
0
2
0
1
1
1
1
1
1
0
2
0
2
0
1
1
0
1
2
0
1
1
1
1
0
0
1
0
1
2
1
0
1
0
2
0
1
2
1
3
2
1
2
0
1
1
1
0
0
2
1
0
1
1
2
0
1
0
2
1
1
0
1
0
0
0
1
0
0
1
0
0
1
1
2
0
1
0
0
2
1
0
0
1
0
1
2
1
1
0
1
1
1
2
2
0
1
1
2
1
0
0
0
0
0
1
2
0
1
1
2
1
0
0
1
0
0
2
2
1
2
0
0
1
4
1
2
1
1
1
2
0
1
1
0
0
1
0
1
2
2
1
0
1
0
0
2
0
2
0
2
1
2
1
0
1
0
2
2
2
0
0
0
0
0
2
0
0
1
2
1
1
2
1
1
2
0
0
1
1
0
1
1
0
1
2
0
1
1
0
0
2
0
1
1
0
1
2
0
2
3
0
0
0
0
0
0
1
0
1
1
1
0
1
2
1
1
0
0
0
1
0
1
0
0
1
0
2
1
1
0
1
1
0
3
0
1
3
1
1
2
2
1
1
0
1
1
2
0
0
1
1
1
0
1
0
2
1
1
0
2
0
2
1
3
0
1
1
1
1
1
0
1
2
0
0
0
1
0
2
1
2
1
0
0
2
0
1
0
0
1
1
2
0
0
0
0
0
0
2
0
0
1
0
2
1
0
2
1
0
1
1
1
2
1
0
0
0
1
1
0
1
1
1
1
1
2
0
1
0
1
0
0
1
1
0
2
1
2
1
1
2
1
0
1
0
1
0
1
1
0
1
1
2
0
1
0
2
1
0
1
2
4
0
1
0
2
1
0
0
4
1
1
0
1
1
1
0
0
1
2
2
2
1
1
0
2
1
0
0
0
0
2
1
0
2
1
2
0
1
0
0
1
0
0
1
1
0
0
1
0
1
0
1
1
1
0
0
1
1
0
2
1
1
1
2
2
0
2
1
1
1
1
0
0
1
1
0
1
0
1
0
1
2
0
1
1
0
0
1
1
0
1
0
2
1
0
1
1
2
0
0
0
0
2
1
1
0
2
2
1
0
2
1
1
0
2
1
1
0
0
1
3
2
0
1
0
1
1
2
1
2
0
1
1
1
1
0
1
2
2
1
0
0
0
1
0
2
0
1
0
0
2
2
1
1
1
2
0
0
0
2
0
1
0
1
1
1
1
0
1
1
1
2
0
2
0
0
0
0
1
0
0
0
1
1
0
1
0
2
2
1
1
0
1
0
0
0
1
2
0
1
2
0
0
1
0
0
2
0
2
0
1
1
0
1
0
1
2
2
2
1
2
2
2
1
2
2
1
1
0
1
1
1
0
2
0
0
0
0
1
0
0
1
1
0
1
2
1
0
0
2
0
1
0
0
0
1
1
0
1
2
2
0
1
1
2
1
1
0
1
0
0
1
0
1
0
0
0
1
0
2
0
1
2
1
1
1
1
1
2
1
1
0
5
2
1
2
1
2
0
1
0
0
0
0
2
0
2
0
0
2
2
0
0
0
2
1
1
1
0
2
1
0
2
1
1
0
1
0
1
0
0
0
0
2
0
0
0
2
2
0
0
2
0
1
1
0
3
1
1
0
1
0
1
0
0
1
1
1
0
2
1
1
2
0
1
0
1
0
0
2
0
1
0
0
1
0
1
0
0
0
1
2
2
2
2
1
0
0
2
1
2
0
0
1
2
1
2
2
0
3
0
0
0
1
1
1
0
2
0
1
1
2
3
0
0
1
2
1
1
1
1
0
1
2
1
0
1
1
0
1
0
0
2
2
0
1
2
1
1
2
0
2
2
1
1
0
0
1
1
0
0
1
1
1
0
0
1
2
2
1
1
1
1
0
1
0
0
2
3
0
0
0
2
1
1
1
1
1
2
0
1
1
0
0
1
1
0
1
0
0
0
2
3
2
1
1
0
0
1
2
2
2
1
2
1
1
2
0
1
0
2
0
2
0
1
1
1
1
0
1
1
0
1
1
1
1
1
2
2
2
1
1
2
0
1
0
2
1
1
2
0
1
2
0
1
1
0
1
1
0
0
0
0
1
2
2
2
1
1
0
1
1
1
2
0
2
2
0
2
2
2
0
2
0
2
0
0
1
3
1
3
0
0
1
0
0
2
2
0
2
2
1
1
2
0
2
0
0
0
1
2
1
1
0
0
1
0
0
1
1
1
0
1
1
2
1
1
0
0
2
1
2
2
2
0
2
2
0
0
2
1
1
1
0
2
0
1
0
2
0
1
0
2
0
2
2
0
0
0
2
0
1
0
1
1
1
0
0
1
1
0
0
0
1
1
2
0
2
1
1
1
4
0
1
0
1
0
0
1
0
1
0
2
0
0
1
1
0
1
0
1
1
0
0
1
1
2
2
0
0
1
1
1
1
1
1
0
1
2
0
0
0
3
0
0
0
0
1
2
1
0
0
2
0
1
0
2
0
2
1
1
0
1
0
1
1
0
1
2
1
2
0
2
0
1
1
0
1
0
2
1
2
0
0
2
1
1
2
1
1
1
1
4
1
1
0
0
0
1
2
2
2
0
2
0
2
1
1
3
1
0
2
1
1
0
0
1
2
2
0
1
2
1
1
1
0
3
2
0
1
0
0
3
1
1
0
1
1
0
1
1
2
0
0
0
0
2
0
2
0
0
0
1
1
2
0
0
1
1
0
1
0
0
1
0
1
0
0
0
0
1
2
1
1
1
1
0
0
2
1
2
2
1
1
0
1
0
2
0
2
0
2
1
0
1
0
2
1
0
1
0
2
2
0
1
0
1
1
1
1
2
1
1
1
2
1
0
2
1
0
2
1
0
0
1
1
0
2
1
1
1
2
2
1
0
2
1
2
1
1
0
1
1
1
2
2
1
1
1
1
2
3
1
2
1
0
1
2
0
1
0
1
2
1
0
1
0
0
1
0
1
0
0
3
0
1
0
0
1
2
1
1
1
1
1
2
2
0
0
1
1
0
1
0
1
2
2
0
0
0
1
0
1
0
0
0
0
0
0
0
1
2
0
0
0
1
2
1
0
0
2
2
0
2
1
1
1
0
1
3
1
2
1
1
1
1
0
0
1
1
0
1
0
1
2
2
2
0
2
1
1
2
1
1
1
1
0
1
0
0
2
0
1
0
1
0
1
1
0
2
1
1
1
1
0
0
2
0
0
0
1
0
1
1
2
0
0
0
1
2
0
3
2
0
0
1
0
1
0
0
0
0
1
2
1
0
1
1
0
0
1
1
2
1
2
0
2
1
2
0
1
0
2
2
1
2
0
2
2
3
2
1
0
2
1
2
0
3
0
0
2
0
0
1
1
0
0
0
0
3
0
2
2
1
2
0
0
0
1
1
0
1
2
1
2
0
0
2
0
1
2
2
1
1
1
1
2
2
1
0
1
2
1
1
1
1
0
2
0
2
1
1
0
2
0
1
0
0
2
0
2
2
1
0
1
2
1
2
0
1
4
1
0
2
0
0
1
1
0
1
0
1
1
1
1
1
0
1
0
1
2
0
0
0
1
1
1
0
0
2
2
1
0
0
1
1
0
1
1
1
0
1
0
0
1
1
2
0
0
1
1
2
1
2
0
0
1
0
1
1
0
1
0
0
2
0
2
1
1
1
0
1
1
1
0
0
0
1
1
1
0
0
0
1
2
0
0
1
2
1
2
1
0
2
1
1
1
1
1
0
3
1
0
0
1
2
0
1
3
0
2
0
0
1
0
0
1
2
0
2
0
0
2
3
1
2
1
0
1
2
1
1
1
1
2
2
1
0
0
0
1
1
1
1
1
0
2
1
1
2
1
2
0
1
1
1
2
1
1
0
1
1
0
0
0
0
0
0
1
0
1
2
0
0
1
2
1
2
1
0
2
1
0
1
1
0
0
0
1
1
1
2
2
1
1
2
0
0
1
0
0
2
1
2
0
1
2
2
3
2
0
1
1
1
0
1
2
0
1
0
0
0
1
1
0
0
1
1
2
2
2
1
1
1
1
1
1
0
2
1
1
1
1
1
2
0
3
1
1
2
1
1
1
1
1
0
2
0
1
1
1
1
0
0
2
0
1
0
3
1
2
1
0
2
1
0
1
1
0
1
0
1
4
3
0
0
2
1
1
1
1
2
2
1
1
1
0
0
1
0
2
2
0
1
1
0
2
0
0
1
1
0
1
0
1
2
2
2
1
0
0
1
2
2
1
0
1
0
1
1
0
0
0
0
2
1
0
1
1
0
2
1
0
0
0
0
2
1
1
0
1
1
0
2
1
0
2
1
0
0
0
0
2
2
0
1
0
0
1
1
1
2
0
2
1
1
1
1
1
1
1
0
2
3
2
0
0
0
2
2
1
1
1
0
0
1
2
0
2
0
0
3
0
1
1
1
2
2
1
0
1
1
1
0
1
1
1
1
2
1
2
2
1
0
1
0
0
2
1
0
1
1
0
0
0
0
0
1
1
1
1
1
1
2
0
0
0
2
2
0
0
0
0
1
1
0
2
0
2
0
1
0
0
2
2
2
0
2
1
1
2
1
2
0
0
0
1
0
1
0
0
1
1
0
0
0
1
0
1
1
2
0
0
2
0
1
1
1
1
0
0
1
2
2
1
1
1
2
2
2
1
0
2
0
2
1
0
0
1
2
2
0
0
0
2
1
2
1
0
0
2
0
1
2
0
1
0
0
1
0
0
1
1
1
2
0
1
0
2
2
1
0
0
1
1
2
0
1
1
1
0
1
0
1
1
0
0
1
1
1
0
0
0
2
0
0
1
1
0
1
0
0
2
2
0
0
1
0
0
1
1
1
0
3
1
0
1
2
2
0
1
2
0
2
2
1
1
1
1
0
2
0
2
1
1
2
0
0
0
0
1
2
0
0
1
2
1
2
0
1
1
1
2
0
0
1
1
0
0
0
1
1
0
0
1
0
0
2
1
1
2
1
1
2
0
1
1
0
2
1
1
2
1
1
1
1
1
0
2
0
1
2
1
0
0
1
0
0
2
0
0
1
0
1
0
2
2
2
1
2
1
0
1
1
1
0
0
0
0
0
1
0
1
0
1
0
1
1
1
2
0
0
1
1
1
1
1
0
1
0
1
2
1
0
2
0
2
2
1
1
0
0
1
1
1
1
1
0
1
1
1
0
1
0
1
2
0
1
2
2
2
1
1
1
2
0
0
1
1
0
2
1
0
1
0
1
1
0
0
1
1
0
1
2
0
1
0
2
2
0
1
1
1
1
1
1
1
4
1
2
0
2
0
1
0
1
1
1
2
0
3
0
0
0
3
0
3
1
0
0
2
2
0
0
1
0
1
0
1
1
1
0
0
1
0
2
0
1
1
2
2
1
0
1
1
2
1
0
1
2
2
0
1
2
0
0
2
1
1
1
1
0
1
0
2
2
1
0
1
2
0
0
0
0
2
1
1
0
0
0
0
2
1
0
0
0
2
1
0
0
2
0
2
1
0
2
1
1
1
0
1
1
2
0
0
0
1
1
2
1
1
0
0
0
0
2
2
2
1
1
1
0
0
2
0
0
2
1
1
0
0
2
2
1
0
1
0
1
0
0
2
1
1
1
0
1
0
1
3
0
1
1
2
2
0
1
1
1
2
0
1
0
2
1
1
0
0
0
2
1
0
1
0
0
1
0
0
1
1
2
0
0
2
0
2
1
2
1
1
0
1
0
1
2
0
0
0
0
1
1
0
2
1
0
1
1
0
2
2
3
0
1
0
2
2
1
2
1
1
0
0
2
0
1
1
0
0
1
1
1
2
1
1
0
0
2
0
0
0
0
0
1
0
1
0
1
2
2
0
1
0
0
1
0
1
2
0
0
0
1
1
0
2
1
0
0
1
1
0
0
1
2
0
0
1
1
1
0
1
2
1
1
1
0
1
1
0
1
2
1
0
1
0
0
0
0
0
0
0
1
1
0
2
1
1
1
1
1
0
1
1
2
2
1
0
1
1
1
0
0
1
0
1
0
0
1
1
2
1
0
0
2
1
1
0
0
2
1
0
1
1
1
1
0
0
0
0
0
2
1
0
1
1
1
0
2
1
1
0
2
1
1
1
1
0
1
1
2
1
1
0
2
0
1
1
0
1
1
1
1
1
0
2
1
1
2
1
1
1
2
1
1
1
2
1
1
1
1
2
1
0
1
2
1
0
2
2
2
1
0
2
0
0
2
1
1
0
1
0
0
1
0
0
3
1
2
2
2
1
1
1
0
1
0
0
2
0
1
1
1
0
1
0
0
0
2
1
1
0
0
0
0
1
1
1
1
1
2
0
0
1
1
0
1
2
0
0
1
2
0
0
2
2
1
1
0
1
1
1
0
0
0
2
0
0
1
1
1
1
0
1
1
1
1
2
1
2
2
1
1
2
0
1
1
1
1
1
0
1
0
1
0
1
1
0
2
2
0
1
3
2
2
2
1
2
3
1
3
1
0
0
1
1
2
1
1
0
1
0
1
0
2
1
1
2
1
0
0
0
0
1
2
4
0
2
1
0
2
1
0
0
0
0
1
1
1
2
0
0
1
1
2
0
1
1
2
0
0
0
0
0
1
1
1
1
1
1
2
2
1
0
2
0
1
2
0
1
1
2
1
1
1
0
0
0
0
1
0
1
2
2
2
1
1
0
1
1
2
1
0
1
1
2
0
1
1
1
2
0
2
1
1
0
5
0
0
1
1
0
1
1
0
1
0
2
2
1
0
2
1
2
1
2
1
2
1
1
1
0
2
2
1
0
1
1
1
1
2
0
0
1
0
4
0
1
1
1
0
1
1
1
2
1
1
0
1
0
2
0
0
0
0
0
0
2
0
2
1
1
2
2
1
1
0
2
1
0
1
0
1
0
0
2
1
0
0
0
0
0
1
2
0
0
2
2
2
2
2
1
2
2
0
1
1
0
0
0
2
1
1
0
2
0
0
1
1
1
2
0
0
0
2
1
1
1
1
2
1
0
1
1
2
2
0
1
0
1
0
2
0
0
0
1
1
2
1
0
0
0
1
0
1
2
0
0
0
1
2
0
0
0
0
2
1
2
0
0
0
2
0
0
0
0
2
1
1
0
2
2
1
2
1
1
0
0
2
1
0
1
1
0
3
0
1
2
0
0
2
0
0
0
0
0
1
0
1
1
1
1
1
0
2
2
0
1
1
2
0
0
1
2
1
0
1
2
0
0
0
0
1
0
1
1
2
1
2
2
0
2
0
2
0
0
0
1
0
1
0
1
1
1
0
2
2
1
3
2
2
1
0
0
2
0
1
0
2
1
0
1
1
1
2
1
1
2
0
1
0
0
0
0
1
1
2
1
0
2
0
1
0
0
2
2
0
1
1
2
2
1
2
0
2
1
1
1
1
0
1
1
1
2
2
0
1
1
2
2
0
2
1
0
1
2
1
0
2
0
0
1
1
0
1
2
0
0
1
2
0
1
1
0
0
1
0
1
2
0
0
1
0
1
0
1
0
1
2
1
2
1
2
1
2
1
3
0
1
0
2
1
2
1
0
1
2
1
2
2
0
1
1
0
1
1
1
0
0
1
1
0
0
0
1
0
2
2
1
0
1
1
0
1
1
0
1
2
0
1
0
1
0
1
0
1
1
0
2
2
1
0
0
2
1
0
2
1
2
1
0
1
0
1
1
0
0
2
1
2
2
0
0
0
2
2
1
1
1
0
1
0
0
2
2
1
2
0
1
0
1
0
0
0
1
2
0
2
0
0
0
0
0
2
0
9
1
0
1
0
0
1
0
1
1
1
1
0
0
1
2
1
1
3
0
0
2
2
0
2
0
2
0
0
0
0
0
0
1
2
0
2
0
0
1
1
1
2
0
0
1
0
1
1
0
0
2
1
2
2
2
2
0
0
1
2
1
1
1
1
0
0
0
1
2
0
1
0
0
1
1
0
0
1
0
1
0
0
1
1
1
0
0
1
1
0
2
0
0
0
1
1
0
1
2
2
0
1
1
0
1
0
1
1
1
0
1
1
2
0
3
1
1
0
0
0
1
1
1
1
2
0
0
1
1
2
0
0
1
2
0
0
1
0
1
0
0
1
1
0
2
1
1
1
1
2
1
0
2
1
0
0
0
2
2
0
2
1
1
3
2
2
2
2
0
0
2
2
1
1
1
1
2
0
1
0
1
1
4
1
1
1
0
1
1
1
1
0
0
1
0
1
1
0
0
1
1
2
0
2
1
1
0
0
1
1
1
0
0
1
1
1
1
1
2
2
2
2
0
0
2
0
1
0
0
1
1
0
1
1
1
1
2
2
1
0
1
0
2
1
0
0
0
1
2
1
1
2
2
0
2
0
0
1
0
1
1
1
0
1
1
1
0
2
1
1
0
1
0
0
1
1
1
1
2
2
1
0
1
1
0
0
0
1
2
1
0
3
1
0
1
0
1
1
1
1
1
1
0
1
2
0
1
0
0
2
1
1
2
0
2
0
2
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
2
2
1
2
1
0
1
0
2
0
0
0
1
0
0
0
2
1
0
1
2
0
0
1
2
0
1
2
3
0
0
0
1
1
1
2
0
1
2
1
1
0
2
2
2
2
0
0
5
2
0
2
0
2
0
0
0
0
1
0
0
0
0
2
2
1
1
0
0
1
0
1
0
1
1
1
0
0
1
0
1
1
2
2
2
0
0
1
2
0
1
2
1
2
0
0
1
2
0
2
2
0
1
0
1
1
0
1
0
2
1
2
1
0
0
1
1
1
0
1
0
1
2
0
0
0
1
0
0
1
0
0
2
1
1
0
2
1
2
1
2
0
0
1
0
1
2
0
2
1
3
0
2
1
0
1
1
0
2
0
2
1
0
0
0
1
1
1
1
0
1
0
2
0
0
2
1
2
1
0
2
1
2
0
1
2
0
2
0
2
1
0
0
0
1
0
0
0
2
1
0
0
1
0
1
0
1
1
2
0
1
1
1
1
1
1
1
0
1
3
1
1
1
1
1
2
2
1
0
0
1
1
1
2
0
0
0
0
2
0
1
1
2
2
0
0
1
1
0
1
1
2
1
1
1
1
1
1
1
2
1
1
4
2
2
1
1
0
0
1
1
0
0
1
1
0
0
1
1
0
0
2
1
0
1
2
1
2
0
0
2
0
2
1
0
2
0
1
0
0
1
0
0
0
0
0
1
0
0
2
1
0
1
0
1
0
1
0
1
3
0
0
0
0
0
1
0
1
0
3
0
1
1
1
1
1
1
1
0
0
1
1
2
0
3
0
0
1
1
0
1
1
1
0
1
0
1
0
0
1
0
0
1
1
1
0
2
1
0
0
1
1
1
0
0
1
2
1
0
1
1
1
0
1
1
1
2
0
1
0
2
1
0
1
1
2
0
1
1
1
2
1
1
1
1
1
2
1
0
0
0
2
0
0
2
0
0
2
1
0
1
0
2
1
2
2
3
0
0
2
1
0
1
2
2
1
0
2
0
1
0
1
2
0
1
1
0
0
0
0
1
1
0
2
0
0
1
2
1
1
0
0
0
1
2
0
2
2
1
2
2
1
0
1
0
1
2
1
0
0
2
1
1
1
1
0
0
0
0
1
1
2
0
2
1
1
1
1
1
0
1
1
1
1
1
1
2
3
0
1
0
0
0
1
1
2
1
0
1
6
1
2
1
2
0
0
1
2
0
0
1
1
0
0
0
0
0
1
0
1
0
2
1
2
1
2
1
1
2
0
0
0
2
0
0
1
1
0
1
0
0
0
0
0
1
0
0
2
0
0
2
1
1
1
0
2
0
0
2
1
0
0
2
2
1
0
0
1
1
1
2
0
0
2
0
0
1
1
1
0
1
1
0
0
1
1
1
1
1
2
1
0
1
1
1
1
2
0
1
1
1
1
1
0
0
1
1
1
1
3
1
2
1
2
1
1
1
1
1
2
0
1
1
0
0
0
0
1
0
0
1
0
1
1
0
1
2
1
0
0
2
2
1
1
2
0
0
0
2
0
2
1
0
0
1
0
1
2
1
1
1
0
0
1
0
0
1
0
2
1
0
0
2
1
2
2
3
1
0
1
0
1
1
1
0
1
1
1
0
1
0
2
1
3
2
0
0
2
1
2
0
0
0
2
2
0
2
2
1
0
1
0
0
0
1
0
2
1
2
0
1
1
2
1
1
1
0
1
2
1
0
1
1
2
0
0
1
1
1
0
0
2
1
2
1
0
0
2
1
1
0
1
0
1
0
2
0
1
0
2
0
0
1
1
1
1
1
1
1
2
2
1
1
0
0
2
1
0
0
2
1
0
0
1
0
0
1
1
0
1
1
1
2
1
0
0
2
0
1
1
0
2
2
1
1
0
2
1
0
0
0
2
0
0
1
2
0
0
0
0
2
0
2
0
2
1
0
0
1
1
1
1
1
0
0
1
1
2
2
1
0
0
2
0
2
0
1
3
1
1
0
1
0
1
1
2
1
1
1
1
2
1
0
1
0
1
1
1
1
2
0
1
1
3
0
0
1
1
0
0
0
1
1
0
1
0
1
0
5
0
0
1
1
2
1
0
1
0
2
1
1
2
1
1
1
1
1
0
0
0
0
1
0
2
0
0
0
0
0
2
1
2
1
0
1
1
1
2
2
1
1
0
1
0
1
1
0
1
0
0
1
2
3
0
0
1
0
1
0
1
1
0
1
2
1
1
1
2
1
1
1
0
0
0
2
1
2
0
0
1
1
2
1
1
0
0
0
2
0
1
0
1
0
1
2
1
2
0
1
0
0
1
0
0
2
0
0
1
1
1
1
0
1
1
2
0
1
0
0
1
1
0
1
1
0
0
0
0
0
2
2
1
0
1
2
0
2
0
1
1
0
0
1
1
1
1
0
1
3
1
1
2
1
1
2
0
1
1
1
3
1
1
0
0
1
2
0
1
0
1
1
1
0
1
1
0
2
0
1
0
1
1
0
0
0
1
0
1
1
0
1
1
2
2
2
0
1
0
2
1
0
0
0
2
0
1
0
1
0
0
2
1
0
1
0
1
0
3
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
2
2
1
0
2
2
0
0
2
0
2
2
0
1
1
0
2
1
0
0
2
2
0
1
0
1
2
0
1
0
0
0
0
1
0
2
0
1
1
1
2
1
0
1
1
0
0
1
2
1
1
1
2
0
3
1
1
1
0
1
1
0
0
1
0
1
0
1
0
0
1
1
0
0
1
2
2
2
1
0
1
1
1
0
1
0
1
1
1
0
0
0
0
1
1
1
0
0
2
1
0
1
1
1
1
1
1
1
0
2
1
0
1
1
1
1
1
0
0
0
1
0
2
1
2
0
0
1
1
1
1
2
3
2
1
1
2
0
2
0
2
1
2
1
0
0
0
0
0
0
1
1
0
1
0
1
1
2
0
1
0
1
0
1
0
2
2
0
0
0
1
1
1
1
1
0
0
0
1
0
0
1
0
1
2
0
0
1
0
1
2
0
1
1
1
0
2
0
0
2
2
2
2
1
1
1
1
2
0
0
0
2
2
0
1
1
0
0
1
3
1
1
1
0
1
1
0
1
1
4
1
0
1
0
1
1
1
0
0
0
0
1
0
1
0
0
0
0
1
1
2
2
1
0
2
1
1
0
0
2
1
1
1
2
0
0
0
1
2
0
1
1
3
0
1
0
1
2
0
1
2
1
0
2
2
2
2
0
0
2
1
1
2
1
0
0
0
0
2
1
2
1
1
0
1
0
0
0
1
1
1
0
2
1
2
1
0
1
0
0
1
2
1
1
1
0
3
3
0
0
1
0
2
1
1
0
1
0
0
2
2
0
0
1
1
0
0
2
0
0
0
0
0
0
1
1
1
2
1
1
0
0
0
1
2
0
1
2
1
0
1
1
0
0
2
0
1
1
2
1
0
1
1
2
1
1
2
0
1
1
0
1
0
2
1
0
0
1
0
2
2
2
1
2
1
1
0
1
0
1
0
0
0
2
0
0
0
0
2
0
1
0
0
1
0
0
1
2
1
1
1
3
2
2
0
2
1
0
1
1
1
1
1
0
0
2
0
2
2
0
0
1
0
1
0
1
0
3
0
1
0
0
2
0
2
1
2
2
2
0
2
1
1
0
0
1
0
1
1
0
1
2
0
1
1
0
0
0
1
0
1
1
1
2
0
1
0
0
0
0
1
0
1
1
2
1
0
0
2
1
1
2
3
0
0
0
1
0
1
0
3
0
2
1
2
0
0
1
1
0
1
0
0
0
1
0
1
2
0
1
2
2
0
0
0
0
0
0
1
1
1
1
1
1
2
2
0
1
1
0
1
2
0
0
1
1
1
2
0
1
0
0
1
1
2
0
3
2
1
0
1
3
0
1
1
1
1
2
0
1
1
2
0
0
0
0
2
1
1
2
0
1
0
2
1
1
1
2
2
0
1
1
1
0
2
0
0
0
0
1
1
0
1
0
0
2
1
0
2
1
1
1
1
1
0
1
0
2
1
2
0
0
0
0
0
3
2
1
1
0
1
1
2
0
0
0
0
1
0
0
2
2
1
1
0
2
0
1
0
1
1
0
0
1
0
2
0
0
1
0
0
0
0
1
2
2
1
2
1
2
0
0
0
1
1
0
1
0
1
2
1
0
1
2
1
0
0
1
1
0
0
0
0
0
2
1
0
1
0
0
0
1
2
1
1
2
0
2
1
2
2
0
0
1
1
0
2
0
0
2
0
2
0
1
0
2
2
1
0
2
2
0
1
1
2
0
2
2
1
0
2
2
3
0
2
0
0
1
0
2
1
1
0
1
1
1
1
0
2
2
0
0
1
2
1
1
1
1
1
0
2
1
0
1
1
2
1
0
0
0
1
2
0
0
0
4
0
2
1
0
1
2
0
3
2
2
1
0
1
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
1
2
1
0
0
1
0
1
0
1
1
2
1
0
1
2
0
1
1
1
1
0
1
0
2
1
0
1
2
2
1
1
1
1
2
0
1
1
0
1
0
1
1
1
1
1
0
2
2
1
0
1
2
2
1
1
1
2
0
0
2
0
0
0
2
0
0
0
2
0
2
2
2
2
1
1
1
1
2
2
2
0
1
1
0
1
0
1
1
2
0
1
0
2
0
1
1
1
3
1
1
0
0
3
1
1
1
0
0
0
0
1
1
2
1
0
1
1
1
1
0
2
1
1
2
3
2
2
2
0
1
1
1
1
0
1
0
0
1
0
0
1
1
0
2
0
1
0
1
1
0
1
2
2
0
2
2
1
2
0
1
2
0
1
0
2
0
0
2
1
2
0
1
0
0
0
0
0
1
0
1
2
1
1
0
1
2
2
1
1
2
0
1
0
1
1
1
1
1
1
1
1
0
2
2
0
2
0
1
1
2
2
1
0
2
1
1
2
0
2
1
3
2
1
2
1
1
0
1
1
0
0
1
0
0
0
1
2
2
1
0
0
1
0
1
2
1
0
0
0
1
1
2
1
1
0
0
0
2
2
0
1
1
2
1
1
2
1
0
2
0
0
1
0
1
0
2
2
1
2
0
2
9
2
0
0
2
0
2
0
1
0
0
1
2
1
2
0
0
0
1
3
1
0
1
1
0
1
0
0
0
0
0
0
1
2
1
1
2
0
1
0
0
0
1
0
0
1
0
1
2
0
1
0
0
2
1
0
1
0
2
1
0
2
1
4
0
1
2
2
0
1
1
2
0
2
1
0
1
0
0
1
4
1
1
2
1
1
1
2
0
0
2
1
0
1
2
2
0
2
0
1
1
1
0
0
1
1
0
1
0
0
0
2
1
2
1
1
0
2
0
0
0
0
1
1
0
0
1
0
0
0
2
0
2
0
2
1
0
3
1
0
0
1
1
1
0
1
0
1
0
3
1
1
1
0
1
1
1
2
1
1
1
1
1
0
0
0
1
1
0
1
0
0
0
0
0
1
2
1
0
2
1
1
0
0
0
1
2
2
0
1
1
1
0
1
1
1
1
1
1
2
0
0
0
0
0
2
0
1
1
1
1
1
1
0
0
1
0
1
1
1
2
0
0
0
2
0
1
2
2
0
0
1
0
2
0
1
2
1
1
1
0
2
1
0
0
1
0
1
2
0
0
0
0
2
0
3
1
0
1
0
3
2
2
1
2
2
0
0
0
0
2
0
2
0
1
0
1
1
1
2
0
0
1
0
0
1
1
0
1
1
1
0
1
1
0
1
2
1
1
3
1
0
0
1
0
0
0
1
0
0
2
1
1
1
1
0
1
1
2
0
0
1
0
1
0
1
0
1
1
0
0
1
0
0
1
0
0
0
0
0
2
1
1
1
0
3
0
0
1
2
1
1
0
1
0
0
0
0
0
1
1
2
0
2
1
0
0
2
1
1
1
0
0
1
2
0
0
2
2
2
1
2
0
2
0
0
0
5
1
4
1
1
1
1
0
2
1
0
0
1
1
2
1
2
1
0
1
1
1
0
0
0
1
1
1
1
1
2
0
0
2
1
1
1
2
1
2
2
2
2
0
0
0
0
2
1
1
1
0
0
0
0
0
0
1
1
4
0
0
1
1
2
0
0
0
0
2
0
0
0
0
2
1
1
1
2
1
2
0
2
1
1
0
1
2
1
0
0
1
0
2
0
1
0
2
1
0
1
2
0
2
1
1
0
1
0
5
0
0
0
0
1
1
0
1
2
1
2
1
1
3
0
2
0
0
2
1
0
0
0
1
0
0
2
1
2
1
1
0
1
1
0
0
1
1
1
2
1
2
0
2
1
0
1
1
0
1
0
1
2
2
1
1
1
1
2
0
0
1
0
2
1
1
0
2
0
0
1
0
2
0
0
1
2
2
0
2
2
0
0
1
2
0
3
1
3
1
1
0
0
2
0
0
0
0
1
1
0
1
1
1
1
2
1
0
1
0
0
3
0
2
0
0
0
2
0
1
1
1
0
0
2
1
0
2
3
3
1
0
0
0
0
0
0
1
1
1
2
1
1
1
1
0
0
1
2
2
1
0
2
2
2
2
0
0
1
1
1
2
1
0
1
0
1
1
1
0
0
1
0
0
1
0
2
1
0
0
1
0
0
1
1
0
0
1
0
2
0
0
0
1
2
2
0
0
0
0
1
1
1
2
2
0
2
3
0
0
1
0
0
0
0
2
0
0
1
1
0
0
1
2
1
1
2
0
2
1
0
0
1
0
2
2
0
2
1
1
1
1
2
0
1
1
2
1
2
1
1
0
0
0
2
1
0
5
0
0
2
1
2
1
2
1
0
1
2
1
1
0
2
3
1
0
1
0
1
1
1
1
5
1
1
2
1
1
0
0
0
1
0
0
2
0
1
1
1
0
0
2
0
1
2
3
1
1
2
1
0
1
0
1
0
0
0
1
0
1
2
2
2
0
0
0
0
0
1
2
2
2
2
1
1
0
2
0
2
0
0
1
0
0
1
1
1
2
1
0
1
2
2
1
0
0
1
1
1
1
0
1
2
1
1
0
0
2
0
2
1
0
2
1
2
0
1
2
1
1
0
2
2
1
0
1
0
0
0
0
1
1
0
2
0
0
2
2
2
1
2
2
2
0
0
0
1
1
1
2
0
0
0
1
1
0
1
0
2
0
0
1
0
0
0
2
1
0
0
2
1
1
1
0
1
0
1
1
1
0
1
2
0
0
0
2
1
0
0
0
2
1
0
0
2
2
0
0
0
1
1
1
1
1
1
2
1
2
1
2
0
2
2
2
0
1
0
1
0
2
2
0
0
0
2
1
1
1
0
1
0
1
0
1
1
2
0
1
1
0
1
1
1
1
2
1
1
2
2
0
0
0
2
1
0
1
1
1
0
0
1
0
0
1
1
2
0
1
0
2
2
1
0
2
1
1
1
1
0
4
0
0
0
2
0
0
0
0
1
2
1
2
2
1
1
0
1
0
2
1
0
0
0
2
1
1
2
0
0
1
3
0
1
1
1
0
0
1
2
1
1
1
0
0
2
0
0
2
0
1
1
1
1
0
1
1
1
1
0
1
0
0
2
2
1
2
0
0
1
0
2
0
1
1
1
0
2
1
2
2
2
3
2
0
2
2
0
1
0
1
1
0
1
2
1
0
0
2
0
1
2
1
4
2
2
2
2
0
1
1
0
1
0
2
2
1
0
1
1
1
2
0
1
1
0
0
1
2
0
0
0
1
0
2
0
2
0
1
1
2
0
1
1
2
1
1
2
1
4
1
1
0
1
2
1
2
0
1
1
0
0
2
0
0
2
2
0
1
2
2
1
0
0
0
0
1
1
2
0
0
1
1
1
1
2
1
0
2
0
0
0
0
1
1
0
0
1
2
1
1
1
0
1
1
1
0
0
3
1
1
1
2
2
1
1
0
0
1
0
2
2
0
2
0
0
1
2
1
2
0
2
0
2
1
1
1
0
0
1
0
1
1
0
1
3
1
0
2
1
2
0
1
0
1
1
0
1
1
2
1
0
2
2
0
0
2
1
1
1
0
1
0
0
0
1
0
1
1
2
2
2
1
1
2
1
1
2
1
0
0
2
0
1
2
2
1
1
2
0
2
0
1
0
2
1
1
0
0
0
1
1
2
0
0
1
0
1
2
2
0
1
1
1
0
1
0
1
1
0
0
0
0
0
2
1
0
1
2
0
1
2
2
0
1
0
0
0
1
2
1
0
0
3
1
0
2
2
0
1
1
0
0
2
0
2
1
1
0
0
0
1
2
1
0
0
1
1
1
1
1
1
0
2
0
0
1
0
1
0
0
1
0
0
2
2
0
0
1
0
1
2
0
0
0
1
1
2
0
0
0
2
1
3
0
0
1
2
0
1
0
1
2
1
0
2
0
0
1
0
2
2
0
1
1
2
0
0
2
1
1
0
0
0
1
1
2
1
1
1
2
0
2
1
0
2
0
2
2
0
2
0
1
0
1
1
0
2
0
0
0
1
0
2
0
1
0
0
0
1
1
1
1
2
0
0
1
0
2
1
0
1
0
0
1
2
0
2
3
0
1
2
1
0
0
2
1
0
1
0
0
2
1
0
1
1
2
0
1
2
0
3
0
1
0
1
1
1
0
0
1
1
1
0
1
1
1
1
0
1
2
1
1
2
0
0
1
2
0
1
1
0
1
0
0
1
2
2
2
1
0
2
2
0
0
1
1
1
1
2
0
1
1
0
0
2
1
1
0
1
1
0
1
0
1
1
0
2
1
2
0
0
1
1
0
0
1
0
1
0
0
1
0
1
0
0
2
0
1
1
2
0
0
2
2
0
0
1
0
0
2
2
0
0
1
1
0
0
1
1
0
1
0
1
1
0
1
1
2
1
0
1
2
2
1
1
1
1
2
0
1
1
1
2
2
2
1
2
1
2
2
2
0
1
0
2
1
1
0
1
2
1
2
0
1
2
2
0
0
2
1
1
1
0
1
0
2
0
1
1
0
1
1
0
0
0
0
1
0
0
0
1
0
0
1
1
1
2
0
1
1
0
0
0
2
2
1
1
1
2
0
1
0
0
2
1
1
1
0
1
2
0
2
2
1
4
0
2
2
0
0
1
2
1
1
3
1
2
1
1
1
0
2
0
1
1
0
0
1
0
1
0
1
2
2
1
0
2
1
1
0
0
0
1
1
0
0
0
1
1
2
0
1
1
0
1
1
1
0
1
1
1
1
1
1
0
1
1
2
0
2
0
1
0
0
0
1
2
0
1
0
2
2
1
0
0
0
0
2
2
0
0
0
2
1
0
1
1
1
10
1
2
2
0
1
2
1
0
1
1
1
1
2
0
0
0
1
1
1
0
0
0
0
1
0
1
0
0
1
1
0
1
0
0
1
1
1
2
0
0
1
1
0
1
1
2
0
0
0
3
3
0
1
0
1
1
1
0
1
1
1
1
1
0
2
2
0
1
2
0
1
1
0
0
1
2
2
0
0
0
0
0
1
1
1
1
1
0
1
1
2
0
2
1
2
0
1
1
1
0
1
1
0
0
1
0
0
2
1
1
1
1
1
1
1
0
3
1
2
4
2
2
2
0
1
0
2
1
0
0
0
1
2
1
0
1
1
0
0
1
1
0
1
1
0
2
1
0
1
0
0
1
2
0
2
1
2
2
2
1
1
0
1
1
2
0
1
1
1
0
1
0
0
0
0
0
0
0
1
2
0
1
2
2
0
1
1
0
0
2
2
1
1
2
2
2
1
2
0
0
0
1
1
0
0
0
0
1
1
1
2
2
1
1
1
0
1
2
2
0
2
6
1
1
0
2
1
1
1
2
3
2
1
2
0
1
1
1
1
0
0
3
1
1
2
0
1
0
0
0
0
1
0
0
0
2
0
2
1
2
0
0
1
1
0
0
1
1
1
1
0
1
1
2
1
0
1
2
0
2
0
0
0
1
2
2
1
1
1
1
1
1
0
1
2
0
2
1
2
0
0
1
2
1
1
0
1
0
1
1
2
2
1
1
0
1
1
1
1
0
3
1
0
2
2
2
1
1
2
0
0
1
3
0
2
1
0
1
2
1
3
1
1
0
0
2
3
1
1
0
0
2
0
2
0
1
1
1
2
0
0
0
1
0
1
2
2
0
0
1
2
2
1
0
1
2
0
2
1
0
0
2
1
1
1
1
1
0
1
2
0
1
1
1
2
1
1
1
0
0
0
1
1
2
0
2
2
1
0
1
0
0
2
2
1
1
2
1
1
1
2
2
0
0
2
1
0
1
1
2
2
1
0
1
0
1
2
0
1
0
0
1
1
0
0
0
0
0
0
1
2
0
0
1
1
0
0
1
1
1
1
1
2
0
1
2
1
2
0
1
1
1
0
0
2
2
2
1
0
1
0
3
2
1
2
3
1
2
0
0
2
1
0
0
1
0
1
1
1
1
1
1
0
0
1
1
1
0
0
0
1
0
2
1
1
1
0
0
0
1
1
1
0
2
0
2
0
0
0
5
2
1
1
2
1
0
0
0
0
1
0
1
1
0
1
1
1
2
1
0
1
1
1
0
1
0
1
2
2
0
2
0
2
0
2
0
1
0
2
1
1
0
0
0
1
0
2
1
2
0
2
0
1
2
1
1
1
1
1
1
0
2
0
2
2
2
2
0
1
2
0
0
0
0
0
2
2
0
0
0
2
1
1
1
1
2
2
0
1
0
1
2
3
1
0
0
0
1
0
0
0
1
2
1
1
0
1
2
0
1
1
1
1
1
0
0
0
2
2
0
1
0
0
1
1
3
0
1
1
1
1
2
0
0
1
1
0
0
0
1
2
1
1
2
0
1
2
2
0
0
1
0
0
0
1
1
1
2
2
2
1
0
1
0
0
2
1
2
0
1
2
1
1
2
2
1
0
0
1
0
1
1
0
2
0
1
2
1
1
0
1
2
0
1
0
0
0
2
2
0
1
1
0
1
0
0
0
0
1
0
1
2
1
2
1
1
1
2
1
0
1
0
0
0
3
1
0
0
0
1
0
1
0
2
0
1
2
2
2
1
0
1
2
1
1
1
0
2
1
1
0
1
1
1
1
0
1
1
0
2
0
2
1
1
1
2
1
0
1
2
1
2
0
1
2
1
0
2
1
1
2
0
1
0
2
1
0
1
1
1
1
1
0
1
0
0
2
1
1
2
0
0
0
2
1
1
0
1
0
1
0
0
1
0
2
1
0
0
1
1
2
2
0
2
2
1
0
0
2
2
0
0
2
1
1
2
2
1
0
0
1
2
0
3
1
1
1
0
1
0
0
1
0
0
1
1
2
2
2
0
2
2
0
1
0
1
1
0
1
1
1
0
1
0
3
0
1
1
2
0
0
1
0
1
2
2
0
0
1
0
0
0
0
2
2
1
0
2
0
0
1
1
0
1
1
1
1
2
2
0
0
0
0
0
1
1
0
1
1
1
1
0
1
1
2
2
1
0
1
1
2
1
0
1
1
0
1
2
2
1
0
1
4
0
1
2
1
0
1
0
1
1
0
1
1
0
0
1
1
1
1
0
1
0
0
1
2
0
1
1
0
0
1
2
2
0
5
0
1
0
1
0
1
0
2
1
0
1
1
0
2
0
2
0
0
0
2
0
0
1
0
0
0
0
1
0
1
2
1
1
0
0
1
1
0
0
1
1
1
2
1
2
2
1
0
0
1
1
1
1
1
0
2
0
0
4
0
1
0
2
0
1
0
1
3
1
1
1
1
2
1
1
0
1
1
0
2
2
0
0
2
0
0
0
0
2
2
0
7
4
2
1
1
0
0
2
0
2
1
1
0
0
2
1
1
2
1
0
0
2
2
1
0
0
2
0
0
0
0
2
0
0
1
2
1
1
2
1
1
0
2
1
0
0
1
1
1
0
0
2
0
1
2
1
0
0
2
2
0
1
1
0
1
3
1
2
0
0
2
0
1
0
0
1
3
0
0
1
2
1
1
2
2
0
2
1
2
1
0
1
1
2
1
2
1
1
1
1
1
1
1
0
2
0
1
0
0
1
2
0
2
0
2
2
0
0
3
0
0
0
1
0
2
1
0
1
2
1
0
1
0
2
1
0
0
0
2
1
0
1
0
1
2
1
2
0
0
1
0
1
2
1
1
1
0
2
1
2
0
0
0
0
0
2
0
1
0
0
1
0
0
1
2
4
2
1
2
1
0
1
0
0
0
0
0
0
1
1
1
0
1
0
2
0
1
1
1
2
1
0
1
0
2
3
0
1
0
1
0
0
0
1
2
2
1
0
1
0
1
2
0
1
0
2
0
0
1
0
0
3
2
0
2
1
2
2
2
0
1
0
0
1
2
0
2
1
0
2
1
0
0
2
1
2
2
2
1
0
1
2
1
2
2
0
0
0
0
1
0
0
1
1
0
1
0
1
1
1
0
1
0
2
0
0
0
0
2
2
0
2
1
0
1
1
1
2
1
1
1
1
0
1
1
2
1
0
1
1
0
0
0
1
1
1
1
0
1
0
2
3
1
0
0
1
1
1
1
1
1
3
0
0
2
1
1
2
1
0
0
0
0
1
2
1
2
1
2
2
0
2
2
1
1
1
0
0
0
0
1
0
0
1
0
0
1
1
5
0
2
0
0
1
2
0
1
0
1
0
0
1
2
2
2
0
1
2
0
1
1
2
1
0
1
3
1
1
1
2
1
1
0
2
1
1
0
0
0
1
1
0
1
0
1
1
1
1
0
1
0
1
0
0
1
1
0
0
1
0
0
0
1
2
0
3
1
0
1
1
2
2
1
0
1
1
0
0
2
0
7
1
0
0
0
2
1
1
1
2
0
0
1
1
0
0
1
2
2
0
0
2
0
2
1
1
2
0
0
0
0
0
1
1
1
1
1
1
0
2
2
0
1
0
2
0
2
0
0
2
2
2
0
0
1
0
0
2
0
2
0
1
2
1
1
1
2
1
1
0
0
0
2
1
2
1
2
2
1
0
2
0
0
1
2
1
0
1
1
1
2
2
0
1
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
1
0
0
1
1
0
2
0
0
0
2
1
0
2
0
1
0
2
2
1
1
0
1
1
0
0
1
0
2
0
2
0
0
0
1
1
1
2
0
2
2
1
1
1
1
1
0
1
2
2
1
1
2
1
1
1
0
2
2
0
1
0
0
2
4
1
0
0
0
1
1
2
1
0
0
1
0
0
1
1
1
1
0
1
1
1
0
0
2
0
0
0
0
2
1
1
2
1
0
0
1
0
0
0
1
0
2
1
0
1
0
1
1
0
0
1
2
0
1
0
1
0
0
0
2
2
2
0
0
2
2
1
1
0
0
1
0
0
0
0
2
0
1
1
2
0
2
1
1
1
0
1
2
1
0
1
1
0
1
2
1
1
2
1
0
1
2
1
2
0
0
0
1
2
0
1
0
0
1
1
2
2
1
0
1
2
1
0
1
0
2
1
0
4
0
0
0
1
0
1
3
2
2
1
0
0
2
1
0
1
1
1
0
0
0
0
1
2
1
0
0
1
2
0
1
1
2
0
1
1
0
1
1
1
2
2
0
2
1
2
1
0
1
0
2
0
2
1
1
0
1
0
0
1
2
0
1
0
0
0
2
1
2
1
1
2
2
1
1
2
0
2
0
1
1
0
1
0
0
2
0
0
2
1
0
0
1
1
2
0
1
1
1
1
0
1
2
1
2
1
1
1
1
2
0
0
1
2
0
1
0
1
1
1
1
0
0
1
0
1
2
1
1
1
1
0
1
0
0
2
1
1
0
1
0
1
1
1
0
2
2
1
2
0
2
2
2
0
1
1
0
1
2
1
2
1
1
0
1
0
0
1
1
2
1
1
2
0
0
1
2
0
1
0
1
0
1
1
1
1
0
1
0
1
0
2
1
0
1
1
0
1
0
1
0
1
1
1
1
1
1
0
1
1
0
0
0
0
1
2
0
1
0
1
1
0
0
1
1
0
0
2
2
0
0
1
1
2
1
1
0
1
0
2
2
3
2
0
2
0
0
1
0
0
1
1
0
1
0
5
2
0
0
0
0
0
1
1
0
0
1
1
1
1
2
2
1
2
1
0
1
0
0
0
0
1
2
1
1
1
1
0
1
2
1
2
0
0
1
1
2
0
1
2
0
1
1
0
1
0
1
1
0
1
0
2
2
3
1
1
0
0
1
0
1
0
1
0
2
1
0
1
1
0
0
0
0
1
0
1
0
1
2
0
1
0
2
1
3
1
1
0
0
3
1
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
1
0
2
1
1
1
2
0
1
1
0
0
0
1
0
0
2
2
1
1
0
0
1
1
1
1
1
1
0
1
0
1
0
1
0
2
1
1
0
0
1
2
1
0
2
1
0
1
0
1
2
2
0
1
1
2
0
2
1
0
0
2
0
2
2
1
2
0
0
2
2
2
1
2
2
2
1
0
2
1
1
1
0
0
0
1
2
1
1
2
0
2
1
0
2
0
1
1
1
1
1
0
0
1
1
0
0
0
2
2
3
1
0
0
0
1
0
1
0
2
0
3
0
0
1
0
0
0
0
2
0
0
1
2
1
0
0
1
1
0
1
1
0
1
1
1
0
2
1
1
1
1
1
1
0
1
1
2
1
1
1
0
1
1
0
0
2
1
0
0
1
1
0
0
1
0
1
1
0
0
0
2
0
0
0
0
2
0
1
1
1
0
0
1
1
1
2
0
1
0
0
1
2
1
1
2
1
1
1
0
0
1
1
0
0
1
1
1
0
0
1
0
2
0
2
2
0
2
2
0
2
1
0
1
1
0
0
1
1
1
4
0
2
0
0
0
1
2
0
0
1
2
2
1
2
0
0
2
1
1
1
2
0
0
2
1
2
0
0
1
0
0
0
0
0
1
0
0
2
0
2
0
0
2
1
2
3
0
1
0
0
2
1
2
2
1
2
1
1
1
0
0
2
1
1
1
2
0
0
0
1
0
1
0
0
1
1
1
2
0
1
2
2
2
2
1
1
1
1
1
2
0
0
0
1
0
0
0
1
2
0
1
2
1
0
1
1
1
0
1
1
0
1
0
0
0
1
2
0
1
0
2
1
0
0
1
0
1
0
0
1
0
0
2
0
1
0
0
1
0
0
2
1
0
2
0
2
1
0
1
1
1
0
2
1
2
1
0
0
0
1
1
0
0
1
0
2
1
1
1
0
3
0
1
1
1
0
0
1
1
1
0
0
2
1
1
1
1
2
2
1
1
1
0
2
2
0
3
1
0
1
1
0
1
1
0
1
0
1
0
1
2
0
1
2
0
0
0
2
1
2
0
1
2
1
1
1
2
1
0
2
2
1
0
0
1
0
1
0
1
1
2
1
2
1
2
2
2
1
2
1
1
1
2
2
1
0
1
1
0
0
0
2
0
1
0
0
1
1
1
1
3
2
0
0
2
0
0
2
2
1
1
2
0
0
2
0
0
0
1
2
1
0
1
1
0
1
0
1
2
2
1
1
0
1
1
0
1
1
2
1
0
2
0
1
0
0
2
0
0
1
1
1
1
2
0
1
0
1
1
1
1
2
1
1
1
0
2
1
2
0
0
2
2
0
1
0
1
2
0
1
1
2
1
1
2
1
0
1
2
0
1
2
1
0
2
1
0
2
1
0
0
1
0
1
2
1
2
1
0
1
1
0
0
1
0
1
0
15
0
2
1
0
1
1
1
1
2
0
1
0
0
0
0
1
0
0
3
0
1
1
0
0
1
2
0
1
1
2
0
1
1
0
1
2
0
0
1
1
1
2
1
0
1
0
0
2
1
1
1
1
1
1
1
1
2
1
2
0
1
0
0
0
2
0
2
1
0
0
1
1
0
2
0
1
1
2
0
2
0
1
2
2
1
0
0
0
0
1
0
0
1
0
1
1
1
0
1
0
2
0
0
1
1
0
2
2
1
2
0
0
0
0
0
2
0
3
0
1
0
2
2
2
2
2
1
0
1
2
0
2
1
0
1
1
1
2
1
1
0
2
2
1
0
1
1
1
1
1
2
0
0
2
2
1
1
1
1
0
2
1
0
4
1
0
1
0
3
2
0
0
0
1
1
1
0
0
1
0
3
0
0
0
1
0
2
2
1
2
1
1
2
1
1
2
2
1
1
1
1
0
0
2
0
0
1
1
1
0
1
0
1
2
0
0
0
2
2
2
0
3
1
2
0
0
0
1
1
0
0
1
1
0
0
0
1
2
2
2
3
1
2
1
0
0
0
1
1
1
1
0
1
1
1
0
2
1
0
0
0
2
0
1
1
2
2
2
0
1
2
1
1
0
0
1
0
0
0
1
0
2
0
1
1
1
1
0
2
0
0
1
2
0
1
1
1
2
0
1
1
0
1
1
2
1
1
0
2
1
0
0
1
2
2
2
2
0
0
1
0
0
1
0
3
0
1
2
0
0
1
1
1
1
1
1
0
1
0
0
1
2
3
0
0
2
2
1
0
1
1
1
0
1
1
1
2
1
2
0
3
2
0
1
2
0
0
1
1
2
2
0
0
0
2
0
1
1
2
1
1
1
0
2
0
0
2
1
1
0
1
1
0
0
2
1
2
1
0
1
0
0
0
0
0
1
2
0
2
0
2
2
2
2
2
1
2
1
1
1
1
1
0
2
1
1
2
2
1
0
1
0
1
0
1
1
1
1
0
2
1
0
0
1
1
0
2
1
0
2
1
2
0
0
1
2
0
0
1
1
2
1
2
0
0
2
1
0
1
0
2
2
2
2
0
1
0
1
0
0
0
0
0
0
2
1
2
0
1
1
2
0
0
0
2
1
0
1
1
1
0
2
0
0
1
1
2
1
0
1
2
0
0
0
1
0
0
0
0
1
1
0
0
1
2
1
1
2
0
0
1
2
2
1
1
3
1
2
0
2
1
2
2
2
2
1
0
1
2
1
0
0
1
2
1
1
0
1
1
2
1
0
1
1
1
0
1
1
0
1
1
2
1
0
3
0
0
0
0
2
1
2
1
1
2
3
1
2
1
1
2
0
0
0
1
2
0
2
0
0
0
0
0
0
1
0
1
1
1
0
0
0
1
2
1
1
1
2
0
0
2
1
2
1
0
0
0
1
1
0
0
2
0
1
0
0
1
2
1
1
2
0
0
1
2
2
0
2
3
0
0
1
1
1
1
1
0
1
0
1
0
0
0
2
2
1
0
1
1
1
0
2
1
0
3
1
1
2
2
1
0
2
1
0
1
1
1
0
1
1
2
1
2
0
1
1
1
2
1
0
0
0
2
0
1
1
2
0
0
0
0
0
2
1
0
2
0
0
2
1
0
0
1
1
1
0
0
1
1
1
0
1
1
2
0
1
1
2
0
0
1
1
0
2
2
0
0
1
1
0
1
2
0
1
1
1
1
0
0
1
0
1
1
1
2
2
2
1
0
1
1
0
2
2
2
0
2
2
2
1
1
0
2
1
1
0
3
1
1
1
1
0
1
1
1
0
2
2
0
1
1
2
0
0
0
0
1
0
2
0
1
1
0
1
0
2
1
1
0
1
0
0
1
1
0
2
0
1
1
1
1
0
0
0
0
2
0
0
1
0
1
1
1
1
1
0
1
0
1
1
1
0
3
0
1
2
0
0
1
0
0
0
0
0
1
2
2
1
1
2
1
0
0
2
2
0
0
1
0
1
1
0
1
1
1
0
2
2
0
1
1
1
1
1
1
1
1
2
0
1
2
0
1
0
0
0
1
1
0
1
2
0
2
0
0
0
1
1
0
1
0
1
2
2
1
0
0
1
1
0
0
0
0
1
2
1
0
2
2
1
0
0
0
1
3
4
0
1
0
1
0
0
0
0
0
0
2
1
1
1
2
0
0
0
0
0
0
3
3
2
2
2
0
1
1
2
0
2
1
1
1
2
0
1
0
2
1
0
1
3
2
1
1
1
0
1
0
6
2
0
2
1
1
1
0
1
1
2
0
0
1
0
1
1
1
2
0
1
0
1
0
1
1
0
0
1
0
0
1
2
2
2
0
2
0
0
1
1
2
1
1
1
1
2
0
1
2
0
1
0
0
0
2
0
2
1
0
2
2
1
1
2
1
2
0
1
0
1
1
2
0
0
1
0
2
0
2
1
0
1
0
1
0
0
1
1
1
1
1
0
1
0
1
1
2
1
1
0
0
1
0
0
0
0
2
2
0
1
1
0
2
2
1
1
2
0
0
1
0
0
2
0
0
0
1
1
1
1
2
0
2
2
1
0
1
2
0
1
0
1
0
0
0
0
2
0
0
0
1
1
1
0
1
0
0
2
2
0
0
3
0
1
1
2
0
1
0
1
0
0
2
1
2
1
1
2
1
0
1
0
2
2
1
0
0
1
1
2
0
0
1
1
0
1
1
1
1
1
1
1
1
1
2
2
1
2
1
1
0
1
1
1
1
2
0
1
0
1
1
2
0
0
0
0
2
0
1
0
1
0
1
0
1
0
1
2
1
1
2
2
1
0
0
0
0
0
1
0
2
1
1
2
1
1
1
0
2
0
1
0
0
1
1
2
0
0
0
0
1
0
1
1
1
1
0
0
3
0
3
2
0
1
1
1
1
1
0
1
1
2
0
0
1
1
1
1
1
2
1
2
2
1
0
1
2
2
2
1
2
0
0
1
1
0
2
0
0
0
1
1
2
2
2
3
1
3
2
0
0
1
1
2
1
0
1
0
1
2
2
1
2
1
2
0
2
1
2
2
0
2
1
1
1
2
0
0
0
0
1
0
1
0
1
2
1
2
1
2
1
2
0
0
1
0
1
1
0
2
1
1
0
1
1
1
2
1
2
0
1
1
0
2
0
0
0
0
0
1
1
0
2
1
1
1
0
1
2
0
0
1
0
0
0
0
0
0
1
1
2
0
1
0
2
1
0
1
1
1
0
1
0
1
0
1
2
2
1
0
2
0
0
0
2
1
2
0
1
0
3
1
0
1
2
1
1
2
1
1
0
2
1
0
2
2
0
0
1
1
0
2
1
0
0
2
1
0
1
2
1
1
1
1
3
2
1
1
0
2
2
0
2
1
1
0
2
0
0
2
1
0
1
0
1
1
1
0
0
2
0
0
2
1
1
1
1
0
1
0
1
1
1
0
1
1
1
1
1
0
0
0
1
0
1
2
0
2
1
2
1
2
0
2
2
1
2
0
1
0
1
1
0
0
1
1
1
1
2
2
2
0
2
1
2
2
1
1
2
0
2
0
1
0
1
0
0
1
1
1
1
1
2
2
0
1
0
2
0
1
1
1
1
0
2
2
0
2
1
2
0
2
0
2
0
0
1
2
2
2
1
2
1
1
3
2
0
1
1
2
1
2
1
0
0
1
0
0
1
1
1
2
0
1
0
1
1
1
2
0
1
0
1
0
2
0
0
2
2
2
0
1
0
1
0
3
0
0
2
2
2
2
0
1
2
1
2
1
0
0
2
1
0
1
0
1
0
0
0
2
0
2
1
0
1
0
1
1
0
1
2
0
0
0
1
2
1
0
2
0
1
1
1
0
1
3
1
0
1
1
0
1
0
0
2
1
2
0
0
2
0
0
2
1
0
1
0
1
0
2
1
0
0
0
2
2
3
0
2
0
0
1
1
0
1
0
1
0
0
1
2
1
1
1
0
2
0
2
0
1
0
1
2
1
2
0
1
2
0
1
1
2
1
0
0
1
1
1
0
0
0
2
0
1
0
1
0
1
1
0
2
2
1
2
0
0
0
0
0
0
2
0
0
1
0
1
1
0
1
0
2
1
0
2
2
0
1
1
1
0
0
2
2
0
1
1
0
1
1
0
0
0
1
0
1
1
2
2
0
1
0
0
2
1
1
0
2
0
1
2
1
0
1
0
2
0
0
2
0
1
0
1
1
3
1
0
1
1
0
2
1
1
0
1
2
0
2
1
2
2
0
0
0
1
0
1
1
0
0
1
0
1
1
1
2
1
1
0
2
2
0
0
1
1
0
1
1
2
5
2
1
2
2
2
1
1
1
1
2
2
0
1
0
2
1
0
0
0
0
0
1
0
2
2
1
1
2
1
1
2
1
1
0
1
0
0
2
1
1
2
2
0
2
1
0
1
1
2
0
1
1
0
0
0
1
2
0
1
0
1
2
0
2
0
1
1
1
2
1
0
3
0
2
2
1
2
0
2
0
1
0
0
1
2
0
1
0
1
1
0
0
3
3
2
1
1
0
0
1
2
2
0
0
1
1
2
1
2
2
2
0
0
0
0
1
1
0
0
2
0
1
1
0
1
0
0
2
1
1
0
1
0
0
1
2
1
0
1
1
1
2
1
1
2
1
0
0
1
0
1
0
1
1
0
0
0
1
1
1
0
1
2
1
2
2
0
1
0
1
1
1
0
1
1
0
1
1
2
1
1
1
1
1
0
0
0
0
2
0
0
0
1
1
1
1
3
1
1
0
0
1
0
1
0
1
1
1
4
0
2
1
2
2
0
1
2
0
0
2
0
0
1
2
3
2
1
2
1
2
1
2
2
3
0
0
1
1
0
0
0
1
1
0
2
0
1
0
0
1
1
0
0
0
1
2
1
0
1
1
0
0
2
0
0
2
0
0
2
1
1
1
2
2
2
2
0
0
1
0
0
1
1
1
1
1
2
1
0
0
2
1
2
1
1
2
1
0
1
2
0
0
2
1
1
0
1
1
0
2
0
1
1
0
1
2
2
1
0
1
0
0
1
0
2
1
0
0
0
2
1
0
0
0
0
1
1
1
1
1
0
0
1
1
0
1
1
1
0
0
0
2
2
1
1
1
0
2
0
0
0
0
1
3
0
2
1
2
2
1
1
0
2
1
1
0
1
1
0
0
1
1
0
0
2
2
1
2
0
0
1
1
0
0
1
1
0
1
1
0
0
1
2
0
1
1
0
0
0
1
1
1
0
2
1
0
0
0
1
0
1
2
1
1
1
1
2
1
1
1
2
2
1
1
0
1
1
1
1
3
1
1
0
2
0
1
0
0
2
2
1
2
1
1
2
1
0
2
2
1
0
0
1
2
0
1
1
0
0
1
1
1
0
2
0
1
1
1
0
1
1
0
0
1
1
1
3
1
0
0
1
0
1
1
1
1
1
4
2
0
1
0
0
2
1
0
1
0
1
0
1
1
1
1
2
2
1
1
2
1
2
2
0
0
0
0
2
0
0
2
1
1
2
0
1
0
0
1
1
2
0
2
0
2
0
0
1
1
0
1
1
1
1
0
1
1
0
1
1
2
2
2
1
2
1
0
0
1
1
0
2
0
1
0
0
1
0
1
2
0
0
0
0
0
0
2
0
2
1
1
2
1
0
0
0
0
0
2
1
0
1
1
2
0
1
0
2
0
0
1
1
1
2
1
3
0
0
0
0
1
2
1
1
1
1
1
2
1
0
1
1
1
1
0
1
0
1
1
0
2
1
2
2
0
2
1
0
1
2
0
1
1
0
2
0
1
0
0
2
0
0
1
2
1
1
0
1
0
1
1
0
1
2
1
1
0
1
1
0
1
0
1
1
1
1
0
0
0
1
1
0
0
0
1
1
1
2
1
0
0
1
1
0
0
1
1
1
0
1
0
1
1
2
0
2
1
0
1
1
0
4
2
0
2
0
2
1
3
0
1
2
1
0
2
1
0
0
2
1
0
1
1
0
0
2
2
0
2
1
0
2
2
1
1
5
2
1
2
2
1
0
1
0
0
1
0
1
0
1
0
0
0
1
0
0
1
1
2
0
0
1
1
0
1
1
1
1
1
1
5
0
1
1
1
2
0
0
0
0
2
2
1
2
0
1
1
0
2
1
0
2
0
2
1
3
0
1
0
2
0
2
1
0
1
0
1
0
1
1
1
0
2
0
1
1
1
1
0
1
0
0
0
1
0
2
0
2
0
1
1
0
0
1
1
1
1
0
2
0
0
1
0
0
2
2
1
1
0
1
2
0
1
0
0
0
0
1
1
2
1
2
1
0
1
1
1
0
1
0
2
1
2
1
0
0
0
2
1
2
1
0
2
2
2
2
2
0
0
2
0
0
1
1
1
1
2
1
2
1
0
0
0
2
1
1
1
0
0
1
1
2
1
2
0
0
1
1
1
0
2
2
0
2
1
0
0
2
1
2
0
1
1
2
0
2
0
0
0
1
2
0
1
0
1
1
2
0
1
0
0
0
0
2
1
1
1
1
1
2
2
0
0
0
1
1
0
2
0
0
2
0
1
0
1
2
1
0
0
0
0
0
1
1
4
0
0
0
0
1
2
2
1
2
0
0
2
1
0
0
0
0
1
1
1
0
0
0
2
0
0
0
1
3
1
2
2
1
0
1
2
0
1
2
0
0
0
0
2
1
2
1
0
1
0
1
2
1
1
0
1
1
1
0
2
0
0
1
0
1
0
0
0
2
0
1
0
1
1
1
2
1
1
1
1
2
2
0
0
2
0
0
1
1
0
1
1
1
1
4
0
0
0
1
1
0
1
1
2
1
2
0
1
2
2
1
1
0
2
1
2
0
0
1
1
1
0
2
1
2
1
2
1
1
0
0
0
1
1
0
1
1
0
1
2
0
0
0
1
1
1
0
1
0
2
1
2
0
1
1
0
1
0
0
1
0
1
0
1
0
0
2
2
0
0
1
0
0
0
1
0
0
0
3
0
3
1
1
1
0
0
0
0
1
1
1
0
1
2
0
1
0
2
2
0
1
1
0
1
0
0
1
1
0
0
1
1
1
0
0
0
1
2
0
0
0
0
1
0
0
2
0
2
1
1
1
1
2
1
2
2
2
1
2
1
4
1
2
2
1
1
0
0
2
1
1
0
1
0
1
1
1
0
1
1
1
1
2
1
1
2
2
1
0
0
0
0
0
0
0
0
1
0
0
1
2
1
0
1
1
1
0
1
0
1
1
0
1
0
2
0
1
1
1
1
2
1
0
1
0
0
2
0
0
0
1
0
0
0
2
0
0
1
1
1
1
1
2
1
1
0
1
0
1
1
1
0
1
2
2
0
0
1
1
2
2
2
0
2
0
2
0
1
1
0
0
1
2
1
0
0
0
2
1
1
1
2
1
2
1
1
1
1
1
0
1
0
1
0
0
0
0
1
1
1
1
1
2
3
0
2
0
2
1
0
0
1
2
0
0
2
0
1
1
0
2
1
1
0
1
1
0
2
1
1
0
2
0
1
1
2
0
2
1
2
1
2
1
1
1
1
1
0
1
0
1
0
1
1
0
0
1
1
1
1
0
1
0
1
1
0
2
0
1
2
0
2
2
0
0
0
2
1
0
1
1
1
1
0
1
1
1
0
0
1
0
0
1
2
1
0
0
0
0
2
1
2
2
1
1
1
2
2
0
2
2
2
2
0
1
1
0
1
0
3
2
1
0
0
2
0
4
1
0
0
0
1
0
1
2
2
1
0
1
0
0
0
0
0
1
1
1
1
0
0
0
1
0
0
1
1
1
0
0
1
1
1
1
2
1
0
1
2
1
1
0
1
0
1
0
1
1
2
0
1
1
0
1
2
0
1
0
0
1
2
2
0
0
2
0
0
1
1
1
0
1
1
1
2
1
2
7
1
0
0
2
0
0
0
1
2
0
0
1
0
0
1
0
0
1
0
0
1
1
1
1
1
1
1
2
1
2
1
1
2
0
2
0
4
0
1
1
6
0
0
0
0
1
0
0
1
0
0
1
1
1
2
1
0
0
2
2
1
0
0
0
1
0
2
0
2
0
4
0
2
0
0
1
0
1
1
0
0
0
0
2
1
1
1
0
0
2
0
2
2
0
2
0
0
2
2
1
1
2
1
2
2
0
1
0
1
1
1
1
1
0
0
1
1
1
1
1
1
1
0
1
1
0
0
1
1
1
0
0
1
1
1
0
1
0
0
1
0
0
3
1
0
1
1
0
1
2
0
0
1
0
1
3
0
0
1
0
2
1
2
0
1
2
2
2
0
1
2
2
1
1
1
0
2
1
0
1
0
1
2
1
2
1
0
0
0
0
1
0
1
0
2
0
2
1
0
0
1
1
1
2
0
0
1
2
2
0
1
2
0
1
1
1
0
2
0
0
1
2
0
0
0
1
0
2
0
0
1
0
0
1
1
1
1
2
0
1
1
1
0
0
0
0
3
1
2
2
2
2
2
2
0
0
1
1
1
0
0
2
2
0
1
0
0
0
0
0
1
2
2
1
2
0
1
1
1
1
0
0
1
0
1
2
1
1
1
2
1
0
1
2
2
1
0
2
0
0
1
0
1
0
1
2
1
1
0
1
1
4
1
0
0
1
2
0
0
1
0
0
1
0
1
2
1
3
1
1
1
2
1
0
1
0
0
1
1
1
2
1
2
1
2
1
2
0
1
0
2
1
1
1
2
1
2
1
0
1
2
0
0
0
2
0
0
1
1
2
0
2
1
1
1
1
0
1
0
1
0
1
2
1
0
0
0
2
0
0
0
0
1
0
1
3
1
1
0
2
0
0
0
1
1
1
2
0
1
0
2
2
2
2
0
2
3
0
0
0
2
0
0
0
2
0
1
0
2
0
1
0
0
0
0
0
1
0
1
2
0
1
1
2
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
1
2
2
2
1
1
1
1
2
2
0
2
0
1
1
0
1
0
0
2
0
1
2
1
4
1
0
0
1
0
0
0
7
1
1
0
1
1
0
2
0
0
0
1
1
0
1
2
1
1
1
0
1
0
1
1
0
2
2
1
1
1
1
1
0
1
0
2
1
1
0
0
1
2
0
0
1
1
0
1
2
1
2
0
1
1
0
0
2
0
0
0
1
2
0
1
0
2
0
0
1
0
2
1
1
0
2
2
1
1
1
0
1
0
0
2
1
0
1
1
0
1
1
1
1
0
1
0
2
1
2
2
0
2
1
1
0
1
2
0
0
1
1
0
0
0
1
1
1
1
1
2
0
0
0
1
1
0
2
0
0
1
0
1
2
1
1
2
1
0
0
1
2
0
0
0
1
1
0
0
0
0
2
1
1
0
1
1
0
1
1
0
1
2
1
2
1
0
1
1
1
1
0
1
0
0
2
0
0
1
1
1
0
1
1
2
0
1
1
1
0
0
2
2
2
2
0
2
0
2
1
1
1
1
1
0
1
1
0
1
0
1
1
1
1
0
0
0
1
2
1
2
2
1
0
1
2
1
1
2
1
0
1
0
1
2
0
1
1
1
0
0
0
1
1
0
1
1
2
0
1
1
2
0
1
0
2
1
1
2
0
0
0
2
2
0
0
0
1
0
1
2
1
1
1
1
0
0
0
0
1
0
0
2
1
1
0
1
0
1
0
2
3
1
2
1
1
0
1
0
0
0
5
2
2
2
1
0
1
1
2
0
3
0
2
0
2
2
0
2
1
1
1
2
1
2
2
0
2
2
1
1
1
0
0
2
4
1
3
2
1
2
1
2
0
3
0
0
2
1
0
1
2
1
2
0
1
1
2
1
0
2
0
1
0
1
0
1
3
0
0
2
3
2
1
0
1
2
1
0
0
0
2
1
0
2
0
0
0
1
1
1
2
1
0
2
2
1
0
2
1
1
0
2
0
2
0
0
1
0
0
1
0
0
0
0
0
1
1
1
1
1
1
0
1
2
0
1
0
1
0
0
1
1
0
1
1
3
1
1
0
0
2
1
0
0
1
1
0
0
2
2
1
1
1
0
0
2
1
1
1
1
2
0
0
0
1
0
1
2
1
1
0
1
2
1
2
1
2
0
2
0
2
0
0
0
0
0
1
1
0
1
0
3
0
2
2
0
1
0
1
1
2
0
1
3
0
1
2
0
1
0
0
1
1
0
1
2
1
0
0
1
1
2
2
0
1
1
1
0
2
1
0
0
0
0
0
1
1
2
0
1
0
2
1
1
0
1
1
2
0
0
1
0
1
0
1
0
2
0
1
2
1
2
0
1
2
2
0
1
1
0
0
0
2
2
0
1
0
2
0
2
0
0
0
1
0
1
2
1
1
2
1
0
3
0
2
1
1
1
0
2
1
2
2
2
2
0
1
1
1
1
1
2
0
0
0
2
0
1
0
0
1
2
1
2
2
2
2
0
1
0
1
2
0
0
1
1
2
2
2
0
2
0
0
0
0
0
1
2
2
1
0
1
0
0
1
2
0
3
1
1
2
0
2
0
2
0
0
1
1
1
1
2
1
1
1
1
0
2
1
1
0
1
0
1
0
0
0
2
1
0
1
0
0
0
2
0
2
0
1
1
0
0
1
1
0
1
0
2
1
1
0
0
0
1
1
2
0
0
2
1
0
1
2
0
0
1
0
2
0
2
0
0
1
0
1
0
1
2
1
0
0
0
0
0
2
1
0
1
2
1
1
1
0
1
1
1
2
0
1
0
0
1
1
1
1
0
0
1
1
1
1
1
0
1
1
0
0
0
1
1
2
1
1
0
3
1
2
1
2
1
1
1
1
3
1
1
1
0
1
1
2
1
0
2
2
2
1
0
1
1
2
1
0
0
1
0
1
0
1
0
1
2
0
2
0
1
1
0
1
1
2
0
1
0
0
0
2
1
1
1
1
2
1
1
2
1
0
1
1
1
1
1
1
0
1
4
1
1
1
0
4
1
1
1
0
1
0
0
0
1
1
1
0
1
0
0
1
0
1
1
0
1
0
0
0
1
0
1
7
1
2
0
1
1
2
1
5
2
2
0
0
1
1
2
1
1
2
2
1
1
1
0
1
1
1
1
0
2
0
0
1
2
1
0
1
1
0
1
1
1
0
2
1
0
1
0
1
0
0
1
1
1
0
2
2
1
0
0
0
3
1
2
0
1
2
0
1
1
0
0
1
0
0
1
1
1
1
2
0
1
1
2
2
0
1
1
0
0
1
1
0
0
0
2
1
0
0
5
0
2
1
2
0
1
1
0
1
1
1
2
0
1
1
2
1
1
2
0
0
1
2
1
0
0
1
3
1
2
1
1
1
1
1
0
2
2
0
1
1
0
1
1
2
0
2
1
2
1
1
0
1
2
0
3
0
1
1
0
1
1
0
1
0
1
1
0
1
0
0
0
0
1
1
2
1
1
0
0
1
0
1
0
0
0
1
2
1
0
1
1
1
2
2
1
1
1
1
0
1
2
0
1
1
2
0
0
2
0
1
0
1
2
1
0
0
0
1
1
1
0
2
0
1
1
0
1
1
1
0
0
1
0
1
1
0
2
0
0
1
1
1
2
1
2
1
0
1
0
1
0
1
1
1
1
1
0
2
1
1
1
0
1
1
1
1
0
1
2
1
1
0
1
1
0
0
0
1
2
8
0
1
1
0
1
0
0
1
0
1
1
1
1
1
0
1
1
1
1
2
1
1
1
3
1
1
1
1
0
1
2
1
2
2
1
2
0
1
1
2
0
0
2
0
1
1
1
1
1
1
1
1
1
0
2
1
0
1
1
1
2
1
2
0
0
1
1
2
1
1
2
1
1
0
1
3
1
2
2
0
0
1
3
1
1
0
0
0
0
2
1
2
1
0
2
2
0
2
2
0
1
0
2
1
1
0
0
0
2
2
2
0
1
1
0
2
1
0
0
3
0
0
2
1
1
2
0
2
0
0
2
1
0
1
1
1
0
1
2
2
1
0
0
2
1
0
1
1
3
0
0
2
0
0
3
2
2
2
2
1
1
1
1
0
1
1
1
2
1
0
1
0
2
2
1
1
0
2
0
0
2
1
1
2
1
2
0
0
3
1
1
1
0
1
0
0
1
1
0
0
1
2
1
0
0
1
1
1
1
0
2
1
2
0
1
2
0
0
1
1
1
2
1
0
2
0
0
2
1
0
1
1
2
1
1
0
0
0
1
1
0
1
0
1
0
1
1
0
0
1
0
0
2
2
3
0
2
1
0
0
1
0
0
0
1
0
2
0
0
1
0
0
0
1
0
0
2
2
1
0
1
1
0
1
0
0
1
1
0
2
2
0
1
2
1
2
2
2
0
1
1
0
1
1
0
2
1
0
2
0
1
1
1
0
1
0
0
1
0
0
0
0
0
2
0
2
1
1
2
0
0
2
0
1
1
0
2
2
0
0
1
1
0
0
0
1
0
1
0
0
2
1
0
1
1
0
1
0
2
1
2
2
2
1
1
1
0
0
0
2
0
1
2
0
0
0
2
1
2
2
2
1
0
2
0
0
0
0
1
0
0
2
1
2
0
0
1
1
1
0
0
1
1
1
0
0
0
0
0
1
1
1
0
0
1
2
2
1
1
1
1
0
2
1
0
1
0
1
1
0
1
0
2
1
1
1
2
2
1
0
2
1
0
0
0
1
1
2
1
0
0
0
0
0
1
1
1
0
0
2
1
2
1
2
2
0
1
2
0
0
1
1
3
0
1
1
0
0
2
1
1
0
0
3
1
2
0
1
2
0
1
1
0
1
2
0
1
2
0
1
1
2
2
0
2
2
0
1
1
1
0
0
0
0
0
0
2
2
2
0
1
2
0
0
0
0
0
1
1
1
0
1
0
0
2
2
1
0
1
1
1
2
2
2
1
0
2
0
1
2
1
1
0
1
0
2
1
0
0
1
2
4
0
0
2
2
0
0
2
1
1
2
0
1
1
0
1
2
0
0
1
1
1
0
1
0
2
0
0
1
1
0
2
0
2
0
0
0
0
2
2
0
1
2
0
1
0
0
1
0
2
2
0
0
0
1
1
1
1
1
2
1
1
0
2
0
1
0
0
1
0
3
0
1
0
0
0
0
0
1
0
1
2
0
2
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
1
0
0
1
1
0
1
1
0
0
1
2
0
0
2
1
2
0
0
2
1
1
2
2
2
1
1
1
0
0
1
1
1
1
1
0
0
1
0
0
1
1
1
2
2
1
1
0
0
2
1
1
0
1
1
0
2
1
0
1
1
1
2
1
1
0
0
3
0
0
0
1
1
2
1
2
1
1
0
2
1
0
1
2
1
1
1
0
2
0
0
0
1
0
0
2
1
0
0
0
1
0
0
1
1
1
1
0
1
0
0
1
0
1
0
0
2
0
1
1
3
2
1
0
0
0
2
0
1
1
2
1
1
1
0
1
1
1
0
1
0
2
3
0
1
0
1
0
0
1
0
1
2
2
0
0
2
2
1
2
2
3
2
0
0
2
0
1
2
0
0
2
1
1
0
0
0
2
1
2
1
0
1
2
0
0
2
0
1
2
0
1
1
0
2
1
2
1
1
0
0
0
0
4
2
1
1
1
1
1
1
2
0
0
1
0
2
2
1
1
2
2
2
2
1
1
1
1
1
0
1
1
0
2
2
0
0
0
1
0
0
1
1
0
1
0
1
0
0
1
1
0
1
0
0
3
1
1
1
2
0
2
3
2
1
2
1
0
0
2
1
1
0
0
2
1
2
2
0
1
1
1
2
2
1
0
1
1
1
1
2
2
1
1
2
0
0
1
0
1
1
0
1
0
1
1
0
2
1
0
0
1
1
0
0
0
0
2
1
0
0
1
0
0
1
1
1
2
2
1
1
0
1
0
0
1
1
1
2
1
1
2
1
1
2
2
1
0
0
2
1
1
1
1
0
2
1
2
1
2
0
2
1
0
1
0
2
0
4
0
1
0
2
1
2
0
0
1
0
1
1
1
2
0
1
0
2
0
1
2
0
4
0
0
1
0
1
0
2
1
1
2
0
1
0
1
2
1
1
2
1
1
0
1
2
1
1
0
2
0
1
0
3
2
1
1
0
0
1
1
1
0
1
1
2
2
1
0
2
3
1
0
2
1
1
2
1
0
0
1
0
0
1
0
1
1
0
0
0
0
0
1
2
0
1
0
0
0
0
2
1
1
2
1
0
2
0
2
0
0
1
2
0
0
1
0
0
1
0
2
0
0
1
0
0
0
2
1
1
1
1
0
1
1
1
0
0
3
0
0
1
1
2
0
0
1
1
0
1
0
1
1
1
0
2
2
1
1
1
0
1
0
0
1
1
3
0
0
1
0
1
0
1
1
1
2
1
1
1
1
2
1
0
0
2
0
1
0
1
1
2
0
0
2
0
1
1
0
0
1
0
5
1
0
1
1
1
2
1
2
1
2
0
0
1
0
2
1
0
1
1
1
0
1
1
0
0
0
1
2
2
1
2
0
0
1
1
1
1
0
1
2
0
0
0
0
1
1
1
2
0
1
0
0
0
1
0
0
0
2
1
0
0
2
0
0
0
0
1
2
2
1
0
0
1
1
0
2
1
1
2
0
0
0
0
1
0
2
0
1
6
0
1
2
1
1
2
1
0
0
0
1
0
1
0
2
0
2
2
0
1
1
1
0
0
0
1
0
1
1
1
0
1
0
1
2
2
2
2
0
2
0
2
0
2
0
0
2
1
1
1
2
1
0
2
0
1
0
1
1
0
0
0
2
2
2
0
1
2
1
0
1
1
1
0
3
2
1
1
1
1
1
1
1
1
2
1
0
0
0
1
0
1
1
0
0
0
1
1
0
3
1
0
1
0
0
1
1
1
1
1
2
1
1
2
1
0
2
1
0
0
0
0
1
2
1
1
0
2
0
0
3
1
1
0
0
2
0
2
2
0
2
0
1
0
1
0
2
0
0
2
0
2
0
1
1
2
4
0
2
0
0
1
1
1
2
1
0
1
2
2
1
0
0
1
2
0
0
1
1
1
0
0
1
1
2
0
0
0
1
0
1
0
1
1
0
2
1
0
1
1
0
1
1
1
2
2
2
0
3
2
1
0
1
2
1
2
2
0
0
1
1
0
2
2
1
0
1
1
2
0
1
1
1
2
1
0
2
1
0
0
0
1
1
1
0
1
2
2
0
0
0
1
1
0
0
0
1
0
0
1
1
2
2
1
0
2
1
0
0
2
1
0
1
2
1
2
2
1
2
1
0
2
2
2
1
0
0
2
0
2
0
1
1
0
1
0
1
1
0
0
2
1
1
0
1
2
1
0
0
1
1
2
0
0
0
1
1
2
0
2
1
1
1
1
1
0
2
1
0
0
0
2
0
2
0
0
0
0
1
1
1
7
1
1
0
0
2
1
1
2
1
1
0
0
1
1
1
0
2
1
1
1
1
1
0
0
0
0
3
0
2
1
1
1
2
0
1
1
1
1
1
2
0
0
0
2
2
1
2
1
1
0
1
0
2
0
1
0
0
1
0
0
2
1
1
2
0
0
0
0
2
1
1
0
4
0
2
0
2
2
1
0
2
2
0
1
2
1
1
1
0
0
0
0
2
1
1
1
1
0
0
1
1
3
0
1
0
1
3
1
0
0
1
1
1
1
1
2
1
1
1
1
0
1
0
2
1
1
0
2
2
2
1
0
1
0
2
2
1
1
2
2
1
0
1
2
0
0
0
1
2
1
0
0
0
3
1
2
3
2
0
0
0
1
0
2
0
0
1
1
0
1
0
2
2
3
1
2
2
2
1
2
1
0
1
2
2
0
2
1
0
1
1
1
2
0
0
0
1
1
1
0
1
2
0
1
0
1
2
1
0
0
2
0
1
1
1
1
1
2
0
2
1
1
0
1
2
1
2
1
0
0
0
2
0
0
0
0
1
1
0
2
2
0
0
1
0
2
0
0
0
1
0
1
2
0
1
0
2
0
0
1
0
0
2
1
2
0
1
0
0
0
2
0
0
0
0
0
2
2
2
0
1
1
1
2
0
1
0
1
3
0
1
1
2
0
1
2
1
0
1
0
0
2
0
1
0
1
1
0
2
1
0
0
2
0
4
1
2
1
0
2
2
2
1
2
0
2
0
1
0
0
1
2
1
0
1
0
1
3
0
1
2
2
0
0
2
0
0
0
0
0
1
2
0
2
1
0
2
0
1
0
1
2
1
0
2
1
1
0
0
1
0
2
1
0
2
2
1
3
0
1
0
0
1
0
0
1
0
1
1
2
1
0
2
0
1
1
1
0
1
2
1
1
2
0
2
0
0
1
1
1
1
0
1
0
1
1
0
2
2
1
1
1
1
2
0
0
2
2
1
0
0
1
0
2
0
0
1
0
0
1
2
1
0
1
1
1
0
1
1
2
1
0
1
2
2
1
1
1
1
2
2
1
1
1
1
1
0
1
1
1
1
2
0
1
1
1
1
1
1
0
1
0
0
0
1
0
1
1
1
1
1
0
2
0
2
0
0
1
0
2
2
0
0
2
1
0
0
1
0
1
0
2
1
0
0
2
2
0
2
3
0
1
0
2
1
1
0
0
1
0
0
1
2
4
2
2
2
0
0
1
1
0
0
2
1
0
0
0
2
0
2
0
1
1
1
2
1
0
0
1
1
0
1
0
0
4
2
1
1
1
0
1
1
0
2
0
0
1
2
1
0
0
1
1
2
2
0
0
0
1
1
0
1
1
2
1
0
0
2
0
1
0
2
1
1
1
0
1
0
0
1
1
0
1
0
1
0
1
1
1
1
1
1
0
1
2
0
1
1
0
2
1
1
0
2
0
0
0
1
0
0
0
0
1
1
2
0
0
0
1
2
1
0
1
0
2
0
3
1
2
1
2
0
0
1
0
0
2
0
0
2
1
0
0
0
3
1
1
1
2
2
2
0
1
1
1
0
1
2
1
1
1
2
2
0
2
2
0
0
2
2
2
0
2
1
0
1
2
0
1
1
0
1
1
0
2
2
3
1
1
1
1
1
1
1
2
0
2
0
0
2
0
2
0
1
1
2
1
0
0
2
0
1
1
1
1
1
0
1
0
2
2
0
1
1
0
1
1
0
2
0
1
0
2
1
1
0
0
1
0
1
2
1
2
0
0
1
1
0
0
0
1
0
1
1
1
1
1
1
3
0
0
0
0
0
2
1
2
1
0
1
0
1
2
1
0
1
0
0
1
0
1
0
0
0
1
2
1
3
1
2
0
0
0
0
1
1
1
1
1
1
0
0
1
0
1
0
0
1
0
1
0
1
1
2
1
1
2
2
0
1
1
0
1
0
2
1
0
2
1
1
1
2
0
0
2
1
0
1
1
1
2
0
0
0
1
1
1
1
2
2
1
2
0
0
0
0
0
1
1
0
1
0
2
3
1
1
1
2
2
1
0
0
1
0
1
0
0
2
1
1
1
1
1
0
1
0
1
1
2
2
0
2
0
1
2
0
2
0
1
2
0
0
0
1
2
1
2
3
1
1
0
2
2
2
1
1
0
1
0
0
0
0
0
1
0
1
1
0
1
1
1
0
0
0
0
1
1
2
1
0
1
0
2
2
0
2
1
1
0
1
1
0
0
0
2
0
0
0
0
2
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
1
1
2
1
0
2
0
2
2
0
1
1
2
0
1
0
1
0
1
0
0
0
1
0
0
2
0
2
1
1
0
0
0
1
2
1
2
0
0
1
1
3
1
1
0
0
0
1
1
2
1
1
2
1
2
1
1
1
1
0
0
1
2
0
2
0
2
1
1
1
2
0
0
2
1
1
0
0
2
1
1
1
1
0
1
0
1
2
1
0
0
1
2
0
1
3
0
2
0
2
2
0
2
1
0
1
1
1
0
0
1
1
2
2
1
2
2
1
3
2
2
1
1
2
2
1
1
2
0
0
2
2
6
1
0
2
0
1
1
0
3
1
0
1
0
0
0
0
2
1
2
0
1
1
2
2
0
0
0
1
2
1
1
0
2
0
0
0
0
0
1
2
1
0
0
0
3
1
1
1
2
1
1
2
1
1
2
3
0
1
0
0
0
1
0
1
0
0
2
0
1
0
1
1
2
0
2
0
3
1
1
1
2
1
1
1
1
0
0
2
0
1
0
1
2
0
2
0
1
1
1
0
0
1
0
1
1
0
1
0
3
2
1
1
0
1
0
1
1
2
0
1
1
0
1
2
0
0
0
0
2
0
0
0
2
0
0
1
0
1
0
0
0
2
0
1
0
2
0
0
0
1
2
5
1
1
1
0
1
2
0
1
1
1
2
0
0
0
0
1
1
0
0
1
0
2
1
0
0
0
1
0
0
1
0
0
1
1
2
0
1
0
1
0
0
0
1
0
0
1
2
0
0
0
0
2
0
1
1
1
1
1
0
1
1
0
1
1
1
0
1
1
2
0
0
1
1
1
1
1
0
2
1
1
1
0
0
2
0
0
2
3
1
1
0
0
0
0
2
1
2
1
0
0
1
0
2
1
1
2
0
2
0
1
1
1
0
1
1
1
0
1
0
1
1
1
1
0
1
0
0
1
1
2
1
0
1
3
1
0
0
1
0
1
1
2
1
0
2
0
0
0
1
1
0
2
1
1
0
0
0
2
1
0
0
1
2
0
0
1
1
1
1
1
2
1
1
2
2
1
1
1
0
2
2
0
1
1
1
2
0
2
1
1
1
0
0
1
0
0
1
0
0
1
1
2
2
0
2
0
0
1
2
0
2
1
2
0
0
1
2
0
0
1
2
1
1
1
2
1
2
1
1
1
1
1
1
0
1
2
1
0
0
1
1
2
1
1
0
1
1
0
0
0
1
1
2
0
0
0
1
2
1
1
2
0
0
1
0
0
2
0
1
0
1
2
2
0
0
1
2
0
1
1
0
0
0
1
0
1
1
2
0
0
0
2
0
0
2
1
0
0
1
1
0
0
2
0
1
1
1
1
2
1
2
0
1
0
0
0
0
0
2
1
1
1
1
0
1
1
0
2
1
1
0
1
0
2
1
0
2
1
3
0
2
2
1
2
0
0
1
0
0
1
1
2
2
1
1
1
1
0
1
0
1
1
1
0
1
1
2
2
0
0
4
2
1
1
2
1
1
1
1
2
0
2
0
1
0
1
0
0
2
0
0
1
2
1
2
1
0
1
2
1
1
0
0
0
1
1
0
1
0
0
0
1
0
0
0
2
0
1
1
3
1
0
2
0
1
0
0
2
0
1
0
1
1
0
0
1
0
0
2
2
2
2
0
0
0
0
1
0
1
1
3
0
1
1
1
1
2
2
2
1
0
1
0
0
0
2
1
2
0
0
1
0
1
1
1
1
0
0
1
1
1
0
2
0
0
2
1
2
2
0
0
0
0
0
0
0
1
1
2
1
0
0
1
2
0
2
1
2
2
1
1
2
0
1
0
1
1
0
0
1
0
1
0
2
1
0
2
0
1
0
1
2
1
1
1
1
2
0
0
2
1
1
0
2
0
1
2
1
0
1
1
1
1
1
1
2
2
0
0
1
0
0
1
0
0
1
1
1
2
2
0
0
2
1
0
2
0
0
0
0
1
1
1
0
1
0
0
0
0
1
1
0
2
0
2
0
0
0
0
0
1
1
1
1
1
2
1
0
2
1
1
0
1
0
1
1
1
1
1
0
0
0
0
0
1
2
2
1
1
2
1
0
0
1
0
0
0
1
2
1
1
1
1
2
1
0
0
0
2
2
1
2
2
1
0
0
1
0
1
1
2
2
0
2
2
1
1
0
1
0
1
1
1
1
1
2
1
0
1
0
2
2
2
2
1
0
0
0
0
1
2
1
0
2
0
0
1
0
1
0
0
2
2
2
0
0
1
1
0
1
0
0
1
1
4
0
1
0
1
1
0
1
2
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
3
2
1
2
0
0
0
2
0
0
0
1
0
0
1
1
2
0
1
1
0
0
0
0
1
1
0
2
0
0
0
0
1
0
0
1
0
2
0
1
1
1
0
2
0
0
0
0
0
2
0
1
0
0
0
0
1
1
0
0
1
2
2
0
1
0
2
0
1
2
2
1
0
1
1
0
1
2
1
0
0
2
0
0
0
2
1
2
0
2
1
1
0
1
1
1
1
2
1
1
1
0
2
2
2
0
0
1
0
2
0
0
1
1
0
0
2
1
1
0
0
1
2
1
0
1
0
2
0
0
1
0
1
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
1
1
2
0
2
1
2
0
1
0
2
0
2
0
0
1
0
0
0
0
2
0
1
1
0
1
1
1
1
3
1
2
0
0
3
1
1
0
1
0
1
1
2
0
1
2
0
0
1
1
2
0
1
0
2
1
1
2
0
1
0
1
2
2
0
0
1
2
1
0
2
0
1
1
2
0
1
1
1
2
0
0
0
0
2
0
2
0
1
1
0
1
0
0
0
1
0
1
0
2
2
0
2
2
2
1
0
0
0
1
2
0
1
2
1
2
0
2
1
2
0
2
2
2
1
2
0
0
0
0
0
1
1
0
1
1
1
0
0
1
0
0
0
0
1
0
0
1
1
2
1
1
1
1
1
1
1
0
0
0
2
1
0
0
0
0
0
0
1
1
2
1
2
2
1
0
0
0
0
1
1
1
1
0
0
0
0
2
0
1
0
1
1
0
0
2
0
1
1
1
0
2
1
2
1
0
1
0
2
1
0
1
1
1
1
0
1
1
3
0
0
1
0
1
0
0
1
1
1
2
1
0
2
0
0
1
0
0
0
1
1
0
1
1
1
1
1
0
0
0
0
0
2
0
0
1
0
1
2
1
5
1
0
1
1
0
2
1
1
1
1
0
1
1
1
0
0
1
3
0
2
2
0
1
0
2
0
0
1
1
1
0
1
0
0
2
0
0
0
1
0
1
1
1
0
1
2
2
1
0
2
2
0
1
1
0
1
1
2
1
1
0
2
1
2
0
1
1
1
0
0
0
1
0
0
0
1
0
2
1
1
2
0
1
0
0
1
0
2
0
0
0
0
0
1
2
1
1
0
2
0
2
0
0
2
1
0
1
0
0
1
1
0
1
1
1
2
1
2
0
2
0
2
1
0
0
2
0
0
1
0
0
2
0
0
0
1
1
2
1
0
0
0
2
0
1
1
0
2
2
1
1
0
1
1
1
1
0
0
0
2
1
1
0
0
0
1
1
0
1
0
2
0
0
0
2
2
1
0
2
1
0
0
1
0
0
0
1
0
0
2
1
1
2
0
0
2
1
0
0
0
0
2
1
2
1
0
1
1
1
0
0
0
1
0
2
0
2
2
1
3
1
0
2
1
1
0
2
1
1
1
0
1
0
0
0
0
1
0
0
1
0
1
1
2
0
0
2
1
2
2
2
1
1
2
1
0
1
1
1
0
2
0
1
1
2
1
2
1
2
0
1
1
2
1
0
1
0
0
1
0
0
0
1
3
1
1
1
0
2
2
1
0
2
0
0
0
1
1
0
0
0
0
2
0
1
1
0
0
2
2
1
0
1
0
1
0
2
1
2
2
1
1
1
2
0
1
1
1
1
1
0
0
1
2
1
1
2
1
1
2
0
0
1
1
0
0
0
1
0
1
2
1
2
0
0
0
1
0
2
2
1
1
0
1
0
2
1
0
1
1
0
2
1
1
1
0
1
1
1
1
0
2
0
0
1
2
0
1
1
1
1
0
2
0
2
1
2
1
0
0
1
1
0
0
1
2
1
1
0
0
1
0
1
2
0
2
0
0
0
1
1
4
0
1
0
2
1
1
1
2
2
1
0
1
1
2
0
0
0
2
0
2
1
0
1
1
1
1
1
1
0
0
1
1
0
0
1
0
1
2
2
2
1
0
1
1
2
1
1
2
0
0
1
1
0
1
1
2
0
0
1
2
2
0
1
2
0
1
2
1
1
0
1
0
1
0
1
0
1
1
1
0
1
1
2
1
1
0
0
3
0
1
0
2
2
2
1
0
0
1
2
1
0
0
1
2
0
1
2
2
1
2
0
1
0
0
2
1
0
2
1
0
0
2
1
3
1
0
2
1
1
0
1
0
1
0
1
1
0
1
0
0
0
1
1
2
0
0
0
0
1
1
0
1
1
1
2
1
1
0
0
1
1
0
0
2
2
0
0
1
0
0
1
1
0
0
1
0
1
0
1
3
1
0
1
1
1
0
0
1
0
2
2
1
0
1
0
0
0
0
1
1
0
2
1
1
2
2
1
0
0
2
1
0
0
0
1
1
0
1
2
2
0
0
0
0
1
2
1
0
0
1
1
2
0
1
1
1
3
1
1
0
1
2
1
1
0
0
2
0
1
1
0
2
2
2
0
1
2
0
1
2
1
0
0
0
1
1
0
1
0
1
0
1
0
1
2
1
1
1
1
1
0
0
1
1
1
0
1
1
0
2
2
2
1
1
2
1
0
0
1
1
1
1
1
1
1
0
2
2
0
1
1
2
0
1
1
1
0
0
1
0
0
0
2
0
0
2
1
1
0
1
1
2
2
0
2
1
1
2
0
1
0
2
1
0
0
2
5
0
1
1
0
0
2
1
1
1
0
1
2
0
2
1
0
0
0
1
0
0
0
0
1
2
1
2
0
0
2
0
1
1
1
0
0
0
2
1
1
2
1
0
1
1
0
0
2
0
1
1
2
1
4
1
0
0
1
1
1
0
2
0
0
1
3
1
1
0
0
0
0
2
0
0
1
1
1
1
0
1
0
1
2
0
1
2
0
1
1
1
1
3
1
1
0
1
0
1
0
0
1
2
0
0
0
0
0
1
0
1
0
0
2
0
0
0
2
2
0
1
1
1
1
2
0
1
2
1
0
2
1
0
0
1
1
1
0
1
1
1
0
2
2
1
0
0
1
0
0
0
1
0
2
1
0
0
1
1
1
2
1
0
1
0
1
1
1
1
1
1
0
2
3
1
1
0
2
1
0
2
0
1
1
1
1
1
0
1
2
2
1
2
1
0
1
0
0
2
2
0
2
2
1
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
1
0
0
1
2
1
0
1
0
0
1
2
0
1
1
0
0
0
1
2
1
0
0
1
1
2
1
2
0
1
2
1
0
1
0
1
1
1
0
0
0
1
1
2
1
0
0
1
1
2
0
1
1
2
2
0
2
1
0
0
1
1
0
1
1
1
1
0
2
1
4
2
2
1
1
0
2
0
0
2
0
2
0
0
3
3
1
0
1
1
1
0
1
1
0
0
1
0
1
2
2
1
4
1
0
1
1
1
1
0
1
1
1
0
0
0
0
1
0
0
1
0
2
1
2
1
1
2
2
0
0
1
0
1
1
1
1
0
0
1
0
0
0
1
1
2
0
1
1
3
0
1
2
0
2
2
1
1
0
0
0
2
1
2
1
1
0
1
1
0
2
0
1
1
0
1
0
1
1
1
2
0
5
1
1
1
2
0
1
1
1
1
0
1
2
2
0
2
1
0
0
1
1
2
2
0
2
1
2
1
1
2
1
2
1
1
2
1
0
1
0
0
1
1
1
0
2
0
0
3
0
1
2
1
1
1
0
1
0
2
1
0
2
1
2
1
1
1
2
1
0
2
2
0
0
2
1
0
2
1
0
2
1
1
0
2
1
3
0
1
1
2
0
0
0
0
2
0
2
0
1
1
1
1
1
2
2
0
0
1
1
3
1
1
2
0
0
0
0
1
0
1
2
1
1
1
0
0
2
2
0
1
0
1
1
2
2
1
1
1
1
0
0
0
1
2
1
1
2
0
1
0
0
0
0
0
1
2
1
0
1
1
0
2
2
0
2
4
0
2
1
1
0
0
1
2
2
0
0
0
2
0
1
1
2
1
0
1
1
0
0
1
1
0
1
1
0
1
0
2
0
0
0
0
2
0
2
2
1
1
1
2
2
2
2
0
2
1
2
2
0
0
2
1
1
0
1
0
0
2
0
0
2
2
0
1
1
0
1
0
1
1
2
0
0
0
0
0
1
1
1
3
2
2
1
0
2
0
0
1
0
0
2
2
0
1
0
1
1
0
2
0
1
0
1
1
0
0
1
0
0
0
0
0
2
0
0
1
0
1
1
0
0
2
1
2
1
0
2
0
0
1
2
2
0
0
1
2
2
2
3
1
1
0
2
2
2
0
1
2
1
2
0
1
1
0
2
1
1
0
0
0
0
1
0
0
1
0
1
2
0
0
2
3
0
1
1
0
0
2
0
1
0
1
2
0
0
0
0
2
1
0
1
2
1
1
0
1
2
2
1
0
2
1
1
2
0
0
0
1
0
1
0
1
2
1
0
0
1
0
0
1
1
2
2
1
1
2
1
0
1
1
0
2
1
1
1
1
0
1
1
2
2
1
0
0
2
1
1
1
2
1
0
3
1
1
1
0
0
0
2
2
1
1
0
1
1
2
1
1
2
3
0
0
1
1
0
1
1
1
0
0
1
0
2
0
2
1
1
3
0
2
2
1
0
2
1
1
0
1
0
1
0
2
1
1
0
1
0
0
1
2
2
1
1
1
1
0
1
2
1
0
0
0
0
1
1
0
1
1
0
0
1
0
0
2
1
0
2
0
2
1
1
2
0
0
0
1
1
0
0
0
0
1
0
0
2
2
1
0
1
2
1
1
1
1
1
2
1
2
1
0
1
0
2
1
0
1
2
2
1
1
1
0
2
0
0
1
0
1
2
2
1
5
0
1
0
0
1
0
1
0
0
1
1
0
0
0
0
1
1
1
0
1
1
1
0
0
2
1
0
2
2
0
0
3
1
3
2
1
0
1
0
1
1
0
0
0
1
0
0
1
0
1
1
1
1
0
0
0
0
1
1
1
1
3
1
2
1
0
2
0
0
0
0
2
2
0
1
2
2
1
1
1
2
1
1
2
0
0
1
1
0
1
0
1
0
0
2
2
1
0
1
0
0
0
1
1
0
0
1
1
1
2
1
1
0
1
0
1
2
1
1
1
2
1
2
2
0
2
1
2
1
1
0
1
2
1
0
2
2
1
1
2
3
0
0
0
1
2
1
1
1
0
1
2
1
1
0
1
1
2
2
0
2
0
1
0
0
2
1
2
0
1
1
0
1
0
1
0
0
1
2
1
0
0
0
1
1
1
1
0
2
0
2
1
0
2
0
0
1
1
0
1
1
0
1
2
2
1
2
1
1
0
0
1
0
2
1
2
0
2
0
0
1
2
1
0
1
0
0
1
0
1
1
1
0
1
1
1
0
1
1
0
1
0
0
0
1
1
2
1
0
1
0
1
6
0
0
0
1
0
1
1
2
2
1
1
0
2
0
0
0
0
1
1
1
0
1
0
0
1
1
0
0
1
0
0
0
2
2
0
0
1
0
1
1
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
2
1
1
2
1
2
2
1
0
2
1
0
2
0
0
2
2
0
1
0
1
0
1
2
2
1
0
0
1
0
0
0
1
3
1
0
1
1
1
0
0
1
1
0
2
1
1
2
2
1
0
3
0
2
0
2
0
1
1
0
0
1
0
0
1
2
0
2
0
0
1
0
1
0
2
0
1
2
2
0
0
0
0
1
1
2
2
0
1
0
2
2
2
1
0
0
1
1
1
1
1
0
1
2
0
1
1
0
0
2
1
0
2
2
0
1
1
3
2
0
1
1
0
0
0
1
1
0
1
0
0
1
1
3
0
0
0
0
1
0
1
1
0
2
1
1
2
0
2
0
1
1
2
0
0
2
0
0
1
1
2
1
1
0
2
1
0
0
0
0
0
2
1
2
0
0
0
0
0
0
1
4
1
0
0
2
2
0
1
1
0
2
1
0
1
0
2
0
0
2
0
0
1
0
2
1
0
0
0
0
0
0
1
0
2
1
0
0
1
1
0
0
2
3
3
0
2
1
1
1
0
2
0
3
1
1
0
2
2
2
1
2
0
1
0
0
2
2
0
2
0
0
1
0
0
0
2
0
2
1
1
0
0
2
2
2
2
2
1
1
2
0
0
0
3
1
1
3
1
0
1
0
0
1
1
2
0
1
1
0
0
1
1
1
1
0
0
1
0
1
0
0
0
1
1
1
1
2
0
2
1
2
2
0
1
0
0
0
0
0
2
0
2
2
1
1
1
0
1
1
1
1
1
1
1
1
2
1
2
0
2
1
0
0
1
2
0
1
2
1
1
1
1
0
2
1
0
2
2
1
1
1
2
0
0
2
0
0
1
0
1
0
1
1
2
0
2
2
0
1
0
1
0
0
1
1
1
0
0
1
2
1
0
1
1
2
1
0
0
1
1
0
2
2
1
0
2
1
2
1
2
1
2
0
0
0
1
1
2
2
0
0
0
0
0
0
2
1
1
0
0
0
0
2
3
1
1
1
1
1
0
0
1
2
2
0
0
0
1
1
0
1
2
1
0
2
1
0
0
0
2
0
1
1
0
1
1
2
1
0
2
0
3
1
3
0
1
0
0
1
0
2
2
1
1
0
2
0
1
1
0
0
2
2
0
0
0
1
2
1
1
2
2
0
0
0
1
4
1
1
0
0
0
0
1
0
2
2
0
0
0
0
1
0
2
1
0
0
1
0
0
2
1
1
0
1
0
1
2
2
10
1
1
1
2
1
2
1
1
0
2
2
0
1
0
2
1
1
0
1
0
1
2
2
0
0
0
2
2
1
1
1
0
1
1
0
1
2
2
0
2
1
0
0
0
2
1
4
1
2
0
0
1
1
1
0
2
2
2
1
0
1
1
0
0
1
1
2
0
2
0
0
0
2
0
0
1
1
0
1
1
1
1
0
1
1
1
0
0
0
1
0
1
1
1
0
1
0
1
1
0
2
0
2
0
1
1
0
0
1
1
0
1
0
0
2
1
1
0
0
1
1
1
0
1
0
0
0
1
1
2
1
0
1
1
2
1
1
0
2
1
1
0
2
1
2
0
0
1
2
1
1
2
2
0
1
1
0
1
1
1
1
1
2
0
2
1
1
3
2
0
1
2
1
0
0
2
0
0
0
1
2
1
2
0
1
2
1
1
1
2
1
1
2
0
0
0
1
1
0
1
0
1
1
0
0
0
0
1
0
2
1
0
1
0
2
0
1
1
0
0
1
1
0
1
2
0
0
0
0
1
1
2
2
2
1
1
1
0
2
1
1
0
2
1
1
2
1
0
1
0
1
1
0
1
0
0
0
2
1
0
1
0
0
1
0
2
0
1
1
0
0
0
1
1
0
2
2
1
0
0
0
0
2
2
1
1
0
2
0
2
2
1
1
1
1
0
0
1
1
1
0
1
0
1
2
0
1
1
2
1
0
1
4
2
1
0
0
0
2
1
2
1
0
1
0
1
0
0
2
0
1
1
0
0
1
1
1
1
3
2
1
1
1
2
1
1
2
0
2
0
1
0
0
1
0
1
0
2
1
2
2
0
1
1
2
1
1
1
2
0
0
0
2
1
2
0
0
0
2
0
1
0
2
1
0
1
0
0
2
2
0
0
0
1
1
5
1
2
1
2
0
1
1
1
1
1
0
1
1
0
1
1
0
0
0
1
1
1
0
0
2
1
2
0
0
1
0
2
1
1
2
2
1
2
0
2
0
0
2
2
0
0
0
1
1
0
1
0
1
4
1
2
1
1
1
1
0
2
1
1
1
0
1
1
0
1
0
1
1
0
0
1
0
1
1
1
3
0
2
1
1
0
1
0
1
1
1
0
0
1
0
2
2
0
1
0
0
1
1
0
1
1
2
0
1
1
0
0
2
2
2
2
0
0
0
1
2
2
1
0
0
2
2
2
1
0
1
0
1
0
0
0
0
0
1
3
0
2
1
0
2
0
0
0
1
1
1
0
2
0
0
1
1
1
0
1
1
0
0
0
0
2
1
0
0
2
0
1
0
1
1
1
1
0
1
1
0
3
1
1
2
0
2
0
0
0
0
1
0
0
1
1
2
1
0
1
0
1
1
0
1
0
1
0
1
1
2
1
4
0
1
1
0
1
0
0
2
0
1
0
2
0
1
2
0
0
0
1
1
0
0
1
2
1
1
1
1
1
0
1
1
0
1
1
0
1
1
2
1
0
2
0
0
1
0
2
1
0
1
1
0
0
0
1
1
2
0
1
2
2
1
0
2
2
1
0
2
0
1
0
3
2
0
2
2
2
0
0
0
0
0
0
1
2
1
1
2
1
1
2
0
0
1
1
0
1
0
2
1
1
0
2
1
0
0
0
2
0
1
2
1
0
4
1
1
0
2
2
1
1
3
1
1
0
2
1
0
0
0
0
0
1
2
0
0
1
0
1
2
1
2
2
0
1
1
2
2
0
2
0
1
0
1
0
1
0
1
1
1
1
1
0
0
0
1
1
1
1
1
1
0
2
1
2
1
1
1
1
2
2
0
1
0
1
0
0
1
2
2
2
2
1
1
0
0
1
0
0
0
2
2
1
1
0
0
2
2
0
0
2
1
1
1
2
1
2
1
2
0
0
1
0
0
0
2
2
2
1
2
0
0
0
2
0
0
2
2
1
0
0
0
0
2
1
0
0
1
2
2
2
1
0
2
2
1
2
0
1
0
1
1
0
1
1
0
0
0
0
1
1
0
0
1
0
2
1
0
0
0
1
0
2
1
2
2
0
1
2
2
2
2
1
0
2
1
1
1
0
2
1
0
1
0
2
3
0
0
2
1
2
0
1
1
0
2
2
2
0
1
1
0
2
0
0
1
2
0
0
3
1
1
1
0
1
1
0
1
0
0
1
2
0
2
1
0
1
2
0
0
0
2
2
0
0
0
0
0
1
1
1
2
0
2
0
0
2
1
1
0
1
0
2
1
2
1
0
1
1
1
0
1
1
1
2
0
1
0
1
1
0
1
1
0
0
3
1
1
0
2
0
1
2
0
0
1
2
0
2
1
0
0
0
2
2
0
0
0
2
1
1
1
2
0
1
1
0
0
2
1
1
1
1
2
1
1
1
2
1
2
1
0
2
1
1
1
1
1
0
1
1
2
1
0
1
1
0
0
2
0
2
1
0
1
0
0
2
0
2
1
0
1
1
1
0
2
1
1
0
0
0
3
2
1
2
1
1
0
2
0
0
1
0
2
0
0
1
1
0
2
0
0
0
0
0
0
1
2
3
1
0
1
2
1
2
0
2
2
1
1
0
2
2
0
2
0
1
0
1
0
2
1
0
2
0
1
2
1
0
2
1
1
1
2
1
2
0
1
0
1
2
0
1
1
2
0
1
1
1
2
1
1
0
0
0
1
1
1
0
1
1
1
1
1
0
0
2
0
1
1
1
0
1
0
2
1
0
0
1
1
2
1
0
1
0
1
1
2
1
0
2
0
2
0
0
0
0
2
2
1
1
0
1
0
1
4
3
2
1
0
1
1
1
2
0
0
1
0
0
0
0
0
3
1
1
1
1
1
0
2
2
0
1
0
0
0
1
2
0
2
1
2
1
0
0
1
1
0
1
0
0
1
0
1
1
0
1
1
0
1
0
1
2
0
0
0
1
2
0
0
2
1
2
1
2
2
1
2
1
1
2
0
1
0
0
1
0
0
0
1
1
0
1
2
6
0
1
0
0
0
2
1
0
0
1
0
0
2
1
1
1
1
1
2
0
0
2
1
0
1
2
1
1
0
1
0
1
2
1
1
2
1
1
1
3
0
1
0
1
1
0
0
1
1
1
0
0
2
0
0
2
1
2
1
1
1
4
2
2
0
2
0
1
1
0
1
0
2
2
0
0
2
0
0
0
2
0
0
1
1
1
0
3
1
3
0
1
0
0
1
1
1
0
1
0
2
0
1
0
0
2
1
0
2
2
1
0
1
1
0
1
1
1
0
2
1
0
1
1
1
5
2
0
0
1
1
1
1
4
2
1
1
2
0
1
2
1
2
2
0
2
0
1
2
2
0
1
1
1
1
2
1
0
0
1
0
0
1
2
0
0
1
1
1
2
2
2
1
0
2
1
0
0
2
1
0
0
2
1
1
2
1
1
2
1
0
1
0
0
0
1
1
2
1
6
1
0
0
0
2
0
0
1
1
2
2
1
0
1
0
0
1
1
0
0
0
0
1
1
0
0
2
1
1
0
0
3
1
0
0
2
0
1
0
1
2
1
1
0
0
2
0
1
0
2
0
1
1
2
1
0
0
1
2
1
0
2
1
0
1
1
3
2
0
0
0
1
0
1
2
1
2
2
1
0
1
0
1
0
0
0
1
2
1
0
0
1
2
0
2
0
0
2
1
0
0
2
2
1
1
0
0
2
0
1
0
0
1
2
1
0
2
2
3
0
1
1
1
2
2
1
0
2
0
0
2
1
0
0
2
0
1
0
2
0
0
0
0
2
1
2
0
0
0
0
2
1
0
1
0
1
1
0
0
0
0
1
1
2
1
0
0
0
1
1
2
1
0
1
1
1
1
1
1
2
1
1
0
0
0
1
1
1
0
1
0
1
1
2
1
0
2
2
1
2
1
2
2
1
0
0
1
1
0
0
2
0
2
0
1
0
1
1
0
0
0
1
1
1
1
0
0
2
1
1
0
1
1
0
1
2
0
1
0
1
7
1
1
2
1
0
1
0
0
1
2
1
0
1
2
1
1
0
1
1
1
1
0
1
1
1
1
1
0
0
0
1
1
0
0
0
0
1
1
2
2
2
0
0
1
2
0
1
1
0
0
2
0
1
1
1
1
3
1
1
2
1
0
1
1
1
1
0
1
0
1
2
0
1
1
2
0
1
2
0
1
2
1
0
1
1
1
2
1
1
0
0
0
1
1
0
1
0
2
1
0
1
2
0
1
0
1
2
1
2
0
1
2
1
0
1
2
1
2
0
2
1
0
1
2
1
0
0
2
1
1
1
0
2
0
0
0
1
0
0
1
2
0
1
1
0
0
0
1
2
2
0
0
0
1
1
1
2
1
0
1
0
1
0
1
1
1
1
0
2
1
0
0
2
1
1
0
2
2
0
0
1
2
0
1
1
0
1
1
0
1
0
2
0
1
0
1
0
0
0
0
1
2
0
1
1
1
1
0
2
0
1
0
0
1
1
2
1
2
2
1
4
0
1
0
2
1
2
1
1
0
0
1
1
1
1
0
3
1
0
1
1
2
0
2
2
2
2
1
0
1
1
1
1
2
0
1
1
0
3
1
1
0
1
0
1
3
1
0
0
1
1
0
1
1
1
2
2
0
1
1
1
0
0
1
2
2
1
1
0
1
1
1
2
1
0
0
0
0
0
0
0
1
2
1
4
0
1
1
0
1
0
0
2
1
1
2
2
1
1
0
0
1
1
1
1
0
1
1
2
1
2
2
2
0
0
0
0
1
0
1
1
2
0
1
2
2
1
0
0
0
2
0
2
0
0
0
1
0
1
1
2
0
0
1
0
1
0
0
2
1
2
1
0
1
1
1
0
0
0
1
0
0
1
1
2
2
1
0
1
0
2
0
1
1
0
1
1
0
1
0
1
0
1
1
2
0
1
2
1
0
1
0
2
0
2
1
2
1
0
2
1
2
1
0
0
2
2
2
1
0
1
0
0
1
0
2
1
1
2
1
0
1
1
3
2
2
2
0
1
2
0
2
2
2
2
2
1
1
0
0
1
0
1
2
1
0
0
0
1
1
2
1
0
2
0
1
1
1
1
1
0
1
1
1
0
1
1
2
1
2
1
2
0
1
0
2
0
1
1
1
1
1
2
1
0
0
2
2
2
1
1
1
0
1
1
0
0
1
0
2
0
1
0
0
0
2
2
0
0
1
0
0
0
0
0
0
1
1
0
0
4
2
0
1
1
0
2
1
0
0
2
1
0
3
1
2
0
0
0
0
2
1
0
1
1
0
2
1
0
1
2
2
0
1
0
1
1
0
2
1
0
2
1
2
2
2
1
2
0
1
0
0
0
1
0
1
2
1
2
1
0
1
1
1
0
0
0
1
0
1
0
2
2
1
0
2
0
0
0
2
0
2
0
0
2
0
0
0
1
2
0
1
2
1
2
1
2
1
1
0
1
1
0
2
1
0
2
1
6
0
0
2
1
1
1
1
2
1
0
2
0
0
2
0
2
0
1
1
1
1
0
3
1
0
0
0
2
2
1
2
1
0
2
1
2
1
1
1
1
2
1
2
1
1
1
0
1
0
2
1
1
0
0
1
0
0
1
1
0
1
1
2
2
2
2
1
0
0
2
1
0
1
1
1
1
1
1
0
1
1
0
2
0
0
1
0
0
2
2
1
0
1
1
2
2
0
1
3
1
2
0
1
1
2
0
2
0
1
1
1
1
1
2
1
1
1
0
0
1
1
1
1
0
1
1
0
1
0
1
0
1
2
2
0
1
0
1
2
1
0
0
0
1
2
1
1
1
1
0
1
0
1
1
1
1
2
1
1
2
0
0
1
1
3
3
0
0
2
1
0
0
2
2
1
0
1
0
2
1
2
1
1
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
2
0
0
1
0
2
0
1
2
0
0
0
1
2
0
2
0
1
0
2
1
1
1
1
0
1
1
0
1
0
3
1
1
0
1
0
1
0
0
0
2
0
2
1
0
2
2
2
1
0
2
0
0
2
0
1
0
2
0
2
1
0
0
1
0
2
1
1
1
1
2
2
0
0
0
1
0
0
2
0
0
2
2
2
0
2
1
0
2
1
2
0
2
1
0
0
2
0
1
2
1
0
1
0
2
1
0
1
1
2
2
1
1
1
1
0
0
0
1
1
0
1
0
1
1
0
1
1
2
1
0
0
0
0
0
0
2
2
1
0
1
2
0
2
1
1
2
0
0
1
1
0
2
2
2
2
1
1
0
0
0
1
2
0
1
1
2
1
1
1
0
2
0
1
0
0
2
0
1
1
1
0
0
0
1
2
1
1
2
0
1
2
0
0
2
1
2
1
0
1
1
0
2
0
0
1
1
1
0
1
0
0
1
1
1
0
0
0
2
0
3
1
1
0
0
1
1
1
2
2
2
1
0
0
0
2
0
2
0
0
1
0
1
2
2
0
1
2
1
0
0
1
2
2
1
0
1
2
1
0
3
0
0
0
0
1
0
0
0
0
1
0
1
2
0
1
2
1
2
1
2
0
2
1
1
1
0
1
1
0
1
1
1
0
1
0
0
2
0
0
0
1
2
1
2
0
1
3
1
1
0
1
2
2
0
0
0
0
2
1
2
1
1
2
0
1
1
0
2
0
0
0
1
0
1
0
1
1
2
0
1
0
0
1
2
0
2
0
1
1
0
1
1
2
1
0
2
2
2
0
0
2
1
1
1
2
1
2
0
2
0
0
1
1
0
0
1
0
1
0
0
0
2
0
2
1
2
0
1
0
1
1
0
1
0
1
2
0
0
1
0
2
0
0
0
0
1
1
1
1
1
2
1
1
1
2
2
0
0
2
1
1
2
0
1
1
0
1
2
0
2
2
1
0
0
1
1
1
0
3
0
1
0
0
1
1
0
0
2
1
1
1
2
1
1
1
0
1
0
2
1
1
0
0
1
1
0
0
1
1
2
2
1
0
0
1
0
1
0
0
1
1
0
0
0
2
1
1
1
1
2
1
1
0
0
1
1
2
0
1
0
1
1
1
1
1
0
0
1
1
2
1
1
1
1
0
1
1
1
2
1
2
0
0
1
3
1
0
0
2
2
0
0
1
1
1
0
0
0
0
0
1
2
2
1
0
0
1
1
0
0
1
1
1
1
1
2
2
2
0
1
1
1
0
1
1
1
0
0
2
0
2
1
0
0
0
0
2
1
1
1
1
1
0
0
0
0
1
2
1
0
2
0
1
1
0
2
0
1
4
1
0
1
0
0
1
1
3
1
0
1
0
1
2
0
0
0
0
1
2
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
2
1
1
0
1
0
0
0
2
0
1
1
1
0
1
1
0
1
2
2
1
0
3
0
2
0
1
0
0
1
1
0
1
1
2
1
1
0
1
1
1
0
0
0
0
0
0
1
2
0
2
1
0
0
0
0
1
2
1
2
0
0
1
2
0
1
1
0
1
2
0
1
1
0
0
1
0
2
0
1
2
1
0
1
1
1
0
0
1
0
2
0
2
0
1
2
2
3
0
1
1
0
0
1
2
0
1
2
1
1
0
0
1
0
2
1
2
0
2
1
2
2
1
0
2
1
1
0
2
1
0
1
0
1
0
1
0
1
0
0
1
1
0
1
0
0
0
1
1
1
0
0
0
2
1
1
1
2
0
0
2
0
1
2
2
2
0
1
0
1
1
1
1
1
2
0
3
0
0
1
1
1
0
1
2
0
1
1
1
0
1
0
0
1
2
1
0
1
0
6
2
2
1
1
2
0
1
0
1
2
1
0
1
1
2
1
2
1
1
1
0
2
1
1
2
0
0
0
2
0
2
0
1
0
0
1
0
0
1
1
0
0
1
0
0
2
1
1
3
0
0
2
0
3
1
0
1
0
0
2
0
1
1
1
2
2
2
1
0
1
0
0
0
1
0
1
1
1
0
1
1
0
0
1
0
0
1
1
1
1
1
4
1
1
0
1
0
3
1
1
1
1
2
0
1
1
2
0
2
1
1
0
0
4
0
0
0
0
0
0
0
2
0
0
1
0
0
2
2
1
1
2
0
2
1
0
1
2
1
0
0
1
2
1
1
0
0
2
2
1
2
0
2
1
0
1
2
1
0
0
2
2
0
0
0
0
0
0
1
1
0
0
0
2
1
0
2
0
2
2
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
1
0
1
1
0
2
1
2
1
0
1
0
1
0
1
2
1
0
2
1
0
0
0
0
0
0
1
0
1
1
1
0
2
0
2
2
0
1
1
1
0
0
1
1
0
1
0
2
1
1
1
1
1
1
0
0
1
1
0
1
1
1
0
0
0
8
0
1
0
0
0
2
1
1
2
1
2
0
1
2
2
1
1
0
0
2
0
1
1
1
0
0
0
0
2
0
0
5
1
1
2
2
0
1
0
0
1
1
1
1
0
1
2
1
1
2
1
1
1
0
0
1
0
1
0
1
1
1
1
1
0
2
0
1
2
1
0
0
1
2
0
1
0
0
1
0
0
0
2
1
0
1
2
2
0
0
1
2
0
0
1
0
1
0
0
2
1
0
0
1
0
1
0
2
0
1
0
0
1
2
0
1
0
2
1
1
1
0
0
1
2
3
1
1
0
1
1
1
1
1
1
0
1
2
1
1
1
0
1
1
1
0
1
0
1
1
0
1
1
1
1
1
1
2
0
1
0
0
0
1
0
1
0
0
3
1
0
2
0
1
0
0
0
0
0
2
1
2
1
1
1
2
0
1
0
1
1
1
2
1
1
1
1
1
1
2
0
1
0
2
1
0
1
0
1
1
1
0
1
1
1
0
0
0
1
1
1
0
1
1
1
1
0
1
1
2
1
0
3
0
1
1
1
1
1
1
1
2
1
1
0
1
2
0
1
2
1
1
1
2
0
1
1
0
0
1
3
1
4
0
1
0
1
2
0
0
1
1
0
0
1
2
1
3
0
0
1
0
1
2
0
1
0
2
3
1
2
1
0
1
1
0
1
1
1
1
0
0
0
1
2
1
0
2
1
1
2
0
1
1
1
1
1
0
1
1
1
1
0
1
1
2
0
0
0
1
0
0
1
2
1
1
2
0
1
0
1
0
1
1
2
1
1
0
2
1
0
0
1
0
0
1
0
2
0
0
1
2
0
0
3
1
1
1
0
1
0
2
1
1
1
0
2
0
0
0
0
2
1
1
0
0
0
2
1
1
1
0
0
0
0
0
1
0
1
0
2
0
1
0
0
2
1
2
0
0
0
1
0
1
1
1
1
0
0
1
0
0
1
1
1
1
2
0
2
0
2
1
2
1
1
0
0
1
2
1
1
0
0
1
1
0
0
1
1
2
0
1
0
2
1
1
2
1
1
3
1
1
0
0
1
0
1
1
2
0
2
1
0
1
1
1
0
1
2
1
1
1
1
0
1
0
2
5
1
1
1
0
1
0
0
1
0
1
0
2
1
1
0
0
2
0
0
0
0
0
0
1
1
0
0
1
1
0
1
2
0
2
0
0
2
0
1
2
0
0
2
1
0
2
1
2
3
1
3
0
0
0
1
1
1
1
0
1
1
1
1
2
0
0
0
0
1
1
1
1
0
2
1
1
1
1
1
0
0
1
0
1
0
0
0
0
1
1
1
0
1
1
1
2
0
2
1
2
0
2
0
3
0
0
0
2
2
0
2
0
1
0
2
0
0
0
1
1
1
4
0
0
0
1
2
0
0
1
0
2
1
1
2
0
1
1
1
1
1
0
1
2
1
1
2
1
2
1
2
1
0
0
2
1
0
1
2
0
1
0
1
1
1
1
0
1
0
0
1
1
0
1
2
0
1
2
1
0
1
0
0
1
2
1
0
2
0
0
0
0
1
2
1
1
1
0
1
1
1
0
1
1
0
2
1
0
0
0
2
1
0
1
1
1
1
0
2
1
2
0
0
1
2
2
1
0
2
2
1
1
0
0
2
0
0
2
2
1
0
2
0
2
0
0
0
1
4
1
0
0
1
2
0
2
0
1
0
1
0
0
1
2
1
2
1
0
0
0
0
2
0
1
1
2
2
2
1
0
2
0
1
0
1
0
1
1
1
0
1
1
0
2
0
1
1
0
0
0
0
0
0
0
0
1
1
2
2
2
2
1
2
1
1
0
0
0
0
2
2
2
0
2
1
2
0
1
2
1
1
1
1
0
0
1
2
3
2
0
0
1
1
0
0
0
0
1
0
1
0
2
1
0
0
0
1
0
2
0
2
0
0
0
1
1
2
1
0
1
2
1
1
2
0
0
1
2
0
2
1
1
0
3
1
1
0
1
1
0
1
0
0
0
0
1
0
2
1
1
1
2
1
2
0
1
0
1
1
1
1
0
1
2
2
2
1
0
0
0
4
0
0
1
1
1
0
0
1
0
2
1
1
0
0
0
1
2
2
2
2
0
0
0
1
1
0
1
0
1
2
0
0
1
1
1
1
1
1
2
2
0
5
1
2
1
1
2
0
0
1
1
1
2
0
1
1
0
1
1
1
1
0
0
1
0
0
1
0
2
0
1
1
0
0
0
1
1
0
1
0
0
0
1
1
1
0
0
1
0
2
1
1
2
2
1
1
0
2
3
1
1
2
0
0
0
0
1
0
0
2
2
0
0
1
0
2
1
0
2
0
2
0
1
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
2
1
1
1
0
1
1
1
1
1
0
0
0
1
1
2
0
0
0
1
1
1
1
1
1
5
1
1
2
1
1
0
2
1
2
2
2
2
2
1
0
1
0
3
0
1
1
0
2
1
2
2
2
0
0
0
0
1
1
0
0
2
0
1
1
0
0
2
0
0
1
0
0
1
1
0
2
1
2
2
2
1
1
0
0
0
1
0
1
2
0
0
0
2
0
2
1
0
1
0
1
1
0
0
2
1
2
2
0
1
1
1
2
0
2
1
0
1
0
0
0
1
2
2
1
1
1
0
0
0
1
2
0
1
1
0
2
2
1
1
0
0
0
2
1
1
0
0
1
0
2
2
2
0
1
1
0
0
2
0
0
1
1
0
1
0
2
1
0
0
1
0
1
0
1
0
0
1
1
1
1
2
1
1
0
1
2
2
1
0
0
0
0
0
1
2
0
0
2
2
2
1
0
2
2
3
0
2
1
1
1
0
0
1
2
1
2
0
2
0
2
1
0
2
1
1
1
1
1
0
2
1
1
1
2
0
1
0
2
0
2
2
0
1
0
1
2
0
1
3
1
1
0
1
1
0
1
0
0
0
2
1
0
0
0
1
0
1
0
2
2
1
2
2
2
1
0
0
1
2
0
2
1
0
1
2
2
2
1
0
1
2
1
0
2
0
2
0
1
0
1
2
0
0
1
1
2
2
2
2
0
0
0
2
0
1
0
0
1
2
1
1
2
0
0
0
1
0
0
1
1
1
3
1
0
0
0
1
0
1
2
2
2
1
2
0
0
1
1
0
0
1
1
0
1
1
0
0
1
1
1
1
0
1
0
1
0
0
2
0
0
1
1
2
2
0
0
0
2
1
2
0
0
1
1
2
2
2
0
1
3
0
0
0
2
1
0
1
0
2
1
2
0
1
1
0
1
0
1
0
0
0
2
1
1
2
0
1
0
0
2
0
5
2
1
0
0
0
1
1
0
0
0
1
0
1
2
0
0
0
1
1
2
0
0
1
0
1
0
0
1
1
0
2
2
2
2
0
1
0
1
1
0
0
2
2
1
1
2
0
2
0
1
0
0
2
1
2
0
1
1
1
0
1
1
0
0
1
2
2
2
2
2
0
2
0
1
1
0
2
0
0
1
1
0
1
1
1
2
0
1
1
1
0
1
1
0
1
2
3
0
1
1
2
2
2
1
1
2
2
1
0
0
2
0
0
0
0
2
1
2
1
0
0
0
1
1
1
0
1
3
0
0
0
0
0
1
1
1
1
0
1
2
0
2
1
1
0
1
0
0
0
1
1
0
0
0
0
2
0
1
0
1
0
1
0
2
1
1
0
1
2
1
0
1
2
1
2
1
2
1
0
0
2
1
0
0
1
1
1
0
2
0
1
1
2
0
1
1
0
2
1
0
2
0
2
0
1
1
1
0
1
1
1
1
0
0
0
1
0
1
2
0
0
1
0
1
0
0
1
2
0
1
0
2
2
1
0
1
3
0
1
0
1
0
1
0
1
1
2
0
1
2
0
0
1
1
0
1
0
1
1
2
0
1
1
0
2
0
0
0
0
1
0
0
0
1
1
0
2
0
0
2
1
2
0
0
0
1
1
1
1
1
0
1
0
0
0
0
0
0
0
2
2
1
1
1
0
2
0
1
0
0
0
1
1
0
2
1
1
2
3
2
0
0
1
2
1
0
1
0
1
2
2
0
1
0
0
0
1
0
1
1
1
1
1
3
0
3
1
1
2
1
1
1
0
0
2
1
2
0
1
1
0
0
0
0
2
1
1
2
1
2
1
0
2
1
0
0
2
2
1
1
0
1
1
1
0
1
1
2
0
0
2
0
0
0
0
0
2
2
0
1
0
0
0
0
0
1
1
1
1
1
1
1
2
0
1
2
0
0
1
2
1
0
1
1
2
1
1
0
1
1
1
0
1
1
1
0
0
1
0
2
0
1
0
1
1
2
1
0
1
1
1
1
1
0
1
1
0
1
1
1
1
2
0
0
2
2
0
0
1
2
0
2
2
1
1
1
1
2
0
1
2
0
1
1
1
0
1
0
0
2
0
2
1
0
2
1
2
0
2
1
0
1
2
2
1
1
0
1
0
1
2
1
0
1
0
1
2
1
1
0
1
2
1
1
0
2
2
0
0
0
0
0
0
0
1
0
1
0
0
1
1
3
1
1
3
1
1
0
2
2
0
0
0
1
1
0
2
0
0
1
0
0
1
2
0
2
1
1
0
0
0
0
2
0
0
1
0
0
1
0
0
1
1
1
1
1
0
0
0
0
0
2
1
2
0
1
2
1
1
0
0
1
2
1
1
0
0
1
0
0
1
3
0
0
5
0
0
1
0
2
2
2
1
1
0
2
0
2
0
1
1
0
0
0
0
0
1
1
1
1
1
1
1
0
1
1
0
1
0
0
2
2
0
2
1
0
1
1
1
0
0
2
0
0
0
1
0
0
1
1
1
2
1
0
1
0
1
1
2
1
0
2
1
3
0
0
1
0
1
1
0
0
1
0
0
0
1
0
3
2
1
0
1
0
1
0
1
2
0
1
2
2
0
0
0
2
1
1
2
1
1
0
2
0
1
3
3
1
1
0
2
0
1
1
0
1
0
0
1
0
1
0
1
1
0
1
0
0
2
1
1
2
0
0
0
0
3
0
1
0
1
1
1
0
1
0
0
1
2
0
2
0
1
1
1
1
1
2
2
1
2
0
3
1
1
3
0
0
0
1
1
1
2
0
2
0
0
2
1
1
2
1
0
0
1
2
2
0
1
0
0
0
2
0
0
0
0
1
1
2
1
2
1
0
3
0
0
0
2
0
0
1
0
2
0
1
1
1
0
1
0
1
0
0
1
1
1
0
1
2
2
0
0
2
0
0
1
1
0
1
2
0
2
0
1
1
0
0
1
2
1
1
1
1
1
1
0
1
1
1
0
2
1
0
1
1
2
1
1
0
0
2
1
0
1
1
0
1
0
0
0
1
0
0
1
2
1
1
1
2
0
2
1
1
2
0
0
1
1
0
0
0
1
0
1
1
2
0
0
0
2
0
1
2
0
2
0
2
1
2
0
1
0
1
1
2
2
0
2
0
0
2
1
1
0
0
1
1
2
2
2
0
1
0
0
0
1
1
2
1
0
1
0
2
1
1
2
1
0
1
2
0
2
0
2
0
0
0
0
1
0
0
0
0
3
1
1
0
1
0
2
1
0
1
1
1
1
0
0
1
1
2
0
0
1
1
2
2
2
0
1
2
1
0
1
0
0
1
0
1
1
2
0
1
0
1
0
2
4
2
0
1
0
1
0
2
1
0
1
0
1
0
2
2
0
0
1
1
1
0
0
1
2
1
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
2
0
0
1
0
1
2
0
0
0
1
1
1
0
1
1
0
1
1
2
1
0
0
1
2
0
1
1
2
2
0
2
1
1
0
1
2
0
0
0
2
1
2
1
2
1
0
0
0
2
2
0
0
2
1
2
1
0
0
3
2
0
1
0
1
0
0
1
1
0
0
2
2
2
0
1
2
0
1
1
0
1
2
1
0
0
1
0
2
0
0
1
0
1
1
0
2
2
0
0
1
0
1
2
0
1
0
0
0
1
0
1
2
1
1
1
0
1
3
2
0
0
0
2
0
1
0
2
0
2
0
2
1
0
0
0
0
0
0
2
1
0
1
1
3
2
1
0
2
1
0
0
1
0
2
0
0
0
0
1
2
1
1
2
0
2
0
0
0
0
1
1
1
1
1
2
0
1
1
1
0
1
1
2
0
1
0
1
0
1
1
0
1
1
0
0
1
1
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
1
0
0
0
1
1
2
1
1
0
1
1
0
1
1
1
2
1
2
1
2
0
1
2
0
2
1
1
2
1
2
0
1
0
0
1
2
1
2
0
0
0
2
1
1
4
0
1
0
0
1
1
0
0
0
1
1
2
2
0
0
0
2
1
1
1
0
0
0
0
1
0
1
2
2
1
1
0
2
1
1
0
1
0
1
1
1
0
2
2
1
2
0
1
1
1
0
0
1
1
0
1
0
2
1
1
0
1
0
1
0
1
0
1
1
0
2
1
1
3
1
0
2
1
0
1
0
0
1
2
1
0
1
2
1
3
0
1
2
1
0
1
1
0
2
2
0
0
0
2
0
0
1
1
2
1
1
0
0
0
2
0
1
2
0
0
2
1
2
1
0
0
0
1
0
1
1
1
0
0
1
0
1
1
1
2
1
0
0
1
0
0
0
2
0
0
1
2
3
1
0
2
1
0
0
0
0
2
1
1
0
0
2
0
0
0
0
1
0
2
0
2
2
2
2
0
0
1
1
1
0
0
2
2
1
1
1
1
1
0
0
0
0
0
0
1
0
0
1
1
3
1
0
1
1
0
2
0
1
0
1
2
2
0
1
1
0
1
0
0
0
0
2
1
0
0
2
1
0
1
1
0
1
1
2
1
0
1
0
0
0
0
1
1
0
2
1
2
1
1
0
2
0
0
2
0
2
1
0
1
1
2
1
2
0
2
1
0
2
1
1
1
1
0
2
1
1
1
1
1
0
0
2
0
1
2
2
0
0
0
1
1
1
2
0
1
1
0
1
0
1
1
2
0
2
2
1
1
0
0
2
1
0
1
0
1
1
0
0
0
1
0
2
0
2
2
1
0
0
1
1
2
0
0
0
2
1
0
0
2
1
0
2
2
2
1
2
1
0
0
0
0
2
1
1
0
0
1
0
1
2
3
1
0
1
1
1
1
3
0
0
0
1
0
1
1
0
0
1
0
1
2
0
2
1
1
0
1
1
0
1
1
1
1
1
0
1
1
3
1
1
2
0
0
0
0
0
1
0
0
0
2
2
1
2
2
0
2
0
2
2
1
1
0
0
2
0
1
2
0
3
1
1
1
3
2
1
0
1
2
1
2
1
0
2
0
1
1
1
1
1
2
1
1
1
1
0
1
0
1
1
1
1
1
1
2
0
0
1
1
1
0
1
0
1
0
3
1
1
2
0
1
0
1
2
1
0
0
3
0
1
1
1
1
1
0
0
1
1
0
1
0
2
0
0
0
1
1
1
2
0
0
1
1
0
0
0
1
1
1
1
2
1
2
0
1
0
0
0
2
0
1
2
0
1
2
0
2
2
2
0
1
2
2
0
1
0
1
2
1
0
0
0
2
0
1
2
0
2
2
0
0
0
0
0
2
1
2
0
1
2
0
2
2
1
0
2
1
2
0
0
0
0
0
0
2
1
1
0
1
1
0
0
1
1
1
0
0
0
2
0
1
2
1
1
0
2
1
1
0
0
1
0
2
1
2
3
2
1
1
2
2
0
2
0
1
1
1
0
0
0
0
0
2
1
0
0
1
0
1
0
0
0
1
2
1
0
2
0
1
0
0
0
0
1
1
0
0
2
0
1
1
0
5
1
1
1
0
0
0
2
1
0
2
1
0
1
0
1
2
1
0
0
1
1
2
3
1
0
1
2
1
1
0
1
0
1
2
1
2
1
1
1
1
1
2
0
0
2
0
2
1
1
1
1
1
2
1
1
0
2
1
0
2
1
3
0
1
1
1
0
0
0
1
2
1
2
2
0
1
0
1
1
1
1
1
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
2
0
1
2
1
0
2
1
1
0
0
0
0
0
0
0
1
0
0
1
1
0
2
1
2
1
1
0
2
0
0
3
1
1
2
2
0
0
0
0
1
1
0
1
1
0
0
0
0
1
2
1
0
0
0
0
0
0
0
1
0
0
1
1
1
2
0
1
1
1
1
0
1
0
0
0
1
1
0
1
0
2
0
2
1
1
1
0
0
1
0
1
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
1
0
1
1
1
1
1
1
1
1
1
1
0
2
1
1
0
1
0
2
1
0
1
0
1
1
0
1
0
1
0
3
1
1
0
5
1
0
0
1
0
1
1
2
1
0
2
0
1
2
0
0
0
0
1
2
2
1
0
0
1
0
1
0
0
2
0
0
1
1
1
1
1
1
1
1
2
0
1
0
2
0
1
0
1
2
2
1
0
2
0
2
0
1
1
2
1
1
1
0
1
0
3
0
1
1
0
0
1
2
2
0
0
2
0
0
0
1
1
1
3
0
1
1
2
2
3
2
1
2
0
1
1
0
0
1
1
0
1
2
0
0
0
0
2
1
1
0
3
0
0
2
2
1
2
2
1
0
1
1
2
1
1
1
1
2
0
0
1
0
0
0
1
0
0
1
0
0
3
2
1
0
1
0
1
2
2
1
0
0
0
0
0
1
0
0
1
0
1
1
0
0
1
2
1
1
0
1
1
1
0
1
0
1
2
0
1
1
0
0
1
0
1
1
1
3
2
0
0
2
1
1
0
0
0
1
0
2
1
2
1
2
0
1
1
0
2
0
0
1
1
0
0
0
2
0
1
1
1
0
2
1
1
1
0
0
1
1
0
2
1
0
1
0
1
0
1
1
0
0
0
0
2
2
0
1
0
0
0
1
0
1
1
1
1
1
0
0
1
1
1
1
0
0
0
2
2
1
0
1
0
0
1
0
1
0
1
5
2
2
2
1
0
1
0
1
2
1
1
0
1
2
1
0
1
0
2
0
1
2
0
1
1
1
0
3
0
2
1
2
1
1
0
1
1
1
0
0
1
1
2
0
0
1
1
0
0
1
2
2
0
1
1
0
0
1
0
0
0
0
1
1
1
1
0
1
0
0
1
0
0
2
0
1
1
0
0
0
2
2
1
1
1
1
0
0
0
0
2
1
2
0
0
1
1
2
1
2
1
1
0
1
0
2
1
1
1
0
2
0
2
1
1
2
0
1
0
0
3
1
1
2
1
0
1
2
1
1
0
1
0
1
3
0
1
1
0
0
0
1
2
0
2
1
1
0
0
2
2
2
0
0
0
0
2
2
0
1
1
1
0
0
0
2
0
1
0
1
0
1
1
2
1
2
1
0
1
1
0
1
0
0
0
2
2
2
2
1
1
1
0
2
0
2
0
0
0
1
1
0
0
1
3
2
0
1
1
1
1
1
2
2
1
1
0
1
1
0
2
1
2
0
0
1
1
0
1
1
0
0
2
2
1
0
0
2
0
0
0
0
1
0
1
0
0
3
0
1
2
2
1
0
5
2
0
2
0
0
1
0
1
0
0
2
2
0
1
0
0
1
1
1
1
1
1
0
0
0
1
1
0
1
0
1
2
1
2
0
2
1
1
1
2
0
0
0
2
1
1
2
0
1
1
1
1
0
1
0
1
1
0
2
1
1
0
1
0
0
0
0
0
0
0
1
3
0
0
0
2
1
2
1
0
2
0
2
1
1
0
1
2
1
1
1
1
2
0
2
1
0
2
0
0
1
1
0
0
2
2
3
1
2
1
1
1
1
1
3
1
0
1
0
1
0
3
0
0
0
1
0
1
0
2
2
0
0
1
1
2
2
0
0
2
2
1
1
0
1
1
0
2
0
2
0
1
2
0
1
1
1
2
2
1
0
1
0
1
1
1
0
1
0
1
1
1
0
0
1
2
0
1
1
1
2
2
2
0
1
1
2
2
0
2
0
0
1
0
2
1
1
2
1
2
1
1
1
1
0
1
2
1
1
0
5
0
0
2
0
0
1
1
1
2
0
1
1
1
1
0
1
2
1
0
0
0
0
0
2
0
2
1
0
1
0
2
2
2
1
2
2
1
0
1
0
1
1
0
2
0
1
0
0
2
2
1
1
1
0
0
0
0
0
0
1
1
0
1
2
1
0
1
0
1
0
1
2
2
0
1
0
1
1
2
2
0
1
2
0
1
0
1
1
0
3
0
0
1
1
0
0
2
1
2
1
0
0
1
0
0
0
0
0
1
2
2
2
1
1
1
1
1
3
0
2
1
0
0
0
1
0
1
0
0
1
1
1
0
2
1
1
0
0
1
1
0
2
0
1
0
0
1
2
1
1
0
1
1
0
0
0
0
0
0
1
1
0
1
2
1
2
1
1
2
1
2
1
0
1
0
1
1
1
0
1
1
2
1
1
2
1
1
1
0
1
1
1
2
0
1
1
0
0
2
2
4
1
2
1
0
0
1
1
1
0
0
2
0
1
0
0
1
2
2
0
1
1
1
0
2
0
2
1
0
0
0
2
2
1
0
1
2
0
1
0
1
0
0
1
0
1
1
0
0
1
3
0
1
1
2
2
2
1
0
1
0
1
0
1
1
0
2
0
1
0
1
0
0
0
1
0
0
1
1
3
1
2
0
1
2
1
0
4
0
2
0
1
2
1
1
0
1
1
0
3
0
1
2
0
0
1
0
0
1
0
1
1
0
0
2
1
1
0
2
0
1
1
0
0
0
1
0
1
1
0
0
1
0
1
1
2
3
1
1
1
0
2
2
4
0
1
0
1
0
1
0
1
2
0
0
2
0
0
0
0
1
1
1
0
1
1
0
0
0
0
0
0
0
1
1
1
1
1
1
0
2
1
1
1
1
1
0
1
0
0
0
2
2
1
1
1
0
1
0
1
2
0
1
0
1
1
0
0
0
1
1
2
0
0
0
0
1
0
1
0
1
2
0
2
0
1
1
1
2
1
2
1
2
2
1
1
0
1
1
0
2
0
0
2
1
1
2
2
0
1
2
0
2
1
1
1
2
0
2
1
2
1
1
0
1
1
2
2
0
1
2
0
0
3
0
0
0
1
1
1
1
0
0
1
2
0
0
2
1
1
1
1
0
2
1
1
2
1
1
1
2
4
1
0
0
0
1
4
2
0
0
0
0
1
2
2
1
0
0
1
1
0
1
1
2
1
2
0
2
0
0
1
2
2
1
1
1
0
2
0
0
0
0
1
0
0
1
1
0
0
1
0
1
0
0
1
1
0
0
2
0
1
0
0
1
1
0
1
0
0
1
0
0
0
1
2
0
1
2
0
0
2
0
0
0
1
2
0
1
1
1
1
3
0
0
1
0
1
2
0
0
1
0
2
0
2
1
0
0
1
1
2
0
3
2
1
0
0
0
2
0
1
1
0
2
1
0
0
2
1
1
1
1
0
1
0
3
2
2
1
0
0
0
0
0
1
2
2
1
0
1
0
2
0
1
1
2
0
2
1
0
0
1
2
3
1
0
1
0
1
1
1
1
1
2
1
0
0
1
0
1
0
1
2
0
3
2
3
0
1
2
1
0
1
1
1
0
2
0
1
2
0
1
1
1
1
1
2
0
1
1
0
2
0
1
1
0
2
2
0
1
1
1
0
2
2
0
1
2
2
0
1
0
1
1
1
0
2
0
0
2
1
2
1
1
1
0
1
0
1
2
1
2
1
0
0
1
0
0
1
0
0
1
0
1
1
0
1
0
0
6
0
0
0
1
1
2
1
1
2
1
2
2
1
0
0
0
0
2
3
1
0
2
0
1
2
1
0
1
1
0
0
2
1
0
1
1
2
2
1
0
0
0
0
1
0
2
3
1
1
1
1
1
2
1
0
1
1
1
0
1
3
2
0
2
0
2
1
1
0
1
2
0
1
0
0
1
1
1
1
1
2
2
1
0
0
1
0
1
0
1
2
1
0
0
1
1
0
0
0
0
0
1
0
1
2
2
1
1
0
0
0
2
1
1
2
1
2
2
0
0
0
0
1
1
0
0
0
0
1
0
0
4
0
0
0
2
0
0
2
2
1
1
1
1
0
0
1
1
1
0
1
1
1
3
1
1
2
1
0
2
1
0
0
0
0
0
1
1
0
2
0
2
0
0
2
1
1
2
0
2
1
1
1
1
0
0
2
1
2
0
2
1
1
0
2
2
2
2
1
2
1
0
1
0
0
1
3
0
1
0
2
0
1
0
1
0
1
0
0
0
0
1
1
4
0
0
0
0
1
0
2
0
0
0
1
1
2
2
1
2
0
1
0
2
0
0
0
2
2
0
0
0
0
0
2
2
0
1
2
0
0
2
1
1
0
0
1
1
2
2
0
0
1
0
2
1
1
0
0
1
1
2
1
1
0
1
0
2
0
2
0
0
2
1
2
0
0
1
1
1
2
1
1
2
2
1
0
1
0
0
0
0
0
2
2
1
1
1
1
2
1
1
2
1
0
0
0
1
1
0
1
2
2
1
1
1
2
1
0
2
2
2
0
1
1
0
1
1
0
1
0
2
2
2
1
1
1
0
0
1
0
1
1
0
0
2
0
1
2
2
1
2
3
1
2
1
0
1
2
2
1
2
0
1
1
2
0
0
0
2
0
1
1
0
2
0
0
0
2
0
0
1
2
1
1
1
0
0
1
0
0
1
2
1
0
1
1
2
1
1
1
0
1
1
0
1
1
1
1
2
1
3
0
1
0
0
2
1
0
1
1
1
0
1
1
0
1
1
1
1
1
2
1
2
1
2
2
2
1
2
1
2
2
0
1
2
1
2
0
1
0
1
0
1
0
0
0
2
2
0
0
0
0
1
1
2
0
0
2
1
0
0
1
0
1
1
0
0
2
0
2
1
2
1
1
0
1
0
1
0
2
0
0
1
1
2
1
1
2
0
1
2
2
1
0
0
2
2
1
1
2
0
2
2
0
0
0
1
4
0
2
0
1
1
1
2
2
1
0
1
1
0
2
1
1
1
1
2
0
2
1
3
3
1
1
1
1
0
1
0
1
2
2
0
0
0
1
2
1
1
0
2
1
0
1
1
0
0
0
2
2
1
1
1
1
0
0
1
2
2
0
0
1
0
1
1
0
1
1
1
2
1
1
1
0
1
3
0
2
1
0
0
1
1
0
2
0
1
1
2
0
1
0
1
0
2
1
0
1
0
2
1
1
1
2
0
0
1
2
2
1
1
0
0
0
1
0
2
1
1
1
1
1
0
1
0
2
0
0
1
1
1
0
0
1
2
1
0
0
1
2
1
2
0
1
2
2
1
0
0
1
2
1
0
1
2
0
0
1
0
1
0
0
2
2
0
1
0
0
1
1
0
0
2
1
0
1
2
2
0
1
1
2
1
1
3
2
1
0
0
1
0
0
0
0
1
1
1
2
2
1
1
1
0
1
0
2
1
0
1
1
1
0
1
2
0
0
0
1
0
0
1
1
0
2
1
2
0
1
2
2
1
1
2
1
0
1
1
0
2
0
3
1
2
0
1
0
0
1
1
0
0
1
0
2
0
1
0
2
1
0
0
2
0
0
1
0
0
1
0
1
1
0
0
0
2
1
1
1
2
0
1
0
0
0
0
0
0
2
1
0
1
1
2
1
2
2
0
0
1
2
0
1
1
1
1
2
0
2
1
1
1
0
2
0
0
0
1
1
2
1
0
0
0
0
1
0
1
0
1
1
0
2
0
0
1
1
2
0
2
0
0
0
0
1
1
0
1
2
0
1
1
1
1
1
0
1
1
0
2
0
1
1
1
0
0
1
1
0
1
0
0
1
3
1
0
1
2
2
2
1
1
2
1
0
2
2
2
0
2
1
1
1
1
1
2
0
0
1
1
2
1
1
2
1
0
1
0
1
0
2
1
1
2
1
0
2
1
2
1
4
1
1
3
1
0
1
2
0
2
0
1
0
2
2
1
0
0
1
1
1
3
1
0
1
1
0
1
0
2
1
2
0
2
0
0
1
0
0
0
2
0
3
1
2
1
2
0
3
1
1
1
0
0
1
1
0
1
1
0
0
1
1
0
0
0
0
0
1
0
1
0
1
1
0
0
2
0
0
1
1
0
1
0
2
2
2
0
1
2
0
2
1
0
1
2
2
1
1
0
0
1
2
1
2
2
1
0
0
1
2
0
2
0
1
2
2
0
0
1
1
0
1
1
1
1
0
0
0
0
2
1
0
0
0
1
0
1
2
1
1
0
0
1
0
2
1
1
3
1
2
0
1
1
1
2
0
0
2
1
0
1
0
2
2
2
0
1
0
2
1
0
1
1
0
0
1
0
1
0
1
0
0
0
2
1
3
2
1
0
2
1
0
0
1
0
2
1
1
1
1
0
2
2
1
1
2
0
1
1
2
1
2
2
0
2
2
1
1
1
2
0
0
2
2
2
1
0
0
1
1
0
2
0
0
1
1
1
0
0
0
2
1
1
1
1
1
1
0
1
1
1
0
2
2
0
0
2
2
1
1
0
1
2
0
0
0
0
0
0
0
1
2
0
3
0
0
0
1
0
2
0
1
1
0
0
1
1
0
1
1
0
1
1
2
1
0
0
1
1
0
1
2
0
2
0
1
1
1
1
1
2
0
0
1
0
2
0
1
1
2
1
1
0
0
0
0
0
1
1
2
2
0
1
0
1
1
1
0
1
0
1
1
1
1
0
0
1
0
0
1
0
1
0
1
0
0
0
0
1
0
1
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
3
1
1
0
1
1
1
0
0
2
0
1
1
1
1
2
0
0
1
2
0
2
1
2
0
2
1
2
2
2
0
1
1
1
2
0
1
1
1
1
2
0
1
0
0
1
0
2
2
2
2
1
0
2
2
0
2
0
2
1
2
2
0
2
2
1
0
0
1
1
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
1
1
1
2
0
1
0
0
1
0
2
1
2
1
1
0
1
0
0
1
1
1
1
1
1
0
0
1
1
2
2
0
1
1
1
1
1
1
1
1
0
0
2
2
0
1
1
2
1
1
1
1
1
0
0
0
1
1
2
1
1
1
1
0
1
0
1
0
2
1
2
1
0
0
1
1
0
1
2
0
1
1
2
1
1
1
1
0
0
0
0
0
0
0
1
2
3
0
1
1
2
1
1
0
2
2
2
2
1
0
0
0
2
1
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
2
1
0
2
0
1
1
1
2
1
0
0
0
1
1
2
2
1
2
0
0
0
0
1
1
0
1
0
0
0
1
0
2
1
1
1
0
1
1
2
1
1
2
0
1
0
0
1
1
1
0
2
2
0
11
1
2
0
2
0
2
2
1
1
2
1
2
1
1
0
0
2
0
2
1
0
0
2
0
1
1
1
1
2
0
1
0
2
0
0
1
0
0
1
0
0
1
2
1
1
2
2
1
0
0
0
2
1
0
1
0
1
2
1
1
1
2
1
0
0
0
3
2
1
1
0
1
0
0
2
1
0
1
0
0
0
0
0
1
0
1
1
1
0
1
0
0
1
0
0
0
1
2
1
1
1
1
2
2
0
0
2
0
0
1
0
1
1
2
0
1
0
1
2
1
0
0
2
1
1
1
0
1
1
1
1
0
2
1
2
0
1
1
1
1
1
6
2
1
2
1
2
1
1
0
1
2
2
0
1
0
0
2
1
0
0
1
1
1
2
1
1
1
0
1
2
0
2
0
2
0
1
1
2
2
1
0
0
0
1
1
1
0
1
0
0
0
0
2
3
0
1
0
0
0
1
0
0
2
1
0
0
1
1
2
0
2
0
0
0
1
0
1
1
2
1
1
2
0
2
1
2
1
0
0
0
0
2
2
0
1
1
1
1
1
2
0
0
1
1
1
0
1
1
1
2
1
0
1
0
0
0
2
2
0
1
2
1
2
0
1
2
1
0
1
0
0
1
0
0
1
0
0
3
0
1
0
1
2
1
1
0
0
2
0
1
0
0
2
0
1
2
1
2
2
0
1
0
0
3
0
1
0
3
1
1
0
0
2
1
1
1
2
0
0
1
2
1
0
1
2
0
3
1
1
2
0
1
3
1
1
0
0
1
2
0
0
0
1
0
3
1
0
0
1
2
2
0
0
0
2
1
1
2
1
1
1
1
0
2
0
0
0
1
0
1
1
1
2
1
2
0
1
1
0
0
1
1
1
0
0
1
1
1
0
2
0
1
1
1
0
11
3
2
2
0
1
1
1
2
0
0
0
2
2
2
1
1
1
0
0
2
1
0
3
0
0
2
0
2
1
0
2
0
2
1
1
1
2
2
0
2
2
0
1
5
0
0
0
1
0
0
2
2
1
0
1
2
0
2
0
2
0
1
0
6
1
0
2
1
1
2
2
2
0
1
0
1
1
3
2
1
2
0
1
0
0
0
1
1
1
1
0
0
1
0
1
2
1
0
1
0
0
0
1
1
1
2
0
1
0
1
2
1
0
1
3
1
0
1
0
0
2
0
2
0
0
0
0
1
2
0
1
1
1
1
0
1
1
1
2
0
2
2
0
1
0
0
2
0
1
1
0
1
2
0
0
2
0
1
0
0
1
1
1
2
0
0
1
1
1
1
0
0
1
2
2
0
1
2
1
1
1
1
0
1
0
1
1
0
0
2
2
0
1
1
0
0
1
1
1
1
1
1
1
2
0
1
2
0
1
1
0
0
2
0
0
2
0
1
0
3
2
1
0
0
1
0
0
0
0
0
1
0
1
2
2
0
1
0
2
2
1
1
0
0
2
1
1
1
0
1
1
2
1
0
1
0
0
2
0
0
1
2
3
1
2
0
2
0
0
2
0
0
0
1
0
0
0
0
1
2
2
0
0
0
2
0
0
1
1
0
1
1
1
1
2
1
0
1
1
0
2
2
1
1
1
0
1
0
0
1
2
2
0
2
1
3
0
0
0
1
2
1
0
1
1
1
1
1
0
0
0
1
0
0
2
0
0
1
1
1
2
1
0
1
1
0
2
0
2
2
0
1
0
1
0
0
1
2
0
0
1
0
0
1
0
0
0
2
0
1
0
1
1
2
0
2
0
0
0
1
1
0
1
0
3
2
1
1
0
0
0
2
1
2
3
2
0
1
1
1
0
0
2
1
2
0
1
0
0
2
2
1
0
2
0
0
1
0
0
0
2
0
1
2
0
2
1
0
2
2
1
1
0
0
1
0
1
0
1
0
2
1
0
1
1
1
0
2
0
1
0
0
2
1
1
1
1
0
0
1
1
0
0
0
1
0
0
3
2
2
3
0
0
0
2
0
0
1
2
1
0
10
0
0
2
1
1
0
2
0
0
1
0
1
1
1
2
0
2
1
0
0
1
1
1
2
2
2
0
1
1
2
1
0
0
1
0
2
1
1
1
1
2
0
0
2
2
0
0
2
1
0
2
2
0
1
0
1
1
2
1
1
2
2
0
0
0
0
1
1
2
0
1
0
1
0
1
3
2
0
0
4
1
2
0
0
1
2
0
1
1
1
0
0
1
1
0
1
0
4
0
0
1
1
1
1
2
1
0
2
1
1
3
2
0
2
1
1
1
1
1
0
2
1
0
1
2
0
1
1
2
0
0
1
1
1
2
0
1
1
1
1
1
2
1
0
0
1
2
2
1
0
0
2
0
0
1
0
2
0
1
2
1
2
1
0
1
0
1
1
1
0
0
1
0
1
2
2
2
1
1
0
2
0
1
1
2
0
0
0
1
0
2
2
1
0
0
1
0
2
1
1
0
2
1
0
0
1
2
2
0
0
2
1
1
1
2
1
0
1
2
0
0
1
0
0
1
2
2
1
0
0
2
1
1
2
2
0
1
1
1
0
2
0
1
0
2
2
2
2
0
1
2
2
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
2
1
0
0
2
0
1
0
0
1
1
0
2
2
0
0
0
0
1
0
0
1
2
0
1
1
2
0
0
2
1
2
0
1
1
0
1
1
0
0
0
1
1
2
0
2
1
1
1
2
2
2
0
1
1
1
0
1
0
0
2
1
1
1
0
2
2
0
0
0
1
1
0
2
1
3
1
0
1
0
0
0
1
0
1
2
3
0
1
0
1
0
0
0
2
1
2
1
1
2
2
2
0
1
0
2
2
0
0
0
2
2
0
1
2
1
1
2
0
0
1
1
0
0
1
0
0
1
1
0
1
2
1
2
0
0
0
1
2
0
1
0
2
2
1
1
2
0
2
1
1
0
0
1
0
0
1
0
2
2
1
1
2
0
2
1
1
0
0
1
2
2
1
1
0
1
2
1
1
2
0
2
1
1
1
1
0
1
0
0
1
1
0
1
1
1
1
0
1
0
2
1
1
1
0
2
2
2
1
1
1
1
0
1
0
1
1
0
1
1
1
1
1
2
2
0
2
1
0
1
2
2
1
0
0
1
2
0
1
0
0
2
0
0
1
1
0
1
0
0
4
0
1
0
1
1
2
0
2
2
1
1
0
0
1
0
1
0
0
1
0
0
1
1
1
1
0
0
2
1
0
0
2
0
0
2
0
1
1
1
0
0
1
2
0
2
0
2
2
2
2
0
2
2
1
1
1
0
2
0
1
2
0
2
0
0
1
0
0
1
2
1
1
0
1
0
0
0
0
2
1
2
0
2
1
0
1
0
0
1
0
0
3
1
1
0
0
0
0
1
2
2
2
0
1
1
1
1
0
3
0
2
2
1
1
0
1
2
2
0
2
1
0
0
0
2
2
2
2
1
0
1
1
0
0
2
1
2
1
1
0
0
1
0
0
1
0
2
1
1
1
3
1
0
1
3
1
1
0
1
0
0
2
1
0
1
0
2
2
0
1
0
0
2
0
1
1
0
1
2
0
1
0
1
1
2
0
2
1
2
2
1
0
0
3
0
3
1
0
0
1
0
1
0
0
0
2
2
1
0
1
1
0
0
0
1
0
0
2
1
0
0
0
2
1
1
1
0
1
0
1
0
1
1
2
1
2
1
0
0
0
1
1
1
0
0
1
1
2
2
0
1
0
1
1
0
1
1
2
2
1
2
2
0
0
2
0
1
1
0
0
1
2
1
0
1
1
1
0
0
1
0
0
0
0
0
2
0
1
1
0
2
0
0
0
2
0
1
0
2
0
0
2
1
0
0
2
0
1
2
2
2
1
1
0
0
0
2
0
4
0
1
1
2
1
0
1
1
0
0
2
0
1
2
2
0
1
1
1
1
0
2
0
1
2
2
0
0
1
0
0
2
3
2
0
1
1
1
1
2
2
1
1
1
1
1
0
2
1
0
2
0
1
2
0
0
2
1
1
2
1
0
0
0
0
2
1
0
0
0
1
1
1
0
0
2
0
1
1
0
1
2
1
3
0
2
1
2
1
0
0
1
0
1
1
1
0
0
1
1
1
0
1
1
0
0
2
1
0
1
1
0
2
0
2
0
0
1
1
1
2
0
2
2
2
0
1
1
3
0
0
1
0
0
0
1
0
0
0
2
0
0
0
1
0
1
1
0
1
2
1
2
2
0
0
1
0
1
0
1
1
1
0
0
0
0
2
0
0
0
1
0
1
2
1
1
1
0
1
0
0
2
1
2
0
0
2
0
2
2
1
0
1
0
0
0
1
1
0
0
1
3
1
1
0
0
2
0
1
1
0
2
1
1
2
1
0
2
0
0
0
1
0
0
2
1
2
0
2
0
1
1
1
1
0
1
1
1
2
0
2
1
1
1
2
1
1
0
2
0
2
1
1
1
1
1
1
0
3
1
1
1
2
0
0
1
1
0
1
1
0
0
2
1
1
1
1
1
0
1
0
1
0
1
1
1
0
0
2
2
2
2
2
2
1
2
4
0
2
1
0
1
1
0
0
1
2
1
1
1
1
2
0
1
1
6
0
2
1
2
2
1
2
1
1
1
1
0
0
2
0
1
1
0
2
0
2
0
1
0
0
0
0
0
1
1
1
1
0
1
1
0
1
1
1
2
2
2
0
0
2
1
1
1
2
2
2
0
2
1
1
0
2
1
1
0
2
1
2
2
1
0
0
2
1
0
1
1
0
1
0
0
0
1
1
0
2
1
2
2
0
0
0
1
0
0
0
1
1
1
1
0
1
1
2
2
1
1
0
1
1
0
1
1
0
1
0
0
0
1
2
2
1
1
1
1
1
0
2
0
1
1
0
1
1
1
2
1
2
1
1
0
2
0
1
2
2
2
0
0
0
2
1
1
1
0
3
0
0
0
1
0
1
1
1
2
2
1
0
2
0
0
0
0
1
0
1
0
0
0
0
1
1
0
2
0
2
1
0
1
1
1
0
1
2
1
2
0
1
1
1
2
2
0
0
4
2
2
1
2
0
0
1
0
1
2
1
0
1
1
0
1
2
1
2
0
1
4
0
0
1
2
2
1
1
1
1
0
1
0
2
0
0
2
0
2
0
2
0
1
0
2
1
0
1
1
0
0
1
1
0
1
1
0
0
0
2
0
1
1
0
1
1
0
1
0
0
0
2
2
2
1
1
0
0
1
1
1
2
1
1
0
0
0
1
1
0
1
0
0
0
0
1
3
0
0
0
3
2
2
0
1
2
0
0
0
2
1
0
0
1
1
0
0
0
1
0
0
0
2
1
1
0
1
0
2
1
1
0
2
1
0
1
2
2
0
2
0
1
1
0
2
2
0
0
2
1
0
0
2
0
1
1
0
1
0
2
1
2
0
0
1
0
2
1
0
0
0
1
1
1
0
2
1
2
1
0
1
1
1
0
0
2
0
0
0
1
0
1
2
1
2
2
0
1
0
2
0
2
0
0
1
1
1
2
1
0
1
1
0
1
1
1
1
0
1
0
1
1
0
0
0
0
2
1
2
0
1
0
0
1
1
0
2
1
0
2
1
1
0
2
0
3
0
0
0
1
3
0
0
0
1
2
2
2
1
1
1
1
0
0
0
1
3
0
0
0
1
1
3
1
0
0
2
0
2
0
1
1
2
1
0
0
0
2
0
0
0
0
1
1
1
0
1
0
0
1
0
1
0
0
1
2
1
1
1
2
0
2
0
2
1
1
1
0
0
0
2
1
0
0
1
1
1
0
0
1
0
2
1
1
1
2
1
0
1
2
2
1
0
0
0
1
2
1
1
1
1
2
1
0
0
2
1
1
1
0
1
2
0
0
0
2
1
1
2
0
1
4
0
2
2
0
0
3
2
1
0
1
1
1
1
1
2
1
0
2
1
1
0
1
0
1
1
0
2
1
1
1
0
1
2
1
1
0
0
0
0
2
1
1
0
0
2
2
1
1
0
1
1
2
0
1
1
1
1
2
1
0
0
1
2
1
4
1
2
0
2
2
0
0
2
0
0
0
2
2
0
0
2
2
0
0
0
1
2
1
0
2
0
0
1
3
0
2
1
2
0
0
2
0
0
1
2
0
2
2
0
1
0
1
0
0
2
1
0
1
0
0
0
0
0
1
1
2
1
1
1
1
0
2
1
1
0
2
0
0
0
0
2
0
0
1
0
2
0
0
1
1
1
1
0
0
2
1
1
1
1
0
0
0
0
0
0
2
1
0
1
0
1
1
1
0
2
1
0
2
1
1
0
1
2
1
1
0
0
1
1
1
2
1
2
1
1
0
0
1
1
0
0
1
0
0
1
2
0
2
1
1
0
2
0
1
2
0
1
2
0
1
1
0
1
1
0
1
1
0
2
1
0
2
2
0
1
1
1
1
1
2
2
0
1
0
1
2
1
0
0
0
1
2
1
1
1
2
2
0
1
1
0
0
0
1
1
1
4
2
0
0
0
1
2
1
1
1
2
1
2
0
0
1
2
2
2
1
0
2
0
1
1
4
0
0
1
1
1
1
0
1
0
1
2
3
1
1
1
0
2
1
2
1
1
0
1
0
0
0
1
0
2
1
1
1
2
1
0
2
1
2
1
1
0
1
2
0
1
1
1
1
1
0
1
2
0
0
1
1
2
2
2
0
1
1
1
2
0
1
0
2
2
1
0
1
0
1
2
1
0
0
0
1
2
2
0
0
1
0
0
0
0
1
1
2
0
2
0
1
0
0
1
1
0
2
1
1
1
1
0
1
0
0
1
2
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
1
2
0
1
1
2
0
1
2
0
0
1
1
1
2
0
1
2
0
1
0
0
1
2
2
2
0
0
1
1
2
2
3
2
1
1
0
0
0
0
0
0
0
1
0
1
0
1
2
0
1
0
2
0
0
2
1
0
0
1
0
0
0
0
1
2
2
2
0
1
0
1
0
0
1
0
0
0
1
2
2
1
0
1
2
1
0
1
0
3
0
0
1
1
0
1
2
2
0
1
0
1
1
0
0
1
1
2
1
1
1
0
0
1
2
0
1
0
1
0
1
1
0
1
0
0
1
1
1
1
2
1
0
1
0
0
2
1
1
1
1
0
0
1
3
2
2
1
2
2
1
0
1
0
1
2
0
0
0
1
3
1
2
0
1
1
1
1
1
0
1
0
2
1
1
1
0
0
3
0
0
1
0
0
0
1
0
1
1
0
1
2
1
1
2
1
1
1
1
2
1
1
0
1
1
0
1
0
2
1
0
2
2
2
2
2
1
1
2
0
2
2
0
2
0
1
1
1
2
2
0
1
2
2
0
2
2
0
1
0
1
2
1
2
0
0
0
1
3
0
0
1
0
1
2
1
0
1
2
2
0
3
0
1
0
0
1
1
0
0
1
0
2
0
0
0
1
1
0
1
2
2
1
0
2
2
2
1
1
1
1
1
0
1
0
0
1
2
1
2
1
1
1
0
0
2
2
2
0
0
1
1
0
2
1
2
0
0
0
0
2
1
3
0
2
1
0
2
0
1
1
1
0
1
2
1
2
2
0
1
0
0
1
0
0
0
2
2
2
1
0
1
1
1
1
0
1
1
2
3
2
1
0
1
0
1
2
1
0
0
0
1
1
1
0
1
1
0
1
1
0
1
1
1
1
1
0
0
1
0
0
2
2
2
0
0
2
0
2
0
1
0
0
1
0
1
3
0
2
0
1
1
0
1
10
0
1
1
1
0
0
1
1
1
1
3
0
2
1
1
1
1
1
1
0
1
1
1
1
1
1
0
1
1
0
2
1
0
0
1
2
1
0
0
0
2
0
1
0
0
2
2
0
1
1
2
1
2
1
2
0
0
1
1
1
2
0
0
0
2
0
0
1
0
0
0
0
2
0
2
2
2
0
1
0
2
0
1
1
0
0
0
0
2
0
1
1
1
1
0
0
0
2
1
2
1
0
1
2
2
1
4
1
1
0
0
1
1
2
0
0
1
1
2
0
0
1
1
1
1
0
1
2
1
1
0
0
2
0
1
2
1
1
2
2
2
1
2
0
0
1
2
2
0
1
0
1
0
0
1
1
0
0
1
0
2
1
2
2
1
0
0
0
2
2
1
1
0
1
2
1
2
1
1
0
0
2
0
2
2
2
1
1
0
0
2
1
1
1
1
1
3
1
0
0
1
0
0
2
0
1
1
0
1
2
2
1
1
1
2
0
1
0
2
2
1
1
0
1
2
1
0
2
0
0
0
1
1
0
1
0
2
1
1
0
2
1
0
0
0
0
0
1
1
0
1
0
0
1
2
1
2
1
0
1
1
1
0
0
1
0
1
1
0
1
2
2
0
1
0
0
0
1
1
3
0
1
1
1
1
2
0
0
1
0
0
2
0
0
2
1
0
0
2
0
0
2
0
1
1
0
1
1
0
0
0
1
0
2
0
1
1
0
0
1
1
0
1
2
0
2
0
2
0
1
2
0
1
1
0
2
0
0
1
1
1
1
1
1
0
1
0
2
1
1
1
2
0
0
1
0
1
1
2
1
2
2
0
1
1
1
1
1
1
1
1
1
0
2
0
0
0
1
1
1
2
1
0
0
2
2
1
1
1
1
0
0
0
0
1
1
0
1
0
2
0
0
0
0
0
1
1
2
2
2
1
0
0
0
1
1
0
1
0
0
1
1
2
2
2
1
2
1
1
0
1
0
2
0
2
2
1
1
1
0
0
1
0
2
2
2
1
1
0
1
0
0
1
0
1
1
0
0
0
2
0
1
1
0
0
0
0
1
1
0
0
1
1
0
1
0
2
1
2
2
0
1
0
1
0
1
0
2
1
0
1
0
1
0
0
1
0
2
0
1
0
1
0
3
2
0
1
1
2
0
0
3
1
1
2
0
0
1
0
0
0
2
2
0
2
0
1
0
1
0
0
1
0
2
0
0
0
0
1
2
1
0
0
1
1
0
1
0
0
2
1
0
0
2
0
0
0
0
1
0
2
0
1
2
0
2
1
1
1
1
0
2
1
2
1
0
0
2
0
2
0
1
2
1
1
1
1
1
2
3
0
0
1
0
0
1
1
1
0
1
1
0
0
1
1
1
1
2
1
3
1
2
1
2
1
1
2
2
1
1
0
0
0
2
0
1
2
1
0
1
1
0
0
1
0
2
2
0
2
1
1
1
0
1
0
2
0
1
0
0
0
1
1
1
1
0
1
2
0
1
0
1
0
1
3
2
2
1
1
0
1
1
0
1
1
1
2
0
1
2
1
1
1
1
1
0
1
1
1
2
1
1
1
2
1
1
1
0
0
2
1
2
0
2
0
0
1
0
1
0
0
0
3
1
0
1
0
1
1
1
2
2
0
2
2
1
2
3
1
0
0
1
0
2
0
0
0
1
1
2
2
0
1
1
1
2
0
0
0
0
0
2
1
1
1
1
1
2
1
1
2
1
0
0
1
2
0
1
2
1
2
1
1
2
0
0
2
2
0
0
0
1
2
1
2
3
1
1
2
2
2
1
0
0
2
1
0
2
2
1
2
0
0
2
1
1
2
1
1
2
1
1
2
1
0
1
0
0
0
0
0
1
1
1
0
1
0
2
0
0
0
0
1
2
2
0
1
1
2
0
1
1
0
0
0
0
0
0
0
2
2
0
2
0
1
0
1
0
0
0
2
1
1
0
2
1
0
1
0
0
1
0
1
0
0
1
1
0
1
0
0
0
0
1
0
2
1
1
1
0
0
1
1
0
0
0
2
1
0
1
0
4
0
2
2
0
2
0
2
1
3
0
1
0
1
0
0
0
3
2
0
2
0
0
0
0
1
1
1
1
1
1
1
2
1
1
1
1
2
1
2
2
1
0
2
0
1
1
2
0
0
1
0
2
1
0
0
0
0
0
1
1
1
2
1
0
0
1
0
0
2
0
2
2
1
2
1
1
0
3
0
11
0
2
1
0
1
1
0
0
1
2
0
2
1
1
1
2
1
1
1
1
1
1
2
0
1
0
1
0
1
1
1
0
1
0
1
1
0
0
0
1
2
1
0
0
1
1
2
0
1
0
0
0
1
2
1
0
0
0
1
1
1
0
0
3
1
0
2
0
2
2
0
1
2
0
2
1
2
0
1
1
0
2
0
1
2
1
2
2
0
0
0
0
0
1
0
1
1
1
1
1
0
1
0
1
1
0
0
0
0
0
2
1
2
2
0
1
2
2
0
2
1
0
0
1
0
1
1
1
2
1
2
1
0
0
1
2
0
0
1
1
1
2
1
0
1
2
1
0
2
1
1
1
0
3
0
0
1
2
2
1
2
1
1
0
2
1
2
1
1
0
0
0
1
1
0
0
1
1
0
1
0
1
1
0
1
3
1
1
0
0
1
1
0
5
1
0
1
0
0
2
1
0
3
1
1
0
1
0
0
1
2
1
0
1
1
2
2
2
1
0
2
0
1
0
1
0
0
1
2
1
0
1
0
0
2
1
1
0
0
1
0
2
1
0
1
1
1
1
1
0
1
1
0
1
0
1
0
1
1
0
1
0
0
0
1
0
0
0
2
1
0
1
2
1
0
1
1
0
0
2
2
1
0
2
0
1
0
2
1
1
0
2
0
0
2
2
1
0
0
2
1
2
1
1
1
0
0
1
0
1
2
0
1
0
1
2
2
0
0
1
2
0
0
0
1
0
0
2
0
2
0
0
1
2
0
1
2
1
1
0
2
2
2
2
0
0
1
1
1
0
1
0
1
0
0
1
3
1
2
1
1
2
2
0
0
2
2
0
0
2
0
1
1
2
1
0
1
1
1
0
0
2
0
1
1
0
1
0
1
2
1
1
2
2
1
1
1
2
2
2
1
0
2
1
3
2
1
0
0
2
0
1
1
1
2
1
0
0
1
0
0
0
0
2
2
1
0
1
0
1
2
1
0
0
1
2
2
0
1
0
1
1
2
0
2
1
0
1
2
1
2
1
0
1
1
1
1
1
1
2
1
2
1
0
1
0
2
0
1
0
1
1
1
1
0
1
1
1
2
1
2
1
1
2
1
1
1
0
2
1
0
2
1
1
1
1
1
0
0
2
2
2
0
2
1
2
0
1
0
2
1
2
2
1
1
0
1
2
0
1
3
0
0
0
2
1
1
1
1
3
2
2
2
0
0
0
3
1
1
0
2
2
1
1
0
0
1
1
0
0
0
1
0
1
2
2
0
2
1
1
1
0
1
2
0
0
2
2
1
2
2
2
0
1
0
0
1
1
0
1
0
0
2
0
0
1
2
1
1
0
1
1
0
1
0
1
0
0
0
1
2
4
0
1
2
0
1
2
1
1
1
4
0
2
1
0
3
1
1
1
2
1
0
0
0
0
1
2
0
2
1
2
1
1
1
0
1
0
0
0
2
1
1
0
0
1
1
1
1
0
0
0
1
0
0
0
1
2
0
1
0
1
2
0
1
1
0
3
2
2
0
1
1
1
1
1
2
0
0
1
1
0
1
1
0
2
0
1
1
2
1
2
0
0
1
0
1
3
0
1
0
1
2
0
0
0
1
1
1
1
1
1
2
2
0
0
1
0
2
1
0
1
0
1
2
0
1
0
0
0
1
1
1
0
0
0
1
1
0
0
1
1
1
1
1
0
2
0
0
1
2
1
2
1
1
0
0
0
2
0
1
1
1
1
1
0
0
0
2
1
1
1
1
1
1
1
2
0
0
1
1
0
0
1
2
2
0
1
1
0
0
1
1
1
1
0
0
1
1
0
2
4
2
1
2
0
1
0
0
0
0
0
0
2
1
0
0
1
0
1
0
1
0
0
1
2
0
1
0
1
1
0
1
1
1
0
2
0
2
0
2
2
1
1
1
0
0
1
1
0
0
0
0
0
2
1
0
0
0
1
1
0
1
1
0
0
1
1
0
0
0
0
1
1
0
1
1
0
1
1
0
1
2
0
0
0
0
0
1
2
1
2
2
1
1
1
1
1
2
0
0
0
1
1
1
1
1
0
1
1
0
2
2
0
0
1
0
1
2
0
1
0
0
0
1
3
1
0
2
0
1
0
0
1
1
2
1
0
2
0
1
0
2
1
0
0
1
1
0
1
0
1
2
2
1
0
0
1
0
1
2
0
0
1
1
2
1
2
2
2
0
1
2
1
0
1
2
0
2
0
2
0
1
2
0
1
2
1
0
1
0
0
1
0
2
1
0
1
2
2
2
2
2
0
0
0
0
1
1
1
1
1
0
0
0
1
1
1
0
0
2
2
2
0
1
1
2
0
1
2
2
0
0
0
0
0
1
2
1
0
1
1
0
2
0
2
1
2
0
2
1
0
1
2
1
0
0
0
1
1
2
0
0
0
3
0
1
2
1
0
1
2
2
1
0
0
0
0
0
1
0
0
1
1
2
2
1
0
2
1
2
1
0
0
0
3
1
1
0
0
0
1
0
1
1
0
2
1
0
1
0
1
1
1
3
0
1
1
1
2
0
0
0
1
1
2
1
1
1
1
1
2
2
1
0
2
1
0
0
2
0
1
2
0
2
0
2
0
1
1
1
0
0
2
1
1
0
0
2
0
1
0
1
2
2
0
2
1
1
2
0
1
1
0
2
2
0
0
1
0
0
0
0
1
2
0
1
1
1
0
0
1
2
1
0
2
0
2
2
0
2
1
2
1
2
2
1
0
1
0
1
0
1
0
2
1
1
1
0
2
1
1
1
0
1
1
1
1
1
1
1
1
2
1
0
2
1
1
1
0
1
0
2
2
0
0
2
1
0
2
0
0
0
2
0
0
2
1
1
1
2
2
1
1
1
2
2
1
1
1
2
1
0
0
1
1
1
1
0
1
0
2
1
1
2
1
1
0
2
1
1
1
1
0
1
0
0
0
0
1
1
1
1
0
0
2
0
1
2
0
0
1
1
1
2
1
1
1
0
0
1
0
2
1
0
2
1
1
0
3
0
1
1
0
0
2
0
0
0
2
0
1
1
1
2
1
1
1
2
0
1
1
0
1
1
0
0
2
0
1
2
1
2
2
1
1
0
2
0
2
1
0
0
1
0
0
1
1
0
1
2
1
1
0
1
0
1
0
1
1
1
1
0
2
0
1
0
0
1
1
2
1
0
1
0
2
1
1
0
0
1
0
0
2
1
2
1
1
0
1
1
3
3
1
1
0
1
1
1
1
2
0
1
1
2
0
0
0
2
0
1
0
0
1
1
1
0
0
0
0
0
0
1
3
0
2
2
1
1
1
2
1
0
2
0
2
2
1
0
0
1
2
1
0
2
2
0
1
1
1
1
0
2
0
1
0
1
1
2
0
1
1
0
0
0
2
1
0
0
2
0
0
0
0
1
2
1
0
0
1
0
1
1
0
1
1
1
1
1
1
1
1
1
0
0
1
1
0
0
0
2
1
1
1
1
0
1
1
1
1
1
2
3
0
0
0
0
2
1
2
0
1
0
1
0
1
2
0
0
1
1
2
1
1
2
1
3
2
1
0
2
1
1
0
2
1
1
2
1
1
2
2
2
0
1
1
1
2
1
0
1
2
1
1
1
0
1
1
1
1
1
2
2
1
2
1
1
2
0
0
0
2
0
0
1
1
1
1
1
0
1
1
1
2
0
1
0
2
2
0
1
0
2
1
0
0
0
2
2
2
1
1
0
1
2
1
1
2
0
1
2
2
0
1
1
1
0
1
1
1
0
0
0
1
0
1
1
1
0
1
0
0
0
1
2
1
1
0
0
0
0
1
0
0
1
0
0
1
0
1
1
2
2
2
0
0
1
2
1
2
1
1
1
2
0
1
2
2
1
2
2
2
0
2
0
0
1
0
1
1
2
0
2
0
1
2
1
1
1
2
1
2
0
2
1
0
0
1
0
0
0
1
0
1
0
1
1
1
1
2
2
0
1
1
1
0
0
1
0
0
1
2
1
0
2
1
1
0
0
2
1
1
2
0
1
2
0
0
1
0
2
2
0
0
2
2
1
0
1
2
0
1
0
0
0
0
1
1
0
0
1
0
2
0
0
1
1
2
0
0
2
0
2
0
2
0
0
0
1
0
0
1
1
2
1
0
1
2
1
1
0
1
0
1
0
1
0
0
0
2
2
0
2
0
0
1
1
1
0
2
0
2
1
0
0
2
2
1
0
1
2
2
2
0
0
0
1
1
1
0
1
1
0
1
2
2
2
0
0
1
1
0
0
1
1
1
2
0
4
0
1
0
0
0
1
2
0
0
0
0
0
1
2
0
1
2
2
2
0
0
2
1
1
0
0
0
0
1
0
1
1
2
2
1
0
1
0
0
1
4
1
1
2
1
1
1
0
1
0
0
1
0
0
0
1
1
2
2
1
1
1
1
0
1
2
2
0
0
1
0
0
0
0
1
1
1
0
0
0
1
1
0
0
2
2
1
1
0
1
0
2
2
0
1
1
0
2
1
1
1
1
2
1
2
1
0
0
0
0
1
0
0
2
0
1
2
5
1
1
1
0
1
0
1
0
2
0
0
1
1
1
1
1
1
0
0
2
1
0
2
2
1
0
1
0
2
0
0
2
0
0
0
1
0
1
0
1
0
1
1
2
1
2
1
0
1
1
1
2
2
1
0
1
2
1
0
1
1
1
1
1
0
1
1
0
1
1
1
1
1
2
0
0
0
3
1
1
0
1
0
2
0
1
1
0
2
0
1
1
1
1
0
1
1
0
2
1
0
0
3
2
0
1
1
2
1
1
2
2
1
1
1
0
2
0
2
1
1
0
2
0
1
0
0
1
0
0
1
0
1
0
3
0
0
1
0
0
1
2
1
1
1
1
2
2
1
2
1
1
1
1
2
2
0
0
0
0
0
1
0
0
1
1
0
0
1
1
0
2
2
0
0
0
2
1
1
2
1
0
1
2
2
1
0
0
1
0
0
0
1
0
1
0
0
0
0
2
2
2
0
1
0
2
0
2
0
1
1
1
1
0
1
0
5
0
0
0
0
1
1
1
1
2
2
0
1
0
0
1
2
2
1
1
1
0
0
1
0
0
2
2
1
1
0
2
1
1
0
0
3
0
1
0
1
2
2
2
1
1
1
1
0
0
0
1
1
0
2
1
0
0
0
1
1
1
0
1
0
0
0
0
1
2
0
0
1
1
1
0
0
1
1
1
2
0
1
0
0
1
1
1
1
0
0
0
0
1
0
1
1
1
0
1
1
1
0
0
1
1
1
2
0
1
1
1
0
0
0
0
0
1
1
2
1
2
1
1
1
4
0
1
0
2
0
0
1
2
3
0
0
2
0
0
1
0
1
0
1
1
0
0
0
1
1
1
2
2
2
0
2
2
2
1
0
1
0
0
1
2
1
0
1
0
1
2
0
1
2
2
1
1
1
1
1
1
2
1
2
1
0
1
1
1
0
1
0
0
1
2
0
1
0
2
1
1
2
0
1
1
1
0
2
1
1
1
1
1
1
1
1
1
2
2
1
1
2
0
1
1
1
0
1
0
1
4
0
1
0
0
0
1
0
2
1
2
0
0
1
2
0
2
0
0
0
0
1
2
1
1
2
0
0
2
0
2
1
1
1
0
2
0
1
2
1
0
1
0
1
0
2
2
1
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
1
2
1
2
1
0
0
1
0
0
0
1
1
2
8
0
2
1
1
0
1
2
1
2
0
1
0
1
1
1
2
1
2
1
0
1
1
0
0
0
1
0
1
0
2
2
0
0
1
1
1
0
0
0
2
1
3
1
0
0
3
0
1
2
2
0
1
0
2
1
0
0
0
0
2
1
0
1
2
0
3
2
0
1
1
1
2
2
1
0
1
0
1
0
1
0
1
0
1
1
0
1
1
0
0
1
1
1
1
1
1
0
1
0
1
0
0
1
1
3
4
0
0
1
1
1
1
1
1
2
0
2
2
0
0
2
0
2
0
2
0
2
2
3
0
2
2
2
0
2
0
2
0
0
2
1
0
0
0
2
0
0
2
0
2
2
0
1
1
1
1
2
1
2
0
0
0
1
1
1
0
2
0
1
1
0
1
0
1
1
0
1
2
1
0
1
1
2
2
0
1
1
0
0
0
0
1
2
0
1
2
0
1
1
1
1
0
1
2
1
1
1
0
0
1
0
2
1
0
0
0
0
1
0
3
0
0
1
0
3
0
1
2
0
0
0
1
1
0
1
1
0
1
1
0
2
1
2
1
1
2
2
0
2
0
0
0
1
1
2
2
1
0
2
0
0
2
1
0
1
0
0
1
0
1
1
0
0
1
2
1
1
0
0
0
1
7
1
1
2
0
1
0
0
0
1
0
0
2
0
0
1
2
1
1
1
0
2
2
1
0
0
0
1
1
1
2
1
0
0
0
2
1
0
0
0
1
0
0
2
1
1
2
0
1
1
0
1
1
0
2
0
0
0
1
0
0
1
0
1
1
0
1
2
1
2
0
0
3
1
2
0
1
0
1
2
2
2
1
1
0
2
2
0
0
0
1
2
1
1
0
0
1
1
0
1
0
1
2
0
0
1
1
2
0
0
1
2
0
2
0
1
1
2
2
2
1
0
2
0
2
0
1
0
0
1
0
2
1
1
2
2
0
2
1
2
2
2
2
0
0
1
1
0
2
2
0
0
1
2
1
1
1
0
0
1
0
1
0
1
1
1
1
2
1
2
1
1
0
2
1
0
0
2
1
1
2
1
2
0
0
0
1
1
1
1
1
1
1
2
1
0
0
0
1
1
1
0
0
0
1
0
0
2
1
1
1
2
1
0
0
0
2
0
0
0
1
2
1
1
0
2
2
0
1
1
0
0
1
0
3
0
2
1
0
1
0
0
1
2
1
0
0
0
1
2
1
1
1
0
0
1
2
1
2
0
0
2
0
1
1
0
1
0
1
2
1
4
0
1
1
0
2
1
1
2
1
0
1
0
0
0
1
0
2
0
1
2
0
2
0
2
1
0
1
2
1
0
1
1
0
1
1
0
1
2
2
0
0
1
1
0
0
7
2
0
1
1
3
1
0
0
1
2
0
0
1
0
3
2
1
4
0
0
1
2
1
1
2
1
0
0
0
4
1
2
0
1
1
1
0
2
1
0
1
0
0
1
2
0
1
1
1
1
2
2
1
0
1
0
0
2
2
0
1
1
0
0
1
0
0
0
0
0
0
2
1
2
2
0
0
0
1
0
1
1
1
1
0
0
0
1
0
0
0
1
0
1
0
1
0
1
2
2
1
1
1
2
2
0
1
0
1
1
1
0
1
0
0
1
1
0
1
1
1
1
2
0
1
0
0
2
2
1
1
0
0
2
1
2
0
1
1
1
0
0
2
1
1
0
2
1
0
0
1
3
0
1
1
1
2
1
2
0
1
0
2
2
0
2
0
0
1
2
1
2
2
1
0
0
0
0
1
0
2
0
0
1
1
1
2
0
2
2
0
2
0
0
1
0
0
1
2
1
0
2
0
2
0
0
0
1
1
1
0
1
2
1
2
1
1
1
2
1
2
1
0
1
0
1
0
0
0
0
1
1
2
1
0
0
1
2
0
0
2
0
0
0
0
0
1
1
0
0
0
0
1
1
2
1
0
0
1
0
0
0
1
0
0
0
1
0
2
0
0
0
1
0
0
2
2
0
0
0
1
0
1
4
0
0
1
0
0
0
0
2
0
1
2
1
1
1
0
0
1
1
0
1
2
0
2
2
1
0
2
1
0
2
0
1
0
0
2
1
2
2
2
1
1
0
1
1
0
0
1
0
0
0
2
2
1
1
1
1
2
0
0
0
1
0
1
1
1
1
1
0
0
1
1
0
0
1
1
1
2
1
1
0
0
0
2
0
2
1
0
1
1
1
0
1
1
1
1
0
1
2
2
2
1
0
0
1
2
0
1
1
1
0
2
0
1
2
0
1
2
0
1
0
1
0
0
0
1
0
0
1
1
1
1
0
0
0
0
1
1
1
0
0
1
1
1
1
0
1
0
1
1
2
2
1
1
2
1
2
2
0
1
0
0
2
1
0
1
2
1
1
1
0
1
1
0
2
0
0
1
2
0
1
2
2
1
0
0
1
0
0
0
1
2
1
0
0
0
2
1
0
0
1
0
1
1
1
0
1
2
2
0
1
2
0
1
2
1
1
0
1
2
1
1
1
2
1
0
0
0
0
1
2
2
1
0
0
0
1
0
1
1
2
0
0
1
1
1
1
1
0
0
1
0
1
1
1
1
1
1
2
2
1
1
0
1
0
2
2
0
1
1
0
1
0
0
0
0
1
0
0
2
0
0
1
1
0
1
0
2
1
0
1
2
1
0
1
0
1
0
1
0
0
1
1
1
1
2
0
1
0
1
1
0
0
0
0
0
0
0
2
2
2
0
2
2
1
1
0
1
0
0
1
0
0
0
0
5
1
1
1
0
1
0
1
0
1
0
2
1
1
1
1
0
1
0
2
2
1
1
0
0
1
2
0
1
1
1
0
0
0
1
1
2
1
0
0
1
0
1
2
1
0
2
0
2
1
1
0
3
0
2
0
1
1
0
1
1
2
2
0
0
2
2
0
2
1
3
1
1
2
0
0
1
2
2
0
1
0
0
0
1
1
1
0
1
1
0
1
0
1
1
1
1
0
0
2
0
2
2
2
3
0
1
1
1
0
0
2
0
1
2
2
0
0
0
2
3
2
1
2
0
2
1
3
0
1
0
0
1
0
1
1
1
1
0
0
0
2
1
1
0
1
0
1
0
0
1
1
1
2
1
2
2
0
1
3
2
0
0
2
1
2
1
0
0
0
1
0
0
1
1
0
0
0
0
2
0
0
2
1
0
0
0
1
1
1
0
3
0
1
1
1
1
3
0
0
0
2
0
1
1
0
1
0
2
2
2
0
2
2
1
1
1
0
2
0
0
1
0
0
0
0
1
1
0
0
2
0
1
2
2
0
0
2
1
1
0
2
2
2
1
2
1
2
0
2
2
2
1
1
0
1
1
2
0
1
0
1
1
1
0
1
1
1
3
0
0
1
3
2
0
0
1
1
1
2
1
0
1
2
1
0
1
1
0
2
1
3
2
2
0
1
1
1
2
2
2
1
1
0
0
1
1
1
1
1
1
1
1
1
1
2
1
1
0
0
2
0
2
1
0
1
0
1
1
0
0
1
1
0
0
1
2
1
0
0
0
2
2
1
1
1
2
1
1
2
0
1
0
1
0
0
0
1
1
0
1
1
2
1
1
2
2
1
0
2
0
2
1
0
1
0
1
2
2
0
1
0
1
0
1
0
2
2
0
0
1
1
1
1
0
0
0
1
1
1
0
0
0
1
1
2
1
0
1
2
2
2
0
1
0
1
0
0
2
1
1
1
1
0
2
2
0
0
0
1
0
1
1
2
3
2
0
2
0
1
0
0
1
0
0
2
0
2
0
0
2
2
1
2
0
0
1
1
1
2
0
2
0
1
2
1
1
0
0
0
0
2
1
1
0
2
1
2
2
1
1
1
0
0
1
0
1
0
1
1
0
0
2
0
1
1
0
2
2
1
2
0
2
1
0
0
2
0
1
2
0
2
2
1
0
0
0
2
0
0
1
0
2
2
1
1
1
1
0
2
1
1
2
1
1
1
1
2
2
1
1
0
0
0
2
1
1
0
2
0
2
2
2
2
0
1
0
1
2
1
0
0
0
0
1
0
1
0
2
2
1
0
1
0
3
1
0
2
1
1
0
1
0
0
1
1
2
1
0
0
0
0
3
2
1
1
0
2
0
0
0
2
0
2
1
2
1
1
1
0
0
1
0
0
2
1
1
1
2
1
0
0
0
1
1
0
0
4
2
2
0
1
0
0
0
0
1
0
2
1
2
0
2
1
0
0
2
1
1
0
0
1
1
1
1
1
0
1
2
1
0
0
0
0
1
0
2
1
0
1
1
1
0
0
1
1
0
1
0
1
1
2
2
1
0
0
2
0
1
0
0
0
0
0
2
0
1
0
2
1
1
0
0
1
1
0
0
1
0
1
2
0
1
2
2
2
1
0
4
1
2
1
2
2
0
1
1
1
0
2
1
1
1
0
0
0
1
2
0
0
1
2
2
2
1
0
2
0
2
0
1
0
1
0
2
1
0
2
1
1
1
0
3
2
1
2
0
1
0
0
0
2
1
1
1
0
0
1
2
0
2
1
1
0
6
0
1
2
2
0
1
1
2
0
0
2
0
2
2
0
1
0
1
0
1
1
2
2
1
1
2
0
2
1
1
1
2
0
2
0
0
2
2
0
2
1
1
1
1
0
0
2
1
0
2
0
0
0
2
1
0
0
3
2
2
2
1
0
1
2
0
2
1
0
0
2
2
2
2
1
1
1
1
1
1
2
0
0
2
1
2
1
0
0
0
2
0
1
2
1
2
0
1
0
2
0
2
0
0
1
0
1
1
2
0
1
0
0
0
0
2
3
1
0
0
0
0
1
0
0
2
2
2
0
1
1
1
1
0
1
0
1
2
0
1
1
1
0
0
2
1
2
2
1
1
0
1
1
1
0
1
2
2
0
1
0
1
0
1
2
1
0
1
2
0
1
2
0
0
2
0
1
0
3
0
0
0
0
2
1
0
1
1
1
0
1
2
1
1
1
1
0
2
0
1
0
2
1
0
2
2
2
0
2
0
2
0
0
1
0
1
2
0
1
1
1
0
0
2
0
1
0
0
1
2
1
0
1
2
0
1
0
0
1
0
1
2
1
1
1
1
0
1
1
1
0
0
2
2
1
0
0
2
1
2
1
2
0
1
0
2
1
2
1
0
0
0
0
1
0
0
1
1
2
1
1
0
2
0
1
0
0
1
3
1
0
1
0
1
1
0
2
0
1
1
0
2
1
1
0
1
0
0
2
2
2
0
1
1
0
1
2
0
1
0
0
0
2
1
1
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
1
0
1
2
2
2
1
1
0
1
1
0
2
2
0
1
0
1
1
1
1
1
0
1
1
0
1
1
0
1
1
0
1
1
2
0
1
0
1
1
2
2
0
2
2
0
0
2
1
0
1
1
2
0
0
2
1
0
1
1
1
2
1
2
0
2
0
0
2
2
2
2
0
2
0
0
1
1
1
0
1
0
0
1
0
0
1
0
1
1
1
0
1
2
2
0
0
0
0
1
2
1
2
0
2
1
1
1
0
0
1
1
0
0
1
2
2
0
8
1
2
2
0
1
2
2
1
1
1
1
1
0
0
1
2
2
2
2
2
1
0
1
0
0
0
1
1
1
1
1
0
0
2
0
1
0
1
0
1
2
2
0
1
1
1
2
0
1
1
1
2
0
1
0
0
2
0
1
0
0
1
2
1
2
0
1
1
0
0
0
2
1
0
0
2
1
0
3
0
2
2
1
0
0
3
1
0
2
1
0
5
0
0
0
2
1
2
1
1
0
2
0
0
0
0
1
2
1
1
2
1
1
1
1
2
0
0
1
3
0
0
0
1
1
1
0
0
0
2
0
0
0
1
0
1
2
0
0
1
0
1
0
1
1
2
0
1
0
2
1
1
1
0
1
0
0
1
1
1
0
2
1
0
0
1
0
0
0
0
0
0
0
2
1
1
0
2
0
0
1
0
1
0
0
1
1
2
0
0
0
1
2
0
1
2
1
1
0
0
2
1
1
1
0
1
0
0
1
0
1
0
1
0
2
0
2
1
1
0
1
0
0
0
1
0
0
1
0
0
1
1
0
2
1
0
5
0
1
1
2
1
2
2
1
0
1
0
2
1
0
0
1
0
2
1
0
0
2
1
0
1
1
0
0
0
2
1
0
0
2
0
0
0
0
0
1
2
2
2
1
0
0
1
0
1
0
2
1
2
1
0
1
2
0
2
0
1
1
1
1
2
0
0
1
0
2
1
1
1
1
1
0
1
0
1
0
1
3
1
0
2
0
1
1
0
0
1
1
0
1
0
0
1
1
0
0
2
0
0
0
2
0
0
2
2
1
0
0
1
1
0
1
1
0
1
0
1
0
0
2
1
0
2
0
0
0
1
2
1
2
0
2
0
0
1
1
0
1
3
0
0
1
0
0
1
2
0
2
1
1
1
1
0
1
1
1
1
0
1
1
2
1
1
0
0
0
1
1
1
2
1
1
0
1
1
0
2
0
1
0
4
1
0
1
1
1
2
0
2
0
1
0
1
1
0
0
1
2
2
1
0
0
1
1
1
0
0
0
1
0
1
1
0
2
2
1
1
2
0
1
0
1
2
0
2
1
0
3
2
2
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
2
0
1
2
1
1
0
1
2
0
1
0
0
1
0
0
1
0
1
0
0
0
0
1
1
1
2
2
0
0
0
0
1
1
1
2
1
0
0
0
0
1
2
0
1
0
1
1
1
3
1
0
0
0
1
0
2
1
1
2
0
2
0
0
1
1
2
1
0
1
1
0
1
0
0
2
0
2
1
0
0
1
1
1
2
1
1
2
0
0
1
2
0
2
0
1
2
1
0
0
0
1
1
0
1
1
1
1
1
2
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
1
1
0
0
0
1
2
1
2
1
2
1
1
1
2
1
0
1
2
0
1
1
1
0
0
1
0
0
0
2
1
2
2
2
1
2
1
2
2
0
2
0
0
4
0
0
1
1
1
2
0
0
1
2
1
2
2
0
1
2
1
1
0
0
0
0
2
0
0
1
0
0
0
2
1
0
0
2
2
1
1
1
2
0
1
2
0
2
0
2
1
0
0
2
2
2
0
1
1
2
0
1
2
0
0
2
1
2
1
0
1
4
0
0
1
0
0
1
0
1
0
1
1
1
0
0
0
0
0
1
1
0
0
1
0
3
0
2
1
1
1
1
1
0
1
0
0
1
1
2
1
1
0
0
0
2
2
0
0
1
1
2
1
2
2
0
1
2
1
2
0
1
0
1
0
2
1
0
2
0
1
1
2
1
1
1
0
0
1
0
2
2
0
2
0
1
2
1
0
1
2
0
2
1
0
0
2
2
0
0
1
1
0
3
3
2
0
1
0
0
0
2
1
0
1
1
2
1
0
2
0
0
0
0
1
0
0
1
2
1
1
0
0
2
2
0
1
0
1
2
2
0
0
1
2
1
1
2
2
1
1
2
1
0
0
2
2
1
1
0
2
0
0
0
0
1
0
0
0
2
1
0
1
0
1
0
0
0
2
0
0
1
3
2
1
0
1
2
0
0
0
0
3
1
2
1
2
0
0
1
0
1
1
2
0
0
1
0
2
0
0
1
0
3
1
0
0
2
0
1
0
0
1
1
0
1
0
2
0
0
0
1
1
2
1
1
1
2
1
2
2
1
1
3
0
1
2
1
0
1
1
1
1
0
2
1
1
1
2
0
0
2
1
0
2
1
1
0
1
0
0
1
1
1
2
2
0
1
0
0
1
2
0
1
0
0
1
1
0
2
2
1
1
1
1
1
2
1
1
1
2
2
2
0
1
0
0
1
2
0
0
1
2
1
0
1
1
0
2
1
1
1
1
0
2
0
2
1
1
0
2
1
1
0
0
0
1
1
0
0
0
0
1
2
1
0
2
0
2
0
0
0
1
1
1
0
2
1
0
1
0
1
1
1
0
0
1
0
1
1
2
1
2
0
1
1
1
1
2
1
1
2
2
0
0
0
1
1
0
0
0
1
0
1
0
0
1
0
0
1
0
1
0
1
1
1
0
2
0
0
1
0
2
1
1
1
1
0
1
0
0
2
1
0
1
2
2
1
1
1
4
0
1
0
2
0
0
0
1
2
0
1
0
2
0
2
1
0
1
2
1
0
0
1
1
2
0
1
1
1
1
1
0
2
2
1
0
1
2
0
1
0
2
0
1
0
1
0
2
0
1
0
0
1
2
0
2
1
0
1
2
1
0
1
2
1
2
1
1
0
1
2
0
0
0
1
2
1
2
0
0
0
1
1
0
2
1
1
0
1
1
1
1
0
1
1
1
2
2
0
1
1
0
1
0
0
0
1
1
1
1
0
2
1
2
2
1
1
0
1
2
1
0
1
2
1
0
0
0
1
2
1
2
1
0
0
2
1
0
0
2
0
2
0
2
1
0
1
1
1
1
0
1
2
1
1
0
1
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
1
0
2
1
1
0
2
1
1
1
2
1
1
2
0
2
2
1
1
1
0
1
1
0
3
2
1
0
1
1
2
2
1
0
1
1
2
0
1
0
2
1
2
0
0
2
1
0
0
1
0
2
2
1
0
2
1
0
1
1
1
0
0
3
1
1
1
1
0
1
1
1
0
0
1
2
1
0
2
0
0
1
0
0
2
2
0
0
0
0
2
1
1
1
2
0
1
2
2
1
1
0
0
1
0
2
0
2
1
1
2
1
2
1
0
2
1
1
1
0
0
2
0
2
0
2
1
2
0
1
1
0
2
0
1
1
1
0
0
0
1
1
0
1
0
0
0
1
1
1
1
2
1
0
0
1
2
1
0
2
2
0
0
2
1
1
0
0
1
1
0
2
1
1
0
1
2
0
1
0
0
1
2
2
1
1
2
0
1
2
0
1
1
2
1
0
2
0
0
0
0
2
1
0
0
0
0
2
2
1
0
2
0
0
0
0
2
0
1
1
0
2
1
1
1
1
0
0
3
0
2
0
0
2
0
1
2
0
3
1
0
0
0
1
1
1
0
0
0
0
1
0
1
0
1
1
1
0
0
2
0
1
0
1
0
2
2
0
1
0
1
1
0
0
0
0
2
1
2
0
1
1
1
2
1
1
0
2
1
2
0
0
1
1
0
4
0
1
0
0
1
0
0
0
0
2
1
0
2
1
0
2
1
0
1
0
0
0
1
2
1
2
0
1
1
0
0
2
1
0
0
0
1
1
2
1
2
2
0
0
2
0
2
0
2
2
1
0
1
0
1
1
2
1
0
0
2
0
1
0
0
1
1
0
0
1
1
0
0
2
0
0
1
0
0
3
0
1
1
2
0
3
1
2
2
1
1
1
1
1
1
2
0
2
2
0
0
0
2
1
0
0
2
2
1
1
0
1
1
1
2
2
0
0
2
1
1
1
1
0
1
1
1
1
2
1
2
0
0
0
1
2
0
3
0
0
0
1
1
2
0
1
0
1
0
0
0
3
1
1
3
0
2
1
0
0
1
0
0
1
2
2
0
1
2
0
1
1
2
1
0
2
1
2
1
2
1
0
1
1
2
1
0
1
1
0
3
0
1
0
1
1
1
1
0
1
2
0
0
0
2
0
2
1
1
1
2
1
1
1
0
1
1
0
0
2
0
2
1
0
1
1
0
1
1
2
0
0
1
0
2
1
1
1
0
2
0
2
2
2
1
0
1
1
1
2
0
0
1
0
1
1
1
1
0
1
0
1
1
2
0
1
2
2
1
0
0
2
1
1
0
0
1
0
0
0
2
1
1
2
1
0
1
0
0
0
0
1
1
0
0
0
0
1
1
1
1
0
0
1
0
0
1
1
1
0
0
1
0
1
1
2
0
0
2
1
0
1
2
0
2
0
6
2
1
2
1
1
0
2
1
0
0
2
1
1
1
0
1
0
1
1
1
1
1
0
0
0
1
0
0
1
1
2
2
0
1
2
1
2
1
1
1
1
0
1
1
1
0
0
0
1
0
1
2
0
1
1
2
0
0
1
0
2
0
0
0
1
2
1
2
2
0
3
1
1
2
1
0
1
0
0
2
1
0
0
0
1
0
1
1
0
2
2
2
0
0
1
1
1
0
1
2
1
1
0
1
1
0
1
0
1
0
1
2
1
1
2
0
1
0
2
1
0
1
1
1
1
1
0
1
1
0
2
2
1
0
0
0
2
1
0
0
1
2
0
2
1
1
0
2
0
2
0
2
0
0
0
1
1
1
0
2
0
0
2
1
2
1
1
1
2
0
2
1
2
1
1
1
0
0
1
0
0
0
1
2
1
2
1
2
2
1
0
2
1
0
1
1
2
1
0
2
2
0
0
1
0
1
1
2
1
1
1
2
0
0
1
1
0
1
1
1
2
1
0
0
0
1
2
0
0
1
0
1
1
1
0
0
1
1
2
1
1
1
0
0
2
1
0
1
2
1
1
0
2
1
2
2
1
0
1
0
5
1
1
1
1
0
2
1
2
0
2
0
1
0
1
0
2
2
2
0
3
1
0
1
1
0
0
1
0
1
2
6
2
1
0
1
2
2
2
1
0
0
2
0
0
1
1
0
1
2
2
1
1
1
0
1
0
0
0
1
2
1
0
0
0
1
0
1
1
1
1
1
0
1
0
0
1
1
2
0
1
1
0
1
1
2
0
1
1
0
1
0
1
2
0
0
1
1
0
1
2
0
1
1
0
1
1
1
2
0
0
1
1
2
1
1
0
1
0
1
2
0
1
1
1
1
0
2
2
1
0
0
2
0
2
1
2
0
0
1
3
2
0
0
1
0
0
2
1
1
2
1
0
1
0
1
0
1
0
1
0
1
0
2
2
2
1
0
0
0
0
1
6
2
3
0
1
0
2
0
0
0
1
2
0
1
0
2
1
1
1
4
2
0
0
1
0
0
0
1
0
3
1
2
1
1
1
2
1
2
0
2
0
0
0
1
0
0
1
0
1
1
0
0
0
1
0
0
1
2
2
1
2
1
2
1
1
1
1
1
2
0
1
1
0
2
0
0
1
1
1
2
1
1
0
2
1
0
1
2
2
0
1
2
2
0
2
0
0
2
2
0
0
1
1
1
2
0
2
0
0
1
2
2
0
1
2
2
1
0
0
0
1
2
0
0
2
0
0
0
1
1
1
2
1
0
1
2
0
1
0
2
0
0
0
0
1
1
1
0
1
1
0
1
2
1
2
2
0
1
0
0
1
2
2
1
1
1
1
0
0
0
1
2
0
0
1
0
0
0
2
2
2
2
1
1
1
1
0
1
1
1
0
1
1
1
0
0
1
0
1
0
1
1
2
0
0
1
1
2
0
0
0
1
1
0
1
1
0
0
2
1
0
1
2
2
1
1
1
2
1
2
0
1
2
2
1
0
1
1
0
1
2
0
0
1
1
1
1
1
1
1
0
2
1
1
0
1
0
1
0
1
0
0
3
0
1
1
0
1
0
0
1
1
1
3
0
2
0
0
0
1
1
0
2
3
2
0
0
1
0
2
3
2
1
2
0
0
0
0
0
2
2
1
1
1
0
2
1
0
3
2
1
1
1
2
1
0
0
1
1
1
1
0
2
0
0
1
0
0
0
0
1
0
2
0
1
0
0
0
0
1
2
0
1
0
0
0
1
1
1
2
1
0
0
0
0
1
0
0
2
0
1
2
1
1
0
0
1
2
1
0
0
1
1
0
0
3
1
2
1
0
2
1
0
1
2
0
2
2
0
1
1
1
1
0
1
0
1
0
4
0
0
0
0
0
2
2
0
1
0
1
1
1
0
0
2
1
2
0
1
3
0
1
2
1
1
1
2
1
1
2
0
2
0
1
2
2
0
1
0
1
2
0
0
1
1
0
0
1
2
1
2
2
2
0
1
2
2
1
0
3
0
1
0
2
2
2
1
2
2
1
2
1
1
2
2
1
0
2
2
0
1
2
0
0
0
1
1
1
1
2
1
0
2
1
0
1
0
0
0
2
2
2
2
1
1
2
0
1
1
2
2
0
1
0
2
2
0
1
0
1
1
0
0
1
1
2
0
0
0
1
0
2
0
1
1
1
1
0
1
0
0
1
0
1
2
0
0
0
0
1
1
2
2
0
1
0
0
2
1
1
1
1
1
1
2
2
0
1
0
1
1
0
0
1
1
1
2
1
2
0
0
0
2
1
0
1
2
0
1
0
0
1
1
0
1
2
1
0
1
1
0
2
0
0
0
0
0
1
1
1
1
0
1
1
1
0
2
0
0
1
1
2
1
1
0
0
1
2
2
1
0
2
0
2
1
0
1
0
1
2
1
1
2
1
0
0
0
2
2
1
1
0
1
0
1
2
2
1
1
0
2
2
2
1
0
0
0
0
1
1
1
0
1
0
0
1
0
0
2
0
1
2
0
0
0
0
0
1
2
0
0
0
0
0
0
1
2
0
0
0
2
0
1
0
0
3
1
0
1
0
0
0
0
0
2
0
1
2
1
2
2
1
1
0
1
1
1
2
0
0
0
1
1
0
1
2
2
0
0
0
2
0
0
1
1
0
0
2
0
0
1
1
1
2
2
0
0
1
1
1
2
1
0
1
0
0
0
1
2
1
0
2
1
2
1
1
2
0
1
0
0
1
0
1
0
0
1
1
1
0
2
1
2
0
0
0
0
0
0
0
0
1
0
2
1
1
1
0
2
2
2
0
1
0
1
0
1
0
1
1
1
1
0
1
0
1
1
2
2
1
2
1
0
0
5
2
1
1
0
1
0
0
1
2
0
1
2
0
1
0
1
1
0
1
1
2
2
1
0
1
1
0
0
0
0
0
0
2
1
1
2
0
1
1
1
0
1
1
0
0
2
5
1
1
1
0
0
1
1
2
0
1
1
1
1
1
0
2
0
2
0
1
1
0
0
0
1
0
2
1
0
2
1
0
0
0
1
0
1
1
2
1
2
2
2
1
1
2
1
0
0
0
2
0
2
1
0
0
1
2
1
0
2
0
2
0
1
1
1
1
1
1
2
0
2
1
1
2
2
1
0
1
0
2
0
3
1
1
2
1
1
0
1
0
0
1
1
2
1
1
1
0
1
0
0
0
3
1
1
0
2
2
0
0
2
0
0
0
0
1
1
0
2
1
1
1
1
1
3
0
0
1
1
0
0
2
2
0
2
2
1
2
1
2
1
3
0
0
0
0
0
2
1
1
0
0
0
1
0
0
1
1
0
0
1
0
0
2
1
0
2
1
0
2
3
1
0
0
1
1
1
0
2
1
2
1
1
0
2
1
1
0
0
0
0
1
2
1
2
0
0
1
0
2
0
0
0
1
1
0
2
1
1
3
2
0
1
1
0
1
2
1
1
0
2
0
2
1
0
2
0
0
0
1
2
0
2
2
1
1
0
1
1
1
2
2
0
0
1
1
1
0
1
0
1
1
0
2
1
2
1
0
1
1
1
1
1
0
2
0
0
0
1
2
1
1
0
1
1
1
0
2
1
1
0
1
0
0
2
2
2
0
0
0
1
0
0
0
1
0
0
0
1
1
0
1
1
0
1
0
1
0
1
1
0
0
0
0
0
1
0
0
2
0
0
1
1
1
1
0
1
2
0
2
0
1
0
0
0
2
0
2
1
1
2
3
1
1
1
1
1
0
2
2
0
1
2
1
0
1
1
0
0
1
1
0
0
1
1
1
2
1
0
1
0
1
0
0
1
1
2
2
1
0
1
0
0
2
2
0
0
1
2
1
2
1
0
0
0
2
1
1
2
0
0
1
2
1
0
0
0
0
1
0
1
0
0
1
0
0
0
1
1
0
1
1
1
0
0
0
0
0
2
0
0
1
1
0
1
1
0
1
2
2
0
1
0
2
1
2
0
1
1
0
0
1
1
0
1
1
2
2
0
2
0
1
0
2
0
2
0
0
1
0
1
1
1
0
1
1
0
1
2
1
2
0
2
1
2
1
0
2
2
2
2
0
0
2
0
0
0
0
1
1
2
0
1
1
0
1
1
0
2
2
1
3
0
0
1
2
0
1
0
0
1
1
1
2
1
1
0
0
0
0
2
0
0
1
0
0
1
1
0
0
1
0
0
1
1
1
1
0
1
2
1
1
0
2
1
0
1
1
2
1
0
0
1
0
0
0
9
0
2
0
0
0
0
1
1
2
2
2
0
0
1
3
0
1
2
1
0
2
0
0
0
2
1
2
0
2
1
3
1
1
2
0
1
0
2
0
0
1
1
1
2
1
2
1
0
0
0
0
1
1
0
2
2
2
2
1
1
1
1
1
2
2
1
0
0
2
2
1
1
0
0
0
2
0
1
0
0
1
0
2
0
0
0
0
1
0
0
0
2
1
2
1
0
0
0
1
1
1
1
1
1
0
1
0
2
0
0
0
2
1
0
1
0
0
0
1
1
1
1
0
1
0
0
2
1
0
0
2
1
0
1
1
0
2
0
0
1
1
0
1
2
1
1
1
0
1
2
0
1
0
0
1
1
1
2
0
1
0
0
0
0
1
0
0
1
0
2
1
2
1
0
1
1
2
1
1
1
1
0
1
1
1
1
0
1
0
2
0
2
0
1
0
0
1
1
0
0
2
0
1
1
0
1
1
0
0
2
0
1
2
2
1
1
1
1
1
2
0
1
0
0
0
0
1
4
2
1
2
2
0
2
1
0
0
0
2
0
0
2
0
3
2
1
0
2
1
0
0
2
1
0
0
1
0
1
2
1
2
1
0
0
2
0
1
2
0
1
3
0
0
0
1
1
1
1
0
2
0
2
0
0
1
2
2
0
0
1
0
2
1
0
0
0
1
0
0
1
0
2
0
0
0
1
1
0
0
1
1
1
0
0
2
2
0
1
0
1
0
2
1
0
2
0
1
1
0
1
1
2
1
0
1
1
0
0
0
1
1
2
1
0
1
1
3
2
1
1
1
1
0
0
2
0
1
1
0
0
1
2
0
0
0
0
1
0
2
0
2
2
0
0
1
0
0
1
0
1
1
1
0
0
1
2
1
0
0
2
0
1
1
2
1
1
0
0
1
0
0
2
0
0
0
1
1
1
0
2
1
1
2
0
2
0
0
2
0
0
1
0
2
1
0
0
0
1
2
0
0
1
2
1
2
1
2
2
0
1
1
4
0
1
1
1
1
2
0
1
1
0
0
2
1
2
0
0
1
1
0
1
1
0
0
0
2
0
0
0
0
2
0
2
1
1
2
1
1
1
0
0
1
0
1
0
0
1
0
1
1
0
1
1
0
1
2
1
1
2
1
0
2
1
0
0
2
0
2
1
1
4
1
0
0
3
1
0
1
0
0
0
2
0
1
1
0
0
1
1
1
2
1
0
1
1
2
2
0
1
1
0
0
0
1
2
0
1
0
0
2
0
1
0
0
0
1
3
2
6
1
1
1
3
4
0
0
1
0
2
0
0
1
0
1
1
1
0
0
2
1
1
1
1
2
1
0
1
0
0
1
1
0
1
0
1
0
1
1
0
0
0
1
1
1
2
0
1
1
1
2
0
2
1
2
1
0
0
1
0
2
1
4
0
0
0
0
1
1
0
2
0
0
2
0
1
0
0
2
0
0
1
0
1
1
1
1
0
2
2
0
1
1
1
0
1
1
1
0
2
1
2
0
0
1
1
0
1
2
0
0
1
2
1
0
1
1
0
1
2
1
0
0
0
1
0
1
1
2
2
1
2
2
2
1
1
0
1
1
1
0
0
0
1
1
0
0
1
0
1
0
1
0
1
1
0
2
1
0
1
1
0
2
2
0
0
1
0
1
0
2
1
1
2
1
1
1
0
2
1
2
1
1
1
0
2
2
1
0
2
1
0
2
1
0
3
1
1
1
1
1
0
2
1
1
0
1
1
0
1
0
0
1
2
0
1
1
2
1
1
1
0
0
1
2
1
2
0
1
0
1
1
1
0
0
2
1
0
0
0
2
0
2
2
1
1
1
3
1
0
1
1
0
1
0
2
1
0
1
2
1
1
0
0
1
0
0
1
0
1
1
2
0
0
2
1
0
2
0
2
2
1
0
0
1
0
0
0
0
1
2
0
2
1
0
0
0
2
1
3
1
2
0
2
1
0
0
0
2
1
0
0
0
2
1
0
0
0
1
1
0
1
2
0
0
1
0
1
1
0
0
1
1
2
0
1
0
1
2
1
1
0
1
1
2
0
0
0
2
1
2
0
0
1
2
1
1
1
1
1
1
2
1
0
0
1
2
1
2
2
1
0
1
0
0
1
2
2
1
2
1
0
0
2
0
0
0
0
0
1
0
2
1
0
0
2
1
1
0
0
2
0
1
0
2
0
2
0
0
2
0
0
1
1
2
0
2
0
1
2
1
0
0
2
2
1
0
1
0
2
1
0
0
1
1
1
2
0
1
1
2
1
1
1
0
1
0
1
2
0
2
2
0
1
2
1
2
0
0
0
0
2
1
1
0
1
1
0
0
2
1
2
0
1
0
0
1
1
0
2
1
2
2
0
0
1
0
1
0
1
2
0
0
0
2
1
0
0
1
1
3
0
0
1
0
1
1
2
1
2
0
0
1
1
1
1
2
0
2
1
0
0
2
0
2
1
1
0
2
0
0
1
2
1
2
0
2
1
1
3
0
2
1
1
2
0
1
1
0
0
1
1
1
1
0
1
1
1
1
1
1
2
1
1
1
1
0
0
0
1
1
0
0
2
0
0
0
2
1
2
0
0
1
4
2
1
0
1
1
0
0
0
0
0
1
0
0
2
0
2
0
1
0
1
0
0
2
1
1
2
0
0
0
1
0
2
1
0
0
2
0
1
0
0
2
1
2
1
1
0
0
1
1
1
0
0
1
0
0
2
1
1
1
1
2
1
1
1
2
1
0
0
1
0
0
1
0
1
1
0
0
2
0
0
2
0
1
0
1
1
2
1
1
1
0
2
2
1
2
0
1
2
1
2
1
1
0
1
0
0
0
1
2
2
1
0
0
1
0
1
1
0
0
0
2
0
0
0
2
1
1
0
1
2
1
1
1
4
0
0
0
0
1
2
1
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
1
1
1
1
1
1
2
1
1
0
2
0
2
2
0
2
2
2
0
1
1
1
2
1
1
0
1
1
1
1
0
0
0
1
0
2
2
0
0
2
2
0
3
2
2
0
0
0
2
0
1
2
0
1
1
2
0
0
1
1
1
1
0
1
2
0
1
2
0
2
0
1
0
2
1
1
0
0
0
0
0
0
0
2
2
0
2
0
0
1
0
2
0
0
1
1
1
1
0
0
2
1
0
0
0
2
2
2
2
1
1
0
1
2
0
2
0
0
0
0
0
0
2
0
0
1
2
2
0
0
2
0
0
2
1
2
2
1
0
0
0
0
1
2
1
1
0
0
2
1
2
1
1
1
1
1
1
0
2
1
2
0
1
2
0
2
1
2
0
0
1
2
1
1
2
0
2
0
0
0
0
1
2
1
0
1
0
0
1
0
0
1
0
2
1
1
1
0
1
1
1
1
0
2
1
2
1
1
1
2
0
2
0
1
0
1
1
1
2
0
1
0
2
0
2
0
2
0
1
2
1
2
0
0
1
0
0
0
0
2
1
0
2
0
2
2
2
0
1
1
0
2
0
0
2
1
2
0
0
2
1
2
2
0
1
2
2
1
1
1
1
5
0
1
2
1
2
1
1
0
1
2
0
0
0
2
1
1
1
0
0
0
2
2
1
2
1
1
1
1
1
0
0
0
2
2
2
1
1
2
0
2
1
1
1
1
2
1
1
2
1
2
2
0
1
0
1
0
0
0
1
0
2
1
1
1
0
1
1
0
0
1
2
0
0
2
2
1
0
1
2
0
2
0
0
0
2
0
2
1
0
0
1
1
1
2
1
0
1
0
0
0
0
0
1
2
0
0
0
2
1
0
0
0
0
0
0
1
2
0
1
3
2
2
1
1
1
0
1
1
1
0
1
1
0
1
0
1
0
2
0
2
1
2
2
0
0
0
1
1
0
0
1
1
1
1
1
2
2
2
1
0
0
0
1
1
2
2
0
0
0
1
1
0
0
0
0
2
0
0
1
1
0
1
1
3
0
0
0
1
0
2
1
0
1
2
0
1
0
2
1
0
0
2
2
0
2
1
2
2
1
0
0
1
0
1
3
2
1
1
0
0
0
0
1
0
0
2
0
2
0
1
2
1
1
0
0
1
0
0
0
0
0
1
2
1
2
0
2
0
0
0
2
0
1
1
1
0
2
1
2
1
0
0
0
0
1
0
2
0
0
0
0
1
1
0
0
1
0
2
0
1
0
0
0
1
0
1
1
0
1
0
0
1
1
0
2
2
1
1
1
1
0
1
1
0
1
0
1
2
0
2
2
0
2
0
0
1
0
1
2
0
1
2
1
0
1
0
0
1
1
2
1
0
1
1
1
0
2
0
1
0
1
0
1
1
2
0
0
0
1
2
0
1
0
1
1
2
1
1
1
1
1
1
2
0
1
0
2
0
2
2
0
1
1
0
1
0
2
1
1
0
0
0
0
1
2
2
0
1
0
1
2
0
1
1
0
1
4
0
1
1
1
0
0
0
1
2
1
2
2
0
1
1
1
0
1
1
1
1
0
1
0
1
0
2
0
0
1
1
1
1
3
0
1
1
1
1
1
2
1
2
1
1
2
2
2
1
0
1
0
0
0
2
0
2
0
1
0
2
0
1
0
0
1
3
1
2
0
1
1
2
3
1
2
1
1
1
2
1
0
1
0
1
2
1
0
0
0
0
0
1
1
1
1
0
1
0
0
2
0
1
0
0
0
0
1
0
0
1
1
2
0
2
1
0
0
0
1
0
2
1
1
0
1
0
0
1
0
1
0
0
0
1
1
1
0
1
1
2
0
0
1
2
1
1
1
0
0
2
0
1
0
0
0
3
2
2
1
2
0
0
0
2
1
0
0
0
1
1
1
0
0
0
0
1
1
0
2
1
0
1
1
0
0
2
0
1
0
0
1
2
2
0
2
1
1
2
0
0
2
0
0
0
0
1
0
3
0
1
1
2
2
1
2
0
0
1
1
1
1
1
1
2
1
0
1
1
0
0
0
0
1
1
1
2
2
1
2
0
2
0
0
3
1
1
1
1
1
0
3
1
1
0
0
1
2
1
1
0
0
0
1
2
2
1
0
1
2
0
2
0
2
0
0
1
0
1
2
2
1
0
1
1
2
2
0
0
0
0
2
1
2
1
0
2
1
1
2
1
2
2
1
0
1
0
1
0
2
0
0
1
1
0
2
2
2
1
2
1
2
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
2
1
1
0
0
0
1
1
0
0
1
2
0
1
0
0
0
1
0
0
0
1
1
2
0
1
2
1
0
2
0
0
1
1
0
2
0
1
0
0
1
0
2
2
2
2
1
1
3
0
0
4
2
0
1
0
0
0
2
0
1
0
1
1
0
1
1
0
2
1
2
1
0
1
1
1
0
1
0
1
1
1
0
2
1
2
2
1
0
1
2
1
1
0
1
3
0
1
0
0
1
0
1
1
3
1
0
0
1
1
2
2
2
2
0
2
1
2
0
1
0
1
2
0
1
2
1
0
2
1
2
1
0
2
1
1
1
0
0
2
1
0
0
1
2
1
0
3
0
1
0
1
1
0
1
2
0
1
2
2
2
0
0
0
0
2
1
0
2
0
1
1
1
2
2
1
0
2
1
2
2
1
2
1
1
1
0
2
2
0
1
1
2
1
0
0
1
0
2
0
1
1
0
0
1
0
1
2
1
0
1
2
2
0
1
1
0
1
1
2
1
1
1
0
2
2
0
0
2
1
1
0
2
1
0
1
0
0
0
1
0
1
1
0
1
1
1
0
1
0
1
0
0
1
1
1
0
2
1
0
0
2
2
1
0
0
1
1
2
0
1
2
0
0
1
1
0
1
2
1
1
0
2
0
0
2
1
2
1
1
1
0
1
0
2
2
0
0
0
1
1
1
2
1
0
2
0
2
0
2
2
2
1
1
0
0
1
1
2
1
0
1
0
1
1
1
2
0
3
0
0
0
0
3
1
0
1
2
0
0
0
1
0
2
1
0
2
0
1
2
2
1
2
1
0
1
2
2
2
0
0
0
1
1
1
1
0
0
1
1
0
2
7
1
1
0
1
0
0
0
0
2
0
2
0
0
0
0
1
0
1
0
2
0
0
1
1
1
1
1
0
1
1
2
0
1
0
0
0
0
2
1
1
1
0
3
1
0
1
1
2
1
0
0
1
0
0
0
0
0
1
0
2
1
1
1
0
1
1
2
1
0
0
2
1
1
1
0
2
2
0
2
1
0
1
1
0
0
0
2
2
2
0
1
0
0
2
1
1
0
0
0
1
0
0
2
1
0
0
0
1
0
2
0
1
0
0
1
1
2
2
0
4
2
2
2
0
2
0
0
0
0
0
0
0
0
1
1
0
0
2
1
2
1
1
2
1
2
1
0
1
2
1
0
0
1
1
0
1
2
0
1
2
0
1
2
1
0
2
1
0
0
1
0
0
0
0
1
0
1
0
1
0
1
1
1
0
0
0
0
1
0
0
0
2
1
1
0
1
0
0
1
0
1
0
2
1
1
1
0
1
1
0
2
1
0
1
2
5
1
1
2
0
2
2
1
1
1
0
0
1
2
0
0
1
1
2
2
0
2
0
2
1
1
0
0
2
1
1
1
2
2
0
2
2
1
0
1
2
0
1
1
0
1
0
2
0
0
1
2
1
0
2
2
1
1
0
1
1
2
1
0
1
1
1
2
0
0
1
1
0
2
1
1
2
0
2
0
1
3
0
0
3
1
1
0
2
2
0
0
0
1
0
2
1
2
0
0
2
1
0
0
1
1
2
0
1
1
0
1
2
0
1
2
2
1
1
1
1
0
2
1
1
1
2
0
1
2
0
2
0
1
0
1
1
1
0
2
0
2
2
0
2
2
2
0
0
0
1
1
0
0
1
0
2
2
2
0
1
1
1
2
1
2
1
0
0
0
1
2
0
2
1
2
0
0
1
1
0
1
1
1
0
2
0
0
0
1
0
0
1
0
1
1
1
0
0
1
1
1
2
0
2
1
0
0
1
1
2
1
0
1
0
0
1
1
0
0
1
2
2
1
0
1
0
1
2
0
1
1
4
1
2
1
1
0
3
1
0
1
1
0
0
0
0
0
0
0
1
1
2
2
1
1
2
1
0
1
1
0
0
0
1
1
1
2
1
0
1
2
1
2
0
0
1
0
1
2
0
1
1
1
2
1
0
1
1
1
2
1
3
0
0
3
2
1
0
0
1
1
1
1
0
2
1
1
2
0
1
1
0
1
1
1
2
1
2
1
2
2
2
0
1
2
1
1
1
1
0
1
0
1
2
0
0
1
1
0
1
0
2
0
0
1
0
0
0
1
1
0
2
2
1
1
1
2
2
2
1
0
1
2
2
0
2
2
2
0
1
2
1
0
0
2
1
0
0
0
0
0
0
2
0
1
0
1
1
0
0
1
1
0
0
0
2
2
0
2
1
0
2
2
0
0
2
2
1
2
0
2
0
2
0
1
1
1
0
1
1
0
1
2
3
0
1
1
0
0
1
1
3
1
0
0
2
1
0
2
0
1
0
2
0
2
0
2
1
0
2
1
0
2
1
2
0
2
1
2
0
0
1
1
2
0
2
1
2
0
0
1
0
1
0
1
1
2
1
0
0
0
2
0
0
1
1
2
0
2
1
1
2
0
4
1
0
0
0
0
0
1
1
2
1
0
1
1
0
1
1
0
2
0
1
1
0
0
1
1
1
1
1
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
1
1
1
2
1
2
0
1
0
3
0
1
0
0
2
1
0
1
0
1
1
0
2
0
0
1
0
1
0
0
0
0
0
2
1
2
1
0
0
1
2
1
3
2
1
1
1
1
2
1
0
1
2
2
0
1
0
1
2
0
1
1
0
1
1
1
1
3
1
0
0
0
2
2
1
1
2
1
1
0
0
0
1
2
0
2
1
1
1
1
2
0
2
1
4
0
0
2
1
1
0
1
4
0
1
2
1
1
1
1
0
1
2
2
0
1
0
0
0
2
1
2
1
1
1
2
1
1
1
1
2
2
1
0
1
1
1
2
1
1
0
0
0
1
1
1
2
1
1
1
1
1
2
2
0
0
0
1
2
1
0
0
0
0
0
0
1
0
2
0
0
0
2
0
1
0
0
0
0
2
1
1
0
1
0
2
0
0
1
1
2
0
1
0
0
0
1
1
1
1
1
0
1
1
1
1
2
2
1
0
1
0
2
2
0
1
1
2
1
1
1
0
2
1
1
1
0
1
2
1
2
2
0
0
1
1
0
2
2
1
1
0
2
1
1
2
0
2
0
0
0
0
0
0
1
0
0
1
1
2
0
1
1
0
0
0
1
0
2
0
1
0
0
1
0
1
0
0
2
1
2
2
1
1
0
1
0
0
1
1
0
0
1
1
0
1
2
0
0
1
1
0
1
0
1
2
1
2
1
0
1
1
1
1
1
2
1
1
0
0
0
0
2
0
1
1
0
0
0
1
0
1
0
2
0
0
1
0
1
2
1
1
1
1
1
1
0
2
0
0
1
2
2
1
0
0
1
2
1
2
1
0
1
0
2
0
0
0
0
0
0
1
1
2
1
1
0
0
1
1
0
0
1
2
0
0
2
1
0
0
1
2
2
1
2
1
1
1
2
0
0
2
1
1
0
0
1
0
0
1
0
1
1
1
1
1
0
2
0
1
1
1
2
1
2
2
1
1
0
0
1
1
2
0
1
0
1
1
0
0
0
0
1
0
1
1
1
1
2
0
1
1
0
1
1
0
1
1
2
1
1
0
0
2
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
2
0
1
1
0
2
0
2
2
2
1
0
0
1
1
0
0
1
0
0
1
0
1
0
1
4
0
2
1
0
0
0
0
0
1
1
1
1
0
1
1
2
1
2
1
2
1
1
0
1
1
1
0
2
1
0
0
1
0
0
0
0
2
0
0
0
1
1
1
1
0
2
2
0
2
0
1
2
0
0
1
0
0
0
1
2
1
0
0
1
1
1
2
1
0
0
1
0
0
1
1
1
1
1
1
4
1
1
0
1
0
0
0
1
0
2
1
0
2
0
0
2
2
0
2
1
1
2
2
1
0
1
2
1
2
2
0
2
1
1
1
1
1
0
0
0
3
0
1
0
0
2
2
2
1
1
0
0
1
0
2
0
0
1
1
1
0
0
1
2
0
1
1
0
1
1
0
0
1
0
1
1
2
2
0
0
1
1
1
2
1
2
0
0
0
1
0
4
1
0
1
1
0
1
0
1
1
1
0
0
1
1
1
0
0
1
0
0
0
2
0
1
2
0
1
0
0
1
1
1
0
0
0
2
2
2
1
1
1
1
1
1
0
1
1
1
0
1
1
1
1
2
0
1
2
1
0
1
1
0
1
1
2
0
2
0
2
2
1
0
2
0
0
1
0
0
0
1
2
1
0
1
0
0
2
1
1
1
0
0
1
0
0
0
1
1
0
1
1
1
0
1
1
1
1
0
0
0
1
1
1
1
0
1
0
1
1
1
1
0
0
0
1
2
0
0
1
1
1
1
0
2
0
1
1
1
2
0
0
1
1
2
2
1
1
1
1
1
0
1
0
2
0
0
0
2
0
0
1
0
0
1
0
1
1
0
1
0
2
1
1
0
4
2
2
2
0
1
1
1
2
0
1
3
0
1
1
2
0
0
2
1
2
0
0
0
0
0
1
0
1
0
0
1
2
0
1
0
1
0
0
0
1
1
0
2
1
1
2
1
1
1
1
0
1
1
1
0
0
2
0
1
0
0
2
0
1
1
0
2
0
0
0
0
0
0
0
0
1
0
0
2
2
0
2
1
0
1
2
1
2
1
1
1
2
0
1
4
1
0
0
0
0
0
0
2
1
2
0
1
1
0
0
1
2
2
2
3
1
2
1
0
1
0
1
0
1
2
1
1
2
1
0
1
1
1
1
0
1
0
1
0
0
2
0
2
0
1
1
0
1
1
1
1
1
2
2
0
5
0
1
2
0
1
2
2
2
1
0
0
2
0
1
0
1
1
1
0
2
1
2
1
0
1
0
2
2
0
1
1
0
1
2
1
1
2
0
0
1
0
1
0
0
1
2
0
1
0
0
0
1
1
2
1
1
0
1
1
1
1
0
2
1
0
0
2
1
2
0
0
0
1
0
2
0
1
0
2
1
0
2
2
1
1
2
0
0
1
2
1
1
2
1
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
2
2
4
3
3
0
0
0
1
0
0
0
2
1
0
0
0
2
2
1
0
0
0
0
3
2
2
0
0
1
2
0
1
0
2
0
1
2
0
2
1
1
1
1
2
0
2
1
0
1
0
1
0
2
1
1
1
2
1
1
2
0
0
0
1
1
0
0
0
1
1
1
1
0
1
0
0
2
1
1
2
1
1
1
0
1
2
1
2
0
0
0
0
0
0
0
3
1
2
2
7
2
0
1
0
1
0
0
1
2
0
0
1
0
1
2
1
0
1
0
2
2
1
0
1
0
2
1
1
0
1
1
1
0
1
1
1
0
0
2
1
0
0
0
0
0
0
2
1
1
1
1
0
0
0
0
2
0
0
1
0
0
1
2
0
0
1
0
2
0
0
2
1
0
0
0
1
1
2
0
0
0
2
1
1
1
0
2
1
1
1
0
2
3
1
0
0
0
2
2
1
0
1
0
1
0
1
0
2
2
1
0
0
1
1
0
2
1
1
1
3
0
0
1
1
2
1
1
0
0
2
2
1
2
1
1
1
2
1
1
0
0
0
1
0
0
2
3
1
0
1
0
1
0
0
1
1
0
1
1
2
0
2
2
0
0
0
1
0
2
2
0
0
1
0
2
1
2
1
0
1
1
0
2
1
1
2
0
1
1
0
1
2
1
1
0
2
0
0
1
2
0
0
2
0
0
0
0
0
0
2
1
2
1
0
1
1
0
0
2
0
0
1
0
0
1
1
1
1
1
1
3
2
1
2
1
0
1
0
2
0
1
2
1
0
2
0
2
1
2
0
0
1
2
0
1
2
2
1
0
1
1
1
0
2
0
2
2
1
0
1
2
1
2
1
4
0
0
0
1
0
2
2
0
1
1
1
1
1
2
0
1
0
0
1
3
1
0
1
0
0
0
0
1
0
0
0
0
2
2
2
1
1
1
1
0
2
0
2
1
1
0
1
1
2
2
1
0
0
1
1
1
2
0
2
1
1
2
1
2
1
1
1
1
3
0
1
2
0
2
1
2
0
1
0
2
2
1
3
2
1
0
0
2
1
2
1
0
0
0
0
1
0
0
1
1
2
2
2
0
0
0
2
0
0
1
0
1
1
1
2
0
2
0
1
1
1
1
2
2
1
1
0
0
0
1
1
0
2
1
1
0
0
1
2
0
1
0
0
1
0
1
1
2
2
0
0
1
3
2
2
1
1
1
0
1
1
0
1
2
1
0
1
1
1
0
2
0
1
0
0
1
0
1
1
0
0
0
2
0
1
3
2
0
2
1
1
0
2
2
0
0
1
1
1
1
1
1
0
0
1
1
1
1
1
0
0
0
1
1
2
1
0
0
1
0
0
0
1
1
1
1
1
1
1
1
1
1
0
2
1
0
2
1
1
2
0
0
1
3
1
0
2
1
0
1
0
0
3
1
2
1
1
1
0
1
2
1
2
0
1
2
2
2
1
0
0
2
2
0
0
0
0
2
0
1
0
1
2
2
0
0
0
1
1
0
1
0
1
1
1
0
0
2
1
2
1
1
1
0
1
2
1
2
0
0
2
1
0
1
2
2
1
0
1
0
0
0
3
1
1
0
0
0
0
1
2
1
2
0
0
0
1
0
0
0
2
0
0
0
1
2
1
1
0
2
0
1
1
1
0
2
2
0
1
0
0
1
0
2
1
1
0
2
1
2
0
0
1
0
0
1
1
2
2
2
1
1
1
0
0
0
2
2
2
0
1
0
2
2
1
2
1
1
1
0
3
0
1
3
0
0
1
0
0
0
1
1
0
1
0
1
0
0
0
1
2
0
2
2
1
1
1
0
0
0
1
1
0
1
2
1
1
1
1
1
0
0
1
1
2
0
1
0
1
1
0
0
1
0
2
1
1
1
1
1
2
2
2
0
2
0
1
1
0
0
0
0
0
1
1
1
0
2
1
2
1
1
0
0
2
0
0
0
2
3
1
2
0
1
0
2
1
2
1
1
0
1
2
1
2
1
1
0
1
0
0
2
1
0
3
0
0
0
1
1
0
0
1
1
2
1
1
0
3
0
0
1
1
1
1
0
0
0
2
2
1
0
0
2
0
2
0
0
0
0
0
1
1
2
2
0
0
2
2
1
1
0
1
0
0
2
1
0
2
1
1
1
1
0
1
1
0
1
0
0
0
1
1
2
2
0
1
1
1
1
1
1
0
0
1
0
0
0
1
0
0
0
0
1
0
2
0
1
2
0
1
0
2
0
1
2
1
1
1
1
2
2
1
0
2
0
0
1
2
1
1
0
1
1
0
0
1
1
2
0
0
0
2
1
1
1
1
0
0
1
1
0
0
0
0
2
0
1
2
1
2
2
0
0
0
1
1
1
1
2
0
3
1
0
2
1
5
0
2
1
2
2
2
0
1
1
1
1
0
1
0
1
0
0
0
1
1
1
1
1
1
1
2
1
0
2
0
0
1
1
0
2
1
0
0
1
2
0
2
1
1
1
3
1
2
0
4
2
1
0
0
0
0
1
2
0
1
0
1
0
0
0
2
0
0
0
1
1
0
0
1
1
1
0
1
0
0
0
2
2
1
1
2
2
0
2
0
1
0
2
2
2
0
2
1
1
1
1
3
1
0
2
1
0
1
2
0
1
0
1
1
0
2
0
1
2
0
0
2
0
1
2
2
1
1
1
2
0
0
1
0
1
0
1
2
1
2
2
2
1
1
0
0
0
0
0
1
1
0
2
2
0
1
1
0
1
1
0
0
1
1
1
0
0
1
1
0
2
1
2
1
0
2
2
1
0
0
1
1
1
0
1
3
0
1
1
1
0
1
0
2
2
0
1
2
0
0
0
2
1
2
1
0
1
0
2
1
0
0
1
1
0
2
1
2
0
0
1
0
1
0
0
0
2
1
2
2
0
1
0
1
1
1
1
1
0
1
2
1
1
0
2
0
2
1
0
1
0
0
1
1
1
0
2
0
2
0
0
0
0
1
2
1
2
1
0
1
0
2
2
0
2
0
1
0
0
1
1
1
2
0
1
1
1
1
0
2
0
2
1
1
2
1
2
2
0
2
0
2
0
2
1
1
0
0
1
1
0
0
2
3
1
1
2
2
0
0
0
0
0
0
0
1
0
0
2
1
2
0
1
0
1
1
0
2
1
1
2
2
1
0
1
2
0
1
2
2
1
0
1
2
1
1
1
1
0
1
2
0
0
0
1
0
2
0
4
1
0
2
0
0
2
1
0
2
0
0
0
0
0
1
0
0
1
2
1
1
1
0
1
2
1
1
0
0
2
0
1
0
1
2
0
2
1
1
0
1
1
1
2
1
0
0
1
2
0
0
3
0
0
1
1
1
1
1
0
0
1
0
0
1
1
2
0
2
0
0
2
0
1
1
1
0
0
0
0
1
0
0
0
0
2
0
0
1
3
0
2
1
0
2
1
0
2
1
1
1
0
0
1
0
0
0
1
1
1
0
1
2
1
0
1
0
1
0
2
0
0
1
2
1
0
1
0
1
1
0
1
2
1
0
0
0
0
2
2
1
2
1
1
2
1
0
1
0
2
0
3
2
0
0
0
1
0
0
0
2
0
1
0
0
1
0
0
0
2
1
0
0
1
0
1
0
0
1
0
1
1
0
0
2
0
0
1
1
1
0
0
1
1
1
2
2
1
1
2
1
0
1
1
0
0
2
2
0
0
0
0
1
2
1
1
0
0
1
1
0
2
1
1
0
2
2
0
1
1
2
0
0
0
2
1
1
1
0
2
0
3
2
0
1
0
0
2
0
1
0
0
0
1
2
1
1
1
1
2
1
2
1
0
1
2
2
0
1
0
0
1
1
0
1
0
1
1
0
1
1
2
1
0
0
0
2
1
1
0
0
1
1
1
2
0
1
1
0
2
1
2
0
1
0
2
1
0
2
0
1
1
1
0
2
0
0
2
0
0
0
0
0
0
2
0
2
0
0
2
0
0
2
1
0
1
0
1
1
0
0
2
2
0
1
0
0
0
2
2
1
1
1
0
2
0
2
1
0
0
0
1
1
0
2
0
1
0
1
1
1
1
1
0
0
0
1
1
0
0
0
1
2
0
0
0
0
1
0
0
1
0
0
1
0
0
1
1
0
2
2
0
0
2
0
2
1
2
3
0
1
0
1
0
0
2
1
2
2
0
1
2
2
0
0
2
2
1
4
1
1
0
0
1
1
1
1
1
0
0
0
1
1
0
1
2
1
2
0
0
0
1
1
1
2
1
1
0
0
0
0
1
2
1
1
1
1
0
0
1
2
1
0
1
0
1
0
1
2
1
2
2
1
1
0
0
0
1
0
1
1
0
1
0
0
0
0
1
1
1
1
1
1
2
0
2
0
1
0
0
1
0
0
1
2
0
2
1
2
3
0
0
2
1
0
0
1
0
2
1
0
1
1
1
0
2
0
0
1
1
0
0
1
0
2
1
0
1
0
1
1
1
0
2
1
2
1
0
2
1
1
0
0
0
1
1
0
1
1
2
1
0
1
0
1
1
0
1
0
1
1
2
0
2
2
0
0
1
0
1
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
2
1
1
0
0
0
1
0
1
2
1
0
2
1
1
0
1
0
0
2
2
0
2
1
1
1
2
0
1
0
1
1
1
0
0
1
2
2
1
0
1
1
0
1
0
1
1
2
1
3
1
0
1
1
0
0
2
0
1
2
1
1
1
1
3
1
1
1
0
0
1
0
0
1
1
0
1
2
0
1
0
0
0
1
2
0
1
0
0
0
1
0
1
0
0
2
4
3
2
5
1
0
1
1
0
2
1
3
0
0
2
1
2
2
0
0
0
2
0
1
2
0
0
1
0
1
0
2
1
0
1
3
1
2
0
1
1
0
1
2
0
0
0
2
1
2
1
0
1
0
0
0
1
0
0
1
0
0
1
0
1
0
0
1
2
0
2
2
1
0
1
2
1
2
0
0
2
1
2
2
0
2
1
0
0
1
0
0
2
1
0
1
0
1
2
0
2
0
2
0
0
1
0
1
0
1
1
2
1
1
1
0
1
0
2
0
0
1
0
1
0
0
1
2
0
4
1
0
1
0
0
1
1
1
0
1
1
0
1
0
2
0
1
2
0
0
2
1
0
1
0
0
0
1
1
2
1
1
1
1
1
1
1
2
0
1
0
2
2
2
1
1
0
1
2
0
0
0
0
0
0
1
1
2
0
2
0
0
1
1
2
0
1
3
1
1
2
1
0
1
1
1
1
1
2
1
1
1
1
0
0
0
1
2
0
1
1
0
1
2
1
0
0
0
2
1
2
1
1
0
0
0
0
0
1
1
1
0
0
2
0
0
1
0
2
2
0
1
0
0
0
2
0
0
0
2
1
2
1
1
0
2
2
0
1
1
1
1
0
2
2
0
1
0
0
0
0
1
0
0
1
1
1
2
0
1
0
1
2
1
1
2
0
1
1
2
1
1
0
1
0
2
1
1
0
1
0
1
2
0
1
2
1
0
1
0
0
0
1
1
2
1
1
2
2
0
2
1
0
2
0
1
0
0
2
2
0
0
1
0
1
0
1
0
0
1
0
2
1
2
0
1
1
0
1
1
1
2
2
0
0
2
1
0
0
0
2
2
0
0
0
0
1
0
1
1
1
0
2
0
1
0
6
2
1
0
0
0
1
0
0
1
1
2
0
1
0
0
0
0
0
0
2
0
0
0
0
1
1
2
1
1
1
1
0
1
0
0
1
1
0
1
0
1
2
0
1
0
1
1
0
2
0
0
0
1
1
1
1
0
1
1
0
0
1
0
1
1
2
0
0
2
0
2
2
1
0
1
3
0
1
1
1
0
1
2
0
1
0
2
2
1
1
2
2
0
0
1
1
0
0
1
2
0
1
0
2
1
1
1
0
1
0
0
0
2
1
0
0
0
0
1
1
0
1
1
2
0
2
0
1
0
1
2
1
0
1
1
0
2
0
2
0
0
1
1
1
0
0
2
1
0
0
2
1
0
0
2
1
2
1
1
1
1
1
2
2
2
1
1
1
1
1
2
2
1
0
2
1
0
2
0
1
2
0
0
2
0
1
0
0
1
0
0
0
0
1
0
1
2
0
2
0
1
2
2
3
1
0
2
2
1
2
0
2
0
0
0
1
0
2
1
0
0
0
0
1
0
3
0
1
2
1
0
1
1
0
1
1
0
2
0
1
0
1
1
2
1
0
0
1
2
1
0
0
0
0
0
0
3
1
0
0
0
2
0
2
0
0
0
1
1
1
1
0
1
2
2
1
1
0
1
1
0
1
2
1
0
1
0
1
1
1
0
1
2
2
1
0
0
0
1
0
2
1
0
0
1
0
1
1
0
1
1
2
1
2
2
0
3
2
1
1
1
1
0
1
2
2
1
0
2
1
1
1
2
0
0
0
2
2
0
1
0
2
0
1
0
1
1
0
2
1
2
0
1
0
1
2
2
0
1
1
0
0
1
0
0
2
2
1
2
1
1
1
0
1
0
0
0
0
0
2
0
0
1
2
0
1
0
0
0
0
1
0
0
0
1
2
1
2
1
1
0
0
1
0
1
1
2
0
0
1
0
0
1
1
1
1
1
1
1
1
0
0
1
1
0
0
1
1
0
1
0
1
1
1
0
0
1
0
2
0
2
0
0
0
0
0
1
2
1
2
0
1
2
1
0
0
0
0
2
1
0
1
1
1
1
0
2
0
2
0
1
1
1
0
1
2
0
0
1
1
1
0
1
1
0
0
0
0
2
2
0
0
2
1
0
1
2
0
0
2
0
1
0
0
1
0
1
1
1
1
1
1
0
0
2
2
1
0
1
0
1
2
1
2
2
0
0
0
0
0
1
0
1
2
2
1
0
1
0
0
2
1
1
1
1
1
1
0
0
1
1
0
1
1
1
1
2
1
1
1
0
1
0
1
1
0
0
1
1
1
0
1
1
0
3
2
2
0
1
2
2
0
0
0
1
0
0
1
2
1
0
0
0
1
1
1
0
0
0
1
1
0
1
0
1
1
1
2
0
0
2
0
2
2
0
2
0
1
0
0
0
0
0
2
0
1
0
0
0
0
1
1
2
3
0
1
0
0
1
0
1
1
1
0
1
0
1
2
0
1
1
1
1
1
2
1
2
2
0
1
1
1
0
1
2
0
0
0
2
0
0
0
2
0
0
0
0
1
1
0
2
2
0
0
2
1
0
1
1
0
0
1
2
1
0
0
2
1
1
0
2
2
0
2
1
1
2
0
0
0
1
1
1
2
0
1
3
2
0
1
0
2
0
0
1
0
1
1
0
0
0
0
0
1
1
2
2
1
0
2
2
0
1
3
1
1
0
0
0
1
0
1
0
2
1
1
0
2
1
2
2
1
1
0
2
1
1
2
1
1
1
0
1
1
0
2
2
0
1
1
1
0
1
2
0
2
0
1
2
1
2
1
3
2
1
1
2
1
0
0
0
0
2
0
0
0
2
0
1
1
1
1
0
0
0
1
0
1
1
2
1
0
0
2
0
0
2
2
0
0
0
1
2
0
2
0
0
2
1
1
0
2
0
0
0
0
1
1
2
1
0
1
1
1
1
1
0
0
0
2
0
1
2
0
0
0
1
2
0
1
0
0
1
0
1
1
0
2
0
0
0
2
1
0
0
0
0
0
0
2
2
1
1
1
2
1
0
1
0
1
1
0
2
1
1
1
0
1
0
2
1
0
1
2
0
1
0
2
2
1
1
0
0
1
1
2
0
3
1
2
0
1
0
1
1
1
1
0
1
1
2
0
0
1
2
0
1
0
0
2
0
0
2
2
0
1
1
0
0
0
0
2
1
0
1
2
2
0
1
2
2
1
0
1
2
1
2
1
0
0
1
0
1
0
2
0
1
1
1
2
0
1
2
2
2
0
2
0
1
0
1
1
0
0
1
1
2
2
0
1
2
1
0
1
1
1
1
1
0
1
1
2
2
1
2
1
1
0
0
0
2
1
1
0
1
0
0
2
0
0
0
2
0
2
3
0
2
1
1
0
0
2
2
0
1
2
2
1
1
1
1
2
0
0
1
1
1
0
0
9
1
2
2
1
1
0
0
1
1
1
0
1
1
1
2
0
0
1
1
1
1
1
2
0
0
0
1
2
1
1
0
0
2
2
0
2
3
1
2
0
0
1
0
0
1
2
1
0
1
1
1
1
0
1
1
1
1
2
0
0
0
2
1
1
0
0
1
1
1
1
0
0
1
3
1
1
2
1
0
1
1
0
2
1
1
1
2
1
1
1
1
0
0
0
2
0
1
1
2
0
1
0
2
1
0
1
0
1
1
2
0
1
2
1
1
1
2
1
0
1
2
0
1
1
1
0
0
0
0
1
2
0
0
1
1
0
0
1
2
2
0
1
0
2
1
1
2
2
1
1
1
0
1
1
1
1
1
0
2
2
2
1
1
1
0
0
1
1
0
1
1
2
1
0
0
1
1
1
0
0
1
2
1
2
0
2
1
1
0
1
0
0
0
2
0
0
1
0
0
1
2
0
0
0
1
1
2
2
1
0
2
1
2
2
2
2
0
1
0
1
1
0
0
2
1
0
1
1
0
0
1
2
1
0
1
2
1
0
1
2
2
1
0
0
2
0
1
1
1
0
1
1
1
0
1
0
0
2
0
1
2
2
2
0
0
2
0
2
0
0
0
2
1
0
0
0
0
1
1
0
4
2
1
1
2
0
2
0
2
1
1
0
0
2
0
2
1
0
1
1
0
2
0
0
0
1
0
0
1
0
2
1
1
1
0
1
2
1
2
1
1
2
1
2
0
1
0
0
1
1
1
1
0
2
0
1
8
1
2
1
0
0
0
0
1
0
1
0
0
1
1
1
1
2
0
1
1
0
2
1
1
2
0
1
2
2
2
2
0
1
0
2
2
1
1
0
0
2
1
2
0
0
1
2
2
0
1
2
2
1
0
0
1
2
0
0
1
1
0
1
0
0
2
2
0
1
2
1
1
2
0
2
0
1
1
2
0
0
1
2
1
1
2
1
1
0
2
0
2
2
0
0
1
2
1
0
2
2
0
0
0
1
0
0
1
0
1
3
1
1
1
3
1
2
0
1
1
2
1
1
1
1
1
1
0
0
1
2
1
0
0
1
1
0
1
0
0
1
0
1
2
1
0
2
0
1
1
0
2
2
2
1
1
0
1
2
0
2
2
1
0
1
1
0
1
2
1
1
0
2
0
1
0
2
0
2
1
0
1
1
1
0
0
0
0
1
1
1
1
1
1
1
1
1
3
0
1
1
1
0
0
1
1
0
1
0
0
2
2
1
1
2
0
1
0
2
0
2
0
2
1
0
0
0
2
1
0
0
0
0
0
1
2
0
2
1
1
1
1
1
2
1
1
0
0
0
0
0
0
2
1
1
1
0
0
0
2
2
1
2
2
0
0
0
1
1
1
1
1
2
1
2
3
0
0
0
0
1
0
1
0
1
1
1
2
0
1
2
1
1
2
1
2
0
1
1
0
1
1
1
1
3
2
1
0
0
0
0
2
0
1
2
1
1
1
0
2
1
2
0
2
1
1
1
1
0
0
0
2
2
0
0
2
1
1
1
2
1
2
1
0
1
1
1
0
1
0
0
1
2
2
2
2
2
0
1
1
1
2
0
1
0
2
0
1
0
1
1
0
2
1
1
0
0
0
1
1
2
1
1
0
1
2
1
2
2
2
1
1
0
1
0
1
0
0
0
3
2
1
2
0
1
2
0
1
2
1
0
1
1
0
2
2
0
0
2
0
1
1
0
0
2
0
1
1
0
0
1
1
0
0
1
1
2
1
0
2
0
2
2
0
0
0
2
0
1
4
0
1
3
0
0
2
0
1
0
2
1
0
0
2
2
3
2
1
2
1
2
1
1
1
0
1
1
0
2
1
0
1
0
0
1
2
0
1
2
1
0
0
2
1
1
1
1
1
1
0
2
0
1
0
1
1
1
0
1
1
1
0
1
0
4
0
3
2
0
0
0
2
0
0
1
0
2
1
0
0
1
1
1
0
1
0
1
0
2
1
0
0
1
0
0
2
2
1
1
0
0
0
1
0
0
1
1
2
2
1
0
1
1
1
1
1
1
0
1
0
2
0
0
0
2
2
1
2
1
1
0
1
0
2
1
0
1
0
0
2
0
2
0
3
1
0
0
0
0
2
0
2
0
0
0
0
0
0
2
1
0
1
1
0
1
1
2
0
2
1
0
0
1
0
0
1
0
1
0
1
1
2
1
1
1
0
0
2
2
1
1
1
1
1
0
2
1
1
1
2
0
2
1
0
0
1
1
0
1
1
2
0
0
2
0
2
2
2
0
0
0
2
1
2
0
0
0
2
1
2
2
2
1
1
0
0
1
2
1
0
2
1
1
0
1
1
0
2
1
2
1
1
2
0
0
0
2
0
1
2
2
0
0
2
0
1
0
1
2
2
1
1
2
0
1
1
0
2
1
1
0
2
0
2
2
0
1
1
0
1
1
0
1
0
0
2
1
2
1
2
1
0
0
1
2
1
1
2
2
0
2
0
0
2
0
0
1
2
0
1
0
0
0
2
0
2
2
0
1
0
1
0
1
1
1
0
1
0
0
1
1
0
0
1
1
2
1
2
0
1
1
2
0
0
1
1
0
2
0
0
0
1
1
1
0
0
2
3
1
2
0
0
0
1
1
1
0
1
0
1
2
1
0
1
0
0
1
0
1
1
0
0
2
1
1
0
1
1
1
0
1
1
2
1
1
1
3
0
0
0
0
2
2
0
0
1
1
1
1
1
0
1
0
1
1
1
0
1
1
2
0
0
1
0
2
1
0
1
1
0
0
1
6
0
0
1
2
0
0
1
0
1
1
0
0
0
0
0
2
0
1
1
2
2
2
1
0
1
2
1
0
2
0
1
1
0
2
2
1
0
4
1
0
0
1
1
2
0
2
1
1
2
0
3
0
1
0
1
2
1
0
0
2
0
1
1
2
0
2
0
0
0
0
2
0
2
0
0
0
2
2
1
0
0
0
1
2
2
0
1
1
1
0
0
1
1
1
0
0
2
1
2
1
1
1
0
0
1
2
0
0
0
0
1
2
0
0
0
1
1
1
1
0
0
0
3
2
0
1
0
0
0
2
0
2
1
2
0
0
4
0
1
1
0
0
0
1
0
3
0
0
0
1
2
1
2
2
0
0
2
1
0
1
1
0
2
1
0
1
0
1
0
2
1
0
0
2
2
2
0
0
0
0
1
2
2
0
1
0
2
1
0
0
2
1
0
0
0
1
1
0
0
1
2
2
1
0
0
2
1
1
0
2
2
1
0
1
1
1
1
0
2
0
1
1
2
0
0
2
1
1
1
8
0
0
1
0
0
2
1
1
1
2
1
0
1
1
1
1
2
0
1
0
0
0
0
0
0
3
2
2
1
1
1
2
1
2
0
2
2
0
2
0
1
0
0
1
0
2
0
0
1
2
1
1
1
1
0
2
0
0
1
0
3
0
0
1
0
2
1
1
1
2
0
0
0
1
1
1
1
0
2
1
0
0
1
0
0
0
2
0
1
1
0
0
1
0
0
1
1
1
0
0
1
1
1
0
1
2
3
0
1
2
1
2
1
2
0
0
0
2
0
1
1
2
1
1
0
2
0
0
1
2
0
0
1
0
1
0
0
1
2
0
2
1
0
2
1
2
0
1
0
1
3
2
2
0
0
1
0
0
0
1
0
0
0
0
1
0
2
0
1
2
2
1
0
0
0
0
0
0
0
2
1
2
2
1
2
1
2
1
2
1
1
2
2
1
1
1
1
1
1
1
0
1
0
2
1
0
0
0
1
0
1
0
1
1
3
1
1
1
0
2
1
2
1
2
0
1
0
0
1
1
1
0
2
1
2
0
0
1
2
2
1
0
1
2
1
1
1
2
1
1
1
2
1
0
1
4
0
2
0
1
0
0
1
0
0
2
1
0
0
1
2
0
2
1
2
3
0
1
1
1
1
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
1
1
0
0
0
0
2
1
3
0
1
1
1
0
1
2
1
0
1
1
0
1
1
1
2
1
1
2
2
0
1
1
1
1
0
0
0
0
2
1
0
0
1
0
7
0
1
2
0
0
0
1
2
1
1
0
1
1
2
1
1
2
0
1
1
1
1
2
1
2
0
1
0
0
0
0
1
2
0
1
0
1
0
1
0
1
0
2
1
1
0
1
1
0
1
2
1
0
0
2
2
0
1
3
1
1
0
0
1
1
0
0
0
2
0
0
1
0
1
1
2
2
1
0
0
1
2
1
1
2
0
0
0
1
3
0
0
2
1
1
1
1
2
1
1
2
1
2
0
2
1
0
0
0
1
1
1
0
1
0
1
0
1
0
1
2
1
1
0
1
0
2
2
1
2
1
1
0
1
1
2
0
1
1
1
1
0
0
1
2
0
0
1
0
0
0
1
2
1
1
0
0
1
2
0
1
2
1
1
0
1
1
1
1
1
2
0
1
2
2
1
0
1
0
1
1
1
2
1
1
1
1
1
1
2
0
1
1
1
1
0
1
1
0
0
1
0
1
2
0
0
0
2
2
0
0
1
0
1
0
0
1
1
0
0
2
0
1
1
0
1
2
1
2
2
1
0
2
1
1
0
4
2
0
1
0
0
2
1
1
0
1
1
0
1
1
0
1
1
1
1
1
1
1
1
1
1
2
1
2
0
1
2
1
3
2
2
1
1
1
0
2
2
1
0
2
1
0
0
2
1
0
2
1
2
0
0
2
0
1
0
2
0
0
2
1
1
2
0
1
0
1
1
1
0
0
2
1
1
1
0
0
2
1
1
0
1
2
1
1
1
0
0
0
0
1
1
0
0
0
2
0
0
1
0
0
1
1
1
0
1
1
1
2
3
1
1
1
0
2
0
1
2
1
2
0
2
0
1
0
1
0
1
1
1
2
0
2
0
0
0
0
1
0
2
2
1
1
0
0
1
1
1
1
1
1
2
1
1
2
4
0
1
0
0
1
1
0
2
0
0
0
0
0
2
1
2
1
1
1
2
2
1
1
0
0
1
1
0
2
0
0
1
0
0
0
2
2
0
0
1
1
1
2
1
1
0
1
1
1
1
0
2
2
2
0
3
0
1
0
0
0
0
0
2
3
0
1
0
1
1
1
2
0
0
1
1
2
0
0
0
1
1
1
1
2
1
1
0
3
0
0
2
1
1
0
1
0
2
0
3
0
0
1
0
0
0
1
1
0
1
1
2
0
0
0
1
0
0
0
1
0
0
0
2
0
1
0
0
1
1
1
0
0
2
1
1
1
0
2
0
0
1
1
1
2
0
0
2
0
0
1
0
0
1
1
0
0
1
1
0
0
2
1
0
0
0
1
1
0
2
1
0
1
0
2
0
1
1
0
0
2
2
0
2
1
0
0
1
1
0
0
1
0
0
1
2
0
2
0
2
2
2
2
1
1
1
1
0
1
1
2
0
2
1
2
2
2
2
0
0
2
1
0
1
0
0
0
0
2
0
1
0
0
2
2
1
0
2
1
0
0
1
0
1
1
1
2
1
0
0
1
2
0
2
1
1
1
1
2
1
0
0
1
1
0
0
2
2
2
0
0
0
3
0
2
1
0
1
2
0
0
0
0
1
2
0
0
0
1
1
0
2
2
1
0
0
2
1
2
1
1
0
1
0
2
0
1
0
0
0
0
0
1
1
1
1
0
0
2
1
1
1
1
2
0
0
1
0
1
0
0
1
1
2
0
2
1
2
1
2
0
1
1
2
2
1
0
1
1
0
0
0
1
0
1
2
1
1
1
1
1
2
0
2
1
2
0
1
1
2
0
1
2
1
1
1
0
2
0
1
1
0
1
2
1
2
1
1
0
0
0
0
1
1
0
1
0
0
1
1
2
0
0
0
1
1
0
1
0
1
1
1
1
2
2
0
0
0
0
0
2
0
0
1
2
0
1
0
0
1
2
0
1
0
1
1
1
0
1
0
1
1
0
0
1
0
1
1
1
0
0
0
0
1
0
0
0
1
1
1
1
1
0
0
0
0
0
0
1
0
2
1
1
1
1
0
0
0
1
1
2
1
0
0
4
1
1
1
2
0
1
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
2
0
0
1
1
2
0
1
0
2
1
2
0
1
2
1
0
0
2
1
0
1
1
1
2
1
1
2
1
0
0
1
1
1
0
1
2
0
0
2
1
0
0
1
1
1
1
1
1
2
0
1
0
1
0
0
1
1
0
1
0
0
0
1
0
1
1
0
0
2
0
0
0
1
1
2
2
1
1
1
0
1
1
0
0
1
1
1
1
1
0
0
3
2
2
1
1
0
0
2
2
0
0
2
1
2
0
0
0
1
0
0
1
3
0
1
1
1
0
0
1
0
1
1
1
1
0
2
0
0
0
0
1
0
0
0
0
1
0
0
1
1
3
2
1
0
1
2
2
1
0
1
1
1
1
2
0
0
2
0
1
2
2
0
1
0
0
0
0
1
0
3
0
2
1
1
2
3
1
0
1
1
1
2
0
1
0
2
2
0
2
1
2
0
1
0
1
1
1
0
1
0
1
0
0
1
1
2
2
2
0
1
0
1
0
1
1
2
2
2
0
2
1
0
2
2
0
0
0
2
1
1
2
2
0
0
1
0
2
2
2
0
2
1
2
3
0
2
1
2
1
0
0
2
2
2
1
0
0
0
2
0
1
1
2
0
0
1
1
1
0
0
1
1
2
2
0
0
2
1
1
1
1
2
1
0
2
0
2
1
1
0
1
1
1
1
0
2
1
1
2
2
0
0
1
2
1
1
1
2
1
2
2
0
1
1
2
1
0
1
1
1
1
0
0
0
0
0
0
0
2
1
0
0
1
1
0
0
1
0
0
2
0
0
2
2
0
0
0
0
1
1
0
2
2
1
1
2
1
2
1
0
1
0
0
1
0
0
3
0
1
0
0
1
2
1
1
1
2
1
1
2
1
1
0
1
0
2
2
1
0
0
1
1
0
2
1
1
0
0
0
2
2
1
0
2
2
1
1
2
0
1
0
0
0
2
1
2
1
2
1
1
0
2
1
1
1
0
1
1
0
0
0
2
2
3
1
0
0
0
2
1
2
1
2
1
2
1
1
2
1
1
2
0
1
0
1
2
1
2
1
1
3
0
1
1
0
1
2
0
2
0
0
1
1
0
0
1
1
1
1
0
1
0
1
0
2
1
0
0
1
0
1
3
1
0
0
0
1
2
2
0
0
0
1
1
0
0
2
2
0
1
0
0
0
2
1
2
3
0
0
0
2
4
3
1
1
1
0
2
1
0
2
1
0
0
0
1
0
1
1
0
1
0
1
1
0
1
0
2
1
2
1
0
0
1
1
0
1
0
0
0
0
0
2
1
3
1
2
2
1
1
2
2
1
1
1
1
1
2
2
1
2
0
2
0
0
1
1
0
0
0
2
0
2
1
1
0
1
1
0
0
0
1
1
1
1
1
2
0
2
0
1
1
1
1
2
0
2
1
1
1
0
1
0
1
1
0
1
3
0
0
1
1
1
1
2
0
1
0
0
2
0
1
0
0
1
1
2
1
1
1
1
0
0
1
1
2
1
1
1
2
1
0
1
1
1
2
1
0
1
6
0
0
2
0
0
0
2
1
1
0
1
1
1
1
1
0
0
2
0
1
1
1
2
1
1
0
3
0
2
1
3
0
0
2
0
2
0
2
0
0
2
0
1
2
0
0
0
2
1
0
0
0
0
2
0
3
0
0
1
0
1
0
1
1
1
1
1
0
0
2
4
1
1
1
0
1
0
2
1
1
2
0
0
1
0
1
0
1
0
1
0
3
2
1
1
1
2
1
1
0
0
1
1
2
1
1
0
0
1
1
1
2
2
2
0
2
1
0
1
1
1
0
1
0
0
0
1
1
1
0
1
1
0
1
0
2
0
0
0
1
0
0
0
1
0
1
0
1
1
1
1
0
1
1
1
2
0
0
0
1
2
2
1
0
0
2
2
1
0
2
1
0
0
0
0
2
1
1
1
0
0
1
0
0
0
2
0
0
1
1
0
0
2
0
2
1
0
1
0
1
0
0
0
1
0
1
1
0
0
0
0
1
1
1
0
0
2
2
2
0
0
1
1
0
6
0
1
0
0
1
1
0
0
3
0
0
4
2
0
1
2
0
2
3
2
2
1
0
0
0
1
0
1
2
4
1
0
2
1
1
0
1
2
1
1
0
3
0
0
0
0
0
2
2
2
0
1
1
0
1
1
1
0
0
2
2
2
2
2
1
0
1
1
0
1
2
1
0
0
0
0
2
1
0
0
1
1
1
1
1
1
0
0
1
0
4
1
1
0
0
0
1
1
2
1
1
1
1
1
2
0
1
2
1
0
1
0
2
1
0
1
1
0
0
3
1
0
0
0
1
1
0
1
0
2
1
0
2
2
1
0
1
1
0
2
2
0
1
0
2
0
2
1
2
1
2
0
2
0
1
1
1
0
0
0
2
0
1
2
1
0
1
1
1
0
1
1
1
0
0
1
1
1
1
2
0
0
0
0
0
1
1
0
1
0
0
1
3
0
2
1
0
3
2
1
1
0
0
1
1
1
0
1
2
1
0
1
0
1
1
0
2
1
1
1
2
0
0
2
1
1
0
1
2
1
2
1
2
1
0
0
0
0
1
1
2
2
0
1
2
0
2
1
1
0
0
1
0
1
0
2
0
1
1
1
1
1
1
2
2
0
1
1
1
7
2
1
0
0
0
1
1
2
0
0
2
1
0
2
1
1
2
1
1
0
2
0
0
2
1
0
0
1
2
0
2
2
0
0
1
2
0
0
0
0
0
1
1
2
2
1
2
1
0
0
0
2
1
0
1
2
1
2
1
1
0
2
2
0
1
0
0
1
0
2
0
1
0
1
0
1
2
2
1
2
1
0
1
2
0
0
2
2
1
1
2
2
0
0
1
0
1
0
0
1
0
0
2
1
0
1
1
1
1
2
1
0
1
2
1
0
1
0
0
2
1
1
1
0
1
0
3
1
1
0
0
1
1
0
1
1
1
2
0
1
1
0
0
1
2
1
0
1
0
0
1
1
1
2
2
1
1
1
0
2
1
0
1
1
1
0
2
2
2
0
2
1
2
0
1
0
0
2
0
0
2
1
0
1
0
1
0
1
1
1
0
0
1
2
2
1
0
0
1
0
1
0
0
0
1
0
2
1
0
1
0
0
2
0
1
0
0
1
1
0
1
0
0
2
0
1
0
1
1
1
2
0
1
0
1
0
1
1
1
1
2
0
0
3
0
1
0
0
2
1
1
0
0
2
0
1
0
3
1
2
2
0
0
0
1
0
0
1
0
1
1
0
1
1
1
2
1
1
1
2
0
1
2
1
0
2
1
0
2
2
0
0
0
1
0
0
1
1
1
2
1
1
0
0
0
1
1
0
1
1
0
2
0
2
1
0
0
0
2
1
0
2
0
1
2
0
0
0
2
1
1
1
3
2
0
1
1
2
1
0
0
1
1
1
0
0
0
0
2
2
1
0
0
0
0
0
1
0
0
1
0
1
1
1
0
1
0
2
2
1
1
1
0
0
1
0
0
1
1
0
0
8
2
1
2
1
1
2
1
1
1
0
0
0
1
2
0
2
0
1
0
2
1
0
0
0
2
0
2
2
1
1
0
2
1
0
0
0
0
2
1
0
1
0
0
1
1
0
0
0
3
1
2
0
1
2
2
1
1
2
0
2
0
0
1
0
2
0
1
1
1
2
0
1
2
1
0
0
2
0
1
0
1
1
1
0
0
0
1
1
0
0
1
0
1
0
0
1
1
1
1
0
1
1
1
0
1
2
1
1
2
1
2
0
0
0
1
2
1
1
1
1
1
5
0
0
0
0
2
0
1
1
1
2
1
0
1
1
1
0
0
2
2
1
1
1
0
0
1
0
2
1
0
1
1
2
1
0
3
1
2
0
1
2
0
1
0
2
1
2
1
0
1
0
2
0
0
0
1
0
0
0
1
1
1
0
0
1
1
1
0
2
0
0
0
1
0
2
2
1
2
0
1
0
2
0
2
0
1
1
0
1
0
0
2
1
0
2
1
0
2
0
0
1
0
2
0
2
1
2
2
1
1
1
1
0
0
1
3
0
1
0
1
0
0
1
2
2
0
0
0
1
0
2
0
2
0
3
0
1
0
1
2
0
0
1
0
1
1
0
1
1
1
1
0
0
0
0
0
0
0
0
1
0
1
2
1
2
0
1
1
0
0
0
1
2
1
0
1
1
0
2
0
1
1
0
0
1
2
0
0
1
0
1
0
2
1
1
0
2
1
0
0
3
2
0
1
2
2
0
1
2
1
3
0
1
1
2
2
1
1
1
1
2
1
1
2
2
2
0
1
1
0
0
0
0
1
2
1
1
1
0
1
2
1
0
3
1
0
1
1
0
0
0
0
1
2
1
0
2
2
1
2
0
1
0
1
1
1
0
1
2
2
1
0
1
1
2
1
1
1
0
1
1
0
2
3
1
0
1
0
0
1
0
0
1
1
0
0
1
0
2
2
1
2
1
0
1
1
2
1
2
2
0
0
1
0
0
1
0
1
1
2
0
1
1
0
0
0
1
0
1
0
1
1
2
0
0
1
1
0
1
1
2
1
0
0
0
2
1
2
1
0
2
2
9
0
1
1
1
1
1
0
2
1
1
1
2
1
3
1
0
0
0
1
0
2
1
2
1
1
2
1
1
1
1
0
27
1
2
0
1
0
1
0
2
1
0
1
2
0
1
2
2
0
1
1
2
1
0
2
1
2
1
0
1
2
1
0
1
0
1
0
1
1
1
0
0
1
1
2
2
0
2
2
1
1
1
1
1
0
1
0
1
0
2
3
1
1
2
0
0
1
0
0
4
0
1
1
1
0
1
1
0
1
2
0
1
1
0
3
1
2
2
1
0
1
1
1
1
1
2
1
1
0
1
0
1
0
1
1
2
2
4
0
1
1
1
1
0
0
2
1
2
1
2
1
1
2
0
1
1
0
0
0
0
0
0
2
1
2
1
0
1
0
3
0
1
0
1
1
1
1
1
1
0
1
3
1
1
1
1
1
2
2
2
0
0
1
1
2
1
0
2
1
1
0
1
0
0
1
2
1
1
0
2
2
1
1
2
1
1
0
0
2
2
0
0
0
1
1
0
0
0
1
1
0
1
0
1
1
0
2
1
2
0
1
0
1
1
2
0
1
2
0
1
0
1
1
0
2
2
2
1
1
0
0
2
2
1
1
1
0
1
1
1
2
1
1
0
1
1
0
0
1
2
1
0
1
0
1
1
0
2
0
1
1
1
1
1
1
0
0
2
0
0
1
0
2
2
2
0
0
1
0
3
2
6
0
1
2
0
0
0
1
0
0
1
0
1
1
0
1
1
1
2
2
0
0
1
0
0
1
1
0
0
2
0
0
1
0
2
0
1
1
1
0
1
0
1
0
2
2
1
0
2
0
1
0
2
0
2
0
1
2
1
1
0
1
1
0
0
1
0
0
2
0
1
1
1
3
0
2
0
2
0
1
1
1
1
1
2
2
1
0
1
0
1
0
2
1
0
1
2
1
1
0
1
0
2
1
0
1
1
1
1
1
0
2
2
2
2
1
2
0
0
2
0
0
1
2
0
0
1
1
0
1
1
1
1
1
1
2
1
0
1
1
2
1
1
2
0
1
0
0
0
1
1
0
0
2
2
2
0
0
1
0
0
2
0
2
0
1
0
1
1
0
0
1
1
0
2
2
2
0
2
2
0
0
2
1
1
1
0
1
0
1
0
0
0
0
2
1
0
1
2
1
1
0
0
1
2
0
2
1
1
0
1
0
1
0
1
2
2
2
2
1
1
2
1
0
2
1
1
0
2
1
0
0
2
0
0
1
1
2
2
1
1
1
0
0
1
1
2
2
1
1
0
2
1
2
1
1
1
1
2
0
1
1
0
0
0
1
2
1
2
1
1
1
0
2
1
1
1
2
1
0
0
1
2
1
1
0
0
0
0
0
1
0
0
1
1
0
0
1
5
1
0
0
1
1
1
1
1
1
1
1
1
2
1
1
1
0
0
1
3
1
1
2
0
2
1
2
0
1
0
1
1
0
0
1
1
0
2
0
1
2
2
1
0
1
0
1
1
6
0
0
2
0
1
0
2
0
0
2
1
0
0
2
0
1
0
0
0
0
1
1
1
1
1
0
0
0
2
1
3
0
1
3
0
0
1
5
2
2
0
1
2
1
0
0
1
0
1
0
1
1
1
1
1
1
1
1
0
1
0
1
0
1
0
1
0
1
1
1
2
0
1
0
0
2
0
0
1
1
1
1
1
1
1
2
0
2
1
0
0
1
2
1
1
2
1
0
2
0
0
1
1
0
1
0
0
0
3
2
1
1
0
1
0
0
1
1
0
1
2
3
0
1
0
0
1
0
0
2
0
1
2
1
2
0
1
2
0
2
0
0
0
0
0
0
1
1
0
0
1
0
1
1
2
0
0
0
1
0
1
0
2
1
2
1
0
1
1
0
2
1
0
1
1
1
1
0
1
3
0
2
1
1
0
2
1
0
0
0
0
2
0
0
1
1
1
2
0
0
2
0
1
0
0
1
0
0
0
1
0
0
2
0
2
0
0
0
2
0
4
2
0
0
1
3
1
2
2
1
1
0
0
1
0
0
2
0
1
0
2
1
1
1
2
1
2
2
1
0
0
0
1
1
1
1
0
1
1
0
2
0
0
3
1
0
1
2
2
2
1
0
1
1
0
2
1
0
2
0
1
1
1
2
2
2
0
1
2
1
2
0
2
2
2
1
2
2
2
0
0
2
2
0
1
0
1
0
0
0
2
0
0
2
1
2
1
1
2
2
1
0
2
1
0
1
0
2
1
1
0
0
2
1
2
1
1
1
0
0
1
0
0
1
0
1
2
1
0
0
1
0
0
1
2
1
1
1
0
1
2
0
0
1
1
1
0
2
1
1
1
0
1
4
2
1
2
2
2
1
1
0
1
1
0
1
1
0
1
1
1
1
2
1
2
1
1
1
3
2
1
0
1
2
1
1
2
1
0
2
1
0
1
1
1
1
1
0
2
2
0
2
2
1
1
0
0
0
0
4
2
1
1
2
0
1
0
2
0
2
1
0
1
2
1
0
1
0
1
0
1
0
1
2
1
0
0
0
0
2
1
1
0
1
2
0
2
1
1
0
2
0
0
0
0
2
1
0
0
1
0
0
1
0
1
0
0
0
1
2
2
2
1
1
1
0
0
0
1
2
1
0
1
0
0
2
0
1
0
1
0
2
1
2
2
1
0
0
0
0
0
0
1
1
0
0
0
2
0
2
0
2
2
2
2
2
0
0
2
0
1
2
1
2
0
0
0
2
1
0
1
1
1
2
1
1
0
2
2
1
1
1
0
1
0
0
0
0
1
2
1
2
2
2
1
1
0
0
0
1
0
0
1
2
0
2
1
0
2
2
0
2
0
2
1
1
0
1
0
1
2
0
0
1
0
0
1
2
0
0
0
1
2
1
1
1
2
1
2
1
1
1
1
0
2
0
2
1
1
2
1
1
0
2
0
1
0
1
2
2
0
0
2
1
2
1
1
0
0
0
1
2
1
2
0
1
0
1
0
1
1
0
1
0
2
1
2
0
1
1
0
1
1
1
2
2
0
0
0
0
0
2
1
1
0
1
1
2
1
2
1
1
4
2
0
2
1
1
0
1
2
1
1
1
0
1
2
0
2
1
2
0
0
0
1
2
1
0
0
1
2
2
0
0
1
2
0
0
1
3
2
0
1
0
1
0
1
0
3
0
1
0
1
2
1
0
0
1
2
0
0
1
1
1
2
0
1
1
1
0
2
1
1
1
2
2
0
2
2
0
1
0
1
0
1
0
0
1
2
1
0
0
1
1
0
1
1
2
0
0
2
1
0
1
0
0
1
1
0
2
1
2
1
0
0
0
1
0
2
0
1
0
0
0
1
1
2
1
2
1
1
2
1
2
2
0
1
1
1
1
1
2
0
0
1
1
1
2
2
0
0
1
1
1
1
0
1
1
0
1
1
0
1
1
0
0
0
0
2
0
0
1
0
0
1
0
0
2
1
1
1
0
1
0
0
1
4
0
1
1
1
1
0
0
1
1
1
0
0
1
0
0
1
1
2
1
1
2
0
1
0
0
0
1
0
0
1
0
1
1
1
1
0
2
1
0
1
2
1
0
0
2
1
2
2
1
2
2
0
1
0
2
3
1
0
1
1
2
0
5
1
0
1
2
2
0
0
2
1
1
1
2
1
1
2
0
2
1
1
0
2
2
2
0
0
0
0
1
2
3
1
0
1
1
0
1
1
0
2
0
1
1
1
1
1
0
0
1
3
1
1
1
2
1
0
0
1
0
2
0
0
1
2
0
0
1
1
2
2
0
2
2
1
0
2
1
2
1
1
0
0
0
0
0
1
1
2
1
1
0
2
2
0
0
1
1
0
0
0
0
0
1
0
2
1
1
0
0
2
1
1
2
0
0
2
2
1
1
0
1
0
1
0
0
0
1
0
0
0
1
2
1
0
2
1
0
1
1
1
0
1
1
0
1
0
2
0
0
2
1
0
1
0
1
1
0
2
2
0
1
0
1
1
2
2
2
1
2
3
1
1
2
1
1
1
1
0
1
2
1
2
1
0
0
1
2
1
0
0
0
1
2
0
0
1
1
3
2
2
0
0
2
0
2
1
1
2
0
2
0
0
1
2
0
0
1
0
2
0
0
2
1
0
2
0
1
1
2
1
0
0
1
1
0
0
0
0
1
0
2
2
0
0
2
1
1
1
0
0
0
0
1
1
1
3
2
2
1
1
2
0
0
2
1
0
1
2
2
0
1
1
0
0
2
0
2
2
1
0
1
0
0
2
1
1
2
0
0
0
1
1
0
1
1
1
2
2
0
0
2
0
1
0
0
2
1
1
1
0
1
0
1
2
1
0
0
0
1
1
1
0
2
1
0
2
0
0
1
0
1
1
0
1
0
0
1
0
1
2
1
0
1
1
0
2
0
1
0
1
1
0
1
1
1
0
1
0
1
0
2
0
1
1
1
2
2
0
1
0
1
1
0
2
1
0
2
1
1
1
2
1
0
2
1
0
1
0
0
1
0
1
2
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
2
1
1
0
1
0
1
2
1
1
1
0
2
1
3
1
0
2
0
2
0
1
0
0
0
0
1
2
1
0
0
0
1
0
1
1
2
1
0
0
1
2
0
1
2
0
2
0
2
0
1
1
2
2
1
0
1
2
1
2
0
1
1
1
0
1
1
0
1
1
2
0
1
2
2
1
0
0
1
1
1
1
0
1
2
1
1
2
2
1
1
0
1
2
1
2
1
1
0
1
1
4
1
2
0
2
0
0
0
1
0
0
2
0
1
0
0
2
1
0
2
1
2
1
0
0
1
0
0
2
0
1
0
1
3
0
1
1
2
0
0
0
2
0
1
1
0
1
3
2
1
0
1
0
0
0
2
1
0
0
2
2
0
1
3
2
0
2
0
0
0
0
1
0
1
1
2
0
1
1
2
0
1
0
0
1
1
1
1
1
0
0
1
0
2
0
1
0
1
1
1
1
2
2
3
1
2
2
0
1
1
0
1
1
0
0
1
3
1
0
0
1
2
1
2
0
2
1
0
0
1
0
0
0
2
3
1
2
1
2
1
0
0
1
1
0
1
0
2
0
1
0
0
1
1
1
0
2
0
0
1
2
0
4
0
2
2
0
1
2
2
1
1
1
1
1
1
0
1
0
1
2
2
1
0
1
2
0
0
2
2
0
1
1
0
0
0
1
1
1
1
1
1
1
2
1
0
1
1
1
1
1
1
1
1
2
0
0
1
1
0
1
2
0
1
1
1
1
1
0
1
2
1
0
0
2
1
0
1
1
1
0
2
0
2
1
1
1
1
0
0
2
0
0
0
1
1
1
0
2
1
0
0
0
1
0
1
0
0
1
2
0
2
1
0
0
0
2
2
0
1
0
1
0
1
1
1
0
1
0
2
0
0
0
1
1
1
0
0
1
2
0
1
0
1
0
2
2
4
0
1
1
1
0
1
0
1
1
0
1
0
0
3
1
1
1
1
1
0
0
1
3
0
1
1
0
2
1
0
0
2
2
1
0
0
0
2
1
0
0
1
2
0
1
2
1
1
0
0
0
2
0
0
1
0
1
1
2
1
0
0
1
1
1
1
1
2
1
1
1
0
1
2
0
1
2
0
0
0
1
1
0
2
0
0
1
2
0
1
2
2
2
2
2
0
1
0
1
1
2
0
2
1
0
1
1
1
1
1
0
0
1
1
1
0
2
3
1
1
1
1
0
0
1
1
1
2
1
0
1
2
2
0
0
1
0
0
1
2
0
1
1
1
0
0
0
0
0
0
1
0
1
0
1
0
2
0
0
0
1
0
1
0
1
1
1
2
1
2
1
1
1
0
1
2
2
1
0
1
1
2
2
0
0
1
0
0
1
0
1
1
1
0
1
0
1
0
1
2
0
2
0
0
1
0
1
2
0
2
1
0
1
1
1
2
0
1
2
2
1
0
0
2
1
1
1
1
0
0
2
1
2
2
0
2
1
0
0
1
1
1
2
0
1
2
0
1
1
1
0
0
1
1
0
0
2
2
2
2
2
0
1
1
0
1
1
1
0
1
0
2
0
0
2
0
0
2
0
1
1
0
0
0
1
1
0
1
1
0
0
2
1
1
1
1
0
0
1
0
1
2
0
2
1
1
2
2
2
2
2
1
2
2
2
0
0
1
2
0
2
1
0
1
1
0
0
0
0
1
0
2
1
1
0
0
1
1
1
0
0
0
2
0
2
0
1
1
1
1
1
1
1
0
1
1
1
0
1
1
0
1
0
0
0
0
3
0
0
0
0
0
2
1
2
2
1
0
0
2
1
2
1
1
0
0
2
3
0
2
1
1
1
0
0
0
1
1
2
2
0
0
0
1
1
1
1
1
1
1
0
1
0
1
0
1
0
0
1
1
1
1
1
1
2
1
0
1
1
0
0
2
1
0
0
0
0
2
0
0
0
2
0
1
0
2
0
2
5
9
1
0
0
1
0
2
0
2
2
2
2
1
0
0
1
1
1
1
1
1
2
1
0
0
1
0
1
1
1
1
2
1
0
0
0
2
0
0
0
2
1
1
1
2
0
2
0
0
1
0
2
1
3
2
1
2
1
0
2
1
0
1
2
1
0
2
0
2
1
1
1
0
2
0
0
0
0
1
1
1
1
1
2
2
0
1
0
2
2
0
1
0
1
2
1
2
1
2
1
1
2
0
2
0
0
0
2
1
3
2
1
0
1
1
1
1
1
1
1
0
1
1
1
2
2
0
1
1
0
2
1
1
0
0
1
0
0
1
2
1
0
0
4
0
1
0
0
1
0
0
1
2
0
0
1
2
0
0
2
0
1
2
1
0
0
2
2
0
0
0
1
0
2
0
2
1
1
1
2
0
0
2
2
0
1
0
1
1
1
1
0
0
0
2
2
1
0
1
2
1
0
1
0
2
0
1
1
2
0
2
2
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
1
0
1
0
1
1
1
1
0
0
0
1
1
1
1
1
1
2
0
1
1
1
1
0
0
2
1
2
1
1
1
0
0
2
0
1
1
2
0
1
1
2
0
0
1
1
1
1
1
0
1
2
1
0
0
2
2
0
2
3
0
1
1
1
2
1
0
1
1
6
1
1
0
2
0
0
1
0
0
0
0
0
1
2
1
1
3
0
1
1
1
1
1
0
0
0
1
1
1
0
0
1
2
1
1
1
0
1
2
1
2
0
0
2
0
1
2
1
1
0
2
2
0
1
2
1
0
2
1
0
1
1
1
2
0
0
0
2
0
2
0
2
1
1
1
1
0
1
0
0
2
0
2
0
2
0
1
1
1
1
0
2
2
2
2
5
1
3
1
0
2
0
1
1
1
1
0
2
1
0
0
2
0
1
0
2
2
0
1
0
1
0
1
1
1
1
0
2
0
1
0
2
2
1
0
2
2
1
0
1
1
1
1
0
0
0
1
1
0
1
1
0
1
3
0
1
0
1
1
1
1
0
2
1
1
1
2
1
3
1
0
1
0
0
1
1
1
1
1
0
1
0
2
0
1
1
1
1
0
0
1
1
0
2
2
0
4
1
2
2
2
0
1
1
1
2
1
1
2
0
0
1
1
1
0
1
0
1
1
1
0
1
1
1
0
0
0
0
2
1
0
1
1
1
1
1
1
0
2
1
2
1
2
0
1
2
2
1
1
0
1
1
1
2
2
1
1
0
2
1
0
1
0
0
2
1
0
1
0
0
1
2
1
2
2
1
0
1
0
2
1
0
0
0
0
0
2
0
0
0
2
1
1
1
2
0
0
0
1
3
0
1
2
1
0
0
0
1
0
0
2
0
1
0
0
0
0
1
1
0
0
2
1
0
0
0
1
2
1
1
1
2
1
1
0
1
0
1
2
1
1
0
1
2
0
2
3
1
2
0
2
0
0
2
1
0
2
1
1
1
1
0
0
0
0
1
1
1
1
1
0
0
2
1
0
2
1
0
1
1
2
2
1
1
1
1
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
1
0
0
0
1
1
2
1
1
0
2
2
0
0
1
1
3
0
1
0
0
1
2
3
0
1
1
1
1
1
1
0
1
0
1
0
2
1
1
0
1
0
1
0
0
1
0
1
0
0
0
2
0
0
1
0
1
1
2
1
0
0
1
1
1
0
1
0
1
1
2
0
1
0
1
0
0
0
1
2
0
0
0
1
1
1
1
1
0
1
1
1
2
0
2
0
0
0
0
1
0
0
1
1
1
2
0
2
0
1
1
1
0
0
1
0
1
0
0
1
1
2
0
1
0
0
0
1
1
1
1
0
2
2
0
0
2
1
0
0
0
1
1
2
0
0
0
2
1
1
1
1
1
1
0
2
0
0
0
2
2
1
0
1
1
0
2
0
0
2
1
1
2
3
1
1
2
1
0
1
0
1
2
2
0
2
1
3
1
2
0
0
0
0
1
0
1
0
2
1
1
1
0
2
1
1
2
2
2
2
0
1
1
0
2
1
1
1
2
2
1
0
0
0
1
1
1
0
0
1
1
0
1
0
0
1
0
0
0
2
0
1
1
1
1
1
1
1
0
2
1
1
0
1
2
1
1
0
1
1
0
1
0
0
0
1
0
2
0
0
0
0
1
1
2
1
0
1
2
1
0
0
1
2
1
0
1
1
1
0
2
0
0
1
1
2
0
1
2
1
2
1
4
1
0
0
2
0
2
0
1
2
0
2
1
1
0
1
2
1
1
1
1
1
1
0
0
1
1
2
0
1
2
2
1
0
1
1
0
1
1
1
2
2
0
3
0
0
2
0
0
1
1
2
1
0
1
1
0
0
0
1
0
1
2
0
0
0
2
0
1
1
1
2
2
0
2
1
0
0
2
2
0
1
0
1
2
0
1
0
2
0
1
1
1
0
0
2
2
1
0
0
1
1
0
2
0
1
2
2
0
0
0
2
0
0
0
0
1
1
0
4
1
0
1
0
1
1
0
2
1
0
0
2
0
1
2
1
0
1
1
0
1
1
2
0
0
1
1
2
0
1
0
1
0
2
0
0
0
1
1
1
1
2
2
1
0
2
2
1
1
0
0
2
2
2
1
0
1
2
1
2
4
1
2
0
0
0
1
1
1
1
2
2
0
1
2
0
1
1
0
0
1
1
2
1
0
1
1
0
1
1
1
0
0
0
2
2
2
1
1
2
1
0
0
1
0
0
1
1
0
1
1
2
1
1
2
2
1
1
1
0
0
0
2
0
2
0
0
0
0
0
1
0
1
1
0
0
2
2
0
0
0
1
1
0
0
0
0
3
1
0
0
0
0
0
0
1
1
2
1
1
1
2
1
0
0
1
0
0
0
1
1
2
2
1
1
1
1
1
1
0
0
1
1
0
2
0
1
0
1
0
1
0
2
0
0
1
3
1
0
0
1
0
0
0
2
1
0
2
1
2
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
2
1
1
2
3
1
0
1
1
2
1
0
0
3
1
2
0
0
1
0
2
1
1
0
2
2
2
2
0
1
2
0
0
0
2
0
0
1
1
2
2
2
1
0
1
1
0
2
1
1
2
0
1
2
1
1
0
0
2
1
2
1
0
1
0
0
2
1
1
0
1
1
0
2
1
1
1
0
0
1
1
2
0
0
1
1
1
1
0
0
2
0
0
0
1
0
1
1
2
1
0
1
0
1
1
2
0
1
1
1
1
0
1
2
0
0
0
0
1
1
0
1
1
0
0
4
2
0
0
2
1
2
1
2
1
1
1
2
2
0
0
0
4
0
2
1
2
0
0
1
0
0
0
0
1
0
1
0
0
0
0
2
1
2
1
1
1
2
1
0
0
0
2
1
0
0
0
0
0
1
2
1
2
2
0
0
0
2
0
1
0
2
0
0
1
0
2
2
0
1
0
1
0
0
0
0
1
0
1
0
1
1
1
0
0
2
1
2
1
0
2
0
1
1
0
2
1
0
2
0
2
1
1
0
2
0
1
1
0
0
0
1
0
1
1
0
0
0
1
1
0
0
0
1
0
1
1
1
0
1
2
0
0
0
2
1
1
1
1
0
0
2
1
0
0
2
1
0
0
2
0
1
1
0
0
0
1
1
2
1
1
0
0
0
1
0
0
0
1
1
2
2
2
3
0
0
2
0
2
2
2
2
1
2
2
2
2
0
1
0
1
1
0
1
0
0
2
1
1
2
2
1
0
0
1
1
0
2
1
2
1
0
1
2
1
0
1
2
2
1
0
0
1
0
0
2
0
1
2
1
1
1
0
1
2
2
0
1
1
0
1
3
2
2
1
1
2
1
0
1
1
2
1
1
1
2
2
2
2
0
0
0
1
0
0
2
2
1
1
1
1
2
1
2
1
0
0
1
0
2
1
2
1
0
1
0
1
0
1
0
2
1
1
0
0
0
0
2
2
2
0
0
0
1
1
0
1
2
1
0
1
2
2
0
0
0
2
2
1
2
3
0
0
1
0
1
0
2
1
1
1
1
1
2
2
0
1
1
2
1
1
1
0
0
0
2
1
1
3
0
2
2
1
0
1
1
2
0
0
0
2
0
0
0
2
1
2
1
2
0
1
0
1
0
2
1
0
0
2
0
2
1
2
2
0
1
2
0
1
1
1
1
2
1
0
0
1
1
0
1
1
2
1
0
2
0
0
1
2
0
0
1
2
0
2
1
0
1
1
1
0
0
1
1
0
0
1
1
0
1
1
1
2
0
0
1
1
0
1
0
0
1
0
1
0
0
1
0
2
0
2
0
0
0
2
1
0
0
1
2
0
2
1
1
2
1
1
1
2
0
0
2
1
0
0
2
1
1
1
1
0
1
1
0
2
1
0
1
2
1
1
1
2
1
2
0
1
1
1
1
2
0
1
0
1
1
1
1
1
1
4
0
0
1
1
0
1
1
0
1
0
1
1
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
1
0
1
1
1
0
1
2
0
1
1
1
1
0
1
1
1
1
1
1
1
2
1
1
0
0
1
1
2
0
1
1
0
0
1
1
2
0
1
1
1
1
1
1
2
0
1
1
0
1
0
1
1
1
0
0
1
0
2
1
0
2
0
1
0
1
2
0
3
1
2
1
0
0
0
2
2
0
1
1
1
3
1
1
3
1
0
0
0
1
1
2
2
1
0
1
2
1
1
2
2
1
2
0
0
2
0
1
0
2
3
2
2
1
1
1
0
2
1
2
1
2
0
2
1
0
0
1
0
2
2
1
0
2
1
0
1
0
1
3
2
1
0
0
2
1
0
0
0
0
0
0
0
0
2
2
0
0
1
1
2
2
1
0
1
0
1
3
0
2
1
1
2
2
2
0
1
2
0
2
1
2
0
0
0
0
1
2
0
3
1
1
1
1
0
0
0
1
2
0
0
1
1
3
0
0
3
0
1
2
2
2
0
1
2
1
0
0
1
1
0
1
0
0
1
0
0
1
1
2
1
1
0
0
2
0
1
1
1
0
0
1
0
2
0
2
0
1
1
1
0
1
2
0
0
1
1
1
0
2
1
2
0
0
1
2
1
0
0
0
1
1
1
1
2
1
1
1
2
2
1
1
1
3
0
0
1
1
2
0
0
1
1
0
1
1
2
1
1
1
1
0
0
0
0
2
1
1
2
0
1
0
1
1
2
1
0
1
1
0
2
1
0
2
1
0
1
1
0
2
0
0
1
2
1
3
2
1
2
0
0
2
1
0
1
2
1
1
1
2
1
2
0
1
2
1
2
0
0
3
0
1
1
1
2
2
1
2
0
0
2
1
2
1
1
1
2
0
0
0
2
1
2
1
1
2
1
1
2
0
0
0
2
0
0
1
0
2
0
1
0
1
1
0
0
0
1
1
0
2
0
0
0
2
1
3
1
0
0
0
0
1
2
2
0
1
2
0
0
1
1
1
0
0
0
0
0
1
1
1
0
0
0
0
2
2
1
2
0
1
1
1
0
1
0
0
1
0
2
1
1
0
0
1
1
1
0
1
1
1
1
2
1
2
1
0
1
0
2
1
1
1
0
0
1
1
0
1
1
1
1
1
2
2
1
0
2
1
1
0
0
1
2
2
0
2
0
0
0
2
2
2
2
1
0
1
0
0
1
0
2
2
0
0
0
1
0
2
1
1
0
0
1
0
1
1
0
2
1
1
0
1
0
0
0
0
2
0
1
1
0
0
1
1
2
0
1
1
1
2
2
1
0
1
1
0
0
0
1
1
0
1
0
1
2
0
1
0
1
0
1
0
2
0
2
1
0
0
0
0
0
0
1
0
1
1
2
1
1
1
4
0
1
1
1
2
1
2
0
2
1
0
1
2
1
1
2
1
2
1
0
2
2
1
2
0
0
1
1
1
1
1
1
0
6
1
1
1
0
1
1
0
1
2
0
0
1
1
0
2
0
0
1
2
1
0
0
0
1
1
1
1
1
0
1
3
1
1
0
1
0
0
1
1
1
2
1
1
1
1
1
2
1
0
1
0
0
0
4
1
2
2
1
0
0
0
1
1
0
1
0
2
2
0
1
2
2
1
1
1
1
1
2
0
0
2
1
0
1
1
0
0
1
1
0
1
0
1
2
1
1
0
1
1
0
0
0
0
0
1
0
1
1
2
2
1
3
2
0
0
0
1
1
1
0
2
1
1
2
2
1
0
0
2
2
0
1
1
0
1
0
0
1
0
0
0
2
2
1
0
3
1
1
2
0
0
1
0
0
0
0
2
1
0
1
1
1
0
0
0
0
1
1
0
1
2
0
1
1
0
0
2
0
1
2
0
0
1
2
0
0
0
0
1
1
0
1
2
2
2
1
1
0
2
1
1
1
2
0
0
1
1
1
1
1
2
0
0
0
0
3
0
1
0
0
2
0
1
0
0
1
1
1
0
1
1
0
0
0
1
1
1
0
0
1
1
0
2
1
2
1
0
2
2
0
0
0
2
0
0
2
0
1
0
1
1
2
3
1
0
0
1
0
0
0
0
2
2
2
0
0
1
0
0
1
0
2
1
2
1
0
1
1
2
0
1
1
0
2
0
2
0
1
0
2
1
1
0
2
3
0
0
0
1
1
1
0
0
0
2
0
1
1
0
0
2
0
0
0
0
1
0
2
1
0
2
0
0
1
0
1
0
0
1
0
0
1
1
0
3
2
1
1
0
1
2
0
1
0
2
1
2
0
0
2
1
0
2
2
1
0
1
1
0
0
1
1
1
0
2
0
2
3
0
2
3
0
2
0
0
0
0
0
1
1
0
0
2
1
1
0
1
1
2
0
1
0
0
0
1
0
0
3
0
0
0
1
2
1
1
1
0
1
1
0
0
2
0
1
1
2
0
2
0
1
1
0
2
1
0
0
2
0
0
2
1
0
2
0
0
1
0
1
0
2
2
1
1
0
1
1
0
1
2
0
0
1
1
1
3
1
0
1
1
0
1
1
1
0
1
1
2
0
0
1
3
2
0
1
1
0
2
0
1
1
0
0
0
0
3
0
1
0
1
2
0
1
1
0
1
0
0
0
0
0
1
2
2
1
2
3
2
1
2
2
0
1
0
0
3
0
0
1
2
1
1
0
0
1
0
2
0
1
2
0
1
2
1
1
1
1
0
1
2
1
1
1
0
2
1
0
0
1
1
1
6
0
1
0
0
1
2
1
1
1
0
1
1
1
0
0
0
1
2
0
1
2
1
0
0
3
0
1
1
0
1
2
0
1
1
1
1
2
1
0
0
0
0
1
0
1
0
2
1
1
0
2
0
1
1
0
0
0
1
0
2
0
0
1
2
1
0
0
0
0
2
0
2
2
1
1
1
0
0
2
0
2
0
1
0
1
0
0
2
2
1
0
1
0
2
1
0
0
0
1
1
2
1
2
2
2
0
0
1
0
1
0
1
2
2
0
1
0
0
0
2
1
1
1
2
2
2
0
1
2
2
2
1
0
1
1
1
2
1
0
2
1
2
0
0
0
1
1
1
1
0
1
2
0
1
1
1
0
1
1
1
2
0
1
2
1
1
1
2
0
2
2
1
1
0
1
0
0
1
1
3
0
0
0
0
1
2
1
2
1
0
1
0
0
0
0
0
0
1
0
2
2
0
3
1
1
1
0
2
0
1
0
1
0
1
1
1
1
1
0
0
1
0
1
0
2
2
1
1
0
0
2
1
1
2
0
2
2
0
2
0
0
1
0
2
0
0
1
1
0
0
1
1
1
2
0
2
0
1
0
0
0
2
1
0
0
0
0
1
3
2
1
0
2
2
1
0
1
0
1
0
0
0
1
0
0
1
2
0
2
1
0
1
2
1
1
1
0
0
2
2
0
0
1
1
0
0
0
2
0
1
0
2
1
0
1
0
1
3
0
1
2
0
1
0
1
0
0
0
1
0
0
0
0
2
0
0
2
1
1
2
1
0
1
0
2
0
0
2
2
1
1
1
1
0
2
0
0
1
1
0
0
2
1
1
0
0
1
1
1
1
1
1
0
0
1
0
1
2
0
1
1
0
1
0
1
2
0
0
0
0
1
1
1
2
1
1
1
0
0
1
2
1
1
1
0
1
0
2
0
2
0
1
1
1
1
2
2
2
0
1
0
0
0
1
0
2
0
1
1
1
0
1
1
0
1
0
0
1
1
1
2
0
1
0
0
0
1
1
0
4
1
1
1
2
0
1
1
2
1
1
2
0
1
1
0
1
0
1
1
2
0
0
2
1
1
2
0
0
1
2
1
0
0
2
0
1
0
0
1
1
0
1
1
2
1
1
0
1
0
2
0
1
0
0
1
1
2
2
1
1
2
1
1
1
1
2
1
0
0
2
1
2
1
2
1
2
1
1
0
0
1
0
0
2
0
0
1
0
1
2
1
2
1
2
0
2
0
1
0
0
0
0
1
1
1
1
1
1
1
1
2
1
1
1
2
0
1
2
1
0
0
1
1
1
0
1
1
2
0
1
0
1
1
1
2
3
0
0
1
1
1
1
0
0
0
0
1
1
1
1
0
2
1
0
1
2
1
1
1
0
2
0
0
1
0
2
0
3
0
3
2
0
1
1
0
2
0
1
1
0
0
1
0
2
2
0
2
0
1
1
2
1
2
1
0
1
0
2
2
3
0
0
0
0
0
1
2
3
0
2
1
1
1
0
1
2
1
0
1
0
1
1
1
1
0
0
1
1
1
1
1
1
0
0
0
0
0
0
1
1
0
1
0
1
1
0
0
0
2
0
0
2
0
2
0
2
1
2
1
0
0
2
0
1
0
2
0
1
1
2
0
0
0
1
0
2
2
0
0
2
0
2
1
1
1
0
0
1
1
1
1
1
1
2
0
0
0
1
1
1
0
2
0
0
1
2
0
2
1
1
2
1
0
0
0
0
1
0
3
1
1
0
1
2
1
0
0
0
0
2
1
1
0
0
1
0
2
0
0
1
0
0
1
0
1
1
1
1
2
1
0
1
1
2
0
0
2
1
0
2
0
0
1
1
0
2
0
0
1
0
1
0
1
0
0
1
1
2
2
0
0
1
2
1
0
0
1
1
0
1
1
1
1
0
2
1
0
1
0
0
1
2
1
0
0
2
1
2
0
0
2
2
0
1
1
1
0
1
0
0
1
1
1
0
2
1
0
0
1
1
0
2
2
1
1
1
2
2
1
0
2
0
0
1
1
2
1
0
1
1
2
0
2
1
2
0
2
1
2
1
1
0
1
0
2
0
0
0
1
0
3
1
1
2
1
0
1
1
1
1
0
2
1
1
1
1
1
0
0
1
1
1
0
2
1
1
0
1
1
0
2
1
1
1
0
2
2
0
0
1
1
1
1
0
3
2
2
1
1
2
0
0
0
2
0
1
2
0
1
2
1
2
1
1
2
0
0
0
1
1
0
1
1
1
0
0
1
0
1
1
0
2
1
2
0
0
2
0
0
1
0
2
0
0
0
1
1
1
2
0
1
2
5
1
2
0
0
1
0
0
0
0
1
0
1
1
1
1
1
0
0
0
0
1
0
0
2
1
0
0
1
0
0
0
0
1
1
0
1
2
0
1
2
0
0
1
2
0
2
1
0
0
2
2
1
0
2
0
0
1
2
1
0
1
2
1
0
0
1
1
2
0
0
0
0
2
0
1
0
1
1
2
1
2
4
2
1
1
0
1
2
0
1
0
1
2
1
0
1
0
0
4
2
2
0
1
0
1
2
0
0
1
0
1
0
1
1
4
1
0
0
0
0
1
1
1
1
1
2
2
1
1
1
1
0
2
0
1
1
0
0
3
2
1
1
1
1
1
2
0
1
1
1
0
1
0
0
0
1
1
0
0
2
1
2
0
0
1
1
0
2
0
0
0
0
2
1
1
1
0
0
1
1
1
0
1
0
2
2
2
1
1
2
0
1
0
0
0
1
0
2
1
0
1
1
0
0
2
1
2
0
1
2
2
1
0
1
1
1
2
0
1
2
2
1
1
0
2
1
0
0
0
1
0
2
0
0
0
0
0
0
0
1
2
1
1
1
2
0
0
1
0
2
0
0
2
1
1
1
0
2
0
1
1
1
1
1
2
0
0
2
1
1
1
2
0
1
1
0
1
0
2
1
1
2
0
1
1
2
2
0
1
0
0
1
1
2
0
1
0
0
1
1
0
1
1
1
0
0
2
2
1
2
0
1
0
2
0
0
1
1
4
2
1
2
2
1
2
2
1
1
1
1
1
1
0
1
2
1
1
0
1
0
0
2
1
0
0
0
2
2
1
0
2
0
1
2
2
1
0
1
0
2
1
1
2
0
1
0
3
2
2
0
0
0
2
1
1
0
2
1
1
0
1
1
0
1
4
0
2
2
1
1
0
3
1
1
0
0
1
0
1
0
1
1
0
2
1
1
1
0
5
0
1
0
2
0
0
1
2
1
1
3
0
1
0
1
2
0
2
0
2
1
1
1
2
1
1
1
0
0
0
1
0
2
1
1
1
0
1
1
1
4
1
1
1
2
2
1
1
0
1
1
1
1
1
0
1
1
0
1
1
1
1
0
0
0
0
0
0
0
1
1
2
2
2
1
1
1
0
1
0
1
1
1
0
1
0
0
1
0
2
1
2
0
0
1
1
1
0
1
2
0
1
0
2
0
2
0
0
4
0
2
1
1
0
0
1
1
0
3
1
0
2
1
0
2
0
1
1
0
2
1
2
1
1
3
0
0
2
1
2
1
1
1
0
1
0
1
2
1
1
0
1
0
0
1
0
1
2
0
1
0
0
1
1
1
0
1
1
3
0
1
2
0
1
1
2
1
0
4
0
0
1
1
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
1
2
2
1
2
0
3
0
2
0
1
1
1
0
1
1
1
0
0
0
1
1
0
1
2
0
2
2
2
0
2
0
1
1
0
1
2
1
1
2
0
1
0
0
1
0
1
1
1
0
0
1
2
0
2
0
1
0
2
0
0
1
1
2
1
1
0
0
0
1
0
1
2
0
1
1
1
0
0
3
1
1
0
0
0
1
1
0
2
1
2
0
2
0
1
1
0
0
1
1
0
1
1
2
0
2
2
0
0
1
0
1
2
2
1
1
0
0
0
0
2
1
0
0
0
1
2
4
1
2
0
0
1
0
1
1
1
2
1
1
2
1
1
1
0
0
1
3
0
0
1
0
1
0
0
2
1
0
0
1
0
2
1
0
0
1
1
1
1
1
0
1
1
1
0
0
0
2
1
0
1
0
0
0
1
1
2
1
2
0
2
1
1
1
1
2
2
0
1
2
1
1
0
2
0
2
0
1
1
1
3
1
1
0
1
2
0
1
1
3
0
1
0
1
1
0
1
1
1
1
2
0
1
1
0
1
2
2
1
1
0
1
0
0
2
1
0
0
1
1
1
2
1
0
2
2
0
2
0
0
1
0
1
1
0
0
2
2
1
2
0
0
0
1
1
2
0
2
1
0
1
0
1
1
3
2
2
1
0
1
1
1
0
1
2
1
1
2
0
1
0
2
1
0
0
0
1
0
1
1
0
1
3
1
1
0
0
2
2
0
1
2
0
0
0
2
1
0
1
2
1
0
1
1
1
2
1
0
0
1
2
0
0
2
2
0
1
2
1
0
0
2
0
1
2
1
1
1
0
1
1
1
0
0
0
1
1
0
0
1
0
1
1
1
9
12
1
0
1
2
1
1
0
1
0
0
1
1
0
0
1
1
2
2
0
0
1
0
2
1
1
0
0
0
1
1
0
0
2
0
2
0
0
0
1
1
0
1
1
0
0
2
0
1
1
1
0
2
1
0
1
2
2
1
0
1
1
1
1
0
0
0
0
0
2
1
1
0
0
1
1
1
0
1
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
2
1
1
1
0
0
0
0
0
2
0
1
1
1
1
1
1
2
0
0
0
1
2
1
0
2
0
2
1
0
0
0
2
0
0
1
0
2
2
1
1
0
0
0
1
0
2
1
2
0
1
1
0
0
1
1
1
0
0
0
0
0
2
0
0
0
2
2
2
1
2
1
2
1
2
0
2
0
1
0
0
0
1
1
1
1
1
0
1
2
2
1
1
2
1
0
1
1
1
1
0
0
1
2
0
0
2
1
0
2
2
1
1
0
1
2
0
0
0
1
1
1
1
0
1
0
0
0
2
0
1
1
1
1
1
2
0
1
1
1
0
1
2
1
0
0
2
1
0
1
2
1
0
1
0
0
1
1
0
1
1
0
0
2
0
0
2
0
2
0
2
2
0
2
0
0
2
2
1
0
1
0
0
0
0
1
1
1
1
0
3
0
1
2
0
2
1
0
2
1
1
0
0
0
0
0
2
0
1
2
0
0
3
1
2
1
2
0
0
2
1
2
2
0
0
0
0
0
1
0
1
2
1
1
0
0
0
2
0
1
0
1
1
0
1
0
0
2
1
1
1
0
2
1
1
0
2
0
0
1
0
0
1
0
2
0
2
2
0
1
1
1
1
2
2
1
1
1
1
1
1
0
0
2
1
1
0
1
0
0
1
0
2
0
0
2
1
1
0
1
0
1
0
2
1
1
0
0
1
0
3
0
0
6
1
0
1
1
2
0
2
0
0
0
0
1
1
0
0
0
0
1
1
0
2
0
1
1
1
0
0
0
0
1
2
1
1
1
2
0
2
0
0
0
1
0
0
0
2
0
1
0
0
0
1
2
2
0
0
0
1
0
1
1
0
1
0
2
0
1
2
0
1
2
1
1
2
1
0
1
0
2
1
0
0
1
1
0
0
0
2
0
1
1
2
0
0
0
2
1
1
1
0
0
2
0
1
1
0
2
2
0
2
1
0
1
1
0
2
0
1
0
2
2
1
2
2
2
1
4
1
0
0
1
0
0
0
2
1
1
2
1
3
3
1
0
2
0
1
0
0
1
0
0
1
1
2
2
0
1
1
1
1
2
1
1
2
1
0
1
0
2
2
0
1
2
2
2
1
2
0
1
1
0
1
1
0
1
6
0
2
0
1
3
0
0
0
1
1
1
0
2
1
0
2
1
0
0
0
0
5
1
2
2
1
2
1
0
1
2
0
1
1
0
0
0
0
1
1
1
1
3
0
1
1
3
2
1
0
0
0
0
1
1
1
1
2
1
0
0
0
0
2
1
2
1
1
1
2
1
1
2
0
0
1
1
1
1
1
0
0
0
0
1
2
2
2
0
1
2
1
2
1
1
0
0
1
1
0
1
2
2
1
0
1
1
1
0
1
2
1
0
0
2
0
2
0
0
1
0
0
1
2
1
1
1
1
1
0
1
1
1
1
0
1
1
0
2
0
1
2
2
1
2
0
1
1
0
1
1
1
0
1
0
2
0
0
2
1
1
1
0
1
0
1
1
0
1
0
1
0
2
1
0
1
0
1
1
2
1
2
4
1
0
2
2
2
0
1
1
2
0
1
1
4
1
0
1
0
1
2
0
0
2
0
0
0
0
1
1
0
1
1
1
0
0
1
1
1
1
1
1
1
1
2
1
0
1
1
2
2
0
1
1
1
0
2
1
2
0
2
0
1
0
0
1
0
0
2
1
0
0
2
1
0
1
0
0
0
4
0
0
1
1
2
0
2
0
0
0
2
0
2
1
0
1
0
0
2
0
0
2
7
0
1
2
2
1
2
0
1
1
2
0
1
0
0
2
1
0
0
2
1
2
0
2
0
0
0
2
1
2
1
2
2
1
1
2
1
1
3
2
2
1
1
0
0
0
2
1
0
1
0
1
2
0
1
0
1
1
1
2
1
0
0
1
0
0
0
1
1
2
2
0
0
0
2
2
1
2
1
0
1
1
1
1
1
1
1
0
0
1
0
1
1
1
0
0
1
1
1
1
1
2
1
2
2
0
1
0
0
1
3
1
0
0
2
1
2
1
1
2
1
1
0
0
1
0
1
2
1
1
1
0
1
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
1
2
0
0
0
6
1
1
1
0
1
2
1
0
0
1
0
2
0
2
1
0
2
1
0
0
1
1
2
1
2
1
1
0
0
0
1
2
2
0
2
0
1
0
2
0
1
2
1
0
1
1
2
1
2
0
1
0
1
0
1
2
2
2
1
0
2
1
1
2
0
2
1
0
0
1
0
1
2
1
1
2
0
1
0
1
1
2
1
0
1
2
2
2
0
0
2
2
2
1
0
1
0
1
2
0
1
1
1
1
2
0
2
1
1
0
1
1
1
1
1
0
1
0
0
1
1
0
0
1
2
1
2
0
0
1
1
2
0
1
1
1
2
2
2
0
1
1
0
1
1
2
0
2
1
1
1
1
1
1
0
2
0
1
1
2
1
2
3
1
0
0
2
1
0
0
0
0
0
0
0
2
1
2
2
2
1
0
0
2
0
1
1
0
0
1
0
0
1
0
0
2
1
1
1
0
0
0
0
1
1
2
1
1
0
2
0
2
1
1
2
0
0
1
0
2
0
1
1
2
0
0
1
1
1
1
1
1
1
0
0
1
2
0
1
0
0
0
0
2
1
0
0
1
1
1
0
1
1
0
0
2
0
0
0
1
2
2
0
2
1
1
1
1
1
0
0
1
0
1
3
0
1
0
0
0
0
1
0
0
1
1
1
0
1
0
0
0
0
2
1
2
1
2
0
0
0
0
1
1
0
0
2
1
0
1
2
1
2
1
2
0
0
2
1
1
1
1
1
1
1
0
1
1
1
0
2
1
0
1
0
0
2
1
3
2
1
1
2
1
2
0
0
0
0
1
3
0
1
0
2
0
0
0
2
0
1
0
1
1
2
2
2
2
0
1
2
1
1
2
1
2
2
1
1
2
0
1
1
1
0
1
1
0
2
1
1
0
2
0
1
3
3
1
2
0
1
1
0
2
1
2
0
2
2
1
3
0
1
1
1
3
2
1
1
1
2
1
1
0
2
1
0
1
2
0
0
0
1
1
0
1
1
1
1
0
0
1
2
1
1
2
0
0
0
1
0
1
0
2
0
0
0
1
0
1
1
1
1
2
1
2
1
3
1
0
1
0
1
0
0
0
1
0
0
0
1
1
2
0
1
3
1
2
1
1
0
2
1
2
2
0
0
0
2
2
1
2
1
1
1
1
1
0
0
0
0
1
0
1
0
2
0
1
1
1
1
1
2
0
2
0
0
1
1
2
2
0
0
0
1
1
2
0
1
0
1
1
1
1
1
1
2
1
2
0
0
2
1
0
0
1
1
0
0
2
0
2
0
1
1
2
0
0
1
0
0
0
0
0
0
0
2
1
1
0
0
1
2
0
0
2
1
2
1
1
1
0
1
2
0
0
1
2
2
1
1
0
1
2
2
1
2
1
1
2
3
0
2
0
0
0
1
2
1
2
0
0
1
0
0
0
0
1
2
0
0
0
0
2
2
0
0
0
0
2
0
0
2
1
1
0
0
0
1
0
1
0
1
2
2
0
1
2
0
1
0
0
1
1
0
1
1
1
1
1
2
1
0
1
2
1
2
0
2
2
0
2
1
0
1
1
1
0
1
2
0
0
0
1
1
1
0
1
0
0
1
2
1
2
1
2
0
1
1
0
2
1
2
2
1
0
1
0
0
1
2
1
0
0
2
1
1
1
0
1
1
1
2
2
0
0
2
0
3
0
1
1
1
1
1
0
3
1
0
1
0
0
3
2
1
2
1
1
1
2
0
0
2
0
0
2
0
2
1
3
0
2
1
2
0
1
2
0
0
1
0
1
1
1
2
2
0
0
0
1
0
2
0
0
0
0
0
2
1
2
1
0
2
0
0
0
1
1
3
0
0
1
1
1
1
0
2
2
0
1
0
0
0
2
0
1
0
1
1
1
1
1
2
2
1
0
2
1
1
2
1
0
0
0
1
2
1
2
0
0
1
1
1
1
0
2
1
1
2
0
0
0
2
0
1
1
1
0
0
3
1
0
0
2
0
0
1
0
2
2
1
0
1
1
2
1
0
0
1
2
0
1
2
0
0
0
1
1
0
1
2
1
1
2
1
0
1
2
1
2
1
0
1
1
2
2
0
0
0
2
1
1
0
2
1
3
1
0
0
0
0
0
0
0
0
1
1
2
1
0
2
0
1
1
1
2
1
1
0
2
0
1
1
0
2
2
1
0
0
2
0
1
1
0
1
1
1
0
0
1
1
2
0
2
1
0
1
0
0
1
2
1
0
3
2
0
2
1
1
0
0
0
1
0
0
2
0
0
1
0
3
1
2
1
0
2
2
1
1
0
0
1
2
2
1
1
0
0
2
2
0
0
1
1
0
2
2
1
2
1
1
0
1
0
2
0
2
0
2
2
0
1
0
0
1
1
0
1
1
1
2
0
0
1
2
0
0
3
0
2
0
0
0
2
2
2
1
1
1
0
1
0
1
1
0
0
1
0
1
2
2
2
1
1
1
1
1
1
1
1
2
0
0
2
0
0
2
1
2
0
2
0
0
0
2
1
1
1
1
1
0
0
1
0
2
0
0
1
0
0
2
1
1
2
1
1
0
1
2
2
1
2
0
1
1
0
2
1
0
2
1
1
1
0
1
2
1
3
1
1
1
1
2
2
2
1
0
1
1
0
2
1
2
2
0
0
1
0
1
1
0
1
1
0
0
1
1
0
2
0
0
0
0
0
1
0
1
2
0
0
0
2
2
1
2
1
0
0
2
1
2
0
2
2
0
0
2
0
1
1
1
1
0
1
1
1
2
0
0
1
2
1
1
0
0
2
1
1
0
2
2
1
2
0
0
0
2
0
0
1
1
0
3
0
2
0
1
0
1
2
1
1
1
1
0
0
4
3
2
0
0
2
1
1
1
0
0
0
1
0
2
0
1
1
0
1
3
1
0
1
1
2
0
1
1
1
0
1
0
0
1
0
2
1
1
1
0
1
0
0
2
0
1
1
0
0
2
1
3
1
2
1
0
2
1
0
0
0
0
0
0
1
0
1
1
1
1
0
2
2
1
0
1
0
0
2
1
2
2
1
2
2
2
1
0
1
1
1
3
1
1
0
1
0
3
1
1
0
1
1
0
1
1
2
2
0
0
0
0
2
2
1
2
0
2
0
2
1
3
0
1
0
1
0
1
2
1
2
1
2
1
2
2
3
1
0
1
0
0
0
1
0
1
2
2
1
1
2
2
2
0
2
2
1
1
0
1
0
2
0
2
1
0
2
1
0
1
1
2
2
2
1
0
3
1
1
0
0
2
0
2
2
1
1
1
0
1
1
0
1
1
0
0
1
1
1
1
1
0
2
0
0
1
2
0
3
1
2
0
2
0
1
1
1
0
0
2
0
2
2
1
0
0
1
1
0
1
1
1
0
2
1
0
1
2
1
1
0
1
1
1
1
2
1
2
0
4
1
1
1
2
2
0
1
1
2
0
1
0
0
2
1
1
0
1
0
1
3
1
0
2
2
1
0
0
0
0
1
1
2
0
1
1
1
1
1
3
0
1
1
1
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
4
2
2
1
1
1
0
2
0
2
1
2
2
0
1
3
0
0
1
2
2
1
2
0
0
1
0
2
0
0
0
2
1
0
2
0
1
1
1
0
2
3
0
2
1
1
2
2
2
0
0
1
1
1
1
2
0
1
0
1
1
0
2
1
2
0
0
1
1
2
0
2
1
2
0
4
0
1
2
2
1
1
1
1
0
1
0
0
1
1
1
1
0
0
0
1
0
2
0
1
0
0
0
2
1
1
0
4
1
0
2
1
2
1
1
0
1
2
1
1
1
0
0
0
1
0
1
1
2
2
2
1
0
2
0
1
3
1
0
2
0
1
0
1
0
1
0
2
0
1
2
1
1
1
2
0
0
0
1
0
1
0
1
2
2
1
0
0
1
1
1
0
1
1
1
2
2
1
0
0
0
1
2
1
1
1
0
1
0
0
1
1
2
1
0
1
1
0
3
1
2
1
0
0
1
1
2
1
2
1
0
5
2
1
2
0
0
2
1
1
1
1
2
0
1
0
2
1
0
0
0
2
1
0
1
1
0
2
1
1
0
1
2
2
0
0
1
0
2
1
0
0
5
1
0
2
1
1
1
1
2
0
1
1
0
0
2
1
1
1
1
0
1
0
0
0
1
1
1
1
0
1
0
0
0
0
0
2
0
1
0
1
0
2
0
2
1
1
0
2
1
1
0
1
1
0
1
0
1
2
1
0
2
2
2
1
1
1
2
0
1
2
1
3
1
0
1
1
2
1
1
0
0
1
0
0
2
0
2
0
1
1
3
0
0
0
0
2
0
2
2
2
1
1
2
2
2
2
2
1
0
2
1
0
2
2
2
2
0
0
0
1
0
1
1
1
1
2
0
1
2
0
0
0
1
3
0
2
1
0
2
0
0
1
0
0
1
0
1
1
0
1
0
0
0
1
0
1
1
1
1
0
2
0
1
1
0
0
1
2
1
2
1
2
0
0
1
3
1
0
1
1
2
1
0
0
2
0
2
1
2
2
0
1
1
0
2
2
1
0
1
0
1
0
0
1
3
1
1
0
1
1
2
1
0
1
0
1
0
1
1
1
1
0
0
2
0
0
1
2
2
1
1
0
0
1
0
0
2
1
0
0
1
1
0
0
0
2
1
1
1
2
2
0
2
1
0
2
1
0
1
1
0
0
0
1
2
1
1
1
0
2
1
1
0
0
0
0
1
0
1
1
0
1
1
1
0
1
1
1
0
2
2
1
0
1
1
1
1
2
1
0
0
2
0
2
1
1
0
1
0
0
1
1
2
1
1
0
1
0
0
1
2
1
2
1
2
1
1
1
0
1
0
1
0
1
0
1
1
2
0
2
0
1
0
1
1
1
0
1
1
1
1
1
1
2
0
0
1
1
0
0
1
1
1
2
1
0
1
1
1
0
2
2
1
1
1
1
0
1
0
0
1
2
0
0
1
2
1
0
1
1
0
0
0
0
1
1
1
0
2
0
0
2
1
2
1
2
1
0
1
2
1
2
0
2
0
0
2
1
0
1
0
0
2
2
0
1
1
1
1
0
0
0
0
0
1
2
0
0
0
3
1
0
1
0
2
0
0
0
2
0
0
1
1
6
1
1
1
0
1
0
0
2
0
0
1
1
0
1
2
1
1
0
0
0
1
0
0
0
0
0
1
2
2
0
2
1
0
1
0
2
0
1
1
1
0
2
1
2
1
0
0
0
2
1
0
1
0
0
1
2
0
0
1
0
0
0
1
0
1
1
0
1
3
1
1
1
0
0
1
0
1
2
1
0
2
1
0
0
1
1
2
0
0
1
2
0
2
1
0
0
1
0
1
0
1
2
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
1
1
2
1
1
0
0
0
0
2
0
0
0
1
0
0
1
0
1
1
2
5
0
1
0
2
0
1
2
0
0
2
0
1
2
0
0
2
0
0
2
0
0
0
0
0
0
0
1
2
0
1
0
1
1
1
0
1
2
2
2
2
2
1
1
1
0
0
1
0
0
2
1
0
0
0
1
1
0
1
1
2
2
1
2
0
0
1
1
1
2
0
1
0
1
2
0
1
0
0
1
1
0
1
0
0
1
2
2
0
0
0
1
0
0
0
2
3
1
1
1
3
0
1
0
1
0
0
0
1
0
1
0
0
0
1
0
1
1
1
2
0
1
0
0
1
1
0
0
1
2
4
0
0
0
0
1
0
2
1
0
0
1
2
0
0
1
2
2
1
0
1
1
0
1
2
2
1
0
0
0
1
2
1
1
0
0
0
2
1
5
0
0
0
1
0
1
3
0
0
1
0
1
1
2
0
1
2
2
2
1
0
0
0
1
1
0
1
1
1
0
0
2
1
0
1
0
2
2
2
1
1
0
4
2
0
1
1
0
1
0
1
2
2
1
1
1
0
0
0
0
0
0
1
2
0
2
2
1
2
0
1
0
0
0
1
2
1
1
0
0
1
0
1
2
0
1
2
2
0
0
2
2
2
1
0
0
0
1
0
2
1
1
2
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
2
1
0
0
0
1
2
1
0
1
1
0
0
1
0
2
0
0
1
0
1
1
0
1
1
1
1
2
1
2
1
0
0
1
1
0
1
0
1
1
2
1
0
1
0
0
1
2
1
1
1
0
1
2
2
0
0
2
1
7
1
0
1
1
0
2
0
0
1
2
0
2
1
0
1
2
0
2
2
1
2
1
0
1
1
1
1
0
0
0
1
1
1
1
2
0
0
1
0
2
1
1
1
2
2
1
1
0
0
1
2
0
0
1
0
0
2
1
1
1
1
1
0
1
1
0
1
1
1
1
0
1
1
0
1
1
1
1
0
0
0
0
1
0
1
2
1
0
2
0
2
1
0
1
0
0
0
2
1
0
1
1
2
1
2
0
1
0
2
1
0
1
1
1
1
2
2
2
0
1
1
1
1
1
0
1
0
0
0
0
1
0
1
0
1
1
0
1
0
1
2
0
1
0
2
0
0
1
1
1
0
0
2
1
0
1
2
2
0
0
2
1
2
2
2
0
1
0
0
0
1
1
0
0
0
0
2
2
0
1
0
4
1
1
2
2
0
1
0
1
0
1
0
2
2
0
2
0
1
0
0
2
0
1
1
2
2
1
1
0
2
0
0
1
1
2
2
1
3
0
1
0
1
1
1
0
0
0
0
1
2
0
2
1
1
1
2
1
0
1
1
1
0
0
0
2
1
1
2
1
0
2
2
1
1
1
1
1
2
0
1
1
1
2
2
0
0
1
1
0
1
0
0
1
1
1
0
1
0
0
0
1
2
0
2
2
1
1
2
1
1
0
2
1
1
0
1
1
2
1
0
2
0
2
2
0
2
1
0
2
0
1
1
1
2
2
0
1
1
0
1
1
1
1
0
1
1
0
1
2
0
1
1
0
1
1
0
0
2
1
1
2
0
0
0
0
2
0
1
0
1
0
0
1
0
2
2
3
0
1
0
1
1
2
2
0
0
2
1
1
1
1
1
0
1
0
1
0
2
0
0
0
2
1
1
0
0
0
2
1
0
1
0
2
1
1
1
1
0
0
1
1
2
0
2
0
1
0
1
2
1
1
0
0
0
1
1
0
0
1
2
0
1
0
0
1
1
1
0
2
1
1
1
0
0
1
0
1
0
0
0
1
1
0
1
1
0
1
1
2
0
0
1
0
1
1
0
0
1
1
0
1
1
1
0
0
2
1
0
1
1
1
2
0
0
1
1
1
1
1
1
0
1
0
0
0
1
0
1
1
1
2
1
1
1
0
0
1
0
1
0
2
0
1
2
2
3
1
2
2
1
1
1
1
1
1
1
1
1
1
2
0
0
1
1
1
1
2
1
0
1
1
1
0
1
1
0
1
2
0
0
1
2
0
1
0
1
0
1
1
0
0
1
0
1
0
1
2
0
0
1
1
1
1
1
1
0
2
2
0
0
0
0
2
2
1
0
1
1
1
0
1
1
0
0
0
0
1
0
1
2
0
1
0
0
1
0
1
0
1
2
1
0
2
1
2
0
2
0
1
0
2
0
0
1
1
0
0
1
1
1
2
0
2
0
0
2
0
0
0
1
0
2
0
1
0
0
0
1
0
0
1
1
0
1
0
4
0
0
2
1
0
0
1
2
1
2
1
1
1
1
0
1
1
0
2
1
1
3
1
2
0
1
0
0
2
3
2
1
1
0
1
1
1
2
4
0
0
1
1
2
2
2
1
2
0
2
2
1
1
1
0
2
1
0
1
0
0
1
0
1
2
1
0
2
1
2
0
0
1
0
0
2
1
0
0
0
0
0
0
1
1
1
1
0
2
0
2
2
1
1
0
2
0
0
1
0
1
1
1
2
1
2
1
0
2
2
2
1
0
1
2
0
0
2
0
0
1
1
2
1
0
0
2
2
1
2
1
2
3
1
2
1
2
1
1
2
1
0
1
0
0
2
1
1
0
0
1
1
1
0
2
0
0
0
2
2
2
2
1
0
2
0
0
1
2
2
1
0
0
0
0
0
0
1
0
0
1
1
1
0
1
1
1
0
0
1
0
0
0
1
1
0
1
1
0
2
2
0
1
0
0
1
0
1
1
1
0
0
2
0
0
1
1
1
1
1
0
0
1
2
3
0
2
2
1
1
0
2
0
1
0
0
2
1
1
0
1
1
1
0
0
0
2
1
0
0
2
1
0
1
1
2
0
0
1
3
1
1
1
0
1
0
1
1
1
2
1
0
4
0
2
0
0
2
1
0
2
1
1
0
0
0
0
2
1
0
1
2
0
1
1
0
2
1
1
2
1
1
1
1
0
0
2
1
2
1
1
0
0
1
1
1
1
0
1
0
1
0
1
1
1
2
0
2
0
2
2
1
0
1
0
1
1
0
2
2
1
0
0
2
1
1
2
1
1
2
0
0
1
0
0
1
2
1
0
1
2
0
1
2
1
2
0
0
1
0
0
1
1
1
1
2
2
0
0
0
0
1
1
0
0
1
0
0
2
1
0
0
1
0
0
1
5
0
0
1
2
1
2
1
0
0
1
1
0
0
0
2
1
1
1
2
1
2
2
1
2
1
1
0
1
1
0
0
1
1
2
1
1
0
0
1
1
0
0
0
1
1
0
2
0
2
2
2
0
0
0
1
0
0
0
1
1
0
1
1
0
0
1
0
0
0
1
1
1
0
1
0
1
1
1
1
0
1
1
0
0
1
2
1
0
1
2
1
2
1
2
0
1
0
2
2
2
2
1
2
0
1
0
1
2
0
2
1
2
1
1
0
1
1
0
1
0
1
2
1
1
1
3
1
1
2
1
1
2
2
1
1
1
0
1
1
1
0
2
0
1
0
0
1
2
0
2
1
0
1
7
0
1
2
2
0
1
2
0
1
1
1
1
1
0
2
0
1
3
1
0
1
0
1
0
1
0
1
2
1
3
1
1
1
1
0
2
2
1
1
1
1
2
1
0
0
0
1
1
1
0
1
2
0
2
0
1
1
0
2
1
0
0
0
1
0
1
1
2
1
1
2
2
2
0
4
2
2
1
0
2
0
1
0
1
2
1
3
0
1
2
1
1
2
1
1
1
0
0
0
2
0
1
0
2
2
1
1
0
0
0
5
0
0
3
0
0
0
2
0
2
0
0
1
0
0
2
2
0
1
2
2
0
2
2
1
1
0
2
0
1
0
0
0
0
0
0
1
2
1
0
2
0
0
1
2
0
0
0
2
0
0
1
2
2
0
1
1
1
2
0
1
1
0
0
0
3
1
2
1
8
0
1
0
0
0
1
2
0
1
0
2
1
0
0
0
0
1
0
1
1
1
0
2
1
0
2
1
2
1
0
2
0
1
2
2
1
0
2
0
1
0
1
0
2
2
0
1
0
0
0
0
1
0
2
1
0
2
2
0
2
1
0
1
2
0
2
0
1
2
2
1
1
0
2
0
2
1
2
1
1
1
2
0
1
3
0
0
2
1
0
0
1
2
0
1
0
1
1
0
0
0
2
1
1
1
1
2
0
2
2
2
2
0
4
0
0
1
2
3
0
2
1
2
1
1
1
1
2
0
2
1
0
1
0
1
0
1
1
0
2
1
0
2
1
2
0
1
0
0
1
2
2
2
0
0
0
0
2
0
0
1
2
0
0
1
0
1
0
0
0
1
2
2
0
0
1
1
2
1
1
1
2
1
1
1
2
0
3
1
1
0
0
0
1
2
1
1
2
1
2
1
2
1
0
1
1
1
1
0
0
2
1
2
0
1
1
2
1
0
2
0
0
1
0
0
2
1
0
1
2
1
2
1
1
2
1
0
4
0
2
1
1
2
1
3
1
2
2
2
0
1
0
1
2
0
2
0
0
1
1
1
0
1
3
0
0
1
0
2
3
2
1
1
0
1
2
1
0
1
2
2
1
2
1
1
0
1
1
3
1
2
0
1
0
1
1
1
0
2
0
0
2
0
2
1
0
0
0
0
0
2
1
1
2
0
1
0
2
1
2
0
1
0
1
0
1
0
0
1
2
0
1
0
0
1
1
1
0
1
0
1
0
2
2
1
1
1
2
1
0
2
0
1
1
1
0
2
1
0
1
1
2
1
1
1
0
0
3
1
0
1
2
0
1
0
0
2
1
1
0
0
2
0
2
2
0
1
2
1
2
1
1
1
0
1
0
1
0
1
2
1
1
0
1
0
1
0
0
0
0
2
1
2
2
2
2
1
0
1
2
0
1
0
1
1
1
0
0
0
1
1
0
0
2
1
1
1
2
0
1
0
1
1
0
2
2
0
1
1
1
1
0
0
0
0
3
0
0
1
0
0
1
1
2
1
0
0
0
1
1
2
0
1
2
1
2
2
0
1
0
1
2
1
1
1
1
0
1
0
0
0
1
0
2
1
2
0
1
2
1
0
0
2
0
1
2
0
1
1
0
1
1
4
1
0
0
2
0
1
1
0
1
0
1
0
1
2
1
1
1
1
2
1
1
0
1
2
1
0
2
0
2
0
0
0
0
1
0
2
1
1
1
0
1
1
2
0
0
0
1
1
2
1
1
1
1
2
0
0
1
0
1
1
0
2
1
0
2
0
2
0
1
1
2
2
1
1
0
1
0
0
1
2
0
2
1
3
0
1
1
0
1
0
1
2
1
1
0
1
2
0
1
0
1
1
0
1
1
2
1
1
0
0
0
0
1
2
1
1
2
1
1
2
1
1
1
2
1
0
2
2
0
1
1
2
2
0
1
1
2
0
1
0
0
1
1
2
0
0
1
1
0
1
1
1
2
3
1
1
0
0
1
0
0
0
1
0
1
0
2
0
0
0
2
0
1
2
0
0
1
0
1
0
2
0
0
0
1
0
2
1
2
2
1
2
1
2
0
1
2
1
1
1
1
0
7
0
1
2
0
2
1
2
2
1
2
1
0
0
1
0
1
1
0
0
1
0
1
2
2
0
1
1
2
1
0
2
1
1
0
1
0
1
0
2
0
0
1
1
0
0
1
2
2
1
1
1
0
0
1
0
0
6
0
2
0
0
3
1
2
0
2
0
1
0
1
1
0
1
3
2
0
2
0
0
1
1
2
1
1
0
1
0
2
0
2
1
1
1
1
1
2
2
1
1
0
2
3
1
1
0
1
0
0
1
0
0
0
3
0
2
1
0
0
1
2
3
2
1
2
0
1
0
1
1
0
0
1
1
0
0
0
0
0
2
2
1
1
1
0
0
1
2
0
0
2
0
1
0
0
1
0
2
1
0
1
5
1
0
0
0
1
0
1
1
0
1
1
0
0
2
2
1
1
2
1
1
1
1
1
1
0
1
1
0
0
0
2
0
0
3
3
1
1
0
1
0
2
0
2
2
2
1
0
1
0
1
2
1
2
0
1
1
1
0
1
1
1
0
0
1
1
1
2
0
1
1
2
1
1
1
0
1
1
1
1
2
0
1
0
2
0
1
2
1
1
2
0
2
0
1
1
0
1
2
2
2
1
0
1
1
2
0
1
1
0
1
0
0
1
1
2
0
1
1
1
1
2
1
0
0
0
1
1
0
0
1
0
0
2
1
1
2
0
1
0
0
0
1
0
2
2
2
1
0
1
2
1
1
0
2
1
0
0
1
1
0
2
0
1
1
0
0
2
0
0
1
0
0
1
0
1
1
1
0
2
1
0
3
1
0
0
0
1
2
0
1
3
1
0
1
0
1
4
2
1
2
1
2
0
0
1
1
0
1
2
2
1
2
0
2
0
1
1
0
1
0
2
0
1
0
2
1
1
1
0
1
2
1
1
2
0
1
2
2
2
0
0
0
0
1
0
1
0
0
0
0
0
1
2
2
1
1
1
0
0
1
0
1
2
0
1
1
0
1
0
0
3
1
0
0
2
0
1
1
0
0
0
1
0
1
1
1
1
0
0
1
0
1
0
1
1
0
1
1
0
0
1
0
1
0
2
0
0
1
2
1
0
0
1
0
1
0
0
1
2
1
2
1
1
0
2
0
2
2
1
0
0
2
1
0
2
2
1
0
1
1
1
0
1
1
0
0
1
1
1
1
0
1
0
0
1
0
2
0
1
0
0
1
1
0
0
0
1
0
0
1
0
2
0
0
1
1
0
2
2
2
0
0
1
0
0
2
0
2
0
1
0
0
2
3
1
2
0
3
2
0
2
1
0
0
1
0
0
0
3
2
1
0
2
1
1
0
0
0
2
0
1
0
0
1
0
3
0
0
0
1
0
0
2
1
1
1
0
0
1
2
1
1
1
0
1
2
2
1
0
0
1
1
0
0
0
1
2
0
0
0
2
0
0
1
1
0
1
0
1
0
1
2
2
0
2
1
0
1
0
1
1
0
0
1
0
0
1
2
1
0
1
0
0
0
2
1
1
2
0
1
1
2
1
1
1
2
1
0
1
2
2
0
0
1
1
0
1
0
0
2
1
1
0
1
1
1
2
2
1
1
0
0
1
0
1
0
0
1
1
1
1
0
1
1
1
2
0
1
0
1
0
0
1
1
0
0
0
0
0
1
2
0
1
1
2
0
2
1
2
1
2
1
1
1
1
0
2
1
2
1
1
2
0
0
1
0
1
1
2
0
2
0
1
2
1
0
1
1
0
0
1
0
0
1
1
0
0
1
1
2
2
0
1
1
2
1
1
1
1
1
1
1
0
2
1
1
0
0
0
1
0
1
0
2
1
0
1
0
1
1
0
1
1
1
1
1
0
1
1
1
1
2
1
1
3
2
0
0
1
1
0
1
3
2
1
1
1
1
1
1
2
2
0
2
1
0
2
0
1
1
1
1
0
0
0
2
0
0
1
0
2
1
2
0
1
2
0
0
0
2
1
1
0
2
2
1
0
3
0
0
2
1
0
0
1
1
1
1
0
2
2
1
3
1
0
0
1
0
1
0
1
1
2
1
0
0
0
1
0
0
0
0
2
0
1
2
2
1
0
1
0
0
2
2
1
1
0
1
0
2
0
2
1
1
1
1
1
0
0
1
1
1
0
1
1
1
1
0
1
0
0
0
2
1
2
1
0
1
0
1
1
2
2
1
2
1
1
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
1
2
1
0
1
2
1
2
0
2
1
0
1
2
1
0
1
2
2
1
1
0
0
2
1
1
1
0
0
2
1
2
1
0
0
1
2
1
2
1
1
2
1
0
0
2
0
1
2
2
0
0
2
1
3
2
1
0
0
2
0
1
2
0
0
0
3
2
1
0
0
0
0
1
1
0
0
0
1
0
0
1
2
1
1
2
1
2
1
1
1
2
2
1
1
2
0
2
2
1
0
1
0
1
1
1
0
0
0
0
1
2
2
0
0
0
3
0
0
2
1
0
1
1
1
0
1
1
1
2
1
1
0
1
2
2
0
2
1
1
1
1
2
1
1
1
1
2
1
1
0
2
1
1
1
0
1
1
2
1
0
0
1
1
1
0
0
0
1
1
1
1
1
1
1
0
1
0
1
1
1
2
1
0
1
1
1
0
0
1
0
0
0
0
2
1
2
0
0
0
1
0
2
2
1
0
0
3
2
1
0
0
0
3
0
0
0
0
1
1
0
1
2
1
1
0
1
0
2
2
2
1
2
0
0
0
2
1
1
2
1
2
0
2
1
1
1
0
1
2
0
0
1
2
0
0
1
0
0
1
0
0
1
2
0
0
2
2
2
3
1
1
2
1
0
0
0
1
1
2
1
0
2
1
1
0
1
1
0
0
2
1
1
1
1
0
0
1
2
1
2
0
2
1
2
0
0
0
1
0
0
0
0
1
1
0
0
2
2
1
0
0
2
5
1
2
1
0
1
1
0
1
1
2
0
1
0
0
1
2
1
1
1
0
1
1
1
0
1
2
0
1
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
1
1
2
0
2
1
0
1
1
0
1
2
1
1
0
1
0
1
1
2
2
1
1
1
0
1
2
1
2
1
0
1
1
1
0
1
1
1
0
1
0
0
1
0
0
0
0
1
0
1
1
1
2
1
1
0
0
0
1
1
2
3
1
2
0
0
1
1
2
0
0
2
1
0
0
0
1
0
0
0
0
0
1
0
0
1
1
2
1
2
1
1
1
1
1
0
0
1
2
0
1
0
1
2
0
0
1
0
1
0
2
1
2
2
0
0
1
0
1
0
2
0
0
0
1
0
1
0
2
0
1
1
1
0
0
1
0
1
2
1
1
2
1
0
1
1
2
1
1
0
0
0
1
1
1
1
1
1
0
0
1
0
0
0
2
0
1
1
1
1
1
1
2
0
1
8
0
0
1
2
1
0
0
1
1
0
1
1
0
1
0
0
1
0
2
1
0
1
2
1
1
0
1
2
2
2
2
0
0
0
2
1
2
0
0
3
1
0
1
0
1
2
0
2
0
1
1
1
2
0
1
0
0
0
0
1
2
1
1
0
0
1
1
0
0
0
0
0
1
1
0
1
2
1
1
0
2
2
1
2
1
2
2
1
2
0
0
0
1
1
1
1
0
1
1
1
0
0
0
1
0
1
1
0
1
1
1
2
0
1
1
2
0
0
0
0
1
2
1
1
2
1
1
0
1
1
0
1
2
2
1
1
2
1
1
0
0
2
2
2
1
1
2
1
2
2
0
1
0
1
0
2
0
2
2
1
1
2
1
1
0
1
1
1
1
2
0
0
1
1
1
2
0
0
1
0
0
2
0
0
1
1
2
1
0
2
0
1
1
2
1
0
0
0
2
2
0
1
2
0
0
1
2
0
1
2
0
2
1
0
2
0
0
1
0
0
1
0
1
1
0
1
2
0
1
1
1
2
1
2
0
1
0
1
2
2
0
3
0
0
2
1
1
1
0
1
1
1
1
0
0
3
1
1
1
1
0
0
2
1
1
0
0
2
0
1
1
0
2
1
0
0
0
0
1
2
1
1
1
2
0
1
1
0
0
0
1
0
0
2
1
2
2
1
0
1
0
1
0
0
1
1
0
1
1
2
0
2
1
2
0
1
2
1
0
2
9
1
1
2
0
1
1
1
2
0
2
1
0
2
0
1
0
0
1
1
0
1
3
0
2
2
1
0
1
0
0
1
2
2
0
1
0
1
0
1
1
1
1
0
1
1
0
0
1
0
0
1
1
1
0
0
1
1
0
0
2
0
0
1
0
1
0
0
0
2
1
2
1
0
0
1
0
2
1
2
0
1
0
1
0
0
0
1
5
0
0
0
1
1
0
1
2
1
1
2
0
0
2
1
2
0
1
0
0
1
1
0
2
1
2
1
1
2
2
0
0
1
0
2
1
0
1
1
1
0
1
1
0
2
2
0
3
0
1
1
0
0
1
0
1
1
1
1
1
1
0
2
1
1
0
0
0
0
1
1
0
0
2
2
0
0
0
1
0
1
1
2
1
1
2
1
0
0
2
1
0
0
0
1
1
0
0
1
2
0
1
0
1
0
1
2
1
1
0
1
1
2
1
2
0
1
0
2
1
0
2
0
1
2
0
0
0
1
1
1
0
1
1
1
2
2
1
0
2
0
3
0
0
1
0
2
0
1
2
0
2
0
0
1
1
0
0
1
2
0
0
1
0
3
0
2
1
0
0
1
2
0
2
2
0
1
0
1
1
0
1
0
2
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
1
0
4
1
1
1
0
2
2
0
0
1
2
2
0
1
1
1
1
1
0
1
3
1
0
0
0
1
1
0
1
2
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
1
2
3
0
2
2
1
1
2
0
1
2
0
2
0
1
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
1
0
0
1
1
1
0
0
1
1
0
1
0
0
1
0
2
1
1
1
0
2
1
1
0
0
0
0
0
1
2
1
0
1
0
0
1
3
0
1
1
0
1
0
1
0
1
1
2
2
1
0
2
1
1
2
1
1
1
1
1
1
0
0
1
0
1
2
1
1
2
2
0
0
0
1
1
1
2
1
3
1
2
0
1
0
2
0
1
0
1
2
0
1
2
0
2
2
0
1
1
0
0
1
1
1
1
0
2
1
0
0
1
0
0
1
3
1
1
2
1
2
1
0
1
0
0
2
1
1
1
0
1
1
0
0
1
0
1
0
2
2
0
1
3
2
2
1
1
4
1
1
0
0
2
0
1
1
1
1
0
0
0
1
0
1
1
2
1
1
1
0
0
2
2
0
1
0
0
0
1
1
0
1
0
1
0
3
1
0
2
2
1
0
1
0
0
2
0
0
1
0
0
2
0
0
1
1
1
0
1
0
0
3
0
2
0
1
0
0
0
1
0
2
0
1
1
3
1
1
1
0
0
1
0
1
0
0
1
1
0
0
1
1
0
0
0
2
0
1
1
2
0
1
0
0
2
0
1
1
1
0
2
2
0
2
1
1
2
2
0
0
2
1
0
2
0
2
1
0
0
0
0
2
1
1
0
0
0
0
1
0
1
0
1
0
2
1
1
2
1
1
1
0
1
1
0
1
1
2
1
0
0
0
1
1
0
0
1
1
1
1
0
0
0
1
1
2
1
2
1
0
0
1
2
0
3
1
1
1
1
0
2
0
2
1
1
0
1
0
2
2
1
0
1
1
2
1
1
0
1
1
0
1
0
2
2
1
2
1
1
0
0
1
0
1
0
3
1
0
3
1
1
0
2
0
2
0
0
0
2
1
0
1
2
2
0
0
2
1
1
1
1
0
1
4
0
1
1
1
7
0
1
1
0
1
1
1
0
1
0
1
0
3
1
0
2
1
1
1
0
0
0
0
1
1
2
1
1
1
1
1
2
0
0
1
0
0
1
1
1
1
0
0
1
1
2
0
1
0
1
1
2
1
1
2
2
1
2
0
0
0
2
2
4
1
0
1
1
1
3
0
0
0
2
2
0
1
2
1
0
0
0
1
1
2
1
0
0
1
2
1
1
1
2
0
2
0
1
1
1
0
0
1
1
0
1
1
0
0
2
1
2
2
2
2
2
1
1
1
0
2
1
0
1
1
1
2
1
2
1
2
0
1
0
1
2
0
0
0
2
0
1
2
3
1
0
1
2
0
0
0
2
1
1
1
1
1
1
0
0
1
1
1
0
2
2
1
1
1
2
1
0
0
0
0
0
1
0
1
1
1
2
1
1
1
1
1
0
2
1
0
1
1
0
0
0
0
1
1
1
1
1
1
1
1
0
0
1
0
1
1
0
0
2
1
1
1
0
2
2
1
1
2
2
2
2
1
2
0
1
1
0
1
0
1
1
0
2
1
2
1
1
1
0
2
2
1
1
0
1
1
1
1
2
0
2
2
0
1
2
1
1
1
2
1
1
1
0
1
2
2
1
2
0
1
1
0
2
1
1
1
2
2
1
0
2
1
1
2
1
1
2
2
0
1
1
0
0
0
2
3
1
1
0
1
0
1
1
2
0
0
0
1
0
0
1
2
1
2
1
0
0
0
0
1
2
2
2
1
1
1
1
2
1
1
0
1
0
2
1
0
2
1
0
0
1
1
2
3
0
2
0
1
1
1
2
1
2
1
1
1
0
0
1
1
1
0
1
0
1
2
0
1
0
1
2
0
0
0
0
2
0
2
1
1
0
0
1
1
1
2
0
0
1
0
0
0
1
1
0
1
1
0
0
0
1
0
1
1
1
2
2
1
0
1
2
0
0
0
1
1
0
2
0
1
3
0
2
1
1
0
1
0
1
1
1
1
1
0
0
2
1
1
2
2
0
1
1
2
0
3
1
0
1
1
1
0
2
1
1
1
0
2
2
1
1
0
2
0
1
1
1
0
1
1
1
0
1
1
2
1
1
1
1
1
0
2
0
1
2
2
1
1
0
1
0
2
0
0
1
0
1
2
1
0
0
1
1
1
2
0
1
0
1
1
0
2
2
1
2
0
0
1
2
2
1
1
0
2
0
1
1
1
0
1
1
0
2
5
2
1
0
0
1
1
0
3
1
0
1
2
1
1
1
1
0
0
1
1
2
1
2
0
2
1
0
1
2
2
0
2
1
0
0
0
1
1
0
0
1
0
1
1
0
1
0
0
0
2
0
0
0
1
0
0
2
0
0
0
2
2
3
1
1
2
0
1
0
3
2
3
1
0
0
1
1
2
3
2
1
0
1
0
2
2
0
1
2
0
1
1
0
0
0
1
0
0
1
1
0
0
0
1
1
1
2
0
0
1
1
1
1
0
1
0
0
1
2
2
0
0
1
0
2
1
0
1
0
1
2
0
1
0
0
1
0
1
0
2
1
0
1
1
0
1
0
2
1
1
1
1
0
1
1
2
1
1
0
1
2
0
0
2
1
1
2
1
0
0
0
1
2
2
0
1
0
2
1
1
0
1
2
0
0
2
0
0
1
1
1
2
0
1
1
1
2
0
1
0
1
0
0
0
2
0
1
1
1
0
0
1
1
0
1
1
1
0
1
0
1
2
0
2
1
2
0
1
0
2
0
0
1
0
0
1
0
2
1
1
2
1
0
0
1
1
0
1
2
2
0
2
0
1
1
1
1
0
0
0
1
1
0
1
0
2
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
2
1
0
1
1
1
1
0
1
1
0
1
0
0
0
1
0
1
0
2
0
1
1
2
0
0
1
0
2
0
2
2
2
1
1
2
0
1
0
2
2
0
2
1
1
1
1
1
0
1
3
0
0
0
1
2
1
1
1
0
1
0
1
0
1
1
1
1
2
1
0
0
0
1
1
2
0
1
1
1
2
1
1
0
2
0
1
1
2
1
0
1
2
0
2
1
0
0
0
2
1
2
0
1
1
2
0
1
0
1
2
2
2
2
1
1
0
0
0
2
1
2
2
0
1
1
1
0
0
2
1
2
1
0
0
0
1
0
1
1
0
1
1
1
1
1
2
0
1
0
1
0
0
1
3
2
1
0
1
1
1
0
1
1
0
1
1
0
0
1
1
2
1
2
1
0
1
1
1
1
0
0
0
1
0
1
1
0
0
1
0
1
0
0
2
0
1
0
2
0
2
1
0
0
0
2
1
1
0
2
2
2
0
6
1
2
1
2
1
0
2
2
2
0
2
1
1
2
1
2
0
0
2
0
1
0
1
1
1
1
1
0
0
0
2
1
2
2
1
1
2
0
2
1
2
2
0
1
0
1
0
0
2
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
3
0
0
1
2
3
1
2
0
1
1
1
1
2
0
2
2
0
3
2
1
1
0
1
1
0
0
1
2
1
0
0
1
2
0
0
2
0
0
1
0
1
1
1
0
1
0
1
1
1
0
0
0
0
1
1
0
0
2
1
1
1
1
2
0
1
2
0
1
2
1
0
1
1
0
1
1
2
0
1
2
0
1
1
0
0
3
0
0
1
0
1
1
0
2
0
1
1
0
1
0
1
1
1
0
2
2
0
0
1
2
0
2
1
0
0
1
0
0
2
0
2
0
1
2
0
1
1
2
1
2
1
1
0
0
0
1
0
1
0
1
2
0
0
1
1
1
0
1
0
2
0
0
0
0
1
1
1
0
1
1
2
0
1
1
2
1
0
0
2
0
2
1
0
1
2
0
2
1
1
0
1
1
3
0
2
0
2
1
1
1
0
1
0
1
0
1
0
1
1
1
1
2
0
0
2
0
0
1
1
2
3
1
0
1
0
2
0
0
1
1
0
1
0
2
0
0
1
1
1
2
0
0
0
1
0
2
1
2
1
0
1
1
1
1
1
1
0
0
2
0
0
0
0
0
1
0
0
1
1
2
1
2
1
0
1
2
0
0
0
1
0
0
0
0
1
1
0
0
1
1
1
1
1
1
0
0
1
1
2
0
0
2
0
1
1
0
2
2
1
2
2
0
2
1
0
0
2
0
1
0
0
0
2
1
1
0
2
2
0
0
1
0
1
0
1
0
1
1
1
0
0
0
1
1
0
0
0
2
0
1
0
2
0
1
0
2
0
0
0
0
0
1
0
1
0
2
1
0
1
1
0
0
0
1
0
0
0
1
1
0
0
2
1
0
1
0
2
0
2
1
1
0
1
2
1
1
1
0
1
2
2
2
1
1
1
1
2
1
0
0
0
0
1
1
1
0
1
2
0
0
1
1
2
2
1
1
2
0
1
1
0
2
1
0
0
2
1
0
2
2
1
0
2
1
2
1
0
0
0
1
0
1
0
1
2
0
1
1
2
0
1
1
1
0
1
0
2
1
1
1
0
2
1
0
0
0
1
1
1
1
0
1
2
0
0
0
0
1
1
2
1
1
0
1
1
1
1
1
0
1
2
2
0
0
0
2
0
1
1
0
2
0
0
2
1
0
0
1
1
0
0
0
0
1
0
1
1
0
0
1
2
0
1
1
2
1
1
1
0
1
0
0
2
0
1
4
0
1
1
0
1
1
1
0
0
1
1
1
0
0
1
1
1
1
1
0
0
0
1
0
2
1
1
0
2
1
1
0
2
0
1
0
2
1
1
2
0
1
2
1
1
0
2
1
1
1
0
0
0
2
2
0
0
2
2
2
1
0
0
0
1
0
1
1
2
2
0
0
1
1
1
0
1
0
1
2
1
1
1
1
2
1
0
1
2
0
0
1
1
1
1
5
0
1
0
0
1
1
2
0
1
0
1
1
1
2
0
0
0
0
1
1
2
0
0
1
3
1
2
2
0
0
1
0
1
0
0
0
1
1
1
1
1
2
2
0
1
2
0
1
2
2
1
0
1
4
0
1
0
1
2
0
2
3
1
0
1
1
1
2
0
0
1
1
2
2
1
0
1
1
0
2
1
2
1
1
1
2
0
0
0
2
2
2
0
0
1
2
0
0
1
0
2
1
2
0
2
2
0
2
2
0
0
0
2
3
2
0
0
1
1
1
1
2
2
1
0
2
0
1
1
1
1
1
1
0
0
2
0
2
0
1
2
0
2
0
0
1
1
1
2
2
0
1
0
0
1
0
2
1
1
2
0
2
0
1
0
0
1
2
1
1
1
2
0
2
2
1
1
1
1
0
2
1
0
2
0
0
1
0
2
1
1
1
2
0
1
1
0
1
0
2
0
1
1
3
1
2
0
1
1
1
0
0
0
0
1
2
0
0
2
2
1
1
0
1
1
2
2
2
1
0
0
2
0
0
0
1
1
1
1
2
1
1
2
0
3
0
2
1
1
1
1
1
1
0
0
1
2
1
2
0
0
0
0
0
1
1
0
1
0
2
2
1
0
2
1
1
0
0
0
1
1
1
0
1
0
1
0
2
0
1
0
0
1
2
1
1
2
0
1
0
2
1
0
1
1
2
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
2
1
2
1
0
0
0
0
0
0
2
1
1
0
1
1
1
1
0
1
0
1
1
0
1
1
0
2
0
2
0
1
0
0
4
2
1
0
2
0
1
1
1
1
0
2
1
2
0
2
1
1
0
2
1
2
0
1
1
1
0
2
0
0
0
1
1
1
0
1
1
1
0
1
0
1
0
1
2
1
1
2
0
1
0
1
0
0
1
2
1
3
1
1
0
0
2
2
0
1
1
2
2
2
0
2
0
2
2
1
1
1
0
1
1
0
0
1
1
0
2
0
0
0
0
1
2
1
2
1
2
1
1
1
1
1
1
1
2
1
1
1
0
0
1
0
1
0
1
0
2
3
0
0
2
1
1
0
1
1
0
1
0
2
1
2
0
1
2
0
1
2
2
0
1
0
1
0
1
0
2
0
2
1
1
0
1
0
2
1
0
0
2
0
2
1
0
2
1
0
0
1
0
1
1
1
0
1
0
1
1
0
1
1
0
1
0
0
0
1
1
2
1
0
1
2
1
0
0
0
2
2
1
0
0
0
0
1
2
0
1
0
0
2
0
1
1
2
2
2
0
1
2
1
1
2
1
0
2
1
0
2
2
2
1
0
1
0
1
0
1
2
0
1
2
1
2
2
0
1
0
1
2
1
1
1
2
2
1
2
1
1
0
0
0
1
0
0
1
0
0
2
0
1
2
0
1
2
1
1
0
3
0
1
1
2
1
5
0
1
1
1
0
1
2
0
1
2
1
0
1
2
0
2
2
0
2
1
1
1
0
2
0
2
0
2
2
3
0
2
1
1
0
1
1
2
1
2
0
2
2
1
1
0
1
1
0
2
0
1
1
0
1
2
0
1
1
1
0
2
0
0
1
1
1
2
0
0
0
1
0
1
1
1
1
0
1
2
1
0
1
0
0
0
2
2
1
2
0
1
0
1
0
0
2
0
0
2
0
0
1
1
0
1
0
2
1
0
0
2
2
1
0
1
1
0
1
0
1
0
1
0
0
2
1
1
1
0
3
0
1
0
2
1
1
1
1
2
1
0
2
1
1
1
0
0
2
1
2
2
1
1
2
0
1
1
1
1
0
2
0
2
0
1
1
0
1
1
2
1
2
0
1
0
0
0
0
2
2
0
1
1
1
1
2
2
0
1
2
1
1
2
1
0
1
0
0
2
0
1
0
0
1
1
2
0
0
1
0
3
0
2
1
1
0
0
2
1
0
0
1
0
1
0
0
2
0
1
1
0
1
1
0
1
0
1
2
1
0
2
1
1
1
2
1
2
2
1
0
2
2
0
1
2
1
1
0
1
0
1
2
0
0
0
0
1
0
1
1
1
0
1
1
1
0
0
1
1
0
0
0
2
2
2
0
2
0
2
1
1
0
0
0
0
2
1
2
2
0
0
1
0
0
1
1
1
2
1
0
1
4
2
0
1
0
0
0
0
1
1
0
1
1
1
0
0
1
1
0
2
1
1
0
0
1
0
1
2
1
0
1
1
1
4
0
0
1
1
1
1
1
2
0
1
0
0
0
0
1
1
0
1
2
0
1
0
0
0
0
1
1
0
1
2
0
1
0
1
2
2
0
2
3
2
2
1
1
0
2
1
1
1
2
1
0
1
1
1
1
1
1
2
1
1
2
1
0
0
1
0
0
1
2
1
0
1
1
2
0
2
2
0
0
1
1
1
0
0
2
0
1
0
1
1
2
0
0
1
0
0
2
1
2
0
1
1
2
2
0
0
1
0
1
0
0
0
0
1
0
0
1
1
1
1
2
1
1
1
1
2
2
1
1
3
1
0
2
1
1
0
1
0
1
2
1
0
2
0
1
0
2
2
1
2
2
1
0
0
2
0
1
0
0
1
1
2
2
0
2
0
1
1
0
1
0
0
2
1
0
2
0
1
0
1
1
1
1
0
2
1
0
1
0
1
1
1
2
0
2
1
0
2
0
0
1
1
2
0
1
1
1
1
0
0
1
1
0
2
0
1
0
2
1
1
2
1
0
1
0
0
0
1
0
1
2
1
0
2
1
0
0
2
0
0
1
1
0
0
1
0
1
2
0
0
2
3
2
0
1
0
2
2
0
1
1
0
1
0
1
1
0
2
0
1
2
0
1
1
1
0
3
0
1
0
1
1
1
0
1
2
0
1
0
1
0
1
1
0
0
0
0
1
1
1
0
0
1
2
1
1
0
1
0
0
1
0
1
2
1
1
0
2
1
2
2
1
1
2
0
1
2
0
1
2
4
1
4
0
1
0
0
1
1
2
0
1
1
1
2
2
2
0
2
0
0
2
2
2
0
2
3
0
1
1
0
2
0
0
0
0
2
2
2
0
1
1
2
2
2
2
1
1
0
1
1
0
1
1
0
1
1
0
1
1
1
0
1
2
2
0
2
0
0
0
1
1
1
2
0
2
1
2
1
0
0
0
1
2
1
1
1
2
1
1
0
0
0
2
0
0
1
0
0
0
0
0
0
1
1
1
1
2
0
2
2
1
0
1
1
2
2
0
1
1
0
1
1
1
0
0
0
2
0
0
0
1
2
1
1
2
1
1
0
1
2
0
1
1
0
1
1
0
2
1
2
1
1
3
2
1
0
0
1
1
2
0
0
6
4
1
1
2
1
1
3
1
1
1
1
2
1
2
1
1
1
0
0
0
1
2
0
0
1
2
0
2
1
1
0
0
2
2
0
2
1
1
0
0
2
2
0
0
2
0
1
0
1
0
0
2
1
0
2
0
1
0
0
0
0
0
1
0
1
0
1
3
0
2
0
0
1
0
0
2
0
1
0
2
1
0
0
1
0
1
2
1
0
2
0
1
1
2
0
1
0
2
2
1
0
0
0
1
0
2
2
1
1
0
0
1
2
2
0
0
2
1
1
0
2
0
1
1
1
2
1
0
1
0
0
0
1
1
1
1
0
1
0
2
1
0
0
2
1
1
1
0
2
0
0
0
1
1
0
1
0
1
2
1
2
0
1
0
12
0
1
1
1
1
0
1
1
1
1
0
2
2
1
0
0
1
1
0
3
0
0
0
0
2
0
1
0
0
1
1
1
0
2
1
2
0
2
0
0
0
1
2
0
0
1
2
0
0
1
0
1
0
2
1
2
0
2
0
2
2
0
0
0
1
1
1
1
0
0
2
0
1
2
0
1
1
2
1
1
2
2
0
2
0
1
1
0
0
2
1
2
1
0
0
0
0
0
1
1
1
0
2
2
1
2
0
1
0
0
1
1
0
2
0
0
0
1
1
0
2
1
1
2
0
1
1
0
2
0
0
1
1
2
0
2
1
1
2
0
2
0
2
2
2
1
1
0
0
0
0
0
0
2
0
0
1
2
0
0
2
0
1
2
0
2
1
0
0
1
1
0
0
0
0
1
0
0
2
0
2
1
1
2
1
0
1
0
2
1
2
0
1
1
2
0
2
2
3
0
1
2
1
2
0
1
1
0
0
1
0
0
1
0
1
1
1
0
1
0
1
1
1
0
0
0
1
1
2
0
2
2
1
1
2
2
1
1
1
1
1
1
1
1
1
0
1
1
0
0
0
2
0
1
0
1
1
0
0
2
0
1
0
2
0
0
1
0
0
1
1
2
0
3
1
0
2
0
0
5
2
1
1
1
1
1
2
2
0
1
0
2
2
0
2
0
1
1
1
1
2
1
0
1
0
1
1
2
1
0
0
2
0
0
2
1
0
2
1
0
2
0
1
1
2
1
2
1
0
0
2
1
0
1
2
0
1
1
1
1
2
0
1
0
0
1
1
2
0
0
1
1
1
1
1
2
0
2
0
1
2
1
1
1
0
4
1
0
1
2
1
2
2
0
0
1
1
1
2
1
1
1
2
0
3
2
0
2
1
1
1
1
0
0
2
1
1
1
1
1
0
1
1
2
0
2
2
0
2
1
1
2
1
1
0
2
0
2
2
1
2
0
1
0
0
0
0
4
0
1
1
1
2
0
0
1
2
1
0
1
1
0
1
2
4
2
2
0
2
0
1
0
0
1
0
2
0
0
1
0
1
1
1
0
1
2
0
1
1
2
0
0
0
0
1
0
0
2
1
0
2
2
0
1
1
1
2
0
1
1
1
1
0
0
2
1
1
0
2
0
2
0
1
1
3
2
1
1
2
0
0
1
0
1
1
1
2
0
1
0
1
1
0
0
0
1
0
2
0
1
1
1
0
1
0
2
0
0
1
0
0
2
1
1
0
0
0
0
0
1
1
2
1
0
1
0
1
1
1
0
1
1
0
1
0
0
0
1
0
0
1
2
2
1
0
1
1
2
0
0
1
1
0
1
1
2
0
0
1
2
1
1
1
0
1
0
0
0
0
1
0
0
0
1
0
1
1
2
1
1
2
0
1
0
0
0
2
0
1
1
0
0
1
1
2
1
0
0
0
0
1
2
1
2
1
0
2
2
1
0
2
2
0
1
0
2
1
0
0
1
0
1
0
1
1
1
2
1
0
1
1
1
0
2
1
0
0
1
2
1
3
1
1
2
2
1
0
3
1
2
1
4
0
0
0
1
0
2
0
1
1
0
0
2
1
0
0
1
0
2
0
0
0
0
2
0
2
1
0
1
0
0
0
0
0
1
1
0
0
0
1
2
2
1
2
2
2
2
1
0
1
3
1
0
1
0
0
1
1
2
1
1
2
1
0
2
0
1
0
2
1
1
2
1
2
1
2
1
2
1
1
1
1
0
2
1
2
1
1
0
1
2
1
0
0
2
1
1
2
1
2
2
0
0
2
1
2
0
2
1
0
7
0
2
0
0
0
0
2
1
1
2
1
2
2
1
4
1
2
1
1
4
2
1
0
2
0
1
1
0
2
0
1
0
1
1
1
0
1
1
1
1
2
1
1
1
0
0
2
0
0
1
0
1
1
1
0
1
0
2
0
2
2
1
2
0
0
0
1
2
1
1
1
1
2
1
0
1
2
1
2
2
1
1
1
0
1
1
0
2
0
0
1
0
0
0
0
0
2
0
2
2
2
0
1
0
1
0
1
1
0
1
2
1
0
0
1
2
2
1
1
1
1
0
2
0
0
1
2
2
0
0
1
0
1
0
2
1
2
1
1
0
1
0
0
1
2
3
2
0
1
2
0
0
1
1
0
1
0
1
1
1
1
2
2
0
2
0
1
0
0
0
1
0
0
0
0
2
1
2
2
0
1
1
0
0
0
1
1
1
0
2
0
1
1
2
0
1
0
2
1
1
0
2
0
0
1
1
2
1
2
1
0
2
0
1
2
1
0
0
1
0
0
0
0
0
1
2
2
0
0
1
0
2
1
2
0
2
2
0
0
2
0
0
1
1
2
0
1
0
1
0
2
0
0
0
1
2
2
0
0
0
0
0
1
0
1
1
1
0
0
0
1
0
0
0
1
0
0
2
1
1
0
1
0
1
0
0
1
0
1
1
0
0
1
2
7
2
0
0
1
1
1
2
1
0
0
1
1
0
1
1
2
1
0
1
1
0
0
2
1
1
2
2
0
1
1
0
0
0
0
0
1
1
1
2
1
0
2
0
0
2
1
1
2
2
0
0
2
2
2
0
1
0
1
2
0
1
2
0
3
0
1
1
1
1
1
2
1
2
0
1
0
0
1
2
0
1
0
1
1
1
1
0
0
2
0
1
0
1
2
0
0
2
0
2
0
0
1
2
0
1
1
1
1
2
2
0
2
0
2
0
1
2
1
1
1
1
0
0
2
1
1
0
0
0
0
0
0
1
1
1
1
2
0
1
1
1
0
0
1
0
1
1
0
2
0
2
0
0
0
1
0
1
0
1
0
2
0
1
2
1
3
1
1
2
0
1
2
2
0
0
1
1
1
1
1
0
2
2
2
0
0
0
1
0
2
1
1
2
1
1
2
2
0
0
1
0
2
1
2
1
1
2
2
2
1
0
2
0
0
1
1
2
1
1
2
2
0
0
2
2
0
1
1
1
2
0
0
1
1
0
0
0
2
0
1
2
1
2
1
0
2
0
0
1
1
1
0
1
2
1
0
1
2
0
1
0
0
0
2
0
2
0
1
1
0
2
2
1
0
2
0
1
1
2
0
1
0
2
0
1
2
0
2
2
1
0
1
1
1
2
0
2
0
0
0
0
0
0
1
0
1
1
0
1
0
2
0
1
0
2
0
0
1
0
1
0
1
1
1
1
1
0
2
1
2
0
1
0
0
1
3
2
0
1
1
2
1
1
1
1
0
0
1
1
1
0
2
1
0
0
0
0
1
3
1
2
2
1
0
0
0
1
0
0
1
1
0
0
2
1
1
2
2
0
0
1
0
2
2
1
0
2
1
0
1
0
1
0
2
0
1
0
3
1
1
1
0
2
0
1
1
0
1
0
1
1
0
0
0
1
1
1
2
1
1
1
0
2
2
1
0
3
2
1
0
0
2
2
0
0
1
1
0
0
1
0
2
1
1
1
1
2
0
0
0
0
0
0
1
2
1
0
2
0
1
0
1
1
0
2
0
1
0
1
2
1
3
1
1
1
0
1
1
1
0
2
1
2
2
1
1
0
1
0
0
1
2
1
1
3
0
2
2
2
1
0
1
0
0
2
0
2
0
2
1
2
1
0
1
2
0
2
1
1
1
1
1
2
0
0
1
1
1
2
0
2
0
0
1
1
2
1
0
2
1
0
0
1
1
1
0
2
2
1
1
1
0
1
0
0
2
0
4
0
1
1
1
0
0
1
2
2
0
0
0
1
0
0
0
0
2
0
1
2
4
1
2
1
0
0
3
0
2
1
0
2
1
1
2
2
2
2
2
0
0
2
0
1
1
1
1
1
1
0
0
0
1
1
1
1
1
0
1
2
0
0
1
2
1
1
0
1
0
0
1
0
0
1
1
1
1
1
1
0
0
0
0
2
1
0
0
1
0
1
2
0
0
2
0
1
0
2
1
0
0
0
1
2
1
2
2
0
1
1
1
2
2
2
2
0
1
0
1
1
2
2
1
2
1
2
4
0
0
1
0
1
1
1
1
1
0
1
0
1
2
0
1
1
1
1
1
0
1
1
3
3
2
1
0
2
1
1
0
2
0
1
0
2
0
0
1
1
1
0
0
2
1
1
0
2
1
0
0
0
0
0
0
1
0
0
2
1
1
0
1
0
0
1
1
0
0
1
1
0
2
2
0
0
4
0
0
1
1
1
0
2
1
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
1
1
0
1
0
1
0
1
0
1
2
1
1
0
1
0
0
0
2
0
1
0
1
1
1
0
1
0
0
0
2
0
0
2
1
0
1
2
1
0
0
0
0
0
1
1
2
0
0
0
0
2
0
1
2
2
0
0
1
1
1
1
2
1
0
1
2
0
1
0
1
2
0
2
0
1
1
1
2
0
0
1
0
1
1
2
0
0
0
0
1
0
2
0
1
2
2
1
1
0
0
1
2
0
1
0
0
1
1
1
1
0
0
0
1
1
0
0
0
1
3
1
1
2
1
2
0
0
1
1
1
1
1
1
0
1
0
0
0
2
0
1
1
1
1
0
2
1
2
0
1
2
1
2
0
0
0
1
0
1
0
0
1
2
0
0
1
1
0
1
1
0
0
0
2
2
1
2
1
2
0
0
2
0
2
0
0
1
1
0
2
1
0
1
0
0
0
1
2
2
1
0
0
1
2
0
0
0
0
0
1
2
2
1
1
1
1
0
2
2
2
0
2
1
2
1
0
0
0
2
1
2
1
1
0
1
1
1
2
0
1
1
0
0
2
0
1
2
0
1
0
1
1
2
0
0
1
0
0
0
0
2
1
0
2
1
0
1
0
1
2
0
1
0
1
1
1
0
1
2
1
0
1
2
1
0
2
1
1
0
3
2
2
0
2
0
0
1
0
2
2
1
1
0
2
2
1
0
1
1
2
1
0
1
0
1
0
1
1
0
2
1
1
0
0
0
2
0
2
0
2
0
2
0
0
0
0
1
0
0
0
0
2
1
0
1
0
2
0
1
3
2
0
1
0
0
0
1
0
1
1
0
2
2
1
2
2
1
0
2
0
2
0
0
1
1
1
1
0
1
0
3
0
1
2
2
0
2
0
2
0
0
2
0
1
1
1
0
2
1
2
0
1
1
2
0
1
0
2
0
1
1
1
1
1
0
1
0
0
1
0
1
1
0
0
1
1
0
1
1
2
0
1
0
0
1
1
2
1
2
2
1
1
0
2
2
1
0
1
1
1
2
0
1
2
0
2
2
2
1
1
0
2
0
0
0
1
1
1
1
0
3
1
0
0
0
0
2
0
4
0
2
1
4
1
1
0
3
1
1
0
0
2
1
3
1
2
0
0
1
1
1
0
1
0
0
0
1
1
0
2
0
1
0
0
2
1
0
0
0
1
1
0
4
0
0
0
0
0
0
0
1
0
1
0
2
0
2
0
1
1
1
1
1
1
1
1
0
1
2
0
1
0
0
1
1
1
1
0
0
2
0
0
0
1
1
1
1
0
1
0
1
1
1
0
1
0
0
0
1
0
1
1
1
2
1
2
0
2
1
2
1
1
1
0
2
1
0
0
1
0
1
1
1
2
1
2
3
2
1
1
1
1
2
2
1
1
0
1
1
1
0
1
1
0
1
0
5
1
0
1
1
0
0
0
0
0
0
1
0
0
1
2
1
2
1
1
2
2
2
1
2
1
1
0
1
2
0
0
0
1
1
1
2
1
2
0
2
2
0
0
0
1
0
1
0
1
1
1
2
2
1
1
1
2
0
0
1
2
1
2
1
1
0
1
1
1
1
0
0
1
1
1
1
2
1
0
1
1
1
1
0
0
2
1
1
1
0
1
1
0
0
2
0
1
3
2
1
0
0
1
1
2
1
1
0
1
0
1
1
1
1
1
0
1
0
1
2
1
0
1
0
2
0
0
2
1
2
0
0
3
2
1
1
2
3
1
1
1
2
1
2
1
0
1
0
1
0
0
2
1
0
0
1
1
0
2
1
2
1
0
0
0
1
0
1
1
0
2
3
0
1
1
0
0
0
1
1
0
1
0
1
0
1
0
1
0
0
1
0
0
2
1
0
2
0
0
1
0
1
1
0
1
0
1
0
0
2
1
2
1
1
1
1
0
2
0
1
1
0
1
0
0
1
1
0
5
0
1
0
1
2
0
0
0
0
0
0
1
1
1
0
1
1
1
0
0
1
1
1
0
0
0
0
0
1
1
0
2
0
3
2
1
0
0
0
0
1
0
1
1
2
1
0
1
0
1
0
0
0
1
1
3
2
0
0
1
1
0
1
1
3
4
2
1
2
0
1
1
0
1
0
0
0
0
1
1
1
0
2
2
0
2
0
2
1
0
0
1
0
0
2
1
0
2
1
1
1
1
2
0
0
0
0
1
2
0
0
1
2
0
0
0
0
1
0
0
0
1
2
0
1
2
1
1
0
1
4
0
0
2
2
2
1
0
1
0
1
0
2
0
2
1
0
0
0
2
2
1
0
1
1
2
1
1
2
0
0
0
0
0
0
2
0
2
2
0
2
1
2
0
2
1
0
1
0
1
0
1
2
2
1
1
0
1
1
0
2
0
1
1
0
1
0
0
1
2
1
1
0
1
1
0
1
1
0
0
0
1
1
2
1
2
1
1
1
1
0
0
1
2
0
2
1
0
1
2
0
2
1
0
1
1
2
1
0
1
0
0
1
0
1
0
1
1
0
2
0
0
1
1
2
1
1
0
1
1
1
1
2
0
1
0
4
1
0
1
0
2
0
2
0
0
0
1
2
2
0
1
1
0
1
0
0
1
1
3
1
2
1
1
1
2
0
0
1
0
1
1
0
0
2
2
1
0
1
1
2
1
1
0
2
1
1
2
2
1
2
2
1
0
0
1
0
0
1
2
1
0
2
2
0
0
1
1
0
2
2
0
0
1
1
1
0
1
0
0
1
0
0
0
0
0
0
2
0
1
2
4
0
0
1
1
0
1
1
2
2
0
2
1
1
1
0
1
0
1
0
0
2
0
0
0
0
1
0
0
0
1
1
0
0
1
1
0
1
2
2
2
0
0
0
0
2
1
1
1
1
2
0
1
1
2
1
2
2
0
0
2
1
0
1
2
1
0
0
0
1
0
1
1
0
0
0
0
2
0
1
2
0
3
2
0
1
1
0
0
1
1
0
0
2
2
0
2
1
0
0
2
1
0
0
0
0
1
2
1
0
2
0
2
1
0
1
3
1
2
0
1
1
1
2
2
2
1
1
1
1
2
2
1
0
0
1
2
2
0
1
1
1
2
0
0
0
0
2
0
0
1
0
1
0
1
0
2
2
1
1
0
1
1
1
0
0
1
2
2
1
1
2
1
0
2
2
2
0
0
1
2
2
0
0
1
2
1
1
2
1
1
2
2
0
1
0
0
1
1
2
2
0
2
0
1
0
1
2
2
2
1
0
0
0
2
2
2
1
1
2
2
2
1
2
2
1
1
3
2
2
0
0
1
1
1
2
1
1
2
0
0
0
2
0
1
2
2
1
0
2
0
0
0
0
2
2
2
0
1
1
1
1
0
0
0
2
1
1
1
2
1
2
1
1
2
0
1
2
2
1
1
0
2
0
0
0
1
2
1
0
0
3
2
0
2
1
1
2
2
0
0
0
0
0
1
1
0
0
0
0
0
2
1
0
1
1
0
0
0
1
1
2
0
0
1
1
0
1
0
1
0
1
1
1
1
0
2
0
0
2
1
0
1
0
3
1
0
0
0
0
1
0
0
1
2
1
1
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
1
2
0
2
1
2
1
1
1
0
0
3
0
1
0
0
0
0
0
1
1
0
0
0
2
0
1
2
0
0
1
2
1
0
2
1
1
0
0
1
1
1
1
0
0
0
0
0
2
2
2
1
0
0
1
2
2
1
1
1
0
2
0
0
2
2
0
2
1
0
1
0
1
2
1
0
0
0
2
1
2
2
2
1
1
0
2
0
2
2
1
0
0
1
2
2
0
0
0
1
1
0
1
1
1
0
1
0
1
1
1
0
0
0
1
0
2
2
1
2
2
0
1
0
1
1
2
1
0
0
1
1
2
2
0
1
0
2
2
2
2
4
3
1
2
0
0
0
0
2
2
1
1
1
1
1
1
0
0
1
0
2
0
1
1
1
2
0
0
0
0
0
1
1
0
2
0
0
0
1
1
2
1
1
2
0
1
0
0
2
0
1
2
1
0
1
0
0
0
2
0
2
2
1
0
0
2
0
2
2
1
0
1
1
0
1
1
2
2
0
1
1
1
0
2
0
2
0
1
1
0
0
1
1
1
0
0
2
0
1
1
1
0
0
0
2
0
1
0
0
2
0
0
1
0
0
0
1
1
0
1
0
2
2
2
1
0
2
0
1
1
2
0
2
0
2
1
0
1
1
2
1
1
1
1
0
0
0
2
1
0
1
1
0
2
1
1
2
2
1
1
1
0
1
0
1
2
1
1
1
1
1
0
1
1
1
0
0
1
1
1
1
0
1
1
0
1
0
0
1
2
2
1
0
1
2
0
0
2
0
1
1
2
0
0
0
1
1
2
1
0
0
2
2
0
1
1
0
2
0
1
2
0
0
1
2
0
1
1
1
1
1
0
2
1
1
0
0
0
2
2
1
0
1
1
1
1
0
0
2
0
0
0
0
1
1
1
1
2
0
0
0
1
2
2
1
1
0
2
1
1
1
0
1
1
1
0
0
2
0
1
0
1
2
1
0
1
0
0
0
0
1
0
1
0
2
2
1
2
1
1
1
1
0
0
0
1
0
0
0
0
2
2
0
1
1
1
0
0
1
1
0
1
1
1
0
0
0
1
1
2
0
1
1
1
2
0
1
0
2
0
1
1
1
2
0
2
1
1
1
1
0
2
1
0
1
0
1
1
1
1
0
0
1
0
1
1
2
1
2
0
1
1
2
1
2
4
1
0
0
0
0
0
1
1
1
3
0
0
0
1
2
1
1
0
0
2
0
2
0
1
2
1
1
0
2
0
1
1
2
1
0
0
1
2
0
0
2
0
1
6
2
1
0
1
1
1
2
0
0
0
0
1
0
0
1
1
1
1
1
1
2
1
0
0
0
2
0
1
1
1
2
2
2
1
0
0
0
1
4
2
0
1
3
0
1
0
0
0
0
2
0
2
2
1
0
0
1
2
1
0
0
0
1
1
1
0
2
1
1
2
1
1
0
2
0
1
0
1
1
1
1
2
0
0
1
1
0
2
2
1
0
1
0
0
0
1
0
2
3
0
0
2
2
1
1
0
0
0
1
1
1
1
0
2
2
0
1
0
1
0
1
1
2
1
1
2
0
1
0
0
0
0
0
1
2
3
0
0
0
1
1
1
0
1
1
2
2
0
1
1
1
1
1
1
2
0
2
1
0
0
1
0
0
2
0
2
2
0
2
1
0
0
1
1
2
2
1
0
2
1
0
2
1
1
0
1
2
0
0
0
1
1
1
1
1
1
0
1
1
1
2
0
0
1
2
1
0
2
1
0
0
0
1
2
2
2
0
0
0
1
2
1
1
0
2
2
1
0
1
0
2
0
0
0
0
2
1
1
2
2
0
0
0
0
1
0
0
1
2
1
2
1
2
1
2
0
1
1
2
0
1
2
0
2
2
0
1
0
2
0
0
0
1
1
1
1
2
2
1
1
0
1
1
2
2
0
0
0
0
1
1
1
2
0
0
2
2
1
1
0
0
1
1
2
1
2
1
1
1
0
1
0
2
2
2
0
0
2
1
0
0
2
1
2
0
0
1
1
1
0
2
0
1
1
1
1
1
1
1
2
0
2
0
1
1
1
0
0
0
0
1
2
0
1
1
1
1
0
0
0
1
0
0
0
1
0
0
0
2
0
2
1
2
0
1
0
0
1
0
2
2
1
1
0
1
0
2
2
2
1
1
2
2
0
1
1
0
1
0
1
1
1
1
0
1
0
0
0
1
2
2
1
0
1
2
1
2
0
1
0
1
1
0
1
1
0
2
2
0
0
2
1
2
1
0
0
0
0
1
2
2
2
0
0
0
0
3
1
1
2
1
2
1
0
1
2
1
1
0
1
2
2
2
1
0
1
1
1
0
0
0
1
0
2
1
0
0
2
0
1
2
0
2
0
1
2
2
0
2
1
1
0
0
0
1
1
1
1
2
0
0
1
0
0
0
1
0
2
1
0
1
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
2
1
1
2
0
0
0
1
0
1
2
1
0
1
0
1
2
1
1
0
2
0
1
2
0
0
0
0
1
1
1
2
1
1
0
1
1
1
2
2
1
1
1
1
1
1
0
2
1
1
2
1
2
0
2
0
2
0
0
2
0
1
1
1
1
1
2
1
1
0
2
1
0
0
1
2
2
1
1
2
1
1
0
1
1
2
2
3
0
0
4
0
1
1
0
1
0
1
1
1
2
1
0
1
1
0
1
2
0
1
1
1
2
1
2
1
2
2
1
4
1
0
1
0
0
1
0
1
0
1
1
0
0
1
2
1
1
1
2
1
1
1
2
2
1
0
1
0
2
1
2
0
0
1
1
1
1
1
1
0
0
1
1
1
5
0
0
2
1
0
0
0
0
1
0
1
0
1
3
0
2
3
0
0
0
0
0
1
0
1
0
0
2
2
2
1
1
0
0
1
2
0
0
2
2
0
2
0
1
0
1
3
0
1
1
0
0
0
1
2
1
0
2
0
0
0
0
2
1
2
1
2
0
0
1
2
0
1
2
0
0
2
1
2
0
1
0
2
2
2
1
1
0
1
1
1
1
0
0
0
1
1
0
1
1
2
0
0
0
0
0
1
1
0
1
1
0
2
4
0
0
0
0
1
0
1
1
1
1
1
0
0
0
2
1
2
1
2
2
2
13
0
1
1
1
0
0
1
1
0
3
1
1
1
0
0
1
1
1
1
0
0
2
1
1
1
0
0
0
0
2
1
2
1
1
0
1
1
1
2
2
1
1
1
0
1
0
2
0
1
1
0
1
0
1
1
2
2
0
0
2
0
0
1
1
2
1
1
0
1
2
1
1
0
2
1
1
0
1
0
1
0
1
0
1
1
0
1
2
1
2
0
1
1
0
1
1
0
0
0
1
1
0
1
1
1
0
0
0
2
0
1
2
0
2
1
0
0
0
0
0
0
0
1
1
1
0
2
3
1
0
1
1
3
0
0
0
2
1
1
0
0
0
0
0
1
1
2
2
0
1
2
2
0
0
1
0
0
1
0
0
0
1
1
2
1
2
1
1
0
2
2
0
0
0
0
1
0
1
2
0
1
1
1
2
0
2
2
1
0
0
3
0
2
0
0
1
2
0
0
1
0
0
2
2
0
1
0
2
0
1
0
0
1
2
0
6
0
0
1
3
1
1
0
0
1
0
1
1
0
1
1
1
1
0
2
1
1
2
0
0
0
0
0
1
2
0
2
2
0
2
1
0
2
0
1
1
0
1
0
0
2
0
2
2
0
1
1
1
0
0
2
1
0
0
0
1
2
0
0
0
1
1
0
1
1
2
0
0
0
1
2
2
0
2
2
2
1
1
1
0
1
0
2
2
1
1
1
0
1
1
1
1
0
0
1
4
0
0
1
2
1
0
2
0
1
1
1
0
0
2
2
0
1
2
0
1
1
0
2
0
0
0
2
1
2
2
0
1
1
0
0
1
1
0
0
1
2
0
1
0
3
0
0
0
0
1
1
0
1
0
1
3
2
1
0
1
1
1
0
0
0
0
1
0
0
1
0
0
2
2
0
0
1
0
0
0
2
1
0
2
1
0
2
1
2
1
2
1
0
0
1
2
1
1
1
4
0
0
0
1
2
1
1
1
1
0
1
0
0
0
1
1
1
0
0
1
0
0
2
1
1
0
2
2
1
1
0
2
1
1
2
0
1
1
2
0
0
2
0
0
0
2
2
2
0
0
0
0
1
1
1
0
1
1
0
1
2
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
2
1
1
1
1
0
0
0
0
0
1
1
1
1
0
0
1
1
0
1
2
1
0
1
1
1
1
0
2
2
2
1
0
0
1
1
1
1
1
0
1
2
1
2
1
1
1
0
1
1
1
0
2
1
1
1
0
1
1
1
1
1
0
1
0
2
2
0
3
1
1
1
1
1
2
1
1
1
1
0
0
1
0
1
0
0
1
1
1
0
2
0
1
0
2
0
1
0
0
0
0
1
1
2
1
2
0
1
2
1
0
1
1
0
0
2
1
1
1
0
1
0
1
1
1
0
1
1
1
1
0
1
0
2
1
1
2
1
0
1
1
2
2
1
1
0
0
0
1
2
0
2
1
0
2
1
2
0
0
2
0
2
2
0
0
2
1
2
0
0
2
0
0
0
0
1
0
0
1
1
0
0
0
2
1
0
2
1
1
2
2
2
1
0
1
1
1
2
2
0
2
0
0
1
1
0
2
0
1
1
1
0
1
0
2
1
2
1
0
2
0
0
1
2
0
1
1
0
1
1
0
1
1
1
1
1
0
0
0
0
1
0
1
2
0
2
2
2
1
1
1
0
2
1
1
1
1
1
2
1
1
0
0
1
1
1
1
0
1
0
2
2
1
0
2
2
2
4
0
2
1
1
0
0
0
0
2
0
1
2
0
0
3
1
1
0
2
1
0
0
1
1
2
0
0
2
0
1
1
0
1
0
2
2
1
1
0
2
0
0
2
0
1
0
0
1
1
1
1
1
2
0
0
0
2
1
0
2
1
0
1
1
0
2
1
2
1
0
0
1
1
2
1
0
1
0
1
1
0
0
0
0
1
2
0
2
1
1
1
2
0
1
2
1
1
1
0
1
0
1
1
1
1
0
0
2
2
1
1
1
1
0
1
1
0
1
1
1
0
0
0
1
0
0
0
0
1
1
0
1
1
0
0
1
2
0
1
0
0
0
0
0
1
0
1
0
0
3
2
1
1
0
1
0
1
2
3
2
1
1
2
2
2
0
1
1
1
0
1
1
2
0
1
2
2
0
2
2
0
1
2
0
1
0
1
1
1
1
2
0
0
0
2
0
0
1
1
1
1
1
1
1
1
0
1
1
1
0
1
1
1
0
2
1
2
0
2
3
2
2
1
2
0
1
0
0
0
1
1
0
2
2
2
0
1
1
1
1
2
0
1
1
2
0
1
2
1
0
2
0
2
0
0
1
0
1
1
1
0
1
1
1
1
0
2
0
0
1
0
1
0
1
1
0
0
2
0
1
0
2
1
1
1
0
0
1
2
2
2
0
1
1
1
2
2
0
1
0
1
1
2
0
2
1
2
2
2
2
2
1
2
0
3
0
3
1
1
1
1
1
0
1
1
0
1
0
0
1
0
0
2
1
1
0
2
1
0
2
0
1
1
1
1
1
1
1
0
0
1
2
1
1
0
2
2
2
2
0
1
0
0
1
2
2
0
1
0
2
1
1
1
2
1
1
0
2
1
1
1
1
1
0
2
0
2
1
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
1
0
0
2
1
1
0
1
1
0
2
1
0
0
0
0
0
2
1
1
1
0
0
0
0
2
2
2
1
1
1
2
1
0
0
0
1
1
0
0
2
0
1
0
0
0
0
0
0
1
0
1
1
0
2
1
0
0
1
1
1
2
2
3
1
2
0
2
0
0
1
0
1
1
1
1
0
1
1
0
1
0
1
1
2
1
2
0
0
0
1
0
1
0
1
1
1
0
2
2
1
0
1
1
1
2
2
1
2
1
2
0
0
1
0
1
2
1
1
1
0
1
1
2
0
2
0
0
1
1
1
1
1
1
2
1
0
0
0
0
2
0
1
1
1
0
1
1
0
2
1
2
0
1
2
1
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
2
0
0
1
1
2
1
1
2
1
1
0
0
0
2
0
2
0
0
0
1
2
0
0
0
2
1
1
0
0
0
0
1
2
1
1
0
0
0
2
1
0
0
1
1
1
0
0
0
3
0
2
1
0
2
0
1
0
1
0
1
0
0
2
0
0
1
1
1
2
1
1
1
1
0
0
1
1
0
0
0
1
0
1
2
0
0
0
0
1
2
0
2
0
1
1
0
0
0
2
1
0
1
0
0
1
1
1
1
2
1
1
1
0
0
1
2
0
1
1
0
2
0
1
1
2
0
0
2
1
0
1
0
2
0
0
2
0
1
0
0
2
1
0
0
2
0
2
2
1
0
2
0
1
0
1
1
1
0
1
1
1
0
2
0
1
2
0
0
1
1
1
1
0
0
2
2
1
1
2
1
1
0
1
1
1
0
0
2
1
1
0
2
1
1
0
0
1
1
1
1
1
1
0
1
0
3
0
1
0
1
3
1
1
1
0
1
2
1
0
1
1
0
1
0
2
1
3
0
1
0
1
0
0
0
1
0
2
1
0
1
1
0
0
1
4
0
1
1
0
2
1
2
0
0
0
1
2
2
1
0
0
2
0
2
1
1
1
1
2
1
1
0
0
1
1
1
2
1
1
0
3
0
0
0
2
0
1
1
2
1
0
2
1
1
0
1
1
1
1
0
0
2
0
1
1
1
1
2
0
2
2
1
3
0
0
1
2
1
0
0
0
0
1
2
0
2
2
1
0
0
1
2
1
2
0
1
0
2
1
1
0
3
1
1
1
0
0
1
1
1
1
0
1
1
2
0
1
2
0
2
0
2
0
1
0
1
1
0
2
0
0
0
0
0
0
1
0
1
1
4
0
0
1
0
2
1
2
1
1
2
0
0
0
1
0
1
0
2
1
0
0
3
2
0
2
0
1
2
2
1
0
1
2
0
0
0
1
0
1
1
0
1
2
2
1
1
0
1
1
1
0
1
1
0
1
1
1
1
1
0
0
1
0
1
1
2
1
1
0
0
1
2
2
1
1
1
0
0
2
1
1
1
1
0
0
0
1
0
2
1
1
1
0
2
2
1
1
0
0
2
1
0
1
0
0
1
0
0
0
2
0
1
1
1
2
0
1
1
1
0
1
2
2
1
2
0
1
1
1
3
0
1
1
2
1
1
1
1
1
1
2
1
2
2
2
2
0
1
1
1
0
0
1
0
0
1
1
1
0
1
1
0
1
0
0
0
0
0
1
1
1
0
2
0
0
0
2
0
0
2
0
0
0
1
2
1
2
2
1
0
2
0
2
0
1
0
0
3
1
1
1
1
2
1
0
1
1
0
1
0
1
2
1
1
1
1
1
1
2
1
1
0
0
0
0
0
1
0
1
2
0
0
2
2
0
0
1
0
1
1
1
1
0
0
0
1
0
0
2
2
0
1
0
1
0
0
2
2
1
1
1
0
0
1
0
0
2
0
1
0
1
1
2
1
1
0
0
0
0
1
2
1
0
1
0
0
0
2
2
0
1
0
2
2
1
2
0
1
0
1
0
1
0
2
1
0
2
1
0
1
0
0
3
0
0
0
1
0
0
1
1
0
1
4
2
1
0
0
0
1
0
0
0
0
0
0
1
0
2
2
2
0
2
1
1
0
0
1
1
0
2
0
1
2
0
1
2
0
1
2
3
0
0
2
1
0
1
1
0
1
2
2
1
2
1
1
1
2
2
0
2
1
1
0
0
1
1
1
0
0
0
1
1
1
0
2
0
0
0
0
1
1
0
0
0
0
0
0
2
2
2
1
0
1
0
3
0
1
2
0
2
0
1
1
1
0
1
1
0
2
0
2
0
0
0
0
1
1
1
1
1
1
2
0
1
0
2
2
2
2
1
2
2
1
1
0
1
0
0
1
0
2
2
2
0
0
0
1
2
0
1
1
0
2
1
0
0
1
1
1
2
1
1
1
2
2
1
2
1
0
2
1
0
0
1
1
2
1
1
1
1
2
1
0
0
0
0
1
1
1
0
2
0
0
2
2
0
2
0
1
1
2
0
1
1
3
1
2
1
3
2
1
0
0
1
1
0
1
0
2
0
1
0
1
0
2
2
2
0
1
0
1
2
0
1
1
0
1
1
1
1
0
0
0
2
1
0
0
0
1
2
1
2
2
1
1
1
0
1
0
0
0
0
1
0
2
0
0
0
2
1
0
4
0
1
1
1
0
0
1
0
0
1
0
2
0
1
1
1
1
0
4
1
2
2
1
1
0
2
0
1
1
1
1
1
1
0
1
0
0
1
1
0
1
2
0
1
2
1
2
0
0
1
0
2
1
2
1
2
1
2
0
0
0
0
0
1
2
2
1
0
0
0
1
2
0
1
0
0
0
1
4
1
1
0
1
2
1
1
0
2
1
3
0
1
0
0
1
2
0
0
1
1
0
1
0
2
1
1
0
0
1
1
0
0
2
2
1
0
1
2
0
2
2
1
0
1
1
2
1
2
1
1
1
2
0
1
1
0
1
2
2
0
0
1
2
0
0
0
2
0
0
0
1
0
1
1
2
0
0
0
1
0
1
1
1
0
0
2
0
0
1
1
2
0
2
2
0
0
0
1
1
2
0
1
1
0
0
1
1
1
0
1
1
0
1
1
1
1
1
1
0
0
1
0
1
2
1
2
2
1
1
1
2
1
2
0
1
2
0
2
1
1
0
0
0
1
3
1
1
0
0
0
2
1
1
2
1
2
2
0
0
1
0
1
0
1
1
0
1
1
1
1
0
1
2
1
0
2
1
1
1
0
2
0
2
1
0
0
1
1
2
1
1
0
0
2
1
1
0
1
0
2
0
2
2
2
1
1
1
0
0
1
0
0
2
1
1
0
1
1
1
1
1
0
1
2
0
1
1
1
1
2
0
0
2
2
2
1
0
0
0
1
2
0
1
1
0
0
1
1
0
1
2
1
2
0
1
0
1
1
0
0
2
1
0
2
0
0
0
2
0
1
1
1
2
1
1
1
0
1
1
0
2
2
1
2
0
1
2
1
0
0
2
0
2
1
1
0
2
0
0
2
0
1
1
1
1
0
1
2
0
2
1
1
1
2
2
1
0
0
1
1
0
1
0
1
0
1
1
1
1
0
1
0
2
2
1
0
3
0
0
1
1
1
0
0
0
0
1
2
0
0
0
0
2
2
2
2
0
0
1
1
1
0
1
0
1
0
2
1
3
2
0
2
1
1
2
0
0
1
0
2
1
2
1
1
2
2
1
1
1
1
0
1
1
0
0
0
1
1
2
0
0
0
0
2
1
0
0
0
0
0
1
0
1
0
1
2
0
2
1
1
2
1
1
0
0
1
1
0
0
0
0
1
1
2
1
0
0
1
2
0
1
0
1
0
1
0
1
1
1
0
0
1
1
0
1
1
0
1
0
2
1
0
0
0
0
1
0
0
1
1
0
1
2
0
1
2
0
1
0
1
1
2
2
1
2
0
0
1
0
1
0
0
0
2
0
1
1
0
1
1
2
1
1
1
1
1
1
0
2
1
1
1
2
0
1
1
0
0
2
1
1
0
1
1
0
1
0
2
1
0
0
1
2
1
0
0
1
0
2
2
0
1
2
1
0
0
0
1
0
1
1
2
2
1
2
1
0
1
2
1
1
2
1
0
1
0
1
2
0
1
1
3
2
1
1
2
0
2
0
2
0
1
1
1
1
1
0
0
2
0
0
1
0
1
2
1
2
2
1
0
1
1
2
0
1
1
1
1
1
0
1
0
1
2
1
1
0
1
0
0
0
1
1
2
1
0
0
1
0
0
0
1
0
0
2
1
0
1
2
2
1
1
1
1
0
0
0
2
2
2
1
1
0
1
0
0
2
1
2
0
0
2
0
0
2
1
1
1
2
0
2
1
1
1
0
2
0
2
1
0
1
2
0
2
1
2
1
1
0
2
2
1
1
2
0
2
1
0
2
2
0
0
0
0
1
2
0
0
2
1
0
0
0
2
2
1
1
1
0
0
1
1
1
1
1
1
2
1
1
0
2
0
2
2
0
1
1
0
0
0
2
1
0
0
0
1
2
0
1
0
1
0
0
2
2
2
2
1
1
0
1
0
1
2
3
2
1
1
2
2
1
0
1
1
1
3
2
0
1
1
1
0
0
0
1
1
2
1
1
2
4
0
1
1
0
1
1
2
0
1
1
0
1
0
0
1
1
0
2
1
0
1
2
0
2
0
1
1
1
0
0
0
0
0
0
1
2
1
2
0
1
1
0
0
0
1
1
1
0
1
0
2
0
2
0
0
2
1
2
1
3
0
2
0
1
2
1
2
0
1
0
1
1
0
1
2
0
0
1
1
2
1
2
0
1
0
1
0
1
1
1
4
0
2
1
0
2
1
1
1
0
0
2
0
1
0
2
1
0
0
2
1
1
2
0
0
2
0
0
0
0
0
0
0
1
2
2
2
0
0
2
0
0
0
1
2
1
0
1
1
1
1
1
0
1
2
0
0
0
1
1
0
0
0
0
1
2
2
1
0
0
1
1
0
0
0
1
0
0
0
1
1
0
1
0
0
0
1
0
0
0
2
0
1
1
2
0
1
0
0
0
2
0
2
1
0
2
0
0
0
1
0
0
2
0
1
2
0
1
1
1
2
3
0
1
1
2
2
1
0
1
0
0
1
1
1
2
0
0
0
0
1
0
0
1
0
1
0
1
2
2
2
1
1
2
0
1
1
1
0
1
2
1
1
1
0
1
0
0
0
0
1
0
0
3
2
3
1
1
0
0
1
0
0
1
1
0
0
1
1
0
0
1
2
1
1
0
0
0
0
1
0
2
1
2
0
1
0
0
2
0
1
0
1
1
0
1
2
1
1
2
2
2
0
0
0
2
1
1
0
2
1
0
0
0
0
2
1
2
1
1
2
0
1
1
1
1
0
5
0
1
1
2
0
1
2
0
0
1
1
1
2
1
0
0
0
2
0
2
1
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
2
0
0
1
1
1
1
1
0
3
0
0
2
2
0
1
2
1
1
2
1
2
1
0
2
0
2
0
0
0
1
1
0
1
0
0
0
2
0
0
0
0
0
2
2
0
1
0
1
2
2
1
2
1
1
3
2
1
0
1
2
0
1
1
1
1
2
2
1
1
0
1
1
0
0
1
1
1
1
6
0
2
1
1
1
0
2
0
2
1
2
1
1
0
0
1
0
0
2
1
0
1
0
0
0
2
3
1
2
1
1
0
0
0
1
1
0
0
0
2
2
0
2
0
1
0
1
0
1
1
1
2
1
1
0
2
2
1
3
1
0
0
1
0
2
0
0
0
1
1
2
2
1
4
0
0
0
1
1
0
1
1
2
1
2
0
1
1
1
1
2
1
0
1
2
0
1
1
2
2
0
2
1
1
1
1
2
0
0
1
1
2
1
0
2
0
3
2
1
0
1
0
0
0
2
1
1
2
0
0
2
2
0
2
0
0
1
1
0
0
1
0
1
1
2
0
2
3
0
0
2
0
1
0
0
2
1
2
0
0
0
1
0
0
0
1
1
0
1
2
0
1
0
0
0
1
0
2
0
1
2
0
0
1
0
1
1
1
0
0
0
0
0
2
2
1
0
0
0
0
2
1
1
1
1
1
1
1
1
0
1
1
1
1
0
2
2
1
2
0
0
0
0
1
1
3
0
1
0
1
1
3
0
1
0
0
0
2
2
0
2
2
1
2
0
1
0
1
0
0
1
2
1
0
2
2
0
0
2
0
0
1
0
1
3
0
0
2
1
1
0
1
2
0
2
1
0
1
0
1
0
1
0
1
0
2
1
0
0
2
0
0
0
1
1
1
0
1
2
0
1
1
3
1
1
1
0
1
0
1
1
1
2
0
2
1
2
1
1
0
0
1
1
0
0
0
0
0
2
0
0
0
0
1
1
0
1
0
2
1
1
2
0
2
0
2
2
1
1
0
1
1
1
1
0
1
2
1
0
0
1
2
0
2
2
1
1
2
1
0
7
0
1
0
0
1
0
2
1
1
2
0
1
2
1
0
2
1
1
1
0
0
1
2
1
2
1
1
1
1
1
0
0
1
1
1
1
2
0
2
1
2
1
1
1
0
0
0
0
0
0
0
1
1
2
0
0
2
1
0
1
2
0
2
0
0
1
0
1
1
1
2
0
1
0
2
2
0
0
0
1
1
0
1
0
2
1
1
2
2
1
1
2
1
1
1
1
0
0
2
1
0
1
2
1
0
1
2
2
0
0
1
2
0
1
1
2
1
1
1
1
2
0
1
0
1
1
1
0
0
2
1
1
1
2
2
1
2
1
1
0
1
1
2
1
0
0
1
1
0
5
0
1
0
2
0
1
0
1
1
1
0
1
1
0
0
0
2
1
0
0
0
1
0
1
2
1
0
1
0
0
2
1
0
2
0
0
1
1
0
1
0
1
0
1
0
1
1
2
1
2
1
2
2
0
1
3
1
1
0
0
2
2
1
0
1
4
0
0
0
2
0
0
0
0
1
1
0
0
3
0
1
1
2
0
0
0
0
1
1
1
2
0
1
1
1
1
1
1
1
2
0
0
0
1
1
2
0
2
0
1
1
1
2
2
0
0
1
0
1
2
0
1
1
1
1
0
2
1
0
2
0
0
0
1
1
1
1
0
0
0
2
2
2
1
2
1
3
0
1
0
1
1
0
0
1
1
1
2
0
1
1
2
1
3
1
2
1
0
0
0
1
0
0
1
1
3
0
1
1
1
0
2
2
0
1
1
0
2
1
0
1
0
2
1
0
1
1
0
0
1
1
0
0
0
1
0
1
0
2
1
1
2
1
2
1
0
2
0
2
0
1
1
2
0
0
2
0
0
1
1
1
2
0
0
1
0
1
0
1
1
1
1
1
1
1
2
1
1
0
1
1
1
1
0
2
1
0
2
0
2
1
1
0
1
1
0
0
0
0
0
1
0
1
0
0
0
2
2
1
0
0
1
1
1
0
2
1
0
2
1
0
0
1
1
2
0
1
1
3
3
0
0
1
0
1
2
2
0
0
1
1
0
0
2
1
1
0
0
1
0
1
2
0
1
0
1
0
1
1
0
2
0
0
2
0
0
2
0
0
0
0
0
2
1
1
2
1
1
0
1
1
1
1
0
2
1
0
1
0
2
1
0
0
0
0
1
1
0
1
1
0
2
0
1
2
0
0
2
0
1
1
2
0
0
0
0
3
1
0
1
1
1
1
2
1
1
0
1
1
1
1
1
0
0
0
1
3
0
2
0
1
0
0
3
2
0
1
1
1
1
2
1
0
0
2
1
1
1
0
0
2
0
1
0
2
0
2
0
1
0
0
1
0
0
0
0
2
0
1
0
0
1
0
0
2
5
1
0
1
0
0
1
1
1
0
1
2
0
0
0
2
1
0
1
1
1
1
2
0
0
0
0
1
0
1
2
0
0
0
1
2
1
0
2
0
2
2
0
0
1
0
2
1
1
0
1
0
0
1
0
0
1
2
0
1
1
0
2
0
0
1
0
1
2
0
0
0
0
1
0
0
1
1
1
0
1
0
0
1
2
0
0
1
0
0
0
1
0
0
1
1
0
0
0
1
1
0
0
1
0
1
1
0
1
2
1
1
0
0
1
1
2
1
1
1
1
2
1
1
0
0
1
2
0
2
1
0
1
2
1
1
0
0
1
2
0
1
0
0
0
2
2
2
0
0
0
1
2
0
0
1
0
2
1
0
0
1
1
2
1
2
1
0
1
0
2
1
1
1
2
0
0
1
0
1
0
0
0
0
1
1
1
0
2
1
1
0
1
2
0
0
0
1
0
0
0
1
2
2
1
2
0
0
2
0
2
1
2
1
0
0
0
0
2
2
0
2
0
0
0
1
1
0
0
0
2
2
1
1
2
1
1
0
0
1
1
1
0
2
2
1
0
0
0
0
0
1
0
2
0
2
1
0
2
2
1
0
1
2
0
2
2
0
0
1
1
1
2
1
1
0
0
2
0
2
0
0
1
1
0
1
1
0
2
1
0
0
1
2
1
0
0
0
2
1
0
2
1
1
0
2
2
1
1
1
0
1
1
0
1
2
1
1
0
1
1
0
0
0
1
0
1
0
1
0
1
2
0
2
1
2
0
4
2
1
0
0
0
0
1
1
1
1
3
0
1
2
0
2
0
1
0
1
0
1
1
1
0
2
0
2
4
0
2
1
0
0
1
1
1
0
1
2
0
0
1
1
0
0
0
1
0
0
1
1
0
0
0
0
1
0
1
2
0
2
1
0
0
1
0
2
1
2
0
1
2
0
1
3
0
2
0
0
0
1
2
0
0
1
0
0
1
0
2
2
2
0
2
0
2
0
0
1
0
2
2
1
2
2
1
0
0
0
1
0
0
1
0
0
1
0
0
4
2
0
2
0
1
1
0
0
1
0
1
0
0
0
0
0
0
2
1
2
1
1
0
2
0
0
1
0
1
1
2
2
2
1
0
0
1
2
1
1
2
2
2
1
0
3
0
1
1
1
0
0
1
2
1
0
0
1
1
1
2
0
1
1
0
1
2
1
0
1
0
0
0
2
0
6
0
1
0
1
0
0
0
1
1
1
0
0
0
1
0
2
0
1
1
0
0
2
0
0
2
0
1
0
0
1
1
1
1
2
1
0
0
1
0
1
1
2
0
2
1
1
0
0
0
0
1
3
2
0
0
1
1
1
0
2
0
1
1
0
0
0
2
1
2
1
2
0
0
0
0
1
0
1
0
1
1
2
1
0
1
1
1
0
0
0
1
1
1
3
2
0
1
2
1
1
0
1
0
1
1
1
1
2
0
0
1
2
2
1
1
2
2
0
0
1
0
1
0
1
1
0
1
0
0
1
0
2
0
1
0
2
0
0
2
0
1
0
0
0
1
0
0
0
0
0
4
1
1
0
0
0
2
1
1
1
0
2
0
0
1
0
0
0
2
0
0
1
1
0
1
1
0
0
1
0
0
0
2
1
2
1
2
0
0
0
0
2
3
0
1
1
0
1
0
1
1
1
0
0
0
0
2
3
1
2
0
1
1
2
1
0
2
2
1
0
1
2
0
0
2
2
0
1
1
0
3
1
0
0
0
0
1
0
1
0
1
0
0
0
2
2
2
1
0
0
1
1
1
0
1
0
2
2
2
2
1
1
0
2
0
1
0
1
1
0
1
1
0
1
0
1
1
1
1
0
0
0
1
1
1
1
0
1
0
0
0
1
2
0
0
0
2
2
0
1
1
1
1
1
1
2
0
0
2
0
0
0
1
1
2
0
2
2
0
2
0
1
1
1
1
1
0
0
2
0
0
0
1
1
0
0
1
0
2
0
0
1
0
0
1
0
2
0
0
1
1
2
0
2
0
0
2
1
1
2
2
0
2
1
0
1
1
2
1
1
1
0
0
1
2
0
0
3
1
2
2
0
0
1
1
0
0
0
2
2
2
2
1
2
0
0
1
1
0
2
0
0
1
2
2
1
0
0
1
1
1
2
2
1
1
0
0
0
0
0
2
1
0
2
1
0
1
0
0
0
1
1
1
1
0
1
1
0
2
1
2
0
1
1
0
2
2
3
0
0
0
1
1
2
0
0
2
1
1
1
1
1
0
0
0
2
1
0
2
1
0
0
1
0
0
1
1
1
1
1
1
2
1
0
1
1
1
3
1
1
0
0
1
0
1
0
1
1
2
0
2
0
0
1
1
0
2
0
1
0
0
1
0
2
1
0
0
2
1
1
2
1
1
1
0
0
0
0
0
1
2
2
0
1
0
0
1
2
0
2
1
2
1
1
0
3
1
0
1
1
1
3
0
0
0
0
0
0
1
2
2
0
1
1
2
2
0
0
1
0
0
3
1
0
2
0
2
0
1
0
2
2
1
1
1
0
0
0
2
1
0
2
2
0
1
1
1
0
0
0
2
0
0
1
1
1
1
0
2
0
1
0
1
1
2
1
1
1
2
1
1
2
0
1
2
1
2
0
0
1
1
1
1
0
0
2
0
1
1
0
0
0
2
1
0
2
2
1
0
2
0
0
1
0
2
1
1
0
1
1
2
0
0
2
0
1
1
1
1
1
1
1
0
1
1
0
2
1
0
1
1
2
0
1
1
1
2
0
1
1
0
1
0
1
1
2
0
0
2
1
1
0
2
2
1
0
1
0
2
0
0
2
0
4
0
2
1
0
0
4
1
1
0
0
1
0
2
0
0
0
0
1
0
0
1
0
2
2
0
2
0
1
0
0
1
2
2
1
0
0
1
0
0
1
1
0
0
1
1
2
2
1
0
1
0
1
0
1
0
0
2
1
0
0
1
2
1
2
1
1
0
1
1
2
1
0
1
0
0
0
2
1
1
2
0
1
1
1
0
0
0
2
0
0
0
2
1
1
0
2
2
1
1
1
2
0
1
2
0
0
0
1
2
1
1
1
2
1
1
2
2
0
0
1
1
0
0
1
0
0
2
1
1
0
0
2
0
0
1
0
1
1
1
0
0
1
2
0
0
0
1
1
1
0
0
2
2
0
1
1
2
1
1
1
0
0
0
0
1
1
1
1
0
0
1
1
0
1
0
1
0
1
1
0
2
1
2
2
2
2
1
2
0
2
1
0
0
0
1
2
0
2
0
1
0
1
1
0
2
1
0
1
0
0
0
1
1
0
2
1
0
1
2
2
0
2
0
2
1
1
1
1
0
0
2
0
2
2
0
1
2
1
1
0
1
1
1
0
1
1
0
0
1
0
0
2
1
1
0
1
1
1
0
1
1
2
2
0
2
1
0
0
0
1
0
4
1
0
0
0
0
1
1
0
1
0
0
2
1
1
1
1
2
0
2
1
1
1
1
0
0
1
0
1
1
2
1
0
0
0
1
2
2
0
0
0
0
0
1
0
1
2
0
2
1
0
1
0
1
0
0
1
1
0
1
1
1
0
0
1
1
2
0
0
0
1
2
0
1
2
0
0
1
0
2
1
1
1
1
1
2
2
1
0
1
1
0
2
2
0
1
1
1
0
1
2
0
2
0
0
1
1
1
0
1
1
1
0
1
0
0
0
1
1
2
0
0
1
1
1
0
0
1
1
1
1
1
0
2
0
0
1
1
1
0
1
0
1
2
2
2
2
1
1
2
1
1
1
1
0
1
2
0
2
0
1
1
0
0
1
2
1
0
0
2
0
2
1
0
1
2
0
0
0
0
2
0
0
3
1
0
1
1
1
0
0
0
1
0
2
2
4
2
1
2
2
0
0
0
0
1
0
0
0
2
2
1
2
0
1
2
0
0
2
1
1
0
2
1
0
2
2
1
0
2
1
2
0
1
1
0
2
1
1
0
0
1
2
0
1
1
2
2
1
1
0
0
1
1
1
0
0
1
1
1
0
1
1
2
0
2
1
1
2
1
2
1
1
1
0
3
1
0
1
3
1
0
1
1
0
1
1
2
2
0
3
1
2
1
1
1
0
2
1
0
1
1
4
0
1
0
1
0
1
0
0
0
2
2
1
1
0
0
1
0
1
1
2
0
2
2
0
0
1
1
1
2
0
0
2
0
1
1
1
2
0
2
2
1
1
0
1
0
1
0
1
2
0
0
0
2
1
1
0
2
1
2
1
1
0
1
1
0
0
2
0
2
0
2
0
2
1
1
1
0
1
2
1
0
1
1
0
1
0
1
1
1
1
0
1
1
1
1
0
1
3
0
1
1
0
0
0
1
0
1
0
0
0
1
0
0
2
0
0
0
2
0
1
1
1
2
0
0
0
0
0
0
1
1
0
1
0
1
1
0
0
2
1
0
1
0
2
1
0
0
0
2
1
1
2
1
0
2
1
1
2
0
0
2
0
0
0
2
1
1
2
0
1
0
2
2
1
1
1
0
2
4
1
3
1
0
0
0
2
0
2
1
0
0
1
2
1
1
2
0
1
2
0
0
1
0
1
0
1
0
0
1
1
0
2
0
1
0
2
3
1
0
0
2
1
1
1
0
2
1
2
0
2
0
2
2
1
1
1
0
1
0
1
1
1
0
0
3
0
1
1
2
0
0
1
1
0
0
1
1
0
1
0
0
1
2
1
0
2
2
1
0
0
1
4
0
0
0
1
1
2
1
0
1
2
0
0
0
2
1
2
1
2
2
1
0
2
0
0
1
1
0
1
0
0
0
2
1
2
0
0
1
2
0
2
1
1
2
0
1
1
1
0
1
1
1
2
1
0
2
1
1
0
1
1
1
0
0
1
0
0
0
1
1
2
2
0
1
1
1
1
0
0
3
1
1
1
1
2
1
0
1
0
1
1
0
0
1
1
1
1
1
0
0
0
0
0
3
1
2
1
0
1
1
1
1
1
1
5
2
0
1
0
0
1
0
0
0
2
0
1
0
1
2
2
0
1
1
2
1
2
0
2
0
1
1
0
0
2
0
0
1
0
0
0
0
2
0
0
2
4
0
1
1
0
0
0
0
0
1
0
0
1
3
1
1
2
1
0
2
2
0
1
0
0
1
1
0
3
1
1
1
1
1
1
0
2
1
0
1
0
0
0
0
2
2
1
2
2
0
1
1
0
1
1
0
1
2
1
2
1
0
1
0
1
1
0
0
2
2
0
1
1
0
1
1
0
0
1
2
1
0
1
0
1
0
0
1
0
0
1
1
0
0
1
2
0
2
0
1
0
1
1
0
1
1
0
1
1
0
2
1
0
0
1
1
1
0
1
1
0
1
0
1
1
1
3
0
1
1
1
1
0
1
0
1
0
1
2
0
1
1
1
1
0
1
0
1
2
3
1
0
1
1
2
1
1
1
0
0
1
1
1
1
2
0
1
0
1
2
1
1
2
0
0
1
2
0
1
1
2
0
0
1
1
1
2
0
0
0
1
1
1
1
1
1
0
0
0
1
0
0
5
1
0
1
1
0
0
0
0
0
2
2
0
2
0
0
0
0
0
1
1
1
1
1
0
1
1
0
0
2
1
0
1
1
0
1
0
2
0
0
1
0
2
1
0
0
2
2
2
1
0
0
0
0
0
1
1
0
1
1
0
1
0
1
1
2
1
1
2
2
0
0
0
1
2
0
0
0
0
1
1
0
2
1
2
0
1
0
0
1
0
1
0
1
1
1
0
1
2
1
2
1
0
2
2
1
2
1
0
0
1
1
0
1
2
2
1
1
1
1
1
2
1
1
0
1
2
2
1
1
1
3
1
0
0
1
0
1
0
2
0
0
2
0
0
3
0
0
1
0
2
1
0
1
1
2
2
0
0
2
1
0
0
1
0
1
0
1
2
0
0
0
2
1
0
1
1
0
1
1
2
0
1
1
2
2
0
1
2
2
2
1
1
1
0
0
1
2
1
0
1
1
1
1
0
2
1
2
0
0
1
2
0
0
1
2
0
2
1
0
0
1
2
0
0
1
0
0
1
2
0
0
2
1
2
1
0
2
0
2
0
0
1
1
2
1
1
1
1
0
2
0
0
0
1
2
0
1
0
3
0
1
1
1
0
0
0
0
0
2
0
1
2
0
2
1
1
1
1
2
1
1
1
0
0
0
1
2
1
2
2
1
0
1
0
1
0
1
2
2
1
1
1
2
0
0
0
1
1
1
0
1
1
0
0
1
0
0
1
1
1
1
0
1
0
1
1
0
2
0
2
0
0
2
0
0
0
2
2
1
0
0
0
1
2
2
0
1
1
0
3
1
1
1
1
1
2
0
2
1
8
0
2
2
1
1
0
1
2
1
0
1
0
0
1
0
1
0
0
1
1
1
1
3
2
0
0
0
0
0
1
2
2
1
2
0
1
1
1
0
3
1
0
1
1
0
0
1
2
0
0
1
2
3
0
1
1
1
0
1
1
1
1
0
0
1
1
2
6
0
0
0
2
3
0
1
0
0
0
1
3
0
0
1
2
2
2
1
1
0
2
2
1
1
1
0
2
2
2
1
1
1
1
0
0
0
1
2
2
1
1
1
1
1
0
2
0
0
0
1
0
2
0
0
2
2
0
1
1
2
2
1
2
0
1
1
0
0
1
0
0
1
1
0
1
1
0
1
0
2
0
3
0
1
2
0
3
0
0
2
0
0
1
0
2
1
2
1
2
0
1
2
2
1
2
2
1
1
0
0
2
0
0
0
1
1
1
1
1
1
0
0
1
0
0
0
2
3
2
1
0
1
0
1
1
1
2
1
1
2
0
0
0
0
1
1
0
0
2
2
1
1
1
1
1
1
0
1
0
1
0
1
2
1
2
0
0
1
0
0
1
1
0
0
1
1
1
2
0
0
0
2
2
1
4
1
0
0
0
2
0
2
1
2
0
1
1
2
0
1
0
0
0
1
2
0
1
0
0
1
1
1
0
2
1
0
0
2
2
2
1
2
2
1
1
1
1
1
0
0
0
0
1
1
2
0
2
2
1
0
1
1
1
2
0
0
2
1
1
1
0
1
1
2
0
1
1
0
1
0
1
1
0
2
4
1
2
1
1
2
0
2
2
0
1
0
0
2
2
1
1
2
1
0
2
2
0
1
0
0
1
3
1
0
0
2
0
2
0
2
2
1
0
0
0
2
1
1
1
1
1
0
0
2
0
1
0
2
1
0
0
1
1
2
2
2
1
2
1
0
0
1
1
2
2
1
2
1
0
2
1
1
0
1
1
1
1
0
0
2
2
0
1
0
0
1
2
0
0
2
0
0
1
3
0
2
1
0
0
0
1
2
1
1
1
0
1
1
1
1
0
0
0
1
1
0
0
1
2
3
1
0
2
2
0
0
1
0
2
2
1
2
0
1
2
0
1
1
0
1
0
0
1
0
2
2
1
2
1
1
2
1
1
2
1
2
2
0
2
0
1
0
2
0
0
0
1
0
2
2
1
0
1
1
0
1
1
0
1
2
0
0
0
1
0
3
1
0
1
0
0
1
2
0
0
1
0
2
0
2
1
1
2
0
0
1
1
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
2
0
1
1
1
2
1
2
0
0
2
1
1
2
1
0
2
0
0
1
0
0
0
0
0
0
0
1
1
2
2
1
1
1
1
0
0
2
1
2
0
1
1
0
0
1
1
2
1
2
2
1
0
0
1
1
0
2
2
1
0
1
1
1
0
0
2
0
1
2
2
2
2
0
2
0
1
5
1
1
1
0
2
0
1
1
0
1
1
2
1
1
1
1
2
1
1
0
1
0
1
0
2
2
0
2
0
0
1
0
0
1
1
2
1
2
2
1
1
1
1
1
1
2
0
1
1
2
2
1
1
0
1
0
1
1
2
1
1
0
1
0
1
1
1
0
2
0
1
0
0
1
0
0
2
0
0
1
1
1
1
0
0
0
1
0
0
0
2
0
1
2
1
1
1
1
0
1
1
2
0
1
1
2
1
0
1
1
1
2
0
0
0
2
1
1
0
2
1
0
2
1
0
1
2
0
2
0
1
1
1
0
0
2
1
2
0
2
0
2
1
1
0
2
1
0
0
1
2
0
1
0
1
0
1
2
1
0
4
3
0
0
0
1
0
2
0
0
2
1
0
0
0
0
1
0
2
0
1
0
0
0
1
1
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
1
2
2
1
2
2
2
0
2
0
0
1
0
0
0
0
1
0
0
0
1
1
1
0
2
1
0
1
0
1
1
0
2
1
0
1
1
1
1
1
0
1
0
2
0
0
2
0
0
0
1
1
0
0
0
1
1
2
0
0
1
2
1
1
1
2
0
2
0
1
1
0
0
0
1
1
1
0
0
0
0
0
1
0
1
1
0
2
1
1
2
0
1
1
1
0
1
1
1
0
0
2
2
1
1
1
0
0
1
1
1
0
1
1
1
0
3
0
1
1
0
2
2
1
1
1
0
1
2
1
1
1
0
0
0
0
2
1
1
2
2
2
0
1
1
0
0
0
0
1
1
0
0
0
2
1
0
2
1
1
1
2
0
2
1
0
0
1
0
0
0
1
2
0
0
2
0
0
0
0
0
0
2
1
0
0
1
2
0
2
0
0
0
1
1
0
1
0
2
2
0
1
0
2
1
2
0
1
0
1
0
0
0
1
0
0
0
1
1
0
1
1
1
0
2
0
2
2
1
0
1
0
0
2
1
0
1
1
0
0
2
0
2
1
1
4
1
1
1
3
0
0
1
2
1
1
1
2
3
4
0
1
1
2
1
2
0
0
0
1
2
0
0
0
1
2
0
0
1
0
1
2
1
0
0
1
1
0
1
0
0
1
2
0
0
1
1
1
2
0
1
1
0
0
1
0
1
0
0
0
1
0
0
1
1
1
0
2
0
1
1
1
0
2
1
0
0
0
0
0
1
2
2
0
0
0
2
1
0
0
0
0
2
1
0
1
1
2
0
1
2
0
0
0
1
0
0
0
1
1
0
0
1
0
0
2
1
0
2
0
1
1
1
1
1
4
0
1
1
2
2
0
0
0
0
1
1
0
0
2
1
0
2
0
1
0
2
0
1
0
0
1
1
1
0
2
2
0
1
0
0
0
1
0
3
2
0
0
1
1
1
2
1
0
2
0
1
0
0
1
0
1
1
0
1
1
0
0
2
0
1
1
1
2
1
1
1
0
1
2
1
0
0
0
1
1
0
3
0
2
1
0
2
0
2
1
2
1
1
1
2
0
2
1
2
1
0
0
2
0
1
1
2
0
1
2
1
2
2
0
0
0
1
0
0
2
0
1
0
1
1
0
0
0
1
1
0
2
1
2
2
1
0
0
2
1
0
0
0
1
1
2
2
1
1
0
0
2
0
0
1
0
0
1
1
2
0
2
1
1
2
1
0
0
0
0
1
2
5
1
1
2
1
1
2
2
2
0
1
1
1
1
1
2
1
2
1
0
2
2
0
0
1
0
2
1
1
0
0
0
2
0
2
3
2
0
1
0
2
1
0
1
0
0
0
0
1
0
0
1
0
1
2
1
1
1
1
1
2
2
2
1
3
0
1
1
0
2
2
2
4
0
1
0
1
2
0
1
1
0
1
0
2
1
2
1
1
1
1
0
0
0
2
1
1
1
0
2
1
1
0
0
0
0
1
1
0
2
1
0
1
1
1
1
0
2
0
2
1
0
0
0
1
1
0
2
2
0
3
1
0
0
0
0
1
2
1
1
2
1
1
2
0
1
1
0
0
1
1
0
0
2
0
2
1
1
0
1
0
1
2
1
2
0
0
1
1
1
0
1
0
2
0
1
0
2
0
3
1
0
0
1
2
2
0
0
0
0
0
2
1
2
2
0
0
0
4
1
2
1
1
0
0
0
0
3
1
1
1
1
1
0
0
0
2
0
0
0
0
0
1
2
2
0
0
0
1
0
0
2
1
1
1
2
1
2
0
0
0
1
0
2
1
1
1
1
1
0
0
0
2
0
1
0
0
2
0
0
1
1
1
0
2
1
1
0
0
0
3
1
2
2
0
1
1
1
2
0
0
2
0
1
0
0
0
0
0
1
1
2
1
2
1
1
1
2
0
0
1
2
1
1
1
0
0
1
0
1
1
0
2
1
1
0
0
0
1
2
1
1
3
1
1
0
1
2
1
1
0
0
2
2
2
0
2
0
0
1
0
0
2
0
0
0
0
1
2
1
2
1
0
1
2
0
1
1
0
2
2
0
0
1
2
0
0
1
1
2
0
1
1
1
0
2
1
2
0
0
0
0
0
1
0
2
0
0
1
1
0
0
0
0
1
0
2
2
0
3
0
0
1
1
1
3
2
0
2
2
0
3
0
1
2
2
1
0
2
0
1
2
1
0
3
1
2
2
0
1
0
2
5
0
1
1
0
1
2
1
1
0
1
2
0
0
0
0
0
1
1
2
2
0
1
1
0
2
1
2
0
0
0
2
2
0
0
3
2
0
1
0
2
1
1
2
1
0
2
2
0
3
1
2
1
1
1
0
1
0
0
0
0
0
0
1
1
1
0
1
0
1
0
2
0
1
2
1
1
0
0
0
0
0
1
0
1
1
0
0
2
0
1
0
0
1
0
0
1
1
0
1
2
1
2
0
0
1
0
0
0
1
2
1
0
0
0
0
0
1
0
1
0
3
1
2
0
0
1
2
1
1
0
2
1
0
1
1
2
0
1
0
0
0
1
2
0
1
1
0
1
1
1
1
2
0
2
1
0
0
1
0
0
0
1
1
1
1
1
0
0
0
1
1
3
2
0
0
0
3
0
2
0
2
1
1
0
0
0
1
1
2
3
1
0
1
2
1
2
1
1
0
1
1
1
1
1
0
1
1
1
0
1
1
0
1
1
1
0
1
1
1
1
0
1
0
0
1
0
1
1
0
1
0
2
3
0
0
0
2
2
0
0
2
1
2
1
1
0
2
0
1
0
2
1
1
0
0
1
2
1
2
1
2
1
0
0
0
0
2
1
2
0
1
1
0
1
1
0
0
2
0
0
0
1
2
1
2
2
2
0
0
1
2
0
0
2
1
0
2
0
2
1
1
1
0
1
2
0
0
1
0
2
3
1
0
0
1
1
1
0
1
1
1
0
0
0
1
0
0
1
2
0
1
0
1
2
0
0
1
1
0
1
3
0
0
0
2
1
2
1
2
1
2
1
1
1
0
1
1
1
0
0
0
0
0
1
2
0
1
2
0
1
2
1
0
1
0
2
1
1
1
2
0
0
0
0
1
0
1
1
1
0
1
1
0
2
0
0
0
0
1
1
1
1
1
1
2
1
0
2
0
1
0
1
0
0
1
1
0
1
1
0
0
2
2
0
0
2
1
1
1
1
1
0
0
2
1
2
2
0
1
0
2
1
1
2
0
0
0
0
0
3
1
0
1
1
1
2
1
2
0
0
0
1
1
0
2
1
1
0
1
0
0
1
2
2
1
0
0
1
1
0
1
0
0
0
1
1
1
0
2
0
0
1
0
0
1
1
2
3
1
0
1
1
1
0
1
1
0
0
2
2
0
0
0
1
0
1
2
3
2
1
2
1
2
1
0
1
1
1
0
2
2
2
1
0
0
1
2
1
1
3
0
1
1
0
1
1
1
0
0
0
0
3
1
1
0
0
0
1
1
1
1
2
0
1
0
2
0
0
0
1
0
0
1
0
1
2
0
2
1
1
0
0
1
0
0
1
0
2
2
0
0
1
1
1
2
0
0
2
1
2
1
0
1
0
0
2
2
1
1
0
0
2
0
0
1
0
2
0
2
1
0
1
1
0
2
0
1
0
0
2
0
1
0
0
1
1
1
0
0
3
0
1
0
1
2
0
2
1
1
1
2
0
1
0
1
0
1
1
2
1
1
0
1
2
1
2
0
1
2
0
1
0
1
1
1
1
0
0
2
1
2
2
1
0
1
1
1
0
0
0
0
0
0
0
1
1
0
1
2
2
0
3
2
1
1
0
2
0
0
0
1
0
0
0
1
1
2
2
1
2
0
1
1
0
0
0
0
1
0
0
1
1
0
0
0
1
1
1
1
0
2
2
2
2
0
0
2
1
0
2
0
1
0
2
2
2
0
0
2
1
1
2
0
2
1
1
1
0
0
0
1
2
2
1
2
0
1
0
1
0
0
3
0
0
2
1
1
0
1
0
0
0
0
1
2
1
0
0
2
2
0
0
0
2
4
1
2
0
1
2
1
2
2
0
0
1
0
0
2
1
1
1
1
0
1
1
3
2
0
1
2
2
0
8
2
0
2
1
2
1
1
1
2
1
2
1
1
0
1
0
1
0
2
2
1
1
0
0
2
0
2
0
0
1
1
0
0
1
1
0
0
1
2
1
1
3
2
0
0
0
1
0
0
0
1
1
1
0
1
0
0
1
0
1
2
0
0
0
1
0
1
0
1
1
2
2
2
2
0
0
0
1
0
0
0
2
2
1
2
0
0
1
0
2
2
0
1
0
0
0
1
0
0
0
0
1
1
2
0
0
1
0
0
0
2
0
0
0
2
2
1
1
1
0
2
0
1
1
1
0
0
0
1
1
2
1
2
1
0
1
0
1
1
0
2
1
0
1
1
0
4
0
1
0
1
0
1
0
1
0
2
0
2
0
1
0
2
2
0
0
1
1
2
1
0
0
2
1
1
0
2
2
0
1
3
1
0
1
1
0
2
1
0
2
0
0
0
0
1
3
0
0
0
2
1
1
1
0
0
2
1
0
1
0
1
1
1
1
0
0
1
0
0
1
0
1
0
1
2
1
0
1
1
0
2
0
1
0
1
1
0
0
3
0
1
0
0
1
0
2
1
1
2
0
0
0
0
0
0
1
1
1
1
0
2
1
1
2
1
1
1
1
2
0
1
2
0
1
1
0
2
0
0
1
1
2
1
0
1
2
2
2
1
0
0
0
0
2
0
1
0
1
2
1
2
2
1
0
0
2
1
2
1
0
2
1
1
0
1
2
0
1
1
0
1
1
0
0
0
0
0
2
1
1
0
1
0
0
0
2
1
0
2
1
0
1
1
1
1
0
1
0
0
1
1
0
2
0
0
0
0
0
1
1
1
2
1
0
1
1
2
0
1
0
0
0
2
1
0
1
1
2
0
1
0
1
1
1
0
1
1
1
0
0
1
0
1
2
1
2
2
1
1
1
0
0
1
0
0
2
2
2
2
1
1
0
0
2
0
1
2
0
0
1
2
2
2
1
0
2
2
0
1
0
0
3
1
2
1
0
2
1
0
2
2
0
2
0
0
0
0
2
2
1
0
1
0
1
0
2
2
1
2
0
1
1
0
0
0
1
1
2
2
1
1
1
0
0
1
0
0
0
0
2
1
1
1
2
2
1
1
0
0
1
1
0
2
0
1
0
1
1
0
0
1
1
2
1
0
1
0
0
2
2
0
2
1
0
1
1
0
1
0
2
1
2
2
1
1
0
1
0
1
1
1
0
4
1
3
0
0
2
0
1
1
1
0
0
1
1
2
0
0
1
2
0
1
0
1
1
1
1
1
0
1
1
0
0
2
1
2
0
1
1
1
0
1
2
2
0
0
1
1
2
1
0
1
2
1
1
0
2
1
0
1
1
0
0
0
0
0
2
1
2
0
1
1
0
1
0
1
0
2
0
1
0
2
0
0
1
1
1
1
1
1
2
0
3
0
0
0
1
0
1
1
0
2
1
0
0
0
0
1
3
0
2
1
3
2
1
0
1
1
2
1
1
1
0
1
0
2
2
0
0
1
1
1
0
0
0
1
0
0
1
1
2
0
1
1
1
0
2
0
0
1
0
2
0
2
1
1
0
2
0
1
2
1
3
0
0
0
2
0
1
0
0
0
2
1
0
2
3
1
2
0
1
0
0
0
3
2
1
0
0
0
0
1
0
0
2
1
1
1
0
0
0
0
3
2
0
3
1
2
1
2
2
2
0
1
1
0
1
2
2
0
1
1
0
0
1
2
1
4
1
2
0
0
0
0
0
1
0
2
0
0
1
2
1
1
2
1
1
1
1
1
1
0
1
1
2
0
0
0
0
0
0
2
1
0
1
2
0
1
1
0
0
0
1
2
1
0
0
0
0
2
0
1
1
1
0
1
3
0
2
1
2
1
1
0
2
2
0
0
0
5
1
0
0
0
0
0
0
2
0
0
2
1
1
0
1
1
2
0
2
0
1
1
1
0
0
1
0
2
1
2
1
0
1
0
0
1
0
1
2
0
0
0
1
2
2
2
2
1
1
1
1
1
0
0
1
1
3
0
2
1
1
2
1
0
1
2
0
2
2
2
1
0
1
1
2
1
1
2
0
1
0
0
2
0
2
2
1
1
1
0
0
0
0
0
0
1
0
0
0
2
1
0
0
2
0
0
0
0
1
1
0
2
2
2
1
0
1
1
1
0
0
2
1
0
0
0
2
0
0
2
2
1
0
0
0
0
1
2
1
2
0
1
0
1
0
8
0
1
0
0
0
1
1
3
0
1
0
1
2
0
1
1
0
1
1
1
0
2
1
0
2
0
0
0
1
2
1
2
1
0
0
1
1
1
2
1
2
1
2
2
1
1
1
1
0
0
2
1
0
0
2
0
2
0
3
2
0
3
4
1
1
0
0
0
0
1
1
2
0
1
2
1
2
0
0
0
0
1
2
1
1
1
2
0
1
0
0
1
0
1
1
1
2
1
0
0
1
1
2
1
1
1
0
0
2
2
0
0
1
2
0
0
0
0
0
0
1
1
1
0
0
2
0
1
2
0
1
1
1
0
0
1
1
2
1
2
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
1
0
0
2
0
2
0
1
2
1
2
1
0
1
2
1
2
1
0
0
0
2
1
2
0
0
1
1
1
1
1
1
0
0
1
1
1
1
1
0
0
2
1
0
0
2
1
1
0
0
0
1
2
0
0
0
1
1
1
2
1
1
1
0
2
2
1
0
1
0
0
1
0
0
1
0
1
0
0
2
0
2
1
2
1
2
0
2
1
1
0
1
1
1
1
1
0
1
0
2
0
0
1
1
0
1
2
1
1
1
0
0
1
0
2
1
1
2
2
1
2
1
1
1
1
0
2
2
0
1
2
1
0
1
0
2
0
1
1
0
2
0
0
0
0
2
0
1
0
1
1
2
2
2
1
0
2
1
0
0
1
0
1
1
0
1
2
1
2
0
1
0
1
2
1
0
1
0
1
1
1
0
0
2
1
0
0
1
2
1
1
0
0
1
0
1
3
1
0
2
0
1
0
1
1
3
0
4
1
1
0
1
0
0
1
0
0
0
0
2
0
2
0
0
0
1
1
2
1
1
1
0
0
1
0
0
1
0
1
2
2
0
1
1
1
1
0
1
1
0
2
0
0
1
1
2
0
1
0
0
0
0
0
2
0
2
2
1
1
2
0
2
0
1
2
2
2
2
1
2
1
0
2
1
0
1
1
0
0
0
2
1
1
0
0
0
2
2
2
0
0
2
2
0
1
0
0
0
2
1
0
0
0
1
0
1
0
0
0
2
0
0
1
1
1
0
0
1
1
1
0
1
0
1
1
2
2
1
1
0
0
1
1
1
2
2
1
0
1
0
1
2
0
1
1
0
0
1
0
1
5
1
2
0
2
1
2
1
2
0
1
2
1
1
0
0
2
0
1
2
0
2
1
0
0
2
1
1
2
0
2
2
2
1
1
1
1
0
0
0
2
1
2
1
1
0
2
2
0
2
1
0
2
2
1
1
0
2
1
0
0
0
1
2
2
0
0
2
3
1
0
1
1
1
1
0
2
2
0
0
0
1
0
2
2
1
0
0
2
0
0
1
0
0
1
1
0
0
1
1
1
1
1
0
1
0
1
2
2
0
0
1
0
2
1
0
1
1
0
1
0
1
1
2
2
0
1
0
0
2
0
0
0
0
1
0
0
8
1
1
1
2
1
0
0
0
2
0
0
1
0
0
1
0
1
1
1
0
2
1
1
1
2
1
0
0
0
1
2
1
0
1
0
2
1
0
1
1
0
0
0
0
1
2
1
1
0
1
0
1
1
2
2
0
1
0
2
0
1
0
2
0
0
0
1
1
0
2
2
0
2
0
1
0
0
1
2
0
1
0
0
1
0
3
0
0
0
1
1
0
0
1
1
0
0
1
0
1
1
1
0
0
1
2
2
0
0
0
1
2
0
1
1
0
0
0
1
2
2
0
0
1
2
1
2
1
1
1
0
1
1
0
0
1
1
0
0
0
1
1
0
0
1
0
2
1
1
0
1
1
2
0
2
0
1
0
2
2
0
0
1
0
0
1
1
2
0
1
0
1
0
1
2
1
0
2
1
2
1
0
3
0
0
1
1
0
0
1
0
0
0
2
2
0
1
2
0
0
1
1
0
1
0
0
0
1
0
0
1
1
1
1
0
0
1
2
0
1
2
1
2
1
0
1
2
1
0
1
2
0
1
0
1
0
1
0
2
0
3
2
1
1
1
0
0
1
0
0
1
1
0
1
1
0
1
1
1
1
1
1
0
0
2
2
2
0
1
1
1
1
0
1
1
1
1
0
1
0
1
1
0
1
0
1
0
2
0
0
2
1
0
2
0
2
1
1
1
0
0
0
1
2
0
2
0
0
0
1
2
0
2
2
1
1
1
2
0
0
1
2
1
1
2
2
1
0
0
0
2
1
2
0
0
0
2
1
0
2
0
0
0
1
0
1
0
0
2
2
0
2
1
1
0
0
0
0
0
0
0
0
0
1
1
1
0
2
0
0
1
0
1
2
1
0
0
0
0
1
1
1
0
0
0
0
1
0
1
0
0
1
0
0
1
1
1
2
1
1
0
0
0
1
0
0
0
1
0
0
1
1
2
2
0
1
2
1
0
0
0
1
2
0
1
1
1
2
0
2
1
0
0
1
0
1
2
0
2
2
2
0
0
1
1
0
1
0
1
1
1
0
1
1
2
1
1
0
1
0
2
1
1
1
0
2
1
1
2
0
0
0
1
0
2
2
3
1
2
0
2
0
0
0
1
0
0
0
0
1
0
1
2
0
0
1
0
0
3
1
1
0
0
1
1
0
2
1
2
2
1
1
0
2
2
1
1
0
0
0
1
2
2
2
3
1
1
2
2
1
1
0
0
0
1
1
1
0
0
0
0
1
2
2
1
1
1
1
0
0
1
1
0
2
1
1
0
1
1
1
1
1
1
1
0
1
2
0
2
0
0
1
0
1
3
0
0
2
0
0
0
1
0
2
0
1
2
1
1
1
2
1
2
1
2
2
0
0
0
1
0
0
0
0
1
2
0
0
1
0
0
0
0
0
2
2
1
2
0
1
0
0
1
1
2
3
2
1
0
0
2
1
1
0
1
1
1
2
1
0
2
0
1
2
2
1
1
0
1
1
0
1
1
1
1
1
0
2
0
0
1
0
0
2
2
1
1
1
0
1
0
1
1
0
0
2
2
0
2
0
1
0
0
2
1
1
2
1
0
2
0
2
1
1
1
1
0
2
0
1
0
2
2
0
1
2
1
2
1
1
0
0
2
0
2
0
0
1
2
1
0
1
0
2
1
2
1
1
0
0
1
1
0
0
0
0
1
1
1
2
1
2
1
0
0
0
1
1
1
0
1
1
1
0
0
2
0
0
2
1
0
2
1
0
0
1
1
0
1
1
2
1
1
1
1
1
2
0
1
0
1
2
1
2
1
1
2
0
3
0
0
0
0
0
1
1
0
0
0
1
1
1
2
1
2
2
0
0
0
0
0
0
1
2
2
1
1
0
0
1
2
2
1
0
2
1
1
1
0
0
2
0
0
0
1
1
1
0
2
1
1
0
0
0
2
1
1
1
0
2
2
0
1
1
0
0
2
1
1
0
0
2
2
0
2
0
1
2
1
1
1
1
2
0
1
2
1
2
0
0
2
0
1
0
0
1
2
0
0
1
2
2
1
1
1
0
1
1
0
1
0
2
1
2
2
2
4
1
0
0
0
0
0
1
0
2
0
2
1
2
0
1
0
0
1
0
1
4
0
1
1
1
1
1
1
1
0
0
1
1
0
2
2
0
2
0
1
1
2
0
2
0
2
0
1
0
1
2
0
2
1
1
1
0
2
2
2
2
0
2
1
2
1
1
1
0
1
0
2
1
1
1
1
2
0
1
1
0
1
0
2
2
2
1
0
1
0
2
0
0
2
1
1
0
1
0
1
1
0
0
0
1
0
2
0
1
1
0
0
0
0
1
0
0
1
0
2
1
0
1
2
0
2
2
1
0
1
0
0
0
1
0
2
2
1
1
0
0
2
1
2
1
1
1
0
0
0
1
1
0
1
0
1
0
1
1
0
3
2
2
1
0
0
1
1
0
0
1
0
1
2
1
0
0
0
1
0
0
2
0
1
2
0
1
0
2
1
0
1
0
0
0
2
0
0
1
2
1
0
0
1
0
0
3
1
0
0
1
1
1
1
2
1
2
1
2
1
2
2
1
0
2
0
1
0
2
0
0
0
1
2
0
1
0
0
1
0
0
1
1
2
1
1
1
0
0
0
2
2
0
0
1
1
1
1
0
0
1
1
1
1
1
0
2
1
0
1
1
0
1
3
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
2
1
0
1
0
2
1
2
0
1
2
0
2
0
2
0
0
0
0
1
2
2
1
0
2
1
0
2
0
2
0
1
1
2
0
0
2
0
2
1
0
1
0
1
0
0
2
2
1
2
0
0
0
1
0
1
1
1
1
1
1
0
1
0
1
1
1
0
1
0
0
0
0
1
0
1
0
0
2
1
0
0
1
2
1
1
0
0
2
0
1
1
0
0
0
2
3
2
0
1
2
0
2
1
0
2
0
0
1
2
1
0
2
0
1
2
1
0
2
1
2
1
0
0
1
1
1
0
1
0
2
1
1
1
1
0
0
1
1
0
0
2
1
2
1
1
0
1
1
2
1
1
1
0
1
0
1
0
0
0
2
0
2
1
2
1
0
1
2
0
1
1
0
1
0
2
1
1
1
1
0
1
2
0
2
0
1
2
0
0
1
2
2
1
1
0
2
1
2
3
0
2
0
0
0
1
0
0
1
1
2
0
0
2
1
1
1
0
1
0
2
2
2
0
0
0
2
2
0
1
0
2
0
0
0
0
0
1
0
1
0
2
1
2
0
1
1
0
0
0
1
0
0
2
1
2
2
1
2
1
0
1
2
0
2
0
1
2
0
2
0
2
1
1
0
0
1
0
2
0
0
1
0
3
1
0
2
3
1
1
2
0
0
2
2
2
1
0
0
2
0
0
1
0
0
3
1
0
1
1
0
1
0
0
1
1
0
0
0
1
1
0
2
1
0
0
3
2
0
1
0
2
1
2
0
1
1
0
1
0
0
1
1
1
1
2
0
2
1
2
0
1
1
1
0
0
1
2
1
1
0
1
1
2
0
1
0
0
0
0
0
0
0
1
0
1
2
1
2
1
0
1
2
0
2
2
0
1
1
1
0
1
1
0
2
2
0
0
0
0
0
0
0
0
0
1
0
1
0
1
2
2
1
1
1
1
1
0
2
2
0
0
1
0
0
0
1
0
2
2
2
1
1
0
1
1
1
1
1
0
0
1
0
0
1
1
2
0
0
1
0
0
1
2
0
1
1
1
1
1
0
1
0
1
0
2
1
1
0
2
0
1
0
0
1
0
1
0
2
0
0
1
0
0
2
1
0
1
1
1
1
1
1
2
1
1
0
2
0
2
3
1
0
2
1
0
1
0
2
1
2
1
1
2
0
0
0
0
1
2
1
0
1
0
2
1
1
2
0
2
2
0
1
0
1
0
1
0
1
1
0
1
0
0
2
1
1
1
1
0
0
0
1
0
0
2
0
2
0
0
1
0
1
0
0
1
1
1
0
2
0
1
0
2
2
2
2
2
1
0
1
1
2
0
1
1
1
1
1
0
1
0
1
0
2
0
0
0
2
0
1
2
0
1
0
2
2
0
1
2
2
2
1
1
0
2
2
0
0
1
2
0
1
2
1
0
1
0
0
1
2
0
0
1
1
1
0
2
1
0
2
2
0
1
2
0
0
0
0
2
1
1
1
1
1
0
1
0
0
2
1
2
1
1
2
1
0
1
1
0
0
2
0
1
0
0
1
0
2
0
0
1
0
1
1
1
1
0
2
1
1
2
2
2
2
2
1
0
0
0
0
1
0
2
1
0
0
0
0
2
0
0
1
0
1
0
0
0
1
2
0
0
1
0
0
1
1
1
3
0
0
1
1
0
1
1
2
1
2
1
0
0
0
0
0
1
2
1
1
1
2
2
0
0
0
2
0
0
2
1
2
1
2
0
1
1
1
2
2
0
0
1
1
1
1
0
1
2
2
2
1
1
1
2
1
0
1
2
2
1
0
1
1
1
2
2
1
3
2
0
1
0
1
1
1
2
0
0
1
2
0
2
2
2
2
0
1
0
0
0
0
1
1
0
1
1
2
1
1
0
0
1
2
2
0
2
1
0
0
0
2
0
2
2
1
1
0
0
0
2
0
0
0
2
0
1
0
1
1
1
2
0
1
0
0
1
1
1
0
1
1
0
0
2
2
1
2
1
1
1
0
0
2
1
1
2
1
0
1
2
0
2
0
2
1
1
1
0
0
1
1
0
0
0
0
1
1
1
0
0
1
0
0
0
0
2
2
2
1
0
1
0
1
2
2
1
1
1
1
0
1
1
0
0
0
0
1
2
1
2
0
2
2
0
0
1
0
2
0
1
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
1
0
1
1
0
0
0
0
1
1
1
0
2
1
1
2
2
1
1
1
1
1
2
2
1
0
0
0
2
1
0
0
0
1
0
1
0
0
2
0
0
0
2
2
1
2
1
0
0
2
0
0
0
0
2
1
2
1
0
0
1
2
0
1
2
0
0
0
3
0
2
0
2
1
1
1
0
0
1
1
2
0
1
0
0
0
2
1
1
3
0
0
2
1
0
1
1
2
1
1
1
1
0
0
0
0
2
2
1
1
0
1
2
0
0
0
1
2
1
5
1
1
0
2
2
1
1
2
0
2
1
2
0
0
1
1
2
1
1
2
0
1
0
0
0
0
0
0
2
1
1
2
1
2
3
1
2
1
0
2
0
0
1
0
1
1
1
1
1
1
2
2
0
1
0
0
0
2
1
2
0
2
1
0
1
0
1
1
1
1
1
1
0
2
0
1
0
1
1
1
1
1
1
1
0
0
0
1
1
2
1
0
0
0
2
2
2
0
2
2
1
0
0
2
0
0
0
2
1
1
1
1
2
1
0
0
1
2
0
0
1
0
1
1
1
0
0
1
2
0
1
2
1
2
0
0
1
1
1
0
1
0
2
1
2
0
0
1
0
0
1
1
1
1
1
3
2
0
0
0
2
0
0
1
2
1
0
0
0
1
0
2
2
1
0
0
0
0
2
0
1
2
0
0
3
0
0
1
0
0
0
1
2
0
0
2
0
1
0
0
1
1
2
0
1
0
2
0
2
1
2
0
2
1
0
0
2
1
2
1
1
0
0
1
1
0
0
1
2
1
1
0
1
1
1
2
0
0
1
2
0
1
1
2
0
0
2
1
0
1
0
1
1
0
1
2
0
1
0
2
1
1
1
0
0
0
0
1
0
0
0
1
0
0
4
2
2
1
2
0
3
0
0
3
1
0
0
0
0
1
1
2
0
1
2
1
1
0
1
0
0
0
0
2
2
0
3
2
0
0
1
1
1
0
1
0
1
2
1
1
2
1
2
2
0
0
0
2
2
0
1
1
1
0
1
2
1
0
0
1
0
0
0
2
0
2
0
2
1
1
1
0
0
0
0
0
1
1
1
2
2
0
1
0
1
2
2
2
1
1
1
1
0
1
0
2
1
0
1
0
0
0
2
1
1
1
4
1
0
0
0
1
1
0
1
2
1
0
1
2
0
1
0
1
0
1
0
1
1
2
0
1
1
0
0
2
2
0
1
0
1
1
0
2
0
0
1
0
0
1
1
0
2
2
2
1
0
0
2
1
1
1
1
1
0
0
2
2
1
1
2
2
2
0
1
1
1
0
1
1
0
0
1
2
1
1
2
1
1
1
0
1
2
1
1
0
1
1
0
0
0
2
1
0
0
5
2
0
0
0
1
2
2
0
1
0
1
0
2
0
1
1
2
1
0
0
2
2
2
1
1
1
1
1
0
1
0
1
1
0
2
1
0
1
0
1
2
0
1
0
1
1
1
0
0
1
0
1
0
1
1
0
0
0
0
1
1
0
1
0
1
0
1
0
1
1
2
1
0
1
2
1
0
1
2
0
0
0
1
0
1
0
0
0
0
1
0
1
0
1
0
0
0
2
0
0
1
1
0
1
0
1
2
1
0
0
2
3
1
2
0
2
1
0
1
1
1
0
2
2
2
2
0
1
0
0
1
2
2
1
1
1
0
2
1
0
1
0
2
2
1
0
1
1
2
0
1
2
2
0
0
2
2
0
0
1
0
0
0
2
0
0
0
0
0
1
0
1
1
2
0
1
2
0
2
2
1
1
0
1
2
0
1
1
2
1
2
1
0
2
2
0
0
1
1
0
1
2
1
0
1
1
2
0
2
0
2
0
1
2
1
0
2
2
1
1
2
1
0
1
1
0
0
0
1
0
0
0
1
2
1
1
2
1
0
1
0
0
2
0
1
0
0
0
0
1
2
2
0
2
0
1
1
1
0
1
2
1
0
1
0
0
0
1
1
2
2
1
0
1
0
0
2
0
1
1
0
0
1
1
0
1
1
1
1
1
1
1
0
0
1
0
1
1
1
1
2
0
0
0
1
1
0
2
0
1
0
1
1
0
2
0
1
1
0
1
2
1
2
1
1
1
0
1
2
1
1
0
3
1
1
0
0
0
0
0
1
1
1
2
0
2
1
2
1
2
3
1
2
1
0
1
0
1
1
0
1
2
0
2
2
2
1
1
0
2
0
2
2
1
2
2
1
1
2
1
2
2
0
0
0
1
2
1
0
1
0
1
0
1
1
1
1
0
2
2
1
2
0
0
2
0
0
1
1
1
0
1
1
1
1
1
0
0
2
2
0
0
2
0
0
2
1
2
1
1
0
1
2
0
0
1
2
2
0
0
0
0
0
0
1
0
0
0
1
2
0
1
0
1
1
1
0
1
2
1
1
1
0
1
1
1
0
0
0
1
0
2
0
2
1
1
1
0
1
1
1
1
0
0
0
1
0
1
0
1
2
1
0
2
1
0
0
1
1
0
1
2
1
0
1
1
1
0
1
1
1
0
1
3
1
1
0
1
0
0
2
0
0
0
0
2
1
0
1
1
2
0
1
2
1
1
1
0
1
1
1
1
0
1
1
1
1
1
0
0
1
1
0
1
0
1
1
2
0
1
2
1
0
1
1
0
0
1
2
2
0
2
0
0
2
0
1
0
0
0
0
1
0
0
0
1
2
1
0
0
0
0
0
1
2
0
2
1
1
1
1
1
0
2
0
1
2
0
1
2
2
1
1
0
1
2
1
2
1
0
1
1
1
0
2
1
1
1
2
1
0
1
0
2
1
1
2
1
2
1
0
0
1
1
0
0
0
0
1
0
0
1
3
0
1
0
0
2
2
0
1
2
1
1
1
1
0
2
1
1
0
1
1
1
2
1
1
1
0
1
0
0
1
2
2
2
1
1
0
1
0
2
1
1
0
1
0
0
0
1
1
1
0
0
0
1
2
1
0
2
0
0
1
0
0
2
2
0
0
2
2
1
0
0
1
0
0
1
1
0
1
1
2
0
0
2
0
0
1
1
0
0
2
0
0
0
0
2
0
0
1
1
0
1
2
0
2
1
1
1
1
1
1
0
1
1
0
1
0
0
2
0
0
1
2
0
1
0
0
1
1
1
1
0
1
1
0
0
1
1
2
0
0
1
1
2
0
2
1
2
2
0
0
2
0
1
1
0
1
0
0
2
1
1
1
2
0
1
0
1
0
0
2
3
1
2
1
5
2
0
2
1
1
1
2
2
1
1
1
1
1
1
0
0
2
1
0
0
0
1
0
2
1
0
1
1
0
2
2
0
1
1
1
1
1
1
2
0
1
2
2
1
0
4
0
2
1
0
1
2
2
2
0
1
0
1
1
0
5
1
1
0
1
1
1
0
0
1
0
1
1
2
1
2
1
2
0
1
1
0
1
2
1
1
2
2
0
1
0
1
0
0
0
1
1
1
0
2
2
0
1
0
0
0
0
2
0
2
1
1
1
0
0
1
1
1
0
2
1
2
3
2
0
1
2
1
1
1
1
0
0
0
0
2
0
2
1
2
1
0
1
2
1
1
1
2
0
2
2
0
2
1
2
1
2
1
1
2
1
1
1
0
1
2
0
0
0
1
0
2
0
1
0
2
0
0
0
1
0
1
1
0
0
2
2
1
0
2
1
0
2
2
1
2
1
0
0
1
1
2
0
3
2
1
0
1
1
1
0
0
0
0
1
1
1
1
4
1
2
0
2
0
2
1
0
1
2
0
1
0
2
0
0
2
0
0
1
2
0
0
1
1
1
0
1
1
1
0
1
1
1
1
1
2
2
3
0
1
0
1
0
0
2
1
1
0
1
1
1
0
0
0
2
0
1
1
2
0
1
0
0
0
1
0
2
1
2
0
1
0
0
0
2
0
1
2
0
0
0
0
0
0
2
0
0
4
1
0
1
0
0
1
1
1
1
0
0
2
1
1
2
1
0
1
0
1
1
1
1
2
1
1
1
2
0
1
0
1
2
1
2
2
0
0
1
2
1
2
0
0
0
1
1
0
2
0
2
1
0
1
0
0
0
0
1
1
0
2
0
0
2
1
1
1
2
0
1
1
2
0
2
0
1
2
0
2
1
2
1
1
1
2
1
1
1
0
0
0
0
1
2
2
2
0
2
2
0
1
3
1
1
1
1
2
1
0
1
0
1
2
2
1
1
2
1
1
1
2
0
1
1
0
0
2
1
1
0
2
0
2
2
0
0
1
0
1
2
0
1
2
2
2
2
0
0
4
1
1
0
2
1
2
0
0
0
2
3
2
0
0
1
1
1
0
0
0
2
1
1
1
2
0
0
2
0
0
1
1
0
2
0
2
1
0
1
1
1
1
1
0
0
1
1
0
1
0
1
1
1
0
0
2
0
1
2
1
0
0
2
0
2
2
1
0
1
1
0
1
1
2
1
2
1
0
0
1
0
2
0
1
0
1
2
1
1
1
0
1
0
2
2
1
1
1
0
1
0
0
0
1
1
2
2
2
0
2
0
2
3
2
0
0
0
1
1
2
0
2
1
0
1
2
1
0
2
0
0
0
3
0
1
1
0
1
1
1
2
1
1
2
0
0
2
0
1
2
0
1
2
1
1
0
0
2
3
1
1
2
0
1
0
0
1
0
1
1
0
1
2
0
0
1
1
1
2
0
2
1
2
0
2
2
0
2
1
1
0
2
3
2
2
2
1
0
0
0
1
1
1
1
0
0
0
0
2
1
2
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
2
0
0
0
6
0
1
1
1
1
1
0
0
2
0
2
1
1
0
0
0
0
1
1
1
2
0
1
0
1
1
0
1
1
0
0
1
0
1
2
0
2
0
0
1
1
2
1
0
0
0
0
2
2
0
1
0
1
0
1
1
0
1
1
1
0
0
1
4
1
0
2
2
0
2
2
2
1
2
2
1
2
1
0
1
2
0
1
1
2
0
0
0
1
0
2
1
1
2
0
0
1
0
0
0
0
2
1
1
4
3
2
0
0
2
0
0
0
0
1
0
0
2
2
2
0
2
2
2
2
1
1
0
0
2
0
1
0
0
1
3
2
0
2
0
1
2
1
1
0
1
0
1
1
3
1
0
0
3
0
0
2
2
1
1
0
0
0
2
1
0
0
0
0
0
2
0
1
0
0
0
1
1
1
0
0
0
2
1
1
0
0
0
2
1
1
0
2
0
0
2
0
1
0
0
1
0
1
1
1
1
0
0
1
0
1
0
0
0
2
2
0
1
2
0
2
1
2
1
0
0
0
1
0
1
0
0
3
2
1
0
0
1
2
0
0
2
0
1
1
1
1
2
0
1
1
1
2
0
0
0
1
2
1
0
0
2
1
0
0
1
2
3
1
0
0
2
1
1
0
2
3
1
1
0
1
1
0
0
0
0
1
0
2
1
1
0
0
1
0
1
2
0
2
1
1
1
0
1
1
1
3
1
1
1
0
0
0
1
2
2
1
0
1
0
0
0
0
0
0
0
1
1
0
1
1
1
0
2
1
0
1
0
0
0
2
1
0
0
2
1
1
2
1
0
0
0
2
2
1
1
2
1
0
0
1
1
2
1
1
1
0
1
1
1
2
2
1
2
2
0
0
1
1
1
1
0
1
1
2
1
0
1
1
0
1
0
1
1
1
1
0
4
1
0
1
1
2
2
2
1
0
1
1
1
0
2
1
0
0
1
1
0
0
0
0
0
8
0
0
2
2
1
1
1
0
0
0
1
0
1
1
0
1
0
0
1
1
0
2
2
2
0
1
1
1
0
0
0
0
1
0
1
1
2
1
0
1
1
0
0
0
2
1
0
1
2
0
0
0
0
1
3
1
0
0
0
2
2
1
2
0
0
1
2
1
2
0
0
2
0
1
1
1
0
0
2
1
1
0
1
1
1
1
0
1
2
2
1
2
1
0
0
2
1
0
2
1
1
0
0
0
0
1
3
0
1
2
1
2
0
2
2
0
0
0
2
2
1
0
3
1
0
1
1
0
1
2
0
1
0
1
1
2
1
0
0
0
1
1
1
0
2
1
1
5
0
1
1
2
1
1
2
0
0
0
0
2
1
0
0
1
2
0
1
1
1
1
4
2
1
0
0
0
2
0
1
1
1
1
1
2
0
2
2
3
0
2
1
2
0
0
1
1
1
0
1
2
2
1
0
2
2
0
3
0
0
0
0
0
0
3
0
2
0
0
1
1
2
0
0
0
0
0
1
0
2
2
2
1
1
1
1
1
0
2
1
0
0
1
0
0
1
2
1
2
2
0
0
2
1
2
2
1
2
1
1
1
0
2
2
1
1
2
2
0
1
2
1
1
2
0
2
1
2
0
2
0
0
1
0
2
0
0
0
0
2
2
2
2
1
2
1
3
0
0
1
1
1
1
0
0
0
0
1
1
0
2
1
1
0
2
0
2
0
0
1
1
0
2
0
2
0
0
1
1
1
2
0
1
1
0
1
2
0
1
1
1
2
0
0
2
1
0
1
0
0
1
1
2
1
0
1
1
1
0
1
0
2
1
2
2
1
3
1
1
0
2
0
1
2
1
0
2
1
1
2
5
0
1
1
1
2
0
2
0
2
1
0
2
3
0
0
0
0
0
1
1
1
2
1
1
1
1
0
3
0
2
1
0
1
0
1
0
0
2
2
3
2
2
1
0
1
1
0
0
0
1
1
0
1
1
1
2
1
2
1
1
1
1
1
1
2
1
2
1
0
2
1
1
1
0
1
0
2
3
1
1
0
0
1
0
0
1
1
0
1
2
0
0
2
1
2
0
1
1
2
2
2
2
1
0
1
2
1
0
2
2
1
2
1
0
1
1
2
0
0
1
1
1
0
1
1
0
1
2
1
0
1
0
1
0
1
1
0
0
0
2
2
2
2
1
0
0
0
2
1
1
1
1
0
0
0
1
0
0
0
2
0
0
1
0
1
1
1
2
1
1
2
2
0
2
2
2
2
1
0
0
1
1
0
1
2
1
1
0
1
1
1
0
0
1
1
0
1
2
0
1
0
0
0
1
1
1
1
2
1
1
0
1
2
0
2
1
2
1
0
0
0
0
1
1
1
1
1
0
0
2
0
0
1
1
0
1
1
0
2
0
0
2
1
1
2
1
1
2
2
1
1
1
1
0
0
2
1
0
1
0
1
2
0
1
0
1
2
2
1
0
2
0
0
2
1
1
1
1
0
0
0
1
0
0
0
1
2
2
1
1
1
2
2
1
1
1
0
1
1
1
2
2
1
0
1
0
2
1
2
0
1
1
1
0
0
1
1
2
0
1
1
3
2
0
0
1
1
1
2
2
0
2
2
1
0
2
1
2
0
2
0
2
2
2
1
0
0
0
1
1
1
1
0
0
0
0
1
1
1
0
0
1
2
0
1
1
2
0
1
1
2
0
0
1
2
1
1
1
0
0
0
0
1
1
0
1
1
1
1
1
1
1
2
1
1
0
2
1
1
1
0
0
1
0
1
0
2
0
4
0
2
0
1
0
0
0
1
1
1
0
1
0
0
2
0
0
0
2
0
0
2
1
1
0
1
0
0
1
2
0
0
0
1
1
0
0
0
0
1
1
2
2
0
0
0
1
0
0
1
0
0
0
2
1
1
3
1
0
0
1
0
1
1
2
0
1
1
1
1
1
0
0
0
0
2
1
0
0
0
0
0
1
0
1
0
1
6
2
0
0
1
2
1
1
1
2
2
2
2
0
2
3
1
1
0
0
1
0
1
2
0
0
0
0
2
0
0
0
2
0
1
2
1
2
2
1
0
1
3
0
1
1
0
1
1
0
0
2
1
2
2
0
0
0
1
1
0
1
1
1
0
1
2
0
2
1
0
1
0
2
1
0
0
2
2
1
1
0
2
0
0
2
0
0
1
0
2
2
0
1
1
0
1
0
1
0
0
1
0
0
0
0
0
1
1
1
2
1
3
1
2
1
3
1
2
1
1
0
1
0
0
0
0
0
0
1
0
0
0
2
1
0
1
2
0
0
1
0
0
2
1
0
2
0
2
2
0
2
0
0
0
0
0
1
0
2
0
0
1
1
0
1
0
1
0
1
1
1
2
2
1
1
1
1
0
1
2
0
1
1
1
1
0
0
0
2
0
1
1
1
0
0
2
0
1
0
0
1
2
1
1
2
2
1
2
0
1
1
0
0
1
0
0
2
0
1
1
0
1
2
1
2
0
2
1
0
0
0
1
1
1
1
0
0
1
1
1
2
2
0
1
1
1
1
1
1
1
2
0
1
2
1
1
2
0
0
2
0
1
2
1
1
2
1
1
0
2
2
0
1
0
3
0
1
2
2
1
0
0
1
2
1
3
0
2
0
1
0
0
2
1
0
1
0
2
0
1
0
1
2
1
2
0
1
0
2
1
0
1
0
0
0
1
0
0
2
0
0
2
0
1
0
0
0
0
1
0
0
1
0
1
0
1
1
1
1
1
2
2
1
0
1
2
1
1
0
2
1
2
0
0
2
0
2
2
0
0
1
1
2
1
1
0
0
0
1
1
2
1
0
0
1
2
2
0
0
2
0
1
1
1
0
0
1
0
1
2
0
1
0
1
0
0
1
0
0
1
0
2
1
2
2
1
0
0
1
1
0
2
1
0
2
0
0
1
1
1
1
1
0
1
0
2
0
2
1
1
2
0
0
1
0
0
0
1
2
0
2
1
2
1
2
0
0
1
2
1
1
0
1
1
2
0
1
1
0
1
0
0
1
2
2
2
1
2
1
0
2
1
1
0
1
1
0
1
2
0
1
0
0
0
0
1
1
0
0
0
1
1
1
0
1
1
2
0
1
1
1
1
2
1
0
0
0
0
0
0
1
1
1
0
1
1
1
1
1
2
1
0
0
0
1
0
1
1
0
1
2
2
2
0
1
2
1
2
0
1
1
1
2
0
2
2
1
3
1
0
1
0
0
1
0
1
0
0
2
0
0
1
0
1
0
1
0
0
2
1
1
0
2
1
0
1
0
2
0
0
0
0
0
1
2
0
1
1
0
2
1
0
1
1
1
2
2
0
2
1
2
2
0
1
0
0
1
2
1
1
0
2
0
1
2
0
1
0
1
0
0
0
2
0
2
0
0
0
1
1
0
1
1
1
0
1
2
1
0
2
0
1
0
2
2
1
2
0
1
0
2
2
0
1
2
1
1
1
2
0
0
2
5
2
0
1
1
1
2
1
2
1
0
1
1
3
1
0
0
2
0
0
1
2
1
1
0
1
2
0
1
2
0
1
1
0
1
2
0
1
0
0
1
0
1
2
1
2
0
2
1
2
1
1
2
0
1
2
2
0
1
2
1
1
1
1
2
1
2
1
2
1
2
0
1
2
0
1
1
2
1
0
1
2
0
0
2
0
0
1
1
0
1
2
1
1
1
2
2
1
0
2
2
2
0
0
0
1
0
0
2
2
0
0
0
1
2
0
0
1
1
1
0
0
1
1
2
1
2
0
1
0
1
2
1
1
0
1
0
1
0
1
1
2
2
2
1
2
0
2
1
1
1
1
1
1
1
0
2
2
0
0
0
0
1
1
2
1
2
2
1
2
1
0
2
1
0
0
2
1
2
1
2
0
0
0
2
0
2
1
2
0
0
2
0
0
1
0
1
1
1
1
2
1
1
1
1
1
1
0
1
0
0
1
1
0
1
1
2
0
0
1
0
0
2
1
1
0
0
0
1
2
1
2
1
0
1
1
1
2
2
0
0
3
2
2
1
0
2
0
0
1
0
4
0
2
1
1
1
1
1
0
2
1
2
0
0
1
2
1
1
0
1
1
1
0
2
0
1
2
1
2
1
1
1
2
1
0
2
3
0
1
2
2
1
2
2
1
1
0
2
0
1
0
0
0
1
0
0
1
1
0
2
0
1
0
2
0
2
2
2
0
1
0
1
2
2
2
1
0
0
1
1
1
0
0
0
1
0
3
1
0
1
0
0
1
1
1
0
0
0
3
0
1
1
0
0
1
0
1
0
1
0
1
1
0
1
0
1
0
1
0
0
1
3
0
0
1
0
2
1
2
1
2
1
2
0
0
1
1
0
0
1
1
1
1
0
0
1
0
1
2
0
1
1
2
0
0
2
2
2
1
2
1
2
1
0
1
1
2
2
1
1
2
0
1
1
0
0
0
1
1
1
0
0
0
1
1
0
2
0
0
2
1
1
0
1
0
0
1
0
1
1
2
0
0
0
1
2
0
1
0
0
1
0
0
1
0
2
1
0
0
0
0
0
0
1
0
1
0
2
0
2
0
0
1
3
1
1
0
0
0
2
1
0
0
1
1
0
1
1
0
1
2
1
1
0
2
2
1
1
0
2
3
1
0
2
0
0
1
1
2
2
1
0
1
0
1
1
0
0
2
2
2
1
1
1
0
0
0
1
0
1
1
0
0
1
0
1
2
0
3
1
1
1
1
2
2
0
1
1
1
2
1
0
1
0
1
1
2
2
0
1
1
0
0
2
0
1
0
1
0
0
1
2
2
0
1
1
0
3
1
2
1
1
1
1
1
0
2
0
0
0
1
0
1
1
1
1
1
1
1
2
1
1
1
1
1
0
1
0
0
2
2
1
1
1
1
1
1
0
0
1
1
2
2
1
1
1
1
2
1
1
1
0
0
0
4
0
0
1
0
1
0
0
1
1
1
1
1
1
1
1
0
1
2
1
1
1
0
0
1
1
2
2
0
0
0
1
0
0
0
1
2
2
0
1
0
1
0
1
1
1
1
0
0
1
1
2
0
0
0
1
1
1
0
2
1
1
1
1
0
1
2
0
1
0
0
1
1
2
0
1
0
0
0
1
0
1
2
0
2
1
2
0
0
0
2
1
0
1
1
1
2
1
2
2
2
0
2
2
0
2
2
0
1
1
1
0
0
0
2
1
0
1
0
0
2
0
1
1
2
3
0
0
2
0
1
2
1
1
2
1
2
0
1
0
1
1
0
2
0
1
2
0
0
0
0
3
0
0
0
3
0
0
1
1
2
0
1
1
2
2
0
1
1
2
1
2
1
1
1
0
2
1
1
3
1
2
1
0
0
1
0
1
0
0
0
0
2
0
2
1
1
0
2
1
0
1
1
2
1
3
2
1
1
1
0
0
1
1
0
0
1
1
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
1
1
1
0
0
1
0
0
1
1
0
1
1
4
0
0
0
1
0
0
1
2
2
0
2
0
0
2
2
2
1
2
2
1
2
2
0
2
0
1
1
0
0
1
0
0
0
0
2
0
1
1
2
1
1
0
1
0
1
0
2
0
3
1
1
0
2
2
0
0
0
0
1
0
1
2
1
0
0
2
1
0
0
1
1
0
2
0
1
1
0
1
2
1
0
2
0
0
1
1
1
1
2
2
3
2
2
1
2
1
0
0
0
1
1
1
0
0
0
0
1
0
2
0
1
0
2
1
1
0
1
0
1
1
1
1
1
1
0
0
3
0
0
2
2
0
0
0
0
1
1
0
0
2
1
1
1
1
1
2
1
1
1
0
2
0
1
0
1
1
0
1
1
0
0
0
1
1
1
0
0
0
0
1
1
0
2
0
2
1
2
1
1
1
1
2
0
1
2
1
1
0
2
0
2
0
0
0
0
1
0
0
2
2
2
1
2
0
1
2
0
2
1
0
1
0
0
0
0
0
0
1
2
2
1
0
2
2
2
0
0
0
1
1
2
2
2
1
1
1
1
0
0
2
1
1
1
0
0
1
0
1
0
0
0
1
0
2
0
0
0
0
2
1
1
1
1
1
1
1
0
1
2
0
1
0
2
0
1
1
1
2
0
1
0
0
2
0
2
1
1
2
1
1
0
0
1
1
0
0
0
1
1
2
0
0
0
1
1
0
2
0
1
1
0
0
0
1
1
0
2
0
2
0
2
1
0
1
0
0
0
1
2
1
0
0
0
1
1
1
0
1
1
0
1
0
0
0
1
1
1
2
1
0
3
1
0
0
0
0
1
2
1
1
0
2
2
2
1
0
2
2
2
2
1
1
1
2
1
1
2
2
2
0
2
0
2
2
2
1
2
0
1
0
1
1
1
2
0
1
1
0
0
0
2
0
0
0
0
0
1
0
2
1
1
1
1
0
1
0
2
1
1
1
1
0
0
1
2
2
0
0
0
0
2
1
2
1
1
0
0
2
1
1
2
1
1
2
2
0
1
1
1
0
2
0
2
2
1
1
1
2
0
0
2
1
0
3
0
1
0
0
2
2
1
2
1
0
1
1
1
0
1
1
1
1
0
0
0
0
2
0
0
2
0
1
2
3
1
2
0
0
0
0
1
0
2
1
1
1
1
1
0
1
1
1
1
0
0
0
1
0
1
0
0
0
1
1
0
0
0
2
0
2
2
0
0
2
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
2
0
1
1
1
1
0
1
0
0
1
0
0
0
0
2
1
1
1
0
2
0
0
1
1
0
2
1
1
2
0
1
1
1
0
2
2
2
2
0
1
0
1
0
0
1
2
1
0
2
1
0
1
1
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
2
0
2
2
1
0
2
1
0
1
1
1
1
1
1
2
0
0
2
0
1
1
0
1
1
1
2
0
1
0
1
0
1
0
2
0
1
0
1
1
0
1
1
0
1
1
0
1
0
0
2
2
1
0
1
2
1
2
2
0
3
2
1
0
2
2
1
2
0
1
2
2
0
0
1
2
1
1
0
1
1
1
2
1
1
0
0
0
0
0
1
2
1
0
1
0
0
2
0
2
1
0
0
1
1
0
2
1
1
1
1
0
1
2
1
1
1
2
2
1
3
1
1
0
1
0
1
3
2
1
0
1
0
0
2
0
0
1
1
2
0
0
1
0
2
0
2
1
0
0
2
0
2
1
0
0
0
0
0
1
0
2
0
1
0
1
2
2
1
0
2
2
0
2
0
1
0
2
2
0
2
0
1
0
2
1
1
1
1
1
1
2
0
1
0
1
3
2
1
1
1
1
1
1
1
1
1
2
0
1
0
1
1
0
2
0
0
1
1
1
1
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
2
0
1
0
2
0
1
0
2
1
1
1
0
0
1
1
0
2
2
0
2
2
0
1
2
1
1
1
0
0
2
1
1
1
1
2
2
0
0
1
0
0
1
2
1
0
1
1
2
0
1
1
0
1
1
1
0
1
1
1
2
2
1
0
1
1
1
2
0
1
2
1
0
0
1
0
0
1
1
0
0
0
3
2
0
0
2
1
0
2
1
2
2
1
0
1
2
1
0
2
2
1
2
0
1
1
1
2
1
1
1
0
2
2
1
0
0
1
1
1
2
2
2
1
0
0
1
2
1
2
0
3
0
1
0
2
0
1
1
1
2
0
1
2
2
1
2
1
2
0
0
2
1
2
2
1
1
0
1
3
0
0
0
1
0
2
1
0
0
1
0
0
0
1
0
0
2
0
1
0
1
0
1
1
2
2
0
1
1
1
1
1
3
0
1
0
1
0
0
1
0
1
0
1
1
1
1
1
1
0
1
1
2
0
0
0
2
1
2
0
0
2
0
2
0
1
0
1
1
0
1
0
2
1
0
0
2
1
0
0
1
0
1
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
1
0
0
1
0
0
1
1
1
0
0
2
1
2
2
2
0
0
1
1
0
1
1
1
0
1
2
1
2
0
0
2
2
0
1
1
1
2
1
1
2
2
1
0
1
1
0
0
2
0
1
1
1
2
0
2
0
3
1
0
0
2
1
0
1
1
2
2
1
1
0
1
1
1
1
0
1
2
1
1
1
1
0
0
1
0
2
0
3
1
1
1
0
1
0
2
1
0
2
0
1
0
1
2
0
1
2
2
2
0
0
1
2
1
2
0
1
1
0
1
1
0
1
1
0
1
2
1
0
2
0
0
2
0
0
2
2
2
1
2
0
2
1
0
1
2
0
1
1
0
2
0
0
0
0
0
0
1
0
1
0
1
0
0
2
0
0
0
1
2
0
0
2
1
1
2
0
0
1
0
0
2
1
0
0
1
0
0
0
2
2
2
2
1
0
0
1
1
2
1
2
2
2
2
1
2
2
0
1
2
0
2
0
1
1
2
0
0
0
0
2
1
1
2
1
1
1
1
2
1
0
0
1
1
0
1
2
0
2
1
1
1
1
1
0
0
1
2
3
1
0
2
0
0
0
0
0
0
2
1
2
2
1
0
1
0
1
0
0
1
2
0
0
0
0
2
1
0
2
2
1
2
1
1
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
1
0
2
0
1
0
0
0
2
2
0
1
2
1
0
0
1
0
2
0
2
1
0
0
2
0
0
1
1
3
0
0
0
1
2
1
2
0
0
1
1
1
0
1
1
1
0
1
1
0
0
1
0
0
2
2
1
0
2
1
1
1
0
0
0
0
0
2
1
1
0
0
1
0
0
1
0
1
1
1
1
1
1
1
2
2
2
2
0
0
1
0
0
0
1
1
0
2
1
1
0
0
1
0
2
1
0
0
0
1
2
0
0
1
1
1
2
0
1
1
0
0
0
0
0
1
0
1
2
1
1
2
1
1
2
1
1
0
0
1
0
2
0
2
1
0
2
2
0
1
2
2
1
0
1
1
2
0
0
0
0
2
2
1
0
0
1
1
2
1
1
1
2
3
0
1
1
0
0
1
1
1
1
1
0
0
1
2
1
0
0
1
2
2
0
0
0
0
1
1
0
0
1
3
0
1
2
0
1
0
2
1
2
1
0
0
2
2
0
1
4
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
1
2
1
0
2
0
1
1
1
1
0
1
1
0
2
1
1
0
1
1
1
2
0
1
2
1
2
1
0
1
0
1
2
0
0
0
2
1
0
1
1
0
1
2
0
1
1
2
0
2
0
0
2
1
1
1
0
0
1
1
0
2
1
0
1
0
2
0
1
1
2
0
1
0
0
1
0
2
1
0
1
1
1
0
1
0
2
0
1
1
1
1
2
0
0
1
2
1
0
2
1
1
2
2
0
0
0
0
0
0
0
0
2
0
0
1
0
1
2
0
2
1
2
1
0
2
1
1
2
0
0
1
1
0
0
1
0
0
1
0
1
0
0
0
1
3
2
0
0
2
1
0
1
1
2
1
2
1
0
3
1
1
0
1
1
0
2
0
0
0
0
0
1
0
1
1
0
1
1
1
0
2
0
1
1
0
1
1
1
1
0
1
0
0
4
0
1
0
2
2
0
0
2
1
1
1
2
2
1
2
0
2
2
1
0
1
0
1
1
2
0
2
0
1
2
2
0
0
0
1
2
1
0
1
0
1
0
1
0
1
0
1
1
0
2
2
2
1
0
0
1
2
1
2
0
1
1
0
1
1
2
1
0
1
0
0
0
0
1
1
0
0
1
2
0
1
0
1
1
1
2
1
1
0
0
1
0
0
1
1
2
0
0
1
1
1
1
1
1
0
0
1
0
0
0
0
0
0
2
1
2
1
1
0
3
0
0
2
2
1
2
0
0
2
0
1
0
2
1
0
2
0
1
1
1
0
2
0
0
0
1
0
1
1
1
1
2
0
1
0
0
3
0
0
1
1
1
2
2
2
0
1
0
0
0
1
0
1
2
2
0
0
0
2
2
1
1
0
1
0
0
2
2
1
2
1
2
2
0
1
1
1
1
0
0
0
0
2
0
1
1
1
1
2
0
0
1
0
0
1
0
0
2
0
2
1
0
0
1
1
2
2
1
1
1
0
1
1
2
3
1
0
0
1
2
1
0
0
2
1
1
1
1
2
0
1
0
0
0
0
2
1
1
2
0
1
0
2
1
0
1
1
0
0
0
2
1
2
1
0
0
0
2
0
1
2
0
0
0
1
1
0
2
1
1
1
1
0
0
2
0
2
1
2
1
1
1
2
1
1
1
3
2
1
1
0
0
0
1
2
1
1
1
0
2
2
0
2
0
0
0
1
2
1
1
1
1
0
1
1
1
0
0
1
0
0
0
0
1
1
0
0
0
1
0
1
0
1
0
0
0
1
0
1
1
2
0
0
1
2
1
1
1
2
1
1
1
1
1
0
2
0
5
1
1
2
0
0
1
0
0
0
2
2
0
1
2
2
0
1
1
0
0
0
2
0
1
2
1
2
0
2
1
2
1
1
2
1
1
1
1
2
0
1
1
0
0
0
0
0
0
1
1
2
2
4
1
1
0
1
0
0
0
0
2
2
2
1
0
1
1
0
1
2
1
2
1
3
0
2
1
1
0
1
2
1
2
0
0
0
0
0
2
0
1
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
2
1
0
0
1
0
0
0
2
1
0
0
0
0
0
1
1
0
0
0
2
0
1
0
0
1
0
1
2
1
2
0
0
2
0
1
0
1
0
1
0
2
2
2
0
1
0
1
1
0
4
2
0
1
1
1
0
0
0
2
2
1
1
0
1
1
0
1
0
0
1
0
0
0
2
0
1
1
1
0
1
0
1
0
2
3
0
0
0
1
0
2
2
2
1
1
2
1
2
0
1
0
0
2
2
2
0
0
0
1
0
2
1
1
1
0
1
0
0
3
0
0
2
0
0
0
1
0
0
0
2
0
0
1
1
2
0
0
0
0
0
1
1
0
0
0
0
0
2
1
0
0
1
0
1
2
1
2
0
0
2
0
0
0
0
1
0
2
1
1
1
1
0
1
0
1
1
0
1
0
0
0
2
2
2
1
0
2
5
1
2
2
1
0
1
0
1
0
1
2
1
1
2
0
2
2
1
1
1
0
2
0
1
0
2
0
2
1
1
0
1
0
0
1
1
0
0
1
0
3
2
1
1
0
2
1
2
3
0
0
2
1
0
0
1
2
0
2
1
0
0
2
0
1
1
0
0
1
2
1
1
0
0
1
0
1
1
0
0
3
1
1
0
0
0
1
0
2
2
1
0
0
1
1
0
2
2
2
1
2
1
2
0
0
0
1
0
1
2
0
0
2
1
0
1
1
2
0
2
2
0
0
1
1
0
1
0
2
3
0
1
1
2
0
1
0
1
0
1
1
0
2
1
1
2
1
1
1
2
0
0
0
1
1
1
2
0
2
1
1
0
2
1
0
4
3
0
0
0
2
0
0
2
1
2
1
2
2
1
2
1
1
1
0
1
0
0
1
2
0
0
0
2
0
1
0
2
0
1
0
1
0
1
1
1
1
0
0
0
0
1
2
1
1
1
0
0
0
1
1
1
2
0
0
1
0
1
1
0
0
1
1
1
1
0
1
1
1
0
0
2
0
0
0
0
1
0
1
1
0
1
0
2
0
0
0
2
1
0
2
1
1
2
2
0
2
2
0
1
2
0
3
1
1
0
0
1
0
0
1
0
1
0
1
0
2
1
0
1
2
0
0
1
1
1
0
0
1
0
0
1
2
1
2
1
2
1
2
1
1
1
0
3
1
1
0
0
2
1
2
0
1
2
0
1
2
0
0
1
0
1
0
0
1
1
2
1
1
0
1
2
1
1
1
1
1
1
0
0
0
0
0
1
0
0
2
2
1
1
0
0
2
1
0
1
1
1
2
1
1
2
0
2
0
2
0
2
0
0
1
1
2
0
2
1
0
1
1
0
0
0
2
2
1
0
1
0
1
0
0
2
1
1
2
0
0
0
0
0
2
0
2
1
1
2
1
0
1
0
0
1
1
1
2
2
1
0
1
1
2
1
0
1
1
1
0
1
2
1
2
0
0
0
1
0
1
1
1
0
1
0
0
1
1
0
2
1
1
1
0
0
2
0
0
1
0
0
1
0
1
1
1
1
1
0
1
0
0
0
1
2
1
2
2
2
1
0
1
1
0
0
2
0
0
2
1
0
1
2
2
0
2
5
0
0
0
1
1
0
0
0
2
0
1
0
2
1
1
2
0
2
2
1
2
0
1
0
0
5
0
2
4
1
2
1
1
2
1
0
2
1
1
1
0
1
0
1
0
1
1
0
1
1
2
0
1
0
1
0
1
0
1
0
2
2
0
0
0
2
0
5
0
1
2
1
2
1
1
0
1
1
0
3
1
1
1
0
1
0
1
1
0
1
1
2
1
1
3
1
0
1
2
2
2
4
1
2
1
0
1
0
0
2
4
2
0
1
2
2
2
0
1
2
1
1
2
1
2
0
0
1
1
2
2
1
1
1
1
1
0
0
1
2
1
2
3
1
0
1
0
0
0
1
0
1
0
1
6
0
1
0
1
1
1
2
1
1
1
2
1
1
2
0
1
0
2
0
1
1
0
0
1
0
1
2
2
1
2
0
1
0
0
0
1
0
0
1
1
0
2
0
1
1
0
1
2
2
0
0
0
0
0
1
2
1
1
0
1
1
1
1
1
1
2
1
0
1
2
0
2
0
1
1
0
2
0
0
0
1
2
0
1
0
0
3
0
0
2
2
0
0
2
1
0
0
1
1
1
1
0
0
1
0
1
0
0
0
1
2
2
2
0
1
2
0
0
0
0
1
1
0
0
0
1
1
0
1
1
0
2
1
2
2
0
1
0
2
1
2
1
1
0
1
1
0
1
1
1
2
2
0
1
0
0
0
1
2
0
2
0
1
2
1
3
1
2
0
2
0
1
3
0
0
0
0
2
0
2
0
2
2
0
2
0
2
2
2
1
1
0
1
0
1
2
1
1
1
1
0
2
1
0
0
1
1
1
1
1
0
0
0
0
1
2
1
0
1
1
1
0
2
1
2
1
1
1
1
1
2
1
1
0
2
2
1
1
0
2
0
1
0
0
1
0
0
2
2
0
1
1
1
1
0
1
1
0
1
3
0
0
0
2
0
0
2
2
1
4
1
0
0
0
1
1
0
1
2
0
2
1
2
1
1
1
0
0
2
1
2
0
1
2
1
2
1
0
1
2
0
1
1
1
1
0
1
2
0
1
1
1
2
1
1
0
2
0
1
1
1
1
1
1
1
1
1
1
1
0
1
0
0
1
2
0
1
1
2
0
1
0
2
0
2
1
0
1
1
0
0
2
2
2
1
0
2
0
1
1
1
0
0
1
1
2
1
1
1
0
1
2
1
0
1
1
1
1
1
1
0
2
0
1
1
2
0
0
1
0
3
1
2
0
2
1
1
2
1
0
1
0
2
0
1
0
1
1
0
1
1
0
1
2
0
0
2
1
1
1
3
1
1
0
1
0
1
1
3
0
3
0
2
1
0
0
1
1
1
2
0
0
1
0
1
0
0
1
2
0
4
2
1
0
2
2
0
1
1
0
0
1
0
1
0
1
2
0
0
1
1
1
0
2
0
2
2
1
2
0
1
0
0
2
0
1
0
0
1
0
2
0
2
1
2
1
1
1
1
0
2
0
0
0
0
1
0
0
2
0
1
0
1
2
0
2
1
1
0
1
1
1
1
1
2
2
1
2
2
0
1
2
2
1
0
0
0
0
1
0
0
1
2
0
1
0
1
1
2
0
0
1
1
1
0
1
0
0
0
2
1
2
1
0
2
1
0
1
1
0
1
0
2
1
1
1
2
1
2
1
1
0
0
2
2
2
1
0
2
0
1
0
2
0
1
0
0
1
0
0
1
2
1
1
0
1
2
0
0
0
1
1
1
0
2
1
1
2
1
2
1
0
1
1
0
0
0
1
0
1
1
1
0
0
1
1
1
2
1
1
0
1
0
1
2
1
0
1
2
1
0
0
1
1
0
1
1
1
0
1
1
2
1
0
1
3
1
2
1
2
1
1
2
1
1
1
0
1
0
0
1
0
2
1
2
1
1
0
1
1
0
0
6
1
1
0
2
1
2
0
2
0
1
1
1
2
1
0
0
0
1
0
2
0
1
1
0
0
0
0
0
0
1
2
1
0
0
0
1
0
1
2
2
1
0
2
1
1
0
2
0
0
0
1
0
1
0
1
0
1
2
0
1
2
1
0
0
0
0
1
2
2
2
0
2
1
1
0
1
2
1
1
1
0
1
1
0
1
0
1
0
0
0
1
0
1
0
1
1
2
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
1
1
1
1
1
0
0
1
0
0
0
1
1
0
1
1
1
0
1
2
0
1
2
0
0
1
0
2
0
0
2
1
2
2
1
1
2
1
0
2
0
1
1
0
1
0
2
0
1
1
2
1
2
2
1
1
2
0
3
0
0
2
2
1
0
0
0
0
1
0
0
0
2
2
1
2
1
1
2
2
0
2
1
3
0
0
2
1
0
1
0
1
0
1
1
0
0
2
0
1
1
0
0
2
0
1
0
2
0
0
2
0
0
1
0
2
0
1
1
1
0
0
2
2
2
1
1
0
1
0
0
0
1
1
2
0
0
0
0
1
0
2
0
1
1
2
2
1
2
0
0
1
0
0
2
1
3
1
0
1
2
0
2
2
1
1
0
1
1
1
0
0
1
2
0
2
0
4
0
1
2
1
1
0
1
0
1
1
0
0
0
0
3
1
4
2
0
1
2
0
1
1
0
0
1
1
1
1
1
1
1
2
0
0
2
2
0
2
1
0
0
2
1
2
2
0
2
0
1
2
0
0
2
2
1
1
2
1
1
3
2
1
1
1
0
1
0
0
2
0
1
2
0
1
3
2
3
2
1
1
1
0
1
0
1
0
1
2
0
1
0
1
2
2
1
1
0
1
2
0
2
0
2
0
2
2
1
0
1
1
0
2
1
2
0
0
1
0
1
1
0
0
1
1
1
1
0
2
0
0
1
1
1
1
1
1
2
1
1
0
1
0
1
0
1
0
1
1
0
0
0
1
0
2
1
0
0
0
1
1
0
0
2
1
1
1
1
1
2
3
1
1
0
2
1
1
1
1
2
0
2
0
0
1
1
0
0
2
1
0
1
2
1
0
1
0
1
0
0
2
0
1
3
1
1
1
0
1
0
0
1
2
0
1
2
1
1
1
1
2
1
0
1
0
1
2
1
2
2
2
1
0
1
0
0
1
0
2
0
0
1
2
1
0
0
0
0
0
1
2
0
2
1
2
0
1
2
1
1
2
0
0
1
1
2
0
1
1
0
0
1
1
1
1
1
1
1
0
0
1
1
1
0
0
1
1
1
0
1
0
1
2
2
0
2
1
0
0
1
1
2
1
2
2
2
1
1
0
1
0
1
1
1
1
1
1
0
0
1
1
0
0
0
2
1
0
1
0
0
0
1
1
2
1
1
1
0
1
1
0
0
0
2
0
1
0
2
1
0
1
0
1
0
1
1
1
1
1
3
2
1
0
1
1
1
1
0
0
1
0
0
0
1
0
1
1
0
2
0
1
1
2
0
1
0
1
1
0
1
1
1
1
0
0
2
2
1
0
2
1
1
0
0
2
2
0
1
0
1
0
1
2
0
0
0
2
0
0
0
1
0
0
0
2
0
2
0
0
1
1
0
0
1
2
1
1
0
0
0
0
2
1
0
0
2
1
0
1
0
1
0
0
3
2
0
1
0
0
2
1
0
0
2
1
0
0
0
2
1
0
2
2
2
1
0
0
1
0
0
0
1
0
2
0
1
1
2
0
2
1
1
0
1
2
0
1
0
0
0
0
1
1
1
2
1
0
2
0
0
0
1
0
3
1
1
0
3
0
2
0
3
0
3
1
1
1
0
1
0
1
2
1
0
3
0
0
2
0
0
2
0
1
1
1
2
0
0
0
0
1
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
1
1
0
1
0
1
2
0
1
2
0
0
1
0
1
3
1
1
0
2
1
1
2
0
1
0
0
2
3
1
1
1
1
0
1
3
1
0
0
0
0
2
2
1
0
1
2
0
1
1
0
0
0
0
2
1
0
0
0
1
0
1
1
0
1
1
2
1
1
0
2
1
2
1
1
1
1
0
1
1
0
0
1
1
2
0
2
1
0
2
1
0
0
1
1
1
3
1
0
0
2
1
2
1
1
1
0
1
1
0
1
0
1
2
0
0
1
2
1
0
1
1
0
0
0
1
2
0
0
0
0
0
1
1
0
2
2
1
0
0
0
0
1
1
0
2
1
0
1
1
0
1
0
0
0
2
2
0
2
0
2
1
2
0
1
2
2
2
0
2
1
0
1
0
2
0
0
1
2
0
1
0
0
1
0
0
1
0
1
2
3
2
0
1
0
1
0
0
1
0
2
0
1
1
1
1
1
0
1
2
1
1
2
1
0
1
1
0
2
2
2
0
0
1
0
1
2
2
2
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
2
1
0
0
1
2
2
2
1
0
1
1
1
1
0
1
0
1
2
0
0
2
2
0
0
2
1
0
2
1
2
1
0
0
0
0
1
0
2
0
2
2
0
2
0
2
1
1
1
1
0
0
1
2
1
0
2
1
2
1
0
0
0
2
0
0
1
0
0
1
1
1
0
1
1
1
2
1
2
0
2
1
1
1
2
2
0
0
1
0
2
2
0
0
2
0
1
0
1
4
1
1
0
2
3
2
0
0
0
0
1
1
1
1
2
0
1
1
2
0
1
1
1
0
1
2
1
2
0
0
0
2
1
1
0
2
0
1
0
4
1
1
0
0
1
0
0
0
2
0
1
0
1
1
1
0
0
0
1
0
1
1
0
0
1
1
1
2
1
0
1
2
0
0
0
1
0
0
0
0
0
1
0
1
0
1
3
2
2
0
0
1
0
0
2
1
2
0
2
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
2
0
1
1
1
0
1
1
0
2
0
0
2
0
2
0
2
1
2
0
2
1
0
0
0
0
2
1
2
1
1
1
0
0
0
2
2
1
0
2
1
1
0
1
0
1
0
2
1
0
0
0
0
0
0
2
0
0
1
0
1
0
2
1
0
2
1
0
0
2
1
0
2
1
1
2
1
0
2
2
0
1
0
0
1
0
1
0
2
1
1
0
1
2
2
0
2
1
5
2
1
1
2
0
0
2
1
1
0
1
1
1
1
0
0
0
0
0
1
1
1
2
0
2
0
1
1
1
0
2
0
2
1
0
0
2
1
1
1
2
1
1
1
1
0
1
0
0
1
1
1
1
1
0
1
1
0
1
1
1
1
2
2
2
1
1
1
0
0
1
0
0
1
1
2
0
0
1
0
0
2
0
1
0
1
0
2
1
0
2
0
2
0
0
1
2
0
2
2
1
0
0
2
2
2
1
2
1
2
1
3
2
1
1
2
0
1
2
2
1
2
4
1
1
0
2
1
1
0
1
2
1
0
2
1
0
1
2
0
2
0
1
1
0
1
0
1
1
0
1
2
1
1
1
0
1
2
0
0
0
2
0
1
1
0
0
2
0
2
0
0
0
1
2
1
0
1
1
0
2
0
0
1
0
0
2
0
2
2
1
1
0
1
0
0
1
0
1
2
1
2
1
1
0
1
1
0
1
1
0
1
1
1
3
1
2
2
2
2
1
1
1
1
1
1
2
0
1
1
1
0
2
1
0
1
0
0
0
2
1
0
2
0
1
1
0
1
0
1
0
1
1
0
0
0
0
1
1
2
1
1
1
0
0
1
0
0
2
1
0
1
0
0
1
1
1
0
1
1
1
1
0
2
1
0
1
1
0
1
1
1
0
1
1
2
0
2
1
0
0
2
2
0
0
0
1
0
0
0
1
1
2
1
2
0
1
2
2
0
1
0
0
1
1
2
0
1
0
0
1
2
2
0
0
1
0
0
0
2
2
0
1
1
2
0
2
1
1
0
1
1
1
1
1
5
0
1
1
0
2
1
1
1
2
1
1
0
1
1
1
6
1
2
0
2
1
1
1
1
2
1
2
1
5
2
0
0
0
1
0
0
1
0
1
1
0
0
1
0
0
0
1
1
2
2
2
1
1
2
2
0
1
0
1
1
1
1
1
0
0
0
1
2
0
2
1
1
0
2
1
1
1
1
1
0
2
2
2
0
1
0
2
0
2
2
1
1
0
2
1
0
0
0
1
1
0
0
1
0
2
0
0
0
0
1
1
1
1
2
2
2
0
0
0
0
2
1
1
1
0
0
1
2
0
1
1
0
2
0
1
1
1
1
1
2
0
0
1
0
2
0
1
0
1
1
0
1
0
1
1
3
2
0
2
0
0
2
1
0
0
1
1
0
0
0
1
1
0
0
0
2
0
0
2
0
2
0
1
0
0
2
0
1
0
0
2
1
1
2
1
1
2
2
1
0
0
0
1
0
3
2
2
2
1
0
1
1
0
0
0
0
0
1
0
0
1
0
2
2
2
0
0
0
2
1
1
0
1
1
0
1
0
0
1
0
1
2
2
1
1
2
0
1
0
0
2
0
1
0
1
2
2
2
0
0
1
1
1
1
1
1
2
1
0
1
1
1
0
1
0
1
0
1
0
2
1
1
1
1
0
1
0
0
1
2
2
1
0
0
2
0
2
1
0
0
1
2
2
1
1
2
0
0
1
1
2
0
3
1
0
1
0
0
2
0
1
0
2
1
0
0
2
1
0
1
1
0
1
0
0
1
0
0
0
0
0
1
2
2
1
2
0
2
1
1
0
1
1
1
0
1
2
1
0
1
0
2
1
1
0
1
1
1
1
2
2
1
1
0
0
1
2
1
0
2
0
0
0
1
2
0
1
0
1
2
1
2
0
0
2
0
1
2
0
1
1
1
1
1
1
1
1
0
0
0
0
0
0
2
0
2
1
2
1
1
1
1
2
1
0
0
1
1
1
4
2
1
0
0
2
1
0
1
0
1
0
1
0
1
1
1
0
1
1
3
1
0
1
1
0
2
1
1
1
1
2
1
2
2
1
1
2
1
0
1
2
0
1
2
0
0
1
2
0
2
0
1
1
1
0
1
0
1
1
1
0
0
1
1
0
1
1
2
0
1
1
2
1
0
1
1
2
1
1
2
1
1
2
2
2
3
0
0
0
0
2
0
0
1
0
1
2
1
2
2
0
0
1
1
1
1
1
1
2
1
1
0
0
1
0
0
0
1
0
0
2
0
1
0
0
0
0
1
0
1
1
0
1
0
0
1
0
2
0
0
1
0
1
1
0
1
1
2
0
1
0
2
2
2
1
0
1
1
0
0
0
0
0
1
0
0
0
1
2
1
2
0
0
1
0
0
2
0
1
0
1
1
0
1
0
1
0
1
2
0
0
0
1
0
1
0
0
1
1
1
1
1
1
1
1
1
0
1
1
2
0
0
0
1
1
1
1
2
0
0
0
1
0
0
2
2
2
1
2
1
0
0
1
0
2
0
1
0
2
1
1
0
0
2
1
1
0
0
2
1
2
2
3
0
2
2
1
0
2
1
1
1
0
0
0
0
2
0
2
0
2
1
0
1
0
2
0
1
1
1
1
1
0
0
1
1
0
1
1
0
0
2
1
0
1
2
0
2
2
1
1
2
1
0
0
2
1
1
2
1
2
1
0
0
1
0
0
1
0
1
0
1
1
0
0
1
2
1
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
1
2
0
0
1
2
1
1
1
1
1
0
2
2
0
0
0
0
0
0
0
1
3
0
1
2
1
0
0
2
1
0
2
1
0
1
1
1
1
0
1
1
1
0
1
2
0
2
1
1
0
1
1
0
0
2
0
1
2
0
1
0
2
0
0
0
2
0
1
1
0
2
0
0
2
0
1
2
2
0
1
0
0
0
1
0
1
0
0
2
1
1
3
0
0
0
0
1
2
2
1
1
0
0
1
2
1
0
0
1
1
0
0
0
2
0
1
1
1
2
0
1
1
0
0
1
2
0
0
1
1
0
1
1
1
1
1
1
2
2
0
2
1
1
0
0
2
1
1
1
1
0
1
0
0
0
0
0
0
0
0
2
1
2
2
0
1
2
1
0
0
2
1
1
2
1
1
1
0
1
0
0
1
0
0
2
1
1
0
0
0
0
0
2
1
2
2
0
1
1
1
2
1
1
0
0
1
0
0
0
1
0
1
1
2
3
0
1
0
1
0
2
0
2
1
0
1
1
1
1
0
1
0
0
1
2
1
1
0
0
1
1
2
0
1
0
1
1
2
0
1
2
0
1
1
2
2
0
2
2
2
2
2
1
0
1
1
1
2
1
0
2
0
2
0
0
1
0
1
2
2
0
0
1
0
0
0
2
2
0
1
0
0
1
2
1
1
0
0
1
1
1
0
1
1
1
1
1
0
1
1
2
2
2
1
2
1
0
0
0
2
1
0
0
0
0
0
1
1
1
1
0
1
1
0
1
0
1
0
0
2
1
0
1
2
1
2
2
1
2
1
1
0
0
2
2
1
0
1
2
0
1
2
0
2
0
1
2
0
1
1
0
1
0
1
1
0
0
0
0
0
0
1
2
2
0
0
1
0
1
0
1
1
1
0
2
0
1
1
0
1
0
1
1
1
0
0
0
1
1
0
0
0
1
1
0
1
0
0
1
0
1
1
1
1
0
0
1
1
0
1
1
3
2
0
1
1
0
0
1
0
0
2
0
2
1
1
0
1
0
1
0
1
1
0
1
1
2
1
0
0
2
2
2
0
0
0
2
1
2
3
1
0
2
1
2
2
0
2
0
2
1
0
2
2
2
0
2
0
0
1
0
0
0
1
1
1
0
2
0
1
0
0
1
1
2
0
1
1
2
1
0
0
0
1
1
1
0
1
0
1
2
0
0
0
1
0
0
2
1
0
1
0
1
1
0
1
1
0
0
0
0
2
0
2
0
1
0
1
0
1
1
1
2
0
2
0
1
0
3
0
1
1
1
0
2
0
1
0
0
0
2
1
2
1
1
2
1
0
1
0
1
1
0
0
1
0
1
0
3
1
0
1
0
1
1
1
1
2
1
0
0
1
0
2
2
0
1
1
0
2
0
2
0
1
0
2
0
0
0
1
2
2
1
2
0
1
1
0
2
0
0
2
0
1
1
1
1
1
2
0
1
1
0
2
0
1
2
1
0
1
1
1
1
0
0
0
0
2
1
1
2
0
1
2
2
0
0
0
1
1
0
0
1
2
2
2
2
2
0
0
2
0
2
1
1
2
1
0
0
0
1
1
2
0
2
2
0
0
0
1
0
1
1
1
1
0
0
0
0
2
1
0
1
0
1
0
2
0
0
1
2
0
1
1
2
1
1
0
2
2
2
0
1
1
0
0
0
2
9
1
0
1
1
0
1
0
0
1
0
1
0
2
1
2
0
1
0
0
0
0
2
1
1
1
1
0
0
0
0
1
1
0
2
2
0
0
1
0
0
1
0
1
1
0
1
0
1
1
0
0
0
0
3
0
2
1
1
1
0
1
0
1
1
0
2
1
0
1
0
0
1
1
1
2
0
2
1
2
1
0
1
1
1
1
0
1
1
1
0
1
0
1
0
1
0
0
0
0
1
1
1
2
0
0
1
0
1
0
2
1
1
1
2
0
1
1
1
2
1
0
1
1
1
0
2
2
2
0
0
0
2
0
2
2
0
2
2
1
1
1
0
2
1
1
0
0
2
1
2
3
0
0
2
4
2
0
0
1
1
1
2
0
1
2
0
0
2
2
1
1
1
0
0
2
1
1
2
0
0
1
1
2
1
0
0
2
1
1
0
1
1
0
0
1
1
3
1
0
0
1
2
1
0
0
0
2
1
2
0
0
2
0
0
1
2
1
0
1
1
2
0
1
1
1
0
2
1
2
0
0
1
2
1
1
0
0
2
0
2
1
0
0
2
1
2
0
1
1
0
2
0
0
0
2
0
1
1
0
0
0
2
0
0
2
2
2
1
1
2
1
1
1
2
1
0
0
1
0
0
1
1
0
0
2
2
1
0
0
0
0
1
0
1
1
0
0
2
1
1
0
1
0
0
1
1
0
2
0
1
1
0
0
2
1
1
0
2
2
0
1
2
0
1
2
2
1
0
0
0
1
1
1
0
1
2
0
1
1
1
1
0
0
1
0
0
1
0
1
4
0
1
1
1
0
1
0
0
0
1
0
2
2
2
0
1
0
0
0
0
1
1
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
2
0
2
2
2
1
0
1
0
2
0
0
0
1
1
0
1
0
2
0
1
0
0
2
0
1
0
0
2
1
2
0
2
0
0
2
1
1
2
1
2
1
0
1
0
2
1
0
0
0
1
1
2
1
1
2
2
1
1
1
1
2
1
0
1
0
0
2
1
2
0
0
0
2
1
1
0
1
1
2
0
0
0
0
0
2
0
1
1
0
0
1
0
1
0
0
1
0
2
1
1
0
1
2
1
1
0
0
1
1
2
1
0
1
1
2
2
0
0
1
2
1
0
0
0
1
2
2
0
2
1
2
2
1
0
1
0
2
0
1
0
1
0
1
0
2
1
1
3
2
1
0
0
1
1
1
0
1
2
0
0
2
3
1
0
2
0
1
0
3
0
1
1
1
1
0
0
1
1
1
2
0
2
0
2
0
0
1
0
0
1
0
4
0
0
0
0
2
0
2
1
2
0
2
0
2
1
0
0
1
0
1
0
2
1
1
1
0
1
2
1
0
0
0
1
1
3
1
0
1
0
1
0
2
1
0
1
0
2
1
2
0
1
2
2
0
0
1
0
1
2
1
0
1
1
3
1
2
0
3
1
2
2
2
1
2
0
0
0
1
0
0
0
1
0
2
0
2
0
1
1
1
0
0
1
1
2
2
0
0
2
1
2
1
0
2
0
0
0
1
2
1
0
0
1
0
2
1
2
2
1
1
2
1
0
2
0
0
0
0
1
1
2
0
0
1
2
1
1
2
0
0
0
0
0
1
1
0
1
2
0
0
2
1
0
2
0
0
1
1
2
2
2
1
1
0
1
1
0
1
2
2
0
1
1
1
1
1
2
0
3
2
2
0
2
2
2
0
1
1
1
0
1
2
0
1
1
0
2
2
0
0
0
2
0
2
1
0
0
1
1
0
0
0
0
1
3
0
1
2
1
0
1
1
2
2
2
1
0
2
1
0
0
1
2
1
3
0
1
2
0
1
3
0
0
2
2
3
1
1
0
2
0
0
1
1
1
0
1
4
1
2
0
1
1
2
0
1
0
0
2
0
1
0
1
1
1
1
1
2
1
0
0
2
1
3
0
0
2
0
0
0
1
1
1
0
1
0
2
0
0
2
1
1
2
2
1
1
0
1
2
0
1
2
0
0
1
0
0
2
0
1
0
0
1
2
1
1
1
1
2
0
1
0
1
1
0
0
1
0
1
0
1
0
1
2
3
0
0
0
0
1
0
1
1
0
1
1
0
0
1
2
2
1
0
0
1
0
1
2
0
0
1
0
0
1
2
2
1
2
1
1
1
1
1
4
1
2
1
2
1
1
0
1
0
0
2
1
0
1
2
1
0
0
2
1
1
0
0
1
1
1
0
2
0
1
0
0
1
0
0
0
0
1
2
2
0
2
2
0
0
0
2
1
1
0
0
2
0
2
0
1
2
1
0
1
2
1
1
0
1
1
1
1
2
0
2
1
0
0
2
2
0
2
0
0
1
0
0
0
0
1
1
0
1
2
0
1
0
1
1
1
1
0
0
1
0
1
0
0
1
1
0
1
1
2
1
2
0
1
1
0
1
0
2
1
0
1
1
0
0
1
2
2
0
1
1
0
0
2
1
1
0
1
2
2
1
2
0
1
1
0
2
0
1
2
0
1
1
1
0
0
0
0
1
2
1
2
1
0
2
2
1
1
1
0
1
0
1
0
2
3
1
1
2
1
0
0
1
1
1
2
0
1
0
2
0
1
0
1
1
2
1
1
1
1
0
1
1
1
0
0
1
0
0
2
1
2
1
2
1
2
2
1
2
2
0
2
0
2
1
1
0
2
1
2
1
1
1
2
0
0
1
1
1
0
1
1
1
1
1
0
1
0
0
0
0
0
0
1
0
2
0
0
1
2
0
4
1
0
0
1
0
1
0
0
2
0
0
2
2
0
1
1
2
0
1
0
2
0
1
1
2
2
1
0
1
0
0
0
1
1
1
1
0
1
1
0
0
0
1
1
2
1
2
2
2
1
2
2
1
1
2
1
1
1
1
0
0
0
2
0
2
1
2
0
0
2
0
2
1
1
1
1
0
2
0
0
0
0
0
2
1
1
1
0
2
1
1
0
2
2
1
2
2
1
0
1
1
2
3
1
2
0
1
0
1
2
1
0
0
0
1
2
0
2
3
0
2
1
1
2
1
0
2
0
1
1
0
1
0
2
0
2
2
2
2
1
1
2
2
1
1
1
1
1
2
0
0
1
1
0
0
1
2
0
3
1
1
2
2
1
2
1
3
1
1
1
1
3
2
0
0
2
0
2
2
1
0
1
1
2
0
1
2
1
0
2
1
1
2
1
1
0
1
1
1
0
0
0
4
0
0
3
1
0
1
1
2
2
0
0
0
0
0
1
0
1
0
0
1
0
1
2
1
1
1
1
1
0
1
2
1
0
1
1
0
2
1
0
1
0
1
1
0
0
1
0
0
1
1
2
2
0
1
1
1
0
1
1
2
0
2
0
2
3
1
2
0
1
1
2
1
1
0
2
2
1
0
0
1
0
0
1
1
0
2
2
1
0
0
1
1
1
2
0
0
2
1
2
1
1
1
0
2
0
1
2
0
0
0
2
1
1
0
1
1
3
0
0
0
0
1
2
1
2
1
2
1
0
1
1
1
0
1
1
0
1
2
0
1
1
2
1
0
1
1
0
1
0
0
0
3
2
1
0
1
1
0
0
2
1
1
0
1
0
0
1
0
0
0
1
2
2
0
2
2
2
1
1
2
2
1
1
7
1
0
0
0
2
2
0
1
1
2
1
0
0
1
0
0
3
0
0
2
2
0
2
1
1
1
0
0
0
1
1
0
0
1
0
0
1
0
1
2
1
2
2
1
1
0
1
1
1
1
0
1
2
2
3
0
0
1
0
0
0
0
1
0
0
0
2
0
0
1
1
1
1
0
1
1
1
0
1
0
1
2
0
1
1
0
0
2
1
1
1
0
2
1
1
1
0
2
5
1
1
1
2
0
1
1
0
0
2
2
0
0
2
0
1
1
1
1
1
1
1
1
1
1
1
1
1
2
2
1
2
2
0
2
1
1
1
0
1
0
2
1
1
1
0
1
2
1
0
0
2
0
0
2
1
1
0
1
1
0
3
0
2
2
1
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
1
1
2
2
1
2
0
1
1
2
0
1
0
2
2
0
2
1
1
1
0
0
1
1
1
0
0
1
1
0
0
0
2
1
2
2
2
1
2
2
0
0
1
1
1
1
0
0
2
4
1
1
1
0
1
1
0
1
0
0
0
0
1
2
1
1
0
2
1
0
0
0
0
1
0
1
2
1
0
1
2
2
1
0
2
2
1
0
0
1
1
1
2
0
0
0
1
1
2
1
0
0
1
1
0
0
0
1
0
2
2
2
1
0
2
0
0
1
2
2
0
1
1
0
0
1
1
0
0
0
0
6
2
0
0
0
1
2
1
1
1
2
2
1
2
1
2
0
1
2
0
0
1
0
2
2
2
1
0
0
2
2
1
2
1
2
1
1
2
1
2
1
0
1
1
2
0
0
0
1
0
1
0
1
0
2
0
1
2
3
0
0
0
0
2
1
1
2
2
2
4
1
1
1
0
1
1
0
2
1
1
1
1
0
1
0
0
0
0
2
2
0
1
0
1
0
0
1
0
0
0
0
2
2
1
1
2
0
2
0
1
1
1
1
2
1
0
1
0
1
0
1
0
1
1
1
1
2
0
1
1
0
0
1
1
1
0
0
1
1
1
1
1
0
1
0
1
1
1
0
0
0
1
0
1
2
0
1
2
0
0
0
1
1
0
0
0
2
1
2
2
0
1
0
1
2
1
0
1
2
2
1
1
2
1
0
1
1
1
1
2
0
2
2
1
1
2
2
0
1
0
2
0
1
0
0
1
1
0
0
0
1
0
1
1
1
2
0
0
0
2
1
1
0
1
2
0
0
2
1
0
1
0
2
1
0
0
1
1
2
0
1
1
0
2
0
0
1
0
0
2
2
1
2
2
1
0
0
1
1
0
1
1
0
0
1
0
1
2
0
1
0
2
2
0
0
1
2
2
2
1
2
2
2
1
1
1
0
0
2
2
0
2
0
0
1
1
1
0
0
1
1
2
1
0
0
1
0
0
2
2
0
1
0
0
2
0
1
0
0
1
0
1
0
2
0
2
0
0
1
2
1
2
0
2
1
0
2
0
2
0
0
2
0
2
1
1
1
1
1
0
1
1
0
0
0
0
0
0
1
0
1
0
3
0
1
0
1
2
1
0
1
1
0
0
2
1
0
0
1
1
1
1
2
1
0
0
0
1
0
0
2
1
2
1
2
1
0
0
0
1
1
0
2
1
1
1
0
0
0
1
0
0
1
0
2
1
3
2
1
2
2
1
0
2
1
0
1
1
2
0
0
1
0
1
0
2
1
1
2
1
1
1
0
2
1
0
0
1
1
2
2
0
1
1
1
0
1
2
2
0
0
1
0
2
2
2
1
2
1
0
1
1
2
0
0
2
1
1
0
0
2
1
1
1
1
1
1
2
2
0
0
2
0
2
1
1
2
0
2
1
0
1
0
0
2
1
0
2
0
1
2
2
0
2
1
0
1
0
1
1
0
2
1
0
1
2
0
2
2
1
2
1
0
0
1
0
1
2
0
0
1
0
0
1
0
0
1
1
0
1
1
1
0
0
5
0
0
1
1
2
0
0
0
0
0
0
0
1
1
0
0
2
1
0
1
0
0
0
1
2
0
0
1
1
0
0
0
0
0
2
1
1
2
1
0
0
1
0
2
1
1
0
1
1
1
1
1
1
2
1
1
0
0
2
0
1
1
0
0
2
2
2
0
1
0
1
2
1
2
1
2
3
0
2
0
0
3
0
0
1
1
1
1
2
0
1
2
0
0
0
0
0
1
0
0
1
1
1
2
0
0
1
1
2
2
1
2
1
0
1
3
0
1
2
5
2
1
0
0
0
0
1
1
2
0
2
0
1
0
0
0
2
3
1
0
0
2
1
0
0
1
0
0
1
1
4
1
2
1
0
0
2
0
1
0
1
0
0
1
0
2
0
0
1
0
0
1
0
1
2
2
2
0
2
0
3
0
1
0
2
0
1
0
1
0
2
2
0
1
2
2
3
0
1
0
0
2
1
1
0
1
0
1
1
0
0
1
1
1
1
2
1
0
2
1
1
0
0
0
0
0
1
1
1
1
0
0
0
1
0
0
0
0
0
1
1
0
2
1
0
2
0
1
1
2
0
2
1
0
3
1
1
1
2
1
1
0
0
0
2
2
1
1
0
0
0
0
2
1
1
0
1
1
1
1
1
1
2
0
0
1
2
1
2
1
1
2
2
1
0
0
0
2
2
0
0
1
1
0
0
1
2
1
0
1
0
1
1
1
0
0
1
2
1
0
1
1
1
0
2
0
0
1
1
1
2
0
1
0
2
1
0
0
0
0
2
2
2
1
0
1
0
1
0
1
1
1
1
2
1
1
0
2
1
2
2
1
1
1
1
3
0
2
1
0
1
2
0
1
2
1
2
1
0
1
1
1
0
0
1
1
0
0
0
2
1
0
1
0
2
0
1
2
1
0
1
0
1
3
0
0
1
0
0
2
2
1
1
2
1
2
2
2
0
0
2
2
2
0
0
0
2
1
0
0
2
1
1
1
1
1
1
2
0
0
1
1
2
1
0
1
0
2
0
1
0
0
1
0
0
2
1
0
1
0
0
1
0
0
2
0
1
0
0
0
2
1
0
0
1
1
1
1
0
0
0
1
0
2
1
1
1
0
1
1
1
1
1
3
0
0
1
1
0
1
1
1
0
0
2
1
0
2
1
1
1
1
1
2
2
2
0
2
0
0
1
0
0
1
1
2
0
0
1
2
1
0
1
1
2
1
2
1
1
2
0
2
2
2
3
0
0
1
1
0
2
1
2
0
0
0
1
2
0
1
0
0
1
1
2
7
2
0
2
1
0
1
1
3
0
1
2
0
0
1
0
1
2
2
1
1
0
1
2
1
1
0
1
2
1
1
1
1
1
2
2
1
2
0
0
2
1
3
1
0
1
0
2
1
0
2
3
2
1
1
1
1
0
1
0
2
0
0
0
0
1
2
0
1
1
1
1
0
0
1
3
1
0
1
1
0
1
1
0
1
1
2
1
0
0
1
2
1
0
0
1
1
0
2
2
1
1
1
0
1
1
0
0
1
1
0
2
1
0
2
0
0
0
0
0
0
1
1
1
0
1
1
2
1
2
1
0
1
1
2
0
0
0
0
2
0
0
1
1
1
1
0
2
0
2
0
0
1
1
1
0
0
0
2
1
3
0
1
1
2
0
0
0
2
2
2
0
0
1
2
0
1
0
1
0
2
1
0
1
1
1
2
0
2
0
1
1
0
2
0
1
1
1
1
0
1
0
0
0
0
0
1
0
1
0
1
1
1
1
0
0
1
0
1
0
2
0
1
0
0
0
1
0
0
1
1
2
0
5
0
1
0
1
2
1
3
2
1
0
1
1
0
1
0
0
2
1
1
1
0
0
1
0
1
0
0
1
1
0
0
0
0
1
1
0
1
2
2
0
1
1
1
0
0
1
2
1
2
1
2
1
1
1
1
0
1
1
1
0
1
0
0
1
1
1
1
1
2
0
1
1
2
0
2
1
0
0
2
0
0
2
0
3
1
2
1
1
0
2
0
2
1
2
1
3
0
1
2
2
2
1
2
1
2
0
1
2
2
2
1
0
1
2
0
1
2
0
2
0
0
1
2
2
0
0
1
0
0
0
0
0
0
1
1
2
0
2
2
1
0
2
1
0
2
1
2
4
0
2
0
1
1
0
0
1
1
0
3
0
0
2
1
1
1
0
0
0
0
1
2
1
2
0
2
2
2
1
2
2
1
0
1
2
0
1
3
2
1
2
1
1
1
0
1
1
1
1
0
2
1
2
1
1
2
2
0
0
2
1
0
1
2
0
0
2
0
1
1
1
1
0
1
0
1
1
1
1
0
1
0
2
1
3
0
1
2
1
0
0
0
1
1
1
1
1
1
0
1
0
1
2
0
1
2
1
0
1
1
1
1
2
1
1
0
2
0
0
1
1
1
0
2
0
0
1
1
2
0
0
2
1
1
2
2
1
0
0
2
0
2
0
2
2
1
0
1
0
1
0
1
0
0
0
2
1
1
1
0
0
0
0
1
1
0
0
1
1
2
0
0
3
2
0
0
1
2
1
0
2
1
0
1
1
1
1
1
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
1
1
0
0
0
1
1
2
0
1
2
1
0
0
0
1
1
1
2
2
0
0
1
0
1
0
1
0
0
0
1
2
1
0
4
2
0
1
2
0
2
1
0
1
0
2
2
0
0
1
0
1
0
0
1
1
2
0
2
1
1
1
2
2
2
0
0
0
1
0
1
1
1
0
1
1
1
2
1
1
2
2
1
0
1
1
0
1
1
1
0
1
2
0
1
0
1
1
1
0
1
1
1
1
1
0
2
1
2
1
0
1
2
1
0
1
0
2
1
0
0
2
0
1
0
0
2
2
0
2
0
0
1
0
0
0
2
1
0
0
1
1
1
0
2
1
0
1
0
0
0
1
0
3
1
1
1
2
2
1
0
1
1
0
1
0
1
0
2
2
3
0
0
0
2
2
2
1
1
2
0
1
0
2
0
0
0
1
2
2
2
2
1
1
1
0
0
0
0
1
1
0
2
0
0
0
1
1
2
0
1
0
1
2
1
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
2
0
0
0
2
1
0
0
2
0
0
0
0
2
0
0
1
2
1
0
1
0
2
1
2
1
0
1
0
0
1
2
0
0
1
2
1
0
0
1
1
0
0
0
0
1
2
1
1
0
2
2
1
0
1
0
1
1
1
0
1
0
0
0
1
1
2
0
0
2
2
0
4
1
1
0
0
0
0
1
2
1
0
1
0
1
0
1
2
0
2
1
3
0
0
0
1
0
1
0
2
1
1
2
0
0
0
1
0
1
1
1
3
2
0
1
0
0
0
2
2
2
1
0
1
0
1
0
2
1
1
0
1
1
1
1
1
0
1
1
0
0
0
3
2
0
2
1
0
2
0
1
0
1
3
2
2
1
1
2
1
5
1
1
0
1
0
2
0
0
0
2
0
0
1
1
1
1
0
0
1
1
2
0
0
1
0
2
0
0
1
0
0
2
0
1
0
2
2
1
0
0
1
0
1
3
0
1
1
2
0
0
2
2
1
1
0
0
1
1
0
0
0
2
1
0
2
1
0
0
1
0
2
1
1
1
1
0
0
0
2
2
0
2
0
1
0
0
0
1
0
0
1
0
1
1
2
3
0
2
2
2
2
0
2
0
0
2
4
0
0
2
0
1
0
1
2
1
0
2
1
0
1
0
3
2
1
1
0
0
1
2
1
2
1
2
1
2
1
2
4
1
0
1
2
2
2
0
1
0
1
0
1
1
1
0
0
0
1
2
2
1
0
0
2
2
0
0
1
2
0
2
2
0
2
2
2
0
2
1
0
0
1
2
1
0
2
1
3
0
0
0
0
2
1
2
0
1
2
1
0
0
1
1
1
0
0
2
2
0
0
1
1
1
0
1
1
1
0
2
1
0
1
1
1
1
1
0
0
1
0
1
0
2
1
1
1
0
0
1
0
0
0
2
1
1
2
0
0
1
0
0
0
0
1
1
0
0
0
1
2
2
0
0
2
2
2
1
0
0
1
1
1
0
1
0
0
0
1
1
1
0
1
1
2
0
1
0
0
0
1
0
0
0
1
1
2
1
2
1
2
2
1
0
1
0
1
3
1
2
1
2
0
2
1
1
0
1
1
0
0
1
1
0
0
1
1
0
0
0
1
2
0
1
1
2
1
0
1
0
1
1
2
0
0
2
0
0
0
2
1
0
2
1
1
0
1
1
2
2
0
2
3
0
2
1
0
0
0
1
2
0
2
0
0
1
1
1
0
1
1
0
1
1
1
0
1
0
1
2
2
0
0
2
1
2
1
0
2
1
0
1
0
0
2
0
1
0
2
1
1
0
2
1
1
1
2
1
1
0
1
0
2
1
0
3
0
0
1
1
1
0
2
1
0
1
0
0
1
2
1
1
2
1
0
0
0
1
1
2
1
0
1
0
0
1
0
1
0
0
1
1
2
2
2
2
1
0
0
0
0
0
0
1
1
1
2
0
1
0
1
0
0
1
1
1
2
2
2
1
1
2
1
0
1
1
0
2
3
1
0
1
1
0
1
1
0
2
0
1
1
2
1
4
0
1
1
1
2
2
0
0
0
1
0
0
1
1
1
1
0
2
2
3
1
0
3
1
1
0
0
1
1
0
1
1
1
1
1
2
1
1
0
1
1
2
2
0
0
0
2
0
3
2
0
0
1
1
0
0
1
1
1
0
0
2
0
1
0
0
0
0
0
1
2
2
2
0
1
1
1
1
2
1
1
1
0
2
2
0
1
1
0
1
0
2
1
0
1
1
1
2
1
2
1
1
1
2
0
1
1
1
1
0
2
2
0
0
2
0
1
2
0
1
1
1
0
1
0
2
1
2
1
2
1
1
2
0
1
1
1
0
1
1
0
0
0
1
1
1
4
0
1
0
0
2
0
1
0
2
0
0
2
2
0
1
2
2
1
0
2
0
0
1
0
2
2
2
1
1
2
0
0
1
0
1
0
2
1
1
1
1
0
0
1
0
2
2
0
2
1
0
1
0
1
1
0
1
0
0
1
1
0
2
1
0
0
0
1
1
0
1
2
0
0
4
2
0
2
1
1
0
0
2
1
1
2
2
0
0
2
0
2
1
2
0
1
1
2
0
1
3
1
0
1
1
2
0
1
0
1
1
2
0
0
0
0
0
1
0
2
2
0
2
2
1
2
0
2
2
0
1
1
2
0
1
1
0
1
1
2
1
0
0
1
0
2
2
1
1
2
0
0
2
1
0
0
1
2
2
0
2
1
1
1
2
1
1
0
1
1
1
2
2
2
2
0
1
2
1
1
0
0
2
0
0
1
0
1
1
1
0
1
1
3
0
1
2
0
1
5
1
1
1
0
0
0
0
0
1
2
1
0
1
0
2
1
0
0
0
0
1
1
1
1
1
0
1
1
1
2
0
0
1
0
0
0
0
0
1
0
1
0
1
0
2
1
0
0
2
2
0
0
0
2
0
2
2
1
0
1
0
1
0
1
2
1
2
0
1
1
0
2
1
0
1
1
0
1
0
2
2
1
0
1
1
1
0
1
0
1
1
0
3
0
1
1
1
2
0
2
0
1
0
0
1
2
1
0
0
1
1
0
1
3
1
1
1
0
1
0
1
2
1
0
2
1
0
1
0
1
1
1
1
2
1
1
1
0
0
0
0
1
0
0
3
0
0
2
1
0
1
2
0
1
1
1
1
2
2
2
0
2
1
0
0
1
0
0
0
0
1
1
0
2
0
2
1
2
1
1
0
2
1
2
2
2
0
0
1
0
0
0
1
0
2
6
1
0
0
0
1
0
2
1
1
0
0
1
1
2
1
2
2
2
2
0
0
0
1
0
1
0
4
2
2
1
1
1
2
1
1
0
2
0
2
1
1
0
0
0
1
0
0
2
0
0
1
1
1
2
0
1
1
1
2
2
2
1
2
2
0
0
0
0
2
2
0
0
0
1
2
1
0
1
0
1
1
0
0
0
1
0
1
0
2
0
3
3
2
1
3
1
1
1
2
2
1
0
2
1
1
1
2
2
1
2
0
2
1
2
1
2
1
0
2
2
0
3
0
2
1
3
2
0
0
2
0
2
2
0
0
3
0
1
0
2
0
1
0
0
2
0
1
2
2
1
2
2
0
1
0
0
0
0
2
1
1
1
1
0
1
1
0
2
1
1
0
1
2
1
0
2
1
0
0
0
2
2
1
0
0
1
0
0
1
0
2
1
2
1
0
0
2
0
0
0
0
1
2
2
0
2
2
1
0
1
1
1
2
1
1
1
2
1
1
1
0
0
2
0
2
1
0
0
0
0
1
1
1
0
2
1
2
0
2
2
2
1
2
0
1
0
2
1
0
0
0
1
2
1
1
0
0
2
1
1
1
1
1
1
2
2
2
0
1
0
2
0
1
1
0
0
0
1
0
1
2
0
3
1
0
1
0
0
0
1
1
0
1
1
1
2
1
0
2
2
0
0
1
1
2
0
2
0
2
2
3
1
0
2
2
0
0
2
0
0
2
1
2
1
0
1
0
2
2
2
1
0
1
0
2
1
1
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
1
2
2
1
1
0
0
1
2
2
0
0
2
2
1
0
2
1
0
0
2
1
0
1
2
0
2
2
0
1
0
0
0
2
3
0
0
1
0
1
1
2
1
2
1
2
0
1
0
1
1
1
0
0
0
1
2
1
1
2
1
1
0
2
4
0
1
1
0
1
1
1
0
2
2
0
0
2
1
1
0
1
1
1
2
0
0
2
2
1
2
0
0
2
2
2
2
2
0
1
2
1
1
2
0
0
2
1
2
1
0
2
2
2
3
1
0
2
1
2
0
1
2
2
2
2
1
0
0
3
0
0
1
0
0
0
1
1
1
1
0
2
1
0
0
0
1
1
1
0
1
2
1
1
2
1
1
1
2
2
1
2
1
0
1
1
2
0
0
2
2
1
0
1
1
1
0
1
0
0
2
0
1
0
1
1
0
1
2
1
1
0
0
2
2
1
2
1
1
2
0
1
1
0
1
0
1
1
1
1
0
0
2
2
2
2
2
2
1
1
0
0
1
2
0
0
0
1
0
0
0
2
1
1
0
2
2
1
0
1
1
0
0
0
0
1
0
1
1
0
2
1
1
1
2
0
0
0
1
2
0
2
0
1
2
1
1
1
0
2
2
0
0
0
1
1
2
2
2
0
1
1
2
1
0
0
0
1
2
1
1
0
1
1
0
2
1
1
1
0
2
0
2
3
2
1
0
2
0
1
2
1
2
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
2
1
1
1
1
0
0
1
0
0
0
0
1
0
2
1
1
1
1
1
0
0
1
1
0
0
1
2
1
0
2
1
1
0
1
1
1
1
1
0
0
1
0
0
3
0
1
2
0
0
1
0
0
1
0
0
0
0
0
0
1
4
2
2
1
0
1
0
2
1
0
0
0
0
0
2
1
1
1
0
0
1
2
0
1
1
0
0
0
0
1
1
1
1
2
1
1
1
2
0
0
0
0
0
2
0
0
1
0
2
0
2
0
0
0
1
2
1
0
0
0
2
2
1
1
3
1
0
2
0
1
2
0
0
2
0
2
1
0
0
2
1
2
1
1
1
1
1
1
1
2
2
0
0
2
0
3
1
5
1
2
1
1
0
2
0
1
1
2
0
2
0
1
0
1
1
2
1
1
0
1
0
1
2
0
1
1
1
1
1
1
1
0
0
0
1
1
2
0
2
0
1
1
1
1
2
2
0
4
0
2
1
1
0
0
2
0
2
0
0
0
1
0
1
0
1
1
0
2
0
0
0
1
2
1
1
1
0
1
0
1
2
2
2
1
0
1
1
1
0
1
0
1
1
1
0
0
0
1
0
1
1
0
0
0
1
1
0
1
0
0
2
0
0
0
2
2
1
2
1
0
1
0
2
1
2
1
2
0
0
1
1
0
2
1
0
0
1
0
1
1
0
0
1
0
1
1
2
2
2
1
0
2
0
1
1
1
1
0
0
1
0
2
1
0
1
0
1
0
1
2
2
1
1
1
1
0
0
0
1
1
0
0
1
0
0
1
2
1
0
0
2
2
2
1
2
2
0
1
0
1
1
0
0
1
1
1
0
1
1
2
0
2
0
2
1
1
1
0
2
1
2
1
0
1
0
2
0
1
2
0
2
0
0
0
0
1
1
1
0
0
2
0
1
2
0
0
1
0
0
0
1
3
0
2
0
1
1
1
1
1
1
0
1
2
1
1
1
0
0
0
0
1
0
2
1
1
0
1
1
1
1
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
1
1
1
1
1
1
0
2
1
2
1
0
1
0
0
2
0
1
1
0
1
0
0
1
1
1
0
0
2
0
1
1
0
1
0
1
0
1
0
0
1
2
0
1
2
1
0
2
1
0
2
0
0
2
0
1
2
0
0
1
1
1
1
0
0
1
0
1
0
0
0
3
1
2
1
0
0
0
1
1
1
1
1
1
0
1
1
2
0
0
0
0
2
2
2
1
1
1
2
0
1
0
1
1
2
2
1
1
1
0
2
0
3
0
1
1
1
2
1
1
0
0
1
3
0
0
0
2
1
2
1
0
0
0
0
2
1
0
0
0
0
0
1
1
1
0
0
1
1
2
0
2
1
1
2
2
0
0
1
2
1
0
0
1
0
0
0
0
1
1
1
1
1
0
1
2
0
1
1
1
1
1
2
0
1
1
1
0
1
1
1
1
1
1
2
2
0
3
1
0
0
1
2
0
0
1
1
1
1
1
1
2
0
2
2
0
1
1
1
0
0
0
0
1
2
0
1
0
0
1
0
1
1
1
3
0
0
1
1
1
1
1
0
0
2
2
2
6
1
0
0
1
0
1
0
0
2
1
1
2
0
1
0
0
3
2
0
0
0
1
0
0
1
0
1
1
1
0
1
1
1
1
0
1
1
0
0
2
2
4
1
1
0
0
1
1
0
1
2
2
0
1
0
2
1
1
0
1
0
0
0
0
0
2
0
2
1
1
0
1
0
2
1
0
0
0
1
1
1
1
0
1
1
0
1
2
1
1
3
1
0
2
0
0
1
0
1
1
1
1
0
0
1
2
0
0
0
0
2
1
2
0
1
7
1
1
0
0
0
1
1
0
0
0
2
1
0
1
0
1
0
1
1
0
1
1
0
2
1
0
1
1
0
0
1
3
2
1
0
1
0
0
1
1
0
0
1
1
0
0
1
1
1
0
1
0
0
2
0
0
2
2
1
2
2
0
0
1
1
1
0
0
1
0
0
2
0
0
0
0
1
0
0
2
0
1
2
2
0
0
0
1
0
1
1
0
0
2
0
0
1
1
1
1
1
0
1
1
2
0
1
0
1
2
3
2
1
3
2
2
2
0
1
2
1
1
0
1
3
0
1
1
1
1
0
2
0
2
2
0
2
1
0
0
1
1
2
0
1
0
2
2
1
1
0
2
2
1
2
1
1
2
1
1
0
0
2
0
0
1
2
0
1
0
0
2
2
0
2
0
0
1
2
0
1
1
0
2
0
1
0
0
1
1
1
3
1
2
0
0
2
2
0
0
0
1
0
1
2
0
1
0
0
1
1
2
0
1
2
1
0
2
2
2
0
0
0
0
0
1
0
2
2
2
0
1
0
1
1
2
3
0
0
0
2
0
0
1
1
1
1
2
1
0
1
0
1
1
2
1
1
1
1
0
1
1
2
0
0
1
1
1
1
0
2
0
3
1
1
1
0
0
1
1
2
0
1
1
0
0
1
1
3
2
0
0
1
0
1
1
1
2
0
0
2
2
2
2
1
2
1
2
1
1
2
0
1
0
0
2
1
0
1
1
1
2
0
0
1
0
0
1
0
2
0
0
2
1
2
0
0
0
2
0
1
0
1
2
1
1
2
1
3
1
0
0
2
1
0
1
1
1
2
0
1
0
0
0
2
1
2
2
1
2
0
1
2
1
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
1
1
0
1
0
1
0
1
1
0
1
1
0
0
2
1
4
0
0
1
1
1
0
0
1
0
1
0
1
1
1
0
0
0
2
0
0
0
2
1
1
0
2
0
0
0
2
2
1
2
1
0
1
2
1
1
3
1
0
0
2
0
1
1
0
1
1
1
0
1
2
0
1
1
3
3
0
0
1
0
1
0
0
1
1
0
1
1
1
2
2
1
1
0
1
2
0
2
0
1
0
1
1
2
1
1
3
1
0
0
2
1
0
1
0
1
0
1
1
1
0
1
0
1
0
1
0
0
0
0
0
1
1
0
1
2
2
0
0
1
1
1
2
0
0
1
0
1
0
0
0
2
2
2
1
1
0
1
0
0
2
2
1
0
2
0
0
0
1
1
0
0
0
1
1
0
1
0
0
1
2
1
0
1
2
2
1
1
1
0
0
1
1
1
0
1
0
1
1
1
0
1
2
1
0
1
0
0
0
0
2
3
1
1
0
2
2
1
1
0
0
1
1
2
0
1
0
0
1
2
0
1
1
1
1
1
0
1
2
0
2
1
0
0
1
3
0
1
1
2
1
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
1
0
4
1
1
0
1
2
0
0
1
1
0
2
0
1
1
0
1
0
0
1
1
0
1
2
0
1
2
1
2
1
0
2
1
3
3
2
1
2
2
0
0
0
0
1
2
1
0
1
1
1
2
0
0
0
1
2
1
0
0
1
0
0
1
1
1
1
0
0
1
1
2
2
0
1
1
2
1
1
0
0
1
1
0
2
0
1
2
0
2
0
0
0
3
2
2
0
0
2
1
2
2
0
2
0
1
2
2
0
0
0
2
2
0
2
0
1
2
2
0
0
0
0
0
2
0
0
1
2
2
1
1
0
2
0
0
0
1
0
0
2
0
1
1
0
1
1
1
0
0
2
1
0
1
1
0
2
0
2
1
0
1
2
2
1
2
0
1
0
0
1
1
0
0
0
0
0
0
1
1
1
0
0
1
1
2
0
2
1
0
0
1
2
0
0
0
2
1
0
0
0
1
0
0
0
1
2
1
1
1
0
0
1
1
1
0
0
0
0
2
1
1
1
1
1
2
0
0
2
2
0
0
1
1
1
2
1
1
1
1
1
0
0
0
1
0
1
1
0
2
2
2
1
1
0
2
0
0
2
1
0
2
1
2
2
0
0
0
1
0
1
0
2
1
0
1
0
0
0
0
1
0
1
1
0
2
0
1
1
2
1
1
2
2
0
1
0
1
0
1
2
2
0
0
1
0
2
1
0
1
0
0
1
0
0
0
1
0
2
0
0
2
0
0
0
0
1
0
0
1
0
2
1
2
0
0
2
0
1
3
1
2
1
0
2
1
0
2
1
3
2
0
0
1
0
0
2
1
2
0
1
0
2
2
1
1
0
1
0
1
0
0
0
0
1
1
1
0
1
1
1
0
0
0
1
1
2
1
0
1
1
0
1
0
0
1
0
1
0
1
1
0
1
1
0
0
1
0
1
1
0
0
1
1
0
1
1
0
0
0
1
1
3
0
2
1
1
1
0
1
2
0
0
0
2
1
1
0
2
0
0
1
2
0
0
0
1
1
0
2
1
0
0
1
1
0
1
0
0
4
0
1
2
2
0
1
2
2
1
0
0
0
2
2
0
0
1
1
2
2
2
0
1
0
1
0
2
1
1
0
0
0
0
1
0
1
0
1
0
0
2
2
2
1
0
1
0
0
0
0
2
1
2
0
2
2
1
1
1
0
0
1
0
1
1
2
1
1
2
2
1
0
2
0
1
1
2
1
0
2
2
0
2
1
1
2
1
0
0
0
1
2
1
0
2
0
3
0
1
2
1
1
0
2
1
1
1
2
1
0
1
0
1
0
1
0
1
0
1
1
1
1
0
0
0
0
2
0
2
1
2
0
1
1
1
1
1
0
0
0
0
0
1
1
2
0
1
2
0
1
1
1
0
0
2
0
0
0
0
1
1
1
0
2
0
0
0
0
0
1
0
0
0
0
2
0
2
1
1
0
1
0
1
1
2
0
1
1
0
2
0
3
1
1
1
1
2
1
1
0
2
0
1
2
2
0
0
2
1
0
0
1
1
1
0
1
1
1
0
1
1
0
0
1
2
1
0
1
1
0
0
2
0
0
0
0
0
2
0
1
1
0
0
1
0
0
1
0
0
2
2
1
0
0
2
1
1
2
2
1
1
1
1
0
1
0
0
1
1
0
0
1
1
0
0
0
2
0
1
0
2
2
0
1
0
2
0
0
0
1
1
0
0
0
2
2
3
1
1
2
0
0
1
0
1
1
0
1
0
3
0
0
1
1
0
2
0
1
1
0
0
1
1
0
0
0
2
1
0
0
1
2
0
1
1
0
0
2
0
0
1
1
0
0
1
1
1
0
1
1
1
0
2
1
0
2
2
1
1
1
0
2
2
1
2
2
0
1
1
1
0
2
1
0
1
1
0
1
0
0
1
2
1
1
1
1
2
0
0
0
1
0
2
2
0
0
0
1
1
1
0
1
0
0
0
2
3
1
0
1
2
1
0
1
1
2
2
0
1
1
0
1
2
0
1
1
1
2
0
0
0
0
2
0
2
0
1
2
1
0
2
0
0
0
2
0
1
0
2
1
1
1
0
1
1
2
0
0
1
2
2
0
1
1
2
1
1
2
1
1
0
2
2
1
2
0
1
1
2
0
1
0
1
2
1
0
0
1
0
0
0
0
0
1
1
1
1
1
0
1
0
2
0
1
0
2
2
1
0
0
2
0
3
0
2
0
2
1
1
1
1
3
0
2
1
1
0
1
1
1
0
3
1
2
0
0
1
0
0
2
0
0
1
1
1
1
1
0
0
1
2
0
1
2
1
1
0
0
1
1
1
1
2
1
0
0
0
0
3
2
2
1
2
1
0
1
2
0
1
1
2
0
1
1
1
0
1
0
1
0
1
1
1
0
1
0
1
2
0
0
1
0
1
0
1
0
2
0
0
0
0
0
0
1
1
2
1
0
2
2
1
5
2
1
0
2
1
0
0
0
1
1
1
1
2
1
0
1
1
0
0
1
0
0
0
1
2
0
0
2
1
0
1
1
1
2
1
1
0
1
0
1
0
2
1
1
3
0
0
1
1
0
1
0
1
2
0
1
1
1
0
1
1
0
2
1
0
1
2
0
1
0
0
2
1
2
2
0
0
1
1
0
1
2
2
2
1
1
0
4
0
1
0
2
0
2
0
1
1
1
1
1
1
1
2
0
2
2
1
0
0
1
1
1
0
0
1
2
0
1
1
1
0
2
0
1
0
0
0
1
0
2
0
0
2
1
1
0
1
0
1
1
1
2
0
2
1
1
1
2
1
1
0
1
2
1
2
1
1
0
2
1
0
0
0
0
0
0
1
0
1
1
1
1
0
2
2
3
0
1
0
1
1
1
1
0
1
0
0
0
1
0
3
1
0
0
0
0
0
2
2
0
1
2
1
1
1
0
0
0
0
1
1
1
1
0
0
1
0
0
0
0
1
0
0
2
1
2
1
0
2
4
1
1
0
2
1
1
1
1
0
2
0
0
1
0
1
2
1
1
2
0
1
0
1
1
1
1
1
0
1
1
2
1
1
2
1
1
1
1
2
1
3
1
0
1
0
2
2
0
1
2
1
0
0
0
1
1
2
2
2
0
0
0
1
0
1
1
0
2
1
1
1
1
0
1
1
1
0
2
1
0
0
0
0
0
0
0
1
0
1
0
0
4
5
0
0
2
1
2
0
1
0
1
0
0
2
0
0
2
2
2
0
3
0
2
1
2
0
2
2
1
0
1
0
1
1
0
1
0
1
1
1
1
0
1
0
2
1
1
1
1
0
0
0
1
0
0
1
1
2
1
1
1
1
0
0
2
1
2
0
2
0
1
2
1
1
0
0
1
2
2
0
2
0
0
1
3
2
1
0
1
0
0
1
2
2
2
1
0
1
1
1
2
0
1
2
1
0
0
0
2
0
0
1
0
1
2
1
0
0
0
0
0
2
3
1
3
2
1
0
2
0
2
2
2
1
3
0
0
0
2
1
1
0
2
0
0
2
1
0
1
1
1
0
0
0
1
2
0
1
0
0
1
0
0
0
1
1
1
0
1
0
0
1
2
2
1
1
2
0
0
0
2
0
1
0
1
0
1
1
0
0
1
1
2
1
1
2
1
1
2
2
2
2
0
2
0
1
1
0
0
1
1
0
1
1
0
1
0
2
0
2
3
0
1
0
0
1
2
1
0
2
2
0
0
1
0
1
0
1
0
1
0
1
0
0
0
1
0
0
1
1
5
1
1
0
1
0
1
0
0
1
0
0
0
0
2
1
0
1
1
0
1
0
0
0
2
0
1
0
1
2
1
0
0
2
1
1
1
1
0
0
0
0
1
1
1
0
0
1
1
0
1
2
1
1
2
1
0
2
1
0
2
1
2
0
0
1
0
2
0
0
2
1
1
2
3
1
1
0
1
0
2
2
0
1
1
1
2
3
1
1
1
0
1
0
1
0
0
2
1
1
0
2
2
0
0
1
2
2
1
0
1
0
1
1
1
0
0
0
1
2
2
0
1
1
1
0
1
1
2
1
0
1
0
0
1
1
1
0
0
2
0
1
1
2
2
2
2
2
1
0
1
2
1
0
1
2
0
0
1
1
0
2
2
0
0
0
2
1
0
0
1
2
0
1
0
1
1
1
2
1
1
0
0
1
0
1
4
2
1
0
1
1
2
2
0
1
1
2
0
2
1
2
1
1
0
0
2
1
1
2
0
1
0
1
1
1
0
2
2
2
1
2
0
2
1
1
0
2
1
0
0
0
0
1
1
0
0
0
1
0
0
0
1
1
0
2
2
1
0
2
1
0
2
0
1
0
1
1
0
0
0
0
1
0
2
0
0
1
0
0
0
1
1
1
0
0
0
2
1
1
5
1
1
1
0
1
1
0
1
0
0
0
1
1
2
1
0
0
1
1
0
0
2
1
1
1
1
1
4
0
1
1
1
0
2
1
1
2
2
1
2
1
1
1
1
1
0
1
2
0
0
2
1
0
2
0
0
0
0
0
0
1
1
1
1
2
2
1
2
0
0
0
0
1
1
2
0
1
0
0
0
0
2
2
1
1
0
2
1
1
2
0
2
1
0
1
0
0
2
1
1
0
1
1
2
1
1
1
1
1
0
1
1
1
0
0
0
0
1
2
2
0
2
1
0
1
1
0
0
0
0
3
2
0
2
2
1
1
1
0
2
1
2
1
2
1
2
0
2
1
0
2
1
0
0
1
0
1
0
1
1
1
2
1
1
2
1
1
0
1
1
0
1
1
7
0
1
2
1
2
1
0
0
1
1
0
0
1
0
1
1
1
2
0
1
1
2
1
1
2
1
0
1
0
2
1
0
0
0
2
1
0
0
2
1
0
2
0
1
1
0
1
2
0
2
2
2
1
2
1
1
0
1
2
1
2
1
2
0
1
1
0
0
0
0
0
0
1
1
0
0
2
0
0
1
1
1
0
0
2
0
1
2
0
1
2
2
0
1
1
1
3
1
0
1
1
0
1
0
2
2
1
0
1
1
0
3
3
0
0
0
1
0
0
1
0
0
1
0
0
1
1
0
0
1
2
1
1
1
2
2
1
2
1
2
1
0
1
2
0
0
0
2
0
0
1
3
0
0
0
2
2
2
1
1
1
0
0
2
2
0
2
2
2
0
0
2
0
1
2
2
2
0
1
2
1
1
1
1
1
0
0
2
1
0
2
0
2
0
2
1
0
1
1
1
0
0
1
1
0
0
2
0
2
0
1
2
1
0
0
1
1
1
0
1
2
1
2
0
0
0
1
2
2
2
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
1
1
1
1
0
1
1
2
1
1
2
0
1
1
0
2
1
0
2
1
2
1
2
1
1
1
1
1
1
1
2
0
0
1
0
1
2
0
0
1
2
1
0
2
1
0
0
1
2
1
0
0
1
2
1
2
1
1
0
2
1
0
1
0
1
1
2
0
1
1
2
0
0
1
0
0
0
4
1
2
1
1
0
0
1
1
1
1
0
3
2
2
0
0
1
1
0
1
1
2
0
1
2
0
1
1
0
0
1
0
2
1
0
2
0
2
0
0
0
0
1
1
2
1
1
2
2
1
1
1
1
1
1
1
0
2
0
1
0
1
1
0
2
1
1
1
0
2
0
1
2
0
0
1
0
1
0
1
0
0
0
1
1
2
1
1
0
1
3
0
0
2
3
2
1
1
0
1
0
0
1
2
0
0
1
0
1
0
0
1
0
1
1
0
0
0
1
0
2
2
0
1
1
0
1
0
1
1
1
2
2
1
1
2
0
0
0
2
1
1
1
0
0
0
1
1
0
0
0
1
2
0
2
3
0
0
2
2
0
0
0
1
0
0
2
2
2
2
1
1
1
1
1
1
0
1
2
2
0
1
1
0
3
2
0
0
0
2
0
1
0
2
2
2
0
2
3
0
2
2
1
1
1
0
1
0
1
2
1
0
0
0
0
0
0
0
0
0
2
0
0
1
2
1
0
1
0
0
0
1
0
1
4
1
0
0
0
0
0
1
1
1
1
1
0
1
1
0
1
0
0
2
1
1
2
0
1
0
1
2
1
2
1
0
0
0
2
0
1
3
1
0
1
0
4
1
1
0
1
0
0
0
1
0
0
1
2
0
1
0
1
1
2
3
1
0
0
0
1
0
0
1
0
1
1
1
0
1
0
0
0
2
1
1
0
1
0
2
2
1
1
0
1
1
1
0
0
0
1
1
0
0
2
0
1
0
0
1
2
1
2
1
1
0
1
1
1
1
0
2
0
1
1
0
1
0
1
0
1
1
1
2
1
1
1
0
1
2
3
2
0
1
1
0
0
0
0
0
1
1
0
0
0
0
1
0
2
1
2
0
0
0
1
1
0
0
0
2
1
1
0
1
0
1
0
1
1
2
1
1
1
1
1
2
1
1
1
2
2
0
0
0
1
2
1
0
1
2
1
1
1
0
2
0
2
1
0
1
0
2
2
2
1
0
1
0
0
2
1
0
0
1
0
0
2
2
2
2
0
1
0
0
2
2
0
0
0
0
1
2
0
3
0
1
0
2
1
2
1
2
0
1
2
1
2
0
2
0
2
1
0
1
3
1
2
0
0
0
1
2
0
2
0
1
1
1
2
2
0
0
2
0
0
0
1
1
0
1
2
2
0
0
2
1
0
1
0
1
0
1
1
2
1
1
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
2
2
0
2
2
1
0
2
1
1
2
2
1
1
1
1
0
1
0
1
2
1
0
0
0
2
1
1
2
0
1
1
2
1
0
1
0
2
1
1
2
0
1
0
1
0
0
2
0
0
1
0
1
2
0
0
1
1
0
1
1
0
1
0
0
1
1
2
3
0
0
1
0
1
1
0
1
1
0
1
1
1
2
1
0
1
2
1
0
1
1
1
0
0
0
0
0
0
2
1
0
2
1
0
2
1
1
2
0
1
1
0
1
1
2
1
2
1
1
2
1
1
0
1
0
1
0
1
0
2
0
0
2
2
0
2
2
0
1
2
1
2
0
0
2
0
1
1
1
1
1
1
0
2
2
0
2
0
0
0
2
2
2
0
1
0
2
0
0
1
0
0
1
1
0
1
2
0
3
2
0
1
1
1
1
1
2
1
0
0
1
1
1
1
1
0
0
2
1
2
0
0
0
0
0
0
2
2
1
1
2
1
2
1
2
1
0
0
2
2
2
1
1
2
0
2
1
0
0
1
1
1
0
0
1
0
1
2
1
0
1
1
0
1
2
0
1
2
0
0
1
1
2
0
0
1
1
1
0
0
0
1
0
1
1
1
2
0
0
2
2
0
0
0
0
2
0
0
1
0
2
0
1
1
1
1
0
0
0
2
0
1
0
1
0
1
2
0
0
0
1
1
2
1
0
2
2
0
2
0
1
1
0
0
2
0
0
1
2
1
1
2
1
1
0
1
0
2
1
1
1
0
1
2
0
1
0
1
3
0
0
0
0
1
2
2
2
0
1
2
0
2
1
1
1
1
0
0
1
1
0
1
1
0
1
1
0
3
2
3
1
0
0
0
0
2
0
1
2
1
2
2
1
1
1
1
0
2
0
1
2
1
1
0
0
1
1
0
2
0
1
2
3
0
2
1
0
1
1
1
0
0
0
1
2
1
1
2
0
1
1
4
2
0
2
0
1
1
1
5
2
0
2
0
0
2
0
0
0
1
2
1
0
2
0
2
0
2
1
0
0
2
1
3
2
2
1
1
1
0
0
2
2
0
1
0
2
2
2
0
1
0
1
0
1
0
1
1
1
1
0
0
1
0
0
0
1
2
1
1
0
2
1
0
2
0
0
2
1
1
1
2
1
2
2
1
0
1
1
1
0
0
0
0
0
0
0
0
1
1
1
2
0
2
1
1
0
0
1
0
2
2
0
2
0
0
1
2
2
1
0
1
2
0
0
0
1
0
1
2
1
2
1
0
1
0
1
0
1
0
1
2
1
0
0
0
0
0
0
1
1
1
0
0
2
2
1
0
0
1
1
1
1
2
0
0
0
2
1
0
0
1
0
2
0
0
2
1
1
1
1
3
0
2
1
1
0
0
1
0
0
0
0
0
1
0
0
0
1
2
0
2
0
2
2
1
0
1
0
1
1
2
2
0
1
2
2
1
2
1
1
1
1
0
0
4
2
1
1
2
0
0
1
1
2
0
1
1
1
0
1
1
0
1
0
0
0
2
1
1
1
1
0
1
1
1
0
0
0
1
2
1
0
0
2
1
1
2
1
1
1
1
2
1
1
0
0
1
0
2
0
2
1
0
1
0
1
1
1
1
0
1
0
0
1
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
1
0
1
1
0
2
0
1
2
0
0
0
2
0
2
1
1
2
1
1
1
0
0
0
0
0
2
0
2
0
1
1
2
0
1
1
1
0
2
1
2
0
0
0
1
0
2
1
0
0
0
0
1
1
5
0
0
0
0
1
2
2
0
0
1
0
1
1
1
1
1
1
1
1
1
0
1
0
0
2
2
1
0
0
1
0
0
1
2
1
2
1
2
1
1
1
2
1
1
1
1
0
1
0
0
1
1
0
0
0
1
0
2
0
5
0
0
3
0
0
0
3
2
1
2
0
0
1
2
0
1
0
2
1
2
1
0
0
1
1
0
2
2
1
0
1
0
1
2
0
0
2
3
0
1
0
1
1
0
0
1
1
2
1
0
0
0
2
2
0
0
1
0
0
1
1
2
0
1
0
2
2
1
1
0
1
2
1
0
1
1
0
0
2
7
1
1
0
1
1
1
0
1
0
2
1
1
1
0
2
0
1
1
2
1
0
1
2
1
2
1
1
0
0
2
0
0
0
1
2
0
1
1
1
0
1
3
0
2
2
2
2
0
2
0
1
0
0
0
2
0
0
2
0
2
0
1
0
0
1
1
0
0
1
0
0
1
2
1
1
1
1
0
2
0
0
2
2
0
2
1
1
2
2
2
0
2
1
0
1
2
2
1
1
1
3
2
2
1
1
3
2
1
2
0
1
0
2
0
2
4
0
1
0
5
0
2
0
1
1
0
0
1
0
2
0
1
0
1
0
1
1
2
0
0
1
1
0
2
2
2
1
0
1
0
1
2
0
0
0
1
1
0
0
0
1
1
0
0
0
2
1
3
1
0
0
0
1
1
1
2
1
1
2
1
0
0
1
0
2
2
0
1
1
0
3
3
0
0
0
0
1
0
2
0
1
0
0
1
1
0
1
1
0
0
1
0
2
1
0
1
2
2
2
0
2
1
2
2
2
1
0
0
1
2
2
1
0
1
1
0
1
0
1
1
1
0
2
1
1
2
0
1
0
0
0
0
2
0
2
1
1
0
0
0
1
0
0
1
0
0
1
1
1
1
0
2
0
0
1
2
0
1
0
0
0
2
2
0
0
2
0
1
0
2
2
1
2
2
0
1
1
0
2
0
2
2
2
2
2
1
0
2
1
1
2
0
0
1
2
1
0
0
1
1
0
2
1
0
2
0
1
1
2
1
0
1
1
2
1
2
0
0
1
0
2
0
0
1
1
0
1
1
0
0
1
0
0
2
0
0
2
0
1
1
2
1
1
0
0
0
1
0
2
1
1
0
1
1
0
1
0
2
2
0
0
2
0
1
0
1
2
0
1
0
2
1
1
1
1
0
0
1
0
1
0
3
0
0
0
0
2
1
2
0
0
0
1
1
0
0
0
0
0
6
1
1
1
2
1
2
0
2
0
1
0
0
2
1
1
0
1
0
1
1
1
1
0
2
2
0
2
0
1
1
0
2
0
1
0
1
2
1
0
1
2
0
1
1
0
1
0
1
1
1
1
0
1
0
0
2
0
0
1
1
0
0
0
1
1
0
0
1
1
0
1
1
2
1
1
2
0
1
2
1
1
1
0
0
1
1
1
1
2
2
1
2
2
2
0
3
1
0
1
1
2
1
0
1
1
0
1
0
1
0
0
2
1
1
1
2
1
1
2
1
0
1
0
0
1
0
0
0
0
0
0
1
1
1
0
1
0
0
1
0
2
0
0
1
0
1
0
0
0
0
0
2
1
0
1
1
0
1
2
2
1
1
0
0
1
1
2
1
0
0
2
2
0
0
1
1
1
2
0
0
1
0
1
1
1
0
1
0
0
0
2
0
0
1
1
1
1
1
1
0
0
1
0
1
2
1
2
1
1
1
1
0
1
0
1
2
0
1
1
0
0
2
1
0
2
0
2
0
0
1
0
0
0
0
1
1
1
1
1
1
1
1
0
1
1
2
2
0
1
1
1
2
0
1
0
2
1
1
1
0
1
0
1
0
0
1
0
0
0
1
0
0
0
2
0
0
0
1
1
2
0
1
0
1
0
2
1
2
1
0
1
0
2
0
1
0
0
1
0
1
1
0
1
1
0
2
1
1
1
0
1
1
0
2
0
0
1
1
1
1
0
2
1
1
0
1
1
1
2
0
0
1
1
1
2
0
1
0
2
2
1
2
0
1
2
2
2
1
2
2
2
1
0
0
1
1
0
0
1
0
1
0
1
1
1
0
1
0
0
1
0
0
1
0
2
2
1
0
1
0
2
0
1
2
2
1
0
1
1
3
2
0
1
2
1
0
1
0
0
2
0
0
0
0
1
1
2
2
0
1
2
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
2
0
2
2
1
0
0
1
0
0
2
1
0
1
0
2
1
0
0
2
1
1
0
0
1
0
0
2
0
1
4
0
0
0
2
2
1
2
2
0
0
1
1
1
2
0
0
0
1
0
0
2
1
1
0
1
1
0
0
1
0
1
2
0
0
2
1
0
2
0
2
2
1
0
1
1
0
0
1
1
2
1
2
2
1
2
0
1
1
1
2
2
1
0
1
0
1
1
2
1
2
2
1
2
1
0
1
0
0
0
1
1
1
1
2
1
0
0
2
1
1
2
1
2
0
2
2
1
0
1
1
2
0
2
1
1
0
0
0
0
1
1
0
0
2
2
2
0
2
2
1
1
1
1
1
0
1
1
0
1
0
2
1
0
2
0
1
0
1
2
3
0
1
1
1
2
0
0
1
1
0
1
4
2
1
2
1
1
0
0
0
0
1
1
1
1
1
2
0
0
0
1
0
1
1
0
1
0
2
2
2
1
0
1
1
3
0
0
0
0
0
1
1
1
0
0
1
0
1
2
1
2
2
1
2
1
0
1
1
2
1
0
1
0
2
2
2
1
2
0
1
0
1
2
0
2
1
0
1
2
2
3
1
1
2
2
0
2
1
0
1
1
1
1
0
2
0
2
2
1
1
0
0
2
0
0
1
1
0
2
2
2
1
0
2
0
1
0
0
0
1
1
0
0
0
1
1
1
0
1
1
0
1
1
1
0
1
3
1
1
0
1
1
1
1
0
0
2
0
1
1
3
1
1
0
0
1
0
0
1
0
0
1
2
2
2
1
1
1
2
0
2
2
1
0
0
0
1
0
0
1
2
1
0
1
0
0
0
1
1
1
1
1
0
1
1
0
0
1
1
0
1
0
1
3
1
1
0
1
0
1
1
0
2
0
1
0
2
2
0
2
0
0
1
1
0
0
1
2
2
0
1
0
0
1
0
0
0
0
0
0
2
0
0
1
2
2
0
1
2
0
1
1
1
1
0
1
1
0
1
2
1
0
0
0
0
2
1
2
0
2
0
0
0
0
2
0
2
1
1
2
1
0
0
1
0
0
0
1
2
1
0
2
1
1
0
0
0
0
1
0
1
2
0
1
1
0
2
1
1
0
0
0
0
0
0
1
0
1
0
0
2
1
2
0
1
0
0
2
2
1
2
2
1
1
2
1
1
0
0
1
2
0
0
2
1
2
2
1
0
0
1
1
0
0
0
1
0
0
0
1
1
1
0
2
1
1
0
0
1
1
0
0
2
0
0
0
1
1
0
0
2
0
2
0
0
1
1
2
0
2
1
0
0
0
0
2
2
1
2
1
0
0
3
2
1
0
0
0
0
2
1
1
0
0
0
2
1
0
0
0
1
0
1
0
1
1
1
2
1
0
0
0
1
0
0
2
1
0
1
1
1
2
0
0
1
1
1
0
0
2
1
1
1
1
2
2
1
1
1
1
0
1
2
2
0
1
0
1
0
1
1
0
1
0
1
2
2
2
0
1
1
1
0
1
1
1
0
1
1
2
1
1
1
0
0
0
1
2
1
0
1
1
0
1
1
2
3
2
1
1
2
2
0
1
1
1
0
1
1
0
1
0
2
2
1
2
0
1
0
0
0
0
2
0
0
0
0
2
0
0
1
2
1
1
1
1
2
1
0
1
1
1
0
2
0
2
0
0
1
2
1
0
0
0
1
0
0
2
0
1
3
1
2
2
1
1
0
0
2
1
2
1
2
1
1
2
0
0
0
0
0
0
0
2
1
3
0
1
1
0
1
2
1
3
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
1
1
0
1
0
1
1
0
0
1
2
0
0
2
1
1
2
1
2
0
2
0
0
1
1
2
1
1
0
2
2
0
1
2
0
3
1
0
1
0
1
1
2
0
0
0
0
0
2
1
0
2
0
2
2
1
1
0
0
1
0
0
1
2
1
1
0
0
2
1
2
1
1
0
2
0
0
2
0
0
0
0
0
0
2
2
2
1
1
0
0
0
2
0
0
1
1
0
0
0
0
2
0
0
2
1
1
1
0
0
0
1
1
2
2
0
0
1
0
2
1
0
1
1
0
0
1
2
1
0
2
0
1
1
0
1
1
0
0
2
1
0
1
1
0
1
0
1
2
1
1
0
1
0
1
1
2
0
1
0
1
0
1
1
0
0
2
0
0
2
0
0
2
0
1
0
0
1
0
3
1
0
0
0
1
0
1
0
1
1
1
0
1
0
1
0
2
0
1
1
0
0
1
1
0
2
2
1
2
0
1
1
1
0
0
2
0
2
0
1
1
1
0
1
2
0
1
1
0
2
2
0
0
0
2
2
1
0
2
0
0
0
1
0
4
1
1
0
0
0
2
3
2
0
0
2
2
1
0
0
2
1
0
2
1
0
1
0
0
1
1
0
2
1
0
0
1
0
1
1
0
1
1
1
2
1
1
1
1
0
0
0
0
0
0
2
0
1
0
1
2
0
1
0
0
2
0
1
3
1
1
1
0
7
1
0
2
0
1
2
0
0
0
1
0
2
0
0
1
2
2
1
0
0
1
1
2
1
2
0
0
0
2
0
0
1
1
1
0
1
0
1
2
2
0
0
2
0
2
1
1
0
1
0
0
2
1
0
0
1
0
2
2
2
2
2
0
0
0
0
2
0
0
1
1
0
1
1
1
0
2
0
1
0
2
2
1
2
0
0
1
1
2
0
0
1
0
2
1
2
1
1
0
1
0
3
0
0
1
0
1
1
2
1
1
1
1
2
0
0
0
1
0
0
0
2
0
1
1
2
1
4
0
2
1
0
1
1
1
2
0
2
0
0
1
0
2
1
2
2
0
1
0
2
0
2
0
0
2
2
0
2
1
1
0
0
0
2
2
1
2
1
2
2
1
0
2
2
2
0
1
0
1
2
1
0
2
1
0
0
0
1
0
2
1
0
2
2
0
1
1
1
1
2
2
0
0
2
1
1
1
1
1
1
1
0
0
3
1
0
1
1
0
2
0
0
1
0
1
1
2
1
0
0
0
1
1
1
2
2
1
1
1
0
1
1
0
3
1
1
3
0
0
0
1
0
2
1
1
0
1
1
1
1
2
2
0
0
1
0
1
2
0
0
1
0
1
1
0
1
0
2
1
1
1
0
0
1
0
0
1
0
0
2
0
1
0
0
2
2
0
1
1
2
1
0
0
1
1
0
1
2
1
2
1
1
1
1
0
1
2
0
1
0
0
1
0
1
1
2
2
2
2
0
0
0
1
1
0
0
0
0
0
2
1
2
1
0
0
0
0
1
1
0
0
2
0
2
1
1
1
1
0
0
3
1
1
2
1
2
0
1
1
1
0
1
0
1
1
1
0
1
2
0
0
0
0
0
0
1
0
1
1
0
1
2
0
1
0
1
1
0
1
1
1
1
1
1
1
0
1
1
0
2
1
1
1
1
0
1
1
0
1
1
0
0
0
1
2
0
0
0
2
1
0
0
1
0
1
2
0
2
1
1
1
1
2
1
1
0
0
1
0
1
1
2
1
0
0
1
1
0
1
0
1
1
2
0
2
3
2
1
0
1
1
1
0
1
4
2
1
2
0
0
2
0
0
0
2
1
1
0
0
0
1
0
1
0
1
0
2
1
1
1
0
1
1
1
2
1
0
2
1
0
0
2
2
1
0
0
1
0
2
1
0
1
2
1
2
2
0
1
2
4
1
1
2
2
1
1
0
1
1
0
1
1
1
0
1
0
1
0
0
0
1
1
2
0
1
2
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
2
2
0
0
1
1
1
1
1
0
1
1
0
0
2
0
0
1
2
0
1
1
1
0
2
0
0
2
0
1
0
0
0
1
1
0
1
1
2
0
0
1
1
1
1
1
2
1
2
1
1
1
2
0
0
1
0
0
1
2
0
2
2
1
0
2
1
2
1
0
0
0
1
2
2
0
0
2
1
1
1
1
0
2
0
2
2
0
1
0
0
1
1
2
2
1
1
1
0
0
1
3
2
0
2
1
0
1
1
1
1
0
2
1
1
0
1
1
1
2
1
1
1
1
1
0
0
1
0
1
0
2
2
0
0
1
0
0
1
1
2
2
0
1
2
0
1
0
0
0
1
1
0
2
0
1
0
2
1
0
1
1
0
1
2
1
0
1
2
1
0
1
1
0
0
1
1
1
1
1
1
1
1
1
1
1
1
0
1
0
1
0
1
1
0
0
2
0
2
1
1
0
1
0
1
2
1
0
0
2
2
0
2
1
0
2
1
1
1
1
0
0
1
1
1
2
0
1
0
0
2
0
2
0
0
2
1
0
2
0
1
2
0
0
0
1
2
0
2
0
1
2
1
3
0
0
0
0
1
0
2
2
1
0
1
0
1
1
2
1
1
0
2
1
0
2
0
2
0
0
0
0
1
0
0
2
0
1
1
1
0
1
0
1
0
2
2
2
1
1
2
0
1
1
1
0
2
2
2
1
2
0
2
0
1
0
2
1
1
0
0
0
1
0
0
2
1
2
0
2
2
0
1
0
1
1
0
3
1
2
1
2
1
5
0
1
1
0
2
1
0
1
0
0
0
1
1
0
1
1
0
1
1
1
1
2
0
1
1
2
1
0
0
1
0
2
2
1
2
1
2
2
1
0
0
2
1
0
1
0
1
1
2
0
0
0
1
0
0
1
0
0
3
1
0
1
2
1
2
2
1
1
0
2
2
0
2
2
0
0
1
1
2
0
1
5
0
0
1
1
0
1
0
2
1
0
2
0
1
0
0
2
1
1
1
0
1
0
2
2
0
1
0
0
0
1
2
1
0
2
1
1
0
2
3
0
1
0
0
0
1
0
1
0
1
0
0
2
2
2
1
0
0
1
1
1
0
2
1
0
0
0
0
1
0
0
0
2
0
1
2
0
2
1
0
0
1
0
1
1
0
0
1
2
0
0
2
0
1
0
0
2
0
0
2
0
2
1
1
1
1
0
0
1
1
1
0
2
2
1
2
1
2
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
2
1
1
0
2
0
1
1
0
1
0
0
0
0
0
1
0
2
0
1
1
1
0
1
2
0
0
0
1
1
1
1
2
2
1
0
0
0
0
1
3
2
1
2
1
1
1
1
0
0
1
0
0
1
2
1
1
1
1
2
1
1
0
2
1
0
1
0
1
1
2
1
1
1
1
2
1
0
1
1
0
1
0
1
2
0
0
0
0
1
0
0
2
0
2
1
2
1
0
0
1
2
3
0
1
2
1
1
1
2
1
0
1
1
1
0
0
1
1
0
2
0
0
0
2
1
2
2
1
2
2
1
0
0
1
1
0
1
0
0
0
1
1
1
1
2
1
0
0
2
2
0
0
1
0
2
0
1
0
2
1
1
2
1
2
2
2
1
2
0
0
1
1
0
1
1
1
1
1
0
0
3
1
0
0
0
1
1
0
2
2
1
1
0
2
1
0
0
2
0
2
1
1
0
0
2
0
1
0
0
0
2
2
1
2
0
2
5
1
1
1
0
0
0
1
1
1
1
1
2
1
2
1
1
1
0
1
1
1
0
0
0
1
0
1
1
0
2
0
1
2
1
0
0
2
1
0
0
1
2
1
1
0
0
1
1
0
1
0
1
2
1
0
0
1
1
0
0
0
0
1
0
0
0
0
1
1
0
2
1
0
1
0
0
0
0
3
1
0
0
1
1
0
2
0
1
1
1
0
1
0
2
0
1
1
2
1
1
0
1
0
1
1
1
2
2
1
2
1
1
0
1
1
0
1
1
0
0
0
1
1
1
2
2
0
1
1
0
1
0
2
0
0
2
0
0
1
0
1
0
1
2
1
1
1
1
2
1
0
1
0
1
1
1
2
0
2
1
0
2
2
1
1
2
1
0
0
1
1
1
2
1
0
1
1
0
2
2
2
1
0
0
0
1
1
0
0
1
1
1
1
1
0
1
0
1
0
0
0
0
0
1
0
2
1
1
0
2
1
1
1
2
0
1
1
1
0
0
1
1
1
1
0
1
2
2
0
1
2
2
1
0
1
0
1
0
0
0
1
0
1
1
1
0
1
1
1
0
0
0
1
0
1
0
1
1
1
0
2
2
0
0
2
0
0
1
1
0
1
1
1
2
2
3
0
1
0
1
1
0
0
2
1
2
0
0
1
2
1
1
1
1
2
2
2
1
2
0
2
1
1
1
0
0
0
1
0
1
0
1
2
2
1
0
0
2
1
1
2
0
0
1
0
0
0
0
0
2
0
1
2
2
0
0
0
1
1
1
1
0
0
1
1
1
0
0
1
2
2
0
0
2
1
2
1
0
1
2
2
2
1
0
1
2
1
1
1
1
0
1
2
2
1
0
2
1
3
0
2
2
0
0
1
1
0
2
0
2
1
0
1
1
1
2
1
1
1
0
1
1
0
1
1
1
2
2
0
0
2
1
1
1
0
0
2
1
1
0
2
2
1
3
1
1
1
2
1
0
0
0
2
0
0
2
1
1
0
1
1
2
0
1
3
0
1
1
1
1
2
0
2
1
7
1
0
2
1
2
1
0
0
1
2
1
0
1
0
1
1
0
0
0
1
0
1
0
1
1
1
2
0
0
1
1
1
0
1
1
0
2
3
1
2
1
0
0
0
1
2
1
1
0
0
0
1
0
2
2
0
0
0
1
2
1
2
2
0
1
1
2
1
1
2
1
0
2
1
0
1
0
1
1
0
0
2
1
0
0
0
1
2
2
0
0
0
1
2
2
1
1
2
2
2
1
2
2
0
1
2
1
1
1
0
1
1
1
1
2
1
1
1
1
1
1
1
0
0
1
0
2
0
1
0
0
0
0
2
1
0
1
1
2
0
1
0
2
2
0
2
0
2
2
1
0
0
1
0
0
0
2
1
0
0
2
1
0
2
1
0
3
1
1
1
1
0
2
2
0
0
1
1
1
0
0
0
0
2
2
0
1
0
2
1
2
2
2
0
1
0
1
1
1
1
2
0
0
1
1
1
1
0
0
2
2
1
0
0
1
1
0
1
1
2
0
1
0
0
2
0
1
0
1
2
0
0
1
1
2
0
1
1
1
0
1
0
2
0
1
0
0
1
1
0
1
2
0
0
1
2
2
1
0
0
2
1
1
2
1
1
2
1
1
0
2
1
0
2
0
0
0
2
2
1
2
1
0
0
1
2
0
2
1
2
2
0
1
1
1
1
1
0
0
2
0
1
1
0
2
1
1
0
7
2
0
2
2
0
2
1
1
0
1
2
2
1
2
2
0
1
0
1
0
0
1
2
0
2
1
1
1
0
1
1
1
2
0
0
1
0
1
2
1
2
2
2
1
1
1
2
0
1
0
0
1
1
0
0
1
2
1
0
1
2
2
2
2
0
0
2
1
0
1
0
2
1
1
2
0
0
1
0
1
1
1
2
4
0
1
1
0
1
1
2
2
2
2
1
0
1
0
2
1
1
2
3
2
1
0
1
0
2
0
1
2
1
1
1
0
1
1
1
0
1
2
2
1
2
0
0
2
0
1
1
0
1
1
1
1
0
1
1
1
0
2
1
0
0
2
2
2
2
1
1
0
0
1
0
0
1
0
2
1
0
0
1
0
0
0
2
0
1
0
1
1
1
0
0
2
0
1
0
0
1
1
0
1
0
1
1
1
2
1
2
0
0
0
1
2
2
0
0
0
1
0
1
1
0
0
1
0
1
0
1
1
0
2
1
0
1
1
2
2
0
1
0
0
2
2
1
0
0
1
0
1
0
1
1
1
2
0
0
0
2
0
0
1
0
1
3
1
1
1
1
0
1
1
1
0
4
1
2
0
1
0
2
1
0
2
0
0
1
1
2
0
2
0
1
1
1
0
0
1
0
1
1
0
0
1
0
0
2
0
1
2
1
2
0
1
0
0
0
0
2
1
1
0
0
1
1
0
1
1
0
1
1
1
1
1
1
0
1
1
2
0
0
2
2
0
1
1
2
1
0
1
0
0
2
0
0
1
0
0
0
0
1
0
1
1
0
0
2
2
2
1
1
0
1
1
1
0
0
0
0
2
1
2
1
1
0
1
1
1
1
1
0
1
0
1
1
0
1
1
1
1
1
0
1
3
0
1
0
1
1
1
1
2
0
0
1
1
2
0
0
1
0
2
2
1
2
2
0
0
1
0
1
1
1
2
1
0
0
1
0
0
1
1
0
0
2
1
0
1
2
0
1
0
2
0
2
0
1
1
1
2
0
0
1
2
0
1
2
0
2
1
1
2
1
1
1
0
0
0
1
0
1
1
1
0
2
0
1
1
0
2
1
0
2
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
1
0
1
1
2
1
2
1
0
3
1
2
1
0
1
2
1
0
0
1
2
1
0
1
0
0
0
1
0
1
1
2
0
1
1
2
0
2
0
1
2
1
2
1
1
0
1
0
1
0
1
2
0
0
2
0
1
1
0
0
0
0
0
0
2
2
0
0
1
1
0
0
1
2
0
3
1
1
1
0
1
2
0
0
1
1
1
2
2
1
1
1
1
0
1
1
1
0
1
2
0
1
0
1
2
0
2
2
0
2
1
2
1
0
1
0
0
0
1
1
1
0
2
1
1
1
2
1
0
2
0
0
1
0
0
2
1
0
2
1
2
0
1
0
0
1
0
3
0
2
0
2
1
1
2
2
1
0
0
1
1
1
1
2
0
0
2
2
2
0
1
1
0
0
1
0
1
1
1
1
1
2
0
1
2
0
1
0
0
2
0
1
1
2
2
1
2
1
0
1
1
1
1
0
0
1
1
0
2
1
0
0
0
0
1
0
3
0
0
0
0
0
1
1
0
1
1
1
0
2
1
1
2
2
0
1
0
0
0
2
1
1
1
0
2
0
1
0
2
2
0
2
1
2
2
0
0
0
2
0
0
0
1
2
0
0
1
0
1
2
1
2
1
0
1
1
1
0
0
0
2
0
2
0
1
1
0
0
0
1
0
2
1
0
1
1
1
0
2
0
0
1
1
1
0
0
1
1
2
1
2
0
0
2
2
1
0
0
1
0
1
1
1
2
1
0
0
0
1
1
1
1
2
0
2
0
1
0
1
2
0
1
0
1
0
2
1
0
1
0
0
0
1
0
0
2
1
2
0
1
2
1
0
1
2
1
1
2
2
1
1
0
2
2
1
0
1
1
0
0
2
1
0
1
2
1
2
0
0
2
1
0
2
1
0
1
2
2
1
0
0
0
2
0
1
0
1
1
1
0
0
0
2
1
2
0
0
0
0
1
2
0
1
1
1
0
2
2
0
2
1
2
1
1
1
0
0
0
2
1
1
2
2
0
1
1
1
0
2
1
0
0
1
0
0
1
2
1
2
0
2
1
0
0
0
1
0
1
0
1
1
2
1
1
1
1
0
2
2
0
2
0
2
0
0
0
2
2
0
3
0
0
0
1
1
0
0
1
1
1
0
1
0
2
1
1
1
0
1
1
1
0
2
1
0
0
0
0
2
0
0
0
0
1
0
2
1
0
1
2
2
0
2
1
2
2
0
1
2
0
2
2
0
1
0
0
0
1
1
2
0
1
0
1
0
2
2
1
0
0
1
0
1
2
0
0
0
0
1
1
1
0
0
2
1
2
0
0
1
0
0
0
1
2
1
1
1
0
1
0
2
0
1
0
2
1
1
1
2
2
0
1
0
2
0
1
1
1
1
0
0
1
1
0
1
0
1
0
1
2
0
1
1
1
1
2
1
2
0
2
1
0
1
2
1
0
1
2
1
1
0
0
2
0
2
1
0
1
0
0
1
0
0
2
1
2
2
2
2
2
1
2
0
0
2
0
0
0
0
0
2
2
0
2
2
0
2
1
1
2
1
1
0
2
0
1
2
2
3
1
1
2
1
2
2
0
0
0
1
0
1
1
1
0
2
0
1
1
0
1
0
1
0
0
2
1
0
0
2
1
0
0
1
1
0
0
1
0
2
1
1
0
0
1
1
0
0
0
1
2
0
2
1
1
1
2
1
0
0
0
1
0
1
0
1
0
1
0
1
2
1
1
0
0
0
1
2
0
2
1
2
2
1
0
2
1
0
1
1
0
2
2
1
1
1
1
2
0
1
1
0
0
0
2
0
1
0
2
0
1
0
1
0
0
1
0
1
1
0
0
0
1
0
2
0
2
0
2
2
0
0
0
0
0
0
1
1
1
1
1
0
1
0
1
1
2
1
1
1
1
2
0
1
1
0
2
0
2
2
1
0
0
2
1
0
1
1
0
2
1
0
1
0
2
2
2
0
0
0
4
2
0
2
1
2
1
2
2
1
0
1
2
0
0
6
0
2
1
0
0
1
2
1
1
0
1
1
2
0
2
2
0
1
0
1
0
1
1
1
0
0
2
1
3
1
0
1
2
2
2
0
1
1
1
0
2
1
0
0
2
0
0
2
1
0
2
1
1
0
0
1
2
0
1
1
2
2
2
1
1
0
0
0
0
1
0
0
1
0
2
1
1
0
1
0
0
1
2
0
1
2
1
1
0
1
0
1
0
1
0
0
2
0
0
1
3
1
0
0
0
1
0
0
2
1
2
2
2
1
2
0
2
0
0
0
0
1
0
0
1
2
1
1
0
0
0
0
1
2
0
1
2
0
2
0
1
1
1
0
1
0
1
0
1
0
1
0
2
0
1
2
0
1
0
1
2
2
2
1
1
1
1
1
2
1
2
1
1
1
0
1
0
0
0
2
0
1
1
2
0
3
1
1
0
2
0
2
0
0
0
0
0
1
1
1
2
0
1
1
0
1
0
0
2
1
0
1
1
0
0
2
1
0
1
1
2
0
0
1
0
1
0
0
0
1
1
0
2
0
1
0
0
0
1
1
0
0
1
2
1
2
1
1
0
1
2
2
1
2
0
2
1
1
1
1
0
0
1
2
1
2
1
0
0
2
0
0
0
2
1
1
1
1
1
2
4
2
1
0
1
2
2
1
1
2
1
0
1
0
1
0
0
3
2
0
0
2
1
2
2
0
1
2
0
0
2
0
0
1
1
1
0
0
0
0
3
1
1
2
1
2
0
2
0
1
1
1
1
0
0
0
0
0
1
1
0
0
1
1
1
0
1
1
0
1
2
2
0
2
0
2
0
0
0
1
1
0
0
0
2
1
0
1
1
0
0
1
0
1
1
0
1
1
0
0
1
2
1
1
0
2
2
2
0
1
1
0
0
1
1
0
2
0
1
0
2
0
0
1
1
1
2
2
1
0
3
0
1
0
1
0
0
2
0
2
0
1
0
2
2
1
0
0
1
0
0
1
2
1
1
0
0
2
1
0
1
1
0
1
2
0
2
1
1
1
1
0
1
0
1
1
0
1
1
0
0
0
0
1
0
1
2
1
0
1
0
0
1
1
2
1
0
1
2
2
0
1
2
1
1
1
1
1
0
0
2
1
0
0
2
1
0
0
4
0
0
1
0
1
1
1
1
1
1
2
0
1
2
1
1
1
1
1
2
0
1
2
0
1
1
2
1
0
1
0
1
1
1
0
1
1
2
3
0
2
0
0
0
0
1
0
0
1
1
0
1
2
2
2
1
1
1
1
1
2
1
2
2
1
2
1
1
1
1
0
1
2
1
1
1
0
0
1
1
2
2
1
2
1
0
0
0
2
0
0
2
1
1
2
1
1
2
0
1
0
2
1
2
0
0
0
2
0
1
0
1
2
1
1
0
0
2
0
1
1
1
2
2
0
0
1
0
1
2
0
0
0
0
1
2
0
1
1
1
1
0
1
0
0
1
0
0
1
0
2
2
1
2
1
0
1
6
1
1
2
2
1
0
1
0
2
0
2
1
0
1
1
1
1
0
2
0
2
1
0
0
1
1
1
1
0
1
1
1
0
1
0
1
0
1
0
1
3
1
1
2
1
0
1
0
0
2
1
1
1
0
2
1
1
2
0
2
0
0
1
1
1
0
1
2
1
2
0
0
1
2
1
0
2
0
2
0
0
1
2
1
0
0
1
3
0
1
2
0
1
1
1
1
1
0
0
1
0
2
2
2
0
1
4
0
1
0
1
3
0
1
1
2
0
3
0
2
2
0
1
1
1
1
1
1
0
0
1
0
2
0
0
0
0
0
1
0
1
1
0
1
0
2
2
1
1
1
0
0
0
0
1
2
1
0
0
1
0
0
1
0
1
2
1
2
0
0
1
1
1
2
1
1
3
1
0
0
0
0
1
0
1
1
0
2
1
1
0
1
0
1
0
0
1
0
2
1
1
0
0
2
1
1
2
1
0
0
1
1
1
0
1
1
0
1
2
0
0
0
3
2
0
0
1
2
0
1
1
1
0
0
2
2
0
2
4
2
1
1
1
0
0
2
1
0
1
1
2
0
0
0
1
2
0
1
2
1
0
1
0
0
0
1
1
2
2
1
1
1
0
1
2
1
1
0
0
0
1
1
1
0
0
1
0
0
0
2
1
1
0
0
0
5
1
1
1
1
1
0
3
2
1
2
0
2
1
0
1
2
3
2
1
1
1
0
0
0
0
1
2
0
1
0
0
0
2
0
0
0
2
0
2
1
2
0
1
2
0
0
1
1
1
2
1
0
0
0
1
2
0
1
0
1
1
1
2
2
3
0
1
1
2
0
0
1
2
1
2
1
1
1
1
1
1
1
0
1
2
0
0
1
0
0
2
0
2
1
0
1
2
1
1
0
1
1
2
1
2
0
0
2
2
1
1
1
0
1
2
1
3
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
2
2
1
0
1
0
0
0
1
0
1
0
2
1
0
0
1
1
1
1
1
1
0
1
0
0
1
0
1
0
0
1
1
0
1
1
0
1
2
0
0
0
1
2
1
0
1
0
0
1
1
0
0
1
1
1
2
0
2
1
1
2
0
0
2
0
1
1
1
1
1
1
1
0
0
1
0
1
1
1
0
1
1
4
2
2
1
0
0
0
2
0
1
1
0
1
1
0
0
1
0
1
0
0
0
0
1
2
0
0
2
0
1
1
1
1
2
1
0
4
1
0
0
1
1
0
0
1
2
1
2
0
0
2
2
1
1
1
2
0
1
0
0
2
0
0
2
0
0
1
2
1
2
4
1
2
1
1
1
2
1
0
0
0
1
2
0
1
1
2
1
2
1
0
1
1
2
0
0
2
0
1
1
0
1
4
2
0
1
1
1
1
2
0
0
0
2
1
2
0
2
1
0
0
2
1
0
0
2
1
1
0
1
0
3
0
1
2
0
0
2
0
1
0
1
0
0
0
1
1
1
1
0
2
1
1
0
0
0
2
1
2
2
0
2
1
0
1
0
1
0
1
1
1
0
1
0
0
0
0
1
1
0
1
1
3
1
1
0
1
0
1
1
0
1
0
2
0
3
2
2
1
1
0
2
1
0
2
1
0
0
2
2
0
2
0
2
2
2
2
0
2
2
2
1
1
1
0
1
1
1
0
0
0
0
2
1
1
2
1
2
2
0
1
1
2
0
2
2
2
0
0
0
2
0
1
2
1
0
1
1
1
2
2
0
2
0
1
1
1
1
1
0
1
0
1
1
1
1
1
0
1
1
0
0
3
0
1
0
0
0
0
1
1
0
2
0
0
0
2
0
0
0
2
1
0
0
1
2
4
1
0
0
2
2
0
1
1
1
2
0
2
0
0
2
1
0
1
0
1
0
0
0
0
1
2
2
0
0
1
1
0
1
0
1
2
0
2
2
1
0
2
0
2
2
1
0
1
2
0
1
0
1
2
2
0
0
1
0
2
1
0
1
0
1
3
2
0
1
1
1
1
1
1
1
1
1
0
2
2
0
1
0
0
0
0
0
1
3
1
2
0
0
2
1
0
0
1
1
1
1
0
1
1
0
2
1
1
0
0
1
2
1
0
0
1
0
1
0
0
2
1
1
3
1
1
1
0
1
2
1
0
0
0
0
1
0
2
1
3
2
2
0
2
2
2
2
2
1
2
1
0
0
1
0
1
1
1
2
0
1
0
1
0
1
1
1
2
1
0
1
1
1
2
0
0
1
1
1
1
0
0
0
2
1
2
0
2
0
0
2
0
1
1
1
0
1
2
0
0
2
1
0
0
1
1
0
0
1
1
0
1
0
0
2
2
1
0
0
1
1
0
0
0
0
0
1
1
1
1
2
2
1
1
2
2
1
1
1
1
0
0
0
0
2
0
1
1
0
0
1
0
0
2
2
2
1
1
3
0
2
1
0
1
1
0
1
0
0
2
0
0
0
1
1
2
0
1
1
1
0
0
1
2
0
1
2
1
1
2
0
2
0
1
1
0
1
1
1
0
1
0
1
0
0
0
1
0
1
0
1
1
1
2
2
2
2
0
0
2
1
1
2
1
0
1
1
2
0
0
4
0
0
1
0
2
0
1
0
0
1
0
0
1
0
0
1
2
2
0
1
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
1
1
2
0
0
0
2
0
2
0
0
2
2
0
0
0
1
0
1
2
0
1
2
1
0
0
0
2
2
1
1
2
0
2
1
1
1
0
1
0
0
2
0
0
0
2
1
2
0
2
2
2
0
1
2
2
2
1
1
1
1
0
2
1
1
1
2
0
2
1
1
0
0
1
1
1
0
1
1
0
0
3
0
0
1
1
2
0
0
1
2
2
0
2
1
0
0
1
1
0
1
1
3
1
0
0
2
1
1
1
5
0
1
0
1
1
1
1
0
0
4
1
1
1
1
1
0
2
0
0
2
2
0
0
1
0
1
1
1
0
1
1
1
2
1
2
0
2
2
0
0
0
1
1
0
2
2
1
0
0
0
1
0
1
1
0
2
1
0
0
0
2
1
2
0
0
2
2
2
1
2
2
2
0
2
0
0
2
1
0
0
2
2
0
1
1
1
1
2
1
2
1
1
0
1
0
0
0
1
1
0
1
0
0
3
1
0
0
1
1
1
1
0
0
0
0
0
1
0
0
0
1
0
2
0
2
1
2
2
0
0
0
2
1
1
1
0
2
2
0
1
0
2
0
1
0
0
1
0
0
2
1
0
0
2
1
3
1
2
1
0
0
1
1
0
2
1
1
2
1
0
0
1
2
1
2
0
1
0
1
2
1
0
2
2
1
2
2
2
0
0
2
1
1
1
0
2
1
0
2
0
1
1
1
0
0
0
1
1
1
1
1
0
1
0
2
1
1
1
2
0
1
1
0
0
2
2
0
1
1
0
0
1
1
1
1
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
1
1
0
1
1
0
0
0
0
1
0
0
1
2
0
1
2
1
0
0
1
2
1
1
1
0
0
1
2
1
0
1
2
0
1
1
1
1
1
1
1
0
1
1
1
1
0
1
2
2
2
0
2
0
1
1
1
2
0
0
0
0
2
2
1
1
1
1
1
0
0
1
0
0
2
0
1
2
2
2
1
0
0
2
2
0
0
1
2
0
1
0
1
1
0
2
2
0
0
1
1
1
1
1
1
0
1
0
0
2
2
0
0
0
0
1
0
0
1
0
1
1
1
1
0
1
0
2
0
1
2
2
1
2
1
2
1
1
0
1
0
0
0
0
1
0
1
0
1
0
1
0
2
1
2
2
1
0
0
0
0
1
1
1
0
0
1
0
1
1
2
1
1
0
2
1
0
1
0
0
0
1
2
1
0
2
0
0
0
1
1
2
0
0
1
0
0
1
2
0
0
0
0
2
2
1
2
2
1
0
1
2
0
1
1
1
2
0
1
2
0
0
2
2
0
1
2
7
1
1
3
0
1
0
2
1
1
1
1
2
3
1
0
1
0
0
1
0
1
0
0
2
1
1
2
2
2
1
1
0
0
0
0
0
0
1
1
3
2
1
0
1
0
2
2
1
0
1
1
0
2
1
1
1
0
0
3
0
1
2
2
1
1
2
1
0
3
1
0
1
0
0
0
0
0
1
4
1
1
0
2
2
1
0
2
0
1
2
1
0
0
2
1
0
0
0
0
2
1
0
0
1
0
1
2
0
1
0
0
0
0
0
2
0
0
2
0
1
4
2
1
1
0
0
1
1
0
1
2
1
2
0
0
2
2
3
2
0
1
2
1
0
1
0
0
0
0
2
0
1
0
0
0
1
1
1
1
1
0
1
0
0
0
1
2
2
2
1
0
1
1
1
1
0
1
1
0
0
2
1
1
2
2
0
0
1
1
4
1
0
1
1
0
1
0
0
1
2
1
0
1
0
0
0
2
0
2
0
0
0
1
1
0
1
0
0
0
0
1
0
0
1
2
2
1
1
2
0
0
1
1
2
2
1
2
1
2
2
2
0
0
0
2
0
0
1
0
1
2
0
2
0
2
4
0
0
0
1
1
0
2
1
1
2
2
1
1
1
0
2
2
0
1
0
1
0
2
0
0
1
2
1
0
1
1
0
0
0
2
0
1
0
1
0
2
1
0
1
1
2
0
0
1
1
1
2
2
2
2
0
2
0
1
0
1
0
0
0
1
2
0
1
0
0
1
1
3
0
1
0
0
1
1
0
1
0
0
1
0
1
1
0
0
0
0
0
1
0
1
2
1
0
0
2
1
0
1
1
0
0
0
0
2
0
0
1
1
1
0
1
1
0
0
1
1
1
2
2
2
2
1
0
2
1
1
3
1
1
2
0
0
1
2
0
1
0
1
1
2
1
0
0
1
1
2
1
0
0
0
2
2
0
0
1
0
1
0
1
0
1
0
2
0
1
1
2
0
1
1
2
1
1
0
0
0
2
0
0
1
0
1
0
0
1
1
0
0
0
0
1
0
1
0
2
0
1
1
0
0
1
1
0
1
0
1
2
0
1
1
2
1
0
1
1
1
0
1
0
1
1
0
1
0
2
1
0
1
0
2
1
0
1
0
1
0
4
2
1
0
0
1
1
0
0
1
1
0
1
0
0
1
2
1
1
2
0
0
0
0
1
0
0
1
0
0
1
1
0
1
2
1
1
2
0
0
2
1
2
1
1
1
2
1
0
1
0
2
1
0
0
0
2
0
1
0
1
2
0
1
1
1
1
1
1
1
1
1
1
0
3
0
0
2
0
2
2
1
1
1
0
0
1
1
0
0
0
0
1
1
1
1
2
0
0
1
0
1
2
1
1
0
1
1
1
1
0
1
1
0
2
0
2
0
0
0
1
2
0
2
2
0
0
0
0
1
2
1
0
0
2
2
1
1
2
2
1
1
1
1
0
1
0
0
2
1
2
2
2
0
1
1
2
0
1
1
2
0
0
0
2
2
0
1
0
1
1
1
1
1
1
0
1
1
0
0
0
1
1
1
1
1
0
1
2
0
0
1
0
1
0
1
0
0
1
1
0
0
1
2
1
0
2
1
0
0
1
2
0
1
2
1
0
0
1
1
0
1
0
1
1
2
0
2
0
2
2
0
1
0
1
0
0
1
2
1
0
2
0
2
1
2
0
2
2
1
1
0
0
1
0
0
2
2
0
1
1
0
1
1
1
1
1
1
0
0
0
1
1
1
0
2
0
0
0
0
0
1
2
1
0
1
2
1
1
0
1
1
1
2
2
1
0
0
0
0
0
0
1
0
0
0
2
1
2
2
1
1
0
1
0
1
1
1
2
2
1
0
1
1
0
1
0
2
1
2
0
0
2
0
1
0
1
1
1
1
1
0
0
0
1
1
0
0
0
0
0
1
1
1
2
1
1
1
1
0
1
2
1
1
0
0
2
1
1
1
0
1
0
0
1
1
2
1
1
1
0
1
0
0
1
0
3
0
2
0
1
1
2
1
1
0
2
1
0
1
2
1
0
0
1
1
1
2
1
2
1
2
2
0
1
1
0
1
0
1
0
2
2
0
1
0
0
0
0
1
0
2
0
1
0
2
0
1
0
0
1
0
1
1
0
1
1
1
1
1
0
0
2
2
0
0
2
2
1
1
2
1
0
2
0
2
2
1
0
2
1
0
1
2
1
0
0
5
1
0
0
1
1
2
0
1
1
0
0
1
0
1
1
2
0
1
0
0
0
1
0
1
2
0
1
0
0
0
1
1
0
2
0
1
0
1
2
1
0
2
0
1
0
2
1
1
2
0
1
1
1
2
0
1
0
2
1
1
0
0
0
1
0
2
1
2
2
1
0
1
0
2
0
0
1
1
2
1
1
0
1
0
1
0
2
1
1
1
1
0
0
1
0
0
0
1
1
0
1
0
1
1
0
1
1
0
2
0
0
4
1
0
0
1
1
1
0
1
0
2
1
0
0
1
1
1
2
2
2
1
1
1
0
0
0
1
1
2
1
0
1
1
0
2
0
1
0
2
0
0
0
1
0
0
2
1
0
1
0
1
2
1
1
1
1
1
2
0
1
1
1
0
1
1
0
0
2
0
2
1
2
1
2
0
0
0
0
1
1
1
1
2
0
0
1
0
0
1
2
2
0
0
1
1
0
1
1
0
2
1
1
1
1
0
1
2
2
0
1
1
1
1
2
0
1
0
1
0
3
0
1
2
1
0
1
2
0
0
1
0
1
0
2
1
0
0
2
1
1
0
2
1
0
0
2
1
0
1
1
0
2
0
2
1
0
0
1
0
1
1
1
0
2
0
0
2
0
1
1
1
1
2
9
1
1
1
2
1
1
0
2
1
1
2
1
0
2
1
1
0
0
1
1
1
2
0
1
0
1
1
0
1
0
2
2
2
1
0
0
1
1
0
0
0
0
0
2
2
2
0
2
0
1
0
0
0
0
1
1
2
0
0
0
2
0
1
2
1
1
0
0
1
1
3
1
1
1
0
0
0
2
1
0
0
1
1
1
0
0
0
0
1
1
2
1
0
1
2
0
1
1
1
2
0
1
2
1
0
2
0
0
1
1
0
2
0
0
1
0
2
0
2
1
0
1
0
0
2
2
0
0
1
0
0
0
0
0
3
1
0
0
0
1
1
2
0
1
0
0
2
1
2
1
0
0
0
1
2
1
2
0
0
0
1
2
0
0
1
0
0
0
1
1
1
0
1
1
1
1
1
0
0
1
0
0
1
0
1
0
1
3
1
1
0
0
2
2
0
1
1
2
1
2
0
2
2
1
0
1
0
2
1
0
0
0
0
0
0
0
1
1
1
1
2
2
2
1
2
0
0
1
1
0
1
1
1
1
2
0
1
1
1
0
2
2
0
2
0
2
0
1
2
1
1
0
2
1
2
0
1
1
1
0
2
2
0
0
0
0
0
0
0
1
1
1
2
0
1
0
1
1
0
1
2
2
1
1
2
1
0
0
2
1
1
0
1
1
1
1
0
0
1
0
1
2
1
0
2
1
1
0
1
0
0
0
1
2
2
1
2
1
1
1
0
2
2
1
1
0
2
0
1
0
0
1
1
2
0
1
1
1
2
0
2
0
1
1
2
1
0
0
2
2
1
0
2
2
2
0
0
2
2
1
0
1
1
1
1
2
0
0
3
2
2
2
3
1
0
3
1
0
0
1
1
0
0
1
2
0
1
0
1
1
1
1
0
2
0
0
1
0
1
0
0
1
1
1
1
1
1
0
1
0
0
2
1
0
2
0
2
1
0
1
0
0
1
0
0
0
1
0
0
1
2
0
2
1
0
1
1
0
0
1
2
2
0
1
0
0
1
1
2
1
1
0
1
1
0
0
0
0
0
1
1
1
2
1
0
2
1
0
1
1
0
1
1
1
2
1
1
2
2
1
1
1
1
0
2
0
0
1
0
1
0
3
1
2
0
2
1
2
2
0
1
0
0
1
2
0
1
2
0
3
1
0
1
0
0
1
1
1
1
1
1
0
1
1
0
0
1
0
0
1
1
1
1
0
0
1
2
1
0
2
0
0
1
1
1
0
1
0
0
0
1
0
2
1
0
1
2
1
3
0
0
2
1
0
0
1
0
2
1
0
1
0
0
1
0
2
1
2
3
1
1
0
2
0
0
1
2
1
1
0
1
0
2
0
0
1
0
1
0
1
1
2
1
0
0
1
1
1
1
0
2
0
2
0
1
0
2
1
0
2
0
0
0
1
1
1
2
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
1
2
1
2
0
0
4
0
1
0
1
1
2
0
2
2
0
1
1
0
2
1
1
1
0
1
0
1
0
4
0
2
0
1
1
0
3
0
2
2
1
0
1
2
1
2
0
0
1
0
1
0
1
2
0
0
0
1
1
1
2
0
0
2
0
0
1
1
0
1
0
0
1
0
0
0
1
0
0
2
1
1
1
1
2
0
1
2
0
1
0
0
1
1
2
2
1
0
0
1
3
0
1
0
0
0
2
0
1
0
2
1
1
0
0
1
1
1
2
1
1
1
0
2
0
1
0
1
0
2
1
1
1
3
0
0
1
2
1
1
1
0
1
1
1
1
1
0
1
2
2
0
0
1
2
0
1
0
0
0
0
0
2
2
0
0
2
0
2
0
1
0
1
1
1
1
3
2
1
1
1
1
3
1
0
1
1
0
1
0
0
0
2
0
1
0
2
1
1
2
1
1
0
0
2
0
0
0
0
0
1
2
0
1
1
1
0
1
0
1
1
0
1
0
0
0
0
0
0
3
0
1
2
1
1
2
0
1
2
0
1
2
2
0
0
0
0
0
0
0
1
0
0
0
0
1
2
1
2
1
1
0
0
1
0
0
0
3
1
1
0
0
1
0
0
2
1
1
0
1
1
0
2
2
1
0
2
1
1
0
0
0
0
0
0
1
2
0
0
1
1
1
0
0
0
2
1
0
1
0
0
1
1
0
0
0
0
3
1
1
2
1
2
2
0
0
1
0
0
0
1
2
1
0
2
1
1
1
0
2
1
0
0
2
0
0
0
2
2
1
1
1
1
1
2
0
0
1
1
1
0
2
0
0
0
2
0
1
0
1
0
0
0
2
3
0
1
0
2
0
0
1
2
1
1
2
2
0
1
0
0
0
0
1
0
1
1
0
2
1
0
2
2
0
3
0
2
1
0
1
0
0
0
2
3
0
0
2
1
0
2
1
1
1
0
1
2
3
2
2
2
0
2
1
1
0
0
0
0
2
2
0
0
1
1
2
2
1
2
0
2
0
0
1
0
1
1
1
2
0
0
1
0
1
0
1
0
1
0
0
0
1
0
1
1
1
2
0
2
2
1
0
0
2
0
1
0
0
0
0
1
1
0
1
0
1
0
0
0
0
2
0
1
0
0
0
2
1
1
0
0
0
1
0
0
1
1
0
2
2
2
1
0
2
0
1
2
0
0
0
0
0
0
0
1
0
1
1
1
1
1
0
1
1
0
1
1
0
0
2
0
1
1
0
1
2
2
0
1
1
0
0
1
1
0
1
0
0
1
1
2
1
0
0
1
1
1
2
1
1
0
0
1
1
0
0
1
1
0
1
2
1
1
0
0
1
0
1
0
2
2
1
1
0
2
1
1
0
0
0
2
0
0
1
2
0
0
0
0
1
0
1
2
2
0
1
0
0
1
1
2
1
1
0
1
0
0
2
1
0
2
0
1
1
1
0
3
1
2
1
0
0
0
1
0
1
1
0
0
0
1
1
0
0
1
2
0
0
1
0
1
1
0
0
1
1
0
0
1
1
2
0
2
0
1
0
2
0
2
2
2
1
0
0
0
1
1
0
1
1
0
1
0
2
1
1
1
1
0
0
1
2
1
2
1
1
1
1
1
2
3
1
0
2
0
0
0
0
2
2
0
2
1
1
1
1
2
0
0
3
0
1
0
2
2
1
2
0
1
2
1
0
0
0
2
1
1
0
0
2
0
1
1
2
0
0
0
2
2
0
0
2
2
2
1
1
1
1
2
1
1
1
2
0
0
1
0
0
0
0
1
1
1
0
0
1
0
0
1
0
0
2
1
0
1
0
0
0
1
0
0
0
1
0
2
0
0
2
2
1
0
1
1
0
1
2
0
0
2
2
0
2
1
0
2
1
1
1
1
2
1
1
1
0
0
0
0
2
0
1
1
2
2
1
2
0
2
1
2
2
1
2
1
0
1
1
1
0
1
1
2
0
0
1
1
0
0
0
3
1
1
1
2
1
2
2
1
1
2
1
2
1
0
1
0
1
1
1
0
2
0
2
2
0
0
1
1
0
1
0
0
0
0
3
1
0
1
1
0
1
2
2
0
1
1
1
0
1
0
1
0
2
2
1
2
0
2
1
0
2
1
1
0
1
1
1
0
0
1
2
2
1
2
0
2
1
0
0
0
1
2
2
0
0
1
1
0
3
1
1
2
1
2
1
1
0
0
1
2
2
1
2
0
0
0
2
1
1
1
2
0
2
1
1
1
0
0
0
0
2
0
3
0
1
1
2
2
1
0
0
3
1
1
2
0
1
1
4
1
1
1
1
4
0
1
0
1
0
0
1
0
1
0
3
1
1
1
1
0
1
2
2
1
2
1
1
2
0
0
1
0
0
1
0
2
0
2
1
0
0
1
1
0
2
3
0
0
0
2
1
0
1
2
0
1
2
0
1
2
1
1
0
2
0
1
2
0
1
1
2
2
0
1
1
0
1
0
1
0
1
2
0
0
1
2
0
0
2
0
2
1
1
2
0
2
1
0
1
1
1
0
1
1
1
1
0
1
0
1
1
0
1
2
1
0
0
0
0
1
2
0
1
2
0
2
2
1
1
2
0
0
1
1
0
1
0
0
0
0
3
0
1
0
0
0
0
1
1
2
1
2
1
1
1
1
2
1
1
1
0
0
2
0
0
0
1
0
2
0
2
0
2
0
2
1
0
2
2
2
0
1
0
1
0
3
0
1
2
0
2
1
0
2
0
1
1
1
1
3
2
0
2
0
0
2
2
0
3
0
2
0
0
1
0
1
0
0
0
2
1
0
1
0
0
2
0
0
1
1
0
0
2
3
1
2
0
0
0
0
0
0
0
1
1
0
0
0
3
0
0
1
2
1
1
1
1
0
2
0
0
1
1
1
0
0
1
1
3
2
2
1
2
0
4
1
1
0
0
0
0
1
0
4
1
1
0
1
0
0
2
2
2
0
0
1
0
1
0
1
1
0
0
1
0
1
0
1
2
0
0
0
2
1
0
0
1
2
2
0
2
1
2
1
1
0
2
1
1
1
4
1
1
1
1
2
1
1
0
1
0
1
1
0
0
0
0
0
0
2
2
1
2
1
0
1
0
0
0
0
0
1
1
2
0
2
0
2
1
1
1
0
2
0
0
2
0
0
0
1
1
1
0
0
1
2
0
2
0
1
0
0
1
1
1
1
1
0
1
3
0
0
1
2
1
1
2
0
2
0
1
1
0
1
0
1
1
0
0
1
0
0
0
2
0
1
0
0
3
1
4
2
2
1
0
2
2
1
2
1
1
2
0
0
1
1
0
0
1
0
1
2
1
2
0
0
0
2
2
0
0
1
0
2
0
1
1
0
1
2
0
0
0
2
2
0
1
2
1
0
0
0
2
0
2
2
0
1
1
0
0
2
2
0
0
1
0
0
1
1
1
2
2
0
1
1
0
1
0
1
0
0
0
1
1
1
2
1
1
2
0
1
2
1
1
1
1
0
0
0
2
1
1
1
1
3
0
1
1
1
0
2
0
0
1
1
2
1
1
1
1
0
0
1
1
0
0
1
1
1
1
0
1
2
0
0
0
1
1
1
0
0
2
0
1
0
0
1
1
1
1
2
0
1
0
1
1
0
1
1
2
1
1
1
1
2
0
1
0
0
0
4
0
0
2
2
0
2
0
1
1
2
1
1
2
0
1
1
0
0
1
0
1
1
0
0
0
0
0
0
1
1
1
2
0
0
0
1
0
2
2
2
0
2
0
0
2
2
0
0
1
2
2
1
0
1
0
0
1
2
1
1
0
1
1
1
2
1
1
1
0
1
2
0
2
1
0
2
0
1
0
0
1
1
0
2
0
1
0
1
0
0
2
2
0
1
2
0
3
3
0
1
0
3
2
1
1
1
0
1
0
0
0
1
0
3
2
2
1
1
2
1
2
2
0
1
0
0
1
0
2
0
1
4
1
2
1
2
2
1
1
0
0
0
1
1
0
0
2
1
0
0
2
2
2
2
0
1
2
1
0
1
1
0
1
1
1
0
1
1
1
0
0
0
0
2
1
0
1
1
0
0
0
0
1
1
0
0
1
0
2
0
1
0
3
2
1
1
0
0
2
2
1
0
0
0
0
2
0
1
0
0
3
1
2
0
0
1
0
1
1
1
1
0
2
2
1
1
1
1
0
1
0
2
2
2
2
0
0
1
2
2
1
2
0
0
1
1
0
1
0
3
1
0
2
0
3
1
1
0
1
2
2
0
2
1
0
0
2
1
2
2
1
0
2
0
1
0
1
1
1
1
0
1
1
0
0
0
3
0
1
2
0
0
2
1
0
1
1
0
0
0
0
0
2
2
0
0
0
1
1
3
0
1
0
1
1
1
1
0
0
0
1
1
0
1
2
2
0
2
2
0
1
0
0
1
0
2
1
1
1
1
2
0
2
0
1
3
0
1
0
0
0
1
2
0
1
1
2
1
0
1
0
2
6
1
1
1
1
2
0
1
2
0
1
0
1
2
0
1
2
3
0
1
1
0
0
0
1
2
2
3
1
1
1
2
2
0
1
0
1
1
0
0
0
1
2
0
1
0
1
0
0
0
2
1
1
0
1
1
0
1
2
0
2
0
1
1
0
1
0
1
0
0
0
2
0
1
2
1
0
2
0
1
2
1
0
0
2
0
2
1
3
1
3
1
1
0
2
1
1
2
0
1
1
0
1
2
0
1
0
1
3
0
1
0
0
1
1
2
0
2
1
0
1
0
0
1
1
0
0
1
1
2
1
1
1
1
0
1
1
1
0
0
0
1
3
1
0
0
1
0
1
1
1
0
1
0
0
0
2
1
2
1
1
1
0
0
2
0
1
1
2
1
0
0
0
0
0
1
1
0
1
1
1
0
2
0
2
1
1
1
1
0
1
1
0
0
1
0
0
1
0
1
1
0
0
0
1
1
0
1
2
1
0
2
0
0
2
0
2
2
1
1
2
2
2
1
0
0
3
1
2
0
0
1
0
0
1
0
0
0
1
1
2
1
1
1
2
0
1
1
1
2
0
1
0
0
0
1
0
2
1
0
1
0
1
1
0
0
2
2
1
2
1
0
1
0
1
2
1
1
0
0
0
1
1
0
1
1
0
0
1
0
1
1
0
1
2
1
1
0
0
2
0
0
2
0
1
1
2
0
1
1
1
0
0
2
1
1
0
1
0
0
1
0
2
2
1
0
0
0
0
0
0
3
0
1
0
1
0
0
1
2
2
2
0
0
0
0
2
2
2
0
2
1
0
1
0
1
1
2
2
0
2
1
2
1
0
2
0
1
2
2
0
2
0
1
7
1
0
0
1
0
0
1
0
2
2
2
0
0
1
0
0
1
1
0
2
0
0
1
0
0
1
2
0
0
1
1
0
0
1
0
2
2
1
0
1
0
1
2
1
2
1
2
0
0
0
1
2
2
1
1
1
1
2
0
2
0
3
0
0
0
0
0
2
1
2
0
1
2
2
0
2
1
0
1
2
1
2
2
0
2
1
0
1
0
1
2
1
1
0
1
2
1
1
1
0
1
2
2
0
2
0
0
2
1
1
0
1
1
3
1
1
3
3
1
0
1
2
1
1
0
1
0
1
0
0
1
0
1
1
0
0
0
1
1
0
1
2
2
0
2
1
0
0
1
2
2
1
1
2
2
2
1
0
0
0
0
1
0
1
0
0
1
2
2
2
2
1
1
0
2
1
0
0
1
0
1
0
0
2
0
0
2
0
1
1
1
1
0
0
0
2
0
1
1
0
1
1
0
0
0
1
1
1
0
0
1
0
2
0
0
2
3
0
0
0
1
2
0
0
2
1
1
0
1
0
3
1
0
1
1
2
2
1
1
0
1
0
1
0
1
0
1
1
1
0
2
1
2
0
1
1
1
2
0
1
1
1
0
1
1
0
2
2
0
2
0
1
2
1
0
1
0
1
0
0
2
0
1
1
1
1
6
0
1
0
1
0
1
0
0
0
1
2
0
0
2
2
0
0
0
1
1
2
0
1
0
1
0
0
2
3
2
0
1
2
2
1
2
1
1
0
0
2
1
1
0
0
0
0
4
0
0
1
2
0
0
1
0
0
0
0
0
0
0
1
1
1
2
0
1
0
0
1
1
0
1
2
0
2
1
1
0
0
1
2
0
0
0
2
1
1
0
1
1
0
1
0
1
1
1
0
2
1
2
0
1
0
0
0
1
1
2
2
2
2
0
1
1
1
0
0
2
1
3
2
0
2
2
1
1
0
1
0
2
2
0
1
0
0
0
1
1
1
2
0
0
0
1
1
0
2
1
0
1
1
2
1
1
2
2
1
2
1
1
1
1
1
1
0
2
2
1
0
0
0
0
0
0
1
0
1
0
0
1
2
2
1
0
1
1
3
0
2
0
1
1
0
0
2
0
0
1
2
0
0
2
2
1
0
1
1
3
0
2
3
0
1
1
2
1
1
1
1
1
0
1
3
0
1
2
1
1
1
1
2
0
1
1
0
1
2
0
0
2
2
1
1
0
0
2
1
0
2
0
1
2
2
2
1
0
1
1
0
0
1
1
0
0
2
0
1
0
0
0
0
1
1
1
1
1
1
0
0
1
2
1
0
0
0
2
1
0
1
2
0
1
2
2
0
1
0
0
1
2
2
0
0
0
1
1
6
0
0
2
2
2
2
0
1
1
1
0
1
1
2
2
2
2
2
0
2
0
1
0
1
1
0
5
2
2
1
2
0
0
1
0
1
1
2
0
2
1
1
2
0
1
0
0
2
1
2
2
0
1
1
0
2
0
2
0
0
1
0
0
0
0
2
1
1
2
1
1
0
1
1
1
0
1
2
2
1
1
2
1
0
0
1
2
0
0
0
1
1
0
1
0
1
1
0
1
0
1
1
1
1
0
2
0
2
1
2
0
2
1
0
1
2
0
2
0
1
0
2
0
1
0
2
2
1
2
0
1
2
0
1
1
1
0
1
1
0
0
0
1
2
1
0
0
2
0
2
0
0
2
0
2
1
0
2
0
1
2
1
0
0
0
1
2
1
1
2
0
0
0
0
0
0
1
2
0
0
2
1
0
0
0
1
0
0
2
0
3
2
1
0
1
1
2
1
1
2
0
1
0
0
0
1
1
3
1
2
1
0
2
1
1
0
1
0
0
0
2
2
0
0
1
0
1
1
2
2
2
1
0
1
0
1
1
2
1
0
1
0
0
3
1
1
0
0
1
2
1
2
0
0
0
0
0
2
1
0
1
0
0
2
3
0
1
0
0
1
0
1
1
1
0
0
1
0
3
2
1
1
1
1
0
0
0
0
0
1
0
5
0
1
1
1
1
2
2
0
0
1
0
1
1
1
0
1
0
1
0
1
2
1
2
0
1
1
0
1
0
0
1
1
0
1
1
0
1
0
0
2
1
1
0
0
0
2
1
0
0
1
1
1
0
1
2
4
1
1
2
0
0
2
0
1
0
1
0
0
2
1
2
0
0
2
2
2
0
1
0
1
2
0
1
0
0
0
1
1
0
1
2
1
0
0
1
1
0
0
0
0
2
1
2
1
2
2
1
1
0
1
2
1
0
0
0
2
0
1
2
3
0
1
3
0
1
1
0
2
0
1
2
1
1
0
1
0
0
1
1
1
1
2
0
1
0
0
1
1
0
0
1
2
3
1
0
0
2
0
2
0
0
1
0
1
1
2
11
0
0
0
2
0
0
0
1
0
1
1
2
0
1
2
0
0
0
2
0
1
0
1
2
1
0
1
0
0
0
1
1
1
0
0
0
1
3
0
0
0
1
0
1
0
0
1
0
2
2
1
1
0
0
2
2
0
0
1
2
0
0
0
2
0
1
2
1
1
1
1
0
0
1
0
0
2
2
1
2
0
1
2
2
0
2
0
0
2
0
0
2
1
1
1
0
2
0
0
1
1
2
1
3
1
1
2
0
2
1
1
1
0
2
1
1
1
2
1
2
1
1
2
2
1
0
0
2
0
1
2
2
0
1
1
3
2
2
1
1
1
1
2
1
1
2
0
0
1
0
1
2
2
1
0
1
0
1
2
0
0
2
0
0
1
1
2
0
1
2
1
0
0
0
0
0
0
0
1
0
2
1
2
0
2
1
1
1
0
0
1
0
1
2
0
1
0
0
1
0
1
1
0
1
1
0
0
1
1
0
2
1
2
1
1
1
1
0
1
2
1
2
0
2
0
3
2
2
1
1
1
1
0
1
3
0
0
0
1
2
0
1
0
3
1
1
0
0
1
0
1
3
2
0
0
0
0
1
1
2
1
1
0
0
1
1
1
1
1
0
1
2
1
1
0
0
2
0
2
0
2
0
1
1
0
1
1
0
0
1
0
2
1
0
0
0
2
0
1
2
0
1
1
0
0
1
2
2
1
2
0
1
0
1
0
1
0
0
0
2
2
2
0
0
1
0
2
2
0
1
1
2
1
1
2
1
2
0
1
0
1
1
2
0
1
0
0
0
0
1
0
0
1
2
2
2
1
1
1
2
1
2
1
0
0
1
1
1
2
1
1
1
1
1
1
1
1
2
1
0
0
3
2
1
0
1
1
2
1
0
1
2
1
1
1
0
1
1
1
0
1
2
2
1
2
1
0
1
2
2
0
0
2
1
0
1
1
2
0
0
1
0
2
0
1
1
0
2
2
1
1
1
1
1
2
1
1
1
2
0
0
0
2
0
1
1
1
2
0
1
0
1
0
2
0
0
2
0
1
0
1
2
1
1
1
0
0
3
2
0
0
0
1
2
0
1
1
0
1
1
0
1
1
1
2
1
0
2
1
1
0
1
2
0
2
1
1
2
1
3
0
2
0
0
0
0
1
1
0
3
1
1
0
1
0
0
2
0
1
1
0
2
1
0
0
1
1
1
1
1
2
0
0
1
2
1
2
1
0
1
1
2
1
2
0
2
1
2
1
1
0
2
0
0
0
2
0
0
1
1
0
2
2
1
0
1
1
1
1
1
0
1
0
1
1
0
1
0
0
0
1
1
0
3
0
0
2
0
2
2
0
0
1
1
2
0
1
0
0
0
1
2
1
1
0
1
1
0
1
1
1
1
1
0
1
0
1
1
0
0
1
0
1
0
1
0
1
0
1
0
0
1
1
1
0
2
2
2
2
2
2
0
0
2
1
2
1
1
0
0
1
1
2
0
0
0
1
0
0
1
0
2
0
0
1
0
1
1
1
0
1
1
1
1
1
0
1
0
1
2
0
1
0
0
1
1
0
1
1
2
1
1
0
1
1
0
1
0
1
0
2
1
0
0
2
1
0
1
0
0
1
2
0
1
0
2
0
1
0
1
1
0
0
0
1
0
0
2
1
1
2
3
1
2
0
1
2
1
2
1
1
2
1
0
1
1
2
2
2
0
2
0
2
1
0
1
0
0
0
0
2
0
0
0
1
0
0
2
0
2
1
0
0
0
1
0
2
0
0
1
1
0
1
0
1
0
1
1
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
1
1
0
1
1
2
2
3
0
1
0
1
1
1
1
0
2
0
0
2
3
2
0
0
0
0
1
1
1
2
0
1
2
1
2
1
0
0
1
1
1
0
1
0
1
0
1
0
0
0
1
1
1
1
0
1
2
0
1
0
0
0
1
0
0
1
1
3
1
0
1
1
0
0
0
0
1
2
0
1
1
1
0
1
1
1
2
1
0
2
0
0
1
1
0
0
0
2
2
2
0
1
1
0
1
1
1
2
1
2
0
0
0
0
0
1
1
2
0
2
1
1
0
0
2
1
3
0
0
1
0
1
1
0
2
0
2
0
1
0
1
1
2
0
0
0
1
1
2
1
1
0
2
0
1
0
2
1
1
2
0
1
1
1
0
0
0
0
1
0
0
1
0
0
0
0
1
1
1
1
1
2
2
0
0
0
1
0
1
1
1
0
1
0
1
1
1
1
3
1
1
0
1
0
0
2
1
0
3
1
1
1
0
1
1
2
1
1
2
1
0
1
1
1
1
0
0
0
0
1
0
1
0
1
1
2
3
0
1
1
0
2
1
2
2
0
0
1
0
1
0
1
0
1
2
2
2
0
0
2
2
1
0
1
0
1
0
1
1
1
1
2
0
0
1
1
0
0
0
0
1
1
1
3
0
1
0
0
0
0
1
1
1
1
2
0
1
1
2
1
0
0
0
2
0
2
0
1
2
1
2
1
0
2
1
1
5
1
1
2
0
2
1
1
1
3
2
1
2
1
0
1
2
1
2
0
1
1
1
2
0
1
1
2
2
1
1
0
1
0
1
1
2
0
1
0
0
1
2
0
0
2
0
1
0
0
1
0
2
1
1
2
0
0
2
0
0
2
1
1
1
0
0
2
2
2
0
1
0
1
2
0
2
1
0
1
1
1
0
1
1
0
0
1
2
2
3
0
1
1
2
1
1
2
1
2
1
1
2
0
1
1
1
2
1
1
1
0
1
0
1
1
0
0
2
1
2
1
0
0
3
1
1
1
0
1
1
1
2
1
2
0
0
0
0
2
0
0
1
1
1
1
1
2
1
0
1
1
2
1
1
0
1
0
0
0
0
1
1
0
2
2
2
1
2
0
1
2
1
0
2
0
0
0
1
0
0
2
0
0
2
0
0
1
0
1
2
2
0
0
2
2
0
1
0
1
1
0
0
0
1
0
2
1
0
0
1
0
0
1
2
2
0
0
1
0
0
2
0
2
2
4
1
0
2
1
0
1
2
2
0
1
0
2
0
1
0
0
1
1
1
0
2
2
0
1
1
1
1
2
0
0
0
0
2
1
1
1
1
0
0
0
0
0
0
1
1
2
1
2
0
1
2
2
0
2
0
2
1
1
1
0
2
0
4
2
1
0
0
1
0
1
1
0
1
1
1
2
0
0
1
2
1
2
1
0
0
0
2
3
2
1
3
0
1
0
1
0
2
3
0
1
0
2
0
2
1
1
0
0
2
0
0
0
2
1
1
0
1
1
1
1
0
1
1
3
2
1
1
1
2
0
0
3
0
2
0
0
0
1
1
2
2
0
1
0
2
0
0
2
1
1
1
0
0
2
2
2
0
1
0
0
0
2
0
2
0
0
2
1
2
2
1
2
1
1
0
1
0
1
0
0
1
0
1
1
0
0
0
2
2
0
1
1
1
0
2
1
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
1
1
0
1
1
2
2
2
2
1
0
0
1
1
1
0
0
0
0
0
1
0
1
1
1
1
0
2
0
2
0
1
2
1
1
1
2
0
0
0
2
3
1
1
1
1
1
1
1
1
0
2
0
0
0
2
1
0
1
2
0
1
1
1
0
1
1
1
1
1
0
0
1
1
1
4
2
1
1
1
0
1
1
1
2
1
1
1
0
0
2
0
1
1
1
1
3
0
0
1
0
0
1
0
0
0
1
0
2
0
2
0
0
0
0
1
1
1
0
1
0
0
1
0
1
2
1
2
0
1
0
0
0
1
1
1
1
1
0
0
1
1
0
1
0
1
0
1
2
1
1
2
1
1
2
1
0
1
0
2
0
1
1
2
2
1
1
0
2
0
1
0
1
0
1
1
1
2
2
0
1
2
1
2
1
2
0
2
1
2
2
1
2
0
2
1
1
1
1
2
0
1
0
1
0
2
0
1
4
1
1
0
2
1
3
0
2
0
1
1
1
0
1
1
1
2
1
1
1
0
0
0
1
0
3
1
1
0
1
1
1
2
1
0
2
0
1
0
1
3
0
1
0
0
0
2
2
1
1
2
0
0
1
0
0
1
1
1
1
0
0
0
1
1
0
1
1
0
2
0
1
1
0
0
2
0
0
1
1
0
0
1
1
0
1
2
0
1
1
0
1
0
1
2
0
1
0
2
0
0
1
1
1
2
0
2
0
1
0
0
1
3
1
0
1
1
0
0
1
0
1
1
1
2
2
0
0
1
1
0
0
0
0
1
0
0
1
0
0
2
2
1
0
1
1
0
2
0
1
0
0
1
1
2
0
1
2
1
1
2
1
0
2
0
1
2
2
2
2
2
0
1
1
0
2
1
1
2
0
1
2
1
1
1
0
2
0
0
0
1
2
0
0
0
0
1
0
1
1
1
2
1
0
0
0
1
1
0
2
1
1
0
0
0
0
1
1
0
0
2
0
0
0
2
1
1
1
2
0
0
0
1
3
0
0
0
1
1
1
1
2
0
1
1
1
1
1
0
1
0
1
1
0
2
1
0
0
0
0
1
0
1
1
2
1
1
1
0
0
1
1
1
1
2
2
0
2
0
2
0
1
1
1
2
1
1
1
0
1
0
1
0
0
1
2
2
0
2
1
2
1
1
1
1
2
2
1
1
0
1
1
0
1
2
2
1
1
0
1
0
0
1
2
1
1
1
1
0
2
2
0
1
0
0
0
1
1
0
0
1
0
1
1
0
1
1
1
2
0
4
2
2
1
1
0
2
1
0
1
1
1
0
1
0
0
1
0
0
2
1
0
0
1
1
1
0
1
2
0
0
1
1
0
2
1
1
1
1
0
0
0
2
2
1
0
2
0
0
1
1
2
1
1
0
2
0
1
1
0
1
2
0
1
0
2
2
1
0
0
0
3
1
0
1
0
2
0
2
0
3
1
2
2
1
1
2
1
0
2
1
2
1
1
0
1
1
1
1
2
1
1
0
0
1
0
0
1
0
1
0
1
0
2
1
1
1
1
2
1
0
2
1
1
1
0
0
1
1
0
1
1
2
0
1
1
2
1
2
1
1
1
0
0
1
1
0
0
2
1
1
1
2
0
2
0
1
0
2
0
1
2
1
0
1
2
0
2
0
1
0
0
1
0
0
2
0
1
1
1
2
2
0
0
1
1
1
1
2
3
0
0
0
0
1
1
2
2
0
0
2
2
0
0
0
2
1
3
2
1
0
2
2
0
2
2
1
0
2
1
1
1
0
1
1
0
1
2
1
0
0
2
0
0
0
1
0
1
0
2
1
0
1
1
1
0
0
1
0
0
2
1
0
1
1
1
1
2
0
0
1
2
1
0
0
1
0
0
2
0
1
2
0
1
1
1
1
0
0
2
1
0
1
1
1
0
0
1
1
1
1
2
0
0
1
1
0
0
1
1
2
1
1
1
2
1
0
0
0
0
3
2
2
1
2
0
1
2
0
0
2
1
2
1
1
0
1
1
1
0
1
0
0
0
1
0
1
2
1
0
2
0
1
2
1
1
2
0
1
1
1
1
0
3
2
2
1
2
2
1
2
2
0
5
1
1
2
1
0
0
0
0
0
1
2
0
0
1
0
2
1
2
0
1
0
0
0
2
1
1
0
1
2
1
0
1
0
1
1
0
1
0
1
2
2
0
2
0
0
0
1
0
1
6
1
6
2
0
1
0
0
0
0
1
1
2
1
1
1
2
2
1
1
2
0
0
1
3
1
2
1
0
2
2
1
0
1
2
0
1
1
0
1
0
0
0
0
2
0
2
0
3
0
1
1
0
1
0
2
1
1
0
2
1
1
1
1
1
1
1
0
0
0
0
1
2
0
2
0
1
2
0
1
0
0
1
1
1
1
1
0
0
1
1
0
2
0
1
1
0
0
1
0
0
0
1
0
0
0
0
2
2
1
1
1
0
2
1
1
1
0
1
2
2
1
0
1
0
1
0
0
1
0
2
1
1
1
1
1
1
0
0
0
1
2
1
0
0
2
0
1
2
0
0
1
1
1
0
2
2
0
1
0
1
1
1
0
1
2
1
1
0
1
1
1
0
1
0
1
0
0
2
0
0
1
1
2
0
0
2
0
1
0
2
1
0
0
0
0
0
1
0
0
1
2
2
2
1
2
1
1
1
1
1
1
0
0
0
3
2
0
0
2
0
0
0
1
0
1
0
2
2
0
1
2
1
1
2
1
0
2
1
0
0
1
0
0
1
0
1
1
0
0
2
1
1
1
2
0
0
0
0
1
0
2
0
0
1
1
2
1
0
2
1
0
1
2
2
2
1
1
0
1
2
1
2
1
0
1
1
1
0
0
2
1
1
2
0
0
1
2
1
0
1
2
1
0
1
2
0
1
1
2
2
0
2
1
1
1
0
1
0
1
0
2
0
2
0
0
1
1
1
1
2
0
1
0
0
1
0
0
0
2
1
2
0
2
1
2
0
2
2
2
1
0
0
1
1
0
0
2
0
0
2
1
0
1
0
1
1
1
2
2
1
0
1
0
1
6
0
0
2
0
0
1
1
1
0
2
0
0
2
1
0
1
1
1
1
2
0
2
0
2
0
0
2
0
2
1
1
1
1
1
0
1
2
0
1
1
0
0
0
1
0
1
1
2
1
2
0
0
0
2
1
2
1
2
3
2
0
2
2
1
1
2
1
0
0
0
0
0
0
1
0
2
1
1
2
1
1
4
0
0
1
1
2
1
3
1
1
2
0
0
1
1
0
1
0
1
2
0
1
2
2
2
1
1
2
2
1
1
0
2
0
1
1
0
0
1
1
1
0
0
1
0
0
1
2
0
0
2
1
0
0
0
1
0
1
1
0
1
1
0
1
0
0
2
1
0
0
0
0
1
1
1
4
1
0
1
1
2
1
0
0
0
1
2
1
0
0
0
1
0
2
1
1
0
2
0
1
2
1
1
1
0
1
0
0
2
0
0
1
2
1
2
1
2
2
0
2
0
1
0
0
0
1
0
2
0
2
2
1
0
1
0
2
2
1
1
1
0
1
0
0
1
1
0
1
1
0
2
2
0
0
1
0
1
1
1
2
0
1
1
0
2
1
1
1
0
0
1
2
1
0
1
0
0
0
0
1
2
1
0
2
1
1
1
0
1
0
1
1
1
0
0
1
0
0
0
0
1
1
1
0
1
2
0
0
1
0
0
0
0
0
1
0
0
1
1
2
0
1
1
1
1
1
1
2
1
2
2
1
1
1
1
0
1
0
0
0
1
1
0
0
0
0
2
1
1
1
0
1
0
1
1
0
0
0
1
0
0
0
2
0
2
1
1
1
2
0
0
1
1
1
1
1
4
1
1
0
0
0
1
1
1
1
1
0
1
0
1
1
2
0
0
0
1
1
1
1
0
0
1
0
1
0
0
1
1
2
0
2
0
1
0
1
0
0
1
0
1
1
1
2
2
2
1
0
1
1
2
2
0
0
1
2
1
1
1
0
0
2
1
1
1
0
1
0
1
2
2
0
0
0
2
1
2
1
0
2
1
2
1
1
2
0
0
0
1
1
4
2
1
0
0
0
0
1
1
0
0
0
0
1
0
2
5
0
2
1
0
0
0
0
0
0
1
0
2
3
0
1
0
1
1
2
1
1
0
1
2
1
0
2
0
1
0
2
1
0
0
0
1
1
1
0
1
0
0
0
1
2
1
2
0
1
0
1
2
0
2
0
0
1
2
0
1
1
0
1
0
1
2
1
1
1
0
2
0
3
0
1
0
0
0
0
1
1
1
0
0
1
0
0
0
0
2
0
1
2
1
2
0
1
2
0
0
1
2
1
2
0
1
1
0
1
0
1
1
0
1
1
2
2
0
2
1
2
0
0
0
1
1
1
0
2
0
0
1
2
2
0
1
0
1
0
1
0
2
1
0
1
1
1
0
0
2
0
0
2
0
3
0
1
2
5
1
1
0
1
1
1
0
0
0
1
1
0
1
1
0
0
0
0
0
0
1
0
3
0
0
0
0
1
2
1
1
2
0
0
0
4
0
1
0
0
1
1
0
0
1
0
2
1
0
1
0
1
0
1
2
0
0
1
1
1
0
1
1
1
0
0
1
1
0
1
0
2
0
1
1
1
2
1
0
1
0
1
0
0
0
0
1
1
1
0
0
1
0
1
2
1
0
1
1
0
0
0
0
1
1
1
0
1
1
2
1
0
0
1
0
0
2
1
1
0
0
2
2
1
1
0
1
2
0
0
0
1
1
2
2
2
1
0
0
2
1
1
2
2
2
1
0
0
0
1
0
1
1
1
3
0
1
0
0
2
2
0
0
1
2
0
1
1
0
1
0
0
1
0
2
0
2
1
1
0
0
1
0
0
1
1
0
1
1
0
0
0
1
1
2
1
1
2
2
0
0
2
0
2
0
0
1
0
0
1
0
1
0
1
1
2
1
0
0
0
1
0
0
1
1
0
2
1
2
1
1
2
1
1
0
1
1
0
0
0
1
1
0
0
1
1
0
1
0
2
2
1
0
0
1
0
1
0
1
0
2
0
2
2
1
1
1
2
0
0
0
1
1
0
1
0
1
1
0
1
1
2
0
1
2
0
1
1
1
0
2
0
2
1
0
1
1
1
0
1
1
1
1
1
1
0
1
0
0
2
2
1
1
1
0
1
0
0
1
1
1
2
1
1
0
1
1
0
0
0
0
1
1
1
0
2
3
0
0
1
1
0
0
2
0
1
1
1
0
2
2
1
1
1
0
0
2
0
1
0
0
0
0
2
0
1
1
0
1
2
0
2
0
2
0
0
1
0
1
1
1
0
2
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
1
1
1
2
3
1
0
2
0
1
0
1
0
1
0
0
1
1
1
1
2
1
0
0
0
0
1
0
2
0
0
0
1
1
1
1
1
0
0
1
0
0
1
1
0
0
0
2
0
1
0
2
2
1
1
1
0
1
0
0
0
1
1
2
1
0
0
1
1
1
0
2
1
1
1
1
0
1
0
1
1
0
2
0
2
1
1
1
1
1
0
1
2
1
0
0
0
1
1
1
0
1
0
1
1
0
2
1
0
2
0
1
2
2
0
1
0
0
0
0
2
1
0
0
0
1
2
1
0
0
0
1
1
1
1
0
0
0
1
1
1
2
2
2
0
1
2
0
2
0
0
1
0
2
1
2
0
1
0
1
1
0
1
0
0
2
1
2
1
2
1
1
0
2
2
0
1
1
0
1
1
2
2
1
0
0
2
3
1
0
2
0
1
0
2
2
1
1
0
0
0
0
0
1
0
1
0
1
1
0
1
1
1
2
1
2
1
1
1
1
1
0
0
1
1
1
1
0
2
1
0
1
1
1
0
1
0
1
0
1
1
1
1
2
0
0
0
1
0
0
1
2
1
0
1
1
1
2
1
0
1
1
0
0
2
0
0
0
1
2
0
0
0
1
0
0
0
0
1
2
2
2
2
0
1
1
0
1
1
1
1
2
3
0
1
0
2
0
1
0
1
1
1
1
0
1
1
2
3
1
1
0
0
1
1
2
0
1
1
0
1
4
0
1
0
1
0
1
0
0
1
1
2
3
1
0
1
1
0
1
1
0
0
0
2
2
0
0
1
1
0
1
0
1
1
0
0
1
2
0
1
1
1
2
1
2
2
1
1
0
0
0
1
2
2
0
2
1
0
1
1
0
0
2
1
4
0
2
0
0
0
0
1
2
0
1
0
2
0
0
2
0
1
0
2
1
0
1
1
2
0
1
2
0
0
0
1
1
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
1
1
0
1
1
2
1
2
0
0
1
1
2
1
2
0
1
1
0
1
0
1
1
0
1
1
1
2
1
0
0
0
0
1
1
0
0
0
0
1
0
1
2
1
0
1
3
1
1
2
0
1
0
1
2
1
2
0
1
0
1
1
0
2
2
1
0
0
2
2
0
1
0
1
1
1
1
0
0
0
1
0
2
2
1
0
0
2
1
2
0
2
0
1
0
0
1
0
1
0
2
2
0
1
2
2
1
0
1
1
0
2
2
1
1
0
0
2
0
0
1
0
2
1
1
1
2
1
1
1
1
1
1
1
1
0
1
0
1
0
1
1
0
2
1
0
1
2
0
0
1
1
1
1
0
0
1
1
1
1
3
1
1
1
2
0
1
1
1
1
0
1
1
1
1
1
2
1
0
1
0
0
0
1
3
0
2
1
0
2
0
2
1
1
2
0
1
1
0
1
1
1
0
1
1
2
1
1
0
2
1
0
1
1
1
1
2
0
1
0
1
1
2
0
1
0
2
0
1
1
0
0
1
0
1
1
0
1
0
0
2
1
0
1
0
0
2
1
1
1
1
1
1
1
0
2
0
0
0
0
0
0
0
0
0
2
1
0
1
1
0
1
0
1
1
1
2
4
0
1
1
0
0
1
1
1
1
1
3
1
1
1
1
0
1
0
2
0
1
0
2
1
1
0
2
0
1
3
2
1
1
1
1
1
0
2
0
1
2
2
0
1
1
1
1
0
2
1
2
0
1
0
1
2
0
1
0
1
0
0
1
0
2
0
1
2
0
0
0
2
0
0
2
0
2
1
1
1
2
0
0
2
1
1
1
1
0
1
2
1
1
0
2
1
0
2
0
1
1
1
0
1
1
2
3
0
1
0
1
1
3
0
3
0
1
1
0
1
0
1
1
0
2
0
0
2
0
1
2
2
0
1
0
3
0
1
1
2
0
1
0
1
2
0
2
0
2
0
1
1
2
2
1
2
1
0
0
0
0
1
1
1
1
1
2
1
1
1
0
2
1
2
1
2
1
1
0
1
0
0
1
0
1
1
0
1
1
2
0
1
1
1
1
2
2
2
2
2
0
0
1
0
0
1
0
2
2
1
0
0
0
1
0
1
2
2
2
2
0
2
1
1
1
1
1
0
0
2
2
1
2
2
1
0
1
1
2
0
1
2
1
0
2
1
0
0
0
0
2
0
1
1
0
2
1
2
0
1
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
2
2
0
1
0
1
0
2
1
0
1
1
0
1
0
1
1
0
1
1
2
0
0
1
1
1
0
0
0
0
2
0
0
0
0
0
1
0
2
1
2
0
1
1
0
3
0
2
1
2
1
0
0
1
0
2
2
2
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
2
0
2
0
0
2
1
1
0
0
0
2
1
1
1
2
1
1
0
1
2
1
1
1
1
2
0
1
1
1
1
0
2
0
0
2
0
0
2
1
0
1
1
1
0
0
0
2
1
0
2
0
0
1
0
2
0
0
2
2
0
0
0
1
1
1
1
2
2
0
2
2
1
2
0
1
1
0
0
0
1
0
1
2
0
1
2
2
2
1
0
0
1
0
1
0
2
1
0
1
0
1
1
2
0
0
1
2
0
0
2
0
1
0
1
0
0
0
0
1
0
0
2
0
0
1
0
1
0
0
2
1
1
0
1
0
0
1
0
1
1
1
2
0
1
0
1
0
0
0
1
4
1
0
1
3
1
1
1
0
0
0
3
2
0
1
1
2
0
0
1
0
0
0
0
2
1
0
1
1
1
1
0
0
1
0
0
1
0
1
1
1
0
1
0
1
0
0
2
1
1
1
1
1
0
1
1
2
1
0
1
2
0
1
1
0
0
0
2
1
1
1
2
1
2
1
0
2
1
0
1
1
1
0
2
0
0
1
1
0
0
0
0
1
1
1
0
2
1
2
1
1
0
2
1
0
1
2
1
1
1
1
0
1
0
0
1
1
1
1
2
0
0
1
2
1
1
1
1
1
0
2
0
2
0
1
2
2
0
2
0
0
2
0
0
1
2
3
0
1
0
1
0
0
2
0
0
1
2
1
3
1
0
1
0
1
2
0
0
0
0
1
0
1
1
1
0
2
1
1
1
1
0
0
2
0
0
0
0
1
1
0
0
1
0
0
0
1
2
1
1
0
1
1
1
0
2
2
0
2
0
2
0
2
1
0
0
0
0
1
1
1
1
1
0
1
0
2
2
0
1
1
2
2
0
0
0
0
0
2
1
1
0
1
1
1
2
2
2
0
0
1
1
1
1
1
2
0
0
1
0
0
1
2
1
0
1
2
1
0
0
0
2
1
1
1
2
1
1
0
3
0
0
1
0
0
1
0
0
2
1
1
1
0
0
2
1
1
0
1
0
0
2
2
0
2
1
2
2
1
2
1
2
1
0
1
1
2
1
2
0
0
0
2
0
0
1
0
2
0
2
2
0
1
0
0
1
1
1
1
1
1
2
0
0
1
0
2
1
0
2
1
0
1
1
0
0
1
1
2
1
2
0
1
0
0
1
0
2
1
0
1
1
0
1
2
3
1
1
0
1
0
1
2
0
1
1
1
2
1
0
0
1
0
0
2
1
0
1
1
0
1
3
1
0
0
0
1
2
2
0
1
1
0
0
0
0
1
2
1
1
2
0
1
0
1
0
0
0
2
0
1
0
0
0
0
1
0
2
1
0
0
2
0
2
0
2
2
0
0
2
0
1
0
0
0
0
1
1
1
1
3
0
1
0
0
0
1
1
0
1
2
1
1
0
0
0
0
1
1
2
2
0
1
0
1
0
0
1
1
1
1
1
0
0
1
1
2
0
1
2
1
1
1
1
1
1
1
1
0
3
0
2
2
0
0
1
0
3
1
2
1
1
0
2
0
1
0
1
2
2
1
1
3
2
0
0
0
1
0
2
2
1
0
0
2
0
0
0
2
3
0
1
1
0
1
0
1
1
0
1
1
2
1
2
0
2
1
0
0
1
0
2
2
1
1
1
1
1
0
1
1
0
1
1
2
2
1
1
1
0
0
1
1
1
1
0
1
0
0
0
0
0
1
1
0
0
0
0
2
0
2
0
0
1
1
2
1
0
1
2
0
0
0
1
1
2
1
1
1
1
1
2
1
3
0
2
2
0
1
1
2
2
2
2
1
2
0
0
0
1
1
1
0
1
1
0
0
2
1
0
1
0
0
1
1
1
1
2
1
2
2
2
0
2
0
2
0
0
1
1
1
1
0
0
1
0
2
1
1
1
0
1
2
0
1
0
1
0
1
2
0
0
1
1
0
1
2
0
2
0
1
0
1
1
0
0
2
0
1
0
1
1
1
2
1
2
1
1
0
1
2
0
5
1
0
1
0
0
1
2
0
1
2
2
1
0
2
1
1
0
2
0
0
0
1
2
2
2
2
0
1
2
1
1
0
0
1
3
2
0
1
1
0
0
2
2
0
1
1
0
1
1
0
0
1
1
0
1
0
2
1
1
2
1
1
1
0
0
0
2
1
0
2
1
0
2
0
2
0
0
0
0
1
1
1
2
1
0
1
0
1
0
0
0
0
2
1
3
2
0
0
0
1
2
0
2
1
0
1
1
0
1
1
1
2
0
1
2
1
0
2
0
1
2
0
0
0
0
1
1
1
1
1
0
2
4
1
1
1
1
2
0
0
1
0
1
0
2
1
2
1
0
0
1
1
0
1
1
1
2
0
0
0
1
1
1
0
0
1
1
0
1
2
0
1
0
2
1
2
0
1
1
2
0
1
2
1
1
1
0
1
0
0
0
0
1
0
0
2
0
1
1
1
0
2
0
1
0
1
2
0
0
2
1
1
1
1
1
0
1
1
1
1
0
2
5
0
1
0
0
0
0
0
1
1
1
1
0
2
1
1
2
1
1
1
2
0
2
1
0
2
2
1
0
0
2
2
1
1
2
0
1
1
1
1
2
2
0
0
0
0
0
0
1
0
1
0
2
6
1
0
2
0
1
1
1
0
2
0
0
2
2
2
0
0
0
0
0
1
2
3
0
0
0
1
1
1
0
0
1
1
0
0
1
1
1
0
1
1
3
1
1
1
0
0
0
1
4
2
1
1
0
0
1
0
1
0
2
1
1
2
2
0
1
1
0
0
4
0
1
1
1
1
0
0
2
1
1
0
1
0
1
2
1
0
0
0
0
1
1
1
0
1
0
2
1
0
1
2
2
1
1
0
1
2
2
1
1
1
2
0
1
1
3
0
0
1
0
2
0
2
1
0
1
0
1
2
1
1
0
0
2
0
1
1
0
1
1
0
1
0
2
2
0
0
0
1
2
0
0
0
0
1
0
2
2
0
1
0
0
1
2
2
2
1
2
0
4
0
0
1
0
2
1
0
0
2
0
2
2
2
0
1
1
0
0
1
1
1
0
1
2
0
1
2
0
2
1
0
1
1
2
0
2
0
0
1
1
3
2
2
0
2
1
0
1
1
2
0
0
2
1
0
1
0
0
1
1
2
1
2
1
2
0
0
1
1
0
2
4
1
0
0
1
1
0
1
2
1
0
0
0
1
0
1
1
2
0
1
1
0
1
2
2
0
1
1
1
1
0
2
2
1
1
1
2
2
0
1
2
2
0
0
1
1
1
2
0
1
1
2
1
2
1
1
0
1
0
2
2
0
1
1
0
1
1
1
1
0
1
1
0
1
1
0
0
1
1
1
2
1
0
1
4
0
0
1
0
0
1
0
2
1
0
2
0
2
0
2
0
0
0
0
2
0
1
1
2
0
2
1
0
0
0
2
1
1
0
1
2
1
1
1
1
1
0
1
2
1
1
1
1
1
1
0
1
1
0
0
1
1
1
3
2
1
1
1
1
1
0
1
0
2
0
0
2
0
1
2
2
0
1
2
0
2
0
1
1
1
2
1
2
2
1
0
1
2
0
1
0
1
2
1
0
1
1
0
0
0
1
0
0
0
3
1
1
1
2
1
1
1
0
0
0
2
0
0
1
2
1
1
1
1
0
1
0
0
0
1
2
2
0
0
2
1
0
0
0
0
0
2
1
2
1
0
2
1
1
0
0
0
0
1
1
1
1
2
1
1
1
0
0
1
1
0
2
0
2
2
0
13
0
0
1
2
1
0
1
1
0
0
2
0
1
1
2
1
2
1
1
1
1
2
0
0
1
1
0
0
2
2
1
1
1
1
0
1
0
2
0
0
4
1
1
1
1
1
2
1
0
0
2
2
0
1
2
0
2
1
0
0
0
0
0
1
0
2
0
1
1
0
1
2
0
1
1
1
0
2
1
0
1
0
0
1
1
2
1
2
0
0
1
1
1
0
0
2
1
0
1
1
0
0
0
1
0
1
2
0
2
1
2
2
0
2
1
1
1
0
0
2
2
1
1
0
0
1
0
0
0
1
2
0
0
2
1
1
0
2
1
1
0
1
1
0
1
1
1
2
2
0
0
2
0
0
0
1
1
1
0
1
0
1
0
0
1
1
1
1
1
0
1
0
1
1
2
0
0
2
1
1
0
0
1
2
2
0
2
1
1
1
0
2
0
1
1
1
0
1
2
0
2
1
1
2
2
1
2
1
2
1
0
1
3
0
0
0
1
0
2
0
1
1
0
0
1
0
0
1
1
2
1
1
0
2
0
2
0
1
0
2
2
0
1
0
2
1
1
1
0
2
0
1
1
1
2
1
0
1
1
2
2
0
0
3
1
2
2
2
1
0
0
2
0
2
0
1
0
1
0
1
2
2
0
0
1
2
0
1
2
1
0
1
0
0
2
1
1
1
1
0
0
1
0
1
0
0
1
0
2
1
0
0
1
2
1
0
0
1
1
0
1
1
1
1
1
1
1
0
2
0
2
3
0
1
1
1
1
1
0
0
1
1
2
1
0
0
1
1
1
0
2
0
1
1
1
0
1
2
1
0
2
0
2
1
0
0
0
0
1
1
2
0
1
2
0
2
0
0
2
0
0
1
1
1
1
1
0
0
0
0
1
1
1
3
0
0
0
0
0
2
2
0
0
1
1
0
2
1
0
0
0
1
1
1
1
1
0
1
0
2
2
0
2
0
2
1
0
1
1
1
0
2
1
1
3
1
2
0
1
0
1
0
1
2
1
0
0
0
0
2
2
1
1
0
0
0
2
1
1
0
0
0
1
1
0
0
1
2
0
0
2
0
0
1
0
1
0
2
0
0
1
1
1
0
1
0
2
1
1
2
0
0
1
0
2
2
2
0
0
1
2
1
0
0
0
3
1
1
1
0
0
0
1
0
0
1
1
1
2
1
0
2
0
0
2
0
1
1
2
2
1
0
0
0
3
0
3
1
1
0
1
2
1
0
0
0
1
0
0
0
2
0
1
1
0
0
1
2
0
2
1
1
1
2
0
1
0
1
0
3
0
0
1
0
1
0
0
2
1
2
0
0
1
2
0
1
2
1
1
1
0
2
0
0
0
2
4
1
0
0
0
1
2
2
2
1
0
1
0
2
0
1
2
0
0
0
1
0
2
0
1
1
0
1
1
0
0
1
1
0
1
1
0
2
1
1
1
0
1
2
0
1
1
1
0
0
1
1
0
1
0
1
0
0
0
0
2
1
0
1
0
1
2
1
0
1
0
0
1
0
1
2
2
1
0
1
0
0
0
2
1
1
1
0
0
0
0
0
0
0
2
0
0
1
0
0
2
1
2
1
2
0
1
2
0
1
3
0
1
2
0
1
0
0
2
0
1
2
2
0
0
2
1
1
1
0
1
0
1
1
0
0
0
0
2
0
0
1
2
1
1
2
0
2
1
2
1
1
1
1
0
0
0
0
1
1
1
2
1
2
0
0
1
1
1
2
0
0
1
0
0
1
2
4
1
1
1
1
1
2
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
2
0
2
0
1
0
2
1
2
1
0
2
0
1
0
2
2
1
2
1
1
2
0
0
1
0
0
1
1
0
0
1
0
1
2
0
1
2
0
0
0
0
1
1
0
1
0
0
0
0
1
2
0
0
1
0
0
1
2
1
2
0
1
2
1
0
1
1
0
0
0
2
0
1
0
4
2
1
0
0
2
1
2
0
0
1
0
0
1
1
1
2
1
1
0
1
0
2
1
1
1
2
0
0
0
1
0
0
1
2
1
2
1
0
0
1
1
2
0
0
1
1
0
0
0
0
2
0
2
1
0
1
1
1
1
0
0
0
1
2
2
2
0
0
1
0
1
0
2
1
2
0
2
2
2
0
1
1
1
3
0
0
2
1
0
1
0
2
1
0
1
0
1
1
1
0
2
1
2
0
0
1
1
2
0
1
0
1
2
2
0
1
1
1
0
0
1
0
2
0
1
2
1
1
2
1
2
0
2
0
0
0
2
1
1
2
2
0
1
2
0
3
1
1
1
0
0
1
2
1
0
1
2
0
0
1
2
2
1
3
1
0
3
0
2
2
0
0
1
2
0
0
0
1
1
0
2
2
0
2
1
0
0
1
2
1
1
0
0
1
0
1
1
2
0
0
1
0
1
0
2
1
1
0
0
2
1
0
2
0
1
0
2
0
1
1
0
1
0
0
0
0
0
1
1
0
1
0
1
1
1
2
0
0
0
2
0
0
2
0
2
1
1
3
0
3
2
1
2
1
1
2
0
2
1
1
0
1
1
1
0
0
0
0
1
1
2
1
1
1
1
0
1
0
2
0
2
1
1
1
1
0
0
2
1
2
0
1
0
2
1
0
0
2
2
0
0
0
1
2
2
0
1
1
1
2
0
1
1
0
2
1
2
2
0
0
1
2
3
1
1
0
2
1
2
2
0
1
1
1
0
0
2
0
0
2
1
1
1
1
0
0
1
2
0
2
2
2
1
1
0
0
1
0
1
0
2
2
0
2
1
1
0
1
0
0
2
2
1
1
0
2
1
0
2
0
0
0
2
0
1
1
0
0
1
0
2
1
0
2
0
0
0
1
2
1
0
0
0
2
0
2
0
1
0
1
1
2
2
1
0
0
1
0
2
1
1
0
1
3
2
0
1
2
1
0
1
1
0
0
2
1
1
1
1
1
0
1
0
0
2
1
1
0
0
2
3
0
1
1
2
0
1
2
0
0
1
1
2
1
2
1
0
0
0
1
0
1
0
1
2
0
0
0
0
0
1
0
0
1
0
2
1
0
2
1
0
0
0
1
1
0
5
1
0
0
0
0
1
0
1
1
1
1
1
1
2
1
2
1
0
5
2
0
1
0
1
1
0
0
0
2
0
1
0
0
0
0
0
2
0
0
1
1
1
0
2
0
1
0
1
1
2
0
1
0
1
2
2
2
1
1
0
2
0
1
0
1
0
1
0
0
0
2
0
0
0
1
0
0
0
0
1
1
1
2
3
0
0
1
0
0
1
0
1
1
0
2
0
1
0
1
0
1
0
1
1
0
2
2
0
1
0
0
0
2
1
2
0
1
0
1
0
2
0
1
0
0
1
2
0
0
1
0
1
0
1
1
0
1
1
1
0
0
1
0
1
0
1
0
1
0
2
1
2
2
2
0
1
1
2
2
0
1
1
1
0
1
0
1
1
1
2
1
1
1
1
0
1
1
1
0
1
1
0
2
1
0
0
0
0
0
1
0
2
1
1
2
2
2
0
1
3
0
3
2
0
0
1
1
1
0
1
1
0
2
0
0
1
1
1
2
2
0
2
1
2
1
1
0
2
1
1
0
1
2
1
3
0
1
1
1
0
2
1
0
1
3
1
1
0
2
1
2
1
0
2
1
2
0
0
1
1
2
0
1
1
0
2
2
0
1
1
1
0
0
0
0
1
2
2
0
1
1
2
0
2
1
1
1
1
0
1
2
0
0
0
0
2
1
0
1
1
0
1
0
1
0
0
1
1
0
1
0
1
1
1
2
1
1
1
1
2
0
0
0
1
0
1
0
1
2
0
2
0
2
2
1
0
0
1
2
1
0
1
1
2
1
1
2
1
1
0
1
1
0
2
1
1
1
0
0
1
0
0
0
1
1
0
1
0
1
2
1
1
0
2
2
1
2
1
2
2
1
1
1
0
1
1
1
0
1
2
2
0
2
1
0
1
1
1
2
2
0
1
0
2
1
0
2
2
2
1
1
1
1
0
1
2
0
0
1
0
1
0
1
0
0
0
2
1
0
1
1
1
1
0
0
1
2
0
0
0
1
1
1
2
2
1
2
0
0
0
2
0
1
2
1
1
1
2
1
1
1
1
1
1
1
1
0
1
1
1
0
1
0
0
1
1
1
1
2
1
0
0
2
2
0
1
2
2
2
1
1
0
3
0
0
1
0
2
1
2
1
2
1
1
2
1
1
1
1
0
0
2
1
1
0
2
1
2
1
2
2
1
0
1
0
1
2
0
0
2
0
0
4
1
0
0
1
1
0
1
0
1
1
0
0
2
0
1
1
0
2
0
2
1
0
1
0
1
0
2
1
1
1
1
2
1
2
1
0
1
0
0
1
1
0
1
1
1
1
0
2
0
0
0
0
0
1
0
0
1
1
0
1
1
0
0
2
0
2
1
0
0
0
2
0
0
2
0
2
1
1
0
0
1
2
0
0
2
2
1
0
3
0
1
1
1
1
1
1
0
1
0
1
2
1
2
0
1
1
0
1
0
2
1
2
0
2
0
2
0
2
0
1
0
1
0
1
1
1
2
2
0
0
5
1
1
1
2
1
2
0
0
0
0
1
1
1
1
0
0
1
1
2
1
2
0
1
1
1
2
2
1
0
0
1
0
1
1
2
1
0
0
0
0
1
1
0
2
1
2
0
0
1
2
1
1
1
0
2
1
1
0
1
1
0
2
1
1
2
3
1
1
0
1
0
0
1
2
1
1
0
0
1
1
1
1
2
2
0
1
2
1
1
1
0
0
0
2
1
1
1
1
0
0
0
1
9
1
1
1
2
0
1
0
1
0
2
2
0
0
1
0
0
2
2
2
1
2
1
2
0
1
0
0
0
0
1
0
2
2
0
0
1
2
1
1
0
1
0
1
1
1
0
1
2
0
2
0
2
0
2
0
0
0
2
0
0
2
0
0
2
3
0
2
1
1
1
1
1
1
0
1
0
0
1
0
2
1
1
0
1
1
0
1
0
1
2
1
1
1
1
1
0
0
1
0
0
2
1
0
0
1
2
1
1
2
2
1
2
0
2
1
2
1
0
2
0
2
1
0
1
2
1
0
0
0
1
2
1
1
2
0
0
1
1
2
0
2
1
1
1
0
0
0
2
0
0
1
2
1
0
0
1
0
1
1
0
2
2
2
0
0
1
0
0
0
1
1
0
0
0
1
1
2
2
2
0
0
1
1
2
0
1
1
0
0
0
0
1
1
1
0
2
1
1
1
1
3
1
1
2
0
1
0
0
2
0
0
1
0
1
2
2
1
1
0
2
2
0
0
0
1
1
0
1
1
2
1
1
1
0
2
1
1
1
1
1
1
2
2
2
3
0
0
0
1
2
2
0
1
2
0
1
1
2
1
2
0
2
1
1
1
0
1
1
2
2
2
1
0
0
2
2
2
1
1
2
0
0
2
2
1
2
0
1
1
0
1
1
2
0
0
1
2
2
0
2
1
0
0
0
1
1
2
1
1
1
1
2
0
0
0
1
2
1
1
1
1
1
1
1
1
0
1
0
1
1
0
0
1
1
1
1
0
1
1
0
1
0
0
0
0
0
1
2
1
1
1
0
2
0
3
0
0
1
2
1
0
1
2
1
2
0
2
0
1
0
1
0
0
1
2
1
0
0
0
0
2
0
0
1
0
2
1
1
1
3
1
2
1
1
2
2
0
1
0
1
2
1
1
3
1
1
0
1
1
0
0
2
1
1
0
2
0
0
2
1
2
0
0
1
0
1
1
0
1
0
0
1
0
1
0
1
1
1
1
2
0
0
1
1
1
2
2
1
1
1
1
1
1
0
1
0
0
2
2
2
2
1
1
0
1
1
1
1
0
2
1
1
0
0
3
1
0
1
2
0
1
1
2
1
0
0
1
2
2
2
0
1
0
0
3
0
2
1
1
1
0
0
1
1
0
0
0
0
0
1
2
1
2
1
1
2
1
0
2
0
0
1
0
1
2
1
0
1
1
1
2
2
0
0
2
1
1
0
1
1
2
1
0
0
0
0
0
2
2
0
0
1
2
1
0
1
0
0
3
1
2
0
0
1
0
2
2
0
1
0
1
5
1
0
1
0
0
1
1
1
2
2
1
1
0
1
1
1
2
1
2
1
0
2
0
2
1
1
1
0
0
2
0
0
1
0
0
0
1
2
0
1
0
0
0
2
0
0
0
1
0
0
0
0
1
1
0
2
1
1
2
1
1
2
2
0
0
1
1
0
2
2
0
1
0
0
0
1
1
1
1
3
1
1
0
0
0
1
0
1
1
0
1
2
0
0
1
1
1
1
3
1
0
2
0
0
0
0
0
0
2
1
1
1
1
0
0
0
0
1
0
2
2
0
4
0
1
0
1
0
1
2
1
1
0
0
3
2
1
1
2
1
1
2
0
1
2
2
0
1
2
1
0
1
0
1
1
0
0
2
1
0
1
2
2
2
2
1
1
1
1
0
1
2
0
2
0
0
2
2
1
1
0
0
0
0
1
0
2
0
1
1
0
2
1
2
2
1
2
1
0
1
0
0
1
0
1
1
1
1
0
0
1
1
3
0
1
0
2
1
0
0
3
1
1
0
0
2
1
1
1
0
0
1
1
1
1
0
0
1
0
0
2
0
0
0
0
2
1
0
2
0
2
0
0
0
1
1
2
2
1
0
0
1
0
1
0
1
2
1
1
1
1
0
1
1
0
1
1
2
0
1
1
1
1
2
1
1
0
1
0
0
0
3
1
1
2
1
0
1
0
1
0
0
0
1
1
2
0
2
0
2
2
2
0
1
1
0
0
0
1
4
0
2
2
2
0
1
1
1
1
0
0
0
1
2
0
1
2
0
1
0
2
2
2
1
2
0
1
1
0
0
1
1
1
1
1
1
0
0
0
0
2
0
2
0
2
2
0
1
0
0
1
0
0
1
1
0
1
1
1
2
1
1
1
0
0
0
0
1
1
2
0
0
2
1
1
1
1
0
1
0
2
1
1
1
2
0
1
0
1
1
1
1
2
0
2
1
0
0
0
0
0
2
1
0
2
0
1
0
1
2
1
1
1
1
0
1
0
1
1
0
1
1
2
1
0
0
3
0
3
1
1
0
0
2
0
0
1
3
1
0
0
1
1
0
0
0
2
0
2
2
3
1
0
1
2
0
2
2
2
0
1
1
0
0
2
0
1
0
1
0
1
0
1
0
2
1
1
1
1
1
1
1
0
2
3
0
1
0
0
0
1
3
1
0
0
1
1
1
2
1
1
0
0
0
1
2
2
0
2
0
2
3
0
0
0
0
0
1
1
2
1
0
1
2
0
2
1
0
1
0
0
1
1
1
1
2
0
0
1
0
0
2
1
1
0
1
2
3
0
2
0
2
0
1
0
1
0
0
2
0
1
1
2
1
0
1
2
1
0
1
0
2
0
0
1
1
1
0
1
2
1
1
2
1
2
1
1
1
2
0
1
0
2
2
2
1
2
1
0
0
1
0
0
0
2
1
2
2
0
2
0
0
0
0
0
0
2
1
2
2
1
0
2
1
0
0
1
1
0
0
1
1
0
0
0
0
1
1
1
0
0
1
0
0
0
0
2
0
0
2
1
1
0
1
0
0
1
1
0
1
1
1
0
0
0
0
1
0
1
0
0
0
2
2
1
1
1
1
0
2
1
1
0
1
1
1
2
1
2
1
1
1
1
0
0
0
0
0
0
0
1
1
1
0
3
0
1
2
1
1
1
0
2
0
1
0
0
1
0
2
0
1
0
0
0
2
0
1
1
0
1
0
0
0
2
0
0
2
1
0
3
1
0
2
1
3
1
0
1
2
0
0
1
2
2
0
0
1
2
2
0
0
1
0
1
1
0
0
1
1
1
1
1
1
1
0
0
0
1
2
1
1
1
1
1
1
1
3
0
2
1
2
1
1
1
2
1
3
0
1
0
0
0
1
2
0
0
1
0
2
1
1
1
0
1
0
1
2
1
2
1
0
1
1
0
1
2
2
1
0
1
0
1
2
0
1
1
1
1
0
0
1
0
1
0
1
0
1
1
2
1
1
0
1
1
1
0
0
1
1
1
0
1
1
0
1
0
1
0
0
0
0
1
0
0
1
0
0
1
1
1
0
1
1
0
2
4
2
1
3
1
1
0
0
1
1
1
0
1
1
0
2
0
1
0
2
0
2
0
1
1
0
3
2
3
0
0
0
2
0
1
2
2
0
0
0
1
2
0
0
1
0
0
2
2
1
2
0
1
1
1
1
1
0
0
0
1
1
2
0
1
0
0
1
1
0
1
1
2
0
0
0
1
2
0
0
0
0
2
0
2
1
1
2
1
0
1
0
1
1
2
0
1
0
0
1
0
2
1
2
0
2
2
1
2
1
0
1
0
0
1
0
0
0
1
0
0
1
0
1
0
0
1
1
1
0
0
1
1
0
2
0
1
2
0
0
1
0
2
0
0
0
1
1
0
1
2
0
2
0
1
1
0
1
2
1
1
0
4
0
2
2
0
1
2
1
0
0
0
2
1
2
0
2
2
1
0
2
0
1
2
2
2
1
2
2
0
0
0
1
1
1
1
1
0
2
0
3
2
1
1
2
1
1
1
0
1
1
1
2
0
3
1
2
0
1
0
0
0
2
0
0
0
1
1
0
2
1
2
1
1
1
2
0
1
1
3
2
1
0
2
2
1
2
2
3
0
1
1
1
2
0
0
1
0
1
0
1
1
2
0
0
1
0
1
1
0
2
1
3
1
0
0
0
2
2
1
1
1
0
0
1
1
1
2
2
0
0
0
0
2
2
2
0
1
0
1
2
2
2
2
1
1
0
0
1
1
2
0
1
1
1
1
1
0
1
1
1
0
2
1
0
0
2
0
0
0
0
2
0
2
1
0
0
1
0
1
1
1
0
1
0
1
0
0
2
0
1
0
0
2
1
2
0
5
1
0
1
1
2
0
0
0
0
0
1
1
0
0
2
1
0
1
1
1
1
2
1
2
1
0
1
1
1
0
0
1
2
1
1
0
0
1
0
0
1
0
1
0
0
0
0
1
1
2
0
0
1
2
1
1
1
1
1
0
1
0
0
1
0
0
1
2
1
1
1
1
1
1
0
1
0
0
1
1
0
0
2
1
0
0
2
0
0
0
2
2
1
0
0
2
1
0
1
1
1
1
0
0
2
0
1
1
1
0
0
0
0
2
2
2
2
0
2
1
1
1
1
2
1
0
0
0
0
1
0
0
0
2
2
2
0
0
1
2
0
0
0
2
1
1
0
4
1
0
0
1
0
1
0
2
1
0
1
0
2
1
2
0
0
0
1
1
2
2
2
1
0
2
1
1
1
2
0
1
0
1
0
1
1
0
2
0
4
0
0
0
0
2
0
2
0
2
0
1
1
3
0
0
0
0
2
0
0
2
1
1
0
1
1
1
1
0
1
0
0
1
0
0
1
0
1
0
2
1
0
2
4
2
1
1
1
2
1
1
2
1
0
0
1
0
1
1
2
1
0
1
1
1
0
2
1
0
1
0
0
0
0
3
1
0
0
1
1
0
2
0
1
0
1
1
0
1
1
1
1
1
1
1
0
2
1
2
0
0
0
1
1
1
1
0
1
0
1
2
2
1
1
2
2
0
0
2
2
2
1
0
1
0
0
0
0
0
0
0
2
0
1
1
1
0
1
1
0
1
1
2
2
0
1
0
1
2
2
4
0
0
1
2
1
1
2
1
0
1
0
1
0
2
2
2
0
1
1
0
2
2
0
0
3
1
0
1
2
1
2
2
0
2
2
1
1
1
1
2
1
0
0
2
2
0
1
0
1
1
1
0
1
2
0
0
0
1
1
1
0
0
1
2
0
1
0
2
1
0
1
0
2
0
0
0
1
0
0
4
1
0
1
0
0
2
0
0
1
0
0
0
0
1
1
1
0
1
0
0
0
0
1
1
1
2
2
1
1
0
0
1
0
1
0
0
1
0
1
2
1
0
0
2
1
1
0
0
1
0
2
2
2
2
1
2
1
0
1
0
0
1
0
1
1
1
0
1
0
1
2
1
0
0
2
0
1
1
2
1
1
0
1
1
1
2
1
1
2
1
0
2
0
1
0
0
1
1
0
0
2
1
1
0
0
2
0
1
2
2
0
1
0
1
2
0
2
1
0
1
2
2
2
1
5
1
1
1
0
0
0
0
2
0
1
3
0
2
2
0
0
1
1
0
0
1
2
1
1
2
1
0
1
1
1
1
1
2
1
0
0
1
2
1
3
0
0
0
0
2
2
1
2
1
1
2
1
0
1
0
0
1
1
2
1
2
0
0
0
1
0
2
2
0
0
0
0
2
0
0
0
0
2
0
1
1
0
0
1
2
0
0
2
0
1
1
0
2
1
1
0
1
1
1
0
2
0
1
0
0
2
0
1
2
2
4
0
1
0
1
0
0
1
2
2
0
0
0
0
0
2
1
2
1
0
1
0
0
0
1
2
0
1
1
0
0
2
1
2
1
1
0
1
0
1
2
2
1
1
2
2
0
1
0
2
2
0
2
2
1
1
0
1
0
0
1
1
1
0
1
2
0
1
1
1
1
0
1
1
1
1
1
2
0
2
0
1
1
1
1
0
0
0
1
1
0
0
0
1
2
0
2
0
0
0
0
0
2
0
2
0
0
1
2
0
1
0
3
1
0
0
5
0
0
0
2
0
0
1
0
0
0
0
0
1
2
0
1
1
0
1
2
0
2
0
0
2
0
1
0
1
0
1
0
2
2
2
1
1
2
0
1
0
0
0
0
0
0
0
0
1
0
0
3
1
0
2
2
2
0
0
1
0
0
1
1
0
1
0
1
0
1
0
1
0
0
2
1
0
1
0
2
0
0
0
2
0
0
2
2
0
2
0
0
1
1
1
2
0
2
0
0
1
1
1
0
1
1
1
1
2
1
1
0
2
1
2
1
1
1
2
0
1
2
2
0
1
0
0
1
1
0
0
0
2
2
0
0
1
0
0
1
0
1
0
1
1
1
1
1
1
1
2
1
0
1
2
0
1
0
1
0
1
1
0
0
1
2
0
0
1
1
0
1
1
1
2
0
1
1
0
0
2
0
0
1
0
0
0
0
2
2
2
0
1
0
1
1
2
2
1
2
1
2
0
1
0
1
1
1
1
1
2
2
0
1
0
1
1
1
1
1
0
1
0
2
2
0
1
1
0
1
0
2
0
1
2
0
0
3
1
1
1
1
2
0
1
1
3
2
0
1
0
1
2
0
1
0
2
1
0
2
1
0
0
0
0
2
2
0
1
1
1
0
0
0
9
2
1
2
1
0
1
0
2
0
0
2
2
1
0
5
0
0
1
0
2
0
0
0
2
0
0
2
2
1
2
0
0
0
0
1
0
0
1
1
0
1
2
0
0
0
0
1
2
1
0
0
0
2
2
0
1
0
2
1
0
1
2
0
0
1
1
1
2
0
1
1
0
0
1
1
1
0
2
0
1
1
2
0
1
2
2
1
1
1
1
2
0
0
2
1
2
2
1
0
0
3
1
1
1
0
2
0
2
0
1
1
1
0
0
0
1
0
0
0
2
1
1
0
1
0
0
2
1
0
0
0
1
1
0
1
2
1
1
2
1
1
0
1
1
2
1
1
0
1
1
1
2
2
0
0
0
1
2
0
2
1
0
1
2
0
0
0
0
2
2
0
1
2
0
1
1
1
1
0
1
1
1
0
0
0
1
1
0
2
1
2
2
2
2
1
0
1
2
1
2
1
0
1
1
0
0
2
0
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
2
0
1
0
1
0
1
1
1
1
1
0
2
1
1
1
0
1
3
0
1
0
2
0
0
1
1
5
1
2
1
0
1
1
2
1
1
0
1
0
2
0
0
0
1
1
0
2
1
1
0
0
0
1
0
1
1
1
1
0
1
0
1
1
1
2
2
1
1
0
1
3
2
0
1
0
0
1
0
0
0
0
0
1
1
1
0
1
4
0
0
0
3
1
0
0
1
1
1
0
0
0
0
0
2
2
1
3
2
0
1
1
0
1
0
0
1
2
0
0
0
0
0
1
2
1
2
1
1
0
1
1
1
1
1
0
1
0
1
1
1
0
1
0
3
1
0
1
0
1
0
2
2
0
1
1
0
1
0
1
2
1
2
0
2
1
1
2
1
2
1
0
1
2
2
0
1
0
2
1
1
1
0
1
2
1
0
1
0
1
0
0
2
0
2
1
0
0
0
0
1
1
2
0
1
0
0
1
1
0
2
0
1
1
1
1
2
1
1
1
0
0
1
1
0
0
2
1
2
1
0
0
0
2
0
1
1
1
0
0
0
2
0
1
3
0
0
1
0
2
4
2
0
2
2
0
1
0
2
0
0
2
2
1
1
1
0
2
0
1
0
2
0
0
1
1
0
2
1
1
0
1
0
2
1
2
0
0
1
0
2
2
2
1
1
0
0
0
0
1
2
0
1
2
2
2
2
0
0
2
2
2
0
1
2
1
0
0
2
1
0
0
0
1
0
3
1
0
1
2
0
0
0
2
2
0
1
0
1
4
2
2
1
1
2
0
0
0
1
0
2
1
0
1
1
0
2
2
1
1
1
1
2
1
0
0
2
0
1
0
2
0
1
1
1
1
0
0
0
1
0
1
1
0
1
2
0
2
2
1
1
2
1
1
1
0
1
0
2
2
0
0
1
0
1
2
1
1
1
0
0
1
2
1
0
0
0
1
0
0
1
0
2
1
2
1
1
0
0
1
2
0
0
1
0
2
1
3
2
1
2
0
1
0
0
1
1
1
2
1
0
1
0
1
0
0
0
2
2
0
1
1
0
1
0
2
1
1
2
1
2
1
2
1
2
1
1
1
2
1
1
0
1
0
1
0
1
0
1
1
0
1
0
2
1
1
0
2
1
2
1
1
1
0
1
2
2
0
0
0
1
1
1
0
2
2
0
2
2
0
1
1
0
0
2
1
0
2
1
1
1
0
0
1
1
0
1
1
1
0
0
2
1
0
2
1
2
2
0
2
1
2
1
2
2
1
1
2
0
1
1
0
0
0
0
2
0
0
0
2
1
0
1
0
1
0
0
0
1
1
0
1
0
1
1
0
2
2
1
2
0
1
2
0
1
0
0
2
1
2
1
2
1
2
0
0
0
2
1
3
1
2
0
2
0
2
1
2
1
0
2
0
1
1
2
3
2
1
0
1
2
0
0
1
1
1
0
0
1
0
0
0
2
0
0
1
0
0
2
1
0
0
1
0
1
0
1
1
0
0
2
2
0
0
2
0
2
1
1
2
0
0
1
2
1
2
1
2
0
1
1
0
1
2
0
1
0
0
1
1
1
0
0
1
2
1
2
2
0
0
1
0
1
0
1
1
0
1
2
1
1
1
0
3
1
0
1
0
1
1
1
2
1
1
1
1
1
1
2
0
2
1
0
0
2
0
1
0
2
1
1
0
0
1
1
2
0
0
2
1
0
0
0
1
2
2
0
1
0
1
1
0
1
1
1
1
1
1
0
0
0
2
1
1
1
1
1
0
0
0
2
1
0
1
1
0
1
0
0
0
0
1
0
1
1
1
2
0
1
1
2
0
2
1
1
1
0
1
0
2
1
1
1
1
0
1
1
1
2
0
1
0
1
1
0
0
1
2
1
1
0
0
2
1
1
0
0
1
0
0
2
0
0
0
2
1
2
1
1
0
1
0
1
1
0
1
0
2
2
2
0
2
1
1
0
1
1
1
0
2
0
1
1
1
2
0
1
2
1
2
0
0
2
1
0
1
0
0
1
0
0
1
2
0
1
1
1
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
1
1
1
2
2
1
2
0
1
2
2
2
1
0
0
0
0
0
0
0
2
3
1
0
2
1
2
2
0
0
2
1
0
2
3
0
0
1
2
0
1
1
1
0
1
1
1
0
3
0
0
0
1
1
0
3
1
3
1
1
1
1
0
2
2
2
1
1
2
0
0
0
1
2
0
2
0
0
1
2
1
1
0
0
2
1
1
1
1
1
1
1
0
1
1
1
2
0
0
0
0
1
0
2
2
0
1
0
0
0
2
0
1
0
1
1
0
0
1
1
0
0
0
0
1
1
1
0
0
0
2
1
0
0
1
1
0
0
0
2
1
0
1
2
0
0
0
0
0
2
0
2
0
0
0
1
2
1
1
0
1
0
0
2
1
2
2
0
0
1
1
0
2
0
0
1
1
1
2
1
0
0
1
1
0
1
1
2
3
1
1
2
0
2
2
0
0
0
0
1
1
0
1
0
1
0
2
0
1
1
2
0
1
0
1
0
1
0
1
1
1
1
1
1
2
0
1
1
0
1
1
0
0
0
1
0
1
1
1
1
0
2
2
1
2
1
0
0
0
0
1
1
0
1
1
0
0
0
0
1
0
0
0
1
0
3
0
2
2
1
1
2
0
0
0
0
1
2
1
2
1
2
0
1
0
0
0
1
1
2
0
0
0
1
1
1
0
1
0
2
2
1
2
1
1
0
2
1
0
2
0
1
1
0
1
2
0
1
0
0
0
2
2
0
1
1
0
1
0
0
2
1
2
2
1
1
1
2
0
0
1
1
2
3
2
2
1
2
0
1
1
0
1
1
0
0
1
1
0
1
1
1
0
0
0
0
1
1
0
2
2
2
0
0
1
1
1
0
1
0
0
0
1
2
1
2
1
1
1
0
1
0
2
0
1
2
0
1
2
0
1
2
0
1
0
1
2
0
0
0
0
0
1
0
1
2
1
1
1
1
1
2
1
0
0
2
1
1
2
1
1
0
1
1
0
2
1
0
0
1
0
1
2
0
0
2
1
1
2
0
0
1
1
3
0
2
0
1
0
1
2
2
1
1
2
0
0
2
0
1
0
1
0
2
1
1
1
1
0
2
0
1
1
0
1
0
1
0
2
0
1
0
1
0
1
1
2
1
2
2
1
1
1
0
1
1
1
1
0
2
2
2
0
2
0
1
3
1
1
0
1
2
2
0
0
0
0
1
2
2
2
0
0
2
1
1
1
2
1
1
2
0
0
2
2
0
2
2
0
1
1
0
3
3
0
1
1
1
1
0
2
0
1
1
1
0
1
3
0
2
0
0
1
1
1
2
0
1
1
1
2
2
0
0
2
1
0
2
0
0
0
1
2
2
2
2
0
1
0
2
1
1
0
2
1
1
0
1
1
0
2
1
1
1
1
1
1
1
0
1
0
2
0
0
1
0
0
1
0
1
2
1
0
1
0
1
1
1
2
1
1
2
2
1
0
1
1
0
1
2
0
1
2
1
2
1
0
1
1
1
2
0
0
2
2
0
0
0
0
0
1
0
2
1
0
2
2
0
1
1
2
1
1
0
2
0
0
2
0
0
2
0
0
1
2
0
0
1
2
0
0
1
0
1
1
0
0
1
0
1
2
0
1
1
2
0
0
0
0
0
0
2
1
2
1
0
2
0
1
1
1
2
1
0
0
0
0
1
0
2
1
1
0
0
1
0
2
1
2
1
0
1
2
1
1
0
1
1
1
1
0
2
0
0
1
2
0
1
1
0
1
2
0
0
1
2
0
2
0
1
0
1
1
2
0
0
1
1
1
1
1
1
0
1
2
0
1
2
1
0
0
0
2
1
0
0
2
0
0
2
2
1
1
1
2
0
2
1
1
1
0
1
1
3
0
0
2
1
2
1
1
1
0
0
0
2
1
1
0
1
1
1
1
1
1
2
1
1
1
1
1
0
0
1
2
2
1
0
1
0
0
1
1
2
0
1
0
0
0
1
0
1
1
1
1
2
0
1
1
1
1
2
0
1
1
1
0
1
0
0
1
1
2
2
1
1
1
0
0
1
0
0
0
0
1
0
1
0
0
1
1
2
1
1
1
0
2
2
1
2
0
1
0
0
2
1
1
0
0
0
1
1
0
1
2
1
0
0
1
2
1
0
1
2
0
0
0
1
0
0
1
0
0
0
0
2
1
1
1
2
2
1
0
2
1
0
0
1
1
1
1
1
0
1
1
1
0
1
4
2
0
2
1
0
0
2
0
1
1
2
0
0
1
2
0
0
1
1
0
1
0
1
1
1
1
1
2
1
0
0
0
1
0
2
0
1
2
2
2
2
1
0
0
0
0
2
0
1
1
2
1
1
1
1
1
2
2
2
1
2
1
0
2
1
2
1
1
1
0
1
0
1
1
1
0
0
0
0
1
1
2
0
0
1
1
1
1
2
1
0
2
0
1
0
1
1
1
0
2
0
2
1
0
0
1
0
1
0
0
0
2
2
2
1
1
1
1
1
0
1
1
2
0
1
1
1
1
1
1
2
2
1
0
0
2
3
2
1
1
1
0
0
15
2
1
2
1
0
2
1
2
0
2
0
2
1
0
0
1
2
0
2
1
2
1
1
0
0
1
1
0
1
3
1
0
2
0
0
0
1
2
1
0
0
1
1
2
0
2
2
1
2
2
0
0
0
0
0
2
1
0
2
2
1
1
0
0
2
1
1
1
1
2
0
2
0
1
1
0
0
0
1
2
1
0
0
1
2
1
1
0
2
1
0
1
0
0
1
0
0
0
0
1
2
1
0
0
1
1
2
1
1
2
0
3
2
2
2
0
1
0
1
1
1
0
1
1
1
0
0
1
0
2
0
0
1
1
2
1
0
0
1
1
0
1
1
1
0
1
1
2
0
0
0
0
2
0
0
2
0
1
1
0
3
0
1
0
1
1
2
1
1
1
0
0
1
0
1
1
1
0
2
1
0
1
1
1
1
2
1
0
2
0
2
2
0
0
2
0
0
3
0
1
1
0
0
1
0
1
0
0
0
1
2
0
1
0
1
0
2
0
0
0
2
1
2
0
2
0
1
0
2
2
0
1
0
2
0
1
0
2
1
0
1
2
0
1
0
2
2
0
0
1
1
0
0
0
2
1
0
1
0
1
0
0
1
0
2
0
1
1
2
1
1
0
1
0
2
1
2
2
0
1
1
1
2
1
1
0
2
0
0
0
0
0
1
1
1
0
0
1
1
0
5
1
1
1
1
0
0
0
1
2
0
0
1
3
0
1
1
2
2
1
0
1
1
2
0
2
0
1
0
0
0
1
1
1
1
1
1
0
0
1
1
1
1
2
2
1
0
1
1
0
2
1
0
1
0
1
0
1
0
0
1
3
1
1
0
0
1
2
0
0
0
1
2
0
2
0
0
0
0
3
2
2
2
0
1
2
1
2
2
1
2
0
0
2
1
1
2
1
2
0
1
2
2
1
0
0
2
2
0
1
0
0
1
1
2
1
2
0
2
0
0
1
0
2
2
2
1
0
2
2
1
1
0
2
1
0
0
1
1
3
1
1
2
0
2
2
1
0
1
0
1
1
0
1
0
0
0
0
0
0
1
1
1
0
3
1
2
2
1
2
1
0
4
2
0
2
1
0
1
1
2
2
0
0
0
1
1
1
0
1
0
1
0
2
0
0
1
1
2
1
1
0
0
1
2
2
0
0
2
1
0
2
0
0
1
0
0
0
1
0
1
1
1
1
0
1
2
0
1
0
2
0
0
0
0
2
0
0
1
1
1
1
0
2
1
2
0
2
2
2
1
2
1
0
0
1
1
1
2
1
0
1
1
0
0
1
0
1
3
1
0
1
0
1
0
2
0
0
0
0
1
2
1
0
2
2
2
0
2
1
2
2
0
2
2
3
0
2
1
1
3
0
2
0
1
2
0
2
0
0
2
0
1
1
0
0
0
0
1
1
1
1
1
1
0
1
0
0
2
1
2
1
0
1
2
0
1
0
1
1
0
0
1
1
1
0
0
0
0
2
0
2
0
0
0
2
2
2
0
2
2
0
0
0
1
1
2
0
1
2
1
0
1
1
0
4
1
0
2
2
1
1
1
1
1
2
0
1
3
1
0
2
2
0
1
0
1
1
1
3
1
1
1
1
0
2
2
0
1
0
0
1
1
1
1
0
2
0
1
0
0
0
1
0
2
0
1
1
2
0
2
0
2
1
0
1
0
1
3
1
2
0
1
0
1
2
1
2
2
0
1
0
1
1
2
2
2
1
0
1
0
0
1
0
0
0
0
0
1
2
1
2
0
2
1
0
1
0
0
2
0
0
1
1
2
0
2
0
0
0
0
2
1
1
1
0
1
2
1
0
2
1
1
1
1
1
1
1
0
1
0
0
0
2
0
1
2
2
1
0
1
0
2
0
2
0
0
0
0
0
0
0
2
0
1
1
0
0
1
2
2
1
1
1
0
0
2
1
2
0
0
0
1
1
0
1
0
0
1
0
1
0
0
2
1
0
1
2
1
0
1
2
2
2
0
1
1
0
1
1
0
1
0
0
0
1
2
1
0
0
1
0
0
0
2
0
1
1
1
0
0
1
1
0
2
0
0
0
0
0
0
3
1
1
1
0
1
0
0
0
1
1
1
1
0
1
2
0
0
1
0
1
0
0
0
1
1
1
0
1
1
1
0
1
2
0
1
1
0
0
0
0
2
2
1
2
0
1
0
2
0
1
1
1
1
0
0
2
0
2
0
1
1
1
0
0
0
1
2
0
0
0
2
0
1
1
1
2
1
1
1
2
2
1
0
0
0
1
1
1
1
1
3
0
1
2
1
2
1
0
1
1
2
1
1
1
0
1
1
1
0
1
2
0
1
1
2
2
0
1
1
1
1
1
2
2
1
2
1
2
1
1
0
1
0
2
0
1
1
2
1
1
1
1
0
1
2
3
1
1
0
1
0
1
0
1
0
0
0
0
0
1
1
2
0
0
1
0
2
1
0
1
0
2
1
1
2
1
1
1
0
1
0
1
0
0
0
1
1
0
1
0
0
1
1
3
1
1
0
3
2
1
1
1
0
0
0
0
2
0
1
1
0
0
0
1
1
0
0
0
3
0
1
0
1
0
2
1
1
0
1
1
0
0
1
0
1
0
2
2
0
1
1
2
1
1
0
0
2
2
2
0
2
0
1
0
1
0
2
0
2
2
2
0
0
1
2
0
0
0
0
0
2
1
2
0
1
0
0
0
0
1
0
2
0
0
0
2
1
1
1
2
2
3
2
1
0
1
0
0
2
0
2
1
1
1
0
0
1
1
2
2
0
0
1
0
2
0
1
0
1
1
0
0
2
1
1
1
0
1
0
0
2
1
0
0
1
1
0
1
0
2
0
0
2
1
1
2
1
2
0
1
2
1
1
2
0
1
1
0
2
1
2
2
1
1
0
2
0
2
1
1
1
0
0
2
2
1
0
0
0
0
1
0
1
0
0
1
0
0
1
1
0
1
0
1
0
2
1
0
1
2
0
2
0
2
1
2
0
0
1
1
1
0
0
0
2
1
0
0
1
0
2
0
1
1
0
0
1
1
0
0
2
0
2
1
1
1
2
1
2
1
1
0
1
0
0
1
2
0
1
0
0
1
1
2
0
0
0
0
1
2
1
1
0
0
0
2
1
2
0
0
2
0
2
0
0
0
0
1
1
2
0
0
0
0
0
0
0
1
1
0
2
1
1
0
1
0
2
2
0
1
2
0
0
1
0
2
0
1
0
1
0
0
2
2
2
1
2
3
0
1
0
2
0
1
1
2
2
1
0
0
0
1
0
3
2
1
1
0
1
2
1
2
0
0
0
3
0
1
2
1
2
1
0
1
3
0
0
2
2
1
0
1
0
0
1
0
0
1
0
0
0
3
1
1
0
2
0
2
0
2
1
2
0
1
1
1
0
1
0
0
0
1
1
1
1
0
1
2
0
1
1
0
1
0
0
1
0
1
2
0
0
0
0
1
1
1
0
2
2
0
1
1
0
0
2
1
1
0
1
1
1
1
0
0
0
0
0
0
2
2
0
2
1
2
1
1
2
0
0
2
2
1
0
2
2
1
2
1
1
0
0
2
2
1
2
2
0
1
0
2
0
1
0
1
0
1
1
0
2
2
0
1
0
0
0
0
2
0
0
1
0
2
0
2
1
1
0
1
0
1
1
2
1
1
1
0
1
1
1
1
1
0
0
2
0
0
1
2
0
0
1
0
0
0
1
0
2
3
0
1
1
0
1
0
0
2
0
1
0
1
0
1
1
1
1
1
1
0
2
1
1
0
2
1
0
2
2
1
2
2
0
0
1
0
1
0
1
2
1
0
0
0
0
0
1
2
2
1
1
0
0
0
1
2
1
2
0
0
1
0
0
0
0
1
0
1
2
2
2
2
1
1
0
2
0
2
0
0
2
0
1
0
0
2
0
2
0
2
0
1
1
0
1
2
0
0
2
2
0
2
0
1
0
2
2
0
1
0
0
1
0
0
1
0
2
0
1
0
2
1
1
2
1
1
1
2
0
0
0
2
1
0
0
0
1
0
0
0
0
2
1
0
1
2
0
0
0
1
1
0
2
1
0
2
2
1
0
2
2
0
2
1
1
1
1
0
2
0
1
0
1
0
1
0
0
2
1
0
0
0
0
2
0
0
1
1
0
0
2
0
0
0
1
0
0
0
1
0
2
1
2
0
0
1
1
0
0
0
1
0
1
2
1
1
0
1
1
1
0
1
1
1
1
1
1
0
2
1
2
0
1
0
0
3
2
0
0
1
1
2
0
1
0
1
1
2
0
1
0
1
0
1
0
1
0
1
1
1
0
1
1
1
2
0
2
0
2
0
0
2
0
1
1
2
0
2
0
0
1
1
2
0
0
2
0
2
1
1
1
0
0
1
1
2
2
0
1
0
0
2
1
1
2
1
2
0
1
0
0
0
0
1
1
2
1
0
0
1
1
1
2
0
2
1
1
1
1
1
2
1
0
1
0
0
2
1
1
0
3
2
1
0
0
0
1
2
0
0
1
1
1
1
1
0
0
1
5
1
0
2
1
2
0
2
0
0
0
0
0
1
1
2
0
1
1
0
1
2
1
0
1
2
0
1
1
2
1
0
1
1
0
1
0
1
0
1
1
1
2
0
0
2
1
0
2
0
0
0
2
1
0
0
2
1
1
1
2
1
0
0
0
2
0
2
3
1
1
2
1
1
1
0
2
1
2
0
2
1
0
1
1
0
1
1
1
3
1
2
0
0
2
1
0
2
0
2
2
1
0
1
2
1
2
1
0
1
0
2
0
2
0
2
0
1
1
1
0
2
2
1
1
0
2
1
0
1
0
2
2
2
1
0
1
1
1
1
1
0
0
1
2
0
0
1
2
1
0
0
0
1
1
1
0
1
2
1
0
1
1
1
0
0
0
0
0
1
2
0
0
1
2
1
1
1
1
1
0
2
0
0
0
1
0
1
1
1
1
0
0
2
2
4
2
2
0
0
1
0
1
1
0
1
0
0
2
2
0
2
1
0
2
1
1
0
0
2
1
1
1
1
1
2
2
0
1
0
0
1
0
0
1
2
1
0
1
0
1
0
1
0
1
0
2
0
1
0
2
1
2
0
0
0
0
0
0
2
1
2
1
0
0
3
1
2
2
1
0
1
0
1
2
0
0
0
0
2
0
2
1
1
1
0
1
0
0
1
2
2
1
0
0
1
0
2
1
1
0
0
2
1
2
0
0
2
0
0
1
0
1
0
0
2
0
1
1
0
0
0
2
0
0
2
2
0
0
0
1
0
0
1
1
1
2
2
0
0
0
0
7
1
1
0
1
0
2
2
2
1
2
0
2
0
1
1
0
2
0
2
1
0
3
1
0
1
1
0
1
1
0
1
1
0
2
1
1
0
1
0
1
2
1
0
1
1
1
1
0
2
0
2
0
2
2
1
1
0
2
0
1
0
0
0
1
0
2
0
0
1
1
0
0
0
1
2
2
2
1
1
1
0
0
0
2
1
0
1
1
1
1
1
2
1
2
0
2
1
0
0
0
1
0
1
1
0
0
0
0
0
2
2
1
1
1
1
0
1
0
1
0
1
0
1
1
1
0
1
0
0
0
1
0
0
1
1
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
1
1
1
0
1
1
0
0
3
2
1
0
2
0
1
0
0
0
0
1
2
0
1
1
1
1
2
0
0
1
3
1
1
1
1
0
1
1
0
0
4
1
0
1
0
1
1
1
0
0
1
1
0
0
1
2
1
3
1
2
0
1
1
1
0
0
2
0
1
1
1
1
1
2
0
0
1
3
0
1
0
0
2
2
2
2
0
1
1
1
1
1
0
1
1
1
0
0
0
1
0
2
1
0
3
1
1
0
0
1
3
1
1
0
1
0
1
2
0
1
2
3
1
0
1
1
0
1
0
2
1
1
1
1
2
2
0
1
0
1
1
0
0
0
2
2
0
1
2
2
1
0
1
1
1
2
1
1
1
0
1
0
2
1
1
2
2
1
0
0
0
2
0
1
1
2
0
2
0
1
2
0
2
0
1
1
2
1
0
0
0
2
1
0
0
2
0
1
1
1
1
1
1
0
0
0
0
0
0
0
2
2
1
0
1
1
1
2
1
1
1
2
1
1
0
0
1
1
1
1
2
2
2
2
0
0
0
0
2
0
2
0
2
2
1
2
2
1
0
1
2
0
1
0
1
0
1
0
0
2
1
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
1
1
0
0
1
0
1
1
1
0
1
1
0
1
1
0
0
1
0
0
1
0
1
2
2
0
0
1
0
1
1
1
2
0
0
0
0
2
0
1
0
2
0
1
0
0
2
2
2
0
1
3
0
0
0
2
2
0
0
0
0
2
1
0
1
3
1
0
2
0
5
1
1
0
0
0
0
1
1
0
1
0
1
0
1
1
0
3
2
1
0
1
1
0
0
1
1
2
0
0
0
0
1
2
0
0
0
2
0
0
0
0
2
0
0
0
1
0
4
0
1
2
2
1
0
1
0
0
1
0
0
0
0
0
2
2
0
1
0
2
0
0
0
2
0
1
1
0
2
0
2
0
2
3
0
0
2
1
1
0
2
3
3
1
2
1
2
1
0
1
0
0
1
0
2
1
1
0
1
0
1
0
2
2
1
1
0
0
0
0
2
1
0
1
0
1
2
2
0
0
0
2
1
0
0
1
1
0
1
2
0
2
1
2
0
0
0
1
1
1
1
0
1
2
0
0
0
1
1
1
3
2
2
2
0
0
2
1
0
2
1
0
0
0
1
1
1
1
1
2
1
0
1
0
2
0
3
1
0
2
0
0
0
1
0
0
2
1
4
1
0
1
2
2
0
1
0
0
1
0
1
2
0
0
2
1
0
0
0
0
1
1
1
0
0
0
0
1
1
0
1
2
0
1
0
0
1
1
1
2
0
1
1
2
1
0
1
3
1
2
3
2
0
0
0
1
0
0
1
2
2
1
1
1
0
0
1
2
0
0
1
0
1
0
1
2
1
1
0
2
0
1
2
0
3
1
0
0
1
0
2
2
1
0
2
2
1
1
0
0
3
5
1
0
1
0
0
0
1
2
1
2
3
2
1
0
0
0
2
0
2
1
0
0
1
1
1
0
1
2
2
0
1
0
0
0
1
0
2
1
0
1
0
1
1
0
1
5
2
1
0
0
1
2
1
1
1
1
0
0
1
0
0
0
0
0
4
0
1
1
0
1
0
1
0
0
1
1
2
1
2
2
2
1
2
0
0
2
0
1
1
0
1
1
1
0
2
0
0
1
1
0
0
2
0
0
2
1
1
2
2
2
2
0
1
0
2
0
1
2
2
2
2
1
0
1
1
1
0
0
0
1
0
1
2
2
1
0
0
0
1
2
1
1
1
0
1
1
0
0
0
0
0
1
2
0
0
1
2
0
0
0
2
0
0
2
2
0
2
1
1
1
1
0
0
1
2
1
1
0
0
1
0
0
1
1
1
1
0
0
0
1
0
3
2
0
1
1
1
2
0
1
0
1
1
2
0
0
1
2
2
3
1
2
0
1
1
2
0
0
1
1
1
0
0
2
0
1
0
0
5
2
1
0
1
2
1
0
0
1
2
2
2
1
1
0
2
1
0
0
2
1
0
1
0
0
2
0
1
1
0
0
0
0
2
1
1
0
1
0
1
1
1
2
0
0
0
2
0
1
2
0
0
1
2
2
2
1
2
0
0
0
1
0
2
0
0
1
0
1
1
1
0
1
0
3
1
1
0
2
2
1
1
1
1
1
1
0
1
1
0
0
1
1
2
2
1
0
0
2
2
2
0
1
1
0
2
0
1
0
0
1
4
2
2
1
0
0
0
1
0
1
2
0
0
1
0
0
1
0
0
0
1
1
2
0
0
1
0
2
1
2
0
0
0
1
1
1
1
1
1
2
0
2
1
1
1
0
2
1
1
0
3
1
0
0
0
2
1
1
2
1
0
0
1
1
1
2
1
1
0
2
2
0
1
0
0
1
1
1
0
1
0
2
1
2
2
0
0
0
2
1
1
1
1
2
1
2
1
0
2
2
1
2
1
2
0
2
2
0
2
0
0
1
1
0
2
0
2
3
1
0
1
1
0
2
1
2
1
0
0
2
2
2
1
1
2
2
0
3
2
0
2
0
0
1
2
4
0
1
1
1
2
2
0
0
1
0
0
1
2
0
2
1
2
1
1
2
0
1
1
1
0
2
2
0
1
0
1
1
2
0
2
1
1
0
1
1
2
1
1
2
0
1
2
1
2
0
1
0
0
0
2
0
1
2
0
1
1
0
0
2
1
0
1
0
1
0
2
1
1
1
1
1
1
0
1
0
1
2
1
0
0
0
1
2
0
2
2
2
1
0
0
0
0
1
1
0
0
0
0
2
0
1
1
1
0
1
2
2
2
3
0
0
6
0
1
2
1
0
0
0
2
0
1
0
1
1
2
1
1
2
2
1
1
0
0
0
1
1
2
1
0
1
2
2
0
1
1
0
1
2
0
1
2
1
1
2
1
0
0
1
0
0
1
1
2
0
0
0
2
0
0
0
2
0
0
0
2
2
0
1
1
1
2
0
1
0
1
0
1
1
2
0
1
0
2
0
2
2
2
0
1
1
1
0
1
1
1
0
0
1
0
2
2
0
1
1
0
1
1
1
1
0
0
0
1
0
2
1
1
1
0
0
1
1
2
2
0
1
0
0
2
1
0
0
1
1
1
1
1
1
1
0
0
1
0
1
0
2
2
1
1
0
0
1
1
2
1
2
0
1
0
0
2
1
0
3
0
0
1
2
1
2
1
0
2
2
0
1
0
1
0
1
0
1
0
1
2
2
2
0
1
1
1
3
1
1
1
1
1
2
0
0
2
2
0
1
2
2
0
0
1
2
0
0
1
0
0
0
1
1
1
1
1
1
2
2
0
2
1
0
2
2
0
0
0
1
2
1
0
1
0
1
1
0
0
1
2
0
1
1
1
0
2
0
2
1
3
2
2
0
0
1
1
1
0
2
1
1
0
0
1
0
0
1
2
1
0
2
1
1
0
1
1
2
1
2
0
0
1
0
2
0
0
0
1
0
1
0
1
4
2
1
0
0
1
0
1
1
0
0
1
2
1
0
1
0
0
0
0
1
0
0
2
0
2
0
1
0
0
0
1
1
2
1
0
2
0
0
1
0
1
2
1
1
1
1
0
0
0
3
0
0
0
1
1
1
0
0
1
0
2
0
1
0
1
0
1
1
1
0
0
1
2
0
2
2
1
1
2
0
0
1
2
0
1
1
0
0
1
0
0
1
0
2
2
0
1
0
0
0
0
0
1
0
1
1
0
1
0
1
2
1
1
1
2
0
2
2
1
3
0
1
2
1
2
0
1
2
0
0
0
0
1
1
1
1
0
1
1
1
1
2
0
1
2
0
0
1
1
1
0
1
0
1
0
1
1
1
0
1
1
1
1
1
1
0
0
2
3
0
0
1
1
1
2
1
0
1
0
0
1
2
1
1
1
2
0
2
0
0
0
1
1
1
1
0
1
1
0
0
0
0
2
1
1
2
0
1
1
0
2
2
0
0
1
2
0
2
0
0
0
0
0
0
1
0
1
1
1
1
0
1
1
2
0
0
0
1
1
0
1
2
0
0
0
0
0
1
1
2
0
2
3
0
0
0
0
1
1
2
1
1
0
0
3
1
0
0
1
0
2
0
0
0
0
0
1
0
1
2
1
0
2
0
2
1
2
1
0
0
2
2
2
0
0
1
1
1
2
1
0
1
0
2
2
1
1
2
1
1
0
1
2
4
2
1
2
1
0
1
0
0
0
1
0
1
0
2
0
1
2
1
2
2
1
0
1
1
0
0
1
0
0
1
1
1
0
0
0
1
0
0
1
0
0
1
1
1
2
1
1
1
0
1
1
1
1
1
1
1
0
0
1
1
0
1
0
1
0
1
2
2
1
2
1
0
1
2
1
1
2
0
1
1
0
1
1
0
0
1
0
0
1
1
1
0
1
0
1
2
1
1
0
0
0
0
1
1
0
2
0
2
0
0
0
0
0
1
0
0
0
1
0
1
0
1
1
2
1
0
2
1
1
1
2
2
0
0
7
0
0
0
2
0
2
1
1
0
0
0
0
1
1
1
2
0
1
1
1
1
0
1
2
1
1
1
1
1
0
2
0
1
0
1
1
2
1
1
1
1
0
1
0
0
0
0
2
0
2
0
1
1
1
0
0
1
0
2
2
1
0
1
1
3
1
0
0
1
0
1
1
1
1
2
1
1
0
1
0
1
0
1
0
0
0
1
1
2
0
0
2
2
0
1
0
2
1
2
2
2
0
0
3
1
1
0
1
1
0
0
2
1
0
1
1
0
1
1
0
1
1
1
1
1
1
2
1
1
2
2
0
1
2
2
0
0
0
0
2
2
1
2
1
0
2
1
1
2
0
1
2
2
0
0
1
1
0
1
1
0
0
2
0
0
0
0
1
0
1
0
2
0
1
1
1
2
0
1
1
1
2
0
0
1
2
1
2
0
1
0
0
0
2
0
0
0
0
2
1
1
1
2
1
1
1
1
0
1
0
1
0
2
2
1
1
0
1
0
0
1
0
1
0
2
1
0
2
1
0
1
0
0
2
0
1
1
0
0
0
0
1
1
0
1
2
0
0
1
1
0
0
1
0
0
1
1
0
2
2
0
1
0
1
0
0
0
1
2
2
0
0
1
2
0
2
0
0
1
0
1
2
1
2
1
0
0
0
1
0
1
1
0
2
0
0
1
2
1
2
0
2
0
0
2
2
1
2
2
0
1
1
0
0
1
0
1
1
1
1
0
1
1
1
0
0
1
0
0
1
2
0
0
2
1
0
1
0
2
2
2
0
1
1
2
1
1
0
2
2
2
0
1
2
0
0
1
0
0
1
0
0
1
2
0
1
1
0
1
1
1
2
1
1
0
1
1
0
0
1
3
0
1
0
1
2
1
0
1
0
0
1
1
0
0
2
2
0
1
0
0
0
0
0
1
1
1
0
0
1
2
1
1
1
1
3
2
1
1
0
1
0
3
1
1
2
2
0
2
1
0
1
1
1
1
0
1
1
0
0
1
0
1
1
1
2
1
1
1
2
2
0
1
1
2
2
2
0
3
0
1
1
1
0
2
2
0
0
1
1
0
1
1
0
0
1
0
0
1
0
1
2
2
0
1
0
0
1
0
0
1
2
0
2
8
0
0
2
2
0
0
0
0
1
0
3
1
0
1
0
2
0
1
2
1
1
0
0
0
1
0
0
1
1
0
2
0
0
0
2
2
2
1
1
2
0
1
1
1
0
0
1
1
1
0
0
1
0
0
0
0
1
1
0
1
0
1
0
0
1
1
1
0
2
1
2
1
3
0
0
1
0
0
0
0
1
0
0
1
0
1
1
0
0
2
2
1
2
1
1
2
1
1
0
1
0
0
0
0
2
2
0
0
0
1
1
0
0
1
2
1
0
1
1
1
2
2
1
0
1
0
1
0
1
3
1
1
0
0
1
1
1
0
1
1
1
0
0
0
0
1
2
1
1
2
3
2
1
1
1
1
0
0
2
1
1
0
2
0
0
1
0
1
1
2
2
2
2
1
1
2
0
1
1
0
2
1
1
1
0
0
0
2
1
0
0
2
1
0
1
0
0
3
2
1
2
1
0
0
1
0
2
0
0
2
0
1
1
0
1
2
1
1
1
0
1
1
0
1
1
0
2
2
0
1
1
2
1
2
1
2
0
0
0
0
0
1
1
1
0
0
2
0
1
2
2
1
1
0
1
2
2
2
2
0
1
0
0
0
2
1
0
1
1
2
0
1
1
0
2
0
1
1
0
0
1
0
0
1
1
1
0
1
0
2
0
2
0
0
1
1
1
1
1
0
0
1
2
0
0
2
2
1
0
0
0
0
1
0
2
0
2
0
2
2
0
0
0
0
2
0
1
0
1
2
0
1
0
0
1
0
0
1
1
0
1
0
1
0
1
1
2
0
2
1
0
1
1
1
0
0
3
0
0
2
1
1
1
2
1
0
2
0
0
2
2
0
2
2
0
0
0
3
2
1
2
2
1
1
1
0
2
1
0
2
1
0
0
1
1
2
0
0
2
1
1
1
0
0
1
1
1
1
0
0
1
1
2
2
2
2
1
1
1
2
1
0
0
0
1
0
0
1
2
1
1
1
2
2
2
1
2
0
1
1
2
1
1
0
1
1
0
1
1
2
0
2
1
0
0
2
0
0
1
0
0
0
0
1
2
1
0
0
2
1
0
2
1
2
1
1
2
1
0
0
2
0
0
0
2
1
2
0
0
0
1
2
1
1
0
2
1
1
0
1
0
1
0
1
0
0
0
2
0
0
1
2
0
0
1
0
0
0
1
1
1
2
1
2
0
0
0
0
0
1
2
3
2
1
0
1
2
1
1
1
0
2
2
1
0
2
1
2
0
1
0
2
0
1
0
2
1
1
2
0
1
2
1
1
0
0
0
1
1
2
0
1
2
0
0
1
0
1
0
2
1
0
2
1
0
0
1
1
1
1
1
1
0
1
0
0
2
0
2
3
0
0
1
2
0
1
2
0
1
1
2
1
1
0
2
1
0
1
1
0
0
0
0
2
0
1
0
1
2
0
0
0
0
1
1
0
1
2
0
1
0
1
2
1
0
3
0
1
1
2
1
1
2
3
1
0
0
1
0
1
0
0
0
1
0
2
1
0
1
0
1
1
1
2
1
0
0
0
1
1
0
0
0
1
2
0
0
1
0
0
2
1
2
0
1
1
2
0
2
0
2
2
0
0
1
1
2
1
0
0
0
0
0
1
1
2
2
1
1
1
2
2
1
0
1
0
1
0
0
1
1
2
0
0
0
1
0
0
2
2
2
2
1
2
0
1
1
0
2
1
1
1
2
0
0
2
1
1
1
1
1
1
0
2
0
1
2
2
1
0
2
1
1
0
1
0
0
0
0
0
0
0
2
1
1
3
0
1
0
0
0
0
2
0
2
1
3
0
3
0
2
1
1
0
0
2
2
0
1
1
1
2
0
2
0
0
1
1
0
2
2
1
1
2
0
0
0
2
1
2
0
0
1
0
2
1
1
0
0
0
2
0
0
0
2
1
2
1
0
1
0
0
2
2
1
0
1
2
0
1
1
1
0
0
0
1
2
0
1
2
1
0
0
0
0
1
1
1
2
0
0
1
1
0
0
0
1
1
0
1
2
1
1
0
1
0
0
3
1
1
1
0
2
2
2
0
2
0
1
1
1
0
1
0
1
1
1
0
1
1
1
1
0
0
1
0
0
1
0
1
2
1
1
2
1
0
0
0
2
0
0
0
2
2
1
1
2
0
0
1
2
0
1
2
0
1
1
1
1
0
2
2
0
1
0
0
1
4
2
1
1
1
1
0
1
2
1
1
0
1
1
1
1
0
1
0
0
0
1
1
1
2
0
2
0
1
0
0
0
2
0
1
1
1
1
0
1
2
1
0
0
0
1
0
1
1
2
3
0
1
2
0
1
1
0
1
0
2
1
1
1
0
2
2
0
0
0
1
0
1
2
2
0
1
2
1
0
0
2
0
3
1
0
1
1
0
0
1
2
0
0
2
1
0
0
1
0
2
2
0
0
1
0
2
0
0
1
0
1
0
2
1
0
1
0
1
0
0
2
1
0
0
0
2
1
1
1
0
0
1
2
2
1
2
0
0
0
1
0
1
0
0
2
0
0
0
0
1
1
1
1
2
0
1
2
1
2
3
0
1
2
0
1
2
1
1
0
0
0
0
0
1
1
1
1
2
0
1
2
2
0
1
1
1
1
2
1
0
1
2
1
1
2
1
2
0
1
0
0
0
0
1
0
2
0
1
1
1
1
2
0
2
2
2
1
0
1
7
0
1
1
0
2
3
1
1
1
0
1
0
2
0
1
1
1
1
2
1
2
2
1
1
0
2
0
2
1
1
2
1
0
0
1
0
1
1
0
0
2
1
2
0
1
1
0
2
0
1
0
2
1
2
1
0
1
2
1
0
1
1
1
0
1
1
0
0
2
0
0
0
2
2
2
1
0
1
1
0
0
2
1
0
3
1
1
2
0
2
0
0
0
2
1
0
2
0
0
1
2
0
1
1
0
0
0
2
1
0
0
0
1
2
1
2
1
0
2
1
0
0
2
0
0
1
0
0
2
1
0
0
0
1
0
0
2
0
1
0
0
1
0
1
0
1
1
0
0
1
1
1
0
0
0
2
1
0
1
0
1
1
0
1
2
1
1
0
1
1
2
0
0
0
0
0
1
2
1
0
0
1
0
2
1
2
1
1
0
1
1
1
1
1
2
0
1
1
1
0
1
1
1
1
2
0
1
0
1
1
1
2
1
0
0
1
2
1
0
1
1
0
1
2
2
0
1
1
0
2
1
3
0
2
2
1
2
2
0
1
1
1
1
2
0
2
1
2
0
0
2
1
0
1
1
1
1
1
0
2
1
1
0
1
2
1
1
1
2
0
1
0
0
1
1
0
2
0
0
1
0
0
1
1
1
0
1
0
1
1
1
0
2
1
1
0
0
0
0
0
0
0
1
2
0
0
2
1
1
0
1
0
1
1
2
0
2
2
0
0
1
2
1
2
0
3
0
1
0
1
1
0
1
1
2
1
2
0
1
0
1
1
5
1
2
2
0
2
0
2
0
1
1
0
0
2
0
0
2
0
2
1
1
2
1
1
0
1
1
2
0
0
0
1
0
1
1
2
2
1
0
1
1
0
1
1
0
0
0
0
1
2
1
1
1
1
0
1
0
2
2
0
1
0
0
0
1
0
0
1
0
1
1
1
2
1
0
1
0
0
0
2
1
1
1
0
1
1
2
1
2
2
2
1
0
2
2
0
1
1
1
1
1
1
0
0
0
2
2
2
1
3
0
1
1
2
0
0
1
0
0
0
1
2
1
0
1
0
0
0
0
0
0
1
0
0
1
2
0
2
2
1
1
1
2
1
2
1
1
0
0
2
2
0
0
1
0
0
0
1
0
0
0
2
1
2
1
1
0
1
1
1
1
2
1
1
0
0
1
0
1
1
1
1
1
1
1
1
1
0
0
0
1
0
1
0
0
0
1
0
0
1
1
1
1
1
1
1
0
1
0
4
1
1
1
1
0
1
2
0
2
0
0
0
1
0
0
0
1
2
1
2
1
2
2
0
0
1
0
0
1
1
0
2
0
0
0
0
0
0
0
1
2
1
1
1
1
0
1
1
0
1
1
0
1
2
2
0
0
2
0
0
1
1
1
2
1
0
0
0
1
2
0
0
1
0
2
1
1
4
2
1
1
0
1
2
1
0
2
2
0
1
0
2
1
1
1
1
1
0
0
1
1
1
2
1
1
1
2
1
2
0
2
0
1
0
1
0
0
1
1
0
1
0
2
1
2
2
1
1
2
0
2
0
0
1
1
1
0
2
2
0
2
1
2
1
0
1
0
1
0
1
0
1
0
1
2
3
1
1
1
0
0
2
0
0
0
1
0
2
0
0
1
2
1
1
0
1
0
0
1
1
1
2
0
1
0
0
0
1
1
1
1
2
1
2
0
0
1
2
1
1
0
1
1
2
0
2
1
0
0
0
0
0
1
2
1
1
0
1
2
0
1
0
1
0
1
0
1
2
1
0
1
2
2
0
2
0
0
0
0
1
1
0
2
0
0
2
0
2
2
0
1
1
1
0
1
0
2
1
1
1
1
0
0
2
0
1
1
2
0
1
1
1
0
0
2
1
1
0
1
0
2
0
5
0
2
0
3
0
0
1
1
2
1
1
1
0
1
1
2
0
2
1
0
0
1
1
0
0
1
2
2
1
0
0
2
2
0
2
1
1
1
1
0
2
2
0
2
0
0
0
1
2
1
1
0
0
2
2
1
1
1
2
1
2
1
1
2
0
0
1
1
1
0
1
0
0
0
0
1
1
0
0
0
1
2
0
1
1
2
2
2
0
0
1
2
1
0
1
1
0
0
0
0
2
0
2
2
1
2
2
0
0
0
1
2
0
1
0
0
2
1
0
1
0
2
2
3
1
1
1
0
0
0
0
1
1
2
2
0
1
1
1
1
1
4
3
1
2
1
0
0
0
1
1
2
0
1
1
0
1
0
2
1
0
2
1
2
2
0
0
1
0
1
2
0
1
1
1
0
1
0
2
2
3
1
0
0
2
1
0
0
1
1
0
2
2
0
1
0
3
0
0
1
1
0
1
2
0
0
1
1
1
1
0
2
1
1
0
2
1
0
1
1
2
0
0
1
0
0
0
2
2
0
1
1
2
1
2
1
2
2
2
0
1
1
0
1
0
1
0
1
1
2
1
0
1
0
0
2
0
0
2
3
2
1
2
2
1
0
1
0
3
0
2
1
1
2
2
2
2
0
2
1
0
1
1
1
0
2
0
0
0
0
1
1
2
1
0
0
3
0
0
0
2
1
2
0
2
1
1
0
2
1
1
2
1
0
1
1
1
0
0
1
0
0
0
0
0
0
1
1
0
1
1
0
1
2
1
2
1
0
2
1
2
1
0
1
2
2
1
0
1
0
1
1
1
1
1
2
1
3
0
1
0
0
0
0
2
1
3
0
1
0
2
1
1
1
1
0
2
0
1
0
1
0
1
1
2
0
1
1
1
1
1
0
2
1
1
0
2
0
1
2
3
1
0
0
0
1
2
1
1
1
0
2
1
1
0
0
1
1
1
2
2
2
0
1
1
0
0
0
0
2
1
1
1
0
1
0
1
1
0
0
0
0
1
1
0
0
0
1
1
1
2
0
1
2
2
0
1
0
0
0
2
1
1
1
0
1
2
1
1
0
0
1
0
0
4
1
1
2
1
2
1
2
1
0
0
2
1
1
2
0
1
0
0
1
0
2
2
1
1
2
0
1
0
1
0
1
1
1
0
2
0
1
0
0
1
0
1
0
1
1
1
1
2
1
1
0
2
2
1
0
1
1
2
0
1
0
0
0
1
1
2
1
0
0
0
2
0
1
1
1
1
0
1
0
1
0
1
0
2
0
0
0
1
1
1
1
1
0
1
1
1
0
2
1
0
1
0
1
0
2
2
0
1
2
0
2
2
1
1
0
0
0
0
1
2
0
0
0
0
1
2
1
0
2
2
1
1
1
0
1
2
0
1
0
2
1
1
1
0
0
1
0
1
1
0
1
1
0
0
1
2
2
1
1
1
0
1
1
2
2
0
1
0
0
0
0
0
2
0
1
0
3
0
3
0
1
0
1
0
0
0
2
1
1
1
2
1
2
0
0
2
0
0
1
2
1
0
2
0
1
2
2
1
1
0
1
1
1
2
2
1
2
0
2
1
1
1
0
1
1
2
3
0
0
1
1
1
0
0
1
0
0
0
2
1
1
1
2
2
0
0
0
1
0
0
0
2
1
0
0
0
1
1
2
2
1
0
0
0
0
2
2
0
0
1
0
0
0
0
1
1
2
1
0
0
1
2
1
2
4
1
0
0
1
2
0
0
0
0
0
1
1
1
0
2
0
0
0
6
1
1
1
1
0
1
0
1
0
2
0
1
2
0
2
0
0
0
2
0
0
2
1
1
2
2
2
2
1
1
1
0
2
0
2
1
2
0
3
0
1
1
1
1
0
0
1
1
1
0
2
1
1
0
1
1
1
0
2
0
0
0
1
0
1
0
2
0
1
3
0
3
1
0
0
3
1
2
0
1
0
0
0
2
0
2
1
1
1
3
0
2
1
1
1
2
1
0
0
1
2
0
0
0
0
0
3
1
2
1
0
2
0
1
1
1
1
1
0
0
1
1
0
1
0
1
0
1
2
1
1
0
1
0
0
0
2
0
2
1
2
0
0
0
0
0
1
0
0
1
1
1
1
1
2
1
1
0
0
0
0
1
1
1
0
1
2
2
1
3
0
1
0
1
0
1
1
2
1
1
1
1
1
1
1
1
0
2
1
0
1
0
0
1
0
1
0
3
2
1
0
2
0
2
1
0
0
0
0
0
0
0
2
2
0
3
1
0
0
1
1
0
2
2
2
0
0
1
1
1
1
0
1
0
0
2
2
1
0
0
0
1
0
0
1
0
0
1
2
1
0
1
0
2
1
0
0
1
2
1
1
0
2
2
0
0
2
1
1
1
0
2
1
2
0
12
2
1
1
1
0
0
0
0
0
0
1
1
1
1
0
0
0
1
2
0
1
0
0
2
1
0
1
1
1
2
2
0
2
1
0
0
0
2
1
0
1
2
0
2
2
2
1
0
0
1
1
1
3
0
1
1
0
2
1
0
1
0
1
0
1
2
2
0
2
2
0
0
2
2
1
0
1
1
1
0
1
2
0
2
1
2
0
3
2
3
1
2
0
0
0
2
1
0
1
0
2
0
1
2
1
1
1
0
0
2
0
1
2
2
0
0
0
2
1
0
0
1
1
1
0
0
0
0
0
0
0
1
2
0
2
1
0
0
0
2
1
3
1
0
1
0
0
1
0
1
0
1
0
1
1
1
2
3
1
0
2
0
1
2
4
1
0
0
1
1
2
0
0
0
2
2
1
1
2
1
1
1
0
2
0
0
0
1
2
0
1
0
1
0
0
1
2
1
0
0
0
1
0
0
1
2
1
3
2
1
0
1
0
1
1
0
1
0
0
1
1
1
1
2
2
1
0
1
2
2
1
1
0
1
1
0
0
1
1
1
0
0
2
0
1
2
0
0
2
1
1
1
1
1
0
1
0
0
0
2
0
1
1
1
1
0
0
2
0
0
1
1
1
1
0
0
1
1
2
0
1
1
1
0
0
0
1
1
1
0
0
2
0
1
1
0
2
1
2
1
2
2
1
0
0
1
3
1
0
0
1
1
0
1
0
1
1
0
2
0
2
0
0
1
2
0
0
2
0
0
1
0
2
0
0
1
2
1
0
1
0
0
1
2
1
2
2
1
1
1
1
0
1
0
2
2
1
1
2
1
2
2
0
1
1
2
1
1
0
2
3
2
2
1
0
0
1
0
0
1
2
0
1
1
1
2
0
2
1
0
2
1
1
1
0
0
1
1
1
2
1
1
0
0
1
1
1
1
0
0
1
1
1
0
2
0
1
1
2
0
2
2
2
0
2
0
2
0
1
0
2
0
3
2
1
0
0
0
0
0
1
0
1
1
0
0
1
1
2
0
1
1
1
2
2
0
1
2
0
2
2
1
1
1
0
0
1
0
1
1
0
1
2
2
2
2
2
1
0
0
1
0
2
0
2
0
1
1
2
0
1
1
1
0
2
1
0
1
1
0
1
1
1
0
0
2
1
2
1
1
1
0
1
1
0
2
1
2
1
1
0
1
0
2
0
1
0
1
1
1
2
3
3
0
0
1
2
2
0
1
2
2
0
2
0
1
1
2
3
1
0
0
1
2
1
1
1
1
1
1
2
3
0
2
0
2
0
1
2
1
0
0
2
1
0
2
1
0
2
0
2
0
1
1
1
0
1
0
0
0
2
1
1
1
1
2
0
0
0
0
0
0
0
1
0
0
0
2
3
2
0
1
2
2
2
2
1
2
1
0
1
2
0
1
1
2
1
2
0
2
2
0
1
1
2
2
1
0
0
0
1
1
0
2
1
2
1
1
1
2
0
1
1
1
0
2
1
0
0
2
2
0
1
1
0
0
1
0
1
2
0
3
0
0
0
1
0
1
1
0
0
0
1
0
0
2
2
2
0
1
0
1
3
0
1
1
2
6
1
2
0
0
2
0
0
0
2
2
0
1
0
1
1
0
0
2
0
0
0
1
1
0
1
0
2
0
0
0
2
2
0
1
0
0
1
1
1
1
0
1
2
0
2
1
0
2
1
0
1
0
0
1
1
2
1
1
1
0
0
0
0
0
0
1
0
1
1
1
2
0
1
2
0
1
1
2
1
1
0
1
0
0
0
1
0
2
0
1
2
0
2
0
1
2
0
2
0
1
1
0
2
0
0
1
1
1
0
0
0
2
0
1
0
0
2
2
2
2
0
1
1
0
0
1
0
1
2
1
0
0
2
1
2
0
0
2
1
0
0
0
1
0
0
1
2
2
6
0
0
2
0
0
0
0
1
0
0
0
0
1
1
2
2
1
0
1
0
1
0
1
0
0
3
0
4
0
1
2
0
0
1
1
0
2
2
0
0
2
0
0
3
0
0
1
1
0
1
1
1
2
1
2
0
1
2
2
1
1
1
1
0
0
1
1
0
1
0
0
2
0
2
0
1
1
0
1
1
1
1
0
0
3
0
0
0
2
2
1
0
3
0
0
0
0
1
2
1
0
0
1
1
0
1
1
1
0
0
1
0
0
1
0
1
0
0
1
1
1
1
2
0
1
1
1
1
2
0
0
0
2
1
1
0
2
1
0
2
0
0
2
0
0
1
2
1
0
0
1
0
1
0
0
0
0
1
0
2
1
1
1
1
0
1
0
0
1
0
0
0
1
0
1
1
0
2
0
1
1
1
0
2
1
1
0
0
1
1
1
0
2
1
1
2
1
2
0
2
0
1
1
0
3
2
0
0
2
0
1
0
2
0
2
0
0
1
2
2
0
2
2
1
2
0
2
0
1
0
1
1
0
0
1
1
0
1
0
0
1
0
0
0
1
1
2
0
0
1
1
1
0
0
1
1
1
0
0
1
1
2
1
0
1
0
1
2
1
1
1
0
0
0
2
0
0
0
2
1
2
1
2
2
0
0
1
0
0
0
0
1
0
1
1
0
2
1
1
2
2
0
2
1
0
2
1
1
0
0
2
0
1
1
1
1
0
3
0
0
1
1
0
0
3
0
0
1
0
0
1
0
1
2
0
1
0
2
0
1
1
0
2
0
1
2
0
0
1
0
2
1
1
1
1
5
0
1
0
0
0
2
1
0
0
2
2
2
0
2
6
0
0
1
1
1
1
0
1
1
0
0
0
0
1
1
1
2
0
0
0
0
1
1
2
1
1
1
1
0
0
0
0
1
1
1
0
1
0
1
2
2
1
2
1
1
1
0
1
2
0
1
1
1
0
1
1
2
2
0
2
2
1
0
1
2
0
0
1
1
0
2
0
0
0
0
1
1
2
1
1
2
2
0
2
1
2
1
0
1
2
0
0
0
2
0
0
0
1
2
2
1
1
1
1
0
2
0
0
0
0
1
1
1
2
1
2
1
0
0
2
1
0
2
0
2
0
1
1
1
2
2
0
0
0
1
1
1
2
0
1
1
4
0
1
0
0
0
0
1
0
1
1
0
2
0
0
0
0
2
1
1
0
0
6
0
1
1
0
1
0
2
1
2
0
0
1
1
0
0
1
1
0
1
1
2
0
1
1
2
0
2
2
1
2
0
1
2
1
0
0
1
0
1
1
2
0
2
1
0
2
1
0
1
1
0
2
1
1
2
0
0
2
2
1
0
0
2
0
2
0
2
1
3
1
0
0
1
0
1
2
2
1
0
1
1
0
0
0
1
1
0
1
1
1
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
1
2
0
0
0
0
0
0
1
1
0
2
2
1
1
0
2
2
2
1
1
2
0
0
1
0
1
2
1
0
0
1
2
3
2
0
1
1
2
0
1
1
0
0
1
1
1
1
2
2
1
0
0
0
2
0
0
1
1
1
0
0
1
1
0
1
0
1
1
2
1
1
1
1
1
0
0
0
1
0
0
2
0
2
0
0
1
0
0
1
1
1
2
0
2
1
1
2
1
0
0
1
2
1
1
1
2
0
2
0
2
0
1
0
2
1
2
0
0
1
2
2
0
3
1
0
1
1
2
0
2
1
1
2
0
0
2
0
1
0
0
0
1
1
2
0
1
0
1
2
0
3
1
0
0
1
1
0
2
1
2
0
1
2
2
0
2
2
2
1
2
2
0
2
0
2
0
0
0
0
2
2
1
0
2
0
1
1
2
0
0
2
1
3
2
2
1
1
0
0
1
1
1
1
0
0
2
1
0
1
2
1
1
1
1
4
0
0
0
0
1
2
2
0
2
1
1
0
0
0
0
0
0
1
0
1
2
1
1
0
2
0
1
0
0
1
1
2
1
0
0
3
0
0
2
0
0
0
2
0
0
0
2
1
0
2
0
0
1
1
0
1
1
0
2
2
2
0
0
1
1
0
1
0
2
0
2
0
1
2
0
1
2
1
2
1
0
2
0
0
2
1
1
0
1
1
0
2
2
0
1
2
1
2
2
2
0
0
0
2
1
1
1
0
0
0
1
1
0
1
0
1
1
1
2
1
2
2
1
0
0
1
1
1
0
1
1
0
1
1
2
1
3
1
1
1
0
1
1
0
0
1
0
1
1
1
0
2
2
1
0
1
0
1
2
1
1
0
0
1
2
2
1
1
2
1
0
2
2
1
0
2
1
0
3
2
1
0
0
0
2
3
1
2
2
1
2
0
0
1
2
0
0
2
1
0
1
0
1
0
2
1
2
2
0
0
0
1
1
2
2
0
1
1
1
0
1
2
0
0
0
2
1
1
1
1
1
0
1
0
0
1
1
0
2
1
1
1
0
1
1
1
1
2
1
5
1
0
0
0
0
1
0
2
1
1
0
2
1
1
0
0
2
0
0
0
1
1
1
0
0
1
1
0
2
0
2
1
0
1
1
0
2
1
0
1
2
1
0
0
0
0
0
0
0
0
3
1
0
2
1
0
0
1
1
2
2
2
1
2
1
1
1
1
2
2
2
0
1
4
1
1
2
1
1
1
0
0
0
0
0
2
1
1
1
2
2
0
2
1
0
1
2
1
0
1
2
1
1
0
0
1
0
1
2
0
0
0
1
2
2
0
1
0
0
2
0
1
2
1
2
3
1
2
2
1
2
1
1
2
1
1
1
0
1
1
1
1
0
1
0
2
0
0
0
1
1
1
0
2
1
1
0
1
1
0
1
0
0
0
0
1
2
2
1
2
1
0
1
1
0
1
1
1
0
1
0
0
2
2
0
1
2
0
1
0
3
1
2
0
1
2
0
1
0
2
1
1
2
1
1
2
0
1
1
2
2
1
0
1
2
0
1
1
1
0
1
0
1
1
1
1
1
0
1
1
0
1
1
1
0
1
1
0
2
0
1
0
0
2
2
0
1
1
0
1
2
0
2
1
1
1
0
2
0
1
1
1
0
2
1
0
2
0
1
0
0
0
2
1
0
2
2
2
1
0
1
1
1
1
0
1
1
0
2
1
1
0
0
2
1
0
0
0
0
1
2
0
0
1
0
1
1
1
0
2
0
1
2
2
2
0
0
3
1
1
0
2
2
2
2
1
1
1
1
2
2
0
2
1
2
1
0
2
1
0
1
0
0
0
2
1
0
1
1
0
0
0
0
2
0
2
0
0
0
1
0
1
0
1
1
1
0
1
0
0
2
2
2
1
1
1
0
2
1
0
1
0
2
1
0
0
1
0
2
1
0
2
0
0
1
0
1
1
1
2
2
0
0
0
1
0
0
0
1
2
1
1
1
2
0
1
1
1
1
0
1
2
0
1
0
1
2
0
1
1
0
0
1
2
0
0
1
2
1
1
1
1
1
0
1
2
0
0
0
1
1
0
0
2
0
0
1
0
2
2
1
0
0
2
1
2
0
2
0
1
1
0
1
0
1
1
0
3
0
1
1
1
2
2
0
2
0
0
1
0
1
0
1
2
1
0
2
0
1
0
0
1
1
0
0
0
0
1
1
0
2
1
0
2
1
1
1
2
1
2
0
1
0
0
1
0
1
0
1
1
1
0
0
1
0
0
0
0
1
2
1
0
0
1
0
0
2
1
1
4
0
0
1
0
2
0
1
1
0
1
0
0
1
0
0
0
2
0
1
1
0
2
2
1
2
1
0
1
1
1
1
0
0
1
1
2
2
1
1
2
0
1
0
0
1
1
1
0
0
2
0
0
1
2
1
0
1
2
0
1
1
2
1
0
1
2
0
0
0
1
1
1
0
0
1
0
2
2
0
1
1
2
1
1
2
2
1
0
1
0
0
1
2
0
1
0
1
1
0
1
1
1
1
0
0
1
2
1
2
1
1
1
2
2
1
1
1
2
0
1
0
1
3
1
0
1
0
3
1
0
0
1
1
0
1
1
0
0
1
0
1
2
0
0
2
0
2
1
0
1
0
0
2
7
1
0
1
1
1
2
0
0
0
2
0
2
1
1
1
0
1
2
0
2
2
1
0
0
0
0
1
1
2
3
0
0
1
1
2
2
1
0
1
1
0
1
0
1
0
0
0
0
1
2
0
0
0
0
2
0
1
2
1
0
2
0
0
2
1
0
1
2
1
1
2
0
0
2
1
0
0
0
1
0
0
1
2
1
1
1
0
1
1
0
0
1
2
1
1
0
0
1
1
2
1
1
0
2
1
0
1
0
1
0
0
1
0
0
2
1
2
2
0
2
1
1
1
1
0
0
1
1
1
0
1
0
1
1
0
2
1
0
0
2
1
1
0
1
0
1
1
1
0
2
0
0
0
0
1
1
1
0
0
1
3
0
0
1
2
2
1
0
0
0
0
0
0
0
1
1
1
1
1
2
1
2
1
2
0
2
0
1
2
1
2
2
1
1
1
1
2
1
1
1
0
1
2
1
1
2
0
0
1
0
1
0
1
1
1
0
2
0
1
2
2
0
1
0
0
0
1
2
1
0
0
2
0
2
2
2
0
0
2
1
1
0
2
0
0
1
0
1
2
0
1
2
0
1
1
1
1
0
1
1
1
2
1
2
0
0
1
1
2
1
1
0
2
2
2
1
0
2
0
1
0
0
2
0
1
1
1
0
1
0
1
0
1
1
0
0
1
0
0
0
0
2
0
1
1
0
2
0
1
1
1
2
2
0
1
1
1
2
0
0
0
2
2
1
1
1
0
2
0
1
0
1
0
0
0
2
1
1
1
0
0
0
1
1
0
1
1
1
1
0
0
1
2
1
0
2
2
0
0
2
2
0
1
1
0
2
2
0
0
0
3
0
0
2
1
0
1
0
1
2
1
1
1
0
1
2
1
0
1
1
1
0
0
2
0
1
0
1
0
2
0
2
1
0
1
1
1
1
3
2
2
1
2
2
1
0
2
1
0
2
1
2
0
0
2
0
0
1
0
1
2
2
0
0
1
0
0
0
2
0
1
1
0
1
1
1
1
0
1
1
1
1
0
3
2
3
1
1
2
0
0
1
2
0
1
1
2
0
1
1
0
1
0
0
1
0
0
0
1
1
1
1
0
1
1
0
0
1
0
2
1
1
1
6
0
2
0
1
1
1
1
0
1
0
0
1
0
1
0
0
2
0
0
1
2
1
2
0
0
1
1
0
0
0
0
0
1
1
1
0
0
0
1
2
2
1
2
2
0
0
0
0
0
0
1
0
2
0
1
0
2
0
0
0
1
0
0
0
0
0
2
1
1
1
0
0
0
1
2
0
0
1
0
0
1
1
1
1
2
0
1
0
1
0
2
1
1
1
1
1
1
0
1
0
1
2
0
1
1
0
0
2
2
1
1
0
0
0
1
1
0
3
0
0
2
2
1
1
0
1
1
1
1
0
1
0
1
0
1
1
0
2
1
1
1
0
1
1
0
1
1
2
1
2
0
1
0
1
1
0
1
1
2
1
0
0
2
2
0
0
0
1
0
1
1
2
1
0
0
1
0
1
2
0
2
0
0
2
1
3
1
1
1
0
1
2
1
0
2
1
1
1
0
2
0
0
1
0
1
1
1
0
1
0
1
0
0
2
1
0
1
1
1
1
0
1
0
2
2
1
1
2
1
1
2
0
0
0
1
3
1
1
0
0
0
0
2
2
1
0
2
1
0
1
1
2
1
0
1
2
0
1
1
1
1
2
1
1
0
2
1
2
0
0
0
1
1
0
0
1
1
1
1
3
1
2
2
2
1
0
2
0
2
1
1
1
0
0
4
1
1
2
2
1
1
1
0
2
2
1
0
1
0
1
0
2
0
0
2
2
1
0
0
2
2
1
2
1
0
1
3
1
2
0
0
0
2
2
0
2
0
2
2
1
1
2
0
2
2
0
0
2
0
0
1
0
1
2
0
1
1
0
1
0
1
0
2
1
0
1
2
1
0
0
0
0
2
2
0
0
2
2
2
0
1
2
1
0
0
0
1
2
1
2
1
0
1
3
0
2
1
0
1
0
1
1
0
2
1
0
1
2
0
1
0
0
0
2
2
1
1
1
2
3
0
0
1
2
1
2
0
2
2
2
1
0
1
1
0
0
0
0
1
0
2
2
2
1
1
0
0
0
0
0
3
0
2
1
0
2
1
2
2
0
2
2
0
1
0
1
0
1
2
1
1
0
0
1
0
0
0
0
0
1
0
2
2
1
2
2
1
2
1
1
1
1
2
1
0
1
2
0
0
0
1
1
1
0
1
0
1
0
0
1
1
2
2
1
1
1
0
1
1
2
1
0
0
2
0
1
2
1
1
1
1
1
1
1
1
1
1
1
0
0
0
0
0
2
0
0
0
2
0
2
1
2
1
0
0
2
1
2
2
2
0
1
0
0
1
0
0
1
1
1
0
0
0
1
0
2
0
2
1
1
2
0
0
0
1
0
2
0
2
1
0
1
0
1
1
1
1
2
0
2
3
1
0
2
0
1
1
1
1
3
2
0
1
1
2
0
0
0
2
0
2
1
2
1
1
1
1
1
2
1
0
0
0
1
1
0
0
0
2
0
0
1
0
1
0
2
2
2
2
0
0
0
1
2
1
1
1
0
1
0
0
0
1
1
2
1
1
0
0
0
1
2
1
0
1
0
1
2
0
0
1
1
1
1
1
1
0
0
1
1
0
2
1
1
2
2
1
0
2
1
0
1
0
1
1
0
1
1
0
1
1
1
1
0
0
0
1
2
0
1
0
1
1
1
2
1
2
0
2
1
1
1
2
2
1
2
1
0
1
0
1
1
0
2
2
1
1
1
0
1
2
0
1
0
0
2
1
0
0
1
0
1
2
0
0
0
3
1
1
0
2
0
0
0
1
1
0
3
1
1
1
2
0
2
1
1
0
2
1
2
2
1
0
0
1
0
2
1
0
2
1
1
2
0
0
2
0
0
1
1
1
1
1
0
2
1
0
0
1
1
1
1
1
2
2
1
0
2
0
2
2
2
0
0
0
0
0
0
1
0
1
0
1
2
0
0
0
2
0
0
0
0
0
1
1
0
2
2
0
0
0
1
0
1
0
0
1
1
0
2
0
0
0
1
1
1
1
0
2
1
0
0
1
1
1
0
1
0
1
1
1
0
0
0
1
1
1
1
1
0
1
0
1
0
0
0
2
2
2
2
0
1
0
2
2
0
0
1
0
0
1
2
2
1
0
0
1
1
1
0
1
2
0
0
0
2
2
1
0
2
2
0
1
0
0
1
0
2
2
2
1
0
0
2
2
0
1
0
1
0
0
0
1
0
1
1
1
0
0
1
1
1
0
1
0
1
1
0
1
0
1
1
1
2
0
0
0
0
0
2
3
0
0
2
2
0
0
1
1
3
0
2
0
1
0
0
2
2
1
0
0
1
0
7
0
1
0
1
0
0
0
0
0
2
1
2
1
1
0
1
1
0
0
0
1
2
0
0
0
1
1
2
3
0
0
1
0
2
1
1
0
0
2
2
2
0
3
1
2
0
1
1
2
0
0
2
1
2
0
3
1
0
1
2
1
1
2
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
2
1
1
1
2
0
1
1
0
1
0
1
1
1
2
2
0
2
0
0
0
0
0
1
0
0
1
2
1
1
2
1
1
0
2
1
1
2
0
1
1
1
2
2
1
0
1
1
2
1
0
2
0
2
2
2
2
2
0
0
1
1
1
1
2
0
1
1
1
1
1
0
1
0
1
1
0
1
0
1
2
0
1
0
2
0
1
2
2
3
0
0
1
1
1
0
2
1
0
1
0
0
1
0
2
2
0
1
0
1
2
1
0
0
0
2
0
1
1
1
1
1
0
0
0
1
1
1
1
1
1
0
2
2
0
1
0
1
2
2
1
2
1
1
1
1
2
0
0
2
2
1
2
1
2
1
2
1
2
2
1
2
1
2
1
1
2
1
2
1
2
2
1
1
1
1
2
2
1
0
1
0
0
0
1
0
0
1
0
1
1
2
0
0
1
1
1
1
1
3
0
0
0
1
0
0
0
0
0
2
1
1
2
1
0
1
1
0
0
1
0
0
1
2
0
2
0
2
1
0
1
0
1
1
0
1
1
2
1
1
2
0
1
1
0
1
1
2
1
1
0
2
3
0
2
2
2
0
0
1
0
0
2
1
0
2
1
1
0
1
1
0
0
1
2
1
0
2
0
1
0
1
2
0
0
0
1
1
1
1
0
2
2
0
1
1
1
0
2
0
1
1
2
0
2
2
1
2
0
1
2
0
2
2
2
2
1
0
1
1
1
0
1
0
2
1
1
0
1
2
1
2
0
1
0
1
1
1
1
1
1
1
2
0
1
2
1
1
1
0
0
0
2
0
2
2
0
2
0
1
3
1
1
0
2
0
2
2
1
1
0
0
2
2
0
2
0
1
2
1
0
2
0
1
0
0
1
1
2
0
1
1
2
1
0
0
0
0
2
2
0
0
0
1
1
0
0
1
1
0
2
0
1
2
0
0
1
2
2
1
2
0
2
1
0
0
1
0
1
0
1
0
0
2
0
1
0
0
0
1
0
1
0
1
1
0
1
1
1
2
0
0
1
2
1
0
1
0
0
1
0
0
0
0
1
1
2
1
0
1
1
1
0
0
2
1
1
0
2
1
1
2
0
0
1
0
1
1
2
1
3
0
1
1
1
1
0
0
1
0
1
2
0
1
2
1
0
1
0
0
1
0
0
0
1
0
2
0
2
0
2
0
2
1
0
0
0
0
2
2
2
2
1
1
1
0
4
2
1
1
1
1
0
0
1
2
0
0
0
2
0
0
1
2
0
1
1
1
0
0
1
0
2
1
2
1
1
4
0
0
2
0
0
1
0
1
2
1
1
0
1
1
1
0
2
0
0
1
0
0
0
2
3
1
2
0
0
1
1
1
1
0
0
0
2
2
1
2
0
0
2
1
1
0
1
2
0
0
1
1
0
2
3
1
1
1
2
1
0
1
1
2
2
2
1
0
0
2
2
0
1
2
0
0
1
2
0
2
0
2
0
1
2
1
2
1
1
1
1
1
0
0
0
0
1
1
0
1
3
0
0
0
1
0
0
2
2
1
1
1
2
2
0
1
0
2
1
1
0
1
2
0
0
2
0
1
1
0
0
0
0
0
1
0
1
1
1
1
0
1
2
2
0
1
2
2
1
1
1
2
1
1
1
2
2
1
2
4
1
2
0
0
1
0
0
0
1
0
0
0
2
0
2
0
1
0
2
2
1
0
0
1
2
0
2
1
2
6
1
2
1
1
0
0
2
0
0
0
0
2
2
0
1
0
1
2
0
0
1
1
0
2
0
1
1
1
2
1
0
1
3
0
2
2
1
0
1
0
1
2
1
0
2
0
1
0
1
1
1
2
2
2
2
0
1
0
1
1
1
1
2
0
0
1
0
1
0
0
2
2
2
1
1
1
1
0
0
2
0
1
1
0
0
2
1
0
1
2
2
1
0
0
0
1
2
0
0
0
2
2
0
1
1
1
1
0
2
1
1
2
0
1
1
1
1
2
0
2
2
1
1
1
0
1
1
0
2
0
0
1
1
2
1
0
1
0
1
2
0
1
0
2
0
1
6
2
2
2
1
0
1
0
0
1
0
2
0
0
1
1
1
1
0
1
2
1
0
0
1
1
1
1
2
2
1
3
0
0
1
1
0
0
1
0
0
1
1
0
0
1
2
2
0
1
1
2
1
1
2
1
1
1
1
1
0
0
1
1
2
1
1
0
2
1
0
1
0
2
2
1
0
0
0
0
4
1
2
1
0
2
2
1
1
1
1
2
1
2
0
2
0
0
0
1
1
2
2
0
1
2
0
0
3
1
1
0
1
3
0
2
1
0
2
1
1
0
0
0
2
1
1
1
1
2
1
0
1
0
0
1
2
1
0
0
0
0
1
2
0
1
0
1
1
1
2
3
1
1
1
3
1
1
1
1
0
1
2
2
2
2
2
1
2
0
0
0
1
1
1
1
1
1
0
1
0
2
1
0
0
2
1
0
0
2
0
1
1
0
1
2
1
1
1
2
2
2
1
1
1
0
0
1
1
0
0
0
1
2
0
0
1
0
0
1
0
1
1
1
0
2
1
0
1
1
1
1
1
2
1
0
2
0
0
1
0
0
0
1
0
1
1
0
1
2
2
0
0
1
2
1
0
0
0
1
0
2
1
0
3
2
0
2
2
0
0
0
1
0
1
0
1
0
1
2
0
1
2
3
1
1
1
0
2
1
2
1
1
0
0
1
1
2
0
1
0
2
0
2
0
0
0
1
2
2
1
1
1
1
2
1
0
1
0
1
0
0
0
0
2
0
0
1
1
0
1
1
0
2
2
0
1
2
0
0
2
1
1
1
0
1
2
1
0
1
0
1
2
0
0
2
0
0
1
0
3
2
1
0
0
0
1
1
1
1
0
0
1
1
0
1
2
1
0
2
1
1
1
2
1
1
2
1
0
2
1
0
0
1
0
2
2
0
1
0
2
2
1
2
1
0
2
0
0
0
1
0
0
0
2
4
1
2
0
0
0
1
1
1
0
1
2
2
0
1
0
1
0
1
0
1
0
0
2
1
2
0
1
0
0
2
2
1
0
1
3
0
2
0
2
1
0
3
2
1
2
0
2
1
0
2
2
0
1
0
0
0
2
0
0
2
1
0
0
0
2
3
1
0
1
1
0
0
1
2
0
2
2
2
0
1
1
0
0
1
1
0
0
0
1
1
2
1
1
1
1
2
1
1
0
1
0
2
0
2
1
1
1
1
2
0
2
0
0
1
0
1
2
1
0
1
0
2
1
1
0
0
1
2
0
1
0
2
0
1
1
1
2
0
0
0
2
2
0
0
2
0
0
0
1
2
0
1
0
0
0
0
3
0
0
1
2
0
1
1
1
1
0
1
1
1
0
2
1
1
0
1
2
2
1
2
2
0
0
1
0
0
2
2
2
0
1
1
3
1
2
3
1
1
0
1
1
0
1
1
1
1
2
2
0
2
0
1
1
3
2
0
0
2
0
0
0
1
1
0
1
1
0
1
2
1
1
2
0
1
0
1
0
2
1
1
1
1
0
0
1
3
2
0
0
1
1
0
1
1
0
2
2
2
2
1
1
1
0
1
0
1
2
2
1
0
2
1
0
2
2
1
1
0
2
1
2
0
1
0
1
0
1
1
2
0
2
2
1
0
2
0
2
2
1
0
1
0
0
2
2
0
1
0
0
0
0
1
1
0
1
0
0
2
1
2
1
2
1
2
0
1
2
2
1
1
0
0
2
1
0
0
1
1
1
0
0
2
1
4
1
1
1
0
0
2
2
3
1
0
1
0
1
0
1
0
0
0
2
1
0
2
1
1
0
1
1
0
0
0
1
0
1
0
1
1
0
2
0
2
2
2
2
2
0
1
0
1
2
2
1
1
3
1
4
0
2
0
3
0
0
0
2
0
2
1
1
0
1
1
1
2
0
0
3
0
0
0
1
2
1
0
0
0
1
0
1
1
0
0
0
2
1
0
0
2
0
0
1
0
1
1
2
2
1
1
1
1
0
0
1
0
0
1
1
1
1
2
2
0
1
0
1
2
0
1
0
1
0
0
2
1
0
0
2
1
2
1
0
1
2
1
0
2
2
2
1
1
2
1
0
0
0
1
0
1
1
1
0
0
1
0
0
0
0
1
0
0
1
0
0
2
2
1
2
1
2
0
0
1
1
2
0
2
0
0
0
0
1
1
1
0
0
1
0
1
0
2
0
2
0
1
1
2
0
1
1
1
0
1
2
0
1
2
2
1
1
0
2
3
1
2
0
1
1
0
0
1
0
1
0
0
0
1
1
1
2
0
1
2
1
2
2
0
1
1
2
0
1
2
1
0
1
1
1
0
1
1
0
1
2
0
0
0
0
0
0
0
0
0
1
1
0
1
1
2
0
1
0
1
0
2
0
3
1
0
2
0
0
2
1
0
2
0
0
1
1
2
3
1
1
1
1
0
2
2
1
2
0
0
0
1
2
2
1
2
0
1
0
0
0
0
0
1
1
2
1
1
0
0
0
1
0
0
2
1
2
2
0
2
1
0
0
0
1
0
1
1
1
0
0
0
1
2
2
1
2
0
1
0
1
1
1
1
2
1
1
0
2
1
0
2
1
1
1
1
2
1
2
0
1
0
0
0
0
0
1
0
1
1
2
2
0
2
0
0
2
0
1
0
1
2
0
2
0
1
1
1
0
4
0
1
0
2
0
1
1
1
0
1
0
0
0
0
2
1
1
2
1
0
1
0
2
0
0
1
2
0
1
2
1
0
0
0
0
0
0
0
2
0
0
0
2
0
2
1
0
0
2
0
0
3
0
0
0
0
0
0
1
0
1
1
1
1
1
0
1
2
0
0
2
0
0
2
0
2
1
0
2
1
1
0
2
0
2
1
0
2
2
1
2
0
0
0
2
2
0
1
0
2
1
1
0
1
1
1
1
2
1
0
2
0
0
1
1
1
1
0
0
2
0
2
0
0
1
1
2
1
1
0
2
1
0
1
2
1
3
2
2
0
1
1
0
0
2
1
2
0
0
0
0
1
1
1
1
1
0
1
0
1
0
1
1
2
0
0
1
0
1
1
0
0
1
1
1
1
1
2
0
2
1
1
1
0
1
1
1
0
0
1
1
0
0
2
1
0
0
0
0
1
0
1
1
2
1
1
1
0
1
2
1
0
2
1
1
0
0
1
1
0
0
1
1
1
0
1
0
0
2
0
1
3
0
0
0
2
2
1
2
0
2
0
1
0
0
0
0
0
2
1
0
1
1
1
2
0
1
1
0
0
1
2
0
1
0
0
1
1
1
2
0
2
1
0
0
0
2
0
2
1
0
1
0
1
1
2
2
1
1
0
0
0
1
1
2
0
1
0
0
0
1
1
1
1
0
0
0
1
0
0
0
1
0
2
0
2
2
0
1
2
0
1
0
1
2
0
1
1
2
0
2
0
2
5
2
1
0
2
1
3
1
0
2
1
0
2
1
2
1
0
2
1
1
2
0
0
1
1
0
1
0
1
0
1
0
1
1
0
2
0
0
0
1
0
1
1
1
1
0
0
1
0
1
1
1
1
5
0
2
0
1
1
1
0
1
0
2
1
2
0
0
1
0
2
0
0
2
0
0
0
1
2
2
1
1
1
0
2
0
1
2
3
1
1
2
0
2
1
0
1
2
0
0
0
1
2
1
1
0
1
0
1
1
0
0
2
0
1
1
1
2
2
0
1
1
1
0
2
0
0
1
1
0
0
1
0
1
2
1
0
0
0
1
1
0
2
1
0
2
0
1
0
0
2
1
2
1
0
0
1
1
0
1
1
1
1
0
2
1
0
0
1
0
2
2
2
0
0
0
0
0
0
2
1
1
1
0
1
1
0
1
0
0
1
1
0
1
0
1
0
1
0
2
1
0
1
2
0
2
0
1
0
1
2
2
1
1
0
0
0
0
2
2
0
2
1
2
2
0
2
0
2
1
1
0
1
2
2
1
0
1
0
3
1
2
2
0
0
1
2
1
2
2
2
0
2
1
0
1
0
1
0
1
0
0
2
1
0
0
0
1
1
1
0
0
1
0
0
2
1
0
2
0
1
0
1
0
1
0
2
1
3
1
1
0
0
1
0
1
0
1
1
0
1
3
2
1
0
0
0
1
1
0
2
0
0
2
1
2
0
0
1
2
1
0
1
1
0
2
1
2
0
1
1
1
1
1
2
0
0
1
0
2
2
3
0
0
0
1
0
1
1
1
0
0
1
1
1
1
1
1
2
1
0
0
2
0
0
1
0
0
2
1
0
0
1
0
0
0
0
1
1
0
0
1
1
1
1
0
1
1
0
1
1
0
1
0
3
1
2
1
1
0
2
1
0
1
0
2
0
2
1
1
2
2
2
2
0
1
0
0
1
1
0
0
2
1
0
1
0
0
1
1
1
3
0
1
1
0
2
1
1
0
2
1
1
0
1
0
0
1
1
3
1
2
1
0
2
0
0
0
0
2
1
1
0
1
0
2
1
1
1
0
0
1
2
0
0
2
2
1
0
0
1
1
1
2
4
1
2
0
2
1
1
0
1
1
0
1
0
2
1
0
2
1
1
0
2
1
1
1
0
1
1
2
0
1
1
2
0
2
0
1
1
1
1
1
0
0
0
0
0
0
1
0
3
0
0
1
1
0
0
1
0
1
2
0
0
1
0
0
1
1
1
1
1
2
0
1
0
1
1
2
0
0
1
1
1
1
1
0
1
2
1
1
1
1
2
1
2
0
2
2
1
1
0
0
0
0
1
0
0
1
0
1
0
0
1
1
0
2
6
0
0
2
0
0
1
2
1
2
0
1
0
1
0
1
0
1
1
2
0
0
1
3
1
1
0
1
2
1
1
1
2
2
1
0
0
1
0
2
1
1
2
0
2
1
0
0
1
1
2
1
4
0
0
2
0
1
2
1
2
2
2
2
0
1
1
0
0
0
2
1
1
1
0
0
2
2
2
2
2
2
3
2
1
2
0
2
0
2
0
0
1
2
1
3
1
0
0
0
0
0
0
1
1
2
0
2
0
2
1
1
1
2
1
1
1
2
2
0
3
0
0
0
5
1
2
0
1
1
0
1
2
0
2
1
0
0
1
0
0
2
1
2
1
1
2
1
1
1
0
1
1
0
1
0
5
0
1
2
2
1
1
2
1
1
1
0
1
1
1
1
0
0
0
0
0
2
0
1
2
1
0
0
0
1
0
1
2
1
1
1
1
2
1
0
1
0
1
0
1
1
2
2
2
0
1
2
2
1
0
1
0
0
1
0
1
2
0
2
1
1
2
2
2
1
2
0
1
3
0
2
1
1
1
1
1
2
1
0
1
2
0
1
0
0
0
0
3
1
1
1
0
1
1
0
1
2
1
3
1
2
0
0
2
2
1
1
1
2
1
0
1
0
2
1
1
0
0
2
1
1
1
0
0
1
2
1
0
0
1
0
0
1
0
1
2
0
1
1
0
0
1
1
1
1
1
2
1
2
1
0
1
1
1
1
0
2
2
1
1
0
2
1
1
1
1
0
2
3
0
0
2
2
2
2
0
1
1
3
0
2
0
1
0
1
1
1
1
0
1
0
2
1
0
1
1
2
1
1
2
1
1
1
1
0
1
1
2
0
2
0
1
1
1
1
2
0
0
0
1
0
1
0
1
0
0
2
1
0
0
0
1
2
0
2
0
1
1
2
1
0
1
1
2
1
1
2
3
1
1
1
1
0
1
0
1
2
1
0
0
1
1
1
0
2
0
2
0
0
0
1
0
0
0
0
2
2
1
0
0
1
3
0
1
1
0
1
0
0
0
0
1
2
1
0
2
1
2
2
1
1
1
2
0
1
3
0
0
1
0
1
1
0
1
1
1
3
1
1
2
1
0
0
1
0
2
0
0
2
0
1
0
1
2
0
0
0
2
0
1
1
1
2
1
0
2
1
1
0
1
1
1
1
0
1
2
4
1
1
1
0
0
1
2
2
1
1
2
2
0
2
0
1
0
1
0
1
1
1
1
2
1
0
0
0
0
0
2
0
0
1
1
1
1
1
0
0
0
0
1
1
0
0
0
0
1
1
2
0
0
1
1
2
0
1
2
1
0
1
1
0
2
0
0
0
2
2
1
0
1
1
1
1
1
1
0
0
4
0
1
0
3
1
1
2
0
1
1
1
0
1
0
1
1
2
2
0
1
1
1
0
2
1
0
1
0
2
2
0
1
1
1
1
2
0
0
0
2
0
0
1
0
0
1
2
1
3
1
2
0
1
1
0
0
0
0
1
1
1
0
1
1
2
1
2
1
2
1
2
1
1
1
1
2
4
1
0
1
2
0
0
1
2
1
2
1
0
0
0
1
2
2
0
1
1
2
0
0
0
2
1
1
2
0
2
0
0
0
2
0
1
0
3
1
1
1
1
1
1
0
0
0
0
0
2
0
0
0
2
0
1
0
1
0
0
2
2
1
0
2
0
0
1
2
0
1
1
2
0
2
0
2
2
1
2
0
1
5
0
1
0
1
1
1
0
1
1
0
1
0
0
2
0
2
1
2
1
0
0
2
1
2
0
2
0
1
0
2
0
0
0
1
1
0
0
1
0
0
1
0
0
2
2
1
1
1
0
0
0
2
1
0
2
1
1
1
2
2
1
1
1
0
1
2
0
1
2
2
1
2
2
1
1
3
1
2
1
2
1
0
0
1
2
1
0
1
1
1
1
2
2
2
0
2
1
2
1
0
1
2
2
0
2
0
1
2
0
2
0
0
0
0
2
0
0
1
1
1
1
1
0
0
2
2
1
2
0
0
2
1
0
2
0
1
2
0
1
1
0
1
1
1
1
1
1
0
0
1
1
0
0
0
1
0
1
2
1
0
1
1
1
0
0
0
2
0
1
0
1
0
1
2
2
1
0
0
0
2
0
0
1
3
1
0
2
0
0
2
1
0
0
1
2
0
0
0
2
1
1
1
1
1
2
0
0
0
1
2
2
2
0
2
0
0
1
2
1
1
0
1
1
1
2
1
0
1
0
0
2
1
1
2
0
2
2
1
1
0
2
0
2
0
1
1
0
1
1
1
1
2
2
3
2
0
2
2
1
2
0
1
1
2
0
1
0
0
0
0
0
0
1
2
1
0
0
1
2
0
2
2
2
0
1
0
1
1
2
1
1
1
0
2
2
0
1
1
0
1
1
2
0
2
2
0
2
0
3
1
1
1
1
2
1
2
0
2
0
0
1
1
0
0
0
0
0
0
0
2
1
1
0
0
2
0
2
0
2
1
1
0
0
1
0
1
0
1
1
0
1
1
1
0
1
0
1
1
0
1
1
0
1
2
1
0
1
0
1
1
1
1
1
1
0
0
1
1
0
2
1
1
0
0
1
0
1
0
1
2
0
0
1
1
2
1
1
1
0
2
0
1
2
1
0
1
1
1
1
1
0
1
1
2
1
0
1
0
1
2
2
1
1
1
1
0
1
0
1
0
0
2
1
0
1
2
0
0
0
1
1
0
3
2
0
0
0
2
1
1
1
0
2
1
2
1
0
0
0
1
0
1
0
0
2
2
1
0
0
0
2
2
1
0
0
2
1
2
1
2
1
2
0
0
0
0
2
0
2
2
0
1
0
1
0
1
1
0
2
1
0
1
0
1
2
0
0
1
1
1
2
0
1
1
1
0
1
1
0
0
1
2
0
1
0
1
1
1
0
1
1
0
0
1
0
1
1
1
1
0
0
1
1
1
2
0
2
1
2
1
0
0
1
0
0
0
1
0
3
0
0
2
1
1
4
1
0
1
1
0
1
1
1
1
2
1
2
1
1
0
3
1
2
2
0
1
2
1
2
2
0
2
1
0
1
0
1
2
1
1
2
2
0
0
0
0
0
3
0
2
1
1
0
2
0
0
0
2
0
1
1
1
1
2
2
1
1
0
0
2
1
2
0
2
1
2
0
2
1
1
0
0
0
1
1
1
2
0
2
1
1
1
1
0
0
0
2
1
1
0
1
0
0
2
2
2
0
0
0
2
0
1
0
2
2
0
0
0
1
0
2
0
1
1
0
0
0
2
0
1
1
0
2
0
2
0
1
0
1
0
0
0
0
1
0
1
0
1
1
0
0
0
1
0
0
1
1
0
1
2
2
2
1
0
0
0
1
0
0
0
0
0
2
0
0
1
0
1
1
0
1
1
1
1
0
1
1
0
2
1
0
2
0
0
1
1
1
2
0
1
1
1
2
0
1
1
0
1
1
2
1
1
1
1
1
0
0
0
0
0
2
1
1
1
2
2
2
2
2
1
1
1
1
1
2
1
1
1
1
2
2
0
0
0
0
0
1
0
1
0
0
0
1
0
2
0
0
2
1
1
0
0
0
0
4
2
1
0
1
0
2
2
0
1
1
1
0
0
1
1
0
0
0
3
0
0
2
0
1
1
1
0
1
0
0
0
1
2
1
0
0
0
2
0
2
0
2
1
2
1
1
0
2
1
1
1
1
2
1
2
0
0
1
0
2
0
1
2
2
1
0
0
2
1
0
1
0
0
0
2
0
1
1
2
0
1
2
2
0
0
0
0
2
0
2
2
0
2
1
0
1
2
0
0
1
0
0
2
1
1
1
1
2
2
0
0
1
1
1
0
1
0
1
0
2
1
0
1
1
1
1
1
1
1
1
1
0
0
0
0
2
2
1
1
1
2
1
1
0
1
2
0
1
0
0
0
0
0
2
0
0
3
1
0
0
0
0
1
0
2
2
1
1
1
1
0
0
1
2
0
1
1
0
2
2
2
2
6
2
0
1
2
0
0
0
0
1
0
1
1
1
1
1
1
2
1
2
1
0
0
5
0
2
1
1
2
2
2
1
0
1
1
2
1
0
0
2
1
0
2
0
1
1
0
2
0
2
1
0
0
0
1
0
2
2
0
0
1
2
0
1
1
1
0
1
0
0
1
1
1
2
0
1
2
1
1
2
1
0
1
1
2
1
0
0
2
0
1
1
0
2
0
0
1
0
1
1
1
1
1
0
0
1
1
0
2
1
1
1
2
2
1
1
1
2
0
3
2
0
2
2
1
0
1
1
0
1
1
0
0
0
1
0
2
0
0
0
1
0
2
0
0
3
0
0
0
0
2
1
1
0
1
0
1
2
1
2
0
0
0
1
2
0
0
1
1
0
3
0
0
2
1
0
2
2
1
2
0
0
0
1
1
0
1
0
0
1
1
0
0
2
1
2
0
1
2
2
1
1
0
0
1
0
0
1
2
2
2
0
1
0
0
2
2
2
0
0
0
1
2
0
0
0
0
0
0
1
1
1
0
1
2
1
0
2
0
0
0
1
2
1
1
0
5
0
2
1
0
0
0
1
1
0
2
2
1
2
1
1
0
0
0
1
1
0
0
0
1
2
0
0
0
0
2
1
2
2
0
1
1
0
2
1
0
1
0
2
0
2
0
0
2
2
2
0
0
0
1
0
1
2
1
1
2
3
2
0
1
2
0
0
0
0
1
2
1
2
1
1
0
1
0
0
0
1
1
1
0
1
2
1
1
0
1
1
0
0
0
2
1
0
1
1
1
1
0
2
0
1
2
0
0
2
0
2
2
2
1
1
1
0
0
0
0
2
0
0
2
0
0
1
1
1
0
0
1
0
1
0
1
1
1
0
0
0
0
0
0
1
1
2
3
0
1
2
1
0
0
1
1
0
0
0
1
2
0
1
0
0
1
2
1
1
1
1
1
6
0
1
1
0
2
0
1
0
2
0
1
0
1
1
2
1
1
0
0
0
2
1
0
1
0
0
2
1
1
0
0
2
0
0
0
1
2
3
0
1
0
2
1
0
0
2
1
2
0
0
1
0
0
1
0
1
0
1
1
1
0
2
1
0
1
0
1
2
0
2
2
2
0
1
0
1
1
1
0
0
1
1
0
0
1
0
0
2
0
1
2
2
0
2
0
0
0
1
2
0
2
1
0
0
0
0
1
2
1
0
0
2
1
1
0
0
0
0
1
3
0
0
0
0
2
2
1
1
1
1
0
2
0
1
2
0
2
1
0
0
2
1
0
0
1
1
1
1
1
0
0
1
0
1
1
1
1
1
0
1
0
2
2
2
0
2
2
0
0
1
1
1
3
0
0
1
2
1
1
0
1
2
2
3
2
1
0
1
0
1
0
2
1
1
2
0
1
1
2
1
0
2
0
0
2
1
0
1
0
1
1
0
1
2
0
5
4
0
1
0
0
0
0
0
1
0
0
0
3
2
1
0
2
0
0
1
0
0
1
1
1
1
1
0
2
1
1
1
0
0
0
1
0
0
2
1
0
0
2
0
1
1
1
0
0
1
0
0
0
2
1
2
0
0
2
2
2
1
1
1
2
2
2
1
1
0
0
1
1
2
2
1
1
2
1
1
1
1
2
0
2
1
0
0
0
2
2
2
0
2
2
0
1
0
0
0
1
1
2
0
1
0
0
0
0
2
0
0
0
0
1
1
1
0
0
2
0
1
0
1
1
0
1
0
1
1
2
1
2
1
1
0
2
1
0
1
2
1
0
2
1
0
0
2
0
0
0
2
1
0
2
2
1
1
1
0
1
0
2
1
2
2
2
0
0
0
2
2
1
1
0
2
0
0
1
0
1
0
2
0
1
1
1
1
2
2
1
1
0
2
1
1
2
0
1
1
0
0
1
2
2
1
1
2
0
0
2
0
0
1
2
2
1
1
2
1
1
2
1
1
1
1
0
1
1
0
0
1
1
1
0
1
2
2
0
1
0
0
0
0
0
1
1
0
2
2
0
2
0
0
0
0
2
1
1
0
0
0
0
1
2
0
0
2
2
1
1
2
0
1
1
0
0
1
0
1
1
1
1
1
0
1
1
1
1
1
0
2
2
1
2
1
2
0
2
1
0
0
1
1
1
0
2
0
0
0
1
0
1
2
1
1
0
2
2
1
1
1
0
0
0
2
2
2
1
1
1
0
1
1
0
1
0
2
1
0
1
1
0
0
2
0
0
1
2
0
0
1
0
0
1
1
2
0
0
0
1
2
0
1
1
2
2
2
1
2
1
0
0
0
2
1
0
0
1
0
2
0
1
2
2
0
1
1
1
2
0
1
1
0
0
2
0
0
1
0
0
3
1
1
1
1
2
1
1
2
0
0
1
0
0
1
0
1
0
1
1
2
0
1
2
0
1
1
0
2
0
0
2
1
1
1
2
1
1
1
1
0
0
0
0
1
0
0
0
1
1
1
2
2
1
1
0
1
1
2
1
0
0
1
0
0
1
1
0
1
1
2
1
1
2
1
2
0
1
0
0
0
0
0
0
0
1
1
1
0
0
1
1
1
0
1
0
0
0
1
1
0
1
1
0
0
1
2
2
1
1
1
1
1
1
1
1
1
0
2
1
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
2
1
1
2
1
1
0
1
2
1
0
0
2
1
2
1
0
0
0
0
0
1
2
1
1
0
1
1
1
1
0
2
3
2
1
0
0
0
1
0
0
2
0
0
1
0
1
1
0
1
0
1
4
0
0
2
1
2
2
0
0
0
1
1
2
1
0
1
1
1
2
1
2
1
1
1
2
2
1
2
0
0
1
2
1
1
1
1
0
0
1
1
2
2
1
2
0
1
1
0
2
1
1
1
1
1
1
2
2
1
0
1
2
1
0
0
1
2
1
0
1
0
0
0
1
0
1
0
0
1
0
1
1
2
1
1
2
0
0
2
1
0
0
2
0
0
1
1
2
1
1
0
1
2
1
1
1
1
1
1
0
0
0
1
1
1
1
1
0
0
1
0
2
1
0
1
2
0
0
1
1
1
0
1
0
1
0
2
0
0
1
0
2
1
0
1
0
0
1
0
2
2
1
1
1
2
1
2
1
0
0
1
1
0
1
0
1
0
0
0
2
1
1
1
1
2
0
2
0
1
1
2
1
0
1
0
2
1
1
0
1
2
0
1
1
1
1
2
0
0
2
1
1
1
0
2
1
2
1
0
2
1
1
2
0
1
1
0
1
0
0
2
1
0
0
2
1
2
0
2
2
1
0
2
0
1
1
0
0
1
2
1
3
1
1
0
1
1
3
0
1
1
0
2
1
0
0
0
2
0
0
2
2
0
0
2
1
0
1
1
0
1
2
2
1
0
1
0
0
0
0
0
0
2
0
1
1
0
2
1
2
1
1
1
2
1
0
0
1
0
1
0
1
0
2
0
3
0
1
0
0
0
1
1
0
0
1
2
0
1
2
2
2
2
2
1
1
1
0
1
0
1
0
1
0
2
1
1
1
2
2
0
2
2
1
0
1
1
1
1
0
3
2
1
1
1
1
0
2
0
1
2
4
0
2
1
1
0
1
0
3
0
0
3
0
2
2
1
0
0
1
1
0
2
1
0
0
1
1
0
1
1
2
0
1
2
1
0
3
2
0
2
2
0
0
2
2
1
1
2
0
1
2
1
1
0
2
0
1
0
0
2
1
0
1
0
0
1
0
1
1
0
0
1
1
2
0
0
1
2
1
1
0
0
0
0
1
2
2
0
2
0
2
0
0
1
0
1
0
0
0
1
0
1
0
1
1
1
0
0
1
0
1
1
2
1
1
2
0
0
0
0
0
2
1
0
1
0
1
2
0
1
0
0
2
1
2
1
0
1
0
1
2
0
2
2
1
0
1
0
2
0
2
1
0
0
2
2
0
0
1
0
0
2
0
1
2
1
0
0
0
1
1
1
1
2
0
1
1
0
2
0
1
2
1
1
2
2
2
1
1
0
1
1
1
2
1
0
1
1
0
2
2
0
0
0
1
1
1
1
0
1
1
0
2
1
0
0
1
4
0
1
0
1
1
0
0
1
2
2
1
0
1
0
1
1
0
0
1
1
2
0
0
0
0
2
1
0
0
1
0
1
1
0
2
1
2
2
0
1
0
1
1
1
0
1
0
1
0
0
0
1
2
1
0
2
0
1
2
1
1
0
0
4
0
0
0
1
2
1
0
0
1
0
0
0
2
1
0
1
1
2
0
1
1
1
0
0
2
2
0
0
2
0
2
1
2
0
0
1
1
3
0
1
2
2
2
1
1
1
1
2
0
1
1
1
2
2
0
1
1
2
2
0
1
1
2
1
0
0
0
0
1
0
0
1
2
1
1
1
0
0
1
1
1
2
1
1
0
0
0
1
2
1
1
0
1
0
0
0
0
1
1
0
2
2
3
0
1
2
1
0
1
2
1
1
2
1
0
2
0
0
1
0
0
0
1
0
2
0
2
1
2
2
2
0
1
2
2
1
2
1
2
2
1
0
2
0
1
1
0
1
1
1
2
2
0
1
2
0
0
2
0
2
1
2
1
1
1
3
1
0
1
0
1
0
1
0
2
2
2
1
0
1
0
0
0
1
3
2
0
2
2
1
2
1
1
0
0
1
1
1
1
2
2
0
2
1
0
1
0
0
0
0
0
2
1
0
1
1
2
0
0
2
0
1
1
1
0
2
0
1
0
0
2
1
2
0
1
0
0
0
1
0
1
2
2
0
1
0
0
0
0
1
0
0
0
1
0
1
2
0
1
0
1
2
0
0
0
2
1
0
0
4
1
0
1
0
0
0
0
1
1
0
1
0
0
0
1
0
0
2
0
1
2
0
2
1
0
0
2
1
0
0
1
0
1
0
0
1
2
0
0
2
0
0
0
2
2
2
1
1
0
1
2
1
0
1
1
0
0
0
1
0
1
1
2
0
2
1
2
2
1
1
1
1
0
1
0
1
0
2
1
0
2
0
1
2
1
1
1
1
1
1
1
0
1
2
0
0
0
0
2
0
2
0
0
0
0
0
1
0
1
1
0
0
2
0
0
0
0
0
1
0
0
1
1
1
2
0
0
1
1
1
2
0
2
0
1
1
1
1
2
0
0
1
0
2
2
0
0
0
1
1
3
1
1
0
0
0
0
0
2
2
1
0
1
0
0
1
0
1
1
0
0
2
2
1
0
1
1
0
1
2
1
1
2
1
0
1
2
1
1
1
1
0
0
0
1
0
1
0
0
2
1
1
0
1
2
1
2
0
1
0
1
0
1
1
0
1
0
1
2
1
0
2
2
1
1
1
0
0
2
2
0
2
1
2
0
2
0
2
1
1
1
0
1
1
0
2
0
1
1
0
0
1
1
2
1
1
1
0
1
1
2
1
1
0
2
1
2
1
2
0
0
0
2
1
0
0
0
1
1
1
1
2
2
1
1
4
0
1
3
0
2
0
0
0
1
1
1
1
1
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
2
1
0
0
2
0
2
0
1
1
1
1
0
1
0
0
2
2
1
0
1
1
1
1
0
0
0
1
0
2
1
0
1
1
2
1
1
0
0
0
2
1
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
1
0
1
1
2
2
2
2
2
1
2
1
2
0
2
0
0
1
2
2
2
0
1
1
2
2
0
1
1
2
3
2
1
3
1
0
1
4
1
1
0
2
2
0
2
1
2
1
1
2
1
1
1
1
1
1
0
0
1
1
1
2
0
0
1
0
2
0
1
1
1
1
1
1
1
1
0
2
1
0
1
1
2
2
1
3
0
0
2
0
2
0
0
1
0
2
0
5
1
0
0
0
2
2
1
1
1
2
2
1
1
0
2
2
0
2
2
0
1
0
2
1
2
1
0
0
1
0
0
2
0
0
0
2
1
1
1
2
0
2
1
2
0
0
0
1
1
0
0
0
1
0
2
2
0
1
2
0
0
0
0
2
2
2
1
1
2
1
2
2
0
1
2
2
2
0
1
1
0
2
0
2
1
1
3
0
0
1
1
2
1
1
0
0
0
2
1
0
1
1
1
1
2
1
1
1
1
1
1
0
2
0
2
0
1
0
1
1
2
1
2
1
1
1
2
1
0
2
1
0
2
0
2
1
2
0
1
2
0
0
2
1
2
1
1
0
1
0
0
1
2
1
1
1
1
1
0
1
0
1
1
0
0
1
0
0
2
1
0
1
0
1
1
1
3
2
0
0
0
0
1
0
1
2
1
0
0
0
0
0
1
1
1
0
2
1
0
0
1
0
2
2
1
0
1
1
3
1
2
1
2
1
0
1
0
2
0
0
1
0
1
0
2
2
0
2
0
0
1
1
1
4
0
2
1
0
2
2
1
2
0
1
3
0
0
1
0
2
3
0
2
0
0
2
2
2
1
0
4
1
1
0
2
2
2
0
0
2
0
1
1
1
2
2
0
1
0
0
1
1
1
0
0
2
1
1
1
1
0
0
0
0
1
2
0
1
0
1
0
0
0
0
2
0
1
3
1
1
0
1
1
1
0
1
2
2
1
1
2
1
0
2
1
0
0
0
0
1
0
1
1
1
0
3
1
1
1
1
0
2
2
2
1
1
2
0
3
0
1
1
1
1
0
1
0
1
0
0
1
0
0
1
0
2
2
1
0
0
1
1
1
1
0
1
1
0
2
1
1
0
2
2
2
1
0
0
0
2
2
0
2
0
2
2
1
1
0
2
1
1
0
0
1
2
0
0
2
1
2
1
1
2
2
0
2
0
1
2
1
0
0
1
0
2
0
1
2
0
0
0
1
0
2
1
1
0
2
1
2
1
1
0
0
2
0
0
1
1
0
0
1
1
0
0
1
0
1
0
2
2
1
0
0
2
0
2
0
0
1
0
0
2
1
0
0
0
1
0
1
2
1
2
0
0
1
0
2
0
1
0
2
1
1
1
1
1
0
2
1
0
1
0
3
1
0
0
2
2
2
1
1
0
1
2
1
1
0
2
0
1
1
1
1
0
1
1
0
1
0
0
0
1
1
1
0
0
0
0
2
1
0
0
0
0
0
1
1
1
1
1
2
0
3
2
1
1
2
0
1
2
0
1
1
0
1
0
1
0
2
2
1
1
2
2
0
1
0
0
1
1
1
1
0
1
2
0
0
1
1
0
1
1
1
0
2
0
1
1
2
2
1
0
2
0
0
1
2
1
1
0
0
1
1
2
0
4
1
0
1
1
0
0
0
0
1
2
1
2
1
0
0
0
0
1
0
2
0
1
0
1
1
0
1
2
0
1
2
2
1
1
0
2
1
2
0
1
2
1
2
2
0
0
1
0
3
0
2
1
2
1
2
1
1
0
1
2
2
2
0
1
0
1
1
0
1
1
3
2
0
1
0
2
0
0
1
0
1
1
0
0
2
1
0
2
2
0
1
0
1
0
0
0
0
0
1
0
0
2
2
0
1
2
0
0
1
0
2
0
1
2
0
0
1
2
1
1
1
0
0
2
1
2
2
2
0
0
2
1
1
0
1
2
2
0
0
2
0
1
1
1
1
0
1
0
1
1
2
1
1
2
1
0
2
0
2
0
1
1
1
1
0
1
0
2
0
0
0
0
0
0
0
0
0
2
2
1
0
2
0
1
2
0
0
1
1
2
1
0
1
0
1
2
0
0
1
0
1
1
0
0
0
2
1
1
2
4
0
1
0
0
2
1
0
2
2
1
2
2
1
1
0
1
1
0
1
1
0
0
1
0
2
0
1
0
1
1
0
1
0
1
2
1
0
0
1
2
1
2
0
1
0
1
0
0
1
0
0
2
0
0
2
1
0
1
0
1
1
2
2
1
1
1
0
2
2
0
0
0
1
2
1
0
0
0
1
0
0
1
0
1
0
0
2
0
2
1
1
7
2
1
0
0
2
0
2
1
0
1
1
0
1
1
2
1
0
0
1
0
1
2
1
0
1
0
1
0
0
2
0
1
2
0
1
1
0
1
1
0
2
0
1
0
0
2
2
0
7
0
2
1
0
0
2
1
1
1
1
1
1
2
1
1
0
0
2
0
1
1
2
0
0
1
0
0
0
1
1
0
0
1
1
1
0
1
1
0
2
0
1
1
1
0
1
1
0
0
0
1
1
0
0
1
1
2
0
1
0
0
1
0
2
1
0
1
2
1
1
1
2
1
0
2
0
0
2
1
1
0
0
1
0
1
1
1
0
1
0
0
0
2
1
1
0
1
1
1
2
0
1
0
0
1
1
1
0
2
1
1
2
2
1
0
1
0
2
2
0
2
1
1
2
1
1
15
1
1
1
2
2
0
2
2
1
0
0
2
1
0
2
1
1
0
2
2
2
0
0
1
2
1
1
0
0
0
0
2
1
1
0
0
2
1
0
2
1
0
1
1
0
1
1
0
2
1
1
0
2
2
2
2
1
0
1
1
0
1
0
0
0
0
1
2
0
1
0
2
1
1
0
1
3
2
1
2
1
1
0
2
2
0
1
1
0
1
2
2
2
0
1
2
1
1
1
0
1
0
0
1
0
0
0
2
2
1
0
2
1
1
0
1
1
1
0
1
2
2
2
2
0
0
1
0
2
0
2
0
2
0
0
0
1
1
3
1
2
1
0
1
3
2
1
0
0
0
2
1
1
1
0
1
1
1
0
2
1
1
1
1
0
2
1
1
0
0
1
1
2
1
1
2
2
0
1
1
0
1
1
0
2
1
2
2
1
0
0
1
0
2
1
1
0
1
1
0
1
1
3
0
0
2
0
1
0
1
1
1
1
0
0
1
2
1
0
0
0
1
0
2
1
1
0
1
0
0
1
2
1
1
1
0
3
2
1
1
1
0
0
0
1
0
0
0
2
2
2
2
1
1
0
0
1
0
2
0
2
1
0
0
1
0
2
1
0
1
0
1
0
0
1
2
1
0
1
1
0
1
0
1
1
2
0
0
1
0
1
1
1
0
1
1
0
1
1
0
1
0
0
0
0
1
0
1
0
0
0
1
1
0
1
1
0
1
3
0
0
0
0
1
1
1
0
0
1
1
0
0
0
2
1
2
0
1
2
1
0
0
1
1
2
0
0
2
0
0
0
2
1
2
2
0
1
2
2
2
2
0
1
1
2
1
0
2
0
1
1
0
0
0
0
1
0
1
2
2
1
0
1
1
0
2
0
1
2
0
1
0
1
2
0
0
2
0
0
1
1
1
1
0
0
0
0
1
0
2
1
0
1
1
1
2
0
1
1
1
1
0
0
0
1
2
0
0
2
1
0
1
1
2
1
0
2
1
2
1
1
0
0
0
1
0
2
3
2
1
1
2
1
0
1
1
0
1
1
2
1
2
0
2
0
1
1
1
1
2
0
1
2
2
0
0
0
1
1
1
1
2
0
0
1
1
1
2
1
1
0
1
1
2
2
0
2
1
0
2
0
2
0
0
2
1
0
2
0
1
2
2
1
1
0
0
2
1
0
1
2
0
1
0
2
1
3
2
2
0
0
2
2
0
0
0
1
0
0
0
1
0
1
1
0
0
1
0
0
0
3
1
2
0
0
0
0
0
1
0
1
0
1
0
0
2
1
0
0
2
1
1
1
2
1
0
1
1
2
0
1
2
2
0
1
1
2
0
1
0
2
0
0
2
1
0
2
1
0
2
1
0
0
1
1
2
0
0
1
1
2
0
0
0
1
0
2
2
1
2
0
1
0
10
1
1
2
1
2
0
0
2
2
1
2
0
0
0
0
2
1
2
2
1
0
0
0
0
1
1
1
1
1
0
0
1
0
0
0
1
1
2
0
2
2
1
0
0
1
1
2
2
0
2
0
1
1
0
1
1
1
0
1
0
0
1
2
0
0
0
1
0
2
1
0
0
0
2
0
1
1
2
0
1
0
1
0
0
2
1
1
1
0
1
1
1
0
2
1
1
0
1
2
0
2
0
2
1
0
1
0
2
1
0
1
0
0
1
0
1
1
1
0
1
0
1
1
2
1
0
1
2
0
0
0
1
1
0
1
1
0
0
1
1
1
1
0
0
1
3
2
0
1
2
1
2
2
0
1
2
0
2
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
2
0
2
1
1
1
1
1
0
1
0
0
1
1
1
2
1
0
0
0
2
0
1
0
2
0
1
0
1
0
0
1
0
1
1
1
1
1
0
2
1
0
0
0
1
2
1
1
2
2
1
1
1
0
0
2
1
1
1
0
0
1
1
2
0
1
2
2
0
2
0
1
2
0
2
1
1
1
0
2
0
2
2
0
1
1
1
1
1
2
2
0
1
0
1
2
0
0
2
1
0
0
0
1
0
1
0
1
1
1
1
2
0
0
2
0
1
0
0
1
0
1
1
0
2
1
0
1
2
1
1
2
2
1
2
0
0
1
0
2
0
1
0
0
2
0
1
0
0
1
1
0
0
0
2
1
1
1
0
0
0
0
0
0
0
2
2
2
1
1
2
0
1
0
0
2
1
0
0
0
1
1
1
1
1
1
1
0
0
0
1
1
0
6
1
1
1
1
0
0
1
0
1
0
0
2
2
1
1
0
1
0
0
1
2
1
0
0
0
1
0
2
2
0
0
0
0
1
2
0
0
1
1
0
0
2
0
2
2
0
1
1
1
0
0
1
1
0
0
0
2
0
1
0
0
1
1
2
0
0
1
1
0
1
1
1
2
2
1
2
2
0
1
0
2
1
0
1
1
0
1
0
0
0
2
2
1
0
2
0
1
1
3
0
0
4
1
1
1
1
2
2
0
0
0
0
0
0
1
2
1
1
1
0
0
0
0
2
1
0
0
0
1
0
0
1
0
1
1
0
0
1
1
1
0
1
1
0
1
2
0
1
1
0
1
2
1
0
1
1
0
0
1
0
1
0
0
0
0
1
0
0
1
2
2
2
0
2
1
2
1
1
1
0
0
0
0
0
0
1
2
1
2
0
1
0
1
1
1
2
0
1
0
1
1
3
2
0
1
2
0
0
0
1
1
2
0
1
1
0
2
1
0
0
0
1
1
1
0
1
1
0
0
2
1
0
2
2
0
0
0
0
2
1
1
1
2
0
1
1
0
0
0
0
0
1
1
0
0
0
2
0
1
1
0
1
1
0
0
1
1
2
1
1
0
1
0
1
0
6
1
1
0
1
2
0
1
0
0
1
0
1
1
2
2
0
1
1
0
0
0
0
0
2
4
2
0
2
1
1
2
2
0
2
0
0
0
2
0
2
1
1
1
0
1
1
0
2
1
2
3
1
0
0
1
1
0
2
2
0
0
2
1
2
0
2
0
1
0
2
1
0
0
1
1
0
2
2
2
1
1
1
1
2
1
1
0
1
2
1
0
2
1
1
2
2
0
1
0
2
1
0
1
0
1
1
0
1
0
0
1
2
1
1
0
2
0
1
1
0
0
0
1
0
1
0
0
1
1
0
1
0
0
2
1
2
0
0
0
0
0
2
1
2
0
1
1
1
0
2
0
1
1
0
0
1
0
1
1
1
1
1
0
1
2
0
0
2
1
0
1
1
2
1
2
2
0
1
2
2
0
2
1
2
1
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
2
1
1
2
1
2
1
1
0
2
1
1
0
1
0
1
1
1
0
3
0
1
0
0
0
2
0
1
1
1
1
1
0
1
1
2
1
1
1
1
1
2
1
2
1
0
0
0
1
0
1
0
1
1
0
1
0
0
0
1
0
0
0
2
0
1
1
0
0
0
2
1
0
0
0
0
0
1
0
2
0
0
2
0
0
1
0
0
0
1
0
0
1
0
0
0
3
1
1
1
1
0
1
1
1
1
1
0
1
1
1
0
0
0
2
0
1
0
2
1
1
0
0
1
1
1
0
1
0
2
1
2
1
0
1
1
1
1
2
2
1
1
1
0
1
2
1
2
0
0
0
2
1
0
1
1
1
1
1
1
0
0
1
0
0
0
1
0
0
2
0
2
1
2
0
0
0
0
1
2
0
1
2
1
1
1
0
1
2
0
0
1
1
0
0
1
1
2
0
0
2
0
1
1
0
1
1
2
1
1
0
1
0
0
1
0
0
2
1
1
1
1
1
2
1
1
0
1
0
1
0
1
2
1
0
1
3
1
1
1
2
0
0
1
2
0
2
1
1
2
0
2
1
0
1
2
0
2
0
0
0
2
2
1
1
0
0
1
0
2
1
1
0
1
0
0
0
1
2
2
2
0
1
0
0
1
2
0
1
2
1
2
1
0
3
1
0
1
0
0
1
2
0
2
0
0
2
1
0
0
1
2
2
1
1
0
0
0
0
3
1
0
0
1
0
0
0
0
1
1
2
1
0
0
0
0
0
1
0
1
1
0
0
0
1
2
0
2
1
2
2
0
2
2
0
1
2
1
0
0
1
1
2
1
1
0
1
0
1
1
0
1
0
2
1
1
2
0
0
0
1
0
0
0
0
2
0
0
0
1
0
2
0
1
1
1
2
1
0
1
2
4
1
2
1
0
1
2
2
1
1
0
1
2
1
0
2
0
1
1
1
3
0
1
1
2
1
1
2
0
0
0
0
1
1
0
2
0
2
0
1
1
2
1
1
0
0
2
0
0
1
1
1
0
1
0
2
1
1
0
0
0
1
0
0
1
0
2
0
1
0
0
0
1
2
1
1
0
2
0
2
0
1
1
0
0
1
0
0
0
1
1
2
0
0
1
0
2
1
0
0
0
1
0
3
0
1
2
1
1
1
0
2
2
1
1
0
0
1
0
2
2
1
2
1
0
0
0
0
2
1
2
0
0
1
1
0
1
1
2
0
1
0
2
0
1
1
1
1
0
1
0
2
0
2
0
1
1
0
2
0
0
0
1
0
2
1
0
1
0
0
1
2
0
2
0
1
1
1
1
2
0
1
0
0
2
1
0
1
1
2
1
1
0
0
1
0
1
1
1
2
1
0
1
0
1
0
1
2
3
0
2
0
0
0
1
1
0
1
1
1
1
1
2
0
1
0
1
1
1
0
2
1
1
2
2
2
1
0
0
1
1
0
1
1
1
1
0
2
1
1
1
1
1
2
0
0
1
0
1
1
0
2
1
1
2
0
1
1
1
0
0
1
1
0
0
0
0
0
1
0
0
0
1
2
0
1
1
0
0
1
0
1
2
1
0
1
1
1
2
2
6
3
2
2
0
0
0
1
0
0
0
0
1
1
1
1
1
0
0
2
3
0
2
0
0
4
0
1
2
1
1
1
0
1
1
0
0
0
2
0
4
3
0
1
0
0
1
1
1
1
0
1
2
2
1
1
0
1
1
0
0
1
0
2
1
0
3
1
1
1
2
0
1
0
2
1
1
0
0
1
1
2
1
0
1
2
0
1
1
1
1
2
1
0
2
2
2
1
1
2
1
1
1
1
0
1
0
1
0
0
0
0
2
2
0
0
0
0
0
0
2
1
2
1
2
0
1
0
0
1
1
0
3
1
1
1
1
1
0
2
1
0
0
1
2
1
0
1
1
0
1
1
0
2
0
1
0
1
3
1
0
1
0
1
2
0
0
2
2
1
1
0
0
1
0
0
0
1
2
1
1
0
0
1
0
2
2
0
0
1
1
0
2
1
2
1
1
1
1
1
1
1
0
1
0
0
0
1
2
1
2
1
1
0
1
0
0
0
0
0
2
1
0
0
0
0
1
1
0
1
1
0
1
1
0
2
0
2
1
2
0
0
0
0
0
0
1
1
1
1
0
1
1
1
0
2
0
1
2
0
1
1
1
1
0
2
0
0
1
0
0
0
0
0
1
0
1
2
0
1
0
2
1
0
2
3
0
0
0
1
1
1
2
0
0
0
0
0
1
3
2
2
0
2
0
1
0
1
0
1
1
1
0
2
0
0
0
0
1
0
1
0
1
0
0
1
2
0
4
6
0
0
2
0
0
0
2
1
2
2
0
1
0
0
1
0
1
1
0
2
1
2
0
0
0
0
1
2
1
0
2
2
1
1
0
1
2
0
0
1
0
2
1
1
1
1
0
1
2
1
0
0
1
1
0
0
0
1
1
0
2
0
1
2
2
1
0
2
2
0
0
1
0
1
1
2
1
1
1
0
0
0
0
1
0
2
0
1
0
0
2
2
1
2
0
1
2
0
1
0
1
0
1
2
0
0
0
1
2
1
2
0
1
1
1
2
1
1
0
1
2
1
0
0
1
0
1
0
2
1
2
1
0
1
0
2
0
1
2
1
1
0
5
0
1
3
0
1
0
1
0
0
4
2
1
2
2
1
0
1
0
1
0
0
1
0
1
1
1
1
1
0
1
1
1
0
1
1
0
0
0
2
2
1
1
2
1
2
2
0
2
1
2
2
3
0
1
1
1
1
1
1
1
1
2
1
0
2
0
1
1
0
0
2
1
1
1
1
1
1
0
1
2
0
0
1
2
0
0
1
0
1
0
1
2
1
0
2
0
1
0
0
0
1
0
1
1
1
1
0
0
0
4
0
0
1
1
9
0
0
2
1
0
0
0
0
1
1
1
1
1
0
0
0
1
1
2
0
1
1
0
2
1
1
1
1
2
1
1
1
1
1
2
0
2
2
1
1
2
1
2
2
2
1
0
0
1
0
0
0
0
2
1
0
2
1
2
1
2
2
1
1
0
1
1
2
0
0
0
4
2
2
2
0
0
3
1
0
0
0
1
0
1
1
1
1
1
0
1
0
0
1
1
1
2
1
0
2
0
0
2
2
2
0
0
0
2
2
1
1
1
2
2
0
2
1
2
0
0
1
2
1
2
1
2
0
0
0
1
2
1
2
2
1
1
1
1
1
1
0
0
1
0
0
0
1
0
2
1
0
2
0
2
1
0
1
0
2
3
0
1
1
2
0
0
0
1
0
1
1
1
2
4
1
1
1
1
2
0
2
1
0
0
2
2
0
1
1
1
0
0
0
0
0
0
0
1
1
2
0
1
1
1
0
0
0
1
1
1
0
0
2
2
1
2
2
2
2
2
1
1
1
0
0
0
0
1
2
0
0
0
1
0
1
1
0
2
0
1
2
0
1
0
1
0
2
1
0
2
1
0
1
2
3
1
1
1
0
0
0
1
0
0
1
2
0
0
1
1
1
2
1
2
0
1
1
1
0
1
0
0
0
0
0
2
0
0
2
1
1
0
0
1
0
1
1
0
1
2
1
2
0
0
2
0
2
1
2
2
0
0
0
1
1
1
2
0
1
2
2
0
2
2
1
2
1
0
0
1
2
0
2
0
0
0
1
1
0
2
0
0
0
1
1
1
1
2
1
0
0
0
1
1
0
0
0
1
1
1
1
0
0
1
1
0
1
1
0
0
1
1
2
1
0
0
0
0
0
1
1
0
1
0
2
1
0
0
2
2
0
0
1
0
0
1
1
0
2
1
0
0
0
0
0
1
0
1
2
1
1
1
0
0
1
0
0
1
0
0
0
0
2
1
0
0
1
0
0
1
1
2
2
0
1
1
0
0
1
1
0
0
1
4
0
2
2
0
1
1
1
0
0
1
1
1
1
0
1
0
1
1
2
2
2
1
2
1
2
0
0
2
1
0
1
1
1
0
1
1
1
0
3
2
1
1
1
0
2
0
0
2
0
0
0
1
1
1
2
1
0
1
1
2
2
0
1
2
2
1
0
1
0
0
0
1
0
1
2
2
0
1
0
1
0
0
1
0
0
1
2
0
1
0
0
0
2
0
1
2
0
2
1
2
0
0
0
1
1
1
3
2
1
1
0
0
1
0
0
0
1
1
1
1
0
0
0
1
1
1
1
2
1
1
2
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
2
0
1
1
2
0
0
0
1
1
1
2
2
1
3
0
0
0
1
2
2
0
0
1
2
2
1
0
1
0
0
1
0
2
3
0
0
3
2
2
0
2
2
2
0
0
2
4
2
1
0
1
2
2
1
2
1
1
2
1
0
1
1
1
0
1
0
2
1
2
1
1
1
1
1
2
1
1
0
1
1
0
0
1
0
1
0
0
1
2
1
0
3
1
0
2
1
0
0
0
0
0
0
1
1
2
0
0
2
1
0
1
0
1
1
0
1
0
1
2
2
0
0
0
1
0
1
1
1
1
0
3
0
2
2
1
1
2
1
0
1
2
0
2
1
0
0
1
1
2
1
2
0
2
0
1
0
0
1
1
1
0
1
0
2
1
1
1
1
1
0
1
2
1
0
0
1
1
1
0
1
4
0
1
0
1
0
0
1
1
0
1
2
1
0
1
1
1
0
0
2
1
0
0
2
0
1
0
1
1
1
0
0
2
1
0
0
1
1
1
1
1
2
3
0
0
0
1
1
2
0
1
1
2
2
0
1
2
0
2
0
0
0
0
1
1
1
2
1
0
2
1
2
1
2
1
2
1
2
2
0
0
0
0
4
1
0
0
0
0
0
0
0
0
2
1
0
0
1
2
0
0
1
1
0
1
0
1
1
1
2
0
2
0
1
0
1
0
0
1
5
2
1
0
0
1
2
1
2
0
1
0
0
1
1
0
0
1
0
0
1
1
0
2
0
1
1
0
0
1
2
1
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
1
1
2
1
2
0
1
0
0
0
0
2
2
1
2
0
2
0
2
0
1
0
1
1
0
0
1
1
1
0
1
0
0
0
0
0
1
0
2
0
0
2
1
2
0
1
2
0
1
0
1
0
2
2
2
2
2
0
1
0
1
1
1
1
0
0
0
2
0
1
1
1
0
1
2
0
0
0
1
1
0
0
1
1
0
1
0
1
1
1
1
1
0
1
1
0
1
2
1
0
1
2
0
0
0
1
0
0
1
1
0
0
2
0
1
1
0
0
0
2
0
1
1
1
1
0
1
0
1
2
0
1
2
0
2
2
1
0
0
0
0
0
1
2
0
1
2
0
2
0
1
1
1
2
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
1
1
0
1
0
1
2
0
1
0
1
1
2
1
2
1
0
0
0
2
1
1
1
1
1
0
0
1
0
0
2
2
1
1
0
0
1
0
0
0
0
2
2
1
2
1
1
1
0
0
1
0
1
1
1
1
0
1
1
2
2
0
0
0
2
0
1
1
1
0
0
0
0
0
2
1
2
0
2
1
2
1
1
1
0
1
1
2
1
1
1
1
2
1
1
1
1
2
0
1
0
0
2
1
0
1
1
1
0
2
1
1
0
0
1
1
0
2
1
0
0
0
0
2
2
1
2
1
1
1
2
1
2
2
2
0
2
1
1
2
1
2
2
1
0
0
0
2
2
1
2
0
1
2
1
0
0
2
1
0
0
1
2
2
1
0
0
0
1
0
4
1
0
2
1
1
0
0
1
1
0
1
0
1
0
1
1
2
0
1
0
0
0
1
1
0
1
0
1
1
0
1
1
1
1
2
2
1
2
2
1
0
0
1
1
0
1
0
0
1
0
1
1
1
1
2
2
1
1
1
1
0
0
0
0
0
0
0
3
0
0
0
1
0
1
1
1
1
1
1
1
3
0
2
1
2
1
2
2
2
1
1
2
1
0
0
2
0
1
0
1
2
1
2
0
2
0
1
0
2
1
1
0
1
0
1
0
1
1
0
1
1
1
1
0
2
1
0
1
1
1
0
2
1
0
2
2
2
1
1
1
0
0
0
1
1
2
1
1
1
2
1
2
0
0
2
1
1
0
0
2
3
0
0
1
2
1
2
1
0
0
0
1
0
2
2
0
0
0
0
0
1
2
1
1
0
0
1
1
2
0
2
2
3
1
0
1
1
2
0
0
0
1
1
0
0
0
2
0
3
2
0
0
2
1
1
2
2
1
1
0
0
0
2
1
1
1
1
0
1
0
1
1
1
1
0
0
1
0
0
1
0
0
2
1
0
1
1
0
0
1
1
1
1
2
2
1
0
0
2
0
0
1
1
1
2
0
0
1
0
1
1
1
1
0
0
1
0
1
0
2
0
2
1
1
0
2
0
0
0
1
1
0
1
1
1
2
0
1
1
0
0
1
2
2
0
0
1
2
2
2
1
1
0
2
0
2
1
1
1
1
1
0
1
0
1
0
2
1
1
1
1
0
1
2
2
1
0
1
0
1
0
0
1
0
2
0
0
0
1
1
2
1
0
1
1
2
0
1
1
2
0
2
1
0
1
0
2
0
1
1
1
1
1
2
1
1
0
1
0
2
1
0
0
2
2
0
2
2
0
0
0
0
1
2
0
1
0
1
2
1
0
0
1
1
1
1
1
0
1
1
1
0
0
0
1
1
1
0
1
2
0
1
1
1
2
0
0
1
1
1
0
1
1
1
0
0
2
2
1
1
1
1
0
0
1
0
1
0
1
0
3
1
0
1
0
1
1
1
0
1
1
1
2
0
2
0
2
1
0
0
1
1
1
1
2
0
0
0
1
1
2
2
0
1
0
0
1
0
0
0
2
2
1
1
1
2
2
0
2
0
0
2
1
2
3
0
1
3
1
1
0
1
0
1
0
1
2
1
1
2
1
1
0
0
0
2
0
1
1
0
1
2
0
0
2
0
1
0
0
0
3
0
0
0
0
1
0
2
2
0
1
2
2
0
1
0
1
0
2
0
1
0
1
0
2
2
0
1
1
0
1
0
0
1
0
0
0
0
2
0
0
0
0
1
2
0
0
2
0
1
0
2
2
0
2
2
2
0
0
1
0
0
1
1
0
3
1
0
1
1
1
1
1
1
2
1
1
0
1
2
1
0
1
1
0
2
0
0
0
1
1
0
0
1
0
2
0
1
2
0
2
1
0
1
1
2
2
1
0
2
0
2
0
0
0
0
2
1
1
0
0
2
1
1
1
2
0
2
0
2
0
2
0
1
0
1
1
1
0
2
1
0
1
0
1
2
2
2
2
0
1
1
1
0
2
0
1
1
1
0
1
1
1
0
3
0
3
0
0
4
1
2
1
1
0
1
2
0
1
0
1
0
2
0
1
1
2
1
0
0
0
0
1
0
0
0
2
0
0
0
1
1
2
2
1
1
0
2
0
2
1
0
0
1
0
1
0
2
2
1
2
1
0
1
1
0
0
2
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
1
2
0
1
0
1
2
2
0
2
0
2
2
2
1
0
0
0
1
0
2
2
1
0
0
1
0
0
0
2
2
1
1
1
1
1
1
1
2
2
0
1
2
1
2
0
0
1
0
1
2
1
0
1
1
0
2
0
0
1
0
0
2
2
0
0
2
1
0
0
0
0
1
2
1
1
2
0
0
2
0
0
3
0
1
2
0
1
0
1
1
2
1
1
0
0
0
1
1
2
0
1
1
2
1
1
1
1
0
1
0
1
0
1
2
0
2
1
2
2
0
1
0
0
1
3
0
1
0
1
1
0
1
1
2
0
0
0
0
1
0
0
2
1
2
1
0
2
0
1
2
1
0
3
1
2
1
1
2
0
2
0
1
0
2
1
0
0
7
2
0
0
0
2
0
2
2
0
0
1
1
0
2
2
1
1
0
0
1
0
0
1
0
1
1
2
1
1
0
0
1
0
0
2
2
1
0
1
1
0
0
1
1
1
0
0
1
2
1
0
0
0
0
1
1
0
1
1
1
0
1
0
1
2
1
1
2
0
0
2
1
2
2
1
1
1
0
0
0
0
1
1
1
0
1
3
1
1
1
0
2
1
0
1
1
2
1
0
0
2
1
2
0
1
1
1
0
2
1
1
2
0
0
0
2
2
0
0
1
4
1
0
1
2
0
1
2
2
1
1
1
2
0
2
1
0
1
1
0
1
2
2
0
2
1
1
1
1
0
0
0
0
1
2
1
0
2
0
0
0
1
0
0
0
0
1
0
2
0
2
2
2
2
1
1
2
1
2
1
0
0
0
1
0
0
1
1
0
0
0
1
1
0
1
0
0
1
2
1
1
1
0
1
2
0
2
0
2
1
0
0
0
2
1
1
1
0
2
1
0
0
0
0
0
0
0
2
0
1
0
1
2
1
0
1
0
1
0
0
0
1
1
0
0
2
1
1
2
0
0
0
1
1
1
1
1
0
0
2
0
1
1
1
1
2
1
0
0
1
0
0
0
0
1
1
1
1
0
1
1
1
1
1
1
2
0
0
2
2
1
1
0
0
0
1
0
0
1
0
1
1
1
0
0
0
0
0
0
1
1
1
2
0
2
0
2
0
2
0
0
2
1
0
0
1
2
0
1
0
0
0
1
2
1
0
0
1
1
0
1
2
0
0
0
0
1
0
1
2
1
1
1
2
0
2
0
1
0
2
1
2
0
0
0
1
0
0
2
0
2
1
0
1
0
1
0
1
2
1
2
0
1
1
0
0
1
0
1
0
0
0
1
1
2
0
2
0
1
1
0
1
2
1
2
1
1
2
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
2
0
1
3
0
1
0
3
0
0
2
2
0
0
2
0
0
2
2
0
1
2
1
0
0
0
1
0
1
0
0
2
1
1
1
0
1
0
1
2
2
1
0
0
0
1
1
1
0
0
0
0
0
2
2
1
2
1
2
0
1
0
1
2
2
1
0
2
0
1
0
1
0
1
1
1
2
1
1
1
0
2
0
1
1
0
0
1
1
0
0
2
0
3
0
1
1
2
3
1
1
2
1
1
2
2
1
1
0
1
0
0
1
2
0
0
1
0
2
2
1
1
1
1
0
1
1
2
0
0
1
1
0
2
1
0
2
0
2
0
0
1
1
0
1
1
1
0
2
2
1
1
0
2
0
0
0
1
2
2
0
1
1
2
1
2
2
0
1
0
2
1
0
0
2
0
0
2
1
1
3
0
0
1
1
2
1
1
2
0
0
3
1
0
0
0
0
2
0
0
2
2
1
0
1
1
2
0
0
0
0
2
1
1
0
1
0
4
1
1
0
0
0
2
2
1
0
0
0
0
2
2
1
0
1
0
1
1
1
2
0
2
1
1
1
2
1
0
0
1
0
2
1
1
1
0
1
1
0
1
0
1
1
2
0
2
0
0
1
2
1
1
0
1
2
1
1
0
0
0
1
1
2
1
1
2
0
1
1
1
0
0
0
0
1
0
1
0
1
0
2
0
1
0
1
2
1
3
0
2
2
0
2
0
0
0
2
1
0
0
2
3
0
2
2
1
0
0
0
0
2
0
1
0
0
1
1
0
3
0
1
1
1
1
1
1
1
2
1
2
0
0
0
0
1
0
0
0
1
0
1
1
0
0
2
2
1
2
0
0
0
1
1
0
0
2
1
0
2
0
2
1
1
1
0
0
1
1
0
0
0
0
1
0
0
0
1
2
1
1
2
1
1
1
2
1
0
0
2
0
2
0
1
1
0
1
1
0
1
2
0
0
1
0
0
0
2
2
2
1
0
0
0
0
1
1
1
1
3
0
0
3
2
1
1
0
2
1
1
0
0
1
0
0
1
2
1
1
0
1
0
0
2
1
2
0
1
0
0
1
2
2
1
0
1
1
1
1
0
2
1
0
1
0
1
0
0
1
0
0
1
1
2
0
0
0
9
2
2
1
5
0
0
1
2
0
0
2
1
0
2
0
0
2
0
0
2
2
1
1
0
1
0
0
1
1
0
1
2
0
0
2
3
0
0
1
1
2
0
1
0
2
2
0
1
1
0
1
4
0
0
1
0
1
2
0
1
0
2
1
2
2
0
2
2
1
0
1
0
0
2
1
2
0
0
1
1
1
0
0
1
1
0
0
0
1
3
3
1
0
2
0
0
2
2
0
1
2
0
2
0
2
2
1
0
0
0
0
0
1
0
1
0
0
0
2
2
0
0
1
3
0
0
0
0
1
0
0
2
1
1
0
0
4
1
1
2
1
1
1
0
0
1
0
0
2
0
1
0
2
1
1
1
1
1
1
1
1
1
0
0
0
1
1
2
0
0
1
2
0
0
1
1
1
1
0
2
3
1
0
1
0
0
2
2
1
3
1
0
1
0
1
0
2
2
0
2
1
0
0
1
1
1
0
1
0
1
1
0
0
0
1
0
1
1
2
0
0
2
1
0
0
1
0
2
1
0
1
2
1
0
2
1
2
1
1
2
1
1
1
1
1
2
1
0
2
0
0
2
1
2
2
1
0
0
1
1
1
2
2
0
1
2
0
1
2
0
2
0
0
0
1
1
0
0
1
1
1
0
1
1
0
1
0
0
2
1
1
0
0
1
1
2
1
2
1
2
0
2
1
0
1
1
2
2
1
0
0
1
0
0
1
0
0
1
2
1
0
1
1
2
2
2
0
0
1
0
0
1
1
0
1
0
0
1
2
0
3
0
2
2
2
2
0
0
1
2
2
1
1
0
0
2
2
0
0
2
1
1
0
2
2
2
2
0
0
1
1
1
1
1
3
0
0
1
2
1
1
2
2
1
0
0
2
1
2
2
1
2
0
0
1
2
0
0
4
1
1
1
0
0
1
1
0
1
0
0
2
0
1
0
1
1
1
0
0
3
3
2
1
1
1
0
0
1
1
0
0
0
0
6
2
0
0
1
0
0
0
1
2
2
2
1
1
0
1
1
1
1
2
1
2
1
1
1
1
2
2
1
1
0
2
1
0
0
0
2
1
2
0
0
1
2
2
1
0
2
2
1
2
1
1
0
1
0
0
1
0
1
2
2
1
1
0
2
0
1
1
1
0
0
0
1
0
0
0
2
3
0
1
1
2
2
1
0
2
0
0
0
0
1
1
0
1
1
1
1
1
0
2
0
2
2
2
0
1
0
1
2
1
1
0
0
2
0
0
2
1
2
0
0
0
0
2
0
0
1
2
0
1
0
0
0
0
1
1
0
0
1
0
1
0
2
1
1
1
1
1
1
1
0
0
0
1
0
1
2
0
0
0
1
0
1
2
0
1
10
0
0
2
1
1
0
0
1
0
1
2
2
0
0
2
1
0
0
0
1
1
2
2
2
2
2
1
2
1
1
1
2
1
1
1
1
0
0
1
1
0
0
1
0
0
2
1
0
1
2
1
1
3
0
0
0
1
2
0
2
0
2
2
1
2
2
2
1
2
1
1
1
1
1
2
1
1
1
1
0
1
2
2
2
0
1
2
2
0
0
0
1
0
0
0
4
2
0
0
1
0
1
1
0
0
0
1
0
2
0
1
0
0
0
1
0
1
0
1
1
0
1
1
0
0
1
0
1
0
1
0
0
0
2
5
2
0
1
0
0
1
2
1
2
1
1
0
0
0
0
2
1
1
0
1
1
2
2
0
0
1
0
1
1
1
2
1
2
1
0
1
0
1
1
0
2
0
2
2
1
2
1
0
1
1
1
1
0
2
1
1
1
1
1
1
1
0
2
1
0
1
2
1
1
1
1
0
1
0
1
0
0
0
2
1
1
1
1
1
0
0
1
1
1
2
0
2
1
0
1
2
1
1
0
0
1
1
1
2
0
2
2
1
4
1
0
2
0
0
1
0
1
1
0
0
0
0
2
1
0
0
1
0
1
1
0
0
0
2
1
1
1
0
0
4
0
0
1
0
3
2
0
0
0
1
2
1
1
0
1
0
1
0
0
1
0
1
0
0
0
0
1
1
2
0
1
1
1
2
0
1
2
0
0
2
1
2
2
1
2
1
1
0
1
2
0
0
3
0
1
2
1
0
0
1
2
1
0
0
1
0
2
2
0
0
2
1
0
0
2
2
1
1
1
1
0
1
1
0
1
1
1
1
2
2
1
2
0
1
2
0
1
1
0
2
1
1
0
1
1
1
0
1
1
1
0
1
1
1
1
0
0
0
2
1
0
2
0
0
0
0
0
1
0
3
1
1
1
0
1
0
1
0
1
1
0
1
0
0
1
0
0
1
1
1
2
1
0
1
2
0
1
1
0
1
0
1
0
0
0
0
0
1
0
2
1
0
0
0
1
1
2
0
1
1
0
1
1
2
2
1
2
2
1
0
1
0
0
0
0
1
1
2
0
1
1
0
0
2
1
0
2
2
2
0
3
2
0
1
1
0
1
0
1
2
0
1
1
0
2
2
1
1
1
2
1
1
1
2
0
2
2
1
1
2
1
2
0
1
0
0
0
1
0
1
0
1
0
0
0
1
0
1
1
0
1
0
1
0
0
1
0
0
1
0
1
0
0
2
0
1
0
0
1
1
1
1
0
2
1
1
0
0
2
1
1
1
0
2
1
1
1
1
1
2
2
0
1
1
2
1
1
1
1
0
3
0
1
1
0
1
1
0
2
2
1
1
2
2
1
0
0
2
1
1
1
1
1
2
3
0
0
0
1
0
1
0
1
2
1
1
1
1
2
0
5
2
0
1
0
0
1
0
0
2
2
1
1
0
0
0
2
0
2
1
1
1
0
2
2
0
2
1
1
1
1
0
0
1
4
1
0
1
1
0
0
1
1
2
1
0
1
2
1
1
0
0
3
0
0
1
1
0
0
1
1
1
0
1
1
0
1
2
0
1
1
0
0
1
1
0
2
0
0
0
0
0
0
0
1
0
2
0
0
2
1
0
2
1
0
2
0
1
2
0
0
0
1
2
1
0
0
1
1
1
1
1
0
2
1
0
0
0
1
2
0
2
0
1
0
1
2
0
0
0
2
0
1
0
2
0
1
3
1
0
1
1
1
2
2
0
2
1
0
0
0
1
1
1
0
1
0
1
2
0
3
1
0
0
0
0
1
1
0
2
0
0
1
1
1
1
1
0
1
1
1
1
0
1
0
0
2
2
0
1
0
0
2
1
0
0
0
0
1
2
2
1
0
1
0
0
2
1
0
0
1
1
2
1
1
0
1
0
1
0
4
2
1
0
0
0
0
0
0
1
0
2
2
1
2
1
0
1
2
1
0
0
0
1
2
0
1
1
1
0
0
2
0
0
1
1
0
1
2
2
2
0
1
0
2
0
1
0
1
1
2
1
1
0
0
2
0
0
1
2
0
0
0
1
0
0
0
0
1
1
1
1
1
0
0
1
1
4
0
1
1
0
1
2
0
0
0
2
2
2
2
0
2
1
0
1
0
1
1
0
0
0
1
1
1
1
2
1
0
1
0
1
0
0
1
0
1
1
0
0
0
3
0
1
1
1
0
0
0
1
2
0
0
2
4
0
1
0
1
1
1
0
1
1
1
2
0
0
0
2
1
0
2
2
2
0
2
0
0
1
1
2
2
1
1
1
0
0
0
0
0
1
1
1
0
0
1
1
2
2
0
1
1
1
2
1
1
2
2
2
0
0
0
0
1
0
1
1
1
1
0
1
1
0
1
1
0
0
2
1
0
2
1
1
1
1
2
0
2
0
1
2
0
1
2
2
3
1
1
1
1
0
0
0
0
1
0
2
0
2
0
2
1
1
1
0
0
2
0
1
2
0
2
0
2
2
0
1
0
1
0
1
1
1
0
0
0
1
0
0
0
2
2
1
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
1
3
1
0
1
1
0
1
1
2
0
0
0
1
2
1
1
0
1
1
0
0
0
2
2
2
1
2
0
2
1
0
1
2
1
1
2
0
0
2
1
1
0
1
0
2
1
0
0
0
0
0
1
0
1
2
2
0
1
0
1
1
0
0
2
0
1
1
0
0
0
0
1
2
2
1
1
0
1
0
2
0
0
0
1
1
0
1
2
1
1
2
2
1
0
0
1
1
2
0
0
2
0
0
4
1
0
0
1
1
1
1
1
2
1
0
0
0
3
2
1
1
0
1
1
1
0
1
1
1
1
1
2
0
1
0
1
2
2
0
0
2
2
1
2
1
0
0
0
0
1
1
2
1
2
1
2
1
1
1
0
0
1
2
2
1
2
0
0
0
0
0
1
1
0
2
0
0
0
1
1
2
0
1
0
0
1
1
2
0
0
1
1
2
1
2
0
1
0
0
0
2
0
1
2
0
2
0
2
1
2
0
2
0
0
0
1
1
1
0
2
2
1
2
0
3
2
1
2
1
1
1
0
2
2
1
1
1
2
1
1
2
1
1
1
1
1
1
1
1
1
2
1
1
1
0
0
0
1
0
1
2
0
1
0
1
1
0
0
1
2
0
0
1
0
1
0
0
1
0
1
0
2
0
1
1
2
2
0
0
0
0
0
2
1
3
0
2
2
1
2
0
0
2
0
0
2
0
0
0
1
2
1
0
1
2
1
2
2
2
0
1
1
0
1
1
0
0
0
2
0
1
0
1
1
0
0
0
0
1
1
2
0
0
0
2
2
0
0
1
1
1
1
2
1
2
1
0
2
0
2
2
2
1
0
0
2
2
0
0
1
1
2
2
2
1
2
0
1
2
0
0
0
0
1
2
1
0
1
1
1
1
1
2
1
0
0
1
1
1
0
1
0
3
0
1
1
1
1
0
1
0
2
2
0
1
0
1
0
1
0
0
2
1
0
0
0
2
2
0
1
0
0
1
1
2
2
0
1
1
0
0
1
4
0
1
0
3
1
1
2
0
2
3
2
0
1
1
4
1
1
1
1
0
0
1
0
2
0
1
0
1
1
1
2
1
2
2
1
0
0
0
2
0
1
0
0
0
1
0
0
2
0
1
1
1
0
1
0
1
2
2
2
0
2
2
0
0
2
1
0
2
3
2
0
2
0
2
0
2
2
0
0
3
2
0
0
0
0
0
0
0
1
0
2
1
2
1
1
0
0
0
1
2
0
1
0
0
1
2
1
0
2
3
1
2
0
0
0
2
1
1
2
1
1
1
2
1
1
1
1
1
2
0
1
1
0
0
0
1
1
1
2
1
0
2
1
1
0
2
0
0
0
1
0
1
0
0
0
0
0
0
1
2
2
2
0
1
1
3
0
0
1
2
2
2
1
1
0
2
2
2
1
1
0
1
1
1
0
1
2
2
0
0
1
0
0
1
1
2
1
1
1
1
2
0
0
1
1
0
1
0
0
0
0
2
0
1
1
2
2
2
0
1
0
0
2
2
2
1
0
1
1
0
2
0
1
2
2
2
1
1
1
2
1
1
2
1
0
1
1
1
1
1
1
0
0
0
0
2
1
0
1
1
0
0
1
1
0
2
2
1
0
0
0
0
1
0
0
0
1
2
2
0
1
1
0
1
2
0
0
2
0
1
1
1
0
1
2
1
2
2
4
0
0
2
0
1
2
0
0
1
0
1
2
1
0
1
1
0
0
0
0
1
2
1
0
2
3
1
1
2
1
1
0
0
0
1
2
1
1
1
2
0
2
1
1
2
0
1
0
0
2
1
0
0
1
0
1
1
0
2
0
2
2
0
1
0
1
1
0
2
1
1
1
2
0
2
0
1
0
1
1
2
1
1
0
2
1
1
1
1
1
0
1
1
0
0
0
0
0
1
2
0
0
1
0
2
2
2
1
1
1
0
1
1
0
1
0
0
2
0
0
1
1
0
2
1
2
1
2
0
1
0
1
0
0
2
1
0
0
1
0
0
1
1
1
1
0
1
0
2
1
2
1
0
0
1
1
0
0
0
2
1
0
2
0
1
1
2
1
1
0
2
1
1
1
1
1
1
1
0
1
1
2
0
2
1
1
0
1
2
1
0
0
1
1
2
1
0
0
1
0
0
1
1
2
1
2
1
0
0
1
1
0
1
0
0
1
0
2
1
2
1
0
0
0
1
0
1
2
1
0
3
0
1
1
1
0
1
1
0
1
1
1
1
2
0
0
2
1
0
1
3
3
1
4
2
1
1
1
1
1
1
1
2
1
0
1
2
0
2
1
0
2
1
0
1
0
1
0
0
1
1
0
1
1
1
0
1
2
1
1
0
0
2
0
1
0
1
0
1
1
1
0
2
1
1
0
2
0
0
2
1
0
2
0
0
1
1
2
0
0
0
2
1
0
1
1
2
2
0
2
0
0
0
0
0
1
0
0
2
1
0
0
1
1
0
1
0
0
1
0
2
3
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
1
2
0
1
1
0
0
0
1
0
0
0
2
0
2
0
0
1
2
1
2
0
0
0
1
1
1
1
1
2
1
0
2
1
0
2
0
0
1
2
1
1
1
1
2
0
0
2
1
1
0
1
0
1
1
0
2
2
0
1
0
0
1
1
2
0
0
1
1
1
0
2
1
0
1
0
0
0
1
1
0
0
0
1
0
1
1
1
1
2
0
0
0
0
0
2
1
2
0
0
0
0
1
1
1
1
1
1
0
0
1
0
2
1
0
1
0
1
0
0
1
2
0
1
1
2
1
2
1
2
1
1
2
1
0
1
1
2
1
0
1
1
2
0
0
0
0
0
1
1
2
0
1
1
0
1
0
1
0
0
2
1
1
1
0
1
0
0
1
1
0
1
0
2
1
2
2
0
2
0
2
2
1
2
0
0
2
1
0
0
1
1
0
0
0
2
1
0
0
2
1
1
1
1
0
1
1
1
2
1
1
0
1
0
2
0
1
1
2
1
0
2
0
0
2
1
1
2
0
2
0
0
2
1
2
1
0
0
1
0
0
1
0
1
1
0
2
0
1
0
2
3
1
1
2
0
1
0
1
1
0
2
1
1
2
2
0
1
0
0
1
2
0
0
1
0
0
0
1
3
1
0
2
1
2
2
0
0
0
1
2
1
2
0
0
0
0
2
0
0
2
0
1
0
1
2
0
0
1
1
1
0
2
2
0
1
2
1
1
1
2
0
1
0
1
0
2
1
0
0
1
1
1
1
1
0
1
1
0
2
2
1
1
0
0
0
3
1
0
3
1
0
1
0
1
1
2
1
2
0
0
1
0
0
0
0
1
1
2
2
0
1
1
1
1
1
0
1
2
0
0
0
2
0
1
0
0
2
1
2
0
1
1
2
2
2
2
1
1
0
3
3
2
0
1
0
2
2
0
2
1
1
0
1
0
1
1
1
0
1
2
0
1
0
1
0
2
1
1
1
0
0
0
0
1
0
0
1
0
0
1
0
2
1
0
0
0
2
1
1
3
0
1
0
1
2
1
0
0
2
0
1
0
0
2
1
2
0
2
1
1
1
1
1
2
0
0
0
0
0
0
0
2
1
1
1
0
1
3
2
2
1
2
0
0
0
0
1
1
2
1
2
0
2
1
1
2
1
1
3
0
2
0
1
0
0
1
0
1
0
2
3
1
1
2
0
0
1
3
0
2
0
1
1
2
0
2
2
2
1
0
1
1
2
1
1
2
1
1
1
0
1
1
2
3
1
0
0
1
4
0
1
2
2
2
1
0
2
3
1
0
1
1
0
0
1
1
1
2
0
2
1
1
2
2
1
0
0
0
1
0
1
1
1
0
0
0
0
1
4
0
0
2
1
2
2
1
0
0
1
1
0
0
0
0
2
1
0
0
2
3
0
2
0
1
2
1
1
1
0
0
1
0
2
0
2
1
1
1
1
0
1
1
2
2
0
0
2
1
0
0
0
0
1
2
1
1
5
0
0
1
0
1
2
2
2
1
0
1
2
3
0
1
0
1
1
1
1
1
0
0
0
1
3
1
1
2
2
0
2
1
1
1
2
2
0
0
0
1
2
0
0
2
0
1
2
1
1
1
1
1
1
1
1
1
2
2
1
0
0
1
0
0
1
2
2
0
0
3
1
0
0
0
0
0
0
2
1
0
1
1
2
0
2
1
2
1
1
2
2
1
1
1
2
1
0
1
0
1
0
0
1
2
1
0
1
0
1
1
1
2
0
1
2
1
0
0
0
0
0
2
1
2
0
0
2
1
1
0
0
1
1
0
0
2
0
0
1
1
1
1
0
0
1
0
1
1
1
1
0
2
0
0
1
1
1
0
0
1
1
1
0
2
0
0
0
0
1
2
1
1
0
1
0
1
2
0
0
1
1
0
1
0
1
0
0
1
1
0
0
1
1
1
0
1
1
1
2
1
2
2
1
1
2
0
0
2
1
0
1
0
2
2
2
2
1
2
1
3
1
2
1
2
1
1
1
0
1
1
1
2
0
0
0
0
0
0
1
1
4
0
0
2
2
1
1
2
0
1
1
1
0
0
1
1
0
0
0
2
1
1
0
2
2
0
0
1
0
0
0
0
1
2
2
1
2
0
0
1
1
0
1
0
0
0
0
1
2
2
1
0
0
2
0
1
1
1
0
1
1
0
1
1
0
2
0
0
0
1
0
2
2
2
2
0
1
1
0
1
1
1
3
1
1
1
0
2
0
2
0
0
2
4
3
2
0
1
0
2
0
0
1
0
1
0
1
1
1
1
1
0
0
0
1
0
0
1
0
2
2
1
1
2
1
0
1
0
1
0
2
1
2
0
0
0
1
0
1
1
2
2
1
0
0
1
1
1
2
1
1
0
1
2
1
1
2
2
1
0
2
2
1
1
2
1
2
1
2
1
1
0
2
1
0
2
1
0
1
2
0
2
2
1
2
1
0
0
0
3
2
1
2
0
1
1
0
0
1
2
1
1
1
4
0
1
2
0
1
1
2
0
4
0
1
1
0
1
1
2
1
0
5
2
1
2
0
1
0
1
0
1
0
2
1
0
1
0
1
1
0
1
1
1
1
0
0
0
2
0
1
0
1
2
1
1
3
1
0
2
1
0
1
2
0
1
1
1
1
1
2
1
1
2
1
1
2
2
0
0
2
2
0
0
2
0
1
2
3
1
0
1
0
0
1
2
2
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
1
0
1
1
1
1
0
1
0
2
1
1
2
1
1
1
0
1
2
0
2
1
0
0
0
0
1
1
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
2
0
2
1
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
2
1
1
0
1
1
1
2
2
1
1
1
0
0
2
2
2
2
0
0
1
2
1
1
0
3
2
1
1
2
1
0
1
2
0
0
0
1
0
0
1
0
1
0
0
2
1
0
2
0
0
1
0
1
2
2
1
1
0
1
1
2
0
0
2
1
1
1
1
1
1
0
1
0
1
0
0
0
1
1
1
2
1
0
0
1
0
1
2
2
1
1
1
1
1
2
0
1
0
0
2
0
0
0
1
0
0
2
1
0
1
2
2
0
0
0
1
1
0
1
2
1
1
0
0
1
1
1
0
2
0
2
0
1
2
0
0
0
0
2
0
1
2
1
2
0
1
1
2
1
0
0
1
2
1
1
1
1
0
1
1
1
1
1
0
0
1
0
2
0
1
0
0
0
2
0
1
1
2
1
0
2
0
0
0
2
1
1
1
1
0
2
0
0
0
2
1
0
2
1
1
0
1
0
2
1
1
0
1
1
1
1
2
0
1
2
0
0
1
1
1
1
1
2
3
1
2
1
0
0
0
0
2
2
1
0
1
0
1
1
0
0
1
0
0
0
0
0
0
1
1
1
0
2
1
1
1
0
2
1
2
2
2
1
2
0
0
1
1
1
2
0
0
1
0
1
1
0
2
0
1
0
1
0
0
0
0
2
1
1
2
0
0
0
0
2
1
0
0
2
0
1
0
2
0
2
0
2
1
1
0
2
2
1
0
1
1
1
2
0
1
1
0
0
1
2
1
2
1
1
2
1
2
2
1
2
2
1
1
1
0
2
0
1
1
0
0
1
1
1
1
6
1
1
2
1
0
1
2
0
0
2
0
1
2
1
0
1
1
0
1
1
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
2
1
0
0
2
0
0
0
1
0
2
2
2
0
1
1
2
0
2
0
0
1
2
2
1
1
1
0
0
1
1
0
0
1
1
1
0
1
2
0
1
1
1
2
2
2
1
0
1
1
0
0
0
3
0
1
2
1
2
1
2
2
0
0
1
0
1
2
0
0
0
0
0
1
0
0
1
1
1
2
3
1
2
0
1
1
2
1
2
0
1
0
0
0
1
0
2
0
1
1
1
1
0
1
1
1
0
1
2
1
1
0
1
2
1
1
2
0
2
0
0
1
1
3
2
0
1
1
1
1
1
2
2
1
1
1
0
1
0
2
2
2
1
1
1
1
0
1
2
2
1
1
1
2
1
0
1
0
0
0
1
1
1
1
0
2
0
1
0
0
1
2
0
2
1
2
0
0
1
2
1
0
1
1
0
4
0
2
1
0
0
1
1
1
1
1
2
2
0
1
0
1
4
0
0
1
0
0
2
1
1
1
0
0
0
1
1
2
2
0
1
1
0
2
0
1
0
0
2
1
0
0
1
0
2
0
0
1
0
0
1
0
1
1
2
0
0
0
2
1
0
0
0
1
1
2
1
0
2
0
0
1
1
0
0
1
1
0
0
0
2
0
0
2
0
0
2
0
0
1
2
0
1
2
1
1
0
0
0
0
1
1
1
0
1
0
2
0
1
1
0
1
0
1
2
1
2
1
2
2
0
0
0
1
0
2
1
1
0
2
1
1
0
1
2
2
1
1
0
0
0
0
0
1
0
1
1
2
1
0
0
0
0
1
1
1
1
2
0
1
0
1
0
1
1
2
1
1
1
0
2
1
1
0
1
2
0
0
0
1
0
0
1
1
0
0
1
1
0
2
1
0
0
2
1
0
1
1
1
1
2
0
1
0
1
0
1
1
1
2
1
2
2
2
0
1
0
1
0
1
0
2
1
0
0
0
1
2
1
2
2
1
1
2
1
0
1
0
0
1
1
2
1
0
1
1
0
0
0
0
0
0
0
1
2
0
1
2
2
2
1
0
1
2
1
0
1
0
0
0
0
1
1
0
2
1
1
1
1
1
0
0
1
0
1
1
0
2
1
1
1
1
1
0
1
1
2
0
0
2
1
0
0
1
0
0
1
1
0
2
1
1
2
1
1
1
0
0
1
1
2
0
0
2
2
2
2
0
1
0
0
0
0
0
2
0
1
1
0
0
2
1
0
0
1
0
1
3
0
0
1
1
1
2
0
1
4
0
1
1
1
1
2
0
1
2
1
0
0
2
1
2
1
1
1
0
0
0
0
0
2
0
0
0
1
1
1
0
2
1
0
2
0
1
2
0
2
1
2
0
0
1
1
1
4
1
1
1
0
1
0
0
1
0
0
0
2
0
1
0
0
0
1
1
0
0
0
0
2
1
2
2
2
0
1
0
2
2
1
0
2
2
2
1
0
3
0
1
0
0
0
0
1
1
0
1
0
0
1
1
1
2
0
1
0
0
1
0
1
0
0
2
1
0
0
0
2
2
0
1
1
1
0
1
0
3
0
1
0
0
0
1
1
0
1
0
0
2
1
2
1
1
1
0
0
2
1
1
1
1
2
1
0
0
2
0
0
1
0
1
2
1
0
1
1
1
0
2
0
1
0
2
1
1
0
0
0
0
0
0
0
0
0
3
0
2
2
0
1
0
1
0
0
1
0
1
0
1
0
1
1
1
2
1
0
2
0
0
0
2
2
3
0
1
1
0
0
1
0
1
1
1
0
1
0
1
2
1
1
2
1
4
2
0
2
1
0
0
1
1
1
0
1
0
2
1
0
0
0
0
1
1
0
2
1
1
0
0
2
0
0
0
1
0
0
0
1
1
0
2
1
0
1
1
1
1
1
1
1
1
2
0
0
0
1
0
0
2
0
0
2
0
2
2
1
0
2
1
0
2
0
2
2
0
1
1
1
1
1
2
1
0
2
2
2
2
2
1
1
0
0
0
2
1
2
1
0
0
1
1
3
0
0
0
0
0
0
1
0
1
1
1
1
2
1
0
0
0
2
0
0
1
0
2
0
0
1
0
1
2
2
0
1
1
1
0
0
0
0
2
0
0
1
1
0
1
1
0
1
2
1
0
2
0
0
0
1
0
0
2
1
0
1
0
0
1
1
1
1
2
0
1
0
2
1
1
0
0
0
1
0
0
0
0
3
1
1
1
1
2
1
2
1
2
0
1
2
1
0
1
0
2
1
2
0
2
1
1
0
1
1
1
1
0
1
2
0
2
0
0
0
0
1
0
0
1
2
2
2
2
0
1
2
1
1
1
0
0
0
0
1
1
1
0
2
0
1
0
0
2
1
0
1
1
1
0
0
1
0
1
2
2
1
0
2
0
0
1
0
1
1
1
2
1
1
2
1
1
2
2
1
1
2
2
0
0
2
2
0
0
1
1
0
1
0
1
0
0
0
1
2
1
2
2
2
0
0
2
1
2
0
0
2
0
1
0
1
1
2
0
2
2
1
0
1
2
2
1
1
1
0
1
0
0
1
0
0
1
0
2
2
0
1
2
0
0
1
1
1
2
1
0
1
0
1
0
1
0
1
1
1
0
1
0
1
0
0
0
1
2
1
1
2
0
1
1
0
1
0
2
2
1
2
0
0
1
1
0
1
1
2
1
2
1
1
0
2
1
0
0
0
0
1
2
1
0
0
1
1
1
1
1
0
2
0
3
0
1
0
1
0
2
0
1
2
1
1
1
0
1
0
0
3
1
0
2
1
1
1
2
2
1
1
2
0
0
0
2
3
1
1
0
0
1
0
1
1
0
0
1
0
1
1
1
2
0
2
2
0
1
1
2
2
1
4
0
1
1
2
2
0
1
0
1
1
1
1
1
0
2
0
0
2
1
0
0
0
1
2
1
1
0
1
0
0
0
0
0
1
0
1
1
2
2
2
1
2
1
2
0
1
0
1
1
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
2
1
0
1
1
0
2
1
1
0
1
1
0
1
1
0
0
1
1
2
1
1
1
0
0
1
0
3
1
2
2
0
1
0
0
1
1
0
1
0
1
2
0
1
0
1
2
1
0
0
1
2
0
1
1
0
2
0
4
0
0
2
0
0
1
1
1
0
0
1
1
1
2
2
2
0
0
2
0
2
1
0
0
0
0
1
0
2
1
2
0
0
1
0
2
0
0
2
0
0
0
2
0
0
2
0
2
0
1
0
1
1
1
1
0
1
2
1
0
1
0
0
1
3
2
2
2
2
0
0
0
0
0
1
1
1
0
0
1
1
1
1
2
0
2
0
0
2
1
1
1
0
0
2
2
0
0
1
0
0
1
0
2
0
1
0
0
0
0
0
1
0
2
1
0
1
1
0
0
0
2
3
2
2
0
1
1
1
1
2
3
2
0
1
1
1
0
0
0
2
0
1
3
2
1
1
0
1
1
0
0
1
2
1
0
0
0
0
0
0
1
0
0
2
0
1
1
0
1
2
1
0
0
2
0
0
1
0
0
1
0
0
1
2
1
2
0
1
0
1
0
1
1
0
2
4
1
1
0
2
1
1
1
0
1
2
0
2
2
1
1
0
2
1
1
1
2
1
1
2
0
1
1
0
0
2
0
1
0
0
0
1
0
0
2
1
1
1
1
0
1
0
1
0
2
2
0
0
1
1
0
1
2
1
0
1
1
4
0
1
0
2
1
1
0
1
1
1
2
2
0
2
1
0
2
0
0
1
2
0
0
2
0
2
1
0
0
0
1
1
0
2
0
2
2
2
0
1
1
0
0
1
1
0
1
1
0
0
0
0
1
1
0
0
1
1
0
1
1
3
2
0
0
0
1
0
2
1
0
0
1
1
0
0
1
0
0
0
1
0
2
1
2
1
1
2
0
1
2
1
1
1
0
2
1
1
2
1
0
1
1
2
2
1
0
1
1
1
1
2
0
1
1
0
1
1
1
2
1
0
1
2
1
1
0
2
2
1
1
0
1
0
1
1
2
0
1
1
0
1
2
0
0
0
0
2
2
0
0
0
0
0
1
1
0
2
2
2
2
1
0
1
0
0
1
2
1
1
2
0
1
0
1
1
0
6
2
0
1
1
1
1
2
0
1
1
2
2
0
1
1
1
0
0
0
2
2
0
0
2
0
2
1
1
2
2
1
2
1
0
1
1
0
1
2
1
1
2
1
0
0
2
1
0
2
1
1
0
1
0
1
1
1
0
1
0
2
1
2
0
1
1
1
1
2
0
2
1
2
2
1
0
2
0
1
1
0
3
2
1
1
1
1
0
2
1
2
1
0
1
1
0
1
0
1
2
1
1
0
1
1
2
1
0
1
1
1
1
2
1
0
1
1
1
0
1
1
2
1
1
1
1
0
0
1
1
1
2
0
1
0
1
2
0
1
1
1
1
1
2
0
1
0
1
0
0
0
0
1
0
1
2
2
1
0
1
1
0
1
2
2
1
1
2
2
2
1
0
0
0
0
0
2
1
0
0
0
1
1
0
1
0
0
0
0
2
2
1
2
1
1
1
0
0
2
0
2
0
0
2
1
1
0
0
1
1
3
0
0
1
0
1
2
0
1
1
1
1
1
1
0
0
1
1
1
1
2
0
0
2
1
2
1
0
0
1
2
1
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
1
0
2
1
2
1
2
1
1
1
1
1
0
0
2
1
2
2
2
0
0
1
1
0
1
1
1
2
2
0
2
1
0
1
1
0
1
0
1
1
0
0
1
0
0
0
0
2
1
1
0
0
0
1
1
1
0
2
2
0
1
1
1
0
1
1
2
2
0
1
0
2
1
0
0
2
1
1
1
2
1
1
0
0
1
1
2
1
1
1
1
2
0
0
1
3
0
2
1
1
0
1
0
0
0
1
0
1
1
1
0
0
1
1
1
0
2
2
1
0
2
0
1
1
0
0
2
1
2
1
2
0
1
1
0
0
1
0
1
1
2
0
1
0
1
1
1
1
1
1
1
1
1
1
0
1
2
0
1
0
0
0
1
1
0
1
1
2
0
0
2
0
0
1
2
0
2
2
1
0
1
0
1
0
0
2
1
1
0
0
0
2
2
2
1
1
2
1
0
1
1
1
2
1
1
0
2
3
0
2
2
1
0
0
1
0
1
2
1
1
2
1
1
1
0
1
2
0
0
1
1
0
2
0
2
0
0
2
0
0
1
0
0
2
0
3
0
1
2
2
1
1
1
1
0
2
0
0
1
1
2
0
1
1
2
0
2
1
1
1
0
2
0
1
0
0
2
0
1
2
0
0
1
1
0
0
2
0
0
0
0
0
1
0
0
1
0
2
2
0
0
1
2
2
0
0
0
1
3
1
0
1
0
2
1
0
0
1
2
2
0
1
0
0
1
2
0
0
2
1
2
1
1
1
0
0
0
2
1
0
0
1
0
2
1
0
0
0
0
0
1
2
1
0
2
2
1
0
2
0
0
2
2
0
1
0
0
0
2
0
1
1
2
2
1
0
1
1
0
0
1
0
1
1
0
2
0
1
0
1
0
1
1
2
1
1
1
2
0
1
0
2
3
1
0
1
0
1
1
1
0
1
0
0
0
1
1
1
0
1
1
2
1
0
2
1
0
0
0
0
2
1
1
2
1
2
1
1
0
2
0
1
1
0
2
0
2
1
0
2
2
0
0
0
3
0
2
2
0
0
0
1
2
0
2
0
1
1
2
2
0
1
0
2
1
1
2
1
1
1
2
0
2
2
0
2
0
2
1
2
0
1
1
2
0
2
1
0
0
0
0
1
1
0
1
0
1
0
1
0
1
0
0
0
1
0
1
1
1
1
0
2
0
1
0
0
1
0
2
2
0
1
1
0
1
0
2
1
0
2
0
0
0
1
1
1
1
1
1
0
0
2
0
2
0
0
1
0
0
1
1
2
0
1
1
0
0
1
0
1
0
1
1
0
2
1
1
0
1
0
0
0
1
2
1
0
7
0
2
0
1
0
1
1
1
0
1
1
10
0
0
4
1
1
0
0
2
1
1
0
1
0
1
2
1
0
1
1
1
1
0
0
0
1
2
3
1
0
0
1
0
0
1
0
0
2
0
1
0
0
2
2
2
1
1
0
2
2
0
1
1
1
0
1
2
0
0
1
1
2
0
0
1
1
0
2
0
1
1
1
0
1
1
0
0
0
1
0
1
1
1
0
2
0
0
1
0
1
1
0
1
1
1
0
1
2
1
2
0
2
2
2
1
0
0
2
3
0
0
0
0
0
1
0
2
1
1
3
1
0
0
2
0
1
2
2
1
0
0
1
1
0
0
2
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
3
1
0
1
1
1
0
1
2
1
0
2
0
2
0
0
1
0
1
0
0
0
1
1
1
1
2
0
2
2
0
0
2
1
1
0
2
2
1
0
2
0
1
2
1
3
0
1
0
1
1
0
1
0
0
1
0
1
0
2
0
1
1
0
0
0
1
1
1
2
0
1
0
0
2
0
1
0
1
1
0
1
0
0
0
1
2
1
1
1
0
1
1
1
1
0
0
0
1
0
2
0
2
1
0
2
0
2
0
1
0
2
1
1
1
1
1
0
2
0
2
0
0
1
0
0
0
2
0
1
0
1
2
1
1
0
2
1
0
1
1
0
0
0
0
1
0
1
0
0
1
0
0
1
0
1
0
0
1
0
0
2
0
1
0
1
2
1
0
1
0
1
2
1
1
2
1
2
2
1
1
1
1
1
1
1
1
0
1
1
2
0
1
2
1
2
0
1
1
0
0
0
0
0
0
1
1
0
0
1
0
1
2
1
0
1
0
0
0
2
2
1
0
0
1
1
0
1
1
1
0
0
1
0
2
1
1
2
1
1
0
1
0
3
0
1
3
1
0
0
0
1
0
2
0
0
0
2
1
0
2
0
1
1
1
2
0
1
1
2
1
1
2
1
0
0
2
1
2
0
1
1
1
0
2
0
1
0
2
1
2
3
1
0
2
2
1
0
2
2
1
1
1
2
2
0
0
1
0
0
2
1
0
0
2
1
2
1
0
0
1
2
2
1
0
0
2
0
0
1
0
0
1
1
1
1
3
0
1
2
1
1
1
1
2
0
2
2
2
0
0
1
0
1
0
1
1
0
0
1
1
0
0
0
2
2
2
1
2
0
0
0
0
0
1
1
2
1
0
2
1
0
2
1
2
1
0
1
1
0
0
2
1
1
0
3
1
1
2
0
1
2
1
2
1
1
1
0
2
1
0
0
2
0
1
0
1
1
2
1
1
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
2
0
0
0
0
0
1
0
1
0
0
0
0
1
1
1
1
2
1
2
0
0
0
0
0
1
1
1
0
0
0
2
1
1
0
1
2
2
0
0
2
0
2
0
1
1
1
2
0
1
1
1
1
0
1
1
2
0
0
1
1
0
1
1
0
1
0
0
2
2
0
2
0
1
4
1
1
2
1
2
0
1
0
2
1
0
2
0
1
1
1
2
1
3
1
2
2
0
1
1
1
2
0
1
0
0
1
1
0
1
1
2
1
2
0
2
3
2
0
0
2
0
0
2
0
0
1
0
0
1
2
1
2
0
2
3
1
1
0
2
0
1
2
0
0
2
0
1
0
1
0
2
1
1
1
0
1
1
1
1
0
0
1
1
1
0
0
3
0
3
1
1
2
0
2
1
1
1
2
1
0
1
0
0
0
0
0
0
0
2
0
1
1
1
0
0
1
0
0
1
0
1
0
2
1
1
0
2
0
1
0
0
1
0
0
1
2
2
1
2
1
0
0
0
3
2
1
2
0
0
2
0
2
1
0
0
1
2
0
1
0
1
2
2
0
1
2
0
0
1
1
1
1
0
0
2
2
0
1
1
1
2
0
0
1
0
1
1
2
0
0
2
2
0
0
1
0
1
2
1
0
1
1
0
2
0
0
1
0
2
1
0
1
0
1
2
0
2
0
1
2
0
0
2
0
1
2
0
1
0
1
1
2
0
0
1
0
0
2
1
2
2
0
1
2
0
0
0
1
1
1
2
2
0
1
1
0
2
1
1
0
2
1
0
1
1
0
1
1
1
0
0
0
1
0
0
0
1
2
0
1
2
1
1
0
0
1
2
1
1
0
1
0
3
2
1
0
1
0
0
2
1
1
0
0
1
2
2
1
1
0
0
2
1
0
1
0
1
0
1
1
1
1
0
1
0
0
2
1
1
1
2
0
1
0
0
1
0
1
1
3
0
2
1
2
1
0
0
2
0
1
0
2
0
0
0
1
1
2
1
3
2
0
1
1
0
2
2
0
0
0
1
1
2
0
0
0
2
1
1
0
0
0
1
0
2
0
1
0
2
0
1
0
2
0
1
1
0
2
2
0
0
0
2
1
2
1
0
1
1
1
0
0
0
2
1
0
0
1
1
1
2
1
1
1
0
0
2
0
1
1
0
0
0
0
0
1
0
0
2
0
1
0
1
1
1
2
1
0
0
0
1
1
2
0
0
2
3
0
0
1
0
0
0
1
1
1
1
2
0
3
1
1
1
1
1
2
1
0
1
0
0
1
0
0
0
2
0
0
1
1
0
0
0
1
2
0
2
0
2
1
0
0
2
0
1
1
0
2
0
0
0
0
1
0
1
0
1
0
4
2
1
1
1
0
2
0
0
0
1
0
0
2
0
0
2
1
2
1
0
2
2
2
2
1
0
0
1
2
1
1
1
1
0
0
1
0
2
0
1
1
1
2
1
2
0
1
1
0
2
1
1
2
2
1
1
1
2
0
0
0
1
1
2
0
0
1
0
1
1
0
1
2
14
1
0
0
1
2
2
1
0
1
0
2
0
0
2
0
1
1
0
1
1
0
0
0
1
0
2
0
1
0
2
0
3
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
2
1
0
2
1
0
0
0
0
2
1
2
1
0
0
0
1
2
2
1
0
4
2
1
0
0
0
0
2
1
1
0
1
1
0
2
2
2
0
0
1
1
2
0
1
2
1
1
1
1
1
1
1
0
1
1
0
0
0
1
2
1
0
0
0
0
1
2
1
1
2
0
2
0
2
0
0
0
0
2
1
0
0
1
0
0
0
2
0
2
1
1
1
3
1
2
1
1
0
0
1
2
2
0
2
0
0
1
2
2
0
1
1
0
1
1
1
1
2
3
0
0
0
1
0
2
0
2
1
0
0
0
0
0
2
0
0
0
1
1
0
1
1
0
0
3
1
1
1
2
0
2
0
2
0
0
0
0
0
1
0
2
0
0
1
1
0
1
2
1
1
1
2
2
1
0
1
1
0
0
0
1
1
1
1
1
0
1
0
0
2
2
2
1
1
2
2
1
1
1
1
0
0
0
1
0
1
0
1
1
2
0
2
0
2
1
1
1
0
0
0
0
0
0
0
1
1
1
0
0
1
2
1
2
1
1
1
3
0
2
1
1
2
2
0
2
0
0
1
0
1
2
0
0
0
2
0
1
0
0
1
1
0
2
0
3
2
0
1
0
0
1
0
2
1
1
1
2
0
1
1
0
0
2
0
2
1
1
0
1
2
1
0
2
2
2
1
1
0
0
1
0
0
2
0
1
1
1
0
0
0
1
2
1
1
1
2
0
1
1
2
1
1
1
2
1
1
0
1
1
0
1
0
2
1
1
1
2
0
3
1
2
0
1
0
2
1
2
2
0
1
0
0
1
1
1
1
0
0
2
0
1
2
0
1
1
1
0
1
1
1
2
0
0
1
0
1
1
1
1
0
0
0
2
2
1
0
2
1
2
0
2
1
1
1
0
1
1
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
1
1
0
2
0
0
2
0
1
0
0
2
2
1
1
2
0
2
0
0
1
1
0
2
1
0
2
1
0
0
1
1
2
0
1
0
0
1
0
0
2
2
1
1
0
1
0
0
0
1
1
1
0
2
1
0
1
2
2
0
1
0
2
1
2
0
2
2
1
0
0
0
1
1
1
1
0
0
1
0
0
2
0
0
2
2
1
2
0
0
0
0
2
1
1
0
1
1
0
2
0
1
2
0
0
1
0
0
0
1
1
0
2
1
2
1
2
1
1
1
0
1
2
1
1
1
1
0
1
1
2
1
2
0
0
1
0
1
1
1
1
0
1
1
2
0
0
0
0
1
0
1
0
0
1
1
2
1
2
1
1
1
5
0
4
0
1
1
0
1
0
1
2
1
2
1
1
0
0
1
0
0
2
0
0
2
1
1
0
0
1
0
0
2
0
0
1
1
0
0
0
1
0
0
2
0
1
0
0
1
0
2
0
8
1
0
0
0
1
0
1
1
1
1
1
2
1
2
0
1
0
2
2
1
2
1
0
0
1
0
0
0
0
1
1
1
1
1
1
1
2
0
0
1
1
0
2
0
0
2
3
1
0
1
0
1
1
1
2
0
1
1
1
2
2
0
0
0
2
0
0
0
0
2
1
0
2
0
1
0
1
2
0
0
1
1
1
1
0
1
0
0
0
0
1
0
2
2
1
0
2
0
0
1
0
0
1
1
1
1
1
1
0
0
2
0
0
1
2
0
2
0
1
2
1
1
2
0
0
2
1
1
1
0
1
0
1
1
2
1
0
1
0
2
0
0
0
0
0
1
0
0
2
1
2
1
0
1
1
0
1
0
0
1
1
1
1
0
1
0
0
0
0
3
1
0
3
2
1
1
1
0
2
0
0
0
0
1
0
1
0
0
2
1
0
0
2
2
2
1
1
0
1
2
1
0
1
0
1
2
2
0
0
0
0
1
1
2
0
1
1
0
0
0
2
0
1
1
0
3
2
0
3
1
1
1
0
0
0
0
2
1
0
2
0
0
0
3
2
0
0
1
1
0
1
0
1
0
1
1
0
2
1
0
2
2
1
0
0
2
0
1
1
1
2
1
0
0
2
1
1
1
0
0
0
2
2
0
0
0
1
1
3
0
1
1
2
1
0
2
0
1
1
1
1
1
1
0
0
2
2
1
0
1
0
0
2
0
0
0
2
0
1
0
0
1
0
2
0
2
1
0
0
1
1
0
1
2
0
1
1
1
2
0
0
0
2
1
1
1
0
2
1
0
0
1
0
1
2
2
0
1
1
0
1
2
1
0
1
0
0
2
1
0
0
2
1
1
2
0
1
1
2
2
0
1
1
1
3
1
0
2
0
1
1
0
13
0
0
1
1
1
2
2
2
0
1
0
0
1
1
1
1
1
1
0
1
2
2
0
1
1
2
0
0
2
0
9
0
1
0
1
1
0
0
2
1
1
0
1
0
1
2
0
2
1
0
0
3
0
1
1
1
0
1
0
0
1
0
2
0
0
0
2
0
1
1
0
4
1
1
1
2
0
1
0
1
2
1
0
2
0
1
0
1
0
0
2
1
0
1
0
1
1
0
0
2
1
0
0
2
2
1
1
0
1
0
2
0
1
0
2
2
0
2
0
0
1
1
0
2
1
2
1
1
1
2
1
2
1
1
0
0
0
0
2
1
3
0
1
1
1
0
1
0
1
0
0
0
2
0
1
1
2
2
1
0
1
2
1
1
0
1
2
1
0
0
1
1
1
1
0
2
0
0
0
2
2
1
2
0
0
1
0
1
0
0
0
0
0
0
1
1
1
0
1
0
2
1
4
2
2
1
1
1
2
1
0
1
0
1
1
1
0
0
1
1
1
1
0
0
0
0
0
2
1
1
2
1
2
1
0
1
0
1
0
0
1
0
2
1
1
2
1
2
1
2
0
3
1
1
0
1
2
0
1
2
0
1
0
0
0
1
0
0
1
1
1
1
1
1
1
1
0
1
0
2
2
2
0
2
2
1
0
1
1
0
0
2
1
1
1
1
0
2
0
0
1
0
0
1
1
2
0
0
0
1
1
1
0
1
2
1
2
1
1
0
2
0
0
2
2
0
1
0
2
0
1
0
0
1
1
0
0
2
2
1
2
1
2
1
1
0
0
1
2
1
2
1
1
1
2
0
0
0
1
1
1
2
0
1
1
0
1
1
2
0
0
0
1
2
0
2
1
1
1
0
0
2
1
1
0
2
1
0
0
0
0
1
2
1
1
1
1
0
1
1
0
0
0
0
1
1
3
0
0
1
1
2
2
0
1
1
0
1
0
2
0
1
1
1
0
0
0
0
2
1
2
0
1
1
0
2
1
0
1
0
1
1
0
2
0
0
1
0
0
2
0
1
0
0
0
1
2
2
1
0
0
1
1
0
2
1
1
0
1
0
1
1
1
1
0
1
0
2
0
1
0
1
0
1
1
1
1
2
1
1
1
1
0
1
1
0
0
0
0
1
2
2
1
1
1
2
0
1
2
1
0
0
0
0
0
1
2
1
0
1
0
1
2
0
3
1
1
1
1
0
0
0
0
1
0
1
1
0
0
1
0
1
1
1
1
1
1
0
0
1
0
2
1
2
2
0
0
2
1
2
1
2
0
1
1
1
0
0
0
2
1
1
1
1
0
0
0
1
1
0
2
1
0
1
1
2
1
2
2
0
1
0
0
1
0
0
2
1
0
0
0
2
0
0
1
1
1
0
1
2
0
0
1
2
1
0
1
1
0
0
0
1
1
1
0
0
1
1
2
0
0
1
1
1
2
0
1
0
2
0
0
1
2
1
1
0
1
2
1
2
1
2
2
1
0
0
2
1
0
1
0
2
0
1
1
0
1
2
2
1
1
1
3
2
1
0
1
0
0
0
0
0
0
1
2
1
1
2
1
1
0
0
2
2
0
0
1
1
3
0
1
1
2
2
0
2
0
0
1
2
0
0
1
1
2
0
0
1
1
0
0
1
1
0
0
1
0
0
1
0
2
0
0
0
2
1
0
1
1
2
2
1
2
0
0
1
1
1
1
0
1
2
0
2
1
0
0
0
0
1
1
1
0
2
1
1
0
4
0
0
1
0
1
1
0
1
2
1
2
1
2
1
0
2
1
1
2
1
2
0
1
3
0
1
2
0
2
2
1
0
1
0
1
1
0
0
1
2
0
0
0
0
2
0
1
1
0
1
1
2
1
1
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
1
1
0
2
0
1
0
0
0
1
1
0
1
1
1
1
2
1
1
2
1
0
0
1
2
1
1
0
1
1
0
1
1
1
0
1
0
1
0
1
0
2
1
0
1
1
2
0
0
0
0
2
1
2
1
0
1
1
1
0
2
2
0
1
1
2
1
0
0
0
0
2
1
0
1
0
0
2
2
0
1
1
0
1
0
0
0
2
3
1
0
1
0
2
2
0
1
1
0
1
0
1
0
0
1
1
1
1
0
1
1
2
2
0
0
2
0
2
0
1
1
1
2
2
1
1
0
1
1
0
2
4
1
1
0
0
1
0
1
0
2
0
0
1
0
0
2
2
1
2
2
0
1
0
1
1
1
0
2
1
1
0
0
0
2
1
0
2
2
2
1
0
0
2
1
1
0
0
3
0
0
1
0
0
0
0
2
1
0
0
1
2
0
2
0
1
1
3
1
2
0
1
1
0
0
1
0
0
2
2
1
0
1
0
1
0
2
0
1
1
1
1
0
1
1
0
0
2
2
2
0
0
0
0
0
2
2
0
1
0
2
0
2
1
1
0
0
0
0
1
1
0
1
0
0
0
1
1
0
1
2
0
1
1
0
1
0
1
0
1
2
0
0
0
1
2
1
0
1
1
2
2
1
1
0
2
0
0
3
1
1
0
2
0
2
1
0
1
0
1
1
0
1
3
1
2
2
1
0
2
1
2
1
0
1
0
1
0
0
2
1
0
1
1
1
2
2
1
2
1
1
1
2
0
0
1
0
1
0
1
2
0
1
0
3
1
0
0
1
1
1
0
1
1
2
3
2
0
1
0
1
1
1
0
0
0
1
1
0
1
0
1
1
1
2
0
1
0
2
2
0
0
1
0
0
1
0
0
1
5
2
1
2
2
1
0
1
1
2
0
1
1
1
0
1
0
0
2
1
2
1
2
0
1
0
1
0
2
0
2
1
1
1
0
0
0
0
0
0
0
0
1
2
2
0
1
1
0
0
1
0
2
0
0
1
0
0
0
2
0
0
1
0
0
1
1
1
1
1
1
0
0
2
1
1
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
1
1
0
2
2
2
0
1
0
1
2
2
0
1
1
2
1
0
1
0
2
2
0
1
1
0
2
0
0
2
2
1
0
0
0
2
1
0
1
0
2
0
0
1
1
1
0
1
0
0
0
1
1
1
2
0
1
2
0
0
1
3
2
2
1
1
1
0
0
1
1
1
3
1
1
1
0
2
2
0
0
0
1
0
1
0
1
1
0
0
1
0
2
0
2
0
0
0
0
0
0
0
1
1
1
1
3
1
2
0
0
0
1
1
2
2
0
0
1
1
1
2
0
2
2
1
0
0
1
0
0
0
0
0
1
1
0
1
2
1
0
1
2
1
0
0
0
2
1
1
0
3
0
1
0
0
0
1
1
0
2
0
0
1
0
1
1
1
4
2
0
1
1
2
0
0
2
0
1
1
2
1
1
2
0
2
1
1
1
0
0
0
0
1
1
1
1
0
1
0
1
2
2
1
0
1
1
0
1
1
0
1
2
0
1
0
0
1
0
1
6
0
0
1
0
1
0
1
2
0
2
2
1
2
2
0
1
0
1
1
1
1
1
2
0
0
1
0
1
1
1
0
1
0
1
1
1
2
1
1
1
0
1
1
1
1
0
1
1
0
1
1
1
0
1
2
0
2
1
0
0
1
0
2
2
2
0
0
1
1
0
1
1
1
0
0
0
1
1
2
1
1
2
1
1
0
1
1
1
0
1
2
1
0
0
2
2
2
0
0
0
2
1
2
2
1
1
0
1
1
2
1
2
1
1
2
0
0
1
1
1
1
0
1
0
1
2
0
0
1
0
0
1
1
1
1
1
1
1
1
1
2
1
0
1
0
2
2
2
0
0
0
0
2
2
1
3
1
0
0
0
0
0
1
1
0
0
1
1
1
0
0
1
0
1
1
0
1
2
0
2
1
1
1
0
0
0
1
1
0
0
2
2
1
0
0
0
1
0
1
0
0
2
0
2
0
1
1
1
0
1
1
0
0
1
1
0
1
2
2
0
0
1
0
0
1
0
2
0
1
0
2
1
0
2
1
1
2
0
0
0
1
0
1
2
1
1
0
1
0
1
0
1
0
2
1
3
0
1
0
2
0
1
2
0
0
1
1
1
0
1
2
2
0
0
2
0
1
1
1
0
1
2
2
0
1
2
0
1
1
1
0
2
1
1
0
1
0
0
2
1
1
2
1
1
0
0
1
1
2
1
1
0
2
0
1
1
2
1
2
1
2
1
0
1
2
1
0
0
0
0
1
0
1
2
1
0
0
2
1
4
1
1
1
0
0
1
1
2
1
1
2
0
1
0
1
1
1
2
0
0
0
1
2
1
0
0
1
0
2
1
0
0
1
1
1
1
1
0
0
0
1
1
1
1
1
1
2
1
0
0
1
0
0
0
2
1
1
0
1
1
1
1
2
0
0
1
0
1
0
1
0
0
1
0
0
1
2
2
0
0
1
2
1
2
0
2
1
0
2
1
1
2
0
2
2
0
1
1
0
2
1
1
1
0
1
1
0
1
0
0
1
0
2
1
1
0
0
1
1
0
1
1
0
2
0
0
0
2
0
1
2
2
0
1
2
1
1
1
0
0
1
2
1
1
1
2
1
0
0
1
1
0
2
0
0
0
0
2
1
1
0
1
2
1
1
1
0
1
2
1
1
0
1
1
1
1
2
0
1
0
1
1
0
0
2
2
1
1
1
2
0
1
1
1
1
2
1
1
0
1
1
1
0
1
2
2
0
2
1
1
0
0
1
2
0
0
0
1
1
0
0
0
2
3
2
1
1
2
0
0
0
3
1
1
1
1
1
2
1
2
0
2
2
1
1
0
1
1
1
2
2
1
0
1
1
1
0
0
2
0
2
1
0
0
1
1
1
0
1
2
2
2
2
1
2
1
2
1
1
0
2
0
0
1
1
0
2
1
0
1
1
2
1
0
1
1
2
1
0
1
0
0
0
2
0
0
0
0
0
0
0
1
2
5
0
0
3
0
2
2
1
0
0
0
1
1
1
1
1
1
1
2
2
0
1
0
0
2
0
0
1
1
2
2
0
0
0
1
1
2
0
0
1
0
1
2
0
0
0
1
2
0
1
1
0
2
1
1
1
0
2
0
1
2
2
0
2
2
1
1
0
0
0
1
1
2
1
1
2
0
0
0
0
1
1
1
1
1
0
0
2
3
1
2
1
0
0
2
1
0
0
0
2
0
1
1
0
1
0
3
1
2
1
1
1
0
2
2
0
0
0
0
2
0
0
1
2
0
1
2
2
1
0
0
2
0
0
1
0
2
0
0
2
1
1
0
2
2
1
1
1
1
2
1
0
1
1
2
0
1
2
1
0
2
2
0
0
2
1
0
1
1
2
1
1
1
1
0
1
0
1
0
2
1
2
0
2
1
1
0
2
1
1
0
1
0
0
0
1
1
1
1
0
2
2
1
1
1
2
0
0
2
0
1
0
1
1
1
2
0
1
1
0
1
1
0
2
2
0
2
2
6
0
1
0
0
2
1
1
1
1
2
0
0
1
2
0
0
1
1
2
0
0
0
0
2
2
1
1
0
1
0
1
1
0
2
1
1
2
0
0
1
0
1
0
0
1
0
0
1
0
2
2
2
1
1
2
1
2
1
2
0
1
1
0
1
1
1
1
1
1
0
1
0
2
0
1
2
1
2
1
1
0
0
2
0
0
0
0
2
0
1
0
0
2
0
0
0
0
1
2
1
1
1
2
1
1
1
1
1
2
0
2
2
0
0
0
0
0
2
1
0
1
0
0
2
1
1
1
0
1
0
2
0
1
0
1
0
1
0
0
2
3
0
1
0
2
0
0
1
0
1
1
2
0
1
0
1
1
1
2
0
0
1
1
0
2
0
1
2
0
2
0
2
1
2
2
1
0
1
2
2
0
0
1
0
2
2
1
2
1
1
0
0
0
0
0
0
0
2
2
2
0
1
1
0
1
2
0
0
1
1
2
0
2
1
1
1
0
0
0
3
1
2
0
2
1
2
2
0
1
1
0
3
1
1
1
1
1
1
0
0
0
0
1
0
1
1
1
2
0
0
1
0
0
1
1
2
0
0
1
1
1
0
0
1
0
2
0
1
2
1
2
1
1
0
2
1
0
0
1
0
2
1
0
0
0
0
0
0
1
2
1
1
1
1
0
2
0
0
0
1
1
2
1
0
0
1
1
1
0
2
0
1
0
1
0
1
0
2
1
1
2
0
2
0
1
0
0
1
0
0
0
1
0
1
0
1
1
0
1
2
1
1
2
2
0
1
1
0
1
1
1
1
1
1
1
1
1
0
1
3
1
1
0
1
0
1
2
1
0
2
0
2
0
0
0
0
0
1
1
0
2
0
1
1
1
1
1
0
0
0
1
3
0
2
0
0
2
0
0
2
1
0
1
2
2
0
2
1
1
2
0
1
2
0
1
1
0
0
1
2
0
1
0
0
0
2
1
1
0
2
0
1
1
2
1
1
0
1
1
1
1
0
0
0
1
1
1
0
1
0
1
1
1
2
0
1
1
1
0
2
2
1
1
0
1
2
2
0
0
0
0
1
1
0
0
2
1
1
1
1
1
0
0
1
2
0
0
1
0
0
2
0
2
2
1
0
1
1
1
2
0
0
0
1
1
1
2
0
0
1
2
0
0
1
2
0
1
0
0
2
0
0
1
1
1
1
1
0
0
1
1
0
2
1
0
4
1
0
1
1
0
1
1
1
2
0
2
0
1
0
1
2
0
1
1
0
2
1
0
1
2
0
2
1
1
2
1
1
0
0
0
1
1
1
0
1
1
0
0
0
1
1
1
2
0
1
2
3
1
0
1
1
0
0
2
0
0
2
2
1
0
0
1
1
1
0
1
0
1
2
0
1
1
0
1
0
0
0
1
3
0
2
2
1
3
1
0
0
0
0
0
4
2
0
2
0
2
0
0
1
0
1
2
3
2
0
1
0
2
1
0
1
0
0
3
1
2
0
2
1
2
1
0
1
1
0
0
2
0
1
0
0
1
0
0
1
0
1
0
0
1
0
1
1
2
1
0
2
1
0
0
1
2
0
0
1
1
1
1
1
1
0
2
2
0
0
2
1
1
1
0
1
1
3
1
2
0
2
0
0
0
0
1
0
0
2
2
2
0
0
0
0
0
2
0
1
0
0
0
1
2
2
2
0
0
2
0
1
1
0
2
1
0
0
1
0
1
1
3
2
1
1
0
1
2
0
0
0
1
1
1
0
0
0
0
0
1
2
2
2
2
1
2
0
0
2
2
1
0
2
1
0
0
1
3
2
1
0
1
1
1
0
0
2
0
0
1
2
2
1
0
1
0
2
0
2
2
1
0
1
0
1
0
1
0
2
2
2
0
1
0
0
0
1
0
1
0
2
0
1
1
1
0
0
2
1
0
0
0
1
1
0
1
0
2
3
0
0
1
0
1
1
1
1
0
1
1
1
0
1
0
1
1
1
1
1
0
1
2
1
1
1
1
0
3
1
1
1
1
1
1
2
1
1
0
2
2
1
1
2
1
0
2
1
1
1
1
1
1
0
0
0
0
2
1
1
0
1
0
0
0
0
0
1
1
0
2
1
0
1
1
1
1
2
0
1
1
1
1
0
1
0
1
0
0
1
0
1
0
1
0
1
0
0
0
0
1
1
3
2
0
1
2
2
1
1
1
0
0
0
1
0
2
0
1
1
0
0
1
1
1
0
1
1
1
1
1
0
1
0
1
0
1
0
1
0
2
0
1
2
1
2
0
1
2
1
1
0
1
2
2
1
1
1
0
1
1
1
2
0
1
1
0
1
0
0
0
0
2
0
0
1
0
0
0
3
1
1
0
1
2
0
2
1
2
0
2
2
0
1
1
0
2
1
2
1
0
0
2
1
2
2
2
1
2
0
1
0
2
0
0
0
0
0
0
0
2
1
0
0
0
1
2
2
1
1
0
1
1
0
1
1
1
0
1
0
1
1
0
2
2
2
1
2
1
1
1
0
0
1
2
0
0
0
2
1
0
0
0
1
1
1
2
2
0
1
1
0
2
1
2
0
1
2
2
2
1
0
0
0
0
1
2
1
1
2
0
1
0
2
0
1
0
0
3
0
1
1
2
0
0
0
0
2
0
1
1
1
1
1
1
1
2
2
0
2
1
0
1
0
2
0
1
1
1
0
1
1
1
2
3
2
0
1
0
0
1
0
2
2
0
0
2
1
1
0
1
1
1
0
2
0
2
1
1
1
0
3
0
0
1
2
0
1
2
1
2
0
1
0
0
0
1
0
1
0
0
1
1
2
1
1
2
0
1
1
1
1
2
0
0
1
1
2
2
1
1
0
1
0
1
1
0
2
1
1
1
0
2
2
1
0
1
0
0
1
0
1
0
2
0
1
0
1
1
1
0
0
2
0
2
1
1
0
3
2
0
1
2
0
0
1
1
0
1
1
0
1
1
0
3
0
0
16
2
0
1
1
0
0
2
2
0
0
0
2
0
0
0
1
1
0
1
1
0
0
0
0
2
0
1
2
2
2
2
2
0
0
0
0
0
1
2
2
0
1
1
1
1
0
0
1
1
0
0
1
2
2
0
0
0
0
2
1
0
0
0
2
0
0
1
2
0
2
0
0
2
1
1
2
1
1
1
1
1
1
2
0
1
0
2
2
2
1
1
1
1
0
0
1
1
0
0
0
1
0
4
0
0
2
1
2
2
2
0
1
1
1
1
1
1
1
1
1
1
0
2
1
0
1
0
1
1
1
1
1
1
0
1
1
2
0
2
0
2
0
2
1
2
1
1
1
0
0
1
0
0
0
1
0
0
1
0
2
1
0
0
1
0
0
0
2
0
2
0
2
1
1
1
8
0
2
1
2
1
2
1
1
0
2
0
0
2
2
0
1
0
1
1
0
2
0
1
2
0
0
0
2
0
0
2
1
0
3
1
0
2
0
2
0
2
1
1
2
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
3
1
2
0
0
1
0
2
2
1
0
2
0
0
2
2
2
1
1
0
0
0
0
0
1
1
0
2
0
2
1
0
0
0
0
1
1
1
2
2
0
1
2
0
1
0
1
0
1
1
0
0
1
0
0
2
1
0
2
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
2
2
0
0
0
1
1
0
0
0
1
1
1
1
1
0
1
0
1
2
0
1
0
1
1
1
2
0
0
2
0
1
0
0
1
0
1
1
2
1
1
0
0
0
2
1
1
0
2
1
0
1
0
1
0
2
1
2
0
2
1
1
0
0
0
0
1
2
2
0
0
1
0
1
2
1
1
0
2
0
2
0
2
1
1
0
1
2
2
2
0
0
0
1
1
0
2
2
0
0
1
0
0
1
1
2
1
2
2
0
0
1
1
1
1
1
1
0
2
2
0
2
0
0
1
0
1
1
1
0
0
0
0
1
2
0
0
1
1
0
1
0
1
0
1
0
1
1
1
0
2
0
0
1
0
1
0
0
1
2
0
2
1
1
2
1
0
1
2
0
1
0
2
2
3
1
2
2
1
2
0
2
1
0
0
1
0
2
0
1
1
3
1
1
2
0
1
2
3
1
0
2
0
1
1
0
0
2
2
0
2
2
0
0
2
0
1
0
0
1
0
0
2
2
0
0
1
1
1
1
2
2
2
0
2
2
1
2
0
2
1
1
1
1
0
0
1
0
2
1
1
2
2
1
0
1
1
0
1
2
3
1
0
1
1
0
0
1
1
1
1
0
0
2
0
0
2
2
1
1
0
0
0
0
1
1
0
1
2
1
2
0
0
0
2
0
0
0
0
2
1
0
1
1
1
1
2
0
2
2
1
0
2
0
1
0
2
1
0
0
0
0
1
1
1
0
0
1
1
0
1
0
4
1
0
2
0
1
1
1
2
1
0
1
0
2
1
1
0
0
2
1
1
0
0
1
0
1
0
0
1
1
0
2
2
1
0
1
1
1
0
0
1
0
2
1
1
0
1
0
2
0
1
0
1
0
0
1
0
0
1
2
1
1
1
0
1
1
1
2
1
1
2
2
1
1
0
0
2
0
0
1
0
1
1
0
2
2
0
1
1
2
2
0
0
2
0
1
0
1
0
1
1
2
1
0
1
1
0
0
2
1
1
1
0
1
0
1
0
1
1
0
1
0
2
2
2
0
0
1
0
2
1
2
0
0
1
0
1
0
1
0
1
2
0
0
1
2
1
2
0
2
2
2
1
2
0
0
0
1
0
0
0
0
1
0
0
0
2
1
0
2
1
0
2
2
1
1
0
0
1
0
1
0
1
0
1
2
2
0
1
0
0
1
2
2
1
2
1
2
1
1
2
2
1
1
1
1
2
1
0
0
1
0
2
1
0
1
0
0
0
0
2
0
1
2
1
0
2
0
0
2
3
2
0
1
0
0
0
0
0
0
2
0
1
0
1
1
0
2
1
1
1
0
3
1
1
2
0
2
2
1
2
0
2
0
0
1
1
0
3
0
0
2
2
0
0
1
0
0
1
1
0
2
1
2
1
1
1
2
2
2
0
0
1
2
2
1
2
2
0
0
0
2
0
0
0
0
2
2
2
1
1
0
0
1
1
2
0
1
1
1
2
1
1
3
0
2
0
1
2
2
2
1
1
2
2
1
2
0
1
0
2
1
2
0
1
0
2
0
0
0
1
2
3
0
0
1
1
0
0
0
2
0
1
0
2
1
1
1
2
2
1
1
1
1
1
0
2
2
2
0
1
0
0
3
0
0
2
0
1
0
2
2
1
3
1
0
2
2
2
1
2
0
1
0
0
2
0
0
0
2
1
2
1
2
1
1
1
2
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
2
0
0
2
0
1
0
0
1
1
0
0
1
0
2
0
0
0
1
0
1
2
2
1
1
0
0
1
0
0
2
0
0
0
0
1
2
2
1
0
1
0
2
1
0
1
0
3
0
1
2
2
1
0
0
2
0
0
0
1
1
0
1
0
1
0
2
1
0
0
1
0
1
1
0
1
2
2
0
2
1
1
1
0
1
1
1
0
0
0
1
0
1
1
1
0
2
1
1
1
2
0
1
2
1
1
0
1
1
0
1
2
0
0
0
1
1
2
0
1
0
1
0
0
4
0
0
0
2
0
1
0
0
0
0
1
1
0
0
0
0
2
1
0
2
0
0
2
0
1
0
2
0
1
0
0
1
1
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
1
1
0
1
1
0
1
1
1
1
0
0
1
1
2
0
1
0
1
0
1
2
1
0
2
1
3
1
0
0
1
1
1
2
1
1
0
0
0
0
1
1
0
1
2
1
0
1
1
2
1
1
0
0
0
0
1
1
0
0
0
1
1
2
1
1
2
0
1
2
0
0
2
2
0
0
1
1
1
2
1
2
1
2
2
1
1
1
1
1
0
2
1
0
0
0
1
2
0
0
2
0
0
2
0
1
1
2
1
1
0
1
2
2
2
0
1
0
2
1
1
1
1
2
2
1
0
1
1
1
1
1
0
1
2
2
1
4
3
2
1
2
0
1
1
1
0
0
2
2
1
1
0
1
2
1
0
0
1
1
2
4
1
1
0
0
0
1
1
0
0
0
2
2
0
0
1
1
1
0
1
1
0
0
0
2
2
1
1
1
2
0
1
0
0
2
1
0
0
1
0
2
2
2
3
1
0
2
0
0
0
7
0
0
1
1
2
0
0
3
0
0
2
0
1
0
0
0
0
20
1
1
0
1
0
2
0
0
1
1
0
1
1
1
0
1
2
2
0
0
2
1
3
2
1
3
0
1
0
0
0
2
0
0
0
0
0
2
0
2
0
2
0
2
0
1
1
2
1
0
0
2
2
0
0
1
0
0
1
1
1
0
2
0
0
1
1
3
0
1
1
1
0
0
2
0
1
2
0
1
0
2
2
1
1
1
0
0
0
2
2
0
0
0
0
1
0
2
0
1
0
1
0
0
1
0
1
2
2
0
0
1
1
1
0
3
1
1
1
0
1
0
0
0
2
0
1
2
1
1
2
1
2
0
1
0
0
0
1
1
0
2
2
1
2
0
1
0
0
0
0
0
1
0
1
2
2
0
1
2
1
1
1
0
2
1
0
0
2
0
0
0
0
0
1
1
1
0
2
1
1
0
2
0
0
1
1
0
1
2
3
2
0
1
0
2
1
1
0
1
2
1
0
1
2
1
1
2
0
1
0
1
2
1
2
2
0
0
1
0
3
1
0
0
0
0
0
1
0
0
0
2
2
0
1
2
0
3
2
2
1
0
0
1
2
0
1
1
2
0
1
2
2
1
0
1
2
0
1
1
2
1
3
0
0
0
0
1
0
1
1
1
0
0
0
1
2
1
1
0
2
1
0
0
1
1
0
2
1
1
1
2
0
2
0
2
1
1
0
0
1
2
2
1
0
0
2
0
1
0
0
2
1
1
0
2
1
0
1
1
1
0
1
0
0
2
0
1
1
0
2
4
2
0
0
1
0
1
0
0
1
0
1
1
2
0
0
1
1
0
1
1
0
0
2
1
1
0
1
0
1
0
0
2
0
1
0
2
0
0
2
0
0
2
2
1
1
1
1
0
0
2
1
0
1
2
5
0
0
2
2
3
2
0
0
0
1
2
0
0
2
0
2
0
2
3
0
1
0
2
2
1
1
1
0
1
0
2
0
0
0
0
0
0
1
2
1
2
1
0
1
0
0
1
1
0
1
0
1
0
0
0
1
0
2
1
1
0
0
1
1
1
0
0
2
0
2
1
1
1
0
2
0
0
1
0
1
0
1
1
2
0
0
0
0
0
0
0
0
1
2
3
0
1
1
1
1
1
0
3
0
1
0
2
1
1
1
0
2
1
1
1
0
0
1
2
1
1
0
1
1
1
1
2
0
1
1
1
1
3
0
0
0
1
3
0
1
0
0
0
1
0
1
2
0
0
0
1
0
0
0
0
2
2
0
0
1
1
1
0
1
1
1
0
0
0
1
1
1
2
1
1
0
2
1
1
0
1
1
1
0
1
2
0
3
0
2
2
2
0
1
1
0
1
1
2
1
0
0
0
3
1
2
0
0
1
2
1
1
1
1
0
0
2
0
1
0
1
0
0
1
0
2
0
0
2
0
1
0
0
2
0
1
0
1
0
1
2
0
2
2
0
0
0
0
2
2
2
2
2
2
2
0
1
0
1
2
0
0
1
0
0
0
0
1
1
1
0
0
1
1
0
1
1
1
0
0
0
1
1
1
1
0
1
2
1
0
2
1
4
0
1
1
2
2
1
1
6
1
1
1
0
1
1
0
2
1
2
0
2
1
2
2
1
0
0
2
0
1
1
1
1
1
2
1
0
0
0
0
0
4
1
1
1
0
2
2
0
0
0
2
1
0
0
0
1
1
2
0
0
2
1
0
1
2
1
1
0
0
2
1
1
0
1
2
1
1
1
1
0
2
2
1
1
2
0
0
1
1
1
2
0
0
0
1
0
1
1
0
1
2
2
0
0
1
1
1
1
1
1
0
0
0
2
0
1
1
2
0
0
0
1
0
0
1
2
0
0
0
1
1
0
0
0
1
2
0
1
0
2
2
1
0
1
0
1
1
1
0
1
0
1
0
1
1
0
1
2
0
0
0
2
2
0
0
2
1
0
0
0
1
1
1
0
0
1
0
1
1
2
1
2
3
0
2
2
1
0
1
0
1
0
1
4
0
0
0
0
1
1
1
1
2
0
1
0
0
3
1
0
1
1
0
0
0
0
1
2
0
0
0
1
0
1
2
0
0
0
2
1
0
2
1
3
1
0
1
1
2
1
1
0
1
0
1
2
2
1
2
1
0
1
1
0
0
2
0
0
0
0
1
0
1
2
1
0
2
0
0
2
0
2
3
0
2
0
4
2
1
1
1
0
0
1
2
2
0
0
1
1
0
0
0
1
0
1
2
2
0
2
6
1
0
1
0
1
1
1
0
1
1
0
0
0
1
1
2
3
0
2
0
2
1
1
0
1
2
2
2
2
0
0
1
1
0
2
1
0
2
1
0
0
1
1
0
1
2
0
1
0
1
1
0
1
0
1
1
0
0
3
1
0
1
1
1
1
3
2
0
1
1
0
0
1
0
2
1
1
1
0
2
0
1
0
0
0
1
0
0
2
1
2
1
2
0
0
1
2
0
0
1
2
0
2
0
0
0
1
1
5
0
1
2
2
0
0
2
1
2
1
1
2
1
1
2
1
1
0
1
1
0
2
0
0
1
0
0
2
0
0
0
0
1
1
1
1
1
1
1
2
0
0
1
2
0
1
1
1
1
2
1
2
0
1
0
1
1
2
2
2
1
1
1
0
0
0
2
0
1
1
1
0
0
1
0
0
1
0
1
0
1
1
0
0
1
1
1
1
2
2
2
0
1
1
2
0
1
2
1
0
1
0
2
1
1
1
1
0
1
1
0
1
1
0
2
0
0
0
2
0
1
0
1
0
0
1
2
0
1
1
1
1
0
0
0
1
2
1
1
2
0
1
2
1
1
1
1
1
0
1
0
1
1
2
1
1
0
2
2
1
0
2
1
0
1
1
0
0
0
1
2
1
1
0
2
0
0
1
2
2
0
0
1
1
1
1
0
1
0
0
2
1
0
2
1
1
0
1
1
1
0
1
0
2
1
0
0
1
1
2
2
0
1
0
0
1
0
0
2
1
0
1
2
0
1
2
0
1
0
2
1
0
0
0
0
1
0
1
1
2
0
2
2
1
0
0
2
0
2
1
0
0
1
0
0
1
1
1
0
0
0
0
1
0
1
1
0
0
1
1
0
2
0
0
2
0
1
1
2
0
0
1
1
2
2
0
1
0
2
0
3
0
0
0
1
0
0
0
2
1
2
0
2
0
1
0
0
1
0
2
1
1
0
1
0
1
0
2
1
0
2
0
1
2
0
1
1
1
2
0
1
2
2
0
1
2
1
1
0
1
2
2
1
0
2
2
0
0
1
1
1
0
0
2
1
2
0
3
0
0
0
1
0
1
2
0
2
0
2
2
0
0
0
0
0
1
2
1
0
0
2
2
1
1
0
0
0
0
1
1
0
2
1
0
0
1
0
0
1
0
1
2
1
1
1
1
0
0
0
0
1
0
1
1
2
1
2
1
2
0
0
2
3
1
2
1
1
1
2
1
1
0
1
0
1
1
0
1
2
2
0
2
1
0
2
1
1
2
0
1
0
1
0
1
1
0
2
0
2
1
0
2
0
2
0
0
0
2
0
0
0
1
0
2
0
2
1
0
2
2
1
2
1
2
2
0
1
3
1
1
1
0
0
0
1
1
1
0
0
1
1
0
1
0
2
1
0
1
0
0
2
2
0
2
1
0
0
1
0
1
0
1
0
2
2
1
1
2
2
0
0
2
1
1
1
0
3
0
0
1
2
0
0
0
2
0
1
2
1
1
1
0
0
1
0
1
1
1
1
0
0
1
1
2
2
1
1
1
1
2
0
0
1
0
1
2
0
1
0
2
1
0
2
0
0
2
0
1
1
2
2
1
0
0
2
1
1
1
1
0
2
2
0
2
0
1
0
1
1
0
2
0
1
1
1
0
1
1
2
1
0
2
0
1
0
0
1
0
2
2
2
0
1
0
1
3
1
0
1
0
0
0
0
1
1
0
0
0
1
2
1
2
0
0
1
0
2
0
0
2
2
0
0
1
1
1
1
0
1
0
1
0
0
0
0
1
1
1
0
1
0
1
2
0
0
0
1
1
0
0
2
0
0
0
0
2
2
0
2
2
1
2
1
2
0
2
1
1
2
0
0
1
1
1
1
2
0
0
0
1
2
1
1
1
0
0
0
1
0
1
1
1
0
1
1
2
0
0
1
1
0
2
2
2
0
0
2
0
2
1
1
0
1
1
2
1
1
1
1
1
1
1
0
0
2
1
1
2
0
1
0
0
2
1
0
0
0
2
0
2
0
2
1
2
1
0
1
1
0
0
0
0
1
0
1
1
2
0
4
5
2
1
2
1
1
1
1
2
2
1
1
1
0
2
1
2
2
0
2
1
2
0
2
0
0
1
2
2
0
2
1
0
2
1
0
0
1
0
4
1
2
2
0
1
0
1
1
1
1
0
2
0
1
2
2
0
2
0
0
0
0
1
1
1
3
1
0
0
0
0
0
1
1
0
0
0
2
0
1
1
0
2
0
1
1
1
0
0
0
1
0
1
0
2
1
3
1
2
1
1
0
0
1
2
0
0
2
0
0
0
0
1
1
1
2
2
2
2
0
1
1
0
1
1
1
1
1
1
0
1
2
1
1
0
2
0
1
1
1
0
1
1
1
2
1
2
1
2
1
1
0
1
2
1
1
0
2
0
0
2
0
2
1
0
0
0
2
3
1
2
1
1
0
0
0
1
2
1
1
0
0
0
1
0
0
1
2
0
0
0
2
1
0
0
2
2
1
1
2
2
2
2
1
2
1
0
1
1
1
0
0
1
1
1
2
0
0
1
0
1
0
1
0
0
0
1
1
2
2
0
0
0
1
1
2
0
1
2
0
0
2
1
1
0
1
1
1
1
1
2
2
1
3
1
0
0
2
1
2
1
0
0
0
0
0
0
2
1
0
1
1
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
2
0
0
0
1
1
1
1
1
1
0
1
2
0
3
1
1
1
3
1
1
2
2
0
1
0
0
1
2
1
0
2
0
0
2
0
0
0
2
0
2
1
1
2
0
0
0
0
0
1
0
1
0
2
2
1
2
1
0
0
0
1
0
1
1
0
0
2
2
1
2
2
1
2
1
0
2
1
0
2
0
0
0
0
2
1
0
1
1
2
1
2
0
1
0
1
0
1
1
0
1
1
2
2
0
0
2
2
0
1
2
1
0
0
2
2
1
1
1
2
0
1
1
0
1
0
2
2
0
1
1
1
0
1
1
2
1
0
0
1
0
2
0
1
0
5
1
1
3
1
1
2
2
0
0
1
0
2
2
1
0
0
2
1
1
1
0
0
0
0
0
1
0
2
0
2
1
2
2
1
0
1
0
0
0
0
1
2
2
1
1
1
1
1
2
0
1
0
1
0
2
2
0
1
0
1
7
2
2
0
0
1
1
2
2
1
1
2
1
1
0
0
1
1
2
0
0
1
1
1
1
0
1
1
1
1
1
2
0
0
0
1
1
2
0
1
1
1
0
0
1
2
0
1
0
0
0
1
0
5
1
1
2
0
2
0
0
0
1
0
1
0
2
1
0
0
0
1
1
0
2
0
1
1
0
0
2
1
1
0
0
2
1
0
0
1
1
1
0
2
2
2
0
2
0
1
3
0
0
0
0
0
0
1
1
1
1
2
1
1
2
0
0
0
0
1
0
1
1
0
1
0
1
1
1
0
2
1
2
1
0
0
2
0
2
1
1
0
2
0
2
0
1
1
0
2
0
2
1
1
2
2
0
7
0
2
1
2
1
3
1
2
0
0
1
1
0
0
0
1
0
5
1
1
1
2
2
0
2
1
0
3
0
2
1
0
0
3
2
2
1
1
0
1
1
0
1
0
2
1
0
0
0
1
5
0
2
2
1
1
0
2
1
0
2
0
0
1
2
1
2
1
1
3
2
0
0
2
0
0
0
2
1
0
2
1
2
2
1
0
1
1
0
0
0
1
0
0
1
1
1
0
0
2
0
0
2
2
0
1
0
0
1
0
0
1
2
1
0
0
4
3
0
0
1
0
2
1
0
1
2
1
0
0
0
2
0
0
0
2
0
1
0
0
1
1
1
1
2
1
1
0
1
1
0
1
1
1
2
0
1
0
2
2
3
0
0
0
0
1
0
4
0
0
0
0
2
3
1
1
2
0
1
2
1
0
2
1
2
2
0
2
1
2
0
0
0
0
0
1
0
2
1
1
1
0
1
1
1
1
2
0
0
0
1
1
0
1
2
1
0
1
0
1
0
0
2
1
0
1
0
0
0
1
1
1
1
2
1
1
0
0
0
2
1
1
0
2
1
1
1
2
1
0
0
0
0
0
2
1
0
0
2
0
0
1
1
1
1
1
2
0
1
2
1
2
0
2
0
1
1
0
0
0
2
0
2
3
2
0
0
1
0
1
2
0
2
0
0
0
1
0
1
1
2
2
2
0
1
2
1
0
2
0
0
1
1
2
2
0
1
4
1
0
0
1
1
0
0
1
0
0
1
1
1
0
1
2
0
0
0
0
1
1
0
1
2
1
0
2
0
0
0
2
3
4
2
1
0
1
1
1
1
0
1
0
2
0
1
2
0
2
0
2
1
1
0
2
1
1
2
1
0
0
0
2
2
1
0
1
0
1
0
1
0
1
2
1
0
2
1
1
0
0
2
1
1
2
2
0
1
0
2
1
1
1
2
0
3
0
0
0
1
2
0
0
1
1
1
0
0
0
1
3
2
2
2
0
2
0
1
0
0
1
0
1
2
1
1
0
0
2
0
1
1
1
1
0
1
0
0
0
0
1
2
1
1
2
2
0
2
0
1
4
0
1
2
1
2
0
0
0
0
0
1
2
0
1
0
1
0
0
1
1
1
2
0
0
1
0
1
1
2
0
1
1
0
1
2
0
1
0
1
0
0
3
2
0
1
2
3
2
1
0
0
1
1
1
0
2
2
0
1
0
2
0
1
0
2
2
2
0
0
0
2
1
0
0
2
0
0
1
0
2
0
2
0
2
1
1
1
0
0
1
1
1
1
2
5
1
0
0
0
1
0
1
0
0
0
1
2
4
0
0
0
1
1
0
1
1
0
0
0
0
0
1
3
2
0
0
2
1
1
0
0
1
2
0
2
0
2
0
1
1
0
2
1
2
2
0
1
0
1
1
0
0
1
1
1
0
1
0
1
1
1
1
0
1
3
2
0
0
2
0
0
2
0
0
0
1
0
2
0
2
1
0
0
1
1
1
1
1
1
0
0
1
2
0
0
1
0
1
2
1
2
2
2
0
1
0
1
0
1
4
0
1
2
2
0
0
0
2
2
0
2
0
0
2
1
1
1
1
1
2
7
0
1
1
0
0
2
0
1
1
1
0
1
1
0
1
0
0
1
1
2
0
1
1
0
0
1
0
0
0
0
2
0
2
2
0
0
1
0
1
0
2
0
0
0
0
3
0
0
1
1
1
0
0
1
1
1
1
1
2
2
0
1
2
1
0
0
0
0
0
5
3
0
1
0
2
0
0
0
0
0
2
2
0
1
1
1
0
2
0
1
2
1
0
2
0
2
0
2
0
2
0
1
0
1
0
0
1
0
2
0
2
0
0
1
2
1
2
2
0
0
1
0
0
0
1
2
0
3
0
0
1
0
2
0
1
2
0
0
1
0
0
0
2
2
0
0
1
0
2
1
2
1
1
2
0
1
1
0
1
2
0
0
1
0
2
1
1
0
0
1
0
0
1
0
1
1
1
0
2
0
1
0
1
2
1
0
2
0
2
1
1
0
1
1
2
2
1
0
1
2
2
1
0
1
1
1
2
2
0
0
0
3
1
2
2
7
0
1
0
2
0
0
0
3
1
0
0
2
0
1
2
0
2
1
1
0
0
0
1
0
0
0
2
1
1
1
0
0
0
0
1
0
2
2
0
2
1
3
0
1
1
1
1
2
1
1
1
0
0
0
0
2
0
0
2
1
2
1
0
1
0
0
1
1
0
0
1
0
1
2
0
1
1
1
3
0
1
1
1
1
0
1
2
1
1
0
3
2
3
2
0
5
1
1
2
0
0
0
1
1
1
1
2
2
2
0
2
1
3
1
2
0
1
1
0
1
2
2
1
1
0
1
1
1
2
2
0
2
1
2
2
0
0
0
1
1
3
0
3
2
0
0
0
1
1
1
0
2
0
0
1
3
0
2
2
0
1
1
0
1
0
2
0
2
1
0
0
2
0
1
2
2
1
1
0
0
1
1
1
0
0
0
1
0
2
1
0
0
0
0
0
0
2
1
2
2
0
1
2
1
0
1
0
0
0
0
3
0
1
2
1
1
1
1
1
1
1
0
1
1
0
2
2
0
0
2
0
0
1
0
0
0
0
2
0
0
2
1
2
0
2
0
2
1
0
1
0
0
1
1
1
1
0
1
2
0
1
6
0
0
0
1
1
1
1
1
1
1
2
2
2
0
2
0
0
0
0
0
0
0
2
0
1
0
0
1
2
1
0
2
0
2
0
0
0
2
0
1
1
0
0
3
2
0
0
1
0
1
2
1
2
1
0
2
0
1
1
0
1
0
0
2
2
3
1
2
0
1
2
2
1
1
0
1
0
1
2
2
0
0
0
0
0
1
0
0
1
1
0
1
2
1
1
0
1
1
0
0
0
0
1
0
1
1
0
2
0
1
1
1
1
0
1
0
1
1
1
0
0
0
0
0
2
0
0
1
0
1
0
2
1
0
0
0
1
1
2
0
1
1
1
0
0
0
1
0
1
2
0
1
0
0
0
2
1
1
0
2
0
1
2
0
1
1
0
2
2
2
3
2
0
0
0
3
1
0
2
1
0
2
1
0
0
0
1
0
1
0
0
1
2
0
1
2
2
1
1
0
1
0
3
2
1
1
0
1
1
0
1
1
1
1
1
0
2
1
1
1
2
2
1
0
1
2
1
2
1
1
1
1
1
0
2
0
1
0
1
0
0
1
0
2
1
0
0
1
0
2
0
3
1
1
0
0
1
0
0
2
0
0
1
2
1
2
0
0
0
1
0
1
1
1
0
2
0
1
1
0
2
0
0
2
1
1
1
0
0
1
2
2
3
0
1
2
1
0
0
1
1
1
3
2
1
2
0
2
1
1
1
0
0
1
0
2
2
0
0
2
2
0
1
0
1
1
1
1
1
0
1
0
0
1
1
1
0
0
1
1
1
0
1
1
1
1
0
1
0
2
2
1
2
0
2
4
1
1
0
0
1
0
1
2
0
1
0
2
2
0
0
0
0
0
0
3
0
1
0
1
0
2
1
2
0
1
0
0
2
2
1
1
0
2
1
1
1
2
2
2
1
0
1
1
1
1
1
1
1
2
1
1
2
1
0
0
1
0
0
0
1
0
1
0
0
0
2
1
2
1
1
1
2
0
2
0
1
1
0
2
1
0
0
1
1
2
1
2
0
2
2
1
1
2
1
0
0
3
2
0
0
1
1
2
1
1
1
0
0
2
1
1
2
0
1
0
0
2
1
0
0
0
0
0
0
1
1
2
2
0
1
1
1
1
0
1
1
1
1
0
0
1
1
0
0
0
1
1
1
1
2
0
2
1
0
1
1
1
1
1
0
0
0
2
2
1
2
0
0
2
2
2
1
0
2
0
1
1
1
1
2
0
2
2
1
2
1
2
1
2
1
3
0
0
2
0
0
1
0
1
1
2
0
2
0
1
1
0
1
1
1
0
1
0
2
0
1
0
1
1
0
2
2
0
0
1
0
1
0
1
1
1
0
2
1
1
1
2
1
0
1
0
2
2
1
2
2
3
3
1
0
1
0
1
1
0
2
0
1
0
2
0
1
0
0
0
0
1
1
0
2
2
0
2
1
1
0
0
3
0
2
1
2
0
1
1
1
1
2
1
2
1
1
0
0
1
1
0
0
0
0
0
0
1
2
2
1
2
0
1
1
1
0
1
2
0
1
0
0
1
0
2
2
1
0
1
1
1
0
2
1
1
0
0
0
1
1
1
1
0
3
1
0
1
1
1
0
2
0
0
1
0
1
0
1
0
0
0
2
0
1
0
0
0
1
0
0
2
0
0
2
1
2
1
1
1
2
0
0
1
0
1
2
0
0
3
1
1
1
0
1
2
1
2
1
0
0
0
2
1
0
0
1
1
0
1
0
0
1
0
1
1
0
1
2
2
1
2
2
0
0
2
0
0
2
1
0
1
0
1
2
1
1
1
1
0
1
1
0
0
1
2
1
1
2
0
0
1
1
2
0
0
0
1
0
1
0
2
2
2
1
3
0
0
1
0
1
1
0
2
0
2
3
2
1
0
0
1
0
0
1
1
0
2
1
0
2
1
1
2
1
2
1
0
1
1
1
2
1
1
1
0
0
0
0
1
1
1
0
2
1
0
0
1
0
2
2
1
1
1
0
2
0
2
1
1
1
0
1
0
0
1
0
0
1
2
2
2
0
0
1
0
0
0
2
1
0
1
1
0
2
1
2
0
1
0
0
0
0
2
1
1
1
0
1
2
0
1
2
2
1
0
1
1
1
0
0
1
0
2
1
1
0
1
1
0
0
0
1
1
0
0
0
1
1
1
0
2
0
0
3
1
1
1
0
1
0
0
1
0
1
1
1
2
1
2
2
1
1
0
1
0
0
2
0
0
0
2
0
0
1
1
2
1
2
0
0
0
0
1
2
1
0
1
0
1
0
0
0
2
0
0
0
3
0
0
1
1
1
0
0
1
1
1
0
1
0
0
0
0
2
0
0
1
1
1
0
2
3
2
1
1
0
1
0
0
1
2
0
0
1
2
2
0
0
2
2
0
1
1
1
1
1
4
0
2
0
1
0
1
0
0
0
2
0
0
2
2
2
0
0
1
0
2
0
1
1
0
1
0
0
2
2
0
2
2
1
1
1
0
1
2
0
1
0
1
0
0
0
0
1
3
2
0
0
0
1
2
2
1
0
0
0
1
1
2
1
0
1
0
0
1
1
1
2
2
0
2
1
0
2
0
2
1
3
2
1
0
1
0
0
1
2
0
1
1
1
0
1
1
1
0
0
1
1
0
1
1
1
1
0
0
1
0
2
0
1
2
5
1
1
2
1
1
0
0
2
1
2
1
0
0
1
1
1
1
1
0
1
0
2
1
1
1
0
2
0
1
0
2
1
1
1
0
0
0
2
2
0
0
2
1
0
1
0
0
1
1
1
0
0
1
1
1
2
2
2
0
2
1
2
1
1
1
0
1
0
2
0
1
0
2
0
0
1
1
1
0
0
2
1
2
1
1
1
0
0
1
0
2
0
0
2
1
0
2
0
0
1
2
1
1
2
0
1
1
0
2
0
1
0
2
1
1
1
0
0
0
1
0
1
1
1
1
0
0
1
1
2
0
0
2
1
2
0
0
1
0
0
1
2
1
1
1
0
0
1
0
1
0
0
0
0
0
0
0
1
1
1
1
1
0
1
2
2
0
0
0
2
1
2
1
1
1
0
0
1
0
0
0
0
2
1
1
1
0
0
0
0
0
2
1
1
1
0
1
0
2
0
1
2
2
0
1
1
2
1
1
1
1
0
1
0
2
1
0
0
1
0
0
1
0
2
1
1
0
1
1
0
1
1
0
0
2
0
1
0
2
1
2
0
2
0
1
1
0
1
1
1
0
2
3
1
0
2
0
1
0
1
2
0
0
0
0
0
2
0
0
0
0
1
1
2
0
0
0
1
1
0
2
3
0
1
2
2
2
1
1
0
0
0
0
2
0
0
1
0
1
1
2
0
0
1
1
0
0
0
1
1
0
1
0
0
1
1
2
0
2
1
0
0
0
1
0
2
0
0
0
1
2
0
0
1
2
0
1
0
1
0
0
0
1
1
2
1
2
1
1
0
1
0
1
1
0
0
1
0
0
2
3
2
0
0
2
1
0
0
2
1
0
0
1
1
1
0
2
0
0
1
3
1
2
2
2
0
2
1
2
2
2
1
1
0
1
1
1
2
0
2
0
1
0
0
0
0
0
0
1
0
1
1
0
1
0
1
2
2
1
0
2
0
1
1
1
1
0
2
2
0
1
1
0
2
0
2
2
0
1
4
0
2
1
0
0
0
0
0
2
0
2
1
1
1
2
1
1
1
0
1
0
1
1
0
1
1
2
2
0
2
0
1
0
1
2
1
2
0
2
1
1
1
0
1
1
1
1
0
1
1
1
0
1
1
0
2
1
0
1
0
2
0
0
1
0
0
0
0
0
0
1
1
1
0
0
2
1
2
2
1
0
0
0
1
1
0
1
0
1
0
0
1
0
1
0
0
0
0
0
1
3
3
0
1
0
1
0
1
2
0
2
1
2
2
1
0
0
3
1
1
0
0
0
0
1
2
1
0
0
0
2
1
1
1
0
0
0
0
0
0
1
0
1
0
0
0
4
0
0
0
1
1
0
2
2
2
0
0
1
1
0
0
1
1
2
0
0
1
0
1
2
0
0
2
1
1
0
1
1
2
2
1
1
0
0
0
0
1
1
0
1
0
2
2
0
1
0
2
0
1
1
0
0
0
0
1
1
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
2
2
0
0
1
1
2
2
2
0
0
1
1
1
0
2
1
1
1
2
2
0
1
1
0
1
2
1
2
2
1
2
1
1
1
1
0
1
0
2
1
2
1
2
0
0
1
2
2
1
1
2
2
1
1
2
0
0
0
1
0
0
2
3
0
1
1
0
1
0
1
2
1
0
1
2
1
1
2
1
0
1
0
0
0
0
1
1
1
3
1
1
0
0
1
1
1
1
0
1
2
1
1
2
0
0
2
1
3
1
1
1
3
1
3
0
1
1
1
0
0
0
0
1
1
2
0
1
0
1
0
1
1
0
1
2
0
2
1
1
1
2
1
1
0
0
2
1
1
0
0
0
1
1
1
1
2
0
1
0
2
3
0
2
2
0
1
0
0
2
1
1
0
0
1
1
2
0
1
1
1
1
0
1
2
1
1
1
2
0
1
0
1
2
0
2
0
0
1
2
0
1
1
2
1
0
1
1
0
1
0
1
1
0
2
0
1
1
0
1
1
2
2
1
1
2
0
0
1
1
0
2
2
2
0
2
0
1
1
0
1
0
1
2
1
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
2
1
1
1
1
1
1
0
0
1
2
0
1
0
0
1
1
1
1
1
1
2
1
1
1
1
0
1
2
1
2
1
1
0
0
1
1
1
0
1
0
2
1
0
1
2
0
0
1
2
1
0
2
0
0
1
2
0
1
1
1
0
1
0
0
1
1
2
1
0
0
0
0
1
1
2
0
1
0
1
1
2
2
2
0
2
1
2
2
0
0
0
1
0
0
0
1
1
1
2
0
2
0
1
1
0
0
0
0
0
0
1
0
1
0
1
0
0
1
2
1
0
2
1
1
0
0
2
0
1
1
0
1
2
0
4
1
1
0
2
0
0
2
2
2
1
1
2
0
1
1
2
1
2
2
2
0
2
0
1
1
1
0
1
0
2
0
2
2
1
1
0
1
0
1
1
0
1
1
1
1
1
1
1
2
1
1
1
1
2
1
2
2
0
0
1
0
2
0
1
2
0
0
0
1
2
1
1
1
0
1
2
1
0
2
1
0
1
0
0
2
2
1
0
0
0
1
1
2
1
0
1
0
0
0
0
0
0
3
0
1
1
1
0
1
0
1
1
0
1
0
1
0
0
2
0
1
1
2
1
1
1
3
0
0
0
0
0
1
0
0
1
1
1
3
0
2
0
1
2
1
0
1
2
0
1
0
1
0
2
3
0
2
1
0
0
3
0
1
2
0
1
0
1
1
0
1
1
1
1
1
0
1
0
1
0
1
0
4
1
1
1
1
1
0
1
1
1
0
1
0
1
0
0
0
2
0
1
1
0
0
1
1
0
0
2
0
2
0
0
2
0
1
0
1
1
1
0
1
2
0
2
1
0
0
2
2
1
0
2
0
0
2
1
2
1
1
0
1
2
0
3
1
1
2
1
0
0
0
0
1
0
0
1
2
0
1
0
0
0
2
1
2
1
0
1
0
1
2
1
0
1
1
1
0
1
0
0
1
1
1
0
0
0
0
1
1
2
2
2
1
1
0
0
1
1
0
1
0
0
1
1
1
2
2
0
0
1
1
0
0
0
1
0
2
0
2
1
1
1
1
1
2
2
0
1
0
0
1
1
2
1
0
2
2
0
1
0
1
1
0
1
0
2
1
0
2
1
0
0
2
1
0
0
0
0
0
0
1
2
0
1
1
1
1
0
1
0
0
0
2
1
2
0
1
0
0
1
2
0
3
0
0
0
0
0
1
1
2
0
1
1
0
1
2
1
0
0
0
0
1
2
0
2
1
0
1
1
1
0
2
0
0
0
0
0
0
1
2
1
1
0
1
0
1
2
1
2
0
1
2
0
1
0
0
1
1
0
1
1
1
1
0
0
2
1
0
2
0
0
1
1
2
0
2
0
0
1
2
1
1
2
2
1
1
0
2
2
0
2
1
0
1
3
1
0
0
1
0
0
1
1
1
1
0
0
1
0
1
1
0
1
1
1
0
0
2
1
2
1
1
0
1
0
0
1
0
1
1
1
0
1
1
1
1
0
0
1
1
1
1
0
2
1
1
1
0
2
1
1
0
1
0
2
1
0
2
1
1
2
0
2
0
1
2
0
0
2
1
1
2
0
0
1
2
0
2
1
1
0
1
2
0
2
2
2
1
0
0
2
0
0
0
2
0
0
1
0
1
0
0
0
1
1
2
1
1
0
2
0
1
0
0
2
1
1
2
1
2
1
2
0
0
1
0
3
1
0
1
2
0
2
1
1
2
1
0
0
0
1
2
1
1
0
2
1
0
1
2
1
0
0
2
1
0
1
1
1
1
1
2
1
0
1
2
1
1
1
0
2
0
1
1
1
0
2
1
0
0
2
1
3
0
2
2
0
2
1
0
1
1
1
2
1
1
1
1
2
1
2
2
0
1
0
1
0
2
0
1
2
0
0
1
1
0
2
0
1
1
0
2
1
2
1
2
1
0
0
0
1
0
1
1
1
1
1
2
1
1
0
2
1
1
0
0
1
2
2
1
1
0
1
0
0
0
0
1
0
1
1
0
1
0
0
1
3
1
0
1
2
2
0
1
1
0
0
1
0
1
2
0
1
0
1
2
0
1
1
0
0
1
1
1
1
0
0
1
1
3
1
1
2
0
2
1
1
0
1
0
1
0
1
1
1
2
0
1
2
0
2
1
0
1
0
2
1
1
1
2
0
2
1
1
0
2
1
2
1
1
0
1
0
2
0
0
2
0
2
1
0
2
0
0
2
1
1
1
0
1
0
0
0
2
0
1
1
1
1
0
1
1
0
0
1
0
0
0
1
1
0
0
1
1
2
0
0
0
0
0
0
1
1
1
0
0
2
0
0
0
1
1
0
0
0
1
0
0
1
0
2
1
1
1
0
2
1
0
0
1
0
0
1
3
0
2
0
0
1
1
2
0
2
2
1
1
1
1
1
0
0
1
1
0
1
0
0
0
2
1
0
2
0
0
1
0
1
1
1
2
2
0
1
1
1
1
0
1
1
1
0
2
0
2
2
1
2
1
1
2
0
1
1
0
0
1
0
2
0
2
2
0
0
1
0
1
2
0
2
0
2
1
1
0
0
1
3
2
1
0
1
0
0
2
1
0
0
0
2
1
1
0
0
1
0
1
1
2
2
2
0
1
0
1
0
1
1
1
2
1
0
1
0
1
0
0
1
0
0
1
0
1
0
0
1
0
0
1
1
0
0
2
0
2
0
1
0
1
2
3
1
2
1
2
1
0
1
1
1
2
2
1
0
2
1
1
0
2
0
0
0
2
0
2
1
2
1
2
0
2
2
2
1
1
2
2
1
1
0
1
0
2
0
1
1
0
0
0
0
1
1
0
0
0
1
2
2
1
1
1
0
1
1
2
1
0
0
1
1
0
0
0
2
0
0
1
1
0
1
0
0
1
1
1
2
0
0
0
0
1
0
1
2
0
2
1
1
1
0
0
1
1
3
1
2
1
1
1
0
0
1
2
2
1
1
1
2
2
3
1
0
2
0
1
0
2
1
1
1
0
1
2
0
0
0
2
1
1
1
1
0
0
0
1
2
1
1
2
0
1
1
0
0
2
2
1
2
2
1
2
1
3
3
2
1
0
0
1
1
0
0
0
0
2
0
1
0
0
1
0
1
0
0
0
0
0
2
0
2
0
1
1
0
0
2
1
2
1
1
1
0
1
0
1
1
1
1
0
0
0
2
1
1
2
0
1
1
3
2
1
2
0
1
1
0
1
2
2
1
0
1
1
0
2
1
0
1
1
1
0
0
1
0
1
1
0
2
0
3
1
1
2
0
1
0
1
1
0
1
0
1
1
1
0
0
0
1
1
0
2
1
2
1
1
1
0
1
1
2
1
0
1
2
3
1
1
1
2
0
0
0
1
1
1
1
0
0
0
0
2
1
1
2
1
2
0
1
1
0
1
2
1
1
1
0
1
2
2
1
1
0
1
1
1
7
0
1
1
0
1
1
2
1
0
1
3
1
2
2
0
0
0
0
0
1
0
2
0
1
0
0
1
2
0
2
8
2
0
0
0
1
0
1
2
0
2
1
1
2
2
0
1
0
0
1
0
2
0
0
1
0
1
0
1
1
0
2
1
0
1
1
0
1
1
0
0
1
0
1
0
1
1
1
0
1
1
0
1
0
0
0
1
0
2
0
1
2
0
0
0
1
0
1
2
2
0
0
2
0
1
1
0
1
2
0
0
1
1
0
0
1
0
1
1
0
1
1
0
1
2
1
2
0
1
2
1
0
0
1
1
0
1
1
1
0
0
0
0
0
0
2
2
0
0
0
1
0
1
1
2
2
1
0
0
1
1
1
1
1
0
0
0
2
0
0
0
2
0
2
2
2
1
2
1
0
1
0
2
0
0
1
1
0
0
1
0
0
1
0
1
0
0
1
0
2
2
0
0
2
2
0
1
0
2
0
1
0
1
1
2
0
1
0
1
0
1
1
2
1
1
1
0
1
0
1
1
1
2
2
1
1
1
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
2
1
0
2
0
1
2
2
1
0
1
2
0
2
0
0
0
1
1
0
2
0
2
0
0
0
0
1
2
1
1
1
1
1
1
0
0
0
0
1
0
1
0
1
1
1
0
2
1
1
1
0
1
0
2
0
2
0
0
0
2
2
0
0
1
1
0
2
1
2
1
1
0
1
0
1
0
1
1
1
0
1
1
1
0
1
0
1
0
0
0
0
0
0
1
0
0
2
1
1
0
0
0
1
0
0
0
0
0
1
2
0
0
1
0
2
2
1
1
1
1
2
0
2
2
0
1
0
1
2
0
0
0
1
1
0
1
0
1
0
1
2
2
2
1
0
1
0
0
0
0
0
2
1
0
1
0
1
1
2
0
0
0
0
1
0
0
1
0
2
0
1
0
1
1
0
0
0
2
1
1
1
0
1
0
3
0
2
0
2
2
1
1
0
2
0
0
1
0
0
1
1
2
1
2
1
0
2
1
1
1
1
1
2
1
0
0
1
0
0
1
0
1
0
0
2
1
0
0
1
0
1
1
1
2
1
1
2
1
0
0
1
0
2
1
0
0
1
3
1
0
0
0
2
0
1
0
2
2
2
0
2
1
0
1
0
0
0
1
1
2
0
1
0
1
2
0
1
2
0
1
0
1
1
1
2
2
1
1
2
1
0
0
2
2
0
2
0
1
2
0
1
2
1
0
1
1
0
0
2
1
1
2
0
1
0
0
2
0
0
2
1
0
0
0
1
0
1
0
1
0
0
2
1
0
0
2
1
0
0
0
0
2
2
0
2
0
2
1
0
1
0
0
0
2
2
0
1
0
0
2
0
1
1
1
2
2
0
1
1
1
0
2
2
2
0
0
2
3
1
0
2
1
0
1
1
1
0
1
1
0
2
2
3
1
1
0
1
0
0
0
1
0
1
2
0
1
1
0
0
1
0
2
1
0
1
2
0
0
2
2
2
0
0
0
0
0
1
1
1
0
2
0
0
0
0
1
1
1
0
0
1
0
2
0
2
2
2
1
0
0
0
1
0
2
2
0
1
1
1
0
1
2
1
2
0
1
1
1
0
1
0
2
2
1
0
1
1
2
2
1
0
0
1
1
0
0
0
1
0
2
0
1
0
2
1
0
0
2
0
1
0
1
2
2
1
0
0
1
1
1
1
2
0
2
1
2
4
2
1
0
0
1
1
1
0
0
1
1
1
1
1
0
1
2
2
2
0
0
0
2
1
0
2
2
0
0
1
1
2
1
3
0
2
2
2
1
1
1
0
0
2
3
0
2
1
1
1
0
0
0
0
0
1
2
1
1
0
0
1
0
1
0
0
0
2
1
2
2
0
1
0
1
2
1
0
2
2
0
0
0
1
0
0
0
4
1
1
0
0
2
2
0
1
0
1
1
0
0
0
2
0
1
1
1
1
1
0
1
0
0
1
0
2
2
0
0
1
1
1
2
1
2
0
2
0
1
0
1
1
0
0
1
2
0
1
1
0
0
2
0
1
0
0
1
1
0
1
0
1
1
0
1
0
0
0
2
0
1
1
2
1
0
2
0
1
0
1
0
0
1
2
1
0
1
1
1
0
0
3
1
1
1
1
1
1
1
0
0
0
1
2
1
0
2
2
0
0
2
1
1
1
1
0
0
1
1
1
0
0
2
0
1
1
1
1
1
2
0
0
1
1
0
2
3
1
0
0
0
1
0
0
0
0
0
0
1
1
0
1
1
0
0
2
2
2
0
0
1
1
0
0
1
1
2
2
1
1
1
1
0
0
0
1
0
2
0
0
0
1
1
1
1
1
2
1
1
1
1
0
0
2
0
2
0
0
0
0
2
1
0
1
0
0
1
0
2
0
0
0
0
0
2
0
2
1
1
1
0
1
1
1
0
2
0
0
0
0
1
0
1
1
0
2
1
1
0
1
1
0
1
1
1
1
1
0
1
0
1
0
2
2
1
1
1
1
1
0
0
1
0
0
2
0
1
2
1
0
2
0
1
1
1
3
2
2
0
1
2
1
1
0
0
2
0
0
0
0
1
1
1
0
1
2
1
3
0
1
1
2
0
0
1
1
0
2
0
1
0
2
2
1
2
0
0
0
0
2
1
0
1
1
1
0
0
1
0
2
0
1
0
0
2
1
0
0
2
2
0
0
1
1
0
0
2
0
1
2
1
1
2
1
2
1
2
0
1
1
0
1
1
1
1
2
1
0
1
1
2
0
1
1
0
0
0
1
1
0
0
2
0
1
2
1
1
0
1
0
1
1
1
1
0
0
2
0
2
3
1
2
1
1
0
0
0
2
1
1
0
0
1
1
0
0
1
0
1
0
1
1
1
0
1
1
0
2
0
2
0
0
0
0
1
0
1
1
1
2
0
1
0
1
2
2
0
0
1
1
1
1
2
2
0
1
2
2
0
2
1
1
0
0
2
1
0
1
1
0
0
0
0
0
2
1
0
2
0
0
2
1
1
1
0
1
0
0
1
1
1
0
1
1
1
0
2
1
0
1
1
0
1
1
2
2
0
0
3
1
1
2
0
1
2
1
0
1
2
1
1
0
2
2
2
0
0
1
0
2
0
1
0
1
0
1
1
0
1
1
0
0
1
0
1
1
0
0
4
1
1
0
0
1
1
2
2
1
1
1
2
1
1
0
0
2
0
2
1
2
2
0
1
0
1
0
0
0
1
1
1
1
1
1
1
1
0
0
0
2
1
2
0
0
1
1
0
0
2
1
1
0
1
0
2
2
2
1
1
2
1
1
1
1
0
0
1
0
1
0
1
2
0
1
0
0
0
0
1
1
1
1
4
2
0
0
1
0
1
0
0
0
1
0
2
2
1
2
1
2
1
0
0
1
2
1
1
2
1
2
0
1
1
0
1
2
1
2
0
1
1
1
1
2
1
4
1
2
0
0
0
3
0
1
0
1
2
0
2
2
2
0
0
2
0
1
0
0
0
1
1
1
1
2
1
2
0
2
1
0
1
0
1
0
2
0
2
1
1
0
0
1
2
0
1
0
0
0
0
1
0
1
0
0
1
1
0
1
2
0
0
1
1
0
2
1
1
0
1
1
0
0
0
0
2
0
1
2
0
0
1
0
1
1
1
1
1
2
1
2
1
1
3
0
2
1
0
0
0
0
2
2
1
0
1
1
0
0
2
0
2
0
1
0
2
0
2
0
0
0
1
2
0
0
1
1
1
0
2
0
2
1
0
1
0
0
1
1
0
2
1
1
0
0
1
1
1
0
1
0
1
1
0
0
1
1
2
1
0
1
0
2
0
2
1
0
0
0
1
0
0
1
0
2
2
0
2
1
2
0
1
0
0
0
1
0
0
1
1
1
0
0
1
0
0
1
1
0
1
2
1
1
1
0
1
0
0
0
1
0
1
1
1
1
1
0
1
0
0
0
1
1
0
1
0
1
1
0
2
0
1
0
1
1
1
1
0
0
0
1
0
1
2
1
0
0
0
0
1
0
0
0
0
0
2
1
2
1
2
0
2
1
0
0
0
0
1
2
2
0
0
1
0
0
0
1
0
1
1
1
1
2
0
1
0
0
1
2
2
2
1
1
1
0
2
0
0
0
0
2
2
0
1
1
0
1
2
1
1
0
1
1
1
2
0
0
0
2
0
0
1
0
1
0
0
0
0
2
0
0
0
1
1
1
1
1
2
1
0
0
0
2
1
2
2
0
2
2
1
2
2
0
0
2
0
0
0
1
2
2
1
1
1
1
0
1
1
1
1
0
0
0
1
2
0
0
1
0
1
0
0
0
1
0
0
0
1
1
2
0
0
1
1
1
2
1
1
0
0
0
1
2
1
0
1
2
1
2
0
0
0
2
1
1
2
1
0
3
1
1
0
3
2
1
0
0
1
0
2
1
0
1
1
1
3
0
1
0
1
0
0
0
1
2
0
1
1
0
0
1
0
1
2
1
1
0
0
2
0
0
1
2
1
1
0
0
0
2
1
3
0
0
2
0
1
0
0
2
1
1
0
0
3
0
1
1
1
0
2
0
0
1
1
2
0
0
0
2
1
0
1
0
2
2
0
1
0
1
2
1
0
2
0
0
0
0
1
0
1
1
0
1
2
1
1
1
1
2
0
0
0
0
2
2
2
3
1
0
0
0
1
1
2
1
0
1
0
0
1
0
0
2
0
0
1
1
1
1
0
0
2
1
0
0
1
0
1
2
1
1
0
1
2
0
1
0
2
0
0
0
1
0
1
1
1
0
0
1
2
1
0
0
0
0
3
1
0
0
0
0
1
2
1
1
0
1
2
1
0
3
0
0
1
1
0
1
2
0
0
2
1
0
0
1
0
0
0
2
0
1
0
2
1
2
2
0
0
2
0
2
2
2
2
2
1
1
1
1
0
2
1
2
0
1
1
1
1
0
1
0
2
2
1
0
1
1
1
1
1
0
2
2
1
0
1
0
0
0
1
1
2
1
0
0
2
2
0
1
0
1
1
0
0
1
0
1
1
0
0
1
1
1
0
2
0
0
2
0
3
1
0
0
2
0
1
1
1
3
0
0
1
0
0
1
0
3
1
1
1
2
1
0
1
2
2
0
1
1
0
1
1
0
2
0
2
2
1
0
1
1
0
2
2
0
5
0
2
1
0
1
1
2
1
0
0
1
1
1
0
0
1
2
0
0
0
2
0
0
0
0
1
0
0
0
1
2
0
2
1
1
0
0
1
1
1
1
1
0
1
0
0
1
0
0
0
1
2
1
2
0
2
2
0
0
1
1
1
2
0
2
1
1
0
0
1
1
0
0
2
2
1
1
0
1
1
0
2
0
2
2
2
1
0
1
1
0
1
0
0
2
0
0
0
1
2
1
0
1
1
1
2
1
0
1
0
2
0
1
0
0
2
0
1
0
2
0
1
1
2
1
0
0
1
0
1
1
0
0
1
0
0
0
1
2
1
2
2
1
1
1
1
0
0
2
1
0
2
1
0
1
2
1
1
1
1
2
0
2
2
1
0
1
1
1
0
0
1
2
2
0
0
1
1
1
1
0
0
2
2
1
0
0
0
2
0
0
3
1
2
1
1
0
1
0
0
1
0
1
1
0
1
0
2
0
1
2
0
2
1
3
1
2
0
0
2
0
0
1
1
1
0
0
1
0
0
0
1
2
1
1
1
1
1
2
1
1
1
2
0
0
2
2
0
0
0
0
1
1
2
0
1
0
1
1
1
2
1
0
1
2
2
0
1
1
2
2
0
2
1
1
2
0
1
2
0
1
1
0
1
0
1
1
1
1
0
0
0
0
0
0
0
2
2
2
1
2
1
0
1
0
0
0
1
0
0
0
1
1
0
1
0
1
2
2
2
2
0
0
1
2
0
0
0
0
1
2
1
0
1
1
1
0
0
1
2
0
0
2
2
0
2
1
0
2
0
1
0
0
0
1
0
1
1
2
1
0
1
1
2
0
1
0
1
2
1
0
0
0
0
2
0
1
0
2
1
1
2
2
1
2
1
1
1
0
0
1
1
0
1
1
0
0
0
1
1
2
0
1
0
0
1
0
0
1
0
0
0
2
0
2
0
0
1
0
0
0
0
1
1
0
0
0
1
2
0
0
2
2
1
1
0
1
2
1
1
2
0
1
0
1
1
0
0
1
0
0
0
2
0
0
2
0
1
2
0
1
2
1
1
0
0
2
2
2
0
1
2
0
0
0
0
1
0
1
2
2
0
2
1
1
1
1
0
0
2
0
0
2
0
1
0
1
1
0
1
2
0
1
1
1
1
1
2
0
1
2
1
0
2
1
1
2
2
0
1
1
0
1
0
1
2
2
2
0
0
0
1
2
1
3
1
0
1
2
0
1
0
1
2
0
1
1
0
4
2
0
2
0
1
2
1
1
2
1
0
0
0
0
1
2
1
0
2
2
1
1
2
2
2
0
2
1
1
0
2
1
0
0
1
0
1
0
0
1
0
1
2
1
2
2
2
0
1
1
0
0
1
1
2
1
0
0
3
2
0
1
0
2
0
0
0
1
0
0
1
1
1
0
2
0
0
0
1
1
1
1
0
0
1
0
2
1
1
1
1
1
1
0
1
0
0
1
1
0
1
1
2
0
2
0
1
1
2
2
1
0
0
1
0
2
2
1
3
0
1
1
1
1
2
1
0
0
1
0
1
1
5
0
2
0
1
2
0
0
2
0
1
1
0
2
0
2
2
1
0
2
0
1
0
2
6
1
0
1
1
0
2
1
0
1
1
2
1
2
1
0
2
2
1
1
0
0
2
0
0
2
0
1
2
1
1
1
0
2
0
1
1
1
0
1
1
0
0
1
1
2
2
1
2
0
1
0
2
2
0
0
2
2
1
0
0
1
2
0
2
0
1
0
0
1
2
1
1
0
2
2
1
2
0
0
0
1
1
2
0
0
1
0
1
1
0
2
2
1
1
1
0
1
0
2
1
2
0
1
1
2
1
0
1
0
0
0
1
0
1
0
0
1
1
1
0
1
0
0
0
2
0
0
0
1
1
1
1
2
1
0
1
0
1
0
0
1
2
2
0
1
1
1
1
3
0
0
2
2
1
0
1
1
0
2
2
1
2
1
2
4
0
0
1
2
0
0
0
1
0
0
0
1
0
0
0
2
2
0
0
0
2
0
2
1
1
1
0
1
0
2
2
2
0
2
0
1
1
0
0
0
1
1
1
0
0
1
0
0
1
0
0
1
1
0
2
1
0
0
1
2
1
0
1
0
0
2
0
2
0
1
0
1
0
0
0
2
1
0
1
0
1
1
1
0
1
0
0
1
1
1
0
0
0
0
2
0
2
0
0
1
0
0
0
2
2
0
0
2
0
0
0
0
0
2
0
1
0
1
0
1
2
1
2
2
0
0
0
0
2
1
2
0
0
1
0
1
1
1
0
1
1
3
0
1
2
0
0
0
1
0
0
1
0
2
1
1
1
0
1
1
1
1
0
1
1
1
2
0
0
2
0
0
1
1
1
0
2
0
0
0
1
0
1
0
1
0
0
2
1
0
1
1
0
0
0
1
0
1
0
0
1
1
3
0
1
0
1
2
2
1
2
2
0
1
1
0
1
0
0
0
2
0
2
2
2
0
0
3
0
1
0
2
0
0
1
1
0
0
3
1
0
1
1
0
1
1
1
1
2
1
1
0
2
0
0
3
1
1
2
2
0
0
2
1
0
0
1
0
1
0
2
2
0
2
2
1
1
1
2
1
1
1
2
0
2
2
1
0
0
1
1
2
2
0
1
0
0
1
2
0
1
0
1
1
1
1
1
0
1
0
0
0
2
0
2
0
0
0
1
0
0
1
1
1
2
2
2
0
1
1
1
2
1
2
0
1
1
0
0
0
0
2
0
0
1
0
1
1
0
1
0
1
0
2
1
0
1
2
1
3
1
0
1
0
1
0
0
0
0
0
1
0
1
1
0
1
1
0
1
1
1
2
2
0
1
1
0
0
2
0
1
1
1
0
1
0
1
1
1
2
1
1
0
2
0
0
1
1
0
1
1
2
1
0
1
0
1
0
0
1
0
2
1
0
1
0
1
0
0
1
2
2
1
0
2
1
0
2
0
0
0
0
1
2
0
3
0
0
1
2
0
2
1
1
0
1
2
1
1
0
0
1
1
2
1
2
1
2
1
1
1
2
1
2
1
2
1
0
0
0
1
1
0
0
1
0
1
1
1
0
2
1
2
2
2
0
0
0
0
2
2
1
1
0
1
0
0
0
1
3
1
0
2
0
0
0
1
0
1
1
0
2
2
1
1
0
2
0
0
2
0
2
1
0
2
1
1
1
2
1
1
2
0
0
0
3
0
1
2
2
1
0
0
1
2
0
0
0
1
0
2
0
0
1
0
2
0
2
0
0
0
0
2
0
1
1
0
0
2
2
1
0
0
0
0
0
3
0
0
1
1
0
2
2
1
1
1
0
1
1
1
1
2
4
0
1
0
1
0
1
1
1
0
1
0
0
3
1
1
1
0
2
1
1
1
1
1
2
1
1
1
0
2
0
1
1
1
2
0
0
2
0
2
1
2
1
0
2
0
0
0
2
0
1
1
2
0
2
1
0
1
2
0
1
0
0
2
1
2
0
1
2
0
0
1
2
1
2
1
1
1
0
2
0
1
0
1
1
0
0
1
0
0
2
1
1
0
1
1
2
0
0
1
1
1
2
0
2
1
1
1
1
1
1
0
0
4
2
0
0
1
1
2
0
0
0
1
1
3
2
1
2
0
0
1
1
1
1
1
2
1
2
1
0
2
0
0
1
0
0
0
0
0
0
3
0
1
1
0
1
0
1
2
0
1
2
1
0
0
0
1
0
2
1
0
2
0
1
0
2
1
2
1
1
0
2
0
0
0
2
1
0
0
0
0
1
0
1
1
2
1
0
1
2
1
0
0
0
0
0
1
1
0
0
1
1
2
2
0
2
1
0
1
0
2
0
1
0
2
0
2
1
1
0
0
1
1
2
0
2
2
0
0
2
0
1
0
0
0
1
1
1
0
0
1
1
2
2
0
1
1
0
1
0
2
1
2
2
1
2
1
3
0
1
1
0
2
2
0
0
0
1
2
0
1
2
0
2
2
0
1
1
2
0
1
0
0
2
0
1
2
1
1
3
1
1
1
1
0
0
1
2
2
0
2
1
0
1
3
1
0
0
2
1
1
0
2
2
0
0
2
0
2
1
1
1
0
0
0
1
1
1
2
0
0
2
1
1
1
0
1
0
0
0
0
1
0
1
0
3
0
1
0
2
2
0
2
2
1
0
2
1
1
1
1
0
1
1
0
0
2
5
1
2
2
0
0
2
0
1
0
1
1
0
0
0
1
1
0
1
2
0
1
0
1
2
2
0
1
0
0
1
0
1
3
2
0
0
0
0
1
0
1
0
1
0
1
1
2
2
1
2
1
1
1
0
1
0
0
0
0
2
2
1
1
0
1
2
1
1
0
0
0
0
2
1
0
2
0
0
1
1
1
0
2
2
0
1
2
1
1
1
1
0
1
1
2
0
1
0
0
0
2
2
1
0
1
1
1
0
0
0
0
3
1
0
1
0
0
0
0
1
0
1
2
1
1
1
0
0
1
0
0
0
2
1
1
0
1
0
1
1
1
0
0
1
2
1
1
1
1
0
0
1
1
1
1
2
1
2
1
2
1
1
0
2
1
0
1
1
0
0
0
0
0
1
0
2
1
2
0
2
2
0
2
1
1
0
0
1
0
0
0
2
0
1
0
0
0
0
1
0
2
1
1
1
1
1
1
0
0
0
1
2
0
1
0
2
1
1
0
2
2
1
1
1
1
0
1
0
0
0
1
2
0
2
2
0
0
2
0
2
0
2
1
0
1
2
0
0
0
0
1
1
1
2
1
2
1
0
1
1
3
2
1
2
2
1
0
0
2
1
0
0
2
0
0
0
0
0
3
0
0
0
2
2
0
1
0
0
1
1
0
0
2
1
1
0
0
2
1
3
2
0
1
0
2
1
1
1
0
0
0
0
0
2
1
2
2
0
1
0
0
2
0
1
0
3
1
1
0
2
0
1
1
0
0
2
1
0
0
0
0
1
1
0
3
1
1
0
2
1
2
1
1
1
1
2
1
0
1
1
0
1
3
2
1
0
0
1
0
0
2
1
1
0
1
0
0
3
0
1
1
0
1
2
2
0
0
0
0
1
2
2
0
0
0
0
1
0
0
0
0
2
1
1
2
0
0
1
1
1
0
1
2
2
1
1
0
0
1
0
1
0
1
4
0
1
1
1
1
1
1
0
0
1
3
2
1
2
2
1
0
2
0
3
1
2
1
1
3
1
1
0
1
1
1
2
1
1
0
2
1
0
1
0
2
0
1
1
2
1
0
1
0
1
0
1
0
0
2
1
0
0
0
2
1
1
1
1
0
0
2
0
2
0
1
1
2
2
1
0
0
1
1
0
0
0
3
2
1
0
0
0
2
2
0
1
2
2
0
2
0
2
2
0
2
0
1
1
1
2
0
0
2
1
0
1
1
0
0
1
0
2
1
1
0
0
2
1
0
1
0
0
2
1
0
2
0
2
0
1
1
2
0
2
2
1
1
2
3
0
0
0
1
0
1
0
2
1
2
1
0
0
2
1
1
1
1
1
2
2
0
1
1
1
0
1
2
0
1
0
1
0
1
0
0
1
1
1
1
2
1
0
1
1
1
0
0
1
3
0
1
2
0
1
1
1
1
1
2
2
0
2
0
2
1
1
0
2
4
2
1
1
0
0
1
0
2
2
1
0
1
0
0
1
1
0
0
1
0
2
0
0
3
1
0
1
2
2
0
0
0
0
0
1
0
2
0
3
1
0
0
0
1
0
2
1
2
1
2
1
0
1
0
0
1
0
0
1
2
2
1
0
0
0
2
1
1
0
1
0
0
2
2
0
1
1
1
0
1
1
0
1
2
0
3
1
1
1
0
0
2
1
1
0
0
2
0
1
2
1
2
0
0
0
2
1
0
1
2
2
0
0
0
2
2
0
1
0
2
0
1
0
2
2
2
2
0
0
1
0
0
1
2
1
0
1
1
1
0
0
1
1
0
1
1
2
0
2
1
2
1
0
0
1
0
1
1
2
0
1
0
1
1
0
0
2
0
0
2
0
2
1
0
1
0
1
2
1
1
2
1
0
0
1
0
0
0
1
0
2
0
0
1
0
0
1
0
0
2
2
0
2
1
0
1
0
0
1
1
0
3
1
0
0
2
2
0
1
1
1
1
1
0
1
1
1
1
2
0
1
2
1
1
1
2
2
2
1
2
1
0
1
1
0
3
1
1
2
0
1
1
2
1
0
1
1
2
1
0
0
1
0
0
2
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
2
1
1
1
1
1
0
0
1
2
0
1
0
1
1
1
0
1
0
1
1
1
0
0
1
0
1
1
1
0
0
1
1
0
0
1
0
1
1
0
1
2
0
1
0
1
0
0
0
2
1
2
1
0
0
0
0
2
0
0
0
1
0
1
1
2
1
1
1
0
0
1
1
2
1
2
0
1
0
0
0
0
1
1
0
1
1
0
1
0
1
0
1
1
1
1
1
1
1
2
2
2
1
1
0
0
1
0
2
0
0
0
1
2
0
2
1
0
2
1
2
0
1
0
0
1
1
0
0
1
0
0
1
1
0
0
2
1
0
0
2
1
0
1
1
0
2
1
2
2
1
0
1
1
1
0
0
2
0
0
0
2
2
1
0
1
0
1
0
1
0
1
1
1
0
1
1
0
0
2
1
1
2
1
0
0
0
1
1
1
2
1
1
2
1
0
2
0
0
0
1
1
3
2
1
1
0
1
0
0
2
0
1
0
2
0
0
1
1
1
0
1
1
1
2
0
1
0
0
1
0
2
2
1
1
0
2
3
1
1
0
1
0
1
1
1
1
0
0
2
2
0
1
2
0
0
0
3
0
1
2
0
1
1
0
2
2
0
2
1
2
2
0
2
0
1
0
1
0
0
2
4
2
1
3
2
0
1
0
2
1
0
1
0
1
2
0
0
2
1
1
1
1
0
1
2
0
1
0
1
1
2
2
1
0
1
0
0
1
1
1
1
0
1
1
2
2
0
0
0
1
1
0
0
0
0
1
0
2
2
0
3
2
0
2
0
0
0
0
1
2
0
4
2
0
1
1
1
1
1
1
1
1
1
0
1
2
1
1
2
1
1
1
1
1
1
1
0
1
1
0
2
0
1
1
1
1
0
0
1
1
0
1
0
1
1
0
0
1
0
0
0
0
0
2
1
0
0
1
1
1
0
0
0
2
1
2
2
0
0
0
0
1
0
2
0
2
0
0
1
0
1
2
1
0
0
1
0
2
0
1
2
3
0
0
2
2
2
2
0
1
1
0
1
0
0
1
0
3
1
0
0
1
1
0
1
0
1
0
1
2
0
0
0
0
1
0
0
2
0
1
1
2
2
2
0
2
2
0
0
0
1
1
2
1
2
2
0
0
2
3
0
2
1
0
0
1
1
1
1
0
1
2
1
0
1
1
2
1
0
2
0
0
0
0
1
1
1
1
1
0
0
1
3
0
1
2
0
0
1
0
1
0
1
0
1
1
0
1
0
1
0
2
0
2
0
0
3
1
1
2
1
0
2
1
0
1
0
1
2
0
0
0
2
0
1
0
2
1
3
1
1
0
0
0
3
2
1
1
1
1
2
0
1
1
0
0
1
2
1
0
0
0
0
1
1
1
0
1
2
2
1
2
0
0
1
0
0
2
0
1
1
0
3
1
1
0
1
0
0
0
2
2
1
2
1
0
0
1
0
0
1
2
0
1
0
2
0
2
2
1
0
0
0
1
2
0
1
2
1
0
1
0
1
2
0
0
1
2
1
0
1
0
1
1
0
0
1
1
1
0
0
0
0
2
1
1
1
0
0
1
2
1
2
1
0
0
1
0
2
0
2
1
0
0
1
1
2
2
0
1
1
1
1
1
2
2
2
1
0
2
1
1
2
0
2
3
0
0
0
1
0
2
2
0
1
2
2
2
1
1
0
0
1
1
0
0
0
1
1
2
0
1
1
0
1
0
0
1
1
0
1
0
0
2
2
2
1
1
0
2
0
2
1
2
1
0
0
2
1
2
0
0
0
0
2
0
1
1
0
0
1
1
1
0
1
0
0
0
1
1
1
1
0
0
0
0
0
2
2
1
1
1
0
1
1
0
2
1
0
0
0
1
0
2
0
0
2
1
0
2
0
0
1
0
1
1
1
1
0
2
2
2
1
1
0
1
1
0
0
1
2
1
0
1
0
1
0
0
1
1
0
2
2
0
1
1
1
1
1
1
1
2
3
2
1
1
0
0
0
0
2
1
1
0
1
1
1
1
2
1
2
1
2
2
1
1
0
1
0
1
0
0
0
1
0
1
2
0
1
2
1
1
0
2
0
0
0
0
1
0
2
2
1
0
2
0
1
0
0
2
0
0
0
0
1
1
1
0
2
0
1
0
1
0
1
1
2
0
2
0
1
0
1
1
0
2
2
0
0
1
3
0
0
0
1
0
1
0
0
2
0
2
1
1
0
2
1
1
1
2
1
1
1
0
0
2
1
0
1
0
2
1
1
2
0
2
1
2
0
1
0
2
0
0
1
1
1
1
1
2
0
2
1
1
0
0
1
0
1
0
1
0
0
1
0
0
0
2
1
0
1
1
1
0
1
1
1
2
0
1
1
1
0
2
1
0
0
1
2
1
1
0
1
1
1
0
1
1
0
0
2
1
1
0
1
1
1
2
2
2
3
1
1
1
0
1
0
0
2
1
1
0
1
2
2
1
0
0
2
1
1
1
1
1
0
0
0
1
1
2
1
1
1
1
2
1
2
1
0
2
2
0
0
2
1
0
1
0
0
1
0
0
1
2
1
1
2
0
2
1
2
1
0
0
1
0
1
2
0
0
0
0
0
2
1
1
0
2
2
1
1
0
2
0
1
1
1
1
2
2
0
0
2
1
1
2
2
1
0
1
0
0
1
0
1
1
1
0
0
0
2
1
0
1
1
2
0
1
1
2
2
2
0
1
1
0
1
1
1
1
0
0
1
1
1
1
1
0
1
1
2
1
0
1
2
0
0
1
1
2
2
0
1
0
2
2
1
2
0
0
2
1
0
1
0
0
1
0
1
0
0
0
1
0
0
0
1
2
0
0
2
1
2
2
1
0
5
2
2
0
1
1
2
0
2
1
0
0
2
1
0
0
0
0
2
0
0
1
0
1
1
0
0
1
0
0
0
0
1
0
1
1
1
0
0
1
1
1
1
2
1
0
2
0
2
1
1
1
0
0
0
1
1
0
1
0
0
1
1
1
1
1
1
1
2
1
1
2
1
1
0
2
3
1
1
0
3
1
1
1
2
2
0
2
1
1
2
1
0
0
0
1
0
1
2
0
0
1
2
1
1
1
0
1
1
4
1
0
2
1
0
1
3
0
2
1
0
0
1
0
2
1
1
1
1
2
5
0
1
1
0
1
0
2
2
2
1
0
2
1
0
2
1
1
0
0
0
1
0
1
1
0
2
0
1
1
1
0
2
0
0
1
2
1
1
0
0
2
0
0
1
1
1
2
1
1
0
2
2
1
1
0
1
0
0
0
0
1
0
0
0
1
0
0
2
1
0
1
1
0
1
0
0
1
1
0
1
2
1
1
0
1
0
1
0
1
2
1
3
1
0
2
2
2
2
2
1
1
1
1
1
0
0
1
0
1
0
1
0
1
2
1
1
1
0
2
2
0
1
1
2
1
0
1
1
2
1
0
2
0
1
0
0
1
2
1
1
1
2
1
1
1
0
1
0
0
0
0
2
1
1
1
1
1
1
1
0
1
1
0
2
1
1
2
1
1
2
1
0
0
1
1
2
1
1
2
2
0
0
1
0
0
1
1
0
1
2
1
2
1
2
1
3
1
1
0
2
1
2
3
1
0
2
0
0
0
2
0
1
1
1
2
0
1
1
0
1
1
1
1
1
0
0
2
2
1
1
0
2
1
2
0
1
3
1
1
1
0
1
2
0
2
0
1
2
2
0
1
2
0
1
1
0
0
0
2
0
0
0
2
1
1
1
1
0
1
2
0
1
2
1
0
3
1
1
0
0
2
0
1
1
0
0
2
0
1
0
0
2
2
2
1
1
1
1
1
2
0
0
0
1
1
1
0
0
0
1
1
2
0
1
1
1
0
2
0
0
2
1
3
1
0
0
0
2
0
0
2
0
2
1
2
0
0
0
2
0
1
0
0
1
0
0
0
0
0
1
1
1
1
1
0
1
4
1
0
2
0
1
0
0
1
0
0
1
0
2
1
1
0
1
2
2
0
1
0
2
0
0
1
0
0
2
1
1
0
0
1
1
1
1
1
1
0
0
0
0
1
0
1
1
0
1
0
0
2
0
1
1
0
2
0
1
1
0
1
1
0
1
1
2
1
2
1
1
0
0
2
1
1
0
1
0
1
1
1
1
1
1
1
2
1
0
2
0
1
0
1
0
1
0
0
0
1
0
0
1
2
1
2
1
1
0
0
3
2
1
0
1
1
1
0
0
1
0
3
0
1
2
2
0
2
1
2
1
0
0
1
1
1
0
0
0
1
0
1
1
0
2
1
1
1
2
0
1
0
0
1
1
1
0
2
1
0
2
0
0
0
1
2
1
0
1
1
1
0
1
0
1
2
0
0
1
1
1
0
0
2
1
2
0
1
0
0
2
1
1
2
0
0
1
0
2
4
1
0
2
0
0
0
1
1
1
0
1
3
1
2
0
0
0
1
0
0
0
0
0
1
1
2
2
1
0
2
1
2
0
1
0
0
0
1
1
1
2
2
0
1
2
1
1
1
1
0
0
2
1
0
0
0
0
1
0
0
1
2
0
0
0
1
2
0
2
2
1
0
0
2
1
2
1
2
1
2
1
0
0
0
0
0
0
0
0
2
2
1
2
0
1
1
0
0
2
2
2
0
0
1
1
1
0
0
1
3
1
1
1
1
1
2
2
1
1
1
0
0
0
1
1
1
1
1
1
1
1
0
1
0
1
2
0
1
1
0
0
0
0
0
1
0
1
0
0
3
0
2
0
2
0
2
0
1
2
2
2
1
2
2
1
0
0
0
0
0
0
2
2
1
0
0
0
2
2
2
2
2
0
1
2
0
0
0
0
2
0
2
2
1
0
2
0
0
0
0
2
2
3
1
0
2
0
0
0
0
1
0
2
0
0
1
4
0
1
1
5
0
1
1
2
1
3
0
0
0
1
1
1
0
1
1
1
0
1
1
1
0
2
0
0
3
0
0
1
1
1
1
1
1
0
1
0
2
2
1
2
1
0
2
1
1
1
0
1
2
1
2
1
1
0
0
0
1
1
1
0
1
1
0
2
1
1
1
1
0
1
1
1
1
0
1
1
0
1
2
0
0
2
0
2
0
1
0
1
0
1
0
0
1
2
0
1
1
1
0
2
1
1
1
0
0
0
0
1
0
0
2
2
1
1
2
1
1
0
1
2
1
1
0
2
2
1
1
0
1
1
2
1
1
1
2
0
1
1
0
0
1
2
1
0
2
2
0
1
0
1
0
0
1
1
1
1
1
1
1
1
2
0
0
1
0
1
1
2
2
1
4
1
2
1
1
0
0
1
2
1
1
0
3
1
0
0
1
0
3
2
1
1
1
1
0
2
1
2
0
1
0
1
2
1
1
1
1
1
0
1
1
0
0
0
1
1
1
0
1
0
1
2
1
3
0
1
2
0
2
0
1
2
2
2
1
2
1
0
1
1
1
2
1
1
0
1
1
0
0
1
0
1
1
1
1
1
1
1
1
1
0
1
0
1
2
0
1
1
2
0
0
1
1
0
0
0
1
0
0
2
1
1
2
0
1
0
1
0
1
2
0
0
1
1
0
0
1
0
0
0
1
1
1
0
1
2
2
1
0
0
0
0
2
0
0
2
1
2
1
0
0
0
0
2
2
0
2
1
0
1
1
2
0
3
0
1
1
2
1
1
1
1
1
0
0
0
0
1
1
1
1
1
0
1
1
2
0
1
2
1
0
2
2
0
0
0
2
1
0
0
0
1
1
0
0
1
1
2
0
1
1
0
2
0
0
0
1
0
2
0
0
0
1
2
1
1
0
1
0
1
0
0
1
0
0
0
0
0
2
0
2
0
2
2
1
0
1
0
1
0
0
2
1
0
0
1
2
1
0
2
1
0
0
2
2
1
2
0
1
0
1
1
0
2
0
0
2
1
2
2
1
0
0
0
1
3
1
0
1
0
0
1
0
2
0
0
0
0
0
1
1
0
2
0
0
0
0
1
1
2
0
0
2
0
1
2
0
1
0
1
0
2
0
0
0
1
0
3
0
0
0
0
2
1
1
2
1
1
0
1
2
2
0
2
0
0
2
2
0
0
0
0
1
1
3
2
1
0
0
1
1
2
2
1
0
2
1
1
2
1
1
2
0
1
1
1
0
2
0
0
0
0
0
2
2
0
0
0
1
0
0
0
1
2
1
2
1
0
0
0
1
0
1
2
1
1
1
2
1
1
0
1
2
0
0
1
1
1
0
0
1
0
0
1
1
0
1
0
1
1
0
2
0
0
0
1
1
2
1
1
0
1
0
1
0
0
2
1
0
0
2
2
1
0
1
1
2
1
1
1
2
0
1
0
1
1
0
2
1
0
0
0
1
1
1
1
1
0
0
2
0
0
1
0
1
1
2
2
0
1
0
2
0
0
2
2
0
0
0
2
0
1
1
1
0
1
1
0
2
0
1
0
0
2
1
1
0
2
0
1
0
1
2
2
0
0
2
1
0
1
0
0
1
0
2
0
1
2
0
1
2
1
0
1
1
1
0
0
1
0
1
1
0
0
0
2
1
0
1
1
0
2
2
0
1
2
1
1
2
1
0
0
1
0
1
1
1
0
1
1
0
1
1
0
0
3
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
1
2
2
0
3
0
0
1
0
1
2
0
2
1
1
1
0
1
2
0
2
2
2
1
0
0
1
1
2
1
1
0
0
1
2
2
0
2
1
0
1
0
0
1
1
0
1
1
1
1
2
0
1
0
0
0
1
2
0
1
1
1
2
0
1
0
1
0
1
0
2
0
1
1
1
2
1
1
2
0
0
0
1
0
0
1
2
1
0
0
2
1
1
1
0
1
0
2
0
1
1
1
2
1
2
0
1
0
1
1
2
0
1
0
0
0
0
1
2
2
2
2
1
1
2
1
1
0
0
2
0
0
1
1
2
1
0
1
0
1
1
0
1
1
0
2
2
0
1
1
1
0
1
1
0
0
2
2
2
0
0
1
1
0
0
2
0
0
0
1
1
1
2
0
1
2
1
0
0
0
2
0
1
0
2
0
0
0
0
0
1
0
0
2
2
3
2
2
0
2
2
0
1
1
0
0
1
0
1
1
0
0
0
1
1
3
0
1
0
2
0
1
2
2
0
0
1
1
2
2
0
2
0
1
0
1
1
1
2
2
1
0
1
1
3
1
1
2
1
1
1
1
1
0
1
2
1
1
2
0
1
1
2
1
0
0
2
4
2
0
1
1
1
1
0
0
0
0
1
0
0
1
1
1
1
1
1
5
1
1
1
2
0
1
0
1
1
1
0
0
1
1
0
0
1
1
1
2
2
1
1
2
2
0
3
1
1
2
0
0
2
0
1
2
2
1
2
1
1
1
2
4
1
1
2
0
1
0
1
0
1
1
1
1
1
2
0
1
2
0
1
1
2
2
0
1
2
1
2
1
0
2
1
3
3
1
0
2
1
1
0
1
0
1
2
2
0
1
2
1
1
0
0
0
0
0
0
1
0
1
1
0
1
3
1
1
2
0
0
1
2
2
0
0
0
2
0
0
0
0
0
1
0
1
1
1
0
1
2
1
1
1
1
0
1
2
2
1
0
1
1
1
0
1
0
1
1
2
2
1
2
0
2
0
1
1
1
0
0
3
1
0
0
1
1
1
0
0
0
1
1
1
0
2
0
1
1
1
1
2
1
1
0
0
2
1
2
0
0
1
0
2
1
0
0
1
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
1
1
2
0
1
0
1
0
2
1
0
0
2
1
1
0
2
1
1
0
1
0
1
1
0
0
1
2
1
0
1
1
2
1
0
0
1
0
1
0
0
1
0
0
0
0
1
2
2
1
0
2
1
0
2
1
2
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
2
0
0
0
0
1
1
1
0
0
1
2
2
0
2
2
1
1
1
0
2
0
0
1
0
1
0
0
0
1
1
0
2
0
2
2
0
1
1
1
0
2
2
1
1
0
3
0
0
0
2
2
2
1
0
1
1
1
1
2
0
2
1
1
1
0
1
2
0
2
0
0
0
0
0
1
0
1
0
0
2
0
2
1
0
0
0
0
1
2
2
2
1
0
2
2
0
0
1
1
0
1
1
1
1
1
1
0
1
2
2
0
2
0
0
2
2
0
1
2
1
2
1
1
0
0
0
2
0
1
2
1
2
1
1
0
1
0
0
2
0
0
2
0
1
2
1
2
1
0
1
2
0
2
1
1
2
1
0
1
1
1
0
2
2
0
2
0
0
1
1
2
0
2
1
0
2
2
0
1
1
0
0
1
0
1
0
0
1
0
0
0
0
1
2
2
2
1
0
1
0
0
2
0
0
1
1
0
1
0
0
1
1
1
1
1
2
2
0
2
1
2
0
0
2
2
1
0
1
1
1
0
1
1
1
1
2
0
0
1
0
2
1
1
1
1
0
0
2
3
1
0
1
0
0
0
0
2
0
0
2
2
1
1
2
0
0
0
0
2
0
2
0
2
0
1
1
0
0
1
0
1
0
0
1
3
0
1
1
0
0
0
2
1
1
1
0
2
0
1
1
0
0
0
2
0
2
2
0
0
1
0
1
0
2
1
0
2
2
1
0
2
0
0
2
1
1
2
1
1
2
1
0
0
1
1
1
0
2
0
0
0
1
2
0
0
5
0
2
0
1
1
0
0
1
1
1
1
0
2
0
0
3
2
0
0
0
2
1
0
0
1
0
0
1
2
1
2
0
2
1
0
0
2
0
0
1
1
1
2
0
1
0
2
0
1
1
2
0
0
1
0
0
2
2
0
0
1
1
1
0
1
2
3
1
2
0
1
2
1
1
4
1
2
0
2
0
1
1
1
1
2
2
0
0
1
0
0
1
2
1
2
0
2
0
1
0
2
1
0
1
2
1
2
1
2
1
1
2
3
0
1
0
1
1
1
2
1
1
0
0
2
0
0
1
1
1
0
0
1
2
0
0
0
1
2
2
1
0
0
2
1
4
0
1
1
2
2
2
2
2
1
0
2
0
0
1
1
2
0
3
1
1
1
1
1
0
2
1
0
0
0
0
0
0
1
1
0
1
1
3
2
0
2
1
0
0
1
0
1
0
2
1
0
1
2
1
0
0
2
0
1
2
1
1
0
1
1
2
1
0
0
0
1
1
1
2
1
2
0
2
0
0
0
1
1
1
0
1
1
1
0
0
1
2
0
1
1
0
1
0
1
0
0
1
1
0
1
1
1
0
2
2
1
0
2
0
2
0
1
0
0
0
1
2
1
1
2
1
0
1
0
0
0
0
1
0
0
1
2
0
1
2
0
1
0
2
1
0
0
1
0
1
0
1
2
2
0
0
1
2
1
1
2
1
1
1
0
0
0
1
0
0
1
0
1
2
0
1
2
1
0
0
2
0
0
0
1
1
2
2
1
0
0
2
0
0
2
0
0
0
0
1
1
0
1
1
1
0
0
0
0
1
2
1
2
1
0
2
0
1
1
0
0
2
0
0
1
4
1
0
1
0
1
2
0
2
0
1
0
1
1
2
2
0
1
0
1
1
2
1
2
0
2
1
2
2
0
0
1
1
0
1
1
1
1
1
0
2
1
2
0
2
1
1
2
1
0
1
2
1
2
0
2
1
0
0
1
1
2
1
1
0
1
1
0
1
0
0
2
2
0
1
1
2
2
0
1
1
0
2
2
1
1
0
1
2
2
1
0
2
0
2
4
0
2
1
1
1
0
0
0
1
2
2
1
0
0
0
1
2
0
2
0
0
1
1
0
1
0
0
0
1
2
0
1
1
0
1
3
2
0
0
1
2
2
1
1
1
2
2
0
2
0
2
0
2
0
2
1
0
1
0
1
0
0
1
0
2
1
1
1
0
0
0
1
1
1
2
2
0
1
2
1
1
2
2
1
1
1
1
0
1
1
3
1
1
0
0
2
0
0
1
0
2
0
0
1
2
0
1
1
1
0
2
1
1
0
0
1
1
2
0
0
1
1
0
2
0
0
1
1
1
0
2
0
1
1
1
1
0
1
2
1
2
1
1
2
1
0
0
2
0
2
0
0
0
1
2
2
1
0
2
4
1
0
2
0
0
1
1
1
2
1
1
0
1
1
0
0
1
2
1
1
0
2
1
1
0
2
0
1
1
0
0
0
1
1
0
0
0
3
1
1
0
2
1
2
2
2
0
0
1
1
0
0
1
1
1
2
1
2
2
2
2
1
0
0
1
1
1
2
1
2
1
2
0
0
0
1
1
0
1
1
1
1
0
1
1
2
0
0
0
1
1
1
1
1
1
1
1
0
2
0
0
1
0
2
2
0
1
1
0
1
0
1
0
2
0
1
0
1
0
2
0
0
0
2
0
0
2
0
0
2
0
0
1
1
0
1
0
0
0
2
0
0
1
0
1
1
0
1
0
2
0
1
1
2
1
0
1
1
1
1
0
2
0
1
1
1
1
1
1
2
1
0
1
2
0
1
1
0
0
1
0
2
1
1
0
2
1
0
1
0
1
2
0
0
1
1
1
2
0
1
0
1
0
0
0
2
1
0
0
1
1
0
1
1
0
1
3
0
1
0
1
0
1
0
0
2
0
1
0
1
1
2
0
1
0
0
2
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
1
1
0
0
1
0
1
3
1
0
0
0
1
1
0
0
1
2
2
1
1
0
1
0
0
1
2
1
2
0
1
0
2
2
1
0
1
1
0
0
0
2
0
0
2
0
2
1
1
0
0
1
0
1
0
0
0
0
2
1
0
1
2
0
1
2
0
2
1
2
1
1
2
1
0
0
0
1
1
0
0
0
1
2
2
2
2
1
0
1
1
2
0
2
1
2
0
1
0
1
0
1
2
2
0
1
1
2
0
0
2
2
1
0
0
0
1
0
1
1
1
0
1
1
2
2
2
0
0
0
0
0
0
2
1
1
1
0
0
1
0
0
1
0
0
1
2
1
0
2
2
2
2
1
2
0
0
0
0
1
0
1
1
2
1
2
2
2
1
1
1
1
1
0
2
1
0
2
2
2
0
2
1
2
0
1
0
0
2
0
2
0
1
1
0
1
0
2
0
0
2
2
2
2
1
1
1
1
2
2
0
1
0
0
0
1
0
2
0
0
0
1
0
1
2
0
1
0
1
0
1
1
2
0
2
0
0
2
1
0
2
2
1
0
0
0
1
1
2
1
0
1
0
1
2
1
1
0
0
0
1
0
0
0
2
2
0
2
0
1
2
1
1
1
1
0
1
0
2
1
1
1
0
1
0
1
0
0
1
0
0
0
2
1
4
0
0
0
1
1
0
1
2
1
0
0
0
0
0
1
1
0
0
2
1
1
2
1
0
0
1
1
1
0
1
0
0
2
0
0
0
0
3
1
0
0
0
0
0
1
2
1
0
0
1
0
0
0
0
2
0
1
0
1
1
0
2
2
0
1
1
2
1
1
3
1
0
2
3
0
0
1
3
2
2
0
1
1
2
2
0
0
0
2
0
2
0
1
0
1
0
1
0
1
0
1
1
2
0
1
0
1
0
0
1
1
1
3
0
0
0
2
1
3
0
0
0
0
1
0
1
1
1
1
0
0
1
1
0
0
1
0
1
1
0
1
0
3
0
2
1
0
1
1
2
0
1
1
0
1
1
0
1
0
1
1
0
1
1
1
1
0
1
2
0
0
0
0
1
1
0
0
1
0
2
1
0
1
0
1
1
1
0
2
1
1
0
1
2
0
1
3
1
1
1
2
2
0
2
1
1
0
1
0
1
0
3
0
1
0
1
0
2
1
2
0
1
0
1
1
1
0
0
0
2
0
0
0
2
1
2
1
0
1
2
3
0
0
2
0
0
2
1
0
0
2
0
1
2
2
1
0
0
3
0
0
1
1
0
2
0
0
0
2
0
1
1
2
2
0
1
1
0
1
3
1
1
0
2
2
0
1
1
0
1
2
1
0
1
0
2
0
1
1
2
1
0
0
1
0
0
0
0
2
0
0
0
1
1
2
4
0
2
0
0
0
1
1
0
1
7
0
1
1
0
0
1
1
0
0
0
2
0
0
0
1
1
2
2
2
1
1
2
0
1
1
0
0
0
0
0
1
2
1
0
5
0
1
0
1
2
1
0
1
2
1
0
0
2
0
2
1
3
1
2
0
2
1
1
0
2
0
1
1
2
0
0
2
1
0
1
1
1
0
0
0
2
1
0
0
1
0
1
1
2
2
1
2
0
2
1
2
2
1
0
1
0
2
0
1
1
0
1
0
2
0
2
0
0
2
0
2
0
1
1
1
1
1
0
0
1
1
2
0
2
1
1
1
2
1
0
0
1
2
1
0
2
2
0
2
1
2
1
0
0
1
1
2
0
1
1
1
0
2
1
1
0
0
0
0
0
0
2
0
2
0
0
1
2
1
2
0
0
2
2
0
2
1
0
1
1
0
1
0
0
0
0
1
0
1
0
2
0
0
1
0
1
0
0
1
5
1
0
0
0
0
0
0
0
2
4
1
0
1
0
0
0
1
2
1
0
0
1
1
1
1
1
1
0
0
1
0
1
2
0
0
1
0
1
1
3
0
1
2
0
0
0
0
2
0
0
2
1
3
2
2
0
4
1
0
1
0
1
1
0
1
0
1
0
0
0
1
1
0
2
2
0
2
1
1
0
1
0
0
0
1
1
0
1
0
0
1
0
0
1
0
2
3
1
2
0
0
0
0
1
0
0
1
1
1
2
0
0
1
0
1
1
2
0
1
0
1
1
2
0
1
0
1
1
2
1
1
4
0
0
0
2
1
0
0
1
1
0
1
1
1
2
2
1
0
0
0
1
1
1
2
0
1
0
1
1
1
1
1
2
1
1
1
1
1
2
1
0
1
0
1
1
1
0
1
0
2
3
1
2
0
2
3
2
1
2
1
0
0
0
1
1
0
1
1
1
2
1
1
0
0
1
2
1
1
0
1
2
1
0
0
0
0
0
0
1
0
2
2
2
2
1
1
0
2
0
1
1
0
0
1
2
0
1
1
0
1
0
2
0
0
1
0
1
0
1
0
2
1
0
0
0
1
0
1
1
1
1
2
0
0
2
0
1
0
0
3
1
1
0
1
1
1
0
1
1
0
2
1
1
2
1
1
1
1
0
2
0
2
1
2
2
1
0
2
0
2
1
2
2
1
1
0
1
1
1
2
0
0
0
2
0
2
0
2
0
0
1
0
1
1
2
1
0
0
2
2
0
2
0
2
0
0
0
2
1
0
1
0
0
2
2
0
3
1
0
0
1
2
0
1
1
2
2
2
1
2
0
0
1
2
1
0
0
1
1
0
0
0
7
0
1
1
0
0
1
1
1
2
1
2
0
0
2
0
1
0
0
1
2
0
2
1
1
1
1
0
1
2
0
1
2
0
0
0
0
1
2
1
0
2
1
1
1
2
0
0
1
1
0
0
0
2
2
2
2
2
1
1
0
1
0
1
1
0
0
1
0
0
1
0
2
1
0
0
1
1
2
0
1
1
2
1
2
1
0
0
2
0
0
1
1
2
0
0
0
1
1
0
1
0
0
1
0
2
0
1
1
0
0
0
2
1
2
3
0
2
2
1
0
2
2
2
1
2
0
2
1
0
1
2
2
2
0
0
1
1
1
1
1
0
1
1
0
1
0
1
1
0
1
0
2
0
0
2
1
0
2
1
1
0
2
1
0
2
0
1
0
2
0
1
1
2
2
1
1
2
2
0
0
1
2
0
1
3
1
2
1
1
0
0
2
0
1
1
1
2
2
1
1
1
1
0
1
1
1
1
0
2
2
1
2
0
1
0
0
1
1
1
1
0
1
1
1
1
1
1
0
0
0
1
2
2
1
1
0
0
0
1
1
1
1
1
0
1
3
1
0
0
2
2
1
1
1
0
2
1
2
0
1
1
1
1
0
0
0
1
0
2
1
0
0
1
0
2
1
2
0
2
1
0
2
0
1
1
1
2
0
1
0
0
2
1
0
1
0
1
2
2
0
2
1
0
1
0
1
2
2
0
1
1
0
0
0
0
1
1
0
0
1
2
1
0
0
0
0
1
0
1
2
1
1
0
1
2
1
1
0
1
0
0
2
0
1
0
0
2
0
1
1
0
0
0
2
1
0
1
2
0
1
1
1
0
1
2
1
2
1
2
2
0
0
1
1
0
0
1
1
2
0
1
0
0
2
1
0
0
0
0
1
0
1
0
1
2
0
1
0
0
1
2
0
0
2
1
1
1
0
0
2
1
1
2
0
1
0
2
1
0
1
0
3
1
1
1
0
0
0
0
2
0
0
0
1
1
1
0
2
2
0
2
1
0
0
2
0
1
0
0
2
1
0
2
0
1
1
1
2
0
1
2
2
0
1
1
1
0
0
2
1
0
0
2
2
0
1
1
1
0
1
1
1
2
3
1
1
1
1
1
0
1
1
0
2
1
1
3
3
0
0
0
1
2
1
2
0
0
0
0
0
1
0
1
0
2
0
1
3
2
1
2
1
0
0
1
0
2
1
0
0
0
2
1
0
1
2
1
1
0
2
0
0
1
1
0
1
1
2
1
0
0
2
0
0
1
2
1
0
1
2
0
1
0
0
2
1
2
0
1
1
0
0
1
0
0
0
1
1
1
0
1
2
1
0
0
0
0
0
1
2
1
1
0
2
0
0
1
1
0
2
1
1
1
0
2
0
2
1
0
1
1
0
0
3
0
1
1
1
1
0
0
0
1
1
1
2
1
0
0
1
1
0
0
1
0
2
2
0
0
4
1
2
1
2
0
0
1
1
1
1
1
1
2
0
0
1
0
2
1
2
0
2
2
0
0
1
0
1
1
1
2
1
2
0
1
1
2
2
1
1
0
1
1
1
0
1
0
0
1
0
0
0
1
1
1
2
1
0
0
1
0
2
1
1
0
0
2
1
1
0
0
2
1
1
1
2
0
2
0
0
0
2
1
2
0
0
1
1
0
0
1
1
1
2
1
0
0
0
0
2
0
1
0
1
0
2
0
1
1
0
0
0
0
0
2
0
0
1
1
2
0
1
1
2
0
3
1
0
0
1
1
0
0
1
1
1
0
1
1
1
0
2
0
2
1
0
0
0
1
1
2
2
0
1
0
2
2
1
1
0
1
2
2
1
1
4
2
0
0
0
0
0
0
0
1
0
1
2
2
0
1
0
1
2
1
1
0
2
1
1
0
1
1
1
2
0
1
2
0
2
1
0
1
1
1
0
1
0
2
1
1
1
1
0
0
2
1
0
2
0
0
2
1
1
0
0
0
0
0
0
0
1
1
2
0
2
1
0
0
1
2
1
0
1
1
1
1
0
1
1
1
1
0
1
0
0
2
0
1
1
0
1
0
2
1
0
1
0
1
1
1
1
1
0
2
0
1
1
1
0
2
1
2
1
0
1
2
1
0
0
1
2
0
0
2
2
0
2
1
2
1
0
0
0
1
2
0
0
1
1
0
2
2
0
2
0
0
0
0
1
2
0
1
1
1
1
1
0
0
1
0
1
1
0
0
0
0
0
1
2
1
2
2
1
2
2
1
2
0
1
2
1
0
1
0
0
2
0
0
1
1
1
1
1
2
2
0
1
1
2
1
2
2
1
1
0
0
0
0
1
1
1
0
1
1
0
0
2
2
0
2
0
1
2
1
0
1
1
1
1
1
0
0
0
0
1
0
2
2
0
1
1
1
1
2
0
2
1
2
1
1
1
1
1
1
2
2
1
2
1
2
1
1
0
1
0
2
1
2
0
0
0
1
2
1
0
2
0
1
1
0
1
1
1
0
0
1
1
1
1
1
0
0
0
0
1
1
1
2
2
0
0
1
0
0
0
0
2
0
2
1
1
0
1
2
1
0
1
1
1
2
0
1
1
1
1
1
2
1
1
1
2
2
1
1
1
0
0
3
2
0
1
0
0
1
1
1
2
2
1
1
3
1
2
0
0
1
1
0
0
0
0
0
0
1
0
0
2
0
1
1
2
0
1
0
1
0
1
0
0
0
1
0
1
1
1
1
1
1
1
2
4
2
0
0
1
1
0
2
2
0
1
1
1
0
2
1
1
0
1
1
1
1
1
1
2
1
0
0
2
2
0
0
0
0
2
0
2
1
0
1
1
1
0
0
1
0
0
1
1
4
2
1
0
1
1
2
0
2
1
0
0
2
0
1
1
0
0
0
0
0
1
1
1
0
0
1
1
1
2
0
0
0
0
2
0
1
0
1
2
1
0
2
0
1
2
0
0
2
2
0
2
0
0
1
0
1
0
2
1
0
1
1
1
0
0
1
2
1
2
0
0
0
1
1
1
0
0
0
1
0
2
0
2
1
0
1
2
0
1
0
0
1
1
0
2
1
0
1
1
1
0
2
0
1
1
2
0
1
4
1
0
1
0
1
1
0
2
0
0
2
0
2
1
0
2
1
1
1
0
0
0
1
1
0
1
1
0
0
1
1
2
1
2
0
1
2
0
1
0
0
1
2
1
0
1
1
0
0
0
1
0
1
0
0
1
0
4
2
3
2
1
2
1
1
1
0
1
0
1
1
1
1
0
0
1
1
1
1
0
1
1
0
2
0
2
2
0
1
1
1
2
1
0
0
0
1
0
2
1
0
1
0
1
0
1
0
2
1
0
1
0
0
0
1
1
1
1
2
2
2
2
2
1
2
3
0
0
1
0
1
1
0
1
1
1
0
2
0
0
0
1
0
1
0
1
1
0
1
0
1
1
2
0
0
0
1
0
0
0
0
1
1
2
1
1
1
1
1
1
2
2
0
1
0
1
1
2
1
0
1
2
1
0
2
0
2
2
0
2
0
0
1
2
0
0
1
0
1
0
3
0
0
1
1
1
2
1
0
1
2
0
2
0
1
3
1
0
0
1
0
2
1
2
2
1
0
2
0
0
1
1
1
2
1
1
2
1
1
1
0
0
2
2
1
0
1
1
0
0
0
2
0
0
0
2
0
1
1
0
2
0
1
0
0
0
2
1
1
1
1
0
2
0
1
0
1
1
2
0
0
2
2
0
2
1
0
2
0
2
0
0
0
2
1
1
1
1
0
2
1
1
0
1
1
1
0
2
0
1
1
0
1
1
1
1
1
1
0
0
1
1
1
0
1
1
1
0
0
1
0
2
3
1
1
2
3
2
1
1
0
1
0
2
1
1
1
1
1
1
1
2
1
2
0
1
2
0
1
0
0
1
2
1
2
0
0
0
0
0
3
2
2
1
0
1
1
1
1
0
1
0
0
1
2
0
0
2
1
1
1
2
2
2
1
0
1
0
1
0
1
1
0
1
1
0
2
0
2
1
2
0
1
1
1
0
0
1
1
0
2
2
0
1
0
0
3
2
0
1
2
0
1
0
2
0
3
0
0
1
0
2
1
1
1
1
2
2
2
1
2
0
0
1
1
0
1
2
1
1
0
2
0
0
5
1
0
1
0
1
1
1
0
0
1
0
0
1
0
2
1
0
1
0
0
0
0
0
2
1
1
2
0
2
0
2
0
2
1
0
0
1
1
1
3
0
2
1
1
1
1
3
0
0
0
1
2
0
0
0
1
2
0
2
1
1
2
0
1
1
1
0
1
1
1
0
0
1
2
2
0
1
2
2
2
1
1
0
1
0
1
0
2
1
2
0
0
2
1
0
0
1
2
1
1
1
0
1
1
1
0
1
0
2
0
0
0
1
1
0
0
1
0
0
0
1
0
1
1
2
1
0
0
0
2
0
1
1
0
0
2
0
0
1
1
0
1
0
1
1
0
0
2
0
1
2
1
0
2
2
0
0
2
0
1
1
2
2
0
0
2
2
1
0
2
0
0
0
0
0
1
1
1
0
1
1
1
1
0
1
0
0
1
0
0
0
1
1
0
1
0
2
0
1
1
2
0
1
1
2
1
2
0
1
1
1
0
0
0
2
2
1
0
0
0
1
1
2
2
0
1
3
1
1
2
0
1
0
1
0
0
2
2
1
1
2
2
2
1
0
0
1
0
1
1
1
0
1
1
0
0
2
0
2
0
0
1
1
1
0
1
1
1
1
1
2
1
0
1
1
1
0
0
0
0
0
1
2
2
1
2
0
3
2
1
1
0
0
0
2
0
1
2
0
0
2
1
1
1
1
1
1
1
0
0
1
1
1
0
2
1
0
1
1
1
1
0
0
0
0
1
1
2
2
0
1
2
2
1
1
1
2
1
0
1
0
1
0
0
0
1
1
2
2
0
0
0
1
2
1
1
0
1
1
1
0
0
0
2
2
0
0
0
1
2
1
1
1
1
0
1
0
0
0
0
1
1
0
2
2
0
0
0
1
1
0
0
0
1
2
2
0
1
2
2
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
2
2
0
1
1
1
1
1
1
1
0
1
1
0
0
1
1
2
1
0
0
2
0
2
2
0
1
0
0
0
0
1
0
1
0
1
0
1
0
3
2
1
1
0
1
2
5
0
0
1
0
1
2
0
1
1
0
0
0
1
1
2
2
0
0
0
1
0
0
1
1
1
1
2
1
0
0
1
0
0
1
1
0
2
0
0
0
1
0
0
0
0
1
1
2
0
1
0
1
2
1
0
1
1
0
1
0
0
2
1
1
1
0
0
2
0
1
0
3
1
2
0
1
0
0
0
1
1
0
0
0
1
1
0
2
0
0
0
2
1
2
0
1
1
1
1
0
2
1
0
1
1
0
1
0
0
1
0
0
0
1
1
1
0
2
2
0
0
1
1
1
1
1
0
0
1
0
1
3
3
2
0
2
0
1
2
2
1
0
2
0
1
2
2
0
1
1
2
1
0
2
1
0
2
0
0
1
1
1
1
0
0
2
1
0
1
0
0
2
2
2
0
1
2
2
2
2
0
1
1
0
2
0
1
1
1
2
1
0
1
1
2
1
1
0
2
2
1
2
2
0
1
2
0
0
1
2
2
3
1
1
2
2
1
1
1
1
0
0
1
0
1
2
0
1
1
1
0
3
0
1
2
0
0
0
2
0
0
1
2
2
0
1
1
2
1
1
0
0
2
1
2
0
1
0
0
1
1
0
2
0
2
0
1
0
0
1
1
0
1
2
0
1
1
0
1
0
2
0
1
1
2
1
1
0
0
0
1
0
0
1
1
1
2
0
0
0
1
0
1
1
2
1
2
0
2
1
0
0
1
1
0
0
1
1
1
0
0
2
1
1
2
0
4
1
2
1
0
0
2
1
0
1
0
1
0
0
2
2
0
1
1
0
1
1
0
1
1
2
0
1
1
0
2
1
1
0
1
0
1
2
1
1
1
2
1
2
1
0
0
1
0
0
0
1
0
1
0
1
0
0
1
1
2
0
2
1
0
1
1
1
1
1
1
1
2
6
1
1
0
0
2
0
0
0
1
1
0
1
1
0
0
2
1
1
0
1
2
0
1
0
2
2
0
2
1
0
0
1
3
1
1
0
1
1
0
0
0
1
1
2
0
0
0
1
0
1
1
2
2
1
2
0
1
2
1
0
1
2
0
0
0
1
1
2
0
1
0
1
1
0
0
1
1
2
1
0
0
1
0
0
1
0
0
0
0
1
0
0
1
1
0
1
0
0
2
1
0
0
0
1
1
2
1
1
2
0
2
0
1
0
0
0
2
0
0
1
2
0
1
3
0
1
2
1
1
0
0
2
1
0
0
0
1
0
0
0
1
2
1
1
2
2
0
0
1
2
1
0
2
0
0
0
2
2
1
0
1
1
0
0
1
1
0
0
1
0
1
1
2
1
1
0
2
1
5
1
0
1
2
2
0
0
0
1
0
0
0
1
1
1
0
0
0
1
0
0
2
2
0
0
0
0
1
2
0
2
1
2
0
0
0
1
0
0
2
0
0
4
2
2
0
0
0
2
0
0
1
0
0
1
3
0
0
0
0
2
0
1
2
0
1
2
2
2
1
0
0
2
1
0
0
0
1
0
0
1
0
0
0
1
2
2
1
1
0
0
0
2
2
0
0
0
1
1
1
2
1
1
0
3
0
2
1
0
2
1
0
0
2
1
2
0
2
1
1
1
0
1
1
2
2
1
2
0
1
2
0
0
0
0
0
2
1
2
2
0
0
1
0
1
1
0
1
1
0
2
0
1
0
1
0
2
2
0
0
0
0
1
1
1
2
1
2
2
2
1
2
0
2
1
0
0
0
0
0
0
0
1
1
0
0
0
2
2
0
0
0
2
1
1
0
0
0
2
1
2
0
2
0
1
1
2
2
2
1
1
0
0
0
0
0
0
1
3
0
1
0
0
0
0
1
1
0
1
3
2
2
1
1
2
0
1
1
1
0
1
2
0
0
0
0
0
1
2
1
1
0
1
0
1
1
1
0
1
0
1
0
2
1
1
0
2
1
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
2
0
0
2
0
0
3
2
1
1
0
0
0
1
1
2
1
1
0
1
1
0
1
0
0
2
1
1
1
0
0
1
2
0
1
3
2
1
1
1
1
2
1
1
2
0
1
0
0
0
2
1
1
0
1
1
0
2
0
1
1
1
1
0
1
0
0
0
0
2
1
1
2
0
1
0
1
0
1
0
0
0
1
0
0
1
2
1
1
1
1
1
1
0
0
0
1
1
0
1
0
0
2
1
1
1
0
0
0
0
0
0
1
1
2
1
1
0
1
0
2
1
2
2
2
1
2
0
2
2
0
1
0
0
1
0
2
1
0
0
1
0
0
2
1
0
0
0
1
1
0
1
0
0
2
2
1
0
2
2
2
1
1
1
1
0
1
0
0
1
0
1
1
1
0
2
1
1
0
2
3
1
2
1
1
0
0
0
2
1
1
0
1
2
2
0
0
0
0
2
1
1
0
1
1
0
2
1
1
1
2
0
1
1
0
2
2
0
1
0
1
1
1
2
2
0
1
1
0
2
0
1
1
0
1
1
1
1
0
2
0
1
0
2
0
2
1
1
1
2
0
2
1
0
2
0
0
1
0
0
0
2
0
1
0
1
1
3
1
1
1
0
0
0
2
1
2
1
0
1
0
2
1
1
1
2
0
1
2
1
2
0
3
0
0
2
0
1
1
1
1
2
0
0
1
1
2
2
1
1
2
0
1
0
0
2
0
1
0
2
0
0
1
0
0
1
1
0
1
0
0
1
0
1
0
1
1
0
2
1
0
1
0
1
0
2
2
0
0
0
2
1
2
0
2
1
0
2
1
0
0
0
1
2
2
0
0
0
2
1
3
1
0
1
1
0
2
1
1
2
0
0
0
1
1
0
1
0
0
0
1
1
0
0
0
1
1
1
2
0
2
0
0
1
0
2
1
0
1
0
2
2
0
2
2
0
0
1
0
2
0
0
0
1
0
1
1
1
1
1
0
2
0
1
0
2
1
1
1
1
1
0
2
0
1
0
2
3
0
1
0
2
1
1
1
1
0
2
2
1
1
0
1
0
1
2
1
2
0
1
2
1
2
0
1
1
0
1
0
0
1
1
0
1
2
1
6
0
1
1
0
0
0
0
1
0
1
2
0
0
0
0
2
0
2
3
1
1
3
1
1
0
2
2
2
1
0
1
0
0
2
0
1
0
1
1
2
0
1
2
1
0
1
1
4
2
1
1
0
1
2
0
1
0
2
1
2
1
1
1
0
3
0
0
0
2
2
1
0
1
0
1
1
0
2
1
0
2
0
1
0
0
1
2
0
1
2
2
0
1
0
1
1
0
1
1
2
6
1
1
1
0
0
1
1
2
2
1
2
1
1
1
0
1
0
1
2
0
1
1
1
0
2
2
1
0
0
1
0
3
2
1
1
2
0
1
2
0
1
1
2
0
0
2
1
1
3
2
2
0
1
2
1
2
2
2
1
2
0
1
1
1
1
1
1
2
2
1
1
0
0
0
1
0
0
0
0
1
0
1
0
2
1
2
0
1
1
0
0
0
1
0
0
1
2
1
1
1
2
1
1
0
0
2
0
1
0
2
0
1
1
1
1
0
1
0
1
1
1
0
1
1
0
0
0
1
1
2
2
1
2
1
3
1
1
2
0
2
2
1
0
3
0
1
1
1
0
1
1
2
1
2
1
0
1
1
0
1
2
1
1
0
0
0
1
0
0
1
0
1
0
1
1
2
2
1
0
2
2
2
1
2
1
0
1
2
0
0
1
0
1
2
0
0
2
2
0
3
1
0
2
0
1
0
0
0
0
1
0
0
2
0
0
0
1
1
1
1
0
0
1
1
0
0
1
0
1
2
0
0
1
0
2
0
0
1
0
1
0
2
1
1
0
2
1
1
0
0
0
1
0
0
1
2
0
0
0
0
1
2
2
2
0
0
1
2
1
0
0
1
0
2
0
0
1
3
1
0
1
0
2
0
0
1
2
0
0
1
1
0
1
1
0
1
1
1
1
1
0
0
1
0
0
1
0
1
1
1
1
2
1
1
0
0
1
0
1
2
1
0
2
2
2
1
2
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
2
1
1
2
2
1
1
0
1
0
1
2
1
1
2
0
2
0
0
0
2
0
1
1
0
0
1
0
1
1
0
0
1
0
0
0
0
1
0
1
1
0
0
1
0
1
1
1
0
1
1
0
1
0
2
0
2
0
2
0
0
1
0
0
0
1
1
0
0
1
0
1
1
1
2
2
2
0
1
1
1
1
0
0
0
1
0
1
1
2
2
0
1
0
2
0
2
3
0
1
2
2
3
1
0
2
1
1
2
0
0
0
1
0
2
1
0
0
1
2
2
1
0
2
0
1
2
1
0
0
2
0
0
2
2
1
2
1
2
1
2
0
1
1
2
1
1
3
1
1
1
1
3
1
0
0
0
0
1
1
1
1
1
0
1
0
2
0
0
2
0
2
2
2
0
0
1
4
0
0
0
0
0
2
1
0
1
2
1
0
0
2
0
0
1
1
0
1
2
2
0
1
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
2
0
2
0
2
0
0
0
2
2
2
0
2
1
2
1
1
0
0
0
2
0
1
0
2
2
0
1
1
2
1
0
1
0
2
1
2
1
2
2
0
1
0
0
0
0
0
1
1
1
1
1
0
1
0
0
0
0
1
1
1
0
1
0
0
0
2
1
0
2
2
2
1
1
1
1
1
2
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
1
2
0
0
2
1
2
1
1
1
5
1
2
1
1
0
2
0
2
0
0
0
1
2
2
1
0
0
2
0
2
1
0
2
0
1
0
2
0
0
0
1
1
1
2
1
0
1
0
1
2
1
0
1
0
2
2
0
1
1
0
0
0
2
0
0
0
1
1
0
0
1
1
0
0
0
1
1
2
0
1
0
2
1
2
2
0
2
0
1
0
2
2
0
2
0
1
1
0
1
1
1
1
1
1
1
1
0
0
0
1
1
1
1
2
1
1
0
0
1
2
0
0
0
1
1
1
0
2
1
0
2
1
0
0
0
1
0
0
1
2
1
0
2
0
2
0
0
1
1
6
1
2
1
1
0
1
1
2
0
1
0
1
0
2
0
1
1
1
2
0
3
0
0
2
0
1
1
2
1
0
0
2
0
2
0
1
0
2
1
1
0
1
1
0
0
0
1
1
0
0
1
3
0
0
0
1
0
2
1
2
0
0
1
0
1
2
2
1
2
2
0
1
3
0
1
0
2
3
1
1
0
0
1
0
0
1
1
1
3
0
1
0
1
1
0
0
1
0
2
2
0
1
0
2
2
1
2
1
0
1
0
0
2
0
2
2
1
1
0
0
0
2
2
0
2
0
2
0
0
2
1
1
0
2
0
0
1
1
0
1
0
1
1
2
1
0
1
1
0
1
1
0
0
0
1
0
1
1
2
1
1
0
2
2
1
0
1
0
0
1
1
1
0
2
0
0
1
1
2
1
1
0
1
0
2
0
1
1
1
2
1
0
1
1
2
2
2
0
0
0
0
1
6
1
0
1
1
0
1
2
1
0
3
1
0
0
2
2
1
2
1
1
0
1
0
2
1
0
1
0
0
1
0
0
2
1
1
1
1
2
3
0
0
0
0
1
1
0
2
2
0
0
0
0
1
0
1
1
0
1
1
2
2
1
0
2
1
0
1
1
0
2
2
1
2
0
2
1
2
1
0
2
1
1
1
0
2
0
1
0
1
2
0
0
1
2
0
1
0
0
1
0
2
0
1
0
0
0
1
1
0
1
4
1
2
0
2
0
1
2
1
1
2
1
0
1
1
0
0
2
0
0
3
0
2
1
0
1
1
0
0
0
0
0
0
2
1
1
0
2
0
1
0
2
0
0
0
0
0
2
2
1
0
0
2
0
2
0
1
0
0
2
0
1
0
1
1
0
0
1
1
0
1
0
0
0
1
0
1
1
0
1
1
1
2
0
2
0
1
0
1
2
2
1
0
2
0
1
0
1
1
1
0
1
0
0
0
0
2
1
1
0
1
1
1
1
1
1
2
1
1
2
1
1
1
0
0
1
0
1
0
0
0
0
0
1
0
0
2
1
1
1
1
0
0
1
1
1
1
1
0
0
1
0
1
1
0
1
1
1
1
1
1
1
1
1
1
0
0
2
2
1
2
1
0
0
1
0
0
1
2
1
0
1
1
0
1
1
0
2
1
1
2
1
1
0
1
1
0
1
1
2
1
2
2
1
2
0
1
0
1
1
1
1
2
1
1
0
1
1
2
1
1
1
2
2
0
1
0
1
1
3
1
2
0
2
2
1
0
2
1
0
5
2
2
0
1
1
1
1
0
1
0
0
0
3
0
0
0
1
1
1
0
2
1
1
0
2
0
0
2
2
0
0
0
2
2
1
1
0
2
0
1
0
1
2
2
1
0
2
0
1
1
1
2
1
2
2
1
1
2
0
2
1
2
2
1
2
0
0
1
1
0
0
0
1
2
1
1
0
2
0
2
1
0
1
0
1
0
0
1
1
1
0
2
0
1
1
2
0
2
1
1
1
1
1
0
1
2
2
0
0
0
0
0
1
2
0
0
0
1
2
2
2
0
2
2
0
1
2
2
0
1
2
2
0
0
0
1
1
1
0
0
0
1
1
0
1
1
1
2
0
1
2
1
2
0
2
2
1
1
0
2
1
0
1
2
1
2
3
1
0
0
0
1
2
1
1
1
1
1
1
0
1
0
1
2
1
2
1
1
1
0
1
0
2
2
2
2
1
0
0
2
1
1
0
0
0
1
0
0
1
0
2
0
1
2
1
2
0
1
0
1
0
1
1
0
2
0
1
0
1
1
1
1
1
0
1
1
0
0
0
1
0
0
0
2
1
1
0
0
1
0
2
0
0
0
2
1
1
0
1
1
0
0
1
1
1
1
0
0
1
2
1
1
2
0
1
1
1
3
1
1
2
0
0
0
1
1
0
0
1
2
2
0
0
1
1
1
0
1
2
1
1
0
2
1
2
2
1
0
0
0
1
1
4
1
2
0
1
1
0
2
0
0
1
1
1
2
1
2
1
1
2
1
2
1
2
0
0
1
2
1
2
1
0
1
1
1
0
1
2
2
0
0
0
0
2
0
0
0
0
1
2
0
1
0
0
2
0
1
0
0
3
0
0
0
2
0
0
2
0
1
0
1
0
0
0
2
1
0
1
1
1
0
2
2
1
1
0
1
1
2
0
0
0
1
0
0
1
1
1
2
0
2
1
2
3
1
1
2
2
1
0
0
3
2
1
2
0
1
0
2
2
0
0
0
2
1
2
2
1
2
0
1
0
1
0
0
1
2
0
1
2
2
0
3
0
1
0
2
0
1
0
1
0
5
2
1
0
2
1
0
0
1
2
0
1
1
1
1
1
2
0
1
0
2
1
0
0
0
0
1
0
3
1
1
3
0
1
0
2
0
1
0
0
1
0
2
1
2
2
0
2
2
3
1
0
1
0
0
2
1
1
0
1
2
0
1
1
2
0
0
0
0
1
1
2
2
1
2
1
2
0
0
1
0
1
1
2
2
0
1
1
1
0
0
1
1
0
1
0
0
1
1
0
1
0
1
1
2
1
1
1
0
1
0
0
0
2
0
2
1
1
0
0
1
0
1
1
1
0
2
2
1
0
1
1
2
0
2
1
0
1
0
1
1
1
1
0
0
0
0
2
2
0
0
1
2
1
0
2
2
1
0
2
2
1
1
0
1
1
0
1
0
0
2
2
1
1
0
2
1
2
2
0
1
1
1
0
1
2
0
1
2
2
0
2
0
1
1
0
1
1
1
1
2
1
2
2
3
0
1
2
1
2
0
0
0
2
1
2
2
1
1
2
2
1
1
1
1
1
0
1
1
1
0
0
0
0
1
0
0
0
2
1
2
1
0
1
0
1
1
0
0
0
1
2
0
1
1
0
0
0
0
2
0
2
0
2
0
0
0
0
1
2
1
1
1
0
0
0
2
0
1
2
0
2
1
1
0
0
1
2
0
1
1
1
0
0
1
2
1
1
2
2
2
0
1
1
2
1
2
1
0
2
2
0
1
0
1
0
1
0
2
0
2
0
1
1
0
1
1
1
2
0
0
1
1
2
1
1
1
0
0
0
3
0
1
1
0
2
0
0
1
0
2
1
2
0
0
1
0
1
2
0
1
1
0
0
0
1
1
1
0
2
2
1
2
0
0
0
0
0
1
2
2
2
2
1
2
0
0
0
0
1
0
1
1
1
1
0
1
0
1
0
2
1
0
0
1
0
1
0
0
2
0
0
1
1
1
0
0
2
0
0
2
1
0
1
1
1
1
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
2
0
1
0
0
0
1
2
2
1
1
1
0
1
0
0
1
0
0
1
1
0
1
0
2
2
2
0
0
0
0
1
1
0
1
2
1
0
0
0
1
2
0
0
1
1
0
1
1
1
1
0
0
1
1
0
0
1
1
0
1
0
1
0
2
2
0
1
2
2
0
0
1
0
0
1
1
0
1
2
1
1
1
1
0
0
1
2
1
0
0
0
2
1
1
0
0
1
0
1
0
0
1
0
1
0
2
2
1
1
2
0
0
2
1
1
1
1
0
1
2
2
0
2
0
0
0
1
0
1
0
0
1
0
0
0
0
1
1
0
0
1
2
0
1
1
0
0
1
2
0
2
2
1
2
1
0
2
1
1
2
1
0
2
1
0
2
0
1
1
2
1
1
1
0
2
2
1
0
1
1
0
4
1
1
1
0
2
2
1
0
1
0
0
0
0
2
1
1
2
2
1
1
1
0
1
2
2
0
1
0
0
0
0
1
0
1
1
1
0
1
2
0
2
0
1
0
1
0
1
0
0
0
0
0
0
1
0
2
0
0
0
1
0
2
1
0
3
0
2
1
1
1
1
2
1
2
0
1
3
1
2
2
1
2
1
2
1
0
0
4
1
0
0
2
0
1
1
1
1
0
0
0
2
0
2
1
1
0
0
1
1
1
1
1
0
1
0
2
1
0
2
0
0
1
2
1
1
2
2
1
1
1
1
0
1
0
0
1
1
1
0
0
0
1
0
1
2
0
1
1
1
2
1
2
1
2
0
2
1
2
0
1
1
0
1
0
2
0
2
1
0
2
1
1
0
0
1
0
2
1
0
2
1
0
2
0
1
1
0
1
2
0
1
0
0
1
0
2
2
0
0
1
0
1
1
0
1
0
1
2
1
1
0
0
2
1
0
1
0
1
1
1
1
3
0
2
1
0
2
1
0
0
0
0
0
0
0
2
0
0
1
1
1
1
2
1
1
2
0
1
2
1
1
1
1
2
1
1
1
0
0
2
2
0
2
0
1
0
0
1
1
3
1
2
1
0
0
1
1
0
1
0
0
0
1
1
2
2
0
1
0
2
2
2
0
2
0
2
2
1
1
0
1
1
3
1
2
1
1
2
2
0
1
2
1
1
0
0
0
0
1
1
2
1
1
0
1
1
1
1
1
2
0
2
1
0
0
1
0
1
0
2
2
0
1
1
2
0
2
0
1
0
2
0
2
2
1
2
1
1
1
0
0
1
1
1
1
1
1
2
0
0
0
1
1
1
0
1
0
0
2
0
0
1
0
1
2
0
2
0
2
0
1
1
0
0
0
1
1
1
2
0
2
1
1
2
0
1
1
2
1
0
1
0
0
1
0
1
1
0
7
1
0
0
0
1
1
1
2
1
1
0
2
2
0
1
2
0
0
1
2
2
1
1
1
0
0
0
2
1
1
2
1
2
1
1
2
0
1
1
1
1
1
0
0
1
0
0
1
1
0
2
0
2
1
0
1
0
0
2
0
1
1
1
1
2
1
0
1
0
1
1
1
1
1
0
0
1
0
0
0
2
0
2
2
1
0
1
0
2
0
0
2
2
1
0
2
0
1
1
0
0
1
1
0
0
2
1
1
1
0
0
1
1
1
0
0
1
1
2
0
1
2
0
1
0
0
2
0
1
2
1
1
1
1
0
0
2
1
0
0
1
1
2
1
1
0
0
0
0
1
1
1
1
1
1
1
1
2
1
1
0
0
1
2
1
2
0
1
1
1
1
2
3
1
1
3
1
1
2
1
0
2
1
0
0
1
2
0
2
2
2
1
4
0
2
1
2
2
1
0
2
0
1
2
0
2
0
0
1
4
2
3
0
0
0
0
0
0
0
1
0
0
0
0
2
1
1
1
0
1
0
1
0
0
2
1
2
1
2
0
2
0
0
1
1
0
1
3
1
1
1
1
0
0
2
0
0
0
0
0
1
1
1
5
2
0
2
1
2
3
2
0
0
0
1
0
3
1
0
1
0
1
1
1
0
1
1
1
1
2
1
1
1
0
1
2
1
0
1
0
2
0
0
2
1
1
2
0
0
1
1
0
2
0
2
2
1
2
0
2
0
1
2
0
1
1
2
2
0
1
1
1
0
2
1
0
0
2
2
0
2
0
2
0
0
1
2
2
1
0
0
1
1
0
0
3
1
1
0
0
0
0
0
0
2
1
0
1
0
1
1
0
0
1
1
1
1
1
1
1
1
0
2
1
1
1
1
1
1
1
0
2
2
1
0
1
1
1
1
0
1
0
0
1
0
2
1
2
1
1
1
1
1
1
1
0
0
0
0
1
0
0
1
0
0
0
2
0
1
1
1
1
1
1
2
0
1
1
1
1
1
2
0
1
0
1
0
0
0
2
0
1
0
0
0
2
2
2
1
1
1
1
0
1
1
0
0
1
1
1
1
2
2
1
1
2
0
2
1
0
0
2
0
1
1
0
1
0
1
0
0
2
2
0
0
1
1
0
2
1
0
0
2
1
2
0
0
2
2
1
0
2
1
2
0
0
2
1
1
1
2
1
1
1
1
1
1
1
2
1
0
1
0
0
0
0
1
1
1
1
1
1
2
2
0
0
0
1
0
1
0
0
2
0
1
2
0
1
0
0
1
1
1
1
1
2
1
2
1
1
0
0
2
0
1
2
0
1
2
1
1
1
0
2
1
1
2
2
1
0
1
0
0
0
1
2
0
1
1
1
1
2
2
1
2
2
0
0
1
2
0
1
1
1
0
1
1
2
2
0
0
0
2
1
0
0
1
0
2
0
0
2
0
1
1
2
0
2
0
0
1
0
0
1
0
0
2
0
0
2
1
1
2
3
1
1
0
1
1
0
2
2
2
2
0
0
0
0
2
2
1
1
2
1
0
0
1
0
1
1
2
1
1
0
1
1
0
0
2
3
2
1
1
1
1
0
1
0
1
1
2
1
0
0
1
0
2
1
1
1
1
0
1
2
0
1
0
0
1
0
1
1
0
0
2
0
2
1
0
2
2
0
1
1
1
3
0
1
1
0
0
0
2
1
0
2
1
0
1
0
1
1
1
2
1
0
0
2
2
1
1
0
1
1
1
1
2
2
1
1
0
0
2
1
2
0
0
0
0
1
0
0
0
0
2
0
1
0
2
2
2
2
0
0
1
2
1
0
0
0
0
1
1
2
0
3
1
1
1
0
5
1
0
1
1
1
0
2
0
1
1
1
1
1
0
3
0
2
1
2
2
2
1
1
2
1
1
1
0
0
2
2
1
1
0
1
0
0
1
0
2
1
0
2
2
0
0
1
1
0
1
1
1
2
2
2
2
1
2
1
1
1
3
2
2
0
1
0
0
2
0
1
1
3
1
1
2
2
2
1
2
0
1
0
0
1
0
1
1
1
1
1
0
0
1
1
0
2
0
2
0
0
1
1
0
1
1
0
0
2
1
1
1
1
0
0
1
1
0
1
0
1
0
2
1
2
2
3
1
1
0
1
2
0
0
1
2
2
1
0
0
2
2
1
4
0
0
0
0
0
1
1
0
1
1
0
0
1
1
0
2
0
0
0
2
0
1
1
1
1
0
2
1
0
0
1
1
1
2
2
0
1
1
0
1
2
0
1
0
0
1
1
0
1
0
1
0
0
1
2
1
3
2
1
2
0
0
1
2
1
1
2
0
0
2
0
2
0
2
0
0
1
2
1
2
2
0
2
2
0
1
2
2
2
1
2
0
1
2
1
1
1
1
0
1
0
0
0
1
1
2
0
0
0
0
0
1
0
0
3
0
0
0
3
2
0
0
0
1
0
0
3
2
0
0
2
2
1
1
1
3
0
1
2
0
0
1
0
1
2
2
0
2
1
1
2
0
2
2
1
0
1
0
0
0
0
1
2
1
0
1
2
0
2
2
2
2
0
0
2
1
0
1
0
1
0
0
2
2
2
1
1
0
1
1
1
0
0
1
1
0
0
0
0
2
1
2
1
2
0
0
1
1
1
0
0
0
1
1
2
2
0
0
2
1
1
0
1
2
2
0
0
0
0
0
0
2
1
0
1
2
2
1
2
2
2
1
2
1
0
2
1
0
1
1
0
2
2
2
1
1
0
1
1
0
1
1
1
0
0
4
2
0
0
2
1
2
1
1
2
1
5
2
1
0
0
2
2
0
0
1
0
0
1
0
0
0
1
2
0
1
2
1
1
2
1
1
0
1
1
0
0
0
2
1
0
2
1
1
2
0
1
1
1
0
0
1
2
0
2
1
1
1
1
0
1
0
1
2
2
0
2
0
2
2
0
1
2
1
1
0
1
0
0
0
2
0
3
1
1
1
0
1
1
1
0
1
1
1
0
0
1
0
1
0
2
1
2
0
0
0
0
0
1
1
0
0
1
1
0
1
2
1
1
1
0
1
1
0
1
1
0
1
2
0
1
4
1
1
0
2
0
0
1
2
0
1
0
1
1
2
0
1
1
1
3
2
0
0
1
2
2
0
0
1
0
1
1
0
0
1
1
0
3
1
1
2
0
0
1
1
1
1
0
1
0
1
1
1
1
0
0
0
0
0
2
2
2
0
0
1
0
0
2
1
2
0
2
0
0
1
1
2
1
3
1
0
2
2
0
0
0
0
3
1
0
2
2
0
1
1
2
3
1
1
1
0
2
1
1
1
2
2
2
0
1
0
0
2
1
0
1
1
0
1
0
1
2
2
1
0
2
0
1
2
0
0
1
1
0
2
3
0
1
0
1
1
3
1
0
2
1
1
0
0
0
1
1
0
3
1
0
0
0
0
0
2
1
0
1
0
2
2
1
0
1
0
2
2
0
1
1
1
0
0
1
0
1
1
0
1
1
3
2
2
2
0
2
2
1
1
0
1
2
0
1
0
1
1
0
1
0
2
2
2
1
1
1
2
1
1
1
1
0
0
1
1
1
0
2
0
1
0
1
1
2
0
2
0
2
1
1
0
0
1
2
0
0
0
0
0
1
1
2
1
1
0
1
1
0
1
1
0
1
0
0
2
1
0
1
0
1
1
0
0
0
1
2
0
2
0
1
2
1
1
0
0
0
1
0
1
2
2
1
1
0
2
2
2
0
0
0
1
1
1
0
0
3
0
0
1
1
2
1
0
0
1
1
1
0
2
2
3
1
1
1
1
0
2
1
1
3
1
0
0
5
0
0
1
2
0
0
1
1
0
0
0
0
1
1
1
0
0
2
0
0
1
2
0
2
0
1
0
0
0
2
1
1
0
1
0
0
1
1
0
2
1
0
2
2
1
0
2
1
1
2
1
1
0
0
1
2
0
2
0
1
2
1
1
0
0
1
1
1
1
1
1
2
0
0
0
0
1
0
2
1
0
3
0
0
2
1
0
0
1
1
2
1
0
1
1
1
0
0
1
1
3
1
2
1
1
0
0
1
1
2
1
2
0
0
1
2
1
0
1
2
0
1
2
1
1
0
1
1
1
0
1
1
1
2
0
0
2
0
2
1
1
2
0
0
0
0
2
2
0
1
1
1
2
1
2
1
1
0
0
0
0
2
1
0
0
0
1
0
1
1
1
0
0
0
1
1
2
0
0
1
1
2
0
0
1
3
0
0
0
1
1
0
0
0
0
2
2
2
2
2
1
2
1
0
1
1
0
1
0
1
1
2
1
0
1
1
2
0
1
1
0
1
1
0
2
1
0
2
1
1
0
1
2
1
1
0
1
2
2
0
2
1
2
0
0
2
1
1
5
1
1
1
1
1
1
2
2
1
3
1
0
2
1
1
0
1
1
0
0
0
0
1
2
0
2
2
0
0
0
1
0
1
0
1
2
2
1
0
0
1
1
1
0
0
0
2
1
0
1
0
1
1
0
0
0
0
2
2
0
1
0
2
1
0
0
0
1
1
0
1
0
1
0
1
1
3
1
1
2
0
0
0
0
1
0
2
2
1
0
0
2
0
0
2
0
0
1
0
1
1
1
2
1
0
2
2
0
2
0
0
0
1
4
2
0
3
2
2
0
1
2
1
0
0
0
1
1
1
0
1
1
1
1
0
2
2
0
0
0
0
0
1
1
0
3
0
2
2
0
2
1
0
1
0
2
1
1
0
0
0
4
0
2
1
0
0
0
1
1
1
0
1
1
0
0
0
0
1
4
1
1
1
2
0
0
0
1
1
2
0
0
3
1
1
0
2
1
1
0
3
1
1
1
2
1
2
1
1
1
1
2
1
0
1
0
2
1
0
0
1
2
0
0
1
2
0
0
2
1
2
0
1
1
0
0
2
0
2
0
2
1
1
0
1
1
2
1
1
1
2
0
1
0
2
0
1
0
4
1
0
0
0
0
2
1
0
1
2
2
1
2
2
1
0
0
2
1
1
1
1
0
2
0
1
0
2
2
2
1
1
2
0
1
1
2
1
1
1
0
1
1
1
2
1
2
2
0
0
0
0
2
2
1
1
0
1
0
1
2
2
1
2
1
1
0
0
2
0
0
0
1
2
0
1
0
0
1
1
2
1
0
1
1
1
0
1
1
1
2
2
0
1
0
1
0
2
0
2
1
1
2
2
0
1
0
2
2
1
2
2
0
0
0
1
1
0
0
2
2
1
0
0
0
0
0
0
1
0
0
1
1
0
0
2
1
1
0
0
1
0
0
0
2
4
0
0
1
2
2
0
0
1
0
0
2
2
1
0
0
0
2
1
0
0
1
1
1
2
0
0
0
0
0
2
0
1
0
1
0
0
1
1
0
5
0
2
0
1
1
1
0
1
1
2
0
0
0
0
0
0
1
1
4
2
3
1
1
0
2
2
0
1
3
0
1
1
2
1
2
0
0
1
0
1
0
0
0
1
0
1
1
1
2
2
2
0
1
1
1
2
1
0
0
1
1
1
2
0
2
0
2
2
1
2
1
0
2
0
0
1
0
1
1
2
1
0
1
0
0
0
0
1
2
1
1
1
1
0
0
0
0
1
0
0
1
2
1
0
2
1
2
2
3
0
1
0
0
1
1
1
2
1
0
0
1
0
0
0
1
1
0
0
0
1
3
2
1
2
3
0
0
2
2
0
0
2
1
0
1
0
0
0
0
1
0
1
1
1
1
2
1
0
1
1
1
2
0
0
2
1
1
0
1
1
0
2
1
2
1
1
1
0
0
1
0
1
2
1
1
0
1
1
0
1
2
1
0
2
0
0
1
2
1
0
1
0
1
1
1
0
0
1
0
1
0
0
1
1
1
1
2
0
1
1
2
1
1
0
2
1
0
1
0
0
0
1
0
1
1
1
0
0
3
0
1
0
0
2
2
0
0
1
0
1
3
0
0
1
2
0
0
0
1
2
0
0
0
1
2
1
2
1
1
0
3
0
1
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
2
1
0
2
0
1
1
2
0
0
2
0
0
0
2
1
1
1
0
0
1
0
0
0
0
1
0
1
0
1
0
0
2
0
0
0
0
0
2
0
1
1
1
1
1
2
0
0
1
1
1
1
1
0
1
2
0
0
0
1
0
1
2
0
1
0
2
0
0
1
2
0
0
0
1
1
2
0
1
0
0
2
1
1
1
1
2
0
2
1
0
0
0
2
1
1
0
0
1
0
0
0
0
0
0
1
0
1
2
2
2
3
2
0
0
1
0
1
0
0
2
1
1
0
0
0
0
0
1
0
2
1
2
0
2
0
0
1
1
0
1
2
0
0
0
1
1
0
1
1
0
0
1
0
0
2
0
0
2
0
0
2
1
0
1
0
1
2
0
0
1
0
0
2
1
2
2
1
0
1
1
1
1
1
0
1
0
2
0
1
0
0
1
2
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
1
1
0
0
1
1
0
1
1
1
2
0
1
1
1
0
0
1
0
2
0
0
0
2
0
0
0
1
1
1
0
0
0
2
1
0
1
1
0
0
0
0
1
2
0
1
1
1
0
0
1
0
1
1
1
2
1
1
0
1
0
4
2
1
0
0
0
1
3
1
2
0
1
1
1
0
1
2
1
1
1
1
0
1
2
1
0
1
1
4
0
1
1
0
1
1
0
1
2
0
1
1
3
2
1
2
1
0
1
0
0
0
1
1
0
1
2
2
0
1
2
1
1
1
0
1
1
2
1
1
2
1
2
0
1
1
2
0
0
1
1
0
1
1
0
2
0
2
2
1
1
2
2
2
1
0
1
0
1
2
1
0
1
1
0
2
1
1
1
0
0
1
2
1
1
0
0
0
2
1
1
1
1
3
2
0
2
1
0
2
1
0
0
2
0
2
2
1
0
1
2
0
2
2
0
1
1
0
1
2
2
2
0
1
1
1
1
2
1
2
1
1
4
2
0
2
0
2
0
0
0
1
0
1
1
1
1
1
0
0
1
0
1
2
1
9
2
1
2
0
3
1
2
2
0
2
1
0
0
0
1
2
1
1
2
1
2
0
0
0
0
1
0
0
0
2
2
0
1
0
2
1
1
1
1
1
1
0
1
1
0
1
1
0
0
0
1
2
0
1
1
0
1
1
0
0
1
0
2
2
2
1
2
2
0
1
2
0
2
1
1
0
1
3
1
0
2
1
0
1
1
2
0
0
1
0
0
0
0
1
1
1
2
1
2
1
0
1
0
1
2
2
0
0
0
3
0
2
3
1
1
0
1
2
1
1
0
2
0
1
0
3
1
0
0
1
1
0
2
0
1
0
1
0
1
0
0
1
2
1
1
0
1
1
0
0
2
0
0
0
0
1
0
1
2
0
2
1
1
0
1
0
0
1
1
0
0
0
0
1
2
2
0
1
1
0
0
1
0
0
0
2
1
2
0
0
1
2
1
1
0
1
0
2
0
2
0
0
0
1
0
1
1
2
2
1
1
2
0
0
0
1
2
1
0
0
1
2
1
0
1
0
0
1
0
2
0
1
2
0
0
0
0
1
0
0
1
1
3
2
0
8
1
2
0
2
1
1
0
2
0
0
2
2
1
2
1
0
1
1
1
1
0
1
0
1
2
1
0
0
1
1
2
0
1
0
2
2
1
2
3
0
0
1
0
2
0
0
0
1
1
0
0
0
2
2
1
1
1
0
0
0
1
1
1
1
2
1
0
1
1
0
1
2
1
1
1
2
0
2
0
0
0
1
2
0
1
2
0
1
2
1
1
0
1
0
0
2
0
2
0
0
0
1
0
1
2
0
2
0
1
2
1
1
2
1
2
2
0
1
0
0
0
0
1
1
2
0
0
0
2
1
1
0
0
1
0
0
1
1
0
1
1
1
1
0
1
1
1
1
0
0
0
0
1
0
2
0
2
0
1
0
2
1
1
2
1
1
0
0
3
0
1
2
0
2
0
0
2
2
0
0
0
0
1
0
1
1
2
0
1
0
1
1
0
0
0
2
0
2
0
1
1
0
0
1
0
2
1
1
0
1
0
0
1
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
2
1
2
0
2
0
0
1
0
2
1
0
0
2
0
2
2
2
1
1
1
2
2
3
2
1
1
0
1
0
1
0
0
1
1
1
0
1
1
2
2
0
0
0
1
1
0
0
1
1
1
1
0
0
2
0
1
0
1
1
0
0
1
0
1
0
1
0
1
0
0
1
2
0
0
2
2
0
1
1
3
1
1
1
0
2
1
1
2
0
0
0
0
2
1
1
0
0
0
2
0
1
1
1
2
1
1
2
1
1
2
2
2
1
0
1
1
2
1
0
2
0
2
1
3
1
0
0
2
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
2
1
0
0
0
2
1
0
0
1
1
0
2
1
1
0
2
1
0
0
2
1
0
0
2
2
0
0
1
0
0
0
2
0
0
0
1
1
0
0
2
1
0
2
2
0
0
0
1
0
2
2
1
1
0
0
1
11
2
0
0
1
0
2
0
1
0
0
0
2
1
0
2
1
0
2
1
0
1
2
0
1
2
0
1
1
0
1
0
0
0
0
1
1
3
2
0
2
0
3
0
1
2
0
0
2
2
1
0
1
1
1
2
2
0
2
0
1
1
0
0
0
0
0
1
2
1
2
0
1
0
0
1
1
0
1
0
0
1
0
1
0
0
0
1
2
2
2
0
1
3
1
0
2
0
0
1
0
1
0
1
1
2
1
0
2
2
2
1
0
0
2
2
1
0
2
1
0
1
0
2
0
2
0
0
1
0
2
2
2
1
1
1
3
2
0
1
1
0
1
2
0
0
1
0
1
1
1
2
2
1
0
0
2
0
2
0
1
0
2
1
1
2
2
2
1
0
1
1
2
1
2
0
1
1
1
2
2
0
2
2
1
0
1
1
0
2
1
0
2
1
0
0
1
1
2
1
1
1
1
2
2
0
2
1
2
1
3
0
0
1
2
1
1
2
0
0
0
0
0
0
2
0
1
0
2
0
2
0
0
1
2
1
3
1
0
0
1
2
1
2
0
0
0
1
1
2
1
2
0
0
0
1
0
2
1
1
1
1
2
1
1
0
0
0
2
2
1
1
2
0
1
0
0
1
0
1
1
0
1
1
2
0
1
0
2
1
1
0
0
1
0
0
1
1
1
1
1
2
1
0
0
0
2
0
2
0
0
0
1
2
2
1
1
0
0
1
1
1
0
1
1
2
0
1
1
0
1
2
2
1
0
1
1
1
1
2
1
1
0
0
1
1
1
0
0
1
2
1
1
2
0
0
2
0
0
3
0
0
1
2
0
0
0
1
2
2
0
1
1
1
2
0
0
2
0
1
1
2
1
0
0
0
1
1
0
2
2
2
2
2
1
0
2
1
0
0
2
1
0
1
2
0
1
2
1
0
0
1
2
0
2
0
1
1
0
0
1
1
2
1
0
2
2
0
1
2
1
1
0
0
2
0
2
1
1
2
1
0
1
3
0
0
1
1
1
0
0
1
1
0
3
2
0
1
2
2
0
0
1
0
2
1
1
1
0
0
1
0
2
0
0
0
0
0
4
1
1
2
2
1
0
1
1
2
0
0
1
0
1
0
0
1
3
0
0
0
1
2
0
1
1
0
0
2
1
0
1
0
0
1
1
1
1
1
1
1
1
1
1
1
2
1
1
1
2
2
0
2
0
1
0
2
1
0
0
0
2
1
2
1
2
0
1
1
2
2
2
1
4
1
1
0
1
0
0
0
0
2
0
0
0
2
1
3
1
0
0
2
0
0
0
1
2
1
1
1
2
0
0
0
2
1
2
2
2
1
0
1
1
0
0
1
1
0
2
0
0
4
2
2
2
0
2
0
0
3
1
1
0
2
1
0
1
0
1
1
4
1
0
0
1
1
2
0
2
0
1
1
1
0
1
1
1
1
1
0
2
1
0
1
1
1
1
0
0
0
0
1
2
1
1
0
0
0
1
0
0
0
1
1
2
1
1
0
0
0
0
1
0
0
2
0
0
1
1
0
0
2
0
1
0
2
2
0
1
1
0
1
0
1
0
1
1
0
1
0
0
0
1
2
1
2
0
2
2
2
0
2
0
1
0
2
0
2
1
1
0
1
0
0
0
3
3
0
1
2
2
0
0
1
0
1
0
1
1
0
0
0
1
0
0
0
1
2
0
0
1
1
1
2
2
2
1
2
0
0
1
0
1
1
1
1
0
1
1
1
0
1
3
0
1
1
2
0
0
2
0
0
0
0
1
0
1
2
0
2
2
0
1
1
0
0
1
1
0
0
1
1
1
0
0
0
0
0
1
2
0
0
1
2
2
1
1
1
1
1
0
2
1
1
1
2
0
1
1
1
0
1
2
0
0
2
2
2
1
0
2
4
0
0
0
3
0
2
0
1
0
1
0
1
2
1
1
1
2
0
1
1
1
1
0
2
2
2
0
1
2
0
1
0
1
2
3
2
2
1
1
0
1
2
0
0
0
2
2
0
1
0
1
1
0
2
0
0
2
0
2
0
1
2
0
2
0
0
0
1
2
0
0
0
0
0
1
1
2
1
1
2
0
1
0
2
1
0
1
0
1
1
0
0
1
0
2
1
2
0
0
1
1
2
2
2
0
1
0
2
0
2
1
1
2
3
0
0
1
0
1
1
0
0
2
4
0
0
0
0
2
3
1
1
1
1
1
0
3
1
2
1
1
5
1
1
1
1
1
0
1
1
0
0
1
1
1
0
1
0
1
2
0
0
1
1
0
2
0
2
1
0
2
1
0
3
2
1
1
0
1
1
0
0
2
0
0
0
1
1
1
2
0
1
1
1
0
1
1
1
1
0
0
1
1
2
2
0
1
0
1
0
0
0
2
1
2
0
0
0
2
0
0
0
1
1
1
1
1
2
0
0
1
0
2
1
0
1
0
2
1
1
1
2
0
0
2
2
0
1
2
0
1
1
1
1
0
2
2
2
1
0
2
2
1
0
0
2
0
1
2
1
0
1
0
1
2
2
0
0
1
0
1
0
2
0
0
0
1
1
0
1
0
0
1
0
1
0
1
1
1
1
1
0
0
0
1
0
2
1
0
1
1
0
0
2
1
1
0
0
0
0
0
1
0
1
1
2
1
1
1
0
1
0
0
0
2
1
1
2
1
0
1
1
1
0
2
1
0
3
0
1
2
0
0
1
0
1
1
0
1
1
2
1
1
1
3
2
2
0
0
0
0
1
0
0
1
1
1
1
1
3
1
0
0
2
1
2
0
0
0
1
2
0
0
0
1
0
1
1
1
0
0
0
0
2
0
2
1
0
0
1
0
0
0
2
0
1
0
0
0
1
2
0
1
2
0
1
0
2
1
1
0
0
0
1
0
0
2
1
2
0
0
0
0
0
0
2
2
0
1
0
1
0
0
1
0
1
0
1
1
0
0
1
0
1
0
0
1
1
2
1
1
0
2
1
2
1
0
1
0
0
0
1
2
2
1
1
1
0
1
1
1
1
1
1
2
0
0
1
0
1
0
0
0
1
1
0
2
0
2
1
0
2
0
0
1
2
0
2
0
1
0
0
2
1
1
2
0
0
0
0
1
1
0
0
0
2
2
2
1
1
2
1
1
0
2
1
0
2
1
0
1
0
1
0
1
0
1
5
1
1
0
3
2
0
1
1
1
1
1
1
0
1
2
1
2
2
0
1
0
0
1
1
0
0
2
1
0
2
1
2
1
0
1
2
0
1
1
0
0
2
1
1
2
0
0
1
2
0
2
1
1
1
1
1
2
2
1
1
1
1
2
0
2
0
1
1
1
2
1
0
0
1
2
1
1
1
2
2
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
2
0
1
1
2
1
0
1
1
2
1
1
1
0
0
2
2
1
1
0
0
0
1
2
1
0
2
1
1
1
2
1
2
1
1
1
0
0
1
0
1
0
2
1
1
0
0
0
2
3
1
2
1
0
0
1
1
1
0
1
1
1
0
1
0
0
0
0
1
2
0
0
1
1
0
2
1
2
1
3
1
1
0
1
2
2
2
1
1
0
0
0
0
3
2
1
0
0
0
1
0
0
0
0
1
2
2
2
1
0
0
1
1
0
0
0
0
0
2
0
0
2
1
0
1
1
2
0
2
0
1
2
1
0
0
2
2
0
1
1
0
5
0
1
0
0
2
1
0
2
1
1
2
0
1
1
1
1
1
1
1
1
2
1
0
1
1
2
0
2
0
0
1
1
2
0
2
2
0
2
1
3
0
2
2
0
1
1
0
0
0
0
0
0
0
1
1
1
1
0
0
0
2
0
0
1
1
1
0
0
2
1
1
1
0
2
1
2
0
0
0
2
1
0
1
0
0
0
2
0
2
0
2
0
2
4
0
0
2
1
1
1
1
0
0
1
1
2
2
0
0
1
2
0
0
1
2
1
0
1
1
0
2
0
2
2
1
2
1
1
0
0
1
1
2
2
0
0
2
0
0
0
1
0
1
2
1
1
1
2
0
0
0
0
2
0
2
1
1
2
1
0
1
2
1
0
1
1
2
1
0
0
0
1
2
2
2
0
0
1
2
0
0
0
0
1
0
1
0
0
0
0
0
1
2
2
1
0
0
0
2
2
3
2
0
0
1
0
2
1
0
2
0
1
0
0
2
0
0
2
2
2
1
2
0
0
1
0
2
1
1
1
2
2
1
0
2
0
0
0
0
1
0
0
1
0
0
1
1
0
0
1
2
1
1
1
0
1
1
2
1
1
0
0
1
0
2
2
1
1
0
3
1
0
0
1
0
0
0
1
2
2
0
0
0
1
5
1
1
0
1
2
0
1
1
1
2
1
1
2
2
2
1
0
0
1
1
0
1
1
1
0
1
1
1
0
1
2
1
0
2
2
2
0
1
2
0
1
0
1
1
0
1
1
2
0
1
2
0
0
1
2
0
1
0
0
1
1
1
0
1
2
1
1
1
2
1
0
2
0
2
0
0
1
0
1
0
1
1
2
1
0
0
1
1
2
3
3
1
1
0
1
0
1
0
2
1
2
0
2
1
1
2
0
1
1
1
1
1
1
1
0
0
1
1
1
0
2
0
0
0
1
1
0
0
0
0
1
1
1
0
1
1
0
0
0
0
1
0
1
0
1
1
0
1
2
0
0
2
0
1
0
0
2
0
4
1
0
1
1
1
0
1
2
0
0
0
0
0
0
0
2
0
0
0
2
1
1
0
0
0
0
1
2
0
0
1
2
2
2
0
1
1
2
1
2
0
1
2
1
0
1
1
1
2
1
0
1
2
1
2
1
0
1
0
1
1
0
0
1
0
0
2
2
0
1
2
1
0
1
1
1
1
2
1
0
1
1
0
1
0
1
1
1
0
2
4
2
1
0
0
2
1
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
1
0
2
1
2
0
0
2
0
0
0
1
1
2
0
2
0
0
2
0
0
0
0
1
1
1
1
0
1
0
0
2
2
0
0
2
2
0
0
0
1
0
1
0
0
2
1
1
1
1
2
1
1
0
1
0
1
1
0
1
2
1
1
0
1
0
1
0
1
1
1
0
1
0
1
2
1
1
2
0
1
0
0
1
0
1
0
1
0
0
2
2
0
1
2
1
0
1
2
0
0
0
2
0
2
2
1
1
1
1
1
0
0
1
0
0
0
1
0
1
2
2
2
2
3
1
1
1
2
1
0
1
1
0
1
0
1
1
1
2
1
0
1
2
2
0
0
0
0
1
1
0
0
1
2
2
2
0
2
1
0
0
1
0
1
0
2
2
0
1
0
2
1
0
1
1
1
2
3
0
1
0
0
0
2
1
1
0
2
2
0
1
1
1
1
1
0
0
2
0
1
0
2
2
2
0
1
0
1
1
1
2
1
1
2
0
1
0
2
0
1
1
0
1
2
1
1
1
2
0
2
0
0
0
0
2
0
1
2
1
2
0
1
1
0
1
2
1
1
1
0
2
1
0
2
1
0
0
0
2
0
0
0
1
1
1
1
0
0
0
0
2
0
0
0
0
1
0
2
2
0
2
0
2
0
0
1
2
0
1
1
2
1
0
1
2
2
0
2
1
0
2
2
1
0
0
2
0
2
0
2
1
1
0
1
1
0
0
1
1
1
0
1
1
0
2
2
0
2
1
2
0
2
1
0
1
1
0
1
1
2
1
1
2
2
1
1
2
1
0
0
1
1
1
0
1
1
0
1
1
0
1
1
0
2
2
0
0
0
2
1
0
0
0
0
0
0
0
2
2
0
2
1
2
1
2
2
1
1
1
2
1
1
2
0
2
0
0
2
0
1
0
0
1
0
1
0
0
2
0
1
1
1
2
2
1
0
0
1
0
0
0
0
1
1
2
2
2
0
2
3
0
0
3
1
1
1
1
0
1
0
0
1
1
0
1
1
0
0
0
2
2
1
0
0
0
0
1
1
2
0
3
0
2
1
1
0
1
0
1
1
2
0
1
0
0
0
1
1
2
2
0
1
0
0
0
0
1
2
0
0
0
0
2
1
1
2
0
0
2
2
0
1
0
0
0
0
1
2
2
1
0
2
0
0
2
2
1
1
0
0
2
1
2
1
1
0
0
0
1
2
0
2
1
1
1
2
1
0
0
2
1
1
0
2
2
2
1
1
1
0
1
1
0
5
2
1
0
0
2
1
2
0
0
1
1
2
0
0
0
2
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
1
1
0
0
1
1
1
1
0
2
1
3
2
1
0
1
0
2
0
0
1
0
1
0
1
1
0
0
0
1
1
2
2
1
0
0
1
1
0
0
11
1
0
2
1
1
0
2
1
0
0
1
0
0
0
2
3
0
0
1
0
1
1
2
0
2
1
1
2
2
1
1
0
2
1
0
2
0
2
0
1
1
0
0
2
0
1
0
2
2
0
0
0
2
1
2
1
1
0
2
0
0
0
1
0
0
0
1
0
2
2
0
2
1
1
2
2
0
0
0
1
1
2
2
1
2
0
1
1
0
0
1
1
1
0
1
1
0
0
1
0
1
1
0
0
0
1
1
0
0
0
2
0
0
1
0
0
2
1
1
1
1
1
1
1
2
0
0
0
0
1
1
0
1
1
2
0
1
1
0
1
0
2
0
0
1
2
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
1
1
1
1
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
2
1
1
1
0
0
1
1
0
1
1
0
0
1
1
0
3
0
2
1
2
5
0
0
2
1
2
2
1
1
0
1
1
1
1
0
1
1
1
0
0
1
0
0
0
2
2
0
1
1
1
2
2
0
0
2
1
0
0
1
0
0
0
0
2
1
0
1
1
2
1
2
1
1
2
0
0
0
0
0
0
2
2
0
0
0
1
1
1
1
0
1
2
2
1
1
2
0
0
0
0
0
2
0
1
0
0
1
0
1
0
1
0
1
0
2
0
0
1
1
1
1
2
1
1
0
2
0
1
1
0
2
0
0
0
2
1
0
0
0
0
0
1
0
0
0
1
0
2
1
1
2
0
1
1
0
1
1
1
0
1
1
0
3
2
1
2
2
2
0
2
1
1
2
1
0
1
1
0
1
0
1
1
0
0
1
0
1
2
2
2
3
2
1
1
2
1
1
1
2
2
2
1
0
2
6
2
1
0
1
0
2
0
1
1
0
1
0
0
1
1
1
0
0
1
2
2
1
1
2
1
0
2
1
0
0
1
0
1
1
1
0
2
1
1
0
0
0
1
2
1
1
1
0
3
0
1
1
0
2
0
1
0
0
2
0
1
2
1
1
1
1
0
1
0
1
1
1
1
1
1
0
1
2
0
0
2
1
0
1
0
1
1
1
1
0
0
1
0
0
0
0
0
1
0
1
0
0
1
1
2
2
3
1
1
1
1
0
1
0
1
0
2
0
1
1
0
0
0
1
1
1
0
2
1
2
0
1
0
1
0
0
0
0
1
0
1
1
2
0
0
2
0
1
1
0
0
2
1
0
1
1
0
2
3
2
1
0
0
1
1
1
3
1
1
0
0
4
1
0
2
1
2
0
1
0
1
1
1
1
1
1
2
2
1
0
1
1
2
1
1
0
0
0
1
0
1
1
0
2
1
0
0
1
2
2
1
0
0
1
0
0
0
1
2
1
1
0
1
3
1
2
0
0
0
1
0
0
1
0
1
0
1
1
1
3
2
1
1
1
0
1
1
1
0
2
0
0
1
2
1
0
0
0
0
0
1
2
1
0
1
3
2
0
2
1
0
1
1
1
0
1
4
0
1
1
2
0
0
1
1
1
0
2
1
0
1
0
0
2
1
0
0
1
1
1
2
0
0
2
2
0
0
4
2
0
1
1
0
1
1
0
0
0
0
0
1
0
0
1
1
1
0
1
2
1
1
2
0
1
0
0
2
2
0
0
0
1
1
0
1
0
2
1
1
1
1
0
1
2
1
0
4
1
0
0
1
1
1
1
0
1
0
1
0
0
1
2
0
0
0
1
1
1
0
1
1
1
0
1
0
1
2
1
1
1
2
2
1
0
2
1
0
1
0
1
0
1
1
1
0
0
0
1
0
1
0
1
2
1
1
0
0
1
2
0
1
2
0
1
1
1
1
1
2
0
2
1
1
0
0
2
1
0
0
2
1
1
2
2
1
1
1
1
1
0
3
0
0
1
2
1
1
0
0
0
0
1
0
0
0
2
1
0
0
1
3
2
1
1
4
0
0
2
0
2
0
0
2
2
1
1
1
0
2
2
0
0
1
2
1
0
0
1
2
0
0
2
1
0
2
0
1
1
2
1
2
1
2
0
0
1
0
0
1
2
1
1
0
0
1
2
2
0
0
1
2
0
1
2
0
1
1
0
1
1
2
2
1
1
1
0
0
1
0
1
2
1
0
0
0
0
1
2
1
0
2
1
0
2
1
1
1
0
1
2
0
1
0
0
0
1
1
1
2
1
0
0
2
1
1
1
1
0
1
1
1
1
1
1
2
0
1
1
2
1
0
0
6
0
1
1
0
1
0
2
0
2
1
0
0
2
1
2
1
1
0
1
1
1
1
1
1
0
1
0
2
0
2
1
0
1
0
1
0
1
0
0
0
1
1
2
1
0
1
1
3
1
1
1
0
0
0
1
1
1
0
1
2
1
1
0
0
1
2
0
0
2
1
2
1
0
1
2
0
1
0
0
0
0
0
0
0
1
2
1
2
2
1
1
1
1
1
2
0
0
0
1
2
1
1
1
3
1
0
0
1
2
2
1
0
0
2
2
1
0
1
2
0
0
0
0
0
2
0
1
1
1
1
0
0
0
0
2
0
2
1
0
0
2
0
1
1
1
2
2
0
1
1
1
2
1
2
1
0
0
0
0
0
2
2
0
2
2
1
0
0
2
0
0
0
0
0
0
0
1
1
0
2
0
1
1
1
0
1
1
1
2
1
1
2
0
0
1
0
1
1
0
0
1
2
1
1
1
5
0
0
1
2
1
0
0
1
1
1
0
1
1
0
2
0
1
1
0
0
0
1
1
0
0
1
0
2
1
0
0
0
0
0
1
1
2
1
2
0
2
1
1
0
1
1
1
2
3
0
0
1
3
0
0
1
1
0
1
1
2
1
2
0
1
0
0
0
1
2
0
1
2
0
1
0
1
1
2
0
0
2
0
1
1
0
1
1
0
0
2
1
0
2
1
1
0
0
0
1
2
0
0
1
0
2
0
0
0
0
2
0
0
0
0
1
1
1
2
0
2
1
0
1
1
0
0
2
1
0
1
2
2
0
1
1
1
1
0
1
1
0
3
0
1
0
0
0
2
0
1
2
0
0
1
1
1
1
2
0
1
1
0
1
0
1
0
1
0
1
0
2
1
1
0
2
2
1
2
0
1
1
2
1
2
1
1
1
1
2
1
2
0
1
1
1
0
1
0
0
0
1
0
1
2
0
0
2
0
1
3
1
2
2
1
0
0
1
0
1
1
1
0
0
2
2
2
2
0
1
0
1
0
2
0
1
3
2
0
1
1
1
0
2
2
2
0
1
1
0
1
2
0
1
1
0
2
0
2
2
1
2
0
1
2
1
1
1
1
0
0
1
3
0
0
0
0
1
1
2
1
1
0
0
1
1
0
2
2
2
0
1
0
1
2
0
0
1
1
0
0
1
0
2
1
1
2
1
2
0
0
0
0
1
2
0
1
1
0
0
1
0
1
0
2
1
0
1
1
2
1
1
0
1
2
0
1
1
2
1
2
1
0
2
1
1
1
0
1
1
1
0
0
2
2
2
3
0
1
2
1
1
0
0
0
1
0
0
0
2
1
0
0
0
1
2
1
1
0
0
0
1
1
2
1
2
2
1
1
1
0
2
0
2
2
0
0
2
0
1
0
1
0
1
2
2
1
0
1
0
0
1
1
1
1
1
0
1
2
0
0
0
1
1
0
0
0
2
1
2
2
1
1
1
1
0
0
0
1
0
2
2
1
1
0
0
2
1
0
1
1
1
2
1
1
0
1
1
2
0
1
3
2
0
1
0
2
1
0
0
0
1
1
1
2
1
0
1
1
0
2
1
2
2
0
1
0
1
2
1
1
2
1
0
1
1
1
1
0
2
0
0
0
2
0
0
2
2
0
0
1
2
0
2
2
0
1
2
1
2
1
1
1
1
2
1
1
1
0
1
0
1
0
0
0
2
1
0
0
0
1
2
0
1
1
2
0
0
0
0
0
1
0
0
2
0
1
1
1
1
0
1
2
2
1
2
2
1
1
1
1
1
1
2
0
1
0
0
2
2
0
0
0
1
2
0
1
1
1
1
0
1
0
1
0
2
0
0
2
0
1
1
1
0
2
2
2
2
1
1
1
1
0
1
0
1
1
1
0
2
1
1
2
1
1
1
1
1
0
1
2
0
1
0
0
0
1
2
0
1
0
1
1
0
1
1
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
1
1
1
0
1
1
0
2
2
1
3
1
0
0
0
1
1
1
0
0
2
2
0
2
0
0
1
1
1
2
0
1
2
1
1
0
0
0
2
1
1
1
2
0
1
1
1
1
0
1
0
2
0
2
0
1
0
0
2
0
0
3
1
2
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
1
2
1
1
1
1
2
0
1
1
1
1
1
1
2
1
1
0
4
1
2
0
0
1
1
0
0
1
0
1
1
0
1
0
1
0
0
1
1
2
1
1
1
0
1
1
1
0
1
0
1
0
1
1
2
0
0
0
2
2
0
1
2
1
2
1
0
1
0
0
2
0
2
1
1
1
1
0
0
0
2
0
2
1
1
2
1
0
1
0
1
2
1
0
0
1
1
2
1
1
2
0
0
2
1
1
2
1
0
0
1
1
2
1
1
1
0
0
0
0
0
2
2
1
0
0
1
1
0
2
1
1
1
1
1
2
2
2
2
2
1
0
2
0
0
0
1
1
0
2
0
2
0
0
0
0
3
1
1
0
1
1
0
1
0
2
0
1
1
1
2
0
1
1
0
1
0
0
0
2
0
1
1
1
0
0
2
1
0
1
0
1
0
1
2
0
2
0
0
0
2
1
1
1
1
0
0
0
1
1
1
0
2
1
0
0
0
1
2
1
2
0
1
0
1
1
0
0
0
2
1
2
2
1
1
0
1
1
1
1
1
2
0
0
0
3
1
2
2
0
0
0
0
1
0
3
0
0
1
0
0
0
3
0
1
1
1
0
0
2
1
2
1
2
2
0
2
3
0
1
0
0
0
0
2
1
1
2
0
1
1
0
0
1
0
2
2
0
1
1
1
0
0
1
1
1
0
0
0
0
0
1
1
0
1
0
0
2
1
0
0
0
1
1
0
2
1
1
1
1
1
1
0
0
2
1
1
0
0
2
0
2
0
0
0
0
2
1
1
0
2
0
2
0
1
3
1
1
1
0
5
0
2
1
1
2
1
1
2
1
2
1
1
2
0
0
2
0
1
1
1
0
1
0
1
1
1
1
1
0
2
1
0
0
2
2
2
1
2
0
1
2
0
0
1
1
2
2
0
0
0
0
2
0
0
0
0
3
0
1
1
1
1
2
0
0
1
0
2
1
1
1
2
1
0
1
2
1
2
1
0
2
0
0
2
2
2
2
2
0
1
0
1
1
2
0
0
0
1
2
0
1
0
0
1
1
1
0
1
0
2
0
1
1
2
0
2
1
0
1
1
0
1
1
1
1
2
2
2
1
1
2
0
0
1
13
1
1
2
2
1
0
1
0
2
1
0
0
1
2
1
1
1
1
0
1
0
2
0
0
1
0
0
0
2
1
1
1
0
0
1
1
1
0
0
1
1
1
1
1
1
1
1
0
2
0
2
0
2
3
2
0
2
2
0
0
0
1
1
0
0
1
0
1
0
1
1
0
0
1
0
1
0
0
2
0
0
2
1
2
1
2
2
0
2
1
3
0
2
0
1
1
1
1
1
0
2
0
0
2
2
2
1
1
0
1
1
1
1
1
2
1
1
0
3
1
0
0
1
0
0
2
1
2
2
0
1
0
1
0
1
3
1
0
0
0
0
0
1
1
0
2
1
1
0
0
2
0
2
1
1
1
2
0
0
0
0
1
2
0
3
1
1
1
0
0
1
2
0
1
2
1
1
1
2
1
1
0
0
1
1
0
2
0
0
1
1
0
1
1
2
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
2
1
2
1
0
1
0
1
0
1
1
0
0
0
0
0
2
1
2
1
0
1
0
0
1
0
2
0
2
1
1
1
2
1
0
1
0
1
0
1
0
1
1
2
2
1
1
1
2
2
3
2
1
2
1
0
1
2
0
1
1
1
2
0
0
0
0
1
1
1
0
1
2
1
2
0
0
1
1
1
2
1
2
2
1
1
2
1
0
0
1
0
1
2
2
2
2
1
0
2
1
0
2
2
1
1
2
0
0
2
1
3
1
0
0
1
1
1
0
0
0
2
0
1
0
2
1
1
2
0
0
1
1
1
1
0
1
0
0
1
2
0
2
0
2
0
0
1
1
2
1
0
0
0
1
1
2
2
2
0
2
2
0
1
1
0
0
1
2
0
0
1
0
0
2
1
0
0
3
0
1
0
0
0
2
1
0
2
0
1
1
0
1
3
1
0
1
0
2
1
2
2
2
0
2
3
2
0
2
1
1
0
0
1
0
0
2
0
0
1
0
0
2
0
2
0
0
1
1
0
0
0
1
0
0
1
1
3
0
1
1
2
2
0
1
1
1
0
1
0
0
0
0
0
1
1
2
1
0
0
0
0
1
1
1
2
0
0
0
0
1
1
0
0
1
1
4
1
1
2
0
1
0
1
0
1
2
0
1
2
2
1
0
0
0
0
1
0
1
1
1
1
0
1
1
1
2
2
1
0
1
1
1
0
0
1
1
0
0
0
0
1
1
0
1
1
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
2
1
1
0
0
0
0
0
1
2
1
0
0
0
1
2
0
1
0
1
2
0
2
2
1
2
2
0
2
0
1
1
2
1
1
2
0
0
1
1
1
1
2
1
0
1
1
2
2
1
0
2
2
1
2
1
2
0
1
0
4
0
0
0
2
0
1
2
1
0
2
1
1
1
1
1
1
0
0
1
1
1
0
1
1
2
2
0
1
0
1
0
0
1
0
2
0
1
0
0
0
1
2
1
1
0
1
0
1
1
1
2
1
0
1
0
1
1
1
0
1
2
2
0
1
0
2
1
2
1
0
1
0
0
1
0
0
0
1
0
1
2
1
0
2
0
0
3
2
3
2
2
1
0
2
2
2
3
2
0
2
1
0
1
0
2
1
1
1
2
1
2
1
1
0
1
0
2
0
1
0
1
0
2
0
0
2
1
1
0
0
0
1
0
0
1
0
2
1
0
1
1
0
1
0
0
1
1
2
1
2
0
1
1
0
0
0
2
1
0
0
1
0
1
2
0
1
1
0
1
1
1
1
0
0
0
1
1
0
0
2
0
0
3
0
0
0
0
1
1
0
1
0
0
1
1
1
2
0
0
1
1
1
1
0
0
2
1
1
0
2
1
1
2
1
1
1
1
1
1
2
0
1
1
2
1
2
1
1
0
1
1
1
0
0
1
0
0
2
0
1
1
3
0
0
1
1
1
0
2
1
2
2
1
0
1
0
2
2
1
0
2
0
0
2
2
0
1
0
2
2
0
0
0
1
1
2
1
1
1
1
1
0
1
1
2
0
1
1
0
0
0
2
1
0
1
1
0
1
1
0
3
1
0
2
0
1
0
0
2
0
0
2
2
0
1
0
1
0
2
0
1
0
0
2
1
0
1
1
0
2
1
1
0
1
1
2
3
0
2
1
0
0
1
1
0
2
0
0
2
0
2
1
0
1
2
0
2
1
1
0
1
1
2
0
1
0
0
1
0
0
0
0
0
2
1
2
0
0
1
2
2
1
0
1
1
1
2
0
0
2
2
0
2
1
1
1
2
1
0
1
1
0
1
0
0
1
0
2
3
1
0
0
1
3
2
1
1
1
0
1
0
0
0
0
2
0
0
1
1
1
0
2
0
1
1
0
0
1
1
1
2
0
0
2
0
4
1
2
0
2
1
1
1
2
0
1
1
0
3
2
1
1
1
0
0
2
0
1
2
0
1
12
0
2
2
0
1
2
0
0
1
2
1
0
2
0
1
1
2
0
1
1
0
0
2
2
1
1
3
2
1
2
0
2
1
1
0
0
0
0
0
1
2
0
1
1
0
2
1
0
2
0
0
0
1
0
1
2
1
0
1
0
1
1
0
0
0
1
1
2
1
1
1
1
0
0
2
0
0
1
2
0
1
0
2
2
0
2
1
2
1
1
1
0
2
0
0
0
1
1
1
1
1
2
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
1
0
2
2
1
0
0
1
2
0
2
3
2
2
2
1
2
0
1
0
0
1
0
0
1
0
0
2
1
1
1
0
1
1
0
1
0
1
1
1
1
1
1
2
2
1
1
1
1
2
0
1
1
3
1
1
0
1
0
1
0
1
1
0
2
1
4
1
0
0
1
0
1
2
0
0
0
2
0
2
1
1
0
1
1
0
0
1
0
0
1
1
0
1
1
1
2
0
1
0
0
0
2
2
0
1
2
2
0
1
0
1
2
1
1
0
3
0
2
2
0
2
1
2
0
1
1
0
2
0
0
1
0
2
0
2
2
1
0
0
1
1
0
0
1
2
0
0
0
1
2
0
1
0
2
1
0
2
2
2
0
2
1
1
0
0
0
1
1
2
0
2
0
2
1
1
1
0
0
3
1
2
0
0
0
1
0
0
1
0
1
1
0
0
2
0
0
2
1
0
1
1
1
0
1
2
0
1
1
2
2
1
2
1
1
1
1
2
1
0
1
1
0
0
1
2
0
1
1
0
0
1
0
1
0
0
0
0
1
0
0
2
2
0
1
0
0
1
1
3
1
0
1
2
0
1
2
1
2
0
1
0
2
1
1
2
1
2
2
1
0
0
2
0
1
1
0
2
2
0
0
0
2
0
2
1
1
0
0
1
0
1
0
0
1
1
1
0
2
2
0
1
0
0
0
2
0
0
0
0
1
0
1
0
0
0
1
1
0
1
1
0
2
0
2
3
2
1
1
0
2
1
2
2
0
1
0
0
2
2
2
1
0
1
1
1
1
1
1
1
1
0
0
2
1
2
2
1
1
0
0
1
0
0
2
2
0
0
0
1
1
1
0
1
2
1
0
2
2
3
1
2
1
0
0
1
2
0
2
0
1
0
0
2
2
0
1
0
0
0
0
1
1
0
1
1
2
0
0
0
2
1
1
2
0
1
2
2
1
0
2
2
1
2
1
2
0
1
2
1
0
2
0
1
1
1
0
0
1
0
1
0
1
0
1
1
0
2
0
0
2
0
1
1
0
1
0
1
0
0
0
0
0
0
1
1
0
1
0
1
2
2
2
0
0
1
2
1
1
1
0
1
2
1
0
1
1
2
2
0
2
0
1
0
0
2
1
0
0
2
1
1
2
2
2
0
1
1
0
0
0
0
2
1
0
0
2
0
1
1
1
0
0
0
0
1
0
0
1
1
1
0
0
0
0
3
1
1
0
2
2
2
1
1
2
0
2
0
1
1
1
0
0
1
2
1
0
0
2
0
0
1
2
0
2
2
1
1
2
0
2
0
0
0
0
1
1
0
1
1
1
1
1
0
2
1
1
0
0
2
0
0
0
0
1
1
2
0
0
1
1
1
2
2
0
2
0
1
1
0
1
1
2
2
1
2
1
1
1
2
0
1
0
0
1
1
0
3
0
0
2
0
0
0
1
1
0
0
1
0
1
0
2
0
1
0
2
1
0
0
0
0
1
1
0
1
1
0
1
2
1
1
0
1
0
1
1
1
1
1
0
2
0
2
1
0
2
2
0
0
2
0
0
2
1
2
1
0
0
1
1
1
0
1
0
2
1
0
1
0
1
0
0
0
0
2
1
1
1
2
1
1
0
0
2
2
1
1
0
0
1
1
0
0
1
1
2
2
0
1
1
1
0
0
1
2
0
1
1
2
1
1
2
2
0
0
0
0
1
1
0
0
0
2
2
1
2
2
0
0
1
1
1
0
2
0
1
1
1
1
0
0
0
0
0
2
1
2
1
2
1
2
2
1
0
0
1
1
2
0
0
0
0
0
1
1
0
0
2
1
0
3
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
0
2
1
0
0
0
1
2
0
0
0
1
2
2
1
1
2
1
0
1
0
1
0
0
2
1
1
0
0
5
0
1
0
1
1
1
2
0
1
2
1
2
2
0
1
0
0
0
0
2
1
0
1
1
1
1
2
0
1
1
2
0
0
2
1
1
1
1
1
2
1
1
1
0
0
0
0
2
1
1
1
0
1
1
0
0
1
1
0
2
1
1
1
2
0
0
1
2
1
0
0
0
0
0
2
0
0
0
2
1
1
1
2
0
0
0
0
1
0
0
1
1
0
1
2
1
1
1
1
0
0
0
0
1
1
0
0
0
0
1
1
2
0
1
0
1
1
0
1
0
2
2
1
0
2
0
0
0
0
2
1
2
1
0
0
2
0
0
1
2
0
2
0
0
2
1
1
2
2
1
1
2
1
1
1
0
0
1
1
1
2
2
1
1
0
1
1
2
1
2
0
2
1
0
0
0
2
0
1
2
1
1
1
0
0
1
0
1
1
0
0
1
0
0
1
2
1
1
1
1
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
2
0
2
2
0
1
0
1
2
0
2
1
1
2
0
0
1
2
0
0
1
0
1
1
2
0
0
0
1
0
0
2
0
1
1
2
0
0
1
0
1
1
0
2
0
0
2
1
1
0
0
2
1
0
0
0
2
2
0
0
0
1
0
1
1
0
1
1
0
0
0
1
1
1
0
0
0
2
1
0
0
1
2
0
1
0
1
0
1
2
1
0
1
0
1
0
1
0
2
1
0
1
2
3
1
1
2
0
1
0
0
0
1
1
0
1
1
0
2
0
1
1
3
2
1
1
1
0
1
0
1
2
2
0
1
1
1
1
0
0
2
2
0
1
0
1
1
1
0
2
0
1
0
0
1
1
2
1
2
2
0
0
2
0
1
0
1
0
2
0
2
2
2
2
2
1
1
1
1
1
1
2
0
0
1
1
2
2
1
1
0
0
1
2
0
0
2
2
2
1
1
1
0
2
1
0
0
0
1
1
1
2
0
0
0
1
0
2
1
1
0
1
0
1
0
2
2
2
0
3
0
0
1
1
3
1
1
2
1
2
0
1
1
0
0
1
3
1
2
2
1
0
1
1
1
2
1
1
3
2
1
2
0
1
2
1
0
0
1
1
0
1
1
0
0
2
1
1
1
1
1
2
1
0
1
2
1
1
1
1
1
1
1
2
1
2
0
2
2
1
1
1
2
0
1
0
0
2
0
0
1
1
0
1
2
0
1
1
2
1
0
0
0
0
1
1
0
1
2
2
1
0
0
0
0
1
1
1
0
0
0
0
1
1
0
0
2
1
1
1
0
0
2
2
2
0
0
1
0
1
0
0
0
2
0
1
2
2
0
1
2
3
0
0
2
0
0
0
0
1
2
2
1
1
1
0
1
2
1
0
1
2
1
1
2
0
0
1
0
1
0
0
2
0
1
0
1
0
1
2
1
2
1
0
0
0
0
1
1
0
1
0
0
0
0
0
2
1
1
2
0
0
3
0
0
2
0
1
1
2
1
0
1
2
0
3
2
0
0
1
0
0
0
0
0
0
1
3
0
2
2
1
1
1
1
0
1
2
1
2
2
2
1
2
0
0
1
0
2
0
1
0
1
1
2
0
0
2
1
1
0
2
3
1
0
1
0
0
2
0
0
1
1
2
0
1
2
1
2
1
1
2
2
1
2
1
0
1
1
0
0
0
0
2
1
1
0
0
1
1
0
1
2
0
0
1
0
1
1
0
1
0
0
0
0
1
1
0
1
1
0
1
1
1
1
2
1
1
1
1
2
0
1
1
0
1
1
0
2
0
1
0
1
1
0
1
0
1
2
2
0
0
2
0
0
2
1
0
1
0
2
2
0
0
0
0
1
0
1
1
0
0
2
2
0
1
1
0
1
0
1
0
0
0
2
1
0
1
0
0
1
0
0
1
1
0
0
2
0
2
1
1
2
0
0
0
1
0
1
2
1
1
0
1
0
0
1
0
0
1
0
0
0
1
0
1
2
2
2
0
0
2
1
0
1
0
1
0
0
0
2
0
0
3
0
0
2
1
2
0
1
2
1
0
1
2
3
1
0
1
0
2
0
0
0
2
1
0
0
0
2
0
1
2
0
1
2
1
2
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
1
0
1
0
1
1
0
2
0
0
1
0
2
1
0
0
0
2
0
1
1
1
2
1
1
1
3
2
1
2
0
0
0
0
1
0
1
1
0
0
1
2
1
0
1
1
0
0
2
1
1
2
0
0
0
0
0
0
2
1
1
1
1
1
0
1
1
1
1
2
0
0
0
2
2
0
0
0
0
1
0
0
0
1
2
0
0
0
0
2
2
1
0
0
2
0
1
0
2
2
1
0
2
2
0
1
0
1
0
1
1
1
2
2
0
4
2
0
1
0
1
1
0
0
1
1
0
2
1
2
1
1
2
1
0
1
2
0
0
0
1
1
0
0
0
1
1
1
0
0
1
0
0
1
2
1
1
0
1
0
1
1
0
1
0
1
3
0
0
2
0
0
1
1
1
1
2
2
0
2
2
0
0
1
0
0
0
0
1
2
1
2
2
1
2
1
1
0
0
1
0
0
0
1
0
0
1
2
1
0
1
0
0
2
0
2
0
1
0
0
1
2
0
4
0
0
7
0
1
1
1
2
1
1
0
0
1
1
0
1
1
1
0
0
0
1
0
1
0
2
0
0
0
0
0
1
0
0
1
0
1
0
0
1
2
2
2
1
1
0
2
1
1
0
0
1
1
2
1
2
1
0
1
0
1
2
1
1
1
1
1
2
2
0
0
1
1
1
1
2
2
2
1
0
1
1
0
0
1
0
0
1
0
1
0
1
1
1
1
1
1
1
0
1
1
0
1
1
1
0
0
2
1
0
0
0
0
0
2
0
0
0
1
0
2
2
0
2
1
0
1
2
2
0
2
1
1
2
1
1
0
0
0
2
0
2
0
0
0
3
0
1
1
2
2
0
2
0
1
0
2
2
1
0
0
1
2
1
1
1
0
2
2
0
2
0
1
1
0
0
0
1
1
1
0
0
1
1
2
0
0
1
2
0
1
1
0
2
1
0
1
1
2
1
1
0
1
1
1
0
0
0
1
3
1
1
1
2
2
0
1
2
1
0
2
2
1
1
1
1
1
0
1
0
0
2
1
1
0
2
2
0
0
2
2
1
1
1
0
1
0
2
2
1
0
1
0
1
2
0
2
2
1
0
1
0
1
1
1
0
0
1
1
0
0
2
0
0
0
1
0
1
0
1
1
3
1
1
2
0
1
0
1
2
2
1
0
2
2
1
0
1
2
1
2
0
1
1
0
1
1
1
1
1
0
0
1
0
4
1
1
1
2
1
2
1
1
0
1
0
3
1
0
0
1
2
1
0
1
0
3
2
1
0
0
0
2
1
2
1
1
0
1
2
0
0
1
0
0
1
2
0
1
1
1
1
0
1
1
0
0
1
2
2
0
1
1
0
1
0
1
0
1
0
1
0
2
0
1
4
1
0
0
1
0
0
0
4
0
1
1
1
1
0
3
1
0
0
2
2
2
1
1
0
1
1
1
0
0
1
1
1
0
0
0
1
1
0
0
2
2
1
1
2
0
0
0
0
0
1
1
1
1
0
1
2
1
1
1
0
2
1
1
2
2
2
1
0
0
2
2
0
0
3
0
2
1
2
0
1
0
1
1
0
2
1
2
1
1
1
1
2
1
0
2
0
1
0
1
0
0
1
1
0
2
1
1
0
2
1
0
1
0
1
0
0
0
0
2
2
0
0
2
1
1
0
4
1
3
3
2
1
0
1
0
1
1
1
1
0
1
0
1
0
2
1
0
2
2
1
0
2
0
2
2
0
1
1
0
0
1
1
0
2
2
0
0
2
1
0
2
1
0
2
0
0
1
2
2
1
0
2
1
1
1
0
0
0
0
0
0
0
0
2
2
1
0
0
1
1
0
2
1
1
0
1
1
0
1
0
0
1
0
1
0
0
0
0
1
1
2
1
0
0
1
1
2
1
2
1
0
1
1
0
2
0
0
1
0
0
0
1
1
0
0
0
1
0
2
1
2
1
1
0
0
2
0
1
1
0
1
0
0
0
2
0
1
0
0
0
0
1
0
0
1
1
0
1
2
1
2
1
0
0
1
0
0
2
1
0
0
2
0
0
1
0
2
1
2
0
0
2
1
0
1
2
0
0
0
1
3
0
0
0
1
2
1
2
1
0
0
0
1
0
0
0
1
0
1
1
0
0
1
2
1
2
1
2
1
2
1
0
0
1
2
0
2
0
1
1
2
2
2
0
0
0
3
1
0
1
1
2
0
1
2
1
1
0
2
0
1
0
1
0
0
2
0
3
1
1
1
1
1
0
1
0
1
1
0
2
0
1
1
1
0
0
1
2
1
0
0
1
1
2
1
0
1
0
0
0
0
0
0
1
2
0
2
0
2
1
2
1
0
1
0
2
1
1
1
0
1
1
1
3
0
1
1
2
1
0
1
0
1
1
1
0
0
0
0
2
0
5
1
0
0
1
1
0
3
1
0
1
1
2
2
2
0
0
1
0
0
1
0
1
1
2
0
0
2
1
0
2
0
1
1
1
1
1
2
0
3
2
1
0
0
0
1
2
1
0
1
2
0
0
1
0
1
2
1
1
0
0
2
0
2
0
2
2
0
2
1
0
1
2
1
0
0
0
2
0
1
1
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
2
0
1
2
1
1
0
1
3
1
0
1
1
2
1
2
0
0
1
1
0
0
2
1
0
2
0
0
0
1
2
0
0
1
0
0
2
0
1
0
0
0
1
3
2
1
2
4
1
2
2
0
0
1
0
1
1
0
1
1
1
0
2
1
2
2
1
2
2
1
1
2
1
2
2
1
2
1
0
1
0
0
1
0
0
0
2
2
0
0
0
2
1
1
1
1
0
0
1
0
1
2
0
0
0
3
0
0
0
0
1
0
0
0
0
1
1
2
1
1
1
4
1
0
1
1
1
0
0
0
3
1
2
0
0
1
1
2
1
2
0
0
1
0
0
1
2
1
0
1
1
1
2
1
2
2
0
0
0
0
2
1
1
1
1
2
0
1
1
2
0
1
0
0
1
0
2
1
2
1
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
1
1
0
0
0
0
2
0
0
1
0
0
1
1
0
0
1
0
2
1
0
0
1
0
1
0
2
1
1
0
1
1
0
2
1
0
2
0
2
1
1
2
1
2
2
1
0
1
0
1
0
2
0
2
2
1
0
0
0
0
1
1
0
1
1
1
1
1
2
0
2
1
0
1
2
1
1
2
0
1
1
3
2
1
1
2
0
0
0
1
2
0
1
1
1
0
2
1
0
1
1
0
2
0
1
2
2
0
0
2
0
0
1
2
1
1
1
0
2
0
1
2
0
0
2
2
1
1
0
0
1
1
1
1
1
0
2
1
0
1
0
0
1
2
0
0
1
1
1
1
2
0
1
2
0
0
1
1
2
0
1
1
0
1
1
2
1
0
2
1
2
1
1
2
0
0
2
0
1
0
2
0
2
2
2
2
0
0
0
0
0
1
2
0
1
1
0
0
1
0
1
0
0
1
0
0
2
1
0
1
2
1
0
0
1
1
1
3
2
0
1
2
1
1
1
0
1
1
1
0
2
2
2
0
0
0
2
0
1
2
1
1
1
2
0
1
3
0
0
0
1
2
0
1
0
0
0
1
1
0
1
4
0
1
0
1
0
1
0
2
1
0
2
2
1
0
2
1
1
1
1
1
2
1
1
0
1
0
1
0
1
0
2
2
1
2
0
1
0
2
0
2
1
1
1
2
0
1
3
2
1
0
2
1
1
2
0
0
1
1
0
1
2
1
1
1
2
3
0
0
2
0
0
0
0
2
0
2
2
1
1
1
1
1
0
2
0
1
2
2
1
1
0
1
0
0
0
1
1
0
1
0
1
2
0
2
1
0
1
1
2
0
1
0
1
2
0
2
1
0
0
1
1
2
1
0
1
1
2
0
2
2
0
0
0
1
1
3
1
0
0
1
0
0
0
0
0
1
0
1
1
1
0
1
3
0
0
0
2
1
0
1
3
0
0
0
1
0
1
2
1
0
0
1
1
1
1
2
1
2
0
0
2
2
1
1
0
1
2
1
2
1
2
3
1
2
0
1
1
0
3
2
0
0
1
0
1
0
2
1
0
0
0
1
0
2
0
1
1
2
1
2
1
1
2
2
0
1
1
1
2
1
1
1
0
2
1
1
1
0
2
2
2
0
0
1
0
1
0
1
0
0
1
1
0
0
1
1
0
0
0
0
1
0
0
1
1
1
2
1
1
0
0
1
0
2
0
2
1
1
3
5
1
1
0
0
1
0
2
0
0
0
1
0
2
0
2
1
1
2
1
1
0
1
1
1
2
0
1
0
2
0
1
0
2
3
2
1
2
0
1
1
0
0
2
1
0
1
1
1
1
0
1
0
0
2
0
1
0
0
1
0
1
2
0
2
0
1
0
1
1
1
0
0
0
0
1
0
2
1
0
2
2
0
0
2
0
1
1
1
0
0
0
0
1
0
1
0
2
0
2
0
0
1
0
1
1
2
1
0
0
2
2
2
0
1
1
0
1
1
0
0
1
2
1
2
0
2
0
0
0
0
0
1
2
2
1
0
1
0
1
1
0
0
0
0
2
0
0
2
0
1
0
1
1
1
0
2
0
1
1
0
0
2
0
1
2
0
2
2
1
1
0
0
2
0
2
1
0
0
1
0
2
2
2
1
2
1
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
1
1
1
1
0
0
2
0
1
1
1
1
1
0
1
1
1
0
3
1
0
1
2
2
0
0
2
1
1
2
2
0
1
2
2
2
0
2
0
3
0
1
2
0
0
2
0
1
2
2
1
1
1
2
0
2
1
2
0
0
1
2
0
2
0
5
1
2
1
0
2
2
1
1
0
2
2
0
0
1
1
2
1
1
2
0
2
1
1
0
1
1
2
1
3
2
0
1
0
0
0
0
2
1
0
1
1
0
1
0
2
0
3
2
4
1
2
1
1
2
0
0
3
0
2
2
2
1
1
1
1
0
0
0
1
0
1
1
0
1
1
1
0
0
1
2
2
1
1
0
2
1
1
0
0
2
2
0
2
2
1
0
1
0
0
2
1
2
2
0
1
2
1
2
1
1
0
1
1
0
2
5
1
0
0
0
1
1
0
1
2
1
2
3
1
0
1
0
1
0
2
1
1
1
0
1
0
1
0
1
0
1
1
0
1
0
0
1
1
1
0
0
0
1
2
0
2
1
0
0
2
2
0
0
1
0
0
2
0
0
1
2
0
1
1
0
0
1
0
2
0
0
0
2
1
1
0
0
2
0
0
2
2
0
0
0
2
1
0
0
1
2
0
2
0
0
1
2
1
1
2
1
1
0
0
1
0
0
1
1
1
0
0
1
1
1
2
0
1
1
0
0
2
1
1
0
3
2
1
0
0
1
0
1
1
1
2
1
1
1
0
1
0
2
2
0
1
1
0
0
1
0
1
1
1
0
0
1
1
2
1
0
2
0
0
0
2
0
1
0
2
1
0
1
1
0
0
0
0
1
2
0
0
1
0
0
1
0
1
2
1
1
3
0
0
2
0
1
1
0
2
0
0
2
0
1
2
0
1
1
2
0
0
1
1
1
0
1
1
1
0
1
0
2
2
1
1
2
0
1
2
3
2
1
0
1
1
1
0
1
1
0
1
1
2
0
0
1
0
1
1
0
1
1
1
0
0
1
2
1
2
0
0
1
2
0
0
1
2
1
0
2
0
1
1
2
3
1
0
2
0
0
2
1
0
1
0
0
0
0
2
0
2
1
1
1
2
0
2
0
2
0
0
0
0
1
0
0
1
1
0
1
0
0
2
0
0
2
2
1
1
1
0
2
2
1
2
1
1
0
1
0
0
0
2
0
0
2
1
0
1
1
1
1
0
0
0
0
0
1
0
2
2
0
2
0
1
0
1
0
1
1
0
0
0
0
0
0
1
1
0
0
1
2
0
1
1
0
3
2
1
0
1
0
1
0
1
2
1
0
0
1
0
1
1
1
1
2
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
2
0
1
1
1
1
0
2
2
0
1
2
1
1
3
1
1
0
1
1
2
0
2
0
1
2
0
0
2
0
0
0
0
3
1
0
2
0
0
1
0
2
2
1
0
1
1
1
0
0
1
2
0
1
0
0
0
2
0
1
3
0
2
0
1
1
2
2
0
0
0
0
2
2
1
2
2
2
0
1
1
1
1
0
0
2
1
1
2
2
0
1
0
1
0
1
2
1
1
1
1
0
1
1
0
0
0
0
1
1
0
1
1
2
2
2
2
2
2
1
2
1
1
0
2
2
0
0
2
0
1
2
2
2
1
0
1
0
1
1
0
0
0
1
0
1
1
0
1
0
1
1
0
1
1
0
0
0
0
0
0
1
1
1
0
2
2
0
0
0
0
2
0
1
0
0
0
1
0
2
0
0
1
2
0
1
1
3
1
0
1
0
2
0
1
1
1
2
2
2
0
1
1
1
2
1
0
1
2
2
1
1
0
1
0
1
1
0
2
1
0
1
1
1
0
1
0
0
0
2
1
0
1
1
0
4
0
2
0
0
1
0
0
0
2
2
0
1
0
0
0
0
2
0
1
0
1
0
2
1
0
1
0
2
0
3
0
1
2
1
0
1
1
1
0
1
1
1
1
1
0
1
1
1
0
0
2
2
1
2
2
0
1
2
1
0
0
1
2
2
1
1
0
0
1
1
1
2
1
0
1
1
0
0
0
0
2
0
0
1
1
1
1
0
1
1
1
2
2
2
1
1
4
1
0
0
1
1
1
2
2
1
2
1
0
0
0
2
1
0
1
0
1
2
1
2
1
1
2
1
1
1
1
0
2
0
0
1
0
2
2
1
1
1
0
1
2
1
1
0
2
0
1
2
2
1
1
2
4
1
1
1
1
0
1
1
1
1
2
2
0
0
0
1
1
0
1
0
1
1
0
1
1
0
0
2
1
0
0
1
2
1
1
1
2
1
0
2
0
1
1
1
1
1
2
0
2
1
0
0
1
1
1
2
0
1
1
1
2
0
2
2
1
1
1
0
0
0
0
1
1
1
1
2
1
0
0
1
1
2
0
1
1
0
1
0
1
0
0
2
2
0
0
1
1
2
2
0
1
1
0
0
0
1
0
1
0
1
1
1
2
0
1
1
1
1
0
2
1
0
2
2
1
0
0
1
1
0
0
0
1
1
0
1
3
1
0
0
0
1
1
2
2
0
1
1
0
0
0
2
1
1
0
2
1
0
0
1
2
2
0
0
1
1
2
2
3
1
0
2
0
0
2
0
0
2
1
0
1
1
1
0
0
0
1
1
2
1
2
1
0
1
1
2
1
0
1
1
2
2
1
0
0
1
1
2
0
0
1
2
1
1
1
1
1
1
0
1
2
1
1
0
1
2
1
0
0
2
0
0
0
0
0
0
1
2
0
0
2
0
1
0
0
1
2
0
1
2
0
0
1
0
2
0
1
0
2
1
1
2
0
0
0
0
1
0
2
0
0
0
1
2
0
0
0
1
2
2
0
0
1
1
0
0
1
2
0
1
2
1
2
0
0
0
2
1
0
1
1
1
0
1
1
2
0
1
0
1
2
0
0
1
2
1
2
0
1
2
1
1
1
1
0
1
3
1
2
0
0
0
1
0
0
0
2
1
1
0
1
3
1
1
0
2
0
2
2
0
2
1
2
1
1
1
0
1
1
1
0
0
1
1
1
0
0
1
0
0
0
0
2
2
0
1
2
1
0
1
0
1
0
2
0
2
0
1
2
0
2
0
0
2
2
0
1
0
1
1
0
0
1
1
0
0
0
0
1
0
2
0
0
2
0
1
0
1
2
2
0
0
1
0
0
0
1
0
0
0
0
0
2
0
1
0
1
0
0
1
1
0
0
0
2
2
0
2
1
0
1
0
1
0
0
0
0
0
1
1
1
0
1
2
1
1
1
0
1
0
0
0
1
1
0
1
1
1
0
0
0
2
0
1
0
1
1
1
2
0
1
2
1
1
0
2
2
1
0
1
0
0
0
1
1
1
1
0
1
1
0
0
0
0
3
0
0
1
0
0
2
1
0
0
1
0
2
2
1
1
1
0
2
1
0
2
0
0
1
1
1
0
1
0
0
2
1
0
1
0
1
1
1
1
2
1
2
0
2
1
1
0
2
1
0
2
1
1
1
0
2
2
2
1
1
1
1
1
0
0
0
0
0
2
2
0
0
2
1
1
1
1
0
0
0
1
1
1
1
0
0
1
1
1
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
2
2
0
1
2
2
1
1
1
0
1
1
0
1
1
0
2
2
1
0
2
2
2
2
0
1
1
1
1
2
0
0
1
2
2
0
1
1
2
0
2
1
1
1
1
1
1
0
1
0
1
1
0
2
1
2
0
2
2
0
2
1
0
1
0
0
1
1
0
0
1
0
0
1
1
0
0
1
1
1
1
0
0
1
1
1
2
2
1
1
0
1
2
2
1
2
1
1
1
1
1
2
0
2
1
0
0
2
0
1
1
1
2
1
0
0
0
2
0
0
1
2
1
0
1
2
1
0
0
0
2
0
1
1
0
0
1
2
1
2
2
1
0
1
2
1
1
1
0
0
1
0
1
0
0
1
2
0
0
0
0
1
2
2
0
1
0
0
2
1
0
0
2
1
0
2
0
0
1
0
0
0
2
2
0
1
0
0
0
1
2
0
1
2
0
0
2
2
2
1
2
1
0
0
2
1
2
1
0
1
0
1
1
2
0
0
1
0
2
1
1
2
1
2
0
2
0
1
2
1
0
0
2
1
1
0
2
1
1
1
1
0
0
0
1
1
1
0
0
1
0
1
1
1
0
0
0
1
2
0
2
0
2
1
0
0
0
2
0
0
1
2
0
2
1
0
3
0
2
1
2
0
2
0
1
0
2
0
1
0
2
2
0
0
1
1
0
2
1
2
1
1
0
0
1
1
0
0
0
0
1
0
0
0
0
4
0
1
2
1
0
0
0
2
0
1
0
3
1
1
1
1
1
2
0
0
0
0
0
0
0
0
2
0
1
0
1
1
1
1
0
1
1
0
0
1
1
2
0
2
1
0
1
0
1
0
2
1
0
0
1
1
1
2
2
2
0
1
2
0
0
0
1
1
2
2
0
2
2
0
0
1
0
2
1
1
0
1
2
0
2
2
0
0
0
1
3
1
0
1
1
0
2
0
2
1
0
0
0
1
1
0
1
1
2
2
0
0
1
0
2
1
2
1
0
1
1
2
1
1
0
2
0
0
1
0
0
1
0
0
1
1
2
0
2
0
2
0
1
0
0
2
0
0
1
0
0
1
0
0
0
2
0
2
1
2
1
0
2
1
1
1
0
2
0
0
2
2
1
0
1
0
1
1
1
0
1
0
2
1
2
1
0
0
0
0
1
0
1
1
2
2
0
0
0
1
0
2
2
0
1
0
0
0
1
1
0
2
0
0
0
0
0
1
0
0
0
1
1
1
1
1
0
1
1
1
1
1
0
2
2
1
0
0
2
0
1
0
1
1
2
3
1
0
2
0
0
0
1
2
0
0
2
1
1
1
1
0
2
0
2
0
0
0
1
2
1
1
2
2
0
0
0
2
1
0
2
2
1
1
0
1
0
0
1
2
1
0
0
1
1
0
0
2
1
0
0
2
0
0
2
0
1
2
3
0
2
1
1
1
0
0
0
0
2
2
2
1
1
2
1
0
1
1
2
0
0
2
1
0
0
2
2
1
0
1
0
0
0
1
2
1
2
1
0
2
1
1
0
2
0
0
0
0
0
0
2
0
1
1
0
1
1
0
0
2
1
1
1
0
0
1
0
1
1
0
1
1
0
0
0
2
1
0
0
0
2
1
0
0
0
1
1
0
1
1
1
1
2
1
1
1
2
1
1
1
2
0
1
2
1
1
1
1
1
0
1
1
0
0
0
0
0
0
2
2
0
0
1
1
0
0
0
0
0
1
1
1
1
1
1
1
0
1
0
1
1
1
0
2
0
0
1
1
2
1
2
4
1
2
2
1
2
0
0
1
0
0
2
1
0
2
1
1
1
2
1
0
2
1
1
1
0
0
0
0
2
0
1
0
0
1
0
1
1
0
1
2
1
0
1
1
1
1
1
1
0
0
1
2
0
2
1
6
2
0
2
0
1
0
2
1
3
1
2
1
0
0
0
1
0
1
1
2
0
2
1
2
3
1
0
0
0
1
0
0
2
2
0
2
1
0
2
0
1
2
1
0
0
3
2
0
1
1
2
0
1
2
2
1
1
1
2
1
0
1
0
1
0
2
1
0
1
1
0
0
1
0
1
1
1
2
0
1
1
1
1
1
2
1
1
1
1
0
1
1
0
0
0
1
0
1
0
1
1
0
1
2
0
0
1
2
1
0
1
1
0
2
0
1
1
1
0
1
2
0
0
2
2
0
0
1
1
0
2
0
0
1
1
0
2
2
1
0
2
0
1
0
0
2
0
0
1
0
0
1
2
1
1
1
1
0
1
0
0
2
1
1
2
1
1
0
1
2
0
1
2
0
1
2
0
1
1
2
0
0
0
1
2
1
1
1
1
1
1
0
1
0
2
1
0
1
0
2
0
1
0
2
0
2
1
0
1
2
1
2
0
1
0
0
1
1
2
1
0
0
1
1
0
0
2
2
1
1
0
1
1
0
1
1
5
0
2
0
0
2
0
0
0
1
1
0
0
0
1
2
1
1
0
0
1
1
2
0
2
0
2
0
1
0
1
1
1
1
0
1
1
1
1
1
2
2
2
0
0
1
1
0
2
2
0
0
0
1
0
1
2
0
2
1
1
2
1
1
2
2
1
0
2
1
1
0
1
1
0
0
1
2
1
1
1
1
0
1
1
1
0
1
1
1
2
1
0
1
0
1
0
1
0
0
0
2
2
0
0
2
3
1
0
1
1
0
0
0
0
1
1
0
0
2
0
0
0
1
0
1
2
1
1
2
1
0
0
0
0
0
2
0
1
0
1
1
0
0
1
1
1
2
0
0
0
1
0
2
1
0
1
2
0
2
0
0
1
0
0
1
0
1
0
2
1
0
0
1
1
0
1
3
2
1
2
0
3
1
0
1
0
3
0
0
1
1
1
1
1
0
1
2
2
0
1
1
2
0
2
1
1
0
2
0
1
1
0
2
1
3
2
1
2
2
1
1
1
2
0
2
1
2
1
0
1
0
1
1
0
0
1
1
2
1
2
0
0
3
1
1
0
2
2
0
0
2
1
0
1
0
0
1
2
2
1
0
0
0
2
0
1
1
0
2
0
0
1
1
0
2
3
1
1
0
2
2
1
3
2
1
0
1
1
2
1
0
0
0
0
1
0
2
1
0
0
2
1
0
0
1
1
2
0
0
0
4
1
0
0
1
2
0
0
2
0
2
1
2
0
1
1
0
3
0
1
0
0
2
1
0
0
1
1
2
1
1
2
0
2
1
0
0
2
2
2
0
2
1
1
2
0
1
2
1
8
0
0
0
2
0
0
1
0
0
0
0
2
1
2
0
2
1
2
0
0
0
0
2
1
1
1
0
1
0
1
0
0
2
0
5
0
0
0
0
1
0
1
1
0
0
1
1
1
1
0
0
2
1
0
2
0
1
0
2
0
0
0
0
2
1
1
0
1
0
0
1
0
0
1
2
0
2
1
2
1
0
0
0
2
2
3
2
1
1
0
1
2
0
1
0
1
1
2
0
0
2
2
1
2
2
0
1
3
2
1
0
0
0
1
1
1
2
0
1
1
4
2
1
0
1
0
2
2
0
0
2
0
1
2
0
5
0
1
1
1
2
0
3
2
1
1
1
0
1
0
1
0
1
1
0
1
0
2
0
2
1
1
1
2
0
1
2
2
0
0
0
1
1
1
1
1
2
2
2
0
1
1
0
1
0
0
0
2
0
0
1
1
0
0
0
0
1
0
0
2
2
1
1
1
2
1
0
0
0
1
0
2
0
1
0
0
0
0
1
1
0
1
0
0
2
1
0
2
1
0
2
0
1
1
2
0
2
0
0
0
0
0
0
1
2
1
0
2
2
1
0
2
2
0
0
0
1
0
2
0
2
1
1
2
3
0
1
0
2
1
1
3
0
1
0
1
1
7
0
1
1
0
1
0
0
2
1
1
0
1
1
1
1
3
1
1
4
2
0
0
0
0
2
2
0
0
0
1
0
3
0
0
1
1
2
1
0
0
1
0
2
1
1
0
1
0
1
0
0
0
1
0
1
1
1
1
1
1
1
3
2
2
2
1
1
1
1
0
1
0
0
2
0
2
1
0
0
2
2
1
1
1
1
1
2
1
1
1
1
0
2
2
1
1
0
0
1
2
2
0
1
2
0
2
1
2
1
1
2
1
1
0
1
0
0
2
1
1
0
2
1
0
0
2
0
1
0
0
0
1
1
2
1
0
0
1
0
0
6
0
1
0
2
2
0
1
2
1
1
1
0
0
0
2
2
2
0
1
1
2
1
2
1
0
0
0
0
0
0
0
2
1
2
1
1
1
2
1
1
2
2
0
2
2
2
0
1
0
1
0
1
1
0
1
0
1
1
1
0
2
0
1
1
0
0
1
0
2
0
0
3
2
1
2
1
1
1
1
2
0
1
1
1
1
0
2
1
1
0
2
0
0
1
0
1
0
0
1
2
0
1
1
2
2
1
0
0
1
1
0
0
0
0
0
0
1
0
1
1
1
1
1
2
0
2
0
1
1
1
1
1
0
1
1
0
0
1
2
0
0
1
0
1
1
1
1
2
1
0
1
3
0
2
1
0
1
2
0
2
0
2
0
0
1
0
4
1
0
0
2
0
0
0
1
2
3
0
1
1
2
1
1
1
1
0
2
2
0
1
0
1
1
1
0
0
1
0
1
0
0
2
2
0
2
0
3
0
1
1
1
1
2
0
1
0
1
1
0
1
0
1
0
2
2
1
0
0
0
1
0
1
0
1
0
1
0
0
1
0
2
2
0
2
5
0
0
2
0
1
2
0
2
1
0
1
0
3
2
1
1
1
1
0
2
0
2
1
1
1
2
1
1
0
1
2
0
2
0
0
0
0
1
0
0
0
1
2
1
2
2
2
0
0
0
0
1
2
1
1
1
1
1
2
0
2
0
2
1
0
1
1
0
1
1
1
0
0
1
1
1
0
2
0
1
0
0
1
0
0
1
1
1
1
0
0
0
1
1
0
2
2
0
2
1
1
1
1
0
1
0
0
2
2
0
1
0
1
1
0
2
1
1
0
1
0
3
0
1
1
1
0
1
1
0
1
1
0
2
1
1
2
2
0
1
0
2
0
0
1
0
0
0
1
0
1
2
0
0
1
2
2
0
2
0
2
0
1
1
0
1
0
0
1
0
1
1
1
0
1
0
1
1
0
1
1
1
0
0
2
3
0
1
1
2
0
2
1
1
1
1
2
0
0
1
2
1
0
1
1
1
2
0
0
1
1
1
0
1
2
0
2
0
0
1
0
0
0
1
1
0
1
0
1
0
1
0
2
0
2
0
1
1
0
1
0
2
2
1
1
0
1
2
1
1
3
1
0
0
1
0
0
1
0
2
1
1
1
0
1
2
1
1
1
0
2
0
1
1
1
2
1
1
0
1
1
1
2
2
1
1
1
2
1
0
2
2
2
1
2
1
2
0
1
0
1
2
0
1
0
2
1
1
2
1
2
1
1
1
0
2
0
1
1
0
0
0
1
1
0
0
0
0
2
0
2
0
0
0
0
0
1
1
0
1
1
0
1
2
2
0
0
2
0
1
1
1
1
1
1
0
1
0
0
0
1
0
1
0
1
1
1
1
1
2
0
2
0
5
0
1
1
0
2
1
0
1
2
1
1
1
1
0
0
0
0
2
0
2
0
0
1
0
0
0
2
1
1
1
0
0
0
2
0
2
1
0
2
0
1
1
1
1
1
1
0
3
0
2
2
0
0
1
1
0
1
2
2
0
0
2
0
1
1
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
1
1
2
1
0
0
0
1
0
0
1
0
1
1
1
1
0
1
1
1
0
1
1
2
0
0
1
0
1
2
0
2
0
0
0
0
0
0
2
0
2
1
1
0
0
1
0
1
0
0
0
0
0
4
1
2
1
0
0
2
1
1
0
0
2
1
2
2
0
2
0
0
0
1
1
2
0
2
1
1
0
1
0
2
1
0
0
1
2
0
2
0
1
2
1
2
0
1
1
2
0
0
3
1
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
2
2
1
1
1
0
0
0
2
1
1
0
0
2
2
0
0
1
1
0
1
4
2
0
1
0
2
0
1
3
0
2
1
2
0
1
1
0
0
1
0
1
2
6
1
1
2
1
1
1
0
0
1
0
1
0
1
0
2
0
1
0
2
1
1
1
0
0
2
2
1
0
2
1
1
1
1
0
0
1
0
0
2
1
1
0
1
1
1
0
1
0
1
1
2
2
3
1
1
2
0
0
1
0
0
1
1
1
0
1
0
1
0
2
2
0
0
0
0
1
0
0
1
0
1
0
0
1
1
2
2
0
0
0
2
0
0
0
0
0
0
1
0
2
1
2
1
1
2
1
2
1
1
1
0
0
0
1
1
1
0
1
2
0
0
0
2
0
0
1
0
1
2
0
0
1
2
0
1
0
0
0
0
2
1
2
0
1
2
1
2
0
0
2
1
1
2
5
0
1
1
0
0
1
0
1
0
0
0
2
1
1
2
0
2
1
1
0
0
1
2
1
0
1
1
0
0
1
1
1
2
1
1
0
1
1
1
1
2
0
2
1
0
0
2
0
2
1
2
2
0
2
0
0
2
1
0
1
1
2
2
1
1
0
1
0
1
1
1
1
2
2
0
1
0
0
0
0
1
1
0
0
2
0
0
0
1
1
0
0
0
1
0
2
1
1
1
0
1
1
1
0
2
0
1
1
1
1
0
1
1
0
1
0
0
0
2
0
1
1
1
1
2
1
0
1
1
0
1
1
0
2
1
1
0
0
0
0
1
0
0
0
0
1
0
0
2
1
2
1
0
0
0
0
0
0
0
0
2
1
0
0
2
1
1
2
0
0
0
1
1
0
1
1
1
0
2
2
1
0
1
0
2
1
2
0
1
0
0
1
1
1
0
0
0
2
0
1
0
0
0
0
2
0
1
1
1
0
1
0
0
0
1
0
0
2
0
0
1
2
0
0
0
2
0
2
1
0
1
1
0
2
0
0
1
0
1
0
1
0
2
1
1
0
0
1
1
2
2
1
1
4
1
1
2
0
0
0
0
0
0
1
0
0
1
1
0
1
0
1
0
0
1
0
1
0
1
1
2
1
0
1
0
2
0
0
1
0
1
0
2
0
2
0
2
0
1
0
0
2
1
1
2
0
1
1
0
2
0
2
1
0
0
0
0
0
1
1
0
1
1
1
0
1
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
1
2
1
1
0
0
2
1
1
1
1
0
0
0
1
2
2
0
0
1
0
2
2
2
0
1
2
0
2
0
0
0
0
1
1
0
0
1
1
1
0
1
0
1
0
1
2
0
0
1
2
0
1
1
0
1
0
1
0
0
1
0
0
2
2
1
2
4
1
1
2
1
0
0
1
1
0
0
0
1
1
0
2
1
0
1
2
2
1
0
1
2
1
1
2
1
0
1
1
2
1
0
2
1
0
1
0
1
2
0
1
1
2
0
1
0
1
0
0
2
2
1
2
0
2
2
1
1
2
1
2
2
0
2
0
0
0
2
2
2
1
2
0
0
2
2
0
1
0
0
0
0
1
0
1
1
1
1
0
0
0
2
1
0
1
1
0
1
0
1
1
0
0
2
1
2
1
0
1
0
1
0
0
2
0
2
2
0
2
1
2
0
0
2
2
0
0
0
0
1
1
1
1
2
2
2
1
1
0
0
1
0
1
0
0
1
1
1
2
1
1
1
1
0
1
0
2
0
2
1
0
1
0
1
0
2
0
0
4
0
0
2
2
2
1
1
2
1
2
0
0
1
0
0
2
1
1
0
0
1
0
2
1
0
0
0
1
0
1
0
1
1
0
2
1
1
0
2
1
0
0
0
1
0
2
1
0
1
0
1
1
0
1
0
1
1
1
0
0
2
1
0
0
2
0
1
2
1
1
0
1
3
2
2
2
0
1
2
0
2
1
2
1
0
1
0
0
2
2
2
0
0
1
0
1
0
1
2
1
0
1
1
3
0
2
2
1
0
0
0
2
1
2
2
2
1
0
0
2
2
0
2
1
1
0
0
0
0
1
0
1
3
2
2
1
0
0
1
1
0
0
1
0
1
2
2
1
0
1
1
0
0
0
0
0
2
2
1
0
2
2
1
1
0
0
1
1
1
1
2
1
1
1
1
0
0
2
0
1
2
0
0
0
0
2
0
0
1
0
1
0
1
0
2
1
1
1
0
0
1
0
3
2
1
0
1
0
2
1
2
2
1
2
1
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
3
2
1
0
0
1
1
1
1
0
2
1
0
1
0
0
1
0
1
0
1
0
1
0
1
2
1
0
0
1
1
1
0
0
0
0
1
2
0
1
1
1
0
2
2
3
2
1
1
0
2
0
1
0
1
1
0
0
1
1
2
0
0
0
2
1
0
2
1
0
2
0
0
1
2
0
2
1
2
0
2
2
1
1
0
1
2
1
2
2
2
0
1
0
1
1
4
1
0
1
0
2
1
0
1
0
2
2
2
1
0
0
2
1
1
1
1
0
0
1
2
1
1
1
0
0
1
0
0
0
0
0
1
0
1
1
0
0
1
1
1
0
0
1
1
1
2
1
1
2
1
2
2
1
1
0
1
1
1
0
2
0
2
0
0
0
1
0
1
0
0
0
0
1
2
1
1
0
1
2
1
1
1
1
0
0
0
1
1
1
1
2
1
1
2
1
1
2
1
2
0
0
1
1
0
1
1
1
2
2
0
2
1
2
0
0
0
0
1
0
1
1
0
0
0
0
2
1
0
1
1
1
2
1
0
1
1
0
1
1
2
0
0
2
0
0
0
1
0
2
0
0
0
0
2
0
0
1
2
1
0
1
0
1
0
0
1
1
0
1
0
0
1
0
0
3
1
0
2
1
0
2
1
0
1
0
1
1
1
2
0
0
0
1
1
3
1
1
1
0
1
1
2
1
0
1
1
0
1
1
0
1
1
0
0
0
2
2
0
1
0
1
0
1
0
1
0
0
1
1
1
0
1
2
2
1
0
2
1
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
1
1
0
2
1
1
2
0
2
1
2
0
1
1
1
0
1
0
0
2
1
4
0
1
1
0
1
1
0
2
1
1
2
0
0
2
1
2
2
1
1
0
1
2
1
2
1
2
0
0
1
1
0
1
2
1
0
1
0
1
1
2
0
0
1
1
0
1
0
1
2
1
1
0
0
0
0
0
0
2
1
1
1
0
1
0
1
2
2
1
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
2
1
0
0
0
0
1
0
1
2
1
0
0
0
2
1
0
1
2
0
1
0
0
0
1
1
3
1
1
1
1
3
1
0
1
1
1
0
2
1
1
1
1
0
1
0
0
1
1
1
0
0
0
0
0
0
0
1
2
0
1
1
1
0
2
0
2
1
2
2
0
2
0
0
0
0
1
1
1
0
1
1
2
1
1
2
0
1
0
0
0
1
0
0
1
1
0
1
2
2
2
1
1
0
1
2
2
1
0
0
0
0
3
2
1
0
1
2
1
0
3
1
0
1
2
2
0
0
1
0
1
1
0
0
3
0
2
0
1
1
0
2
0
0
0
0
1
1
2
1
0
0
0
0
1
0
0
1
1
1
1
1
1
1
3
2
2
0
0
1
0
0
1
0
1
0
2
2
2
0
1
1
1
1
1
0
0
2
0
0
1
2
0
1
0
0
1
0
1
0
3
1
2
2
1
4
0
1
1
0
1
0
1
1
1
0
0
0
2
2
0
0
2
0
1
2
1
2
1
0
0
1
1
1
1
0
0
1
0
0
0
1
2
0
2
2
0
0
2
0
1
2
3
1
0
1
0
2
1
0
0
1
1
0
1
2
0
1
1
0
1
0
0
2
1
1
1
1
1
1
0
0
0
1
0
0
0
0
2
0
1
0
1
2
0
1
0
2
2
0
2
2
1
2
2
0
3
0
2
1
2
2
1
0
2
1
0
0
2
1
0
0
1
1
1
0
1
1
2
0
1
2
1
0
1
0
1
1
0
1
1
1
0
2
1
0
1
2
1
0
1
2
1
2
1
0
2
1
0
1
0
0
0
1
0
1
0
0
1
1
2
2
0
0
1
0
2
0
1
1
2
1
1
1
0
0
0
2
1
0
1
2
1
1
1
1
1
1
0
2
1
2
0
0
1
2
2
2
0
0
2
0
0
1
1
4
0
1
0
0
1
1
1
1
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
1
1
0
2
1
1
1
1
0
2
0
0
1
0
1
1
0
0
0
1
2
0
1
0
1
1
0
1
0
0
1
1
1
0
2
1
2
0
0
0
2
1
2
0
1
0
1
0
1
1
0
2
1
1
0
3
2
1
1
0
2
1
0
0
2
0
1
2
2
2
0
1
1
2
3
1
0
1
0
1
0
2
2
2
1
1
2
0
1
2
0
0
0
2
0
0
0
1
1
2
0
1
1
1
2
2
0
4
0
1
0
1
0
0
0
0
1
0
1
0
0
1
0
1
0
0
1
0
2
0
2
2
1
0
1
2
2
0
1
1
1
0
0
1
1
0
1
0
1
2
2
2
1
0
2
1
1
1
1
0
1
0
1
1
2
0
1
1
1
1
0
1
0
0
1
1
0
0
2
1
1
1
1
0
1
2
2
2
2
2
1
0
0
0
1
2
0
2
1
0
1
1
2
0
2
1
1
1
0
0
0
0
1
1
1
0
2
1
0
0
1
1
0
1
0
2
1
1
2
1
1
1
2
0
1
1
0
1
0
0
0
0
1
0
0
3
0
0
4
1
2
0
0
0
0
2
1
1
0
2
1
1
1
0
1
2
3
0
0
0
0
1
1
1
1
1
1
0
1
0
1
1
2
2
1
1
0
1
1
1
1
2
0
0
1
2
1
0
1
1
0
2
2
0
1
1
0
0
1
2
1
1
0
1
0
0
1
1
1
0
0
0
0
2
0
1
0
3
1
2
0
0
2
0
1
2
1
2
0
2
2
1
0
1
2
1
0
2
2
0
1
1
0
1
1
2
0
0
2
2
2
1
0
0
1
0
2
1
2
0
0
0
2
0
1
2
1
1
1
2
0
0
1
3
2
0
1
0
2
0
2
1
1
1
1
0
1
0
1
0
1
0
0
0
2
0
0
2
1
1
1
2
1
0
0
2
1
2
0
0
1
2
1
0
0
1
0
2
0
0
0
0
0
1
2
1
0
0
0
0
0
0
1
1
0
0
1
2
0
2
1
2
1
1
1
1
1
0
0
0
2
1
1
0
1
2
0
0
1
2
1
1
2
2
1
2
1
0
1
0
2
1
1
0
1
1
2
1
0
0
0
1
1
2
0
1
2
2
0
1
0
0
2
2
1
0
1
1
1
2
1
0
0
0
1
2
0
1
1
0
0
1
1
0
1
0
1
1
0
1
0
0
0
1
0
0
1
1
0
1
1
0
0
0
0
1
1
0
0
0
1
1
1
1
1
1
0
1
1
1
1
1
0
0
0
0
3
1
1
2
0
0
1
2
1
2
1
1
1
2
1
1
1
1
0
0
1
1
0
2
2
2
0
1
0
2
2
1
0
1
0
0
0
2
0
2
0
0
0
0
0
2
0
1
1
2
1
1
1
1
1
0
0
0
1
1
3
1
1
2
0
1
1
2
1
0
1
1
2
1
0
1
1
0
1
0
0
2
1
2
1
0
0
0
1
0
2
0
2
1
0
1
0
0
2
1
0
0
6
2
1
0
2
0
1
2
2
0
2
1
1
0
1
0
2
0
0
0
1
1
0
1
1
1
1
0
0
0
1
0
0
2
1
5
0
1
1
0
1
0
0
0
1
0
1
2
0
0
0
0
1
0
0
1
2
1
2
2
1
2
0
1
0
0
1
1
1
1
0
0
0
0
0
1
1
0
1
1
1
0
0
0
3
2
0
1
3
2
0
1
0
0
1
1
2
1
1
0
1
1
0
1
0
1
2
1
1
1
2
2
3
0
1
0
1
1
1
1
1
1
1
1
0
1
0
1
1
0
1
0
0
2
0
2
0
2
0
2
1
1
0
0
1
0
0
2
0
0
1
0
0
0
1
1
1
0
1
0
0
0
0
1
0
2
1
0
1
2
1
1
0
0
1
0
2
1
2
0
1
1
0
1
0
2
1
1
0
0
0
1
1
2
2
0
0
2
0
1
1
1
0
2
1
1
2
0
1
0
2
0
0
2
0
1
0
2
0
1
1
0
2
1
0
1
2
1
2
0
1
2
1
1
2
2
2
2
0
1
1
2
3
0
0
2
0
2
1
0
0
2
0
0
0
1
1
0
2
2
2
0
0
0
1
1
2
0
0
1
0
0
0
1
1
1
0
0
1
0
0
0
1
1
0
1
0
1
1
0
1
0
0
0
2
0
0
0
0
0
1
1
2
0
0
0
1
1
2
0
1
1
0
0
1
1
1
0
0
0
1
0
0
2
0
3
1
0
2
1
0
0
0
2
1
1
1
1
2
0
0
0
2
0
1
1
0
1
1
2
1
0
1
1
0
1
0
1
0
1
1
2
0
1
0
2
0
2
0
0
2
0
1
1
1
0
1
0
0
2
0
0
0
0
2
1
1
2
2
0
1
2
0
0
1
1
2
0
0
0
0
1
0
2
0
1
1
1
0
1
1
2
1
2
1
1
0
0
2
2
0
2
2
1
1
0
0
1
2
1
1
0
1
1
0
2
0
0
1
1
0
1
2
1
0
0
1
0
1
1
0
0
4
0
1
0
1
1
0
2
0
0
0
0
2
0
2
2
2
0
1
2
0
1
1
0
1
1
0
1
1
1
1
2
2
0
0
1
2
0
2
2
2
3
2
1
2
0
2
1
0
0
1
0
1
1
1
2
0
0
2
0
2
0
0
1
0
2
0
0
1
0
0
0
2
0
1
3
1
0
0
1
0
1
2
0
0
1
1
2
0
1
0
1
2
0
1
2
1
2
0
0
2
2
0
1
1
2
0
0
0
2
1
0
1
0
1
1
1
0
1
0
1
2
1
0
2
1
1
1
1
1
2
1
2
1
3
0
0
2
1
1
2
1
1
1
0
0
0
1
0
1
1
1
0
0
1
0
1
1
1
0
1
0
1
1
2
2
0
1
2
0
1
0
0
2
2
0
1
1
2
0
1
0
2
0
0
2
1
1
0
0
1
1
1
0
1
1
0
1
0
1
1
1
1
2
0
1
0
1
0
1
2
0
1
1
2
0
1
1
0
2
1
1
1
2
0
0
0
0
0
1
1
2
1
3
0
1
0
2
2
2
0
2
1
0
0
1
2
1
1
1
1
2
0
1
0
1
1
1
1
1
1
1
0
0
0
0
1
2
1
0
0
0
0
2
2
4
1
1
2
0
1
1
2
1
1
1
1
1
1
0
1
1
0
0
1
1
0
0
0
1
1
0
2
2
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
1
2
2
0
1
0
2
0
1
1
0
2
1
1
1
1
1
1
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
1
2
1
1
1
0
0
0
0
2
2
4
0
2
0
2
0
2
6
0
2
0
2
0
1
0
2
0
1
0
0
1
0
2
0
1
1
0
0
1
0
1
0
2
1
1
1
2
1
0
1
0
1
1
0
0
1
1
1
0
1
1
1
1
1
0
3
0
1
4
2
0
1
0
0
0
1
2
0
1
0
2
0
1
2
2
2
1
0
1
1
1
0
2
0
1
1
0
0
1
0
2
0
1
2
1
0
0
2
0
2
1
1
0
0
1
1
0
1
1
1
2
0
0
1
1
1
0
1
0
1
0
0
3
0
1
0
0
0
1
0
1
1
2
1
0
0
1
2
0
0
0
1
1
1
0
0
0
1
2
1
2
1
1
2
0
0
2
2
0
0
0
0
1
10
1
1
1
0
0
1
1
1
1
2
1
1
0
0
1
2
2
0
1
0
0
1
1
0
1
1
0
2
2
1
2
0
0
0
2
0
1
1
0
2
0
1
0
1
2
1
1
0
1
1
0
0
2
2
0
0
0
1
0
2
1
0
0
0
1
1
0
0
0
2
1
2
1
0
0
1
1
1
0
0
2
1
1
1
0
1
0
1
0
2
0
0
0
0
2
0
1
0
2
1
0
1
0
1
1
2
2
0
2
1
2
2
0
1
1
1
1
1
1
0
1
2
1
1
0
2
1
1
0
0
1
0
0
0
1
1
0
1
0
2
0
0
1
1
1
2
1
1
2
0
1
2
2
4
2
2
0
1
1
1
0
2
1
0
0
3
1
0
0
0
0
0
1
1
3
0
0
1
0
1
2
1
0
1
1
1
1
1
0
1
2
1
0
1
0
3
0
0
1
0
0
1
1
2
1
1
1
1
0
1
2
0
1
0
1
1
2
1
1
0
1
0
1
1
0
1
2
2
2
0
2
0
2
0
0
2
2
1
1
1
0
0
1
1
0
1
2
2
2
2
1
2
0
2
0
1
0
0
1
1
1
1
1
1
1
1
1
0
1
1
0
2
0
1
1
0
1
0
1
2
2
1
0
1
2
1
0
1
0
2
0
1
0
2
1
0
0
1
0
1
2
0
1
3
0
0
3
0
2
1
2
0
1
1
1
1
0
1
2
1
0
0
2
1
1
0
2
1
1
1
1
0
0
1
2
1
1
0
1
0
1
2
0
0
0
1
0
2
1
0
1
2
1
0
0
1
0
2
1
1
0
1
0
0
1
0
1
1
1
2
0
0
1
0
2
1
2
1
0
1
1
1
0
1
2
1
1
0
2
2
0
1
1
1
1
1
2
0
7
0
0
0
1
0
1
0
1
0
0
0
1
1
5
0
1
1
1
0
0
1
0
0
1
1
0
0
2
1
0
2
1
0
2
1
0
2
0
0
2
1
1
1
1
0
2
0
0
0
1
2
1
2
1
0
1
1
0
0
2
0
2
0
2
1
0
3
0
2
1
2
0
1
0
0
2
1
0
2
0
0
1
1
0
2
0
1
1
0
0
0
0
2
1
2
1
1
1
4
2
1
1
1
0
2
1
0
0
1
2
0
1
2
3
2
2
1
1
0
0
0
0
2
1
1
0
1
0
1
0
0
2
0
1
3
1
2
0
1
0
0
0
1
1
0
0
0
2
1
1
2
0
2
0
0
1
0
0
2
0
0
1
0
2
1
1
0
1
2
2
1
1
2
2
1
1
0
2
0
1
0
0
0
1
0
2
0
0
1
2
2
0
2
1
0
1
1
1
0
1
1
0
2
3
0
2
0
0
1
2
2
2
1
1
0
1
1
1
2
1
1
1
2
2
1
0
2
0
1
1
1
1
2
1
0
2
1
1
0
2
0
1
0
0
2
2
1
0
2
1
2
0
0
0
0
1
0
0
2
2
2
1
2
2
0
0
0
0
1
0
0
0
0
0
0
1
2
3
0
1
1
1
2
1
1
1
0
0
0
0
2
2
2
0
1
2
0
1
0
0
1
0
0
0
0
2
0
2
1
0
1
0
1
0
1
2
2
0
1
1
0
2
2
1
0
1
1
0
1
1
1
1
0
0
1
0
0
1
2
1
1
0
1
0
0
2
1
1
2
2
1
1
1
1
0
1
0
0
1
2
1
2
2
1
0
1
1
2
0
0
1
0
0
1
2
1
1
0
2
2
0
1
5
2
1
0
0
1
1
0
0
1
0
1
2
1
0
0
2
0
0
2
1
0
1
1
1
2
0
2
2
1
0
1
0
0
2
1
0
1
0
0
0
0
1
1
0
1
1
2
1
0
1
1
2
1
1
2
1
2
0
0
1
2
0
2
2
2
1
1
1
0
1
0
1
1
2
0
1
1
0
0
1
0
1
7
1
1
0
2
0
1
1
0
1
1
1
0
1
0
0
1
0
1
2
1
2
0
1
0
0
0
2
1
2
2
1
1
2
1
0
1
2
1
2
1
0
0
0
0
0
1
0
1
0
1
2
1
1
0
1
0
1
0
1
0
1
1
2
2
2
1
0
2
2
1
0
1
1
1
0
0
1
0
2
0
1
0
1
1
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
2
1
2
1
0
0
1
0
1
0
2
2
2
1
0
1
1
0
3
1
1
0
1
1
0
2
0
1
1
2
0
1
1
1
0
2
0
1
1
0
0
0
0
0
0
1
2
2
2
0
1
0
2
2
0
1
1
1
1
0
0
0
0
0
0
1
0
1
1
2
0
1
1
0
2
2
1
0
1
1
2
2
1
0
0
2
2
1
1
0
2
2
0
0
1
2
0
1
0
1
1
2
1
1
2
2
1
1
2
2
1
1
1
2
2
2
1
0
2
2
0
0
2
0
0
1
2
2
2
1
0
2
2
0
2
2
2
1
2
0
2
0
1
2
1
2
0
1
1
1
0
2
0
0
1
2
1
2
0
1
1
0
3
1
2
0
0
2
0
2
0
1
0
1
1
1
1
3
0
1
0
0
0
1
1
0
4
1
2
0
0
1
0
2
0
0
0
2
1
0
1
1
1
1
1
2
1
1
1
0
2
2
1
2
1
0
1
2
0
1
1
1
1
1
1
1
0
0
2
2
1
1
0
1
1
2
1
1
1
0
0
0
2
1
1
0
1
2
0
1
1
1
4
1
1
1
0
1
0
1
0
2
1
2
1
1
0
1
1
1
1
1
0
0
0
1
0
2
1
1
1
2
1
1
2
1
0
0
2
0
1
1
0
0
0
2
0
0
0
2
0
0
1
1
1
2
0
0
0
0
1
1
0
0
1
1
1
1
1
2
0
1
0
2
2
1
2
0
2
1
0
0
0
1
0
2
2
0
0
1
0
0
0
1
0
1
1
0
1
0
2
0
0
1
0
0
1
2
1
2
2
1
1
0
2
0
0
0
1
1
0
0
0
0
1
0
1
0
0
1
1
0
1
2
1
3
2
1
1
1
1
1
2
0
2
0
0
1
2
0
0
2
1
1
0
0
1
0
1
1
2
0
1
0
0
1
1
2
2
3
0
1
1
2
0
2
0
0
0
1
1
0
0
1
1
1
1
0
0
2
0
2
1
0
3
2
1
0
2
1
0
1
2
0
1
0
3
1
1
1
1
0
0
1
0
1
2
1
1
0
0
5
1
0
1
0
2
1
2
1
1
0
2
1
1
0
1
1
0
1
0
1
0
1
2
2
3
1
2
2
1
1
2
1
1
1
0
1
1
2
2
6
0
2
2
0
2
2
1
2
0
0
1
0
1
0
1
1
0
2
2
1
2
0
0
1
1
2
2
0
0
0
2
1
3
0
2
1
0
1
1
1
2
0
1
1
1
1
0
1
0
0
2
0
0
2
1
2
1
0
1
1
2
1
1
1
1
1
0
1
0
1
1
0
1
0
1
1
0
1
1
0
1
0
0
0
0
0
1
0
1
0
1
0
0
1
1
1
0
0
1
0
1
2
1
1
2
0
1
1
1
1
0
1
1
0
0
1
0
0
1
2
2
0
2
0
0
1
1
1
1
1
1
0
0
1
1
1
1
0
0
1
0
0
0
0
0
2
0
0
1
1
0
1
0
2
1
0
2
0
0
1
0
1
1
2
0
1
1
2
0
1
1
0
1
0
0
0
0
1
1
2
1
0
0
0
1
3
1
0
1
1
1
2
1
0
2
1
1
2
0
0
2
1
2
2
0
2
0
2
1
0
0
2
0
0
1
0
1
0
1
0
0
1
2
1
1
0
0
2
1
2
1
1
0
1
1
2
2
0
2
2
2
1
1
1
0
2
1
1
1
1
0
1
1
0
1
1
0
0
2
1
1
0
1
0
1
0
0
0
0
1
0
1
1
0
0
2
0
1
0
0
2
0
1
0
1
1
1
1
0
1
0
2
0
2
1
2
0
2
0
5
1
0
3
2
1
2
0
0
1
0
2
0
2
1
1
0
1
1
1
1
1
0
0
1
1
3
0
2
1
0
0
2
1
1
1
0
0
2
0
0
1
1
2
1
0
2
1
1
1
0
0
0
0
0
0
1
0
0
0
1
2
1
1
0
2
0
2
2
1
0
0
2
0
1
0
1
1
1
1
3
1
1
3
1
2
3
1
1
1
0
0
1
0
1
0
0
1
2
0
1
0
1
0
4
1
0
0
1
2
1
0
0
2
0
1
0
0
1
2
0
2
1
0
2
1
1
0
0
6
1
1
1
3
0
1
0
0
0
0
0
2
2
1
2
1
1
0
0
0
0
0
0
2
1
0
2
0
1
2
1
1
1
1
0
0
2
2
0
1
1
0
1
0
2
0
0
1
2
0
2
2
0
1
0
0
2
0
3
2
0
0
0
2
2
0
1
0
1
0
1
0
2
0
0
0
0
3
0
2
0
0
2
0
2
1
1
0
1
0
0
2
2
1
1
1
1
0
1
1
1
1
0
1
2
0
0
0
2
1
1
2
2
2
0
0
1
2
2
2
1
1
1
0
1
1
2
0
2
0
0
1
0
2
0
2
1
1
0
1
1
0
1
0
0
2
0
1
0
1
2
1
2
1
2
0
1
2
2
2
0
0
0
2
1
1
1
0
1
1
1
2
2
1
0
2
0
0
1
2
0
1
1
0
0
1
1
2
0
2
1
1
1
1
2
1
0
1
0
0
1
0
1
0
1
2
1
1
0
1
0
0
2
1
0
1
1
1
0
1
1
0
0
1
0
2
2
0
1
1
0
1
0
3
2
0
1
1
0
1
2
1
0
0
1
2
2
1
0
2
2
0
2
1
0
0
0
0
1
2
0
0
2
0
1
1
0
0
1
0
0
0
0
0
1
2
1
0
1
2
1
1
1
2
0
1
1
2
0
0
0
1
0
2
2
0
0
1
0
1
0
0
0
1
1
1
0
2
1
0
1
0
1
1
0
0
0
1
1
1
0
1
0
1
0
1
1
0
1
2
2
1
1
2
1
0
2
0
0
1
2
0
1
1
1
0
1
0
1
1
2
0
1
0
1
0
1
1
1
2
0
1
1
1
0
1
0
1
1
1
2
2
0
2
1
2
0
1
1
1
0
1
0
0
1
0
1
0
0
0
1
2
1
1
0
0
1
1
0
0
0
1
2
1
1
1
1
1
2
1
1
0
2
0
1
1
1
1
1
0
0
1
0
0
2
4
1
0
1
1
0
1
1
0
0
1
0
2
1
1
1
1
0
0
0
0
1
1
0
1
1
1
1
2
0
0
0
1
1
0
0
0
2
0
1
1
0
1
2
1
0
1
0
2
1
1
0
0
0
2
0
2
2
0
2
0
2
1
3
1
1
2
1
1
1
1
0
0
0
0
0
1
0
0
2
2
0
0
0
1
1
0
0
0
3
1
2
1
1
2
1
0
1
2
0
1
1
3
2
0
0
1
1
1
1
0
1
1
0
0
0
1
2
0
1
1
0
2
1
1
2
1
1
0
1
1
1
1
1
1
1
1
2
2
0
0
1
0
0
1
2
0
1
1
0
0
0
0
1
0
1
2
1
2
0
0
0
2
0
1
3
2
2
0
1
0
0
0
0
0
0
0
1
0
0
2
0
1
2
1
0
1
2
1
0
2
2
1
2
2
0
1
0
1
1
0
1
1
0
1
1
1
1
0
2
2
2
1
0
0
0
0
1
1
0
1
1
2
0
1
1
1
1
2
1
3
0
2
0
0
0
0
2
0
0
2
1
0
1
1
2
1
0
2
2
1
1
2
1
0
1
2
1
2
2
1
1
1
2
1
2
1
0
0
2
0
1
0
1
0
1
1
2
0
1
1
0
1
1
0
1
1
2
0
1
1
0
0
2
1
0
1
0
2
1
1
2
1
2
2
0
1
2
1
4
1
0
2
1
2
1
1
2
0
0
1
2
0
1
1
0
3
2
1
1
2
1
0
2
0
1
0
0
1
0
0
1
1
2
0
2
0
0
1
1
1
3
1
0
0
1
2
2
2
0
2
0
0
2
0
2
0
0
0
1
2
0
2
1
1
0
2
2
2
1
2
2
0
0
0
1
0
1
1
1
0
0
0
1
0
1
1
0
0
1
1
0
1
1
0
2
0
1
0
1
1
2
0
2
1
1
1
1
2
0
2
1
1
2
1
0
2
0
0
0
0
0
1
1
0
0
0
0
1
1
1
0
1
1
1
1
1
0
1
0
1
0
1
1
0
2
0
1
2
0
0
2
1
0
0
1
0
0
2
1
1
1
1
1
1
0
1
1
0
1
0
1
0
1
1
0
1
1
1
2
1
1
1
0
0
0
2
1
0
1
0
2
0
0
1
1
0
1
0
1
0
0
0
1
1
3
0
1
0
1
1
1
1
1
0
1
5
0
2
1
0
1
1
1
0
3
0
1
0
1
0
1
0
3
2
0
2
1
0
1
2
0
0
0
1
0
1
2
1
1
1
2
1
2
2
0
0
0
0
0
0
1
0
1
0
1
1
1
0
0
1
2
0
0
1
1
1
1
1
0
0
1
1
1
2
2
1
1
1
0
4
0
2
1
0
0
2
1
2
1
1
0
2
1
2
2
1
2
0
1
2
0
0
2
1
1
1
0
1
2
1
1
0
1
2
0
0
0
1
1
0
2
1
0
0
0
1
0
0
0
2
0
1
0
1
1
1
1
2
0
1
2
2
3
3
0
1
1
0
0
1
2
1
0
2
1
0
1
0
1
1
1
0
1
1
1
0
2
1
0
0
1
0
0
0
0
1
1
1
0
0
1
1
1
2
0
1
0
2
0
1
2
0
0
0
2
2
0
1
2
0
1
0
1
0
0
0
1
2
2
1
1
0
1
1
0
0
1
0
2
0
0
1
0
1
1
2
0
2
2
1
2
0
1
1
1
1
0
1
1
2
3
2
0
1
1
1
1
0
0
0
0
1
0
8
1
2
1
0
1
1
2
0
0
0
0
1
1
0
0
1
0
1
0
0
1
0
1
2
0
4
0
1
0
2
1
0
0
1
1
2
0
2
0
1
2
0
1
3
1
2
2
0
2
1
1
0
1
1
0
0
0
2
1
1
0
0
0
1
1
1
1
2
1
0
0
1
0
0
1
2
2
1
0
1
0
1
1
1
0
0
1
2
1
2
1
1
0
0
0
0
1
1
1
0
1
1
1
1
0
1
1
0
0
0
2
0
2
2
2
1
2
1
1
1
2
0
1
1
2
1
1
0
0
1
0
0
2
0
0
0
2
0
1
1
1
2
1
2
0
1
0
1
1
2
0
0
2
1
0
0
1
0
1
1
1
0
1
1
1
1
1
1
2
1
2
2
1
0
0
2
0
2
0
2
0
2
2
1
1
1
2
1
0
0
1
1
1
0
0
0
2
0
1
1
0
0
0
1
1
2
1
1
2
2
0
0
2
1
0
1
0
0
1
0
0
0
0
2
2
0
1
2
1
2
0
2
1
2
0
1
0
2
1
0
1
0
1
2
1
1
3
0
4
0
2
2
2
0
0
1
2
2
0
1
0
1
0
1
1
2
2
1
0
2
0
0
1
1
1
0
0
0
0
1
1
1
0
2
0
0
2
0
1
1
1
1
0
2
1
2
1
1
0
1
0
1
1
0
1
0
0
2
0
2
0
0
0
2
1
0
0
0
2
0
0
1
0
1
1
2
2
2
1
0
0
2
0
0
0
0
1
0
1
0
1
2
1
0
1
2
0
1
2
2
1
0
1
1
0
1
2
0
0
1
0
2
0
0
1
1
1
0
1
0
0
1
1
0
2
1
2
0
1
0
0
0
0
1
0
0
1
2
1
1
2
1
0
0
1
2
2
0
1
1
0
1
1
1
2
2
2
4
1
1
0
1
2
2
4
1
0
2
0
1
1
0
1
0
1
0
2
2
0
2
0
1
1
0
2
1
1
2
3
1
1
1
2
1
0
1
1
1
1
2
2
2
2
1
1
1
1
0
0
1
0
0
1
1
0
1
1
1
1
1
2
1
2
1
1
2
3
0
1
1
0
0
1
1
1
0
1
1
1
0
2
0
0
2
1
0
2
0
1
0
0
0
0
2
1
0
0
2
0
0
2
1
2
0
1
2
0
0
4
2
2
0
0
0
1
0
0
1
0
3
2
1
0
1
1
0
1
2
1
1
0
0
0
0
0
2
1
0
2
2
0
0
1
0
1
1
1
0
2
3
0
0
2
1
2
0
2
3
1
2
0
0
1
2
0
1
1
2
1
1
2
0
1
1
0
0
2
2
0
3
2
0
1
0
1
1
0
1
0
0
1
1
0
2
0
2
2
0
0
1
1
1
2
0
0
0
2
1
0
0
0
1
1
1
3
2
2
1
0
1
1
1
1
1
0
0
0
1
1
0
0
0
1
2
3
0
2
3
0
2
1
0
1
2
0
2
1
0
1
3
1
0
1
0
1
1
0
0
0
0
2
0
1
1
0
1
1
0
1
1
0
2
0
2
2
1
1
0
2
1
2
0
2
1
1
0
1
1
0
0
1
0
0
0
1
1
1
0
1
1
1
1
1
1
2
1
1
1
0
0
0
0
1
0
1
2
2
2
0
0
1
0
0
0
2
0
1
1
1
0
0
2
1
2
1
0
1
1
1
1
1
1
0
1
0
1
2
0
0
1
1
0
0
0
1
0
0
1
2
0
1
2
1
0
0
1
2
2
1
0
1
0
2
0
1
1
2
0
0
1
0
2
1
1
2
2
0
1
0
1
1
1
2
0
0
2
3
1
1
1
1
3
0
0
1
0
0
1
1
1
1
0
1
1
0
0
1
0
1
0
0
2
0
0
0
1
2
0
2
1
1
0
1
1
1
0
0
0
0
0
2
0
1
0
0
0
1
2
0
0
2
2
2
0
2
0
1
0
2
1
2
0
0
0
0
0
1
1
1
0
0
1
1
0
1
2
1
2
1
1
2
0
1
0
2
1
1
0
2
2
1
2
1
2
0
2
1
0
1
2
0
1
0
2
1
2
1
0
0
0
1
1
0
0
1
2
0
0
0
0
1
1
0
1
2
1
1
0
0
2
2
1
1
1
1
1
0
0
0
0
1
1
1
0
3
0
1
1
0
0
1
2
1
2
2
1
1
0
2
1
2
2
2
0
0
0
0
0
2
0
1
0
0
1
0
0
2
0
2
1
0
0
1
0
2
1
2
1
1
2
1
2
1
0
0
2
0
0
2
1
2
2
0
1
0
0
0
1
0
1
0
2
2
0
0
1
1
1
0
0
0
0
1
0
2
1
2
1
2
1
0
2
1
1
0
0
1
1
1
0
1
1
0
0
0
1
1
1
1
0
2
2
2
1
0
1
0
0
0
0
0
0
0
1
0
1
2
3
0
1
1
0
1
1
3
0
2
4
0
1
0
1
1
2
2
0
2
0
1
0
0
0
0
2
0
0
0
2
0
2
0
0
0
2
1
0
1
1
1
2
0
0
1
0
2
1
1
1
0
2
0
0
1
2
3
1
1
0
0
0
1
0
1
0
1
1
2
0
0
1
0
0
3
0
3
0
1
1
0
0
3
1
0
0
0
1
1
1
0
2
2
1
0
1
0
1
2
0
2
1
0
0
2
1
1
0
0
1
0
0
0
2
0
2
0
0
1
1
2
0
1
1
2
0
2
1
0
1
0
0
2
0
0
2
1
1
0
2
0
0
1
1
2
0
0
2
2
1
0
1
2
2
1
0
1
1
1
2
0
0
0
1
0
1
1
0
1
0
2
1
0
1
2
1
1
2
1
0
1
1
1
2
0
2
0
1
1
1
0
0
0
1
1
0
1
0
2
2
0
1
0
3
0
0
1
2
0
0
0
0
1
0
1
2
1
0
0
2
2
1
1
0
1
0
0
2
1
1
0
0
2
1
2
0
1
0
0
2
0
0
0
1
1
3
0
2
0
2
2
1
2
0
0
0
0
1
0
0
0
0
1
1
1
1
2
0
1
1
0
1
0
0
1
1
2
0
2
2
2
1
2
0
1
0
0
2
0
2
1
1
2
1
2
1
0
0
2
2
0
1
2
1
0
0
0
1
0
2
1
0
1
0
0
0
2
1
2
1
1
3
0
1
2
2
0
1
1
1
1
1
2
1
2
1
1
1
2
1
1
1
1
0
1
0
1
0
0
2
0
1
1
0
1
0
0
2
1
1
1
0
0
1
1
2
2
1
2
1
1
1
1
0
0
0
1
0
2
0
1
1
0
1
2
0
2
0
0
1
0
0
0
1
0
1
0
1
0
0
1
0
1
0
0
1
2
2
1
0
0
1
0
2
1
2
2
1
2
1
0
1
0
1
0
1
0
2
2
0
2
1
1
1
1
2
0
0
1
2
0
0
1
1
0
1
0
2
0
0
1
1
2
1
1
0
1
0
1
1
3
0
1
0
1
0
0
0
0
2
0
1
1
1
0
2
1
0
0
1
1
1
1
1
0
1
1
1
2
2
0
0
1
0
1
1
0
0
1
0
0
2
1
1
0
2
1
1
1
1
1
1
1
1
0
1
1
1
1
0
0
2
1
2
1
0
1
2
1
0
1
0
1
0
0
1
1
2
0
2
0
1
1
0
2
1
0
0
1
1
0
0
3
2
2
2
1
1
2
1
1
1
0
1
2
1
0
1
1
0
1
0
1
0
0
1
0
1
0
1
1
1
0
2
1
1
2
1
1
1
2
0
1
2
0
0
0
1
1
0
1
1
1
0
0
1
2
2
1
1
2
5
1
1
0
0
0
0
0
0
2
1
0
1
2
1
0
0
1
0
0
1
2
2
0
0
0
0
0
2
1
1
0
2
1
0
0
1
1
0
1
0
1
1
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
2
1
0
2
1
0
0
0
1
1
1
0
1
1
1
2
0
0
1
1
0
0
1
0
0
0
0
2
2
2
1
1
0
1
2
2
0
0
0
0
2
2
0
1
1
0
2
1
0
2
1
1
1
1
0
0
2
1
0
2
1
1
2
0
0
1
1
1
1
0
1
1
2
0
1
2
2
1
1
0
0
1
0
0
0
1
0
1
2
2
2
1
2
1
1
0
0
1
0
2
1
1
1
0
2
0
1
1
0
1
0
0
0
2
2
0
2
2
1
0
1
0
1
0
1
0
0
1
0
1
2
1
0
2
1
1
2
0
2
0
1
2
1
0
0
0
1
0
1
0
0
0
1
0
2
1
0
2
0
0
0
1
2
0
1
0
0
3
2
1
0
1
1
3
2
1
1
2
2
0
3
0
0
0
1
0
1
1
1
0
2
1
1
2
2
1
1
0
1
1
0
0
0
0
1
0
1
0
1
1
0
1
0
0
0
1
1
1
1
2
0
0
0
0
2
1
0
1
0
1
0
0
1
0
2
0
0
2
1
1
1
2
0
1
2
2
1
2
1
2
0
1
1
1
1
3
0
1
2
0
1
2
0
1
0
0
2
1
1
2
0
0
0
0
1
2
2
0
2
1
1
1
0
0
2
1
0
1
0
0
0
1
1
1
1
2
2
1
2
1
1
0
0
0
0
0
0
1
0
1
0
2
1
1
1
0
0
1
2
0
0
2
2
2
1
0
0
0
0
0
1
0
1
2
1
2
0
1
2
1
0
1
1
1
2
2
1
1
2
1
1
0
2
1
1
0
1
0
0
2
1
0
2
2
1
1
2
0
1
0
1
0
2
1
1
0
2
1
0
1
1
1
0
2
1
0
0
0
0
2
0
0
0
1
0
2
2
1
0
0
2
2
2
0
1
1
1
0
1
0
0
1
0
0
1
1
1
1
1
0
1
2
1
0
0
0
1
1
1
0
1
0
2
1
0
1
1
0
0
2
1
0
0
0
2
1
1
1
2
0
1
2
0
1
2
0
0
1
0
1
1
1
1
1
1
0
1
2
0
3
0
1
2
2
3
1
0
2
1
0
1
0
2
1
1
0
1
1
0
1
0
0
0
2
0
2
3
0
2
0
2
1
1
2
0
0
2
4
1
1
1
2
1
2
1
1
0
1
0
2
1
1
0
0
2
2
1
2
1
0
0
9
1
0
0
2
0
0
1
2
0
0
1
1
1
1
1
1
0
1
0
1
0
1
1
1
1
2
1
0
1
0
1
3
1
1
0
2
0
1
0
1
1
3
0
1
1
0
2
1
2
2
1
1
1
2
0
1
0
1
0
0
0
2
0
2
1
1
0
0
0
1
1
1
0
0
1
2
1
0
1
2
0
0
2
0
1
1
2
0
2
1
0
0
1
1
1
1
1
1
1
0
0
2
1
1
0
2
0
0
1
1
0
2
0
0
1
1
0
2
0
2
1
2
1
1
0
0
1
0
2
1
1
1
1
1
2
2
2
2
2
0
1
0
0
1
1
0
0
2
1
1
1
2
1
0
1
0
1
1
1
2
1
0
0
0
2
0
2
1
1
0
0
2
0
0
1
2
2
0
1
0
2
1
0
1
2
2
1
0
1
0
0
2
0
2
1
1
1
0
1
0
2
0
0
1
0
1
0
0
0
2
1
0
0
1
1
0
2
1
2
1
2
0
2
0
1
0
3
0
1
1
0
1
2
0
0
2
0
1
0
0
3
0
1
0
0
1
1
1
1
2
0
0
1
1
2
1
0
1
0
1
5
0
0
1
2
2
0
2
2
2
1
1
2
0
1
0
1
0
2
1
2
0
0
1
1
3
0
0
1
1
2
0
1
2
2
1
1
0
0
2
2
2
0
2
1
1
0
1
0
0
2
0
0
1
0
0
0
1
1
1
0
1
1
0
0
1
1
0
1
1
3
1
1
1
1
1
0
1
0
1
1
1
2
0
1
0
0
2
0
0
0
2
2
2
1
1
1
0
0
2
0
0
2
0
1
2
2
1
1
1
0
0
1
0
0
1
2
0
1
0
0
0
0
1
2
0
0
1
0
1
1
1
2
1
2
0
1
1
0
0
2
2
2
0
1
2
0
2
1
1
0
1
1
0
2
0
1
0
1
0
1
0
0
2
2
2
1
1
1
1
1
1
2
1
2
2
1
1
1
2
1
2
2
1
1
0
1
0
2
0
1
1
2
2
2
1
2
0
1
0
0
2
2
2
0
2
1
1
0
0
0
0
1
0
0
1
0
1
2
0
1
2
2
1
1
0
2
1
0
0
2
0
2
2
1
2
1
2
1
0
2
1
2
1
0
0
2
0
0
0
2
2
0
0
1
1
1
1
1
3
1
0
1
0
0
2
1
1
1
0
1
0
1
0
1
2
2
1
1
0
0
2
1
0
2
3
0
0
1
1
0
0
0
0
0
0
1
2
1
0
2
0
2
2
1
0
1
0
1
0
0
1
1
1
2
2
2
0
1
2
0
2
0
1
2
1
2
0
1
0
1
2
0
0
1
1
1
3
0
0
0
0
1
2
0
0
0
1
2
1
2
0
2
1
1
1
0
1
0
1
1
0
0
0
2
0
0
0
3
2
1
0
0
1
1
0
2
0
0
0
1
0
1
0
0
2
0
2
1
1
1
2
0
0
0
0
2
1
0
0
0
2
1
0
1
0
1
0
1
1
1
1
1
1
1
0
1
2
1
1
2
1
0
1
0
0
3
0
1
2
3
1
2
2
0
1
0
2
1
1
1
1
0
1
0
1
0
0
1
0
2
1
1
2
0
0
1
2
0
1
2
1
0
0
2
0
2
2
0
2
1
1
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
1
1
0
2
2
1
0
1
1
1
1
0
0
2
1
0
0
0
2
0
1
1
1
0
1
0
0
1
1
1
1
2
1
1
0
1
0
2
1
2
0
1
2
0
2
0
2
1
1
1
1
0
0
0
0
1
0
2
2
0
1
0
0
1
0
1
0
0
1
1
1
2
0
1
2
1
0
1
1
1
0
2
1
2
1
1
0
0
0
2
0
1
2
0
0
0
0
0
0
0
1
0
0
2
2
2
1
0
2
1
1
1
1
0
1
0
1
1
2
2
2
0
0
0
1
2
0
0
1
0
1
2
1
2
0
1
0
1
0
1
1
2
2
1
0
1
2
2
2
2
0
2
0
1
1
2
0
0
0
3
1
1
0
1
2
0
1
0
1
2
1
1
0
0
2
1
1
2
1
1
1
0
0
1
1
1
1
1
0
1
0
1
2
0
0
1
1
1
0
1
1
2
0
1
1
0
0
2
1
0
0
1
0
1
2
2
0
1
1
0
0
0
1
0
2
1
2
2
1
0
1
0
0
0
0
1
0
1
0
0
2
0
0
0
0
1
1
1
0
2
1
0
2
3
0
1
0
1
2
2
1
0
0
2
1
1
0
0
1
2
0
0
0
1
1
2
1
2
0
0
0
0
0
2
0
0
0
1
1
2
1
0
1
2
0
0
1
0
2
1
0
0
2
0
1
2
0
0
2
2
2
0
2
2
0
2
1
1
1
0
1
0
0
1
2
1
1
0
1
2
0
1
2
2
1
0
1
2
1
0
2
2
0
1
1
0
2
1
2
1
1
2
0
2
1
0
1
0
0
0
2
0
0
0
1
1
2
2
1
1
1
0
0
0
2
1
2
1
0
1
0
1
0
0
0
0
1
0
2
2
1
0
0
0
0
0
1
1
0
0
0
1
1
1
0
1
1
1
3
0
0
1
2
0
0
0
2
1
2
2
1
0
1
2
1
0
1
1
0
0
0
1
1
2
0
0
0
1
0
1
2
2
0
0
3
0
1
2
1
1
1
0
1
2
1
0
0
2
0
2
0
2
2
1
1
0
1
1
0
1
2
2
2
0
2
2
2
4
2
1
0
0
0
1
1
1
1
1
1
0
3
0
2
2
0
1
0
0
2
1
0
1
2
0
1
0
0
0
1
0
1
1
0
1
0
1
1
2
0
0
0
0
1
0
1
0
0
1
2
0
1
1
1
2
0
0
1
1
0
1
1
0
1
2
2
0
0
0
0
2
1
0
0
2
1
0
0
1
1
0
2
0
1
1
1
1
0
1
0
0
2
0
3
1
1
1
2
2
1
1
1
2
1
2
1
1
2
0
1
1
1
1
1
1
1
1
0
1
0
0
0
2
0
0
1
1
2
1
1
1
1
1
0
1
1
1
0
1
0
1
1
1
2
1
0
2
2
1
1
0
0
1
1
1
1
0
1
1
2
1
1
2
0
1
1
0
1
0
1
0
0
0
1
1
1
2
0
0
2
2
0
0
0
0
0
0
0
1
0
1
1
2
1
1
1
0
0
1
2
0
1
0
0
0
2
0
0
1
0
0
1
0
1
0
1
2
2
0
0
1
0
1
3
1
1
0
1
0
1
0
1
2
0
1
1
1
1
0
1
2
0
2
1
1
0
1
2
1
1
1
2
1
2
1
2
2
2
0
2
1
1
1
1
1
0
1
0
0
2
1
0
2
1
1
1
0
0
0
1
0
1
2
0
1
0
1
1
1
2
2
0
0
0
0
0
0
1
1
1
1
2
0
3
0
1
0
1
0
2
0
0
1
1
0
1
1
0
0
0
0
1
1
2
1
1
1
0
1
0
1
2
1
1
0
1
0
1
1
0
2
0
1
1
1
0
2
0
1
1
0
1
2
0
2
0
2
2
2
1
0
1
1
0
2
0
3
1
1
1
0
1
1
1
0
1
2
1
1
1
0
0
1
2
0
2
0
1
0
0
1
1
2
2
1
1
2
1
1
1
2
4
0
0
1
2
1
0
0
2
1
0
1
2
0
2
0
2
1
0
1
0
1
1
2
1
1
0
2
0
0
2
0
3
1
1
1
2
1
1
2
2
1
1
0
3
1
2
0
2
1
2
0
2
1
2
1
2
0
2
2
2
0
1
0
1
1
1
2
2
0
0
0
0
2
2
2
0
1
0
0
1
0
0
0
1
1
0
1
0
1
0
1
0
0
2
2
2
0
0
1
1
0
1
1
2
2
1
2
0
0
1
1
0
1
1
0
0
0
1
2
1
1
1
2
2
0
0
0
1
2
2
0
0
1
0
0
0
0
0
2
0
0
0
1
2
2
2
1
1
2
0
0
0
2
0
2
1
0
1
0
1
1
0
2
1
1
2
1
1
0
0
2
1
1
2
2
1
1
1
2
0
0
0
0
0
2
1
0
1
2
1
0
1
0
1
1
2
2
0
1
0
2
0
1
1
0
1
2
0
1
0
1
0
1
0
1
0
2
1
1
0
0
0
0
0
1
0
1
0
1
2
1
0
2
0
1
0
0
0
1
1
1
2
2
1
1
2
2
1
2
1
1
1
1
1
0
1
2
2
0
0
0
0
0
0
1
1
2
2
0
1
1
2
2
1
2
0
0
1
1
1
0
0
1
2
0
1
2
1
0
2
1
1
1
1
0
3
0
1
0
2
0
0
1
1
0
0
1
1
0
0
1
0
0
0
2
0
1
0
1
2
1
1
2
0
1
1
2
1
1
2
1
2
1
1
1
2
1
1
2
2
1
0
1
0
0
0
1
2
2
1
0
0
1
1
0
1
0
0
1
1
1
2
0
1
0
1
1
0
1
1
0
1
0
0
0
1
1
1
1
0
0
1
1
2
0
1
0
1
0
1
0
3
0
1
2
1
1
1
0
0
2
0
1
1
2
2
0
1
1
1
1
1
0
2
0
0
0
1
0
0
2
1
1
0
1
2
0
0
0
5
1
1
0
0
2
1
0
0
0
1
2
0
0
0
1
1
1
1
0
0
5
2
2
1
1
0
0
0
0
2
1
1
0
1
2
2
1
2
2
1
1
1
0
0
0
0
2
0
1
1
2
1
1
0
2
0
1
2
1
0
2
1
1
0
0
2
0
0
0
0
1
1
0
0
1
1
1
2
2
1
1
2
2
2
0
0
0
1
1
0
2
0
2
0
2
1
1
1
1
1
2
0
1
0
0
0
1
0
1
2
1
0
2
1
0
2
0
0
0
0
1
1
3
1
0
3
0
1
1
0
0
1
0
0
0
3
4
1
0
1
0
0
0
2
0
1
1
0
0
2
1
1
1
0
1
1
0
2
2
0
2
2
1
2
2
0
1
1
1
0
1
2
1
0
0
1
1
0
1
0
0
1
2
1
2
1
1
2
2
1
0
2
1
2
0
0
1
0
1
0
1
1
2
0
0
0
0
0
0
1
1
1
1
1
0
1
0
0
0
0
1
0
1
1
1
1
1
2
1
2
2
1
0
2
0
0
0
2
0
0
1
0
0
2
1
1
0
0
2
2
0
2
0
1
0
0
1
0
0
0
0
1
0
0
1
2
1
1
1
2
0
0
2
1
1
1
0
2
0
0
0
0
2
1
0
0
2
1
0
0
2
2
0
1
1
0
0
0
0
1
0
1
1
0
2
2
0
0
0
1
2
0
2
3
1
1
1
0
0
0
0
1
0
0
1
2
1
1
2
1
2
1
2
2
0
0
2
1
2
0
1
1
2
0
1
0
2
2
0
0
0
0
1
1
1
0
0
2
0
0
1
1
1
0
3
0
1
2
1
0
0
0
0
1
2
1
0
2
0
1
4
0
0
1
1
2
2
2
3
2
2
1
0
0
2
1
1
0
2
1
1
1
0
2
0
1
1
3
2
1
1
2
1
2
2
1
1
1
0
2
0
1
2
1
1
2
0
1
1
0
1
1
2
1
2
2
0
2
0
0
1
0
0
0
1
0
1
2
1
2
0
1
1
0
0
1
2
1
0
1
1
1
0
0
0
0
1
3
2
2
0
0
0
0
0
0
0
1
2
1
1
0
1
1
1
2
0
0
3
0
0
1
0
0
1
1
0
2
2
2
0
1
0
1
2
1
2
1
1
1
1
1
1
0
1
2
1
1
1
1
0
2
1
1
1
2
1
2
0
0
1
0
2
1
0
1
1
0
1
1
1
0
0
0
0
1
1
1
0
1
1
0
0
0
1
0
0
0
1
0
1
2
1
0
1
1
7
0
0
0
0
1
1
1
1
0
0
0
1
0
2
0
2
2
0
0
0
1
3
1
1
0
2
2
1
0
1
0
0
0
1
0
2
0
0
1
0
0
1
2
0
1
0
2
1
1
1
1
0
2
0
1
3
2
2
0
2
0
0
1
1
1
0
1
1
1
0
2
1
2
0
0
2
0
0
0
2
1
2
0
0
2
1
1
1
1
1
2
1
1
0
1
0
1
0
1
2
0
0
0
2
1
1
1
1
2
2
1
0
2
1
2
0
1
2
1
0
0
1
1
1
1
0
2
0
0
0
0
0
2
0
1
0
2
0
1
1
2
1
2
1
2
1
0
5
1
0
0
0
0
1
1
0
1
2
1
0
1
2
2
0
0
0
1
2
1
0
1
2
1
0
2
1
1
1
1
2
0
1
1
1
0
2
2
0
0
0
0
2
1
1
0
1
0
1
1
1
0
2
2
0
0
4
1
1
1
1
0
1
0
0
2
1
1
0
1
0
2
0
0
2
2
2
1
0
1
1
1
0
1
1
0
0
0
1
0
0
0
1
0
2
0
1
1
1
2
2
1
1
2
2
0
0
0
0
1
2
0
5
1
1
0
2
1
0
3
2
1
1
0
0
1
0
1
1
0
1
0
2
2
2
1
0
1
0
0
0
2
0
1
3
2
1
0
0
0
1
1
0
0
0
0
1
0
0
0
1
1
1
1
2
1
0
0
1
2
0
1
1
1
0
0
1
1
1
1
0
1
1
0
2
0
1
0
1
1
2
1
1
1
0
2
1
1
2
1
2
1
0
1
2
1
1
2
0
0
1
2
2
2
1
1
3
0
2
2
1
1
1
1
0
1
1
2
1
2
1
1
2
0
1
0
0
2
2
0
1
0
0
2
1
1
1
0
0
2
0
1
0
4
1
0
2
2
1
1
2
1
0
0
2
1
0
0
0
1
1
0
1
1
1
0
1
1
1
1
1
1
2
1
1
2
0
0
2
0
1
1
1
2
1
1
2
1
1
0
1
2
0
1
0
0
2
1
1
1
0
1
1
2
2
2
2
1
0
0
0
0
1
0
0
0
2
1
2
0
0
2
2
0
1
1
0
1
1
1
1
0
1
2
1
2
0
1
1
2
0
1
0
1
0
1
0
1
2
1
1
0
0
0
0
2
0
1
0
0
0
1
0
1
0
2
1
0
1
0
1
2
3
2
1
1
1
1
1
0
2
2
1
3
0
1
0
2
2
1
0
1
2
0
1
1
0
1
1
0
0
2
1
0
2
0
0
2
0
0
0
1
0
1
2
1
1
0
2
2
0
0
0
2
0
2
0
2
0
0
1
2
0
2
0
0
1
2
2
1
0
2
0
0
1
2
0
1
0
0
1
1
1
2
0
3
0
2
0
0
1
2
2
0
1
0
0
1
2
2
0
1
1
0
1
0
2
1
2
1
0
0
2
2
1
0
1
1
2
2
0
0
2
1
1
0
1
0
0
0
1
1
1
0
1
0
0
0
0
1
2
0
1
1
0
1
5
2
0
1
1
0
0
1
0
0
1
1
1
0
1
0
1
0
0
1
1
1
2
1
1
0
0
1
0
2
0
0
0
0
1
0
1
1
2
1
1
1
1
2
0
9
1
0
1
1
1
2
2
1
2
1
2
1
2
0
1
0
2
0
0
1
0
0
1
1
0
1
0
0
1
0
0
1
0
0
0
1
1
0
0
1
1
0
1
0
0
0
1
0
1
1
0
2
1
1
1
1
1
0
2
0
1
0
1
0
0
1
0
1
1
1
0
1
0
0
2
2
1
0
1
2
2
0
1
0
1
1
0
0
1
0
1
1
1
2
0
0
1
2
0
0
1
2
0
2
1
1
2
1
1
0
0
0
0
0
1
1
0
2
1
2
1
2
2
0
1
0
1
2
0
2
0
2
1
0
2
1
1
1
1
1
0
0
1
2
1
1
1
1
2
1
2
1
2
2
0
0
1
1
0
1
0
1
0
0
1
0
2
1
0
1
1
0
0
0
0
0
0
1
2
2
2
0
2
1
0
1
0
1
1
1
2
1
1
1
1
1
0
0
1
0
0
0
1
2
0
1
1
1
3
1
0
2
0
1
1
0
0
1
0
0
1
2
2
2
1
2
1
0
0
0
1
1
2
2
1
0
0
2
1
0
1
0
0
0
2
2
1
0
0
0
2
1
0
3
1
0
2
1
0
0
0
1
1
0
0
0
0
1
1
2
0
2
0
0
0
0
2
0
1
0
0
2
2
2
2
0
0
2
0
0
1
1
1
3
0
1
2
2
0
0
2
0
1
1
1
2
0
1
2
2
0
0
2
0
2
2
1
2
0
1
0
0
2
2
1
0
0
2
0
0
1
1
1
1
1
1
0
1
0
2
0
2
1
1
1
0
0
2
0
0
1
0
0
1
1
1
2
0
0
7
2
0
0
2
1
0
1
1
1
1
1
0
1
0
2
1
1
0
0
0
1
1
0
1
1
1
0
2
0
1
1
1
0
0
1
1
1
2
1
1
0
0
1
1
0
2
2
1
2
2
1
0
1
2
1
1
0
1
2
2
2
2
1
2
1
2
1
0
1
0
0
0
0
2
0
1
0
0
3
1
0
2
1
1
0
2
0
0
1
0
0
0
0
1
1
0
0
1
0
1
1
2
0
1
0
0
1
1
2
0
1
0
1
0
1
0
2
0
0
1
2
1
1
0
1
1
1
0
0
0
3
0
0
1
3
0
1
1
0
2
1
2
0
0
1
0
0
1
2
2
1
0
0
1
0
0
0
2
1
0
1
1
1
2
1
1
0
2
4
1
0
1
1
0
2
1
1
1
1
1
2
0
3
2
1
0
1
3
1
1
0
1
1
1
0
2
0
0
1
1
0
1
1
1
1
0
0
0
1
2
0
0
1
1
1
1
2
1
3
1
0
2
0
0
1
0
2
0
1
0
2
1
0
1
1
2
1
0
1
1
0
2
1
1
1
0
0
0
1
2
0
1
2
0
2
0
1
0
1
1
1
2
1
2
1
0
0
0
1
2
1
2
1
2
2
2
0
2
0
1
0
0
1
2
3
0
1
0
0
1
1
0
0
2
0
1
0
0
0
2
1
1
1
1
0
0
2
0
1
1
2
1
1
2
1
0
0
1
1
2
1
2
2
2
1
0
2
0
1
2
2
0
2
0
0
0
0
1
0
0
1
1
2
0
1
1
2
0
1
0
1
1
0
0
1
1
2
1
0
2
0
0
0
1
0
0
1
1
1
2
0
0
1
1
1
0
0
0
1
0
0
1
1
2
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
1
0
2
1
0
0
2
1
0
1
0
1
0
2
0
2
1
2
2
0
1
0
1
1
0
1
1
0
0
0
0
1
1
1
2
1
1
0
1
1
1
0
0
2
0
1
1
2
0
0
3
2
0
1
0
0
0
0
2
0
1
0
2
6
1
2
2
0
1
0
1
1
1
1
1
0
0
0
1
0
0
2
0
1
2
1
2
1
1
0
1
0
0
1
2
2
0
0
0
0
1
0
2
0
0
2
1
2
0
0
0
0
1
2
0
2
0
1
0
0
1
1
1
0
1
0
2
1
0
1
1
0
1
1
2
2
2
1
2
1
2
1
2
1
0
0
0
2
0
1
1
2
1
1
0
1
2
1
2
0
2
6
1
5
3
1
1
1
0
0
0
0
1
0
0
2
0
0
1
1
0
1
1
1
0
2
0
0
1
1
2
0
2
2
0
0
0
0
1
1
1
2
0
0
1
1
0
0
0
0
1
1
1
2
1
1
1
0
0
0
0
2
0
1
1
2
1
2
1
1
1
2
0
0
1
0
0
0
2
1
0
0
0
1
0
2
0
0
2
0
1
1
2
1
2
2
0
2
0
2
0
1
1
0
0
0
2
2
2
1
1
1
0
0
1
1
1
1
2
0
2
3
2
0
2
1
2
1
2
1
1
2
1
0
1
2
0
2
1
0
2
0
1
0
2
1
2
1
1
0
1
1
0
0
1
3
2
0
0
1
1
1
2
1
1
0
2
1
1
0
1
1
1
0
1
1
1
0
0
0
0
2
1
1
1
1
0
1
0
1
0
2
2
1
0
1
0
0
0
1
1
0
2
3
1
2
3
2
0
0
1
1
2
1
1
1
0
1
1
0
0
2
1
2
0
0
2
1
0
1
0
2
0
0
0
0
0
1
0
1
2
2
0
1
2
2
2
2
0
1
0
0
0
2
0
1
2
0
0
0
0
2
1
2
2
2
0
1
0
1
1
1
1
1
1
1
2
0
2
1
2
0
0
2
1
2
0
0
0
1
0
1
0
1
0
0
2
0
6
2
1
1
2
1
2
1
1
0
1
1
2
2
0
1
0
1
0
0
0
0
2
2
0
0
2
0
2
0
0
0
0
0
1
2
2
2
1
1
1
2
0
2
0
2
1
0
0
2
1
2
2
1
1
1
0
1
1
1
0
0
0
1
0
2
1
0
1
1
1
1
0
0
0
0
1
1
0
0
1
0
1
2
1
0
0
1
0
1
0
1
1
2
0
0
2
1
0
1
0
1
0
2
1
2
0
0
0
1
0
1
0
2
2
1
1
0
1
1
0
2
1
1
1
1
0
0
1
1
2
0
0
0
1
1
2
1
2
1
1
2
1
0
0
0
1
2
1
1
1
0
2
0
1
1
2
2
1
0
3
6
0
0
2
1
0
0
0
0
0
0
1
1
1
1
1
1
1
0
0
1
1
0
1
1
1
1
1
0
2
1
0
0
1
2
0
1
0
1
1
0
1
1
1
2
2
0
1
0
0
0
2
1
2
0
1
0
2
1
1
1
1
2
1
0
1
1
1
0
1
1
0
1
1
2
1
7
1
0
0
0
0
1
1
1
2
0
1
1
0
10
0
0
0
0
0
2
0
0
0
1
0
1
2
1
2
0
1
1
1
0
1
2
0
2
0
0
0
1
2
1
0
2
1
0
1
2
2
1
1
0
1
0
2
0
1
0
2
1
0
0
1
0
0
0
1
1
1
1
0
1
0
1
2
0
0
0
1
2
0
2
0
1
0
1
1
0
0
1
1
0
1
1
0
2
1
0
1
0
0
0
1
0
2
0
1
3
0
1
1
0
1
1
0
0
1
1
1
1
0
1
2
0
1
2
1
1
0
0
0
1
1
0
2
0
2
4
0
1
0
0
1
1
0
1
0
1
0
3
2
1
0
1
0
0
1
0
1
2
0
0
1
1
0
1
0
1
1
0
2
0
1
0
0
0
1
1
1
1
2
1
2
1
1
0
1
1
2
2
2
0
0
0
0
0
0
2
0
0
1
1
2
0
1
0
1
0
0
2
1
0
1
1
1
1
1
2
1
1
1
1
2
1
1
0
2
0
0
0
0
2
1
1
0
1
1
2
0
3
0
0
0
1
1
0
1
1
0
1
0
1
1
1
0
0
1
1
1
0
1
1
0
2
2
0
0
1
1
1
1
1
0
0
0
2
0
0
1
1
1
1
0
1
0
1
0
1
2
0
0
1
0
0
1
0
2
2
1
0
2
2
0
1
1
1
1
1
0
2
2
1
0
0
1
2
0
0
1
1
1
1
1
1
1
0
1
0
2
1
2
0
0
0
1
2
0
0
0
2
0
0
1
0
1
1
0
1
2
0
0
1
1
0
0
0
0
1
1
1
0
1
1
2
0
1
0
2
0
0
1
1
1
0
0
2
2
2
0
1
0
0
2
0
1
2
0
0
0
1
2
1
2
1
1
1
1
2
0
0
0
1
1
0
2
2
1
1
0
0
2
0
0
2
2
0
0
1
1
0
1
2
0
0
3
2
1
0
0
0
0
0
0
2
2
1
0
3
2
1
0
0
2
0
0
0
2
0
2
1
0
0
1
0
0
0
1
1
0
1
0
1
2
1
1
2
1
1
1
1
1
0
1
0
0
0
1
3
0
0
1
0
0
2
1
1
2
0
0
0
2
0
0
0
1
1
3
1
0
1
0
0
1
1
0
1
1
0
1
1
1
0
1
1
1
0
1
0
2
1
1
2
2
0
1
0
0
1
2
1
1
1
0
1
2
2
1
2
1
1
1
0
1
1
1
1
2
0
2
0
0
0
1
0
1
1
2
1
0
1
1
0
1
0
0
0
1
0
2
2
1
2
1
3
0
1
0
0
1
2
1
2
2
1
1
0
0
1
1
3
0
0
1
2
1
1
1
0
1
2
2
1
1
1
1
0
1
1
2
1
0
0
2
1
0
0
1
2
1
1
2
1
0
1
1
0
1
2
2
0
2
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
2
1
1
0
0
0
4
2
2
2
2
0
3
0
1
1
0
2
2
1
0
1
1
2
2
2
2
1
1
0
2
0
0
0
2
0
0
1
1
1
0
1
0
4
0
2
0
1
1
1
1
2
1
0
0
0
1
0
1
0
2
2
0
1
1
0
2
1
1
2
4
0
3
2
0
2
1
1
1
2
2
0
1
0
1
1
0
0
2
2
2
1
1
0
1
0
1
0
4
2
0
1
0
0
1
0
0
1
2
0
1
2
1
0
2
0
1
0
0
2
1
2
0
0
1
2
2
0
2
0
0
1
2
2
2
2
1
1
0
1
1
0
1
2
1
1
0
0
0
1
1
2
1
1
2
1
1
2
1
0
0
1
1
0
0
1
2
1
1
1
1
1
0
1
0
3
0
1
0
1
2
0
0
1
0
1
0
1
1
2
0
1
1
0
0
0
1
1
2
1
0
2
1
2
1
0
1
0
1
2
0
2
2
1
2
2
2
0
1
0
1
0
1
2
1
1
0
0
1
1
0
0
2
2
0
0
1
0
0
1
0
1
2
1
1
2
2
0
0
0
2
0
2
0
1
0
1
1
1
0
2
0
1
0
1
1
0
1
1
2
1
1
2
1
0
0
1
0
1
0
0
3
1
1
1
0
1
1
2
0
0
0
0
0
1
3
0
1
2
1
1
0
0
0
0
0
1
0
0
2
2
1
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
1
2
0
1
0
0
0
1
1
2
1
2
1
1
2
1
0
2
2
1
2
2
2
1
0
0
0
2
2
0
1
3
0
0
0
2
1
1
2
1
0
0
0
0
2
1
0
2
0
1
2
0
1
1
1
1
1
0
0
0
2
0
1
1
0
2
0
1
0
0
0
0
1
2
0
2
1
0
2
1
2
1
1
0
2
2
1
2
0
2
2
0
0
0
1
1
0
0
2
0
0
1
0
1
1
1
0
0
1
1
0
1
1
1
1
1
1
0
3
0
2
1
1
1
2
0
2
2
1
0
0
2
1
0
0
1
1
1
0
0
0
1
2
2
0
0
1
2
1
2
2
3
0
2
0
1
0
1
0
1
0
2
1
1
1
2
0
1
1
0
0
0
1
0
1
0
0
0
1
0
0
0
1
2
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
4
1
1
0
1
2
0
1
2
1
0
2
0
0
0
1
0
1
1
1
0
0
1
0
1
0
1
2
1
2
1
1
1
2
0
0
2
0
0
1
0
1
2
0
1
1
1
1
1
1
0
2
1
1
1
2
1
0
0
2
1
1
0
1
1
1
1
1
0
0
0
0
0
1
1
2
0
0
0
2
1
0
1
2
1
1
2
0
0
0
0
0
1
2
0
0
1
1
1
0
1
1
2
1
1
1
2
1
1
0
0
1
0
1
0
1
1
1
0
3
2
1
1
0
2
1
0
2
1
3
1
2
0
1
0
1
1
0
0
0
0
0
0
0
0
1
2
1
0
0
1
0
1
0
2
1
0
1
0
1
0
1
0
2
2
0
1
0
0
1
0
1
1
2
1
2
2
0
1
0
0
0
2
1
1
1
1
0
2
3
0
0
1
2
2
4
0
2
1
1
0
2
2
0
2
0
1
1
2
1
0
1
3
1
1
0
1
2
1
0
1
0
1
1
0
0
2
0
0
0
1
0
1
3
1
2
0
0
2
1
2
2
1
0
1
0
1
0
2
0
1
1
1
1
1
0
0
0
1
0
0
2
0
1
1
2
2
1
2
2
1
1
1
0
0
1
0
1
2
0
1
0
1
0
1
0
0
2
0
1
2
1
0
1
0
0
2
2
0
4
0
1
0
0
0
0
2
0
1
1
2
0
1
2
1
3
2
0
0
1
0
1
1
2
0
0
1
2
2
2
1
1
1
0
1
1
1
1
1
0
1
1
3
2
2
0
0
0
3
0
0
0
0
0
0
1
2
3
2
1
2
2
0
1
1
1
0
0
1
0
0
1
0
2
1
1
0
1
2
2
0
1
1
0
2
1
1
1
2
0
0
2
0
0
0
0
1
0
0
0
2
2
0
1
1
0
0
1
1
1
3
2
1
0
0
2
1
1
1
0
1
1
1
1
1
0
1
0
0
1
2
1
0
1
0
2
0
1
1
1
0
5
2
1
1
0
1
1
1
0
0
0
0
2
0
2
1
0
2
1
0
0
1
0
0
0
2
2
0
1
2
1
0
2
2
0
1
0
1
2
1
2
0
0
0
1
0
1
0
1
2
0
2
1
0
2
1
1
1
2
1
1
2
2
1
2
0
1
0
2
1
4
0
2
1
0
0
1
2
0
0
1
1
1
1
1
0
0
0
1
0
0
2
1
0
0
0
0
0
1
1
2
1
3
0
1
1
2
2
1
1
0
0
1
0
2
2
1
1
1
1
0
0
1
1
0
2
2
1
1
1
2
0
1
1
2
2
0
1
3
1
1
1
1
1
2
1
1
1
0
2
1
2
1
0
1
2
1
1
0
2
2
0
1
0
2
2
1
2
1
0
2
2
1
1
1
0
1
0
0
0
1
1
0
0
1
1
0
0
1
2
0
1
2
0
2
2
0
0
1
1
1
0
1
1
1
1
0
2
0
0
2
0
1
2
1
2
1
0
0
1
0
2
1
2
2
1
3
1
0
1
2
1
1
0
2
1
0
1
2
1
0
1
0
0
1
2
1
0
0
2
0
1
1
1
1
2
2
2
0
0
1
0
1
0
2
2
0
1
2
2
2
2
1
2
1
4
0
0
0
2
1
2
2
2
1
1
1
0
1
1
0
0
0
0
0
0
0
1
2
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
1
2
1
0
0
2
1
1
0
1
0
0
2
0
0
0
1
0
1
2
0
0
1
2
2
2
2
2
0
0
0
0
0
1
1
2
2
0
1
1
1
0
1
1
1
1
1
1
0
2
3
2
1
0
0
0
2
0
0
0
0
0
1
1
0
1
0
1
0
0
1
2
0
1
1
0
2
0
0
0
1
1
0
2
0
1
0
1
2
2
1
1
0
1
0
2
1
2
1
1
2
0
0
1
0
0
2
2
2
0
2
1
0
4
1
1
2
1
1
4
1
1
1
1
2
2
2
0
0
1
2
0
2
2
0
2
2
1
1
0
0
1
2
1
0
1
0
1
1
0
0
1
0
1
0
0
0
0
1
0
1
1
0
2
2
0
0
1
0
0
1
1
1
1
1
0
2
3
1
0
1
2
0
0
1
0
0
0
0
1
1
0
1
2
3
2
2
1
0
2
0
0
1
2
1
2
2
2
2
0
0
1
0
2
2
1
1
1
1
0
0
0
0
0
0
1
2
2
0
1
1
1
0
1
0
1
0
0
1
0
1
1
1
1
0
1
2
0
0
1
1
1
1
0
1
2
1
1
0
0
1
1
1
2
1
1
0
0
1
0
0
0
0
2
2
1
0
1
0
0
0
2
0
1
1
1
0
1
1
0
0
2
1
2
1
2
1
0
1
1
0
2
1
0
1
0
1
0
0
0
0
1
0
1
0
0
2
2
1
2
1
1
1
1
0
0
1
0
0
1
0
0
1
2
1
0
1
1
1
0
1
2
0
0
0
2
0
1
1
2
1
0
2
2
1
1
0
1
1
2
0
0
1
1
0
1
1
1
2
1
0
1
1
0
1
0
1
0
1
2
1
0
1
2
1
1
0
2
0
3
1
1
1
1
1
1
0
1
2
0
0
0
2
0
0
1
0
1
2
1
0
0
0
0
1
0
1
0
1
1
1
0
0
0
1
0
0
1
2
2
0
1
0
2
0
0
1
1
2
1
2
2
2
0
2
0
1
3
0
0
1
0
1
1
2
0
2
0
1
1
1
1
0
1
1
0
1
0
0
1
1
1
0
1
0
1
0
1
0
1
1
2
2
0
0
1
2
0
0
0
0
1
1
2
0
1
2
1
0
1
0
0
2
1
1
1
1
1
0
0
1
0
0
2
1
0
0
0
1
3
2
0
1
0
2
2
1
0
1
2
0
1
0
2
0
1
1
3
0
1
0
0
0
1
1
0
1
0
1
2
0
2
0
0
1
0
2
2
1
0
2
1
0
2
1
1
0
2
1
0
1
0
0
0
0
1
2
0
1
2
0
0
1
1
3
0
1
0
0
1
1
1
2
2
2
0
0
1
2
2
2
1
1
0
0
0
0
0
0
1
1
1
2
0
1
1
1
0
0
1
0
1
1
0
2
0
0
1
0
1
1
1
0
1
1
1
2
1
2
1
1
2
0
0
1
0
1
0
0
1
1
2
1
1
1
0
0
1
1
0
1
1
1
1
1
0
3
1
2
1
0
2
0
0
0
1
1
2
2
1
1
1
0
0
2
1
1
2
1
1
0
1
2
1
2
0
1
0
0
1
0
1
1
1
2
3
1
0
0
2
0
1
2
0
1
1
0
0
2
1
1
1
2
2
0
1
0
1
2
2
1
1
2
2
0
2
0
0
2
1
2
1
2
2
0
0
1
2
2
2
1
0
0
1
2
2
1
1
2
1
0
0
1
1
1
1
1
1
0
0
2
0
1
2
0
0
0
1
0
1
0
0
0
1
0
1
1
0
0
0
1
0
0
1
0
1
1
1
0
1
2
1
2
1
0
1
0
1
1
1
1
1
0
1
1
0
0
0
2
0
1
1
0
0
2
0
2
3
1
0
1
2
2
0
0
1
0
0
2
0
1
0
1
2
2
0
1
0
1
1
2
0
1
0
1
2
0
1
0
0
1
2
0
2
1
0
0
1
0
0
0
0
0
1
1
1
1
0
0
2
0
2
0
1
1
2
3
0
1
1
0
0
0
0
0
1
0
0
2
1
0
0
0
1
1
2
2
0
3
0
1
0
0
1
0
0
0
0
1
1
1
0
1
0
0
1
2
1
0
2
2
0
0
2
2
0
2
1
0
0
1
2
2
0
1
1
2
1
1
1
0
0
1
0
1
2
1
2
2
0
0
1
1
1
2
0
0
0
0
2
2
0
5
1
2
1
2
2
1
2
0
1
0
2
2
0
0
0
0
0
1
1
1
1
0
1
0
0
0
2
0
1
1
1
2
0
0
0
0
0
0
0
2
2
2
2
1
0
1
0
1
1
2
0
1
0
0
1
1
0
1
1
1
1
0
0
1
0
2
0
1
0
2
1
2
2
1
1
2
0
1
1
0
1
1
1
2
1
0
0
0
0
1
0
0
2
0
0
0
0
2
1
1
0
0
2
0
2
1
0
0
2
4
1
0
0
0
1
3
2
1
0
1
2
3
1
0
0
2
0
0
0
1
1
0
1
0
3
1
0
0
0
1
1
0
0
1
1
1
1
2
2
2
1
0
2
0
1
0
0
1
0
1
2
0
2
1
2
0
0
1
1
0
0
0
3
2
1
2
1
0
0
3
1
1
1
1
0
2
0
1
1
0
1
0
1
0
1
1
0
1
1
2
2
1
1
0
2
1
3
1
1
2
0
0
1
0
2
1
0
0
0
0
0
1
0
0
1
1
0
1
2
2
0
1
2
0
1
1
1
2
0
2
1
1
0
2
2
2
2
1
2
1
2
1
1
0
0
0
0
2
0
0
0
2
1
2
2
0
0
0
2
1
0
1
2
2
1
1
1
1
1
0
2
2
0
1
1
0
1
1
0
1
1
0
1
2
0
2
0
0
1
1
0
1
0
2
1
0
0
3
0
1
1
1
1
2
2
1
1
0
0
0
1
1
1
1
1
0
0
2
0
0
0
0
1
1
1
2
1
0
0
2
2
0
2
1
1
1
0
0
1
2
2
1
1
0
1
1
0
1
0
1
0
0
1
1
2
1
1
1
2
2
1
1
0
0
1
1
2
1
3
0
0
2
0
1
1
0
1
2
0
1
0
1
0
1
1
0
1
0
1
1
1
0
0
1
0
0
0
2
0
0
2
0
2
2
0
1
2
0
0
2
1
0
0
1
1
1
0
1
2
1
0
0
1
1
1
1
1
0
1
2
0
1
1
2
0
2
1
1
0
0
0
1
1
5
2
0
1
1
0
2
1
0
0
0
1
0
1
1
2
2
2
2
0
1
0
0
1
1
2
3
0
0
1
1
1
2
1
1
1
0
2
2
1
2
2
1
2
0
2
0
0
4
2
0
0
0
0
3
1
1
1
1
1
1
3
1
2
1
0
2
1
0
2
0
0
0
2
0
0
0
1
0
0
2
1
2
0
0
0
0
0
2
1
0
1
2
1
0
0
2
0
1
1
1
2
2
2
1
1
0
0
1
1
0
1
2
0
0
0
1
2
1
1
0
0
0
1
0
0
1
2
2
2
0
0
3
1
1
3
0
3
1
1
1
0
0
0
1
1
2
1
2
1
1
1
0
0
1
1
0
2
0
2
2
0
1
1
0
1
0
2
0
1
2
0
0
0
0
0
1
0
1
1
2
1
2
0
0
1
1
1
0
1
2
1
1
0
1
0
2
2
0
1
0
0
1
2
2
1
1
1
1
2
1
2
0
2
1
0
0
2
1
1
1
0
2
1
1
1
0
1
0
0
0
0
2
0
1
1
1
0
0
1
0
0
0
1
2
0
1
1
0
1
0
4
0
2
0
1
0
1
0
0
0
2
2
0
0
3
2
2
1
1
1
0
3
0
1
7
1
2
1
1
2
2
0
0
2
2
1
0
1
0
0
0
1
0
0
1
0
1
1
2
1
1
2
1
1
1
0
1
0
1
1
1
0
0
1
0
0
2
2
1
0
2
2
0
1
0
2
1
0
2
2
1
0
1
2
2
1
1
1
1
1
0
1
4
0
0
1
1
0
1
0
1
0
2
1
1
1
0
1
1
0
2
1
0
0
2
0
0
1
1
2
1
1
0
2
1
1
2
0
1
0
2
1
0
1
1
2
1
1
0
1
2
0
2
0
0
2
2
1
2
1
1
2
2
2
0
1
1
1
1
1
1
1
0
2
2
1
1
0
2
1
1
0
3
1
2
1
2
1
0
2
0
0
1
1
1
0
0
1
0
0
0
1
1
0
0
2
0
0
3
2
1
0
2
1
0
1
0
0
1
2
0
1
2
2
1
2
2
1
1
2
0
0
0
0
0
0
2
2
2
1
0
1
0
0
1
1
0
1
2
1
1
0
0
1
0
0
1
2
1
0
0
0
1
1
2
1
0
2
0
0
1
0
1
1
3
0
1
2
2
2
0
1
0
1
0
1
1
2
1
0
1
2
2
2
0
0
0
1
2
1
0
1
0
0
1
2
1
1
2
1
1
3
0
0
1
1
1
0
1
0
1
0
0
3
2
1
1
1
1
1
2
0
0
3
0
1
0
0
0
2
1
1
1
1
1
0
1
1
0
1
0
1
0
0
2
0
2
1
1
2
2
0
1
1
1
0
1
2
2
1
1
0
1
0
1
1
0
1
0
0
1
0
1
1
0
0
0
3
0
1
1
1
0
1
0
1
2
1
1
2
1
0
1
0
3
1
1
2
1
0
2
0
1
1
2
2
0
1
0
0
2
1
1
0
2
1
1
0
2
1
1
0
1
0
1
0
1
0
3
3
2
1
0
1
1
1
2
1
1
2
1
1
0
0
0
2
1
4
1
0
1
1
0
0
1
0
2
1
0
0
0
1
1
1
0
0
1
1
2
1
2
0
0
0
1
0
0
0
0
1
1
1
0
0
0
2
1
0
1
1
1
0
1
2
1
0
0
2
2
1
1
1
1
2
0
1
2
2
0
0
3
0
1
2
1
0
1
0
0
1
0
1
0
2
0
1
0
2
1
0
0
2
1
0
1
2
0
2
0
2
0
3
1
1
1
2
2
0
1
1
1
0
0
1
1
1
2
0
2
1
0
2
0
0
1
2
1
1
1
0
0
1
1
1
1
1
0
0
2
5
0
0
1
1
0
0
0
1
2
1
4
1
1
0
0
0
0
2
2
1
0
1
1
2
0
2
0
1
0
1
1
0
2
0
2
0
0
1
1
0
0
1
2
0
1
0
2
2
1
0
0
1
0
1
1
1
0
2
1
0
1
2
1
2
0
1
0
2
1
0
1
2
2
0
0
0
1
0
0
0
0
2
0
2
0
1
0
2
2
1
2
0
1
0
0
11
2
2
1
2
3
1
1
0
2
0
2
1
1
1
0
1
0
0
0
1
1
0
0
0
2
1
1
0
1
1
0
1
1
0
0
2
1
1
0
2
0
0
0
1
1
1
1
0
2
5
0
0
1
0
0
2
1
2
0
1
0
1
1
1
0
2
1
0
0
0
0
0
1
0
1
0
1
2
2
0
1
0
0
0
2
1
1
0
0
2
2
1
1
1
1
2
0
0
1
0
0
3
0
2
1
2
1
0
0
1
1
1
0
2
1
1
2
0
0
2
0
0
1
2
0
2
2
0
1
2
1
0
1
1
2
13
1
0
0
1
1
0
0
0
1
2
1
2
2
2
0
1
1
2
0
0
0
0
1
2
1
1
2
0
1
0
1
1
1
1
0
2
1
0
0
0
1
2
1
1
2
2
0
0
0
1
1
0
0
0
1
1
0
1
0
1
1
2
2
1
0
2
1
1
1
0
1
1
0
1
2
1
0
1
16
1
2
1
1
2
3
2
0
2
0
0
0
1
1
1
0
0
0
0
1
1
0
1
2
0
1
1
1
1
0
1
1
1
2
1
1
1
1
0
0
1
0
0
1
1
1
1
0
1
2
1
1
1
1
1
0
0
1
2
0
1
0
0
0
2
1
1
0
1
2
2
0
2
0
0
1
1
1
1
1
0
1
1
0
1
0
2
1
2
2
0
0
0
2
0
0
0
2
2
2
2
0
2
1
1
0
0
2
1
1
2
1
2
0
1
2
2
1
0
0
1
0
1
2
2
1
1
0
0
2
0
1
1
0
1
2
1
1
1
1
0
0
1
0
0
0
0
2
0
2
0
0
2
0
0
1
1
2
0
1
1
1
1
2
0
1
0
1
2
1
1
0
2
1
1
1
1
0
0
0
2
3
0
1
0
1
0
0
2
1
1
0
0
0
0
1
0
1
1
2
0
1
0
0
1
1
0
2
1
0
1
0
0
2
0
1
0
0
1
0
0
1
0
1
1
1
1
1
0
1
2
0
1
0
2
0
0
0
2
2
0
0
0
3
0
1
2
0
1
1
0
1
1
3
0
1
1
2
1
1
2
0
1
2
1
1
1
0
2
0
1
3
1
1
1
0
0
0
2
1
1
2
1
1
1
0
2
2
1
2
0
0
1
0
2
2
1
2
1
2
1
1
2
0
0
0
0
1
0
1
2
0
2
1
2
0
1
0
1
0
1
1
2
1
1
0
1
1
0
0
2
0
0
1
2
1
2
0
0
0
0
1
1
1
0
2
1
1
1
1
0
1
0
0
1
11
1
2
0
1
1
2
0
2
0
1
1
2
0
1
2
1
1
0
1
0
0
0
0
1
1
2
3
0
2
1
0
1
1
0
0
1
2
1
1
1
0
0
0
0
3
1
0
0
0
0
0
0
2
1
1
1
2
1
1
2
0
0
1
0
1
0
1
1
1
0
2
0
2
1
1
0
1
1
0
1
1
0
2
0
1
1
1
1
2
1
0
0
2
2
2
0
0
1
0
0
1
0
1
1
1
1
1
1
1
1
0
1
1
2
0
1
2
1
0
2
1
1
0
0
1
2
2
1
2
2
1
0
2
0
0
0
1
1
0
3
0
0
1
0
0
1
1
1
0
0
2
2
1
2
0
1
0
0
0
1
2
2
1
1
0
2
1
2
1
0
2
1
1
0
0
0
1
0
0
0
2
2
2
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
2
1
2
0
0
0
0
1
1
1
2
1
1
0
1
0
0
0
1
0
3
1
1
1
1
1
0
1
0
0
0
1
0
2
1
2
1
1
1
0
0
0
0
0
1
0
2
0
0
1
0
1
0
1
0
1
0
1
0
0
1
2
0
0
1
1
0
0
7
0
0
1
1
1
2
0
0
0
0
0
1
2
2
1
1
0
1
2
1
0
1
2
2
0
1
0
0
0
1
0
2
0
1
2
0
2
1
1
1
0
2
1
0
2
1
1
2
0
1
0
0
1
2
2
0
0
0
0
0
0
2
1
2
2
0
2
1
2
2
2
0
1
0
1
0
1
0
0
2
1
0
0
1
0
1
0
0
1
1
1
2
1
0
0
0
1
1
1
0
0
0
2
2
0
1
2
1
2
2
0
1
0
1
1
2
1
0
1
0
2
0
0
0
1
2
1
1
0
1
0
0
1
0
1
1
1
1
2
0
0
2
1
0
2
2
0
0
0
2
2
1
3
1
1
2
1
0
1
1
2
1
0
0
0
0
1
0
0
1
1
0
0
1
1
0
0
1
0
2
1
1
2
2
3
0
2
1
0
1
2
1
1
0
2
1
3
0
1
1
1
1
0
0
0
1
2
0
0
1
0
1
0
1
1
0
2
1
2
1
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
4
1
2
0
1
0
2
2
1
1
2
0
0
1
0
0
0
1
1
1
1
0
0
1
0
1
1
1
0
0
2
1
0
2
0
0
0
1
0
0
1
0
0
0
2
1
2
2
0
1
2
1
0
2
1
1
2
1
2
0
1
1
0
1
1
1
0
2
2
2
2
1
1
1
1
1
1
0
0
1
1
1
1
3
1
2
1
2
2
1
0
1
1
1
1
0
1
0
0
0
0
1
2
2
0
0
1
2
1
1
0
1
0
0
1
2
0
3
0
3
1
0
2
0
0
1
2
1
0
0
0
1
0
0
1
1
0
0
0
0
1
1
0
1
0
0
2
1
2
1
0
1
1
2
1
1
2
1
0
0
0
1
0
1
2
1
2
0
1
1
0
0
1
1
1
1
1
0
1
1
2
0
2
1
1
1
2
2
1
2
2
1
1
0
0
0
1
0
1
2
1
0
1
0
2
1
1
1
1
0
2
0
1
1
0
0
1
1
0
1
0
0
2
1
1
1
0
0
2
0
1
2
1
2
2
1
1
1
0
0
1
2
0
2
0
2
0
2
1
0
1
1
0
0
0
0
1
0
0
1
2
0
1
2
2
1
2
1
1
0
0
1
1
2
1
0
1
1
0
2
0
1
1
1
1
1
2
0
0
0
0
1
1
2
2
0
1
0
1
0
1
2
1
1
1
0
1
0
1
0
1
0
1
1
2
1
1
0
1
0
0
1
2
2
0
1
0
0
0
1
2
2
1
3
1
0
0
2
0
1
2
2
2
2
1
2
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
2
0
1
2
2
2
0
0
0
1
1
0
1
0
1
1
2
0
1
0
0
0
2
0
1
0
2
0
0
2
1
2
2
1
1
0
1
1
0
1
0
2
0
0
0
0
2
1
1
1
0
0
0
2
0
0
1
2
0
1
1
0
1
0
0
1
1
1
1
2
1
0
1
1
1
0
2
1
1
1
2
0
0
0
3
2
0
0
2
0
0
0
1
2
2
2
1
0
0
1
0
1
1
1
0
0
1
0
0
1
3
2
1
2
1
0
2
1
1
1
0
0
0
0
4
0
2
0
2
2
1
0
1
1
2
2
1
0
0
2
1
3
0
2
1
0
1
1
1
0
0
2
2
2
1
1
0
0
0
1
0
1
0
1
1
0
1
0
0
0
1
1
1
0
2
2
0
0
0
1
2
2
1
2
0
0
1
0
2
1
2
0
0
0
0
0
2
1
2
0
0
0
1
0
1
1
1
2
1
2
0
0
1
0
0
1
1
1
2
1
1
1
2
2
1
1
1
0
2
0
0
0
2
1
1
1
3
2
0
0
0
2
1
1
0
2
1
2
1
2
1
0
1
1
1
0
1
2
2
1
1
0
1
1
0
1
0
0
2
0
0
1
0
1
1
2
2
1
1
0
1
0
1
0
2
0
1
0
0
1
1
0
0
0
0
0
4
0
1
1
0
1
1
0
1
1
0
2
0
2
1
2
1
2
0
0
2
0
0
0
0
0
0
1
3
0
1
1
0
2
1
1
2
2
0
0
0
0
0
0
0
2
0
1
2
0
0
1
1
1
2
0
0
0
1
1
1
1
1
0
1
2
0
0
0
2
0
1
1
1
1
0
1
1
2
1
1
0
2
1
1
0
0
0
1
1
0
2
1
2
0
1
1
1
1
0
1
0
2
0
0
1
0
2
1
2
2
0
3
1
2
0
1
0
1
2
0
3
2
1
1
0
1
2
0
2
1
2
0
0
0
1
1
1
1
0
1
0
1
1
1
1
0
0
0
0
0
0
2
3
0
1
0
1
0
0
2
1
1
2
2
0
1
0
1
0
1
0
2
1
1
0
1
0
0
1
1
1
1
0
0
1
0
3
4
0
0
1
0
1
0
3
0
0
1
0
1
0
0
1
0
1
0
1
0
1
0
0
1
1
0
0
1
1
2
1
1
2
0
3
1
0
2
0
2
0
1
2
2
1
0
1
1
2
1
2
0
1
1
1
0
1
0
0
2
1
1
0
1
0
2
1
2
1
0
1
1
0
0
0
0
0
2
0
1
2
2
0
0
2
0
1
0
0
2
1
0
2
1
0
2
2
2
1
0
0
1
2
2
1
1
1
0
2
0
0
2
1
0
2
1
1
0
2
0
0
0
0
2
1
2
1
1
1
2
1
2
1
1
1
0
3
1
1
1
0
0
2
1
0
1
1
0
1
1
2
2
1
1
0
1
1
2
1
0
1
0
1
1
0
1
1
2
0
1
4
1
0
2
0
1
0
1
1
2
0
2
0
0
2
0
2
1
1
1
0
0
1
1
0
0
1
2
2
0
0
0
1
0
1
0
0
0
0
1
0
1
1
0
1
1
1
1
1
0
2
1
1
0
2
2
1
0
0
0
2
1
1
2
1
1
0
1
0
1
0
1
1
2
0
1
1
0
1
0
0
0
1
0
0
1
1
1
2
2
1
2
1
0
1
0
0
2
1
0
1
0
2
1
1
0
1
1
0
0
0
1
0
0
0
1
0
0
1
0
2
1
0
1
2
1
0
0
2
0
0
0
1
1
1
1
1
1
2
1
1
1
2
0
1
2
2
1
0
2
2
0
2
2
1
1
1
0
1
1
2
0
0
1
0
0
1
2
1
0
2
2
2
2
1
2
0
0
0
1
2
2
1
1
0
0
0
1
1
1
2
0
1
0
1
0
1
1
1
0
2
2
6
0
0
0
0
2
2
1
1
0
0
2
2
0
1
2
4
2
0
0
1
1
0
2
1
2
3
1
0
2
1
0
1
1
0
0
1
0
1
0
1
1
1
1
3
0
0
2
1
1
0
1
1
0
0
0
0
0
0
1
1
1
1
1
0
1
0
1
2
0
2
0
0
2
1
1
3
3
0
0
1
0
0
0
0
2
0
0
2
1
0
1
2
1
0
1
2
0
1
2
1
2
1
1
1
1
2
0
0
0
2
1
0
1
0
2
0
1
1
2
0
4
0
1
2
1
0
1
1
0
1
1
1
1
1
0
0
1
1
1
1
0
1
2
2
2
1
0
0
0
0
3
0
1
2
2
0
1
0
2
0
1
0
0
0
1
2
0
1
2
1
0
2
0
1
1
3
0
1
1
2
0
1
0
0
0
1
0
2
1
0
1
2
0
3
0
0
1
1
0
1
2
1
0
1
1
1
1
2
1
0
0
1
0
1
2
1
0
0
2
1
0
0
0
1
0
1
0
0
1
0
1
0
2
0
2
1
1
1
1
1
1
0
1
1
2
0
0
1
0
1
1
0
0
2
1
0
1
0
0
2
0
1
1
2
1
0
1
1
2
1
1
0
1
1
2
1
0
0
1
0
0
0
2
0
1
1
1
1
0
1
3
0
1
1
0
0
0
0
0
0
1
2
1
1
0
2
2
0
0
2
1
3
2
0
2
1
0
0
0
0
1
1
0
0
2
0
0
0
0
2
1
2
2
1
1
1
0
0
1
0
1
0
1
3
0
1
1
0
1
1
2
1
0
2
1
1
2
2
1
2
1
2
2
0
3
0
0
2
2
1
1
2
2
1
2
0
1
2
0
1
1
2
1
0
1
1
1
2
0
2
0
0
0
0
0
1
2
1
1
0
0
1
0
1
0
2
5
1
0
1
0
1
0
0
0
1
0
1
0
1
0
1
1
2
1
2
0
1
0
3
2
0
1
0
2
2
1
0
1
1
0
0
1
1
2
0
0
2
0
2
1
2
1
1
1
0
2
2
1
0
0
1
1
0
0
0
0
1
2
2
0
0
0
1
0
2
0
0
0
0
2
0
2
1
1
1
1
0
0
2
0
0
0
1
1
0
1
1
1
0
0
1
1
3
1
2
1
1
0
1
1
1
1
0
3
2
1
2
0
2
2
2
1
1
1
0
0
1
0
1
1
2
1
2
2
1
2
1
1
2
0
0
0
1
0
2
2
0
1
1
0
0
2
1
0
0
0
1
2
2
1
0
2
0
0
0
1
0
0
0
2
1
2
1
0
1
2
1
0
2
1
0
2
0
0
1
1
1
1
0
0
0
1
2
1
0
0
0
1
1
1
1
1
1
0
1
0
2
1
1
2
0
1
0
1
1
0
1
0
1
0
0
1
0
1
2
0
2
0
1
0
2
0
0
1
0
0
0
0
2
2
1
0
0
0
0
6
1
1
1
0
1
2
0
2
1
1
2
1
0
1
1
1
0
0
0
1
2
2
0
1
1
2
1
0
0
2
2
1
1
2
1
0
0
0
0
0
0
1
1
0
1
0
0
1
0
2
0
0
1
2
2
1
0
2
0
2
1
1
0
2
0
0
1
0
0
0
1
2
1
1
1
1
1
1
1
1
1
0
2
2
1
1
1
1
0
0
0
1
1
2
1
0
1
0
0
2
1
1
0
1
0
0
0
0
1
0
1
1
0
0
1
1
1
1
2
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
1
1
1
2
1
0
0
2
0
0
3
0
0
0
1
1
0
0
0
2
2
2
0
1
2
1
1
2
0
0
1
1
1
2
1
0
0
0
2
1
2
1
0
1
0
0
1
1
2
0
0
1
0
0
1
0
1
1
0
1
1
0
1
0
0
0
2
1
0
0
0
0
1
0
1
1
1
1
0
2
1
1
2
3
0
1
0
1
1
1
1
1
0
1
0
2
0
2
2
1
1
2
1
0
0
0
2
1
0
1
2
2
1
0
4
1
1
2
2
0
4
1
1
0
0
0
0
0
0
1
0
1
1
0
1
2
0
0
1
1
0
1
2
0
3
2
0
0
1
0
1
2
0
0
0
0
0
1
1
0
2
1
0
1
1
1
0
0
0
1
2
0
0
3
0
0
3
1
0
0
1
0
0
1
1
1
2
1
0
1
1
1
0
2
1
1
2
2
1
0
0
1
1
0
2
0
0
0
1
0
1
2
1
1
2
3
2
1
0
2
0
2
2
2
1
2
0
1
2
2
1
0
1
1
1
1
1
2
4
2
0
2
0
0
1
1
0
1
1
2
0
1
1
1
0
0
2
2
0
1
2
0
1
0
0
2
0
2
1
1
0
1
1
1
0
0
0
1
1
1
0
0
0
2
2
0
1
0
0
2
1
1
2
1
0
1
1
4
1
2
1
1
0
0
2
0
0
2
2
1
0
1
1
1
0
0
1
4
0
1
1
1
1
1
0
1
2
0
0
2
1
1
0
1
1
1
1
0
1
1
1
0
2
0
2
2
2
1
1
2
0
1
1
1
1
1
1
2
0
1
2
0
0
0
2
2
3
0
0
0
0
1
0
0
0
0
1
1
1
1
2
2
1
2
2
1
1
0
1
1
1
2
1
0
2
1
1
0
0
1
2
1
1
1
0
2
2
1
0
0
0
1
2
2
0
1
1
1
0
2
2
1
1
1
1
0
0
0
0
1
1
0
0
0
0
1
1
1
1
2
11
0
1
1
0
0
1
1
1
2
1
1
1
1
1
0
0
1
1
1
1
2
0
2
0
2
2
0
0
1
2
0
1
1
0
1
0
0
1
0
1
2
0
2
0
0
1
1
1
0
1
0
0
1
0
1
1
2
1
0
1
0
1
2
0
0
1
1
1
0
0
2
1
1
0
1
0
2
2
0
0
0
2
2
1
0
0
1
0
0
1
0
1
0
0
0
1
2
2
0
2
1
0
0
2
1
2
1
1
1
1
1
0
0
1
0
1
1
0
1
1
0
0
1
1
0
0
1
0
0
0
0
1
0
1
1
1
2
1
1
1
1
1
1
0
1
0
2
1
1
0
2
0
1
1
1
1
0
0
2
2
0
2
0
2
1
1
1
0
0
1
1
0
1
0
1
1
1
1
1
1
1
0
0
1
1
2
1
1
0
1
0
0
1
2
0
0
1
2
0
1
1
0
2
1
2
0
0
2
1
1
1
2
2
1
2
1
1
1
0
1
0
0
1
0
2
0
1
1
1
2
2
1
0
2
1
0
1
2
0
2
0
3
2
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
2
1
1
1
1
0
1
0
0
0
0
2
1
1
2
3
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
2
0
0
0
0
0
0
0
0
1
1
1
1
1
0
1
1
0
1
1
0
2
1
0
1
1
0
2
1
1
2
1
0
0
1
0
1
2
1
1
0
1
0
0
1
0
1
1
0
2
1
1
0
1
0
1
0
0
0
0
1
1
2
0
0
1
2
1
0
0
2
0
0
0
1
1
1
1
0
0
0
1
1
0
2
0
0
1
1
2
0
0
1
1
0
0
0
0
1
0
0
0
1
1
2
0
0
1
0
0
1
1
0
1
1
2
1
1
1
0
1
0
1
2
2
2
0
1
0
1
1
1
2
1
0
1
0
0
0
0
1
0
1
0
1
1
1
0
1
1
0
0
4
0
2
2
1
1
0
1
0
0
0
1
2
1
0
1
1
1
0
1
1
1
3
1
0
0
1
0
1
0
3
0
1
2
0
0
1
0
1
0
0
1
2
0
0
2
1
0
1
1
0
0
0
1
1
1
0
2
1
0
2
1
0
0
0
2
0
0
0
0
0
2
1
2
0
1
1
1
1
1
1
2
0
2
1
1
1
2
0
0
0
1
1
0
0
0
0
1
2
0
0
0
1
0
1
1
0
0
2
0
0
0
1
1
1
0
2
0
0
0
2
1
0
0
1
3
2
1
0
0
2
1
2
1
2
1
1
0
0
0
1
0
2
1
0
1
1
1
1
2
0
1
1
2
2
1
1
0
2
2
0
0
1
0
1
1
0
1
1
0
1
1
1
1
0
3
2
0
0
1
2
0
0
0
0
1
2
1
1
1
0
0
0
1
0
2
0
0
1
2
2
2
0
1
1
0
2
2
1
0
1
1
0
0
2
2
0
0
0
1
0
2
0
2
0
0
2
0
0
0
0
2
2
2
0
1
1
0
2
2
1
0
1
0
1
0
1
1
2
0
1
2
2
0
0
0
0
1
2
1
2
1
2
0
1
1
1
0
1
0
0
0
1
0
1
2
1
2
0
0
1
2
2
6
0
0
1
1
0
1
1
1
1
0
0
1
0
2
1
0
1
0
0
1
1
1
0
0
2
1
0
0
0
2
0
0
1
0
1
0
1
2
0
0
1
2
2
1
3
0
0
0
1
1
2
1
1
0
1
2
2
1
0
0
0
1
2
0
1
0
4
0
1
0
6
1
1
0
2
1
1
1
2
0
0
2
2
1
1
0
1
0
2
0
0
1
2
0
1
1
0
1
0
0
1
0
0
1
1
0
0
2
0
1
2
2
1
1
0
1
0
1
0
2
2
2
0
2
0
2
1
1
0
0
0
0
2
1
0
1
2
0
1
2
1
1
0
1
0
0
1
1
1
0
0
0
1
0
0
1
1
0
0
0
1
1
2
0
1
1
1
1
0
2
1
0
1
0
1
2
2
0
0
1
0
3
0
0
0
2
0
0
0
0
1
1
0
1
1
0
2
0
0
1
0
1
0
0
1
2
0
0
2
2
0
1
2
2
0
2
0
1
2
2
1
1
0
0
2
1
2
1
0
0
1
0
2
1
2
1
1
2
2
1
1
0
1
1
0
2
0
2
2
0
0
0
0
1
1
0
1
2
1
2
2
1
0
0
1
1
1
1
1
0
2
1
0
0
2
0
1
1
0
0
0
0
1
0
0
6
1
1
0
0
0
1
2
1
1
2
0
4
2
2
2
2
1
1
1
2
0
1
1
2
2
1
0
0
0
0
0
1
1
1
1
1
2
2
2
2
2
0
0
0
1
2
0
2
0
0
0
1
0
2
1
0
0
1
2
2
0
1
0
2
2
1
1
0
0
2
2
1
0
3
1
2
0
0
1
1
0
2
0
2
2
0
2
0
1
0
0
0
1
0
1
1
2
1
0
1
0
1
0
0
2
2
0
2
0
1
0
1
2
0
2
2
1
1
1
1
0
1
0
3
2
2
2
1
0
1
0
1
0
2
1
1
1
0
2
2
1
0
1
2
0
0
2
1
0
0
2
0
0
0
1
1
0
1
1
1
1
1
0
1
1
1
1
1
1
0
1
2
0
0
0
1
1
1
0
0
1
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
1
2
0
0
0
0
0
1
0
0
1
2
1
1
1
2
0
1
1
2
1
1
2
1
2
0
1
0
1
0
2
0
0
0
0
0
1
2
0
1
1
1
1
0
1
1
2
1
0
0
0
1
2
0
1
1
2
0
0
0
1
0
2
1
0
2
1
0
2
2
0
1
1
0
2
0
1
0
1
0
0
2
0
0
0
1
0
1
1
1
0
1
1
1
0
2
2
1
2
0
1
0
1
0
0
0
2
0
3
0
0
1
1
0
0
1
0
4
2
0
0
0
1
1
0
0
1
2
0
1
0
1
1
1
1
0
0
1
0
1
1
0
1
0
1
1
2
1
2
1
2
2
3
1
2
2
1
0
0
0
1
2
0
0
1
1
1
0
0
1
1
0
2
1
2
2
0
2
1
2
1
1
0
1
0
1
2
1
0
2
0
0
0
4
1
1
2
1
0
1
0
1
0
1
3
1
1
0
0
0
2
0
0
0
0
0
1
1
0
1
0
2
0
0
0
2
0
1
2
1
1
1
0
0
0
0
2
1
0
2
0
2
0
0
0
0
1
0
1
1
0
1
2
0
1
0
0
1
1
0
0
0
0
1
0
1
1
1
0
1
0
1
0
1
1
0
1
0
0
0
0
2
2
1
1
1
2
0
2
1
2
1
0
0
0
1
2
0
2
2
1
0
0
0
1
0
1
1
0
2
2
1
1
0
0
1
1
0
1
1
0
0
0
0
1
1
1
2
0
1
1
1
1
3
1
1
1
1
2
0
1
2
1
0
2
2
1
2
1
2
1
1
2
0
1
1
0
1
0
2
1
2
2
1
2
0
0
1
3
0
0
1
2
0
5
0
1
0
2
0
0
1
2
2
1
1
1
2
1
1
1
1
2
1
2
2
2
1
1
1
1
2
1
0
1
0
1
1
4
1
1
1
2
0
0
1
1
0
0
0
1
1
0
1
1
2
1
1
7
1
1
1
2
0
1
1
2
1
1
0
1
1
1
0
1
1
1
2
1
1
1
2
1
0
1
0
0
2
0
1
0
0
2
1
0
0
1
2
0
1
2
0
1
2
1
0
1
2
0
1
1
1
2
0
1
1
3
2
1
0
4
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
2
1
0
0
1
0
2
2
1
0
1
1
0
2
0
0
0
1
0
1
1
2
2
0
1
2
1
0
0
2
0
1
1
0
1
1
0
1
0
1
1
2
1
0
0
0
1
0
0
1
1
0
0
1
1
7
2
1
1
2
0
0
2
0
0
1
0
1
1
1
0
1
1
0
0
0
1
0
0
0
2
1
1
0
0
0
2
1
1
2
2
1
0
0
1
1
0
3
2
1
1
0
2
1
1
2
0
0
1
2
0
0
1
0
0
6
0
1
1
0
0
0
1
2
2
1
0
0
2
2
1
0
1
1
3
1
1
0
1
1
0
3
0
0
0
2
0
0
0
1
1
0
1
0
1
2
1
0
0
1
0
1
1
0
2
1
0
0
2
1
1
2
0
1
0
0
1
0
3
1
1
2
0
1
1
1
1
0
0
2
0
1
2
0
1
0
2
0
0
0
2
2
1
0
2
0
1
1
1
1
2
0
1
1
1
0
0
1
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
1
1
1
1
0
2
1
0
1
0
3
2
1
1
0
0
1
1
2
1
0
1
2
1
0
0
0
0
0
1
0
1
2
0
1
1
0
1
0
2
1
1
0
0
1
0
1
1
0
1
0
1
1
1
0
0
0
2
0
1
0
0
0
2
2
1
0
1
0
0
3
1
1
0
1
2
1
1
1
1
2
1
2
1
1
1
1
1
0
0
1
0
1
1
0
1
1
2
1
2
1
0
2
0
1
2
1
0
2
0
1
0
1
1
0
1
1
1
0
0
0
1
0
0
1
1
1
0
2
0
0
2
1
1
1
1
1
0
2
0
2
0
2
2
1
0
0
0
0
1
0
1
2
0
0
1
2
0
2
0
0
1
0
0
0
0
2
2
1
0
0
1
0
1
1
1
0
1
0
0
0
1
1
0
0
0
2
0
2
1
1
0
0
2
2
2
1
0
1
1
0
1
2
0
1
0
1
0
0
2
1
2
1
1
0
0
0
0
2
2
2
0
0
0
0
1
1
2
12
3
0
2
0
2
4
2
0
1
0
1
0
1
2
0
0
0
1
0
0
0
0
1
1
0
2
1
1
0
1
0
2
1
0
1
0
0
2
0
1
0
0
1
1
1
0
0
2
0
1
1
1
1
2
2
1
1
0
0
2
1
1
0
0
0
1
2
1
0
1
0
0
2
0
0
1
2
1
2
1
0
0
1
0
1
1
1
0
0
1
0
1
0
2
2
1
0
1
1
1
1
0
0
1
0
1
0
1
1
1
1
2
2
0
1
1
1
0
2
2
1
1
2
1
1
0
2
1
2
1
0
2
0
2
2
2
1
0
0
1
1
1
1
0
0
1
0
1
2
1
0
2
1
1
1
2
1
0
1
1
0
1
1
0
1
0
1
0
1
2
0
1
0
0
1
0
0
2
1
0
1
0
1
0
1
0
0
2
0
0
1
1
0
0
0
3
1
1
2
0
2
0
2
1
0
0
0
0
2
2
1
1
4
1
1
1
0
0
1
2
1
0
1
1
0
1
1
0
1
0
1
1
1
0
2
0
0
2
0
2
2
1
1
5
0
0
0
2
0
1
0
1
2
0
0
1
0
0
0
2
0
2
0
0
0
1
1
1
0
0
2
0
0
1
0
2
1
0
0
0
2
0
1
2
0
2
0
0
0
1
0
0
1
0
0
0
1
0
2
0
2
0
3
2
0
1
0
1
0
2
1
2
2
2
1
1
1
0
1
0
1
0
2
1
1
1
0
0
2
0
2
1
1
2
2
0
1
0
0
0
1
0
1
2
1
1
0
1
2
1
3
0
1
1
0
1
2
2
0
2
0
1
0
2
1
1
1
2
2
1
0
1
2
0
0
0
1
0
2
0
2
1
0
0
2
1
1
2
2
1
1
0
1
2
1
0
0
1
0
2
0
2
1
1
1
2
1
0
1
1
1
1
1
1
0
0
0
1
2
0
1
1
1
1
2
0
0
0
1
0
0
0
0
0
0
4
0
0
2
2
0
1
0
2
6
2
1
0
0
2
0
1
0
1
1
0
1
1
0
0
2
1
0
1
1
1
0
1
0
0
1
2
1
1
1
0
0
2
0
1
0
0
1
0
1
2
1
1
0
0
1
0
1
1
0
0
0
1
1
0
2
1
0
0
1
1
0
0
0
1
1
1
0
2
1
0
0
0
0
2
1
1
0
1
0
1
4
0
1
0
1
1
1
0
1
1
3
0
0
1
0
2
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
1
2
1
0
1
1
0
1
1
1
2
1
1
0
0
2
0
1
0
1
1
1
0
1
3
1
1
0
0
2
1
0
0
2
0
1
2
0
0
1
0
0
0
0
1
0
1
1
1
2
0
1
0
0
0
3
2
0
0
2
1
1
1
0
1
2
1
1
1
2
0
2
0
1
0
1
2
2
0
1
0
1
1
2
1
2
1
2
1
1
2
0
2
0
0
1
1
0
2
0
0
1
2
1
2
1
0
2
1
2
2
1
2
1
1
1
0
1
0
0
0
2
2
0
1
1
1
1
0
0
0
0
0
0
1
0
0
2
1
0
1
0
2
1
1
2
0
2
1
1
0
2
2
0
1
0
1
2
0
1
0
1
0
0
0
2
1
1
1
0
2
0
0
0
2
2
0
1
1
0
1
1
2
1
2
0
2
0
2
0
1
0
0
1
2
1
0
1
0
2
0
0
1
0
1
0
1
0
0
0
2
1
1
1
0
0
0
0
0
2
1
0
0
1
0
0
0
0
2
1
0
2
1
1
2
0
1
1
0
0
0
2
2
0
2
0
2
1
0
2
0
1
0
0
1
2
0
0
0
1
2
0
0
0
0
0
2
2
1
1
0
2
1
1
1
2
2
2
0
1
0
1
0
2
1
1
1
1
1
1
2
1
0
1
0
0
1
1
1
1
1
2
1
1
1
0
0
1
2
2
2
2
0
1
1
2
0
1
0
2
1
1
0
3
1
0
1
0
1
4
0
1
1
0
4
0
0
2
2
1
0
1
1
0
1
0
1
2
1
2
2
0
0
1
0
0
1
0
1
1
1
0
0
1
0
0
2
2
1
1
2
2
1
2
0
0
0
2
2
0
0
1
0
0
0
0
2
0
2
0
0
1
2
1
1
1
0
1
1
0
0
1
0
1
1
1
1
2
0
1
2
2
2
1
2
0
2
1
1
0
0
1
1
1
0
2
0
1
0
2
0
1
1
1
1
2
1
0
0
0
0
1
1
0
0
1
0
1
0
0
2
1
0
0
0
1
1
0
3
0
2
1
0
2
1
1
2
0
2
1
2
0
2
0
1
1
0
1
1
1
0
0
1
0
1
2
1
2
1
0
0
2
0
0
1
0
0
0
0
0
0
0
1
2
0
1
0
2
2
0
1
1
1
1
0
1
1
1
1
2
1
1
2
0
1
1
1
2
0
0
0
0
1
0
2
0
1
1
1
1
0
1
1
1
1
0
0
0
1
0
0
0
1
2
2
0
1
1
2
2
0
1
0
1
2
0
1
1
0
0
1
0
2
0
2
0
2
2
1
1
1
0
2
1
0
1
1
0
1
0
0
1
1
0
2
0
0
1
0
0
2
0
0
2
1
1
1
1
1
0
2
0
1
1
2
1
1
2
0
0
1
3
0
1
0
0
1
2
1
0
0
0
2
1
1
0
1
1
0
2
0
1
0
1
0
0
1
1
0
1
2
2
2
1
1
0
0
1
1
2
2
2
3
0
1
2
2
0
0
0
2
1
1
1
2
2
0
0
0
0
0
1
0
0
0
0
1
0
1
1
2
2
0
0
0
1
1
0
0
0
2
0
1
2
0
2
0
2
2
0
4
0
1
1
0
0
0
0
1
0
1
1
0
2
0
1
1
2
0
0
0
0
0
2
0
0
2
2
0
1
0
0
1
0
0
0
2
0
0
1
1
0
2
2
0
2
0
0
1
0
0
2
2
1
0
1
0
1
0
2
2
0
1
1
0
1
2
0
2
0
1
0
2
2
0
2
0
1
0
2
1
1
2
1
0
0
2
1
0
1
1
1
2
1
1
1
1
0
0
0
1
1
1
2
0
0
1
0
1
0
0
1
0
1
1
0
0
1
0
0
2
2
2
2
2
0
1
1
0
1
1
1
1
1
2
0
1
1
0
0
1
0
1
1
0
1
2
2
1
1
1
0
0
1
2
1
1
0
0
2
1
2
1
1
1
0
0
1
2
1
0
1
2
2
0
1
0
1
1
1
0
0
2
2
2
1
1
1
2
0
0
0
2
0
2
0
0
2
2
1
1
0
2
2
1
0
1
1
1
2
0
1
1
1
2
1
1
1
0
1
0
0
2
1
2
0
0
2
0
0
0
0
1
1
1
0
0
1
2
1
1
2
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
2
1
1
1
0
2
1
0
0
1
0
0
2
0
1
1
1
1
1
0
3
1
0
0
1
1
0
1
0
1
0
0
1
1
1
1
0
0
0
2
0
2
0
0
1
2
2
1
0
0
2
1
1
2
1
2
1
1
0
1
1
1
2
1
0
1
1
0
0
2
2
2
0
2
0
0
2
2
0
0
0
0
2
1
1
0
2
1
1
0
0
0
1
1
2
2
0
1
1
1
1
0
0
1
1
0
2
0
1
1
1
2
0
1
2
0
1
0
1
1
1
0
1
0
2
1
0
2
0
1
0
0
0
0
0
0
1
1
2
0
1
2
0
1
0
0
0
1
2
1
1
0
0
2
0
1
1
1
1
0
0
1
2
1
1
0
1
2
2
1
1
1
0
1
1
0
3
1
0
1
2
0
1
0
0
1
0
2
0
1
2
0
1
0
0
1
0
2
2
1
0
1
0
1
1
1
2
1
1
0
0
1
3
0
2
1
2
0
0
2
0
2
2
2
1
1
0
1
2
1
1
0
0
1
3
1
0
2
2
1
2
0
0
0
1
2
2
0
4
0
0
0
0
0
0
1
1
0
0
2
1
1
1
0
0
0
0
2
0
1
1
1
0
0
0
0
0
0
0
1
1
1
2
1
1
0
1
2
0
0
2
0
2
2
4
0
0
0
0
0
0
1
2
1
0
0
0
1
1
2
2
0
2
1
0
1
2
1
0
1
1
1
0
1
1
0
1
1
0
1
1
1
1
1
0
1
1
1
1
1
1
1
0
1
2
1
0
2
2
2
1
0
0
0
2
0
1
2
0
1
1
0
0
1
1
2
2
1
3
2
2
0
1
0
0
1
0
2
1
1
2
0
0
0
1
0
1
0
2
0
3
2
2
1
0
1
1
1
1
0
1
2
2
0
0
1
2
0
1
0
0
0
0
2
1
1
1
0
1
1
1
0
1
1
2
0
0
1
2
0
1
2
3
1
1
0
1
0
1
2
0
1
1
4
2
1
0
2
1
1
2
2
2
0
0
1
0
0
1
1
3
1
1
1
0
1
2
0
1
1
1
1
0
2
0
2
2
0
0
1
0
2
0
1
1
2
2
0
0
2
1
1
0
1
1
2
2
1
2
0
1
0
1
1
1
2
1
0
2
1
0
2
2
2
1
2
1
1
0
0
0
1
1
1
1
2
1
0
1
1
1
2
1
0
1
0
0
0
0
1
1
2
0
0
0
0
1
1
0
0
0
0
0
1
2
0
0
0
1
0
1
1
1
0
0
1
1
0
0
1
2
0
1
0
1
0
2
1
0
1
0
0
1
0
1
0
1
1
1
1
0
2
1
0
0
1
0
1
1
1
2
1
1
0
2
0
2
0
0
0
1
2
1
2
1
0
0
3
1
0
1
0
1
0
2
2
0
1
0
1
2
1
1
0
0
1
0
0
0
1
1
1
0
3
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
2
0
1
0
1
1
2
0
1
1
1
0
1
1
1
0
0
1
0
1
0
1
2
1
1
1
1
0
1
2
0
1
0
1
0
3
2
1
0
2
2
0
0
0
1
1
0
1
2
2
2
1
1
1
0
2
2
0
0
1
1
0
0
1
0
3
0
0
2
0
2
1
2
0
0
1
1
0
1
0
0
0
2
2
1
1
0
2
1
1
1
0
0
1
1
0
1
2
1
2
1
1
0
1
1
1
0
2
0
1
0
1
0
1
0
1
2
2
2
1
1
0
1
2
1
0
1
0
0
1
1
1
0
1
1
2
1
0
0
2
1
0
0
1
2
2
1
0
2
0
0
1
0
1
2
2
1
2
1
0
1
1
0
1
1
2
1
0
1
0
0
1
0
1
1
1
0
0
2
1
1
1
1
0
1
1
1
1
0
0
1
0
0
2
1
0
0
0
0
1
0
0
0
0
1
0
1
2
2
1
0
1
0
2
2
1
2
1
0
0
0
0
1
0
1
1
1
0
0
2
3
1
2
1
1
0
1
2
0
2
0
0
0
1
0
0
2
0
1
0
1
0
0
2
0
1
0
0
1
1
1
0
0
0
0
0
2
1
1
0
0
0
0
1
1
1
3
1
1
2
1
2
2
0
0
0
0
0
1
1
3
2
2
1
1
1
2
0
1
0
0
1
0
1
0
1
2
0
1
2
1
1
2
0
2
1
1
2
2
0
1
2
0
0
0
1
0
1
1
0
0
0
0
0
2
0
0
1
1
0
0
1
1
0
1
2
1
0
0
0
2
0
0
2
0
1
2
1
1
1
0
0
1
1
1
2
1
2
1
0
1
1
0
1
1
0
0
0
1
0
0
1
0
1
1
2
2
0
2
0
2
0
2
2
1
2
0
0
1
0
0
2
0
0
3
1
1
2
2
0
2
2
2
1
2
0
2
0
0
0
0
1
1
0
2
1
0
1
2
3
1
4
1
2
0
2
0
0
0
2
2
0
1
1
0
2
1
0
0
2
1
1
1
2
0
2
1
0
0
0
2
1
2
1
2
1
0
0
1
1
0
2
2
1
0
1
0
1
0
0
1
1
0
0
1
0
3
0
0
0
0
1
1
0
0
0
1
1
0
0
1
1
2
2
1
0
0
2
1
1
0
1
0
2
2
2
0
1
0
1
1
0
0
0
0
1
1
1
2
1
1
2
2
1
1
0
0
0
0
0
0
2
2
0
1
1
0
1
1
1
1
2
1
0
1
0
0
1
1
1
1
0
3
0
1
1
0
1
1
0
2
2
0
1
1
0
2
0
0
1
0
0
1
0
2
1
2
0
0
2
2
1
0
2
0
1
0
0
1
2
2
0
0
1
0
2
1
2
0
2
2
2
0
1
0
0
1
0
1
1
1
0
0
1
0
0
2
1
1
2
0
0
2
4
0
1
1
0
2
0
1
2
0
2
4
1
1
0
2
0
0
0
1
1
0
1
0
1
0
1
0
0
2
3
0
1
0
1
2
3
1
0
4
0
1
0
2
1
1
1
2
1
0
0
0
1
1
0
1
1
0
1
2
0
1
3
2
1
2
1
2
0
2
1
2
1
0
1
0
2
0
0
0
0
2
0
1
0
0
0
2
1
1
0
1
2
2
0
2
2
2
1
1
2
1
0
0
1
3
1
2
0
1
0
1
1
0
1
0
1
1
1
0
1
0
0
0
0
0
1
2
0
1
0
1
2
0
2
0
2
3
0
0
2
0
1
1
0
1
0
2
0
5
0
2
2
1
0
2
2
1
0
2
2
0
2
2
0
2
0
0
1
0
1
0
0
0
1
2
1
2
1
0
1
1
0
1
1
0
1
2
1
1
0
2
2
2
1
1
2
1
0
0
0
0
1
1
3
2
2
1
0
2
0
0
1
2
2
1
0
0
1
1
0
0
0
1
0
0
1
2
1
0
0
1
1
2
0
1
0
0
1
1
0
0
0
2
0
0
0
1
1
2
0
2
1
0
10
2
2
1
2
1
6
0
1
1
1
0
2
0
0
0
1
1
1
3
0
2
2
0
2
1
0
0
3
0
1
1
1
0
2
2
0
1
2
2
1
0
3
1
2
1
0
0
1
0
1
1
1
1
2
1
1
1
1
0
1
0
0
0
0
0
1
1
1
1
1
0
2
0
0
0
1
1
0
0
0
1
0
1
0
1
1
1
1
1
0
1
0
1
1
0
0
0
2
1
0
1
2
0
1
1
1
0
2
1
2
0
2
0
0
0
0
0
0
2
0
1
3
1
0
0
0
0
0
1
0
2
1
1
2
0
0
2
1
0
1
2
1
1
0
2
1
1
1
2
0
1
0
0
0
0
0
2
0
3
0
0
1
1
1
1
1
1
0
1
1
0
0
2
0
0
1
2
1
1
0
1
0
0
2
1
1
2
0
2
1
1
0
0
1
1
1
1
0
1
0
1
1
1
2
0
1
0
0
0
1
1
1
1
0
2
0
0
0
0
0
2
2
2
2
1
1
0
1
1
1
0
0
2
2
1
0
1
1
1
1
1
2
1
0
1
1
1
2
0
2
0
0
1
1
0
2
0
0
2
1
0
1
0
1
1
2
0
1
0
0
1
0
0
0
2
1
0
2
0
2
1
2
2
0
0
2
0
0
0
0
2
2
1
2
2
2
1
0
0
1
1
1
0
2
2
1
0
1
0
1
0
1
1
1
1
0
1
1
0
2
0
1
1
0
1
2
2
1
1
2
2
1
0
2
2
1
0
1
2
2
2
0
2
1
2
0
0
0
2
2
2
0
2
3
0
1
0
0
0
1
2
1
0
2
0
1
3
1
1
0
0
0
0
1
1
3
1
1
0
0
1
0
2
1
1
0
0
1
0
0
0
0
2
1
1
0
1
1
2
2
1
2
0
0
0
1
1
2
0
0
1
1
1
1
1
0
0
2
1
1
2
0
3
1
1
1
0
1
0
1
0
0
0
1
2
1
0
1
1
1
1
0
0
0
1
1
0
0
1
1
0
1
0
1
3
0
1
1
0
0
0
2
0
0
3
1
1
1
0
1
2
3
1
0
2
1
1
0
1
1
1
1
1
1
1
0
0
1
1
0
1
1
0
1
0
3
1
1
0
2
2
1
1
1
1
1
1
1
1
2
0
2
1
2
1
3
1
1
0
2
0
1
2
1
2
0
1
0
1
0
2
0
1
0
1
1
0
0
1
1
2
1
0
0
1
1
2
2
2
0
1
3
1
2
1
1
1
1
2
0
1
1
2
1
2
0
0
1
0
1
1
2
1
1
2
2
0
1
1
1
1
2
0
2
2
1
0
2
0
2
0
0
2
2
0
1
0
0
1
1
2
0
0
0
2
1
1
1
2
1
0
1
0
2
2
0
0
2
2
1
1
2
2
1
0
2
1
0
2
2
1
1
1
0
0
1
1
2
0
0
0
0
1
0
1
0
1
1
0
3
0
0
1
2
0
1
1
1
2
0
0
1
0
2
2
0
1
1
1
0
2
0
0
1
0
1
0
1
0
1
1
2
1
1
0
2
1
2
0
1
0
2
1
0
1
1
2
1
2
1
1
2
0
0
1
1
0
3
0
2
1
2
1
1
0
1
1
1
2
2
2
1
0
0
3
0
1
0
1
0
0
0
0
0
2
0
1
0
0
1
1
1
1
0
1
1
1
0
1
0
1
6
0
0
1
0
1
2
2
1
1
1
1
1
1
2
1
1
0
1
2
0
0
2
0
0
1
1
1
0
1
2
0
1
0
0
0
1
2
2
0
1
0
2
1
1
3
1
2
0
2
0
0
2
0
1
0
1
1
0
0
2
2
2
2
2
0
1
0
0
0
0
2
2
1
1
2
1
1
1
0
1
0
2
1
1
0
0
0
0
0
0
1
1
1
0
1
1
1
0
1
1
2
2
0
1
0
0
0
1
2
0
1
2
0
4
2
2
1
1
0
0
2
1
0
0
1
0
2
0
0
1
1
1
0
0
1
1
0
0
0
1
1
2
1
2
0
1
0
1
1
1
1
2
1
1
1
1
0
0
0
0
1
0
0
0
0
2
1
2
2
0
2
1
1
1
1
0
0
1
1
1
0
1
1
1
1
1
1
3
1
1
2
1
0
2
0
2
1
1
0
3
0
1
0
0
0
0
1
1
1
0
2
1
1
2
2
0
0
0
0
1
0
2
1
0
0
1
1
0
1
2
1
2
1
0
1
2
1
2
1
0
2
2
1
2
0
2
1
0
0
0
0
0
0
0
0
1
1
0
0
1
2
0
2
2
3
0
0
0
3
3
1
0
0
1
1
2
1
1
0
1
1
1
0
1
1
1
1
0
1
1
1
0
1
0
0
0
0
0
3
1
1
1
0
2
1
0
0
0
2
0
1
1
1
0
2
2
0
0
0
2
0
0
0
1
0
1
0
1
0
1
2
0
0
0
0
1
0
0
2
0
0
0
0
1
1
0
1
1
1
0
1
1
0
1
1
0
0
1
0
0
1
1
0
0
1
2
3
0
1
0
2
1
0
1
1
2
0
1
3
2
0
1
1
2
0
1
1
0
1
1
1
1
1
1
0
0
0
0
1
1
1
0
0
1
0
0
0
2
0
0
1
2
1
0
2
0
1
0
1
1
2
1
1
1
1
1
1
0
0
2
0
2
1
0
0
0
1
1
1
0
2
0
1
0
2
1
0
1
1
2
0
0
0
1
1
1
2
0
1
2
1
1
0
1
1
0
1
2
2
1
2
1
1
0
1
0
1
2
0
1
0
0
1
1
2
1
0
2
0
0
0
1
1
0
2
0
0
0
0
2
2
0
0
1
2
0
0
0
2
0
1
2
0
0
2
0
0
3
1
3
1
1
2
1
2
2
1
1
0
0
1
1
1
2
1
0
1
0
2
0
1
0
1
2
1
1
0
0
0
0
1
1
0
1
1
2
0
1
0
0
1
1
0
1
0
2
1
0
2
0
1
0
0
0
1
0
0
1
0
1
0
0
8
0
1
0
2
1
1
2
1
1
2
3
1
1
1
1
0
0
1
0
1
1
0
1
0
1
0
1
1
3
0
0
2
1
2
1
0
4
0
0
1
2
0
0
1
2
0
0
1
1
0
2
1
1
2
1
0
0
0
1
0
1
2
1
2
0
0
1
0
0
1
1
2
2
2
1
1
2
1
1
0
3
0
1
1
1
1
1
1
2
1
0
0
1
2
0
1
1
1
1
0
1
1
1
0
0
0
0
0
2
1
2
1
1
1
1
0
1
2
0
2
2
0
0
0
0
0
1
2
0
0
0
1
2
1
0
3
1
0
1
2
2
0
2
1
2
2
0
2
0
0
0
1
1
1
1
1
0
1
0
0
0
1
0
0
0
1
0
0
0
1
1
4
1
2
1
1
0
0
1
0
0
0
1
1
1
2
2
1
1
0
1
1
1
1
0
1
1
0
1
1
1
1
1
1
0
1
1
1
2
1
0
1
0
1
1
1
0
1
0
2
0
0
0
0
1
1
1
1
1
2
1
1
1
0
0
1
0
2
1
1
2
1
0
0
0
1
2
0
1
2
1
0
1
0
0
0
1
1
0
0
1
0
0
0
1
0
2
0
1
0
0
1
0
1
2
0
0
2
0
1
1
1
2
0
0
0
2
1
0
0
2
0
0
0
2
0
0
1
0
0
1
0
1
1
1
1
2
0
1
1
0
0
1
0
1
0
0
1
1
3
1
1
1
1
1
1
0
0
2
2
1
3
1
0
1
1
2
0
1
1
0
0
1
0
1
2
1
2
1
0
2
0
0
2
1
1
1
2
1
1
1
1
0
1
2
0
1
1
2
1
1
0
0
1
0
1
1
0
2
0
0
1
1
1
0
0
0
1
1
1
0
2
2
0
0
1
0
0
0
0
1
1
0
1
2
2
2
0
1
0
0
0
2
1
0
1
0
1
2
0
0
4
2
0
0
2
1
0
2
1
0
0
1
0
1
0
1
1
1
1
2
1
1
0
0
1
0
0
1
0
0
0
2
1
2
1
1
0
0
1
0
0
2
1
0
1
1
0
1
1
2
0
5
1
2
1
1
0
1
1
0
1
1
1
2
2
2
0
1
2
0
0
1
2
0
1
1
0
3
0
0
1
2
2
2
0
1
1
1
1
0
0
0
0
2
1
1
1
1
0
0
0
2
1
1
0
2
1
1
0
0
0
0
0
1
0
0
0
0
1
1
1
1
1
0
2
1
2
1
0
1
1
2
2
0
0
0
1
0
1
1
1
1
2
0
1
1
2
2
2
2
1
0
0
2
0
1
0
0
0
0
0
1
0
1
1
1
2
0
1
2
1
1
0
0
0
1
1
0
1
1
0
1
1
0
2
0
1
0
2
1
0
1
1
2
1
1
1
2
1
1
1
1
0
1
1
0
1
1
2
1
1
0
1
0
0
0
1
1
2
1
2
2
1
1
1
0
0
2
1
0
0
0
0
1
1
0
2
1
0
1
1
1
2
0
1
1
1
0
0
1
2
0
1
0
0
2
1
0
1
1
0
2
0
0
0
1
0
0
2
1
4
0
0
1
1
0
1
1
2
0
1
0
0
1
0
0
0
1
1
0
2
1
0
0
2
0
0
1
1
1
0
1
2
2
0
2
0
0
2
3
0
1
1
0
2
2
1
1
0
0
2
1
2
2
1
0
1
0
1
0
0
1
0
1
2
3
0
1
0
2
1
0
1
1
2
1
1
1
1
1
1
1
0
2
1
0
2
1
1
1
2
2
2
2
0
1
0
1
0
1
1
2
1
2
1
2
1
2
0
1
0
2
0
0
1
2
0
0
0
0
0
1
0
1
1
1
0
2
0
2
1
1
2
1
0
2
2
2
1
2
2
1
1
2
0
1
0
0
2
1
2
0
0
2
1
0
0
3
0
0
2
0
2
1
1
0
1
0
0
0
1
1
0
3
1
1
0
0
0
1
0
1
0
2
1
2
2
1
0
2
1
2
0
1
1
0
0
1
0
2
1
0
1
2
0
0
0
2
0
1
2
2
1
0
1
1
0
0
2
1
1
1
0
1
1
1
2
0
2
2
0
2
0
1
0
0
0
0
2
0
1
0
1
3
0
1
0
1
0
0
1
2
0
0
2
0
0
1
1
0
2
0
0
2
1
0
2
0
0
2
2
1
0
1
0
0
1
1
0
0
1
0
0
1
0
2
0
1
1
1
0
1
2
0
0
1
0
1
0
1
1
0
0
0
1
0
0
2
1
1
1
1
1
2
0
0
0
2
0
1
2
2
0
0
1
1
0
1
0
0
2
1
0
0
1
1
2
0
1
0
0
0
1
1
1
1
1
2
1
0
1
0
0
0
1
0
2
0
1
3
1
2
1
0
1
0
1
2
1
0
1
2
2
0
0
1
2
2
0
2
1
0
2
0
1
0
0
0
0
0
2
2
1
0
1
0
1
1
1
2
1
0
1
0
2
0
1
0
0
0
0
2
1
1
1
1
0
1
1
0
1
0
2
3
1
1
2
2
0
0
2
0
1
0
2
0
2
0
2
1
0
1
1
0
0
1
1
1
2
2
1
0
0
1
2
0
1
1
0
2
1
0
0
2
2
0
1
1
0
0
0
1
1
1
0
1
2
0
0
0
1
0
2
2
0
0
1
0
0
0
0
0
1
2
2
2
0
1
1
1
2
0
0
2
0
1
0
0
1
1
1
1
2
0
1
0
0
1
1
0
1
0
1
1
0
1
2
0
0
1
1
2
1
0
0
2
0
1
0
1
0
1
0
0
2
1
1
0
0
0
0
0
0
1
0
0
1
0
1
1
2
0
0
1
0
2
1
0
0
2
0
1
2
2
0
0
0
1
0
0
2
0
2
0
1
2
1
1
1
1
1
0
2
1
0
1
0
0
1
0
0
0
1
2
0
1
2
0
1
0
2
1
0
0
0
0
1
0
1
1
1
2
1
2
1
0
0
1
1
1
2
1
1
1
0
0
2
3
1
3
0
1
1
1
1
0
1
2
1
1
1
3
2
2
0
1
0
1
0
1
1
0
2
1
2
0
0
1
3
0
0
0
1
0
1
2
0
1
0
0
0
2
2
0
0
0
1
2
1
2
0
3
2
1
2
1
2
0
2
1
0
2
1
1
1
0
0
2
2
1
3
0
1
0
0
2
1
2
0
2
1
2
1
1
1
2
0
0
0
1
2
0
0
1
2
0
1
1
0
1
1
0
2
0
2
1
2
0
1
2
1
0
0
1
1
1
0
0
2
2
0
1
2
0
2
0
1
0
1
0
1
1
1
0
1
0
0
1
1
1
2
0
1
2
3
2
3
1
0
0
0
0
2
2
1
2
0
2
1
0
1
1
1
1
3
1
2
0
0
1
1
0
0
1
0
2
1
0
2
1
1
1
0
2
0
0
1
1
2
0
0
1
0
0
0
2
0
0
0
1
1
1
1
2
1
2
1
0
0
0
1
0
1
2
0
1
1
1
0
1
0
1
0
1
0
2
1
0
1
2
1
1
2
1
0
2
1
0
0
0
0
2
1
1
1
1
1
1
1
1
1
0
1
1
0
0
1
0
1
1
1
1
1
1
2
2
1
0
2
0
2
2
0
2
1
0
1
0
0
3
1
0
0
1
1
1
0
1
1
2
1
0
1
2
1
3
2
0
1
2
1
0
1
1
2
1
1
0
1
0
0
1
0
2
2
3
2
2
0
0
1
1
1
1
3
0
0
1
0
1
1
1
1
0
0
1
1
2
1
2
1
2
1
0
0
1
2
1
0
0
1
0
0
1
2
0
0
2
0
1
2
1
2
2
1
0
1
0
0
2
1
1
1
0
1
2
2
2
1
2
2
0
0
2
1
0
2
3
1
1
1
0
0
0
0
1
1
0
0
0
1
1
1
0
0
0
1
0
0
0
2
1
0
0
2
2
1
0
0
0
0
1
0
3
1
0
1
1
0
0
2
0
0
1
0
0
2
0
0
2
0
2
0
1
0
2
0
0
2
0
2
2
4
1
1
0
0
1
1
0
0
1
2
1
1
0
1
0
2
2
1
1
1
1
0
0
1
0
1
2
1
1
0
1
2
0
2
1
2
0
0
0
0
1
1
1
0
0
1
4
3
2
1
0
2
1
0
0
0
1
1
2
2
0
0
0
2
2
0
1
1
1
2
1
1
0
0
2
2
3
0
0
4
0
0
1
0
0
1
0
1
1
1
1
1
1
0
1
0
2
0
0
1
1
1
0
1
1
1
1
2
1
1
1
1
1
2
1
1
1
1
1
1
1
2
0
2
1
0
2
0
1
1
1
1
2
1
0
0
1
1
0
0
0
1
0
1
0
0
1
0
1
1
0
0
0
0
2
1
3
0
1
0
1
0
1
0
1
2
0
1
0
1
1
0
0
1
1
0
0
2
4
1
0
1
2
0
1
0
3
1
2
0
1
2
0
1
1
1
0
0
1
1
0
1
2
0
2
1
0
1
0
1
2
1
0
2
2
1
1
1
1
2
0
2
1
1
1
2
0
1
1
1
0
0
2
1
1
0
2
1
0
0
0
2
1
1
0
0
1
2
1
1
0
2
0
1
3
0
2
1
1
1
0
1
1
1
0
1
2
1
1
1
2
1
0
0
1
1
0
2
1
0
1
2
0
0
1
0
2
2
1
1
2
1
1
0
1
0
0
0
1
1
1
0
2
0
1
1
1
1
2
0
2
1
0
1
0
1
2
1
0
1
0
1
0
0
0
2
1
1
2
1
0
2
2
1
0
2
2
0
1
2
0
2
0
1
0
2
1
0
1
0
0
0
2
1
1
1
0
0
1
1
1
0
1
0
2
1
2
0
2
1
2
0
2
2
2
1
1
0
1
0
0
1
2
1
0
1
1
1
0
1
2
0
1
0
2
1
0
0
2
1
2
1
0
1
0
0
2
2
1
2
1
0
2
1
1
0
1
1
1
0
1
0
1
0
2
2
0
1
2
1
0
2
2
1
0
1
2
0
1
0
0
1
2
1
0
1
0
1
2
0
0
1
0
0
0
2
0
2
2
2
2
2
1
0
0
1
1
1
2
1
0
1
1
0
1
1
1
2
1
0
0
1
0
1
2
0
2
1
1
1
2
0
2
1
1
0
1
1
1
2
1
0
0
1
1
2
0
1
0
2
1
2
1
1
0
2
0
0
1
0
1
1
0
1
0
1
0
2
1
0
2
0
0
0
0
0
1
1
0
1
1
2
1
0
1
1
1
1
1
1
1
1
2
0
2
1
1
1
1
1
1
1
1
1
1
0
2
2
0
0
0
1
1
0
0
1
0
1
0
1
1
0
2
1
1
2
0
2
2
1
2
2
1
0
0
1
2
1
1
1
2
0
2
0
2
0
2
0
0
1
1
1
0
0
1
0
0
2
1
2
1
2
2
2
0
2
0
1
1
0
2
2
0
2
2
0
1
1
0
0
1
1
2
1
1
2
3
1
1
2
3
0
0
0
0
3
1
2
0
2
1
1
2
1
0
0
0
1
0
1
1
1
0
0
1
2
0
1
2
0
1
1
0
0
1
1
0
2
1
0
0
1
0
1
2
1
3
2
2
0
1
2
0
1
2
0
0
2
0
1
2
3
1
1
1
1
1
0
2
1
0
2
1
0
0
0
0
2
0
1
1
1
2
1
1
1
1
0
3
0
0
0
2
2
0
2
0
1
0
0
0
1
0
0
0
1
2
0
2
1
0
1
0
1
1
0
0
0
0
0
0
1
1
1
0
0
2
1
1
0
2
1
2
1
2
2
0
2
2
1
0
0
1
0
2
0
0
0
2
0
1
0
0
1
1
2
1
2
1
2
0
0
2
0
0
1
0
2
2
2
2
1
0
0
1
2
2
0
0
2
1
1
0
2
1
1
0
0
0
0
0
0
2
0
1
0
2
1
0
1
0
2
0
1
2
1
0
0
2
1
2
0
1
2
2
2
1
1
2
1
0
1
1
0
1
0
0
0
2
1
1
1
1
0
1
0
0
1
1
2
1
3
3
2
3
1
2
2
1
2
2
1
1
1
0
0
0
0
2
1
0
0
0
0
1
1
2
1
0
0
0
0
3
0
1
2
0
2
0
0
1
1
1
1
0
0
1
1
2
1
2
0
2
0
1
1
1
1
0
1
0
0
1
2
2
1
0
1
2
1
1
0
0
0
0
4
1
0
2
0
1
1
0
1
1
0
1
1
0
0
2
2
1
2
0
1
0
2
1
0
1
1
0
1
0
0
0
1
0
1
0
1
1
0
2
0
1
0
1
0
0
0
1
1
1
0
1
3
2
1
0
0
2
0
2
2
1
0
1
0
1
0
0
1
0
1
0
0
0
2
1
2
0
0
0
1
1
2
0
1
1
0
0
2
1
1
1
0
0
0
2
1
0
0
0
2
1
1
1
0
1
0
1
1
0
1
0
1
0
1
1
0
0
1
2
2
1
0
0
2
0
0
0
0
0
0
1
1
2
0
0
1
2
1
2
2
2
0
1
2
0
1
1
2
0
4
2
1
0
7
1
1
1
0
0
3
0
0
0
2
1
0
0
1
1
1
1
1
0
0
0
0
1
1
1
1
2
0
2
1
1
1
2
1
1
2
0
1
0
1
1
1
0
1
1
0
1
0
1
1
0
1
0
0
2
1
0
0
0
2
1
1
0
0
0
1
0
2
2
1
0
3
0
1
1
1
1
0
0
1
0
1
2
1
1
1
1
0
0
0
1
2
2
0
2
2
0
1
0
4
0
3
1
0
1
1
0
1
1
0
1
0
1
1
1
2
1
1
0
0
2
2
1
0
0
0
1
0
0
0
0
1
1
2
0
0
0
0
1
0
0
1
1
0
0
0
0
1
2
0
1
0
0
1
1
0
0
1
1
0
1
0
1
1
1
1
0
2
0
1
0
1
2
0
0
2
0
0
1
2
0
1
0
1
2
2
1
1
0
0
1
1
1
2
4
1
2
0
1
1
1
1
2
1
2
1
0
0
0
1
2
2
1
1
0
2
2
0
1
2
2
1
1
2
0
1
1
0
1
0
0
1
0
0
0
1
0
1
1
2
0
2
2
0
0
0
0
1
1
2
0
1
0
2
0
2
1
1
0
1
0
1
0
0
0
2
0
2
0
1
1
0
2
2
0
2
0
1
0
1
1
0
0
1
0
1
1
1
1
1
2
0
0
2
2
2
1
0
1
1
1
0
0
1
2
0
1
0
1
1
1
0
1
0
0
0
1
0
0
0
1
2
0
0
2
1
1
1
0
2
2
1
0
1
0
0
2
0
2
1
0
1
1
1
1
1
0
2
2
1
0
2
2
2
1
1
0
0
1
2
1
2
2
1
1
0
1
1
0
0
1
2
2
0
0
0
0
0
0
1
1
1
0
2
2
2
0
1
0
0
1
1
0
1
0
0
2
1
1
1
0
0
1
2
1
0
1
2
1
1
2
0
1
0
1
1
1
0
1
1
1
1
0
0
0
1
1
1
0
1
0
1
0
1
0
0
1
2
0
0
1
2
0
0
0
0
0
2
1
2
2
1
2
1
0
1
0
1
1
0
1
2
1
1
2
0
2
1
2
2
2
2
2
0
2
0
2
1
1
1
0
0
0
0
1
0
2
1
2
0
0
2
1
0
1
2
1
1
0
1
1
2
0
0
1
1
0
0
1
1
0
0
0
0
2
0
1
0
2
0
0
0
1
0
1
2
1
0
0
2
0
2
1
0
1
0
1
1
1
1
1
0
1
0
2
0
1
1
1
0
1
0
0
0
1
1
11
0
0
0
1
1
1
2
0
0
2
0
0
0
0
3
0
0
1
1
2
2
2
2
1
1
1
0
2
1
0
1
2
0
2
0
2
0
0
1
2
1
1
1
2
1
0
2
2
0
2
0
1
2
2
0
1
0
0
0
1
0
2
1
1
0
0
0
2
3
0
2
2
1
2
1
2
0
0
1
1
2
0
2
0
0
1
2
0
0
2
0
0
6
2
1
0
2
1
2
1
2
0
2
2
0
1
2
1
0
0
0
1
1
2
0
2
0
0
2
0
0
0
1
0
0
0
0
1
1
0
2
1
2
1
1
2
0
1
0
1
1
0
1
0
1
0
0
2
2
0
2
1
1
1
0
1
0
1
0
0
2
1
1
3
0
2
2
0
0
2
1
0
0
1
0
2
0
1
1
0
2
1
1
0
0
1
1
0
0
1
2
0
1
0
1
0
2
1
1
1
0
0
1
2
1
0
2
0
1
1
0
2
0
1
1
0
1
2
1
0
0
1
0
1
3
1
0
1
1
0
0
2
1
2
1
0
2
1
2
1
0
0
0
0
0
2
0
0
1
2
2
0
0
0
0
1
0
1
0
0
1
1
2
1
0
0
0
2
0
0
2
0
1
0
2
1
0
1
2
1
2
0
1
1
1
0
2
2
2
4
2
0
0
1
1
1
2
2
0
1
1
1
2
0
1
0
0
2
0
3
2
2
2
1
0
1
2
1
0
0
2
1
2
1
1
0
0
0
3
2
2
0
0
1
1
0
1
2
0
1
0
1
0
1
1
1
0
2
2
0
1
1
1
1
2
1
1
0
0
1
2
0
1
0
0
2
2
0
0
1
1
1
2
2
1
2
1
0
1
1
0
1
0
1
0
2
1
0
0
0
0
0
1
1
2
2
1
2
0
0
1
0
0
2
0
0
1
1
1
0
1
1
1
1
2
0
1
2
2
2
0
1
1
0
0
0
1
1
1
1
0
2
2
1
2
0
1
1
1
1
1
0
0
2
0
2
0
0
1
0
0
0
1
0
2
1
2
2
0
0
1
3
1
2
0
2
2
1
0
0
0
1
1
2
1
0
1
2
0
1
0
0
0
1
1
0
1
0
1
2
2
2
2
1
0
1
4
1
1
2
0
0
0
0
0
1
1
0
0
1
1
0
0
1
2
0
2
0
0
0
0
1
0
1
2
1
0
0
2
0
0
1
1
0
0
1
0
1
1
0
1
2
2
0
1
0
1
2
1
0
1
1
0
2
3
1
0
1
2
1
1
3
1
1
0
0
0
0
0
0
0
2
1
1
2
0
0
1
1
0
2
1
2
1
2
0
1
0
2
2
1
1
2
2
0
0
0
1
1
0
0
2
1
0
1
0
0
1
1
0
2
2
0
2
1
1
0
1
0
1
0
2
2
1
0
1
0
0
0
1
1
0
3
1
1
2
2
0
2
2
1
0
5
1
1
2
2
1
0
0
2
0
1
0
0
0
0
1
2
0
3
0
1
1
1
0
1
1
0
1
0
1
1
2
2
1
1
0
1
1
0
1
0
0
0
0
1
2
2
2
0
0
1
0
1
0
2
2
1
1
1
1
0
2
1
1
1
0
1
0
1
0
0
1
2
0
0
2
2
2
1
2
1
2
2
1
2
1
0
0
0
3
1
2
0
0
0
0
0
1
0
1
0
0
1
2
0
1
0
1
1
1
0
0
1
0
2
2
1
1
2
0
1
0
0
0
0
2
0
1
1
1
1
0
2
0
1
2
1
0
1
1
0
0
1
1
0
0
0
1
0
1
1
0
2
0
1
0
0
0
1
0
1
2
1
2
0
2
2
0
1
0
0
1
2
0
0
0
1
1
2
0
1
1
2
1
1
1
0
1
0
0
1
2
1
1
0
1
2
0
1
1
1
2
0
0
0
0
1
1
3
4
1
0
4
0
1
2
1
1
2
1
1
1
0
0
2
0
1
0
2
1
0
0
1
0
0
2
0
1
1
1
0
0
0
1
1
2
0
0
0
3
0
1
2
0
1
1
1
1
0
1
1
1
2
0
1
0
1
2
0
1
1
7
0
0
1
2
0
2
2
0
0
0
1
2
1
0
1
3
1
1
2
0
0
2
0
1
0
2
1
3
2
3
0
2
0
1
2
0
2
2
0
0
2
1
0
1
2
1
2
0
1
2
2
0
0
2
2
1
1
0
1
0
1
1
0
1
1
0
0
0
0
0
0
0
1
2
1
1
3
1
2
1
1
0
2
2
1
1
1
0
1
1
1
0
1
0
2
1
1
2
0
1
2
1
0
1
0
1
1
2
2
0
0
0
0
1
1
1
1
1
1
1
0
1
1
0
0
0
1
0
2
1
0
0
0
0
1
0
0
0
1
1
2
2
0
0
1
0
0
0
2
0
2
1
2
0
0
0
0
2
1
1
0
2
0
1
1
0
0
0
2
0
0
0
0
2
3
1
0
1
2
2
1
0
0
0
0
2
3
0
0
1
2
0
1
0
1
2
1
3
1
1
0
2
0
1
1
1
0
0
0
0
1
1
1
0
1
0
0
0
1
1
1
2
0
1
2
0
1
0
0
1
0
2
1
1
0
0
1
2
0
2
0
0
1
2
0
0
1
0
1
0
0
0
2
0
1
1
1
0
1
2
1
1
0
1
0
1
0
0
0
0
2
1
1
0
0
1
2
1
0
0
1
1
2
0
1
0
1
1
0
1
0
1
2
0
1
0
0
1
0
0
1
1
0
0
2
2
0
2
1
3
0
0
0
1
0
1
1
1
0
2
3
1
1
1
1
1
2
0
1
0
0
1
0
2
1
1
0
0
1
1
0
0
0
1
2
2
0
0
0
2
0
2
2
0
0
0
1
0
1
0
1
1
1
1
2
2
2
2
1
0
0
0
2
0
1
0
0
0
0
1
0
2
1
0
0
1
2
0
2
0
0
0
0
2
0
1
0
1
1
0
0
2
0
0
1
0
0
2
2
0
1
1
1
0
2
2
1
3
1
2
1
1
1
0
0
0
0
1
0
1
2
2
2
2
2
0
1
0
0
0
0
0
1
0
1
0
1
2
2
0
0
0
0
2
0
2
1
0
0
1
2
3
2
0
2
0
2
2
22
0
0
0
0
1
1
0
0
2
2
0
2
1
3
1
1
1
1
2
0
1
1
0
0
2
1
1
1
0
2
0
0
1
2
0
1
0
2
0
0
0
2
0
2
0
2
0
1
0
0
1
0
1
1
2
2
1
2
0
0
0
0
0
2
2
1
0
1
1
0
1
0
1
2
0
1
1
0
0
0
1
1
0
1
1
1
0
2
3
0
0
1
0
1
0
1
0
0
0
2
2
1
0
0
0
1
0
2
1
2
0
1
2
2
0
0
0
0
1
1
1
1
0
2
2
1
1
3
1
2
1
0
1
0
1
0
0
1
0
0
1
1
2
1
0
0
1
2
2
2
1
0
0
0
2
0
0
1
1
2
0
1
1
2
3
2
1
1
1
1
2
0
0
0
2
0
0
2
0
1
1
0
1
1
0
1
0
0
2
1
0
1
0
2
2
1
2
0
1
1
1
0
1
0
0
0
1
0
2
0
0
1
0
1
1
2
1
2
1
1
0
1
0
0
1
1
1
0
2
0
1
1
2
2
1
0
1
2
1
0
0
2
0
2
0
2
2
2
0
2
2
2
0
2
2
1
2
0
1
0
2
1
1
1
1
1
2
1
2
1
0
0
1
0
2
0
1
0
1
0
2
1
1
0
0
3
0
0
2
0
1
2
0
2
1
1
0
2
1
0
0
0
0
0
2
0
1
1
1
0
2
0
1
3
1
2
0
1
0
2
2
1
2
0
1
2
0
1
1
0
2
2
2
1
1
1
1
0
1
2
0
1
3
0
1
0
1
1
2
0
0
0
0
2
1
0
2
1
1
1
1
1
1
2
2
0
0
1
0
1
2
0
2
2
0
2
0
0
0
0
0
0
1
2
0
0
0
2
2
1
1
0
0
0
0
1
1
1
1
1
0
1
1
2
1
2
1
2
1
0
0
1
1
0
0
0
2
1
2
1
0
0
1
1
1
1
0
2
1
2
0
2
1
2
3
1
0
1
0
0
0
2
2
1
1
1
1
1
1
2
1
0
1
0
2
0
0
1
0
2
1
0
1
2
1
2
0
0
0
1
1
0
0
1
1
4
1
2
1
2
1
0
1
2
2
1
4
0
0
2
2
1
2
0
2
0
1
0
4
2
2
0
0
1
1
1
0
1
2
0
0
0
2
0
1
0
3
3
0
1
1
0
0
1
0
0
0
0
2
1
2
3
0
2
0
1
0
0
1
1
0
0
2
1
1
0
0
1
0
0
0
1
1
0
1
1
1
1
1
2
0
0
0
0
0
0
1
2
2
3
0
0
2
1
0
1
1
0
0
4
0
0
2
0
0
1
0
0
1
0
2
2
2
0
1
3
0
1
1
1
0
0
2
2
1
1
0
1
2
2
0
1
3
1
1
0
2
1
0
0
1
2
1
0
0
0
2
1
1
1
1
0
1
1
2
0
1
0
1
1
0
0
0
2
2
0
0
1
1
1
1
1
1
1
1
2
0
0
0
2
1
2
2
1
1
0
1
1
0
0
0
2
0
2
1
0
0
0
1
2
0
0
0
1
0
2
1
2
2
0
0
1
1
0
1
1
1
0
2
2
2
2
0
1
0
2
0
0
1
2
3
1
1
1
2
2
1
2
0
2
2
0
1
2
1
2
1
0
1
0
1
2
0
0
0
1
0
0
1
3
1
1
1
1
1
0
1
0
0
0
1
1
1
2
0
1
0
2
1
1
1
1
1
1
0
1
2
0
6
2
1
1
0
0
2
2
0
1
1
2
2
2
1
0
0
2
2
0
0
0
0
2
2
0
0
2
1
0
0
1
1
0
3
0
2
0
0
2
0
1
1
0
1
2
1
1
1
0
1
0
1
0
1
1
1
1
1
1
0
0
1
0
2
1
1
0
2
2
0
0
1
2
1
0
0
0
1
0
1
1
1
1
1
0
0
0
0
1
0
1
0
2
1
1
0
0
2
1
3
1
1
2
2
0
0
2
0
1
0
0
1
1
1
0
1
0
0
1
0
1
2
2
1
1
0
2
0
1
1
0
1
0
1
1
1
1
2
2
1
1
2
1
1
2
0
0
2
0
1
2
0
0
0
0
0
1
0
1
0
0
2
1
1
2
0
1
1
0
1
1
0
1
1
2
2
1
0
2
1
0
0
0
0
0
0
0
0
0
1
1
1
2
0
0
1
1
0
0
2
1
0
0
2
0
0
2
1
1
0
0
0
1
1
0
0
1
0
1
2
1
1
1
2
0
1
1
1
0
0
0
1
0
0
0
1
1
2
4
1
0
2
0
0
1
2
1
0
2
0
0
2
0
3
1
1
1
1
2
0
0
0
1
0
6
0
0
1
1
2
1
1
0
0
0
0
1
1
1
0
0
0
2
2
3
1
2
1
1
0
2
1
0
0
1
0
2
2
3
1
0
0
1
1
2
1
0
0
2
2
0
0
1
0
0
0
0
2
0
0
0
1
2
1
1
1
1
0
0
0
2
0
0
2
1
0
0
2
3
0
1
1
1
2
0
1
1
1
1
0
0
1
0
0
2
2
1
2
0
1
1
1
1
1
0
0
1
1
0
0
1
1
1
1
1
1
1
2
2
0
1
1
0
0
1
1
0
2
1
0
1
1
2
2
1
1
0
0
1
2
1
1
0
0
1
1
3
2
0
0
0
2
0
0
1
1
2
0
1
1
0
1
0
1
0
0
0
0
0
1
0
1
6
0
0
1
0
1
0
0
1
0
1
2
1
1
1
0
0
0
1
0
0
2
2
3
0
2
0
1
0
0
0
0
0
1
0
2
1
2
1
0
1
0
1
7
0
1
0
0
2
0
0
1
0
2
0
0
1
1
0
1
0
1
1
2
0
1
1
0
0
2
0
0
0
2
1
1
1
1
1
2
2
1
2
0
0
1
2
1
2
1
2
2
0
1
1
1
0
0
2
1
2
1
2
1
1
1
0
1
0
2
0
2
0
2
0
0
0
1
0
0
1
0
0
1
1
0
1
0
3
0
1
1
0
0
2
0
2
0
1
0
0
2
0
1
2
4
0
1
0
0
1
1
1
2
2
1
1
0
1
1
0
2
0
2
1
2
0
1
2
1
1
1
1
0
1
2
2
1
1
0
0
2
2
0
0
1
2
0
0
0
0
3
0
1
0
0
1
0
2
0
0
0
1
2
5
0
0
1
2
0
1
0
1
1
1
2
1
0
1
0
2
2
1
0
2
1
2
1
0
0
1
0
1
2
1
1
2
0
0
1
1
1
1
0
0
0
2
1
1
0
1
0
0
0
1
0
0
0
0
2
2
1
0
0
0
1
1
0
2
1
1
2
1
2
1
1
0
0
1
0
1
2
0
2
1
0
0
2
1
1
0
0
1
2
0
2
0
2
2
1
1
1
0
0
2
1
1
0
0
0
0
1
0
0
1
0
2
0
1
1
0
0
0
0
0
1
0
1
3
1
1
1
0
4
5
1
1
2
2
0
1
2
0
0
0
0
0
1
1
0
0
1
1
3
0
1
1
1
2
0
0
2
0
0
1
0
2
1
1
2
2
0
1
1
1
1
1
1
1
0
1
1
1
3
0
0
1
1
3
1
0
1
0
1
1
1
0
0
2
1
1
0
1
0
0
0
1
2
1
0
0
1
1
1
0
0
3
0
0
0
1
1
2
2
1
0
1
0
1
1
1
2
0
0
1
1
0
0
1
0
2
1
0
1
2
0
0
2
1
1
1
1
0
2
2
0
1
2
1
2
0
1
0
0
0
0
0
1
1
0
0
0
1
2
1
2
2
1
1
1
0
2
2
2
0
2
0
2
0
1
2
0
2
1
0
0
2
0
1
2
1
1
1
2
2
1
2
0
1
1
0
0
1
1
1
0
1
0
2
0
2
2
1
0
0
2
1
0
1
2
1
0
1
0
1
0
0
0
1
2
2
0
0
1
1
2
8
1
0
2
2
1
1
1
1
1
1
1
1
2
0
0
0
1
1
1
2
2
1
2
2
0
0
0
0
0
1
2
2
2
0
1
0
0
2
2
1
0
0
0
1
1
0
0
2
1
1
1
0
0
0
1
1
1
3
0
0
1
1
1
1
1
0
1
1
0
2
1
0
0
1
0
1
1
2
1
0
1
1
1
0
0
0
1
0
0
2
0
0
1
1
1
2
2
1
1
2
1
1
0
1
2
1
2
1
2
0
0
0
1
0
0
0
0
1
1
2
1
1
0
0
0
0
2
2
1
1
1
0
1
3
0
2
1
1
1
1
0
1
2
3
1
2
0
2
0
1
2
1
0
0
0
2
0
2
2
0
1
1
1
1
1
1
2
0
1
3
0
1
2
1
1
0
2
1
0
0
0
1
1
0
0
0
1
1
2
0
1
1
1
0
2
0
0
0
0
1
1
2
1
2
0
0
1
1
0
2
1
1
1
1
1
1
2
1
0
1
0
1
3
1
3
1
4
0
0
1
2
2
1
1
2
3
2
0
2
2
1
0
0
2
0
0
1
0
0
1
2
1
2
1
2
1
0
2
2
1
2
0
0
1
0
0
1
0
0
2
1
1
1
0
2
1
1
0
1
1
2
1
2
0
1
1
2
1
0
1
2
1
0
2
0
1
1
0
2
0
0
0
0
1
1
2
0
1
1
1
1
0
1
1
0
0
1
2
1
1
2
1
0
4
0
2
2
0
1
0
1
0
0
0
1
0
2
2
2
0
2
0
0
1
0
0
0
1
0
3
1
1
1
1
1
0
2
1
1
1
1
0
1
1
1
1
0
0
2
0
1
0
2
0
1
1
2
0
1
2
0
0
1
0
2
0
2
2
1
0
1
1
1
2
2
1
0
2
1
2
1
2
2
0
1
1
1
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
1
1
1
0
2
1
2
0
1
0
2
2
1
1
1
1
2
1
0
0
0
0
1
0
1
2
1
1
1
0
0
2
2
1
4
2
1
0
2
0
0
0
2
0
2
0
2
1
1
1
1
1
0
2
0
0
0
1
1
2
0
0
0
1
1
1
0
1
1
2
0
0
2
1
0
2
1
2
2
1
2
1
1
1
0
1
2
0
0
1
2
1
0
1
0
0
2
1
2
1
2
0
2
0
1
1
2
0
0
1
1
1
0
2
0
0
0
1
1
0
1
2
0
1
1
0
1
0
0
1
0
0
2
1
2
1
1
0
0
2
1
1
1
0
0
0
1
0
2
0
0
0
0
0
1
1
2
0
1
0
0
1
2
0
2
0
0
0
2
3
0
0
1
0
2
2
0
0
1
0
0
2
2
1
0
2
1
2
0
0
1
0
1
2
0
2
1
1
0
1
0
0
0
0
1
2
0
1
0
1
1
1
1
2
1
0
2
1
2
0
0
1
2
2
1
0
1
3
2
1
0
1
0
1
0
1
1
1
1
1
1
2
2
1
0
2
0
0
1
0
2
0
1
0
1
1
1
1
2
1
1
0
0
1
0
1
1
2
0
1
0
1
0
4
0
1
3
1
0
1
1
0
0
2
1
0
1
2
0
1
0
0
0
1
1
0
0
0
1
1
1
2
0
0
0
0
0
0
1
1
1
1
0
0
0
1
0
2
0
2
0
0
1
1
2
1
1
3
0
0
1
0
0
0
1
2
0
1
2
1
1
1
2
0
0
0
0
2
1
2
1
0
1
0
2
2
0
2
1
1
0
1
1
0
2
1
1
2
0
1
0
0
0
2
2
0
2
1
2
0
1
0
0
1
2
2
1
1
0
1
0
1
0
0
2
2
1
1
0
2
0
0
0
1
2
1
2
2
1
0
2
0
2
1
1
0
0
1
0
1
1
1
0
1
1
1
1
1
1
0
1
0
1
2
1
0
2
1
0
0
0
1
1
0
1
1
2
1
2
2
0
1
0
1
1
2
1
1
2
1
1
0
0
2
2
1
0
1
2
1
2
0
0
1
2
0
0
2
0
1
1
0
0
0
0
0
0
2
2
2
2
2
1
1
1
0
2
0
0
2
1
1
0
1
1
0
2
0
1
1
2
1
0
3
0
2
1
2
0
0
2
0
1
2
1
0
2
1
0
0
1
3
1
1
1
1
1
2
2
1
0
0
1
0
0
0
2
0
1
0
0
2
0
0
0
1
0
1
0
0
1
0
1
0
0
0
2
0
0
1
0
0
1
0
1
1
0
2
0
0
0
0
1
0
1
1
2
1
1
2
0
2
0
0
2
1
1
0
0
1
0
1
0
2
1
0
1
2
2
0
1
0
1
2
0
0
0
0
0
2
0
0
0
1
0
1
1
1
0
0
2
2
0
1
0
0
1
1
2
2
1
1
1
2
0
1
0
1
0
1
3
1
1
1
1
2
0
0
0
2
2
0
1
0
1
0
2
1
1
2
1
1
2
0
1
0
0
1
0
1
1
1
0
1
0
2
1
0
0
0
3
0
0
0
1
0
2
2
1
0
1
0
1
0
1
1
1
0
2
0
1
0
1
1
0
1
0
0
0
0
1
1
0
2
1
1
2
1
2
0
0
0
2
1
2
0
1
0
0
1
0
1
1
2
0
3
0
2
2
1
0
0
0
2
1
1
1
0
1
1
0
0
1
1
0
1
0
1
0
0
1
2
0
2
2
1
1
0
1
1
0
2
2
0
1
0
1
2
0
0
2
0
1
2
0
1
2
0
2
1
0
0
1
0
0
2
2
1
1
0
1
0
2
0
2
0
2
1
1
2
1
1
2
0
1
0
0
0
1
1
1
1
2
0
0
0
1
0
0
1
0
1
1
0
2
1
2
0
0
0
1
0
0
0
2
2
1
1
0
1
0
2
2
0
1
1
0
0
0
1
1
2
1
2
0
1
1
1
0
2
0
0
1
2
1
2
1
0
2
0
1
2
0
1
0
0
1
0
1
1
0
0
2
2
2
2
1
1
1
1
0
1
1
2
1
1
1
1
0
0
0
1
1
2
2
2
0
1
1
0
1
0
0
1
0
0
0
0
0
0
1
1
0
1
2
1
2
1
0
2
1
0
1
2
2
0
1
1
0
1
0
2
0
0
1
0
2
1
1
0
2
1
2
1
0
2
1
2
1
2
1
1
1
0
0
2
0
2
2
0
1
1
1
0
0
2
1
0
0
2
0
1
1
1
1
0
0
0
0
0
0
1
1
0
0
0
1
0
2
2
1
1
2
2
0
1
1
0
0
1
1
0
0
1
1
2
2
0
1
1
1
1
1
0
0
1
1
1
1
0
1
1
0
2
0
1
2
0
2
1
1
0
1
1
0
0
0
1
1
0
0
1
0
0
1
0
2
1
0
1
2
2
0
2
0
2
0
1
0
1
0
0
0
2
1
1
0
1
1
0
1
1
2
1
0
1
2
1
2
2
0
1
0
0
0
0
1
2
0
2
0
2
1
0
0
1
3
0
2
0
0
1
0
0
1
0
1
1
0
2
2
1
1
2
0
0
1
1
0
1
2
1
1
0
1
1
1
0
1
1
2
1
0
0
0
1
0
2
0
0
0
2
0
1
1
2
0
0
3
0
0
1
1
0
0
2
2
1
1
1
0
1
1
1
1
2
1
2
0
1
1
2
2
2
1
0
1
0
1
1
2
2
0
2
0
0
0
0
1
1
2
2
1
1
2
1
2
2
1
1
0
0
1
1
0
1
0
0
0
0
1
0
2
2
1
1
2
0
1
2
1
2
0
2
0
0
5
0
0
0
1
2
0
0
1
0
0
2
2
1
1
1
0
0
1
2
0
0
2
2
1
0
1
2
2
0
1
2
1
0
0
2
1
2
0
0
0
1
0
1
1
1
1
0
0
1
0
1
2
0
1
0
2
2
1
0
0
0
0
1
1
0
2
1
2
2
0
0
1
0
2
3
1
0
1
1
1
2
2
2
0
0
2
1
0
1
1
2
0
1
1
1
0
2
0
1
0
1
0
0
0
0
1
3
0
0
1
0
0
2
0
1
0
1
1
0
2
0
1
0
0
1
2
0
0
1
2
0
0
1
1
1
1
1
0
0
1
0
0
1
1
2
1
0
0
0
1
1
2
1
0
0
1
0
0
0
2
1
1
0
0
2
1
0
2
0
2
2
1
1
0
1
1
1
1
0
2
2
2
2
0
1
1
0
1
0
1
1
1
0
1
0
0
0
2
1
2
1
1
2
2
1
0
2
0
1
2
0
0
0
1
0
1
0
3
0
0
0
2
1
2
0
1
1
0
1
0
1
2
0
0
0
2
1
1
1
0
2
0
0
1
1
2
1
0
0
1
0
0
0
1
0
0
0
2
0
0
1
0
1
0
3
2
2
1
1
0
0
0
1
1
1
1
1
1
0
1
0
0
0
0
1
0
1
1
2
0
1
1
1
1
0
0
0
0
2
0
2
0
4
1
0
0
1
0
0
1
1
0
0
0
0
2
0
1
0
0
3
0
0
2
2
2
0
0
1
0
1
1
0
0
0
1
2
0
1
0
0
2
0
1
1
2
1
0
0
1
0
0
1
2
1
2
0
1
1
1
1
0
1
2
0
0
0
0
2
0
0
1
0
0
1
1
0
0
2
5
1
0
1
0
2
1
1
1
2
2
0
1
0
0
1
0
0
0
2
2
0
1
2
0
0
0
2
1
2
0
0
1
1
1
0
2
2
1
2
1
1
1
2
2
0
2
0
0
2
1
0
2
0
1
1
0
0
1
1
0
1
1
0
1
1
0
0
2
2
0
1
0
0
0
0
0
2
0
0
0
1
0
2
0
2
0
1
1
0
1
2
1
2
0
0
1
1
1
0
1
1
2
0
1
0
1
0
0
0
1
0
0
0
1
1
0
0
2
1
1
0
0
1
2
1
0
1
2
1
2
0
2
0
1
4
2
1
0
0
2
1
2
1
1
2
0
1
0
2
0
1
2
1
1
0
0
1
3
0
2
0
0
2
2
1
0
0
1
1
1
1
0
1
2
0
1
0
1
1
1
0
0
1
2
1
2
1
1
2
0
2
0
1
1
2
1
2
0
2
1
0
0
2
1
1
1
1
0
0
1
0
2
0
0
2
2
1
0
1
3
0
1
2
0
2
0
1
1
2
0
1
0
1
1
2
0
1
1
1
0
2
0
2
1
1
0
0
1
1
2
0
1
1
1
0
1
1
1
2
2
1
2
2
0
1
1
0
1
1
2
0
1
1
2
1
2
1
2
0
0
0
0
0
0
1
0
1
1
1
0
2
0
2
0
1
0
1
2
0
1
0
2
1
0
0
2
1
0
2
0
0
2
0
1
1
1
0
1
1
1
1
0
0
0
0
2
2
0
0
0
0
0
2
2
0
1
1
1
1
0
1
0
2
0
0
0
1
1
0
1
1
2
2
1
3
2
1
2
1
1
0
1
0
0
0
1
1
2
0
0
0
0
0
1
1
1
2
0
4
1
0
0
2
1
0
1
1
3
1
2
0
0
0
0
2
0
2
1
0
2
1
1
1
0
0
2
2
0
1
1
2
1
1
0
1
0
1
2
1
0
1
0
0
2
2
1
0
1
2
0
0
0
1
0
2
1
2
2
0
0
0
0
0
2
1
0
1
0
0
1
1
2
1
1
2
0
2
1
1
1
1
0
0
0
0
2
0
0
1
0
0
1
0
1
2
0
0
2
1
1
0
1
1
2
0
1
0
0
0
1
0
2
1
1
1
2
1
2
0
1
1
0
2
0
1
2
1
2
2
1
1
1
0
0
0
0
0
2
0
0
3
0
0
2
0
0
2
0
2
2
0
1
0
1
0
2
1
0
0
0
2
1
0
0
1
0
0
0
0
2
1
2
1
1
0
0
0
1
0
2
2
0
0
2
0
0
1
1
1
2
0
1
1
1
2
2
1
1
0
2
1
0
0
2
0
1
0
1
2
0
1
0
0
0
0
0
2
1
0
1
1
0
0
1
2
1
0
1
1
1
0
1
2
2
0
0
2
1
1
2
0
1
1
1
1
0
0
1
0
1
0
1
1
1
0
2
1
0
0
2
1
2
0
1
0
2
1
2
2
1
2
1
2
1
1
1
0
1
1
3
2
0
1
0
1
1
0
2
1
0
2
1
3
2
1
1
0
2
1
2
0
2
1
0
1
1
2
0
1
0
0
0
0
0
1
2
1
0
1
3
2
1
0
2
1
1
0
0
0
0
0
1
1
1
1
1
0
1
1
1
0
0
1
1
1
1
1
0
1
1
1
3
1
0
2
1
2
0
0
1
1
0
0
0
1
1
2
2
0
0
1
1
2
2
0
1
1
1
0
0
1
1
0
1
1
2
0
1
0
1
2
0
1
0
1
0
2
0
2
2
0
0
1
1
1
2
1
2
1
1
1
0
0
0
0
0
1
1
1
1
2
0
1
0
0
1
2
2
0
0
1
2
0
0
1
0
0
0
2
1
1
0
1
0
1
1
1
0
1
0
0
2
1
2
1
2
1
3
0
1
1
0
1
0
0
0
0
0
2
0
0
2
1
1
1
2
0
2
0
2
1
1
2
2
1
0
0
1
2
1
1
0
2
0
0
2
0
2
0
1
1
0
0
0
1
1
0
1
1
2
1
1
1
0
1
1
1
2
0
2
1
2
1
3
0
2
2
0
1
2
0
0
0
1
1
0
4
0
1
0
1
1
0
0
1
1
0
1
1
0
0
2
0
1
0
0
1
2
0
1
2
2
0
0
1
1
2
2
0
1
2
1
0
2
2
1
2
1
1
0
1
1
3
2
0
2
2
1
2
0
1
1
0
1
1
2
1
0
1
0
1
2
2
1
2
0
1
0
1
1
1
2
0
0
1
3
2
1
1
2
0
0
1
1
0
1
0
0
0
1
1
1
2
1
0
0
0
2
1
0
2
1
1
1
1
1
1
2
0
0
1
0
1
1
1
1
1
0
2
2
0
2
0
2
0
0
2
1
0
1
0
1
0
2
0
1
0
0
1
4
2
0
0
0
1
1
1
1
0
0
1
0
1
1
0
1
3
2
1
1
1
0
1
1
0
0
1
0
0
0
0
1
2
0
1
2
0
1
0
1
2
0
0
1
2
0
0
0
0
0
2
2
4
1
0
0
2
0
0
1
1
0
0
2
0
1
1
0
2
0
2
0
1
2
1
2
1
2
1
2
2
1
0
0
2
2
0
1
0
2
0
2
0
3
1
0
2
0
2
0
1
2
1
0
0
2
0
0
2
1
0
0
1
1
2
2
0
2
0
1
0
1
1
1
1
2
3
1
1
0
0
0
2
1
2
1
2
2
1
0
1
0
0
1
1
0
2
2
2
2
0
1
2
2
2
2
1
1
1
0
0
1
2
2
2
0
1
1
0
2
2
1
0
0
1
0
0
1
0
1
1
1
2
1
1
1
3
0
1
2
0
1
0
2
1
0
0
2
0
1
0
3
0
0
0
1
0
1
0
0
1
0
2
2
0
1
0
0
0
0
1
0
0
1
0
0
3
0
1
0
0
2
0
0
2
2
1
2
0
2
1
1
0
0
0
0
0
1
2
0
0
1
0
0
2
1
1
0
1
0
2
1
2
0
1
0
1
0
2
0
2
2
0
2
1
1
1
0
0
1
0
2
0
1
1
2
0
0
1
0
1
0
1
0
1
1
0
0
2
2
2
1
0
0
0
0
1
0
1
0
2
2
1
0
2
1
0
0
1
1
2
1
0
0
2
0
1
1
1
2
0
0
0
0
2
2
0
2
0
2
1
2
0
0
1
1
1
0
0
2
2
0
1
2
0
0
1
1
1
0
0
1
2
1
0
1
0
0
1
0
2
0
3
1
0
2
0
0
0
0
2
2
0
0
1
1
1
0
2
1
0
1
1
0
1
1
1
1
0
1
3
1
1
2
0
0
2
0
0
0
0
1
0
0
0
2
1
1
2
2
1
0
2
1
2
0
1
0
0
1
0
1
1
0
1
1
0
1
0
1
1
2
3
2
1
1
0
2
0
0
1
1
1
0
0
2
1
2
0
2
1
1
0
1
0
1
1
2
1
0
1
3
0
1
0
1
1
2
1
0
0
0
1
0
0
2
2
1
1
0
2
1
1
1
1
2
1
1
2
0
2
0
0
1
2
0
1
0
1
2
0
0
2
2
1
0
1
0
2
0
0
0
0
2
1
0
0
2
0
1
2
2
2
0
1
2
0
1
0
0
1
2
2
0
1
1
1
2
1
1
0
1
1
1
0
2
2
0
1
2
2
1
2
0
0
1
1
1
2
0
1
0
1
1
1
1
1
0
1
2
2
1
2
0
1
2
1
1
0
1
0
0
1
0
1
2
0
1
1
1
2
1
0
1
0
0
1
1
2
1
2
0
0
1
0
2
1
1
0
0
0
0
0
1
2
0
0
2
2
2
1
2
0
1
1
1
0
1
0
1
0
2
1
1
3
0
1
0
1
1
1
0
2
2
2
0
0
1
0
0
1
1
1
3
1
2
1
1
0
2
1
0
2
0
1
0
3
1
0
1
0
1
1
2
0
1
3
0
1
0
0
1
1
1
1
0
1
0
0
1
0
0
0
0
2
1
1
1
0
1
0
2
1
0
0
1
1
0
1
1
2
1
1
0
0
1
1
0
1
0
0
0
1
0
1
0
0
1
3
2
0
2
0
0
1
2
1
0
1
0
0
0
0
0
1
1
0
1
0
0
1
3
0
1
2
0
1
2
0
1
1
1
1
2
2
0
0
0
1
0
0
1
2
2
3
1
0
1
0
1
1
0
0
1
0
1
1
0
0
1
2
0
2
0
2
1
1
1
2
1
1
1
1
0
0
1
3
1
1
0
0
0
0
0
0
1
0
0
2
1
0
0
0
1
0
1
0
1
0
0
0
0
2
0
0
1
0
2
0
0
1
0
1
0
1
1
0
1
2
0
2
0
0
0
0
0
0
2
2
1
1
0
2
0
1
2
2
1
1
1
1
0
2
0
0
0
2
1
0
0
0
0
1
1
0
1
0
0
0
1
1
2
1
0
0
1
0
0
1
1
0
1
0
2
0
0
0
3
0
1
1
1
0
1
1
2
1
1
1
2
1
1
0
0
0
0
1
0
0
1
0
1
0
1
0
2
0
2
2
0
0
1
0
0
0
2
0
1
0
0
0
0
0
1
1
0
0
0
0
1
2
3
1
0
0
0
0
2
0
0
1
2
2
0
0
0
1
0
0
2
1
1
1
0
0
0
0
2
0
1
1
0
0
0
2
0
1
1
1
1
0
2
1
0
0
0
1
1
1
0
1
2
0
1
1
1
2
1
0
1
3
1
1
1
0
0
1
0
0
0
0
1
2
2
0
1
0
2
1
5
0
1
3
0
1
1
1
1
0
2
0
0
0
0
0
1
1
0
1
2
2
0
1
1
1
2
3
1
2
1
1
0
2
1
1
1
0
1
0
2
1
0
2
1
0
0
1
2
1
0
1
2
2
0
0
0
2
1
3
1
0
0
1
1
0
2
0
1
0
0
1
1
0
1
1
1
1
2
1
0
1
1
1
0
1
0
0
0
0
2
1
1
0
0
2
1
1
1
1
0
1
1
0
1
0
1
1
0
0
1
1
2
0
0
0
2
0
0
1
1
1
0
1
0
1
1
0
2
3
0
1
0
0
1
1
0
1
0
2
0
0
1
2
1
1
0
1
0
1
1
4
0
0
2
2
0
2
0
0
0
0
1
0
0
0
0
0
1
1
1
1
0
1
0
0
2
1
2
0
1
2
0
1
0
0
0
1
0
0
2
1
1
0
0
0
1
2
0
1
0
1
2
1
2
2
1
1
1
1
2
1
0
0
1
1
2
1
0
2
1
0
2
1
2
1
1
0
0
1
2
1
1
0
0
1
0
2
1
0
1
0
1
0
1
1
1
2
0
0
1
2
0
0
1
0
1
1
2
1
3
0
1
2
1
2
0
1
2
2
2
0
0
1
4
2
1
0
0
2
0
1
0
0
2
1
1
1
1
2
0
0
0
0
1
0
1
1
0
2
1
1
1
0
1
2
1
0
2
0
2
1
2
0
1
1
0
0
0
0
0
1
1
1
0
0
1
2
2
0
1
0
1
1
0
0
0
0
1
1
1
0
1
1
0
2
1
2
0
0
0
0
0
2
4
0
1
0
0
1
1
1
1
2
1
2
1
2
1
0
0
1
0
2
2
0
0
0
1
1
0
0
0
2
1
0
1
0
2
1
0
1
1
2
1
3
0
1
1
2
0
1
1
2
2
0
0
1
2
0
2
0
0
0
1
2
2
1
2
0
1
0
1
1
0
0
0
2
1
1
0
0
2
1
0
1
0
0
1
1
0
1
1
2
0
3
0
1
0
2
0
2
0
1
1
0
0
1
0
0
1
2
0
0
1
0
1
0
1
1
0
1
2
0
1
0
2
0
1
1
1
1
0
2
0
0
1
0
2
1
0
2
1
1
0
0
0
2
1
0
0
4
0
1
1
0
1
1
2
3
1
1
3
1
1
2
0
0
0
1
1
1
0
0
1
0
2
2
0
1
2
2
0
0
0
0
1
1
2
3
2
1
0
0
1
2
1
1
0
1
1
0
1
2
0
0
2
0
1
2
1
2
1
1
0
1
1
0
0
2
1
0
1
0
2
0
1
2
0
2
0
1
2
0
2
0
0
1
0
1
1
1
1
2
2
2
1
1
0
1
1
0
0
1
1
1
1
0
0
1
0
1
0
0
0
1
2
1
1
0
1
1
0
1
1
0
2
1
2
0
2
0
0
2
1
0
0
1
1
1
0
1
0
1
1
1
0
0
1
1
1
0
2
0
0
2
1
0
0
1
0
2
1
2
1
2
0
1
1
1
1
2
1
1
2
1
0
0
0
0
0
1
1
2
1
1
1
0
0
1
1
0
0
1
0
1
1
0
0
0
1
1
1
0
1
1
0
1
1
0
1
1
1
1
0
1
1
0
1
1
0
0
1
1
0
0
1
0
2
0
0
1
1
2
1
0
1
2
2
1
2
0
0
1
1
2
0
2
0
1
0
0
1
2
1
0
2
1
0
1
0
3
0
0
1
0
1
1
1
1
1
1
0
1
1
2
2
1
3
1
2
0
2
1
1
0
0
0
0
0
3
2
2
1
0
1
0
0
0
2
1
2
2
1
0
1
0
2
0
1
0
0
1
1
2
0
2
0
2
1
1
1
1
1
2
0
0
0
0
2
1
0
0
0
2
1
1
1
1
0
1
0
0
0
2
2
1
2
1
0
1
0
0
0
1
1
2
1
0
1
0
0
0
1
2
0
2
1
1
1
0
1
2
0
0
2
2
1
1
1
1
0
0
1
0
0
0
5
1
0
0
0
1
0
1
1
0
0
0
2
1
1
0
2
0
0
0
1
1
1
0
1
0
1
2
0
2
0
1
1
0
1
0
2
2
2
1
0
2
0
0
2
0
0
0
7
1
1
0
2
1
0
1
1
0
0
0
2
1
2
1
0
1
0
1
0
0
2
1
2
0
1
3
1
0
1
0
1
1
0
1
1
1
2
0
1
2
1
0
0
0
1
1
0
1
1
2
0
2
1
1
1
1
2
1
2
0
1
1
1
1
1
2
2
1
1
2
0
0
2
3
0
1
2
0
1
1
1
2
2
1
2
0
1
1
1
1
0
2
1
0
0
1
1
0
1
1
1
2
2
1
0
1
1
1
2
2
0
1
0
3
2
0
1
0
0
1
0
0
0
1
2
1
1
0
1
0
1
0
0
1
0
0
1
1
1
0
2
0
1
1
1
2
2
0
1
0
1
2
0
0
1
0
1
1
1
1
0
1
2
0
1
1
0
0
0
0
2
1
0
0
2
2
1
1
0
1
0
1
0
1
1
2
2
1
0
0
1
0
1
1
0
0
1
1
1
2
1
2
0
0
1
0
0
1
1
1
1
1
1
2
0
1
0
0
1
1
0
2
0
1
1
2
2
0
3
2
1
1
1
1
1
1
2
1
0
1
3
0
1
1
0
0
2
1
2
1
0
0
2
2
0
1
2
1
1
0
1
0
0
1
0
0
0
0
1
0
1
0
1
0
1
0
0
1
1
1
0
2
0
1
0
2
1
0
0
1
0
1
2
1
2
1
2
1
0
1
2
2
0
0
1
0
0
0
0
0
1
1
0
0
1
0
1
2
0
1
2
0
2
1
1
0
0
1
1
2
1
2
1
0
2
0
1
0
1
1
2
0
0
0
1
2
0
0
1
1
1
1
1
0
0
1
1
1
0
0
0
2
1
0
1
3
1
2
0
1
1
2
0
0
1
1
0
2
1
1
2
1
2
0
0
2
1
2
0
1
0
0
2
2
1
0
0
0
1
1
2
2
0
1
1
3
0
1
1
1
0
0
6
0
2
0
1
1
0
0
0
2
1
0
1
0
1
2
2
1
2
0
1
2
2
2
2
1
0
0
5
2
0
2
1
1
0
2
1
1
1
1
0
1
0
2
1
0
0
0
1
1
2
1
2
3
2
1
1
2
1
0
2
0
0
1
1
2
0
1
2
1
1
1
2
2
0
0
2
1
1
0
1
1
0
1
0
1
2
1
0
0
0
1
1
0
0
1
1
0
0
0
1
1
0
1
0
1
0
0
1
2
1
1
1
0
0
1
0
2
1
1
1
0
1
1
2
2
0
2
0
0
1
0
0
1
1
2
0
0
2
1
0
1
0
1
2
0
1
2
1
0
1
0
2
1
0
1
1
2
1
3
2
0
1
0
1
1
0
1
1
2
0
1
1
0
0
1
0
0
1
0
1
1
2
0
1
2
1
0
2
2
0
0
0
2
0
0
1
0
1
1
0
1
1
2
0
0
1
1
2
2
1
2
2
0
0
0
2
1
0
1
1
1
0
2
1
0
0
2
0
1
1
1
2
1
0
0
0
1
1
0
0
1
0
0
0
0
2
0
0
0
0
1
0
2
2
2
1
1
1
1
0
1
1
2
1
1
1
1
1
0
0
1
1
0
1
0
2
1
1
2
1
2
0
0
1
1
1
0
0
1
0
0
1
0
1
0
2
0
0
1
1
0
0
2
1
0
0
0
2
0
1
1
1
2
0
2
1
2
0
1
2
0
1
0
2
1
0
2
0
1
2
1
0
1
0
2
1
0
2
2
1
0
2
0
0
0
1
1
0
0
1
0
1
2
1
0
1
1
0
2
1
4
1
0
0
0
1
2
1
0
1
2
0
1
1
1
1
0
0
0
0
2
2
1
0
1
1
2
1
2
0
1
0
1
1
2
0
1
1
2
0
1
1
0
1
0
1
3
0
0
2
0
0
1
1
2
1
1
1
2
1
0
0
0
0
2
1
0
1
0
1
2
0
2
1
1
0
1
1
2
0
1
0
1
2
0
2
1
1
1
1
2
1
0
2
1
2
1
2
2
0
1
0
1
1
0
2
1
1
2
0
0
1
0
2
0
3
1
1
2
1
0
0
3
2
2
1
1
2
2
2
0
2
2
2
0
2
0
2
0
0
1
0
0
1
2
0
2
1
2
2
0
0
0
0
1
0
0
2
1
0
2
0
1
0
0
0
1
0
0
0
2
0
0
0
1
0
0
1
0
0
0
1
1
0
2
1
2
0
0
2
0
0
0
1
0
1
2
0
0
0
1
2
1
0
0
0
2
2
2
0
0
1
0
0
2
1
1
2
0
0
1
0
1
0
1
0
1
1
1
0
1
1
0
0
0
1
1
0
0
1
1
0
0
1
1
0
0
2
0
0
1
2
2
1
2
1
1
0
1
4
1
0
1
0
1
1
1
1
0
1
0
3
0
1
1
1
0
1
0
0
3
2
1
0
1
0
2
2
1
0
1
0
0
2
0
0
1
1
2
1
1
0
0
2
2
0
1
2
1
2
0
2
1
1
2
0
3
0
1
0
3
0
2
1
1
1
1
2
2
1
1
2
0
0
1
0
1
1
0
1
1
1
1
2
0
0
0
2
0
2
0
0
1
1
1
0
1
1
1
1
2
1
1
2
2
0
1
0
0
1
1
4
0
1
2
0
0
2
0
2
0
2
0
2
2
1
2
0
0
1
0
0
0
0
2
0
0
1
1
1
1
2
2
0
2
1
0
1
0
1
0
2
1
1
1
1
1
3
1
1
2
1
1
2
2
2
0
4
0
2
0
1
0
1
2
1
1
0
1
4
1
0
1
1
1
1
0
1
1
1
1
0
2
2
1
3
1
1
0
1
0
1
0
1
1
1
1
0
0
2
0
1
1
2
2
1
1
0
1
1
2
0
0
0
1
1
1
0
1
1
1
1
2
1
2
0
1
2
1
0
2
2
2
0
1
1
2
0
1
0
1
2
0
2
2
3
0
0
0
0
1
1
1
0
1
2
0
0
0
0
2
4
0
0
2
1
1
2
2
0
0
2
1
2
2
0
1
0
1
2
1
0
1
1
1
1
1
1
1
1
1
1
0
0
0
1
2
0
1
2
1
1
1
2
2
1
1
2
0
0
1
2
1
0
1
2
0
0
1
0
0
1
0
2
1
1
1
1
1
1
0
1
1
0
1
0
0
2
0
2
1
1
1
2
0
0
0
2
0
1
2
3
2
2
0
1
2
1
1
0
0
2
1
1
1
0
2
2
2
1
1
1
0
2
2
0
2
1
1
2
2
0
0
1
1
2
1
2
0
0
0
1
0
2
0
1
0
0
2
2
1
2
0
1
2
2
0
0
1
0
1
0
0
0
1
0
0
0
1
0
2
0
0
1
0
0
1
1
0
4
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
2
1
0
2
0
0
0
2
2
1
0
2
2
1
0
1
1
1
0
0
1
0
2
0
1
0
0
0
2
1
1
2
0
0
0
2
0
2
2
2
1
0
1
1
1
2
1
0
1
1
1
1
1
1
0
0
0
2
1
0
1
2
2
1
0
2
0
0
1
0
1
0
1
1
0
2
2
0
0
0
1
0
0
2
0
1
0
1
1
0
0
2
0
0
2
1
0
1
0
0
0
0
2
1
0
0
0
0
1
1
0
1
0
2
0
1
0
1
2
1
1
1
1
0
0
2
2
1
0
0
2
0
0
0
0
1
2
0
1
1
1
1
0
0
1
1
0
1
0
0
2
2
0
2
0
1
2
0
1
2
1
1
2
0
0
1
2
0
1
0
1
0
2
2
0
1
0
0
1
2
1
1
0
0
1
0
0
0
2
0
1
1
1
0
1
0
0
0
1
1
1
0
0
2
1
2
2
0
0
1
0
0
0
0
1
2
3
1
2
0
1
0
0
1
1
0
1
1
0
2
1
2
3
2
1
1
1
0
0
0
0
0
1
1
0
2
1
2
0
0
1
1
0
1
1
1
1
0
0
1
2
0
0
1
2
0
0
2
1
1
0
1
1
1
1
1
1
1
1
2
1
0
1
1
2
2
0
1
1
1
0
1
0
1
0
0
1
1
1
2
2
2
1
2
1
0
1
1
1
1
0
1
0
0
1
2
2
1
0
0
2
1
0
1
0
0
1
0
1
1
0
0
1
2
0
1
1
1
1
2
2
0
0
0
3
1
0
0
1
0
1
0
1
0
2
2
1
0
3
5
1
2
2
1
2
1
2
2
1
0
0
1
2
1
1
0
0
0
1
1
0
2
2
0
1
1
2
0
2
1
2
2
1
0
2
2
0
2
0
0
2
0
1
0
0
0
0
2
1
0
3
0
2
0
0
1
2
0
2
2
2
0
1
1
2
0
1
2
1
1
1
0
0
1
1
0
1
2
2
0
0
2
0
1
1
1
1
1
1
0
1
1
0
0
0
1
2
0
0
1
2
1
1
1
1
0
0
1
0
0
2
0
2
2
0
2
0
1
0
0
1
2
0
1
1
4
1
1
2
1
1
0
0
2
0
1
1
0
1
0
1
2
0
0
2
0
0
1
0
0
1
1
1
1
0
2
2
2
2
1
0
0
0
0
1
1
0
0
1
1
0
0
1
1
1
2
3
1
0
0
1
2
0
2
0
1
1
0
2
1
1
0
0
0
0
0
2
0
0
0
2
0
1
1
1
0
1
1
1
0
1
0
0
0
0
0
0
1
0
0
1
0
2
1
0
0
0
1
2
1
0
1
1
1
1
0
1
0
1
1
0
1
1
1
0
0
1
0
1
0
1
1
0
2
1
0
0
1
1
2
0
0
0
6
0
1
0
1
0
1
0
0
2
0
1
1
2
0
2
0
1
0
0
1
1
1
0
2
1
1
1
2
1
2
1
0
1
2
1
1
0
0
0
0
2
0
1
2
1
1
0
0
0
1
1
1
1
1
1
1
0
0
2
1
2
1
0
0
1
1
0
2
2
0
0
0
0
1
1
1
1
0
2
1
0
2
2
2
1
1
1
0
2
0
1
1
0
2
2
1
1
1
1
1
2
2
0
0
2
1
1
0
0
1
1
1
0
1
0
1
0
0
1
0
0
0
1
0
0
1
0
0
2
0
0
0
1
1
1
0
1
0
0
0
2
2
1
0
0
1
0
2
1
2
1
1
0
1
2
2
0
2
2
0
0
2
0
1
0
0
0
1
1
0
0
2
2
0
0
2
0
0
1
1
1
0
2
0
0
0
1
2
1
2
0
2
2
0
0
1
1
0
0
1
2
1
2
0
0
0
1
1
0
0
0
0
1
1
0
2
1
1
0
1
0
2
0
1
1
1
1
1
0
1
0
1
1
0
1
0
0
1
2
1
1
2
2
1
0
2
1
0
1
1
1
1
0
0
2
0
0
1
0
0
2
0
1
1
1
0
2
1
1
1
2
0
0
0
2
1
2
1
2
1
1
0
0
1
0
0
1
0
1
0
0
0
1
2
0
0
0
3
1
0
3
2
1
0
1
0
1
2
0
0
1
0
2
0
1
2
0
0
0
1
1
0
1
2
2
0
1
0
1
0
1
0
1
3
1
1
1
1
1
0
2
1
1
2
0
0
0
0
1
2
0
0
0
1
1
0
0
2
0
0
0
1
1
1
0
1
0
2
0
0
1
1
1
3
0
0
1
1
0
2
1
2
1
1
1
1
1
1
0
0
1
1
0
2
2
2
0
2
1
1
1
1
2
1
2
1
0
0
1
1
1
0
1
0
0
0
2
0
0
0
0
1
1
1
2
1
1
2
1
1
2
1
0
2
0
2
2
1
2
0
2
0
1
3
1
0
0
1
0
0
2
0
2
1
1
0
2
1
1
1
0
0
0
1
0
0
0
1
1
2
1
1
0
1
2
2
0
1
0
0
0
0
0
0
1
1
1
0
1
2
1
1
0
2
0
1
1
1
0
0
0
0
2
2
1
1
0
1
1
2
0
2
0
1
1
1
0
1
1
0
1
0
1
1
0
0
2
0
0
2
0
2
1
2
2
0
0
2
1
1
1
1
0
0
0
0
0
0
1
1
0
0
1
0
1
1
1
1
0
1
1
2
0
1
2
2
2
2
1
1
2
1
0
1
1
0
1
1
2
0
2
1
0
1
2
0
1
1
0
2
1
0
0
3
0
0
2
2
0
0
2
0
1
1
1
0
1
2
0
0
1
2
1
1
0
2
0
3
1
1
0
0
0
2
0
2
2
1
2
1
1
0
2
1
0
0
1
0
1
0
2
0
2
1
0
2
2
1
0
2
2
2
1
0
1
0
0
0
0
1
0
1
1
0
1
1
2
1
2
0
0
2
1
1
1
1
2
2
2
0
0
1
0
0
0
3
1
1
0
1
2
1
0
0
0
2
0
2
1
1
1
0
0
1
0
2
0
1
0
1
1
2
0
0
0
2
1
0
0
0
1
1
2
1
1
0
1
1
2
0
1
2
1
2
0
0
1
0
0
0
1
1
0
1
0
1
2
1
1
0
2
1
0
1
2
0
2
0
0
0
1
1
1
2
1
1
0
1
2
1
0
0
1
0
1
2
0
2
1
1
1
1
1
3
1
1
1
0
2
2
0
4
0
0
0
0
0
2
1
2
2
0
2
0
0
1
1
1
0
1
1
2
0
3
0
1
0
0
0
1
0
1
0
0
1
0
0
2
1
0
0
0
2
0
0
1
2
1
1
2
1
2
0
2
0
2
0
0
2
0
1
1
1
2
1
1
0
1
1
0
0
0
1
0
1
0
0
1
1
0
0
0
3
1
1
2
0
1
1
0
2
1
2
2
1
1
1
1
2
2
1
0
0
0
0
0
2
4
0
2
0
0
2
2
2
1
0
0
2
1
2
0
2
0
0
0
0
0
0
2
1
2
2
0
1
1
0
1
0
0
1
2
1
2
1
1
2
2
1
1
0
1
2
1
1
0
2
1
1
0
0
0
0
0
0
1
0
2
0
2
0
2
0
1
1
1
1
3
0
1
0
0
1
1
2
1
1
1
0
1
1
2
1
0
1
0
0
1
1
0
0
0
1
1
1
0
1
1
0
1
1
2
2
1
1
0
1
1
1
2
2
0
0
0
2
2
0
2
2
0
0
1
1
1
1
1
0
2
1
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
1
2
0
3
0
0
1
1
0
0
2
1
0
0
1
0
1
2
2
1
0
0
0
0
1
0
1
1
0
2
1
2
1
1
1
2
1
0
0
2
2
0
2
1
0
0
1
1
0
1
0
1
1
0
1
0
1
3
0
0
1
2
1
0
1
0
1
0
0
0
1
0
0
1
1
1
2
0
1
2
1
0
1
0
1
1
1
1
0
0
2
0
0
1
1
0
1
0
0
0
2
0
0
1
0
1
1
0
0
2
1
2
0
0
4
2
1
0
0
0
2
1
0
0
2
2
0
1
2
1
1
0
2
0
2
1
2
0
0
1
0
0
2
0
0
1
1
0
0
1
0
0
0
1
2
0
0
0
1
0
1
0
2
0
0
0
2
0
1
0
0
0
0
1
1
0
0
2
1
0
2
0
1
2
0
2
0
0
0
1
0
0
0
1
0
1
1
0
1
0
2
0
1
1
1
0
2
1
2
1
0
0
0
0
0
0
0
3
1
1
2
1
0
1
0
1
2
1
1
1
0
2
2
1
1
1
1
1
2
1
1
0
0
1
0
1
2
1
0
1
3
1
0
1
1
1
1
0
0
2
1
1
2
1
0
0
2
0
1
2
1
1
1
0
3
2
2
2
1
0
1
0
0
0
0
2
2
0
1
2
2
0
0
1
1
0
2
1
0
3
1
0
1
4
1
0
1
1
1
0
0
0
2
0
0
1
2
0
0
2
1
2
0
2
1
1
0
1
2
2
0
0
0
1
1
0
1
0
2
1
1
0
1
2
1
0
1
1
2
0
1
0
1
0
0
1
2
1
2
1
1
1
1
1
0
0
1
1
1
0
0
1
1
2
0
0
1
1
1
1
1
2
2
1
0
0
2
2
2
1
2
1
2
0
1
0
1
0
2
0
1
1
0
1
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
1
2
0
2
0
1
1
1
0
2
0
1
0
0
1
2
1
0
0
2
0
0
0
0
2
0
1
0
1
2
2
1
0
1
0
1
3
0
2
1
0
2
1
2
0
0
0
0
0
0
1
0
1
3
0
1
2
2
1
1
2
1
0
0
0
1
1
0
0
0
0
2
2
0
0
2
1
0
0
1
0
1
1
1
0
0
1
0
2
1
2
2
0
0
2
0
0
2
0
0
0
0
1
2
0
1
1
0
1
1
0
0
0
0
1
1
2
1
1
2
0
1
1
1
2
1
1
2
1
0
0
0
0
1
1
1
2
0
1
2
1
0
0
2
0
1
2
2
0
0
1
2
2
2
0
1
2
1
0
0
1
0
1
0
1
2
2
1
1
2
1
1
1
1
1
1
0
0
1
0
1
1
1
8
0
0
1
2
1
2
1
0
1
0
0
0
1
0
2
1
1
2
0
2
1
1
1
0
0
0
1
1
0
1
2
2
0
1
2
1
0
0
2
2
2
0
2
1
1
1
0
0
0
1
1
0
1
0
0
2
2
0
1
2
0
0
0
0
0
2
0
0
1
0
0
0
0
2
1
2
0
1
0
2
1
0
1
2
1
0
1
2
1
0
2
1
0
0
0
2
1
2
0
2
1
2
0
1
2
2
1
1
2
2
0
2
0
0
2
1
2
3
1
2
0
0
0
1
1
1
0
0
0
0
1
1
2
1
1
0
2
2
0
1
0
1
1
1
2
2
0
1
0
0
1
0
0
1
1
11
0
0
1
1
0
1
1
1
0
0
1
2
1
2
1
1
1
2
0
0
7
0
0
0
1
2
0
1
2
0
1
1
1
1
1
0
0
3
2
1
0
1
1
2
0
2
2
1
1
0
1
1
1
2
1
2
2
0
0
0
0
1
1
0
2
5
2
0
1
0
0
2
1
1
1
1
1
2
2
1
1
1
0
0
1
0
2
1
2
1
1
0
0
1
0
0
0
1
0
0
2
1
2
0
0
0
0
0
0
0
2
1
2
1
2
0
1
0
0
1
0
0
1
1
2
2
1
1
0
1
1
0
0
1
0
1
0
0
0
2
0
1
0
0
1
0
0
1
0
1
1
1
0
1
2
1
1
1
1
1
2
1
0
1
1
0
1
0
0
0
1
1
4
1
2
1
2
0
1
1
2
0
2
0
0
1
2
1
1
1
0
0
0
1
1
0
2
0
2
2
1
1
2
0
1
2
1
2
1
2
0
1
1
0
1
0
0
2
1
1
0
0
0
2
1
0
1
1
2
0
0
2
0
2
0
0
2
1
0
0
1
0
2
0
1
0
3
0
1
0
0
1
1
1
1
2
1
0
0
1
1
2
1
0
1
0
2
0
1
1
2
0
0
0
1
1
1
1
0
2
2
1
3
0
0
0
2
0
1
2
0
1
0
2
1
1
1
1
1
0
0
2
0
1
1
0
1
1
0
1
1
0
2
0
1
2
2
2
2
0
1
0
0
1
2
0
1
0
0
1
1
2
0
1
0
2
1
1
0
1
2
1
1
1
0
0
0
0
1
1
0
0
0
1
0
1
3
0
0
0
1
2
1
0
2
1
0
2
1
1
1
2
0
0
1
3
1
3
1
1
2
2
2
1
2
0
2
0
1
0
1
0
2
0
2
2
2
1
2
2
1
0
0
0
1
2
1
1
0
2
0
0
0
0
1
1
2
0
2
0
0
1
0
0
1
1
0
1
1
2
1
1
2
1
0
1
2
1
2
1
3
2
2
2
0
0
0
2
1
0
1
1
1
1
1
0
1
2
2
1
2
3
1
0
2
2
0
0
0
0
0
0
0
2
1
1
0
0
0
0
2
0
1
2
0
0
0
0
1
1
0
0
0
1
2
1
0
0
0
1
2
0
1
0
5
1
0
1
2
1
0
1
2
1
0
0
0
0
1
1
2
2
0
0
1
1
2
2
0
0
1
0
2
0
0
0
1
1
0
1
0
2
1
1
2
0
1
1
0
0
0
0
0
0
0
1
1
1
2
0
0
1
0
1
0
0
2
1
2
1
1
0
2
2
2
0
1
0
0
0
2
1
0
1
2
2
1
1
0
1
2
1
1
1
1
2
1
2
1
0
1
2
0
1
1
1
1
1
2
2
1
1
2
0
2
0
1
0
1
2
0
1
0
0
1
1
1
1
0
0
1
1
2
1
1
1
2
0
1
1
0
1
1
0
1
0
0
1
1
2
0
0
2
1
1
1
2
1
1
0
2
1
2
2
1
3
1
1
1
1
1
2
1
0
2
2
2
1
0
1
1
1
3
0
0
0
0
1
3
1
0
0
1
1
1
2
0
0
0
1
1
1
1
1
2
1
1
1
1
2
0
2
3
1
0
1
1
0
1
2
0
1
1
1
0
1
1
1
1
0
1
0
0
2
0
1
0
1
0
0
0
0
2
2
1
1
0
1
2
0
2
0
0
0
1
1
0
2
1
1
0
0
2
1
2
2
0
1
1
0
1
1
1
0
0
1
1
1
0
2
2
0
0
1
2
1
2
0
0
2
3
2
0
1
2
0
1
0
2
1
1
0
1
2
0
0
4
2
0
0
2
0
1
2
0
1
1
1
0
1
1
1
2
0
0
0
1
2
1
0
1
0
1
0
1
1
1
0
1
1
0
0
2
1
1
1
1
0
1
0
0
0
2
1
1
1
0
2
2
0
2
2
0
0
0
2
0
1
2
1
2
0
1
1
2
0
2
1
0
0
1
1
1
3
0
1
0
1
2
0
0
1
2
2
1
0
0
2
0
1
0
0
1
0
1
0
1
0
1
0
2
1
0
1
0
0
2
2
0
2
0
2
2
1
0
2
1
2
1
0
1
2
0
0
0
1
0
1
1
0
1
0
0
0
2
2
0
3
0
0
1
1
2
1
0
0
2
1
1
2
1
2
2
0
2
0
0
2
1
0
0
1
1
2
2
1
1
3
2
0
2
1
0
2
0
0
0
0
2
2
2
2
1
0
0
0
2
1
0
1
0
2
1
1
2
0
2
2
1
0
2
0
1
1
0
1
1
2
0
2
1
1
0
1
0
1
0
1
2
1
0
1
2
0
0
1
2
0
1
1
1
2
0
1
1
2
1
1
0
2
1
1
1
2
1
0
1
2
1
2
0
1
1
0
1
2
2
2
2
2
0
0
0
0
0
2
2
1
1
1
2
0
1
0
0
2
2
0
0
1
2
2
1
2
2
0
0
2
0
0
0
2
2
3
0
0
1
1
0
2
0
0
0
0
2
0
1
1
1
2
2
0
0
0
1
0
1
1
2
2
0
1
0
2
2
2
0
1
1
1
0
1
0
0
1
1
0
0
1
2
2
2
2
3
0
0
0
3
0
0
2
1
1
0
2
2
1
1
1
2
0
1
0
1
0
1
1
0
1
2
2
2
2
0
1
1
0
2
1
0
0
1
1
1
0
0
3
2
2
0
2
0
1
0
0
0
0
1
1
2
1
0
1
0
1
2
0
2
0
0
1
1
1
1
0
0
1
0
1
1
0
0
0
0
2
0
1
0
0
1
0
2
2
2
1
1
1
1
0
0
0
1
0
1
0
1
0
2
0
2
0
0
1
0
0
1
1
1
1
1
0
1
0
1
2
0
2
1
2
0
1
1
2
0
0
0
1
0
1
1
1
0
2
2
1
0
0
0
2
2
0
0
1
1
1
1
0
0
0
1
0
0
0
0
0
2
0
0
1
2
1
0
1
1
1
1
1
0
0
0
1
1
1
0
0
2
0
2
1
0
0
0
1
0
0
1
1
2
1
0
1
2
1
0
0
2
1
1
0
2
1
1
0
1
1
0
2
1
0
1
0
0
1
0
0
0
1
1
2
1
1
0
1
1
0
2
2
0
1
0
1
0
1
0
1
1
1
1
0
0
1
1
0
0
0
1
1
2
2
0
2
1
0
1
0
1
0
0
2
0
1
0
0
1
1
1
2
2
0
0
1
0
0
1
1
1
2
2
1
2
1
1
0
0
0
2
1
0
2
1
1
2
1
1
0
1
0
2
1
1
1
0
2
1
1
1
0
1
2
0
1
0
1
1
0
3
0
1
2
0
0
0
0
0
1
0
0
1
1
0
5
1
1
1
2
2
2
0
0
0
0
1
1
2
2
1
0
0
1
1
1
2
1
2
0
2
0
0
1
1
1
0
1
0
1
1
2
2
1
0
0
0
0
0
1
1
0
2
1
1
1
1
2
0
1
2
1
2
0
1
1
0
3
1
1
1
2
2
0
1
1
1
1
2
1
0
2
3
0
1
0
1
0
1
0
0
2
2
0
0
1
0
0
0
1
1
0
2
0
1
1
2
1
2
0
0
1
0
0
0
1
1
1
0
2
2
1
1
0
0
1
1
0
0
1
1
1
1
1
0
0
0
1
0
1
0
1
1
1
2
1
0
0
0
3
0
0
1
0
1
2
1
2
1
1
2
1
0
1
2
2
4
1
0
2
1
1
2
0
1
0
1
1
1
1
1
0
1
0
1
2
0
0
0
2
1
1
0
0
0
0
0
0
2
1
1
2
1
0
0
0
2
0
0
1
1
0
1
1
1
1
0
0
2
2
0
0
1
2
0
0
2
1
2
0
3
0
1
0
0
2
1
0
0
2
0
3
1
1
0
0
0
1
1
0
2
2
0
1
0
1
2
1
1
1
0
1
1
0
0
0
0
1
1
0
1
1
2
1
0
2
2
1
2
1
0
2
1
1
1
1
0
0
1
1
1
0
2
2
1
0
0
1
1
1
0
0
1
0
0
0
2
2
0
3
1
2
1
1
0
2
0
1
0
0
1
2
2
1
0
1
1
0
2
0
0
0
0
2
1
0
2
2
0
0
0
1
1
0
0
1
2
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
1
1
0
0
0
1
2
1
1
0
0
2
0
0
1
2
1
2
0
0
1
2
2
2
0
0
0
1
3
1
2
0
3
0
1
2
0
1
1
1
1
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
2
0
2
1
1
2
0
0
0
0
2
1
2
0
0
1
1
0
1
2
0
0
0
0
2
1
1
2
0
2
0
2
0
2
0
2
2
0
1
1
0
1
0
0
0
1
0
0
2
1
0
1
0
0
0
0
1
1
0
0
1
0
0
1
1
1
0
0
0
2
2
0
1
1
0
1
0
1
0
2
0
2
1
0
0
1
0
1
2
2
1
1
1
0
1
1
1
2
1
0
0
0
1
0
1
1
0
1
0
1
0
0
0
1
0
2
0
0
1
0
1
0
1
2
1
0
2
0
0
1
2
0
1
1
2
1
0
2
1
2
0
0
1
2
1
0
0
2
2
0
0
1
2
1
2
2
0
0
0
0
1
1
1
2
2
0
0
1
1
1
1
2
1
0
2
1
2
1
0
0
0
2
1
0
1
0
0
2
0
0
2
1
0
2
1
0
2
0
0
1
2
1
1
1
2
0
1
1
0
1
0
0
2
0
2
1
1
1
0
2
0
0
1
0
1
0
2
0
0
0
0
1
0
2
0
0
1
1
0
1
2
0
1
0
0
1
1
2
0
0
1
0
1
1
1
0
1
0
0
1
1
1
1
0
0
2
1
0
3
1
0
1
0
2
1
1
1
2
0
0
1
0
1
1
2
0
2
1
1
0
1
2
0
1
0
1
1
2
1
1
2
1
2
1
1
1
0
1
0
1
1
3
1
0
1
0
2
0
2
1
0
1
2
1
1
2
0
1
2
1
0
1
0
0
1
0
1
0
2
2
0
1
1
0
0
1
0
2
0
1
0
1
0
2
0
1
0
0
0
0
0
1
1
2
2
1
2
2
0
1
1
1
1
0
1
2
0
2
0
2
0
1
0
0
0
1
1
1
0
0
2
1
0
1
0
1
2
1
0
1
1
2
1
1
1
1
1
0
1
0
0
1
2
1
3
2
1
2
0
2
2
1
1
1
0
1
0
0
0
2
2
1
1
1
1
1
0
0
0
0
0
0
0
6
0
2
2
1
1
2
1
0
1
2
1
1
0
0
1
0
1
1
1
1
1
2
2
1
0
2
0
0
2
1
0
1
1
2
1
0
0
2
1
2
1
2
1
1
0
2
1
0
0
0
0
0
1
0
1
1
1
1
2
0
2
2
1
2
2
0
1
1
1
0
0
1
0
1
2
0
1
1
2
2
1
0
1
1
0
0
2
1
0
2
1
1
2
1
1
2
0
0
1
1
2
0
1
0
1
1
0
0
2
0
1
1
1
1
4
0
0
0
1
1
0
0
0
1
1
1
1
0
0
1
0
2
0
1
1
1
1
1
0
0
1
2
0
0
0
0
1
1
1
0
1
0
0
1
1
0
0
0
2
2
0
0
0
0
0
0
0
1
1
0
1
3
2
2
2
2
0
0
0
0
1
0
0
3
1
0
1
0
1
1
0
0
0
1
0
1
0
2
0
0
1
1
0
0
1
0
2
1
3
0
2
1
1
2
1
2
1
0
8
0
4
0
2
2
3
0
2
2
0
2
1
2
1
0
0
0
0
0
2
1
0
1
0
1
1
1
1
3
0
1
1
1
0
0
1
1
2
0
1
0
2
2
0
1
2
1
2
0
1
1
1
2
0
1
1
0
1
0
0
0
1
0
1
1
1
1
0
0
1
1
0
1
2
1
2
1
1
1
2
2
0
1
2
1
0
1
0
1
0
0
1
0
0
2
1
0
0
0
1
0
2
0
2
1
1
0
2
1
1
1
0
0
2
1
1
0
0
1
2
1
1
2
0
1
0
0
2
0
1
2
0
1
2
2
1
2
2
1
1
0
1
2
0
1
1
1
1
2
0
0
1
0
0
2
1
0
0
1
0
0
0
2
0
0
0
0
0
0
2
1
1
1
0
1
0
2
1
1
1
2
0
0
1
1
0
1
2
2
0
1
1
0
2
1
1
0
1
1
1
0
0
0
0
1
1
0
1
0
1
0
0
1
2
2
1
2
2
1
1
2
1
0
2
2
1
0
1
1
0
1
0
1
1
0
2
0
0
1
0
2
0
1
0
1
2
2
0
3
0
1
0
1
1
1
2
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
2
0
1
2
1
1
1
2
1
0
2
0
2
1
1
2
1
1
1
0
0
0
0
1
1
1
1
1
1
0
0
2
2
1
0
1
0
0
1
2
1
1
0
0
1
2
0
0
0
2
0
0
0
0
2
1
1
1
1
0
0
0
0
1
0
2
1
1
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
1
1
2
2
0
0
0
0
0
1
1
1
3
1
1
1
0
1
1
1
2
2
0
0
1
0
1
1
0
0
1
0
0
1
1
0
1
0
0
1
0
1
1
1
0
1
1
0
2
1
2
1
0
1
0
0
1
0
0
1
2
0
0
2
0
0
0
2
1
2
2
0
0
1
1
0
0
2
0
1
1
0
0
1
1
0
0
0
2
1
1
0
1
0
0
1
0
2
0
0
0
1
1
0
1
1
1
1
3
1
2
2
0
1
0
2
2
1
2
3
1
0
0
2
2
1
1
2
1
1
1
2
0
1
0
0
2
2
1
1
2
2
0
0
0
0
1
0
0
0
1
0
0
2
2
3
2
0
0
0
2
2
0
0
0
0
0
0
1
0
1
2
1
0
2
2
1
0
1
1
0
1
1
1
0
0
1
1
1
2
2
0
1
1
1
1
1
0
0
2
1
1
2
0
0
1
2
3
0
1
1
0
0
1
0
2
2
1
0
0
0
2
0
1
0
0
2
0
0
0
0
1
0
1
2
0
0
1
2
2
1
0
1
1
1
2
2
1
2
1
1
2
0
1
0
0
0
1
2
0
1
1
0
1
1
0
0
1
2
2
1
0
2
2
0
1
0
0
0
0
0
1
1
2
1
0
1
0
2
1
2
0
0
1
1
0
1
2
0
1
0
0
1
2
2
1
1
0
0
0
2
2
0
0
1
1
0
2
2
0
1
1
1
1
2
1
2
0
0
1
0
1
1
1
3
0
0
1
0
2
0
1
0
2
0
0
1
2
0
1
0
0
1
2
0
0
0
0
1
1
0
2
3
1
0
0
0
1
0
1
0
2
0
1
0
1
1
1
1
1
2
2
2
2
1
2
0
0
1
0
2
0
2
0
1
1
1
1
0
2
0
2
0
2
1
0
0
2
1
2
0
0
1
1
1
0
2
1
1
0
0
1
2
1
0
1
1
0
1
0
1
2
0
1
1
1
0
0
0
0
0
1
0
1
1
0
0
1
1
2
2
0
0
0
0
0
1
3
1
1
1
1
1
1
1
0
2
1
2
0
1
2
4
0
0
1
2
0
1
1
0
0
2
3
1
0
1
0
0
0
2
1
2
1
1
0
1
0
1
0
0
2
0
0
1
1
0
1
1
1
0
1
0
0
0
1
0
0
1
0
1
0
2
1
2
1
1
1
0
1
0
0
2
1
1
1
0
0
1
3
0
0
1
1
0
2
4
1
0
0
0
0
1
2
1
0
0
1
1
0
1
0
1
1
0
1
1
0
0
1
2
1
0
2
1
1
3
1
0
0
0
0
1
2
0
0
1
2
0
1
2
0
1
1
2
1
1
2
0
0
0
1
2
1
0
1
0
0
1
0
0
0
1
1
1
0
2
1
1
1
1
1
2
1
2
1
1
2
0
2
1
1
1
1
2
1
0
0
2
0
0
0
1
2
0
1
1
1
1
0
2
2
0
0
1
0
1
1
2
0
1
1
0
0
0
1
2
2
0
1
2
1
0
2
2
0
0
0
2
1
1
1
0
1
0
2
0
1
1
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
1
1
1
1
1
0
2
1
1
1
2
1
1
0
1
2
2
1
1
1
1
0
0
1
0
1
3
1
1
0
1
0
2
1
1
0
2
0
1
0
1
0
0
0
1
1
0
2
1
1
1
1
1
0
1
0
1
2
1
1
2
2
1
2
1
0
0
0
2
0
0
2
1
0
0
2
0
2
2
1
1
0
0
1
1
1
0
0
0
1
1
1
1
1
1
2
1
0
2
0
1
0
0
1
0
0
0
1
1
0
0
0
1
0
1
1
1
0
2
0
1
0
1
1
1
2
1
1
1
3
0
2
0
2
0
1
0
1
1
1
2
0
1
0
1
1
1
0
1
2
0
0
0
0
2
0
0
0
0
1
1
1
0
2
1
0
0
0
2
0
1
1
0
1
1
2
1
1
2
0
0
1
0
0
0
0
1
0
2
2
0
0
0
2
1
1
1
0
0
2
1
0
1
0
1
2
1
1
0
2
1
1
2
0
0
0
1
1
2
0
1
2
0
0
2
1
2
0
0
1
0
0
1
0
1
0
0
1
2
1
1
0
0
0
1
0
1
0
1
0
0
0
1
2
2
2
0
0
0
0
0
1
2
0
0
0
2
0
1
2
2
2
0
0
2
0
1
0
1
0
0
0
0
1
11
3
1
1
0
2
2
2
2
0
2
0
0
1
1
1
1
1
0
2
0
1
0
1
2
0
0
2
0
1
2
0
2
1
1
0
0
0
1
2
0
2
5
1
0
2
1
1
3
0
0
1
1
2
2
1
1
1
0
0
2
0
0
0
1
3
0
0
1
2
2
1
1
2
0
2
0
2
1
0
1
0
1
0
1
0
1
0
1
3
2
0
2
1
2
0
1
0
0
1
0
0
2
0
0
2
1
1
0
1
1
0
0
0
0
1
2
0
0
2
1
1
2
1
0
1
0
1
1
1
0
1
1
1
0
0
0
0
0
1
1
0
1
1
1
0
1
1
0
1
0
2
1
1
1
2
1
2
1
1
0
2
1
1
0
1
1
1
2
0
0
0
1
1
2
1
1
0
1
4
0
2
0
2
0
1
2
1
1
1
0
2
2
1
0
0
1
0
1
0
2
2
1
1
1
0
2
0
2
3
0
1
1
2
0
1
1
2
0
2
2
0
3
0
2
3
2
1
1
0
2
0
0
0
2
1
0
1
1
1
2
1
1
1
0
1
0
0
2
2
1
0
1
2
1
0
1
1
1
1
0
1
2
0
0
0
0
2
1
2
0
1
2
1
0
0
0
2
1
0
2
1
0
0
1
0
0
2
2
0
1
2
4
0
0
1
2
0
1
0
1
0
1
0
2
3
0
1
1
1
1
1
1
0
1
0
0
0
0
2
2
1
1
2
2
1
2
0
2
1
2
0
1
0
2
1
0
2
0
0
1
1
0
1
0
1
1
2
2
0
0
1
0
1
2
2
0
1
0
2
1
0
0
0
1
3
2
1
1
2
1
1
0
0
2
1
0
1
0
0
0
0
1
1
1
1
2
1
1
0
2
1
0
1
1
1
1
0
1
2
1
0
0
1
0
1
2
0
0
1
1
0
1
0
0
1
1
1
0
1
1
1
0
2
0
0
2
1
0
2
1
0
1
0
1
1
0
1
1
0
0
2
2
0
1
1
0
1
1
0
0
0
1
2
1
2
0
0
1
1
0
1
0
2
1
2
2
2
1
1
2
1
2
0
0
0
1
1
1
1
1
0
2
1
0
0
1
2
1
1
1
0
0
1
0
0
2
0
2
1
0
0
1
1
1
0
0
0
0
1
0
2
1
1
0
2
2
0
0
0
0
0
0
1
1
1
1
1
6
0
0
1
0
0
1
1
3
4
2
2
1
0
0
0
1
0
0
0
1
2
0
2
1
1
0
0
0
0
1
1
0
0
1
1
1
1
1
0
2
0
1
0
0
0
2
0
2
0
2
0
2
2
1
0
1
0
3
2
0
0
1
1
0
2
0
0
1
0
0
0
2
1
0
0
0
1
0
1
2
2
0
0
1
1
0
2
1
1
1
0
1
2
1
2
0
1
2
1
0
1
1
2
0
1
1
1
2
1
0
0
1
1
1
2
2
0
0
1
0
0
2
1
0
0
2
1
0
1
2
1
0
0
2
1
3
1
0
1
2
0
1
0
0
0
2
1
0
1
0
0
1
1
0
1
1
1
1
1
1
0
0
0
0
0
1
1
2
0
0
0
0
1
1
0
1
2
1
2
1
2
0
0
0
1
2
2
1
1
1
0
1
0
1
1
0
0
1
2
1
1
2
0
2
1
2
1
1
1
1
1
2
1
0
1
0
0
0
1
1
0
0
1
1
1
1
0
0
0
1
0
2
0
0
1
1
1
0
2
0
1
1
2
1
2
0
1
0
1
1
1
1
0
0
2
1
0
1
0
2
2
0
1
1
0
0
1
1
0
1
0
1
0
1
0
0
0
0
1
2
0
2
1
0
2
2
0
1
0
1
1
2
2
2
2
0
0
0
0
0
1
0
0
0
0
0
2
1
0
1
1
1
0
2
0
2
0
2
2
2
0
1
0
1
2
0
0
1
1
2
1
0
1
0
0
0
2
1
2
2
1
1
0
0
1
1
2
0
0
1
1
0
1
3
0
1
0
2
1
0
0
0
1
0
1
0
0
1
1
2
1
1
1
1
2
0
0
1
0
1
1
0
2
1
1
1
1
0
0
2
2
0
0
0
0
0
1
2
2
1
2
1
1
0
0
1
0
0
1
3
1
0
0
0
1
2
1
0
1
1
1
2
1
0
1
1
0
1
1
1
1
1
1
1
1
1
0
1
0
1
2
1
0
0
0
0
0
0
1
0
0
0
1
0
3
0
2
1
0
1
1
1
0
1
2
0
1
1
1
0
1
1
1
0
0
2
0
0
2
2
0
2
1
1
0
1
1
1
1
2
1
0
1
0
1
1
0
0
1
2
2
1
2
1
0
1
1
0
1
1
1
0
0
1
0
0
1
2
1
1
1
2
0
1
1
2
1
0
1
1
2
0
1
2
0
1
0
1
0
0
0
2
2
2
0
1
1
1
0
0
0
0
0
1
2
1
1
1
1
1
1
1
1
2
1
1
2
0
1
1
1
0
0
1
1
1
0
2
1
0
1
0
0
1
1
1
1
0
3
0
0
2
1
2
0
1
0
1
0
2
1
2
1
1
1
2
1
0
0
1
0
1
0
1
2
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
2
0
0
2
1
0
0
1
1
0
0
2
0
0
2
1
2
1
0
1
0
1
2
0
0
1
1
1
0
1
0
2
0
0
0
1
0
1
1
1
3
1
1
1
3
0
1
1
1
0
1
2
0
0
0
0
1
0
0
2
1
1
2
1
0
2
1
1
1
1
1
2
0
0
1
0
0
0
1
1
2
1
2
2
0
1
0
1
1
2
0
2
2
1
0
0
2
0
0
1
1
1
0
1
0
1
0
1
0
0
1
1
1
1
1
1
2
0
0
2
1
1
2
1
1
1
0
2
0
0
0
1
2
0
1
0
0
2
1
2
1
1
2
1
1
0
0
0
2
1
1
1
1
1
2
1
1
0
2
0
1
1
0
0
1
0
1
0
0
2
1
1
0
0
1
0
3
0
2
0
1
0
3
1
0
0
2
2
1
1
1
1
1
1
1
1
0
1
0
1
0
1
1
1
0
0
1
3
2
1
0
0
0
0
1
1
0
2
0
1
1
0
1
2
0
2
1
1
0
0
0
0
1
1
1
2
1
0
0
1
1
0
2
2
0
0
0
0
1
0
1
1
2
0
0
0
0
0
1
3
0
0
2
1
0
2
1
1
0
0
1
1
2
2
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
2
1
1
2
1
0
1
0
0
0
2
0
0
0
1
0
1
0
1
2
1
0
0
2
1
1
0
0
0
1
0
0
1
0
0
0
1
1
2
1
1
2
2
1
0
1
1
2
0
1
0
0
2
1
1
0
0
1
1
0
1
2
1
1
0
1
2
1
2
2
2
1
1
0
1
1
0
0
0
1
1
0
2
0
0
2
2
1
1
0
1
0
0
1
0
0
1
0
0
0
0
2
0
1
0
1
0
1
1
1
1
0
2
0
1
0
0
0
1
2
2
1
0
0
1
1
0
0
1
1
1
0
2
0
1
0
0
1
0
0
2
1
2
0
0
0
0
1
1
0
0
1
1
1
0
1
1
1
1
0
1
0
1
0
0
0
2
1
2
2
1
0
0
1
0
4
0
0
0
0
1
2
1
1
5
1
2
2
0
1
1
0
0
1
0
0
0
1
1
0
1
0
1
1
2
1
2
1
2
0
2
2
0
1
2
1
1
2
0
1
0
0
1
0
0
1
0
0
0
1
1
0
1
1
0
1
2
0
1
1
0
2
2
1
0
1
1
0
1
2
0
2
1
0
1
0
0
0
0
1
3
2
2
1
1
2
2
1
1
1
1
1
1
1
1
0
0
1
0
0
0
1
0
1
1
0
2
0
1
1
0
0
2
1
2
0
0
2
0
1
1
1
0
1
0
1
2
1
2
0
1
1
2
1
1
2
1
0
0
1
1
0
0
0
1
2
0
1
1
1
1
0
1
2
3
1
0
1
3
1
0
1
0
2
1
2
1
2
0
0
0
1
0
0
2
1
0
0
1
0
1
0
2
2
1
1
1
2
0
0
1
1
0
0
1
1
1
1
2
1
0
0
2
0
1
0
0
1
0
0
1
2
0
2
0
0
1
1
1
2
1
0
0
1
1
0
2
2
2
2
0
1
0
1
0
1
2
0
0
1
0
1
1
0
2
1
0
1
0
1
0
0
0
0
0
2
0
0
0
0
1
0
2
1
2
0
1
1
1
0
1
1
1
3
1
1
2
1
3
0
1
0
0
1
0
1
1
1
1
1
0
0
1
0
3
0
1
1
0
0
1
0
2
0
0
1
2
2
0
2
1
0
1
1
2
2
1
0
1
2
0
0
0
0
1
0
0
1
1
1
0
1
0
1
1
1
1
0
2
1
0
0
1
1
1
2
2
0
1
1
0
2
1
0
2
0
2
2
2
0
0
0
0
0
0
0
1
0
2
1
1
0
1
1
1
0
1
1
1
2
1
1
0
2
1
2
1
0
2
0
1
0
2
1
1
0
0
2
0
1
1
1
1
0
1
1
0
1
0
0
1
1
1
0
1
1
2
0
0
1
2
2
2
0
1
2
1
2
2
1
0
0
1
1
0
0
2
0
0
0
2
1
2
2
1
0
0
1
2
1
1
2
1
1
0
1
2
0
1
0
1
0
0
2
1
0
0
1
1
2
0
2
2
1
1
1
2
1
1
2
1
1
2
0
2
4
2
0
2
1
0
0
0
0
2
0
0
0
1
0
1
1
0
1
2
0
0
1
1
0
2
0
0
1
2
0
0
0
1
1
1
2
1
0
1
0
1
2
0
2
0
2
2
2
2
0
0
0
1
0
0
1
2
0
0
1
1
0
1
0
0
0
1
0
1
0
1
1
2
0
1
0
2
1
1
1
2
0
0
0
2
0
0
1
1
0
0
1
2
0
1
0
1
1
2
1
2
2
1
0
2
0
0
1
0
2
0
2
1
1
1
0
1
1
1
1
0
1
2
0
0
0
1
1
0
0
1
0
1
1
2
3
0
0
1
0
1
1
1
1
2
1
1
0
1
0
2
2
1
1
2
1
0
1
2
2
0
0
2
1
1
1
0
3
1
1
0
0
0
0
0
1
0
1
1
0
1
0
0
1
0
2
0
0
1
1
1
0
1
1
0
0
2
0
1
0
1
1
2
1
0
0
0
0
2
1
0
0
2
2
1
1
0
0
0
1
1
1
0
1
1
0
0
0
1
1
7
2
0
0
0
2
1
1
0
1
1
0
2
0
2
0
2
2
0
5
1
1
1
0
1
0
0
2
0
1
1
1
1
2
1
1
1
1
1
0
1
1
1
1
1
0
2
0
2
1
2
1
0
0
1
0
1
0
1
1
1
2
1
1
0
0
0
0
2
2
1
2
3
1
1
0
0
0
1
0
0
1
1
1
1
1
2
1
0
1
1
2
2
2
1
1
1
0
0
0
1
1
0
1
0
1
0
1
0
1
0
1
2
1
1
0
1
1
0
0
0
1
0
0
0
2
1
1
2
1
1
2
1
1
2
1
1
0
1
1
1
2
1
1
1
2
0
1
0
0
0
1
2
1
1
0
1
1
0
0
1
1
0
0
0
0
2
0
2
0
0
0
0
2
3
1
0
0
3
1
0
1
1
0
0
1
3
0
0
1
0
0
1
1
0
1
1
0
2
2
1
0
0
1
0
0
1
1
0
1
1
1
2
0
0
1
0
0
1
2
1
0
0
1
2
0
1
1
0
0
0
0
1
0
2
2
0
1
2
1
2
0
2
2
2
0
1
1
1
1
1
0
0
2
1
0
1
2
1
0
1
1
0
2
2
0
0
2
0
0
0
0
1
0
0
2
0
2
0
2
1
0
0
1
0
0
0
0
0
2
0
2
1
2
2
0
0
0
2
1
0
2
1
2
2
0
1
2
1
0
1
0
2
2
0
0
2
1
1
0
0
1
1
2
0
0
0
1
0
1
0
0
0
1
0
0
2
2
1
0
0
1
1
0
1
1
0
2
1
1
2
1
1
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
2
2
1
0
2
1
0
1
0
1
0
1
0
1
2
1
0
1
2
1
1
1
1
1
1
0
1
0
1
0
2
2
1
0
0
1
2
3
3
0
1
0
1
0
0
1
1
1
1
0
1
1
0
1
1
0
0
1
0
1
1
1
1
1
0
1
1
0
0
0
1
1
2
1
0
2
1
1
1
1
0
1
0
1
2
3
2
0
0
0
1
0
1
0
0
0
1
1
1
0
0
1
1
1
1
1
1
0
1
1
1
2
1
2
1
2
2
1
0
1
1
2
2
0
0
1
0
0
0
0
1
0
2
1
1
2
2
1
0
0
0
2
1
0
2
0
0
1
0
0
0
1
1
3
2
0
1
0
2
1
0
0
0
1
1
0
1
1
1
1
1
1
1
1
0
1
0
0
1
2
2
0
1
1
0
0
1
0
2
1
0
1
1
1
0
0
0
1
0
4
0
1
1
1
1
1
0
2
0
1
0
1
1
1
2
0
1
0
0
2
2
0
0
1
2
2
2
1
0
1
2
1
0
1
2
0
0
1
0
2
2
1
0
2
1
0
1
0
1
0
0
1
0
2
0
1
1
2
1
2
0
1
1
0
2
1
0
0
1
2
1
0
0
0
1
0
2
0
0
0
1
0
0
0
0
2
0
1
2
0
1
1
1
0
0
1
0
2
0
1
1
2
1
1
1
2
1
1
0
1
2
0
1
2
2
2
0
0
1
0
2
1
2
1
1
1
1
0
0
0
0
2
0
1
1
0
0
1
1
1
0
0
0
1
2
0
0
1
1
0
2
0
2
1
1
2
2
0
0
1
1
2
0
1
0
1
1
2
0
2
2
2
2
0
3
1
1
0
0
2
0
1
1
0
3
1
0
2
1
1
2
0
2
1
2
1
3
0
0
1
1
1
3
1
0
1
2
2
2
1
1
2
0
2
1
0
0
0
2
1
2
0
2
0
1
2
0
0
1
2
0
0
2
2
0
0
2
1
1
2
0
2
0
2
0
2
2
1
1
1
0
0
0
2
2
0
0
1
0
1
1
2
0
1
0
0
1
0
1
2
1
0
1
2
0
1
0
0
2
1
1
1
0
0
1
2
0
0
2
0
0
3
0
0
0
0
2
0
0
1
0
1
0
0
0
1
0
1
1
1
1
1
0
1
1
0
1
1
1
0
0
2
1
0
1
0
0
1
1
0
0
1
0
2
0
1
0
1
1
1
2
1
2
1
1
1
4
0
0
2
1
1
0
1
2
2
0
1
0
0
1
2
1
1
0
1
0
2
0
1
1
2
0
1
0
1
0
2
0
1
2
2
0
1
0
1
0
1
0
1
0
0
1
0
2
0
0
1
0
1
2
3
1
1
1
1
1
1
2
1
0
1
1
0
2
0
0
0
2
2
0
0
0
1
1
1
1
0
1
2
2
1
1
0
2
1
1
2
2
0
1
1
0
0
0
1
1
2
0
1
1
1
0
1
0
2
0
2
1
1
1
0
1
0
0
0
0
0
2
1
0
1
1
2
0
0
1
1
2
0
0
0
2
0
1
0
1
3
0
0
1
2
2
1
2
1
1
1
2
1
0
1
1
0
1
0
2
0
1
1
1
1
0
1
2
2
2
1
3
1
2
2
0
0
0
2
0
2
1
0
2
0
0
0
0
0
2
1
0
0
1
0
1
1
0
1
0
1
0
2
0
0
0
0
1
1
1
2
0
0
0
1
0
1
1
0
1
0
1
0
0
1
2
2
0
0
1
1
2
0
1
1
0
2
1
2
0
1
1
1
0
0
2
0
2
0
1
2
0
1
2
2
1
2
0
0
2
1
0
1
1
0
2
0
2
3
0
1
1
0
2
0
0
0
1
1
2
2
2
1
1
1
0
1
1
1
0
1
0
1
0
2
2
0
1
0
0
2
0
0
1
0
1
0
1
0
1
1
2
2
1
1
0
1
0
0
0
1
1
0
1
0
2
0
2
1
1
0
0
0
0
0
1
0
1
1
1
0
1
0
1
1
2
0
0
0
1
0
0
0
1
1
0
0
2
1
0
2
2
0
1
2
1
0
1
1
1
0
0
0
0
1
1
1
1
1
1
1
1
0
1
2
2
1
0
0
2
2
0
2
0
0
2
1
1
1
0
2
0
0
1
0
0
0
1
2
0
0
1
1
1
1
2
0
1
1
1
1
2
1
2
1
1
0
0
1
0
0
0
0
1
0
1
1
2
1
1
0
2
0
0
2
0
1
4
1
1
1
1
0
1
1
2
1
1
1
1
1
0
1
2
0
2
2
2
0
0
2
0
0
1
1
1
1
1
0
0
2
1
1
0
3
2
0
1
2
0
0
1
0
2
0
0
2
2
1
1
1
1
1
1
0
0
0
2
0
1
2
1
1
0
0
0
1
1
1
1
2
0
1
0
1
1
0
0
1
0
1
0
2
1
1
1
1
0
1
1
0
1
2
1
2
2
2
1
0
2
2
0
0
0
0
1
0
1
0
0
1
2
1
0
1
1
2
2
1
1
0
0
1
0
0
0
0
2
0
1
0
0
1
0
1
1
1
0
1
1
2
2
0
1
1
0
2
0
2
0
1
1
2
1
0
2
1
1
1
0
1
0
1
2
1
0
1
2
0
0
0
0
0
1
1
2
0
0
0
1
0
1
0
2
0
1
1
0
0
0
0
2
1
1
2
2
0
1
1
1
0
2
0
0
2
1
0
1
1
1
1
2
2
1
2
3
2
1
2
2
1
2
1
1
1
7
0
0
0
0
2
1
1
1
0
0
0
1
0
0
0
2
0
1
0
2
1
1
0
0
1
0
1
2
2
0
0
1
0
1
2
0
1
0
2
0
0
0
0
0
0
1
2
0
1
1
1
0
0
2
0
1
0
0
1
2
2
1
2
0
0
0
2
1
1
2
0
0
0
1
2
1
0
0
0
2
0
1
1
0
0
0
1
0
1
1
2
1
0
1
2
1
0
1
0
0
1
2
1
0
0
1
2
0
1
1
1
2
1
0
1
0
2
0
0
1
2
1
0
1
1
0
1
2
1
2
1
1
1
3
1
1
1
1
1
0
0
1
2
1
1
2
2
2
1
1
1
0
0
0
2
1
0
0
0
1
2
0
0
1
0
1
0
1
2
1
1
0
2
1
3
0
1
1
0
0
2
0
0
0
1
1
0
1
1
1
2
1
1
1
2
1
0
2
2
1
3
1
0
0
0
1
1
1
0
0
2
0
2
1
2
2
0
0
0
1
0
1
0
0
1
2
1
1
2
1
1
1
0
1
1
0
2
1
0
0
2
1
2
1
0
2
2
0
1
0
0
1
2
0
1
0
0
0
1
0
1
1
2
0
1
2
2
0
0
1
2
0
1
1
0
0
1
1
1
0
1
2
0
0
0
2
2
0
0
0
1
0
0
0
1
0
1
0
0
2
1
1
2
2
1
0
1
1
2
1
0
2
1
0
0
3
1
0
0
2
1
2
1
1
1
0
0
1
0
0
1
1
2
0
1
2
0
1
0
0
2
0
1
3
0
2
1
0
1
1
0
1
2
2
0
0
2
1
1
1
1
0
2
0
0
2
1
1
2
1
0
2
1
1
0
0
0
0
0
3
1
0
2
0
0
0
1
0
1
0
0
0
0
0
1
0
1
1
0
1
0
0
0
2
2
2
0
0
0
0
1
0
1
0
0
1
1
1
0
1
1
2
0
1
1
1
0
2
2
1
0
0
0
0
0
1
1
1
0
1
1
0
0
1
2
1
2
0
2
1
1
0
2
1
0
1
2
0
1
2
1
2
2
0
1
1
2
0
0
0
1
1
0
0
1
0
1
1
2
6
2
1
0
1
1
0
0
0
0
0
1
0
2
0
2
0
1
2
1
1
0
2
1
2
0
1
2
1
2
1
0
1
0
2
1
1
2
1
0
0
0
2
2
0
1
2
2
1
1
1
0
0
0
1
3
0
1
1
2
2
0
1
0
1
0
1
0
0
1
0
2
1
1
0
2
1
0
1
0
1
0
2
1
2
0
1
0
0
1
1
0
2
0
0
1
0
2
2
1
0
0
1
1
0
1
0
0
1
0
0
2
0
2
0
1
1
1
1
1
2
0
0
0
2
0
2
0
1
0
1
1
2
1
2
0
0
2
0
0
0
0
1
0
0
1
0
0
3
0
0
2
0
0
1
0
0
1
0
2
0
1
3
4
2
0
2
2
2
0
1
0
1
1
2
1
0
1
0
0
1
0
2
2
1
0
0
0
2
1
2
0
1
0
1
2
0
1
0
2
0
1
0
2
0
1
1
2
1
0
0
0
0
0
2
0
2
0
2
1
4
0
0
1
1
1
0
0
2
2
2
0
1
1
0
1
1
1
0
1
0
1
1
1
0
0
0
0
0
0
1
1
1
2
0
1
1
0
1
1
0
0
0
2
0
0
2
1
0
0
0
2
1
0
1
0
0
0
0
2
1
2
1
0
0
1
3
0
1
1
0
2
1
0
0
1
1
0
1
0
2
0
0
0
2
2
1
2
0
1
0
1
2
0
2
2
2
1
2
1
0
0
1
1
1
1
2
0
1
0
0
1
1
1
0
1
2
0
2
1
0
1
1
1
0
1
2
1
0
2
0
0
1
0
0
0
0
1
1
4
0
2
0
0
2
0
1
1
0
2
1
0
0
0
1
1
1
1
0
1
2
1
2
1
1
0
0
2
0
1
0
1
0
0
0
1
0
2
1
1
0
1
1
1
0
0
1
0
2
0
2
1
2
1
1
0
2
2
1
1
2
0
1
0
0
2
1
0
1
2
2
0
1
0
0
0
1
1
1
2
0
2
2
0
0
0
1
0
2
0
2
2
1
1
0
1
0
1
1
1
1
1
0
3
1
0
0
2
0
2
1
0
0
1
0
3
0
2
0
0
1
0
1
0
0
1
0
0
1
0
0
1
0
1
1
0
1
2
0
0
3
0
2
1
2
1
1
1
2
1
2
1
1
1
1
0
0
1
2
0
1
1
0
3
1
1
1
0
1
1
1
2
0
2
0
1
0
1
1
2
2
1
0
0
0
1
1
2
0
1
2
1
1
2
1
1
0
1
0
1
1
2
1
0
0
0
3
1
0
1
0
0
2
0
0
2
1
2
0
0
1
2
2
1
1
2
0
1
0
0
1
1
0
0
1
1
0
1
0
0
0
0
1
0
1
0
2
0
0
2
2
2
1
2
2
2
2
2
1
0
2
0
0
1
1
1
2
0
1
1
0
0
1
1
2
3
1
1
2
0
0
2
2
3
2
1
1
0
2
1
0
1
1
1
2
0
1
1
2
1
0
0
1
1
1
1
0
0
1
1
2
1
0
0
0
1
0
1
1
0
2
2
1
0
2
3
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
2
1
4
0
0
0
2
1
2
1
2
1
1
0
2
2
0
3
0
1
0
1
1
0
1
1
1
1
0
1
0
0
0
1
0
0
2
0
0
0
1
3
2
1
2
1
0
1
0
1
1
0
1
1
0
1
1
0
0
0
1
2
0
2
1
0
0
1
2
0
1
1
0
2
2
2
1
1
1
1
0
0
0
1
0
1
1
3
1
0
0
2
1
0
0
1
0
1
0
1
1
1
3
1
2
2
2
2
1
0
1
1
1
0
2
2
1
1
0
1
0
0
0
0
2
1
1
0
0
2
1
0
0
2
1
2
1
0
0
0
2
3
2
1
1
1
0
2
0
0
1
0
1
0
0
0
0
2
0
1
2
0
0
0
0
2
1
1
1
0
0
0
1
2
0
2
1
0
2
0
0
1
0
1
0
0
1
1
2
1
2
1
0
1
0
1
1
0
0
0
1
2
0
0
0
2
2
0
0
1
0
1
0
1
2
0
2
2
2
2
1
0
0
2
0
0
1
0
0
1
1
0
0
1
0
2
2
1
1
1
1
0
2
1
0
2
0
1
0
0
1
1
1
0
2
1
0
1
2
2
1
1
1
1
0
2
0
0
2
1
3
0
0
2
1
1
0
1
1
2
0
0
3
0
2
1
1
1
1
2
1
0
1
0
0
2
1
0
1
0
1
0
2
2
0
2
1
0
0
0
2
1
2
1
2
0
0
0
2
1
0
1
1
1
1
2
1
1
0
1
2
1
2
0
0
1
1
1
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
2
1
1
1
1
0
1
2
0
1
2
1
1
0
1
0
1
2
0
1
1
2
0
0
0
1
2
1
0
2
2
1
1
1
0
2
2
2
0
2
1
0
1
0
0
0
1
0
0
0
0
0
3
2
0
2
2
1
0
2
1
1
0
0
1
0
0
0
1
0
1
0
2
0
0
2
0
0
0
2
0
0
2
2
0
2
1
0
1
0
1
1
0
0
2
5
1
1
0
1
1
2
0
0
0
2
0
0
2
0
2
1
0
1
0
1
1
2
1
0
0
1
0
0
1
2
0
1
1
0
1
1
0
0
2
1
0
1
0
2
1
2
2
0
1
1
2
0
2
1
0
0
2
0
0
1
3
2
2
2
1
0
0
1
2
3
0
1
1
1
1
2
0
1
0
0
0
2
0
2
3
1
1
2
2
1
0
2
0
0
1
2
0
0
1
0
1
1
2
0
2
0
1
0
0
0
2
1
1
2
2
2
0
1
0
2
2
1
0
0
0
0
1
1
3
1
2
2
1
2
0
1
0
1
0
1
1
2
1
2
1
2
1
2
0
1
0
1
2
1
2
0
2
2
3
2
0
1
2
0
2
0
1
1
0
0
0
0
0
2
1
2
0
1
0
1
1
1
1
0
0
1
1
0
1
1
1
0
0
0
2
0
0
1
1
1
1
0
1
0
2
2
0
1
0
2
0
0
1
1
0
2
2
1
1
1
1
1
1
0
1
0
0
1
3
1
2
0
0
0
1
1
0
0
1
2
1
1
0
0
0
2
2
1
1
0
0
0
1
1
0
0
0
0
4
0
1
0
0
1
1
1
0
1
0
1
1
0
0
1
1
0
1
0
0
0
0
0
1
2
1
0
0
0
1
0
0
2
2
0
2
1
2
0
0
2
0
1
2
1
0
0
1
2
1
1
0
0
1
2
0
0
2
1
2
1
1
1
1
1
0
0
0
0
0
1
1
0
2
2
1
0
1
1
0
1
2
0
2
1
0
0
0
1
0
1
1
1
0
0
2
1
2
0
2
2
1
0
1
0
0
2
1
1
1
1
1
2
1
1
2
0
1
0
0
3
0
1
0
2
0
1
2
2
1
1
0
1
1
0
0
2
0
0
1
0
0
0
1
0
0
2
0
1
2
0
0
0
2
1
1
2
0
0
0
0
1
1
0
4
1
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
1
1
2
1
2
1
1
0
0
2
2
2
0
2
0
1
1
0
0
2
2
1
0
1
1
0
1
0
1
1
0
0
1
1
0
1
0
1
1
1
0
0
1
1
1
0
1
1
2
1
1
2
1
1
1
0
1
1
1
2
1
1
0
4
1
2
1
1
0
0
1
2
0
0
1
2
0
2
0
0
0
2
0
0
1
1
2
0
2
1
0
1
2
0
0
1
2
2
0
2
1
1
0
2
1
0
1
1
1
1
1
1
0
1
1
2
1
1
1
6
2
2
1
0
1
0
0
1
1
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
1
1
1
0
2
0
0
1
1
2
0
0
0
2
0
1
1
2
1
0
0
0
0
1
0
1
0
1
0
0
1
1
0
1
1
0
1
1
3
2
0
1
0
2
2
0
2
1
1
0
0
2
0
2
1
1
1
1
2
1
0
0
1
1
2
0
0
0
0
2
0
0
1
0
1
2
0
0
0
2
0
2
0
0
0
0
0
3
1
1
2
0
2
0
0
1
2
2
1
0
1
2
0
0
2
2
1
0
0
1
2
0
2
2
1
0
0
0
2
1
2
0
1
0
0
2
2
0
0
0
14
2
0
1
0
0
0
0
2
0
1
2
0
1
2
1
1
2
1
1
1
0
2
3
0
2
0
2
0
0
0
1
1
2
0
1
0
0
1
2
1
1
1
1
0
2
2
0
0
2
2
2
1
1
1
0
1
2
1
1
0
0
2
0
1
2
1
2
2
2
0
1
0
1
0
1
1
1
1
0
0
1
0
0
1
0
1
1
1
2
0
1
1
0
1
0
1
0
1
0
0
0
1
2
0
2
0
0
1
0
1
0
2
0
2
1
1
1
2
1
2
1
0
2
0
2
0
1
1
1
1
0
1
0
1
1
2
0
0
2
1
3
1
1
1
1
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
2
2
0
2
1
0
0
0
1
1
2
2
1
1
0
0
1
0
0
2
0
0
1
2
2
0
2
0
0
1
0
0
2
1
0
0
0
0
1
2
0
2
2
1
0
0
0
2
1
2
1
0
1
0
1
0
0
0
0
0
0
1
1
0
2
2
1
0
0
0
0
2
0
0
2
0
1
0
1
0
1
1
0
0
0
1
0
2
0
1
2
1
1
1
0
0
1
2
0
1
0
2
1
0
2
1
0
2
0
2
1
1
0
2
1
1
0
2
1
1
1
1
1
0
0
1
2
2
0
2
1
2
1
1
0
0
0
0
1
1
0
0
2
1
0
1
1
1
0
1
1
1
0
1
2
0
2
0
0
1
1
0
2
0
2
1
1
2
0
1
2
1
1
1
0
2
2
1
0
1
0
0
0
0
0
1
0
1
1
0
1
1
0
0
2
0
0
0
0
1
1
0
2
1
1
1
2
0
0
1
0
1
1
1
1
2
1
0
1
0
0
2
1
0
0
0
1
2
1
0
1
0
1
0
1
1
2
1
0
1
0
2
0
1
1
1
1
2
1
1
1
1
1
1
0
1
0
1
0
0
3
2
1
2
2
0
2
0
0
1
2
0
0
1
1
1
0
2
1
0
0
2
1
1
2
0
2
1
0
1
1
1
1
0
0
0
0
1
1
1
0
0
2
1
0
0
1
2
1
2
2
2
1
1
1
0
1
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
1
1
1
1
0
1
0
1
2
1
1
0
1
1
1
2
2
0
0
0
1
2
0
4
1
1
1
1
1
0
1
1
1
0
1
0
2
0
1
2
2
1
0
0
1
1
2
1
2
1
0
1
1
0
0
1
2
1
1
1
1
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
1
1
1
3
1
1
0
3
1
0
1
2
1
0
0
1
4
0
0
1
1
1
0
0
2
1
0
2
1
2
2
1
1
1
1
0
2
1
2
0
1
1
2
1
1
1
1
0
2
1
1
0
3
1
0
0
0
1
0
2
0
2
1
1
0
0
0
0
2
0
1
0
1
1
1
1
2
0
1
0
1
1
2
1
1
2
1
1
0
1
0
0
0
0
0
0
0
0
1
2
1
1
2
0
2
0
0
0
1
0
1
1
0
1
2
0
2
1
0
2
1
1
1
1
1
1
0
0
1
1
1
1
1
0
0
2
0
0
2
0
0
1
3
0
1
2
1
0
2
1
0
1
0
2
2
0
1
0
2
0
0
2
1
0
0
2
1
2
0
1
1
1
0
0
1
1
1
1
0
3
1
2
2
0
0
1
1
1
0
2
1
0
0
1
1
2
2
0
2
0
0
2
1
0
0
0
1
1
0
1
0
0
0
2
2
0
1
3
2
1
1
2
0
0
2
1
1
2
1
0
0
2
1
0
1
0
1
1
1
0
1
0
2
1
1
1
2
1
0
3
0
2
1
0
1
1
0
1
0
0
3
1
0
0
1
2
1
0
1
1
2
1
1
0
2
0
1
1
1
1
0
1
2
2
0
0
1
1
0
0
1
1
2
0
0
1
0
1
1
1
2
2
0
0
2
2
1
0
2
1
1
2
1
1
1
1
0
1
2
2
0
0
0
2
0
0
1
2
0
0
1
2
0
0
0
0
2
0
0
1
0
1
1
2
3
6
1
1
0
1
1
1
1
2
3
1
1
0
0
2
1
1
0
0
2
2
0
1
1
0
0
0
1
0
2
1
1
0
0
0
0
1
0
1
2
1
0
0
1
2
1
0
1
1
2
0
2
0
0
1
2
0
1
1
0
0
1
0
0
0
0
0
0
0
1
1
2
1
0
2
1
2
1
2
0
2
2
1
0
1
1
0
0
1
0
0
1
0
2
2
2
0
1
0
1
1
1
1
0
1
2
1
0
0
1
0
2
1
0
0
0
1
1
0
3
1
1
1
2
0
0
1
0
0
0
0
2
1
1
2
0
0
2
0
2
2
2
2
0
0
1
1
1
0
0
1
0
0
0
0
0
0
1
1
1
0
0
2
1
1
2
0
0
1
2
1
0
1
0
1
1
0
1
2
2
2
1
0
1
1
1
0
1
0
1
0
2
2
1
0
0
0
1
2
1
1
1
0
1
2
0
1
1
1
1
1
0
2
2
2
1
2
1
1
2
1
0
2
0
0
0
0
0
0
2
1
2
2
0
0
1
1
2
1
2
0
2
2
0
2
0
2
1
0
2
1
0
1
3
1
0
2
0
0
1
0
2
0
1
0
0
0
0
0
0
0
1
1
1
0
1
1
1
0
1
0
2
1
1
1
2
3
2
0
2
1
1
0
1
0
1
1
2
1
2
2
1
0
1
2
0
1
1
0
1
1
0
1
0
1
1
0
2
0
0
0
1
0
1
2
0
2
0
1
1
0
0
0
2
1
2
0
2
1
0
2
0
0
2
1
0
1
2
1
1
1
1
1
0
0
2
0
0
0
1
0
0
2
1
1
0
1
1
0
1
0
1
1
0
2
2
0
2
1
1
2
0
2
1
0
0
1
2
1
0
0
0
0
1
2
0
3
2
1
1
0
0
0
0
1
2
0
2
0
1
1
1
2
2
1
1
2
0
0
2
2
0
1
1
2
1
2
0
1
0
2
1
0
0
2
1
0
1
0
0
3
1
0
0
1
0
1
2
1
0
1
2
2
0
2
1
1
0
1
0
1
2
1
0
0
3
0
1
2
1
2
3
1
0
0
1
1
0
0
0
1
2
1
0
1
0
0
1
1
1
0
1
1
2
0
1
1
0
1
3
0
1
2
0
0
1
0
1
0
0
2
1
0
1
1
2
2
1
2
0
0
0
1
0
2
1
0
2
1
1
0
1
1
1
0
1
0
1
1
0
1
0
1
1
0
1
2
1
2
1
1
0
0
1
2
0
1
2
2
0
0
1
0
1
1
0
1
0
1
0
1
2
2
1
2
0
0
1
2
0
0
0
0
0
2
1
1
1
4
2
2
1
0
0
1
2
1
0
2
0
4
1
0
2
2
0
0
0
1
2
2
1
2
0
1
2
1
1
0
0
1
1
1
2
2
1
1
1
1
1
2
0
1
1
2
0
1
2
1
1
1
1
0
1
2
2
1
2
0
1
2
1
0
1
1
1
1
0
0
0
2
2
2
2
1
0
1
0
0
0
0
0
1
0
0
2
1
0
0
0
2
3
2
0
0
1
0
1
0
2
1
2
1
1
0
0
1
0
1
2
0
1
0
0
0
0
0
1
0
2
1
0
0
0
2
1
0
1
0
1
1
0
2
2
1
0
0
2
2
0
0
1
0
1
2
0
0
1
0
1
1
0
1
1
0
0
0
0
2
2
1
1
0
0
1
0
0
0
0
0
1
0
1
0
0
2
2
1
1
1
1
0
1
1
1
0
0
0
1
0
1
0
0
0
0
0
1
2
0
1
0
1
1
0
0
0
0
1
0
1
2
1
0
1
0
1
1
1
1
1
1
9
2
0
1
0
0
1
1
1
1
0
1
0
2
1
1
2
2
1
2
2
1
1
2
0
1
1
2
2
1
2
1
1
1
0
2
2
0
2
2
2
0
0
2
1
1
2
0
2
1
0
1
1
1
1
2
0
0
1
1
2
1
0
1
0
0
1
1
2
2
0
2
0
1
1
1
0
0
0
0
1
0
1
1
1
2
0
0
1
0
1
0
2
2
0
1
1
0
0
1
0
0
1
0
0
0
1
2
1
2
0
0
0
0
2
2
0
1
0
1
2
1
1
1
0
2
0
1
1
0
0
1
0
0
2
1
0
0
0
0
1
1
1
0
0
1
0
1
0
0
0
2
1
0
1
1
0
1
2
3
2
1
0
0
1
0
0
2
1
1
0
0
0
1
2
0
2
1
1
2
0
0
1
1
0
2
2
2
3
0
0
1
0
2
0
1
1
1
2
0
0
1
2
0
1
0
0
0
0
1
0
0
0
0
0
3
1
0
0
2
2
1
2
1
0
1
1
1
1
2
0
3
0
2
2
1
1
1
1
1
0
1
0
0
0
0
1
0
1
2
1
0
2
3
0
0
1
0
1
0
1
4
0
2
0
4
1
2
1
0
0
0
2
0
1
1
1
0
0
0
0
1
1
1
0
1
1
2
2
1
1
0
0
1
1
0
1
1
1
0
1
0
0
1
1
1
0
1
2
0
1
1
1
0
1
3
1
1
0
0
1
1
1
0
2
1
1
0
2
1
1
1
1
0
2
1
0
1
1
2
1
1
2
0
0
1
0
0
0
1
2
2
0
0
0
1
0
1
0
0
1
1
1
1
0
2
1
1
1
1
2
0
1
0
1
0
0
2
1
0
1
1
0
1
0
2
1
0
0
0
0
1
0
1
1
0
0
1
2
6
2
0
1
1
2
2
1
1
1
1
2
1
0
1
2
1
1
0
1
2
0
0
1
2
1
1
1
2
1
2
2
0
0
0
1
2
0
4
2
2
1
2
1
1
0
0
0
0
1
1
0
0
0
0
0
1
3
0
1
1
1
2
1
2
1
0
0
0
2
0
0
0
1
2
0
1
0
0
0
1
1
1
2
2
0
0
0
1
2
1
1
2
1
1
2
1
1
0
2
1
1
1
0
0
3
1
0
2
0
0
0
2
0
0
1
1
1
1
0
2
2
0
2
1
1
0
2
0
1
0
0
1
4
1
0
0
0
1
1
3
1
0
1
1
0
0
1
1
1
1
1
1
1
1
1
1
0
2
1
0
0
1
0
0
1
2
1
2
2
0
1
1
1
2
2
1
0
1
1
2
2
1
1
0
0
2
1
2
0
0
2
1
0
0
2
1
0
0
2
2
0
1
0
0
0
0
2
0
1
3
0
1
2
0
1
0
0
1
0
0
0
1
2
1
0
2
0
1
1
2
0
0
0
1
0
1
1
0
1
0
0
1
5
1
2
1
0
2
1
1
0
1
2
1
0
1
2
0
0
2
1
0
0
0
1
1
2
1
0
1
1
1
5
0
0
0
1
0
1
0
1
1
2
0
0
0
2
1
2
0
1
0
1
0
0
1
2
1
1
5
1
1
0
0
0
0
1
0
1
0
1
0
0
0
0
1
2
2
2
1
2
2
0
1
1
1
2
1
2
2
0
1
0
2
1
1
1
3
0
1
2
1
1
1
1
1
1
1
2
1
2
1
1
1
2
0
0
0
1
1
2
1
1
1
2
1
0
0
1
2
0
0
1
1
0
1
0
1
0
2
2
1
0
1
1
2
2
1
1
0
1
2
0
1
0
1
0
0
1
2
1
2
0
1
0
0
1
1
0
0
0
0
0
1
0
2
0
1
0
0
0
0
2
0
2
2
0
1
2
1
0
0
1
1
0
2
0
0
2
0
0
1
0
1
0
0
1
1
1
1
1
0
1
2
2
3
1
0
1
2
1
0
1
1
0
0
2
1
0
0
0
1
0
1
2
2
1
1
2
1
1
0
1
0
0
0
1
1
0
1
2
2
0
0
1
1
1
2
1
1
1
1
1
1
1
1
2
1
1
0
2
2
0
1
1
0
1
0
2
1
1
1
0
1
1
0
2
0
2
1
0
0
2
1
2
1
0
1
1
2
0
0
0
2
0
0
2
0
0
0
1
0
2
1
0
1
0
0
0
3
1
0
2
1
0
1
0
1
1
0
0
0
1
1
1
0
2
0
0
1
1
1
1
0
1
0
0
0
0
2
1
1
0
2
0
0
0
2
0
0
0
1
0
5
1
2
1
2
2
2
0
0
1
0
1
0
1
1
1
1
1
0
1
2
2
1
0
0
0
2
1
2
2
0
0
0
2
0
2
0
0
1
0
0
1
1
0
0
0
2
1
0
1
1
1
1
0
1
1
1
1
1
1
2
1
1
0
0
1
2
1
1
0
1
0
1
2
0
0
3
1
2
2
1
0
2
1
1
1
0
2
0
1
1
0
2
1
0
1
1
0
1
1
1
1
2
1
1
1
0
0
1
0
1
1
3
1
0
0
0
0
0
0
0
0
2
0
0
1
0
2
1
1
1
0
0
0
0
1
1
0
1
0
1
1
1
1
2
0
0
0
1
1
0
1
1
1
1
1
1
1
1
1
2
0
0
2
0
1
0
1
0
2
1
0
1
1
0
0
1
2
2
1
0
1
1
0
0
0
0
0
2
1
2
2
0
0
3
2
2
1
1
0
1
0
2
1
0
0
2
0
1
1
2
0
2
1
0
1
0
1
1
1
0
0
2
0
0
0
1
0
0
1
2
0
0
1
0
0
1
0
1
1
0
0
0
0
1
3
0
1
0
1
2
1
0
0
1
0
1
0
1
0
1
0
1
0
0
0
1
0
1
1
1
0
2
0
0
1
1
0
1
1
0
2
0
2
1
0
1
1
1
0
1
0
0
1
0
1
1
1
1
1
2
2
0
4
0
2
0
1
2
0
1
2
1
2
0
1
0
1
0
0
1
1
1
2
0
0
1
2
1
0
1
0
2
1
2
0
0
2
1
0
0
1
1
0
0
1
0
2
0
0
0
1
1
0
1
1
1
1
0
1
1
0
1
1
1
0
0
1
0
0
0
0
1
2
2
2
2
1
2
0
0
1
2
0
0
1
1
0
0
0
1
1
2
2
0
1
0
0
1
0
1
1
0
1
0
0
2
1
0
2
1
1
1
0
0
2
1
1
0
2
2
1
0
1
0
0
2
0
0
1
1
0
0
0
1
1
2
1
3
0
1
1
1
0
1
0
2
0
2
1
3
0
0
1
0
1
2
2
0
0
1
1
0
1
0
2
0
2
1
1
0
2
2
1
1
1
1
1
0
1
0
1
1
0
2
2
0
0
0
0
2
1
1
2
1
0
1
2
0
1
0
1
0
1
0
0
0
1
1
0
1
1
1
1
0
2
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
2
2
1
0
0
0
0
0
2
1
0
2
2
1
1
1
1
1
0
1
1
1
1
1
0
0
1
0
0
3
1
0
1
1
0
0
0
2
0
0
0
1
0
1
3
0
0
2
1
0
0
1
0
0
1
0
2
2
0
1
1
2
2
2
0
1
1
0
1
1
0
0
2
0
0
0
1
2
2
0
4
1
0
1
2
1
2
0
0
0
0
2
0
2
0
1
1
1
0
1
1
0
0
2
1
1
2
0
2
0
1
1
1
1
1
1
3
1
0
1
0
0
1
1
1
0
1
1
2
0
2
0
0
1
1
1
0
0
1
1
1
0
2
1
0
2
0
2
2
0
0
0
0
2
0
1
0
1
3
0
0
0
0
2
1
1
0
2
1
0
1
0
1
1
1
0
2
3
1
1
2
1
1
2
0
1
1
2
0
1
1
1
0
0
0
1
1
0
2
1
1
0
1
0
0
4
3
1
0
1
0
0
0
1
1
2
2
0
0
1
0
2
2
2
0
0
0
1
0
0
2
1
0
0
1
1
0
0
0
1
1
1
0
0
2
0
1
2
3
1
1
2
2
2
3
0
1
2
0
2
1
1
2
0
2
2
0
1
0
1
1
2
0
2
2
2
1
0
1
2
2
1
1
1
1
0
2
0
1
2
2
1
1
0
3
0
0
2
2
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
1
1
1
0
0
1
0
0
0
2
1
1
0
2
0
1
1
1
0
1
1
2
2
0
0
2
0
0
1
0
0
1
1
1
1
0
1
0
0
0
1
1
0
0
0
0
0
2
1
1
2
1
0
2
1
0
0
1
0
3
1
0
0
0
2
1
1
1
1
0
0
0
1
2
0
2
0
2
0
0
0
0
0
1
1
1
0
2
1
1
2
0
3
0
1
1
2
1
1
0
1
0
0
1
1
1
2
1
1
0
1
0
1
0
0
0
0
0
2
0
0
2
2
1
0
1
0
1
1
0
1
1
0
0
0
1
0
0
1
1
2
0
1
0
1
0
2
2
0
5
2
1
0
1
3
1
0
2
0
0
1
0
0
0
0
2
1
0
0
0
0
0
1
0
2
1
0
0
2
0
2
1
0
2
2
0
0
0
0
0
1
1
2
1
1
0
0
0
0
1
1
0
0
1
1
0
2
0
2
2
2
1
2
0
1
0
0
0
0
1
0
1
0
2
1
0
2
0
0
1
0
1
0
0
0
0
0
1
0
2
0
1
1
1
1
2
1
0
1
0
0
1
0
2
1
0
0
1
1
1
1
0
0
0
0
0
1
0
0
1
1
1
1
2
1
0
0
2
0
1
0
1
0
0
3
1
0
0
0
1
2
0
2
2
0
2
0
0
1
2
1
1
0
1
1
2
2
1
1
2
2
1
2
0
1
0
0
1
0
2
1
1
1
0
0
0
1
0
1
0
2
0
0
0
0
2
1
2
2
3
0
0
1
0
0
1
2
1
2
1
2
2
0
1
2
0
1
2
0
2
1
2
0
0
2
0
1
2
1
1
2
0
1
0
0
0
1
2
0
0
1
0
0
0
0
3
1
2
2
1
0
1
0
1
2
1
1
0
0
0
2
0
1
1
2
1
0
0
1
2
2
0
1
1
1
0
0
2
1
1
1
0
0
2
0
0
0
1
2
1
2
1
0
0
0
2
0
2
0
1
0
2
0
0
1
0
1
2
0
0
1
0
1
0
0
1
1
1
1
0
1
0
0
2
0
1
1
3
0
1
1
2
1
2
0
1
1
1
0
0
2
1
0
1
1
2
0
2
1
0
0
0
1
1
0
0
1
1
1
1
2
0
0
0
0
0
2
0
0
1
2
0
2
0
0
0
0
1
1
1
0
0
0
1
1
2
2
2
2
2
0
2
0
1
0
1
0
2
0
1
0
2
0
0
1
0
0
1
0
0
2
1
0
2
0
0
1
1
0
1
0
1
1
0
0
1
1
1
0
1
2
0
0
0
1
1
0
1
0
1
2
2
1
1
0
1
1
0
0
2
1
1
0
1
0
1
2
1
1
1
0
0
0
1
1
1
0
1
1
0
2
1
1
1
1
2
0
1
1
1
1
0
1
0
0
0
1
1
1
4
2
1
1
0
0
1
0
3
0
0
1
0
3
1
1
2
1
1
1
1
0
0
0
0
1
0
1
0
0
0
3
1
0
1
2
0
2
1
1
0
1
1
1
0
0
1
1
1
1
1
0
2
2
0
0
1
0
0
1
1
1
0
0
0
1
0
1
0
1
1
1
1
1
0
1
0
0
2
0
1
0
0
2
1
1
0
0
2
0
0
0
1
0
0
0
2
2
1
1
0
0
2
1
1
0
1
0
0
1
0
0
0
2
1
1
1
1
2
0
0
1
0
0
2
0
0
2
0
0
1
1
2
0
0
2
0
1
0
0
1
0
0
2
2
1
0
0
0
0
1
1
2
2
0
0
3
0
2
2
1
2
1
0
1
2
1
1
1
0
1
0
1
0
1
2
2
0
0
0
2
2
1
0
1
0
1
2
2
1
0
0
0
2
0
1
1
1
0
1
0
2
2
1
0
3
1
0
1
1
1
0
0
0
0
1
1
1
2
2
2
0
0
1
1
1
2
0
1
0
1
2
3
1
1
0
1
1
1
1
1
1
1
3
1
0
0
0
0
2
1
1
4
0
2
2
1
1
0
1
1
2
1
0
2
1
0
1
1
0
2
4
0
1
0
1
1
1
0
0
0
1
1
0
2
0
1
1
1
1
0
0
0
0
1
0
0
0
1
1
1
2
1
0
0
0
0
1
1
1
2
1
2
1
1
0
0
2
0
1
2
1
1
0
2
1
2
1
3
0
1
0
2
1
0
0
1
1
1
1
0
0
3
1
0
0
0
0
1
0
1
0
2
0
1
2
2
0
0
0
0
0
0
0
2
1
1
0
1
0
2
0
0
2
0
0
1
2
2
0
0
2
1
0
1
1
1
0
1
1
1
1
1
0
1
0
0
1
0
2
1
3
0
3
1
1
2
1
0
1
2
2
2
0
1
0
0
0
1
2
0
1
1
0
1
1
1
2
0
1
1
1
0
0
2
0
1
1
0
0
0
1
1
4
3
1
0
0
1
2
3
1
1
2
0
1
1
2
1
2
2
0
1
0
1
2
0
1
1
0
1
0
2
1
1
0
0
0
1
2
3
0
0
0
1
0
0
0
1
1
2
0
0
2
2
0
2
0
1
1
1
1
0
1
2
1
0
0
0
2
1
2
1
2
1
0
0
0
0
1
2
1
1
2
1
1
0
0
0
1
1
0
1
1
1
1
1
1
1
1
1
0
0
2
0
2
2
1
2
0
2
1
1
0
1
1
1
0
1
0
1
1
2
1
1
1
1
0
1
3
0
1
1
2
0
0
0
1
1
1
1
1
2
0
0
0
0
0
0
1
3
0
1
1
0
0
3
1
1
1
1
2
1
1
2
0
1
1
0
0
2
0
0
1
0
1
1
1
2
1
2
0
1
2
0
1
1
1
2
0
1
0
1
2
1
1
1
1
0
0
0
1
0
0
0
0
1
2
1
0
0
2
3
1
1
0
2
1
0
0
1
2
1
1
0
0
0
1
4
0
2
0
0
1
1
0
0
2
1
0
0
0
1
2
2
1
0
1
2
1
0
0
1
1
1
0
2
3
0
0
1
0
0
1
0
1
1
2
0
2
0
0
1
2
2
2
1
0
0
1
0
0
2
0
0
2
1
0
1
3
1
1
1
0
0
2
1
0
0
1
1
2
1
0
0
0
0
1
2
1
1
1
0
0
2
2
0
1
1
2
1
0
0
1
0
0
0
2
1
0
1
2
0
1
0
2
1
0
2
2
1
1
0
0
0
1
1
1
1
1
1
1
0
0
1
2
0
0
1
1
0
1
0
1
1
2
0
1
1
1
1
1
1
1
1
0
2
0
1
1
2
1
2
0
0
1
2
0
0
0
0
1
1
1
0
2
0
0
1
0
1
2
1
0
0
0
0
1
2
0
1
1
0
1
1
0
0
2
1
0
1
2
2
1
1
1
1
2
1
1
1
1
1
0
1
1
0
0
0
1
0
1
2
0
2
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
2
1
1
1
1
1
0
3
1
1
0
1
1
0
0
2
0
1
2
2
0
0
2
0
2
2
1
1
1
1
0
2
0
1
1
0
2
2
2
2
0
2
1
0
1
1
1
0
1
1
2
0
1
1
2
1
1
0
2
2
0
1
1
2
0
2
1
1
0
2
3
1
0
2
1
0
0
1
1
1
1
2
2
1
1
1
1
1
1
0
0
1
1
1
0
2
1
0
0
2
6
1
0
1
1
2
1
1
2
2
1
0
0
0
0
1
0
2
0
1
1
0
1
1
2
0
1
0
1
1
0
1
0
1
1
0
2
2
2
1
0
1
0
1
1
0
2
1
1
2
1
2
0
1
0
1
1
0
1
1
1
1
1
1
2
1
0
3
0
2
2
0
1
2
0
0
1
0
1
2
1
1
1
0
1
0
0
0
0
2
0
1
1
2
1
1
2
0
1
2
2
0
2
2
1
1
0
1
1
1
1
2
1
2
0
0
0
2
0
2
1
1
2
0
2
1
0
2
0
1
2
0
1
0
2
2
1
1
1
1
1
1
0
1
1
1
0
0
1
1
1
1
2
1
2
2
1
1
1
2
2
0
2
0
0
1
2
0
2
2
0
2
2
0
2
1
0
0
1
1
0
0
1
0
1
0
1
2
0
0
0
1
1
1
1
2
2
1
2
0
0
1
0
0
1
0
1
2
2
2
1
2
2
1
2
2
1
2
2
1
1
0
0
1
1
0
2
1
1
0
0
0
1
0
2
2
1
1
1
0
1
2
1
0
1
0
0
1
0
0
1
1
0
0
2
1
0
0
1
2
0
1
1
1
2
1
1
1
1
1
2
2
2
1
0
1
1
2
0
0
1
0
2
0
0
0
2
0
1
0
1
1
2
0
0
2
1
1
2
2
1
1
0
2
1
1
2
1
4
2
2
0
0
0
1
2
0
0
1
0
3
0
0
1
1
1
2
0
1
1
0
0
1
2
2
1
2
0
1
1
2
0
1
0
0
5
1
2
1
0
1
0
1
0
0
2
0
0
1
1
2
0
2
0
1
0
0
1
0
0
1
1
2
0
2
1
1
1
0
1
2
0
1
0
2
1
0
2
2
0
2
1
0
2
2
2
1
2
1
1
0
0
1
1
0
1
1
1
1
1
1
1
1
0
4
1
1
1
1
2
1
0
1
2
2
1
0
0
0
0
1
0
2
1
1
1
1
1
0
0
2
0
1
1
1
0
2
1
1
1
1
0
1
0
1
1
1
1
1
0
0
0
0
3
0
0
1
2
0
1
2
1
2
2
0
3
1
1
0
1
2
0
2
2
1
0
0
2
1
1
2
1
1
1
2
0
0
0
0
0
1
1
1
2
0
1
2
0
2
0
1
2
1
0
1
1
1
0
0
1
1
1
2
2
0
0
1
1
2
1
1
1
2
0
0
0
1
0
1
1
2
1
1
1
2
1
0
2
1
3
1
0
1
0
0
1
1
3
1
1
2
1
0
1
0
0
2
1
2
1
1
0
0
1
2
1
0
1
1
1
1
1
1
0
1
0
2
0
1
1
2
3
1
1
1
2
1
0
2
0
0
3
1
0
1
1
2
3
0
1
1
0
0
0
1
0
0
0
1
1
1
2
0
2
0
0
1
0
1
2
0
2
0
0
0
1
0
0
0
2
1
0
2
2
0
0
1
2
2
0
1
0
0
1
0
2
0
2
2
0
1
1
0
0
2
1
0
1
0
1
1
2
1
1
1
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
3
2
1
0
0
0
2
0
1
2
2
2
2
0
0
0
0
1
0
2
2
1
3
0
0
1
1
1
0
0
0
0
0
1
1
0
0
1
0
2
0
0
1
2
0
1
2
1
2
0
2
2
1
1
0
0
2
0
2
1
0
1
2
0
0
2
0
0
1
0
0
0
1
2
1
0
0
0
1
1
0
0
1
2
0
1
0
0
1
1
1
2
0
0
0
0
2
1
2
0
0
1
0
1
0
2
1
0
1
0
1
1
0
1
0
0
0
2
0
1
1
0
1
0
2
0
1
2
2
1
0
0
1
0
1
3
1
0
0
3
0
0
2
0
0
0
1
1
0
1
0
1
0
2
1
2
0
0
2
1
0
0
2
1
0
2
0
1
0
1
1
1
2
2
0
0
1
1
2
1
1
0
1
0
0
1
1
1
0
0
2
0
0
1
0
1
0
1
1
0
2
1
0
2
1
0
1
2
1
2
1
0
1
0
0
0
1
2
1
1
1
2
0
2
0
0
0
1
2
2
1
1
0
1
1
2
0
2
2
1
1
0
1
0
2
0
1
0
0
0
1
0
0
1
0
2
0
0
0
0
2
1
1
1
1
1
0
1
2
0
0
1
0
0
1
0
1
2
2
2
1
0
2
2
2
0
1
1
1
2
1
1
0
0
1
1
0
0
1
1
1
1
1
1
2
0
0
0
2
1
0
1
0
0
2
1
3
1
2
0
0
1
0
1
3
2
2
1
0
0
2
3
1
1
0
2
1
0
1
1
2
1
2
0
0
2
2
0
1
2
2
2
0
0
0
1
0
0
1
0
0
0
0
1
1
2
0
1
0
0
0
0
1
1
1
0
0
1
2
0
0
3
0
1
0
2
0
0
2
0
2
0
0
1
2
0
3
1
1
1
0
0
0
1
0
0
0
0
1
2
1
1
0
0
0
1
1
2
2
0
0
2
0
0
1
2
1
1
3
1
1
0
0
1
0
0
1
0
1
0
1
2
2
2
0
1
2
2
1
1
2
2
0
0
1
0
0
1
1
1
0
2
0
0
1
1
0
2
0
1
2
0
2
0
0
1
1
1
2
0
1
1
2
1
0
0
0
0
0
2
2
3
2
0
0
0
7
1
1
1
1
1
2
1
0
0
1
2
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
1
1
2
1
0
0
0
1
0
0
1
2
1
1
0
1
0
1
1
2
1
0
0
1
1
0
1
1
2
1
2
3
0
2
0
3
2
2
0
0
2
0
1
2
0
0
0
0
1
2
1
1
0
5
1
0
1
2
0
1
1
1
1
0
0
0
1
1
0
0
1
0
2
0
1
0
0
1
1
0
1
2
1
0
0
0
0
1
2
0
1
1
2
0
1
0
0
2
0
1
1
1
0
0
1
0
1
1
0
1
1
0
1
1
0
0
1
1
2
1
1
0
2
1
1
0
2
0
1
2
1
3
2
1
1
0
1
2
0
2
0
0
1
3
1
1
2
2
1
0
0
1
0
1
1
1
1
1
2
2
0
0
1
2
1
1
1
1
1
0
1
1
0
1
1
0
1
1
2
2
2
0
0
1
0
0
1
3
0
1
1
1
1
2
1
1
2
1
2
1
1
2
1
0
0
1
2
0
0
0
1
1
1
2
2
0
2
2
0
1
1
0
2
1
1
1
2
2
2
1
0
0
1
1
0
0
2
1
2
0
0
1
2
2
1
0
1
0
1
0
1
2
1
1
0
0
2
0
0
0
1
0
0
2
1
1
0
2
0
1
2
0
1
1
0
2
1
0
2
1
1
0
1
2
0
2
0
2
0
1
0
0
1
0
0
1
0
0
0
1
2
1
0
1
1
0
0
1
0
0
1
0
0
1
2
0
0
2
0
1
1
0
1
1
0
0
1
1
0
1
2
2
0
1
2
2
1
0
1
2
3
1
1
2
1
0
0
1
1
1
1
1
0
0
1
0
0
0
1
0
0
0
2
2
1
1
1
1
2
2
2
1
1
0
0
2
1
3
0
0
0
1
0
3
0
0
0
2
1
0
1
0
1
1
2
2
1
0
2
0
3
1
0
1
1
1
0
1
0
0
1
2
0
2
0
0
2
0
1
1
1
1
1
1
1
1
1
1
0
1
2
2
0
0
1
0
2
1
1
1
0
0
0
1
2
2
1
0
2
2
0
1
1
1
0
1
2
2
1
0
0
1
1
1
2
3
0
1
2
1
0
2
3
0
1
0
2
1
0
1
2
0
1
1
1
2
0
0
1
3
1
0
1
1
0
2
2
2
1
0
1
1
2
0
0
0
0
3
0
1
1
2
2
1
1
2
1
2
0
2
3
1
1
2
0
2
0
0
1
2
2
2
1
1
0
2
0
1
1
2
1
0
0
0
1
1
2
2
0
2
0
2
2
1
0
1
0
1
0
1
3
0
0
1
1
0
0
1
1
1
0
1
1
2
1
1
1
1
2
2
1
1
1
1
1
1
0
2
0
0
1
0
1
1
1
1
0
0
1
2
1
0
1
0
2
0
2
3
1
1
2
1
2
1
1
0
0
0
1
1
1
0
1
0
1
2
3
0
1
2
1
1
0
0
0
1
1
0
0
0
1
1
3
0
2
2
1
0
2
0
1
1
1
2
1
0
2
2
0
1
2
0
0
1
1
2
2
0
0
2
0
1
1
0
1
1
0
0
0
0
0
1
1
0
2
1
1
0
1
2
0
1
1
1
3
0
3
2
0
1
1
2
0
2
2
1
0
2
1
0
2
0
0
1
1
1
0
1
1
1
2
0
1
1
0
0
0
0
2
2
2
2
0
1
1
1
1
1
0
1
1
2
0
0
1
1
0
0
0
1
1
0
0
0
1
0
1
0
0
2
1
1
0
0
1
0
1
1
2
0
1
1
0
0
1
1
1
1
0
0
0
2
0
1
0
1
0
0
1
0
1
0
0
0
0
2
0
1
0
0
1
0
1
2
1
0
1
0
0
1
0
0
0
0
0
0
1
0
1
1
2
1
2
1
0
0
1
1
2
0
4
1
2
0
1
2
0
2
1
1
0
2
1
1
1
0
1
2
2
1
1
1
2
1
1
2
0
1
0
0
0
2
0
0
1
0
1
0
0
2
1
2
0
1
2
1
2
0
0
2
1
1
0
0
0
0
2
0
1
1
1
1
1
1
0
1
1
2
0
0
2
3
1
0
1
1
0
1
0
2
0
1
1
0
0
1
0
1
3
2
2
0
1
2
0
2
0
0
0
1
1
1
1
0
0
1
2
0
1
1
2
0
0
0
1
0
0
0
1
0
2
2
1
1
2
1
0
0
2
2
1
1
2
1
0
1
1
1
0
2
1
0
0
1
2
0
0
0
2
1
0
1
1
1
1
0
0
0
1
0
0
1
1
1
0
1
1
1
2
2
0
1
2
0
0
0
1
0
1
1
0
0
1
0
1
0
1
1
0
1
1
1
0
1
0
1
1
1
1
0
1
1
1
1
2
1
2
0
0
1
0
0
0
1
0
2
0
0
0
1
0
0
0
1
1
1
1
1
0
0
0
0
1
0
2
1
0
0
2
0
0
0
1
2
0
1
1
1
0
2
2
0
1
0
2
1
1
2
2
2
0
2
1
2
1
0
0
0
0
0
0
2
1
2
0
1
3
1
0
2
0
1
1
1
1
1
2
1
0
2
1
0
0
1
0
2
0
1
1
0
2
0
0
1
0
1
0
0
3
1
0
0
1
1
0
2
0
1
2
0
2
0
1
0
0
0
0
1
0
2
0
0
1
2
2
1
1
0
0
1
1
0
0
1
1
1
2
0
1
1
1
1
0
0
1
1
2
0
1
1
0
1
0
0
1
0
0
0
3
0
1
0
1
0
0
1
0
1
1
0
2
0
0
2
0
1
2
0
1
2
0
1
0
0
2
2
1
1
0
0
1
0
2
1
0
0
1
1
0
1
0
0
1
0
1
0
2
2
1
0
0
1
0
1
1
1
2
0
1
2
1
2
2
0
1
2
1
1
0
0
0
0
1
0
3
0
1
0
2
2
2
1
1
1
0
0
1
2
1
0
2
0
0
0
0
1
1
0
0
1
1
0
1
1
1
1
2
1
1
0
0
0
0
1
1
0
1
2
2
1
1
2
0
0
1
1
0
0
0
1
1
2
0
1
1
0
2
1
2
1
2
1
0
1
0
1
2
1
2
1
2
2
1
0
0
2
1
0
0
2
1
1
1
1
0
0
1
2
2
2
2
2
1
0
1
0
0
1
1
2
0
0
2
1
2
2
2
0
0
0
1
1
1
3
2
0
1
1
0
1
1
1
0
1
0
0
1
0
0
1
0
0
0
0
0
1
2
0
1
0
1
0
0
2
0
1
0
0
0
0
1
0
0
1
0
1
1
1
1
1
0
0
0
0
0
2
2
1
1
1
0
1
2
1
0
0
0
2
0
1
0
0
2
0
1
1
0
1
4
1
1
1
1
0
0
2
1
0
2
1
1
2
2
0
1
0
1
0
1
1
1
1
1
2
1
1
0
1
2
4
0
0
2
2
1
2
1
0
0
0
1
0
1
2
0
2
2
0
0
0
0
0
2
0
2
0
0
0
0
1
1
1
0
1
1
2
2
0
2
1
1
0
1
1
1
1
1
1
1
0
0
2
1
0
0
1
0
1
0
1
0
0
0
1
0
0
1
2
2
1
2
3
0
0
1
2
0
1
0
1
1
1
1
2
0
0
0
1
0
1
2
2
2
3
0
0
0
0
1
0
2
0
0
1
1
0
2
0
0
2
2
1
1
1
1
2
0
0
0
1
1
0
1
0
2
1
2
0
0
2
0
1
1
0
2
0
1
0
1
1
1
2
1
0
1
2
0
1
1
1
0
0
1
0
0
1
0
0
1
0
1
1
0
1
1
0
0
1
1
1
1
0
2
4
0
0
1
1
1
0
1
1
2
0
2
1
0
1
0
0
1
1
1
3
0
1
1
0
1
2
3
0
0
2
0
2
1
2
1
2
2
0
0
1
0
1
1
2
0
1
0
0
1
1
1
2
0
0
0
2
1
1
2
1
0
2
2
0
1
1
1
0
2
1
1
1
1
0
0
0
1
0
0
0
1
2
0
1
2
0
2
0
0
1
1
0
0
1
1
0
1
0
2
0
1
1
1
3
1
2
1
0
0
1
1
1
0
2
2
2
0
1
2
0
0
0
2
0
0
1
0
1
1
2
1
1
0
0
0
1
2
2
1
0
1
0
1
0
0
2
2
3
1
1
1
1
1
0
0
1
1
1
1
0
3
0
1
2
3
1
0
2
0
0
1
2
1
0
1
1
0
0
0
0
0
1
0
2
1
1
0
1
2
1
2
0
1
0
1
0
0
2
1
0
1
0
2
1
1
0
1
1
0
1
0
1
1
2
3
1
0
1
1
2
0
0
1
0
0
0
2
1
0
1
0
1
2
2
0
0
2
0
0
0
1
2
0
2
1
1
1
0
0
0
0
1
1
2
0
0
2
2
0
0
1
0
1
2
0
0
1
0
1
0
0
0
1
2
0
1
2
0
0
2
1
1
0
0
0
1
1
1
1
1
1
1
1
1
1
0
1
0
2
3
1
1
0
0
1
0
0
2
0
1
1
0
1
1
1
0
1
1
1
2
0
0
2
0
1
0
0
0
0
1
0
0
1
0
0
1
2
1
0
1
2
2
2
0
1
2
0
0
1
1
0
0
1
0
2
1
0
1
2
2
0
2
0
2
2
2
0
0
1
1
0
2
1
1
2
1
0
1
2
0
0
2
1
2
1
0
1
3
1
0
1
1
0
0
1
2
1
1
1
0
2
1
1
2
0
1
2
1
0
1
3
1
1
0
2
2
1
1
1
2
0
0
0
1
0
0
2
0
2
1
0
3
1
1
1
1
2
1
1
1
2
0
0
1
1
0
1
2
0
4
0
1
0
2
0
2
0
1
0
0
0
0
2
0
0
1
2
0
1
1
1
0
1
1
2
0
1
0
2
1
2
1
0
1
1
0
1
0
0
2
2
6
2
9
1
1
0
1
1
0
1
0
1
1
1
0
1
0
0
0
2
0
0
2
1
2
1
2
1
1
2
0
0
0
0
1
0
0
1
2
1
2
2
1
0
0
0
0
1
0
0
1
1
0
1
0
1
0
1
1
1
1
1
1
1
4
2
0
1
0
0
1
0
1
1
3
2
0
1
0
1
1
0
0
2
1
2
0
0
1
1
1
0
0
1
1
2
0
0
2
1
0
2
1
1
2
1
0
0
1
1
1
0
0
0
2
2
1
1
3
2
1
1
0
2
1
2
0
0
0
1
1
2
2
1
2
0
1
2
2
1
1
0
1
0
2
4
2
0
1
0
2
0
1
1
1
0
1
1
1
1
1
2
2
1
0
1
2
1
1
0
1
1
0
1
1
0
1
2
2
2
1
1
1
2
2
0
1
1
1
1
2
0
2
2
1
0
2
0
1
1
2
1
0
0
2
1
0
3
0
0
1
0
0
2
2
1
0
2
1
0
2
0
1
1
0
1
0
0
0
0
1
0
0
2
1
0
2
3
0
1
2
1
1
1
1
3
1
0
1
1
0
0
0
1
0
0
1
0
2
0
0
1
0
1
0
1
0
1
0
1
2
1
1
0
2
1
0
2
1
2
0
2
2
0
0
0
0
0
1
2
0
0
1
2
2
1
1
0
0
0
1
0
0
0
0
0
1
1
0
1
1
0
0
0
1
2
2
1
0
0
0
2
2
1
2
0
1
1
1
1
1
1
0
1
1
1
0
0
2
0
1
1
0
1
1
0
1
3
1
1
0
1
0
1
2
2
1
0
1
2
1
1
0
2
2
0
1
1
2
1
0
0
2
2
2
0
2
2
0
0
0
2
2
1
1
0
0
1
0
1
0
1
1
0
0
0
1
0
2
0
0
0
0
1
2
1
1
1
0
1
0
1
1
1
0
1
0
1
1
0
1
1
0
0
1
1
0
0
1
2
0
1
0
0
1
0
0
0
0
0
0
1
1
1
1
2
0
2
1
2
0
2
0
1
0
2
0
1
1
2
1
3
1
0
2
0
2
0
1
0
1
0
2
0
1
1
0
2
2
1
2
0
1
2
1
0
1
0
0
1
1
1
1
1
2
0
2
2
1
0
0
1
1
1
1
1
2
1
1
1
1
2
0
1
0
2
1
0
2
1
0
0
0
1
1
2
1
1
0
0
0
2
0
0
1
0
0
1
1
2
1
0
1
1
0
2
1
1
0
2
2
1
0
2
0
2
0
0
0
0
1
2
1
1
0
0
0
1
2
2
2
1
2
0
2
0
0
0
0
2
0
1
2
0
0
0
1
2
0
0
0
0
0
0
0
1
1
1
1
1
1
2
0
1
1
1
1
1
0
2
2
2
0
1
2
2
2
1
1
0
0
2
1
0
2
1
0
1
0
1
1
1
3
0
0
2
0
0
0
0
1
1
0
0
1
0
0
0
1
2
1
1
0
0
0
1
1
1
2
1
0
1
1
0
2
1
1
0
2
0
0
1
0
2
2
2
1
0
2
1
0
1
2
1
0
0
0
0
1
0
0
2
0
1
0
1
0
0
0
2
0
1
0
0
1
2
0
1
2
1
1
2
0
0
1
1
0
0
2
1
0
1
0
1
0
2
2
0
1
2
0
0
0
1
1
1
0
0
0
2
0
1
1
2
2
1
0
1
4
1
1
0
1
0
0
1
0
0
2
0
2
2
0
1
0
2
1
1
2
3
1
2
1
0
0
1
1
2
0
1
1
0
0
0
1
1
1
1
3
0
0
0
1
2
1
1
1
2
2
0
0
0
0
0
1
2
0
1
0
1
2
0
1
2
2
0
0
0
0
2
1
2
2
0
1
1
1
0
1
1
0
0
0
0
0
0
2
1
2
0
0
0
0
0
1
1
0
1
0
1
1
0
3
0
1
0
1
1
1
0
0
1
1
2
1
1
1
1
1
1
2
0
1
1
1
0
2
0
1
1
2
0
1
0
0
1
0
0
2
2
2
0
0
0
1
2
1
1
2
1
1
1
1
1
2
0
2
3
0
0
2
0
0
0
2
1
0
1
1
2
1
1
0
2
1
1
0
1
0
1
1
2
0
1
2
2
0
2
0
2
0
1
1
0
0
1
0
2
1
1
0
2
1
3
1
1
0
0
0
0
0
1
1
1
1
0
3
2
0
1
2
1
2
0
0
1
1
0
1
2
1
0
0
2
1
2
2
1
1
4
1
0
2
0
1
1
2
0
0
0
0
0
1
0
0
1
1
0
0
1
2
1
1
0
1
1
1
1
0
1
0
1
0
2
0
2
0
2
3
1
1
0
0
0
0
0
1
1
0
0
1
2
3
2
2
1
2
2
0
0
1
1
2
0
0
1
0
1
0
1
0
2
1
0
0
2
0
1
0
2
3
1
1
1
1
0
1
1
2
2
0
1
0
2
1
2
0
0
0
0
0
1
0
2
1
0
1
0
2
0
0
2
1
0
0
0
0
1
0
0
0
0
1
0
0
2
1
1
2
0
2
2
1
1
1
1
1
0
1
1
1
0
0
2
2
2
0
1
2
2
2
0
2
1
1
0
1
1
2
1
3
0
0
2
0
1
0
2
0
1
2
1
2
1
0
1
0
2
0
0
1
1
1
0
2
0
0
1
1
2
1
1
0
0
0
0
1
0
0
0
1
0
1
1
1
0
0
0
1
1
0
4
0
1
1
0
1
3
2
0
2
0
1
0
0
1
2
1
2
1
0
0
1
1
2
0
2
0
0
2
2
0
0
1
1
2
0
2
0
2
1
1
2
0
0
2
1
0
2
3
1
0
0
1
0
0
0
1
2
0
2
1
0
1
0
0
1
1
2
0
1
2
1
0
0
1
3
1
0
0
1
0
1
0
1
0
1
1
0
0
2
0
2
1
1
0
0
1
0
1
1
1
2
0
1
1
0
0
0
1
2
2
2
1
2
0
1
0
0
2
0
2
1
0
0
2
2
2
2
1
2
0
0
1
1
0
0
0
0
2
1
1
1
1
2
2
2
0
1
2
1
2
2
0
1
0
1
1
1
0
2
0
0
1
2
3
0
0
0
0
0
1
2
1
0
1
1
0
0
1
0
2
0
0
1
1
2
1
1
0
1
1
1
0
0
1
0
1
1
1
0
0
0
0
1
2
1
0
2
1
1
0
0
0
0
3
1
1
1
0
1
2
1
2
0
1
1
0
2
0
0
0
1
0
1
1
1
0
2
1
0
2
0
1
0
1
1
2
1
1
2
1
0
2
0
2
2
2
1
1
1
0
1
1
1
2
1
1
0
1
0
1
0
1
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
1
2
1
0
1
2
2
2
0
0
1
1
1
0
1
2
1
0
2
1
0
1
2
1
1
1
1
1
2
1
2
1
0
0
0
0
0
1
1
2
1
0
0
3
0
0
1
2
2
0
0
1
0
1
1
0
0
0
1
1
1
1
2
0
2
2
0
0
0
1
0
2
0
1
0
0
0
1
1
0
3
0
1
1
1
1
1
2
1
0
0
2
1
1
0
2
0
0
2
3
0
0
0
0
0
1
1
0
0
2
0
1
2
1
0
0
2
2
1
1
2
0
2
0
0
1
0
0
1
1
0
3
1
2
2
1
0
1
1
4
2
2
1
1
0
1
1
0
1
1
2
2
1
0
1
0
5
1
1
1
1
0
0
2
1
2
2
1
2
0
2
0
1
0
0
1
0
1
1
0
0
0
1
0
1
1
0
2
1
0
0
1
0
1
0
0
2
1
2
1
2
1
0
1
2
2
2
2
1
0
1
2
0
1
1
2
0
3
1
0
1
1
0
2
0
1
1
2
2
1
1
0
1
4
1
2
1
2
1
0
1
2
1
1
1
1
2
2
3
2
0
0
1
0
1
0
2
2
1
0
0
0
0
2
0
0
2
1
0
0
0
2
0
1
2
1
1
0
2
1
0
1
0
2
0
0
0
1
1
0
0
0
0
2
0
0
0
1
0
1
0
1
2
1
0
2
1
0
0
1
1
0
0
0
1
2
2
0
1
2
0
2
1
0
0
1
1
1
0
2
2
2
0
1
1
0
0
1
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
3
0
1
1
0
1
1
2
2
2
2
2
0
1
0
0
1
1
2
2
0
0
0
2
0
1
0
0
0
1
0
0
2
0
1
1
2
1
0
1
2
0
0
0
2
1
1
1
1
1
1
1
0
0
2
1
0
1
2
0
1
2
0
3
1
2
0
3
2
0
0
0
2
2
2
2
2
0
1
0
0
1
0
1
1
0
1
1
0
2
2
0
1
1
0
0
1
1
3
0
0
2
1
0
2
2
1
0
2
1
0
2
0
0
1
1
1
2
2
3
0
1
1
2
0
2
0
1
1
1
0
2
1
0
1
0
1
0
2
0
1
1
0
2
0
0
3
1
1
1
0
2
1
1
0
1
1
1
2
2
1
0
2
0
1
0
1
2
0
1
1
1
2
4
1
1
0
0
2
1
1
1
0
1
0
0
1
1
0
2
0
1
2
0
0
0
0
0
1
1
0
0
2
0
1
0
0
2
1
0
0
1
0
0
1
0
1
1
0
1
2
1
9
2
1
2
1
2
0
1
2
0
0
0
6
2
1
2
1
0
0
0
0
2
1
2
1
1
0
0
1
2
1
0
2
0
2
0
1
0
0
0
1
2
1
1
0
0
1
2
1
0
1
1
1
0
1
1
1
1
2
2
0
0
1
0
1
0
0
1
1
1
0
0
1
0
0
0
1
1
1
2
2
0
2
0
1
0
0
1
1
0
3
1
2
2
1
1
2
1
1
2
2
0
0
1
1
2
1
0
2
0
1
0
2
0
0
1
4
0
0
1
2
1
0
0
1
2
0
1
1
1
2
0
1
3
1
1
0
0
1
0
0
0
1
1
1
2
0
3
1
1
0
0
0
1
0
1
2
2
1
1
2
1
0
2
1
0
0
0
2
0
2
1
2
2
2
1
0
1
0
1
0
1
1
0
1
2
1
0
0
1
1
2
1
2
1
0
0
2
1
2
1
0
0
3
0
2
0
1
2
1
1
0
0
1
1
0
2
1
0
1
1
1
1
2
1
0
0
0
1
1
1
0
0
2
1
2
0
1
0
0
1
1
0
1
1
0
2
1
2
2
1
0
0
1
0
1
0
1
0
0
1
1
0
1
1
0
0
0
0
0
1
0
2
0
0
1
1
1
1
1
2
0
0
0
1
1
1
1
0
0
0
0
1
0
1
0
1
1
1
1
2
0
1
0
0
0
0
2
0
0
0
2
2
2
1
1
1
0
2
2
1
1
1
0
0
1
0
1
1
2
1
2
0
1
0
1
2
0
0
0
1
1
0
1
0
1
0
1
2
1
0
0
1
1
1
2
1
3
0
1
0
2
0
1
1
0
2
0
1
1
2
0
1
0
1
0
0
2
1
0
8
1
3
2
5
2
1
0
1
0
2
1
1
0
2
1
0
0
0
2
0
2
1
1
0
2
0
1
1
2
2
1
0
0
0
2
2
2
0
1
0
0
0
0
0
2
2
0
1
1
0
0
1
0
1
1
0
1
0
1
2
0
1
0
2
1
0
0
1
0
1
1
0
1
1
0
1
1
0
2
2
2
0
0
0
1
0
2
2
2
0
1
0
2
0
2
1
0
0
0
0
1
1
1
0
0
0
0
0
0
2
1
2
2
1
0
1
1
2
1
0
0
2
2
1
0
0
1
1
0
0
1
3
0
0
0
1
0
0
0
1
1
0
0
1
1
2
1
1
1
2
2
0
0
1
1
1
1
2
2
0
1
1
0
1
1
2
0
1
0
0
2
2
1
2
1
1
0
0
0
1
1
1
0
1
1
1
1
1
1
0
2
2
0
0
0
1
0
0
0
1
1
0
2
1
1
1
1
0
1
0
2
0
0
1
0
3
2
0
0
1
1
2
1
2
0
1
0
2
1
0
1
2
1
0
0
1
1
0
2
2
3
1
1
1
0
0
0
1
0
1
1
2
1
1
2
0
2
1
0
1
1
1
0
0
0
0
0
0
2
0
2
0
0
1
0
2
2
0
2
0
2
2
1
0
2
2
1
1
1
1
0
0
1
1
0
1
0
0
2
0
1
2
2
1
2
0
1
1
2
1
0
1
0
2
1
1
0
1
0
0
0
1
1
1
2
0
1
0
1
2
1
2
1
0
1
1
2
0
1
0
1
1
0
2
2
0
1
2
2
1
2
0
1
0
0
0
1
1
0
1
1
1
0
0
0
0
0
1
0
4
0
1
1
2
1
0
1
0
0
1
1
1
2
1
0
1
2
2
1
0
2
1
0
1
1
1
1
1
0
0
0
1
2
0
0
2
2
1
1
2
1
0
1
0
0
2
2
0
2
1
1
1
0
1
0
0
2
0
0
2
0
1
0
1
0
2
0
1
2
1
2
2
0
1
1
2
0
0
0
0
0
0
0
1
1
1
2
1
0
0
0
0
1
1
1
1
0
0
1
0
2
0
2
2
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
2
1
1
2
0
0
3
0
1
1
0
2
1
1
1
1
2
0
1
2
0
0
1
2
0
2
0
0
1
0
1
1
0
1
2
2
1
0
1
0
2
2
0
0
1
2
1
0
0
1
0
1
2
0
1
1
1
1
1
1
1
0
2
0
0
1
0
0
2
1
0
2
1
1
2
2
0
1
0
0
1
1
0
1
1
1
1
1
0
1
0
1
1
3
0
1
0
2
1
2
0
2
0
2
3
2
2
1
2
0
1
1
0
0
1
1
1
0
0
1
0
1
0
0
2
0
2
1
0
0
0
2
1
0
1
1
2
2
3
1
0
0
2
0
1
1
1
0
0
1
0
1
0
0
1
2
0
1
2
0
2
2
2
0
1
0
0
0
0
0
2
0
2
0
0
1
0
1
2
2
1
0
1
2
1
0
0
2
2
0
1
0
1
1
2
0
5
2
1
0
0
1
1
1
1
1
2
1
2
2
1
3
1
0
1
0
0
0
0
0
2
0
0
1
1
0
0
1
1
1
1
0
0
0
2
0
1
0
2
1
2
2
0
1
0
2
0
1
1
1
0
1
1
0
1
0
1
3
0
0
0
0
0
1
0
1
1
1
0
0
0
1
0
1
0
1
2
2
0
1
1
1
0
0
0
2
1
1
0
2
1
0
1
0
1
0
2
1
0
1
1
1
0
1
0
0
0
2
1
1
0
0
2
1
1
2
1
2
0
0
0
2
0
1
0
0
1
0
1
0
0
0
0
0
1
0
1
1
2
2
0
0
1
1
0
3
2
1
2
0
0
2
1
0
2
3
0
0
2
0
0
0
2
1
1
2
0
2
3
0
0
0
0
2
1
0
0
2
1
2
1
2
0
1
0
1
1
0
2
1
0
0
0
0
0
0
0
1
1
0
0
0
3
0
2
0
0
0
1
0
2
2
2
1
0
2
1
0
1
1
1
3
1
2
1
0
0
0
1
0
2
0
1
1
1
2
2
0
1
0
1
1
1
1
2
1
1
1
1
0
0
0
2
0
1
0
1
0
0
0
1
2
0
0
0
1
2
0
1
0
2
0
0
0
0
0
1
0
1
1
0
1
1
1
1
0
0
0
1
1
1
1
0
0
2
0
1
1
0
2
1
0
1
2
1
0
1
3
0
1
2
1
0
2
1
0
1
1
1
0
0
0
0
0
1
1
0
1
0
1
2
1
0
1
0
2
0
0
0
2
2
0
2
0
1
5
1
0
0
1
0
0
0
1
2
0
1
0
1
1
1
0
2
2
2
1
0
2
2
1
0
1
2
1
3
1
1
0
1
1
1
0
2
1
0
2
1
2
0
1
1
0
1
0
1
1
0
0
0
1
1
0
0
1
1
0
2
2
2
2
0
2
0
1
1
0
0
0
1
1
1
1
0
0
0
0
1
1
0
1
2
2
2
0
0
2
2
1
1
2
1
2
0
0
0
0
1
0
0
0
1
0
1
1
2
2
1
2
0
1
2
1
1
0
3
1
0
0
1
0
1
1
0
1
1
1
1
1
1
0
0
0
0
0
0
1
1
2
0
2
2
1
0
0
0
0
3
1
0
1
0
1
0
2
0
0
2
0
2
0
2
0
0
1
0
2
0
0
0
0
1
2
0
2
0
1
2
1
0
1
2
2
1
1
2
0
0
1
1
2
1
0
2
2
2
2
0
1
1
1
1
1
0
1
0
0
1
2
1
1
2
2
0
1
3
2
1
0
1
1
1
0
1
2
1
0
0
2
0
0
1
2
1
0
1
1
0
0
1
2
1
1
1
1
2
1
0
0
1
1
0
2
0
0
1
0
0
0
1
0
0
2
1
0
1
2
2
1
1
2
2
0
0
0
2
0
1
2
2
1
1
2
1
2
1
2
1
1
0
1
0
0
0
1
0
0
1
2
0
1
1
3
0
1
2
2
1
1
0
0
0
0
0
0
1
0
2
0
1
0
1
0
0
0
0
0
2
1
2
0
2
1
1
2
3
0
0
1
1
1
1
2
0
2
3
2
0
2
1
2
0
0
0
2
0
1
0
2
1
2
0
0
0
0
0
2
2
2
1
0
1
1
2
1
0
0
0
1
2
0
1
1
2
0
2
0
0
1
2
1
0
0
0
0
1
0
1
3
0
0
0
0
2
1
3
1
1
2
1
2
1
2
0
0
1
0
1
0
0
2
0
0
2
0
1
0
3
0
0
1
0
0
2
3
1
0
2
1
3
2
0
0
2
1
0
1
2
0
1
0
1
0
0
0
0
0
1
0
1
1
0
1
2
1
0
2
2
1
2
1
0
1
2
1
1
0
2
2
1
0
0
2
1
0
2
1
1
2
2
1
1
0
0
0
2
1
1
1
1
2
0
0
2
2
0
0
0
1
0
1
1
1
0
1
1
0
1
0
1
1
0
1
1
1
0
0
1
0
0
1
1
2
2
1
0
1
2
0
1
1
0
2
0
0
0
0
2
2
0
0
0
3
1
2
2
0
0
0
1
0
0
1
1
0
1
0
1
0
2
0
2
1
0
0
1
0
0
1
2
0
1
0
2
1
0
2
0
0
0
2
0
1
0
0
1
2
0
0
0
1
1
5
0
1
1
0
1
1
1
1
0
2
2
1
1
1
0
0
0
1
0
1
1
2
2
1
1
0
2
2
0
2
0
0
0
2
1
2
1
2
2
2
1
0
0
1
2
2
0
2
1
1
1
2
0
0
2
0
0
0
1
2
0
0
0
1
1
1
2
0
1
1
0
1
1
1
1
1
1
0
1
1
1
1
0
0
2
1
0
0
2
0
1
0
2
2
2
0
0
2
0
0
2
0
1
2
2
1
0
1
1
0
0
0
2
1
2
1
1
0
1
2
1
0
2
2
1
1
2
2
1
1
0
2
0
0
2
0
1
1
2
0
0
2
0
0
0
1
0
1
1
1
1
1
0
1
0
0
1
1
0
0
2
0
1
1
2
1
0
0
1
0
2
1
2
0
1
0
2
0
0
1
0
0
1
1
2
1
0
1
2
3
1
1
2
2
0
0
1
0
0
0
0
2
0
2
0
1
0
1
1
4
0
2
2
1
2
1
1
1
2
1
0
0
1
1
0
2
0
0
0
1
2
0
1
2
0
0
2
1
0
1
2
3
0
0
1
1
0
0
2
2
1
3
1
1
0
2
0
0
0
1
1
1
0
2
1
0
1
1
2
0
0
1
0
0
0
0
0
1
1
0
1
0
2
1
0
0
0
0
0
0
1
1
1
2
0
0
2
1
0
2
2
0
1
0
2
2
0
2
1
0
1
1
1
0
0
0
0
1
1
1
2
1
0
0
2
2
1
2
0
1
1
0
2
2
0
1
1
0
1
1
1
1
0
1
2
1
0
2
0
0
0
1
1
1
1
2
1
2
2
1
0
1
0
0
1
0
2
2
4
1
1
2
1
1
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
2
0
0
0
0
2
2
1
1
0
0
1
1
1
1
1
0
1
2
2
0
1
2
2
2
1
0
0
0
1
1
1
2
0
0
2
1
2
0
2
2
0
1
1
0
1
0
0
1
2
1
0
0
1
1
1
1
2
1
0
1
2
2
1
1
0
1
0
2
2
2
3
1
2
1
0
1
0
0
2
1
0
0
1
0
0
2
3
0
0
1
1
1
1
1
2
1
1
0
0
2
0
1
2
1
1
0
1
1
2
0
2
1
1
2
1
0
1
0
1
1
1
2
1
0
1
1
0
1
0
1
0
1
0
1
1
0
2
1
0
2
0
0
1
1
3
0
0
0
0
0
2
1
0
0
0
1
0
1
1
0
2
0
0
1
1
1
1
0
2
1
2
2
1
0
0
0
1
2
0
0
2
1
0
2
1
0
1
2
0
1
0
0
1
0
0
1
1
1
1
1
0
1
2
2
0
1
2
1
1
1
0
0
2
2
2
1
0
0
0
1
1
0
0
0
1
0
1
1
0
1
1
0
0
0
1
0
0
0
1
0
2
2
0
1
2
0
1
1
1
0
1
0
0
0
2
1
0
0
0
0
1
1
0
0
6
0
2
2
0
2
0
1
1
1
0
0
0
0
0
1
0
0
2
0
0
2
1
0
0
2
2
0
0
2
2
2
0
1
1
1
2
1
1
0
1
1
0
1
1
1
1
2
0
1
0
1
0
1
1
0
0
0
0
1
1
0
2
0
1
1
0
1
2
0
1
0
1
0
0
2
1
1
1
1
4
2
1
1
2
1
0
1
0
1
0
2
0
2
0
0
1
0
0
2
1
0
2
0
1
1
2
0
1
0
1
1
0
0
1
1
1
0
0
1
0
1
1
2
1
0
2
2
0
2
1
1
1
1
2
2
1
4
0
2
1
1
1
1
2
2
1
0
1
2
1
0
2
1
1
2
2
2
2
0
0
0
2
0
0
0
0
0
1
0
1
1
1
2
0
0
1
2
1
0
1
0
1
1
1
0
0
0
0
0
0
1
1
3
0
1
0
1
1
1
1
2
1
1
0
2
2
3
1
1
1
1
0
0
1
2
2
1
0
1
0
0
1
1
1
0
0
0
1
0
2
0
1
1
0
1
0
1
2
0
1
0
2
0
1
0
1
2
1
1
0
1
2
1
0
1
1
1
1
0
0
2
2
1
2
0
5
2
1
0
1
0
0
0
0
1
0
2
0
0
2
0
1
1
1
1
1
2
0
0
1
1
2
0
1
0
2
3
1
0
0
1
1
1
1
1
0
2
0
0
2
1
1
1
1
1
1
3
2
0
1
0
0
0
0
0
1
0
0
1
2
2
0
1
0
0
1
0
1
0
1
0
0
1
2
1
1
1
0
1
2
2
1
0
1
0
0
2
0
0
0
0
1
1
0
0
2
1
2
1
1
0
1
1
2
0
1
0
1
2
1
0
1
1
1
2
1
0
0
1
0
0
2
1
1
1
1
1
1
0
1
0
0
0
0
1
0
0
1
2
1
2
1
0
1
1
2
0
0
1
0
1
2
1
0
1
1
0
0
0
1
4
0
2
1
1
0
1
1
1
1
2
2
1
2
1
0
2
2
1
2
0
1
1
0
1
0
1
1
0
2
0
0
0
2
2
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
2
0
2
2
2
1
0
1
2
0
2
0
2
1
2
2
2
2
2
0
1
1
2
2
0
1
2
1
1
0
0
0
0
1
1
2
0
2
0
1
0
2
0
2
1
0
2
1
0
1
1
2
1
0
0
2
1
1
1
0
1
2
1
0
1
2
2
1
0
2
1
0
2
0
2
0
1
3
0
2
0
0
0
0
1
2
1
2
1
1
0
0
1
0
0
1
0
0
1
0
0
1
1
1
0
1
1
2
1
1
2
1
1
0
1
1
0
0
0
2
0
2
2
1
1
0
0
2
0
1
0
2
1
0
2
0
2
1
0
3
0
3
0
1
2
0
0
0
0
1
0
1
2
3
1
0
1
0
0
0
1
1
1
0
2
1
0
2
1
1
1
0
1
1
0
0
1
0
0
0
0
2
2
2
2
0
2
0
1
4
1
1
1
2
1
2
0
0
0
1
1
0
1
1
1
2
0
0
1
2
0
2
1
0
0
0
0
0
0
0
2
1
1
2
2
2
2
2
0
0
1
2
2
1
1
1
0
0
1
0
1
0
2
0
0
0
1
0
0
0
1
1
1
1
1
0
2
1
2
2
0
0
0
0
0
2
2
1
0
2
0
1
2
0
2
1
1
0
0
0
2
0
0
1
1
0
0
1
2
0
0
0
0
2
1
1
0
0
2
1
1
2
1
0
1
1
1
0
0
2
1
2
2
1
2
0
0
0
0
2
1
1
1
0
3
1
0
2
0
1
0
0
1
1
1
0
1
2
1
1
0
0
0
2
0
1
1
1
2
2
0
2
0
2
0
2
0
1
0
2
2
1
0
2
0
1
0
2
1
1
1
1
0
0
1
0
1
1
1
0
0
1
2
0
1
0
1
0
2
1
2
1
2
3
2
2
1
1
1
2
0
0
0
2
0
0
0
0
1
0
1
0
0
0
2
0
2
2
3
1
0
0
1
1
1
1
0
1
1
2
2
2
1
0
0
1
1
2
2
0
2
0
1
0
2
1
2
1
1
0
1
1
3
1
0
0
1
2
1
0
0
1
0
0
1
1
2
1
1
1
3
1
2
1
2
0
2
2
1
0
2
0
1
1
1
2
0
0
1
0
0
1
0
0
1
1
2
1
1
1
2
0
0
1
0
1
1
2
0
1
1
1
1
1
0
1
1
1
2
1
0
2
1
2
1
0
0
0
0
0
1
0
0
2
0
1
1
1
0
0
0
2
1
1
1
2
1
1
0
4
1
0
0
1
2
2
1
1
0
0
0
1
1
1
1
1
2
0
1
1
0
0
1
1
2
0
1
2
2
2
0
0
0
1
0
1
1
0
1
1
0
1
0
1
3
0
1
0
1
0
1
0
1
2
0
0
0
0
1
2
0
1
1
1
1
0
1
2
0
0
1
2
0
1
0
0
1
1
1
1
2
0
1
0
1
0
1
1
2
0
2
1
2
1
2
0
1
2
1
0
2
1
0
1
2
2
2
1
1
2
1
1
1
2
2
0
0
0
1
1
0
0
1
0
1
0
2
0
0
2
0
0
2
0
0
1
0
0
2
0
1
1
2
2
1
1
1
2
1
1
1
1
1
0
2
0
0
1
1
0
1
0
0
1
0
2
2
2
0
1
2
1
0
6
1
0
0
1
0
0
3
2
2
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
2
1
2
0
0
2
1
0
0
1
0
0
1
2
0
1
1
2
0
2
1
0
4
0
0
1
2
0
0
0
3
2
2
1
1
1
0
1
0
1
2
0
1
1
1
0
0
1
2
0
1
2
0
0
1
1
0
0
0
0
1
0
2
0
0
1
0
1
1
0
0
2
0
1
0
0
1
2
1
0
0
1
0
2
1
1
1
0
1
0
0
0
1
1
1
1
1
1
0
1
1
0
2
0
0
0
1
1
0
2
1
2
0
1
0
0
1
1
0
0
0
0
2
1
2
1
3
1
1
1
0
0
0
1
2
2
0
2
0
2
0
0
2
1
0
0
1
0
1
0
2
0
1
0
2
2
0
2
0
0
0
0
2
0
1
0
0
1
2
1
1
2
0
0
1
0
1
0
2
0
1
0
0
0
3
1
0
2
1
1
1
0
1
0
0
1
0
0
1
1
0
1
1
1
2
1
1
1
1
0
0
1
2
1
0
1
1
0
1
0
1
1
0
0
0
2
1
0
1
0
0
1
2
1
1
2
1
1
0
1
0
1
1
0
1
1
1
0
0
1
2
0
1
0
2
1
1
1
2
2
1
0
2
2
1
2
2
0
0
0
0
1
2
0
2
0
1
0
2
2
0
2
0
1
0
2
1
0
0
2
1
2
1
2
0
1
1
1
0
1
1
2
2
0
0
1
1
1
1
0
0
1
1
0
0
0
0
0
0
0
2
0
1
1
1
1
0
1
0
2
2
2
0
1
0
0
0
1
2
0
0
2
0
0
1
0
1
1
2
2
2
1
1
1
0
0
0
1
1
1
0
1
1
1
0
3
0
1
0
1
2
0
0
0
1
2
0
0
1
0
0
1
1
2
0
1
2
1
0
1
0
0
2
0
1
0
1
0
1
2
1
0
0
1
2
1
1
2
1
0
1
2
1
0
0
1
1
2
0
1
1
2
0
2
1
1
1
1
2
1
1
2
0
2
1
1
2
0
1
0
0
2
1
1
1
2
0
2
2
2
0
0
0
1
2
1
2
0
2
0
0
0
0
1
0
0
1
1
0
0
1
0
1
2
2
0
1
1
1
2
1
1
0
1
1
1
1
1
0
0
2
1
1
1
0
1
0
0
0
1
0
0
1
1
2
2
1
2
1
2
1
1
2
0
1
2
0
2
1
1
1
2
0
0
0
1
2
1
1
0
1
0
1
0
1
1
1
2
0
2
0
1
1
1
2
1
0
0
1
0
1
1
0
0
0
0
1
1
1
1
1
2
2
2
1
1
2
1
1
0
1
0
0
0
2
1
2
0
3
1
2
1
1
1
2
0
1
0
0
1
1
1
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
4
0
1
0
1
0
0
1
1
0
1
2
1
1
0
2
0
0
0
0
0
0
1
1
2
2
0
0
1
0
3
2
1
0
0
0
1
2
2
0
3
1
2
2
3
0
1
1
0
0
0
1
0
2
1
2
2
1
0
1
1
1
1
0
1
3
1
0
1
2
1
1
2
2
2
1
1
2
0
3
0
0
1
2
2
2
0
1
1
0
2
0
3
1
1
2
0
0
0
1
0
1
1
0
1
1
1
1
1
0
1
2
0
2
2
2
0
0
1
1
2
2
1
3
2
1
1
1
1
1
2
0
1
2
1
0
0
0
1
1
2
0
1
2
1
0
1
2
0
1
0
0
0
2
0
1
0
0
0
1
0
0
1
1
1
0
1
1
1
0
1
1
3
3
2
1
0
1
1
0
2
1
1
1
2
1
1
0
0
1
1
1
0
2
1
0
1
1
0
0
0
1
1
0
0
0
0
2
1
1
1
1
0
3
1
1
0
0
1
1
0
1
2
0
0
1
2
3
2
1
1
1
1
0
2
1
2
0
0
1
2
1
2
0
1
0
1
2
1
0
0
2
0
0
2
0
0
0
0
1
0
1
1
1
1
1
2
2
1
1
2
1
0
1
1
0
0
2
0
0
0
1
2
1
0
0
0
1
1
2
1
0
1
3
0
1
1
2
1
0
0
0
0
0
1
0
0
1
2
1
1
1
0
1
1
0
0
0
0
1
2
1
2
4
0
1
0
0
3
2
1
0
2
1
0
1
0
0
1
3
2
1
1
0
1
1
1
1
1
0
1
1
2
1
1
1
1
1
2
3
0
1
1
0
2
1
1
0
5
0
2
1
1
0
0
3
2
1
1
1
0
2
2
2
1
2
2
0
0
1
1
0
0
0
0
2
0
1
2
1
0
1
0
1
0
2
2
1
1
1
2
1
0
0
1
1
1
1
1
0
5
0
0
0
0
0
1
0
2
1
0
0
1
1
1
0
2
0
0
0
1
0
1
1
3
2
0
2
1
0
2
0
1
0
1
1
0
1
0
1
0
2
2
0
1
2
2
0
2
1
0
2
1
2
0
1
0
1
1
0
0
0
0
0
2
2
0
0
0
1
0
1
1
0
1
0
1
0
1
2
1
1
2
1
2
1
1
1
0
2
1
0
2
1
2
1
0
0
1
1
1
2
0
2
0
1
0
1
2
1
1
0
0
0
1
0
0
0
1
2
0
1
0
1
0
1
2
2
0
2
1
1
2
2
1
0
2
0
1
2
2
1
2
1
1
1
1
0
0
1
1
0
0
1
2
2
2
0
1
2
0
0
0
1
1
0
1
1
0
0
0
1
1
2
2
0
0
1
0
1
1
2
1
0
1
0
0
1
0
1
1
1
0
0
0
2
2
1
0
2
1
2
2
0
1
1
1
0
0
0
2
1
1
2
1
0
0
1
2
1
0
0
0
0
1
2
1
2
1
2
0
0
1
0
2
1
2
0
1
0
0
0
2
0
1
2
1
2
0
0
1
1
1
1
2
2
0
0
1
0
1
0
0
2
0
0
1
0
1
1
2
0
1
2
0
1
0
0
1
1
0
0
0
2
0
1
1
0
2
1
1
2
1
0
1
0
1
0
1
1
2
2
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
1
2
0
0
0
1
1
1
0
1
2
1
0
0
0
1
0
1
0
0
1
1
2
0
1
0
1
2
0
2
2
2
1
1
1
0
1
0
1
2
1
2
0
1
1
2
1
0
1
1
0
1
2
5
0
0
0
1
1
1
1
2
0
1
2
1
0
1
0
1
1
1
0
0
0
1
1
0
0
1
0
0
2
0
0
1
3
1
1
1
0
0
1
1
2
0
1
1
0
0
1
0
0
0
2
1
1
2
0
3
2
1
1
2
1
0
1
0
1
0
1
0
1
1
0
2
0
1
0
1
0
1
0
2
2
1
0
1
0
1
2
2
1
0
0
1
0
2
0
1
1
1
2
0
1
0
3
2
2
2
2
1
0
1
1
2
1
2
1
0
0
1
0
0
1
0
0
2
1
2
0
0
0
1
1
0
1
0
0
1
4
1
3
1
1
1
1
1
2
0
1
0
2
0
2
2
0
0
0
0
0
1
1
1
0
1
3
1
0
0
1
1
1
2
0
1
0
1
2
0
2
0
1
0
0
1
2
0
1
1
0
0
0
0
0
1
2
1
2
1
2
1
1
0
0
0
1
1
1
1
2
2
0
1
0
2
1
2
1
2
0
0
1
2
2
2
0
1
1
1
1
1
0
2
1
0
0
0
2
2
0
2
2
1
1
0
1
2
0
1
1
0
1
0
1
0
1
2
0
1
1
1
0
2
1
1
0
1
1
0
1
1
1
1
0
1
1
1
0
0
0
0
0
0
2
3
1
0
0
1
2
0
2
2
1
1
2
0
1
1
0
0
0
0
0
1
0
1
2
0
1
1
0
2
2
0
0
0
1
0
0
3
1
0
1
1
0
2
1
0
1
1
1
2
0
1
0
1
1
1
0
0
0
1
2
1
0
0
1
0
1
0
0
2
0
0
1
1
1
0
1
2
1
2
1
2
1
2
2
0
0
1
2
1
1
2
0
1
2
1
1
2
2
0
0
1
0
1
1
1
0
0
1
0
1
0
1
2
1
1
0
2
0
1
0
0
2
2
2
0
1
2
0
2
0
1
0
0
0
1
1
0
0
1
0
5
1
1
1
0
1
0
0
1
0
2
2
1
1
2
1
1
1
0
2
0
1
2
1
1
2
1
1
1
0
0
1
1
1
2
1
0
2
0
0
1
0
0
1
2
1
1
1
1
2
2
1
0
0
2
2
0
1
1
2
2
1
2
1
1
1
1
0
1
1
0
0
0
2
1
1
1
0
1
0
0
0
1
0
1
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
1
2
0
0
1
1
1
1
1
1
0
0
1
1
1
0
0
9
0
0
1
0
0
1
1
0
0
2
2
0
0
2
1
0
1
2
2
2
1
0
1
2
1
1
0
1
1
0
1
1
0
0
1
1
2
1
0
1
1
1
0
0
2
2
0
1
0
1
2
1
0
2
0
2
0
2
1
1
2
0
1
2
1
0
0
0
2
2
0
2
0
1
0
1
0
0
0
2
1
0
1
0
1
0
2
1
2
1
1
1
1
1
0
0
0
0
1
2
0
2
0
0
0
2
2
2
1
0
1
1
1
0
0
2
1
1
0
1
1
0
0
2
2
1
2
2
0
0
1
0
0
2
1
0
2
1
0
2
0
0
1
0
1
2
1
1
2
0
2
0
0
1
0
1
1
1
0
0
1
1
1
1
0
0
2
1
0
1
1
0
0
0
0
0
2
2
0
0
1
0
0
0
2
1
0
0
0
1
0
1
0
0
0
0
0
2
1
0
3
1
0
1
1
0
0
1
0
1
0
1
0
2
0
1
1
1
0
4
0
0
0
0
2
1
1
2
2
1
1
0
2
0
4
1
1
0
1
2
0
1
1
1
1
1
2
1
2
1
1
0
1
1
0
0
1
2
1
0
2
1
1
2
0
0
1
1
1
1
1
1
2
1
2
0
0
2
1
0
1
0
0
2
0
2
2
1
0
1
0
1
0
0
2
1
2
0
0
0
1
2
1
0
1
0
0
2
0
2
2
2
0
0
3
2
1
1
0
1
0
1
0
1
0
0
1
0
2
2
1
0
1
0
2
1
0
2
1
0
2
2
1
0
1
1
2
1
1
1
0
1
1
0
0
1
1
0
0
0
0
0
0
2
0
2
2
2
2
0
1
3
0
0
4
1
2
1
0
1
1
2
0
1
0
1
1
2
1
0
0
0
1
1
1
2
0
0
1
0
1
0
0
0
0
2
0
0
1
0
0
0
1
2
1
1
0
0
0
2
1
1
2
2
0
0
1
0
1
2
1
2
2
1
2
1
0
1
1
1
0
0
0
1
1
0
1
0
0
0
0
0
2
1
1
0
0
2
1
1
2
0
2
0
2
1
3
1
1
1
2
2
0
1
1
1
1
1
1
0
1
1
0
1
2
0
1
1
0
1
2
0
0
1
0
1
0
1
0
0
1
3
1
1
0
3
2
2
1
1
2
0
1
1
1
2
1
1
1
1
0
2
0
1
0
1
0
1
1
0
1
0
0
0
2
1
1
1
0
1
0
0
1
1
2
0
1
3
1
7
1
0
0
2
0
2
2
2
2
0
1
0
0
2
0
1
2
1
0
1
1
2
0
0
0
1
1
1
1
0
2
0
1
0
1
1
0
1
1
0
1
0
1
0
2
1
1
0
0
2
1
1
0
1
0
1
2
0
0
0
2
1
1
0
2
1
2
3
1
0
0
0
1
0
0
2
0
0
0
1
1
1
0
1
0
2
1
0
1
0
1
3
2
2
0
0
2
1
2
3
1
2
1
0
2
0
0
1
1
1
2
1
0
0
2
2
1
1
1
0
2
2
1
1
1
0
5
1
1
1
0
1
0
1
0
1
0
1
2
1
0
0
0
1
2
0
0
0
0
1
2
1
1
2
1
1
0
1
2
0
1
0
1
1
1
3
0
0
0
0
0
1
0
1
1
0
0
0
2
0
1
0
3
0
2
0
0
0
1
3
1
0
1
1
2
0
0
1
0
0
1
0
1
1
0
2
1
1
1
0
2
0
2
0
0
2
1
0
1
0
1
1
0
0
1
0
0
0
0
1
0
2
1
1
1
1
0
1
2
0
0
1
1
1
2
0
0
0
1
1
1
0
0
2
1
2
1
1
1
2
1
2
0
2
0
0
1
0
0
1
1
0
0
1
1
2
0
1
2
1
2
2
2
0
2
0
0
2
2
1
0
2
0
0
1
2
0
2
0
0
0
0
1
2
1
0
2
0
2
0
1
1
0
1
0
0
3
0
0
1
1
0
1
1
1
0
1
2
0
1
1
0
1
0
1
0
1
2
0
1
2
0
2
2
1
1
0
0
1
1
0
1
0
1
1
0
1
0
1
1
0
0
2
0
2
0
2
1
1
1
0
0
2
1
1
0
1
1
0
1
1
1
0
2
1
1
0
0
1
1
1
0
0
2
2
0
0
0
1
2
0
1
1
1
0
1
2
4
0
1
0
0
0
1
0
0
0
1
1
1
1
2
0
1
2
1
2
0
0
0
2
2
2
0
1
1
0
0
1
1
0
0
3
2
1
2
1
1
1
1
1
2
2
2
1
0
0
0
1
1
0
1
1
1
0
1
0
3
0
0
0
0
0
1
1
1
1
1
1
1
0
2
2
2
1
2
1
1
1
0
0
1
0
1
3
1
2
1
4
0
0
1
1
2
0
1
0
1
2
1
1
0
2
0
2
0
0
2
0
1
0
0
1
2
0
1
2
1
0
1
0
0
0
2
1
2
2
0
0
1
0
0
1
0
1
0
2
2
1
2
2
0
0
1
0
0
0
1
1
1
0
2
1
0
0
1
1
1
0
1
0
1
2
1
0
0
2
2
2
0
1
1
0
2
1
0
0
1
0
1
1
0
0
1
1
0
1
1
1
2
1
0
2
0
0
0
1
1
0
0
0
1
1
2
0
0
2
1
2
1
1
1
2
0
2
1
2
2
2
1
1
0
0
3
0
2
0
2
1
1
1
2
1
2
1
1
2
0
0
1
1
1
0
0
1
2
0
1
2
1
1
1
2
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
1
0
1
1
2
1
2
0
0
0
1
2
0
1
1
1
2
1
0
1
0
1
1
0
0
2
0
1
1
1
1
0
0
1
2
0
1
1
0
1
0
0
1
1
2
0
2
1
0
2
0
2
2
0
1
1
2
0
0
0
1
2
0
1
2
0
1
0
1
0
0
1
0
2
2
0
0
2
0
0
1
2
1
1
1
1
0
1
0
0
1
1
0
0
0
1
7
0
1
1
0
1
2
0
1
0
0
0
0
1
2
2
0
2
2
0
1
1
1
1
1
2
1
2
1
2
0
1
1
1
0
0
0
1
1
1
0
2
2
1
3
1
0
1
1
0
0
1
1
1
1
1
0
0
1
0
2
2
2
0
2
1
1
1
0
1
1
0
1
0
2
0
0
2
1
1
1
2
1
0
1
2
0
0
1
2
1
1
1
1
1
1
1
0
1
0
0
2
2
2
1
2
0
1
0
1
0
1
1
2
2
0
0
0
0
2
1
1
0
2
0
2
2
0
1
0
1
1
1
2
1
1
1
2
1
1
0
1
2
0
0
1
1
1
1
1
0
2
0
2
1
1
1
1
0
0
1
1
2
0
1
1
0
2
1
1
1
0
2
1
0
1
1
2
1
0
2
2
0
0
1
1
2
0
1
1
1
2
0
0
0
0
1
0
2
1
0
0
2
0
2
2
2
2
1
0
0
5
1
2
0
0
1
2
2
2
0
1
0
1
2
2
0
1
2
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
1
1
0
1
0
1
0
1
0
3
1
0
0
1
2
1
2
0
0
1
2
0
0
1
1
2
2
0
0
0
0
1
0
2
0
1
0
2
1
2
0
0
1
1
1
0
0
1
0
1
1
1
0
1
1
2
0
1
2
0
0
2
1
0
0
1
2
0
2
0
2
0
1
0
1
1
1
1
1
2
0
1
0
1
3
1
1
1
1
0
0
2
0
2
0
1
1
0
2
0
0
0
4
4
2
1
0
1
1
1
0
2
1
1
0
0
1
0
1
2
2
0
2
1
0
0
1
2
0
0
0
0
2
1
1
0
0
0
2
0
0
1
3
0
1
1
2
0
1
1
1
0
1
1
1
0
1
0
0
1
2
0
0
1
4
2
2
1
2
0
0
1
0
1
2
0
1
3
2
1
1
1
2
1
1
1
0
0
0
2
1
1
2
1
2
2
2
1
1
0
0
0
0
2
0
1
0
1
1
1
2
1
0
2
2
0
0
1
1
2
2
1
0
1
1
0
2
0
0
1
1
2
4
2
0
2
1
1
1
1
0
2
0
0
0
0
1
2
0
0
2
0
1
2
1
2
1
2
1
2
1
2
0
0
1
0
0
3
2
0
0
0
0
1
1
0
3
0
0
1
1
0
0
0
0
0
1
2
0
0
1
1
1
1
0
1
0
0
0
2
1
0
1
1
0
1
0
1
0
0
1
0
0
1
0
0
1
1
1
1
2
0
2
2
1
0
1
0
1
0
2
2
0
1
1
1
1
0
1
0
2
0
1
0
0
0
0
2
0
0
1
1
2
0
0
1
0
0
1
1
1
0
1
0
0
1
1
2
1
1
1
0
0
2
2
0
3
1
1
1
2
1
1
2
1
0
0
1
2
1
1
0
2
0
0
1
1
0
1
0
2
0
1
2
0
1
0
1
2
2
0
0
0
0
2
1
2
1
1
1
0
2
1
0
0
1
0
0
1
2
1
0
2
2
2
2
0
0
1
1
1
1
1
0
1
2
0
2
1
1
1
1
0
1
1
2
1
1
1
1
2
0
2
0
1
0
2
0
0
1
1
1
1
0
0
1
2
0
1
2
0
0
1
1
0
0
1
2
1
1
1
2
1
0
1
0
1
0
0
0
0
0
0
0
2
0
1
2
1
1
1
1
1
1
0
0
0
1
0
1
1
0
0
0
0
2
1
0
1
0
2
1
1
0
1
1
2
1
2
1
1
1
0
1
0
0
1
1
2
0
1
0
0
1
0
1
2
0
0
2
2
0
1
0
0
2
2
1
1
0
2
0
0
0
3
3
2
0
0
0
3
1
1
2
1
1
0
1
2
0
0
1
1
2
0
0
1
0
0
0
0
2
1
1
0
1
0
1
2
0
0
2
2
0
1
1
1
1
2
0
1
0
0
0
0
2
1
0
2
2
0
1
1
1
0
0
0
1
0
1
1
1
2
2
0
0
0
2
2
4
0
1
2
0
0
1
0
0
0
0
10
0
0
1
0
1
0
1
2
1
1
0
1
2
1
1
1
0
1
1
1
2
0
2
0
0
0
0
1
2
1
0
1
0
1
1
1
1
1
0
1
1
1
2
1
0
2
1
0
0
1
1
1
0
2
1
0
0
0
0
1
0
2
1
1
1
0
1
1
2
2
0
0
1
0
1
0
0
2
0
0
0
0
1
2
1
0
0
1
1
0
0
0
0
0
0
0
2
2
2
0
0
2
0
2
0
1
1
0
0
2
1
2
2
0
0
0
1
0
0
0
0
1
1
1
0
1
0
0
3
2
2
0
0
1
1
1
1
1
1
1
0
5
2
1
1
1
1
0
0
1
0
1
0
1
0
3
1
1
2
0
0
1
4
2
0
2
0
1
0
0
0
0
2
0
2
1
1
2
1
2
1
0
2
1
1
0
1
2
1
1
0
2
1
0
1
0
1
2
0
0
0
2
2
1
0
1
1
1
0
0
0
0
1
0
0
0
0
1
3
0
0
0
1
1
0
3
1
0
0
2
1
1
1
1
1
2
1
0
0
1
2
2
2
1
3
0
2
2
2
0
0
0
1
0
2
1
2
1
1
0
0
0
0
1
0
1
1
0
0
0
1
0
1
2
2
1
2
1
0
1
1
2
1
0
2
0
2
0
0
0
1
2
0
1
1
0
0
0
2
2
2
3
0
1
1
0
0
1
1
0
1
1
1
0
0
1
1
1
0
1
2
0
0
1
2
1
0
0
0
2
1
1
2
0
3
0
0
1
2
2
0
0
0
1
2
0
0
1
2
1
1
1
1
2
1
0
2
3
2
0
0
2
0
2
1
1
1
1
1
0
1
1
0
1
2
0
1
0
1
2
1
0
0
1
1
1
1
1
2
2
0
2
2
2
0
0
0
0
1
1
1
0
1
0
0
1
1
0
0
0
1
0
1
1
0
2
0
1
0
1
0
0
0
2
0
1
1
1
2
1
1
1
2
0
2
1
1
0
1
0
2
1
2
0
1
2
0
0
1
2
2
1
2
2
0
2
0
1
2
0
0
2
0
0
0
2
2
2
1
1
1
1
0
1
1
2
1
0
1
1
0
1
2
0
2
1
0
1
1
1
1
2
0
1
0
2
2
0
1
0
2
0
2
0
0
0
1
2
1
2
2
2
0
0
1
0
0
1
0
1
2
1
0
2
0
0
1
2
1
1
0
1
1
2
2
2
1
0
1
0
2
1
2
0
0
0
0
0
0
0
2
0
2
0
1
1
0
1
1
0
2
1
0
1
0
4
1
0
0
0
1
0
1
1
2
0
2
1
0
1
1
1
0
2
2
1
0
1
0
1
1
0
0
0
2
0
2
1
0
0
0
1
0
0
1
2
2
3
1
1
0
1
2
1
0
1
1
0
1
1
1
1
0
1
4
1
1
0
1
0
1
1
1
0
1
0
0
1
1
2
2
0
1
0
2
0
1
0
2
0
0
2
1
0
2
1
0
0
1
0
1
1
0
1
0
1
2
2
1
0
0
2
0
0
1
1
1
0
0
1
0
0
0
1
2
0
1
1
1
0
2
1
0
0
2
0
0
0
1
1
3
1
1
0
0
1
2
0
2
1
0
4
2
0
1
0
1
1
0
1
0
2
0
0
1
1
0
2
1
1
0
0
0
0
0
1
2
0
0
0
1
2
1
0
2
1
2
1
0
0
1
2
2
1
0
1
0
0
1
2
1
2
1
0
0
1
0
2
1
2
0
1
2
1
0
1
0
0
1
1
1
1
0
1
0
2
2
1
1
2
0
2
1
1
3
1
1
0
1
2
1
0
1
0
0
0
0
1
1
0
0
0
2
0
1
0
0
0
2
2
2
1
1
1
2
2
1
0
1
1
0
0
3
1
0
0
1
1
0
0
1
2
1
1
1
2
2
0
1
1
1
2
1
1
2
1
0
0
1
1
1
0
2
0
0
1
1
0
3
0
0
1
0
1
1
0
0
1
1
1
2
2
0
0
1
0
0
2
2
1
1
1
1
2
2
0
1
0
2
2
1
1
0
0
2
2
0
1
1
1
1
1
1
0
1
2
1
0
2
1
2
2
0
1
1
0
2
0
1
0
1
2
0
1
1
1
2
1
0
0
0
0
1
1
2
0
0
2
1
0
1
1
1
0
1
2
0
2
2
1
1
2
1
1
0
1
0
0
0
0
1
1
2
2
0
5
0
1
2
0
0
2
0
0
1
1
1
1
2
1
2
2
1
1
1
1
1
1
1
1
0
1
1
2
0
0
1
0
2
0
0
0
0
1
2
2
0
0
1
0
0
1
0
1
1
1
2
2
1
1
1
1
0
0
0
2
1
0
2
0
2
2
0
0
1
1
1
0
1
1
0
2
2
1
2
0
0
2
1
0
0
0
0
2
2
2
1
0
0
1
1
0
1
1
0
1
0
1
0
1
0
0
0
1
0
2
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
2
1
2
1
0
0
0
1
1
0
2
1
0
1
0
1
0
1
0
1
0
2
1
1
1
0
2
0
1
2
2
0
1
1
0
0
0
2
1
0
2
0
0
0
0
1
1
2
1
1
0
1
0
2
0
0
0
2
2
1
1
0
0
0
2
0
1
1
1
2
0
2
0
1
2
0
0
1
0
1
0
0
0
2
0
2
1
1
1
1
0
1
2
2
2
2
1
2
2
1
1
1
0
1
2
0
1
0
0
1
1
1
1
0
0
0
1
1
0
0
2
1
1
0
0
0
1
1
1
1
1
1
2
0
3
2
2
0
0
2
0
0
1
0
1
0
1
0
0
1
1
0
2
1
2
0
2
0
2
0
2
2
0
0
0
1
0
2
0
2
2
0
0
0
0
1
0
0
0
2
1
1
1
0
2
0
1
0
0
2
2
2
0
0
2
0
0
0
2
0
0
1
1
2
0
1
1
0
0
1
2
0
0
0
0
0
0
2
2
2
1
1
1
1
1
1
1
2
1
2
1
0
0
0
0
1
1
1
0
0
0
2
0
0
0
1
0
0
1
2
0
1
0
2
0
1
1
0
4
1
0
2
1
2
0
1
1
1
0
2
1
0
1
2
1
0
2
0
1
1
1
1
0
1
0
0
1
0
2
1
2
0
1
0
0
1
1
0
1
1
2
1
1
1
0
1
0
1
0
0
2
2
1
0
2
0
1
0
0
0
1
2
0
0
0
1
1
1
0
1
2
0
0
0
1
2
0
2
0
1
0
1
1
2
2
2
2
1
2
0
0
2
1
1
1
2
1
0
1
0
0
1
2
1
2
1
2
0
1
1
1
0
0
1
2
0
2
2
0
1
1
1
0
0
0
0
0
1
1
1
0
0
1
0
1
2
0
1
2
2
1
0
1
0
2
1
2
2
1
1
2
0
0
0
1
2
2
0
1
0
0
1
2
0
0
0
0
0
2
0
0
0
0
1
1
1
0
0
0
0
2
1
1
1
1
1
1
1
1
1
2
0
2
3
0
1
1
1
1
0
0
2
1
2
2
0
0
1
0
2
1
1
0
1
3
0
1
0
0
1
1
0
1
1
1
1
1
1
2
0
2
1
2
0
1
2
0
0
1
1
1
0
0
0
2
0
2
1
0
1
1
2
1
1
0
0
1
1
1
0
0
0
1
0
0
1
1
0
1
0
0
2
1
1
0
2
1
2
1
0
1
1
2
0
2
1
1
0
1
2
0
0
0
2
0
1
0
2
0
1
1
1
1
2
0
1
1
0
0
0
1
0
1
2
2
0
0
1
0
2
1
0
0
1
2
0
0
0
0
0
1
0
1
0
0
1
1
1
1
1
1
1
0
1
2
2
0
1
1
2
0
2
1
0
1
3
1
1
1
2
1
1
1
0
2
0
4
2
0
1
0
0
3
0
2
1
0
2
0
2
1
0
1
0
2
1
2
0
3
0
1
0
1
1
0
2
0
0
0
0
0
2
0
1
1
1
1
2
2
0
1
2
3
1
0
0
0
2
2
0
0
0
1
1
2
2
2
2
1
0
2
1
4
1
0
0
0
2
2
0
2
0
1
2
0
1
0
1
1
0
1
2
1
2
0
1
1
2
0
2
1
1
0
2
0
0
1
1
2
0
0
0
2
1
0
1
1
1
0
1
1
1
0
0
0
1
2
0
1
1
1
1
0
1
1
1
1
0
2
2
1
0
1
1
1
2
1
1
0
0
0
1
1
1
3
0
1
1
0
0
1
2
1
0
2
0
0
2
0
0
0
0
1
1
0
1
0
1
0
2
1
2
2
0
1
1
2
2
1
0
1
0
1
0
1
0
1
2
0
0
0
0
1
1
1
1
2
1
0
0
0
0
0
2
2
0
0
1
0
2
1
2
1
1
0
0
0
1
0
0
1
0
1
0
0
1
0
0
1
1
1
0
2
0
0
0
1
2
1
0
0
0
1
0
1
0
3
3
1
1
0
1
0
2
1
1
0
0
2
1
0
2
1
1
1
2
0
1
1
0
1
1
2
0
0
1
0
1
2
2
2
2
2
1
2
0
0
0
0
0
1
0
2
1
2
1
0
2
1
1
2
2
0
2
2
0
0
0
0
2
5
1
2
1
1
2
1
3
1
0
2
0
1
0
1
0
2
1
0
1
1
0
1
0
0
0
0
1
2
2
1
0
2
0
2
2
0
1
2
1
2
0
2
2
2
2
2
0
2
0
1
1
1
1
1
0
3
0
2
1
0
0
0
2
1
0
0
1
2
1
2
0
2
0
0
0
1
0
1
0
2
1
0
2
0
1
1
0
1
0
0
1
2
0
0
0
2
1
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
1
1
2
0
3
2
1
1
0
1
1
0
0
1
1
0
0
2
1
5
1
1
0
0
1
2
0
1
0
2
1
0
1
1
2
0
2
0
0
0
2
1
1
1
0
1
2
0
2
0
0
1
2
1
0
0
1
0
0
1
0
0
2
2
0
2
1
0
1
0
0
0
0
1
0
0
2
1
0
0
0
1
2
0
1
1
0
2
2
1
2
2
0
0
0
0
1
1
0
1
1
0
1
0
2
0
1
2
1
0
1
0
1
1
1
1
1
0
1
1
0
0
0
0
0
0
2
0
1
1
1
1
0
2
1
1
1
2
1
1
0
1
1
0
1
0
1
2
1
1
2
2
1
0
0
0
0
0
0
0
2
2
0
1
0
2
3
0
0
0
2
0
2
0
0
1
2
1
2
2
2
1
0
0
1
2
1
1
0
0
1
0
0
0
0
1
2
0
1
2
3
0
2
2
0
0
0
0
0
0
2
1
0
0
2
1
1
0
1
1
1
2
0
2
0
1
1
2
2
0
1
1
0
1
1
1
1
0
0
1
0
0
3
0
1
0
2
0
0
1
1
0
1
2
0
0
1
5
2
0
2
0
1
0
1
1
1
0
0
2
2
0
0
0
0
2
0
0
2
2
0
3
1
1
2
1
1
1
1
2
2
1
1
1
2
0
1
2
1
1
2
1
1
0
2
2
2
1
1
0
2
2
1
0
0
0
0
1
2
1
2
1
1
1
0
1
0
2
2
1
2
0
1
0
2
2
0
2
2
2
1
2
2
1
3
1
0
1
0
2
2
0
1
1
2
1
0
0
0
1
1
1
1
1
2
0
0
0
0
2
1
1
1
0
0
0
2
0
1
0
0
1
0
1
1
0
2
2
1
0
0
0
1
0
0
1
1
1
2
0
0
0
0
2
2
0
0
0
2
0
2
1
1
1
0
1
0
1
1
1
0
2
1
0
2
0
1
0
1
0
0
1
1
1
0
1
2
1
0
2
2
2
2
0
1
1
1
0
1
2
0
1
2
0
1
1
2
1
0
0
1
0
0
2
0
0
2
0
1
0
1
2
0
0
0
1
2
1
0
2
2
1
2
1
0
0
0
1
1
3
0
1
1
2
1
1
1
2
0
1
0
5
1
0
1
1
1
0
1
4
1
2
1
2
0
0
0
0
1
2
1
2
2
1
1
0
1
0
1
0
2
0
0
3
0
1
3
1
0
2
2
0
0
0
1
2
1
1
0
2
1
1
0
1
1
0
2
2
3
0
3
1
0
0
1
1
1
1
2
0
1
2
1
2
1
1
0
0
1
0
0
2
1
1
2
0
1
2
0
1
2
0
1
0
1
0
1
0
1
1
1
2
1
1
0
0
0
0
2
2
2
0
1
0
0
1
2
0
0
1
2
1
0
1
2
1
0
1
1
0
0
1
1
1
1
2
1
0
1
1
1
2
1
0
1
0
0
1
0
1
1
2
0
0
1
1
1
2
0
1
1
2
1
1
2
1
0
1
0
0
0
0
0
1
2
0
0
0
1
1
1
1
1
0
0
2
1
2
2
1
0
0
0
0
0
2
1
2
0
1
0
3
0
0
2
2
0
0
1
1
0
0
2
0
0
0
0
0
1
1
0
1
0
0
0
2
1
2
1
0
1
0
1
1
0
0
0
0
0
0
1
2
1
0
2
2
0
1
1
1
2
1
2
1
1
1
0
0
2
0
0
0
0
0
1
1
2
0
2
1
0
1
0
1
0
0
0
1
1
1
1
0
0
0
0
3
1
0
1
1
1
1
1
0
1
0
0
1
2
0
1
0
0
0
1
0
2
2
1
1
1
2
0
1
2
1
1
0
2
0
2
2
1
0
0
1
1
1
1
1
2
1
0
2
2
1
0
1
2
1
0
1
0
1
1
0
0
0
1
2
0
0
2
2
1
0
1
0
0
1
0
1
0
1
0
1
2
1
1
2
0
0
0
1
1
2
1
1
0
0
1
1
0
1
2
0
1
2
1
0
1
1
0
0
2
0
1
2
1
0
2
2
1
1
0
1
0
0
2
2
0
1
0
2
2
2
0
1
1
1
0
1
1
2
2
0
0
1
2
1
2
1
1
0
2
1
0
0
2
1
1
3
1
2
1
0
1
1
0
0
0
2
1
2
2
0
2
1
2
0
0
2
0
2
2
3
1
0
1
1
1
1
1
0
1
1
0
3
1
0
0
1
0
2
1
1
1
1
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
1
1
0
1
0
1
1
0
1
0
0
0
2
2
0
2
2
1
1
0
2
2
0
1
1
2
2
1
0
0
2
0
1
0
0
0
1
2
1
2
0
2
0
2
0
1
0
2
1
1
0
0
0
0
1
1
1
1
0
0
0
2
1
0
1
0
1
0
1
1
1
0
0
0
0
0
0
0
1
2
1
1
0
1
0
0
1
3
2
1
0
2
1
0
1
1
1
1
0
2
2
2
1
2
2
0
0
0
2
0
0
2
1
1
0
3
1
1
0
1
1
0
0
2
0
0
0
0
0
0
0
0
1
1
2
2
1
0
0
0
1
2
1
1
0
1
1
2
1
2
1
1
1
1
2
1
0
0
1
2
2
1
2
2
2
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
1
2
2
1
1
1
1
0
0
0
2
1
1
1
0
2
2
0
7
1
2
1
0
1
0
1
2
0
1
2
0
2
0
2
1
2
1
1
1
0
1
0
1
0
0
0
2
0
0
0
1
2
2
0
0
0
1
0
1
1
0
1
2
2
1
1
1
0
0
1
1
0
0
0
0
1
1
1
6
1
0
2
0
1
0
2
1
2
0
0
1
2
1
0
2
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
1
1
1
2
1
0
2
2
0
0
0
0
0
1
0
1
1
1
0
1
1
2
2
0
2
0
0
0
2
2
0
0
0
0
2
0
0
1
0
0
0
1
0
0
1
0
2
0
0
0
1
0
0
2
1
1
0
0
1
1
1
6
0
1
0
1
1
1
0
1
1
0
1
1
1
1
1
1
2
0
1
2
0
0
0
0
1
0
0
1
1
0
1
1
0
0
1
1
1
2
0
2
0
1
1
2
0
1
0
1
2
1
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
1
0
2
2
1
0
0
1
0
1
2
1
1
1
2
1
2
2
0
1
1
0
1
2
1
0
4
0
1
0
0
0
0
1
0
0
1
1
0
0
0
1
1
0
1
1
1
1
2
0
0
1
1
2
1
0
1
1
2
1
2
1
1
2
1
1
1
2
1
0
1
2
0
1
2
2
0
0
0
2
0
2
1
2
1
1
0
0
0
0
0
2
0
1
1
0
0
2
0
0
0
1
2
0
1
0
2
0
0
1
1
2
1
0
2
1
0
0
1
1
1
1
0
0
2
1
1
0
2
1
1
2
1
1
2
2
0
0
2
0
0
0
1
2
1
2
1
0
1
0
1
0
1
1
1
2
1
2
2
1
1
0
1
2
1
0
0
2
1
2
2
1
0
2
2
1
1
0
2
0
1
1
2
3
0
1
2
1
1
0
1
1
1
0
2
1
1
0
0
1
0
2
0
1
0
0
0
2
1
0
0
1
1
0
2
0
1
2
0
2
1
0
0
1
0
2
0
2
1
1
2
0
1
2
1
0
1
1
2
1
1
0
1
1
1
0
1
1
0
1
1
2
0
0
8
0
1
0
0
0
2
1
0
0
0
2
2
2
0
0
0
1
0
1
0
1
2
2
1
0
1
0
2
0
1
0
0
2
0
1
1
2
0
1
2
0
0
0
0
1
1
0
1
1
0
0
1
1
1
2
1
1
2
0
0
1
1
2
0
1
0
1
0
2
2
0
1
1
1
1
2
1
0
3
0
0
1
1
3
1
1
1
0
0
0
2
1
1
1
0
0
0
0
0
0
2
1
1
1
1
0
0
1
0
0
2
1
2
0
0
2
2
0
1
0
1
1
0
0
2
1
0
2
1
1
2
0
2
1
0
0
1
4
1
3
1
1
1
1
0
1
2
3
2
0
0
0
2
1
0
2
1
1
0
0
1
0
1
0
1
1
0
1
0
0
2
1
0
2
2
1
1
2
1
1
0
2
2
1
0
0
1
0
0
0
0
1
1
1
2
0
1
1
0
1
2
1
0
0
0
0
0
2
2
0
1
0
1
0
0
1
0
1
2
1
2
0
2
2
1
0
2
2
2
1
1
1
1
1
0
2
0
1
0
1
1
0
0
0
0
1
1
2
1
1
1
1
0
0
1
1
1
2
2
1
1
0
1
0
1
1
1
1
0
1
0
1
1
0
0
1
1
1
2
0
2
1
0
2
0
0
1
2
2
0
2
3
0
0
0
0
1
0
0
1
2
1
1
1
0
1
1
1
1
0
0
0
2
2
1
0
0
1
0
0
2
2
1
2
0
1
3
0
0
1
2
1
2
0
1
1
0
0
0
1
1
1
1
0
1
2
0
1
0
2
1
1
0
2
2
0
2
1
0
1
0
1
0
2
1
0
0
1
0
0
1
1
1
1
0
0
0
0
1
1
1
1
0
1
1
2
1
0
1
1
1
2
0
2
1
0
2
0
1
0
1
1
0
1
0
2
0
0
1
0
0
1
1
2
1
2
2
1
0
2
1
1
0
1
2
0
0
0
1
0
2
2
2
0
2
2
1
0
0
0
2
1
1
0
2
1
1
0
1
0
1
1
1
1
0
1
1
0
1
1
1
1
0
0
1
0
1
1
1
1
0
1
1
0
0
0
1
3
1
0
2
1
1
0
1
0
1
1
0
1
0
1
2
0
1
0
2
0
0
1
1
2
0
2
0
1
0
1
0
0
0
1
2
6
2
1
0
1
2
0
1
0
0
1
1
1
0
1
0
1
2
2
1
0
0
2
0
1
0
1
0
0
1
0
1
1
0
0
1
2
1
1
2
2
2
1
0
0
0
2
1
4
0
0
1
1
2
1
1
2
2
1
0
1
0
2
2
1
0
1
0
1
1
1
0
3
2
0
1
0
1
0
1
1
0
1
2
0
0
1
1
0
0
2
2
0
0
0
1
1
0
1
1
2
0
0
0
0
1
1
0
1
0
3
0
1
2
1
1
0
2
2
1
0
3
1
1
0
0
2
1
1
0
1
1
3
0
0
2
2
0
1
1
1
0
1
0
2
1
0
2
0
0
1
1
0
1
1
1
2
1
1
2
1
1
2
1
1
1
2
2
1
0
2
2
2
0
0
1
1
0
2
1
0
0
2
0
2
1
0
0
1
0
0
0
3
2
0
1
1
2
2
1
0
1
0
1
1
0
0
0
0
2
0
0
2
2
0
1
1
2
1
0
1
2
0
2
1
1
0
0
1
0
1
0
1
1
2
1
1
2
2
0
1
0
1
0
2
0
0
1
2
1
2
0
0
0
0
1
3
2
0
0
1
1
1
2
0
0
0
1
3
2
1
0
0
1
1
1
0
2
2
2
1
0
1
0
0
0
1
1
1
0
0
2
0
1
0
1
0
1
1
0
2
1
0
1
1
0
1
1
0
0
2
0
1
1
0
1
2
1
1
1
1
0
0
0
2
0
0
1
1
0
1
0
0
1
1
1
3
0
2
0
0
1
3
2
1
2
2
0
0
0
1
0
0
0
2
0
0
1
1
0
0
0
1
2
1
0
1
1
0
2
0
2
2
1
1
1
1
0
0
1
0
0
1
3
1
3
0
0
2
0
2
0
0
0
0
0
1
0
0
0
1
2
2
0
0
1
1
1
3
1
1
1
1
1
1
0
0
0
1
2
0
1
1
2
1
2
0
1
1
1
1
1
1
3
2
0
0
2
1
0
1
0
1
2
0
2
0
0
1
0
0
0
1
0
0
0
1
0
0
1
2
2
0
1
1
1
1
1
0
0
0
0
0
0
2
0
1
2
0
0
1
0
1
2
2
0
2
0
1
0
0
2
1
0
2
0
2
0
0
0
0
0
2
1
2
2
1
0
1
2
1
2
2
1
1
1
1
0
1
0
0
2
0
1
0
3
0
0
1
1
1
2
0
1
1
1
2
2
2
0
2
2
1
2
1
2
0
0
2
2
2
0
1
0
1
1
2
0
2
0
1
0
1
1
2
0
2
0
0
1
1
0
1
0
0
0
1
0
1
0
1
2
0
1
0
1
1
1
1
1
1
2
1
2
2
1
0
1
1
0
1
0
1
0
2
0
1
1
1
2
0
1
1
1
0
2
1
1
2
1
2
0
0
0
0
0
0
1
1
5
2
0
1
0
2
1
1
0
2
1
2
1
0
1
0
1
1
0
0
2
0
2
0
2
0
0
0
0
1
2
1
0
2
1
0
2
1
2
2
1
0
1
0
0
1
0
1
0
2
1
1
0
0
0
1
0
1
1
1
1
0
0
0
1
0
1
0
0
1
1
0
0
2
0
1
2
0
2
1
1
2
1
2
2
0
0
0
2
2
0
1
0
0
1
0
0
0
1
1
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
2
2
0
2
1
1
0
1
1
1
1
1
3
0
2
0
1
1
0
1
2
0
0
0
2
0
1
0
1
2
0
0
3
1
1
2
2
1
1
1
0
1
2
1
0
1
1
1
1
0
2
0
0
1
1
2
2
0
0
1
1
0
0
0
0
2
0
0
1
2
0
2
2
1
0
1
0
1
0
0
0
0
2
0
0
2
2
2
1
0
1
0
1
1
0
2
1
0
1
0
0
2
0
1
0
1
1
0
0
3
1
0
0
0
0
1
1
1
2
0
0
0
1
3
1
0
1
1
2
0
0
1
1
2
0
2
1
0
1
2
0
1
2
0
1
1
1
2
1
0
1
1
0
1
1
1
1
1
1
2
1
0
0
1
1
0
0
1
2
0
0
2
0
1
1
1
1
0
2
1
1
0
2
0
0
2
0
0
0
1
0
2
1
0
0
1
1
1
2
1
0
0
1
1
0
1
1
0
1
0
1
3
0
1
1
1
0
2
1
0
0
1
1
0
2
1
1
1
1
3
0
0
1
1
1
1
0
1
0
1
0
1
0
0
0
1
1
0
0
0
2
0
0
2
0
0
1
1
1
2
2
0
1
1
2
1
0
1
0
0
1
2
1
0
1
0
2
2
2
0
0
2
1
0
0
0
0
1
1
0
0
2
0
1
1
0
0
1
0
1
2
0
0
1
1
0
2
2
0
2
2
2
2
1
1
0
0
1
0
2
2
0
1
0
1
2
0
1
2
1
2
1
1
2
1
0
0
0
0
0
1
2
1
1
1
2
1
0
0
2
0
1
0
2
2
0
1
2
1
0
1
0
1
0
1
2
2
2
1
2
0
1
1
0
0
1
1
2
0
1
0
0
0
2
0
2
1
1
0
2
0
0
0
0
0
0
1
1
0
2
0
0
1
1
0
1
1
1
0
0
2
0
0
4
0
1
1
2
2
0
0
2
1
1
2
1
0
0
3
1
2
1
1
1
0
1
1
0
1
1
1
2
1
1
0
1
0
1
3
2
0
2
1
0
1
0
1
0
2
1
0
0
1
0
0
0
2
4
1
2
0
2
1
0
0
1
1
1
1
1
0
2
0
1
0
2
1
0
1
1
0
1
0
1
1
0
0
0
1
0
0
3
2
1
0
0
1
1
1
2
2
1
2
1
0
3
0
2
1
0
2
0
1
0
0
0
2
0
1
0
1
0
2
0
1
1
2
2
2
1
0
2
1
3
2
1
1
1
0
1
0
1
1
0
0
4
1
1
1
0
0
1
0
1
0
0
2
2
1
2
0
1
1
1
1
2
0
1
2
1
1
1
1
1
0
0
1
2
1
0
0
2
0
1
1
1
2
1
0
2
1
1
2
0
0
1
1
0
0
0
0
0
0
0
1
2
0
1
0
1
1
0
0
0
1
1
0
1
0
1
0
0
1
0
0
1
2
1
1
1
1
0
3
0
1
1
0
1
2
1
0
1
0
2
0
1
1
2
0
0
0
1
1
0
0
1
0
0
0
2
2
0
1
1
1
1
1
0
0
1
1
0
1
0
0
1
0
0
0
0
1
1
1
0
0
2
1
1
2
0
1
2
2
2
1
1
0
0
0
0
0
1
1
1
1
0
2
2
2
2
1
2
0
1
2
0
0
0
1
1
2
1
1
0
1
1
1
2
1
1
1
2
0
1
1
0
2
0
0
1
0
1
0
1
2
3
1
1
0
0
1
1
0
0
1
0
1
2
2
0
2
0
0
1
0
1
1
1
0
2
2
1
0
1
0
0
2
2
0
1
2
2
0
2
2
0
2
0
2
2
1
0
0
0
1
2
0
2
2
1
1
1
0
2
1
1
2
0
1
1
2
2
1
0
1
2
0
1
2
2
2
0
1
0
1
1
0
2
1
2
0
0
2
1
1
1
0
1
0
2
1
0
1
1
0
1
0
0
1
1
2
0
0
0
0
2
0
0
1
2
1
1
3
0
1
1
1
2
1
0
0
1
2
1
1
0
0
0
1
1
2
1
0
0
1
2
2
0
0
0
2
1
1
0
1
1
1
0
2
2
2
1
0
0
0
1
0
0
0
2
1
1
2
0
3
3
0
0
0
2
2
1
1
0
2
1
0
0
0
2
2
2
1
0
0
2
1
0
1
1
1
1
1
0
0
0
0
0
2
1
2
0
2
1
1
1
0
0
1
2
0
2
0
0
0
2
1
1
0
0
1
0
1
0
0
0
0
3
1
1
0
1
0
3
2
0
0
3
0
2
2
0
1
1
2
0
1
0
0
2
0
2
0
0
1
2
0
0
0
0
1
1
1
0
1
0
1
1
1
1
0
2
1
1
1
3
2
1
1
1
1
0
1
0
1
3
0
1
1
2
0
2
0
1
1
0
1
2
1
1
0
0
1
0
0
0
1
1
1
0
2
0
2
0
0
0
2
3
1
1
1
2
2
1
0
0
1
2
0
0
1
1
2
1
2
2
2
2
1
2
2
1
0
2
0
1
2
1
2
0
0
1
0
1
1
2
0
2
1
1
0
1
2
2
2
1
0
1
0
2
2
0
2
2
1
2
1
2
1
2
1
1
1
1
0
1
1
0
0
1
1
0
1
2
1
0
1
1
1
1
0
1
0
1
2
1
0
1
0
0
2
1
0
0
1
0
2
1
0
1
2
0
0
1
0
1
0
0
1
2
0
2
0
0
2
1
1
0
1
1
0
2
0
1
2
1
0
0
2
0
0
1
2
1
1
1
2
1
0
1
1
1
1
0
1
1
0
1
2
0
1
1
1
1
2
0
2
1
0
2
0
1
0
1
2
0
1
1
0
2
1
2
2
0
0
2
2
1
0
1
1
0
2
1
0
1
1
1
1
0
0
0
0
2
0
2
1
0
1
0
1
1
0
1
1
1
1
0
1
2
2
1
0
0
2
0
0
2
1
1
0
0
1
1
1
4
1
1
1
1
2
1
0
1
0
2
0
1
1
2
2
1
2
0
1
0
0
0
0
1
0
0
1
0
2
0
2
0
2
2
0
0
0
1
1
2
3
0
0
3
0
1
0
1
0
0
0
2
1
2
0
1
0
1
2
0
0
1
2
2
2
1
0
0
1
0
0
2
1
0
0
1
0
0
0
1
0
0
0
1
1
0
2
0
1
3
0
0
2
1
2
0
0
1
0
0
0
0
0
1
1
0
1
0
0
1
1
0
2
1
1
0
0
0
2
2
1
1
0
0
1
0
2
0
1
1
2
0
0
0
2
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
2
0
1
0
0
1
1
1
1
2
1
0
0
1
0
2
1
0
1
2
1
0
0
0
0
2
0
1
0
0
2
1
2
1
1
2
0
2
2
0
0
2
1
2
1
1
1
2
0
0
0
0
2
0
0
1
0
2
1
0
1
2
1
1
2
2
0
2
2
0
1
1
0
1
0
1
1
2
1
2
0
0
1
0
0
0
0
2
2
0
2
1
1
3
1
2
1
1
1
0
1
0
1
2
2
0
1
0
1
1
0
0
1
2
0
1
2
3
1
2
1
2
2
1
1
1
0
1
0
0
1
2
0
2
2
1
1
0
1
1
0
2
0
0
2
1
2
0
3
1
0
0
2
0
2
0
0
1
0
0
0
1
1
0
1
2
0
0
1
1
1
2
1
1
0
0
2
2
0
2
1
1
0
2
0
0
1
1
1
0
1
0
1
1
0
0
1
1
1
1
2
0
2
1
1
1
0
2
1
1
0
1
0
0
2
1
0
1
1
0
1
1
2
2
1
1
0
1
1
1
0
1
0
1
0
0
2
1
1
0
1
0
1
0
0
0
1
2
0
1
0
0
1
1
1
2
1
0
0
1
0
1
2
1
1
1
0
1
0
2
2
0
1
1
1
2
1
0
1
1
0
1
1
0
1
0
1
0
1
0
2
0
0
0
0
0
0
0
1
1
2
0
0
2
2
0
2
2
1
1
0
0
0
1
0
1
0
0
0
1
0
1
2
1
1
1
1
0
0
0
2
1
0
0
0
1
1
1
1
0
3
0
1
1
1
2
1
1
1
0
0
2
0
0
1
0
2
1
1
2
2
1
1
0
1
1
2
2
0
2
2
2
2
0
1
0
1
0
2
2
0
1
2
0
1
1
1
3
1
1
0
2
1
1
0
0
1
1
0
1
2
2
0
1
0
0
0
1
0
0
0
2
0
0
3
2
0
2
2
0
0
2
1
1
0
1
1
1
0
1
1
0
0
2
2
2
0
0
0
1
2
1
0
0
0
2
2
0
0
1
1
0
1
1
1
2
0
0
1
0
1
1
1
1
2
1
0
0
0
2
0
1
0
1
2
0
1
0
2
0
1
0
1
2
0
0
0
2
2
2
0
1
2
1
2
1
0
0
1
2
0
0
2
2
0
1
0
1
1
1
2
0
0
2
1
1
1
0
2
0
0
2
0
0
1
2
2
0
1
1
1
1
0
0
0
2
1
2
1
1
1
1
0
0
1
1
0
0
1
1
0
3
0
2
0
5
1
0
2
1
0
2
0
2
0
0
0
2
1
2
2
1
2
1
0
1
2
2
2
1
0
0
1
2
2
1
0
2
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
1
1
0
2
0
1
1
0
0
1
1
1
0
1
1
0
0
2
0
1
0
1
0
1
2
1
2
0
2
0
1
0
2
0
0
1
0
2
2
2
0
2
0
1
2
1
1
2
1
2
1
0
1
2
1
0
3
1
1
2
2
1
0
1
0
1
0
2
1
2
1
1
0
2
1
4
1
1
0
0
2
0
0
0
2
1
1
1
2
0
1
1
0
0
0
1
1
0
0
1
0
0
2
1
1
0
0
0
0
0
2
0
1
0
2
0
0
1
1
1
1
1
2
1
1
2
0
0
2
0
0
2
2
1
1
1
1
1
0
2
2
0
2
2
0
2
1
1
1
2
0
2
2
0
2
2
0
2
1
0
1
0
0
2
1
1
0
0
0
0
2
1
0
2
0
0
0
2
1
0
0
2
0
1
2
1
0
0
0
2
0
1
0
0
1
0
0
0
1
0
0
2
1
0
1
1
1
1
0
0
0
0
2
0
1
1
0
1
2
1
2
0
1
0
1
0
2
1
1
0
0
0
1
1
1
1
1
1
0
2
0
0
0
1
0
0
2
0
0
2
1
1
0
1
0
0
2
2
1
0
2
1
2
1
1
0
1
2
1
0
0
0
1
1
1
1
3
1
0
1
0
0
0
2
1
0
1
0
0
2
0
2
1
2
5
1
2
0
1
0
0
1
1
0
0
0
0
2
0
1
4
2
1
1
1
1
1
1
1
0
1
1
2
1
1
1
0
0
1
0
1
1
0
7
2
0
1
0
0
0
2
0
0
2
0
3
1
0
1
0
0
2
2
1
0
0
1
0
1
1
0
1
0
1
0
0
1
0
0
1
1
0
2
0
2
0
0
2
1
0
1
1
1
1
1
0
0
2
2
2
0
1
1
0
1
3
1
0
0
1
2
1
2
1
1
0
0
1
1
1
0
0
1
1
3
1
1
2
0
0
1
2
0
0
1
1
1
0
2
2
1
0
0
1
1
0
1
2
0
0
2
2
1
3
1
0
2
2
1
0
0
1
0
0
2
0
0
1
0
0
1
0
2
1
1
0
1
1
1
0
2
1
0
0
2
0
1
1
3
1
0
1
2
0
0
0
2
1
0
0
1
2
1
1
0
1
0
2
1
2
1
0
0
0
2
1
1
0
0
1
0
2
0
0
1
0
1
1
2
2
0
1
2
2
0
1
1
0
2
5
0
2
0
2
0
1
1
1
0
0
2
2
1
1
1
1
1
1
0
1
2
1
1
1
0
0
0
1
1
0
2
2
3
1
0
1
1
0
1
0
1
1
0
0
2
0
2
1
0
0
2
0
1
0
0
1
0
1
2
1
0
1
1
2
0
2
1
0
0
1
2
0
1
2
0
1
2
1
1
0
1
1
1
2
1
1
0
0
1
2
1
0
2
0
3
1
1
1
2
2
0
1
1
0
2
0
1
1
1
2
0
0
1
0
1
2
1
0
0
1
0
6
2
2
0
1
0
1
0
2
1
0
1
1
2
0
2
0
2
2
1
1
0
0
2
0
2
0
1
0
1
1
1
0
1
2
0
0
0
0
2
1
1
2
0
0
1
0
0
1
1
0
1
2
1
1
1
1
0
1
1
2
2
0
2
1
1
0
1
0
0
5
1
2
0
0
1
0
2
2
2
0
0
1
2
0
1
1
1
1
1
2
1
1
1
1
1
0
1
0
0
1
0
0
1
1
1
1
0
0
2
1
2
1
1
2
2
0
1
2
0
0
1
1
2
0
13
2
2
2
0
2
1
1
1
1
0
0
0
3
1
2
0
1
2
1
1
0
0
4
1
0
1
2
0
0
0
1
1
0
2
1
0
0
1
1
2
1
2
0
1
0
1
0
0
1
0
0
2
0
1
0
1
1
0
0
1
1
0
2
0
1
0
2
1
0
0
1
0
2
0
0
1
0
1
0
0
0
1
1
0
0
1
1
0
0
0
1
0
0
0
1
0
2
0
2
0
2
1
1
2
0
1
0
1
2
0
1
2
0
0
0
1
1
0
2
0
2
2
7
0
0
1
0
1
0
0
2
2
1
1
2
0
0
1
0
2
0
1
2
1
0
1
0
2
0
1
1
1
1
0
1
2
1
0
0
2
2
2
1
1
1
0
1
0
1
0
0
1
0
0
2
1
2
1
1
1
0
1
0
0
1
0
0
1
1
1
2
2
2
2
2
0
0
1
0
1
1
1
2
2
0
0
2
1
1
1
1
0
0
0
2
1
0
0
1
1
2
1
0
0
1
0
1
1
1
0
0
1
2
0
2
2
2
1
1
2
1
0
1
1
2
1
1
0
1
1
1
0
1
1
0
0
1
0
2
0
0
2
0
0
1
3
1
0
1
1
1
2
0
0
0
0
2
0
1
1
0
0
1
0
2
1
1
2
1
1
1
0
1
2
2
0
0
0
0
2
0
1
1
0
1
3
0
1
0
2
0
1
1
1
1
1
1
0
1
1
0
0
2
0
0
0
0
1
1
2
2
1
2
1
1
0
1
2
2
0
0
1
1
0
2
1
1
2
0
1
0
1
1
1
2
1
0
1
1
1
0
1
1
2
0
1
0
0
0
2
1
1
0
0
1
1
1
1
0
0
1
0
1
0
1
2
1
0
1
2
2
2
2
1
0
1
0
1
0
0
1
0
1
3
2
0
1
0
2
2
2
1
0
1
2
0
3
1
1
0
1
2
0
1
0
0
0
2
0
2
2
2
1
0
0
0
0
0
1
1
1
0
1
0
2
1
1
2
1
2
2
1
2
0
1
2
0
0
1
0
2
1
2
0
0
1
2
1
1
0
1
2
0
1
0
2
1
1
1
2
1
0
2
2
1
2
2
1
2
1
1
0
1
2
0
0
0
2
0
0
0
1
0
1
0
1
0
2
1
0
1
0
0
0
0
2
0
0
0
1
1
2
2
2
0
1
1
1
2
1
0
0
0
0
2
0
0
2
2
1
2
1
1
0
2
2
0
0
1
1
1
1
1
2
2
2
1
1
1
1
2
0
0
0
1
0
0
1
0
0
0
2
0
2
0
1
2
1
2
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
2
1
0
2
2
0
0
1
1
1
0
0
2
1
0
0
0
0
0
1
2
1
0
2
1
1
2
1
0
0
1
0
1
1
2
1
0
1
0
0
2
0
0
0
1
0
2
0
0
1
0
1
1
2
2
0
2
2
1
1
2
0
2
2
1
1
1
0
0
0
2
0
2
1
2
0
2
0
1
1
0
0
1
1
0
0
1
0
1
1
0
1
0
1
0
2
1
0
0
0
1
1
1
3
0
0
1
2
0
0
2
2
0
0
1
0
0
1
1
2
2
0
1
1
1
0
0
1
1
1
0
2
1
1
2
1
1
0
2
0
2
1
2
0
0
0
2
0
0
0
1
1
0
0
0
1
1
2
1
0
0
0
0
0
0
2
1
1
1
0
2
1
0
1
0
1
1
1
0
2
1
0
1
0
1
0
0
0
0
1
0
0
1
2
2
1
1
2
1
2
0
0
2
1
0
1
1
1
2
1
0
0
0
0
1
0
0
0
0
0
0
2
2
0
3
2
2
1
2
0
0
2
1
0
3
1
1
1
1
2
3
0
1
1
1
0
1
0
0
0
0
0
0
0
0
2
2
1
1
2
0
1
0
0
1
0
1
0
0
1
1
0
2
0
2
0
0
1
2
1
0
1
1
3
2
1
1
0
1
0
3
0
1
9
2
2
1
0
2
2
0
1
1
1
1
1
2
0
0
1
2
0
1
0
1
1
0
0
0
0
1
0
1
1
1
0
1
2
1
0
2
0
0
1
1
2
1
0
0
0
1
1
0
0
2
1
0
0
1
2
1
0
1
0
1
1
0
1
0
1
1
1
1
2
1
1
0
1
1
1
1
0
0
1
0
0
2
1
0
1
0
0
1
0
1
0
1
1
1
0
1
1
0
1
0
1
0
1
1
1
2
1
1
0
1
1
2
1
1
2
1
2
0
1
2
4
0
1
1
1
1
2
1
1
0
2
1
1
0
1
2
0
1
1
1
1
1
1
1
1
3
1
2
2
2
0
0
2
1
1
1
1
0
0
1
1
1
2
2
0
1
2
0
2
0
0
1
2
1
1
1
1
2
1
4
2
2
0
1
0
0
0
2
1
2
1
2
1
0
1
0
0
1
0
0
4
0
1
2
0
2
0
2
0
2
0
1
4
0
0
1
2
0
0
1
2
1
1
0
1
0
2
2
2
2
0
0
0
0
0
2
2
2
2
1
2
0
0
1
0
1
1
1
0
0
2
0
0
1
0
2
1
1
1
0
1
1
0
1
2
2
2
0
0
1
0
1
0
0
2
2
2
1
1
0
1
0
1
2
2
2
0
0
0
1
0
1
2
2
0
0
2
0
1
2
1
2
1
2
0
2
1
0
0
0
0
3
2
2
0
2
1
2
1
1
2
1
2
2
0
0
1
1
1
0
1
0
0
0
2
1
2
1
0
1
0
0
1
1
0
2
2
1
0
0
1
0
0
1
0
2
1
0
1
2
1
0
1
0
2
0
1
1
0
0
1
1
2
0
1
2
0
1
1
1
1
0
2
2
0
1
2
0
0
0
1
0
0
1
0
2
0
1
0
1
1
0
2
1
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
1
1
0
1
2
0
0
0
2
2
2
0
0
1
0
2
2
0
1
0
0
1
0
0
1
0
0
1
2
1
2
1
2
1
2
1
1
5
1
0
0
1
0
1
1
1
2
1
0
2
1
2
1
0
1
1
0
1
0
2
0
1
2
1
2
2
0
1
2
1
0
1
2
0
1
2
0
0
0
0
0
1
1
1
1
2
0
0
1
1
0
0
3
2
1
0
1
2
1
1
1
0
0
2
1
0
0
1
2
1
1
1
0
0
2
1
1
0
2
1
0
1
2
1
1
0
0
1
2
2
0
0
0
1
0
0
1
0
2
0
1
0
0
0
2
1
1
0
0
0
2
0
1
2
0
2
1
1
1
2
1
1
0
0
1
0
2
2
0
1
0
1
0
1
1
1
0
1
1
1
2
2
1
2
0
3
1
2
1
1
1
1
1
0
2
2
2
1
1
0
0
0
0
2
1
2
0
1
0
1
1
2
2
1
1
1
2
2
0
3
1
1
0
1
0
1
0
2
2
2
2
2
2
0
1
0
0
0
0
1
0
0
1
0
0
2
1
1
1
1
2
0
0
1
1
1
1
1
2
0
0
1
0
2
0
2
0
2
1
0
1
1
2
1
0
0
1
2
0
0
1
2
0
1
1
0
0
1
1
0
1
2
0
0
1
0
0
1
1
2
1
0
2
0
1
2
0
0
1
0
3
1
0
2
2
0
1
1
0
0
2
1
0
0
1
0
0
2
1
1
0
2
0
0
1
0
0
2
2
1
2
1
1
3
0
2
0
2
2
0
0
0
1
0
2
0
2
1
3
2
1
1
1
0
0
0
1
0
2
1
0
0
1
0
0
2
0
1
0
1
1
0
0
1
1
0
2
2
1
0
1
0
0
0
1
0
1
1
2
0
0
0
0
1
0
2
1
1
0
2
1
0
1
2
2
0
0
2
1
0
0
0
0
1
0
0
0
1
2
1
1
1
0
1
4
1
1
0
0
1
0
1
0
0
0
2
2
0
2
1
1
2
0
0
0
1
0
1
0
0
0
1
1
2
0
1
1
1
2
0
1
1
1
0
1
0
0
1
1
1
3
0
0
0
2
0
0
1
2
0
2
1
0
2
1
2
0
2
1
1
0
0
2
1
2
1
2
3
1
1
1
0
2
0
1
0
1
1
1
0
1
0
3
0
0
1
0
1
1
2
1
1
1
1
2
2
1
1
0
1
1
1
1
0
0
1
1
1
0
3
1
1
1
1
0
0
0
1
0
2
0
3
1
0
1
0
2
1
1
2
0
0
1
1
1
0
0
1
0
2
0
0
0
0
1
1
1
1
1
0
1
0
2
0
2
1
1
2
2
1
0
1
1
0
1
1
0
1
2
0
3
0
2
1
1
1
1
1
0
1
0
2
0
0
2
1
0
1
0
1
1
1
1
0
0
2
2
1
0
0
2
1
0
1
2
0
0
0
0
1
2
0
1
2
0
3
0
2
0
1
0
0
2
0
1
1
1
1
0
0
2
0
2
4
0
2
0
2
2
1
1
1
2
1
0
0
1
1
1
2
0
0
0
0
2
1
1
1
0
1
0
0
0
0
1
2
0
1
1
0
2
0
1
2
1
0
2
1
2
0
0
1
0
0
1
2
0
1
1
2
1
0
0
1
1
0
0
2
0
0
0
0
0
0
2
2
1
1
0
0
0
0
2
0
2
1
5
2
1
2
2
0
2
1
0
1
2
0
0
0
1
1
0
2
0
0
0
0
0
1
2
0
0
2
0
0
1
0
1
0
0
1
1
0
2
0
1
2
0
0
0
0
1
0
5
0
1
2
1
0
1
1
1
1
0
1
1
0
1
0
0
0
0
2
0
0
1
0
3
2
0
0
0
2
2
0
1
2
1
0
1
1
2
1
0
1
0
1
0
1
1
1
1
1
0
1
0
0
0
1
0
1
0
1
0
1
0
1
1
0
3
2
0
2
0
0
0
1
0
1
2
1
2
0
1
1
1
2
0
1
0
0
0
0
0
0
0
3
1
0
1
0
1
1
0
1
1
2
1
2
0
1
0
1
0
1
2
1
0
1
1
0
0
1
2
1
1
0
1
0
2
1
1
0
1
2
0
2
1
1
0
0
1
0
2
0
2
2
1
1
1
2
0
1
0
1
0
0
0
0
1
2
1
1
0
0
0
1
2
1
0
1
0
1
1
1
1
0
0
0
0
2
1
0
0
1
2
1
0
0
1
0
1
0
1
1
0
0
0
1
2
0
1
1
0
0
1
0
0
4
0
2
2
0
1
2
1
0
0
1
0
2
2
0
1
0
1
1
0
1
0
1
1
1
1
0
1
1
1
2
0
1
1
0
2
2
2
0
1
2
1
0
4
2
2
0
1
1
0
1
2
2
0
2
2
0
2
2
0
0
1
0
1
0
1
0
0
1
1
1
2
2
1
0
1
1
0
0
2
1
2
0
0
2
1
2
0
0
1
0
2
0
0
0
0
2
0
1
0
1
0
0
2
2
1
1
0
0
2
0
0
1
1
0
0
1
1
2
2
0
2
2
2
0
0
1
2
0
1
1
0
2
0
1
0
1
0
2
0
0
1
0
2
2
1
1
1
2
0
2
0
0
3
2
1
1
1
0
2
1
0
0
2
1
1
1
1
2
1
0
2
0
1
0
1
2
2
1
0
2
1
2
0
1
0
1
2
2
0
2
2
0
0
2
0
0
2
2
0
1
0
2
0
1
0
2
1
0
0
1
1
4
1
0
2
3
1
0
0
2
0
0
2
2
0
1
0
2
1
1
1
1
4
1
2
1
1
1
2
0
0
0
1
2
1
1
2
1
1
1
0
0
2
1
1
2
0
1
1
0
0
2
1
1
0
2
0
0
0
0
1
3
0
1
1
2
0
2
1
0
0
1
0
0
0
0
1
1
0
0
1
2
1
1
2
0
0
3
2
0
2
0
1
2
1
1
0
0
1
2
0
2
0
2
2
1
0
0
2
2
2
1
0
0
2
0
0
0
0
1
0
1
0
0
0
1
2
1
2
0
2
2
1
1
1
2
1
0
2
0
2
1
0
0
3
1
1
0
0
0
1
1
0
0
0
0
1
0
0
1
2
2
1
0
1
0
1
0
1
2
1
1
1
1
1
0
0
1
2
1
2
1
0
3
0
0
0
1
1
2
2
2
0
0
0
0
2
1
1
0
1
0
0
1
0
1
2
3
0
1
2
1
0
0
1
0
1
1
0
1
0
1
0
1
3
0
0
0
0
1
0
2
1
2
1
0
1
0
1
1
1
2
2
1
1
0
2
0
1
1
1
0
1
0
1
0
0
0
1
0
1
1
2
1
2
1
2
1
0
2
1
1
1
0
4
1
1
0
0
1
1
0
1
0
1
2
0
0
2
2
0
2
0
1
2
2
0
2
0
2
1
0
1
2
1
0
1
2
1
1
2
1
0
0
2
2
1
0
1
1
0
1
0
2
1
0
0
2
0
0
1
0
2
2
1
2
1
0
1
0
2
0
0
1
0
0
3
0
6
2
2
0
0
1
0
0
0
1
2
1
0
3
2
0
0
0
1
2
2
2
0
0
1
2
0
1
1
1
1
0
2
0
1
1
0
2
1
0
0
1
0
1
1
1
2
1
0
1
1
1
0
0
0
0
1
0
0
1
2
1
1
1
1
0
0
1
0
2
1
1
0
2
1
0
0
2
2
0
0
0
2
1
2
0
0
0
0
1
2
0
0
0
0
1
2
1
2
2
2
0
2
1
0
1
0
0
1
1
0
1
1
0
1
1
2
0
0
0
2
0
1
0
1
0
0
1
1
1
0
2
1
0
2
2
0
0
0
1
0
1
2
2
0
2
0
0
0
1
1
1
1
0
1
0
1
0
0
2
2
1
1
1
1
0
1
0
0
0
1
1
1
0
0
0
3
1
2
2
2
1
0
2
1
1
2
1
2
0
0
2
0
0
0
1
2
1
0
1
0
1
0
0
1
2
0
0
2
0
0
2
1
0
0
1
0
1
1
1
1
1
0
1
0
3
1
2
2
1
1
0
1
1
1
2
2
0
0
2
0
0
1
1
1
0
0
2
1
1
0
0
2
1
2
1
3
1
1
0
0
2
2
1
0
1
1
0
0
1
1
1
1
1
1
2
2
2
0
0
1
3
2
1
0
1
0
0
0
0
2
0
2
2
3
1
0
1
0
1
2
2
0
0
1
0
1
1
1
2
2
1
0
0
0
1
0
1
2
0
1
0
1
0
1
0
0
0
1
2
0
1
1
2
1
0
0
2
1
1
2
1
1
0
0
1
1
2
0
2
1
0
0
0
1
0
1
2
0
2
1
4
0
1
0
1
0
0
1
1
2
1
2
0
2
0
1
2
0
2
0
0
0
1
1
0
0
2
0
0
0
1
0
1
0
1
2
1
0
0
0
0
0
0
0
0
4
1
0
1
2
1
0
1
0
0
3
0
2
1
0
0
0
2
0
1
1
2
1
1
1
2
2
1
0
2
0
2
2
1
0
1
0
0
2
1
0
3
0
1
0
1
1
0
0
0
1
1
1
1
0
2
0
1
2
2
1
1
0
0
0
1
2
1
2
2
2
1
1
1
1
1
2
1
0
0
2
0
1
1
1
1
2
2
2
0
2
1
2
1
0
1
1
2
0
1
1
2
1
1
1
1
1
2
2
1
0
0
1
2
2
1
0
1
2
1
1
1
1
1
0
1
1
0
0
1
0
1
0
1
1
0
2
0
2
1
1
0
1
0
0
1
1
2
0
1
0
2
0
0
1
2
2
0
1
2
0
1
0
2
1
1
0
1
1
2
1
0
1
1
0
0
0
2
1
1
0
0
2
0
0
2
2
2
2
2
1
2
2
0
0
1
0
2
0
1
0
2
2
1
0
0
1
1
1
0
1
1
1
0
0
0
1
1
0
0
2
0
1
0
1
0
1
2
2
2
2
0
1
0
2
0
1
1
1
0
0
0
0
1
1
2
0
1
1
1
0
1
0
1
0
0
2
1
2
1
1
1
1
0
0
1
1
0
0
2
2
0
0
1
1
1
0
2
2
0
0
2
1
0
0
2
0
1
2
0
0
2
0
0
2
2
1
1
1
0
0
2
2
3
0
1
1
0
0
0
1
1
0
1
0
1
0
1
1
1
1
1
1
0
1
1
1
1
1
1
1
0
0
0
0
1
2
2
0
2
1
0
0
1
2
1
2
0
2
0
0
1
1
2
0
1
0
0
0
3
0
1
1
0
1
1
1
0
0
0
0
0
1
2
1
0
0
2
1
0
1
0
2
0
0
2
2
0
0
0
0
1
1
2
1
0
1
0
0
1
0
0
0
1
2
2
1
1
0
1
1
2
1
1
1
0
0
1
1
1
0
2
0
1
1
2
1
1
0
0
1
0
2
1
0
0
2
0
1
0
1
0
0
0
1
1
2
1
1
1
2
0
1
1
2
0
1
0
0
1
0
2
2
0
1
3
1
0
2
0
1
0
1
1
1
0
0
0
1
1
1
1
0
1
2
1
1
0
0
2
1
0
2
1
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
2
2
1
2
0
1
0
1
1
0
0
0
1
1
1
0
1
1
2
1
0
2
0
0
0
0
0
1
1
0
1
0
0
1
2
0
2
2
1
0
0
0
1
0
2
1
2
1
0
1
1
1
1
1
2
0
0
2
1
0
2
0
0
0
2
1
2
0
1
0
0
1
1
1
1
0
0
1
1
3
1
0
0
0
2
0
3
2
2
1
3
2
1
1
0
0
0
0
1
1
0
1
0
2
1
2
1
0
2
1
2
2
2
0
0
1
0
1
0
1
1
2
1
0
0
0
0
0
0
1
1
0
0
2
1
1
0
0
0
1
0
1
0
0
1
1
1
1
0
1
1
1
2
1
0
0
2
0
1
0
1
1
1
2
1
0
1
0
1
1
1
2
0
1
1
2
0
1
0
0
1
2
0
1
0
1
0
0
2
1
1
0
0
0
1
0
1
0
0
1
2
1
2
1
1
2
1
1
0
1
2
1
0
0
1
0
0
0
1
1
0
0
2
0
1
1
1
1
2
1
1
2
1
1
1
1
2
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
2
0
2
1
1
1
2
0
0
1
0
2
1
1
2
2
2
0
0
1
0
0
2
1
2
0
0
1
1
0
1
0
0
1
0
0
0
0
1
1
0
1
2
1
1
1
0
1
2
0
2
1
0
0
0
0
1
0
1
1
1
1
1
1
0
2
1
2
1
2
2
1
1
2
0
1
1
1
0
0
1
1
0
0
2
0
1
1
2
1
3
1
1
2
2
0
0
0
1
2
0
0
0
2
1
0
0
1
0
2
1
2
0
1
0
0
1
0
1
2
1
1
1
0
1
1
1
0
2
0
1
2
1
2
2
1
0
1
0
0
0
0
0
1
2
1
0
2
0
1
2
1
1
2
2
1
1
0
0
0
1
2
0
0
1
0
0
2
2
1
1
0
2
0
0
1
1
1
1
1
0
1
2
0
2
0
2
2
1
1
0
0
2
1
2
1
0
3
2
0
2
0
1
1
2
1
2
3
2
0
1
0
1
1
0
1
0
2
1
1
1
0
2
2
0
1
1
1
1
0
2
1
0
0
0
0
1
0
2
0
1
0
1
2
2
0
1
2
0
0
1
2
1
1
0
2
2
3
3
1
2
1
2
2
2
2
1
1
1
1
1
1
0
2
1
1
1
2
2
0
1
1
0
0
1
0
0
1
1
2
0
0
0
1
1
1
1
1
2
9
2
1
1
2
1
2
1
2
2
2
0
0
2
0
0
1
0
2
2
0
2
0
1
0
0
1
1
0
1
2
0
0
2
1
1
1
1
1
1
1
2
1
2
1
1
0
1
2
1
1
1
1
0
0
2
1
0
0
0
0
0
0
1
0
1
1
0
1
0
0
3
2
0
1
0
1
2
0
0
0
2
2
1
0
0
1
0
0
3
1
0
1
2
1
0
1
0
0
0
1
0
1
0
2
0
1
0
2
1
0
1
0
0
1
0
1
0
2
2
0
0
3
2
1
0
1
3
2
0
1
1
2
0
1
1
1
0
0
2
2
1
1
2
2
1
1
1
0
1
2
1
1
0
1
1
1
0
0
1
0
1
0
2
0
0
1
1
0
2
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
5
0
0
2
0
0
0
1
0
2
0
0
2
1
3
1
0
1
0
1
1
2
1
0
0
1
1
1
1
2
0
2
0
1
1
2
1
1
3
2
0
3
1
1
1
2
1
1
0
0
0
1
0
1
1
4
1
2
0
1
1
2
1
0
1
2
0
1
2
0
1
2
0
0
1
0
0
1
1
0
2
0
1
2
0
2
0
2
2
2
0
1
0
1
1
0
1
0
0
1
1
2
0
0
0
1
1
2
1
0
1
0
1
1
0
1
0
0
1
1
0
1
0
2
1
0
2
0
0
1
1
2
0
0
0
0
2
2
1
0
1
2
1
0
2
0
1
0
0
0
1
2
2
1
0
0
0
2
0
0
0
1
0
1
2
0
2
1
2
2
1
0
1
0
0
0
1
1
1
2
2
1
2
1
0
0
1
0
1
1
1
0
1
1
0
1
1
1
0
0
1
1
1
2
0
0
0
1
1
2
1
0
0
0
0
2
0
1
0
1
1
1
1
0
0
1
2
0
0
1
0
1
0
2
0
0
2
0
0
0
2
2
1
1
2
1
1
1
0
0
0
1
0
0
0
1
1
0
1
0
1
0
2
0
1
0
2
2
2
1
2
1
1
0
2
1
1
0
2
1
1
0
2
0
1
2
1
2
0
1
1
0
2
0
1
0
1
1
0
1
0
1
0
2
2
0
0
1
0
1
0
2
1
0
1
0
0
1
2
0
1
1
2
1
2
0
1
1
1
2
0
2
0
1
0
1
1
0
1
2
2
1
0
0
0
2
5
0
0
1
0
2
0
0
1
0
0
1
0
1
1
0
1
1
0
0
2
1
0
2
0
2
0
1
0
0
2
1
1
1
0
1
0
0
2
2
0
0
1
0
0
1
2
2
0
0
2
0
2
1
0
2
1
0
2
1
2
0
2
0
0
1
2
0
0
1
2
2
0
2
2
1
0
1
1
1
1
1
2
0
1
1
2
2
1
1
1
1
1
0
1
1
0
0
1
0
0
2
0
2
2
0
0
0
1
1
1
2
0
0
0
1
0
0
0
2
0
1
1
0
0
0
1
0
0
0
0
1
3
0
2
1
0
1
2
0
1
0
2
0
1
1
0
0
1
2
3
0
2
0
1
1
2
0
0
0
0
1
0
1
1
2
1
0
2
0
0
0
1
0
0
1
1
0
2
1
3
1
0
2
1
1
2
0
0
1
1
0
1
1
0
1
0
0
1
4
1
2
2
1
0
2
1
0
0
1
2
0
0
1
1
0
1
2
1
0
0
0
1
1
1
3
0
1
0
1
1
0
0
0
0
1
2
0
1
1
2
0
2
1
1
0
0
0
0
1
1
0
1
2
2
0
0
2
0
3
0
0
2
0
1
1
1
0
1
0
0
0
1
0
2
0
0
2
1
2
2
2
1
1
1
1
2
2
0
0
3
1
1
0
0
1
2
1
1
2
1
0
0
0
2
0
0
1
1
0
0
1
0
1
2
0
2
2
1
0
0
1
1
2
1
2
0
2
1
0
0
2
2
1
1
2
0
0
3
0
1
0
2
1
2
2
1
0
1
0
0
1
0
1
2
2
1
2
1
0
1
0
0
0
1
0
1
2
0
1
1
0
1
1
2
0
0
0
0
0
1
0
1
0
1
0
1
2
0
2
0
1
0
1
0
0
1
0
1
0
0
1
0
0
1
1
1
2
0
1
1
1
0
0
1
2
0
0
0
2
0
2
2
2
0
2
0
2
2
1
2
0
2
0
1
0
1
1
0
0
1
0
1
0
0
1
2
2
1
1
2
1
2
2
1
0
1
0
0
0
1
0
2
0
0
1
0
1
1
1
1
0
1
1
2
0
2
1
2
0
1
0
0
2
0
1
1
1
1
1
0
0
1
1
1
2
0
1
1
0
1
2
0
0
2
0
0
0
1
2
0
1
0
1
0
1
2
0
2
0
1
1
2
0
2
0
2
0
1
1
2
2
0
1
2
2
0
1
0
1
1
1
2
1
1
1
0
0
1
1
0
1
1
2
1
1
1
2
0
1
1
2
2
1
1
0
3
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
2
0
1
2
0
4
0
0
0
3
0
1
1
2
1
0
1
1
2
0
2
0
0
1
1
1
1
0
2
1
0
1
1
1
1
1
1
0
0
1
0
0
0
2
0
1
2
0
2
2
0
2
1
1
0
0
1
2
1
1
1
2
0
0
1
0
1
2
1
2
2
2
1
0
1
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
1
1
2
1
2
1
1
2
2
0
0
1
1
0
2
1
0
2
2
2
0
0
2
0
0
1
1
2
2
0
1
0
0
0
2
2
0
3
1
0
2
2
0
1
0
1
3
0
1
0
0
2
2
0
1
2
0
1
1
0
0
2
1
2
2
1
1
0
0
1
0
1
0
0
0
0
1
0
0
1
1
2
0
2
1
1
0
2
0
1
3
1
2
1
1
1
1
1
1
2
0
1
1
2
2
2
0
2
2
0
0
0
2
1
0
2
0
1
0
2
1
1
1
1
1
0
0
1
2
0
0
2
0
0
0
0
1
2
1
0
1
0
0
0
0
2
1
2
0
2
1
0
0
1
0
1
0
2
3
0
0
2
2
0
1
0
1
1
0
0
0
1
2
1
0
1
1
1
0
1
0
2
0
0
1
0
0
0
2
0
1
1
0
0
1
0
0
0
0
0
0
1
1
2
1
2
1
1
1
1
4
0
0
1
0
0
0
1
1
2
0
2
0
0
0
0
0
1
1
1
0
2
1
1
0
2
1
2
1
1
2
0
1
1
2
0
0
0
1
1
1
1
1
0
0
2
2
0
0
0
0
0
0
1
1
0
1
1
2
2
1
0
2
2
1
0
0
0
1
3
0
1
0
0
2
1
0
1
2
1
1
0
2
0
2
1
1
0
1
2
1
1
0
1
0
1
0
2
2
0
1
2
3
1
1
0
2
1
1
0
1
3
2
0
1
1
0
2
1
0
1
0
0
0
1
1
1
0
1
0
1
1
1
0
1
0
0
2
0
1
1
1
1
0
0
2
2
2
2
0
1
0
0
0
2
1
1
0
2
0
0
1
1
2
2
1
1
2
1
0
0
2
2
1
2
0
0
0
0
0
1
1
0
0
2
2
1
1
2
2
2
1
2
0
2
1
1
0
2
2
0
1
1
0
1
1
2
1
1
2
0
1
0
2
1
1
1
1
0
1
1
2
1
0
0
0
1
0
0
1
1
0
0
1
1
1
2
1
0
1
1
1
1
0
0
2
0
1
0
0
0
1
1
1
0
0
1
0
1
0
1
2
0
2
2
2
1
1
1
1
0
0
1
1
0
0
0
2
2
0
1
1
0
1
0
0
1
2
0
1
2
1
0
1
1
0
1
1
0
2
1
0
2
2
1
1
1
0
2
2
2
0
0
1
2
3
1
2
0
0
0
2
1
0
2
2
0
0
0
1
0
0
2
0
0
0
0
1
2
2
0
1
0
1
0
1
1
1
2
0
1
2
0
3
1
0
0
0
2
3
1
4
1
0
0
0
0
0
0
2
1
1
2
0
2
1
0
1
1
1
2
2
1
0
1
2
1
2
0
2
0
1
2
3
0
2
2
0
0
0
2
1
0
2
0
1
0
2
2
0
2
2
0
0
0
1
2
2
1
1
2
0
2
2
1
0
2
0
0
2
2
0
1
1
1
1
1
1
2
1
0
1
0
0
2
0
0
2
1
1
1
1
1
1
0
1
0
2
1
2
1
0
1
0
1
1
1
2
0
1
0
0
2
0
1
0
2
1
0
0
0
1
0
1
1
2
0
2
0
0
1
0
1
1
1
1
0
1
0
0
1
1
1
0
0
0
0
1
0
3
1
0
2
0
2
0
1
1
1
1
1
1
0
1
0
2
1
0
1
0
2
0
1
2
1
1
2
1
0
1
1
1
1
2
1
1
1
1
2
1
0
0
1
0
1
1
1
2
0
0
1
0
1
1
0
2
0
2
1
0
1
0
2
0
4
0
0
1
1
1
1
1
0
1
1
1
0
1
0
2
1
0
0
2
1
0
0
3
1
0
2
1
1
0
0
2
0
0
2
2
2
2
2
1
0
0
0
0
1
2
2
2
1
0
2
2
1
1
0
2
1
1
0
0
0
0
2
1
3
0
1
1
2
1
2
1
2
0
0
0
0
0
2
1
0
2
0
0
2
2
1
0
3
1
0
1
0
2
0
0
0
1
0
0
1
2
1
1
0
1
2
1
0
1
0
1
0
2
2
1
1
1
1
0
1
0
1
2
0
1
0
1
1
1
1
1
1
2
1
2
0
1
0
0
1
0
1
0
1
1
1
1
1
1
2
1
0
1
2
2
2
1
0
2
0
0
1
2
1
2
0
2
1
1
0
2
0
0
2
1
2
0
4
2
0
1
1
2
0
0
0
2
0
0
2
2
2
0
0
1
1
2
0
0
0
0
0
0
0
0
1
3
1
2
1
2
2
2
1
2
2
1
0
2
0
1
0
0
0
2
0
0
0
1
1
0
0
1
0
1
1
1
1
0
2
0
0
1
1
1
0
0
2
2
0
0
0
2
1
0
0
0
1
1
1
2
2
3
2
2
0
0
1
0
0
1
0
2
2
1
0
1
2
1
1
0
0
1
4
1
1
0
0
0
0
0
2
0
1
1
1
1
1
1
2
1
1
0
1
1
2
0
1
1
1
0
3
0
2
1
1
2
0
0
2
0
1
2
0
3
0
2
0
0
0
0
1
2
0
1
2
1
1
0
0
1
1
0
2
2
0
2
2
0
1
0
1
1
1
0
1
1
1
0
3
2
1
1
0
1
0
1
0
0
1
0
2
0
0
0
0
0
0
1
0
1
0
2
1
1
2
2
1
2
0
2
0
1
1
1
2
1
1
0
1
0
1
0
1
2
1
2
4
1
1
0
2
1
1
0
0
1
1
2
1
0
1
0
2
0
1
0
0
1
0
1
1
2
1
1
1
1
1
0
2
0
1
2
0
1
2
1
5
0
0
1
1
0
0
1
1
2
0
0
2
0
2
1
0
0
1
1
1
1
0
0
1
0
2
2
1
1
1
1
2
0
0
1
1
0
1
1
0
1
0
0
0
2
2
1
1
2
2
0
3
1
0
0
1
1
1
2
0
2
2
1
5
2
0
0
0
1
1
0
4
1
0
1
1
1
2
2
2
0
1
0
0
2
1
1
0
1
0
2
0
0
1
1
0
0
0
0
0
1
0
1
0
0
1
2
2
0
1
1
1
0
1
1
1
0
0
1
0
0
0
1
0
1
0
1
1
1
1
0
0
0
2
0
0
0
1
1
1
2
0
0
0
1
0
2
1
2
0
1
1
1
1
0
1
1
0
0
0
0
2
2
0
2
0
3
2
0
0
1
1
1
1
2
0
1
1
1
2
0
0
2
0
2
1
1
0
2
2
1
2
1
1
1
2
0
0
1
1
1
5
1
1
1
0
0
1
0
0
1
0
2
0
0
0
1
0
0
1
1
0
0
1
2
1
1
0
1
1
1
1
1
0
0
1
1
0
0
1
1
0
0
0
3
0
0
1
1
2
2
3
0
1
1
1
2
2
0
0
0
0
1
1
0
1
0
0
2
1
1
0
3
0
2
0
0
2
0
1
1
2
1
2
0
0
0
0
1
1
1
3
1
1
2
0
0
1
2
0
2
0
1
0
1
2
1
0
1
2
0
1
1
0
1
0
0
1
0
0
0
2
1
0
4
1
2
0
0
1
1
2
1
2
0
0
1
0
0
1
0
0
1
2
0
0
1
0
3
1
0
2
1
1
1
1
0
0
1
0
1
0
0
1
1
0
0
1
1
0
1
0
0
0
0
2
1
0
1
1
0
1
0
0
1
2
2
1
1
1
2
2
1
1
2
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
1
1
0
0
1
0
0
1
0
0
0
0
1
2
1
1
2
0
1
1
0
1
1
0
1
0
1
0
0
1
0
1
2
1
1
1
4
0
1
0
0
0
1
1
1
0
0
0
1
0
0
1
0
0
2
1
0
1
2
1
0
1
1
1
0
0
1
1
1
0
1
0
0
0
2
0
1
0
1
1
1
0
0
1
1
1
0
1
2
2
1
1
2
2
1
1
5
0
0
0
0
1
0
0
1
1
0
1
0
0
1
1
0
1
0
2
1
2
0
0
0
1
1
0
0
0
0
1
0
2
2
2
1
2
1
0
0
1
0
0
1
0
0
2
2
0
0
0
0
3
0
0
1
1
0
1
0
0
1
1
1
0
1
2
2
1
1
0
1
2
0
0
2
0
1
0
2
0
0
1
1
1
2
2
0
0
2
2
1
0
1
0
1
1
1
2
0
1
1
0
1
2
0
1
1
1
2
0
0
0
1
0
1
1
0
2
1
2
2
4
0
3
2
0
3
2
0
0
0
0
2
1
2
0
1
2
1
2
0
2
2
1
1
2
0
0
0
1
0
0
2
3
1
0
2
1
0
0
1
2
0
2
1
0
1
2
0
2
2
1
0
2
1
0
0
2
0
1
1
1
1
2
0
0
0
2
0
0
0
1
0
1
0
1
0
1
2
0
1
1
2
1
3
1
1
1
1
1
1
0
0
0
1
2
1
1
1
0
0
1
2
2
1
1
1
1
1
1
1
1
1
0
1
2
1
0
0
0
1
2
0
0
1
1
0
1
1
0
1
1
1
2
0
1
1
1
1
1
1
1
2
1
0
1
1
0
0
0
2
0
1
1
0
0
0
0
0
0
1
0
2
0
1
1
0
0
0
0
1
2
2
0
1
1
0
0
0
0
3
0
1
1
1
1
0
0
1
2
0
1
0
1
2
1
0
0
1
1
0
0
1
1
1
0
2
0
1
0
2
1
1
1
0
1
2
2
1
0
1
2
1
1
0
1
1
2
1
1
1
0
2
0
2
1
0
0
1
0
1
2
2
1
1
0
2
1
1
0
0
0
1
2
0
0
0
2
0
1
0
1
2
0
2
1
1
0
1
0
1
2
0
0
0
2
2
0
0
1
1
1
0
0
1
0
1
0
1
1
0
1
0
1
2
0
1
1
1
1
0
2
0
2
1
1
2
1
0
1
2
0
0
1
2
2
1
1
0
0
2
1
1
1
2
1
0
1
2
0
1
0
2
1
0
0
0
2
1
0
0
1
1
2
2
0
1
1
1
2
0
0
0
0
1
0
1
1
1
1
0
1
0
0
2
2
1
1
1
2
0
2
2
1
0
0
0
1
0
0
2
1
1
0
2
1
1
0
0
1
1
0
0
1
1
1
1
0
0
2
0
2
1
3
2
1
0
1
0
0
1
0
0
2
1
1
0
0
0
1
1
1
1
1
0
0
1
2
1
0
2
1
1
0
0
1
1
0
2
2
2
0
2
1
1
1
1
1
1
0
2
2
1
1
1
0
0
2
1
0
0
1
2
0
2
0
1
0
1
1
1
2
0
1
2
1
1
2
2
0
0
1
1
0
2
0
1
0
0
1
2
2
0
0
3
1
1
0
2
1
0
1
0
2
1
1
0
1
1
2
2
0
2
2
2
2
0
1
1
0
1
5
1
0
0
1
0
0
0
0
0
2
0
0
1
0
2
0
0
1
2
0
1
1
1
1
1
1
2
0
0
0
1
0
1
1
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
2
0
1
2
1
0
0
0
1
2
0
1
2
0
2
1
0
1
1
0
1
1
3
1
0
2
0
2
1
0
1
3
0
0
2
1
2
0
1
1
1
0
2
1
0
0
3
1
1
0
1
0
0
1
2
1
0
0
2
2
0
2
1
0
0
1
0
1
0
0
2
0
1
0
0
0
0
0
0
1
1
1
1
0
2
2
1
0
1
1
2
1
0
2
0
0
0
0
2
0
2
1
1
2
0
2
1
1
1
2
1
2
2
1
2
1
0
1
1
0
0
1
2
1
2
1
0
0
1
1
3
1
1
2
1
2
0
0
1
1
0
1
1
0
2
2
0
2
0
0
4
0
0
0
1
2
0
0
2
1
0
1
1
0
0
2
1
1
1
1
0
2
1
1
2
1
1
0
1
0
0
2
0
0
3
1
0
2
2
1
0
0
2
0
1
0
0
0
0
1
0
2
0
1
0
0
1
1
0
0
1
2
1
0
0
0
1
0
1
1
0
2
2
0
1
1
0
1
1
1
0
0
1
0
3
0
1
0
2
0
0
0
2
1
1
1
1
0
2
0
1
0
1
2
0
1
1
1
1
0
0
2
1
1
0
2
1
0
1
1
0
2
0
1
1
1
2
0
2
0
1
2
1
0
5
2
1
2
2
1
0
2
0
1
1
1
0
0
0
0
0
2
0
1
1
2
0
0
0
1
1
2
0
1
1
0
0
0
0
0
0
1
0
1
0
0
2
0
0
2
0
0
1
1
0
0
1
0
1
1
0
0
0
0
1
1
0
0
1
1
1
1
1
1
2
1
1
2
1
2
0
0
1
1
0
1
1
2
0
2
1
0
0
0
0
0
2
0
0
2
0
1
1
1
0
1
1
0
1
0
1
0
1
1
0
1
0
1
1
0
1
2
0
1
0
2
0
2
2
1
2
0
0
0
0
0
1
2
3
0
1
1
2
2
0
1
2
1
0
1
1
1
2
0
1
2
0
0
2
0
1
1
0
1
2
0
2
2
1
2
1
0
1
1
0
0
1
1
1
0
1
1
2
0
0
0
0
1
2
2
1
0
2
2
2
0
1
0
1
1
2
1
0
1
1
1
0
0
0
1
2
0
1
1
1
1
3
1
0
1
0
0
0
1
2
0
2
0
0
1
1
1
2
1
1
2
0
1
0
2
1
0
2
2
0
1
1
1
2
2
1
1
0
0
2
2
1
0
1
0
1
1
0
2
0
2
0
0
1
0
0
2
0
1
0
2
2
1
0
2
1
1
1
2
2
1
1
0
1
1
1
0
1
2
0
1
1
3
0
1
1
0
0
0
2
2
0
2
1
0
1
1
0
1
1
1
1
1
2
1
2
2
1
2
1
1
1
1
1
1
2
1
1
1
1
0
1
1
1
1
0
2
1
0
0
1
0
1
1
0
1
0
0
0
0
0
2
0
0
1
1
2
2
1
1
0
2
3
0
1
2
2
1
2
1
1
0
0
0
0
0
0
1
1
1
0
0
0
2
0
0
0
0
1
1
2
2
1
1
1
1
1
1
0
1
1
2
0
1
0
0
1
1
0
0
0
0
0
0
2
2
1
1
1
1
1
2
1
2
0
1
0
0
1
2
1
0
2
1
0
0
0
0
1
1
1
0
2
2
1
3
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
2
1
0
1
0
1
1
1
0
1
1
0
1
0
1
2
2
0
2
2
0
0
2
1
1
0
2
0
2
1
1
1
0
0
0
0
0
0
2
0
0
1
0
2
1
2
0
2
3
0
2
0
1
2
2
2
1
1
0
1
0
1
1
0
2
1
1
0
0
1
2
1
2
1
1
1
2
1
1
1
0
1
2
0
1
0
1
2
1
1
1
0
2
0
0
1
2
0
0
1
1
0
1
0
1
1
2
2
1
0
0
2
2
2
0
2
1
1
0
1
0
0
2
1
1
0
1
1
1
1
1
0
0
0
1
1
1
2
0
0
2
0
0
1
0
1
0
1
0
1
2
2
2
1
1
1
2
1
0
1
0
1
1
2
2
2
2
1
2
1
1
0
2
2
1
0
1
2
2
0
0
1
2
1
1
2
1
0
0
1
1
0
0
1
0
0
0
0
1
2
1
0
3
2
2
1
3
1
0
1
0
1
2
0
1
0
1
1
1
0
1
0
2
1
0
1
0
1
1
1
2
0
1
2
1
2
1
1
0
1
1
1
0
1
0
1
0
0
0
1
2
1
0
0
2
2
0
1
2
0
2
1
2
2
2
1
1
0
0
1
1
0
2
2
0
1
0
0
1
1
1
2
1
2
1
0
0
1
2
0
2
0
1
1
0
2
1
0
1
0
0
1
2
1
1
2
2
1
0
0
0
1
0
1
2
1
0
0
0
0
1
1
0
0
4
1
0
0
0
1
0
1
2
1
1
2
0
1
2
2
1
0
0
1
1
0
3
1
0
1
1
0
1
1
1
1
1
0
0
0
0
1
1
0
0
2
0
0
1
2
1
1
2
0
0
0
1
1
1
0
0
0
0
0
1
1
1
1
1
0
1
1
0
2
0
2
1
0
0
2
0
2
1
1
1
1
1
1
1
1
0
2
2
1
0
0
2
1
1
0
1
2
0
1
0
0
0
2
3
2
2
0
0
1
0
0
1
1
1
0
1
1
0
0
0
2
1
1
2
1
0
2
0
2
2
1
1
1
1
0
0
0
1
1
3
2
0
2
2
1
2
2
0
0
1
1
1
2
0
1
1
1
1
0
2
0
1
1
1
1
0
2
1
1
2
1
0
2
0
1
1
1
1
1
1
1
0
1
1
0
3
2
1
1
2
0
0
1
0
0
0
1
1
0
0
2
1
2
1
2
0
1
1
2
1
0
0
1
1
1
2
0
1
0
1
0
1
1
0
1
0
1
0
0
1
1
1
0
1
1
1
2
2
0
2
2
1
2
0
1
0
2
1
1
2
1
0
0
0
1
0
0
1
2
1
1
1
2
2
2
0
0
0
2
0
0
1
1
0
0
1
0
1
3
1
2
2
1
0
2
0
1
1
2
3
1
0
0
1
1
1
0
0
1
0
0
1
1
0
2
2
1
0
1
0
0
0
1
1
2
0
0
1
1
1
1
1
0
0
0
1
0
1
0
1
1
1
1
2
0
1
1
1
2
0
0
1
2
0
1
1
0
0
0
1
1
2
0
1
2
1
1
0
0
1
0
2
1
1
0
1
0
0
1
0
1
0
0
1
1
0
0
0
1
2
2
2
0
0
1
1
2
0
2
0
0
1
1
2
0
2
0
0
0
0
3
0
0
1
2
0
0
1
1
1
0
0
1
1
0
2
0
0
2
1
2
1
0
0
0
1
1
1
1
0
2
1
0
1
1
0
0
2
0
0
1
1
2
1
1
0
0
1
2
1
1
1
0
0
0
1
2
0
1
1
2
4
1
1
1
2
1
1
1
1
0
2
1
0
1
1
0
0
0
1
1
0
1
0
0
1
1
1
1
0
0
1
2
0
1
0
2
0
1
1
0
1
1
0
1
2
1
0
1
2
1
1
1
1
0
1
1
1
0
1
1
1
1
0
1
2
0
0
1
0
2
1
0
1
1
2
0
1
2
2
1
0
1
0
0
2
0
1
1
1
0
2
0
2
2
0
0
0
2
2
0
2
0
1
0
0
0
0
2
1
2
0
1
2
0
1
1
0
1
0
1
2
1
3
1
1
0
1
1
0
0
2
0
2
2
0
0
1
1
0
0
0
1
1
2
0
0
1
3
0
3
1
0
1
1
0
1
1
1
0
0
1
0
0
0
0
1
4
0
2
2
2
0
0
1
0
0
1
1
0
2
2
2
0
1
0
2
0
2
0
0
1
2
1
1
1
2
1
1
0
1
1
0
1
2
0
1
1
0
0
1
0
2
0
1
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
1
1
1
2
2
0
1
0
1
1
1
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
1
1
3
0
0
0
1
0
1
1
1
1
0
1
1
0
2
0
1
0
0
0
0
0
0
2
0
1
2
1
1
0
0
2
0
2
1
1
2
0
1
2
0
2
0
0
1
1
1
2
2
0
1
1
1
2
0
2
2
1
0
1
10
1
0
0
0
0
1
1
1
2
1
1
1
1
1
0
0
0
1
0
1
0
1
0
2
0
0
2
3
2
1
2
1
1
2
1
1
1
1
0
1
0
0
1
2
1
0
0
1
2
0
1
0
0
1
1
0
0
1
2
0
0
0
0
0
0
0
2
1
0
0
0
0
1
1
0
2
0
0
1
0
0
0
1
0
2
1
1
1
0
1
1
0
0
0
1
1
1
0
0
1
0
0
1
1
2
0
1
2
0
0
0
0
3
2
2
1
0
1
1
0
1
2
0
0
1
2
0
1
2
1
1
1
1
1
1
2
0
0
1
1
0
2
0
0
0
2
1
2
2
0
0
0
1
1
0
1
1
2
0
0
0
2
2
0
1
1
2
4
2
0
0
1
1
0
1
0
1
1
2
1
1
0
2
0
1
2
1
2
2
0
0
1
0
0
1
0
0
0
0
2
0
0
0
2
0
1
0
3
1
1
0
1
0
0
1
2
0
0
1
0
0
1
1
0
1
0
0
2
1
1
1
0
0
2
1
0
0
0
3
1
0
2
1
2
0
1
1
0
1
1
2
1
1
0
1
1
2
1
0
1
2
1
3
1
1
0
1
3
2
2
0
1
0
0
1
0
1
0
1
0
1
2
0
1
1
2
0
0
0
1
2
0
1
1
0
0
2
2
2
1
2
2
1
1
1
0
0
1
0
2
1
1
0
2
0
0
1
1
1
0
0
1
1
0
1
0
0
0
3
1
2
1
2
2
2
0
1
1
0
0
0
1
1
1
2
0
1
2
1
0
2
1
0
1
1
0
2
1
0
0
0
0
2
2
0
0
0
0
1
0
0
1
2
0
1
1
0
1
2
0
0
1
0
2
2
0
2
1
0
0
2
1
0
0
0
0
0
1
0
2
2
1
1
0
2
2
0
2
1
1
1
0
0
0
0
0
2
2
1
1
1
0
1
2
1
2
0
1
1
0
0
0
0
0
0
1
0
2
0
2
2
0
1
2
0
0
1
2
1
0
1
1
0
1
1
0
1
2
1
0
2
2
0
2
0
1
2
1
2
0
0
2
0
1
1
0
1
1
0
0
1
2
1
1
0
1
1
0
2
2
1
2
2
0
0
1
2
1
0
0
1
0
0
0
2
1
0
1
1
1
2
2
1
2
0
1
0
1
1
0
0
2
0
0
0
0
2
0
0
0
1
1
2
0
1
1
0
0
1
1
1
2
1
0
0
2
0
1
2
0
1
1
1
0
0
0
2
1
0
1
1
0
2
0
1
2
0
2
0
2
1
1
2
0
2
1
1
0
2
0
1
1
0
1
1
1
2
0
0
1
2
0
4
0
1
2
0
0
1
0
0
2
0
1
0
0
1
1
2
2
0
2
0
2
0
1
0
1
0
0
1
1
1
0
0
2
2
2
0
2
2
2
0
1
0
2
0
1
1
2
0
1
0
0
0
0
0
2
2
1
1
0
2
3
1
1
0
0
1
0
0
1
1
0
1
1
1
0
1
1
1
0
1
1
1
0
0
1
0
0
2
0
2
2
0
0
2
1
1
1
0
1
2
2
1
0
0
1
2
1
1
0
0
0
2
1
1
1
0
1
0
1
0
2
0
2
0
1
1
1
1
2
0
0
0
0
2
1
0
1
1
2
2
2
0
1
2
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
1
1
1
1
2
1
1
2
1
0
0
1
1
0
1
0
0
1
2
0
1
0
1
1
1
0
6
0
0
0
1
1
1
2
2
2
2
0
0
1
1
0
3
2
2
1
1
2
1
0
0
0
0
0
0
1
0
2
2
0
1
1
2
1
2
0
1
2
0
1
2
1
2
1
1
2
1
0
0
1
1
0
2
1
0
2
1
1
0
0
0
1
0
0
2
0
1
2
1
0
0
2
0
0
0
1
0
0
2
0
0
1
1
0
0
2
2
1
0
1
2
0
0
0
0
0
0
2
0
1
0
2
1
0
0
2
1
0
3
1
2
2
2
1
0
1
0
2
2
1
1
2
1
0
1
0
2
2
1
1
1
1
0
1
4
1
2
0
0
1
2
1
1
2
1
1
1
1
0
1
0
1
1
1
3
1
1
0
1
1
0
0
1
1
1
2
4
0
0
2
2
1
1
0
2
1
0
1
1
1
0
1
2
2
0
2
1
0
0
2
2
0
1
1
1
0
1
0
1
2
0
1
1
2
1
1
1
0
1
2
1
3
1
0
2
0
0
0
0
2
0
1
2
0
2
1
1
1
0
0
1
2
1
0
0
1
1
1
0
2
2
0
1
0
1
0
2
0
1
1
0
1
2
1
0
0
2
2
2
1
0
2
2
1
1
1
2
2
0
2
0
0
0
1
2
1
1
0
0
0
2
0
2
2
1
2
1
0
1
1
1
0
0
0
1
3
2
0
0
0
1
1
3
1
1
0
0
1
0
1
0
0
2
0
1
2
2
1
0
0
2
1
1
0
1
1
2
1
1
1
2
1
1
1
0
2
1
2
1
2
0
2
0
1
0
1
0
0
1
1
0
1
1
0
0
0
2
0
1
0
0
0
0
0
1
2
0
0
1
2
1
1
2
1
1
2
0
1
0
1
2
1
1
1
1
2
0
1
1
2
0
4
2
1
2
0
0
0
1
0
0
0
0
2
1
0
1
0
0
2
0
0
0
1
2
1
1
2
0
0
2
1
0
1
2
0
0
1
1
1
0
1
1
0
2
1
2
0
0
2
2
0
1
2
1
0
1
2
0
0
1
1
2
1
1
0
0
0
1
0
0
1
0
2
1
0
1
0
0
1
1
2
1
1
2
2
0
1
0
1
2
1
2
0
1
1
1
2
0
1
1
0
0
2
0
0
1
1
1
1
1
0
1
1
1
1
1
0
0
0
0
2
0
0
0
2
0
0
1
2
0
1
1
0
2
1
0
0
0
0
1
1
0
0
2
0
0
2
2
1
2
1
1
0
1
0
0
0
1
2
0
2
0
2
0
0
0
0
1
0
2
1
1
1
0
1
1
1
1
0
2
2
2
1
0
1
0
2
0
2
2
1
0
0
1
2
1
0
1
2
1
1
1
1
1
0
0
1
1
1
0
1
0
1
0
0
1
0
0
0
1
1
2
2
2
2
2
0
0
1
0
0
0
0
0
1
0
2
1
1
1
1
0
2
0
0
1
0
1
1
0
0
0
2
1
2
1
0
0
0
1
2
1
0
1
1
1
0
0
0
0
2
0
0
0
1
2
1
2
0
2
1
2
0
1
0
0
0
1
2
0
0
0
1
1
1
0
2
0
1
2
0
0
1
2
2
1
1
0
1
2
2
3
0
0
0
2
1
3
1
0
0
1
1
1
1
2
1
1
1
2
0
0
0
1
1
0
1
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
1
1
1
0
1
1
0
1
2
2
1
0
2
0
0
1
1
2
1
1
1
0
1
2
0
2
2
1
0
1
1
2
0
2
1
1
2
0
1
0
0
1
0
1
1
1
1
1
2
2
1
2
1
0
1
1
0
1
0
2
0
2
0
0
1
0
0
0
1
1
0
2
1
1
1
2
2
1
1
1
2
0
0
0
1
2
1
1
3
1
1
0
0
1
2
2
1
1
2
2
1
0
2
1
0
2
2
2
1
0
0
1
1
1
2
2
1
2
1
1
1
0
0
2
1
1
0
2
0
0
2
0
1
1
2
1
1
0
2
0
4
2
0
0
0
1
0
2
3
2
0
1
1
0
1
2
0
1
1
2
2
1
2
1
1
1
1
1
1
2
0
0
2
0
2
0
1
1
1
1
0
1
2
0
2
2
0
1
2
0
0
2
0
0
0
1
0
0
1
1
1
2
1
1
2
0
0
1
0
1
0
1
1
1
1
0
0
0
1
0
1
1
1
1
1
2
1
1
0
0
1
1
1
0
2
0
1
1
1
1
2
1
0
0
2
1
1
0
1
1
0
0
0
2
2
1
1
0
1
1
2
1
0
2
1
0
1
0
2
0
0
1
0
0
0
1
0
1
2
1
0
1
0
2
1
2
1
0
2
0
1
2
2
1
1
0
0
0
0
1
1
0
0
2
0
1
1
2
0
2
1
0
2
1
0
1
0
1
1
1
1
1
0
1
1
2
0
2
0
2
1
1
0
0
0
0
1
1
1
1
2
2
0
1
2
1
1
0
0
0
1
0
0
0
1
0
1
1
0
0
0
3
1
0
0
1
2
0
1
0
0
1
2
1
0
0
2
0
0
1
0
0
1
0
1
2
0
1
2
0
0
3
0
0
0
1
0
0
1
2
0
0
0
0
1
1
0
2
0
1
1
2
1
2
1
0
2
1
1
1
2
3
2
1
1
1
3
1
0
1
1
0
1
0
2
0
2
1
1
2
0
2
2
3
1
1
1
2
1
1
2
2
1
1
2
2
1
2
1
1
0
1
0
1
0
2
0
0
0
1
2
0
1
1
1
1
2
1
1
0
1
1
1
1
2
0
1
1
1
0
1
0
0
0
0
1
2
1
0
0
3
1
1
2
1
1
0
0
1
1
1
1
2
1
1
1
1
1
1
1
0
1
2
0
0
1
1
1
1
1
0
0
0
1
0
1
1
0
1
1
0
0
1
0
2
0
1
0
0
0
2
2
1
0
0
1
1
0
1
0
1
1
1
1
0
1
0
0
0
1
0
2
1
1
0
1
1
1
0
0
1
0
1
1
1
1
0
0
1
2
0
0
1
2
0
2
0
0
1
1
0
0
2
1
1
0
1
0
1
1
1
2
1
0
1
2
0
1
0
2
1
0
1
0
1
1
0
0
0
2
0
0
0
2
2
1
1
2
2
1
0
2
0
1
1
2
0
1
1
0
2
2
1
2
2
0
0
0
2
0
1
2
0
1
0
2
0
0
1
0
1
0
1
0
1
1
0
0
1
0
0
0
0
1
0
1
0
0
1
0
1
1
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
1
0
1
1
1
0
2
0
0
2
0
0
0
2
1
1
2
0
1
1
0
1
4
1
1
1
1
0
1
2
0
2
1
1
0
2
1
1
0
1
2
0
1
0
0
2
2
0
1
2
1
0
1
2
1
1
0
0
0
1
1
1
2
1
1
1
1
2
2
1
1
0
0
1
2
1
2
1
1
1
0
0
2
0
0
1
0
1
0
0
0
0
0
1
2
1
0
1
0
2
0
1
1
1
0
2
2
0
2
1
1
0
1
1
0
0
0
0
0
2
2
1
0
1
1
1
0
1
1
0
1
0
1
1
1
0
1
1
0
0
0
0
2
2
1
1
0
1
0
0
2
0
2
0
1
1
2
1
1
0
1
1
2
0
0
2
1
0
2
1
2
1
1
1
0
1
0
1
0
0
1
1
1
0
1
2
0
0
1
0
2
1
0
1
2
0
0
1
0
2
0
0
0
1
1
1
0
0
2
1
0
2
0
1
1
0
1
0
1
1
3
1
1
2
1
0
0
1
0
0
0
1
1
1
0
1
1
0
0
0
2
2
3
0
0
1
0
0
1
0
0
1
1
1
2
1
2
0
0
1
2
0
0
1
0
1
0
1
1
1
2
2
1
1
0
1
1
0
0
0
2
1
0
1
2
1
1
2
0
1
2
1
1
2
0
2
0
1
1
1
0
2
1
2
1
0
0
1
1
0
1
1
0
1
0
1
1
0
1
0
1
1
1
1
2
1
2
1
0
1
2
1
0
0
2
2
0
0
2
0
0
0
0
1
1
1
1
0
1
1
0
2
2
2
0
0
1
0
1
1
1
4
0
0
2
0
0
0
0
2
2
1
2
1
1
1
0
1
0
1
1
0
0
0
1
1
1
2
2
1
0
0
0
0
0
2
1
2
1
1
0
0
1
2
0
1
1
0
0
0
1
0
2
1
0
0
1
0
0
0
0
1
0
0
1
1
1
0
1
0
1
0
2
1
1
2
2
2
2
0
1
2
2
2
0
0
2
2
2
1
2
0
1
4
2
1
1
1
1
0
0
1
0
0
1
0
0
0
0
0
2
2
0
1
2
2
0
1
1
1
0
0
1
3
0
1
0
2
1
1
0
0
0
2
0
1
0
2
1
2
1
1
1
2
2
1
2
1
0
1
3
1
1
1
0
1
0
1
0
0
0
1
1
1
2
1
1
1
0
1
0
1
1
1
0
1
0
0
1
2
2
0
1
0
1
1
1
1
1
0
1
0
1
0
1
0
0
0
1
3
1
0
2
3
0
1
0
1
1
0
1
2
1
1
0
2
2
0
1
0
1
1
1
1
2
1
2
1
0
1
0
1
0
1
0
0
0
1
2
1
0
0
1
0
1
1
0
0
2
1
2
1
0
1
0
0
0
0
1
0
0
2
1
1
1
3
1
0
1
1
0
2
1
0
2
0
2
0
0
1
0
2
1
0
1
1
0
1
0
1
0
0
2
2
0
0
1
1
0
0
1
0
0
0
2
1
0
2
1
1
0
1
2
0
0
0
2
0
1
0
0
0
1
0
0
2
0
3
1
1
2
3
0
0
0
1
0
1
2
0
0
1
0
0
0
0
0
1
0
1
1
1
0
2
3
0
0
0
1
0
3
1
3
1
0
1
2
0
0
2
0
0
0
1
1
0
0
1
1
0
0
1
1
1
0
2
1
0
0
1
1
1
0
1
0
2
0
0
1
1
2
0
0
2
2
0
0
1
0
0
0
1
1
1
0
2
1
0
2
0
0
1
0
1
1
1
2
0
2
2
0
0
0
2
1
1
1
1
1
2
1
1
2
0
0
0
1
0
2
0
1
2
2
0
2
1
0
1
1
0
1
1
2
1
1
0
1
2
1
0
2
0
1
1
0
2
1
0
0
0
0
1
0
0
1
2
0
1
2
0
1
0
2
1
0
1
1
0
0
1
1
2
0
1
2
2
1
1
0
2
1
0
0
1
3
0
0
2
1
0
1
0
1
1
0
1
1
2
1
0
1
1
1
0
1
2
0
0
0
0
1
2
0
0
1
0
1
2
2
1
2
1
1
0
1
1
0
2
0
0
2
0
2
1
1
1
1
2
0
0
0
1
1
0
1
1
1
0
1
0
1
0
2
1
1
0
0
2
1
1
0
3
2
0
0
1
0
2
0
0
0
2
1
2
2
0
1
1
2
0
0
1
1
2
2
0
1
0
0
0
0
1
1
0
2
0
0
1
0
0
2
0
1
1
0
0
2
1
2
2
0
1
0
1
0
2
1
1
1
2
1
0
1
0
0
0
0
2
1
2
1
1
2
2
1
1
0
1
0
0
1
0
2
1
0
0
1
1
1
0
2
2
1
1
1
2
0
1
0
0
2
2
0
0
0
1
1
1
2
1
2
2
0
1
1
1
1
0
1
2
1
1
0
0
0
0
0
2
2
2
1
2
1
1
1
1
2
0
0
0
1
2
0
1
0
1
0
1
1
0
1
0
0
0
1
0
2
1
0
1
1
0
2
0
2
2
0
1
1
1
1
1
1
0
0
1
0
2
1
1
0
0
1
1
1
0
1
1
0
0
1
1
0
2
1
0
2
1
0
2
0
1
1
1
1
2
0
1
1
0
1
2
1
2
1
2
1
0
1
0
1
1
0
1
1
0
1
2
2
1
0
1
1
1
0
1
2
0
1
1
0
1
0
0
0
1
1
0
0
1
0
1
1
1
2
1
0
2
2
1
0
0
1
1
1
1
0
1
0
0
2
2
0
1
0
1
2
1
1
0
0
1
1
0
1
0
2
1
1
1
0
1
0
0
1
2
1
0
1
2
0
1
2
1
0
0
2
2
0
0
2
2
1
1
0
1
1
1
0
2
0
0
1
0
1
1
0
1
0
2
2
2
1
2
1
1
1
1
0
0
1
0
1
0
0
1
1
1
0
1
0
1
1
0
1
0
0
1
1
1
0
0
1
0
2
0
1
3
1
1
1
2
1
1
0
1
2
1
1
2
2
1
0
2
2
1
1
1
0
0
0
1
0
0
2
2
2
1
1
0
2
2
2
1
1
2
0
0
1
2
2
1
1
0
0
0
2
1
0
0
1
0
2
0
0
0
1
1
1
0
0
1
0
1
2
1
1
2
0
0
2
0
2
1
0
0
0
1
0
2
1
1
0
0
1
2
0
1
1
0
2
0
2
0
1
1
1
3
1
0
2
1
1
0
0
2
0
2
0
0
1
1
1
1
1
2
0
0
0
0
0
1
1
0
0
1
0
7
2
1
1
1
1
0
1
0
1
2
0
1
0
0
2
0
0
0
0
1
0
2
2
1
1
1
0
0
1
1
0
1
1
2
0
0
0
0
0
1
2
1
2
2
1
2
0
1
0
2
1
1
2
1
1
0
1
2
0
0
1
1
1
1
1
0
0
0
0
0
1
0
0
1
1
0
1
1
1
2
1
1
0
2
0
0
1
1
3
1
1
0
1
1
1
2
1
1
1
0
0
1
0
2
0
0
0
0
0
1
0
2
1
1
0
1
0
1
1
0
0
1
1
1
0
0
0
1
1
1
1
0
1
0
0
0
1
1
0
1
0
0
1
1
1
1
2
1
1
0
0
0
0
1
0
0
1
2
1
0
1
1
0
1
1
0
0
0
2
2
2
0
0
0
2
1
1
0
1
2
0
0
1
0
1
2
0
1
0
2
1
1
2
0
0
1
0
0
0
2
0
1
1
1
0
1
0
2
0
0
1
0
0
1
2
2
1
2
3
2
0
0
1
0
1
1
1
1
1
0
1
1
1
1
1
1
0
2
0
0
2
0
0
2
1
0
1
1
2
2
1
1
0
0
2
1
3
0
1
0
0
0
1
2
1
1
0
1
1
1
0
1
0
0
0
1
0
1
2
0
1
0
0
1
0
1
1
0
1
0
0
1
2
0
2
0
0
1
2
2
0
0
0
2
0
1
2
2
0
0
1
0
1
0
0
1
2
1
2
0
1
1
2
1
0
1
1
0
0
1
2
2
2
0
1
1
0
0
1
1
3
2
2
0
0
0
2
0
0
1
1
0
1
0
1
1
2
0
1
0
1
1
1
0
1
0
3
0
0
1
1
1
0
2
1
1
1
2
1
1
1
1
1
3
2
1
0
0
1
0
2
0
0
1
0
1
0
0
0
1
1
1
1
0
0
0
0
1
0
1
0
0
2
0
2
1
1
0
0
2
1
0
1
0
1
0
0
0
2
1
0
1
0
0
1
1
0
0
1
0
2
0
1
1
4
0
0
0
1
1
0
2
0
0
0
1
1
1
1
1
1
1
0
2
0
1
1
0
1
0
1
1
0
0
0
0
9
0
0
0
1
0
0
0
0
2
1
0
1
0
1
1
1
1
1
1
0
1
2
2
2
0
0
1
3
0
1
0
0
1
2
1
1
3
2
1
1
0
0
0
0
1
2
1
2
1
1
1
1
2
0
2
0
2
2
2
1
2
0
0
1
0
1
1
0
1
0
1
2
0
2
0
2
0
0
1
1
1
1
1
0
1
1
1
2
2
2
1
0
0
0
1
0
1
3
0
1
1
2
1
2
0
2
0
0
1
0
0
5
0
1
1
0
0
0
0
1
2
2
0
0
0
0
0
1
1
0
0
1
2
0
1
1
1
0
0
1
0
2
2
1
0
1
1
2
1
0
1
1
0
1
0
1
0
1
0
0
1
1
0
1
2
0
0
1
0
1
1
1
2
1
0
0
1
1
1
0
0
1
2
0
1
1
1
1
0
0
1
1
1
0
0
0
0
0
0
1
0
2
2
1
0
1
0
0
2
0
2
1
0
0
2
0
1
0
0
1
1
2
1
1
1
3
0
2
2
0
0
0
0
0
2
1
1
1
1
1
2
1
0
2
2
2
1
1
0
1
2
1
0
1
2
2
1
0
1
2
0
1
0
1
1
0
0
0
2
0
2
2
1
2
0
0
1
0
1
2
1
1
2
0
2
2
2
2
0
1
1
1
2
0
2
2
1
1
0
0
1
0
0
0
0
2
2
0
0
0
1
0
0
0
2
1
0
0
1
1
1
0
2
0
1
2
0
2
1
0
0
2
1
0
2
2
2
1
1
1
1
2
2
0
2
0
2
1
1
1
0
1
0
0
2
0
0
0
2
0
1
0
1
1
1
2
1
1
1
2
0
0
0
1
2
0
1
4
1
0
1
2
0
2
1
1
1
1
0
1
0
1
0
2
1
0
2
2
1
0
0
1
0
1
0
0
0
0
1
0
3
1
1
0
0
1
0
0
0
1
1
1
0
1
1
1
1
0
0
2
1
1
2
2
0
2
2
1
0
1
0
1
1
0
0
2
1
0
0
2
1
0
1
0
1
0
2
0
0
2
0
0
1
1
2
2
2
3
0
0
1
2
0
1
1
0
0
1
1
1
0
1
1
3
2
2
1
0
1
2
1
1
1
1
1
1
2
2
1
0
2
1
2
0
2
0
0
0
0
1
1
1
2
0
0
1
0
1
2
5
0
0
2
1
3
0
0
1
1
1
0
2
1
1
1
1
1
0
0
1
0
1
1
1
2
1
1
2
0
0
0
0
0
1
0
2
0
1
3
0
0
1
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
1
1
1
2
0
0
0
0
0
1
2
1
0
1
0
1
1
2
0
0
0
0
1
1
1
1
2
1
1
0
0
1
0
0
0
1
1
2
0
0
0
1
1
1
0
1
2
1
1
1
2
1
6
0
0
1
1
0
1
2
0
1
1
2
2
1
1
2
2
0
2
0
3
2
1
1
0
1
0
2
1
1
1
0
2
0
1
1
2
2
1
1
0
1
1
0
2
0
1
1
1
0
1
1
2
2
0
0
0
0
0
0
0
2
2
1
1
0
0
1
1
2
2
1
3
0
1
1
0
0
0
2
1
2
0
1
1
2
0
0
0
1
1
0
2
0
2
0
0
1
1
1
2
1
2
0
1
0
0
0
0
0
0
0
1
1
1
0
0
2
2
0
0
0
2
2
0
0
1
0
0
2
1
1
0
0
1
2
0
1
2
2
3
0
1
2
1
0
0
0
0
0
1
1
1
1
2
0
1
2
1
2
0
1
0
0
3
0
2
0
1
0
0
2
1
1
3
2
1
1
1
1
0
1
1
2
0
0
1
0
0
2
2
0
0
0
2
2
1
0
0
2
1
1
1
1
2
0
0
1
0
1
2
0
0
1
0
1
1
0
1
0
1
1
2
0
1
2
3
0
0
0
2
2
0
1
0
0
0
0
1
2
1
0
0
0
0
1
2
2
2
0
0
1
1
1
1
0
1
0
3
0
1
0
1
1
1
0
2
1
1
0
2
0
2
1
1
2
1
0
0
1
0
0
1
1
3
1
1
1
0
1
2
0
2
0
1
0
0
1
1
1
1
0
0
2
2
1
0
1
1
0
1
2
1
2
1
0
2
1
0
1
0
0
1
2
1
1
1
1
1
1
2
0
2
2
2
2
0
1
0
0
0
1
2
0
0
2
0
1
0
1
1
0
1
2
2
2
1
0
0
1
2
1
0
1
0
0
0
1
0
1
0
1
0
0
0
0
2
0
2
0
1
0
1
0
2
2
1
0
0
1
0
1
0
1
1
1
2
0
2
2
2
1
1
1
1
2
1
2
0
0
1
0
1
0
2
2
0
0
1
1
0
1
2
4
1
0
2
0
0
1
0
1
1
0
1
0
2
0
0
0
0
2
1
0
0
1
2
2
0
0
0
0
1
1
0
0
2
2
1
1
0
2
1
1
0
2
0
0
2
0
2
0
1
0
1
2
2
0
1
0
1
1
2
0
0
1
1
0
1
2
1
1
2
1
2
1
0
0
0
1
1
0
0
0
1
3
1
1
3
1
1
0
1
1
2
2
0
1
0
2
2
0
1
1
1
2
1
1
1
1
1
0
0
0
2
2
1
1
0
0
0
0
2
1
1
0
0
0
1
1
0
0
2
1
0
0
1
2
0
0
2
2
0
1
1
0
2
0
0
0
0
0
3
0
2
2
0
2
2
0
1
1
1
0
1
1
1
0
2
1
0
0
1
2
0
0
1
0
2
1
0
0
0
1
1
0
1
0
1
0
0
1
1
0
0
0
1
2
2
2
1
1
0
1
0
0
0
3
0
0
1
0
1
2
2
0
2
1
2
2
1
1
1
1
1
0
0
0
1
2
0
0
2
1
2
0
2
0
1
0
2
1
1
2
0
0
2
0
1
1
0
0
0
2
0
1
1
2
0
1
0
1
1
1
1
0
1
1
0
0
1
0
0
0
0
1
2
0
0
0
2
1
1
1
2
0
1
0
1
2
1
0
1
0
2
1
1
1
0
2
2
1
1
0
1
0
2
1
2
1
0
0
1
1
0
1
2
0
0
1
2
1
1
3
2
1
0
1
1
0
0
2
0
0
0
0
1
2
1
1
1
1
0
1
1
2
0
0
2
2
0
0
1
0
0
1
2
1
2
0
1
2
2
0
1
0
0
0
0
1
1
0
0
1
1
2
2
1
0
1
2
1
1
1
2
1
1
2
0
0
1
1
0
1
0
1
0
0
0
1
1
2
1
0
0
0
2
1
2
0
1
0
1
0
0
2
0
1
1
1
1
0
2
1
0
2
0
0
0
0
0
0
2
1
0
0
2
2
1
1
4
0
2
0
2
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
1
0
1
0
1
1
0
2
0
0
1
3
0
0
0
0
0
0
2
0
1
1
0
2
1
0
1
0
0
1
0
0
0
0
1
1
0
0
1
1
1
0
2
0
0
1
0
2
1
0
0
1
1
2
0
0
0
2
1
0
0
0
1
3
1
0
1
0
0
2
0
0
1
2
0
2
0
1
1
0
0
3
1
1
0
1
1
0
0
1
0
1
1
1
2
2
0
1
1
2
0
1
2
0
2
0
1
0
0
1
1
2
0
2
1
1
0
2
0
0
0
1
2
0
0
1
1
1
5
0
0
1
0
2
1
2
2
1
0
1
1
0
1
0
0
1
0
2
2
1
0
1
1
3
2
0
0
1
2
1
1
1
1
1
3
1
0
1
1
2
2
1
0
0
2
0
0
0
1
1
0
2
2
0
0
2
1
0
0
0
0
1
2
1
1
1
1
0
0
1
0
1
2
2
0
1
0
1
0
0
1
2
0
1
0
3
0
1
2
0
0
0
0
0
0
1
1
0
1
0
3
0
1
0
0
0
2
1
1
0
0
1
0
0
0
1
1
1
0
1
1
1
1
2
1
1
1
1
2
0
1
2
0
0
1
1
2
1
1
2
1
1
3
0
1
1
0
0
1
1
0
1
1
0
1
0
1
2
1
2
1
0
1
0
0
1
1
2
1
1
1
0
0
0
0
1
0
0
1
2
0
1
0
2
2
1
1
0
1
1
2
1
0
0
1
2
1
0
2
1
0
1
0
1
0
2
2
1
0
2
2
1
0
1
0
0
0
1
2
1
0
1
1
1
0
2
1
1
1
4
1
3
0
0
1
2
1
1
1
1
1
2
2
1
2
1
0
0
0
0
1
0
0
1
0
0
3
2
1
1
0
1
1
2
1
2
0
0
0
1
1
1
1
0
2
1
0
1
1
0
0
1
1
0
2
2
1
1
2
2
0
1
1
0
0
1
0
2
1
1
1
0
0
2
2
1
1
2
0
1
0
1
2
1
0
0
2
1
2
5
1
1
2
2
2
0
2
0
1
1
0
0
0
0
1
0
1
3
2
0
1
1
0
1
0
0
0
1
1
1
0
2
0
1
1
1
0
1
1
0
0
0
0
0
0
0
2
1
2
1
1
0
2
2
0
1
2
2
1
0
1
1
1
1
1
1
0
2
0
1
0
1
0
1
0
0
0
0
0
2
0
1
0
0
2
1
1
2
1
0
1
1
0
0
0
2
0
0
0
1
0
2
1
2
0
1
1
1
0
1
1
1
1
1
2
0
0
0
1
1
1
0
0
0
1
2
1
0
2
1
0
0
1
0
0
1
1
1
1
1
2
0
0
0
1
1
0
0
0
2
0
0
0
0
2
1
1
2
1
0
1
1
1
0
2
3
0
0
2
1
0
2
2
0
2
3
2
1
1
1
2
0
0
1
1
1
0
1
1
0
2
1
0
0
1
1
0
1
0
0
0
1
1
2
1
1
0
0
1
0
0
1
1
2
0
1
1
0
0
0
1
2
0
2
0
1
0
1
3
0
1
2
1
1
1
2
0
2
0
2
2
0
0
1
0
0
2
7
2
0
0
0
1
1
2
0
0
1
1
0
1
0
1
0
0
0
1
0
0
0
0
2
1
0
1
0
1
0
2
0
1
0
0
2
1
1
1
0
1
0
2
0
0
1
1
0
1
0
2
0
1
2
1
0
1
2
0
0
1
3
0
2
1
2
0
1
1
2
1
0
1
2
1
1
0
2
0
1
2
1
2
1
0
1
0
0
1
0
2
0
2
0
0
2
2
1
0
2
2
0
1
2
0
1
2
0
1
2
1
1
0
0
1
1
1
1
1
1
0
0
1
0
3
2
0
3
0
0
1
0
0
1
0
0
1
0
3
1
1
2
0
0
0
0
0
1
0
0
2
2
0
0
0
2
1
2
1
1
1
0
1
2
1
1
0
0
1
2
1
1
2
0
0
1
0
0
0
1
2
0
1
2
1
0
1
0
1
1
0
1
1
0
0
1
2
2
2
0
1
1
2
0
0
0
0
0
1
1
2
0
0
0
0
0
1
0
0
2
2
2
2
2
0
3
2
0
0
0
0
0
3
1
1
0
1
0
1
2
1
0
1
0
0
1
0
0
0
1
2
2
0
1
1
0
1
2
0
0
1
0
2
2
0
0
0
1
0
0
2
1
1
0
0
1
0
1
1
0
3
1
1
0
0
0
2
2
2
1
2
0
2
1
1
1
1
0
0
0
1
1
2
0
1
1
2
2
1
0
2
3
2
1
0
2
2
0
1
1
1
0
2
2
1
2
0
0
0
0
2
0
1
0
1
0
2
1
0
1
2
2
0
1
1
0
2
0
2
2
2
1
1
0
1
2
0
0
1
1
0
2
1
0
0
1
0
0
1
0
0
1
2
0
1
0
0
1
0
1
3
1
1
1
0
1
1
5
0
2
1
0
1
2
0
1
0
0
1
2
0
0
1
1
0
2
0
0
1
0
2
1
0
0
0
2
0
1
0
1
1
1
1
0
1
0
0
1
0
0
2
0
1
0
0
1
1
2
2
1
2
2
0
0
2
0
1
1
1
0
2
1
2
0
2
0
0
1
1
2
0
1
1
1
1
0
2
0
1
1
2
1
2
1
2
0
1
1
0
1
0
0
2
1
1
0
2
0
0
2
1
2
0
0
2
1
1
1
2
0
0
1
0
3
2
2
1
1
2
0
2
0
1
0
0
1
0
0
1
1
1
1
1
2
0
0
0
0
2
0
0
1
0
0
1
1
1
1
2
0
1
1
0
1
0
1
1
1
1
2
1
1
0
0
1
1
0
1
1
0
1
1
1
2
1
1
0
1
1
2
2
2
0
2
1
1
1
0
0
1
2
0
0
2
1
1
0
1
1
0
1
1
1
2
0
0
1
0
1
0
1
1
2
1
1
1
1
0
1
0
0
2
1
1
1
0
0
1
0
1
1
1
2
2
0
0
1
1
0
2
0
0
0
1
1
0
2
1
0
2
2
0
2
2
2
1
0
1
1
0
2
1
2
0
2
0
0
0
2
1
0
0
0
2
1
2
2
2
1
1
1
1
0
2
1
2
0
1
1
0
2
0
0
0
0
1
1
0
0
1
1
2
1
1
1
2
1
0
1
0
1
2
2
0
1
0
0
1
3
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
1
1
1
0
0
0
2
0
1
2
1
0
0
1
2
0
2
1
1
0
1
1
0
0
0
1
1
1
0
2
1
0
2
0
2
1
1
2
1
2
3
1
0
2
2
1
1
0
0
0
2
2
2
0
2
2
0
0
1
1
1
1
1
1
2
0
2
0
0
1
2
1
1
0
0
1
2
2
0
1
0
2
1
2
0
2
1
0
1
0
1
0
2
1
1
2
2
1
0
1
0
1
1
0
2
0
1
0
2
0
1
0
2
0
0
1
0
1
0
0
5
0
1
2
0
0
1
1
1
1
0
1
1
2
0
2
0
0
1
0
1
2
2
0
1
1
0
1
0
1
2
2
1
0
2
0
0
0
1
0
2
0
0
2
0
1
2
0
0
2
1
0
1
2
1
2
1
0
2
4
1
2
1
2
0
2
1
1
1
1
0
1
0
2
0
2
2
1
0
0
1
0
1
2
0
5
0
1
1
1
2
1
2
1
0
2
0
1
0
2
1
1
2
0
2
1
2
1
1
1
1
1
2
0
1
3
0
1
0
0
1
0
1
2
0
0
0
2
0
3
2
0
0
0
1
0
2
2
0
1
0
2
0
0
1
1
2
1
0
2
0
0
0
0
2
2
0
1
2
0
0
0
0
1
0
1
1
1
0
0
1
1
0
0
2
2
1
1
2
0
0
1
0
0
0
1
0
0
0
1
1
1
2
0
0
1
1
2
1
1
1
1
0
0
1
0
1
1
2
0
0
0
0
1
1
1
2
2
0
0
0
2
2
1
1
0
1
1
1
1
0
1
1
0
2
3
1
0
0
0
2
0
1
3
2
1
2
0
0
0
0
0
0
0
1
0
2
0
2
1
2
1
0
0
2
0
2
2
1
1
2
2
2
0
1
1
2
2
0
1
1
1
2
2
2
2
2
1
0
1
1
0
2
0
1
0
0
0
1
0
0
0
1
1
0
1
1
1
0
0
0
1
0
0
0
0
2
1
0
0
0
0
1
2
0
0
1
0
1
1
2
0
0
2
1
2
0
1
1
1
0
1
0
0
2
1
1
0
1
1
2
0
0
0
2
0
1
2
2
2
1
1
2
2
2
0
0
1
0
0
0
0
0
0
1
1
2
1
0
2
0
3
1
1
0
1
1
0
0
1
0
0
0
1
0
0
0
0
1
2
1
0
2
2
0
1
0
2
0
1
1
1
4
0
0
2
2
2
1
0
0
2
1
0
1
0
0
1
0
1
2
1
0
1
0
0
2
0
1
2
2
1
0
1
2
1
1
0
1
1
1
0
0
2
1
2
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
2
1
1
0
0
2
1
0
0
1
2
0
0
0
1
1
0
1
1
2
2
0
1
1
0
2
0
2
1
1
0
0
2
0
0
0
1
1
0
0
1
1
0
1
2
2
1
1
0
0
2
1
1
1
0
0
0
1
2
1
2
0
1
1
0
0
2
1
1
1
0
0
3
1
2
0
0
0
0
1
2
1
1
2
1
1
1
0
0
0
0
2
0
3
1
1
0
2
0
0
0
0
2
0
0
1
2
2
0
2
2
1
1
2
0
1
1
1
0
0
0
0
1
2
2
1
1
0
0
1
1
1
0
1
2
0
1
0
1
2
0
1
1
1
2
2
0
1
3
1
3
2
1
0
0
1
2
2
0
1
0
1
2
0
2
1
1
0
1
1
0
2
0
1
1
0
0
0
1
0
1
0
1
0
1
0
1
1
0
2
2
2
0
0
0
2
1
0
0
1
0
2
2
0
2
1
0
1
0
1
0
0
0
0
0
0
0
1
1
0
1
2
1
0
1
0
1
0
1
0
0
0
2
0
1
0
0
0
1
0
2
1
2
2
0
0
2
1
0
0
0
1
0
0
1
2
1
1
1
0
1
1
2
1
2
0
1
2
1
2
1
1
1
1
3
2
2
1
1
0
1
0
1
2
0
2
2
1
2
1
1
2
0
0
0
4
1
2
1
3
1
0
2
1
0
2
0
0
0
0
0
0
0
2
1
2
0
2
2
0
1
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
1
1
2
2
0
0
0
2
1
3
3
1
0
0
3
2
2
0
1
0
2
0
0
0
1
2
0
1
2
0
1
2
1
1
1
0
1
2
1
2
1
1
0
0
0
0
2
2
0
2
1
0
0
1
0
0
1
0
1
2
2
2
1
1
1
2
0
1
1
0
1
1
1
0
1
0
1
1
1
0
1
1
0
1
1
1
2
0
1
0
2
1
0
2
0
1
0
2
1
3
2
2
2
1
0
0
1
2
0
1
0
0
1
1
1
0
0
2
1
0
2
0
1
2
0
1
1
0
1
0
2
3
1
0
2
0
0
2
1
1
0
1
1
1
1
1
1
2
0
0
1
0
1
1
2
1
0
0
1
2
1
1
1
1
2
2
2
0
1
1
0
0
0
2
0
0
2
2
1
1
1
0
1
2
1
1
0
2
0
2
2
1
0
1
1
1
1
1
0
0
0
1
0
2
0
0
1
0
1
2
0
2
0
1
4
0
1
1
1
2
0
0
1
0
5
1
1
0
2
0
2
0
1
1
0
2
1
0
0
2
2
2
2
1
1
0
1
0
2
0
1
1
1
0
1
1
1
0
1
0
0
2
1
0
0
1
1
1
1
1
0
0
1
1
1
1
4
0
0
0
2
1
2
2
2
0
0
2
1
1
1
3
1
0
2
0
0
2
0
0
0
1
1
0
0
0
0
0
0
1
1
0
1
1
2
2
1
0
1
0
1
0
1
0
2
0
0
1
0
1
1
1
0
1
1
1
0
1
1
0
1
2
0
1
0
1
1
0
2
1
1
0
1
0
0
1
2
2
1
2
1
1
0
1
2
0
1
2
0
0
0
2
0
1
1
0
0
0
2
2
1
2
2
2
0
0
1
1
2
1
1
1
0
1
1
1
0
2
1
0
1
0
2
0
0
2
3
0
2
0
1
0
0
1
1
1
1
0
1
3
0
2
1
1
1
1
1
0
2
0
0
1
0
2
0
0
0
2
0
0
1
2
0
1
1
0
0
1
0
1
1
1
1
2
2
1
1
0
1
0
0
0
1
1
0
0
1
0
0
2
0
2
0
1
2
1
2
1
0
0
1
0
0
0
1
0
1
1
0
2
1
0
0
1
0
0
0
1
1
1
0
2
0
1
2
0
1
1
1
0
1
0
2
0
0
0
3
1
0
2
1
0
1
0
1
0
0
2
2
1
2
0
1
1
0
0
1
1
1
3
2
1
0
1
2
0
1
0
2
1
0
0
0
1
1
1
0
0
2
2
2
1
2
1
2
0
0
1
1
0
2
1
0
0
1
1
2
1
1
1
1
2
0
0
1
1
0
0
1
0
1
0
0
1
0
1
2
0
1
0
2
0
1
0
1
8
0
3
2
0
0
1
0
0
0
1
2
0
2
0
1
0
0
0
0
0
0
0
2
0
2
3
2
1
1
1
0
0
0
1
1
1
1
0
0
0
0
1
0
0
0
1
0
1
1
0
1
0
1
0
1
0
0
0
1
0
1
1
1
4
1
0
0
1
2
1
1
2
0
0
0
0
0
1
1
0
0
0
1
1
0
1
2
0
1
0
0
3
1
0
0
2
2
0
2
0
1
0
0
0
2
1
1
0
0
1
2
0
0
1
2
1
0
2
2
1
1
0
2
1
0
1
1
1
0
2
0
0
0
0
2
1
0
1
0
1
0
0
2
1
1
1
1
2
1
1
0
2
0
0
1
1
2
0
0
2
2
0
1
0
0
1
2
2
2
0
1
0
1
1
2
1
3
2
2
2
0
1
0
2
1
1
6
1
0
0
2
1
1
0
1
1
2
2
2
0
1
0
0
2
0
0
1
1
0
2
0
0
0
1
0
0
0
1
1
0
1
0
0
2
0
2
2
2
0
1
2
1
1
1
0
1
1
0
1
0
0
0
2
0
0
0
0
2
0
0
1
1
0
3
0
1
0
0
1
0
2
1
0
1
1
0
0
0
1
0
2
1
1
1
1
1
4
1
1
0
1
1
0
0
0
0
1
2
0
0
0
1
2
1
0
1
0
2
1
1
1
2
2
3
1
0
0
0
0
2
0
0
1
2
0
0
1
2
0
1
3
1
1
2
2
1
0
1
2
2
2
1
1
2
1
1
0
0
1
1
0
0
1
0
1
2
1
1
0
0
2
2
0
2
1
3
1
0
0
0
0
1
0
1
0
0
2
2
0
1
0
1
1
2
2
0
1
1
0
0
0
1
0
0
2
0
0
1
1
2
1
0
1
0
0
1
2
1
2
1
0
1
0
0
0
2
1
1
1
2
0
0
2
1
1
1
2
2
2
1
0
1
0
0
0
2
0
3
1
2
0
2
0
0
1
1
1
2
0
4
1
0
1
0
1
2
1
1
1
1
0
1
0
1
2
1
2
0
1
1
0
2
0
1
2
0
0
2
0
1
2
0
0
0
0
1
0
0
1
1
0
0
0
0
1
1
2
1
1
1
1
1
1
0
1
0
2
1
1
2
1
2
1
1
0
1
1
0
0
1
2
1
1
0
0
1
0
1
1
1
1
0
1
1
0
1
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
1
0
1
1
1
0
1
2
1
1
1
2
2
1
2
1
1
1
2
1
0
1
2
1
0
0
1
2
0
0
2
1
3
2
0
1
1
0
2
1
1
2
1
0
0
1
0
1
0
0
1
0
0
2
2
0
0
1
2
1
1
2
0
3
1
0
1
0
0
0
0
1
1
1
0
0
0
2
0
0
1
2
0
2
2
2
1
2
1
2
2
1
0
0
2
2
0
0
1
1
2
0
0
2
0
2
1
1
0
1
2
2
0
1
2
1
0
0
1
0
2
0
0
0
0
1
0
2
0
2
0
1
0
0
0
0
1
2
0
0
0
0
2
1
2
1
2
2
1
0
0
0
0
1
1
0
0
0
1
2
0
2
0
1
0
2
0
1
1
2
0
0
0
2
1
0
1
0
0
0
0
0
2
1
0
2
0
0
0
1
0
2
0
7
1
1
0
2
0
0
0
0
1
0
1
1
0
1
2
0
0
1
0
0
1
0
0
2
1
1
0
0
1
1
1
0
0
0
1
0
0
1
2
1
0
1
0
0
1
0
1
1
1
1
2
0
2
1
2
0
1
2
1
0
1
1
2
0
1
1
0
1
1
0
0
1
2
2
2
0
0
1
0
1
0
0
0
2
1
1
1
0
2
1
0
0
1
1
0
1
0
1
1
0
2
2
1
2
1
2
2
0
0
0
0
0
0
1
1
1
1
2
1
1
0
1
1
1
1
2
2
0
1
1
0
0
0
0
2
0
2
1
0
0
3
1
0
1
0
2
1
0
0
1
0
1
0
0
0
1
0
2
1
1
2
1
1
1
0
0
8
0
2
2
1
0
0
0
1
1
2
0
0
0
2
1
1
0
0
1
0
1
1
1
2
0
0
2
1
0
1
0
0
1
0
0
0
2
2
3
0
0
2
2
0
1
1
0
1
0
2
1
1
0
1
0
1
1
1
1
1
0
1
2
2
1
1
2
1
2
1
2
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
2
1
0
0
1
1
0
1
2
0
1
1
1
2
1
3
0
2
0
1
1
1
1
1
2
1
0
1
0
0
0
1
1
1
2
0
2
2
1
0
2
0
0
1
0
1
2
0
2
0
2
1
2
2
0
1
1
0
2
1
1
1
2
1
1
1
2
1
0
1
0
0
0
0
2
2
2
2
2
2
1
0
2
0
2
1
1
0
1
2
0
2
2
0
1
2
0
2
1
1
1
1
1
0
0
1
1
2
0
0
0
1
1
3
2
0
1
1
0
1
0
1
0
1
1
1
1
0
0
1
0
2
0
0
1
1
0
1
0
1
3
1
0
0
0
0
0
1
1
0
1
1
0
1
1
1
2
0
1
0
1
0
0
2
1
1
0
0
0
0
1
0
1
1
2
0
0
0
0
0
1
1
0
2
1
0
2
0
1
0
1
0
1
1
0
1
0
2
1
0
1
0
1
0
0
0
0
0
1
0
1
2
1
1
1
0
2
2
0
1
2
1
0
2
2
2
0
0
2
1
0
0
0
0
0
1
1
2
0
0
1
1
0
1
2
1
0
2
0
2
1
1
0
2
1
1
0
1
1
1
1
2
0
1
0
0
0
0
1
1
0
0
0
1
2
0
1
2
2
1
1
1
1
1
3
3
1
1
2
2
2
0
0
0
2
1
2
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
1
1
1
0
0
0
2
1
2
2
0
1
0
0
1
0
1
1
1
1
0
1
1
1
2
0
2
1
2
0
0
0
1
1
1
2
0
0
1
0
2
1
1
0
1
0
2
1
0
1
1
1
0
0
1
0
2
0
0
0
0
0
0
2
1
2
1
1
1
2
0
2
0
2
0
1
1
2
0
0
2
1
2
1
1
0
0
0
1
1
1
1
1
2
0
1
1
0
1
1
1
1
3
1
2
2
1
1
1
0
2
2
1
1
1
1
2
1
1
2
2
0
0
1
1
1
1
2
1
2
2
1
2
1
0
0
0
1
3
2
0
1
0
0
1
1
4
1
1
0
2
0
0
0
0
2
0
1
0
0
1
1
0
0
0
2
1
0
1
0
0
1
1
1
2
2
2
2
1
1
2
0
2
0
0
2
0
0
0
2
0
0
1
0
1
0
0
0
2
2
0
1
1
0
0
1
1
0
2
0
2
1
0
1
1
2
1
1
2
0
0
1
1
0
2
0
0
1
1
1
4
2
0
2
0
0
0
1
1
0
1
1
1
1
0
1
1
0
1
1
2
2
3
0
1
1
1
0
0
0
1
0
0
1
1
1
1
0
1
0
2
1
3
0
1
2
3
0
1
1
0
0
2
0
0
0
0
0
1
1
1
1
0
0
2
0
1
1
0
2
0
1
0
0
1
1
2
0
0
0
1
0
1
2
1
1
1
2
1
1
0
3
1
1
1
1
0
1
0
0
2
1
0
1
1
1
0
2
0
1
1
0
0
0
1
2
0
0
0
0
1
0
0
0
2
2
0
0
2
0
1
0
0
0
1
1
0
2
0
0
0
2
1
0
0
0
2
1
2
2
1
1
0
1
0
1
0
2
2
0
2
0
1
1
1
2
3
1
0
2
0
2
2
1
2
1
1
0
1
0
1
0
0
0
0
1
0
1
3
1
2
1
1
1
1
1
2
1
0
1
2
1
1
0
0
1
1
1
2
0
0
2
1
0
0
2
1
1
1
1
2
1
0
1
1
0
0
2
1
2
1
1
0
0
0
1
2
0
0
1
2
1
0
1
1
2
1
1
2
2
0
1
3
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
2
1
0
0
1
0
0
0
1
1
0
2
1
0
1
1
0
1
0
2
1
0
1
2
1
2
0
1
0
0
2
1
0
1
1
1
0
0
1
0
1
0
1
0
0
1
2
2
0
1
1
1
0
0
0
2
2
0
1
0
0
2
2
1
0
0
0
2
1
0
0
1
0
2
0
1
1
0
1
1
1
2
0
3
1
0
2
1
1
1
0
1
1
1
0
0
0
2
1
1
1
0
2
0
1
1
1
3
0
0
0
1
1
0
0
1
0
0
1
0
2
1
0
0
2
2
1
1
0
2
2
3
1
0
1
0
1
2
0
1
0
2
2
0
1
1
0
1
1
0
0
0
1
0
0
1
1
1
2
0
1
2
0
1
1
0
1
2
1
1
0
1
2
1
0
1
1
2
1
1
1
0
0
0
3
1
1
0
0
0
2
1
1
0
1
0
1
0
0
1
0
0
1
2
1
2
2
1
0
1
0
1
1
1
1
0
1
0
3
1
1
0
0
0
1
0
1
0
1
1
1
1
1
0
0
0
0
1
0
1
0
0
2
1
2
1
2
1
0
0
2
1
2
0
2
1
1
1
0
1
1
0
0
0
0
1
0
1
1
1
0
2
2
1
0
2
1
1
1
1
2
2
1
1
2
0
0
1
3
1
1
0
0
2
3
2
0
1
2
1
1
0
0
1
0
0
0
0
2
4
1
1
0
2
0
3
0
0
1
1
2
0
1
2
2
0
0
0
0
1
2
1
1
1
2
1
0
0
1
1
0
1
1
1
2
1
0
3
2
1
2
0
1
1
1
2
1
1
0
1
1
3
1
1
0
2
0
0
2
1
1
1
1
2
0
2
0
0
2
0
0
0
2
1
0
1
2
0
0
1
1
1
1
4
1
1
1
1
2
0
0
0
0
1
1
3
0
0
2
0
1
0
2
2
0
0
2
1
1
2
0
2
1
2
0
1
0
2
1
2
0
0
0
1
2
2
1
1
1
1
2
0
1
2
1
1
1
1
2
1
0
1
2
0
2
1
2
1
0
0
1
1
1
0
1
1
1
0
0
1
2
0
0
0
2
0
0
0
2
0
3
1
0
1
0
0
0
0
0
0
1
1
2
0
1
1
1
1
0
0
2
1
1
2
1
2
0
0
0
1
3
1
1
0
0
2
0
0
1
0
0
1
0
2
1
1
1
0
0
2
1
1
0
0
1
2
1
1
0
1
1
2
0
0
2
0
1
0
0
1
0
1
0
1
1
2
0
2
0
1
1
0
0
1
1
0
0
1
1
3
1
1
1
0
0
2
1
0
2
0
0
0
0
1
2
0
0
0
1
0
0
0
0
1
1
1
2
0
2
0
1
0
0
1
0
1
1
1
0
1
1
0
3
1
0
0
0
1
0
0
0
2
1
0
1
1
0
1
1
0
1
1
0
0
0
0
1
2
1
1
0
1
1
2
2
1
1
1
0
1
2
1
0
0
1
0
1
0
2
1
1
1
0
0
2
0
0
1
1
1
1
1
0
0
0
0
1
2
2
2
1
0
1
1
2
0
0
1
0
1
0
2
2
0
1
1
1
2
3
0
0
2
1
2
0
0
1
2
0
1
2
0
2
1
0
1
1
0
0
1
2
1
0
0
0
0
1
1
1
0
0
0
2
1
0
0
0
0
0
1
2
2
0
1
1
0
1
1
1
2
1
1
1
0
0
2
1
1
1
0
1
0
1
1
0
0
0
2
2
0
0
1
0
0
2
1
0
0
0
0
3
0
0
0
1
2
0
1
1
2
0
1
3
1
0
1
1
0
1
1
1
0
2
1
0
0
0
0
1
0
1
3
1
1
0
0
1
2
1
1
0
1
1
0
0
1
2
1
1
2
1
2
0
0
0
0
0
1
1
2
2
0
1
1
1
2
0
2
2
2
2
2
0
1
1
1
1
2
2
1
1
0
0
0
1
1
1
0
2
1
0
2
1
1
0
2
1
0
0
2
2
3
0
1
1
1
1
0
0
1
0
1
0
0
1
2
1
1
1
2
1
2
0
1
2
0
0
1
1
0
0
1
0
0
0
0
2
1
1
0
1
2
1
0
0
1
0
1
0
2
0
1
0
2
1
1
0
2
1
2
1
0
1
0
0
2
1
1
0
0
0
2
2
0
1
1
0
1
2
2
0
1
0
9
0
0
2
0
2
2
1
1
0
1
1
2
2
0
0
1
2
0
0
0
2
1
2
0
1
1
1
2
1
1
0
2
2
2
0
0
0
4
3
1
1
0
1
2
1
1
1
2
0
1
0
5
0
1
2
0
0
0
2
0
0
0
0
2
1
1
1
2
2
1
1
2
1
0
0
2
0
0
1
1
1
0
1
0
1
2
2
2
0
0
1
2
0
0
0
2
3
0
1
2
1
0
1
2
2
1
2
0
0
1
0
1
1
1
0
0
1
1
1
1
1
1
2
3
1
2
0
2
0
1
1
0
2
1
0
0
1
1
2
1
0
1
1
0
1
1
1
0
0
0
2
0
0
1
1
2
1
0
0
0
1
1
1
1
2
0
0
1
0
2
1
0
2
2
0
1
2
2
0
2
1
0
2
1
1
3
0
0
1
1
2
1
2
2
1
1
0
2
0
0
1
1
2
0
0
2
2
1
1
1
1
1
1
2
0
1
2
1
0
1
1
1
2
0
0
2
1
0
2
1
0
1
1
1
0
1
1
1
1
0
0
2
0
1
1
2
2
1
0
1
0
2
3
1
0
0
2
0
0
1
0
1
0
2
1
1
1
1
0
0
1
1
1
0
0
0
1
1
1
1
2
1
1
0
1
2
0
1
1
0
2
0
0
0
2
1
0
2
3
1
0
2
2
1
0
0
1
1
1
0
1
1
1
1
1
1
0
1
2
1
2
2
0
1
0
0
0
2
1
1
2
1
1
0
0
1
2
2
0
4
1
1
1
1
0
0
0
2
2
0
1
1
0
1
0
1
1
0
1
1
0
2
2
0
3
1
1
0
2
0
2
2
1
0
0
1
0
0
1
0
1
0
1
0
1
0
1
1
1
0
2
2
0
0
2
2
1
0
1
1
0
1
1
0
0
0
1
0
1
3
2
0
2
0
2
2
2
1
0
1
0
1
1
0
2
0
1
0
1
0
1
0
0
0
0
2
3
1
1
2
1
2
1
1
2
3
0
1
1
0
0
0
0
1
1
1
1
1
2
0
2
1
0
0
0
0
1
0
1
2
1
1
0
1
1
0
0
0
1
2
0
2
1
2
1
1
1
1
0
0
0
2
0
1
1
0
1
2
0
1
0
1
2
0
0
0
1
2
1
2
2
1
0
1
0
0
0
1
0
2
0
0
1
1
0
1
1
1
0
1
0
1
2
1
2
0
1
2
1
0
2
1
0
0
0
0
0
0
1
0
1
0
0
1
2
0
1
2
0
2
1
2
2
0
1
0
2
2
0
1
1
0
1
0
1
2
0
1
2
1
2
0
2
0
1
0
1
1
1
0
1
1
0
1
1
0
0
1
2
0
2
1
2
0
2
0
1
1
1
2
2
1
2
1
0
1
1
0
0
2
2
2
0
1
0
2
0
0
2
1
1
0
1
0
1
1
0
0
2
0
0
1
1
0
1
0
1
2
2
1
2
1
1
2
1
0
2
2
0
2
0
2
3
2
0
1
0
3
0
1
0
2
0
1
1
1
1
0
0
1
2
2
2
2
1
0
0
1
0
0
1
0
0
0
0
0
1
2
1
0
1
0
0
1
2
1
0
1
2
2
1
0
2
0
0
0
1
0
0
2
2
0
0
1
1
0
1
1
0
1
1
1
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
1
1
2
0
1
0
0
1
1
1
0
2
0
1
0
0
2
2
2
1
2
1
2
0
0
2
2
0
0
1
1
0
1
1
0
1
2
1
12
0
0
2
0
2
1
1
2
2
0
1
2
1
0
0
0
1
2
1
2
0
2
1
0
1
1
1
0
0
2
1
0
1
0
0
0
1
3
1
1
1
1
0
1
0
0
2
2
1
0
0
0
2
0
2
0
0
1
0
1
1
2
2
0
0
1
0
1
1
1
1
1
2
2
1
1
2
0
2
0
2
2
2
0
2
0
0
2
0
1
1
0
1
0
1
0
0
0
1
1
0
1
1
1
0
1
0
1
1
0
0
0
0
0
0
1
1
2
0
0
0
0
1
1
1
2
2
2
0
2
1
0
1
1
0
2
1
2
2
0
2
2
1
1
1
0
0
1
2
1
3
0
2
0
2
0
1
2
1
1
0
0
0
1
0
1
0
0
0
0
1
0
1
2
0
0
1
1
0
2
0
1
0
0
0
0
0
2
1
1
0
2
1
1
1
2
0
0
2
0
1
0
0
0
1
0
1
1
2
0
2
1
1
0
0
3
2
0
0
1
1
0
0
2
2
0
2
1
1
0
0
1
0
1
1
2
2
1
2
0
0
0
0
0
1
2
1
1
0
0
1
0
2
1
0
1
1
1
1
2
1
1
0
1
2
1
1
2
0
1
2
1
0
1
1
1
0
1
0
1
0
2
2
2
0
0
0
1
1
0
1
0
0
2
0
0
1
1
2
1
1
0
1
1
0
2
0
1
2
0
0
1
2
2
1
0
1
0
2
0
2
0
0
0
2
1
2
0
0
1
2
0
0
1
2
2
1
1
0
1
1
2
1
1
1
2
1
0
2
0
0
0
1
0
1
2
1
1
2
1
0
2
2
0
1
1
1
0
2
0
1
0
1
1
2
0
1
1
0
1
0
1
2
1
0
2
2
2
1
0
1
1
1
0
1
1
0
1
1
0
0
0
3
0
2
1
1
2
0
2
2
1
0
1
0
2
0
2
1
1
1
1
2
1
0
0
0
1
1
2
1
1
1
1
1
0
2
1
0
0
1
1
2
0
1
0
0
1
1
3
1
0
2
1
0
1
0
2
2
1
0
0
2
0
1
1
0
1
0
2
0
0
0
1
1
1
1
2
1
0
1
1
1
1
1
0
0
1
0
1
1
0
0
1
2
1
0
0
0
0
1
0
1
1
1
0
0
0
0
1
0
0
0
0
1
2
2
1
0
0
1
1
6
0
1
2
2
2
1
1
2
1
0
2
0
2
0
0
0
0
1
1
2
2
1
1
0
0
1
1
2
0
2
0
2
2
0
2
1
1
2
1
1
1
0
1
1
1
1
1
2
1
1
2
0
0
2
0
1
2
2
2
2
0
3
1
0
2
0
0
1
0
1
0
2
0
0
3
0
1
1
0
0
2
1
0
2
1
2
1
2
0
1
2
2
0
0
2
0
1
0
0
1
2
1
1
1
1
0
1
1
1
0
1
0
0
0
1
1
1
1
0
0
1
0
1
1
1
0
1
2
0
0
0
1
1
2
1
0
1
1
0
0
1
0
2
0
0
0
0
0
1
2
2
2
2
0
0
2
1
1
1
1
0
2
0
0
0
0
2
0
0
2
0
1
2
2
1
0
2
0
1
1
0
0
2
2
0
1
0
0
0
0
1
1
0
2
1
1
0
0
1
0
0
1
2
0
0
2
0
0
1
1
0
1
1
1
0
0
0
1
2
0
0
2
2
2
1
1
1
1
1
1
1
1
1
4
0
0
0
1
1
0
0
1
0
0
1
1
1
0
0
1
0
1
2
1
0
2
2
1
0
1
1
2
0
0
0
0
1
1
1
1
1
2
2
0
1
2
1
1
2
0
0
0
1
1
2
0
1
0
1
0
1
2
1
1
1
0
1
1
0
2
1
0
0
0
2
0
0
1
0
2
0
2
1
0
1
0
0
0
0
1
0
2
1
1
1
2
1
1
1
1
0
1
0
1
1
0
0
1
0
2
1
0
0
1
0
0
0
0
0
0
1
1
0
2
2
0
2
1
0
1
0
1
0
1
2
0
1
1
1
1
1
1
0
1
0
1
1
2
1
0
1
1
0
1
1
0
2
1
1
0
0
1
2
1
1
2
0
1
2
1
1
1
0
0
0
2
2
1
3
0
1
1
0
1
1
0
0
1
2
0
2
0
1
1
0
0
2
1
1
2
1
0
1
2
2
0
1
0
1
2
1
0
1
3
2
1
0
1
1
1
1
1
1
1
0
0
1
0
1
1
2
0
0
2
1
0
1
1
1
1
0
1
0
0
1
2
0
1
0
2
1
0
0
0
0
0
1
1
1
2
0
2
0
0
1
1
0
0
0
1
0
2
1
1
2
2
1
0
0
0
1
0
1
0
0
0
1
0
1
0
0
2
0
1
1
1
1
0
2
1
0
1
1
2
0
0
2
0
2
0
2
0
2
0
0
1
1
1
2
1
2
1
0
1
1
0
2
0
0
1
1
1
0
2
0
0
2
2
0
2
3
0
0
2
2
0
0
0
0
1
2
1
0
1
1
1
3
0
0
1
0
0
0
0
1
1
1
0
2
1
2
2
0
0
0
1
1
3
1
0
1
1
1
1
1
1
1
1
0
2
0
0
1
2
2
0
1
0
2
1
0
1
2
0
2
0
1
0
0
2
1
1
1
1
0
2
1
1
1
0
2
1
0
1
1
0
0
1
1
0
1
1
2
2
1
2
1
0
1
1
2
0
2
1
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
2
0
1
1
1
1
0
0
0
0
2
1
0
1
2
1
4
0
1
1
0
1
0
0
0
1
1
0
2
2
1
0
1
1
0
2
0
1
2
0
1
1
1
0
1
2
0
1
0
1
2
1
1
1
2
1
1
0
2
0
1
1
0
1
0
1
0
1
2
1
0
2
2
0
0
2
0
0
0
1
0
1
0
1
2
2
1
0
0
0
0
0
1
1
0
1
0
2
0
0
1
1
0
1
0
1
0
2
0
1
0
1
0
0
1
2
0
1
0
2
1
0
0
1
0
1
0
0
3
2
0
1
1
2
2
1
2
1
0
1
0
0
1
0
0
0
1
1
1
0
2
1
0
0
1
2
2
1
2
0
1
1
1
1
1
0
1
1
0
1
1
1
2
0
0
0
0
0
0
1
1
1
1
1
1
2
0
1
1
0
0
0
1
2
0
0
1
0
1
0
2
2
0
2
0
1
0
1
1
2
2
1
1
0
0
1
1
1
2
0
1
1
0
1
2
1
2
0
0
0
0
0
0
0
1
2
0
1
1
2
1
0
0
1
0
1
2
0
0
1
0
0
1
1
1
1
1
1
1
0
1
1
0
1
0
0
2
0
2
1
0
1
1
0
0
0
0
1
1
2
0
0
1
0
2
1
0
1
1
1
1
0
0
0
0
2
0
0
2
0
1
2
1
1
0
0
0
0
2
0
1
1
1
0
2
1
2
0
0
0
0
0
0
1
2
0
1
2
0
1
1
0
4
0
1
0
0
0
2
1
0
2
0
0
1
2
1
2
0
2
2
1
1
1
0
0
1
0
1
1
2
1
0
2
0
0
2
0
0
0
0
1
1
0
2
1
0
1
2
1
2
1
1
1
0
0
2
1
2
1
1
0
1
3
0
0
1
1
0
2
2
0
0
0
1
0
0
2
4
1
1
1
0
0
1
0
2
0
2
2
0
0
1
0
1
0
0
1
2
0
1
0
1
0
0
0
0
0
1
2
0
0
2
0
1
0
1
0
0
1
1
0
1
2
2
2
2
1
2
2
1
1
0
0
1
2
0
2
1
2
2
2
2
2
0
1
1
1
2
1
1
0
1
0
2
0
0
0
1
0
0
1
0
0
1
1
4
1
0
1
2
0
0
0
1
0
3
1
1
1
0
2
2
0
1
0
0
1
1
2
0
1
1
0
0
1
1
0
0
2
0
2
3
1
0
0
0
2
1
2
0
0
0
2
0
1
2
1
1
1
2
1
1
1
0
1
0
0
0
1
1
2
0
0
2
1
1
0
2
1
1
1
0
0
1
0
0
1
1
0
2
0
0
0
0
2
0
2
1
0
3
0
1
2
1
0
2
1
1
1
0
0
1
1
2
1
1
1
1
2
2
2
0
1
0
1
2
1
0
1
1
1
0
0
2
0
1
1
0
1
1
1
0
0
0
0
0
2
0
0
0
1
1
2
1
0
0
1
2
2
2
2
2
0
0
1
1
0
1
1
1
0
0
1
1
1
1
2
1
0
0
2
1
2
1
2
2
1
0
0
1
2
2
1
1
0
1
3
0
2
0
1
2
0
0
3
1
1
1
0
1
0
1
1
1
1
2
0
0
0
0
1
0
0
0
2
0
0
2
2
1
1
0
1
0
1
0
0
2
2
0
0
1
1
0
1
0
1
1
1
1
1
2
0
2
0
0
1
0
1
0
2
1
0
1
2
0
0
0
0
1
2
1
1
0
2
1
0
1
1
2
0
0
1
0
0
1
1
0
1
0
0
2
0
1
0
2
1
2
0
1
2
1
1
1
1
2
0
1
1
0
0
1
0
0
2
1
1
2
0
1
1
0
0
0
0
0
2
1
2
0
2
1
0
1
0
2
0
1
0
0
2
0
1
2
1
2
2
2
0
0
2
3
1
0
1
2
2
0
0
1
0
0
2
1
0
2
0
1
0
2
1
0
0
0
1
1
0
0
1
1
0
1
0
0
2
0
1
2
0
0
2
0
2
2
1
2
1
1
0
1
2
1
1
0
0
1
1
3
1
0
1
0
3
0
2
0
1
1
0
0
1
0
2
1
2
1
2
2
0
1
1
0
2
1
1
0
1
0
1
2
1
0
1
2
0
1
2
0
0
0
0
0
2
1
1
2
1
1
2
1
1
1
1
2
2
1
0
1
2
1
2
2
1
1
1
1
0
0
1
0
0
0
1
0
1
1
1
0
0
2
1
0
0
1
0
1
0
1
1
1
2
1
1
0
2
1
2
1
3
1
1
2
1
0
1
1
1
1
0
0
1
1
2
0
1
2
1
0
1
0
0
0
4
1
0
0
1
1
0
0
1
1
2
1
1
0
1
2
1
1
1
0
0
0
2
1
1
1
0
0
2
0
1
2
0
0
2
2
0
2
0
1
1
1
0
1
2
0
0
2
1
1
0
0
0
2
1
1
1
1
1
2
2
0
0
3
0
1
0
0
1
0
1
2
0
1
0
0
1
1
2
1
0
2
0
0
1
2
0
0
1
0
2
0
3
1
0
0
0
0
2
1
2
1
1
0
2
1
0
1
0
2
1
0
0
2
1
0
1
1
2
2
0
0
2
2
1
1
1
2
1
0
1
2
2
0
1
0
0
0
1
0
1
1
0
3
1
0
1
1
0
2
3
1
0
0
0
0
1
0
1
2
0
0
0
1
0
1
2
2
0
0
1
1
2
2
1
1
0
2
0
0
2
0
1
0
2
1
1
2
2
1
1
2
0
1
1
0
1
0
1
0
2
0
1
1
3
0
1
2
0
0
0
2
1
1
1
1
1
1
0
0
1
1
0
1
0
1
1
0
1
2
0
0
0
2
1
0
0
2
1
1
0
0
1
0
0
0
1
2
0
0
1
2
0
0
1
2
2
0
2
0
1
1
1
2
0
0
0
2
0
0
0
1
1
1
0
0
0
0
2
0
2
0
0
1
1
2
0
0
0
0
1
2
0
1
0
0
0
0
0
2
2
0
0
0
0
0
1
0
1
0
0
2
0
2
1
3
1
1
0
0
0
1
0
0
1
1
1
1
0
2
0
2
0
0
1
0
0
0
0
0
1
2
0
0
1
1
0
1
2
1
1
0
1
1
1
2
0
1
0
1
0
1
1
2
0
1
0
0
1
0
1
1
1
2
0
3
2
2
1
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
1
1
0
1
0
0
2
1
1
2
1
2
2
0
2
0
1
2
1
1
1
0
1
0
1
1
0
1
2
1
1
0
0
0
0
0
0
2
1
0
2
3
1
0
1
0
0
0
2
2
0
1
0
0
1
1
1
1
0
1
0
1
2
0
0
1
0
2
1
1
0
2
2
0
1
0
0
0
0
1
0
1
1
0
1
2
0
0
2
1
0
1
3
1
1
0
2
1
2
3
2
1
1
0
0
0
0
1
0
0
2
1
1
0
1
0
1
0
1
2
1
0
0
1
1
2
0
1
2
2
0
1
0
0
0
1
0
0
0
3
2
0
0
1
0
1
1
1
1
1
0
0
3
2
1
0
1
1
1
2
0
0
1
2
0
0
1
1
1
0
2
1
1
1
0
0
1
2
0
2
1
1
0
0
0
1
1
0
0
0
0
1
1
0
1
0
3
2
0
1
1
1
0
0
2
0
0
0
0
1
0
2
1
0
0
1
0
1
0
0
2
1
0
2
0
2
1
0
0
0
0
1
1
0
0
0
1
2
1
1
0
0
2
2
2
1
0
1
1
0
1
0
4
0
0
1
0
0
2
0
0
1
1
0
2
1
1
1
0
0
2
1
0
1
0
0
0
0
2
0
1
0
2
1
0
2
1
3
2
1
0
2
1
1
2
1
1
0
1
1
1
2
1
1
0
2
0
1
0
1
2
0
0
0
0
0
0
2
1
1
1
0
0
0
1
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
1
0
0
1
1
2
0
1
0
2
0
1
0
0
0
1
2
1
2
2
0
1
1
0
0
1
2
4
1
1
1
1
0
2
1
1
0
2
2
1
0
0
2
0
0
3
1
1
2
1
2
1
1
0
1
0
0
2
0
1
2
2
0
0
0
0
0
1
2
0
0
0
1
0
0
1
2
2
0
1
0
0
1
1
0
0
2
0
1
2
2
0
0
2
1
2
2
1
0
0
2
0
1
0
0
1
0
0
2
2
0
1
2
0
1
0
2
1
0
0
2
1
0
0
1
0
1
0
2
1
2
1
0
1
1
0
1
0
0
1
1
0
1
0
0
2
0
1
0
0
1
0
0
1
0
0
1
0
0
2
0
1
1
0
2
1
1
0
0
0
1
2
1
0
0
1
0
1
1
2
0
0
1
0
1
1
1
0
1
1
0
1
0
1
1
2
1
0
1
2
1
2
1
1
2
0
2
0
0
1
1
0
1
0
0
0
1
0
1
1
2
1
2
1
1
2
1
0
0
0
1
1
1
1
2
0
1
0
1
1
1
2
1
1
2
0
1
1
0
2
0
1
1
0
0
1
1
1
2
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
1
1
1
1
1
2
0
0
2
0
0
1
1
2
0
0
0
0
0
1
2
0
1
2
2
0
0
0
1
2
1
2
1
2
0
0
1
0
0
1
2
2
0
2
1
2
1
0
0
2
0
1
2
1
0
1
0
3
2
0
1
0
0
0
2
0
0
0
1
0
2
0
0
2
1
1
2
0
1
0
2
0
0
0
0
0
1
1
1
1
1
0
1
0
0
2
2
2
0
0
1
1
0
0
0
0
2
0
0
0
1
1
0
1
1
1
2
1
2
0
1
1
1
0
2
0
1
1
1
1
0
1
1
0
0
1
1
2
2
0
0
1
0
0
1
0
0
0
1
0
2
2
0
1
1
0
2
2
0
1
1
3
0
0
0
0
0
1
0
0
1
1
0
1
0
2
1
0
1
3
0
1
1
1
0
1
1
0
1
1
0
1
1
1
2
1
1
0
0
1
2
1
1
1
3
0
0
2
0
1
2
0
2
0
2
0
1
0
1
2
0
0
2
1
2
2
2
1
1
1
1
1
1
2
1
0
1
0
2
1
2
0
0
0
1
0
2
1
2
1
0
1
2
2
1
2
0
1
1
0
2
0
2
0
1
0
0
1
0
0
2
1
2
0
2
0
0
1
1
2
0
2
1
1
1
0
0
0
0
2
0
0
1
2
0
0
0
1
2
1
0
2
1
2
0
0
1
1
1
1
0
1
1
0
0
1
1
1
1
1
2
3
1
1
0
0
2
1
0
1
0
1
1
0
1
0
3
0
1
0
1
1
0
1
2
1
1
3
1
1
1
0
2
0
0
0
0
0
0
0
2
1
1
1
0
0
0
2
0
0
0
2
1
1
2
2
2
2
1
1
1
1
1
1
0
1
0
2
0
2
1
0
0
1
0
0
1
1
0
0
0
1
1
2
1
1
0
1
0
1
0
1
2
2
1
0
2
0
0
0
2
1
1
0
2
1
0
0
0
2
1
0
1
4
1
0
0
0
0
1
2
1
2
2
0
1
2
2
0
2
1
1
1
2
0
0
0
2
1
0
1
0
1
0
2
2
2
0
1
0
2
0
2
1
2
0
0
0
0
2
1
1
0
2
3
0
0
0
2
2
2
0
0
0
1
1
0
1
2
1
2
2
1
0
0
1
1
0
3
1
0
1
2
0
1
1
1
2
2
1
1
0
2
0
2
0
0
0
0
1
0
1
0
1
0
1
1
1
2
1
0
1
2
1
2
0
2
0
0
0
0
1
1
0
2
0
2
1
0
0
0
2
0
2
2
0
1
0
1
0
2
1
0
2
2
1
1
0
0
0
2
0
0
2
1
1
1
1
1
0
0
2
2
2
1
1
2
0
1
0
1
1
0
1
2
0
3
1
2
1
0
0
1
1
1
2
2
0
2
0
1
0
0
0
1
0
0
0
0
0
0
2
1
2
2
1
0
1
2
2
2
0
0
0
0
2
0
2
1
0
2
2
2
3
1
2
0
1
1
3
0
0
1
0
2
2
2
2
0
0
0
0
0
1
2
1
0
0
1
2
1
1
2
1
0
0
1
1
0
0
0
1
1
0
2
2
2
0
0
0
2
1
0
1
2
1
2
2
1
1
0
0
2
2
1
2
0
1
2
1
1
2
0
0
1
1
2
1
0
1
0
0
2
1
1
1
2
2
0
1
0
0
1
0
2
1
0
1
0
0
0
2
1
0
3
0
1
2
1
2
0
0
0
0
2
0
1
1
1
1
1
2
0
0
1
1
1
0
0
0
2
1
0
0
1
0
1
1
0
1
1
1
0
2
1
1
0
2
1
1
2
2
1
0
0
1
3
0
0
2
1
0
0
2
0
1
1
0
1
0
2
0
0
1
1
0
0
2
1
0
0
2
0
2
0
1
1
1
1
0
1
2
0
0
1
1
1
2
0
0
1
1
1
2
0
1
2
2
1
0
2
0
1
0
0
0
0
0
0
1
1
1
1
1
0
0
1
1
1
2
1
2
0
1
0
0
1
1
2
1
1
1
3
0
0
0
0
0
0
0
1
1
1
0
0
1
0
1
1
2
0
2
0
1
0
0
2
1
1
1
1
0
2
1
0
0
1
0
0
2
1
1
1
2
1
1
0
0
2
1
1
1
1
2
1
1
0
0
1
1
1
3
3
1
0
2
1
0
0
2
1
1
0
0
0
1
2
0
1
0
1
2
0
0
1
0
0
0
0
1
0
2
1
2
0
0
0
1
2
0
2
0
1
2
0
2
0
2
0
0
1
1
1
1
1
1
1
0
2
0
2
2
1
2
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
1
0
1
1
2
2
0
1
0
1
0
0
1
1
1
1
0
1
0
1
0
1
0
0
1
3
1
0
0
1
1
1
1
0
0
0
0
1
1
0
2
2
1
0
1
1
1
2
1
0
1
2
2
1
2
0
1
1
2
1
1
0
2
0
2
1
1
1
2
2
0
1
2
0
0
1
1
1
1
2
1
0
0
0
2
2
0
0
1
1
2
1
1
1
1
2
1
2
2
0
0
1
0
2
0
0
0
0
2
0
1
2
1
0
0
3
1
2
0
2
0
1
3
2
0
1
2
0
2
1
1
0
1
2
2
1
2
1
1
0
2
2
0
1
1
1
0
1
2
0
2
1
2
2
1
0
0
1
0
1
2
0
2
0
1
0
2
1
1
1
2
2
0
0
2
2
0
1
1
2
1
1
0
1
2
1
0
0
2
1
1
1
0
2
0
2
1
3
0
2
0
1
1
1
1
1
1
1
0
0
1
1
0
0
1
0
0
1
1
1
1
0
1
0
1
0
1
2
1
0
2
1
1
0
0
0
2
2
1
2
1
1
0
0
0
2
2
1
0
0
2
0
3
1
0
0
2
1
1
2
0
2
1
1
2
0
0
0
3
0
0
1
1
1
1
0
3
2
1
2
1
1
0
0
0
1
0
0
1
2
1
0
0
1
1
0
3
2
0
2
0
2
0
1
0
1
2
1
1
2
1
1
0
2
2
0
1
1
0
0
1
1
0
0
0
2
0
1
1
1
0
3
1
2
0
2
0
1
0
2
1
1
0
2
1
1
1
0
1
0
1
2
0
2
0
2
0
2
1
1
0
0
0
0
0
1
1
0
2
1
2
0
1
1
2
1
0
1
1
1
1
1
0
1
0
0
2
2
1
1
1
1
1
0
1
2
2
0
2
2
0
2
0
1
2
0
0
2
1
1
1
2
0
0
0
0
0
0
1
0
2
1
1
2
2
1
0
1
0
1
0
1
1
0
1
1
1
2
1
1
0
1
1
0
1
1
1
2
1
2
0
0
0
0
1
1
3
0
2
1
1
1
1
0
0
1
0
0
0
2
0
1
0
2
0
0
2
1
1
2
2
0
0
0
1
1
1
2
1
1
0
1
0
1
3
2
0
1
1
0
2
0
0
2
0
1
0
0
0
1
1
0
2
0
1
0
0
0
0
0
0
1
0
1
0
2
2
0
1
0
0
1
1
0
1
1
1
0
1
0
0
0
1
2
0
2
1
1
0
0
0
0
1
2
0
1
1
1
2
1
1
1
0
0
1
2
1
2
0
2
2
0
0
0
2
0
0
2
0
2
0
2
0
0
1
0
2
0
1
0
2
1
2
0
1
0
1
0
1
0
1
0
1
1
0
2
0
0
2
0
0
0
1
1
1
2
0
0
0
2
0
2
0
1
1
1
1
1
2
0
1
1
2
0
0
2
2
2
0
1
1
1
0
2
1
1
0
0
0
1
0
0
2
2
0
1
0
2
2
0
2
1
0
1
0
0
0
0
2
0
0
1
1
0
0
3
0
0
1
1
1
1
0
1
2
0
2
1
1
0
1
0
2
0
2
2
1
1
1
1
0
2
3
1
1
1
0
0
1
0
1
0
1
2
0
1
1
2
1
0
0
1
1
0
1
0
0
0
1
2
1
0
2
0
1
3
0
0
0
1
1
0
1
0
0
0
2
2
1
2
0
1
1
0
1
0
1
0
1
1
0
1
0
1
1
0
1
1
0
1
2
1
2
1
1
1
0
1
1
0
0
1
0
1
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
3
0
1
1
0
1
1
0
0
2
0
0
0
1
0
1
1
0
1
1
1
1
2
1
1
1
0
0
0
1
1
2
0
1
0
2
1
0
0
2
1
0
1
2
0
1
1
0
0
1
0
1
1
1
0
0
1
1
1
1
2
0
1
1
1
0
0
2
2
0
2
1
0
0
0
1
0
1
2
0
1
2
0
0
0
0
0
0
1
0
0
1
0
1
0
2
0
1
0
2
0
0
0
0
2
2
1
0
0
1
1
1
2
2
0
0
1
0
0
2
1
0
1
2
0
0
2
2
1
0
2
0
1
0
0
1
0
0
2
0
1
2
1
1
1
0
0
1
2
2
0
1
0
1
1
2
1
0
0
2
1
1
0
1
1
1
2
1
2
2
1
2
0
0
2
0
0
2
0
1
0
0
0
1
1
0
0
1
2
2
0
1
1
0
0
0
1
1
2
0
2
2
1
0
1
2
1
2
0
1
0
1
0
0
2
1
0
2
1
1
2
1
0
1
2
1
0
0
1
1
1
1
1
1
1
1
0
0
0
2
1
0
2
1
0
3
2
2
2
0
1
1
2
2
1
0
0
1
1
1
2
1
2
2
0
1
0
0
0
1
1
0
1
1
0
2
2
1
1
1
1
0
0
0
1
0
0
0
1
1
2
0
2
1
0
0
0
0
1
3
1
0
0
1
1
2
0
2
2
1
1
1
0
1
2
1
0
2
1
0
0
0
2
0
2
0
1
1
1
0
2
1
0
0
1
1
1
1
0
0
2
0
0
3
1
1
0
1
0
2
2
1
0
2
0
1
1
1
1
2
0
1
0
0
1
2
0
2
0
2
0
2
0
0
1
0
1
0
2
1
0
1
0
0
0
1
1
0
0
0
0
1
1
1
0
2
0
1
0
2
2
2
0
1
0
2
0
2
2
1
1
0
1
1
0
0
2
1
1
2
2
2
0
1
1
0
1
0
3
1
1
1
2
1
0
3
1
1
0
0
1
1
1
1
0
2
0
3
0
2
0
2
0
0
2
0
2
1
1
1
1
1
0
0
1
1
1
1
1
1
1
1
0
0
2
2
0
1
2
0
0
0
2
1
1
2
2
1
1
1
1
2
0
2
1
0
0
1
0
2
1
0
1
2
0
0
2
0
2
0
2
0
2
2
2
0
1
1
0
0
1
1
1
2
2
1
3
1
0
1
2
0
2
2
0
1
0
0
1
1
0
3
0
1
0
1
1
0
0
0
1
0
1
0
1
2
1
2
1
1
1
0
2
2
1
1
0
1
1
0
1
0
0
0
1
1
0
0
0
0
1
2
4
2
0
0
1
1
2
1
0
2
2
0
1
1
2
0
0
0
0
0
2
1
0
0
1
0
1
2
1
1
0
1
0
1
0
1
1
1
2
0
2
2
0
1
0
0
2
2
1
1
0
1
2
2
1
0
0
1
1
0
0
0
1
2
0
2
1
0
2
2
0
2
0
2
1
1
0
0
1
0
0
1
0
1
1
0
1
2
1
1
2
0
1
1
0
0
1
2
1
1
2
1
4
0
0
0
2
1
0
0
0
1
0
0
0
0
2
2
1
0
0
3
0
0
0
0
0
0
0
1
0
0
2
0
0
1
1
1
2
1
1
3
0
0
1
0
0
0
2
1
0
0
0
0
1
0
1
0
1
1
0
1
1
2
1
1
2
0
0
2
0
2
0
1
0
0
1
2
1
0
0
0
2
0
0
0
1
1
1
2
0
0
2
2
1
1
1
1
2
2
0
2
2
1
0
1
2
1
0
1
1
1
0
0
3
1
3
1
1
1
1
1
0
0
0
0
0
2
0
2
1
0
0
2
1
1
1
0
1
1
1
2
2
0
1
2
1
0
0
0
0
1
1
2
0
1
1
0
1
2
1
0
1
2
0
1
0
2
1
2
0
1
2
1
0
2
1
0
1
1
0
1
0
0
0
0
1
2
0
1
2
0
0
0
1
2
1
1
1
0
0
1
0
0
2
0
1
2
1
2
1
0
0
1
1
0
1
0
1
0
1
1
0
1
2
0
0
0
2
2
0
2
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
2
1
2
0
1
1
0
0
0
0
1
0
0
1
0
1
0
1
1
0
0
0
1
2
0
1
0
0
0
0
1
0
0
4
1
0
1
2
1
0
0
0
0
2
1
1
1
2
0
0
0
1
1
0
2
2
0
0
1
0
0
1
1
0
2
0
0
1
0
2
2
0
0
2
1
2
2
3
0
1
0
1
0
0
1
0
1
1
1
1
1
2
0
2
0
0
0
4
1
0
0
1
2
0
2
1
0
1
2
0
0
1
1
1
2
1
1
0
0
0
1
2
0
0
0
2
3
0
1
1
1
0
1
1
1
0
1
1
1
0
1
1
0
1
1
1
2
0
0
1
1
0
0
1
1
1
2
1
0
1
1
1
2
1
0
0
1
0
1
0
2
2
0
1
0
1
0
3
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
2
0
2
1
0
0
0
1
0
0
0
1
1
0
2
2
0
0
0
2
0
1
2
1
0
0
0
6
0
2
1
0
0
2
1
1
0
1
1
1
0
0
2
0
2
2
0
2
2
1
1
1
0
1
1
1
0
2
1
0
1
1
2
1
0
2
0
0
1
0
2
1
2
0
0
3
0
0
0
1
2
1
0
1
1
0
1
0
1
2
1
0
1
2
0
0
0
1
0
2
1
2
0
1
1
0
1
2
1
1
0
1
2
1
1
1
1
0
0
0
0
1
1
0
0
0
0
2
1
0
1
0
1
0
0
0
0
2
1
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
1
0
1
1
2
0
0
1
2
1
0
1
1
1
0
1
2
2
1
0
0
0
0
4
1
1
2
2
1
1
1
2
0
1
1
1
2
2
0
1
2
1
1
1
2
1
1
0
1
1
1
2
1
1
0
2
2
0
0
2
2
0
0
1
2
1
0
0
0
1
2
0
2
0
0
1
0
0
0
0
1
2
1
0
1
1
0
0
0
1
2
1
0
0
1
1
1
1
1
0
0
2
1
2
1
0
0
1
0
0
0
0
2
1
1
0
1
0
0
1
0
1
0
1
1
0
0
0
2
1
1
0
0
1
1
2
2
2
0
1
1
0
2
1
1
1
0
2
2
0
2
0
1
2
2
1
1
2
0
0
0
1
2
1
2
2
2
0
1
2
1
1
0
2
1
0
1
1
1
0
0
1
0
0
1
1
2
0
2
0
1
0
0
1
0
1
0
1
1
1
1
0
2
0
2
0
0
1
1
1
1
1
2
0
1
1
2
2
0
0
2
0
1
0
3
1
0
0
0
1
0
0
1
1
0
0
1
1
0
1
2
1
1
1
1
1
0
0
0
0
0
1
0
2
2
1
0
0
0
0
1
0
1
0
1
1
1
1
1
0
1
2
2
0
0
1
7
1
0
2
0
0
1
0
1
2
1
0
1
0
1
2
2
0
2
0
1
0
2
1
0
0
2
0
0
1
0
1
0
0
0
0
0
2
1
0
1
3
1
1
1
2
1
0
2
2
1
0
0
2
0
1
0
1
2
0
0
0
2
2
0
0
0
2
0
2
2
0
2
2
1
0
2
2
0
1
1
0
2
1
1
1
0
1
0
0
0
1
1
0
2
1
2
1
0
0
0
0
0
1
1
0
0
1
1
0
2
0
2
2
1
1
1
0
2
1
1
0
1
0
0
2
1
1
1
0
0
0
2
2
0
1
2
1
1
0
1
1
2
1
0
2
2
0
2
0
1
2
0
1
1
3
1
1
1
1
0
0
2
1
2
2
0
1
1
1
2
0
1
2
1
1
1
0
0
0
2
1
2
1
0
0
1
1
1
2
2
1
1
1
0
1
0
0
0
1
2
1
0
1
0
0
0
2
0
0
0
2
1
0
1
2
0
1
0
2
1
0
2
1
1
0
1
1
0
1
2
1
0
0
1
0
1
1
0
1
0
1
0
1
0
2
1
0
0
0
1
1
0
1
0
0
1
0
1
0
2
0
2
1
1
1
0
0
1
2
1
0
1
0
0
2
0
1
0
0
0
2
0
0
0
1
1
2
0
0
1
2
1
0
1
0
1
1
0
2
2
1
1
1
0
0
1
1
0
0
1
0
0
2
1
0
0
1
2
1
2
1
2
1
2
1
1
2
2
0
1
1
0
1
0
1
2
0
2
2
1
2
0
0
2
0
0
2
1
0
1
2
1
1
0
1
1
1
2
1
1
0
2
0
0
0
2
1
1
1
2
2
0
2
1
0
0
1
0
2
2
2
2
2
0
0
1
1
1
2
2
1
1
1
2
0
1
0
1
0
0
0
0
2
2
0
1
1
0
1
1
0
0
1
1
2
0
1
0
0
0
1
1
0
0
1
1
1
1
1
2
2
0
2
4
1
0
0
1
1
1
2
1
2
0
0
0
1
1
0
2
2
0
1
1
1
2
1
0
2
0
1
1
3
1
0
0
1
1
2
1
1
1
1
2
0
2
1
0
1
0
2
0
1
1
1
1
2
2
0
2
1
1
2
0
0
1
0
1
1
1
0
0
0
1
0
1
0
0
1
1
0
0
1
0
0
1
1
2
0
2
1
1
1
1
0
0
0
1
1
1
0
0
0
0
1
2
2
1
2
0
1
0
0
2
2
1
0
0
0
1
1
0
0
2
1
1
1
2
0
1
1
2
0
1
2
0
1
0
2
0
1
2
1
0
1
1
0
0
0
0
0
1
0
1
1
0
0
5
1
1
0
0
0
0
2
0
1
0
1
1
1
1
2
0
0
1
0
1
1
1
0
1
1
0
1
0
1
2
0
1
1
0
1
0
1
1
1
1
3
2
1
1
0
2
1
0
2
2
0
1
3
1
0
2
0
0
1
0
2
1
0
0
2
0
1
1
1
0
1
0
1
0
1
1
1
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
2
2
0
2
1
0
1
0
2
0
2
1
1
0
2
1
0
0
0
0
1
0
0
1
1
1
1
1
2
2
1
1
1
0
2
1
0
0
3
0
1
1
1
0
0
2
0
2
1
1
0
0
0
0
0
0
2
2
2
2
1
1
0
2
2
1
1
0
2
0
2
2
2
1
2
1
0
2
0
1
0
0
1
0
0
1
1
1
1
1
0
1
1
2
2
1
1
2
2
0
0
1
1
1
1
1
2
1
2
0
1
2
0
1
2
1
0
2
2
1
1
1
2
2
0
1
0
0
0
2
1
0
1
2
2
1
0
0
1
0
1
0
3
2
1
1
1
0
2
1
2
1
0
0
1
2
1
0
0
1
0
1
2
0
0
1
0
2
1
1
1
0
1
1
0
0
2
0
1
0
1
0
1
1
3
0
0
1
1
1
1
1
1
0
0
2
2
0
0
1
2
0
1
0
1
2
1
0
0
1
1
1
0
2
1
0
2
1
2
0
0
0
1
1
1
2
0
1
1
2
1
1
1
0
0
2
2
2
2
0
0
0
1
0
0
0
2
1
2
0
0
1
0
1
1
1
1
1
0
1
1
0
0
1
2
1
2
0
0
0
2
2
2
1
1
1
1
1
1
0
1
1
0
1
1
1
3
1
3
1
1
0
1
1
1
2
0
0
1
0
2
0
2
0
1
1
0
0
0
1
0
2
2
0
1
0
2
2
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
1
0
1
1
2
2
1
0
2
1
0
1
0
0
1
2
0
2
1
2
1
0
3
2
0
0
1
0
1
2
1
0
1
0
0
0
1
0
0
1
2
0
3
0
1
1
1
0
1
0
1
0
0
2
2
0
0
0
0
1
0
0
2
1
2
1
1
2
1
0
0
1
2
0
1
0
2
0
1
0
1
1
2
0
1
0
0
1
1
1
1
0
0
1
2
2
1
1
2
0
1
0
0
2
0
2
0
1
0
0
0
1
0
1
1
0
0
2
0
1
2
0
1
2
0
2
1
1
2
1
1
1
2
0
2
2
0
1
1
2
2
1
0
0
1
1
2
1
0
1
0
0
1
1
1
2
0
1
0
2
0
0
1
1
0
0
0
2
1
0
2
1
1
0
1
2
3
2
1
1
1
0
1
2
0
1
0
0
2
1
1
0
0
0
0
1
0
1
1
1
1
3
1
1
1
1
2
2
1
1
1
2
1
1
2
0
1
1
2
1
2
1
1
1
0
1
0
1
0
0
0
0
1
2
1
0
0
1
2
0
1
1
0
2
0
0
0
1
1
0
0
1
0
2
1
0
1
2
0
2
0
1
1
2
1
1
0
2
0
1
0
2
2
1
1
2
0
1
2
2
1
0
0
3
1
0
2
0
1
0
0
2
1
1
1
1
1
0
2
1
0
0
0
0
0
1
1
1
1
1
1
0
2
0
1
1
1
0
1
1
0
0
0
0
0
1
6
2
0
2
0
1
0
1
2
0
0
0
2
1
1
3
1
1
2
1
1
0
0
0
1
0
1
2
0
1
0
1
2
1
1
0
1
3
0
0
0
1
0
0
2
0
1
1
2
0
3
1
1
0
3
1
3
0
2
0
2
1
0
2
0
1
0
1
0
0
1
0
1
2
1
1
2
0
2
3
2
5
1
0
2
3
2
0
0
2
0
0
2
1
0
0
0
0
1
0
0
1
1
0
0
1
1
0
2
1
1
2
0
1
1
0
1
0
2
0
0
1
2
1
0
0
1
0
1
1
0
0
0
1
0
0
0
1
1
0
0
1
0
1
1
1
0
0
1
0
2
1
0
0
1
1
2
0
1
0
2
0
1
2
1
0
0
0
1
1
1
1
2
0
0
2
2
1
0
1
0
0
2
1
1
2
0
1
0
0
1
1
0
2
0
1
1
1
0
0
1
0
1
0
1
0
0
0
1
5
1
1
2
1
1
0
1
2
2
1
0
0
2
1
0
0
0
2
0
2
1
0
0
1
1
2
2
0
2
1
2
0
2
1
0
0
2
0
0
0
2
2
0
0
1
1
1
1
0
1
1
0
1
2
2
2
2
0
0
0
0
0
0
0
1
0
2
1
3
0
0
3
1
1
0
0
1
1
2
0
0
1
0
1
0
0
0
0
1
1
0
2
0
0
1
2
1
1
0
0
0
1
2
1
0
1
0
2
2
2
2
0
0
0
0
2
0
0
2
1
2
3
0
0
0
0
1
1
2
0
0
1
0
1
0
2
1
1
1
0
0
0
2
1
2
0
2
1
3
2
2
0
2
1
1
1
2
0
0
0
2
2
0
0
1
2
2
2
1
2
3
2
1
0
0
1
0
0
1
0
2
1
0
2
1
1
0
1
1
2
0
0
2
2
1
0
2
1
1
1
0
0
1
0
0
1
1
1
1
1
1
2
2
1
2
1
0
2
1
2
2
0
1
2
1
0
1
2
0
2
1
1
0
2
0
0
0
0
0
0
0
0
2
2
0
1
0
1
1
2
0
2
0
2
1
1
2
0
0
0
1
0
1
0
0
0
1
0
1
0
0
1
0
1
0
2
0
0
0
2
0
1
0
1
1
1
2
1
0
1
1
1
2
1
0
1
0
2
0
0
1
1
1
2
1
0
1
2
0
0
3
1
1
0
0
0
0
3
1
0
1
1
0
2
0
0
0
1
2
1
1
2
1
0
1
2
0
4
1
1
0
1
1
0
1
0
0
0
0
1
1
1
0
0
2
2
0
0
0
1
1
0
2
0
0
0
0
1
2
1
0
4
2
0
0
1
0
0
0
2
1
1
1
2
0
0
0
1
1
0
1
0
1
2
0
1
1
0
1
1
0
1
0
0
0
1
1
0
2
0
0
2
0
2
2
2
2
0
0
0
1
2
2
0
1
0
0
2
1
0
1
0
0
2
2
1
1
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
2
0
0
0
0
1
2
2
1
0
0
2
1
1
1
2
2
1
0
0
0
1
0
1
2
0
1
1
1
0
1
1
0
0
2
1
1
0
2
2
2
1
0
1
1
1
0
0
0
1
0
2
1
2
0
0
0
2
1
2
1
1
1
1
1
1
0
0
1
0
1
1
2
2
1
0
1
1
1
0
1
0
0
1
1
2
1
1
1
0
1
2
1
0
2
1
2
0
0
2
0
0
1
0
1
2
2
0
2
0
0
1
0
0
0
0
0
0
0
1
2
1
1
0
3
1
1
0
1
1
0
1
1
0
0
2
1
0
1
0
0
1
0
0
1
1
2
0
1
1
2
1
0
1
0
1
0
0
1
1
1
0
0
1
1
2
0
0
0
1
0
1
0
1
0
2
1
1
0
2
0
2
1
1
1
2
1
2
0
1
0
0
1
1
0
1
2
2
2
1
0
2
0
0
0
1
0
2
0
2
1
1
2
2
0
2
0
0
0
0
0
2
2
2
2
1
1
0
2
0
2
1
1
2
0
1
2
1
1
1
0
1
1
0
1
0
0
1
0
2
0
1
2
1
0
0
1
1
1
2
0
1
1
1
1
0
2
1
2
1
2
0
2
0
1
1
0
0
1
1
0
2
1
2
0
2
0
1
0
2
0
2
0
1
2
1
1
0
0
2
2
0
0
2
1
1
2
0
1
1
0
2
2
2
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
1
1
0
2
1
0
0
0
3
0
3
1
1
0
0
1
1
1
1
1
0
0
1
2
1
0
1
1
0
0
1
0
0
2
0
0
1
1
0
2
0
1
0
0
1
3
2
0
0
2
0
2
1
0
2
0
1
2
2
0
1
1
1
1
0
0
0
2
2
0
1
1
0
0
1
0
0
1
1
1
1
1
2
0
1
1
1
2
1
1
0
1
0
0
2
0
2
2
0
1
1
0
2
2
1
1
2
2
1
0
0
2
0
2
0
1
0
2
0
1
0
2
1
0
0
0
1
0
0
1
2
3
1
1
0
0
0
1
0
0
2
0
1
1
2
1
1
0
2
0
1
1
0
1
0
1
1
0
1
0
1
1
0
2
2
0
2
1
0
1
0
0
0
2
0
0
1
2
0
2
0
0
1
0
0
0
1
1
0
0
0
1
1
1
0
1
2
0
0
0
0
0
0
1
2
1
1
1
2
1
0
0
2
0
1
1
1
0
1
3
1
1
0
2
1
0
0
2
0
1
2
1
1
0
2
0
0
0
1
1
0
1
0
2
1
0
2
1
0
0
2
1
0
1
1
0
0
0
0
0
1
2
1
0
1
1
0
0
1
1
2
0
1
2
1
2
1
1
0
2
0
1
0
0
0
2
1
0
0
2
2
0
1
1
0
1
4
0
0
2
1
0
0
0
3
1
0
0
0
4
2
1
0
0
2
0
2
0
1
0
1
1
1
0
0
1
1
0
0
0
1
1
1
0
1
0
1
2
2
2
1
0
2
1
0
0
1
0
1
1
1
1
2
1
1
2
0
1
2
2
1
0
1
0
0
1
3
2
2
0
0
1
2
1
1
1
1
2
1
2
0
1
0
1
2
1
1
1
0
0
0
2
1
1
0
2
2
1
1
0
1
0
0
2
1
1
0
3
0
1
1
1
3
0
0
1
0
1
0
1
2
0
1
1
2
2
2
0
1
1
0
1
0
1
1
1
1
0
1
1
0
2
0
1
1
1
0
2
0
2
1
2
1
0
1
1
2
1
1
0
1
0
0
3
2
0
0
1
1
2
1
0
0
2
0
2
0
0
0
2
0
0
0
0
1
2
0
0
0
0
2
1
1
2
0
0
1
1
1
0
1
1
1
1
1
1
1
0
1
1
1
2
2
2
1
0
0
1
0
1
1
0
1
1
1
0
0
1
1
2
2
1
1
2
3
1
1
1
1
0
1
1
1
0
0
2
1
0
1
1
0
0
1
0
1
2
1
1
2
2
1
0
2
0
0
1
1
1
0
0
1
0
2
3
0
1
0
1
0
3
0
1
0
0
0
1
1
0
1
1
2
1
0
2
0
1
0
2
0
0
0
0
0
1
2
0
1
0
1
1
1
0
2
1
1
0
0
1
1
1
1
1
1
0
2
0
1
2
0
0
2
1
1
2
1
0
1
1
1
1
0
1
3
1
2
1
1
0
3
0
1
0
2
0
0
1
1
1
0
0
0
0
0
0
2
1
1
1
1
0
0
0
1
0
1
1
0
2
1
0
4
2
1
1
6
1
1
0
0
0
1
2
1
0
0
1
1
0
1
1
1
0
0
1
1
0
0
1
2
1
0
2
1
2
1
1
0
1
0
1
1
2
2
1
2
1
3
1
0
0
0
2
0
0
0
1
1
0
0
1
0
1
2
0
1
0
1
2
1
1
1
1
0
0
1
0
0
0
0
1
0
1
2
2
1
4
0
3
1
0
2
1
1
0
2
2
1
1
1
1
0
0
2
1
0
0
0
1
0
1
0
2
0
0
1
0
0
2
1
0
1
1
1
0
0
1
2
1
1
1
0
1
2
1
2
0
2
1
1
0
2
2
0
1
1
2
1
1
2
1
1
1
1
0
1
1
1
1
1
0
1
1
1
3
0
1
0
0
0
1
2
0
1
2
0
1
0
1
0
1
0
0
0
0
3
2
1
0
1
1
1
0
3
1
1
0
1
0
0
0
1
2
1
0
1
1
2
0
2
1
1
0
1
1
0
1
0
0
1
1
1
1
2
1
0
0
1
1
2
1
0
2
1
1
0
2
2
1
0
0
2
1
1
0
1
0
0
0
0
0
2
2
1
1
0
0
1
1
0
1
2
1
2
1
1
1
1
1
0
2
1
1
0
1
1
0
0
0
1
1
0
0
1
0
1
1
1
3
0
1
0
1
0
2
2
2
0
0
2
0
0
1
2
1
0
1
0
2
2
0
1
2
0
1
0
0
3
2
2
2
2
1
1
1
0
0
1
1
2
1
2
2
0
1
2
2
1
0
0
1
0
1
0
1
1
1
2
1
1
1
1
1
1
1
2
1
2
1
2
2
1
1
1
1
0
1
0
0
0
1
1
0
0
1
0
1
1
1
1
1
0
0
2
1
2
0
2
2
1
1
0
1
2
1
0
0
0
2
2
1
0
1
2
0
1
1
1
3
2
3
0
0
2
0
2
2
0
0
2
1
2
1
0
0
0
0
1
2
0
2
1
0
0
0
1
0
1
1
0
2
1
1
0
1
2
0
0
1
0
2
0
2
0
2
3
0
1
1
0
1
0
1
1
0
0
0
1
1
0
0
0
1
1
1
0
0
0
0
1
1
1
2
0
1
1
1
0
0
0
0
0
1
0
2
0
1
2
0
1
0
1
1
1
1
0
2
2
0
2
2
2
1
0
0
2
2
1
2
0
2
1
0
1
1
1
2
2
1
0
1
0
0
0
1
1
1
2
1
2
0
0
1
0
0
2
0
2
0
0
0
0
1
1
2
0
2
0
0
0
2
1
1
0
0
0
3
1
0
1
2
0
0
0
2
1
0
0
0
0
0
2
1
0
2
1
0
2
4
1
1
0
2
0
0
2
0
0
1
1
1
0
1
1
1
1
0
1
1
1
1
1
0
0
1
0
2
1
1
1
1
0
1
0
0
1
5
1
0
1
1
0
0
1
1
0
1
0
0
2
0
0
0
0
2
1
2
1
0
0
2
2
2
2
1
1
2
2
1
0
0
1
1
0
2
1
1
0
2
1
0
1
0
0
4
2
3
1
1
3
1
2
0
0
0
2
0
1
1
1
2
2
0
2
1
0
1
2
1
0
0
0
1
1
1
0
0
0
0
2
1
1
1
1
1
2
1
1
1
2
0
0
1
0
0
0
2
1
1
1
1
2
0
0
0
0
1
2
1
1
1
1
0
2
2
0
1
0
1
0
0
1
3
2
0
0
2
0
1
0
1
2
0
0
0
1
1
0
1
0
0
1
1
1
0
0
0
1
0
1
0
2
0
0
0
0
0
2
6
0
0
1
0
0
1
1
1
0
1
1
2
0
0
0
1
2
0
3
2
0
1
0
0
0
1
2
1
0
0
1
1
0
1
2
1
0
0
1
0
1
1
1
0
0
0
0
2
1
1
1
0
1
0
1
1
0
1
1
2
1
0
0
2
0
0
1
2
2
2
3
2
1
0
1
1
4
2
0
1
0
1
1
2
0
1
1
0
2
2
2
2
1
0
1
1
1
0
1
2
2
0
0
1
2
1
1
1
2
0
0
0
0
1
1
0
1
2
1
1
0
1
0
0
0
3
1
1
1
2
3
0
1
1
2
0
0
0
1
2
1
0
3
1
1
1
0
2
0
0
0
2
0
0
1
2
0
1
1
1
0
0
0
1
0
0
3
1
2
1
2
1
2
0
0
0
0
1
2
0
0
0
2
0
0
1
0
1
1
1
2
0
1
2
1
2
1
1
2
0
1
1
0
0
1
1
1
1
0
2
0
2
0
1
1
0
0
1
1
0
0
0
1
0
2
1
1
1
0
2
2
2
2
1
0
2
0
1
0
2
0
1
0
0
1
1
0
2
2
1
1
1
2
1
1
0
1
1
1
1
1
2
0
0
1
2
0
1
1
1
2
1
2
1
1
1
2
2
1
1
1
1
0
0
1
1
1
0
0
1
1
1
1
0
0
0
0
0
2
0
1
2
0
1
2
2
0
1
1
1
2
0
0
1
0
0
0
1
1
0
0
0
2
0
2
2
1
2
1
1
0
0
0
0
1
0
1
1
1
0
1
2
0
1
1
0
1
0
0
2
1
2
1
1
2
1
0
0
0
0
0
0
0
2
0
2
1
1
0
2
1
0
1
2
0
2
0
2
0
2
1
0
0
0
0
1
1
2
1
0
0
1
1
0
2
1
1
1
2
0
1
0
2
0
1
1
1
1
1
2
0
0
1
0
0
0
1
1
1
1
0
1
2
0
1
1
0
1
2
1
0
0
1
0
1
0
0
1
0
2
0
0
2
1
0
1
1
0
1
0
0
1
0
2
0
1
3
0
1
2
0
2
0
1
2
1
3
1
1
0
0
2
2
1
1
2
2
1
0
0
1
1
0
2
0
1
1
1
2
0
0
0
0
1
2
2
1
1
1
1
0
1
0
0
1
0
0
1
0
0
1
2
1
1
0
2
0
1
0
1
2
1
0
0
1
0
1
0
3
1
1
0
0
1
0
0
1
1
2
0
1
3
2
2
1
0
4
0
0
2
3
0
1
2
1
0
2
1
1
2
2
1
1
0
0
2
2
1
2
0
1
0
1
1
0
0
1
1
2
0
0
1
1
1
0
2
0
1
1
2
0
0
1
0
0
1
0
0
1
0
0
2
2
2
1
0
1
2
1
1
1
0
1
2
0
2
1
1
0
0
1
0
1
2
1
1
0
1
2
1
2
2
1
2
2
1
0
2
0
1
1
0
0
0
1
0
1
0
0
0
0
1
1
2
0
2
0
2
0
1
2
1
0
1
2
2
1
2
2
0
1
1
1
1
0
1
0
2
0
1
0
1
0
2
1
2
1
0
0
1
0
1
0
0
0
0
0
1
0
1
1
1
0
1
1
0
2
0
1
1
0
1
0
0
2
1
0
1
1
0
1
0
1
0
1
0
1
2
0
2
1
2
1
1
0
2
0
0
2
1
1
0
0
3
1
0
2
1
0
0
1
1
2
0
0
1
2
2
2
0
1
1
0
2
0
0
0
0
2
1
1
0
1
1
2
0
0
2
0
1
0
0
0
0
0
1
0
2
1
0
2
2
1
2
0
0
0
0
1
0
1
1
0
2
1
0
0
2
2
2
0
1
1
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
2
2
1
0
2
1
2
1
2
0
0
0
1
1
0
0
2
1
0
1
3
1
1
1
0
0
0
0
0
0
1
1
0
0
1
2
0
2
1
0
0
1
0
2
1
0
1
2
1
2
0
0
0
1
1
0
0
1
1
1
0
1
1
0
2
1
0
0
0
2
0
0
1
1
1
1
1
2
0
1
2
1
1
2
2
1
0
1
2
1
2
0
1
1
1
1
1
1
1
3
1
0
2
2
0
1
0
2
1
2
2
1
0
0
1
0
1
0
2
0
2
2
0
2
0
0
1
1
1
3
2
0
1
1
2
2
2
2
1
0
0
0
0
2
2
0
0
2
1
2
1
1
0
2
1
1
0
0
2
2
1
0
0
2
1
1
0
1
2
2
2
2
1
4
2
0
1
1
0
0
1
0
1
1
0
0
2
2
2
0
0
1
0
1
2
0
0
0
0
2
0
1
0
1
0
2
2
1
3
1
1
1
1
2
0
2
1
4
1
1
1
1
1
1
1
0
1
0
0
1
0
1
0
2
0
0
1
1
2
1
0
1
2
2
0
0
2
1
0
0
2
0
0
2
1
0
0
0
0
0
2
0
1
0
1
2
0
0
0
0
1
0
0
0
0
1
0
0
0
6
1
0
3
0
0
1
0
2
2
0
0
1
1
0
1
0
0
0
0
0
1
0
1
1
1
2
0
1
0
2
0
2
0
0
0
1
1
1
1
0
1
1
2
1
1
2
1
0
1
1
0
1
1
0
1
0
0
0
0
0
0
0
1
1
1
1
2
1
1
0
1
0
1
1
0
1
5
1
1
1
2
0
2
2
1
2
1
1
1
1
2
1
1
1
1
1
1
0
0
1
1
0
2
0
1
1
1
0
1
1
0
0
0
1
1
2
0
2
0
1
1
2
0
2
1
2
1
1
2
2
2
1
0
2
0
1
0
0
1
1
1
1
0
2
0
0
0
0
1
0
0
1
0
1
1
1
1
2
0
0
1
1
0
2
1
1
0
0
0
0
2
1
2
1
0
1
0
1
1
1
1
0
1
1
0
0
1
1
3
0
0
2
0
2
0
1
2
0
1
2
1
2
2
1
2
2
0
1
1
1
1
1
2
2
1
2
1
0
0
1
3
1
0
0
0
0
0
1
0
1
0
2
1
1
0
1
0
1
2
1
0
1
0
2
0
2
0
1
0
0
2
1
0
0
2
2
2
1
1
0
1
2
1
3
0
0
0
0
1
0
2
2
0
1
2
1
0
0
2
1
1
0
0
1
2
0
0
0
1
0
2
1
0
1
0
0
0
0
1
0
1
0
0
1
1
2
2
1
1
1
0
0
1
0
0
2
0
2
1
0
0
1
1
0
1
0
1
2
0
1
1
0
2
2
2
0
1
2
2
0
1
2
1
1
1
1
1
1
0
2
2
1
1
1
2
1
2
2
1
0
1
1
0
0
1
1
1
1
1
1
1
0
0
0
2
1
0
3
1
2
1
4
2
0
0
0
1
1
1
1
2
2
0
1
1
0
1
0
1
2
1
1
0
1
1
0
0
2
0
0
1
2
0
1
1
0
2
0
0
0
0
1
1
1
1
1
1
1
1
0
1
1
1
1
1
0
0
1
0
1
2
0
2
1
2
1
1
0
1
1
0
0
2
0
1
0
2
0
1
0
0
0
0
0
1
0
0
0
1
2
0
0
2
1
0
3
1
1
2
2
2
0
0
0
0
3
0
0
0
0
0
2
0
1
1
0
2
1
0
1
0
2
0
0
2
1
1
0
0
2
0
2
2
1
0
2
2
2
2
0
0
0
1
0
0
2
1
0
0
1
1
2
0
0
0
0
2
1
0
1
2
2
1
0
2
0
0
1
0
1
1
0
2
2
0
2
1
1
1
1
0
0
2
1
0
0
0
0
1
1
0
0
0
0
2
2
1
0
1
0
1
1
0
0
1
0
2
0
1
1
0
0
1
2
1
1
1
1
0
0
0
2
3
0
1
0
0
0
1
1
2
4
1
0
1
1
1
0
1
1
1
1
1
0
1
1
0
0
2
0
1
1
2
1
1
1
0
1
0
1
0
1
1
1
0
1
1
1
0
1
2
0
0
0
1
0
1
1
1
2
0
1
0
0
0
2
1
1
1
1
1
1
1
2
0
2
0
1
0
2
2
2
2
1
2
0
1
2
1
1
2
1
2
1
2
0
2
1
1
1
1
1
2
0
1
1
0
1
3
1
2
0
0
2
2
0
1
1
1
3
0
2
1
2
0
0
0
2
2
0
0
1
1
1
0
1
0
2
1
2
0
1
1
2
0
1
1
0
0
1
0
1
1
1
1
0
3
0
1
0
0
2
0
1
0
2
1
1
1
0
0
1
2
1
2
0
2
2
1
1
1
1
0
1
0
1
0
2
1
1
1
2
0
2
2
0
0
0
0
2
0
2
2
2
2
2
1
1
2
0
2
0
0
1
1
0
2
1
1
0
1
0
1
0
1
1
2
1
0
1
4
1
2
0
2
0
1
0
2
2
0
3
0
0
0
1
1
1
1
2
1
1
2
1
0
2
0
1
0
1
2
1
1
0
2
1
1
0
0
1
1
2
1
1
1
1
0
1
1
0
0
0
0
1
2
2
1
0
1
2
2
2
1
0
1
2
0
2
0
1
0
0
0
0
1
0
1
2
1
2
0
1
0
0
1
1
1
0
2
1
0
0
2
0
1
2
2
1
2
5
1
2
1
1
1
2
1
0
2
0
2
2
1
1
1
0
0
1
2
0
2
0
2
0
1
0
1
2
0
2
1
1
0
1
1
0
1
0
0
2
1
2
1
1
1
1
0
2
0
0
0
2
1
0
1
0
0
0
1
0
1
1
2
0
1
2
2
2
1
0
1
2
1
0
1
1
0
1
2
0
0
1
1
0
1
0
1
1
1
0
1
1
1
0
0
0
2
0
1
1
0
0
3
0
1
0
2
0
1
3
2
1
0
1
0
1
1
2
2
1
1
2
1
1
2
0
1
1
0
2
0
0
1
1
0
0
1
1
0
2
0
0
0
1
0
0
2
1
1
1
1
2
5
0
1
0
1
0
0
1
2
0
1
2
1
0
1
2
0
2
2
0
0
0
0
1
2
0
2
0
1
0
2
2
2
0
1
0
0
1
1
2
2
2
0
1
2
0
1
0
1
1
1
2
0
2
1
1
2
0
1
0
2
1
0
2
0
1
0
2
2
1
0
2
0
0
2
0
0
0
1
2
0
0
1
1
2
1
0
2
1
0
0
0
2
2
0
0
0
1
1
0
1
1
0
1
1
0
1
0
2
1
0
1
0
0
0
0
1
0
0
2
1
1
1
0
0
1
2
0
0
0
2
1
0
1
1
0
2
0
0
1
2
1
2
1
1
0
0
1
1
1
1
0
1
1
0
1
2
0
3
0
1
1
0
0
0
1
2
0
1
0
0
0
1
0
1
2
0
0
0
2
1
0
2
0
1
1
1
2
0
2
0
1
3
2
2
1
1
0
1
0
1
2
2
2
0
0
1
0
0
0
1
0
0
0
2
1
2
0
1
0
0
3
1
1
1
2
0
2
0
1
1
1
1
2
1
0
1
0
0
1
2
2
0
1
0
1
2
4
0
0
1
1
1
1
2
1
0
1
0
2
0
1
0
0
1
2
1
0
2
0
0
2
0
1
0
1
2
1
0
1
2
1
0
0
0
0
1
1
1
0
1
1
0
0
0
2
1
0
2
1
0
1
0
0
1
2
1
1
0
2
2
0
0
0
0
0
1
0
2
0
1
2
0
1
0
2
0
0
0
1
0
1
0
1
2
1
1
1
1
0
0
2
1
0
0
1
1
1
0
1
0
2
1
2
1
0
0
1
1
0
0
1
2
0
1
1
0
0
0
1
0
0
0
2
0
3
0
1
0
0
2
0
0
1
1
0
2
0
0
0
1
0
1
0
2
1
1
0
2
2
0
0
2
0
0
0
3
0
1
1
0
0
0
1
2
1
1
1
0
0
1
0
1
1
1
0
1
1
1
1
0
1
2
0
0
0
0
1
2
2
1
0
1
0
1
1
0
2
1
1
0
1
1
1
0
0
0
0
1
0
0
2
1
2
1
0
2
1
0
2
2
1
0
1
0
0
2
1
0
0
0
1
1
0
0
2
1
2
0
2
2
2
2
0
1
1
0
2
1
0
2
1
2
2
2
1
1
1
2
1
0
1
2
0
0
1
1
1
1
1
1
2
0
0
0
1
1
1
0
2
0
1
0
0
0
0
0
1
0
2
0
0
1
0
1
0
0
2
1
0
1
1
1
0
1
0
2
2
0
2
0
0
2
0
0
1
1
2
2
1
2
1
1
1
0
2
0
1
0
2
0
0
1
0
0
2
2
1
1
1
2
0
2
0
1
1
0
0
1
0
1
2
2
0
1
1
2
0
1
1
0
1
0
0
2
0
0
2
0
1
0
1
1
0
1
1
0
1
0
2
1
0
2
0
1
2
0
0
1
0
0
3
1
1
0
0
0
0
0
2
2
0
0
1
2
0
2
0
1
0
1
2
0
1
1
0
0
2
0
0
1
2
1
1
1
1
2
1
0
2
0
1
0
1
0
2
1
0
0
1
0
0
1
1
2
1
0
0
1
1
2
1
0
0
1
2
1
2
0
1
1
0
2
1
1
1
2
0
2
1
1
2
1
0
0
1
0
1
0
0
1
1
0
2
0
0
0
1
0
1
1
1
1
1
0
1
0
1
1
1
1
0
2
2
1
2
0
2
1
1
1
2
0
2
0
1
1
2
2
1
2
1
1
1
2
1
0
0
0
2
1
0
0
0
0
2
1
0
2
0
1
1
1
1
2
1
1
2
0
0
0
2
0
2
2
1
0
2
0
1
1
0
1
0
1
0
1
1
0
0
0
0
1
1
0
0
1
2
1
0
0
3
0
0
0
2
3
2
0
0
0
0
0
0
2
0
1
0
0
3
0
1
2
0
0
0
0
0
1
1
2
1
0
1
2
1
1
1
1
2
1
2
1
1
1
1
1
0
2
1
1
1
1
0
1
0
2
1
1
1
0
2
0
1
0
2
2
1
0
0
3
0
1
0
1
1
2
0
2
1
1
2
0
1
0
1
0
1
0
2
0
2
1
0
0
2
1
1
0
0
0
1
1
1
1
1
0
2
2
0
0
2
1
1
1
0
2
2
0
2
4
1
0
1
0
0
0
1
0
2
2
0
1
0
1
2
1
0
1
2
1
1
0
2
0
1
0
1
2
0
1
1
1
0
0
1
1
1
0
1
0
0
2
0
1
1
2
1
1
0
0
2
1
0
1
0
2
2
1
0
0
1
1
0
0
0
2
1
2
0
1
0
0
0
1
2
0
1
1
1
1
0
0
0
1
1
3
1
1
1
2
2
2
0
1
0
0
1
1
0
1
0
1
0
1
2
0
1
2
2
1
2
0
0
0
0
0
2
0
1
0
1
2
1
0
0
0
1
1
0
0
1
0
0
1
1
2
0
1
1
1
2
1
0
0
1
1
1
0
0
0
1
0
5
1
0
0
0
2
1
0
1
0
2
0
2
0
0
0
2
1
3
1
0
0
0
0
0
0
1
1
1
2
1
0
0
0
0
1
1
1
1
1
0
0
0
0
0
2
2
0
3
0
2
1
1
0
2
2
2
1
2
1
2
1
1
1
2
0
0
1
1
1
1
1
1
1
0
2
0
1
1
1
1
0
2
1
2
1
2
2
1
1
1
2
2
0
1
0
1
2
1
0
1
1
2
3
0
2
1
0
0
2
1
0
2
0
1
0
1
0
1
1
0
1
0
0
0
1
1
2
0
1
1
1
0
0
1
1
0
2
1
1
0
0
1
1
0
2
0
1
1
0
0
0
1
0
0
1
0
1
0
2
0
1
2
0
0
0
2
1
1
0
0
1
0
1
2
0
1
1
0
1
0
0
0
1
2
1
2
2
0
1
2
1
1
1
0
1
1
0
2
1
2
0
0
1
3
0
0
2
1
1
1
0
1
1
1
1
1
0
2
0
2
3
1
1
1
0
2
0
2
0
8
0
2
2
0
1
2
0
1
2
1
0
2
0
0
0
1
2
0
0
1
1
0
2
1
1
1
0
1
1
2
1
0
2
0
1
1
0
0
2
2
2
1
1
1
2
0
1
0
1
0
1
0
2
1
1
0
0
0
1
0
1
0
1
0
1
1
0
0
0
2
2
0
0
1
1
2
0
1
0
1
2
0
2
0
1
0
1
1
0
0
1
1
0
0
1
2
0
1
1
0
4
1
2
1
1
1
1
0
0
0
1
1
1
0
2
0
0
0
2
0
0
1
1
1
0
1
0
1
0
2
1
0
0
1
0
2
2
2
2
0
0
1
1
1
2
1
0
0
2
0
0
1
2
0
1
2
2
1
0
1
0
0
0
0
0
0
1
2
1
2
1
1
1
2
1
2
1
1
0
0
2
1
1
0
0
0
1
0
2
0
0
1
1
0
0
0
2
0
1
0
1
1
1
0
0
1
1
2
1
0
2
1
1
0
0
2
1
0
0
1
0
1
1
2
1
2
0
1
1
1
1
1
2
1
0
2
0
0
2
1
0
1
0
1
2
1
0
1
1
0
0
0
0
2
0
2
2
2
1
1
1
1
1
1
0
2
0
1
2
1
0
1
2
1
1
0
2
1
2
0
2
1
1
0
0
1
1
1
1
2
1
1
2
1
0
0
1
1
2
0
0
1
1
2
2
0
1
2
0
0
2
0
1
0
1
0
0
0
2
0
1
1
2
0
1
0
1
2
1
2
0
0
2
0
1
2
0
1
1
0
1
1
1
1
1
0
2
0
1
2
0
2
0
0
1
3
1
2
2
2
0
1
1
2
0
2
0
0
1
1
1
2
0
1
0
2
0
0
2
0
0
0
0
2
1
1
1
0
2
1
0
1
2
0
0
2
1
0
1
1
0
1
1
1
2
0
0
1
0
0
0
0
2
1
1
1
1
0
0
2
1
2
0
0
0
0
4
1
0
0
2
0
1
0
1
1
0
0
0
1
1
0
1
0
1
1
0
0
1
0
1
0
2
0
0
2
1
0
2
1
0
2
0
1
1
2
2
0
1
0
1
0
1
2
0
0
1
2
1
1
0
1
1
2
2
2
1
1
2
0
1
1
2
1
0
1
1
1
0
2
0
1
0
1
2
1
0
0
2
0
0
2
0
2
1
1
3
0
0
2
1
1
0
1
1
1
1
1
0
0
1
1
2
0
2
1
1
1
1
0
1
1
1
0
1
0
0
2
1
1
1
0
0
1
1
0
0
1
2
1
0
1
1
0
0
2
0
2
1
1
0
1
1
0
0
0
0
2
0
1
1
1
0
2
0
0
0
0
2
0
0
1
2
0
1
0
3
1
1
0
0
1
1
2
0
3
1
2
2
0
0
3
2
0
0
0
1
2
0
0
0
0
0
2
0
2
0
3
2
1
3
1
0
0
1
1
2
0
2
0
1
1
1
0
0
4
1
2
1
2
2
1
0
0
0
0
2
1
0
0
0
0
2
1
1
0
1
2
2
0
1
0
0
0
0
2
0
0
1
2
2
1
1
2
0
1
0
2
0
1
1
0
2
4
1
0
0
0
0
1
0
1
3
0
0
0
2
1
2
0
1
0
0
0
0
0
0
1
2
3
0
0
2
0
0
0
1
1
0
1
0
1
2
0
2
1
1
0
1
0
1
1
1
1
1
1
0
2
2
0
1
2
1
2
1
1
0
3
2
1
1
0
0
1
0
1
0
2
0
1
2
2
1
3
1
1
1
0
2
2
0
0
0
1
0
0
2
1
1
0
0
2
2
0
0
1
2
0
1
1
1
0
1
2
2
0
0
0
1
1
1
0
1
2
0
2
2
1
2
1
0
1
1
1
1
2
0
2
1
0
3
0
0
0
1
1
0
0
2
1
0
2
1
1
4
0
2
0
1
1
0
0
0
2
0
1
0
1
1
1
0
2
2
0
0
2
1
2
1
2
1
0
1
0
2
2
0
1
1
1
1
0
1
0
0
0
1
0
0
1
1
2
0
2
1
0
0
2
0
1
1
2
0
0
2
2
1
2
0
0
1
2
1
3
0
1
0
1
0
1
1
0
1
2
0
2
1
2
1
0
1
1
1
2
1
1
1
2
2
2
1
0
1
1
2
1
1
1
1
0
1
0
0
0
2
0
2
0
0
1
0
1
1
1
1
0
2
1
2
0
1
0
0
2
2
0
1
1
2
0
2
1
1
2
0
2
2
0
0
0
2
1
0
1
0
0
2
0
1
0
1
0
1
1
2
1
1
0
1
2
0
1
0
0
1
1
0
0
0
1
0
1
0
0
1
0
2
2
1
2
0
0
1
2
1
1
0
2
0
0
0
1
1
1
0
0
0
0
0
2
1
1
1
0
1
1
1
0
1
4
0
0
0
0
0
1
1
1
1
0
0
1
1
2
1
0
0
0
1
1
1
1
1
2
0
1
0
1
0
0
0
1
1
2
0
2
1
0
2
1
0
0
0
0
1
0
2
0
0
2
0
0
1
0
1
1
3
1
0
1
2
2
0
0
0
1
1
1
1
0
1
1
2
1
0
1
1
2
0
1
2
2
1
0
1
1
1
0
0
0
2
1
2
1
0
0
2
0
0
1
1
1
0
1
2
0
0
0
2
0
1
2
2
0
1
0
0
0
0
2
0
1
0
2
1
1
1
0
0
1
0
2
0
0
0
1
1
1
0
0
0
0
1
0
1
0
0
1
2
2
2
1
1
1
0
2
2
1
0
0
1
1
0
2
2
1
2
0
2
2
1
0
0
1
1
0
1
2
1
0
0
1
1
0
1
0
0
2
1
0
1
1
0
0
0
1
2
0
0
0
1
0
0
1
1
1
0
0
1
1
0
1
0
3
1
0
1
2
0
2
1
0
2
0
2
0
0
2
2
0
1
2
0
2
1
2
1
1
0
1
0
0
2
0
1
1
1
0
3
2
0
0
0
2
0
1
2
2
0
1
2
1
1
2
0
0
0
1
0
0
0
1
1
1
0
0
0
1
0
1
1
0
1
2
2
0
1
0
2
0
0
0
2
1
2
2
1
1
0
1
2
0
0
2
0
1
1
0
0
1
3
1
1
1
2
4
2
0
0
1
1
0
0
0
0
0
4
0
0
1
0
1
0
2
1
0
1
0
0
2
0
0
2
2
1
1
0
0
2
0
1
1
1
0
2
0
2
0
1
1
1
0
1
2
1
2
0
2
2
2
2
0
1
1
0
1
0
0
1
0
1
0
1
2
0
2
0
1
0
1
1
2
1
0
1
0
0
1
2
1
1
2
2
3
0
2
0
2
0
0
0
0
2
0
1
0
1
1
2
2
1
2
0
1
1
1
2
2
1
2
2
1
2
0
2
1
2
1
0
1
1
1
0
0
2
1
2
1
1
1
4
1
0
0
0
1
1
1
0
1
0
1
1
1
0
0
2
1
2
1
1
0
0
0
0
0
2
0
1
1
0
2
0
1
0
2
1
2
1
2
1
0
0
4
1
0
2
1
2
2
1
0
0
0
0
1
2
1
1
0
0
2
0
1
1
0
2
0
1
2
1
2
0
0
1
0
1
0
2
0
4
1
1
0
0
2
0
2
1
1
2
0
2
0
2
2
1
1
0
0
0
1
0
1
0
2
2
0
1
1
0
0
0
1
1
2
0
0
1
0
0
0
0
1
0
2
1
0
1
2
1
0
0
1
2
0
2
1
1
1
0
0
0
1
2
1
1
2
0
1
0
2
2
0
1
1
1
2
2
1
0
1
0
0
2
1
0
0
1
0
2
0
2
0
0
1
0
0
0
0
0
3
1
0
0
2
0
1
0
2
1
1
0
0
0
1
1
1
0
0
1
1
1
2
0
2
0
1
1
1
1
1
0
2
1
1
2
0
0
0
0
3
0
1
0
0
0
1
1
1
0
2
1
0
1
1
2
1
2
2
1
0
0
2
0
1
0
0
2
1
1
0
0
0
1
2
1
0
1
1
2
3
1
0
1
0
2
2
1
0
2
1
1
0
1
1
2
0
1
0
1
1
0
2
2
1
0
1
0
0
2
1
0
0
1
2
1
0
0
1
0
1
1
1
0
2
1
2
0
2
1
2
1
3
0
0
0
2
1
0
2
1
1
1
2
1
0
0
1
1
1
2
1
3
0
0
2
0
2
0
1
1
0
0
2
0
0
2
2
2
1
1
2
1
0
2
2
1
1
2
3
1
2
2
1
2
1
0
2
1
2
0
1
1
1
0
0
2
2
0
2
0
2
0
0
1
0
1
0
1
1
0
0
1
1
1
0
1
4
0
1
0
0
0
0
1
0
0
0
1
1
1
2
2
1
0
1
0
0
1
1
0
0
1
1
1
0
2
2
2
1
2
1
1
1
2
2
0
2
1
1
0
0
2
1
2
2
1
2
1
0
0
1
2
0
1
1
1
1
1
0
3
0
2
2
0
0
2
1
2
1
0
0
2
1
1
1
0
2
0
1
0
0
0
2
2
0
1
1
0
0
1
1
0
0
1
1
0
0
1
1
2
1
0
3
1
2
0
1
1
0
2
0
1
0
2
0
1
0
0
1
2
0
1
3
1
0
0
2
1
2
1
0
1
2
2
0
0
0
0
2
2
2
1
1
1
1
1
1
0
0
0
1
1
1
0
0
1
0
0
2
0
0
2
1
0
0
1
0
1
1
0
0
2
1
2
2
0
0
2
0
1
1
1
2
1
0
1
0
2
3
4
2
1
0
0
1
0
1
2
1
0
2
0
1
0
0
1
0
0
1
0
1
1
0
1
1
0
1
0
0
2
2
2
1
1
1
0
0
1
2
2
0
1
1
1
0
1
2
0
1
0
2
2
1
2
2
2
1
1
0
0
0
1
1
2
2
1
0
0
1
1
2
3
1
1
0
1
1
2
1
0
2
2
2
0
4
1
0
1
1
2
1
0
1
2
2
2
0
1
1
0
0
0
0
1
1
1
2
1
0
0
0
1
0
0
0
1
0
0
1
0
0
1
2
0
1
1
1
1
1
0
2
0
0
2
2
1
0
1
2
0
0
1
2
0
0
0
1
1
1
4
0
0
0
0
1
0
2
0
2
0
0
0
2
0
1
0
1
1
0
1
1
0
2
2
2
0
0
0
1
2
0
1
0
1
2
0
1
0
1
2
1
2
3
0
0
1
1
1
1
0
2
1
2
2
0
0
1
1
0
2
0
0
2
0
0
1
0
1
1
0
1
1
2
1
0
0
1
1
1
0
1
3
0
0
2
0
1
0
2
1
1
1
0
0
0
0
0
2
1
4
2
0
0
0
1
0
0
1
1
1
1
1
0
1
1
1
1
0
1
1
0
0
3
1
0
2
1
1
2
1
0
1
1
1
1
2
1
1
2
2
2
1
1
0
1
2
0
2
0
1
1
0
2
1
1
0
0
2
0
1
2
0
0
1
0
1
0
1
1
1
1
2
1
0
1
2
1
0
1
2
2
1
0
1
2
0
0
0
1
1
1
1
0
0
1
0
0
1
1
2
0
1
1
0
1
0
1
1
2
1
0
0
0
0
1
2
0
2
2
1
2
0
1
0
0
1
0
1
1
1
2
0
0
2
1
1
1
0
1
0
1
1
1
2
0
1
1
0
1
1
1
0
2
1
1
1
0
0
1
2
2
2
1
1
0
2
2
0
1
2
2
2
3
0
0
1
0
0
2
0
0
0
0
1
2
1
0
1
1
0
2
2
1
0
1
0
3
1
0
1
2
2
1
0
0
1
1
1
0
1
1
0
1
0
1
0
1
0
2
2
1
1
1
3
2
1
0
0
1
0
2
1
1
1
2
0
1
2
2
1
2
1
2
0
1
0
1
0
0
1
0
0
0
1
1
1
0
1
1
0
1
2
2
0
1
1
0
0
0
0
0
1
1
1
1
0
0
0
1
1
1
2
2
0
2
0
2
1
0
0
0
1
0
0
0
0
0
2
1
0
1
1
2
1
2
1
0
1
1
0
0
0
0
1
0
0
1
0
0
2
1
1
1
1
1
0
2
1
1
2
2
1
0
2
0
1
2
1
0
0
1
1
1
1
0
2
1
2
2
2
1
1
1
1
1
2
0
0
1
1
2
2
0
2
0
1
0
0
0
0
1
1
1
1
1
3
2
0
0
0
2
1
1
0
3
2
1
2
1
1
0
1
0
0
1
0
2
1
2
1
1
1
1
1
1
2
0
1
0
1
1
2
2
0
0
2
0
1
1
1
1
0
2
1
2
1
1
1
0
2
0
2
1
1
0
0
2
0
1
1
1
2
0
5
1
1
1
1
0
1
0
1
3
1
1
2
0
2
1
0
2
0
1
0
2
0
0
0
0
0
0
2
0
2
0
0
0
1
1
0
1
0
1
1
2
1
2
2
2
0
1
1
0
2
0
1
0
1
1
0
1
2
0
1
0
0
0
2
1
1
0
2
1
2
0
1
0
1
0
0
0
1
1
1
1
1
1
1
2
0
2
2
0
0
1
0
2
0
1
1
1
1
1
0
0
0
1
2
1
0
1
0
1
1
0
0
1
0
0
0
0
2
3
2
0
0
0
0
0
1
2
1
2
2
1
0
0
1
1
1
0
2
0
1
1
0
0
0
0
2
1
1
2
1
3
0
0
0
1
0
2
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
1
2
1
1
0
0
1
1
2
0
1
0
0
1
0
1
1
1
1
2
1
0
1
2
2
2
1
1
0
0
0
1
3
2
2
3
1
0
1
0
1
1
0
0
1
0
0
1
1
1
1
0
1
2
1
2
2
1
1
1
0
0
1
1
0
0
1
0
0
1
2
1
2
0
1
0
0
2
0
2
0
2
1
2
2
0
0
0
0
0
1
0
0
0
0
2
1
2
0
0
2
1
0
1
0
0
0
1
0
1
0
2
0
0
2
0
1
0
1
0
0
1
0
0
1
5
2
1
1
0
1
1
2
1
3
1
1
1
3
0
0
1
2
1
0
0
1
1
2
1
0
2
1
1
2
0
1
2
1
1
2
1
2
0
1
1
0
0
0
0
1
1
0
2
0
1
1
0
1
2
1
0
0
1
0
1
0
1
0
0
1
0
0
0
2
0
0
1
0
0
2
1
2
0
0
1
0
0
0
1
0
2
0
0
0
2
0
0
2
1
0
1
0
3
1
2
1
0
1
0
1
0
0
0
2
0
2
0
1
1
1
2
1
0
1
0
1
2
1
0
3
1
2
1
2
1
1
1
0
0
2
1
3
0
0
1
0
2
0
1
1
2
0
0
0
1
0
0
2
1
1
2
0
2
1
2
0
1
0
2
0
0
1
2
2
0
0
1
2
0
1
1
0
2
2
1
1
0
2
0
1
1
0
0
0
2
0
0
1
0
3
2
0
1
2
2
0
0
1
1
0
1
1
2
2
0
1
1
0
2
0
0
0
0
1
1
2
2
0
0
1
1
0
1
1
2
0
1
0
0
2
1
1
1
1
0
1
2
2
3
0
0
0
2
1
2
1
1
2
3
1
1
2
0
0
0
1
0
2
1
1
0
1
2
1
1
2
1
1
2
2
0
1
1
1
2
0
0
0
0
0
2
2
1
2
0
2
0
0
1
0
1
1
1
0
0
2
0
2
1
2
0
0
0
2
1
1
1
1
1
1
0
1
0
2
1
1
1
1
0
0
1
1
2
0
1
0
2
1
1
0
2
1
0
2
1
0
2
1
0
0
1
0
1
1
0
1
1
1
2
0
1
3
1
0
0
1
0
0
0
1
1
2
1
0
1
1
1
1
2
0
0
1
0
2
1
2
0
2
2
1
2
0
1
2
2
1
0
1
0
1
0
0
1
0
1
1
1
2
1
1
0
1
1
3
2
0
0
2
2
1
2
1
3
0
1
2
0
1
0
0
0
1
0
5
3
1
0
2
1
0
0
2
1
2
0
0
3
1
2
1
0
1
2
1
0
0
0
1
0
1
0
2
3
0
0
1
1
0
1
1
1
1
2
0
1
1
0
0
1
0
0
2
0
1
1
1
1
2
1
1
0
1
1
1
2
1
2
2
1
0
1
1
1
1
1
0
0
0
1
2
1
2
2
1
0
0
0
1
2
1
1
2
0
1
2
2
0
2
2
1
1
0
0
0
1
0
1
1
2
1
1
0
0
0
1
1
0
1
0
0
1
1
1
1
0
1
1
2
0
2
0
0
0
1
1
1
2
2
0
1
2
2
0
1
4
1
0
0
1
0
1
1
1
1
2
0
1
1
0
2
1
0
0
0
0
1
0
1
1
0
3
1
0
0
0
2
0
0
1
2
0
0
0
0
1
1
0
0
0
0
0
2
1
2
2
0
1
3
0
0
0
2
0
2
2
2
0
1
0
0
2
1
1
1
0
1
1
2
0
1
0
1
0
0
1
0
0
0
2
0
2
1
1
0
2
0
0
2
2
0
2
1
1
0
0
0
0
1
1
0
0
1
0
0
2
2
0
1
1
1
1
0
1
1
0
1
0
1
1
1
1
1
0
0
1
1
0
0
1
1
0
1
0
0
0
0
1
1
3
0
2
2
1
1
1
3
1
0
1
1
1
1
0
1
0
1
0
2
1
0
0
0
0
1
2
0
0
0
1
2
0
1
1
2
0
0
0
0
0
0
0
2
1
1
1
0
0
0
2
0
1
2
1
0
1
1
0
1
1
0
2
0
0
1
1
0
1
1
1
0
0
1
0
0
1
1
1
2
2
1
2
0
0
2
0
2
0
0
2
0
1
1
0
1
1
0
0
0
1
0
2
1
2
0
0
2
0
0
1
0
2
2
1
0
0
0
1
0
1
0
0
0
1
1
1
2
0
1
1
0
1
2
1
2
2
3
1
1
0
0
1
1
1
1
1
0
1
0
1
1
2
0
1
1
2
2
1
1
1
0
2
0
0
2
0
1
2
1
1
1
1
2
0
0
2
1
3
0
1
1
1
0
1
0
0
1
1
2
0
0
4
0
0
2
0
1
0
1
3
0
2
1
0
1
1
0
0
0
2
1
2
0
1
0
0
0
0
1
2
0
1
0
1
2
1
2
1
1
1
1
1
0
0
0
0
1
0
2
1
1
2
1
0
1
2
0
1
1
3
1
0
0
1
0
2
2
1
1
1
1
1
1
1
1
1
2
0
1
1
0
0
0
2
0
0
2
1
0
2
2
4
2
0
2
0
0
1
0
1
1
0
2
1
1
0
2
1
4
0
0
1
0
1
1
2
0
3
2
2
1
0
1
1
0
1
0
1
2
1
2
0
0
0
2
1
2
1
2
0
1
0
1
1
1
1
0
0
1
1
1
1
1
1
0
0
2
3
0
1
1
2
2
0
1
1
2
1
1
1
1
3
1
2
0
1
2
1
1
0
2
2
1
2
1
0
0
0
1
0
1
0
2
1
0
1
1
1
2
2
2
2
0
0
2
1
0
2
0
0
0
1
1
1
2
1
2
1
0
1
1
0
1
2
0
0
1
1
1
2
2
2
1
0
2
2
1
0
2
1
0
2
2
2
0
0
2
1
2
0
1
1
1
2
1
0
0
0
0
1
0
1
1
1
1
2
2
1
0
1
0
0
1
0
1
0
0
1
0
1
1
1
2
2
0
0
2
2
1
0
0
2
4
0
0
1
2
2
1
3
1
1
1
1
3
2
2
1
1
3
0
0
0
0
0
1
0
1
2
0
2
1
0
0
2
1
1
2
3
1
1
1
1
2
0
0
0
1
0
1
1
0
2
0
1
1
2
2
0
0
1
1
0
1
1
0
0
0
2
1
0
1
1
0
1
0
0
0
0
2
1
0
2
0
0
1
0
2
1
1
1
2
0
1
1
0
2
1
1
1
1
0
0
1
0
0
1
0
0
2
1
0
0
2
1
1
1
1
1
2
0
1
1
2
0
0
2
1
1
0
1
1
0
1
0
1
2
1
0
1
1
0
0
1
1
0
2
1
1
1
1
1
0
0
0
3
2
0
2
2
1
3
0
1
1
0
0
2
2
1
1
0
1
0
0
1
0
1
1
2
1
0
1
0
1
1
0
2
1
2
0
0
2
2
1
0
1
0
2
0
0
2
1
1
1
0
1
2
0
0
2
1
2
1
2
0
0
0
0
1
0
1
0
1
1
2
1
1
0
1
0
1
0
0
1
1
2
0
2
0
1
0
1
1
0
0
1
0
0
1
0
1
2
2
0
2
0
1
0
0
2
1
0
2
0
0
1
1
2
0
1
1
1
1
2
0
1
0
0
2
0
2
0
0
1
2
3
0
1
2
1
0
0
2
1
1
0
1
0
1
1
0
0
1
1
1
0
0
1
2
1
1
0
1
1
0
1
2
1
0
1
2
0
1
1
0
0
2
2
1
1
1
1
0
1
2
0
2
0
1
2
2
0
1
0
0
0
0
1
1
0
2
0
1
2
1
1
1
2
1
1
0
0
1
0
2
2
1
0
1
1
0
1
2
0
3
1
0
2
0
0
1
0
0
0
0
2
0
1
1
0
1
2
2
0
0
0
1
0
0
1
0
1
1
0
1
0
0
1
1
0
2
2
2
1
0
0
2
0
1
1
1
1
0
1
2
1
1
0
1
1
1
0
0
0
1
0
0
2
0
2
0
1
0
2
0
0
0
1
0
1
2
2
2
0
1
1
0
1
1
1
1
2
1
1
1
0
2
1
0
2
0
0
1
1
0
0
0
0
2
1
2
1
2
2
0
0
0
1
0
0
0
1
0
1
1
1
0
1
1
1
0
1
2
0
0
2
0
2
0
0
0
0
2
1
1
1
0
1
0
0
0
1
2
2
0
0
1
1
2
0
1
0
2
1
2
0
2
0
1
1
2
0
0
0
2
0
0
1
0
0
0
0
0
1
2
0
1
0
1
0
1
1
1
1
1
1
0
2
1
1
1
0
0
0
0
1
2
0
1
1
1
1
0
0
1
1
0
2
1
0
2
1
1
1
0
2
1
1
0
2
1
0
2
0
0
2
0
0
0
0
0
2
0
0
0
1
2
0
1
1
2
0
0
0
0
1
1
2
2
0
0
2
1
2
0
1
1
1
1
0
1
2
2
1
0
0
0
1
1
1
1
1
2
2
0
0
1
1
0
0
2
3
0
0
1
1
1
2
1
1
1
2
1
0
0
1
2
1
0
0
0
0
2
2
1
2
1
2
1
0
0
1
0
1
0
0
1
1
1
1
2
0
1
0
0
0
0
2
1
1
1
1
0
1
1
1
0
0
1
0
2
1
0
0
0
1
1
2
2
0
1
0
0
0
3
1
2
1
0
2
1
2
1
1
1
0
1
1
3
2
1
3
1
2
1
0
1
0
1
0
1
0
0
0
1
1
1
2
2
1
0
1
0
0
1
0
2
0
0
0
0
0
1
2
1
0
1
2
1
2
0
2
1
0
0
1
0
1
1
1
2
1
0
1
1
2
0
1
0
2
0
1
0
0
0
1
1
1
0
1
0
2
1
0
0
1
1
0
1
0
0
0
1
2
0
0
2
1
1
0
2
0
2
0
1
0
0
1
3
1
0
1
1
0
0
1
2
0
1
0
0
0
1
2
1
2
1
0
0
2
0
4
1
2
2
1
0
2
0
1
0
0
0
2
2
2
2
2
1
1
0
1
0
1
0
2
2
0
1
1
0
0
4
2
0
5
0
1
0
1
2
1
1
1
0
0
0
2
2
2
0
2
2
0
0
1
1
0
0
0
2
1
2
0
2
2
1
0
0
1
0
0
0
0
1
0
1
0
2
0
1
1
0
1
2
2
2
1
2
0
0
2
1
1
1
0
0
1
0
0
1
1
2
3
0
1
1
2
1
1
0
2
3
0
2
0
2
2
1
1
2
0
1
0
2
0
0
1
1
0
1
1
0
0
2
2
0
2
0
0
1
1
0
0
2
1
1
1
0
0
1
0
1
1
1
2
0
1
1
0
0
2
1
0
0
2
2
0
1
1
2
2
1
1
0
0
1
2
1
1
0
0
1
0
2
0
0
1
4
0
1
2
0
0
2
2
0
2
1
1
3
0
1
1
1
0
1
1
0
0
0
0
1
2
0
1
1
0
1
1
0
1
0
1
2
2
5
1
1
0
0
1
1
0
1
1
2
1
1
1
2
1
1
1
0
2
2
1
1
0
0
2
2
1
1
2
0
2
0
0
2
0
0
2
1
0
2
0
1
1
2
0
0
0
0
1
0
0
1
0
2
1
0
2
2
1
2
0
0
0
2
1
1
1
0
1
2
2
0
1
0
1
0
0
1
0
0
2
0
0
0
2
1
1
2
2
0
1
0
0
0
1
0
1
0
1
0
1
0
1
1
2
1
0
0
1
1
2
1
2
4
1
1
1
1
0
1
0
0
0
1
2
0
2
0
1
2
0
1
1
0
1
1
1
2
0
2
2
0
0
2
1
0
2
0
0
2
1
1
0
1
1
0
2
1
0
1
1
2
0
1
2
0
0
0
1
0
0
1
0
0
0
0
1
0
2
0
1
0
1
0
0
1
0
1
1
0
1
1
1
1
1
0
1
1
1
1
1
2
0
0
0
0
1
0
0
0
0
0
2
0
1
2
2
0
2
0
2
2
3
1
0
0
0
0
1
2
1
2
0
1
0
2
0
0
0
0
2
0
1
0
0
1
2
0
1
2
1
2
0
0
0
0
1
1
2
3
2
0
1
2
1
0
1
0
0
0
2
0
2
0
1
0
1
2
0
0
2
1
0
0
0
0
1
1
0
1
2
2
1
0
2
0
1
0
0
2
2
2
1
0
1
1
0
1
1
1
0
1
1
1
0
0
1
2
1
0
2
0
1
0
0
1
2
0
1
1
2
0
2
1
2
1
2
1
2
1
1
2
0
3
2
2
0
1
1
1
0
0
0
0
1
1
0
1
1
3
1
2
0
0
1
2
1
0
0
1
1
2
1
2
1
1
2
1
1
1
0
2
1
1
1
0
0
1
1
0
0
1
0
2
1
0
0
1
1
1
2
1
2
0
1
2
0
1
1
2
2
1
0
0
2
1
1
1
2
2
1
0
1
0
0
1
0
0
1
3
1
2
0
1
1
0
1
1
0
0
2
1
1
1
0
2
1
0
1
0
0
1
0
1
1
0
0
1
0
1
1
0
0
1
2
0
1
0
1
0
0
2
1
2
1
0
1
0
2
0
0
1
1
1
2
1
0
0
2
2
1
1
0
2
1
0
0
2
0
1
0
2
1
0
0
1
0
1
1
1
0
0
2
0
3
0
2
0
0
1
1
2
2
2
2
0
4
1
0
1
0
0
0
1
0
2
0
1
0
1
1
0
0
0
0
1
2
0
1
0
1
2
1
0
0
1
1
1
1
1
2
1
3
2
0
2
2
1
1
1
0
0
0
0
0
1
2
0
0
0
0
2
2
2
1
0
2
1
0
0
1
0
1
0
0
1
1
0
1
0
1
1
1
2
0
2
2
1
1
0
0
0
2
0
1
0
2
1
1
0
0
0
0
1
1
1
1
0
1
1
0
0
1
0
0
1
0
0
0
0
2
1
1
1
2
1
0
1
0
2
1
0
0
2
1
2
1
1
1
2
1
4
0
0
1
1
2
0
1
1
0
1
2
0
3
1
1
1
1
2
0
1
0
2
0
1
0
1
1
0
1
1
1
1
0
0
2
1
0
0
1
0
0
0
2
1
0
0
0
2
0
1
1
0
0
1
2
0
1
1
1
0
1
1
1
1
0
0
1
1
1
0
3
0
2
0
0
1
1
1
1
0
0
0
2
1
0
0
2
0
1
1
0
0
0
1
1
0
2
2
0
0
0
2
1
0
0
0
2
1
1
1
0
2
0
1
1
0
2
0
2
0
0
1
1
0
1
1
0
0
1
1
1
3
1
0
1
1
0
1
1
1
1
0
0
1
0
2
1
2
0
0
1
0
0
0
1
1
1
0
2
1
0
1
1
1
2
1
1
2
2
1
2
2
1
0
1
1
1
0
1
2
2
2
1
0
0
1
2
0
0
1
0
0
0
0
2
1
0
0
1
0
1
1
1
1
0
0
2
2
0
1
2
1
1
1
0
0
0
3
0
0
0
1
1
1
0
2
1
1
2
1
1
3
0
1
0
9
0
2
2
2
0
1
0
2
2
0
1
0
2
0
1
2
2
0
2
1
2
1
1
0
0
0
0
0
0
2
1
1
1
1
0
1
1
1
1
0
1
2
2
0
2
1
0
2
0
2
1
1
1
3
0
2
0
1
0
0
1
2
2
2
1
2
0
1
0
2
1
2
0
1
2
2
0
0
1
2
0
0
1
1
1
1
3
0
1
0
2
1
2
0
0
1
1
1
0
2
2
2
0
0
1
1
0
4
1
0
1
0
1
3
2
0
2
2
1
0
2
0
1
1
1
2
0
3
0
1
0
1
1
2
1
1
1
0
0
1
0
1
1
0
0
2
0
0
0
2
1
0
0
1
1
1
0
1
3
1
2
0
2
1
2
2
0
0
0
0
1
0
1
2
2
0
0
0
0
1
2
0
1
2
0
1
0
1
1
2
1
1
1
0
0
0
0
2
1
0
1
1
0
1
1
1
2
0
0
0
0
1
0
1
0
0
3
0
0
0
1
1
0
1
1
1
0
1
0
0
0
2
0
1
1
1
1
0
0
1
1
1
0
0
1
0
0
2
1
2
0
0
1
2
3
0
1
0
2
1
2
0
1
0
1
1
0
0
1
0
0
1
1
0
2
1
2
0
1
1
2
1
0
2
0
0
0
0
2
1
1
2
2
0
0
4
0
0
0
1
0
1
0
1
0
1
1
0
1
2
0
0
1
0
0
1
0
2
0
0
1
0
1
1
1
0
2
2
0
0
0
1
0
0
0
1
0
0
1
1
2
1
0
0
1
0
0
1
0
1
0
1
2
0
0
0
1
2
0
1
2
2
1
3
1
2
0
1
0
0
1
1
0
0
0
0
2
2
1
1
0
1
0
1
4
1
0
1
2
1
2
2
2
0
0
2
1
0
0
2
2
2
2
0
0
0
1
1
0
0
1
2
2
0
0
1
1
1
0
2
0
0
2
2
0
1
1
1
2
0
2
0
2
0
1
1
1
0
0
1
1
1
1
2
2
3
1
1
1
0
2
1
0
0
2
2
3
3
0
2
1
0
0
1
0
1
0
0
0
1
2
0
2
2
1
0
1
1
1
0
0
1
1
0
0
0
1
0
1
1
0
3
0
1
2
0
1
1
1
1
1
0
0
1
1
1
0
0
0
2
1
2
0
0
1
2
1
1
0
2
0
0
1
1
0
0
2
1
0
0
0
1
1
1
1
1
0
2
0
0
1
2
2
1
0
0
0
2
0
0
2
1
0
0
0
1
0
1
1
1
0
1
0
0
1
0
2
0
1
0
1
0
1
2
1
0
1
0
1
0
0
0
0
0
1
1
0
1
1
1
1
1
1
4
1
1
0
1
0
2
1
1
1
1
1
1
2
1
1
1
1
1
0
1
2
2
0
0
1
1
0
0
0
0
0
0
0
2
2
2
0
0
2
0
2
1
0
1
0
0
1
2
2
1
1
1
1
0
1
1
1
0
1
1
1
0
2
0
0
0
0
1
1
0
0
2
1
2
1
0
0
1
1
1
0
0
0
0
0
1
0
0
0
2
0
0
2
1
2
0
0
2
0
4
2
1
0
1
0
1
1
0
2
2
1
1
0
0
1
1
0
2
2
0
1
0
1
0
1
0
0
0
1
2
1
0
0
1
0
1
0
1
1
2
0
3
0
2
2
0
2
1
2
2
1
0
0
0
0
1
1
0
2
1
1
0
1
2
3
2
0
1
2
1
2
0
0
1
1
2
0
0
0
0
0
1
1
0
1
1
1
0
1
0
1
0
2
0
0
0
0
0
0
1
0
0
0
1
1
0
1
2
1
1
1
1
1
0
0
1
2
0
1
1
1
0
0
0
0
0
1
1
1
0
0
3
1
2
0
0
1
1
1
1
2
2
0
0
1
2
0
0
0
0
1
0
2
0
1
0
1
1
0
1
1
1
1
0
0
2
0
1
0
2
1
2
2
1
0
1
1
1
0
1
1
2
0
1
1
1
1
0
2
0
1
1
1
0
0
0
1
1
1
1
0
1
2
2
2
1
0
4
1
0
2
0
1
1
0
0
1
1
2
1
1
1
2
1
1
2
2
0
2
1
1
1
1
0
2
1
0
0
0
1
1
2
1
2
1
1
1
0
0
0
1
0
1
0
0
2
0
0
1
0
1
1
2
2
0
1
0
0
0
1
1
0
0
0
1
2
0
0
0
0
0
0
1
0
1
1
1
0
1
0
0
1
2
0
0
2
1
1
2
0
1
2
0
2
2
0
0
0
0
0
0
0
2
1
1
1
2
1
0
1
1
0
1
0
0
0
3
0
0
1
1
0
0
1
0
0
2
2
0
2
0
1
0
1
0
1
1
1
1
1
0
0
0
0
0
0
1
2
1
1
1
0
1
1
0
0
2
2
0
0
1
2
2
2
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
1
0
0
1
1
0
0
1
0
1
1
1
2
0
2
1
0
3
2
0
1
1
0
1
2
1
0
0
1
2
0
1
0
1
2
2
2
1
2
2
0
1
1
0
0
0
1
1
0
3
1
1
0
1
0
2
1
1
1
2
1
2
0
1
2
1
2
2
2
1
2
0
0
2
0
1
1
2
0
3
0
0
1
2
0
2
0
1
1
2
1
0
0
2
2
0
1
1
0
1
2
0
2
0
2
1
2
1
0
2
0
0
1
0
1
1
0
1
0
0
1
2
1
0
1
1
1
1
1
1
1
2
0
2
0
2
1
1
1
1
0
1
2
0
1
0
2
2
0
0
3
0
1
4
2
2
1
4
1
0
1
2
0
2
0
0
1
0
0
0
1
1
1
1
1
0
0
1
1
0
1
0
1
0
0
1
1
0
0
0
1
1
2
1
1
2
0
1
2
2
0
2
0
1
1
1
0
0
0
2
1
1
2
1
0
1
0
1
0
1
3
0
1
0
1
0
0
2
1
0
0
1
1
0
1
1
0
0
2
0
1
0
2
1
0
0
0
2
0
1
0
1
1
2
0
2
0
0
2
0
2
0
2
0
2
1
1
0
3
1
1
0
0
1
0
2
1
1
1
0
1
0
1
1
0
1
0
0
0
1
0
1
1
2
5
1
2
0
0
0
1
0
0
2
1
0
1
1
0
1
0
1
2
2
0
0
0
1
1
1
2
2
2
1
0
0
0
0
0
1
0
1
0
3
1
1
0
0
1
2
0
1
2
1
1
2
1
0
2
1
1
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
2
1
3
2
0
0
2
0
2
1
0
1
0
2
0
1
0
1
1
0
2
0
1
2
0
0
1
1
1
1
1
4
0
1
0
0
1
0
0
0
1
1
0
1
0
0
2
2
0
1
0
0
0
0
1
0
0
2
1
0
1
2
0
1
1
1
2
0
1
0
1
2
0
0
0
1
1
0
0
1
2
1
1
1
0
1
0
0
1
1
1
1
1
1
1
0
0
6
2
2
0
2
1
0
0
0
2
2
0
0
2
1
0
0
0
1
1
1
0
1
1
1
0
1
0
0
2
0
1
1
2
1
1
0
2
1
0
2
0
0
2
0
2
1
0
1
0
1
0
0
1
0
0
1
0
2
0
1
1
2
1
3
0
0
0
0
1
2
2
0
0
1
0
2
1
0
0
1
2
1
0
2
0
0
0
0
0
1
0
0
1
0
1
2
0
2
0
0
0
0
2
2
1
0
1
0
1
0
0
0
1
1
0
0
0
0
2
0
2
0
2
1
0
0
2
1
0
0
0
0
1
1
1
1
0
4
1
1
2
1
1
0
2
2
1
1
0
0
1
1
0
0
0
1
1
2
2
0
0
2
1
0
2
1
0
0
1
1
0
2
1
0
1
0
0
1
0
0
0
2
2
1
0
1
2
0
0
2
0
1
3
1
0
1
1
0
2
1
3
0
0
2
1
0
0
0
3
0
0
2
1
1
1
2
1
1
1
2
1
1
2
2
0
0
0
1
1
1
1
1
0
0
0
0
0
2
0
1
0
1
2
1
1
2
0
1
0
1
1
2
2
0
0
0
1
0
1
0
0
1
0
1
2
1
0
2
1
2
0
0
0
1
0
0
1
0
1
1
2
0
2
1
1
1
1
2
1
0
0
1
1
0
0
0
2
0
1
0
2
0
1
0
0
0
1
1
0
1
1
0
0
1
1
1
2
0
1
2
2
1
2
2
0
1
1
2
0
1
1
1
1
0
1
1
2
2
0
1
0
1
1
0
0
2
1
0
1
2
2
1
1
0
1
0
0
2
1
1
1
2
2
0
1
1
1
1
1
1
2
2
1
1
0
0
0
2
1
3
0
0
2
0
0
0
0
1
0
1
1
1
0
1
0
0
0
1
1
0
0
1
0
2
0
0
1
2
0
2
0
0
0
2
2
0
0
0
2
2
0
2
2
1
1
0
0
2
1
0
1
0
1
2
2
0
0
3
0
1
0
2
0
1
1
1
2
0
2
0
2
0
2
2
0
1
1
1
1
1
0
1
0
1
0
1
0
2
1
2
1
1
1
2
0
0
0
0
0
1
1
0
0
1
0
1
2
0
2
0
1
1
1
1
2
0
0
2
2
1
0
1
2
0
1
2
1
2
2
0
0
2
1
1
1
0
0
0
2
2
1
1
1
1
1
0
1
0
1
2
1
2
1
0
1
1
1
0
0
0
2
0
1
0
0
2
3
2
0
2
0
2
0
0
0
1
0
0
1
0
0
0
0
1
2
2
2
0
1
1
0
0
0
2
0
1
0
1
0
1
0
1
1
0
1
1
2
2
1
0
0
2
0
3
1
0
2
1
2
1
0
0
0
2
4
2
0
2
0
2
2
1
0
1
0
1
0
1
1
1
2
1
0
1
2
2
2
2
2
1
2
1
0
3
0
2
0
2
1
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
2
2
2
2
1
1
2
0
0
2
1
0
1
1
2
1
1
1
1
0
1
1
1
2
1
2
1
0
2
1
1
1
0
0
1
1
1
0
0
2
0
0
1
0
0
1
0
1
1
2
0
1
2
1
3
1
0
0
1
1
2
1
0
0
1
1
1
2
2
2
1
1
1
0
0
0
0
1
1
1
0
2
0
1
1
2
2
0
0
0
1
1
1
0
2
0
1
1
1
0
0
1
0
0
2
1
1
0
2
3
0
2
2
0
1
1
0
1
2
1
0
0
1
1
1
0
4
1
2
0
1
2
1
0
1
0
0
0
0
1
0
1
0
2
4
0
0
1
1
1
1
2
1
0
1
1
1
0
2
1
1
0
1
1
2
1
0
1
0
1
1
2
4
0
1
1
0
1
1
2
0
2
2
1
0
1
0
1
0
0
0
0
0
0
2
0
0
1
1
1
1
1
0
2
1
1
0
1
2
2
0
0
1
0
0
1
1
1
0
2
0
2
0
2
1
2
2
2
1
1
1
1
0
0
1
2
0
1
1
2
1
2
1
0
0
0
1
0
1
0
1
2
1
0
2
0
1
2
0
0
0
0
2
1
0
0
2
3
2
0
1
1
1
0
0
0
0
0
2
2
1
1
0
2
1
2
0
1
1
0
2
2
1
1
1
2
2
1
2
1
2
2
2
2
0
1
0
2
0
2
3
0
1
0
0
1
0
1
0
2
1
1
1
1
0
0
0
0
1
1
1
0
1
0
1
0
0
2
0
0
1
0
1
1
0
2
1
2
1
0
0
2
2
0
2
2
0
1
0
0
0
0
2
1
2
1
2
0
0
1
2
0
0
1
1
0
1
0
2
1
0
2
0
0
0
1
0
1
0
0
0
1
1
1
2
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
1
1
0
0
0
3
0
0
0
1
1
2
0
0
0
0
0
0
1
1
0
2
0
1
0
0
1
2
0
1
1
1
2
0
2
0
0
0
0
0
0
1
0
1
2
2
1
1
0
0
0
0
1
1
2
1
2
1
2
0
1
1
2
0
0
1
0
0
2
2
0
1
1
1
0
1
2
0
1
0
1
1
0
0
1
1
1
1
0
2
1
1
1
1
0
1
1
2
0
1
8
1
0
0
0
0
0
1
0
1
0
2
2
1
0
0
1
2
0
1
1
1
2
1
2
2
0
1
0
1
0
2
2
0
0
0
1
0
2
0
0
1
0
0
0
1
1
0
1
1
0
1
0
2
0
1
1
1
1
0
0
1
0
1
1
0
1
0
0
2
0
0
1
2
1
0
1
1
1
1
2
0
1
1
0
0
1
2
2
0
0
0
1
0
0
0
2
1
1
0
0
0
0
1
0
1
2
0
0
1
1
1
1
1
1
1
2
2
1
0
1
1
1
0
0
0
2
2
0
0
1
1
2
2
0
2
0
0
1
0
0
1
0
1
0
2
1
1
0
1
0
1
2
0
0
1
0
0
1
2
2
2
3
2
0
2
2
2
0
1
1
2
0
1
2
1
0
1
0
1
1
2
1
1
1
1
1
1
2
0
0
1
0
1
0
1
1
1
1
1
1
0
1
1
1
0
2
0
2
0
1
2
1
2
2
0
0
0
0
2
1
1
0
1
1
0
1
1
1
1
2
2
0
2
1
2
1
2
0
2
2
1
0
2
2
0
0
1
1
1
0
2
0
2
1
0
0
0
0
1
2
1
1
3
0
0
0
1
2
0
1
2
1
0
0
1
1
0
0
1
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
1
2
0
2
1
2
0
1
0
1
0
0
2
0
2
2
1
1
1
0
2
1
0
0
0
0
1
1
2
0
2
2
1
1
1
0
1
0
1
1
2
0
2
2
1
4
4
1
2
1
2
1
0
0
1
2
1
1
0
0
0
1
1
0
2
1
0
0
1
1
1
0
0
0
0
1
2
2
0
1
1
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
2
1
0
0
1
0
0
0
1
0
1
1
0
0
1
2
0
0
1
2
0
1
1
0
2
1
2
0
0
1
1
1
1
1
0
1
1
1
2
0
0
1
1
1
0
1
1
1
2
0
0
0
0
2
1
0
1
0
0
0
1
1
1
0
2
0
2
2
0
1
2
0
1
0
0
0
1
1
2
2
2
0
2
1
0
1
0
1
2
1
0
0
0
1
1
0
0
1
0
0
0
1
0
2
1
2
3
1
1
1
1
0
1
0
1
0
1
0
2
0
1
1
1
4
0
2
0
1
1
0
0
0
0
2
1
1
0
1
2
0
2
1
2
0
0
1
1
2
1
2
1
1
0
0
1
0
0
0
2
2
1
2
1
2
2
1
0
0
2
1
0
0
1
1
2
0
1
2
0
0
2
1
1
1
1
1
2
1
0
2
0
1
1
1
0
1
2
0
1
1
0
0
2
2
0
0
2
0
0
0
1
0
0
0
0
1
1
1
0
1
1
1
0
1
5
2
0
0
1
1
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
2
0
0
0
0
0
1
1
1
1
2
1
2
0
1
1
2
2
0
0
1
0
1
1
1
2
0
1
1
0
1
2
0
0
2
1
1
0
2
0
0
1
0
0
1
0
0
1
1
2
1
0
2
0
1
1
1
1
2
0
0
0
1
2
2
0
0
1
2
2
0
0
3
1
0
0
2
1
0
0
0
3
0
0
0
2
0
1
0
2
1
1
0
0
1
1
1
0
1
0
0
0
1
0
0
0
1
1
1
0
1
0
0
1
0
2
1
0
1
1
1
4
2
0
0
2
2
0
2
1
1
1
1
1
0
0
2
1
0
0
2
1
1
1
1
3
1
1
0
0
2
0
0
2
2
1
1
2
0
2
1
2
0
2
0
1
0
1
2
1
2
1
1
1
1
1
1
1
1
2
0
1
2
0
2
0
1
1
2
1
0
1
0
0
1
0
0
0
1
0
1
0
1
2
1
1
1
0
1
2
0
1
0
1
1
2
0
1
1
1
1
3
0
1
1
0
0
0
1
2
1
0
1
0
1
1
0
1
2
2
1
1
1
0
1
0
0
2
2
1
1
1
1
0
0
0
0
0
1
0
2
2
1
0
1
2
2
1
2
0
2
0
0
2
0
0
1
1
0
0
0
0
2
0
0
1
0
1
2
2
2
1
1
1
1
0
2
2
1
0
0
0
1
0
0
0
2
0
0
2
2
1
2
1
1
0
2
1
0
0
0
0
2
0
0
2
2
1
2
2
1
0
1
2
1
1
1
1
1
1
0
1
0
2
2
2
1
1
1
1
2
2
0
1
0
1
1
0
2
0
0
1
1
0
2
1
1
2
1
1
2
2
3
1
1
2
1
1
0
0
1
0
1
1
1
2
0
1
2
0
3
0
0
0
0
0
0
0
0
4
2
1
2
1
2
1
0
1
1
1
1
0
1
0
1
1
0
1
1
1
0
1
2
1
4
1
2
0
2
2
0
2
1
1
1
1
0
0
0
0
1
2
0
1
1
0
2
2
1
0
1
1
1
0
1
2
1
0
2
0
0
1
2
1
0
0
0
1
0
1
2
0
0
0
0
2
1
2
0
0
3
1
2
1
0
0
1
2
1
0
2
2
0
2
1
0
1
0
1
0
1
1
2
2
1
1
2
2
0
2
0
0
2
1
1
2
0
0
1
1
1
1
1
0
1
1
1
0
1
0
0
0
0
1
1
0
0
1
2
1
2
1
2
0
0
0
0
1
0
0
1
1
1
1
1
1
2
0
2
0
0
0
0
0
1
2
1
0
1
0
1
1
2
1
0
2
1
0
0
2
1
1
0
0
3
0
0
0
1
1
1
1
0
1
0
1
0
2
1
1
2
0
0
1
1
0
0
0
1
0
2
0
0
1
2
1
8
2
1
2
0
0
2
0
0
1
1
0
1
1
2
2
1
1
2
0
1
0
1
1
0
1
0
1
0
0
0
0
1
0
0
1
2
5
2
1
1
1
0
0
1
1
0
1
4
0
2
1
0
0
0
2
0
0
2
0
2
2
2
1
0
0
1
0
0
1
0
0
0
1
1
0
1
2
1
0
1
1
1
2
2
1
0
0
0
1
1
1
0
1
0
1
1
0
1
1
1
1
1
2
2
2
1
1
0
2
0
0
2
0
0
1
1
0
2
0
0
0
2
2
0
2
0
2
0
1
0
0
0
1
1
1
0
1
0
2
1
1
0
2
1
0
2
0
0
1
1
2
1
0
2
1
0
0
1
1
1
1
0
1
2
1
1
0
0
1
1
1
0
2
1
0
1
1
2
0
0
0
2
1
1
1
0
0
1
0
2
2
0
2
0
0
1
0
1
1
2
0
1
1
0
0
2
0
0
1
1
1
0
1
0
1
1
0
2
1
0
2
1
1
0
1
0
1
2
2
0
0
0
0
2
0
0
0
1
1
2
0
1
0
2
1
0
0
2
1
0
0
0
0
1
0
0
1
1
2
3
1
2
0
1
1
0
2
1
0
0
1
0
1
1
2
2
0
1
1
0
1
0
4
0
1
0
0
1
0
1
2
1
1
0
2
1
1
1
4
2
0
0
2
0
0
2
1
0
2
2
2
0
0
0
0
1
0
0
1
0
2
1
1
2
0
1
0
1
0
0
0
0
0
1
0
0
0
2
1
2
2
1
1
0
1
0
1
0
0
0
0
0
1
1
0
2
1
1
1
1
1
0
1
0
1
0
1
0
2
1
0
1
1
0
0
1
1
0
2
4
0
0
0
1
0
1
2
2
1
1
0
0
0
1
1
0
0
2
1
0
2
1
3
1
0
0
1
1
0
0
2
1
0
0
1
1
0
1
1
1
4
2
0
0
0
2
1
0
1
1
0
1
2
0
0
0
0
1
1
1
0
1
2
1
0
1
0
1
1
1
0
0
0
2
1
1
0
0
1
1
1
0
0
0
1
0
1
1
0
0
1
2
1
2
0
0
3
0
1
1
2
0
1
0
1
1
2
0
1
4
2
2
0
1
1
1
2
1
1
0
2
1
2
1
1
2
1
1
1
1
2
2
2
1
0
2
0
0
0
0
2
2
1
2
0
2
0
0
0
4
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
2
1
1
0
2
1
1
1
1
4
1
0
1
2
1
2
0
1
0
1
1
1
1
1
2
1
1
0
1
0
0
1
1
1
0
1
2
2
1
1
2
2
0
0
1
0
1
1
3
0
0
1
0
0
1
2
0
0
2
0
3
0
0
2
1
1
0
0
0
1
0
1
1
1
1
0
1
2
0
0
1
0
0
1
1
0
0
2
1
1
0
0
0
2
0
1
0
0
0
2
0
1
1
2
2
1
0
1
1
1
1
1
0
1
0
1
1
1
0
0
0
0
0
2
1
2
2
1
0
0
2
1
2
1
1
0
1
1
2
1
3
1
1
1
1
4
0
2
1
2
1
1
0
1
1
1
0
0
1
2
1
0
3
1
2
1
0
0
0
1
2
1
1
2
0
2
2
2
0
0
1
2
0
0
2
1
1
0
1
0
0
0
0
1
1
1
2
0
1
2
1
1
1
2
1
2
1
1
2
3
0
0
0
0
1
3
1
0
1
0
1
0
0
1
1
1
0
1
2
0
1
5
1
0
0
0
1
0
1
0
1
0
2
1
0
2
0
1
0
0
1
1
1
0
1
0
0
0
3
1
0
1
0
1
1
2
0
1
0
1
0
2
2
0
1
3
1
1
2
3
2
2
2
0
0
0
0
1
1
1
0
2
1
1
0
0
0
0
3
1
2
0
0
0
0
1
0
1
1
1
0
2
0
1
0
1
2
1
2
0
0
1
2
0
1
0
0
1
1
2
2
0
1
5
0
2
0
2
1
0
0
1
2
0
0
1
1
0
2
2
2
2
1
1
0
0
0
1
0
1
1
0
1
1
0
1
0
0
0
0
0
0
1
1
0
2
1
1
1
1
2
2
0
1
0
1
1
1
0
2
2
0
0
0
0
1
1
0
1
0
2
1
0
1
2
1
1
1
0
0
0
0
1
0
2
0
1
0
1
1
1
0
0
1
3
1
0
0
0
0
1
1
2
2
2
0
1
2
1
2
0
2
0
1
1
1
1
0
1
0
0
2
1
1
0
0
2
1
1
2
0
2
0
0
1
2
1
1
1
2
1
0
0
0
0
0
1
2
1
0
0
0
0
1
1
1
2
1
2
0
0
1
0
1
1
1
1
1
1
0
0
0
0
1
2
2
0
0
1
2
0
2
0
2
1
0
0
0
0
1
2
0
1
0
0
1
0
2
1
1
1
1
1
1
1
1
1
0
0
0
0
1
1
0
1
1
0
2
1
1
1
0
1
1
2
1
0
0
1
2
1
2
2
3
0
0
2
0
0
1
0
1
1
1
1
1
2
1
2
1
1
0
0
0
1
0
1
0
2
1
1
1
1
0
1
2
1
2
2
1
1
2
0
2
0
0
1
1
1
2
1
1
1
0
0
0
0
0
1
1
1
0
0
0
0
2
0
2
1
1
1
0
0
0
2
0
1
0
2
0
0
0
1
0
1
2
0
2
1
2
0
0
1
1
1
1
0
1
2
1
2
0
1
2
2
1
1
0
1
2
0
1
1
1
0
0
2
1
2
0
2
0
1
0
0
1
0
0
1
0
0
0
1
1
2
0
1
1
0
2
0
2
1
2
1
1
1
1
1
2
1
2
0
2
1
0
2
1
1
2
1
2
0
1
2
0
1
2
0
1
0
0
2
0
0
0
2
2
1
1
1
0
1
1
2
1
0
1
2
0
1
2
0
0
0
1
1
1
1
2
1
0
0
0
1
1
1
2
2
0
1
0
2
0
2
2
2
0
0
0
2
1
1
2
1
1
0
2
0
2
1
0
1
1
0
1
2
2
2
2
1
1
0
1
1
0
0
0
0
0
0
1
1
0
0
1
0
2
0
2
0
1
2
0
1
1
1
0
0
0
1
2
1
0
0
0
0
1
0
1
0
3
0
1
0
1
0
0
1
0
1
2
1
0
2
0
2
0
0
1
1
1
0
0
0
0
1
1
5
0
0
1
1
2
2
0
1
2
1
2
1
2
1
1
0
0
0
0
0
1
1
1
1
1
0
0
2
1
0
1
0
2
1
1
0
2
1
1
1
1
1
0
0
1
2
2
1
1
2
0
1
1
1
2
1
1
0
1
0
1
0
1
2
0
0
0
2
0
1
0
0
2
1
2
0
0
2
1
2
0
0
2
1
1
1
1
0
0
1
1
0
2
1
1
2
1
0
1
0
2
1
1
0
1
0
1
0
0
2
0
0
1
1
2
1
1
1
2
0
0
0
1
4
0
0
0
0
0
0
1
0
1
0
2
0
2
1
0
2
3
0
0
2
0
0
1
0
0
1
0
1
0
2
0
0
1
0
0
1
1
2
0
2
1
1
2
1
0
1
0
1
2
0
0
0
1
0
1
0
1
2
1
0
1
2
1
1
2
0
1
1
0
1
0
1
2
1
2
0
1
2
1
1
2
0
1
0
2
1
2
1
2
0
1
1
1
2
1
0
2
1
1
0
1
0
0
0
0
0
0
2
2
1
1
1
0
0
0
0
1
1
1
0
1
0
0
0
0
1
0
2
1
1
2
0
1
0
1
0
1
0
1
2
0
1
2
1
1
0
0
0
2
0
2
0
1
2
1
1
1
1
2
2
1
1
1
0
0
2
1
1
1
1
1
1
0
1
1
2
0
1
0
1
0
1
0
1
2
2
2
2
2
1
0
2
2
1
1
0
2
2
2
1
1
2
0
2
1
0
2
1
1
1
2
1
2
1
1
2
1
4
0
0
0
1
2
0
2
0
0
2
0
1
1
1
1
2
0
1
0
1
1
1
0
1
2
0
1
1
1
1
1
1
0
0
1
0
1
0
0
1
1
1
1
1
2
1
1
1
2
1
0
1
1
1
1
0
2
0
0
1
2
2
1
0
0
0
1
1
0
2
2
1
0
2
0
0
1
1
1
0
0
0
1
0
0
2
2
1
0
1
1
1
1
2
1
1
2
0
0
2
0
1
2
1
1
3
2
1
0
1
1
1
1
2
1
1
2
0
0
1
1
0
0
1
0
0
0
2
0
0
0
0
2
0
0
2
0
1
1
0
1
2
0
2
0
1
1
2
2
2
1
0
2
2
1
2
1
2
2
0
1
2
1
2
0
0
0
0
1
2
0
1
0
1
0
0
2
2
0
2
1
1
1
1
1
1
0
0
1
1
2
1
2
2
0
1
0
2
2
1
1
0
1
0
1
1
1
1
1
2
0
0
2
0
2
0
0
1
1
2
2
0
0
1
0
0
3
0
2
1
1
0
1
1
0
1
2
8
2
1
0
1
0
0
0
2
1
0
1
0
0
2
0
0
0
1
2
0
1
0
1
0
0
1
0
0
1
1
1
2
1
1
0
0
0
2
1
1
2
0
2
1
2
1
0
0
0
1
1
3
2
0
0
1
1
1
0
1
0
0
0
0
0
1
1
1
0
0
1
1
2
1
1
1
2
1
1
1
0
1
0
1
2
2
1
0
0
0
1
1
1
1
1
0
1
0
2
0
0
0
0
1
0
1
1
0
2
0
1
0
0
1
0
1
0
0
2
1
0
0
2
1
0
0
1
2
2
0
1
1
0
1
2
0
0
0
1
0
2
0
1
1
0
1
0
1
0
0
0
1
1
1
1
1
2
0
1
0
2
1
0
0
1
1
1
1
0
0
1
1
0
0
1
1
2
1
1
1
2
1
2
0
1
1
0
2
0
0
0
1
0
0
0
1
0
1
2
1
0
2
2
1
1
1
1
1
1
1
0
1
1
1
0
0
2
1
2
2
0
2
2
0
2
0
1
2
1
2
1
1
2
2
1
1
1
0
0
1
1
0
0
1
0
1
2
1
0
0
0
0
2
1
1
2
2
3
0
0
2
0
0
1
0
0
1
1
1
0
1
2
2
1
1
1
0
0
1
0
0
1
1
0
1
0
1
0
0
0
1
1
0
2
1
0
1
0
0
0
1
1
0
1
1
1
1
0
0
1
1
1
0
2
0
1
2
2
1
2
1
0
1
2
0
0
1
3
1
1
0
0
1
2
2
0
0
0
1
0
1
0
0
0
1
1
0
1
0
0
0
0
0
2
1
2
2
0
1
1
1
0
2
0
2
0
2
0
1
0
1
1
1
0
0
1
1
1
1
0
1
1
1
2
0
0
0
0
0
1
2
2
1
0
0
1
0
1
1
0
1
0
1
1
1
2
2
0
0
0
2
0
1
0
2
0
1
1
1
0
1
2
2
1
2
1
1
2
0
0
3
0
1
0
1
2
0
2
1
2
2
1
0
0
1
1
3
0
1
2
0
2
0
2
1
1
2
2
1
2
0
0
2
1
2
0
0
1
1
0
2
0
0
2
0
0
2
0
0
1
0
2
0
2
1
0
1
1
0
2
0
1
0
0
1
1
1
2
0
1
1
0
3
0
0
0
0
1
0
1
0
0
1
1
0
1
0
0
2
1
0
0
1
0
1
2
2
2
1
0
1
0
2
3
1
0
1
2
2
1
1
0
0
0
0
0
0
1
1
1
2
0
0
1
2
0
0
0
1
1
3
0
0
0
2
1
2
0
0
2
2
1
0
2
0
2
2
1
1
1
1
1
2
0
0
2
2
1
1
2
1
0
0
1
0
2
0
1
1
0
2
1
1
2
2
1
0
0
2
0
1
0
1
1
0
1
2
1
1
0
1
0
0
0
1
2
0
2
0
0
2
1
0
1
0
0
0
0
2
1
0
0
2
2
1
1
0
2
1
1
1
0
1
2
1
0
1
1
1
1
0
0
0
1
1
0
1
1
1
0
1
2
2
3
2
1
0
1
1
2
1
0
1
2
2
1
2
1
1
0
1
1
1
1
1
1
1
0
2
2
0
0
1
2
1
1
1
0
0
1
2
0
0
1
1
2
0
1
0
2
0
0
0
2
0
0
2
1
0
0
1
1
0
0
2
1
0
1
2
0
1
1
1
0
2
0
1
1
1
0
2
0
0
0
2
0
2
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
2
0
0
0
1
1
2
0
1
1
0
0
0
1
1
2
1
1
0
0
0
1
0
1
0
2
1
2
2
1
0
2
0
0
0
2
1
0
0
3
0
0
0
1
0
2
2
1
1
2
2
1
0
1
1
2
0
0
1
2
1
1
0
0
0
1
1
2
0
1
2
0
1
1
0
1
1
0
2
2
1
1
0
0
2
1
1
1
1
0
1
2
1
2
1
0
0
0
1
0
0
0
1
0
1
1
2
1
1
1
2
0
1
0
0
1
0
1
1
1
0
1
0
2
0
1
1
0
0
1
2
1
0
0
1
0
0
0
4
1
0
1
1
2
0
2
0
0
0
0
2
2
0
2
0
2
0
2
0
1
1
0
0
0
1
0
2
1
1
1
1
1
1
2
0
0
1
1
1
0
1
0
0
1
0
2
0
0
1
2
2
0
1
0
1
1
2
1
2
1
2
1
0
0
1
0
1
0
1
0
0
0
2
2
0
1
4
1
1
1
2
0
1
1
1
0
0
2
2
1
2
0
1
0
2
1
0
0
1
1
1
0
2
0
0
2
2
1
0
0
0
2
0
1
0
1
0
0
1
1
0
1
0
1
1
2
1
1
0
1
2
2
0
2
0
1
0
2
2
0
1
1
1
1
1
1
0
2
3
0
0
0
0
1
0
1
1
1
2
5
2
0
1
1
2
0
2
1
2
1
1
1
0
1
1
2
0
1
1
0
0
1
1
1
2
0
1
1
0
1
1
1
1
0
1
0
0
2
1
1
1
0
2
1
1
1
1
1
2
0
0
0
1
1
0
1
1
0
1
0
0
0
0
1
0
8
2
1
1
1
0
0
1
0
1
2
0
1
4
0
2
1
2
0
2
2
2
0
0
2
0
0
2
1
3
1
0
0
0
1
1
2
0
1
0
1
2
3
4
0
0
2
0
1
0
0
1
0
0
2
0
2
1
0
0
0
1
0
2
2
1
1
0
1
1
1
0
0
1
2
1
0
1
0
1
3
0
1
0
1
0
2
0
0
1
2
1
0
0
0
0
1
1
2
0
0
1
2
0
2
0
2
1
2
1
1
5
0
0
1
2
2
2
2
0
0
1
1
1
1
0
1
1
1
0
1
1
1
1
0
0
1
0
1
1
0
2
2
0
1
2
1
2
0
0
2
2
0
1
0
0
0
1
0
0
2
1
2
1
0
0
0
2
0
0
0
0
2
2
0
1
2
0
1
0
0
0
1
2
1
1
0
0
0
1
0
1
0
0
1
0
0
1
1
1
0
0
1
0
0
0
2
1
0
0
1
1
1
2
2
2
0
1
0
1
2
1
2
1
0
0
1
2
2
2
1
1
1
0
1
2
1
1
0
0
1
0
1
0
0
1
2
0
1
0
2
0
1
0
1
0
1
1
1
1
1
0
0
0
1
1
1
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
2
1
0
2
0
1
1
4
1
2
2
2
1
1
1
1
1
1
0
0
0
1
0
2
1
1
1
1
2
0
0
0
2
1
2
0
0
2
1
1
0
2
2
0
0
2
0
1
0
0
2
1
1
0
0
0
1
0
1
0
1
1
0
1
2
1
0
1
3
1
1
0
1
2
2
2
2
0
0
0
1
1
1
2
2
0
0
1
0
1
0
2
0
1
0
1
1
0
0
1
1
1
1
1
0
1
2
0
2
0
0
1
0
2
1
4
0
1
0
0
2
1
1
1
1
1
2
1
2
1
0
2
0
2
2
2
1
0
0
1
2
1
1
0
0
2
1
2
0
2
1
1
2
2
3
0
1
1
1
2
1
3
1
1
3
1
0
2
0
0
0
2
2
0
0
1
3
1
2
1
1
1
2
1
0
1
0
2
2
1
0
0
1
0
1
0
2
1
1
1
2
0
1
0
2
2
1
1
0
0
1
1
0
1
0
2
3
0
0
2
1
2
1
0
2
0
0
0
1
0
0
1
1
0
1
0
0
2
0
1
1
0
1
0
0
1
0
1
0
0
1
1
2
2
1
1
0
0
1
1
1
0
0
0
2
0
0
0
1
2
2
2
3
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
1
1
1
0
1
1
0
0
0
2
0
1
0
2
0
1
0
1
2
0
1
2
1
2
0
0
1
1
1
0
0
0
1
1
2
2
2
2
2
2
0
2
1
1
2
0
1
0
0
0
1
0
1
2
1
0
1
0
2
0
2
1
0
1
0
0
1
2
0
1
0
2
2
2
2
1
1
1
0
1
1
1
1
2
2
1
0
1
0
2
0
0
0
0
1
0
2
1
0
1
1
0
0
0
0
1
2
0
1
0
1
0
1
0
1
2
1
1
1
0
1
1
1
1
0
0
0
1
1
0
2
2
1
0
0
0
1
1
0
1
2
1
0
1
2
0
1
1
0
1
1
3
1
2
1
1
0
2
1
1
2
2
1
0
0
1
0
0
1
1
0
2
0
2
2
1
2
0
0
1
0
0
0
2
0
2
1
1
1
1
1
0
2
1
1
0
1
1
2
1
2
0
1
0
1
1
1
2
0
1
0
2
0
2
0
1
0
1
0
0
2
1
0
0
0
0
2
2
1
0
1
1
2
1
2
0
2
2
0
0
2
1
0
0
1
0
1
1
2
0
2
1
0
0
0
2
2
1
0
0
0
0
1
0
1
0
2
0
2
1
2
1
1
0
1
0
0
0
2
0
0
1
0
0
1
0
1
0
1
0
0
0
1
0
1
1
1
1
2
0
1
0
1
1
2
0
0
0
2
0
0
2
1
0
0
0
0
0
0
2
1
0
0
1
2
1
0
1
1
1
1
0
2
0
2
0
0
1
0
1
0
2
1
2
0
1
2
0
1
1
0
1
2
0
2
1
1
0
0
0
2
0
1
0
0
0
1
3
2
2
0
1
1
2
1
1
0
1
0
1
0
2
0
1
0
1
1
0
1
1
1
0
2
1
0
0
0
1
0
2
0
1
0
2
2
0
1
1
0
0
1
1
1
0
0
1
1
2
1
1
0
0
0
2
1
1
1
1
0
1
1
1
2
0
3
1
0
2
1
2
0
0
1
2
2
1
1
3
0
1
1
0
1
1
1
0
4
1
2
0
0
0
0
1
1
0
1
0
2
2
0
0
0
1
0
2
1
0
0
0
1
0
1
1
1
1
1
2
1
0
1
0
0
1
0
0
0
0
0
1
2
1
1
2
2
0
2
1
0
1
1
2
0
1
4
1
2
2
0
1
0
1
0
2
0
2
0
1
2
1
1
2
2
0
0
1
1
1
0
1
1
0
0
2
1
0
0
0
1
1
2
1
0
0
2
0
0
0
0
0
2
1
0
1
2
1
1
0
0
1
0
1
1
1
1
0
1
1
0
1
0
1
2
1
1
1
1
1
2
0
0
0
0
1
0
0
2
0
1
2
1
0
2
1
0
0
0
0
0
1
0
1
0
0
1
0
2
1
1
0
1
1
2
2
0
0
1
1
0
0
0
0
2
1
2
1
1
1
1
1
0
2
0
1
0
1
1
2
1
1
0
0
1
0
1
1
0
1
2
1
0
1
0
1
0
1
0
0
1
0
2
0
1
0
0
1
0
1
1
2
1
1
1
0
1
0
1
1
2
1
1
0
2
0
1
2
1
0
0
0
2
2
2
1
0
0
0
1
0
0
1
2
1
1
0
0
0
0
1
0
2
0
0
1
1
0
0
1
2
0
0
1
2
1
1
4
1
1
1
2
1
2
2
2
1
0
2
1
0
1
1
0
2
1
0
1
0
2
1
0
0
5
0
1
0
1
2
0
0
2
1
1
1
0
1
1
0
0
0
1
1
1
2
1
0
1
0
0
0
2
1
0
1
1
1
1
2
1
1
0
1
3
0
0
2
0
0
0
0
0
2
0
2
1
2
1
1
1
2
0
2
0
0
2
1
2
1
1
1
0
0
0
1
1
1
0
0
2
0
0
1
1
0
1
1
0
1
1
2
1
1
0
0
1
1
0
2
2
0
2
0
1
1
2
1
1
1
1
1
2
2
0
0
2
1
0
1
0
1
0
0
0
2
0
1
1
1
0
1
1
0
1
1
0
0
0
2
2
0
1
0
3
0
0
1
2
2
0
0
1
0
1
1
0
2
1
1
0
0
1
0
1
1
1
0
0
1
0
1
0
1
1
2
1
0
1
0
2
1
0
0
1
0
1
1
0
0
1
0
1
0
0
0
2
1
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
1
1
0
1
1
1
1
2
2
0
1
0
1
0
2
0
2
1
0
1
0
0
1
1
0
1
1
1
1
2
1
1
1
2
0
0
0
0
1
0
2
1
2
2
1
2
1
1
0
0
2
1
2
1
0
2
1
0
1
1
0
1
1
1
1
1
0
2
0
1
0
1
1
2
2
0
0
2
1
1
2
0
0
2
1
2
1
2
0
0
2
1
1
0
0
2
2
0
2
1
0
2
1
0
1
1
0
1
0
0
2
2
1
2
0
0
2
1
0
1
1
2
0
2
1
1
3
2
1
0
0
1
3
0
1
0
0
1
2
0
2
2
1
1
1
0
0
0
0
1
2
2
0
2
0
0
0
0
2
2
1
1
1
0
0
1
0
2
0
2
1
2
0
0
0
2
0
0
1
2
2
1
2
0
0
2
2
0
1
1
2
2
0
0
2
2
0
2
0
0
2
0
1
0
0
1
0
2
0
0
0
2
0
1
0
1
1
1
0
2
0
1
2
1
1
1
0
0
0
2
0
2
0
0
0
1
0
0
1
1
1
1
0
0
0
2
1
0
1
0
1
0
0
1
2
1
0
0
1
1
0
0
1
1
2
0
0
1
0
0
1
1
0
1
1
0
2
2
1
0
1
0
1
0
0
2
1
0
2
0
1
1
0
0
0
3
0
0
0
2
1
1
0
0
1
1
1
0
1
0
1
4
2
1
1
2
0
0
0
1
2
3
2
0
2
2
2
1
2
0
2
1
0
0
1
0
2
0
1
1
0
0
1
2
0
0
2
2
0
2
1
0
2
0
1
0
0
0
1
2
0
0
1
2
2
1
1
2
0
0
2
0
1
1
2
1
0
2
2
0
2
1
1
0
0
2
0
3
1
1
0
2
0
0
0
1
2
1
0
1
1
1
1
0
0
0
2
0
1
2
0
0
8
0
1
1
0
2
0
1
1
0
1
0
3
1
1
0
1
1
2
0
1
1
2
3
2
0
2
0
2
1
0
0
1
0
1
0
0
0
0
1
0
1
1
1
1
3
1
1
1
0
0
1
1
1
0
1
0
1
0
0
1
2
0
1
0
0
1
0
0
2
0
1
1
2
2
1
2
0
0
0
0
2
0
0
2
0
1
0
0
1
0
0
2
0
1
0
1
1
1
3
0
1
2
1
0
0
2
2
2
2
2
2
1
0
0
1
0
1
2
0
2
0
2
1
1
1
1
1
1
1
1
0
1
1
0
0
1
1
1
2
0
1
1
1
1
1
1
2
0
0
2
2
2
2
0
1
0
1
2
1
1
0
2
2
1
1
2
2
0
2
0
1
1
1
0
2
0
1
1
6
1
0
2
0
1
1
1
2
1
1
1
0
0
1
1
0
1
0
0
2
0
1
1
1
1
1
0
0
0
2
0
1
2
1
0
0
2
0
0
1
0
1
1
0
1
0
0
0
2
2
1
1
2
2
0
2
1
1
0
2
0
1
0
0
1
1
0
1
0
1
1
2
0
1
1
1
0
1
1
1
0
1
0
1
1
0
2
0
1
1
1
1
0
1
1
2
2
1
2
0
1
1
2
1
2
1
1
0
2
0
1
0
0
1
0
1
1
1
1
1
0
1
0
0
0
0
1
1
1
2
2
0
1
2
0
2
2
1
1
0
0
1
0
1
0
1
2
0
0
1
1
1
2
0
2
1
2
2
1
0
2
0
1
2
0
2
1
2
2
2
1
2
1
0
1
2
4
1
0
0
1
1
1
0
1
0
0
0
1
1
0
2
2
0
1
1
1
2
1
0
2
1
0
0
0
1
1
0
1
2
1
2
2
2
1
2
0
1
1
2
1
2
0
2
1
1
0
0
0
0
0
0
1
0
0
2
0
1
1
2
4
0
2
0
0
1
0
3
0
0
0
1
0
1
0
0
1
1
0
2
1
1
1
1
6
2
0
1
1
2
0
1
0
0
0
1
1
1
1
0
2
2
0
1
0
2
3
1
1
0
0
1
2
0
0
0
0
0
0
1
1
1
1
1
1
0
1
3
2
2
1
2
0
0
2
1
1
1
2
0
1
2
0
2
1
1
0
1
0
2
1
0
0
1
3
1
0
0
0
1
1
1
1
1
1
1
1
0
1
2
2
1
0
1
1
1
1
1
1
2
1
0
3
1
0
1
2
0
1
0
2
2
1
0
0
1
0
1
1
1
0
1
1
2
0
0
0
1
0
0
0
0
0
1
0
2
2
0
2
0
1
1
1
1
1
2
0
1
1
0
0
2
0
2
1
2
1
1
0
1
1
1
1
1
1
0
1
2
2
2
4
1
2
0
0
0
2
1
0
0
0
3
0
0
2
2
0
0
0
3
0
0
1
0
1
0
0
2
1
1
2
0
1
2
1
0
1
2
1
0
1
0
1
0
0
1
1
1
0
0
1
0
1
1
0
1
2
2
0
2
0
1
1
2
0
0
2
0
0
1
0
2
0
2
0
0
0
0
2
2
2
0
1
0
1
1
0
2
2
3
0
0
0
2
0
2
1
0
0
0
1
2
2
0
2
0
0
1
0
1
0
0
0
1
1
0
2
2
0
0
2
1
1
1
1
0
0
0
0
1
2
2
2
2
1
2
1
1
0
0
0
2
1
0
0
1
1
1
1
2
1
0
1
1
1
3
1
2
0
0
0
0
2
0
1
0
2
1
1
0
1
1
2
0
0
1
1
1
1
0
1
0
1
0
0
1
2
1
0
1
2
1
2
0
2
1
0
0
1
0
0
1
0
2
0
1
2
1
1
6
0
0
0
3
1
1
0
2
0
1
1
1
0
1
2
0
2
1
2
1
1
2
0
0
0
0
2
0
0
1
0
1
2
0
1
1
1
1
2
1
1
2
1
0
1
1
1
0
1
2
0
0
0
1
2
1
0
0
0
1
1
0
1
0
1
2
2
2
0
1
1
2
2
1
0
1
0
1
0
1
1
1
0
1
1
1
2
0
0
1
3
0
0
0
0
0
2
1
0
2
0
0
2
2
1
0
1
0
0
0
2
1
2
0
0
0
2
2
1
0
1
0
1
0
1
1
0
1
2
1
0
1
2
0
1
0
0
1
0
2
0
0
0
2
2
0
0
0
2
2
0
0
1
2
1
0
1
1
1
0
0
2
1
1
0
3
2
2
0
1
0
1
0
0
2
0
0
0
1
2
0
0
2
0
2
1
0
1
0
1
2
0
1
1
0
2
2
1
1
2
1
0
1
1
0
0
0
0
1
1
0
2
2
0
0
1
0
0
0
2
0
0
0
1
2
2
1
1
0
0
0
2
2
1
1
0
0
0
0
0
1
1
0
2
2
2
0
1
0
0
0
1
2
0
0
0
0
1
0
0
2
1
1
2
1
1
0
0
1
2
1
2
2
0
2
0
0
1
1
2
1
0
2
0
0
1
2
0
0
1
1
2
0
1
2
0
1
2
1
2
0
1
0
1
1
0
1
2
1
2
1
0
2
1
1
2
2
2
2
1
1
1
0
2
2
1
0
2
0
0
1
1
1
0
2
1
1
1
0
1
1
2
1
1
2
0
0
2
0
1
0
1
0
1
0
1
2
1
0
2
0
0
3
2
1
0
2
0
2
0
1
0
2
0
1
0
2
0
0
0
2
1
1
0
0
1
2
2
0
1
1
1
1
0
1
0
2
0
1
1
1
0
2
2
2
1
1
0
0
2
1
0
2
0
1
0
0
4
1
2
2
0
1
0
2
1
1
2
0
0
2
0
2
2
0
2
0
3
1
1
2
0
0
2
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
1
0
0
1
2
0
1
0
0
0
0
1
0
1
0
2
2
0
0
0
1
1
0
0
1
0
0
1
1
1
0
0
2
2
0
2
2
1
0
1
0
2
1
2
0
2
1
2
0
1
1
1
1
1
0
2
2
1
1
1
1
2
1
0
0
1
1
0
1
0
0
2
0
2
0
1
1
0
0
0
0
0
0
1
0
1
2
0
2
1
2
2
1
0
1
0
0
0
0
0
1
1
1
2
1
0
1
0
1
1
1
0
1
0
1
0
1
0
1
0
1
1
1
1
0
2
1
2
1
0
2
1
0
0
1
0
1
2
2
0
1
1
0
1
1
2
1
1
2
1
0
0
1
0
2
2
1
0
1
1
2
0
2
1
1
0
1
0
0
0
0
1
2
2
0
0
0
0
0
1
1
1
0
0
1
0
1
1
0
0
0
1
0
1
2
0
0
1
0
3
2
1
1
0
2
2
0
0
1
1
1
1
0
1
0
2
2
1
1
1
1
0
0
1
0
1
1
1
2
0
0
1
2
2
1
0
1
1
0
1
1
2
0
1
1
1
1
1
0
1
0
0
2
2
1
0
0
1
0
1
0
1
0
1
0
0
1
0
2
0
0
0
1
1
0
0
1
1
0
1
2
2
1
1
0
1
0
2
2
0
2
1
0
2
0
1
0
1
1
1
0
0
1
1
0
1
2
1
0
1
1
1
2
1
2
1
0
0
0
0
2
0
1
2
1
2
0
1
2
1
2
0
0
0
0
0
1
1
2
1
1
2
2
0
1
0
2
2
1
1
1
2
2
3
1
2
2
1
1
0
1
1
0
0
2
1
2
1
1
0
0
0
0
1
0
1
0
2
0
2
0
1
0
1
1
2
4
0
0
1
1
0
2
1
1
1
0
1
0
0
1
1
2
1
0
1
1
1
1
0
1
0
2
1
1
2
0
0
1
0
1
1
0
0
0
1
0
0
1
0
1
2
2
1
0
1
2
0
0
0
0
1
1
0
2
0
1
1
1
0
0
2
1
1
0
0
1
1
1
1
0
0
1
1
0
0
1
0
0
3
2
1
1
0
1
1
2
0
0
0
0
1
1
0
0
1
1
2
1
2
0
2
2
2
2
0
0
2
1
2
2
1
0
0
2
1
0
0
2
1
2
0
1
0
0
1
1
1
1
1
2
1
0
0
0
3
1
0
1
1
0
1
1
1
2
1
1
1
2
0
2
0
1
1
0
0
1
1
1
1
1
1
2
1
0
2
0
1
0
1
1
1
2
1
2
1
2
1
0
2
0
2
0
0
0
2
0
0
0
1
1
0
0
0
1
1
0
2
0
2
1
1
0
2
1
1
2
0
0
1
0
2
1
1
1
1
0
1
0
0
2
1
1
0
1
2
2
2
0
1
1
0
1
0
1
0
2
0
2
1
1
0
1
1
1
1
0
1
0
0
0
0
0
2
0
1
0
2
0
2
0
1
0
1
2
2
2
1
0
1
0
0
1
2
1
2
2
0
1
0
2
1
2
2
0
0
0
2
0
1
1
0
4
0
0
0
2
2
1
2
1
0
0
1
2
0
1
1
1
3
1
1
0
0
0
2
1
0
1
2
0
1
2
1
1
5
0
0
2
1
0
1
0
1
0
0
2
0
0
2
0
1
0
2
1
1
1
0
1
0
1
1
0
0
0
0
0
2
1
2
1
1
2
1
1
0
1
0
1
2
2
1
2
1
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
2
1
2
1
1
1
1
2
2
2
2
1
1
1
2
1
0
1
0
0
1
0
0
2
2
1
1
1
0
1
2
1
0
1
1
2
0
0
0
3
1
1
0
1
2
2
1
2
0
1
2
2
1
0
0
0
2
1
1
0
1
1
0
0
1
3
0
1
2
1
2
2
0
2
0
0
1
0
0
2
2
1
0
0
2
2
1
1
0
0
1
1
2
1
1
1
2
0
1
1
2
1
0
0
1
2
2
1
1
0
2
1
0
1
0
1
2
1
0
1
0
1
0
0
2
1
3
0
4
1
1
1
1
1
1
0
0
0
1
1
0
1
0
1
1
1
1
1
2
1
0
0
2
0
1
1
1
1
0
1
2
2
0
0
0
0
1
1
0
0
1
2
0
0
0
1
2
0
0
0
2
2
1
0
2
1
0
1
2
1
1
1
1
0
0
1
0
1
0
0
1
2
1
2
1
1
1
0
0
3
0
1
0
2
1
2
2
0
1
1
0
2
2
2
2
0
1
0
1
0
2
1
2
1
2
2
2
2
2
1
1
2
0
2
1
0
1
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
2
1
1
2
0
0
2
2
1
2
0
0
1
1
0
0
0
1
2
1
0
0
2
0
0
2
1
2
0
1
0
0
0
1
0
0
2
1
2
2
2
0
0
2
2
1
0
1
1
1
1
1
2
0
1
1
1
3
2
1
0
2
0
0
0
0
0
1
0
1
2
1
0
0
1
0
0
0
0
2
1
1
0
2
0
3
2
2
1
0
2
0
0
0
1
1
1
2
0
1
1
2
0
1
0
1
1
1
0
0
1
2
0
1
1
1
1
1
0
1
0
0
1
2
2
0
2
2
1
1
2
0
2
0
0
0
0
0
1
1
0
2
0
2
2
1
2
0
0
2
1
0
1
0
0
2
1
0
0
2
1
2
1
0
0
2
1
1
1
1
1
1
1
1
2
2
1
0
2
0
0
1
1
0
1
1
2
2
0
0
1
0
2
0
0
1
1
1
1
2
1
1
0
0
0
1
0
1
0
1
1
0
0
1
1
1
2
2
0
1
2
0
0
1
1
2
1
0
0
1
0
0
2
0
1
1
2
0
0
0
1
0
2
2
2
2
0
2
2
1
0
1
1
1
0
0
1
0
0
0
2
0
1
0
0
0
0
1
0
1
0
1
1
0
0
1
0
0
1
0
0
1
1
3
2
2
2
2
0
1
0
0
1
0
0
1
3
2
1
0
2
1
0
0
0
2
0
1
2
2
1
0
2
0
1
2
1
0
0
1
2
0
0
0
1
1
0
0
1
1
1
1
0
0
2
1
2
0
1
1
0
1
1
0
0
1
1
2
0
0
2
0
2
2
1
0
0
0
2
2
0
1
1
0
1
1
0
1
1
3
2
2
2
2
1
0
1
1
0
1
0
1
0
1
0
1
0
1
1
0
2
2
1
1
2
2
0
1
1
0
0
0
1
0
2
1
2
0
0
2
1
0
2
1
0
2
1
1
2
2
0
0
2
1
0
0
0
0
1
2
1
0
1
1
1
0
0
2
1
2
1
0
1
1
0
0
0
0
0
1
1
1
2
1
2
1
1
1
2
1
1
0
1
1
2
2
2
0
1
1
1
2
2
1
0
1
1
0
0
2
2
1
0
2
0
0
0
1
2
0
1
1
1
2
1
0
3
0
0
1
2
0
1
2
0
2
1
2
2
2
1
1
0
0
1
2
0
1
0
0
0
2
1
1
2
0
0
1
1
1
2
0
0
2
0
1
0
1
0
1
1
1
0
0
0
0
0
1
1
0
0
2
1
0
1
3
1
0
0
1
0
1
1
1
0
2
1
1
1
2
0
0
1
0
1
2
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
2
1
1
2
1
1
0
0
0
2
0
0
2
0
1
1
1
0
1
2
2
1
1
1
1
1
2
0
0
0
1
1
1
1
1
0
1
1
2
1
1
1
2
0
0
2
0
0
0
1
1
3
1
0
1
0
0
0
2
1
1
1
0
0
0
0
0
1
1
0
1
2
1
2
0
1
1
0
3
2
0
0
0
0
1
0
1
1
0
0
2
0
1
5
1
0
1
0
1
0
1
2
1
0
2
2
1
1
1
1
1
0
0
2
1
1
1
0
1
0
1
0
1
1
1
1
0
0
0
2
2
3
1
0
2
1
0
2
0
1
2
0
1
2
0
1
1
0
2
0
0
1
1
1
1
2
1
2
0
1
2
2
1
1
0
0
2
2
2
2
1
1
1
1
1
2
0
4
1
2
1
0
0
1
1
1
1
1
1
0
2
2
2
0
2
2
2
1
2
4
0
2
2
2
0
0
2
0
0
0
0
1
1
1
1
2
2
0
1
0
2
0
2
3
1
1
0
0
1
1
0
1
0
0
2
2
1
2
0
1
1
0
2
1
0
0
2
0
0
0
1
1
1
1
2
0
1
1
0
5
2
1
1
0
1
1
0
2
0
2
2
0
1
3
0
0
0
2
1
1
0
2
1
0
0
1
0
2
0
2
0
2
2
1
1
0
1
1
1
0
1
0
2
1
0
0
1
1
2
1
0
1
0
1
2
1
2
1
0
0
1
1
0
0
2
0
0
2
1
2
1
0
0
0
1
1
2
1
2
1
1
0
0
1
1
1
2
1
0
0
1
1
1
0
2
1
2
2
1
0
1
1
0
2
1
1
2
1
0
1
0
0
1
0
2
1
1
1
0
1
0
2
0
2
0
0
0
1
1
0
2
1
1
0
0
1
1
0
2
2
2
0
2
0
0
0
0
1
0
0
1
2
1
1
1
2
1
1
0
2
2
1
2
1
2
2
0
0
1
0
2
0
1
2
0
0
0
1
1
1
0
1
0
3
0
1
0
1
2
2
0
2
2
0
0
1
1
0
1
0
0
2
1
0
2
2
0
0
0
1
0
0
0
0
2
1
1
1
2
0
1
2
2
1
0
1
2
0
1
0
1
2
1
1
0
2
0
1
1
1
1
1
0
1
2
0
2
2
0
1
1
0
0
0
2
0
0
1
0
0
2
1
0
1
0
1
1
0
0
2
2
1
2
0
1
2
1
0
1
1
0
0
0
3
0
0
1
0
2
2
0
1
0
1
1
2
1
2
1
1
1
1
0
0
0
2
0
2
0
0
0
0
2
0
1
2
0
0
1
0
0
0
0
1
1
1
0
0
1
1
0
0
1
2
0
2
2
0
1
1
1
0
2
2
2
1
1
0
1
1
1
1
1
2
0
2
0
0
0
0
2
1
0
1
1
2
0
1
0
1
0
4
0
2
1
0
0
0
1
1
2
0
2
1
0
3
0
0
0
1
0
1
1
0
2
1
2
1
2
1
0
0
1
1
0
0
0
0
2
1
2
0
1
0
0
0
0
0
1
1
2
1
1
2
0
2
1
0
1
0
0
0
1
0
2
0
2
0
1
2
1
0
1
1
0
0
1
0
1
1
1
1
1
1
0
2
1
0
0
0
2
2
1
1
1
0
0
1
1
1
2
1
1
1
2
0
0
0
2
1
2
2
2
1
0
0
0
1
1
2
1
0
1
1
1
1
1
2
1
1
2
1
2
0
2
2
0
1
0
1
2
1
1
2
2
2
2
0
1
0
0
1
2
1
0
0
0
2
1
2
1
2
0
1
0
2
0
1
0
1
2
1
2
1
1
3
1
1
0
0
1
0
1
0
0
2
1
0
0
0
1
0
1
2
2
0
0
1
1
2
1
1
1
0
2
0
1
0
2
2
0
0
1
0
0
2
0
1
1
0
0
1
2
0
0
1
1
1
1
0
2
2
1
2
1
2
2
1
0
0
0
1
1
1
0
1
2
2
2
2
2
1
2
1
1
1
1
1
0
0
1
0
2
1
1
1
1
0
0
2
1
2
2
0
2
0
0
0
0
1
2
1
0
2
1
0
0
0
1
2
0
2
2
1
0
1
1
1
1
1
1
1
1
0
1
2
0
0
0
2
1
1
1
1
1
2
2
0
1
1
1
0
1
0
1
0
2
2
1
0
0
1
2
0
2
1
1
2
1
1
0
2
2
1
0
0
0
1
2
1
0
2
1
0
0
1
2
2
1
2
0
0
0
0
0
2
1
1
2
0
1
1
0
0
2
0
2
1
1
1
1
0
1
0
2
1
0
1
2
0
0
1
2
2
1
0
0
1
1
1
1
0
0
1
0
0
1
1
1
1
0
0
0
1
0
1
1
0
0
2
0
0
2
2
1
0
1
1
0
1
0
1
2
2
0
1
1
0
0
1
2
0
0
0
0
0
0
1
2
2
2
1
0
0
1
1
2
0
1
0
0
0
0
1
1
0
1
1
1
1
0
0
1
1
2
0
0
0
2
1
0
1
1
2
0
2
1
0
0
1
2
1
2
3
1
1
1
1
1
1
0
0
1
0
1
1
2
0
1
0
1
1
1
2
0
1
2
1
1
2
0
1
0
2
1
0
1
1
1
0
0
2
0
1
1
0
1
0
0
1
0
0
1
0
1
0
2
1
0
2
1
1
0
0
1
1
0
0
2
0
0
0
2
1
2
1
0
1
1
1
0
2
0
1
0
0
1
2
1
0
2
1
1
1
1
1
1
1
0
0
0
0
0
0
0
1
2
2
0
0
0
0
2
1
0
2
1
1
0
2
2
1
2
0
1
1
2
1
2
2
1
1
0
2
1
1
0
0
1
3
3
2
1
1
0
0
1
0
2
0
1
1
1
1
0
2
0
3
1
0
0
0
1
0
1
0
1
1
1
2
0
1
2
1
1
0
1
0
2
1
0
1
0
0
1
0
1
0
2
0
1
1
0
0
1
0
2
0
0
1
1
2
0
0
2
2
1
0
1
2
1
0
3
0
0
1
0
2
0
1
0
0
0
2
0
0
0
1
2
0
2
1
1
1
0
1
0
1
0
0
0
0
1
0
0
1
1
1
0
0
1
2
0
1
2
1
1
0
1
0
0
1
0
0
1
1
0
2
0
1
1
1
1
0
0
1
0
0
1
1
1
0
0
0
1
0
0
2
0
2
2
0
1
0
1
1
0
1
0
2
2
1
0
2
2
0
0
0
0
3
2
1
1
0
0
0
2
1
0
1
2
2
0
0
1
0
0
0
2
0
0
0
0
1
0
1
1
1
1
2
0
0
1
2
0
2
0
2
2
0
2
1
1
2
0
1
0
1
1
1
1
2
1
2
0
2
1
0
0
0
2
1
2
1
1
1
0
0
3
0
1
2
1
1
1
1
1
1
1
0
0
2
0
1
0
1
2
0
1
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
2
0
0
1
0
0
0
1
2
2
0
0
3
1
1
2
2
0
1
0
0
0
2
3
1
1
2
1
0
0
0
1
0
1
2
0
2
1
1
2
0
1
2
0
1
2
2
1
0
0
0
0
1
2
1
1
0
0
2
0
1
1
0
0
1
2
1
2
2
0
1
3
1
2
0
1
2
0
1
1
1
1
1
0
0
2
0
1
0
1
1
1
1
0
0
1
0
1
2
0
1
1
1
2
2
0
0
0
0
0
2
1
2
0
0
1
2
0
1
2
1
0
1
0
0
0
0
0
3
1
2
1
0
0
1
2
0
0
1
1
1
1
0
1
2
2
1
0
2
1
1
2
0
0
2
0
1
1
1
1
2
0
1
1
1
0
2
0
4
2
1
2
1
1
1
0
1
2
0
0
0
1
0
1
1
1
0
1
1
2
1
0
2
2
1
1
0
2
1
0
0
2
0
2
0
1
1
1
1
2
0
1
2
0
1
1
0
0
0
1
2
0
0
2
2
2
0
0
1
0
0
1
1
2
0
0
2
0
0
2
2
1
2
1
0
0
0
1
1
2
0
0
0
1
2
2
2
0
1
1
0
1
0
0
2
0
0
1
2
1
3
1
2
2
0
1
0
1
0
0
0
0
1
0
3
0
2
1
0
0
1
2
1
2
0
2
1
2
1
1
0
2
0
0
4
1
1
0
0
2
1
0
1
2
2
0
2
1
0
1
0
0
0
2
2
0
1
0
0
1
2
0
1
1
0
1
0
2
0
2
0
4
2
0
1
0
0
1
1
1
2
1
0
1
1
1
2
1
1
0
2
2
1
0
0
1
0
0
0
1
1
1
2
1
1
0
2
0
0
1
0
2
0
0
1
0
0
2
0
2
2
0
2
1
1
2
2
2
2
0
1
0
1
1
0
0
1
2
1
0
0
1
1
0
2
1
0
1
2
0
1
0
0
0
0
0
0
1
0
1
0
1
2
1
3
2
1
2
0
1
1
0
0
0
2
0
2
0
0
0
0
0
0
1
0
1
0
0
2
1
1
1
0
2
1
0
2
1
0
0
0
0
0
1
1
0
2
2
0
1
1
1
1
2
0
0
1
0
0
1
2
1
1
0
2
3
2
0
0
0
0
0
2
0
1
0
1
2
1
1
1
0
1
2
0
0
2
2
0
0
2
1
2
0
2
0
2
1
1
1
0
1
1
2
0
2
1
1
0
2
2
1
1
2
0
0
0
2
2
1
1
1
2
1
0
2
1
1
1
0
0
2
0
0
1
0
1
1
0
0
2
3
0
2
2
1
1
0
1
1
0
0
2
1
0
0
1
0
0
0
2
1
1
1
1
0
1
2
0
0
0
1
5
0
2
3
1
1
1
0
1
2
0
1
1
1
0
1
0
1
0
0
0
1
1
1
1
2
0
0
1
1
0
0
1
2
0
0
0
1
0
1
0
1
0
0
2
0
0
0
1
0
0
2
2
0
2
2
1
3
0
0
1
0
1
1
1
1
1
0
0
1
1
1
0
2
1
1
0
0
2
2
1
0
2
1
2
1
2
0
1
1
2
1
2
1
2
2
1
0
1
1
0
0
1
0
0
1
2
2
0
2
2
2
2
1
1
2
0
0
2
1
0
2
0
2
0
0
0
0
2
1
1
2
0
0
0
1
0
4
0
0
1
2
0
0
1
1
2
2
1
0
1
4
0
1
2
0
1
3
1
2
1
0
2
1
0
2
2
0
2
0
0
2
2
1
0
1
1
2
0
0
0
0
1
0
2
0
0
2
1
2
1
2
2
1
1
2
0
1
1
0
2
1
1
2
0
0
0
2
0
1
0
1
1
2
0
1
0
1
0
0
0
1
1
0
0
1
0
2
0
2
2
2
0
0
1
2
2
2
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
1
0
0
2
0
2
2
0
1
1
1
0
1
0
0
2
1
1
1
0
0
1
1
1
0
0
1
1
2
0
1
0
0
0
1
1
0
1
1
1
0
1
1
1
0
2
1
2
0
0
0
1
1
2
0
1
1
0
0
2
1
0
1
0
1
0
2
1
0
2
0
0
2
1
0
1
0
1
1
1
0
1
2
1
0
1
1
0
2
1
1
2
0
2
1
1
0
0
1
0
0
1
1
1
2
2
0
1
2
2
0
0
2
1
0
1
2
0
0
0
1
2
0
2
1
1
0
1
1
0
0
2
0
2
1
0
1
1
1
0
1
0
1
0
1
0
0
2
0
1
0
0
1
0
1
2
0
1
0
0
2
2
0
0
1
1
0
1
0
1
0
2
2
1
1
1
0
0
1
2
1
1
2
1
0
1
0
0
2
1
1
1
1
1
0
0
0
1
1
0
1
1
0
5
1
0
1
1
0
0
1
2
1
1
0
2
1
1
1
2
2
2
2
0
2
1
1
0
0
1
2
2
1
1
1
1
0
0
2
0
1
2
0
1
2
0
0
0
0
1
0
1
0
2
2
1
0
1
1
0
1
1
2
0
1
1
0
1
0
1
1
1
1
1
1
1
1
0
0
1
2
0
2
0
0
1
0
0
2
2
0
0
1
0
0
0
1
0
1
2
0
0
2
2
1
2
1
2
1
2
1
0
1
1
1
0
1
1
0
2
1
0
0
2
2
2
1
2
0
0
0
0
1
1
1
1
0
1
1
0
0
1
1
1
0
2
1
0
1
0
1
2
0
2
0
2
0
0
0
1
1
0
1
1
0
1
1
0
0
2
0
0
2
0
0
2
0
1
1
1
0
0
2
1
1
1
1
1
0
1
0
2
2
0
0
0
2
3
0
0
0
0
0
1
1
1
1
2
1
0
1
0
1
1
0
0
1
0
1
1
1
2
2
1
0
2
1
1
0
0
2
2
0
0
2
1
1
1
2
1
0
0
1
0
1
0
1
0
2
0
0
2
0
0
1
0
1
0
0
1
0
2
1
1
0
0
2
0
2
0
1
0
1
1
0
1
2
0
0
0
0
0
1
1
1
1
2
0
1
1
0
2
2
0
0
1
0
0
1
1
1
0
1
0
0
0
2
1
1
1
1
0
1
1
1
1
1
1
1
0
1
1
2
2
1
0
0
1
1
1
1
0
2
2
1
0
0
2
1
0
0
1
0
2
0
1
0
2
1
2
0
1
1
1
1
1
1
2
0
1
1
2
0
0
0
0
0
0
2
0
0
1
2
2
1
0
1
1
0
1
0
0
2
1
3
1
0
1
1
1
1
1
0
0
0
3
1
0
0
1
0
0
0
0
2
1
2
0
1
1
1
2
1
0
1
2
1
0
0
0
3
2
0
1
0
2
0
0
1
2
0
1
0
2
0
1
1
1
1
0
0
0
2
0
2
0
0
0
0
0
1
0
1
0
2
2
1
0
0
1
2
0
1
1
0
1
1
2
0
1
2
1
1
0
1
0
0
1
1
1
1
2
2
1
1
1
2
0
1
1
1
0
0
2
0
1
1
1
1
2
1
0
2
0
0
0
2
2
1
2
0
1
2
2
0
2
1
1
1
1
2
1
1
1
1
0
0
3
1
1
0
1
0
1
0
3
2
0
1
1
2
0
2
0
1
2
0
0
0
0
1
1
2
1
4
0
0
0
0
0
0
1
1
1
1
2
2
1
0
2
2
0
0
1
0
2
0
1
1
0
0
2
1
0
2
1
2
2
3
2
4
1
1
1
1
1
2
1
0
1
2
2
0
2
0
2
1
1
1
0
0
1
1
0
1
0
0
0
1
1
0
0
1
0
1
1
0
0
0
0
2
1
2
0
0
0
2
1
0
1
1
2
2
1
2
2
0
1
0
2
2
1
2
1
0
0
1
0
0
1
0
0
1
0
2
2
1
1
1
2
0
1
0
0
2
1
1
2
0
0
0
2
0
1
1
0
1
0
2
0
1
1
1
0
1
0
2
0
2
0
1
0
0
1
0
1
1
0
1
2
0
0
0
0
0
1
0
0
0
0
0
1
1
1
1
0
0
0
2
1
1
1
0
0
1
1
0
2
1
1
0
0
0
1
2
0
0
0
1
1
2
1
0
0
0
2
0
0
0
1
0
3
2
1
2
2
0
1
0
1
1
0
1
0
3
1
1
0
0
0
1
1
0
0
0
0
1
0
1
2
1
0
2
1
3
1
0
1
2
0
2
1
1
0
0
2
1
1
2
1
1
1
1
1
1
2
1
0
0
0
0
1
0
0
5
1
2
0
1
1
1
0
1
1
2
0
0
0
0
2
1
1
0
0
0
0
1
1
0
0
1
2
2
0
0
0
2
2
1
1
0
2
1
2
1
1
0
2
1
0
2
2
1
0
0
3
0
0
0
0
2
2
0
1
4
0
0
0
2
0
1
1
1
1
0
0
2
0
0
0
0
0
1
0
1
0
2
0
1
1
0
1
2
0
1
1
0
1
2
1
0
1
0
2
0
1
2
1
0
0
2
1
0
0
0
1
1
0
0
1
1
0
0
0
2
1
1
1
1
1
0
1
0
0
1
1
2
0
0
1
1
0
1
1
1
0
0
1
1
2
2
0
0
1
2
0
0
2
0
1
0
1
1
0
2
1
0
1
1
0
0
2
0
1
1
1
0
1
0
1
1
1
2
1
1
0
2
0
1
0
1
1
0
0
1
0
2
1
0
1
2
2
2
1
1
0
0
1
0
2
0
1
0
1
1
0
1
0
0
1
1
1
2
0
1
3
2
2
2
2
1
1
0
0
2
1
0
2
2
2
0
1
1
0
0
2
1
0
0
1
0
0
0
2
1
0
0
1
0
0
2
0
1
0
0
0
2
2
0
0
1
2
0
2
1
2
0
0
1
0
1
2
0
2
1
1
0
0
0
1
1
1
0
0
0
1
5
2
2
2
0
0
0
0
1
0
1
2
1
2
2
1
0
1
0
0
3
2
2
1
1
0
0
4
2
2
1
2
1
1
2
0
1
2
1
0
1
1
1
2
0
1
1
1
1
0
1
1
0
2
1
2
1
2
4
1
1
1
3
1
1
2
0
1
1
1
0
0
0
2
0
0
1
2
1
2
0
2
1
1
1
1
0
0
1
0
0
0
2
0
0
1
0
2
1
0
0
1
1
0
1
1
1
1
2
2
0
2
1
1
0
0
1
0
1
0
1
1
0
0
0
2
0
1
0
1
0
0
2
1
1
0
2
1
1
0
0
0
2
2
1
2
2
0
1
2
0
1
2
0
1
1
0
0
1
0
0
0
0
0
1
1
0
2
0
2
0
0
0
1
1
0
1
1
0
0
0
0
2
2
2
2
1
0
2
2
2
0
2
1
2
0
1
0
0
2
1
0
0
0
0
2
2
0
2
0
0
1
1
0
0
1
0
0
1
2
0
0
2
1
0
1
1
1
1
1
0
0
1
1
2
1
1
1
1
0
0
1
2
0
2
0
1
2
1
2
0
1
0
2
1
2
3
2
1
0
1
2
0
1
1
0
1
2
3
1
0
0
0
0
1
1
0
2
1
2
1
0
0
2
1
2
0
1
1
0
1
0
0
0
1
1
0
3
1
1
1
1
1
0
0
1
2
0
1
0
1
1
2
0
0
1
2
1
0
1
1
0
0
1
0
2
2
1
0
0
2
2
1
0
0
0
0
2
2
0
1
2
0
0
1
2
1
1
1
3
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
1
1
2
1
0
0
0
2
2
0
1
0
12
0
1
0
0
1
1
1
1
2
1
0
0
0
0
1
0
1
2
0
0
1
1
2
0
1
1
0
2
0
0
1
1
0
3
1
0
1
0
2
0
2
1
1
1
0
1
0
1
2
1
0
0
1
2
0
2
1
1
0
2
1
0
1
1
0
0
0
1
1
2
1
0
0
1
0
1
2
1
1
1
0
0
0
1
1
2
0
2
1
2
0
0
2
2
2
1
2
0
2
1
0
1
2
1
0
1
1
0
2
0
2
0
5
1
1
0
2
1
2
2
2
0
0
0
2
2
0
0
1
1
0
0
2
1
0
1
0
0
2
1
1
0
0
0
1
0
1
1
1
1
4
2
1
0
1
1
2
0
2
0
2
1
0
1
1
1
0
0
2
2
0
2
1
1
0
0
2
0
2
2
2
2
0
1
0
0
2
2
0
2
0
0
1
1
1
1
2
1
2
2
1
1
1
2
2
2
1
0
1
0
0
1
1
0
0
0
0
1
1
2
0
1
0
0
1
1
0
1
2
2
1
0
0
0
0
0
0
1
1
0
0
1
1
0
0
1
1
0
0
1
0
2
1
1
1
0
0
1
2
0
0
1
2
1
0
2
1
2
1
1
2
1
1
0
1
2
0
2
0
1
2
1
1
1
0
0
0
1
1
2
2
2
1
1
0
0
0
0
0
0
0
0
2
1
0
1
0
2
0
0
2
1
0
2
1
0
1
1
2
1
1
2
1
0
0
1
0
1
2
2
1
2
2
1
0
1
2
1
2
1
0
2
2
0
0
1
1
0
1
2
0
1
0
2
1
2
2
1
1
1
2
0
0
0
1
2
1
2
1
2
0
1
0
0
2
0
0
0
1
1
2
1
0
0
2
2
1
1
0
1
1
2
0
1
1
2
2
1
2
0
2
2
0
0
1
2
0
0
0
1
1
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
2
2
2
2
2
0
0
1
0
0
2
0
2
0
0
0
2
2
1
0
0
2
0
0
0
2
0
0
1
0
1
1
2
0
1
2
3
1
0
0
0
1
0
2
0
2
0
0
0
2
2
2
1
0
0
1
0
0
2
1
1
0
1
2
0
2
1
0
2
0
1
2
0
2
1
0
1
1
1
0
0
2
0
0
3
0
1
1
0
0
0
1
2
0
2
1
2
1
1
1
0
2
2
0
1
1
1
1
0
0
0
1
1
1
0
1
3
1
0
0
0
1
0
0
1
1
1
2
1
0
2
1
0
1
2
0
1
0
1
1
0
1
2
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
1
0
0
2
2
2
1
1
2
0
1
0
1
0
1
1
0
1
0
0
1
2
0
0
2
2
2
0
0
1
1
0
1
2
0
1
2
0
1
1
1
0
1
1
2
0
1
2
1
0
2
2
0
1
1
0
0
1
2
0
1
0
0
0
0
2
0
1
1
2
1
1
0
1
2
1
0
2
1
0
1
0
0
0
1
0
0
1
1
1
0
0
0
0
0
1
1
0
0
1
1
3
0
1
2
2
1
0
0
0
0
0
0
3
1
2
2
1
1
1
2
1
1
0
2
0
0
1
2
1
0
1
1
2
0
3
0
1
1
0
0
1
0
1
0
1
1
1
2
1
1
1
0
0
2
0
0
1
0
1
0
0
2
0
1
1
1
1
1
2
0
1
2
0
1
4
1
0
2
1
1
2
0
0
2
1
1
0
0
1
1
2
1
0
1
2
1
1
0
0
1
0
1
1
1
0
1
0
1
2
1
0
0
1
2
0
0
2
2
0
0
1
1
0
2
2
2
0
1
0
2
1
0
3
1
1
0
3
0
2
0
0
0
1
2
0
2
0
0
0
1
1
1
1
0
2
4
0
2
1
0
0
1
0
0
0
1
1
2
0
1
0
0
0
1
1
1
0
0
2
0
0
0
2
0
0
0
2
0
0
1
0
1
1
2
2
0
1
0
0
1
2
1
2
1
0
1
2
1
0
1
2
1
1
2
0
1
0
3
1
0
2
0
1
2
0
0
0
1
1
0
1
0
1
1
1
1
2
2
0
1
1
0
1
2
2
0
0
1
0
2
0
0
0
1
1
0
2
2
0
0
0
2
2
2
0
0
1
0
0
2
1
1
1
2
1
0
0
3
1
1
1
1
0
0
2
1
1
2
0
0
0
1
1
0
2
1
0
1
0
1
0
0
1
0
1
1
1
0
0
2
2
0
0
1
0
0
1
2
2
1
1
1
0
1
0
1
0
1
0
2
1
1
3
2
0
2
0
1
1
2
1
2
1
0
0
0
0
1
1
2
1
0
0
0
2
0
0
2
1
2
1
0
0
2
1
0
0
0
1
1
1
1
0
0
2
2
2
1
0
2
0
1
2
2
0
2
2
0
2
2
0
1
0
0
1
2
0
1
0
0
2
0
0
2
0
1
1
0
0
1
1
1
0
0
0
1
0
1
0
0
0
2
2
2
1
2
0
1
2
1
1
0
1
2
0
1
0
1
0
0
1
1
2
1
1
1
1
0
1
0
0
2
0
1
0
2
1
0
2
1
0
0
0
2
2
1
2
2
0
0
1
4
1
1
1
1
0
0
0
0
0
3
1
1
0
2
0
1
0
1
1
1
1
0
2
1
1
0
0
2
2
0
1
0
1
2
1
0
4
0
0
2
0
0
1
0
0
0
0
0
2
1
2
1
0
0
2
0
1
1
1
1
0
1
0
1
0
1
0
1
2
1
0
1
2
1
0
1
0
1
1
2
1
1
0
0
0
1
1
2
0
1
1
0
2
0
0
0
1
0
0
0
1
2
0
0
1
1
2
0
2
2
1
1
0
2
3
0
2
1
0
1
1
0
1
1
1
1
1
0
2
2
0
3
1
1
2
0
0
1
1
0
0
1
1
3
1
0
1
2
0
4
0
2
0
3
0
1
0
1
2
0
1
0
0
0
0
1
0
0
0
2
0
1
0
2
0
0
1
1
0
0
0
1
0
1
0
3
1
1
1
1
2
2
2
0
0
0
2
1
0
2
1
0
3
1
2
2
0
0
1
2
1
0
0
1
0
1
0
0
0
1
1
1
2
0
1
2
2
3
0
2
0
1
3
1
1
1
0
1
2
1
1
0
2
2
2
2
0
0
2
0
0
0
0
0
0
2
1
1
1
0
2
1
1
2
0
2
2
0
1
2
3
1
0
0
0
2
1
1
2
1
0
2
1
0
1
1
0
3
2
0
0
1
1
2
0
1
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
1
0
1
2
1
2
2
0
1
1
1
1
0
0
2
2
0
2
1
2
2
2
0
0
0
0
1
2
3
1
1
1
0
0
1
2
0
1
0
2
2
2
0
1
2
0
2
0
0
1
2
0
1
2
1
0
0
2
1
0
1
0
0
1
1
2
1
1
2
2
0
1
0
1
1
2
1
1
1
0
0
2
2
0
1
0
2
2
1
1
0
0
0
0
1
0
0
0
1
0
2
1
2
0
1
0
2
1
1
0
2
2
1
1
0
0
1
0
1
0
1
1
0
1
0
1
2
0
1
1
1
1
1
0
0
1
0
1
0
2
1
2
1
2
1
1
1
2
0
1
0
1
2
2
0
0
1
1
1
0
0
1
2
2
0
1
0
0
2
1
2
0
1
1
0
0
0
1
2
1
1
1
0
0
0
1
0
0
0
0
0
2
1
0
2
1
2
1
0
2
0
1
1
2
2
0
0
2
0
1
0
0
1
0
0
2
1
1
1
1
2
1
2
0
1
0
2
0
3
2
2
1
1
1
0
2
0
2
0
1
0
0
5
2
1
1
0
0
0
2
1
0
0
1
1
1
2
1
1
0
0
1
0
0
0
0
1
1
1
0
1
1
2
1
0
1
0
1
1
0
2
1
0
0
0
0
0
2
2
0
1
2
1
1
2
1
0
1
1
1
0
2
0
2
0
2
1
1
0
2
0
1
1
1
2
0
1
1
0
0
0
0
2
1
1
2
2
2
1
1
1
0
0
2
1
0
1
1
2
0
0
1
1
0
2
2
0
0
0
1
0
2
1
1
1
0
2
0
0
0
0
0
0
1
1
2
0
0
1
1
1
1
1
1
0
0
1
0
0
1
0
0
0
2
1
1
1
0
1
1
0
1
1
1
0
1
0
1
0
1
0
1
1
0
1
1
1
0
1
0
0
0
1
1
1
1
0
2
1
0
2
0
1
1
0
1
2
0
0
0
1
0
1
1
2
0
0
1
3
1
0
2
1
0
0
1
4
1
2
0
0
3
1
2
0
0
1
1
1
2
0
0
1
1
0
0
1
2
0
2
0
2
1
2
1
0
0
2
1
0
1
2
0
1
2
0
0
1
0
3
1
2
2
1
1
0
0
1
1
0
0
2
0
1
0
1
2
0
3
0
1
1
0
2
2
1
1
1
1
0
2
1
0
1
2
2
2
0
1
1
1
2
2
1
2
1
1
1
1
1
0
1
1
1
1
1
0
0
1
2
2
0
1
2
0
0
0
1
1
0
1
1
1
2
2
0
0
2
1
2
1
2
1
1
1
1
0
0
0
0
1
1
1
1
1
2
0
1
2
0
0
1
1
2
0
1
0
0
0
0
2
1
1
0
1
1
0
1
0
1
2
1
0
0
0
2
2
1
0
3
1
2
2
1
1
0
1
0
1
0
1
0
2
1
0
1
1
2
1
2
1
0
0
1
2
0
1
0
2
1
0
2
1
2
1
2
4
0
1
3
0
0
4
0
1
1
1
0
0
1
3
0
1
1
0
0
1
0
0
1
3
0
0
2
2
2
2
2
1
1
0
0
0
1
2
1
1
0
0
2
3
0
0
0
1
1
2
0
2
0
0
2
2
3
0
0
1
2
0
0
1
1
0
1
2
0
0
0
0
0
0
1
1
0
0
1
1
0
1
1
2
1
0
1
0
0
1
0
0
2
1
2
1
0
0
0
0
2
2
2
1
1
0
2
1
2
0
2
0
0
0
2
2
2
2
0
0
1
2
2
1
1
0
0
1
0
2
2
2
1
0
1
2
0
0
1
0
1
0
0
2
0
0
1
2
2
1
0
0
1
1
0
0
2
0
0
3
1
1
0
0
1
1
0
0
0
1
1
2
0
1
2
0
0
0
0
2
0
2
1
1
1
1
2
1
1
1
1
1
0
2
2
1
0
0
1
0
1
0
0
0
1
1
1
1
0
0
0
1
0
0
0
0
0
1
0
0
1
2
1
1
1
1
1
1
2
0
1
0
0
0
2
0
1
1
0
0
0
0
0
0
1
1
0
2
0
0
0
0
1
2
0
1
2
0
1
0
2
1
2
0
0
1
2
0
0
0
0
0
0
2
2
2
1
1
1
0
2
0
2
0
1
0
0
2
0
0
1
2
2
1
0
0
1
1
1
3
0
2
1
1
0
1
1
1
1
1
1
1
0
1
0
1
2
2
1
2
2
0
0
0
0
0
1
1
1
1
1
0
1
0
1
4
0
3
1
2
0
1
0
1
0
0
2
1
0
1
0
1
1
2
2
2
0
0
1
1
1
0
1
0
0
0
1
0
2
1
1
0
1
0
0
1
0
0
0
3
2
0
1
1
1
0
1
2
1
2
1
0
1
1
1
0
1
0
0
0
2
0
2
2
0
1
1
1
0
2
1
0
0
1
0
0
1
1
1
0
0
0
2
0
0
1
0
0
1
0
0
0
1
2
1
0
2
1
3
3
1
1
0
2
0
1
0
0
1
2
1
0
2
0
0
2
0
0
0
0
1
1
0
1
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
1
0
0
1
1
1
1
0
0
1
1
1
0
4
0
0
0
2
0
1
2
1
0
1
2
0
1
2
0
2
0
0
2
1
0
0
1
0
1
0
2
1
2
1
0
2
2
2
1
0
1
0
0
1
0
0
0
1
1
0
0
0
2
1
1
1
1
1
0
1
1
1
0
1
0
0
0
0
1
1
0
1
1
1
3
1
1
1
1
0
2
0
1
0
1
3
0
2
2
0
1
0
1
0
1
0
1
0
1
1
0
3
1
0
0
0
1
2
0
1
1
0
1
2
1
0
2
1
0
2
0
0
1
1
0
2
2
0
2
1
0
0
0
0
2
0
1
1
0
1
0
1
2
0
2
0
2
1
0
0
1
0
1
2
1
6
0
1
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
2
1
0
2
2
0
1
0
1
1
0
1
0
0
1
1
2
0
1
1
0
0
2
1
0
0
0
1
1
0
1
0
2
1
1
0
1
1
1
1
1
1
2
1
2
1
0
0
0
1
0
0
0
1
0
0
1
2
0
1
0
1
1
2
0
0
1
0
0
1
1
0
1
0
1
0
1
2
2
2
0
2
1
0
1
1
0
0
1
2
2
0
1
1
2
1
0
2
1
1
0
2
0
0
1
0
1
1
2
0
1
0
2
1
0
1
1
0
2
2
1
1
0
0
1
1
1
1
2
0
2
2
0
4
0
1
1
1
1
0
1
0
3
2
0
0
2
1
0
2
2
0
2
0
0
0
1
2
0
0
1
1
0
0
1
0
0
0
1
1
0
2
0
2
1
0
0
1
1
1
1
1
0
1
1
1
2
0
0
1
1
0
1
1
2
1
1
2
0
0
0
0
0
1
0
0
0
2
0
1
0
2
6
0
1
1
0
0
0
1
2
0
3
0
2
0
1
2
1
2
1
2
0
1
2
2
0
1
1
3
0
1
0
1
5
1
0
2
1
2
0
2
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
2
0
2
0
0
2
0
1
0
2
1
1
0
1
0
0
1
1
0
0
0
1
2
1
2
1
0
0
0
1
0
0
1
1
0
1
1
1
1
2
0
1
1
2
0
0
2
0
1
0
1
1
0
0
2
0
1
0
1
2
0
0
0
0
2
1
1
0
1
0
1
0
0
1
0
0
1
0
1
1
0
2
0
2
7
2
1
2
2
1
2
2
2
1
1
1
1
1
0
1
1
2
0
0
2
1
1
0
1
0
1
0
0
1
1
0
0
1
1
0
0
0
1
1
0
0
0
1
2
0
1
0
1
1
2
3
1
0
0
2
0
1
0
1
1
1
4
1
1
0
1
0
1
0
3
0
1
1
2
1
0
2
0
1
0
1
1
0
0
1
2
2
2
1
2
0
1
1
1
0
0
0
0
2
2
1
2
0
1
0
2
0
0
0
2
1
0
1
2
1
5
1
1
1
1
1
0
0
1
1
1
1
0
2
2
0
1
1
2
1
2
2
2
1
1
2
0
1
0
1
1
2
2
0
1
2
1
1
0
0
2
0
1
0
0
2
1
1
1
0
0
0
1
1
2
2
2
1
0
2
2
0
2
2
0
1
0
1
2
1
0
0
2
0
0
0
0
0
0
1
0
2
1
2
0
2
1
2
1
0
1
2
1
1
3
1
1
2
0
1
0
2
1
0
0
0
1
1
0
1
0
1
2
0
0
1
0
1
0
2
0
1
0
0
1
0
0
2
1
1
1
0
0
1
1
2
1
1
1
1
2
0
1
0
0
1
2
1
1
0
1
1
0
3
0
0
2
0
0
0
0
0
2
0
0
3
0
0
1
0
1
1
1
1
0
0
0
2
2
2
0
0
0
1
1
2
2
2
0
0
0
0
0
0
1
1
0
1
0
0
0
1
1
1
0
0
2
0
0
1
0
0
1
2
0
0
1
0
1
1
0
1
0
1
2
1
0
0
1
2
1
0
0
0
2
0
0
0
1
1
2
0
1
0
1
2
0
2
1
1
1
2
2
1
0
0
2
0
0
1
1
2
1
0
1
1
1
1
0
1
2
0
0
1
0
1
0
0
0
1
0
1
1
2
2
1
1
1
1
2
0
0
0
2
0
0
3
1
1
1
1
2
1
1
0
0
0
1
2
1
0
2
0
1
1
0
0
0
0
0
1
2
1
2
0
1
1
1
0
1
1
0
1
0
0
1
2
0
0
1
1
1
1
0
1
1
1
0
0
1
0
2
1
0
1
0
1
2
1
1
2
2
1
0
2
1
1
1
1
2
1
0
1
2
0
0
0
0
2
1
0
1
0
0
0
0
1
0
0
1
1
1
0
1
0
0
0
1
0
3
0
0
0
0
0
2
0
1
0
1
1
1
1
1
1
1
1
1
1
3
0
1
0
1
0
1
1
2
1
1
0
0
0
2
0
1
1
0
0
2
1
0
1
0
1
0
0
1
2
2
1
1
2
0
3
0
2
2
1
0
0
2
0
2
1
1
2
1
1
0
2
1
1
1
1
1
0
1
0
1
1
3
1
0
0
1
0
1
2
2
0
0
1
0
0
0
1
1
2
0
1
2
0
1
1
1
1
2
0
1
2
1
0
0
0
2
1
0
2
2
2
0
1
0
0
0
1
1
1
1
2
0
1
0
1
1
0
2
1
1
2
5
0
1
0
2
0
0
1
1
0
0
0
1
1
0
1
2
0
1
2
2
0
0
2
0
1
2
1
0
2
1
0
0
0
1
1
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
1
2
0
0
2
0
0
0
1
2
2
2
0
1
0
1
2
1
2
1
0
0
1
1
2
1
0
1
1
0
2
1
0
1
1
2
0
0
2
1
0
2
0
1
0
1
0
2
0
1
0
2
2
0
1
1
0
1
1
0
0
1
1
0
4
1
1
0
0
1
2
1
0
1
1
1
0
1
0
2
2
0
0
3
1
3
0
1
0
1
1
2
1
2
1
1
1
0
2
0
0
0
0
2
0
0
0
1
0
0
2
1
0
0
0
1
1
1
0
0
1
0
1
0
4
0
0
0
0
2
1
0
1
2
1
2
2
1
2
1
0
0
0
1
0
0
0
0
1
1
2
1
1
0
2
1
1
0
0
2
2
3
0
0
2
1
0
1
1
0
0
1
1
0
2
2
1
3
0
1
2
1
2
1
0
1
1
0
0
2
3
0
1
0
0
1
0
1
0
2
1
1
1
0
0
0
1
0
2
1
0
1
0
1
0
2
1
0
0
1
0
0
1
0
1
2
1
0
1
0
2
0
0
2
1
0
1
2
1
2
0
1
0
0
2
0
1
1
0
0
1
1
2
0
1
2
1
1
0
0
0
0
0
0
1
1
0
0
2
0
1
0
0
1
0
0
1
1
1
2
0
1
0
0
1
1
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
2
1
1
1
1
0
2
2
1
0
1
1
1
1
1
1
2
1
0
0
2
1
1
0
1
0
0
2
1
1
0
1
0
0
1
0
2
2
0
1
0
1
1
0
0
1
1
1
2
4
0
0
0
2
0
2
0
1
0
2
0
0
1
1
0
0
2
1
0
2
1
0
1
0
1
1
0
1
1
2
0
0
0
0
0
1
0
2
1
1
2
1
0
1
0
0
2
1
0
3
1
0
0
0
0
0
2
1
0
1
1
2
0
2
0
0
0
1
1
2
1
1
0
2
2
1
1
1
1
0
0
0
0
0
2
1
0
1
0
0
1
1
0
0
0
1
0
1
1
1
1
1
1
2
1
2
2
1
0
2
0
0
0
3
3
0
2
0
1
0
2
3
1
1
2
1
0
1
0
2
1
0
1
1
2
2
0
0
2
1
0
1
2
0
0
1
0
1
2
2
0
1
0
1
1
0
1
0
1
0
0
0
1
1
3
1
0
0
0
0
1
0
2
0
0
2
1
2
2
1
0
1
2
0
0
0
1
1
2
2
3
0
0
1
2
0
2
1
2
1
2
1
0
1
0
0
2
1
0
0
1
0
0
0
0
3
0
1
1
0
1
0
1
0
0
2
2
1
1
1
1
0
0
1
2
2
1
0
2
1
0
0
1
1
2
2
0
1
2
0
1
1
0
0
3
0
0
1
0
0
0
1
0
1
0
1
2
1
1
0
0
1
1
1
0
3
2
1
2
0
1
0
0
0
1
2
1
0
1
0
2
0
0
0
1
2
1
0
1
2
0
1
0
2
0
2
1
0
2
0
0
0
1
1
0
0
0
1
1
0
1
1
1
0
0
0
1
0
0
1
2
0
0
0
0
2
1
0
0
0
2
1
0
0
1
0
3
0
1
0
1
0
1
2
0
0
1
2
1
1
1
2
0
1
0
2
3
0
1
0
2
0
0
2
0
0
0
0
0
1
2
0
0
1
0
1
0
2
1
1
1
0
0
0
0
1
0
1
1
2
2
2
2
1
1
1
2
1
1
1
1
0
1
0
1
0
0
1
1
1
0
0
0
1
2
1
1
0
0
1
1
0
0
1
2
0
2
2
2
1
1
1
1
1
2
0
1
0
1
1
0
0
1
0
2
1
1
1
1
0
2
1
0
0
2
2
0
2
2
0
2
1
0
0
1
1
1
1
2
2
0
2
1
1
2
1
2
0
1
2
2
0
0
0
1
1
0
1
0
1
0
0
1
0
2
0
0
0
0
2
2
1
0
2
1
0
0
1
0
2
1
1
0
0
1
1
2
2
1
1
0
0
1
1
2
0
2
2
1
1
1
1
0
2
2
3
1
0
0
2
1
0
1
1
1
0
1
2
2
0
1
2
2
2
0
1
0
1
0
2
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
2
2
1
0
0
0
2
2
0
1
1
0
0
2
1
1
2
1
2
2
0
1
1
1
0
1
0
2
1
0
0
0
2
1
0
1
2
0
1
0
1
0
0
1
1
1
2
0
1
1
2
0
0
0
1
1
0
1
0
2
2
0
1
1
1
1
2
1
0
0
1
0
1
1
1
0
1
0
2
0
2
0
0
2
0
1
2
2
1
2
0
3
0
1
1
1
0
1
0
0
1
2
2
1
0
2
0
1
0
3
1
1
1
1
1
0
0
2
3
0
2
1
1
1
1
0
1
1
0
0
2
1
2
1
0
0
1
0
0
1
2
0
0
1
0
0
1
1
2
2
1
1
0
3
1
0
2
2
1
0
0
1
0
1
2
1
2
0
0
2
1
1
0
1
0
0
1
0
1
2
2
2
1
2
0
1
1
1
0
0
1
2
0
0
1
0
1
1
0
1
2
0
1
1
2
2
1
0
1
1
2
0
2
1
1
1
2
0
0
1
0
2
0
2
1
1
0
1
1
2
1
0
3
0
1
2
0
0
0
0
0
0
1
1
1
0
0
1
2
0
1
1
2
1
1
0
1
1
1
2
0
2
1
1
0
2
2
1
1
1
0
0
2
3
1
2
1
2
1
0
1
1
1
0
4
1
1
0
1
0
1
1
0
1
0
0
1
1
1
1
1
2
0
2
0
0
1
1
0
1
1
1
2
1
1
1
0
2
2
1
0
0
2
1
0
1
1
0
1
0
1
2
0
1
0
2
2
0
0
1
1
1
2
1
1
0
0
1
2
2
0
1
0
3
2
1
2
1
2
0
0
1
1
1
0
1
2
0
2
1
0
0
2
1
0
1
1
0
0
1
3
2
3
0
0
1
1
0
0
0
0
1
1
0
0
0
1
1
0
2
1
2
1
1
1
2
0
0
0
0
2
2
2
1
0
2
2
1
0
0
1
0
0
1
1
1
2
1
1
0
2
0
0
0
0
1
1
1
1
2
0
1
0
1
0
2
4
0
1
1
0
0
1
0
4
0
1
2
4
2
0
3
0
2
2
1
0
0
2
0
0
2
1
2
2
1
1
0
1
1
1
0
2
2
1
7
2
0
1
0
1
1
0
1
1
1
2
1
1
0
1
0
1
0
1
1
0
0
1
3
1
1
2
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
1
1
1
0
1
0
0
0
1
1
1
1
0
0
1
0
4
1
1
1
0
1
0
1
1
1
1
1
1
2
1
0
2
1
0
1
2
1
1
1
2
1
1
0
0
1
0
1
1
2
0
0
2
1
1
0
1
0
0
0
0
0
1
0
2
1
0
2
2
0
1
0
1
1
1
1
2
1
1
0
1
2
0
4
0
1
0
1
0
0
1
0
0
1
1
2
1
1
1
1
0
2
1
1
1
0
1
4
0
1
1
0
2
4
1
0
1
0
0
0
1
1
0
2
0
1
0
1
0
2
0
1
2
0
0
0
1
0
0
2
0
2
0
2
0
2
0
0
1
1
0
0
0
0
0
0
1
0
0
2
1
1
2
2
0
1
0
0
1
1
1
2
0
2
0
0
1
1
2
1
1
1
1
0
2
0
1
1
2
0
1
1
2
2
0
1
0
0
0
1
2
0
0
1
1
1
0
0
0
1
1
1
2
0
1
2
0
1
2
0
0
1
1
0
0
1
0
1
1
1
2
0
1
1
0
1
2
3
0
2
2
1
1
2
4
3
2
0
0
1
0
1
0
0
2
1
1
2
0
0
0
0
2
2
2
0
1
2
2
2
0
2
0
1
1
2
0
0
1
2
2
1
1
1
2
1
1
0
0
2
1
2
1
0
2
0
2
2
1
1
0
4
1
2
0
1
0
2
1
0
0
0
0
1
1
4
2
0
1
1
2
2
0
1
2
2
2
1
1
0
2
1
1
1
1
0
0
2
1
0
0
0
2
1
0
1
0
1
2
3
1
2
1
1
2
0
2
0
2
2
0
1
1
0
1
1
0
2
0
0
1
0
2
1
0
0
0
0
1
0
0
1
0
0
2
0
0
0
1
1
2
1
1
0
0
0
1
1
0
0
1
1
2
2
0
2
1
1
2
0
0
2
1
0
2
2
2
2
1
1
2
1
0
2
0
0
0
1
0
1
0
2
1
1
1
0
0
1
0
0
1
0
1
0
2
0
1
2
1
1
0
0
0
0
0
2
1
1
0
0
2
3
1
2
1
1
1
1
0
1
2
0
0
1
0
1
1
2
0
2
2
0
0
1
1
2
0
2
1
0
0
4
1
2
0
2
0
2
0
2
1
0
0
1
0
1
0
1
0
0
0
0
1
1
0
1
0
0
1
1
0
1
0
0
0
0
0
1
1
2
1
1
2
0
1
1
0
1
0
1
0
2
0
1
0
1
0
0
0
0
2
1
0
0
0
1
0
2
2
2
1
0
1
1
0
2
1
1
0
1
0
1
0
3
0
0
0
0
0
1
1
1
2
0
1
1
3
1
0
0
1
2
0
2
2
3
1
0
0
2
0
0
0
1
0
0
0
2
1
1
0
0
0
2
0
2
2
0
1
1
0
1
0
0
1
0
0
1
1
0
1
0
0
0
0
1
0
1
0
2
1
1
2
1
0
1
2
1
0
0
0
2
1
2
1
0
1
2
0
0
1
0
2
1
1
1
1
2
2
1
1
1
0
0
1
2
1
0
1
0
1
0
2
0
0
0
0
0
2
0
1
0
1
1
1
0
1
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
2
2
0
1
0
1
2
1
0
1
2
1
2
2
0
2
1
2
0
0
2
1
1
0
1
0
1
1
0
1
1
1
0
0
0
0
1
1
1
1
2
1
1
2
1
2
0
2
1
1
2
1
0
0
1
1
0
1
2
2
2
0
0
1
0
0
1
1
2
0
2
1
1
0
1
1
0
2
0
0
0
1
1
1
1
1
0
1
0
0
2
0
1
1
6
2
1
0
1
0
2
2
0
0
1
0
1
1
2
0
1
0
0
1
2
0
2
0
2
1
2
0
0
0
0
1
1
2
0
2
1
0
1
0
0
2
2
1
1
1
0
0
0
0
1
0
0
0
1
0
1
1
2
1
1
0
1
0
0
1
1
0
0
1
1
1
0
2
1
0
1
1
1
1
0
0
1
0
1
1
2
0
2
0
0
0
0
0
2
0
0
1
1
2
1
0
2
1
0
0
2
2
0
1
0
0
0
1
0
0
2
1
1
1
1
0
1
1
0
0
1
2
0
0
1
2
0
1
1
1
0
0
1
2
1
1
1
2
1
0
1
2
4
2
0
1
1
1
2
0
0
1
0
0
1
2
0
1
0
1
0
1
2
0
2
0
0
0
1
0
0
1
1
2
0
1
0
1
0
0
0
0
2
0
0
1
2
0
0
2
0
2
1
0
2
0
1
3
0
0
1
1
0
0
0
2
1
1
0
1
0
2
2
0
1
0
0
1
1
1
1
0
0
2
0
1
1
2
2
1
0
1
2
1
0
0
0
3
0
0
0
0
2
0
1
0
0
1
1
0
0
0
1
0
1
0
1
1
1
2
1
2
1
0
0
2
1
1
1
1
0
1
0
2
0
2
2
0
2
1
0
1
0
2
0
0
2
3
1
0
1
1
0
1
1
1
0
0
2
0
0
1
1
0
2
0
0
2
1
0
1
0
0
0
1
1
0
1
1
0
1
0
1
1
0
1
2
1
2
2
1
1
1
1
2
0
0
0
2
0
0
0
1
1
0
2
2
0
0
0
2
0
0
0
2
1
2
0
1
2
0
1
2
1
2
0
0
1
2
0
0
1
1
0
0
0
0
1
2
0
2
0
1
1
0
0
1
3
0
0
1
1
1
1
2
0
1
0
0
1
1
1
1
2
1
0
1
0
1
0
1
0
1
1
0
1
1
1
1
1
0
1
0
0
1
1
2
1
0
0
0
0
1
1
1
0
2
0
2
0
1
1
0
0
0
1
1
1
1
2
0
0
2
2
1
0
1
0
2
1
2
0
0
0
1
1
0
2
1
0
0
2
0
1
1
1
1
1
0
1
1
1
0
0
0
0
0
1
2
0
2
2
0
1
1
1
1
1
0
1
1
1
2
0
0
0
1
1
2
0
1
0
0
0
2
2
1
2
0
0
0
1
0
0
0
2
2
0
0
1
1
1
1
1
2
1
0
0
1
1
0
0
0
0
1
5
1
1
0
1
1
1
1
2
2
2
2
2
1
1
1
0
0
2
2
1
1
0
1
2
1
1
0
4
1
0
0
0
1
0
0
2
1
0
2
1
1
0
1
0
1
0
0
2
2
2
2
0
1
0
2
1
0
0
1
1
1
1
0
2
2
1
2
1
0
2
0
1
0
0
0
0
2
1
0
1
2
1
1
1
0
2
0
1
0
2
0
0
1
3
1
1
0
1
0
1
0
1
1
1
2
2
2
0
0
2
0
0
2
0
0
0
2
2
0
2
2
0
1
2
0
0
1
2
3
2
0
1
1
0
0
1
0
0
0
1
1
0
0
1
0
2
0
2
2
1
0
0
1
0
1
1
0
1
1
0
2
0
1
1
0
0
0
2
0
2
0
1
1
1
0
0
1
0
1
0
1
1
0
1
0
1
1
1
1
1
0
0
1
0
0
1
1
2
1
0
2
0
1
1
2
0
0
1
1
1
1
0
0
0
0
2
3
1
1
0
0
0
3
0
2
1
0
2
1
2
0
0
0
2
0
0
0
2
2
0
0
0
1
1
1
0
0
1
2
0
1
0
3
3
2
0
2
0
1
3
2
0
0
0
0
2
1
1
1
1
1
0
1
0
1
1
2
1
0
1
1
2
1
0
2
1
1
0
2
0
0
1
1
0
0
0
1
0
2
1
2
1
0
0
0
0
1
1
1
2
1
3
1
0
0
0
2
1
2
2
0
0
2
2
0
1
0
2
0
0
0
1
2
2
0
1
1
0
1
1
0
0
2
1
1
0
1
0
2
1
0
1
0
2
2
1
2
1
1
1
0
2
0
0
0
0
0
3
1
0
1
5
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
1
1
1
1
2
1
2
0
0
0
0
1
1
0
1
0
2
0
2
1
1
1
1
2
0
2
2
1
1
1
2
0
0
1
1
0
2
1
1
0
2
0
2
1
0
1
0
1
0
0
2
2
0
0
0
0
1
2
0
0
1
1
1
0
0
1
5
1
1
0
2
1
0
0
2
0
0
1
2
3
0
0
1
0
1
1
1
2
0
0
0
2
1
1
0
0
2
1
2
1
2
0
0
0
0
0
0
1
1
1
2
0
2
1
1
2
1
1
1
1
1
2
1
1
1
0
2
0
0
3
0
0
1
2
3
0
2
1
0
1
0
1
2
0
0
1
0
2
2
1
4
0
1
0
1
1
1
2
0
0
1
0
0
1
1
1
0
0
1
2
1
2
0
2
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
2
1
0
0
0
1
1
0
2
0
0
0
1
2
0
0
1
1
0
0
0
1
2
1
1
0
1
0
0
2
1
1
0
0
3
0
1
1
2
1
2
2
0
0
1
1
0
0
0
0
0
0
0
1
0
2
1
1
0
2
2
0
2
0
0
2
1
0
1
1
2
0
0
2
1
0
2
1
1
0
1
0
2
2
2
0
0
0
1
0
3
1
2
1
0
1
2
2
0
1
0
0
1
0
0
1
1
1
3
1
1
1
2
1
0
0
1
2
0
2
0
1
0
1
1
0
2
0
2
2
2
0
0
0
0
2
1
0
1
2
0
1
0
0
1
1
1
0
4
0
1
0
2
2
2
0
1
1
0
0
2
0
0
2
0
0
0
1
0
1
0
1
0
1
0
2
1
0
0
0
0
0
0
0
0
1
1
0
2
2
1
1
0
0
2
1
0
0
0
0
1
2
0
0
0
1
2
2
0
0
0
2
0
1
1
1
2
2
1
1
0
2
1
1
0
2
1
0
0
0
0
0
1
1
2
1
1
0
0
0
2
0
1
0
0
3
0
0
0
0
2
0
1
1
2
0
0
0
2
0
3
2
0
0
0
0
1
2
1
1
1
1
0
0
0
1
1
1
0
2
0
1
2
0
0
1
1
0
2
1
4
1
0
1
1
0
2
0
1
0
2
0
0
1
0
1
0
1
0
0
0
0
1
0
0
2
1
2
2
1
0
2
0
5
0
0
1
1
0
2
0
0
0
2
2
0
1
1
2
1
1
1
0
1
0
0
1
1
0
3
1
0
2
2
0
0
0
1
2
2
0
1
1
0
1
0
0
2
1
0
2
0
0
0
3
0
0
0
2
2
2
3
1
1
0
1
2
0
0
2
2
0
1
0
1
1
1
1
1
1
1
0
2
0
1
1
0
0
1
0
2
0
0
0
0
2
0
0
1
0
1
1
3
1
0
2
1
2
2
0
1
1
0
0
2
0
1
0
2
1
0
1
1
0
2
2
2
0
0
0
1
1
0
0
1
2
1
2
0
0
0
0
0
0
1
0
1
0
1
0
1
1
0
1
1
1
1
0
2
1
2
0
1
0
2
0
0
0
0
0
0
1
0
2
1
0
1
1
1
0
2
0
1
2
2
2
2
0
0
0
0
1
0
0
1
1
1
2
0
1
1
0
0
1
0
1
1
2
3
1
1
0
1
2
2
1
0
2
1
1
1
1
0
0
1
1
0
2
2
0
1
0
1
0
1
1
2
0
1
1
0
1
2
2
2
1
0
1
0
1
0
1
1
3
0
0
1
1
0
1
0
1
0
0
3
1
2
0
0
1
0
0
0
0
1
2
0
2
2
1
1
2
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
1
0
0
1
1
2
1
0
0
1
1
0
0
1
0
0
1
1
0
1
1
1
0
1
1
3
0
1
1
0
1
2
0
2
1
0
2
0
0
1
0
0
0
0
2
1
1
1
1
2
0
0
1
0
1
3
2
0
1
1
1
2
0
1
0
0
0
2
0
1
1
0
0
1
1
1
0
0
1
0
1
0
0
2
0
0
1
0
2
0
2
0
0
1
1
2
0
2
0
0
0
0
1
1
1
1
3
1
2
2
1
0
1
3
1
1
1
0
1
3
0
0
1
0
1
1
0
1
0
0
2
3
1
1
1
1
0
1
2
1
2
2
1
1
0
0
1
1
2
0
1
1
1
1
2
1
1
0
0
2
1
2
1
1
1
1
1
0
1
1
0
1
1
0
1
2
2
2
1
0
1
0
0
0
1
0
1
4
2
2
0
0
2
2
2
1
1
2
1
2
0
2
2
1
2
1
0
0
1
1
2
1
2
0
0
0
1
1
1
1
0
1
0
0
1
1
1
0
3
1
0
0
1
1
1
2
1
2
0
1
2
2
1
1
0
2
0
0
2
0
1
1
2
0
0
0
1
1
0
0
0
1
0
1
2
0
0
1
1
1
1
1
1
1
0
2
0
2
0
1
1
1
0
0
0
0
0
1
1
3
2
0
1
1
2
1
2
1
2
0
0
1
0
1
1
0
1
1
1
1
0
1
1
1
0
2
2
1
3
1
1
1
0
1
0
1
1
2
1
2
1
1
0
3
0
2
3
2
1
2
0
1
2
0
1
1
0
0
2
1
2
1
2
0
0
0
1
0
0
0
1
2
2
2
4
0
1
2
0
1
0
0
0
2
1
2
1
0
2
0
1
1
0
0
3
0
0
0
1
1
1
0
0
1
1
2
1
2
1
1
2
1
1
1
1
1
2
1
2
2
2
2
0
1
2
0
0
0
1
0
1
1
0
0
2
2
1
2
0
1
1
1
0
1
1
1
2
0
0
1
2
1
2
1
1
0
1
0
0
1
1
0
0
2
3
0
1
2
0
0
0
2
2
1
0
2
1
1
1
2
1
7
1
1
1
2
0
2
1
1
2
1
1
1
1
1
0
2
1
1
2
0
1
1
0
1
1
0
2
0
1
0
0
0
0
1
1
0
1
2
2
1
1
1
0
0
1
1
2
1
1
0
1
1
0
1
0
0
1
1
0
2
3
0
1
1
2
2
1
1
0
1
2
1
1
0
0
1
1
0
1
1
1
0
1
2
2
1
1
0
2
2
1
1
1
0
1
0
2
2
3
0
0
0
0
1
2
1
1
2
0
2
0
1
0
1
0
1
1
1
0
1
0
1
0
2
0
1
1
0
0
0
0
2
0
1
2
1
0
1
0
0
1
0
0
1
1
1
1
2
1
1
1
1
0
0
1
0
1
2
1
2
0
0
1
0
2
1
3
0
0
0
0
0
1
0
0
1
0
0
1
2
0
1
1
2
1
2
0
0
2
1
0
2
1
2
0
1
1
1
0
0
1
0
1
2
1
1
0
1
1
0
0
1
0
0
1
1
2
2
2
0
1
1
1
1
1
1
0
1
0
1
0
0
1
2
2
1
1
0
2
0
2
2
1
0
1
1
2
1
0
2
1
0
2
0
1
0
2
2
1
1
0
0
0
1
0
1
0
0
1
0
1
0
2
1
1
1
1
1
2
0
2
0
1
2
0
1
0
1
0
0
1
0
2
0
0
0
0
0
0
0
1
2
1
0
0
1
1
2
0
2
1
2
1
0
2
1
0
0
0
2
2
0
0
0
0
1
2
0
1
0
1
0
1
0
2
0
1
0
1
0
1
0
0
0
0
1
1
1
1
0
1
0
0
2
0
0
0
1
0
2
1
0
2
1
1
2
1
1
0
1
0
1
2
2
0
0
1
1
2
0
1
1
1
0
2
1
0
0
1
1
1
0
1
0
0
3
1
0
2
0
1
0
1
1
2
0
0
0
0
2
0
0
2
2
2
0
2
2
0
0
1
0
2
0
0
1
1
2
1
1
0
1
1
1
0
2
0
0
2
0
0
3
1
1
1
2
0
0
0
2
0
0
0
0
2
1
1
0
1
2
1
2
1
2
0
1
0
0
0
0
0
2
1
0
2
1
1
0
0
1
2
0
2
2
1
2
1
0
2
1
2
0
0
1
0
0
1
0
1
0
2
1
0
2
0
1
2
1
0
2
1
2
2
1
1
1
2
0
1
0
0
2
1
0
1
0
1
1
1
1
0
0
0
2
2
1
2
0
1
0
2
0
2
1
0
1
0
1
1
1
0
1
2
0
0
1
1
1
2
0
0
0
0
1
1
2
2
0
0
2
1
1
1
0
2
1
0
1
0
0
0
0
1
0
1
0
0
1
0
1
1
1
0
1
0
1
0
0
0
2
1
1
0
2
0
0
1
0
1
0
0
2
0
1
0
0
0
1
2
0
0
1
1
2
0
2
1
0
1
2
0
0
1
0
2
1
1
1
0
0
0
0
0
0
0
3
0
0
2
0
1
2
1
0
2
1
0
1
1
0
1
0
4
1
0
0
2
1
0
0
2
2
1
0
1
0
1
1
2
1
1
2
1
2
2
2
0
1
1
1
0
4
3
1
2
0
0
1
0
1
0
2
1
0
2
2
2
3
0
1
2
1
2
1
0
2
1
0
0
0
2
1
0
1
1
1
0
1
1
0
0
0
0
2
0
2
0
2
1
0
1
0
1
0
0
2
0
1
2
2
0
2
2
0
1
2
0
0
1
1
0
0
0
1
1
1
1
2
1
2
1
1
1
0
0
0
1
2
3
0
1
1
0
0
0
2
0
0
0
0
0
0
1
1
1
2
2
1
0
0
1
0
1
0
1
1
2
2
2
1
1
2
0
2
1
1
2
0
0
1
0
1
0
0
0
1
1
1
1
2
1
0
0
1
1
1
2
2
2
1
0
1
2
0
0
0
2
0
1
0
2
0
0
0
1
1
1
1
0
1
0
1
0
0
1
1
1
0
2
2
0
0
2
0
2
3
1
1
1
0
0
2
2
0
1
2
0
2
2
0
2
1
2
2
0
1
0
2
2
0
0
0
2
0
1
0
1
1
0
2
0
0
0
1
0
1
0
1
0
2
0
0
2
0
0
0
1
0
1
2
0
1
1
2
1
1
1
0
0
1
0
2
0
1
0
1
1
2
1
0
2
0
1
2
2
1
1
1
0
1
0
0
1
0
1
2
0
2
1
1
0
1
2
1
1
2
1
1
2
0
1
1
1
0
1
3
1
1
0
0
1
1
0
1
1
0
2
0
1
3
0
1
1
2
0
2
0
2
0
0
0
1
0
0
1
1
1
1
0
1
0
1
0
0
1
1
0
1
1
0
0
1
0
1
2
1
1
1
1
0
0
0
0
2
0
2
1
0
1
1
0
0
2
1
1
1
1
1
0
0
0
1
0
1
2
1
0
2
0
0
2
0
1
1
0
0
1
0
1
2
1
1
0
1
2
2
0
0
1
2
1
0
1
1
3
0
0
1
2
0
2
2
0
0
0
0
1
1
2
0
0
1
1
2
1
0
1
0
1
0
2
1
1
1
0
2
0
1
2
0
1
0
1
0
2
0
2
0
0
1
0
2
0
0
0
0
1
2
1
0
2
1
0
0
1
1
1
2
1
1
1
1
0
0
1
0
1
0
0
0
1
0
2
1
2
1
0
1
0
0
1
1
1
1
0
1
0
0
1
1
0
2
2
1
0
0
2
2
1
1
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
1
1
0
2
1
1
1
1
0
2
0
0
1
1
1
0
2
1
1
1
0
0
1
0
1
0
1
0
1
2
1
1
1
2
1
0
0
1
0
1
1
1
1
1
2
2
2
0
1
2
1
1
2
2
0
2
1
1
1
1
1
0
2
1
0
1
1
1
2
1
0
1
2
1
1
2
0
2
0
1
2
0
0
1
1
2
2
0
2
2
0
1
2
1
0
0
2
6
0
2
1
2
1
2
2
0
0
0
3
2
1
1
0
0
1
0
0
0
2
2
0
1
1
2
1
0
1
0
0
1
0
0
0
1
0
1
0
1
2
1
1
1
1
1
1
3
0
0
1
0
0
0
0
0
2
1
1
1
0
1
0
0
1
0
0
1
2
2
0
1
2
1
0
1
0
2
2
1
2
1
1
0
1
2
1
2
0
1
1
1
0
1
0
2
1
0
1
1
2
1
1
2
2
1
2
2
2
1
1
2
0
2
1
1
0
1
0
0
0
2
1
1
0
0
0
1
1
0
0
0
0
0
0
2
1
0
0
1
1
0
1
0
1
0
2
0
3
0
0
0
1
1
0
3
1
1
0
0
2
2
2
1
0
1
2
1
0
0
0
0
0
0
2
1
1
1
0
1
1
0
2
1
1
0
0
0
0
0
2
2
2
2
2
2
1
1
1
2
2
1
2
2
2
1
0
1
0
2
1
1
1
1
1
0
0
1
1
2
0
1
1
0
2
1
0
0
0
1
1
1
1
2
0
2
0
0
1
1
0
0
1
0
0
3
2
1
0
1
1
1
1
0
0
2
0
1
2
0
2
0
0
0
2
2
0
0
2
1
2
1
2
5
1
1
0
2
1
0
1
1
0
1
1
2
0
1
0
0
3
1
0
1
0
1
0
2
0
2
2
1
0
1
1
1
2
1
0
1
1
1
1
0
0
1
1
2
2
0
1
1
0
0
0
1
0
0
0
1
1
3
1
2
0
1
1
1
0
0
0
0
0
1
2
1
0
2
0
0
0
1
0
2
2
0
1
1
1
2
1
3
0
0
0
1
0
0
1
1
0
2
0
1
0
0
0
1
1
2
1
0
1
2
1
0
0
1
0
0
0
0
1
1
0
2
2
0
1
1
1
1
2
0
2
1
1
1
2
0
1
1
2
2
1
1
0
2
1
1
0
1
0
0
0
2
1
1
0
1
0
1
1
1
1
2
2
3
1
2
0
0
1
0
0
0
1
0
1
1
2
0
0
0
0
0
1
1
2
1
0
0
0
1
1
0
2
0
2
0
0
2
2
0
2
1
0
2
0
2
1
1
0
0
2
1
0
1
0
2
0
1
2
1
2
2
2
1
0
0
1
2
0
0
2
1
1
2
1
0
0
0
0
2
1
2
0
2
2
0
0
1
0
0
2
1
1
1
0
0
1
0
1
1
2
1
0
1
2
2
0
0
1
0
0
1
0
0
0
0
0
0
1
0
2
2
0
1
1
0
0
1
1
1
0
1
2
0
0
0
1
2
0
2
2
1
0
0
0
0
0
0
2
1
1
1
1
0
1
2
2
2
1
0
2
0
0
0
1
0
2
0
0
0
0
0
2
2
1
1
2
2
1
1
0
0
1
0
1
2
2
0
0
0
2
0
1
2
2
0
1
0
0
1
1
1
2
2
1
1
1
2
1
1
0
2
1
0
0
1
0
3
0
2
1
0
1
0
0
1
2
1
2
0
1
0
0
1
0
1
0
1
2
0
0
0
2
0
3
1
2
0
0
1
2
0
0
1
1
0
1
0
2
2
0
1
1
1
1
2
0
2
2
0
0
1
0
0
0
1
2
0
1
2
1
0
2
1
0
2
1
0
2
0
0
1
1
1
0
1
2
0
1
2
0
0
0
0
1
1
1
0
0
1
2
0
0
2
2
2
1
2
0
0
0
1
2
0
2
0
1
1
2
0
1
2
2
0
0
1
0
2
1
2
0
2
0
0
1
1
2
0
1
0
1
0
1
2
2
2
0
1
1
0
1
2
1
1
1
2
1
0
1
1
1
0
2
0
0
0
2
0
1
0
1
2
1
1
0
0
3
2
0
2
0
1
1
0
2
0
0
1
2
2
0
0
0
2
2
1
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
1
1
0
0
0
0
1
1
2
2
1
0
1
1
2
3
0
0
0
1
0
0
1
1
2
0
0
0
1
2
2
1
0
2
1
1
1
1
0
0
1
1
1
0
0
2
1
1
0
1
0
2
1
0
0
0
0
0
1
1
0
0
0
0
0
2
1
1
0
0
0
1
2
1
2
0
0
1
0
1
0
0
1
0
1
0
0
1
1
0
0
1
0
1
0
0
2
2
0
1
0
1
2
0
1
1
0
2
2
0
1
1
0
0
0
2
2
0
0
0
9
1
1
0
0
0
0
1
0
1
0
0
1
1
1
1
0
2
1
1
2
1
0
1
2
1
0
0
0
0
1
0
1
2
1
0
0
0
1
1
1
0
0
0
0
0
1
0
1
0
1
2
1
1
1
1
2
0
1
0
1
1
0
2
2
2
1
1
1
2
1
2
1
1
1
1
1
0
0
1
0
0
1
1
1
1
1
1
0
1
0
1
0
1
2
1
2
2
1
1
2
2
1
0
1
2
1
1
0
1
1
0
0
0
3
1
0
1
1
1
0
2
1
0
0
1
0
1
0
0
1
1
2
1
1
2
0
0
2
0
0
1
1
1
0
1
0
1
2
1
0
2
0
0
2
1
1
0
2
1
1
2
1
0
0
0
1
1
0
0
1
1
0
0
2
0
0
0
1
0
1
0
1
2
1
2
2
0
0
0
1
2
0
1
0
1
0
0
2
1
1
2
0
1
1
0
0
2
0
1
1
1
0
1
0
1
1
4
2
1
0
0
0
2
0
0
0
0
1
1
1
1
0
1
0
1
0
1
1
2
1
1
0
2
0
0
0
1
2
0
1
1
1
0
1
0
1
0
0
1
0
0
0
0
0
0
1
1
1
0
1
1
0
0
1
2
0
0
1
1
2
1
0
0
2
0
0
0
2
1
1
1
1
0
1
0
1
1
1
0
0
2
0
2
0
2
0
0
0
1
0
2
1
1
2
1
2
2
0
0
0
0
1
0
1
2
0
0
0
1
1
0
1
1
0
0
0
3
2
2
0
0
2
1
1
0
1
0
0
1
1
0
0
0
0
0
1
1
0
1
0
1
0
1
2
2
1
2
1
2
1
4
0
1
2
2
4
2
0
1
2
2
1
2
1
0
1
0
1
0
1
2
2
0
1
2
2
2
0
2
0
2
1
0
1
2
0
1
0
0
2
2
0
1
0
1
0
2
1
0
1
1
2
1
2
0
2
0
0
0
1
0
0
0
2
1
0
0
0
0
0
1
0
1
0
1
2
1
1
0
1
0
1
0
0
0
1
1
1
2
0
2
0
0
1
0
2
1
2
1
2
0
0
1
0
0
2
1
0
0
2
1
0
0
2
0
1
1
1
0
1
0
1
0
1
1
0
0
1
0
2
1
0
0
1
2
1
0
1
2
0
0
2
2
0
2
0
0
0
1
2
0
0
1
1
2
0
1
0
0
0
1
0
0
0
2
1
1
0
0
1
1
0
0
0
2
2
1
1
1
1
2
0
0
1
3
2
1
0
0
2
0
0
0
2
0
0
0
0
1
2
1
0
1
0
0
1
1
1
0
1
0
2
1
1
0
0
0
2
0
1
1
0
1
2
1
0
1
1
0
0
2
2
0
0
2
1
0
2
1
2
0
0
0
0
0
0
1
1
1
1
2
0
1
0
2
1
2
1
0
0
1
2
2
1
2
0
1
1
2
0
0
0
1
0
1
0
0
1
4
1
0
0
2
0
1
2
0
1
1
2
0
1
0
0
2
2
2
0
0
1
1
0
1
1
1
2
0
0
2
1
1
1
1
1
2
0
1
2
0
0
0
0
0
2
1
2
0
1
0
0
1
1
2
0
0
0
1
0
0
1
2
1
0
0
0
0
0
2
2
0
0
1
0
2
0
0
2
2
1
1
1
1
0
2
0
2
1
1
1
1
2
2
2
1
0
1
2
0
2
2
1
1
0
1
0
0
1
1
0
2
1
1
1
0
2
0
0
0
1
1
0
2
1
2
0
2
1
0
0
0
1
1
2
0
1
1
2
1
1
1
1
0
0
1
0
0
0
1
0
0
4
2
0
1
0
0
1
0
0
1
0
1
0
2
0
1
0
0
1
1
1
0
0
2
1
0
2
1
0
0
0
1
0
0
1
0
2
2
2
1
1
1
0
0
1
0
1
1
1
1
0
1
1
0
1
2
2
1
1
2
2
0
1
1
2
0
2
2
0
0
1
2
0
1
0
0
1
0
0
1
0
1
0
2
1
1
0
0
0
0
1
0
1
0
0
2
2
2
2
0
1
1
2
0
1
0
0
1
3
0
0
1
0
0
0
1
0
1
2
0
0
1
0
1
0
2
1
0
1
1
1
0
2
0
0
0
1
0
1
2
2
1
1
1
0
1
1
0
2
1
2
2
2
1
0
0
0
1
0
1
1
1
2
2
0
0
0
1
0
1
0
1
1
0
0
1
1
2
1
2
1
0
1
2
1
1
1
1
1
0
0
0
1
0
1
1
1
0
0
0
1
1
0
4
0
0
2
0
1
1
1
0
2
0
0
0
0
0
0
1
2
2
0
1
0
1
1
1
1
1
1
2
2
0
1
2
2
1
2
1
1
0
0
1
1
1
0
0
2
0
1
0
0
0
5
0
1
1
2
2
0
1
0
0
1
2
0
1
0
0
0
0
1
1
1
1
0
1
0
0
3
1
2
0
1
1
1
0
1
2
1
2
2
0
2
1
0
0
1
0
1
0
2
0
0
0
2
1
0
2
2
2
2
0
3
0
0
0
2
1
1
0
0
0
0
0
1
1
0
3
2
1
0
0
1
0
0
1
1
1
2
4
0
2
1
1
3
2
0
1
0
0
2
1
0
2
0
0
2
2
0
2
0
2
0
1
0
1
1
0
0
2
0
0
2
1
1
2
0
0
0
0
3
1
0
0
0
1
0
1
0
0
0
3
1
1
2
1
1
0
1
2
2
2
0
2
2
0
0
0
0
1
0
1
0
1
1
1
1
0
0
0
0
2
0
1
2
1
1
0
0
2
0
0
0
1
1
0
0
2
1
0
2
1
1
2
0
0
1
1
1
0
0
0
2
0
0
1
2
0
1
0
0
2
0
3
1
0
1
1
1
0
2
1
0
1
2
0
0
1
0
2
1
1
1
0
1
1
0
1
0
0
0
1
2
0
1
2
0
2
0
0
0
0
1
2
1
1
1
1
1
1
0
0
2
1
0
1
0
0
2
2
2
2
2
1
1
0
0
1
2
0
4
2
2
2
0
0
2
1
2
1
1
0
2
2
2
1
0
1
1
1
0
0
1
2
1
3
1
2
1
0
0
0
0
0
2
1
1
0
0
0
0
1
2
1
0
0
0
1
1
1
1
0
0
0
0
1
1
0
1
0
1
0
0
0
2
1
1
1
0
1
2
1
1
1
0
0
2
1
0
1
2
0
0
0
0
1
0
0
0
1
1
0
1
2
0
2
0
1
0
1
1
2
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
1
1
0
2
0
0
0
1
1
1
1
1
0
1
0
0
0
0
1
1
0
2
1
2
1
0
0
1
2
0
0
2
1
0
2
1
0
1
2
1
2
1
0
0
1
1
2
1
4
1
1
2
1
1
0
0
0
1
0
2
0
2
0
0
2
0
1
0
2
0
0
1
1
0
1
0
2
0
0
2
2
1
0
1
1
1
1
1
2
0
2
0
1
0
1
0
1
1
1
1
3
1
0
1
0
1
1
2
0
2
0
2
0
1
0
3
2
0
2
0
1
1
0
1
0
0
1
1
1
1
0
0
1
1
1
2
1
0
2
1
1
0
0
1
0
0
1
1
2
2
1
1
0
0
0
0
0
0
1
1
1
1
1
0
1
2
2
0
5
1
1
1
0
2
2
0
0
1
1
1
0
0
1
1
1
1
0
1
0
0
1
0
0
1
2
0
1
0
0
1
0
0
1
1
1
0
1
1
2
0
0
0
1
1
2
1
2
1
0
1
0
1
0
0
1
2
2
0
3
1
1
0
1
2
1
2
0
0
1
2
0
0
1
1
0
0
0
1
0
2
2
1
2
2
1
0
0
1
0
0
1
0
0
2
2
2
2
2
1
0
1
2
0
1
0
1
0
0
1
0
2
2
0
0
1
0
1
0
0
0
1
0
1
1
0
0
1
2
3
2
0
1
1
1
1
0
0
2
0
0
0
0
2
0
2
2
0
0
0
0
0
2
0
0
2
4
0
1
0
1
1
0
1
0
1
0
2
2
0
0
1
0
0
4
2
0
1
0
1
3
0
2
1
1
1
0
2
2
0
0
0
1
2
2
1
2
2
2
0
1
0
0
2
0
0
2
2
1
1
0
0
1
0
1
0
2
0
1
1
2
2
2
0
0
0
0
1
1
0
1
1
2
0
0
7
0
1
2
1
0
0
1
0
2
2
0
3
1
2
1
0
2
0
0
0
1
0
1
0
0
0
0
0
2
0
0
2
1
0
0
0
2
2
0
1
0
2
1
1
0
0
1
2
0
0
1
0
0
1
0
1
2
1
0
0
2
2
0
1
1
0
0
1
2
1
2
1
0
0
1
1
2
0
0
1
1
1
1
1
0
0
0
1
0
1
1
2
1
0
0
2
0
2
0
0
0
1
2
0
0
1
0
0
0
0
0
1
0
2
0
1
1
0
1
1
0
1
1
1
0
3
2
2
0
0
0
0
1
1
1
2
1
3
0
1
1
0
0
1
1
1
0
1
2
1
0
0
0
1
0
2
0
0
2
1
0
1
1
1
1
0
1
1
0
2
1
0
2
0
0
0
1
0
2
2
1
1
2
1
0
0
0
2
0
0
0
2
1
0
0
0
0
0
1
0
1
2
0
0
2
2
0
1
0
0
0
2
0
1
1
1
2
1
0
0
1
2
2
0
1
0
0
0
1
0
1
1
0
3
1
0
0
1
1
0
1
0
0
0
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
0
0
2
0
1
2
1
0
1
2
0
0
1
0
0
0
1
1
1
0
0
2
3
1
2
1
1
2
2
0
1
0
3
2
2
1
1
0
0
0
2
1
1
0
0
1
1
1
1
1
0
2
0
1
1
0
0
0
0
1
1
0
1
0
2
2
1
2
0
0
1
1
1
2
0
1
1
1
1
0
0
1
0
1
1
0
0
2
2
2
1
0
2
0
1
0
1
1
0
0
0
2
0
2
0
0
2
1
1
0
0
0
0
2
1
2
0
1
1
1
1
0
1
2
1
0
1
0
0
1
2
1
1
0
1
2
0
1
0
1
1
0
1
0
2
0
4
0
0
1
1
1
0
0
0
2
1
1
0
0
1
0
1
2
1
0
0
2
1
1
0
1
1
0
1
2
2
1
1
2
0
1
0
1
2
0
1
2
1
1
0
2
1
0
0
1
0
2
1
1
1
2
1
1
0
0
1
1
0
0
0
0
1
2
1
0
0
0
0
1
1
1
0
2
1
0
0
1
2
1
1
0
1
2
1
1
1
0
1
2
2
0
0
0
1
0
1
0
1
1
0
2
0
1
1
1
1
2
0
1
2
0
1
1
2
1
1
2
2
2
0
1
2
0
2
1
0
2
3
0
0
0
1
1
1
1
1
1
2
0
1
0
0
1
1
1
2
1
0
0
0
0
2
1
2
1
2
2
1
2
1
0
1
0
3
1
1
1
1
2
1
0
0
0
1
2
0
0
0
1
1
1
0
0
0
1
2
0
1
0
0
0
0
1
1
2
1
2
1
1
1
0
1
1
0
0
1
2
1
1
1
1
2
0
2
0
0
2
1
1
0
1
0
1
0
1
2
1
1
2
0
1
2
0
0
2
0
0
2
1
3
0
0
1
0
0
1
2
0
2
1
2
0
0
2
1
0
0
2
1
0
2
0
0
2
1
1
1
0
1
1
1
1
0
1
2
0
0
1
0
2
1
1
1
0
1
1
0
2
3
2
0
0
0
0
1
0
0
0
0
1
1
2
1
1
0
1
3
2
0
1
0
1
1
0
2
1
3
1
2
2
0
0
0
1
1
1
1
0
2
0
2
0
1
2
1
1
1
1
0
0
0
1
1
1
1
1
1
6
2
1
2
2
0
1
0
0
0
1
0
1
0
1
0
0
1
1
0
1
0
0
1
2
0
1
0
1
1
1
0
0
1
0
0
0
0
1
1
0
1
2
0
5
0
1
2
0
0
1
1
2
3
0
1
0
1
1
2
0
2
0
1
2
2
2
0
0
0
0
0
0
2
0
0
1
1
0
0
1
0
0
1
0
0
0
1
0
2
1
1
1
1
1
1
0
0
4
0
0
2
0
0
2
2
0
0
2
2
0
2
0
2
0
1
0
2
0
0
0
0
0
1
1
1
1
0
1
0
2
2
0
2
0
0
0
0
4
1
0
1
0
1
0
2
1
0
1
0
0
1
1
2
0
1
0
1
0
1
1
0
0
0
1
2
0
2
0
1
0
0
1
0
1
0
0
0
2
1
1
0
0
1
1
2
2
1
3
0
0
0
0
1
1
0
2
0
0
0
1
3
1
0
0
1
1
0
1
2
1
0
2
1
2
1
2
1
0
1
2
0
0
1
0
1
1
0
0
0
0
0
0
0
0
2
1
0
3
0
2
0
2
2
1
0
2
2
1
1
0
0
2
1
0
1
0
0
2
1
3
2
0
0
0
0
0
2
2
0
8
1
0
1
0
1
1
0
0
1
2
0
1
1
1
1
1
1
2
1
0
2
0
1
2
1
2
1
1
1
1
1
0
0
0
1
1
2
2
1
0
2
1
0
1
1
2
0
0
1
1
0
0
0
1
1
0
2
1
0
1
2
1
2
1
1
0
2
0
0
1
1
0
2
1
0
2
2
1
0
1
0
1
1
0
1
1
1
1
0
0
0
0
0
2
0
1
1
1
0
2
3
2
0
1
1
1
0
0
1
2
3
0
2
0
2
2
1
0
2
0
0
0
2
2
0
2
1
0
1
0
2
0
0
1
0
1
0
0
2
0
1
0
1
0
2
0
0
2
1
1
0
2
0
0
2
2
2
0
0
0
1
2
1
0
0
1
1
3
1
0
0
0
1
4
1
1
2
0
1
0
1
2
1
1
2
0
1
2
0
0
1
1
0
2
0
1
2
0
0
1
4
0
1
2
0
0
0
1
2
2
0
0
1
1
0
0
1
1
1
1
2
1
2
0
1
1
1
1
0
1
2
1
0
2
0
1
1
0
2
2
0
0
1
1
0
0
0
2
0
1
2
1
1
0
2
1
1
1
1
2
2
1
0
1
0
1
2
0
2
0
1
2
1
0
1
1
1
0
1
2
0
0
0
1
0
0
1
1
0
1
1
0
1
2
1
0
0
0
0
0
0
1
1
0
1
1
1
1
0
1
2
2
0
1
0
0
2
2
1
0
1
0
0
0
1
1
0
1
2
2
0
0
1
0
0
1
0
2
0
0
0
2
1
1
0
0
0
2
0
1
1
2
1
1
0
1
2
1
1
1
2
0
2
1
1
1
1
1
2
0
2
2
0
2
0
2
1
2
1
1
2
1
0
2
0
0
2
0
2
1
0
1
0
1
2
3
2
0
1
0
1
0
0
3
0
0
2
1
0
1
1
1
1
1
2
1
0
0
0
1
0
4
2
0
1
0
2
1
0
2
0
0
0
2
0
1
1
0
1
1
0
0
0
0
0
1
0
0
1
0
2
1
2
2
0
1
2
3
0
0
0
0
1
0
6
1
0
2
2
2
1
2
2
2
2
2
1
1
1
1
2
1
1
0
0
0
1
1
2
0
1
2
0
2
1
1
2
0
2
1
0
2
0
1
2
0
2
1
2
0
0
1
1
0
0
1
0
2
1
1
1
1
0
2
1
2
0
1
1
2
1
1
1
0
0
0
3
0
2
1
1
0
2
0
2
0
2
2
2
0
1
0
0
2
2
0
0
1
2
0
0
0
0
2
0
1
2
2
1
2
0
1
1
0
0
0
2
2
0
1
0
1
1
0
0
1
2
3
0
2
0
1
1
1
0
2
0
1
1
0
1
0
0
1
1
0
1
0
0
1
1
0
0
1
1
1
1
0
0
0
1
0
1
1
0
1
0
1
0
0
0
1
2
0
2
1
0
0
2
0
2
2
1
1
0
1
0
3
1
0
0
1
0
0
2
0
0
0
1
1
1
0
0
0
0
0
1
1
0
1
1
1
1
0
1
0
1
1
0
1
2
1
0
1
1
0
1
2
0
1
0
1
2
0
0
0
0
0
0
0
3
1
0
1
0
1
0
0
0
0
0
0
2
1
2
0
0
1
0
0
1
1
1
2
1
0
2
1
1
1
0
1
1
1
0
1
2
1
0
2
2
0
0
1
0
0
1
0
2
0
0
1
0
2
0
1
0
1
2
1
1
0
0
1
0
0
1
1
0
0
2
0
1
0
0
2
2
0
2
1
2
1
1
1
1
1
2
1
1
1
1
2
2
1
1
1
1
2
1
1
1
2
1
2
0
0
1
0
0
1
0
0
1
1
2
0
0
1
1
2
1
0
2
1
2
0
1
0
1
2
0
0
0
1
0
0
2
0
1
1
1
0
0
2
1
0
0
2
0
2
2
2
1
1
0
0
2
1
0
1
1
0
0
0
0
0
0
0
2
3
0
1
0
2
1
0
1
2
0
0
1
1
1
0
2
0
1
1
2
3
2
0
2
1
1
1
1
0
1
0
2
2
1
1
2
0
1
2
2
2
1
2
1
0
0
0
0
2
2
0
0
0
0
1
2
0
1
1
2
1
1
0
1
1
0
0
1
2
1
0
1
0
0
1
1
2
1
1
1
0
0
1
0
1
0
2
0
1
0
2
2
0
0
0
2
1
0
2
1
1
1
0
2
2
0
1
1
1
1
1
2
2
1
0
1
0
0
0
2
2
0
0
1
0
1
1
0
2
1
2
2
0
1
0
0
1
0
1
1
1
0
1
1
0
0
1
0
2
0
2
0
2
0
0
1
1
0
1
2
2
2
0
1
1
0
1
2
0
1
0
1
1
0
0
1
1
0
0
0
1
0
1
1
2
1
1
0
2
0
0
1
0
1
2
0
0
2
0
2
0
0
1
1
1
0
0
0
0
0
2
1
1
1
0
1
1
0
0
1
0
2
1
1
0
0
1
1
0
2
1
0
2
1
0
2
0
0
0
1
0
0
1
1
1
2
0
1
1
0
1
0
1
0
1
1
1
0
1
1
0
2
1
0
0
2
0
0
1
1
1
1
0
0
2
1
1
0
0
0
1
2
0
0
1
1
0
0
1
1
1
1
1
1
0
0
0
0
1
0
0
3
1
2
2
1
2
1
0
1
2
2
1
1
2
0
2
1
2
1
0
1
2
1
1
1
2
1
1
0
1
0
1
0
2
1
1
0
0
0
1
1
0
0
0
1
2
2
1
0
2
0
0
1
1
1
0
2
0
1
2
0
1
1
0
0
2
1
0
2
1
1
0
0
0
1
0
2
1
2
1
0
0
0
1
2
0
2
0
1
0
2
0
0
0
0
2
0
0
0
1
2
1
0
0
0
1
2
0
0
0
1
0
0
0
1
0
2
0
0
2
1
0
2
2
0
2
0
1
0
1
2
0
1
0
0
0
2
1
2
0
1
1
0
1
0
0
0
1
1
1
0
1
1
1
0
1
1
1
2
0
1
2
2
1
1
1
1
0
2
0
0
1
2
2
0
0
2
0
0
1
0
2
1
1
1
1
0
1
0
1
0
0
1
0
1
1
0
2
1
1
0
2
1
0
0
0
0
1
3
1
1
0
1
0
0
1
2
2
0
0
0
1
1
0
1
0
1
0
0
2
1
0
1
0
0
2
0
0
0
1
1
1
1
1
1
2
0
0
1
0
1
2
0
2
0
0
1
1
2
0
2
2
1
0
1
2
1
1
1
0
2
3
0
1
1
2
1
0
2
2
2
2
1
0
0
1
0
1
1
0
1
0
0
0
0
2
1
2
1
1
1
0
0
1
0
0
0
0
2
2
1
2
1
0
2
0
2
1
1
1
2
1
2
2
2
0
0
1
0
2
2
0
2
1
3
2
1
1
0
1
1
1
1
0
1
1
0
2
1
0
3
0
1
0
1
0
2
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
1
0
1
1
1
0
0
0
0
1
2
1
1
1
1
2
0
1
0
1
0
0
3
1
2
1
0
1
0
1
0
1
1
0
1
0
0
0
1
0
0
0
0
0
2
0
1
2
1
0
1
1
2
0
1
0
0
2
0
2
3
3
0
2
0
1
2
2
0
1
1
0
2
0
1
0
2
0
0
1
0
1
1
2
1
1
1
1
0
1
2
0
1
0
1
0
0
1
1
2
2
1
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
2
1
3
0
0
0
0
0
0
0
2
1
1
1
0
1
1
0
2
1
1
2
0
1
0
1
0
1
0
2
0
1
2
2
1
2
5
0
0
0
1
0
0
2
1
0
1
1
0
0
1
1
0
1
2
0
1
1
0
3
1
1
1
1
1
0
0
0
1
0
0
0
1
0
1
2
0
1
1
1
2
0
1
0
2
1
1
1
1
1
1
1
0
1
0
1
1
1
1
2
1
1
1
0
0
2
0
1
1
1
0
1
0
1
0
2
0
0
0
0
1
0
2
2
1
1
0
2
0
1
1
1
1
2
1
1
1
0
1
0
0
1
1
0
1
1
0
1
2
0
0
1
1
1
3
1
2
2
1
0
1
0
0
0
2
1
1
1
0
0
0
0
1
0
0
2
1
2
0
1
1
1
0
0
1
0
0
1
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
2
0
1
0
0
0
0
2
0
1
0
1
0
1
1
0
1
0
1
0
2
0
1
1
0
0
2
2
2
0
0
2
1
0
2
0
2
0
1
1
2
1
1
0
2
1
0
1
0
2
4
0
0
1
1
0
0
5
1
0
0
0
2
1
2
0
1
0
1
1
1
0
2
2
2
0
0
1
2
2
0
0
2
1
1
0
1
0
1
0
2
0
1
1
0
0
0
1
2
1
0
2
3
0
2
0
0
0
1
1
0
0
0
0
1
0
0
1
1
0
1
0
1
0
0
0
0
0
0
3
3
1
2
1
0
2
1
0
1
1
0
2
2
0
1
0
1
1
0
1
1
0
2
0
0
0
0
1
2
1
1
2
1
0
3
2
1
1
0
2
0
0
2
1
0
0
0
2
1
0
0
0
0
1
1
1
0
0
1
0
1
4
2
1
1
2
0
1
0
1
1
0
1
0
1
1
0
0
0
1
2
2
2
2
0
0
0
0
2
2
0
0
0
1
1
2
0
1
0
1
0
2
0
0
1
1
0
0
0
1
0
0
0
2
0
0
1
0
1
1
1
2
2
0
2
0
2
1
2
0
1
1
1
0
1
1
0
0
1
0
1
1
2
0
2
1
2
0
0
2
2
1
2
1
1
1
1
1
1
2
0
1
0
2
1
0
1
2
1
1
1
2
1
1
0
2
0
2
0
1
0
0
1
1
2
1
1
0
0
2
2
1
2
1
0
1
1
2
2
1
2
2
2
0
1
1
1
0
0
0
0
1
0
0
1
0
1
0
1
1
0
1
1
0
2
1
2
1
0
0
1
2
1
0
1
1
0
0
0
0
2
0
1
2
0
0
0
0
1
2
2
2
1
2
1
1
1
2
1
0
0
2
1
0
1
1
1
0
1
1
1
0
1
2
1
1
1
0
0
0
1
2
0
0
0
0
2
2
0
1
2
0
1
1
0
2
1
0
2
0
0
0
1
2
0
4
0
2
2
2
1
0
2
1
1
2
2
0
0
2
0
1
1
1
1
0
0
0
2
0
0
0
0
1
2
2
1
0
2
2
0
0
1
1
0
0
2
2
1
0
2
1
0
1
1
0
1
0
0
0
2
0
0
2
1
0
2
1
1
1
0
0
0
0
3
2
1
1
0
3
1
2
0
1
1
2
0
0
0
0
2
0
0
0
1
2
0
2
2
1
1
1
2
1
2
1
2
2
1
0
3
2
1
1
2
1
2
3
0
1
1
1
0
0
0
1
1
1
0
0
2
2
0
0
1
0
1
1
0
1
1
0
1
0
1
1
2
2
1
2
1
0
1
1
1
0
0
1
0
1
2
0
2
0
1
1
0
1
1
0
1
2
1
0
0
1
1
1
1
1
1
1
0
1
0
0
1
1
0
0
0
1
1
0
0
1
0
0
1
1
2
1
0
1
0
0
0
1
1
2
0
2
2
0
2
1
0
1
0
0
1
2
2
1
1
1
2
1
2
1
2
0
1
0
0
0
0
0
0
1
2
0
1
1
1
1
1
1
2
0
0
1
2
0
0
0
2
2
1
2
0
0
1
1
1
0
1
1
2
2
0
0
0
2
2
0
0
0
2
2
1
1
1
2
0
2
0
0
1
1
2
0
0
1
0
0
0
0
0
0
0
0
2
1
1
2
1
2
0
0
1
1
0
2
0
0
1
1
2
0
1
1
0
2
0
1
2
1
1
0
0
0
1
2
1
1
1
2
1
1
1
2
1
0
0
2
0
1
1
0
0
0
3
1
1
1
1
0
2
0
0
0
2
1
0
0
2
0
0
1
0
1
1
0
1
2
2
0
0
1
1
1
2
2
2
2
0
8
1
1
0
2
0
1
0
2
0
1
0
0
1
1
0
1
0
1
2
2
0
0
1
0
2
1
1
0
1
1
1
0
1
0
1
0
0
1
0
2
0
0
0
0
2
1
2
0
1
2
0
1
1
0
2
2
2
0
0
1
2
1
1
1
1
1
0
2
0
1
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
1
2
1
1
2
2
1
1
0
2
0
0
1
1
0
1
0
2
0
2
2
1
1
0
2
2
0
0
3
1
0
2
0
0
2
1
0
1
0
2
0
0
1
1
0
1
1
0
1
2
0
1
1
1
0
1
0
1
0
0
2
0
1
1
0
0
0
0
0
2
1
0
1
0
1
1
0
0
2
1
1
0
2
1
1
0
1
1
0
1
1
2
0
0
1
1
1
1
1
0
0
1
0
0
0
0
0
1
0
2
0
0
0
2
1
2
0
0
0
0
0
1
1
2
0
0
2
2
2
1
0
0
0
2
0
1
2
1
0
0
2
2
1
2
0
0
2
0
0
0
1
0
1
2
1
1
0
0
0
2
0
2
1
1
0
0
0
0
2
1
1
2
1
1
0
0
1
1
0
0
2
0
1
1
0
1
0
1
1
1
0
3
1
0
2
0
1
0
0
0
0
0
0
0
0
1
2
0
0
2
2
0
0
0
1
1
0
2
1
2
0
0
0
0
0
1
2
2
0
1
2
2
1
2
2
1
3
0
0
1
2
0
2
1
0
1
1
1
0
1
0
0
0
2
1
2
0
0
1
0
0
2
2
2
2
2
1
2
2
0
2
0
1
2
0
0
1
0
2
1
2
2
1
0
0
0
0
0
1
0
2
1
0
0
1
1
1
2
1
0
2
0
0
1
1
0
0
2
0
2
0
2
0
0
1
0
0
2
2
0
2
1
1
2
1
2
1
0
1
0
1
0
0
0
1
1
2
1
0
1
2
1
1
1
7
0
0
1
1
2
1
0
1
0
0
1
0
0
2
1
0
2
0
0
1
0
1
0
1
2
0
2
0
5
1
0
0
1
0
1
2
0
0
0
1
2
1
1
0
0
1
1
2
1
1
1
0
2
1
2
1
0
1
0
0
0
0
1
0
1
0
0
1
0
1
0
1
2
2
2
2
0
1
1
0
0
1
2
1
0
0
0
1
2
1
1
0
2
2
0
1
0
2
0
0
1
1
1
2
0
1
1
0
0
0
1
0
1
0
1
1
0
0
1
0
0
2
1
0
0
0
1
0
0
0
2
1
1
0
0
1
1
1
2
2
2
0
1
1
0
1
0
1
2
2
0
0
0
0
0
1
1
1
2
1
1
0
1
0
0
2
0
1
1
3
1
2
1
0
2
0
2
0
0
3
1
0
1
1
2
1
0
0
0
2
0
0
0
1
0
1
1
1
0
2
0
0
2
1
1
2
2
1
1
1
1
0
2
2
1
0
1
2
0
0
0
2
1
0
2
1
0
0
1
1
0
1
0
2
1
3
1
0
0
0
2
0
1
0
0
3
1
1
1
0
0
2
2
1
0
1
2
0
1
1
2
1
1
1
0
0
0
0
0
0
2
2
1
0
1
1
1
3
1
0
1
2
0
0
0
0
3
1
1
1
2
1
1
0
0
0
0
0
0
0
0
1
1
0
0
2
1
2
0
2
1
0
2
2
0
0
0
1
2
1
1
0
1
0
1
0
0
2
1
0
1
0
1
0
2
1
2
1
0
1
0
0
1
2
0
1
1
0
0
1
1
0
0
0
2
0
1
0
1
1
2
2
2
0
0
2
0
2
1
0
0
1
1
0
1
1
0
0
1
0
0
2
2
0
1
0
2
0
0
0
1
0
1
0
1
0
0
2
1
0
1
1
1
0
0
2
3
2
1
2
1
0
1
1
1
2
0
1
0
1
1
0
1
0
0
2
0
1
1
0
1
0
0
0
0
1
1
0
0
1
2
1
1
0
0
1
0
0
0
1
0
0
1
0
1
0
0
2
1
1
1
1
2
2
2
1
1
1
1
0
2
1
0
1
1
0
1
1
0
2
1
3
0
1
1
1
2
0
0
1
1
2
0
0
1
1
1
0
3
1
1
2
1
2
2
0
1
1
1
3
2
0
1
2
2
2
1
0
1
0
1
1
1
0
1
0
0
2
1
2
2
2
1
2
0
0
0
1
0
2
1
0
0
1
1
1
2
1
0
1
1
0
0
0
1
1
1
2
1
1
4
2
1
0
1
2
1
0
2
2
0
1
2
1
2
2
0
0
1
1
2
2
1
1
1
0
2
0
1
1
2
2
1
0
0
0
2
1
0
1
1
0
0
0
2
2
1
1
0
2
0
1
1
0
0
2
2
1
0
1
1
0
2
0
0
2
2
1
2
1
1
0
1
0
0
2
1
0
0
2
2
1
1
1
1
1
0
2
1
0
1
0
0
1
0
2
0
0
2
0
2
0
1
0
1
0
0
2
0
1
0
0
1
0
0
2
1
0
0
2
0
2
0
1
0
2
0
1
0
1
0
1
0
0
1
0
1
1
2
1
0
2
1
1
0
1
0
1
0
2
0
2
0
0
1
1
2
0
2
1
0
1
1
1
1
0
2
2
1
0
1
2
1
1
0
0
0
1
0
2
1
1
0
0
1
0
0
0
0
1
0
0
2
1
0
1
1
1
1
0
2
0
1
1
1
0
0
0
1
1
2
0
0
1
0
0
1
0
2
1
0
1
1
0
2
0
0
2
1
3
1
0
0
1
1
1
1
0
0
0
1
0
2
0
1
1
0
0
0
1
1
2
0
1
2
1
2
1
0
1
1
0
0
0
0
0
1
1
1
2
0
2
0
1
0
0
2
1
2
2
0
1
1
1
0
2
0
2
1
1
1
1
2
1
2
0
0
1
0
0
0
1
0
1
1
2
2
0
0
2
2
0
1
0
1
1
0
0
0
1
0
0
1
0
2
0
1
1
0
1
0
1
2
2
2
1
1
2
1
1
1
2
1
1
1
2
1
1
0
0
0
1
0
0
1
0
0
0
2
1
0
1
1
2
1
2
0
0
0
0
1
0
0
2
2
1
0
0
2
0
1
0
1
0
0
2
0
0
0
1
2
1
1
1
1
0
2
2
0
2
0
2
1
2
1
2
1
0
0
2
0
0
1
1
1
1
2
1
0
1
2
2
0
1
2
0
1
1
0
1
1
0
1
1
0
1
1
0
0
1
0
1
1
0
2
0
0
0
0
1
0
0
1
0
1
1
1
0
2
0
2
0
2
1
1
0
1
1
0
0
0
1
2
1
0
3
0
4
1
2
1
0
2
1
1
0
1
1
1
1
0
1
0
1
1
2
0
1
0
3
2
1
0
0
0
1
1
0
1
1
0
0
0
0
1
2
0
0
0
0
0
0
1
0
2
1
0
2
0
1
2
0
0
0
1
0
1
0
0
2
1
1
1
2
1
1
1
1
2
2
1
0
2
0
1
0
0
0
0
2
0
1
2
0
1
2
1
0
1
2
0
1
1
2
0
1
0
1
0
2
2
0
2
2
0
0
1
0
0
1
1
1
1
0
2
1
0
1
1
0
0
0
1
2
1
0
0
1
2
0
0
1
1
1
1
0
1
1
2
0
0
0
1
1
1
2
1
1
1
0
1
0
1
1
1
0
1
1
1
0
1
2
1
1
1
2
1
2
0
1
1
2
0
1
0
0
0
1
1
1
2
2
1
0
1
1
1
1
1
1
1
1
2
2
0
0
0
1
0
0
4
0
1
0
0
1
0
0
1
0
0
1
2
0
1
1
2
1
1
0
1
0
0
0
0
2
0
1
0
0
1
0
0
1
1
0
3
0
0
0
2
1
0
0
0
1
2
0
1
1
0
0
1
0
2
0
1
1
1
2
0
1
1
2
1
0
0
1
0
0
1
0
1
2
0
3
1
1
0
1
2
1
1
0
0
1
0
2
2
0
2
2
6
1
1
1
0
0
2
0
2
0
0
1
2
1
1
2
0
0
0
1
0
1
0
0
1
1
0
0
1
4
1
1
2
1
1
2
1
1
1
1
1
1
1
0
1
0
1
1
1
1
1
1
1
0
0
1
1
0
1
0
0
0
0
0
1
1
2
2
0
1
2
0
1
0
0
2
0
2
0
1
1
0
1
1
2
1
2
2
0
0
1
1
2
2
0
2
1
0
1
1
2
1
0
2
1
0
0
1
2
1
0
0
0
0
2
0
1
1
0
2
2
1
0
0
1
0
0
2
3
2
0
1
0
1
0
0
0
1
1
0
1
1
0
1
0
1
0
2
1
2
1
1
2
2
1
1
0
0
1
0
1
2
1
1
2
0
0
0
1
0
1
2
0
0
0
1
0
3
1
1
2
1
0
1
2
1
0
1
2
2
1
1
2
3
1
1
0
1
2
0
2
0
2
1
2
1
1
1
1
0
0
1
2
0
0
0
1
1
1
1
0
0
3
0
1
1
1
1
1
0
2
1
0
1
1
0
2
0
1
2
0
0
1
0
2
0
1
3
0
1
2
0
1
0
0
0
2
1
0
2
1
2
1
0
2
2
0
1
2
2
2
0
0
1
0
3
2
0
0
0
1
1
1
0
0
0
1
0
0
1
1
2
0
0
0
1
0
1
1
0
0
0
2
0
3
0
2
0
1
0
0
0
1
0
2
1
0
1
1
1
1
2
0
0
1
2
0
1
1
0
0
0
0
1
1
1
2
0
1
3
0
1
2
0
2
1
1
0
0
1
1
0
0
1
0
0
0
1
1
2
1
1
0
0
0
0
1
1
1
1
0
2
0
1
1
0
0
2
2
0
0
1
1
1
1
2
0
0
0
0
0
2
2
2
2
1
0
1
0
0
0
1
1
2
0
1
1
1
0
2
2
1
1
3
1
0
0
0
1
0
1
2
2
2
3
0
2
1
0
1
1
1
1
0
0
0
1
2
0
0
1
1
0
2
0
2
2
0
0
1
1
1
2
0
2
0
1
0
0
0
2
0
0
0
0
0
1
0
2
0
1
0
2
1
0
2
2
1
0
1
1
0
0
2
0
0
2
1
0
1
0
0
1
2
0
2
0
1
0
2
1
0
0
0
1
1
1
1
1
0
0
2
0
0
2
2
0
0
3
0
2
2
2
2
0
0
1
1
2
2
0
1
1
0
0
2
1
2
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
2
1
2
0
2
1
2
0
1
2
1
1
1
0
2
1
2
0
1
0
0
2
1
0
0
0
0
0
1
1
0
1
2
1
1
0
1
1
0
2
1
2
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
1
1
1
1
0
2
0
0
1
0
0
2
2
2
2
0
1
0
0
0
2
0
1
1
1
0
0
0
2
1
0
1
2
2
1
0
0
0
2
1
0
1
0
1
1
1
0
0
1
2
2
1
2
1
0
2
0
0
0
1
1
1
0
0
1
0
0
1
0
0
1
2
0
2
0
0
1
0
1
1
0
0
2
0
1
1
1
2
0
0
1
1
0
1
0
1
0
2
0
2
0
1
1
1
1
1
0
1
0
1
0
0
0
0
0
2
0
1
2
1
1
1
0
0
2
1
1
2
0
0
1
0
2
2
1
0
1
2
0
1
2
0
0
0
0
0
3
1
0
0
0
1
0
0
2
2
2
0
1
1
0
0
0
0
1
1
0
1
1
2
1
0
2
0
0
1
0
2
2
2
2
0
1
1
1
1
0
0
0
1
1
0
0
0
2
1
2
0
2
1
0
2
1
0
0
0
0
2
1
0
1
0
2
0
0
0
1
0
1
0
1
0
2
0
2
0
0
1
1
1
0
1
1
1
0
1
0
2
0
1
0
2
1
2
1
1
1
1
1
0
0
2
0
0
1
1
0
1
1
1
0
0
1
2
1
1
2
2
2
0
2
1
3
2
0
0
1
0
0
2
2
2
0
1
1
0
1
1
1
0
0
0
1
3
0
0
1
0
0
1
1
0
3
3
1
2
1
0
1
2
2
0
0
0
0
1
0
2
0
0
0
0
2
1
0
1
3
0
1
1
1
0
0
1
2
2
0
2
1
2
0
2
1
0
0
2
2
1
0
1
2
1
0
0
1
0
2
0
0
1
1
0
2
2
0
2
1
1
0
2
0
0
0
3
0
0
0
1
0
1
3
0
0
2
0
1
0
1
0
0
0
0
0
0
2
3
1
2
2
2
0
1
2
0
2
1
2
0
1
0
0
2
0
0
1
1
0
2
1
1
3
0
2
1
1
1
1
3
2
1
1
0
2
1
0
1
1
1
1
0
0
1
0
2
1
0
1
0
0
1
1
1
0
2
0
0
0
2
0
0
0
2
0
0
1
0
0
1
1
0
1
1
0
0
1
1
1
1
0
0
2
1
0
1
2
0
1
1
2
0
2
1
1
2
1
0
2
0
2
1
0
2
0
1
1
2
0
2
0
1
0
0
0
0
0
2
0
1
2
2
1
1
1
1
0
2
1
0
1
1
0
2
1
0
2
0
0
1
1
0
1
0
1
0
2
2
0
2
0
1
0
0
1
1
1
2
1
0
1
0
0
2
0
2
2
1
1
1
0
0
0
0
1
1
0
1
1
1
1
1
0
0
1
0
1
1
1
1
1
0
2
1
0
0
2
1
0
1
0
0
0
1
2
0
0
2
0
0
1
0
0
1
0
1
1
0
2
1
2
0
1
0
1
2
0
0
1
1
0
0
0
0
0
0
0
2
0
2
1
2
0
1
0
1
1
1
2
2
0
2
0
0
1
1
0
0
2
4
0
1
0
0
0
0
1
2
0
0
1
0
1
0
0
0
1
0
0
0
0
1
1
0
0
1
0
2
1
4
1
2
2
0
0
2
2
2
1
1
1
0
0
1
2
0
1
1
1
2
0
0
1
2
0
2
1
1
4
0
0
0
2
0
1
0
0
1
0
0
0
0
2
2
1
0
1
1
1
2
0
0
1
2
2
2
3
0
0
0
2
1
1
2
2
0
1
0
1
0
0
1
0
2
0
0
2
2
0
2
1
0
1
0
1
1
1
1
0
0
2
0
1
2
1
0
2
2
0
0
2
1
0
0
0
0
2
0
2
1
1
2
0
0
2
1
2
1
0
2
2
1
2
1
1
0
1
0
1
1
2
0
2
1
0
0
0
0
2
0
1
1
1
2
2
2
0
1
0
1
3
1
1
1
1
1
0
0
0
0
2
1
0
0
0
0
1
1
1
1
0
0
0
0
0
7
1
0
0
2
1
1
1
0
0
2
2
2
1
0
2
0
2
1
0
1
1
1
0
0
0
0
0
0
1
0
0
1
1
0
0
2
0
0
1
0
2
1
2
2
0
2
1
1
0
0
0
0
3
1
3
1
0
0
2
0
0
0
0
1
1
0
0
0
0
1
2
1
1
1
1
1
2
0
0
1
0
2
0
1
1
0
1
0
0
0
1
0
2
0
0
2
1
0
2
0
1
1
1
0
2
1
1
0
1
0
2
2
0
0
2
0
1
2
2
1
1
2
0
0
1
1
1
0
0
1
2
1
1
1
0
1
2
1
0
1
1
1
0
0
1
0
0
0
1
0
2
1
0
2
0
1
1
2
2
1
0
2
1
2
1
2
2
1
1
0
0
0
1
0
0
2
0
2
2
1
1
0
1
0
1
1
2
1
1
3
0
2
0
0
0
0
1
1
1
0
2
0
0
1
1
5
1
0
0
0
2
0
2
0
2
0
0
1
0
1
0
2
0
0
2
2
1
1
2
0
0
1
0
0
0
0
2
1
1
0
0
1
1
2
1
1
2
0
1
1
2
0
1
0
0
0
1
0
0
1
1
1
0
0
0
0
1
1
1
0
1
0
0
0
1
1
2
1
0
2
0
0
1
1
1
1
0
1
2
2
0
1
0
2
1
1
1
1
1
2
0
1
2
1
2
2
1
0
0
0
0
1
0
2
0
2
2
0
1
0
1
0
2
0
1
1
1
2
2
0
1
1
2
3
3
0
2
1
0
0
2
1
1
0
3
2
1
2
0
0
1
1
0
0
0
0
0
2
2
1
1
0
0
0
1
2
0
0
0
4
1
1
0
0
0
0
1
2
0
2
1
2
1
1
2
1
0
2
1
1
1
2
0
2
1
5
0
2
0
0
2
2
2
0
1
2
2
0
2
2
2
2
1
1
1
0
2
2
1
1
1
0
1
1
0
0
1
2
1
0
0
0
1
3
2
0
1
1
0
0
0
1
1
0
1
0
0
0
0
2
0
2
0
2
1
2
0
0
0
2
1
1
1
2
0
1
0
0
0
2
0
1
0
0
1
1
0
0
3
1
0
2
1
0
0
1
0
0
1
0
1
1
1
2
1
1
1
1
1
1
1
1
0
1
1
0
1
2
0
0
3
0
0
0
1
0
1
1
0
0
0
0
1
0
0
2
0
0
1
2
0
1
0
1
0
0
2
2
2
2
1
0
1
0
0
0
2
1
2
0
0
1
1
2
1
0
1
2
0
2
0
1
0
0
0
1
0
1
0
0
1
0
0
2
2
0
0
1
1
1
0
0
1
1
0
0
0
0
0
1
0
1
2
0
0
0
0
0
1
0
2
0
2
0
1
1
2
0
4
5
0
2
1
2
0
6
1
2
1
0
1
0
1
0
2
1
4
1
2
2
0
0
0
1
0
0
0
1
3
0
0
1
1
2
2
1
0
1
0
0
2
0
1
0
1
2
0
2
0
1
0
0
3
0
0
0
2
0
4
1
0
2
0
1
2
2
2
1
0
1
1
1
0
1
1
3
0
0
0
1
2
0
2
1
2
1
1
1
0
1
2
1
0
1
1
0
1
2
0
2
1
2
0
0
2
0
0
2
0
2
0
2
0
0
1
0
0
0
1
2
0
1
0
2
1
1
0
1
1
1
2
0
1
2
0
0
1
2
1
2
1
2
0
1
0
0
0
0
1
0
2
1
1
0
0
1
1
0
1
0
0
2
0
0
0
0
0
1
0
0
1
0
0
1
2
1
1
2
2
0
0
0
1
1
2
2
1
0
2
1
2
0
0
4
2
0
1
1
1
3
1
0
1
1
0
0
0
1
1
0
0
1
1
1
1
0
2
0
2
1
2
1
0
0
1
0
2
0
2
0
2
0
1
1
2
2
0
1
2
0
2
0
0
0
0
1
1
1
2
2
0
1
0
0
1
1
0
3
1
1
1
0
0
2
2
1
2
0
0
2
1
1
0
0
1
1
0
0
0
0
1
2
1
2
0
0
1
0
2
0
0
2
1
2
2
0
1
0
1
2
0
1
1
1
3
1
1
1
1
0
0
0
1
1
2
0
1
0
2
0
0
0
0
1
0
2
0
0
2
0
1
2
0
2
1
1
2
2
1
0
2
1
1
1
0
0
1
1
2
0
1
0
1
2
1
1
0
1
0
1
2
1
0
1
1
0
0
0
1
1
1
0
1
1
2
0
1
0
1
0
0
1
0
1
0
2
2
0
0
0
2
1
2
2
1
1
0
1
0
0
0
0
1
2
0
1
3
2
2
0
1
0
0
1
1
2
0
1
1
0
4
1
2
0
0
1
0
0
0
0
1
1
1
1
1
2
0
1
0
1
0
0
1
0
1
0
2
2
1
1
2
0
1
1
2
1
1
0
1
1
0
1
0
1
0
1
1
1
1
0
0
1
1
2
0
1
2
1
1
1
2
2
1
1
1
0
0
0
2
0
1
0
0
0
1
1
1
1
1
1
0
0
1
0
1
1
2
1
0
1
1
1
1
1
0
1
1
2
2
2
0
1
2
2
0
1
2
0
2
1
0
0
1
0
1
0
0
1
0
0
1
2
1
2
1
0
0
0
0
0
0
2
0
0
1
1
2
0
0
0
1
1
0
1
1
2
0
0
2
1
2
0
1
1
2
0
1
1
1
1
2
0
0
2
0
2
1
0
1
1
0
1
2
1
0
1
0
1
0
0
1
2
0
1
1
0
0
0
0
0
2
0
2
0
0
0
2
0
0
1
0
1
0
1
3
1
1
0
1
0
1
2
2
2
1
0
1
0
0
3
0
1
2
2
1
0
2
0
2
0
2
2
0
1
1
2
0
1
0
0
1
2
1
0
1
2
1
1
2
0
2
1
1
2
0
1
0
1
0
0
2
0
0
1
2
2
1
0
0
0
2
0
1
1
0
1
1
0
1
1
0
0
1
3
0
1
1
1
1
0
1
0
1
1
1
1
1
1
1
1
2
0
0
0
1
0
1
0
1
0
2
2
0
0
1
1
1
1
1
2
1
0
0
1
1
0
2
2
1
0
1
0
2
1
0
1
0
3
0
0
2
0
1
0
1
0
0
0
0
0
1
1
1
1
1
2
0
2
1
1
2
0
1
1
2
0
0
1
3
1
0
1
1
0
1
2
1
1
0
0
1
0
2
2
2
1
2
1
0
1
1
0
1
2
1
0
0
0
0
2
0
1
1
2
0
1
0
1
2
0
1
1
2
1
2
1
0
1
1
0
2
1
0
1
1
2
0
0
1
1
0
1
0
1
1
2
1
2
2
3
1
0
1
2
1
1
0
0
0
0
1
0
2
1
0
1
0
1
1
2
0
1
1
0
0
0
1
0
2
0
0
0
1
1
1
1
0
2
1
1
2
1
1
1
2
1
1
1
1
1
0
0
1
1
0
0
2
2
1
2
2
2
0
0
1
0
1
0
1
2
1
0
1
2
1
0
0
1
1
1
0
0
1
0
0
2
2
0
0
0
0
1
2
1
0
0
0
0
0
0
2
1
0
0
1
1
2
0
1
1
1
1
0
1
1
1
1
0
0
0
0
1
1
0
1
0
1
1
2
1
1
0
1
1
2
0
0
1
2
1
2
1
1
0
0
0
0
3
0
0
0
0
1
1
1
1
0
1
1
0
1
0
2
2
1
0
0
0
2
1
0
1
1
0
1
1
3
0
2
2
1
1
1
2
2
0
2
1
1
1
0
1
0
1
2
0
0
0
1
0
0
0
0
1
0
1
1
0
2
2
0
0
2
1
0
1
2
0
0
0
0
0
1
0
0
1
2
3
2
2
1
1
1
1
0
1
0
1
0
0
2
0
1
1
2
2
0
0
1
0
1
1
1
1
0
1
0
1
0
2
0
1
0
0
0
1
0
0
1
1
2
2
1
0
0
0
0
1
1
0
1
1
1
2
0
0
2
1
2
1
1
2
2
1
2
0
1
0
1
2
1
0
0
2
0
1
1
1
1
1
1
1
0
2
1
1
1
1
1
1
2
0
1
6
0
1
1
0
1
0
0
2
1
2
1
1
0
1
1
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
2
1
0
0
1
0
0
0
1
1
0
0
2
1
1
2
0
1
1
1
0
2
0
2
2
0
2
1
0
0
2
1
1
1
0
0
0
0
1
0
0
1
2
0
0
2
2
1
2
0
1
1
0
1
0
0
2
2
0
1
1
1
1
0
0
1
1
1
2
0
2
1
0
2
1
1
0
0
1
0
0
1
0
1
1
1
0
1
1
1
0
2
2
1
1
2
0
0
1
2
1
0
2
0
0
0
1
0
1
0
0
2
2
0
0
0
0
2
1
1
1
0
1
0
0
1
2
0
1
0
2
2
2
0
0
0
1
1
0
2
0
0
3
1
1
1
1
0
1
1
1
0
1
0
0
0
0
1
0
3
1
0
2
2
1
0
2
2
0
1
0
1
2
1
1
0
0
2
2
0
1
1
2
0
0
0
2
0
1
1
0
1
0
2
0
1
2
1
0
2
0
0
0
1
2
1
1
2
0
0
2
2
0
1
0
0
0
0
1
0
1
0
1
0
1
2
1
0
0
2
1
0
0
0
2
2
2
0
0
1
1
0
0
2
0
0
0
1
0
2
0
1
1
0
0
0
0
1
1
2
2
1
0
1
0
0
0
0
2
2
0
0
1
2
0
0
1
0
0
2
1
1
1
0
0
2
2
1
1
0
1
2
0
1
0
1
1
0
0
0
2
1
2
1
1
1
1
1
1
0
2
1
2
2
2
2
0
1
2
0
0
0
0
1
0
1
0
0
1
0
1
1
1
0
0
1
3
1
2
1
0
2
0
0
0
1
1
3
2
1
0
0
2
1
2
1
2
2
2
0
1
0
0
1
1
0
1
2
1
0
0
1
1
1
4
1
1
2
1
1
2
0
2
2
2
1
2
0
0
0
0
0
0
1
0
2
0
0
0
2
2
0
0
2
0
0
1
1
0
2
0
2
2
0
0
0
0
1
1
1
0
2
0
0
1
2
0
0
0
1
1
3
0
2
0
1
0
1
1
1
2
0
1
1
1
1
0
0
1
4
0
1
0
2
0
2
1
2
0
0
1
2
2
1
0
0
1
1
2
2
1
1
0
1
0
0
1
0
1
0
0
0
0
2
0
1
0
0
2
1
4
0
0
0
1
1
2
0
0
2
1
1
1
1
2
2
2
1
0
2
1
2
0
0
1
1
1
0
0
1
1
0
0
1
1
1
2
1
2
1
0
0
1
1
1
2
2
2
0
2
1
0
2
2
1
1
0
1
3
1
0
0
0
0
2
0
0
1
0
1
0
0
1
0
0
1
0
0
1
0
1
0
0
0
2
2
0
0
1
0
1
2
2
1
1
1
1
0
0
0
2
0
2
0
0
0
1
2
1
1
1
1
1
2
2
1
1
1
0
0
2
0
0
0
1
1
1
1
2
0
0
1
1
1
2
2
0
2
2
1
0
1
0
1
2
1
0
0
0
0
2
1
0
0
0
1
0
0
2
1
0
0
1
1
1
1
1
0
1
1
1
1
1
1
2
2
1
0
1
0
1
0
2
1
0
1
4
1
1
1
0
0
1
0
1
0
1
1
0
0
0
1
1
1
0
0
1
0
2
0
1
0
1
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
1
2
1
2
1
1
0
1
1
1
1
1
1
1
1
2
0
1
2
1
0
1
0
1
0
1
3
0
0
0
0
0
0
0
0
1
1
1
2
0
0
1
1
1
0
0
1
0
1
0
1
0
1
2
0
1
1
0
1
2
0
2
1
0
1
0
1
0
0
0
2
3
0
1
0
2
1
2
0
0
0
0
1
1
0
2
0
1
1
1
2
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
1
0
1
2
1
1
1
0
1
2
2
2
1
2
2
1
1
0
1
0
0
3
0
1
0
0
0
2
2
2
1
2
1
1
1
1
0
1
0
0
2
0
0
2
0
1
1
1
0
2
0
1
0
0
1
0
1
6
0
1
1
2
0
1
1
0
1
1
0
2
2
0
1
1
2
1
1
1
1
2
0
0
0
1
0
0
0
0
0
1
0
0
4
1
0
0
0
1
1
1
0
2
2
1
1
1
1
4
1
1
0
1
0
2
1
1
2
1
0
0
1
2
0
2
2
1
0
1
1
0
0
0
1
0
0
1
0
1
1
0
0
3
1
1
2
1
2
1
0
1
1
0
1
0
1
1
2
1
0
1
1
0
1
0
1
1
1
2
2
1
1
0
0
1
1
0
0
0
1
0
0
0
0
0
1
2
1
1
0
1
1
0
0
1
0
0
1
4
0
2
0
2
1
0
0
0
2
1
1
2
0
0
2
1
0
1
0
1
1
1
2
1
2
1
0
2
0
1
1
1
0
1
0
0
1
2
0
2
1
2
1
0
2
0
2
0
0
1
0
1
1
0
0
0
1
2
1
1
1
1
1
1
1
0
2
2
0
1
2
1
0
1
1
2
0
1
2
0
0
2
2
0
0
2
2
1
0
1
0
2
0
2
1
0
0
1
1
1
2
0
1
0
2
2
0
0
1
0
1
1
1
0
0
0
0
1
1
1
0
1
2
1
0
0
0
2
0
0
0
2
2
2
0
0
0
0
0
1
0
1
0
0
0
2
2
1
0
0
0
1
1
1
0
0
0
1
1
1
0
0
2
0
2
2
1
2
0
1
0
1
0
1
1
0
0
1
1
0
1
2
0
0
2
1
1
0
2
0
0
0
1
0
2
1
1
1
1
1
1
1
0
1
0
2
1
1
0
0
1
1
1
1
1
1
0
0
0
2
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
1
0
0
3
1
1
1
2
0
1
2
0
1
1
1
0
8
0
0
0
2
2
1
0
1
1
1
2
1
0
1
2
0
2
1
1
0
2
1
1
2
0
1
2
2
0
1
0
1
2
1
0
3
1
2
1
1
1
1
0
0
0
0
1
2
0
0
2
2
2
2
1
1
0
0
0
0
1
1
0
0
0
1
2
2
0
0
2
2
0
2
0
1
0
1
2
0
1
0
0
1
0
2
1
0
2
2
0
1
1
0
2
2
1
1
1
1
0
0
0
0
0
0
0
2
2
1
0
1
1
1
2
1
1
1
0
2
2
2
1
1
1
1
0
0
0
0
0
3
1
0
0
0
1
1
0
0
0
1
3
2
2
0
0
0
2
1
0
0
1
0
1
0
1
1
0
0
0
2
0
2
2
0
1
2
0
1
0
0
1
0
2
0
0
0
1
1
0
0
0
1
0
0
1
1
0
1
1
0
0
2
1
1
0
1
1
0
0
0
1
1
0
0
1
2
0
0
1
2
2
0
1
1
0
1
2
1
2
0
1
0
0
1
0
0
0
0
0
0
2
0
0
1
0
3
0
2
0
2
0
1
2
0
1
2
0
1
0
0
0
0
2
0
3
1
1
0
0
0
0
0
1
0
2
0
0
0
1
0
0
2
1
0
0
2
1
0
0
1
2
1
0
0
0
2
1
0
0
0
0
1
1
1
1
2
1
2
0
1
0
1
1
2
1
1
2
0
1
2
0
0
2
1
0
0
0
2
0
0
0
3
2
0
0
1
1
1
2
1
3
0
0
0
0
1
0
3
0
0
2
1
0
1
0
2
0
0
1
0
0
0
2
3
0
1
0
1
2
0
0
2
1
1
0
0
1
2
0
1
1
1
2
0
1
2
1
0
0
1
0
1
0
1
0
0
0
2
1
0
0
0
1
1
2
2
1
1
1
2
0
2
0
1
1
1
2
1
1
0
1
0
2
2
1
0
0
0
2
0
1
1
0
0
2
0
1
1
0
1
1
1
0
0
1
0
0
1
2
2
1
1
1
0
2
0
1
1
1
0
0
2
0
1
0
0
1
1
3
2
1
0
0
0
1
1
0
0
1
1
2
0
1
0
1
0
0
0
0
0
1
1
0
1
2
0
0
2
1
1
1
0
1
1
0
1
0
1
1
1
2
1
0
3
1
1
2
2
0
1
0
1
1
1
0
1
2
0
0
0
1
2
1
1
1
0
2
1
0
0
0
0
1
1
1
0
1
1
1
0
0
0
0
1
2
1
2
2
2
1
0
2
0
2
1
0
0
0
0
0
0
1
1
1
0
2
2
1
0
0
0
1
0
2
0
1
1
2
1
0
0
2
0
2
6
0
2
1
1
2
1
1
0
1
2
0
2
1
0
0
0
1
2
0
0
1
0
0
0
1
0
1
2
1
2
0
1
1
1
1
1
1
1
0
1
1
0
2
0
0
0
0
3
0
2
0
0
0
1
2
2
1
1
0
0
2
1
2
0
0
0
1
1
2
1
0
2
0
1
2
1
1
0
0
0
2
2
1
0
0
1
0
2
0
1
1
1
0
0
0
0
0
1
0
0
2
0
1
1
1
2
1
0
0
1
0
1
0
1
0
0
0
2
1
1
0
1
1
2
1
2
0
0
1
2
3
0
0
2
1
1
0
0
2
2
2
1
0
1
0
1
1
2
2
1
6
2
0
3
1
2
1
2
0
1
1
0
1
0
0
0
1
1
1
0
1
0
1
0
0
3
0
0
0
0
2
0
2
0
0
2
0
0
1
0
1
1
1
0
5
1
1
1
0
2
0
0
0
1
0
1
0
2
1
0
2
1
1
0
1
2
1
1
0
1
1
0
1
2
1
1
1
1
0
0
1
0
2
0
1
6
0
1
1
1
0
1
0
2
1
2
1
2
1
0
1
2
3
2
1
0
1
1
2
0
1
1
0
2
3
1
1
5
0
0
1
0
0
0
0
1
2
2
1
0
1
2
0
0
1
1
0
0
0
0
2
0
1
0
0
1
0
1
1
0
1
2
0
0
0
0
0
0
0
1
0
0
0
2
1
1
0
0
2
1
0
1
0
0
1
3
1
1
0
1
2
2
2
0
1
1
1
1
1
2
1
0
2
2
0
1
0
2
0
0
0
1
0
2
0
1
1
0
2
1
0
0
0
0
1
1
0
0
1
1
1
2
1
0
2
1
2
1
1
0
2
0
1
2
2
1
0
1
0
1
1
0
2
1
0
1
0
1
1
1
1
0
3
0
2
0
2
0
0
0
2
1
1
1
0
1
2
1
1
2
1
2
0
1
0
0
2
1
1
0
1
1
1
2
0
2
1
0
1
1
2
1
0
1
1
1
0
0
0
1
0
0
1
0
0
0
1
0
1
1
1
2
0
0
1
0
0
1
1
0
0
2
1
0
2
1
1
0
0
3
0
1
2
2
1
2
1
1
1
0
2
0
2
1
0
0
0
3
1
1
1
1
2
1
2
1
0
0
1
1
0
1
1
2
1
0
1
2
0
2
1
0
2
2
2
0
1
0
2
0
0
1
0
1
0
0
1
0
0
1
0
3
1
0
0
1
0
0
0
1
1
1
0
1
0
2
0
2
0
0
1
0
1
1
2
0
1
1
0
0
1
2
1
0
1
2
2
2
2
0
1
0
0
2
0
2
1
2
3
2
2
0
1
0
0
1
0
1
0
1
2
0
0
0
1
1
2
0
0
2
1
0
1
1
0
0
0
1
2
0
2
2
2
1
1
2
1
0
2
0
1
1
0
1
1
1
0
2
0
0
0
0
1
1
1
1
1
2
1
1
1
0
1
1
0
2
1
1
0
1
2
1
0
1
1
0
1
0
2
2
2
2
0
2
1
1
0
0
1
1
0
1
2
0
0
1
1
1
2
1
1
2
3
3
1
1
1
0
0
0
1
1
1
0
0
2
0
0
2
2
1
1
0
1
1
1
2
0
0
0
0
1
0
0
2
1
2
2
0
1
1
2
1
2
0
0
1
0
2
1
1
3
0
1
1
1
0
1
0
1
2
1
0
0
1
1
1
2
0
1
1
1
1
1
0
2
0
2
1
2
2
0
0
1
0
2
0
1
1
1
0
0
0
2
1
0
0
0
0
0
0
1
0
1
1
0
1
1
0
1
0
0
0
0
0
1
0
0
1
2
1
1
1
0
1
3
1
0
2
1
1
1
2
1
1
0
1
0
0
5
2
0
0
2
1
0
0
1
0
2
0
1
0
0
1
0
0
2
0
1
2
1
1
1
1
2
0
1
2
0
1
1
1
1
2
1
0
0
0
0
0
1
0
1
0
2
2
1
0
2
1
0
2
1
1
1
2
0
2
0
2
1
0
2
0
0
2
0
0
1
2
0
1
1
1
2
0
0
1
1
2
0
0
1
1
2
0
0
0
1
0
1
0
1
0
2
2
2
0
1
1
2
1
1
1
1
2
1
2
0
2
2
1
1
0
0
0
0
0
2
0
2
0
2
1
1
0
0
0
1
0
1
1
0
2
1
1
0
1
2
0
1
7
1
1
1
0
0
2
1
0
2
0
1
2
0
0
1
0
2
0
1
2
0
0
0
0
1
0
0
0
0
1
0
0
1
2
2
2
5
2
0
0
1
0
1
2
0
0
0
0
2
1
2
1
2
0
0
2
1
0
0
0
2
0
2
0
1
0
1
0
1
1
1
1
0
0
2
2
1
2
0
2
1
1
0
1
2
1
0
0
1
1
0
0
0
0
2
2
1
1
1
2
1
1
1
0
2
1
2
1
2
2
1
1
3
1
1
1
1
1
1
1
2
1
1
1
3
2
1
2
0
1
0
2
2
1
1
1
2
1
0
1
0
2
2
0
0
1
0
1
0
2
1
0
2
2
2
1
2
0
0
1
0
0
0
1
2
2
0
1
0
1
0
3
1
2
0
0
0
0
0
2
0
2
2
0
1
2
1
2
1
1
3
0
1
0
0
1
1
0
0
2
2
0
0
6
2
0
0
0
0
1
1
1
0
1
0
2
1
0
0
0
1
0
0
1
1
2
1
1
1
1
0
1
1
1
0
2
0
1
0
1
2
0
2
1
2
1
0
0
1
1
0
0
0
1
1
1
0
0
2
0
0
2
0
1
0
0
0
0
1
2
0
1
1
1
0
0
0
1
0
2
1
1
0
1
0
1
0
3
1
0
2
2
0
1
0
2
0
1
0
1
0
1
2
1
1
0
1
0
0
3
0
0
1
0
3
2
0
0
1
2
0
0
0
1
1
0
0
2
0
1
2
1
1
1
1
0
1
1
0
2
2
0
0
1
0
1
0
0
2
1
2
1
0
0
0
1
2
1
0
1
2
1
0
1
0
1
0
0
0
2
1
2
1
0
0
4
1
0
1
1
0
0
1
1
1
1
1
1
1
2
0
2
2
1
1
1
2
1
1
1
1
2
0
1
1
1
1
1
0
2
6
0
0
1
2
0
2
0
2
2
2
0
1
0
1
0
0
1
0
2
2
0
0
1
0
1
1
0
2
1
1
0
1
1
2
0
1
4
0
2
0
1
0
0
1
0
2
2
1
0
0
0
1
0
1
0
0
2
0
2
1
2
1
1
0
1
0
2
1
0
0
1
1
0
1
0
1
1
1
1
0
0
1
0
0
2
2
1
0
0
1
0
0
0
1
0
1
1
0
1
2
2
2
1
1
2
1
1
0
1
0
1
0
2
0
0
1
0
1
0
1
2
0
0
1
1
1
0
1
0
0
1
2
0
2
1
1
2
0
0
2
2
2
2
0
3
2
1
2
2
1
1
1
0
1
1
0
1
0
1
0
1
0
1
2
1
1
0
2
2
0
1
1
2
1
1
0
0
1
1
1
0
2
2
1
1
2
1
1
0
0
1
1
0
0
2
1
0
1
2
1
2
2
0
1
1
1
2
0
0
0
0
2
0
1
0
1
2
0
1
1
2
0
0
1
1
0
0
0
1
0
1
0
1
1
0
3
0
0
1
1
0
1
2
0
0
1
2
2
0
0
1
0
2
1
0
0
1
0
0
1
1
1
0
0
1
1
1
0
0
1
1
2
0
1
0
1
1
0
1
2
1
1
0
2
0
1
0
2
1
0
0
1
1
0
1
0
1
0
1
2
0
1
1
0
1
2
2
2
1
2
0
2
0
0
0
0
2
0
0
1
1
0
0
1
2
2
1
1
0
0
0
1
0
0
1
2
0
2
1
2
1
2
1
0
0
1
2
2
0
0
1
0
2
1
0
0
2
2
1
0
0
0
0
1
2
1
2
0
2
2
0
0
1
1
1
1
0
2
0
1
2
2
0
0
1
0
2
0
1
3
1
0
0
2
3
2
0
0
0
1
2
1
0
1
0
1
1
0
0
1
0
1
0
1
0
0
0
1
0
1
2
0
2
0
1
3
2
1
0
0
2
1
1
1
4
0
0
0
2
0
0
1
1
0
2
0
1
2
0
0
1
0
0
1
0
0
1
0
2
2
0
1
2
2
2
0
2
2
1
0
2
1
0
0
1
1
1
1
0
0
2
1
3
0
2
1
2
2
1
0
1
1
0
2
1
0
0
1
1
1
2
0
1
2
0
1
1
2
0
1
1
1
0
2
1
0
0
2
1
0
2
1
1
1
2
2
0
1
1
2
1
0
2
0
0
1
2
1
0
0
0
0
0
0
0
0
1
2
0
2
1
0
1
2
0
2
0
1
2
0
2
1
1
2
0
2
0
1
0
1
0
1
2
1
0
2
2
1
0
2
1
0
0
0
1
0
1
2
1
1
1
0
1
2
0
1
1
0
2
2
0
0
1
2
1
0
1
0
1
0
2
1
1
0
2
1
2
0
1
1
1
1
0
0
1
2
0
1
0
1
2
0
0
0
1
2
0
1
0
0
1
1
1
1
0
1
2
0
1
1
0
0
1
0
2
1
0
1
1
0
2
0
0
0
0
0
0
2
2
1
1
0
1
1
1
2
1
0
0
1
0
0
1
0
1
1
1
0
1
0
1
1
0
0
2
0
1
1
1
1
1
1
1
1
0
0
0
2
1
2
0
0
0
0
1
0
0
0
1
2
0
1
2
2
1
0
2
1
0
1
0
0
1
1
2
2
2
1
1
0
1
1
0
1
0
0
0
1
2
0
0
1
0
0
0
1
0
2
2
1
2
0
0
0
1
0
1
0
0
0
1
2
1
1
2
0
0
0
0
0
0
1
0
1
0
0
0
1
1
1
4
1
0
1
0
1
2
0
0
1
2
0
0
1
1
1
1
0
1
1
1
1
1
1
2
0
2
0
1
1
1
0
1
0
0
0
0
0
0
1
2
0
1
1
0
1
0
0
1
1
0
1
1
1
2
1
2
1
1
2
0
0
1
0
0
0
2
0
1
1
2
1
0
1
0
2
1
2
1
1
1
2
0
0
1
2
0
0
2
0
0
1
2
0
1
2
1
0
0
1
0
2
1
2
2
0
1
0
2
1
0
1
0
0
2
1
2
1
2
1
0
0
0
0
1
1
0
0
6
0
2
0
0
2
0
0
2
1
0
0
0
1
3
0
1
1
2
0
1
2
1
1
1
0
0
3
0
0
1
0
1
0
1
2
0
2
2
2
1
1
1
1
1
2
0
0
1
2
0
0
1
0
1
1
1
0
1
0
1
0
0
0
2
1
1
2
1
1
2
1
1
1
2
0
1
0
0
1
0
2
1
0
0
0
0
0
2
0
0
1
0
0
0
2
2
0
2
0
1
0
0
0
0
2
0
0
5
0
2
2
0
1
1
2
0
1
2
3
0
3
0
0
2
1
2
0
1
3
8
0
2
0
1
0
0
1
1
0
1
1
2
0
0
1
3
0
2
0
1
1
0
1
0
1
1
2
0
0
1
0
1
0
2
2
2
1
3
0
0
0
2
2
1
1
2
2
1
1
2
1
0
1
2
1
1
0
2
0
0
0
2
1
1
1
1
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
2
0
0
2
1
1
1
0
0
2
0
0
1
2
1
0
2
0
1
1
1
0
1
2
1
0
1
1
0
1
0
0
1
1
0
0
1
0
0
0
0
2
1
0
0
1
2
0
0
0
1
0
1
1
1
0
1
1
1
0
2
2
0
0
0
0
0
0
0
1
1
2
2
1
1
0
1
2
3
1
2
0
1
1
1
2
2
2
1
0
4
1
2
1
1
0
0
1
1
1
0
2
0
2
0
0
2
0
0
2
1
0
0
2
1
0
0
1
1
2
0
0
1
2
0
0
1
0
0
1
1
4
0
0
2
2
2
1
3
1
0
0
0
0
1
0
1
2
1
0
0
1
0
0
0
0
1
0
0
1
1
1
0
0
0
1
2
0
0
2
0
0
0
1
0
0
1
1
0
0
2
1
0
0
0
0
2
1
0
0
1
2
2
1
0
1
0
2
1
0
1
2
0
2
0
1
3
0
1
0
1
1
2
0
0
1
0
1
0
0
0
0
1
0
0
0
1
1
1
0
1
0
2
2
1
1
2
2
1
0
2
1
0
2
2
2
0
0
1
1
1
1
1
0
0
2
1
0
3
0
2
0
0
1
1
2
1
1
0
1
1
1
0
0
1
0
2
1
0
1
1
1
0
2
1
0
1
1
1
2
1
2
0
0
1
0
0
1
1
0
0
1
1
0
1
0
0
0
1
0
2
0
0
1
1
0
2
2
2
2
1
0
0
0
0
1
0
1
1
1
0
2
1
1
1
1
0
1
1
1
1
1
2
0
0
1
1
0
0
1
1
0
1
1
1
0
2
1
1
0
0
0
0
0
0
2
1
1
2
0
1
0
0
1
1
0
0
2
0
0
1
1
0
1
0
1
1
2
1
1
0
0
1
0
1
2
2
0
1
2
2
0
0
1
2
1
0
0
0
1
1
1
1
0
2
2
0
0
2
2
1
0
0
2
2
1
0
0
0
1
0
0
7
2
1
2
2
0
2
1
2
0
0
2
1
0
1
1
0
1
0
0
1
2
2
0
1
2
0
2
1
1
2
0
0
2
2
1
2
2
1
1
1
0
0
2
2
0
2
1
2
0
0
0
0
0
1
0
1
1
0
1
1
1
1
1
1
0
0
1
1
1
1
0
1
0
2
1
0
1
0
1
0
0
1
1
3
1
1
0
1
1
1
2
1
1
1
0
0
1
2
1
0
0
1
0
1
1
1
2
0
1
2
1
2
3
1
2
1
1
2
1
4
1
2
0
1
1
1
0
2
1
1
0
0
1
0
1
2
1
1
1
1
1
0
2
1
2
0
1
1
3
0
1
2
0
1
0
0
1
1
0
4
2
1
1
2
2
1
1
1
1
0
0
5
2
1
2
0
3
0
0
0
0
0
2
1
1
1
0
2
1
2
0
0
2
1
0
0
0
1
0
1
2
2
0
0
1
2
0
1
0
2
2
0
1
1
2
1
0
1
0
0
2
2
0
2
2
0
0
0
0
2
1
0
1
0
1
1
0
0
1
0
0
0
2
1
0
2
1
1
0
2
2
0
0
0
1
0
0
2
0
0
0
1
0
1
0
1
0
1
0
2
1
2
0
2
1
0
0
1
0
0
0
1
2
0
1
0
1
0
2
0
0
0
2
2
1
0
1
0
0
0
1
1
0
1
1
2
2
0
1
0
2
1
2
2
1
1
2
0
1
1
1
0
1
0
1
0
2
0
1
0
1
6
1
1
1
0
3
0
1
0
1
1
1
1
1
2
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
2
1
0
0
2
0
1
1
2
0
2
1
0
2
1
0
1
0
1
1
0
2
0
3
0
1
1
2
1
1
1
0
2
1
2
1
2
2
0
0
0
0
1
1
2
2
2
2
0
1
2
0
1
0
0
1
1
0
0
1
1
1
1
1
0
2
0
0
1
2
1
0
0
0
0
2
0
0
1
1
1
1
2
1
0
0
0
2
0
1
1
1
0
1
2
0
1
0
3
1
0
0
1
0
0
1
0
0
2
1
1
1
0
0
0
1
1
1
2
0
1
1
0
0
0
0
0
1
0
2
1
1
2
1
0
1
3
1
1
0
0
2
0
2
0
2
1
2
1
1
0
2
0
2
0
0
1
2
1
0
0
2
0
1
0
0
1
2
0
0
0
0
0
1
2
1
1
2
1
0
0
0
0
1
2
0
1
1
1
1
0
2
0
0
0
0
0
0
0
0
0
2
2
2
2
2
0
0
1
0
1
1
2
1
1
1
1
3
2
0
1
0
0
2
2
0
0
0
1
0
1
0
1
2
2
0
0
0
0
0
1
1
3
1
1
0
1
1
0
1
2
1
1
1
2
2
1
0
0
2
1
1
2
0
0
0
2
0
1
0
0
0
1
0
1
1
1
0
2
0
1
2
0
1
1
0
2
1
2
2
1
0
0
2
1
2
2
2
1
0
1
2
2
0
1
1
1
1
0
1
1
0
0
2
2
1
2
0
1
6
0
1
1
2
0
0
5
1
0
1
2
0
0
0
1
0
0
2
0
1
0
0
0
2
2
1
2
2
1
1
0
0
1
1
1
2
0
2
1
1
0
1
0
1
3
2
2
2
1
0
0
0
1
0
1
1
0
2
1
2
1
0
1
2
0
0
1
0
1
0
0
2
0
1
1
2
3
1
2
2
2
1
0
0
1
0
2
2
1
1
0
0
1
1
1
1
1
1
1
0
1
2
3
0
1
1
1
1
0
0
2
0
0
0
1
2
1
0
2
1
0
0
1
1
0
0
1
1
0
1
0
1
2
0
0
0
1
2
1
1
0
2
0
1
0
2
0
1
1
2
0
0
1
2
2
0
2
1
0
0
0
1
1
0
1
3
0
1
1
0
0
2
1
0
0
2
1
1
2
3
1
1
1
0
0
1
0
1
1
0
0
0
2
0
0
2
0
0
2
2
1
1
2
2
0
1
2
0
1
0
2
0
1
1
0
0
0
1
1
1
2
2
2
0
0
1
5
0
0
0
2
3
0
0
0
0
2
0
0
2
1
1
0
0
1
0
0
2
0
1
1
0
2
1
2
0
1
2
3
1
0
0
1
2
1
0
0
0
1
2
1
1
1
2
1
2
0
1
0
1
0
0
0
0
0
0
0
1
1
1
0
1
2
0
1
1
2
1
0
0
2
0
1
0
0
2
0
0
0
0
1
0
1
1
0
1
1
1
0
0
2
2
2
1
0
0
0
1
0
1
1
2
0
0
2
2
0
2
0
0
1
0
0
1
0
0
0
2
0
1
0
0
1
0
2
2
2
1
1
2
1
0
1
1
0
1
0
1
1
1
2
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
1
2
0
1
0
1
0
1
9
1
0
4
0
0
1
0
2
0
0
2
1
0
0
0
0
0
1
1
0
1
0
1
2
0
2
1
1
0
1
0
0
0
0
0
0
3
0
1
1
1
2
0
0
1
0
0
1
2
0
0
1
0
1
1
0
1
0
1
2
0
1
2
0
1
0
1
0
1
1
0
0
1
0
1
1
2
0
0
1
1
1
2
0
0
0
1
1
0
0
1
0
2
0
2
0
0
2
1
0
0
1
1
0
1
1
0
0
1
1
2
0
2
1
0
1
1
2
0
1
0
0
2
3
1
2
1
2
0
2
1
0
0
1
0
6
0
0
0
1
0
1
1
2
1
3
1
0
0
1
0
2
0
1
1
2
2
0
2
1
1
0
1
1
0
0
0
0
0
0
0
3
1
0
1
0
0
0
0
1
0
0
2
1
1
0
2
1
0
1
1
2
0
0
0
2
0
0
1
2
0
2
0
0
2
2
2
0
3
1
0
0
1
0
2
2
1
1
1
2
1
1
1
1
0
1
1
1
2
2
1
1
0
2
1
1
2
2
0
0
1
0
0
1
0
0
1
1
1
1
0
0
2
2
1
0
0
2
0
0
0
0
1
2
2
0
2
1
0
0
2
0
0
0
1
0
3
0
2
1
2
0
0
1
0
2
1
0
2
2
1
0
2
0
2
0
1
2
2
3
1
0
1
1
0
0
1
2
0
0
0
0
2
0
0
1
0
1
0
2
1
0
0
0
1
1
0
1
2
0
1
0
0
1
2
2
1
3
1
0
0
0
4
1
0
0
0
0
0
2
0
1
0
0
2
0
1
0
2
0
2
0
2
0
2
1
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
2
1
1
1
1
2
1
2
0
0
0
0
0
0
2
1
2
1
1
2
0
1
0
1
1
2
0
1
1
2
2
0
2
1
1
1
1
2
0
1
0
1
1
2
1
0
1
1
1
1
0
0
0
1
1
1
0
0
1
2
1
2
1
0
1
1
2
0
0
3
1
0
1
1
0
0
0
1
1
0
1
0
1
1
2
2
0
0
1
1
1
0
1
1
0
0
1
2
1
2
0
0
2
0
1
0
1
2
1
2
2
2
1
2
2
1
0
2
1
1
1
1
0
0
0
0
2
1
1
1
1
0
1
0
1
11
1
0
0
3
0
0
1
1
2
2
1
1
1
0
0
0
1
2
0
0
2
0
0
2
1
1
0
0
1
0
0
1
2
2
0
0
0
1
0
0
1
0
2
0
1
2
2
0
0
0
2
1
1
1
0
0
1
2
2
1
0
2
1
1
1
0
1
2
2
2
2
0
2
2
1
0
3
1
0
2
1
2
0
0
1
1
1
0
0
0
0
0
0
1
0
1
1
1
2
0
0
2
0
1
1
1
0
2
1
0
0
0
2
0
2
1
1
0
3
0
2
0
0
2
1
0
0
2
1
0
2
0
2
1
0
1
1
1
0
2
1
1
1
1
1
0
1
0
1
1
2
1
1
2
1
2
0
0
5
0
0
1
0
0
2
2
0
0
1
1
1
1
1
2
0
2
0
0
0
0
0
1
0
0
0
0
0
1
1
3
0
1
1
2
1
0
1
0
1
1
1
1
2
1
0
0
0
0
0
2
0
1
2
1
2
0
2
0
1
1
2
0
1
1
1
1
0
0
0
0
0
1
1
1
0
1
1
1
0
1
1
0
1
2
2
0
0
0
0
1
1
2
1
0
0
0
0
2
1
2
0
0
1
1
2
1
0
0
0
0
2
1
0
0
0
0
0
1
0
2
1
2
1
1
1
1
3
0
1
0
1
1
0
0
1
1
1
0
0
0
1
2
1
1
1
2
0
1
0
0
1
2
1
0
0
0
0
1
1
1
0
1
1
1
1
0
0
1
1
1
2
3
2
0
2
3
0
0
2
1
0
1
2
0
2
0
3
2
0
2
0
0
0
2
1
0
2
1
1
1
3
1
2
0
1
0
1
2
1
2
0
0
1
1
1
1
1
1
1
2
1
0
1
2
0
0
2
1
0
2
1
1
1
2
1
0
1
2
2
1
1
2
2
2
1
2
1
0
0
0
0
2
2
1
1
0
0
1
1
2
1
0
0
0
1
0
2
2
1
2
0
1
0
1
0
0
2
1
0
0
0
0
5
0
0
2
1
2
1
0
1
3
1
1
1
0
1
1
1
0
0
1
0
1
1
2
2
2
0
1
1
1
3
1
1
0
0
2
2
0
2
3
1
2
2
0
0
2
0
0
2
2
1
1
1
2
0
0
0
0
1
2
2
0
2
0
0
0
0
0
0
2
0
0
1
2
1
0
2
0
0
0
0
0
0
2
1
1
1
0
0
1
1
1
1
0
2
1
3
2
1
0
1
0
1
1
1
0
1
2
1
2
1
0
2
1
0
1
0
2
1
1
0
0
2
0
1
0
1
1
2
2
2
1
1
1
0
0
2
0
0
0
1
1
1
2
1
2
0
0
1
0
0
0
0
2
1
1
0
2
2
1
0
0
1
0
1
0
1
3
0
1
1
1
1
2
0
0
3
2
1
2
0
0
0
2
0
0
1
1
1
0
1
1
0
2
0
1
2
3
2
2
0
0
0
2
2
1
0
0
0
0
2
0
0
1
0
1
0
0
1
1
1
0
1
1
2
0
0
1
1
0
0
2
1
0
2
2
0
2
0
2
1
1
0
2
2
1
0
0
0
2
1
1
1
0
0
1
2
2
2
1
0
2
1
1
2
1
1
1
0
2
1
1
1
2
0
0
0
0
1
0
0
1
1
2
0
2
2
2
2
2
1
1
0
2
1
1
0
0
2
2
0
1
1
2
0
1
2
2
1
1
1
0
1
0
0
0
1
1
2
0
1
1
1
0
2
2
2
0
1
1
1
2
1
2
1
1
0
1
0
2
1
1
0
2
0
2
2
2
1
2
0
0
0
2
1
0
0
0
1
0
1
1
1
1
1
1
1
0
2
2
2
2
2
2
2
0
1
0
0
0
1
0
0
1
0
0
1
1
1
1
0
2
0
3
0
0
0
2
2
0
0
0
0
1
1
1
1
0
1
0
0
1
1
0
1
1
2
0
1
1
2
1
0
2
1
1
2
2
0
0
1
0
0
1
1
1
0
1
3
1
0
2
2
1
2
0
0
1
2
2
0
1
0
2
0
0
2
1
1
2
1
2
2
1
0
1
0
2
0
1
0
1
1
0
1
1
2
0
1
4
0
0
1
0
0
1
2
3
1
1
0
4
1
0
0
0
1
2
1
1
1
1
1
0
1
2
0
0
1
2
2
1
0
0
0
2
2
1
0
2
0
0
1
2
0
1
0
0
1
0
1
0
0
2
2
0
0
1
2
2
2
2
1
2
0
2
1
0
1
2
1
1
2
0
1
2
1
2
1
1
0
1
0
0
0
1
1
1
2
0
1
0
1
0
1
1
1
1
1
0
0
1
1
0
1
3
0
2
0
1
1
2
0
0
0
1
0
2
2
1
1
2
1
0
1
0
1
0
1
1
2
2
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
2
6
1
1
0
1
2
1
0
1
2
1
0
0
0
0
0
1
1
4
2
1
1
1
1
0
0
1
2
0
0
1
0
2
1
1
1
1
1
1
1
2
0
3
1
1
1
1
1
2
2
1
0
2
0
1
2
0
2
1
0
1
2
1
0
2
0
1
2
1
0
0
0
2
1
0
0
0
2
1
1
1
1
2
0
0
1
1
1
2
0
1
1
0
0
2
1
1
0
1
2
2
2
1
1
0
0
0
1
1
1
1
0
2
0
1
1
1
2
0
2
1
1
3
3
0
2
1
4
0
2
2
0
2
0
2
1
1
0
1
0
0
0
1
2
1
1
0
2
0
1
1
0
0
0
0
1
0
0
1
0
2
2
1
0
0
0
0
1
2
3
1
2
0
1
1
2
0
0
0
2
2
0
0
2
0
1
0
2
2
1
0
5
1
0
0
0
2
1
1
2
0
3
2
0
0
0
2
0
0
2
1
0
1
1
1
1
2
1
0
0
1
0
0
2
1
0
0
0
1
0
1
0
1
1
0
0
2
1
1
0
1
2
0
2
0
0
0
0
0
2
0
1
0
2
2
0
0
0
0
1
3
1
1
1
0
1
0
0
0
1
0
2
0
2
2
1
1
0
1
1
2
0
0
2
1
0
2
0
2
0
1
1
0
0
2
0
0
2
0
2
1
0
0
2
0
2
0
0
2
2
0
0
0
1
2
1
0
0
1
0
0
1
0
1
0
1
1
0
1
1
1
1
0
1
2
1
2
1
1
2
0
2
0
0
1
1
1
2
0
0
2
0
1
0
2
0
1
1
1
0
0
1
1
2
1
1
1
1
2
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
2
1
1
1
2
0
1
0
2
1
0
0
0
1
2
0
0
0
1
2
1
0
3
0
2
2
1
1
1
0
1
0
1
0
1
1
0
0
1
0
1
0
2
1
0
0
1
0
0
0
0
0
2
1
1
0
1
0
1
0
0
0
1
1
3
2
1
1
1
0
2
1
0
1
0
1
2
1
1
0
0
0
1
0
1
2
2
3
0
1
1
0
1
0
2
1
1
1
0
0
2
0
0
0
2
0
1
0
1
1
0
0
2
0
0
0
3
0
2
1
0
1
2
2
2
1
2
0
1
0
1
2
0
0
1
1
1
0
1
2
1
2
1
0
1
1
1
1
1
1
2
1
0
3
0
0
1
1
2
2
2
1
2
0
0
1
0
0
2
0
0
0
1
1
2
0
1
2
1
1
0
2
1
2
2
0
0
1
0
1
0
1
0
0
0
0
0
2
1
1
0
0
1
1
2
1
0
0
2
1
0
1
0
0
0
2
1
2
0
1
0
0
2
0
0
0
1
1
1
1
1
0
0
0
0
0
1
2
1
2
2
0
1
1
1
0
2
0
0
1
1
0
0
2
2
1
1
1
1
2
0
2
1
1
0
2
1
1
0
1
1
0
0
1
2
2
1
0
0
0
0
1
2
1
1
0
0
0
2
2
2
0
0
0
2
0
1
2
0
2
1
0
0
1
2
0
0
1
0
0
0
1
0
0
0
1
2
1
3
0
1
0
0
1
2
0
1
2
2
0
1
0
1
2
0
0
0
1
2
0
2
0
0
1
2
0
0
1
1
2
1
1
2
0
1
0
1
0
2
0
0
1
0
2
0
1
2
0
0
1
2
0
0
0
0
0
2
1
1
0
1
0
1
0
1
0
1
2
1
0
1
0
1
4
1
0
0
0
1
1
2
1
2
1
2
0
2
0
0
1
0
1
3
0
0
0
2
0
1
1
1
1
2
0
1
2
2
0
0
1
1
1
0
0
0
1
2
0
1
0
1
1
0
0
0
1
1
1
1
0
2
1
2
2
0
2
0
0
1
2
1
0
1
0
0
2
0
0
0
0
0
0
2
0
1
1
1
1
2
1
0
2
3
2
0
0
2
0
0
1
0
0
0
0
2
1
2
2
1
0
1
2
1
1
2
2
0
0
1
1
0
0
1
0
0
2
1
1
2
2
0
1
2
1
2
1
0
0
2
2
0
1
0
0
0
0
1
1
1
2
1
2
0
2
2
0
2
1
0
2
1
2
1
0
2
1
1
0
0
1
0
1
0
2
2
1
1
1
0
1
0
1
1
1
2
1
1
1
0
1
1
2
0
1
0
2
0
0
2
0
1
2
0
1
0
1
0
1
0
1
0
0
0
1
0
4
1
0
0
1
0
1
1
0
1
0
0
2
0
1
0
0
3
2
0
2
0
1
1
2
1
1
2
0
1
2
0
1
1
2
0
1
0
1
2
1
1
1
1
0
6
2
0
1
1
2
2
0
1
1
0
1
0
1
0
2
1
1
1
2
0
0
2
0
2
1
2
2
1
0
2
1
0
2
1
0
0
0
0
0
3
1
1
0
0
2
0
0
1
0
1
2
1
2
0
1
0
0
0
0
2
1
1
1
7
0
1
0
0
0
1
1
2
0
1
1
1
0
2
0
0
0
0
0
2
1
1
0
0
0
2
0
2
1
0
0
0
1
2
2
0
1
1
2
0
3
0
0
0
1
2
2
1
2
1
1
0
0
2
0
2
0
0
2
1
0
0
0
0
1
2
0
1
0
0
1
2
1
0
1
0
2
2
0
1
2
0
0
0
2
0
0
0
0
0
0
2
1
1
1
0
2
2
0
0
1
2
2
1
2
1
2
1
1
3
1
0
2
1
2
1
0
1
0
0
0
1
0
0
2
0
1
1
0
1
0
2
1
1
1
1
0
1
2
0
1
0
1
1
2
0
2
2
1
0
2
2
0
0
1
0
1
1
0
0
2
0
0
2
1
1
0
0
2
1
0
2
0
1
1
2
1
1
2
1
0
1
0
2
1
1
1
1
1
0
1
2
4
0
2
0
2
1
0
2
2
1
0
0
1
0
0
1
0
0
1
1
1
0
0
1
0
0
0
1
0
1
0
2
1
4
0
0
0
1
1
1
1
1
0
1
0
2
1
3
0
1
1
1
0
0
2
1
0
1
1
1
0
2
0
1
0
1
1
0
2
0
0
0
0
0
0
1
1
0
0
2
2
1
1
1
1
2
1
1
0
1
1
0
1
1
0
0
2
1
1
0
1
1
0
1
0
1
0
0
2
2
1
2
0
1
0
1
0
0
2
2
0
0
2
0
0
0
1
0
1
0
0
2
0
1
2
0
1
1
0
2
1
1
1
2
0
0
1
1
1
1
1
1
0
0
0
0
1
0
0
1
0
0
1
1
0
1
2
0
1
1
0
1
0
0
3
0
2
1
1
1
1
2
1
0
2
0
2
0
1
0
0
0
1
0
0
0
0
1
2
1
1
1
1
1
2
2
0
2
2
1
2
1
1
0
0
0
0
0
1
2
1
1
0
1
2
1
0
1
0
1
0
1
0
2
0
0
1
1
0
0
1
1
0
0
0
2
0
1
0
2
0
1
0
0
0
1
1
2
2
0
2
1
1
1
0
1
1
1
0
2
1
0
1
1
1
4
0
1
2
1
0
0
1
1
0
0
0
0
2
1
2
1
3
1
0
2
3
0
1
2
0
2
1
1
3
0
0
2
0
2
2
0
0
0
2
0
1
1
0
2
1
0
0
1
3
1
0
1
1
0
0
0
0
2
1
0
1
2
0
2
1
2
2
2
1
1
1
0
2
2
0
1
0
0
1
0
1
1
2
1
1
1
1
0
3
1
1
2
4
3
2
0
0
0
0
2
0
1
0
1
1
0
1
2
2
0
1
2
0
1
1
0
0
0
3
0
0
1
0
0
1
2
1
0
0
0
1
1
1
0
2
2
1
0
0
1
1
2
1
0
2
1
0
2
1
0
1
1
2
0
0
1
5
2
2
1
1
2
0
0
2
1
4
1
0
0
0
0
2
1
1
0
1
1
0
1
0
1
1
1
1
1
0
3
2
0
0
0
1
0
1
0
1
2
0
0
1
0
0
2
0
2
1
0
2
1
0
0
0
0
0
1
0
0
2
1
1
0
1
4
2
1
1
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
1
0
0
1
0
1
1
0
1
2
2
1
1
1
0
4
1
1
0
1
0
1
0
1
1
1
1
2
2
0
1
0
1
2
0
0
0
2
2
1
1
0
1
0
0
1
2
2
2
1
0
0
0
1
1
0
0
0
0
0
0
1
1
2
0
1
1
2
0
0
2
1
0
1
0
0
0
2
2
0
3
0
2
0
1
2
1
2
0
1
2
2
1
0
1
0
2
2
1
0
1
2
0
0
1
0
2
2
1
0
1
0
2
0
2
0
1
3
0
1
1
2
0
0
1
1
0
0
0
3
2
1
0
2
2
2
1
0
0
2
1
1
0
0
0
0
2
0
2
1
0
1
2
0
2
1
1
0
0
0
2
1
0
0
0
0
0
0
0
0
1
2
1
1
0
0
3
1
1
1
0
2
0
2
0
0
2
1
0
0
1
1
1
1
1
2
0
0
0
0
3
1
2
1
1
0
2
1
0
1
0
2
1
2
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
2
0
0
1
1
1
0
2
0
1
1
2
0
1
1
2
0
0
0
0
2
0
0
1
1
0
2
2
1
1
0
1
0
2
0
0
1
0
3
0
2
0
1
2
1
0
1
0
1
0
2
1
0
0
3
0
1
0
0
2
0
1
0
0
1
0
0
2
2
1
2
0
0
0
0
0
1
0
0
1
0
2
0
1
2
0
2
1
0
0
2
1
0
0
2
0
0
2
0
1
0
0
4
1
2
0
2
1
1
1
1
0
0
0
1
1
1
0
1
0
2
1
0
0
2
1
0
0
0
1
0
0
2
0
1
1
0
0
2
1
1
2
0
0
1
0
1
1
0
1
2
0
0
2
1
0
2
2
2
0
0
2
3
0
2
0
2
2
2
0
0
1
1
0
0
1
0
1
2
1
0
1
1
2
1
0
0
1
0
1
1
0
2
1
0
1
2
0
0
1
1
2
1
1
1
1
1
0
1
0
0
1
1
2
0
1
0
1
0
2
1
0
1
1
0
1
1
1
0
2
0
0
0
3
0
1
0
1
2
2
1
2
0
2
0
1
0
2
1
1
1
0
1
2
0
0
0
0
0
0
0
0
1
2
1
1
0
0
0
2
2
0
0
0
4
1
2
0
0
1
0
2
0
2
0
0
2
0
2
0
0
1
0
1
2
1
1
2
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
2
1
1
0
1
1
1
2
1
0
0
1
0
0
0
2
2
0
0
0
2
1
0
0
2
0
0
3
1
2
1
0
0
0
0
1
0
1
2
1
1
0
0
1
1
0
0
0
0
1
0
0
1
1
2
0
2
0
1
0
1
1
0
1
2
2
1
0
2
2
0
0
1
0
0
0
0
2
1
0
0
0
0
2
1
0
2
0
0
2
1
1
0
1
0
0
1
0
1
0
2
0
1
0
1
0
2
0
0
2
3
0
2
2
1
0
1
0
1
1
0
0
0
1
0
1
0
0
0
1
0
2
0
0
2
0
0
0
1
1
0
0
0
0
1
0
2
0
2
1
2
1
1
1
2
2
0
0
1
1
0
1
0
0
2
1
1
2
1
2
1
0
0
0
0
0
1
1
2
0
1
1
1
1
0
1
0
0
1
2
1
2
1
0
0
2
0
1
2
4
3
1
3
0
0
0
0
2
1
0
1
2
2
0
1
0
1
1
1
0
1
0
0
2
0
2
0
1
1
0
0
1
1
2
0
0
0
2
0
2
2
1
1
1
0
0
0
0
0
0
0
0
1
0
0
1
1
1
1
0
0
1
2
0
1
0
1
1
0
1
2
1
0
1
0
1
1
0
1
0
1
1
0
2
1
2
1
2
1
1
1
2
0
2
0
2
2
0
0
0
0
1
1
0
2
1
0
0
4
0
0
2
2
2
1
0
0
1
1
0
1
2
1
1
1
2
2
0
2
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
1
0
2
0
1
0
0
1
0
0
1
1
0
0
1
2
1
0
1
0
1
0
0
0
0
0
0
1
1
1
1
0
2
1
4
0
1
0
0
1
0
1
1
1
1
0
1
0
1
1
1
2
2
2
1
1
1
2
2
1
0
0
0
2
0
0
0
1
2
1
1
0
0
1
3
2
2
1
0
0
1
3
1
1
0
0
2
1
0
0
2
0
0
0
1
0
1
2
0
2
2
0
0
1
0
2
2
0
1
0
1
2
1
0
0
0
0
0
1
0
1
1
0
1
1
0
2
2
2
1
2
1
2
1
0
0
0
1
1
0
0
1
1
0
1
2
2
0
2
2
2
0
1
0
1
1
0
1
2
0
0
0
2
0
1
0
1
1
0
2
2
2
2
2
2
2
0
1
1
2
0
1
1
0
1
2
1
0
2
0
0
1
1
0
1
1
0
0
0
2
1
0
2
2
1
2
0
3
0
0
1
2
1
2
0
1
0
1
1
1
1
0
1
0
0
2
1
1
0
0
1
1
0
2
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
2
1
1
0
1
1
2
2
1
1
1
2
0
2
2
0
2
2
0
1
0
1
2
1
3
0
1
1
0
2
1
1
0
0
1
2
0
0
1
3
1
0
1
1
2
0
1
1
2
0
2
1
0
0
1
1
0
1
1
3
0
0
1
0
1
1
2
1
1
1
1
0
0
1
0
2
1
0
1
2
1
2
0
0
1
1
2
1
1
0
1
1
3
1
0
2
2
1
0
0
0
1
1
0
1
0
1
1
1
1
1
0
2
1
0
2
1
0
1
1
1
1
1
0
1
0
1
0
1
0
1
0
0
1
1
0
1
0
1
0
1
1
0
1
2
1
0
1
1
2
2
1
2
2
2
0
2
2
0
1
0
1
2
0
0
1
1
0
0
0
0
2
0
1
1
0
1
1
1
1
1
1
1
0
2
1
0
2
0
1
1
0
2
1
1
1
1
0
2
1
2
1
0
0
2
2
0
1
1
1
1
3
0
0
0
2
1
0
1
1
1
1
1
1
0
0
1
0
1
2
2
0
2
1
0
2
0
0
0
0
1
0
2
2
0
2
1
2
0
2
0
2
2
0
0
0
0
0
0
0
0
1
0
2
0
1
2
0
0
0
1
1
1
1
1
0
2
0
0
0
0
1
0
1
2
1
1
0
0
2
0
1
1
0
1
1
0
1
1
1
1
1
2
0
1
1
0
1
1
0
1
2
0
0
1
1
1
0
1
0
1
0
0
0
0
1
2
1
2
1
1
2
0
0
0
1
0
0
0
1
0
0
3
1
3
2
2
0
1
1
1
0
1
1
0
1
0
0
0
1
1
1
1
1
0
1
0
0
0
2
1
0
1
1
2
0
0
0
2
1
2
1
0
0
0
0
1
2
0
0
0
0
1
0
0
1
2
1
1
0
1
0
1
0
1
0
3
0
0
1
0
0
0
0
0
1
0
1
2
1
1
2
1
1
1
2
0
0
0
1
2
0
0
1
1
1
1
1
1
1
2
1
0
0
1
0
0
0
1
0
0
0
0
1
3
0
2
0
0
1
0
0
0
2
1
2
0
0
0
1
1
1
1
0
0
0
1
0
1
2
0
1
1
2
1
1
1
0
2
0
0
2
0
0
0
2
1
2
0
1
0
1
1
2
1
3
0
1
0
0
0
0
1
0
1
2
0
1
0
0
0
0
2
0
3
0
1
1
1
1
1
0
1
3
1
0
1
1
1
2
2
0
1
0
0
1
1
1
1
0
1
0
2
0
0
1
0
0
2
0
1
2
0
2
0
0
0
1
0
2
1
0
1
0
0
2
1
1
2
2
0
1
0
1
1
1
0
1
1
0
1
0
1
1
0
2
0
2
0
0
1
0
1
0
0
2
2
0
2
1
1
0
0
1
1
0
2
0
2
0
0
0
0
1
1
1
0
0
1
2
0
1
1
1
1
0
2
2
0
2
2
0
0
2
0
2
1
1
2
0
1
0
1
1
2
2
1
2
1
2
3
1
2
0
2
3
1
1
0
0
1
2
0
1
0
1
0
0
0
1
0
0
0
1
1
1
1
0
2
1
0
1
0
1
0
0
1
0
1
1
0
1
0
2
1
0
1
0
0
1
2
2
2
0
0
1
0
2
2
0
1
2
0
2
0
1
1
2
1
0
0
1
1
0
1
2
1
1
0
0
0
0
0
1
2
1
0
1
0
1
2
0
0
0
2
0
1
1
2
0
1
0
0
1
1
2
0
0
1
1
1
2
0
0
0
1
1
1
0
1
0
2
0
1
2
1
1
1
2
0
1
0
2
1
2
1
1
0
0
2
2
0
0
1
1
0
2
0
2
1
1
0
1
2
0
2
0
2
0
1
2
0
2
1
2
1
0
0
1
1
1
2
0
0
2
0
1
0
1
1
1
1
2
0
1
0
1
1
1
1
0
2
0
0
0
1
0
1
0
1
2
0
2
0
0
2
2
0
1
0
2
1
0
0
0
1
0
1
0
2
1
2
0
0
2
3
2
2
2
1
1
0
1
2
1
0
1
0
1
1
2
2
2
1
1
1
2
1
1
0
1
1
1
1
1
0
2
2
0
2
1
1
1
2
0
1
2
0
0
1
0
0
2
0
0
0
1
0
0
0
1
0
2
1
1
1
0
1
0
0
1
0
0
0
0
1
2
0
0
0
0
4
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
2
1
0
1
2
1
2
1
1
1
0
0
1
1
0
0
1
0
2
0
0
0
2
2
1
6
1
1
1
0
0
1
2
1
1
0
2
2
0
1
0
0
1
1
2
2
1
1
0
2
1
1
1
1
1
0
0
1
2
1
2
1
1
0
1
0
1
0
0
2
0
2
0
2
2
0
0
2
0
2
1
2
1
2
1
1
1
0
1
2
1
2
0
1
2
1
1
1
0
1
0
2
2
0
0
0
1
1
2
0
0
1
1
2
0
1
2
1
1
1
0
1
0
1
1
0
1
1
1
1
1
0
0
3
0
0
0
0
0
2
1
1
1
1
2
1
0
0
2
0
1
0
1
0
1
1
1
1
0
0
1
0
0
0
1
2
0
0
0
0
2
1
0
1
0
2
0
2
1
1
2
1
1
1
1
0
1
1
0
2
0
1
1
0
2
0
0
0
2
2
2
0
0
2
1
2
0
1
1
0
2
1
0
0
0
2
1
1
0
2
1
2
0
1
2
1
1
1
2
1
1
1
1
0
2
1
0
0
1
2
1
1
1
3
2
0
1
2
0
0
0
1
1
0
0
2
2
2
1
1
0
0
0
2
1
1
2
0
0
1
0
0
0
2
0
1
1
2
0
0
0
1
3
0
0
0
4
0
0
2
0
0
2
1
0
2
0
2
0
0
0
1
1
1
0
1
2
1
0
1
0
1
0
3
1
1
0
0
0
1
2
0
1
0
1
1
0
1
2
1
1
3
1
1
2
3
1
0
0
0
0
2
0
1
1
1
1
2
1
0
1
0
2
2
1
0
0
2
0
1
2
2
0
1
0
1
0
1
0
1
1
1
0
0
0
0
1
0
0
0
0
1
0
1
1
1
1
1
0
0
0
2
2
0
1
2
2
1
1
2
1
2
1
0
0
1
0
1
1
1
0
0
1
2
0
1
0
0
0
2
0
1
1
1
0
2
0
0
0
2
1
0
0
0
0
0
0
2
1
1
1
0
1
0
0
1
0
1
1
1
2
0
1
1
2
0
1
1
0
2
1
1
2
2
0
0
2
1
1
2
0
1
2
1
0
1
0
1
0
1
2
0
1
1
2
1
2
1
0
0
0
1
1
0
1
0
0
2
2
0
0
2
1
2
1
0
0
1
1
0
0
1
0
2
1
1
1
0
1
1
2
0
0
0
0
1
1
2
0
0
1
1
2
1
2
1
0
1
2
2
0
1
2
0
0
2
1
0
0
1
2
1
0
1
1
1
1
0
1
0
0
0
0
1
1
1
1
0
0
0
0
2
0
1
1
2
2
0
1
2
1
0
0
2
0
0
1
1
0
0
0
0
0
0
2
0
1
2
0
0
1
2
1
0
0
0
1
1
0
0
0
1
1
0
1
0
2
0
1
0
2
1
0
2
0
0
0
2
0
0
1
0
0
2
0
2
0
0
0
0
2
1
0
1
3
1
0
0
0
2
2
0
1
1
0
1
2
0
1
0
0
0
1
0
1
0
1
1
1
1
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
2
1
0
2
0
0
0
0
0
0
0
0
2
2
0
2
1
2
1
0
1
0
1
1
1
1
0
0
0
1
3
2
2
1
0
1
0
0
1
0
2
1
0
2
0
1
0
1
0
0
2
2
1
1
1
1
0
1
0
0
0
1
2
2
2
1
3
2
0
1
1
1
0
3
0
1
0
1
0
0
0
1
2
1
0
1
1
0
1
1
2
0
2
0
0
0
1
2
1
0
0
2
3
2
0
1
2
1
0
0
1
1
1
0
1
0
1
1
0
1
2
1
3
2
0
0
1
1
2
2
0
1
0
1
2
2
1
1
1
0
0
0
2
2
2
0
0
0
1
2
0
1
2
1
1
0
0
0
1
0
3
0
0
0
1
1
1
1
1
0
1
0
1
2
0
2
0
1
1
1
1
1
0
2
1
0
0
2
0
1
2
1
0
0
1
1
1
1
2
0
1
1
2
0
1
1
0
0
0
2
1
1
1
1
0
1
2
2
2
2
0
2
0
0
4
1
0
0
2
1
0
1
1
1
2
1
1
0
1
0
2
0
1
2
1
1
0
0
0
0
2
1
0
0
2
2
0
1
2
1
0
0
0
1
0
1
1
1
1
0
1
2
0
1
2
1
1
1
1
0
1
2
1
0
0
2
1
2
0
1
0
0
2
0
1
0
1
1
0
1
1
0
0
0
2
1
2
2
0
0
1
0
2
1
0
0
1
0
0
1
1
0
1
1
1
2
0
0
0
3
0
2
2
4
2
1
1
1
1
0
0
1
1
0
0
2
0
1
0
1
2
1
2
1
2
0
0
2
0
2
0
0
0
0
1
0
0
2
1
1
0
0
1
1
2
0
1
1
0
0
4
1
0
0
5
1
2
2
0
2
2
1
0
0
0
1
0
0
0
2
1
1
0
0
1
0
0
1
0
0
1
0
0
3
1
2
0
0
1
0
2
2
1
1
2
0
0
0
1
1
1
1
2
1
0
1
0
0
1
1
0
0
0
0
0
0
2
0
1
1
0
2
0
0
0
0
0
0
2
0
1
1
0
0
3
0
2
0
1
1
0
1
2
0
1
0
2
0
3
1
3
0
1
2
2
0
1
2
2
1
0
0
0
1
1
2
1
2
0
0
1
1
1
1
0
2
0
1
1
1
0
0
0
1
1
2
0
1
0
2
0
0
0
0
2
1
0
3
1
1
2
2
1
1
2
0
1
0
1
0
0
1
1
0
2
0
1
2
1
0
2
1
2
0
1
0
1
2
0
1
0
1
0
0
0
0
0
1
0
1
1
2
1
1
2
1
2
1
2
1
0
3
0
0
0
0
1
2
2
2
1
0
1
0
1
1
0
1
2
1
0
1
2
2
2
0
0
1
1
1
1
1
0
1
1
0
1
0
2
1
0
1
0
1
2
1
0
0
0
0
2
0
0
0
1
1
1
0
0
2
1
1
1
0
0
0
2
1
0
1
1
0
1
1
1
0
0
1
1
1
1
2
0
4
1
2
2
0
0
0
0
1
0
0
1
2
0
2
0
2
1
1
2
2
0
2
0
2
2
1
1
2
2
1
1
1
2
1
1
1
1
0
0
1
0
0
2
0
2
1
0
1
3
1
0
2
0
2
1
1
2
1
0
1
1
1
0
2
2
1
1
1
0
1
0
0
1
1
0
1
0
0
0
0
1
1
0
1
0
0
0
1
1
0
0
1
0
1
0
0
2
2
0
3
1
0
1
2
2
2
1
1
2
0
0
0
0
1
1
1
1
1
1
0
1
1
0
1
2
1
0
1
0
2
1
1
0
2
1
1
1
2
0
1
0
1
2
2
1
2
1
0
0
2
1
0
1
1
0
1
1
0
1
1
1
1
0
1
2
0
2
1
0
2
2
1
0
0
2
1
1
0
1
1
1
3
1
1
2
2
1
0
1
2
1
2
2
1
1
1
2
1
2
0
2
1
0
2
2
0
1
2
0
1
1
0
1
1
0
1
0
2
3
0
0
1
1
2
0
2
1
1
0
1
2
3
0
0
1
1
0
0
0
1
2
0
1
1
2
0
0
1
0
0
0
2
2
1
1
0
1
1
2
2
1
0
1
0
1
1
1
0
0
0
1
2
2
0
2
1
1
0
2
1
2
0
1
0
0
0
2
0
0
0
1
1
0
1
1
0
0
2
1
0
0
1
1
0
0
2
1
2
1
0
1
1
0
1
1
2
1
0
0
1
1
1
1
2
1
1
1
2
0
0
1
4
2
1
2
1
2
1
0
0
0
1
0
0
1
1
1
1
1
0
1
2
0
1
1
0
1
0
0
0
0
1
2
0
1
1
2
0
2
0
0
1
0
0
0
2
1
1
0
1
0
0
2
2
2
1
0
0
0
1
1
0
1
1
1
0
1
1
2
0
1
1
1
1
0
1
0
0
2
2
0
2
1
0
2
0
0
0
0
1
2
0
0
2
0
2
0
0
0
0
1
0
0
1
1
1
2
1
1
0
0
0
0
1
0
0
0
1
0
1
1
2
0
0
1
2
0
2
1
0
1
0
1
0
1
2
2
0
1
1
0
0
0
1
0
1
0
1
1
1
0
0
1
1
1
0
0
1
1
2
3
1
2
0
1
2
1
0
1
2
0
1
0
0
0
2
2
0
3
2
0
2
1
1
1
1
1
0
2
0
4
0
0
0
1
0
2
0
1
0
0
0
0
1
1
0
2
0
0
0
0
0
1
1
0
2
1
1
0
1
1
0
0
1
0
0
0
1
1
2
2
3
0
0
2
2
1
0
1
0
2
1
0
0
1
0
0
1
0
1
2
0
2
0
1
2
1
0
0
1
0
1
0
1
0
2
2
1
0
1
1
2
0
2
1
3
1
1
3
2
0
0
2
0
1
1
1
0
1
2
1
1
0
1
2
0
0
1
1
1
3
1
3
0
0
0
0
0
0
2
2
0
2
1
2
0
1
1
2
0
1
2
0
1
0
1
1
2
1
0
1
0
0
0
1
0
2
2
1
0
1
1
2
0
0
0
1
1
0
0
0
1
2
2
0
1
0
0
2
1
0
0
1
0
0
0
0
2
2
1
1
0
1
0
0
0
2
1
2
1
0
1
0
0
2
1
0
1
2
1
2
2
1
2
1
1
0
0
1
0
1
2
2
0
1
2
0
1
2
1
0
1
0
0
2
0
2
1
2
1
2
1
0
1
3
0
1
0
1
0
1
2
1
0
0
1
1
1
0
1
1
1
1
0
0
1
1
0
0
0
0
1
1
1
2
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
1
1
0
2
1
0
0
0
1
0
1
1
1
2
1
2
1
0
1
0
1
2
0
1
1
0
2
1
1
0
0
0
0
2
1
0
0
1
2
0
2
2
2
0
2
2
1
0
1
0
0
1
1
1
0
1
1
1
1
1
2
1
0
1
0
2
2
2
0
0
1
1
1
1
0
1
1
2
0
0
1
1
0
0
2
1
1
0
0
1
0
2
1
1
0
1
0
1
1
1
1
0
0
1
1
1
1
1
0
0
2
1
1
3
0
0
2
1
0
0
0
0
1
0
1
1
3
1
0
1
1
0
1
0
1
2
2
1
0
3
2
1
0
2
2
0
2
0
1
1
1
1
0
0
1
2
0
0
1
5
0
1
1
0
0
0
0
2
2
0
1
0
0
0
0
1
1
0
2
2
1
3
1
0
0
1
1
0
0
0
1
1
0
0
0
1
0
1
2
2
1
0
2
1
2
0
0
1
1
0
2
0
1
0
1
1
0
0
1
1
2
2
1
2
1
0
1
1
2
1
1
1
0
0
2
2
0
0
0
1
0
2
0
0
2
1
0
1
1
0
2
1
1
2
1
0
0
0
0
1
0
2
1
2
1
1
1
2
2
0
2
1
1
2
1
0
1
0
0
1
0
0
0
0
1
0
0
2
1
1
0
0
1
2
0
0
0
0
1
0
1
1
0
0
2
3
1
0
1
1
0
0
2
3
0
0
1
1
0
1
1
0
0
5
0
1
1
0
0
0
0
1
1
1
2
0
0
0
1
1
0
0
0
1
1
0
1
0
1
0
0
1
1
0
1
1
1
1
0
0
2
2
0
0
0
1
2
0
1
0
2
1
0
2
0
2
1
0
0
2
2
1
2
2
0
0
1
0
0
1
1
0
0
1
1
0
1
0
0
2
0
2
1
2
1
0
1
0
0
0
2
2
2
2
0
1
1
2
2
0
0
0
1
0
0
2
0
0
1
0
0
1
0
2
0
0
1
1
1
1
1
0
1
0
0
1
1
1
1
2
0
2
1
2
1
0
1
1
2
0
0
1
0
2
2
2
1
1
0
1
1
0
1
3
0
1
1
0
1
0
1
1
1
1
0
2
1
1
0
1
1
1
2
1
1
0
1
1
0
1
0
1
0
0
2
2
1
2
0
0
1
1
1
0
2
1
1
2
0
0
1
1
0
1
1
1
1
0
0
0
2
0
0
1
1
0
2
0
0
3
1
1
0
0
0
0
0
0
1
1
0
2
0
0
0
1
0
0
1
1
1
1
1
1
1
8
0
1
1
2
1
1
2
1
1
1
1
0
1
0
2
0
1
2
1
0
0
1
0
2
0
0
2
1
1
0
1
2
2
1
1
0
1
0
1
2
1
6
0
0
1
0
0
0
2
2
2
0
1
3
0
1
1
0
1
2
0
1
0
1
1
2
1
0
0
0
0
0
2
0
1
0
0
2
1
0
1
1
2
1
0
1
0
1
2
0
2
0
0
2
0
0
2
1
1
1
1
2
0
0
0
2
1
1
1
0
1
1
1
1
0
0
1
1
1
1
2
2
0
0
1
2
2
0
1
1
2
1
0
2
2
0
1
0
1
1
2
1
0
2
1
1
0
1
0
1
1
0
1
2
0
2
0
1
1
1
1
0
0
0
2
1
1
1
2
0
2
0
0
1
2
0
1
0
2
1
2
2
0
0
0
1
1
2
2
0
2
0
1
1
2
0
0
0
1
2
0
1
1
1
1
1
2
1
1
0
2
0
2
1
2
1
1
1
0
0
1
1
1
2
0
0
0
1
2
1
1
0
2
0
2
0
1
1
0
2
1
1
0
0
1
1
0
0
0
1
1
2
0
2
0
1
1
0
1
2
1
1
0
2
1
2
1
2
2
1
0
1
2
1
1
0
2
1
1
0
2
0
0
1
1
1
1
0
0
0
0
1
1
2
0
0
0
1
2
2
0
1
0
0
1
0
2
0
1
1
1
0
0
0
0
0
1
0
0
2
0
1
1
2
1
0
1
1
1
1
1
0
1
2
1
1
2
0
0
1
2
1
2
2
1
1
0
0
2
0
2
2
1
1
1
0
1
2
2
0
0
0
2
1
0
1
1
1
0
1
0
3
2
1
0
1
0
1
1
1
1
2
2
1
1
0
0
0
0
2
0
1
1
1
2
3
1
1
0
0
0
0
2
0
1
0
2
0
2
0
0
1
2
1
1
0
0
2
2
1
0
1
0
1
0
1
1
1
1
1
0
2
1
2
1
0
0
0
1
2
2
1
1
2
0
0
2
0
0
1
1
2
1
0
1
3
0
1
1
1
1
0
1
1
0
1
0
2
1
0
0
2
1
1
1
2
0
0
0
1
1
2
0
0
1
0
2
1
0
1
2
1
3
0
0
1
2
1
0
0
1
0
1
1
1
0
1
2
0
0
0
1
2
0
1
0
2
0
2
1
0
0
0
1
1
0
0
3
1
2
1
1
0
0
2
1
1
1
0
1
1
2
2
0
0
1
0
4
0
0
1
0
0
2
1
0
2
0
2
1
0
1
2
2
0
0
0
0
2
0
0
1
1
1
1
1
0
0
1
1
2
0
0
0
2
0
2
1
0
1
1
2
0
1
0
0
1
1
0
0
1
2
0
2
0
2
0
1
1
1
1
1
2
0
2
2
0
0
0
2
0
1
1
0
0
0
1
2
2
1
1
0
0
1
0
2
0
2
1
0
2
1
1
0
2
1
1
1
0
2
0
1
0
1
0
2
0
0
2
0
1
1
0
0
0
2
0
0
0
0
1
1
2
1
1
2
3
1
1
1
2
1
1
1
1
1
2
2
0
1
0
0
1
1
0
1
0
2
1
0
1
0
0
0
0
1
2
0
0
1
0
3
0
0
0
0
0
1
1
0
2
2
1
1
1
1
0
1
2
1
0
2
2
0
1
0
0
1
2
1
1
1
1
2
2
0
2
0
2
0
2
0
0
2
1
0
0
0
0
0
0
0
2
1
1
1
2
1
2
1
0
0
1
1
0
0
0
1
0
0
1
0
2
0
1
2
0
0
1
1
2
0
1
0
1
1
2
0
0
1
1
1
1
1
0
2
0
1
2
0
1
1
0
0
0
1
2
1
2
5
0
2
0
1
4
1
1
0
1
1
0
1
1
0
1
1
0
1
0
0
0
2
2
0
2
0
1
0
2
2
1
1
0
1
1
2
0
1
2
1
2
1
1
0
1
0
0
2
1
2
0
0
1
1
0
2
2
1
1
2
0
0
2
0
1
1
0
2
0
0
1
0
0
0
1
0
1
2
2
0
0
0
1
2
0
1
1
1
0
0
0
0
0
0
0
0
3
1
0
2
0
0
1
1
0
2
0
0
1
0
0
2
1
2
0
1
2
0
2
1
1
1
0
0
2
0
1
1
2
2
1
0
2
1
0
2
0
1
0
2
1
0
1
0
2
0
0
0
0
1
0
0
0
1
2
0
0
0
1
2
0
1
1
1
2
1
0
1
0
1
3
0
2
0
1
0
2
2
1
1
2
0
0
1
1
1
0
0
1
0
0
1
0
1
0
0
2
2
1
1
1
2
2
0
2
2
0
1
0
1
0
1
0
1
0
2
0
1
2
0
1
0
1
2
1
1
0
2
1
1
2
1
1
1
2
1
0
2
2
1
1
1
1
2
1
1
1
0
1
2
1
1
3
0
2
0
1
1
0
0
0
1
1
0
2
0
0
2
0
0
0
0
0
1
0
1
0
0
0
2
1
1
0
1
0
0
0
0
1
1
0
0
1
0
0
0
2
1
0
1
0
0
1
1
0
1
0
1
1
1
0
0
0
1
0
0
1
0
0
2
2
0
1
2
1
0
2
2
0
0
0
0
0
0
0
0
2
2
1
2
1
2
0
2
1
1
0
2
1
0
1
1
1
2
0
2
2
0
1
0
0
1
0
0
2
2
0
2
2
1
1
2
1
1
2
1
0
1
1
0
2
2
0
0
0
1
0
0
1
0
1
0
1
0
1
0
0
2
1
0
0
0
0
1
0
1
3
0
0
1
0
2
2
1
0
2
2
0
1
0
1
0
1
0
1
1
0
0
0
0
1
1
2
0
0
0
1
0
1
0
0
1
0
1
2
0
1
1
1
0
1
2
0
1
0
0
1
2
2
1
2
2
1
1
1
1
0
1
0
2
0
1
0
1
1
0
1
1
0
2
2
2
2
2
1
1
2
1
0
1
0
1
2
0
1
0
1
2
2
0
1
0
0
1
1
1
2
0
1
1
1
0
1
0
0
0
1
1
2
2
0
0
2
1
2
2
0
0
0
1
0
1
1
2
0
3
1
1
1
1
1
0
0
0
1
1
0
0
1
0
1
1
0
2
1
1
2
2
1
0
0
2
2
0
1
1
0
1
1
0
1
1
1
1
0
2
1
1
1
0
0
1
1
0
1
1
0
0
2
0
0
1
0
2
1
1
2
0
0
2
0
0
0
1
0
1
0
1
1
1
1
0
1
0
1
0
2
0
0
0
2
1
2
1
1
2
0
0
2
0
0
0
2
1
2
0
1
0
2
2
1
1
1
0
0
0
0
1
1
0
0
0
2
0
1
0
1
0
0
1
1
1
0
0
0
1
0
2
1
1
1
1
0
1
1
0
2
2
2
0
0
1
0
0
0
2
0
0
1
1
1
0
1
2
1
0
1
2
0
2
0
0
2
2
0
0
0
0
2
1
0
2
0
2
0
2
1
0
1
1
2
1
1
2
0
0
0
1
1
3
0
1
1
2
6
2
0
2
1
1
1
0
0
1
2
1
1
1
1
1
0
0
2
1
0
2
0
1
2
0
2
1
0
1
0
0
1
2
1
2
1
1
0
0
1
0
2
2
1
1
0
1
0
0
0
0
1
1
0
1
1
0
0
1
1
0
1
1
1
1
0
2
2
2
0
1
1
2
2
0
0
0
1
2
0
0
0
0
2
0
0
1
0
2
2
1
1
0
1
1
0
1
0
1
1
1
0
2
2
0
0
1
2
2
1
0
3
2
0
0
1
2
0
2
1
2
0
2
2
1
1
0
0
2
1
0
0
0
1
0
2
2
2
1
1
2
1
1
0
0
0
1
0
0
2
0
2
1
1
1
1
0
0
2
1
2
1
0
1
1
2
0
2
0
2
0
3
0
1
1
0
0
0
2
1
1
0
2
2
0
2
1
1
1
1
0
1
0
0
2
0
0
0
0
1
1
0
0
0
0
1
1
0
0
2
1
0
2
0
1
0
1
0
0
2
0
1
2
1
0
1
0
1
0
0
0
0
0
1
2
1
0
0
2
0
0
1
0
0
0
0
0
1
2
0
2
2
2
0
2
0
1
0
1
1
0
1
0
1
0
0
1
2
1
1
0
2
0
0
0
1
2
2
0
1
0
2
1
1
1
0
2
1
1
0
1
0
2
0
0
1
2
0
1
1
2
0
1
0
2
1
0
1
0
0
1
1
0
1
1
1
1
2
1
1
0
1
1
0
1
1
1
2
0
2
0
1
0
1
0
1
2
1
2
0
1
1
1
1
2
1
1
2
2
0
2
1
1
0
1
0
0
1
1
1
2
1
1
0
1
2
0
2
0
2
0
2
1
0
0
2
0
1
0
3
2
1
0
0
1
4
0
1
1
1
1
3
1
0
0
1
2
0
0
1
1
1
1
1
2
0
1
0
0
0
0
1
1
1
0
0
0
0
2
0
9
0
1
1
0
0
2
1
0
0
2
0
0
0
0
0
0
0
2
2
1
0
1
0
0
0
2
0
2
0
0
1
1
1
2
0
0
1
0
0
0
1
1
0
0
0
2
0
1
1
2
0
2
1
0
1
2
0
1
2
2
2
1
1
0
2
0
1
0
2
1
1
1
1
1
1
0
0
1
0
0
2
1
1
0
1
2
2
1
0
0
0
2
2
1
0
0
0
0
1
1
1
0
1
1
1
1
2
0
0
2
1
0
3
0
1
0
1
1
1
2
0
1
2
2
2
2
2
1
1
0
2
0
1
1
1
0
1
0
0
0
1
0
2
1
2
2
1
1
1
1
1
2
1
1
0
0
1
0
0
1
1
1
1
0
0
0
1
2
2
2
1
1
1
0
1
1
3
1
1
0
2
1
1
0
1
0
0
0
2
0
1
3
0
2
2
1
1
0
0
1
1
0
2
2
1
1
1
0
1
2
1
2
2
1
1
1
1
2
2
1
1
1
2
1
0
2
2
0
1
2
0
2
2
0
2
1
2
0
0
1
0
1
0
2
1
1
2
1
0
0
2
2
0
1
0
2
1
0
0
0
1
2
0
1
0
0
2
1
0
0
0
1
0
0
1
0
0
2
2
0
0
1
2
1
1
0
0
1
2
1
1
0
2
2
0
2
1
2
2
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
1
1
1
0
0
1
1
0
1
0
0
1
1
1
1
2
1
1
2
1
0
0
2
0
1
0
1
2
0
1
1
1
1
0
1
1
1
1
0
1
0
0
1
1
1
0
0
1
0
1
2
2
0
3
1
0
0
1
1
1
1
2
1
0
2
1
2
2
0
2
2
0
0
1
1
2
1
1
0
0
2
1
1
2
1
1
1
2
1
1
0
2
0
1
1
1
1
1
1
2
1
2
1
0
1
1
0
1
0
0
0
1
0
0
2
1
0
1
1
1
2
0
0
0
1
3
0
1
0
2
0
0
2
0
1
1
0
0
2
2
0
1
1
1
1
0
0
2
0
0
1
0
0
1
4
1
1
1
2
0
3
0
0
2
2
2
1
0
1
1
0
0
0
2
0
0
0
0
2
1
0
0
2
0
1
2
2
2
0
0
0
1
1
1
2
0
2
1
0
0
0
2
0
2
1
1
1
2
2
1
2
0
0
2
1
0
2
0
1
1
1
0
1
2
1
1
0
1
0
2
1
0
0
2
2
2
0
2
2
0
2
0
0
1
1
1
0
1
1
1
2
1
2
2
2
0
1
1
1
0
2
2
0
1
1
1
2
0
0
0
2
0
2
2
1
2
0
2
1
0
0
0
0
0
0
1
2
1
0
0
2
2
3
0
1
2
0
0
2
1
0
1
0
1
2
1
1
1
0
0
0
0
0
1
1
0
1
2
0
1
2
0
1
1
2
2
1
0
0
0
1
0
0
0
1
1
0
0
2
0
1
0
0
0
0
0
1
1
0
0
0
1
1
2
0
0
1
0
2
1
1
0
1
0
0
2
1
0
0
1
1
0
0
1
1
2
0
0
0
1
0
0
1
1
1
2
1
1
0
0
1
1
2
2
0
0
0
1
0
0
1
0
1
1
1
1
0
1
2
0
0
1
0
0
0
1
2
0
1
2
0
1
1
1
2
2
0
2
2
3
0
0
1
2
2
0
2
0
0
2
1
0
0
0
0
0
0
1
1
1
1
1
0
2
1
0
0
1
1
0
1
0
1
1
1
1
0
2
1
1
2
2
0
1
0
0
0
1
2
1
2
2
0
2
0
0
0
0
2
1
2
1
0
1
0
2
1
0
1
1
0
1
0
0
1
2
0
0
1
0
1
1
0
1
1
2
0
0
0
0
0
1
0
0
0
1
1
1
1
1
1
2
0
1
1
2
0
0
0
2
1
1
2
1
1
1
0
0
1
1
1
1
0
1
2
1
0
0
1
0
0
0
2
1
0
2
3
1
1
2
2
2
2
2
2
1
0
1
1
0
1
1
0
0
1
0
0
0
0
2
1
1
1
0
1
0
1
2
0
0
2
0
0
1
0
2
2
1
1
2
0
1
1
1
1
0
1
0
0
0
0
1
0
2
0
1
0
1
1
2
2
1
0
1
2
1
1
1
0
2
0
0
1
1
1
1
0
0
1
1
0
1
0
0
1
0
0
1
0
2
1
0
2
1
2
0
2
0
0
1
2
1
0
1
0
1
0
1
1
0
0
0
0
2
0
1
2
1
0
0
2
2
2
0
1
0
1
1
1
1
2
0
0
1
0
1
0
1
0
0
2
1
1
1
0
1
1
1
1
0
1
1
1
0
0
0
1
1
0
0
0
2
0
0
1
1
2
1
0
1
2
0
1
1
2
0
0
0
1
0
0
0
0
0
2
1
1
1
1
3
0
2
0
0
2
0
0
1
1
2
0
0
1
0
1
0
1
1
1
1
2
2
1
0
0
0
1
1
1
0
2
0
0
0
1
0
1
0
2
1
0
0
1
2
0
0
1
2
2
1
2
1
1
0
0
0
0
0
1
0
2
1
0
0
0
0
2
1
2
0
0
0
2
0
1
0
0
1
2
0
1
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
1
1
0
2
1
2
0
2
2
1
1
0
1
0
0
0
1
2
0
0
2
2
0
0
2
1
0
0
2
1
0
1
1
2
0
1
0
2
0
0
1
0
0
0
2
0
1
1
1
0
0
2
2
0
2
0
1
1
1
1
0
1
1
0
1
0
1
0
0
1
1
1
1
0
0
1
0
0
3
0
0
1
1
1
1
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
2
1
2
1
1
1
2
0
1
2
2
0
0
0
1
1
2
1
0
1
0
1
1
0
1
1
1
0
1
0
0
1
1
1
0
1
2
1
0
0
0
1
1
0
1
1
1
1
2
1
1
0
1
0
2
2
1
0
0
0
2
0
2
0
1
1
2
0
0
1
2
0
1
1
0
1
1
0
0
0
1
0
1
1
0
0
1
0
2
1
1
1
1
0
1
1
0
1
0
1
1
1
0
0
2
0
1
1
1
1
1
2
1
0
2
2
1
0
0
2
0
0
1
1
2
2
0
2
1
0
1
0
1
1
1
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
1
0
1
0
0
0
0
0
1
1
0
2
1
2
0
1
0
0
1
0
1
0
1
1
1
2
1
0
1
0
1
0
1
0
1
1
2
1
1
2
0
0
1
0
0
0
1
2
3
1
1
1
1
1
0
1
1
2
1
2
1
2
1
1
0
0
1
2
0
0
0
1
1
0
2
1
1
1
2
1
1
2
0
2
0
0
0
1
0
2
0
0
1
0
1
2
3
1
1
0
0
0
1
0
0
1
5
1
2
1
1
2
1
1
2
1
0
1
0
2
1
0
2
0
1
1
1
0
1
2
1
0
1
0
0
0
1
0
2
2
0
2
0
2
1
1
1
1
1
0
1
0
0
1
1
0
2
1
0
0
0
0
2
0
2
1
1
0
2
1
1
0
1
2
1
2
0
1
1
1
1
1
1
1
2
2
1
0
0
0
0
3
2
0
1
2
0
1
0
2
2
0
1
0
1
0
0
1
1
1
1
0
0
0
1
0
1
1
1
1
1
0
1
2
1
1
0
1
0
2
2
3
0
2
1
0
1
0
0
1
1
2
1
1
2
0
1
2
2
1
1
0
1
7
2
2
1
1
1
2
0
1
1
2
0
1
1
0
0
0
1
1
1
0
1
1
1
0
1
1
0
0
2
0
0
0
0
0
1
0
2
1
1
1
1
0
1
0
1
1
2
1
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
1
2
2
1
1
1
1
2
1
0
0
0
0
2
0
1
1
1
0
1
0
0
2
2
1
0
0
2
0
0
1
2
0
0
1
2
1
1
0
1
0
2
0
1
2
1
0
2
0
2
0
2
1
1
2
0
1
1
1
1
2
0
1
2
1
1
0
1
1
2
0
0
1
0
1
2
1
1
1
1
2
1
1
0
2
0
1
3
0
0
2
2
0
1
0
2
1
1
1
0
2
1
0
0
1
2
1
1
1
0
0
0
1
0
0
0
0
1
1
1
0
2
1
2
2
1
2
2
0
0
2
2
1
1
1
2
1
0
2
0
0
0
2
0
0
1
1
2
0
2
0
1
2
2
1
0
1
0
0
0
2
1
1
2
1
0
0
1
1
5
0
1
1
2
0
0
2
0
2
2
0
0
1
0
1
0
0
0
1
2
1
2
1
0
0
1
2
0
0
1
0
1
0
1
1
0
0
0
0
1
0
1
1
1
0
1
1
1
1
0
0
2
1
0
0
1
0
0
0
2
0
0
1
2
1
1
1
2
0
0
0
0
0
1
1
0
0
1
0
0
1
1
2
1
0
1
0
1
0
1
0
1
1
0
2
0
1
0
0
0
2
1
0
0
0
1
1
1
1
1
0
0
0
0
1
0
0
0
1
0
1
0
1
2
1
2
2
0
0
0
0
0
1
2
0
1
0
1
1
1
0
0
1
1
1
0
1
3
0
0
2
1
0
1
0
1
0
1
4
0
0
0
1
0
1
2
0
0
1
2
0
1
0
1
1
2
1
1
0
1
2
1
0
1
2
1
1
2
1
1
0
1
1
1
2
2
0
1
1
1
0
0
1
1
2
0
1
0
0
1
2
1
0
1
1
1
0
2
0
0
1
0
1
2
0
1
1
1
0
2
1
1
0
1
0
2
0
1
0
1
2
2
0
2
1
1
2
1
1
1
0
1
1
0
0
0
0
2
1
1
0
1
2
1
1
2
1
2
0
1
1
1
2
1
0
2
2
0
1
1
2
1
0
0
0
2
2
1
0
0
1
0
0
1
1
0
1
0
2
0
0
0
2
1
2
3
1
0
0
0
0
1
1
2
1
2
1
0
0
2
0
2
0
1
1
0
1
0
0
2
0
0
2
0
0
0
1
1
1
1
2
0
1
0
0
1
0
4
0
0
2
2
0
2
2
0
0
1
2
1
2
0
0
1
0
1
1
0
1
2
3
1
2
0
1
0
2
0
0
2
2
1
1
0
2
0
1
2
2
1
1
2
1
2
0
2
1
1
0
2
5
0
0
1
2
0
1
0
0
2
0
2
1
0
1
2
2
1
1
0
1
0
0
1
0
0
1
2
1
2
9
2
1
2
1
3
1
0
0
1
0
0
1
2
0
1
0
1
1
0
1
0
1
1
1
2
2
0
2
1
1
0
0
17
0
2
2
0
0
2
1
0
1
0
2
0
2
1
1
1
1
1
1
1
1
0
1
2
0
2
2
2
1
0
0
1
0
0
1
1
2
1
1
1
1
1
1
2
2
2
0
0
2
1
2
1
1
1
1
1
1
1
2
2
1
0
1
1
1
2
2
1
1
0
0
0
1
0
0
0
2
2
1
0
1
0
1
0
0
2
0
0
0
1
0
0
1
2
1
0
0
1
0
0
1
1
0
1
2
0
0
0
1
3
2
2
1
1
1
0
0
1
1
2
1
3
1
0
1
2
1
0
0
1
1
2
0
2
0
0
1
2
1
1
2
1
0
1
0
0
1
0
2
1
1
0
0
2
0
0
0
0
1
2
1
1
0
2
2
0
2
1
1
0
0
1
0
0
1
1
0
0
1
0
1
0
2
0
0
0
2
1
1
0
2
1
2
1
1
0
0
0
1
0
1
0
1
1
0
1
1
2
1
1
2
2
0
0
0
0
0
1
0
1
2
1
1
0
2
0
0
2
1
0
4
0
0
1
0
2
0
1
2
0
0
1
1
1
0
2
0
1
0
1
0
1
2
0
1
0
2
1
0
1
1
2
2
2
0
1
1
0
2
2
0
1
1
1
2
2
1
0
2
0
1
0
0
2
2
0
1
1
1
0
0
1
1
1
2
0
0
0
0
2
0
1
0
1
0
0
0
1
1
1
1
0
0
1
2
1
2
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
2
2
1
0
0
0
1
0
0
1
1
2
1
0
0
1
1
0
1
1
1
1
0
1
2
0
0
2
1
2
0
0
1
0
1
0
0
0
0
1
1
0
1
0
0
0
0
1
1
0
2
1
0
0
2
1
0
2
2
2
1
2
1
1
0
1
1
0
1
1
0
3
1
0
0
0
0
0
2
2
0
1
1
0
1
3
2
1
1
2
0
1
1
2
0
0
1
1
1
0
2
1
1
0
2
2
1
0
1
0
0
2
0
2
0
2
0
1
0
2
1
0
2
0
2
2
1
0
2
3
0
0
1
1
1
2
1
2
0
0
0
0
2
0
2
1
0
2
1
0
0
1
0
2
0
0
1
0
2
1
0
2
2
2
1
2
2
2
0
1
1
2
0
1
0
1
1
0
2
0
0
1
2
1
1
0
0
1
3
2
1
1
1
2
0
0
2
0
2
0
1
0
2
2
0
2
1
1
0
0
2
0
2
0
0
2
0
0
1
1
2
1
0
1
0
1
0
1
1
1
1
0
0
1
1
0
0
0
1
0
2
0
1
1
0
2
0
1
2
0
0
1
0
1
3
1
2
1
0
2
0
1
0
2
2
0
2
0
3
0
0
1
0
0
1
0
0
1
2
1
0
1
2
0
1
0
2
5
1
2
1
0
1
1
1
0
1
1
0
1
1
1
1
0
2
1
0
1
0
1
2
0
1
0
0
0
1
1
1
1
1
2
0
0
2
2
0
2
1
0
2
0
2
0
0
0
1
1
0
1
0
1
0
1
2
1
2
0
2
0
1
1
2
0
0
2
1
2
0
1
0
1
1
2
2
0
1
1
2
2
1
0
1
1
0
2
0
1
2
1
1
1
1
2
1
0
3
0
0
0
1
0
0
0
1
2
1
1
1
1
0
1
0
0
0
0
1
2
0
2
0
1
2
2
1
0
1
2
6
0
2
0
0
0
1
2
1
2
0
0
2
0
2
2
2
0
1
0
0
0
2
2
2
0
0
1
0
0
1
1
0
0
0
0
0
1
2
1
0
2
2
0
1
1
0
1
1
0
0
1
2
1
0
0
2
0
0
1
1
1
0
1
3
0
1
0
1
1
1
2
1
1
1
0
0
1
1
0
1
0
0
1
2
1
1
1
1
1
2
2
0
2
0
1
1
1
1
2
1
0
1
1
2
1
0
1
0
0
0
3
1
0
1
0
2
0
2
0
1
0
1
0
1
2
0
1
0
1
1
0
1
0
2
1
1
1
0
0
1
1
3
1
1
0
0
0
2
0
0
0
0
2
1
0
0
2
0
0
0
1
0
2
1
0
0
0
1
1
1
1
1
2
1
2
0
0
0
2
1
1
0
2
0
1
0
0
1
0
1
0
0
1
0
1
1
0
2
0
2
1
2
0
1
0
2
0
0
1
0
1
1
1
0
0
1
2
0
1
1
0
1
1
2
0
1
2
1
1
2
0
1
0
0
0
0
1
1
1
0
0
1
0
2
0
1
2
0
1
1
2
2
1
0
0
0
1
0
2
1
0
1
1
1
0
1
0
1
1
2
0
2
0
0
1
0
1
1
2
2
0
1
2
0
0
1
1
2
0
0
1
0
0
2
0
0
0
1
2
1
1
2
1
1
1
1
0
2
1
1
2
1
1
1
2
1
1
0
1
2
2
0
0
0
0
1
1
0
0
1
0
1
1
0
0
1
0
1
0
0
0
1
2
0
0
1
2
0
0
1
1
2
0
0
0
0
1
0
1
1
2
0
1
1
1
0
1
1
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
1
0
1
1
0
0
0
0
2
3
0
0
0
0
1
1
2
0
2
2
1
1
1
1
1
3
1
2
1
2
2
0
2
1
0
1
1
3
2
0
1
1
2
1
1
1
1
0
0
0
0
0
2
0
2
0
1
4
0
1
1
1
1
1
0
0
0
2
2
2
0
1
2
1
2
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
3
2
0
1
1
0
1
0
2
2
2
2
1
0
1
1
1
1
2
1
0
0
0
1
2
2
3
0
2
1
1
2
1
2
1
1
2
0
0
1
0
1
1
1
0
3
2
2
1
1
2
0
1
0
2
1
1
2
4
1
1
1
1
2
0
1
1
2
0
0
2
0
0
0
2
0
3
2
1
2
0
0
1
0
0
2
0
2
1
0
1
1
0
1
2
2
0
0
1
1
1
0
0
1
1
2
1
1
1
0
1
1
0
2
0
0
0
1
1
1
0
1
0
2
1
1
2
1
1
15
0
1
2
2
0
2
2
0
1
0
1
1
1
0
2
1
0
2
2
0
1
1
1
0
0
2
1
1
2
0
0
2
1
1
2
1
0
0
2
2
2
1
1
1
0
0
2
0
1
0
2
1
0
1
2
0
1
2
0
1
1
1
1
1
0
0
0
0
1
0
1
1
0
0
2
1
0
0
0
0
1
0
1
0
1
1
0
1
1
0
2
1
0
1
1
0
1
2
1
1
2
0
1
1
1
0
2
1
0
2
2
2
2
1
1
1
1
1
0
0
2
0
1
0
2
1
1
1
2
0
1
1
2
0
1
0
2
0
1
0
1
0
0
0
0
1
1
0
2
1
1
2
0
0
0
2
3
0
2
0
0
1
3
2
0
1
0
2
2
0
1
1
1
0
0
0
0
1
0
1
0
1
0
1
2
1
1
1
2
1
2
0
0
1
1
1
0
0
1
2
1
0
2
0
0
0
2
1
1
1
1
0
1
1
0
0
1
0
2
2
2
1
1
0
2
0
3
1
2
0
1
2
0
1
0
1
0
1
1
2
1
0
0
1
1
0
0
1
1
2
2
2
1
0
3
1
1
1
0
1
1
2
1
1
2
1
0
0
1
2
0
0
0
0
1
2
0
1
0
2
0
1
2
0
1
1
1
0
2
0
0
2
2
0
1
0
0
0
0
0
0
2
2
2
0
2
1
0
0
2
1
1
2
1
2
0
1
1
0
1
0
1
2
1
2
1
2
1
0
1
0
0
0
3
1
0
2
1
2
1
2
2
2
0
1
2
1
0
2
0
2
1
1
1
1
1
0
2
0
0
0
1
0
2
2
0
0
1
1
2
0
1
1
1
1
0
1
1
1
0
2
0
0
2
1
0
1
1
1
1
2
0
1
0
1
1
2
1
1
1
0
0
2
0
2
2
1
0
2
0
2
0
1
0
1
1
1
2
1
1
0
1
0
0
1
0
2
2
0
0
1
2
0
0
1
1
1
0
0
1
0
2
2
0
2
0
1
1
1
0
2
2
0
0
1
2
0
0
0
1
2
1
1
2
2
1
0
0
0
2
0
1
1
0
2
0
1
2
0
0
0
0
0
2
1
1
0
0
0
0
2
0
1
0
2
1
2
0
0
2
2
0
1
0
2
1
0
0
2
1
1
0
0
0
0
1
0
1
0
2
0
1
2
0
1
1
1
1
0
0
1
1
0
1
1
1
0
1
0
1
1
1
1
2
0
2
2
1
2
1
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
4
1
2
0
2
1
1
2
0
0
0
2
1
1
1
2
1
0
1
0
1
0
1
0
0
2
0
1
2
1
1
1
2
2
1
0
1
2
1
1
1
1
1
0
0
2
1
0
1
1
2
0
1
1
0
1
0
1
0
0
1
0
4
0
2
1
0
0
0
1
0
0
0
1
1
1
1
1
1
0
2
1
2
1
1
2
0
0
1
0
0
0
1
2
0
0
2
0
0
1
1
1
0
0
0
1
1
0
0
0
0
1
0
1
0
0
2
0
2
1
1
0
0
0
2
1
1
0
0
0
2
2
1
0
0
1
1
0
0
1
1
1
2
1
3
1
0
1
2
1
1
0
1
0
0
1
1
1
1
2
2
0
0
1
0
1
0
2
0
2
2
2
0
1
0
0
0
0
1
2
1
2
1
0
2
0
0
2
2
0
0
0
2
0
0
0
0
2
0
1
1
2
0
2
0
2
0
2
0
1
3
0
0
1
1
1
1
0
1
1
2
3
1
0
2
0
1
1
0
1
1
1
1
1
1
2
0
1
1
0
0
0
2
0
0
0
1
2
0
1
1
0
2
1
0
0
0
0
1
2
2
1
2
4
2
2
0
0
0
0
2
0
2
1
1
1
0
1
1
2
0
0
2
1
0
0
1
2
0
0
1
0
1
1
1
0
0
0
2
0
0
2
0
0
1
0
1
0
1
1
0
0
2
2
1
0
1
0
0
0
0
1
1
1
1
1
0
0
0
1
1
0
1
2
0
1
1
0
2
0
2
0
0
1
1
1
0
1
1
1
0
2
0
0
1
0
1
0
2
0
0
0
1
1
2
2
0
1
1
1
0
0
0
1
0
0
2
1
3
1
0
1
1
1
1
2
0
1
0
2
0
0
2
0
2
2
2
1
0
0
1
2
1
1
0
0
0
1
1
1
0
2
2
0
1
0
1
1
0
2
0
2
1
1
0
0
0
1
0
2
0
2
1
1
0
1
0
1
1
1
1
1
0
0
0
3
0
0
0
1
2
1
0
0
0
1
0
1
0
0
1
1
0
0
1
0
1
2
1
0
2
0
2
2
0
1
1
2
0
0
0
2
0
0
0
0
0
1
0
0
0
1
1
0
2
0
0
1
2
0
0
1
1
1
1
0
1
0
1
0
1
2
1
0
0
3
1
1
0
0
2
1
1
1
0
3
0
2
1
0
1
1
0
2
1
0
0
1
1
1
1
1
2
3
1
0
0
1
0
0
0
1
1
0
0
1
2
0
0
0
1
2
0
0
2
1
1
3
0
0
1
2
0
1
2
1
2
0
1
2
0
1
1
2
0
1
2
2
1
0
1
0
0
1
2
2
1
2
2
0
1
1
1
1
0
1
0
1
0
1
1
0
0
0
0
2
0
0
0
3
1
0
1
2
0
1
0
0
1
1
2
0
0
0
2
2
0
0
0
1
2
0
1
0
1
0
4
1
2
1
0
2
2
3
1
1
0
0
0
1
1
2
1
1
1
1
0
0
2
1
0
0
1
0
1
0
0
0
0
0
0
2
1
2
0
2
0
1
0
1
0
0
0
2
0
0
1
1
2
1
2
0
1
1
1
1
1
0
0
0
1
1
0
2
1
0
0
1
0
1
0
1
0
1
0
0
1
2
2
1
1
1
1
2
1
1
0
1
1
0
1
1
1
0
0
1
0
2
1
0
0
0
1
1
1
0
2
2
0
2
1
0
0
1
1
3
2
0
0
1
2
0
2
0
0
0
1
2
1
1
1
3
1
1
1
1
2
2
2
0
0
2
0
2
1
1
1
0
1
0
1
1
0
3
0
2
1
1
0
0
1
2
0
2
1
0
1
0
2
1
2
0
2
0
1
1
2
0
1
0
1
0
0
1
1
0
0
1
0
2
0
0
0
0
0
1
0
1
0
1
2
1
0
2
2
3
2
2
1
0
0
1
0
3
0
0
2
0
1
0
0
2
0
1
0
1
0
0
1
2
1
0
0
1
1
2
2
0
1
1
1
1
0
2
0
2
0
1
0
0
1
0
1
1
0
2
0
0
0
2
0
2
0
1
2
1
1
0
0
1
0
1
2
0
2
0
0
2
0
0
2
1
0
0
1
0
1
2
2
0
1
0
2
2
1
0
1
1
2
1
1
1
1
0
0
0
0
1
1
0
1
1
1
2
2
1
2
0
1
0
0
2
2
2
0
0
1
0
2
0
0
0
2
1
0
1
1
0
1
0
3
2
0
2
1
1
0
0
1
2
0
1
0
1
1
0
1
1
1
1
1
1
0
0
2
1
1
1
0
1
1
1
2
0
0
1
0
1
1
2
1
2
0
0
2
1
2
0
1
1
0
0
2
0
0
1
0
2
0
1
0
2
1
0
0
1
0
1
0
1
1
1
4
0
1
0
0
0
0
0
2
0
1
1
1
0
1
0
1
2
2
1
0
2
1
7
1
0
1
1
0
1
1
0
0
0
1
0
0
3
1
1
1
0
0
2
1
1
0
1
1
1
0
1
0
0
1
1
1
0
0
0
1
1
1
0
1
1
0
0
1
1
1
0
1
1
0
2
1
1
0
0
0
2
0
2
1
1
2
1
2
0
2
0
1
0
1
1
0
0
2
0
1
0
2
0
2
0
1
1
1
0
1
2
0
0
1
1
0
2
1
0
1
1
1
2
1
0
2
0
1
0
1
1
2
0
0
0
0
3
1
1
1
1
1
2
0
0
1
2
2
0
0
1
0
1
1
1
1
1
0
0
1
0
1
2
1
2
2
0
1
2
0
1
0
1
0
2
0
0
1
1
0
1
1
2
1
0
2
1
2
1
2
1
1
0
1
2
0
2
2
1
0
1
1
0
2
1
2
0
1
0
1
1
1
0
1
1
0
0
2
1
0
1
0
1
2
2
1
0
0
2
2
1
0
1
0
1
0
0
1
0
1
0
1
1
1
0
1
1
1
1
1
1
0
0
2
3
1
2
3
0
2
1
2
0
1
1
1
2
0
1
2
2
1
2
1
0
0
1
1
1
0
0
1
2
2
1
0
1
2
0
0
2
1
1
1
2
1
0
0
0
0
1
1
0
1
2
0
0
2
0
1
1
0
1
0
0
0
2
0
1
2
1
1
1
1
2
1
1
1
2
2
0
2
2
0
0
1
1
0
1
0
0
0
1
1
0
0
2
0
2
2
0
0
0
2
1
1
2
2
1
0
0
0
1
2
0
0
1
0
0
2
0
1
0
1
0
1
0
1
2
0
2
1
1
0
1
1
0
1
1
0
1
0
1
0
1
1
0
1
3
0
2
0
1
0
0
2
1
0
0
1
1
2
2
1
2
0
2
0
1
1
1
1
1
0
1
1
1
1
1
1
1
1
0
0
0
0
1
2
1
2
0
0
0
1
2
0
0
2
2
1
0
0
0
0
1
2
0
0
1
1
1
1
0
0
0
1
1
0
0
0
2
1
0
2
2
2
0
2
1
2
0
2
1
2
1
0
0
2
1
0
1
0
0
1
1
2
1
0
1
2
1
0
0
1
1
1
0
0
0
2
2
1
1
1
0
2
1
1
1
1
2
0
0
1
0
0
1
4
0
0
1
1
2
1
2
0
0
0
0
0
1
1
2
1
0
0
2
1
0
2
0
2
1
2
2
1
1
2
0
1
2
0
1
0
0
2
1
1
2
0
2
0
0
2
0
0
2
0
0
0
1
0
2
0
0
2
1
1
0
1
1
0
0
0
0
1
0
0
0
3
0
1
0
1
2
0
1
1
1
1
0
1
1
0
0
0
1
1
1
0
0
0
2
1
3
1
2
2
0
1
2
0
0
0
0
0
1
2
1
1
1
1
1
0
1
1
1
1
1
0
1
0
2
1
0
2
1
0
1
1
1
2
2
2
0
1
0
2
0
0
0
1
0
0
2
1
2
1
2
1
1
1
2
1
0
0
2
2
1
2
0
0
0
0
1
1
0
0
2
1
1
2
0
2
0
0
0
1
1
0
0
2
2
0
0
0
0
1
0
0
0
1
2
1
0
1
1
0
2
1
1
0
1
1
1
0
1
0
1
0
0
0
2
1
0
0
2
0
2
1
2
1
2
1
1
0
0
2
1
0
0
0
2
1
0
1
1
0
0
1
0
1
2
0
1
1
2
2
0
0
1
0
0
0
1
0
1
1
0
1
1
1
0
0
1
0
0
0
1
1
2
0
2
0
1
0
1
0
2
1
0
2
2
1
1
2
0
1
0
2
1
2
1
0
1
1
1
8
2
2
1
0
1
1
1
2
1
1
1
0
2
2
2
0
1
0
1
0
1
1
1
2
1
0
1
0
1
0
2
0
0
1
0
1
0
0
0
0
2
2
1
1
0
0
1
1
1
1
0
1
2
0
0
1
0
1
0
0
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
0
0
0
1
2
0
2
0
0
0
2
1
1
1
0
1
0
1
1
2
1
1
1
0
1
0
1
0
0
1
0
1
0
0
0
2
2
2
0
1
2
0
0
2
1
0
0
2
2
1
0
2
0
0
0
0
1
2
1
0
0
0
2
1
2
1
2
1
2
2
0
1
2
0
2
1
2
0
3
1
1
0
2
1
0
0
2
1
1
1
1
0
0
1
2
1
0
1
2
1
0
0
0
1
0
0
1
0
2
0
0
0
1
1
0
2
1
1
1
3
1
2
1
0
0
0
0
0
0
1
0
1
1
1
2
3
1
2
0
0
0
1
1
2
1
1
1
3
1
2
1
1
0
2
3
0
0
1
2
0
1
0
0
2
0
2
0
1
2
1
2
2
2
1
1
1
0
0
1
2
2
0
0
3
1
1
1
2
1
2
1
1
0
0
1
0
2
2
2
0
1
1
1
2
0
0
0
2
1
1
0
1
1
2
0
1
0
0
1
1
0
0
1
1
0
0
2
1
1
3
2
1
0
1
0
0
1
0
0
1
1
0
0
2
0
1
0
0
0
0
2
1
0
1
0
2
1
2
1
2
1
2
0
1
1
2
1
1
2
0
2
1
1
1
1
0
0
1
1
2
1
1
0
0
1
2
1
1
3
0
0
1
1
0
1
1
0
2
0
1
0
3
2
0
0
2
0
0
1
0
2
0
0
2
1
1
0
1
1
1
2
0
0
1
0
0
0
1
1
2
1
1
1
0
0
1
1
0
1
0
1
1
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
1
0
0
1
2
1
2
0
0
1
0
2
1
2
1
1
1
0
1
1
0
1
0
1
1
0
0
1
2
1
0
0
2
1
0
1
1
0
1
0
0
1
1
1
2
1
0
0
0
0
0
1
0
2
0
2
2
1
2
1
0
0
2
0
0
0
0
0
1
0
0
1
1
2
2
0
1
1
1
0
2
1
1
1
2
1
1
2
2
1
0
0
1
4
1
1
2
1
0
1
1
3
1
0
0
1
0
0
0
0
2
1
0
1
1
1
0
1
0
0
1
1
2
0
2
1
0
1
0
1
1
1
0
2
0
1
0
0
0
1
1
1
0
1
1
2
1
1
0
0
0
1
0
2
0
0
1
2
0
0
1
1
1
1
0
1
2
0
0
1
3
1
0
0
0
1
3
0
2
0
1
3
0
1
2
1
2
1
0
0
1
1
0
2
2
0
1
1
0
2
0
0
0
1
1
1
0
0
0
1
0
2
0
2
1
1
0
2
2
0
1
0
0
0
1
0
2
2
0
1
1
0
0
1
0
0
0
0
1
1
0
1
5
0
0
1
1
1
1
0
2
0
0
0
2
0
1
1
0
2
1
0
0
1
1
2
1
0
0
0
0
1
1
1
0
1
1
1
0
0
1
1
0
0
0
0
2
0
1
0
0
1
3
1
1
0
0
1
3
1
0
1
1
0
1
2
0
0
1
1
1
0
1
0
0
1
0
1
2
0
0
1
1
0
2
1
1
0
0
1
2
0
0
2
0
2
0
1
0
1
2
0
0
0
2
0
0
2
2
1
1
1
2
3
1
0
2
1
1
2
2
2
2
2
0
1
1
0
2
1
0
1
0
2
1
2
0
0
0
1
0
1
2
1
0
1
2
1
1
2
1
2
0
2
2
0
0
1
1
2
0
1
1
0
2
0
0
0
2
1
1
1
2
0
0
1
0
0
0
0
0
0
2
1
0
0
0
2
1
1
0
0
2
1
2
0
1
2
2
2
0
0
1
0
1
2
1
0
2
1
1
1
1
0
0
0
1
1
2
0
1
0
1
0
0
2
1
2
2
1
0
1
0
0
0
1
0
1
2
1
2
2
1
1
1
1
1
0
1
1
0
1
1
0
0
1
1
2
3
1
1
0
1
1
1
1
1
1
1
0
1
2
2
0
1
2
1
1
1
0
1
2
0
2
1
0
1
2
1
1
2
1
0
0
2
0
2
2
0
2
0
1
1
1
0
1
2
0
1
0
2
4
2
2
1
0
2
0
1
0
1
1
1
1
1
0
0
2
1
0
1
0
1
1
1
0
2
1
0
1
0
2
1
1
0
2
0
0
0
0
1
1
0
3
0
1
2
0
1
4
0
0
0
1
1
0
2
1
2
0
0
1
0
1
2
1
0
2
1
0
1
1
1
0
2
0
0
2
0
0
1
1
1
0
0
2
2
1
1
2
1
0
1
0
0
0
1
0
0
2
0
1
0
1
0
0
0
0
1
2
0
1
1
0
0
2
2
0
0
0
0
0
1
0
2
0
3
2
0
0
2
1
2
0
2
1
2
1
2
5
1
0
0
1
2
1
1
0
2
0
1
0
1
1
1
1
1
1
1
0
1
2
2
1
0
1
0
1
1
2
0
0
0
1
1
0
0
0
1
1
0
0
1
1
1
1
2
0
2
0
2
1
0
0
0
2
0
1
1
1
1
1
1
0
2
2
0
2
0
2
0
1
1
0
0
0
1
0
2
1
2
1
0
1
1
0
1
1
1
1
0
1
1
0
2
0
0
1
1
1
0
0
2
2
2
0
0
2
0
1
2
1
1
0
1
0
0
4
0
1
2
1
2
1
0
0
0
2
1
1
1
1
0
0
2
0
0
0
0
2
0
1
0
1
1
1
0
2
0
0
3
1
1
1
2
2
0
0
2
0
0
1
1
2
0
0
1
0
2
2
1
0
2
2
1
0
1
2
1
0
1
2
1
0
2
2
2
2
0
1
0
0
0
1
1
1
1
1
1
1
0
1
1
0
1
0
2
2
1
3
0
1
0
2
0
0
1
1
0
0
0
2
0
2
1
3
0
0
2
2
1
2
0
0
0
0
0
1
1
3
1
0
1
2
0
0
0
2
0
2
2
2
1
0
1
2
2
0
0
0
2
1
0
2
1
1
1
0
0
2
1
0
2
2
1
1
0
2
0
1
0
0
2
1
2
1
0
2
0
2
1
0
1
2
4
1
1
0
1
0
1
1
2
0
0
1
1
2
1
1
0
0
3
1
0
0
2
0
0
1
1
2
0
3
1
2
2
0
0
1
1
1
0
3
1
1
1
0
0
2
0
1
2
1
1
1
0
0
1
2
1
1
2
2
0
0
1
1
2
2
0
1
0
1
0
1
1
2
2
0
1
0
1
0
1
1
3
1
2
2
0
1
2
1
2
1
1
0
2
0
1
1
0
0
1
0
1
1
0
1
1
0
2
2
0
1
1
0
1
0
2
0
1
0
0
2
0
2
1
1
2
1
0
2
1
1
0
1
1
0
2
1
2
0
0
2
1
0
0
3
2
0
1
0
2
2
0
0
0
2
2
1
0
1
2
2
1
0
1
1
2
1
1
0
2
2
0
1
1
1
1
2
2
0
0
0
1
2
1
2
1
1
1
1
1
3
2
1
0
2
0
1
0
0
2
0
0
0
0
1
0
2
2
1
1
2
1
0
0
1
0
1
1
0
2
0
2
0
0
2
0
1
1
2
0
0
2
1
1
0
1
0
0
1
2
1
1
0
1
0
1
1
2
1
1
0
0
0
0
2
0
1
1
1
1
1
2
1
1
0
1
0
0
0
1
0
1
2
2
1
1
2
1
1
0
1
2
0
2
0
1
1
2
0
1
0
0
0
0
2
1
1
1
1
0
1
0
1
1
0
0
0
1
2
1
0
0
1
6
2
0
1
1
0
2
0
1
0
2
0
0
1
1
0
0
0
0
0
0
0
2
0
0
1
2
1
2
2
1
2
2
3
0
1
0
1
1
0
0
1
2
1
0
0
0
0
0
2
1
0
4
1
0
1
2
0
0
0
1
2
1
2
0
0
1
0
0
1
0
2
0
0
2
2
1
2
0
0
1
2
0
0
0
0
1
1
0
1
1
1
0
0
0
1
2
0
1
2
0
1
0
0
2
0
1
1
2
1
1
2
0
2
0
0
1
0
0
0
2
0
2
1
0
2
0
0
1
1
0
0
0
1
2
1
0
0
2
0
2
0
2
1
0
1
0
0
0
2
1
2
0
1
0
0
2
1
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
1
2
1
0
1
0
2
1
3
1
0
0
2
1
1
2
1
1
1
0
2
0
0
1
1
2
0
1
0
1
1
1
0
1
2
1
1
1
1
3
0
1
1
1
1
1
2
2
0
0
2
1
1
1
2
0
1
0
2
2
2
0
2
0
2
2
0
1
1
0
1
1
2
0
0
0
2
2
1
0
0
1
1
1
1
2
1
1
1
1
1
0
0
1
0
1
0
2
1
2
1
0
0
1
2
0
2
2
1
1
2
1
2
0
1
1
1
0
1
1
0
0
1
1
2
1
2
2
1
1
1
1
2
2
2
1
4
1
0
1
0
1
0
2
0
0
0
2
1
2
2
0
0
0
2
0
1
0
1
1
1
1
0
2
1
1
0
0
1
1
1
0
2
2
0
2
1
1
0
0
1
2
0
1
2
1
2
1
0
2
1
2
1
1
0
0
1
1
1
3
1
1
2
2
0
1
1
2
1
0
1
0
2
2
0
1
1
1
0
0
0
2
0
0
0
1
2
1
1
0
0
1
0
0
1
1
2
1
1
1
1
1
1
0
2
0
0
0
0
1
0
1
1
1
1
2
0
1
1
1
1
1
2
2
1
0
1
2
1
2
0
2
1
0
2
0
2
3
1
0
1
0
2
2
0
0
0
2
2
1
0
2
2
1
0
2
1
1
0
1
0
1
0
1
2
2
0
2
2
1
2
1
0
0
0
1
2
1
0
0
1
0
1
0
1
0
0
2
1
2
0
0
1
1
1
2
2
0
0
0
0
1
0
0
0
1
1
0
1
0
1
1
1
0
0
2
2
1
0
1
0
2
1
1
1
2
0
0
2
1
1
1
1
2
0
0
1
0
0
0
2
2
0
0
2
0
0
1
1
0
2
0
1
0
1
0
1
1
0
0
2
1
1
0
0
0
1
0
2
0
1
2
0
0
2
1
1
1
0
2
2
1
0
1
0
1
2
1
2
0
1
0
3
0
1
2
2
1
1
0
1
0
0
3
1
0
0
2
1
0
1
1
0
1
1
0
2
2
2
1
2
0
1
0
3
0
2
2
0
0
2
0
1
0
0
1
1
0
1
1
0
0
0
1
1
1
1
1
1
1
0
0
1
1
2
1
0
0
1
0
0
2
0
1
1
2
0
1
0
0
1
1
2
1
1
0
1
2
0
0
2
1
0
1
0
1
0
1
1
2
0
0
0
1
0
0
1
2
0
1
2
1
0
1
0
1
1
0
2
2
1
1
1
2
1
0
1
0
1
0
0
0
2
0
0
2
0
0
0
1
2
0
0
0
0
2
0
2
1
1
0
1
0
1
1
0
0
0
0
1
2
1
2
0
1
2
0
0
0
2
0
0
2
0
0
2
1
1
0
1
0
0
1
1
2
0
0
1
1
0
2
0
0
1
0
1
2
1
2
2
0
0
1
0
0
2
0
2
0
1
0
0
0
0
0
0
2
2
0
0
2
0
0
1
0
1
0
1
0
0
1
1
0
0
0
1
1
2
1
0
0
0
0
2
4
0
3
1
0
0
1
2
0
0
1
1
3
0
2
0
1
0
1
1
4
1
1
1
0
2
0
1
1
0
0
2
2
1
1
1
0
0
0
1
1
1
0
3
2
0
0
1
2
0
1
2
1
0
1
0
0
1
1
0
0
2
0
1
1
0
2
2
2
0
0
1
0
0
1
1
0
1
1
3
2
1
1
2
0
0
0
0
1
0
2
0
1
1
1
1
0
1
1
1
1
1
2
0
3
1
0
1
0
2
1
0
1
0
2
0
1
0
0
0
2
2
2
2
1
1
1
0
0
2
2
0
2
2
1
1
3
0
0
1
0
1
1
1
0
1
0
2
1
0
1
0
0
0
2
1
0
2
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
0
1
1
1
1
0
0
0
1
0
0
0
2
3
0
1
1
1
1
0
0
1
1
1
0
5
1
2
2
2
0
1
0
1
0
3
2
0
1
1
0
0
2
0
1
0
0
2
1
1
2
1
0
0
0
1
0
0
1
0
2
1
1
1
0
0
0
1
0
0
0
0
0
1
2
0
2
0
1
1
1
0
1
0
0
1
0
1
0
0
0
1
1
0
2
1
1
2
1
2
1
0
2
0
3
1
1
1
0
0
0
1
1
1
1
0
1
0
2
1
0
0
1
2
1
1
1
0
1
2
1
0
0
1
1
2
1
0
0
0
2
2
2
0
1
0
1
1
0
2
2
0
0
2
2
1
0
0
1
2
1
2
0
0
0
1
1
0
2
0
2
2
0
0
2
1
1
2
1
1
0
0
1
2
3
0
1
1
0
0
3
1
0
1
1
1
2
1
2
0
2
0
0
3
1
0
2
2
0
2
1
0
0
1
0
0
1
1
2
1
0
1
1
0
1
2
0
1
1
1
2
2
2
0
2
1
1
1
0
0
1
0
0
0
0
1
1
2
1
0
2
0
2
2
2
1
2
1
1
1
0
0
2
1
0
0
1
0
2
0
0
1
0
2
0
2
1
1
1
2
1
1
1
0
2
0
1
1
0
0
1
0
1
1
1
1
1
2
1
0
2
1
3
0
2
0
0
1
0
1
0
2
0
0
2
2
1
1
0
1
1
0
2
1
2
1
0
1
1
1
1
1
0
2
1
0
0
2
2
2
0
2
0
2
2
2
2
1
1
1
2
0
0
0
1
2
1
2
0
1
2
0
0
2
1
2
1
0
0
0
1
0
1
1
1
2
1
0
0
0
2
0
2
0
2
0
1
0
0
0
1
1
1
2
1
2
0
1
2
0
2
2
1
0
0
0
0
1
2
0
1
1
0
0
1
2
0
1
1
0
2
1
0
1
1
1
1
0
0
2
2
3
0
0
0
2
0
1
1
1
0
1
0
2
1
0
2
0
1
2
1
1
0
0
1
0
0
1
0
2
2
0
2
0
0
0
2
0
0
0
2
0
0
1
1
0
0
1
2
0
1
1
2
0
0
1
1
2
1
0
0
1
1
0
1
2
1
1
0
0
0
2
1
1
2
0
1
0
0
0
0
0
0
1
1
0
2
2
2
0
1
1
1
0
0
0
0
0
2
1
2
0
2
0
1
1
1
0
1
2
0
2
0
0
1
1
1
1
0
0
2
1
0
0
0
2
0
0
1
0
0
0
0
2
1
2
0
1
3
2
1
0
1
0
1
1
1
1
0
1
0
1
0
2
0
0
2
0
7
1
1
1
1
0
0
0
0
1
1
1
0
0
0
1
1
1
1
0
1
0
1
2
2
1
1
5
2
1
1
0
0
0
1
0
0
1
2
1
0
0
0
0
2
1
0
0
2
0
0
1
0
0
1
0
0
1
2
0
0
1
1
0
1
2
1
2
1
1
1
1
2
0
0
0
0
2
1
0
0
1
0
0
0
0
2
2
0
0
0
3
2
0
2
0
2
1
0
1
7
3
1
1
0
1
1
1
1
0
1
0
0
1
1
1
2
0
1
0
1
0
0
0
1
1
1
0
2
0
0
0
1
1
0
0
1
0
2
0
0
1
0
1
0
1
1
1
0
2
0
0
1
1
1
1
2
0
2
1
1
1
1
1
1
2
2
0
1
0
2
2
0
0
2
5
1
0
1
1
1
1
0
0
2
2
0
1
2
0
1
1
0
0
0
0
1
2
0
1
0
0
1
0
2
0
2
2
0
0
1
0
0
0
0
0
1
2
0
1
1
0
1
1
0
1
0
0
1
1
2
2
1
0
0
0
0
1
0
0
0
0
1
0
0
0
2
1
0
2
1
1
1
0
2
1
0
1
1
0
0
2
0
0
0
0
0
0
1
1
1
0
0
0
1
0
1
0
0
0
1
2
1
1
1
0
0
2
0
1
0
1
1
0
2
0
2
2
1
0
0
1
0
0
0
1
1
0
2
1
0
2
0
0
0
2
0
0
1
0
0
0
0
2
1
0
1
3
1
1
1
1
0
0
2
1
0
0
1
1
1
1
0
0
0
0
1
1
1
0
1
2
1
0
1
0
1
0
1
1
1
0
0
0
1
2
2
1
0
1
0
0
1
1
0
2
1
1
1
0
0
1
1
0
0
2
0
0
1
2
2
1
2
1
0
0
0
0
1
0
0
2
0
0
1
0
3
2
1
1
0
1
2
1
1
1
2
0
0
1
0
0
0
1
0
1
1
2
1
1
0
1
1
0
1
0
0
0
0
2
2
2
0
2
1
0
0
1
1
0
0
0
0
1
1
0
1
1
1
0
1
0
0
1
0
2
5
0
3
0
2
0
2
0
1
0
0
1
1
0
2
0
1
1
0
0
0
0
0
2
2
0
0
0
0
2
1
0
1
1
3
1
2
0
1
0
0
1
0
1
0
1
1
1
1
0
1
1
0
0
1
1
2
1
0
1
2
0
0
0
1
0
0
1
0
2
2
0
1
2
1
2
0
0
2
1
0
1
1
3
2
2
2
0
2
1
1
1
0
0
1
0
0
1
1
0
0
1
2
1
2
1
0
1
2
1
1
0
0
2
1
0
1
1
0
0
1
0
1
0
0
0
0
1
0
1
0
1
0
1
2
1
0
0
1
2
1
1
0
0
1
0
1
2
2
1
1
0
0
2
0
1
1
1
2
0
2
1
4
0
0
1
0
2
1
1
1
1
2
1
1
0
0
2
0
0
1
1
1
0
1
0
1
2
1
0
2
2
0
1
0
0
1
2
0
0
2
0
2
1
0
0
2
2
2
0
1
1
1
1
1
2
0
1
1
0
2
0
3
2
2
1
0
0
0
0
0
2
2
0
1
1
0
0
0
1
1
0
1
0
2
2
1
2
0
1
2
1
0
3
0
2
1
2
0
1
1
0
1
1
0
2
1
0
0
0
0
1
2
1
1
2
2
1
2
2
0
1
2
2
0
0
0
0
0
2
1
1
2
0
1
0
0
2
0
1
2
2
1
1
1
0
0
2
0
1
0
0
1
1
1
0
1
1
0
1
1
2
0
0
2
2
2
1
0
1
1
1
0
0
2
2
2
0
0
0
1
1
0
2
0
1
0
2
2
0
1
0
0
0
1
1
1
1
0
2
0
2
1
1
1
1
0
1
2
1
1
0
0
2
2
2
1
2
0
0
0
1
0
0
1
2
1
0
2
2
1
0
2
0
1
0
0
2
0
0
0
0
2
3
2
1
0
2
2
0
1
1
0
1
1
0
0
1
2
0
0
1
2
0
2
1
1
1
0
0
0
1
2
1
0
1
1
1
0
1
0
2
1
0
1
1
1
1
2
0
1
2
1
2
0
1
1
2
2
3
1
1
1
0
0
1
3
1
0
1
0
2
2
0
0
0
1
1
0
2
1
0
2
1
0
0
1
1
2
0
1
1
2
1
0
2
1
0
2
1
1
0
2
1
2
1
1
2
0
0
0
0
0
1
0
2
1
1
1
0
1
1
1
1
0
1
0
0
0
1
2
0
0
0
0
0
1
0
2
1
1
0
1
2
0
0
2
2
1
0
0
1
1
0
1
2
0
0
2
1
0
1
0
2
0
1
2
1
3
2
0
0
0
2
1
2
2
0
0
1
0
1
1
2
2
1
1
2
2
2
1
1
1
0
2
0
1
0
0
1
1
1
1
0
0
2
1
0
2
0
1
0
2
0
1
1
0
1
0
1
1
2
2
1
1
0
1
0
1
1
0
1
1
0
2
2
0
1
2
0
1
1
1
4
0
0
1
0
1
0
1
0
2
0
2
0
0
0
2
3
1
0
2
0
0
2
1
0
1
0
0
0
0
1
0
1
2
1
0
1
1
1
2
1
1
1
0
1
1
0
2
0
2
1
0
2
1
2
1
2
0
1
1
1
1
3
0
2
1
2
0
1
1
2
0
2
1
0
0
0
1
1
0
3
1
1
0
0
1
0
2
0
0
1
1
0
1
0
1
2
1
0
1
4
0
0
2
0
0
0
1
0
0
0
0
2
1
1
0
0
0
2
0
0
0
0
2
1
0
1
0
2
0
1
2
2
1
0
1
2
1
1
1
1
1
3
1
0
1
1
2
0
0
1
0
2
0
1
2
0
2
0
1
0
0
0
0
0
0
1
1
1
1
1
0
0
0
2
1
2
1
0
1
1
1
1
0
1
0
0
1
0
0
0
0
1
0
2
1
2
2
0
2
2
1
1
0
2
2
1
1
1
0
2
0
2
1
1
0
1
2
0
0
1
2
1
1
2
1
0
0
0
1
2
0
2
0
3
1
0
1
0
0
0
2
2
0
5
1
2
0
0
1
2
0
0
1
2
3
1
1
0
1
2
1
1
0
0
0
0
2
1
2
1
0
2
2
0
2
1
1
2
2
2
0
2
1
0
1
1
2
0
0
1
0
0
0
1
1
1
0
0
0
2
1
0
0
1
1
1
0
2
1
0
1
2
1
1
0
0
0
0
1
0
0
1
2
1
0
2
1
1
0
2
2
1
0
1
1
1
0
1
0
2
2
2
2
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
2
0
1
1
1
0
1
1
1
1
1
0
0
1
2
1
1
2
1
2
0
0
1
0
1
1
1
2
2
0
0
0
0
0
0
0
2
1
0
0
2
1
1
2
0
0
0
1
0
2
1
0
2
0
1
0
1
0
1
1
1
0
1
1
2
2
1
1
1
0
1
1
0
2
0
0
1
1
0
1
1
1
1
0
0
1
1
1
0
1
1
1
0
0
0
0
1
1
0
0
0
0
0
0
2
1
2
0
1
1
1
1
0
0
0
0
2
2
1
2
1
2
2
1
0
0
1
0
1
0
1
0
0
0
3
2
1
1
0
1
1
2
0
1
3
1
0
0
1
0
1
0
1
1
0
1
0
1
0
0
1
1
0
0
1
1
1
2
1
1
1
0
1
0
0
1
0
1
0
1
0
1
0
0
1
0
1
0
2
0
2
2
0
0
1
0
1
1
1
2
1
1
1
0
0
1
2
0
0
3
0
0
1
0
0
0
1
0
0
1
1
1
2
0
0
0
0
2
1
1
0
2
1
1
0
0
2
0
1
0
1
0
1
2
1
0
0
0
1
1
1
1
0
0
1
1
1
1
1
2
0
0
1
1
1
0
0
1
2
1
0
1
2
0
2
0
2
0
0
0
1
0
1
1
0
2
0
1
1
2
0
2
0
1
2
0
0
1
0
0
0
1
2
2
0
1
1
1
1
1
2
0
1
1
1
2
0
0
0
0
0
1
0
1
0
1
1
0
2
0
0
0
0
1
1
1
0
0
1
0
0
2
2
1
1
0
2
2
2
1
2
2
2
0
0
0
1
0
1
3
1
0
0
2
1
0
1
1
1
1
2
0
2
1
0
1
0
1
2
1
0
1
0
1
1
0
0
0
0
0
0
2
0
1
2
0
1
1
1
0
0
1
1
0
0
1
1
2
2
2
2
0
0
1
0
0
1
1
1
2
1
1
2
1
0
1
0
0
1
0
1
1
2
2
1
2
2
2
0
0
2
1
1
0
2
1
0
1
1
0
1
1
1
0
2
1
1
2
1
2
0
1
1
2
0
2
2
2
0
1
1
1
0
2
0
0
1
1
1
0
0
2
0
1
2
1
1
4
2
0
0
1
1
2
1
0
0
0
1
2
1
1
0
0
0
2
2
2
0
1
1
0
1
0
2
2
1
2
0
0
0
0
2
1
0
0
0
1
0
2
1
1
0
1
1
0
1
1
1
1
0
0
2
1
0
1
1
0
0
0
0
0
0
0
0
2
2
0
0
3
1
1
1
0
0
0
0
1
2
0
0
2
1
0
2
2
1
4
0
0
2
0
0
0
1
2
0
0
1
0
1
1
1
1
1
0
1
2
2
0
0
1
0
1
2
0
1
1
1
0
0
1
2
0
2
0
1
1
0
0
1
1
0
0
1
0
0
2
2
2
1
2
1
0
1
1
0
2
0
1
2
1
2
1
1
1
2
0
0
0
0
0
1
1
0
0
0
0
3
2
2
1
1
2
1
0
1
0
0
0
0
1
1
2
0
0
1
0
1
0
1
0
2
0
0
2
1
2
0
0
0
1
2
1
2
2
1
2
2
2
2
0
0
1
1
0
0
1
0
0
0
1
0
2
0
2
2
1
1
2
0
0
0
0
2
0
1
1
0
2
2
0
1
2
1
2
0
1
1
2
0
1
1
1
1
1
1
1
1
1
2
1
2
2
0
1
0
0
0
1
0
1
2
0
2
1
0
2
2
1
1
1
3
0
0
2
2
1
2
1
2
1
1
2
0
2
0
0
0
1
1
0
2
1
1
0
1
3
0
0
0
2
1
1
2
2
0
2
2
2
1
2
1
2
1
3
0
0
1
2
0
1
1
0
1
0
2
1
1
0
0
0
1
0
1
0
1
2
0
2
1
3
0
0
0
1
1
1
0
1
1
0
5
0
0
0
1
0
0
1
1
2
2
1
1
0
1
2
2
1
1
2
1
0
0
2
2
0
0
1
0
0
1
1
2
1
1
1
0
1
1
0
1
1
1
0
2
0
0
2
2
0
0
0
0
2
1
1
2
0
2
1
2
1
1
1
1
0
1
0
0
2
1
2
1
0
1
0
0
2
1
2
0
1
2
2
0
1
1
0
1
1
0
0
0
1
0
0
2
2
2
1
3
1
0
1
2
1
1
0
0
0
1
1
1
0
1
0
1
1
0
0
0
1
0
1
0
1
0
2
0
2
1
0
0
2
1
0
0
1
1
0
1
1
0
0
0
0
1
0
1
1
0
1
0
0
1
1
1
0
0
1
0
2
0
1
1
3
0
0
2
0
0
1
1
1
1
2
1
1
0
1
0
2
2
1
0
1
1
0
2
0
1
1
1
0
1
1
0
1
2
3
1
0
2
2
1
1
0
0
1
1
1
0
2
1
0
2
1
0
1
2
2
2
0
0
0
0
1
1
0
0
1
1
1
0
1
0
0
2
0
1
1
1
1
1
2
2
0
1
1
0
1
1
2
2
2
1
0
2
0
2
0
0
1
1
2
0
1
0
2
2
1
1
1
1
1
2
0
0
1
1
4
0
0
0
0
1
1
1
0
1
2
3
1
2
2
2
0
1
1
2
1
0
0
0
1
0
0
0
2
1
2
2
2
2
2
0
1
3
2
0
1
1
2
0
1
2
1
2
0
1
1
2
1
1
2
1
2
0
0
1
0
3
0
0
1
0
1
0
1
2
2
0
1
2
2
0
0
2
1
1
0
0
1
0
1
1
1
2
0
2
1
0
2
2
0
0
0
0
1
0
4
0
0
0
2
1
1
0
0
0
0
1
1
1
2
2
0
2
2
1
1
0
1
0
2
1
1
2
0
1
1
1
1
0
1
2
0
2
0
0
1
2
1
2
2
1
1
1
0
0
0
0
1
1
1
1
3
1
0
2
1
1
2
1
0
2
1
1
0
1
1
1
2
0
3
0
0
0
2
0
0
1
0
1
2
0
1
0
0
1
2
2
0
0
0
1
1
0
2
1
0
0
0
1
0
1
0
2
1
2
0
1
0
2
2
0
0
2
1
1
3
1
0
1
0
0
3
0
1
2
0
1
0
1
0
0
0
1
0
1
0
0
2
0
2
0
2
2
1
1
0
0
2
1
0
1
1
1
1
1
3
2
1
1
1
0
1
2
0
0
0
0
0
0
1
0
1
0
1
3
0
0
2
0
2
1
2
1
0
2
0
0
0
1
1
1
0
2
0
0
1
0
1
0
2
1
0
2
2
0
0
1
1
0
0
1
1
0
1
0
0
2
0
2
2
1
0
2
2
0
2
1
3
1
1
0
0
0
2
1
2
1
1
1
2
0
2
0
2
1
1
2
1
1
2
1
1
0
2
0
3
0
0
0
0
1
1
0
2
2
1
0
1
0
0
1
0
1
0
2
1
0
0
0
1
1
2
1
2
0
0
1
1
1
0
1
1
0
1
0
2
0
0
1
0
0
1
2
2
0
1
2
0
0
1
2
1
2
0
0
1
0
1
0
0
2
1
1
0
0
2
0
2
1
0
0
0
0
1
2
1
0
0
1
1
0
1
1
0
1
0
0
2
2
2
2
0
2
2
2
1
1
2
1
1
2
1
1
1
1
1
1
1
2
0
2
0
0
0
0
1
0
0
0
1
2
1
1
1
2
1
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
1
1
2
0
0
1
0
1
1
1
1
0
0
1
4
1
1
1
0
0
0
0
1
1
2
1
4
0
0
1
2
1
0
1
0
2
1
0
1
1
0
0
0
1
1
1
2
0
0
1
2
0
0
0
1
2
1
1
0
0
0
0
2
0
0
2
0
0
1
0
1
2
0
2
1
1
1
2
2
0
1
1
0
1
2
0
0
0
1
1
2
0
0
1
0
1
0
1
1
0
0
1
1
1
1
0
0
0
1
0
2
2
1
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
1
0
0
1
1
0
1
1
2
0
1
0
2
1
0
0
1
0
1
3
0
1
0
1
2
0
0
1
2
0
1
3
2
0
0
1
0
0
2
2
2
0
0
0
1
1
1
0
0
2
2
0
1
2
0
0
1
0
2
0
0
1
1
0
1
1
2
0
0
0
1
2
1
0
1
1
0
1
0
1
0
0
0
2
1
0
0
1
1
2
1
1
1
0
2
1
7
1
0
1
1
0
0
2
0
0
0
0
2
0
0
1
0
0
0
1
2
1
0
1
0
1
0
2
3
0
2
0
2
1
0
1
0
1
2
0
1
1
1
0
0
1
2
0
2
1
2
1
2
0
2
0
0
1
1
3
0
0
0
2
0
0
1
0
0
2
0
0
2
0
1
1
0
0
0
1
2
0
0
1
1
0
2
0
1
2
1
2
0
2
2
3
0
0
1
1
0
1
0
0
2
2
0
1
0
1
1
0
2
0
1
0
1
2
1
0
0
1
1
2
0
0
1
1
1
0
0
0
2
0
0
1
0
1
0
1
1
0
1
0
2
2
1
2
0
1
0
2
1
0
1
2
1
2
0
0
0
2
1
1
0
1
0
0
0
1
0
1
1
0
0
1
0
1
2
1
1
1
0
2
1
0
1
1
2
0
1
0
2
0
2
0
0
2
0
0
0
0
1
0
2
0
1
1
1
1
1
0
1
0
1
1
2
0
0
1
0
0
2
1
0
1
2
0
1
0
1
2
1
0
0
0
0
0
0
1
2
2
0
1
1
1
1
1
2
1
2
1
0
0
1
1
1
2
0
1
0
0
0
2
0
0
0
2
1
1
1
1
1
2
0
0
0
1
1
1
0
1
1
0
2
2
1
0
1
2
1
0
0
1
1
0
1
0
1
0
2
0
1
1
1
1
1
2
0
2
2
1
2
1
0
0
2
0
1
0
0
2
2
2
0
1
2
1
0
0
1
1
2
1
2
0
0
1
2
0
0
2
1
1
0
0
0
0
0
1
0
2
2
0
0
1
1
0
1
2
2
0
4
0
1
1
0
0
1
2
1
0
2
0
2
0
2
1
3
0
0
1
1
1
2
1
7
1
2
2
1
0
1
2
1
1
1
1
2
1
2
1
1
2
2
2
2
0
1
0
1
0
0
1
1
2
0
0
2
0
0
0
0
1
0
2
2
1
1
1
1
0
0
1
2
1
1
0
1
0
0
0
1
0
2
0
1
0
0
2
0
0
0
2
0
1
1
0
1
0
0
0
0
0
0
2
1
0
1
2
1
2
1
0
1
1
2
0
0
2
0
0
0
0
1
1
1
1
0
1
0
0
1
0
2
1
1
1
1
0
2
1
1
2
1
1
3
1
0
1
2
1
0
1
0
0
0
0
1
0
0
2
2
1
1
0
1
0
0
0
2
1
1
1
1
1
1
0
1
0
0
2
2
1
2
0
0
1
0
1
1
0
0
0
0
0
1
0
2
1
2
0
0
0
0
0
1
0
1
0
2
1
0
0
0
0
0
0
0
1
0
1
2
0
2
1
0
0
2
2
0
0
0
0
2
1
1
0
0
0
0
3
2
0
1
0
3
0
0
1
0
1
0
1
1
1
1
0
1
1
1
1
1
0
1
2
0
1
1
0
2
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
2
2
1
1
2
1
1
0
0
1
1
1
1
0
0
1
2
1
0
1
1
2
1
1
0
1
0
1
0
1
1
1
2
0
1
2
2
0
1
0
0
1
0
1
2
1
2
0
0
0
0
2
0
0
1
2
1
1
0
0
1
1
1
1
0
0
1
0
0
2
0
1
1
1
1
0
1
0
2
1
0
1
0
0
0
0
1
0
0
1
1
0
1
0
1
1
2
0
1
1
2
1
1
1
1
1
0
0
1
2
1
0
1
0
1
1
1
0
0
1
1
2
0
1
0
0
1
1
0
1
2
0
2
1
0
1
2
0
1
0
2
2
2
3
0
1
1
1
1
0
1
1
1
1
2
1
2
2
0
2
0
2
2
0
0
3
0
2
0
2
0
0
2
0
0
1
1
1
0
0
1
0
3
2
1
0
0
2
1
0
0
0
3
1
1
1
1
0
1
1
0
2
0
1
0
0
1
0
1
2
2
0
0
1
0
2
1
2
1
0
0
1
1
1
0
1
0
1
1
2
0
2
0
0
1
0
0
1
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
4
2
1
1
0
0
0
0
0
0
1
2
2
0
1
0
2
2
1
1
1
1
1
2
0
2
2
0
1
1
0
3
1
0
1
1
0
0
0
1
0
1
0
1
1
0
0
1
0
1
4
1
0
2
2
1
1
1
2
0
0
1
1
1
1
0
0
2
0
1
0
1
1
1
1
0
1
1
0
0
1
1
0
0
2
0
1
0
2
1
2
1
1
1
1
0
2
0
1
0
1
1
1
1
0
1
0
2
2
0
1
0
2
1
1
2
2
0
1
1
1
1
0
0
1
0
2
0
2
1
1
1
2
0
1
2
0
2
0
1
2
1
0
1
0
1
1
0
1
0
0
0
1
1
0
2
2
0
2
0
1
0
1
2
0
1
1
1
1
0
1
0
2
0
1
0
1
1
0
0
0
2
0
1
1
0
0
0
1
1
0
0
0
0
2
0
0
1
1
0
1
0
1
1
1
1
2
2
0
0
0
2
0
0
2
2
0
1
0
0
2
0
0
1
1
1
0
2
1
1
0
0
0
1
3
1
1
2
1
0
1
2
2
1
0
0
0
1
0
0
0
3
0
2
0
1
2
2
1
0
0
1
0
0
0
0
1
0
0
1
0
1
0
1
1
1
2
0
2
0
0
0
2
2
0
1
2
2
2
1
1
0
1
0
1
1
2
0
1
1
1
2
1
1
0
2
1
0
0
1
0
0
1
1
0
1
1
0
0
0
1
0
0
1
2
1
0
2
2
2
2
0
0
1
1
2
0
4
0
0
1
0
1
2
2
0
1
0
0
0
1
1
2
0
0
2
0
0
0
2
1
2
0
0
0
0
1
1
2
0
1
2
0
1
0
1
0
1
1
0
1
0
0
1
0
1
0
0
0
1
0
2
0
1
2
1
0
1
0
1
1
2
4
1
1
4
0
0
0
0
0
0
2
0
1
2
1
2
1
0
3
0
2
2
0
1
0
1
0
0
0
0
1
2
1
1
0
1
0
0
1
2
1
2
0
1
2
0
0
1
0
2
1
2
1
0
2
2
1
2
1
2
3
1
0
0
2
0
2
1
2
2
1
0
2
1
1
1
0
1
0
0
0
0
3
1
2
0
1
2
1
1
2
2
2
0
1
0
1
0
2
2
0
0
1
0
0
0
0
0
1
1
0
1
2
0
1
2
0
1
2
0
1
0
0
0
2
1
0
2
0
0
1
2
1
0
0
2
2
1
1
0
3
0
0
0
2
1
1
2
0
0
0
0
1
0
0
0
0
0
1
1
2
1
1
0
0
2
2
1
1
3
3
1
2
2
2
0
0
2
0
0
1
2
0
1
0
1
0
1
1
0
0
0
0
3
1
2
2
0
0
1
1
1
0
1
0
0
1
0
2
1
0
2
1
2
3
2
0
2
1
1
2
1
1
0
2
0
0
2
2
1
0
1
0
0
2
1
0
0
1
0
1
3
2
1
1
0
1
0
0
2
1
0
0
0
0
0
2
1
1
1
2
0
1
2
1
2
0
0
0
1
1
0
1
0
0
1
1
3
1
0
0
1
0
0
0
2
0
1
1
1
1
2
1
1
2
2
2
1
2
0
1
1
1
1
4
1
1
2
1
0
1
1
0
1
0
1
1
1
0
1
1
1
2
0
0
1
0
2
0
2
1
0
0
0
0
0
2
1
0
2
2
1
0
0
3
2
0
0
0
0
2
2
1
3
0
2
0
1
0
0
0
0
0
0
0
0
1
0
1
1
1
1
2
1
0
2
0
1
0
0
0
1
0
0
6
2
2
1
0
0
0
1
0
0
0
0
0
2
0
1
1
1
1
0
0
0
0
1
2
0
1
1
1
0
0
2
0
1
0
0
1
1
2
1
1
0
0
1
0
0
1
1
2
1
1
0
0
2
1
2
0
1
0
0
0
0
0
2
1
1
0
0
2
0
0
1
1
1
2
0
0
2
1
0
1
1
1
0
1
1
1
0
2
0
1
1
0
1
1
0
0
2
1
0
0
2
0
0
0
1
1
1
1
0
0
0
1
0
2
1
1
0
0
1
2
0
1
2
2
0
0
1
2
0
2
1
1
0
0
1
1
2
0
1
1
1
0
0
0
2
2
0
0
2
1
0
0
0
0
0
2
1
0
0
0
0
0
1
1
2
0
2
1
1
1
1
0
1
1
2
1
0
1
1
0
1
0
1
1
2
1
1
0
1
1
1
1
1
2
2
3
2
0
1
1
0
1
0
1
0
2
1
0
1
0
0
1
2
0
2
0
1
1
1
0
1
0
2
0
1
1
1
0
1
0
1
2
2
0
2
0
0
2
2
1
0
1
1
2
1
0
2
0
1
0
1
0
0
2
1
1
0
2
2
0
0
0
2
0
1
0
1
1
1
2
0
5
0
0
1
0
1
2
2
2
0
2
1
1
2
1
0
0
1
1
0
0
0
0
1
1
0
1
0
0
1
0
0
2
1
1
1
2
2
0
1
1
2
1
1
0
0
1
5
0
1
1
0
0
1
1
1
0
1
2
1
0
2
1
1
0
2
0
2
0
0
2
2
0
0
0
1
0
1
0
0
0
4
1
0
2
1
3
0
3
6
1
0
0
5
2
1
2
0
0
0
0
1
0
1
1
0
0
0
1
1
2
0
1
1
0
2
2
0
2
0
1
0
0
0
1
2
1
2
0
2
0
1
1
0
1
1
2
0
2
0
0
1
0
1
0
0
1
0
0
0
0
2
2
1
1
1
1
0
2
0
1
1
1
0
1
1
0
2
2
0
1
2
1
1
1
1
0
0
0
0
0
0
2
1
2
0
1
2
1
0
1
0
0
1
2
0
0
2
2
2
0
2
0
0
1
0
2
1
2
1
1
0
1
0
2
3
2
1
1
2
2
1
2
0
1
2
3
2
2
1
1
0
2
0
1
0
1
0
0
0
1
1
0
2
0
1
1
2
2
0
1
1
1
2
0
0
2
1
0
1
0
0
1
0
1
0
1
1
0
0
0
0
0
1
0
0
1
0
1
1
0
1
0
0
1
1
1
2
0
0
0
1
0
0
0
1
1
1
0
1
1
0
1
1
0
0
1
0
1
1
2
1
0
2
1
1
1
1
0
0
1
2
0
1
0
1
2
1
0
2
0
1
0
0
2
1
0
0
0
1
0
2
2
1
2
1
0
1
1
0
1
1
0
1
0
1
1
1
0
2
1
1
1
1
0
1
1
2
1
1
2
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
2
0
0
0
1
2
0
1
0
0
0
0
2
1
1
2
1
2
0
1
1
0
0
2
1
3
1
0
1
2
1
2
1
1
3
0
0
1
0
1
2
0
1
0
1
0
1
3
2
1
1
1
0
1
0
1
0
1
0
1
1
0
0
1
1
1
0
1
0
0
0
0
1
0
0
1
0
2
0
1
3
1
1
1
2
0
0
2
0
0
1
0
2
1
0
2
1
0
2
0
2
0
2
0
1
0
1
2
1
0
2
2
0
1
0
0
2
1
0
1
0
2
0
1
3
1
2
0
2
0
1
0
1
2
1
1
1
2
0
0
1
0
2
1
1
0
0
1
0
1
1
1
1
1
2
2
2
1
2
0
2
1
2
1
0
1
0
2
0
2
0
1
1
1
1
2
0
1
0
1
1
0
2
1
0
0
0
0
1
1
0
1
2
1
0
2
0
2
0
0
0
1
2
1
0
0
1
1
1
1
0
1
1
2
2
1
2
1
2
5
0
1
0
1
2
2
0
2
1
2
2
1
0
3
1
0
0
1
0
0
2
1
0
0
1
0
1
0
0
0
0
0
1
0
1
0
1
1
1
1
1
2
2
1
0
0
0
0
0
3
1
1
0
1
0
1
0
0
0
2
0
9
2
1
0
0
1
2
0
0
1
1
3
1
0
0
1
1
1
1
0
1
1
1
1
1
2
0
1
0
0
1
2
0
1
1
2
0
1
2
1
2
1
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
1
1
1
2
1
0
1
1
1
0
1
1
1
0
1
2
1
0
3
0
0
0
0
0
1
0
2
1
0
1
3
2
0
0
1
0
1
0
1
0
0
0
1
1
0
2
2
2
0
2
1
0
1
2
0
2
0
1
0
0
1
2
1
1
2
1
1
1
1
0
1
1
1
1
2
0
0
0
0
2
2
1
2
0
2
0
2
0
1
2
0
0
0
3
1
2
0
1
1
2
1
0
1
0
0
1
1
0
1
0
1
2
2
1
0
0
0
0
0
0
0
1
1
0
0
0
0
4
1
1
1
0
2
0
1
0
0
1
1
0
1
1
2
1
0
1
2
2
2
1
0
3
0
0
1
0
1
2
2
1
1
1
0
0
2
1
0
1
1
0
2
1
0
1
2
2
1
1
2
2
0
1
0
1
1
2
2
1
1
1
1
0
0
1
1
1
0
0
1
0
0
2
1
2
2
0
1
1
0
0
1
0
1
1
1
0
1
2
1
0
2
2
2
1
2
0
0
2
1
1
1
0
2
0
0
1
0
2
0
2
2
1
2
0
1
0
0
1
1
0
0
2
1
1
0
0
1
0
0
1
1
0
2
1
0
0
0
1
1
1
0
1
0
0
2
1
0
1
0
0
0
0
2
1
1
2
0
1
1
0
2
2
2
1
0
1
0
1
0
0
2
1
1
1
0
2
1
1
0
1
1
0
2
1
0
0
0
0
1
0
2
0
2
0
0
2
0
1
0
1
1
0
0
1
1
1
1
0
1
0
0
3
1
0
2
1
1
2
2
1
2
1
0
2
1
0
0
2
0
2
2
1
0
1
0
2
1
0
1
1
1
1
0
1
0
1
0
0
1
5
0
1
2
4
0
0
1
0
1
1
0
2
2
2
0
1
2
0
0
1
0
1
0
1
1
1
0
0
1
1
0
1
0
0
1
0
0
0
1
1
2
2
1
0
1
2
1
1
1
2
0
0
1
1
2
0
1
1
0
1
0
1
2
0
1
1
2
2
1
1
0
0
0
0
1
0
2
2
2
1
0
2
1
1
0
0
0
2
1
0
1
2
0
1
1
1
0
1
2
1
0
3
0
0
0
1
2
0
0
1
1
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
1
0
2
0
2
1
1
0
0
0
2
0
1
1
0
2
0
0
1
0
0
1
0
1
0
2
0
0
1
0
1
1
0
0
0
2
1
0
0
1
0
0
0
0
1
0
1
1
2
0
0
1
1
0
1
1
0
0
0
0
0
1
1
0
0
1
0
0
2
2
1
0
1
1
0
1
0
0
0
0
1
2
0
0
1
0
0
0
2
2
1
0
1
0
0
0
1
0
1
1
1
0
2
1
2
2
1
0
2
1
0
2
1
0
1
0
2
1
1
1
0
0
0
1
0
1
0
0
1
1
1
1
2
4
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
3
0
1
3
2
2
0
0
2
2
0
0
1
2
1
1
2
0
1
1
0
1
0
2
2
3
1
1
1
0
1
1
2
1
0
0
1
2
0
1
1
2
1
0
1
2
0
1
0
2
1
0
0
2
1
0
0
1
0
1
2
0
2
2
0
0
0
1
1
2
1
2
1
1
1
1
1
1
1
1
0
1
0
0
0
0
2
1
2
1
2
0
1
0
1
0
0
1
0
1
0
2
2
1
1
1
1
1
2
0
2
0
2
0
0
0
1
1
1
1
1
2
0
1
1
0
1
1
0
1
1
0
2
0
1
1
1
0
0
0
1
0
1
0
2
1
2
0
0
0
0
1
0
1
0
0
1
2
1
1
0
0
1
1
0
0
0
0
1
2
0
1
0
1
0
0
1
1
2
1
1
2
1
0
0
0
0
1
0
1
1
1
1
2
0
2
2
1
1
2
0
1
1
1
0
0
0
2
2
1
2
2
0
2
2
2
1
1
1
0
1
1
1
0
1
1
0
2
0
1
1
1
1
2
4
2
1
1
1
0
1
2
0
1
0
2
0
0
2
2
0
0
1
0
1
1
2
2
1
0
2
2
0
1
1
1
0
1
1
1
0
0
1
0
1
2
0
0
1
0
1
0
0
0
1
1
0
2
2
2
1
2
0
0
0
1
1
1
2
0
2
2
2
2
2
1
0
0
2
1
2
0
2
0
1
2
1
0
2
1
2
0
1
0
1
1
0
1
1
0
3
0
1
0
1
0
1
0
1
1
1
1
2
1
0
1
1
0
0
2
0
0
2
0
1
0
1
0
0
1
0
1
1
0
1
2
1
0
0
1
0
0
0
1
0
2
2
1
1
2
0
1
0
2
1
1
1
1
0
2
2
0
1
1
1
0
1
2
2
0
0
2
0
1
1
1
2
2
5
0
0
2
0
2
0
0
0
1
0
3
1
2
1
1
0
1
0
0
2
1
2
1
1
1
1
0
2
1
2
0
1
1
1
1
1
3
2
1
0
0
0
1
0
1
2
2
1
1
0
1
0
1
0
2
0
1
1
1
0
1
0
1
2
0
1
0
1
0
1
0
0
1
1
0
0
0
1
1
2
0
2
1
1
2
0
2
1
0
0
1
0
0
0
1
1
0
0
1
2
0
0
0
1
1
1
0
0
1
0
2
1
1
0
3
2
0
0
0
3
2
0
1
1
0
1
0
0
1
0
0
0
1
0
1
1
1
1
0
2
0
1
0
2
0
1
0
1
0
0
0
0
1
1
1
1
0
0
3
1
0
0
0
2
0
0
0
1
0
2
2
0
2
0
2
1
0
1
0
0
1
0
1
2
0
1
2
2
1
1
0
2
0
2
2
0
0
1
0
0
0
0
1
1
1
1
1
0
0
0
0
0
1
0
0
0
2
2
1
1
1
0
1
3
0
0
0
0
0
0
1
0
1
0
1
1
1
2
2
1
1
0
0
1
0
1
2
0
0
1
0
0
1
1
0
1
1
2
1
2
1
0
2
1
1
1
1
2
1
1
1
1
1
1
0
0
0
1
0
0
1
1
1
1
0
3
1
0
2
0
1
2
0
1
1
1
1
3
2
0
2
1
2
0
3
3
0
0
1
2
1
0
0
1
1
0
0
0
0
2
1
2
0
2
0
0
1
1
0
1
1
1
0
0
2
1
1
0
1
1
2
2
1
1
3
1
1
1
0
0
1
0
1
1
0
0
0
1
0
1
0
2
0
1
1
0
0
0
1
0
2
0
0
0
0
2
2
0
2
1
0
0
0
1
1
1
0
0
0
2
1
0
1
0
0
1
1
1
0
0
1
0
0
2
1
0
1
0
0
1
2
2
0
0
1
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
2
0
1
1
1
1
0
2
0
1
0
0
1
1
1
2
0
0
1
1
2
2
1
0
2
0
1
0
1
0
0
2
1
3
1
1
0
1
1
1
0
0
0
0
1
1
0
0
0
0
0
0
1
3
1
1
0
0
1
1
0
1
0
1
1
0
1
1
0
2
1
0
1
0
1
2
0
1
1
0
1
0
1
1
0
0
2
0
0
0
0
0
2
2
1
1
2
0
0
1
2
2
0
3
1
5
1
1
2
0
0
0
1
0
2
2
0
2
0
1
0
1
1
2
1
0
0
0
1
0
1
1
2
1
1
17
1
0
0
2
2
1
0
0
1
2
1
2
1
0
1
2
1
1
0
1
2
1
0
2
1
1
1
0
0
1
1
0
1
1
0
2
1
1
2
1
1
1
0
1
0
1
0
1
0
2
2
1
0
1
0
0
1
2
2
1
0
1
0
1
0
0
1
0
0
0
1
2
0
1
0
0
2
1
1
1
1
2
2
2
0
2
2
2
0
1
1
0
1
2
0
2
0
0
1
0
0
1
1
0
1
0
0
2
1
2
2
2
0
1
2
2
0
0
0
0
0
0
1
1
4
1
0
2
0
0
2
1
0
2
0
2
1
2
0
0
3
0
1
1
1
1
1
1
0
1
2
1
2
1
0
2
0
1
0
0
0
2
1
1
0
2
1
0
0
0
2
0
2
2
0
1
2
0
0
11
1
0
2
1
1
2
2
1
0
0
0
0
0
1
1
0
2
1
0
2
0
2
2
1
0
0
1
1
0
1
1
1
0
1
2
2
1
0
0
1
0
1
1
1
0
0
2
0
2
0
1
0
1
0
0
1
1
0
2
1
1
0
1
0
2
2
1
0
0
1
1
0
1
1
0
0
1
2
2
2
2
1
2
0
0
1
0
1
0
1
2
0
1
1
1
0
0
1
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
2
2
1
0
1
0
1
0
1
1
0
0
0
0
1
2
1
2
1
1
0
1
1
1
1
1
0
2
0
2
2
1
4
0
0
0
0
0
1
2
0
1
2
1
1
2
0
1
0
1
1
0
1
2
1
1
0
1
0
2
2
0
0
0
2
1
1
1
2
1
2
1
1
0
1
0
1
2
0
1
0
1
2
0
0
3
1
0
2
1
0
2
1
1
1
0
1
0
1
0
1
2
1
1
1
0
0
1
0
1
1
1
1
1
1
2
1
1
0
0
1
0
0
1
1
0
1
0
2
2
1
0
0
0
1
0
0
2
2
1
0
0
0
1
0
1
0
0
1
2
2
0
0
0
1
2
1
3
2
1
0
1
1
1
0
0
0
1
0
1
3
0
1
2
1
0
1
0
0
0
1
1
2
0
0
1
0
0
1
0
1
1
0
0
2
2
2
0
0
2
0
1
2
2
1
0
2
2
0
0
0
0
0
2
0
0
1
0
1
1
1
2
0
0
1
2
0
0
1
1
1
0
1
2
1
1
0
0
1
1
2
0
1
0
1
0
1
0
1
1
0
1
1
0
0
1
1
1
0
2
1
1
1
1
0
1
2
0
1
1
1
0
2
1
1
1
0
1
0
0
1
2
2
2
1
0
2
1
1
0
0
1
0
1
2
0
1
2
1
1
2
2
0
1
0
1
0
2
4
1
2
1
0
1
2
2
0
1
0
0
0
0
0
1
0
2
1
3
2
3
0
1
0
1
0
1
0
1
1
2
1
2
0
1
0
1
1
0
2
1
0
2
0
1
0
0
1
2
1
0
0
0
2
1
0
1
0
1
1
0
0
2
1
2
1
1
0
0
0
0
3
0
0
1
0
1
1
1
2
0
0
3
0
0
0
2
2
2
1
1
0
0
1
1
1
1
1
1
0
1
0
0
1
2
0
2
2
1
0
1
0
0
1
1
0
0
1
0
2
0
2
1
0
2
1
0
2
2
1
1
1
1
1
1
1
0
1
1
2
0
1
0
0
0
0
2
1
0
0
1
2
1
0
2
2
0
2
1
0
1
0
2
0
1
0
0
1
2
2
1
3
2
1
0
1
1
1
0
0
2
1
1
0
0
0
1
0
2
0
1
0
1
1
1
0
1
0
2
1
0
3
2
1
0
0
0
1
0
1
0
2
2
0
0
1
2
1
0
2
2
1
1
0
0
2
1
1
0
2
0
1
0
1
2
1
1
1
2
2
1
2
1
0
0
1
0
1
1
0
0
0
0
0
1
2
0
1
2
2
1
0
1
1
0
2
1
1
0
2
1
0
0
0
2
1
2
2
1
1
0
0
1
1
0
1
1
2
2
1
1
1
1
1
2
0
2
0
1
0
2
2
1
0
1
0
0
1
2
1
0
0
0
1
0
1
2
1
1
0
1
1
0
0
1
2
0
1
2
0
0
1
1
1
2
2
1
0
1
0
1
1
1
1
0
0
0
1
1
0
0
1
1
0
1
0
1
0
2
2
2
1
2
1
0
1
2
0
0
1
1
0
0
2
0
1
1
0
0
2
0
2
0
0
1
1
0
1
1
2
1
2
0
1
0
0
0
2
2
0
1
1
1
1
1
0
2
0
2
0
1
0
1
2
0
2
1
2
0
0
0
0
1
1
2
2
1
1
1
2
1
2
1
1
1
1
0
1
2
1
0
0
0
0
0
0
0
1
0
1
2
1
1
0
1
2
0
2
0
2
0
1
1
0
0
1
2
0
0
1
1
1
0
1
0
1
2
1
0
1
1
2
0
1
1
0
2
2
2
1
1
1
1
0
2
1
3
0
1
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
1
3
1
1
1
0
0
1
0
0
2
1
1
1
2
0
1
1
2
1
1
1
1
0
0
1
1
0
0
1
1
1
1
1
0
0
1
2
0
0
4
1
2
2
2
1
1
0
0
0
2
2
2
0
0
1
2
1
0
0
2
0
1
3
1
1
0
0
2
0
1
1
1
2
1
1
1
0
0
0
0
1
1
0
0
2
1
1
0
1
0
3
0
1
0
1
1
0
0
0
2
0
2
1
0
0
0
1
1
0
0
2
1
1
3
2
0
0
2
0
2
1
1
1
0
2
0
0
1
1
0
0
0
1
1
0
1
1
0
2
0
0
0
1
0
0
0
2
0
2
0
1
1
0
2
1
0
0
0
2
0
0
0
1
1
0
1
1
1
1
0
1
0
2
1
1
0
0
2
1
0
0
0
0
1
1
2
1
0
1
1
1
1
0
1
0
1
1
1
2
1
0
1
0
1
0
0
0
0
1
0
0
0
0
1
1
1
1
1
1
2
2
0
1
1
0
2
2
0
0
0
1
2
1
1
0
1
2
0
1
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
1
0
2
0
0
1
0
0
1
0
0
0
2
1
2
0
2
0
0
0
1
0
0
0
1
2
1
0
0
2
0
1
1
2
1
6
0
1
1
0
1
0
2
1
1
0
0
2
2
2
1
1
0
0
2
1
1
0
2
0
1
2
0
1
3
1
1
1
2
0
1
0
2
0
2
2
0
1
0
1
2
0
0
4
0
2
0
1
0
3
1
2
2
0
0
0
1
1
0
2
0
2
1
0
0
2
2
1
0
0
0
1
1
1
0
1
1
1
2
2
1
0
1
1
1
2
1
0
2
2
1
1
2
1
1
0
0
1
1
0
1
1
2
2
0
2
1
2
0
0
2
1
0
1
0
1
1
1
1
2
0
1
2
0
1
0
0
0
0
0
0
2
1
2
4
1
2
1
1
0
2
0
0
0
1
2
2
1
0
1
0
0
1
1
1
1
0
0
2
1
0
1
2
3
2
1
2
1
0
2
1
0
1
1
0
0
0
0
1
0
1
1
1
1
0
1
1
2
2
0
0
2
1
1
1
0
0
1
0
0
0
2
0
2
3
1
0
2
2
1
0
1
0
1
0
1
1
2
1
2
0
0
1
3
0
1
0
1
1
2
1
0
2
0
0
0
0
0
1
0
1
0
0
1
1
0
0
1
0
1
2
1
1
1
1
1
2
1
1
0
1
0
2
1
1
4
3
1
0
2
0
0
0
0
1
2
2
0
2
0
1
1
0
0
0
1
0
0
2
2
1
1
1
2
0
1
2
1
0
0
1
1
2
0
2
2
2
1
0
2
0
2
0
0
2
2
0
0
2
1
0
1
0
1
0
0
1
0
2
1
2
2
2
0
2
1
1
2
0
1
2
1
0
1
1
0
2
0
2
1
1
0
0
1
0
1
1
0
0
0
1
0
2
2
0
0
2
0
0
2
1
1
0
1
1
1
1
1
0
1
0
2
1
1
1
1
2
0
2
1
2
0
1
2
2
0
0
2
2
1
0
1
1
0
0
2
1
0
2
2
1
1
1
0
1
2
0
1
0
0
1
1
1
2
1
1
1
1
0
1
1
1
0
1
2
0
1
1
2
1
0
0
0
1
2
3
2
0
0
1
0
1
2
0
1
1
1
0
1
0
0
0
1
0
2
1
0
0
2
0
2
2
2
2
1
1
1
0
0
2
1
0
0
1
1
2
1
1
0
2
6
2
0
1
0
0
1
1
1
0
1
0
2
1
2
0
0
1
0
2
0
2
2
0
2
0
3
1
1
2
0
2
0
1
1
2
0
1
1
0
0
0
0
1
1
2
1
0
1
0
1
0
0
0
1
0
1
0
0
1
1
0
0
0
0
2
1
0
1
0
0
2
1
0
1
1
2
1
2
2
1
2
1
1
1
0
1
1
1
1
2
1
0
1
0
1
1
1
0
0
1
2
1
0
1
1
0
1
1
1
0
1
1
1
1
0
2
1
1
1
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
1
0
1
1
2
0
1
1
1
0
1
1
2
1
0
2
2
0
2
1
1
1
0
1
0
0
2
1
1
2
1
1
0
0
1
1
1
2
0
2
1
0
0
0
2
0
2
1
0
0
1
0
1
0
2
1
2
0
1
2
1
1
0
1
0
1
2
1
0
2
0
2
0
1
0
1
0
1
1
0
1
0
0
0
1
0
0
1
0
2
2
0
1
2
1
2
1
0
0
1
0
1
2
0
2
2
0
0
3
0
2
0
0
1
1
2
1
0
2
1
1
1
0
1
2
0
0
0
1
2
0
0
0
1
1
1
2
1
1
0
0
1
2
1
0
1
0
1
0
1
1
0
1
0
1
1
0
1
0
1
0
1
2
1
2
2
0
0
0
1
1
1
1
2
0
0
2
0
0
0
0
0
1
0
0
1
2
0
1
1
0
2
0
2
0
3
1
0
1
0
0
2
3
0
0
2
2
0
1
0
2
1
0
2
0
0
1
0
0
0
1
1
0
0
0
1
1
0
1
1
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
1
1
0
0
2
0
0
0
2
0
1
1
0
1
2
0
0
2
0
0
0
0
1
0
1
2
1
3
2
1
1
0
1
0
1
0
2
2
1
2
0
0
1
0
1
1
0
0
1
2
2
0
2
2
2
1
0
1
1
2
0
0
2
0
1
1
0
2
2
0
0
0
0
1
2
0
0
1
1
0
1
0
0
1
2
0
2
0
1
1
1
1
0
1
1
0
0
0
1
2
0
0
2
0
0
0
0
0
1
1
0
1
1
0
0
1
0
0
0
1
0
0
2
2
0
0
1
0
0
2
1
2
1
1
2
1
0
0
2
0
1
0
0
1
1
0
0
1
0
2
0
1
0
1
0
0
1
0
0
0
0
2
0
1
0
0
0
1
0
2
0
1
0
1
2
1
0
2
0
0
0
2
1
0
2
1
1
0
1
0
1
0
0
0
2
1
1
0
1
1
1
0
1
2
2
0
1
2
1
1
3
0
0
1
0
0
2
1
0
0
1
0
2
0
0
1
1
0
0
1
1
0
1
1
0
0
1
0
0
1
1
2
1
1
2
1
0
0
0
2
1
1
1
1
0
2
0
1
0
2
0
2
0
0
0
1
0
0
0
1
0
1
0
2
0
1
0
0
2
1
0
2
2
1
1
1
0
1
2
1
2
0
1
0
0
2
0
2
0
1
0
0
0
0
0
1
1
1
1
2
2
0
1
0
0
0
2
0
1
0
1
0
0
2
0
0
0
2
1
1
2
0
0
1
2
1
1
0
2
0
0
0
2
1
1
5
2
1
0
0
0
1
1
0
0
1
1
1
0
2
1
0
1
0
1
1
1
0
2
1
2
1
1
2
0
3
1
1
0
2
1
1
2
3
1
0
1
2
2
0
0
0
0
0
1
2
2
1
0
0
0
1
0
0
0
0
1
0
1
0
2
0
0
2
0
1
1
2
2
0
1
0
1
1
4
1
0
0
2
0
0
1
0
0
0
1
0
1
0
2
0
0
1
2
0
1
0
1
0
1
0
0
1
0
1
1
0
0
2
0
1
0
0
0
1
1
1
1
1
0
1
2
1
2
2
0
0
2
2
0
2
0
1
1
2
2
1
1
2
2
2
0
0
2
0
3
0
0
2
1
0
1
2
0
4
0
1
0
2
0
1
0
0
2
2
0
2
1
0
0
0
0
2
2
0
2
1
1
1
2
2
1
0
1
0
2
0
0
2
1
1
2
1
1
1
0
0
2
0
1
0
1
0
1
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
2
1
0
0
3
0
2
0
1
0
1
1
0
0
0
0
2
0
2
1
0
0
1
1
2
2
2
1
0
0
1
1
0
1
2
1
2
3
0
1
1
2
1
2
1
2
0
0
0
1
1
1
1
0
2
2
2
0
2
2
0
1
0
0
0
1
2
1
0
0
2
0
1
0
1
2
1
0
0
1
0
0
1
1
1
1
0
2
1
2
1
0
1
0
1
1
0
0
0
0
1
2
1
4
0
2
0
1
0
1
3
2
1
2
1
0
0
0
1
0
3
0
2
1
0
1
1
1
2
1
2
1
1
1
0
1
0
2
4
0
4
0
2
1
0
1
0
1
0
1
0
1
0
0
1
1
2
0
0
1
1
0
0
3
1
1
2
2
2
2
0
1
1
1
0
2
2
0
0
2
0
0
2
0
1
2
1
0
0
0
2
1
1
1
0
2
0
1
0
1
1
1
0
2
1
1
0
1
0
2
0
2
1
0
0
1
0
1
2
2
0
2
1
0
0
0
2
1
0
0
1
1
0
1
1
2
1
1
2
0
2
2
2
1
1
2
2
2
1
1
1
1
1
1
0
0
0
1
2
2
0
1
0
2
1
0
0
2
1
0
3
2
1
1
2
1
1
1
0
0
2
0
2
0
1
1
0
0
2
0
3
1
0
0
0
1
2
1
2
2
0
1
1
0
1
2
2
1
1
0
1
0
1
0
0
1
2
1
0
1
0
1
0
2
1
2
0
1
2
1
1
1
2
0
1
1
1
0
1
2
2
1
1
0
1
1
0
0
0
1
1
1
1
0
0
0
1
0
1
1
2
1
1
0
1
0
0
2
1
0
1
0
0
0
0
0
0
2
0
1
1
1
0
0
0
1
1
0
2
1
1
0
2
1
2
1
0
1
0
0
0
1
0
1
1
2
2
0
0
1
2
2
1
2
1
0
1
2
2
2
1
1
0
0
1
0
1
0
1
0
0
1
1
0
0
1
0
0
2
1
0
1
0
0
2
0
1
0
1
0
2
1
0
1
0
1
2
1
0
2
1
0
0
2
1
1
1
2
1
0
0
1
2
1
0
1
0
2
1
0
1
0
1
0
1
2
2
0
0
1
2
1
2
0
1
0
0
0
0
0
3
1
2
2
0
2
2
0
2
0
1
1
0
0
0
2
2
1
1
2
1
0
1
1
0
0
1
1
1
1
0
0
0
0
0
2
1
1
1
1
0
0
0
2
0
0
1
2
0
1
0
2
0
2
1
1
2
1
0
0
0
1
3
1
1
4
0
0
1
0
0
2
1
0
1
1
0
4
1
2
2
2
1
0
2
0
1
0
2
1
2
1
0
0
0
0
0
0
1
1
0
1
1
1
0
0
1
1
2
2
2
1
1
3
2
1
0
1
0
1
2
0
0
2
2
0
0
1
1
2
1
1
0
1
1
1
0
2
2
1
0
0
2
2
0
1
1
1
0
2
1
2
0
0
2
1
0
0
1
3
0
1
0
0
2
1
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
1
1
0
1
1
0
0
0
2
0
0
1
2
4
1
0
0
0
1
0
0
4
1
0
2
0
1
1
2
2
0
1
1
1
1
1
1
1
0
1
2
1
2
1
1
1
2
1
0
2
0
0
2
2
0
1
1
2
2
1
0
0
1
2
2
1
0
1
0
1
2
1
1
0
1
1
0
0
1
0
0
1
0
1
0
2
1
0
2
1
1
0
0
0
0
2
1
0
0
0
1
1
2
1
2
2
1
1
1
1
0
0
0
0
0
0
1
0
1
2
1
1
2
0
0
1
5
1
1
1
0
1
0
1
2
2
0
0
2
0
0
2
0
2
1
0
1
0
2
1
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
2
1
2
3
0
0
1
2
1
0
0
1
0
1
1
0
1
1
2
2
0
0
0
1
3
1
0
1
0
0
0
1
0
0
1
0
0
1
0
1
1
2
0
1
0
2
0
2
1
0
1
1
0
0
1
1
0
0
2
2
0
1
2
0
2
2
2
0
0
3
0
1
1
1
2
2
0
1
1
1
0
1
2
0
1
0
2
1
0
1
2
1
0
2
1
2
0
0
1
1
1
0
1
0
0
0
0
1
1
1
1
1
1
1
0
0
2
0
1
0
0
1
2
1
0
0
2
0
1
1
1
1
0
0
0
2
1
1
0
1
1
1
0
0
1
1
1
2
1
0
0
2
0
2
1
2
1
1
1
0
2
0
2
1
0
2
2
2
1
2
0
2
0
0
1
0
1
1
2
0
1
0
1
1
1
1
1
3
2
1
1
0
2
0
1
0
0
0
3
0
1
0
1
0
1
1
0
0
1
0
1
0
0
1
0
0
1
0
0
2
0
2
0
0
1
1
0
1
0
0
0
2
1
1
0
0
1
0
1
0
2
0
1
2
0
1
1
2
1
1
1
1
0
0
0
1
0
1
1
0
1
0
0
2
0
2
2
1
1
2
0
0
1
1
2
0
1
2
0
0
1
0
2
0
2
2
2
1
2
0
0
0
0
1
1
2
3
0
1
1
0
0
0
1
1
1
0
1
0
0
1
1
1
2
1
1
1
1
0
2
0
2
2
0
1
0
1
1
1
1
1
1
1
0
2
0
1
1
0
0
0
2
1
1
0
1
0
0
1
2
0
0
1
1
1
2
1
2
0
1
2
0
0
2
0
1
2
2
1
1
1
2
0
1
2
1
1
1
1
2
0
0
0
0
0
1
0
1
1
1
1
0
2
1
0
0
4
3
1
0
1
0
2
0
1
2
0
2
2
1
2
1
0
0
2
1
2
2
2
1
0
0
0
2
2
1
1
1
0
2
0
1
1
2
2
2
1
1
1
2
0
0
1
2
1
1
1
1
1
0
0
0
2
1
1
1
1
1
1
1
1
1
2
0
1
0
1
0
1
2
1
0
0
1
0
0
0
1
1
1
0
1
2
0
0
1
1
0
0
1
1
0
1
1
1
1
7
0
3
0
1
0
0
2
0
1
0
0
0
0
2
0
1
1
0
0
0
0
2
1
0
1
1
1
2
2
0
0
0
1
1
2
1
0
1
0
1
2
3
2
0
1
0
2
1
0
0
0
1
0
0
0
0
2
0
1
0
1
0
0
0
0
0
1
1
1
0
0
0
1
1
0
3
0
0
2
2
0
0
1
2
0
0
1
1
0
0
1
0
0
0
1
0
0
1
2
1
0
1
0
0
1
1
1
2
2
2
1
2
2
1
1
1
2
1
0
2
0
1
2
0
2
0
1
0
1
1
2
1
0
2
1
1
2
0
1
1
1
0
0
0
1
2
0
1
1
1
1
0
1
0
2
0
0
3
1
1
1
1
1
0
1
1
1
1
1
2
1
0
1
0
1
2
1
1
2
0
2
1
1
0
2
0
1
1
0
2
0
0
2
0
1
0
1
1
0
1
1
0
0
2
2
0
1
2
1
0
0
2
1
1
1
0
0
1
2
1
0
1
1
1
0
0
0
2
1
0
1
1
0
1
2
13
1
2
2
0
1
0
1
1
2
0
0
0
1
0
2
0
0
0
0
0
1
1
1
2
1
0
1
0
1
2
0
0
1
1
0
2
0
1
0
1
2
1
0
0
0
2
1
0
2
1
0
1
1
1
0
2
0
1
0
0
0
1
2
2
0
1
0
1
1
2
2
0
2
0
2
2
0
4
0
2
2
0
1
0
1
1
0
1
1
0
1
2
0
1
1
1
2
1
2
0
1
1
0
1
0
1
2
2
0
1
0
0
2
0
0
1
0
2
0
1
0
0
0
1
2
2
0
1
1
2
1
2
0
0
1
1
1
1
0
1
1
0
0
0
0
2
0
2
0
0
0
1
0
0
1
1
1
0
1
2
2
0
1
3
0
1
0
1
1
2
1
0
0
0
0
1
2
2
0
1
1
0
2
1
0
1
1
0
0
0
1
1
1
1
0
0
0
2
1
0
1
0
2
1
0
2
1
0
3
0
2
1
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
2
1
1
0
3
1
0
1
1
1
0
0
0
0
0
1
2
2
1
0
1
1
0
0
1
0
0
0
0
2
0
0
1
0
2
1
1
0
0
1
1
1
0
0
0
0
2
1
0
0
0
0
0
1
0
1
1
0
1
0
2
1
0
1
0
1
0
0
0
2
2
1
2
0
0
2
1
1
1
3
1
0
2
1
0
2
2
1
2
1
0
2
1
2
1
1
1
2
0
2
0
1
0
0
1
1
1
2
1
0
0
0
3
0
0
1
2
0
1
0
1
1
1
0
0
1
0
1
0
1
3
1
1
0
0
1
1
1
0
2
1
0
1
1
2
2
2
2
1
0
0
1
0
0
0
1
1
1
1
1
0
0
1
1
0
1
0
0
1
0
0
0
2
3
0
0
0
1
1
1
1
1
2
1
1
2
4
0
2
2
1
0
0
1
1
1
2
2
1
0
0
0
1
2
0
1
4
0
2
1
2
0
0
1
2
0
0
0
2
0
0
1
1
1
2
0
0
0
0
0
0
1
1
1
0
0
1
0
1
1
1
3
2
1
1
0
0
1
0
1
2
0
0
1
0
0
0
1
0
2
3
0
0
1
0
0
2
1
1
1
0
0
1
0
1
2
0
2
0
4
1
0
2
1
2
0
0
0
0
0
0
1
2
1
2
2
0
0
2
0
0
1
2
2
2
1
0
0
0
1
1
2
0
1
0
0
1
2
0
0
0
0
0
0
2
0
1
1
3
0
2
7
0
0
0
0
0
1
1
0
1
1
1
0
1
2
0
1
0
1
1
1
1
1
1
0
0
2
2
2
2
1
0
0
0
1
0
2
2
2
1
2
0
2
1
1
1
0
2
1
1
1
1
0
0
0
0
1
1
2
2
3
0
1
1
0
0
1
1
1
0
0
1
0
2
0
0
0
0
0
1
2
2
0
1
1
2
1
1
1
1
0
1
0
0
1
0
1
0
0
0
1
2
1
1
1
0
2
0
1
1
0
0
0
0
1
0
1
0
1
0
1
0
1
2
1
0
0
1
1
2
1
2
1
3
1
0
2
0
0
0
2
0
2
2
2
2
0
1
1
0
1
0
2
2
0
1
1
0
1
0
1
1
2
1
2
2
0
1
1
2
1
0
0
0
0
1
1
2
2
1
2
1
1
2
0
2
0
2
0
0
0
1
0
2
1
1
0
1
2
0
2
2
0
1
2
1
0
0
2
0
1
2
0
0
1
2
2
1
1
2
1
0
1
0
0
0
3
1
1
1
0
0
1
0
1
0
2
1
2
1
1
1
1
0
0
1
1
0
0
0
0
2
1
0
2
1
2
2
0
0
1
0
2
1
0
1
0
0
2
1
0
2
0
2
1
1
1
1
1
0
1
1
1
0
1
2
0
1
2
0
1
1
1
1
2
1
0
2
2
0
0
0
0
1
1
0
0
1
1
1
0
1
1
1
0
1
2
2
2
0
0
1
1
0
1
0
1
1
1
1
0
2
1
2
2
0
1
1
2
2
2
1
1
1
1
1
0
1
2
1
1
1
0
1
1
2
1
0
0
1
1
1
0
1
2
1
3
2
0
0
1
2
1
0
2
2
0
1
2
2
2
2
2
1
0
1
0
1
1
0
2
0
2
2
0
1
0
0
1
2
1
0
0
1
1
1
1
0
1
1
0
2
1
0
1
2
1
0
1
2
0
1
2
0
2
1
1
1
0
1
2
0
0
0
0
1
0
2
0
0
1
1
1
0
0
3
1
0
0
0
0
0
1
0
1
2
0
1
0
1
0
1
0
4
0
0
1
2
0
0
0
1
0
2
2
0
0
0
0
1
0
1
2
0
1
0
0
1
1
0
0
2
1
4
0
1
0
0
1
1
0
2
1
0
2
0
1
2
0
0
1
1
0
1
1
0
0
0
1
2
0
0
1
1
1
2
0
1
1
1
2
0
1
0
1
2
0
0
1
1
0
1
2
0
1
1
1
1
1
1
1
0
0
0
2
2
2
0
2
0
2
0
0
2
2
0
2
0
0
1
2
2
2
1
3
2
1
0
0
0
1
1
0
1
0
1
0
1
1
1
1
0
3
1
1
2
0
0
1
2
2
1
2
1
2
0
1
0
1
1
1
1
2
0
1
2
0
2
2
1
0
0
0
1
2
3
1
2
1
2
2
0
0
0
0
1
2
0
0
0
1
2
0
0
2
2
2
0
1
0
2
2
1
0
0
0
1
3
0
1
1
1
0
1
0
4
2
0
1
0
0
1
1
2
0
0
0
1
1
0
0
1
1
1
0
1
0
0
0
1
2
3
0
0
1
1
1
0
1
1
1
0
1
0
2
1
2
1
1
0
1
0
0
0
0
0
2
0
0
2
2
2
2
0
0
1
1
3
0
0
0
0
1
0
1
0
1
1
0
2
1
1
1
0
0
1
2
1
2
0
0
1
0
0
2
2
0
2
2
1
0
1
1
0
1
1
1
0
0
2
1
1
1
1
2
0
1
1
1
0
2
0
2
1
0
2
0
1
0
0
1
0
1
1
1
0
1
0
0
0
0
2
2
2
2
2
1
0
1
1
1
2
3
0
1
2
0
1
2
0
2
2
1
1
0
1
0
0
0
0
3
1
1
0
0
2
0
1
0
1
2
2
0
1
1
0
0
2
0
0
2
1
0
1
1
1
2
0
1
1
2
0
1
1
0
2
2
0
1
2
1
2
1
2
1
1
2
2
1
1
2
1
0
1
1
2
0
0
2
0
0
2
1
1
1
0
1
1
2
1
0
1
0
0
2
0
1
0
2
0
2
0
1
0
2
0
2
0
2
2
0
0
1
1
0
1
1
0
0
1
0
0
0
2
0
1
0
1
1
2
1
0
1
1
0
0
1
0
0
0
2
1
2
0
2
2
0
1
1
0
0
0
0
0
0
1
1
0
0
2
1
0
0
0
0
1
2
1
0
1
1
0
0
2
2
0
1
1
1
1
0
0
2
2
2
0
0
0
0
1
0
2
1
2
0
2
1
0
1
2
2
0
1
0
2
0
1
2
0
0
1
1
0
0
0
0
0
2
0
1
0
1
0
0
0
0
1
0
0
2
0
0
1
1
2
1
0
1
0
1
0
1
0
1
1
0
0
0
1
0
0
1
1
1
1
2
1
0
1
2
0
1
1
0
1
0
0
1
1
1
1
2
2
0
2
2
0
1
1
0
1
1
1
1
0
0
1
0
0
1
1
0
1
0
0
1
0
2
1
1
1
1
1
1
0
0
1
0
1
2
0
1
2
0
1
0
0
1
1
0
1
0
0
1
3
2
1
1
0
1
0
0
1
2
2
2
1
0
0
0
1
0
0
2
0
0
2
1
0
1
1
0
0
0
2
1
2
2
1
2
0
1
1
1
1
1
0
1
2
1
2
1
0
0
0
2
1
2
1
1
2
0
1
4
2
2
0
0
1
1
1
1
1
0
2
0
1
2
1
2
1
0
0
1
1
1
0
1
1
2
0
1
1
1
0
2
2
0
0
0
1
0
1
1
1
1
0
2
2
1
0
2
0
1
2
1
2
1
1
2
1
0
0
2
2
0
1
0
1
2
0
0
0
2
0
0
0
0
2
0
1
1
1
2
1
1
0
0
2
0
2
1
2
0
0
2
1
1
0
0
1
0
0
0
2
1
2
0
0
0
0
1
2
2
2
0
0
0
1
2
1
0
0
2
0
2
2
0
1
1
2
0
0
2
2
2
1
1
0
0
1
0
0
0
1
1
1
0
0
1
0
2
0
1
2
1
1
1
0
1
2
0
2
0
0
0
0
1
2
0
1
0
1
1
1
0
1
2
0
0
0
1
2
2
1
2
0
0
1
0
0
0
2
2
0
0
1
1
1
0
0
0
1
0
3
2
0
2
1
0
0
0
1
2
2
0
2
0
2
0
1
2
2
1
1
1
1
0
1
1
2
2
0
0
0
2
0
2
1
1
3
0
0
1
1
0
1
1
0
0
2
0
2
2
1
0
0
3
2
1
0
1
0
1
0
2
0
1
2
1
1
2
1
4
0
1
0
0
1
2
0
1
2
1
2
1
1
0
0
1
1
1
0
0
2
2
2
2
0
1
1
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
1
1
1
1
1
1
0
0
1
0
1
0
3
1
1
0
0
1
2
1
1
0
2
1
0
1
1
2
0
0
0
0
0
2
1
1
0
0
0
0
1
1
0
1
1
1
1
1
1
0
2
0
2
0
0
1
0
1
2
1
1
2
0
0
2
2
0
0
0
1
0
2
2
2
0
1
1
0
3
0
1
1
0
0
2
1
0
1
2
3
1
1
1
2
1
1
1
0
0
2
0
1
0
1
0
0
1
0
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
0
0
0
0
1
2
2
2
2
0
0
0
2
1
1
2
2
0
1
1
1
0
0
1
1
0
3
0
1
0
1
2
0
0
2
0
1
1
2
1
1
0
1
0
1
0
0
0
0
2
1
1
0
1
0
0
0
1
1
1
2
0
0
1
2
1
0
1
1
0
0
0
0
2
0
3
3
0
0
2
1
0
2
0
0
1
0
1
0
1
1
1
2
0
2
2
1
0
0
1
1
1
1
2
2
0
1
3
0
1
0
0
1
2
0
0
2
1
2
0
0
0
2
2
0
0
1
0
0
1
2
1
2
2
2
1
2
0
0
1
2
0
1
0
1
2
2
2
2
0
1
0
1
1
1
0
1
1
0
1
1
0
0
2
2
2
0
0
0
0
1
2
1
0
1
2
0
2
0
2
2
0
0
0
0
0
2
0
1
2
1
1
0
1
1
0
1
1
1
2
2
0
0
1
0
1
2
1
0
1
1
1
0
0
2
1
1
1
1
1
1
1
2
3
2
0
1
1
0
0
0
0
1
0
0
1
0
0
0
2
0
1
1
2
0
0
2
1
0
0
2
0
0
1
0
0
0
1
2
1
0
2
0
0
1
0
0
0
2
1
0
0
1
1
1
1
1
2
2
1
0
1
1
1
2
0
0
0
2
2
0
2
0
0
0
1
2
2
2
0
1
2
1
2
0
1
2
1
0
0
0
1
0
1
0
1
7
1
1
0
2
1
0
2
0
1
2
1
2
0
2
1
2
1
0
2
0
2
0
0
2
0
1
2
1
0
1
0
2
1
0
2
1
0
1
2
2
0
0
2
1
0
1
2
0
0
0
1
1
1
0
2
0
1
1
2
0
0
2
1
0
0
0
0
2
1
0
0
0
1
2
0
2
1
0
0
0
2
1
0
1
1
1
0
1
0
0
0
0
0
2
1
0
0
1
1
4
0
0
5
2
0
2
0
3
1
1
1
0
0
1
1
0
0
1
2
2
1
1
1
2
0
0
2
2
2
0
1
2
1
0
1
1
0
1
2
0
0
2
1
0
1
0
2
2
0
0
1
0
1
1
2
0
2
0
1
1
0
0
1
0
0
0
0
0
0
0
1
2
1
2
3
0
0
2
2
2
0
1
1
2
0
0
1
1
1
0
2
1
1
2
2
1
0
3
0
0
1
1
1
0
2
1
2
1
2
3
1
1
0
1
1
2
0
1
0
0
4
0
1
2
0
0
0
0
1
1
0
2
0
2
2
1
0
2
0
1
1
1
0
0
1
0
1
2
0
0
0
0
1
0
1
2
0
1
0
0
1
2
0
0
1
0
3
0
0
2
1
1
0
1
0
0
1
2
1
1
0
0
0
0
1
1
1
0
0
0
0
1
0
1
1
0
0
0
2
0
1
0
2
0
0
0
4
0
2
2
0
2
0
1
1
2
0
1
2
1
1
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
2
2
0
1
1
0
0
1
1
0
0
4
1
1
0
0
0
1
1
0
1
2
2
1
1
2
2
0
1
2
0
1
0
0
0
0
1
2
0
2
1
1
2
1
0
0
1
0
1
0
0
1
2
0
0
0
1
1
0
2
1
0
1
0
1
1
1
1
2
0
1
1
2
0
0
0
0
0
1
0
2
2
0
2
0
1
2
1
0
0
0
0
1
2
0
1
0
0
0
0
2
2
1
2
0
1
0
2
0
1
1
0
1
0
1
0
2
1
0
2
1
0
1
0
1
0
0
0
0
2
2
1
0
0
0
2
0
1
2
1
2
0
0
1
0
0
1
1
2
1
3
2
1
1
1
1
1
2
1
0
0
1
0
5
0
1
2
1
0
0
0
0
1
1
2
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
2
1
0
1
1
0
1
0
0
2
1
2
0
1
0
2
1
1
0
0
1
1
1
1
0
0
0
0
2
2
0
0
0
1
0
0
0
1
0
0
0
1
2
1
1
1
1
0
1
0
0
0
1
0
1
1
1
0
2
0
1
2
2
1
0
2
2
0
0
2
0
0
0
0
1
1
1
0
1
2
0
0
1
1
0
0
1
2
1
1
1
1
1
1
0
2
0
1
0
2
2
2
1
0
1
1
0
0
0
1
1
0
2
1
2
0
0
0
0
0
1
1
0
2
1
1
0
1
2
1
0
0
0
1
2
0
2
2
2
1
2
0
0
1
0
0
0
2
1
0
0
2
1
1
0
2
1
1
1
0
1
1
1
0
0
0
0
0
1
1
0
2
0
0
2
1
1
1
2
1
1
1
0
1
0
0
0
0
2
0
0
0
1
0
1
1
0
1
2
0
1
1
0
1
0
0
0
0
0
1
1
1
2
1
0
1
0
0
2
0
0
1
1
1
2
2
0
0
2
1
2
0
1
0
0
1
1
0
0
1
1
1
1
1
0
2
2
1
0
1
0
0
1
0
2
2
3
3
0
3
1
1
2
1
1
1
1
0
0
0
1
1
2
0
0
1
2
0
1
0
0
0
0
1
1
3
1
0
6
3
0
2
1
1
1
0
1
2
0
0
1
2
1
1
2
2
2
0
0
2
1
0
1
0
2
0
1
1
1
1
2
1
0
0
1
1
1
0
1
2
1
0
0
0
2
1
0
3
1
1
2
1
1
2
1
0
2
0
0
2
0
2
0
1
0
2
6
2
0
1
0
1
0
1
2
2
0
1
1
2
1
1
0
1
3
1
0
1
1
1
1
1
0
0
2
0
0
1
1
1
2
0
2
1
0
2
0
1
2
1
1
1
0
1
0
2
2
2
1
1
0
0
2
1
1
0
0
1
2
0
1
1
1
2
1
1
2
1
0
1
1
0
2
1
1
0
1
1
1
1
1
1
3
2
2
1
2
1
1
0
1
1
0
1
0
2
2
0
2
0
1
1
3
1
2
1
0
0
2
2
1
1
2
2
1
0
2
1
0
0
1
1
1
0
1
0
1
2
0
0
0
2
2
0
1
1
0
0
1
2
1
2
0
1
1
2
0
0
1
1
0
0
2
1
1
2
0
1
0
2
0
1
0
0
0
2
1
1
2
1
0
3
0
2
8
0
0
0
0
1
0
1
0
1
2
1
0
0
1
0
1
1
1
2
0
0
0
1
2
0
0
2
1
2
1
1
1
1
0
1
0
1
1
0
0
0
0
0
1
2
2
2
0
2
2
1
1
1
2
1
2
0
2
1
0
0
0
0
1
1
1
0
1
2
1
0
2
1
0
0
0
1
1
1
0
1
2
1
0
1
2
0
2
1
0
1
0
2
1
0
1
1
0
1
0
1
1
1
0
0
0
0
0
0
3
0
2
1
0
1
2
1
0
0
0
1
0
0
1
2
2
1
0
2
2
0
2
0
1
0
2
1
0
1
0
0
3
1
2
0
0
0
0
5
1
0
0
0
2
0
1
0
2
1
1
0
2
0
1
2
0
0
0
2
0
0
1
0
0
0
1
1
0
0
0
2
0
1
3
0
1
0
0
1
2
1
0
0
2
0
1
1
2
1
0
0
0
2
1
0
1
1
2
1
1
2
2
0
0
1
3
3
0
1
1
0
1
0
0
1
0
1
1
1
0
2
1
0
1
0
2
2
1
1
1
0
2
0
1
1
1
0
0
0
1
0
1
1
1
0
2
0
0
2
2
2
2
1
0
1
0
0
1
2
2
1
0
0
0
2
2
1
1
0
1
1
2
0
0
0
1
0
1
0
1
1
2
1
1
2
1
0
1
1
1
0
0
1
2
1
1
1
0
0
1
1
2
2
0
2
1
2
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
1
1
0
0
0
2
0
1
1
0
0
1
1
0
1
1
1
1
2
0
2
0
0
0
1
0
1
2
0
0
0
2
1
1
0
1
0
0
1
1
0
0
2
0
0
0
0
1
0
5
0
2
1
0
1
1
2
0
2
2
1
2
0
0
0
1
2
1
1
0
0
0
1
0
1
2
2
1
0
3
2
0
1
0
1
2
1
0
3
2
1
1
1
0
0
0
0
1
0
0
2
0
2
0
1
1
0
0
0
0
1
0
0
0
2
0
2
1
2
0
0
2
2
2
1
0
1
1
1
2
0
1
1
1
1
2
1
2
1
2
0
1
4
0
1
0
1
2
0
0
1
0
0
1
0
0
0
1
2
0
0
1
0
2
0
1
2
0
1
1
0
0
1
2
2
2
1
2
1
2
1
0
0
1
1
0
0
2
1
1
1
0
2
1
0
1
1
1
2
2
1
1
1
0
0
0
2
1
0
0
2
1
1
0
1
0
2
0
1
1
0
0
0
2
2
0
0
2
2
3
1
0
0
2
0
1
0
1
0
1
1
0
2
1
1
1
2
2
0
1
1
1
2
2
1
1
1
2
0
2
0
0
0
5
0
2
1
1
1
1
0
0
1
0
1
1
1
1
1
1
1
1
0
1
2
2
0
2
0
0
2
2
1
2
0
1
1
0
0
0
0
2
1
0
0
2
0
1
0
1
2
0
0
1
0
2
1
0
0
0
1
2
0
1
2
1
3
1
0
0
0
1
1
1
1
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
2
2
0
0
0
0
0
0
0
1
0
0
1
0
1
2
1
2
0
0
1
4
2
1
0
0
3
0
0
1
0
1
1
2
0
0
2
1
0
3
1
2
2
2
1
0
1
0
1
1
0
0
1
2
1
2
2
2
0
0
0
3
0
0
1
0
0
2
1
2
0
2
0
0
2
1
0
0
2
2
1
1
0
32
1
0
0
0
0
0
1
0
0
2
1
2
1
2
2
0
2
0
0
1
0
0
1
2
2
0
0
1
2
0
1
1
0
2
1
0
1
1
2
1
2
1
0
0
0
1
0
0
2
1
2
0
2
1
1
2
1
0
3
0
2
2
2
2
1
0
0
1
2
2
1
0
0
0
1
2
2
1
0
1
0
0
2
1
1
1
1
0
2
0
1
1
1
0
1
1
0
1
0
0
0
1
2
0
0
0
0
0
2
1
1
0
2
0
0
0
0
0
1
2
1
1
0
1
1
2
1
0
0
2
0
1
0
0
1
1
1
2
0
1
0
0
1
2
0
1
2
1
0
1
1
0
1
2
0
0
1
1
0
1
0
1
1
1
1
1
2
1
1
0
2
1
0
0
0
0
2
1
0
0
1
0
3
0
1
0
0
1
2
1
2
1
1
0
0
1
0
1
1
0
1
1
0
1
0
0
0
0
2
0
0
1
0
0
0
0
1
1
0
0
1
0
0
1
1
2
0
1
1
1
1
1
2
2
0
0
1
0
2
1
0
2
3
0
0
0
0
1
1
0
1
0
2
0
0
1
1
2
0
0
0
0
0
3
0
2
1
1
0
3
1
0
0
0
0
2
1
0
0
1
1
0
0
0
1
1
2
0
2
0
0
1
0
2
1
1
0
1
2
1
0
0
0
0
1
2
0
1
1
0
0
2
0
1
2
1
0
2
2
0
0
1
1
2
0
0
1
1
0
1
0
0
1
1
1
1
0
1
0
0
2
0
0
1
0
1
1
1
1
1
1
1
1
1
1
0
0
0
0
1
1
0
1
1
2
2
2
1
1
2
1
1
2
1
1
2
2
0
8
2
1
2
1
1
0
0
0
0
0
2
1
1
1
0
0
2
2
1
3
0
1
2
0
2
0
2
2
1
0
0
1
0
1
0
1
0
1
2
2
0
0
0
0
0
0
0
2
0
2
1
3
2
0
1
1
0
2
1
1
2
2
2
2
2
0
1
1
1
0
0
2
0
1
0
1
0
0
0
2
1
0
0
0
1
0
0
1
1
0
1
0
0
3
1
0
0
0
0
2
1
1
1
2
1
1
0
0
0
0
1
1
0
2
0
1
1
2
1
1
2
2
1
2
1
0
6
1
0
2
0
1
0
0
0
0
1
0
0
0
0
2
1
1
2
1
0
0
0
0
1
1
0
1
0
1
1
1
0
1
1
1
2
1
2
2
1
1
0
1
0
0
0
0
0
1
1
1
1
1
0
1
2
0
1
1
0
2
2
0
1
3
1
0
0
0
0
0
1
1
2
1
0
0
2
0
1
1
0
1
1
4
1
0
2
1
0
2
0
0
0
1
1
0
5
2
1
1
1
0
1
0
2
1
2
1
0
1
1
0
1
2
2
2
0
0
1
1
0
2
0
2
0
2
0
2
0
2
0
2
0
2
2
0
2
0
1
2
1
2
1
0
1
2
0
1
0
0
2
0
0
0
1
0
1
1
2
0
1
1
0
1
2
0
1
0
1
1
4
1
1
1
1
2
0
1
0
0
0
0
1
2
0
0
0
1
2
0
0
2
0
3
0
0
1
1
2
2
1
1
0
3
0
1
3
0
1
0
1
2
2
1
0
0
1
2
2
0
0
3
0
0
0
2
1
0
0
0
0
0
0
1
1
1
1
2
0
0
0
1
0
1
0
2
2
0
0
2
0
0
1
0
1
2
1
0
2
0
1
1
0
1
2
0
1
1
1
1
1
1
0
1
1
1
0
2
0
2
1
0
0
2
1
2
0
0
0
1
1
0
1
1
0
1
1
1
0
0
2
0
1
1
1
0
1
0
1
2
0
2
1
1
0
0
2
2
2
1
2
1
1
1
1
1
2
1
1
1
1
2
1
2
0
0
0
1
1
0
2
1
1
0
0
1
0
2
1
0
0
1
0
0
1
1
2
1
0
0
0
1
0
0
1
2
0
2
0
0
2
0
2
0
2
2
1
0
0
1
0
0
1
2
0
1
0
1
0
0
1
1
2
1
1
2
1
1
2
0
1
1
1
0
2
0
1
1
0
1
1
1
1
0
1
2
7
1
1
2
2
0
1
0
0
1
1
2
1
0
3
1
0
1
1
0
0
1
2
1
2
2
1
0
1
1
0
2
1
0
0
1
0
0
1
1
1
1
1
0
2
1
2
0
1
0
1
1
1
2
2
1
2
0
0
0
0
0
1
0
0
0
2
0
1
0
0
1
1
0
2
1
0
1
0
0
0
0
0
2
0
2
0
1
0
0
2
0
1
0
1
2
0
0
0
0
2
2
0
2
0
0
1
2
1
0
2
0
1
0
1
2
1
2
0
0
2
0
1
1
0
0
1
2
0
3
0
1
0
1
0
0
1
1
0
0
2
1
0
1
2
2
1
2
0
2
1
0
0
1
1
1
2
2
0
1
5
2
1
0
0
3
0
1
0
0
1
0
1
0
1
0
2
1
2
0
1
1
2
0
1
0
0
0
1
1
0
2
1
1
1
0
1
1
1
2
1
2
0
1
2
0
0
0
1
2
0
0
0
1
1
1
2
1
2
1
1
1
0
1
0
0
0
2
0
1
0
1
1
1
1
1
1
1
0
1
1
0
1
2
2
2
1
1
1
2
1
0
2
0
0
0
0
1
2
0
0
1
0
0
1
1
1
0
0
1
1
1
1
1
2
1
0
1
1
2
0
2
0
1
1
1
2
2
1
0
2
1
2
1
1
0
2
1
1
2
0
2
1
0
2
2
1
0
0
0
1
0
2
2
2
1
1
2
1
1
0
2
0
1
0
0
2
0
1
2
1
0
0
1
0
1
2
1
2
1
1
1
0
0
2
0
1
2
1
1
1
1
0
0
1
1
0
1
0
1
0
0
0
2
1
0
0
1
0
0
0
0
1
2
0
0
1
2
0
0
0
2
0
0
1
0
2
2
1
1
1
0
1
1
0
1
1
0
1
0
2
0
1
2
0
1
1
1
2
1
3
1
0
0
2
2
0
1
0
1
1
1
1
0
1
1
0
0
1
0
0
2
1
0
0
0
1
0
1
1
2
0
0
0
0
0
0
1
1
1
0
1
1
1
1
0
0
2
2
1
0
0
1
0
1
1
2
1
1
0
1
0
0
1
0
2
0
2
1
2
0
0
2
0
1
1
0
0
0
1
2
1
1
3
2
0
1
0
2
0
0
1
2
1
0
0
0
1
1
0
2
2
1
0
1
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
2
2
1
1
2
0
0
0
0
1
1
1
2
2
2
1
2
0
2
0
0
1
2
2
0
0
1
1
0
0
1
1
1
0
0
0
0
2
0
1
0
1
0
1
1
0
0
0
0
0
0
1
1
1
0
0
0
1
1
1
0
2
0
0
0
1
2
0
1
0
1
0
1
0
1
1
0
0
0
2
2
1
2
1
2
0
1
0
0
0
1
2
0
0
0
0
1
0
2
0
0
1
2
0
0
1
2
0
0
0
0
1
1
2
0
1
1
0
0
1
2
0
0
0
1
0
0
0
1
1
1
0
1
1
0
4
2
0
1
2
0
1
0
2
1
5
2
0
0
1
1
1
2
1
0
0
0
0
0
0
0
1
1
1
1
2
0
2
1
1
1
2
2
1
0
0
0
2
1
3
0
2
1
0
0
2
0
2
0
0
1
0
2
2
0
0
2
0
0
1
0
2
1
0
1
0
1
0
1
0
1
0
0
2
1
0
1
0
1
1
1
2
1
1
0
1
2
1
2
0
0
0
0
2
1
1
2
0
0
0
0
0
0
1
1
0
1
1
1
0
0
1
0
1
1
0
1
1
2
0
1
1
1
0
2
1
2
1
0
0
2
1
0
1
1
0
0
0
1
0
0
0
0
2
1
2
0
0
0
3
1
1
1
0
1
0
1
0
1
1
0
1
3
1
1
2
0
2
2
2
1
2
1
0
2
2
1
0
1
2
5
1
0
1
0
1
0
1
0
0
2
1
1
0
0
1
0
0
1
1
2
0
0
1
2
1
1
1
2
2
0
1
0
0
0
0
0
2
0
1
0
0
0
1
1
2
2
1
2
0
2
0
1
1
2
1
0
2
2
2
1
0
1
0
2
1
1
3
0
2
0
0
2
1
1
1
0
0
0
0
1
0
1
0
1
0
0
0
1
3
1
1
2
0
1
1
1
1
0
0
0
2
0
1
2
1
0
0
1
1
0
1
0
1
2
1
2
2
0
1
0
1
1
0
1
1
1
1
0
1
0
1
1
1
0
2
0
1
0
1
1
1
1
9
1
0
0
2
1
1
1
0
2
0
1
0
1
1
2
1
3
1
1
2
1
1
0
2
1
1
0
1
1
0
2
0
2
1
1
1
0
0
2
1
2
2
2
0
1
0
1
1
0
2
1
2
0
0
0
1
2
0
1
0
0
1
1
0
2
1
1
0
0
0
1
1
2
1
2
0
2
2
1
2
2
3
1
1
1
0
2
0
2
1
1
0
0
1
2
2
2
0
1
0
0
1
1
0
1
0
1
1
1
0
2
0
2
0
0
2
0
0
2
2
0
0
1
1
0
2
1
0
2
0
0
2
2
0
1
0
0
0
0
1
3
0
2
1
0
0
2
0
2
2
1
2
0
0
0
0
1
2
0
2
1
0
1
0
1
1
0
0
0
1
2
0
1
1
1
0
1
0
1
1
0
0
0
4
0
2
1
1
1
0
1
1
0
0
0
0
0
0
0
1
1
1
0
1
0
0
2
2
2
1
0
0
1
0
1
0
0
1
2
1
0
0
0
2
2
0
7
2
2
1
1
1
0
0
0
0
0
0
0
2
1
1
0
1
1
0
1
0
0
0
2
1
2
0
0
1
1
1
1
1
0
2
1
1
0
3
0
0
1
1
0
0
2
0
0
1
1
1
0
1
0
1
0
1
0
0
1
0
0
1
1
0
0
0
2
0
2
0
1
0
1
1
0
0
1
1
0
1
1
0
0
2
1
1
1
1
0
0
0
1
2
0
3
2
0
0
2
0
0
1
0
1
1
1
2
0
2
2
1
1
1
0
1
1
0
1
1
3
1
1
0
2
0
4
1
0
2
1
0
1
0
1
1
0
0
2
0
1
1
0
0
0
2
2
1
0
1
0
0
2
0
0
0
1
1
1
2
0
0
0
0
2
0
1
1
1
1
0
0
2
1
2
1
0
0
0
1
0
2
1
0
2
2
0
0
1
0
2
2
1
1
0
0
0
1
1
1
0
1
1
1
1
1
1
1
0
0
2
2
1
2
1
1
0
2
0
2
2
1
2
1
2
1
4
0
1
0
0
0
1
1
1
0
0
1
1
2
1
1
1
0
0
0
2
0
0
0
2
1
0
0
1
0
1
2
1
2
0
2
1
0
1
1
1
1
1
0
0
1
1
2
1
1
0
2
0
2
0
1
0
1
0
0
1
0
0
0
0
1
0
2
0
0
2
1
1
1
0
2
0
1
0
1
0
3
1
1
2
0
1
2
0
0
2
1
2
1
0
1
1
1
0
0
2
1
2
1
2
0
0
0
1
0
0
1
0
0
0
1
0
1
1
2
0
0
0
2
1
0
0
1
0
0
2
0
2
1
2
0
0
0
0
1
0
2
0
1
2
0
0
1
0
1
1
0
1
2
1
0
0
0
1
0
2
1
1
1
0
0
1
0
0
0
0
1
0
1
1
1
0
1
0
3
0
0
0
1
1
1
1
1
0
1
0
0
1
1
0
1
1
1
0
0
0
2
0
2
2
0
0
0
0
0
2
1
1
2
0
1
0
2
0
1
0
1
0
0
2
1
1
0
1
0
0
0
2
0
0
0
2
2
2
1
1
2
0
2
2
0
0
2
0
2
1
0
1
2
0
1
0
3
1
1
1
1
0
1
1
0
1
2
0
1
2
0
1
1
0
0
1
3
1
0
0
2
0
0
0
0
1
1
1
0
2
3
0
1
0
0
1
0
1
1
2
0
0
1
3
0
3
1
1
2
1
0
2
0
0
1
1
0
1
0
0
1
2
1
1
1
1
0
2
1
2
1
1
1
1
1
1
0
1
1
2
1
2
2
1
0
0
1
1
2
0
1
0
2
0
1
1
0
2
0
2
1
0
0
1
1
0
1
1
3
1
1
0
0
1
0
0
1
2
0
2
1
0
1
1
1
0
1
1
1
0
2
1
0
1
1
1
1
1
2
0
1
2
0
0
0
1
1
3
1
0
0
2
1
1
0
0
0
0
1
1
0
6
0
0
2
2
0
1
0
0
1
1
2
1
1
0
1
0
0
0
2
1
1
1
0
2
1
0
0
1
2
2
1
0
2
2
1
2
0
1
2
1
0
1
2
1
1
1
0
2
2
1
2
0
0
1
3
0
1
0
0
0
1
0
1
2
1
0
0
0
0
1
1
0
2
0
1
2
2
1
1
1
0
2
0
0
0
0
0
0
0
0
2
1
2
0
0
2
0
0
2
1
0
1
0
2
2
0
1
1
1
1
1
1
0
2
0
2
1
0
0
0
0
1
2
2
0
0
1
0
4
0
2
0
1
1
0
0
2
0
1
1
3
0
1
0
1
2
2
1
0
1
0
1
1
0
1
0
1
0
0
0
0
0
1
1
0
2
0
2
1
0
0
2
0
2
0
0
0
1
1
1
0
1
0
0
1
0
0
1
0
0
2
1
0
1
1
0
2
2
2
1
1
0
0
2
0
2
2
0
0
1
0
1
0
0
2
0
0
0
1
1
0
0
1
2
0
1
1
0
1
1
2
2
0
1
1
1
1
0
1
0
2
0
2
1
2
0
2
1
1
2
0
1
1
1
1
1
1
1
1
1
0
1
0
2
1
0
1
1
1
1
0
0
2
0
1
0
2
1
1
1
2
0
0
1
2
0
0
2
0
2
2
0
2
0
2
0
0
0
2
1
2
2
2
0
0
1
3
2
1
1
1
0
1
5
0
0
0
1
0
0
0
1
1
0
0
1
2
1
2
1
2
2
0
1
0
1
0
1
0
1
1
3
1
1
0
1
2
1
0
2
1
1
2
0
0
0
0
2
0
2
3
2
2
0
0
0
0
2
2
1
1
0
0
2
1
1
0
3
0
1
0
2
1
1
0
1
0
0
0
2
0
2
1
2
0
1
0
0
0
1
1
0
1
2
1
2
0
1
0
0
1
2
0
2
0
2
1
2
0
1
3
1
2
2
0
0
1
3
0
0
1
1
3
0
1
1
0
0
2
2
1
1
1
1
0
2
0
0
0
7
1
0
2
1
0
2
1
1
1
2
0
0
2
0
1
1
0
0
2
0
0
2
0
0
0
2
1
1
0
2
0
1
0
2
1
1
0
1
0
0
0
2
0
1
0
2
1
0
2
2
2
1
2
0
1
2
0
2
2
0
2
0
0
1
2
1
0
1
0
2
1
0
0
1
0
0
0
0
0
2
1
1
1
0
1
0
1
0
1
0
2
0
2
1
1
2
0
1
0
1
2
0
0
1
1
0
0
0
0
2
0
2
0
0
0
2
1
0
1
0
2
1
2
0
0
2
3
0
1
0
1
2
2
2
0
1
0
1
0
1
1
1
1
0
1
0
0
0
1
2
2
0
5
0
0
2
0
0
1
1
0
0
1
1
1
1
2
1
1
0
0
2
2
1
0
2
0
1
1
0
2
2
2
1
1
1
0
0
0
2
0
2
1
2
1
1
0
1
1
1
1
0
1
1
0
0
1
0
2
1
0
2
0
0
1
1
1
0
2
1
2
1
0
2
1
2
1
1
0
1
0
0
1
0
0
1
1
0
0
1
1
2
1
2
1
2
1
1
2
2
1
0
0
1
3
1
2
0
2
2
0
2
1
2
0
2
1
0
1
0
0
0
0
2
1
0
2
0
2
1
1
1
0
0
1
1
1
1
2
1
3
0
0
0
0
0
0
0
1
1
0
0
0
1
1
1
0
1
1
1
2
1
1
1
2
2
1
3
1
2
1
1
2
0
0
1
0
1
1
0
0
1
0
0
2
0
0
2
1
0
2
0
1
2
1
2
0
0
0
1
2
2
0
1
1
1
2
0
0
1
0
0
1
0
0
1
1
0
0
0
0
1
2
2
0
3
1
0
2
0
1
1
1
0
0
1
1
0
1
0
0
1
1
2
2
1
2
2
0
2
0
1
1
2
0
0
2
1
1
0
1
1
1
0
1
2
1
1
0
0
0
2
0
0
1
0
2
0
0
2
1
0
2
1
2
0
2
0
1
1
0
2
0
2
0
0
2
2
2
1
1
0
2
2
1
1
5
1
0
1
0
0
0
1
1
0
2
1
0
1
1
1
0
2
2
1
0
0
1
0
1
0
0
0
0
1
1
0
0
1
1
2
0
0
1
1
0
0
3
1
0
1
0
1
1
1
1
0
2
0
0
2
0
2
0
0
0
0
1
2
0
2
0
0
1
2
1
1
0
0
3
0
1
1
1
0
0
0
0
1
1
1
0
2
1
1
0
1
0
0
1
1
0
1
0
0
0
0
1
0
1
0
1
1
2
0
1
0
1
1
1
0
0
0
1
2
0
0
2
0
0
1
0
1
2
0
0
0
0
2
0
1
0
1
2
2
1
1
0
1
0
2
3
2
0
0
1
2
0
0
2
0
2
1
1
0
1
1
1
0
0
0
1
0
1
1
0
1
2
1
0
0
0
2
2
0
0
1
2
0
0
0
2
2
2
1
0
1
0
1
1
2
0
2
1
1
0
1
1
0
1
2
2
1
0
0
1
1
0
2
0
0
0
1
3
0
1
1
2
1
1
1
1
2
1
1
2
2
0
0
2
0
1
0
1
2
0
1
2
1
0
1
0
2
0
2
0
0
0
2
0
0
1
0
0
0
1
0
1
1
1
2
2
0
1
1
1
2
0
0
0
1
0
1
0
1
1
0
2
0
0
1
1
0
0
0
2
1
0
2
2
1
0
1
0
0
0
1
1
0
1
2
1
2
2
1
2
1
0
1
0
0
0
2
1
1
1
1
1
0
2
0
0
2
1
0
1
0
1
1
2
0
0
1
3
0
2
1
1
2
2
2
1
1
2
1
2
0
1
0
2
2
2
1
1
2
0
0
2
1
1
0
0
1
0
0
1
0
0
1
0
0
0
2
1
0
0
1
2
1
1
0
0
0
1
0
1
0
0
1
1
1
0
1
1
1
0
2
0
12
0
1
1
3
1
0
0
0
0
1
0
0
0
0
0
0
1
1
2
2
1
1
0
0
0
1
0
0
1
2
1
1
1
0
0
0
1
2
0
1
2
0
2
1
0
1
2
0
0
2
0
1
0
0
1
1
2
1
1
3
0
0
0
2
1
0
0
0
0
0
2
1
2
1
1
0
2
1
1
0
0
0
1
0
1
0
2
1
1
0
2
1
2
1
2
2
2
1
0
2
1
1
2
1
0
2
2
1
0
1
2
2
0
1
0
1
1
0
0
1
0
2
1
2
0
0
1
1
0
1
0
2
1
1
0
0
1
1
0
0
2
1
0
0
0
0
3
2
0
1
1
1
2
0
2
0
0
2
0
1
1
1
2
1
0
0
0
1
0
0
1
1
0
1
0
0
1
1
0
1
1
0
2
2
0
1
0
1
1
1
1
1
0
1
0
1
0
0
1
1
0
0
0
0
2
2
0
2
1
0
1
0
2
1
1
1
1
2
1
1
0
1
0
2
0
1
1
1
0
0
2
1
0
1
0
1
1
0
1
1
2
0
0
1
1
0
0
2
0
1
1
0
3
1
1
2
1
0
0
2
1
0
1
0
0
1
0
1
0
0
1
2
0
1
2
2
2
2
0
0
0
1
0
1
0
3
1
0
1
0
1
0
1
0
0
2
0
1
0
1
1
1
1
2
1
2
2
0
0
0
1
3
2
1
1
3
1
2
0
2
1
1
1
2
0
1
1
0
0
0
1
0
1
2
0
0
1
1
1
1
0
0
0
0
1
1
1
0
1
1
1
0
1
2
1
0
2
0
0
0
1
1
2
0
0
1
0
2
1
1
0
0
0
1
2
0
1
1
0
1
0
0
1
1
0
0
0
0
1
0
0
2
1
2
0
0
1
1
1
1
0
2
2
0
1
1
1
0
1
1
0
1
2
0
2
0
1
0
0
2
0
2
0
0
0
2
1
0
1
0
2
2
1
2
2
1
1
0
0
0
0
2
0
1
1
2
0
0
0
0
1
0
1
2
1
1
1
2
0
0
1
1
2
2
2
1
2
0
1
1
1
0
1
0
0
2
1
1
1
1
2
1
1
1
1
2
1
1
2
2
0
2
0
0
1
0
0
1
1
1
2
1
0
1
1
0
0
0
1
0
1
0
1
1
3
2
1
2
1
0
0
2
0
1
1
1
1
1
1
1
0
1
0
2
2
2
0
0
2
0
1
2
0
1
0
1
1
1
1
2
1
0
0
0
0
1
1
0
0
2
1
2
2
0
2
2
0
2
2
1
0
2
0
2
0
2
1
0
1
0
0
0
2
2
0
1
1
2
1
1
0
1
1
0
0
2
0
0
0
0
2
1
2
0
0
3
1
0
1
1
2
1
2
1
2
1
1
1
2
0
0
0
1
1
0
2
2
2
0
0
0
1
1
2
2
0
0
0
1
2
0
0
1
1
0
0
1
2
2
0
0
1
0
0
3
2
0
1
2
0
0
0
1
3
0
1
1
1
0
0
0
0
0
0
0
1
1
2
0
2
0
1
1
1
0
0
0
0
1
0
0
0
1
2
0
0
2
1
0
2
1
5
2
1
0
1
2
1
1
1
2
2
0
2
0
1
0
1
1
1
2
1
2
2
2
1
0
0
0
1
2
1
0
1
0
1
2
0
0
2
2
1
0
1
1
0
0
2
0
1
2
0
1
1
0
2
1
0
0
2
1
2
1
1
0
0
0
2
1
0
2
1
1
1
0
2
0
1
1
1
2
0
2
0
0
1
1
2
1
1
1
1
1
2
0
0
1
1
0
0
2
1
1
0
1
2
2
1
1
0
0
3
2
1
0
2
0
1
0
1
0
1
2
1
1
1
0
0
1
0
0
1
2
0
1
0
1
0
2
1
1
0
0
0
1
0
1
1
1
0
0
2
0
2
1
0
2
1
0
2
1
2
0
0
1
0
2
1
1
0
1
0
0
1
1
2
1
2
2
0
0
0
0
1
1
2
1
1
1
1
0
0
1
0
0
1
1
0
1
0
1
1
1
1
2
1
2
3
0
1
1
2
2
1
1
1
1
3
0
1
2
1
0
0
1
3
2
1
0
2
2
2
1
0
4
0
0
0
1
1
0
0
0
1
2
0
0
0
2
1
2
0
1
2
0
1
0
2
2
2
0
1
1
1
0
1
0
0
1
3
0
1
2
2
1
2
2
1
0
2
2
0
1
0
1
2
0
1
1
1
1
2
1
0
0
1
2
1
1
1
1
2
2
0
0
2
1
0
1
0
1
0
0
1
0
2
1
2
1
1
1
1
0
0
2
1
2
2
3
1
1
1
1
0
1
1
2
0
0
1
1
1
0
1
2
1
0
2
1
0
2
1
1
1
1
2
0
1
2
0
1
2
1
1
0
0
0
0
1
1
0
1
2
2
2
1
1
1
1
2
0
0
0
0
2
1
0
2
2
1
1
0
1
1
0
0
2
0
0
1
1
0
0
1
1
2
1
3
2
0
1
2
0
0
1
0
0
2
0
1
0
0
0
2
3
0
1
0
1
0
2
4
0
0
2
0
2
2
1
1
1
0
1
1
0
1
2
0
1
1
1
1
2
0
0
1
0
0
2
0
1
1
0
3
1
0
2
1
2
0
0
0
2
1
1
2
0
2
0
1
0
1
1
1
2
0
1
1
2
0
0
2
2
0
0
1
2
0
1
1
0
2
1
2
0
1
2
0
1
2
0
2
1
1
2
0
2
2
0
1
1
1
0
1
1
1
0
0
0
0
0
2
0
2
0
0
2
0
2
2
0
0
0
0
1
0
1
0
0
0
1
1
1
1
1
1
1
1
0
0
1
1
1
0
1
0
2
0
1
1
2
0
0
1
1
0
2
0
0
1
0
0
1
1
0
1
1
0
4
2
1
0
0
2
0
1
1
0
1
0
0
2
2
1
1
0
0
0
2
1
1
1
2
0
0
0
2
0
0
2
0
1
1
0
0
1
2
0
1
1
0
0
1
2
2
0
0
0
0
1
2
1
0
0
2
2
2
0
1
2
0
2
0
0
2
1
1
1
2
3
2
0
0
1
1
0
1
1
0
1
1
0
0
1
0
0
1
0
1
0
0
1
1
2
0
1
1
2
2
1
0
0
1
1
1
0
0
1
1
1
1
1
0
1
1
1
1
1
0
1
0
0
0
0
1
0
0
0
0
2
0
1
0
1
1
1
0
0
2
1
1
1
0
1
2
1
1
1
3
0
2
2
1
1
1
0
0
1
1
2
1
0
1
1
0
1
1
0
0
0
0
1
0
1
0
0
1
0
0
1
0
1
0
1
0
2
1
1
0
1
1
0
0
2
3
2
1
1
1
0
0
2
0
1
1
1
1
1
2
0
1
1
1
1
1
0
4
0
2
0
1
0
2
1
1
1
2
0
0
0
0
1
1
0
2
1
1
1
0
1
2
1
0
1
1
1
1
1
0
0
0
0
1
2
0
0
1
2
1
2
0
2
3
1
2
1
1
2
2
0
2
0
1
0
1
0
0
0
0
1
2
1
1
1
2
1
2
0
4
1
0
0
0
1
2
0
0
1
0
1
0
2
1
1
1
1
0
0
1
0
1
1
0
2
0
2
0
0
0
1
0
0
1
1
1
0
1
2
1
0
0
2
1
1
2
1
1
1
0
1
1
0
0
2
0
0
1
1
2
1
1
0
2
1
2
0
0
0
1
0
0
2
2
0
1
2
1
0
1
2
0
0
0
2
1
2
3
0
0
2
1
1
0
0
2
0
1
1
0
2
1
0
0
1
1
0
1
0
3
1
0
1
0
0
0
0
0
2
2
1
3
1
0
0
0
1
1
1
2
0
2
0
0
2
0
2
2
0
0
1
0
0
1
1
1
1
1
1
1
0
1
2
0
2
0
1
1
1
0
2
2
0
4
2
0
0
1
0
1
1
0
2
0
0
2
0
0
0
0
0
1
1
1
2
0
1
1
0
0
1
2
1
1
0
0
1
2
0
0
0
1
1
2
1
0
0
4
1
1
0
0
1
1
1
0
0
0
2
1
0
0
0
0
0
0
1
1
2
0
1
2
1
1
2
1
2
1
1
2
1
2
0
1
3
2
1
0
0
0
1
1
0
1
2
0
0
0
2
0
0
0
0
1
0
0
1
0
2
2
0
2
1
2
1
1
0
1
3
2
0
1
1
1
1
2
1
1
0
2
0
2
1
0
0
0
1
2
0
0
0
0
0
1
1
2
0
0
1
0
0
1
1
0
1
2
0
0
2
1
2
1
0
1
1
2
2
0
2
0
1
0
1
1
0
1
1
0
0
0
2
0
0
1
2
0
0
1
1
1
0
2
0
0
0
1
1
0
0
0
0
1
0
2
2
1
0
0
2
1
0
1
1
0
1
1
0
1
2
1
1
2
0
2
0
0
0
2
1
0
0
0
0
1
1
1
1
1
1
1
0
2
0
1
0
2
1
0
2
0
1
0
2
0
2
0
0
0
0
1
1
1
1
1
0
0
0
0
1
2
1
2
1
0
1
1
2
1
0
2
1
1
2
0
0
1
2
0
3
0
2
0
1
0
1
4
0
0
0
0
0
0
0
0
3
2
1
1
0
0
0
0
1
1
0
1
0
0
1
2
2
1
1
1
0
0
1
2
0
0
2
1
0
1
2
1
2
1
0
1
0
1
1
0
1
1
1
1
1
2
0
2
0
0
2
1
0
1
4
1
1
0
1
1
0
2
0
2
2
2
1
0
0
0
2
1
1
1
0
0
1
0
1
2
1
2
0
0
0
0
1
1
0
2
1
2
0
1
1
1
2
0
1
0
2
1
0
2
0
0
1
0
1
2
2
1
3
1
0
0
2
1
0
0
0
0
1
0
1
0
0
1
1
0
1
0
1
1
0
1
0
2
2
2
0
0
0
1
2
0
1
0
2
1
1
2
2
0
0
1
2
0
2
1
1
0
1
0
1
0
0
1
1
1
0
2
1
1
1
1
1
1
0
1
2
1
0
1
1
1
1
0
1
1
1
0
0
1
1
0
0
0
0
1
0
3
4
1
2
1
1
0
0
1
1
2
1
0
0
1
1
2
2
2
0
1
1
2
1
1
2
1
1
0
2
1
1
0
2
1
1
2
1
0
0
0
0
1
1
0
0
0
1
0
1
1
0
2
0
0
1
2
0
1
0
2
3
0
1
1
2
1
1
0
0
1
0
2
0
0
2
0
0
2
1
1
2
1
0
0
2
0
0
1
1
2
1
1
1
0
0
0
0
1
1
0
0
0
0
2
1
1
1
1
1
1
1
1
0
0
1
1
1
1
1
2
0
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
1
1
1
2
1
2
1
0
1
0
0
1
2
0
1
1
0
1
1
0
2
0
0
1
2
0
1
2
7
0
0
2
1
0
0
0
1
2
1
0
1
0
0
1
1
0
0
2
1
0
2
1
1
0
1
2
1
0
1
0
2
1
0
2
2
1
2
1
1
2
2
0
0
2
2
0
2
1
1
0
2
1
0
0
2
1
0
0
0
2
2
0
0
2
0
2
1
1
1
2
2
0
2
1
1
2
0
1
1
1
2
2
0
1
0
0
2
2
1
0
0
0
0
3
1
0
1
0
0
2
1
0
1
2
1
1
0
1
2
1
0
1
3
1
1
2
0
1
0
0
1
1
0
2
2
0
0
1
1
0
1
1
1
1
0
0
2
2
0
2
0
1
0
4
0
0
1
0
1
1
1
1
2
1
0
1
2
0
1
0
0
3
1
0
1
0
1
0
0
2
1
1
0
1
2
2
2
0
0
1
1
0
0
0
0
0
2
4
1
0
2
2
0
1
1
1
0
0
2
1
0
0
0
1
0
1
1
1
0
0
1
1
0
0
2
1
1
1
1
0
0
2
2
1
0
0
1
2
2
0
0
0
1
2
2
2
1
1
0
2
1
0
1
2
0
0
1
0
1
1
2
1
0
4
0
2
0
2
0
0
1
1
1
0
1
1
0
0
1
1
2
1
0
1
2
1
1
2
0
1
1
1
0
2
2
0
1
2
0
0
1
0
2
1
0
0
2
1
1
0
1
1
1
1
0
0
1
2
0
1
0
1
0
2
1
1
2
0
0
2
0
1
1
1
2
0
0
1
3
1
0
1
0
0
1
1
0
1
2
0
1
0
1
0
1
1
0
0
1
0
3
1
0
1
1
1
2
1
0
0
2
1
0
2
1
1
0
0
0
2
1
3
1
3
1
2
1
0
0
0
0
1
0
0
2
0
1
0
1
2
0
2
1
0
0
0
1
1
1
0
1
2
1
2
0
2
1
0
2
3
0
0
1
0
1
1
1
1
1
0
1
0
1
0
1
0
0
2
1
0
3
1
0
0
2
0
0
0
0
1
2
2
0
1
2
1
0
1
1
1
0
1
4
2
0
1
1
1
1
0
0
1
2
0
0
1
0
2
2
0
0
0
0
0
1
0
0
0
2
0
1
0
1
2
0
1
1
0
1
0
2
2
1
2
1
0
2
1
0
0
0
0
0
0
0
0
2
2
1
0
2
1
0
2
0
0
1
1
2
1
2
2
2
0
1
1
0
0
0
0
2
3
2
0
0
1
1
1
1
1
0
2
0
0
0
1
1
1
1
1
0
0
2
0
1
2
1
0
2
0
1
1
0
2
0
1
1
0
0
1
2
1
1
0
0
2
1
0
1
0
1
1
0
0
0
0
0
2
0
2
0
1
2
1
1
0
2
0
0
0
2
1
1
0
0
1
1
0
1
1
1
0
2
2
1
1
2
2
0
0
1
0
0
2
1
1
2
2
2
0
0
1
1
1
3
2
0
2
1
0
7
2
1
0
2
1
1
1
1
0
2
2
2
0
1
1
1
0
0
2
1
0
1
1
0
3
0
0
0
1
1
1
0
1
1
2
1
0
0
1
1
1
0
0
1
2
1
0
1
1
1
2
0
1
1
1
1
0
2
0
1
0
0
2
1
3
0
0
0
2
0
1
1
1
1
1
0
0
1
1
1
0
0
1
0
2
3
1
0
1
0
0
1
2
0
3
0
1
1
0
0
0
0
2
1
0
0
0
1
0
1
0
0
1
1
1
0
0
0
2
1
0
5
1
2
0
0
2
1
1
2
0
1
1
1
1
0
0
1
1
0
0
3
0
1
0
2
0
0
0
0
0
2
2
1
0
1
0
0
0
1
0
2
0
1
1
1
2
1
0
0
1
0
0
1
2
0
1
1
2
0
1
0
2
2
1
0
1
2
1
0
1
3
2
1
0
0
2
1
0
1
3
0
2
0
1
1
1
0
1
0
1
0
0
1
1
0
2
1
1
0
2
0
2
2
0
1
1
0
3
0
0
0
1
1
1
1
2
0
1
0
1
1
0
0
2
0
1
0
0
0
1
0
2
1
2
0
1
0
0
1
2
0
2
2
0
1
0
2
0
1
1
1
1
1
0
2
1
0
1
0
2
0
1
0
2
0
0
0
2
0
1
2
1
0
1
1
0
0
1
0
1
2
2
1
0
0
1
0
2
2
2
2
0
0
1
2
1
0
0
1
1
1
0
0
2
1
0
2
2
0
0
1
1
1
0
0
0
1
1
1
1
0
0
1
2
1
1
1
0
0
0
2
0
0
1
2
2
1
0
1
0
0
1
2
1
0
2
0
1
1
0
1
2
2
0
2
0
0
0
1
0
0
1
1
1
2
1
2
2
2
2
1
2
1
2
1
1
1
2
1
1
2
2
3
2
0
0
1
0
0
1
2
2
0
0
1
1
1
1
0
0
0
1
1
1
0
0
0
2
1
1
2
1
1
1
0
1
0
0
0
0
1
2
0
1
0
3
3
0
0
1
2
1
0
1
1
1
1
1
0
1
0
2
0
0
0
0
1
1
2
1
0
1
0
0
1
0
2
0
2
1
0
0
0
0
0
1
0
2
0
1
1
0
1
0
1
0
2
0
0
1
1
0
1
0
0
2
0
3
1
1
2
1
1
2
2
2
1
1
0
2
2
0
1
2
1
0
0
1
2
1
0
0
0
3
2
2
0
0
0
1
2
0
1
0
0
0
2
0
1
1
0
2
1
1
0
2
1
1
1
1
0
0
1
0
0
0
1
2
1
0
0
1
2
0
0
0
0
0
0
1
2
2
1
0
0
0
1
0
0
1
0
0
0
1
2
1
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
2
0
3
0
2
2
2
2
1
0
0
2
0
1
0
1
0
0
2
1
1
0
0
1
2
0
0
0
0
2
4
0
1
1
1
0
1
0
2
1
2
2
1
1
0
1
0
1
0
0
1
2
0
0
1
0
1
0
0
1
1
2
1
0
0
1
1
2
1
1
0
1
0
1
0
2
1
0
1
1
1
2
2
0
2
1
0
1
1
0
0
2
1
0
0
0
0
0
2
0
0
1
0
0
1
4
1
0
1
2
2
0
2
1
1
0
1
2
0
0
0
0
3
0
1
0
0
0
0
0
1
2
1
0
2
0
1
0
2
1
2
0
0
2
0
0
1
0
1
1
0
1
1
2
0
2
0
2
0
0
1
2
0
1
1
1
1
1
2
0
2
1
1
0
0
0
1
0
1
1
0
2
0
0
0
0
0
0
1
1
1
1
2
2
1
0
0
0
2
2
0
1
0
2
1
2
1
1
1
1
1
1
1
2
0
1
4
2
2
1
1
0
0
6
1
2
0
2
1
1
1
0
3
2
0
1
0
2
0
0
1
0
0
1
0
1
1
1
1
1
2
2
1
1
2
0
0
1
0
0
2
0
0
0
1
0
1
1
0
1
1
0
2
1
2
1
0
1
1
0
0
0
1
0
2
1
1
1
1
0
0
1
0
0
1
2
0
1
2
0
1
2
1
4
1
1
1
1
1
0
1
1
0
2
1
0
1
0
0
0
1
0
2
1
1
1
1
1
1
0
1
1
0
1
0
1
0
0
0
2
1
1
1
0
2
0
0
0
0
2
1
2
1
1
2
0
0
1
1
2
1
1
0
1
2
0
1
0
1
2
0
0
4
0
0
0
0
2
1
0
0
1
1
1
1
0
0
2
0
1
2
1
0
0
1
0
0
2
1
0
0
0
0
1
1
0
0
1
1
1
0
0
1
1
2
1
1
0
0
0
2
1
2
0
0
0
1
0
1
2
1
0
0
0
2
1
1
0
0
1
1
0
1
1
1
1
0
2
2
1
1
1
2
1
0
1
1
0
1
1
0
0
1
0
1
1
2
1
2
0
4
0
2
2
0
1
0
2
0
2
0
0
2
0
2
0
0
0
1
0
0
0
1
1
1
1
2
0
0
0
2
0
0
0
1
0
0
1
1
1
1
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
1
1
0
0
1
0
1
1
0
0
1
2
0
0
0
1
0
0
1
0
1
0
2
0
1
1
1
0
1
1
0
0
1
1
0
1
0
0
1
0
1
0
0
0
1
1
0
0
0
0
1
1
1
0
1
0
2
0
0
1
0
1
2
2
3
1
0
1
1
1
1
2
0
0
0
1
1
1
0
0
1
1
0
1
3
0
2
1
1
0
0
2
2
1
2
1
0
2
2
1
2
2
2
0
0
2
2
1
2
2
0
1
0
1
2
2
0
0
0
0
0
1
0
1
0
0
0
2
2
0
1
0
1
0
1
0
0
1
1
1
1
1
1
1
0
1
0
1
2
0
2
0
1
1
0
1
2
0
1
1
0
0
1
1
3
0
0
1
2
2
1
0
2
1
0
2
1
1
0
1
0
1
0
1
0
0
1
0
0
1
1
1
1
1
0
1
0
1
1
1
2
2
0
0
2
0
0
0
1
1
0
1
2
2
2
1
2
1
2
2
1
0
1
0
0
1
2
1
0
0
2
0
0
0
2
0
2
0
0
2
0
2
1
1
1
2
1
1
2
2
0
0
1
1
0
2
2
2
1
1
0
0
1
1
0
1
0
0
1
0
0
0
1
0
2
2
0
1
0
1
0
1
1
0
1
2
2
0
2
2
1
0
0
1
0
1
1
0
1
1
0
0
0
1
1
1
1
1
0
0
2
1
0
0
0
1
0
1
2
2
0
1
0
1
1
1
2
2
0
0
0
1
0
2
1
1
1
0
1
0
2
1
1
0
2
2
2
1
1
1
0
0
2
0
0
2
1
1
1
1
0
1
1
0
0
1
1
0
0
1
0
2
1
1
2
0
1
1
1
1
1
0
2
1
1
1
0
0
0
1
1
0
0
1
0
0
0
1
0
0
2
0
0
0
1
1
1
0
2
1
0
0
2
2
1
1
1
0
0
1
2
2
0
0
2
2
1
0
1
1
1
0
0
0
1
0
0
2
2
1
1
2
0
1
1
0
1
0
0
0
2
1
0
2
2
0
0
0
0
2
2
1
1
0
0
1
0
0
2
0
2
0
1
2
1
1
1
0
1
1
2
0
1
0
1
1
2
0
1
1
0
2
0
1
1
1
1
2
0
1
1
1
1
2
3
0
1
1
1
0
2
1
1
2
1
2
0
0
0
1
2
2
1
2
2
1
2
2
0
0
1
0
2
0
2
0
0
1
0
2
0
0
0
1
0
0
0
0
1
0
1
3
2
2
2
1
2
1
1
0
0
0
0
1
0
0
0
0
1
0
2
1
2
1
0
2
2
2
1
3
1
0
1
1
1
1
1
1
0
1
0
0
0
2
1
0
0
1
1
2
1
1
1
0
2
0
2
1
2
1
2
1
0
2
0
1
1
0
0
1
1
0
0
0
1
1
0
0
2
1
1
0
0
1
2
1
1
0
1
0
2
0
2
0
1
2
2
1
1
1
0
1
1
1
0
0
0
0
2
1
1
0
0
2
0
1
1
0
2
2
2
1
0
2
1
2
0
1
1
2
1
0
1
0
2
2
0
1
2
0
1
1
0
2
2
1
1
1
1
0
0
2
2
0
1
2
2
2
0
1
1
1
0
1
0
0
0
0
0
1
0
1
0
2
1
0
0
0
2
2
0
1
1
0
0
2
0
2
1
1
0
0
1
1
0
2
1
0
0
0
0
1
1
0
1
0
0
2
1
0
1
2
0
0
0
0
3
0
0
1
1
2
1
0
0
0
4
1
1
1
2
0
1
0
2
1
1
1
1
2
2
1
0
0
2
0
1
0
0
1
2
0
0
2
1
0
0
0
1
0
1
0
2
0
0
2
1
0
0
1
2
1
1
1
2
6
2
1
0
1
1
1
2
1
2
0
1
1
0
1
2
1
2
0
2
0
2
1
2
1
0
0
2
0
1
1
0
1
1
1
1
2
0
0
1
2
0
1
0
0
0
0
0
1
1
0
1
0
2
0
2
0
2
0
1
0
1
2
0
1
2
0
1
1
1
0
2
2
0
0
1
2
2
1
0
0
1
1
1
0
1
1
1
0
2
0
0
2
3
1
1
1
0
2
0
1
0
2
0
0
2
1
0
1
1
1
0
1
0
1
0
0
1
1
1
1
0
1
0
2
1
1
1
1
2
1
1
1
1
0
0
1
1
1
2
0
0
1
1
2
1
0
0
2
0
1
3
0
0
0
1
2
1
0
0
0
1
2
1
1
0
1
2
0
2
0
0
0
0
0
2
0
2
0
1
2
2
0
0
3
1
0
1
0
0
0
0
0
0
0
0
1
2
1
1
1
2
0
2
1
1
0
2
2
1
1
2
0
1
1
1
4
0
0
0
2
2
2
1
0
1
1
2
0
2
1
1
2
0
0
2
1
0
0
2
1
0
1
0
2
1
1
0
0
1
0
0
2
2
1
2
2
1
0
0
2
1
0
1
2
2
1
0
0
2
1
0
0
0
1
0
0
0
0
1
0
2
1
1
1
1
0
1
2
1
1
0
1
0
1
0
2
2
0
0
0
1
0
1
2
0
0
1
3
1
0
1
0
2
1
0
1
1
0
1
0
0
0
2
0
1
0
1
0
1
1
1
1
1
0
0
1
2
0
0
1
1
1
2
0
0
1
0
0
0
1
0
4
0
1
1
0
1
1
0
2
2
0
0
2
2
0
2
0
0
1
1
1
0
0
1
0
1
0
0
1
2
1
1
0
2
0
1
1
2
1
6
2
1
1
2
0
1
0
1
0
0
0
2
1
1
2
1
1
0
1
0
1
0
1
1
1
0
2
2
1
0
0
0
1
1
1
1
2
0
0
2
1
0
0
0
1
0
2
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
2
1
2
1
0
1
2
0
2
0
1
1
0
2
0
0
0
1
1
2
1
0
1
0
1
2
0
2
1
0
1
2
0
1
1
0
2
0
0
1
1
2
0
1
2
0
2
2
0
2
0
0
2
0
2
2
0
0
1
2
0
0
1
0
1
1
0
2
1
1
0
1
2
3
1
0
2
0
2
1
1
2
1
1
1
0
1
0
0
0
0
1
0
0
0
2
2
1
1
2
1
2
0
0
0
2
0
1
0
1
1
2
3
1
0
1
2
1
1
1
2
1
0
0
0
1
1
2
0
1
1
1
1
1
0
2
0
1
1
2
1
1
0
1
0
0
2
0
1
1
0
2
1
0
2
1
0
0
0
0
1
1
2
0
0
1
0
0
0
2
1
2
1
2
0
0
1
0
0
2
1
0
1
1
1
0
2
2
1
0
0
2
0
1
1
0
1
1
1
1
0
2
0
1
0
0
1
1
1
2
1
1
1
0
0
1
1
2
0
1
1
0
2
0
0
0
1
1
1
0
1
1
2
1
0
0
2
0
0
0
0
0
1
1
0
1
3
0
2
1
0
1
1
2
2
2
1
0
1
2
2
0
0
2
0
0
2
2
1
0
0
2
2
0
1
1
2
1
0
1
2
1
0
0
0
1
0
1
1
0
1
1
0
0
0
1
0
0
0
0
0
1
0
2
0
1
0
0
0
2
2
2
1
2
2
2
1
0
2
1
0
0
0
1
0
2
0
0
1
1
0
0
1
2
1
0
2
1
0
1
1
2
0
1
2
1
0
1
3
1
2
0
2
0
2
0
1
2
1
2
1
1
1
0
0
1
2
0
1
0
0
2
1
0
2
0
2
1
0
0
2
1
0
0
0
1
0
2
1
1
1
1
0
0
0
1
1
0
1
1
1
0
0
1
0
1
0
1
0
0
2
1
0
1
2
1
0
0
1
0
2
1
1
2
0
0
0
1
1
0
0
1
2
2
1
1
2
0
0
1
2
1
0
0
1
0
1
0
2
0
0
1
0
1
1
0
2
1
0
0
1
2
2
1
0
1
0
0
1
1
0
0
0
0
0
1
0
1
0
1
2
2
1
0
0
0
1
0
0
0
0
0
0
2
2
0
1
0
1
2
1
1
0
0
0
1
1
0
0
1
2
1
2
0
1
0
0
1
1
2
2
0
0
1
2
2
1
0
2
2
1
0
0
1
1
0
2
1
0
1
1
2
2
2
0
1
2
1
2
2
2
0
0
0
0
1
0
3
0
1
0
1
0
1
0
1
1
1
2
0
0
2
1
1
1
2
2
0
1
2
0
0
0
1
1
1
0
1
0
0
1
0
2
1
1
0
2
1
2
1
1
1
2
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
1
0
1
0
1
0
0
2
2
2
2
2
2
0
2
0
2
0
1
1
1
0
1
2
1
1
1
1
0
1
0
0
2
2
1
0
1
1
0
1
0
0
2
1
0
1
0
0
0
1
0
0
1
0
2
0
2
1
2
0
0
1
0
0
3
1
0
2
0
0
1
0
1
2
0
0
0
1
1
1
2
2
1
2
1
0
0
1
1
1
0
0
2
0
0
2
0
0
1
1
1
0
0
0
1
0
1
1
0
0
2
0
0
1
1
2
1
1
0
0
0
0
1
1
0
0
1
0
1
2
1
0
1
2
0
0
0
0
0
0
1
1
0
2
0
1
2
0
0
4
1
1
0
1
2
0
0
0
2
0
0
0
1
0
1
0
1
0
0
1
1
1
1
0
0
0
0
0
0
0
2
1
0
0
1
2
1
1
0
0
1
2
2
1
1
1
1
2
1
0
1
0
1
1
0
0
1
0
0
0
0
0
0
2
0
0
2
1
2
1
0
1
0
0
1
1
0
0
0
0
1
2
2
1
0
0
2
0
0
2
0
0
0
2
1
1
1
0
1
1
1
1
0
0
0
0
0
0
1
3
1
1
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
2
0
1
1
0
0
1
2
1
1
0
0
1
1
2
0
2
1
0
1
2
0
1
0
1
0
1
0
0
0
0
4
1
1
2
1
1
1
1
0
0
1
1
1
1
0
2
1
0
1
1
0
1
0
0
1
0
1
1
1
0
1
1
1
0
0
1
1
2
1
1
1
1
1
1
1
0
0
2
0
0
1
1
1
1
1
0
0
2
0
0
1
0
2
1
1
1
1
1
1
1
2
3
0
1
1
2
1
2
1
0
2
2
1
1
0
0
2
0
2
0
0
2
2
0
0
1
1
2
0
0
0
1
3
0
0
0
3
2
0
0
0
2
1
0
0
0
1
0
0
2
0
0
1
2
0
0
2
0
0
0
1
1
2
0
1
1
2
1
2
2
0
1
1
2
0
2
1
1
0
0
1
1
1
1
2
1
0
2
0
1
0
2
0
2
4
0
1
1
0
0
1
0
2
2
1
1
2
1
1
0
2
2
0
1
0
0
0
1
0
0
1
0
0
0
0
2
0
1
1
1
0
2
0
1
2
1
2
1
1
1
1
0
2
3
1
0
1
1
0
0
0
0
2
1
2
1
1
1
2
0
1
0
0
0
0
1
1
2
0
0
1
1
1
0
1
1
1
2
1
0
1
1
2
1
2
0
1
1
0
2
2
0
1
1
1
0
2
0
2
0
1
0
0
1
1
0
2
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
1
0
1
0
1
0
2
2
1
1
0
1
0
1
0
1
0
2
0
1
2
1
0
0
1
2
0
0
0
0
0
0
0
1
1
1
2
1
2
0
2
0
1
1
0
0
2
0
1
0
2
0
0
0
1
1
0
0
0
1
0
0
0
2
1
2
1
1
0
0
1
0
2
2
0
0
1
2
1
0
3
1
0
0
1
0
0
2
0
2
0
1
0
0
0
0
1
2
1
0
2
0
1
1
0
0
0
1
2
0
2
1
2
0
0
0
0
1
0
1
2
1
2
0
0
0
1
0
1
1
1
1
1
1
1
1
5
1
0
1
0
1
2
0
1
2
0
1
2
1
1
1
1
1
1
1
1
0
2
0
1
1
2
1
1
1
2
0
1
2
0
2
1
1
0
0
1
2
0
0
1
2
0
0
3
2
2
3
3
1
0
0
1
0
2
2
2
0
1
2
0
0
2
2
1
2
1
2
1
2
0
0
0
2
2
0
1
1
2
0
2
0
0
0
0
0
1
2
1
0
0
0
2
0
0
2
0
1
0
1
2
2
0
1
2
0
1
0
1
0
1
1
2
1
2
0
0
1
1
1
0
2
0
0
0
0
2
2
1
1
1
2
1
0
0
0
0
2
2
2
0
0
1
0
1
0
0
1
0
1
1
0
1
0
0
2
1
1
0
2
1
0
0
1
0
1
0
1
1
1
1
2
1
1
1
0
0
5
0
0
1
1
2
2
2
2
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
2
0
2
0
1
0
0
1
0
1
0
0
0
2
0
1
2
1
0
0
1
1
1
1
1
0
0
1
1
1
0
1
2
0
0
2
2
2
1
0
0
1
0
0
0
2
2
2
2
1
0
0
0
1
0
1
0
1
0
1
0
2
0
1
1
0
1
4
1
1
0
3
3
0
2
2
1
1
0
0
0
1
1
2
1
1
1
2
2
0
0
1
0
2
1
1
3
1
2
0
2
1
2
1
1
1
1
0
2
0
2
2
0
2
2
1
2
0
1
1
2
0
1
1
0
1
0
2
0
2
2
1
3
0
0
0
1
1
1
0
1
1
0
2
1
1
1
0
1
2
2
2
1
0
0
1
2
0
1
0
2
1
2
0
2
0
0
1
0
0
0
0
1
0
2
0
1
2
1
1
1
2
0
0
1
2
0
1
0
2
0
0
1
1
2
0
0
0
0
0
1
3
0
1
1
1
0
2
1
1
1
1
1
0
0
0
0
0
0
0
1
1
0
0
0
2
0
1
2
0
0
1
0
2
2
0
1
1
1
0
2
1
1
1
1
1
0
1
2
1
1
1
1
1
0
2
1
1
3
1
1
1
1
1
1
0
0
0
1
1
1
0
2
2
0
2
2
1
2
2
3
1
0
1
0
1
0
0
2
2
0
1
0
1
2
0
0
0
2
2
1
0
2
2
3
2
2
0
1
2
1
2
1
2
2
0
1
2
1
0
0
0
0
2
2
0
1
1
1
1
1
0
1
1
0
1
3
1
1
0
1
1
0
0
0
1
1
1
2
1
0
0
1
2
1
1
0
1
1
0
0
2
2
1
1
1
1
1
1
1
0
0
0
1
0
3
0
1
0
0
1
0
0
2
1
0
1
0
1
0
0
2
1
5
0
0
0
2
2
2
2
1
1
1
1
0
2
0
0
1
3
2
1
1
0
1
1
1
0
0
0
0
0
1
0
1
2
0
1
2
0
0
0
1
1
1
2
1
1
0
1
2
2
1
0
0
1
0
2
1
0
2
1
1
1
1
2
2
2
1
0
1
0
0
0
1
0
1
1
2
1
2
1
0
1
1
1
0
0
0
1
1
1
1
2
1
0
0
2
0
0
1
1
1
1
2
1
0
0
1
0
0
1
2
0
1
0
1
1
1
0
0
2
1
0
1
0
1
1
0
0
1
2
0
0
0
1
1
0
0
0
0
1
1
0
1
1
0
2
2
0
5
0
1
1
1
0
1
0
1
2
1
1
0
2
0
1
0
0
1
1
0
2
1
3
0
1
2
0
1
1
2
0
2
1
2
2
3
1
2
2
1
1
1
1
0
1
0
1
0
2
2
2
1
2
1
1
0
2
0
2
2
0
0
0
0
2
1
1
1
0
2
1
0
2
0
0
1
1
2
2
0
1
0
9
0
1
1
1
1
1
1
0
2
2
1
0
2
0
0
1
2
2
0
1
2
1
2
1
1
2
0
0
0
1
1
1
1
1
2
0
1
0
0
0
2
0
0
1
0
1
0
2
0
0
2
1
1
0
1
2
0
0
2
0
3
2
1
0
2
2
3
1
1
0
1
2
0
1
0
1
2
2
1
1
0
2
0
2
1
0
2
2
0
1
1
1
0
2
0
2
1
1
0
2
0
2
0
0
1
0
1
1
0
1
0
1
1
1
1
0
0
1
1
1
0
0
0
0
1
2
1
0
1
0
1
0
0
2
1
1
0
1
1
1
1
2
1
0
0
0
0
2
1
2
1
1
2
1
0
0
0
3
0
0
0
2
1
0
2
0
1
0
0
0
0
0
2
1
0
1
2
1
2
1
1
0
2
1
1
1
2
2
0
1
1
0
1
1
0
0
2
1
0
0
0
1
0
1
0
0
2
1
0
0
0
1
0
0
0
2
0
0
2
1
2
1
2
1
1
0
0
0
1
1
0
2
1
0
0
2
1
1
1
3
1
0
1
1
2
1
1
1
2
1
1
0
0
2
0
1
2
2
0
1
0
1
2
1
1
0
1
0
1
1
0
1
0
1
0
1
1
0
1
0
0
1
1
2
1
2
1
0
2
0
1
1
1
1
0
1
3
1
1
1
0
0
2
1
0
1
1
2
2
0
1
1
0
2
1
0
0
0
1
1
0
1
1
1
0
0
1
2
2
1
2
2
0
1
1
1
1
2
2
1
2
1
2
2
0
0
0
0
0
2
2
1
0
1
1
2
0
1
0
0
1
1
2
0
1
0
0
3
3
1
0
0
4
1
0
2
1
1
1
0
1
1
1
2
0
1
2
0
1
1
1
2
1
1
3
2
2
0
2
2
1
2
0
2
2
0
2
2
0
1
0
1
1
1
1
0
2
0
1
1
1
0
1
1
1
2
0
2
2
0
0
2
2
0
0
0
0
2
2
0
1
0
0
0
1
1
0
1
1
0
0
2
0
2
1
0
1
1
0
2
0
2
2
0
1
1
1
1
1
0
1
0
2
0
1
3
1
1
0
1
0
0
2
1
0
1
0
1
2
0
0
1
2
0
2
1
0
0
2
2
2
1
0
0
2
1
2
2
1
0
0
2
0
0
0
0
0
2
1
2
1
1
0
0
1
0
0
0
1
0
1
0
1
0
1
2
0
2
1
0
1
1
0
0
0
2
1
2
0
4
1
2
0
0
1
0
1
2
0
1
1
1
1
0
1
2
0
2
1
0
0
2
2
0
2
1
1
2
0
0
1
2
2
0
0
1
0
0
0
2
0
0
0
1
0
1
1
1
0
0
2
1
0
2
1
1
2
2
1
0
1
1
1
1
0
1
1
1
0
1
1
0
1
1
0
2
0
2
2
1
0
0
1
0
0
2
1
2
2
0
1
1
0
1
0
0
1
1
1
2
1
0
1
1
1
2
0
0
1
1
0
2
1
1
0
1
0
0
2
0
1
1
2
0
2
0
1
0
2
1
0
0
1
0
2
0
2
0
0
0
1
2
1
1
0
0
1
0
0
1
0
1
0
0
2
1
1
1
1
0
1
1
0
2
1
2
0
2
1
2
0
1
1
1
2
1
0
1
2
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
1
1
2
2
1
1
2
1
2
2
0
0
0
0
1
1
0
1
2
1
1
1
1
0
1
0
0
1
2
0
0
0
0
1
0
1
2
1
0
2
1
2
2
0
0
2
0
2
2
0
1
0
1
2
1
1
0
2
1
0
0
0
1
1
0
0
1
2
2
2
1
0
0
2
1
3
1
2
1
1
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
1
2
1
0
1
0
1
1
0
0
0
1
2
1
0
1
1
2
2
2
0
2
1
2
0
0
2
1
1
1
0
1
0
0
0
2
0
1
1
1
1
0
2
1
0
1
1
2
2
1
2
0
1
1
0
1
1
0
0
0
0
2
1
1
1
3
1
0
1
0
1
0
1
0
0
0
1
0
1
2
2
2
1
1
0
1
2
2
0
0
1
2
2
0
0
1
1
0
1
1
0
2
0
0
0
0
0
0
1
1
1
0
2
1
0
1
1
0
2
0
1
0
2
0
0
1
0
0
2
2
2
0
0
1
0
0
2
0
1
0
1
0
1
2
0
0
0
0
2
1
2
1
0
0
1
0
1
2
0
1
0
0
2
1
0
2
0
2
1
2
0
0
1
1
0
5
0
1
0
0
0
1
1
1
1
0
1
2
2
0
1
1
1
2
0
0
2
2
1
0
0
1
1
0
2
2
1
1
0
3
4
1
0
1
0
0
1
2
2
1
1
0
1
0
0
1
0
1
1
0
0
1
3
1
0
0
0
0
0
1
0
0
2
3
1
0
0
1
0
1
1
1
2
1
1
1
0
1
1
1
0
0
1
0
3
1
2
1
2
1
0
1
1
0
1
0
0
0
0
0
1
1
1
1
1
0
0
1
0
2
2
0
1
0
0
1
2
1
0
2
0
0
0
0
0
1
0
1
0
0
1
1
2
0
0
1
1
0
1
1
1
0
2
0
0
0
1
0
0
0
0
1
0
0
2
1
2
1
2
3
1
2
1
1
1
0
1
0
2
1
0
0
1
0
1
2
0
0
2
2
1
0
0
0
1
0
0
2
1
1
1
0
2
0
1
1
1
0
0
2
1
0
2
1
2
1
1
2
0
1
0
0
1
1
1
0
1
1
1
0
0
1
2
2
2
0
1
2
0
0
0
1
2
0
5
0
2
0
2
0
0
1
0
1
0
0
1
1
1
0
1
1
0
0
0
0
2
1
1
1
1
0
0
0
0
0
2
1
0
1
1
0
1
1
0
1
0
0
2
2
0
0
0
0
2
1
0
1
2
0
1
2
1
0
1
0
2
2
2
0
0
0
1
1
1
2
1
1
1
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
1
2
2
0
0
0
1
0
0
0
1
1
0
0
2
1
5
0
1
0
1
1
0
1
2
0
1
1
2
3
1
1
2
0
1
1
1
2
1
0
1
1
2
1
2
0
1
0
0
1
2
1
0
0
2
1
0
0
1
1
0
2
0
1
2
0
1
2
0
4
2
2
1
0
1
0
2
1
2
0
0
0
1
1
0
0
0
2
2
1
0
4
0
1
1
0
0
0
1
1
0
1
0
0
1
0
2
0
1
1
1
0
0
0
0
1
0
0
1
1
0
0
0
0
1
2
0
1
1
0
0
3
0
1
0
0
3
2
2
1
1
0
0
1
1
1
1
0
0
0
2
1
0
1
1
2
0
1
0
1
1
1
1
0
0
0
0
1
1
0
0
1
1
1
1
1
0
0
0
2
2
2
0
1
1
1
0
2
1
1
2
1
0
1
2
0
1
1
2
0
0
2
1
1
2
2
0
1
0
3
2
0
0
0
0
0
0
0
2
0
0
1
1
1
0
1
0
0
0
0
0
0
1
1
1
1
0
1
2
1
1
2
2
1
2
0
2
0
1
0
2
0
1
0
1
1
0
0
1
2
1
0
2
0
1
1
0
1
0
2
1
0
1
0
1
0
2
1
1
0
2
2
2
1
2
1
1
0
1
1
1
2
2
1
1
1
1
0
2
2
0
2
1
1
1
1
0
1
2
0
1
2
0
1
1
1
1
1
0
0
2
0
0
1
0
3
1
2
2
1
0
0
0
4
0
2
1
1
1
0
1
2
1
0
2
0
0
0
0
1
0
0
0
0
1
2
0
1
0
1
1
0
0
1
0
1
1
0
2
0
2
2
1
0
0
1
0
1
0
1
1
2
2
1
0
1
0
0
0
0
0
1
1
2
0
0
2
2
0
1
1
2
2
0
0
0
0
1
3
0
0
0
2
0
2
2
0
0
0
1
2
2
1
2
1
0
2
0
0
0
0
1
1
1
0
1
1
0
1
1
0
1
0
0
1
1
1
0
1
1
2
3
1
1
1
0
0
0
1
2
0
1
0
2
0
0
1
0
0
1
1
2
0
1
1
0
1
1
1
0
1
0
0
1
0
0
0
2
0
2
2
0
1
0
0
1
3
0
2
2
0
0
1
1
2
1
1
0
2
0
2
0
1
0
2
1
2
1
0
1
0
1
1
2
0
0
2
0
0
1
0
1
0
1
0
1
1
0
1
0
2
0
1
0
0
2
0
0
2
1
1
1
1
0
1
2
0
0
1
2
1
2
2
2
1
0
0
1
0
0
2
0
1
1
2
0
1
1
0
1
0
2
1
2
1
1
0
1
0
2
0
0
0
0
1
2
2
2
2
1
4
0
2
0
0
0
3
1
1
2
0
0
0
1
1
1
1
2
1
1
1
1
2
0
0
1
1
0
2
2
1
1
1
1
0
2
1
2
1
0
0
1
0
0
0
2
1
0
0
0
0
2
0
0
1
0
1
1
0
0
2
3
0
0
1
1
2
1
0
1
1
1
0
1
0
2
1
1
0
0
0
0
1
1
0
1
0
0
0
1
1
0
1
0
2
1
1
0
0
0
2
0
1
1
0
0
0
0
1
0
0
1
0
0
0
1
1
1
1
3
1
1
1
0
0
2
1
1
1
0
1
2
1
0
1
0
1
2
1
0
0
0
1
1
1
0
0
0
0
1
1
1
2
1
0
1
0
0
2
0
1
1
0
1
2
0
0
1
1
2
1
0
0
1
0
0
1
0
0
1
1
0
1
1
1
1
1
0
1
1
1
4
1
0
0
1
1
1
1
0
2
0
0
1
1
2
0
1
0
0
2
1
1
0
0
1
0
1
2
1
0
1
1
0
0
2
0
0
1
0
1
0
0
1
0
0
0
1
0
1
2
0
1
0
0
0
0
1
1
2
1
0
2
1
0
0
2
1
1
2
0
0
1
1
2
0
1
2
0
1
1
0
0
1
0
2
0
2
0
1
2
0
0
2
1
0
0
1
1
1
1
1
2
2
1
2
1
1
0
1
1
1
0
0
0
1
2
1
0
2
0
0
0
1
1
2
0
1
0
2
1
0
0
2
1
0
0
0
1
1
0
0
0
0
1
2
1
0
1
0
0
0
1
0
0
1
1
1
0
1
1
2
1
0
1
0
1
1
1
1
0
1
0
1
2
1
1
0
1
0
1
2
1
1
0
0
0
2
0
1
0
1
1
2
2
0
0
2
1
1
0
1
2
2
5
1
1
1
1
0
1
1
0
2
2
0
1
1
1
2
0
1
2
2
0
0
1
0
4
1
0
0
0
2
0
0
1
0
0
2
1
1
0
2
1
2
1
1
2
2
1
1
1
0
1
0
0
3
2
2
1
1
2
1
0
0
1
1
0
1
0
0
1
0
1
0
2
0
0
0
0
1
1
2
1
1
1
1
0
1
2
0
1
1
0
1
0
1
1
1
0
0
1
0
0
2
0
0
2
2
1
2
2
0
1
0
1
1
2
1
1
2
0
3
1
2
1
1
1
1
0
0
0
1
1
1
0
1
0
1
0
0
2
1
2
1
0
0
0
2
0
0
2
0
1
1
0
2
1
1
0
0
1
1
0
1
1
0
1
0
0
1
2
0
0
0
0
0
1
0
2
1
1
2
0
2
0
1
1
0
1
2
0
1
1
1
0
2
1
1
1
0
2
1
1
0
2
0
0
0
1
1
0
2
0
2
2
1
1
0
2
1
1
0
1
2
2
0
1
2
2
1
1
0
0
0
1
0
2
1
1
0
0
1
1
0
0
1
0
1
1
1
1
0
0
0
1
1
2
0
2
0
0
1
0
1
2
2
0
1
1
1
2
1
0
0
1
1
0
0
1
0
1
0
1
1
0
1
1
1
1
1
0
2
0
1
1
1
1
1
0
1
0
1
1
1
2
0
1
1
1
1
0
0
1
1
1
0
0
0
1
0
3
0
0
1
1
0
1
0
0
0
0
1
2
2
0
0
0
0
0
2
1
1
0
1
0
1
0
0
2
1
0
0
2
1
1
0
0
1
2
1
1
0
0
1
0
0
2
1
1
1
0
1
2
0
1
1
1
1
1
1
2
1
0
1
0
0
0
0
0
0
1
1
1
0
0
1
0
2
1
2
2
0
1
2
0
1
1
1
0
1
2
1
1
1
0
1
1
1
0
1
2
0
2
0
2
1
1
0
0
0
1
1
1
0
3
0
2
0
1
0
2
1
2
0
1
2
0
0
1
1
1
0
0
0
1
1
1
2
0
1
0
0
0
0
0
1
0
1
0
0
1
1
2
1
1
2
2
2
2
1
2
1
1
1
2
1
2
1
1
1
2
0
0
2
0
0
1
0
0
0
1
1
2
1
0
2
0
0
1
0
2
0
1
0
0
0
0
2
2
1
0
1
1
1
0
0
1
2
1
1
1
1
0
1
1
1
0
1
1
2
0
0
2
3
1
2
1
0
1
2
0
2
0
0
1
2
0
2
0
0
0
1
0
1
0
1
0
2
0
1
1
1
0
1
0
1
1
2
1
3
1
2
0
0
1
1
1
2
0
1
0
0
1
0
2
2
1
0
0
1
1
2
1
0
0
0
0
1
1
0
2
2
0
2
12
0
1
0
0
2
1
0
2
2
2
1
1
0
2
0
0
0
0
1
0
1
1
1
1
0
2
1
0
1
1
2
0
1
2
0
1
2
0
0
4
1
1
1
1
2
3
0
0
2
2
2
1
2
0
2
0
0
1
0
1
1
0
1
1
0
1
2
0
2
2
0
1
0
1
1
0
1
2
0
0
1
1
0
0
0
0
1
1
1
1
1
0
1
1
2
1
0
1
1
0
1
1
0
2
0
2
0
1
1
0
0
1
1
0
1
1
0
1
1
1
0
1
1
1
1
1
1
3
0
1
2
1
2
2
0
1
3
2
0
0
2
0
2
0
1
1
0
2
1
2
2
0
1
0
2
1
0
1
2
2
0
1
0
0
1
0
2
1
0
1
2
2
1
0
0
1
1
0
2
0
0
1
0
1
0
1
1
1
1
0
1
1
1
2
3
1
1
1
1
0
0
0
0
1
1
2
1
1
2
0
0
2
2
0
2
0
0
1
1
1
1
0
1
2
0
0
1
0
0
0
1
1
3
0
0
1
0
2
0
0
0
1
1
0
2
1
0
0
1
0
0
0
1
1
1
0
0
0
0
1
0
2
0
2
0
0
2
0
0
1
0
1
0
0
0
3
0
0
0
0
1
1
1
2
0
0
2
0
0
0
0
2
0
2
0
1
1
0
0
1
0
1
0
1
1
2
1
1
1
0
1
1
0
1
1
1
2
0
0
2
4
1
0
0
1
0
1
1
2
1
0
0
2
0
2
0
0
0
0
0
1
2
1
0
1
1
2
0
2
0
0
0
2
0
0
1
1
1
0
1
2
2
0
2
1
0
1
1
2
1
2
0
0
1
0
1
2
0
0
2
1
1
1
1
0
1
0
0
1
2
0
0
1
0
0
5
1
0
3
2
1
0
1
1
1
0
1
0
2
1
1
2
0
0
1
0
0
0
1
1
1
1
0
1
2
0
0
0
2
0
1
0
1
1
1
0
1
1
0
2
2
0
1
0
0
0
2
0
0
0
1
2
1
0
0
1
0
2
0
1
0
1
1
1
0
2
1
0
0
1
3
0
0
0
0
4
1
1
2
0
0
2
0
1
1
1
0
2
2
0
1
0
0
0
0
0
2
0
1
0
1
1
0
0
1
0
2
1
0
1
2
1
1
0
1
2
0
2
1
0
2
2
2
0
0
1
1
0
1
2
2
0
0
0
1
1
2
2
1
1
0
1
0
2
1
2
0
2
0
0
3
0
1
0
1
2
0
0
0
2
1
0
0
1
3
0
1
1
2
1
2
0
0
0
1
0
1
1
2
0
2
0
2
1
0
0
0
0
0
0
2
1
0
0
0
3
0
0
0
0
0
0
1
2
1
0
1
1
1
0
0
1
2
0
0
2
1
2
0
1
1
0
1
0
1
1
1
0
2
0
0
0
1
2
2
1
1
0
1
0
1
2
2
2
0
2
2
1
1
1
1
1
0
0
2
0
1
1
2
0
1
1
1
1
2
0
0
2
0
0
1
1
2
0
0
1
2
1
0
0
1
0
1
1
1
0
2
1
1
2
0
0
0
0
1
1
0
0
2
0
2
1
0
1
0
1
1
1
0
2
1
0
2
1
0
1
1
2
1
1
0
1
1
1
1
0
0
5
0
0
1
0
1
0
0
1
0
0
1
1
0
1
1
2
0
2
0
1
1
1
0
0
1
0
2
0
0
1
2
1
1
2
1
2
2
1
1
0
0
1
0
0
1
2
2
0
1
1
2
1
1
0
1
1
2
1
1
1
0
1
2
0
1
0
0
0
1
0
1
2
0
1
0
1
0
1
1
1
1
1
2
0
0
0
1
2
0
0
1
2
1
1
1
0
1
1
2
2
1
0
2
1
2
1
2
1
2
0
0
1
1
1
1
0
0
0
1
0
0
0
3
0
0
0
1
0
0
2
2
2
0
2
0
0
0
1
1
1
1
0
1
0
0
1
1
2
1
1
1
0
2
2
0
1
0
2
0
0
0
0
0
0
1
3
0
1
1
0
1
0
0
1
1
2
0
2
2
0
0
2
2
3
1
0
0
1
0
1
2
0
1
0
0
2
0
0
0
0
2
1
1
1
0
1
1
1
1
0
0
1
1
1
1
1
2
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
1
0
3
0
1
2
0
1
0
2
1
1
0
0
3
1
0
1
0
1
1
2
2
0
1
0
0
1
1
0
1
0
0
2
0
2
2
0
1
2
0
0
1
1
1
1
3
0
1
2
0
2
0
2
2
1
1
1
0
0
0
0
1
0
1
1
2
0
1
2
3
1
1
2
0
1
2
0
2
0
1
1
0
1
0
1
0
0
2
1
2
0
1
2
0
1
0
0
0
2
0
1
3
1
1
0
0
2
1
0
1
0
1
0
0
1
0
2
1
2
0
1
1
2
0
1
2
0
4
0
1
1
0
0
0
0
2
1
1
0
1
0
1
2
1
0
1
0
0
1
2
1
1
0
2
0
1
1
1
0
1
0
1
1
0
0
1
0
0
0
1
1
2
0
1
0
1
1
1
0
1
3
0
2
1
0
2
0
0
0
2
1
0
0
0
1
0
2
1
1
0
0
0
3
1
1
0
0
0
0
0
0
1
1
0
0
1
0
5
1
1
0
1
0
4
1
0
0
1
1
1
1
2
2
3
1
0
1
1
1
1
0
0
0
0
2
1
1
1
0
1
2
0
1
1
1
0
0
0
0
0
2
1
0
2
1
0
0
2
0
2
0
1
0
0
1
0
0
0
1
0
1
0
1
0
2
0
2
0
0
0
1
2
1
1
0
0
0
2
0
0
0
1
2
1
1
0
0
1
1
0
1
0
1
0
0
2
0
0
2
0
0
1
1
1
1
2
2
1
1
0
2
0
0
3
2
0
1
1
0
1
0
0
1
1
1
0
0
2
1
0
2
0
2
1
0
0
0
1
0
0
0
0
2
2
2
0
0
1
1
3
1
1
1
0
0
1
1
2
1
3
2
0
0
1
1
2
2
1
2
2
0
0
0
0
1
2
0
0
2
0
0
0
1
2
0
1
2
0
2
0
1
0
0
1
0
0
1
1
0
1
1
2
1
0
0
1
0
1
2
1
1
1
0
1
1
1
1
1
1
0
0
1
0
0
0
0
0
1
1
1
3
0
0
1
0
2
1
1
0
0
0
0
2
1
1
0
1
0
0
0
2
2
0
1
1
0
1
0
0
0
0
0
1
1
1
1
1
1
0
1
3
0
0
2
0
0
1
0
0
0
2
1
0
0
0
1
2
0
2
1
1
0
1
1
0
0
1
1
1
1
2
1
1
0
1
0
1
0
1
1
0
1
0
1
3
0
0
1
1
2
1
1
2
0
1
0
1
0
1
0
1
0
2
2
0
0
2
0
1
1
1
1
0
1
1
1
0
0
0
1
0
0
0
0
1
1
0
1
0
1
1
2
0
0
1
0
1
0
0
1
0
2
1
2
1
0
1
1
0
1
2
1
1
2
0
1
2
4
2
1
0
0
0
0
2
0
1
0
1
2
1
2
0
2
0
1
0
0
2
0
2
1
1
1
1
1
2
0
1
2
2
1
0
1
0
0
1
3
0
1
2
0
1
0
1
3
0
1
2
0
1
0
1
0
0
1
3
1
1
1
2
0
1
1
2
1
2
2
0
1
1
3
1
1
2
0
0
3
1
2
2
1
2
0
1
1
2
1
0
2
1
1
0
0
0
2
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
1
1
1
2
2
2
1
0
1
1
1
0
0
1
0
0
2
0
1
2
0
1
1
1
1
0
0
1
1
1
1
2
1
0
1
0
0
1
1
0
0
1
2
0
1
1
1
1
2
3
2
2
1
1
1
2
0
1
2
0
1
0
2
1
0
2
1
1
2
0
1
1
0
0
0
2
1
0
0
1
0
0
0
1
2
2
2
0
0
2
1
0
1
0
2
0
0
2
1
1
0
1
1
2
0
1
1
0
0
1
0
1
1
0
2
1
1
0
0
0
0
2
0
0
2
1
0
2
1
1
2
0
2
0
0
3
2
0
1
1
0
1
2
1
0
1
1
2
2
1
1
1
2
0
0
0
1
0
0
1
2
1
2
1
2
1
0
1
2
1
0
0
2
1
0
2
1
0
2
0
1
0
1
1
0
1
0
1
0
2
1
1
0
2
2
0
1
2
1
0
1
0
0
0
0
1
1
0
1
1
0
1
0
0
1
1
1
1
0
1
1
1
1
0
0
0
0
0
1
0
2
1
0
0
3
2
0
2
2
1
1
1
1
1
0
1
3
0
0
1
1
0
2
1
1
1
2
0
0
2
2
2
0
1
0
1
1
0
0
0
1
2
0
1
1
0
1
0
1
1
0
1
1
0
0
2
0
0
0
0
1
0
1
2
0
2
0
0
2
0
1
1
1
1
1
0
1
2
2
2
1
2
2
1
2
0
0
2
2
1
1
2
1
0
1
0
1
2
1
0
2
1
1
0
1
1
1
1
2
2
1
2
2
0
0
0
0
1
1
1
0
0
0
2
1
2
0
1
0
1
1
0
0
0
1
0
0
0
1
3
1
0
1
1
1
0
1
1
2
2
1
0
1
1
1
1
1
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
2
1
1
2
2
1
1
1
0
0
0
1
0
3
2
0
0
1
1
1
1
1
0
0
1
1
0
2
0
0
0
0
1
0
0
2
0
1
2
1
0
1
2
0
0
0
0
1
1
1
2
2
1
0
1
2
2
2
2
1
0
2
1
0
1
1
1
0
2
2
0
1
2
0
0
2
1
0
0
2
0
2
0
0
0
0
0
1
2
1
2
0
1
1
0
0
2
0
1
0
0
1
0
1
0
2
0
1
0
1
0
2
1
1
0
0
0
0
1
0
1
0
1
0
1
2
1
1
1
0
1
0
0
0
2
0
0
0
0
0
1
1
0
0
1
1
1
1
0
0
1
1
0
0
1
1
0
0
1
1
0
1
2
0
0
0
2
0
0
0
1
1
2
3
1
2
1
0
0
0
1
0
1
0
0
1
2
0
0
1
2
1
1
0
1
1
0
1
0
1
0
1
1
0
1
0
2
2
2
0
0
2
1
0
1
2
3
0
0
0
0
2
0
1
1
0
0
1
1
0
0
0
1
2
0
0
0
2
1
0
0
1
0
1
0
2
0
1
0
1
0
0
0
0
0
1
1
2
0
0
0
1
3
0
2
1
1
0
1
2
1
0
1
1
1
0
2
1
2
1
0
1
2
0
1
0
0
1
2
1
0
2
0
1
2
1
2
1
0
0
2
0
0
0
1
1
0
0
1
0
0
1
1
2
0
2
1
0
1
2
2
2
0
2
2
0
1
0
0
0
0
2
0
0
0
0
1
1
1
2
1
1
0
3
0
1
1
2
1
8
1
2
1
0
2
1
0
0
2
0
0
5
0
1
0
0
1
1
0
1
2
2
0
2
2
0
0
2
1
0
2
0
2
1
0
0
0
0
0
0
1
1
0
1
2
0
1
0
1
1
1
1
1
0
0
1
1
2
2
0
2
0
1
0
1
1
0
0
0
0
2
0
1
0
0
2
2
0
0
2
3
1
0
1
0
0
2
1
1
1
1
2
1
0
0
2
1
1
1
1
0
0
0
1
2
1
1
2
1
0
2
0
2
2
0
1
0
0
2
0
0
2
0
0
0
0
1
1
0
1
0
1
1
1
1
0
1
0
1
2
0
0
1
0
1
0
1
0
0
1
1
1
1
0
0
2
0
1
1
0
0
1
0
0
0
1
1
0
2
1
0
0
1
2
2
1
1
0
1
1
1
1
0
2
0
1
2
2
2
1
1
0
1
1
0
0
1
0
0
1
1
0
2
1
0
1
2
0
0
2
1
1
1
1
3
0
0
1
1
1
2
1
0
2
1
1
0
0
0
1
0
0
0
0
1
2
0
4
2
0
1
0
1
0
1
1
2
2
1
0
0
0
1
1
1
1
3
1
1
0
1
2
1
5
1
2
1
0
0
0
2
0
0
1
0
0
1
1
0
2
2
0
0
1
2
1
0
2
1
1
2
1
0
0
2
1
0
0
1
1
0
0
0
1
2
2
0
0
1
0
1
2
0
0
1
1
1
0
0
1
0
2
1
1
2
2
1
0
2
10
0
1
2
0
1
1
0
0
2
2
1
1
0
0
0
2
1
1
1
2
0
0
1
0
1
1
2
1
0
0
0
1
0
0
3
1
0
2
2
1
2
1
2
1
0
1
2
0
2
1
1
0
1
2
0
0
1
1
1
1
1
2
0
2
0
2
0
1
1
0
1
0
0
0
1
2
1
0
2
0
1
0
1
1
0
1
2
0
4
1
1
0
0
1
0
1
2
1
0
0
2
0
0
1
1
2
2
0
0
1
1
0
2
0
1
2
1
1
0
2
1
0
2
0
1
2
0
0
1
1
0
2
1
1
0
0
0
2
0
1
1
0
0
1
0
0
1
0
1
1
1
2
1
2
2
2
0
0
2
2
0
2
1
0
3
1
1
3
1
2
1
2
0
0
2
1
1
1
2
1
0
1
2
2
2
0
0
1
3
0
1
1
2
2
2
1
1
2
0
0
1
0
0
1
0
0
0
2
2
1
1
1
1
1
0
1
2
1
0
0
1
0
0
2
2
0
0
2
1
0
2
0
1
0
1
2
1
1
2
1
0
2
2
1
0
0
2
0
0
1
1
0
1
2
1
2
2
2
2
0
1
2
1
2
2
1
2
1
1
2
0
1
1
3
1
0
1
1
1
0
0
1
0
0
2
0
1
0
2
0
0
1
1
2
0
2
1
0
1
1
0
0
1
0
1
0
2
0
2
0
1
1
1
1
1
0
1
0
0
1
0
1
1
0
0
0
0
2
1
0
0
0
2
0
1
0
0
1
2
1
1
2
2
1
2
0
1
0
1
1
1
0
0
1
1
2
0
0
0
0
2
0
2
0
2
0
0
0
2
1
2
0
1
1
2
1
1
1
3
0
0
1
2
1
1
0
1
0
0
0
1
0
1
2
1
2
2
0
0
1
0
0
1
0
2
1
2
0
0
0
2
0
0
1
1
2
2
0
1
0
1
1
1
2
2
0
0
2
1
1
0
1
0
1
3
0
0
1
0
1
0
1
0
1
1
1
0
1
0
1
2
1
0
2
0
0
2
0
0
1
2
1
1
1
0
0
2
1
0
0
1
0
1
2
2
3
1
0
1
1
0
2
1
1
1
0
0
0
0
1
1
0
2
0
0
1
1
2
0
1
0
1
0
0
0
0
1
1
1
1
0
0
2
2
0
1
0
0
1
1
1
0
0
2
0
1
2
0
0
0
0
0
2
0
1
0
0
1
1
1
3
2
0
0
1
2
0
0
0
0
2
1
0
1
1
2
0
0
1
0
2
0
1
2
0
2
1
3
1
0
1
0
0
0
0
0
0
0
2
0
1
1
2
1
0
0
0
1
0
0
0
0
1
0
2
0
0
0
1
1
1
0
1
0
0
1
0
2
2
1
0
1
1
1
0
1
2
2
1
1
2
0
1
2
1
2
2
0
1
0
1
2
0
1
0
0
1
2
1
0
2
0
0
2
1
0
1
1
0
1
1
0
2
1
2
2
0
1
0
2
1
1
5
1
1
1
1
0
1
0
2
0
2
0
2
1
0
1
0
1
0
1
1
0
0
4
1
1
0
1
0
0
2
0
0
1
1
1
0
1
2
0
0
0
1
2
0
1
2
0
1
0
1
0
0
1
1
0
0
0
0
1
0
1
0
0
2
1
0
0
1
0
2
0
1
2
1
1
3
0
0
1
2
1
0
0
1
1
0
1
1
1
1
0
1
0
1
2
0
1
2
2
0
0
0
3
0
0
0
1
0
1
1
0
1
2
0
2
2
2
0
0
0
1
2
0
0
2
1
1
1
1
2
0
2
2
0
1
1
1
1
0
1
0
2
1
0
0
1
1
1
0
0
1
1
0
1
1
0
2
0
2
1
0
1
1
0
0
1
1
0
0
2
1
0
0
0
0
1
0
0
2
0
1
1
0
1
1
2
1
1
1
2
1
2
1
0
2
1
2
0
2
0
0
1
1
2
0
0
0
1
0
1
2
2
1
1
2
0
0
1
0
0
2
0
0
1
0
2
2
2
1
0
1
1
0
0
2
0
1
2
0
0
1
1
2
2
0
2
0
2
0
2
1
2
0
0
0
2
0
1
2
2
1
1
0
0
1
1
1
0
0
1
2
1
0
0
0
1
0
1
1
0
1
1
1
2
0
2
2
0
2
1
1
2
0
1
1
0
0
0
0
1
2
0
1
1
1
1
0
2
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
1
2
2
0
0
1
1
0
1
0
1
2
0
0
0
1
1
0
1
1
0
1
0
0
2
1
1
0
0
1
2
1
2
1
2
0
2
0
2
2
0
0
1
2
1
1
1
2
0
1
1
2
0
2
1
0
0
1
0
0
1
1
1
0
0
0
0
0
1
2
1
2
2
0
0
0
2
0
1
0
1
1
2
2
1
0
1
1
0
1
0
1
2
2
1
1
0
1
0
0
1
1
1
0
0
0
0
0
1
2
2
0
0
0
2
1
1
2
0
1
1
1
1
0
0
0
1
2
1
0
2
2
0
1
2
2
1
0
1
0
3
2
0
2
2
2
1
2
0
0
0
2
0
1
0
1
0
1
2
1
1
1
2
1
1
1
0
1
3
1
1
1
1
2
2
0
1
0
0
0
0
1
1
0
1
1
0
0
2
0
0
1
1
2
1
1
0
2
0
2
0
1
1
0
1
1
1
0
0
0
1
1
1
1
2
1
2
2
0
0
2
0
0
0
2
2
0
2
0
1
1
1
0
0
0
1
2
1
0
1
0
1
0
1
1
0
2
0
0
2
1
0
0
7
1
1
2
1
0
1
1
1
2
0
0
1
2
1
1
0
2
2
1
0
2
0
2
0
1
0
0
0
1
1
1
0
0
1
0
0
0
0
0
1
0
0
2
1
1
1
1
1
1
0
2
1
1
3
1
0
0
2
1
0
1
0
0
0
0
1
0
2
1
0
0
0
0
1
1
1
1
0
0
0
1
1
0
0
2
1
1
1
1
1
1
2
2
2
1
0
1
0
0
4
2
0
0
1
0
1
0
1
1
1
2
0
2
3
1
0
0
1
2
2
0
1
1
1
0
0
0
1
0
1
0
0
1
1
3
2
2
2
0
2
0
1
2
0
1
0
1
2
1
3
1
1
0
1
2
1
0
1
0
2
0
0
2
2
2
1
0
2
0
1
1
0
1
0
0
0
2
0
1
0
2
2
2
1
0
0
0
2
1
1
1
0
0
2
0
1
2
1
2
0
1
1
0
1
0
1
1
0
1
0
1
2
0
0
0
0
0
0
0
0
1
1
0
1
2
0
1
1
1
2
2
0
2
0
1
2
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
1
1
1
1
1
2
1
0
0
2
1
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
2
0
1
0
1
1
1
1
0
2
1
0
1
0
1
2
2
0
1
1
1
0
3
1
0
0
0
0
0
2
1
2
1
1
1
0
1
1
1
0
1
2
1
1
1
1
1
2
0
0
2
1
0
1
0
1
2
1
0
0
2
0
0
0
1
0
1
0
2
1
2
1
1
1
0
1
2
0
2
6
0
2
0
2
1
1
1
2
1
0
1
0
2
1
1
2
0
0
1
2
2
2
0
0
0
0
1
2
0
2
0
1
1
1
1
2
0
1
1
0
2
0
1
2
0
1
1
1
2
0
0
1
1
1
1
1
0
1
2
1
1
2
0
1
0
0
1
1
1
1
0
1
0
0
2
1
0
2
1
2
0
1
0
2
1
0
2
2
0
0
1
0
2
2
1
2
2
1
1
1
1
1
0
2
0
0
0
1
2
2
1
2
1
1
0
1
2
1
2
0
0
0
2
0
0
2
2
1
1
1
2
0
1
2
2
1
0
1
1
1
1
1
1
3
0
1
1
1
0
0
2
1
0
0
0
2
0
0
2
0
0
0
2
1
2
1
0
1
0
2
0
0
0
1
2
0
0
0
0
1
0
2
0
0
0
1
2
1
0
1
0
1
1
3
1
1
1
1
0
0
0
2
1
1
0
1
0
2
0
0
2
1
1
1
0
1
0
2
0
1
2
1
0
2
1
1
0
1
2
1
1
0
1
0
1
1
1
1
1
1
1
0
0
1
2
0
1
1
1
0
1
0
1
0
2
1
2
0
1
0
0
0
1
2
1
0
0
2
0
0
0
0
1
0
1
2
1
1
0
1
2
2
1
0
0
0
0
1
1
1
1
0
1
1
2
0
1
2
2
0
0
2
1
0
1
0
1
1
2
0
2
2
1
1
1
1
2
1
0
3
2
0
0
2
0
0
0
1
0
0
0
0
2
0
1
2
1
0
0
0
1
1
2
0
2
0
0
1
1
1
0
1
0
1
0
1
1
2
0
0
2
0
0
2
1
2
0
2
2
1
0
2
0
0
2
0
1
0
0
1
1
1
1
1
0
0
2
2
1
1
0
1
1
2
2
1
0
2
0
0
1
0
1
2
1
0
7
0
1
1
1
0
0
0
0
1
1
3
0
1
0
0
0
0
2
1
1
0
2
0
1
2
2
0
0
1
1
2
0
1
0
1
0
0
0
0
0
1
1
1
0
0
1
0
1
0
1
2
1
0
2
2
2
0
0
0
1
0
0
0
0
2
0
2
0
1
1
0
1
1
0
1
1
0
0
2
0
1
0
0
1
2
2
0
1
1
0
0
1
0
1
0
1
0
1
0
0
0
0
0
1
0
0
1
1
1
0
1
1
1
2
0
0
1
0
1
1
0
0
2
1
1
0
0
2
2
0
2
1
1
1
1
0
2
1
1
1
0
0
1
0
0
1
1
0
0
0
1
1
0
1
1
1
1
2
0
1
1
1
2
0
1
1
2
0
0
0
1
0
0
0
0
0
2
0
1
1
1
1
0
1
2
0
0
0
1
0
2
0
2
0
1
2
2
0
0
1
0
0
1
2
0
0
1
2
1
0
0
2
2
0
1
1
2
1
1
1
1
2
1
0
1
0
1
2
0
1
0
0
1
0
2
0
0
0
0
0
1
1
0
2
3
1
0
2
2
1
1
0
0
0
0
0
4
2
0
1
1
1
0
1
2
0
0
2
0
0
1
0
0
2
1
0
1
3
0
0
1
2
0
1
1
0
0
1
2
0
0
1
2
2
0
1
0
1
0
0
0
1
2
0
1
0
1
2
0
0
0
1
0
1
0
2
0
0
1
1
0
0
1
0
0
2
0
1
2
2
0
0
2
2
1
1
1
2
2
0
1
0
1
1
0
1
1
2
0
1
1
2
0
0
0
2
1
1
1
2
0
0
0
1
0
1
2
2
1
0
1
1
0
2
1
0
1
2
2
2
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
2
1
1
2
0
1
0
1
2
0
2
0
0
0
1
2
0
1
1
1
0
0
0
2
1
0
3
2
1
1
0
1
0
0
2
0
1
0
2
0
2
1
2
0
0
1
0
1
2
1
2
1
1
1
1
0
2
2
1
1
1
1
2
0
1
1
1
4
3
1
0
1
0
1
1
2
0
0
1
2
0
1
0
0
0
1
2
0
1
0
0
2
2
1
1
0
2
0
0
2
0
1
0
0
0
1
1
1
0
1
0
1
1
0
1
0
0
1
1
1
0
1
1
0
0
1
0
1
2
0
1
0
1
1
1
2
1
1
1
0
0
0
2
1
1
1
2
2
0
2
2
1
1
0
1
0
0
10
1
0
1
2
3
1
1
0
2
1
0
2
1
2
1
0
0
0
1
1
0
0
0
1
0
2
1
2
2
1
0
0
0
2
0
2
0
1
1
1
1
0
2
1
2
1
1
2
1
1
2
0
0
0
2
0
1
1
0
1
1
2
0
0
1
2
0
0
0
2
2
0
1
1
0
0
0
1
0
0
0
1
2
0
5
0
0
0
0
2
1
0
0
2
1
2
2
2
1
2
2
1
2
1
1
1
1
1
2
2
0
0
1
1
1
2
0
0
2
1
1
1
0
0
1
0
0
0
2
1
1
0
0
0
1
0
2
2
2
1
1
0
1
1
2
0
2
0
0
1
0
0
1
0
2
0
2
0
0
1
0
1
2
1
0
2
1
0
1
1
0
0
0
0
2
0
0
1
1
0
1
0
2
1
2
1
2
0
0
4
1
1
0
0
2
1
1
0
0
1
1
0
0
1
2
0
2
0
2
0
0
2
0
2
2
2
0
0
0
0
1
0
1
0
4
1
2
2
1
0
0
1
0
0
2
0
2
1
0
1
2
1
2
0
1
2
0
0
1
0
0
0
2
0
0
2
1
1
1
2
0
2
0
1
0
0
1
0
0
0
1
2
1
1
2
1
1
0
2
1
1
2
2
0
1
0
0
1
0
1
0
1
2
2
1
0
1
2
1
1
1
0
2
1
1
0
1
0
1
1
2
1
2
1
0
1
0
0
1
1
1
2
1
1
1
0
0
0
0
0
0
1
1
2
0
0
0
0
0
1
2
0
1
0
1
0
0
0
1
1
0
1
2
0
1
2
2
2
1
2
1
0
1
0
0
0
1
0
0
2
1
0
0
1
2
0
1
0
1
0
1
1
0
2
2
2
2
0
2
2
1
0
0
1
0
0
1
2
1
0
1
1
0
0
1
2
2
1
0
2
2
0
2
2
0
0
0
2
0
1
1
2
1
1
1
0
2
1
2
0
1
1
1
1
3
2
1
0
0
0
0
0
0
1
0
2
0
1
1
0
2
0
2
1
0
2
2
0
0
0
0
2
1
1
0
0
1
1
1
2
0
1
0
2
0
1
2
1
1
2
1
0
0
2
0
0
0
0
0
2
0
2
1
0
1
1
1
1
2
0
0
0
1
1
1
0
1
2
2
1
2
2
3
1
0
1
1
1
1
2
2
0
0
1
2
1
1
2
1
1
1
0
0
0
1
0
1
1
0
1
0
2
0
1
1
0
1
1
1
0
1
1
1
0
1
0
0
1
0
1
0
1
2
2
2
0
0
1
2
0
0
0
0
1
1
0
1
1
2
1
0
2
0
2
2
0
0
1
1
2
1
0
0
0
0
1
3
2
2
0
0
1
0
1
0
0
1
0
2
1
1
2
0
0
0
0
1
0
0
0
1
0
1
0
1
0
2
2
2
1
0
1
1
1
2
1
1
1
2
0
0
2
1
2
0
2
0
1
2
0
1
0
0
0
0
2
0
1
0
0
1
1
2
2
2
0
1
0
0
0
1
0
1
2
0
0
1
1
0
2
0
1
2
2
1
0
0
1
0
0
0
0
2
2
2
1
2
0
1
1
0
1
1
2
2
1
0
2
0
0
1
1
0
0
0
1
0
0
1
1
2
0
1
1
0
1
0
0
2
1
1
1
1
2
2
2
1
0
0
2
1
1
1
2
0
1
1
1
1
0
0
1
0
3
1
0
2
2
1
0
1
0
0
2
1
0
1
1
2
0
1
0
2
1
0
0
0
1
2
1
1
0
2
0
1
1
2
1
0
2
0
2
0
1
1
2
1
1
0
0
1
0
1
0
1
0
0
2
2
1
0
2
1
2
0
0
2
2
0
0
0
1
1
2
0
2
1
0
0
1
0
1
0
1
1
2
1
0
0
0
2
1
0
1
2
1
0
1
0
1
0
0
1
3
1
0
0
0
0
1
0
2
0
1
1
0
1
2
2
2
1
1
1
0
1
2
5
0
1
1
1
0
0
2
0
0
1
1
0
2
2
0
0
2
1
0
0
0
2
1
1
1
0
1
2
3
1
0
1
0
0
0
0
1
0
0
0
2
0
0
1
2
0
1
2
0
2
0
1
1
0
1
2
1
0
2
2
1
0
1
0
0
0
1
1
0
0
2
0
0
1
1
2
1
0
3
1
0
0
2
2
0
2
1
0
1
0
0
2
1
1
0
0
0
1
1
1
1
1
0
0
1
2
1
2
1
2
0
0
0
1
4
0
0
1
0
0
0
0
2
0
1
0
0
1
2
2
1
1
1
2
1
0
2
0
2
1
2
2
1
1
2
1
1
0
1
0
0
0
1
2
0
0
1
0
1
0
2
1
0
0
0
0
0
1
2
1
2
1
2
1
0
0
0
0
1
0
0
2
2
2
0
1
0
1
0
1
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
2
0
1
0
0
1
3
1
0
2
1
1
0
1
1
1
1
2
0
1
2
1
0
1
1
0
1
1
2
0
0
0
2
2
1
0
0
0
1
1
2
1
1
0
0
0
1
0
2
1
1
2
1
0
1
1
2
0
1
2
2
0
2
1
1
0
0
2
1
0
0
0
2
0
1
1
0
1
1
0
0
1
0
1
1
0
1
1
1
2
1
1
1
2
0
0
2
2
1
2
0
1
1
1
0
0
1
4
0
1
1
0
0
1
0
2
1
0
1
3
1
0
0
2
1
0
2
2
2
0
1
1
2
0
3
1
0
0
2
1
0
1
1
2
1
2
1
2
0
0
0
1
1
2
1
1
1
0
0
1
1
1
1
0
2
1
0
1
1
0
1
2
1
0
2
0
1
1
1
12
0
0
1
2
1
2
1
1
0
1
0
1
2
1
0
2
0
0
1
0
2
0
0
2
2
3
1
1
2
0
1
0
0
1
0
1
0
0
0
2
1
1
0
2
1
2
0
0
0
1
0
0
2
0
0
1
0
0
2
0
2
0
1
0
1
3
2
1
0
0
0
0
0
0
1
1
0
0
2
1
1
1
0
2
1
1
0
0
0
1
1
1
0
2
1
0
2
2
0
1
0
1
2
0
2
2
0
1
0
0
2
0
0
2
0
0
0
1
0
0
0
1
2
0
1
1
1
1
1
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
2
2
0
1
2
0
0
0
1
0
0
1
2
1
0
0
1
1
1
0
0
1
4
0
0
1
2
0
1
1
1
0
0
1
1
1
1
1
0
0
0
0
0
0
0
0
1
0
1
2
1
0
1
1
0
0
1
1
0
1
0
1
1
0
0
0
0
0
1
1
3
1
0
2
0
0
0
0
1
1
0
2
0
2
1
1
0
1
2
0
1
1
1
1
0
2
1
1
0
1
0
0
1
0
0
2
0
1
1
0
1
1
0
0
0
0
0
1
0
0
1
2
0
0
1
2
0
0
1
2
0
0
2
2
1
1
1
0
1
2
2
1
2
2
2
1
0
1
0
0
0
0
2
0
0
1
0
1
0
1
2
0
0
2
1
2
1
0
1
0
1
3
0
1
0
0
2
1
0
2
1
0
0
1
2
0
2
2
0
2
1
2
0
1
1
0
12
2
1
0
0
0
1
1
1
2
0
0
2
1
0
2
0
0
1
0
0
0
0
0
0
2
0
0
1
1
2
0
0
0
0
0
1
0
1
0
2
1
0
0
1
1
0
0
3
2
0
1
0
0
2
0
0
1
0
0
1
2
2
1
0
0
1
2
1
2
1
0
3
0
2
0
2
0
1
0
1
1
1
0
0
0
0
1
1
2
1
0
0
1
3
1
2
1
0
1
2
0
0
2
0
2
0
0
0
1
3
0
2
0
0
1
1
2
2
1
0
1
1
0
0
1
1
1
1
1
0
1
0
0
0
0
1
0
1
1
2
1
2
0
1
1
0
1
0
0
0
1
2
0
1
1
0
1
0
1
1
1
1
0
2
0
1
1
0
2
1
0
2
1
1
0
0
0
1
2
0
2
1
0
1
2
2
0
2
1
1
2
0
0
2
0
0
1
0
0
1
0
1
0
1
1
0
2
3
2
2
0
0
2
2
2
0
2
1
0
1
2
0
1
1
2
2
1
2
2
0
2
1
0
0
1
2
1
0
2
1
1
0
0
1
1
2
2
0
2
1
1
0
1
0
0
0
0
1
1
0
2
0
2
1
1
2
0
0
1
2
1
1
2
0
1
0
0
2
0
1
2
1
1
2
1
0
0
1
2
0
2
0
0
1
0
0
2
0
0
2
1
1
0
1
1
1
0
2
0
2
0
2
0
1
1
0
1
0
1
0
2
0
0
0
1
0
0
2
0
0
2
1
1
2
0
0
1
1
2
1
0
0
1
0
3
0
0
1
1
1
1
0
0
1
0
2
2
0
0
0
0
1
1
0
0
1
0
1
1
1
2
1
1
2
0
0
1
0
0
0
0
1
0
2
0
1
2
0
0
0
0
0
1
2
1
7
2
0
0
1
1
1
0
0
0
2
0
1
0
1
0
1
1
0
0
2
0
0
1
1
2
1
2
1
1
1
0
0
1
0
0
1
1
0
0
0
0
2
1
0
0
1
2
2
2
2
0
2
1
1
1
0
0
1
1
2
1
2
2
1
0
1
2
1
0
1
1
1
0
0
1
1
2
1
2
1
1
1
0
4
0
1
1
1
0
0
1
2
1
2
0
1
1
0
0
1
0
1
0
1
1
0
1
0
0
1
1
1
0
0
0
2
1
1
0
0
2
2
0
1
0
1
0
0
0
0
0
1
2
1
0
1
0
0
2
0
0
2
0
1
1
1
0
2
0
1
0
1
1
0
0
1
1
1
0
2
1
1
0
1
1
0
0
1
1
2
1
0
1
0
1
0
0
1
0
1
1
1
2
1
0
2
0
1
1
1
1
1
1
0
1
1
2
0
0
2
0
0
0
1
2
0
2
0
1
2
0
0
1
1
4
0
1
1
1
1
0
1
0
1
0
1
0
2
1
2
2
2
1
1
2
0
1
1
1
1
1
2
1
1
0
2
0
0
0
2
2
0
0
1
1
1
1
1
0
0
1
1
2
2
3
2
1
0
1
1
0
1
1
0
0
0
1
1
1
2
2
0
1
1
1
1
1
2
2
1
1
0
0
0
1
0
0
0
0
1
0
0
0
2
2
2
0
1
1
0
0
2
1
0
1
1
1
1
0
0
0
0
0
1
2
1
0
0
0
2
0
1
0
0
1
0
1
0
1
2
0
0
1
0
2
1
1
1
1
0
0
1
0
0
0
0
0
1
0
1
0
0
1
2
0
0
1
1
1
2
0
0
1
1
0
1
2
1
1
1
1
1
2
2
1
1
2
0
1
2
1
0
1
2
1
0
1
0
1
0
1
1
0
0
1
1
0
2
1
0
0
1
2
1
0
0
1
0
1
1
3
0
0
1
0
0
1
2
1
2
1
2
2
2
0
2
1
2
2
1
0
0
1
1
0
1
0
0
1
1
2
0
1
1
1
1
2
2
0
0
1
2
2
1
1
0
3
0
1
0
2
2
1
1
0
0
0
0
0
2
2
0
1
2
0
1
1
0
1
0
2
0
3
0
2
1
0
1
0
1
1
0
0
0
2
0
1
2
0
0
1
2
1
0
0
0
0
0
1
2
0
1
1
1
2
2
2
2
0
2
1
0
1
1
0
1
2
0
1
2
1
2
2
0
1
1
0
1
1
1
1
3
1
1
1
1
1
0
2
0
2
1
2
2
1
1
0
2
1
1
1
2
2
1
1
2
1
0
0
0
0
1
1
0
0
0
0
1
0
2
1
1
0
2
0
2
1
0
0
0
0
1
0
0
0
1
0
0
2
0
0
2
0
1
3
0
1
0
0
0
1
1
1
2
2
2
1
0
0
0
0
2
1
2
0
2
1
1
0
2
1
1
1
1
1
1
0
2
2
0
0
0
1
0
0
1
1
1
0
0
2
1
1
0
1
0
2
2
0
0
1
0
2
0
1
3
1
1
0
2
1
0
0
0
1
0
2
0
0
0
2
2
1
0
1
0
0
0
1
0
2
0
0
2
1
1
0
1
0
2
0
0
0
0
2
0
2
2
0
1
1
2
0
0
0
2
1
1
0
1
1
0
0
0
0
1
0
3
1
0
1
1
1
1
2
1
0
1
1
2
0
1
0
2
0
2
2
2
1
0
2
1
2
2
1
1
1
1
0
0
3
0
1
0
1
1
1
1
2
0
0
2
2
5
0
1
0
0
0
0
1
2
0
0
0
0
2
0
0
3
1
1
2
4
0
0
2
0
2
0
1
2
2
1
0
0
1
2
0
0
3
1
1
0
2
2
0
2
2
2
0
0
1
0
0
1
0
1
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
2
1
2
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
1
0
2
1
0
0
1
0
1
1
1
0
0
2
0
1
1
2
0
0
1
1
2
1
0
1
0
2
0
0
0
1
1
2
0
0
0
1
2
1
0
2
2
3
0
1
1
1
2
1
1
1
0
0
2
1
0
0
1
0
0
1
0
0
2
1
1
1
0
2
0
2
0
1
1
1
0
2
2
1
0
0
1
1
0
0
3
1
2
1
1
1
1
2
0
1
0
2
0
0
0
1
1
1
0
1
1
1
2
2
1
1
0
2
0
2
1
0
0
0
1
2
1
1
0
1
1
2
1
1
0
0
0
1
0
1
1
2
0
0
5
1
0
1
0
2
1
1
0
0
2
0
0
0
0
2
2
0
1
2
0
0
0
1
1
1
2
0
1
0
1
2
2
1
0
1
1
2
2
1
2
0
0
1
0
2
2
2
1
0
0
2
0
1
0
1
0
1
0
2
1
1
0
1
1
0
2
1
1
1
2
0
1
2
0
0
1
0
2
2
0
2
2
1
0
0
0
0
2
0
0
2
1
2
0
0
1
1
1
2
1
1
0
0
1
0
0
1
1
1
0
1
1
2
2
2
0
1
1
0
0
0
0
1
2
0
0
2
0
1
1
1
0
1
1
2
0
3
0
1
1
0
1
1
1
1
1
0
0
0
0
0
2
1
1
2
1
0
1
0
2
1
0
2
2
3
2
0
1
2
1
0
1
1
1
0
0
0
0
1
0
1
1
0
2
1
3
1
2
0
0
0
1
0
1
2
1
0
0
0
0
0
2
0
0
0
2
1
2
1
1
2
0
1
0
0
0
0
0
0
0
2
2
2
2
1
0
2
0
0
1
0
1
2
1
0
0
1
0
0
0
1
1
2
0
1
0
1
1
1
1
0
1
1
0
0
2
3
2
1
1
1
2
0
1
1
2
2
0
0
1
1
0
1
0
0
2
1
1
2
0
0
0
0
0
1
0
1
1
0
1
1
0
1
2
1
1
0
2
0
1
0
0
0
1
1
0
0
0
0
2
1
1
1
0
0
1
0
1
2
0
2
1
1
1
2
6
0
2
1
0
1
0
0
1
1
0
0
1
0
0
0
2
2
1
1
2
0
0
2
2
0
0
2
1
1
2
0
1
1
0
0
0
1
0
2
1
2
0
1
0
0
0
1
1
0
2
0
2
1
1
0
2
0
3
0
0
0
1
1
0
2
1
1
1
1
1
0
0
1
2
0
1
0
0
0
0
2
2
0
0
1
1
0
2
1
0
0
1
1
2
0
0
1
1
1
1
2
0
1
1
2
0
2
1
0
0
0
0
0
1
1
2
1
0
1
1
3
2
0
1
0
2
2
2
2
0
1
0
1
0
3
0
2
1
0
0
1
1
0
0
0
1
0
0
2
1
1
0
2
2
1
2
1
0
0
1
1
3
1
2
3
1
0
1
2
1
2
1
1
1
0
2
2
2
2
1
1
0
2
0
1
0
0
1
1
0
0
2
2
1
0
2
1
0
0
0
2
0
2
2
1
1
2
1
2
1
1
1
1
2
1
2
1
0
1
1
1
1
0
2
0
2
1
1
2
2
1
2
0
2
1
0
0
1
0
2
1
0
1
0
0
2
2
1
2
1
0
1
2
0
0
0
0
0
1
1
0
2
2
1
0
2
1
0
1
0
0
0
2
2
2
2
0
1
0
0
1
1
0
1
0
1
1
1
1
2
1
1
0
2
0
0
0
0
2
0
2
0
0
0
1
0
0
1
1
1
1
1
1
0
1
2
1
0
1
2
1
0
1
1
1
1
1
2
0
1
2
0
1
0
0
0
1
0
2
1
0
0
1
0
2
1
0
0
2
2
0
1
1
0
1
0
0
0
0
2
0
0
3
0
0
0
0
2
0
1
1
2
2
0
1
0
0
0
0
0
1
1
0
0
1
0
1
1
2
1
0
1
0
1
0
1
0
1
0
0
0
1
1
2
1
1
0
0
0
0
1
0
1
1
0
2
1
0
2
0
2
0
1
1
1
2
0
0
1
2
0
1
0
0
0
0
0
0
0
0
2
2
1
2
2
2
1
1
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
2
1
1
1
1
2
0
1
0
1
1
0
2
0
1
2
2
2
0
0
2
0
1
0
0
1
1
0
1
2
0
1
1
1
0
0
1
0
1
1
0
2
0
0
0
0
0
1
1
0
1
1
1
0
1
0
0
0
1
1
1
0
1
1
0
0
1
0
0
2
2
1
0
0
2
0
1
1
2
0
2
0
0
1
1
1
1
1
2
1
1
1
0
1
1
2
1
1
0
0
0
1
2
0
2
2
1
1
0
2
1
0
1
3
0
1
1
1
1
1
0
2
1
0
2
0
1
2
0
1
2
1
0
0
1
0
0
1
2
1
0
0
1
0
1
0
2
0
0
2
1
0
0
2
2
1
2
1
2
1
1
1
1
0
1
0
1
1
0
1
0
0
1
1
3
1
2
0
1
2
1
2
0
1
0
1
0
0
0
1
0
0
0
2
0
1
0
1
1
1
1
2
0
2
1
0
0
0
2
1
0
1
1
0
2
0
0
1
2
1
0
0
1
1
2
1
2
1
0
1
0
2
1
0
2
1
0
2
0
1
1
1
0
0
1
1
0
0
2
0
1
0
0
1
2
1
1
1
0
1
2
1
1
0
1
0
0
1
1
2
1
2
2
0
0
2
0
1
1
1
1
1
0
0
0
2
0
2
2
1
1
0
1
1
0
0
2
2
1
0
0
1
0
2
0
0
0
0
0
0
1
0
2
2
0
1
0
1
1
3
0
0
0
1
1
1
2
2
0
1
1
0
0
1
1
2
0
2
0
0
0
1
2
2
1
1
0
0
0
1
0
1
1
1
1
1
0
0
1
0
1
3
0
2
2
0
0
0
0
1
0
1
0
1
2
0
1
1
1
0
1
1
1
1
1
0
1
2
2
1
0
1
1
0
0
3
0
1
2
0
0
0
1
0
0
0
0
0
1
1
1
1
1
2
1
1
1
1
1
2
2
1
1
0
1
1
0
0
1
0
2
1
1
0
3
0
1
1
0
2
0
1
2
2
1
2
0
1
0
2
1
0
0
0
1
1
5
0
1
0
1
0
2
0
1
1
1
2
2
2
0
0
1
1
2
0
2
1
2
1
0
1
0
1
1
1
0
2
1
2
0
0
1
2
3
2
3
0
2
2
0
0
0
2
1
2
2
0
1
2
1
1
1
0
0
0
2
1
1
0
1
0
1
1
2
0
0
2
0
0
0
0
0
2
0
1
1
1
0
1
2
1
1
1
0
0
2
1
0
0
2
2
0
0
2
1
0
1
2
2
1
0
2
1
1
1
0
0
2
0
0
0
1
1
0
1
0
1
0
1
0
0
0
0
0
2
0
2
2
1
0
1
1
0
1
0
1
1
1
0
1
0
0
1
1
2
0
0
0
0
0
0
2
1
1
0
1
0
0
1
0
2
1
0
0
0
2
1
0
0
0
1
0
1
0
0
2
0
1
1
0
1
0
0
2
0
0
0
0
0
0
0
3
1
0
0
0
1
1
2
1
0
1
1
0
1
0
1
2
2
2
0
0
1
0
0
1
0
0
1
1
1
2
0
4
0
2
1
1
2
0
1
1
1
2
1
1
2
1
1
2
1
0
0
1
1
0
1
0
2
1
0
0
0
0
2
1
0
0
1
0
1
0
1
0
1
2
2
2
0
0
1
1
0
2
0
0
0
2
0
1
1
2
2
0
1
0
2
0
1
0
0
2
0
1
0
2
0
1
2
0
1
2
1
2
2
0
2
1
1
2
1
2
2
1
0
2
1
2
1
2
2
0
0
1
0
1
0
0
1
2
1
2
2
3
0
1
1
2
0
2
2
2
0
0
0
2
2
1
2
0
1
0
2
1
1
0
0
2
1
1
0
0
1
1
2
0
1
0
1
2
1
4
1
1
0
0
1
2
0
1
0
0
1
0
2
0
1
1
1
0
0
0
1
0
1
0
3
0
2
2
0
0
0
0
0
2
2
0
1
0
0
1
2
0
1
0
0
1
1
1
1
2
1
0
0
0
1
2
0
2
1
1
1
0
0
1
1
1
1
0
0
1
0
2
1
6
0
0
3
0
1
0
1
1
0
0
0
2
1
1
2
2
0
0
2
2
0
0
1
0
2
1
0
2
2
1
1
1
1
0
0
1
2
1
1
1
2
0
1
0
2
1
0
0
2
1
0
0
0
1
1
1
2
1
1
1
0
0
0
0
0
0
2
1
0
3
1
0
2
1
1
0
2
2
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
2
2
1
1
0
1
2
0
0
0
0
0
0
0
0
2
1
2
2
0
1
1
0
1
0
1
1
0
0
2
1
3
0
1
3
1
1
1
1
0
0
3
1
0
2
1
0
2
1
1
1
0
2
1
1
1
0
0
0
0
2
0
2
2
1
0
0
2
2
1
2
0
2
0
1
0
1
2
1
1
1
3
1
1
0
1
0
1
1
1
1
1
1
1
0
0
1
1
1
0
0
1
1
4
1
1
2
2
0
0
0
0
1
3
0
0
2
3
2
0
1
0
0
1
1
0
0
0
0
2
0
1
1
0
1
0
1
2
0
1
2
0
1
1
2
1
0
0
0
0
0
1
0
0
1
1
2
2
1
1
0
1
1
0
0
2
1
0
1
1
1
1
2
2
0
1
2
2
0
1
1
0
2
0
1
0
0
3
2
2
2
0
2
1
2
0
2
1
1
0
0
2
1
1
2
0
1
0
0
2
1
2
1
1
0
0
0
1
0
0
1
1
1
1
2
1
0
0
2
0
1
2
1
1
2
0
0
0
1
0
1
1
0
0
1
1
0
2
0
0
0
1
2
1
2
1
0
1
2
1
1
1
2
1
2
1
1
2
1
0
0
0
2
1
2
1
0
3
0
0
0
0
3
0
1
1
0
1
0
0
0
2
0
1
1
0
0
2
1
1
0
1
1
2
1
2
1
1
1
1
2
1
2
1
2
0
0
0
2
1
1
1
1
3
0
2
0
0
1
1
1
2
0
0
0
0
1
2
1
0
2
0
0
1
0
2
0
2
2
0
3
1
2
0
0
1
2
0
1
0
1
1
0
0
0
2
0
1
2
1
0
0
0
0
2
1
1
1
1
0
1
1
0
0
0
1
1
0
2
2
1
1
1
2
1
0
0
2
1
1
0
1
1
2
0
2
0
2
2
1
1
0
0
1
1
1
2
1
2
1
2
1
1
1
0
1
1
2
0
0
1
0
1
0
0
1
0
2
1
1
0
0
1
2
0
2
1
0
1
0
2
0
1
0
1
0
1
0
2
0
0
0
1
1
1
2
1
1
1
1
1
2
2
0
0
1
2
1
1
0
1
0
3
0
1
1
0
2
0
1
0
1
0
0
0
0
0
1
0
1
1
1
0
1
0
0
1
1
2
1
2
2
1
0
0
0
2
1
1
1
0
0
0
0
1
1
0
0
0
0
2
0
1
0
1
1
1
1
2
2
1
0
0
1
1
2
1
1
0
0
2
1
2
2
0
2
0
0
2
0
1
2
2
0
2
1
0
1
0
1
1
0
0
2
1
1
1
1
2
2
0
1
0
0
0
2
2
1
3
2
0
0
0
2
0
0
0
1
0
1
1
0
0
1
1
2
1
0
0
1
0
0
2
0
1
0
0
0
1
0
0
1
0
2
1
1
1
0
3
0
1
0
0
0
2
1
2
0
0
0
0
0
2
1
0
2
2
0
0
2
3
1
0
1
1
2
3
1
0
0
2
1
1
2
1
1
2
2
0
0
2
2
1
2
2
1
1
0
1
1
1
1
1
0
2
1
0
0
1
0
0
0
0
0
2
1
1
2
2
0
1
0
1
0
1
1
1
1
0
1
0
0
0
1
0
1
1
0
1
0
2
1
0
1
1
1
0
1
1
2
0
1
2
1
2
0
1
1
2
2
2
1
1
0
0
0
0
1
1
1
0
0
1
0
0
2
1
2
1
2
1
2
1
1
2
1
2
1
1
3
1
0
2
0
2
1
0
2
1
0
0
0
0
2
1
0
1
0
1
0
2
0
0
1
1
1
2
2
1
2
1
0
1
2
2
1
0
0
1
0
2
0
1
1
0
1
1
0
0
0
0
0
0
2
2
2
0
2
1
1
0
0
2
0
1
0
1
0
0
1
1
0
1
1
2
0
1
2
1
0
1
0
1
0
0
1
2
1
1
1
0
2
1
1
1
1
2
0
0
2
2
0
2
0
1
2
1
1
1
0
2
1
1
0
0
2
1
1
0
0
2
0
1
2
4
0
1
1
1
0
0
1
1
2
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
2
0
0
2
1
1
2
1
0
1
0
2
0
0
0
0
1
2
0
0
1
1
1
1
0
1
1
3
1
1
1
0
0
1
1
1
1
0
2
0
2
0
1
1
2
0
1
1
0
0
0
0
1
1
1
0
0
0
1
1
1
2
2
0
0
1
1
1
0
1
1
2
1
5
0
0
0
1
2
0
1
0
2
1
0
0
1
0
1
1
0
0
2
0
2
1
0
0
3
2
1
1
1
1
1
1
2
0
2
3
0
1
0
1
2
2
0
7
1
0
1
1
1
0
1
0
2
0
2
2
0
2
1
0
0
0
1
0
0
1
1
0
1
0
2
2
0
1
2
0
0
0
0
1
1
2
0
2
1
0
3
1
0
1
0
1
1
3
0
2
1
2
1
0
0
0
5
0
1
0
2
2
1
1
0
1
2
2
1
2
0
0
2
0
2
1
0
1
0
2
1
0
0
1
0
0
0
0
3
0
1
2
2
0
0
0
0
0
1
1
0
2
0
1
1
1
0
2
0
1
1
1
1
0
2
0
0
2
2
0
0
0
2
1
2
2
1
2
0
0
1
0
1
2
1
1
1
1
2
3
0
1
0
0
0
1
2
0
1
1
1
1
2
0
1
2
0
1
0
2
0
0
2
0
1
1
0
0
2
0
2
1
2
2
1
0
0
0
2
2
0
1
0
0
0
2
1
1
0
2
1
1
1
0
0
1
2
2
1
2
2
2
0
1
2
2
0
0
1
1
2
0
1
0
1
2
0
0
1
0
1
1
0
1
1
4
2
4
1
0
2
0
0
0
1
0
1
2
1
1
0
0
1
1
2
0
3
1
1
0
1
2
0
2
1
1
2
0
1
1
1
1
0
2
0
1
1
1
2
5
2
1
0
2
2
1
0
2
1
0
0
0
0
1
1
0
0
0
3
1
1
1
1
0
1
2
1
1
0
2
0
0
1
0
1
0
1
1
1
1
0
2
0
1
0
5
2
0
0
0
2
1
0
0
0
1
2
1
1
0
0
1
1
1
2
0
0
1
0
1
0
0
0
2
0
0
0
2
1
0
0
1
1
1
1
0
0
2
0
0
1
1
0
1
1
0
1
1
2
2
1
0
0
2
3
1
2
0
0
2
2
1
1
1
0
0
0
1
1
1
2
1
2
0
1
1
0
0
2
0
2
0
1
0
2
1
0
0
1
1
4
0
0
1
1
0
0
3
1
3
0
0
9
0
1
3
2
1
1
1
2
0
0
1
0
2
0
0
1
2
0
1
0
2
2
2
0
0
0
0
0
0
0
1
1
0
0
1
0
0
2
0
0
0
1
1
1
0
1
2
1
2
0
2
2
1
2
0
1
1
2
1
1
0
0
1
1
0
1
0
0
1
0
1
0
0
0
1
1
1
2
0
0
1
0
1
1
1
1
0
0
1
0
1
1
1
1
2
0
1
0
1
0
2
1
2
0
2
0
0
2
0
1
1
1
0
1
0
1
0
2
0
0
0
1
1
0
1
0
1
1
2
0
0
0
0
1
0
0
0
0
1
1
1
1
0
0
1
1
2
1
1
1
0
1
1
2
1
0
1
1
3
2
2
2
2
1
2
2
1
1
0
1
0
1
0
1
0
1
0
1
2
1
1
1
0
1
3
1
0
1
0
1
1
2
1
1
2
0
0
0
0
0
0
0
2
0
1
2
2
0
2
2
0
1
1
1
0
1
1
2
1
0
0
0
0
3
1
1
2
1
2
0
1
0
0
0
1
0
0
0
0
1
4
1
1
1
1
0
2
0
2
1
1
0
2
0
1
2
2
1
1
1
2
1
2
1
2
1
0
0
0
0
0
0
0
1
1
0
0
1
0
1
1
1
2
0
2
1
1
1
2
0
1
0
0
0
1
1
1
0
2
0
2
1
0
0
1
2
1
2
2
0
1
2
0
0
2
1
1
0
0
1
0
0
2
1
1
2
0
1
1
0
0
1
1
0
0
0
0
1
1
1
1
2
2
0
0
0
2
1
0
0
0
1
2
0
0
0
1
1
1
1
1
1
1
2
0
0
1
0
0
2
2
0
1
1
1
1
0
1
0
0
0
1
0
2
0
1
0
1
1
0
2
2
3
1
2
0
0
1
1
1
2
2
2
1
2
1
2
1
1
1
0
0
0
2
2
1
0
0
1
1
0
0
0
1
1
1
1
1
1
0
0
1
0
0
0
1
2
1
0
1
1
2
0
2
2
0
1
1
1
0
0
2
0
0
1
1
1
0
0
1
1
1
2
2
2
1
2
2
0
2
2
1
0
1
0
2
1
1
1
1
0
1
2
1
0
1
1
1
0
1
1
0
0
1
0
0
2
0
1
1
0
1
1
1
1
1
1
0
0
1
1
1
1
1
1
1
0
0
2
2
0
1
1
0
1
0
2
1
0
1
0
2
1
1
1
1
1
0
2
1
2
1
0
1
1
2
0
0
1
1
1
0
0
0
2
0
1
1
2
0
2
0
0
2
1
1
2
4
0
2
1
1
0
1
1
2
2
2
2
0
0
0
1
0
0
0
0
0
2
1
2
0
2
0
0
1
1
1
1
1
2
2
1
1
0
0
1
0
0
1
1
1
2
1
0
2
1
0
2
1
2
1
1
0
0
2
1
2
2
1
1
0
0
0
3
1
0
1
2
0
1
0
0
0
0
1
0
2
0
1
0
0
1
2
2
0
0
0
0
0
2
0
0
0
1
1
1
0
0
2
1
2
2
1
1
2
1
2
1
2
2
0
1
1
1
1
0
1
0
2
3
0
2
2
2
0
2
0
2
1
2
1
1
1
1
0
0
0
1
3
2
1
1
0
1
2
0
1
1
1
1
1
2
1
2
0
1
1
0
1
0
2
1
0
2
2
0
2
1
2
1
1
1
3
3
1
2
0
1
1
1
0
0
1
4
0
0
2
1
1
2
1
1
1
1
0
0
2
2
0
1
0
0
2
1
0
2
2
2
1
2
1
0
1
1
1
0
0
0
2
1
0
1
2
0
1
1
0
2
0
0
1
0
1
1
0
0
0
1
0
1
0
1
0
0
0
2
2
2
0
0
0
0
1
1
1
4
1
1
1
2
0
0
0
1
0
2
0
1
0
1
2
1
0
2
1
0
2
1
0
0
1
2
0
0
0
2
2
2
2
0
0
1
2
0
1
0
0
1
1
1
0
0
1
0
1
2
0
1
0
1
0
1
1
2
0
0
0
0
1
2
1
0
0
0
0
2
1
2
0
0
1
1
1
2
0
0
1
1
2
1
1
4
1
1
1
1
1
1
1
1
1
0
0
2
2
0
0
0
1
0
0
0
0
2
2
0
1
0
1
3
0
2
2
1
1
2
1
1
1
1
0
0
0
2
0
1
2
0
2
1
2
2
0
0
2
2
0
0
0
0
1
0
2
1
0
0
0
0
0
0
1
0
1
1
1
0
0
2
2
1
2
1
1
0
1
1
1
2
1
0
2
0
0
2
0
0
2
1
1
0
1
0
1
2
2
0
0
0
1
1
0
1
1
1
0
1
1
0
1
0
1
2
2
0
3
1
0
0
0
2
1
2
0
0
1
1
1
1
0
2
0
2
1
2
1
0
1
0
2
0
2
1
1
2
2
1
0
1
0
0
0
0
3
0
0
2
1
1
1
0
1
1
0
0
0
2
2
2
0
0
0
2
2
1
2
1
1
2
1
1
1
1
1
0
0
0
1
2
0
1
1
1
2
1
1
1
2
1
0
0
1
2
0
1
2
0
0
0
2
1
1
1
1
2
1
1
0
1
1
1
0
0
1
1
0
2
0
0
1
2
1
1
0
1
1
1
2
1
0
0
0
1
0
1
2
0
2
0
0
2
0
1
2
0
0
1
0
2
0
0
2
0
0
0
1
0
2
2
0
0
1
0
1
0
1
2
1
0
2
0
1
0
0
1
0
0
0
2
0
2
0
1
0
1
2
0
0
1
1
2
1
1
0
1
1
1
3
2
1
2
2
0
0
0
2
1
2
2
1
1
0
0
1
1
1
1
0
1
0
0
0
2
1
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
1
1
2
2
2
0
2
2
2
2
0
0
0
1
2
1
0
2
2
1
0
3
0
0
1
2
1
1
0
2
1
2
2
0
1
1
0
2
1
1
1
1
1
0
3
1
0
2
0
0
0
1
2
0
0
2
2
0
0
1
1
1
1
0
0
3
0
0
0
0
0
0
1
1
2
1
0
0
0
2
0
3
2
0
2
1
1
2
1
0
0
0
1
0
1
2
1
0
0
1
2
0
0
0
1
2
0
2
0
2
0
0
0
0
2
0
0
0
0
1
2
0
0
2
2
0
0
0
0
0
2
0
1
0
1
2
1
2
0
0
2
0
0
1
1
1
1
0
1
0
2
1
1
0
2
2
2
0
2
1
2
0
2
0
2
2
0
1
1
0
0
0
1
1
0
1
1
1
0
0
2
0
0
1
0
1
1
1
1
1
1
1
1
0
1
0
1
1
1
0
0
0
2
0
1
2
0
1
2
0
0
0
2
0
2
0
1
1
0
1
1
1
0
0
0
1
0
0
1
1
2
2
0
1
2
0
0
0
1
1
2
0
0
0
1
1
0
1
1
1
1
0
1
1
1
0
0
0
1
2
2
1
1
1
0
1
1
0
1
0
0
0
0
2
1
0
0
1
2
2
1
0
2
2
0
0
1
1
0
1
0
0
0
1
2
2
1
0
1
1
3
1
2
0
0
1
1
1
0
2
1
1
0
0
1
2
1
1
2
0
0
2
1
1
0
1
2
1
2
2
0
0
1
1
0
1
2
1
1
1
0
2
1
1
2
1
1
2
0
1
0
1
1
0
1
0
0
1
0
0
2
1
0
0
1
1
2
0
0
2
1
1
1
1
2
0
2
0
0
2
0
1
1
0
0
1
0
2
0
1
0
1
1
0
0
3
0
1
0
1
0
0
2
1
0
1
1
1
2
1
1
1
1
1
2
0
1
1
1
2
0
1
0
1
0
0
2
0
2
2
2
1
0
2
2
1
1
2
2
1
1
2
1
0
1
0
1
1
2
1
0
0
0
1
0
2
0
0
1
2
2
1
0
2
0
1
2
0
0
1
1
0
1
0
0
0
0
0
0
2
0
1
0
1
1
1
0
1
1
0
1
1
2
2
4
0
1
2
0
1
0
0
0
0
0
2
1
1
2
1
0
2
1
2
0
1
4
0
0
0
1
1
1
1
1
1
1
0
2
0
0
1
0
1
1
1
1
0
1
1
2
1
0
0
1
2
0
1
2
0
0
2
0
1
0
1
0
0
0
0
1
2
1
2
2
1
0
0
2
1
1
2
1
1
1
2
0
0
2
1
1
0
0
2
1
0
1
2
1
2
0
2
0
1
1
2
1
1
0
1
2
0
0
1
3
0
0
0
1
2
0
0
0
0
2
0
2
0
0
1
1
0
0
2
1
1
1
1
1
1
2
2
0
1
0
0
0
0
1
0
1
1
1
2
0
0
0
0
1
0
0
2
0
0
0
2
1
2
2
0
2
1
0
0
0
0
2
0
0
0
1
0
1
1
0
0
0
0
2
0
0
0
1
1
0
0
0
1
0
0
1
1
2
0
0
2
0
1
2
1
1
1
0
1
0
1
2
0
0
0
1
1
1
1
0
1
1
2
1
0
0
1
0
1
1
2
1
0
1
1
1
2
2
2
0
3
1
0
1
0
0
0
1
1
2
1
2
0
0
1
1
1
0
2
0
3
0
1
1
0
0
1
1
0
0
2
1
2
1
2
0
0
2
0
2
1
1
1
0
0
1
2
2
1
0
0
0
0
1
0
1
2
0
0
2
0
1
1
1
0
0
0
0
0
1
1
0
0
0
0
0
3
0
0
0
2
0
2
1
1
0
1
2
0
0
1
0
2
0
1
1
2
2
1
1
2
0
0
2
2
1
0
1
0
0
0
1
0
2
0
2
1
0
0
1
0
0
1
0
1
0
1
0
1
1
1
0
2
0
0
1
1
1
0
0
0
0
1
1
0
2
0
1
1
1
1
1
0
2
0
2
1
1
1
1
0
0
0
0
2
0
0
2
2
1
2
2
1
1
1
0
0
1
0
0
2
1
1
0
0
1
1
2
0
1
0
1
2
0
1
0
0
0
0
0
1
2
1
1
1
0
1
1
0
0
2
3
2
1
1
2
1
0
2
1
0
1
1
1
1
0
0
3
1
1
2
1
0
1
0
0
0
1
1
2
0
0
0
0
2
0
0
1
2
0
1
0
1
0
0
1
2
1
0
0
2
1
0
0
1
2
2
2
0
1
1
2
1
0
0
1
0
0
1
0
1
0
1
4
0
0
1
0
0
1
1
1
2
1
1
2
0
1
1
0
1
1
0
2
2
0
1
1
0
1
2
1
2
0
1
2
1
2
0
2
2
1
0
0
1
2
0
2
0
8
0
2
1
1
0
2
0
0
2
1
1
0
0
1
1
0
0
1
3
1
0
1
1
2
0
1
1
2
1
1
1
2
2
0
2
0
1
0
0
1
0
2
2
2
1
0
1
2
2
0
2
0
0
0
0
0
1
2
0
0
1
1
2
1
0
0
2
0
0
1
0
0
0
1
0
1
2
1
2
0
0
0
0
2
0
2
1
1
2
1
2
2
1
0
0
0
1
1
1
0
1
0
0
1
0
1
1
0
1
1
1
3
2
0
2
0
1
0
0
0
0
1
0
2
2
1
1
0
0
1
2
2
0
0
0
2
1
1
1
0
1
0
0
2
0
2
0
0
0
0
1
0
0
2
0
2
3
0
0
0
0
2
0
2
1
0
2
1
0
0
2
1
0
1
2
0
1
2
0
0
3
1
2
2
0
0
2
0
1
0
1
2
0
2
0
1
1
1
0
1
0
2
1
1
1
1
1
1
0
0
1
0
0
0
0
2
1
1
1
1
1
1
1
2
1
1
0
3
0
1
0
0
1
1
1
0
0
1
2
0
1
1
1
3
1
1
1
0
1
0
1
1
2
1
0
1
2
0
0
1
1
0
1
2
0
1
1
1
2
1
0
1
1
2
1
1
0
1
1
0
1
1
1
0
0
0
0
2
1
0
2
0
1
2
0
1
1
2
1
2
1
1
0
1
1
2
0
1
1
0
2
0
1
1
1
0
1
1
1
2
0
0
0
1
0
2
1
0
1
0
2
1
1
0
0
0
2
2
0
0
2
0
1
1
0
1
0
0
0
0
1
2
1
0
0
0
0
1
0
1
1
0
2
0
1
0
0
2
0
1
2
1
2
0
0
0
1
2
0
0
0
1
0
0
0
0
1
1
1
2
1
1
0
1
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
1
2
1
0
0
0
2
1
0
0
1
1
1
3
0
0
1
2
2
1
0
0
1
2
2
0
2
1
0
1
0
1
2
0
2
0
1
1
1
1
1
1
2
1
0
0
0
1
1
1
0
2
1
0
0
1
1
1
1
0
0
1
0
0
2
0
0
1
0
0
0
0
0
1
1
1
0
1
2
1
0
1
2
0
1
2
0
1
1
0
2
2
0
1
1
1
0
1
2
0
1
1
0
1
1
1
0
0
2
1
0
1
2
1
0
1
1
0
1
1
0
2
2
0
1
1
2
2
3
2
1
1
1
0
0
0
1
0
2
1
1
1
1
0
1
2
0
1
1
0
1
2
1
0
2
2
0
1
0
0
1
1
0
0
2
1
5
0
1
2
1
1
3
0
0
1
1
0
0
0
1
1
2
2
1
1
1
0
1
0
0
1
0
0
0
0
2
0
1
1
0
1
1
1
0
2
0
0
2
0
0
2
1
0
1
1
1
1
2
1
1
0
0
1
1
1
0
2
0
2
1
1
1
1
1
0
1
1
1
0
1
3
0
1
0
2
1
0
1
1
1
2
1
2
0
0
2
2
1
1
1
1
0
0
0
2
1
2
2
2
2
1
1
0
1
0
1
1
1
0
1
2
2
2
0
1
1
2
1
2
0
1
1
0
2
1
0
2
1
0
1
0
0
0
1
1
1
3
0
1
1
0
0
0
0
2
1
0
2
1
0
0
0
1
1
2
0
0
1
1
1
0
0
1
0
2
2
1
1
0
0
2
1
0
0
1
1
0
2
1
2
1
1
1
0
0
0
0
0
0
1
0
1
2
1
1
0
0
0
1
0
1
2
0
1
0
0
1
0
2
0
1
0
1
0
2
0
1
2
0
1
2
2
1
0
1
0
2
0
0
0
1
0
0
0
0
0
0
1
2
1
2
1
1
0
0
0
1
1
0
0
0
2
0
1
1
0
0
3
0
1
0
1
0
0
0
2
0
0
0
1
1
1
1
2
1
3
1
0
0
0
1
1
0
0
2
0
2
0
2
1
2
2
0
0
1
1
0
2
1
2
1
1
0
1
0
0
0
1
0
0
2
1
0
0
0
1
0
0
0
1
1
0
1
0
0
0
1
0
0
3
2
1
1
1
0
0
1
0
0
1
0
1
1
2
2
1
1
1
1
1
1
2
1
2
2
0
0
1
0
0
1
1
2
1
2
1
1
1
1
0
1
0
2
2
0
5
1
2
0
1
1
2
1
1
0
0
3
0
2
2
0
1
1
1
0
2
1
1
0
0
2
1
1
0
1
0
1
0
0
1
0
0
1
1
1
1
2
0
0
1
0
0
1
0
1
1
1
2
0
1
0
2
2
0
1
0
1
0
0
1
0
2
0
0
2
2
0
0
1
0
1
0
1
0
1
0
0
1
0
0
1
1
0
1
2
1
0
1
1
0
0
0
0
1
0
1
0
0
2
1
0
0
0
1
1
0
0
1
2
0
1
2
2
0
2
2
2
0
0
1
1
1
0
2
2
1
1
0
1
1
1
0
1
1
0
1
1
1
0
0
0
1
0
1
1
0
0
1
0
1
0
0
3
0
0
1
2
1
1
0
0
2
1
1
0
0
1
2
0
1
1
0
0
1
0
0
0
1
2
1
0
2
3
0
1
2
0
0
1
1
2
0
0
0
2
0
1
0
0
0
1
2
1
0
0
1
1
2
2
1
1
2
1
1
0
1
1
0
0
0
1
0
1
1
1
2
1
1
0
1
2
1
1
1
1
0
0
1
0
0
0
0
1
0
2
0
2
2
1
1
1
2
0
1
0
1
0
1
1
2
1
1
1
2
2
1
1
0
0
0
1
3
1
2
2
0
1
0
2
0
0
0
0
1
1
1
0
2
1
0
2
0
0
0
1
1
0
0
0
1
1
1
1
0
0
1
1
1
0
2
1
4
1
0
0
1
0
0
0
2
0
1
0
0
1
1
1
1
2
0
0
1
1
0
0
1
0
1
1
0
0
0
0
2
1
1
2
0
1
1
0
2
0
1
1
1
0
0
0
0
0
1
0
1
1
0
0
0
0
2
1
0
0
1
0
0
2
1
0
0
1
1
1
0
1
0
2
0
0
1
1
0
0
0
1
0
1
1
1
1
1
1
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
2
1
0
1
2
3
1
0
1
1
0
0
0
1
1
1
0
0
1
2
1
1
0
0
0
2
3
1
1
1
0
2
0
0
1
0
2
0
0
2
2
0
1
0
2
1
0
2
1
0
1
0
0
1
0
1
0
1
0
0
0
1
1
1
0
2
0
1
0
0
0
1
1
1
1
1
1
0
2
0
0
2
0
1
1
0
0
1
2
2
0
2
0
1
2
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
1
1
0
1
2
1
2
1
2
0
2
0
1
0
2
0
1
0
0
0
2
0
1
1
0
0
1
0
1
0
3
2
1
0
0
1
0
0
2
1
0
0
0
1
2
0
0
1
2
1
2
0
1
0
1
1
0
2
0
4
2
0
1
1
0
1
0
2
0
1
2
1
1
0
1
1
0
2
0
0
0
2
0
1
1
0
0
2
1
1
1
0
0
0
1
0
1
1
1
1
1
0
0
2
0
1
0
1
0
1
0
0
0
0
1
1
0
0
2
1
0
0
2
2
1
0
1
1
1
2
0
0
1
2
1
1
0
1
2
1
1
0
1
1
0
2
0
0
1
1
1
2
0
1
2
1
1
0
2
0
2
0
0
2
1
1
1
0
0
2
1
0
1
0
1
0
1
2
0
0
1
3
0
0
0
1
2
2
1
2
1
0
2
1
0
1
1
1
1
1
0
1
2
1
2
0
1
2
1
1
0
0
0
2
0
0
0
0
1
2
2
0
0
0
1
0
2
0
1
0
1
1
0
2
2
0
2
0
2
2
1
0
1
1
0
1
0
0
0
2
0
1
1
2
1
0
0
2
1
2
0
0
1
0
1
1
0
1
2
2
1
0
2
1
2
1
1
1
1
1
1
1
0
1
2
1
2
0
0
2
1
0
1
1
1
0
0
2
2
1
1
2
1
0
0
1
0
1
1
1
2
1
1
1
0
1
0
1
2
2
1
2
0
1
1
0
0
1
1
1
0
0
1
0
0
1
3
0
1
2
1
0
1
1
3
1
2
0
0
0
2
1
1
0
0
1
2
1
2
0
1
1
0
0
1
2
0
1
0
1
0
0
0
1
0
1
0
0
0
0
2
0
2
0
1
2
1
0
1
3
2
2
0
0
0
0
2
0
0
2
2
1
0
2
1
2
1
0
1
0
0
0
2
1
1
0
1
1
0
0
0
1
0
1
2
2
2
0
0
0
1
0
1
2
2
0
0
2
2
0
1
2
1
1
1
0
1
0
1
0
0
2
1
0
2
2
0
1
0
0
1
2
1
0
1
1
0
0
0
0
2
2
1
0
0
0
0
1
1
0
1
1
1
2
2
1
1
1
1
1
1
2
0
0
0
2
1
0
0
1
0
1
0
4
0
1
0
2
1
0
0
2
1
2
0
0
1
1
2
1
2
0
2
0
3
1
1
0
1
0
1
2
2
1
0
1
2
0
0
1
0
2
1
1
2
1
1
1
1
2
1
3
0
2
1
0
1
0
1
2
0
0
0
2
1
0
1
0
2
1
0
2
0
1
1
2
2
0
0
2
1
0
1
0
2
0
1
1
1
1
2
1
0
1
0
1
2
0
1
1
2
2
0
2
2
0
1
1
0
1
2
0
0
0
2
2
0
0
1
1
0
0
1
0
0
0
2
0
1
1
0
2
0
1
1
0
1
0
2
1
0
2
1
1
1
0
1
1
0
1
2
1
0
1
1
0
1
1
0
2
2
0
0
0
1
0
0
0
0
1
2
2
1
0
0
2
1
1
0
1
2
0
1
2
1
0
0
2
1
0
0
1
0
1
1
0
1
1
1
0
0
0
0
1
2
1
1
1
1
1
2
1
0
1
1
1
0
1
2
1
0
0
0
1
1
0
0
2
0
0
2
1
0
1
2
2
0
2
1
2
0
1
0
0
1
1
1
0
1
2
0
1
1
0
1
1
0
0
1
1
1
0
0
2
0
0
0
1
1
1
2
1
0
1
1
2
0
0
0
0
1
1
3
1
2
0
0
1
1
1
0
1
0
1
0
1
0
0
1
2
0
1
0
0
1
0
0
1
1
1
0
1
2
0
2
2
0
0
1
1
2
0
1
1
0
0
0
1
1
1
2
1
0
1
2
0
1
0
1
2
0
1
0
1
1
0
1
1
1
2
1
0
0
0
0
1
0
0
0
1
1
0
2
1
4
2
0
0
2
1
0
0
1
1
1
2
0
1
0
0
1
0
0
1
2
1
2
1
1
2
2
1
1
1
0
2
2
0
1
1
0
3
2
1
1
1
0
2
1
2
1
0
0
0
1
0
0
1
1
0
2
0
0
0
0
0
2
2
0
1
1
0
0
0
1
0
0
0
2
1
0
0
2
1
0
1
2
1
1
1
0
1
1
0
1
3
2
0
2
2
0
0
2
1
0
1
1
1
2
1
2
0
3
1
1
1
1
1
2
1
1
0
1
1
1
1
1
0
0
2
2
2
2
1
1
1
0
0
0
1
0
0
0
0
2
1
2
2
2
0
1
1
2
0
1
2
1
0
2
1
0
2
0
1
0
0
1
1
1
0
0
0
5
2
0
1
1
1
0
0
0
0
0
0
0
1
1
2
0
1
0
1
1
1
1
1
2
0
1
2
0
0
1
0
1
2
1
1
1
0
1
1
1
1
0
0
1
0
0
1
0
2
0
2
0
0
0
2
0
3
1
1
1
0
2
1
0
1
0
1
1
0
1
1
1
0
0
2
1
0
1
1
1
0
1
0
0
0
1
1
0
0
0
0
2
2
0
0
0
1
1
0
1
1
1
6
1
1
1
2
0
0
0
1
0
0
1
2
1
2
0
2
2
0
2
0
1
1
0
1
0
0
0
1
0
0
2
1
2
2
0
1
2
0
2
0
2
2
0
0
1
1
0
1
1
0
0
1
1
1
2
2
0
0
1
0
0
2
1
1
0
0
1
1
0
0
1
2
2
1
0
0
0
1
1
0
1
0
3
1
0
1
1
0
1
2
1
2
0
2
2
1
1
2
1
1
1
0
0
0
1
1
0
2
1
1
1
0
1
0
0
0
0
1
2
1
0
0
0
1
2
3
2
2
1
2
0
1
1
1
0
1
1
0
0
2
2
2
0
1
1
0
1
1
1
0
1
2
2
1
1
0
0
2
0
2
0
1
1
0
1
2
1
1
1
0
1
1
0
0
1
0
2
1
0
0
1
0
1
0
0
1
0
2
0
2
0
0
1
2
1
1
1
1
1
0
0
0
6
0
2
0
0
2
3
0
1
0
0
2
0
0
0
2
1
1
2
3
1
0
0
2
0
0
0
0
1
1
1
1
1
2
1
1
1
0
0
4
1
2
1
0
1
0
2
0
0
2
0
1
1
0
0
0
0
2
1
1
3
1
1
1
0
0
0
2
2
0
1
2
0
1
1
0
0
0
0
0
2
0
0
0
0
2
1
1
1
0
0
0
1
2
0
1
2
0
2
0
1
2
1
0
0
0
0
1
2
0
0
0
0
2
0
0
0
1
2
0
2
1
0
1
1
2
0
0
0
0
1
0
2
1
0
0
2
0
2
0
1
0
1
1
0
0
1
1
1
0
2
1
1
2
0
1
2
4
0
2
2
0
0
0
1
0
1
1
3
0
0
1
1
0
1
2
0
2
1
1
0
1
1
0
0
1
2
1
1
1
0
1
0
1
2
2
0
2
2
0
1
2
0
1
2
0
1
1
0
0
1
0
1
1
1
1
0
0
1
2
0
0
0
0
0
1
2
1
1
0
1
0
0
0
2
0
0
0
1
2
0
0
2
2
1
0
1
1
1
0
2
0
0
1
1
0
0
1
1
1
1
1
0
0
2
1
2
1
1
0
2
0
0
1
2
0
2
1
1
0
2
1
1
1
0
1
2
1
1
1
2
2
1
0
0
2
1
1
0
1
2
0
1
0
0
0
1
0
1
2
1
0
1
1
0
1
2
1
0
2
0
2
1
1
0
1
1
1
2
0
0
1
0
0
2
0
0
1
2
0
0
2
1
1
1
2
1
0
1
0
1
1
1
1
0
0
0
1
1
0
0
1
0
1
4
1
3
1
2
2
0
0
0
1
1
2
1
2
2
0
2
1
0
1
0
0
1
1
1
1
0
0
0
1
2
1
1
3
1
1
2
1
0
1
0
0
1
1
0
0
2
2
1
0
1
0
0
0
0
0
2
1
1
1
2
2
1
1
0
1
2
2
0
1
2
0
0
1
3
0
0
1
1
1
1
1
0
1
0
1
1
1
0
2
1
1
1
1
2
1
1
1
2
0
0
0
1
1
1
4
0
2
0
2
1
0
0
1
1
1
0
0
1
1
1
2
1
2
1
2
3
0
1
0
2
0
0
1
0
0
0
1
1
0
4
0
0
2
0
0
0
2
0
0
2
3
1
1
1
1
2
0
1
1
0
1
0
1
1
2
0
0
1
0
1
0
2
0
1
0
3
0
2
0
0
0
0
1
2
2
0
0
0
1
2
0
0
0
2
1
1
1
1
1
3
2
2
0
2
0
1
1
1
2
2
0
0
0
0
1
1
0
1
2
2
0
1
2
0
0
0
2
0
0
2
1
0
2
3
1
0
1
2
1
0
1
0
2
2
0
0
0
1
0
0
1
0
0
0
1
2
1
2
1
3
2
0
0
2
3
2
2
1
0
0
0
2
1
1
2
0
2
1
1
2
0
2
0
0
1
0
1
0
1
1
2
1
2
0
0
0
2
2
1
1
1
0
0
0
0
1
1
2
1
1
0
0
2
1
1
0
2
0
0
2
1
1
2
2
1
1
0
1
2
2
2
1
0
0
0
0
0
0
0
0
0
0
0
2
2
1
2
0
1
1
0
1
0
0
2
1
1
2
0
1
2
0
2
0
2
0
1
1
3
1
1
1
0
1
0
1
0
0
0
1
0
1
1
1
1
1
2
2
2
0
0
0
1
2
0
2
0
2
0
1
2
1
0
0
0
2
0
0
1
2
0
1
0
1
1
1
0
1
1
1
1
1
1
0
0
1
1
0
0
1
2
0
0
1
2
1
1
2
0
1
1
0
3
1
0
0
0
1
0
0
2
0
0
0
2
1
0
1
0
2
1
0
0
1
1
1
1
1
1
1
1
0
1
2
2
1
2
0
2
0
0
0
1
0
3
0
1
1
0
2
0
1
0
0
2
1
0
0
1
2
1
0
0
0
1
2
1
0
1
2
1
1
2
0
2
2
2
1
2
0
3
0
0
0
2
0
2
1
0
1
0
1
0
0
2
1
1
1
0
0
1
1
3
1
2
0
0
1
1
0
0
0
1
2
1
0
0
1
0
0
0
2
2
1
1
1
1
2
2
2
0
1
2
1
0
2
1
1
1
1
2
1
0
1
1
0
0
1
0
0
1
2
2
2
2
2
0
2
0
2
0
1
1
0
1
2
2
0
0
2
1
1
1
0
2
0
0
1
0
0
0
2
1
2
0
1
0
1
1
0
1
0
1
0
0
1
1
2
1
0
0
1
0
2
1
1
2
1
0
2
2
1
1
1
1
2
0
0
2
1
2
1
2
2
2
2
0
0
0
0
1
0
1
0
0
0
1
0
0
2
0
1
1
1
1
1
2
2
1
2
2
1
1
1
1
2
1
2
1
2
0
0
0
1
0
2
2
1
1
1
1
0
1
1
0
2
1
0
0
2
0
0
0
1
1
0
0
2
0
0
1
1
2
1
1
0
2
2
2
0
0
2
2
0
2
4
0
0
0
0
0
0
2
0
0
0
2
0
2
2
1
0
0
0
0
1
1
0
0
1
1
1
0
0
2
0
1
1
2
1
1
1
0
1
2
1
1
1
0
0
2
2
0
1
0
2
0
0
0
1
1
1
0
1
0
0
2
0
2
0
2
1
1
1
0
0
0
1
1
2
2
0
0
0
1
0
2
1
2
2
0
0
1
1
2
0
0
1
0
0
0
0
1
1
1
0
0
1
1
1
0
0
1
1
0
1
1
0
1
2
2
1
1
1
0
0
1
0
1
2
1
0
1
0
2
0
2
0
2
1
1
0
1
0
0
0
1
1
0
1
2
1
1
0
1
0
1
0
2
0
1
1
1
0
2
2
2
1
0
1
0
0
0
3
2
0
2
0
3
2
0
1
0
1
0
0
2
0
0
1
1
2
0
1
1
0
0
1
0
2
1
0
1
2
0
2
1
0
2
1
1
2
0
1
3
1
3
2
0
0
0
0
0
1
3
2
1
2
0
2
0
1
0
0
1
0
1
0
1
1
2
0
0
1
1
0
0
1
1
0
0
2
2
0
0
0
1
0
0
1
0
1
0
0
1
1
1
2
1
0
2
0
0
0
0
0
1
2
1
0
0
0
0
0
0
1
2
0
1
0
2
2
1
1
0
1
0
0
1
1
2
4
0
2
1
1
1
1
0
0
2
1
1
0
0
0
0
0
1
1
0
2
2
0
3
0
1
1
3
2
0
1
0
0
0
1
0
2
0
0
1
1
2
1
1
2
1
2
0
1
1
2
1
1
2
2
0
2
1
1
2
1
1
2
2
1
1
1
2
1
1
1
0
0
0
1
2
0
1
0
4
1
1
0
2
0
0
1
0
2
2
1
2
1
2
1
1
0
0
1
2
2
1
0
2
1
0
0
0
0
2
1
1
0
1
0
0
0
1
1
0
2
0
0
0
1
2
1
1
1
3
0
1
1
2
0
2
0
1
0
0
0
2
0
0
1
1
0
1
1
0
0
2
0
1
1
0
2
1
0
1
0
0
0
1
2
2
2
1
0
1
1
0
2
0
1
0
1
2
2
1
0
1
2
1
2
1
2
1
1
0
1
1
1
2
2
0
0
0
2
1
0
1
1
1
0
0
2
2
1
1
1
1
0
1
1
1
1
2
1
2
1
2
1
2
0
0
0
1
2
0
0
0
1
2
1
2
2
0
0
0
1
2
2
1
2
0
2
2
2
1
1
1
0
2
1
1
1
0
1
0
1
2
0
0
0
2
0
2
2
2
3
2
2
0
0
1
1
1
1
2
2
1
0
0
0
1
0
0
1
1
1
0
1
0
0
2
2
1
0
1
1
2
2
1
0
1
0
1
2
2
0
1
1
0
0
1
0
1
0
1
0
1
1
0
1
0
0
2
0
0
0
2
2
1
2
0
1
0
0
2
2
0
0
0
1
0
0
0
1
1
0
2
0
0
1
0
0
2
1
0
1
1
0
0
0
0
1
1
2
2
1
1
2
1
1
1
1
2
1
1
1
3
0
1
0
2
2
0
0
2
0
0
0
1
0
0
2
0
0
1
1
2
0
0
0
0
0
0
1
2
0
0
0
0
0
1
1
0
0
0
0
0
1
3
0
1
0
1
1
1
1
2
2
0
2
2
0
0
0
1
1
2
0
2
1
0
0
1
2
1
2
1
0
2
1
1
2
2
0
0
1
2
0
1
2
0
0
0
1
0
3
2
1
2
0
1
0
1
1
0
0
2
0
1
1
0
0
0
3
2
1
0
0
7
1
2
1
1
2
0
0
1
1
0
1
1
2
0
0
0
1
1
0
0
0
0
0
0
1
1
1
1
2
2
0
1
1
0
2
0
1
1
0
1
1
1
1
2
1
2
1
1
0
1
1
0
2
0
1
0
1
2
2
0
1
1
0
0
2
1
2
1
2
0
1
1
0
0
0
0
0
0
1
0
1
1
1
1
2
0
1
2
1
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
2
0
1
0
1
1
1
2
1
0
1
2
0
0
2
2
1
1
1
3
0
0
0
1
0
1
1
1
1
0
0
0
0
1
1
2
2
1
0
0
1
1
2
1
2
0
0
1
4
2
0
0
0
1
2
1
0
1
1
0
0
0
2
2
0
1
0
0
0
0
1
1
2
0
1
2
1
1
0
1
1
0
0
0
0
1
1
1
0
1
1
0
0
1
2
0
0
1
0
2
1
2
1
0
0
1
1
0
0
2
1
1
1
0
0
1
0
1
2
1
0
0
2
1
1
2
1
0
0
2
1
0
2
2
0
0
1
0
0
1
0
1
0
0
2
1
0
2
0
1
2
1
1
0
1
1
1
2
2
0
1
0
3
0
0
0
0
1
2
0
0
1
1
0
0
1
1
0
0
1
1
2
1
0
0
1
0
0
1
1
1
2
0
1
2
0
0
1
0
0
1
0
2
0
0
1
2
0
2
2
1
1
1
0
1
0
0
1
0
2
1
2
1
1
0
0
1
0
1
1
0
1
0
1
1
0
0
2
2
0
0
1
1
1
2
2
1
1
1
2
0
2
0
1
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
1
0
1
2
0
2
1
2
0
2
0
1
2
2
0
0
1
1
0
0
0
1
2
3
2
1
1
0
2
0
1
1
2
2
0
1
1
1
0
1
1
1
1
0
2
1
2
1
1
1
2
0
2
1
0
1
0
3
1
0
1
1
2
2
1
2
1
1
0
0
3
1
0
0
2
4
2
1
3
0
2
0
3
1
0
1
1
1
0
1
1
0
0
0
0
0
0
1
0
0
1
1
2
3
0
0
1
0
0
1
3
1
2
0
2
0
0
0
1
2
1
2
1
0
2
1
1
1
1
1
1
0
2
1
1
0
0
0
0
22
1
2
1
1
1
1
1
1
0
0
2
1
1
0
2
0
1
0
2
2
1
2
0
2
1
2
0
1
1
0
2
0
2
0
0
2
1
0
2
0
0
0
0
2
1
1
2
1
0
0
1
0
2
1
1
1
1
2
1
2
0
1
0
0
0
0
2
1
1
1
0
1
0
1
0
4
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
2
1
2
2
0
0
2
0
2
0
1
1
1
0
1
1
1
0
0
1
0
0
0
2
1
1
0
1
0
0
2
2
0
1
0
1
2
2
1
1
1
1
0
1
0
0
0
2
2
0
0
2
1
1
1
1
0
1
1
1
1
2
1
1
0
0
0
1
2
0
2
0
1
1
2
1
1
1
2
0
2
2
0
0
0
1
1
0
2
2
0
2
2
0
0
1
1
1
0
0
1
1
0
1
0
2
0
1
1
0
1
0
0
0
0
2
1
2
0
0
0
0
1
2
1
0
1
0
2
0
1
1
0
1
0
0
2
4
3
3
0
0
0
1
0
0
2
0
0
1
0
0
0
1
1
0
1
0
1
0
0
1
2
1
0
1
0
1
1
0
2
1
1
0
0
1
1
1
1
1
0
1
1
1
1
0
0
1
0
1
1
1
1
0
0
1
0
2
2
1
1
3
1
0
0
0
0
0
1
5
0
1
0
2
1
2
1
1
2
1
0
1
0
1
0
1
0
1
1
0
1
0
0
1
3
0
1
0
0
2
0
1
0
1
1
5
0
1
0
0
0
1
1
2
1
1
0
3
2
2
1
0
1
0
1
1
0
0
1
1
0
1
1
2
0
1
1
0
0
0
1
0
2
0
1
1
0
0
1
1
0
0
0
1
1
1
0
2
2
1
0
0
0
3
1
0
0
0
1
0
2
2
3
2
1
1
1
2
2
0
2
2
1
0
0
1
0
1
2
1
0
1
0
1
2
2
1
1
0
1
0
0
1
1
1
1
1
2
0
2
2
0
0
2
0
1
1
2
0
0
1
1
0
0
2
0
1
2
0
1
0
0
1
0
2
1
0
1
1
0
2
2
1
1
2
3
1
0
0
1
2
0
0
2
2
0
1
1
1
0
1
1
1
1
1
1
0
0
0
1
1
2
0
0
1
1
1
0
0
1
0
1
0
2
0
1
3
2
1
2
1
0
0
2
0
1
0
0
0
1
1
1
0
0
2
0
1
2
0
0
0
2
1
0
0
0
0
0
1
4
0
1
0
1
1
1
0
6
2
1
0
0
2
2
0
0
2
0
2
1
0
0
1
0
0
1
0
2
1
0
0
1
0
0
0
1
0
0
2
1
2
2
2
2
1
1
0
0
0
1
2
0
1
0
0
1
0
0
1
2
1
2
0
0
1
1
1
0
1
1
1
0
0
0
2
1
0
0
0
0
2
0
0
0
1
0
1
1
2
1
1
0
2
3
0
0
1
1
2
0
1
0
4
3
0
0
0
0
1
2
2
1
1
0
1
1
1
2
1
1
1
1
0
0
1
2
0
0
0
0
1
1
0
2
0
0
0
1
1
0
1
0
2
2
0
2
0
2
2
1
0
0
1
1
0
0
2
0
0
0
2
1
1
0
2
2
2
0
2
1
0
1
1
0
1
1
1
1
0
0
1
2
0
0
1
1
0
1
0
0
1
0
0
1
1
1
0
1
1
0
1
0
0
1
0
1
0
2
1
0
1
0
2
0
2
0
0
1
1
1
0
0
0
1
1
1
1
0
1
2
1
0
0
3
0
0
1
1
0
1
0
2
1
0
0
0
0
1
0
1
0
0
1
1
1
1
2
2
2
1
0
0
0
0
0
2
0
2
0
0
1
0
2
0
2
1
2
2
1
1
1
1
1
0
2
0
0
1
0
0
0
0
0
1
0
0
0
2
0
2
0
1
1
0
0
1
1
1
1
1
1
0
0
0
1
2
1
0
1
1
1
0
1
0
2
0
1
1
1
2
1
1
1
2
2
1
1
0
2
0
0
1
1
2
0
2
1
1
1
0
1
0
1
2
0
1
0
0
0
1
0
1
2
2
1
0
0
0
2
0
1
0
0
1
1
1
1
1
0
0
1
1
0
2
1
2
0
0
0
0
1
0
1
0
2
1
0
1
0
2
1
0
1
2
0
0
1
0
0
1
0
1
2
2
0
1
2
1
2
0
0
1
0
2
1
0
0
0
2
0
2
0
2
0
2
0
2
0
0
0
2
0
0
1
1
1
0
1
0
0
2
0
1
0
0
1
0
2
0
3
0
0
0
1
2
0
0
3
1
0
1
1
0
0
2
0
0
1
0
0
1
0
1
0
1
1
0
1
0
1
1
0
2
0
1
0
0
2
0
0
1
0
1
1
0
1
0
2
0
1
2
0
2
0
0
1
0
0
1
1
0
1
0
0
1
1
1
2
0
0
2
0
2
2
1
1
0
0
2
0
2
0
1
0
1
1
1
0
0
1
1
0
1
0
0
0
1
2
1
2
2
2
1
0
1
2
2
1
0
0
0
0
1
1
1
0
1
0
0
0
1
1
1
1
1
0
0
1
1
2
2
1
0
2
1
2
2
2
1
1
0
1
2
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
1
1
1
1
1
0
1
1
0
0
2
0
1
2
1
2
1
1
0
0
1
0
2
1
1
1
0
2
0
2
0
0
2
0
2
2
0
1
0
0
2
0
2
2
0
0
1
1
1
0
0
3
0
2
1
1
0
2
0
2
0
1
2
1
1
0
0
1
0
1
1
1
1
0
0
0
2
0
0
1
2
0
2
0
1
1
1
0
2
0
1
3
1
0
1
1
2
0
0
1
2
0
1
1
0
1
0
0
0
1
0
0
0
1
0
1
0
1
1
2
0
0
0
0
0
2
1
2
0
0
1
1
2
1
1
1
1
1
1
1
0
0
0
1
0
0
0
0
1
0
0
2
2
1
1
0
0
0
0
1
1
2
0
0
1
2
0
0
0
0
1
0
1
1
0
1
2
2
2
0
0
1
3
1
0
0
1
2
0
1
0
0
0
2
1
0
1
0
0
0
2
0
0
2
1
1
1
0
0
1
2
1
2
0
0
0
2
0
0
1
1
0
0
1
3
0
2
2
1
2
0
1
0
1
2
2
0
0
2
1
1
1
2
0
2
1
1
2
1
0
1
0
1
1
4
0
0
1
1
0
3
1
0
2
0
2
0
0
1
1
0
1
0
1
2
1
1
0
0
1
1
1
1
1
0
0
2
2
1
2
1
0
0
0
0
1
1
0
1
1
0
0
1
1
0
0
0
0
1
1
1
0
1
2
1
2
0
1
1
1
0
1
0
1
1
1
0
1
1
1
1
5
2
1
1
0
2
1
1
1
1
1
2
1
1
1
2
0
0
1
1
0
1
0
1
2
1
1
0
0
0
0
2
1
0
2
2
1
1
1
1
0
2
1
0
1
0
0
0
0
2
1
2
0
1
4
1
0
0
0
0
1
1
0
1
0
1
0
1
0
2
0
0
0
0
0
1
2
1
1
2
2
1
0
2
1
0
2
1
1
0
1
1
2
2
0
0
0
0
1
1
2
1
0
2
1
0
2
2
0
2
4
0
1
1
2
2
2
1
1
0
1
0
2
0
1
0
1
2
2
0
1
0
2
0
1
0
1
1
2
1
2
0
0
0
1
2
2
1
1
1
1
1
1
2
3
1
1
0
0
1
2
0
0
0
1
1
0
0
1
2
0
1
0
0
1
2
0
0
1
0
1
0
0
0
2
1
0
1
2
1
2
0
0
0
2
0
0
1
1
1
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
1
1
0
2
1
0
2
1
2
0
2
1
0
0
0
1
1
1
1
0
1
1
2
0
2
2
0
0
2
0
1
0
1
2
0
2
1
2
0
1
2
1
0
0
0
2
1
1
0
2
2
1
0
1
2
1
0
2
0
2
0
0
1
1
2
0
0
1
2
2
1
0
1
4
0
0
0
0
2
1
2
0
0
1
2
0
1
2
0
2
1
2
0
1
0
1
0
2
1
1
1
1
0
0
3
0
2
0
0
0
1
4
2
1
0
0
3
2
1
0
1
2
0
4
0
1
1
0
0
1
0
1
0
1
0
0
0
0
1
1
1
0
0
2
0
1
1
1
0
1
1
1
0
2
2
1
0
2
2
1
2
0
1
1
0
2
1
2
3
0
0
0
0
3
1
0
0
0
0
1
0
2
2
1
2
0
0
1
0
2
1
0
1
1
2
0
1
1
0
0
1
0
0
1
1
1
0
0
1
0
0
2
2
0
0
1
0
1
0
0
0
1
0
1
1
1
0
2
1
2
1
0
2
0
0
2
0
1
0
2
0
0
0
0
1
0
2
2
2
1
2
1
0
0
1
0
1
0
0
0
1
0
1
0
2
0
0
0
2
0
2
1
0
1
1
1
1
0
0
1
2
1
0
0
1
1
0
0
1
1
1
2
0
0
2
1
0
1
1
1
1
1
1
2
0
2
0
2
2
0
0
1
0
0
1
0
1
0
0
1
2
2
1
0
0
1
1
1
2
2
0
0
2
1
0
0
0
1
1
1
0
0
3
1
3
1
1
1
1
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
1
2
0
0
0
1
1
0
0
1
2
2
1
1
1
0
1
1
1
0
0
0
0
2
1
0
0
0
1
2
2
0
2
0
0
0
1
2
0
3
1
0
2
0
0
0
0
2
0
0
2
1
0
1
0
0
0
1
1
1
1
0
1
0
1
0
1
0
1
1
0
0
0
0
1
0
1
1
1
1
0
1
1
0
0
0
0
0
2
1
0
2
1
1
0
0
0
1
1
1
0
0
1
0
1
2
1
0
0
1
1
1
2
0
2
0
2
1
0
1
0
0
2
2
2
0
0
2
2
1
1
1
1
1
0
2
0
1
1
0
1
2
0
2
1
1
0
0
1
1
2
1
2
1
1
0
0
1
0
2
2
0
0
0
1
1
0
0
1
1
0
1
0
1
0
0
0
2
1
0
1
1
0
1
1
1
1
0
1
1
0
2
1
0
2
0
1
0
1
1
1
0
0
0
2
1
0
1
2
0
2
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
1
1
1
0
1
0
0
2
2
0
1
1
1
0
1
1
0
0
2
0
0
2
0
0
0
0
0
2
2
1
1
2
1
0
3
0
2
0
1
0
0
1
1
0
0
1
1
2
1
1
0
0
2
0
0
0
1
0
1
0
1
2
1
1
0
1
0
0
0
0
1
1
1
0
2
2
1
1
1
0
0
1
1
1
0
1
0
1
0
1
0
2
2
0
0
0
0
2
1
0
0
2
1
0
1
1
0
1
2
1
2
0
0
1
0
0
0
0
1
2
0
0
2
0
2
1
0
0
2
2
1
1
1
2
3
0
2
1
0
2
2
1
1
0
1
0
0
1
1
0
1
1
0
0
1
1
0
0
1
1
1
0
1
0
0
1
3
1
1
1
0
1
0
0
1
1
0
0
0
1
0
1
1
2
1
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
1
1
2
2
1
1
2
1
1
0
1
0
1
0
2
0
2
1
1
1
0
1
2
2
1
0
1
2
1
2
2
1
0
1
1
1
0
0
1
1
2
2
0
1
0
1
0
1
0
1
0
1
1
0
1
1
0
1
1
0
1
0
1
2
1
1
0
3
1
1
1
0
0
2
1
2
2
1
1
0
1
2
0
0
2
0
1
0
0
1
1
0
0
1
1
0
1
0
0
0
1
1
2
0
0
1
0
1
2
0
0
1
1
1
2
0
2
1
0
2
2
0
2
1
1
0
2
1
0
1
2
2
2
1
0
1
1
0
2
2
1
1
1
1
0
2
1
1
2
1
1
0
0
2
2
1
0
1
2
0
0
1
0
1
2
2
0
1
2
0
0
0
2
0
0
0
0
1
1
2
1
1
1
0
1
3
1
1
1
1
0
1
0
1
0
1
1
2
0
0
0
1
3
1
1
0
1
1
1
0
1
1
0
1
2
1
1
1
1
0
2
1
1
1
0
0
0
2
0
1
0
1
1
1
1
0
0
3
0
1
2
0
0
2
2
2
2
2
2
1
2
0
1
2
0
0
0
0
0
1
0
0
2
2
1
1
0
1
1
2
1
1
2
0
1
1
0
2
1
1
2
0
1
0
1
1
1
1
0
1
1
1
1
0
0
2
2
1
3
1
1
1
0
1
2
1
0
1
1
0
1
1
1
1
0
2
1
0
0
1
1
1
0
0
0
0
1
1
1
0
1
2
1
0
1
1
0
0
1
0
0
2
0
0
1
2
0
2
2
0
0
2
0
2
0
0
2
0
0
1
2
2
0
2
1
0
0
2
0
0
1
2
0
2
0
2
1
0
1
1
2
0
2
0
2
1
2
2
2
2
1
2
1
1
0
1
0
0
1
0
1
1
1
2
0
1
0
0
0
1
0
2
1
2
2
2
1
0
1
0
0
0
0
1
2
1
1
1
0
0
0
2
1
0
0
1
0
0
1
1
1
1
1
0
0
0
2
0
1
0
1
2
0
0
1
2
0
1
0
0
0
2
0
1
0
0
0
3
2
2
1
2
1
1
0
0
2
0
0
1
0
0
2
2
1
1
1
0
1
0
1
1
0
2
0
0
1
2
1
1
0
1
0
1
1
1
0
0
2
2
0
1
0
2
2
1
2
0
1
1
1
0
1
0
0
1
0
0
1
1
1
1
2
2
0
0
0
0
2
1
2
2
0
1
1
2
0
0
1
0
1
1
2
2
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
2
1
0
2
0
1
0
1
0
0
1
1
1
1
0
1
1
1
0
2
1
0
1
0
1
1
0
0
3
0
0
1
0
0
1
0
2
2
0
1
2
1
1
1
2
0
0
0
0
0
1
1
0
0
1
1
1
1
0
0
1
0
0
1
0
0
0
0
2
2
0
0
0
1
0
1
0
1
0
0
1
1
1
2
0
1
0
1
2
0
2
2
1
0
0
2
1
0
0
1
1
0
2
2
0
3
0
0
0
1
1
0
0
0
1
1
2
0
0
0
1
0
1
2
2
0
1
1
2
1
1
1
1
1
1
0
3
1
2
2
2
0
0
0
1
0
0
1
2
1
0
2
0
0
2
1
2
1
2
2
0
0
0
0
1
1
0
2
1
2
0
0
2
2
2
0
0
4
1
2
2
0
0
0
0
1
1
0
2
0
1
1
0
1
0
2
1
0
1
1
0
1
1
2
1
1
1
1
0
0
2
1
0
0
0
0
1
1
1
2
1
0
1
2
1
0
2
0
1
1
1
1
1
2
0
0
0
0
0
1
1
0
0
1
0
2
0
0
0
2
1
1
1
2
1
1
0
0
2
1
1
2
1
0
1
1
1
0
1
0
1
0
1
0
0
1
0
0
1
2
1
2
1
1
1
1
0
2
2
0
1
1
1
0
0
2
1
0
0
2
0
4
0
0
0
0
0
0
0
0
1
0
2
2
1
2
2
1
1
1
1
2
1
0
1
0
2
0
0
0
1
1
2
1
0
1
1
0
0
2
2
0
2
1
2
1
1
1
1
1
2
1
0
0
1
1
0
1
0
1
2
0
1
2
0
2
2
1
2
0
0
0
1
2
2
1
0
2
0
0
2
2
1
2
0
1
2
0
1
0
0
0
1
2
0
0
0
3
1
0
1
0
3
0
1
1
1
0
0
0
0
0
1
2
0
1
0
0
1
1
1
1
1
2
1
0
1
1
0
0
0
2
1
0
1
0
0
0
0
1
0
1
1
0
1
1
0
1
0
0
0
2
2
0
1
2
1
0
1
0
0
0
0
1
0
1
2
2
1
0
0
1
0
1
1
2
2
1
1
2
2
0
1
1
1
1
1
0
1
2
0
0
4
0
1
0
2
1
2
0
1
1
2
0
1
1
0
2
0
0
1
2
1
0
1
1
1
0
1
2
1
1
0
1
0
1
1
2
1
0
2
0
0
2
0
1
2
2
0
2
3
1
0
0
0
1
1
0
1
0
0
2
0
1
0
0
2
0
1
2
1
1
0
2
1
0
1
0
0
2
2
1
1
0
0
0
1
1
0
0
0
0
1
1
0
1
1
0
0
0
1
1
1
0
0
1
2
2
1
2
1
2
0
0
0
2
0
0
1
0
1
0
1
1
0
0
0
0
1
1
2
1
1
1
1
1
0
1
0
0
0
1
0
2
0
0
1
1
1
0
2
1
0
0
0
1
2
0
0
1
1
0
0
0
1
0
0
1
0
1
0
1
0
2
1
2
1
1
0
1
0
4
1
1
1
0
1
1
0
2
0
2
1
0
0
0
0
2
0
2
1
1
1
0
1
0
1
2
2
0
1
1
1
0
0
0
0
1
2
1
1
0
1
1
1
2
1
2
0
2
1
0
0
1
1
2
1
1
1
1
0
2
0
2
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
2
1
0
0
1
1
1
0
0
0
0
2
2
0
0
1
1
1
0
1
1
0
0
0
0
0
0
1
1
1
1
2
0
1
2
0
1
1
0
1
0
1
0
1
0
1
1
1
1
0
1
0
1
0
1
1
1
1
0
2
0
2
1
1
0
1
0
0
1
2
0
2
0
1
0
2
0
0
2
1
0
1
2
0
1
1
0
1
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
2
1
1
2
1
0
2
0
0
1
0
0
5
2
1
0
0
1
2
0
0
0
1
2
0
0
1
2
1
1
0
0
0
0
0
0
1
1
2
0
1
0
0
0
1
1
1
1
1
2
1
1
1
0
2
0
0
1
1
2
0
1
1
1
0
0
0
1
0
0
1
1
2
0
0
2
2
1
0
1
1
2
0
0
1
1
0
0
1
1
1
2
1
2
2
1
1
0
0
2
1
0
1
1
1
2
0
0
1
3
0
0
1
0
0
0
1
1
2
2
1
0
0
1
3
1
0
1
0
1
0
0
0
1
2
0
1
2
0
2
1
1
0
1
1
0
0
0
1
1
0
0
2
0
0
2
0
1
0
2
0
0
0
0
1
0
0
0
1
0
2
2
1
0
1
0
0
2
1
0
1
2
0
1
3
2
1
2
0
0
2
1
0
0
1
0
1
4
1
2
1
1
0
1
2
1
1
0
0
1
2
0
1
0
3
1
1
1
1
1
1
0
0
0
1
0
2
0
0
1
0
2
1
0
1
1
1
0
1
1
1
1
2
0
0
0
3
0
3
1
0
2
0
1
1
0
0
0
1
0
1
0
0
0
2
0
0
1
1
1
0
1
0
0
0
0
2
1
0
1
0
1
2
1
2
3
0
0
1
1
1
0
0
3
0
1
1
1
1
0
2
0
1
2
2
2
0
0
2
1
1
0
0
0
0
2
1
2
1
1
2
0
3
1
2
1
2
2
1
0
2
1
1
0
0
0
0
0
1
0
2
0
0
1
0
1
2
0
0
1
0
2
1
0
2
0
2
1
1
0
1
1
0
1
0
0
1
0
0
2
0
1
1
0
1
0
2
1
0
2
2
2
2
0
0
0
2
0
0
2
2
0
1
1
0
0
0
1
0
0
0
2
0
2
0
1
2
2
0
1
0
0
0
1
0
0
1
1
2
1
2
1
1
1
0
1
1
0
2
1
1
1
0
0
2
1
0
1
1
2
0
1
1
2
0
1
0
0
1
1
2
0
0
1
1
0
1
1
0
1
0
0
1
0
1
1
0
1
2
1
2
2
0
2
0
0
1
2
0
1
0
3
2
1
2
1
2
1
2
0
1
0
0
1
1
1
1
1
1
1
0
2
0
1
0
0
2
1
2
0
0
0
1
0
0
2
1
3
0
2
1
2
0
3
1
2
2
0
0
0
0
0
1
2
1
0
2
1
1
0
0
1
2
1
1
1
1
0
1
1
0
2
0
1
0
0
2
2
2
2
2
1
0
1
2
2
1
1
1
0
2
1
1
0
1
2
1
0
2
2
0
1
0
1
2
0
0
0
1
2
2
0
0
1
0
1
2
2
1
0
4
1
1
1
2
1
0
0
0
1
1
2
1
2
0
1
1
2
0
2
1
1
0
0
2
1
1
1
0
0
2
2
1
1
2
0
1
0
1
2
1
1
0
0
0
0
0
0
3
1
1
1
0
1
1
1
3
1
0
2
1
0
2
1
1
1
0
2
2
1
2
1
2
0
0
0
2
0
2
1
1
0
2
0
2
1
1
1
0
2
1
0
0
1
0
1
0
0
2
2
1
0
1
3
1
0
0
0
1
0
1
1
0
0
1
1
0
0
1
0
1
0
1
1
2
2
0
0
2
0
1
2
1
0
1
1
0
0
2
0
1
0
1
2
1
2
0
0
1
1
0
2
0
1
2
2
1
0
3
1
0
1
1
0
1
0
0
0
0
0
0
1
0
0
1
1
0
2
2
0
1
0
1
1
2
1
1
0
1
1
0
1
2
0
0
0
1
2
0
1
0
2
3
0
4
2
0
1
0
1
1
0
1
0
3
1
1
2
2
2
0
1
1
1
0
0
2
2
0
0
0
1
1
1
1
0
1
0
1
0
1
2
2
0
2
2
3
1
1
1
2
0
0
2
0
0
2
2
1
1
0
1
0
0
0
0
2
3
1
2
2
0
0
1
2
0
1
1
2
0
0
1
2
0
0
0
0
1
2
1
0
0
1
1
0
0
0
2
1
2
0
0
0
0
1
2
0
1
0
2
1
2
0
2
0
1
1
0
1
0
0
2
2
0
1
0
1
0
1
1
2
1
1
0
6
1
0
2
1
0
0
1
1
1
2
0
1
1
2
0
0
1
2
0
1
0
1
1
1
3
2
2
0
0
1
0
1
2
0
1
0
0
0
1
0
1
1
0
2
1
0
1
0
0
2
2
10
2
0
1
2
0
1
0
2
0
1
1
0
1
2
0
0
0
1
1
1
0
1
0
1
1
1
2
1
1
0
1
0
2
1
0
0
1
0
2
1
0
0
2
2
0
2
1
0
0
0
0
2
2
0
2
2
1
1
0
1
1
1
2
1
2
0
0
1
2
1
0
0
0
0
0
1
0
1
0
1
0
1
1
1
2
3
1
2
0
2
1
0
0
2
2
1
1
0
0
1
0
0
0
2
0
0
0
2
1
2
0
0
0
0
0
0
0
2
1
1
2
2
0
2
1
0
1
0
2
1
2
1
2
1
2
1
2
1
1
1
1
2
1
1
0
1
1
2
0
0
0
0
0
2
2
1
2
1
0
1
2
2
2
1
1
0
1
2
0
0
1
1
1
2
0
0
1
3
0
0
2
2
1
1
2
2
2
1
0
1
1
1
0
0
2
1
0
2
0
0
1
1
2
0
1
0
0
3
1
3
1
1
0
1
1
1
1
0
0
2
2
1
0
1
2
0
1
1
3
0
1
2
2
1
1
3
1
1
1
2
1
0
0
0
0
1
1
0
0
2
1
0
2
2
1
2
0
2
0
2
0
0
2
1
0
1
3
0
1
0
0
1
0
2
1
0
2
1
2
2
0
0
0
0
0
0
0
2
0
1
1
0
1
0
0
1
2
3
0
2
1
2
2
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
1
2
1
2
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
2
1
1
1
1
2
1
0
2
0
2
1
0
0
0
1
0
2
0
0
1
2
0
1
2
0
1
0
1
0
2
1
0
2
0
0
0
0
0
2
2
1
3
1
0
2
0
1
0
2
0
1
1
0
1
1
1
0
0
4
2
0
2
1
1
0
2
0
1
0
2
1
4
2
1
2
1
2
2
0
1
2
0
1
0
1
0
0
1
1
2
0
0
1
1
0
0
2
0
1
0
2
2
2
0
1
0
1
1
0
1
1
2
2
0
0
2
1
1
1
1
1
0
0
0
1
2
0
2
0
0
0
0
0
1
1
0
1
0
1
1
1
1
2
2
0
0
0
0
2
1
1
0
1
7
1
2
0
1
0
0
0
0
1
0
2
2
0
0
2
1
0
1
0
1
3
3
1
0
0
0
1
1
0
2
0
0
2
0
0
0
1
0
1
0
1
0
0
4
0
0
2
1
0
0
2
0
1
1
0
1
0
0
0
1
0
0
1
1
0
1
0
1
1
0
1
3
0
2
0
0
0
0
1
1
0
1
1
1
0
0
1
0
1
1
0
0
2
3
2
0
0
1
1
1
0
1
1
0
2
0
1
0
0
1
3
2
0
1
0
1
0
0
1
0
2
2
0
1
1
0
0
0
0
0
1
0
0
0
0
3
0
1
0
2
0
1
1
2
0
2
0
0
0
2
1
0
0
1
1
1
1
1
1
0
1
0
0
0
0
0
2
0
0
1
1
0
0
0
0
2
1
2
0
1
2
0
2
0
3
1
0
1
1
1
1
1
1
2
1
0
3
4
1
0
1
1
0
0
2
1
0
0
1
0
0
1
2
1
0
0
0
1
1
0
1
0
1
1
1
1
0
0
2
0
0
1
1
0
0
1
2
1
0
0
3
1
0
0
1
1
0
0
0
1
1
2
0
2
1
3
0
1
1
2
0
1
2
2
2
1
1
0
1
0
1
1
1
1
1
2
1
2
0
2
0
0
0
0
1
0
1
1
1
1
0
0
1
2
2
2
0
2
2
1
2
0
1
1
0
1
1
1
0
1
1
0
1
1
0
0
1
2
1
0
2
2
1
0
0
0
0
2
1
0
1
0
2
0
0
0
2
0
0
0
0
1
1
1
2
0
0
2
2
0
0
0
0
0
2
2
1
1
1
1
1
0
1
2
0
2
1
0
1
1
1
0
0
1
0
1
1
0
0
2
2
0
3
1
0
0
0
2
1
1
1
0
2
1
2
2
1
0
1
2
2
2
0
0
2
0
1
1
0
2
2
1
2
0
1
1
1
2
2
1
1
1
1
1
1
1
0
1
0
2
2
0
1
0
0
0
1
3
1
1
1
2
0
2
0
1
0
0
1
1
0
1
1
0
2
1
1
2
0
2
2
0
0
0
0
1
1
0
2
1
1
2
0
2
2
0
1
0
1
1
0
0
0
2
2
1
2
0
3
2
0
1
1
0
0
0
2
0
1
1
0
0
2
1
1
0
2
0
1
2
0
0
0
1
1
0
0
1
0
0
0
1
0
2
0
1
1
0
1
0
0
2
1
1
1
0
1
1
0
2
1
1
1
1
2
1
0
0
1
0
0
0
2
2
2
2
1
1
0
0
1
0
2
2
0
0
2
1
0
1
0
1
0
1
0
0
0
1
0
0
2
1
0
1
1
1
1
3
0
1
1
0
1
0
1
4
0
1
1
0
0
1
0
2
1
2
0
1
0
1
0
2
2
0
1
0
1
1
0
2
0
1
2
1
1
0
0
0
2
0
1
1
2
0
2
2
1
2
2
1
1
1
0
2
2
2
2
1
0
1
2
1
2
0
1
2
0
2
0
0
1
0
1
1
0
0
2
0
0
1
0
1
2
1
0
1
0
2
2
0
0
0
1
0
2
1
0
1
2
2
1
1
0
1
2
0
0
2
0
2
1
1
2
0
3
0
4
2
0
0
1
0
2
2
2
2
0
6
1
0
2
1
0
0
2
2
1
0
0
8
0
0
1
1
1
2
1
2
1
1
1
0
1
1
2
0
0
1
0
1
1
0
1
1
1
1
1
0
0
0
0
1
1
0
1
1
2
1
0
1
0
0
2
2
0
1
0
0
1
1
0
0
0
1
0
2
0
1
0
0
1
1
1
1
2
2
1
0
1
0
0
2
2
1
1
0
0
0
1
0
1
0
1
0
0
1
2
1
0
1
1
0
1
0
1
0
1
1
0
0
0
1
0
1
0
1
0
1
2
0
1
1
0
0
1
2
1
0
4
2
0
0
0
2
2
1
2
2
0
1
0
1
0
1
0
1
0
2
0
1
0
2
1
1
1
1
0
1
1
0
0
0
1
2
3
0
2
0
1
1
1
0
1
2
1
1
0
2
0
0
2
1
0
0
2
0
0
3
1
1
1
0
0
1
1
1
1
1
2
2
0
1
0
1
0
0
2
1
1
3
0
1
0
1
2
0
1
0
1
2
2
0
2
2
2
0
2
0
2
0
0
0
1
0
1
1
0
2
2
0
0
2
1
3
1
2
0
1
0
2
1
0
0
1
1
1
2
2
0
0
2
1
2
0
1
1
1
1
1
0
2
0
0
1
0
0
2
0
0
2
1
0
0
1
0
0
1
1
1
0
0
0
2
0
2
0
2
0
1
1
0
1
1
0
0
2
2
1
0
2
1
1
2
0
1
2
0
1
0
0
0
0
0
1
1
3
0
2
0
0
0
1
0
0
1
0
1
0
0
0
1
2
2
0
0
1
0
0
2
2
0
1
1
1
1
0
2
1
1
2
1
1
1
0
0
1
0
1
0
0
1
0
1
1
2
1
0
1
0
1
3
1
0
1
2
0
2
2
1
0
0
2
1
0
1
1
1
0
1
1
2
2
1
1
2
1
0
2
0
2
0
1
1
2
2
2
0
0
2
1
0
0
1
0
2
2
2
1
1
0
0
2
2
1
0
1
1
0
2
0
2
1
1
0
1
0
2
0
1
0
1
0
1
0
0
1
1
1
1
0
0
0
1
1
0
0
2
0
0
2
0
0
1
0
0
2
0
2
2
1
1
2
2
2
2
1
0
0
1
0
2
1
1
1
0
2
1
1
1
1
2
1
0
1
0
1
2
2
1
1
2
2
1
2
0
1
0
2
0
0
1
0
0
2
0
1
0
0
2
0
1
2
1
2
1
2
1
0
0
0
2
0
2
1
0
2
0
1
1
2
1
2
1
2
1
1
1
2
1
2
2
1
0
1
0
0
0
2
1
2
0
0
2
0
1
1
1
0
2
0
2
0
0
0
2
1
1
1
0
2
2
0
0
0
2
2
0
1
0
1
1
1
0
2
3
0
0
1
1
0
2
0
1
0
0
0
1
1
1
0
0
2
0
0
1
1
1
1
2
3
0
0
2
0
0
0
0
0
2
0
2
1
0
1
2
2
0
1
0
1
3
2
1
1
2
1
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
1
1
2
2
1
2
1
0
1
1
1
0
0
0
1
1
0
2
1
1
1
0
1
0
1
2
0
1
0
0
2
0
0
0
1
0
0
0
0
1
2
0
0
0
1
2
1
2
0
0
0
2
0
1
2
2
0
0
0
1
0
1
1
1
2
1
1
1
1
0
1
0
1
0
2
2
1
0
1
1
1
0
0
0
1
0
2
0
1
0
2
1
1
2
2
1
2
0
1
0
0
2
2
2
0
2
2
1
0
1
0
1
1
0
0
1
1
0
1
2
2
1
0
1
1
0
0
0
1
1
0
2
1
0
0
0
2
0
1
0
0
0
2
2
1
0
0
0
1
0
2
0
1
0
2
2
0
1
0
0
1
0
0
1
0
2
0
2
0
1
0
0
0
3
0
0
1
0
0
2
0
0
1
1
2
2
0
0
0
1
1
0
0
1
0
2
0
0
2
0
0
1
0
1
0
1
1
2
2
0
0
2
1
3
1
2
1
3
2
2
2
0
1
0
0
0
0
2
1
2
0
1
0
0
1
1
1
1
2
0
2
2
0
0
1
1
1
1
0
2
0
1
0
2
0
0
1
1
1
1
1
1
0
0
2
2
2
1
0
0
0
0
1
2
0
1
1
2
1
1
0
1
1
1
2
1
1
1
0
1
0
2
0
2
0
2
0
0
2
1
1
1
0
1
0
1
2
2
0
0
0
1
0
2
0
2
1
0
0
0
1
0
1
1
0
1
2
0
2
2
1
2
2
1
0
2
1
0
0
1
1
1
1
0
0
0
0
1
0
2
1
0
1
0
1
1
1
2
0
0
0
0
0
1
0
1
2
2
1
2
0
0
1
0
1
1
0
0
0
0
1
1
0
0
1
1
0
0
1
1
0
0
1
1
0
1
1
1
3
2
2
1
2
1
0
4
0
1
1
2
0
0
1
1
1
2
1
1
0
0
1
2
2
2
3
1
1
0
1
1
0
0
1
0
2
1
0
0
0
2
0
1
1
1
0
1
0
1
1
2
0
2
0
1
0
1
2
1
1
1
1
1
1
2
2
2
1
0
0
2
0
1
1
0
1
2
0
1
1
1
1
0
0
0
1
2
1
1
1
2
1
1
1
2
2
2
1
1
2
3
0
0
2
0
0
0
1
1
1
0
2
1
2
0
0
0
0
2
1
1
0
2
1
0
1
1
1
0
2
0
0
1
0
0
1
0
1
0
2
2
1
2
1
2
2
0
0
0
1
1
0
1
0
0
2
0
0
2
0
0
0
0
0
1
1
0
1
1
0
1
0
0
4
1
1
1
1
1
0
1
2
1
0
0
1
0
0
2
1
0
0
1
0
1
1
2
1
1
1
2
0
1
2
0
0
2
1
0
0
0
0
0
2
1
3
1
1
1
0
0
0
0
2
0
2
0
0
0
1
0
2
0
0
2
1
1
2
1
1
0
0
1
1
4
1
0
2
0
1
3
2
1
0
0
1
1
2
1
2
2
0
2
2
1
0
0
1
1
1
1
0
0
1
2
2
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
2
0
1
0
2
0
1
1
1
0
1
2
1
1
0
1
0
0
1
2
1
1
1
0
0
0
0
1
2
0
1
0
2
0
1
2
0
0
0
1
0
0
1
0
2
0
2
0
2
1
0
0
2
3
1
0
0
2
0
2
0
2
2
1
2
1
0
0
1
0
2
1
0
1
0
0
0
1
0
1
0
0
2
2
2
0
1
1
1
2
2
1
1
2
0
2
2
1
0
0
1
0
2
0
0
1
0
1
1
1
3
0
2
1
0
2
1
0
2
2
1
1
1
1
1
0
1
1
0
1
0
1
0
1
0
1
1
0
1
0
1
0
0
1
0
0
1
0
0
0
3
0
2
2
1
1
2
0
0
0
2
0
1
2
0
0
2
1
0
2
0
0
1
0
0
1
0
0
2
0
1
1
1
1
0
2
2
0
0
1
0
1
0
0
1
2
2
1
0
1
1
1
2
1
1
1
1
0
1
0
0
0
4
2
1
1
2
2
0
1
0
0
1
2
0
0
2
1
0
1
2
1
2
1
0
1
0
2
0
0
1
1
1
0
0
1
2
1
1
1
0
0
1
2
0
0
0
1
2
2
1
0
2
2
1
2
1
0
0
0
0
1
0
1
0
1
0
1
0
1
1
1
0
0
1
1
1
2
1
0
2
2
2
0
2
0
2
0
2
0
1
0
0
1
0
2
0
0
2
1
0
0
0
2
2
1
1
1
0
1
1
1
0
1
1
1
0
1
0
1
2
2
0
1
1
1
0
0
0
0
2
0
0
1
1
0
2
0
0
2
1
4
1
0
1
1
2
0
1
2
1
1
2
1
2
0
1
2
2
0
2
2
1
1
1
1
2
0
1
2
2
1
0
0
0
2
1
2
1
1
1
0
2
1
0
1
0
0
0
1
0
2
0
0
1
1
2
1
1
1
0
2
1
1
0
0
1
0
0
0
1
0
0
0
1
1
1
0
2
1
0
0
2
1
2
1
0
0
1
1
1
2
0
1
0
1
0
1
0
2
1
1
1
1
1
0
1
0
0
0
0
2
0
0
0
2
0
0
0
2
0
1
1
2
1
1
0
1
1
0
0
2
0
1
0
2
0
1
2
2
0
1
2
3
1
0
0
0
0
2
1
0
0
1
0
1
0
1
1
2
1
0
1
1
1
0
0
1
2
1
2
1
0
2
0
0
0
2
0
0
1
0
1
0
1
0
0
2
0
0
1
2
1
1
0
0
1
1
0
2
1
2
0
3
1
0
2
1
1
2
0
0
0
0
1
0
1
1
2
0
0
0
0
2
0
2
1
0
1
1
1
1
2
1
0
2
2
1
3
1
1
0
1
0
1
1
1
1
2
1
1
0
1
0
0
1
0
2
0
1
1
2
2
0
0
2
0
1
0
0
2
1
1
0
0
3
2
1
0
2
1
1
0
1
1
1
0
2
0
2
0
0
1
1
1
1
3
0
1
0
1
1
0
1
0
1
0
2
1
0
1
0
1
1
1
0
2
2
1
1
1
2
1
0
1
2
0
2
0
1
1
1
1
0
0
0
1
2
1
2
0
0
1
0
1
2
0
0
1
0
0
1
0
0
0
0
0
1
0
0
2
2
1
0
2
1
0
1
1
0
2
0
1
0
1
0
1
0
1
1
1
1
1
1
0
1
0
0
0
1
0
3
0
2
0
0
0
1
1
2
0
0
1
0
2
1
2
2
2
0
1
0
1
1
0
1
1
1
2
1
2
0
1
0
0
1
0
0
0
2
1
1
1
1
0
0
2
1
1
1
0
2
2
2
1
2
1
0
0
2
0
2
1
2
2
3
0
0
1
0
1
2
2
3
1
1
1
0
1
0
1
1
1
1
0
1
0
0
1
1
2
0
1
0
1
1
1
1
2
1
0
1
0
2
1
1
0
2
1
1
0
1
1
2
1
0
0
1
0
1
2
3
3
1
0
0
0
2
2
2
1
0
1
1
0
1
1
2
2
1
1
2
2
2
0
1
0
0
0
1
0
0
2
0
1
1
0
1
1
1
1
0
0
0
0
0
2
1
0
0
1
0
0
2
1
0
0
2
2
2
0
2
0
1
0
2
1
2
1
1
0
1
0
1
1
1
0
1
0
1
0
0
0
0
2
1
0
0
0
2
0
1
1
1
0
1
2
2
1
0
0
2
1
0
2
0
2
1
2
2
2
1
0
0
1
0
1
2
1
1
1
0
2
1
2
1
1
0
0
0
1
1
1
0
0
0
2
0
4
0
1
2
2
1
0
1
0
1
1
0
1
0
1
1
1
0
1
0
0
2
1
0
0
1
0
1
2
1
1
0
1
1
1
0
2
1
0
1
1
1
1
3
0
0
2
0
0
2
0
0
2
0
1
0
1
2
1
1
0
0
0
2
0
0
0
1
2
2
2
2
1
0
2
2
0
1
1
2
0
1
0
0
2
0
1
2
2
1
1
1
1
0
2
0
0
0
1
0
0
2
0
0
0
3
1
2
1
1
0
0
5
2
2
0
1
0
2
2
2
1
2
1
2
1
2
2
0
0
0
1
0
0
0
0
1
2
0
1
1
0
1
2
2
2
2
1
0
1
0
2
0
1
3
1
0
0
0
1
0
0
1
1
1
2
2
0
1
1
2
0
0
0
0
1
0
0
1
0
2
2
0
0
0
2
0
0
1
0
0
1
0
2
0
0
3
0
1
1
0
1
1
0
0
2
0
1
0
0
1
1
2
0
1
0
0
0
0
2
0
2
1
5
1
1
1
1
1
0
0
1
0
3
0
2
2
2
0
0
1
1
0
0
2
2
0
0
2
2
1
0
0
1
2
1
3
1
0
2
1
0
0
0
1
1
1
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
2
2
0
2
1
2
0
0
0
0
1
1
0
1
1
0
1
1
2
2
1
2
0
1
1
1
1
2
2
2
0
0
0
0
0
1
0
0
0
2
0
1
2
2
0
1
0
0
2
0
3
1
2
0
2
0
0
1
1
1
2
1
0
1
1
1
1
0
0
2
1
0
1
0
1
2
1
2
2
2
0
2
1
0
2
2
0
0
0
0
0
1
2
0
1
0
1
0
1
2
1
2
2
2
2
2
1
0
1
1
0
1
0
1
0
2
1
1
0
0
2
2
0
1
1
0
2
0
0
1
0
0
0
1
0
0
0
2
2
0
1
0
1
0
0
6
1
0
0
2
1
0
0
1
1
2
2
1
3
1
0
1
1
1
2
1
2
1
0
0
0
0
1
2
1
0
1
0
1
1
0
2
1
1
2
2
0
1
2
2
0
2
1
1
2
2
0
2
2
0
1
1
1
2
1
1
1
2
0
0
1
0
0
1
2
0
2
0
1
0
2
2
1
1
2
1
0
0
0
1
2
1
1
0
0
1
2
0
1
0
0
1
1
2
1
1
1
1
1
2
2
1
2
2
0
1
1
0
0
0
1
0
2
2
1
0
0
0
1
1
0
2
2
1
1
2
3
0
0
2
2
1
0
0
2
2
0
1
1
0
0
3
0
2
1
1
1
2
2
2
2
2
1
0
2
1
1
1
1
2
2
0
2
1
2
2
0
0
1
0
0
2
2
0
0
2
1
1
2
2
1
0
1
0
0
2
1
1
0
0
1
2
0
1
0
1
0
1
0
2
1
1
2
1
0
2
1
0
2
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
1
0
1
0
0
1
2
1
2
2
0
0
2
2
0
0
0
1
2
2
0
1
0
0
0
2
1
0
0
7
0
0
2
1
2
1
1
1
0
0
2
2
0
1
1
1
1
0
0
0
0
0
3
0
0
0
1
2
2
1
3
1
0
0
1
1
1
0
0
0
0
2
1
0
1
2
1
2
2
0
1
0
0
0
1
1
1
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
1
0
1
1
2
0
1
1
2
1
0
1
1
0
0
0
0
2
2
2
1
1
1
1
1
0
1
2
0
1
0
0
1
1
1
2
1
0
0
1
1
0
0
2
0
1
0
1
0
1
0
0
2
1
2
3
1
1
0
0
0
1
0
1
0
0
1
1
1
2
0
1
1
0
1
1
1
0
2
0
1
1
1
2
1
0
1
1
2
2
2
1
0
0
0
0
0
1
0
1
0
0
0
1
2
2
0
0
0
0
2
0
1
1
0
2
2
0
0
1
0
2
1
0
0
0
1
0
0
0
0
1
2
2
1
1
2
0
2
0
1
0
0
0
1
4
0
0
1
2
1
0
1
0
1
1
0
1
0
2
1
0
1
0
1
0
0
0
0
0
0
1
1
0
1
0
2
0
1
0
1
1
1
0
1
2
0
0
0
2
2
0
2
1
1
2
0
1
2
1
1
1
0
2
1
0
0
0
0
0
2
2
1
0
0
0
2
1
0
1
0
1
1
0
1
1
1
1
2
2
0
2
1
1
1
2
6
1
0
0
2
0
1
0
1
1
1
0
1
1
2
1
0
0
2
1
2
1
1
0
1
0
0
0
1
1
0
0
0
0
1
1
1
2
0
0
2
1
0
2
0
0
2
1
1
1
1
0
0
1
2
0
0
1
2
0
0
1
2
1
0
0
0
0
2
0
0
2
2
0
0
0
1
0
0
1
1
2
0
0
1
0
1
0
1
2
0
0
1
0
1
0
0
0
1
2
2
0
1
2
1
1
2
1
0
1
1
1
1
1
2
1
2
1
1
2
0
1
0
1
2
0
1
0
1
0
0
2
2
1
0
1
0
0
2
1
2
0
1
1
0
0
2
1
0
0
0
0
0
1
1
2
1
1
2
0
0
0
2
1
1
0
0
2
0
1
0
2
2
1
0
1
0
0
2
1
2
1
2
1
1
1
1
0
1
1
0
0
0
0
1
0
1
0
1
1
0
1
2
1
0
1
0
0
0
0
0
0
2
1
0
2
0
1
1
0
1
1
1
2
0
0
0
1
0
1
1
0
1
0
2
3
1
1
0
0
1
0
1
0
0
1
2
1
0
0
0
1
1
0
0
0
2
0
0
2
0
0
2
2
2
3
0
0
1
1
0
1
1
2
1
3
0
1
2
0
1
0
2
1
0
0
0
0
2
0
0
2
3
1
2
0
1
1
1
1
1
0
1
1
2
2
0
0
2
2
1
0
0
1
2
3
0
0
1
1
1
0
0
1
0
1
2
1
0
1
0
1
2
2
0
0
1
0
1
0
1
2
0
1
1
2
1
0
0
1
0
1
1
0
0
0
1
0
0
1
1
1
0
1
0
2
1
1
2
1
1
0
1
2
1
0
0
2
0
1
2
0
2
0
1
1
0
2
0
0
1
0
1
1
0
0
0
0
0
1
2
0
1
2
1
0
1
2
1
1
2
1
2
0
0
1
1
1
2
0
0
0
0
1
2
0
0
2
2
0
3
1
1
0
1
2
1
1
0
0
1
0
0
0
0
2
0
2
0
0
0
2
0
1
2
1
1
0
0
1
2
0
0
0
0
2
1
0
1
1
0
0
0
0
2
0
0
0
1
1
2
1
0
2
0
1
0
2
0
2
0
1
2
1
1
2
2
1
1
0
2
0
1
2
0
0
0
0
1
1
1
0
0
0
1
0
1
1
0
0
1
1
2
0
2
0
0
2
1
1
2
0
2
0
1
0
0
1
1
1
1
2
0
0
2
2
1
1
0
1
2
1
0
0
0
0
2
1
2
0
0
2
1
1
1
1
2
2
0
0
0
0
0
0
1
0
0
1
0
2
1
2
1
0
0
1
3
1
1
0
0
1
2
0
1
0
0
1
0
2
1
0
1
1
0
1
1
1
1
1
2
2
0
1
1
2
4
1
4
2
1
1
2
2
0
1
0
1
1
0
0
1
0
0
1
1
2
2
1
0
2
4
1
2
0
1
1
1
0
2
2
1
2
0
0
1
1
1
1
1
2
0
2
2
0
1
1
0
0
1
2
1
2
1
0
1
1
0
0
0
0
2
1
0
0
1
1
2
1
2
2
2
1
2
1
2
1
1
0
0
1
0
0
0
2
0
0
2
0
1
0
1
0
0
1
1
1
0
1
0
2
0
1
2
0
1
0
0
1
0
0
1
0
1
1
0
1
2
2
0
4
1
1
2
1
0
0
1
0
1
0
1
1
1
0
2
1
0
0
1
0
0
0
0
0
0
0
2
0
1
1
0
0
1
0
1
1
2
0
0
1
1
2
1
0
2
0
1
2
0
0
1
0
0
1
1
0
1
0
0
0
1
1
0
0
0
0
0
0
2
2
1
0
2
2
1
1
1
2
0
0
1
0
1
0
1
1
1
2
0
0
2
1
0
0
2
1
0
1
1
0
0
0
1
0
0
2
1
0
2
2
1
1
0
1
2
1
0
0
0
0
1
0
1
0
1
0
0
2
2
1
1
1
0
2
1
0
0
2
0
0
2
0
0
0
0
2
0
2
1
1
0
0
2
0
0
0
1
1
1
0
1
2
2
0
1
0
1
1
0
0
1
1
1
0
0
0
0
0
1
1
0
1
2
0
1
1
1
2
1
0
3
0
1
0
1
0
0
1
1
2
0
0
0
1
1
0
2
2
2
0
1
1
1
0
1
0
2
0
1
0
0
2
2
0
1
0
0
0
2
0
4
1
2
2
1
0
2
0
1
1
0
0
0
0
1
1
1
2
3
1
1
0
1
1
1
2
2
2
0
1
1
0
0
2
0
2
2
1
0
2
0
1
1
0
2
1
0
1
0
2
1
1
2
0
0
1
0
1
1
2
1
1
2
0
1
1
1
3
1
2
0
2
0
1
2
0
0
0
0
1
1
2
2
2
0
2
0
0
0
1
1
2
1
2
1
1
0
1
1
2
0
0
1
2
0
0
0
1
0
3
0
2
0
2
0
1
1
2
0
2
2
0
1
0
3
1
1
2
1
0
0
1
2
0
0
0
1
2
0
1
2
2
0
0
2
0
0
0
2
2
0
1
2
0
0
1
3
1
1
0
0
0
1
0
1
1
0
0
0
2
0
1
1
0
1
2
0
1
1
0
0
2
1
0
0
0
3
1
0
1
0
0
0
1
0
1
0
0
2
2
0
1
0
0
0
1
1
0
2
1
0
0
2
1
0
1
0
2
1
0
1
1
0
2
1
2
0
1
0
0
0
0
2
0
1
2
1
2
0
1
1
1
1
1
1
0
1
0
1
0
3
2
2
2
1
0
1
0
2
1
2
1
1
1
0
0
0
0
1
2
2
1
1
2
1
1
1
0
1
0
1
2
1
0
1
0
0
2
2
1
1
2
0
2
0
0
0
0
1
2
2
1
2
0
0
2
0
1
0
2
0
0
0
0
0
1
0
2
2
1
0
1
1
1
0
0
2
1
1
1
1
1
0
0
0
1
1
1
1
1
1
0
1
2
0
1
2
0
0
1
0
0
2
2
3
0
2
1
0
1
1
2
0
1
1
1
0
0
1
1
1
0
2
1
1
0
3
0
0
1
2
1
0
1
0
2
0
1
1
0
1
0
3
2
0
2
1
2
1
1
0
0
0
1
2
1
2
1
0
2
1
2
0
1
2
1
0
2
0
0
0
1
4
1
1
0
1
0
0
0
1
2
0
1
0
1
1
1
2
2
2
1
1
1
0
2
0
0
0
2
1
1
0
1
1
0
0
2
0
0
0
1
0
0
1
1
2
2
1
0
0
1
1
1
0
0
1
0
1
2
1
3
0
0
0
0
1
1
2
0
0
1
0
1
2
0
0
1
0
1
1
1
0
1
0
1
0
0
0
0
0
0
1
5
3
1
1
1
0
1
1
1
3
0
2
0
0
1
0
0
0
0
0
1
1
1
2
0
0
0
2
2
2
0
0
0
1
1
0
1
0
2
0
1
1
1
0
1
1
1
1
1
0
0
0
1
0
0
0
0
1
0
1
2
0
2
0
0
0
1
1
2
1
0
0
2
0
1
1
0
1
0
1
0
0
2
1
2
3
1
1
2
0
1
2
0
1
0
0
0
0
2
0
0
2
1
2
0
2
1
2
0
2
1
2
0
0
1
1
0
2
0
2
1
1
2
1
1
0
1
0
1
0
1
1
0
2
1
3
1
0
1
1
2
1
2
0
0
1
0
0
0
1
0
1
1
0
1
0
0
2
1
1
0
2
0
2
2
2
1
2
0
1
2
0
1
2
2
0
1
2
0
0
1
1
1
0
1
1
2
0
1
0
2
2
0
1
0
0
1
1
1
0
0
1
0
1
1
0
0
0
0
1
0
1
0
2
0
2
1
1
1
1
0
1
0
0
1
0
0
0
1
2
1
1
0
1
1
1
1
2
1
0
2
0
1
0
0
1
1
2
1
2
0
2
1
0
0
0
2
2
2
1
0
1
0
1
0
0
0
2
0
1
1
0
0
0
2
0
1
1
1
0
2
2
1
2
0
0
0
1
2
2
0
1
0
1
2
2
1
1
0
1
0
2
2
1
0
1
0
1
0
1
2
2
1
1
0
0
2
2
0
2
0
0
1
2
1
1
1
2
1
1
2
1
2
1
1
1
2
0
2
0
1
2
1
1
1
0
2
1
2
0
0
1
1
2
0
1
2
1
2
2
0
2
0
1
1
0
0
1
1
1
1
2
1
0
0
0
0
0
2
0
0
0
2
2
2
0
1
0
2
1
1
0
0
1
2
1
0
2
0
1
0
1
0
1
2
2
0
0
0
0
1
2
1
1
2
2
2
0
1
0
2
0
1
1
2
0
1
0
0
1
0
0
1
2
1
1
0
0
1
0
2
0
2
1
0
1
0
1
2
0
0
0
1
1
2
0
0
1
2
3
0
1
0
1
2
2
2
1
0
0
1
2
1
0
0
2
3
1
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
2
0
2
3
0
0
1
0
0
0
1
0
0
0
0
1
1
1
1
1
1
0
1
2
0
0
2
2
0
2
2
1
2
2
2
0
1
2
1
0
1
0
2
1
1
1
1
1
1
2
0
0
2
1
1
10
1
1
1
1
2
0
2
0
0
0
0
1
1
0
1
1
1
1
1
0
0
0
1
0
2
1
0
0
0
0
0
1
6
1
0
2
2
2
0
0
0
1
0
1
0
0
2
1
0
2
0
0
2
0
1
0
0
1
1
0
0
0
0
1
2
0
1
0
0
1
2
1
3
2
1
1
1
2
1
0
1
1
1
0
1
1
2
2
0
1
2
2
0
2
0
0
0
0
2
2
0
0
0
1
0
0
0
2
1
0
0
1
0
1
3
0
1
0
1
1
2
1
0
0
0
2
3
2
1
1
1
2
2
1
0
1
0
2
2
1
1
0
1
0
1
0
1
2
0
1
2
2
1
0
1
0
0
0
1
1
0
2
0
1
1
1
2
2
1
1
1
1
1
1
1
0
2
2
0
5
1
3
1
2
0
0
0
2
0
1
2
1
0
0
2
0
2
1
4
0
2
0
0
0
0
1
0
2
2
0
0
2
2
0
1
1
0
1
0
0
2
0
0
0
1
0
0
0
0
2
1
0
0
0
0
1
0
2
3
1
0
1
1
2
2
2
1
0
4
2
2
0
0
0
1
2
0
0
1
1
0
2
0
1
1
2
2
0
0
0
0
0
0
1
1
1
0
2
1
1
1
1
2
0
2
1
1
0
2
0
3
0
0
2
1
1
0
0
0
0
2
2
0
0
1
1
0
0
1
1
1
2
1
1
2
0
0
2
0
3
1
1
1
2
2
0
0
2
0
0
1
2
1
2
2
2
0
1
0
0
2
1
0
1
0
0
0
0
0
3
2
0
1
1
1
2
1
0
0
1
1
2
0
0
2
0
0
1
0
1
0
0
1
0
1
2
1
3
1
0
2
2
1
2
1
0
2
1
1
0
0
2
1
1
0
1
0
0
2
0
2
2
2
1
1
2
1
2
2
0
0
0
0
0
1
1
0
2
1
1
2
2
1
1
1
2
1
0
2
1
0
2
0
2
1
0
1
1
1
0
2
0
2
0
0
0
0
2
1
1
0
1
1
1
2
0
2
1
0
1
0
2
1
3
2
0
0
0
1
1
0
0
2
1
1
2
2
0
0
1
2
0
1
1
1
2
0
1
1
1
1
0
1
0
0
1
1
1
1
2
1
1
2
0
1
1
0
0
0
0
4
1
1
2
0
1
0
0
1
0
2
0
2
1
2
0
1
2
1
0
0
2
0
2
2
0
0
0
0
1
0
2
1
0
2
1
0
0
0
0
1
1
3
2
1
1
0
3
0
0
0
1
0
0
0
0
2
2
0
2
0
1
2
2
0
2
1
1
0
2
0
0
1
1
0
1
1
1
2
0
0
2
1
0
2
0
1
2
0
0
2
0
2
1
0
0
2
1
1
3
1
0
0
0
0
0
1
1
1
0
0
2
0
1
0
0
1
0
1
0
0
0
0
1
2
1
0
1
1
0
0
0
1
1
1
0
2
2
0
0
1
0
1
4
0
1
1
2
0
1
1
1
2
0
1
1
0
1
1
1
0
0
2
0
0
1
1
0
0
0
1
0
2
0
0
2
1
0
1
2
2
0
1
2
0
0
0
1
0
1
1
1
2
1
1
1
2
0
1
2
2
0
1
0
2
0
0
0
0
1
1
0
1
1
2
2
0
0
1
1
1
2
1
1
0
1
0
1
1
0
2
1
1
0
1
0
0
2
1
0
2
0
2
2
1
1
0
1
0
1
1
1
0
2
2
2
0
0
1
1
0
1
1
2
1
1
0
1
1
0
2
0
2
2
1
0
1
0
3
0
1
0
0
5
1
0
0
1
0
1
3
0
1
0
0
3
2
0
0
1
0
1
2
1
0
0
2
1
2
0
1
2
2
0
1
0
2
0
1
0
0
3
1
1
1
0
1
1
2
2
1
2
1
1
1
1
0
1
1
1
1
0
0
1
2
0
1
1
1
0
2
1
1
0
1
0
2
1
0
0
1
0
2
1
0
0
0
0
0
1
2
2
0
0
1
0
0
0
1
1
0
0
2
0
1
0
2
0
2
0
1
2
0
1
0
2
0
0
1
1
0
1
1
0
0
0
1
0
0
0
2
0
3
0
0
2
1
1
6
0
2
1
0
2
1
2
2
2
1
0
0
1
0
1
1
2
2
1
0
0
0
1
0
1
2
1
1
1
0
0
2
1
0
2
0
0
2
1
1
2
0
2
0
1
2
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
1
1
1
0
1
0
0
0
2
0
3
1
2
2
0
2
1
1
0
1
0
0
1
2
0
1
0
0
2
0
1
1
1
0
0
2
1
0
0
1
1
1
1
2
0
0
0
3
1
2
2
0
2
2
0
0
1
1
1
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
3
0
1
0
0
0
2
0
1
1
1
2
1
1
0
0
0
2
1
0
2
1
0
1
1
1
1
0
2
0
0
2
0
2
0
2
2
1
0
2
1
0
1
0
2
0
1
1
1
1
2
0
0
1
2
2
1
1
0
0
1
0
0
3
2
0
1
1
1
2
1
3
1
1
0
0
3
1
1
1
1
1
1
0
2
1
0
0
1
0
0
1
0
0
2
0
1
2
1
0
2
1
0
0
1
0
1
1
1
1
2
1
0
2
0
0
0
1
2
1
1
0
1
1
1
0
2
2
0
0
0
0
1
0
0
2
0
0
1
0
0
0
1
1
1
1
1
2
1
0
0
1
1
2
1
2
0
2
2
0
0
1
2
0
0
0
0
1
0
1
0
2
1
1
1
0
0
1
0
2
1
1
1
0
1
0
2
1
2
1
0
2
2
1
0
0
0
1
0
1
2
1
1
1
0
2
0
1
3
1
1
2
0
1
2
2
2
2
2
0
2
1
2
3
2
2
2
2
1
0
1
4
1
1
1
1
0
0
1
2
2
1
0
1
1
1
0
2
2
2
2
0
1
1
3
2
2
0
0
1
1
1
0
0
2
3
0
0
0
1
1
1
2
0
1
0
2
1
7
1
0
1
0
2
1
2
2
1
2
2
2
1
0
1
0
2
1
2
1
1
0
1
0
1
1
1
2
2
1
1
1
1
0
0
0
0
1
0
1
0
0
2
2
2
0
2
0
1
1
2
0
2
1
0
1
0
2
1
1
0
1
1
0
2
0
2
0
2
3
1
1
0
2
1
1
2
0
1
0
2
2
1
1
2
0
1
1
0
0
0
0
2
1
0
0
0
0
1
1
1
2
0
1
1
0
0
1
0
1
2
1
1
0
1
2
0
2
0
1
0
2
0
1
2
0
0
1
1
0
2
0
1
1
1
0
1
0
3
1
0
2
1
1
2
2
1
1
0
0
0
0
2
2
1
1
2
0
2
1
1
0
2
1
1
2
0
0
1
1
1
0
0
2
0
0
1
0
0
0
3
1
0
1
2
0
0
1
0
0
2
2
2
0
1
2
1
0
0
2
1
2
0
1
1
0
1
1
2
0
0
0
1
0
0
0
1
1
1
2
2
0
1
1
0
2
1
2
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
4
2
1
0
1
1
1
0
1
1
1
0
1
2
0
0
2
1
0
0
2
1
1
1
0
2
0
0
1
0
1
0
0
3
1
0
0
1
0
2
0
0
2
4
1
0
0
0
1
2
0
2
1
1
0
1
0
0
1
1
1
0
0
2
1
0
0
1
0
1
1
3
0
0
0
1
1
0
2
0
2
0
1
1
0
2
2
1
2
0
0
2
1
1
1
0
3
0
0
1
1
1
1
2
1
3
1
1
0
1
0
0
1
2
0
2
1
0
0
2
1
1
1
0
1
1
0
1
2
2
2
0
3
1
0
1
1
1
1
1
0
1
0
2
2
1
0
0
1
0
0
1
0
2
1
1
0
3
0
0
1
1
2
2
0
2
0
0
1
0
0
2
1
1
0
1
1
1
2
0
2
0
1
0
1
2
1
1
0
0
1
1
0
1
0
1
1
1
1
0
0
1
2
2
1
3
0
2
1
1
1
1
0
2
2
0
0
0
1
1
2
1
1
4
0
2
1
1
1
1
1
1
0
1
0
2
2
1
2
0
2
2
0
1
1
1
1
0
2
1
1
2
1
2
2
0
0
1
0
1
1
0
0
0
2
0
0
1
2
0
1
0
1
0
0
0
1
0
0
0
2
1
1
2
2
0
1
1
0
1
2
2
1
0
2
0
1
0
1
1
0
1
0
0
1
1
0
0
2
2
3
2
1
0
0
0
1
2
1
1
1
2
2
2
1
0
0
1
1
2
1
0
1
1
1
0
1
0
0
1
1
0
0
0
1
2
2
1
0
1
0
1
1
0
0
1
2
1
1
1
0
0
2
1
1
0
0
1
0
0
1
1
2
0
3
1
2
1
1
2
0
0
2
1
0
0
1
2
1
0
0
2
1
2
1
2
0
1
1
1
1
0
0
1
5
0
1
2
1
1
1
0
0
2
2
1
0
0
2
2
0
1
2
1
0
1
2
0
2
1
1
0
2
1
0
0
0
1
1
0
2
2
1
1
1
0
1
0
1
1
1
0
1
1
2
2
0
0
0
1
0
0
1
1
2
2
0
0
2
1
1
1
0
2
2
1
2
3
1
3
1
0
1
2
0
0
1
1
2
0
2
2
1
2
1
1
0
1
0
2
1
1
0
1
1
0
0
1
1
1
0
2
0
1
1
0
2
0
2
1
0
2
3
2
1
1
2
1
0
0
2
0
1
1
0
1
0
0
0
2
1
0
1
1
1
2
0
1
1
2
0
0
1
2
2
0
1
1
1
0
0
0
1
1
0
1
0
0
1
1
0
2
1
1
1
0
1
0
1
1
2
1
2
0
1
2
1
2
1
0
1
0
2
2
2
0
1
1
2
2
1
1
1
0
1
2
2
1
0
1
1
0
0
0
1
1
1
0
2
0
0
1
0
1
1
1
1
1
1
0
1
2
0
4
0
2
1
0
0
0
2
0
0
1
0
1
0
1
0
2
4
2
2
1
0
0
1
2
4
1
0
2
0
0
2
3
1
0
1
0
0
0
2
0
0
1
1
1
0
1
2
2
2
1
1
1
0
0
2
1
1
2
0
2
1
2
2
1
2
3
1
0
2
1
0
2
0
1
0
2
1
2
0
1
1
3
1
0
0
2
0
0
0
1
0
0
2
1
0
1
2
0
2
2
0
2
0
0
1
0
1
2
2
0
2
1
1
0
1
0
0
1
0
2
0
0
2
1
1
0
1
2
2
1
0
0
2
0
2
1
1
1
1
0
1
1
0
1
0
0
0
2
1
0
2
0
1
0
2
1
2
1
1
0
0
1
0
1
1
5
0
0
0
1
0
0
2
1
2
2
0
2
0
1
0
0
0
2
0
0
1
1
0
2
2
3
0
1
1
2
1
2
1
2
2
0
0
1
1
2
0
0
1
2
1
1
2
0
2
1
0
3
0
1
2
1
0
0
1
2
1
0
2
3
2
1
1
2
1
1
0
1
1
0
0
2
2
0
0
8
2
0
0
0
0
1
2
1
0
0
1
0
2
1
2
0
2
0
2
0
3
1
2
0
1
2
1
0
2
0
1
1
2
0
1
0
1
2
1
0
0
2
0
1
0
1
1
0
0
1
0
0
1
0
1
1
1
0
1
2
1
2
1
0
0
2
1
2
0
2
1
1
0
1
1
2
1
2
1
2
1
1
0
1
1
1
1
2
1
1
2
0
0
1
2
0
1
0
0
0
1
2
1
0
0
5
1
1
1
1
1
0
1
0
0
0
0
0
2
1
0
1
1
0
0
0
2
0
0
2
0
2
1
0
1
1
0
0
2
2
0
0
0
0
1
1
0
0
1
1
2
1
2
0
1
1
1
2
0
1
1
1
1
0
2
2
0
0
2
1
1
2
0
1
2
2
1
2
0
1
1
1
0
1
2
0
0
2
0
0
0
2
0
0
1
0
0
0
0
1
2
1
2
0
1
0
3
1
2
1
1
0
1
1
1
2
2
1
1
1
1
2
2
2
0
3
0
2
1
2
1
1
0
2
0
1
0
1
1
1
0
1
0
1
1
2
0
0
1
1
1
1
2
0
0
0
0
0
2
1
1
0
1
2
0
1
0
1
1
0
0
2
2
0
2
2
1
1
0
0
0
2
2
1
2
2
0
1
1
1
2
0
0
0
3
0
1
1
1
2
2
2
0
1
0
1
0
0
1
2
1
2
2
0
0
0
0
0
0
2
0
2
0
2
1
1
1
1
1
2
1
0
1
3
2
1
1
1
3
0
2
0
0
1
0
1
1
1
1
1
0
1
1
1
0
0
0
2
1
2
1
0
0
0
1
0
0
1
0
0
0
2
1
2
1
0
0
1
1
1
2
1
0
0
0
1
0
1
1
1
2
0
1
0
2
0
2
0
0
0
1
1
1
2
2
0
0
2
2
1
1
0
1
1
1
1
0
2
0
2
2
1
2
1
1
0
0
2
0
0
2
1
0
2
1
0
1
1
1
3
3
0
1
0
0
1
1
0
1
0
1
0
1
1
1
1
1
0
2
0
2
1
1
1
1
2
0
1
1
0
1
2
2
1
0
2
0
0
0
1
2
2
2
2
1
1
1
0
1
1
1
1
1
0
0
1
1
0
0
1
2
0
0
1
1
0
1
0
0
2
0
3
1
0
0
0
1
2
0
0
1
1
0
2
2
0
0
0
0
1
0
0
0
1
1
0
0
0
1
1
0
0
0
1
0
1
0
0
1
1
2
0
0
2
0
2
0
1
0
0
2
0
1
1
0
0
1
2
0
1
1
1
1
1
2
0
1
0
2
1
0
0
0
2
0
2
0
2
1
0
1
0
2
0
2
1
0
1
1
2
0
2
0
1
0
0
0
2
2
0
3
1
0
1
1
0
1
0
0
0
0
1
1
0
0
0
2
1
2
1
2
0
1
1
1
0
1
2
1
1
0
2
1
1
2
1
1
1
2
0
0
0
0
0
2
1
1
1
0
2
1
1
1
0
1
0
1
0
1
3
1
2
2
1
1
0
1
0
0
1
1
1
2
1
1
0
2
1
0
1
0
2
1
1
1
2
1
0
0
0
0
1
0
0
1
2
1
1
0
2
2
0
2
2
2
2
1
1
2
0
0
2
0
0
0
0
2
0
0
0
0
1
0
2
0
1
1
2
0
3
0
0
0
0
1
2
1
0
0
0
0
0
2
2
0
1
2
0
1
2
2
2
1
1
1
0
0
1
0
0
1
1
0
2
2
1
0
0
0
1
2
0
0
0
1
1
1
0
1
1
1
0
1
1
0
0
0
0
1
1
2
1
2
0
1
1
1
0
1
0
2
2
1
0
2
0
0
1
2
0
0
1
0
1
2
2
2
2
0
0
1
1
1
1
1
0
1
1
0
0
1
1
0
0
1
0
0
2
1
2
2
1
0
1
2
0
1
2
0
0
1
1
2
0
0
2
0
2
0
0
0
1
1
0
1
0
0
1
0
1
2
0
1
2
0
0
1
1
1
0
1
1
0
0
0
0
1
1
1
3
1
0
2
0
0
0
2
1
0
1
0
0
2
0
0
2
1
1
1
1
0
2
0
2
2
2
0
1
1
0
0
0
1
0
0
1
2
1
2
0
1
0
2
0
0
1
0
0
2
2
2
2
0
1
0
1
1
1
1
0
1
2
2
0
0
1
0
2
2
0
0
0
0
1
2
0
2
1
0
1
0
1
2
0
0
1
1
2
0
0
1
0
1
0
1
1
1
0
0
0
0
2
1
2
0
0
0
0
1
0
2
0
2
1
1
2
2
2
1
2
2
1
1
0
0
1
0
0
0
0
0
0
0
2
1
2
0
0
0
1
1
1
0
2
0
2
2
1
0
0
2
2
1
2
0
1
0
2
1
1
2
0
2
1
2
1
1
2
0
3
0
1
2
1
0
4
1
1
1
1
1
1
1
2
0
1
0
2
2
2
2
0
0
2
0
2
2
2
1
1
1
0
0
1
1
1
0
0
1
1
0
2
0
0
0
2
0
0
0
1
0
1
0
1
1
0
1
2
1
2
1
0
0
1
0
0
1
0
0
2
0
1
0
1
2
0
2
1
0
0
2
2
0
0
2
3
2
1
0
0
2
1
0
2
0
2
2
4
2
1
0
0
1
0
1
0
2
0
0
0
1
2
2
1
1
2
1
4
0
0
0
0
2
1
0
4
0
0
1
0
0
2
0
0
0
1
0
3
0
1
0
1
2
1
1
0
0
0
1
2
0
0
1
3
1
0
0
2
1
0
1
0
0
1
1
2
0
1
0
0
0
1
1
1
1
0
0
0
0
0
0
1
0
2
1
0
0
1
0
0
1
1
2
4
2
1
0
0
0
1
0
2
1
1
1
0
2
0
1
1
1
2
0
0
2
0
1
1
0
0
1
2
1
0
0
1
1
0
1
0
0
2
0
1
0
0
0
1
0
1
0
1
0
1
0
1
0
0
0
2
0
1
0
1
0
2
0
1
0
2
0
0
2
0
4
1
1
2
1
1
2
1
0
1
2
0
2
0
1
1
0
0
0
1
2
2
0
1
1
0
0
0
2
1
0
0
0
2
0
1
1
1
1
0
0
1
1
1
1
2
0
2
1
0
1
2
1
1
1
0
0
0
2
2
1
1
0
0
2
1
1
0
1
0
1
1
0
0
1
2
1
0
1
0
2
0
1
4
2
2
1
2
0
1
0
0
2
1
1
0
1
1
0
1
3
0
1
0
1
1
2
1
1
1
1
0
2
0
1
1
2
1
1
2
2
1
0
2
1
0
0
0
0
1
0
0
1
1
1
1
1
0
0
2
0
2
1
1
0
0
1
0
1
0
0
2
0
0
0
1
2
1
0
1
0
2
2
0
2
0
1
1
1
1
2
1
0
2
1
1
0
0
0
2
0
1
0
0
0
1
1
0
2
2
1
1
2
0
2
2
1
2
0
0
0
0
1
1
0
2
1
1
0
2
1
0
2
0
1
1
0
2
1
2
0
0
1
0
1
1
1
0
2
0
0
14
1
1
0
0
1
0
3
0
2
1
2
1
2
1
0
3
2
0
2
0
1
1
0
2
2
0
1
2
2
0
0
2
4
0
0
1
2
1
0
2
2
2
0
1
1
2
1
0
2
2
2
1
1
0
0
2
0
2
1
2
1
1
1
1
1
0
1
1
1
2
1
0
0
1
0
0
2
1
0
1
0
0
1
0
0
0
0
1
2
0
1
6
0
0
0
0
1
0
0
1
1
1
1
1
0
2
0
0
0
1
0
3
1
0
2
1
0
2
2
1
2
0
1
2
0
2
1
1
1
2
1
0
1
1
1
1
1
1
2
1
0
2
0
1
0
2
0
0
0
2
0
1
2
1
0
1
1
1
2
1
2
1
1
1
2
1
0
0
0
2
2
0
2
1
2
1
0
0
1
0
1
1
0
1
2
0
0
0
2
1
0
1
2
1
1
0
1
0
0
2
3
0
1
0
0
0
2
0
1
0
2
2
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
2
0
2
2
0
2
0
2
0
0
2
0
0
0
1
0
1
2
0
1
1
2
0
0
0
1
0
1
1
0
0
0
0
0
1
1
1
1
0
1
0
2
1
1
0
2
0
1
2
0
1
1
1
0
0
0
0
1
0
1
0
2
0
1
1
0
2
0
0
1
0
2
1
0
0
2
2
0
1
0
1
3
1
2
1
1
1
2
1
0
0
1
1
2
0
1
1
0
1
0
1
2
1
1
0
0
1
2
0
0
0
1
1
1
0
1
0
0
1
0
1
1
0
1
1
0
1
0
0
1
0
5
1
0
0
1
0
0
0
1
1
1
0
2
2
1
0
0
0
1
0
0
2
1
1
2
1
0
0
2
0
1
1
1
2
1
0
0
0
2
2
0
0
0
1
2
1
0
0
1
0
1
0
1
0
0
0
2
1
1
1
1
1
2
2
2
2
0
2
1
1
2
2
0
0
1
0
1
0
0
1
1
1
1
3
1
1
1
0
0
1
0
0
2
0
0
0
1
0
0
0
1
0
0
2
2
1
0
0
1
0
0
1
1
1
1
0
0
0
0
1
2
0
1
0
0
0
0
1
2
1
2
2
0
1
2
3
2
0
2
0
0
1
1
0
0
1
1
2
0
1
0
0
0
2
2
0
0
1
0
1
1
0
0
0
1
1
2
2
0
3
0
1
1
2
0
1
2
0
1
1
1
1
0
0
0
0
0
0
0
2
1
0
0
0
1
1
0
2
0
0
1
1
1
1
2
0
1
0
1
0
2
0
0
1
2
1
0
0
1
0
1
1
0
0
1
0
1
0
1
0
1
0
0
0
0
1
1
1
0
0
0
1
0
2
0
2
0
1
0
0
1
0
1
0
1
0
2
0
2
3
0
2
0
0
4
1
0
1
0
0
1
1
0
1
2
0
1
2
0
0
0
0
2
1
0
2
2
0
2
0
2
2
0
1
0
1
1
0
2
1
0
2
2
0
1
1
1
1
2
1
0
1
1
2
1
1
1
1
1
0
2
1
1
1
0
0
0
4
1
2
2
1
0
3
1
2
0
0
0
0
2
1
1
1
1
0
0
2
1
1
0
2
1
1
0
0
1
1
1
0
1
1
2
2
2
2
1
1
0
1
2
1
1
1
1
0
0
2
2
1
1
1
1
1
1
1
0
1
2
2
0
2
0
0
1
2
0
1
0
1
1
4
1
0
0
1
0
2
0
2
1
0
1
2
2
2
2
1
0
1
0
0
2
0
1
0
1
1
1
2
0
1
2
0
0
1
1
2
2
0
0
1
1
0
3
0
1
1
0
1
1
2
1
1
1
1
0
2
2
1
2
1
0
0
1
2
0
1
1
1
0
1
1
3
1
2
1
1
0
1
0
1
2
2
2
3
2
0
1
1
1
0
1
1
1
1
1
1
0
2
3
2
1
0
1
0
0
2
1
0
0
2
0
1
1
2
3
1
0
0
1
1
1
1
1
1
0
1
1
0
1
2
2
1
1
1
1
1
0
0
0
0
2
0
0
1
0
1
1
1
1
1
2
2
0
0
1
2
2
0
2
0
3
1
1
1
0
0
1
0
1
0
1
2
1
0
1
0
1
0
0
1
1
1
0
0
1
1
1
1
0
1
0
2
1
0
1
1
1
2
1
0
2
0
1
2
0
1
2
0
0
0
0
1
1
1
3
1
1
0
0
1
1
0
1
2
1
0
2
0
2
1
1
0
1
1
1
2
2
1
1
1
0
1
1
1
0
0
1
1
2
1
1
2
1
1
2
1
2
0
1
0
3
0
2
1
0
1
0
0
3
1
1
0
1
0
2
1
0
1
1
0
0
0
2
2
2
2
2
0
2
0
0
1
1
1
1
1
0
0
0
0
1
0
1
2
1
0
0
1
2
1
0
2
0
0
0
1
1
0
0
0
1
1
0
1
0
1
1
0
1
1
2
1
0
0
1
2
0
1
1
1
0
0
1
0
0
2
0
0
2
1
1
1
1
2
0
2
0
1
0
0
1
0
0
2
2
0
2
0
0
0
0
2
0
1
2
0
0
1
0
0
2
1
0
1
2
2
0
1
0
0
0
0
0
2
2
1
0
1
0
1
2
1
0
0
2
0
2
1
2
2
2
0
1
1
2
0
1
0
1
1
0
0
2
1
0
2
1
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
2
1
2
0
1
0
1
0
0
1
0
0
1
2
2
1
1
0
0
0
0
2
1
0
1
0
2
0
0
1
1
0
1
0
1
1
2
1
0
0
1
2
1
0
1
1
2
2
1
2
1
1
0
2
2
0
2
2
1
2
0
1
0
0
1
1
1
0
1
1
0
1
1
2
0
2
1
0
0
0
1
1
2
0
2
2
2
0
0
0
4
0
1
1
1
2
1
1
0
2
1
0
2
1
1
2
0
1
0
1
0
0
2
0
1
0
2
1
1
0
1
2
0
1
1
2
1
1
0
2
0
2
1
0
1
0
1
2
0
2
1
1
1
0
2
2
0
1
0
0
1
1
1
0
1
2
1
0
0
2
1
0
1
2
1
2
2
1
1
1
0
1
0
0
0
0
0
1
2
2
1
0
2
1
0
0
1
0
2
2
1
1
1
1
1
1
1
2
1
1
0
0
1
2
1
0
1
2
2
3
0
0
0
0
0
0
1
1
1
2
0
2
1
1
0
0
0
1
2
0
1
1
0
2
0
1
1
0
2
1
2
1
0
0
1
0
1
1
2
0
1
0
2
1
2
2
1
1
2
0
0
0
0
1
0
1
1
2
1
2
0
1
0
1
0
3
0
0
0
0
0
2
1
2
2
2
1
0
1
0
0
0
2
0
1
0
1
1
0
0
2
0
1
0
0
0
0
1
0
1
0
6
1
0
1
2
0
0
0
1
2
1
0
1
1
0
0
1
0
2
1
0
0
2
0
2
0
1
0
0
0
1
2
0
1
2
1
0
0
0
0
0
4
1
0
2
2
1
1
1
1
1
1
2
0
2
0
1
0
0
0
2
2
0
0
1
0
0
0
1
1
1
0
1
0
1
1
1
2
1
1
0
1
0
2
0
1
2
0
2
2
0
0
0
1
0
2
1
2
1
1
1
1
2
1
2
0
1
2
0
2
0
1
1
2
1
2
1
1
0
1
1
2
1
0
1
1
0
1
1
2
1
1
0
1
1
1
2
0
2
0
0
1
1
1
0
2
1
2
0
0
1
0
1
2
1
1
1
1
1
0
0
0
0
1
2
2
1
0
0
1
0
1
1
2
2
0
2
1
1
2
3
0
1
1
1
0
1
0
0
1
0
0
0
2
1
1
1
0
0
0
0
0
0
1
2
1
2
2
0
0
1
1
0
0
0
1
0
2
2
2
1
0
1
1
2
0
2
0
2
2
1
0
0
1
1
1
0
0
2
0
2
2
2
0
1
5
0
0
0
0
1
1
0
2
0
0
2
0
0
0
0
1
2
2
1
0
1
0
0
0
1
2
1
1
0
1
0
1
0
0
0
1
0
2
1
1
2
2
2
0
1
1
0
0
2
0
2
1
1
2
0
0
1
0
2
0
0
0
2
2
1
0
0
1
1
0
0
2
0
1
2
0
1
0
1
1
2
0
1
0
1
1
1
0
0
2
0
1
1
0
0
0
2
1
1
0
2
0
1
2
0
0
0
1
1
0
0
1
1
0
0
1
1
1
2
0
0
0
1
1
0
2
0
3
1
0
1
1
0
1
2
2
0
2
0
0
1
0
0
0
0
1
1
0
1
2
0
2
1
1
0
1
0
0
0
1
1
0
0
1
0
0
2
0
0
1
1
1
1
0
2
1
0
2
0
0
0
0
2
1
0
0
3
0
0
1
0
2
1
0
2
0
0
2
1
0
0
1
2
1
1
0
0
2
2
1
0
0
2
0
1
1
0
0
0
1
1
0
1
1
1
0
1
1
1
1
1
0
1
0
0
1
1
1
0
1
2
1
1
1
2
1
0
2
1
0
0
0
0
3
1
0
0
0
2
1
2
1
0
0
1
0
1
0
0
1
1
0
1
2
1
1
0
2
0
2
0
0
1
1
2
2
0
2
0
1
1
2
1
0
2
1
1
0
0
0
1
1
2
1
0
1
1
1
0
0
2
0
0
2
0
0
0
1
0
1
2
1
0
1
0
0
0
1
1
1
1
4
0
2
0
0
0
0
2
1
2
1
0
0
1
1
1
0
0
1
2
0
0
1
2
2
0
7
0
1
1
2
0
0
1
1
1
1
2
0
0
0
1
1
0
0
1
1
1
2
1
0
2
2
0
1
1
2
1
0
2
2
1
0
1
1
0
1
0
1
1
0
0
0
1
1
1
1
1
0
0
0
1
2
2
0
1
2
2
0
0
0
2
0
2
1
1
1
0
2
1
2
2
1
0
0
2
2
1
2
0
0
0
1
1
0
3
1
2
0
2
1
0
1
0
0
2
2
1
0
0
2
1
0
1
1
1
1
1
1
1
1
1
0
0
4
0
1
0
1
0
0
1
0
1
2
1
1
2
0
1
1
0
1
1
1
1
1
0
0
0
0
0
2
1
0
0
1
0
1
0
0
0
1
2
1
2
1
2
1
2
0
1
2
0
2
0
0
0
1
0
2
2
1
1
1
0
2
0
1
1
1
0
1
1
0
1
2
0
1
1
0
3
1
0
0
1
2
1
1
0
1
0
1
1
0
2
0
0
1
2
1
0
1
0
1
0
0
2
0
1
1
1
1
1
0
0
1
1
1
1
1
1
1
1
0
0
0
1
2
1
0
1
0
0
2
1
1
1
1
0
0
0
0
1
0
1
1
0
0
0
2
1
1
0
2
2
0
0
1
0
2
0
1
2
0
0
1
2
0
0
1
2
1
0
0
2
2
0
1
0
2
1
0
1
2
1
0
1
1
1
1
2
1
0
1
1
1
1
1
0
1
0
1
2
1
1
2
2
1
1
1
1
2
1
1
2
1
1
0
1
2
2
0
1
0
0
0
2
0
1
1
2
0
0
0
2
1
1
1
1
1
1
2
1
2
0
1
1
0
1
0
2
0
2
2
1
1
2
1
1
2
0
1
1
1
1
0
0
0
1
1
1
0
2
0
1
2
1
2
0
1
0
1
1
2
1
0
1
1
1
1
1
1
0
1
1
1
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
2
0
2
1
1
2
2
0
0
1
2
2
0
0
0
1
1
1
0
1
2
2
1
1
2
2
0
2
0
0
1
1
1
0
1
1
0
2
0
1
1
1
0
0
2
2
0
2
0
0
1
0
0
2
1
0
2
1
0
0
2
0
0
1
0
0
0
1
1
0
0
2
1
3
0
1
1
0
1
0
0
0
1
1
0
0
1
2
1
0
1
1
3
0
0
1
2
1
1
2
2
1
4
0
0
1
1
3
0
1
3
2
1
0
1
0
0
0
0
0
0
2
0
1
0
0
3
0
0
1
1
2
2
0
2
1
1
1
1
2
1
2
0
1
2
0
1
0
0
1
1
1
1
1
1
0
1
2
1
1
1
1
0
0
1
0
1
2
1
1
2
2
2
1
0
2
2
0
2
0
1
0
0
1
1
0
3
1
0
1
1
1
1
2
0
1
0
1
2
0
1
1
0
0
0
0
1
1
1
0
1
1
0
1
0
1
1
0
2
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
1
0
1
0
1
0
0
1
1
2
2
0
0
1
0
1
2
0
1
1
0
2
1
0
1
0
1
2
1
0
0
3
0
0
1
0
1
2
2
1
0
0
2
2
2
1
1
2
0
0
2
1
1
0
0
0
1
1
1
1
2
1
1
1
1
2
2
1
0
0
2
1
1
2
0
0
0
0
0
1
2
0
0
1
2
1
1
1
0
0
1
0
0
1
2
1
1
2
0
2
0
2
1
0
1
0
1
1
0
1
2
1
0
0
0
1
0
0
0
2
2
1
1
0
0
2
2
1
0
2
0
1
0
1
0
2
0
0
1
2
1
1
0
2
2
1
0
2
2
1
0
0
0
0
1
0
2
0
0
1
1
1
1
1
2
2
2
0
1
0
1
2
0
1
1
0
2
0
0
1
0
0
2
0
0
1
0
1
0
1
2
1
1
0
1
2
0
2
0
0
0
1
2
1
0
2
0
0
1
1
2
0
0
1
0
0
2
2
0
0
2
0
1
0
2
0
1
2
2
0
1
1
1
2
2
1
2
0
2
1
2
0
2
1
0
1
0
0
0
0
1
0
1
1
2
1
0
0
1
0
0
0
0
1
1
1
2
1
2
1
1
1
2
1
1
2
2
1
0
0
1
1
2
2
2
1
1
1
0
0
2
0
1
1
2
0
0
0
0
1
0
2
0
0
0
1
0
2
0
2
0
0
0
1
0
0
1
2
1
1
1
1
2
1
0
1
1
1
0
1
0
1
0
1
2
0
0
1
1
0
1
2
1
1
2
0
0
0
0
1
2
0
0
1
1
0
1
1
1
0
2
1
1
0
1
0
2
3
0
0
0
1
2
0
0
2
1
0
0
0
1
2
1
0
1
0
0
2
0
0
0
2
0
0
1
3
1
0
1
1
2
0
0
0
0
1
0
2
2
1
0
2
2
0
0
0
0
0
0
0
1
2
0
1
0
2
2
2
1
1
1
1
1
0
0
0
1
1
1
2
0
0
1
0
1
1
0
0
0
2
2
1
2
2
1
0
1
0
1
0
2
2
1
1
1
1
2
0
0
3
0
0
0
1
0
0
1
2
1
1
2
1
1
1
0
1
0
1
2
2
0
1
0
2
0
1
0
1
0
0
2
2
0
1
0
0
1
1
0
0
0
2
2
2
0
4
3
2
0
1
1
0
1
1
1
2
1
0
0
0
1
1
0
1
1
2
1
1
2
0
0
1
1
0
0
2
0
1
0
0
0
1
2
0
2
0
2
0
1
1
0
0
0
1
1
0
0
0
0
0
1
2
2
1
2
1
0
2
0
1
1
0
2
1
0
0
1
2
5
1
1
2
2
2
1
0
1
2
1
0
1
0
0
0
0
1
2
0
1
0
0
4
1
1
0
0
2
1
2
2
1
0
0
0
1
0
3
2
0
1
2
1
2
0
1
2
1
0
0
0
0
0
1
0
0
1
0
0
1
2
1
0
0
1
0
2
1
1
1
1
2
0
1
1
1
2
2
1
0
2
0
1
0
0
1
0
2
1
2
1
1
0
1
1
0
0
1
1
0
1
0
0
0
0
2
1
2
1
1
0
0
2
0
1
1
0
2
1
0
2
1
2
0
2
1
0
1
2
1
1
1
0
0
0
1
0
0
0
2
0
0
1
0
0
0
2
0
0
2
0
1
0
1
0
1
0
1
1
1
1
0
2
2
0
2
2
1
1
0
1
0
0
2
0
1
1
1
1
0
0
1
1
0
2
2
0
0
1
0
0
2
0
1
1
2
0
2
0
0
0
0
0
0
1
1
1
0
2
0
0
1
2
2
0
1
0
1
2
2
0
2
2
1
0
1
0
1
0
1
1
0
0
2
0
0
0
0
0
0
1
1
0
1
1
1
0
0
1
1
0
2
0
1
1
1
0
0
0
1
1
1
0
1
0
1
1
0
1
0
1
0
0
0
1
0
1
1
2
1
2
0
1
2
0
0
1
0
0
0
1
1
1
1
0
0
1
0
0
0
1
2
1
0
2
0
1
0
1
1
0
0
1
0
2
2
1
1
1
0
1
2
2
1
0
1
0
1
1
5
2
1
1
0
0
0
1
2
0
0
0
0
2
2
2
2
2
0
0
1
2
1
2
2
0
1
1
1
1
1
0
1
0
0
2
1
2
1
1
1
1
1
1
0
2
0
0
2
2
0
0
2
1
1
0
2
1
1
0
1
0
0
0
1
1
1
1
0
1
0
1
2
1
0
1
0
2
1
1
0
0
2
0
1
0
2
0
1
1
0
1
2
0
1
1
1
2
3
0
1
0
2
1
1
1
0
0
0
3
2
1
0
0
2
0
3
0
1
1
1
0
1
1
1
1
1
1
2
1
2
2
0
2
0
2
0
2
0
0
0
1
2
1
1
1
0
0
1
0
1
1
2
1
0
1
2
1
2
1
0
1
1
0
0
2
0
1
1
0
1
1
2
1
3
2
1
1
1
1
1
1
2
1
0
0
1
1
0
2
0
1
2
2
2
0
2
1
0
0
1
0
1
1
1
1
1
1
0
2
1
0
0
1
0
1
1
2
1
1
0
2
1
1
2
1
0
1
0
0
0
1
2
1
1
0
0
0
1
0
0
0
0
2
1
0
2
2
0
1
2
1
1
1
2
0
0
0
1
1
2
0
0
0
0
2
2
0
2
0
2
1
0
0
1
1
1
2
1
1
1
1
1
2
1
0
2
1
0
0
0
0
1
1
0
1
1
0
0
0
1
2
0
2
1
0
0
0
2
0
1
1
1
0
2
0
0
0
0
1
2
0
0
0
0
2
1
0
0
0
0
0
2
0
1
2
1
1
0
1
1
0
0
3
3
0
0
0
0
1
1
2
1
1
1
1
1
0
0
0
1
0
1
1
0
1
1
1
2
1
1
0
2
0
0
2
2
1
1
1
2
1
1
1
1
1
1
1
1
0
1
2
1
0
1
1
0
2
3
0
1
0
2
2
0
2
0
0
0
2
0
1
0
2
1
1
1
0
1
2
0
0
1
2
0
0
1
2
1
2
0
2
0
1
1
2
0
0
0
1
0
2
0
1
1
1
1
1
1
1
2
2
2
0
2
0
1
1
2
1
2
2
0
0
1
3
1
1
1
2
1
2
0
1
2
0
1
1
2
0
0
2
0
0
1
1
0
1
1
1
1
0
0
1
1
2
0
2
1
1
1
0
0
1
0
2
1
1
0
1
1
0
0
2
0
1
1
0
0
0
1
3
0
1
0
2
1
1
1
3
2
1
1
0
2
2
1
0
1
2
0
0
1
2
2
0
1
1
3
2
0
2
0
0
2
0
0
1
2
1
2
1
0
1
1
2
0
0
1
0
0
0
1
0
0
0
1
1
0
0
1
1
0
1
1
0
0
0
1
2
2
1
0
2
2
1
1
0
2
0
0
1
1
0
0
1
0
1
0
3
0
1
0
0
1
2
0
0
3
1
0
0
1
0
0
1
0
0
0
2
0
2
1
0
1
1
0
2
2
0
0
1
2
0
1
2
0
0
2
0
1
1
0
1
2
1
0
1
2
1
0
1
1
0
2
1
1
1
2
0
1
1
1
0
0
2
0
0
1
2
1
1
0
2
1
1
1
0
2
1
1
0
2
1
1
0
1
2
0
0
1
1
2
0
1
2
0
1
1
1
1
2
0
1
1
0
1
1
2
0
1
0
0
0
1
2
0
0
1
0
2
0
0
0
1
0
0
0
0
1
1
2
0
0
2
0
0
0
1
0
2
0
2
1
1
1
1
1
1
1
1
1
1
0
2
2
1
1
2
1
0
1
0
0
1
0
1
2
2
0
0
1
0
0
2
0
1
0
1
1
1
2
0
1
1
0
0
2
0
2
1
0
0
1
0
0
1
1
0
2
0
0
3
1
2
0
1
2
1
1
0
1
0
3
2
4
0
0
2
1
0
0
0
2
2
0
0
1
1
2
1
2
1
1
1
0
0
2
0
3
2
2
0
1
0
1
0
2
1
1
1
2
0
0
1
0
2
0
1
0
2
1
0
2
0
1
1
0
2
2
2
0
2
0
0
0
0
1
2
2
1
0
0
2
0
0
0
0
2
0
2
0
1
0
1
1
1
0
0
0
0
1
1
0
1
1
1
0
1
1
0
0
1
2
1
0
1
0
1
0
0
0
0
2
1
2
0
1
0
0
0
1
2
0
0
0
0
0
2
0
1
0
1
0
1
0
2
1
1
1
0
3
2
2
1
2
0
3
1
2
1
2
1
0
2
2
1
1
0
0
0
2
0
2
1
2
1
0
1
0
1
1
0
0
2
0
1
1
0
1
1
2
1
1
3
0
1
0
2
1
2
0
0
1
1
1
2
1
2
2
1
0
1
1
1
2
1
0
2
0
1
1
2
3
0
2
0
1
1
0
2
0
1
2
0
0
1
0
1
0
1
2
2
0
0
2
1
1
2
1
0
1
2
1
1
1
0
1
1
1
2
0
1
1
0
2
2
1
0
0
0
0
1
2
0
0
0
1
2
1
1
0
1
2
1
0
1
1
1
2
2
0
1
2
0
1
1
0
0
2
0
0
2
0
0
1
1
0
1
0
0
0
2
1
1
0
0
0
0
3
1
1
1
2
0
0
0
1
1
2
1
0
0
0
2
1
1
2
0
2
1
0
0
1
1
1
0
1
2
2
1
1
0
1
2
2
3
1
0
2
2
2
0
1
0
0
1
0
1
0
2
0
0
0
0
0
2
0
2
0
1
0
0
2
1
1
1
1
2
1
0
0
2
0
1
0
3
4
0
2
1
1
1
2
1
2
2
0
1
2
1
0
1
0
1
2
2
0
0
1
0
2
2
0
0
0
0
0
0
0
1
1
1
2
0
2
0
0
1
1
0
2
2
1
1
2
1
1
0
1
2
2
1
1
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
2
1
0
0
1
1
0
0
1
1
0
1
0
0
2
1
0
1
1
2
0
1
3
0
1
0
0
1
2
0
0
1
2
2
0
2
2
2
0
0
0
1
2
0
1
3
0
1
2
1
1
1
1
2
2
0
1
2
1
0
1
1
0
2
0
0
0
2
0
1
0
2
1
2
1
1
1
1
1
1
1
1
0
1
0
1
0
0
0
2
2
1
1
0
0
0
0
0
1
1
1
2
1
0
1
0
1
0
1
1
0
2
0
0
1
0
2
0
2
2
0
1
0
0
1
0
1
0
0
1
2
0
1
1
1
1
0
0
2
2
1
0
1
0
0
1
0
0
0
0
2
0
0
0
0
1
1
2
0
2
0
0
2
1
0
1
0
1
0
1
1
0
2
1
2
1
1
1
1
0
0
0
0
1
0
0
0
1
0
2
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
1
0
1
0
0
0
3
2
1
0
2
1
1
2
0
1
0
1
2
2
0
2
2
1
2
0
0
2
1
0
0
2
2
0
1
2
2
0
1
0
0
0
2
2
0
1
1
2
2
1
0
0
0
0
0
1
0
0
1
0
0
0
1
2
0
0
1
1
2
1
1
1
2
0
0
0
1
1
1
0
2
1
2
2
0
1
0
2
1
0
2
1
1
1
0
1
0
1
1
1
1
3
2
0
0
1
0
1
0
2
2
1
1
1
0
1
2
1
0
2
1
1
1
0
1
1
0
0
1
2
0
2
1
0
0
0
0
0
0
0
1
0
0
1
2
0
2
1
1
1
2
1
2
2
0
2
1
0
1
0
1
0
1
0
2
2
1
1
1
0
0
1
1
1
1
1
1
0
2
1
1
1
1
1
0
0
1
1
1
1
0
0
0
2
1
0
0
0
1
2
1
0
0
0
2
0
0
0
1
2
0
0
2
0
1
0
1
0
0
2
2
2
1
1
2
1
0
0
1
0
1
1
1
0
2
1
2
1
0
0
1
1
1
1
0
0
0
1
0
1
0
2
1
1
0
0
2
1
0
1
2
1
1
0
2
0
2
0
1
0
0
1
1
1
0
2
1
0
2
1
0
2
2
0
0
0
1
0
2
2
0
0
1
1
0
1
0
0
2
1
2
1
1
1
1
1
2
1
0
0
0
0
1
2
1
2
0
0
2
1
1
2
0
0
2
2
0
1
0
2
1
2
2
0
0
1
0
1
1
0
1
4
1
0
0
2
0
2
1
0
1
3
0
1
0
0
0
1
0
1
1
1
0
0
1
2
1
0
0
1
1
0
1
1
1
1
1
1
1
2
1
3
1
1
2
2
0
1
0
1
1
2
0
0
0
1
1
1
0
1
0
2
2
1
0
1
1
2
2
3
1
0
2
2
0
1
2
0
2
2
1
0
1
0
2
1
0
0
0
1
1
1
1
0
1
1
2
1
2
1
0
0
1
2
0
1
1
0
1
1
0
2
1
2
1
2
1
1
1
1
0
0
1
2
1
2
0
2
0
0
0
0
1
0
0
2
0
2
1
1
2
3
2
0
0
0
2
0
1
2
0
2
1
2
2
0
1
0
1
2
0
1
2
0
0
2
2
1
0
0
1
0
0
2
0
1
0
2
0
1
1
1
1
0
0
1
0
1
2
0
0
0
0
1
2
0
2
1
0
2
0
1
0
2
1
0
1
0
1
1
2
2
0
2
0
0
0
0
0
1
1
1
0
1
0
0
1
0
0
0
0
0
0
1
2
2
2
0
2
0
1
0
0
1
2
1
0
1
1
0
1
1
0
0
1
1
0
2
1
0
1
1
2
1
0
2
0
0
1
2
2
1
1
0
1
1
0
0
0
1
0
2
0
1
2
1
1
1
1
0
0
1
3
1
1
0
0
0
1
1
2
0
0
2
1
0
0
0
1
1
1
2
2
0
1
0
1
1
1
1
2
1
1
0
2
1
1
1
2
1
1
0
1
1
2
0
2
1
1
1
0
1
1
1
2
0
1
0
1
0
0
0
0
2
1
1
1
1
1
0
0
0
1
1
0
1
0
1
2
1
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
1
1
0
5
1
1
0
2
0
1
0
0
2
0
2
2
1
1
0
2
1
1
0
0
2
0
2
1
0
1
1
2
1
0
0
1
0
0
0
1
2
0
1
1
0
0
1
0
0
0
1
0
0
2
0
1
2
2
1
0
1
1
2
1
2
0
1
1
1
0
0
1
1
2
0
0
0
0
0
1
1
1
1
0
0
1
0
2
1
2
2
2
0
1
2
0
0
5
0
0
2
2
2
0
0
0
0
0
2
0
0
1
2
0
1
1
2
0
1
0
2
1
0
0
0
0
0
2
1
0
0
0
2
1
0
1
0
0
0
0
0
1
0
0
1
1
0
2
1
0
0
0
0
2
2
2
1
1
0
0
2
1
1
0
2
0
1
0
0
0
0
0
1
1
1
0
2
1
2
1
2
0
0
2
2
1
1
0
2
0
0
1
0
0
0
1
1
1
1
1
2
0
0
1
1
0
1
2
1
0
0
1
0
0
0
0
0
2
1
1
1
1
1
1
2
0
1
2
2
0
1
1
2
1
0
0
0
1
1
1
2
0
0
2
0
0
0
2
0
0
1
2
1
0
1
0
2
1
0
0
0
1
2
0
0
0
0
0
2
1
0
1
2
1
1
0
0
2
1
0
0
1
0
2
1
1
0
1
2
1
2
0
0
1
1
0
0
0
0
1
2
0
1
0
0
0
2
2
2
0
1
0
0
1
1
1
0
1
2
0
2
1
2
2
2
1
1
1
2
1
2
2
0
0
1
2
1
0
1
2
0
4
1
2
0
1
2
0
0
2
1
0
1
2
1
0
0
1
0
2
1
0
1
0
0
0
0
2
0
2
1
1
0
2
0
0
0
1
1
1
0
0
1
1
0
0
0
2
1
0
1
0
1
0
0
0
0
0
2
0
1
0
0
2
1
1
2
2
2
2
0
0
1
1
1
1
2
2
1
0
1
1
0
0
0
1
1
0
2
0
0
2
1
1
1
0
0
0
0
1
1
0
1
0
0
1
1
0
1
2
2
0
2
2
2
1
2
1
1
1
0
0
0
1
1
2
0
1
0
3
1
2
0
1
2
1
0
2
0
1
1
0
2
0
0
0
0
2
1
2
0
0
0
2
0
0
0
1
0
0
1
1
0
1
3
0
1
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
2
0
1
1
0
0
3
0
0
1
1
1
0
1
0
0
2
2
1
1
1
0
0
0
0
1
0
1
2
2
1
1
1
1
1
2
1
0
1
1
0
1
1
0
1
0
1
1
2
0
0
1
0
1
0
2
2
1
2
2
1
1
0
2
0
0
1
0
0
2
0
4
0
0
1
1
0
0
0
1
3
1
1
0
1
2
1
1
1
1
3
2
1
1
2
0
2
0
0
0
1
1
0
2
1
0
1
1
0
0
0
1
0
1
1
0
0
1
0
0
1
2
3
0
0
1
1
1
0
0
2
1
0
1
0
0
0
1
1
2
0
1
0
2
1
2
2
1
0
1
1
0
0
1
0
2
1
0
0
0
1
1
2
2
1
1
0
0
0
2
0
0
2
1
1
0
0
0
0
0
2
0
2
0
2
0
0
1
0
0
2
1
2
1
1
0
0
1
2
2
1
2
0
0
1
1
1
1
0
1
2
2
1
2
0
1
0
0
1
1
1
2
0
2
0
1
0
2
0
0
1
0
1
0
2
0
1
1
1
0
1
2
0
0
1
0
1
1
0
2
1
0
0
0
1
1
1
2
1
0
1
1
1
0
1
2
1
0
2
2
2
0
0
1
1
0
0
1
2
1
2
0
1
2
1
0
2
2
0
0
1
2
1
3
0
1
1
2
0
0
0
3
0
2
0
1
1
0
1
1
1
1
1
1
1
1
0
0
1
1
0
0
2
0
2
1
1
1
1
2
1
1
0
0
2
1
2
0
0
0
2
0
0
2
1
0
1
0
1
1
2
0
1
1
0
1
0
1
0
1
0
0
1
0
1
1
2
2
2
1
9
0
1
1
0
1
0
0
1
0
0
1
0
0
1
0
1
0
0
0
2
2
0
1
1
0
1
0
2
1
1
1
0
0
1
2
0
1
1
2
1
0
0
2
1
2
1
1
3
1
0
1
2
0
1
0
0
1
0
1
1
0
0
2
2
0
0
0
1
1
0
1
1
0
1
2
1
0
0
1
1
1
1
2
2
1
1
0
1
1
1
2
0
2
1
1
0
1
0
1
0
0
1
0
0
1
1
1
1
1
2
0
2
2
1
1
0
1
1
1
2
2
0
2
1
0
1
1
1
2
0
1
2
0
0
0
0
1
1
0
1
2
2
2
0
0
0
1
1
0
0
1
2
2
1
1
2
0
0
2
0
1
1
0
1
2
1
2
2
2
0
2
2
1
1
3
2
1
1
2
1
2
2
2
1
1
0
2
0
0
0
1
2
2
1
1
0
1
1
0
1
0
0
0
1
0
0
0
2
0
0
1
1
1
1
1
1
2
2
0
1
1
3
1
0
1
1
0
2
2
1
0
0
0
1
1
1
3
2
2
2
1
1
2
0
2
1
0
1
2
0
1
0
0
0
2
0
0
1
1
0
1
0
0
2
1
0
0
2
0
2
1
0
0
2
1
1
0
6
0
0
0
1
0
0
2
2
1
4
1
1
2
0
1
1
0
1
2
2
0
2
2
0
1
1
0
1
1
2
1
1
1
1
0
1
1
1
0
2
0
2
0
0
1
1
0
1
0
0
0
2
1
0
0
0
1
2
2
0
1
1
1
2
2
0
2
1
1
1
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
2
1
0
1
0
1
0
1
1
0
1
0
0
1
2
1
1
0
1
2
2
0
1
2
0
0
2
1
1
1
2
0
2
1
2
2
3
1
1
0
1
1
0
2
0
1
0
1
0
0
0
1
2
1
1
1
0
0
1
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
2
1
2
0
0
0
0
2
0
2
0
1
3
0
0
2
0
2
1
0
1
1
1
0
0
1
1
0
0
1
2
1
2
1
2
2
0
1
0
2
1
1
1
2
0
0
1
1
0
0
2
0
0
1
0
1
1
0
2
0
0
0
0
3
0
0
0
0
2
1
2
0
2
1
1
2
1
0
1
2
1
2
0
1
1
0
2
0
2
1
0
0
0
0
0
0
1
2
0
1
0
1
1
2
1
0
0
0
0
1
1
2
2
1
3
0
1
1
0
1
2
0
1
0
0
1
1
2
1
0
1
2
1
2
1
0
1
0
0
4
1
0
0
2
1
2
1
2
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
1
1
0
1
1
1
1
1
1
4
3
0
1
1
2
1
1
0
1
0
1
1
1
1
1
2
0
2
1
2
0
1
0
0
2
0
2
2
0
0
2
1
0
1
1
2
2
0
0
0
0
2
1
2
2
0
0
1
1
1
0
0
3
1
0
0
1
2
2
1
0
1
2
0
1
1
0
1
4
1
1
1
0
1
0
1
1
0
0
2
1
3
1
2
1
0
2
0
1
1
1
1
2
0
0
1
0
0
2
1
2
1
1
0
0
2
1
0
1
1
0
1
0
0
2
1
1
1
2
1
0
1
0
1
0
1
1
1
2
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
2
2
1
2
0
0
1
2
1
1
0
0
1
1
0
0
1
0
2
0
0
0
2
1
1
2
1
0
0
0
2
0
0
2
2
0
0
1
1
1
2
0
2
3
2
1
1
0
1
2
1
0
1
1
0
0
1
1
1
2
1
1
1
0
3
0
0
1
0
0
1
1
2
2
1
1
1
1
0
1
2
1
1
0
0
0
0
1
0
1
1
0
1
0
0
1
0
1
0
0
1
1
2
1
0
1
1
2
1
0
0
0
0
0
0
1
1
1
0
0
0
1
0
1
1
0
0
1
1
0
0
0
1
1
0
2
1
1
0
0
1
1
2
0
1
3
0
0
2
2
0
0
0
0
1
0
0
0
1
1
2
1
0
2
0
2
2
2
1
1
1
2
2
1
1
1
0
0
1
0
2
0
1
1
0
1
0
1
1
0
2
1
0
0
1
1
1
1
0
0
3
1
0
0
2
2
0
1
1
1
1
1
1
0
1
0
1
1
0
0
1
1
0
0
0
1
0
2
2
0
0
1
0
2
4
0
1
0
1
2
0
0
0
0
1
2
1
2
1
1
1
1
0
2
1
2
1
0
2
2
1
0
0
0
1
1
0
0
1
0
1
1
1
1
0
2
2
0
1
0
2
0
0
2
0
1
1
1
0
1
0
2
0
1
0
1
0
0
3
1
1
0
1
1
0
1
1
1
0
0
2
1
0
2
1
2
0
1
1
0
2
1
0
1
2
1
1
0
0
0
2
1
1
2
0
1
1
2
0
1
0
1
1
0
1
2
1
2
1
0
0
1
1
0
0
1
2
0
0
1
2
1
2
2
1
0
0
0
0
2
0
1
1
0
2
1
0
2
0
0
0
2
0
1
0
1
1
0
0
0
0
2
0
0
1
1
2
1
2
0
2
2
0
1
2
1
2
2
2
1
0
3
2
1
1
0
2
1
0
1
1
1
2
0
1
0
0
1
1
2
2
1
1
0
2
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
1
0
1
1
2
0
0
2
1
3
0
1
0
1
2
0
0
1
0
1
2
0
0
1
1
1
0
1
1
0
1
2
0
1
1
0
1
0
2
1
1
0
0
0
0
0
1
1
1
0
2
2
1
1
0
1
1
1
2
2
0
2
2
0
2
0
1
1
2
0
1
1
1
2
0
1
0
2
0
1
0
0
1
0
1
2
1
2
0
0
1
1
2
2
0
0
0
1
1
0
1
2
0
1
2
1
1
0
1
0
0
2
1
2
1
2
0
0
0
1
2
1
0
2
0
1
1
0
0
0
2
0
0
0
0
1
0
2
1
1
1
3
1
0
2
2
1
1
0
0
2
1
1
0
1
0
1
0
2
1
0
0
1
1
1
2
0
1
1
1
0
0
1
2
0
1
2
1
0
0
1
1
2
0
0
1
1
2
0
0
2
1
0
0
1
1
0
1
1
0
1
0
0
1
2
0
1
1
1
0
1
0
1
1
2
2
2
0
1
1
1
2
1
0
0
0
1
0
0
0
1
0
2
0
1
0
1
1
0
0
2
0
2
0
2
1
1
4
0
2
1
0
1
1
1
0
1
2
0
0
0
0
1
1
0
1
2
0
0
0
0
0
0
1
0
1
2
1
0
0
2
0
1
2
0
0
0
2
1
0
1
2
0
0
0
1
2
1
2
1
1
0
0
0
0
0
2
1
1
1
0
2
0
1
0
1
0
0
1
0
0
1
1
1
0
1
0
1
0
2
4
2
2
1
0
1
0
1
0
1
1
1
1
1
1
3
2
1
0
1
0
1
1
1
2
0
0
1
2
0
1
2
0
0
2
2
0
0
0
1
1
0
0
0
1
0
1
2
0
1
0
1
0
1
0
1
2
0
1
2
1
2
0
0
2
2
2
0
3
3
2
2
0
0
1
3
1
0
1
0
1
2
2
1
3
1
1
2
2
1
0
1
0
0
1
1
2
2
2
2
2
2
1
1
2
1
0
0
0
0
2
0
0
1
0
2
0
1
0
1
2
2
1
0
1
2
1
2
0
1
1
1
2
1
0
1
0
0
1
1
1
0
0
1
0
1
2
0
1
0
2
2
0
3
1
9
1
0
1
1
1
0
1
2
3
0
0
1
0
2
2
1
1
2
2
0
2
0
1
2
2
1
1
1
1
1
0
1
1
0
0
2
0
0
1
1
1
1
1
0
0
1
0
1
2
2
1
2
0
1
1
0
1
1
1
0
1
1
2
1
0
0
0
0
1
0
1
2
1
0
0
0
1
0
0
0
0
1
1
2
1
0
0
1
0
2
0
0
0
0
0
0
0
0
1
1
0
2
0
1
2
1
0
3
0
0
1
1
1
1
0
1
0
1
0
1
0
0
2
0
2
1
0
1
0
1
0
1
0
1
0
1
0
0
1
1
2
2
1
0
0
1
0
0
2
0
1
0
1
0
2
0
1
1
1
1
0
0
1
1
1
1
1
0
1
0
1
1
1
0
2
0
2
1
2
2
1
2
1
0
0
1
1
1
1
0
0
1
2
0
1
1
2
1
0
0
0
0
1
1
0
1
2
1
1
1
0
1
0
2
1
0
1
0
1
0
0
0
1
1
0
1
0
1
2
1
1
0
1
0
1
0
1
3
0
1
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
2
0
0
0
2
0
0
1
1
0
1
1
0
1
1
2
0
1
2
2
1
1
1
0
0
0
0
1
1
0
2
3
2
1
1
1
2
0
2
1
1
2
0
0
2
0
0
0
0
1
2
0
1
0
1
2
0
2
2
1
2
0
1
0
0
0
2
1
1
1
0
1
0
2
1
0
1
2
0
0
2
0
2
0
0
0
0
1
2
0
0
1
1
2
0
1
0
2
1
0
0
2
1
1
0
2
1
0
0
1
0
0
1
1
0
0
1
1
1
0
1
1
0
0
1
1
2
1
1
0
0
1
0
1
2
2
1
1
1
0
0
0
1
1
0
1
0
0
1
0
0
0
2
2
0
1
1
1
2
0
0
2
0
1
1
2
1
1
0
2
0
0
1
1
0
1
1
0
1
3
1
0
1
2
1
1
0
1
1
2
0
0
0
0
1
1
0
1
1
0
0
0
1
1
2
0
0
2
1
0
0
1
1
2
1
1
0
2
0
2
1
1
2
0
1
2
2
1
1
2
0
1
0
2
0
1
1
1
2
0
1
0
1
0
0
2
0
1
1
0
1
1
0
1
1
1
0
4
0
0
2
1
0
0
0
1
0
0
1
0
0
5
0
0
0
1
0
0
1
0
2
2
1
2
1
0
1
0
0
0
1
0
1
1
0
2
2
2
1
1
0
0
0
1
1
2
2
1
0
1
0
0
1
2
1
1
0
2
0
2
2
1
0
0
2
1
1
0
1
0
2
2
1
0
2
0
2
2
0
1
1
1
2
2
0
1
1
0
1
1
0
2
0
1
2
1
2
0
2
1
1
0
1
1
1
1
1
2
2
1
0
1
0
1
1
2
2
0
0
0
0
1
0
0
1
0
0
1
0
0
2
0
1
2
0
2
1
2
3
0
0
0
1
1
0
0
0
2
0
3
2
1
1
1
1
0
1
0
1
0
0
2
1
2
1
0
1
2
0
0
2
2
0
0
2
0
2
1
0
2
0
2
2
0
2
1
1
0
0
2
0
2
0
1
0
1
1
1
0
1
1
1
0
0
0
1
0
1
0
1
1
2
0
1
0
1
1
2
3
0
1
2
0
0
1
1
2
0
1
2
1
0
1
0
1
1
2
0
2
2
1
1
1
2
2
0
2
0
2
0
2
2
0
1
0
0
0
2
0
1
0
1
0
0
1
0
2
2
1
0
2
0
1
2
2
0
0
2
0
1
0
2
3
1
0
1
0
0
0
1
1
0
0
0
3
0
0
2
1
1
1
1
3
2
2
0
0
1
0
2
2
1
1
0
0
0
3
1
1
1
2
1
2
0
0
0
2
2
0
1
3
1
2
2
0
0
1
2
1
1
0
0
2
0
1
0
1
2
2
1
0
3
1
1
0
1
1
2
2
1
2
0
1
1
1
0
1
0
1
1
0
1
1
0
1
1
0
1
0
0
2
1
1
2
0
0
3
0
0
1
1
0
2
3
1
2
0
0
0
1
2
1
1
1
1
2
1
1
2
1
0
1
0
1
0
0
1
2
0
0
0
1
2
0
1
0
1
1
0
2
0
2
1
2
1
2
1
0
2
1
1
1
0
0
0
0
2
1
0
3
0
0
0
0
1
1
1
1
2
0
0
2
0
0
2
0
0
2
2
2
1
1
0
1
1
2
1
1
0
1
0
3
2
0
0
1
0
0
1
0
1
0
0
1
0
0
0
2
1
1
2
1
1
0
0
1
1
1
1
1
1
1
2
2
0
0
1
0
2
1
0
2
1
1
1
1
1
0
0
1
1
2
1
1
0
2
1
1
1
1
1
1
1
1
0
2
2
2
0
0
1
0
2
0
1
1
0
1
0
2
2
0
1
2
1
2
0
1
0
2
1
2
0
0
0
0
1
1
1
1
2
2
0
0
1
2
0
1
1
2
1
2
0
0
1
0
2
2
0
2
0
0
0
1
3
2
1
0
1
1
2
1
0
1
0
0
2
1
0
0
0
0
0
1
1
1
1
2
0
0
1
1
0
0
0
1
0
1
2
0
0
1
0
1
0
1
2
0
0
1
7
1
1
1
0
3
1
1
0
0
0
1
0
0
1
0
0
2
1
3
0
0
1
2
1
0
1
0
1
1
0
2
2
1
1
1
2
1
0
2
1
0
0
0
0
1
2
0
0
1
1
1
1
2
1
1
0
1
0
0
1
1
1
2
1
0
0
0
0
0
2
0
1
0
0
0
0
2
2
0
0
2
1
0
1
1
2
0
1
1
0
1
0
1
0
1
2
2
3
0
0
0
0
2
1
0
2
0
0
2
3
1
0
0
2
0
2
1
0
0
0
1
0
1
0
1
1
1
1
0
0
1
2
0
1
1
0
1
0
2
2
3
0
0
2
2
0
2
0
0
1
0
2
0
2
1
1
0
0
0
0
0
0
1
1
2
1
0
0
0
1
0
1
0
3
0
0
0
1
1
0
0
2
0
2
0
2
2
0
1
3
2
1
0
2
0
1
1
2
2
0
2
0
2
0
2
0
2
2
0
0
0
0
0
0
1
2
1
0
1
1
2
1
0
0
1
0
1
2
1
0
1
2
2
0
5
1
0
1
1
1
1
1
0
1
1
0
1
0
0
1
0
0
1
0
0
0
1
2
2
1
0
0
0
0
0
0
0
0
1
0
0
0
2
1
1
2
2
1
1
0
0
0
1
2
1
1
1
2
2
2
1
2
1
0
3
3
1
0
1
1
1
1
0
0
1
2
1
0
3
2
0
0
1
0
0
0
1
2
0
0
1
0
1
1
2
1
6
1
2
0
1
0
0
2
0
2
0
1
1
1
0
1
1
2
0
0
3
1
1
0
0
0
2
0
2
1
0
2
0
0
1
0
0
0
0
1
1
1
0
3
0
0
0
1
1
1
1
0
2
1
0
0
1
2
1
1
0
1
0
1
2
0
2
1
1
1
2
0
2
0
0
0
1
1
2
0
2
2
0
0
1
0
0
0
1
0
3
0
2
1
0
0
0
2
2
1
0
1
0
0
1
2
1
0
1
2
1
0
1
1
1
1
0
1
0
2
0
0
2
3
0
1
2
0
3
2
0
1
1
0
2
2
2
3
2
0
0
2
1
1
1
1
1
2
1
0
1
1
2
2
0
1
2
1
2
0
0
1
2
0
0
2
2
1
0
2
2
0
0
0
1
0
1
0
0
1
1
1
1
2
2
2
2
1
1
0
0
1
0
0
2
1
1
0
5
0
1
1
1
0
2
0
1
1
1
1
1
0
0
2
2
0
0
0
0
1
0
0
2
1
0
0
1
1
0
2
1
1
1
2
1
1
0
0
2
1
0
1
2
0
1
2
0
0
0
1
1
0
0
0
1
0
1
0
1
1
0
0
0
1
0
1
2
2
0
0
0
1
3
1
3
0
2
0
1
0
2
0
0
0
0
1
0
0
3
1
1
0
1
0
0
2
1
0
0
1
0
0
0
2
2
0
0
0
0
2
1
2
0
1
0
1
1
0
2
2
2
0
1
1
2
2
1
2
0
2
1
0
1
2
1
1
0
0
1
1
0
1
2
2
1
2
0
0
0
2
2
1
2
2
3
0
2
1
2
1
1
2
0
1
0
2
1
1
2
0
1
1
0
1
2
0
1
0
2
1
2
0
0
2
0
2
0
0
0
1
0
0
0
1
1
2
1
1
1
1
0
0
1
1
0
2
2
1
2
4
1
0
2
1
0
0
0
0
1
1
1
0
1
0
0
0
2
0
0
1
0
1
1
1
1
0
1
1
1
2
1
0
1
0
4
0
2
0
2
1
0
0
1
0
1
1
0
1
1
0
0
0
1
0
1
1
2
0
2
0
1
0
0
2
1
1
0
1
0
2
0
0
0
1
3
1
1
0
2
2
2
2
2
1
1
0
0
2
1
2
0
1
1
0
3
2
1
1
0
1
2
2
1
2
0
1
0
2
0
1
1
0
0
0
0
1
1
1
1
1
1
0
1
0
1
2
0
0
1
2
1
1
1
0
1
1
1
0
1
0
0
2
2
0
0
0
1
1
2
1
2
0
1
1
1
0
2
1
0
0
0
2
0
1
0
2
0
2
1
0
0
3
1
0
0
1
0
0
0
0
0
1
0
0
1
1
1
3
2
1
1
0
0
2
0
0
0
1
1
0
2
1
0
0
2
0
2
0
0
0
0
1
2
0
0
2
2
0
0
0
2
1
0
0
2
0
1
1
2
0
0
1
1
2
0
0
0
0
1
0
1
1
0
1
0
1
1
1
1
1
1
1
2
0
1
0
1
0
2
0
0
3
1
1
2
2
1
0
1
2
0
2
0
2
0
0
0
2
0
1
0
1
0
0
1
2
0
0
2
2
2
0
2
0
0
0
0
0
0
0
0
1
1
0
1
1
1
2
1
0
1
1
1
0
2
0
0
1
1
0
1
0
2
2
0
1
2
2
0
1
2
0
0
2
1
0
1
2
2
1
1
2
0
1
1
0
0
0
0
1
0
3
2
0
0
3
2
1
1
1
0
1
1
0
1
1
0
2
0
0
0
1
1
3
2
1
1
2
0
1
1
1
0
1
0
2
1
1
0
1
1
1
1
0
2
1
0
2
1
1
2
2
0
1
1
1
1
0
0
2
1
2
0
1
1
2
0
1
1
2
0
1
1
0
0
1
0
1
2
0
1
1
0
1
1
0
2
0
1
0
1
2
0
0
2
2
0
1
0
0
1
0
1
1
2
2
0
1
2
1
2
0
0
0
0
0
2
0
1
0
1
0
0
2
0
0
1
1
0
2
1
2
0
0
1
1
0
1
2
1
1
1
2
1
1
0
0
0
1
2
0
1
2
0
0
0
0
0
0
2
1
0
2
1
2
1
0
1
0
0
0
0
1
2
1
0
1
1
2
2
0
1
1
0
0
0
0
2
0
2
1
3
1
0
1
1
1
3
1
1
0
1
0
1
2
0
0
1
2
0
0
1
0
1
1
0
0
2
1
2
1
0
0
0
2
0
1
0
0
1
0
0
2
1
2
0
0
2
0
0
2
1
0
0
1
1
1
0
0
1
0
0
2
1
1
2
0
2
0
0
0
2
1
1
1
0
2
2
0
0
2
2
3
1
0
1
1
1
2
1
0
1
0
2
1
0
0
1
0
2
2
1
2
0
1
1
0
0
2
1
1
0
0
1
1
2
2
0
2
2
0
2
2
0
0
0
0
2
1
1
1
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
2
1
0
0
0
1
1
0
1
0
1
2
0
0
1
0
0
2
0
1
1
2
1
2
0
2
1
0
2
1
0
0
1
1
2
0
1
1
1
1
2
1
1
1
2
1
2
1
0
1
0
1
0
0
0
1
1
1
2
0
0
0
2
0
0
0
1
1
0
1
1
2
0
1
2
1
2
0
1
0
0
0
1
1
0
2
2
2
1
0
0
0
0
1
1
0
1
2
0
1
0
0
1
0
0
0
1
0
1
2
2
1
1
1
0
1
0
1
4
0
1
0
1
2
1
2
0
1
2
0
1
1
1
1
2
1
1
0
1
2
0
0
0
1
0
0
0
0
1
1
1
1
1
3
2
1
1
1
0
3
0
1
1
0
2
0
0
1
0
0
1
0
0
1
1
0
1
0
1
2
0
0
1
0
2
0
1
2
1
0
1
0
2
0
2
2
0
0
2
1
0
1
2
2
0
2
2
0
0
0
1
2
1
1
1
4
2
1
0
2
0
1
0
1
0
1
2
0
0
0
0
0
0
0
1
1
1
2
1
1
2
0
0
0
7
0
0
2
2
2
0
0
0
5
0
1
0
1
2
0
1
2
1
0
1
1
0
1
0
1
0
0
0
0
1
2
2
1
1
2
1
1
1
0
0
1
2
1
0
2
1
1
0
2
1
2
0
0
2
0
3
0
2
1
1
1
2
1
2
0
0
1
0
1
1
2
1
1
1
0
0
1
1
0
0
0
0
1
2
0
0
1
2
0
1
0
2
0
1
1
1
0
2
0
2
1
1
1
0
4
0
2
1
1
0
1
1
0
1
2
1
0
0
0
1
0
2
0
2
1
2
2
1
0
1
2
1
0
1
0
3
1
0
1
2
0
1
1
1
1
0
1
1
0
0
0
0
1
0
0
1
0
1
1
0
1
0
0
0
2
0
0
1
2
0
1
1
1
1
2
2
0
1
0
0
0
0
0
0
1
2
1
2
2
0
1
1
2
2
2
0
0
2
1
1
1
1
1
1
2
0
1
1
1
2
0
0
2
1
1
1
2
0
0
1
1
0
0
2
1
0
0
0
1
1
1
1
2
1
1
0
0
0
1
1
1
2
1
2
2
0
0
2
0
2
1
0
1
2
0
0
2
0
1
0
1
0
1
1
1
0
1
2
0
1
0
2
0
2
0
0
0
2
2
2
1
1
2
0
0
1
0
1
0
2
2
1
0
1
0
2
1
1
0
0
1
1
0
0
2
0
1
1
0
0
2
2
1
0
2
1
0
0
0
0
3
0
1
2
2
2
0
1
0
2
1
0
0
2
1
2
0
0
0
0
0
1
0
0
1
0
2
1
0
1
0
0
2
1
0
2
1
1
0
2
2
1
0
2
2
1
0
2
1
0
0
1
2
2
0
0
0
1
1
1
2
0
1
0
1
3
2
2
0
0
1
1
1
2
0
2
1
1
0
0
1
0
2
0
0
2
2
0
1
1
1
0
0
0
0
0
0
0
1
1
1
0
2
0
1
1
0
0
1
0
1
2
0
0
1
1
1
4
2
1
0
0
0
0
2
0
1
2
0
0
2
1
0
0
1
0
0
0
0
1
1
1
0
0
2
0
0
1
2
1
0
1
1
1
0
1
1
1
1
1
0
2
2
1
1
1
0
1
0
1
2
1
2
0
1
1
1
2
1
2
2
0
0
1
2
2
3
1
2
1
1
0
0
2
1
2
1
1
0
0
1
2
1
0
4
1
2
0
1
1
1
1
1
0
2
0
0
0
2
1
0
2
0
1
0
0
1
1
2
0
2
0
1
0
2
0
0
2
0
1
1
2
1
2
0
0
0
0
2
0
1
0
0
1
1
2
0
0
0
1
0
1
2
1
1
0
1
1
1
0
1
2
1
2
1
1
0
2
0
2
0
0
1
0
0
1
0
4
2
1
1
1
3
1
1
1
1
0
1
1
1
1
2
1
2
1
0
0
0
1
2
1
1
1
2
0
1
0
0
1
0
1
0
0
1
1
2
1
1
1
4
1
2
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
1
3
0
1
0
1
2
1
0
0
0
0
0
1
2
0
2
0
0
0
0
1
1
1
0
0
1
0
1
1
1
1
1
1
0
2
1
1
0
1
0
0
0
1
0
2
0
1
2
0
1
1
1
0
2
2
0
2
1
2
1
1
0
1
2
2
2
0
2
2
1
1
2
0
1
2
1
0
0
3
0
0
0
0
2
0
1
2
0
1
0
1
0
2
1
0
0
1
1
0
0
1
1
1
1
0
2
0
0
2
0
0
0
0
1
2
0
2
2
2
0
0
0
2
2
0
0
0
0
1
2
0
1
1
1
1
0
1
1
1
1
0
2
1
1
0
1
1
1
1
0
0
1
2
1
1
1
2
0
1
5
1
0
1
1
1
0
0
0
1
2
0
3
1
0
2
1
3
0
0
0
2
2
0
1
0
0
1
2
2
2
1
1
0
1
0
0
2
0
0
0
2
1
3
1
1
2
1
2
0
1
0
1
0
1
0
0
1
1
1
0
2
0
0
1
0
0
0
1
1
0
0
2
1
1
1
2
2
1
1
2
1
0
1
2
3
0
1
2
1
0
1
0
0
2
2
2
1
0
2
2
0
1
0
0
0
0
1
0
0
1
0
2
0
0
0
3
2
0
1
0
1
2
0
2
0
0
1
2
2
1
0
3
0
1
0
0
1
0
2
1
0
2
1
1
0
1
2
0
0
2
0
1
0
1
1
0
1
0
2
0
0
0
1
1
1
0
1
1
0
1
0
0
0
1
2
1
1
1
1
1
2
1
0
0
0
1
0
2
1
2
1
0
1
2
1
2
0
0
2
0
1
2
2
1
2
1
0
1
2
0
0
2
1
1
2
1
1
0
0
0
0
0
0
2
2
1
0
0
1
0
1
1
1
0
1
1
1
0
1
0
0
0
1
0
1
1
1
0
0
2
0
1
2
1
2
1
1
2
0
1
0
0
1
1
2
1
1
1
0
1
1
1
1
1
0
0
0
2
0
1
2
2
0
0
0
0
2
0
1
1
0
3
0
1
0
1
1
2
0
3
0
0
0
1
0
2
1
0
1
1
1
0
1
0
0
2
2
2
1
2
0
1
1
1
0
0
2
1
1
1
1
1
2
2
0
0
0
1
0
1
0
1
1
2
2
2
2
2
1
0
0
0
0
1
1
0
0
2
1
1
2
0
0
1
1
1
0
1
1
0
0
1
1
2
2
0
0
0
1
3
1
3
2
0
0
1
0
1
1
1
2
0
0
0
1
2
2
0
1
2
0
1
1
1
2
1
0
1
0
1
0
1
1
0
1
2
1
1
1
1
2
1
1
1
2
1
0
0
0
1
1
1
2
0
2
0
1
0
2
0
1
1
1
1
0
0
1
2
1
0
1
0
1
0
0
1
0
1
1
1
2
0
0
1
0
0
0
3
1
0
0
0
0
1
1
0
1
1
0
0
2
2
1
0
1
1
1
0
2
1
0
1
0
0
1
1
0
2
0
1
5
1
0
0
1
0
2
0
1
0
0
0
1
0
1
0
0
1
1
2
1
1
0
0
1
0
0
0
1
2
1
0
2
0
1
2
0
0
1
0
1
0
1
2
1
1
1
1
1
1
1
1
0
2
1
1
1
1
2
2
0
0
2
0
0
0
2
0
0
0
0
1
1
1
2
2
0
2
0
1
1
2
2
2
1
0
1
0
1
1
1
1
0
1
1
2
1
0
1
1
0
2
1
2
0
0
1
1
1
2
0
0
0
1
1
0
2
2
0
1
1
1
1
1
2
0
0
0
5
2
2
1
0
0
0
0
0
0
1
0
1
1
1
1
1
0
2
1
1
0
0
0
1
1
1
2
0
1
0
1
2
1
0
0
0
1
0
2
0
0
2
1
2
2
0
1
0
2
0
1
0
0
2
2
1
0
1
0
1
0
1
2
0
1
0
2
1
0
1
0
1
2
2
0
2
1
1
0
3
2
1
1
2
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
2
1
0
0
0
3
0
1
0
1
1
2
2
0
1
2
0
2
1
2
1
2
2
0
0
1
2
1
0
0
1
2
2
1
0
0
1
0
2
0
1
0
1
2
1
1
0
1
1
2
1
0
1
1
1
0
1
2
1
0
1
2
0
2
0
0
1
0
0
1
0
2
1
1
1
0
2
0
2
1
2
0
1
2
2
2
0
0
0
2
0
2
0
0
0
1
1
1
1
0
0
1
2
2
0
1
0
0
1
1
0
2
0
2
2
0
0
2
2
0
0
0
1
1
0
1
1
1
0
1
1
1
1
0
0
1
0
1
1
0
0
1
1
0
2
0
2
0
1
2
0
1
0
0
0
0
1
2
0
0
1
1
0
0
0
1
2
0
2
0
0
2
2
1
0
3
2
1
2
0
0
2
1
1
0
0
0
1
1
0
0
1
2
2
0
1
0
0
2
1
0
2
2
2
0
2
1
0
1
0
1
1
2
0
1
0
0
0
0
2
1
2
0
1
0
0
2
1
0
2
2
0
0
2
0
1
0
2
0
1
1
0
0
1
3
1
0
2
1
1
0
0
1
0
2
0
2
0
1
0
1
0
0
2
1
2
1
0
0
1
1
1
0
0
1
0
1
2
0
2
0
0
0
0
0
2
1
2
0
2
1
0
1
2
2
0
2
0
0
1
1
0
2
1
1
2
1
1
1
0
1
2
0
0
1
0
0
1
0
0
0
0
0
2
0
2
1
1
0
1
2
1
1
0
2
2
1
2
1
2
2
1
0
2
1
0
1
1
1
0
2
1
1
0
2
1
2
2
1
2
0
0
1
1
2
0
0
1
1
1
1
0
0
0
2
1
1
0
1
2
0
2
1
0
1
1
0
2
0
1
1
1
1
0
1
0
1
2
2
0
1
1
1
2
1
0
1
2
1
1
0
0
0
0
0
0
1
0
3
0
1
1
2
1
1
0
2
2
1
0
2
2
2
1
2
1
0
1
1
0
1
0
1
0
2
2
3
0
0
0
0
2
1
1
1
2
0
1
1
0
0
1
2
0
2
0
1
0
0
1
0
1
0
2
1
0
1
0
1
1
0
1
2
1
1
2
1
1
1
0
1
1
0
2
2
0
1
0
1
0
2
1
1
0
1
0
1
0
2
0
0
0
2
0
0
0
4
0
0
0
1
0
0
0
2
1
0
0
1
1
1
0
1
0
1
2
1
1
1
2
2
0
4
1
2
0
0
0
1
0
1
1
0
0
0
1
0
1
2
0
1
0
0
0
1
1
1
1
1
0
0
0
1
0
0
1
0
0
0
0
1
0
1
1
0
2
0
0
1
1
0
1
1
1
0
0
0
1
1
0
0
1
1
2
2
1
1
1
2
2
1
2
0
3
0
1
0
1
0
0
1
0
1
0
1
0
0
3
0
0
0
1
0
0
0
1
0
1
1
1
2
1
1
1
0
1
0
1
1
1
0
4
1
1
1
2
2
0
0
0
1
0
0
2
2
0
2
0
1
0
2
0
1
0
2
0
1
1
0
1
2
2
0
1
2
0
1
3
2
1
3
1
1
1
1
0
0
1
0
0
1
1
1
0
1
2
1
1
0
1
1
0
1
1
0
2
2
2
2
1
0
0
1
3
3
1
0
0
0
0
1
2
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
2
1
1
0
0
0
1
1
1
0
1
0
0
1
2
1
1
2
0
2
1
2
1
0
0
1
1
0
1
1
2
1
0
2
1
1
1
0
1
0
0
1
0
1
2
2
0
1
1
0
1
1
1
2
1
0
1
2
1
2
2
0
0
2
0
1
2
0
0
1
1
1
0
1
0
2
1
1
1
0
1
1
1
1
0
0
2
1
1
1
0
0
1
1
2
0
0
0
1
1
0
2
2
0
0
1
1
1
1
0
1
1
0
1
2
1
2
2
2
2
0
0
1
0
1
2
0
1
2
2
2
1
1
2
2
0
0
2
1
1
1
0
1
1
0
1
1
1
1
2
2
0
1
0
0
0
0
1
1
1
1
2
0
3
2
0
1
1
0
0
1
0
0
1
1
1
2
1
0
0
0
1
1
1
1
1
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
1
1
0
2
2
1
1
2
1
1
2
0
1
2
0
2
3
3
0
0
1
1
1
0
1
1
0
2
0
0
0
1
1
0
1
1
0
1
0
0
0
2
2
0
1
2
1
0
2
1
0
1
0
0
0
0
0
2
0
0
1
0
0
1
0
0
2
0
2
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
2
0
1
0
6
0
0
2
1
3
2
0
1
1
1
1
0
0
0
0
1
2
1
1
1
0
1
1
0
2
1
0
2
0
2
1
1
0
1
1
1
0
0
0
0
1
1
0
0
1
1
0
0
1
0
0
1
1
0
2
0
0
0
0
0
1
1
0
2
1
3
1
0
0
1
1
1
1
1
1
1
1
0
1
2
2
1
0
2
1
3
0
4
0
2
0
2
0
2
0
0
0
2
1
0
1
2
1
1
0
3
1
1
2
2
1
2
0
1
1
2
1
2
2
1
1
1
0
2
0
1
0
2
1
0
1
1
1
0
2
2
2
3
2
1
2
2
1
2
0
2
1
1
1
1
0
1
0
0
1
0
0
0
2
1
1
0
1
0
0
0
0
0
1
1
0
2
0
1
1
1
1
1
2
0
1
1
1
0
2
2
0
0
2
2
0
0
2
2
1
1
2
0
1
0
0
2
1
2
0
2
1
1
1
0
1
0
0
2
1
2
1
1
0
1
1
0
1
1
0
1
2
0
1
3
1
2
0
1
1
2
0
2
1
0
1
1
2
0
1
1
1
0
1
1
0
0
0
1
2
0
0
1
1
0
0
1
1
1
1
1
1
0
0
1
1
1
0
2
2
1
0
2
0
0
2
1
1
1
1
2
1
0
1
0
0
1
2
2
1
0
1
1
2
2
2
1
0
1
1
0
0
0
0
2
0
1
2
2
1
0
1
1
1
1
2
1
0
1
1
1
0
1
0
2
1
0
1
1
1
0
0
0
1
2
0
0
1
1
1
0
2
3
0
0
0
1
1
2
1
3
0
0
1
0
2
2
1
2
0
2
3
1
1
2
1
1
0
2
0
0
0
1
2
0
1
0
1
1
2
2
2
2
0
1
0
1
1
1
1
1
0
0
1
1
1
2
1
0
0
1
0
2
2
1
1
0
0
0
1
3
1
1
1
1
1
0
1
1
1
0
0
0
1
2
0
3
0
1
1
0
0
2
0
2
2
2
0
1
0
3
1
1
0
1
2
1
0
0
0
0
0
2
1
0
1
1
0
1
1
0
2
1
2
2
1
0
2
0
0
2
1
0
2
0
2
4
0
1
0
2
1
0
0
2
1
0
1
2
0
2
1
0
2
1
1
1
0
1
1
2
3
0
0
0
1
0
2
1
2
2
1
0
2
1
0
0
0
1
2
0
0
0
0
0
1
0
1
1
0
0
2
4
1
1
1
1
0
0
0
0
1
2
2
1
0
0
1
1
0
0
0
1
0
2
0
2
2
2
0
0
1
0
0
1
1
1
0
2
1
2
0
1
2
2
2
2
0
2
1
4
1
1
0
2
0
1
1
3
0
2
1
0
2
1
0
0
0
1
1
1
2
0
2
0
1
1
0
1
1
1
0
2
0
2
0
1
0
1
0
1
0
1
0
1
1
2
0
0
0
0
1
1
0
1
1
2
2
2
0
2
1
2
0
0
5
2
1
0
1
1
1
2
0
1
1
0
1
1
0
0
2
1
1
1
0
2
1
0
2
0
3
2
0
1
2
2
0
0
1
1
0
0
1
2
1
1
2
0
1
0
1
1
1
1
1
0
2
2
2
0
0
1
1
0
1
0
0
0
1
0
1
1
1
2
0
2
0
0
1
1
0
1
0
0
2
0
0
0
1
1
1
1
2
1
0
0
1
0
1
1
1
2
0
0
1
1
1
0
2
1
0
1
1
1
0
0
0
0
2
0
0
1
1
1
0
0
0
2
2
1
0
1
0
2
1
2
1
1
0
0
1
1
1
1
2
1
1
1
0
0
0
1
0
1
1
2
1
0
2
1
2
1
1
1
1
1
0
0
0
0
1
1
2
1
0
2
1
0
1
1
1
2
0
1
2
0
0
1
0
2
0
1
1
0
0
3
1
2
1
0
1
0
0
2
1
0
2
0
1
2
0
0
2
1
1
2
1
0
0
1
0
1
1
1
0
1
1
1
1
0
1
2
2
2
1
0
0
1
1
1
1
1
2
1
0
1
2
2
1
2
0
2
2
2
2
1
2
1
0
2
2
2
0
1
1
0
1
0
0
1
0
2
1
2
1
0
1
1
1
0
0
4
1
1
0
0
2
0
2
0
0
1
0
0
0
2
1
1
0
2
1
1
0
2
1
1
3
0
1
2
0
2
1
2
1
0
2
0
2
2
2
1
1
0
1
0
1
1
1
2
1
1
0
1
1
0
1
1
0
2
1
0
0
0
1
1
0
2
2
0
0
0
1
0
0
2
2
1
1
0
0
0
1
0
1
0
0
2
2
0
2
1
0
2
0
0
0
2
2
0
1
0
1
1
1
1
1
0
3
1
1
0
2
2
0
1
1
0
2
1
1
1
2
0
0
2
0
0
0
2
1
0
1
1
0
1
1
0
2
1
2
0
2
2
0
1
0
1
2
2
2
0
0
2
2
0
0
1
2
0
1
0
1
1
0
0
1
2
2
0
0
1
0
2
0
0
1
0
0
1
0
1
0
0
2
1
0
0
0
0
1
1
1
0
0
0
0
1
0
1
0
1
2
1
0
0
0
2
2
2
0
1
1
2
0
1
1
0
3
1
2
1
0
0
0
1
1
0
0
1
1
0
0
2
0
0
0
0
1
2
1
1
4
2
1
1
2
1
0
1
1
0
0
1
1
1
2
0
2
2
0
1
0
2
0
0
0
0
0
2
1
1
0
2
0
0
1
0
1
1
1
0
2
1
1
1
2
0
1
0
2
2
1
0
0
0
0
0
0
2
1
1
0
2
0
2
1
0
0
1
0
0
1
1
1
1
0
0
0
0
0
1
0
2
0
0
0
2
1
2
0
2
1
0
2
1
0
1
1
0
1
1
0
1
1
2
0
2
1
1
1
1
0
1
1
0
0
0
2
0
2
1
2
0
0
1
1
2
1
1
0
0
0
1
1
1
1
0
1
1
0
1
2
1
1
1
1
1
1
1
2
1
1
1
2
0
0
2
2
1
0
2
2
1
0
0
1
0
1
2
0
0
1
2
1
2
2
6
1
0
0
0
2
0
0
1
2
0
0
0
1
1
0
1
1
0
2
2
0
0
0
1
0
0
1
2
0
0
3
1
1
0
1
1
1
2
1
2
0
2
2
1
0
2
1
0
1
2
0
1
1
1
2
1
0
1
1
1
1
2
1
0
2
1
1
2
0
1
1
1
1
1
0
1
2
0
1
1
1
2
0
1
0
1
0
0
1
1
1
2
1
0
0
0
0
0
2
2
0
2
2
2
2
1
2
0
2
1
2
1
0
1
1
0
2
0
1
0
2
2
1
0
2
1
1
0
1
0
0
1
0
0
1
0
0
2
0
1
0
2
2
2
2
1
1
0
2
0
0
0
2
0
0
1
0
3
0
0
0
0
1
0
0
2
0
2
1
1
1
1
1
0
0
2
1
0
1
2
1
2
1
1
1
0
0
0
0
2
2
0
0
2
1
0
0
0
1
1
1
1
1
2
0
0
1
0
1
1
1
0
0
0
1
2
0
1
1
2
0
1
1
1
2
0
2
0
1
1
2
0
0
0
0
1
1
1
2
1
0
1
0
0
0
1
1
2
2
2
2
0
1
1
0
0
1
1
1
0
0
1
1
0
0
2
2
2
0
0
1
1
1
1
1
0
2
1
0
2
1
2
2
1
0
0
0
0
1
2
1
0
0
0
1
1
1
2
2
1
1
2
0
1
1
1
2
2
1
0
2
1
0
1
0
0
1
0
1
1
1
2
0
0
1
2
0
2
1
1
0
0
0
0
2
0
0
1
0
1
0
2
2
2
2
0
1
2
0
2
2
0
0
2
0
1
0
0
1
2
1
2
2
0
2
2
1
1
0
1
1
0
1
1
0
0
2
0
0
0
2
1
0
1
2
1
0
0
2
1
2
0
1
2
2
1
0
1
1
2
1
2
1
2
0
0
1
1
1
0
2
2
0
3
0
0
0
1
1
3
1
1
1
2
2
0
1
0
0
0
1
0
2
1
1
1
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
2
0
2
0
2
0
0
1
0
1
0
0
0
1
2
2
1
0
0
2
1
2
0
1
0
1
0
1
0
1
1
1
1
1
2
0
0
1
0
2
0
2
0
1
1
1
1
4
1
2
0
0
1
2
2
1
1
0
1
2
1
1
1
0
1
0
1
0
1
1
0
2
0
1
2
0
0
0
1
2
1
1
1
1
0
0
0
2
0
2
1
0
1
0
0
1
0
1
1
2
1
0
2
1
2
0
0
2
2
0
2
1
1
1
1
2
2
2
2
1
0
2
1
1
0
0
0
0
0
1
2
1
0
2
3
2
0
5
1
1
1
0
1
1
0
1
2
2
0
1
2
2
1
0
0
0
1
1
0
1
0
2
1
0
2
0
1
0
1
0
2
0
1
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
2
1
1
1
0
0
0
3
0
1
0
0
0
2
1
1
1
1
0
0
0
1
1
0
2
0
1
1
2
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
1
2
0
4
0
1
2
0
1
1
0
0
2
1
2
0
1
0
0
1
1
1
1
0
1
2
1
0
0
2
2
0
0
1
0
0
1
1
0
2
0
0
0
2
0
0
0
1
1
0
1
0
0
1
0
1
2
1
1
1
2
0
1
0
1
0
2
2
0
1
1
0
2
2
1
0
0
2
1
0
2
0
0
1
2
0
0
1
0
1
0
1
2
1
0
1
1
2
2
1
1
0
0
0
2
3
0
0
0
3
0
0
0
1
0
3
1
0
0
4
0
1
2
1
0
0
0
1
2
2
0
0
1
1
2
0
1
0
0
2
0
0
0
0
1
1
1
0
1
0
0
1
1
1
2
1
0
0
0
2
2
0
0
1
1
2
0
0
1
1
2
1
2
0
0
2
0
1
2
0
1
0
0
0
1
1
0
0
2
0
0
1
2
1
0
1
0
0
8
3
0
0
0
0
2
2
1
1
2
2
1
1
1
0
3
0
0
1
1
0
0
0
0
1
2
0
1
3
0
0
1
0
0
1
0
0
0
0
1
0
0
1
1
1
1
0
1
1
0
1
0
2
0
0
1
2
0
1
1
0
0
1
1
0
0
1
0
0
1
0
0
0
0
2
0
3
0
0
0
1
0
1
0
1
2
1
0
3
0
1
0
1
1
1
1
2
2
1
0
0
1
0
2
0
1
0
0
2
1
1
2
2
0
2
0
1
2
0
2
0
2
0
0
0
1
1
1
0
0
0
2
1
0
0
1
1
0
1
4
1
1
2
0
2
1
3
0
1
2
0
2
1
1
1
2
0
2
1
2
1
1
1
2
1
1
1
1
0
1
2
1
1
0
1
1
1
1
1
0
0
1
1
2
0
1
0
1
2
0
2
1
2
2
0
1
2
0
0
2
0
1
1
2
1
1
1
2
1
1
1
1
1
0
0
2
2
1
1
0
1
2
0
1
1
1
2
1
1
2
1
1
2
2
0
3
0
1
0
1
0
0
0
2
1
1
0
0
0
0
2
0
1
1
2
1
1
0
1
0
0
1
0
1
1
2
0
0
2
0
0
1
2
0
0
1
0
1
1
0
0
1
2
1
0
1
1
1
1
0
0
1
1
0
1
0
0
1
2
1
1
1
2
1
1
0
0
2
1
1
1
0
0
1
1
2
1
1
0
2
0
0
4
1
0
1
2
0
1
2
1
0
0
1
1
2
1
1
2
0
0
3
2
2
1
0
1
3
1
1
0
1
0
2
1
2
2
0
1
2
1
1
3
2
1
1
1
1
2
1
1
0
1
1
1
4
0
1
1
1
2
2
1
1
0
1
1
1
0
0
0
1
0
0
2
0
0
1
0
1
1
1
2
0
1
2
0
1
0
1
0
2
0
0
1
0
1
1
0
2
0
0
0
0
0
0
0
0
2
2
2
0
1
0
1
1
0
1
2
1
1
0
0
2
0
1
2
1
2
2
2
1
1
2
1
0
0
1
1
0
2
1
0
1
2
2
0
2
1
1
1
0
0
1
1
0
2
1
0
1
1
1
1
2
0
0
2
2
1
1
1
1
0
1
2
1
2
0
0
0
0
1
1
2
2
2
0
0
2
1
1
0
0
3
2
2
0
0
0
0
0
0
0
0
2
0
2
1
0
0
2
2
1
1
0
1
1
1
1
0
0
0
0
1
1
0
1
0
0
0
2
0
0
1
2
1
0
0
0
0
0
2
1
1
0
1
1
0
1
1
1
1
0
2
1
0
0
0
1
2
0
1
2
2
1
2
0
2
1
0
1
0
1
1
0
0
0
0
1
2
0
0
1
1
0
1
0
0
0
0
1
0
0
2
0
1
1
0
0
2
1
1
1
1
1
1
0
0
2
1
1
1
0
1
0
0
0
1
0
0
1
0
1
0
0
2
0
1
1
1
2
0
1
1
0
0
2
0
2
1
0
2
0
2
0
1
0
1
0
3
0
0
0
1
1
2
0
1
2
0
2
1
1
0
1
0
1
2
2
2
0
2
1
0
0
2
0
1
0
0
0
2
0
1
1
0
3
1
0
0
0
0
1
1
0
2
1
0
0
0
1
1
1
1
1
2
1
2
1
2
1
0
2
0
1
2
1
1
1
0
1
1
0
1
1
1
2
2
2
1
1
1
0
2
1
0
2
0
0
1
0
2
1
0
2
0
1
0
0
0
1
2
0
0
1
1
1
3
2
2
3
2
2
0
2
1
0
1
1
1
1
1
2
0
0
1
1
1
1
2
1
1
2
1
2
2
1
0
0
0
0
2
0
0
0
2
0
0
1
2
0
2
0
0
0
1
2
0
2
1
0
2
1
0
1
1
0
1
0
0
1
0
1
1
1
2
0
1
0
0
0
0
0
4
2
0
0
0
1
0
0
1
0
1
1
2
0
0
1
0
0
1
1
1
0
1
2
0
0
0
1
2
2
0
1
1
1
1
0
2
1
1
1
0
0
2
0
0
0
1
3
1
2
2
1
1
1
0
0
0
1
0
1
1
1
0
2
0
1
0
2
1
1
0
1
0
0
0
1
2
0
2
0
1
5
2
1
1
2
2
0
1
2
1
1
0
2
0
0
1
1
0
1
2
0
2
1
1
0
1
1
1
1
1
0
1
0
1
2
2
2
0
1
3
0
1
0
2
2
1
2
1
1
2
0
0
2
1
1
0
1
2
1
2
1
0
1
1
1
0
0
0
1
0
1
1
1
1
1
1
1
2
0
0
0
0
1
1
2
2
1
1
0
1
2
1
1
0
0
0
0
1
2
1
1
0
2
1
0
1
1
1
0
1
1
0
0
1
0
1
1
0
1
1
1
0
1
0
0
1
2
1
0
0
1
0
0
0
1
1
1
1
2
1
2
1
0
3
0
0
1
1
0
1
0
0
1
1
1
1
2
1
0
0
2
1
2
0
2
1
1
2
2
0
0
0
2
0
0
0
1
1
1
0
2
1
1
0
1
0
2
1
1
0
0
1
2
2
1
1
1
0
1
0
3
1
2
0
2
0
1
0
1
1
0
0
1
0
0
2
0
0
1
0
0
2
0
0
0
0
0
1
2
0
1
0
1
1
0
1
1
1
0
0
2
0
2
1
1
0
1
1
1
2
2
0
2
2
1
0
2
1
0
2
1
1
0
1
2
2
1
1
1
2
1
0
0
1
1
1
1
1
0
1
1
0
1
0
0
0
1
0
1
1
0
1
1
0
0
2
0
1
0
0
1
2
2
0
0
1
1
1
0
1
1
1
1
0
0
0
2
1
0
1
1
0
0
1
1
1
0
2
2
2
0
0
1
0
2
0
0
1
0
2
0
1
2
1
0
2
1
1
0
0
1
0
0
0
0
0
0
1
1
2
0
1
8
0
1
1
0
0
1
0
1
0
1
0
2
1
0
2
1
2
0
1
0
0
0
0
1
1
1
1
0
1
0
0
1
1
2
0
1
0
0
2
1
0
1
0
2
0
1
1
2
0
0
1
1
1
0
2
1
1
0
0
1
0
0
0
0
1
0
1
0
1
2
0
1
2
0
2
1
1
2
2
0
0
0
1
0
0
0
2
1
0
1
0
2
1
0
0
2
0
1
1
2
1
0
1
0
1
0
1
1
0
0
1
1
1
0
0
2
0
1
1
1
1
1
1
1
1
2
1
1
0
0
0
0
1
1
0
2
1
0
1
1
0
1
0
1
1
1
1
0
1
1
0
0
1
1
2
0
3
2
2
2
2
1
1
1
0
1
1
0
0
0
0
1
0
1
0
1
1
1
1
3
1
1
0
1
1
2
2
0
0
0
0
2
0
1
1
2
2
0
2
2
2
0
1
2
1
1
1
1
2
1
2
0
2
3
0
2
1
0
0
0
2
2
0
0
1
1
1
2
1
2
2
0
2
2
1
1
0
0
2
0
0
1
1
1
0
0
1
0
1
1
1
0
1
1
2
0
1
1
1
0
1
1
0
1
2
2
1
1
1
0
1
1
2
2
0
1
1
1
0
0
1
0
1
2
1
0
0
2
1
0
1
0
1
2
1
0
0
3
1
1
1
0
1
2
0
3
2
0
0
0
2
0
0
0
0
2
0
2
2
1
0
1
1
1
1
0
2
1
1
2
0
1
0
0
1
1
2
1
1
1
1
2
0
1
0
1
1
0
0
5
1
1
0
2
2
1
1
0
0
0
3
0
0
1
1
1
0
0
0
1
1
1
0
1
1
0
0
1
0
0
0
2
2
1
0
3
1
2
0
2
2
0
0
0
0
0
2
1
0
0
2
1
1
1
1
2
0
0
2
0
1
1
0
0
1
1
2
2
0
0
1
1
0
1
0
1
0
1
1
1
0
1
1
0
2
0
0
1
0
1
1
0
2
1
1
2
0
1
2
1
1
2
0
0
1
0
1
0
1
1
0
0
1
1
1
2
0
1
0
0
0
1
0
2
2
0
0
1
2
1
3
1
1
0
1
1
0
0
0
0
0
1
0
1
0
2
0
1
1
0
0
2
0
2
0
2
0
0
1
0
1
0
1
1
0
0
1
2
2
0
1
1
1
1
0
1
0
0
1
2
1
2
1
1
0
0
0
2
1
2
2
2
1
0
1
0
1
1
0
0
1
2
1
1
1
0
1
2
0
0
1
0
1
1
0
1
1
0
2
0
0
1
2
0
1
0
1
2
4
0
1
1
0
1
0
1
1
1
0
1
2
1
0
0
0
0
2
2
1
1
0
2
2
1
0
0
0
1
1
2
1
0
1
0
0
0
1
0
0
2
1
0
0
0
0
0
1
0
1
0
0
1
1
0
0
2
0
2
2
0
0
0
1
2
0
1
2
0
2
0
1
2
2
1
1
0
2
2
0
0
4
0
2
2
2
1
1
1
1
0
2
2
0
1
1
0
1
0
1
1
1
2
2
0
2
0
1
0
0
1
2
2
1
3
1
1
2
0
2
0
0
0
1
0
1
2
0
1
2
1
0
0
0
1
1
0
0
1
1
1
0
1
0
2
0
1
0
0
0
0
1
0
0
0
0
1
0
1
1
1
0
1
1
0
1
0
1
2
1
0
0
1
0
0
2
0
0
1
1
2
0
1
1
2
1
0
0
2
2
0
2
3
1
1
2
0
0
1
0
0
0
2
1
1
2
0
0
0
2
2
2
1
1
2
2
1
0
0
0
1
0
0
0
1
1
2
2
2
0
1
0
0
1
0
2
1
0
0
2
1
0
0
2
2
2
1
1
1
2
2
1
1
2
1
1
0
1
0
0
1
0
0
2
0
1
1
1
1
0
0
0
0
0
1
0
0
2
2
0
2
0
2
1
0
0
1
2
1
2
0
2
2
0
1
0
0
1
2
0
0
0
3
2
1
2
0
1
0
1
1
2
1
2
1
0
2
2
2
0
2
1
2
0
0
2
0
0
1
1
1
2
3
0
1
2
1
0
2
0
1
0
1
3
0
0
0
1
1
0
0
1
0
2
0
1
0
0
0
0
0
1
0
1
1
2
4
1
0
1
0
1
2
0
1
1
1
1
0
0
1
0
2
0
0
2
0
0
0
2
0
0
1
2
0
0
2
0
1
0
0
1
1
2
2
0
1
2
5
1
0
1
1
0
0
2
1
1
0
2
0
1
2
0
2
0
0
0
0
2
0
0
1
0
1
2
0
1
3
1
1
1
0
0
2
1
2
0
1
1
1
2
2
2
0
1
0
0
0
0
0
1
1
1
1
0
2
1
3
1
1
2
1
0
0
1
1
1
1
1
3
0
1
1
0
1
0
0
0
1
1
2
2
0
0
0
0
4
1
0
0
2
2
0
3
1
1
1
2
1
2
0
1
2
0
1
2
2
3
1
1
0
0
1
0
0
0
0
3
1
0
0
1
1
3
0
2
0
2
1
2
2
1
0
2
2
2
0
2
2
0
1
2
1
2
0
1
1
0
0
1
0
1
0
0
0
0
2
1
1
1
2
0
1
0
2
0
2
1
0
1
0
0
1
1
0
0
1
0
1
3
1
2
2
1
2
1
0
1
1
2
1
1
1
0
1
1
0
1
0
0
0
3
1
1
0
1
0
1
1
1
0
2
2
0
1
0
1
1
0
0
0
0
2
0
2
0
0
1
2
1
2
1
0
0
1
2
1
1
2
1
0
1
0
1
1
0
1
1
2
0
3
0
0
2
0
1
2
1
0
1
2
0
1
0
0
1
0
1
0
2
1
1
1
1
1
0
1
0
2
0
2
0
0
1
0
0
2
1
1
1
2
2
0
0
0
1
1
1
0
0
1
1
1
3
2
0
0
0
1
2
1
1
2
1
2
1
1
1
0
2
0
1
1
0
1
1
1
0
0
0
1
2
2
1
0
0
0
2
1
1
0
0
1
0
1
0
2
2
0
0
0
1
0
3
1
0
1
2
1
0
2
2
1
0
0
0
1
0
2
1
2
2
0
0
1
0
0
1
2
0
0
2
2
2
2
0
0
2
0
0
1
1
2
1
1
2
2
1
1
1
1
0
0
1
1
1
0
0
1
0
0
1
0
0
0
0
0
0
1
1
1
1
0
0
0
2
0
0
0
2
0
1
0
2
1
2
2
0
1
0
0
2
1
0
0
0
0
0
1
1
0
1
1
0
1
0
1
0
0
1
1
0
0
2
1
1
1
1
0
2
0
1
1
2
1
1
0
0
2
1
1
2
1
0
1
1
3
1
0
1
0
0
1
0
2
0
1
1
1
0
0
0
0
0
0
1
3
0
0
1
1
2
1
1
2
0
1
2
0
1
0
0
0
0
0
3
2
0
1
2
0
0
3
1
0
2
2
1
1
1
1
2
0
2
1
0
0
1
0
0
0
0
1
1
1
0
0
0
1
0
1
2
0
0
0
1
0
1
1
2
0
0
1
0
0
1
1
1
0
1
1
1
0
1
0
1
1
0
1
2
0
0
0
0
0
0
0
2
0
0
1
0
0
2
1
1
1
2
0
1
1
1
1
0
1
1
2
0
1
4
0
1
0
0
1
1
2
1
0
0
2
0
0
0
0
1
0
1
1
0
0
1
0
1
1
0
0
0
2
0
0
0
0
2
2
1
2
1
1
1
0
0
1
0
0
0
1
0
0
1
1
0
2
2
0
2
1
1
0
1
2
0
0
0
1
1
0
2
1
0
1
0
0
1
0
1
1
1
2
1
0
2
0
1
2
1
1
1
1
0
1
1
0
2
1
2
1
0
0
1
1
1
1
0
1
1
2
0
2
0
1
2
2
1
0
1
1
0
1
1
1
0
0
1
1
0
1
0
0
1
1
2
1
1
2
0
2
1
2
1
2
2
1
0
0
0
0
2
0
2
1
1
0
1
0
1
0
1
1
1
1
0
0
0
2
0
0
0
0
0
1
1
4
1
0
0
1
2
2
1
1
2
0
0
2
1
1
0
1
4
0
1
2
0
2
0
0
0
2
0
0
0
1
0
2
2
1
0
2
1
1
0
1
0
0
3
1
2
0
2
0
0
2
2
0
1
2
1
1
2
0
1
1
0
1
1
1
1
2
0
1
1
0
2
0
0
1
0
2
1
0
1
0
1
0
1
0
0
0
1
1
2
1
1
1
0
0
1
1
1
2
0
1
2
1
2
1
1
1
0
1
2
0
0
1
0
0
2
1
0
0
2
0
0
1
0
0
1
3
1
1
0
0
0
2
1
0
0
1
0
1
0
1
2
0
1
1
0
0
0
2
2
1
1
1
0
0
3
2
0
1
0
1
0
2
0
0
1
0
2
1
1
0
1
1
0
1
0
1
2
0
2
1
1
1
0
0
1
0
3
1
0
0
1
1
1
2
2
2
0
1
1
1
0
1
1
0
1
0
2
0
0
1
2
1
1
1
2
0
0
1
2
0
0
1
0
2
0
1
1
0
2
0
0
0
1
0
2
2
0
0
1
1
0
3
1
1
2
1
1
0
0
1
2
1
1
1
1
0
2
1
0
0
2
4
1
0
0
0
1
2
0
1
1
0
2
1
1
2
2
0
0
0
1
1
0
1
1
2
6
2
0
0
0
2
1
1
1
0
0
1
2
3
1
0
0
2
1
1
2
2
0
1
1
0
0
0
2
1
2
2
3
1
1
0
0
0
0
1
2
2
0
1
0
1
0
2
1
1
0
0
1
1
1
1
1
0
2
1
0
1
1
1
0
0
1
1
1
2
0
2
0
1
1
1
1
2
1
1
1
0
1
0
2
1
1
1
2
2
0
1
2
1
0
2
2
0
0
0
2
2
1
1
0
1
0
1
0
2
2
0
1
1
1
2
2
1
1
1
1
2
0
1
2
1
1
1
2
0
1
2
2
0
1
0
1
2
2
1
2
0
0
0
0
1
0
1
1
0
0
4
1
1
0
2
1
2
1
0
1
1
2
0
1
0
0
0
0
0
1
0
0
0
1
1
1
1
2
2
2
1
0
1
2
0
0
1
1
1
0
0
3
0
2
1
2
0
1
2
0
0
1
0
1
1
0
1
2
1
2
2
2
1
2
2
0
0
1
1
2
2
1
1
1
0
0
0
0
0
0
0
0
2
2
1
1
0
2
0
1
0
2
0
0
1
2
0
0
1
2
2
0
1
0
0
1
1
1
0
1
1
0
2
1
1
0
1
0
1
3
0
0
2
0
2
2
1
1
0
1
1
0
1
0
0
0
2
1
1
1
1
1
1
1
1
0
0
0
2
1
0
0
2
1
0
2
2
1
2
2
1
0
0
3
0
0
1
0
1
1
1
0
0
0
0
0
1
0
2
0
2
1
0
0
0
0
1
2
1
3
1
0
1
1
1
1
1
1
0
0
2
1
0
2
0
0
0
0
1
1
1
1
0
0
1
2
2
2
2
0
0
0
1
2
2
2
1
1
1
0
1
1
1
0
1
0
2
1
1
2
0
3
0
1
0
2
0
0
0
0
0
1
2
0
1
2
0
0
0
1
1
0
2
0
1
0
1
0
1
1
1
1
2
1
1
1
1
1
0
0
1
0
1
1
1
2
2
1
1
1
1
0
1
2
2
0
2
0
1
1
3
1
0
2
1
0
1
1
1
0
0
1
0
1
0
2
2
3
0
2
1
0
1
0
0
0
0
0
0
2
0
0
1
3
0
0
2
1
1
0
2
1
0
0
0
0
1
0
0
0
0
0
2
0
2
1
0
0
2
1
0
1
1
1
1
1
1
2
1
1
0
2
0
1
2
0
0
0
1
1
2
1
2
0
0
2
0
1
1
0
2
0
1
2
2
0
0
1
0
0
1
0
0
1
0
1
0
2
1
2
1
0
2
0
2
2
0
2
0
1
0
1
1
1
1
1
1
0
1
1
1
0
1
2
1
1
0
0
0
2
0
1
0
1
0
1
0
1
1
1
2
2
1
2
0
3
0
2
0
1
2
0
0
0
1
0
0
1
0
2
1
2
2
0
0
2
0
2
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
1
0
3
0
2
0
1
0
0
0
0
0
1
0
1
2
0
1
1
1
1
0
1
1
2
2
1
1
2
2
2
2
7
1
0
0
0
0
1
0
0
1
2
2
0
2
1
5
1
0
2
2
0
1
1
2
1
2
0
2
1
0
1
2
0
0
0
2
0
1
0
0
0
1
1
0
0
1
0
1
0
0
0
1
1
1
2
0
2
1
2
0
2
0
0
1
0
1
2
0
1
1
1
0
1
0
0
1
1
2
0
0
0
0
0
1
0
0
0
2
0
3
1
0
0
2
2
1
0
1
1
1
2
1
1
2
1
0
0
0
1
0
2
0
2
2
0
1
1
0
2
0
1
1
1
1
2
0
1
0
0
0
1
2
0
1
0
1
0
0
1
1
0
0
0
2
0
0
1
1
0
1
2
0
1
0
1
2
0
0
0
1
1
0
0
2
0
1
2
2
1
0
0
2
0
2
2
0
1
2
1
0
0
1
1
1
0
1
1
0
1
0
1
1
1
1
0
0
2
0
0
2
1
2
0
1
2
1
0
2
0
0
0
2
1
0
0
2
1
1
1
0
1
0
1
1
0
0
2
2
1
1
0
1
2
0
1
1
2
2
0
1
0
0
1
1
0
0
2
1
1
1
2
0
0
0
3
0
0
0
0
1
0
2
1
1
1
1
2
1
0
1
0
2
1
1
0
1
0
1
0
1
0
2
0
0
1
0
2
1
1
0
0
2
0
0
0
1
1
0
0
0
1
1
2
3
1
1
1
0
2
1
1
0
0
0
1
0
1
0
1
0
0
2
0
0
1
0
2
1
0
1
0
2
0
1
1
1
1
0
1
0
0
0
0
0
3
0
1
0
2
1
0
1
1
0
0
0
0
0
0
1
0
1
1
3
2
1
2
0
2
1
0
2
1
1
0
0
2
1
2
1
2
2
2
2
0
2
0
0
1
0
0
1
1
2
1
1
1
1
1
2
2
1
0
1
0
1
1
3
0
1
2
0
2
0
0
1
1
1
1
0
0
0
1
0
0
0
2
1
2
0
2
2
2
1
1
1
0
1
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
1
0
0
1
2
1
2
1
1
1
0
0
0
2
1
0
2
2
2
0
0
2
0
0
1
0
1
2
0
1
1
0
1
1
1
1
1
0
1
1
2
1
1
1
2
0
0
0
2
1
0
2
0
0
1
0
0
0
1
0
0
1
0
1
1
2
2
0
1
0
1
0
0
1
0
3
0
0
0
2
1
0
2
1
0
0
2
0
1
0
0
2
0
2
0
2
1
2
2
0
0
1
0
2
1
1
1
3
2
2
1
0
0
0
0
1
1
1
0
0
0
0
0
2
1
1
4
2
0
0
1
1
0
0
0
1
0
4
0
2
0
0
2
1
1
0
2
1
2
0
0
0
1
2
2
3
0
1
2
0
0
0
1
2
1
0
2
1
1
0
0
0
0
1
1
0
1
1
0
1
1
1
2
0
0
0
1
1
1
0
1
1
1
0
0
2
0
0
1
1
0
0
1
2
1
0
0
1
1
0
0
1
0
1
1
2
2
1
1
0
1
0
0
1
0
2
0
1
1
1
1
2
0
1
1
1
1
1
1
0
0
1
2
2
2
0
0
0
0
1
0
1
2
1
0
1
0
1
1
0
1
0
2
1
0
1
2
1
0
1
1
0
1
1
1
0
0
0
1
0
0
0
0
2
0
1
1
0
1
1
1
1
1
2
0
0
0
1
0
1
0
1
0
1
0
2
0
1
0
0
0
0
0
0
2
2
0
2
1
0
1
1
0
1
1
1
1
0
0
2
2
0
0
1
1
1
2
0
1
1
1
0
0
1
2
2
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
2
1
1
1
1
0
0
1
0
0
1
1
0
0
0
0
1
0
0
2
0
2
0
2
0
1
1
1
2
0
1
2
1
1
0
0
0
2
1
0
1
1
2
0
0
3
1
0
0
1
0
2
2
1
1
1
2
0
1
1
2
1
1
0
1
1
2
0
0
0
1
0
1
1
1
1
2
1
2
0
0
0
1
1
1
0
0
0
1
0
2
1
0
0
2
1
0
4
0
2
2
2
1
1
1
0
0
0
2
2
2
0
0
1
0
2
1
1
1
0
0
2
0
2
0
5
0
0
0
0
1
1
0
0
2
1
0
1
1
2
0
0
2
2
1
1
1
0
0
2
1
2
1
1
2
1
1
1
2
0
0
0
0
2
1
1
0
2
1
1
0
0
0
0
1
2
2
2
1
0
1
0
2
0
2
1
1
1
2
0
2
0
2
1
0
0
2
1
2
0
1
0
0
1
2
1
1
1
1
0
1
0
2
0
0
1
2
1
1
0
0
0
0
1
2
2
0
1
0
1
1
1
2
0
0
0
0
0
2
2
0
0
2
0
0
0
1
2
0
1
1
1
2
1
2
2
1
1
2
0
0
1
2
1
1
0
1
2
0
0
0
0
2
0
1
0
1
0
0
1
1
2
1
0
0
1
2
0
1
1
1
2
2
1
1
0
2
2
0
1
1
0
1
1
0
1
2
2
1
0
1
1
3
0
1
1
0
2
1
1
0
1
0
1
1
2
0
2
0
1
0
0
2
2
1
1
0
0
0
0
1
0
0
0
2
0
1
1
0
1
0
0
1
0
0
1
0
0
1
0
0
1
0
1
0
0
2
1
0
3
1
0
2
2
0
0
0
1
1
1
1
1
1
0
1
0
0
0
2
2
0
1
0
2
0
1
0
3
1
2
2
1
0
1
2
1
1
0
1
0
2
1
2
2
0
0
1
0
1
1
0
2
2
1
0
1
0
1
2
3
1
1
0
2
1
1
0
1
3
2
0
1
0
2
1
2
2
1
0
0
2
1
2
1
0
0
0
1
1
1
1
1
0
2
1
2
1
1
2
2
0
2
1
0
0
0
1
0
2
1
2
0
1
1
1
1
2
2
1
0
2
1
0
1
1
1
1
0
1
2
1
1
0
1
0
1
2
1
3
2
0
1
0
1
1
1
2
0
0
2
2
0
2
1
0
1
2
0
1
1
1
1
0
1
1
1
1
1
2
0
1
1
0
2
1
0
0
0
2
0
0
0
1
0
1
1
1
0
2
1
2
1
0
1
3
0
2
0
1
0
0
0
1
1
0
2
0
0
0
0
2
1
1
2
0
1
1
2
1
2
2
2
1
1
2
1
0
0
1
0
2
2
1
0
1
1
1
1
1
0
0
2
0
0
1
0
2
1
2
2
0
0
1
0
2
1
1
2
0
0
0
1
2
1
0
1
1
1
0
0
0
0
2
0
0
20
0
0
0
1
0
1
0
2
1
2
2
1
1
2
0
1
1
0
0
3
1
1
2
0
0
2
2
1
0
1
1
0
1
0
0
2
1
1
0
0
0
1
4
0
1
0
2
1
1
0
0
0
0
0
0
1
1
1
0
0
1
0
1
2
0
0
3
2
2
0
2
0
0
2
1
1
1
1
1
1
2
1
0
1
1
0
1
1
1
0
0
0
1
0
1
2
1
1
1
0
0
1
1
0
2
0
1
1
1
1
2
0
0
2
3
0
1
1
1
0
2
1
0
0
0
0
2
1
0
1
1
0
2
1
0
0
2
1
1
1
1
2
2
1
0
1
2
0
2
0
1
1
0
1
1
1
0
1
1
0
0
2
1
0
0
1
1
1
0
1
0
1
2
2
0
0
0
1
1
2
0
1
1
1
0
1
2
0
0
1
1
2
1
0
0
1
1
2
2
1
1
2
2
2
0
0
1
2
2
1
1
0
1
1
1
2
1
0
2
2
0
2
2
1
1
1
2
1
1
0
1
1
1
0
1
1
2
2
0
0
1
0
2
1
2
3
2
0
1
1
0
2
2
1
2
0
1
1
2
2
0
0
0
0
1
0
0
0
0
1
2
0
0
1
2
0
1
2
2
0
1
1
2
1
1
1
0
0
2
1
0
2
1
1
0
1
0
2
0
0
1
0
2
0
0
1
2
2
0
2
2
1
0
0
0
2
1
1
0
0
2
1
1
2
1
0
1
1
0
2
0
1
0
0
2
1
1
0
1
0
0
1
0
1
2
0
2
1
2
0
1
2
0
1
0
0
1
0
0
1
1
0
1
1
0
0
0
1
0
0
1
1
0
0
2
2
1
1
0
1
0
0
0
1
0
1
0
0
1
2
1
2
0
1
0
2
1
0
1
0
2
1
1
1
0
2
1
1
1
1
1
0
1
1
1
0
1
0
2
1
0
1
0
2
1
1
0
2
1
1
0
0
3
0
2
0
2
2
0
0
1
1
2
0
2
0
1
1
2
1
0
0
1
0
1
0
2
0
0
0
1
2
1
0
1
0
0
1
2
1
0
1
0
1
0
0
2
0
1
1
1
0
2
1
2
0
1
2
1
1
1
2
1
1
1
2
3
1
1
1
1
1
1
0
1
1
1
2
0
0
1
0
0
2
1
2
0
2
1
0
0
0
0
0
0
0
0
2
0
1
2
1
1
0
1
0
0
0
0
1
1
1
2
0
1
1
0
1
2
1
1
1
1
1
3
0
0
1
1
0
2
2
0
1
2
0
1
2
0
1
0
2
0
2
1
0
0
1
1
0
0
0
0
0
1
1
0
1
2
0
2
0
1
0
0
2
0
1
0
2
1
1
2
0
2
2
2
0
2
0
0
1
1
0
1
0
1
1
0
0
0
0
0
0
0
1
1
2
1
2
2
2
0
2
2
2
0
1
0
1
0
1
0
2
1
0
2
0
1
1
2
0
0
2
2
2
2
1
0
2
1
0
0
1
1
0
2
1
0
0
0
0
1
1
0
1
2
1
1
1
1
0
1
1
1
0
2
0
0
0
1
1
0
2
1
0
0
0
2
2
0
1
0
0
0
1
0
1
0
0
0
1
0
0
1
2
2
0
0
0
0
2
0
0
1
0
0
0
2
0
1
1
1
1
1
1
0
0
0
2
1
1
2
0
0
0
2
2
0
2
1
1
1
1
1
0
0
1
2
0
1
1
2
1
0
2
1
0
1
1
2
1
2
1
0
1
0
0
4
0
0
1
3
0
1
1
0
1
2
1
2
1
1
0
0
1
2
2
1
0
0
1
0
0
0
2
1
2
1
1
1
1
1
2
0
0
0
2
0
2
0
0
1
2
1
1
1
1
1
1
1
0
0
1
0
2
2
1
1
0
0
3
2
2
1
1
1
0
1
1
0
1
2
1
2
2
0
1
3
0
2
1
1
3
1
3
1
1
1
0
0
1
1
0
0
1
2
0
1
1
1
2
1
1
0
0
1
0
0
2
2
0
0
0
2
0
2
0
2
0
1
0
3
0
0
0
1
1
1
0
1
1
2
0
2
1
0
0
0
1
1
1
3
0
1
0
1
1
1
1
0
0
1
0
1
1
1
2
0
0
2
2
0
2
1
0
1
1
1
1
2
0
1
2
0
3
1
1
2
0
2
0
2
2
2
1
1
1
2
1
0
1
2
1
2
1
1
1
0
1
0
2
3
2
1
0
1
1
2
1
1
1
1
1
1
2
1
1
1
2
1
1
0
1
0
2
1
0
0
0
0
0
1
0
1
0
1
0
1
2
0
0
0
1
4
0
0
1
1
1
2
0
1
0
1
0
1
0
2
0
0
1
0
2
0
1
0
1
1
2
0
0
1
2
0
1
1
1
0
0
0
1
1
1
4
3
0
0
0
0
2
2
2
2
0
0
1
0
2
2
1
0
0
1
1
0
0
2
1
0
0
0
0
2
0
0
1
2
1
0
1
0
0
2
1
0
1
0
1
0
1
0
0
2
0
0
1
0
2
1
0
0
0
1
0
1
0
0
2
2
1
2
1
2
0
2
2
2
0
0
1
1
1
1
0
2
1
1
0
2
0
2
1
2
0
1
0
1
0
1
2
1
2
0
1
0
1
0
1
0
2
1
1
1
1
0
1
0
0
1
1
2
0
2
1
0
1
2
2
0
0
0
1
0
1
0
2
0
0
0
2
2
0
2
1
1
0
0
1
0
1
1
1
2
0
2
3
0
0
0
0
0
1
0
2
1
2
1
0
1
0
2
0
1
0
1
1
0
2
2
0
0
0
1
1
0
0
0
1
0
2
1
1
1
0
2
0
0
0
1
1
1
0
2
1
1
1
1
1
1
1
1
2
1
1
2
0
0
0
2
1
2
2
0
0
0
1
0
0
0
2
0
1
1
0
1
0
0
2
2
1
1
0
0
2
0
2
0
2
2
0
1
1
0
2
1
1
3
1
1
0
1
0
1
1
1
0
2
0
1
0
2
0
2
2
3
2
0
1
1
0
1
0
0
0
2
1
0
0
0
1
0
1
1
1
1
0
1
1
0
1
2
0
2
0
1
0
0
2
1
2
1
1
1
2
0
0
0
2
0
1
0
2
2
0
1
0
0
1
0
1
1
0
1
1
1
1
0
2
0
1
1
0
1
0
0
0
2
1
0
0
0
1
4
0
2
1
1
2
1
2
1
1
0
1
1
1
2
1
0
1
0
1
1
1
1
7
1
0
0
0
1
0
0
0
1
1
2
0
2
1
1
0
1
2
0
1
0
2
2
1
2
0
1
1
2
0
1
0
5
2
0
1
1
0
0
0
0
0
0
0
1
1
4
1
0
2
0
2
0
1
1
1
1
0
2
0
1
1
1
2
2
3
0
0
1
1
1
0
1
1
0
0
0
1
1
1
2
0
1
0
1
0
0
1
0
3
0
0
1
2
0
3
1
1
0
0
1
2
0
0
1
1
0
0
0
1
0
2
0
1
1
2
0
1
0
0
2
1
1
1
0
0
0
0
2
0
0
1
2
1
0
0
0
1
0
1
0
0
1
2
0
1
0
1
3
2
1
2
1
1
3
3
0
1
1
2
1
0
2
0
0
0
0
2
3
0
1
0
0
0
0
1
1
0
2
1
3
0
0
0
0
0
2
1
1
1
2
0
1
0
3
1
3
1
2
0
1
0
0
2
0
0
0
0
1
2
1
1
2
2
1
0
1
1
1
1
0
1
0
0
1
0
2
1
1
1
0
0
3
2
0
2
1
2
1
0
1
3
0
1
0
1
0
2
0
0
1
0
2
1
2
1
1
1
1
0
2
0
1
0
0
2
1
0
0
0
1
1
2
0
1
0
0
0
1
1
1
1
2
0
1
0
0
2
1
0
1
1
1
1
0
0
1
1
1
2
0
2
0
1
2
2
1
0
1
2
2
0
0
0
0
0
0
0
1
0
2
1
0
0
1
1
2
2
2
1
3
0
2
1
1
2
2
0
1
0
1
0
0
0
1
0
0
1
0
0
1
2
1
1
0
0
0
0
0
1
2
1
2
0
0
0
0
4
0
1
0
2
1
1
1
0
0
1
1
2
1
0
2
0
0
0
2
1
1
0
0
0
2
1
8
0
0
0
2
1
0
0
0
0
1
3
0
1
0
1
2
0
0
1
1
2
0
0
0
0
0
2
0
1
0
1
1
2
0
0
2
0
3
1
2
1
1
0
0
2
2
0
0
1
1
1
2
2
0
0
2
1
2
0
0
0
0
0
1
2
1
1
1
0
1
0
1
2
2
0
0
1
1
0
0
0
1
2
1
1
0
0
1
1
1
0
0
0
0
2
1
1
1
1
1
1
0
1
0
0
0
0
1
0
2
1
1
2
0
1
2
0
2
2
0
0
2
0
2
0
2
1
1
1
0
1
1
0
1
2
3
1
1
0
0
2
0
1
2
0
0
1
0
1
1
3
0
0
2
1
0
0
2
1
0
1
1
0
1
0
2
1
1
1
1
0
0
1
1
2
0
1
1
2
1
0
1
0
1
0
1
0
0
1
2
0
1
1
1
0
2
2
2
0
2
1
1
3
0
3
0
2
1
0
0
2
2
2
0
1
0
2
1
0
1
0
0
1
1
0
0
3
2
2
1
3
0
1
1
0
1
0
1
1
0
1
2
1
1
2
0
1
0
0
1
2
0
1
0
1
1
2
0
2
0
1
0
0
1
2
1
1
1
0
0
2
1
1
1
0
0
1
0
1
0
0
2
0
0
2
1
0
1
0
1
1
2
0
0
1
1
0
1
0
1
1
1
0
0
1
0
0
2
2
0
1
1
1
1
2
1
0
1
1
0
1
2
2
1
1
1
2
1
2
1
2
0
1
0
0
2
0
0
2
2
0
2
1
2
1
0
1
1
1
1
1
1
0
0
2
0
2
2
2
1
1
0
1
0
2
0
0
2
0
1
0
0
1
0
0
0
2
1
0
1
2
3
2
0
1
1
2
0
1
2
0
1
0
0
0
0
2
0
2
2
0
1
2
1
0
0
0
0
2
1
0
2
1
1
0
1
0
0
0
0
1
1
0
1
0
1
1
1
0
0
1
0
1
1
0
2
1
0
0
0
2
1
2
1
1
2
0
0
2
0
0
2
2
1
1
1
0
2
1
1
2
2
1
2
1
1
1
0
1
2
0
2
1
2
0
2
2
1
1
2
2
0
0
2
2
0
1
0
0
0
0
0
0
1
0
2
0
0
1
1
0
1
0
1
3
0
0
1
0
1
0
1
0
5
2
0
1
1
2
0
2
3
0
1
0
0
0
0
0
0
2
1
1
2
0
0
2
2
1
1
2
1
0
0
1
1
3
1
2
1
0
0
1
2
1
1
1
1
1
0
1
1
0
0
0
2
0
1
0
1
1
0
1
2
0
1
2
1
0
0
1
0
1
0
1
0
1
0
1
0
0
1
0
1
0
0
1
3
1
1
1
1
1
1
1
0
2
0
1
0
0
1
2
1
1
0
1
0
0
0
0
0
0
1
0
1
0
1
0
1
1
0
1
0
1
2
0
0
2
1
1
0
0
1
0
0
0
0
1
1
1
2
0
2
1
1
2
1
0
2
0
1
0
1
1
2
0
0
0
1
1
2
0
1
1
1
0
0
2
0
1
1
2
1
1
2
1
0
2
1
0
2
1
2
0
0
1
2
1
0
0
0
1
2
1
0
0
0
2
1
1
2
0
2
0
0
1
0
2
0
0
1
1
0
1
0
0
1
0
1
0
2
1
1
1
0
1
0
0
1
0
1
0
0
1
2
1
1
0
0
2
2
0
0
0
0
1
2
0
2
0
0
3
0
1
1
0
2
1
2
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
2
2
0
2
1
4
1
0
1
0
2
1
1
0
1
1
0
1
0
0
2
2
0
1
1
1
0
2
1
2
1
0
1
0
2
1
2
0
2
1
0
1
1
1
1
0
1
1
0
1
0
2
1
1
0
1
0
1
2
0
1
0
1
1
0
0
1
0
2
1
0
1
1
2
1
1
1
0
0
2
1
2
0
1
0
0
0
2
1
0
0
1
1
2
1
1
0
2
0
1
0
0
0
2
1
1
0
1
1
0
0
1
2
1
3
1
0
0
0
0
0
1
2
1
0
1
1
0
2
0
0
1
1
1
1
0
0
0
1
0
0
0
0
1
1
0
1
1
0
1
0
2
1
1
0
0
1
3
1
2
0
2
1
2
1
0
0
0
2
0
1
0
1
1
1
2
1
1
1
0
0
2
1
0
2
1
0
1
0
2
0
1
0
1
2
2
0
2
1
2
1
0
2
0
2
0
0
0
1
1
0
0
1
1
0
0
0
0
0
2
0
2
0
0
2
0
2
1
0
0
1
0
0
1
0
2
0
0
1
0
1
1
2
1
2
2
2
1
2
0
1
1
1
2
2
1
1
1
0
1
0
1
1
2
1
1
1
1
0
1
1
0
1
1
1
2
0
4
0
0
1
0
0
0
5
2
0
0
1
0
0
1
0
1
1
0
0
1
1
0
1
0
2
0
1
0
1
0
0
0
1
1
0
0
0
2
2
1
0
1
2
0
2
0
0
1
0
2
1
1
0
2
0
0
1
1
1
0
2
0
1
2
1
2
0
1
0
2
1
0
1
1
0
2
2
1
1
1
0
1
1
2
1
0
1
1
1
1
7
0
1
2
1
0
1
0
0
0
1
1
0
1
1
1
1
1
2
0
1
1
0
2
1
2
0
0
2
0
0
0
2
1
1
1
1
0
1
0
0
1
0
1
1
0
0
0
1
1
2
0
0
2
0
2
1
2
0
0
1
1
2
1
1
1
0
1
1
1
1
0
0
1
0
2
1
0
0
0
2
0
1
2
1
4
2
0
0
1
2
1
1
0
1
2
0
2
1
2
0
1
2
1
0
0
1
1
1
0
3
2
0
0
2
0
2
2
0
0
0
0
1
0
1
0
0
1
0
0
0
2
0
1
0
0
1
1
2
2
2
1
1
2
0
0
0
2
0
1
1
1
2
1
1
0
1
2
2
0
0
0
1
1
1
1
2
1
1
1
0
0
1
0
0
2
1
0
2
2
0
0
1
0
1
0
1
1
0
1
1
1
1
0
0
0
2
2
0
2
0
0
1
0
2
2
0
1
0
1
1
1
0
0
0
1
3
3
2
2
1
2
2
0
0
1
3
0
2
0
1
0
2
0
0
2
0
1
0
0
1
1
0
1
1
2
2
0
1
0
1
0
1
2
3
1
1
0
1
0
0
1
2
2
1
0
0
2
1
1
2
2
1
1
1
0
2
1
2
0
2
0
2
2
1
0
0
1
0
1
1
0
0
1
1
0
1
2
0
0
0
0
2
0
1
2
0
2
0
0
2
3
0
0
2
0
1
1
1
0
1
2
1
0
2
1
0
0
1
1
1
1
1
2
1
1
1
1
0
1
1
0
1
1
1
0
1
1
4
1
0
0
0
1
1
1
0
0
0
2
0
0
0
1
2
2
0
0
2
0
1
0
0
2
2
0
1
0
1
1
0
1
1
1
0
2
1
0
0
0
0
1
1
5
0
2
1
1
2
2
2
1
0
0
0
1
1
1
2
1
0
0
1
1
0
0
1
1
0
1
1
0
1
2
0
0
0
0
1
1
1
0
0
1
0
1
2
0
0
1
2
0
0
1
1
2
2
1
4
1
1
2
1
2
0
0
1
1
1
0
0
1
1
0
2
0
0
0
0
0
0
0
2
0
2
1
2
0
1
1
0
0
2
0
0
1
1
0
1
0
2
0
1
2
0
1
1
0
2
0
2
2
4
0
2
1
1
0
2
2
2
0
1
0
2
2
0
1
1
2
0
0
2
1
0
0
1
1
1
1
1
1
2
0
2
2
1
1
0
0
1
1
0
0
1
0
1
1
0
2
1
0
0
0
0
0
2
0
0
0
1
2
1
0
0
2
0
0
0
1
2
0
1
1
1
2
2
1
2
1
1
0
1
2
0
1
0
0
0
1
1
1
1
0
2
2
2
0
0
0
1
0
1
1
1
2
2
1
1
1
0
1
0
0
0
0
0
2
1
1
0
0
2
2
1
1
2
2
0
0
2
1
1
0
1
2
1
2
2
1
0
1
0
0
0
1
0
1
0
1
1
1
0
1
2
0
0
1
0
1
1
1
1
0
0
0
1
1
1
1
1
2
1
1
2
0
0
1
2
0
0
0
1
0
1
1
1
2
1
1
2
1
0
2
1
1
1
1
0
0
1
2
0
0
1
2
0
0
2
1
1
0
6
0
2
0
1
0
2
0
0
2
2
2
1
2
2
1
0
3
1
1
2
0
0
0
1
0
2
0
0
2
1
0
0
1
1
2
0
0
0
1
0
0
2
0
0
0
1
1
1
0
1
0
0
0
2
0
1
0
1
0
1
0
1
1
0
2
0
3
0
0
0
3
1
0
2
2
1
2
2
0
1
1
2
0
0
1
0
0
1
2
0
0
1
0
0
0
1
4
1
1
1
2
1
1
1
0
0
2
1
0
1
2
2
1
1
1
2
1
0
2
2
0
1
0
1
0
1
2
1
0
0
2
2
0
1
2
0
0
0
1
1
0
1
0
2
0
0
3
1
1
0
1
1
1
1
0
0
0
1
0
0
1
1
2
1
3
0
2
2
0
2
1
2
2
0
1
2
3
1
1
1
1
0
0
0
1
1
0
0
1
1
2
1
1
1
1
1
0
2
1
1
0
2
2
1
1
1
1
2
1
1
0
1
1
0
2
1
1
0
0
0
0
1
1
2
0
0
0
1
1
1
1
1
2
0
2
2
0
2
1
2
1
1
1
0
1
2
0
4
2
1
1
0
0
2
2
1
2
1
1
0
1
0
0
2
2
1
2
1
1
0
2
1
1
2
1
0
2
1
2
1
1
1
0
1
0
1
1
2
1
2
0
1
0
0
1
2
1
2
1
0
0
1
0
0
0
0
1
0
2
1
1
2
2
0
0
0
1
1
0
1
2
2
0
0
2
0
0
1
2
0
1
0
0
1
1
2
1
1
0
2
1
0
1
1
0
0
1
2
0
1
0
2
0
1
2
3
2
1
1
0
0
1
2
2
1
1
0
0
1
2
1
1
0
1
2
0
1
1
1
2
0
0
0
2
1
1
1
0
2
0
1
0
2
1
0
1
1
0
1
0
1
1
0
0
0
2
2
1
2
0
2
2
2
1
1
2
1
1
0
3
0
1
0
0
1
1
1
0
2
1
1
1
1
1
2
0
2
1
0
3
1
1
1
0
1
1
1
0
0
0
2
2
1
1
0
2
0
3
1
2
2
0
0
1
1
0
2
1
2
0
0
0
1
0
1
1
0
2
0
1
0
0
2
0
1
2
2
2
2
1
0
1
2
1
0
1
1
2
0
1
1
0
0
2
0
1
1
2
1
1
1
1
0
0
0
0
0
1
1
0
3
1
2
0
1
2
2
2
1
1
2
1
1
2
2
1
2
1
1
2
0
0
3
0
2
1
1
1
1
1
1
0
0
0
0
2
0
2
0
1
2
0
1
2
0
1
1
2
0
2
2
0
1
1
1
1
1
1
0
0
0
2
0
0
2
0
0
0
2
1
2
2
2
0
0
1
2
2
0
0
2
0
0
0
0
1
0
0
0
2
0
1
0
0
0
1
0
0
0
2
0
0
1
2
0
0
0
0
0
2
0
0
1
1
1
1
2
1
0
1
0
1
1
2
1
2
1
0
2
1
0
0
0
2
1
1
2
0
2
1
1
1
0
0
0
2
1
2
0
0
1
1
0
1
0
1
1
1
0
2
0
0
1
2
0
0
1
1
1
0
1
1
2
1
0
1
2
1
1
2
0
0
1
0
2
0
0
2
1
0
0
1
2
0
1
0
1
0
0
1
2
2
1
3
2
0
2
2
1
2
1
2
0
0
0
0
1
1
1
1
0
0
2
2
1
1
0
0
1
0
0
2
1
1
2
0
1
1
0
2
2
1
0
0
1
0
1
0
1
1
1
2
1
1
1
2
0
0
0
1
2
0
1
2
0
0
1
1
0
2
0
0
1
1
0
2
0
2
2
1
0
1
1
0
0
1
1
1
0
2
1
2
0
0
0
2
1
0
2
2
2
1
1
0
0
2
2
1
0
0
2
1
0
0
1
2
1
1
1
1
1
1
2
3
2
1
1
2
0
1
1
2
2
0
1
0
2
2
4
2
1
0
2
1
1
1
0
0
0
0
1
2
1
0
0
1
1
4
1
0
1
2
2
0
2
1
1
0
0
2
2
0
0
1
1
0
0
2
1
0
1
1
1
0
0
2
2
1
1
0
1
1
1
0
0
0
1
2
0
0
0
0
0
1
0
0
1
0
1
0
2
1
0
0
0
1
0
0
2
1
2
2
1
0
0
1
1
0
2
1
0
3
1
0
3
0
0
1
1
1
1
2
2
0
2
2
1
1
1
1
3
2
0
0
2
2
1
1
1
0
1
1
0
2
0
1
1
1
1
1
0
2
0
0
0
1
2
1
1
0
1
0
0
0
2
1
1
2
1
0
0
1
2
1
1
0
1
1
0
1
2
1
1
1
2
0
0
1
1
0
1
0
2
1
1
2
0
1
0
0
0
1
1
1
0
2
1
0
0
1
1
1
0
2
1
0
0
1
0
0
1
0
1
2
2
1
0
2
2
1
0
2
2
2
0
2
1
0
2
0
0
0
0
1
2
2
1
0
2
2
1
1
1
0
2
0
2
2
1
1
2
0
0
2
0
0
0
0
2
0
2
1
0
0
1
0
2
2
2
0
0
0
2
0
1
0
2
0
2
2
2
0
1
0
0
2
2
1
0
2
0
0
1
2
1
1
0
2
0
0
1
1
1
1
3
1
2
0
0
1
2
0
1
0
1
2
1
0
0
1
1
0
0
0
2
1
2
1
2
1
1
1
2
1
1
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
1
1
0
1
0
0
0
2
0
0
1
0
0
1
0
1
1
1
1
0
2
0
2
0
0
0
0
1
0
0
0
1
1
1
2
1
0
1
0
0
0
0
1
1
0
0
2
0
2
1
1
3
2
1
0
0
0
0
1
1
1
0
2
1
0
0
1
0
1
0
0
0
0
0
2
2
3
2
0
2
1
1
1
0
1
2
2
2
0
4
1
2
1
0
0
2
1
1
1
0
1
1
1
0
0
0
0
2
1
0
1
0
0
1
0
0
2
0
0
1
0
4
2
0
1
1
0
2
0
1
0
3
0
0
0
2
2
1
1
0
1
1
2
1
1
2
1
0
0
2
0
0
0
0
2
0
3
1
2
0
0
0
2
1
1
1
1
1
1
2
1
2
1
0
2
2
0
0
0
0
0
0
0
1
2
1
1
1
2
0
1
0
0
1
2
0
2
0
0
1
0
0
1
1
1
0
0
1
2
0
0
1
4
0
3
1
1
0
0
2
1
1
1
0
2
0
0
1
3
1
2
0
0
1
0
1
1
2
1
2
1
0
0
0
1
1
0
0
2
0
1
1
0
1
0
0
1
0
2
1
1
1
1
0
0
2
1
0
2
0
1
0
1
0
1
0
0
1
0
0
2
0
2
0
0
2
1
1
0
2
1
1
1
0
2
0
0
1
0
2
2
1
1
1
3
1
2
1
0
2
1
2
2
0
0
0
0
1
2
1
1
2
1
0
2
0
0
0
2
1
0
0
0
0
1
1
2
2
1
2
0
2
0
1
2
1
0
0
0
1
1
2
0
2
0
2
0
1
2
0
0
3
0
1
1
1
0
2
1
0
2
0
1
1
1
0
0
1
1
2
0
2
0
2
0
0
1
1
0
1
0
0
1
1
0
1
1
0
2
1
3
2
1
1
0
2
2
0
0
1
2
0
1
1
0
0
0
0
0
1
0
0
2
2
0
0
1
0
0
0
0
1
0
0
2
3
0
1
1
2
0
0
0
1
2
2
0
0
0
0
2
0
2
0
1
1
0
0
0
1
2
2
0
1
2
1
0
1
0
2
1
0
2
1
0
1
1
1
0
0
2
1
1
0
1
0
1
0
2
1
0
1
2
0
0
0
2
1
1
0
1
0
0
0
0
2
2
2
0
1
2
0
1
0
0
0
2
0
2
1
1
2
0
2
1
1
2
1
1
2
1
0
1
1
1
0
1
0
0
1
2
1
1
3
4
1
2
2
1
0
1
1
1
0
1
0
0
0
1
1
0
1
1
1
0
1
2
1
2
0
0
1
0
2
3
1
3
1
1
2
1
0
0
0
1
1
2
1
2
2
0
1
1
0
0
0
0
0
0
1
3
2
0
2
1
1
1
1
0
1
0
0
0
0
1
0
0
0
1
1
1
0
2
1
0
0
2
0
0
2
0
1
1
0
1
0
0
1
1
0
1
0
0
1
0
2
0
1
0
1
1
1
0
1
2
0
0
0
1
0
0
1
2
0
1
1
0
1
0
1
0
2
2
3
1
0
0
4
0
0
0
0
1
2
3
0
2
2
0
1
0
1
3
0
1
1
1
1
0
0
2
0
1
0
1
1
0
1
1
2
1
2
0
0
1
0
2
1
0
2
0
1
0
0
0
1
0
0
4
0
1
1
1
2
2
1
1
2
1
0
1
1
6
0
5
1
2
0
2
2
1
1
1
0
1
2
1
1
2
0
1
0
0
0
0
1
1
0
0
1
1
1
0
0
0
1
2
0
2
1
0
1
0
0
0
1
2
1
2
2
1
2
1
0
0
1
0
1
0
2
0
0
1
1
0
1
1
2
1
1
1
0
1
1
0
0
0
1
0
0
0
0
0
2
1
2
0
1
0
0
2
3
0
1
0
1
1
0
1
0
2
1
0
0
0
2
0
1
0
1
0
2
0
0
0
1
1
1
0
0
1
1
1
1
1
1
0
2
0
0
0
0
0
2
2
1
0
0
1
1
0
0
1
0
2
2
0
1
2
1
1
1
1
0
1
1
1
0
0
0
0
0
2
2
1
2
0
2
2
1
1
0
0
1
2
0
1
1
1
1
1
2
1
0
1
1
0
1
1
0
2
0
1
1
1
1
2
1
0
0
2
0
0
0
0
0
1
1
1
1
1
0
0
1
0
2
0
1
2
1
2
1
2
1
1
1
1
2
2
1
0
1
0
1
1
1
1
1
2
2
1
1
0
1
2
1
1
0
1
0
1
0
1
1
2
1
1
0
2
0
0
2
2
0
1
1
0
0
3
0
1
2
2
2
2
1
1
1
1
2
1
2
1
0
1
1
1
2
0
0
0
0
0
2
0
1
2
0
1
0
2
0
0
1
1
0
1
0
0
0
1
0
1
2
0
1
2
0
2
0
2
0
0
0
1
0
2
0
2
0
2
1
0
2
1
1
1
2
2
2
2
1
0
0
1
1
0
1
2
1
0
0
0
2
2
2
0
1
0
0
0
0
2
0
2
0
1
0
0
0
0
1
0
0
1
1
1
0
1
0
1
0
2
0
0
2
0
1
0
0
0
1
2
4
2
1
0
0
0
1
1
0
0
1
2
2
0
0
0
1
1
1
0
0
0
1
1
1
2
2
0
2
0
0
2
1
3
1
1
1
0
0
2
1
0
2
1
1
1
1
1
2
1
1
1
1
0
2
1
2
0
1
0
1
1
2
1
0
0
2
0
1
0
2
1
0
1
1
1
0
0
0
0
0
2
1
2
1
1
0
2
1
1
1
0
0
1
2
0
0
1
2
0
0
0
3
2
0
1
0
0
2
1
0
0
0
2
0
0
0
1
0
1
0
1
2
1
1
1
2
1
2
1
1
0
2
2
0
0
1
1
0
1
1
1
1
1
1
0
1
0
0
2
1
0
0
2
2
0
2
0
1
0
2
2
0
0
1
1
2
1
1
0
1
0
0
1
0
1
0
1
0
1
1
1
0
1
1
2
1
0
1
1
2
0
0
1
1
1
0
2
1
2
0
1
0
0
0
2
1
0
2
2
2
2
0
0
0
2
1
0
0
1
1
0
0
0
2
1
1
1
1
1
1
2
0
2
0
2
1
1
1
0
1
0
1
0
2
1
0
1
0
0
1
0
2
1
0
2
1
2
3
0
1
2
2
1
1
2
2
0
0
1
1
2
1
1
0
0
0
1
0
0
1
0
1
2
1
1
2
0
2
1
1
0
0
1
0
0
1
1
0
1
0
1
1
1
2
0
1
2
0
0
1
2
0
0
1
2
2
4
0
2
1
1
2
1
2
1
0
2
0
2
0
3
1
1
1
0
0
1
1
0
0
1
1
0
2
2
2
0
0
0
1
2
0
0
1
2
1
1
0
2
0
0
1
2
2
0
0
1
0
1
0
0
0
1
1
0
0
2
0
1
2
0
1
3
1
0
0
1
1
2
1
2
1
1
0
1
1
2
2
3
1
1
0
0
1
1
0
0
1
2
1
1
1
0
1
1
0
0
1
0
0
1
1
0
0
1
0
0
0
0
2
1
1
1
1
0
0
1
1
2
1
0
0
1
1
1
0
1
1
1
1
2
1
0
1
2
0
2
2
1
1
0
1
0
0
0
2
0
0
0
0
0
1
1
1
1
1
2
2
1
1
1
2
1
2
1
1
1
0
2
2
2
2
1
0
0
2
2
1
0
1
1
0
2
2
1
0
3
0
0
0
0
1
2
2
2
1
1
1
1
2
2
1
1
0
0
2
2
2
1
0
1
1
1
1
1
0
2
0
2
1
1
1
1
1
0
0
1
2
2
1
1
1
2
1
1
2
0
0
1
2
0
1
2
1
0
2
0
1
0
1
1
0
1
1
0
1
1
2
0
1
1
1
1
0
2
1
3
2
0
1
1
0
1
1
2
1
0
0
1
0
0
0
1
0
0
1
0
0
2
4
0
1
1
2
1
1
0
1
2
0
0
1
1
0
1
1
0
2
2
1
1
3
1
1
0
2
1
0
1
0
0
1
2
2
1
1
1
1
1
1
0
0
0
0
1
2
1
2
1
2
1
2
1
1
0
1
2
1
1
0
3
1
2
2
2
0
0
0
2
0
2
1
0
0
1
0
2
1
0
0
1
0
2
0
0
1
0
0
0
2
1
0
0
3
2
0
1
2
0
1
1
0
1
2
0
0
2
1
0
1
1
0
0
1
0
0
1
1
0
0
1
0
1
1
0
0
1
3
1
1
0
1
0
1
0
1
0
2
1
2
1
3
0
0
0
1
1
1
0
2
1
2
1
1
2
1
1
1
1
0
1
1
1
1
1
0
1
1
0
1
1
0
0
2
1
0
0
0
2
0
0
0
2
0
0
0
0
2
2
2
0
1
1
2
2
0
0
1
0
1
1
1
1
0
2
1
2
2
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
2
1
0
1
1
1
1
3
0
0
0
1
1
1
0
0
1
1
0
0
1
2
2
1
3
1
1
1
2
0
0
1
1
2
0
0
1
0
0
0
0
0
1
1
1
0
1
1
0
0
1
0
0
2
2
0
0
2
1
0
1
0
1
1
1
0
1
1
1
1
1
2
3
1
2
0
0
1
0
1
1
1
0
0
0
0
1
0
0
1
1
1
1
1
1
1
0
0
0
1
0
2
0
2
1
0
1
0
2
0
0
0
0
0
0
1
0
1
2
0
1
0
1
1
0
0
2
0
1
1
1
1
2
0
0
2
0
0
1
1
0
0
2
1
1
2
0
0
2
1
1
0
0
1
1
0
6
0
1
2
2
2
0
0
0
0
0
1
0
0
2
1
0
2
0
0
1
1
0
1
1
1
0
1
0
0
0
0
0
1
0
1
0
1
1
1
0
1
2
3
0
1
1
1
2
0
1
1
1
0
2
2
0
3
1
0
0
0
1
0
1
2
1
2
2
1
0
1
0
2
2
3
2
0
0
1
2
2
0
2
1
0
1
0
0
1
1
2
1
2
1
1
0
0
1
1
1
1
0
2
0
2
1
0
1
1
1
1
1
1
0
0
2
2
0
1
0
0
1
2
0
0
0
5
1
0
1
1
1
4
0
2
0
2
1
0
2
0
0
0
2
0
2
0
2
2
0
2
1
0
2
1
1
0
1
2
0
1
1
2
1
0
2
1
1
0
2
1
0
0
0
1
0
2
0
3
2
0
0
1
1
1
0
0
0
0
2
1
0
0
1
0
0
1
0
1
2
1
1
0
3
0
1
0
1
2
1
0
1
2
1
0
0
6
2
1
1
1
1
3
1
1
0
1
0
1
1
1
1
1
2
3
0
0
1
0
1
3
1
0
1
2
2
2
0
0
1
2
0
1
0
2
1
2
1
2
0
0
2
0
1
1
0
0
1
1
0
0
2
1
2
1
1
0
0
1
1
1
2
0
1
0
1
2
0
1
1
0
0
0
0
1
0
0
2
2
0
0
0
1
1
1
0
0
1
0
1
1
0
0
0
1
1
1
0
1
0
0
2
0
2
1
0
1
0
2
2
1
0
2
0
1
1
0
0
1
1
0
1
1
1
0
0
1
1
0
2
0
0
2
0
1
2
0
0
0
0
1
0
1
1
1
2
2
1
1
1
2
1
1
1
0
1
0
0
1
0
2
0
2
1
2
0
2
0
0
1
2
1
1
1
0
2
0
1
2
0
2
1
1
1
1
0
0
1
2
1
1
2
0
1
1
1
1
1
0
0
1
1
0
1
2
0
1
0
0
0
0
0
1
1
2
1
1
2
2
0
0
2
1
0
0
0
1
2
1
2
0
1
0
1
0
0
2
1
0
0
2
0
0
2
0
1
1
2
1
1
2
1
0
1
1
0
0
0
2
0
2
1
1
1
2
1
2
1
2
0
1
0
1
1
0
0
1
2
0
2
0
0
2
1
0
1
1
0
0
2
2
1
1
0
1
1
0
1
2
0
2
0
0
0
0
2
0
0
1
0
2
1
1
0
2
0
2
0
1
0
1
0
1
1
1
2
2
0
1
2
1
2
1
0
1
2
1
0
2
0
0
2
2
2
1
0
1
0
0
1
1
2
1
0
1
1
0
0
1
0
2
1
0
0
0
0
1
1
2
1
1
7
0
1
2
0
1
1
0
1
0
0
0
0
3
1
1
1
1
0
0
0
2
1
0
0
0
0
2
1
0
2
1
2
2
0
2
0
0
0
0
1
0
2
2
2
0
1
1
2
0
0
1
1
2
2
0
1
1
2
2
1
0
2
1
1
1
0
1
0
0
1
2
0
1
0
0
0
2
1
2
2
2
2
2
0
1
0
0
0
1
1
1
1
0
1
1
2
1
1
2
2
0
0
0
0
0
1
2
2
1
1
0
1
2
2
1
1
2
0
0
1
1
1
0
1
2
1
0
0
1
1
0
1
0
1
2
1
0
0
2
1
1
0
0
0
0
0
0
1
2
2
0
0
0
0
0
2
1
0
0
1
0
2
1
0
0
1
1
0
2
0
0
0
0
0
1
1
1
1
2
3
0
1
1
2
1
0
0
2
0
2
1
0
2
2
0
1
0
2
1
0
0
1
1
0
1
0
2
1
2
0
0
0
2
0
0
0
0
2
0
2
0
0
0
2
0
1
1
2
0
0
0
2
2
0
1
1
0
1
1
2
1
2
2
0
1
2
0
2
1
1
0
1
3
2
1
0
0
0
1
1
0
1
1
0
0
1
2
0
0
1
0
0
0
0
2
1
0
0
1
1
1
0
0
0
0
1
0
1
1
1
1
1
0
0
0
1
1
0
2
1
2
1
1
0
0
0
0
1
1
1
2
0
2
1
1
1
0
1
0
0
0
2
2
1
1
1
1
0
2
0
0
1
1
1
1
2
1
2
1
0
1
1
0
0
1
1
0
1
0
2
1
1
0
2
2
0
2
1
2
0
0
1
2
0
2
0
1
2
1
2
2
0
0
0
0
0
2
0
0
1
2
2
1
1
0
0
2
0
0
0
1
0
0
2
0
1
1
0
2
1
1
1
1
2
1
0
1
2
2
0
1
0
0
0
0
1
1
2
1
0
0
2
1
2
1
2
2
1
1
0
0
1
0
2
0
2
0
0
0
1
0
0
0
0
2
0
1
0
0
1
0
2
2
2
1
1
1
0
0
1
0
0
0
2
1
1
1
0
0
1
0
1
2
1
0
0
1
1
1
1
1
2
1
1
0
0
2
1
1
2
0
0
1
1
0
1
0
2
0
0
1
1
0
1
0
1
1
1
1
2
0
2
1
1
1
0
0
1
0
1
0
1
0
1
2
1
0
2
2
1
0
0
1
0
0
1
2
1
1
0
0
1
0
1
1
2
1
0
1
0
0
0
1
1
0
2
1
1
1
2
0
0
0
2
0
2
0
1
0
2
2
0
1
0
0
2
2
0
2
0
2
2
2
1
0
2
0
2
1
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
1
1
2
1
1
2
0
1
2
0
2
0
1
1
0
0
1
0
0
0
1
2
0
1
0
1
1
1
1
0
0
2
0
2
2
1
0
2
1
0
0
2
2
0
0
0
0
1
2
1
0
0
1
0
2
0
0
1
1
3
1
1
0
1
1
1
2
0
1
2
1
1
1
0
2
1
0
0
1
2
3
0
1
0
0
1
2
2
1
1
2
0
2
1
0
1
1
0
1
2
0
2
0
0
0
1
0
1
0
2
2
1
3
2
2
1
1
1
2
2
1
2
0
0
1
0
0
0
1
0
1
0
2
2
0
2
2
0
0
0
2
2
3
1
1
1
1
1
2
2
2
1
2
0
2
1
0
0
2
2
2
2
0
1
0
1
0
0
2
2
0
0
1
2
1
0
0
1
2
2
2
2
1
0
0
1
1
0
1
1
0
0
2
2
0
0
1
0
2
0
2
1
1
1
2
0
1
1
0
1
1
0
0
1
0
0
1
1
2
1
1
2
2
4
0
1
1
1
2
2
0
0
1
0
0
1
1
1
0
0
1
2
3
1
0
1
1
1
1
0
1
1
2
2
1
2
0
0
4
1
1
1
1
0
0
1
0
0
2
0
1
1
1
2
2
1
1
1
2
0
1
1
0
3
2
0
1
0
1
1
1
1
0
0
0
1
1
1
1
0
0
0
0
1
0
2
1
1
0
1
1
2
1
1
2
2
0
2
1
1
0
1
1
2
0
1
0
1
2
0
0
0
0
1
0
2
2
1
1
0
2
2
0
1
1
2
1
0
1
0
0
0
1
2
1
1
0
0
0
1
2
1
0
0
2
0
1
1
0
0
1
0
1
2
1
0
0
1
2
0
0
2
1
0
1
0
2
0
2
1
2
1
1
2
0
0
0
1
1
0
0
0
2
1
2
3
0
1
2
1
2
0
2
2
1
2
0
0
1
1
0
0
1
1
0
1
1
2
1
1
2
1
0
1
0
2
2
0
0
2
1
0
0
2
0
2
2
0
1
1
1
1
0
0
1
0
0
4
1
2
0
2
0
1
0
2
0
0
2
1
2
2
1
1
1
1
1
2
0
1
2
0
1
1
2
0
1
0
0
0
0
0
1
0
0
0
1
2
3
1
2
0
0
2
1
2
1
2
2
2
0
2
0
1
0
2
2
0
0
2
2
1
2
0
1
2
0
0
1
1
2
2
0
1
1
1
2
1
0
0
2
1
2
0
1
1
0
0
0
1
2
0
0
1
1
2
0
0
0
0
0
0
2
1
1
1
1
1
1
1
0
2
1
2
1
1
0
1
1
2
0
1
0
2
0
4
0
1
0
0
1
0
2
1
2
0
1
0
2
2
0
1
0
1
0
0
2
4
1
0
0
0
2
0
1
1
2
0
1
1
1
2
0
0
0
1
1
1
0
2
0
0
2
0
2
0
0
0
0
0
1
1
1
2
1
1
2
2
0
1
0
0
0
2
0
1
2
0
0
1
2
0
0
1
0
0
4
1
0
2
0
1
2
0
0
2
1
0
0
1
1
0
0
0
0
1
1
0
0
1
0
1
0
2
1
1
1
1
1
0
1
1
0
0
2
1
2
0
1
2
2
1
2
1
4
1
1
2
1
1
1
0
1
2
2
1
0
1
0
1
1
0
1
1
0
0
0
2
0
2
0
2
2
2
0
1
0
1
0
0
1
0
0
2
0
0
0
0
2
0
2
1
0
1
2
0
0
1
2
0
0
2
0
0
0
2
0
2
2
1
1
2
0
2
0
1
1
1
1
0
1
1
1
1
1
2
0
0
0
2
1
1
1
0
1
0
1
1
0
0
1
1
0
1
0
1
1
1
0
0
0
1
2
2
1
0
2
0
0
1
0
0
1
0
2
2
1
0
2
0
2
1
1
2
1
2
2
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
1
0
1
1
0
0
2
0
1
1
1
2
1
1
0
2
0
0
0
1
0
0
1
1
0
1
2
0
1
1
1
1
0
1
0
1
1
0
2
0
2
2
1
1
0
0
0
1
1
1
0
1
1
1
0
0
2
0
0
3
2
0
0
1
1
0
0
1
2
1
1
1
0
0
0
1
2
1
0
2
0
0
0
2
0
0
0
2
1
0
2
1
1
0
1
2
1
1
0
0
0
1
0
0
1
4
1
2
0
1
1
3
2
0
0
0
1
0
3
0
1
2
0
0
2
1
1
0
1
0
1
1
1
1
0
0
1
2
1
1
0
2
0
0
1
1
0
1
2
2
2
1
1
2
1
1
0
1
0
1
1
0
3
0
1
1
0
1
0
2
1
1
1
1
1
2
3
1
2
0
0
0
2
2
1
1
0
0
2
1
1
0
0
0
0
1
0
1
0
0
2
1
0
0
2
2
1
2
1
0
1
1
0
0
0
1
1
1
1
1
1
0
0
0
0
0
0
1
1
2
1
2
1
2
0
0
3
1
0
0
0
0
0
1
0
1
2
1
0
1
1
2
0
2
2
0
0
0
1
2
1
2
0
2
2
2
0
1
2
0
0
1
0
1
2
0
1
1
1
1
0
0
0
2
1
3
2
2
2
1
2
0
2
1
2
0
0
2
2
1
0
0
0
0
2
3
1
2
2
0
1
4
1
0
1
1
0
0
1
2
2
1
1
0
0
1
1
0
2
1
1
0
0
0
2
1
0
1
0
0
2
0
1
0
0
2
2
0
2
1
1
1
0
2
0
1
1
1
0
0
2
2
1
2
1
1
0
1
0
1
0
0
0
0
0
0
0
1
0
1
2
2
2
0
0
1
0
2
1
1
0
0
2
2
0
0
2
1
0
0
1
1
0
0
0
0
0
2
1
0
1
2
0
0
1
2
0
1
1
0
0
2
0
1
2
1
1
0
0
3
2
0
0
0
0
2
1
1
0
1
1
1
1
1
0
1
1
1
2
2
2
0
0
2
0
1
1
0
0
2
0
0
0
2
1
1
1
0
1
0
1
0
0
2
1
0
1
1
0
0
1
0
0
1
0
0
2
0
0
2
1
1
1
0
1
1
0
1
0
1
0
0
1
1
0
0
1
0
1
0
0
0
1
0
0
2
2
4
0
2
0
0
1
0
2
0
1
2
1
0
2
2
1
3
0
1
1
0
1
0
1
1
1
1
1
2
1
2
1
1
0
0
0
3
2
1
1
1
0
1
0
0
1
0
0
1
0
0
1
1
1
2
0
1
0
2
1
1
0
2
1
1
2
0
1
2
0
2
2
1
1
1
0
2
2
2
0
0
0
0
0
1
1
2
0
0
0
1
1
0
0
0
1
2
0
1
1
1
2
1
0
2
2
2
0
0
0
1
1
1
2
2
1
0
2
0
2
1
0
1
0
0
0
2
2
1
0
1
0
2
1
2
0
1
1
2
0
1
0
1
0
1
1
1
0
0
0
1
1
2
1
2
1
1
1
0
0
0
1
1
0
2
0
1
0
0
0
0
2
1
1
0
2
0
0
0
0
1
0
2
2
7
0
2
2
0
0
1
0
0
1
0
1
0
0
1
2
1
2
1
2
1
0
2
1
1
2
0
0
0
0
0
0
0
1
0
2
1
0
2
2
2
1
0
0
1
2
0
2
1
1
0
1
2
1
2
0
2
1
0
0
2
1
1
2
4
0
1
1
0
1
1
1
0
2
1
1
4
0
1
0
1
0
0
1
0
0
1
1
2
2
2
1
0
0
0
1
0
1
2
0
0
0
1
2
2
1
1
3
2
1
2
0
0
2
2
1
2
0
1
0
0
2
1
1
1
0
0
0
1
0
1
0
2
1
0
0
0
1
3
3
2
0
1
0
2
0
2
1
0
1
2
0
0
0
1
0
3
1
2
2
1
0
1
1
1
1
1
1
0
1
1
0
2
1
2
2
1
1
1
1
1
1
2
0
1
0
0
2
0
0
2
1
2
0
2
0
1
1
2
2
1
0
1
0
0
1
0
1
1
0
0
0
1
0
2
1
0
0
1
2
0
1
1
0
0
1
0
0
0
1
2
2
2
1
1
0
0
0
2
2
1
0
1
0
3
2
2
2
2
1
0
0
2
0
2
0
2
2
0
2
0
0
1
1
1
0
0
1
0
1
1
1
1
0
2
1
0
0
0
1
1
0
1
1
0
0
2
1
1
1
1
0
1
1
2
1
1
2
1
2
2
0
0
0
1
0
2
1
1
1
0
2
0
1
1
1
1
0
0
2
2
0
0
2
0
1
0
0
1
1
0
0
0
1
0
0
0
1
2
2
2
5
1
2
0
1
2
0
1
1
1
1
0
2
1
0
2
2
1
1
2
2
2
1
1
0
1
1
0
0
1
0
0
2
0
0
1
1
1
1
0
0
0
0
1
2
1
2
3
0
0
1
2
1
0
1
1
1
1
0
1
1
1
1
0
2
1
1
0
0
0
0
0
1
2
0
1
1
0
1
0
2
1
1
1
0
1
2
0
2
1
1
0
0
0
1
0
2
1
1
1
2
1
0
0
1
0
1
0
1
2
1
0
0
2
0
0
2
2
1
1
0
2
2
2
0
1
0
1
1
1
0
1
1
0
1
1
0
0
0
1
1
1
0
0
1
0
1
1
1
2
0
1
2
1
1
0
0
0
2
0
0
2
2
2
0
2
0
3
1
1
1
1
0
1
2
2
0
1
1
0
0
0
0
2
1
2
0
0
2
0
0
1
0
3
2
2
1
0
0
1
2
0
1
0
1
1
1
2
1
1
2
1
0
0
1
0
1
0
2
0
1
2
1
0
2
0
1
1
0
1
2
1
1
2
0
0
1
0
0
0
2
1
1
1
1
0
1
1
0
2
0
2
0
1
0
1
0
0
1
0
0
2
3
1
0
0
0
0
1
0
1
1
0
0
0
1
0
0
1
1
0
0
1
0
2
0
1
0
0
0
1
1
0
2
0
0
1
1
0
1
1
0
2
0
1
0
1
0
0
0
1
1
2
0
0
1
0
0
1
0
2
0
1
0
0
0
2
0
0
0
2
0
1
0
0
0
0
1
0
0
2
1
0
1
1
5
1
0
0
0
0
1
1
0
2
1
2
3
0
0
2
0
0
1
0
0
2
1
0
2
0
0
2
1
0
1
1
1
1
0
1
0
2
2
2
1
0
1
0
1
2
2
0
1
0
2
1
1
2
1
1
0
2
0
1
0
0
0
0
0
2
1
0
0
1
0
2
1
0
0
2
2
0
0
1
2
1
0
2
0
2
1
1
1
2
0
2
0
0
0
0
1
1
1
0
1
2
2
2
1
1
1
1
1
0
1
0
1
1
0
0
1
0
1
0
1
1
2
0
0
0
0
2
1
2
0
1
2
0
0
0
0
2
1
0
0
0
2
1
1
0
1
0
1
1
2
0
1
0
1
2
1
0
1
0
1
0
2
0
0
2
1
1
0
1
2
0
0
1
0
0
1
2
1
1
1
0
1
1
0
1
0
2
1
0
1
1
0
0
1
1
0
1
2
0
0
1
2
0
1
1
0
0
1
0
2
0
5
0
0
0
1
2
2
1
0
0
2
0
1
1
2
4
0
1
0
1
0
0
0
0
0
0
2
2
0
2
2
1
1
2
1
0
1
0
1
1
0
1
0
1
0
2
0
0
1
0
2
0
1
0
1
1
0
0
1
0
2
1
1
0
2
2
2
0
2
0
1
0
1
0
2
0
2
0
1
1
5
1
1
0
0
1
1
0
1
1
1
0
2
1
2
0
2
1
0
2
0
1
1
3
1
1
1
1
0
0
1
2
0
2
0
2
1
0
2
1
1
0
2
0
0
0
2
0
0
1
1
1
0
1
1
2
0
0
2
0
2
1
1
8
2
0
1
1
1
2
1
2
0
0
1
1
1
1
0
1
0
2
1
2
3
1
2
1
2
0
1
0
1
1
0
0
0
0
0
2
1
2
2
0
0
1
0
1
0
0
0
1
0
2
2
1
0
2
2
0
2
0
0
2
1
2
0
0
2
0
0
0
0
2
1
0
1
0
1
0
0
1
2
2
0
0
0
1
4
2
0
2
1
0
1
2
2
1
2
1
0
0
2
2
2
0
2
2
1
1
0
1
0
0
1
1
2
1
0
0
0
0
0
1
1
1
1
1
1
1
3
0
2
1
0
0
2
1
0
0
0
2
3
1
1
0
1
1
1
2
0
2
2
2
1
2
0
0
0
0
1
0
1
0
2
0
2
2
1
1
0
1
0
1
2
1
1
0
1
0
1
0
0
0
1
0
2
0
0
0
1
1
2
1
1
0
0
0
2
0
0
0
0
1
1
0
1
1
1
1
0
1
0
1
0
0
0
0
1
1
1
0
2
1
1
1
0
2
0
1
1
1
0
2
0
1
1
0
0
0
1
0
1
1
1
2
0
1
1
1
2
0
1
1
0
0
2
0
0
1
0
1
0
1
0
1
1
1
0
0
1
1
0
0
1
0
1
0
0
1
0
2
1
2
4
1
1
1
0
2
0
0
2
2
1
2
0
0
2
0
0
0
1
1
2
0
2
0
1
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
1
1
1
1
2
0
2
0
1
0
3
1
1
2
1
0
1
0
1
1
0
1
0
0
0
0
2
0
1
0
0
1
1
1
1
1
0
0
0
0
0
1
1
2
1
0
0
1
0
2
1
2
0
2
0
1
1
3
1
2
2
0
0
0
0
2
0
2
2
1
1
0
1
1
0
1
1
1
2
1
0
0
0
1
0
0
2
0
2
2
0
4
0
0
1
0
0
2
0
2
2
1
2
1
1
0
3
2
1
1
0
1
1
0
2
2
1
0
1
1
1
2
2
1
0
1
2
0
1
2
1
1
1
0
1
0
2
1
0
1
0
1
1
0
1
0
0
2
1
0
1
0
1
4
0
2
0
0
2
1
0
0
0
0
3
1
1
0
0
0
0
0
2
1
1
0
1
1
1
0
1
1
2
2
1
0
1
2
0
2
0
0
1
0
0
1
1
0
0
1
0
1
1
1
1
0
0
0
0
1
0
1
1
0
0
1
0
0
0
1
1
1
1
0
0
0
0
1
1
0
0
0
1
0
1
2
0
0
1
2
1
0
3
0
1
0
1
0
0
0
1
0
0
1
0
2
1
0
1
1
0
0
4
0
0
2
1
1
0
0
1
2
2
0
0
2
0
1
1
2
0
0
0
0
1
1
1
1
0
1
0
0
2
1
2
0
2
0
1
1
1
0
2
1
1
0
0
1
0
1
1
0
0
2
1
0
0
1
0
0
2
0
0
1
1
0
0
1
2
1
0
1
0
2
0
2
0
2
1
1
0
2
1
0
1
2
1
0
1
0
1
1
0
3
2
1
1
1
2
1
0
1
2
2
1
1
1
0
1
1
1
1
1
2
1
3
0
1
2
1
2
0
1
3
0
3
0
0
0
0
2
0
1
2
0
0
1
2
1
0
0
1
0
0
1
0
0
0
0
1
2
1
2
0
1
2
0
0
0
1
3
0
2
1
0
1
1
1
1
2
1
2
1
1
0
2
0
2
1
2
2
2
2
3
1
2
0
0
0
1
0
0
2
1
0
0
1
2
4
1
0
1
0
2
1
1
1
3
2
2
1
2
0
1
0
1
1
0
1
0
1
1
2
2
1
0
1
1
1
0
0
0
1
1
0
1
0
0
0
0
1
1
2
1
1
2
1
2
1
0
1
0
2
1
1
2
0
1
0
0
2
2
0
2
0
1
0
1
0
0
1
1
2
4
0
1
0
0
0
0
0
1
0
0
2
1
6
0
0
0
0
1
1
1
2
0
1
2
2
0
1
0
0
0
1
0
2
1
2
1
1
0
1
0
1
2
1
1
2
1
0
0
1
0
2
2
0
1
1
0
1
2
1
1
2
2
2
0
0
1
1
0
0
1
1
1
1
0
2
2
0
2
2
0
1
2
0
2
2
2
1
0
1
1
0
0
1
1
1
0
1
1
2
0
1
2
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
2
0
1
2
0
2
3
0
2
1
1
0
1
0
1
0
1
0
2
0
0
1
1
0
0
1
0
1
2
0
0
1
1
1
1
2
1
1
1
1
1
0
2
0
1
0
1
0
2
2
1
2
0
1
2
0
2
1
1
2
1
2
1
1
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
2
2
2
1
0
1
1
1
4
0
0
0
0
0
1
0
2
1
1
1
1
1
0
1
2
1
1
1
1
1
0
0
0
1
1
1
1
0
1
1
1
0
1
2
1
1
2
0
2
2
0
2
1
0
2
0
1
1
0
1
1
0
0
0
1
0
1
1
1
2
0
0
0
0
2
0
3
1
1
0
1
0
0
2
2
0
0
2
1
1
1
0
1
0
1
0
1
0
1
1
2
2
0
1
1
1
1
0
0
2
1
1
2
1
1
1
0
2
0
2
0
1
0
0
1
1
2
0
1
2
0
0
2
0
0
0
2
2
0
0
1
1
1
2
2
1
0
1
0
1
2
2
0
2
0
0
0
0
0
0
1
0
0
2
1
0
0
2
0
0
1
1
3
0
1
3
1
1
1
0
2
2
0
1
0
0
1
0
1
1
1
2
2
0
1
2
0
2
1
1
0
1
0
0
2
0
0
0
3
0
0
1
1
1
1
1
1
1
0
2
1
0
0
2
0
0
1
0
2
1
3
6
0
0
1
1
1
0
1
2
1
2
1
0
0
0
1
1
1
0
1
1
0
0
0
2
0
0
0
1
0
0
0
0
2
1
0
1
0
1
1
1
1
1
1
0
0
1
0
1
0
1
0
1
0
2
0
0
1
1
1
1
0
0
0
1
1
1
0
0
1
0
0
0
2
0
2
0
2
2
0
2
2
0
0
1
0
1
1
2
1
0
0
0
0
1
1
1
1
2
0
2
0
1
0
1
1
0
0
0
0
2
0
0
0
1
0
2
0
1
0
2
0
0
2
1
0
0
0
1
2
0
1
0
1
2
2
2
0
1
0
0
0
2
1
1
1
0
1
1
0
0
1
0
0
0
1
1
0
1
1
0
1
0
1
0
0
2
0
1
0
1
1
1
2
0
1
0
2
1
0
0
0
0
0
0
1
0
1
2
1
1
1
2
2
0
1
1
2
2
2
1
1
1
1
0
0
0
2
2
1
0
0
0
0
1
1
2
1
0
2
0
0
2
2
1
0
0
2
0
0
1
1
0
1
1
0
2
0
1
1
1
0
0
1
0
1
1
2
0
0
2
0
1
2
1
1
2
0
1
1
0
0
0
1
2
0
1
2
1
0
0
1
0
1
1
0
1
0
2
0
1
2
1
1
3
1
2
0
1
0
0
1
1
1
0
0
2
0
0
2
1
1
0
6
2
2
1
1
0
1
1
2
1
0
0
0
1
1
2
0
2
1
1
1
2
3
2
0
0
1
1
1
1
1
1
2
1
0
1
0
1
1
2
3
2
0
0
2
1
0
1
2
0
1
1
1
0
1
0
1
1
1
1
1
0
1
1
0
1
0
0
0
0
0
0
1
2
0
2
2
0
1
0
3
0
0
1
0
0
2
1
1
0
1
1
2
1
2
0
1
2
2
2
0
1
1
0
0
2
2
1
2
1
1
2
2
2
0
0
2
0
0
0
0
2
0
0
2
0
1
1
1
1
1
0
0
0
0
0
1
1
2
1
0
3
1
0
0
0
1
1
1
0
1
0
2
1
0
1
0
1
0
0
1
1
2
0
1
0
1
2
2
0
1
1
0
0
0
0
1
2
0
0
0
0
2
1
0
0
1
2
2
1
0
0
1
2
3
1
1
0
0
0
0
1
0
0
1
1
1
2
1
0
3
0
0
0
0
0
1
1
0
1
0
1
1
0
1
0
0
0
0
2
1
2
2
2
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
2
2
0
0
2
2
0
0
2
0
3
2
0
0
2
0
0
5
0
0
1
1
0
2
1
2
0
0
2
0
2
2
0
1
2
1
0
0
0
2
0
1
2
1
2
1
1
2
0
1
0
0
2
1
0
2
1
2
1
1
0
0
1
1
0
0
2
1
0
1
1
1
2
0
1
1
0
1
1
1
0
0
0
2
0
2
1
1
1
2
0
0
0
1
0
1
2
2
2
1
0
1
2
0
1
2
1
0
0
4
1
0
0
1
1
1
1
1
2
2
1
2
0
2
0
1
1
2
1
0
2
2
0
1
3
0
0
1
1
1
1
0
2
1
0
0
0
1
1
2
6
0
1
1
0
0
2
2
0
2
2
1
1
2
1
0
2
0
0
1
1
1
1
0
1
0
2
1
1
1
0
0
0
0
1
0
0
1
0
2
0
2
1
0
0
2
0
1
1
2
0
0
2
0
0
0
1
0
1
0
1
2
0
0
0
0
0
0
1
1
2
0
7
0
1
2
2
0
0
2
1
1
1
0
2
1
0
1
2
0
2
1
0
1
1
0
5
1
2
1
0
3
2
0
0
1
0
1
1
0
4
1
1
1
0
2
4
0
1
1
1
0
2
2
1
1
1
1
4
0
2
1
2
1
2
0
2
1
0
1
0
0
0
1
2
0
1
2
1
0
1
1
0
0
0
0
1
0
0
0
2
0
1
1
1
1
1
1
2
2
0
2
0
1
0
2
1
0
1
0
1
2
2
1
0
2
0
2
0
0
0
1
2
2
3
0
1
1
0
0
1
0
1
0
0
1
1
0
1
2
2
0
0
1
0
1
0
1
1
3
1
0
1
1
1
2
0
0
0
2
2
1
1
1
0
0
1
1
1
1
1
1
1
0
2
2
2
1
1
0
2
0
2
2
2
1
0
0
2
0
1
1
1
1
1
0
1
0
0
1
0
1
1
1
0
1
2
1
2
2
1
1
1
0
0
1
2
0
1
2
0
1
2
0
0
1
2
2
0
0
0
2
1
0
1
0
1
0
1
0
0
2
0
0
3
0
0
0
2
2
1
2
1
2
1
0
2
0
2
1
2
0
1
0
0
0
1
0
2
0
0
1
2
1
1
1
1
0
1
1
1
0
0
1
0
0
0
1
1
0
0
0
1
2
1
0
1
0
1
0
2
0
0
1
1
1
1
2
0
1
0
2
0
0
0
2
2
0
0
1
2
2
1
0
1
0
0
0
0
0
1
0
1
2
0
2
0
2
0
0
2
0
0
1
0
2
0
1
2
0
0
1
0
0
0
2
0
2
1
1
1
1
0
1
1
1
1
1
1
0
0
1
1
0
1
1
0
1
0
1
0
0
2
0
0
1
1
2
1
4
0
1
1
0
0
1
0
2
0
1
2
1
1
0
1
0
1
1
0
2
0
1
1
0
2
1
0
0
2
0
0
1
1
0
0
0
1
0
1
1
0
0
1
0
0
0
1
0
2
0
1
2
0
2
0
0
0
2
0
0
1
1
0
1
0
0
1
0
0
0
0
2
1
0
1
1
1
2
0
0
1
2
0
0
2
0
1
0
0
0
1
0
2
1
0
1
1
1
2
1
1
0
1
1
1
0
1
2
1
1
1
0
1
2
2
0
2
1
0
1
2
0
2
1
1
1
1
1
1
0
1
2
1
0
2
1
2
0
1
0
2
2
1
1
1
0
2
1
1
0
0
1
1
0
2
1
2
0
0
1
1
2
1
1
0
2
0
0
0
0
1
1
0
1
2
2
0
0
2
1
1
1
2
1
2
1
3
0
0
4
2
1
1
1
0
1
0
2
1
1
1
0
1
1
0
0
1
2
0
0
0
1
0
3
0
1
1
2
0
1
0
1
0
1
0
2
2
1
1
2
1
2
0
0
0
0
0
1
2
0
2
0
1
1
1
3
1
1
1
0
1
0
1
1
1
1
1
0
1
1
2
3
1
0
0
1
2
1
1
1
2
1
0
2
2
0
0
2
0
1
0
4
1
1
1
1
2
0
1
2
2
2
0
2
2
1
1
1
0
0
1
5
2
1
0
0
0
2
0
1
0
0
0
3
1
0
1
2
0
0
1
1
0
2
1
1
0
2
1
2
1
3
1
1
0
1
0
0
0
1
1
1
3
1
1
1
1
0
1
0
0
1
0
2
0
1
0
0
2
0
0
1
0
1
0
2
0
0
0
1
1
1
2
2
1
1
2
2
0
0
1
1
1
1
2
2
2
1
1
0
0
2
1
1
2
2
2
0
2
1
0
2
3
2
0
0
0
0
2
1
1
0
0
0
1
1
1
2
1
1
0
2
1
1
0
0
1
1
0
2
1
0
1
0
0
2
0
0
0
1
1
1
0
1
2
2
1
2
0
0
0
1
2
1
0
0
1
1
0
0
1
1
1
2
1
1
1
2
1
2
1
2
0
2
0
0
1
2
0
1
2
1
0
0
0
1
2
0
1
2
1
0
0
1
0
0
0
0
2
1
2
1
1
2
2
0
0
0
1
2
2
1
0
0
2
0
1
0
1
0
1
1
1
0
0
2
2
1
1
2
2
1
1
2
1
1
1
1
0
0
1
0
0
1
0
1
2
2
0
1
2
1
0
0
1
1
0
1
0
1
1
0
1
1
1
0
0
0
1
0
1
1
0
1
1
0
3
2
2
2
2
1
2
1
1
1
2
0
1
1
0
2
1
1
0
0
2
0
1
2
0
0
0
1
1
1
0
2
0
1
1
1
0
0
2
2
1
0
1
3
2
1
2
1
1
1
1
1
1
0
0
2
0
1
2
0
1
2
0
0
1
1
1
1
0
2
0
2
0
0
1
1
0
1
1
1
0
2
1
1
2
0
1
0
0
0
1
1
0
2
0
1
2
1
2
1
0
1
0
0
0
2
1
0
1
2
1
1
0
0
0
2
0
0
0
0
1
1
1
0
1
0
0
0
1
1
0
0
0
1
0
0
0
2
0
1
1
1
0
2
0
1
1
2
1
2
1
1
2
0
0
0
0
1
2
0
2
2
0
0
0
1
0
0
0
2
0
0
2
0
1
0
2
1
1
1
0
1
0
0
3
2
1
1
2
2
1
0
2
0
1
0
1
1
0
1
2
2
0
0
1
1
0
0
2
1
0
0
1
1
1
0
2
0
0
1
0
0
1
1
0
2
1
2
2
1
2
1
0
0
0
2
1
0
1
3
0
1
1
1
0
0
0
0
1
2
0
2
2
0
2
0
1
0
0
1
1
0
2
0
0
1
0
2
0
1
0
0
0
2
0
2
0
1
0
1
1
1
1
0
1
1
0
0
1
1
2
0
0
1
0
2
1
0
2
2
0
0
0
1
1
1
2
0
1
1
1
1
0
0
1
1
0
0
2
0
1
2
0
1
0
0
0
0
1
2
0
1
2
1
0
2
1
0
0
1
0
2
1
1
1
0
2
1
0
1
1
2
0
0
2
0
0
0
0
0
0
1
0
2
0
0
1
1
2
0
2
4
0
0
1
3
1
3
0
1
1
2
0
2
0
0
0
2
1
0
0
0
1
0
0
1
0
0
0
0
1
0
1
2
2
1
0
0
1
0
0
0
0
1
0
1
1
1
0
0
0
3
0
2
0
1
1
2
1
1
1
2
0
1
2
2
2
1
0
2
0
0
0
0
1
1
0
1
2
1
0
0
0
0
3
0
1
2
2
0
1
2
1
2
1
0
1
2
1
0
0
1
0
0
0
1
0
0
1
1
0
1
2
2
1
2
0
2
0
0
1
2
2
1
0
0
0
2
1
1
0
0
0
0
1
2
1
0
1
2
1
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
2
0
0
0
0
2
0
0
0
1
1
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
2
0
2
3
1
0
2
1
0
1
0
1
1
0
1
2
2
0
0
0
1
1
2
0
0
1
1
1
1
2
1
2
2
1
2
1
1
0
0
1
1
1
0
2
0
0
2
2
2
2
1
0
0
2
0
0
1
2
2
1
1
2
1
1
0
1
0
1
0
1
1
0
0
2
2
1
0
2
0
2
1
0
1
1
2
1
2
0
1
0
0
1
2
2
0
0
0
1
0
0
0
1
3
0
1
0
1
1
1
0
2
2
0
0
0
2
0
2
1
1
2
1
2
1
1
1
0
1
0
2
0
2
0
1
0
0
1
2
0
0
1
1
1
0
0
2
0
1
1
0
0
0
1
0
2
2
2
1
0
1
1
1
1
2
1
1
0
1
0
0
1
1
0
1
0
2
2
0
2
0
1
1
0
2
2
1
3
1
1
2
1
1
0
0
1
0
0
1
1
1
2
1
1
1
1
2
1
1
0
0
1
1
0
1
1
0
0
0
0
1
1
0
1
0
0
0
1
0
2
1
0
3
1
1
0
0
0
0
1
1
0
1
0
2
0
2
2
1
2
1
0
2
0
0
1
0
0
0
1
1
1
0
1
0
0
1
0
2
1
2
2
2
0
0
1
0
2
1
0
2
0
0
1
1
2
2
0
0
1
0
0
2
0
0
0
0
1
1
1
1
1
1
0
0
1
1
1
1
0
2
1
0
0
2
0
1
1
0
1
0
0
1
1
1
1
0
2
1
0
0
1
1
0
0
1
1
2
2
2
1
2
1
2
0
0
1
0
1
1
1
0
0
1
2
0
0
0
2
1
2
1
2
0
1
1
0
1
1
0
2
0
1
1
0
2
1
0
1
0
0
1
0
2
2
1
0
2
1
0
1
0
2
1
2
0
1
2
2
0
0
0
1
1
0
1
1
1
0
2
1
0
2
0
1
0
1
1
0
0
0
1
1
1
2
0
0
0
2
2
0
2
0
1
2
0
0
1
1
1
0
1
2
1
0
0
0
0
2
0
0
1
1
1
1
0
1
2
0
1
1
2
0
1
0
2
1
0
0
1
0
0
1
0
1
2
2
0
0
0
2
0
1
0
2
0
0
0
2
1
2
0
1
0
0
2
2
1
1
2
0
0
2
1
0
1
1
0
0
1
2
0
0
0
1
0
2
1
1
2
1
1
0
1
0
1
2
0
2
0
2
2
1
1
1
0
0
0
2
0
0
0
1
0
1
0
0
2
0
0
1
1
0
1
1
1
1
0
1
1
0
2
1
0
1
0
0
2
1
2
1
0
2
0
1
0
2
1
1
0
0
2
0
1
1
0
1
0
0
0
0
0
0
2
2
1
1
1
0
2
0
0
0
0
0
1
1
2
0
0
0
1
3
0
0
1
1
1
0
2
0
2
1
2
1
1
1
0
2
1
2
0
1
0
0
1
0
0
0
2
1
0
2
0
1
1
1
2
1
0
0
1
1
0
0
2
0
1
0
1
0
0
1
0
0
1
2
1
0
0
2
0
0
0
1
2
1
1
0
2
0
0
1
1
2
3
0
1
0
0
1
0
1
2
2
0
2
1
0
2
1
1
0
2
0
0
1
2
2
0
1
0
2
0
2
1
0
1
1
1
1
0
0
5
0
2
1
0
2
2
0
2
1
0
2
1
0
0
2
0
1
2
0
0
0
0
1
0
0
0
0
2
1
1
0
0
0
1
0
1
1
1
1
1
2
1
1
0
1
0
1
0
0
0
0
1
1
0
1
1
0
0
0
0
1
0
1
0
1
1
0
0
2
0
1
1
0
0
0
1
2
2
2
0
0
1
0
1
2
2
2
3
1
0
1
0
7
0
0
1
0
2
2
0
1
0
2
1
0
2
2
1
0
1
1
0
1
1
1
1
1
1
0
0
1
2
0
1
1
0
2
2
2
0
2
1
0
1
0
0
1
0
0
2
0
1
1
1
4
1
0
1
2
0
1
2
1
0
0
0
1
1
1
2
1
0
2
2
2
0
0
0
1
2
0
1
2
1
1
2
0
0
1
1
1
2
0
0
0
1
0
0
1
0
1
2
1
0
2
2
2
0
0
1
0
2
1
1
0
1
0
1
1
2
0
0
0
1
1
0
1
1
1
1
0
0
1
1
1
1
1
0
2
0
0
2
0
1
1
1
0
1
0
0
0
0
1
0
0
0
0
2
2
0
1
0
0
1
1
2
0
0
2
0
2
0
0
1
0
0
1
2
2
1
0
3
0
1
0
0
0
2
0
0
1
2
1
0
0
0
1
0
2
0
0
1
2
0
0
2
1
1
1
2
0
1
0
2
1
2
0
0
2
0
0
0
1
1
0
3
1
1
0
1
0
1
0
0
2
1
0
2
2
0
1
0
0
2
2
1
0
0
0
2
1
2
1
0
1
0
1
2
1
1
2
2
0
1
2
1
4
0
1
2
2
2
2
0
2
0
1
2
1
1
0
0
0
1
0
1
0
0
3
1
2
1
0
1
0
1
0
4
0
0
1
1
1
0
0
0
0
0
1
0
0
0
1
0
2
0
2
2
1
1
1
2
2
1
1
0
1
0
0
2
1
0
1
1
1
1
4
1
1
1
3
1
0
1
1
0
0
1
2
2
2
1
0
0
1
2
1
1
0
1
1
1
1
0
0
0
0
2
2
1
0
1
2
0
0
2
1
0
0
1
1
3
0
0
0
0
2
2
2
0
1
0
1
0
1
0
1
0
0
1
0
2
0
2
1
0
1
2
1
0
0
0
2
0
0
0
0
1
2
2
1
0
1
0
2
1
1
0
1
0
1
2
2
0
2
0
0
1
0
0
1
2
2
1
1
1
0
0
0
0
2
3
1
2
1
1
1
0
1
1
0
0
2
1
1
0
1
0
1
0
1
1
0
0
0
0
0
1
1
2
0
0
1
1
2
2
3
2
0
1
0
1
0
0
0
1
0
1
0
0
2
0
1
0
0
2
2
3
0
1
0
0
2
0
0
0
0
1
0
0
0
2
0
2
2
0
0
0
3
2
0
1
2
0
1
1
2
1
1
2
1
0
0
2
2
0
0
2
1
1
1
0
2
0
1
2
1
2
0
1
1
0
1
0
1
2
0
4
2
1
0
2
2
0
0
1
0
0
1
0
1
2
0
1
0
2
0
0
1
2
1
0
1
0
1
2
2
0
0
1
0
2
0
1
0
1
0
1
0
1
0
0
1
0
2
2
0
1
0
0
1
0
1
0
1
1
0
1
0
0
0
0
1
2
0
2
0
0
0
1
0
1
2
1
0
1
1
0
1
2
0
0
1
0
0
0
1
1
2
0
1
2
2
1
2
0
0
1
0
0
1
1
1
1
1
0
1
1
2
0
1
1
0
2
1
1
1
0
2
1
1
0
2
1
0
1
0
2
0
2
1
2
0
2
0
0
1
0
0
0
2
1
2
2
0
0
0
2
0
2
1
1
1
1
1
1
2
1
1
1
1
1
0
0
2
1
1
1
0
0
0
0
0
1
1
1
1
2
0
0
1
3
2
2
1
2
1
0
2
2
1
2
1
2
1
0
1
0
1
0
1
0
0
0
1
2
2
1
2
1
1
0
0
2
1
0
1
1
1
2
2
0
1
1
3
1
2
0
1
1
0
2
0
0
0
0
0
2
1
0
0
0
1
2
0
0
0
1
1
2
1
0
1
0
0
0
0
1
1
0
0
1
2
3
0
5
3
0
2
1
1
0
2
1
0
1
2
2
0
2
0
1
0
1
0
0
0
0
0
1
0
2
0
0
2
1
2
2
2
1
0
2
1
1
1
0
1
5
1
0
2
2
1
1
1
1
1
0
2
2
0
0
2
2
3
0
0
2
0
1
0
0
3
2
1
0
0
1
1
1
0
0
1
2
0
2
1
1
2
1
0
0
2
0
1
1
0
0
1
1
0
0
0
1
1
0
2
1
0
1
1
1
3
2
1
0
2
1
1
0
1
0
1
0
2
0
1
2
1
2
2
1
0
1
0
0
1
0
1
0
2
0
0
2
2
2
0
2
2
0
2
1
0
1
2
1
1
1
1
0
0
1
1
1
1
1
1
0
2
1
1
1
2
0
1
2
2
1
2
1
1
0
1
1
1
0
1
1
0
2
2
1
5
1
0
2
0
0
0
0
0
0
3
2
0
0
1
2
0
2
1
1
2
0
0
1
2
0
0
1
0
2
1
1
2
1
0
0
0
2
0
2
0
0
0
0
0
0
1
1
1
2
1
1
0
0
0
1
0
1
2
2
0
1
0
1
1
0
2
0
2
0
1
1
1
0
1
0
1
0
0
2
0
0
0
2
0
1
2
0
1
1
0
1
2
1
0
0
0
2
1
0
1
1
1
1
1
1
2
0
2
0
0
0
2
1
0
3
0
0
1
1
0
1
0
0
0
0
1
1
0
0
2
2
2
0
1
0
1
2
1
1
1
2
0
0
1
0
2
2
2
2
1
1
1
0
1
0
0
0
0
1
2
1
1
1
2
0
1
0
1
0
2
1
1
3
0
0
1
0
2
0
0
2
0
1
0
0
1
1
1
2
0
1
0
0
1
2
0
1
1
0
0
1
1
3
2
0
2
2
0
2
3
1
0
1
0
2
0
2
0
0
0
0
1
4
2
0
1
2
2
0
0
2
2
0
1
2
1
1
1
0
0
1
0
2
0
0
1
1
2
1
0
1
0
1
0
2
0
2
1
0
0
0
0
1
1
1
1
1
0
1
1
1
0
1
2
2
0
0
1
1
1
1
0
0
1
0
2
1
0
1
2
1
1
2
2
0
1
1
2
0
1
2
0
1
0
0
1
0
2
0
1
0
1
1
1
0
2
0
1
2
1
0
2
1
0
0
0
2
1
0
1
0
0
2
1
2
5
2
0
1
2
0
0
0
2
0
0
1
0
1
0
2
1
2
0
1
2
2
0
0
2
1
0
1
1
0
1
2
2
1
7
1
0
1
1
1
1
0
0
2
0
2
0
0
2
0
1
2
2
0
0
0
2
2
2
0
0
1
2
0
0
0
2
2
2
1
0
2
2
1
3
0
0
0
1
2
1
1
2
0
1
0
1
1
0
1
0
1
2
0
1
1
0
0
0
1
0
0
1
0
0
0
2
2
2
1
1
1
2
0
2
0
0
1
1
0
0
1
2
0
1
1
0
1
0
2
0
1
0
1
0
1
0
2
2
2
1
2
0
2
1
1
1
1
0
2
0
0
1
1
1
0
1
2
1
2
2
0
4
1
1
2
0
2
0
0
2
2
0
0
1
0
0
0
1
1
2
2
0
2
1
2
1
0
0
0
1
3
1
0
1
0
2
2
0
2
2
0
0
1
0
2
1
1
1
2
2
0
1
0
1
2
1
0
1
0
1
2
1
1
0
1
0
1
0
2
0
1
0
0
1
0
0
2
2
0
0
2
1
1
0
2
1
1
0
2
1
0
0
1
1
1
2
1
0
1
0
2
3
1
1
2
1
1
1
2
2
1
1
0
1
0
1
2
0
1
0
1
1
1
1
1
0
0
1
1
0
1
2
1
1
0
2
1
2
1
3
2
1
1
0
1
2
2
5
0
1
1
1
0
1
0
1
0
0
1
1
1
1
2
2
1
1
0
0
0
2
2
2
1
1
2
0
2
2
2
1
1
0
2
1
2
0
2
2
2
0
0
2
2
2
0
1
2
1
4
0
1
0
0
0
1
2
0
2
1
1
2
1
0
1
1
1
1
0
1
1
2
0
0
0
1
0
2
0
0
0
1
2
1
2
0
2
2
1
0
1
1
1
0
1
1
0
1
0
1
2
0
1
1
1
1
2
1
0
1
1
0
1
0
2
0
0
1
2
1
3
1
0
1
0
2
1
0
0
0
1
0
0
1
0
0
1
1
1
1
0
0
1
0
0
3
1
2
0
0
1
1
0
0
0
2
2
2
0
2
2
0
0
1
0
2
0
2
2
2
1
0
1
2
0
1
1
0
0
2
0
1
3
1
1
0
1
0
1
1
0
1
2
1
2
2
0
1
0
0
1
0
1
2
1
0
3
1
1
0
1
1
1
1
1
2
0
1
2
0
1
1
0
1
0
1
0
2
0
1
1
2
1
0
0
0
2
1
1
1
2
1
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
2
1
1
0
1
1
1
1
1
0
0
0
0
1
0
1
0
0
2
3
1
1
1
0
0
1
0
2
1
0
2
0
2
2
0
2
1
1
1
2
1
1
0
0
0
0
1
1
4
2
1
1
0
2
1
0
0
0
0
1
1
1
2
0
1
1
1
1
1
2
0
1
0
0
2
2
1
0
1
1
0
1
1
1
1
2
0
2
1
1
1
1
2
1
2
0
2
2
1
1
1
1
0
2
0
1
2
0
1
0
1
4
0
2
2
0
0
2
2
2
2
0
2
3
0
0
0
1
0
1
1
0
2
2
2
2
0
2
0
0
1
0
0
0
0
1
1
0
1
2
2
1
2
0
1
0
0
1
1
0
2
0
2
0
1
0
0
1
0
0
1
0
2
2
0
0
1
1
2
0
0
0
3
1
1
0
0
1
1
0
1
0
2
2
1
2
0
0
2
0
2
1
2
0
0
1
2
2
0
0
0
1
2
1
2
1
0
0
0
0
1
0
0
0
0
2
0
0
2
0
1
1
0
0
0
0
0
1
0
0
1
1
1
1
2
2
1
0
2
1
1
1
1
2
1
0
1
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
2
0
0
2
0
0
2
0
3
0
2
0
0
1
2
0
0
0
0
1
0
0
0
1
0
1
2
0
2
0
0
3
2
0
0
1
1
0
0
1
0
0
0
1
1
1
0
0
0
1
2
1
1
2
0
1
0
1
2
1
2
2
1
1
1
2
1
1
0
1
0
0
0
0
2
0
0
0
0
0
1
2
0
1
0
1
1
0
0
1
0
2
0
1
0
1
1
0
1
1
0
0
2
2
0
1
1
0
0
0
0
1
0
0
2
0
1
1
0
1
3
2
0
0
0
1
2
0
0
2
0
0
1
0
1
1
1
2
1
1
0
0
1
0
0
2
2
1
0
0
0
2
2
1
1
2
0
0
0
0
1
0
2
0
2
1
1
1
2
0
0
1
1
2
2
1
1
1
1
0
1
1
0
2
1
0
0
0
0
2
2
1
0
0
1
0
0
1
0
0
1
1
0
0
1
1
1
0
2
0
1
1
0
0
2
0
0
1
2
2
1
1
1
0
1
0
2
0
4
1
0
1
0
0
1
0
0
0
0
2
0
1
1
1
0
0
1
0
2
0
0
2
2
0
2
1
0
0
2
2
2
0
2
1
1
1
1
0
2
2
1
1
2
3
0
0
2
0
1
0
2
0
1
1
0
0
2
0
1
0
0
0
0
1
1
2
0
2
1
1
0
2
2
0
1
1
0
0
0
0
2
1
1
0
1
0
1
0
0
1
1
0
1
1
1
2
1
0
1
0
0
2
1
1
0
2
0
0
1
1
1
1
0
0
0
1
1
0
0
0
1
1
0
1
2
1
2
0
0
2
1
2
2
1
1
0
2
0
1
1
2
2
2
3
2
2
0
0
0
1
2
0
0
4
0
1
3
2
0
0
0
2
1
2
3
0
0
0
1
2
0
1
1
2
1
0
1
0
0
1
1
0
0
1
2
2
0
1
0
0
1
1
0
0
1
1
0
1
1
1
2
3
1
1
0
1
1
0
0
0
0
2
1
1
1
0
2
2
0
1
0
2
1
0
1
1
2
0
1
0
0
1
0
0
1
0
2
2
2
0
1
0
1
0
0
0
0
1
1
1
1
1
1
1
0
0
2
2
0
1
1
2
1
0
2
0
1
2
1
0
1
1
0
0
1
2
0
0
1
1
0
2
1
1
1
0
0
1
1
0
0
1
0
1
2
0
0
0
0
1
1
0
0
2
0
1
1
0
1
0
1
0
0
0
1
1
1
2
0
0
1
2
0
1
0
1
0
0
2
1
0
2
0
2
1
1
1
1
0
0
1
2
0
1
2
0
0
1
0
1
0
2
0
1
1
1
1
1
1
1
0
1
0
0
0
1
0
1
0
2
0
0
2
1
0
1
1
0
0
0
0
1
2
0
1
0
1
0
2
1
0
0
0
0
0
0
0
1
1
2
1
0
0
1
3
1
1
0
1
2
1
1
0
1
2
0
1
2
1
1
1
3
2
0
1
2
2
1
1
1
2
0
0
1
2
0
1
0
1
0
0
0
3
1
1
0
1
0
1
4
2
0
0
0
1
1
3
2
1
1
0
0
2
1
1
0
1
1
2
1
0
1
1
0
2
0
0
1
1
0
0
2
2
1
1
3
1
0
0
2
0
2
0
2
1
1
1
0
1
0
0
1
0
1
0
1
0
0
1
1
0
0
2
0
0
1
0
2
4
1
1
1
2
1
0
2
0
1
3
2
2
1
0
0
0
2
0
0
0
3
1
1
2
0
2
0
1
2
1
1
1
2
2
2
2
2
0
2
1
0
1
0
0
1
0
0
2
2
0
2
1
1
2
1
1
0
2
0
2
0
1
2
1
0
3
0
2
0
0
1
2
2
0
0
1
0
0
2
3
1
0
0
0
4
0
0
2
2
2
0
2
0
1
0
1
1
0
2
0
2
1
0
1
1
2
0
1
2
1
2
2
2
0
1
0
0
1
0
1
0
0
1
0
1
1
0
1
1
0
3
1
1
5
1
0
3
0
1
1
0
0
1
1
2
1
0
1
0
0
0
2
2
2
1
1
2
0
1
0
0
0
1
1
0
2
0
1
1
2
1
1
0
0
2
1
2
1
4
1
1
1
2
0
0
1
1
1
1
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
2
1
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
2
1
2
1
1
2
1
1
0
1
1
1
1
0
1
0
0
1
1
0
1
1
2
0
1
1
1
2
0
2
0
1
0
0
0
0
1
1
2
0
2
0
2
0
0
2
2
1
1
2
3
1
1
1
0
0
0
2
1
2
0
0
0
1
2
1
1
0
0
0
1
1
1
0
0
0
1
1
2
0
2
0
1
0
0
0
1
0
4
2
0
0
1
1
0
1
0
0
0
2
0
0
0
0
2
2
1
1
1
1
0
1
1
0
0
0
2
0
1
0
0
1
2
0
2
0
1
2
2
1
1
0
1
0
0
1
1
1
0
0
0
0
0
1
1
1
0
0
1
2
1
1
2
0
0
0
2
0
0
1
0
2
0
1
0
1
1
2
2
0
0
1
0
1
0
0
1
0
0
1
2
0
2
0
1
0
2
1
0
1
2
1
2
1
1
0
0
2
1
2
2
0
2
2
2
1
1
0
0
2
0
0
2
2
1
0
1
2
1
0
3
0
0
2
1
0
1
1
1
0
1
0
1
0
0
2
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
1
2
1
1
0
0
1
1
0
0
0
2
0
0
1
0
0
0
0
2
2
1
0
1
0
1
2
1
0
1
0
1
0
2
0
1
3
2
2
1
2
0
0
2
1
1
1
1
2
1
2
1
1
2
0
2
0
2
0
1
0
1
2
0
1
0
0
0
0
0
1
0
0
2
1
0
1
4
1
1
0
3
0
2
1
1
1
0
0
1
0
0
2
1
1
0
3
2
0
2
0
0
0
0
0
0
1
2
0
2
1
2
0
1
1
2
1
0
1
1
0
1
1
2
1
0
2
2
1
3
1
0
2
0
2
1
2
1
0
2
1
0
1
1
2
1
0
1
0
2
0
2
2
1
2
0
1
3
1
2
1
0
2
1
2
0
1
1
0
8
0
0
0
0
0
0
1
1
0
1
0
1
2
1
2
1
0
1
2
4
1
0
0
0
1
2
0
1
0
0
2
1
2
0
0
0
2
1
0
1
0
0
0
1
1
0
0
1
1
0
1
1
0
2
0
0
1
0
1
2
1
1
1
0
0
1
2
0
2
1
1
0
1
0
2
0
1
0
1
1
2
0
0
1
2
1
2
2
0
0
1
1
1
3
0
0
1
2
1
0
1
0
2
2
2
2
2
1
1
0
0
0
1
0
0
1
0
0
1
1
1
0
0
2
1
1
0
0
1
1
0
1
2
0
0
1
0
1
2
1
0
1
2
2
1
1
1
0
1
1
1
1
1
0
0
0
1
0
2
2
0
0
1
2
2
1
1
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
1
1
0
2
1
0
1
0
0
0
1
2
0
0
0
1
2
2
0
0
2
2
1
1
0
1
0
1
1
0
0
1
1
1
0
0
0
0
0
0
1
1
2
3
0
0
2
1
0
1
1
0
0
0
2
1
1
1
1
0
2
2
2
0
1
1
0
0
2
2
2
2
1
2
0
1
1
0
0
2
2
0
0
1
1
1
1
3
0
0
1
2
0
2
1
0
2
0
1
0
1
0
2
0
0
0
1
1
1
1
0
1
3
1
2
0
1
2
0
1
0
1
2
2
1
1
2
0
0
0
2
0
0
0
0
1
0
2
3
0
1
1
1
1
1
2
0
2
0
1
2
0
1
1
1
0
1
0
3
1
1
2
1
2
0
1
1
0
0
1
0
0
1
0
2
2
0
1
1
0
2
0
0
4
2
0
1
2
1
2
0
0
0
1
2
1
1
1
0
0
0
0
1
1
0
0
0
2
0
2
0
0
2
1
1
1
2
0
1
5
0
1
2
1
0
1
0
2
0
0
1
1
0
1
2
2
1
0
1
0
0
2
1
0
1
0
2
2
1
2
2
1
0
3
0
0
0
0
0
1
1
1
0
0
0
1
0
0
2
0
2
0
1
0
1
0
1
2
2
0
2
2
0
1
1
1
2
1
0
0
0
0
2
0
0
1
1
0
1
1
1
0
1
1
1
0
1
0
0
2
0
2
1
2
1
2
0
0
1
2
1
1
2
0
1
0
0
2
0
0
0
0
0
1
1
1
0
1
2
0
0
1
0
1
0
2
1
2
1
0
3
0
0
1
0
0
2
1
0
0
2
0
1
0
0
2
0
0
1
2
0
0
1
0
0
0
1
0
2
1
1
0
0
0
0
2
2
0
1
2
1
0
0
2
1
1
0
0
1
2
0
2
0
0
0
1
0
1
2
0
1
2
1
0
0
1
0
0
0
0
2
1
0
0
2
3
1
1
2
0
1
0
1
1
1
0
0
1
0
2
0
1
0
1
0
1
0
1
1
0
1
1
2
0
1
1
0
0
2
0
0
2
1
1
0
1
0
0
0
1
1
0
1
2
1
0
0
2
2
0
0
2
0
0
1
0
1
0
1
1
0
0
0
0
2
1
1
0
1
0
2
0
2
0
2
1
1
1
0
0
1
1
1
1
2
1
0
1
0
0
2
0
0
1
0
2
1
2
0
1
1
0
0
1
2
1
0
0
1
2
0
2
0
0
1
1
1
1
0
1
0
0
1
0
0
1
0
0
0
0
1
0
2
1
2
0
0
1
0
1
0
0
1
1
0
1
1
1
1
0
1
1
1
0
1
2
2
2
1
1
1
0
2
1
1
0
0
2
1
0
1
0
1
1
0
1
1
1
0
1
2
0
3
2
0
0
1
0
1
0
0
1
0
2
1
1
1
1
1
0
0
0
1
1
0
0
2
0
1
2
0
2
2
1
1
2
1
1
0
1
1
0
0
0
1
1
1
1
0
0
0
0
2
2
0
2
0
0
2
0
1
1
0
2
1
1
1
2
0
2
1
0
0
2
0
0
2
0
0
0
2
1
1
0
1
0
0
2
0
0
1
1
1
2
1
0
0
1
2
2
0
0
0
2
0
1
1
1
0
2
0
1
0
0
0
0
0
3
1
1
0
1
0
1
1
2
0
1
1
1
2
2
0
0
2
0
0
1
1
2
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
2
1
1
2
1
1
0
0
2
0
1
0
1
1
2
1
0
2
1
1
2
0
1
1
0
1
1
0
3
0
1
2
1
1
1
1
2
1
0
1
2
1
0
1
1
1
1
1
0
1
1
2
0
1
1
0
1
1
1
1
0
2
2
0
2
0
1
0
0
0
0
0
1
1
1
1
0
0
1
1
0
0
0
2
1
0
0
0
1
1
1
1
1
1
0
2
1
1
0
2
0
0
2
2
0
0
3
1
2
0
3
1
2
2
0
1
1
0
0
1
1
1
0
1
1
0
2
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
1
2
2
1
2
1
0
0
2
0
0
0
1
2
1
0
2
1
0
2
0
0
0
2
2
0
2
0
1
0
0
1
1
1
1
2
0
0
2
1
0
1
0
1
0
0
0
0
0
1
0
1
0
2
2
1
0
0
1
2
0
0
1
1
2
1
2
1
2
1
1
2
1
0
1
1
3
2
1
1
1
1
0
0
1
0
1
0
2
1
1
1
1
0
1
0
0
2
0
0
2
1
0
0
1
0
0
1
0
1
0
2
1
0
1
1
1
2
0
1
1
1
0
0
1
1
2
0
2
1
0
0
1
1
0
2
2
1
1
1
1
1
0
1
3
1
0
0
0
0
0
1
0
1
2
1
2
2
0
0
0
1
0
1
1
1
0
0
0
1
2
2
0
0
0
1
2
0
1
2
1
3
2
0
1
1
0
0
2
1
2
0
0
0
2
0
1
0
1
2
1
2
1
2
0
1
0
0
0
1
1
0
3
1
2
0
0
1
2
0
1
1
0
0
2
2
1
2
1
2
1
1
0
1
0
0
2
1
0
0
1
0
0
1
0
1
1
0
0
0
0
0
2
0
1
1
0
0
1
2
2
2
0
2
1
1
0
1
1
1
1
0
2
1
1
1
1
2
1
0
0
1
1
2
2
0
0
2
0
2
2
0
1
0
1
2
1
0
1
1
0
0
1
0
0
0
0
1
0
2
1
1
2
1
2
1
0
1
1
0
0
0
1
1
1
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
2
1
2
1
0
2
0
1
2
0
1
0
0
0
0
0
1
2
0
1
0
1
2
1
1
0
2
2
0
0
0
1
0
1
2
0
1
0
1
0
1
2
0
1
1
1
2
1
1
0
0
0
1
0
0
2
1
0
1
0
2
2
1
1
2
0
1
1
2
1
1
1
2
0
0
0
0
0
0
0
1
2
1
2
2
0
1
1
0
1
0
0
1
0
1
1
3
2
1
2
0
1
2
0
0
1
0
2
2
2
1
0
2
1
2
1
0
0
2
2
0
0
1
2
1
1
1
1
0
1
0
2
0
0
0
1
0
0
0
1
0
0
1
3
0
1
1
1
1
0
0
0
1
0
2
2
0
0
1
2
0
1
1
2
1
1
1
1
1
2
0
1
0
0
2
2
1
4
1
2
1
2
1
2
0
1
0
1
1
1
1
1
1
2
0
1
0
2
1
1
0
1
0
1
1
2
1
3
1
2
0
0
0
1
1
0
1
0
2
1
0
1
1
2
0
0
0
1
2
1
1
0
3
2
0
1
1
0
1
1
1
2
0
0
1
0
1
0
2
0
1
2
0
1
0
0
2
1
0
2
0
0
1
0
0
0
1
0
2
0
2
1
1
1
0
1
0
0
1
1
2
1
2
0
2
1
2
0
0
0
1
1
1
2
2
0
1
2
1
1
0
0
1
0
1
1
1
1
0
0
1
0
2
1
0
0
1
0
1
0
1
0
2
1
0
2
1
0
2
0
0
0
0
1
1
3
0
1
2
0
0
1
0
2
1
2
2
1
1
1
1
1
0
0
1
1
0
0
1
1
0
2
1
2
2
0
0
2
0
0
2
0
1
0
0
2
0
0
0
0
0
0
1
1
0
0
0
1
0
1
1
0
1
2
0
0
1
1
2
2
1
1
1
2
0
0
0
2
1
0
1
1
0
1
1
2
1
2
0
0
0
1
0
0
0
2
0
2
0
1
0
0
1
0
1
0
0
0
0
1
0
1
1
0
2
1
2
0
0
0
2
0
2
1
0
1
1
1
0
1
1
0
0
0
2
0
1
2
0
0
1
1
2
0
1
1
1
0
1
0
2
2
6
2
2
2
0
1
1
1
1
0
0
0
0
0
0
1
2
1
1
0
1
1
0
1
1
2
0
2
0
0
1
3
0
0
1
0
2
2
2
0
0
0
2
0
0
0
0
1
0
0
0
2
0
1
0
0
1
2
2
0
0
0
2
1
0
1
1
3
1
2
0
0
0
0
1
2
2
2
1
1
2
0
0
1
2
0
2
0
1
1
0
0
1
0
1
1
1
0
0
0
0
1
2
0
0
0
2
1
1
0
0
0
1
1
1
2
0
0
1
1
1
0
0
1
1
0
1
3
0
0
1
1
1
1
0
1
0
0
0
1
1
1
0
1
1
2
0
2
1
1
1
0
1
0
1
2
0
1
1
4
0
0
2
0
0
3
0
2
0
0
2
2
0
0
1
0
0
0
2
0
0
0
2
2
1
2
2
1
1
0
0
0
2
2
1
0
0
0
1
3
1
0
0
2
1
0
1
1
1
0
2
0
2
2
2
2
2
1
1
1
1
1
4
0
1
1
0
2
1
2
0
0
0
2
3
1
9
0
2
0
0
1
1
2
1
1
1
1
3
0
0
1
0
2
1
2
0
1
0
2
1
0
1
1
2
0
1
1
2
1
0
1
3
1
2
2
1
0
0
1
1
2
0
1
1
1
2
0
1
1
1
1
0
1
1
1
0
0
1
1
1
1
2
0
0
1
0
0
1
0
0
1
1
0
0
1
2
0
0
0
1
1
0
0
0
1
2
1
1
0
2
0
2
0
1
2
1
0
1
1
0
0
0
2
2
0
1
2
0
1
1
1
0
5
0
1
0
1
0
1
2
0
1
1
0
1
0
0
0
2
0
0
0
2
2
1
1
0
2
0
1
5
0
0
2
1
0
2
0
0
0
1
1
2
3
0
1
1
1
0
0
1
2
1
1
2
1
1
0
1
1
2
2
0
2
1
1
0
1
2
2
1
2
1
2
1
0
2
0
1
1
1
1
2
0
0
1
0
1
1
0
0
1
1
1
3
0
0
1
0
0
0
1
2
1
1
0
1
0
1
1
1
0
0
0
1
1
0
1
0
1
2
1
1
0
1
0
0
1
1
0
0
0
1
0
1
2
0
2
0
0
1
0
2
0
1
1
1
2
0
2
0
1
0
1
1
0
2
1
3
1
2
0
2
1
2
0
0
1
0
2
0
1
2
2
2
1
1
1
1
0
0
1
1
0
0
1
2
0
0
1
0
0
0
1
1
0
1
1
2
1
1
3
0
1
1
2
1
1
1
1
0
1
1
0
0
0
2
1
1
1
2
1
1
1
1
0
1
1
1
2
0
0
2
1
1
1
2
0
1
0
0
2
1
2
0
0
2
0
0
1
3
2
1
2
0
0
2
0
2
0
0
0
0
1
1
1
0
1
0
0
0
1
1
1
1
0
0
1
1
1
1
2
1
1
0
2
0
0
0
1
1
1
1
2
1
1
1
2
1
0
2
1
2
1
1
1
1
0
2
0
2
2
2
1
1
1
1
1
1
0
1
1
0
0
0
1
1
1
1
2
1
0
0
2
1
1
1
0
1
1
2
0
1
1
0
1
0
0
0
0
1
1
0
2
1
0
0
0
0
1
0
1
1
1
0
0
0
1
1
1
0
2
1
2
0
0
0
2
0
1
0
1
1
1
1
0
0
1
0
1
0
0
1
1
2
1
2
0
1
1
0
0
1
2
2
0
1
0
1
1
1
1
0
1
1
2
1
2
1
2
1
2
0
1
1
2
1
2
2
1
2
0
1
0
0
0
0
1
0
0
0
1
0
2
0
0
0
1
0
0
2
0
1
2
1
2
2
1
2
1
1
1
1
0
0
0
1
0
0
0
1
2
2
0
1
0
2
1
0
1
0
0
1
1
1
1
2
1
0
0
1
2
0
2
2
1
2
0
0
1
1
1
0
2
2
0
0
2
2
0
0
1
2
0
1
1
2
0
0
1
2
0
1
1
0
0
1
2
1
1
0
0
0
2
0
1
0
2
1
2
1
1
1
0
0
0
1
0
2
1
1
2
1
0
1
0
1
0
0
1
1
2
1
0
0
2
0
0
0
0
0
0
2
0
1
1
2
0
0
1
0
0
2
1
0
0
0
2
0
2
0
2
0
1
2
0
0
2
0
0
0
0
0
0
1
0
0
1
1
1
2
2
0
2
0
1
0
0
0
0
1
1
1
0
2
0
0
0
2
0
1
0
0
1
1
1
1
1
1
0
1
0
0
1
2
0
0
2
0
0
2
2
2
0
0
1
1
0
1
0
1
1
1
0
1
0
1
2
0
1
0
0
1
1
2
0
0
2
1
1
0
0
1
1
0
1
1
0
1
1
0
0
1
2
0
0
2
0
2
0
2
1
0
2
0
0
1
1
0
2
1
1
0
0
2
0
1
0
0
1
1
0
0
0
0
0
0
1
2
1
1
0
1
1
1
1
0
2
1
2
0
0
0
0
1
0
2
2
1
1
1
0
0
0
0
2
1
0
2
2
2
1
1
0
0
2
0
1
1
0
1
1
0
2
1
0
0
1
3
1
0
1
1
2
0
0
0
2
3
2
0
1
1
0
2
1
1
2
0
0
0
0
0
1
1
0
0
1
2
1
1
1
2
3
1
1
2
0
1
0
3
2
1
1
0
1
4
1
0
2
0
0
2
1
1
0
2
0
1
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
2
2
0
2
0
0
1
1
1
1
0
1
2
2
0
1
1
0
1
0
0
2
1
1
0
2
1
0
1
0
1
2
3
0
0
0
2
1
0
1
1
0
1
0
0
1
1
1
1
1
2
0
1
0
2
0
0
1
1
0
0
1
0
2
1
1
2
1
0
1
2
1
0
1
0
0
2
0
1
0
0
0
2
0
0
2
1
1
2
1
0
1
2
0
1
1
0
1
0
2
0
0
0
1
2
2
0
1
2
1
1
0
0
2
1
1
0
0
0
1
1
1
0
1
0
0
0
0
0
2
1
0
1
2
0
1
0
1
1
2
2
1
0
0
0
0
0
2
1
1
2
0
2
0
1
0
0
1
2
0
2
2
0
1
3
0
0
1
0
0
2
2
1
1
0
1
0
1
1
1
0
1
0
3
0
2
1
1
0
1
0
2
1
1
1
1
0
1
2
0
2
2
0
0
2
1
0
0
1
0
1
0
1
0
0
1
0
1
1
1
2
1
1
0
1
0
1
1
1
0
1
2
0
0
0
1
1
2
2
1
0
1
2
0
1
0
2
0
1
1
0
1
2
1
0
2
0
0
2
0
0
1
0
1
2
1
1
0
0
1
1
2
1
0
2
0
1
1
2
0
1
1
0
1
0
2
0
1
0
1
0
1
2
1
0
0
0
1
1
2
1
1
1
0
2
0
2
0
2
0
2
2
1
0
1
2
1
1
1
0
0
1
2
2
0
1
1
2
0
1
1
1
0
0
1
1
0
1
1
0
2
0
0
1
3
2
1
0
0
0
0
2
0
1
1
1
0
1
0
2
0
1
0
0
0
1
2
0
2
0
0
2
1
0
0
2
0
0
0
0
1
1
2
2
0
0
0
0
1
0
0
1
1
1
0
0
1
1
0
1
0
1
1
1
1
1
1
0
1
1
0
0
0
0
1
0
2
0
1
1
1
2
0
0
1
2
2
0
1
2
0
2
1
0
1
1
1
0
0
0
1
1
2
1
2
1
0
0
1
1
0
2
0
0
0
0
0
0
0
2
2
1
2
1
0
1
0
0
0
1
0
1
1
1
1
2
1
2
1
2
0
0
0
2
1
2
2
1
1
2
2
1
0
1
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
2
1
2
2
2
0
1
2
0
0
0
0
0
1
0
2
0
2
1
0
1
1
0
1
0
0
1
0
1
0
2
1
0
1
0
2
1
1
0
1
0
0
0
2
0
2
1
0
1
1
0
1
0
2
1
0
0
0
0
2
2
2
1
1
0
1
2
1
0
2
1
1
1
2
1
2
2
1
1
1
1
0
0
1
1
0
1
2
2
0
2
1
1
1
0
1
0
2
1
2
3
2
0
3
0
0
0
0
1
2
2
1
2
0
1
0
3
1
0
1
1
1
2
1
1
2
0
1
0
2
3
1
0
0
0
1
2
0
0
2
0
1
1
0
1
0
2
2
1
0
0
3
0
2
1
1
1
2
0
1
0
2
2
2
0
1
1
0
0
1
1
2
1
0
0
1
0
0
3
1
3
2
0
0
1
2
3
1
0
0
1
0
1
1
0
1
0
1
0
1
2
0
0
2
2
0
0
1
0
1
2
1
2
0
0
0
1
1
2
2
2
0
0
0
0
1
1
0
0
0
2
0
1
0
1
1
0
2
1
1
1
0
1
0
1
2
1
0
0
2
2
1
1
1
0
1
0
1
1
1
1
0
1
1
2
1
0
1
0
2
1
1
1
0
2
0
1
0
2
1
0
0
1
1
2
0
0
0
1
1
2
1
1
2
2
0
1
1
1
1
0
0
0
5
1
2
0
2
1
0
0
0
1
0
1
0
2
1
0
1
0
1
0
0
1
1
1
1
0
1
1
1
0
0
0
0
1
2
1
2
1
0
1
2
0
1
2
0
0
1
0
0
2
0
0
2
1
1
0
1
0
1
0
1
1
1
0
1
3
2
0
0
1
1
2
0
2
0
1
2
0
1
2
1
1
1
2
0
0
0
0
1
1
1
0
2
2
3
0
1
1
2
0
0
2
1
0
0
1
0
1
1
2
0
0
1
1
2
1
1
0
1
2
1
1
0
1
0
2
0
0
1
1
2
0
1
1
1
0
1
0
1
1
0
0
0
0
1
2
1
0
0
2
0
0
2
2
1
1
0
0
0
0
0
1
1
1
2
0
0
1
0
1
1
2
0
1
0
1
3
0
0
1
1
0
0
0
2
0
0
1
1
1
1
1
0
2
0
0
0
1
0
0
1
2
2
1
2
1
0
0
1
2
0
2
1
1
2
1
0
1
2
0
2
0
2
1
0
2
1
1
0
0
0
0
1
0
1
1
0
1
0
0
0
1
1
1
0
1
2
2
0
0
1
1
1
1
1
0
0
1
0
1
0
0
1
0
0
2
2
0
1
0
0
0
1
0
0
0
2
0
0
2
2
0
0
0
2
1
0
2
0
0
0
0
0
0
1
1
0
2
0
1
0
0
1
3
1
2
1
2
0
0
0
2
1
2
3
1
0
0
1
0
2
0
0
0
0
1
0
0
0
0
7
1
3
1
0
0
1
1
0
0
0
1
0
3
1
1
0
0
0
0
1
0
2
0
1
0
0
2
1
0
1
0
0
1
1
0
2
0
1
0
2
2
2
3
0
2
0
0
1
2
1
1
0
1
2
1
1
0
2
0
0
0
2
0
0
0
1
1
0
0
2
1
1
1
0
2
0
1
0
1
1
1
2
0
2
1
0
1
1
1
0
1
0
0
1
0
1
1
0
1
1
1
0
2
0
2
0
2
0
0
2
0
2
2
0
1
0
0
1
0
2
0
0
0
2
0
1
0
2
0
2
1
1
3
1
1
0
0
1
0
0
1
2
0
2
0
1
1
1
1
2
0
0
1
1
0
1
2
2
0
2
1
0
1
2
0
0
0
0
2
0
2
1
2
1
1
2
0
0
0
0
1
1
0
0
1
1
1
0
2
1
1
2
2
2
1
2
0
5
0
2
0
1
0
0
0
1
1
1
3
1
1
0
0
2
0
0
0
1
2
3
1
0
1
0
1
1
0
2
1
2
2
0
1
0
1
1
0
1
0
1
2
1
0
0
1
2
0
1
2
2
0
0
1
2
0
0
0
1
0
0
1
1
1
0
2
1
2
0
2
1
1
1
1
0
1
0
0
1
1
1
0
1
3
1
0
2
0
2
1
0
1
0
0
0
1
0
2
0
0
1
2
0
2
2
1
1
0
1
0
0
1
2
1
2
0
1
0
1
1
1
0
2
1
0
2
2
0
1
0
0
1
1
2
0
1
1
1
1
2
0
0
0
1
0
0
0
1
1
2
2
1
0
1
1
2
1
1
0
1
1
1
1
0
1
2
2
0
1
0
1
1
0
0
2
3
1
0
1
1
2
0
1
2
2
1
0
0
0
0
2
0
1
1
0
0
2
2
2
0
0
2
0
2
1
0
1
1
0
0
1
0
1
0
1
2
0
0
1
0
1
1
0
0
0
1
1
1
3
1
0
1
1
0
3
2
2
2
2
1
0
0
2
0
0
1
2
2
0
0
0
0
0
0
1
1
2
2
0
0
1
1
2
2
5
0
0
0
0
0
0
1
1
1
2
1
3
0
1
1
0
0
2
0
1
1
2
0
1
0
1
0
2
1
0
0
2
2
1
0
0
0
0
2
1
2
2
1
1
0
0
1
1
1
1
1
1
2
1
1
0
0
1
0
1
0
2
0
0
2
0
0
0
0
2
2
1
1
1
1
0
1
0
1
1
1
1
1
1
1
0
2
1
1
2
2
0
1
1
2
0
1
0
1
1
2
2
0
0
1
1
0
1
0
0
1
1
2
0
1
1
1
1
0
0
2
1
0
0
1
1
2
0
0
1
1
0
1
0
1
0
0
1
1
0
0
1
0
2
2
0
3
0
2
0
0
0
1
2
0
2
0
2
1
2
0
2
1
0
1
1
0
2
0
1
0
0
2
0
0
0
2
0
1
0
0
3
1
1
0
1
0
2
1
2
1
2
1
1
1
1
0
0
0
2
1
1
1
1
2
0
0
2
1
1
1
0
0
1
1
1
0
0
1
0
2
1
0
0
2
0
0
1
0
2
1
1
1
0
0
0
0
0
2
2
0
2
1
0
0
1
1
1
1
0
1
1
0
0
0
2
1
0
0
0
0
1
0
1
0
0
1
0
2
1
0
0
0
1
1
0
0
0
1
0
1
0
1
2
1
0
0
1
1
0
1
1
0
0
2
2
0
1
2
0
0
0
1
1
1
0
2
2
0
1
0
2
2
1
2
2
2
1
0
2
1
2
0
0
1
0
1
1
0
0
2
0
1
2
1
1
1
2
0
1
0
0
1
0
0
2
1
2
0
1
0
0
1
1
0
2
1
1
1
2
1
1
1
1
2
0
2
1
1
1
2
0
1
2
0
0
0
0
2
0
2
1
2
2
0
0
0
0
1
0
2
1
2
1
0
0
0
0
0
0
0
2
1
1
0
3
1
1
2
0
0
2
1
0
1
0
0
1
0
1
0
0
2
0
0
1
1
0
0
1
0
1
0
0
2
2
0
0
1
2
0
0
1
0
0
0
1
0
2
1
1
1
1
0
0
1
2
0
0
1
0
1
1
0
0
1
0
1
2
1
2
1
0
1
0
1
2
0
0
1
0
1
2
2
2
3
2
0
0
0
0
0
0
0
1
1
0
1
1
1
0
1
1
0
1
2
0
0
0
0
1
2
1
0
1
2
0
0
1
0
1
1
1
2
1
0
0
2
2
0
2
0
1
1
1
1
1
1
1
1
1
0
0
0
2
0
1
1
1
2
2
2
5
1
0
1
2
0
1
0
2
0
0
0
0
1
1
1
1
0
1
0
1
0
0
1
2
0
0
0
0
0
0
1
1
1
0
0
0
1
0
2
1
0
1
0
0
0
1
0
2
0
2
0
1
1
1
0
2
0
1
0
1
1
1
1
1
2
0
1
2
1
1
0
1
2
1
1
3
0
3
0
0
0
1
0
2
1
0
0
1
0
0
0
1
2
0
1
1
1
0
0
1
0
2
1
1
1
0
0
0
5
1
0
0
1
0
1
2
2
1
2
2
0
2
2
0
1
0
1
3
1
0
0
0
0
0
0
1
2
0
0
0
1
1
1
1
0
1
0
1
0
0
2
0
0
0
1
1
2
0
0
0
1
0
4
2
0
1
0
1
1
0
1
1
1
1
0
1
1
1
0
2
0
0
1
0
1
1
2
1
1
0
2
0
0
0
1
0
0
1
1
1
1
2
2
1
4
0
0
1
1
2
0
1
1
1
0
1
1
0
0
1
1
0
1
1
2
1
1
0
2
2
0
0
0
0
0
2
1
0
1
0
0
0
0
0
1
2
0
1
2
2
0
0
1
1
1
1
2
0
0
0
1
1
1
0
1
2
0
2
0
0
1
2
1
1
1
0
2
1
1
2
1
0
0
0
2
0
1
2
1
2
0
0
0
2
0
1
0
0
1
1
0
2
0
2
0
1
0
1
1
0
2
0
1
0
0
0
0
0
1
1
0
0
0
0
0
2
2
2
1
0
1
1
0
2
0
0
1
0
0
0
0
2
2
1
2
0
1
2
1
0
0
2
1
1
1
1
1
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
1
0
0
2
1
1
0
1
1
0
0
0
1
2
0
2
0
0
0
0
1
2
1
2
2
1
0
0
2
2
1
3
0
1
2
2
1
1
2
1
0
1
1
1
2
2
1
1
1
1
1
1
1
0
1
1
1
1
3
0
2
1
1
1
1
0
0
0
0
0
2
2
0
1
1
0
2
1
1
1
0
2
0
1
0
0
2
2
0
0
1
1
1
2
0
1
1
0
0
1
0
0
0
0
0
2
1
1
0
1
1
0
2
2
1
1
2
0
0
2
2
2
1
5
2
0
1
0
1
0
0
0
1
1
1
1
1
0
1
1
1
0
1
2
0
1
2
1
0
3
0
0
0
1
0
1
2
0
0
0
0
1
1
1
2
2
0
1
1
1
0
2
1
3
1
0
2
0
0
0
0
2
1
0
1
1
2
1
2
0
2
0
1
0
0
1
0
1
1
1
1
1
0
1
2
0
2
0
0
0
2
1
2
1
1
0
0
0
0
0
2
2
1
0
1
2
2
1
0
2
1
0
1
1
1
0
1
2
0
1
1
2
1
1
0
1
2
0
1
0
1
1
1
1
0
0
0
1
1
1
1
3
0
1
2
0
1
2
0
0
1
1
0
1
1
2
2
0
0
2
1
2
0
2
2
0
0
0
1
1
0
1
0
0
0
2
0
2
0
0
0
1
0
0
1
0
1
2
0
1
1
2
1
0
0
0
2
0
0
1
2
2
1
2
0
0
1
0
0
0
0
0
2
1
2
0
0
1
2
0
1
1
1
0
1
0
0
2
1
0
1
1
0
1
1
2
1
1
1
1
2
1
0
1
0
2
1
1
2
2
1
0
0
2
1
0
1
0
1
1
0
0
0
2
0
2
1
0
2
1
1
2
2
2
0
1
0
0
2
2
1
0
1
0
1
0
0
0
2
0
1
0
0
0
1
0
1
0
0
1
1
1
0
0
2
2
1
2
1
1
1
1
0
0
2
0
1
0
0
0
0
1
0
0
0
1
0
1
0
2
1
2
0
1
0
3
0
2
1
0
2
1
2
1
2
1
2
1
1
0
0
0
0
1
1
1
1
1
1
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
2
2
2
1
1
1
0
0
0
0
0
2
0
1
1
0
1
1
1
0
1
1
0
0
0
1
3
0
0
0
2
1
2
1
2
1
0
2
0
0
1
0
2
0
1
1
1
0
2
2
0
2
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
1
0
1
1
2
0
1
0
0
1
0
1
2
2
1
0
0
0
0
2
1
2
0
1
1
1
0
1
2
2
1
2
1
0
3
0
1
2
1
1
0
1
1
1
1
0
1
1
1
1
0
1
0
2
0
0
0
1
1
0
1
2
0
2
0
2
1
1
0
0
2
2
2
2
1
1
0
1
2
0
1
0
2
2
1
0
1
6
0
2
2
1
1
0
0
1
1
1
1
0
1
0
0
0
0
2
1
2
2
0
0
0
2
3
0
2
1
1
2
1
0
2
2
1
2
1
1
1
0
2
0
1
1
1
1
2
1
2
2
2
2
0
0
0
1
1
2
0
2
0
0
0
1
1
1
0
0
1
0
0
0
0
1
0
1
0
3
1
1
0
1
1
1
1
0
1
0
2
1
1
1
1
0
1
1
0
1
1
0
1
0
0
0
0
2
2
1
0
2
2
2
1
0
2
1
1
2
1
0
1
3
2
0
0
2
1
0
2
1
1
1
1
1
1
1
0
0
0
0
1
1
0
1
2
2
1
0
0
0
2
0
2
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
2
0
2
0
1
1
0
4
0
0
0
0
0
0
0
2
2
1
2
2
0
1
1
1
0
1
0
0
2
0
0
1
1
2
0
0
0
1
0
2
1
1
1
0
2
1
2
0
2
0
0
0
1
0
1
0
0
0
0
2
0
0
1
1
0
0
0
1
0
0
2
1
0
2
0
2
2
0
1
0
0
0
0
0
0
1
0
1
1
2
2
1
2
0
1
0
0
1
1
0
0
2
1
0
0
0
1
2
0
1
2
1
2
1
2
0
2
1
0
1
2
1
0
1
0
3
0
1
1
0
1
4
1
4
1
1
0
2
1
1
0
1
0
2
0
1
1
2
1
1
0
3
1
0
0
0
0
0
0
1
0
0
0
1
1
1
1
2
1
2
1
1
1
1
0
1
0
2
2
1
0
0
1
0
2
1
1
0
1
2
1
1
1
0
0
1
1
0
0
2
0
1
1
1
0
1
0
0
2
2
0
0
1
0
0
2
1
0
1
2
1
0
1
1
1
2
3
0
1
0
1
0
0
2
2
0
1
0
1
0
2
0
0
0
2
2
2
0
1
2
1
0
2
2
1
1
0
2
2
0
0
1
0
1
1
2
1
0
1
0
0
1
0
2
1
1
1
0
0
0
0
2
2
2
0
1
0
2
0
0
1
0
1
1
0
1
0
1
2
0
0
1
1
0
0
1
2
0
0
1
1
0
1
2
2
2
0
0
0
2
0
1
0
0
1
0
0
1
0
0
0
1
2
2
0
0
2
1
1
1
2
2
1
1
1
0
0
1
0
0
0
0
2
1
0
1
1
1
0
1
0
0
1
0
1
1
2
1
0
0
1
2
2
0
1
2
0
0
0
0
0
0
0
1
1
0
1
3
2
1
0
1
2
1
1
1
1
1
1
1
2
0
0
1
2
1
2
1
0
0
1
0
1
2
0
2
2
3
0
2
0
1
2
1
0
1
1
1
2
0
1
2
1
0
1
2
0
2
0
1
0
0
2
1
1
0
1
0
0
0
1
0
0
2
1
0
0
1
0
0
0
2
0
1
0
0
1
0
1
0
0
0
4
1
1
0
1
0
0
1
1
2
1
1
1
0
1
0
0
0
1
0
1
1
2
0
0
2
1
1
2
2
1
1
1
0
0
1
1
0
2
0
0
1
0
2
0
0
2
0
2
0
2
0
3
1
0
0
0
1
1
2
2
1
0
2
0
2
0
0
1
0
2
1
1
0
1
1
2
1
2
1
0
0
1
0
1
1
2
0
0
2
1
2
1
0
1
0
1
2
2
3
1
1
2
1
1
1
1
1
0
0
1
1
1
0
0
0
0
0
1
1
0
2
1
0
1
2
1
0
1
1
1
1
1
1
1
2
0
1
2
0
2
0
1
0
2
2
1
2
2
1
1
3
1
0
2
0
1
2
1
1
1
1
0
0
0
1
1
0
0
1
0
1
2
3
2
2
2
0
1
0
0
1
1
1
2
1
1
1
0
1
1
2
0
1
1
0
2
2
2
1
0
0
1
2
0
0
1
2
1
2
0
2
0
2
0
2
1
1
0
1
1
0
0
0
1
2
2
0
1
0
0
2
0
2
0
1
1
0
1
1
1
2
0
1
0
0
1
1
0
0
1
2
0
2
1
0
1
1
0
0
1
1
1
1
0
3
3
1
2
2
1
2
0
1
0
1
2
2
1
2
0
2
0
2
0
0
1
2
2
1
2
0
1
0
1
0
0
1
1
1
0
1
0
2
0
1
2
2
0
3
0
0
0
1
1
2
0
2
0
2
3
1
0
2
0
0
1
1
0
0
0
1
0
0
1
0
0
2
1
1
1
0
1
2
1
1
0
0
1
0
2
1
1
1
2
1
1
0
1
0
0
0
1
0
0
1
0
0
0
1
1
1
0
2
1
0
0
0
3
2
1
1
0
1
2
0
2
2
1
0
1
1
0
0
0
0
1
0
2
1
0
1
2
0
2
2
1
2
1
3
2
1
0
2
1
2
1
1
2
1
1
1
0
0
0
1
1
0
1
2
1
0
2
1
0
0
1
1
1
0
2
1
0
0
1
1
1
0
0
2
1
1
0
0
1
1
0
0
1
2
2
1
2
0
0
0
0
2
2
1
1
0
1
1
1
0
0
2
0
0
2
1
0
1
1
0
0
1
1
1
0
0
2
1
2
0
1
0
1
1
0
2
0
0
1
0
1
1
0
1
0
0
0
0
0
2
0
0
1
2
2
1
0
2
3
1
0
0
0
1
2
0
0
0
1
2
1
2
0
1
1
0
0
1
2
0
3
0
1
1
0
0
2
1
0
0
0
0
0
1
0
0
1
1
0
0
2
2
0
1
1
1
0
0
1
1
0
0
1
1
1
1
1
0
0
0
0
2
0
1
1
1
0
0
2
1
0
0
0
0
1
0
0
2
1
2
2
0
0
0
1
1
0
2
1
1
1
1
1
1
0
2
0
1
2
1
0
0
0
2
1
1
3
0
2
0
1
0
1
0
0
2
2
0
2
1
2
1
2
0
1
0
2
0
1
1
1
2
1
1
2
2
2
0
0
0
1
1
1
0
0
1
0
2
1
0
1
1
0
2
0
0
1
0
1
0
1
1
1
0
0
1
2
1
0
2
1
1
0
0
0
2
0
2
1
0
1
1
0
0
1
0
1
1
0
1
3
0
0
0
0
0
1
0
1
0
0
1
0
2
2
0
0
1
0
0
1
1
0
0
0
1
1
0
2
1
1
4
1
0
2
0
1
0
1
1
0
0
0
0
0
1
2
0
0
0
1
2
0
1
1
1
0
0
0
3
1
0
0
0
0
1
2
0
1
4
0
0
1
0
0
0
2
1
2
1
1
1
1
0
0
1
1
2
0
0
1
1
0
0
0
0
1
0
1
1
1
1
2
2
2
0
2
0
1
0
0
0
1
0
0
1
0
0
1
1
0
1
0
0
1
0
0
1
1
0
0
2
0
0
4
0
0
0
1
2
0
2
0
0
2
0
1
2
2
0
2
0
0
1
0
1
0
1
0
0
0
1
0
1
1
2
1
0
1
1
0
0
1
1
1
1
0
2
2
1
2
0
1
1
1
2
2
1
1
0
2
1
0
1
0
3
2
1
0
0
3
0
2
1
0
0
0
3
2
0
1
1
0
1
0
2
0
1
2
0
1
2
1
0
0
0
2
1
0
2
4
0
1
1
0
0
2
1
1
2
2
2
0
1
1
0
2
1
1
0
1
1
1
0
3
1
2
2
1
0
1
0
0
1
1
0
2
1
2
0
0
0
1
3
1
0
2
3
0
1
2
1
0
0
0
0
0
1
1
1
1
3
0
1
1
0
0
1
2
1
0
1
1
0
1
1
0
2
0
1
0
0
0
2
0
1
1
7
0
2
0
2
0
1
0
0
0
1
0
1
1
2
1
0
0
1
2
1
0
2
1
1
1
0
1
2
1
1
0
2
0
2
0
2
1
0
1
1
0
0
1
2
3
0
2
0
2
1
1
0
0
0
1
1
0
0
1
1
0
0
0
0
2
0
1
0
0
1
0
1
1
0
2
1
1
1
0
1
0
1
1
0
1
2
0
5
1
1
1
2
1
1
1
0
1
0
0
2
2
1
1
1
1
0
0
0
1
0
1
1
0
2
2
0
0
1
0
0
2
0
1
1
1
0
0
0
0
1
1
1
2
0
1
1
0
2
1
1
0
1
1
0
0
0
1
2
0
2
0
3
1
2
1
1
1
2
0
1
1
0
1
0
5
2
1
1
0
1
2
0
1
0
0
0
0
0
0
1
2
0
1
5
0
1
2
0
0
2
0
2
1
1
0
2
1
1
1
1
0
1
0
0
0
0
0
0
0
1
1
2
2
0
0
0
0
0
0
0
1
1
0
0
2
1
0
1
0
2
0
0
0
0
0
2
1
1
0
0
1
0
0
0
1
0
1
1
0
0
0
1
0
1
1
0
0
0
1
0
1
0
0
1
1
1
1
0
1
1
0
0
1
0
0
0
2
4
1
1
2
1
0
1
0
1
3
1
2
0
0
3
1
0
0
1
1
1
2
2
2
1
2
0
2
1
2
2
1
1
0
0
0
2
2
2
1
1
3
1
1
1
3
1
1
0
1
0
2
0
0
0
1
2
1
2
0
1
1
0
1
1
0
0
0
1
1
0
2
0
0
2
2
0
1
1
0
2
0
0
1
0
1
1
1
0
0
1
2
0
0
0
0
2
0
0
2
0
0
0
1
2
1
0
1
2
0
2
0
0
0
0
1
2
0
2
0
1
0
1
1
1
1
0
0
0
2
0
0
1
2
0
1
1
1
1
1
1
0
0
0
0
2
0
1
0
0
2
2
0
1
1
1
1
0
1
1
0
0
2
1
1
0
1
0
1
0
1
0
2
1
2
0
0
1
0
0
0
2
5
0
0
1
1
1
3
0
1
0
0
1
0
1
0
2
1
1
1
2
1
1
0
1
1
0
0
0
0
2
0
1
2
2
1
2
1
2
1
2
1
0
1
2
1
0
0
2
1
0
2
0
0
0
2
0
0
1
1
1
1
2
2
0
0
1
0
0
1
1
0
1
0
1
1
0
2
1
0
3
1
0
2
1
1
1
1
2
1
2
1
0
2
1
1
2
2
1
1
1
1
0
0
1
0
1
1
2
2
0
1
0
1
1
0
0
1
2
0
2
2
0
0
1
0
0
1
3
1
2
0
3
2
1
2
2
0
1
2
0
0
1
1
0
0
1
0
0
0
2
1
1
1
0
0
1
1
1
1
1
0
0
2
0
1
1
0
2
2
0
0
2
0
2
2
2
1
1
1
1
2
2
2
1
1
0
1
1
1
0
2
1
0
1
0
1
1
0
0
1
1
0
1
1
1
0
0
1
1
2
2
0
1
1
0
1
0
2
3
0
0
1
0
2
0
1
2
0
1
0
2
2
2
1
2
0
1
2
0
1
0
0
1
1
0
2
1
1
1
1
0
1
2
1
1
0
2
2
0
2
1
1
3
2
0
2
1
1
1
2
0
1
2
2
0
0
1
0
2
1
2
2
1
0
1
2
2
1
0
2
2
0
2
0
1
1
1
0
1
2
0
1
1
0
0
2
1
0
0
1
2
1
2
2
0
0
2
0
1
1
2
0
0
0
0
1
2
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
1
1
2
0
0
2
1
0
0
0
0
0
0
1
2
0
0
1
0
2
1
0
2
1
0
0
0
0
1
2
0
2
1
2
0
2
0
1
0
0
0
0
0
0
0
1
1
1
0
1
1
1
0
2
0
2
0
0
0
1
0
0
2
2
1
0
0
2
1
0
2
1
0
2
1
1
1
1
0
0
0
1
0
0
1
0
0
0
1
2
1
0
0
2
2
2
1
1
0
2
0
0
2
1
0
1
0
0
0
1
2
2
0
1
1
0
0
1
1
0
2
1
1
2
0
1
2
3
1
1
0
0
2
1
2
0
2
1
1
0
1
1
0
2
0
1
0
2
2
2
0
1
0
1
0
2
1
2
1
5
0
1
1
1
1
2
0
1
0
0
2
0
1
2
2
0
0
1
3
2
2
0
1
0
1
0
0
0
0
1
0
2
0
0
0
0
0
1
0
1
0
1
2
0
0
0
2
0
0
0
1
0
0
1
1
0
0
0
2
1
0
1
1
0
1
3
0
2
0
1
1
2
1
1
1
0
2
0
2
1
1
2
0
0
2
0
2
1
0
1
0
1
1
0
0
2
0
1
0
1
2
0
1
1
2
1
1
0
0
2
0
2
0
1
0
0
2
1
0
0
0
2
1
1
1
0
0
4
2
1
0
0
0
1
1
0
2
1
1
1
1
1
1
1
1
0
1
0
2
2
0
0
0
1
1
2
0
1
1
0
0
1
0
1
1
1
2
0
1
1
1
1
2
1
0
0
0
0
2
1
1
1
0
2
1
2
2
0
1
0
2
2
2
2
2
1
0
0
0
1
2
0
1
1
0
0
2
0
1
0
2
1
0
0
0
1
0
0
0
0
0
1
0
2
2
0
1
1
0
2
3
1
0
1
1
0
0
1
1
1
1
1
0
0
2
1
2
2
0
0
0
1
1
0
1
0
0
0
3
2
0
0
0
1
0
1
0
0
0
1
0
0
0
1
1
2
0
0
2
1
0
0
2
1
1
1
0
1
1
0
0
1
0
2
0
1
1
1
2
2
1
2
1
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
2
0
1
0
2
0
2
2
0
0
2
0
1
1
0
0
0
1
1
0
1
0
1
1
0
0
1
0
1
2
1
0
1
0
1
0
0
0
1
1
1
0
2
0
0
0
2
0
2
0
1
0
0
0
2
0
1
2
0
1
1
0
1
1
0
2
0
0
1
1
1
0
1
1
0
2
1
1
1
0
0
1
0
1
1
1
1
1
0
0
2
1
0
1
0
0
0
1
0
2
1
0
0
1
2
2
1
2
2
1
2
0
0
1
1
0
2
1
0
0
0
0
2
2
1
1
0
0
0
0
2
0
1
1
1
2
1
0
1
1
1
1
1
1
2
2
1
0
2
0
0
1
2
1
1
2
2
2
1
1
1
1
0
1
1
1
1
0
1
2
0
2
1
1
1
2
0
1
0
0
1
2
0
0
1
2
1
0
0
1
0
1
1
1
0
1
0
0
2
1
2
0
0
1
0
1
1
2
1
1
1
2
2
1
1
0
1
2
1
1
1
1
1
0
0
0
1
0
0
1
1
2
1
2
1
2
1
0
1
0
2
1
0
1
0
0
1
1
1
2
0
2
1
0
0
0
0
1
2
0
3
0
0
0
0
0
0
0
0
1
2
1
1
1
1
0
0
1
1
0
1
0
0
1
2
1
1
0
2
1
0
1
2
1
1
1
0
1
2
1
0
1
0
0
2
0
2
1
0
2
0
0
3
1
0
1
0
1
1
0
0
0
1
1
2
1
0
1
2
0
2
1
0
1
1
1
0
1
0
0
1
1
2
0
0
2
0
1
1
0
0
1
0
0
2
2
1
0
0
0
1
1
0
2
0
1
0
2
1
0
3
1
0
1
2
2
1
1
1
0
2
1
0
1
0
1
2
1
0
1
1
3
0
1
2
0
2
1
0
1
0
0
0
1
1
0
0
0
1
1
1
1
0
2
0
0
0
0
1
0
2
1
0
0
0
0
2
1
0
0
1
2
1
1
0
1
0
1
0
0
2
0
0
0
2
0
1
2
0
0
1
0
1
0
0
1
2
0
1
2
0
1
1
2
0
1
0
0
1
2
0
1
3
1
1
2
2
2
1
1
2
3
1
1
1
1
1
2
0
0
1
1
1
1
1
0
0
1
1
3
0
2
2
0
0
0
2
2
0
1
1
2
3
1
0
1
1
1
2
0
1
0
2
0
1
0
0
0
0
1
0
0
2
0
1
1
1
2
2
2
1
1
2
1
1
2
1
2
2
1
0
0
0
1
1
0
1
1
1
1
2
1
0
2
1
2
0
1
0
1
0
0
1
0
0
0
0
1
2
0
0
2
0
3
0
0
0
2
0
1
3
0
0
0
1
0
2
1
1
0
0
1
0
1
1
1
2
2
2
1
2
0
1
1
1
0
0
2
0
0
0
0
2
1
2
2
2
1
1
1
1
2
0
2
1
2
1
0
1
1
1
2
1
0
3
0
0
0
1
1
0
1
0
0
0
0
2
2
0
0
0
0
1
0
0
0
1
2
0
2
0
0
0
0
2
1
0
0
0
1
1
0
1
0
2
1
0
0
0
2
0
1
0
0
0
0
0
2
0
1
2
2
0
1
0
1
2
0
0
2
0
0
2
2
0
0
1
1
1
1
0
1
2
1
2
2
0
1
0
0
0
2
1
1
2
1
0
0
1
0
2
1
0
0
1
2
0
1
1
0
1
0
0
2
2
1
1
1
1
0
0
2
0
1
0
2
1
1
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
2
0
0
1
0
0
1
3
0
1
2
2
1
2
1
1
1
1
2
0
0
2
0
1
0
1
1
0
0
1
0
0
1
2
0
0
1
0
2
0
1
2
1
1
1
0
0
1
2
2
0
2
1
2
0
2
1
0
2
2
1
0
2
1
1
0
0
2
1
0
0
0
1
1
0
0
0
2
0
1
1
0
1
1
2
2
0
0
1
1
1
0
1
2
1
0
0
1
0
0
1
1
0
2
0
2
0
0
0
0
2
0
0
1
0
2
0
0
0
1
0
0
0
1
2
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
1
1
0
1
1
1
2
0
1
1
1
1
1
1
2
0
1
2
1
1
1
0
1
1
0
2
0
0
1
0
1
1
0
0
1
1
1
0
1
1
1
1
0
0
2
0
1
1
0
2
1
1
1
2
1
0
1
2
1
3
0
1
1
0
2
1
1
1
0
0
2
0
1
0
0
0
0
1
1
1
0
1
1
1
0
1
0
0
1
0
2
2
1
0
1
0
1
0
0
1
1
1
0
0
1
2
0
1
1
0
1
0
1
1
0
0
0
0
1
2
1
0
0
1
2
0
1
1
0
0
1
1
2
1
1
0
1
2
0
0
2
0
1
3
2
0
2
0
0
0
0
1
1
1
0
2
0
2
2
2
1
2
2
0
1
2
1
0
1
0
1
2
0
0
0
1
0
0
1
0
0
1
0
1
2
0
0
0
1
1
0
0
0
1
1
1
2
0
1
0
0
1
2
0
0
1
0
2
0
0
2
2
0
0
1
1
1
0
1
0
0
1
1
1
0
2
2
2
0
1
1
3
1
0
1
1
1
2
0
0
2
1
1
0
0
1
1
0
1
2
1
1
1
1
2
2
2
1
2
0
1
0
1
0
0
2
0
0
1
1
2
1
1
1
1
0
1
2
1
0
1
2
1
1
3
0
0
1
2
2
0
2
1
0
1
1
1
1
1
0
2
1
0
0
1
1
1
1
0
2
1
0
0
1
1
0
0
0
1
1
0
0
0
2
1
2
0
0
2
1
0
0
1
0
1
0
1
0
1
2
0
0
2
1
0
1
1
2
0
2
0
0
0
1
2
0
1
2
0
0
0
1
1
0
1
2
2
2
1
2
0
1
0
0
1
0
2
0
2
0
0
2
2
0
2
2
0
1
0
1
1
0
2
1
0
0
0
0
1
0
1
2
2
0
0
0
1
0
0
0
2
0
1
2
0
1
0
1
1
2
2
1
0
1
1
2
2
2
1
1
2
0
1
0
0
0
1
1
2
2
1
1
1
0
0
2
0
1
1
2
0
0
0
1
1
1
2
1
0
2
1
0
1
0
1
3
0
1
0
0
1
0
0
2
1
1
1
1
0
1
0
1
0
1
0
2
1
2
2
0
1
1
0
1
0
2
0
0
1
1
0
1
0
1
1
0
1
2
0
0
0
2
0
0
0
1
0
0
1
1
0
1
0
1
1
2
2
0
0
2
2
0
0
2
1
0
1
1
0
1
2
1
0
1
0
2
0
1
1
2
0
1
1
0
1
1
0
0
2
2
2
2
1
1
0
0
2
0
1
0
2
1
2
1
0
0
1
2
2
0
1
1
0
2
0
1
1
0
0
0
0
4
1
1
1
1
0
0
0
0
0
0
1
2
1
1
0
0
0
1
1
1
0
1
2
0
0
0
0
2
0
0
2
0
1
0
0
2
2
0
1
0
0
0
2
2
0
0
1
2
0
2
0
0
0
1
1
1
0
1
0
0
1
1
0
0
2
0
1
0
0
1
0
2
0
0
0
2
0
1
1
0
0
1
0
2
0
0
1
0
2
0
1
2
3
0
1
1
2
1
0
1
1
0
2
2
1
0
1
0
0
1
0
0
1
0
1
2
2
1
2
1
2
2
2
0
0
2
1
0
1
0
0
1
1
1
1
1
1
0
0
1
0
1
2
0
0
2
1
2
2
2
2
1
1
1
2
2
2
0
1
0
0
0
1
0
0
1
0
1
1
2
1
1
1
0
0
0
2
2
0
0
0
1
1
1
0
0
1
1
2
0
0
0
0
2
2
2
2
2
0
1
1
1
2
1
0
1
0
1
1
1
0
1
0
1
1
0
2
2
1
2
0
0
1
2
0
2
0
1
1
2
2
0
0
1
2
0
0
1
1
1
2
0
0
2
0
2
0
2
1
0
1
0
0
0
1
0
1
2
1
1
1
2
1
0
0
2
0
2
1
1
0
1
0
2
1
1
1
0
1
2
2
2
1
2
0
0
0
1
1
0
0
0
1
0
0
1
2
1
1
1
0
1
2
1
3
0
0
1
1
1
0
1
2
1
0
1
1
1
1
0
1
0
1
1
1
1
0
2
1
1
2
1
1
2
1
1
0
1
1
1
0
1
1
0
2
0
0
2
1
2
0
0
1
0
2
1
0
1
0
2
1
0
0
0
0
2
0
1
0
1
0
0
0
1
1
1
0
0
1
2
1
0
2
0
0
0
1
0
1
1
2
1
0
1
2
1
1
1
0
0
1
0
1
3
1
0
2
1
2
0
2
0
2
1
0
2
1
1
0
2
0
1
2
0
1
0
2
2
2
4
1
0
2
0
1
0
1
2
2
2
0
0
1
0
0
2
1
2
2
0
2
2
1
1
2
2
0
1
1
0
0
1
1
0
0
2
1
2
0
0
0
1
1
0
0
1
0
0
3
2
3
1
0
0
1
0
0
1
0
1
0
1
0
2
1
0
0
2
2
2
0
1
0
4
1
1
0
1
1
2
1
0
1
1
1
2
1
1
2
1
1
1
0
1
0
2
0
0
1
0
0
0
0
0
3
0
3
1
0
2
1
1
0
0
0
1
0
2
2
0
0
2
0
0
2
1
2
1
1
0
1
0
0
1
0
2
2
0
1
1
1
0
0
1
1
1
1
2
1
1
2
1
0
0
0
1
0
0
2
1
1
0
0
1
1
0
0
1
0
0
1
1
0
2
2
1
0
0
1
1
3
1
0
0
2
1
1
1
1
1
2
0
1
1
0
0
0
2
1
0
0
2
0
1
1
0
0
2
0
0
0
0
1
1
1
2
2
1
2
1
2
0
2
2
0
1
0
0
2
0
1
1
0
0
1
0
0
0
2
1
0
2
1
1
0
1
2
0
2
0
0
2
1
0
1
2
1
1
0
1
2
1
0
0
0
0
0
1
1
1
2
0
1
0
2
1
0
1
0
1
1
0
2
0
1
1
0
1
1
1
1
0
0
0
0
1
0
0
2
1
2
1
0
0
1
0
2
0
1
2
1
2
1
0
0
2
1
0
0
0
5
2
1
2
2
2
1
0
0
0
2
1
1
0
0
1
2
0
0
2
1
0
0
1
0
0
0
1
2
2
0
1
0
1
1
1
3
1
2
1
1
1
1
0
0
1
0
1
1
0
0
1
0
2
0
2
1
0
2
0
1
0
0
0
1
2
0
1
1
0
2
2
1
0
0
1
1
1
0
1
2
1
0
0
1
0
0
1
1
2
1
0
1
1
2
0
0
1
1
0
0
0
0
0
0
3
1
0
0
1
0
1
0
1
1
1
0
1
1
0
2
2
1
1
0
0
0
1
2
1
0
0
1
2
1
2
0
1
3
2
0
3
1
0
0
1
0
0
2
1
1
1
1
1
0
0
1
0
0
1
0
1
2
2
0
1
2
4
0
1
1
1
0
0
3
2
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
1
1
1
0
0
0
1
1
1
1
2
1
1
0
1
1
0
0
1
0
0
0
1
1
0
0
1
0
2
0
0
1
0
0
0
0
1
1
0
0
2
0
1
2
0
2
0
0
0
2
0
1
2
2
2
1
1
1
1
1
0
1
0
3
2
1
1
0
1
1
3
0
2
0
0
2
1
2
0
0
1
0
2
1
2
1
0
1
0
1
0
1
0
1
1
3
1
1
0
3
0
2
0
1
1
1
0
0
0
2
1
1
1
1
3
0
1
0
1
1
1
1
2
0
0
1
1
0
1
1
0
2
1
1
0
2
0
1
0
1
0
2
0
4
1
1
5
3
2
0
0
0
0
0
0
0
2
1
1
2
2
2
0
2
1
1
0
1
2
0
0
2
2
1
0
0
1
0
2
2
0
0
1
0
0
0
1
1
2
0
1
0
1
1
0
1
2
2
2
1
1
3
0
2
1
1
1
0
1
0
2
2
1
1
0
1
1
0
1
1
0
2
0
6
2
0
1
0
1
0
0
2
1
1
1
0
1
1
0
0
1
1
0
0
0
0
0
2
0
0
1
0
1
1
0
1
2
2
0
0
0
1
0
1
0
1
1
2
2
0
0
3
1
0
2
1
0
2
0
1
0
0
2
0
0
0
2
0
1
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
1
0
1
1
1
0
1
0
0
2
1
1
0
2
0
2
0
1
0
2
0
0
0
2
1
2
1
1
1
1
0
0
1
0
2
2
0
2
1
0
1
0
2
1
0
1
2
0
0
0
3
1
0
1
1
0
0
0
2
1
2
0
2
1
1
2
0
1
1
1
2
1
1
2
3
2
0
0
3
1
1
0
2
1
0
0
0
1
2
0
1
1
1
1
0
0
1
1
0
2
0
0
1
0
0
0
1
1
1
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
2
2
2
1
1
1
2
1
1
1
0
0
1
0
0
1
0
0
1
0
2
0
0
0
2
4
1
2
1
1
0
1
0
1
1
2
0
2
1
1
2
1
0
1
0
1
1
2
0
0
1
2
0
1
1
1
1
1
2
0
1
1
1
2
0
0
0
2
1
0
1
0
2
1
1
2
0
2
1
0
0
2
2
1
1
0
2
2
1
0
1
2
1
0
2
1
0
0
0
2
1
0
1
2
0
1
1
0
1
1
1
1
1
3
1
0
2
1
1
0
0
0
2
1
0
0
0
2
0
1
1
1
0
2
1
1
1
1
0
2
1
1
0
2
0
0
1
0
0
1
3
0
4
1
2
0
1
0
0
0
2
2
1
1
2
1
1
0
2
3
1
0
1
2
0
1
1
0
1
1
1
1
1
2
0
0
1
2
2
2
2
1
0
0
0
0
2
1
2
0
0
0
0
2
1
2
1
0
1
0
2
2
0
0
1
0
1
2
1
0
1
1
0
2
2
1
2
2
1
1
0
1
0
1
1
0
2
0
0
0
1
2
1
1
0
3
0
2
0
0
0
0
1
0
0
2
1
0
1
2
0
1
0
1
1
1
1
0
1
0
1
0
0
1
1
2
0
0
1
1
0
0
2
1
2
2
0
1
1
0
0
0
1
1
1
1
1
1
2
2
1
1
0
0
2
1
2
1
1
1
1
0
1
1
2
2
1
1
1
0
1
0
3
0
1
2
0
0
1
0
2
0
0
0
3
2
2
0
0
1
2
1
2
1
0
1
2
2
1
1
1
1
0
2
1
1
2
1
0
0
1
0
1
0
2
0
1
1
1
2
0
1
1
1
0
1
1
0
1
2
0
1
2
2
0
1
0
1
1
1
1
0
1
1
1
2
0
1
2
1
0
1
0
1
0
0
0
1
0
1
1
2
1
0
2
2
0
0
0
2
1
0
0
0
0
2
1
0
0
1
1
0
0
1
2
0
2
1
0
0
1
0
0
0
1
0
0
0
0
1
1
1
0
1
0
2
1
2
1
2
1
1
0
1
1
1
1
2
0
0
1
0
0
1
1
0
2
1
0
1
2
1
1
0
0
1
1
0
0
1
2
1
1
1
0
0
3
0
0
0
2
0
1
0
1
2
0
0
1
2
1
0
1
1
0
1
0
0
1
1
1
0
2
0
0
2
1
0
2
0
2
0
0
0
0
0
0
2
0
2
0
1
1
0
1
1
1
1
2
0
1
1
2
2
1
1
1
2
1
2
1
0
1
1
2
1
0
1
0
0
2
0
1
0
1
0
2
1
0
0
0
0
0
0
1
2
1
2
3
0
0
2
0
0
1
0
1
0
1
2
0
1
1
1
0
1
0
1
2
0
0
0
1
0
2
0
1
0
0
0
2
0
0
1
2
3
1
0
0
2
1
1
0
0
0
0
0
0
1
0
1
0
2
0
3
0
0
1
1
0
2
1
0
1
2
1
1
0
0
0
2
2
1
1
0
1
2
1
1
0
0
0
1
1
2
0
1
1
0
2
0
1
0
1
0
1
2
0
1
0
0
1
0
2
1
1
1
1
1
1
2
0
0
1
0
2
1
0
0
0
2
0
2
0
0
0
0
0
2
0
2
0
1
1
1
2
1
1
2
2
2
2
0
0
0
0
1
1
2
1
2
0
1
0
1
0
1
0
2
0
0
0
1
0
0
1
0
2
2
0
0
2
0
1
1
0
0
0
1
1
0
1
1
1
1
0
0
0
0
0
0
2
0
1
2
2
2
0
2
0
0
1
1
2
0
0
1
0
0
0
0
0
0
2
1
0
1
1
0
2
2
2
0
0
0
1
1
1
1
1
2
0
1
2
2
0
0
1
1
0
0
2
0
0
0
2
1
0
2
1
2
0
1
2
1
1
2
2
1
0
0
0
1
1
0
4
1
2
0
1
1
1
2
1
3
1
1
1
1
0
1
0
0
2
0
0
0
0
4
0
1
0
0
1
0
2
1
0
0
1
0
0
0
1
0
2
1
0
0
0
2
1
0
1
2
2
1
1
1
2
1
0
1
3
0
0
1
0
2
2
1
0
1
0
2
2
0
0
1
1
1
0
1
2
0
1
0
0
1
0
1
1
1
0
2
1
2
1
0
1
1
0
0
0
0
0
2
2
2
2
1
2
1
2
0
1
0
1
0
2
2
0
0
2
0
1
0
0
0
0
0
0
1
2
0
3
2
0
2
2
2
1
1
0
0
0
2
0
0
2
0
0
0
2
1
0
0
0
1
0
1
2
0
2
2
0
0
1
1
0
0
2
0
0
1
2
1
2
1
2
0
1
2
1
2
0
0
0
2
0
0
0
1
0
2
2
2
0
1
2
0
0
2
1
2
1
0
3
2
2
1
1
0
0
0
2
0
1
1
0
0
1
0
0
3
2
0
0
0
1
2
1
1
1
1
0
2
0
0
2
1
2
1
0
1
1
2
2
0
2
1
0
1
1
1
1
0
0
1
1
0
1
1
1
1
0
0
0
0
1
0
1
1
0
1
0
0
0
0
2
0
2
1
1
1
2
1
0
2
1
1
2
0
1
1
1
1
1
0
0
2
3
1
3
1
1
2
2
1
0
1
0
1
2
1
0
0
0
1
0
1
2
2
1
1
1
0
0
1
1
0
0
2
1
1
0
0
0
2
0
2
0
1
0
1
3
0
1
1
0
0
2
0
1
1
2
2
1
1
0
2
2
1
2
2
0
2
2
2
0
0
0
0
2
0
3
1
2
1
0
1
1
0
1
2
1
0
1
1
2
0
0
0
0
2
1
0
1
1
1
2
0
1
0
1
0
1
0
0
0
0
1
0
1
2
1
1
0
1
2
1
1
1
1
0
0
1
1
1
0
2
0
0
2
0
1
1
2
0
1
3
1
2
1
1
0
2
0
0
2
1
1
2
1
2
0
2
0
2
1
1
1
1
0
1
0
2
0
2
3
0
2
0
0
0
0
0
0
1
0
1
0
2
0
1
1
2
0
2
0
0
0
0
0
0
1
0
1
0
2
0
1
0
0
0
0
0
2
1
0
1
1
0
1
0
2
2
1
0
1
0
0
0
0
2
0
1
0
1
0
0
0
1
0
1
1
0
1
0
1
0
1
1
1
0
2
1
2
1
2
1
2
1
0
2
1
0
0
2
1
0
2
0
1
1
1
0
2
0
1
2
2
0
0
1
0
0
2
1
1
1
2
2
0
2
1
0
1
2
1
0
1
2
2
1
0
2
0
2
2
1
1
2
0
0
1
0
1
2
3
0
0
0
1
1
0
2
1
1
1
1
2
0
2
0
0
0
2
0
0
1
0
1
1
0
1
2
0
0
2
0
0
1
2
0
0
2
1
2
1
2
0
1
1
1
2
0
2
0
2
2
0
0
3
1
1
0
0
0
0
0
0
2
1
1
0
1
0
2
0
2
2
0
2
0
1
2
0
1
1
1
1
1
0
0
1
1
0
0
1
0
2
1
3
0
1
1
2
0
0
1
2
1
0
0
1
0
0
0
2
1
2
0
2
1
1
1
0
1
1
0
2
0
2
1
1
1
0
2
1
1
2
1
1
0
1
0
1
2
0
2
0
0
1
0
1
2
5
0
1
1
0
0
1
2
0
1
2
0
1
2
2
1
1
1
1
1
1
2
0
1
1
1
0
1
2
0
1
0
1
0
1
2
0
2
2
0
1
0
1
1
0
3
0
2
0
2
2
1
2
2
0
2
1
0
1
0
0
2
1
0
0
1
2
0
0
0
1
0
1
1
0
0
2
1
2
1
1
2
2
3
0
2
1
2
1
0
0
0
0
0
1
1
7
1
2
2
2
1
1
0
1
1
1
0
0
2
2
0
0
0
0
0
1
1
2
1
0
0
5
0
1
2
1
1
2
1
1
2
2
0
2
0
1
1
1
0
2
2
1
1
0
2
0
2
2
1
0
0
0
1
2
0
1
0
2
1
1
0
1
2
2
0
1
0
2
1
0
1
2
1
1
0
3
0
5
2
0
0
0
2
0
1
1
0
0
0
2
2
0
2
1
0
1
2
1
1
2
1
0
1
0
1
1
0
0
0
0
0
1
2
1
0
0
0
0
1
0
1
0
2
1
1
0
1
0
1
1
3
1
1
1
0
0
1
2
0
1
1
0
2
0
2
0
0
2
1
0
2
0
1
0
1
0
1
2
0
0
0
1
3
0
0
3
2
1
0
2
2
1
0
1
2
0
1
0
1
2
1
0
0
1
2
0
0
1
2
0
0
0
1
2
1
3
0
0
0
0
0
0
0
2
1
0
1
1
1
0
2
0
1
1
1
0
0
2
0
0
0
1
0
1
0
0
1
0
2
1
1
0
2
0
0
2
1
2
1
1
2
0
1
2
1
2
2
2
1
2
0
0
1
0
0
2
2
0
1
0
1
2
1
1
1
1
0
1
2
0
0
2
1
0
1
1
1
2
0
1
2
1
0
1
0
2
2
1
2
0
2
2
2
2
0
2
1
0
0
2
0
0
0
0
0
0
2
0
1
0
0
1
1
0
2
1
0
0
3
1
2
0
2
1
1
0
1
1
0
0
1
0
0
0
1
2
0
0
1
1
1
1
2
0
0
2
0
2
0
0
0
1
0
1
2
0
1
0
0
0
0
2
0
0
1
1
1
2
0
3
0
2
2
0
0
0
0
1
1
0
0
0
0
1
0
1
1
0
0
0
0
1
0
2
0
1
0
2
0
2
0
1
0
0
0
0
0
1
1
0
0
0
2
2
1
2
1
0
1
1
1
1
1
0
0
2
1
0
0
1
0
3
2
0
1
1
0
4
0
1
1
0
0
0
2
0
0
0
1
0
1
1
2
0
0
2
2
0
1
0
0
0
2
2
0
1
1
1
0
1
1
0
0
0
0
2
2
0
0
2
0
2
1
1
0
1
1
0
1
2
1
1
2
1
1
2
1
2
0
0
1
2
0
2
1
0
0
2
1
2
1
1
1
0
2
2
0
0
0
1
1
1
1
0
0
2
1
1
0
2
1
0
3
1
0
0
1
3
1
0
0
1
1
2
1
0
1
2
2
1
1
1
1
1
0
0
2
2
0
0
1
1
1
0
1
0
2
2
1
1
0
0
1
0
0
2
1
0
2
0
2
1
2
1
1
2
0
2
0
0
1
0
0
0
2
1
0
1
0
1
1
1
0
0
1
0
1
1
1
0
0
1
1
0
0
2
1
1
0
1
1
0
0
0
0
1
0
1
0
4
1
1
1
1
2
1
1
2
1
2
2
1
1
1
2
2
1
0
1
0
0
0
1
0
2
1
1
0
2
0
0
0
0
1
2
0
1
1
2
2
0
2
0
0
1
0
1
1
2
0
0
3
2
1
0
0
1
0
0
1
1
1
0
1
0
0
3
0
2
0
2
0
0
0
1
0
2
1
1
1
1
0
1
1
1
1
1
1
1
4
2
1
2
1
0
1
2
0
0
0
1
2
1
0
0
0
0
1
1
0
1
0
2
0
0
1
0
1
1
0
2
1
2
2
1
0
0
1
1
1
1
1
1
0
1
1
2
1
1
1
0
1
2
0
1
0
0
1
1
0
0
1
0
0
0
0
2
1
0
0
2
1
3
1
1
1
0
2
0
1
1
0
0
1
2
1
1
0
0
0
3
1
2
0
0
1
0
1
1
1
1
2
0
0
0
1
2
0
0
0
1
1
0
1
0
1
1
1
0
2
2
2
1
0
0
1
0
0
1
2
0
1
1
0
1
1
0
1
1
0
1
1
0
0
0
0
2
0
2
0
1
2
2
2
0
2
0
2
1
0
0
0
1
1
0
1
0
1
2
0
1
2
1
0
1
1
0
1
2
0
0
1
0
1
1
0
1
1
1
1
2
2
0
1
1
2
0
2
0
0
0
2
1
1
2
0
0
0
1
3
0
0
2
0
2
2
1
0
1
0
1
0
2
1
1
0
1
2
0
2
0
1
0
2
0
1
2
1
2
1
1
0
1
1
1
0
0
1
1
0
1
0
0
2
0
1
1
2
1
1
1
1
1
0
1
0
0
1
1
1
2
1
1
1
2
0
0
0
1
1
2
0
1
1
2
0
0
1
0
0
0
1
1
2
0
0
2
1
1
0
0
1
0
0
3
2
0
0
1
0
2
2
0
0
0
0
1
0
0
0
1
2
1
1
0
2
1
0
2
2
0
0
1
0
1
1
0
1
1
1
2
0
2
0
0
0
1
2
1
1
2
0
0
0
2
0
5
2
1
2
2
0
1
0
0
0
0
1
1
0
0
1
2
1
1
0
0
2
1
1
1
0
1
1
0
0
1
1
0
2
0
1
2
0
2
0
0
2
1
1
0
2
1
1
0
2
0
1
1
0
0
1
2
2
2
1
0
0
2
0
1
0
1
0
0
0
1
1
0
3
1
0
1
1
0
0
1
0
0
1
0
2
1
0
0
2
0
2
1
1
3
2
1
2
1
0
1
1
2
0
0
1
0
1
2
0
0
0
1
0
1
0
1
1
2
1
0
0
0
0
1
1
1
0
1
0
2
0
1
0
0
2
0
1
1
2
0
0
0
2
2
1
1
1
0
1
2
0
0
0
1
0
0
0
3
8
1
0
1
1
1
1
1
0
2
0
2
2
0
0
1
2
1
1
1
1
1
1
1
0
0
2
2
2
1
0
0
1
2
1
2
1
0
1
0
1
1
1
1
1
0
1
2
0
1
1
1
0
1
2
2
2
0
1
1
0
0
0
0
2
1
1
1
1
0
0
2
0
1
2
1
1
0
2
2
1
1
0
0
1
0
0
1
1
0
2
1
0
1
0
0
0
1
2
1
0
2
0
0
1
2
0
2
2
0
2
1
2
2
1
0
0
0
0
1
1
0
1
0
2
1
0
1
0
0
2
1
1
1
2
2
1
0
2
0
2
2
2
2
0
0
0
0
1
1
1
1
1
1
0
1
2
1
2
1
1
2
1
2
0
1
1
1
2
1
0
0
1
1
2
1
1
0
1
0
1
0
0
0
1
1
2
1
0
0
2
2
0
1
2
2
0
0
0
3
0
1
1
0
0
0
1
0
0
2
2
1
2
0
0
2
0
2
2
2
0
1
1
1
1
1
0
2
1
2
2
0
1
0
1
1
1
1
2
0
2
0
0
1
2
2
0
1
3
1
2
0
0
1
1
0
1
0
0
2
1
0
2
1
3
1
2
1
0
1
0
0
1
1
1
0
1
1
0
1
1
1
0
0
1
0
2
1
1
2
1
0
1
1
2
2
1
1
1
0
0
0
0
0
1
0
0
0
1
2
1
0
0
0
1
0
1
1
0
1
2
0
2
3
1
2
0
2
1
0
1
0
0
1
2
2
1
1
2
0
1
0
1
1
1
1
1
2
0
1
0
1
2
0
1
0
1
1
2
1
2
1
1
2
1
2
0
3
3
1
0
2
1
2
0
0
1
2
1
0
1
0
0
2
1
0
2
1
1
0
1
0
0
1
1
0
1
0
1
2
0
0
0
0
1
0
1
1
2
2
1
0
0
1
0
1
1
0
1
0
1
1
0
1
0
0
1
2
2
2
0
1
0
1
0
1
2
0
1
1
2
2
0
2
0
1
1
1
0
2
1
1
0
0
1
2
0
0
2
1
0
0
0
1
2
0
1
0
1
1
0
1
1
1
2
0
2
1
1
1
0
1
0
0
0
0
2
1
1
0
1
1
0
1
0
2
1
0
1
0
1
1
1
2
0
0
0
1
0
2
1
2
0
1
0
1
0
0
0
0
1
1
2
1
0
1
0
2
0
2
1
2
2
1
1
1
2
1
1
0
1
2
1
0
1
2
1
1
1
1
2
0
0
0
1
1
1
0
1
1
1
0
1
0
0
0
0
2
0
1
0
1
1
0
1
1
0
1
0
1
2
0
1
1
0
2
1
1
1
1
0
1
1
0
0
1
1
0
1
2
0
0
0
1
0
0
0
1
0
2
1
2
0
1
2
1
2
1
2
1
2
1
1
0
1
1
0
0
2
2
1
2
1
0
0
0
1
1
0
1
0
0
0
1
1
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
1
0
0
2
0
1
1
0
2
1
1
1
1
3
2
1
3
2
0
1
0
0
2
1
2
1
1
1
0
0
1
2
0
0
1
1
0
0
0
1
1
0
1
0
1
0
0
3
1
0
0
1
2
2
1
3
2
1
0
2
0
1
2
2
1
0
1
0
2
0
2
0
0
1
0
0
0
4
0
1
1
0
0
0
1
0
2
1
1
5
1
2
0
0
1
0
1
1
2
1
2
0
1
0
2
0
0
1
1
2
0
2
2
1
2
1
2
0
2
0
0
2
1
1
0
1
1
2
1
1
2
1
0
1
2
0
1
1
1
0
0
2
2
2
2
1
1
2
1
1
0
1
0
1
0
0
2
1
1
1
2
2
0
2
0
0
0
0
1
1
0
0
0
0
1
2
0
2
1
1
0
1
3
2
0
0
1
0
2
0
2
0
1
1
2
0
0
0
0
0
2
1
1
0
1
0
0
3
1
2
2
2
0
1
1
1
1
1
1
0
0
0
1
2
1
0
0
2
0
0
1
2
0
1
2
1
2
0
0
1
2
1
0
2
2
0
1
0
0
2
2
2
2
1
1
0
0
0
2
0
2
2
2
1
0
0
0
2
1
1
0
1
2
0
1
0
0
0
0
0
0
2
2
0
0
1
2
1
2
1
2
3
0
3
1
1
0
2
1
0
0
1
0
0
1
2
2
1
1
0
0
0
2
7
0
1
1
2
1
1
5
0
1
0
0
0
1
0
1
1
0
0
1
2
2
1
1
1
3
0
0
1
2
0
0
1
1
2
1
1
0
1
1
0
1
1
0
2
2
0
2
1
0
1
1
1
0
2
1
1
1
1
0
1
1
0
1
1
0
1
0
0
0
2
0
2
1
0
2
1
0
0
1
1
0
1
1
1
0
1
0
0
2
1
2
0
0
0
1
1
2
1
2
1
0
1
1
1
1
0
1
1
1
3
0
0
0
0
1
0
2
1
3
1
2
0
0
1
2
2
2
0
0
1
1
1
0
0
0
0
2
1
1
2
0
0
2
0
0
0
0
0
0
2
0
1
1
0
1
2
0
1
2
1
1
0
0
0
1
0
2
0
0
2
0
0
0
1
0
1
1
2
2
1
2
1
0
1
2
1
1
0
0
1
1
1
0
0
0
2
1
1
1
0
0
2
0
0
1
4
1
2
1
0
0
0
0
1
1
2
0
1
2
1
2
0
1
0
1
0
0
1
0
3
0
1
2
0
1
0
2
0
0
2
0
1
2
1
2
0
0
0
2
1
2
1
0
2
1
2
0
2
2
1
2
1
0
2
0
0
1
1
1
0
1
2
1
0
0
1
0
2
1
1
0
1
1
1
2
1
0
1
0
1
0
0
0
3
1
1
1
0
2
0
2
2
0
0
0
0
4
0
1
2
2
2
0
2
1
1
1
2
0
0
0
0
2
3
0
0
2
0
0
2
2
2
1
1
0
2
1
2
1
2
0
2
2
1
2
2
0
1
2
0
1
1
2
2
1
0
2
0
1
1
0
0
1
1
1
2
0
1
1
0
2
1
2
0
1
2
0
0
2
1
0
0
1
1
1
1
0
0
0
0
0
0
1
1
1
1
1
1
2
2
1
0
0
0
1
0
1
0
0
0
0
0
0
0
2
2
0
1
0
0
2
0
0
0
0
0
0
1
0
1
7
0
0
1
1
2
1
0
2
0
0
1
1
0
0
1
1
2
1
2
0
1
2
3
1
1
5
0
7
0
0
1
1
2
0
2
2
2
2
1
1
2
2
2
2
0
0
1
0
2
1
2
0
0
0
0
1
0
0
1
1
2
0
0
1
0
1
0
0
0
0
0
2
1
1
1
1
1
0
0
0
0
1
0
2
0
0
1
2
0
1
1
0
0
1
1
2
1
1
1
2
1
3
1
2
2
0
1
2
2
0
2
0
1
1
2
0
2
1
2
0
0
0
1
0
2
2
1
0
0
0
1
1
1
2
0
0
0
1
1
1
1
3
0
0
2
1
0
0
0
1
1
1
1
1
0
1
2
0
0
0
0
0
1
1
0
1
0
0
1
0
2
1
0
2
0
0
0
0
0
0
1
0
1
1
2
0
2
2
2
1
1
1
0
0
0
0
2
1
1
1
0
2
2
0
2
2
1
1
1
0
1
0
1
1
0
1
1
1
0
1
0
1
0
0
2
0
2
3
1
1
1
1
0
2
0
1
2
0
0
0
1
3
0
1
0
1
0
2
2
2
0
0
0
0
1
1
0
2
0
1
2
0
2
0
0
0
0
0
2
0
1
1
0
2
1
1
0
1
1
1
1
2
0
1
2
0
1
2
0
1
0
1
0
0
2
1
1
2
1
1
2
1
1
1
1
0
0
0
2
0
0
1
1
1
0
0
2
1
0
1
2
1
0
0
2
0
1
0
1
1
0
0
2
2
1
0
1
2
0
1
2
0
1
2
2
0
1
2
0
0
0
2
1
1
2
0
2
1
0
2
1
0
1
2
0
2
0
2
1
0
1
0
1
0
0
1
2
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
1
1
1
0
1
2
0
0
2
1
1
2
2
0
0
2
0
1
2
0
1
2
2
1
2
0
0
2
2
0
0
1
1
0
0
1
0
1
1
1
0
2
1
1
1
0
0
0
2
1
2
9
0
2
2
0
1
1
0
0
2
0
0
1
0
1
1
2
2
2
2
1
2
1
1
1
1
0
0
2
0
0
1
2
2
0
0
3
1
1
2
0
0
1
2
0
0
1
2
2
3
1
1
1
2
0
0
0
2
0
2
1
1
0
2
1
1
1
1
0
1
0
2
1
2
0
1
1
1
0
0
2
0
0
1
1
2
2
0
2
1
2
2
3
0
0
2
1
0
1
1
1
0
1
0
3
1
0
2
0
0
0
0
0
3
0
1
0
0
0
2
1
2
0
2
1
1
1
1
1
0
1
2
1
0
0
2
2
1
1
0
0
0
1
1
2
1
2
0
2
1
0
0
0
0
2
0
0
0
0
1
2
1
0
0
1
0
2
0
0
2
1
2
1
1
2
0
2
2
2
2
2
0
1
0
1
2
0
0
0
1
2
0
0
0
1
0
0
2
1
2
1
0
0
1
0
0
0
3
1
0
1
1
0
0
1
0
1
2
2
0
0
1
0
1
3
1
0
0
1
0
2
1
1
2
0
0
0
0
0
0
0
0
2
0
1
2
0
2
0
0
1
2
0
1
1
2
2
1
1
0
0
2
1
1
0
2
0
0
0
0
1
1
1
1
0
0
1
2
3
0
0
10
4
1
1
0
1
2
0
0
1
0
1
1
1
2
1
0
2
1
0
0
1
0
1
1
0
1
1
2
2
2
0
0
1
1
0
0
1
2
2
2
0
0
0
0
1
2
1
1
0
0
1
0
1
0
0
0
0
1
1
1
1
1
2
1
1
2
1
0
0
1
0
1
2
1
1
1
2
0
1
1
2
0
0
1
0
0
0
1
2
1
1
0
1
0
1
0
2
2
1
1
0
1
0
1
0
0
0
1
1
1
1
0
0
0
0
1
0
0
0
1
0
0
1
2
2
0
1
1
1
1
2
2
1
1
0
0
1
1
2
0
1
0
2
0
2
2
0
0
2
2
1
0
2
2
0
0
1
0
0
0
0
0
2
2
0
0
1
0
1
1
0
0
0
2
1
0
0
0
2
0
0
1
1
1
0
2
1
2
1
2
2
1
0
1
1
0
0
1
1
1
5
1
0
0
0
1
2
0
0
1
0
0
1
2
2
0
1
0
2
1
1
0
0
0
0
1
0
2
1
0
0
1
1
0
1
0
1
1
0
1
2
1
2
0
0
0
0
2
0
1
1
1
0
1
0
0
1
2
0
2
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
1
2
1
2
0
2
1
0
1
1
0
0
0
0
1
1
1
1
1
1
0
1
0
0
0
1
1
1
0
0
0
0
0
0
1
1
2
0
0
0
3
1
0
0
2
2
2
0
0
0
1
1
0
2
1
1
0
1
1
0
1
1
1
1
1
1
0
1
0
0
1
1
1
0
2
0
2
0
1
1
0
1
2
0
2
0
2
1
2
2
0
1
1
0
0
0
0
0
1
0
1
1
1
1
0
1
1
1
0
2
0
1
0
0
1
1
0
2
2
1
1
2
2
2
2
0
1
2
1
1
1
2
2
0
0
2
2
2
1
1
1
0
2
2
0
2
1
0
1
0
2
0
2
2
0
1
1
0
0
0
0
1
0
1
0
0
0
1
0
2
0
2
0
2
2
0
3
0
2
1
1
0
0
0
1
3
1
2
1
2
1
1
1
0
1
2
2
0
1
0
0
2
2
1
0
0
1
1
1
1
0
0
1
1
0
0
1
2
2
0
1
2
1
2
0
2
0
2
0
0
2
1
1
2
1
1
0
2
1
0
1
1
1
1
0
1
0
2
0
1
2
0
1
1
1
2
0
2
1
1
0
1
0
1
0
1
1
2
2
0
2
0
1
2
2
2
0
0
0
1
2
0
2
1
0
2
0
0
0
2
2
2
1
2
2
1
1
0
2
0
1
2
1
0
1
1
1
2
1
0
0
0
3
1
4
2
1
1
0
2
1
0
1
0
0
5
2
1
1
0
0
1
2
1
0
0
0
2
0
1
2
1
0
2
2
0
1
0
1
0
1
0
1
0
0
0
0
0
1
1
1
2
2
0
1
1
1
1
1
1
1
0
0
1
2
0
1
1
1
2
1
1
0
1
1
1
1
2
3
2
0
0
1
1
2
1
1
0
0
0
2
0
0
0
0
1
1
0
0
1
0
0
1
0
1
0
1
1
1
0
1
3
1
1
2
2
2
1
0
0
1
0
0
2
1
1
1
1
1
0
2
0
1
1
2
1
1
1
0
0
1
0
2
1
0
0
2
1
1
1
1
1
0
1
2
0
0
1
1
0
1
0
1
1
1
1
1
0
0
0
2
1
1
0
1
0
1
1
0
0
0
2
0
1
1
1
0
1
2
1
3
1
1
1
1
1
0
1
0
2
0
0
2
2
1
2
1
0
0
0
0
0
1
2
0
1
2
1
0
1
1
0
1
1
2
0
0
0
2
0
0
1
0
1
0
1
0
1
0
1
0
0
1
1
1
0
0
0
0
0
8
0
0
0
2
1
0
2
0
0
1
1
7
0
0
1
1
0
1
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
1
2
1
3
2
0
2
1
1
1
1
1
3
2
0
0
1
0
0
0
0
0
0
2
0
0
1
0
1
2
0
0
0
0
2
2
0
1
1
0
0
0
0
0
1
0
0
1
0
0
1
0
2
1
1
0
1
1
2
2
2
1
1
1
2
1
1
0
1
0
1
1
0
3
0
1
1
0
2
1
0
0
1
1
0
1
0
2
0
1
0
1
1
1
0
0
0
0
1
2
2
0
1
1
2
0
1
2
0
2
0
1
1
2
1
1
2
0
1
1
0
1
1
1
0
2
1
2
0
1
0
0
0
0
0
1
1
0
0
2
1
2
2
0
1
1
1
1
3
2
0
2
1
1
1
1
1
1
0
1
0
1
2
1
1
1
1
2
2
0
1
1
0
0
0
0
2
2
1
0
1
2
0
0
0
1
2
0
1
1
0
2
2
0
0
0
1
0
0
0
0
2
0
1
1
0
1
1
0
0
0
0
0
0
0
0
1
0
1
1
2
2
0
0
2
0
1
0
3
1
0
0
0
0
2
1
0
0
4
1
0
0
1
1
1
1
0
1
2
0
0
1
0
0
1
0
0
0
1
1
1
0
0
2
0
1
1
0
1
0
2
0
0
0
1
0
1
1
1
1
1
1
0
1
1
3
2
0
1
2
1
1
1
0
0
2
0
0
0
2
1
1
1
1
0
1
2
0
0
0
0
1
0
1
1
1
2
0
1
2
1
1
1
2
0
2
3
0
0
0
0
1
4
1
1
1
3
0
0
0
2
1
1
0
2
1
0
0
0
0
0
1
0
2
0
2
1
0
0
2
0
1
0
0
1
1
0
2
2
0
1
1
1
1
0
0
2
2
2
1
0
1
0
0
0
0
1
0
0
2
1
2
0
1
2
1
2
0
2
1
0
0
0
0
0
0
2
1
1
1
0
0
2
1
1
1
0
1
0
1
0
2
1
1
2
2
1
0
1
2
0
0
1
1
0
0
0
0
0
1
1
0
0
1
0
1
1
1
0
1
1
4
0
0
1
2
1
0
0
1
1
1
1
0
2
1
0
0
0
0
2
2
1
0
1
2
0
0
1
0
0
2
1
0
1
2
1
1
1
1
0
1
1
1
0
1
1
2
1
1
1
3
2
2
1
1
0
2
0
0
2
1
1
1
1
0
0
1
2
2
1
0
1
0
0
1
1
1
2
1
0
0
1
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
1
1
0
0
2
0
0
0
0
0
0
0
0
2
2
0
1
2
0
1
2
2
1
1
0
0
1
2
1
2
1
1
0
3
1
0
1
1
2
2
0
0
1
1
1
0
0
0
1
1
1
1
3
2
0
0
1
2
0
3
1
0
0
1
1
0
0
0
1
1
0
1
2
2
2
2
1
0
1
2
1
1
2
1
1
1
0
1
1
2
0
0
0
0
2
1
2
2
0
0
2
0
0
1
0
2
1
1
2
0
1
1
1
0
0
0
0
1
0
1
2
0
1
0
2
0
0
2
0
0
0
0
0
1
0
0
1
0
1
2
2
0
1
0
4
1
1
0
0
0
0
1
2
2
1
0
0
1
0
0
0
0
0
0
0
0
2
0
1
2
1
0
2
2
1
1
0
1
1
0
1
0
0
0
1
0
1
2
1
1
0
0
0
1
0
0
1
0
2
1
0
1
2
2
0
0
1
2
1
2
0
1
0
0
0
3
2
0
1
0
0
0
0
1
0
1
2
2
0
1
1
0
1
0
0
1
0
2
0
0
0
0
1
1
0
2
2
0
0
1
0
0
1
1
0
1
0
1
1
1
1
0
1
2
0
0
1
1
1
0
1
1
1
1
1
0
1
1
1
1
2
1
1
2
1
2
0
0
0
1
2
1
2
2
1
1
2
0
1
0
0
1
1
2
0
0
0
1
1
1
1
2
1
2
2
1
2
0
1
0
0
1
0
0
1
2
0
1
1
1
0
0
0
0
0
1
0
2
2
0
0
0
0
1
1
1
1
2
2
1
1
2
1
2
0
1
1
1
1
0
0
1
0
0
1
0
2
1
0
0
0
0
2
0
1
0
1
1
2
0
0
1
2
2
0
3
2
0
0
3
2
0
0
1
2
2
2
2
0
2
0
2
0
2
1
0
1
1
2
1
1
1
0
1
1
1
0
1
0
1
0
0
1
0
0
1
0
0
1
1
0
2
1
2
2
1
1
0
0
0
0
1
1
1
1
0
0
1
2
0
0
0
0
2
1
2
0
2
1
1
1
1
0
0
0
2
1
1
0
2
0
1
3
2
0
2
1
1
1
1
0
1
0
1
0
0
1
1
0
0
2
0
0
0
1
2
2
1
1
1
2
0
1
0
0
1
2
1
1
0
1
1
0
0
1
1
1
1
1
3
1
0
2
0
1
0
1
0
1
2
1
0
1
0
3
1
0
1
1
1
0
0
1
1
0
1
0
2
0
0
2
1
0
0
0
0
1
2
2
0
2
1
1
2
0
1
0
1
1
0
1
0
1
1
2
1
1
2
2
0
0
0
0
2
1
0
0
0
2
0
2
2
0
0
0
0
0
2
0
0
2
1
1
2
1
2
2
0
2
0
1
1
1
1
1
1
0
2
0
2
1
0
6
0
0
0
0
0
1
1
1
0
0
0
1
2
2
1
0
1
3
1
2
1
1
0
0
1
2
0
0
2
0
0
0
1
0
1
1
0
0
2
1
1
2
0
0
1
0
0
0
1
2
1
1
1
1
2
2
0
1
2
0
0
1
1
0
0
0
0
1
1
0
1
0
0
1
1
1
1
1
1
0
1
2
0
0
0
0
1
0
0
1
0
1
1
2
2
1
0
0
0
1
1
0
0
3
0
1
1
1
1
0
2
0
1
2
1
0
0
0
0
1
0
2
0
2
0
0
2
1
0
1
1
0
0
1
1
0
1
2
0
1
0
0
1
1
3
0
0
0
0
0
0
2
1
1
0
2
1
2
0
1
1
2
1
1
2
2
1
0
0
1
0
2
2
1
0
1
0
2
0
1
0
0
0
0
0
2
1
1
0
1
1
0
2
0
1
1
1
1
0
2
1
0
0
1
1
1
2
1
2
2
0
0
1
2
0
1
0
2
1
1
0
0
1
1
0
2
1
1
0
1
0
1
1
0
0
2
2
1
0
0
1
0
0
0
2
1
1
1
0
0
2
1
3
1
1
2
1
1
2
0
1
2
2
1
1
0
1
1
2
1
0
0
0
1
0
0
1
0
2
2
2
2
1
0
1
0
1
0
2
0
0
2
0
1
0
2
1
0
2
1
1
0
2
1
1
1
0
0
1
0
2
1
1
2
0
2
1
0
1
1
2
1
2
0
1
0
1
0
1
0
1
2
2
0
0
0
2
1
0
0
1
0
1
0
1
1
1
2
0
0
0
1
2
0
0
0
0
0
1
0
0
1
2
2
2
1
2
0
0
2
0
1
2
2
1
0
1
0
1
1
1
1
1
1
0
2
0
1
1
1
1
1
0
1
1
0
0
1
0
0
1
2
1
0
1
2
0
1
0
2
1
2
0
1
0
1
0
0
3
2
0
1
0
3
2
2
0
2
0
0
0
0
1
2
0
0
2
1
1
2
1
1
0
0
0
2
1
1
2
0
1
1
0
2
0
2
2
0
1
1
0
0
0
0
0
2
1
0
1
1
1
1
0
0
2
1
1
0
1
0
1
1
0
0
0
0
1
1
2
1
0
1
0
2
0
1
0
1
1
1
0
2
2
0
0
0
0
0
2
1
0
0
0
1
2
2
1
0
1
0
2
0
2
0
2
0
2
1
0
0
1
0
0
1
1
1
0
0
2
1
2
0
2
1
2
1
2
2
0
2
2
1
1
2
1
1
0
0
1
0
0
2
2
1
0
2
0
1
0
0
0
2
1
3
3
1
0
1
1
0
1
0
2
0
0
2
0
2
1
1
1
5
2
1
0
1
1
0
1
0
1
0
1
0
1
2
1
1
1
1
1
0
1
1
0
0
3
0
1
0
1
1
2
0
0
1
0
1
1
1
0
1
0
0
1
1
2
1
1
2
2
2
1
2
1
2
0
1
1
2
1
0
0
0
1
0
0
0
0
0
3
0
1
1
0
1
1
1
0
2
2
0
0
0
0
0
0
1
0
1
2
0
2
2
1
0
0
1
3
1
0
0
1
1
1
2
0
1
0
1
1
0
1
1
1
0
1
0
1
0
1
0
1
0
2
0
0
1
0
1
1
1
0
1
0
0
1
2
0
0
1
0
3
1
0
0
2
2
2
1
0
0
1
0
1
2
0
0
1
2
0
1
0
0
2
1
0
1
2
0
2
0
1
0
0
1
0
1
2
1
1
0
0
2
0
1
1
0
0
1
1
1
0
0
0
2
0
1
2
1
0
1
1
1
0
1
1
2
0
1
1
0
0
2
0
1
2
1
1
1
0
0
0
1
2
0
0
1
1
0
1
0
0
1
2
0
0
2
0
0
0
1
1
1
2
0
0
2
1
1
1
1
1
1
1
1
0
0
2
0
0
1
0
2
0
0
2
0
1
1
1
1
2
0
0
0
1
0
1
1
1
0
0
0
2
0
2
0
0
0
0
0
1
0
0
1
4
0
0
0
0
2
2
0
0
1
0
0
1
0
0
0
2
2
1
1
2
1
1
0
0
0
0
1
0
2
1
1
1
2
1
1
1
0
2
0
1
1
0
2
1
0
0
1
0
0
2
0
1
2
0
1
1
0
2
2
1
0
1
0
0
2
1
0
1
1
0
2
0
2
0
1
1
1
1
2
1
0
0
0
2
0
1
0
1
0
0
0
1
1
0
1
1
2
1
0
1
1
1
1
2
2
0
1
2
0
0
1
1
1
0
1
0
0
1
2
2
1
1
1
1
0
0
1
2
0
0
2
2
2
0
0
0
2
0
1
1
1
2
0
1
0
0
1
0
2
2
1
0
1
2
3
1
0
1
0
0
4
2
0
1
0
1
0
1
0
1
1
1
1
4
0
1
0
1
1
1
0
0
0
1
0
0
0
1
0
1
1
2
2
1
2
1
2
1
1
0
0
2
1
0
1
1
0
0
0
1
1
2
3
0
2
2
0
0
0
1
2
2
2
1
1
2
0
1
3
0
1
1
2
1
0
1
0
1
0
0
1
1
0
0
0
0
1
2
0
1
1
0
0
1
1
0
2
1
0
1
0
0
2
1
1
0
0
2
1
2
0
0
0
1
3
0
0
2
0
0
2
1
2
1
0
0
0
0
1
2
0
1
0
0
0
0
1
1
0
1
2
1
0
1
0
2
1
0
1
1
0
2
2
0
1
1
2
0
0
2
0
0
2
1
1
0
1
0
0
0
1
1
2
1
1
2
1
1
2
1
1
1
1
3
0
0
1
1
0
1
0
0
2
2
2
0
0
3
1
1
2
0
1
2
0
0
0
1
0
1
0
2
2
0
2
1
0
1
0
1
0
0
2
1
1
0
2
1
0
0
2
2
1
0
1
2
0
0
1
1
2
1
1
0
0
0
1
0
0
2
1
0
0
1
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
1
1
1
2
1
0
1
0
0
2
0
0
2
0
1
0
0
0
0
0
4
1
0
2
0
1
4
0
0
1
2
0
1
1
1
2
0
2
0
2
0
1
0
1
1
0
0
1
1
0
1
2
0
0
0
1
1
1
0
0
0
1
2
1
2
0
0
0
1
0
1
2
1
0
0
1
2
0
1
0
1
0
0
1
0
0
0
2
2
1
0
0
0
0
2
0
1
0
2
0
0
1
0
0
1
1
1
1
1
0
1
1
1
2
1
1
0
2
0
1
0
1
2
1
0
0
2
2
0
0
2
1
1
0
0
0
2
0
0
0
0
0
2
1
1
0
0
1
1
0
0
2
0
0
3
2
1
1
2
1
1
0
1
0
1
3
0
0
0
0
1
1
1
1
0
0
0
1
0
2
0
0
0
1
1
1
1
1
2
0
1
0
1
0
1
2
2
2
0
0
0
0
2
2
0
1
2
2
0
1
1
0
1
0
1
0
0
1
0
0
0
2
0
0
0
2
0
1
0
2
0
0
1
1
2
2
2
1
0
0
2
1
0
1
1
2
1
2
0
0
0
1
1
1
0
1
2
0
0
0
1
1
2
1
1
4
1
0
0
0
1
0
1
3
1
0
1
1
2
1
0
1
2
2
1
0
1
1
1
2
0
1
0
1
1
1
2
0
2
1
1
0
1
1
2
0
0
1
1
1
1
2
1
0
0
0
2
0
1
0
1
0
0
2
0
0
0
0
1
1
0
0
1
1
2
1
0
1
0
1
2
1
2
1
0
1
1
3
0
1
2
0
1
2
2
0
1
1
2
2
0
1
1
1
1
1
0
2
1
3
1
3
2
0
0
1
1
0
1
1
0
0
2
2
1
2
3
0
2
0
1
2
0
0
2
0
1
0
0
1
2
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
1
0
0
1
1
1
0
0
0
1
1
1
0
2
2
1
0
1
0
1
2
0
1
0
1
1
0
0
0
1
2
1
0
1
0
1
0
2
1
1
0
1
0
0
2
1
0
0
1
0
1
2
1
0
1
1
0
2
2
2
0
1
0
1
2
0
0
0
1
1
3
0
1
1
1
1
0
1
1
2
1
1
3
1
1
1
1
0
1
2
2
1
1
0
0
0
2
0
0
1
0
1
1
2
1
2
1
1
2
0
0
1
2
0
2
3
1
0
0
1
1
2
1
2
0
0
1
1
1
0
1
0
0
0
0
2
2
1
0
1
0
1
0
1
0
0
1
1
1
1
0
2
0
0
1
1
1
1
2
1
0
0
1
2
2
2
2
2
0
1
0
2
2
0
1
2
0
0
2
1
0
0
1
1
0
1
2
1
0
2
1
1
1
0
2
0
2
0
2
2
2
1
0
1
0
1
2
0
0
2
2
0
2
0
0
1
0
2
0
0
2
2
0
1
0
2
1
0
1
2
0
0
1
0
1
1
0
2
0
1
1
0
1
0
0
1
0
1
1
1
1
0
1
0
2
0
2
1
0
3
1
0
1
1
0
1
2
0
0
2
1
0
1
1
2
1
2
1
0
1
0
0
1
0
0
1
1
0
1
2
2
1
0
0
1
0
0
1
0
2
0
0
0
0
1
2
2
2
2
0
1
2
2
1
2
0
2
1
0
1
1
1
3
1
1
1
0
0
1
0
0
1
1
0
1
1
0
1
0
2
3
0
0
1
0
2
1
0
0
1
1
1
1
0
0
0
0
0
0
1
1
0
1
0
2
1
2
0
0
1
2
2
1
0
2
2
1
0
2
0
1
3
0
2
0
1
1
0
1
0
0
1
1
1
0
0
1
2
1
0
1
1
1
2
1
0
2
1
0
1
0
1
0
1
1
1
1
1
1
2
2
0
1
0
1
0
0
1
0
2
1
1
1
0
2
0
1
0
1
0
2
1
0
2
0
0
1
0
1
0
1
0
0
2
0
0
1
0
0
2
1
0
1
1
1
1
1
0
1
1
1
0
1
0
1
1
1
1
0
1
0
2
1
2
0
0
0
2
1
0
0
1
0
0
3
1
1
0
2
0
2
0
0
2
1
1
2
0
1
2
1
1
2
3
2
1
2
0
0
0
1
2
1
0
0
1
1
0
0
0
1
1
1
0
2
1
1
1
0
0
2
1
1
0
0
0
1
1
0
1
3
0
1
1
1
0
1
2
9
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
1
1
0
0
2
1
0
1
0
0
1
0
0
2
0
2
1
0
1
0
2
0
0
1
0
1
2
0
0
0
1
0
0
2
0
2
0
0
0
3
0
0
1
0
1
1
2
2
1
1
1
0
1
1
1
0
0
1
1
0
0
1
1
2
2
0
1
1
2
1
0
0
1
1
0
1
1
0
2
0
1
0
0
0
1
2
1
2
0
1
0
0
1
1
2
1
1
1
1
1
0
0
1
1
1
0
1
1
1
1
0
0
1
2
1
0
1
3
0
1
3
0
1
1
0
2
0
2
0
2
1
0
1
0
2
0
2
0
2
0
0
0
0
1
2
0
2
1
0
0
1
2
0
0
0
2
2
0
0
2
0
2
1
1
0
2
0
0
1
2
1
0
2
2
0
1
1
0
0
0
2
2
1
2
2
1
0
1
0
0
1
2
2
0
0
1
1
1
2
0
0
2
2
0
0
2
1
2
0
2
0
0
0
0
0
1
1
1
1
0
0
0
0
1
1
1
2
0
0
0
2
1
1
2
1
1
0
2
0
2
2
1
0
2
0
1
1
1
1
1
0
1
2
0
1
1
1
1
1
1
0
2
1
1
0
1
0
0
1
1
0
1
2
0
1
2
2
0
1
0
1
0
1
0
2
1
1
0
0
0
1
1
0
2
1
1
0
2
3
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
1
0
1
1
0
2
1
1
0
0
0
0
2
1
2
0
1
0
1
2
1
2
0
2
0
1
2
2
2
2
2
0
2
0
0
1
0
0
0
1
0
1
2
0
1
2
1
1
1
0
1
0
2
1
2
1
2
1
0
2
2
0
0
2
1
0
2
1
0
1
1
1
0
2
1
2
0
0
1
1
1
0
1
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
1
1
1
0
2
1
0
2
2
1
1
1
2
1
0
0
1
3
1
1
1
0
0
0
0
1
0
1
2
0
1
1
1
0
1
1
2
1
1
2
1
1
0
0
2
1
2
0
2
1
0
0
0
0
1
1
0
0
2
0
1
1
1
2
2
1
2
2
1
1
2
0
1
1
1
2
0
0
1
2
0
2
2
2
0
1
0
1
0
0
1
2
1
0
2
2
0
2
0
0
0
0
2
2
2
1
1
1
0
2
0
1
0
0
1
1
1
1
2
1
1
1
1
0
0
1
0
0
0
0
1
1
0
0
1
1
2
1
0
2
0
1
1
2
2
3
1
1
2
1
0
2
2
2
0
1
2
1
0
1
0
1
0
1
2
1
0
1
1
0
1
1
0
2
0
1
1
6
1
1
2
0
0
0
1
2
0
2
1
1
1
2
0
0
0
1
0
0
0
0
0
1
4
0
2
0
1
1
0
0
1
1
1
1
0
0
0
1
1
0
0
1
1
1
0
1
3
1
5
1
1
0
0
2
1
2
0
0
0
0
1
0
1
2
0
0
2
0
0
0
0
0
1
0
1
1
0
0
1
0
2
0
0
0
0
1
2
2
2
0
1
0
1
2
0
1
1
0
0
1
1
1
0
1
2
1
0
0
1
0
0
1
0
0
0
1
0
0
0
2
0
2
1
2
0
0
0
1
1
0
2
1
0
0
0
0
0
0
0
0
0
1
0
1
2
2
2
1
1
0
0
1
1
0
2
0
1
0
1
2
2
0
3
0
2
1
2
1
0
1
1
0
0
1
0
1
2
0
1
0
1
2
0
1
0
1
2
2
1
0
1
0
0
0
0
0
2
2
1
1
1
0
2
2
0
2
0
0
3
1
1
0
0
0
1
0
2
2
1
1
2
1
1
1
0
4
1
0
0
0
2
0
1
1
0
0
1
1
1
0
2
1
0
0
0
1
0
5
1
1
1
1
0
0
2
2
1
1
0
2
1
2
1
1
0
0
1
0
0
3
0
0
0
1
0
1
2
0
2
0
0
1
0
1
1
0
1
2
0
1
2
1
0
1
2
0
0
1
1
0
2
1
2
0
0
0
0
0
1
1
1
1
2
0
1
0
1
1
0
0
1
2
2
1
1
0
1
1
0
0
0
0
1
2
1
0
1
1
1
0
1
1
1
0
2
2
1
1
1
1
0
0
1
0
1
0
0
1
1
11
0
0
0
1
1
0
1
0
3
1
0
0
2
1
1
1
0
0
0
2
1
3
0
1
0
0
1
0
1
2
0
1
0
2
0
1
1
0
1
1
0
1
3
1
0
2
0
1
1
0
2
0
1
1
1
1
0
1
1
1
0
3
0
1
2
0
2
0
0
2
0
4
1
0
1
0
1
1
1
1
1
0
1
1
1
0
1
0
0
0
0
0
1
2
0
1
0
1
0
0
2
2
0
0
0
1
2
1
1
1
0
2
0
2
0
1
1
1
0
1
1
0
2
1
0
0
1
2
0
4
2
1
1
2
0
0
0
2
0
1
0
1
1
0
2
1
2
0
0
0
1
1
1
1
1
0
1
0
1
1
1
0
1
0
1
0
0
1
1
2
1
2
2
0
0
0
2
2
1
2
0
2
0
1
0
0
2
1
4
2
0
0
1
3
1
0
1
0
1
1
1
0
0
0
2
0
1
2
0
1
2
1
1
1
0
2
1
0
2
1
1
1
1
0
1
0
0
0
2
2
0
1
1
1
1
0
0
4
1
1
1
2
2
0
0
1
0
0
1
1
0
2
2
2
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
2
0
1
2
0
1
2
0
2
3
1
2
1
0
2
1
2
1
2
0
0
0
1
0
0
1
2
0
2
0
0
1
0
0
0
2
1
1
1
1
0
0
2
0
0
2
1
2
1
0
3
0
1
2
0
1
0
0
1
0
0
1
0
0
0
0
0
1
1
0
1
0
0
3
2
1
2
1
1
2
0
0
1
1
0
0
2
1
4
0
0
0
0
0
2
0
1
0
0
2
0
1
0
0
0
0
0
0
1
1
2
1
2
0
2
2
0
2
1
2
0
2
0
0
2
0
2
0
1
1
2
1
2
1
2
0
2
0
0
0
2
2
0
0
1
1
1
0
2
1
2
0
0
0
0
1
1
0
1
0
0
1
2
0
1
0
0
0
1
2
1
0
3
0
1
1
1
1
2
1
0
0
1
0
1
1
0
0
2
2
1
0
1
0
1
0
0
0
2
0
2
1
1
1
0
0
2
1
0
2
1
0
1
2
0
0
0
0
0
0
0
1
1
2
0
0
1
0
0
0
0
0
0
1
0
1
2
2
0
0
1
1
2
2
0
1
0
2
2
2
1
0
1
0
1
0
0
2
0
2
0
2
1
1
4
0
0
1
0
1
1
1
2
1
0
1
1
1
0
6
1
1
1
0
2
2
0
0
1
0
2
0
2
2
2
1
0
1
1
1
1
0
0
2
0
1
2
0
1
2
2
1
0
1
0
0
0
2
1
0
0
2
1
0
2
1
1
0
0
0
0
0
1
0
0
0
2
0
1
1
0
0
1
1
0
1
5
2
2
0
0
1
1
2
1
2
2
0
1
2
0
0
0
0
1
0
1
1
0
2
1
1
0
0
0
0
1
3
1
1
0
0
1
1
0
0
0
1
1
0
0
2
0
1
1
1
0
2
1
1
1
1
0
1
0
0
1
2
0
0
2
0
1
1
0
1
6
2
2
1
2
2
1
0
0
1
0
0
1
1
0
2
0
1
0
1
0
0
1
0
0
1
0
1
1
0
0
1
0
1
0
2
1
1
1
0
2
2
2
1
0
1
0
1
1
1
0
1
1
0
1
0
1
0
1
0
1
1
1
0
1
2
1
1
2
1
1
1
0
0
2
1
0
1
2
1
0
2
0
0
0
1
1
0
0
1
0
1
0
0
1
1
0
2
0
0
0
2
0
0
0
0
2
0
1
0
0
0
1
1
2
1
2
1
0
0
2
0
0
1
2
2
2
2
0
0
0
2
0
0
0
1
2
0
0
1
0
0
1
0
2
0
0
1
0
0
1
1
0
1
1
1
1
1
0
1
0
0
1
2
1
1
0
2
1
1
1
0
0
2
1
0
2
1
1
0
0
2
0
3
1
1
2
2
0
0
2
0
2
0
2
0
1
0
1
0
2
0
1
1
1
1
0
1
3
0
2
1
2
0
1
0
2
0
0
2
2
1
2
0
0
2
2
0
1
2
1
0
2
2
0
2
0
1
0
0
1
1
0
1
0
0
0
1
1
1
1
1
0
2
0
2
2
0
1
0
0
0
1
0
6
1
1
0
1
0
1
0
3
2
1
1
0
3
2
0
1
1
0
0
0
1
1
0
4
2
0
1
0
0
1
1
0
1
0
1
1
0
1
1
0
0
0
4
1
1
1
1
0
1
0
1
2
1
2
1
1
1
2
1
1
2
1
2
2
0
2
0
1
0
0
2
2
1
0
0
1
0
0
1
0
2
1
1
0
0
1
1
1
1
1
0
0
1
2
2
1
0
2
2
1
2
2
2
1
1
0
0
6
1
1
0
0
2
0
1
1
2
1
2
0
0
0
1
1
2
0
0
1
1
2
0
0
0
0
0
0
0
0
0
1
1
1
1
0
2
1
1
1
0
1
0
1
1
0
2
0
1
1
1
1
1
1
1
1
2
2
2
2
1
1
1
2
2
1
0
0
2
0
0
0
0
1
0
0
2
2
0
1
1
2
1
1
0
1
0
0
0
1
1
2
0
0
0
1
1
0
2
0
0
2
1
2
1
0
1
1
0
0
1
2
1
1
1
0
1
0
0
0
1
1
1
5
1
2
0
0
1
1
0
1
1
1
0
0
0
1
0
1
1
0
1
0
0
0
0
2
1
0
0
1
2
2
2
0
1
1
1
2
1
2
2
1
2
0
0
0
0
1
0
1
0
2
0
0
0
0
1
0
0
2
0
1
2
5
1
2
1
1
0
0
2
2
2
2
2
0
0
0
0
0
1
2
0
1
0
0
2
2
1
0
0
0
2
2
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
3
0
1
0
2
1
0
0
2
0
1
0
1
2
2
0
2
0
2
1
1
1
0
2
0
0
2
2
1
1
0
0
2
0
0
1
1
0
1
0
3
1
1
0
0
2
2
2
0
1
0
2
2
1
1
2
0
1
0
0
0
1
2
1
2
0
0
1
2
0
1
0
1
2
0
0
0
2
1
1
0
2
1
1
2
0
0
0
1
0
1
0
0
0
0
1
0
0
0
2
0
2
0
1
2
0
1
2
1
2
1
1
0
0
1
0
2
0
1
2
1
1
1
1
0
1
0
1
2
1
1
0
2
1
0
0
1
0
2
0
2
1
0
1
0
0
0
1
0
9
1
0
0
1
2
0
1
2
0
1
0
0
2
1
1
1
1
1
0
1
2
1
1
1
0
1
0
1
0
0
1
0
2
1
1
1
1
2
1
0
0
0
1
2
0
1
2
2
1
0
1
1
0
0
0
1
0
0
2
0
0
1
1
5
0
1
2
0
1
1
1
0
2
1
0
0
1
1
0
2
0
2
0
0
1
2
0
1
0
2
0
2
1
0
0
0
0
1
0
1
1
2
0
0
1
2
1
1
0
1
1
1
0
1
1
1
1
0
0
1
1
3
0
0
0
0
0
2
1
1
0
1
1
2
2
0
0
0
1
2
2
2
1
1
1
0
0
1
2
0
0
0
1
1
0
1
0
0
1
0
0
2
1
0
0
0
0
2
1
0
1
1
0
0
1
1
0
1
1
1
1
1
0
0
1
0
1
1
1
0
1
1
1
2
1
1
0
0
1
1
0
2
0
1
0
2
0
0
1
2
0
2
1
2
2
1
0
2
1
0
0
1
0
0
2
0
0
1
1
0
1
1
0
1
1
0
0
1
0
1
1
0
0
1
0
0
1
1
2
0
0
0
0
0
1
0
0
1
0
2
1
1
0
0
1
0
0
1
1
1
0
0
1
1
1
1
1
1
2
0
1
1
2
0
1
1
0
2
0
2
1
0
1
1
2
1
0
1
1
3
1
1
0
0
2
0
0
1
0
1
1
1
0
1
0
0
0
0
1
0
2
1
1
1
2
0
0
0
1
0
0
0
1
1
2
1
1
0
1
0
0
0
2
2
1
2
0
3
1
1
0
0
1
1
0
2
1
0
0
3
0
2
1
1
2
2
0
2
1
2
0
1
2
0
1
0
0
0
1
2
1
1
1
2
0
1
2
1
0
1
1
1
1
1
2
2
1
1
1
0
3
1
1
1
1
1
0
1
2
0
1
0
0
2
1
1
2
3
0
1
2
0
0
1
1
2
0
1
1
1
1
0
1
2
2
2
0
0
0
0
1
1
1
1
2
1
0
1
0
1
0
1
1
0
2
1
0
2
1
0
0
0
0
0
0
1
2
0
1
0
2
2
0
1
0
0
0
2
2
0
1
2
0
1
1
0
1
1
2
0
1
1
0
0
0
1
1
2
0
1
0
2
1
2
1
0
0
0
2
0
0
0
2
0
1
2
0
1
2
1
2
1
1
2
1
1
1
1
0
0
1
0
0
1
2
1
1
1
1
2
1
2
1
1
1
2
0
1
1
1
0
1
2
1
2
1
0
0
1
1
0
0
1
1
2
1
1
1
0
2
2
0
2
0
2
0
1
0
0
1
1
1
1
2
1
1
1
1
1
1
0
0
1
0
0
1
1
1
0
2
0
0
0
0
1
2
2
0
0
0
1
0
0
1
1
1
1
2
2
0
3
1
0
0
2
0
1
1
0
0
0
0
1
3
1
2
2
0
0
2
0
0
0
0
1
1
0
1
2
2
1
0
1
1
2
0
0
0
1
1
1
0
0
1
0
1
0
1
0
0
1
1
0
1
0
0
0
1
1
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
1
1
2
2
2
0
1
2
2
0
2
0
1
0
0
1
1
0
1
1
2
2
2
1
0
0
2
0
0
2
1
2
0
0
0
1
0
0
1
2
0
0
1
0
1
0
1
1
1
0
1
0
1
1
1
0
1
0
0
2
2
0
0
0
1
0
0
1
0
0
6
0
2
1
0
1
0
1
1
1
0
1
0
2
2
1
2
0
1
1
2
0
1
0
2
2
0
0
1
1
2
0
0
2
1
0
0
0
1
1
2
2
1
0
1
0
0
2
0
1
0
0
1
1
2
2
2
1
1
1
1
0
3
1
0
0
0
1
1
0
0
0
1
1
2
2
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
2
0
1
2
2
1
0
1
1
1
0
2
0
0
0
0
0
0
2
2
2
1
0
1
0
1
2
2
0
0
0
0
1
1
1
1
0
1
2
1
1
2
0
2
0
1
0
2
2
0
1
0
1
0
1
1
1
0
0
0
0
0
0
1
2
2
2
0
1
1
1
0
1
2
1
1
1
1
0
2
2
0
1
2
0
2
2
1
0
0
0
1
1
2
1
2
1
1
2
4
2
1
0
0
0
0
0
0
0
1
0
1
1
0
2
1
0
0
1
1
0
2
1
1
1
0
2
0
0
1
0
1
1
0
0
0
1
0
2
3
0
0
0
2
0
1
0
1
0
1
1
0
2
0
0
1
0
0
1
2
0
0
1
0
0
0
0
1
0
0
1
0
0
2
2
2
1
0
0
0
0
0
0
0
2
0
2
1
1
0
0
1
0
0
1
2
0
1
2
1
0
0
0
0
0
2
1
0
0
1
0
1
0
1
0
0
0
2
2
1
1
1
0
0
2
0
2
0
0
2
0
0
0
0
1
1
2
2
0
1
1
1
2
1
0
0
1
2
1
2
0
1
1
1
1
1
1
0
1
0
0
9
1
0
2
0
2
0
0
0
2
0
0
0
2
1
0
1
1
1
2
2
1
0
1
0
0
2
0
1
0
0
1
0
0
1
0
0
2
1
3
1
2
1
1
1
2
1
1
1
0
2
0
0
0
0
1
1
0
0
1
1
1
1
0
1
2
0
0
0
0
1
3
0
0
1
0
1
0
1
1
1
1
3
1
1
0
1
1
0
1
1
1
1
0
1
1
2
2
2
0
0
1
0
0
1
0
0
1
0
1
0
0
1
2
1
1
0
2
0
2
1
1
2
1
0
0
0
2
1
0
0
0
12
0
1
0
0
2
2
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
1
2
1
2
0
0
1
1
1
0
0
0
1
1
2
0
2
2
2
1
2
0
1
1
1
2
2
1
0
0
0
1
1
0
1
2
1
0
1
2
1
1
0
2
0
0
0
0
1
1
0
0
2
1
0
0
1
0
0
1
1
2
2
1
1
2
0
0
2
0
2
1
0
1
1
0
0
1
0
2
1
1
0
1
3
1
0
2
0
2
0
2
1
0
0
0
0
0
0
1
1
2
0
0
2
2
1
0
2
1
2
0
1
1
1
0
1
1
0
2
1
0
0
0
2
0
0
4
0
0
1
1
0
1
1
1
1
0
2
0
1
1
0
0
2
1
1
2
2
1
1
0
0
2
1
1
0
1
0
2
0
1
1
2
0
2
1
0
1
1
1
2
2
1
1
1
0
2
1
0
1
2
1
1
2
1
1
0
2
2
2
2
1
0
1
0
1
0
1
2
2
1
1
3
1
1
0
2
0
1
1
0
0
0
2
0
1
1
1
0
1
2
0
1
0
1
0
1
0
0
1
0
0
1
1
2
0
0
0
0
0
1
1
0
3
4
0
2
1
0
2
3
0
2
1
0
0
1
0
1
2
1
0
0
1
1
0
2
2
0
2
2
0
2
1
1
2
1
2
2
2
1
0
1
2
0
0
0
0
2
0
0
1
0
0
2
0
0
2
0
2
1
0
0
1
1
1
2
0
0
1
0
0
0
1
0
2
2
2
2
2
0
1
1
2
1
1
0
1
0
1
1
0
2
0
1
1
0
0
0
1
0
0
0
1
1
1
1
1
0
2
1
1
0
1
2
1
1
0
1
0
0
0
0
1
3
0
0
2
0
1
2
0
1
2
0
1
0
0
0
0
1
1
1
1
2
0
1
1
0
2
0
1
1
0
1
2
1
3
1
0
2
0
1
2
1
0
1
1
2
2
0
0
0
1
1
0
0
1
3
1
1
2
1
1
1
1
2
1
1
1
2
1
2
1
1
0
0
2
3
2
2
0
0
1
1
0
1
1
1
1
1
1
2
2
0
1
1
2
0
1
2
1
1
0
0
1
0
0
1
1
2
1
0
1
0
2
2
2
0
1
2
0
0
0
2
0
0
1
1
1
1
0
0
2
1
1
0
1
0
0
2
2
0
0
1
1
1
0
0
0
0
1
1
0
2
1
1
1
0
1
0
0
0
0
0
0
1
2
1
0
1
1
2
2
0
0
1
2
2
0
0
0
1
0
2
1
2
1
1
1
1
0
2
0
0
0
0
1
1
1
0
1
0
1
0
2
0
2
1
1
0
1
2
2
1
0
0
2
1
2
0
2
0
0
0
1
1
2
0
2
2
1
1
2
0
2
0
2
1
0
1
2
0
0
2
2
0
0
2
1
1
2
0
1
1
2
0
1
2
0
0
0
2
0
0
2
1
2
2
0
0
0
2
1
0
1
0
2
1
1
0
0
1
2
1
1
2
0
0
0
2
0
1
0
0
0
1
2
1
1
0
1
1
0
1
0
1
1
1
2
1
0
0
2
2
1
0
2
2
2
0
0
1
0
0
1
0
1
1
1
0
1
0
1
1
0
2
2
1
0
2
2
2
1
1
1
2
1
1
0
1
1
0
0
2
2
0
0
0
2
0
1
1
0
0
0
0
1
2
0
1
1
2
1
1
2
2
1
3
0
0
1
0
2
1
1
1
0
1
0
1
0
2
1
2
1
2
1
1
2
2
1
1
1
1
0
2
2
0
2
0
0
0
1
1
0
1
1
1
1
1
0
0
0
2
0
3
0
1
0
1
0
0
1
1
1
0
0
1
0
0
0
1
1
2
1
1
1
0
0
0
0
3
0
0
2
1
2
0
1
1
0
1
2
1
2
1
0
0
2
2
0
1
1
0
0
0
1
0
2
2
0
1
0
2
0
1
0
0
2
0
0
1
2
1
2
0
2
2
1
1
3
1
0
1
1
0
0
1
2
0
2
0
0
0
1
1
2
0
1
2
0
0
2
0
1
1
0
0
1
0
0
0
0
0
0
0
1
1
3
1
0
3
2
2
1
2
1
1
1
0
0
0
0
1
0
1
2
0
0
1
1
0
0
1
1
2
0
1
0
1
2
1
1
0
1
2
2
2
0
0
0
2
0
0
0
1
0
0
2
1
1
0
2
2
0
0
1
1
0
0
1
0
0
2
0
1
1
1
2
1
1
0
2
0
0
0
1
0
0
1
1
1
1
0
2
0
0
0
0
2
2
2
2
0
1
0
2
0
0
2
1
1
0
1
0
3
2
1
0
1
1
0
0
1
1
2
2
1
2
2
1
0
0
1
0
0
1
1
1
2
2
1
1
2
2
1
1
2
1
0
1
0
2
6
1
0
1
0
0
0
1
1
0
1
1
1
1
1
1
0
1
2
1
0
0
0
1
0
1
3
0
2
0
0
1
1
0
2
2
1
0
1
1
1
1
0
2
2
0
2
0
1
0
1
0
0
0
0
1
2
0
1
2
2
1
0
2
1
0
0
2
1
1
1
0
2
1
1
0
1
1
2
0
0
2
1
0
1
0
2
1
1
0
0
0
1
1
0
0
0
0
2
2
0
1
1
0
2
0
1
0
0
2
1
1
0
1
1
2
0
0
0
0
1
1
1
1
2
0
0
2
1
1
1
2
1
0
0
0
1
0
1
1
1
0
1
1
0
1
1
0
1
1
0
1
2
2
0
0
2
1
0
0
1
1
0
0
1
1
1
2
1
3
1
0
0
1
0
0
1
0
2
2
0
2
2
1
0
2
1
0
2
2
0
1
0
0
2
2
1
0
1
0
1
1
1
0
2
0
1
3
0
0
1
2
2
2
0
0
1
1
1
0
0
1
1
0
2
0
2
1
0
2
0
3
0
1
0
0
2
0
0
0
1
0
0
1
2
1
1
1
4
0
1
1
0
1
0
1
1
1
1
1
2
2
2
2
2
1
1
1
2
1
1
0
1
1
2
0
2
0
0
1
2
1
0
1
2
0
0
1
0
1
2
1
0
0
0
0
1
0
2
0
2
0
0
1
2
1
0
1
1
1
1
0
0
0
0
3
0
1
2
0
1
1
2
1
0
1
1
0
0
0
1
0
1
0
1
0
0
0
1
2
2
1
1
1
0
1
2
0
1
0
2
1
0
3
0
1
1
1
0
1
1
2
2
0
1
1
0
0
0
0
2
1
2
1
1
0
1
0
0
0
0
2
1
1
1
2
1
1
0
1
1
2
2
0
0
1
0
1
1
1
1
2
0
1
0
1
0
1
1
0
1
5
0
1
0
1
0
1
1
2
0
0
2
0
0
1
0
0
1
0
2
1
2
0
2
2
1
1
0
2
1
1
2
2
1
1
1
0
2
1
1
0
1
1
2
2
1
2
2
1
1
2
0
0
4
2
0
1
0
0
1
2
1
0
0
3
1
1
2
0
0
1
2
2
2
1
2
2
0
1
0
0
1
2
0
0
0
0
2
0
0
0
0
1
0
2
1
1
0
1
1
1
0
1
1
1
1
2
1
0
2
2
0
2
2
2
2
0
1
0
1
0
2
0
2
1
1
0
2
0
0
1
0
1
1
0
4
1
0
2
0
1
2
1
0
1
1
1
0
2
0
0
1
1
2
0
1
1
0
1
0
0
2
0
0
1
1
0
1
2
0
0
2
1
0
1
0
0
0
2
0
1
1
0
0
0
1
0
1
0
0
0
2
0
0
1
0
1
1
1
2
0
2
0
0
2
3
0
2
0
2
1
0
2
1
1
0
0
2
0
1
1
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
1
1
2
0
2
0
2
1
2
0
0
1
1
0
1
0
2
1
1
2
1
0
0
1
0
1
1
0
0
1
0
2
1
1
0
2
1
2
2
1
1
2
0
2
0
1
1
1
0
1
1
0
0
1
0
0
2
1
1
1
1
0
0
1
1
2
0
0
1
0
2
0
1
1
1
0
0
0
0
2
1
0
0
0
1
0
1
1
2
1
1
2
0
0
1
0
0
1
2
1
0
0
1
0
1
1
0
0
0
2
1
3
2
2
0
1
0
0
1
0
0
2
1
0
0
0
0
2
1
0
1
1
1
0
0
1
3
1
1
0
0
0
0
1
0
0
2
2
1
2
0
2
1
0
0
1
0
0
1
0
0
1
0
2
0
0
1
0
1
2
2
2
0
0
0
1
2
2
2
2
1
1
1
0
0
2
2
0
1
0
0
1
1
0
2
2
1
1
1
1
1
1
1
0
0
0
1
1
0
0
2
2
0
0
2
0
1
2
0
1
3
0
0
0
0
1
2
0
0
1
1
1
1
0
0
0
1
0
0
1
1
0
0
2
1
0
1
0
0
0
2
0
2
0
0
1
1
1
1
0
2
1
1
0
0
1
1
2
1
2
1
0
1
0
1
1
1
2
0
1
1
1
0
0
1
0
1
0
1
0
2
0
1
1
1
0
0
1
2
1
2
1
2
1
1
0
0
0
0
0
1
0
0
0
2
2
1
1
2
0
1
1
0
1
0
0
2
1
2
1
0
0
0
1
0
0
0
2
0
0
0
0
1
1
0
1
2
0
1
1
2
0
1
2
0
0
0
1
0
1
2
1
1
0
3
2
0
0
1
2
2
2
0
1
1
0
0
1
1
1
0
0
1
2
0
0
1
1
0
0
2
0
2
1
0
1
1
1
1
1
2
2
0
0
0
0
0
1
1
1
1
0
1
1
0
0
1
1
2
0
1
3
1
1
2
0
2
0
0
0
0
0
2
1
0
0
1
0
1
2
1
1
0
1
0
2
0
0
1
1
0
0
2
1
2
1
2
1
0
0
2
0
0
1
2
2
2
1
0
1
0
0
0
1
0
1
2
0
2
0
0
1
2
0
2
0
0
2
1
1
1
0
1
2
0
0
0
1
2
2
0
0
0
2
0
0
1
0
0
1
1
2
0
0
0
2
1
2
1
0
0
0
2
0
1
1
2
0
2
1
2
1
1
2
0
0
1
2
1
0
0
0
1
1
2
0
2
0
2
1
0
0
1
0
2
0
1
1
1
1
1
2
0
0
2
0
1
0
1
2
1
3
1
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
1
0
0
0
2
0
1
1
2
1
0
2
1
1
0
0
2
2
1
1
1
2
1
2
0
0
0
0
0
2
1
0
0
1
0
0
1
1
1
0
1
2
0
0
1
0
0
2
0
1
0
0
2
0
0
1
1
2
0
1
0
0
0
1
2
0
0
1
1
1
2
1
6
1
2
2
2
0
2
0
2
1
0
2
1
0
1
2
1
1
2
3
1
0
2
2
0
1
0
1
0
0
0
2
0
1
1
1
0
3
1
0
1
0
2
0
1
2
1
1
1
0
1
2
2
2
0
2
2
1
1
0
1
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
1
0
1
1
0
0
1
0
0
2
1
2
0
0
2
0
1
1
0
0
0
0
0
0
2
0
2
1
2
1
1
0
0
1
1
0
1
0
0
2
0
2
1
2
1
1
1
0
0
0
0
1
2
0
1
1
1
1
2
0
0
2
1
0
1
0
0
1
0
0
2
0
2
2
2
3
0
2
0
1
2
0
0
0
0
1
0
2
2
2
2
1
1
0
0
2
0
0
0
1
1
0
1
2
0
1
2
1
2
1
0
1
1
0
1
0
0
2
1
1
0
0
2
1
0
0
0
1
0
1
0
2
0
2
0
0
2
1
1
2
2
0
0
1
1
0
2
3
1
2
2
2
2
0
1
0
0
1
1
2
2
1
0
1
3
1
1
0
1
0
0
1
2
0
2
1
2
2
0
0
2
0
0
0
0
1
0
2
0
0
0
1
2
0
1
2
2
2
0
1
1
2
0
0
2
0
0
0
1
1
0
1
0
0
0
1
1
1
0
1
0
2
0
0
2
0
0
2
2
0
2
1
2
0
0
1
1
1
0
0
1
0
1
0
1
1
1
2
0
0
1
1
0
0
1
0
1
2
0
2
0
0
1
0
2
1
0
0
2
0
1
0
0
2
2
0
0
0
1
0
1
2
0
2
1
0
3
0
0
1
0
1
0
1
2
0
0
0
1
1
0
1
0
0
2
2
1
1
0
0
2
0
2
2
1
2
2
0
0
1
1
1
2
1
1
1
1
0
0
0
0
0
2
0
0
2
1
0
1
0
1
1
1
1
0
1
0
1
0
0
1
0
0
0
1
0
0
1
1
0
2
1
1
0
1
0
1
2
0
0
1
2
1
1
4
1
0
0
0
0
1
0
1
1
0
2
1
0
0
0
0
0
0
0
1
0
0
1
1
2
2
0
1
1
0
0
3
2
0
0
2
1
2
1
2
0
1
0
1
1
0
0
0
1
1
0
1
1
2
0
0
1
2
0
1
1
1
1
1
1
1
0
1
2
0
0
1
2
0
2
1
0
0
0
2
1
0
0
0
2
0
1
0
2
0
2
0
0
0
2
2
0
0
0
0
0
1
1
1
1
2
1
1
2
0
1
0
0
1
0
0
2
2
0
0
1
1
1
1
1
2
2
1
1
0
0
2
1
0
1
1
1
2
2
0
0
2
1
0
0
0
2
1
2
0
0
0
2
2
1
1
0
0
0
1
1
2
1
1
2
1
3
0
0
0
1
0
1
1
2
2
0
0
2
1
0
0
0
0
1
1
0
0
1
0
1
1
1
0
0
0
0
2
2
0
1
2
1
1
0
1
0
1
1
0
0
1
0
1
1
0
0
1
2
0
2
1
2
2
1
1
0
2
1
0
0
1
1
1
0
2
7
1
0
1
0
1
0
0
0
1
0
0
1
0
0
0
1
0
1
0
2
2
1
1
1
0
1
1
0
0
0
1
1
1
2
0
0
1
1
1
1
3
1
0
0
1
2
2
0
1
1
1
2
1
2
2
0
0
1
1
0
0
0
1
0
0
1
0
1
2
2
1
0
2
2
1
0
0
2
1
1
0
0
2
1
0
0
1
0
0
2
2
0
0
0
2
0
1
0
1
0
3
0
2
1
2
0
0
0
2
1
1
1
0
1
0
0
1
1
0
1
1
2
0
1
2
1
0
0
0
1
1
1
2
0
1
2
2
0
0
0
2
1
3
0
3
1
1
0
1
1
1
2
0
1
0
1
0
1
0
0
2
0
2
0
2
0
0
1
0
1
0
0
0
0
2
1
0
0
1
0
1
1
2
0
0
0
3
2
0
0
1
1
1
0
2
0
0
1
0
0
2
0
0
2
1
1
2
0
3
0
0
0
0
0
0
2
2
0
0
0
1
1
1
1
0
0
2
1
0
1
0
1
0
0
0
1
0
0
2
0
1
1
0
0
0
1
2
1
0
1
2
1
2
1
0
0
1
0
0
1
1
2
0
2
2
0
0
1
2
1
1
0
1
2
0
0
2
1
2
2
1
1
0
1
1
0
0
0
1
1
0
1
1
2
2
1
1
1
1
0
0
0
2
1
0
1
1
1
2
1
0
0
1
0
2
1
0
2
0
2
1
2
2
1
0
1
1
1
1
1
0
2
1
0
1
1
0
1
2
1
0
1
2
3
0
1
2
1
0
1
0
2
1
0
1
1
2
2
0
2
0
0
2
2
0
0
0
1
0
0
1
2
0
2
0
3
2
1
2
0
0
2
0
0
0
1
0
0
0
0
2
2
2
0
0
0
2
1
1
1
0
1
0
2
2
1
1
1
1
2
1
0
1
2
1
0
0
1
0
1
1
2
0
1
1
2
0
0
1
1
0
1
0
1
1
1
1
0
2
4
1
2
1
0
0
1
1
2
1
2
2
0
2
0
0
1
0
2
2
2
1
1
1
0
1
2
1
1
0
1
1
2
1
0
0
0
1
0
0
2
1
0
0
1
0
0
0
2
0
2
1
2
0
2
1
1
0
1
1
0
0
2
1
0
0
0
0
0
1
1
0
0
0
0
2
0
1
0
1
0
2
1
2
1
1
2
2
2
1
0
1
1
0
0
1
2
0
1
1
0
5
1
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
2
0
2
1
0
1
1
0
0
1
2
2
0
0
2
0
0
0
1
1
1
1
1
1
0
0
1
1
0
0
2
0
3
1
2
0
0
0
0
0
0
0
2
2
0
0
1
0
2
1
0
0
0
0
1
0
0
0
0
0
1
1
1
2
2
2
0
2
1
0
2
1
2
0
1
0
1
0
1
0
0
1
0
1
0
1
2
1
0
0
2
0
2
1
1
0
1
0
0
0
1
2
0
1
0
1
0
0
2
1
1
1
1
2
0
0
1
1
0
0
0
0
0
2
0
1
0
1
0
0
2
0
1
0
1
2
1
0
2
0
0
1
0
0
2
2
0
1
1
2
1
0
1
6
1
0
0
0
2
1
0
2
0
0
0
1
2
0
1
1
2
2
0
1
0
0
0
2
1
1
1
1
2
0
1
0
2
0
0
0
0
2
2
2
1
0
0
1
1
0
2
0
2
1
0
2
1
2
1
1
1
0
2
1
1
2
2
1
1
2
0
2
2
2
0
2
1
2
0
1
0
0
1
0
0
2
0
1
0
0
1
2
2
0
0
2
0
0
2
0
1
1
0
2
2
0
1
1
1
0
0
1
1
1
0
1
0
1
1
0
1
0
2
0
2
1
1
2
0
1
0
0
0
0
1
1
0
0
1
0
0
0
1
0
2
2
0
1
1
0
1
1
2
0
0
1
1
2
0
1
2
1
1
1
0
1
1
0
1
2
1
0
1
1
2
1
0
0
2
0
2
2
0
0
1
2
1
1
1
1
2
1
0
2
0
0
1
2
2
0
0
1
1
1
1
2
1
0
1
1
2
0
0
1
1
0
1
0
0
0
0
1
1
2
0
0
0
1
1
0
2
0
0
0
2
0
0
1
1
0
0
1
1
2
1
1
1
0
1
0
0
1
0
5
1
1
1
1
0
1
1
0
1
1
1
1
0
1
0
2
1
0
2
0
1
1
0
0
1
1
3
0
1
2
1
0
0
2
1
0
0
1
2
0
2
1
1
1
0
0
1
1
1
0
0
0
1
2
1
1
2
0
2
0
1
1
1
0
1
1
0
1
1
1
2
1
0
0
0
2
1
0
3
0
1
1
1
0
0
2
2
1
1
0
0
1
0
0
1
0
1
0
1
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
1
0
2
0
0
1
1
3
1
2
0
0
2
0
0
1
0
0
0
2
0
0
0
0
2
2
2
1
0
2
0
2
0
0
2
1
1
2
0
2
2
1
1
3
1
0
0
1
2
1
0
0
1
0
1
1
1
0
1
3
1
1
0
1
1
2
0
2
1
2
2
1
0
1
2
1
2
0
2
0
0
0
0
1
2
1
0
0
0
0
1
1
0
0
0
1
2
2
0
2
0
2
1
1
1
2
2
0
1
1
0
0
1
0
1
2
0
2
0
1
0
1
1
0
1
1
0
1
1
1
1
1
2
1
2
1
1
1
1
1
0
0
2
1
1
2
1
1
0
1
0
1
2
0
1
1
1
2
1
0
1
1
0
2
1
0
1
0
0
1
2
0
0
1
1
1
0
1
1
1
2
2
2
0
1
2
1
0
1
1
1
2
2
1
2
0
0
0
0
2
0
1
1
0
0
2
0
1
1
2
1
0
0
0
0
1
1
0
0
0
0
1
2
1
2
2
0
2
1
1
2
2
1
1
2
0
0
0
2
1
0
1
1
2
0
2
2
0
1
0
0
0
0
0
1
1
0
0
0
2
1
0
0
0
1
2
1
1
1
2
0
0
0
1
0
0
1
1
2
0
2
1
0
0
0
2
2
0
0
2
1
1
0
0
2
0
2
1
0
0
1
1
1
0
0
1
1
0
1
2
0
1
2
1
1
2
0
0
0
0
1
1
1
1
1
1
0
0
0
1
2
1
1
1
0
0
1
0
1
2
0
0
0
0
2
1
1
0
2
2
1
2
0
1
0
1
1
0
1
0
0
1
1
2
0
0
0
1
0
1
0
0
1
0
0
1
0
1
0
1
1
1
1
1
0
1
1
0
1
2
1
1
0
1
0
0
0
0
0
0
0
1
2
1
0
1
2
0
3
1
2
1
0
0
1
0
0
2
0
1
0
1
0
2
2
1
1
1
1
0
3
0
3
0
0
1
0
0
0
0
0
0
2
2
1
2
1
1
3
1
1
2
0
1
1
1
3
1
2
1
1
0
0
0
0
2
1
1
0
1
1
1
1
2
1
2
1
2
0
1
0
0
1
1
1
1
0
2
0
1
1
0
1
2
2
1
0
1
1
1
0
1
0
0
1
1
2
1
1
1
0
0
1
0
2
1
0
0
0
2
0
2
0
1
0
0
1
1
0
1
1
2
1
0
1
2
2
2
0
1
1
0
0
0
2
0
0
0
0
1
1
2
1
1
0
1
0
0
1
1
0
0
1
0
2
0
1
1
2
1
1
1
1
2
0
5
0
0
2
1
2
0
2
1
1
0
1
0
0
0
0
0
1
0
1
0
1
2
1
0
0
0
2
0
2
1
1
1
0
0
0
1
0
0
1
0
0
0
2
1
1
0
0
1
1
0
0
0
0
0
0
0
1
1
0
2
2
1
1
2
0
1
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
2
0
1
1
0
1
0
2
0
2
1
0
1
2
0
0
1
0
1
0
0
0
0
1
2
0
3
1
0
2
1
3
1
1
0
2
1
0
1
0
1
0
0
0
0
1
3
0
0
0
1
1
2
0
0
0
2
2
1
1
1
1
0
0
0
2
2
0
1
1
0
2
1
2
1
0
1
0
0
0
0
1
1
0
0
0
0
1
1
2
0
0
0
1
2
1
1
0
0
0
2
1
2
0
0
1
0
0
0
0
2
1
1
1
0
3
1
2
1
0
1
0
0
0
1
0
2
1
0
1
0
2
0
0
1
0
1
1
0
2
1
0
0
1
0
0
2
0
0
0
1
0
1
2
2
1
0
0
1
2
1
3
2
0
0
0
2
0
0
1
1
2
1
1
0
0
0
2
2
0
1
1
0
0
1
0
1
1
1
0
0
0
2
1
2
0
0
0
2
1
2
1
1
0
1
1
2
1
0
2
1
0
0
0
0
1
2
0
2
2
0
0
0
3
2
2
0
0
1
0
1
0
1
1
1
0
2
2
0
0
2
1
1
1
2
0
0
2
1
1
2
1
1
1
1
2
2
1
2
2
2
1
1
2
2
1
1
3
2
0
2
0
2
0
0
0
2
2
0
0
1
1
0
2
1
1
1
2
0
0
0
0
0
0
0
0
2
0
2
2
1
1
3
2
3
1
0
1
1
0
0
0
0
1
2
1
0
1
0
1
0
0
1
2
1
0
1
1
0
0
0
0
1
1
1
2
2
2
1
1
0
0
2
0
0
1
1
1
0
1
1
2
2
0
2
1
0
1
3
0
1
1
2
1
0
2
2
4
2
1
0
1
1
0
1
2
0
0
2
1
1
2
0
1
1
0
1
0
0
0
2
0
2
2
0
4
1
0
1
0
2
0
0
0
0
2
0
1
1
1
1
0
1
0
1
2
1
2
0
0
1
0
1
0
2
1
1
0
0
0
0
2
0
1
1
1
0
2
1
0
1
2
0
1
2
1
1
0
1
0
3
0
0
1
2
0
1
2
2
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
1
1
1
0
1
1
1
0
0
0
2
1
1
0
1
2
0
1
2
1
0
2
0
1
0
1
2
1
1
1
0
1
0
0
0
0
1
1
1
0
1
2
0
1
1
1
0
1
2
0
0
0
1
0
0
1
0
0
2
0
0
0
1
0
0
0
1
1
0
2
0
0
0
0
0
2
2
1
0
0
1
0
2
2
2
1
1
2
0
0
2
8
2
2
2
1
1
2
1
0
3
0
1
1
2
0
1
0
2
1
0
1
0
2
5
0
1
1
0
0
1
0
2
0
2
2
1
1
2
2
0
1
1
0
1
0
1
0
1
0
1
0
2
1
2
0
4
1
2
1
2
0
1
0
0
2
1
0
2
1
0
0
3
0
2
0
0
1
2
2
0
2
1
1
2
1
0
0
1
0
2
2
2
1
2
0
2
2
2
0
0
2
0
2
2
0
1
2
0
1
1
2
1
0
0
0
2
0
1
0
0
1
2
0
2
2
1
2
0
1
2
0
0
0
1
1
2
2
2
1
0
0
2
1
1
0
0
2
2
0
0
0
2
0
1
0
0
2
1
1
1
1
1
1
0
0
0
1
1
1
1
1
2
0
2
0
2
2
0
2
0
0
3
0
1
0
0
0
2
0
0
1
1
0
1
0
2
0
0
2
1
0
1
2
0
2
2
2
0
0
1
0
2
2
1
2
0
2
2
0
1
0
0
0
0
1
1
0
1
1
0
1
1
0
0
2
1
1
2
1
0
1
1
1
1
1
1
0
1
0
2
2
2
1
0
0
0
0
2
1
1
1
0
0
2
0
0
0
0
0
1
1
2
1
0
0
0
2
0
0
0
0
2
0
1
0
0
1
1
1
0
2
0
1
0
2
0
0
1
2
0
0
1
0
0
0
2
0
0
2
1
0
1
0
1
1
0
2
1
0
2
0
0
1
0
2
0
0
1
1
1
1
1
1
2
0
1
0
1
1
1
0
1
1
1
1
0
1
0
2
0
0
2
1
1
2
2
1
1
2
2
0
0
2
2
0
1
2
0
2
0
2
0
0
0
0
0
1
2
0
0
1
0
0
1
0
1
1
0
0
0
0
1
1
2
1
0
2
0
0
0
1
2
0
2
0
2
0
2
0
0
1
0
2
0
1
0
1
2
1
1
1
0
0
0
1
0
1
1
1
0
1
1
0
1
0
0
1
0
1
1
1
0
2
1
0
0
0
1
1
1
0
1
0
0
1
0
1
0
1
1
0
1
2
0
2
0
0
0
0
1
0
0
0
0
1
0
1
1
2
1
2
1
0
1
2
1
0
2
1
1
2
0
1
0
1
1
0
0
0
1
1
0
1
2
2
0
0
1
0
2
0
1
0
1
0
0
1
0
1
1
0
0
1
0
1
0
2
1
2
0
0
0
0
0
0
1
0
0
2
0
1
0
1
0
0
2
1
2
2
1
1
0
0
0
0
0
1
0
1
0
0
2
0
1
1
0
0
0
0
1
0
1
1
0
2
1
1
0
0
1
1
1
0
2
1
0
1
2
1
0
0
1
0
0
1
2
0
0
0
0
1
1
0
1
1
2
2
2
0
1
1
0
1
0
2
2
0
2
0
0
1
1
2
1
2
2
0
1
0
2
2
0
0
1
2
1
2
1
1
1
0
1
3
0
1
1
0
2
1
0
0
0
2
1
1
0
0
2
0
1
2
0
2
0
0
0
0
0
1
1
0
0
2
0
2
1
1
1
0
1
2
1
2
3
0
5
0
1
1
1
1
0
2
2
0
1
1
0
2
0
1
2
2
1
1
2
0
1
0
0
2
0
1
0
0
0
0
1
0
0
1
2
0
2
0
1
1
1
2
0
1
1
0
1
1
1
0
1
1
1
0
2
1
1
1
0
1
0
0
0
2
0
0
0
1
0
2
0
1
0
0
2
1
1
0
1
0
1
0
1
0
1
2
4
1
0
0
2
0
0
1
1
2
1
1
1
1
0
0
1
0
1
0
0
2
2
2
0
0
0
1
0
1
2
1
0
1
2
0
1
1
2
0
0
1
0
1
1
2
2
1
0
0
1
1
2
0
0
1
1
2
0
0
2
1
1
0
0
0
0
0
0
1
2
1
1
2
1
1
0
2
0
2
2
0
0
0
2
0
0
0
1
2
1
1
0
1
1
1
1
0
0
1
1
1
0
0
0
1
1
0
0
1
2
2
1
1
0
0
1
1
0
0
0
1
2
2
0
2
0
1
1
0
1
0
1
1
1
1
2
0
1
2
1
0
1
0
1
1
0
1
0
0
0
0
1
1
2
0
0
0
2
1
1
2
1
1
1
0
1
0
1
0
2
1
0
2
1
1
1
1
0
1
0
1
1
0
2
2
0
0
1
0
2
0
0
0
0
1
0
3
1
2
0
2
0
2
0
2
0
0
1
0
2
1
0
0
1
1
0
0
2
1
1
0
1
1
1
0
0
1
0
0
0
1
2
1
2
1
1
1
2
0
1
1
2
0
0
1
1
0
1
0
2
1
0
0
0
0
0
2
1
0
1
0
0
2
0
0
0
2
2
0
0
0
1
1
0
2
1
1
0
0
0
0
0
1
0
0
0
0
1
1
1
1
2
1
1
2
0
0
1
2
2
0
0
1
1
1
0
2
1
1
1
0
1
0
1
0
1
0
2
0
1
0
0
1
0
2
0
0
1
0
0
1
2
1
2
0
2
1
3
1
1
0
2
0
1
1
3
0
1
0
1
1
0
1
0
1
1
0
2
0
2
0
2
2
1
1
0
0
0
0
0
0
2
1
1
1
3
0
0
2
1
0
2
1
1
0
2
2
1
2
0
0
0
1
1
0
0
1
1
1
1
1
0
1
0
0
1
2
1
2
1
2
1
1
0
0
2
0
1
1
2
1
0
1
1
3
1
0
0
0
2
0
0
2
1
0
1
0
0
0
0
0
1
1
1
0
0
0
2
2
7
0
1
1
1
0
1
2
0
1
2
0
1
2
1
1
0
0
2
0
1
1
1
1
1
0
0
0
2
1
1
0
2
0
1
0
0
0
1
0
2
0
0
0
1
2
3
1
0
2
1
0
1
0
1
1
1
0
1
1
1
0
1
0
0
0
0
2
1
0
2
1
1
0
2
2
1
0
0
2
1
0
0
1
1
0
0
1
0
0
1
1
1
2
1
0
1
1
1
1
0
1
1
0
1
0
2
1
0
1
0
2
1
1
1
1
0
1
2
0
1
0
0
0
1
0
0
2
3
1
1
2
1
0
0
2
1
2
1
0
1
1
0
1
1
0
0
0
1
2
1
1
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
2
2
3
2
1
2
1
2
2
0
1
1
0
0
0
1
0
0
1
1
0
2
1
1
0
2
0
1
1
1
0
1
1
0
0
0
1
0
0
0
2
0
1
2
1
1
0
0
0
1
0
2
0
2
2
0
0
2
0
1
2
0
0
1
2
0
1
0
0
2
0
2
0
2
2
1
0
0
0
2
0
1
1
0
2
1
1
2
2
1
2
0
0
0
2
0
2
1
2
0
0
1
1
2
0
1
0
1
0
2
2
1
1
1
1
0
2
0
0
2
0
1
1
1
1
0
0
2
1
1
1
0
0
0
1
0
0
2
0
1
1
0
0
2
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
9
0
1
0
1
0
2
2
1
0
3
2
0
0
1
2
0
0
2
0
2
0
1
2
2
0
1
1
1
0
1
0
1
0
0
1
0
2
2
1
1
0
0
0
0
1
2
0
1
1
0
0
2
2
1
2
0
1
2
2
1
0
1
2
1
1
2
1
1
2
0
2
1
1
2
0
0
1
1
1
1
0
1
0
0
1
1
1
0
1
2
2
2
0
2
2
1
1
0
0
2
1
1
2
0
0
1
0
3
2
2
0
1
0
1
2
2
0
1
1
2
1
4
0
1
1
0
1
0
1
0
0
1
0
2
1
1
1
0
0
0
1
2
0
2
1
2
1
1
1
0
2
1
1
0
2
1
1
1
1
1
0
1
0
2
2
2
0
1
2
0
2
0
1
3
2
2
1
0
1
0
0
1
0
1
0
0
1
0
1
0
1
1
1
0
2
3
1
0
0
1
1
1
2
0
1
0
1
0
2
1
1
0
1
1
2
1
0
0
0
1
2
2
1
1
2
1
0
1
1
1
0
0
1
2
1
0
1
0
0
1
2
0
2
0
1
2
1
0
0
4
0
1
0
2
2
0
2
0
1
2
0
0
2
1
1
1
2
2
1
0
0
2
1
0
2
2
1
2
2
2
1
0
1
1
0
3
1
2
1
1
0
2
2
1
0
0
0
2
3
1
2
1
2
2
2
0
0
0
0
2
1
1
2
1
0
2
4
0
2
0
1
0
1
1
1
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
2
1
1
2
1
2
0
1
0
0
0
2
0
1
2
0
0
1
1
0
2
0
0
0
2
2
2
2
0
0
0
1
1
0
0
1
0
2
0
1
0
0
1
1
2
1
1
2
1
0
2
2
1
0
2
1
0
0
0
1
2
1
1
0
0
1
2
0
2
1
1
1
1
0
0
2
1
1
0
1
2
1
1
1
1
1
3
0
1
1
1
0
1
0
1
0
2
0
0
1
1
1
0
0
2
2
1
0
0
1
2
0
0
0
1
2
1
1
0
1
2
1
0
0
0
0
2
0
0
0
2
2
2
0
1
1
2
0
2
0
0
1
2
2
2
2
1
2
0
1
2
0
2
2
2
2
1
4
0
1
1
0
0
0
1
1
2
0
0
0
2
2
2
0
1
0
2
1
2
0
1
1
0
0
3
0
1
0
1
1
1
2
2
2
1
0
1
0
2
0
2
2
0
0
1
1
0
0
2
0
1
2
1
1
0
0
1
1
1
1
1
0
0
1
0
1
1
0
1
2
0
0
0
0
0
0
0
2
1
3
2
1
1
0
1
0
2
0
0
0
0
1
1
0
1
0
2
1
0
2
0
1
0
2
2
0
0
2
0
1
0
0
1
2
1
1
1
1
2
1
2
1
2
2
2
0
1
2
1
1
0
1
0
2
1
4
0
1
1
0
1
0
1
0
2
2
1
0
2
0
1
2
2
0
2
1
2
0
2
0
2
0
1
3
2
0
2
0
0
1
0
2
1
1
0
2
2
0
1
1
1
1
1
0
0
1
1
0
0
0
0
1
1
0
0
1
1
0
0
0
0
1
1
1
0
1
2
1
1
2
1
1
0
0
1
0
2
0
1
1
1
0
0
1
0
1
0
1
1
0
0
2
1
1
0
7
2
0
0
4
0
1
3
1
0
2
1
1
0
1
1
0
1
1
0
1
1
0
1
1
2
1
0
0
0
1
0
1
1
0
0
1
1
0
1
1
1
1
0
0
1
1
2
1
1
2
0
1
1
0
2
2
1
2
1
0
0
1
3
1
1
1
2
0
2
1
0
1
1
0
2
0
1
0
1
1
0
2
0
1
1
0
1
0
2
0
0
0
1
0
1
0
0
1
0
0
2
2
0
1
1
2
1
0
1
0
0
1
1
1
4
0
1
0
0
0
0
0
0
1
2
1
2
1
0
1
0
1
0
0
1
0
0
2
0
0
2
0
1
1
0
2
0
0
2
0
1
2
0
1
0
0
1
0
2
1
2
0
1
2
2
0
0
1
0
1
0
1
2
1
0
1
2
0
1
0
2
1
2
1
0
1
2
0
1
1
2
1
2
1
2
1
1
0
2
2
0
1
1
0
1
0
1
0
1
0
0
2
1
0
1
2
0
0
2
2
1
2
0
2
0
2
1
2
1
0
1
2
2
0
0
1
1
0
0
0
1
2
2
0
0
0
2
1
0
0
2
2
1
1
2
0
1
0
0
1
1
0
1
2
0
0
0
2
2
1
1
0
0
0
1
2
2
1
2
2
1
1
2
0
2
2
2
2
0
1
1
0
1
1
4
0
2
0
0
0
2
2
2
1
0
0
0
2
1
0
0
2
2
0
1
2
0
1
0
1
0
0
0
0
1
0
1
0
0
1
1
1
2
1
1
1
0
0
2
0
1
2
0
2
0
1
0
1
0
1
0
0
2
0
1
3
2
0
0
1
1
1
0
1
1
0
2
2
0
2
0
0
0
1
0
1
2
0
1
1
0
2
0
1
1
2
2
0
1
1
1
1
2
0
0
1
1
2
0
1
2
0
0
0
1
1
0
0
2
0
0
0
0
0
2
0
1
2
1
1
1
1
1
0
0
0
0
1
2
1
1
2
0
1
0
1
0
0
1
1
1
0
2
0
0
0
2
1
2
2
3
0
2
1
1
0
0
1
0
1
0
2
3
1
0
0
0
0
0
0
0
1
2
0
1
1
0
1
0
2
2
1
1
5
1
2
1
0
2
0
2
0
1
1
2
0
1
0
2
2
0
1
1
1
2
3
1
0
1
0
0
1
1
1
1
1
0
1
0
0
1
0
1
1
0
0
1
0
2
2
0
1
0
0
0
0
0
0
1
3
0
0
0
0
1
2
0
3
0
2
0
0
2
1
2
0
1
2
1
2
2
1
1
1
0
0
1
1
2
1
0
0
2
2
0
0
2
0
0
0
1
0
1
1
1
0
1
0
0
1
1
0
0
1
0
1
0
1
0
2
1
1
1
1
1
1
1
1
1
2
1
0
2
0
1
0
1
2
0
3
2
0
2
1
2
1
0
0
0
1
0
1
2
0
2
2
0
2
0
0
1
0
1
2
1
0
0
0
1
1
0
2
1
1
0
2
1
0
2
0
2
2
0
0
1
1
0
1
2
1
0
1
0
2
0
1
0
1
2
0
2
2
0
2
0
0
1
1
2
0
1
1
1
0
2
1
1
1
0
2
2
2
1
1
0
1
1
1
2
1
0
1
2
0
0
1
2
0
1
1
2
1
0
0
1
0
1
0
0
1
0
1
1
1
1
1
0
0
2
1
0
0
2
1
1
2
1
1
1
1
1
2
0
2
1
1
0
2
0
0
0
0
0
0
1
2
2
1
0
1
0
2
2
1
2
0
2
2
1
2
1
1
1
0
0
2
2
1
0
2
1
1
1
2
0
0
1
2
1
1
1
1
0
0
0
2
0
2
1
1
0
0
0
0
0
1
0
1
0
2
0
1
0
0
1
1
1
0
1
0
0
2
3
2
1
0
2
1
2
0
1
0
1
0
0
0
1
0
2
1
2
0
0
0
1
2
0
0
1
2
0
2
2
0
1
0
0
2
1
2
1
1
0
1
1
2
2
1
0
0
1
0
0
1
0
0
2
0
2
1
1
0
1
2
2
1
1
1
2
2
1
3
2
1
0
1
0
0
2
0
1
1
2
2
1
0
2
1
1
1
1
2
1
1
2
1
0
0
0
2
0
1
1
1
1
1
1
0
0
0
0
1
1
0
0
1
2
2
2
1
0
0
1
0
2
1
0
1
0
0
0
3
0
0
2
1
1
0
0
0
1
0
1
2
2
1
0
1
1
0
2
0
2
0
1
0
0
2
1
1
1
0
1
1
0
1
0
0
0
2
0
0
1
0
2
0
0
1
2
1
1
2
0
1
0
0
1
0
2
0
0
1
0
1
0
0
1
0
2
4
2
0
2
0
1
0
1
1
1
0
1
1
0
0
1
0
0
0
0
0
1
0
2
0
3
1
1
0
1
0
5
0
1
1
0
0
2
0
2
2
2
0
1
0
1
1
0
0
0
3
0
1
1
2
2
0
0
0
0
1
1
1
0
0
1
3
1
0
1
1
1
1
0
0
1
0
2
1
1
0
0
2
1
1
0
0
0
1
1
1
0
1
3
1
2
1
3
2
0
0
0
0
1
0
2
0
1
2
0
1
0
1
1
1
1
2
1
0
1
0
2
0
2
0
2
1
0
1
0
0
1
2
1
1
0
0
1
0
1
0
0
2
0
1
0
1
0
0
0
1
0
0
1
2
1
1
1
1
2
0
0
0
0
1
0
1
0
0
0
2
0
1
0
1
0
0
1
0
1
0
0
3
0
1
1
1
0
2
1
1
1
1
1
1
2
0
1
2
0
1
1
0
0
1
1
1
0
0
1
0
1
0
1
0
1
2
2
0
2
1
2
2
2
0
0
2
1
1
1
0
1
1
1
1
2
0
1
1
1
1
1
0
0
4
0
1
0
2
1
2
0
1
1
0
0
3
2
0
2
1
1
0
2
0
0
1
0
2
1
0
3
2
0
0
0
0
0
0
0
2
2
2
2
1
2
2
0
0
2
1
1
1
2
1
2
0
1
0
0
0
0
0
0
2
1
1
0
1
3
1
1
0
0
0
0
1
0
1
1
1
0
1
0
2
0
2
2
2
1
0
1
1
0
1
1
0
0
2
2
2
2
1
1
1
2
2
2
0
1
4
2
0
2
2
0
2
0
1
1
2
1
1
2
1
1
2
0
0
1
1
1
1
1
1
1
0
0
2
1
0
0
0
2
1
0
0
1
0
1
0
2
0
0
0
1
0
1
0
1
1
0
0
1
1
0
0
0
0
0
1
0
0
0
2
0
0
1
1
0
1
0
2
1
0
1
0
1
0
1
3
2
0
1
1
1
2
1
0
2
0
0
2
0
2
0
1
0
1
0
0
1
3
0
0
1
1
0
2
4
0
2
0
1
2
1
1
0
1
2
0
1
2
2
2
1
1
2
1
0
0
1
2
0
2
1
1
1
1
2
1
2
0
2
1
1
0
2
1
0
2
1
0
0
1
1
1
0
1
4
2
1
0
4
0
1
0
1
1
2
1
1
0
2
2
2
0
1
1
0
1
1
1
2
1
2
2
1
0
1
1
1
1
1
0
1
2
2
2
2
1
1
0
1
2
1
2
2
2
0
1
0
1
0
3
1
1
0
1
1
0
2
3
1
2
1
0
1
0
1
2
1
2
0
0
1
0
1
0
1
1
1
0
0
0
0
0
1
1
0
1
1
2
1
1
2
0
2
2
2
0
2
1
1
0
1
0
1
1
0
1
2
0
0
2
0
0
0
2
2
3
1
1
0
1
0
2
0
0
2
0
1
1
2
3
2
2
0
1
0
1
1
0
3
1
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
1
0
2
0
1
2
1
0
0
1
0
0
0
0
1
2
1
2
0
2
0
1
0
2
0
2
1
0
0
1
0
2
1
2
0
1
0
0
1
1
0
1
1
1
0
2
0
2
2
3
1
1
2
0
0
2
1
1
0
2
0
0
1
2
1
2
1
0
0
1
2
2
0
0
2
0
0
1
0
2
1
0
0
1
2
0
0
0
1
1
1
2
0
1
0
0
2
0
0
2
1
1
1
0
0
0
2
2
0
1
2
0
1
0
0
1
0
1
2
2
1
0
0
0
1
0
0
0
0
1
2
0
1
0
0
1
0
2
2
1
1
1
0
1
0
2
1
2
1
2
1
1
0
0
0
0
2
2
2
0
1
2
2
0
0
1
0
1
1
0
1
2
0
2
0
2
1
0
1
2
0
0
2
0
1
0
0
0
0
1
1
0
0
3
3
2
1
1
2
0
1
0
0
1
1
1
1
0
1
2
0
2
0
0
2
0
1
0
0
1
1
1
0
0
0
1
1
1
0
0
1
0
0
0
1
2
0
1
0
1
0
1
2
0
1
2
0
0
2
1
1
0
1
3
1
1
0
1
1
1
0
0
0
1
2
0
1
2
2
0
1
1
0
1
1
0
1
1
1
2
1
1
0
0
0
1
2
1
2
0
0
2
1
0
1
2
0
0
0
2
0
0
1
0
0
1
1
2
1
0
0
0
0
1
1
0
1
1
1
1
0
2
2
0
0
0
0
2
0
0
0
1
0
2
2
0
0
2
0
0
1
3
1
2
2
0
0
0
0
1
1
2
2
0
0
0
0
1
2
0
1
1
1
2
1
3
0
0
1
1
1
1
2
0
0
1
1
1
1
2
1
0
1
0
1
0
2
2
1
1
1
0
0
0
2
0
0
0
0
2
1
1
0
1
2
2
3
2
3
0
1
1
0
1
1
1
1
1
2
2
0
0
0
0
1
2
0
1
1
0
0
1
0
1
0
1
0
1
0
1
0
1
0
0
1
1
1
1
0
0
3
0
0
0
0
2
2
1
3
2
1
1
1
0
0
1
2
0
0
0
0
0
1
0
0
2
0
2
0
1
0
2
0
2
2
0
1
2
0
1
1
2
0
1
2
1
0
2
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
1
1
1
1
0
3
1
2
1
1
1
1
2
0
0
1
0
1
2
1
1
0
2
0
1
1
0
2
2
1
0
0
0
1
1
0
1
0
1
1
2
2
2
1
1
2
0
0
1
2
0
0
0
1
0
0
0
0
0
0
1
0
2
1
0
1
1
1
0
0
0
1
0
1
1
0
0
0
0
0
1
1
0
1
1
0
0
0
0
1
0
0
2
2
2
3
2
1
0
1
0
1
1
1
0
0
0
0
0
1
2
0
1
0
2
0
2
1
1
2
1
1
1
2
1
4
2
0
0
1
2
1
1
2
0
0
0
2
0
1
2
0
0
1
0
1
1
1
0
2
1
0
1
1
1
0
0
0
0
1
1
2
2
0
1
1
0
1
1
0
1
0
0
1
1
4
0
0
0
0
0
2
0
1
0
3
0
0
1
1
1
0
0
2
2
3
0
0
0
2
0
0
3
2
0
1
1
0
0
2
2
1
0
1
1
1
2
0
0
0
0
2
0
1
1
2
0
0
0
1
3
2
1
1
1
2
0
0
1
0
1
2
1
5
2
0
1
0
2
1
1
0
1
2
2
1
0
0
0
2
1
1
1
0
0
2
2
2
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
2
0
0
0
0
1
1
0
2
0
0
2
0
0
2
0
2
0
0
1
2
0
2
2
0
0
1
0
2
0
1
1
1
1
0
0
1
0
0
1
0
1
2
1
0
0
2
1
2
1
2
2
1
1
2
1
0
0
0
4
5
0
1
0
1
1
0
0
2
1
0
1
0
1
0
0
1
0
0
1
1
0
0
2
1
0
0
0
2
2
0
2
1
1
1
2
1
0
2
1
3
0
2
0
2
0
2
0
0
1
1
2
1
2
1
1
1
2
1
2
0
1
0
2
1
1
3
0
0
1
0
0
1
2
1
2
1
2
0
1
0
1
1
1
0
0
1
1
1
1
1
0
1
1
0
1
1
0
2
0
1
0
0
1
1
1
1
2
0
2
1
1
0
0
1
2
1
0
0
0
0
0
0
0
1
1
2
0
0
1
0
1
0
2
1
1
1
0
2
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
2
0
2
1
1
1
1
1
0
0
0
0
1
0
2
2
1
0
1
0
1
1
1
1
2
0
1
1
1
1
0
0
2
0
1
0
2
0
1
0
1
0
1
1
0
0
0
0
0
0
2
2
1
0
1
0
2
0
0
0
0
2
2
1
2
1
2
0
1
0
1
2
0
2
0
0
0
0
0
0
1
1
1
0
0
1
1
1
0
2
0
1
1
0
0
1
1
0
1
2
2
0
1
2
0
0
1
1
1
1
2
1
1
0
0
2
0
0
2
2
1
0
1
2
1
1
1
0
0
0
0
0
0
0
2
0
3
0
0
0
0
1
0
2
1
1
2
1
2
2
0
1
0
0
1
2
0
1
0
1
0
5
0
2
0
2
2
2
0
2
1
1
2
0
0
1
2
0
2
1
1
0
0
1
0
2
1
0
0
2
1
1
1
1
1
0
0
0
0
4
1
1
2
2
0
1
2
0
0
1
0
0
0
2
1
0
0
0
0
2
0
0
2
2
0
0
0
0
1
1
1
1
0
1
0
0
2
0
0
1
2
2
1
1
0
0
3
1
0
1
0
1
1
1
0
1
1
2
2
2
0
1
0
1
0
1
1
3
1
1
0
1
3
2
2
1
1
2
1
2
2
0
0
0
0
0
0
2
2
2
0
1
1
0
2
1
2
0
1
1
2
0
3
0
0
0
0
2
0
0
0
2
1
1
0
0
1
1
0
2
0
1
0
2
1
2
0
2
0
3
0
0
0
1
0
1
2
1
2
2
1
0
2
3
0
3
0
0
0
0
1
0
1
2
0
1
2
0
0
2
0
2
0
1
2
0
2
0
0
0
1
1
0
3
2
0
2
1
0
0
1
0
0
2
0
2
1
1
2
0
0
2
1
2
1
1
1
2
0
0
0
1
1
0
0
0
0
1
2
2
0
0
1
1
2
0
1
0
1
1
2
1
0
2
0
0
0
0
0
0
2
0
0
1
1
1
1
2
1
0
0
1
0
0
0
0
2
2
1
2
2
1
1
1
2
1
1
2
0
0
1
0
1
0
2
0
2
0
0
0
2
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
1
2
0
2
0
1
2
0
0
1
0
1
1
1
0
0
2
1
0
0
1
0
0
1
0
1
0
1
0
0
0
0
1
2
1
0
2
0
1
0
0
0
0
0
0
1
2
0
1
0
0
1
1
0
2
0
0
0
0
2
0
2
0
1
1
0
2
0
0
1
0
2
3
0
0
1
2
0
1
7
1
1
1
2
1
1
0
0
1
1
0
0
1
2
1
0
1
1
2
1
0
0
0
2
0
0
3
2
2
1
1
0
0
1
2
0
0
2
1
1
2
0
0
1
1
1
2
1
0
0
0
1
2
1
4
1
0
0
0
1
0
0
1
1
0
0
0
0
0
2
2
1
1
1
0
0
1
2
0
2
1
0
2
2
1
0
0
2
2
1
2
1
1
2
1
1
1
1
0
1
1
1
0
1
0
0
1
0
0
0
1
1
1
2
0
0
1
2
1
0
1
2
2
0
0
1
1
3
1
0
1
2
0
1
0
1
3
1
0
2
0
1
2
0
2
0
0
2
1
0
1
0
0
2
2
1
0
1
1
1
0
1
0
2
0
0
0
0
0
2
1
1
0
2
0
0
0
0
0
1
1
1
0
0
1
1
1
2
0
2
2
0
2
1
0
1
1
0
0
1
2
0
2
0
0
1
0
1
0
0
0
2
2
1
0
2
1
1
0
0
1
0
0
0
1
2
1
0
1
0
1
1
1
2
1
2
2
0
0
0
0
2
0
2
0
0
1
1
2
1
0
1
1
0
1
1
0
2
1
1
1
2
1
0
2
1
1
0
0
0
0
0
1
2
0
0
2
0
1
1
0
1
1
0
1
0
0
0
0
1
0
0
1
0
1
1
0
0
2
1
0
0
2
1
1
2
0
2
2
0
0
1
1
1
0
1
0
2
0
0
1
0
0
2
2
0
1
2
1
2
0
1
1
0
0
0
0
0
2
1
2
1
1
1
1
1
1
2
2
1
0
1
1
1
2
0
2
0
2
0
1
0
0
4
2
0
1
1
1
0
3
0
0
1
0
1
1
1
2
1
1
2
1
0
0
2
0
0
0
2
1
0
2
1
0
1
1
0
2
0
1
2
0
1
0
1
2
1
2
1
0
1
2
1
1
1
2
2
0
2
3
0
1
1
0
2
2
0
1
1
0
1
1
1
2
0
1
0
0
2
1
1
0
0
1
0
0
0
1
2
0
1
1
2
0
1
1
1
0
2
1
0
1
1
0
1
0
2
2
2
1
1
0
1
2
1
0
1
1
0
2
0
2
0
1
1
0
2
0
2
2
0
2
0
1
1
0
1
1
1
1
1
0
2
0
1
0
1
1
0
1
1
1
1
0
2
0
0
2
2
0
1
1
1
0
2
1
0
1
2
1
0
1
2
1
2
2
0
0
2
2
1
1
1
0
0
0
2
0
0
0
1
2
0
1
3
2
0
2
0
1
1
2
0
0
1
0
2
1
1
2
2
0
1
2
1
0
1
1
0
2
2
0
0
1
0
2
2
1
3
2
2
0
0
1
1
0
1
0
2
2
1
1
3
0
0
2
0
1
0
1
0
0
4
5
1
1
0
0
1
1
0
0
1
1
0
0
1
1
1
0
0
0
2
1
1
1
0
1
2
1
2
2
1
1
2
0
2
1
2
0
2
1
1
2
1
2
2
0
1
1
2
0
0
0
0
0
2
1
1
1
1
0
2
1
1
0
2
1
1
1
1
0
0
0
1
0
0
0
0
0
1
2
0
0
2
1
2
2
2
0
0
2
1
1
1
0
1
2
0
0
1
1
1
1
0
1
2
1
1
0
2
1
2
1
2
0
2
0
1
0
0
1
1
2
3
1
0
2
0
0
0
0
0
0
1
1
2
1
1
0
1
1
0
1
0
0
0
0
0
0
2
0
1
0
1
0
0
2
2
1
1
0
1
1
1
1
2
0
2
0
1
2
2
2
2
1
1
2
0
0
1
2
1
2
0
0
0
2
0
0
2
0
0
1
2
1
1
1
1
3
0
1
0
1
0
0
0
1
0
2
0
1
2
0
1
2
2
1
0
0
2
1
2
0
1
0
1
1
0
1
1
1
2
0
1
2
2
0
1
1
1
1
2
2
2
0
2
3
0
0
0
1
0
0
2
0
0
1
1
1
0
1
0
0
1
2
1
2
1
2
2
0
1
0
0
1
0
1
1
0
2
0
0
0
2
2
0
0
0
1
0
0
2
0
0
1
2
3
1
0
1
1
0
0
1
0
0
1
0
4
1
3
1
0
0
0
2
0
0
1
0
2
0
0
1
0
2
1
1
0
1
0
0
0
0
2
1
2
0
2
2
1
0
2
0
0
1
1
2
1
1
0
0
1
0
0
0
2
1
1
1
0
0
0
1
1
0
2
0
2
1
0
1
0
0
0
1
2
1
0
2
0
1
1
1
1
0
2
0
1
1
0
0
1
0
0
1
3
1
3
0
1
2
2
0
1
0
0
1
1
0
0
0
1
0
2
0
0
0
2
1
2
0
0
0
1
1
1
2
0
1
0
2
1
1
0
1
0
0
0
1
0
0
1
1
0
2
1
1
1
0
0
0
1
2
2
0
0
2
2
1
2
0
0
1
1
2
0
2
4
2
0
0
2
0
0
2
0
0
0
1
2
1
2
2
2
1
2
0
1
1
0
2
1
1
1
0
2
0
1
1
0
0
0
0
1
0
1
0
1
1
0
1
0
2
1
2
2
1
0
1
0
2
1
2
0
0
0
1
1
1
1
0
0
2
1
1
0
1
1
0
1
2
1
2
0
0
1
0
3
1
2
0
0
0
1
2
1
0
0
1
2
0
0
0
1
2
1
3
0
0
0
2
2
0
4
0
1
1
0
0
1
0
0
1
1
1
1
0
1
3
0
0
1
1
2
0
2
2
1
2
2
1
0
1
1
0
0
0
1
0
0
0
0
2
2
1
0
0
0
0
0
1
1
1
0
1
1
1
0
2
2
1
2
1
0
2
0
2
2
1
2
1
0
0
0
0
1
1
0
2
1
2
1
2
1
0
1
0
0
1
1
2
0
1
2
1
2
0
1
0
1
2
0
2
2
0
2
1
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
1
2
0
0
2
1
1
0
1
1
2
0
2
0
1
1
0
1
1
2
0
1
0
1
1
1
2
1
1
1
1
1
1
0
0
0
1
1
1
2
2
0
1
0
2
1
1
1
2
0
3
1
0
0
2
0
0
1
0
2
0
1
0
1
0
0
2
1
3
3
0
0
0
0
0
3
2
1
1
0
0
2
1
1
0
0
2
0
1
2
1
1
0
0
2
0
0
3
1
1
2
0
1
0
2
2
0
1
1
2
1
0
2
2
1
1
0
0
0
0
1
0
1
1
0
2
0
1
1
0
0
1
2
0
1
2
2
1
0
1
0
1
2
1
0
0
1
1
0
0
0
0
0
2
2
1
0
2
2
1
2
0
3
1
1
2
2
1
1
2
0
2
0
0
1
0
1
1
1
0
2
2
1
1
1
2
1
0
2
2
0
1
2
0
1
1
0
2
1
1
0
0
0
0
0
0
1
1
1
0
0
1
0
1
1
1
0
0
1
2
0
1
0
2
0
0
0
2
2
0
0
2
1
1
0
0
0
0
1
0
1
1
0
0
1
0
1
1
0
2
1
1
0
2
2
0
2
0
2
1
2
0
1
1
0
1
1
2
2
0
1
0
1
0
0
1
1
0
0
1
0
1
0
2
0
1
0
1
1
0
1
0
1
1
1
2
0
0
2
0
2
2
1
0
3
1
1
2
0
1
0
2
1
3
0
2
1
1
0
1
2
0
0
1
1
2
0
0
0
0
0
2
2
0
0
1
0
2
0
2
0
0
0
1
2
2
1
0
1
1
1
0
1
2
1
0
0
1
0
2
1
0
2
2
3
0
1
1
1
0
0
1
1
2
1
2
0
2
0
0
1
1
0
0
2
1
1
0
0
2
1
2
2
1
2
1
0
0
0
1
1
1
1
2
1
2
0
3
2
2
3
1
3
0
1
0
1
1
0
0
0
2
1
1
1
0
0
1
0
0
0
0
0
2
0
1
1
0
1
2
0
2
1
2
0
0
1
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
1
1
0
1
1
1
0
1
2
0
2
0
2
0
0
0
1
0
0
0
1
2
0
1
0
2
1
1
1
1
0
0
0
0
2
0
0
0
1
0
0
1
0
2
1
1
1
0
0
1
0
1
0
1
0
3
1
0
0
0
0
2
0
2
0
1
1
2
2
1
1
2
0
0
1
1
0
0
2
1
0
1
0
2
1
2
1
2
3
0
0
0
0
0
0
2
0
0
1
1
0
2
0
1
1
0
0
2
0
2
2
0
2
0
0
0
1
0
0
1
1
0
0
2
3
0
1
1
1
0
1
0
1
2
2
1
1
0
1
0
2
1
4
1
2
0
1
0
1
0
1
1
4
0
0
1
1
0
1
0
1
1
2
1
0
0
2
2
1
0
0
1
1
2
2
1
1
0
2
0
1
2
1
2
0
0
1
0
0
2
0
0
0
2
3
2
1
0
2
2
0
1
0
1
2
2
0
1
1
0
0
1
1
0
2
1
0
4
0
2
1
0
0
1
0
2
0
1
0
2
1
1
1
0
3
0
1
2
1
0
0
1
1
0
2
1
0
0
2
0
0
0
0
1
0
1
0
0
0
1
2
2
0
2
1
0
2
1
1
0
1
2
2
1
2
0
2
0
1
1
0
1
1
1
2
1
0
0
1
0
0
2
1
2
2
1
0
1
2
2
2
0
0
0
1
2
0
0
1
1
0
1
2
1
0
0
1
2
1
0
0
0
1
1
2
0
1
2
0
1
1
2
2
0
2
0
0
1
1
2
2
1
0
0
1
0
1
0
0
0
0
2
0
1
1
1
0
2
1
1
0
2
0
0
0
2
0
0
0
2
1
1
1
0
0
1
1
0
0
1
1
0
2
2
1
0
0
1
0
1
0
1
1
1
1
4
0
1
0
1
0
2
0
0
0
2
1
1
0
2
1
1
0
0
0
0
0
2
0
1
0
0
1
1
2
1
1
2
1
2
1
2
2
2
0
0
2
1
0
2
1
2
2
0
2
1
1
1
2
2
0
1
2
0
0
2
2
0
1
1
1
1
2
2
1
1
2
1
2
0
1
1
0
0
2
0
0
2
0
0
2
0
1
1
1
0
1
1
0
0
1
1
2
2
2
2
3
1
2
2
1
1
0
0
2
0
0
2
1
0
0
1
1
1
3
0
1
0
1
1
0
2
2
0
1
1
1
1
1
2
0
0
1
0
0
1
1
2
0
1
0
0
1
0
0
2
2
0
0
1
2
0
1
0
0
2
1
0
1
1
0
1
0
1
0
1
1
1
1
1
1
0
1
2
0
1
0
0
2
0
0
1
0
1
1
1
3
3
0
0
0
0
2
0
0
0
1
0
1
1
1
1
1
2
2
1
0
0
1
0
1
0
2
0
0
1
0
1
0
2
1
2
0
1
0
2
1
1
1
5
1
1
0
1
0
1
0
0
1
1
1
0
0
0
2
0
2
0
1
0
2
0
1
0
1
0
2
1
1
0
0
0
0
1
1
1
3
2
0
1
0
1
3
0
0
0
1
0
0
2
2
0
1
2
1
0
1
2
1
0
2
1
0
0
2
2
0
4
0
0
0
0
1
2
0
0
1
0
1
1
2
1
1
0
1
1
0
0
0
2
2
1
0
0
0
1
2
2
1
1
1
0
0
0
0
1
1
0
1
1
0
1
0
0
0
1
1
1
0
0
1
1
0
0
0
0
1
0
0
0
0
2
1
3
0
0
2
2
2
1
2
0
0
1
0
0
2
0
0
1
0
2
2
1
0
0
1
1
0
1
1
2
1
2
1
0
0
0
1
2
0
1
0
0
2
0
0
0
1
0
0
0
1
2
3
0
0
2
1
1
1
1
0
0
0
1
1
1
3
2
2
0
2
1
1
1
2
0
2
1
2
1
2
1
2
2
0
2
2
1
0
2
1
1
2
1
0
0
2
0
0
1
0
0
1
0
1
2
3
0
2
1
1
2
2
1
2
1
0
2
0
2
0
1
0
0
0
0
0
1
0
1
1
1
1
1
0
0
1
2
2
1
1
0
1
1
0
0
1
0
2
1
0
0
0
0
0
3
0
1
0
1
1
0
0
4
1
1
1
2
0
1
0
2
1
0
2
2
1
0
1
1
1
1
1
0
1
0
2
0
1
1
0
1
1
1
0
2
0
1
1
1
0
1
0
1
1
1
2
0
1
0
0
0
6
0
0
3
1
1
4
0
2
0
0
1
0
0
1
1
2
0
0
0
1
0
2
0
0
1
0
0
0
2
1
0
1
2
1
0
2
0
0
0
1
1
0
1
2
0
0
1
2
0
2
1
0
1
1
0
0
1
1
2
1
0
1
1
0
1
0
0
3
1
0
2
1
1
1
3
0
0
0
2
1
0
1
2
1
2
1
0
0
1
1
1
0
0
1
0
2
0
1
0
0
2
0
1
0
0
2
0
2
1
0
2
1
3
1
2
1
0
2
1
1
0
1
2
0
1
0
1
0
2
0
2
1
3
0
0
2
1
1
1
1
1
2
2
2
0
0
2
2
0
1
2
1
2
0
0
0
0
1
1
0
0
3
2
0
1
2
2
2
1
2
0
1
1
1
0
1
2
1
0
2
2
1
0
0
2
1
0
2
2
2
3
0
2
2
1
0
0
0
1
1
1
2
1
2
1
1
2
1
1
1
1
1
2
0
1
0
1
0
0
0
1
1
1
0
1
2
2
1
2
2
0
1
2
0
1
0
0
0
2
0
0
2
2
0
0
0
1
2
2
1
0
0
1
2
1
1
1
3
1
1
2
1
1
0
1
2
1
0
0
1
1
2
1
0
2
0
0
2
1
1
0
1
1
2
1
1
0
1
0
1
1
0
2
0
0
2
2
2
1
0
0
1
1
1
0
0
1
0
2
0
1
1
2
0
0
2
2
0
1
0
0
1
0
1
1
0
0
1
2
2
0
0
0
0
1
4
1
1
1
0
1
2
1
0
0
1
1
1
1
0
0
0
1
0
2
1
0
1
0
1
0
0
1
1
2
0
2
2
0
0
1
2
2
0
0
0
0
0
1
1
0
1
1
1
0
0
0
1
2
1
3
1
1
2
2
1
2
0
0
0
0
1
0
0
0
2
1
0
1
0
0
2
0
2
1
0
0
2
1
0
0
1
0
1
1
1
0
2
1
1
0
1
2
0
1
1
2
0
0
1
1
1
0
0
0
1
2
2
0
0
3
2
0
1
3
1
3
1
0
3
1
0
0
2
1
0
0
0
1
1
1
0
0
0
2
2
0
1
2
0
0
1
0
0
2
1
1
1
1
0
0
2
0
1
0
0
2
1
0
2
1
3
0
2
1
1
0
1
1
1
1
0
2
1
2
2
2
5
1
0
1
0
1
1
0
0
1
1
1
1
0
2
1
0
1
2
0
1
1
1
0
1
1
2
0
1
2
2
2
1
1
1
2
2
0
1
1
0
0
0
2
2
0
0
1
0
0
1
2
1
0
1
0
2
0
4
1
0
1
2
0
1
1
0
0
1
0
2
0
0
0
2
1
0
0
1
2
1
0
1
1
1
2
2
0
1
0
0
1
2
0
0
0
1
1
2
2
1
0
0
0
0
2
1
1
1
2
1
1
2
1
1
0
0
1
1
0
0
0
0
1
0
0
0
1
0
1
0
1
0
1
1
2
0
1
2
2
1
0
1
0
1
0
2
2
2
1
0
2
0
2
1
0
1
2
1
1
2
0
0
0
0
2
0
1
0
1
2
1
1
2
2
0
1
1
2
0
1
0
0
0
0
2
0
1
0
1
2
1
1
1
1
0
4
2
1
1
0
2
2
0
1
1
1
1
0
0
0
0
1
1
1
0
2
1
0
0
1
0
0
3
1
1
0
0
0
1
1
1
2
1
0
0
2
1
1
0
2
0
0
0
1
0
1
0
0
0
1
1
1
2
0
1
1
2
0
0
2
0
0
1
0
1
0
0
0
2
1
0
1
0
1
0
1
0
2
0
3
0
2
0
0
2
2
2
2
1
0
0
2
4
0
2
2
0
2
2
2
1
0
3
1
0
2
0
0
0
2
0
2
0
0
0
1
1
0
0
2
0
0
1
1
0
1
0
2
0
1
2
1
1
0
0
1
0
0
0
2
2
1
0
2
0
0
1
1
1
1
1
1
2
0
1
2
0
0
0
0
2
2
2
1
1
1
0
0
0
2
0
0
0
1
2
1
1
2
4
0
1
1
2
2
1
3
1
1
2
0
0
0
1
0
1
3
2
0
0
1
1
0
0
0
0
0
0
2
1
2
1
2
1
1
2
1
2
0
1
1
1
0
0
2
0
1
1
0
1
0
0
0
1
1
2
0
1
1
2
1
0
0
2
1
1
2
1
0
0
0
1
2
1
0
1
1
1
1
1
1
0
1
0
2
2
2
1
0
1
0
1
1
2
0
0
1
2
1
0
0
1
0
0
0
0
2
0
2
1
1
1
1
0
0
0
0
1
0
0
1
0
0
1
0
2
2
1
1
1
0
0
1
0
1
2
0
2
0
3
0
0
1
0
0
1
1
1
1
0
1
1
0
2
1
1
0
1
0
2
0
1
1
0
0
0
0
1
0
0
0
1
2
2
1
2
1
1
0
0
1
0
1
1
0
2
1
1
1
0
0
0
0
0
1
1
1
0
3
1
0
1
0
1
2
2
1
0
1
0
0
0
0
0
2
2
0
0
1
1
0
2
0
0
2
0
1
0
1
1
2
0
2
0
1
1
2
0
0
2
0
2
0
1
2
2
0
1
0
1
1
0
1
2
1
2
2
2
1
2
0
2
1
1
2
1
1
2
2
0
2
0
2
0
0
0
0
0
1
2
0
0
1
0
1
1
1
3
0
1
1
1
1
1
0
0
2
1
2
2
1
0
2
1
0
1
2
0
1
3
2
1
1
1
1
1
0
1
1
2
0
1
0
0
1
0
1
0
0
1
1
1
0
0
1
0
2
0
0
0
1
0
0
0
0
1
1
0
1
2
0
0
1
1
1
0
2
0
1
0
0
0
0
0
1
1
2
0
0
0
1
1
0
1
1
1
0
2
1
1
1
1
0
0
0
0
0
2
1
0
1
0
1
0
2
1
1
0
2
1
0
1
1
0
1
2
1
0
2
1
1
0
2
1
1
1
1
1
1
0
2
0
2
1
0
1
1
2
0
0
0
2
2
0
2
0
2
0
1
1
1
1
0
3
0
0
0
1
2
1
0
0
0
2
0
0
2
1
2
1
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
1
0
2
2
1
0
2
1
1
0
0
1
0
0
0
2
1
2
0
1
1
1
2
1
2
1
1
0
1
1
1
2
1
0
2
0
1
0
2
2
1
1
0
1
0
0
0
1
1
2
2
1
2
2
0
0
0
0
0
1
2
1
0
2
2
0
1
1
1
1
1
1
0
1
1
0
1
0
1
0
1
2
1
0
1
1
1
0
2
1
1
2
1
0
0
1
0
0
2
0
0
0
1
1
2
0
0
0
2
2
1
1
2
2
4
2
0
0
0
0
2
1
1
1
2
1
0
1
0
0
0
2
0
1
2
1
0
1
0
0
1
0
0
0
1
0
2
2
2
0
0
0
0
1
1
1
0
1
0
1
3
2
0
1
2
0
2
2
0
1
1
0
2
0
2
0
0
0
1
1
1
0
0
1
1
0
1
1
1
1
0
0
0
2
1
0
1
2
1
1
0
0
0
1
0
1
1
1
0
1
0
0
2
0
1
0
0
1
1
1
1
0
2
2
2
2
0
2
2
2
0
1
2
1
1
1
0
0
2
1
0
1
2
1
0
2
1
1
0
0
2
3
0
1
2
0
2
0
1
2
1
1
0
1
2
1
1
1
0
2
0
0
0
0
0
0
1
1
2
1
2
2
0
6
1
0
1
2
1
1
0
1
1
0
0
1
0
1
1
0
2
0
1
0
1
0
0
1
2
0
0
0
0
0
2
0
2
1
0
2
0
2
2
0
1
1
1
1
1
3
0
0
1
1
1
2
2
1
1
1
2
2
0
0
0
1
0
0
2
1
1
1
1
0
0
1
0
2
1
1
0
2
0
1
0
1
2
1
0
1
0
0
2
1
0
1
2
0
2
0
0
1
0
0
2
0
2
0
0
1
1
1
3
2
2
1
2
2
0
2
2
1
0
0
1
1
0
1
2
0
0
2
2
1
1
1
1
0
1
0
2
1
3
1
2
0
0
0
2
2
1
1
0
0
1
2
0
2
2
0
1
2
1
0
0
0
0
1
0
0
2
0
1
2
0
0
2
1
1
0
1
1
0
1
1
2
2
2
1
0
2
2
2
1
1
1
0
2
0
2
0
0
1
0
1
0
0
1
2
0
0
1
0
0
0
1
0
1
1
1
2
0
0
1
2
2
0
4
0
0
2
2
0
3
0
1
2
2
2
1
2
0
2
2
1
0
1
0
0
0
1
2
0
0
1
1
0
2
0
1
2
0
1
1
1
0
2
1
0
1
1
1
1
2
1
0
1
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
1
0
0
2
1
0
2
2
1
0
2
0
0
3
1
0
0
1
0
2
1
0
1
2
1
2
0
0
0
0
2
2
0
1
1
0
1
0
0
0
0
0
1
1
1
0
0
1
1
0
2
1
2
0
0
2
2
1
0
0
1
2
2
2
1
1
0
1
2
1
1
0
5
1
0
0
1
1
1
3
1
1
2
2
0
0
1
0
0
0
0
0
2
2
2
1
0
0
0
1
1
2
0
0
0
1
0
0
1
0
1
0
1
1
0
1
2
1
0
0
0
0
0
1
1
1
1
0
1
1
0
0
0
0
2
0
1
0
1
1
3
1
2
0
1
2
1
0
2
1
1
1
0
1
1
0
1
1
0
1
1
1
1
0
1
2
0
1
0
0
0
3
0
0
0
2
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
2
0
1
0
1
2
1
2
0
1
0
0
0
2
1
0
1
0
0
0
1
0
2
0
2
1
0
2
2
2
0
0
1
2
0
1
1
2
1
1
0
0
1
0
2
0
0
1
1
3
0
1
0
2
0
2
1
0
0
0
0
2
1
0
2
0
1
0
0
0
0
1
2
2
1
2
0
1
1
1
0
0
1
0
1
0
0
1
1
1
2
0
2
2
2
1
2
1
0
1
3
0
3
0
2
0
0
2
2
0
2
0
0
0
0
1
2
2
0
0
1
0
2
1
1
0
0
1
2
1
2
2
1
0
2
0
1
1
0
0
0
2
0
1
0
1
1
1
0
0
2
1
0
0
0
1
1
0
1
1
0
2
1
1
1
2
2
0
0
0
2
1
2
0
2
0
0
1
2
2
0
2
0
1
1
2
2
1
1
0
1
1
1
0
1
0
0
0
1
0
0
0
1
1
1
1
1
1
2
3
2
1
2
0
1
2
0
0
2
1
0
2
1
0
0
1
1
1
0
0
2
1
2
0
0
1
0
1
0
0
0
0
1
0
1
2
2
2
1
0
1
2
1
1
2
0
2
1
0
0
1
0
2
0
0
2
1
2
0
2
2
1
1
0
1
0
2
0
1
1
1
2
1
1
0
2
0
2
2
2
0
0
0
0
0
1
0
0
2
1
1
2
0
1
1
0
1
1
2
2
1
0
2
0
0
2
1
2
0
0
0
0
0
0
1
1
1
0
1
0
2
0
1
1
0
0
2
2
1
1
1
1
0
2
0
0
1
1
0
2
2
1
0
1
0
0
0
0
2
0
2
0
1
1
1
2
2
1
0
1
1
1
2
0
1
0
1
1
0
0
1
0
1
0
0
1
0
2
0
2
0
3
1
0
1
1
3
1
1
0
1
0
1
2
1
1
0
1
1
2
0
1
1
0
2
0
2
0
0
1
0
1
1
0
1
1
1
0
1
0
1
1
7
2
1
1
3
1
1
0
1
1
1
0
2
1
2
0
0
0
0
0
2
1
0
1
0
2
1
2
1
1
0
1
1
0
2
1
1
0
1
2
0
1
1
1
1
2
2
1
0
1
1
0
2
1
1
0
0
1
2
0
0
1
1
2
0
1
2
2
1
0
1
0
0
1
1
0
0
0
0
2
2
0
0
1
0
0
0
1
0
0
1
0
0
1
1
2
0
0
2
1
0
0
2
0
1
1
1
1
1
0
0
0
0
1
1
0
2
0
2
1
1
1
2
0
2
2
2
1
0
0
1
2
0
2
1
0
0
0
1
0
0
1
0
1
1
2
0
2
2
0
1
1
2
1
2
0
2
1
2
1
1
1
1
0
3
0
2
2
1
0
0
1
0
2
0
2
0
1
0
1
0
0
2
0
0
0
0
0
0
0
2
1
1
3
1
0
1
1
2
0
1
0
0
2
0
1
0
0
2
2
1
0
1
1
1
0
2
2
2
2
1
1
0
0
0
1
6
1
0
0
0
2
0
0
0
2
1
0
2
2
0
0
1
0
1
1
0
0
1
0
0
2
1
0
1
0
0
0
1
1
1
1
0
0
1
2
1
1
2
1
2
1
1
1
1
1
2
1
0
1
0
0
0
0
1
1
1
1
1
2
0
1
0
1
2
1
1
1
1
1
0
1
1
0
0
1
2
0
2
1
1
1
0
0
2
0
1
1
2
1
1
1
1
2
1
1
1
1
2
1
1
1
2
0
0
0
0
1
1
0
1
0
2
2
2
1
0
0
1
1
1
3
2
0
1
0
1
0
0
0
1
0
2
0
1
2
1
1
0
0
2
0
0
0
1
0
0
0
0
0
1
1
2
1
1
1
0
1
0
2
1
1
1
3
1
0
0
1
1
1
0
1
2
2
0
0
0
1
0
1
1
0
0
1
1
2
0
2
0
1
0
0
0
0
1
1
0
1
1
1
0
0
0
2
0
0
2
0
0
0
3
4
1
1
1
2
1
0
0
1
1
1
0
0
1
2
1
0
2
2
1
2
0
0
0
0
0
0
1
2
1
2
1
1
0
0
2
0
1
0
1
1
1
1
0
1
2
1
3
1
1
0
1
1
3
0
1
0
0
2
0
0
0
1
0
1
1
0
2
2
2
0
0
1
0
1
1
2
0
2
1
2
0
1
0
1
2
0
1
1
2
2
7
0
1
1
0
0
1
0
0
1
1
2
0
1
1
2
1
1
0
3
1
0
2
0
0
1
0
1
2
1
0
0
2
1
1
1
2
1
2
1
2
1
1
2
0
1
2
1
1
0
2
0
0
0
1
0
2
0
0
0
1
0
1
1
0
0
1
1
0
1
1
0
1
1
1
2
0
2
2
0
2
0
1
1
0
0
1
0
0
1
1
0
1
0
0
0
0
0
1
2
1
0
1
0
0
0
0
1
1
0
2
1
0
1
0
2
0
1
0
0
1
0
1
0
0
0
1
1
1
0
2
0
0
0
0
1
0
2
2
1
1
1
0
2
1
0
1
0
2
0
0
0
1
1
0
1
0
1
0
1
0
1
0
0
0
0
0
1
3
1
2
0
0
1
2
1
0
2
2
0
1
0
0
1
0
1
2
2
2
2
1
1
2
0
1
2
1
1
2
1
2
0
1
2
2
0
2
2
0
1
4
1
1
0
0
2
0
0
1
0
2
0
2
2
1
0
0
2
0
0
1
0
1
0
0
0
1
0
0
1
0
0
2
0
0
1
2
2
0
1
0
1
0
0
1
2
1
0
0
2
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
2
1
2
0
0
3
0
1
2
0
1
1
1
0
1
0
1
1
2
0
1
0
0
1
2
2
2
0
0
0
2
0
0
0
1
2
0
1
1
1
0
0
0
2
0
1
0
1
4
1
1
0
0
1
2
1
1
1
0
0
0
1
2
1
2
1
0
2
2
0
1
2
1
2
1
1
2
0
1
0
1
0
0
1
0
1
0
1
1
0
1
1
2
0
3
1
0
0
0
0
0
0
0
1
1
1
2
1
2
0
3
0
1
2
1
1
1
1
0
2
1
2
1
1
2
1
0
1
0
1
1
2
2
0
0
0
0
1
2
0
1
0
1
2
2
2
1
1
1
3
0
0
0
2
1
3
0
1
1
0
1
2
1
1
0
1
1
2
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
1
1
1
2
0
0
2
2
0
2
0
1
2
0
2
1
0
0
1
2
2
0
0
1
0
2
2
1
0
0
0
1
0
0
1
1
3
0
0
1
0
0
0
0
1
1
1
0
0
1
0
0
0
0
1
1
2
1
0
2
0
2
1
0
3
2
0
0
0
0
2
1
0
1
0
0
2
1
1
2
2
0
0
0
1
0
1
0
2
1
1
2
1
0
1
1
0
2
0
2
0
1
0
0
0
1
2
1
2
2
1
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
1
2
1
1
1
0
1
0
2
0
0
1
1
1
1
0
0
1
1
2
1
1
0
1
2
2
0
0
1
1
1
1
1
0
0
1
1
0
1
0
0
1
2
2
0
2
0
1
0
1
0
0
2
0
2
1
2
0
2
1
1
0
2
1
1
0
0
1
1
2
0
1
0
3
1
1
1
1
1
1
0
0
1
0
1
1
0
1
0
1
1
0
1
2
2
1
1
2
0
0
0
1
0
2
0
1
0
0
0
0
2
2
2
2
0
0
1
0
0
2
1
0
2
1
1
1
1
0
2
0
1
0
0
1
2
2
1
1
0
1
0
1
0
0
0
0
0
2
2
0
2
1
0
1
0
1
0
1
0
0
1
1
2
0
1
0
2
2
2
2
1
1
1
2
2
0
3
0
2
1
1
0
1
0
2
1
1
0
0
1
0
0
0
1
0
2
2
0
1
2
2
1
0
0
0
1
2
0
0
0
0
0
1
2
2
0
1
0
0
2
0
1
0
0
0
1
1
0
0
0
2
1
3
0
0
0
1
0
0
1
1
1
1
2
1
1
0
0
1
0
0
1
0
2
0
1
1
1
2
0
0
0
1
1
0
1
2
2
2
2
0
0
1
0
1
0
1
0
1
0
2
0
1
1
0
1
2
1
1
0
0
0
0
1
2
1
0
2
2
0
0
0
1
1
1
0
1
0
0
1
0
1
2
0
1
0
1
1
2
1
1
1
0
1
2
2
1
1
0
1
1
1
1
2
0
0
0
1
1
1
1
3
0
1
1
2
0
2
1
2
2
0
1
2
1
1
1
1
2
2
0
1
0
0
0
0
0
0
0
0
2
1
0
1
1
0
0
2
0
2
0
0
1
1
0
1
0
1
0
0
1
0
0
0
1
1
0
0
1
0
0
1
0
1
0
2
0
1
1
0
1
2
1
1
2
1
1
0
1
0
1
0
1
0
1
1
1
2
0
1
1
2
0
0
1
2
1
0
2
0
1
0
0
2
2
0
0
0
0
0
0
2
2
1
1
0
0
0
0
1
1
1
1
2
0
2
0
2
1
0
2
0
0
1
0
2
1
0
1
3
0
2
0
2
0
0
1
1
1
0
3
2
0
2
2
2
2
1
1
0
2
0
2
2
1
1
0
1
0
2
1
0
2
0
0
2
1
1
2
1
0
1
0
0
0
2
1
1
0
1
1
3
0
0
0
0
0
1
2
0
0
1
1
0
3
0
1
1
2
0
0
0
1
0
0
1
1
3
0
0
1
1
0
0
1
0
0
0
1
0
0
0
1
2
0
1
0
1
2
2
0
1
0
0
0
0
0
0
2
0
1
1
0
0
0
1
0
2
2
0
1
1
0
1
0
2
0
0
0
0
0
0
2
2
1
0
0
0
0
1
2
2
0
0
0
2
0
0
1
1
1
0
1
1
0
0
1
1
2
0
1
1
0
0
0
2
1
1
1
2
0
0
0
0
1
0
2
0
0
0
2
0
1
1
0
0
0
1
0
0
0
0
1
0
2
1
2
0
0
1
1
2
2
2
0
2
0
2
0
1
0
1
2
2
0
1
2
1
0
0
2
0
1
2
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
2
0
2
2
0
2
1
0
0
2
0
2
1
0
0
1
1
1
0
1
1
0
2
2
3
2
0
0
1
0
0
0
1
1
2
1
1
0
1
0
2
1
0
1
0
0
0
0
0
0
0
1
0
1
2
1
1
0
2
2
2
1
1
1
0
0
1
0
0
1
2
0
0
0
0
0
1
0
0
0
1
0
0
0
1
2
1
0
1
2
1
1
0
0
0
0
0
2
0
0
0
0
2
0
1
0
2
1
0
1
0
0
2
1
2
1
1
0
0
3
2
1
4
0
2
0
0
0
0
1
0
2
1
2
2
0
0
1
2
0
1
2
2
1
0
0
2
2
2
2
1
0
1
1
0
2
0
0
2
2
2
1
1
0
0
1
0
1
0
0
0
1
2
0
0
3
0
0
0
2
1
0
0
0
0
1
0
2
1
2
2
0
0
1
2
0
0
0
1
0
1
3
0
2
1
2
1
1
2
0
1
1
1
0
1
0
2
0
1
2
2
0
2
1
0
3
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
1
0
0
1
1
4
0
0
1
0
0
0
1
1
3
2
2
1
1
0
1
0
0
0
1
2
1
1
1
1
0
2
1
1
0
0
0
1
1
1
1
1
1
1
1
0
1
0
2
1
1
2
1
2
1
1
1
5
1
0
1
1
2
1
1
0
0
2
0
1
0
0
2
0
0
1
0
2
0
1
0
0
0
1
0
0
2
1
1
1
1
0
1
1
1
0
1
1
2
1
0
1
1
0
1
1
0
1
0
1
0
0
2
2
2
1
1
0
0
0
0
1
0
1
2
1
0
1
1
1
1
1
2
1
0
2
1
0
1
0
2
0
2
0
1
1
1
2
1
1
2
2
2
0
2
0
1
2
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
1
1
0
1
1
0
0
2
1
0
1
1
1
1
0
2
2
1
1
2
2
0
1
1
1
1
1
1
2
1
0
0
0
1
2
1
1
1
1
0
1
1
2
0
0
1
1
1
0
0
0
1
1
0
1
0
0
1
0
1
2
0
1
2
0
1
1
1
0
2
2
1
1
0
1
1
0
1
2
1
0
1
1
1
2
0
0
1
0
2
0
1
2
2
0
2
1
0
1
0
1
2
2
1
0
0
1
1
1
0
0
0
1
0
1
0
1
0
0
1
0
0
1
0
0
0
0
1
1
2
1
1
1
2
2
1
0
0
1
0
0
1
1
1
1
1
1
2
2
1
1
2
0
1
2
1
0
2
2
0
0
2
0
2
1
2
0
0
2
1
0
3
2
0
0
1
0
2
1
1
1
1
1
1
1
2
2
0
0
0
0
1
0
1
0
1
1
0
1
2
0
1
2
1
3
2
0
0
1
1
2
0
1
0
2
0
0
0
2
0
1
1
1
1
0
0
1
2
2
2
0
1
0
0
2
2
2
1
0
1
1
0
1
1
1
2
1
0
1
0
2
1
2
1
0
1
0
0
0
1
1
1
0
1
0
0
1
2
0
1
1
1
1
0
1
1
0
2
1
0
0
3
2
0
0
1
1
1
1
0
1
1
1
1
2
2
1
3
0
2
1
0
2
1
1
1
2
0
1
1
2
1
1
1
0
0
1
11
0
1
1
1
1
0
1
0
0
1
1
0
2
1
1
0
0
0
3
1
2
1
0
0
1
1
3
0
1
0
1
2
1
0
0
1
0
0
0
0
1
0
1
2
1
0
0
1
1
0
1
1
2
1
0
0
1
0
0
0
2
0
0
1
1
1
2
1
2
0
1
1
1
0
1
1
1
0
1
1
2
2
2
1
0
0
1
1
2
2
1
0
2
0
1
0
1
0
1
2
0
0
1
2
0
0
0
1
1
2
1
2
1
2
1
1
0
2
2
0
0
1
0
2
1
0
0
0
1
0
1
1
0
2
0
0
2
0
0
0
0
1
0
0
2
1
0
1
2
0
1
1
0
2
0
0
2
0
1
0
0
2
1
2
0
0
2
1
1
2
2
1
2
1
1
2
1
1
0
2
1
0
0
2
0
0
0
2
0
1
1
1
1
2
2
0
0
0
0
0
0
2
2
2
2
1
0
1
0
2
1
1
1
1
0
0
0
2
1
2
2
1
1
2
1
2
1
1
1
2
0
2
1
2
1
0
1
1
0
2
1
1
2
1
1
2
1
0
0
0
0
0
2
0
0
1
2
2
1
2
1
0
0
0
0
1
0
1
2
1
2
1
0
0
0
1
2
1
1
2
2
1
0
2
0
1
1
1
0
1
0
0
1
0
1
0
1
1
0
3
0
1
1
1
2
1
1
2
1
1
0
1
1
2
0
0
0
2
0
1
2
0
2
2
2
0
3
2
0
0
1
0
1
1
2
1
2
0
1
1
1
0
0
0
0
1
0
0
1
0
1
0
0
1
1
2
0
0
0
0
0
1
0
2
1
1
0
1
1
1
1
0
0
0
2
1
1
1
0
2
2
0
1
2
0
0
0
0
0
0
1
1
5
0
0
0
2
0
1
1
0
2
2
1
1
2
0
0
0
1
1
0
0
1
0
2
0
0
1
2
0
0
2
0
2
3
0
0
0
0
0
1
1
0
1
0
0
1
1
0
0
1
0
2
0
0
0
1
2
1
0
2
0
1
2
1
1
0
1
1
1
0
0
1
2
1
0
0
1
0
0
0
0
1
1
2
1
0
0
1
1
2
1
0
1
0
0
0
1
2
1
1
0
1
3
2
1
1
1
1
1
0
1
1
0
1
1
0
1
0
0
3
2
2
1
2
0
0
0
1
1
1
2
1
1
2
0
0
0
0
0
0
0
0
1
1
0
0
1
2
0
1
0
1
1
1
1
0
1
1
0
2
2
1
0
1
0
1
1
2
0
1
1
2
2
0
2
0
2
5
1
0
1
1
1
1
1
1
0
1
1
0
1
1
0
1
0
2
1
0
4
0
1
0
0
0
2
0
1
0
2
1
2
0
1
0
0
2
1
0
2
0
2
0
1
0
0
2
0
0
1
1
1
0
0
2
1
0
1
2
2
1
0
0
0
1
1
1
2
1
0
1
1
0
0
0
0
1
1
0
2
2
2
0
0
2
1
1
0
2
0
1
1
0
1
0
1
0
2
0
2
1
0
1
2
0
0
0
1
1
0
2
2
2
0
1
0
3
1
0
1
2
0
2
0
0
2
2
0
1
0
1
2
0
1
1
1
1
1
0
1
1
2
1
2
1
1
1
0
1
0
0
1
2
0
1
0
0
0
1
1
1
2
0
0
1
4
0
1
1
1
0
0
0
1
0
2
1
1
2
0
1
1
0
1
2
1
2
1
1
2
1
1
2
1
1
0
0
0
0
2
1
1
0
1
4
2
0
0
0
0
0
2
1
1
0
0
1
0
0
0
1
1
1
2
2
1
2
0
1
0
0
0
2
1
4
2
1
1
0
2
2
2
1
1
0
3
2
1
0
2
1
2
1
1
1
2
1
2
2
0
0
1
0
0
1
1
1
0
8
1
0
0
0
0
0
1
2
1
2
2
2
2
2
1
0
1
0
0
1
0
0
1
0
2
1
0
0
2
2
1
0
0
1
2
0
0
0
1
2
1
1
2
1
0
2
0
1
2
0
1
1
2
2
2
0
1
0
0
0
1
0
2
2
0
1
0
1
0
0
1
1
0
0
1
0
0
2
0
2
0
2
1
2
0
0
1
2
2
1
0
1
2
2
0
0
1
0
1
2
0
0
1
0
2
0
1
3
1
0
0
1
1
0
0
0
0
1
2
2
0
2
0
2
1
1
2
1
2
1
2
0
1
1
0
1
0
0
0
0
2
2
1
1
0
1
2
0
0
0
2
2
2
1
1
0
1
0
0
0
2
1
1
0
0
0
1
2
0
1
2
2
0
1
1
1
1
2
0
0
1
1
2
1
1
1
0
0
2
0
0
0
3
0
0
0
1
1
1
1
0
0
1
0
2
1
0
0
0
1
1
1
0
1
0
1
0
1
1
0
0
0
1
2
1
1
2
1
1
0
1
2
1
2
2
1
2
2
0
0
1
0
2
2
0
2
1
0
0
1
0
2
0
0
1
2
1
2
2
2
2
1
2
0
0
0
2
0
0
0
1
1
0
0
2
1
0
2
2
2
1
2
0
2
1
2
0
2
0
1
1
1
0
0
2
0
1
0
0
1
1
1
0
0
0
2
0
2
1
2
0
0
0
0
0
1
2
0
1
0
3
0
2
0
1
0
2
2
2
0
0
2
1
0
0
1
2
0
0
0
0
1
1
0
1
1
1
0
0
1
1
2
1
1
0
0
1
2
1
2
1
1
2
0
0
0
1
2
0
0
1
0
0
2
1
1
0
0
0
1
1
1
7
1
1
1
0
2
2
0
1
5
2
1
1
2
0
0
2
0
2
3
0
0
1
2
1
2
2
2
1
1
1
0
0
0
0
0
0
1
2
1
0
1
1
2
0
1
2
0
0
1
1
0
1
2
1
0
1
2
1
0
1
1
2
7
1
0
0
1
2
2
1
0
0
2
1
0
1
3
0
1
2
1
1
0
2
1
0
1
0
1
0
1
2
0
1
2
1
1
2
2
1
0
2
0
4
0
0
0
0
1
1
0
0
0
0
1
1
0
1
1
1
1
0
1
2
0
0
0
2
2
1
1
1
0
2
2
0
1
1
1
0
2
1
0
0
1
2
1
0
1
2
0
1
1
0
1
1
2
2
0
1
1
1
2
2
0
0
1
0
9
0
1
2
0
0
0
1
1
1
0
0
0
0
1
0
2
1
0
0
2
2
0
0
0
6
1
1
1
0
2
2
0
2
0
0
2
1
0
1
1
0
1
1
0
0
1
0
0
0
2
2
2
2
2
1
1
1
0
0
1
0
0
1
1
0
2
1
1
2
0
2
1
1
0
2
0
2
0
2
0
1
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
1
2
0
1
0
1
1
0
3
0
1
1
1
0
2
0
3
0
1
1
0
2
0
1
2
1
2
2
0
1
2
2
0
2
1
0
1
2
2
0
2
0
2
2
0
0
1
1
1
2
1
1
1
0
1
0
0
0
2
0
0
1
2
1
1
0
2
1
0
1
1
2
1
0
3
0
0
0
0
1
0
2
0
0
2
1
4
1
2
0
2
0
1
1
1
0
0
0
0
0
0
0
1
1
1
0
1
0
1
1
1
0
2
1
0
0
0
0
0
1
1
1
0
1
0
2
3
1
2
1
2
1
0
1
0
1
0
0
1
0
1
0
1
2
1
1
0
0
1
0
0
0
1
0
2
0
1
1
2
0
1
1
2
1
0
1
0
1
1
0
1
1
0
1
0
0
0
0
0
1
0
0
0
1
2
0
2
0
0
2
2
0
2
0
1
0
0
1
1
2
2
1
1
0
2
0
1
0
1
0
0
3
2
2
2
0
1
1
1
1
0
2
1
1
1
1
1
2
1
0
2
2
2
2
0
2
1
0
0
0
0
0
0
2
0
0
0
1
0
0
1
2
0
2
2
1
0
1
1
1
1
0
2
2
1
1
1
1
1
1
1
1
1
0
2
0
0
0
1
1
0
0
0
1
2
0
1
1
0
0
0
0
0
0
1
0
1
2
1
1
2
2
0
1
0
0
2
0
1
1
2
0
2
1
2
3
2
0
0
0
1
2
2
1
1
1
0
1
0
2
1
0
0
2
2
1
1
1
1
2
2
1
1
1
0
2
1
0
2
0
1
2
1
1
0
1
3
1
1
0
1
0
0
1
2
0
0
1
2
0
0
1
1
1
1
1
0
1
1
2
2
2
2
1
1
1
0
2
0
0
1
2
0
0
1
2
0
0
1
2
0
2
1
0
1
0
1
0
2
0
1
1
1
1
0
0
0
0
4
1
2
0
0
2
0
1
2
0
0
0
1
1
2
2
1
0
1
1
1
0
1
2
0
0
1
1
1
1
2
0
1
1
0
2
0
1
1
1
0
2
0
1
0
2
1
0
0
1
0
0
2
1
1
0
2
1
1
1
1
1
2
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
1
0
1
1
1
0
1
1
1
2
2
1
2
1
0
0
2
2
2
0
0
0
0
2
1
1
2
1
3
0
0
0
1
1
1
1
1
2
0
1
1
1
0
2
0
2
3
1
1
1
0
0
1
2
2
1
0
1
1
2
1
0
1
1
0
0
1
2
0
1
1
2
1
0
0
0
2
1
1
1
1
0
2
1
1
0
0
1
3
1
1
1
1
1
2
1
0
2
0
0
0
13
1
3
2
1
0
1
0
2
1
0
0
1
0
0
1
0
1
1
0
0
0
2
2
1
1
0
0
1
1
0
1
1
1
0
2
2
1
0
1
0
0
0
1
1
1
1
1
3
2
1
0
2
0
1
0
0
2
1
1
0
1
0
2
1
1
0
1
0
0
2
1
0
1
0
0
1
0
1
0
1
0
0
0
1
1
1
2
0
1
2
1
2
2
1
1
1
1
1
0
0
1
0
2
1
1
0
0
2
2
0
0
0
2
1
0
0
1
1
0
2
0
1
0
1
2
1
2
0
2
1
2
1
0
1
0
0
0
0
1
2
0
2
1
1
1
1
0
0
0
2
0
2
1
1
2
0
1
0
1
2
0
0
2
1
1
2
2
0
1
1
1
1
0
0
2
2
0
0
1
0
0
1
1
1
1
0
1
2
0
2
3
0
0
2
0
0
1
2
1
0
1
1
2
1
1
0
0
1
0
2
0
2
1
0
0
2
2
0
2
1
0
0
1
0
0
0
0
1
1
2
2
1
1
0
0
0
1
0
0
2
2
2
1
0
1
0
0
0
2
2
1
0
1
1
0
1
2
1
2
0
1
1
1
0
0
1
0
0
1
1
1
1
1
1
2
1
0
0
1
0
1
0
0
0
2
0
1
0
1
0
1
3
1
0
0
2
1
1
0
0
0
0
2
0
2
2
0
0
1
2
2
2
1
2
0
1
0
1
2
0
1
0
1
1
1
1
0
0
1
0
1
0
2
1
0
1
1
1
0
0
1
0
1
0
1
0
2
1
0
2
2
0
1
2
3
2
0
1
1
1
2
1
1
0
0
2
0
1
0
2
2
2
0
0
0
0
0
2
0
2
1
1
0
1
0
1
0
1
2
2
2
0
0
0
2
0
0
0
1
0
2
0
3
0
0
0
1
2
2
0
0
2
0
1
1
1
0
1
1
0
1
1
1
2
5
0
0
0
0
0
1
2
0
1
2
2
0
0
1
0
0
1
1
0
1
1
0
1
1
2
1
2
0
0
0
1
2
0
2
2
2
1
0
1
0
0
0
0
0
0
1
2
0
1
1
1
0
2
0
2
0
1
2
3
1
1
0
0
1
0
2
2
0
1
2
1
1
2
1
2
0
0
1
0
0
0
0
0
2
0
0
1
1
1
0
1
0
2
0
0
0
0
1
1
1
1
0
1
2
1
1
0
2
1
3
0
0
4
0
0
1
0
1
2
1
0
0
0
1
0
0
1
0
1
2
1
0
1
0
0
2
0
1
1
0
1
1
1
1
2
0
1
2
0
1
2
1
0
1
1
0
3
0
0
0
0
0
1
1
1
2
1
2
2
1
1
1
1
0
1
0
0
0
2
1
0
1
0
1
0
1
0
1
0
1
1
1
1
0
2
0
0
1
0
0
2
2
0
0
0
0
0
2
1
0
1
0
1
0
1
0
1
2
1
0
0
3
1
1
2
1
1
0
2
1
0
2
0
2
1
2
1
0
0
0
1
1
1
1
1
1
2
1
1
1
1
3
0
2
2
1
1
1
0
1
2
2
1
0
1
3
0
0
0
1
1
1
0
1
1
1
1
0
0
2
0
1
0
1
1
1
0
0
1
0
0
0
0
1
0
1
2
0
1
0
2
0
1
2
1
2
0
0
2
1
0
1
0
2
0
1
1
2
1
0
0
1
1
2
0
2
0
2
2
0
2
2
0
0
0
0
0
0
0
1
0
0
1
1
1
1
0
0
1
1
1
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
4
1
1
2
2
0
1
0
1
0
0
1
2
1
1
1
0
1
0
0
0
2
1
1
0
2
1
1
1
0
0
0
1
0
0
1
2
0
0
0
2
2
1
0
2
3
1
0
1
2
2
1
1
0
1
0
0
0
0
1
1
2
2
1
1
1
0
0
1
0
2
0
1
1
0
1
1
1
1
1
1
0
1
2
0
2
0
1
2
3
0
1
2
1
0
0
1
0
2
1
2
1
2
0
0
2
0
3
1
0
0
1
1
1
1
0
2
1
1
1
0
0
1
0
0
1
1
1
0
2
2
1
1
1
0
2
2
2
0
0
0
0
0
2
1
0
1
0
1
2
1
2
0
1
0
0
0
2
1
1
1
1
1
0
0
0
0
1
0
2
2
0
0
1
0
0
1
0
0
2
2
1
2
2
1
0
1
0
0
2
0
2
0
0
2
2
2
1
0
0
0
0
0
0
2
2
1
0
0
0
1
0
1
0
1
0
1
1
1
0
0
0
1
0
0
1
0
0
0
0
2
0
1
1
0
0
0
2
0
1
0
0
2
1
0
0
0
0
0
0
0
1
0
1
1
1
1
0
0
1
2
0
2
1
0
0
2
1
1
0
1
1
2
0
1
1
0
0
0
2
0
2
1
0
2
0
0
1
0
1
0
1
0
0
2
2
0
0
0
0
0
1
0
1
1
0
0
0
2
3
0
0
1
2
0
5
1
1
1
1
0
0
0
0
1
0
1
1
0
0
1
2
1
2
1
0
0
0
2
0
1
1
2
2
1
0
0
1
2
1
0
1
0
2
0
1
0
2
1
0
1
1
2
1
2
0
1
0
0
1
0
1
2
2
1
0
1
0
0
0
2
1
1
0
2
2
0
1
1
2
1
1
2
1
1
1
1
2
1
0
1
2
0
0
0
2
2
0
0
1
0
0
0
2
2
0
1
0
1
2
0
0
0
1
1
2
1
1
1
0
0
0
2
1
1
1
2
0
2
2
1
2
3
0
0
1
1
1
2
0
0
1
1
0
1
2
0
2
1
0
0
0
0
1
0
1
1
2
1
2
2
1
0
1
1
1
2
2
2
0
0
0
0
2
0
2
0
0
0
0
1
0
1
2
1
1
2
2
0
0
2
0
1
1
0
1
2
3
0
3
1
0
1
0
0
0
2
2
0
1
0
1
1
2
1
0
0
1
1
1
3
1
0
2
1
1
0
1
2
2
0
0
1
0
1
0
0
0
0
1
2
1
1
0
1
0
1
0
1
1
2
0
1
0
1
2
0
1
1
1
0
1
1
1
0
0
0
4
1
1
1
0
1
0
0
0
1
1
0
0
0
0
1
1
0
1
0
1
0
0
1
0
0
0
0
1
2
0
0
0
0
2
1
0
4
1
2
1
1
3
1
1
3
0
0
0
2
0
2
1
0
0
1
1
0
1
2
0
3
1
1
0
0
0
1
0
2
2
2
2
0
0
0
0
1
0
0
6
1
0
1
1
0
0
1
0
0
1
0
2
0
0
1
0
1
0
1
0
0
0
1
2
1
1
2
2
1
2
2
1
1
0
1
1
0
2
2
1
2
1
0
1
1
0
2
2
1
1
2
1
1
0
1
1
2
0
2
2
0
2
0
1
2
0
0
2
0
0
1
1
2
0
0
2
1
2
1
0
2
0
0
2
1
0
0
2
0
0
0
2
0
0
0
1
4
0
1
2
0
0
0
1
2
1
0
0
1
1
1
1
0
1
1
2
0
1
1
0
2
1
1
1
1
2
2
0
1
2
1
1
1
3
0
2
1
0
0
2
0
2
0
2
0
0
0
1
1
1
1
0
1
0
2
1
1
0
0
0
1
0
1
0
1
0
2
0
0
0
2
0
0
1
0
1
0
0
1
0
1
1
1
1
2
2
1
1
2
0
1
0
2
0
2
1
2
1
0
0
0
0
2
1
1
0
1
0
1
3
0
2
1
0
0
0
0
1
1
2
0
2
2
1
1
1
1
0
1
1
0
0
0
2
2
0
2
1
2
0
0
0
0
1
1
2
1
0
1
1
0
0
1
1
2
1
0
0
2
1
0
2
1
1
0
1
0
2
1
0
1
0
2
2
2
1
0
0
0
0
1
2
0
0
1
1
0
0
4
1
2
0
0
3
1
3
2
0
0
1
0
0
2
0
0
2
0
1
2
0
1
0
4
1
2
0
0
1
1
2
1
0
2
6
0
2
2
0
0
0
2
1
1
0
1
0
0
1
1
1
1
0
1
0
1
0
0
2
1
1
1
0
1
1
0
0
0
0
0
2
2
0
1
1
2
1
2
1
0
1
1
0
1
0
0
2
2
1
0
2
0
0
0
1
0
0
2
2
2
0
0
0
1
1
1
0
2
0
0
1
1
1
1
0
2
2
0
3
0
1
0
0
1
1
0
0
1
1
0
0
0
0
2
0
0
2
1
0
0
1
1
2
0
1
2
0
2
1
0
0
1
1
1
0
0
2
0
0
0
2
2
2
0
2
2
1
1
0
2
2
0
1
2
0
1
1
1
2
2
1
1
0
1
1
2
2
0
0
1
2
2
1
1
2
1
2
0
0
0
2
1
1
0
1
1
2
1
0
0
2
1
1
0
2
0
0
1
2
2
1
2
1
0
1
1
1
1
0
0
0
0
2
0
1
1
1
2
1
2
1
2
0
2
0
2
0
1
2
0
1
2
1
1
2
2
1
1
2
1
1
0
1
0
1
1
2
0
0
0
0
1
1
1
0
1
2
1
0
0
0
0
1
2
0
1
0
1
3
2
0
0
1
1
0
1
0
0
0
1
2
1
0
0
2
0
0
1
2
2
1
0
2
2
2
0
0
0
0
1
1
0
1
2
1
0
0
2
1
0
0
0
0
0
2
2
0
1
1
0
0
1
0
0
0
1
2
1
0
0
0
1
2
0
0
1
1
0
1
2
2
0
2
2
1
0
2
2
0
3
0
0
1
1
2
1
2
2
2
0
1
2
2
1
1
0
1
1
2
0
0
1
0
1
0
1
0
0
0
1
1
2
2
4
0
1
2
0
1
2
0
0
2
0
0
2
0
1
0
0
1
0
1
1
1
0
1
1
1
1
0
2
0
0
0
1
1
0
1
2
1
0
1
1
2
0
1
1
0
2
0
1
0
0
0
0
1
0
2
0
0
2
1
0
0
2
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
5
2
1
2
1
1
2
0
0
0
0
1
2
0
1
0
1
0
3
0
0
0
1
0
1
0
0
0
2
0
1
1
0
0
0
2
1
0
2
0
2
1
0
1
0
1
0
1
1
2
2
0
1
1
2
2
0
0
1
0
0
1
0
0
1
2
2
0
2
0
0
0
1
1
2
0
1
1
0
0
0
2
2
1
2
1
2
1
1
0
0
0
0
1
0
0
0
1
0
1
1
0
1
2
0
0
1
0
1
0
2
2
2
1
1
1
0
1
1
2
0
1
0
0
1
0
0
1
0
1
0
1
1
1
0
0
0
1
2
0
0
1
0
1
0
0
0
1
1
1
0
0
1
1
1
1
1
2
1
2
0
2
0
0
0
0
2
0
2
2
1
0
0
1
2
1
2
0
1
0
1
1
1
0
0
2
2
0
2
0
0
1
2
0
0
1
0
1
0
1
0
2
1
0
0
2
1
1
0
0
2
0
1
1
0
0
1
1
1
1
1
0
2
1
2
0
0
0
2
1
0
2
0
2
2
2
0
2
2
2
1
0
0
1
2
0
0
0
1
1
0
1
0
0
0
2
1
0
1
2
0
2
0
0
0
1
0
0
0
1
0
0
0
2
0
0
1
1
1
0
1
1
1
1
1
0
1
0
0
0
1
1
0
3
0
1
1
2
0
1
0
1
0
1
0
2
2
1
0
0
0
2
1
1
2
2
2
1
2
0
0
0
2
1
2
0
4
0
0
0
0
2
1
4
2
2
2
1
2
1
1
1
0
2
0
0
1
1
1
0
1
0
0
0
0
1
0
0
1
0
2
1
1
1
1
1
0
0
0
1
2
0
1
1
0
2
0
1
0
0
3
1
1
0
1
0
0
0
1
2
0
1
2
1
2
2
0
1
1
2
0
2
2
1
2
1
2
1
0
1
1
2
0
0
1
1
0
1
2
2
0
1
2
0
2
0
2
0
0
0
0
0
0
1
0
1
1
1
2
1
0
0
0
1
0
1
2
1
1
0
1
1
0
1
0
0
1
0
0
2
3
2
1
1
0
1
0
1
0
1
1
1
1
0
1
0
1
0
2
2
2
2
2
1
1
1
2
2
3
3
3
0
1
0
0
1
1
2
0
1
0
0
0
0
1
0
1
0
1
0
2
1
0
0
2
0
1
0
0
1
1
2
0
2
1
1
2
0
1
0
1
0
1
1
0
1
1
0
1
0
0
0
0
1
2
1
0
1
0
0
2
1
1
1
0
0
2
1
1
0
0
0
1
2
0
1
2
0
1
0
1
1
0
0
0
1
1
0
1
2
1
1
0
1
2
0
1
0
0
0
0
0
0
1
1
0
1
1
1
1
0
1
1
0
1
1
1
1
0
1
2
0
1
0
1
1
0
2
2
2
0
0
2
1
1
2
1
2
2
1
2
0
1
0
2
0
2
0
1
2
2
1
0
0
1
1
0
3
2
0
1
0
0
2
2
0
0
2
0
0
1
0
0
1
0
0
1
2
0
0
1
1
2
0
0
1
1
1
0
1
0
2
0
1
0
0
2
0
0
1
1
1
1
0
0
1
0
2
1
0
1
1
2
0
1
1
0
2
0
0
1
1
1
0
0
2
1
2
0
0
1
0
2
1
1
2
0
1
1
1
2
2
0
1
1
0
1
0
1
2
2
0
0
1
0
0
0
1
1
2
1
1
1
0
0
1
0
0
0
1
1
0
1
2
0
0
0
0
1
2
0
0
0
1
0
1
2
3
2
0
0
0
1
3
0
0
0
1
1
1
2
0
2
0
1
2
1
2
0
0
1
1
0
1
1
1
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
1
0
0
1
0
0
0
0
1
0
0
0
1
2
2
0
0
0
0
0
1
1
0
1
0
1
0
2
0
1
1
0
1
2
0
0
0
0
1
1
1
1
0
0
2
0
2
0
0
1
0
0
1
0
1
0
0
1
1
2
1
2
1
1
1
2
2
2
0
1
0
0
2
0
2
1
1
2
1
0
0
1
3
0
0
1
0
1
0
1
1
1
1
0
0
0
0
1
0
0
1
2
3
0
1
0
0
0
0
1
0
0
2
1
2
2
2
1
0
2
1
0
0
0
0
0
0
0
2
0
0
2
1
2
1
1
1
1
1
2
0
1
1
1
2
2
1
1
2
1
0
0
1
2
0
1
2
0
2
4
0
0
1
1
0
1
2
0
0
0
0
0
1
0
1
0
1
1
0
2
0
2
0
0
1
1
0
0
3
0
0
0
1
2
0
0
1
0
0
2
0
1
1
1
2
1
2
0
0
1
1
1
0
3
2
1
0
2
1
0
1
1
0
0
1
0
1
2
2
1
0
0
0
1
0
1
2
2
0
1
1
1
1
0
2
2
2
0
1
1
1
2
0
0
0
0
1
1
1
2
2
1
1
2
2
0
2
1
1
0
1
2
0
1
0
1
1
2
2
2
0
0
1
1
1
1
0
1
0
0
1
1
1
1
0
1
0
0
1
1
0
1
1
0
2
1
1
0
2
0
1
1
1
2
1
2
1
1
0
2
2
0
0
1
0
2
2
0
1
0
1
2
1
1
2
0
0
0
0
1
0
1
2
1
0
1
1
0
1
1
2
0
1
0
2
1
1
0
1
0
0
2
1
1
0
0
1
1
0
0
1
2
1
1
2
2
0
0
2
1
2
2
2
1
1
0
1
1
1
0
1
0
0
2
0
2
2
1
1
0
1
1
0
1
0
0
0
1
1
0
1
1
1
1
2
1
1
1
2
2
0
1
1
0
3
1
1
0
1
0
2
1
2
0
1
0
2
2
0
0
1
1
0
2
1
1
0
2
0
0
1
2
1
1
0
2
2
0
0
0
1
1
0
0
1
2
0
1
2
0
0
0
0
0
0
0
2
0
1
1
2
1
2
1
0
1
0
0
2
1
0
0
2
2
0
1
2
1
1
0
1
2
0
1
0
0
0
0
0
1
2
1
0
1
0
1
0
1
1
0
1
0
0
1
0
2
2
2
1
1
1
0
2
0
1
1
1
1
0
1
0
0
1
0
1
2
0
1
0
1
0
1
0
0
1
1
1
1
0
2
1
1
1
0
0
0
0
2
0
1
1
0
0
1
1
2
1
1
0
0
2
0
2
1
0
1
1
1
0
1
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
1
0
2
1
0
2
3
2
1
0
2
2
0
1
0
1
1
1
0
2
1
0
0
2
1
0
0
0
0
0
0
1
1
1
0
2
1
2
2
2
1
1
0
0
2
0
0
1
1
2
3
1
0
1
1
1
2
0
0
0
2
2
2
1
2
1
1
0
0
1
1
2
1
1
0
0
1
1
1
1
0
1
1
0
1
2
2
1
1
2
1
2
1
0
1
1
0
0
2
0
2
0
1
0
1
0
1
1
2
1
0
1
1
2
0
1
0
1
1
2
1
2
0
1
1
0
1
1
1
2
2
0
1
1
1
2
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
1
2
0
0
0
1
1
0
0
2
0
1
0
0
1
0
0
2
1
0
0
1
0
1
2
1
1
0
1
3
0
0
1
1
3
1
0
2
2
0
1
1
0
2
1
1
1
2
1
1
2
0
2
1
0
2
0
0
1
0
0
1
0
1
2
2
1
1
1
0
0
1
0
1
1
2
2
2
1
1
2
1
2
1
0
0
1
0
2
2
0
1
1
0
1
1
1
1
0
2
2
0
2
0
1
0
0
0
0
2
1
1
1
0
1
0
1
1
0
1
0
1
0
0
0
1
1
0
0
4
1
2
0
0
1
0
0
0
0
1
1
0
0
0
1
0
1
0
1
0
2
0
0
0
0
0
0
0
1
1
0
1
1
0
1
1
1
0
2
2
0
0
0
3
1
1
2
0
0
0
0
0
1
1
1
2
2
2
1
1
1
1
1
0
0
0
1
2
3
0
0
2
2
2
0
0
0
2
3
1
2
1
0
1
1
0
1
0
0
0
0
0
1
2
0
0
0
2
0
1
1
1
2
2
1
1
2
0
2
2
1
3
0
0
1
0
1
1
2
1
0
0
0
2
0
1
1
2
1
2
0
1
3
0
1
1
2
1
0
1
2
2
0
1
0
2
0
2
1
1
0
0
1
2
1
1
0
2
1
2
2
1
0
0
1
0
1
1
0
0
3
0
1
1
0
0
1
1
2
1
0
0
0
0
1
0
0
2
1
1
1
1
2
0
2
0
1
2
0
0
0
1
0
0
0
2
0
0
1
1
2
0
0
2
2
0
2
1
0
1
0
0
1
2
0
2
0
0
0
0
1
2
1
0
2
0
0
0
2
0
0
1
1
2
0
1
1
0
0
0
1
1
1
1
1
2
0
1
0
0
2
1
2
1
1
0
0
2
0
1
1
1
2
0
2
0
3
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
1
1
0
2
2
2
0
0
0
1
1
2
1
1
1
0
1
1
2
0
1
2
1
0
1
0
1
0
0
0
0
1
1
1
2
1
0
0
2
0
0
0
1
1
0
1
1
1
2
2
1
1
1
0
0
4
1
1
1
0
1
1
1
2
0
2
0
1
0
0
1
1
1
2
1
2
0
0
2
1
0
2
1
1
2
0
0
0
0
1
1
0
0
0
1
1
1
2
1
0
0
0
0
2
0
0
2
2
1
0
0
2
1
1
1
2
1
0
2
1
0
1
2
2
2
2
2
0
2
1
0
0
1
0
1
1
0
1
2
2
1
1
2
0
0
0
1
0
1
0
0
0
1
1
0
0
1
0
2
2
0
1
1
0
2
0
0
0
1
2
0
0
0
2
2
1
2
2
1
1
0
1
0
2
1
1
1
1
1
0
2
1
1
0
0
0
0
2
2
0
1
0
0
0
0
0
0
1
2
0
0
1
1
0
0
1
0
1
0
0
0
2
0
1
2
2
0
2
2
0
1
2
1
1
2
0
2
0
1
1
0
0
1
1
1
1
0
2
1
1
1
0
2
1
1
2
0
0
1
1
1
1
2
1
0
1
0
0
0
0
2
1
1
2
1
2
0
1
0
1
1
0
0
0
0
1
1
2
2
0
2
2
2
0
0
0
1
1
0
1
2
1
5
2
1
0
0
1
1
1
0
0
2
1
1
3
1
2
1
1
0
2
1
0
0
1
0
0
0
2
0
3
2
0
0
1
1
0
1
0
1
0
2
1
1
0
0
1
2
0
0
9
0
0
1
0
1
0
1
0
1
0
1
1
0
1
1
2
0
2
1
0
2
2
0
2
1
0
3
0
1
1
1
1
2
0
1
0
0
2
4
0
1
1
2
1
2
1
2
0
0
2
0
0
2
1
0
2
0
0
1
0
0
0
1
1
0
1
1
0
0
0
0
2
1
0
0
1
0
1
1
0
2
0
1
2
1
2
0
2
2
0
1
0
2
7
3
1
2
2
1
0
2
2
2
0
1
0
1
0
0
1
0
1
1
0
2
1
0
2
2
2
0
0
1
0
2
1
4
0
0
1
1
2
1
1
0
0
2
1
0
0
2
0
1
1
0
1
0
0
1
0
2
1
0
0
2
2
0
1
0
0
1
0
0
2
0
2
1
1
1
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
2
0
1
1
1
1
2
2
1
0
0
2
1
0
1
1
1
0
1
1
0
0
0
0
0
0
2
0
1
0
0
1
0
1
0
1
2
0
0
0
0
1
0
0
2
0
2
0
2
0
2
0
0
1
2
1
0
1
1
1
0
3
1
0
2
1
0
0
1
0
1
0
0
0
0
0
0
0
2
3
1
0
3
1
0
1
2
0
0
0
2
2
1
0
1
2
3
0
0
1
0
1
1
2
0
2
1
0
2
1
1
0
0
1
2
1
2
1
1
0
2
1
0
1
2
0
0
0
1
2
0
1
2
1
2
2
0
0
0
1
1
0
1
1
0
1
1
0
3
0
0
0
1
1
1
1
1
2
1
0
3
1
0
0
0
0
1
2
1
1
0
0
0
1
1
2
2
0
1
2
1
1
1
2
1
1
0
2
0
0
2
1
1
1
0
0
2
0
0
0
1
1
0
1
2
0
0
1
3
1
2
0
1
2
2
0
0
0
0
1
1
2
1
0
0
1
1
0
0
0
0
2
1
2
0
0
2
1
1
1
1
0
0
0
1
1
0
2
0
3
0
1
0
1
1
2
0
1
0
0
1
0
0
1
1
1
2
2
0
2
1
1
1
1
1
0
1
0
2
1
1
1
0
2
1
2
1
2
1
1
1
1
1
2
1
0
1
1
2
0
1
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
1
1
0
1
2
0
2
0
2
1
2
0
0
1
0
0
1
1
2
2
0
1
2
1
1
2
0
0
1
1
2
1
2
2
0
2
1
0
1
1
1
1
2
1
0
0
0
2
1
0
0
0
0
1
1
0
0
2
1
2
0
1
1
1
3
1
1
0
1
2
2
1
0
1
2
2
0
1
1
1
0
0
2
1
1
0
2
1
2
0
0
0
1
0
2
2
0
1
0
0
0
1
1
1
1
1
0
0
1
1
0
1
2
0
1
2
1
0
0
1
0
1
1
0
1
2
2
1
0
1
1
3
1
1
2
0
1
0
2
0
0
2
2
1
1
1
1
1
0
2
0
0
1
0
1
1
1
0
0
0
2
0
1
1
1
1
1
2
1
1
0
1
1
2
0
2
0
0
0
1
0
1
0
2
2
2
0
0
1
1
0
1
1
1
0
1
1
0
0
1
0
1
0
1
1
0
2
0
1
1
0
0
1
2
0
1
0
0
1
4
1
1
2
0
0
0
2
2
2
1
0
1
0
0
2
0
1
2
1
1
0
1
1
0
0
0
1
1
0
0
0
0
2
0
2
2
2
2
0
1
2
2
1
0
2
1
2
2
1
0
1
0
0
0
3
1
2
0
1
3
1
1
1
3
2
0
0
3
1
0
1
1
1
2
1
0
2
0
1
0
0
1
0
1
1
1
1
1
0
1
1
1
2
0
0
2
1
0
0
0
0
0
0
3
2
1
1
2
1
2
1
1
3
0
0
0
0
1
0
2
0
0
0
2
2
1
2
1
2
0
0
2
0
2
0
0
1
2
1
1
0
1
0
0
0
1
0
1
2
1
0
1
1
1
1
0
2
0
3
1
0
0
0
0
0
2
0
1
1
2
1
1
1
1
0
2
1
2
1
0
1
1
1
0
2
1
0
2
0
1
2
0
1
0
0
1
0
1
0
1
2
0
1
0
0
2
2
2
1
1
1
0
1
2
0
1
0
0
0
0
1
0
0
1
0
1
0
1
1
1
1
1
1
2
1
0
1
0
0
2
1
0
0
2
1
1
1
0
1
2
2
1
0
0
1
0
1
1
0
0
0
2
1
0
0
2
0
0
2
1
2
1
0
0
0
1
0
1
1
2
2
1
0
1
1
0
1
0
0
0
1
1
1
2
0
2
0
0
1
1
2
0
0
0
1
0
0
0
1
0
3
1
1
0
0
1
1
0
2
1
2
0
0
2
1
2
2
2
2
2
0
2
1
2
2
1
2
1
2
1
0
1
1
1
0
0
0
2
5
1
0
0
1
1
1
0
0
0
1
2
2
2
0
0
1
0
0
0
1
2
1
2
0
0
1
2
1
0
0
0
2
1
1
1
0
0
1
0
1
0
1
1
0
0
1
1
4
2
0
0
1
2
1
0
0
2
1
0
2
1
1
0
2
1
0
1
1
0
4
0
1
1
1
1
1
2
1
1
0
0
0
0
2
1
0
1
1
3
0
1
2
0
2
1
2
0
1
0
0
0
0
1
1
1
0
0
1
2
1
2
1
0
1
1
1
2
2
1
1
1
2
0
1
0
0
1
2
0
0
0
0
1
1
2
2
1
1
2
0
0
2
1
1
1
1
2
0
2
1
1
2
2
1
1
3
2
1
2
2
2
0
2
0
0
2
0
2
0
1
0
1
1
0
0
1
0
0
2
0
0
0
1
2
0
1
1
1
0
1
0
0
1
0
1
2
0
0
1
2
2
0
0
2
2
1
1
0
2
0
1
2
0
0
1
0
2
2
0
0
1
2
1
0
0
0
0
0
1
0
2
1
1
1
0
1
0
0
1
0
1
1
1
0
2
1
0
0
1
1
3
0
0
2
0
0
1
0
1
0
1
0
1
0
0
0
0
1
0
1
1
0
1
1
2
0
0
1
1
2
1
2
2
0
1
3
2
1
1
1
2
2
0
0
0
2
0
2
7
1
2
2
0
0
1
1
1
2
1
2
2
1
1
1
1
0
2
0
0
1
2
0
0
0
0
1
1
0
1
0
1
1
0
0
0
2
0
1
1
2
0
2
1
1
0
2
0
2
1
1
0
0
2
0
2
1
2
2
1
0
2
1
1
1
1
3
5
0
0
0
0
1
0
3
0
0
1
1
1
1
0
2
1
1
0
1
0
1
0
0
2
1
0
2
0
1
0
0
0
0
1
1
1
2
0
0
0
1
0
0
1
0
1
0
0
0
1
2
2
0
0
2
1
2
0
0
0
0
0
0
0
2
1
1
0
1
0
2
1
0
1
1
1
0
3
0
0
1
1
1
1
1
0
1
1
0
0
0
0
2
0
1
0
2
1
4
0
1
0
0
0
0
2
1
0
2
2
1
2
0
2
1
0
1
1
1
0
0
0
0
0
2
0
0
1
0
2
2
0
3
0
1
0
0
0
1
0
1
0
1
1
0
0
2
0
2
0
1
2
2
0
1
0
1
0
2
0
0
2
0
0
0
1
3
1
0
4
2
0
0
0
0
1
1
0
1
0
0
2
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
2
1
2
1
2
1
0
1
2
0
0
1
0
0
0
1
0
2
2
2
1
0
1
0
1
0
2
3
1
0
0
2
1
2
2
0
3
1
2
0
0
0
1
1
0
1
0
1
1
1
0
1
0
1
1
0
0
2
2
1
1
2
1
2
0
0
3
2
0
2
2
0
0
2
2
1
2
0
2
1
1
2
1
2
1
1
1
0
2
0
0
3
1
0
3
1
0
0
0
2
1
1
0
1
0
0
2
0
1
1
0
1
0
0
1
1
1
1
1
5
0
1
0
0
2
1
0
0
1
1
2
2
1
0
1
1
1
1
0
1
0
0
0
2
1
0
4
1
1
2
2
1
0
2
1
1
1
1
1
0
0
0
2
2
0
2
2
3
1
0
0
2
2
1
1
1
0
3
0
1
0
1
0
0
0
0
0
1
1
0
0
1
0
1
1
0
1
2
0
4
1
1
0
1
0
0
0
0
1
1
1
1
0
0
0
0
0
2
0
1
2
0
1
1
1
1
0
0
0
1
1
0
0
1
0
2
0
1
0
1
2
0
0
1
1
0
2
0
0
0
2
0
1
1
0
0
2
2
0
3
2
0
2
0
1
1
2
1
1
1
0
1
1
0
0
0
1
1
0
0
1
2
0
1
0
2
0
2
1
1
0
0
1
1
1
2
2
5
2
0
0
1
1
0
0
1
0
3
1
1
2
0
2
1
0
0
2
0
0
1
1
1
2
0
0
0
2
2
0
2
1
0
2
1
1
2
0
1
0
2
5
2
1
0
2
2
1
0
0
1
2
0
0
1
0
0
1
1
0
0
1
2
1
0
0
0
0
0
1
0
2
1
1
1
0
1
1
0
0
2
0
2
0
2
1
0
2
0
1
1
2
0
1
1
0
0
0
2
1
1
0
1
1
0
0
0
2
2
1
0
3
2
0
1
1
0
1
2
1
1
2
0
3
1
0
1
1
2
0
1
2
0
0
1
1
4
1
1
1
2
0
1
0
1
1
2
1
0
2
2
1
1
0
2
0
2
2
0
1
0
1
0
0
2
1
1
1
0
0
0
1
0
1
0
0
2
1
1
1
0
1
1
1
0
2
1
1
2
2
0
4
0
1
1
2
1
2
0
1
2
1
0
1
0
1
0
0
1
0
1
1
0
0
1
0
0
0
0
1
1
0
2
0
0
2
2
1
1
0
0
0
1
2
0
1
2
1
2
1
0
1
1
0
1
2
1
0
1
1
0
1
0
0
1
0
2
0
0
0
2
2
1
0
0
1
0
1
1
0
0
2
2
2
0
0
1
1
0
1
2
0
2
0
0
1
0
2
1
0
2
0
0
2
2
2
1
3
1
0
0
2
1
1
1
2
2
1
2
0
0
1
0
1
0
1
1
0
0
2
0
1
0
2
0
0
2
1
2
1
1
0
1
2
0
1
2
1
1
0
2
1
0
0
1
2
0
1
1
1
0
0
1
0
0
1
0
0
0
0
2
1
1
1
0
2
0
1
2
0
1
0
1
0
1
1
5
1
2
1
0
0
1
0
1
1
1
0
2
0
1
1
2
0
2
0
2
1
0
1
2
1
0
1
0
0
2
1
2
2
2
1
2
1
0
1
0
0
0
1
2
0
1
1
1
1
1
0
0
0
1
1
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
1
1
0
2
1
0
0
2
1
0
2
1
2
1
0
1
0
2
0
0
1
2
0
2
0
2
0
0
1
1
0
1
0
1
3
0
0
0
2
0
2
0
1
3
0
0
1
2
1
1
1
1
2
0
0
2
0
0
2
2
1
1
0
2
0
0
2
0
3
1
0
1
0
0
0
0
0
0
0
1
1
2
0
1
0
0
0
1
0
1
1
1
0
1
1
0
2
1
2
1
1
2
0
2
0
1
0
0
0
0
0
1
1
2
0
1
1
1
0
1
1
2
1
1
2
0
1
1
0
0
2
1
1
0
0
2
0
1
2
1
1
0
1
1
0
2
2
0
0
2
2
0
0
0
0
1
1
0
1
1
0
0
0
1
1
2
1
2
1
2
0
2
0
3
0
1
0
0
0
2
0
0
0
0
1
1
0
1
1
1
0
2
2
1
1
0
0
4
1
0
2
0
0
0
2
0
0
1
2
1
1
1
1
0
1
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
2
0
0
0
2
0
1
3
1
1
2
1
1
1
1
1
1
1
1
0
0
0
0
2
0
0
2
0
1
0
0
0
2
1
1
0
2
0
1
0
2
2
2
0
0
1
0
1
2
1
1
2
1
1
1
0
2
0
1
0
2
2
0
2
0
0
0
2
0
0
0
1
0
2
0
2
1
0
1
2
1
1
1
1
1
1
0
0
2
0
1
0
1
3
1
0
1
1
1
0
2
2
0
1
0
2
0
1
0
0
1
2
0
1
0
1
0
0
1
0
2
0
0
0
0
0
2
1
0
1
1
0
2
1
1
0
1
2
2
3
2
1
2
1
1
2
0
1
0
1
1
0
0
1
2
0
0
1
0
1
0
2
1
1
0
1
0
2
2
1
0
2
0
1
2
1
1
2
1
0
0
0
1
2
0
0
0
0
1
1
2
1
1
1
0
2
0
0
0
0
0
1
0
0
1
0
1
2
0
1
1
1
1
1
0
0
1
0
2
0
2
0
1
0
0
1
1
1
1
0
1
1
0
2
0
2
0
0
0
2
1
1
0
1
2
1
2
2
1
0
1
0
1
1
2
0
1
0
1
0
1
1
2
0
0
1
0
2
1
2
1
2
1
1
2
0
0
1
1
0
1
0
1
0
1
2
1
1
2
1
1
0
1
1
2
0
1
1
2
1
1
0
2
1
0
1
1
2
0
1
1
1
1
0
0
0
0
0
2
0
0
2
1
1
1
1
2
0
2
1
1
1
1
0
1
0
1
1
0
2
1
0
1
1
1
1
0
2
0
1
0
0
2
1
0
0
1
0
0
1
0
1
0
2
0
2
1
1
0
0
0
0
0
0
0
2
0
1
0
0
0
1
1
2
0
0
0
2
0
2
1
0
0
1
1
2
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
1
1
0
0
0
2
1
0
0
0
1
0
0
1
1
2
1
2
1
0
0
2
1
1
0
0
2
1
0
1
1
1
1
0
0
0
2
0
0
0
2
1
1
4
0
2
0
1
0
0
0
2
1
0
1
0
0
0
1
0
3
1
1
0
1
0
0
2
4
0
0
1
1
1
0
0
3
2
2
1
2
0
0
1
2
2
0
0
0
1
2
1
1
0
2
2
1
0
1
3
0
0
0
2
0
0
1
0
0
0
2
0
2
1
1
3
2
2
0
2
2
0
3
0
1
2
2
0
1
1
2
0
2
0
1
1
1
0
1
2
0
0
2
1
0
1
3
0
1
1
0
1
1
1
0
1
1
1
2
0
1
1
0
1
1
2
2
1
0
1
1
1
1
0
1
1
1
1
1
2
2
2
2
0
0
1
2
1
0
1
1
1
1
1
1
0
0
1
0
1
1
0
0
1
1
0
1
2
0
3
1
1
1
1
2
0
0
1
0
0
0
0
1
1
2
1
1
2
1
0
2
1
1
1
0
0
0
1
0
0
2
0
0
0
0
1
2
1
1
0
2
1
1
0
0
1
1
2
0
1
1
0
2
1
2
0
1
1
2
1
1
1
0
2
2
2
1
1
1
2
0
1
1
1
1
2
0
1
1
0
1
2
2
3
1
0
0
1
0
0
2
0
2
0
2
0
0
1
0
2
0
0
0
2
1
1
0
2
0
1
0
1
1
1
2
0
1
1
1
1
1
2
0
1
1
1
2
0
1
1
0
1
0
1
0
1
2
1
0
1
0
0
0
1
0
0
1
0
0
1
0
0
1
2
0
1
1
2
2
0
1
0
1
0
2
2
1
1
2
2
2
1
2
0
2
1
1
0
1
1
1
1
1
2
0
1
1
2
2
0
0
1
0
0
0
2
1
0
2
0
2
0
0
1
0
1
1
1
2
0
1
2
1
2
1
2
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
2
0
1
0
0
0
1
1
1
0
2
1
1
0
2
0
0
1
1
0
0
0
0
0
0
1
2
0
2
1
0
0
0
0
0
0
0
0
2
1
0
2
1
1
1
3
1
1
1
0
0
1
0
1
2
0
1
0
0
2
1
1
1
0
0
0
1
2
1
1
0
0
2
0
1
1
0
2
1
0
1
0
0
0
1
0
0
0
1
0
2
0
1
0
0
1
0
0
1
1
0
2
1
2
2
1
2
0
0
1
0
0
2
1
0
0
0
0
1
0
0
0
2
0
0
0
1
0
1
1
2
2
2
1
1
2
1
1
0
0
0
1
0
0
0
2
0
1
2
0
1
0
0
0
1
1
2
0
2
1
1
1
0
1
0
2
1
2
1
2
2
0
1
0
1
0
0
3
0
0
0
0
1
1
0
2
0
0
1
1
0
0
1
1
0
2
2
1
2
0
1
0
2
2
1
2
0
2
2
0
0
0
1
0
0
0
1
0
0
0
1
1
1
1
1
1
0
1
1
0
2
0
2
0
1
1
0
1
1
0
2
1
0
0
2
1
0
3
3
0
1
1
0
0
0
1
1
1
1
1
0
1
2
1
0
2
1
1
0
2
1
3
1
1
0
1
0
2
0
0
0
1
1
2
0
0
3
2
0
0
1
2
0
0
0
0
0
0
1
0
2
1
1
2
1
0
0
0
0
2
2
0
0
1
0
0
1
0
2
0
1
0
2
1
0
1
1
0
1
0
1
0
0
0
1
1
1
0
2
2
1
1
1
1
0
1
0
0
1
0
1
1
2
0
0
2
0
2
1
1
1
0
2
2
0
1
0
1
1
0
0
2
1
0
1
0
0
0
0
0
0
1
2
2
1
0
1
1
1
0
1
0
1
1
1
1
0
1
1
0
0
1
1
2
0
0
0
2
1
2
0
1
0
2
0
0
0
0
0
1
1
0
2
0
0
0
1
2
0
2
1
0
0
1
0
1
1
2
0
2
2
0
2
0
1
2
2
0
1
2
1
2
0
0
1
0
0
0
1
0
1
0
1
2
0
0
2
2
1
0
1
0
0
0
2
1
2
1
0
1
1
1
0
1
1
1
1
2
2
0
0
1
0
0
0
0
2
1
0
1
2
2
1
1
0
0
0
1
2
7
1
1
1
1
1
2
0
0
0
2
0
1
0
0
0
0
1
1
0
0
0
1
1
2
1
0
0
1
1
1
1
1
0
1
1
1
1
2
0
0
1
0
1
1
1
2
0
1
1
1
1
0
1
0
1
0
0
1
0
1
2
2
0
0
0
2
0
0
0
1
0
1
1
0
1
2
2
0
1
2
1
1
0
0
0
2
1
2
2
0
1
1
1
1
0
0
0
1
0
0
0
0
0
1
2
2
0
2
4
0
0
0
2
1
1
0
0
1
0
1
1
2
1
0
1
1
1
2
0
2
2
0
1
1
1
2
1
1
1
1
0
2
1
0
2
1
5
1
1
0
1
0
0
0
0
1
0
1
0
1
1
2
1
1
3
0
0
0
2
0
0
1
0
2
2
1
1
2
0
0
0
1
1
2
0
0
1
0
1
1
1
0
1
1
0
0
1
0
1
0
1
1
1
0
1
0
1
0
0
1
1
1
0
1
0
1
1
0
1
1
0
0
1
2
0
0
0
2
1
0
0
1
0
0
0
1
1
1
1
2
2
0
2
2
1
1
1
0
0
0
1
1
1
1
1
2
1
0
0
0
1
0
1
1
2
1
0
2
1
1
2
0
2
1
1
2
1
0
1
2
0
0
0
0
2
2
0
2
0
0
2
1
0
0
1
1
2
0
0
1
0
1
1
1
1
1
1
0
2
2
2
3
2
1
0
2
0
0
0
0
0
0
0
1
1
0
1
0
0
1
1
2
1
1
0
1
0
1
2
0
1
0
2
0
1
1
1
0
0
0
0
0
0
1
2
1
0
2
1
0
1
0
0
0
1
2
0
0
2
0
1
0
2
0
1
1
0
0
1
3
2
1
0
0
0
0
2
1
1
1
1
1
0
0
2
1
2
1
1
1
1
0
0
1
2
2
2
1
1
1
0
0
0
0
1
0
1
2
1
2
0
2
0
3
1
1
0
2
1
0
0
1
0
0
1
0
1
0
2
1
0
0
2
2
1
4
2
1
2
0
2
2
2
1
2
1
1
2
0
1
0
1
0
2
0
0
1
0
1
0
0
2
2
0
0
1
2
1
2
0
2
2
0
1
2
3
1
0
2
0
2
2
0
0
0
1
1
2
2
1
0
0
1
0
1
0
0
0
1
2
1
1
1
0
1
3
0
0
2
0
2
2
2
1
0
0
1
0
1
1
2
1
0
2
1
1
1
1
2
0
2
2
0
4
0
0
1
0
2
0
1
1
0
0
1
1
1
0
2
2
2
0
1
0
0
2
0
2
2
0
0
0
2
1
1
1
0
0
1
2
1
1
2
1
1
2
0
0
0
0
2
0
2
0
2
0
1
2
0
1
0
1
1
0
1
1
0
0
2
0
1
1
1
0
2
1
0
0
0
1
1
0
0
1
0
1
0
1
0
1
1
0
0
0
1
0
0
1
0
1
2
0
1
1
0
1
0
1
0
1
0
1
0
1
1
0
0
0
2
1
0
1
0
2
2
2
2
2
1
1
1
1
0
2
0
0
1
0
1
1
2
2
2
0
0
1
2
2
0
2
1
3
1
1
0
1
0
0
0
0
0
0
1
1
1
1
3
0
3
0
0
0
2
0
0
0
1
0
1
1
1
2
1
1
2
0
1
1
2
2
1
1
2
0
0
1
0
2
0
0
0
2
1
0
0
2
0
0
0
2
0
1
1
1
2
3
3
2
0
2
2
1
0
1
1
0
1
0
0
1
1
1
0
1
0
2
2
2
1
1
0
0
2
1
0
1
0
0
0
3
0
1
2
1
1
2
1
0
0
0
2
1
1
1
1
1
0
2
1
1
0
0
2
2
0
2
1
2
2
1
2
1
1
2
0
0
0
0
2
1
0
1
2
0
1
0
1
0
2
1
2
1
1
1
0
0
1
1
1
2
0
0
1
2
0
0
0
1
0
2
0
1
1
0
1
0
0
2
0
2
0
0
1
1
1
1
0
2
0
1
1
0
0
1
0
1
0
0
1
0
0
1
0
0
0
2
1
1
0
0
0
1
1
1
1
1
0
2
1
1
0
0
0
1
3
0
1
2
2
1
1
1
0
2
0
1
2
0
1
1
1
0
2
1
0
1
1
0
2
0
0
1
0
0
1
0
0
0
1
0
0
1
1
0
0
2
0
1
2
0
1
2
0
0
1
1
0
3
1
2
1
0
0
1
0
2
1
0
1
1
1
0
2
0
1
1
2
0
0
1
0
0
1
0
1
1
1
1
1
1
1
0
0
1
1
0
1
1
2
2
2
2
0
2
1
0
1
1
1
0
1
1
1
1
0
1
2
1
2
2
0
1
2
1
2
0
0
0
1
1
0
2
2
0
1
0
0
1
0
0
2
1
2
0
1
0
2
0
1
0
2
2
0
1
1
1
1
1
0
1
1
1
1
1
0
0
1
2
0
1
0
0
2
0
1
1
1
0
0
0
0
1
0
0
2
1
2
1
0
1
0
0
1
0
0
0
1
1
2
0
0
0
1
1
1
0
0
1
2
1
0
1
0
1
2
0
0
1
0
2
3
3
0
0
1
1
1
2
0
1
1
2
5
0
1
0
2
1
3
1
0
1
1
1
0
0
0
1
2
0
0
0
1
1
0
1
2
1
0
1
0
1
0
0
1
2
1
2
0
1
0
0
0
2
0
2
2
0
2
2
1
2
0
3
0
1
0
0
0
1
1
1
0
0
0
0
1
0
1
1
0
0
1
1
2
0
0
1
1
0
0
1
1
1
0
0
1
0
3
1
0
0
1
1
1
0
1
0
2
2
0
0
1
2
1
1
1
1
1
1
1
1
2
0
1
0
1
0
2
1
0
0
1
2
0
2
0
0
0
0
1
1
0
1
1
0
2
0
1
0
2
1
0
0
0
3
0
0
0
2
1
2
0
1
1
1
1
0
0
1
0
1
0
1
0
0
1
1
0
0
1
2
0
1
1
0
0
1
2
1
0
3
2
0
2
1
0
0
1
0
0
1
2
1
2
1
2
1
1
1
1
0
0
0
0
0
2
1
0
0
0
1
0
1
0
0
2
2
1
1
0
1
1
1
1
1
1
0
0
0
0
2
1
0
0
0
0
1
0
0
0
2
0
0
1
2
0
1
1
2
0
0
0
1
2
2
0
0
0
0
2
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
2
0
1
1
1
1
0
0
0
1
0
2
1
0
1
0
2
0
0
1
2
1
1
0
2
3
2
2
1
0
0
0
1
0
1
1
0
0
0
1
1
2
0
0
0
0
1
0
1
1
2
2
1
2
1
0
0
1
0
2
1
0
2
2
0
0
0
0
1
1
1
1
1
0
1
2
2
0
2
2
2
0
1
1
0
1
1
0
1
3
1
1
0
1
0
0
1
1
1
1
1
0
1
1
2
1
1
2
0
0
0
0
1
2
2
0
1
1
0
1
0
0
3
2
2
0
0
2
0
0
0
1
2
1
2
0
0
1
1
1
1
0
0
0
1
2
0
0
0
2
0
0
1
1
0
3
1
1
1
0
1
1
1
1
1
1
0
1
1
0
0
1
1
0
0
1
3
1
0
1
0
0
1
0
0
2
1
2
1
2
2
1
1
1
0
0
1
2
2
0
1
0
1
1
1
1
2
1
0
0
2
1
1
2
0
0
2
0
0
0
1
0
1
1
0
1
2
1
1
0
0
3
1
1
2
0
0
1
2
0
0
1
0
0
1
1
2
2
2
0
2
2
1
1
0
1
1
3
0
1
1
2
2
2
2
0
2
0
0
1
2
1
1
0
2
0
1
1
1
1
0
1
0
1
1
0
1
0
0
2
1
1
0
3
1
0
1
1
1
1
0
2
2
0
1
1
1
0
0
0
0
0
0
2
0
1
1
0
2
1
0
1
1
1
0
0
0
0
2
1
0
4
1
1
0
1
1
1
2
1
0
1
1
2
1
2
0
2
0
1
0
1
0
2
3
2
0
0
0
0
1
0
1
2
0
1
1
1
0
1
2
0
3
1
0
0
1
1
0
1
0
0
0
1
0
0
1
1
2
1
1
5
2
1
1
2
1
1
4
1
2
0
1
0
0
3
1
1
1
0
1
1
0
1
1
1
2
1
1
3
1
1
2
0
2
0
0
0
0
2
1
2
2
0
0
1
1
2
0
2
0
1
0
0
0
1
0
1
2
0
0
0
0
0
2
0
1
1
1
1
0
1
2
0
0
0
0
0
2
0
1
2
1
0
0
0
2
1
1
2
2
1
2
1
0
1
0
2
1
2
0
0
0
1
0
0
1
1
0
1
0
0
1
1
2
1
0
2
2
1
1
1
2
2
2
0
1
1
1
0
2
3
2
2
1
2
0
0
0
2
2
1
0
0
0
2
0
2
1
0
0
0
2
0
0
2
1
0
0
0
1
1
2
3
0
0
2
0
2
0
0
0
1
1
1
1
1
1
2
0
2
0
0
1
1
2
2
2
2
0
0
2
2
2
2
0
1
0
0
1
0
0
0
2
1
1
2
2
1
1
0
0
2
2
0
1
1
1
2
1
0
1
2
2
1
2
2
1
1
1
0
1
1
0
1
2
2
0
1
1
0
0
1
0
1
1
0
0
1
0
0
0
2
0
2
0
1
1
0
0
1
0
1
1
2
0
0
0
1
0
0
0
1
0
1
0
0
2
1
0
1
1
1
0
2
2
0
1
0
2
1
0
1
0
0
1
2
1
1
0
1
2
0
0
3
1
2
0
0
1
0
1
0
1
0
1
1
2
0
0
1
0
0
1
0
2
1
0
1
0
0
1
0
0
2
0
0
1
0
2
2
2
2
0
0
0
0
1
1
2
0
0
0
1
1
0
0
2
2
1
1
1
2
1
0
0
0
1
2
1
1
0
1
1
0
1
0
1
1
1
0
2
2
1
2
0
1
1
1
1
2
2
0
1
0
0
1
1
6
1
1
2
0
2
0
1
1
0
1
0
0
0
0
1
0
0
1
1
0
1
2
0
0
0
2
1
0
2
2
0
0
0
0
1
0
0
2
0
0
1
0
0
0
2
0
0
1
2
0
1
1
1
1
1
2
2
1
1
0
2
0
2
1
0
1
0
0
0
0
1
2
3
1
2
0
2
2
0
1
2
1
2
1
0
0
0
2
0
0
1
0
2
1
0
0
2
1
1
2
1
2
2
0
0
1
0
1
1
2
0
0
3
2
0
0
1
1
1
0
1
2
0
1
1
0
2
2
1
0
1
0
0
0
0
1
1
2
1
2
1
0
1
2
0
2
2
1
1
1
1
1
1
0
1
0
1
1
2
1
1
2
0
1
2
0
1
1
1
0
0
1
0
0
2
2
2
2
2
0
0
0
2
1
0
2
0
0
1
0
2
0
0
1
1
0
0
1
0
1
2
0
2
1
0
1
2
1
0
2
1
2
0
0
1
0
1
0
1
2
1
1
0
0
1
0
0
0
1
1
0
1
0
0
2
1
1
0
1
1
1
0
1
0
1
0
2
0
0
0
1
1
2
2
1
2
0
1
0
0
1
1
0
1
2
2
1
0
0
0
2
1
0
1
0
0
0
0
1
0
2
1
2
0
1
0
1
1
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
2
2
1
0
1
1
0
1
0
1
1
0
1
0
0
2
0
0
2
1
0
2
0
0
1
1
0
1
0
1
1
1
0
0
1
0
0
2
1
0
2
0
2
1
0
0
0
0
0
2
1
1
1
1
3
1
0
1
2
2
0
1
1
1
0
1
1
1
0
0
2
1
2
2
1
0
1
1
9
2
0
2
1
0
0
0
1
0
1
0
0
1
1
2
1
1
0
1
1
1
0
1
2
0
1
0
0
0
0
0
0
1
2
1
2
2
1
1
0
1
0
1
0
0
1
1
1
0
0
1
0
0
3
0
2
1
2
1
0
5
0
4
1
1
0
0
0
2
1
1
0
0
1
0
0
2
1
0
2
1
1
0
0
2
3
0
0
1
2
2
0
0
1
2
0
1
1
2
1
0
0
2
0
1
1
1
2
4
1
1
0
0
1
2
0
0
1
1
1
1
0
1
0
0
2
0
2
1
1
1
0
1
2
1
1
0
1
2
0
1
1
0
2
1
3
1
0
1
2
1
0
2
2
1
1
0
2
0
1
1
1
0
0
1
0
1
0
0
0
0
0
2
1
2
2
0
0
1
0
1
1
1
2
0
0
0
2
0
2
0
2
2
0
1
2
1
0
0
1
0
0
2
1
2
0
0
1
0
1
0
0
1
0
0
1
0
1
1
1
0
1
0
1
0
1
2
0
2
1
0
0
0
0
0
1
1
1
0
1
0
2
1
1
1
1
0
2
0
2
0
2
1
2
2
2
1
0
0
1
0
1
0
1
0
1
1
2
0
1
0
1
0
0
1
0
0
1
1
0
1
2
2
0
1
3
1
1
0
0
0
2
0
0
2
1
0
1
2
1
1
2
1
2
0
1
1
1
0
1
0
0
2
1
1
2
0
0
2
1
0
2
1
1
0
2
1
1
1
1
0
0
2
0
0
1
0
0
0
1
1
1
2
0
1
1
0
1
2
1
0
1
0
2
1
2
0
1
1
1
2
1
0
2
2
1
1
1
1
2
1
2
0
3
0
2
1
0
0
0
0
2
0
1
0
0
1
2
2
2
1
0
1
0
0
1
1
1
2
0
0
1
2
2
1
0
1
1
4
0
0
0
0
0
1
1
1
0
2
0
0
0
2
0
2
1
2
0
2
1
2
1
2
1
1
0
1
1
1
1
1
1
1
0
1
0
2
1
1
0
0
1
1
0
1
1
1
0
0
2
2
2
2
0
0
1
0
1
2
0
1
3
0
1
0
2
2
0
1
1
1
0
0
0
3
0
0
0
0
0
1
0
2
1
1
2
0
0
2
2
1
2
2
0
2
0
1
0
1
0
0
0
0
1
1
1
0
2
0
0
0
1
1
0
0
0
2
0
1
1
1
1
1
1
1
2
1
0
0
1
0
0
1
1
1
1
1
1
1
2
1
1
2
1
1
0
1
1
1
0
1
0
1
1
1
1
0
0
0
1
2
0
0
1
1
1
0
2
1
0
1
1
0
2
2
1
1
1
2
1
0
0
0
0
1
2
0
0
1
1
2
1
2
1
2
0
2
2
0
1
3
1
2
1
0
0
0
1
1
2
1
1
1
0
2
0
1
1
1
1
2
0
0
1
2
0
0
0
0
1
1
0
0
1
0
2
0
0
1
2
2
2
2
2
0
1
1
0
2
2
0
1
0
1
1
2
2
1
0
1
0
0
1
1
1
1
0
2
2
0
1
1
0
0
1
2
2
0
1
1
0
2
0
0
1
1
2
1
1
2
1
2
2
0
0
0
1
1
2
1
0
3
0
1
0
0
1
0
0
1
0
0
0
1
2
2
0
1
0
1
0
2
2
0
0
0
0
1
0
1
1
2
1
1
0
1
0
2
0
0
0
1
2
2
1
1
1
2
1
2
0
1
2
2
0
0
0
0
2
0
0
1
1
0
1
0
0
1
0
0
1
0
2
0
0
0
2
2
0
0
0
0
1
2
0
0
0
0
2
1
0
2
2
0
0
2
0
0
1
1
1
1
1
1
1
1
2
1
1
1
1
0
2
1
0
0
1
2
1
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
2
2
1
0
2
1
1
0
1
1
1
2
0
1
0
2
1
0
1
1
1
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
2
3
2
1
2
0
0
1
1
0
0
0
1
1
1
0
0
1
0
0
1
0
1
0
0
0
0
2
0
1
2
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
3
2
2
2
0
0
1
2
0
1
1
0
2
0
1
1
0
0
1
0
0
0
1
1
0
0
0
3
0
1
0
0
0
0
0
2
1
2
1
0
2
1
1
0
0
0
0
0
1
0
0
0
0
0
2
1
1
0
0
2
0
0
1
2
1
2
0
2
0
0
0
0
1
2
1
0
0
0
2
0
1
3
1
1
0
1
0
2
1
2
0
1
0
0
0
0
1
1
1
1
1
2
0
0
0
2
1
0
2
1
2
1
0
0
0
1
1
2
2
3
0
1
1
0
1
0
1
1
0
0
0
1
0
0
0
2
1
2
2
1
1
1
1
2
0
1
2
0
0
1
2
2
0
2
2
1
2
0
2
1
1
0
2
1
0
0
0
1
0
1
0
2
1
0
2
2
0
2
1
1
2
0
1
2
1
2
0
0
1
2
0
0
0
0
0
1
0
2
0
1
2
0
0
0
0
0
2
2
1
2
2
0
2
1
0
1
0
1
0
0
0
0
1
0
0
1
1
0
0
0
2
1
1
1
1
0
1
0
0
1
1
2
2
2
1
0
1
1
0
0
2
2
0
0
0
1
1
2
0
2
1
1
1
0
0
1
0
0
0
1
1
1
2
2
1
2
1
1
0
2
1
1
0
0
2
0
0
0
0
0
0
1
1
2
0
1
0
0
1
2
2
0
0
2
1
0
1
0
1
1
1
2
2
1
1
0
1
0
1
0
1
0
0
2
0
1
1
0
1
0
1
0
0
1
0
0
1
2
0
0
0
1
0
2
1
1
1
1
1
1
1
0
1
0
1
0
2
2
1
1
1
1
0
2
1
0
0
3
2
2
0
0
2
1
1
2
1
0
1
2
0
2
1
0
1
0
0
1
2
1
0
1
2
1
0
1
0
0
1
0
0
0
2
0
0
0
0
0
1
1
1
1
0
0
1
1
0
0
0
1
1
0
1
0
0
1
2
2
0
2
1
2
0
2
2
2
0
0
1
0
1
1
0
1
1
2
0
0
0
1
0
1
0
0
1
1
2
0
0
1
0
1
1
2
1
2
0
1
1
2
0
0
1
0
0
0
2
2
2
1
0
1
1
2
1
1
0
2
1
0
2
1
0
1
1
1
0
0
1
0
2
1
1
1
0
0
0
0
1
1
1
1
1
3
2
1
0
1
0
1
2
0
0
0
0
1
1
10
0
1
0
0
1
1
2
0
2
2
2
2
2
1
0
0
0
2
1
2
2
2
2
0
2
2
1
0
0
1
2
0
0
0
0
2
0
0
2
1
1
2
2
0
2
0
1
2
1
0
2
1
2
1
1
2
0
1
1
0
0
0
2
2
2
0
2
0
0
2
0
1
1
1
0
1
1
0
0
1
0
0
1
1
1
0
0
0
0
1
1
1
1
0
0
0
0
1
2
1
0
2
0
0
1
2
0
0
0
1
1
2
0
1
1
1
2
2
1
1
2
0
1
3
1
2
2
2
0
0
2
0
1
0
2
1
1
0
1
1
0
1
0
0
2
2
1
2
1
2
0
2
1
1
0
1
1
1
0
0
1
1
0
0
2
1
1
2
0
0
0
0
1
0
2
1
1
1
2
2
0
0
2
1
2
1
2
0
1
1
1
0
1
1
2
0
0
0
0
0
1
0
0
2
0
0
0
1
0
1
1
0
0
1
0
0
2
0
0
1
1
1
0
1
1
1
0
0
1
0
1
0
0
1
1
1
1
0
0
2
0
1
1
2
0
0
1
0
0
0
0
1
1
0
1
2
0
2
1
0
2
0
1
1
0
0
1
1
0
3
1
0
2
3
1
0
0
0
0
1
2
1
2
2
1
0
1
2
0
0
2
0
0
2
0
1
1
2
0
0
1
1
0
1
1
1
0
1
1
1
0
1
0
2
2
1
0
1
1
0
0
1
0
0
1
0
0
2
1
3
0
2
2
0
2
2
1
1
1
0
1
0
2
1
0
0
0
2
1
1
0
1
2
1
0
0
1
1
1
0
1
2
0
0
2
0
1
2
1
0
1
1
0
0
0
2
2
1
1
0
0
1
0
1
1
4
1
0
1
1
0
2
1
1
2
1
0
1
1
1
0
1
1
2
0
1
1
1
2
0
0
0
0
0
0
0
1
1
0
0
0
1
1
1
0
1
0
0
0
0
1
1
1
0
1
0
0
1
2
1
0
1
1
0
2
2
2
0
1
1
0
1
2
1
0
0
0
1
0
2
1
2
1
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
1
1
2
0
0
1
0
0
2
0
0
0
2
1
1
0
1
1
1
2
2
2
1
2
1
2
2
1
0
1
0
2
0
2
0
2
1
0
0
0
1
1
2
1
2
1
1
1
0
1
2
0
0
1
2
1
1
0
1
0
0
0
2
0
2
0
1
2
2
1
0
1
1
2
0
2
1
0
0
3
0
2
2
1
1
0
2
3
3
1
2
2
1
2
0
0
2
1
2
0
0
0
0
0
0
1
1
0
1
2
0
3
0
0
1
1
0
2
1
2
1
0
0
0
0
0
2
0
1
2
2
1
2
1
1
2
0
0
1
1
2
1
1
1
2
1
2
1
1
0
0
2
3
1
1
1
0
0
2
2
0
1
0
1
4
2
1
2
0
0
2
2
0
2
1
2
0
1
1
1
0
2
0
0
0
1
1
1
1
0
1
1
1
1
0
2
0
0
1
0
2
0
0
1
1
1
0
1
1
2
0
0
1
2
0
0
0
1
1
1
0
2
0
0
2
0
2
1
1
1
0
0
1
0
0
1
0
0
1
1
0
2
0
1
1
0
0
1
0
1
2
0
0
1
1
0
0
1
0
0
1
0
2
1
0
1
2
1
0
2
0
0
0
1
0
1
2
0
1
0
2
0
0
2
1
2
1
0
2
0
0
0
1
0
1
0
2
1
1
1
1
0
1
2
2
2
0
1
2
1
0
2
0
2
0
1
1
0
2
0
1
2
0
1
0
0
0
1
0
0
0
3
3
1
2
1
0
0
0
1
0
0
0
1
2
0
0
1
0
0
1
0
1
0
0
2
1
1
1
1
0
0
1
0
1
1
1
0
0
1
2
1
0
0
0
0
0
1
2
0
1
0
1
1
0
1
0
1
0
2
0
0
1
1
0
1
1
2
1
1
1
1
0
0
0
0
0
1
1
2
0
2
2
1
0
0
2
2
1
0
1
0
0
1
1
0
0
1
0
2
0
1
1
4
1
2
1
0
1
0
1
2
1
0
1
0
0
1
3
1
1
1
0
1
1
1
1
2
2
1
2
0
2
1
1
2
1
0
1
1
0
0
1
0
1
2
0
0
2
1
1
0
0
2
0
0
1
2
1
0
0
1
1
0
0
1
2
2
2
1
0
0
1
0
0
1
0
1
2
0
1
2
1
0
1
0
1
0
0
1
1
1
2
2
0
1
1
1
0
0
0
0
2
2
0
1
0
1
1
1
1
0
1
0
0
0
0
1
2
1
1
1
1
1
1
0
1
1
1
2
1
1
0
1
2
0
0
2
1
0
1
0
0
0
2
0
2
2
0
0
2
2
2
2
1
1
0
1
0
0
0
0
2
1
0
0
1
0
0
0
2
1
1
1
2
0
0
1
1
0
2
1
1
1
1
0
0
0
1
3
1
1
0
2
2
2
0
2
0
0
2
2
0
0
2
0
1
2
0
0
1
0
2
0
1
0
1
0
2
2
0
0
0
2
0
0
2
2
2
1
0
0
2
2
2
1
0
1
1
3
0
0
0
1
0
2
0
0
2
1
1
1
2
1
0
0
1
0
0
0
1
0
0
1
1
2
1
0
1
0
2
1
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
1
1
1
1
1
0
0
1
0
1
0
0
1
2
1
1
0
1
0
1
0
1
2
2
2
1
2
1
0
1
2
0
2
0
1
0
1
0
0
2
3
0
1
0
0
1
3
1
1
1
1
1
0
0
1
1
1
2
2
0
1
1
0
0
1
3
0
1
0
0
1
1
1
2
2
0
1
0
1
1
0
0
0
1
1
0
0
1
0
2
2
1
1
1
2
0
2
0
0
1
0
2
0
1
1
1
0
0
1
1
0
0
1
1
0
1
3
0
0
0
1
1
0
1
1
3
0
0
0
1
0
0
1
2
0
1
0
0
0
2
1
0
1
0
1
0
1
1
0
2
2
1
0
0
1
1
3
2
0
0
1
0
0
2
1
1
0
0
0
0
3
2
0
0
0
1
0
0
2
0
0
2
0
1
2
0
0
1
2
1
1
1
1
0
1
1
1
0
2
1
1
2
1
1
0
0
1
2
0
2
2
0
1
1
0
0
2
1
1
1
0
0
3
0
1
0
0
1
2
0
1
0
2
1
0
2
0
0
1
0
1
1
0
1
0
0
0
0
1
1
0
0
2
2
1
2
1
2
2
2
0
1
0
0
0
0
1
2
0
2
1
0
1
1
2
0
3
1
1
0
2
1
0
2
2
0
1
1
0
0
2
0
0
2
2
1
0
0
1
2
2
2
0
1
0
0
1
1
1
1
1
0
1
1
1
1
1
0
2
0
0
1
1
2
0
1
2
1
0
0
2
1
0
0
0
0
0
0
1
2
2
0
0
0
1
0
1
1
1
1
0
0
0
1
0
0
0
0
2
1
1
1
1
0
2
0
0
1
1
0
1
1
2
0
0
2
0
1
2
1
0
0
1
0
0
0
0
1
1
0
1
1
2
0
1
2
2
0
1
1
4
1
0
1
0
1
0
0
1
1
0
2
0
0
3
0
2
1
2
0
0
1
2
0
0
0
0
1
2
0
0
3
2
1
1
1
1
0
1
2
1
0
1
0
0
1
1
0
2
0
1
0
1
1
2
0
0
0
0
0
2
1
0
2
0
1
1
1
2
0
0
1
0
1
2
1
3
0
0
1
0
1
0
2
1
1
1
1
1
0
0
1
0
1
2
2
2
1
1
0
1
0
0
0
0
2
0
0
0
1
0
0
2
2
0
3
2
2
3
1
2
2
0
1
0
2
1
1
1
0
1
1
1
0
1
1
0
1
1
2
1
2
0
1
2
0
0
1
0
1
1
1
1
1
0
0
1
1
1
1
0
0
0
0
0
1
0
0
1
0
0
1
0
2
0
1
1
1
1
2
1
1
1
3
1
1
1
1
1
1
2
2
0
1
2
1
0
0
0
3
0
0
3
0
0
0
0
2
0
0
1
1
1
0
0
0
1
1
0
0
1
0
1
1
1
1
1
1
0
0
0
0
0
1
1
1
1
0
2
1
1
1
1
1
0
0
0
1
0
1
1
0
1
2
3
1
1
3
0
3
2
2
0
0
0
0
1
0
0
1
1
0
1
0
1
1
1
1
0
0
3
0
0
0
2
0
0
0
0
1
0
0
2
1
0
0
1
2
0
0
1
2
0
0
1
0
3
0
3
1
0
1
0
1
1
0
2
0
1
1
0
2
0
0
1
4
1
1
0
1
1
2
2
0
0
2
1
0
2
1
0
1
0
0
2
1
0
0
0
1
1
1
0
2
2
0
0
1
1
0
0
1
1
1
0
2
0
1
1
0
1
0
2
0
1
1
1
1
2
0
0
2
0
2
2
1
0
1
1
2
1
2
1
0
1
1
1
1
1
2
0
0
1
2
2
1
2
1
0
0
0
0
0
1
3
1
0
1
0
0
2
0
2
0
0
2
1
0
1
2
1
1
4
1
1
1
0
0
1
2
1
1
0
1
1
0
1
0
2
2
1
2
0
2
1
0
1
0
1
0
1
0
0
0
0
1
0
0
0
3
0
2
1
0
0
0
2
1
0
1
0
0
1
1
0
0
1
0
1
0
1
1
2
1
1
0
2
1
0
0
1
2
0
0
0
2
2
1
0
1
1
1
2
4
1
0
1
2
1
2
2
1
0
1
1
0
1
1
1
1
1
1
0
2
1
0
1
1
2
2
1
1
0
0
0
0
1
2
0
0
0
0
1
0
0
1
0
1
2
1
2
1
3
0
1
1
2
0
1
1
0
1
1
0
0
0
1
0
0
0
2
1
0
1
0
0
0
0
1
0
1
2
2
3
0
0
3
2
1
0
1
2
1
1
1
0
2
0
0
0
0
1
2
0
0
1
1
0
0
0
0
0
2
1
0
0
2
2
0
0
0
1
3
1
0
1
0
1
1
2
1
1
1
0
0
2
0
0
1
0
0
0
1
0
2
1
0
0
1
2
1
1
1
1
1
2
0
0
2
0
0
1
1
0
1
1
2
0
0
1
1
1
0
2
1
1
1
1
0
2
2
0
1
2
1
0
1
2
0
2
1
0
1
2
1
2
2
1
1
0
1
0
2
0
2
2
0
2
0
1
2
2
1
1
0
1
0
2
1
1
0
0
2
0
0
0
0
0
0
0
0
2
1
2
2
3
1
1
0
1
0
0
0
2
1
1
1
0
2
0
1
1
1
0
1
0
2
1
0
0
0
0
1
2
2
1
2
0
0
1
0
1
1
1
0
0
1
1
0
2
1
0
0
1
0
2
1
2
1
1
0
0
0
0
0
0
1
1
0
0
1
2
0
2
0
1
0
1
0
2
0
1
0
3
1
1
0
1
0
1
2
0
2
0
3
1
2
0
0
1
2
1
1
0
0
2
0
1
0
0
2
0
1
0
1
0
0
0
2
0
1
2
0
0
1
0
2
0
0
0
0
0
1
3
2
0
0
1
0
1
0
1
1
0
1
2
0
1
2
1
0
1
1
2
2
1
1
1
1
2
2
2
1
1
0
0
1
0
2
0
0
1
1
1
1
0
0
2
1
0
2
2
1
0
0
1
1
1
3
1
0
2
1
2
0
0
0
0
1
1
2
2
1
2
1
2
2
1
2
0
1
0
0
0
2
2
0
0
0
0
1
0
1
1
2
1
2
0
2
1
0
1
0
1
2
0
1
1
1
1
0
1
2
0
0
1
0
0
0
0
0
1
1
1
1
2
2
0
1
1
1
0
2
1
2
1
0
0
0
0
0
1
0
1
0
1
0
1
1
0
0
0
2
2
1
0
0
1
0
1
1
0
1
1
0
2
0
2
0
1
3
0
1
1
1
1
0
0
2
1
0
1
1
2
1
1
2
1
0
1
3
0
1
0
0
1
2
0
1
0
1
1
0
1
0
1
1
1
2
1
0
0
0
2
1
1
1
1
2
1
1
0
0
0
0
1
1
2
1
2
1
0
1
1
1
0
3
1
0
1
4
1
1
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
1
1
0
1
2
2
1
3
0
0
0
0
2
2
0
1
0
1
1
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
2
0
1
1
0
1
1
0
1
1
0
0
2
1
1
0
0
0
0
1
1
0
1
2
1
1
1
0
1
1
2
1
0
0
1
1
0
1
1
2
2
1
0
0
3
2
0
0
2
3
1
1
1
0
2
0
2
2
0
0
2
1
1
1
1
1
2
0
1
1
0
1
1
1
0
1
1
0
0
0
0
0
1
0
2
1
0
0
1
0
1
0
0
0
1
3
1
1
2
1
1
2
2
2
0
1
1
2
1
2
2
2
0
1
0
0
2
0
2
0
3
1
0
1
0
0
0
3
1
0
1
0
1
0
1
1
1
2
2
0
0
2
0
1
2
2
1
0
1
0
0
0
1
1
1
0
1
0
1
0
0
1
1
2
1
0
0
1
1
2
1
1
0
2
2
2
0
2
0
1
1
2
0
1
0
0
1
0
2
2
0
2
2
0
0
0
2
0
1
0
0
2
1
0
1
2
0
0
1
1
1
1
1
0
1
1
0
2
0
4
2
0
0
2
1
0
0
4
1
1
1
1
2
2
1
1
2
0
0
1
1
2
2
2
0
1
1
0
0
0
0
0
1
0
1
1
3
0
1
3
0
0
1
0
1
1
2
0
0
0
1
1
1
1
1
1
0
1
3
1
0
1
1
0
0
1
1
1
1
2
1
1
0
1
1
0
0
1
2
1
1
1
0
1
0
0
0
2
0
1
2
1
0
1
1
2
4
1
0
2
2
2
0
1
1
1
0
0
0
1
2
1
0
0
1
0
0
2
0
0
0
0
2
1
2
2
1
1
0
2
0
1
1
0
2
1
0
0
1
2
1
0
1
1
0
2
2
1
2
2
2
0
1
0
1
1
0
0
1
2
0
1
0
4
1
1
1
0
1
0
0
2
2
0
1
1
2
2
0
2
1
2
2
0
1
1
1
1
0
0
3
1
1
1
1
1
1
0
0
0
0
1
0
2
0
0
0
1
1
2
0
0
1
1
2
2
1
0
2
1
1
1
0
2
0
1
0
0
1
0
0
0
0
2
0
2
0
1
1
1
0
1
2
2
1
1
1
1
0
0
1
0
2
0
1
1
1
1
3
1
0
0
0
0
1
2
1
0
2
2
0
0
0
1
1
0
2
2
2
0
0
0
0
1
0
0
0
1
0
1
3
2
1
0
0
0
1
2
0
2
0
1
2
0
0
1
1
0
2
0
1
1
2
0
1
0
1
0
0
0
2
0
0
0
0
1
0
1
0
1
0
2
0
1
1
0
0
1
0
2
0
0
1
2
0
0
1
0
2
0
0
0
3
0
0
2
0
1
1
2
0
1
2
1
1
0
2
0
1
2
1
5
1
1
0
0
0
1
1
1
1
1
0
1
0
2
1
1
2
0
1
0
0
0
1
1
0
2
1
0
1
1
0
1
2
1
1
1
0
0
1
1
2
2
3
0
2
0
2
1
0
0
0
1
0
1
0
0
1
0
1
0
1
1
1
0
2
1
1
1
1
0
2
1
0
1
0
0
0
2
0
0
0
1
1
1
2
2
2
1
2
1
2
0
2
0
0
1
0
2
0
0
0
1
0
2
0
0
3
1
0
1
0
1
0
1
1
3
0
0
1
2
0
0
0
1
1
0
1
1
1
1
0
1
0
0
2
1
2
0
0
0
1
0
1
0
1
2
1
1
0
0
1
2
2
0
0
2
0
1
0
2
0
0
0
1
0
2
0
1
1
0
2
0
1
0
2
2
1
0
1
1
2
2
2
0
0
2
1
1
1
1
0
0
1
0
1
2
1
1
1
0
1
1
0
0
0
1
0
1
0
2
0
0
1
1
0
2
1
0
0
0
1
2
0
0
1
1
1
0
1
0
0
0
2
2
1
1
2
0
2
0
0
0
2
1
1
0
0
2
0
2
1
0
0
2
0
0
0
1
0
1
0
1
2
0
0
2
0
1
1
0
0
0
1
1
0
0
0
1
0
1
2
0
0
0
1
0
0
0
1
0
0
0
2
1
1
2
1
0
0
0
12
4
1
0
0
0
0
0
0
0
1
0
0
1
0
1
1
1
1
0
0
1
0
2
0
2
1
1
1
2
1
0
1
0
1
2
2
0
1
0
1
1
0
1
1
0
2
1
1
1
0
1
1
2
1
0
0
0
1
0
0
1
2
0
1
1
0
1
1
0
1
0
1
1
0
2
0
0
1
1
0
1
1
0
0
0
1
1
0
0
1
1
1
1
1
2
2
0
0
1
0
0
1
2
2
2
2
2
0
1
2
2
1
0
4
2
0
1
0
0
0
0
1
1
0
1
0
2
0
0
0
2
1
2
2
0
0
1
2
1
0
1
0
2
2
1
1
1
1
2
1
1
2
2
1
2
1
2
1
1
0
1
1
0
1
0
1
0
2
3
2
0
1
1
0
2
2
1
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
2
0
1
2
1
3
1
0
0
2
2
0
0
1
1
1
2
2
2
1
0
1
1
0
1
0
2
1
3
0
0
1
4
0
2
2
1
2
1
1
1
0
1
1
1
1
2
0
1
2
2
1
0
0
0
1
0
1
1
2
0
1
1
0
1
0
1
0
2
1
0
1
0
2
0
2
1
1
0
2
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
2
0
0
1
0
1
0
2
0
1
2
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
1
0
2
0
1
2
0
0
1
1
0
0
0
0
2
1
3
2
0
0
0
0
2
1
3
2
1
2
0
1
3
1
2
2
0
0
1
1
0
1
0
2
1
0
0
0
1
0
2
1
0
1
1
0
1
0
1
0
1
0
1
0
2
0
0
1
0
0
1
1
1
0
1
0
1
1
0
1
0
2
1
1
0
1
1
1
1
0
0
0
1
1
0
0
0
1
2
2
2
2
0
0
1
1
2
1
0
1
1
5
1
1
1
1
0
0
1
2
1
0
1
1
1
1
0
0
0
0
1
2
2
1
1
1
0
1
0
1
0
1
0
1
0
1
0
1
1
1
2
0
2
1
1
1
0
0
1
0
1
2
1
1
2
0
0
1
1
1
1
0
0
1
0
1
1
1
1
0
0
0
1
0
1
1
1
2
2
0
1
2
0
1
1
2
1
1
1
0
2
1
0
1
1
0
0
0
2
1
1
0
0
2
2
2
1
2
1
1
0
1
0
2
1
1
1
0
0
1
0
1
0
1
0
0
1
0
0
0
1
0
2
1
1
0
0
0
1
0
0
1
2
4
1
1
1
0
0
2
2
2
0
2
2
2
0
1
1
1
0
0
1
0
1
2
2
1
1
0
0
0
0
1
2
1
0
0
2
0
0
0
2
0
1
1
0
0
0
1
0
0
2
0
1
1
0
1
0
0
0
0
0
1
1
2
0
2
0
0
2
2
1
2
0
2
1
1
1
1
0
0
0
0
0
1
0
0
1
2
1
2
1
0
0
0
0
2
0
1
2
0
1
0
0
0
0
2
2
2
1
0
0
0
2
0
1
1
1
1
0
0
1
0
0
1
0
1
0
1
2
1
0
0
2
0
1
2
1
2
0
0
0
0
1
1
1
2
0
1
1
2
0
1
1
0
2
2
0
1
0
0
2
2
1
0
1
1
0
0
0
1
0
1
0
0
1
0
2
0
0
0
1
2
1
1
0
1
1
1
2
2
0
1
2
0
0
1
2
1
1
2
1
2
0
0
0
2
1
1
2
2
0
1
2
1
1
0
1
1
2
1
1
0
2
0
2
2
0
2
1
0
1
0
2
2
0
2
1
1
2
0
0
1
0
2
1
1
0
0
0
1
1
0
0
1
1
1
0
1
1
1
1
1
0
1
1
1
0
2
0
1
0
0
0
2
0
2
1
1
1
0
2
0
1
1
3
0
0
1
0
0
0
0
2
2
1
2
1
1
0
0
0
0
2
1
0
0
5
1
0
1
0
1
1
0
2
0
1
0
1
1
1
0
0
0
2
0
0
2
0
1
0
0
0
1
0
1
0
5
2
2
0
1
2
0
1
2
1
2
2
1
1
1
2
1
1
1
0
2
2
1
1
2
1
1
1
0
0
0
0
1
0
1
1
0
1
0
0
0
1
2
0
1
2
2
0
1
1
1
1
1
0
1
0
1
2
0
1
0
1
2
1
2
1
0
1
2
1
2
1
1
1
0
2
0
1
1
2
0
1
1
2
0
0
0
1
0
1
0
0
0
0
1
1
0
2
0
1
4
2
1
1
2
0
2
1
0
1
0
0
0
1
0
3
1
0
1
2
1
0
2
0
0
1
0
0
1
0
2
0
1
0
2
1
2
0
0
1
0
1
2
0
1
1
1
0
1
0
1
2
0
0
2
1
2
2
2
1
1
1
0
2
0
0
0
0
0
1
2
1
0
1
3
1
1
0
0
1
0
1
1
0
0
1
0
1
0
0
0
2
2
0
0
0
1
0
0
1
1
1
1
1
1
1
1
0
2
2
1
2
0
0
0
0
1
2
1
0
1
1
1
0
1
2
1
2
0
0
0
0
0
1
2
0
0
0
2
1
2
1
1
2
0
0
1
1
2
1
2
0
0
2
2
0
1
2
0
1
0
2
1
2
1
2
0
0
0
0
1
0
1
1
0
2
1
1
0
2
1
0
2
2
1
2
0
0
0
2
2
1
0
0
0
2
0
2
2
0
0
0
1
3
0
1
2
0
0
1
2
0
1
1
0
0
1
0
1
0
2
1
0
1
2
1
13
2
0
2
1
1
2
0
1
1
1
0
1
0
2
1
2
0
1
1
2
0
1
1
1
1
1
1
0
0
2
2
1
1
0
1
0
1
0
2
0
2
1
1
0
3
1
0
2
1
0
2
1
1
0
2
0
0
0
1
1
0
0
1
1
2
2
0
1
1
1
0
1
1
0
1
0
2
2
1
1
0
0
0
0
2
2
2
2
1
0
2
0
0
2
1
2
1
0
2
1
2
0
1
0
1
1
0
1
1
2
0
0
1
1
0
2
0
0
2
0
0
1
1
0
0
0
2
0
0
2
0
1
0
2
1
0
1
0
1
0
0
2
0
2
0
1
2
1
0
1
2
2
1
1
2
1
2
1
1
0
2
0
0
1
1
1
0
0
2
2
0
1
3
0
0
1
0
1
0
1
1
2
1
0
3
1
1
0
1
1
2
0
1
1
1
0
1
1
0
2
0
0
0
0
0
0
2
1
1
0
0
0
2
0
1
2
1
0
0
1
2
0
1
2
1
1
1
0
0
0
1
0
0
0
0
1
2
0
2
1
1
0
1
1
2
0
2
2
2
3
1
2
1
0
1
0
0
0
0
0
1
0
2
1
0
1
1
1
0
0
2
1
3
1
2
1
1
2
1
0
0
1
1
0
2
1
0
0
15
0
1
2
0
1
2
0
1
0
0
0
0
0
0
1
1
1
1
2
0
0
1
0
0
0
0
2
0
2
0
2
2
2
1
1
0
1
2
1
0
3
1
1
3
3
2
1
2
1
1
1
0
0
1
2
2
0
1
0
1
2
1
0
2
1
2
0
0
2
0
0
1
5
1
0
0
0
2
0
1
0
0
1
3
0
1
0
2
0
1
2
1
1
1
0
1
1
0
0
1
0
1
0
1
1
1
2
0
1
3
1
1
0
0
2
0
2
1
0
1
2
0
0
0
2
2
1
2
2
2
1
3
1
0
2
1
0
0
0
1
1
0
2
1
2
1
2
0
0
1
0
0
1
1
1
0
0
1
0
1
0
0
1
0
2
0
1
2
1
0
0
2
1
0
1
1
0
1
0
0
2
0
1
0
0
0
2
0
0
2
0
2
1
0
0
1
1
0
0
2
2
2
0
0
1
2
0
2
0
0
2
0
3
1
2
0
1
1
0
0
0
0
2
2
2
0
0
0
2
2
0
0
1
2
2
1
1
0
1
2
0
0
2
1
1
3
1
0
2
1
1
2
1
0
1
0
0
1
1
2
1
2
1
1
0
1
2
0
0
1
1
0
2
0
1
1
0
1
0
1
2
0
2
2
1
0
1
1
0
1
1
0
3
0
1
0
0
2
0
0
0
2
2
2
1
2
1
0
0
1
0
2
2
1
2
0
0
0
0
1
1
0
0
1
0
2
1
2
2
0
1
2
2
2
1
0
1
1
0
0
1
1
2
2
0
1
0
0
1
0
0
0
0
1
0
1
0
1
2
1
2
1
2
1
1
0
0
1
2
3
1
2
2
2
1
2
0
0
1
1
0
2
0
1
1
1
0
0
1
0
2
1
0
1
1
0
1
2
1
2
1
0
1
0
1
2
1
1
2
0
2
2
0
1
2
2
2
0
2
1
0
2
1
0
2
1
0
0
2
0
1
0
1
2
0
0
1
2
0
0
0
0
0
1
1
1
2
0
2
0
1
1
0
2
0
0
1
1
0
0
0
1
1
1
2
1
0
2
1
1
0
2
1
1
1
0
1
0
2
1
1
0
0
0
3
1
0
1
0
1
0
1
0
0
1
1
0
1
1
0
0
0
2
0
1
1
1
0
0
1
0
2
3
0
1
2
1
1
0
1
1
1
2
1
1
0
2
1
0
0
1
1
0
2
0
1
1
0
1
0
1
0
0
1
7
0
2
1
0
0
0
0
2
1
0
0
1
1
0
1
1
0
1
1
2
2
2
1
1
0
0
0
0
0
0
0
1
1
0
1
2
0
2
3
0
2
0
0
0
2
1
2
1
2
2
0
1
1
0
0
1
2
0
1
1
1
1
1
1
0
1
0
0
0
2
1
3
1
2
1
0
0
3
0
1
1
2
2
1
1
2
1
1
0
1
0
1
0
0
0
0
0
1
1
2
0
0
0
0
2
0
1
2
1
2
0
1
1
2
1
2
1
0
0
2
0
0
0
0
0
0
0
0
1
2
0
1
2
0
2
2
2
0
0
1
1
1
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
2
1
1
0
1
2
2
1
1
1
1
2
0
2
3
0
4
1
1
2
0
0
1
2
0
1
0
1
1
1
0
1
1
0
0
1
1
1
1
0
2
1
2
0
0
2
0
0
2
0
1
2
1
1
1
1
1
1
0
1
1
1
1
1
0
1
3
1
0
0
0
1
1
0
1
0
1
1
0
1
1
2
7
1
0
3
2
2
0
1
1
1
2
1
1
0
2
2
0
0
3
2
1
2
0
0
0
2
0
1
2
2
0
1
1
1
0
0
1
1
2
1
0
1
1
2
1
0
1
0
1
1
0
0
1
2
0
0
0
1
1
1
1
0
0
0
0
2
1
0
1
1
0
0
1
0
0
1
3
1
0
0
2
0
1
0
1
2
1
2
1
1
0
0
1
1
0
3
2
1
0
1
0
2
0
1
1
2
0
0
0
0
0
2
0
2
1
0
0
2
0
1
1
0
1
0
1
1
1
1
2
0
0
2
0
1
0
2
0
0
1
2
0
1
0
2
1
0
0
0
2
0
2
1
0
2
0
1
0
0
0
0
1
0
2
2
3
0
2
1
1
1
1
1
0
1
1
0
0
0
0
1
1
0
1
0
1
1
2
0
0
0
1
0
0
0
2
0
1
1
2
0
0
1
2
0
1
1
1
1
0
1
0
0
2
1
1
1
1
2
0
0
2
0
1
2
2
1
2
1
0
1
0
1
1
1
0
0
1
0
1
1
1
0
0
1
1
0
2
0
1
0
0
0
0
2
0
1
1
1
0
1
1
2
0
1
1
1
0
1
1
0
0
0
1
1
0
2
1
0
0
1
0
1
1
1
1
1
0
0
0
0
0
0
0
1
0
1
0
2
0
2
1
1
1
1
1
1
1
1
2
0
1
1
0
0
0
1
0
1
2
3
0
1
1
0
0
0
2
1
1
0
2
1
1
2
1
0
2
0
0
0
0
0
1
0
1
1
1
0
1
2
1
0
1
2
2
1
0
0
1
0
1
0
2
2
0
2
0
0
0
1
0
1
1
1
2
1
1
3
0
1
2
0
0
1
1
1
3
0
0
0
0
1
1
1
2
1
0
0
2
0
0
1
0
0
0
2
1
0
2
0
1
1
0
0
0
1
1
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
1
0
0
1
1
2
1
0
2
1
2
1
0
2
2
3
1
1
0
1
1
0
0
0
0
0
1
1
0
2
0
0
2
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
2
1
1
1
0
1
0
1
0
1
0
1
0
2
1
2
1
2
1
1
1
0
0
1
1
0
1
1
2
0
2
0
1
2
1
0
2
1
2
0
0
0
1
1
2
0
1
0
0
0
0
1
1
0
1
2
0
0
1
0
1
1
0
0
1
1
0
1
0
0
0
0
2
2
0
0
0
0
1
1
2
0
2
2
1
2
1
1
0
1
0
1
0
0
1
0
0
1
0
0
1
0
0
1
5
1
1
0
0
1
0
1
0
0
1
2
1
0
0
0
0
1
0
0
0
0
1
1
1
0
2
1
1
1
1
0
1
1
1
1
0
0
1
0
0
1
0
1
1
1
1
1
1
2
0
1
0
0
2
0
0
1
0
0
0
0
1
1
0
1
0
0
2
0
0
0
1
2
0
1
1
2
2
3
0
0
0
0
0
0
1
0
1
1
0
0
3
1
1
2
2
1
1
1
1
1
2
2
0
2
1
1
0
2
2
0
0
1
1
1
2
2
0
1
1
5
2
0
1
0
1
0
0
0
5
0
1
2
0
1
2
2
0
0
1
0
1
0
0
2
1
2
2
1
2
0
1
0
2
1
1
2
1
1
0
2
0
0
2
1
1
0
0
0
2
1
2
0
1
1
1
2
2
1
1
0
1
0
1
0
0
1
1
0
1
0
2
2
2
2
0
0
2
0
0
1
1
0
1
1
0
0
1
1
0
0
1
0
1
0
0
1
1
2
3
1
3
0
1
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
2
1
1
1
0
2
2
1
2
0
0
2
1
0
0
2
1
0
1
1
2
2
1
2
1
1
1
2
2
2
0
0
1
0
1
1
1
1
2
1
1
0
1
2
1
1
1
0
1
0
0
1
1
0
0
1
1
1
2
0
1
1
0
0
0
2
0
2
1
0
1
2
1
3
1
0
2
1
0
2
1
1
1
1
2
0
1
1
0
1
0
1
1
2
2
1
0
2
1
0
1
0
0
0
1
0
0
1
2
0
1
1
1
0
1
2
0
0
2
1
1
1
0
1
2
0
1
1
0
0
2
0
0
2
0
0
1
1
0
0
0
0
2
2
0
2
0
1
0
2
1
0
0
0
1
1
0
2
1
2
0
0
1
2
1
0
0
0
1
0
0
1
2
1
0
1
0
0
1
0
1
0
0
0
1
0
1
1
2
0
0
1
1
0
1
1
0
2
1
3
1
0
2
0
0
1
1
0
0
1
1
1
0
0
0
1
2
2
2
0
1
0
2
1
0
0
0
1
0
0
0
1
0
1
0
1
2
0
2
1
0
0
0
1
0
1
2
1
0
2
0
0
2
0
2
1
0
1
2
0
0
1
1
1
0
0
1
1
0
2
2
2
0
0
1
1
0
2
0
0
1
0
0
1
0
0
2
0
1
2
1
1
0
2
2
0
1
1
0
2
0
1
2
1
0
2
0
0
1
0
0
0
1
0
0
1
1
2
1
1
0
0
0
0
1
1
2
1
1
0
1
1
0
1
1
1
1
0
1
1
2
0
2
0
1
2
2
2
1
2
1
2
0
0
0
0
0
1
0
1
1
0
0
1
0
1
0
2
1
2
0
2
0
0
1
1
2
0
0
1
1
0
2
1
0
1
0
1
2
0
0
1
1
0
1
1
6
1
0
1
0
0
2
1
0
1
1
1
1
0
0
2
0
0
1
0
0
2
1
2
0
2
1
0
1
2
2
1
2
1
1
2
0
0
0
1
2
0
0
2
0
1
2
0
2
1
1
1
0
1
1
0
1
0
0
0
0
0
1
1
0
2
1
1
1
0
1
1
0
2
1
0
0
1
1
0
1
0
1
1
1
0
0
1
0
2
0
0
1
0
0
0
1
0
0
0
1
2
0
2
0
2
1
0
0
1
1
1
1
0
1
0
1
1
2
1
0
2
1
1
0
1
1
0
1
0
1
0
1
1
1
0
1
0
0
1
0
1
1
3
1
1
0
0
0
1
0
2
2
1
1
0
0
0
1
1
1
1
1
2
2
1
2
1
1
1
1
0
0
1
0
0
0
2
1
2
1
1
2
0
2
1
1
1
2
0
0
0
2
0
2
1
0
0
1
1
0
0
0
2
0
2
1
1
1
0
0
0
2
2
8
2
0
1
0
1
1
0
0
1
2
0
1
0
1
1
1
0
0
0
1
1
2
1
1
1
2
2
1
1
0
2
2
1
1
0
1
0
2
1
1
2
1
1
0
1
1
2
1
2
1
1
0
1
1
0
0
0
0
1
0
0
5
0
1
2
0
1
2
1
2
4
1
1
1
1
3
0
1
3
0
1
2
1
0
1
1
0
0
1
1
1
2
2
3
0
2
0
0
0
0
1
0
2
2
2
0
2
0
1
0
0
0
1
2
2
1
1
1
1
0
1
1
1
0
0
2
2
5
2
0
1
1
2
1
1
2
1
2
2
1
0
1
1
1
2
0
0
0
0
1
0
0
0
2
1
1
0
0
0
0
1
0
1
1
0
2
0
0
1
2
0
2
1
1
2
1
0
0
0
1
1
4
0
1
1
0
2
1
0
0
1
1
0
0
1
2
1
0
0
1
0
2
2
2
1
1
1
2
2
1
4
0
1
0
1
0
0
1
0
2
0
1
1
0
0
1
0
0
0
0
3
0
3
0
0
1
2
2
1
3
0
2
1
0
0
2
1
0
1
2
1
1
2
2
0
1
1
1
0
2
0
1
0
0
0
2
0
2
0
0
1
2
1
1
0
1
1
2
2
1
1
2
2
0
0
1
0
2
2
2
0
0
2
0
2
0
1
1
1
1
1
1
2
2
2
1
0
1
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
2
1
2
0
1
2
2
1
1
0
0
2
0
2
2
1
0
2
2
1
0
1
0
2
0
0
0
1
0
1
0
1
2
1
0
0
2
0
1
0
0
2
1
0
2
1
0
0
0
2
0
1
0
0
1
1
2
1
1
0
2
0
1
0
0
2
1
1
1
0
0
1
1
0
0
0
2
1
1
0
2
2
1
1
0
2
1
1
0
1
2
0
0
1
1
0
2
0
0
2
0
0
0
1
1
1
0
1
0
0
2
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
2
1
2
1
0
1
0
1
1
2
1
0
0
2
0
1
0
1
0
1
1
0
2
0
2
0
2
1
2
1
1
2
1
1
1
2
0
0
0
1
2
2
1
0
0
3
1
1
1
0
1
2
2
0
1
0
0
2
1
0
1
1
1
1
0
2
1
2
1
0
0
1
1
0
0
0
2
1
0
1
0
0
0
0
2
2
0
1
0
2
1
0
2
0
2
0
1
1
0
0
2
1
1
1
1
2
2
1
2
1
0
2
1
2
0
1
1
0
0
2
1
1
1
0
2
1
0
0
0
2
2
0
2
2
1
0
2
0
0
1
0
1
2
1
0
0
1
1
1
0
0
1
2
1
1
0
0
1
0
1
0
1
0
0
2
0
1
1
0
0
0
1
1
0
2
2
1
0
0
1
0
1
2
0
0
1
1
1
0
0
1
1
2
2
2
2
1
1
1
1
2
0
0
2
1
0
0
1
0
1
0
1
2
0
1
1
1
0
2
0
2
0
2
2
1
0
0
0
2
1
0
2
1
0
2
0
1
1
1
1
1
2
2
2
2
0
2
0
1
0
0
1
1
1
0
1
1
2
0
0
0
0
0
1
0
1
2
0
0
0
0
1
1
0
1
0
1
1
2
0
1
1
0
0
1
0
0
0
1
0
0
1
0
0
2
2
2
2
0
1
0
2
1
1
2
1
1
1
2
2
0
1
2
1
1
1
0
0
1
0
2
1
1
0
1
0
1
0
1
1
0
1
2
1
0
1
2
2
2
0
0
2
3
2
0
2
0
1
0
1
1
1
1
1
1
0
0
0
1
2
1
1
2
0
0
2
1
1
0
0
0
0
1
1
1
0
1
2
2
0
2
0
0
0
2
0
1
1
1
0
3
0
0
0
1
2
1
0
1
0
1
1
1
0
1
2
1
0
2
0
1
0
1
0
1
3
1
2
0
2
1
0
2
1
1
0
0
2
1
2
1
2
0
1
1
0
0
0
1
0
2
1
0
0
0
0
2
1
0
1
1
0
0
1
1
0
1
0
0
1
1
1
0
0
2
0
0
2
0
3
0
2
0
1
1
1
1
2
1
2
2
0
2
0
0
0
5
1
1
1
3
0
0
0
0
0
0
0
0
1
1
1
1
0
1
1
1
1
2
1
2
0
1
2
1
1
0
1
0
1
0
1
3
1
0
0
2
1
1
2
2
0
1
0
0
0
2
0
0
1
1
1
1
1
1
0
1
1
0
1
2
1
1
2
0
2
3
1
0
2
2
2
1
1
1
2
0
0
1
0
1
1
0
1
2
1
0
1
0
3
1
0
0
1
1
0
1
0
0
0
0
1
2
0
1
1
2
1
2
2
0
0
0
0
0
0
2
0
0
1
2
0
1
0
1
1
1
2
1
0
2
2
2
0
1
1
1
0
1
1
1
2
1
4
2
0
1
1
1
2
2
0
0
2
0
1
0
1
2
0
1
0
1
1
2
1
0
0
1
0
1
2
1
0
1
1
0
1
0
2
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
1
1
2
1
0
0
1
2
1
1
2
0
0
0
1
1
2
1
0
1
1
0
1
1
2
1
1
1
0
1
0
0
2
0
1
0
0
1
0
0
0
1
0
1
1
2
0
0
2
1
0
1
1
0
0
2
1
1
1
2
0
0
2
2
1
0
0
0
0
0
0
1
2
1
0
2
1
0
1
1
1
2
1
2
0
0
0
2
2
2
0
2
1
0
2
1
0
1
1
0
1
0
1
1
0
2
1
2
3
1
2
2
3
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
2
0
1
1
2
0
0
3
1
2
0
1
2
1
0
2
1
1
0
0
1
2
0
0
3
2
2
1
1
0
2
2
0
0
0
1
1
2
2
2
1
0
0
0
1
1
0
2
1
2
0
1
1
0
0
1
0
0
0
0
0
0
2
0
1
1
1
1
0
0
0
0
0
1
0
1
0
0
1
0
2
1
1
3
0
1
0
0
0
0
2
0
0
2
0
2
0
0
0
2
1
1
0
0
2
0
1
2
1
2
2
1
0
1
4
1
0
2
2
0
1
0
0
1
0
0
0
0
0
0
2
1
2
1
1
0
0
0
1
1
0
0
2
2
0
1
1
7
0
0
0
1
1
1
0
0
1
0
1
1
2
0
1
1
2
2
1
1
2
0
0
1
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
1
1
0
2
0
1
1
1
0
0
2
1
1
0
0
0
0
0
1
0
1
2
0
0
1
3
3
2
1
1
0
0
1
1
0
2
1
0
2
2
1
1
1
1
2
2
0
1
2
1
1
1
2
2
1
2
0
1
2
0
3
1
2
1
1
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
2
0
10
0
0
1
1
0
0
0
0
0
2
1
0
0
1
2
1
1
0
0
0
2
0
0
1
1
0
1
0
0
0
1
0
2
0
0
1
1
0
0
1
0
0
2
1
2
0
2
0
1
1
0
1
1
0
1
1
1
1
0
1
2
2
1
0
2
0
1
0
1
1
0
0
2
1
0
2
1
0
1
2
1
1
2
2
0
1
1
1
1
0
2
0
2
1
1
0
2
1
0
2
2
0
1
1
0
2
0
0
2
0
0
0
0
0
2
0
2
0
1
0
0
0
0
1
1
0
1
1
0
0
2
0
0
1
0
1
3
0
2
1
0
1
1
0
0
0
1
2
0
2
2
1
1
1
1
1
1
0
0
0
2
1
2
1
0
0
0
1
0
0
1
1
0
2
1
1
0
1
0
0
1
0
1
1
0
0
1
0
0
0
2
1
0
1
0
1
1
1
2
1
1
2
0
1
1
2
1
0
1
0
1
2
0
0
0
1
2
0
1
2
1
1
0
0
1
0
1
0
1
2
0
2
2
0
0
1
0
0
1
0
1
3
1
3
1
1
1
0
1
2
0
1
2
2
2
1
0
1
1
0
0
1
0
0
1
2
1
1
1
0
0
0
0
2
0
0
2
1
2
0
0
1
0
2
0
0
0
1
2
0
0
2
2
1
1
0
0
0
0
0
2
0
0
2
1
0
0
1
0
2
2
0
1
1
1
0
0
1
2
0
0
0
0
0
1
1
0
2
1
1
1
0
0
1
0
0
2
2
0
1
2
2
1
0
2
0
2
1
0
1
2
1
0
0
2
1
0
1
2
1
1
1
1
1
0
0
1
2
1
0
0
1
1
0
1
0
0
1
1
2
2
1
2
1
2
0
3
0
1
2
1
0
2
0
0
1
0
0
0
1
0
2
1
0
0
2
1
2
2
0
0
0
0
1
2
2
0
0
0
0
1
0
3
0
0
1
0
1
1
1
1
2
0
1
0
1
2
1
1
2
1
1
0
1
1
1
1
1
0
2
8
0
1
1
1
1
2
0
3
0
1
0
2
0
1
2
2
0
0
0
1
1
0
0
2
0
0
1
0
0
0
2
1
1
0
2
0
1
0
0
1
1
1
0
0
1
0
3
2
0
0
2
0
1
0
2
2
2
1
0
1
0
2
1
0
1
1
0
0
2
1
1
2
2
1
0
2
1
1
1
2
0
0
1
1
1
1
0
0
1
2
1
0
0
2
2
1
0
1
0
1
0
4
2
0
0
0
2
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
2
2
0
0
1
0
0
0
0
0
1
0
0
1
0
2
0
2
0
0
2
0
1
0
0
0
0
1
0
0
0
1
1
0
2
0
0
0
2
0
1
0
1
0
0
0
1
2
0
1
2
2
0
1
1
2
1
1
0
0
0
2
1
0
2
0
1
1
1
1
1
0
2
2
0
1
1
1
2
1
2
0
2
2
3
0
0
0
1
1
1
1
1
1
1
0
2
0
0
0
0
0
1
1
3
1
0
0
1
2
0
2
1
2
0
0
1
0
1
2
1
0
2
0
1
0
2
2
1
0
2
2
2
3
2
2
0
2
1
1
0
1
1
1
1
1
2
0
1
0
2
2
0
2
1
0
0
1
0
1
0
0
0
2
0
1
2
0
0
0
1
0
1
1
1
1
3
3
0
1
0
1
1
3
0
1
0
0
0
1
1
0
1
2
1
0
0
0
2
2
0
0
1
2
1
1
2
0
0
0
0
0
2
1
0
0
0
0
1
1
1
1
1
0
0
1
0
0
0
1
1
1
0
0
0
1
0
0
0
0
1
1
0
0
2
2
1
2
1
1
0
0
1
1
0
0
1
1
1
1
2
1
1
2
0
1
0
1
1
1
2
1
1
1
0
2
0
0
0
1
0
0
0
2
1
0
3
0
1
0
0
1
0
3
0
2
0
1
1
1
0
2
2
1
1
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
1
1
2
0
1
0
0
1
0
0
0
1
0
1
0
1
1
0
1
1
1
2
1
2
2
2
2
1
1
2
1
1
0
0
11
0
0
2
1
1
1
1
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
2
2
0
1
0
2
0
0
0
0
1
2
0
0
0
1
1
1
0
1
0
0
1
0
2
0
2
0
1
1
0
0
2
0
0
2
2
0
0
1
1
0
1
0
0
2
2
1
0
1
1
0
2
1
0
1
2
1
2
2
0
0
2
0
0
1
1
1
1
1
0
0
4
0
2
1
1
2
2
3
1
0
0
0
1
1
1
2
1
0
1
1
0
0
1
1
1
2
0
2
2
0
1
1
0
2
0
0
0
1
2
1
2
0
2
0
1
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
1
1
2
0
0
2
0
0
1
1
1
2
1
0
2
1
0
0
1
1
1
0
1
1
0
2
1
2
1
0
1
0
0
0
2
0
0
0
1
1
2
0
1
0
2
2
1
1
1
1
1
0
1
1
1
0
1
1
1
1
0
1
2
0
1
1
0
0
1
2
1
1
0
0
1
0
1
1
2
1
3
0
2
1
0
0
0
2
0
1
1
1
0
1
2
1
1
1
1
1
0
2
2
1
2
1
2
0
2
0
0
2
2
2
0
2
1
1
0
1
3
0
0
0
0
0
1
0
1
0
0
1
1
1
0
2
1
1
1
0
2
1
1
1
1
2
0
0
1
1
1
1
2
0
0
1
1
1
1
1
2
1
2
1
2
2
1
0
2
1
0
2
0
0
0
0
2
1
2
0
0
0
1
2
1
3
1
1
1
0
2
1
2
1
1
0
1
0
0
0
0
2
2
2
1
0
0
1
0
0
1
1
1
0
0
0
1
0
2
0
2
1
2
0
1
1
1
2
1
0
0
2
0
0
1
2
1
0
2
0
0
1
1
1
0
1
1
0
0
1
1
0
0
0
1
2
1
1
0
0
1
0
1
0
1
0
2
0
0
1
0
2
1
2
0
2
1
1
0
1
2
0
2
0
1
1
2
0
0
0
1
1
2
2
0
1
1
0
0
2
1
0
1
1
2
1
2
0
1
2
1
1
0
0
1
1
0
0
1
1
2
1
0
0
1
1
0
1
0
0
0
2
2
2
1
1
0
0
2
1
2
0
0
2
1
2
0
1
0
0
1
1
1
0
0
2
0
0
1
2
0
1
0
1
1
1
0
1
2
2
1
3
0
1
0
0
1
1
1
1
1
0
2
2
0
1
2
0
1
2
0
2
0
1
0
2
2
2
1
0
0
0
1
0
2
1
1
2
2
1
2
0
1
0
1
1
2
0
0
0
1
2
2
1
0
0
1
2
2
1
0
0
1
0
2
1
0
2
2
1
0
0
0
0
1
2
1
2
0
0
1
0
0
1
2
1
0
0
1
0
0
1
0
0
1
1
1
2
0
0
0
2
1
0
0
0
1
0
2
1
0
2
3
0
1
2
2
1
1
2
1
1
1
2
1
1
0
0
1
2
0
0
2
0
1
2
0
1
1
2
2
1
2
1
2
1
0
0
0
1
2
0
0
0
1
0
1
1
1
2
0
1
1
0
0
0
2
1
2
2
1
0
1
0
0
1
1
2
2
0
1
1
0
0
0
1
0
1
0
1
1
2
1
1
0
1
0
1
2
1
0
1
1
1
0
2
2
0
0
0
1
2
1
0
1
1
1
2
0
0
0
2
1
1
0
0
1
0
0
0
2
2
0
0
1
0
1
1
0
2
1
0
1
0
0
1
0
1
1
0
2
1
1
0
1
1
0
1
1
1
0
2
0
1
2
0
0
0
3
0
1
1
2
1
1
0
0
1
0
1
2
2
0
0
0
2
2
0
0
2
0
2
2
0
0
1
2
1
0
2
1
2
1
0
0
0
2
2
0
0
2
1
0
1
2
1
0
2
0
1
0
1
0
0
0
0
1
0
1
2
2
1
0
0
1
0
1
0
0
1
1
0
1
0
2
0
1
0
1
1
0
1
2
2
1
1
2
2
0
1
0
0
0
3
4
0
2
0
1
0
1
2
2
2
2
1
1
1
2
1
0
2
2
2
5
0
1
1
2
0
1
0
1
2
0
1
1
2
2
0
1
1
2
2
0
1
1
2
0
1
1
1
1
1
0
2
2
0
2
1
1
0
1
2
2
2
0
0
1
0
2
1
1
1
2
0
2
1
1
2
2
0
1
1
1
2
1
1
0
0
2
1
1
1
1
1
0
2
1
1
1
0
1
2
0
2
0
1
0
2
0
2
1
1
1
2
0
0
0
0
0
2
1
2
0
2
0
2
0
0
1
0
0
0
0
0
1
1
1
0
2
1
2
0
1
2
0
0
0
1
1
1
1
0
2
1
0
2
0
0
2
0
0
0
2
0
1
0
1
2
0
1
2
0
2
0
1
1
1
0
2
0
1
0
0
2
1
1
0
0
1
0
0
0
0
2
0
1
1
2
0
4
1
0
0
2
0
0
2
0
1
1
1
0
2
0
1
0
0
1
1
1
0
0
1
0
0
1
0
0
1
2
1
1
2
0
2
0
0
2
1
1
1
0
1
0
2
0
0
0
2
0
0
0
0
2
2
1
1
1
1
0
0
1
0
0
2
1
1
0
2
2
2
2
0
1
2
2
1
1
2
1
0
0
2
1
0
1
1
1
2
3
1
1
2
1
2
1
1
0
2
1
1
1
1
3
1
1
1
5
1
1
4
1
1
1
0
0
0
0
1
0
1
1
0
1
0
1
0
1
0
2
0
0
1
2
1
0
0
1
1
1
2
0
1
1
1
0
2
0
1
1
0
0
0
1
1
1
1
2
2
2
1
1
2
3
1
0
0
0
0
0
1
0
2
0
0
0
0
1
1
0
1
1
1
1
0
2
0
2
1
0
0
0
0
0
0
1
0
0
1
1
1
1
1
0
1
2
1
2
0
1
1
2
1
1
2
0
1
1
0
0
0
0
1
0
1
0
1
0
1
0
1
0
0
2
1
1
2
0
0
1
1
0
2
1
2
1
0
4
0
2
0
4
0
0
0
1
1
0
1
1
0
3
0
0
0
2
1
2
0
1
0
0
2
0
0
1
2
0
1
1
1
0
0
0
2
1
2
2
0
3
2
1
1
2
0
1
0
2
1
1
0
1
0
0
0
1
1
1
0
1
1
1
0
0
0
0
1
2
1
2
0
0
1
0
0
1
2
0
0
2
0
1
0
1
0
1
0
1
0
2
0
2
1
1
2
1
0
0
1
0
0
1
1
2
1
0
2
5
2
1
0
2
3
1
0
2
1
0
1
1
0
2
1
0
0
2
0
0
0
0
2
2
2
1
2
1
0
0
2
1
0
0
1
0
0
2
2
0
0
1
0
0
1
1
1
1
0
0
2
0
0
1
1
1
0
0
0
0
0
1
1
0
2
0
0
2
2
1
2
0
1
1
0
0
3
1
0
0
0
0
0
0
2
1
0
1
0
0
3
1
0
1
0
1
0
1
0
0
0
1
2
2
0
1
1
0
2
0
0
0
0
0
1
0
0
0
0
1
1
0
0
2
0
1
0
0
2
1
0
1
1
1
1
1
0
1
0
1
1
1
1
0
1
0
0
0
0
1
0
1
1
0
0
1
0
1
2
0
2
2
1
0
2
1
0
1
2
1
1
1
0
2
0
0
2
2
0
0
1
0
1
1
0
0
0
0
2
2
1
1
0
1
2
1
1
1
1
1
1
2
1
0
0
0
2
1
2
1
0
2
2
0
2
0
0
0
2
0
2
1
2
0
2
0
3
0
1
1
2
0
1
0
0
0
1
0
0
1
2
0
1
1
1
1
1
1
0
1
0
0
1
2
0
0
0
2
1
0
0
5
2
1
0
2
1
0
1
1
0
1
0
1
0
1
2
2
2
0
2
1
1
2
1
2
0
0
1
1
0
1
2
0
1
1
1
0
1
1
0
2
1
2
0
2
0
0
2
1
2
1
2
1
0
1
1
0
1
1
0
1
0
0
1
0
0
2
1
0
0
1
0
0
2
1
1
2
2
1
2
2
2
0
0
1
1
0
0
1
0
0
0
0
0
0
2
1
1
0
0
1
1
0
2
0
2
3
1
2
0
3
1
1
1
1
1
0
1
1
1
1
1
0
1
0
3
1
2
1
1
2
1
2
1
1
0
1
1
1
2
2
0
1
2
0
1
0
1
0
0
1
2
1
1
0
2
0
0
1
1
0
1
2
1
0
1
0
1
0
1
1
0
1
0
0
1
1
1
0
0
1
0
0
2
1
1
0
0
0
0
0
2
0
0
0
2
1
0
1
2
0
0
0
1
0
1
1
1
1
1
1
0
0
2
1
0
1
0
1
1
2
1
0
1
0
1
1
2
1
1
1
0
1
1
1
0
1
1
0
0
1
0
0
2
1
0
1
1
2
1
1
2
2
0
0
0
0
1
0
0
0
1
2
1
2
2
1
3
1
0
1
0
0
1
0
2
1
2
1
2
0
0
1
1
1
1
2
1
1
1
2
1
2
0
1
0
1
3
0
0
0
1
1
1
0
0
0
0
0
2
1
0
2
0
0
0
1
1
0
1
0
1
0
2
0
0
0
0
1
2
1
1
0
3
1
1
0
0
1
1
1
2
1
0
1
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
2
2
1
0
0
1
0
1
0
0
0
2
2
0
1
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
2
2
2
0
1
0
1
4
1
1
1
1
1
0
2
1
0
1
1
0
1
0
1
0
0
1
1
0
0
0
1
1
0
1
2
0
1
1
0
2
0
0
0
2
0
0
0
1
0
3
0
0
1
1
0
2
1
0
1
1
0
2
2
2
1
1
0
1
1
0
0
2
0
1
0
0
0
0
2
2
2
1
1
0
1
1
1
2
1
2
1
1
2
1
1
1
0
0
2
1
1
2
1
0
1
2
0
1
1
0
2
0
1
0
1
1
0
1
0
0
2
2
1
0
1
0
0
0
1
0
0
0
0
2
0
2
2
2
0
0
1
2
0
1
1
1
1
0
1
0
2
0
2
0
0
1
0
0
0
1
0
1
1
1
1
0
1
1
0
1
0
0
0
5
1
0
2
2
0
0
1
2
0
1
0
0
0
0
2
0
0
1
0
1
0
0
1
1
1
1
1
0
2
2
2
0
1
2
0
1
0
1
0
2
0
0
1
1
1
0
1
0
2
0
0
1
1
0
0
1
1
2
1
0
1
2
1
1
0
2
1
0
1
1
0
0
1
0
2
0
1
0
2
1
1
0
0
1
1
1
2
0
0
0
0
1
1
0
1
0
1
0
1
0
2
0
0
1
0
1
2
2
0
0
0
2
0
2
0
2
1
1
0
1
0
0
1
0
0
0
0
0
0
1
0
1
1
2
0
0
2
0
2
1
0
0
2
0
0
1
1
1
0
1
0
1
1
0
0
1
1
2
0
1
1
0
0
3
0
1
0
1
0
1
0
1
1
0
1
0
1
1
2
1
2
0
1
2
0
0
0
0
4
0
1
0
2
1
0
2
2
0
1
0
1
0
1
1
0
2
0
2
1
1
2
1
2
0
1
1
1
1
0
1
1
1
0
1
1
1
1
1
0
0
1
2
0
1
2
2
0
2
1
1
0
1
1
2
1
1
0
0
0
1
0
2
2
0
1
0
1
0
0
0
0
2
1
0
2
1
0
0
0
1
0
0
2
2
0
1
1
2
0
0
1
0
0
1
1
0
0
2
0
0
1
0
0
2
1
0
0
1
0
2
1
0
3
2
1
0
0
0
1
0
0
1
0
0
2
0
0
2
0
1
0
0
1
2
1
0
2
2
2
1
0
1
1
1
0
0
0
2
0
1
1
1
0
2
1
0
2
0
0
1
0
1
0
1
2
0
0
1
1
0
1
1
0
3
0
0
1
0
1
0
1
0
1
2
2
2
0
0
1
1
1
2
2
0
0
0
3
0
2
0
2
0
1
0
0
1
0
0
0
1
0
0
2
0
1
1
2
0
1
2
0
2
0
1
0
0
1
1
1
0
1
0
1
0
1
1
1
0
1
0
2
1
0
1
0
3
2
0
2
2
2
1
2
1
0
0
2
0
0
1
0
1
2
0
0
2
1
1
0
2
1
0
1
1
1
0
1
1
0
1
0
1
0
0
0
0
0
1
1
2
0
0
0
0
1
2
1
0
0
2
2
1
1
1
1
1
1
0
0
1
0
0
0
1
1
0
1
1
0
2
3
0
0
1
1
2
2
0
2
1
1
0
1
0
0
0
1
0
0
0
2
0
2
1
1
1
0
1
0
3
2
2
1
1
1
0
0
0
1
1
2
0
1
3
1
0
0
1
0
2
1
0
1
1
1
0
2
1
0
1
1
1
1
2
0
0
3
1
0
2
0
0
0
1
1
0
0
2
1
0
0
0
2
0
2
1
0
3
2
3
0
0
0
0
0
0
1
0
0
2
0
2
1
1
1
0
1
2
1
1
1
2
2
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
2
1
1
1
0
2
1
2
1
0
0
1
1
1
2
0
1
1
1
1
2
0
1
1
1
2
1
1
0
0
3
2
1
1
0
2
1
1
0
2
1
1
1
1
2
1
2
0
0
1
1
2
2
0
0
0
1
0
0
1
1
0
0
1
0
1
0
0
4
0
0
0
0
1
0
0
0
1
0
0
1
1
2
1
2
2
2
1
1
1
0
1
0
0
0
1
0
0
1
1
1
1
1
0
0
1
2
0
2
2
1
2
0
0
0
0
1
1
0
1
1
1
0
2
1
1
1
1
0
1
0
0
1
0
1
0
0
0
1
1
2
0
2
0
1
1
1
1
1
2
1
2
1
1
0
2
1
1
2
0
2
2
1
2
0
0
0
2
2
1
1
0
0
0
0
1
2
1
1
0
2
1
0
1
2
2
1
0
1
2
0
1
0
1
1
3
1
1
2
0
2
2
0
2
0
2
0
0
1
0
2
0
1
2
0
2
0
0
1
0
1
1
1
1
1
1
1
0
3
2
0
0
2
2
2
1
0
2
2
1
0
2
0
2
0
1
0
0
1
2
0
2
0
2
1
1
0
0
0
1
1
2
1
0
0
1
1
2
0
1
1
2
1
1
1
1
0
0
0
1
0
0
1
0
1
2
1
0
1
2
1
1
0
2
1
2
0
1
1
2
2
1
1
0
1
2
0
0
1
0
2
1
1
0
0
0
1
2
2
0
1
1
0
0
0
0
2
2
1
1
2
2
1
0
1
0
1
0
2
1
2
0
0
1
0
0
0
1
0
0
1
2
0
0
0
1
0
0
1
0
1
0
0
1
0
1
2
2
0
1
1
2
2
0
2
2
2
2
1
2
0
2
0
2
1
1
2
1
1
1
0
0
2
0
0
1
0
0
1
0
0
1
2
2
0
2
0
1
1
1
1
0
0
0
2
1
1
2
0
0
1
2
0
1
0
2
0
0
1
2
0
0
1
3
1
2
1
0
2
0
2
2
0
2
2
1
0
0
1
0
1
2
1
1
2
1
0
1
10
1
0
1
1
1
1
1
0
0
2
1
0
0
0
0
0
0
0
2
0
1
0
3
2
1
1
0
4
0
2
2
0
1
4
2
1
1
2
0
1
0
0
2
0
1
1
0
0
2
0
2
0
0
0
2
2
1
2
0
1
1
1
1
2
1
0
0
0
0
1
1
1
1
2
1
0
0
2
1
1
1
2
0
1
0
0
1
1
2
0
1
1
0
1
0
0
2
1
0
1
0
0
2
3
1
0
2
0
0
1
0
0
1
2
0
1
0
0
2
2
0
1
2
0
1
3
1
2
0
0
3
2
0
1
2
1
0
0
0
2
1
1
2
0
2
4
1
2
0
1
3
0
2
0
0
0
2
0
0
0
0
1
1
0
0
1
2
0
0
0
0
0
2
0
2
1
0
0
1
1
0
0
1
0
1
2
1
0
0
1
2
2
2
2
1
0
1
1
1
2
1
1
1
0
0
0
1
1
1
0
0
1
2
2
2
0
0
0
0
0
1
1
0
2
2
1
1
1
0
0
2
1
1
1
1
0
1
0
0
2
2
0
0
0
2
1
0
1
0
0
1
0
0
2
0
0
1
1
1
0
0
2
2
0
1
1
2
2
0
0
2
1
2
0
0
0
0
0
3
2
0
1
0
0
1
0
2
3
2
1
0
0
0
1
1
2
2
2
0
1
1
1
0
0
1
0
1
0
0
0
1
0
2
4
1
0
1
0
1
0
1
0
0
1
1
1
1
0
1
0
1
0
2
1
0
0
1
0
1
1
1
0
0
1
0
1
0
0
3
2
1
2
1
2
1
0
2
2
2
0
0
0
2
1
0
2
0
0
0
0
1
0
0
2
2
1
0
1
1
1
1
3
1
2
2
1
0
1
1
0
1
0
0
2
1
1
0
0
1
1
0
0
1
0
0
1
1
1
2
0
2
0
1
2
1
2
0
0
0
1
1
1
0
0
2
0
1
0
0
3
1
0
0
0
2
1
0
1
1
0
0
0
2
0
0
2
2
1
0
1
1
0
0
0
1
0
2
2
1
0
0
0
0
1
1
0
1
1
0
1
1
0
2
1
2
1
0
1
1
0
1
0
1
1
0
0
2
1
0
0
1
1
1
0
1
0
1
0
1
0
0
1
0
1
2
0
3
1
1
0
0
1
0
2
1
0
2
1
2
0
1
1
0
1
2
1
1
0
0
0
0
1
1
0
0
1
1
2
1
2
0
0
0
1
1
0
1
1
0
2
0
2
1
1
1
1
1
0
1
2
2
1
2
1
0
1
1
0
0
1
1
1
2
0
2
0
2
0
0
0
0
0
0
2
1
1
0
2
1
0
6
1
1
1
0
1
1
1
0
1
2
0
0
1
1
2
2
1
1
2
0
1
1
0
2
1
2
0
2
2
1
1
0
0
2
2
0
2
2
0
2
0
0
1
1
1
0
0
0
1
1
0
0
2
2
2
0
1
0
0
1
0
1
2
2
0
2
1
3
0
1
0
1
2
0
0
0
1
0
0
0
1
1
2
1
1
0
1
2
2
1
0
0
1
2
1
2
0
1
1
1
1
2
0
2
0
0
0
0
0
1
1
0
2
1
1
0
2
1
0
1
1
0
0
1
0
2
0
1
1
1
2
1
1
1
0
0
1
2
2
1
2
1
0
0
0
0
1
0
2
3
0
1
0
1
0
1
1
2
1
2
0
0
2
1
0
1
0
0
0
0
2
1
1
0
2
1
1
0
2
0
2
1
0
1
0
1
1
3
1
0
1
0
1
0
0
3
2
0
0
0
1
1
0
1
0
0
1
0
1
2
1
1
0
0
2
0
0
0
1
0
1
0
0
2
1
1
2
0
0
1
2
1
0
0
1
2
2
1
1
1
1
2
2
1
2
2
0
1
0
0
0
1
1
1
0
0
0
2
1
0
0
2
6
2
0
1
2
1
0
1
2
1
0
0
1
1
1
1
0
1
1
2
1
1
1
0
1
0
0
0
1
0
1
1
2
2
1
1
0
2
1
1
0
0
0
1
0
1
2
0
0
1
2
0
1
1
1
1
0
1
0
1
0
0
0
1
1
1
2
2
0
0
1
0
1
0
0
0
0
1
1
1
0
0
0
1
1
1
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
6
4
0
1
0
0
2
2
1
1
1
0
2
2
0
0
2
1
2
1
1
1
1
0
2
1
2
1
1
2
0
0
0
2
2
2
0
1
0
0
0
1
2
0
1
3
0
1
0
1
2
1
0
0
0
1
1
2
1
0
1
0
1
0
0
2
1
1
2
2
0
0
1
1
0
2
0
0
1
2
2
0
2
0
0
0
1
0
0
1
0
1
1
1
0
2
2
0
0
2
0
0
0
1
2
0
2
0
0
2
1
2
1
0
2
0
0
1
2
1
1
1
1
1
2
3
1
0
0
2
0
0
1
1
0
1
1
2
2
1
0
1
0
0
0
1
1
1
1
3
0
0
0
1
0
0
0
0
0
3
2
0
3
0
0
1
0
2
0
0
0
2
1
0
3
0
0
1
1
1
0
1
1
1
0
2
0
2
2
0
2
2
0
1
0
1
1
0
0
0
0
0
1
1
0
2
0
1
2
1
2
0
1
2
0
2
0
2
2
0
0
0
9
2
0
0
2
0
0
0
1
2
3
1
2
1
0
1
2
0
1
1
3
2
1
0
1
2
2
1
0
1
1
1
2
0
2
1
1
0
1
1
0
1
1
2
7
2
1
1
2
1
0
0
0
2
1
1
1
1
1
0
2
1
2
0
0
0
1
1
0
0
2
2
1
0
2
1
1
1
2
1
0
0
1
1
5
1
0
1
0
0
1
0
0
1
0
1
0
1
2
0
0
0
0
2
0
0
0
1
0
0
0
2
1
0
3
0
1
0
1
1
1
1
0
0
0
1
0
0
1
1
0
0
2
0
1
1
1
0
1
1
1
1
1
0
0
1
0
1
0
2
0
0
1
1
0
0
1
1
1
0
0
1
0
1
1
0
2
2
0
0
0
1
1
1
1
1
0
0
0
1
2
1
1
0
1
0
0
2
1
1
1
3
0
2
1
1
1
1
0
0
0
1
1
1
1
0
0
0
0
2
0
1
2
0
2
1
0
2
2
2
1
0
2
2
1
0
0
2
2
2
0
0
2
0
1
0
1
0
1
0
0
0
2
1
3
1
0
1
0
2
2
0
1
2
1
1
0
1
1
1
2
3
0
2
1
1
1
0
1
1
0
1
1
2
0
2
0
1
1
0
1
1
0
1
0
1
0
2
0
2
0
0
0
2
1
2
1
0
2
0
0
1
1
1
0
1
0
0
1
2
1
1
0
0
0
2
0
0
1
1
1
0
1
0
1
1
0
0
0
2
2
0
2
1
0
1
1
3
1
0
0
1
0
2
0
0
2
0
0
1
0
3
0
1
1
2
0
2
0
4
0
1
0
2
0
0
2
1
1
1
0
0
0
0
1
2
0
0
2
1
0
2
0
1
2
0
2
0
1
0
2
0
2
1
0
0
0
1
2
0
0
1
1
2
1
2
0
0
2
0
2
1
0
1
0
1
0
0
0
0
1
2
0
0
0
1
2
0
1
1
0
2
1
1
1
2
1
2
0
3
1
2
0
1
0
2
0
0
0
1
0
2
0
1
0
1
1
0
0
2
1
0
0
1
1
2
0
0
0
1
0
0
2
1
2
0
2
0
0
3
2
0
0
0
0
1
0
2
1
0
2
1
3
2
0
2
0
1
0
2
0
1
3
0
1
0
0
1
0
0
0
1
0
1
2
0
1
2
1
0
0
0
0
2
1
0
0
1
0
1
2
3
1
0
0
1
2
1
1
1
1
0
0
0
1
1
0
0
0
0
0
1
2
2
0
0
0
0
0
2
0
1
1
1
2
2
1
1
0
1
1
0
1
2
1
2
0
0
2
0
1
1
1
0
4
1
0
0
0
1
1
0
1
1
1
1
1
2
0
2
2
1
1
0
0
1
2
0
0
2
1
0
2
1
1
0
2
0
2
1
2
0
1
1
1
0
0
0
1
1
1
2
0
2
0
0
0
2
1
2
0
1
0
0
0
2
2
0
0
1
1
1
1
1
2
1
1
1
0
2
0
0
1
0
0
0
0
1
0
2
0
0
0
1
1
0
1
0
1
1
0
2
0
1
1
0
0
2
0
1
1
2
0
3
0
0
1
0
1
1
0
2
2
0
1
0
0
1
1
0
0
1
0
1
1
1
0
1
0
2
1
0
0
1
1
2
1
1
1
1
2
0
1
1
3
1
0
0
1
0
1
2
0
1
2
1
2
3
3
0
1
3
1
2
1
0
2
1
0
0
0
1
0
1
0
2
0
1
0
0
1
0
2
2
0
1
0
0
0
1
0
2
1
1
0
1
1
0
1
1
0
1
0
1
0
0
1
1
1
0
0
1
1
2
2
2
2
1
2
1
0
2
0
3
2
2
0
0
1
0
2
2
1
1
1
1
0
0
1
0
0
1
0
0
0
0
0
1
1
1
2
0
4
0
0
0
1
1
0
1
1
2
1
1
0
1
2
0
0
1
1
0
0
1
1
0
1
0
1
0
0
0
0
2
0
0
0
0
3
0
1
0
1
0
1
0
0
0
1
2
1
1
1
1
0
2
1
2
1
2
1
0
0
1
1
1
2
2
1
1
0
1
1
0
1
1
2
1
0
1
1
2
1
2
0
1
0
0
2
2
1
2
1
0
0
0
2
2
1
1
0
0
1
2
0
2
1
1
2
0
2
0
0
0
0
0
2
2
0
2
0
0
0
0
1
1
0
0
0
0
1
0
0
1
2
0
0
0
1
0
1
5
1
0
1
1
0
2
0
0
2
2
1
0
1
0
1
0
0
1
2
1
0
2
1
0
1
0
0
0
0
0
1
0
1
0
1
1
0
1
0
0
1
0
1
0
2
0
0
0
0
0
1
0
1
0
1
2
2
1
0
0
0
2
2
2
1
0
0
1
0
1
0
0
2
1
0
1
2
0
1
0
0
2
1
0
0
2
2
0
1
0
0
0
1
2
3
2
2
1
1
0
1
0
2
0
1
2
2
0
1
1
1
2
0
1
0
2
2
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
1
2
0
0
0
1
0
0
2
0
1
1
0
1
0
1
0
1
0
1
0
1
2
2
1
1
1
2
0
1
1
0
0
2
2
0
1
1
1
0
1
1
0
1
1
1
2
1
3
0
1
2
1
2
2
1
2
0
1
0
2
2
0
0
1
1
2
0
1
0
1
3
1
0
2
1
0
1
1
0
1
0
1
0
0
0
0
2
1
1
0
1
1
2
1
1
0
0
0
2
0
2
2
0
1
0
2
2
2
0
0
0
1
0
0
1
0
2
0
2
0
0
2
1
0
0
3
1
0
0
0
1
0
1
0
2
2
0
1
1
0
0
1
1
0
0
1
0
2
0
0
1
1
1
1
0
1
0
2
0
1
1
2
1
0
0
1
1
0
0
1
0
0
1
0
0
2
2
1
1
0
0
2
0
1
0
0
0
0
0
2
2
1
1
0
2
0
2
0
1
0
1
0
0
2
1
0
0
0
0
1
0
1
0
2
0
0
1
2
0
1
1
0
3
1
1
0
0
1
0
0
0
0
1
2
1
2
1
1
0
0
1
0
1
1
1
1
0
2
1
1
0
1
2
2
1
1
2
0
0
2
0
1
2
1
0
0
1
1
0
0
1
0
0
1
1
1
2
0
1
2
0
0
1
0
0
1
1
1
2
1
1
2
1
2
0
2
1
0
2
2
2
0
0
0
1
2
1
2
0
0
0
0
0
0
0
1
0
3
0
2
0
2
1
0
0
2
0
9
0
1
1
0
0
0
1
1
0
0
0
2
0
0
0
0
1
0
2
1
1
0
1
1
0
1
0
0
2
1
1
1
0
0
2
1
0
0
0
0
0
0
0
1
0
1
0
1
0
2
0
0
2
0
0
2
0
1
1
0
1
0
0
2
1
2
0
1
2
0
1
0
0
1
0
0
2
0
0
0
2
1
0
1
0
1
0
0
1
0
1
2
1
1
0
1
1
0
0
1
1
0
0
2
1
0
1
1
2
0
0
0
1
1
0
0
2
1
2
1
1
0
2
0
0
1
2
4
1
0
0
0
1
2
2
1
1
1
1
0
0
1
1
0
0
0
0
1
2
1
0
0
2
1
0
0
1
1
1
0
0
2
1
1
2
1
1
2
2
1
1
1
0
0
0
1
1
2
0
2
2
2
2
1
2
0
2
1
0
1
0
0
0
0
1
1
0
1
1
2
1
2
1
0
0
2
0
0
0
1
1
1
0
0
1
0
0
0
0
2
2
2
2
0
1
1
0
1
1
0
0
0
0
2
2
2
0
2
0
0
1
1
2
1
2
1
1
1
0
2
0
0
0
2
0
0
1
0
3
1
0
0
1
1
0
2
0
2
0
1
1
0
1
0
2
0
1
1
1
1
2
2
1
0
0
2
3
1
1
0
2
0
0
1
2
0
1
1
1
0
0
1
0
0
0
2
3
0
1
0
1
1
1
0
1
1
2
0
1
2
0
0
1
1
0
1
0
0
1
3
0
0
0
1
1
0
1
0
2
0
2
0
1
1
2
0
0
0
1
0
1
0
2
1
0
1
0
1
1
2
0
1
1
0
0
2
1
0
1
0
2
2
0
1
0
0
0
2
0
1
0
1
1
0
0
1
2
0
2
0
0
1
0
1
0
0
1
0
0
1
0
0
0
1
2
0
0
0
1
0
0
1
0
0
2
2
2
2
1
1
1
0
1
2
2
1
0
1
0
1
2
1
0
1
0
3
1
1
1
1
0
0
0
2
1
2
0
0
0
1
2
2
0
1
2
1
1
0
0
0
0
1
0
1
1
1
0
0
0
0
0
1
1
0
1
0
1
2
3
1
1
0
0
0
1
1
0
1
0
0
1
0
0
2
0
1
1
1
2
1
2
1
0
0
0
0
0
0
2
2
1
1
2
1
0
2
2
1
0
2
1
0
1
1
0
1
1
0
1
2
0
1
2
1
0
1
0
0
0
0
1
2
0
2
0
1
1
0
1
1
0
0
0
2
0
0
0
2
0
1
1
2
2
0
1
0
1
1
1
1
1
1
3
0
2
2
0
1
0
0
0
1
1
1
1
1
0
0
1
0
2
1
2
2
1
0
2
0
2
0
2
1
0
1
0
1
0
1
0
2
1
0
0
1
0
1
1
1
0
1
0
2
0
1
2
2
1
0
1
1
1
0
0
1
0
1
3
1
0
3
0
1
0
1
0
2
1
2
1
2
0
1
2
0
0
1
0
1
0
0
0
0
0
0
0
0
2
1
1
0
2
2
0
0
2
0
1
1
1
1
0
2
1
1
1
1
0
0
1
0
1
1
0
1
2
1
0
0
0
0
1
2
1
1
0
2
0
1
2
0
2
1
1
1
0
1
1
0
1
0
1
1
0
0
1
1
0
2
0
0
1
2
1
2
1
1
1
1
1
0
1
1
2
0
0
0
2
1
0
0
2
2
1
0
1
1
0
0
2
2
1
0
0
0
0
1
0
0
1
1
1
1
0
1
0
0
0
0
0
1
0
1
2
0
0
1
1
0
0
2
0
1
2
2
1
0
1
0
0
0
0
1
1
2
1
0
1
0
1
0
1
0
0
1
1
2
1
1
2
2
0
1
0
2
2
0
1
1
2
0
0
0
1
0
1
1
1
2
0
0
1
2
1
2
0
1
0
2
2
0
0
0
0
1
2
0
2
0
0
1
1
2
0
0
2
1
0
2
1
1
0
0
1
1
1
0
2
3
0
0
0
1
0
1
2
0
0
0
1
1
0
0
2
1
0
0
2
0
0
1
0
1
1
2
3
1
1
1
1
1
0
0
0
0
1
2
0
0
2
1
1
0
1
1
0
0
2
0
0
2
0
0
0
0
2
1
1
1
1
0
2
2
1
1
2
1
0
0
0
0
0
1
1
2
1
1
1
1
2
0
2
1
2
0
1
0
2
1
2
1
2
1
0
2
0
1
2
2
2
2
2
2
2
1
0
0
1
0
1
1
0
0
0
2
0
1
1
2
1
1
1
0
1
0
0
1
1
1
1
0
0
1
1
1
0
2
1
0
2
1
1
1
1
1
0
0
1
1
1
1
1
0
0
0
2
1
0
2
0
0
2
1
0
2
0
1
1
2
0
0
2
1
7
0
1
2
0
1
1
1
0
0
2
0
0
0
2
1
1
0
2
2
2
2
2
3
0
1
0
1
1
0
2
1
0
1
2
2
1
1
3
0
0
1
1
1
1
2
0
2
1
2
1
1
1
0
1
1
2
3
1
1
1
0
0
2
2
0
0
0
0
0
0
0
1
0
1
4
0
2
1
0
0
1
0
2
2
2
0
0
1
0
0
0
0
0
0
2
1
1
3
0
2
2
1
2
0
0
2
2
1
1
2
0
1
1
0
0
0
0
1
1
1
2
0
1
2
1
1
0
1
2
0
0
0
1
1
3
1
0
0
0
0
1
0
0
1
0
2
0
2
0
0
1
0
1
1
1
1
2
0
0
0
0
0
1
2
1
1
0
0
2
1
3
2
1
1
0
0
1
0
0
2
2
1
1
0
2
0
0
2
0
1
2
2
0
0
1
0
0
0
1
0
2
0
1
0
0
2
2
1
0
2
0
3
0
1
0
1
1
0
0
1
0
1
1
1
1
2
1
1
2
1
1
0
2
1
1
0
0
1
0
0
0
2
0
2
0
2
1
0
1
2
2
1
0
1
0
0
1
1
1
1
0
1
0
1
2
4
1
1
1
0
0
0
1
0
2
2
1
1
1
1
2
0
1
1
1
1
0
1
1
1
1
1
0
0
0
2
1
0
2
1
1
1
0
1
0
2
1
0
0
0
0
0
1
2
0
1
1
2
0
2
0
0
0
0
0
2
0
0
0
0
2
1
2
2
1
0
1
1
0
1
1
1
0
2
0
2
0
0
0
1
1
2
0
0
0
0
0
1
0
0
0
0
0
0
2
2
2
2
2
0
1
0
0
3
0
1
0
0
0
1
3
2
2
0
2
1
1
1
2
1
0
0
0
3
0
2
0
1
1
1
1
2
1
0
1
0
0
0
0
1
2
2
0
2
1
1
0
1
0
0
1
1
0
2
0
0
2
1
1
0
2
2
0
1
2
0
1
0
1
2
0
1
2
1
2
2
2
2
0
0
0
1
2
1
2
1
1
0
1
0
0
0
0
0
1
1
1
1
0
0
2
2
0
0
0
0
0
0
1
0
2
0
1
1
1
2
2
2
0
1
1
0
0
1
0
0
1
0
0
1
0
2
1
0
2
1
1
0
1
0
2
2
2
2
0
0
2
2
2
2
1
1
0
0
1
0
2
1
2
0
0
1
0
1
0
2
0
0
0
1
0
1
1
2
0
1
1
0
1
5
1
0
1
0
0
1
0
1
1
1
1
0
0
1
0
2
2
0
0
1
1
0
0
0
1
0
0
5
0
0
1
2
0
1
1
0
1
2
2
1
1
0
0
2
2
0
2
3
0
0
1
1
2
1
0
0
2
0
1
0
1
0
1
2
1
1
0
0
0
0
1
1
0
1
0
1
2
1
0
0
0
0
1
0
1
0
2
1
1
1
0
0
1
0
1
1
1
0
0
1
1
1
1
2
1
0
0
1
0
2
0
1
1
1
1
2
2
0
2
0
0
0
2
0
2
0
1
0
1
0
0
1
1
2
0
1
0
0
2
1
2
2
0
2
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
3
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
2
2
2
0
1
1
1
0
2
0
2
1
1
2
1
1
1
0
2
0
1
0
1
0
0
0
1
0
0
0
0
0
2
1
2
1
2
0
2
1
1
2
0
2
0
0
0
1
1
1
0
3
1
0
0
0
0
2
2
1
1
2
0
1
0
0
2
1
1
1
1
1
0
1
2
0
0
1
1
0
0
1
1
1
2
1
0
0
0
1
1
0
1
0
0
2
0
1
1
2
0
1
1
0
1
1
0
1
2
0
1
0
1
1
2
1
1
1
1
1
1
1
2
0
0
2
1
0
1
0
2
1
2
1
1
0
1
0
1
1
2
1
0
1
1
0
0
1
1
0
1
0
0
1
1
0
2
0
0
1
1
1
1
1
1
0
0
1
2
0
1
2
0
0
1
1
0
0
2
2
1
0
0
0
0
1
2
0
1
2
0
1
2
0
1
2
1
2
0
0
3
1
2
1
0
2
1
0
0
0
5
1
1
3
0
0
1
1
1
0
1
0
0
2
1
0
1
1
0
0
0
0
0
2
1
2
1
1
1
1
0
0
1
0
1
1
0
1
0
2
1
0
2
1
2
0
0
0
0
1
0
0
0
2
2
2
1
2
1
1
1
1
0
1
1
2
2
1
1
1
0
0
1
0
0
0
1
0
0
1
0
0
2
1
2
0
0
1
0
1
0
1
2
0
2
2
1
0
0
0
2
0
1
1
0
1
2
2
1
1
0
1
0
3
0
2
0
0
0
1
0
1
0
1
1
0
0
0
0
0
2
0
0
2
1
1
1
1
0
0
0
1
1
1
2
0
0
1
1
2
0
0
0
2
0
1
1
1
1
1
0
0
0
1
0
0
0
1
1
0
1
0
0
2
0
2
2
0
0
1
2
2
0
1
0
1
0
2
1
2
1
1
1
0
1
0
0
1
2
1
0
0
1
2
0
1
0
2
0
2
2
2
0
0
2
0
2
1
0
1
2
1
2
0
0
2
2
1
1
0
2
0
0
1
1
0
1
2
1
2
2
0
1
1
1
0
1
1
1
0
2
0
1
1
1
1
1
1
0
1
1
0
0
2
1
1
2
0
1
2
2
1
0
0
0
0
2
0
0
1
1
1
0
2
0
1
2
1
4
0
0
1
0
2
1
1
2
0
1
0
1
0
0
0
1
1
2
0
1
0
0
0
0
0
1
0
1
0
0
0
2
0
0
2
0
0
0
0
1
1
0
1
1
0
1
1
1
0
2
0
2
1
0
1
0
1
0
2
1
0
1
1
0
1
1
0
0
0
0
1
1
2
1
1
1
0
1
0
1
0
0
0
2
2
1
1
3
0
0
3
0
0
1
2
0
1
2
1
0
1
2
2
2
0
1
1
0
0
0
2
3
0
0
0
3
1
1
0
2
0
0
0
0
1
2
1
2
0
0
0
0
2
1
1
0
0
0
1
0
1
1
0
2
1
1
0
0
0
2
2
1
1
0
2
0
0
0
2
2
1
0
0
1
0
1
0
2
0
2
0
0
1
2
2
1
1
1
2
0
1
0
0
0
1
0
1
1
2
2
0
1
0
1
2
1
0
0
1
4
0
1
0
1
1
0
1
0
0
2
2
0
1
1
0
0
1
6
1
2
0
2
0
2
1
0
2
0
1
3
2
1
0
0
1
1
0
1
0
0
1
1
0
1
0
1
0
1
1
1
1
1
2
5
0
0
0
2
1
1
1
1
1
0
1
0
0
1
0
5
0
1
1
0
1
2
1
0
0
1
0
0
1
1
2
2
0
0
2
1
0
0
2
1
1
2
0
2
1
3
0
0
1
0
2
2
2
2
1
0
0
0
2
0
2
0
1
2
0
0
0
2
1
0
0
0
1
1
1
1
0
0
0
1
0
0
0
1
3
1
0
0
3
1
1
2
0
0
0
2
1
1
1
0
1
1
2
0
2
1
2
1
0
1
1
2
1
0
0
1
0
1
0
2
0
1
2
1
0
1
0
1
2
2
2
1
1
0
1
1
0
2
1
1
1
2
1
2
1
2
0
0
2
0
1
0
0
2
1
0
2
1
1
2
2
0
0
1
0
1
0
1
1
0
2
0
1
1
2
1
0
0
2
0
1
0
1
2
0
0
1
2
0
2
0
0
1
0
0
1
1
2
1
0
1
2
1
1
1
0
2
1
0
0
0
2
2
1
1
1
1
0
0
2
1
2
0
1
1
0
0
1
0
2
2
1
2
1
1
1
0
0
1
0
1
1
1
0
1
0
0
1
0
0
1
0
2
0
2
1
1
0
0
1
1
1
1
0
0
1
0
1
1
2
1
1
2
2
0
2
0
1
1
0
0
0
0
0
1
1
0
0
2
1
0
2
0
0
2
3
1
0
0
1
0
1
2
1
0
0
2
2
0
2
1
2
1
0
0
0
1
1
0
1
2
1
0
0
1
0
0
0
2
0
0
3
1
0
1
2
1
0
0
1
2
1
0
0
1
0
1
0
0
1
1
1
0
2
1
2
0
1
0
1
1
2
3
0
1
1
0
2
0
0
2
1
0
1
1
0
1
2
1
1
1
1
0
0
2
0
0
0
0
1
1
0
1
2
0
1
2
2
0
2
1
1
1
0
1
1
0
2
0
1
1
1
2
0
2
0
0
0
2
0
2
1
0
1
3
0
1
1
0
1
0
1
2
1
0
0
2
0
0
1
1
1
1
2
1
0
1
0
2
0
1
0
1
0
1
0
0
2
0
2
1
0
0
0
1
0
0
2
0
0
1
0
1
2
1
2
0
0
1
2
1
0
1
0
0
1
1
1
2
0
1
2
1
2
0
1
1
0
1
2
1
1
1
1
1
2
1
0
0
0
1
2
2
2
2
1
1
0
1
1
0
0
1
0
0
1
2
2
0
2
2
2
0
1
1
0
0
1
0
2
0
0
1
1
0
1
0
1
1
2
2
2
2
0
1
0
1
2
0
1
0
1
1
0
1
1
2
1
0
1
0
0
1
2
1
2
2
1
0
2
0
0
1
1
2
0
0
1
0
1
0
0
2
0
1
1
1
1
1
2
1
1
0
0
0
0
1
0
0
1
1
1
2
1
2
1
1
0
2
1
1
1
1
1
1
0
0
0
1
0
1
2
2
2
1
2
1
0
0
1
1
0
2
2
0
0
2
1
0
1
2
0
0
2
0
0
1
0
1
1
0
1
1
1
1
1
1
1
0
0
0
1
2
0
2
0
0
2
0
3
1
0
1
2
0
2
2
1
0
0
0
1
1
1
0
1
0
1
1
1
1
0
1
1
0
2
2
1
0
0
0
1
1
2
0
2
1
0
0
0
1
2
1
2
2
0
1
2
1
2
1
0
2
0
1
1
0
1
0
1
2
0
2
1
1
2
1
2
0
1
1
1
0
0
1
0
1
0
0
2
0
1
2
2
1
1
0
2
0
1
1
2
2
0
1
1
1
0
0
0
1
2
1
1
2
0
4
2
0
0
3
0
0
0
0
0
3
3
1
1
2
2
1
0
2
1
1
0
1
2
1
0
0
0
1
1
1
2
0
2
0
1
2
0
1
3
1
1
2
0
0
3
2
2
0
1
1
0
0
0
2
2
0
0
0
2
0
0
1
1
1
1
1
1
0
1
0
1
1
0
1
0
0
0
1
2
0
1
0
2
0
2
1
0
0
1
2
2
0
1
1
2
0
0
2
1
2
1
0
2
0
0
0
0
0
0
0
0
0
1
1
0
6
2
0
0
1
0
1
0
0
2
0
1
2
0
0
1
0
1
1
0
2
1
1
0
1
1
1
0
0
1
1
0
0
0
0
1
0
0
1
1
1
0
3
0
1
0
2
0
2
2
1
2
0
1
2
1
0
2
1
1
0
2
1
1
0
2
1
0
2
0
1
0
0
1
1
1
0
0
1
2
0
1
0
0
1
2
0
0
2
1
0
2
0
2
2
0
2
0
1
0
0
0
0
2
0
1
0
2
0
1
1
0
1
0
0
1
0
1
1
0
1
1
0
1
2
1
0
2
1
2
1
1
1
0
2
1
0
0
0
1
1
0
1
0
2
0
1
2
2
0
1
1
0
1
2
0
0
0
1
1
3
0
0
2
0
0
1
1
2
1
2
1
1
2
0
1
0
0
1
0
1
2
1
0
0
0
0
1
1
1
0
0
2
1
3
0
0
1
0
1
1
1
0
2
2
0
0
0
0
1
0
1
1
0
0
1
2
0
2
1
0
2
1
0
1
1
1
0
1
2
0
1
1
0
2
2
1
0
2
1
0
3
1
1
0
1
0
1
2
2
0
1
2
0
2
0
1
2
1
1
0
2
1
1
0
1
2
2
0
0
1
0
2
3
2
0
0
1
0
0
0
1
1
1
0
0
0
0
2
0
1
3
1
0
0
0
0
1
0
0
0
0
1
1
1
1
1
2
0
1
1
1
0
2
0
2
1
0
1
1
0
1
0
2
1
2
0
0
2
0
0
0
1
0
2
1
1
0
0
2
1
0
2
0
14
2
2
0
1
1
2
2
2
1
2
1
0
2
1
1
0
2
1
2
1
0
2
0
0
0
2
1
0
1
0
0
1
0
2
0
1
2
1
1
2
1
0
1
1
0
0
1
1
1
2
0
0
1
2
0
1
1
0
0
2
1
0
0
0
2
1
0
2
0
1
0
0
0
0
1
0
2
1
1
0
2
1
0
2
3
2
2
2
0
0
1
0
1
1
1
1
2
1
0
1
0
1
1
0
2
2
1
0
1
0
0
0
1
0
1
0
1
1
1
1
1
2
1
0
0
0
0
0
0
3
1
2
2
0
1
2
0
1
2
1
0
1
1
0
0
1
1
2
0
2
2
1
1
0
0
2
0
3
1
1
2
0
1
1
2
2
0
4
0
1
2
0
1
1
0
0
1
0
1
1
1
0
1
0
0
2
0
1
1
0
2
1
0
2
0
1
0
0
0
2
0
0
1
0
1
2
1
0
1
1
0
1
1
1
0
2
0
1
1
0
0
1
1
0
2
2
0
1
1
0
0
1
1
0
0
0
0
1
0
1
0
0
1
1
1
2
0
0
2
3
0
2
1
0
0
2
0
0
0
2
2
1
1
0
2
0
2
0
2
0
1
1
0
2
0
0
0
2
0
1
2
0
2
0
0
0
0
1
0
2
1
2
0
2
1
1
2
1
1
0
1
0
0
0
1
1
2
2
1
1
1
0
1
0
3
1
0
0
0
0
0
0
1
3
1
1
0
1
1
2
1
1
0
2
1
0
1
1
2
2
1
0
0
2
2
1
0
0
0
3
2
0
1
0
1
0
0
0
1
1
2
0
1
0
0
0
1
1
2
0
0
0
1
1
0
0
0
2
0
2
1
1
1
1
1
1
0
0
0
1
2
0
1
0
3
0
0
3
2
1
0
1
1
0
0
2
1
0
0
0
1
1
1
1
0
2
0
0
1
1
0
0
1
0
0
2
2
1
1
0
1
0
0
1
1
2
2
0
0
0
1
2
2
1
0
1
0
0
0
0
1
1
1
0
1
0
0
1
1
2
1
1
0
3
1
2
1
0
0
0
0
0
1
0
1
2
0
0
2
1
3
1
0
0
0
0
2
0
2
3
1
1
0
0
2
0
2
1
0
2
1
0
1
0
2
1
1
0
0
0
1
0
0
2
1
1
1
1
1
0
0
1
0
0
0
1
2
0
0
1
0
3
1
1
4
1
1
1
0
2
0
1
2
2
1
1
1
0
2
1
2
2
0
1
1
0
0
0
0
2
0
0
1
1
1
1
3
0
1
2
2
0
0
2
1
1
0
0
1
1
2
0
2
0
0
1
1
0
0
1
1
0
2
1
0
0
1
1
2
2
2
0
1
0
1
2
1
0
1
1
2
0
1
1
1
1
1
0
0
0
0
1
2
2
1
2
0
2
0
2
2
2
1
1
1
1
1
1
1
0
0
1
1
0
2
0
0
1
0
0
2
0
1
0
1
2
0
1
1
1
0
1
2
0
0
2
1
1
0
1
0
2
1
0
0
0
0
1
4
2
1
1
0
0
0
1
0
0
0
1
1
0
2
2
0
2
0
1
2
5
1
2
2
1
1
1
0
2
0
0
1
2
2
0
0
1
1
2
0
1
1
1
0
1
1
0
1
0
0
2
0
0
1
1
1
1
1
2
0
0
0
0
1
1
1
2
1
1
0
0
0
0
2
0
0
0
0
1
0
2
2
0
0
0
1
1
2
1
3
1
3
0
0
1
0
1
0
0
1
1
1
1
1
2
1
2
2
1
0
2
1
1
0
1
1
0
0
1
0
1
0
0
1
1
1
0
0
2
0
0
1
2
0
1
2
0
0
2
1
0
0
0
0
2
1
0
1
2
1
1
0
1
0
2
1
1
0
1
0
2
0
0
0
2
1
1
0
0
1
1
0
1
2
1
2
0
0
1
0
1
1
0
2
1
0
0
0
0
0
0
2
0
0
0
1
3
0
1
1
1
1
1
1
2
2
2
0
2
1
0
1
1
0
0
0
0
1
0
2
1
1
1
0
0
0
0
0
1
0
2
1
0
3
1
0
1
1
1
2
1
0
0
0
2
1
0
2
1
1
0
2
1
0
1
1
1
0
2
0
1
0
0
0
1
2
1
1
2
5
0
0
1
0
2
1
0
0
2
1
0
1
3
2
1
2
1
1
1
2
2
1
2
2
0
2
0
2
1
1
0
1
2
0
2
1
1
2
0
0
1
0
2
2
1
0
0
2
1
0
0
2
1
0
0
0
0
0
1
2
1
0
1
0
1
2
0
0
1
1
0
0
1
1
2
2
1
0
1
1
0
1
1
0
0
2
1
1
1
0
1
0
2
0
0
1
1
0
0
0
0
0
2
1
0
1
0
2
0
0
1
1
1
1
2
3
1
0
1
2
2
1
1
2
1
0
0
0
1
0
2
1
0
2
0
2
1
1
0
0
1
1
1
1
0
3
0
1
1
1
2
0
0
0
2
0
2
0
1
0
1
1
0
1
0
1
2
0
0
0
0
1
1
1
2
2
1
1
1
1
1
1
0
1
0
2
1
1
2
0
0
0
0
0
1
1
1
1
2
0
1
1
0
1
1
1
1
0
1
0
0
2
1
1
1
0
1
0
2
0
2
0
0
1
1
0
1
1
1
1
1
2
2
0
1
2
2
0
1
0
0
1
1
0
0
2
2
0
1
0
1
0
0
2
8
1
0
2
0
1
1
0
2
1
0
2
2
1
2
1
0
0
0
2
2
1
1
2
1
0
2
1
1
0
2
2
2
0
1
1
2
0
1
0
0
1
1
1
0
0
1
1
0
1
1
0
2
2
1
0
2
1
2
0
0
0
0
1
0
2
0
0
1
1
0
1
2
0
2
0
1
1
2
1
0
0
1
0
2
1
1
2
1
1
1
2
0
2
2
1
1
3
0
2
2
2
2
2
1
1
2
1
0
2
1
2
0
0
2
0
0
1
0
0
0
0
1
1
0
1
1
0
2
1
0
0
2
0
1
2
2
2
0
1
2
0
2
1
0
2
0
0
0
2
0
2
1
2
0
1
0
1
2
1
1
0
1
1
2
0
1
1
0
1
0
1
1
2
0
0
2
1
0
1
1
2
1
1
1
1
2
1
1
0
2
0
0
1
1
1
2
0
1
0
0
1
2
1
2
2
1
1
0
0
1
0
2
0
0
0
1
2
2
1
1
0
1
1
1
0
1
1
1
1
0
0
2
0
0
0
1
0
2
2
0
2
1
1
0
0
0
2
0
1
0
0
1
1
0
0
2
1
2
1
1
2
0
1
0
0
0
2
2
0
0
0
1
1
0
2
1
2
2
0
0
0
1
1
0
0
1
0
0
0
0
0
1
2
1
1
2
2
1
0
2
2
1
1
0
2
2
1
1
0
0
0
0
0
1
1
0
0
4
1
0
2
1
2
2
0
0
0
2
2
1
1
0
3
0
2
1
1
0
0
0
3
1
0
1
2
0
0
0
2
0
1
0
0
1
1
2
0
0
0
0
0
1
1
1
1
1
2
1
2
0
1
1
1
2
0
2
2
2
0
0
0
0
2
2
0
2
0
2
0
2
0
0
0
0
1
2
0
1
1
1
1
0
0
0
1
4
1
2
1
1
1
1
1
2
3
0
1
0
1
1
2
0
0
0
0
1
0
0
2
0
1
1
0
2
1
1
1
1
0
0
1
0
0
0
1
1
1
0
0
0
0
3
1
1
0
0
0
1
0
0
1
0
2
2
1
1
0
1
0
0
1
0
0
1
1
1
1
0
2
1
0
1
2
1
2
0
0
1
0
1
1
0
0
1
0
0
1
1
1
1
0
1
0
0
1
0
1
0
0
0
3
1
3
1
0
1
2
0
1
1
0
0
1
2
1
2
0
1
0
1
1
1
1
0
1
2
0
0
1
0
1
1
0
2
1
1
0
1
1
2
2
0
2
1
0
1
0
1
1
1
0
0
1
1
0
0
1
1
0
0
1
1
2
1
0
2
2
0
1
0
2
2
1
2
0
0
1
2
1
0
1
1
0
1
0
1
1
1
0
0
0
1
1
2
1
0
0
0
1
0
0
2
1
0
0
2
0
1
1
0
1
1
0
1
0
0
0
1
0
0
2
1
0
2
1
1
0
1
0
2
1
2
1
1
1
1
0
0
1
1
0
2
0
0
0
0
1
0
0
1
1
0
1
0
1
0
2
1
2
0
0
1
0
1
1
0
1
3
2
0
1
1
1
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
1
0
2
1
0
2
0
0
2
0
1
0
0
1
0
1
2
2
0
1
1
0
1
1
0
1
1
1
0
2
1
0
1
1
0
0
0
1
0
1
2
1
1
2
1
2
0
0
1
3
0
2
2
0
0
2
1
0
2
0
0
1
0
2
0
0
0
1
1
0
0
2
1
1
1
2
1
1
0
0
0
0
1
0
1
0
1
2
1
1
2
0
1
0
0
0
0
4
1
2
0
1
1
2
1
2
0
0
0
2
1
2
0
1
2
3
1
1
1
1
0
0
1
1
1
0
0
3
0
1
0
0
2
1
0
0
2
0
0
1
1
1
1
0
0
0
0
1
2
2
0
1
1
0
0
0
1
2
0
2
1
1
0
2
0
1
0
0
0
1
1
0
0
0
2
0
2
0
0
0
0
1
0
1
0
0
1
0
2
1
0
1
1
0
2
0
1
1
2
1
0
1
0
1
0
1
0
0
2
0
1
2
0
1
0
1
1
1
0
2
1
1
0
0
1
1
0
2
0
1
1
0
2
0
0
1
1
1
0
1
0
1
1
0
2
0
0
1
3
1
2
1
2
2
1
2
0
0
4
0
1
0
0
0
0
1
0
1
0
2
0
2
1
3
1
1
1
0
0
0
2
1
1
0
1
0
2
0
1
0
1
1
1
2
0
0
1
0
1
0
2
1
2
1
0
2
1
0
2
0
0
1
2
1
0
1
0
1
0
0
1
1
2
1
1
2
1
0
1
0
0
1
0
1
0
1
2
0
1
1
0
1
0
1
0
1
0
1
0
0
0
2
0
0
2
0
1
1
0
1
2
1
1
0
0
2
1
0
1
0
1
0
1
2
0
1
1
0
0
0
1
0
0
0
2
1
0
3
1
2
1
1
0
2
0
1
0
0
1
0
0
0
1
1
1
3
0
0
0
0
0
1
0
3
1
2
1
0
0
1
0
1
1
1
1
0
1
2
0
1
2
0
0
1
2
2
0
1
2
0
0
0
2
0
2
2
2
2
0
1
2
1
0
1
0
1
0
0
1
0
1
2
2
0
0
2
1
0
2
0
0
1
2
2
1
0
1
1
1
1
0
1
1
2
1
0
2
0
1
1
1
0
1
1
1
0
0
2
1
1
0
2
0
2
0
1
0
2
2
0
0
0
2
2
1
2
2
0
2
1
0
0
0
1
1
0
1
1
2
1
2
2
0
1
2
0
1
1
1
0
0
1
1
2
2
0
2
1
2
1
2
0
2
2
0
0
0
0
0
0
1
0
0
2
1
0
0
0
2
0
0
0
1
0
0
1
0
0
1
1
1
1
1
0
0
1
1
1
0
1
2
0
0
1
0
0
0
1
2
1
2
2
1
0
0
2
1
0
1
2
1
0
1
1
0
0
1
2
0
1
2
0
2
1
0
2
1
1
0
2
0
2
0
0
1
2
1
1
1
2
2
0
1
0
2
0
1
1
0
0
1
1
1
0
2
0
2
2
1
1
1
1
1
0
2
1
0
0
0
1
1
1
1
0
2
2
1
1
1
1
1
1
1
2
1
0
0
2
1
1
0
1
1
1
2
2
0
1
0
2
0
1
2
0
1
1
0
3
2
1
2
2
2
0
1
2
1
0
2
0
0
0
0
2
1
1
0
1
2
2
0
1
0
0
0
1
0
2
0
1
2
4
0
1
1
0
1
1
1
0
0
1
1
0
1
0
1
1
0
0
1
0
1
2
0
1
1
0
2
0
1
1
1
0
1
0
0
0
0
2
1
1
0
0
5
0
0
0
3
0
1
1
1
2
2
3
1
1
1
1
0
1
0
0
0
0
1
3
0
0
0
0
0
0
1
4
1
1
1
1
1
1
1
1
1
1
0
2
2
1
1
2
2
1
2
0
0
1
2
1
2
1
0
0
1
0
0
0
2
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
2
0
2
1
1
3
2
2
1
0
1
1
0
1
0
2
0
1
1
1
1
1
0
2
0
1
2
0
1
0
1
1
1
2
1
2
1
1
1
0
2
0
1
0
1
1
1
1
2
1
1
0
2
0
2
0
1
0
1
2
0
3
2
0
0
1
0
3
0
1
0
2
3
1
2
1
2
0
0
0
1
1
0
9
1
0
1
0
1
0
2
0
2
0
2
2
0
1
1
0
0
0
1
1
0
1
0
2
0
1
0
0
1
0
0
2
1
1
0
1
1
1
1
1
1
0
3
1
0
0
0
0
1
0
0
0
1
1
0
1
3
1
1
0
1
1
2
3
1
2
1
0
0
0
0
7
1
0
0
0
0
0
0
0
2
1
2
0
1
2
0
0
0
0
2
0
1
1
2
1
1
1
0
1
0
2
1
1
1
0
2
0
1
2
1
1
1
1
0
0
1
1
1
0
0
0
1
1
1
1
0
1
1
1
0
2
2
0
0
3
0
1
0
0
1
0
1
0
0
1
0
0
1
2
0
1
2
0
1
1
0
0
2
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
1
0
1
1
0
1
1
0
0
0
1
0
0
0
2
1
0
2
0
1
2
2
2
1
0
0
2
0
1
2
0
0
0
2
1
0
1
1
1
1
1
1
0
2
1
1
1
1
0
2
0
0
0
0
0
1
1
1
0
0
0
1
1
1
1
0
1
1
0
2
0
2
1
1
2
2
1
0
0
0
2
2
2
1
1
0
1
1
0
2
2
1
0
0
1
1
0
2
1
1
0
0
0
1
2
1
0
2
0
0
2
1
1
2
0
2
1
0
0
0
1
0
2
0
0
0
0
1
1
2
1
0
0
1
0
0
1
1
1
0
0
2
0
0
0
0
0
1
2
2
0
0
1
1
1
0
2
2
0
1
0
0
0
1
2
1
0
0
0
0
1
2
0
2
0
1
0
0
0
1
2
0
2
0
0
2
0
0
1
1
0
0
1
0
1
2
1
2
0
0
0
0
1
1
0
2
2
2
0
0
0
0
1
2
2
1
0
1
0
0
2
1
1
1
0
0
0
1
0
1
0
1
0
2
1
0
1
0
0
2
0
0
1
1
2
0
0
2
1
2
1
2
2
1
0
0
2
1
2
1
0
0
0
0
2
0
2
1
1
1
0
2
0
1
0
2
0
1
1
1
1
1
1
0
0
0
0
2
2
0
0
0
1
0
1
0
1
0
2
0
0
1
0
0
0
0
0
1
3
1
2
0
0
0
1
0
0
0
0
1
2
0
0
1
1
1
2
0
1
1
1
0
2
1
2
1
2
1
1
0
1
2
0
1
2
0
1
0
1
0
2
3
0
2
0
2
1
2
0
1
1
3
2
1
1
2
0
1
0
1
1
0
0
2
0
1
1
2
0
1
1
1
1
0
1
0
0
0
0
0
1
1
1
0
2
2
0
1
1
1
0
1
1
0
2
0
0
1
0
1
1
2
1
1
1
0
0
0
1
1
1
1
0
2
1
2
3
1
0
0
1
2
1
0
0
0
1
1
0
2
0
2
0
0
0
0
1
2
1
1
1
2
0
1
2
0
1
1
1
2
0
2
2
1
1
1
1
0
1
1
2
0
1
2
2
1
2
0
0
1
2
1
2
0
0
1
1
4
0
0
2
1
1
2
0
2
1
0
0
1
0
1
0
1
1
0
0
3
0
2
2
1
0
0
1
0
0
2
0
0
1
1
1
0
0
0
0
1
0
1
0
0
0
0
1
0
2
1
0
1
1
2
0
2
1
0
1
2
1
1
0
0
0
1
1
0
2
2
0
1
0
0
2
0
0
1
1
0
1
0
0
1
0
0
1
0
1
1
1
2
0
1
1
0
0
1
1
0
1
2
0
1
0
0
1
0
2
1
1
1
1
0
1
0
0
2
1
0
0
1
0
1
2
0
1
1
2
1
3
0
0
0
1
1
2
1
1
0
2
1
0
0
0
1
0
1
0
0
2
1
2
1
0
1
0
1
0
1
2
2
1
0
0
1
1
0
0
0
0
0
0
1
1
0
0
1
2
1
1
0
2
0
2
1
1
1
3
1
2
0
0
0
1
1
1
0
1
2
0
1
0
0
0
1
0
1
0
2
2
0
2
0
2
0
1
2
1
0
0
1
2
1
0
1
0
1
0
0
1
1
0
2
0
0
1
2
0
1
0
0
0
2
1
2
1
2
0
0
0
2
1
1
0
0
1
0
1
0
1
0
1
3
2
0
0
4
1
1
1
1
1
2
1
1
0
1
1
1
0
1
0
1
0
0
1
0
2
0
3
1
0
1
2
1
1
0
0
0
0
1
2
2
2
0
1
0
1
0
0
1
0
1
0
0
1
2
1
2
0
0
0
1
0
0
1
0
1
0
0
0
1
0
2
1
1
2
1
0
0
2
0
1
0
2
2
0
2
1
0
0
1
0
0
2
1
1
1
0
0
1
2
0
2
0
3
0
1
0
1
1
0
1
0
1
1
1
1
3
0
0
0
0
1
1
1
1
0
1
0
1
2
1
1
2
0
1
0
0
0
2
0
0
1
2
0
0
2
2
0
1
1
1
1
1
0
1
1
0
1
1
0
1
2
2
1
1
2
2
2
0
0
0
0
1
1
1
0
2
3
0
1
1
2
1
2
0
1
2
0
0
0
0
0
0
1
1
0
0
0
0
2
1
0
0
0
0
0
0
1
1
1
0
0
0
1
2
1
0
0
0
0
1
2
1
1
0
2
0
1
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
2
2
1
0
0
0
0
1
0
2
0
1
2
1
0
0
0
4
2
1
1
2
0
1
2
2
1
0
1
1
0
0
1
1
1
1
0
0
0
1
1
0
1
0
1
0
1
0
2
1
0
1
1
0
0
1
2
0
1
1
0
0
1
1
2
2
0
3
1
2
1
1
1
0
2
2
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
1
2
0
2
0
1
1
1
1
1
0
1
4
2
1
1
0
1
0
0
1
0
0
0
2
2
1
0
2
0
1
0
2
0
2
2
0
1
0
0
0
1
0
0
1
1
1
1
1
0
1
2
0
0
2
1
0
0
1
0
1
1
0
1
3
0
1
2
0
0
3
1
0
1
1
2
1
1
0
0
0
1
2
0
1
1
1
0
1
1
0
0
2
0
2
0
1
1
1
2
1
1
0
2
0
1
1
2
0
1
0
1
0
2
3
1
0
1
1
1
2
2
1
0
2
1
1
1
1
0
0
2
1
0
1
1
0
1
0
1
1
0
2
0
0
1
0
1
1
1
0
0
1
2
0
1
1
2
0
2
1
1
0
2
0
2
1
1
1
0
0
1
1
1
2
0
1
0
0
0
0
1
2
1
0
1
1
1
2
2
2
1
0
1
1
1
2
1
1
2
1
3
0
0
0
1
0
0
1
0
0
2
0
0
0
2
1
2
1
0
0
1
3
0
0
2
1
0
0
1
0
0
1
0
2
0
0
1
1
0
0
1
0
0
1
1
0
0
0
1
0
2
1
1
1
3
0
0
2
1
2
0
1
1
1
1
0
0
0
0
1
1
0
0
0
1
2
0
0
2
2
2
0
1
0
2
0
0
1
2
0
0
2
2
1
0
1
0
0
0
2
0
0
2
0
2
0
2
0
0
1
0
2
1
1
0
1
0
0
2
1
1
1
1
3
0
0
1
0
0
1
1
1
0
1
2
1
0
1
0
1
2
0
1
2
0
0
2
1
1
2
0
0
0
7
2
2
1
0
1
0
0
2
1
1
2
0
2
2
2
0
0
0
0
1
0
1
0
0
2
1
0
0
0
0
1
0
3
0
0
1
1
1
0
0
0
0
1
0
1
2
0
1
1
1
2
2
0
1
1
1
0
2
0
0
2
1
0
0
2
2
1
0
1
0
1
0
3
0
1
1
1
1
0
0
0
2
1
0
0
0
2
0
1
0
0
2
0
0
1
0
1
1
2
0
0
1
1
2
0
0
1
2
2
1
2
1
0
0
0
0
0
1
1
0
1
0
2
1
0
0
0
0
1
0
0
0
1
0
0
0
1
2
0
1
2
1
1
2
1
0
1
2
0
1
1
0
1
1
1
1
2
1
0
1
0
1
2
1
0
1
2
0
1
0
2
2
1
0
0
0
0
2
0
1
2
1
1
1
1
2
0
0
1
0
1
1
1
0
0
0
0
2
0
1
0
1
0
2
1
2
0
3
1
1
2
1
0
0
3
0
1
0
1
2
2
0
2
2
2
2
1
0
2
2
0
2
0
1
1
1
0
2
0
1
0
3
1
1
0
1
1
2
1
0
0
2
0
0
2
1
2
1
2
1
1
1
0
2
0
2
1
0
2
0
3
0
1
0
1
1
0
1
1
1
0
0
1
2
1
2
2
3
0
1
0
0
1
2
1
0
0
1
1
0
1
1
0
0
1
1
1
0
0
0
0
0
1
1
0
1
1
1
0
0
1
1
0
0
1
2
0
1
1
1
2
0
1
1
1
1
0
0
0
0
0
1
1
1
1
0
0
0
9
6
0
0
2
2
1
1
1
2
1
1
1
1
1
0
2
0
2
1
1
0
2
0
0
1
0
1
2
1
2
0
0
2
2
2
1
2
0
2
2
0
2
0
1
1
2
0
2
1
0
2
0
0
0
2
1
2
1
2
2
3
0
1
1
2
3
0
0
1
3
1
2
2
1
1
0
1
3
0
0
0
1
0
2
2
2
0
2
0
0
0
0
1
2
2
1
2
2
1
2
0
0
0
2
1
1
2
0
0
0
0
1
0
2
1
0
2
0
2
1
1
0
2
0
1
2
1
1
0
1
0
1
1
1
0
1
2
1
2
1
1
0
0
0
0
0
1
0
0
2
0
0
0
0
2
1
1
0
1
1
1
1
2
0
0
1
2
0
2
0
2
3
0
3
1
1
2
0
2
2
2
0
0
1
0
0
0
0
0
1
5
0
2
1
0
2
0
2
1
0
0
1
1
0
0
1
1
0
1
2
0
1
0
1
0
1
0
0
2
1
0
0
1
0
0
2
1
1
1
0
2
0
1
0
0
0
2
2
0
2
1
2
1
2
1
1
2
2
1
1
1
1
0
1
1
0
1
1
1
1
1
0
0
0
2
2
1
0
1
1
1
1
0
1
0
1
1
2
0
2
0
1
0
0
2
0
1
0
0
0
0
2
0
1
1
0
0
0
0
4
2
0
0
0
2
1
1
2
0
0
0
1
1
1
0
2
1
1
1
2
1
2
0
2
0
3
3
1
2
1
0
3
1
0
1
2
2
0
1
0
0
1
1
1
1
0
0
0
1
0
2
0
0
0
0
0
2
0
2
0
1
0
2
0
0
0
0
1
1
2
3
0
1
0
2
1
2
1
0
1
2
2
0
0
1
1
2
0
0
1
2
0
1
2
0
1
0
0
2
1
0
0
1
0
1
0
1
0
0
2
2
1
1
1
0
2
0
0
0
0
2
1
0
0
0
1
0
2
0
0
2
0
1
2
0
0
1
0
0
2
0
1
1
0
0
1
0
0
0
1
3
1
0
3
0
0
1
2
2
0
1
1
0
1
0
2
0
1
0
0
1
0
1
2
1
1
2
2
2
1
2
0
1
2
0
0
0
1
2
1
0
1
2
1
2
2
1
1
1
0
1
1
0
2
1
1
0
2
1
0
1
0
1
0
1
0
2
1
1
1
1
1
1
1
0
1
0
0
0
0
1
0
1
1
1
0
2
0
1
1
0
0
0
2
1
1
2
1
1
2
1
0
0
1
0
0
1
2
0
0
1
1
3
0
1
0
1
0
0
0
0
1
0
0
1
1
0
1
2
1
1
1
3
1
2
2
2
1
0
2
1
2
2
3
2
2
1
1
1
1
2
1
3
0
1
1
2
0
1
1
2
1
3
1
0
1
1
1
0
0
1
0
1
0
2
2
3
0
1
1
1
1
1
0
2
2
2
1
1
1
0
2
0
0
0
0
0
2
2
0
0
1
1
1
1
0
0
0
0
0
2
1
0
2
1
4
1
1
0
0
0
0
0
0
0
1
0
0
1
1
1
1
1
3
0
2
0
0
2
2
0
0
1
1
0
2
1
0
1
0
1
1
0
0
0
2
2
2
1
0
1
0
2
0
1
1
0
3
2
0
0
0
1
0
0
2
1
2
2
1
0
0
1
1
1
1
0
2
0
2
0
1
0
2
1
0
1
1
0
2
1
0
1
1
0
1
4
0
0
2
2
1
0
2
2
1
1
0
0
2
0
0
2
1
1
0
0
0
0
1
2
1
1
0
1
0
1
1
0
1
2
1
1
0
1
2
0
1
2
2
1
0
1
1
0
1
0
0
1
0
0
0
0
2
0
1
2
0
1
1
1
0
0
0
0
1
1
0
1
2
1
1
1
1
1
0
0
1
1
0
0
2
1
1
6
1
1
2
0
1
1
0
1
1
0
0
1
0
0
0
1
2
1
3
1
0
0
2
1
0
0
1
0
0
1
1
3
0
0
1
0
1
1
2
1
0
4
0
0
0
1
0
1
1
0
1
1
1
2
2
0
0
0
1
1
1
1
0
1
1
4
0
1
2
0
0
0
0
2
2
0
0
1
1
1
2
1
1
0
2
1
1
0
1
2
0
2
2
0
1
2
1
0
1
0
0
1
0
0
1
0
0
0
4
1
1
0
0
0
1
2
1
1
0
0
0
1
2
0
1
4
0
0
2
1
2
1
1
0
1
2
1
1
0
1
0
0
1
1
0
0
1
1
2
1
1
0
1
1
1
0
1
1
1
1
1
0
2
1
0
1
2
1
2
2
0
0
0
1
1
0
1
2
0
0
1
0
0
1
1
0
0
0
1
2
0
1
2
0
0
3
3
2
0
2
0
2
2
1
1
1
0
2
1
0
0
0
0
0
2
2
0
0
0
0
2
1
0
1
2
1
0
0
1
0
1
1
0
1
0
1
1
1
0
0
1
0
2
1
1
0
1
0
0
0
1
0
1
1
1
2
0
1
0
2
1
2
2
0
0
2
0
2
1
0
2
0
1
0
0
1
0
0
0
1
2
0
0
2
1
0
1
0
1
1
0
1
0
1
1
2
2
1
0
1
0
0
0
0
0
2
2
0
3
1
1
0
0
0
0
0
0
1
1
0
2
0
1
2
1
0
0
0
0
1
1
0
1
1
0
0
0
1
2
1
1
0
1
1
2
0
2
1
1
0
1
0
1
0
1
0
0
1
0
2
1
1
2
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
1
0
2
0
1
2
0
0
4
2
1
1
0
3
3
0
1
1
1
1
1
2
0
0
0
2
1
1
1
1
1
0
2
2
0
0
0
0
1
1
0
2
0
0
1
0
0
0
0
0
3
0
1
1
0
0
1
1
0
0
2
0
0
0
0
1
0
0
2
1
2
1
1
1
0
1
0
1
1
0
1
0
2
0
1
2
2
0
1
1
2
0
0
0
2
1
1
2
0
2
0
1
1
1
1
2
0
1
1
2
2
0
1
0
2
1
2
1
1
0
0
1
2
0
1
2
0
1
1
1
1
0
1
1
0
1
0
2
1
1
0
0
2
2
1
1
1
0
2
2
0
1
0
1
0
0
0
2
1
2
2
1
3
1
0
1
0
0
0
0
2
0
1
1
0
1
2
2
2
0
1
2
1
2
1
1
0
0
1
0
0
2
4
2
0
2
1
0
1
0
0
0
3
1
1
0
0
1
0
0
2
0
1
0
2
1
1
1
1
0
2
0
0
0
1
2
2
1
1
1
2
1
1
0
1
1
0
0
0
2
1
2
1
1
0
0
0
1
0
1
0
0
1
0
1
1
1
1
0
2
0
0
0
1
2
0
0
0
2
0
0
2
0
2
1
0
3
3
2
0
1
0
0
2
2
0
1
0
3
0
1
2
0
1
1
0
0
2
0
2
2
0
1
1
2
0
0
2
0
2
0
2
1
1
2
0
1
2
1
1
2
2
2
0
1
0
1
0
1
1
0
3
0
2
0
2
2
0
1
0
0
0
1
1
1
1
0
0
0
1
1
1
1
2
1
0
0
1
1
2
2
1
2
2
1
1
0
2
1
1
0
0
2
0
0
1
0
1
1
1
1
1
2
2
1
1
1
0
1
1
0
2
3
2
0
1
2
0
1
0
1
0
2
1
0
1
1
2
2
1
2
1
2
1
0
0
1
2
1
0
1
1
1
1
0
1
1
2
0
1
0
0
2
0
0
0
0
1
1
0
1
0
0
1
0
1
1
3
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
1
0
0
2
1
2
1
2
2
0
2
0
2
0
0
1
1
1
1
1
0
2
1
1
2
0
0
2
0
2
0
0
0
1
0
1
2
1
1
1
1
1
2
0
2
0
1
0
2
0
1
0
1
0
0
1
1
2
0
0
1
0
0
2
1
0
2
1
0
0
1
1
2
0
2
0
1
1
0
2
0
2
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
1
1
2
1
0
1
0
1
0
1
1
2
2
0
0
1
2
0
0
2
0
3
0
0
0
0
2
2
1
0
0
1
2
2
1
2
1
2
0
1
0
0
1
2
1
2
0
0
0
1
1
1
1
1
1
0
2
1
1
2
2
2
2
1
2
1
2
0
0
0
2
0
2
0
0
1
3
0
1
1
2
0
1
0
1
1
2
0
0
0
1
1
1
0
0
0
0
0
1
1
2
0
1
1
2
2
1
0
1
0
1
2
0
2
1
0
1
0
2
2
1
1
0
2
0
2
2
1
0
1
1
0
0
2
1
0
2
1
0
2
1
0
1
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
1
0
0
0
1
1
0
2
2
1
0
2
1
1
0
0
0
2
1
0
0
1
0
2
1
1
1
2
0
2
2
1
1
2
0
2
2
2
0
0
1
0
0
3
2
1
1
1
2
1
0
2
1
1
1
2
0
0
0
1
0
0
0
1
0
2
1
1
1
1
2
1
1
0
1
7
1
0
0
2
1
0
0
0
1
1
1
1
2
0
1
2
2
1
2
1
0
0
0
0
0
3
0
1
1
0
2
0
0
1
1
1
0
0
0
1
1
0
1
0
0
2
2
1
1
2
0
2
2
0
2
1
0
2
0
1
0
0
0
0
2
1
1
1
0
0
2
2
1
1
0
0
0
0
2
2
2
2
1
1
2
0
2
1
0
1
1
0
1
0
0
1
0
1
0
0
1
1
2
1
2
0
2
1
1
0
0
0
1
1
2
1
0
0
2
1
2
1
1
1
0
0
2
2
1
2
0
1
1
2
1
1
1
1
2
1
0
1
0
0
0
1
1
3
2
0
0
0
2
1
2
1
0
1
2
1
0
1
2
0
0
0
0
2
2
1
0
1
0
1
0
0
1
1
1
0
0
0
0
2
1
2
2
3
1
2
0
0
2
0
2
1
1
0
0
0
1
0
1
0
1
0
2
4
0
0
1
1
1
1
1
0
1
0
1
1
0
0
1
0
2
0
2
3
0
0
2
0
2
1
0
0
0
1
1
1
1
0
2
2
1
0
2
0
1
0
1
0
1
0
1
1
0
0
2
0
2
1
1
0
2
1
1
1
2
2
1
1
0
2
2
2
1
2
2
2
0
1
1
1
2
2
2
0
0
0
0
0
1
0
0
2
0
1
1
2
0
0
0
1
0
0
2
0
1
0
2
2
1
0
1
0
1
1
1
2
1
0
1
0
2
2
0
0
1
0
2
0
0
2
2
2
0
1
1
0
2
2
1
2
1
1
1
1
1
1
0
2
0
1
1
1
1
2
0
0
0
1
0
0
0
1
0
2
1
0
0
1
2
2
1
1
2
1
0
0
1
4
0
1
1
1
1
0
2
1
2
1
0
1
1
1
0
2
1
1
0
1
0
2
2
1
0
2
0
1
0
1
2
0
0
2
0
2
0
2
0
1
0
0
1
1
0
0
1
2
1
0
1
0
0
1
2
1
1
1
1
1
0
0
5
1
2
2
2
0
1
0
0
0
0
1
2
0
0
1
1
0
2
1
0
1
0
0
0
0
0
2
0
1
0
0
1
1
1
1
0
2
2
0
0
0
1
0
1
0
0
1
1
0
2
0
1
0
0
1
0
1
0
1
1
2
0
0
0
1
0
0
0
1
2
1
0
0
2
1
0
0
0
0
0
2
1
1
2
2
0
0
1
1
2
1
0
0
1
0
0
2
1
1
1
1
0
1
1
0
0
0
1
2
0
1
0
1
1
0
0
1
1
0
0
0
0
0
0
2
0
0
2
1
2
1
0
0
0
3
1
1
1
0
0
0
0
1
1
2
0
0
2
3
1
0
2
1
0
0
1
0
0
2
1
0
1
1
0
2
1
0
2
0
0
2
0
1
0
0
0
1
2
2
0
2
2
1
2
1
1
0
0
0
1
2
1
0
0
0
2
1
0
1
0
2
0
0
1
0
1
1
1
2
1
1
0
0
1
0
0
0
1
1
2
1
2
0
0
1
1
0
2
0
1
1
0
0
1
2
1
2
1
0
2
1
2
0
1
0
0
1
2
0
2
2
1
2
1
1
2
1
0
1
0
0
3
1
2
0
0
0
1
0
1
2
2
0
0
1
1
0
1
0
0
2
1
2
0
1
2
1
0
2
0
1
1
2
0
2
0
0
0
1
0
0
0
1
0
1
0
0
2
2
0
1
0
1
1
0
1
0
0
0
1
1
2
2
0
1
1
0
1
0
1
2
1
0
0
1
2
1
1
0
2
0
2
1
2
0
1
0
2
2
0
3
1
0
1
0
2
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
2
1
0
1
1
1
1
2
0
2
1
0
1
2
1
0
0
0
0
0
0
0
1
1
1
1
0
2
0
1
0
0
1
0
0
2
1
1
1
1
1
1
2
0
2
1
1
0
1
2
0
2
0
2
2
1
2
2
0
1
1
0
0
1
0
1
1
2
0
0
2
0
0
0
2
1
2
0
1
1
1
0
1
1
0
0
0
1
0
0
0
3
0
1
0
1
0
2
0
1
0
1
1
2
1
0
0
1
0
0
0
1
1
2
1
1
2
1
0
2
0
2
1
1
0
1
0
1
0
1
2
0
1
1
2
1
3
0
2
1
1
0
2
0
2
1
0
0
2
2
0
1
0
2
2
0
0
1
1
1
0
1
2
3
1
1
0
1
0
2
2
2
0
2
1
0
0
0
2
1
2
0
0
0
0
0
2
0
0
3
0
2
1
0
0
1
1
0
0
1
1
0
1
1
1
1
1
1
0
0
1
1
1
1
0
0
3
1
1
1
2
1
1
0
1
1
0
0
1
1
1
2
1
1
1
2
2
0
0
2
2
2
1
0
0
0
1
1
0
1
0
2
2
2
0
1
0
0
0
1
0
1
1
2
0
1
1
0
0
0
0
2
2
1
0
0
1
1
2
1
0
0
0
0
2
0
0
1
0
0
2
0
1
0
1
1
1
0
0
1
2
1
0
7
1
0
0
1
0
1
1
1
0
3
3
1
0
0
0
1
0
1
0
0
1
0
2
0
0
1
0
0
0
2
0
1
2
0
0
0
1
6
1
1
0
1
0
0
1
1
0
0
1
1
2
0
0
0
0
0
1
0
0
1
1
0
3
1
1
0
1
0
1
2
1
0
0
2
0
2
2
0
0
0
2
0
2
2
1
0
1
1
1
0
1
1
2
1
2
0
0
0
1
1
0
0
2
0
1
1
3
2
1
0
0
1
0
0
2
0
2
0
0
2
2
1
0
1
1
2
1
0
0
0
0
2
0
0
0
2
1
1
2
1
1
2
0
2
2
1
2
2
2
2
1
1
1
0
0
0
0
1
0
2
1
0
2
2
0
0
1
2
0
1
1
2
2
1
2
0
1
2
2
0
0
0
1
2
2
2
0
1
0
2
1
1
0
0
2
1
1
0
2
2
1
2
1
0
0
1
2
0
1
0
0
0
0
2
0
1
0
0
0
0
1
0
1
1
1
0
1
2
1
2
2
0
1
1
1
1
0
0
2
2
2
2
2
0
0
0
0
0
2
2
1
1
2
1
1
0
1
0
0
1
1
2
1
0
1
1
0
1
0
3
0
0
1
1
2
1
2
2
1
1
0
1
1
0
0
2
1
1
0
0
1
0
1
1
0
1
1
1
0
2
0
0
0
0
0
1
3
1
2
1
2
0
0
1
1
1
2
1
0
1
2
1
0
2
0
0
0
2
0
0
1
1
1
0
0
1
1
1
1
0
3
0
2
0
0
1
2
1
0
0
1
1
1
1
0
1
2
1
3
1
1
0
0
1
0
0
1
0
1
1
1
0
1
0
1
1
1
0
2
1
1
0
0
2
1
0
1
2
2
2
0
0
2
2
1
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
1
0
1
0
1
0
2
0
0
0
1
0
0
1
0
1
2
0
0
4
0
0
0
1
2
1
1
0
0
1
0
0
0
2
1
1
1
0
1
2
1
1
0
0
0
0
2
1
0
2
1
0
0
1
0
0
1
1
0
0
0
2
0
1
1
0
0
2
1
1
1
1
1
1
1
1
0
0
2
0
1
2
2
1
1
0
0
1
2
0
0
1
0
0
1
3
2
0
1
0
1
2
2
0
2
0
1
1
2
1
1
0
1
0
2
0
0
0
0
1
1
1
1
2
0
1
1
1
0
1
0
1
0
1
0
0
0
0
0
2
1
0
1
1
2
2
2
2
0
1
1
1
1
1
1
2
1
0
0
0
0
0
0
2
0
1
0
0
2
1
1
0
0
1
0
1
2
0
1
1
0
2
1
1
0
1
0
1
1
0
0
2
0
1
0
0
1
1
0
1
0
1
0
0
0
1
0
1
0
2
1
1
0
1
1
1
0
2
2
1
0
0
0
0
2
0
0
0
0
0
2
1
2
2
0
2
0
1
0
1
2
0
2
0
1
0
0
2
0
1
0
1
2
0
1
2
1
2
0
1
0
0
1
2
0
0
1
2
1
1
0
2
0
1
1
1
2
0
1
0
2
0
1
1
0
3
0
2
1
1
0
0
1
1
0
0
0
0
0
1
0
1
2
3
0
2
0
1
2
1
0
0
1
0
0
0
0
0
1
0
2
2
0
0
0
1
1
0
0
1
3
0
0
1
0
0
0
1
1
2
1
1
0
2
3
1
0
1
1
1
2
0
2
0
0
0
1
2
1
0
1
1
0
0
1
1
1
0
1
1
1
1
1
0
0
0
1
2
0
0
1
0
1
0
1
1
2
0
0
0
0
2
1
2
0
1
0
1
1
2
0
2
1
2
0
2
2
1
1
0
1
1
1
1
0
1
0
1
0
2
0
1
1
1
0
1
1
0
0
1
1
1
1
2
0
1
2
0
0
0
3
0
0
0
1
0
1
1
2
1
1
1
0
1
0
1
2
2
1
1
0
0
1
0
1
0
0
1
0
0
1
0
1
0
1
2
0
2
2
0
2
1
0
0
0
1
1
0
1
1
1
1
1
0
2
0
1
0
2
2
0
0
1
2
1
1
2
1
0
0
0
1
1
0
1
0
1
1
0
2
1
0
1
1
0
2
2
0
1
0
1
0
1
1
0
3
1
0
1
4
1
0
2
0
1
0
2
1
0
1
1
1
2
1
2
0
0
0
1
0
0
2
2
0
1
0
3
0
0
0
0
1
0
1
1
1
0
0
2
0
1
0
2
2
0
0
0
0
1
2
2
1
2
0
0
0
2
1
0
1
1
2
3
0
1
0
0
0
0
2
1
0
0
0
1
0
0
1
1
1
0
2
3
0
1
2
2
0
2
3
0
2
1
1
1
1
1
1
0
0
1
0
0
2
1
1
1
1
0
0
0
1
0
1
1
0
0
1
1
1
0
1
0
1
1
1
2
0
0
0
2
1
1
0
0
0
3
0
1
2
0
1
1
0
1
1
0
1
2
0
1
1
0
0
0
1
2
1
1
0
1
3
2
0
0
2
0
1
1
1
0
0
0
1
0
1
0
0
1
2
2
1
1
1
2
1
2
0
0
0
1
1
2
1
1
1
0
3
0
1
0
0
1
1
0
1
1
1
1
0
1
2
2
1
1
1
1
0
0
0
3
1
1
0
2
0
0
1
2
1
0
0
1
0
2
0
0
0
0
1
0
1
1
1
2
0
2
0
0
1
1
2
0
0
0
0
0
0
2
1
2
1
1
1
0
1
0
0
2
1
1
2
0
2
1
2
2
2
0
0
2
2
0
0
2
2
1
2
1
2
0
0
0
0
2
1
1
2
0
0
0
1
1
2
1
1
1
1
2
2
2
1
0
1
1
0
1
0
0
1
1
1
2
1
0
2
1
0
1
3
1
0
0
0
0
2
0
2
0
1
1
0
2
0
0
1
1
0
0
0
0
0
1
0
2
1
1
1
1
0
2
1
2
2
1
0
1
0
1
0
0
1
0
0
0
1
0
1
1
1
0
1
3
0
0
0
0
1
2
4
0
1
2
1
1
0
1
1
0
1
2
0
0
0
0
0
0
0
0
0
0
2
2
1
1
3
0
1
2
1
0
0
1
1
2
1
0
0
1
1
0
0
1
0
0
0
0
0
1
2
1
0
2
2
1
0
1
1
0
0
0
2
1
2
0
0
2
0
0
2
2
2
0
2
1
2
0
1
1
1
2
0
0
0
1
0
0
1
1
0
1
0
1
0
1
0
1
0
1
2
0
0
2
1
1
0
2
0
1
0
0
1
0
2
2
2
0
1
1
0
0
1
0
0
0
1
0
1
2
2
2
2
0
1
1
0
2
1
2
0
1
1
0
1
0
0
2
0
2
1
1
2
1
0
0
2
1
1
0
0
1
1
1
0
1
0
1
0
1
2
1
1
1
1
0
0
2
1
0
0
0
2
0
1
1
0
1
2
1
0
0
0
1
0
1
2
1
0
1
2
1
0
5
2
0
1
0
2
1
1
0
2
2
1
2
0
0
1
0
1
0
1
0
2
0
1
1
1
0
1
0
0
1
0
1
2
0
0
0
0
2
1
1
1
0
1
1
0
1
0
1
1
1
0
0
1
0
0
0
1
2
1
0
1
1
1
0
0
1
1
2
0
1
1
0
1
1
0
2
1
2
0
1
2
0
0
1
0
1
0
1
0
1
1
1
0
0
2
1
1
1
1
0
1
0
2
1
0
0
0
0
1
0
0
0
0
0
1
2
1
0
1
0
2
1
1
2
1
0
1
0
2
1
2
0
2
1
0
0
1
2
2
0
1
4
1
2
0
1
1
1
0
0
1
2
2
1
0
0
0
2
1
2
1
1
2
2
1
0
2
1
0
0
0
1
1
1
0
1
0
0
0
2
0
0
0
2
1
2
1
0
1
2
0
1
2
1
2
1
0
0
0
2
1
2
0
0
0
2
1
1
1
0
0
1
0
1
0
0
2
0
0
0
0
1
2
0
0
0
2
2
1
0
1
2
2
1
0
2
0
1
1
0
0
0
0
1
0
2
2
2
0
2
0
1
1
0
1
1
1
2
1
1
2
0
1
1
0
1
1
2
2
0
2
0
0
1
0
2
1
0
1
2
2
2
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
1
1
2
1
1
0
0
0
1
1
2
1
0
2
0
0
1
0
0
1
2
0
2
2
1
0
0
1
1
0
1
0
0
1
1
0
1
0
0
2
0
0
1
1
0
1
1
0
0
0
2
0
2
0
0
1
0
1
2
0
1
0
0
0
3
0
0
0
1
0
1
2
0
0
0
0
2
0
1
1
2
1
1
1
1
2
0
2
1
2
0
0
0
0
1
0
1
0
1
1
1
1
1
0
1
0
1
0
0
1
1
2
1
1
1
0
0
0
1
1
2
1
0
2
0
1
1
0
0
2
0
0
2
2
2
0
0
0
0
1
1
0
0
3
1
1
0
1
0
1
0
1
1
0
1
1
1
0
0
0
0
0
2
0
0
0
1
0
0
2
1
1
0
1
1
1
1
1
1
1
1
1
1
0
2
1
2
0
0
0
0
2
2
0
0
2
2
1
1
2
2
1
0
2
1
1
1
2
1
0
0
0
3
0
0
1
0
0
1
2
1
0
0
0
0
2
0
2
0
1
0
2
1
2
0
1
0
0
1
2
1
1
2
1
0
1
0
0
0
2
1
1
2
0
1
0
2
1
2
1
2
0
1
0
1
1
0
2
1
1
0
1
2
0
1
0
1
1
0
2
1
1
0
1
1
1
7
1
0
1
2
0
2
0
1
2
0
0
1
1
2
2
0
0
1
0
1
1
1
1
1
2
1
2
2
0
0
0
0
0
2
1
0
1
1
1
1
2
0
2
0
2
0
0
0
0
0
1
0
0
2
2
0
1
2
1
1
2
1
1
0
0
1
1
1
0
1
1
1
0
2
1
0
1
3
2
0
1
0
0
1
0
3
0
1
0
1
2
1
1
0
1
0
0
1
0
0
2
0
0
1
1
1
2
0
1
0
1
0
1
0
2
0
0
0
1
2
1
0
2
2
1
0
2
2
1
0
1
1
0
0
2
0
0
0
0
0
0
0
2
1
0
0
1
1
2
1
0
2
2
0
2
0
0
2
1
0
1
0
1
1
2
1
0
0
0
0
0
2
0
0
0
0
2
0
1
0
1
1
2
2
2
2
0
1
1
1
1
2
2
2
1
0
0
1
1
1
1
1
1
1
3
2
0
1
1
2
2
1
1
1
2
0
1
1
1
0
0
1
0
1
2
2
1
1
0
0
1
1
0
0
1
2
2
0
0
1
1
0
1
0
0
2
2
2
2
1
0
0
2
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
1
0
0
2
2
0
1
1
1
0
0
0
1
2
0
2
0
0
0
1
0
0
3
2
1
0
2
0
1
3
0
1
2
0
1
2
2
0
0
1
2
0
0
0
1
1
0
3
0
1
0
1
0
0
1
1
1
2
0
2
1
0
0
0
0
2
0
1
0
2
2
0
0
1
1
2
2
0
1
3
0
2
4
0
2
0
1
1
1
1
2
1
0
0
0
0
0
2
1
0
2
0
1
2
0
2
1
0
0
1
2
1
1
0
0
2
2
0
0
1
1
2
1
0
0
0
1
0
0
1
0
3
0
1
0
0
0
0
1
1
0
0
3
0
0
2
1
0
0
1
2
1
1
1
1
0
1
1
0
0
1
0
1
1
2
0
0
0
1
2
1
2
1
3
1
1
0
0
2
0
1
2
1
0
1
2
2
1
0
2
0
0
1
1
1
0
0
1
0
2
0
3
0
2
2
0
0
0
0
2
2
0
1
2
1
0
1
0
1
1
1
0
1
2
0
0
1
1
1
0
0
2
1
1
1
0
1
0
1
0
0
0
1
5
1
2
0
1
0
0
2
1
2
1
2
0
2
0
0
0
0
0
2
1
2
1
0
2
2
0
2
0
0
0
2
1
2
2
2
1
2
2
1
0
0
2
0
0
1
0
1
2
2
2
1
0
0
1
2
2
2
0
0
0
0
1
1
1
0
1
0
0
0
1
0
1
2
1
0
1
0
2
0
1
3
1
1
0
1
1
0
2
1
2
1
2
1
1
1
1
0
0
0
2
0
2
0
0
0
1
1
0
1
0
2
0
2
0
0
2
0
0
0
0
2
3
2
0
0
1
0
0
1
0
2
0
0
1
1
2
1
0
0
0
0
1
0
0
1
0
1
0
1
0
1
2
1
1
2
1
2
1
0
0
1
0
1
0
2
0
1
1
2
0
2
2
0
2
0
1
0
2
2
0
0
2
0
2
0
0
1
2
0
0
1
2
5
0
0
1
1
2
2
0
1
2
1
1
1
2
1
2
0
1
1
0
2
0
1
0
1
2
0
1
0
0
1
0
0
2
1
2
1
0
2
1
0
2
1
0
0
2
0
0
0
0
1
0
1
1
0
1
0
0
1
2
0
0
1
0
1
1
2
0
1
1
0
1
1
2
0
2
1
0
2
0
1
1
2
0
0
3
1
2
2
2
2
1
0
0
2
1
1
0
1
1
0
2
2
1
2
0
0
2
0
2
1
3
2
1
2
1
0
1
1
0
0
1
1
0
0
1
0
0
0
1
1
0
0
1
0
1
0
2
0
2
0
2
0
2
1
0
0
2
1
0
0
1
2
1
1
1
1
0
1
2
1
2
1
1
2
0
1
1
0
2
5
1
0
2
0
1
1
0
2
0
2
0
2
0
1
0
1
2
1
0
0
1
0
1
2
0
0
3
1
1
1
0
1
2
0
3
0
0
0
0
0
1
0
0
1
1
2
1
0
0
1
0
1
1
0
1
0
0
2
1
2
1
0
0
1
1
0
2
2
2
2
2
1
0
0
1
0
0
0
0
1
0
0
2
1
0
0
0
1
1
2
1
0
1
1
1
1
0
1
0
2
0
2
1
2
1
2
1
2
1
0
1
0
2
2
1
1
1
2
2
1
0
0
2
1
0
1
2
2
1
0
1
1
0
0
0
2
0
0
1
0
0
0
0
2
1
0
2
0
0
0
0
1
1
0
0
2
0
0
1
2
1
0
0
1
2
2
1
0
1
2
3
2
2
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
2
1
1
2
2
2
0
2
0
0
2
1
1
1
1
1
0
1
1
1
2
0
1
1
1
0
2
1
0
0
1
0
1
1
0
0
2
0
0
1
0
1
2
2
2
1
2
3
2
0
1
0
0
0
0
1
1
0
1
0
1
0
1
1
1
0
2
1
0
0
2
2
1
2
2
0
0
0
0
2
1
0
2
0
1
0
1
2
0
0
2
0
1
2
1
2
1
2
0
0
0
0
0
0
0
0
2
1
2
0
0
1
2
0
1
0
0
1
1
1
1
1
0
1
1
0
1
0
1
1
1
0
1
1
2
1
6
0
1
0
1
0
1
1
1
1
0
1
0
0
1
1
2
0
0
1
0
2
1
2
0
0
1
1
0
1
0
1
0
0
0
1
1
0
0
2
1
1
1
1
2
0
1
2
0
0
0
2
2
0
0
1
0
1
0
1
2
1
0
2
2
0
0
2
0
0
0
0
0
2
3
0
1
1
1
2
0
0
0
1
0
1
1
1
5
0
0
0
1
2
1
2
1
2
1
1
0
0
0
2
2
1
0
2
2
1
0
1
2
1
2
0
0
1
1
2
0
0
0
1
2
0
0
2
1
1
0
0
1
1
1
1
3
2
1
0
1
0
2
0
0
0
1
0
3
0
1
1
1
0
0
1
0
1
0
1
2
2
2
0
2
2
0
2
1
2
1
3
1
0
0
2
0
1
2
1
0
0
0
0
0
1
1
1
1
2
1
1
1
0
1
1
1
2
1
2
0
1
1
2
1
0
1
0
0
0
1
1
1
0
1
0
0
0
2
1
0
2
2
1
0
2
3
1
0
2
0
0
0
1
1
2
0
2
1
1
1
1
1
0
2
0
0
0
1
0
1
1
0
0
2
1
1
0
2
2
2
1
0
0
0
2
0
0
0
1
0
0
0
1
0
0
2
0
1
1
1
0
2
0
1
0
2
1
0
0
1
0
1
0
0
1
1
2
2
1
2
0
2
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
7
0
1
0
2
0
0
0
2
0
0
0
1
0
0
2
0
0
2
0
1
3
0
1
0
1
1
2
2
0
0
2
0
1
2
2
1
2
0
0
1
0
0
1
1
0
0
1
0
2
0
2
1
0
0
1
0
0
1
0
0
2
0
2
1
0
0
1
1
1
1
0
0
1
2
0
0
0
1
1
0
2
2
1
0
4
1
1
0
0
1
0
1
0
0
1
2
1
0
1
0
0
2
0
0
0
0
2
0
1
0
0
0
0
2
2
0
0
2
1
1
1
0
0
0
2
0
2
1
2
2
0
0
0
1
0
0
1
0
0
0
0
2
0
1
4
0
0
1
0
1
0
0
1
0
0
0
0
1
2
1
3
1
1
1
0
1
2
2
0
0
1
0
0
1
3
2
2
0
0
0
0
0
0
0
1
1
2
2
2
0
1
2
1
0
0
1
2
2
1
0
1
0
0
2
0
0
1
2
1
0
2
0
2
2
1
1
1
2
0
0
2
0
0
1
0
0
0
1
2
0
0
0
0
0
1
2
0
1
0
0
2
1
1
0
0
1
0
1
1
0
1
2
0
2
1
1
0
2
0
0
1
0
0
0
1
0
0
2
2
1
1
2
1
0
1
0
0
1
0
2
1
0
2
1
1
0
0
3
1
0
2
0
2
1
1
1
2
2
0
0
1
0
1
2
0
1
0
2
0
1
2
1
1
1
2
1
0
0
0
1
0
1
0
0
2
2
2
1
0
1
1
0
1
1
0
1
1
0
0
0
1
1
2
0
1
2
0
1
1
1
1
0
1
1
1
1
0
1
0
2
0
1
1
1
0
0
1
2
0
1
1
1
2
1
0
0
0
2
1
1
2
0
1
1
0
0
0
1
0
1
0
0
0
1
0
1
2
1
0
2
0
1
2
1
0
0
0
1
1
0
2
1
1
2
1
0
2
2
0
1
1
0
1
2
1
2
1
0
1
0
1
3
1
4
1
1
0
0
0
1
0
0
1
1
0
0
1
3
0
0
1
0
1
0
1
0
2
1
2
3
2
1
2
2
0
1
1
1
0
0
0
0
1
0
0
1
2
2
1
0
0
0
0
1
0
1
0
1
0
0
2
1
1
1
2
0
1
2
1
2
0
0
1
1
0
0
2
1
4
2
1
2
0
1
1
1
2
3
0
1
0
0
2
2
2
0
0
1
0
0
1
1
0
0
1
0
1
2
0
1
1
0
2
0
1
0
2
0
0
1
1
0
1
1
1
0
2
2
1
1
1
1
0
1
0
2
0
2
2
1
1
0
2
1
1
1
0
0
1
1
2
2
0
1
0
1
0
2
1
1
0
2
1
1
0
1
0
0
0
1
0
1
3
2
1
2
1
0
0
1
0
1
1
1
0
0
0
0
1
1
0
0
0
2
0
0
1
2
0
0
0
1
0
1
1
1
1
2
2
0
0
0
0
1
2
2
1
1
0
0
2
0
1
0
0
1
0
0
1
1
3
0
2
0
2
1
2
3
0
1
2
0
0
1
1
0
0
1
1
1
1
0
0
2
2
4
0
1
1
0
1
4
0
0
0
0
0
1
1
2
0
2
0
1
2
1
1
0
1
2
2
0
2
1
0
2
2
0
3
2
2
0
2
0
2
0
0
1
1
1
1
2
1
2
0
1
0
3
0
2
1
0
1
2
0
0
1
0
1
1
1
1
0
0
0
1
2
0
0
2
0
2
0
0
2
1
1
0
0
0
0
0
0
2
0
0
1
1
2
1
0
0
1
1
1
1
0
1
1
1
0
0
1
1
1
2
2
2
1
1
2
2
0
2
1
2
1
1
0
1
2
1
0
1
0
0
1
3
2
2
2
0
0
1
0
1
1
1
1
2
0
1
2
0
0
1
0
0
1
2
2
0
1
2
0
0
0
1
0
0
0
0
2
1
0
1
2
3
2
2
0
1
1
1
0
0
0
0
1
2
2
0
1
1
1
1
1
1
2
0
1
1
0
1
2
0
2
0
1
1
0
0
1
0
1
1
0
1
0
2
0
0
0
2
1
2
1
2
1
1
2
1
1
0
1
1
1
0
0
1
0
0
1
2
1
0
2
2
0
0
1
2
0
3
1
0
2
0
0
2
1
0
0
1
2
0
1
2
2
0
0
0
0
1
0
1
1
1
2
0
1
1
0
1
0
1
1
2
2
2
0
0
1
1
1
0
1
0
2
0
3
1
1
2
2
1
2
0
1
0
0
1
0
0
1
2
0
0
1
0
2
1
0
0
0
2
0
0
0
0
2
0
0
0
0
1
2
0
0
0
1
2
2
2
0
1
1
0
0
0
1
2
2
2
2
0
2
0
1
2
0
1
0
2
0
1
1
1
1
2
2
2
0
2
0
0
2
1
0
0
1
1
1
0
0
1
2
1
1
0
0
1
2
4
1
1
1
1
0
0
2
1
1
1
0
0
1
0
0
0
1
1
0
0
1
1
0
2
0
2
2
2
1
0
0
0
2
1
0
0
1
0
1
2
0
2
2
0
1
1
1
0
1
0
1
0
0
0
0
0
2
1
2
2
0
1
1
1
2
1
1
0
1
1
1
1
0
1
0
0
0
2
2
0
0
0
1
0
0
2
1
0
2
2
0
0
0
1
0
2
2
0
1
1
2
0
0
1
1
1
0
2
0
0
0
0
1
0
2
1
0
1
2
0
1
0
0
1
0
0
0
1
1
1
1
0
1
1
2
0
0
0
3
0
1
0
1
1
1
1
1
0
3
0
0
1
1
1
2
2
1
2
2
1
2
2
0
1
1
1
2
0
1
1
2
0
0
1
1
0
2
1
1
2
2
1
2
1
0
0
0
0
1
1
2
1
1
0
0
1
0
1
1
3
3
1
0
1
0
2
0
1
0
0
0
0
0
1
1
2
1
1
0
2
0
1
1
0
2
1
1
0
1
0
0
0
0
0
0
2
2
0
1
2
1
1
0
0
0
0
2
1
1
2
0
1
1
1
3
0
1
2
2
2
1
1
0
2
1
1
0
0
1
1
1
1
0
0
0
2
0
1
0
1
0
2
1
1
2
0
0
0
0
2
0
1
2
1
0
2
1
0
0
1
0
0
0
1
0
0
0
0
1
1
1
2
1
0
0
1
0
1
1
0
1
0
0
1
2
1
1
1
0
2
2
1
0
5
0
0
0
1
1
0
1
0
2
1
0
0
0
0
1
0
0
1
1
0
1
0
0
0
2
1
1
2
1
0
1
1
0
2
1
1
1
0
0
0
0
1
1
1
0
2
0
1
0
1
2
1
1
2
0
1
0
1
1
1
0
1
2
2
0
0
0
0
0
3
1
0
1
2
1
0
1
1
1
2
0
0
0
0
0
0
0
0
0
1
1
1
0
1
4
0
1
1
0
1
1
1
0
2
1
0
2
2
2
2
1
1
0
1
2
0
0
2
2
2
1
1
1
2
2
2
1
1
1
2
1
2
1
2
1
2
1
1
1
2
0
0
0
1
0
0
1
1
0
2
1
1
1
1
2
0
2
0
0
0
1
1
1
1
1
1
2
0
0
2
1
0
1
0
0
0
0
0
0
1
2
0
3
1
1
2
1
0
0
1
1
0
0
2
2
2
0
1
0
1
1
0
1
1
0
2
0
1
0
0
0
2
1
0
0
1
3
0
0
1
1
0
1
1
0
2
1
2
1
1
1
2
3
1
2
1
1
1
0
0
0
0
0
0
1
1
1
0
3
0
1
2
0
0
0
1
1
0
1
0
2
1
0
0
0
2
1
0
2
1
1
1
2
0
1
0
1
0
1
2
3
2
1
2
0
2
2
0
1
0
0
1
0
0
2
1
1
2
0
0
1
1
1
0
1
1
1
1
3
0
0
1
0
0
1
7
0
0
1
2
2
0
0
0
2
0
1
0
2
2
0
1
2
1
0
0
0
0
2
2
0
0
0
0
1
1
0
1
0
1
0
0
2
0
0
0
0
2
1
0
0
1
1
1
1
0
0
1
1
0
5
1
1
1
2
1
0
2
1
2
0
0
1
0
1
2
1
1
2
0
1
0
1
0
1
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
1
1
0
0
0
0
2
2
0
0
2
0
0
2
2
0
0
1
0
2
1
2
1
1
1
2
0
2
1
1
0
0
0
2
2
1
1
2
1
2
0
2
1
2
0
0
0
0
0
0
0
1
2
0
1
4
2
1
0
1
0
0
0
0
0
2
1
1
2
1
1
1
0
2
2
1
1
1
0
2
0
1
2
2
2
1
1
1
0
0
0
0
2
2
1
1
2
6
1
1
1
1
0
1
1
0
1
1
2
2
0
1
1
0
0
1
0
0
0
0
2
2
1
2
2
1
1
0
1
2
2
0
0
1
0
1
0
1
1
1
2
0
1
0
2
1
0
0
2
0
0
2
2
2
1
0
1
0
1
1
2
0
0
0
1
0
0
2
0
0
0
0
1
3
0
0
1
0
3
2
1
0
1
2
1
0
0
1
0
0
1
0
2
1
0
1
2
1
0
1
1
1
0
0
1
2
1
1
2
1
0
0
0
0
1
2
0
0
1
0
1
0
0
1
3
0
1
1
1
0
1
2
0
1
2
1
0
1
1
0
1
1
2
1
1
2
0
2
0
0
1
0
1
0
0
0
0
0
0
0
2
1
1
1
2
2
0
1
2
1
2
0
2
2
0
1
1
1
4
0
1
1
0
2
1
0
1
2
2
1
0
0
0
0
1
0
0
0
2
0
1
0
1
0
1
0
2
0
1
0
0
0
1
1
2
1
1
0
0
1
0
1
3
2
1
1
1
0
0
1
0
2
2
2
0
2
1
1
2
1
1
2
0
1
0
0
2
0
0
1
2
2
2
0
0
1
1
1
0
2
1
0
1
1
0
1
1
0
2
0
0
1
1
0
1
1
0
1
1
1
1
0
1
0
2
0
1
1
2
2
2
0
0
1
1
0
2
0
0
0
3
1
1
1
2
2
0
1
0
0
0
1
0
0
2
1
0
0
6
1
2
2
2
1
1
1
0
2
1
0
1
2
2
3
2
1
1
1
2
0
1
1
0
6
2
1
0
0
0
1
2
1
0
2
2
2
0
5
0
1
2
1
2
0
1
2
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
1
2
0
1
1
1
0
1
0
2
0
0
0
0
2
1
0
1
1
1
1
0
2
1
1
0
0
2
1
1
1
1
2
0
2
1
0
0
1
1
1
1
1
0
1
2
0
0
1
1
1
0
0
2
1
2
1
1
2
2
0
0
0
0
2
0
0
1
0
0
1
2
2
2
0
1
0
0
0
1
1
2
1
1
1
1
1
0
1
1
1
2
0
0
1
0
0
2
2
0
0
1
2
0
2
1
2
0
0
0
0
0
0
0
1
0
0
0
2
1
2
0
0
2
0
0
0
0
1
1
1
0
1
0
1
1
1
0
0
2
1
1
0
0
1
2
1
0
0
0
0
0
0
0
0
1
0
1
0
1
2
2
1
1
0
2
0
0
2
2
0
2
0
2
2
1
0
0
1
0
2
2
0
1
2
0
2
1
0
2
0
1
0
0
0
0
0
2
1
0
0
0
1
0
2
0
0
1
0
2
1
1
1
2
2
0
2
2
2
0
2
1
0
0
0
0
1
0
2
2
0
1
1
1
2
1
1
0
0
1
2
1
0
1
2
2
0
0
0
0
0
1
0
0
0
0
1
1
2
0
3
0
1
0
1
1
1
1
1
1
1
0
2
1
0
0
0
0
0
1
1
0
1
0
1
3
2
2
0
2
1
0
2
1
0
1
0
0
2
0
0
2
1
0
0
1
1
1
0
1
0
0
2
1
2
1
0
1
2
1
0
0
0
2
1
2
2
1
0
1
1
1
2
3
0
0
1
1
0
2
0
2
1
1
0
0
1
2
1
0
2
3
0
0
2
2
0
0
1
0
2
0
2
0
1
1
2
1
0
2
0
0
0
0
0
2
0
0
1
0
0
2
1
1
1
2
1
0
1
0
1
0
0
1
1
0
0
1
2
1
1
2
0
1
1
2
1
0
2
1
1
0
0
1
0
1
0
0
1
1
1
0
0
0
0
0
0
1
1
3
0
2
1
3
1
0
1
2
1
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
2
1
0
1
0
0
0
1
0
0
1
1
1
1
0
0
1
1
1
0
0
0
0
0
1
0
1
0
3
1
1
0
1
0
2
0
2
0
0
1
2
1
0
1
1
0
0
1
2
0
1
2
0
0
1
1
2
2
1
0
2
0
1
1
0
0
1
0
2
1
2
1
0
1
2
0
0
2
0
0
2
2
1
0
0
2
1
0
2
2
0
0
1
0
2
2
0
1
0
2
0
0
1
0
1
0
2
2
2
0
0
0
2
1
2
0
2
2
0
1
1
1
0
0
0
0
3
2
0
2
0
1
1
0
0
2
1
2
1
0
0
0
2
1
1
3
0
3
0
0
1
0
1
0
0
1
0
1
0
1
0
0
1
0
2
1
0
2
1
3
2
1
2
0
0
1
1
2
2
2
1
1
0
1
1
1
0
0
0
1
1
0
1
0
2
3
0
2
1
1
2
1
1
1
1
0
1
1
1
2
2
1
2
2
1
1
2
1
0
0
0
0
2
0
2
1
0
2
0
1
0
2
1
1
1
1
0
0
2
1
2
2
2
0
2
0
1
0
0
2
1
1
0
2
1
1
1
1
0
1
1
0
0
2
1
1
0
1
1
0
0
0
1
0
0
1
2
1
0
1
1
1
0
0
2
2
0
1
0
0
1
0
2
2
2
0
0
0
0
2
0
0
0
2
2
1
0
0
0
1
0
2
0
0
2
2
1
0
0
0
1
1
0
0
1
0
2
2
1
1
1
0
0
0
1
1
1
1
1
1
0
0
1
2
1
2
1
2
2
0
0
1
1
0
2
0
0
2
0
1
2
2
3
0
0
1
2
1
1
1
0
1
0
1
0
0
0
0
0
0
0
0
2
0
2
1
4
1
0
1
0
2
1
1
1
0
1
1
0
1
0
0
0
1
3
1
0
0
0
1
2
2
1
0
0
1
0
1
2
2
1
0
1
2
1
0
0
0
0
0
1
3
0
1
3
0
0
4
2
0
0
0
1
0
2
1
1
0
1
2
0
2
0
0
1
0
2
0
0
1
0
1
1
0
1
0
0
0
0
2
2
1
1
2
1
0
2
1
0
1
2
1
0
1
1
0
0
1
2
0
0
0
0
0
3
1
1
2
2
0
0
2
0
2
0
0
0
3
2
0
1
0
2
0
0
1
0
1
4
1
0
2
1
1
0
0
0
1
1
2
0
3
1
2
0
0
2
0
0
1
1
1
1
0
1
0
1
2
2
0
0
2
1
1
2
0
1
0
1
0
0
1
1
1
0
0
1
0
1
0
2
1
1
0
1
1
1
0
4
0
0
1
1
2
2
0
0
0
0
2
0
0
0
2
2
0
2
0
1
1
0
1
1
1
0
0
0
1
1
1
3
0
0
2
2
1
0
0
1
0
1
0
3
2
2
0
2
0
0
0
2
0
3
1
1
1
1
2
1
2
1
0
0
0
1
2
1
2
1
1
1
1
1
1
0
1
3
0
1
0
1
2
2
2
0
0
0
1
0
2
0
1
0
4
1
1
0
1
1
0
0
2
2
0
0
1
1
1
2
1
1
1
0
0
1
1
0
1
0
0
2
3
2
2
1
1
2
1
0
1
1
0
0
1
0
2
0
0
0
0
0
1
0
0
2
1
1
0
1
1
2
0
1
2
1
5
2
1
0
2
2
0
2
2
0
1
2
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
2
1
1
0
2
0
2
1
0
0
1
1
1
1
0
2
0
0
2
1
0
1
1
0
1
1
1
2
0
1
1
1
1
1
2
0
1
0
0
0
1
1
2
0
0
0
0
0
1
0
1
0
0
0
2
0
0
1
4
2
1
2
0
0
2
1
3
0
0
1
0
0
1
1
0
0
1
0
0
0
2
0
0
2
2
0
1
1
0
0
3
1
1
0
0
0
2
0
0
0
2
0
1
1
0
0
1
0
0
0
0
2
0
1
0
1
1
1
1
0
0
0
2
1
2
1
1
1
1
2
1
1
0
1
5
0
1
1
0
1
0
0
0
0
2
1
1
0
0
1
0
0
0
1
0
1
0
1
0
0
1
0
1
2
0
0
1
1
0
2
2
1
1
0
0
1
1
0
1
2
1
1
0
0
2
1
1
0
0
2
1
1
0
1
1
2
1
1
0
0
1
0
1
0
1
0
0
1
1
1
0
2
1
0
1
1
2
1
0
1
2
0
2
1
0
1
1
2
2
1
1
1
0
0
1
0
1
1
0
0
1
2
0
0
1
1
1
1
0
1
1
0
1
0
0
0
2
0
2
0
0
2
2
3
2
1
2
2
2
0
0
1
1
0
0
2
1
0
1
2
0
0
1
2
2
1
1
1
1
1
2
0
2
0
1
2
0
1
1
1
0
0
0
1
0
0
2
1
0
0
1
2
1
0
2
1
0
0
1
2
1
0
0
0
2
0
2
1
1
2
0
2
0
0
0
1
2
0
2
1
2
1
1
1
2
1
2
1
0
0
0
2
2
1
0
0
0
1
2
1
1
0
0
1
0
1
2
0
1
0
1
0
0
0
1
1
1
0
1
2
0
1
2
2
2
1
2
2
1
2
1
0
1
0
1
0
0
0
0
1
0
1
1
1
1
1
0
1
1
0
0
2
2
2
1
0
2
1
2
1
1
1
1
1
0
1
1
1
0
2
0
3
1
1
2
0
2
1
0
1
2
1
0
0
1
1
1
0
2
1
0
2
0
2
1
1
2
1
1
2
1
2
2
2
0
1
1
0
1
1
0
0
1
1
2
0
1
0
0
2
3
2
1
2
2
1
1
0
1
0
2
1
2
0
2
0
1
0
1
1
2
1
1
12
0
1
1
0
1
1
1
0
2
1
0
1
0
0
1
1
2
1
1
1
1
0
2
1
0
1
0
0
1
2
1
1
2
2
1
0
1
1
0
0
1
2
1
1
0
1
2
1
1
0
1
1
1
2
1
1
0
0
0
1
0
2
1
1
0
1
2
1
1
0
2
3
0
1
0
1
2
0
1
1
0
1
0
0
2
2
0
2
1
0
2
0
1
2
0
0
0
0
0
1
1
1
0
2
1
0
1
2
0
2
2
0
0
1
1
1
0
2
2
2
1
1
0
1
1
0
0
0
0
2
0
0
2
1
1
2
0
0
0
2
1
2
0
2
2
0
2
0
0
1
2
0
2
1
0
0
0
2
0
2
1
2
1
2
2
1
1
1
0
0
2
0
1
0
1
0
0
1
0
0
0
0
1
1
2
2
0
1
1
1
2
1
5
1
0
1
1
1
2
1
2
1
0
0
1
1
1
2
1
0
1
0
1
2
2
2
0
0
0
0
1
1
1
1
0
1
2
0
1
0
1
0
0
0
0
2
1
1
1
0
0
2
1
0
2
3
0
1
1
1
1
0
0
1
0
1
0
0
0
1
0
0
0
0
2
0
1
0
2
1
2
0
0
0
0
0
0
0
1
1
2
0
2
0
0
1
1
1
2
0
0
1
0
1
2
0
2
0
1
1
2
0
2
2
0
1
0
0
1
1
0
1
1
2
1
1
1
0
1
1
1
1
1
1
0
0
0
0
0
1
2
1
0
1
2
0
1
1
0
0
2
0
0
0
0
3
0
1
3
0
0
1
1
0
0
0
1
2
1
0
0
0
2
1
1
0
0
1
1
1
0
0
1
1
0
2
0
0
0
0
1
1
2
0
2
1
0
2
0
1
1
1
1
2
1
0
1
0
0
2
0
0
1
0
2
0
2
0
1
1
1
0
2
2
0
2
0
1
0
0
1
0
0
2
1
0
2
1
0
0
0
1
0
0
0
2
1
1
0
0
3
2
1
0
1
0
1
0
0
0
0
0
1
0
0
2
2
1
0
0
1
0
1
0
0
0
0
0
1
2
0
1
1
0
1
1
0
1
1
0
2
1
0
1
0
0
2
2
1
0
1
0
0
2
0
2
0
2
1
1
0
0
1
1
0
0
0
0
1
0
1
2
0
0
1
1
1
1
0
0
0
0
0
1
0
1
2
1
0
0
1
0
2
1
0
0
2
1
1
2
1
0
2
2
1
2
0
1
1
1
0
2
1
2
1
0
0
1
0
2
0
1
0
0
0
1
3
0
0
0
0
0
1
0
1
2
1
0
2
1
1
1
2
2
2
0
0
2
0
1
0
1
1
2
0
1
0
0
0
0
1
1
2
1
1
2
0
2
1
0
1
2
1
0
2
2
1
1
1
2
2
2
2
1
0
2
2
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
1
0
1
0
0
1
0
2
0
0
0
1
0
1
0
0
0
2
0
2
0
0
1
0
1
2
2
2
0
2
2
0
1
0
2
1
0
2
0
1
1
1
0
0
0
0
0
0
2
0
0
2
0
2
0
1
1
2
2
2
0
1
0
0
1
0
1
2
0
0
2
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
2
1
0
0
0
1
0
1
1
3
1
1
0
2
2
1
0
1
1
2
2
2
0
2
0
0
2
1
0
0
1
0
0
0
1
1
0
2
1
1
2
0
2
0
2
0
1
0
1
1
2
1
0
2
0
1
0
1
1
1
2
1
0
1
0
2
1
1
1
0
0
1
1
0
0
1
0
0
1
0
0
1
0
2
1
1
2
0
1
1
1
1
0
2
1
1
0
1
2
0
2
0
1
1
0
0
0
1
0
0
2
0
0
1
0
0
0
0
1
3
0
1
1
1
1
0
1
2
1
0
0
2
0
0
0
0
0
0
2
0
1
1
1
0
1
1
0
1
0
0
0
1
0
2
1
1
0
0
0
1
0
1
1
1
0
1
1
1
0
1
1
1
2
1
0
0
1
2
1
1
1
0
1
0
0
2
2
1
1
0
0
0
1
1
0
0
2
1
1
0
2
1
0
0
1
2
1
1
1
1
0
0
0
0
1
1
1
1
2
2
0
0
0
0
2
0
0
0
2
1
2
0
0
1
2
0
0
0
2
2
1
1
1
2
2
0
3
0
0
0
2
1
2
2
2
0
0
2
1
1
0
0
2
0
1
2
1
2
0
1
1
0
0
1
1
1
1
2
0
2
0
1
1
1
1
0
0
1
2
0
0
2
1
0
1
1
1
0
2
1
1
0
0
0
0
0
0
1
1
2
0
1
2
1
1
2
0
0
2
1
2
0
0
1
1
0
0
1
0
0
2
1
0
0
1
1
1
1
2
1
0
2
1
0
2
1
0
0
1
0
0
0
1
0
0
1
0
5
2
1
0
1
2
1
0
0
0
0
2
0
4
1
1
2
0
0
1
2
2
2
1
1
1
0
0
1
1
2
2
0
0
1
0
0
0
1
2
1
1
1
0
2
1
1
1
1
0
0
0
0
1
1
0
1
1
1
0
3
0
1
1
1
0
1
1
2
0
2
1
0
1
0
1
2
1
0
1
1
1
0
1
1
1
0
0
1
1
2
2
2
1
1
1
1
0
1
0
1
0
2
0
0
0
0
1
0
0
1
1
2
0
2
1
1
0
2
0
0
2
0
1
0
0
0
0
0
1
1
0
0
1
0
2
1
0
1
0
1
1
2
1
5
0
0
1
3
1
0
0
1
0
1
0
1
2
0
0
2
1
0
0
0
1
0
0
0
1
1
0
0
2
1
2
0
1
0
1
2
0
0
1
1
2
0
0
0
0
1
1
0
1
1
2
1
1
0
0
1
0
0
2
1
2
2
0
2
1
0
2
2
0
1
0
0
2
2
1
0
0
1
1
0
2
1
2
0
1
1
1
1
0
0
2
1
2
0
0
0
1
1
0
1
1
0
1
0
1
0
2
0
0
2
0
0
2
1
1
0
0
1
0
2
0
1
4
0
0
2
0
1
1
0
1
0
2
0
1
0
0
1
0
2
0
1
0
0
0
1
2
0
2
2
0
1
1
0
0
0
1
2
0
2
1
0
3
1
0
3
0
0
0
1
0
1
0
0
0
0
1
0
2
0
2
1
0
0
1
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
2
0
1
1
1
1
1
1
0
2
1
1
2
1
2
2
0
2
1
1
2
4
1
1
1
2
1
2
2
2
0
0
1
1
1
1
1
0
1
1
1
0
1
2
0
1
0
1
0
0
1
0
3
1
1
0
0
1
0
1
2
3
2
0
1
1
0
0
2
1
0
0
0
1
0
1
1
1
0
0
0
2
2
0
0
0
0
2
1
0
0
0
1
2
1
1
0
1
0
0
1
1
0
0
1
1
1
0
0
1
1
2
0
0
0
2
2
0
2
1
0
2
1
1
1
2
1
0
1
2
0
0
1
0
0
1
1
0
1
2
0
1
1
0
0
1
0
1
1
1
1
2
0
0
2
2
1
1
0
0
1
1
1
2
1
1
2
1
0
1
1
1
1
1
2
0
1
1
0
1
1
2
1
0
1
0
0
2
1
2
0
0
0
0
0
2
0
0
2
1
1
0
2
0
1
0
1
0
1
2
1
0
1
2
0
0
2
1
1
0
0
0
1
1
2
1
1
0
2
1
1
2
1
1
2
0
1
2
2
1
0
2
0
0
1
1
2
0
1
3
2
1
2
0
1
0
0
2
1
0
3
1
1
4
0
0
0
0
1
0
2
1
2
1
0
0
1
1
0
1
2
2
1
0
2
1
0
0
1
1
1
0
0
1
1
0
0
1
1
1
0
2
2
0
0
0
1
1
0
2
0
0
2
0
2
4
1
0
2
2
0
0
0
1
0
0
0
0
2
2
0
1
1
1
0
0
0
0
1
1
0
2
0
0
1
1
0
0
0
1
2
0
1
2
1
0
1
2
0
0
0
1
1
0
0
0
2
2
1
1
2
2
0
1
2
1
2
1
2
1
7
1
1
1
1
0
0
2
0
4
0
1
1
2
1
0
1
1
0
0
3
2
0
2
2
1
1
2
0
0
1
1
2
0
0
1
1
1
0
0
2
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
2
0
0
0
1
1
0
0
1
1
2
0
0
0
0
0
2
1
0
0
1
1
1
0
1
1
0
0
1
2
0
0
1
2
3
0
1
2
0
1
0
2
0
2
1
3
2
0
0
1
0
0
0
1
0
1
0
1
1
0
1
1
2
0
0
2
0
0
2
0
1
2
2
2
0
0
0
1
2
2
1
0
1
1
0
2
2
0
1
1
1
0
1
2
0
1
0
1
2
0
2
0
0
1
0
1
2
1
2
0
2
2
0
0
2
2
2
0
0
0
2
0
0
1
0
0
1
0
1
0
1
1
1
1
0
0
2
3
2
2
1
1
1
0
0
0
1
0
0
0
2
2
1
1
2
1
1
1
1
2
1
1
0
1
2
0
0
3
1
0
0
1
0
1
0
0
0
1
1
3
1
0
2
1
0
1
0
2
0
1
1
0
2
1
2
0
1
2
1
1
2
1
0
0
5
0
0
0
0
0
1
0
0
0
0
2
1
0
2
2
1
1
1
1
0
2
1
2
0
0
0
1
2
2
1
1
1
0
0
2
1
2
0
1
0
2
1
0
1
1
0
0
0
2
0
1
2
2
0
0
1
1
1
0
1
1
1
2
1
1
2
0
0
1
0
0
2
0
0
2
1
1
0
2
0
1
0
1
0
0
1
0
1
1
0
2
1
1
2
2
1
0
1
0
0
0
2
1
1
0
1
1
1
0
0
0
0
0
1
0
2
0
0
1
2
2
1
1
0
1
0
1
1
0
1
2
0
1
1
1
3
0
1
1
2
1
1
0
0
1
1
0
2
0
0
0
1
1
2
1
0
1
2
1
0
1
0
0
0
0
0
1
0
2
0
1
0
2
0
0
0
2
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
2
1
2
0
0
0
1
1
0
0
2
1
1
0
0
1
2
1
2
0
1
0
1
1
1
1
2
1
0
1
0
1
0
2
2
1
0
1
0
0
2
0
0
0
1
2
0
0
1
2
2
0
1
0
2
0
1
0
0
0
0
1
1
0
1
1
0
1
1
0
2
3
0
1
0
0
0
0
0
0
0
1
0
1
2
1
2
1
1
0
1
1
1
0
0
0
1
2
1
1
2
0
0
1
1
1
1
1
0
0
1
1
1
0
0
0
1
1
3
2
1
1
0
1
2
1
1
0
1
1
1
1
1
1
1
0
0
1
1
2
2
1
0
0
0
0
2
1
0
1
0
0
1
0
0
1
2
1
0
0
0
0
0
1
0
0
1
1
0
0
0
2
4
1
0
0
1
0
2
2
1
0
2
1
1
0
0
2
0
1
0
3
0
2
1
0
2
1
2
0
0
1
3
0
1
0
1
1
1
2
1
0
0
0
0
2
1
3
1
2
1
1
0
0
0
0
0
1
2
0
1
0
1
0
1
0
0
1
2
0
1
0
0
1
1
2
0
0
0
1
1
2
0
2
0
0
0
1
2
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
1
1
2
1
0
0
1
2
2
2
1
0
1
1
0
1
0
0
0
0
0
0
2
2
1
1
2
0
0
0
1
0
1
2
0
0
0
0
2
1
0
1
2
2
0
1
1
1
1
0
0
2
0
0
0
2
1
0
0
0
0
1
2
0
0
0
1
0
1
0
1
0
2
1
2
1
1
0
0
0
1
1
0
1
0
2
1
0
2
1
0
0
1
1
2
1
3
1
2
1
0
0
1
0
2
1
2
2
0
1
0
1
0
2
2
1
1
2
2
2
1
3
0
2
0
0
0
0
0
1
0
0
1
1
0
2
0
2
0
0
1
0
0
0
2
0
1
0
0
1
1
1
3
0
0
2
0
1
0
0
1
1
0
0
1
2
1
2
0
0
0
0
1
1
1
1
0
1
0
1
0
0
0
1
2
2
2
0
2
2
1
1
2
1
0
1
0
0
2
0
1
1
0
2
0
2
0
0
1
1
0
0
1
0
2
0
0
1
1
0
2
0
1
1
1
2
1
2
0
1
1
0
2
1
0
0
0
2
2
1
2
1
0
2
1
1
1
1
0
0
0
0
1
0
2
0
1
1
0
0
1
0
1
1
0
0
2
0
0
2
0
2
0
0
1
1
2
0
0
1
2
2
1
2
0
0
1
1
0
0
1
2
0
2
0
0
0
0
0
0
0
0
1
0
2
0
1
0
1
1
0
1
0
0
1
1
1
2
2
1
0
0
0
1
2
1
1
0
0
2
0
0
0
2
1
1
0
2
0
1
0
1
2
1
0
2
2
2
0
1
1
1
1
0
1
1
1
0
3
0
0
1
1
0
2
1
0
0
2
0
0
0
2
2
0
2
2
0
2
1
2
0
2
2
1
0
0
0
1
0
2
1
0
2
2
1
0
2
1
2
1
0
0
1
2
0
2
2
1
0
0
0
3
0
0
1
0
0
1
2
1
1
1
2
1
2
0
0
1
2
1
0
1
1
0
2
0
2
0
0
1
1
0
1
2
1
1
0
0
0
0
0
1
1
1
1
0
1
0
0
1
0
0
0
0
0
2
1
0
0
0
2
2
0
2
0
1
0
2
0
1
2
0
2
1
2
1
1
2
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
2
0
1
1
0
0
1
1
0
2
1
1
0
0
1
0
0
1
0
0
0
1
11
0
0
2
1
1
2
0
0
0
1
2
0
1
1
1
1
1
0
0
0
0
0
0
2
2
1
2
0
0
0
1
2
0
0
0
1
2
1
2
0
2
1
0
1
1
2
0
0
0
0
0
2
0
0
2
1
2
0
1
1
0
0
0
2
2
1
1
0
0
0
2
1
1
1
2
0
2
1
2
2
1
2
1
1
1
1
2
1
1
0
0
0
0
1
0
1
1
2
0
1
0
0
0
2
1
0
1
1
1
2
0
0
2
0
2
1
1
0
0
1
2
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
2
0
2
0
4
1
0
0
0
1
1
2
1
0
0
2
2
0
1
1
2
0
0
1
0
1
0
0
2
2
0
1
0
0
3
1
1
2
2
1
0
0
1
0
1
2
0
0
1
1
0
0
1
1
1
0
1
1
2
0
0
0
0
1
0
1
1
0
2
1
2
2
0
0
1
2
0
2
0
1
1
0
1
1
0
2
2
0
0
0
0
0
0
0
2
2
1
1
1
0
1
0
1
0
1
0
1
0
1
2
1
2
1
1
1
0
2
1
0
1
2
2
3
0
2
1
1
0
0
1
0
0
1
1
1
0
2
0
2
0
0
0
1
1
2
1
0
2
0
1
0
1
0
2
1
2
1
1
1
1
1
1
0
0
2
0
1
0
1
1
2
0
0
1
1
0
0
0
0
1
2
0
1
0
1
1
0
0
0
2
0
2
0
0
2
0
0
0
2
1
1
4
0
1
0
0
0
1
1
2
0
0
1
0
0
0
1
0
2
1
1
0
2
0
0
1
0
0
2
1
0
0
1
2
0
0
0
1
2
2
0
5
0
0
2
0
1
1
1
0
2
2
10
1
1
0
2
1
0
0
1
0
1
1
1
1
0
2
0
2
0
1
0
0
0
0
0
0
1
1
1
0
0
0
1
2
0
1
2
1
0
1
1
0
2
1
1
0
1
0
0
0
0
1
2
0
0
0
2
1
0
0
0
0
1
0
1
1
1
0
0
1
1
0
2
0
0
1
0
0
0
1
0
1
1
1
0
1
2
0
0
2
0
0
1
1
1
2
1
1
2
3
0
1
0
0
1
0
1
1
0
1
2
1
1
2
1
1
1
1
0
1
3
2
0
0
0
0
1
2
2
0
0
1
0
1
0
1
3
1
0
1
1
1
2
0
1
1
0
1
2
2
1
2
0
0
1
0
1
2
1
1
2
0
1
0
2
1
0
1
0
1
0
2
1
1
0
0
1
0
0
1
1
1
1
2
0
0
2
0
0
0
0
1
1
1
0
0
0
3
2
1
0
2
1
1
1
3
1
0
0
2
0
0
0
1
0
0
2
1
0
1
1
1
0
0
0
1
1
1
1
2
1
1
0
1
1
0
1
0
0
0
1
2
0
0
1
2
0
2
1
0
2
0
0
1
0
2
2
0
1
2
1
1
0
2
1
0
0
1
2
1
1
2
2
1
2
2
0
1
0
0
0
0
2
2
2
0
1
2
2
2
0
2
0
1
1
0
0
1
1
0
2
1
1
2
0
1
1
2
1
1
0
0
2
1
2
0
2
0
2
1
0
1
0
2
1
1
0
1
0
0
1
1
0
1
2
0
1
1
0
1
1
2
1
2
1
1
1
1
1
0
0
3
2
0
0
2
0
0
2
0
1
0
1
2
0
1
1
1
1
1
0
1
1
0
1
0
0
0
0
0
2
0
1
2
1
2
0
1
1
1
1
0
1
0
0
1
0
1
1
0
0
1
0
1
1
0
1
1
0
1
2
1
1
2
0
1
4
1
0
0
0
0
2
0
2
0
1
0
1
0
0
2
1
1
1
0
2
0
1
0
0
1
1
0
1
1
1
0
0
0
2
0
1
1
1
0
0
0
0
2
1
2
2
0
1
1
0
0
2
1
1
2
1
1
1
0
0
0
1
2
0
2
1
0
0
2
0
0
0
2
0
0
1
0
1
0
0
0
2
0
2
2
1
2
0
0
0
1
0
2
1
2
0
1
0
1
2
1
1
2
1
1
1
1
1
0
0
0
1
2
1
2
0
0
2
1
2
0
1
1
1
0
4
2
2
2
0
1
1
2
3
0
2
1
1
0
0
1
0
1
1
1
1
1
0
2
0
0
0
1
1
2
1
1
1
2
0
1
0
3
0
1
2
1
1
2
2
1
1
2
0
0
0
0
1
0
2
0
0
0
2
2
0
0
0
2
0
0
2
0
1
0
0
0
1
0
0
1
1
1
2
0
2
1
2
1
0
1
2
1
1
0
1
2
0
0
0
2
0
1
0
1
1
1
2
2
0
3
1
0
2
1
2
1
5
2
0
0
2
1
1
1
0
0
1
1
1
0
1
2
1
2
2
2
0
1
0
0
0
4
0
1
2
0
1
1
1
0
1
2
1
1
0
0
2
1
1
0
0
0
1
1
0
0
1
1
1
0
0
1
2
0
12
2
1
1
0
0
1
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
2
1
1
1
1
2
1
0
0
2
0
2
0
1
1
0
2
2
2
2
2
1
0
2
0
0
1
0
0
1
1
1
1
2
0
0
2
0
0
1
1
0
1
0
1
0
0
2
0
1
1
2
0
0
2
1
0
0
1
1
2
1
6
0
3
0
0
0
0
1
0
1
0
0
1
2
0
0
2
1
0
1
2
1
3
0
2
1
1
0
3
0
2
0
0
1
0
1
2
0
1
1
1
2
0
1
2
3
2
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
2
0
1
0
1
0
1
1
0
0
1
1
1
0
2
0
1
1
1
0
1
0
0
0
0
1
1
2
2
1
0
1
1
1
0
3
2
2
0
1
1
1
1
1
2
2
0
0
0
0
1
2
1
1
0
0
0
0
0
0
1
1
1
2
1
1
0
0
1
0
0
2
0
2
0
1
2
2
1
1
0
0
2
2
3
2
1
0
0
2
3
1
1
0
0
3
0
0
0
0
1
2
1
1
0
0
1
1
0
1
1
1
1
0
1
1
1
1
1
1
2
1
0
2
1
0
1
1
0
0
2
0
0
2
1
1
1
0
0
1
0
0
0
1
0
0
1
1
2
0
3
1
0
1
1
2
0
1
1
0
1
0
1
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
1
2
1
1
0
1
1
1
0
1
0
3
2
2
1
0
0
1
1
0
1
1
1
0
1
0
0
0
0
0
2
1
0
1
0
0
1
1
1
0
1
0
0
3
1
0
1
1
0
1
0
0
1
1
2
0
2
2
1
0
2
1
1
2
1
0
0
0
1
0
0
0
0
2
0
1
1
0
1
1
1
0
1
0
1
0
0
1
1
2
2
0
0
1
0
2
0
0
1
0
1
1
1
2
1
0
0
0
0
0
1
0
1
2
1
0
0
2
0
0
2
0
1
0
1
0
2
1
3
1
1
2
1
0
0
1
1
0
2
1
2
1
0
1
0
0
0
1
0
0
0
1
1
0
0
1
2
3
2
0
0
1
1
1
0
0
1
1
2
8
0
2
0
2
1
1
1
2
0
1
0
1
0
2
0
2
2
2
0
1
0
0
1
1
1
2
0
0
0
1
1
3
1
1
2
0
1
1
0
4
0
1
1
2
0
0
0
0
1
1
0
1
1
0
2
0
1
0
1
0
2
1
2
0
2
2
1
0
2
0
1
0
1
1
0
1
0
0
0
1
1
2
1
0
0
0
1
2
1
0
0
2
1
0
1
2
0
0
0
1
0
2
1
2
0
0
1
0
0
0
1
1
0
2
2
0
2
1
2
0
0
0
0
0
1
1
2
2
1
2
2
0
0
2
0
0
1
1
0
0
1
1
0
1
2
2
0
1
1
1
1
0
2
3
1
2
0
0
0
1
1
1
0
1
2
1
2
0
1
0
1
2
2
0
2
0
1
1
0
1
1
2
1
2
0
1
0
0
0
1
0
0
1
0
1
0
0
1
0
0
1
1
0
0
2
1
1
0
1
1
0
0
1
1
1
1
0
0
0
0
2
2
0
1
0
0
0
2
0
1
0
1
1
1
2
0
1
1
2
0
1
0
0
1
2
0
1
2
2
2
2
0
0
0
0
1
1
1
0
1
1
2
3
1
3
0
0
0
1
0
0
2
1
1
1
0
2
2
1
1
1
2
2
2
2
1
0
1
0
0
1
1
0
3
2
0
0
0
0
0
0
2
2
1
0
0
1
0
2
1
1
0
0
2
1
2
0
2
0
2
1
0
1
0
0
0
0
1
1
0
1
2
2
1
2
1
2
1
0
0
0
1
0
1
1
1
1
0
3
0
1
0
0
2
1
1
1
1
1
1
2
2
2
2
0
1
0
1
2
0
1
1
1
1
2
0
2
2
0
1
1
0
3
0
1
1
0
0
1
0
3
0
0
0
0
2
0
0
0
0
1
1
0
2
10
1
0
1
1
0
1
0
1
0
0
0
1
0
1
0
2
0
2
0
1
0
1
1
0
0
0
0
0
2
1
1
1
1
1
0
2
2
2
0
1
0
0
1
0
2
0
1
0
1
1
0
0
1
1
1
2
0
2
0
0
1
2
0
0
0
1
0
0
1
1
0
0
0
1
0
1
1
1
0
1
1
1
1
0
1
1
0
2
0
1
0
1
2
1
1
0
0
0
1
0
1
2
0
1
1
2
2
0
2
0
1
0
0
1
0
0
2
2
2
2
0
3
0
0
1
1
2
0
1
3
0
0
1
2
1
1
0
1
0
0
0
0
1
2
2
1
2
0
1
0
2
2
1
1
2
2
1
1
0
0
0
1
0
0
1
0
0
1
2
1
0
0
0
2
0
1
0
0
1
1
0
1
0
0
1
0
2
2
0
1
0
1
1
2
0
0
0
1
2
0
0
1
0
1
0
2
2
1
1
2
1
1
2
0
0
0
2
1
0
1
0
0
0
2
2
1
0
0
2
2
0
1
1
1
0
2
0
1
3
0
0
1
2
0
1
1
1
1
0
0
2
0
1
2
2
2
1
0
0
1
1
0
0
2
2
1
0
0
1
1
0
0
1
0
0
2
1
0
0
1
2
1
0
1
1
2
1
2
0
0
1
1
3
2
3
0
1
1
1
0
0
1
3
1
0
2
2
0
1
0
1
1
2
1
1
2
1
2
0
0
2
0
1
2
1
1
3
0
1
1
0
1
2
0
1
2
0
1
0
1
0
2
0
0
1
2
2
0
0
2
0
2
2
2
0
0
1
0
1
1
1
0
0
2
2
0
0
0
0
1
0
1
0
2
1
1
0
0
0
1
0
2
1
1
2
2
0
0
2
1
0
0
2
1
0
0
1
2
1
1
1
0
2
1
0
1
2
0
0
1
2
2
0
0
2
5
1
1
0
2
0
1
0
0
1
2
0
1
0
0
1
1
0
0
0
2
1
0
1
0
0
2
2
0
0
3
1
0
1
2
0
1
0
1
2
0
0
0
0
0
1
1
0
0
2
0
4
2
2
1
0
1
1
0
1
1
0
0
3
2
0
1
0
0
0
1
1
1
0
0
1
0
0
1
1
0
1
0
0
1
0
1
1
0
0
1
0
0
1
1
2
1
0
1
1
1
1
1
2
0
1
0
2
0
0
0
1
0
2
2
1
2
1
1
4
1
0
1
1
0
1
2
1
0
0
0
1
0
0
1
2
2
0
1
1
1
1
1
0
3
0
2
0
0
0
1
2
0
0
1
0
0
0
2
0
1
2
0
0
0
1
0
0
1
1
0
1
1
2
0
0
0
0
0
1
0
0
3
1
1
0
2
0
2
1
2
0
0
0
2
0
1
1
0
2
1
0
1
0
0
1
0
0
2
1
1
2
0
2
0
0
0
1
1
2
0
1
0
2
0
1
0
1
1
0
0
2
0
1
1
1
1
1
1
2
0
0
0
0
0
0
0
0
2
0
3
0
0
1
1
1
1
1
1
0
2
2
2
1
1
1
1
0
0
1
1
0
2
2
0
0
0
1
0
0
0
1
2
2
0
1
1
1
0
1
0
1
1
2
1
1
0
2
1
1
0
0
2
1
1
0
1
0
1
1
0
1
2
0
1
0
0
0
0
1
0
1
0
2
0
0
1
0
1
2
0
1
0
0
1
1
1
1
2
1
0
2
0
0
1
0
1
1
0
0
0
1
1
1
2
2
0
0
2
1
2
2
0
0
0
0
1
0
2
2
1
0
1
1
1
1
1
1
0
0
0
1
1
0
0
2
1
0
1
2
0
0
0
1
2
0
1
2
1
1
1
1
0
2
0
1
1
0
0
1
0
0
0
1
1
0
0
1
0
1
0
1
2
0
0
0
1
0
1
2
0
1
2
1
0
2
0
0
0
1
2
0
0
2
0
0
2
0
1
1
1
0
0
1
0
1
0
1
0
2
0
0
2
1
1
0
1
1
1
0
0
3
0
0
2
2
0
0
0
1
0
5
2
1
0
2
1
1
0
0
1
0
1
2
1
2
0
0
0
1
0
1
1
2
0
1
2
2
1
1
2
1
1
2
2
1
0
2
1
2
0
0
2
0
1
2
1
1
1
1
0
0
0
0
0
0
1
1
1
1
0
1
1
0
1
0
0
1
1
1
0
1
1
1
0
0
1
2
1
0
2
0
0
2
0
0
1
1
0
0
2
2
1
0
1
1
0
0
1
1
0
1
2
2
1
0
1
2
1
0
2
0
1
1
2
1
1
0
1
0
1
0
0
0
0
1
0
2
1
0
0
1
0
1
0
1
0
0
1
0
0
0
2
0
0
1
0
2
1
0
1
1
2
2
2
2
1
0
1
1
2
0
1
2
2
1
0
2
2
2
0
0
0
0
1
1
0
0
0
2
0
0
1
2
2
1
1
0
0
1
0
1
1
1
1
0
1
0
1
1
0
0
0
2
2
1
1
0
1
1
0
0
1
0
0
1
0
1
1
0
1
1
1
1
1
0
0
0
1
2
1
0
1
1
0
0
1
0
2
2
0
2
1
1
2
0
0
0
1
0
1
0
2
0
0
0
0
1
0
0
0
2
1
1
1
1
1
1
1
0
0
3
1
1
2
1
1
0
1
1
1
0
0
0
3
0
1
1
0
1
1
0
3
1
0
0
1
1
2
0
0
0
0
1
0
1
2
1
1
0
0
0
1
0
2
1
2
2
1
2
2
0
1
1
1
1
1
1
0
1
1
0
1
2
4
0
1
0
0
0
0
0
1
2
1
1
0
1
0
2
2
0
0
0
0
2
3
1
2
0
2
1
1
0
2
3
1
1
2
2
2
0
1
0
1
1
0
2
0
0
0
1
2
1
0
1
1
0
0
2
2
2
1
0
2
2
1
0
0
0
2
0
1
1
0
0
0
0
1
1
1
1
1
0
1
1
1
1
2
1
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
1
1
1
2
1
1
2
0
0
0
2
1
0
0
0
1
0
4
0
0
0
0
2
2
1
0
0
1
2
0
2
0
1
2
1
1
2
2
0
1
1
1
0
0
2
0
2
1
1
0
0
1
1
1
0
3
1
1
0
1
1
0
1
1
0
1
1
0
1
0
1
0
0
2
0
1
2
1
2
2
1
0
2
0
1
1
0
0
0
1
1
0
0
0
1
1
0
3
0
1
2
1
1
2
1
2
0
0
2
0
0
0
1
2
0
0
0
1
1
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
2
1
1
0
1
0
1
1
1
0
1
1
1
1
2
1
1
0
1
0
1
1
0
2
1
4
1
1
1
1
1
1
0
0
0
1
1
0
1
0
0
1
0
1
0
2
1
1
2
1
1
1
0
0
1
1
0
0
1
2
1
0
0
0
2
2
0
1
2
0
4
0
1
0
0
1
1
1
2
0
2
0
0
0
0
0
0
2
1
1
0
1
0
2
1
0
1
0
1
1
0
2
1
0
1
2
0
0
0
1
0
0
0
0
1
0
0
2
0
1
2
1
1
0
0
1
0
0
1
0
1
0
0
2
1
1
1
2
2
1
1
2
0
0
1
0
0
1
0
0
0
0
0
0
2
2
0
0
1
2
0
1
0
2
0
2
1
2
2
2
0
0
0
1
1
1
1
1
0
0
0
0
0
0
2
2
0
1
0
1
1
0
0
2
2
2
0
0
1
0
0
1
0
1
1
0
0
2
0
1
0
0
2
1
2
0
0
0
1
0
1
1
0
2
2
2
1
1
0
1
2
0
0
1
0
1
0
2
1
0
2
2
0
1
0
2
0
2
1
2
3
0
4
1
1
0
1
0
0
2
0
2
1
1
2
0
2
1
1
1
2
0
2
0
0
0
0
1
0
0
0
0
2
0
1
1
1
0
2
1
0
0
1
1
1
2
1
1
1
0
2
0
2
0
2
1
2
1
0
0
0
2
2
0
0
0
1
2
0
0
0
0
2
0
1
0
1
1
1
0
0
2
2
2
0
0
0
0
2
3
1
0
2
2
1
0
2
1
0
1
1
1
1
0
1
1
0
2
0
0
1
0
2
0
1
0
0
0
1
0
0
0
1
0
1
0
0
1
1
0
0
1
1
0
2
0
0
0
1
2
1
2
2
0
0
0
1
1
2
1
2
1
1
2
2
1
0
1
0
0
1
0
0
2
0
0
1
0
0
3
2
0
1
0
0
3
1
2
1
2
0
0
0
0
0
2
1
1
0
0
1
0
2
1
0
1
1
0
0
0
1
2
2
0
2
1
3
0
0
2
2
1
0
2
0
0
0
2
1
2
0
2
0
0
1
2
2
0
2
0
0
1
1
1
0
1
0
2
1
1
0
1
1
2
0
0
0
0
1
0
0
0
2
0
1
3
2
0
0
1
1
1
2
1
0
1
4
0
1
1
1
1
1
2
1
0
1
0
1
3
2
2
0
0
0
1
0
1
0
0
1
0
0
0
2
0
0
0
0
1
2
1
0
1
0
2
2
0
0
0
2
1
2
2
0
2
1
1
0
1
2
0
1
0
1
2
0
0
0
0
1
0
0
0
2
2
2
1
2
2
0
2
0
2
1
2
1
1
2
1
2
1
1
0
1
0
1
0
1
0
0
1
2
1
1
1
1
2
1
1
0
1
0
0
0
0
2
1
0
1
1
1
0
0
2
2
1
0
0
0
2
0
1
1
0
0
0
0
1
2
2
1
1
1
1
0
0
0
0
0
0
0
0
2
2
0
1
0
2
1
0
1
1
0
0
0
1
1
1
2
0
1
2
0
1
1
2
1
1
0
3
0
1
0
0
0
1
2
2
1
1
0
1
1
0
0
0
2
0
2
0
2
1
0
0
2
0
0
1
2
0
2
0
1
1
0
2
0
1
0
2
2
1
0
0
1
2
0
1
0
1
2
2
0
3
1
1
1
1
0
0
0
0
1
1
3
1
0
0
2
0
1
0
2
0
0
0
0
1
1
1
1
0
2
0
0
0
0
0
1
2
1
1
1
2
0
2
2
1
1
0
2
1
2
0
1
0
0
0
2
1
0
2
2
2
1
0
0
2
2
0
0
0
0
1
0
1
1
1
0
0
0
2
1
0
1
1
1
0
1
1
0
1
1
1
1
2
1
0
0
1
0
2
0
0
1
0
0
0
0
3
1
0
1
0
1
1
0
2
2
0
1
1
1
0
0
1
0
1
2
1
0
2
2
1
0
2
0
1
1
3
2
0
0
2
2
2
3
0
0
0
0
0
0
1
0
1
2
0
2
1
0
2
1
1
1
0
0
2
1
0
2
2
0
1
0
0
1
1
0
1
0
1
0
1
0
0
0
0
0
2
0
1
3
0
1
1
2
0
1
2
1
2
0
1
0
1
2
1
0
0
1
0
2
1
0
1
1
0
0
0
0
0
1
2
0
2
1
0
1
0
2
0
0
0
2
0
2
0
0
0
1
2
0
0
0
0
0
2
1
1
0
0
0
2
0
0
0
1
0
0
2
1
2
0
1
1
1
0
0
2
1
2
0
0
1
2
0
1
2
1
2
0
3
1
1
1
0
1
2
0
5
2
2
1
1
1
0
1
0
0
2
4
1
1
0
0
2
0
1
1
0
0
0
0
1
2
0
1
1
2
1
2
1
2
0
1
0
0
0
1
0
1
2
2
1
1
2
1
1
1
1
0
1
1
1
2
0
2
1
0
2
1
1
0
0
1
1
2
2
0
0
1
1
1
0
0
1
0
1
0
2
1
2
2
2
2
2
2
0
1
1
2
1
1
0
1
1
1
1
1
0
0
1
2
1
1
0
0
0
1
0
0
1
0
1
0
1
2
0
1
3
1
1
2
7
2
0
0
0
0
1
0
0
1
2
1
0
1
1
0
2
1
0
1
0
0
0
0
1
2
0
1
2
1
1
1
2
1
0
0
1
2
1
1
2
1
1
0
0
2
0
3
2
0
0
1
0
1
0
0
1
1
0
2
1
1
1
0
1
0
1
1
1
0
1
1
1
2
1
1
2
1
1
2
2
1
0
1
0
2
1
0
2
0
1
0
1
0
0
2
1
4
0
2
1
0
1
0
0
2
1
1
1
0
1
3
2
1
0
2
1
2
2
0
0
0
0
0
0
0
0
0
1
0
3
1
0
0
2
1
1
1
0
0
0
2
0
2
0
2
0
0
1
2
1
2
1
1
1
1
2
0
0
1
0
1
1
1
1
1
0
2
0
3
1
2
2
0
1
0
0
1
0
2
0
1
0
0
0
1
0
2
0
0
0
0
1
0
1
1
1
0
0
2
0
2
1
1
2
2
1
1
0
1
2
0
2
2
2
0
2
2
2
2
1
2
1
1
2
1
1
2
2
0
1
1
0
1
0
1
0
1
1
1
2
1
1
1
1
0
2
1
2
0
1
2
0
3
1
1
2
1
0
0
1
1
0
0
1
2
1
3
0
0
2
3
1
1
2
0
0
0
2
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
1
0
0
1
2
1
0
0
1
0
0
0
1
2
2
1
1
1
2
0
1
1
0
0
0
0
1
0
0
1
2
1
2
1
1
1
2
0
0
2
0
0
2
0
1
0
1
0
1
0
1
1
0
1
0
1
1
2
1
0
2
2
2
1
1
2
1
2
0
0
1
1
2
1
0
1
1
1
1
2
1
0
2
0
0
1
0
2
0
1
0
0
1
0
0
0
0
0
0
2
1
0
0
0
1
1
0
0
1
0
0
2
0
0
2
0
1
1
2
2
2
1
1
0
0
1
0
2
1
0
1
0
0
2
0
2
1
2
1
1
0
2
1
1
2
1
1
0
0
0
1
2
1
0
0
2
1
0
1
1
1
2
1
0
2
2
2
0
2
2
0
0
0
0
0
0
0
0
3
0
2
1
1
0
1
2
0
1
0
1
0
2
2
2
2
1
1
1
1
1
0
0
2
0
0
0
0
0
1
1
2
2
0
0
0
2
0
1
2
6
1
1
1
0
1
0
1
2
0
1
2
0
1
0
1
1
0
0
1
2
0
1
1
0
2
0
1
0
2
0
1
1
1
0
1
1
1
2
0
1
0
0
0
2
2
1
0
2
1
2
1
1
1
2
1
0
2
1
1
1
0
2
2
1
1
1
1
1
2
0
0
0
1
1
1
1
0
0
2
0
0
2
2
1
0
1
2
0
1
1
1
1
2
1
1
0
1
0
2
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
1
1
2
1
1
0
1
1
1
2
2
1
0
0
1
1
0
1
0
1
1
0
1
0
0
1
0
1
1
0
2
1
2
0
3
0
2
1
0
0
0
1
0
0
1
1
1
0
1
0
2
1
0
0
2
1
0
0
0
1
2
1
1
3
2
1
2
1
0
1
0
2
0
0
2
1
0
2
2
0
0
1
0
0
0
1
1
0
0
2
1
0
1
1
0
0
0
1
2
0
2
0
0
1
1
3
0
0
0
1
1
1
1
0
0
1
1
0
0
2
2
0
2
0
0
0
0
1
2
1
0
1
1
0
1
1
0
0
0
0
2
1
0
1
2
1
0
0
1
2
0
2
2
1
0
0
1
1
2
0
2
1
2
1
1
2
0
2
0
0
0
2
0
1
1
0
1
2
0
0
0
0
1
2
2
2
0
0
2
0
2
1
1
1
0
1
0
0
0
0
0
2
0
1
1
1
1
2
1
0
1
0
1
2
0
1
0
1
2
0
1
1
0
2
2
1
0
0
0
0
0
0
1
0
0
0
1
2
0
1
1
0
0
1
1
0
1
1
2
0
1
2
1
0
4
1
0
2
1
0
0
1
0
1
2
1
0
1
1
0
1
0
1
2
1
0
1
0
2
2
0
1
1
0
1
0
1
2
1
1
0
1
3
1
2
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
1
1
0
1
0
0
2
0
2
1
0
0
2
1
0
1
1
1
0
0
2
2
2
0
0
1
2
1
1
0
2
0
1
0
1
0
1
2
1
0
0
0
0
0
0
2
1
1
0
1
0
0
0
0
0
1
0
0
2
0
1
3
1
2
1
2
0
0
0
1
0
2
0
1
0
0
2
0
2
1
0
0
1
0
2
1
0
0
1
1
1
0
0
0
1
1
1
1
1
1
1
0
1
0
0
1
0
0
0
0
0
0
2
0
1
0
1
1
1
0
2
1
0
1
1
0
0
0
0
1
0
0
0
2
1
1
1
1
0
0
0
2
2
2
1
0
1
1
3
1
0
0
1
0
2
1
1
0
1
0
0
0
2
1
1
1
1
0
2
0
6
0
0
0
2
0
0
2
0
1
0
0
0
1
1
0
1
0
2
0
1
0
2
0
1
0
1
1
0
1
0
1
0
3
0
2
1
0
1
1
0
2
1
1
0
1
0
0
0
3
0
0
0
0
4
0
0
2
0
1
0
2
0
0
0
2
0
1
0
0
2
0
1
2
0
1
0
0
1
0
0
1
0
1
0
1
2
0
0
2
0
1
0
4
0
1
0
0
0
1
0
2
0
1
0
0
0
2
1
2
1
0
1
2
0
1
2
0
1
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
1
1
1
1
0
3
1
3
0
2
2
0
0
0
1
0
0
0
1
0
1
1
1
1
0
0
2
1
0
0
0
1
0
2
1
0
2
2
0
1
1
1
1
0
1
0
2
1
1
0
1
2
1
0
0
1
1
2
0
0
0
3
0
1
1
2
2
2
0
0
0
0
2
0
0
0
1
1
1
0
0
0
0
2
2
1
0
0
1
1
0
2
0
1
0
2
1
2
0
0
0
0
1
1
1
2
1
2
1
0
2
0
0
2
1
1
0
1
1
2
1
0
0
2
0
2
2
0
1
0
0
1
1
1
1
0
1
0
1
1
0
1
0
0
1
1
0
1
0
0
0
1
3
2
0
2
2
2
1
1
1
0
0
1
0
1
2
0
2
2
2
0
1
2
1
0
3
0
0
0
2
1
0
1
0
1
0
0
0
2
0
1
3
2
2
0
1
0
1
1
0
0
0
0
0
0
0
0
1
2
1
2
0
1
2
2
2
0
1
2
1
2
1
0
0
2
0
0
0
1
2
0
1
0
1
0
1
2
1
2
1
2
0
0
1
1
0
1
2
0
1
0
0
0
1
1
0
0
0
0
0
2
2
2
1
2
1
1
1
0
0
1
2
1
0
1
1
0
2
2
2
0
1
0
0
1
0
0
0
0
2
2
1
0
0
1
0
0
1
3
1
2
2
1
0
2
1
1
0
0
1
0
1
1
1
0
0
1
2
0
0
1
2
1
1
1
0
1
1
2
2
1
1
0
0
0
1
0
0
1
1
0
0
1
2
0
0
0
0
1
1
1
1
1
0
2
0
1
0
1
1
0
0
0
1
1
0
2
0
1
1
1
1
0
2
1
1
0
1
1
0
2
1
2
1
2
0
2
1
1
0
0
3
0
0
2
1
0
1
1
0
1
1
0
0
2
1
1
2
0
1
3
2
0
1
2
2
1
0
0
0
2
0
1
2
0
1
0
1
1
0
0
0
2
0
2
1
0
0
0
1
0
2
2
0
2
0
0
2
1
1
0
0
2
0
0
0
0
1
0
0
1
2
0
0
0
2
1
2
1
0
0
1
3
2
1
0
0
2
0
0
1
2
0
0
0
1
1
0
1
0
0
0
1
1
0
2
5
0
1
2
0
2
0
0
1
1
0
0
1
0
1
1
2
2
0
0
2
1
2
0
1
0
0
0
0
0
2
2
0
0
0
0
0
1
1
0
2
1
2
1
0
1
0
0
1
2
2
1
1
1
1
1
1
2
2
0
0
0
0
2
0
1
2
2
2
1
0
1
0
1
0
0
2
1
1
1
0
2
1
0
2
0
1
1
1
1
1
1
1
0
1
1
1
1
1
0
1
1
1
2
2
1
0
0
1
0
0
1
1
0
1
1
2
1
2
1
1
0
1
0
1
1
1
1
0
2
0
0
0
0
1
2
0
1
1
1
0
2
1
0
1
1
2
0
0
1
0
1
1
2
0
0
1
1
2
2
0
3
0
1
1
0
2
0
0
2
0
1
1
1
1
2
1
1
1
1
1
0
0
1
2
1
1
0
1
0
2
1
1
1
1
0
0
2
1
0
1
1
0
2
1
1
2
0
1
0
2
2
1
0
0
2
2
1
1
1
0
1
0
3
0
2
1
1
1
0
1
2
2
1
4
1
2
0
0
0
2
3
1
1
1
2
0
1
1
1
2
3
2
0
1
0
0
2
2
0
1
1
1
1
1
0
1
0
0
2
2
0
0
0
1
2
1
0
2
0
2
1
2
0
1
2
1
0
0
1
0
1
1
1
1
0
1
0
1
1
2
1
0
1
0
0
0
0
2
1
0
2
1
0
0
1
0
0
1
0
3
2
2
1
0
2
1
2
1
1
1
1
1
1
1
0
0
2
1
0
1
2
0
0
0
1
0
1
1
1
2
1
0
1
2
1
1
0
1
1
0
2
2
2
1
2
2
2
0
0
0
0
1
1
1
1
1
1
1
2
1
2
0
1
0
1
0
1
1
0
0
1
2
0
2
1
1
2
0
0
0
0
0
1
2
0
0
2
0
1
2
2
1
1
2
0
0
2
1
0
1
0
0
2
1
1
1
0
2
0
0
1
1
0
1
0
0
1
1
2
2
1
1
2
0
0
1
0
0
1
1
0
2
0
0
1
3
2
2
0
2
0
0
0
1
0
1
1
1
0
0
1
1
1
1
1
1
0
1
2
0
1
1
0
0
1
0
2
0
2
2
0
2
1
0
0
0
2
0
0
0
0
1
0
1
0
1
1
2
0
0
0
1
0
2
1
2
2
2
1
1
2
0
1
1
1
0
2
0
2
1
1
1
1
1
0
0
0
2
3
1
0
1
2
2
1
0
0
1
1
2
1
1
0
0
2
1
0
1
0
0
1
2
0
2
2
0
2
2
0
2
2
1
2
0
2
1
0
0
1
0
2
2
0
2
2
0
0
1
1
2
0
0
0
0
1
1
2
0
1
0
1
1
0
0
0
2
0
1
1
0
1
1
2
0
1
1
0
1
2
0
1
1
2
0
0
2
2
1
0
1
0
1
0
2
0
2
0
0
0
1
0
0
1
2
1
1
1
0
0
1
1
0
0
0
0
0
1
4
0
2
1
0
1
0
1
0
1
1
1
1
1
1
0
0
2
1
2
0
0
0
2
1
0
0
0
0
1
2
2
1
1
2
0
0
0
1
0
0
0
1
0
1
0
2
0
1
1
3
1
0
1
1
0
0
1
1
0
1
2
1
2
2
1
2
1
1
0
0
1
1
1
0
0
1
0
0
1
0
2
1
1
5
1
1
1
0
0
0
2
0
1
1
0
2
2
1
0
1
2
2
0
0
1
1
2
0
2
0
0
2
2
2
1
1
0
0
1
0
2
0
0
0
2
0
0
0
1
0
0
0
1
2
0
2
0
0
0
1
2
0
1
0
0
2
0
1
1
2
1
0
1
0
1
2
1
1
1
0
1
1
0
1
1
1
0
0
0
0
1
1
2
2
1
1
2
0
0
1
0
1
2
0
0
1
0
1
0
1
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
2
0
1
0
0
0
0
1
0
0
1
1
1
0
1
0
2
3
0
1
1
1
0
0
1
2
1
0
0
2
2
1
0
0
1
2
2
1
3
1
2
0
1
1
0
0
2
0
1
0
2
0
0
2
1
0
0
1
1
1
3
0
1
1
2
1
0
1
0
0
1
3
2
0
0
1
0
0
2
2
1
0
1
0
0
0
2
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
2
1
2
0
1
2
2
2
4
1
0
1
0
0
2
1
1
0
0
1
2
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
2
1
0
2
2
0
0
0
1
2
0
1
2
0
1
0
0
1
2
1
1
2
0
1
1
1
1
1
0
1
0
0
0
0
1
1
0
0
0
1
2
1
2
2
1
2
0
3
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
1
1
2
1
1
0
1
1
2
2
1
0
0
2
1
0
0
0
0
1
2
2
1
0
0
1
0
2
1
2
1
1
1
1
2
2
0
1
0
2
0
1
0
1
1
0
0
0
2
2
2
0
3
0
0
0
0
1
1
1
0
0
1
2
1
1
2
2
0
2
1
1
1
1
0
1
2
0
2
0
0
0
0
2
0
2
2
0
0
0
0
1
1
0
1
0
0
2
0
1
2
1
1
0
0
1
1
0
2
0
1
2
0
0
1
0
0
1
1
2
0
0
0
2
1
1
1
0
2
1
0
0
0
1
1
2
0
1
0
0
0
1
1
2
1
2
0
0
1
0
1
3
0
0
0
4
1
1
3
1
1
0
0
0
2
1
0
1
2
1
1
0
2
0
0
1
1
1
1
2
1
1
2
0
0
2
0
0
0
1
2
2
1
1
2
2
2
0
0
1
2
2
0
1
1
0
1
0
0
2
1
0
2
0
1
2
1
0
2
0
0
0
0
0
0
0
1
0
0
2
2
2
0
1
0
1
0
2
0
0
1
0
0
2
0
2
0
0
2
0
2
1
3
1
1
2
0
0
1
0
1
0
1
0
1
1
2
1
2
2
1
1
2
1
1
1
4
2
1
0
1
0
2
1
2
1
0
1
1
0
1
0
0
1
1
1
1
0
0
1
2
2
1
2
0
1
2
0
0
1
2
0
2
1
0
2
0
0
0
1
1
0
1
2
1
0
1
1
1
2
1
0
1
0
1
1
3
1
1
1
0
2
0
2
1
0
1
5
1
0
2
2
1
0
2
1
1
2
2
2
2
2
2
2
0
2
2
2
0
2
1
2
0
0
0
2
1
1
1
2
0
1
0
1
1
2
1
1
2
2
2
0
0
0
1
1
1
0
2
2
2
0
1
0
1
1
1
0
0
2
0
0
2
1
1
1
2
1
3
0
1
1
1
1
0
1
0
0
2
0
0
0
2
0
1
1
1
0
1
0
0
0
0
1
0
1
2
1
1
0
1
1
2
2
2
0
0
3
0
1
0
0
0
0
1
2
2
0
1
1
1
1
2
2
1
1
1
1
0
1
1
0
1
2
0
2
0
2
1
1
1
1
1
2
0
0
0
1
0
2
2
0
2
1
0
1
2
2
2
1
1
2
2
1
1
0
1
0
1
2
2
0
1
2
2
1
0
1
1
1
0
2
0
0
0
0
1
0
0
2
0
1
3
0
0
1
0
0
0
0
1
0
0
1
0
0
1
1
0
0
2
0
3
0
2
1
1
2
1
1
2
2
1
1
2
0
1
2
1
2
1
1
0
1
2
0
1
1
1
0
1
0
1
0
1
0
1
0
3
1
0
1
2
1
1
0
0
1
1
0
0
2
1
0
1
0
0
2
2
0
1
2
2
2
0
0
2
0
0
0
1
0
0
0
1
1
1
0
1
1
0
0
1
0
0
1
2
1
0
0
1
1
2
2
0
1
0
0
0
2
2
0
0
0
0
1
1
0
1
0
1
1
1
0
1
0
2
2
1
1
1
1
0
1
2
0
1
2
2
2
0
1
2
0
0
2
1
6
1
1
0
1
1
1
1
0
1
2
0
1
1
2
2
1
2
0
1
1
0
1
2
0
1
1
0
0
0
1
1
0
0
0
1
0
0
1
2
1
2
0
0
1
2
0
0
0
0
0
0
1
5
2
1
0
2
2
2
2
0
1
0
1
0
0
1
1
2
0
1
0
0
1
1
2
0
1
0
2
1
2
0
4
0
1
0
1
1
1
2
2
0
1
0
0
1
1
1
1
1
0
1
2
1
2
0
1
2
0
2
0
0
0
1
1
1
0
0
0
0
1
0
0
1
1
1
0
0
2
1
1
0
1
1
1
0
1
2
0
1
1
0
0
0
0
2
0
0
0
1
0
1
2
0
1
1
1
0
2
1
0
2
2
2
2
2
2
0
0
1
0
1
0
0
1
1
1
0
0
1
1
0
2
0
2
2
1
2
1
2
1
0
1
0
0
0
1
1
0
1
0
1
0
2
1
0
1
0
0
1
0
0
1
1
2
1
1
0
0
1
1
4
2
0
0
0
2
0
1
0
0
1
2
0
1
1
1
1
2
2
2
1
0
0
0
1
1
1
0
3
0
0
1
0
2
0
0
1
0
0
2
2
2
2
1
2
0
0
0
0
1
1
0
0
1
0
0
2
2
2
1
0
0
1
0
2
2
2
1
1
2
1
2
2
1
0
1
2
0
2
3
1
0
1
1
2
0
0
1
1
0
1
1
0
1
0
1
1
1
1
1
0
0
1
0
2
0
2
2
1
0
0
0
0
1
0
3
1
0
1
1
1
1
0
1
0
1
0
0
0
1
0
1
1
0
1
0
0
0
0
1
1
0
1
2
0
0
1
2
2
2
0
1
1
2
1
0
0
0
0
0
0
2
1
1
1
1
0
0
1
1
1
2
2
1
1
2
2
1
2
1
0
2
0
1
0
2
2
2
0
0
2
0
1
1
2
2
1
0
1
0
0
0
1
0
1
0
2
0
2
2
1
0
1
0
0
2
1
2
1
2
1
0
1
0
0
1
0
0
2
0
1
3
0
1
1
1
1
1
0
1
0
0
1
0
0
0
2
1
1
1
2
0
1
0
1
1
1
3
1
0
0
0
0
1
2
0
1
0
2
2
1
2
1
0
0
0
0
2
1
1
1
2
4
2
0
2
0
0
2
0
1
3
0
1
2
0
0
0
2
2
1
2
2
0
0
1
0
1
1
0
1
1
1
2
0
2
1
1
1
0
1
0
0
1
0
0
1
0
1
0
0
1
1
1
1
0
1
2
1
1
0
1
0
1
0
0
1
1
1
1
0
0
0
2
1
1
1
1
0
0
1
0
1
0
2
1
0
0
0
1
0
0
0
0
0
1
1
1
1
2
1
0
1
1
2
0
1
1
2
0
1
2
0
1
1
2
2
1
1
1
1
0
1
0
1
0
0
0
1
0
0
0
1
2
2
1
0
0
1
0
1
0
0
0
0
0
2
2
0
1
1
1
1
0
1
2
1
0
2
1
0
0
0
1
3
2
0
0
1
0
2
0
1
1
0
1
2
0
2
0
1
0
0
0
0
1
2
2
0
1
0
0
2
1
2
1
2
0
0
1
1
0
1
1
2
1
1
2
0
2
3
1
0
1
1
2
1
0
0
1
1
0
1
0
1
1
0
1
1
0
1
2
1
2
2
2
0
0
0
0
0
1
1
0
0
2
0
1
0
0
0
1
1
0
0
3
0
2
2
0
0
0
1
1
0
0
2
2
0
1
0
0
1
1
1
1
1
0
0
1
1
1
1
1
0
0
0
0
1
2
0
1
0
0
2
1
2
0
1
2
2
0
0
0
0
0
0
0
1
0
1
1
0
1
2
1
0
1
0
2
0
1
1
0
2
1
0
1
2
2
2
1
1
1
1
1
1
1
1
1
0
0
0
1
0
0
2
0
0
0
0
1
2
2
0
0
0
0
0
1
0
2
0
0
1
1
0
1
2
1
0
0
0
0
0
0
0
0
0
2
1
1
0
1
1
0
0
1
0
2
0
0
0
1
0
1
0
0
2
0
0
0
1
0
1
1
1
1
0
0
2
0
1
0
0
1
2
0
0
1
0
1
2
0
1
0
2
1
3
0
0
0
2
0
1
0
0
1
1
1
2
1
0
0
0
0
2
0
0
1
2
0
1
1
2
0
2
2
1
0
3
0
0
4
0
2
2
2
2
1
0
2
0
0
1
0
0
0
1
0
1
0
0
0
1
1
0
1
1
2
0
1
0
1
0
1
1
2
3
0
0
1
0
0
1
1
1
1
0
0
2
0
0
1
0
1
0
0
2
0
0
2
0
2
0
1
0
0
0
1
0
2
3
2
0
1
1
0
1
1
0
0
2
1
0
2
2
2
0
1
0
1
1
1
1
1
1
1
0
0
1
1
0
0
1
0
1
0
0
0
0
2
2
1
1
2
1
1
2
0
0
0
0
1
3
0
2
2
0
0
1
1
0
0
2
1
4
0
2
0
2
0
0
1
0
1
1
2
0
0
2
0
2
0
1
0
0
0
0
1
0
1
1
0
1
1
0
0
0
0
3
1
1
1
0
0
1
2
1
1
0
1
1
0
1
1
0
2
0
1
0
1
0
1
1
0
0
0
2
0
0
1
0
0
0
1
0
1
1
0
0
2
0
1
1
1
1
1
0
1
2
0
2
0
0
1
1
0
1
1
2
0
1
1
0
0
0
1
0
1
0
1
2
3
1
1
1
3
1
0
2
1
0
0
0
0
0
2
0
2
0
0
0
1
1
2
0
1
1
2
0
1
0
2
0
1
0
1
2
2
2
1
1
0
0
1
0
1
0
0
2
2
1
1
0
1
0
0
1
2
2
0
0
2
1
1
1
1
2
0
1
0
0
1
0
0
1
1
1
2
2
1
2
1
1
1
2
0
0
2
0
0
0
2
1
1
2
0
0
1
1
0
0
1
1
1
1
0
0
0
0
3
0
0
1
0
0
1
1
0
1
2
0
0
0
2
0
1
1
2
2
1
1
0
2
2
2
0
2
2
1
0
2
0
2
0
0
2
1
1
2
1
0
0
1
1
1
2
1
1
1
2
2
1
0
1
2
1
1
0
0
0
0
1
2
1
1
1
1
1
1
0
2
1
2
3
1
0
1
2
1
2
0
0
0
2
2
1
0
0
2
0
2
2
1
1
0
3
1
1
1
0
0
0
1
0
0
0
0
1
1
1
0
1
3
0
1
1
1
0
0
1
1
1
2
2
2
1
1
0
0
1
1
1
2
2
1
0
0
0
1
1
1
0
2
1
0
2
1
0
2
2
0
2
0
0
2
2
0
1
1
1
0
1
1
1
0
0
0
2
0
0
0
0
2
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
2
1
0
1
1
2
2
1
2
1
1
0
0
2
2
2
0
0
0
0
0
0
2
0
0
0
1
1
0
0
1
0
2
0
1
1
0
1
1
0
2
0
1
1
0
0
1
1
0
0
1
2
0
0
1
1
1
1
1
3
0
0
0
2
0
1
1
2
0
1
1
1
1
2
0
0
2
0
2
2
0
1
2
1
1
1
2
2
0
1
2
2
1
2
1
3
1
1
2
0
2
1
0
1
1
0
0
1
0
0
3
0
2
1
0
1
1
1
0
0
1
1
2
1
0
0
0
0
0
3
1
0
1
1
0
1
0
2
2
0
1
2
0
0
1
1
2
0
1
2
0
0
2
0
2
2
0
0
2
1
1
0
0
1
1
1
2
1
0
2
1
0
0
1
0
1
0
0
0
0
2
1
0
3
0
1
0
2
1
1
0
1
1
1
1
0
0
0
2
0
1
0
2
0
1
1
1
1
0
0
0
1
1
0
0
1
0
1
0
2
1
1
0
1
1
2
2
1
1
2
1
1
0
0
0
2
1
2
0
0
0
0
0
1
0
0
0
1
0
2
1
2
0
0
0
1
2
1
2
0
2
1
1
0
0
1
1
2
0
1
1
1
2
1
2
2
0
0
0
2
1
1
2
1
1
1
1
2
0
0
0
0
2
1
0
0
0
1
0
1
1
3
0
9
1
0
2
1
1
1
2
0
1
1
0
1
1
2
0
1
1
0
1
2
0
1
0
0
2
0
1
0
0
1
0
0
1
3
1
2
2
0
1
2
1
0
2
0
0
0
1
1
3
1
1
0
0
1
2
0
0
1
1
1
1
0
0
1
1
0
2
1
0
0
0
0
0
2
1
0
0
0
1
1
1
1
0
1
2
2
1
1
0
1
0
0
1
1
1
1
0
0
1
2
0
0
2
0
2
1
2
1
2
0
0
2
1
6
0
1
1
0
1
0
2
1
1
0
0
2
1
1
1
2
0
0
2
2
1
1
0
0
0
2
0
1
1
1
2
2
0
1
0
1
1
0
1
0
1
0
2
0
1
1
0
1
0
1
1
0
0
0
1
1
3
1
0
3
1
1
0
0
1
0
2
1
2
1
0
2
0
2
0
0
0
2
0
0
1
0
0
0
0
1
2
0
0
0
0
0
2
0
0
2
0
2
2
2
1
1
0
2
0
0
1
1
2
1
4
2
2
2
0
1
0
0
0
1
6
1
1
0
1
1
0
1
0
0
2
1
1
0
1
0
2
0
0
1
0
1
2
0
1
1
0
1
0
0
0
1
2
1
0
1
1
1
0
2
1
1
2
0
1
0
0
0
0
2
0
0
1
1
0
0
1
0
1
1
0
0
0
0
0
1
0
1
1
0
1
1
2
1
1
0
2
1
3
0
2
0
2
2
1
0
1
2
0
2
0
1
2
1
1
1
0
1
3
0
2
1
0
1
0
1
0
2
0
0
1
1
2
0
0
1
0
1
0
1
0
0
1
0
0
0
1
1
0
1
1
2
0
0
0
0
0
0
0
0
0
1
1
1
1
2
2
1
1
0
0
0
0
0
0
1
1
0
1
0
1
0
1
1
0
0
1
2
1
1
1
2
1
2
0
4
1
1
2
1
0
1
1
1
0
2
0
0
1
1
0
0
0
2
1
0
1
2
1
0
0
2
0
0
0
1
1
0
1
2
1
1
0
0
1
2
1
0
0
1
2
2
0
0
0
2
3
0
1
1
0
2
0
1
1
2
2
2
2
0
1
1
0
2
1
0
2
0
1
0
2
1
1
0
0
0
0
2
2
1
0
1
0
0
0
1
1
0
0
0
1
0
0
1
0
1
2
2
1
2
0
1
1
1
1
0
0
2
2
1
0
1
0
1
0
2
1
0
2
1
0
1
0
2
0
1
1
1
1
0
1
1
2
0
2
1
1
0
0
1
2
0
1
0
1
1
2
2
2
1
1
1
1
2
2
2
1
0
0
3
0
2
0
1
1
0
0
0
2
0
0
1
2
1
0
0
2
2
2
2
1
0
0
0
0
0
0
2
1
1
1
0
1
0
1
1
1
0
1
1
1
0
2
2
0
1
2
1
0
2
1
0
0
0
0
2
0
0
2
0
1
1
0
1
0
1
1
1
2
1
1
0
1
0
1
1
0
0
0
0
3
0
1
0
1
0
0
1
2
2
0
0
0
1
0
2
0
3
0
1
3
1
1
0
1
1
0
1
1
0
1
1
0
2
1
1
0
0
1
0
2
2
2
0
2
0
0
2
0
1
1
1
1
1
0
1
0
1
0
2
0
0
3
2
1
0
2
1
0
2
0
1
1
1
0
0
2
0
2
0
2
0
0
3
0
2
2
0
0
2
1
1
1
1
1
1
1
1
1
1
1
0
0
0
0
1
0
1
1
0
1
1
0
1
2
0
0
1
1
0
3
1
0
2
1
2
1
2
0
0
0
1
0
0
0
1
0
0
0
1
0
0
3
1
1
1
0
0
1
2
0
0
0
0
0
1
1
1
1
1
2
0
1
0
1
1
1
1
1
1
1
1
0
2
0
1
0
0
0
1
1
0
2
0
2
0
2
1
0
0
1
0
1
0
0
2
0
0
0
0
2
1
2
2
1
1
1
1
0
1
0
0
1
1
0
0
2
1
2
1
2
0
2
2
4
0
0
2
1
0
1
0
1
1
0
0
1
1
0
1
0
1
0
2
0
0
0
2
0
1
0
1
0
1
0
0
0
0
0
0
1
0
2
0
1
0
1
1
0
1
4
1
1
0
0
1
1
0
2
0
0
0
1
2
0
2
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
1
1
2
0
1
1
0
1
1
0
1
0
0
0
0
1
1
1
1
1
0
1
0
0
0
0
1
1
1
0
1
2
0
1
2
1
1
1
0
0
1
1
1
1
1
0
1
1
3
0
0
1
0
2
2
2
2
2
1
1
0
0
1
0
2
0
0
0
0
0
1
0
0
2
1
1
1
2
0
0
1
0
0
1
1
1
1
2
1
2
0
0
2
1
1
0
1
0
0
2
1
0
2
1
1
2
2
0
0
0
2
4
1
1
1
1
2
0
0
0
0
0
0
1
0
1
0
0
0
0
2
1
1
1
0
1
2
1
1
2
1
0
1
0
0
0
1
0
1
0
0
1
2
0
0
1
2
0
0
0
0
0
1
0
1
0
2
1
2
2
0
2
0
1
1
0
3
0
1
1
2
2
1
0
0
0
0
1
2
1
1
0
1
3
2
2
0
0
0
0
0
0
1
3
0
1
0
0
2
0
0
0
1
0
1
1
0
0
0
2
1
2
3
0
1
2
1
1
2
0
0
1
2
1
0
3
1
2
0
2
0
0
0
2
1
1
0
0
0
1
2
2
0
1
0
0
2
1
0
2
2
0
1
0
1
1
0
1
1
1
1
2
0
2
0
2
2
2
1
0
1
0
2
0
0
0
1
0
1
2
0
1
0
1
1
1
1
1
4
0
1
1
1
0
2
1
0
1
0
1
0
0
0
1
1
1
1
0
1
0
1
1
2
1
1
2
1
1
3
0
0
0
0
1
2
0
0
0
1
2
2
1
1
0
1
1
1
0
0
1
1
2
1
0
0
0
0
0
2
2
0
0
1
0
0
1
2
1
0
1
1
0
0
1
0
2
2
3
1
1
1
0
1
0
2
0
0
0
1
0
1
4
0
1
1
1
0
0
0
0
0
0
0
1
0
0
2
2
1
1
1
0
0
2
2
0
0
1
1
2
0
1
0
1
1
0
0
0
2
1
0
2
0
0
0
1
0
0
0
2
2
0
1
2
0
1
0
1
1
0
0
1
0
1
0
2
1
1
1
2
2
0
1
2
1
1
1
0
1
2
0
1
0
2
1
2
1
0
1
0
2
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
2
2
2
0
0
1
0
2
1
0
0
0
0
2
0
0
1
1
1
1
1
1
2
0
1
0
3
1
2
1
0
0
1
0
2
1
0
2
0
3
0
2
1
0
1
0
1
2
0
2
3
0
1
1
0
2
1
2
1
0
1
2
0
0
0
0
2
2
1
1
1
2
2
1
2
0
0
1
2
1
0
0
1
1
0
0
0
1
0
0
0
1
4
2
1
0
1
0
0
0
0
0
2
2
2
1
0
0
1
1
2
3
1
1
2
1
2
1
0
2
0
2
2
1
1
0
1
2
1
0
0
1
1
1
1
0
2
2
0
2
2
0
0
1
0
0
2
2
0
1
1
0
1
1
1
1
2
2
0
0
0
0
0
1
1
0
0
1
2
0
0
1
0
0
2
0
0
0
1
0
1
1
0
0
1
1
0
0
0
0
1
1
1
0
0
1
0
1
0
0
1
2
0
2
0
2
0
1
0
2
0
0
1
0
0
2
1
1
1
2
1
2
1
0
2
1
2
2
0
0
0
0
1
1
1
1
1
1
0
0
2
0
2
0
1
0
3
1
2
1
0
3
1
3
0
0
1
0
0
1
1
1
0
2
2
2
2
0
2
1
0
2
0
0
1
2
2
1
2
0
2
2
2
0
1
0
0
2
0
1
1
0
1
1
1
0
1
1
0
0
2
1
1
0
1
1
2
1
0
1
0
0
2
2
1
0
0
1
1
1
0
2
0
0
0
0
1
0
2
5
1
1
0
1
0
0
0
2
1
1
0
1
0
0
2
2
1
0
2
2
2
0
0
0
1
0
1
1
2
2
0
0
2
1
1
2
0
0
1
0
0
2
3
1
0
0
2
1
0
1
0
0
2
0
0
1
0
0
0
0
1
0
0
2
2
0
1
1
1
3
1
1
1
2
0
2
1
0
1
1
2
1
1
0
1
2
0
1
1
1
1
1
0
2
2
1
1
0
1
0
0
2
0
2
0
2
0
0
0
1
0
1
1
0
0
0
2
1
1
2
2
2
2
2
0
2
1
0
1
1
2
0
1
1
1
1
0
1
0
1
0
1
1
1
0
0
3
0
0
2
2
1
1
1
2
0
0
0
1
1
2
0
1
0
1
2
1
1
1
0
1
2
2
0
0
0
2
0
0
1
1
0
2
0
0
0
2
2
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
2
0
1
2
1
1
1
1
0
2
2
2
2
0
0
1
2
0
0
0
0
0
2
1
2
1
0
0
0
2
1
0
1
1
1
1
1
1
1
0
0
1
0
2
2
0
1
0
1
0
0
0
0
0
0
1
0
0
3
0
2
1
1
1
1
1
0
2
0
0
0
0
1
1
0
1
1
2
0
1
1
1
1
1
0
0
2
2
1
0
2
0
0
1
1
1
1
1
1
0
0
0
0
1
1
0
1
1
0
0
2
1
2
1
1
0
0
0
1
2
1
1
1
0
5
0
0
0
0
0
0
1
1
1
0
0
2
0
1
0
0
1
2
2
1
0
0
1
2
1
2
1
3
0
2
0
1
0
0
2
0
1
1
2
1
0
1
2
1
0
0
1
0
0
0
2
1
0
1
2
0
0
2
1
1
1
2
2
0
1
1
0
1
1
1
0
1
2
2
0
0
0
0
2
0
2
2
1
1
0
0
1
0
0
0
1
0
1
0
0
1
1
1
1
1
0
0
0
1
0
2
1
0
1
0
1
2
1
0
0
0
0
2
2
2
2
1
1
0
1
0
1
2
1
0
0
1
1
1
1
0
0
2
1
1
0
0
1
1
0
1
1
0
2
0
0
1
1
1
0
1
0
1
0
0
1
3
1
0
0
1
1
1
1
1
0
0
0
2
1
3
2
1
1
0
1
0
0
0
1
1
1
0
1
1
1
0
0
1
4
1
0
1
1
2
0
1
1
1
1
2
1
1
1
1
2
1
1
3
4
1
1
0
1
1
0
2
0
1
1
2
0
1
0
0
1
1
1
2
0
0
2
1
2
1
2
1
1
1
0
1
1
1
0
0
1
0
2
2
0
0
1
2
0
0
0
0
2
0
0
1
1
1
0
0
1
1
0
0
1
1
1
2
2
1
2
1
0
0
1
1
0
0
1
0
2
1
2
0
1
1
2
1
2
0
1
2
1
2
0
0
1
0
1
2
0
1
2
0
1
2
1
1
2
0
1
1
1
0
2
1
1
0
1
2
1
1
2
0
0
1
0
1
1
1
0
0
0
1
0
1
0
1
1
2
0
0
0
1
1
1
0
2
1
0
1
2
0
2
1
2
0
0
2
1
1
2
0
1
1
2
0
1
0
0
0
2
1
1
2
0
0
1
0
1
1
0
1
1
1
0
0
1
0
0
1
1
1
0
2
2
1
2
0
0
1
0
1
2
1
0
0
2
2
1
1
1
0
2
2
2
2
2
3
1
0
0
0
0
1
2
1
1
0
1
0
1
1
1
0
0
1
0
1
2
1
2
1
2
0
0
1
0
1
0
0
0
0
1
1
2
2
0
1
0
0
0
1
1
0
1
0
1
0
1
2
2
2
0
1
0
0
1
1
0
0
1
2
1
1
3
1
1
0
0
2
0
0
0
2
0
0
3
2
1
0
0
0
1
2
2
0
1
0
0
0
1
1
1
0
1
3
1
1
1
0
0
0
0
1
1
0
1
2
0
2
1
0
1
1
1
1
0
2
2
0
0
0
2
0
1
0
0
1
0
1
1
1
1
0
2
1
0
1
0
1
3
1
0
0
0
1
2
0
1
1
3
1
1
0
0
2
1
0
1
0
1
0
1
0
0
0
0
1
1
4
0
0
0
1
0
0
0
2
1
1
1
3
1
0
0
0
0
2
0
0
2
0
0
1
1
1
2
0
2
0
1
0
2
1
1
0
0
1
1
1
0
0
1
1
1
1
1
1
1
4
1
1
0
0
0
0
0
1
1
1
1
0
1
1
0
2
1
1
0
2
0
0
0
1
1
1
2
1
0
0
0
1
0
2
2
0
2
0
0
2
2
0
1
1
0
1
0
1
0
2
0
2
2
1
1
0
1
0
1
2
1
1
2
2
2
1
2
0
0
2
0
1
1
1
0
1
0
1
1
1
0
1
0
2
1
1
0
0
1
0
1
0
1
2
1
0
2
2
2
1
0
0
2
0
0
2
0
2
0
1
1
0
2
0
2
2
0
0
2
0
2
1
0
1
2
3
1
1
2
0
0
0
2
1
2
0
1
2
0
1
0
0
0
1
0
2
1
0
0
0
2
1
1
1
2
0
4
0
2
0
2
1
0
0
1
0
0
2
2
0
3
2
1
1
1
1
1
0
1
0
0
1
1
2
2
0
2
0
1
0
0
0
0
1
0
6
1
0
0
2
1
2
2
0
0
1
1
0
0
1
1
2
0
0
2
0
1
2
1
2
1
0
0
0
1
0
0
1
1
2
0
1
1
0
1
0
0
0
0
0
2
1
1
1
0
1
1
1
0
0
4
0
1
0
1
0
2
1
1
0
1
2
0
1
1
0
1
2
0
1
0
2
1
1
2
0
1
0
1
3
2
0
0
0
1
1
2
3
2
0
0
0
0
4
2
1
0
0
0
0
2
0
2
1
1
4
2
0
1
3
3
0
0
3
0
0
1
0
1
2
0
0
0
0
0
1
1
0
2
2
0
1
2
0
1
0
1
1
1
1
2
2
2
1
0
1
0
0
0
1
1
0
0
1
2
1
2
1
1
0
1
1
1
2
0
0
1
1
1
2
1
0
0
0
0
1
2
2
2
0
0
1
0
0
2
0
0
2
1
0
1
1
2
1
0
0
0
0
3
2
0
0
2
1
0
1
0
2
0
2
0
1
1
1
2
2
1
0
2
0
0
2
0
1
1
0
1
1
2
3
1
0
0
0
1
0
1
1
1
2
2
1
0
1
2
0
1
1
1
1
0
2
0
0
1
1
2
2
0
2
0
0
1
0
3
0
0
1
1
2
2
0
1
0
3
0
1
0
2
1
2
0
1
1
0
3
3
2
1
0
0
1
1
1
1
1
1
0
1
0
1
1
2
2
2
2
0
0
1
1
0
2
0
1
1
1
2
1
1
1
0
0
1
0
0
1
0
0
2
2
1
2
1
0
2
1
1
1
0
2
0
0
1
1
2
0
1
0
1
1
1
1
0
0
2
0
0
0
2
0
0
2
2
2
0
1
0
2
1
2
2
1
1
1
1
1
0
2
1
2
0
1
0
1
2
1
2
1
1
1
0
0
2
2
1
0
0
0
0
2
2
0
1
1
2
2
2
0
2
1
0
0
1
1
1
1
1
0
2
1
0
1
0
0
1
0
0
0
2
1
2
1
1
0
0
0
1
0
4
0
2
2
1
1
0
2
1
0
0
0
0
0
2
0
1
1
1
1
0
1
1
0
1
0
1
0
1
1
0
0
0
1
0
1
2
1
1
1
3
0
0
1
3
0
1
0
0
0
0
1
2
1
1
2
1
2
0
1
1
2
1
0
2
1
1
0
2
0
1
0
0
1
2
1
2
2
0
2
0
2
1
0
3
1
0
0
0
2
2
1
1
1
2
2
1
2
2
0
0
1
1
2
1
2
1
1
1
1
0
0
2
1
2
0
1
1
0
0
2
0
0
0
0
1
0
0
1
5
0
5
0
2
0
1
0
0
1
0
0
2
0
0
2
0
1
0
2
1
0
1
0
0
1
4
1
1
0
0
0
0
1
0
1
2
0
1
1
2
0
2
0
0
2
2
1
2
0
2
2
1
0
0
1
0
1
1
0
0
1
1
0
0
2
2
0
1
7
0
1
1
0
1
2
2
1
2
0
2
2
0
1
0
0
1
2
2
0
1
0
0
0
2
1
1
0
1
2
1
2
2
0
1
0
1
1
1
0
0
0
0
0
1
0
0
0
1
1
1
1
0
2
1
2
1
1
1
0
0
0
2
1
1
1
2
0
2
2
2
1
1
1
0
1
1
1
1
0
1
1
1
0
1
1
1
0
2
0
0
2
1
1
1
0
1
1
1
1
2
3
0
2
1
3
2
0
0
2
0
0
2
2
0
1
0
0
2
0
0
2
0
2
1
1
0
0
0
0
0
1
2
1
0
2
1
0
1
0
1
0
1
0
1
0
2
1
1
0
0
1
1
1
1
2
2
1
1
0
1
1
0
1
1
0
1
1
1
0
0
0
0
1
0
1
3
1
1
1
1
1
0
0
0
1
1
1
2
1
1
0
1
2
1
1
0
0
1
1
0
1
0
1
1
0
2
2
0
1
1
1
1
1
0
0
3
0
0
1
1
1
1
1
0
1
0
2
1
0
0
1
2
0
1
2
1
0
0
1
0
1
1
0
1
1
1
2
2
0
0
1
0
0
2
1
1
1
1
0
0
0
1
0
1
2
1
0
1
0
1
1
2
0
1
0
0
0
2
0
1
1
1
1
1
1
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
1
1
1
4
0
0
0
0
1
0
2
0
1
3
1
0
1
0
1
0
0
1
1
1
1
0
0
0
2
0
2
2
1
1
1
1
0
0
1
1
1
0
0
1
0
1
0
1
1
0
1
0
0
0
1
1
0
0
0
0
2
0
2
0
1
0
1
0
0
0
2
0
0
1
1
0
0
0
1
1
1
0
0
1
1
1
2
0
0
1
1
1
2
1
0
1
1
1
1
2
0
2
1
1
0
2
1
1
0
0
1
0
1
0
1
1
2
2
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
1
2
3
2
1
2
1
0
2
1
1
1
1
0
1
0
0
1
1
1
0
0
1
1
1
1
0
1
4
0
0
0
2
2
0
2
1
0
0
0
2
0
1
2
1
0
1
2
0
1
2
2
0
0
2
0
1
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
2
1
2
1
0
0
1
2
1
0
1
1
1
2
0
2
1
1
1
0
1
1
0
0
0
1
2
0
0
1
1
0
1
2
2
0
1
0
1
1
0
1
1
0
0
0
0
0
1
2
1
1
2
1
0
0
0
0
2
1
0
1
1
2
1
1
0
1
2
1
1
2
3
1
0
0
1
0
0
3
0
1
1
2
0
2
1
0
0
1
1
0
1
1
0
2
0
1
0
1
3
1
1
2
1
1
2
1
0
1
1
1
2
2
0
1
0
1
0
1
1
1
0
1
0
0
2
0
0
1
0
0
0
0
0
2
0
2
2
1
1
2
2
0
2
0
0
2
1
1
0
1
1
2
2
1
1
1
0
1
1
1
1
2
1
0
0
0
0
0
0
0
2
2
2
0
1
0
0
2
0
0
1
2
2
0
1
2
1
2
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
2
1
1
1
2
2
2
2
1
1
0
0
0
0
2
1
0
2
0
1
0
0
2
1
1
2
1
1
0
0
3
1
0
1
1
2
0
0
2
2
1
1
2
1
0
0
0
1
0
2
2
1
0
3
0
0
2
0
0
0
1
0
2
0
1
1
1
1
0
1
1
0
1
2
1
1
0
1
2
1
1
1
0
1
2
0
0
0
1
0
0
0
2
0
0
0
0
0
2
2
0
1
1
0
1
1
2
1
0
2
0
2
2
0
0
0
0
1
0
1
0
1
1
2
2
1
0
0
2
1
1
0
2
1
4
0
0
0
2
1
0
0
0
0
0
1
0
0
0
2
1
0
1
0
2
1
0
1
0
0
2
1
1
1
0
0
0
2
1
2
1
0
1
2
1
0
1
2
1
1
1
2
1
0
3
1
2
2
1
2
0
2
0
2
1
0
2
1
0
0
1
1
3
1
0
0
2
1
0
0
2
2
0
2
1
1
0
1
0
6
0
2
0
0
2
1
1
0
1
0
2
0
3
0
0
2
1
0
1
2
2
0
1
2
1
1
0
1
1
2
0
1
0
0
0
1
1
2
2
0
0
0
2
1
1
0
0
0
0
2
0
2
0
0
1
1
2
2
0
2
2
2
1
2
1
2
0
3
1
1
2
0
0
1
2
2
1
2
0
0
2
0
2
2
0
0
1
1
1
1
1
0
1
0
1
0
0
0
1
1
0
0
2
1
1
1
0
1
1
2
1
0
1
0
2
0
0
1
2
0
0
0
3
0
2
0
1
2
3
1
1
6
0
0
1
0
0
1
1
0
2
0
2
0
0
0
2
2
1
1
1
1
0
2
1
0
1
0
1
0
0
1
1
0
0
1
2
0
0
0
0
1
2
1
2
2
1
1
1
0
1
1
1
0
1
1
1
2
1
2
2
2
0
1
0
1
2
1
2
2
0
0
2
0
0
1
0
2
1
2
0
0
1
1
1
2
0
1
0
2
1
0
0
0
1
2
0
2
1
2
1
1
0
0
2
1
1
1
1
1
1
0
1
0
0
1
0
0
0
2
0
0
0
2
0
1
1
1
2
0
1
1
1
1
0
0
0
0
1
0
1
0
5
1
2
1
2
2
0
0
1
0
2
0
2
0
1
1
0
2
0
1
1
1
0
1
0
2
2
0
2
0
1
1
0
1
2
1
1
1
0
1
0
0
2
2
2
1
1
0
2
0
0
0
1
1
1
2
1
1
2
0
0
1
0
0
0
0
0
0
4
0
0
0
1
2
1
2
0
1
0
1
0
1
0
1
0
0
1
0
1
0
1
1
0
0
1
0
2
0
0
1
2
1
0
0
4
2
0
0
0
1
1
2
0
0
1
1
0
2
1
1
0
0
0
2
1
0
1
0
2
2
0
0
1
1
1
1
2
1
1
0
0
1
1
2
1
0
0
1
2
0
1
0
2
0
0
0
1
0
1
1
0
0
2
0
1
0
2
0
1
1
2
0
2
0
1
1
1
1
1
1
1
1
2
0
0
1
1
1
1
1
2
1
1
0
0
0
1
1
2
1
2
0
2
0
2
0
0
2
0
0
1
1
1
1
0
2
0
0
0
0
1
1
0
0
0
1
0
0
0
0
2
2
1
0
0
1
2
1
1
0
0
2
0
0
2
3
0
1
3
1
0
3
3
0
2
0
0
2
1
0
0
0
2
0
0
2
1
1
2
2
0
1
0
2
2
0
0
2
1
0
0
1
2
0
1
1
0
0
2
1
1
0
1
1
2
2
0
1
1
2
2
0
1
0
1
1
0
0
0
0
0
1
1
1
1
1
0
3
1
1
1
1
0
0
0
0
0
2
3
0
1
2
2
2
1
2
0
0
2
0
1
2
0
2
1
1
1
0
0
0
2
0
0
0
1
0
0
0
0
2
1
0
1
1
0
2
0
0
0
0
2
1
2
0
2
1
1
2
0
0
3
0
0
1
0
2
0
1
0
1
0
0
1
0
1
2
2
0
2
1
0
0
0
0
1
0
1
1
0
2
1
0
2
2
1
0
0
0
0
2
0
2
0
1
0
0
2
1
1
0
2
0
0
0
0
1
3
0
1
1
1
0
1
0
2
1
0
1
1
1
1
1
0
1
0
0
2
0
2
0
2
2
1
0
1
1
0
1
2
0
1
1
0
1
0
0
2
0
0
3
2
0
0
1
2
0
1
1
2
0
0
2
1
1
2
0
2
0
1
0
0
2
2
0
0
1
0
0
1
0
2
0
1
1
0
1
1
0
0
0
0
0
1
2
2
0
1
0
1
2
0
1
1
2
1
0
2
2
0
0
0
2
1
0
1
0
1
0
1
1
1
0
2
0
2
2
0
0
0
1
1
2
0
1
2
0
2
1
2
0
0
2
1
0
0
1
1
3
2
0
0
2
0
0
0
0
0
1
0
1
1
1
0
0
1
1
1
0
1
0
1
0
0
1
1
2
0
0
2
0
1
2
2
2
0
0
2
1
0
0
2
2
0
0
0
0
1
2
0
0
0
0
2
0
0
0
2
1
1
0
0
0
1
1
1
1
0
0
1
0
1
1
0
0
0
1
2
2
0
1
1
0
0
2
0
3
0
0
1
2
3
2
2
0
1
0
1
0
0
2
3
0
0
1
0
0
2
1
2
2
1
1
2
0
0
0
0
2
0
1
0
2
1
0
0
0
1
0
2
0
0
1
1
1
0
0
1
2
1
0
1
2
5
0
0
0
0
0
1
1
1
0
1
1
1
1
0
0
1
0
4
1
0
2
0
2
1
2
2
0
0
1
2
0
2
0
3
0
2
0
2
0
0
0
1
3
1
1
1
0
2
1
0
1
2
0
1
2
1
2
1
2
1
2
0
0
2
2
0
0
2
1
2
2
2
0
1
0
0
2
1
0
0
0
1
0
1
2
2
2
1
1
1
0
4
0
0
0
0
1
0
0
2
1
0
1
0
1
1
1
1
0
0
2
1
1
2
1
1
2
0
0
2
3
2
1
0
2
0
0
2
1
0
1
0
1
0
1
0
0
0
0
0
0
0
1
2
1
0
0
1
2
0
1
0
2
0
1
1
0
1
0
1
0
0
2
1
1
1
2
1
1
1
0
1
0
0
0
1
1
0
1
0
2
2
1
1
2
1
0
0
0
2
0
0
0
2
1
1
0
1
1
1
1
1
0
0
1
1
3
0
0
1
1
1
0
2
0
1
0
2
1
0
1
2
1
1
1
1
2
0
0
0
1
0
0
2
1
3
0
0
2
1
0
2
1
0
1
0
0
0
1
1
0
1
1
0
0
1
3
1
1
0
2
1
1
1
0
1
2
1
1
1
1
2
1
2
1
0
0
0
0
0
0
1
0
2
0
0
2
1
0
1
0
1
1
0
2
0
1
2
0
0
0
0
2
0
1
3
1
0
2
0
1
0
0
2
1
2
2
2
0
1
0
0
1
2
1
2
1
1
0
0
1
0
2
1
0
1
2
0
1
0
2
2
0
0
1
1
1
2
0
0
1
0
0
1
2
0
1
2
1
1
0
1
2
1
1
0
0
1
0
0
1
1
0
2
2
0
0
2
1
2
1
2
0
0
0
4
1
1
1
1
0
2
0
1
2
0
0
0
2
0
0
1
0
1
0
0
0
2
1
1
0
1
0
0
0
0
0
0
0
1
1
0
0
1
1
1
1
0
2
1
0
0
2
0
0
1
1
2
2
2
1
0
0
0
1
0
1
2
2
1
0
2
2
0
1
0
1
0
2
0
0
1
2
2
1
1
1
2
0
2
2
1
2
0
1
2
2
1
0
0
4
2
0
0
1
1
0
0
1
2
2
0
1
0
1
0
2
2
1
1
1
1
1
1
2
1
2
2
0
0
0
0
1
2
2
1
1
0
0
0
0
1
0
1
0
2
0
0
1
2
2
0
0
1
0
0
2
1
2
0
0
2
0
0
2
0
2
0
2
1
1
1
2
1
0
0
0
2
2
1
0
2
1
2
0
0
0
0
0
0
0
0
1
0
2
1
2
1
2
0
2
0
1
1
0
0
1
0
0
0
1
1
0
1
0
0
1
1
3
0
0
0
1
0
0
1
1
1
4
2
0
1
2
2
2
3
2
1
0
0
2
1
0
1
1
1
0
0
4
0
2
0
0
1
0
0
2
1
1
2
0
1
0
0
1
2
0
2
1
0
0
2
1
0
2
2
1
1
1
1
1
2
2
0
0
0
0
0
0
1
0
1
1
2
2
0
0
1
1
2
0
1
2
1
0
1
2
1
1
1
0
2
0
2
1
1
0
0
1
0
2
0
0
2
2
2
2
0
1
0
0
2
0
0
2
1
1
1
0
1
0
0
0
1
2
2
1
1
0
2
0
1
0
0
0
0
4
2
1
0
2
0
1
1
2
0
2
0
0
2
0
0
1
1
1
2
0
2
2
0
0
2
0
0
0
1
1
0
0
2
2
0
2
1
2
0
0
0
1
0
0
0
0
0
2
2
1
0
1
0
1
0
3
1
2
1
1
0
0
0
0
0
0
1
1
2
0
1
1
3
1
0
0
0
1
0
0
1
3
0
0
1
1
0
2
0
1
2
1
1
0
1
0
2
0
1
0
2
1
0
1
0
1
1
1
0
1
1
1
1
2
0
1
2
0
1
0
0
0
1
2
1
0
0
0
0
1
1
2
2
1
0
0
2
2
2
1
0
5
0
0
1
0
0
0
2
2
0
0
1
0
2
0
2
3
0
1
1
0
2
1
2
0
1
3
0
0
1
1
1
1
0
0
1
0
2
2
0
0
0
0
1
1
0
1
1
1
0
0
1
2
0
0
1
1
0
1
0
2
0
0
1
0
0
1
2
2
1
2
1
0
1
0
0
1
0
1
2
0
3
0
2
0
1
2
1
1
1
2
0
0
1
1
1
0
0
1
2
1
0
2
1
0
0
1
0
1
1
1
0
0
0
0
1
2
0
0
1
1
2
1
2
1
0
2
0
1
0
2
0
0
0
1
0
2
1
0
0
0
1
2
1
1
0
1
0
1
0
0
0
2
0
0
0
1
1
1
0
1
1
0
1
0
0
2
1
0
1
1
0
1
0
2
1
0
0
0
1
1
1
0
0
0
1
0
1
1
1
0
0
2
1
0
0
0
0
1
0
1
2
0
2
0
0
0
0
0
1
2
2
1
1
1
2
2
0
0
1
1
1
1
1
0
0
1
0
1
0
0
2
0
1
0
1
0
2
0
1
2
1
2
0
0
1
0
0
1
1
2
1
0
0
1
0
3
2
0
0
0
0
2
0
1
2
2
1
0
1
1
0
0
0
2
1
0
1
0
1
0
0
1
0
2
1
0
2
0
0
1
0
1
1
1
1
0
0
1
0
0
2
2
2
2
0
0
0
1
2
1
0
0
1
2
1
1
1
0
1
1
0
0
2
0
0
0
0
0
1
1
1
0
2
0
1
0
1
1
2
2
0
0
2
0
1
0
0
3
1
2
1
1
2
1
2
1
2
0
1
3
2
2
0
1
0
0
1
1
0
0
1
2
0
2
1
1
1
0
2
0
0
0
1
1
0
2
1
0
2
0
0
2
0
2
2
0
2
1
2
2
1
1
1
0
1
1
0
0
0
2
2
0
1
2
0
1
1
0
0
1
1
0
0
0
0
2
1
2
0
0
2
2
2
2
2
0
1
2
0
2
0
1
3
1
2
2
1
1
2
1
2
1
0
0
0
1
1
2
0
2
1
2
1
0
0
2
0
0
0
2
0
2
0
1
0
1
0
0
1
0
2
0
2
2
1
1
0
0
2
1
1
1
2
1
0
1
0
0
0
0
2
1
1
1
0
1
1
1
2
0
1
0
1
2
2
1
2
0
0
1
2
0
1
0
0
0
1
1
1
2
1
0
0
6
0
0
1
1
2
0
0
0
2
0
1
7
1
2
2
1
1
0
2
2
2
0
1
2
1
1
1
1
2
1
2
2
1
2
1
0
1
0
0
2
0
2
1
1
1
2
0
1
0
0
1
1
0
0
1
1
2
1
1
2
1
1
0
0
1
0
2
1
0
0
2
1
1
0
0
2
0
0
2
0
0
1
2
0
1
0
0
1
0
1
1
2
0
1
1
0
2
0
2
1
0
3
1
0
1
0
3
0
1
1
0
2
2
2
0
0
1
0
1
0
0
1
0
0
2
2
0
1
2
2
1
0
2
0
1
1
1
1
0
3
1
1
0
1
2
0
0
1
0
1
2
0
0
1
1
0
2
1
0
0
2
2
1
3
2
0
0
1
2
1
1
1
1
1
2
1
0
0
1
0
2
1
0
0
0
0
0
0
0
0
2
2
1
0
1
1
1
0
2
1
0
0
2
1
0
1
0
0
0
2
1
0
0
1
0
1
0
0
1
0
1
0
1
2
0
1
0
0
1
1
0
1
0
1
1
0
0
1
1
2
0
0
0
0
2
1
1
1
0
1
1
3
0
1
2
0
0
1
0
2
0
2
0
0
0
0
0
2
2
0
1
0
0
2
2
0
1
0
0
1
0
1
2
0
0
0
0
1
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
1
2
1
0
3
0
0
0
0
0
1
2
1
0
0
1
1
2
1
1
2
2
0
0
1
2
0
0
0
2
1
2
0
0
2
0
0
1
1
1
2
0
0
2
1
0
0
1
1
2
2
1
1
1
1
0
1
1
2
0
0
1
2
1
0
1
1
1
0
1
1
0
2
2
2
1
1
1
3
1
1
0
0
1
1
0
0
1
2
0
1
1
0
1
2
1
1
2
1
0
2
1
4
0
0
0
0
2
0
0
1
0
0
2
1
0
2
2
1
0
1
0
1
2
1
1
0
1
0
0
2
0
1
0
1
2
1
1
2
2
0
1
2
0
1
1
1
0
0
0
0
0
2
3
1
2
0
0
0
0
1
0
0
1
2
3
2
0
1
1
1
0
0
0
0
0
1
1
0
1
2
0
2
0
2
1
3
1
0
0
2
0
1
0
1
2
0
0
1
1
1
0
0
2
0
0
2
0
2
1
0
1
2
2
1
1
1
1
1
2
1
0
0
1
0
0
0
2
1
0
1
2
2
1
1
1
0
0
0
2
1
2
3
1
0
1
2
0
0
0
0
2
0
0
1
3
0
0
2
1
1
2
1
2
0
1
1
2
1
1
1
0
1
0
0
0
2
1
0
1
1
0
1
1
3
2
0
0
1
0
1
1
1
0
1
1
0
0
1
2
2
1
1
0
0
0
2
2
2
0
2
0
1
2
1
2
2
0
0
1
1
2
2
0
1
0
2
0
1
2
0
3
2
1
1
0
3
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
2
0
0
0
1
0
0
1
1
0
0
2
1
1
0
2
0
0
2
1
0
0
0
1
2
0
1
0
0
1
2
2
2
1
0
0
0
0
2
0
0
2
0
1
2
1
1
0
1
2
0
0
2
0
1
0
0
0
0
1
1
2
0
3
1
1
1
0
0
1
0
0
0
1
1
0
1
0
0
2
1
1
2
1
0
0
1
0
0
0
1
0
0
0
0
0
1
2
0
2
1
1
1
0
0
1
0
3
0
1
0
1
0
0
0
1
2
0
0
1
2
0
1
1
0
2
1
2
2
2
1
0
1
0
0
2
0
0
2
0
2
2
1
0
1
2
2
2
0
1
0
0
0
0
1
0
0
1
0
2
1
0
0
1
2
0
0
0
2
1
0
3
1
1
1
3
1
1
0
0
1
0
1
2
0
0
1
0
0
2
2
2
0
0
1
2
1
0
1
2
1
1
2
2
0
1
0
2
1
1
2
0
2
1
0
2
0
0
2
2
1
1
1
1
3
0
1
3
3
0
1
0
0
1
0
0
0
1
1
1
0
1
1
2
0
1
0
0
3
2
1
1
1
2
2
1
1
1
6
1
1
1
0
1
1
2
0
1
0
2
0
0
0
2
1
1
0
4
1
1
0
2
1
1
0
1
0
0
0
0
2
1
2
1
1
0
0
2
2
1
1
2
0
0
1
0
1
0
1
0
1
1
1
0
1
0
0
0
1
2
0
0
2
1
1
0
1
1
0
2
0
1
2
0
1
2
2
1
0
0
0
2
1
1
0
2
2
0
1
2
2
0
0
2
1
2
0
2
0
1
0
1
0
0
0
3
0
0
1
0
0
1
0
0
2
0
0
2
1
1
0
2
1
1
1
2
0
0
0
1
1
0
1
0
0
1
1
0
1
2
1
0
0
1
1
1
0
1
0
2
1
2
2
1
0
0
0
1
1
2
2
1
0
1
0
1
1
1
1
1
1
1
0
1
0
1
1
1
0
0
2
2
1
1
0
0
0
1
1
2
0
2
1
1
0
1
0
0
0
2
0
0
1
0
1
1
3
0
1
0
0
0
0
1
0
1
1
2
0
0
2
0
0
0
1
2
1
2
0
1
0
0
2
1
1
8
1
0
0
0
0
1
0
2
1
2
0
1
2
2
1
0
0
0
1
0
0
2
0
0
0
2
1
0
0
0
0
2
0
1
2
2
0
0
1
0
2
0
2
2
0
1
1
2
1
2
0
1
2
2
2
0
0
2
2
1
2
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
3
1
2
0
0
0
0
0
0
1
0
2
1
0
0
0
0
1
1
2
1
0
0
0
0
1
2
2
0
0
1
0
0
2
0
0
0
1
2
1
0
0
1
1
0
0
1
0
4
1
1
0
2
1
1
1
2
2
1
1
1
2
0
0
2
1
3
1
0
0
1
2
1
0
2
0
0
0
0
0
0
2
1
0
0
2
1
2
0
0
2
2
1
0
0
0
0
2
0
1
1
0
1
0
0
1
2
0
1
1
1
2
1
0
1
0
0
1
1
2
1
1
1
0
0
0
1
0
1
2
0
1
2
1
0
0
1
1
2
2
0
1
1
1
2
0
2
1
1
0
2
1
1
1
0
1
0
1
0
0
0
2
0
1
0
1
0
2
0
1
0
1
0
0
0
0
0
1
0
2
0
0
1
0
0
1
0
0
0
0
0
2
2
1
1
0
2
2
0
1
0
1
0
0
0
0
1
1
1
0
1
0
0
1
0
1
2
1
2
0
1
1
1
1
1
1
1
2
1
1
0
0
0
0
1
0
2
0
0
3
0
3
0
2
2
1
0
0
1
0
0
2
0
2
0
1
2
2
2
2
1
0
0
0
0
1
2
1
1
0
1
0
0
1
1
0
2
1
1
2
0
0
2
1
0
2
0
2
7
2
1
1
0
1
2
0
0
0
0
0
0
2
0
1
2
1
0
0
2
1
0
2
1
2
1
2
0
0
0
0
0
0
0
0
1
2
0
0
2
2
0
2
1
4
1
0
2
0
1
1
2
1
1
1
2
0
2
0
0
1
1
0
0
2
1
1
1
0
1
1
0
0
0
1
1
2
0
0
1
1
0
1
5
0
2
1
1
1
0
1
0
1
1
1
2
0
1
1
0
0
0
0
0
0
0
2
0
1
1
2
2
1
1
1
0
1
1
0
0
1
0
2
1
0
0
1
2
0
1
1
0
1
0
1
1
0
1
1
2
2
2
1
2
1
1
1
0
0
1
0
1
2
0
1
2
0
0
0
2
1
0
0
1
0
0
0
1
0
1
1
0
2
0
2
1
2
2
2
0
1
0
1
0
1
1
1
0
1
1
0
0
1
2
1
1
1
4
1
0
0
1
0
0
1
0
0
1
1
0
2
2
1
0
2
1
0
0
1
0
0
3
2
2
2
0
0
0
0
0
1
2
1
2
1
1
1
0
0
0
1
2
2
0
1
0
2
2
2
0
0
0
1
2
1
1
1
1
1
2
0
2
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
1
2
0
0
0
1
1
0
1
1
2
1
1
0
1
0
0
0
2
0
1
3
0
0
1
0
1
0
0
2
0
0
0
0
1
1
2
0
1
3
1
1
0
0
1
1
2
0
1
0
2
2
1
0
0
1
0
3
2
2
1
0
0
0
0
2
1
1
2
1
1
3
0
1
0
1
1
1
1
2
1
0
1
3
1
2
0
2
0
1
3
2
0
0
1
1
0
0
1
0
0
0
1
1
1
0
1
1
1
0
0
1
0
1
1
0
0
2
1
2
0
0
0
1
2
0
0
1
2
3
1
2
2
1
0
1
1
1
0
0
1
1
2
1
1
1
1
1
0
2
2
1
1
2
1
1
1
0
0
1
0
0
1
0
0
1
1
2
0
1
0
1
3
1
1
1
0
0
0
1
0
0
1
0
1
1
0
1
1
2
0
1
0
1
2
2
1
0
1
0
2
0
0
0
0
1
1
0
2
2
2
0
1
2
1
1
1
1
2
0
2
2
1
0
1
1
3
0
0
1
0
1
1
0
0
2
1
0
0
1
1
1
0
1
1
0
0
2
0
1
0
2
0
2
1
0
0
2
0
2
1
1
0
2
2
2
1
1
1
0
1
2
0
2
0
1
0
1
0
1
1
1
1
2
1
1
1
1
1
2
1
1
2
0
1
0
1
0
1
0
1
0
1
1
0
0
0
2
2
0
1
2
1
0
1
0
0
2
1
1
0
0
2
1
0
1
1
0
1
1
2
0
0
2
2
0
1
0
2
2
0
0
0
0
0
0
3
1
1
2
2
0
1
0
2
2
0
0
2
1
1
0
1
1
1
0
2
1
1
0
2
1
0
0
1
0
0
1
3
1
0
1
0
1
0
2
1
0
0
1
1
0
0
0
0
2
0
2
0
1
0
2
1
2
1
1
1
2
1
1
0
2
1
1
1
1
0
0
0
2
1
2
1
0
2
0
2
0
0
0
0
2
0
1
0
0
1
0
1
0
2
2
0
1
2
0
2
1
0
2
3
1
1
1
2
1
0
1
0
0
0
0
2
1
0
1
2
1
0
0
0
2
0
0
0
1
2
1
1
2
1
0
2
1
0
1
0
1
1
3
0
0
1
3
1
0
2
0
1
1
1
1
1
0
0
1
0
0
1
0
1
1
0
0
0
0
1
2
1
1
2
2
1
1
1
2
1
0
1
0
2
1
0
0
1
2
2
0
0
2
2
0
0
1
1
2
3
1
2
1
0
0
1
0
1
1
0
1
0
0
0
0
0
0
1
1
1
1
1
1
1
2
1
2
0
1
1
1
2
0
0
0
1
0
2
2
6
0
2
1
1
0
0
2
0
0
2
0
0
1
0
2
2
2
0
0
2
1
2
2
0
1
2
0
0
0
1
2
0
2
1
1
1
2
2
1
0
1
0
0
1
1
0
0
1
1
1
1
0
1
1
0
1
1
0
1
0
0
1
1
1
0
1
0
0
1
1
1
1
0
0
1
1
2
1
1
0
1
0
1
2
2
0
0
1
0
1
1
0
0
1
0
0
0
2
0
2
2
0
2
1
0
2
1
2
2
1
2
1
3
1
0
0
0
1
1
1
2
2
2
2
0
1
1
1
0
0
0
1
1
2
2
4
0
1
2
0
2
0
2
0
1
1
1
0
0
0
3
2
1
2
2
2
1
0
1
0
2
3
2
1
0
0
0
0
1
1
1
2
1
0
0
1
0
0
0
0
0
0
1
2
1
0
1
1
2
2
0
2
1
1
2
2
0
0
1
0
0
2
1
0
2
0
0
2
0
2
0
0
1
1
0
0
1
0
0
1
0
1
1
0
4
0
1
0
0
0
2
1
0
1
2
1
1
0
0
2
1
1
1
1
1
0
0
1
1
1
1
1
1
0
2
1
1
0
1
0
1
1
2
0
0
0
0
1
1
1
1
0
0
3
0
0
0
4
1
0
2
0
1
0
2
2
1
1
0
0
2
0
0
0
0
2
1
2
1
1
2
0
0
2
1
1
1
0
1
1
1
3
0
0
1
0
1
0
1
0
1
0
2
1
0
0
0
0
1
0
1
0
0
1
0
1
1
0
2
0
0
0
2
1
1
0
1
2
0
1
1
2
1
0
1
0
0
0
1
1
0
0
0
3
2
0
2
1
0
0
1
0
2
1
0
1
1
0
2
1
1
2
1
2
1
1
0
1
0
0
3
0
0
2
1
0
0
0
0
0
1
0
2
0
0
1
1
0
0
0
0
2
0
1
2
1
2
0
1
1
0
2
2
2
2
2
0
0
2
0
2
0
2
0
2
0
2
0
2
0
1
0
1
0
2
0
0
1
0
0
2
2
0
0
0
2
1
0
2
1
0
0
1
0
0
1
2
0
0
1
0
1
0
0
3
0
0
2
0
0
1
2
1
2
1
1
0
2
1
2
2
1
0
0
2
3
0
1
1
2
2
0
0
0
1
0
1
0
2
0
2
1
0
2
1
0
0
2
0
0
1
0
0
0
0
1
0
2
4
0
0
0
1
1
1
0
1
2
1
2
0
1
0
2
0
0
1
2
1
2
0
1
1
0
1
1
1
1
0
0
1
2
1
2
1
0
0
2
0
2
1
2
1
0
1
0
0
1
2
0
0
2
1
0
0
1
1
1
2
1
1
1
1
0
0
1
1
0
0
1
2
0
1
0
0
0
2
1
2
0
1
1
0
2
0
2
1
1
1
0
1
1
0
1
1
1
1
0
0
0
0
0
0
2
2
0
0
1
0
1
0
2
1
2
2
0
0
0
0
0
2
2
0
1
1
1
1
1
1
1
1
2
0
0
0
0
2
0
1
0
0
1
0
2
2
5
1
0
0
1
1
2
2
2
1
0
0
0
0
0
3
4
0
0
1
0
2
2
2
0
1
0
1
1
1
1
0
1
1
2
2
0
1
1
1
0
2
0
2
2
0
0
0
0
1
0
1
1
2
2
0
0
2
2
1
2
1
1
0
0
0
1
1
0
0
0
0
1
1
1
1
0
1
0
0
0
2
0
1
1
6
0
1
1
0
2
1
0
0
1
1
2
0
1
2
1
2
1
0
2
1
1
2
1
2
0
1
1
1
2
0
0
1
1
1
0
0
1
0
2
0
0
1
0
0
2
0
1
0
1
0
2
0
1
0
2
1
0
0
0
1
2
1
0
0
2
1
2
1
2
1
0
2
2
0
0
1
0
0
0
1
1
0
1
1
0
0
1
1
1
0
1
0
1
0
1
2
2
2
1
0
2
0
0
0
2
0
2
1
2
0
2
1
0
0
0
0
2
2
1
1
2
0
2
1
0
1
1
2
0
0
0
2
0
3
0
0
1
1
1
1
2
0
2
4
1
0
0
0
0
1
1
1
1
1
1
2
1
0
0
1
0
2
0
0
0
1
1
1
1
1
1
0
2
1
2
1
0
1
1
0
2
3
0
1
0
2
0
1
1
0
1
0
0
2
0
1
0
1
0
0
0
2
3
1
0
0
1
0
2
0
0
1
1
1
0
0
1
0
0
2
1
1
1
0
1
1
0
1
0
1
2
0
0
1
0
1
0
0
0
1
0
1
1
0
2
0
2
0
1
2
1
0
1
2
0
1
1
0
1
1
0
0
1
0
0
1
1
1
0
2
1
2
0
1
1
0
2
2
0
0
1
1
0
1
1
1
1
0
0
2
0
0
0
1
1
0
2
0
1
0
2
2
1
0
0
0
1
1
2
0
0
1
1
0
2
2
0
0
2
0
1
0
1
0
0
4
0
2
0
2
0
1
0
2
0
0
2
0
2
0
1
1
0
0
2
2
2
0
2
0
1
0
0
0
0
0
3
1
0
2
1
1
1
0
0
1
1
1
0
2
0
0
0
1
2
3
2
2
0
1
0
1
1
2
0
0
2
4
0
0
0
1
2
0
0
0
0
2
0
1
0
0
1
0
0
0
0
1
2
0
1
0
1
1
0
0
1
0
2
2
1
1
1
1
3
0
0
2
0
0
1
2
2
1
0
0
1
1
0
0
1
0
0
2
0
1
0
1
2
0
0
1
2
1
1
2
0
0
0
2
2
2
2
0
2
1
1
2
1
0
1
2
1
0
0
0
0
0
2
1
0
1
1
0
0
5
0
2
2
0
1
2
1
1
1
0
0
2
2
1
2
0
1
2
2
0
2
2
0
2
1
0
0
0
2
1
1
1
0
0
1
0
4
2
0
0
2
0
1
1
0
0
0
2
1
1
0
1
2
1
1
1
1
0
2
0
2
1
1
0
0
0
0
1
2
0
0
0
0
1
1
0
1
1
1
3
0
0
2
0
0
1
2
2
0
1
1
0
0
1
1
2
1
0
2
0
0
0
1
0
2
1
2
0
0
0
2
2
1
0
0
0
2
1
0
1
0
0
2
1
2
0
0
2
0
0
1
1
1
1
2
0
2
0
1
0
1
0
0
0
1
1
0
2
1
2
1
1
1
0
1
0
1
0
1
1
1
1
0
1
1
2
1
0
0
2
0
0
0
2
1
1
1
0
0
1
1
0
1
1
2
0
1
0
2
0
1
0
0
1
2
1
1
3
1
1
2
0
1
1
1
0
2
1
1
0
1
2
1
0
1
0
0
0
1
1
0
1
1
0
0
0
0
2
0
0
1
0
0
0
1
1
0
0
1
0
1
2
0
0
1
0
2
0
0
2
1
1
1
0
2
1
0
0
1
2
0
2
0
0
1
0
0
2
1
1
1
0
1
0
0
0
2
0
0
2
0
0
0
2
0
0
0
1
1
0
1
0
2
2
1
1
2
0
0
0
0
1
0
1
0
0
1
1
0
1
0
0
0
2
6
2
1
0
1
2
0
1
0
0
1
1
0
0
1
1
0
1
2
0
0
0
1
2
2
0
1
0
0
0
0
0
0
2
1
1
0
1
1
0
2
2
0
0
2
0
1
1
0
1
0
1
0
1
0
1
1
2
1
1
1
0
2
0
1
1
0
2
1
0
1
0
0
1
1
1
1
0
0
0
0
2
1
2
2
0
2
0
0
0
0
2
1
0
2
1
3
0
1
2
1
1
0
0
0
2
1
2
2
0
1
1
0
0
1
0
1
1
0
0
1
1
0
0
0
2
2
1
1
1
1
1
0
0
1
0
0
1
0
1
1
0
1
1
1
1
0
2
2
0
1
1
0
1
1
0
2
0
1
2
1
1
1
1
0
0
2
1
1
1
1
0
0
1
0
1
1
0
0
1
1
1
1
0
2
0
1
1
1
2
2
0
1
2
0
0
0
0
1
0
1
0
1
1
2
0
1
0
0
1
0
2
0
1
1
1
2
0
2
0
0
2
0
0
0
0
4
1
2
2
1
0
1
0
1
1
1
0
2
2
2
1
1
2
1
0
1
1
0
1
0
0
2
1
0
1
1
2
0
1
1
1
1
2
1
2
0
0
2
2
1
0
0
2
1
4
0
2
2
1
1
0
1
0
1
2
0
0
1
2
2
0
0
0
1
0
0
1
3
0
2
0
2
0
2
2
2
1
0
1
1
1
2
1
2
2
2
0
1
2
1
1
1
1
2
0
1
1
1
0
1
1
1
1
2
2
1
0
1
0
0
1
1
0
1
1
0
1
2
0
1
2
0
1
0
1
1
2
0
0
1
0
0
0
0
0
1
1
2
1
1
1
3
2
1
0
0
1
2
2
0
0
0
0
0
0
0
0
0
1
2
1
2
1
0
1
1
1
1
1
0
1
1
2
2
1
2
0
2
2
1
0
0
2
2
2
1
0
0
0
0
0
1
0
0
1
2
0
1
0
1
0
0
0
1
5
0
1
1
0
1
0
2
2
0
2
0
1
1
2
0
2
0
1
0
1
0
1
0
0
0
0
2
1
1
2
2
2
0
0
1
0
1
2
1
1
2
0
3
1
0
0
2
0
2
0
2
1
1
1
1
0
1
2
0
2
1
2
0
2
2
1
1
2
0
0
0
2
0
2
0
1
0
0
2
1
0
2
2
0
0
1
0
1
0
1
1
2
0
0
2
1
0
2
1
2
0
3
1
1
2
1
0
2
0
2
0
1
1
1
1
2
0
2
1
1
1
0
1
2
0
0
1
2
0
0
1
1
1
0
2
2
0
1
2
0
0
1
1
0
1
0
0
2
1
0
1
0
1
0
1
1
0
1
0
0
0
2
0
1
0
0
1
1
2
2
2
1
0
0
0
0
1
0
0
1
1
0
1
1
0
0
1
1
2
1
2
0
0
1
2
1
1
1
2
1
1
0
2
1
2
2
1
0
0
2
2
1
0
2
0
0
0
1
0
1
2
3
1
0
2
1
1
0
1
0
0
0
2
1
0
0
0
1
0
1
0
0
2
0
1
1
0
2
2
1
0
2
2
0
1
2
2
1
2
1
0
1
0
0
1
1
1
1
0
0
0
0
1
1
0
1
1
2
2
1
0
1
1
0
1
1
1
1
1
1
1
2
1
1
2
0
1
0
0
0
3
1
1
1
2
1
0
1
1
1
0
0
0
1
2
0
0
0
1
0
1
0
0
0
0
1
2
1
0
0
0
0
1
2
1
0
0
2
1
1
0
1
2
2
1
1
1
2
1
0
1
0
4
1
1
2
1
1
0
1
0
3
1
0
0
1
0
0
1
1
3
0
1
1
0
0
0
1
2
0
0
0
0
0
2
2
2
1
0
1
2
0
0
1
0
0
1
0
1
2
0
2
2
1
0
0
0
1
0
0
0
1
0
1
2
2
1
0
0
2
2
0
1
0
0
1
2
1
1
2
0
1
0
1
1
0
1
0
1
0
5
2
2
0
0
0
0
0
0
0
2
1
0
1
1
1
0
1
0
1
1
0
0
2
1
0
2
1
1
1
0
0
2
2
0
1
0
1
0
2
0
0
2
0
1
0
2
0
1
2
2
1
0
1
3
0
0
2
0
2
2
2
1
1
0
0
0
1
2
0
2
0
0
0
1
1
2
2
2
0
1
1
0
1
1
3
2
0
2
2
0
0
1
0
1
2
0
2
1
0
32
0
1
1
1
1
0
1
0
0
2
0
1
1
2
1
1
0
0
1
0
1
0
1
2
2
1
0
2
1
3
1
1
1
1
2
0
1
1
2
1
0
2
0
0
0
0
0
2
1
0
1
0
0
1
0
1
0
2
0
1
0
1
1
0
2
0
1
1
0
1
1
1
1
0
0
0
2
0
1
1
0
2
1
1
1
1
0
0
1
1
2
1
0
1
0
0
0
1
1
4
1
0
2
1
0
0
2
1
0
2
1
0
2
0
0
1
0
0
1
3
1
1
0
0
1
1
0
1
0
0
2
2
0
1
0
1
1
2
1
1
1
0
2
0
0
2
0
0
0
1
0
1
0
1
1
2
1
1
0
1
3
0
0
1
1
2
1
2
2
0
0
1
0
2
0
0
0
1
0
0
1
1
1
0
1
0
0
1
0
2
0
0
0
0
2
0
1
2
2
2
1
1
2
0
1
0
0
1
1
1
0
0
1
0
2
0
2
0
1
1
0
1
1
0
1
1
1
0
1
2
2
0
1
0
2
1
1
1
1
1
1
0
2
1
0
1
1
1
1
1
2
0
1
0
1
1
1
1
1
2
1
0
1
0
1
0
0
0
1
1
0
0
0
1
1
2
1
2
0
2
0
0
2
0
2
0
1
0
0
1
1
1
9
2
2
1
0
1
0
1
2
1
0
1
2
2
0
1
0
5
1
1
2
0
1
0
1
2
1
0
1
0
0
1
1
1
2
0
2
0
1
0
2
0
1
2
1
2
0
0
0
0
0
2
2
0
0
2
1
1
0
1
0
2
1
2
2
1
2
0
1
0
1
1
1
0
0
0
0
1
2
1
1
0
0
1
1
0
1
0
2
1
1
3
1
1
1
1
0
0
0
1
0
2
1
1
0
0
0
1
1
1
1
2
0
2
0
2
0
2
1
1
2
1
0
2
1
1
1
0
2
0
0
1
0
1
0
1
2
1
1
2
0
1
1
1
0
0
0
1
2
1
0
3
2
0
1
1
2
0
1
1
0
1
1
2
1
1
2
1
1
1
1
0
1
2
1
2
1
0
0
1
1
1
1
1
1
0
1
2
0
2
1
1
0
0
0
2
2
0
0
1
0
1
0
1
1
1
2
2
0
2
2
1
0
1
2
0
1
0
0
1
0
1
0
1
2
1
1
1
1
1
0
1
0
0
0
1
1
2
0
0
1
0
1
0
1
3
0
0
0
0
0
2
1
1
0
0
1
1
2
1
1
1
1
2
0
0
1
1
3
0
1
2
1
0
1
1
0
2
0
0
2
2
0
0
1
1
1
1
1
2
0
0
0
0
0
1
1
2
0
1
0
0
1
0
0
2
0
2
0
0
2
1
0
0
1
0
1
0
0
0
2
2
2
0
1
0
1
2
2
2
1
2
0
0
0
1
2
1
1
1
1
2
0
0
2
0
0
2
0
0
2
1
2
2
0
2
2
2
1
0
2
2
0
2
1
1
1
1
0
0
2
1
1
1
0
1
1
0
1
2
1
0
0
1
1
0
2
1
0
0
0
0
0
1
0
2
0
0
1
1
1
0
2
0
0
1
2
1
1
2
2
2
1
0
0
0
1
0
1
0
0
0
2
0
0
1
0
1
1
1
1
1
0
0
1
1
0
1
2
0
2
2
0
0
0
0
1
1
1
1
1
0
2
2
1
0
0
0
1
0
1
1
0
1
0
1
1
1
1
0
0
0
1
0
1
0
1
1
1
0
1
1
0
1
2
1
0
1
0
0
1
1
0
0
0
0
0
0
3
2
0
2
0
0
1
1
0
1
0
0
1
0
1
2
1
0
0
3
1
0
0
1
1
1
0
2
2
1
0
0
4
1
0
0
0
0
0
0
0
0
1
1
2
1
1
1
1
1
0
1
1
2
0
2
1
1
2
2
1
2
1
1
1
1
0
1
0
0
0
0
0
0
1
0
0
1
0
2
1
0
1
0
2
1
1
1
1
1
0
0
2
1
1
1
0
0
0
1
1
2
0
2
0
1
2
1
2
1
0
1
2
2
2
1
0
1
2
0
1
0
1
2
1
1
0
0
1
2
2
1
0
1
2
2
1
2
0
2
1
2
0
2
0
0
0
0
1
0
0
0
0
0
2
1
1
0
0
2
0
1
0
1
2
2
1
1
2
2
1
1
0
0
1
2
2
1
0
1
0
2
0
0
0
0
2
1
2
1
1
1
0
0
2
1
0
0
1
0
1
0
2
0
2
2
2
1
0
0
0
1
0
2
1
0
0
1
1
0
0
2
0
1
0
1
0
1
2
0
1
0
2
1
1
0
0
1
2
1
0
2
0
1
0
1
0
0
2
0
1
2
2
1
2
1
0
2
1
1
1
0
0
0
2
0
0
1
2
0
1
1
0
2
2
1
1
0
1
0
0
0
1
2
0
1
0
1
2
0
0
0
0
1
1
2
0
3
2
2
1
1
1
0
0
1
0
2
2
1
2
1
1
0
0
0
2
0
0
2
0
0
0
2
0
0
1
0
2
0
0
0
0
1
1
1
3
2
3
2
1
0
0
2
0
2
1
0
0
0
0
0
0
0
3
0
1
1
0
2
0
0
0
0
1
0
1
0
1
0
0
0
1
0
1
2
0
1
0
0
0
0
1
0
1
0
7
2
2
2
0
0
1
2
1
1
0
1
1
0
0
1
1
0
0
2
0
0
1
2
2
1
0
2
2
0
2
0
0
0
1
2
3
2
0
1
0
0
0
2
0
0
1
0
0
0
0
1
2
0
0
2
2
1
3
0
1
1
0
2
2
0
0
0
0
0
1
0
1
1
1
1
0
0
1
1
1
0
0
0
1
1
0
3
2
0
2
0
3
2
0
1
0
0
1
1
1
1
1
1
2
2
0
0
0
0
0
2
0
1
2
0
0
0
0
1
2
1
1
0
1
2
2
1
0
3
1
0
2
2
0
1
0
0
2
4
3
2
0
0
2
2
2
0
1
3
1
2
1
1
0
2
2
2
0
0
2
0
0
1
1
1
2
0
0
0
1
0
1
3
1
0
2
1
0
1
1
1
2
2
2
1
2
2
0
2
2
0
0
0
2
1
0
0
2
2
1
2
0
1
0
1
0
1
0
0
2
1
0
2
1
0
2
1
0
0
1
1
0
1
1
0
1
0
2
0
2
2
1
0
0
1
1
2
1
1
2
0
2
2
3
0
0
1
0
0
0
0
0
2
1
2
0
2
2
1
2
0
0
2
2
2
1
0
1
0
1
0
2
1
2
0
1
1
0
2
0
0
2
0
0
2
1
0
0
0
1
1
1
0
0
0
0
1
1
0
0
1
2
2
0
0
0
0
1
0
0
0
0
1
2
2
2
1
2
3
0
0
0
2
1
0
1
1
0
2
0
2
0
1
1
0
1
1
2
1
1
1
1
2
0
0
4
0
0
2
0
3
2
2
1
2
0
2
1
1
0
0
2
1
0
0
0
0
0
2
0
0
1
1
4
1
2
0
1
0
2
0
2
2
1
0
0
1
2
0
2
1
0
0
2
1
0
1
1
1
1
4
2
1
2
0
0
1
2
2
1
0
0
0
0
0
0
1
2
1
1
1
2
2
0
1
0
0
1
0
0
1
1
1
1
1
1
2
2
2
1
0
1
0
1
0
1
1
1
1
1
3
1
2
4
1
2
1
2
1
2
2
1
0
1
0
0
1
1
1
1
0
1
2
1
0
1
2
0
1
0
2
0
1
1
1
0
2
2
0
1
1
0
0
0
0
1
1
2
1
1
2
0
1
1
0
0
1
1
0
0
1
0
2
2
1
0
1
0
1
0
0
1
0
0
1
0
2
1
2
2
3
0
0
0
0
1
0
2
2
0
0
0
2
2
1
1
1
1
0
1
0
0
1
1
0
0
0
3
1
2
2
1
1
1
1
0
1
0
0
0
1
0
0
0
0
1
2
2
0
0
0
1
0
0
1
0
2
1
1
1
2
2
1
2
2
2
1
2
2
0
0
2
2
1
2
0
0
1
1
0
0
1
3
0
2
2
2
0
0
0
0
1
1
1
1
0
0
2
1
2
1
2
1
1
2
3
0
1
0
1
0
1
1
1
1
0
0
1
1
0
2
2
1
0
0
0
0
0
2
0
1
1
0
1
0
2
1
0
2
1
3
0
1
1
0
1
0
1
2
2
3
0
0
2
1
0
1
1
2
1
0
0
0
1
2
1
1
1
0
0
0
0
0
1
2
2
1
1
2
1
1
1
2
0
2
1
0
0
1
2
1
0
1
0
1
1
3
0
1
0
2
1
1
2
1
0
4
1
1
2
2
0
1
1
1
1
2
0
2
0
0
1
3
1
2
1
1
1
0
2
1
1
1
0
1
0
1
0
1
1
1
1
1
1
0
1
2
2
0
1
0
0
2
0
1
1
1
1
0
0
1
0
1
2
0
0
0
0
2
0
1
0
1
1
0
1
0
1
1
2
1
0
1
1
1
2
1
0
0
0
1
0
1
1
2
0
1
0
0
2
1
2
3
1
2
2
2
0
2
2
1
0
2
0
1
2
0
0
0
2
0
1
2
1
1
0
2
0
1
0
1
0
2
1
2
2
0
1
2
2
0
2
2
1
1
1
0
0
0
0
2
2
2
0
2
0
2
2
1
0
1
2
1
1
0
1
1
1
1
1
0
0
1
1
0
0
0
1
0
0
0
3
2
0
2
2
0
1
0
1
0
0
0
1
1
2
1
1
1
1
0
0
1
0
2
0
0
0
2
0
1
0
0
0
0
1
0
1
2
1
2
1
0
0
0
0
2
1
1
0
0
0
2
1
2
0
2
2
1
0
0
0
1
0
0
1
1
0
0
2
0
0
2
2
0
0
0
1
2
1
2
1
1
2
0
1
1
1
1
1
0
2
1
2
0
1
0
0
2
2
2
1
2
2
2
1
2
3
1
0
1
0
1
1
0
1
0
0
2
1
2
1
2
2
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
1
2
1
0
1
0
2
0
0
0
1
2
1
1
1
0
0
0
0
1
2
1
2
1
1
1
0
0
0
0
2
2
1
1
0
2
1
0
1
1
0
0
2
0
2
0
0
0
1
0
0
0
2
0
0
2
2
1
1
0
0
0
3
0
0
0
1
0
1
0
2
1
1
0
1
1
1
1
2
1
0
1
0
3
1
0
1
2
0
2
1
0
0
0
0
0
1
1
0
1
1
0
0
0
0
1
0
1
1
0
0
0
2
0
0
1
0
2
0
0
1
1
1
1
0
0
1
0
0
0
1
1
2
0
1
1
0
2
0
1
1
0
2
1
0
0
1
1
4
2
1
0
2
1
2
0
1
0
0
0
1
1
1
1
2
1
2
1
0
1
0
1
0
2
1
1
1
1
0
0
1
1
2
1
0
0
0
2
1
0
1
1
2
0
0
0
1
2
1
1
0
3
1
1
2
0
1
1
0
0
2
0
3
2
2
1
2
1
1
0
1
0
1
1
1
0
1
0
2
0
1
2
0
1
2
0
0
0
2
0
0
0
0
0
1
0
0
2
2
1
2
2
1
1
0
1
0
1
1
1
1
1
0
0
1
0
2
2
2
0
1
2
1
1
0
1
2
2
0
2
1
1
1
2
1
1
2
0
0
0
1
2
0
2
0
1
2
0
2
1
0
1
0
0
2
2
0
0
1
2
1
0
1
0
1
1
0
0
2
1
1
1
0
1
1
0
1
1
2
1
1
1
0
3
1
0
2
0
2
0
2
0
0
1
2
0
3
0
0
2
0
2
1
2
0
1
1
1
0
2
0
1
0
2
0
0
2
2
1
0
0
0
1
0
2
1
2
1
2
1
0
1
1
2
0
0
2
0
0
1
1
0
0
0
1
0
0
1
1
0
0
1
2
0
0
2
1
0
2
5
1
0
3
0
2
0
0
2
1
0
1
1
1
2
1
0
1
0
1
0
1
1
2
2
0
0
0
0
0
0
0
0
1
0
1
2
1
1
1
1
0
0
2
2
1
1
1
2
1
1
3
1
2
0
1
0
0
0
1
1
1
0
2
0
0
0
1
0
2
2
1
0
0
2
0
1
1
0
0
0
0
0
1
2
1
2
0
2
3
3
0
1
1
1
2
0
1
0
0
2
1
1
2
0
2
2
0
0
2
0
0
2
2
0
0
0
3
0
0
0
1
0
0
1
1
2
2
2
0
1
0
1
1
0
1
1
1
0
0
0
2
1
1
2
0
0
1
0
1
0
1
1
1
0
1
0
0
0
0
1
1
1
1
1
2
1
0
0
1
2
2
2
0
1
1
0
1
1
2
0
0
1
0
0
0
0
4
1
1
2
2
0
1
0
1
1
1
1
2
2
2
1
1
0
1
1
0
1
1
2
1
1
0
2
1
1
2
1
1
2
0
0
1
1
1
0
0
2
1
0
2
1
2
1
0
0
2
1
2
0
2
0
1
1
1
1
2
0
0
1
1
0
2
1
1
1
1
1
1
1
1
1
0
1
1
1
0
0
1
1
0
3
1
0
1
0
2
1
1
0
1
1
0
1
1
0
0
1
5
0
1
1
0
2
0
1
1
2
1
1
0
1
1
0
1
1
1
0
1
1
0
3
0
1
2
1
0
1
0
0
2
1
0
1
2
1
0
0
0
1
0
1
0
0
0
0
1
0
2
1
1
1
1
0
0
2
0
1
1
1
0
1
0
0
0
1
1
0
0
0
1
1
0
0
2
1
1
1
1
3
2
0
1
2
1
0
0
1
1
0
2
1
0
2
0
1
1
0
0
1
0
0
1
1
1
0
2
1
1
0
1
1
1
0
1
2
0
1
3
0
0
3
2
2
0
0
0
1
1
0
0
2
2
2
1
0
0
0
1
2
1
0
0
2
1
1
1
0
1
2
1
2
0
0
1
1
1
2
1
1
0
1
0
0
2
2
2
2
0
0
0
1
2
2
1
0
1
0
0
0
0
1
1
2
0
1
0
1
0
2
1
2
0
0
0
1
0
1
1
0
0
1
2
0
1
1
0
2
1
0
0
1
1
0
0
0
1
0
1
0
2
2
2
1
2
1
2
2
0
1
2
0
1
1
2
0
1
1
0
0
2
0
0
1
1
2
0
0
0
0
0
1
2
1
0
2
0
0
0
1
0
1
0
0
2
0
0
0
1
2
0
1
0
0
1
1
1
0
1
1
2
1
1
1
5
0
1
2
2
0
2
0
2
0
0
0
0
1
0
0
1
1
1
0
0
0
0
1
0
1
2
2
0
2
1
1
0
1
1
1
0
0
0
1
1
0
2
0
0
1
0
1
0
0
1
0
1
1
1
0
0
0
0
0
0
0
1
1
1
2
0
1
0
0
1
1
2
0
1
2
2
1
2
0
0
0
2
1
0
0
1
0
2
0
0
1
1
1
0
2
0
0
0
0
1
1
0
1
1
1
1
0
1
0
1
0
1
0
2
0
1
1
0
0
1
1
0
0
0
0
0
2
1
0
1
2
1
0
1
0
1
1
1
1
1
0
3
1
0
0
0
0
0
2
0
0
0
1
2
0
0
1
0
0
1
2
0
2
1
0
0
1
2
0
0
2
2
1
0
2
2
1
0
1
0
0
1
0
1
1
0
2
2
0
2
0
2
1
1
1
1
1
0
1
0
1
1
0
0
0
2
1
1
1
1
2
2
0
2
8
0
0
2
2
2
2
0
1
0
2
1
2
0
0
2
0
0
1
1
0
0
0
0
1
1
0
2
1
2
0
0
0
1
0
1
0
0
2
0
1
2
0
2
0
0
0
0
0
0
1
0
2
1
0
1
0
1
0
0
0
0
1
1
2
2
0
0
1
2
1
1
0
1
1
1
1
0
1
2
2
1
1
1
2
1
1
0
1
1
2
1
2
0
1
2
2
0
1
2
3
1
1
1
2
0
1
0
2
2
1
0
2
0
0
0
1
0
1
2
0
1
1
0
0
1
1
0
0
0
2
3
1
3
1
0
0
1
0
0
0
2
0
0
2
1
0
1
0
2
2
1
1
0
2
1
0
0
0
0
2
1
1
2
2
4
0
0
0
1
2
1
1
0
3
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
4
1
0
1
1
1
3
2
1
4
0
1
0
0
0
2
1
0
2
0
2
2
0
0
1
0
0
0
2
0
0
0
1
0
1
1
1
0
1
1
1
0
0
1
0
0
1
0
1
0
2
2
2
0
2
1
2
0
1
1
0
1
0
2
1
1
2
0
0
2
3
0
1
0
0
1
0
0
3
1
0
1
0
0
0
1
1
0
0
1
0
0
1
1
0
1
1
2
1
0
0
1
0
2
0
1
0
1
1
1
0
3
1
0
1
0
1
0
0
2
0
1
0
1
0
1
2
0
0
0
0
1
2
1
0
3
2
1
0
2
0
0
1
0
0
0
1
2
1
0
0
2
1
3
2
0
1
1
1
0
1
2
1
0
2
1
2
2
2
2
2
2
0
1
1
0
1
1
0
0
0
0
2
0
2
1
1
2
2
2
0
0
0
1
1
1
1
1
0
0
0
1
0
0
1
2
2
0
1
2
1
1
1
0
1
1
0
0
1
2
0
0
1
1
0
0
1
1
2
0
0
2
0
0
1
1
2
1
2
1
0
2
0
0
2
1
2
2
0
0
0
0
1
1
1
0
0
0
1
2
1
0
1
0
0
0
2
1
0
1
0
1
1
1
0
1
2
0
0
1
2
2
1
2
0
0
0
1
1
0
0
0
0
0
0
1
2
1
0
1
1
0
0
0
0
2
2
0
0
1
2
1
1
0
3
0
0
1
1
1
1
0
0
0
1
0
1
4
1
3
0
0
1
0
2
0
0
1
0
2
1
2
0
1
2
1
1
1
1
2
1
1
2
1
1
2
0
0
1
0
0
2
2
1
0
0
2
1
1
1
1
1
1
0
2
2
0
1
1
1
1
2
1
2
2
2
0
2
2
0
0
0
0
0
2
0
1
1
0
1
1
0
2
1
0
0
2
1
0
2
0
2
1
0
0
1
0
1
1
1
1
0
2
2
1
1
0
3
1
0
1
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
1
2
1
2
1
1
0
2
0
1
1
1
0
0
1
1
0
0
0
0
0
2
0
1
2
0
1
2
0
2
1
0
0
1
1
1
1
0
0
2
0
1
1
3
0
1
2
0
2
2
0
0
2
1
1
0
2
0
1
1
1
1
0
0
0
1
0
2
0
0
0
0
0
0
3
2
0
1
1
1
0
0
0
0
0
2
0
0
0
1
0
1
1
0
0
1
0
2
1
1
1
0
1
1
1
0
0
2
2
0
1
2
0
3
2
1
2
0
2
1
1
1
0
0
2
0
1
2
1
1
1
1
1
1
1
1
0
0
1
2
1
1
1
1
0
1
2
0
1
1
0
2
0
1
0
0
1
1
1
0
2
1
1
1
2
1
1
1
0
0
0
3
3
2
0
0
2
1
0
0
0
1
1
0
1
1
2
0
2
0
0
1
1
0
0
3
0
1
1
0
2
2
0
0
0
2
0
2
0
1
0
0
1
1
2
2
2
0
0
2
2
2
2
1
1
0
1
1
0
1
1
2
0
0
1
1
0
0
0
3
0
1
0
2
1
1
0
0
0
1
1
6
2
0
2
1
0
2
4
0
0
0
1
1
1
0
2
0
0
1
1
0
1
2
1
1
0
2
1
2
1
1
2
2
1
0
1
1
0
0
2
1
0
1
2
2
0
0
2
1
0
0
2
1
0
1
0
2
1
2
2
1
2
2
0
0
2
0
0
2
0
1
1
0
0
1
2
2
0
1
2
1
2
0
0
2
0
1
0
2
1
0
0
1
0
0
0
2
0
2
0
0
2
1
2
0
1
0
2
1
1
0
1
2
0
2
0
0
1
1
0
0
1
0
2
1
2
1
1
0
1
2
1
2
1
0
2
0
2
1
2
2
0
1
2
0
1
1
1
0
1
1
1
0
0
0
1
2
0
1
2
1
0
1
1
0
2
0
1
2
1
1
1
1
0
0
0
2
0
0
1
1
0
1
0
0
0
1
2
0
0
1
2
0
0
0
0
1
0
0
0
2
1
2
0
1
1
2
0
1
2
0
2
1
0
1
1
0
1
0
1
2
1
1
0
2
2
1
1
0
2
2
0
2
0
0
0
0
2
1
0
0
3
0
0
3
1
0
1
1
2
2
0
0
0
0
1
1
1
1
0
2
2
2
0
1
3
1
2
0
0
1
0
1
0
1
2
0
0
0
1
2
2
1
2
1
0
1
0
1
1
0
1
2
4
0
0
0
1
0
0
1
2
1
2
3
1
0
2
4
1
1
1
0
1
1
0
0
0
1
0
2
0
2
1
1
0
0
0
2
0
1
1
1
2
0
0
0
1
1
4
0
4
0
1
0
0
2
2
0
1
0
0
2
1
2
1
0
0
0
1
0
0
0
1
2
0
2
0
1
2
1
0
0
1
1
1
1
1
2
0
2
1
1
1
2
0
1
1
0
2
2
0
2
2
3
1
1
1
1
2
1
0
1
0
2
0
0
1
0
1
0
2
1
0
0
0
1
1
0
2
1
5
0
2
1
1
1
2
1
2
2
1
1
0
0
0
0
0
2
0
0
0
1
2
3
0
0
0
0
1
1
2
2
1
0
1
1
0
0
0
2
3
0
1
0
1
0
0
0
2
1
1
1
1
3
1
0
0
1
2
2
0
1
0
0
1
1
1
1
1
1
0
0
1
3
1
0
0
0
1
0
0
1
0
1
1
0
1
1
0
1
2
1
0
1
1
1
0
2
0
0
1
0
2
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
1
2
0
0
1
0
1
2
1
1
3
0
0
1
2
0
0
2
2
1
1
0
2
1
1
1
2
0
1
0
0
1
0
1
0
1
2
0
0
1
1
0
0
1
0
0
1
1
0
0
0
0
1
1
0
0
0
2
2
1
1
1
0
1
1
2
0
1
0
1
1
0
2
0
1
0
0
0
0
1
0
1
1
0
3
1
0
0
2
0
0
0
2
1
3
3
1
2
2
0
0
3
0
1
1
1
2
1
0
0
2
0
1
1
5
2
2
0
1
0
0
0
1
2
0
1
1
0
0
0
2
2
1
0
0
1
0
1
2
0
0
0
1
0
0
0
1
2
1
0
1
0
2
0
0
0
1
0
3
1
1
2
0
0
0
1
1
0
0
1
1
0
1
1
1
2
0
1
2
1
0
0
1
1
2
1
1
0
5
1
1
2
0
1
2
1
0
2
1
2
1
0
2
0
0
1
0
1
2
1
0
2
1
0
2
2
2
1
0
0
1
0
1
0
1
0
1
0
0
0
1
2
1
0
1
1
2
1
2
2
1
0
4
1
0
0
2
0
0
0
0
2
2
1
1
2
1
1
1
1
2
0
1
2
0
0
1
1
1
1
0
2
2
2
2
2
1
2
1
2
1
2
0
0
0
1
1
0
0
1
0
0
0
3
0
0
2
1
1
1
1
1
0
1
1
1
0
0
1
0
1
0
1
0
1
2
0
2
0
0
1
1
1
0
1
0
1
1
0
0
0
0
2
1
2
1
2
1
1
1
0
0
1
1
1
1
1
1
0
1
2
2
1
0
0
0
0
2
0
0
0
1
2
2
0
1
0
1
1
1
1
0
0
0
0
2
1
0
0
0
2
0
2
1
1
0
1
0
0
0
2
2
0
2
1
1
2
1
2
0
1
2
0
0
1
0
2
1
1
1
0
0
0
0
1
1
2
0
0
2
2
2
0
1
1
0
1
1
1
0
2
1
0
1
0
0
0
0
0
3
1
1
0
1
1
1
1
0
0
0
2
0
1
0
0
1
2
1
2
1
0
1
0
1
1
0
0
0
2
1
1
0
0
1
1
3
2
0
3
1
2
0
0
5
2
1
0
1
2
2
0
1
2
2
1
0
2
1
0
2
0
1
1
2
2
0
0
2
0
0
0
2
2
1
1
0
2
1
1
1
0
1
1
0
0
0
2
1
1
0
1
1
2
0
0
0
2
1
0
0
1
0
2
0
0
0
0
0
1
0
0
2
0
0
2
0
1
1
1
1
0
1
1
2
1
0
0
1
0
0
0
2
1
2
1
0
1
1
1
1
0
1
0
0
0
2
1
2
1
1
0
0
0
0
0
0
0
1
1
1
0
0
1
2
1
2
2
2
1
1
1
0
1
0
1
1
0
0
0
1
1
0
2
1
1
2
0
2
2
2
0
2
1
1
0
0
1
0
1
1
0
0
1
1
0
0
2
0
2
0
2
1
3
0
1
1
1
2
0
0
0
1
1
0
0
0
1
1
0
0
2
1
2
0
0
2
0
0
2
2
1
3
1
0
2
1
0
0
0
0
1
0
1
1
2
1
1
0
1
0
1
0
0
0
1
0
2
1
2
0
1
0
0
0
2
0
1
2
1
2
2
2
0
0
1
0
1
0
2
1
0
1
0
3
1
2
0
0
1
0
0
0
2
0
2
1
2
0
1
1
0
1
0
0
2
0
2
2
1
1
1
1
1
1
1
1
1
0
0
0
1
1
2
2
1
2
0
0
0
1
1
0
0
0
0
1
1
2
4
1
1
1
0
0
1
1
0
0
1
0
0
0
0
2
1
2
1
0
0
0
1
0
1
1
0
1
1
1
1
0
0
2
2
1
1
0
1
0
0
1
2
0
1
1
0
0
0
1
1
2
1
1
1
0
2
1
2
1
0
1
2
0
2
2
2
1
0
0
1
0
0
2
1
0
0
0
2
0
1
1
0
1
0
3
0
3
0
0
0
0
1
1
1
2
0
0
0
0
0
0
2
4
1
1
0
0
0
1
1
2
1
1
0
2
0
1
1
0
0
2
0
2
0
2
0
0
1
1
0
1
1
2
1
1
2
0
1
2
0
0
0
0
2
2
3
0
0
0
2
1
2
2
1
0
1
1
0
1
1
0
1
0
0
2
0
1
1
1
0
2
1
1
0
0
0
1
2
0
2
1
0
0
4
0
1
1
0
1
1
1
0
0
0
0
1
3
1
1
0
0
0
1
2
0
0
1
1
1
1
0
2
1
0
1
1
1
0
1
2
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
1
1
1
0
1
1
0
1
1
1
2
1
0
0
2
2
1
2
0
2
0
1
0
2
1
1
2
1
1
0
2
1
0
0
1
1
2
2
0
1
0
2
2
1
0
1
0
0
2
0
2
0
2
3
1
0
1
0
1
0
2
0
2
2
2
2
1
0
0
2
1
0
2
2
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
1
1
0
0
0
1
1
1
2
1
0
2
1
0
0
0
0
0
1
2
1
2
0
0
0
2
1
0
1
0
1
1
1
0
1
1
0
0
0
1
1
1
1
2
1
1
1
1
1
2
2
0
2
0
1
1
2
1
1
2
0
1
1
0
1
1
2
1
0
1
1
1
0
1
1
1
1
0
0
1
1
2
1
1
0
0
1
0
1
2
0
0
0
1
3
1
1
1
0
1
0
3
0
0
2
1
0
1
0
2
1
0
1
0
2
3
0
0
2
0
1
1
1
1
1
2
0
2
0
1
1
1
0
0
0
0
2
0
0
0
1
2
0
0
1
0
1
0
1
0
2
2
2
1
2
0
0
0
1
1
0
0
1
1
0
2
2
0
1
0
1
1
0
0
0
1
1
0
0
1
2
1
2
0
1
0
0
0
1
0
0
2
2
0
0
1
0
0
0
3
1
2
1
0
0
2
0
1
0
1
0
1
0
0
0
1
0
0
1
0
1
1
2
0
1
1
0
0
0
0
2
0
0
1
1
2
0
0
0
0
0
1
0
2
1
0
1
1
0
0
1
2
1
1
0
2
1
1
0
0
1
1
0
0
1
0
0
1
1
1
0
2
0
2
1
0
0
0
0
1
2
0
0
0
2
0
0
0
1
2
0
2
1
0
0
3
1
0
0
2
0
0
1
2
0
1
0
0
1
0
2
1
1
2
0
1
2
0
1
0
1
1
0
1
2
0
3
2
1
2
2
0
1
1
0
1
0
0
2
0
2
1
3
2
2
1
1
1
2
1
1
2
0
1
1
1
1
0
0
0
0
1
1
0
0
1
1
0
1
1
0
0
1
0
0
1
2
2
1
1
0
1
1
2
0
0
0
1
1
2
0
1
1
0
2
0
1
2
2
1
0
0
0
1
2
0
1
0
2
2
0
1
0
0
0
2
0
4
1
3
0
0
1
6
0
1
1
2
1
1
1
1
1
2
1
0
2
1
0
2
0
1
0
1
1
2
1
1
2
1
0
2
1
0
1
1
1
0
0
1
2
1
1
0
0
1
1
0
0
0
1
2
0
1
1
0
2
2
1
0
1
2
0
0
1
1
1
0
0
1
1
0
0
0
0
0
2
1
1
0
1
0
0
1
1
0
0
0
0
2
2
0
1
0
4
2
1
1
0
2
0
2
1
1
1
1
1
0
1
1
0
1
1
1
2
2
0
1
0
2
1
0
0
0
0
2
1
0
2
1
1
1
2
3
2
1
0
1
0
0
1
0
2
0
2
0
0
1
1
1
0
0
3
1
0
1
0
0
1
0
0
1
1
1
1
0
0
2
2
1
1
1
0
1
1
0
1
3
0
1
2
1
1
2
2
1
1
1
2
0
3
2
1
1
0
3
0
2
1
2
1
0
0
0
1
1
0
0
1
2
0
2
0
1
1
2
2
0
2
2
1
2
2
0
2
0
1
1
0
1
1
0
0
0
2
0
1
0
0
1
0
2
2
0
0
1
0
0
0
2
1
1
2
1
0
0
0
2
0
0
1
1
1
2
2
1
2
0
2
2
2
0
0
0
1
0
1
1
0
1
0
0
2
2
2
1
0
2
0
0
0
0
2
1
2
1
2
1
1
2
0
1
0
2
2
2
0
0
0
0
2
1
0
2
2
1
1
0
1
0
0
1
2
1
1
1
2
2
0
1
0
0
2
0
0
2
0
2
2
2
1
1
0
1
0
0
2
2
2
0
0
1
0
1
0
0
0
0
0
0
1
1
1
0
0
1
0
1
1
2
1
1
1
1
1
0
2
2
0
0
1
1
2
1
0
0
0
1
2
1
0
0
0
0
0
1
1
0
0
0
0
1
1
2
0
2
1
1
2
0
1
0
0
0
1
2
2
0
2
0
0
2
0
2
1
0
1
1
1
0
1
0
1
1
1
2
1
0
0
1
0
2
0
1
0
2
0
2
2
2
1
0
2
1
1
2
1
2
0
0
2
1
0
2
0
1
1
0
1
1
2
0
0
1
0
1
1
2
0
0
0
1
2
0
1
2
1
2
1
0
0
0
2
0
2
1
5
0
1
1
0
0
0
0
2
0
1
1
1
2
0
0
1
2
1
1
1
1
1
0
2
1
1
0
0
0
2
2
0
1
2
1
2
0
2
2
2
0
2
0
0
0
1
0
1
1
0
0
1
0
0
2
0
0
1
1
1
1
1
1
0
0
1
1
1
2
0
0
0
2
2
0
0
1
1
1
2
3
1
0
0
0
1
2
1
1
1
2
1
1
2
1
2
1
2
0
0
2
1
0
1
1
0
2
1
2
0
2
0
0
0
1
2
0
1
0
0
0
1
2
0
0
1
2
2
1
0
1
1
2
0
3
1
2
1
2
0
1
2
0
0
0
1
0
1
1
0
1
2
0
2
1
0
0
1
1
0
2
0
3
1
0
1
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
2
1
0
0
1
0
1
0
1
1
0
0
2
2
1
1
1
0
1
0
0
1
2
0
1
1
0
1
1
0
1
2
0
1
1
0
0
1
0
0
0
2
0
1
0
2
1
1
0
1
0
2
0
1
1
2
2
1
1
1
2
1
0
0
0
1
2
1
0
0
1
1
1
1
2
2
2
2
0
0
0
0
0
1
2
0
0
2
0
1
1
0
1
0
0
0
0
1
0
1
1
1
7
1
2
1
0
1
2
1
2
1
1
1
0
0
0
2
0
0
0
0
1
1
2
1
1
0
2
7
2
1
1
0
1
1
2
1
1
1
1
0
1
0
2
0
1
0
1
0
0
0
1
1
2
1
1
1
2
0
0
1
1
1
0
1
1
1
1
0
1
2
1
2
0
0
1
0
1
0
2
1
0
1
2
0
2
1
0
1
2
2
0
1
0
0
2
0
2
0
0
1
1
0
0
2
0
2
1
0
2
2
1
0
1
0
2
0
0
0
1
2
3
1
2
0
0
2
0
1
1
1
1
1
2
0
2
0
0
0
2
0
1
0
1
1
1
1
0
0
1
0
2
1
0
0
0
0
0
1
2
0
1
0
1
2
2
2
0
2
2
2
0
0
0
2
0
2
2
2
1
1
0
0
2
0
1
2
0
2
0
0
2
2
0
1
0
2
3
1
0
0
2
1
0
2
1
2
1
1
1
0
1
1
0
2
0
0
1
2
0
1
1
1
1
0
0
2
0
1
0
0
2
0
1
2
0
0
1
1
0
1
1
1
2
0
0
1
0
1
0
1
4
1
2
0
1
0
1
1
0
2
1
1
1
0
2
0
0
2
1
2
0
1
0
1
2
4
1
0
1
0
0
1
0
2
0
0
2
1
1
1
1
1
0
0
0
2
0
1
2
2
0
2
2
1
1
1
0
2
1
2
1
0
0
1
0
0
0
1
2
1
0
2
0
0
2
0
0
0
0
0
0
1
1
0
0
1
2
0
2
0
1
0
1
0
3
1
2
0
2
1
1
0
0
1
0
0
1
1
0
0
2
0
1
0
1
2
0
1
1
3
0
2
0
1
2
0
0
1
1
1
0
0
1
0
1
1
2
2
1
2
1
2
0
0
2
2
0
2
1
1
0
1
0
2
0
2
1
2
1
0
1
2
0
0
1
0
1
0
0
1
1
2
0
0
1
0
2
1
1
0
1
1
1
4
2
1
0
0
0
2
1
0
1
1
2
2
0
0
0
1
0
1
0
1
2
1
1
1
1
2
1
1
2
0
1
0
0
1
0
0
0
1
1
0
0
2
2
0
1
0
0
2
0
0
0
1
1
0
0
1
0
0
0
0
1
1
1
0
1
2
0
1
0
0
1
0
2
2
1
1
1
2
2
1
2
1
1
0
1
0
0
1
0
1
1
0
1
0
0
1
2
0
1
0
0
0
0
1
1
0
0
1
2
2
1
0
1
0
2
1
1
0
0
1
2
1
0
0
0
0
0
1
1
2
0
1
0
0
1
0
0
0
2
0
0
1
2
0
0
1
0
0
1
2
2
1
0
2
2
1
1
2
0
0
0
1
1
0
1
1
2
0
2
2
2
1
0
1
2
2
2
2
0
2
0
2
2
1
1
1
1
2
1
0
2
2
2
1
1
2
1
2
0
0
0
1
1
1
2
0
0
0
1
0
2
0
0
0
2
2
0
1
0
1
1
2
0
2
0
0
0
1
0
0
1
2
1
2
2
3
1
0
0
1
1
1
1
0
2
0
0
2
2
2
0
2
1
0
2
0
0
0
2
0
1
1
2
1
2
1
1
1
3
1
1
0
0
1
2
0
1
2
1
1
0
2
2
1
1
0
0
1
2
1
2
0
1
1
0
2
1
0
2
3
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
1
0
2
0
0
1
2
2
0
1
1
0
0
2
1
1
2
0
2
0
2
0
1
2
0
1
1
1
2
0
2
2
1
0
0
0
2
0
2
2
2
1
0
0
2
0
1
0
1
1
1
0
0
1
0
0
0
2
2
0
0
0
0
2
1
1
2
1
0
1
1
1
0
1
1
1
1
0
0
0
0
1
1
1
1
0
1
1
1
0
0
0
2
2
0
1
2
0
0
0
0
2
2
1
2
1
2
0
1
2
2
0
2
1
0
0
0
0
1
0
2
1
2
1
0
1
1
1
1
0
0
2
1
1
1
2
0
2
0
0
0
1
2
1
0
2
0
0
0
0
1
1
1
2
1
0
0
1
1
1
2
0
0
0
1
1
0
1
0
1
5
0
1
1
1
0
3
1
1
1
2
1
2
2
0
0
0
0
1
0
1
1
1
1
0
0
1
0
1
1
0
1
1
0
2
2
0
0
2
1
2
1
0
0
0
2
2
3
1
2
0
0
1
2
0
0
2
0
0
0
3
2
0
0
2
1
0
1
2
0
1
0
1
2
1
0
1
1
0
0
2
0
1
0
2
0
1
1
0
0
2
0
0
0
2
0
0
1
0
1
1
0
0
0
1
0
0
0
2
0
3
1
1
0
2
1
0
1
0
0
1
0
2
1
0
0
0
0
2
1
1
0
1
0
2
0
0
0
1
1
2
0
1
1
2
2
5
1
1
1
0
0
1
1
1
0
0
0
2
0
0
0
2
0
1
0
0
1
1
0
2
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
1
1
1
0
0
1
0
1
1
1
0
1
0
0
0
0
2
1
0
0
2
1
1
2
2
1
2
2
2
0
0
2
0
0
0
2
1
1
1
0
0
2
0
0
0
0
2
2
1
0
1
2
0
0
0
0
0
0
1
2
0
0
1
1
2
0
1
1
0
0
1
1
1
1
1
0
0
0
0
1
0
0
0
0
2
0
1
1
0
0
2
2
1
1
2
0
2
0
1
0
1
3
0
2
0
0
0
2
1
0
0
1
1
1
1
1
4
1
0
0
0
0
2
2
2
0
0
2
0
0
2
0
1
1
2
0
0
1
1
1
2
1
0
0
0
1
0
0
0
2
1
2
1
1
0
2
0
1
0
2
1
2
2
0
2
1
0
0
1
0
2
0
1
0
1
1
1
0
0
2
0
0
1
0
2
2
2
2
1
0
1
2
0
2
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
2
0
0
1
4
1
1
2
3
0
2
2
2
0
1
0
0
1
2
0
2
2
1
1
0
1
0
2
3
1
0
0
2
2
0
2
1
0
2
1
1
1
0
1
2
1
2
3
1
0
1
1
1
1
1
1
2
1
0
0
1
0
1
0
0
1
0
2
1
1
0
2
0
2
0
0
1
1
2
2
1
0
2
2
1
0
3
3
0
0
1
1
1
0
0
1
0
0
2
2
1
0
3
0
1
2
0
1
2
1
1
0
1
2
1
2
2
0
2
0
1
1
2
0
1
1
1
0
1
1
0
1
2
0
2
1
2
0
1
2
0
1
2
0
2
1
0
1
1
0
0
1
3
1
0
2
0
0
0
0
1
0
1
1
0
1
1
2
1
3
1
1
2
1
1
2
1
0
0
1
0
1
1
0
2
0
1
1
0
1
0
2
1
2
0
0
1
2
1
0
1
0
0
2
0
1
1
1
1
0
1
0
1
0
0
1
0
1
0
2
1
0
0
0
0
2
0
2
2
1
0
1
1
1
1
1
0
0
1
3
1
2
2
1
2
1
1
0
2
1
2
1
1
2
0
2
1
0
1
1
2
1
2
2
0
2
2
2
0
0
2
0
0
1
1
0
0
2
1
1
2
1
1
0
1
1
0
0
0
0
2
2
0
0
0
2
0
2
1
0
1
0
0
1
0
0
0
2
2
0
0
1
1
0
0
2
1
1
0
1
0
1
0
0
1
1
2
2
0
2
1
1
2
0
2
1
0
0
1
1
0
0
1
0
1
1
1
2
0
0
0
0
2
1
0
0
0
2
1
0
1
2
1
2
1
1
2
2
2
0
1
2
0
1
0
0
0
1
0
1
1
0
1
0
2
2
2
3
0
0
1
2
0
1
2
0
0
2
0
1
1
2
1
1
0
0
1
0
0
2
2
2
2
0
0
1
1
0
1
0
0
1
1
0
2
0
1
1
0
1
0
2
0
0
1
1
1
2
2
0
0
2
0
1
2
1
1
0
0
0
2
1
1
0
0
1
1
0
0
5
0
1
0
2
0
1
2
5
0
2
2
0
0
0
2
0
1
0
0
1
1
0
1
1
1
1
0
0
1
1
1
2
2
1
1
0
1
1
2
6
1
1
1
1
1
0
0
1
0
1
0
1
2
0
0
2
0
1
1
2
0
0
1
2
0
0
1
2
0
0
0
0
2
1
2
1
0
0
0
0
0
1
2
2
1
0
0
0
0
1
0
1
2
0
1
1
0
0
0
0
0
1
2
1
0
2
2
3
1
0
0
0
0
3
0
0
2
0
2
0
2
0
1
1
0
1
1
0
0
2
0
2
2
1
2
2
0
2
1
1
0
0
0
1
1
1
0
2
1
2
2
0
2
1
2
1
0
2
0
2
1
1
2
1
2
0
1
1
0
2
3
2
0
0
0
1
0
0
1
1
2
2
1
1
0
0
0
1
1
0
0
0
0
2
1
1
1
1
1
0
1
1
1
2
0
1
2
0
0
2
2
2
0
1
1
1
2
2
1
1
1
1
1
1
0
1
0
0
1
3
0
0
0
1
1
1
0
0
0
0
2
1
0
2
0
2
0
1
2
1
0
1
1
2
1
2
0
1
1
0
0
0
2
1
2
2
0
1
0
2
0
0
0
2
0
0
1
0
2
0
0
1
2
0
1
0
1
0
0
1
0
2
0
1
0
2
0
0
2
1
2
0
0
2
0
1
6
0
1
1
2
2
0
2
1
1
0
0
1
0
1
1
0
0
2
0
0
1
2
1
1
2
0
0
2
2
1
3
0
2
0
0
0
1
1
1
1
1
0
2
1
1
0
0
0
1
0
1
1
2
0
0
2
2
2
0
0
0
1
0
2
1
2
0
0
0
0
0
2
0
1
0
0
0
0
1
1
2
2
0
1
1
2
1
1
1
1
0
1
0
1
3
0
0
0
2
2
0
0
0
1
0
2
2
0
0
0
2
2
2
2
0
2
2
6
1
2
0
0
0
2
2
2
1
1
1
0
2
0
2
1
0
1
2
1
1
1
0
2
0
0
0
0
1
0
0
3
0
0
1
1
2
1
1
2
2
1
0
0
1
2
1
0
0
0
1
0
2
0
0
1
1
0
0
1
1
0
1
2
0
1
1
2
0
1
2
0
2
1
0
2
2
0
0
1
1
0
1
0
3
0
2
0
1
2
0
1
1
1
0
1
0
1
1
1
1
3
1
2
0
1
0
0
0
2
2
0
0
1
0
0
2
0
2
1
1
1
1
0
1
2
0
2
2
1
0
0
2
1
2
0
0
1
2
1
1
0
0
0
2
0
2
1
2
1
0
1
0
0
0
0
2
1
1
0
1
2
0
0
1
0
0
1
2
1
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
2
1
1
1
0
1
1
0
2
1
1
0
0
1
0
0
1
1
1
1
0
0
2
0
1
0
0
0
2
1
0
0
0
0
0
1
0
0
1
1
1
1
0
1
1
2
1
1
0
1
1
0
1
1
0
0
1
1
1
2
1
1
1
1
0
0
2
1
1
0
0
1
1
0
2
0
1
1
0
1
0
0
2
0
0
1
2
1
1
1
0
2
4
2
0
0
0
2
1
1
2
1
1
1
1
0
0
2
2
0
1
0
0
1
1
0
1
0
0
0
0
0
0
2
0
2
1
0
2
1
1
0
1
0
2
1
1
0
0
0
2
2
1
1
0
1
2
0
1
1
2
0
1
0
2
1
1
0
1
0
0
2
0
1
1
0
0
0
2
0
1
1
0
0
4
1
0
1
0
0
1
2
2
0
1
1
1
0
0
2
1
1
0
0
0
1
2
1
0
1
2
0
0
0
1
1
2
1
1
0
1
1
2
2
0
0
0
2
1
0
1
1
0
0
1
0
0
0
0
2
1
0
0
0
0
2
0
2
0
2
1
0
1
1
0
2
0
1
2
1
0
0
0
0
0
1
0
0
0
1
1
2
1
1
0
1
0
2
1
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
1
1
0
1
2
0
1
1
2
1
2
2
1
1
0
0
1
2
2
1
1
2
0
1
2
0
2
1
2
2
0
0
0
0
0
2
1
1
0
0
1
1
1
1
0
0
2
2
2
0
1
0
0
0
0
2
2
1
2
2
0
0
1
0
0
0
2
2
1
1
2
2
1
0
1
1
1
0
2
25
1
1
0
0
1
1
1
2
1
0
0
0
2
0
0
0
2
2
2
1
3
2
0
0
2
3
0
1
3
0
1
0
0
0
0
0
0
1
0
2
0
0
0
1
0
2
1
0
1
0
1
1
2
1
1
0
1
1
0
4
1
0
1
0
0
1
1
1
1
1
2
0
0
2
0
0
1
2
0
0
0
0
2
1
0
2
0
1
0
1
1
0
1
0
2
1
0
0
0
0
0
2
1
0
0
1
0
1
0
1
0
0
1
0
2
0
1
0
0
2
2
1
1
0
0
1
1
0
1
0
0
2
1
1
1
2
1
0
0
0
0
1
1
0
1
0
0
1
0
0
2
0
2
1
1
0
2
2
2
2
1
0
2
0
4
1
1
0
1
0
2
0
2
0
2
6
0
1
0
1
0
1
0
0
0
1
0
0
1
1
0
1
1
1
0
2
0
1
2
5
0
2
2
0
1
0
1
0
0
2
2
6
2
2
0
1
1
0
1
2
1
0
0
1
0
2
2
0
2
1
0
1
1
1
1
0
2
0
2
0
0
2
1
1
0
1
1
0
0
1
1
1
1
1
0
0
2
2
3
3
0
2
1
0
2
2
2
0
0
1
0
0
1
2
1
1
1
0
0
0
1
1
0
0
0
0
2
0
0
1
2
1
2
1
0
1
0
1
1
0
0
0
1
2
0
1
0
1
2
1
1
1
3
1
2
0
0
0
0
0
1
2
1
0
1
1
0
1
0
0
0
1
0
1
2
0
2
0
0
1
0
0
1
0
0
1
1
2
0
0
0
2
0
0
0
0
0
2
1
1
2
2
1
1
1
0
0
0
1
1
1
1
0
1
1
0
0
1
2
0
0
2
0
0
1
0
0
0
1
1
0
1
0
0
2
0
1
1
0
2
0
0
0
1
0
0
0
2
1
0
1
1
0
1
1
2
0
0
1
1
1
0
0
3
1
0
0
3
1
0
1
0
0
0
2
4
1
0
1
0
1
1
1
2
0
0
2
2
1
0
0
1
2
0
1
0
0
2
0
1
2
1
1
1
1
0
0
0
1
0
0
1
0
0
1
0
1
2
2
1
0
0
1
2
0
0
2
1
0
2
0
1
1
2
2
1
2
0
2
2
1
2
0
1
2
1
2
0
1
2
1
1
0
0
1
1
1
2
1
0
0
2
1
1
0
0
1
0
2
1
1
2
1
2
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
2
1
1
1
1
0
2
0
0
1
1
1
1
2
1
0
1
0
1
2
0
1
1
0
2
0
1
1
0
1
1
1
1
0
2
1
0
1
2
2
1
2
0
1
1
0
1
0
1
0
2
3
1
0
2
1
1
0
1
0
1
1
2
2
0
1
0
1
0
0
1
0
0
2
0
2
1
1
1
0
0
1
1
0
1
2
0
0
0
1
2
0
1
0
1
0
0
2
1
1
0
2
0
2
0
2
1
1
1
1
1
0
2
2
2
1
1
0
0
1
0
1
0
0
1
1
0
0
0
0
1
0
0
0
2
1
1
2
2
0
1
1
0
0
1
0
0
1
0
0
2
1
0
0
2
0
1
1
1
0
0
0
0
1
2
0
1
0
1
1
1
1
0
1
1
1
1
1
1
0
1
0
1
0
0
1
1
2
2
0
1
1
1
1
2
2
0
1
0
0
0
0
0
0
0
2
1
1
1
1
2
1
0
2
1
0
1
3
1
0
0
0
1
1
0
0
1
2
1
1
0
0
1
1
0
1
1
1
0
2
0
1
0
1
0
0
0
2
2
0
0
3
1
0
0
0
1
0
1
0
1
1
2
0
0
1
2
1
2
1
0
1
1
2
2
1
1
2
0
1
0
2
0
0
0
0
1
2
2
1
2
1
0
0
2
0
1
1
0
0
1
1
1
0
0
1
1
0
0
0
2
0
2
1
1
0
1
1
0
0
1
1
0
0
1
2
1
0
0
1
1
1
0
1
0
0
0
2
1
2
1
2
0
0
2
0
1
1
1
0
0
0
1
1
2
1
1
2
1
0
0
0
2
0
0
0
1
0
1
1
0
1
2
1
0
0
0
1
0
2
1
1
0
0
1
1
2
1
0
0
1
0
0
1
2
2
0
1
1
0
2
1
2
0
1
0
1
1
0
1
1
0
1
1
1
0
1
0
1
2
0
2
2
3
0
2
0
1
1
2
2
1
1
0
0
1
2
0
0
1
2
1
1
2
0
2
1
1
1
2
1
0
1
0
0
0
0
2
0
2
2
1
2
0
0
0
1
2
2
0
2
0
2
2
0
1
2
0
1
0
1
0
0
0
1
0
1
2
0
1
1
0
1
2
2
1
2
0
0
1
1
0
0
2
0
1
1
0
2
1
1
1
0
0
1
1
0
0
1
0
0
2
1
2
1
1
0
1
0
0
1
1
2
0
1
1
1
2
0
0
1
1
1
0
1
0
0
2
1
2
0
0
0
1
0
1
2
0
1
0
2
0
3
0
1
2
1
1
1
1
1
1
0
2
1
1
2
1
0
0
0
0
1
0
1
1
0
1
0
1
1
1
1
1
1
0
3
0
0
2
0
1
1
1
2
0
1
0
0
0
0
1
0
1
2
0
1
3
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
2
2
2
1
0
1
1
0
1
2
1
2
0
0
1
2
0
1
1
2
0
2
1
0
1
1
0
0
1
1
3
2
0
0
0
0
2
0
2
1
0
0
1
2
0
0
1
0
1
1
4
0
0
1
1
0
2
1
0
1
0
1
2
0
0
0
0
1
0
0
1
2
0
0
1
1
0
0
1
0
1
1
0
0
0
1
0
1
1
1
1
0
2
1
0
1
0
1
2
0
2
2
0
0
2
1
0
2
1
0
1
0
0
2
2
1
0
0
2
0
1
1
2
1
2
0
0
1
0
0
2
0
0
3
1
0
1
0
0
1
2
0
1
0
0
1
0
0
1
10
0
1
1
1
2
1
0
1
1
1
0
0
1
0
1
1
3
2
1
0
1
2
2
1
0
0
0
0
0
0
0
2
1
0
1
1
1
1
0
0
0
1
1
1
0
0
2
2
1
1
1
0
1
0
1
1
1
1
1
1
0
0
1
0
2
0
1
0
3
0
0
1
0
1
2
1
1
1
1
2
2
2
2
0
2
2
0
0
0
0
1
1
1
0
1
1
0
1
0
2
1
1
0
0
1
1
1
1
0
1
0
1
0
2
2
1
0
1
1
0
1
1
1
2
2
1
1
0
1
1
0
0
2
1
0
0
2
0
1
1
1
0
0
1
0
0
1
1
0
1
1
1
1
1
1
0
1
2
1
2
0
0
0
0
0
0
1
0
0
1
0
0
0
2
2
0
1
1
1
0
2
2
2
1
0
1
2
0
1
1
0
1
2
1
2
1
0
0
0
0
0
1
2
0
0
0
1
1
0
0
1
1
1
0
2
0
1
0
2
0
0
2
2
2
0
1
1
1
2
2
2
0
2
1
0
0
0
2
1
0
1
2
0
1
0
0
1
2
2
1
2
1
0
0
2
1
1
1
0
2
0
0
0
1
0
0
0
3
0
0
2
1
2
1
1
0
2
0
0
0
1
1
1
1
0
1
1
2
1
0
1
1
1
1
2
0
0
1
1
0
1
2
0
0
1
0
1
2
2
1
0
1
0
0
0
0
0
1
2
2
2
0
1
2
1
1
1
0
0
2
2
1
0
1
1
0
1
0
0
1
2
2
0
0
1
1
1
0
2
1
1
0
0
0
2
0
0
1
0
0
1
0
1
1
0
2
0
2
2
2
1
0
1
1
2
0
0
0
1
0
1
0
1
0
2
1
0
1
1
2
0
0
0
1
1
0
0
2
0
1
0
1
0
1
0
2
0
0
1
1
1
1
1
0
0
2
1
1
2
0
0
0
1
1
1
0
0
2
1
0
0
2
1
2
2
0
2
0
1
1
1
1
2
0
0
1
1
1
0
0
0
0
1
0
2
2
0
1
0
0
0
2
2
2
0
0
1
0
1
1
1
0
0
2
2
1
1
1
1
0
1
0
2
0
1
2
1
1
1
0
0
0
2
0
0
0
0
0
0
2
1
0
1
2
0
1
1
0
0
0
2
4
1
0
0
0
0
0
2
0
1
0
1
1
0
1
0
0
0
0
1
1
0
0
2
6
1
2
3
1
1
1
1
1
1
0
1
1
1
0
0
1
0
2
0
0
1
0
0
0
2
1
0
0
0
1
0
2
1
2
0
1
0
0
0
1
1
1
1
0
0
1
1
1
1
1
1
1
0
0
2
0
0
1
0
1
2
0
2
1
0
0
1
0
2
0
0
1
2
0
1
1
2
2
0
0
0
1
2
0
1
0
0
2
1
1
3
2
1
1
1
1
0
1
1
0
1
2
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
2
1
1
2
0
1
1
0
1
2
2
1
0
2
0
0
0
1
2
1
1
1
1
0
1
0
0
2
0
0
2
1
2
1
0
1
1
1
2
0
0
2
2
1
1
0
1
0
0
0
1
1
2
0
0
0
0
0
0
2
0
1
2
0
0
1
0
1
0
0
0
0
1
0
2
1
0
2
1
1
2
2
0
0
1
0
1
2
0
1
2
2
1
1
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
1
2
1
0
0
1
1
0
0
0
2
1
0
0
0
0
1
2
2
3
0
2
1
2
0
2
1
1
1
1
2
2
1
2
1
1
1
2
0
0
1
0
1
1
1
1
0
1
0
1
0
1
2
1
0
0
1
0
0
0
0
1
1
1
2
0
1
1
2
1
0
0
2
2
0
1
1
1
0
2
2
0
0
0
1
0
0
0
0
2
2
0
1
0
1
1
2
1
0
0
2
2
1
1
2
1
0
0
1
1
2
0
0
1
0
0
1
2
1
0
0
1
1
1
2
3
1
0
0
1
1
2
1
0
0
2
0
1
2
0
1
0
0
1
0
5
0
0
1
0
0
1
2
1
0
0
0
2
0
0
2
1
1
0
0
2
2
2
1
1
1
0
0
2
2
1
0
2
2
1
1
0
1
2
1
1
1
0
1
2
2
2
1
0
0
1
2
2
1
0
0
0
1
1
0
0
1
1
1
1
0
1
0
0
1
1
2
1
0
0
0
0
0
2
2
2
2
0
1
1
1
1
0
0
1
1
1
2
1
0
0
2
0
1
0
1
2
1
0
0
1
0
0
0
1
1
0
1
1
0
1
1
1
1
0
0
2
0
2
1
1
0
2
3
2
2
2
0
1
1
1
0
0
0
1
1
1
1
0
2
0
3
0
0
0
1
1
1
0
2
1
1
0
1
0
1
0
1
1
0
0
1
2
2
0
0
0
0
0
1
0
0
0
2
0
1
2
0
0
0
0
1
3
3
0
0
1
2
1
0
2
0
0
0
1
0
0
1
0
2
1
2
2
1
2
2
1
2
0
0
1
2
0
0
0
0
1
2
0
0
1
2
0
2
2
2
0
1
1
1
1
1
0
1
0
1
1
1
2
1
0
2
0
3
0
0
1
2
1
2
1
1
0
0
0
1
0
2
0
2
1
0
0
0
1
2
0
1
1
1
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
2
0
1
0
0
1
1
0
1
0
1
2
1
1
0
1
1
2
1
1
0
0
2
0
1
0
1
0
1
0
0
2
0
1
2
1
1
0
1
1
1
3
0
0
1
1
2
3
0
1
0
0
0
0
1
1
1
1
1
1
3
2
1
0
0
0
0
1
0
1
0
2
1
0
0
2
0
1
1
1
0
1
2
0
0
0
2
1
0
1
1
0
2
1
0
1
0
1
0
1
0
1
0
1
1
0
1
0
0
0
1
2
0
1
0
1
0
1
0
2
0
1
1
1
1
0
0
1
1
0
0
0
0
1
2
1
0
1
1
1
1
1
1
1
2
2
0
0
1
1
2
2
2
0
0
1
0
1
0
0
0
1
0
0
1
1
1
0
1
2
0
1
1
0
0
2
2
2
1
2
1
1
0
0
0
0
1
2
2
1
1
0
0
1
0
1
1
0
2
0
1
1
2
1
1
0
1
0
2
0
0
0
1
0
0
2
2
1
0
2
0
2
2
3
2
0
3
1
0
1
2
2
2
1
1
1
2
2
0
2
0
0
0
0
0
0
0
0
0
2
1
1
2
0
1
0
0
1
1
0
1
0
0
2
0
2
1
1
1
0
1
1
1
1
1
1
2
1
1
0
0
0
1
0
4
1
1
1
2
1
3
0
0
0
1
2
0
0
2
1
1
2
1
0
0
0
1
1
0
0
1
1
1
0
1
2
0
2
1
0
0
0
1
2
0
0
1
0
2
2
1
0
2
2
0
0
1
0
1
0
0
2
4
1
0
0
1
2
0
0
1
1
1
0
1
1
0
1
0
2
0
2
0
2
1
1
1
2
0
2
0
2
1
2
1
0
0
0
1
2
0
4
0
1
0
2
0
2
0
2
0
0
1
2
0
1
1
1
0
1
0
1
2
0
0
1
1
1
0
1
3
1
2
0
1
2
2
1
0
2
1
0
1
1
0
1
1
1
1
1
2
1
1
1
1
2
1
1
0
2
0
0
0
2
0
0
0
2
0
0
0
2
1
2
1
3
1
2
0
0
1
0
3
1
2
0
0
0
0
1
1
0
2
0
1
0
0
3
0
1
0
0
0
0
1
1
0
1
1
1
1
1
2
1
0
0
0
1
2
0
0
0
0
0
1
4
0
0
1
0
1
1
0
2
0
0
0
1
0
1
0
1
2
0
0
1
0
2
2
0
1
0
2
2
0
0
0
1
0
1
0
0
1
2
1
2
1
0
2
1
0
1
1
0
0
1
1
1
1
1
1
2
0
0
12
2
0
2
1
1
2
1
0
1
1
0
2
1
0
2
1
2
0
2
1
1
0
1
2
0
1
0
0
1
1
1
0
0
1
0
2
2
0
0
2
1
1
1
0
1
0
2
0
1
1
1
0
0
1
0
2
1
1
1
3
0
0
0
2
2
2
1
1
0
3
2
1
2
1
1
2
2
1
0
2
2
1
1
0
2
0
3
0
0
2
2
0
2
0
0
1
1
0
1
1
0
0
0
0
0
2
2
0
2
1
1
2
0
1
0
7
1
1
0
0
1
0
0
0
1
0
1
0
1
2
2
0
1
2
1
1
1
0
2
0
0
1
2
1
1
0
1
0
1
1
0
2
2
1
1
1
1
1
1
2
5
0
3
0
2
0
2
1
0
2
0
2
0
2
0
0
1
1
1
0
0
0
0
1
1
0
1
2
0
1
3
1
2
0
0
0
0
1
0
1
0
2
0
0
1
1
3
0
2
1
2
0
3
0
0
0
1
2
1
0
1
0
1
0
0
3
2
0
0
1
1
1
1
0
2
2
1
1
2
2
1
2
1
0
1
1
1
1
2
2
0
2
1
0
0
2
0
0
2
0
1
2
0
2
2
0
0
0
4
0
1
1
1
0
1
2
2
1
0
1
0
2
1
2
2
1
2
2
2
0
0
1
0
0
2
1
1
2
2
1
0
2
2
3
1
2
0
2
1
1
1
0
0
1
1
0
2
1
1
0
0
3
0
1
0
0
1
1
0
1
0
1
0
2
2
1
2
0
1
1
2
0
1
1
1
0
0
1
1
1
0
0
1
1
0
2
0
2
0
1
3
1
0
1
0
0
2
1
2
0
1
0
2
0
0
1
0
1
1
1
2
0
1
0
0
1
1
0
1
2
2
1
0
1
2
0
1
1
0
2
1
5
0
0
1
2
0
0
0
2
0
1
1
2
2
1
2
1
1
0
0
1
1
0
0
2
2
2
1
1
1
0
0
0
2
1
1
0
1
1
2
0
0
2
0
1
0
1
0
2
2
2
0
1
0
1
0
0
1
0
1
0
1
2
1
1
3
1
1
1
1
0
1
1
2
1
0
2
0
0
2
0
0
1
2
2
0
0
1
1
3
1
0
0
1
1
0
1
0
0
0
2
1
1
3
0
3
2
0
1
2
0
1
0
1
0
0
0
0
1
2
1
1
1
1
1
1
2
1
0
0
0
0
1
0
1
1
0
2
1
1
2
2
0
0
1
1
0
1
2
2
1
1
0
1
2
1
0
2
0
1
1
1
1
1
1
0
0
1
1
0
1
1
1
0
1
0
0
1
1
0
0
2
0
0
0
1
2
2
2
1
1
0
0
1
1
0
0
0
0
1
1
1
1
1
0
0
0
1
1
2
5
1
0
2
2
1
0
0
0
0
1
1
1
0
1
2
1
0
2
2
0
1
0
1
0
1
1
0
1
0
0
2
1
1
2
0
1
0
1
0
1
1
1
2
2
2
1
0
2
1
1
0
0
0
0
1
1
0
2
3
1
0
0
0
1
1
0
0
0
2
3
2
0
0
2
0
0
0
1
0
0
0
2
1
0
1
1
0
0
1
0
3
2
1
2
2
0
2
2
2
0
0
0
0
2
1
1
0
0
0
1
1
2
0
2
0
0
2
2
2
0
0
1
1
1
1
1
1
2
1
0
1
2
0
1
1
2
0
2
2
1
3
0
0
1
2
1
2
1
0
0
2
2
0
2
0
1
0
2
1
0
0
2
2
1
0
0
2
1
2
0
0
0
0
0
1
0
0
1
2
1
2
1
0
1
1
0
1
0
1
0
1
0
1
1
2
1
0
2
2
1
1
1
1
0
1
0
1
2
0
1
0
0
2
1
0
0
0
2
0
0
0
1
1
1
0
2
0
0
0
0
0
1
1
1
1
0
1
1
0
1
1
0
0
1
0
0
1
2
2
1
1
0
2
2
0
0
0
1
0
2
0
2
1
1
1
0
0
1
2
0
0
0
1
2
1
1
2
1
0
0
1
0
1
1
2
1
2
2
1
0
0
2
1
1
1
2
1
1
0
0
1
0
1
0
0
0
0
0
0
2
1
1
0
1
1
1
0
0
1
0
0
0
3
3
2
0
0
1
1
0
0
2
1
1
0
3
2
2
0
2
0
1
0
1
1
1
0
1
3
3
2
2
2
2
0
0
0
1
1
6
0
0
1
2
0
1
5
1
0
2
1
0
1
2
2
0
0
0
1
1
0
0
0
1
0
1
0
0
1
1
1
1
1
2
1
2
1
1
2
0
2
1
2
0
2
0
0
0
1
0
0
1
1
0
1
1
1
0
0
0
2
0
0
1
0
1
1
0
2
1
1
1
0
1
1
0
1
1
1
1
1
1
2
1
0
1
0
1
1
0
2
1
0
1
1
0
0
0
0
0
0
2
0
2
0
0
0
2
0
1
1
0
0
1
0
2
0
1
0
0
1
1
2
3
2
0
0
1
2
0
0
1
2
1
2
0
1
1
2
0
1
1
2
1
2
1
1
0
0
2
1
0
0
2
1
0
0
1
0
0
0
1
3
0
1
2
0
2
2
0
1
2
2
1
0
0
2
1
2
3
0
0
1
2
2
2
1
2
0
2
1
2
1
0
2
0
1
1
1
1
1
0
2
0
0
1
2
0
1
1
1
2
0
0
0
0
1
1
1
3
2
0
1
1
0
0
1
1
1
0
1
1
2
0
0
1
0
0
1
0
0
1
1
0
1
2
0
1
1
1
1
2
2
1
1
2
2
1
2
1
0
0
0
1
0
3
1
1
2
1
0
0
1
1
1
1
1
1
1
1
0
2
1
0
1
0
1
2
1
2
1
2
0
1
2
1
0
3
0
2
1
1
1
0
0
0
0
0
1
0
2
0
0
1
0
0
0
2
0
0
1
1
2
1
1
2
0
1
2
2
0
0
2
1
1
0
0
1
2
2
1
0
1
2
2
1
1
0
0
0
2
2
2
0
1
1
1
2
1
1
0
2
1
2
1
0
0
1
1
2
1
2
2
0
2
1
1
1
0
1
0
0
0
2
1
2
1
0
0
0
3
1
1
1
0
0
1
1
2
0
2
1
1
2
0
1
0
0
1
1
0
1
1
2
0
1
2
2
0
1
2
1
0
1
0
0
1
1
0
1
1
1
1
2
1
0
0
0
1
1
0
0
1
1
1
2
0
1
1
0
0
0
1
0
1
0
1
0
1
0
0
0
1
1
0
0
1
0
1
2
1
1
0
1
0
1
0
0
0
1
2
1
0
2
0
1
1
1
3
2
1
0
1
2
1
0
1
1
0
1
0
1
2
1
0
1
2
1
2
1
1
1
3
1
2
2
0
1
1
1
0
1
0
1
0
2
1
0
2
0
0
2
1
2
2
1
1
1
0
1
1
0
2
1
0
1
1
0
2
2
0
2
1
0
0
0
0
1
1
1
2
0
1
0
0
1
0
1
0
1
3
0
1
1
1
1
3
2
0
0
2
1
1
1
1
0
0
1
0
2
1
1
0
2
1
0
2
0
1
1
2
1
0
1
0
0
2
2
0
2
1
1
1
0
1
2
1
1
0
0
2
2
1
0
2
0
1
1
0
0
1
1
0
2
2
0
1
1
1
1
1
0
1
1
2
1
1
0
2
0
2
0
1
0
1
0
0
1
0
0
0
1
2
2
1
1
0
0
0
2
1
0
2
0
1
0
0
0
1
2
0
0
0
1
0
1
0
1
0
0
1
1
1
1
1
0
2
0
2
1
0
1
2
2
1
0
0
0
2
2
1
4
0
2
0
1
0
2
0
1
2
0
1
0
1
1
1
1
1
1
1
2
1
0
0
1
1
0
2
0
0
2
2
1
1
0
2
0
1
2
1
0
0
2
0
0
0
1
1
1
1
1
1
2
1
0
1
0
1
0
1
0
1
0
0
1
1
0
0
2
0
1
2
1
1
2
2
0
2
2
2
0
1
1
0
1
2
1
0
0
0
2
1
1
1
1
2
1
1
0
1
0
4
0
1
0
1
2
1
1
1
1
0
2
1
1
2
0
1
2
2
1
1
0
0
0
0
1
0
2
0
1
0
1
1
2
2
0
0
2
3
0
0
0
1
1
2
0
0
2
0
1
1
1
3
1
1
1
1
0
2
0
1
1
0
2
1
1
2
1
0
1
1
1
2
0
1
1
0
1
1
4
1
0
1
2
0
2
0
2
1
2
0
0
2
0
3
1
0
1
2
0
1
1
1
2
0
0
2
2
2
2
0
1
1
1
0
0
1
2
0
0
0
1
0
0
1
1
0
0
0
1
0
1
0
0
1
2
1
3
1
0
4
0
2
0
0
1
0
1
0
3
2
1
0
1
1
0
1
2
1
1
0
1
0
2
0
0
1
0
0
2
1
0
0
2
1
2
2
0
2
0
1
0
2
2
2
0
0
0
0
2
0
1
2
0
1
0
1
0
1
2
2
0
0
1
1
0
0
1
2
0
1
2
1
2
0
0
0
0
1
2
2
0
1
0
0
0
0
1
0
1
0
0
0
1
2
0
1
0
2
0
2
1
1
0
0
2
0
2
0
0
0
1
2
1
1
1
0
1
2
1
0
2
1
1
0
2
2
0
1
0
1
2
2
1
0
1
1
1
1
2
1
2
0
0
1
1
0
1
0
2
2
0
0
0
1
0
1
0
2
0
0
1
0
1
2
0
1
1
0
2
1
1
1
0
0
0
0
1
2
1
2
0
1
1
0
2
0
2
1
1
1
0
0
0
1
1
1
1
2
1
0
1
0
0
1
1
2
1
0
2
0
1
1
0
2
2
1
1
1
1
2
2
1
0
2
2
1
1
2
2
0
1
0
0
2
2
2
1
1
0
2
0
2
0
0
0
0
0
0
0
2
1
1
0
2
1
0
1
0
0
1
0
0
0
0
1
0
2
2
2
1
1
1
1
1
0
1
1
2
2
2
0
2
2
1
0
2
1
2
1
1
0
0
0
0
2
1
2
0
2
3
2
0
2
1
0
1
0
0
2
0
2
1
2
2
2
0
0
1
0
1
0
0
0
2
0
0
0
1
1
0
1
0
1
1
1
0
1
2
0
0
1
4
2
0
0
1
1
1
0
0
0
1
1
1
1
1
1
0
1
1
1
4
2
2
3
0
0
1
0
2
0
1
1
0
1
1
1
1
0
2
0
0
0
0
0
0
0
1
2
1
0
1
1
1
0
1
2
3
0
2
1
1
0
2
0
2
0
1
0
2
2
1
0
0
1
5
0
0
1
0
0
3
0
0
0
2
1
1
0
0
0
2
6
0
0
3
2
0
0
0
2
0
0
0
0
0
0
1
0
1
0
1
1
0
1
0
0
0
0
0
1
2
1
0
1
1
1
0
1
2
2
0
0
2
0
2
0
2
1
2
2
1
1
1
1
1
0
1
1
0
1
1
2
1
0
0
1
0
2
1
2
1
0
1
1
1
1
2
1
1
0
0
0
0
1
1
2
0
1
0
0
1
1
0
0
0
1
2
1
1
1
0
2
1
1
1
1
0
1
0
1
0
1
0
1
0
0
1
1
3
2
2
1
1
1
1
2
1
1
0
0
0
0
2
1
1
0
2
2
3
0
2
0
0
2
0
0
0
1
1
1
2
0
1
0
1
2
0
1
1
1
1
0
1
1
0
1
0
1
2
0
0
0
0
0
0
0
1
2
0
1
1
2
2
0
0
1
1
3
2
2
0
0
0
0
2
0
0
1
1
0
1
0
0
0
2
0
0
1
2
2
1
0
1
1
1
0
1
1
2
0
1
0
2
2
2
2
1
2
1
1
2
0
2
0
2
0
0
2
0
1
0
0
2
0
0
0
2
0
1
0
0
2
0
0
1
1
2
0
2
1
0
1
2
0
2
2
0
0
2
0
1
1
2
0
1
0
1
0
1
2
1
2
1
0
2
1
2
0
2
1
1
1
0
0
3
0
2
1
1
0
0
1
0
1
1
2
0
0
1
2
0
2
2
2
2
0
0
1
0
2
2
0
0
2
1
2
2
1
2
1
1
1
0
0
1
1
0
0
1
3
0
1
0
1
0
1
0
0
1
0
1
0
0
2
0
0
1
0
1
1
2
0
0
1
2
1
1
2
2
0
1
2
2
0
1
0
0
0
1
0
0
1
1
2
0
2
1
0
0
1
0
2
0
0
1
1
0
2
2
0
1
2
0
0
0
1
1
1
0
0
1
0
1
1
0
0
2
2
0
1
2
0
1
0
1
0
1
0
0
0
1
0
1
1
2
1
3
1
1
0
0
2
0
0
1
0
0
1
2
0
0
1
1
0
0
2
1
1
2
0
1
1
0
2
0
1
2
1
1
1
2
2
2
0
2
0
0
0
0
0
0
2
0
0
0
1
2
1
1
1
2
1
1
1
1
1
0
0
1
1
2
1
2
1
2
0
1
0
0
1
1
2
0
2
2
0
2
0
0
1
0
2
1
2
0
1
1
0
0
1
1
1
1
0
1
1
0
0
0
0
0
1
1
1
0
0
1
2
2
0
0
0
0
1
0
1
2
1
0
1
1
0
1
0
1
1
0
0
1
1
1
1
0
0
1
2
0
2
0
0
1
1
2
1
1
0
0
2
0
0
0
1
1
2
2
1
1
1
0
1
1
1
1
2
1
2
0
1
1
0
1
0
1
1
0
2
0
1
1
1
0
1
1
2
0
3
0
1
1
2
0
1
2
0
0
0
0
0
0
1
1
1
1
1
1
0
0
1
0
0
1
0
0
1
0
2
0
1
1
0
1
1
3
1
1
1
1
1
0
0
2
0
1
0
0
0
0
2
0
0
2
0
1
1
1
1
0
0
2
3
0
0
1
2
1
1
0
2
1
0
2
2
0
2
0
1
1
2
1
0
0
2
1
0
0
0
1
0
2
1
0
2
1
1
1
2
2
3
1
0
1
2
1
1
1
1
0
0
2
2
0
0
1
0
0
1
0
0
0
0
0
2
1
0
1
2
0
1
0
1
1
0
0
1
1
2
0
2
1
2
0
2
0
1
0
0
1
1
0
1
0
2
2
0
1
0
1
0
0
0
0
0
1
0
1
0
1
1
0
0
2
1
2
1
0
2
2
2
0
0
0
2
1
2
1
2
0
2
0
0
2
2
0
2
0
1
1
1
2
1
0
0
2
0
0
1
1
1
0
0
1
2
2
2
0
0
0
1
1
0
0
1
0
0
2
1
1
2
0
0
1
2
1
3
2
1
1
2
1
0
2
1
0
0
0
2
1
2
1
0
2
1
0
0
1
2
0
0
1
2
0
0
2
1
1
0
0
0
2
1
1
0
2
0
0
1
1
1
2
2
1
0
2
0
1
1
1
0
1
0
2
1
1
1
1
2
2
0
1
0
1
1
2
0
0
0
1
0
0
2
1
1
2
0
0
0
0
0
0
2
1
0
2
2
0
1
1
2
2
0
0
2
0
2
0
0
1
0
2
0
0
0
2
0
0
0
2
1
1
0
0
0
1
0
2
1
2
0
0
2
2
1
0
0
2
2
1
0
0
1
0
1
2
9
1
1
0
1
0
1
1
1
2
0
1
2
1
2
0
2
2
1
0
0
2
2
1
2
0
0
2
0
2
1
0
1
1
1
3
2
0
0
1
0
1
2
1
2
0
2
2
2
2
1
1
0
1
3
2
1
1
1
1
1
1
1
2
0
1
0
0
0
0
0
2
2
0
2
0
0
2
0
1
0
2
2
0
1
1
0
0
1
2
1
0
0
1
2
0
0
1
2
0
2
0
0
1
0
0
0
1
0
0
0
1
1
1
1
1
0
2
0
2
1
1
2
1
1
0
0
1
0
2
0
0
1
0
0
1
0
0
0
2
1
0
1
0
1
0
0
1
0
0
0
1
1
2
0
0
2
0
0
0
0
1
0
1
1
2
0
2
1
2
0
0
1
0
2
2
2
1
2
0
1
2
0
1
0
2
0
4
0
2
1
2
0
0
1
1
0
1
0
1
0
0
0
2
0
1
2
1
0
1
1
2
0
1
1
0
0
0
1
1
0
1
2
0
0
1
0
2
0
0
0
0
0
1
0
0
2
0
0
1
1
0
0
1
0
0
2
0
1
1
1
2
1
1
0
0
1
0
1
0
0
0
1
0
1
2
2
1
0
1
1
0
0
2
1
2
0
0
1
0
0
1
1
2
0
0
1
1
1
1
0
1
2
2
0
0
1
1
0
0
1
1
0
0
0
0
0
2
2
0
0
2
5
1
2
0
2
2
0
0
0
0
2
0
1
1
1
2
0
0
0
0
0
1
2
0
1
1
1
0
1
2
1
0
0
0
1
2
1
2
1
2
1
2
0
3
1
0
2
2
1
0
0
0
2
0
0
1
1
2
1
1
1
2
1
0
1
0
1
0
2
0
0
1
0
0
0
0
1
0
2
0
1
2
0
0
0
1
0
0
0
0
1
2
0
1
0
0
1
1
2
1
1
1
0
2
0
1
2
0
1
2
0
0
0
1
0
0
2
1
0
0
0
0
2
0
1
1
2
1
2
1
1
0
0
0
1
1
0
2
1
0
2
0
1
2
1
2
2
0
0
2
1
1
1
0
0
2
1
1
0
2
0
0
1
0
2
0
1
0
1
0
1
0
0
0
2
0
2
0
0
0
0
1
0
1
0
0
1
2
1
2
0
0
0
1
2
1
0
0
1
0
2
0
0
1
2
0
1
2
0
1
2
0
0
0
1
0
0
1
1
0
1
1
0
0
0
0
1
1
1
2
2
1
0
1
0
2
0
2
0
1
0
0
2
2
2
0
0
1
0
0
2
0
0
2
1
1
0
0
1
1
2
1
0
0
0
0
1
2
2
0
0
0
0
2
1
1
2
2
1
0
2
1
0
2
2
0
0
0
2
2
1
1
0
1
2
1
2
0
1
1
2
2
1
0
3
1
2
1
1
2
1
1
0
1
0
1
2
4
0
2
1
0
0
1
1
0
0
1
0
1
1
1
0
2
1
2
2
0
0
0
1
2
1
2
2
0
0
0
2
0
0
0
1
0
1
0
0
2
2
0
1
1
1
2
1
1
2
0
1
2
1
2
1
1
1
0
1
1
0
0
1
1
1
0
1
1
2
2
3
0
2
0
3
2
1
0
0
1
2
0
0
2
0
0
0
1
0
0
1
0
0
0
2
0
2
0
2
2
0
0
1
0
0
0
1
0
0
0
1
2
2
0
1
1
1
0
0
2
4
1
0
1
0
0
2
1
0
0
0
0
0
0
2
1
2
0
0
1
1
1
1
0
1
2
1
2
2
0
0
1
0
1
0
1
0
2
2
2
1
0
1
0
0
0
1
2
0
1
0
1
1
1
0
1
0
0
1
1
2
0
1
0
2
1
2
0
1
1
1
0
1
0
0
0
2
0
2
0
1
1
0
2
2
1
1
1
0
2
2
2
1
2
0
2
2
0
0
0
2
0
2
3
2
0
0
0
1
1
1
1
1
0
1
0
0
0
1
1
0
0
1
0
1
0
0
1
1
2
0
1
0
2
0
0
1
0
1
2
1
3
2
0
0
1
1
0
2
1
1
2
1
2
0
1
0
0
2
0
3
0
0
0
1
0
1
0
0
1
5
0
0
1
0
2
1
0
2
0
1
0
1
2
0
1
2
1
1
1
1
1
2
2
0
1
0
1
0
0
2
0
1
0
1
2
1
0
1
1
0
2
1
0
0
2
1
1
0
0
0
1
0
1
1
1
0
2
0
1
1
1
0
1
1
1
1
2
2
1
0
2
0
0
0
1
0
1
0
2
2
0
1
2
0
2
1
1
0
0
1
0
2
0
2
1
0
1
1
1
1
2
1
1
1
1
0
0
0
0
1
0
1
1
1
2
1
0
1
1
1
3
1
1
2
2
1
2
1
1
2
0
1
0
1
1
1
1
2
1
0
1
1
0
0
1
1
1
0
0
1
1
0
2
0
2
1
2
0
0
2
0
1
1
0
2
0
0
1
2
1
2
1
2
0
1
1
0
1
0
1
1
1
0
0
1
0
2
0
0
2
1
2
1
1
2
1
0
1
0
1
0
1
2
1
1
0
0
2
0
2
0
0
1
0
2
2
0
2
0
1
2
0
0
2
2
1
2
3
0
1
1
0
0
0
0
1
1
0
2
2
1
1
1
1
2
1
1
0
2
0
0
1
2
1
0
0
0
1
2
1
0
0
1
1
2
0
1
0
0
0
2
1
0
1
1
1
2
0
1
0
1
0
2
0
2
1
1
1
0
1
2
3
2
2
1
0
0
1
0
3
2
0
1
0
0
0
2
0
1
2
1
1
2
2
1
1
0
2
0
0
1
2
0
0
2
1
2
1
0
0
0
2
0
2
1
1
1
1
1
0
0
0
0
1
1
2
0
2
2
1
0
1
1
0
0
0
1
0
0
1
1
0
0
2
1
1
0
0
3
0
0
0
0
0
2
0
0
1
1
3
0
1
0
1
1
0
1
1
0
2
2
1
0
0
0
0
0
2
1
1
1
0
1
0
0
1
1
1
3
0
0
2
2
1
1
1
0
1
1
2
1
0
0
2
1
2
1
1
1
0
1
1
2
0
1
0
1
0
1
0
0
1
1
0
1
0
1
0
1
1
0
0
0
1
2
0
0
0
1
0
2
0
1
0
0
1
0
2
0
2
2
1
2
2
0
1
2
1
0
0
1
1
0
0
2
1
2
0
1
2
0
2
1
0
0
2
0
1
0
1
1
1
1
0
0
0
0
1
0
1
1
0
1
0
1
0
0
2
2
0
2
2
0
1
2
0
1
0
1
1
1
0
0
2
0
1
1
0
0
1
2
0
2
2
0
0
0
1
1
0
1
2
2
0
0
0
1
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
1
1
2
0
1
2
1
1
1
2
1
0
0
0
0
0
1
1
0
2
2
0
1
0
0
2
2
3
0
0
2
0
0
2
0
1
0
1
0
0
1
2
3
0
0
0
2
0
0
1
0
1
2
1
0
0
0
1
2
2
0
0
0
1
2
2
0
2
1
2
0
1
2
1
0
3
2
0
1
0
2
2
2
2
0
1
1
0
2
0
2
2
1
1
0
1
2
2
1
1
1
0
0
0
0
0
0
1
1
2
0
2
1
1
1
1
0
0
0
0
1
0
2
0
0
2
0
1
1
1
2
1
1
0
1
0
0
1
1
1
1
1
1
1
1
2
0
0
2
2
1
2
0
1
1
2
3
1
1
1
1
0
0
0
1
1
1
2
0
2
0
0
1
0
0
0
1
1
3
1
1
1
0
1
0
1
0
2
0
2
0
0
2
2
2
0
1
1
0
1
2
0
0
0
0
1
0
0
1
0
0
5
0
1
0
0
0
1
2
2
1
0
0
0
0
1
0
1
2
1
1
1
1
1
0
1
0
0
0
0
1
0
1
0
2
0
2
0
2
1
1
1
2
0
1
1
1
0
1
2
1
1
0
1
2
1
1
1
1
1
2
3
2
3
0
0
1
1
1
1
0
1
0
2
0
1
2
1
0
1
0
0
3
0
2
0
1
0
1
0
1
1
0
1
1
0
0
1
0
0
2
1
0
1
1
0
1
0
1
1
1
1
1
1
0
1
0
1
2
0
1
0
2
2
1
0
0
2
1
1
0
2
1
0
1
0
2
2
1
1
1
0
0
1
1
0
2
0
3
0
0
0
1
1
2
0
0
0
1
0
1
1
1
0
2
1
2
0
0
0
1
0
1
1
1
0
0
0
1
1
1
0
1
0
2
0
2
2
1
1
2
0
1
1
1
1
0
0
1
0
1
0
0
1
1
1
0
2
0
1
2
0
0
1
1
2
1
0
5
1
1
0
1
1
0
0
0
1
2
0
0
1
1
0
0
0
1
1
1
1
0
2
0
2
1
0
1
2
2
1
1
0
1
2
0
1
2
1
1
0
1
0
0
0
0
1
1
1
0
0
1
0
0
0
0
1
0
0
0
2
1
1
0
0
2
1
0
1
0
1
1
1
2
0
0
1
0
0
0
1
1
2
0
2
2
2
0
1
0
1
1
1
0
1
0
1
2
1
1
1
0
1
0
0
0
1
1
2
1
0
0
1
2
0
1
1
0
1
0
2
0
0
0
2
1
1
0
1
2
0
1
2
1
0
1
0
1
1
0
2
0
2
2
1
1
0
0
1
2
0
0
0
0
2
0
1
1
0
2
1
2
1
0
0
2
0
2
1
2
0
1
0
0
0
1
0
2
1
1
1
1
1
0
2
1
0
0
1
0
0
0
1
0
1
0
1
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
2
1
2
1
1
1
1
1
0
0
1
0
2
2
0
1
0
1
3
1
0
2
0
1
1
2
0
1
0
2
0
1
2
1
3
2
3
0
1
1
2
0
2
2
2
1
2
2
1
1
1
0
1
0
1
1
2
2
0
1
0
1
0
1
2
1
0
1
1
1
0
0
1
1
1
0
2
1
0
2
1
0
0
1
2
0
0
2
0
2
0
0
1
1
1
1
1
0
0
1
2
1
0
2
1
1
1
3
2
2
1
2
2
0
1
2
0
0
2
2
0
1
1
0
2
0
1
0
1
0
0
2
1
0
2
0
0
1
0
0
0
0
2
0
0
1
2
0
1
0
2
2
1
1
1
1
0
0
0
2
1
0
1
1
78
2
0
0
1
1
0
0
2
2
0
1
0
1
1
0
0
1
0
2
0
2
0
1
0
0
0
0
0
0
1
1
1
1
1
0
0
1
0
1
0
0
0
0
0
1
0
1
1
2
0
0
0
1
1
0
2
0
1
1
1
1
0
0
1
2
0
0
1
1
2
0
1
0
0
0
2
1
2
0
1
0
1
1
1
1
0
1
1
1
1
1
2
1
1
0
0
5
3
1
1
0
1
1
1
0
0
0
2
0
2
4
2
1
0
0
0
1
1
0
2
0
2
1
0
2
0
1
0
0
2
1
0
0
0
1
1
0
0
2
0
0
0
2
2
0
0
1
0
1
2
0
0
0
0
1
1
1
0
1
0
2
1
1
1
1
1
0
2
1
2
0
1
0
1
1
0
0
0
1
0
1
1
0
0
1
1
0
2
0
0
0
2
1
3
0
1
2
2
0
0
1
1
0
0
0
2
2
1
0
0
0
0
1
1
0
1
1
2
1
1
1
1
0
0
1
2
1
0
1
0
2
0
2
2
1
1
0
0
1
0
1
2
1
0
2
0
2
2
1
1
0
1
0
0
1
1
0
1
2
0
1
0
1
1
2
2
1
1
1
0
1
2
1
1
1
2
0
1
1
2
0
0
2
0
0
1
1
0
2
0
0
2
0
0
1
1
0
1
0
1
0
0
1
1
1
2
0
0
2
2
0
0
1
1
1
2
1
1
2
2
1
0
0
0
1
3
0
1
1
2
0
0
1
1
2
1
0
1
0
1
2
0
1
1
2
1
1
0
0
1
2
2
2
0
2
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
1
0
3
1
0
1
1
0
2
0
0
1
2
0
1
1
0
1
1
1
0
2
1
0
0
1
1
1
2
1
1
1
1
1
0
0
2
0
1
1
1
1
0
1
0
1
2
1
0
1
0
0
1
0
2
0
1
1
1
2
0
0
0
1
0
0
0
1
1
1
2
2
1
1
1
0
0
0
2
2
0
2
0
0
1
2
1
1
1
1
2
1
1
0
0
2
2
2
2
1
1
0
1
2
0
2
0
1
2
1
2
1
1
1
1
0
1
1
1
1
0
1
2
2
1
0
0
0
1
0
2
1
2
2
0
0
0
0
0
0
1
1
1
2
2
0
2
1
1
1
1
0
1
2
0
1
0
2
1
1
0
0
0
1
1
1
2
1
2
1
0
1
1
3
0
0
0
0
0
1
1
0
2
0
2
3
1
0
1
2
0
0
2
0
0
1
0
0
0
0
2
1
2
0
2
2
0
0
1
1
0
2
0
0
2
1
0
1
1
2
1
0
1
0
0
0
1
1
0
1
2
2
0
3
1
1
0
1
0
0
1
0
2
0
0
0
1
1
1
1
0
0
1
1
1
0
1
1
0
0
1
2
0
1
1
0
1
2
0
1
0
0
1
0
1
0
0
2
0
0
2
2
0
0
2
0
1
0
0
0
0
0
3
1
0
2
2
1
1
1
2
1
1
1
0
1
0
2
2
1
0
1
1
3
2
1
0
2
1
1
2
1
0
0
2
1
0
1
1
0
1
0
0
0
0
3
1
2
1
0
3
0
1
0
0
2
2
0
1
1
2
1
1
0
1
2
1
1
2
2
1
0
0
0
1
1
1
1
0
0
0
1
0
0
2
0
1
3
1
0
1
0
0
0
2
1
0
2
0
1
0
1
1
0
0
1
1
1
2
1
0
1
2
1
2
2
1
0
2
1
1
1
0
1
1
0
0
2
0
0
1
1
1
1
1
2
2
0
2
2
0
1
0
0
2
3
0
0
1
1
2
1
1
2
1
0
1
2
0
1
0
1
0
0
0
1
1
0
1
0
2
1
1
0
1
0
0
1
2
0
2
0
0
0
0
3
1
0
2
0
1
0
0
2
0
0
1
0
0
0
1
0
0
0
2
1
1
2
0
1
0
0
2
0
1
1
2
3
1
0
0
1
1
0
3
2
1
0
1
1
2
0
1
2
0
3
0
0
0
0
0
0
2
2
2
1
0
0
2
1
1
1
0
0
2
1
0
0
0
0
1
0
0
1
0
0
1
2
1
1
0
1
1
1
1
0
0
2
2
0
0
2
0
1
0
0
0
1
1
2
0
1
0
0
0
0
1
0
0
2
2
1
2
0
1
1
2
0
0
0
1
1
0
1
1
0
2
2
0
0
0
1
0
1
0
0
1
0
1
0
1
0
1
1
2
1
1
0
0
2
1
2
1
1
0
2
1
2
2
1
1
0
1
1
2
1
0
0
0
1
1
1
0
0
0
0
2
2
0
1
2
0
1
2
0
0
1
0
1
2
0
0
1
0
1
0
1
1
1
2
1
1
0
1
0
1
0
4
1
1
1
1
1
0
1
0
2
2
0
0
1
1
0
3
1
1
0
1
0
0
1
1
1
1
2
1
0
1
1
2
0
2
1
1
1
1
0
2
0
1
0
0
2
0
1
1
2
2
1
0
0
2
0
1
0
1
0
0
0
2
0
1
2
0
0
2
2
1
2
0
1
0
1
0
0
1
0
1
0
0
2
1
1
0
0
3
1
0
1
2
1
0
1
0
1
0
2
1
2
2
0
0
0
0
0
0
1
0
0
2
0
2
2
1
1
0
1
0
1
1
0
0
1
2
1
0
1
2
1
1
0
1
1
2
0
0
2
2
0
2
1
2
0
0
0
2
1
1
1
1
2
0
1
1
2
1
0
2
0
1
0
0
1
1
1
1
0
0
0
1
1
2
0
0
1
2
3
0
2
0
1
1
0
0
0
1
2
0
0
1
0
1
2
1
2
2
1
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
1
3
2
1
0
1
2
0
0
0
2
2
3
2
1
1
0
1
1
0
0
3
0
1
2
0
1
0
0
1
1
1
2
0
4
1
0
1
2
1
1
1
1
1
2
1
2
0
0
0
1
0
0
2
1
1
0
0
0
1
0
1
0
0
1
1
1
2
1
0
1
2
2
0
1
1
2
0
1
2
3
2
1
1
1
0
1
1
0
0
0
2
0
0
1
1
2
1
1
2
0
2
1
1
0
0
0
0
0
1
0
0
2
0
1
2
1
0
1
0
0
2
0
0
0
2
0
1
1
1
0
0
1
0
1
2
1
1
1
0
1
0
0
0
1
2
1
1
0
0
0
0
1
1
2
2
1
1
1
0
0
1
5
0
1
1
0
0
1
0
1
3
1
1
2
0
1
2
2
0
1
0
0
1
1
1
2
0
0
2
0
0
0
1
0
2
1
0
3
0
1
1
0
0
1
0
2
1
2
1
0
2
0
2
0
1
0
3
0
1
0
1
1
0
2
0
1
1
1
2
0
0
1
0
0
0
2
2
0
4
0
2
2
1
0
2
0
0
1
0
1
1
0
2
0
0
0
0
2
0
0
3
0
0
0
1
0
2
1
2
0
1
1
0
0
2
0
2
1
1
0
2
3
2
0
2
1
1
0
1
1
0
0
1
1
0
1
1
1
2
2
0
0
0
0
0
0
1
0
0
0
1
0
2
2
0
1
2
2
0
2
1
2
0
1
0
0
0
1
0
0
1
0
1
1
0
1
0
2
0
2
0
3
1
0
2
1
1
0
2
0
1
0
1
0
1
0
1
1
2
0
2
0
0
4
0
1
2
0
1
1
1
2
0
1
1
1
0
0
1
2
1
1
1
1
1
1
0
2
1
0
1
1
1
1
0
2
0
0
2
2
2
0
2
1
1
0
0
2
0
1
2
1
2
1
0
1
0
0
1
1
0
2
2
1
1
2
0
0
1
2
2
1
1
0
0
2
0
2
0
2
0
2
0
2
0
1
0
1
2
2
0
1
1
0
2
2
0
2
0
1
0
1
1
0
1
0
1
0
0
2
2
1
1
0
2
0
0
1
1
1
1
0
2
2
2
0
1
0
0
0
0
2
1
1
2
1
0
2
0
1
0
0
2
0
3
0
2
0
1
1
1
2
1
0
2
1
0
1
0
1
1
0
0
0
0
1
2
0
1
1
1
1
1
1
2
1
0
1
0
0
2
1
1
0
2
0
2
1
0
0
0
0
1
1
1
0
0
1
1
1
0
0
1
0
0
1
0
0
2
2
1
1
1
0
2
1
2
1
1
0
1
0
2
2
0
1
0
1
2
1
2
2
0
2
1
0
1
1
0
3
2
1
0
1
0
1
0
0
0
0
1
1
1
2
0
3
1
0
1
0
1
0
0
0
2
2
2
0
0
1
0
0
1
0
1
1
0
2
0
1
0
1
0
0
2
1
0
0
0
1
0
0
1
0
2
0
0
0
0
1
2
0
2
1
1
1
1
0
1
0
0
0
0
1
1
1
1
2
1
0
2
0
1
1
0
1
0
0
2
0
0
0
1
0
0
0
0
0
1
1
0
2
2
1
1
0
2
0
0
1
0
2
0
1
1
0
1
2
2
2
0
0
2
1
1
1
0
0
0
2
0
1
0
0
2
0
2
1
0
1
2
2
1
0
1
3
0
0
1
1
2
0
1
2
1
2
1
1
2
0
2
1
1
0
2
2
5
0
0
0
1
2
0
2
0
1
1
1
1
1
0
0
1
2
0
0
1
1
0
1
0
1
0
0
0
0
2
1
1
0
0
6
1
0
0
1
2
1
1
0
0
1
1
1
2
0
0
2
0
0
2
1
1
1
0
0
2
2
0
1
2
1
0
3
3
1
0
1
1
0
2
0
0
1
1
0
0
0
2
0
1
1
0
1
1
0
2
1
1
0
1
1
1
1
0
2
0
0
0
1
1
0
0
1
0
2
1
0
0
1
0
0
1
0
0
0
1
1
1
0
0
1
0
0
2
1
3
1
0
2
1
0
2
0
0
0
0
2
0
0
1
1
1
1
2
1
0
1
0
1
0
0
0
1
0
2
1
1
1
0
0
1
2
0
0
1
0
1
0
0
0
1
2
2
0
0
2
2
0
0
0
0
2
0
3
0
2
1
0
1
2
0
1
1
0
1
0
0
1
1
2
0
0
0
1
2
0
1
1
0
1
1
0
2
1
0
1
1
1
1
0
0
0
0
1
1
0
0
0
0
2
1
0
2
1
1
0
1
0
0
1
0
1
1
1
1
1
1
1
1
2
0
0
1
1
0
2
1
0
0
0
1
1
1
1
0
4
1
1
0
1
0
2
1
0
0
2
1
0
1
0
2
1
1
1
0
0
0
0
0
0
0
1
1
0
2
0
2
0
0
0
2
1
0
2
1
0
1
1
0
0
2
0
0
2
1
2
1
0
2
0
0
0
2
0
1
2
1
0
2
1
1
0
2
1
0
0
2
1
0
0
0
2
1
1
2
0
0
1
2
0
0
0
0
0
1
0
1
0
1
0
1
0
0
2
2
1
1
2
2
2
1
1
1
1
1
0
1
1
2
1
0
0
1
1
1
1
2
1
0
0
3
0
1
2
0
1
0
1
3
0
1
2
0
0
0
1
0
2
1
1
0
2
1
0
0
2
1
1
1
2
2
2
1
0
2
0
2
1
0
2
2
2
1
1
0
0
2
0
0
2
3
2
1
1
2
0
1
1
1
2
0
0
0
1
2
0
2
1
1
1
0
1
2
2
1
1
1
2
0
0
0
2
0
1
1
1
1
1
0
2
0
1
0
1
1
1
1
1
0
0
2
2
2
1
0
0
0
0
0
2
1
1
0
0
1
1
2
0
1
2
0
0
1
0
1
1
2
1
1
1
1
1
1
0
1
2
2
2
0
1
2
2
0
0
0
1
2
1
2
2
1
1
1
0
1
2
1
2
0
1
1
1
2
2
2
3
1
2
2
0
0
0
0
3
0
0
1
1
2
2
1
0
2
0
1
2
1
0
1
1
1
2
2
0
1
0
1
1
0
4
1
1
0
0
1
1
0
1
0
2
0
1
0
1
1
1
2
1
0
0
1
0
0
2
1
0
2
0
0
0
0
2
1
0
1
0
0
0
4
3
1
1
1
4
2
0
1
0
0
1
2
1
0
1
1
1
1
1
0
1
1
1
2
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
2
0
1
0
2
0
0
1
0
2
1
1
0
1
1
1
0
0
0
0
0
2
0
0
3
1
0
0
0
1
1
1
1
0
0
0
1
0
0
2
1
0
0
2
1
1
0
0
1
1
2
0
1
2
2
2
1
1
1
1
0
0
0
2
1
1
1
2
0
2
2
1
2
2
2
1
1
2
2
1
0
2
1
0
1
1
1
2
1
0
2
2
0
1
0
1
1
1
2
2
1
0
1
2
0
1
0
0
0
1
2
0
1
0
0
0
0
0
2
0
0
1
1
2
1
0
0
3
0
1
1
0
0
0
1
1
0
0
1
2
1
0
1
2
2
1
0
1
1
1
0
2
1
0
0
1
0
0
2
2
1
0
1
0
0
2
1
2
2
0
1
0
1
0
1
2
0
1
0
0
1
0
0
2
3
0
1
0
1
0
2
0
1
0
2
2
0
2
0
0
0
2
0
0
1
0
2
1
1
2
0
1
0
1
6
1
3
0
2
2
1
1
0
1
0
1
0
0
0
1
2
0
0
0
2
1
2
2
2
1
1
0
1
1
1
0
1
2
2
1
1
0
2
2
2
2
0
0
0
0
1
2
1
1
0
1
0
1
1
0
0
0
1
2
0
1
1
0
1
0
2
2
1
0
0
0
1
0
1
0
1
0
2
0
2
2
0
3
2
1
0
2
1
1
1
0
0
0
1
0
1
1
1
2
0
0
1
2
1
0
2
2
0
2
1
1
4
0
1
0
1
1
0
2
0
0
0
1
0
1
1
1
0
2
2
0
0
1
0
2
0
2
0
2
1
0
0
2
2
1
0
1
1
1
1
0
2
1
0
0
2
1
1
1
0
1
1
1
0
2
0
1
1
2
0
2
2
0
1
2
0
0
1
0
1
0
0
0
2
0
1
1
1
1
1
1
0
1
1
2
0
0
1
1
1
1
0
1
0
1
0
2
1
1
1
0
1
0
0
0
2
1
1
1
0
0
2
1
0
0
1
2
1
0
1
1
0
0
2
1
0
0
2
0
3
0
0
1
2
0
0
1
2
0
0
0
1
0
2
0
2
1
1
1
0
1
0
0
1
1
2
2
1
1
0
1
2
2
2
1
0
0
1
0
1
0
1
0
2
1
1
0
2
2
1
0
1
2
1
2
0
0
1
1
2
1
1
2
1
0
1
2
2
0
0
2
0
0
1
1
0
0
0
0
2
3
2
1
0
1
0
2
1
2
1
0
1
1
1
0
3
0
0
2
1
0
0
2
0
2
0
1
0
0
0
0
0
0
2
0
1
0
3
0
0
2
3
2
0
0
0
0
0
1
2
2
1
0
0
2
0
0
0
0
0
0
2
1
2
1
1
1
0
1
4
2
1
2
0
0
0
0
1
1
0
2
1
1
0
2
0
0
2
0
0
1
1
0
2
0
1
0
2
1
1
1
2
1
0
1
1
2
0
1
1
2
2
0
0
3
1
0
2
1
2
2
2
0
1
0
0
1
2
3
1
0
0
2
0
1
2
1
1
0
2
0
1
2
0
2
2
0
2
0
2
1
0
0
0
0
1
0
2
0
0
1
1
0
0
0
0
1
2
2
1
1
1
0
0
1
0
0
0
0
0
0
0
1
1
1
1
2
0
2
3
0
0
1
0
0
2
1
0
1
1
0
2
2
1
1
0
2
1
1
1
0
2
0
0
1
0
2
1
1
2
0
1
1
2
2
1
2
4
1
1
0
0
0
0
0
1
1
1
0
2
3
0
1
0
1
1
1
0
0
0
1
2
1
0
2
0
1
1
2
1
0
1
1
1
2
2
2
2
1
0
1
2
2
1
0
1
2
0
0
1
2
1
0
0
0
0
0
0
2
0
1
0
1
0
3
1
0
0
2
2
1
1
1
2
0
2
0
1
1
0
1
0
0
2
0
1
0
2
0
0
0
1
1
1
1
2
2
0
0
2
2
0
2
1
2
1
1
1
1
1
2
5
0
0
2
2
0
1
1
0
3
1
2
1
2
2
1
0
0
2
2
0
2
2
2
0
1
1
0
0
1
0
1
1
1
2
0
2
2
2
0
0
0
0
0
1
1
1
3
1
0
1
1
2
2
2
0
1
1
2
0
0
2
2
0
0
0
0
2
0
1
1
1
1
1
1
0
1
2
3
0
1
1
0
0
1
1
2
0
0
0
0
1
2
0
0
1
0
0
0
0
2
2
1
1
0
1
1
3
0
3
0
2
1
0
2
1
0
0
1
0
0
0
0
1
0
0
1
1
1
1
0
0
2
1
0
2
0
1
2
1
2
1
0
1
1
0
2
0
1
1
1
1
1
2
1
1
0
0
0
1
2
1
0
1
1
1
0
0
1
0
0
0
2
2
0
1
1
1
1
1
1
0
1
2
0
2
0
1
0
1
0
2
1
2
0
0
0
0
1
0
1
0
1
0
0
1
0
2
0
2
0
2
2
1
0
0
3
0
0
1
0
0
0
1
2
0
5
1
1
1
1
1
2
1
1
0
1
2
0
1
2
1
1
0
1
0
2
0
1
0
2
3
0
1
0
1
1
1
0
1
1
3
1
0
0
0
1
0
1
1
0
0
1
1
2
1
0
0
0
1
1
1
2
2
0
0
0
1
2
1
1
1
0
0
2
0
0
1
0
0
1
4
2
1
0
0
2
0
0
2
2
0
2
3
2
0
3
0
2
0
1
9
0
2
0
0
3
1
2
0
1
0
1
1
0
1
1
1
1
0
1
1
2
1
2
0
1
0
2
1
0
1
0
1
1
2
0
2
0
1
0
0
0
1
0
1
0
1
2
0
1
1
1
1
0
1
0
0
0
1
0
0
2
0
1
0
2
0
1
0
1
2
1
2
1
0
1
1
0
0
1
0
0
0
1
0
1
0
2
2
2
2
0
0
0
2
0
1
0
2
2
1
2
0
0
2
2
2
1
1
1
1
1
1
1
0
2
2
0
0
1
0
0
2
0
0
2
1
0
0
2
0
0
2
1
0
0
1
0
0
1
1
1
0
1
2
2
4
0
0
1
2
0
0
0
1
2
4
0
1
0
0
2
2
1
1
1
0
1
0
0
1
0
1
1
1
1
0
0
1
2
1
0
2
0
0
1
0
0
0
3
0
2
1
0
0
1
0
1
1
0
1
0
2
1
0
1
1
1
0
1
0
0
1
1
1
1
1
1
2
1
0
0
1
1
1
0
1
0
0
2
0
2
2
1
2
1
2
0
0
0
2
1
0
1
1
1
0
0
1
2
1
2
0
0
1
2
0
1
1
0
0
1
0
0
0
1
2
0
1
2
1
0
1
0
0
0
2
1
1
0
1
0
0
0
2
0
0
1
1
1
0
1
1
1
0
1
2
0
1
0
0
1
1
2
1
0
1
2
1
0
1
0
1
2
1
0
0
1
1
2
3
0
0
1
0
2
1
2
1
0
0
2
0
3
2
1
1
0
1
0
1
1
2
1
1
0
2
1
1
3
0
0
1
0
2
1
0
1
2
2
1
1
0
2
1
1
2
0
2
1
5
2
0
2
0
1
0
2
0
0
0
0
0
1
2
1
0
0
2
1
2
1
0
0
1
2
0
1
0
2
0
0
0
0
0
1
2
0
1
0
1
0
2
0
0
0
1
0
0
1
1
1
1
2
0
1
1
1
0
0
1
0
1
0
2
0
1
2
0
0
1
2
0
1
0
2
1
0
0
1
1
1
1
0
0
0
0
0
1
0
0
2
1
0
1
0
1
0
0
2
0
0
0
0
2
0
0
0
0
1
1
3
0
1
2
1
0
1
1
1
0
2
0
0
1
1
0
1
0
0
2
2
2
1
0
0
2
0
3
2
2
1
2
1
0
2
1
1
0
1
2
1
2
1
0
1
2
0
0
1
2
2
0
0
0
0
2
1
1
1
1
2
0
0
1
2
0
0
2
0
0
2
2
2
0
2
0
1
1
1
0
0
1
3
0
1
0
0
1
0
0
1
2
1
1
0
2
1
0
0
0
1
1
2
1
0
1
1
0
2
0
2
0
0
1
1
0
0
1
0
3
0
1
0
2
0
2
0
0
1
1
1
2
2
0
0
2
2
0
1
1
1
2
0
0
0
0
0
2
1
0
2
2
0
1
2
2
0
1
0
0
1
2
0
0
0
1
1
1
0
2
0
2
1
0
2
0
3
0
2
2
0
1
0
1
1
2
0
0
1
1
0
1
0
2
1
1
1
1
0
1
0
0
0
1
1
0
2
0
2
0
1
2
0
1
0
0
0
2
1
2
0
0
1
1
1
0
0
2
0
0
1
1
1
0
0
0
0
0
1
0
2
0
0
0
1
0
1
0
1
1
0
0
1
0
2
1
0
0
1
0
1
0
1
0
1
1
1
0
0
2
1
0
1
0
1
1
0
2
1
2
3
0
2
1
1
2
1
2
0
1
0
1
0
2
1
1
0
1
0
0
0
0
1
0
2
2
2
0
1
1
2
0
0
0
1
0
0
1
0
1
0
0
0
1
1
1
0
0
1
0
0
1
1
1
0
1
0
2
0
0
2
1
1
2
0
2
2
2
0
1
1
0
0
2
0
0
0
1
1
1
0
0
1
2
0
0
0
1
1
2
2
0
2
0
0
1
2
1
2
2
0
0
0
1
0
1
3
1
0
2
0
1
1
1
1
0
2
1
0
1
0
0
0
0
0
0
0
2
0
1
1
0
0
2
2
1
1
0
2
0
0
0
1
1
1
2
1
1
0
1
1
0
2
0
3
1
0
1
1
1
1
0
0
0
2
2
1
0
2
2
0
2
2
0
0
2
1
0
0
0
1
1
0
0
0
0
0
0
1
3
0
2
1
0
0
2
0
0
1
1
1
1
2
0
2
0
2
1
0
0
1
2
2
1
0
0
1
1
0
0
1
1
1
1
2
1
2
0
1
0
1
1
0
2
0
1
2
1
1
0
1
0
0
1
2
0
2
0
1
1
1
1
0
1
1
2
0
2
2
0
2
0
1
1
0
1
1
1
0
1
1
0
2
0
0
0
2
1
0
0
2
1
0
0
0
1
0
3
2
1
2
2
2
1
1
0
0
0
1
2
0
0
0
1
1
1
1
4
1
2
1
1
1
2
1
1
1
0
2
2
0
1
1
1
1
1
1
2
1
1
2
1
2
1
0
1
0
2
1
2
1
1
1
1
0
0
0
2
0
0
0
1
1
1
2
2
0
0
1
2
0
1
1
1
0
0
2
1
0
1
1
1
0
1
0
2
1
1
1
1
2
0
1
0
1
0
0
2
0
1
2
2
3
0
2
2
1
0
0
1
2
1
1
2
0
0
0
1
1
2
1
2
1
2
1
2
1
0
1
0
1
2
2
1
1
2
0
1
0
0
0
0
0
1
0
2
0
1
0
1
0
1
0
0
0
1
1
0
0
1
1
1
0
0
1
1
0
1
2
1
2
0
0
0
0
0
1
1
0
0
1
0
2
0
0
1
1
0
2
2
1
1
0
1
0
0
0
0
0
1
0
1
0
1
3
0
0
2
0
2
1
0
0
0
2
0
1
0
1
2
0
2
0
1
2
1
1
1
2
1
1
0
1
0
1
0
1
0
1
2
0
0
2
0
2
2
0
1
0
0
2
0
1
0
0
2
0
0
0
2
1
0
2
0
3
1
0
1
2
0
1
1
0
1
1
1
0
1
0
1
1
1
1
0
1
1
2
1
0
0
0
0
1
2
0
1
1
2
1
2
2
0
0
0
0
0
1
0
1
1
0
1
0
1
1
1
2
0
2
0
0
1
0
4
1
2
1
0
1
2
2
0
1
1
1
2
0
1
2
0
6
2
0
2
1
0
1
1
2
0
0
0
0
1
2
2
0
0
2
2
0
1
0
2
0
0
1
0
0
0
0
1
1
1
0
2
0
1
5
0
0
1
2
0
1
2
1
0
1
0
2
0
5
2
1
0
0
1
2
1
2
0
1
1
0
0
1
2
0
0
0
4
2
0
2
0
1
0
0
1
2
2
3
0
2
2
3
2
0
0
0
1
1
1
1
0
0
1
1
0
2
1
2
0
0
2
0
0
0
2
1
1
1
1
0
2
2
2
2
1
2
1
1
0
0
0
1
2
1
1
2
0
1
1
1
0
1
0
1
0
0
3
0
2
2
1
0
0
0
0
1
1
0
0
1
0
2
1
0
1
2
1
2
0
1
0
1
2
1
0
1
1
0
0
1
1
2
1
0
1
0
1
2
1
1
1
1
0
0
0
0
0
1
0
1
1
0
2
1
0
1
1
1
1
1
2
1
0
1
0
2
0
2
2
0
1
1
1
4
2
0
1
0
0
1
0
1
1
0
1
1
0
1
0
2
2
2
2
1
1
0
0
0
1
1
0
1
0
2
1
1
0
1
2
0
1
2
0
0
0
1
3
1
1
1
1
0
1
2
0
1
0
0
2
1
2
1
0
1
1
2
1
1
2
1
0
0
3
1
0
2
0
0
1
2
1
0
2
0
1
0
3
0
1
1
0
1
1
2
2
4
0
0
1
1
1
1
2
1
1
0
0
0
1
1
2
1
0
2
0
0
1
2
2
1
0
3
1
1
0
3
0
0
0
0
1
1
0
1
0
1
0
1
2
2
0
0
1
1
1
0
2
0
1
1
1
2
1
1
0
0
0
0
2
1
0
1
0
0
2
1
0
1
1
2
1
0
1
0
1
2
2
2
2
0
2
0
2
2
2
2
4
1
0
1
0
2
0
0
2
2
0
1
1
2
0
0
1
2
0
1
0
0
0
0
1
1
1
1
1
0
0
1
1
3
0
2
1
0
2
0
1
1
1
0
0
0
1
1
0
1
1
0
2
2
0
1
1
0
1
1
1
0
0
0
1
2
0
2
1
0
1
0
2
1
0
2
1
0
0
2
2
1
0
1
0
0
0
2
1
0
1
0
0
0
2
1
0
1
2
1
0
0
0
1
0
1
3
1
0
1
1
0
0
0
2
1
2
2
1
2
1
1
2
1
2
1
1
0
1
0
1
0
0
0
0
0
2
1
1
1
0
2
2
2
1
2
2
2
0
1
1
2
0
0
1
1
0
2
2
1
0
1
0
0
3
1
0
0
2
0
1
1
0
0
0
2
1
2
1
0
0
1
0
0
1
2
2
1
1
1
1
1
2
2
0
0
0
1
0
1
0
1
1
0
0
2
2
0
3
0
1
0
1
0
1
0
0
1
0
0
0
2
2
0
2
0
0
0
0
1
0
1
0
1
0
0
2
1
2
2
2
0
1
1
1
1
0
0
0
1
4
2
1
2
0
0
1
2
0
5
1
1
0
1
1
1
0
0
0
1
0
0
1
1
0
2
0
1
0
0
1
0
2
0
1
0
1
0
2
0
0
2
1
2
1
0
0
1
1
1
2
1
1
0
0
1
2
3
0
1
0
1
1
3
2
0
0
3
1
2
0
0
0
0
1
2
2
1
0
2
0
1
1
0
1
1
1
0
1
0
0
1
0
0
5
1
0
1
1
1
0
0
0
1
0
0
1
2
1
2
0
0
1
0
0
3
1
1
1
2
0
1
2
1
1
0
0
1
1
0
0
1
1
1
0
1
0
4
0
0
2
1
0
2
1
0
1
2
2
2
0
2
1
0
0
1
1
1
2
0
1
0
0
0
1
0
0
1
2
1
2
0
0
0
1
0
0
0
1
2
2
1
0
2
1
1
0
0
1
3
1
0
2
0
0
1
0
1
1
1
1
1
1
1
0
1
0
1
1
0
0
1
0
1
1
0
1
1
0
0
1
0
0
1
1
0
0
1
2
2
0
1
1
2
1
1
2
0
0
1
2
1
2
2
3
0
0
0
0
2
1
1
1
1
2
0
2
0
0
1
0
1
2
2
0
0
0
1
0
1
0
1
1
0
0
1
1
0
1
0
1
2
0
1
0
0
1
1
0
1
1
0
2
1
1
1
0
0
0
0
0
0
2
1
1
0
1
2
1
1
1
1
0
0
2
2
0
2
0
1
1
1
1
1
0
2
1
0
1
1
1
2
2
2
0
0
0
0
1
2
1
1
0
2
0
1
3
2
1
0
1
0
0
0
0
1
0
0
0
2
2
0
2
2
1
2
0
1
0
0
1
1
1
1
0
2
1
0
2
0
2
0
1
1
1
0
0
0
2
2
0
2
3
0
3
1
1
1
1
1
2
1
0
1
1
2
0
2
0
1
0
1
0
2
1
1
1
1
2
1
2
0
1
1
1
0
1
2
0
1
1
0
1
0
2
0
2
0
0
1
0
1
0
2
1
1
2
0
2
3
0
0
0
0
2
1
0
1
0
1
1
1
0
1
1
2
0
1
0
0
1
1
1
0
2
0
2
1
1
2
2
1
2
0
2
1
1
1
2
1
2
0
0
0
1
0
1
0
0
1
1
0
2
1
2
0
0
0
0
2
2
0
1
2
2
0
2
0
1
1
0
2
1
1
1
3
1
0
1
0
2
0
1
1
0
3
1
1
1
2
0
1
1
0
0
0
0
0
1
1
2
1
0
2
0
0
1
0
0
0
0
1
0
0
1
2
0
0
0
1
2
1
2
3
0
1
1
1
2
2
1
0
0
2
2
0
1
0
0
0
0
2
1
1
0
0
0
2
0
1
0
0
1
1
0
1
2
2
2
2
0
0
1
0
2
0
0
0
1
2
0
0
2
2
2
0
1
1
0
0
0
1
2
1
2
1
1
2
0
0
2
2
2
1
0
2
1
2
0
0
1
3
4
1
0
2
0
2
1
1
2
0
0
1
2
0
2
0
1
0
2
1
1
1
1
1
1
0
0
2
0
0
1
0
1
0
0
2
1
1
0
2
1
1
2
0
0
2
0
0
2
2
0
0
1
1
0
0
0
2
1
2
1
1
0
0
0
2
0
0
1
1
0
2
1
1
2
0
0
0
0
1
2
0
1
2
1
2
0
0
0
0
0
2
1
1
0
1
0
2
0
0
1
1
1
2
2
1
0
1
1
1
0
2
0
1
0
1
0
2
0
1
1
2
1
0
0
0
1
1
1
0
2
0
2
1
1
1
0
0
3
1
0
0
1
1
0
0
0
1
1
1
2
2
0
2
0
2
0
2
1
1
0
1
0
0
1
0
2
0
1
1
0
1
2
2
1
0
2
1
1
2
1
1
2
2
2
1
0
0
0
0
0
1
1
1
1
0
0
0
1
0
0
1
1
2
2
1
1
0
0
1
2
1
0
0
0
1
1
0
1
1
1
1
1
0
3
0
2
0
2
0
1
1
2
0
0
1
2
1
0
2
2
2
0
0
0
0
1
1
2
1
1
0
2
1
0
1
1
1
1
1
2
1
1
1
2
0
0
2
2
2
2
1
0
0
0
1
0
1
2
0
0
1
0
1
0
1
0
2
0
2
0
2
0
0
2
0
0
0
2
2
2
0
1
1
0
0
0
0
2
0
1
2
0
1
0
1
1
0
3
2
0
1
0
1
1
2
1
0
1
0
1
2
0
3
0
1
0
2
0
0
0
0
0
0
0
1
1
6
2
1
1
0
2
0
1
0
1
2
0
1
0
1
1
1
0
0
0
1
0
0
0
0
2
0
0
1
0
0
1
1
0
1
2
2
0
0
2
2
1
1
1
0
2
2
2
2
1
2
0
2
1
1
0
2
2
0
2
0
0
2
1
2
0
1
3
0
0
2
1
2
0
0
2
1
0
1
0
0
2
3
2
1
2
0
2
1
0
0
0
0
2
1
1
1
1
0
1
0
0
1
1
1
0
2
0
2
1
2
2
0
1
1
0
0
1
2
0
1
0
0
1
1
0
2
0
1
0
2
0
1
0
0
2
4
0
0
0
0
2
0
2
1
1
1
2
0
0
0
0
2
1
0
0
3
0
1
0
1
0
1
0
0
2
0
2
1
1
1
1
1
2
1
1
0
0
0
0
1
0
1
0
0
1
2
1
0
1
0
1
2
1
1
5
2
0
1
0
1
0
0
0
0
2
0
0
0
1
0
0
2
2
2
0
0
0
1
1
1
2
1
1
1
1
2
0
0
2
2
1
0
0
2
2
1
2
1
0
0
1
2
1
1
0
0
0
1
1
1
2
0
1
2
1
1
1
0
2
0
1
0
0
1
0
0
0
1
0
0
1
1
0
1
0
1
1
1
1
0
1
2
1
0
2
0
0
2
0
1
0
1
0
1
1
0
0
0
0
0
2
1
1
2
0
1
0
2
1
0
2
2
1
1
1
1
1
1
2
2
2
0
1
0
0
0
2
2
0
1
1
1
1
0
0
1
1
0
1
0
2
0
0
1
2
1
0
0
0
2
1
1
0
0
2
2
1
1
2
1
2
2
0
0
0
2
1
1
1
1
1
2
0
2
0
2
1
1
1
0
0
1
0
0
1
1
1
0
0
0
0
2
0
0
3
0
1
0
0
0
2
0
1
0
0
1
2
1
1
2
1
1
2
0
1
0
1
0
0
0
2
1
0
1
1
1
0
0
0
0
0
0
0
0
0
3
2
2
0
1
2
1
0
0
1
1
1
0
0
1
0
0
0
1
1
1
2
0
1
0
0
2
1
0
0
0
1
0
2
2
1
1
1
0
1
2
2
1
0
1
0
0
1
0
0
0
0
0
1
0
1
1
1
2
2
0
0
0
1
1
1
2
0
1
2
0
0
0
1
0
1
0
2
2
0
1
2
0
2
2
3
0
0
1
1
1
1
1
0
0
2
1
0
2
2
0
1
2
1
0
2
1
1
0
2
0
1
0
0
1
0
2
0
1
0
1
0
1
0
2
0
1
2
2
0
1
2
2
0
1
8
0
0
1
0
2
1
0
2
2
0
1
0
0
2
0
0
0
0
1
0
0
2
3
1
0
0
0
0
1
1
0
2
1
2
3
1
0
1
2
2
2
0
1
0
0
1
2
0
1
2
0
2
0
0
3
0
1
0
2
2
1
0
2
1
2
0
0
1
1
1
2
0
0
0
1
2
3
1
1
1
0
1
2
2
1
1
0
0
1
0
0
2
1
2
0
1
2
0
0
1
1
2
0
0
1
1
0
0
2
0
1
1
1
1
0
1
0
1
1
1
0
0
0
1
2
1
0
1
1
0
0
0
2
1
2
1
0
0
0
0
2
0
0
0
1
1
1
2
1
1
0
1
1
0
1
0
0
1
2
0
2
1
0
2
0
0
2
1
1
0
0
0
1
0
0
1
2
0
0
0
0
7
0
2
0
1
1
1
1
2
0
0
1
1
0
0
1
0
0
0
0
1
0
1
2
1
2
1
1
0
1
0
2
0
0
0
0
0
0
1
1
2
2
2
0
1
3
0
1
1
0
0
0
1
0
3
0
1
0
2
1
2
1
0
2
1
2
3
2
0
0
3
1
0
0
0
1
1
1
0
1
0
0
1
2
0
1
2
0
0
0
1
0
1
4
0
0
0
0
1
1
1
0
0
0
1
1
1
0
1
0
1
1
1
0
1
0
0
0
1
0
2
2
1
1
0
1
1
2
0
1
1
0
0
0
2
1
0
1
1
0
3
0
1
2
0
2
2
2
0
2
2
1
2
1
0
2
0
0
1
1
0
1
1
0
1
1
1
2
0
0
0
0
0
1
0
1
3
2
0
0
2
2
2
1
0
0
2
0
1
1
0
2
1
1
1
0
2
1
1
2
0
0
1
0
1
1
0
0
1
2
1
1
2
5
0
1
0
2
3
0
1
2
1
0
0
0
2
2
0
0
0
2
0
0
1
1
0
0
0
2
1
1
1
0
0
1
0
0
1
1
0
0
1
1
0
0
0
2
1
1
1
1
0
1
0
1
1
0
0
0
1
1
0
2
0
2
2
1
0
0
0
2
1
3
0
0
2
1
2
2
2
1
1
2
2
1
0
0
0
2
3
2
0
1
1
0
0
0
1
0
0
3
0
0
2
0
2
0
0
0
1
1
1
0
0
1
1
2
1
2
1
2
1
0
1
0
0
1
0
1
3
0
2
2
0
1
0
2
1
2
2
0
1
1
0
0
0
1
1
0
2
0
1
1
1
1
0
1
2
1
1
0
0
2
2
0
0
2
1
1
2
1
2
2
1
0
2
0
2
1
2
1
0
1
2
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
2
1
0
1
0
1
1
0
3
0
2
0
1
0
0
2
2
0
0
0
0
1
2
1
1
0
0
1
0
2
1
1
1
2
0
2
1
2
1
0
1
1
1
1
1
1
0
1
0
2
1
1
2
0
2
0
2
1
0
1
0
0
1
2
1
1
2
2
1
1
3
0
0
1
1
0
1
1
1
0
2
1
1
2
2
0
3
1
1
1
0
0
0
0
0
0
1
2
1
1
1
1
1
0
1
0
2
0
2
0
1
2
0
0
2
2
0
1
1
1
0
1
0
2
1
1
0
0
1
0
2
0
0
1
0
3
1
2
2
0
2
1
0
0
5
0
1
0
1
1
2
2
1
1
1
2
0
1
1
1
1
1
3
1
0
1
0
2
0
1
1
1
1
0
1
0
1
1
1
0
1
1
1
1
1
2
0
0
1
1
1
2
0
0
2
1
1
1
2
0
0
1
0
1
2
3
2
1
0
1
2
0
0
0
0
2
2
0
2
1
0
1
1
0
0
1
0
0
0
1
1
1
1
1
0
3
1
0
2
2
0
0
2
1
1
1
1
0
1
1
2
0
1
2
0
0
2
0
0
1
0
1
0
0
0
2
0
2
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
1
1
1
0
2
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
2
2
1
0
0
0
0
2
1
0
2
2
2
2
0
1
0
0
0
2
0
0
0
0
1
1
0
2
0
2
0
1
0
1
0
0
1
2
3
1
2
2
0
2
2
2
1
3
1
0
2
1
1
0
1
1
3
0
2
0
1
0
1
1
1
0
1
0
2
1
0
0
0
2
2
2
1
2
1
0
0
2
0
0
0
1
0
1
0
1
0
2
1
1
1
2
1
1
1
0
0
0
0
1
1
2
0
0
0
0
0
2
3
6
0
2
0
0
2
0
0
1
0
2
1
3
0
2
0
1
1
2
1
2
2
2
0
1
0
2
0
1
0
1
2
1
1
0
0
0
0
2
1
0
2
2
2
1
0
2
0
1
0
3
1
0
1
0
0
2
2
3
1
1
0
0
0
0
1
2
1
1
1
2
0
1
2
1
1
1
0
1
1
2
1
1
0
1
0
2
2
0
1
0
0
1
1
1
1
0
2
0
0
0
1
0
2
1
0
0
0
0
1
0
1
1
1
1
0
1
2
2
1
0
1
0
0
0
2
0
0
2
1
2
1
0
1
0
2
0
0
0
2
1
0
0
0
0
0
2
1
1
0
1
0
1
0
1
0
0
0
1
1
1
1
0
1
1
2
0
1
0
2
1
0
1
2
0
1
0
1
1
1
0
0
2
0
2
0
0
0
1
2
1
1
0
1
0
0
0
1
1
2
1
1
0
1
0
2
1
0
0
2
0
1
1
1
0
1
0
0
0
0
0
2
1
0
1
1
0
1
1
0
0
0
1
1
1
1
1
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
2
2
0
2
2
2
2
0
3
2
0
0
2
1
0
2
0
0
0
0
1
1
1
0
0
1
2
0
1
1
0
1
2
0
0
1
1
0
2
2
2
0
1
2
2
1
0
0
2
0
0
3
0
2
2
0
2
0
2
0
2
0
2
1
2
0
1
1
2
0
0
2
0
1
0
0
0
3
3
0
2
0
3
1
0
0
0
0
1
1
2
2
2
0
1
1
2
0
1
0
0
0
2
2
1
2
2
0
2
0
0
0
1
2
1
2
0
2
2
1
1
1
1
0
0
2
2
1
0
2
0
0
0
0
1
1
2
0
1
1
1
1
1
0
0
2
0
0
1
0
1
1
1
0
1
0
0
0
0
1
2
1
1
2
2
0
0
1
0
0
1
3
1
0
0
0
1
1
1
1
1
2
0
0
0
1
0
1
0
0
3
3
0
0
1
1
2
0
0
2
1
0
1
2
0
1
2
1
0
1
0
2
2
1
0
0
2
2
2
3
0
1
1
1
0
1
1
0
0
0
1
0
2
1
0
0
1
0
0
1
1
2
0
1
1
1
0
0
0
0
0
2
1
0
0
0
1
0
0
2
0
0
0
1
0
0
2
1
1
1
1
1
2
2
1
2
1
0
1
0
1
2
0
0
1
2
1
0
0
0
1
1
2
1
2
1
0
1
0
1
1
1
1
1
2
1
2
0
0
0
1
2
0
0
0
1
2
1
1
0
2
1
1
1
0
0
0
1
2
0
0
1
1
2
0
1
2
1
1
0
1
0
0
2
2
2
1
2
0
0
0
0
0
0
1
0
2
1
3
1
0
2
2
1
1
2
1
1
1
0
0
0
0
1
0
0
2
2
0
1
2
0
0
1
0
0
2
2
0
1
1
1
0
1
0
0
0
0
1
1
0
2
1
1
1
0
0
0
0
1
0
0
2
1
0
0
4
0
2
0
0
1
2
0
0
1
1
0
0
0
1
2
1
1
0
1
1
1
2
0
0
0
2
0
1
1
1
1
0
1
4
2
1
1
1
2
1
1
0
3
1
0
1
1
0
0
1
1
0
1
3
0
0
1
0
1
0
1
0
1
2
2
1
1
0
0
1
0
0
1
1
2
0
1
1
0
1
1
2
1
0
0
1
2
2
0
1
2
1
0
2
1
0
0
0
2
0
1
1
0
1
0
2
2
2
2
0
0
0
0
0
2
1
0
1
1
0
2
1
2
0
1
0
0
0
1
2
0
1
1
0
2
0
2
1
0
1
0
4
2
2
1
1
2
1
2
1
0
1
0
2
0
0
0
0
0
1
1
1
0
2
1
2
0
2
0
0
2
0
1
1
0
1
2
1
1
0
0
0
1
1
0
1
2
1
2
2
0
0
1
1
1
1
1
0
0
1
0
0
0
2
0
1
0
0
0
2
1
0
0
1
0
3
0
1
2
0
0
1
1
2
1
1
0
2
1
2
1
0
1
2
0
2
2
1
1
0
1
0
2
2
2
1
1
0
1
0
1
0
2
2
1
1
0
1
0
1
2
0
1
0
0
0
2
0
0
1
1
0
1
1
0
0
1
0
1
1
1
0
0
2
3
1
2
1
2
2
2
0
0
1
0
0
0
2
1
2
2
2
2
0
0
0
1
1
1
2
1
0
2
1
0
2
0
3
0
2
1
2
1
2
1
0
1
1
1
0
0
1
2
1
0
1
0
1
0
1
1
1
0
2
0
1
1
0
0
1
0
1
0
1
1
2
1
1
2
0
1
0
1
1
2
2
1
2
0
2
2
0
0
0
2
0
2
1
2
2
1
1
1
0
2
1
1
2
0
0
2
1
1
2
2
2
2
0
0
0
0
2
0
3
0
0
0
0
1
1
1
2
0
2
0
0
0
0
0
1
1
2
1
0
0
0
1
0
1
1
1
0
0
2
2
2
0
0
1
1
2
2
1
1
1
1
2
0
1
1
0
2
0
1
2
2
1
3
1
1
0
2
2
2
0
0
0
1
1
2
0
1
0
2
2
2
0
0
2
1
1
0
0
1
2
0
0
2
1
1
2
0
2
1
0
0
0
1
0
1
0
0
0
0
2
2
1
2
0
2
1
2
0
1
0
1
0
1
1
1
0
0
1
0
0
1
0
0
1
1
0
0
0
1
1
1
0
0
1
2
0
0
0
2
1
0
1
2
0
0
1
0
0
1
2
1
0
2
1
0
0
2
0
1
1
2
1
0
1
1
1
1
2
1
0
0
1
2
2
1
2
1
0
1
1
1
1
0
1
1
1
2
0
2
1
0
0
1
0
1
0
1
1
1
2
0
2
0
1
0
0
0
2
0
1
1
0
1
1
0
0
0
0
2
2
1
2
2
0
1
1
1
0
0
0
0
2
1
3
1
2
1
0
2
1
0
1
1
1
1
0
0
0
1
2
0
1
0
3
0
1
0
2
1
2
1
0
2
1
0
1
2
1
0
1
2
2
1
2
1
2
1
0
1
0
1
2
1
1
0
0
2
2
1
0
1
0
1
3
2
2
0
1
1
0
1
0
0
0
2
2
1
0
2
2
3
2
0
1
0
2
1
0
1
1
0
2
0
0
0
1
0
1
1
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
1
2
0
0
0
1
2
0
0
0
2
1
0
0
2
1
2
0
1
1
1
1
1
2
0
0
0
1
0
2
1
2
1
2
0
1
0
1
1
0
0
1
0
0
0
0
1
0
2
2
0
0
0
0
0
1
0
0
2
1
1
0
0
1
2
0
2
0
1
1
1
2
1
1
1
0
0
2
0
1
1
0
0
0
1
1
1
2
1
0
0
0
1
2
1
1
0
2
0
1
0
1
0
1
1
1
0
1
0
0
0
2
1
1
0
2
1
2
0
2
2
1
0
2
2
0
0
0
0
1
1
0
0
1
0
0
0
2
1
0
1
1
0
2
1
2
0
0
1
1
1
0
1
0
1
0
1
0
1
2
1
0
0
2
1
1
0
1
0
2
0
0
1
0
0
0
0
1
0
0
1
0
1
0
1
0
2
2
0
0
2
2
2
0
1
1
2
0
2
1
2
0
2
1
0
1
0
2
2
0
2
0
2
1
2
2
1
0
1
1
0
0
2
0
1
2
1
0
0
1
0
1
1
1
0
1
0
0
1
2
2
2
1
1
1
1
0
1
2
0
1
0
1
0
0
2
2
0
0
0
1
2
2
0
1
2
1
0
1
2
2
1
0
0
1
0
0
0
0
2
0
3
0
2
2
2
2
0
0
0
1
0
0
1
2
1
1
1
1
0
1
2
1
0
1
1
0
0
0
2
0
2
1
2
0
0
1
1
0
1
2
0
1
1
0
1
1
1
0
2
0
1
0
1
2
0
2
0
0
0
1
0
0
0
1
2
1
0
0
1
0
4
0
0
1
0
1
1
0
2
1
1
1
0
0
1
0
0
0
1
2
1
0
1
1
1
2
0
2
2
0
1
2
0
1
0
1
1
0
0
0
3
1
1
2
1
2
0
0
1
0
1
0
1
2
0
1
0
0
0
2
1
2
1
2
1
1
0
0
0
0
0
1
0
1
0
0
2
2
2
2
0
1
2
0
2
2
0
0
1
0
0
1
0
1
1
2
1
2
2
1
1
0
0
0
2
0
0
0
2
2
1
1
1
1
1
1
2
2
1
1
0
0
0
1
2
1
3
1
2
0
0
0
0
0
1
1
0
2
2
2
2
0
1
2
0
0
0
2
0
1
2
1
0
1
0
0
0
0
0
0
0
2
2
0
0
0
1
1
1
0
0
0
1
0
1
1
1
1
1
1
0
0
2
1
0
1
0
0
0
2
2
2
0
0
2
3
2
0
1
2
2
0
2
0
0
1
1
0
0
0
1
0
0
1
0
0
2
1
0
0
1
2
1
0
0
1
1
2
0
2
0
2
0
1
0
2
2
0
2
3
0
3
1
2
1
1
0
2
0
1
0
3
0
1
2
0
1
2
1
1
3
1
0
1
1
0
2
1
2
1
0
1
1
1
2
0
2
2
0
1
0
1
1
1
2
1
1
1
1
0
1
0
0
1
1
1
2
0
1
0
0
0
0
1
0
1
2
2
0
0
1
1
0
0
1
0
1
2
1
0
0
0
0
0
2
1
1
0
0
1
1
1
2
0
1
1
2
1
1
1
1
2
0
2
1
1
0
0
1
2
0
0
0
0
1
1
2
2
0
1
1
1
0
2
1
1
0
0
1
1
0
0
1
1
0
1
2
1
0
1
2
2
2
0
1
0
2
0
0
0
0
1
0
0
0
2
0
1
1
1
0
0
1
0
0
1
1
0
0
1
1
2
0
1
0
1
1
1
0
1
1
1
0
2
1
0
1
0
0
1
1
0
0
1
2
1
0
0
1
0
2
0
0
1
1
2
1
1
0
1
1
1
1
0
1
2
2
1
2
1
0
0
1
2
1
0
1
0
0
1
0
2
1
2
0
2
0
0
2
1
2
1
0
1
0
0
0
2
0
1
1
0
0
0
0
1
2
0
2
2
1
1
0
0
1
1
0
0
1
0
0
0
4
2
1
1
0
0
0
1
1
0
0
0
0
1
2
0
0
0
0
1
0
1
2
1
2
0
0
0
0
0
0
1
1
2
1
1
0
1
0
2
2
2
0
2
0
1
1
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
2
2
0
0
0
0
1
0
1
0
0
0
0
1
1
0
1
1
1
2
2
0
2
1
0
0
0
0
1
0
1
2
1
2
0
3
0
2
0
1
0
1
0
1
1
0
0
0
0
3
0
0
0
2
0
2
0
0
0
2
1
1
1
0
0
2
0
0
0
1
0
0
1
0
2
2
2
0
1
2
1
0
1
1
0
0
0
0
0
0
1
0
0
1
2
0
0
1
0
0
0
1
0
1
1
1
1
0
1
1
1
1
1
1
1
2
0
0
2
1
0
1
0
1
2
0
0
1
0
0
0
0
2
0
0
1
0
2
2
1
2
1
1
1
1
1
0
1
1
0
2
2
1
2
0
0
0
1
0
0
1
1
1
0
1
2
0
0
0
0
1
0
1
1
2
1
0
1
0
0
2
0
1
1
2
0
0
2
0
2
1
1
0
1
0
0
2
2
0
0
0
1
2
2
3
1
2
0
0
1
1
1
0
2
3
0
2
1
1
0
2
0
1
0
0
1
0
1
0
1
0
0
2
1
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
1
2
1
1
2
1
0
2
0
0
1
0
1
1
2
0
0
1
2
0
1
0
2
1
0
1
1
0
0
1
0
1
0
0
0
0
1
2
1
0
1
4
1
2
2
0
1
1
2
0
1
0
0
0
0
0
0
1
0
1
1
1
0
2
0
3
0
1
2
1
0
0
2
1
1
2
0
0
1
1
0
0
0
0
2
0
1
1
1
2
0
0
0
2
0
1
1
1
1
0
2
0
1
0
3
0
0
1
1
1
1
0
1
0
1
2
0
2
2
1
1
0
1
0
1
1
0
1
1
2
0
4
2
0
2
0
2
1
1
0
0
1
0
2
1
0
0
2
1
0
0
1
1
0
1
0
2
2
1
1
0
0
2
0
0
0
1
0
2
1
2
0
1
2
1
0
0
0
0
0
0
1
0
0
2
2
3
0
2
2
1
0
0
1
1
1
1
2
0
1
0
1
0
2
0
1
2
1
0
0
1
1
2
0
1
2
1
2
0
1
1
0
0
0
1
2
2
1
1
0
2
0
0
1
0
1
2
1
0
1
1
0
1
1
1
1
0
1
2
1
0
0
0
1
1
0
0
2
0
1
1
2
1
1
0
1
0
2
1
0
1
0
2
1
2
1
0
1
1
2
0
0
0
2
0
1
0
1
0
1
1
1
1
1
0
1
1
0
0
1
0
0
2
2
1
0
1
1
0
0
0
2
0
0
1
0
1
1
0
0
1
0
0
1
0
0
2
2
0
0
2
0
0
0
2
0
2
0
1
1
0
1
0
1
1
0
0
1
1
1
1
2
2
1
2
0
1
0
2
0
2
2
1
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
2
0
1
1
1
1
0
2
0
1
1
1
4
2
0
1
1
1
0
0
0
2
2
1
2
1
0
1
0
0
2
0
0
0
0
1
0
1
2
3
0
1
0
1
0
1
1
0
2
2
1
0
0
2
2
1
0
1
1
2
0
1
0
2
1
0
0
0
0
0
2
2
1
2
1
1
2
1
0
2
0
2
0
0
1
0
1
0
1
0
1
1
1
1
1
2
0
1
1
0
0
2
1
4
2
0
1
2
0
2
0
1
0
0
0
1
1
1
0
0
0
1
2
0
1
2
0
0
1
0
1
1
1
2
1
0
2
2
1
1
1
2
1
2
0
1
1
0
1
1
0
2
0
2
0
1
2
1
3
2
1
1
1
1
0
1
2
1
0
0
1
1
0
0
0
0
1
2
0
0
1
1
2
2
1
1
1
1
1
2
0
0
2
2
0
0
1
0
2
1
3
1
0
0
0
0
0
2
2
0
1
0
1
2
1
0
0
1
1
2
0
2
0
0
1
0
1
1
1
1
1
1
1
0
1
1
0
0
1
0
1
2
0
2
1
0
0
0
0
0
1
0
0
1
1
0
0
0
2
3
0
0
1
0
1
2
1
1
0
0
0
1
1
0
0
0
0
2
0
1
1
2
0
1
2
9
1
2
1
2
1
1
0
0
0
1
0
1
0
1
1
0
1
0
0
0
2
1
0
0
2
1
0
1
1
1
0
1
2
0
0
1
0
0
1
0
3
0
1
0
1
1
1
1
0
1
2
1
1
0
1
2
1
0
1
1
1
2
2
1
0
1
2
1
0
1
0
0
0
1
0
1
2
2
0
0
0
0
1
0
0
2
1
0
0
1
1
1
1
2
2
0
3
2
0
3
2
0
1
0
1
2
1
1
2
0
2
2
0
3
2
2
0
1
1
0
0
2
0
1
2
1
2
0
0
0
0
2
2
1
2
2
0
1
0
0
0
0
2
0
1
2
1
2
1
2
1
1
0
1
1
2
1
1
2
1
2
1
1
2
0
0
0
0
1
0
1
1
0
2
0
1
1
1
1
0
1
0
1
1
1
1
0
1
1
1
0
0
0
1
0
0
0
0
0
2
0
1
0
2
0
0
2
0
0
1
2
1
1
0
0
0
2
0
1
0
1
1
0
1
0
1
1
2
1
0
1
1
1
1
1
1
1
0
1
1
0
1
0
2
0
0
1
1
1
0
0
0
0
0
1
2
0
1
2
0
1
2
0
2
0
1
2
0
1
0
0
0
1
0
1
1
0
0
0
2
0
0
0
0
1
0
1
0
1
0
3
0
1
0
1
1
2
2
1
1
0
0
1
0
1
0
0
1
0
1
1
0
1
1
0
2
0
1
2
0
1
2
2
1
1
1
1
1
2
0
1
1
4
0
0
0
0
2
0
0
1
1
2
1
2
0
0
0
1
2
1
2
1
2
0
1
0
1
1
1
1
2
1
2
0
2
0
0
0
1
1
1
0
1
1
0
2
0
0
1
0
0
0
2
0
2
3
0
2
4
0
1
1
1
0
2
0
2
3
1
0
1
0
2
0
0
1
2
2
0
2
2
2
1
0
1
2
1
4
0
2
0
0
2
0
2
2
1
0
0
0
0
1
0
2
1
0
3
1
2
0
1
0
0
0
0
2
0
0
1
0
1
1
2
1
0
1
1
0
1
1
0
0
0
1
0
2
1
0
0
0
1
1
1
0
0
1
0
0
2
1
1
0
0
0
0
0
1
1
2
1
1
1
1
2
1
0
1
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
2
1
1
1
1
2
0
2
1
1
1
0
0
2
0
0
2
1
0
1
0
1
3
1
0
2
0
2
0
0
1
1
1
2
1
0
2
2
1
0
0
2
0
1
0
0
0
0
2
0
0
1
0
1
1
2
1
0
0
1
0
0
0
4
1
2
2
1
0
0
3
1
2
1
2
1
0
2
2
1
0
1
1
1
2
1
1
0
0
3
1
1
0
0
0
1
1
0
0
0
1
1
0
1
2
0
0
1
2
0
0
1
0
2
1
2
0
9
3
0
0
2
0
0
0
0
0
2
4
2
1
1
0
2
0
1
0
0
2
1
2
1
0
1
0
2
0
2
1
0
1
1
2
1
1
0
1
0
1
2
0
1
2
1
1
1
1
1
2
1
0
2
2
2
0
0
0
1
1
0
2
0
0
0
0
0
0
1
2
2
1
2
0
2
1
1
2
0
0
2
1
0
0
2
2
1
1
1
0
0
1
1
1
0
0
1
0
0
1
0
2
1
0
3
2
0
0
1
0
1
1
1
1
1
2
0
2
1
1
0
2
0
0
0
2
2
1
1
1
0
0
1
1
0
1
1
1
1
1
0
0
0
1
0
2
1
0
1
0
1
0
2
1
0
2
2
2
0
1
0
0
0
2
1
3
1
0
2
1
0
1
0
1
1
0
1
2
1
2
2
1
2
0
2
0
1
0
1
1
0
1
0
0
0
0
1
0
1
2
0
1
2
0
1
0
0
0
0
0
1
2
0
1
1
0
2
0
1
0
0
0
1
0
0
0
0
0
1
1
1
1
1
1
2
0
0
2
1
0
0
1
2
1
0
2
1
1
0
1
1
1
0
1
0
0
2
1
2
0
1
1
1
2
0
1
0
0
2
2
0
0
0
1
0
1
1
1
0
0
1
1
0
1
0
0
0
1
1
0
2
2
0
1
0
1
0
2
1
2
0
1
1
1
2
0
1
1
1
1
2
0
1
1
1
1
1
2
1
1
2
0
0
0
1
1
0
2
2
3
2
1
0
2
1
1
1
1
0
2
2
0
0
1
0
1
0
1
0
1
0
0
0
0
2
0
0
1
2
0
2
0
0
2
0
2
0
0
0
0
0
0
1
0
2
0
0
1
1
0
1
1
0
1
2
2
0
1
1
0
0
2
0
2
2
0
0
3
0
0
2
2
0
2
1
1
0
0
1
1
1
2
2
0
1
2
1
0
1
0
1
3
0
1
0
2
0
0
0
1
2
4
2
0
2
1
1
0
1
0
0
0
2
2
2
0
1
0
2
2
1
1
2
0
1
2
2
1
0
2
0
0
1
1
2
0
1
0
2
1
0
2
2
2
2
0
0
0
1
1
1
2
0
0
0
2
1
0
0
0
2
1
1
0
0
1
0
4
0
2
0
2
0
1
2
0
1
1
1
1
0
0
1
0
0
1
0
1
3
1
0
0
1
1
3
1
2
1
0
2
1
0
0
1
1
1
0
1
1
0
0
1
1
2
2
1
2
2
2
2
0
1
1
0
1
0
0
0
1
1
1
1
1
0
2
0
1
0
2
1
0
1
1
0
1
1
1
1
1
1
0
2
1
0
0
0
1
0
1
0
0
1
1
1
1
0
2
2
1
2
0
0
1
0
1
3
1
1
0
1
1
1
0
0
0
1
1
0
1
1
1
0
1
0
2
2
2
1
0
2
1
1
1
0
1
1
1
2
1
1
2
0
0
0
0
0
2
0
1
1
1
0
0
1
2
0
1
1
0
0
1
1
1
1
2
0
2
0
2
0
1
2
0
1
0
2
1
0
1
0
0
1
2
0
0
0
1
0
1
0
1
1
0
0
2
3
2
1
2
0
2
1
1
1
0
0
2
0
1
0
0
0
0
1
0
1
1
1
0
3
0
2
0
0
1
0
2
1
2
0
2
1
0
0
3
2
1
0
1
0
1
0
0
1
2
0
0
0
2
1
1
1
1
1
2
0
0
2
0
1
0
1
1
2
1
0
1
0
2
0
1
0
2
0
0
0
1
0
1
3
1
0
0
0
1
1
2
0
0
0
1
1
0
1
1
0
0
2
2
0
0
0
2
1
0
0
0
2
0
1
2
1
0
0
2
1
1
2
2
0
0
1
1
2
0
1
1
2
2
0
1
2
0
0
1
0
1
1
0
1
0
1
2
1
2
2
1
0
0
0
0
2
1
0
1
2
1
0
0
0
2
0
1
1
0
1
0
0
1
1
1
0
1
1
2
0
1
2
0
1
1
0
1
0
1
1
1
1
1
0
2
2
0
1
0
0
2
0
1
0
0
1
0
0
1
1
0
0
0
0
2
0
0
0
2
0
0
1
1
1
0
0
1
3
0
1
1
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
1
2
3
0
1
1
1
0
0
0
2
0
2
0
0
1
1
1
1
1
1
2
1
1
3
2
0
1
0
1
1
1
0
0
0
2
0
1
2
1
2
0
3
2
0
1
0
1
1
0
1
0
2
1
0
0
1
2
1
0
1
2
0
0
0
1
2
0
0
0
1
1
0
1
2
0
2
0
1
2
0
0
0
1
1
2
2
1
0
1
0
0
0
2
2
0
2
3
2
0
1
1
2
1
0
0
0
0
1
1
0
0
0
1
4
2
0
1
1
1
0
2
0
1
0
1
2
1
1
1
0
0
0
0
0
1
0
1
0
0
0
1
1
2
1
0
2
1
1
2
1
0
0
0
0
1
2
1
0
0
1
1
1
2
1
1
1
1
2
1
1
1
0
0
0
0
1
2
2
1
0
2
1
2
1
0
0
0
0
1
0
0
0
1
1
0
1
1
0
1
2
1
0
2
0
1
0
0
3
2
2
0
0
0
2
0
1
1
0
0
0
0
0
0
3
0
1
2
2
1
0
2
1
0
0
1
2
0
0
1
1
0
0
7
1
1
0
0
0
1
3
0
2
0
1
1
2
0
0
2
2
2
0
1
0
1
0
0
1
1
0
0
2
1
0
0
2
1
0
0
2
1
0
1
1
1
1
0
0
1
2
0
1
0
0
2
0
0
0
1
2
0
0
2
1
1
0
1
0
1
0
2
1
3
0
1
1
0
2
1
0
1
1
4
1
2
1
0
0
0
2
2
1
0
2
0
1
1
3
0
1
2
2
1
2
1
2
2
0
1
1
1
2
0
0
1
2
0
1
0
2
1
0
5
1
0
0
1
0
2
2
1
0
3
0
1
0
2
1
2
0
1
0
2
1
1
1
0
0
1
1
1
0
0
1
0
0
1
1
1
1
2
1
0
2
1
2
1
0
2
2
2
1
0
0
0
0
1
0
2
2
2
1
0
0
1
0
1
1
2
2
1
1
2
2
2
0
0
1
2
0
0
1
0
0
0
0
0
2
2
0
1
0
2
0
1
0
2
2
1
0
2
0
1
1
2
0
3
1
1
2
1
2
0
0
0
1
2
0
2
1
1
2
2
2
2
0
0
0
0
2
1
2
0
0
0
1
0
2
2
0
1
1
0
0
0
0
0
1
2
1
2
0
0
0
1
1
0
0
0
1
0
1
0
1
1
2
1
1
0
2
3
1
0
1
1
2
0
0
2
0
0
1
2
1
1
2
2
0
0
0
1
2
1
0
0
2
2
0
0
0
1
0
1
0
1
1
0
1
1
3
2
1
1
0
2
0
0
0
0
2
0
0
2
2
2
2
2
1
0
3
0
0
2
1
0
1
0
1
2
0
1
0
2
0
1
1
0
0
0
0
1
1
0
0
2
0
0
1
1
0
1
1
2
1
2
0
1
1
0
1
0
0
1
1
0
2
1
1
2
0
0
1
1
1
1
1
2
1
0
2
3
0
1
1
1
0
1
2
0
0
1
2
1
2
0
0
0
3
1
1
1
1
2
2
0
0
0
2
2
2
1
2
1
0
5
2
0
0
0
2
2
2
0
0
2
0
0
1
0
1
0
0
0
2
1
0
1
1
0
0
0
2
1
0
1
0
0
2
2
0
1
0
2
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
2
0
0
1
0
1
0
1
0
0
0
0
1
2
1
2
0
0
1
2
2
0
0
1
0
1
0
1
1
0
1
1
1
1
0
1
0
0
1
0
2
2
0
1
2
1
1
0
1
2
2
1
0
2
0
1
0
1
0
1
1
2
1
0
2
2
2
1
0
0
1
0
0
0
0
1
0
2
0
1
1
2
1
1
0
0
0
0
2
2
1
0
1
1
0
0
1
0
2
0
0
1
0
0
0
1
1
0
1
1
0
0
1
1
2
0
0
1
1
0
0
0
1
0
1
0
2
0
2
1
0
0
2
2
1
0
0
2
0
0
0
0
0
0
1
0
1
1
1
1
0
1
0
2
0
0
0
2
0
0
2
1
2
0
0
0
2
0
2
0
0
3
0
1
1
0
0
1
1
2
2
2
1
0
2
1
0
1
1
1
0
2
1
2
0
1
0
1
0
2
1
1
2
0
4
0
0
2
0
1
1
0
0
1
0
0
2
2
1
2
1
1
2
0
1
1
3
1
1
0
1
1
1
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
1
1
1
1
0
1
0
0
1
0
1
0
0
1
0
0
2
2
2
0
2
0
0
0
0
0
0
0
1
1
0
2
0
1
0
2
1
0
1
2
1
1
0
2
0
2
2
1
0
1
0
1
1
2
0
1
1
2
0
2
1
1
0
0
0
2
2
1
0
0
0
2
0
2
1
0
1
0
1
1
1
1
2
1
2
1
4
0
1
2
1
1
0
1
2
2
1
0
0
0
0
0
2
0
1
1
1
1
0
1
2
1
2
1
0
2
2
1
1
0
0
1
0
1
0
0
2
2
0
1
0
1
1
1
2
0
0
1
0
0
1
1
0
2
0
2
1
1
1
0
0
2
0
0
1
0
1
1
3
1
1
1
0
0
0
1
1
0
0
2
1
2
1
2
0
2
0
0
1
1
0
0
1
2
0
0
1
2
1
0
0
1
0
1
1
1
1
0
1
1
1
1
1
1
0
1
1
0
0
1
0
1
1
2
1
0
1
1
2
1
1
1
0
1
2
1
0
0
2
0
0
0
1
0
0
1
3
1
2
1
1
1
1
0
1
1
0
1
0
2
1
0
1
2
0
0
0
1
2
1
1
1
1
0
0
0
2
1
0
1
1
3
0
0
0
1
1
2
1
0
0
1
2
1
0
0
2
1
0
0
1
0
1
0
0
2
0
1
0
1
2
0
1
0
2
0
2
1
1
1
2
2
0
0
0
0
0
0
0
0
0
2
1
0
0
1
2
2
0
0
2
0
1
1
0
0
2
2
1
2
1
0
1
0
0
0
1
0
2
2
1
0
0
0
1
2
3
2
1
1
2
0
0
1
1
0
0
1
2
0
0
2
0
0
2
0
2
1
1
2
0
0
1
0
3
0
0
0
2
0
1
0
1
2
0
1
1
2
1
0
1
0
0
0
1
2
0
0
1
0
0
1
0
1
0
0
0
0
1
1
1
2
0
1
0
0
1
1
2
0
0
0
0
1
0
3
2
1
0
1
0
0
1
1
0
0
1
2
2
1
2
1
2
1
2
2
1
2
0
1
2
0
0
0
1
0
2
0
0
0
0
1
2
0
0
1
1
0
0
0
1
2
0
1
1
0
1
0
0
0
2
1
0
1
0
1
0
1
1
2
0
1
1
2
1
0
0
0
1
1
1
0
0
0
0
1
1
0
0
0
1
0
2
0
0
1
0
0
1
2
1
2
1
1
2
0
0
2
1
1
1
1
0
2
1
1
0
1
2
2
0
0
0
2
2
0
1
1
1
2
0
0
1
0
0
0
0
1
0
1
0
2
0
1
0
1
0
0
1
1
1
0
0
0
2
0
2
1
1
1
1
0
2
1
0
0
0
1
0
1
0
0
0
1
0
3
2
2
0
1
1
2
1
0
0
0
0
2
0
1
0
0
0
1
0
1
1
0
1
2
1
0
0
2
2
2
1
0
1
0
0
1
0
1
1
2
0
2
0
0
1
0
1
2
1
0
0
2
0
0
1
0
1
0
1
0
0
1
2
2
1
2
0
1
1
1
0
1
1
0
2
0
1
0
0
0
1
2
0
2
0
1
0
2
2
2
1
0
3
0
1
1
1
1
1
1
0
2
1
0
1
1
1
1
0
2
1
1
0
3
0
3
0
0
0
2
0
2
0
0
2
0
1
0
0
0
1
2
0
0
1
0
0
0
3
1
1
1
0
1
3
0
3
0
0
0
2
1
2
1
0
0
2
1
1
0
1
1
2
1
0
0
0
1
1
0
3
0
0
1
1
2
0
2
2
0
1
0
0
0
1
0
2
0
1
0
1
1
1
1
2
1
2
0
0
0
1
0
0
1
1
0
0
0
2
1
0
1
1
0
1
0
2
0
0
0
0
2
0
0
2
1
1
1
1
0
2
2
2
0
0
2
1
0
1
1
0
1
2
1
0
0
1
0
0
2
2
1
2
0
1
1
2
2
1
0
1
0
0
1
0
0
0
1
1
1
0
2
1
1
0
1
1
0
2
1
1
0
0
0
0
0
0
1
1
0
0
1
0
1
2
0
0
0
1
0
0
0
1
0
2
0
0
3
0
0
2
0
1
1
0
0
2
0
2
0
0
0
3
0
0
2
0
0
1
2
1
1
1
0
0
1
0
2
0
2
0
0
0
2
0
1
0
2
1
1
2
1
1
0
1
1
0
1
1
0
1
1
0
3
2
2
0
0
1
0
0
0
2
1
1
2
1
2
1
1
1
1
0
2
0
0
1
0
0
0
1
1
1
0
1
1
2
0
0
1
0
1
1
0
0
2
0
1
2
0
0
0
0
0
2
0
1
1
2
1
1
1
2
0
1
1
1
1
0
0
1
2
0
2
2
0
0
3
1
1
1
0
0
0
1
0
1
0
0
1
1
1
1
0
2
0
2
1
2
1
0
0
0
1
2
0
0
1
0
0
0
1
0
0
2
1
0
0
0
1
2
0
1
0
0
0
0
0
1
1
1
1
1
1
1
1
0
2
0
1
1
2
0
1
0
0
0
0
1
1
0
2
0
4
1
2
0
0
2
1
1
1
2
0
0
0
1
1
1
0
1
1
2
0
1
2
1
0
0
3
1
0
2
0
1
2
1
0
0
1
1
2
0
2
1
1
2
0
1
0
1
2
1
3
0
1
2
0
0
1
0
0
2
1
0
1
1
0
0
0
0
2
2
0
2
1
0
1
0
2
0
0
1
2
2
1
0
5
0
0
1
2
0
0
0
2
0
1
1
2
1
0
2
0
0
0
2
0
1
1
1
3
2
1
2
0
0
1
0
1
0
2
1
0
3
0
0
0
1
1
1
0
0
0
3
1
2
1
1
0
0
0
3
1
0
1
1
0
0
2
1
2
2
0
0
1
2
0
0
2
0
0
0
1
2
1
2
2
1
2
1
1
0
0
1
0
0
0
0
0
1
0
0
0
2
1
2
1
1
0
0
1
1
2
0
0
1
2
0
2
1
0
0
1
0
0
0
1
1
0
0
1
1
0
1
0
0
2
2
3
1
1
1
2
0
0
1
0
1
0
0
1
1
1
1
1
1
1
2
0
1
1
1
0
1
0
0
0
0
0
1
0
1
1
1
3
0
2
1
2
1
0
0
0
0
0
2
0
1
0
2
2
2
0
0
0
1
0
0
0
1
1
0
2
1
3
1
0
1
1
2
1
1
1
2
0
1
2
1
0
0
0
0
1
0
1
1
1
0
3
2
0
1
0
2
1
0
1
1
0
0
0
1
1
1
0
0
1
0
0
1
1
1
1
0
1
0
1
2
1
0
0
0
0
2
0
0
3
2
2
2
2
0
1
0
1
1
1
2
0
0
1
1
0
0
2
2
4
0
0
1
1
2
0
1
1
1
2
0
1
2
2
1
2
0
1
0
2
1
0
1
1
0
0
1
0
2
0
2
1
1
2
2
0
0
2
0
1
0
1
1
1
0
0
1
0
2
1
1
1
0
1
0
1
0
0
0
1
0
2
0
1
0
0
0
1
2
0
0
0
2
1
1
0
1
8
0
1
1
0
0
2
0
2
1
1
2
1
2
2
1
0
0
0
1
2
3
0
0
1
1
1
0
1
0
0
2
0
2
0
10
2
1
2
0
2
0
2
1
0
2
0
0
0
0
0
0
1
0
1
0
1
2
1
2
2
1
0
0
0
1
3
1
2
1
1
1
0
1
0
0
2
2
0
0
0
1
2
2
2
0
0
1
0
1
0
1
0
1
1
0
2
2
1
2
0
2
2
0
0
1
1
1
1
2
2
0
0
2
0
0
2
2
0
2
1
0
0
1
1
0
0
1
0
2
0
0
1
1
1
2
0
1
0
1
0
1
2
0
1
0
0
3
1
1
2
0
1
0
1
1
1
1
1
0
2
2
0
0
0
2
1
0
0
1
0
0
0
0
0
2
2
1
1
0
0
2
1
0
0
2
0
0
0
2
0
1
0
2
0
0
2
1
2
0
0
0
0
1
1
2
0
0
1
0
0
1
1
0
0
0
0
1
0
1
2
0
2
3
0
1
2
2
1
0
0
1
0
1
0
1
0
0
2
0
2
0
0
1
1
0
1
0
0
0
0
0
0
1
1
1
0
1
1
2
1
1
0
2
1
0
0
1
1
0
1
2
3
1
1
2
2
0
1
2
0
2
1
0
1
1
0
1
1
2
1
2
2
0
0
2
2
0
0
1
1
0
1
0
0
1
2
0
2
1
0
0
1
1
0
0
1
0
1
1
2
1
1
2
0
0
1
0
1
0
2
1
0
0
2
2
1
1
1
0
0
1
0
2
0
1
0
1
0
1
0
0
1
1
1
2
0
0
0
0
0
0
2
0
2
1
1
2
1
0
0
2
1
2
0
2
2
1
0
0
1
1
0
2
0
2
1
1
0
0
2
0
2
0
1
1
0
0
1
2
0
1
2
0
1
1
1
1
1
0
0
1
1
0
0
2
2
0
1
2
1
0
2
1
1
0
1
1
2
0
0
2
1
2
2
2
1
0
0
2
4
2
1
0
0
0
2
2
0
0
2
1
0
1
2
0
2
2
3
1
1
2
0
1
1
1
2
0
1
1
2
0
1
0
1
0
1
3
1
0
0
2
0
0
0
0
0
1
0
0
1
0
0
2
0
2
1
1
2
6
2
2
0
1
0
0
0
1
1
1
0
0
0
0
2
0
2
1
2
1
0
2
1
0
0
2
0
2
0
0
0
2
3
1
2
0
2
0
1
0
1
1
1
1
0
1
2
1
2
0
0
1
0
0
1
1
2
1
1
1
1
0
1
0
2
1
0
1
1
0
0
0
0
0
2
2
0
2
1
1
1
1
1
0
1
0
2
1
2
1
2
2
1
1
3
1
1
2
0
0
0
0
1
2
2
2
0
1
2
2
1
0
1
0
2
0
0
1
1
1
1
0
1
1
0
1
0
2
1
1
1
1
1
1
0
0
1
1
1
1
1
1
0
1
0
1
2
1
1
1
1
1
1
0
1
0
2
0
2
1
0
0
0
0
1
0
1
0
1
0
1
2
0
0
0
1
2
1
1
2
2
2
0
1
1
0
0
0
3
0
0
2
2
0
0
1
1
0
0
0
0
2
0
0
2
2
0
1
0
1
0
2
1
1
0
1
1
0
2
1
1
1
0
1
1
0
0
0
1
1
1
0
0
0
1
2
0
0
0
2
0
1
1
0
1
2
1
0
1
1
0
0
0
1
1
0
1
1
1
0
2
0
0
0
2
2
0
0
0
1
1
1
1
2
0
0
1
1
1
2
1
0
0
1
0
0
1
0
1
0
1
0
0
0
0
1
2
1
2
2
1
1
1
0
0
1
0
0
0
2
0
0
0
2
2
2
2
1
0
0
0
1
1
0
0
1
0
2
1
0
1
0
2
0
1
0
1
2
0
0
0
0
0
0
2
1
0
1
1
2
2
1
0
1
1
0
0
1
1
1
0
1
0
0
1
0
2
1
0
0
0
1
0
1
2
1
2
0
2
2
2
0
1
1
0
1
0
0
1
0
0
0
0
0
2
0
2
0
1
1
1
1
0
2
1
0
1
0
2
2
1
0
0
0
2
0
1
1
1
3
1
1
0
2
0
1
1
1
1
1
0
0
1
1
0
0
3
1
0
1
1
1
2
0
2
1
1
3
0
0
2
0
2
1
2
1
1
2
1
2
1
1
0
0
0
1
2
1
2
1
0
1
2
1
2
2
2
0
2
0
0
0
1
1
0
2
1
0
1
1
0
1
0
2
1
0
1
0
1
1
0
0
2
0
0
1
1
0
2
2
2
2
0
1
1
0
1
0
1
2
2
1
1
0
1
1
1
1
0
2
2
0
0
0
0
2
3
0
0
0
2
1
1
0
0
1
1
0
0
2
0
0
1
0
1
2
0
2
1
1
1
0
2
1
0
1
0
2
3
1
0
1
1
1
0
0
1
1
2
0
1
0
0
1
1
1
1
1
1
1
1
0
1
1
0
1
1
1
1
2
1
0
1
2
0
2
0
1
0
1
0
0
0
1
1
0
2
2
1
1
0
0
1
2
1
0
0
0
1
1
1
0
0
1
0
2
1
0
1
0
0
1
0
0
1
2
0
0
1
2
2
0
0
1
1
0
2
2
0
1
0
1
0
1
1
1
1
0
1
0
0
0
0
1
1
0
1
0
0
0
1
1
0
1
0
0
1
0
1
1
1
1
1
2
0
1
0
1
0
1
2
2
1
1
0
1
1
1
1
0
0
0
1
2
2
1
0
0
2
2
1
1
1
0
1
1
0
1
1
2
1
2
2
1
1
0
0
2
1
0
1
1
0
3
0
1
0
0
2
0
0
0
0
1
0
0
1
1
1
1
0
2
0
0
0
2
2
2
1
0
1
0
2
1
2
1
1
2
2
1
1
2
1
1
2
2
2
0
0
0
2
0
1
0
1
0
1
0
0
1
1
0
1
0
1
2
0
0
1
2
1
2
1
0
0
0
1
1
1
1
1
1
2
1
1
2
1
1
2
1
1
0
0
1
1
0
0
1
0
0
1
0
2
1
1
0
1
0
0
1
1
1
1
1
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
1
2
1
0
2
1
0
1
0
2
0
0
1
1
2
0
2
0
0
1
0
2
2
2
1
0
2
1
1
1
0
0
1
2
2
1
0
0
1
2
1
1
0
0
0
0
0
0
2
2
2
1
1
0
0
0
0
2
1
1
1
1
0
1
2
2
1
1
0
0
0
1
1
0
0
1
1
2
1
1
1
0
2
0
0
2
0
0
0
0
2
2
0
1
2
1
1
2
0
0
0
1
0
0
0
0
1
2
1
2
0
1
0
0
2
0
1
1
0
0
0
1
2
2
1
0
0
2
0
1
0
1
1
1
2
1
1
1
0
1
0
0
2
0
1
0
0
2
0
0
1
1
0
2
0
0
1
1
0
2
0
0
0
2
0
1
1
0
1
0
2
0
1
1
1
2
0
0
1
0
3
2
0
2
2
0
1
0
0
0
0
1
1
0
2
1
0
0
1
2
1
0
0
4
0
0
1
3
1
0
2
1
1
2
2
0
2
0
1
0
2
1
0
1
1
1
0
0
0
0
1
0
0
2
2
1
0
0
1
0
1
0
0
0
1
0
2
2
1
0
1
0
0
2
0
0
1
1
2
0
1
0
1
0
0
2
2
2
1
1
1
1
1
0
1
0
0
1
1
2
1
0
1
0
0
0
2
2
4
1
1
1
0
0
2
1
1
2
1
2
1
0
0
0
1
0
1
2
0
0
1
2
0
0
2
2
0
1
2
1
0
1
1
3
1
0
0
2
0
1
1
2
1
0
2
1
1
0
0
0
1
0
0
1
1
0
1
1
1
0
1
1
2
1
1
0
0
0
1
0
2
0
0
2
1
1
1
1
3
0
2
1
1
1
1
2
0
2
0
2
1
1
1
0
1
0
2
1
2
1
2
1
0
2
0
0
0
0
1
0
2
0
2
0
0
1
1
0
1
0
0
0
0
2
1
1
0
1
2
0
1
1
1
0
0
1
2
1
1
0
0
2
1
2
1
0
2
1
0
3
0
1
2
0
1
1
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
1
1
1
1
1
1
1
1
1
0
1
1
0
1
1
0
1
0
1
3
0
1
1
2
1
0
1
0
2
1
1
7
1
1
3
1
0
1
2
0
2
1
1
2
0
1
1
0
0
1
3
0
2
1
1
0
1
2
1
1
1
0
0
2
1
2
1
1
1
2
0
0
2
0
0
2
1
0
0
1
1
0
0
0
1
2
1
1
0
0
2
2
2
2
0
0
1
0
0
0
1
1
0
0
0
1
0
1
2
1
1
0
1
2
0
2
0
1
1
0
1
0
1
2
1
1
2
1
1
0
1
1
1
1
2
0
0
0
0
1
2
1
2
2
2
1
2
1
2
1
0
0
2
0
0
0
0
2
0
0
1
0
2
0
2
1
1
1
1
2
0
2
2
0
3
1
1
2
1
1
0
0
0
0
0
2
0
0
0
0
0
0
1
1
1
0
1
2
0
2
0
2
1
0
1
0
1
1
2
0
1
1
2
0
0
1
1
0
1
1
0
3
1
0
1
0
2
0
1
1
1
2
1
0
0
1
2
2
0
0
0
0
1
0
1
1
0
1
1
0
0
0
0
0
0
1
1
1
0
0
0
2
0
1
0
0
0
1
0
2
1
0
2
1
2
1
1
0
2
3
0
2
2
0
0
2
1
1
1
0
0
0
1
2
1
2
2
1
1
3
0
2
1
0
0
2
2
0
2
1
0
0
0
1
1
3
0
2
0
1
0
1
1
0
0
1
1
2
2
1
1
1
1
2
0
1
0
1
0
2
1
0
1
2
1
1
0
1
1
0
2
2
1
2
1
1
0
0
0
0
2
2
0
1
2
2
0
1
0
2
1
1
3
2
0
1
0
2
1
0
1
2
2
1
1
0
0
0
2
1
0
0
0
0
1
0
2
1
1
1
0
0
0
0
1
0
2
2
0
0
0
0
0
1
0
2
1
1
0
0
0
0
0
1
1
2
1
1
2
1
2
0
1
0
2
0
1
1
1
0
4
0
2
0
1
0
2
1
2
2
2
1
0
0
1
1
0
4
1
0
2
2
0
1
2
0
2
2
2
2
0
0
1
1
2
0
2
2
0
2
0
0
0
1
1
0
2
0
1
0
1
0
0
2
0
1
0
1
1
0
0
2
1
0
0
2
1
2
1
1
1
1
0
1
0
0
0
2
1
1
0
0
2
1
0
1
1
0
1
4
0
0
1
0
1
0
0
1
1
5
0
0
0
2
0
1
0
0
1
2
1
2
0
1
0
0
1
1
1
1
1
2
0
0
0
1
1
1
1
0
1
1
0
0
0
1
1
2
2
2
1
1
0
2
0
1
1
1
1
0
1
1
1
2
1
1
2
1
1
1
2
0
0
2
0
0
0
2
2
0
1
0
2
0
1
2
1
2
0
1
1
0
2
0
1
0
2
0
2
0
1
1
1
0
2
4
2
2
0
1
0
2
3
2
2
1
2
2
2
1
0
0
1
0
2
0
0
0
0
0
1
1
1
0
0
1
1
1
2
1
0
2
2
0
1
0
0
2
2
1
1
0
0
2
1
1
0
0
0
2
2
1
1
1
1
1
1
1
1
2
0
1
2
2
1
2
1
2
1
0
2
1
1
1
0
2
1
2
2
0
1
1
1
1
2
1
0
0
1
1
3
2
1
0
0
0
0
1
0
1
0
1
0
0
0
0
1
2
0
0
1
0
0
0
0
0
1
0
1
0
1
1
1
0
1
0
1
1
0
2
2
1
0
1
0
0
1
0
0
0
1
1
2
1
2
1
1
3
0
0
0
1
1
1
2
1
2
1
1
2
1
2
1
1
1
0
0
1
1
1
0
0
1
1
1
2
1
1
1
0
0
0
1
0
0
0
0
0
1
1
0
0
1
2
0
1
0
1
2
2
2
0
0
1
1
1
0
2
1
1
1
0
1
0
0
1
1
1
2
2
0
2
0
2
0
1
1
0
0
1
0
1
1
1
1
1
0
1
1
1
1
0
1
1
1
1
1
0
2
2
0
0
1
1
1
0
0
2
1
0
0
0
0
1
0
1
0
2
1
2
2
0
0
2
0
0
1
1
0
2
2
2
1
0
0
2
2
1
1
2
0
3
1
0
0
1
1
2
1
0
2
1
0
1
0
0
1
0
0
0
0
0
0
2
2
0
0
2
1
0
0
3
0
0
0
1
0
0
0
2
2
0
2
0
1
0
0
1
0
1
1
1
2
0
1
1
2
1
1
1
1
1
0
1
1
1
2
0
1
2
0
2
0
0
1
2
1
1
0
0
0
1
2
0
2
1
1
0
1
1
1
0
0
0
2
1
1
0
1
1
0
0
0
2
0
0
1
0
1
1
0
2
1
0
2
1
0
0
1
1
1
0
1
1
2
0
2
1
1
0
0
1
0
0
1
2
1
1
1
2
2
1
0
2
1
1
0
2
2
1
1
0
0
2
0
0
1
0
0
0
2
0
0
0
0
2
1
1
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
1
1
0
2
0
0
0
0
1
2
0
1
1
1
1
0
0
1
4
0
1
0
0
1
1
2
1
1
0
0
1
0
2
2
0
0
2
1
2
1
0
0
3
0
2
0
1
2
0
1
1
1
0
1
0
0
1
3
1
2
0
2
0
1
2
0
0
0
0
0
0
0
2
1
2
2
2
1
1
0
0
1
0
0
0
1
2
3
2
1
1
3
0
1
0
1
0
1
1
0
1
2
0
0
0
0
2
1
0
1
0
0
1
0
2
0
1
0
2
0
0
1
1
0
1
1
1
0
1
0
1
0
2
0
1
0
0
1
2
0
1
0
0
0
0
1
0
0
0
2
1
1
1
1
0
1
1
2
0
0
1
1
2
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
2
0
0
1
0
2
2
2
1
1
2
0
1
0
1
1
1
1
0
0
1
1
2
0
0
2
0
0
0
0
1
0
2
1
2
1
1
0
0
2
1
0
0
0
2
2
2
0
0
0
1
1
2
0
0
0
1
2
1
2
0
1
1
0
2
0
1
1
0
0
0
1
2
1
1
1
0
0
1
1
1
0
2
2
1
0
2
0
0
1
0
0
0
1
0
0
0
2
0
0
0
2
2
1
0
0
1
2
0
2
0
1
1
0
0
0
0
1
2
1
0
0
0
2
2
0
1
2
1
1
0
1
2
1
0
0
3
1
1
2
1
2
1
0
0
0
0
2
1
1
2
0
2
0
1
1
1
0
0
1
2
2
1
1
1
0
1
0
1
0
0
0
1
2
2
0
0
0
1
0
2
1
1
0
0
1
0
0
0
0
2
2
0
0
0
3
1
0
2
0
1
1
2
0
1
0
0
1
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
1
1
2
1
2
1
1
0
1
0
1
1
0
1
0
1
1
0
1
0
0
1
0
0
0
0
0
1
1
1
2
1
0
2
0
1
0
0
0
0
0
1
2
2
2
2
0
0
0
0
0
2
1
2
1
1
0
2
0
2
0
1
0
1
2
0
0
0
0
2
0
1
0
2
1
0
0
0
0
2
2
2
0
0
2
0
0
0
1
1
0
0
1
0
1
1
0
1
1
0
2
0
0
1
0
1
2
1
1
0
0
0
0
0
1
2
2
2
0
1
1
0
0
0
0
0
2
0
1
0
3
1
1
1
2
2
0
1
2
2
2
0
0
2
0
0
1
1
3
0
1
2
0
0
1
2
1
0
1
1
2
2
0
0
1
1
2
1
0
2
1
0
0
0
2
2
1
1
1
1
1
0
3
1
0
2
1
1
0
3
0
1
0
4
1
1
0
1
0
2
1
1
0
0
1
1
1
2
0
1
1
1
1
2
1
0
0
0
1
2
2
0
0
1
0
1
0
0
2
2
1
0
0
1
0
0
0
2
1
0
1
0
1
1
1
1
0
0
2
1
1
1
0
1
2
2
2
0
1
0
1
1
1
1
0
1
1
0
1
0
1
1
2
2
0
1
1
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
1
1
0
2
0
0
0
2
1
1
0
2
0
0
0
1
2
1
1
1
0
0
0
2
1
1
0
1
1
0
0
1
1
0
0
1
2
2
2
0
1
2
0
1
0
0
1
2
2
0
1
1
1
1
2
1
0
1
1
0
1
1
0
0
0
1
1
2
2
1
1
1
0
0
1
1
0
1
1
0
1
0
2
1
1
0
0
0
1
1
0
0
1
1
0
2
1
0
0
1
2
1
2
0
0
0
0
1
1
0
1
1
2
1
0
3
2
1
1
1
2
2
1
1
0
0
1
0
1
1
1
0
0
2
1
1
2
1
1
0
2
3
0
0
1
2
1
1
0
2
1
0
0
3
0
1
0
0
0
2
1
3
2
1
0
0
0
2
0
1
2
1
0
0
2
0
0
0
0
1
2
0
0
0
2
0
1
0
1
0
0
2
2
2
3
0
1
0
1
2
1
0
2
0
1
3
2
2
0
0
0
0
0
1
1
0
2
0
0
0
2
0
0
1
1
0
0
0
2
1
0
1
0
2
1
0
1
0
2
0
1
0
1
1
1
2
2
1
2
0
1
0
2
1
0
1
0
2
2
2
0
1
1
2
0
1
0
1
1
1
1
1
0
2
2
2
0
1
2
0
1
0
0
1
2
1
0
0
1
1
1
2
1
0
0
0
2
0
1
0
0
0
0
0
0
1
1
2
0
2
0
0
1
1
2
1
0
2
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
2
1
1
0
2
0
0
1
1
0
0
2
2
2
3
2
0
2
0
0
0
0
2
1
0
0
2
1
0
0
1
0
1
1
3
0
0
0
1
0
1
0
2
1
0
0
1
0
1
1
1
0
1
1
0
0
1
0
0
2
1
2
1
0
1
0
0
2
0
0
0
0
0
1
2
2
2
3
1
0
1
1
0
2
0
0
2
2
1
0
2
1
0
0
1
2
0
0
0
1
1
0
0
1
0
2
1
0
0
2
0
1
1
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
1
2
0
0
2
1
1
2
2
2
1
0
0
0
0
1
1
0
0
1
1
1
0
1
1
1
1
2
0
1
0
0
1
2
1
0
2
2
1
2
0
0
1
0
1
0
2
2
1
0
0
0
0
1
2
1
0
0
1
0
0
0
0
1
0
0
0
1
1
1
1
0
1
0
2
0
0
2
1
1
2
1
1
2
0
0
0
0
1
0
1
1
1
0
0
1
0
3
3
0
1
1
0
2
0
1
1
0
2
2
1
0
0
3
1
1
0
0
2
0
0
0
1
2
2
1
1
2
0
2
0
0
1
0
0
0
0
1
1
2
2
1
2
1
0
0
0
1
0
0
1
1
0
1
0
0
0
2
1
1
2
0
0
0
2
0
1
0
0
2
1
0
2
2
0
0
0
1
0
1
1
1
0
3
0
1
0
2
2
0
0
2
0
0
0
1
0
0
1
1
0
0
0
1
0
0
1
0
1
0
1
1
0
1
0
2
0
0
1
0
1
1
1
1
2
1
1
2
0
1
1
0
1
0
0
0
0
0
2
1
0
0
1
1
0
1
1
1
2
1
2
1
2
0
1
0
0
1
1
0
0
0
2
0
1
1
0
0
1
0
1
1
1
1
1
0
1
1
1
0
1
2
0
0
1
1
0
0
2
3
1
1
1
1
2
1
2
0
1
0
2
2
0
1
1
1
0
0
0
0
1
0
1
1
1
1
1
1
2
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
1
1
1
2
1
0
0
0
0
1
2
0
1
0
2
1
1
2
2
1
2
0
0
1
1
2
0
2
2
0
1
1
0
0
1
2
1
0
1
2
2
1
2
0
0
0
0
1
0
2
1
1
1
2
1
1
1
1
2
1
0
1
2
0
1
2
0
0
1
2
2
2
1
1
0
1
0
1
1
1
1
2
1
1
0
1
1
1
1
1
2
0
0
0
0
1
0
1
1
0
1
0
0
0
1
2
1
0
2
1
1
0
0
1
2
0
0
1
1
0
0
0
0
0
2
1
2
0
4
0
0
2
1
1
0
0
1
1
0
0
2
0
0
2
0
0
1
0
1
1
1
0
2
1
0
0
1
0
3
1
1
0
0
0
0
2
0
1
0
0
2
0
1
1
0
0
0
0
0
0
4
2
0
1
1
1
0
1
0
0
2
1
1
0
1
1
1
1
1
1
0
1
3
1
1
0
1
1
1
1
2
2
0
2
1
1
2
1
1
2
0
2
1
1
0
0
1
1
2
0
2
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
2
1
2
3
1
0
1
0
2
0
2
1
1
0
0
0
0
2
1
1
1
2
1
0
1
1
2
0
2
2
1
0
1
0
1
0
2
0
1
0
2
1
1
1
0
2
1
1
0
0
2
0
0
0
0
1
0
0
0
0
1
1
1
2
0
1
2
0
1
0
1
1
0
0
0
2
1
1
0
0
2
1
1
2
0
0
0
0
1
2
0
1
0
1
0
2
0
0
0
2
2
1
0
1
1
0
2
0
0
1
2
1
1
0
0
0
0
2
0
1
0
1
0
1
0
2
0
2
0
1
0
1
2
0
2
0
1
2
1
1
0
0
0
1
0
1
2
2
1
1
2
1
1
2
1
0
1
1
0
2
1
1
1
1
1
0
2
2
2
0
1
0
3
2
0
1
0
0
2
0
1
0
0
0
1
0
0
0
2
0
0
0
1
0
0
2
2
1
0
0
0
0
2
0
0
2
1
1
1
2
2
1
0
3
1
2
1
1
2
0
0
0
2
0
1
0
1
1
1
0
1
0
1
1
1
0
0
1
0
1
2
2
1
1
0
0
1
0
1
0
0
0
0
0
2
0
0
0
3
0
1
1
1
1
1
3
2
0
0
0
0
1
1
1
1
2
0
1
1
0
1
1
2
1
0
0
1
1
0
0
1
0
0
2
1
0
0
0
2
0
2
1
0
1
0
0
2
2
0
0
0
2
1
0
0
1
1
1
2
2
1
0
0
1
1
1
1
0
0
1
0
2
0
0
1
2
1
0
0
1
1
2
2
1
2
1
2
0
1
0
1
2
0
2
2
0
1
0
2
3
1
1
2
1
1
2
0
0
1
2
0
1
0
0
1
2
0
1
0
2
0
0
0
0
0
2
2
1
3
0
0
2
0
2
1
1
0
0
0
2
0
1
0
0
2
1
1
0
0
2
1
2
2
1
2
0
1
0
1
1
1
2
0
0
1
0
0
1
0
1
1
0
2
0
0
0
1
0
3
2
1
0
1
0
1
0
2
1
2
2
1
1
2
1
1
1
0
0
1
1
0
1
0
0
1
2
0
0
0
0
1
0
1
0
1
1
2
0
0
0
0
2
1
2
0
2
1
0
0
5
0
0
0
1
1
0
1
1
0
1
0
0
1
0
1
0
0
0
0
2
1
0
1
0
0
2
0
3
1
5
2
1
0
0
1
1
0
0
0
1
2
1
2
0
2
2
0
2
0
1
1
0
0
0
0
0
0
2
0
1
0
1
1
2
1
0
1
0
1
1
0
1
2
1
0
0
1
1
1
0
0
0
0
2
0
2
1
1
0
0
1
1
0
1
1
0
0
2
1
0
0
0
1
1
1
0
0
1
0
0
1
1
1
0
2
1
0
0
1
0
0
2
2
1
1
1
0
2
0
5
1
0
2
0
0
2
2
2
1
1
0
2
1
0
0
1
0
2
2
1
9
0
0
1
2
0
0
0
1
1
0
1
0
1
0
0
1
1
1
1
0
1
1
0
1
2
0
1
0
2
1
1
1
3
0
2
0
0
1
0
2
1
0
0
1
1
0
1
0
2
0
1
1
0
2
1
2
1
0
0
1
3
3
1
2
0
0
2
2
0
0
1
2
2
1
0
2
0
2
2
0
0
0
0
1
2
0
1
1
0
1
0
0
0
0
0
0
1
0
2
1
0
0
1
0
0
0
0
0
0
0
1
0
1
1
2
3
2
0
0
0
1
0
1
0
1
0
0
1
0
0
1
1
0
2
1
2
0
0
1
1
0
0
1
0
0
1
1
0
0
0
1
1
0
0
0
0
2
0
1
0
0
1
1
0
2
1
1
0
0
1
2
2
4
1
2
0
1
2
0
1
1
2
0
1
2
1
2
2
0
2
2
2
1
0
0
0
1
1
0
1
2
2
2
1
1
1
0
2
1
0
1
1
0
1
1
0
0
1
2
2
0
1
2
1
2
0
1
0
1
0
0
0
0
2
2
0
0
2
2
1
1
2
1
1
1
2
2
0
1
1
2
0
0
2
0
0
0
2
1
2
0
0
0
0
0
0
0
1
1
0
2
1
2
0
1
0
0
2
0
2
1
0
1
2
1
1
1
0
0
0
1
0
0
1
1
1
0
2
0
0
0
1
0
0
1
0
0
3
1
0
1
0
0
1
1
0
0
2
1
1
1
2
2
1
1
0
1
0
2
2
0
1
0
1
1
1
1
1
2
1
1
1
1
0
0
0
1
1
0
0
0
0
1
0
2
0
1
0
0
2
1
1
0
1
2
1
3
0
2
0
0
1
0
1
0
1
2
1
2
1
4
1
0
0
1
1
1
0
0
1
1
0
1
1
0
1
0
2
1
1
2
1
1
1
1
0
1
1
2
1
1
1
2
1
0
0
0
0
1
1
1
1
0
1
1
1
0
0
0
1
2
0
2
2
0
1
0
0
0
0
1
2
1
3
1
0
0
1
1
2
0
2
0
2
0
1
1
2
0
2
1
1
0
0
0
2
0
1
1
1
0
1
0
0
0
0
0
0
2
0
1
2
1
0
0
1
1
1
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
1
2
0
1
2
2
1
2
2
3
2
1
1
2
2
0
2
0
0
0
1
0
1
0
1
1
1
0
2
1
0
1
1
0
2
0
2
3
1
0
0
0
0
2
0
2
0
1
0
2
1
0
2
2
1
1
0
1
0
0
1
0
0
0
1
0
1
0
0
1
0
1
2
2
0
0
0
2
1
2
0
0
0
0
0
2
1
1
1
2
1
2
1
3
2
0
0
0
2
0
2
2
0
0
0
0
0
0
0
1
0
0
0
3
1
2
1
2
1
2
0
2
0
0
0
0
2
0
1
1
1
2
0
1
1
0
0
0
1
0
1
0
1
2
5
1
1
0
1
2
2
1
0
1
0
1
1
1
2
0
0
1
0
1
1
1
2
2
2
1
1
2
1
0
2
0
1
0
0
2
2
0
0
0
1
0
2
0
2
1
1
1
1
2
0
0
0
0
0
0
2
2
1
1
1
1
0
1
1
2
1
2
0
0
1
0
0
1
1
0
1
2
0
0
1
0
1
1
1
0
0
0
0
1
2
1
1
1
1
2
1
0
1
1
1
1
0
1
0
0
1
2
2
2
1
1
2
4
2
1
1
0
2
0
1
0
0
0
1
0
1
0
1
2
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
2
0
0
1
1
1
0
0
2
0
1
1
1
0
1
1
0
0
1
0
2
1
1
0
0
0
0
0
1
1
1
2
0
1
1
1
1
0
0
3
1
1
2
0
1
1
0
1
1
3
2
0
0
3
1
1
1
0
1
0
0
1
2
1
0
2
0
1
0
0
0
0
1
1
2
0
0
1
2
1
1
0
1
0
0
1
1
0
2
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
2
2
0
0
1
0
0
1
0
2
1
2
2
0
1
2
2
0
0
1
1
1
0
0
1
1
2
1
0
2
1
0
1
1
1
0
1
1
0
0
1
1
2
1
1
0
0
0
1
2
0
1
1
0
1
0
1
0
0
0
2
1
1
1
0
0
1
2
3
1
5
2
1
0
1
0
1
2
0
1
0
2
1
2
0
0
0
0
0
2
2
0
1
0
0
0
1
0
1
0
0
0
2
0
0
2
2
0
2
0
1
0
2
2
1
1
0
0
0
1
2
0
1
2
0
0
1
0
2
1
2
2
0
2
2
2
2
0
1
0
0
0
1
2
0
1
1
1
2
1
1
1
2
0
0
3
0
0
0
0
0
2
1
0
0
2
0
2
2
1
2
0
0
0
2
0
0
2
0
2
0
0
1
0
1
1
0
1
0
1
2
0
0
0
1
2
0
0
0
2
1
2
1
0
0
1
0
0
0
0
1
1
0
0
2
2
1
1
1
2
2
0
1
0
1
0
0
2
1
1
1
0
0
0
0
0
0
2
1
0
1
0
0
2
1
2
1
0
1
0
0
2
1
1
1
0
1
2
1
1
2
0
1
0
2
1
0
2
1
0
1
1
1
1
1
1
1
2
1
1
1
1
3
2
0
0
1
0
0
1
1
1
1
1
0
1
2
1
0
1
0
0
0
0
1
2
2
0
1
2
2
0
0
0
1
2
1
2
0
0
2
0
0
0
0
2
0
0
1
2
0
2
1
2
2
1
1
2
0
1
0
1
1
0
0
0
0
2
1
2
1
0
2
2
2
0
1
0
1
0
1
0
2
1
0
1
1
2
1
1
1
1
1
2
1
0
1
0
2
1
2
1
2
1
0
2
1
0
0
1
1
0
0
0
0
2
0
1
1
1
0
0
1
1
1
0
1
0
1
1
1
1
2
0
0
1
1
0
0
0
1
0
0
0
1
2
0
1
0
2
1
0
1
0
2
2
0
1
0
0
1
0
0
0
0
0
2
1
1
1
0
0
0
2
1
0
1
0
0
1
1
0
1
0
0
0
1
1
0
1
1
0
2
0
2
2
0
2
1
0
1
0
2
4
0
1
0
1
1
4
1
0
0
0
0
1
0
1
0
1
0
1
2
0
1
1
0
1
0
2
0
1
1
0
1
1
0
2
1
0
2
2
0
2
0
0
0
1
0
1
2
2
0
0
1
0
1
2
1
1
0
1
1
0
0
0
1
2
2
0
0
1
1
1
1
1
1
2
0
1
2
0
1
1
0
1
0
2
0
0
0
2
2
0
0
1
2
1
2
2
0
0
1
0
1
1
0
1
0
2
0
1
0
3
2
1
1
0
0
0
0
2
2
0
1
1
0
2
0
0
1
0
0
1
1
1
0
2
0
1
1
2
0
2
1
0
2
0
2
1
2
2
2
1
1
1
0
0
0
2
1
0
2
0
1
0
2
0
0
2
0
2
0
0
0
2
1
1
0
1
0
1
0
1
1
2
0
0
2
1
0
0
2
1
1
1
1
0
1
0
1
2
0
0
0
0
1
1
2
1
1
2
0
1
0
0
0
1
1
1
0
1
2
0
1
0
1
1
1
0
1
3
1
0
0
0
0
0
1
2
0
0
1
1
1
1
0
3
1
0
2
1
1
2
2
0
1
0
0
1
1
0
2
1
2
0
1
0
2
1
0
2
1
2
1
1
1
1
0
1
2
1
0
0
1
1
1
1
2
0
1
0
0
0
0
1
2
2
0
1
0
0
2
2
0
1
1
1
1
1
0
1
0
0
1
1
1
2
0
1
2
4
0
2
0
0
0
1
0
3
2
2
0
0
0
0
0
1
3
0
1
0
0
1
0
1
0
1
2
0
1
0
1
1
1
1
1
3
2
1
0
1
1
2
0
1
3
0
1
1
1
2
1
0
2
1
1
1
1
1
0
1
1
1
0
1
1
1
0
0
0
1
0
2
0
2
0
1
0
0
1
0
1
0
2
2
0
1
2
2
1
2
1
0
0
0
2
0
0
0
1
1
0
3
2
1
1
0
0
3
1
1
0
0
0
0
1
2
0
0
0
0
0
2
2
0
1
2
1
1
2
1
2
0
2
0
0
2
0
1
2
2
0
0
0
1
0
1
1
2
1
1
0
2
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
1
1
0
1
2
0
0
0
2
1
0
1
2
0
1
2
1
1
1
0
0
0
2
1
0
2
2
1
1
0
0
1
2
1
1
1
2
0
1
1
2
0
2
2
1
2
0
0
1
1
1
1
1
2
1
0
0
0
2
2
1
2
0
2
0
0
2
0
2
2
2
1
0
1
0
1
0
0
2
2
1
2
1
1
0
0
0
1
1
0
2
1
0
0
0
2
1
1
0
2
1
1
1
1
2
1
1
2
0
1
0
1
2
1
2
1
2
0
0
1
1
1
0
0
1
1
1
0
0
2
1
1
2
0
1
1
0
2
0
2
0
1
1
1
2
1
1
2
1
0
2
0
1
2
1
0
1
0
2
2
1
1
2
0
1
2
2
1
0
1
1
0
0
0
1
0
2
1
1
2
1
0
0
0
2
1
1
0
0
1
2
1
1
2
0
1
0
0
0
0
0
1
0
1
0
1
2
2
0
0
2
2
0
2
1
0
2
0
1
0
2
0
2
2
2
0
2
1
1
0
0
2
1
2
2
0
1
1
1
0
1
0
1
1
1
1
1
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
1
4
2
2
1
0
0
1
1
0
0
1
0
1
1
1
1
2
1
2
1
0
0
0
0
2
0
2
2
1
0
2
0
1
1
0
0
0
2
0
2
0
1
1
2
1
0
0
1
0
0
1
2
1
3
1
0
2
0
1
0
2
0
1
0
0
0
2
2
0
0
0
1
1
1
1
2
2
2
0
1
2
0
0
2
0
0
1
1
0
1
0
1
1
0
3
2
2
1
0
2
2
1
1
0
1
1
0
0
0
0
0
2
0
1
1
2
1
0
0
1
0
1
0
0
2
0
0
0
1
0
2
0
1
2
0
0
2
1
2
0
0
1
0
1
0
2
2
0
1
2
1
2
3
0
0
2
1
1
2
2
0
1
0
1
0
1
1
1
2
1
1
0
0
1
0
1
0
0
0
2
0
0
0
2
0
0
0
0
2
0
1
0
1
1
0
2
1
1
1
0
1
1
1
0
2
1
1
0
0
0
0
0
1
2
0
0
2
1
0
0
1
2
1
1
0
2
2
1
0
0
1
1
0
1
2
1
2
0
1
2
0
2
0
0
1
0
2
0
0
1
0
0
1
1
1
1
0
0
1
1
1
2
0
2
1
1
0
2
0
1
0
0
2
0
1
1
0
2
0
1
2
2
1
2
1
3
1
0
1
0
2
2
1
1
0
2
1
0
0
0
0
0
0
0
1
1
0
1
1
0
2
2
2
1
1
1
1
0
0
2
1
1
1
0
0
1
1
0
1
0
0
0
0
0
0
2
2
1
2
1
1
0
0
0
2
0
1
1
0
2
1
1
0
0
0
1
1
1
1
0
1
2
0
1
0
0
1
0
1
2
0
1
2
1
1
1
3
1
1
1
0
1
2
0
1
3
1
1
0
1
0
0
1
1
0
1
0
2
1
1
1
0
0
1
1
1
1
1
2
3
0
1
1
0
1
0
0
1
1
1
1
0
0
0
0
2
3
0
2
1
1
0
1
2
2
1
1
2
1
0
1
0
0
0
1
1
1
2
1
1
2
2
1
1
1
1
0
0
2
2
2
0
1
0
0
1
0
0
1
0
2
0
0
1
1
0
0
2
0
1
0
2
1
1
0
0
0
0
0
2
0
2
1
1
0
1
1
2
2
0
0
0
1
1
0
0
3
0
2
1
2
0
1
2
1
0
2
0
2
0
1
0
0
1
1
0
1
1
2
3
1
2
1
1
0
1
0
1
2
0
2
2
0
1
0
1
2
1
0
0
0
1
2
0
1
1
1
0
1
1
0
1
2
0
1
0
0
0
1
1
0
0
1
0
0
2
0
1
1
1
1
1
0
1
2
0
1
1
1
1
0
1
0
0
1
1
0
4
0
0
0
2
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
3
0
0
2
1
0
1
0
1
1
0
1
1
0
2
1
2
0
2
1
0
1
0
0
3
1
1
2
1
0
3
0
1
0
0
2
0
0
0
0
1
0
2
0
2
1
0
2
1
1
0
1
0
0
0
0
1
2
3
2
1
1
1
1
0
1
0
1
0
0
2
2
1
0
1
0
1
1
1
2
1
0
1
0
1
0
0
1
0
2
0
0
0
0
2
0
2
1
0
1
1
2
1
2
0
1
2
2
2
1
1
2
1
0
1
0
0
0
1
1
0
1
0
0
0
0
1
2
0
1
0
0
0
0
1
1
2
2
1
0
2
0
2
0
1
0
0
2
2
2
1
1
2
1
0
0
0
2
1
0
0
1
0
1
1
0
2
1
1
2
2
2
1
2
1
1
0
0
1
0
0
0
0
0
1
0
2
2
2
0
2
3
1
1
1
0
1
0
0
1
1
1
1
0
1
0
0
1
1
1
0
1
0
0
1
0
0
1
0
2
2
0
1
0
1
2
1
1
1
0
0
2
1
0
1
2
0
2
1
1
0
0
1
0
2
0
0
1
0
0
2
0
3
2
1
0
1
0
0
0
1
0
1
0
1
0
1
1
0
1
2
0
2
0
2
0
1
0
1
2
1
1
0
0
1
0
0
2
0
0
2
2
2
0
1
0
0
0
0
1
1
2
2
0
0
2
1
0
1
1
0
0
0
1
1
2
1
2
1
2
0
1
0
0
0
1
2
0
0
1
0
2
0
0
1
1
0
0
1
1
0
1
0
0
2
2
0
0
0
3
1
1
0
0
0
0
1
0
2
0
0
1
2
1
2
1
1
2
0
1
0
0
2
0
0
1
1
0
0
1
1
1
1
4
1
0
0
2
2
1
1
1
0
0
1
3
2
0
0
2
0
2
2
0
1
1
1
2
1
1
0
0
2
0
2
1
1
0
1
0
1
0
0
1
0
1
0
0
1
1
0
2
1
1
1
2
0
0
1
1
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
1
1
2
1
1
0
1
0
2
1
0
0
1
1
1
1
1
2
0
1
1
2
0
0
2
0
2
1
2
1
2
1
0
1
1
2
0
0
0
1
0
0
0
1
2
2
1
0
0
0
1
0
0
2
2
0
1
1
1
0
1
1
2
0
1
1
0
3
0
0
1
1
1
1
1
0
1
1
0
1
1
0
0
2
1
1
1
1
0
0
0
0
0
1
4
1
0
3
0
0
0
1
0
0
1
0
0
2
2
1
1
0
1
2
1
1
2
1
1
1
1
0
0
0
0
4
0
2
2
1
0
1
0
1
0
1
2
1
1
1
0
0
0
1
0
1
2
3
2
0
2
1
1
1
0
1
0
0
0
1
1
0
1
2
0
2
10
1
0
1
2
1
1
0
0
1
0
0
1
0
1
0
1
2
1
2
0
1
0
0
0
1
0
0
0
0
1
0
1
0
2
1
1
1
2
0
2
0
0
2
1
1
0
1
1
1
0
0
1
1
2
0
2
1
0
0
0
1
2
0
2
0
2
0
1
2
1
1
2
1
0
0
0
0
1
0
2
1
1
1
1
1
0
2
0
2
0
2
0
1
1
1
1
0
1
1
0
1
0
0
3
1
0
2
1
0
1
0
1
1
0
0
1
0
1
0
0
0
0
0
1
0
2
2
1
0
1
1
0
2
1
1
2
0
0
2
0
0
1
1
1
2
2
1
0
0
1
2
0
0
2
0
1
2
1
0
2
0
0
0
1
0
1
0
2
0
0
0
1
0
1
1
1
1
0
0
0
0
0
2
0
1
2
1
0
0
0
1
1
1
1
0
2
2
1
2
2
3
1
2
0
1
1
2
1
1
1
0
2
0
2
0
2
0
0
0
2
0
0
0
0
2
0
0
1
2
0
2
3
3
1
0
1
0
0
3
1
0
0
1
2
1
2
0
2
1
0
0
0
0
0
0
1
2
0
2
1
1
0
2
0
0
0
2
1
2
1
1
0
1
0
1
0
1
0
0
1
1
2
2
1
1
0
2
0
0
0
0
2
0
1
0
0
0
0
0
1
2
0
1
2
0
2
1
1
1
2
0
0
1
0
1
0
1
0
1
2
0
0
0
0
2
0
0
0
0
2
0
2
0
0
1
1
1
1
1
1
0
1
2
1
0
1
2
0
1
1
2
1
1
0
0
0
0
1
0
1
0
2
2
1
1
1
0
0
1
0
0
1
0
0
0
0
0
0
1
1
1
0
0
1
1
0
0
1
0
0
1
2
1
2
0
1
0
1
0
0
0
1
2
1
0
0
0
1
3
1
1
1
2
1
1
0
0
0
1
2
1
0
1
2
1
1
1
0
1
1
1
0
1
0
1
0
0
0
0
1
0
1
1
0
2
2
0
1
1
1
1
1
0
1
0
1
0
0
2
1
1
0
1
0
2
1
0
1
1
1
2
0
2
0
1
0
0
2
3
0
0
0
2
2
1
0
3
0
0
2
2
1
1
0
1
1
0
1
2
1
0
1
2
0
0
1
1
1
1
1
1
1
0
0
1
1
0
0
0
0
0
2
0
1
0
1
1
0
0
1
1
2
1
1
0
0
0
1
0
2
0
0
1
1
1
1
2
0
1
1
1
0
0
3
2
3
1
0
2
0
2
2
1
1
0
2
1
1
0
1
1
1
2
0
2
0
2
0
2
1
1
0
2
0
2
1
2
0
2
1
1
2
3
1
1
1
0
1
2
1
1
0
0
0
1
1
0
1
1
1
0
1
2
0
0
0
1
1
2
2
0
0
1
0
0
0
0
0
1
1
2
1
0
0
2
0
1
1
0
1
1
1
0
0
0
0
1
0
0
3
1
2
0
0
0
0
0
0
0
1
1
1
1
0
1
0
0
1
0
0
1
2
1
0
2
1
0
1
0
1
1
0
1
2
0
2
0
0
1
0
1
1
0
0
0
0
1
0
0
1
1
1
1
1
2
1
0
0
0
2
0
0
0
0
0
0
1
0
1
0
1
1
0
0
1
2
0
2
1
1
1
3
0
0
3
0
1
1
0
1
1
0
0
2
0
1
0
0
1
1
0
0
0
0
0
2
2
0
2
1
0
2
1
2
0
1
2
1
1
2
1
2
1
2
1
2
2
2
1
1
1
1
1
1
1
0
0
0
0
0
0
0
1
0
1
1
0
1
2
1
0
1
0
1
2
1
2
2
3
0
1
1
1
0
2
1
2
0
0
0
1
1
0
0
2
1
0
2
0
2
1
0
2
2
0
1
2
0
1
0
2
1
1
1
0
1
1
1
0
1
0
2
0
0
0
1
0
0
0
0
1
2
0
1
0
1
0
1
1
1
1
0
2
2
0
1
2
0
0
1
1
2
0
1
0
1
0
1
0
1
0
1
0
1
1
0
1
0
0
0
0
0
0
2
0
0
2
0
1
1
2
2
2
0
0
1
0
1
1
0
1
1
1
1
1
0
0
1
1
0
1
0
1
0
1
0
2
0
1
1
1
1
1
0
1
2
0
0
1
0
0
1
2
1
0
1
2
1
0
1
0
1
1
2
0
0
1
3
0
2
2
2
1
1
1
0
0
1
1
1
0
1
1
2
1
2
2
1
2
1
1
0
0
0
0
2
0
0
1
3
0
0
1
0
1
0
4
2
1
0
0
1
0
1
0
0
1
1
0
1
0
0
1
0
1
2
0
3
0
0
2
0
2
0
0
0
1
0
2
2
1
2
1
0
0
1
0
0
1
0
1
1
0
0
2
0
2
1
0
2
0
0
0
0
0
1
2
2
2
1
1
0
1
2
2
2
1
0
1
1
0
1
2
0
2
1
1
0
0
0
0
0
0
1
1
0
1
1
3
0
0
1
0
2
0
2
0
0
2
0
0
0
0
0
1
1
0
0
0
2
0
0
2
0
1
1
0
2
1
0
0
0
2
0
0
0
0
0
0
2
0
2
1
0
1
0
0
1
0
1
2
0
1
0
0
2
0
1
0
1
0
0
0
1
0
0
1
1
2
0
0
0
0
1
0
1
0
1
1
1
1
1
0
0
0
0
2
0
1
2
0
3
0
2
2
2
0
0
2
0
0
0
1
2
1
1
0
1
2
1
1
2
0
1
0
1
0
0
1
1
2
0
1
2
1
0
1
0
1
0
1
0
1
3
0
2
2
0
1
0
0
0
2
2
0
0
0
1
0
1
1
1
0
0
0
0
0
1
1
1
1
1
1
0
1
1
0
1
0
0
0
0
1
1
0
1
2
0
1
0
2
1
0
1
0
2
1
1
2
2
0
0
2
0
2
2
0
0
0
1
2
1
2
0
0
0
2
0
1
1
0
1
0
1
1
1
1
1
2
1
0
1
0
1
1
0
2
0
0
1
0
2
0
0
0
2
0
0
1
2
1
2
0
2
1
0
0
0
0
1
0
1
0
2
0
2
1
2
0
1
1
1
2
0
1
1
0
1
0
2
0
0
0
0
0
0
1
0
0
1
0
0
1
2
0
2
1
1
1
0
1
1
1
1
1
1
0
1
1
1
0
1
0
1
1
1
1
0
2
2
0
0
1
1
0
0
1
0
2
1
1
0
2
0
1
1
1
0
2
1
0
0
0
1
2
0
0
2
2
2
1
2
2
2
1
2
2
1
1
0
2
3
0
0
0
0
0
1
1
0
1
0
0
1
1
1
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
1
1
2
0
1
2
1
1
2
0
1
0
1
1
0
1
0
1
1
1
1
1
0
0
2
2
2
0
2
0
2
0
1
0
1
1
1
1
0
2
0
1
3
1
2
1
0
1
0
0
1
1
1
1
2
1
1
1
1
2
1
0
0
0
2
0
1
0
0
1
1
0
1
0
1
0
1
1
1
0
1
1
0
1
0
0
1
1
0
1
1
1
0
0
1
1
0
1
0
0
1
1
0
0
0
1
2
1
0
2
2
1
0
0
2
2
0
1
0
1
1
1
2
2
1
2
0
0
0
2
2
0
1
1
2
2
0
2
1
0
0
1
0
2
1
1
0
0
1
2
0
0
0
0
0
2
0
0
1
0
1
1
2
2
0
0
0
1
0
0
0
0
0
0
2
1
1
0
0
0
0
1
2
1
2
0
0
1
2
1
0
0
0
1
0
2
2
0
1
0
0
0
2
2
2
0
0
0
2
0
2
0
0
1
0
0
2
1
1
2
1
2
0
1
0
1
1
0
1
0
1
2
2
0
3
2
0
0
0
0
0
3
1
1
0
1
1
2
1
0
0
1
1
0
0
0
1
0
2
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
2
0
1
2
0
1
2
2
0
0
1
0
1
0
0
0
0
1
0
1
2
0
0
2
2
1
0
0
3
0
0
0
0
1
0
0
1
1
2
0
2
2
1
0
1
1
0
1
0
2
0
2
2
1
2
1
2
1
0
1
1
1
0
1
0
0
0
1
2
2
1
1
1
2
2
1
1
1
1
1
0
2
1
2
1
2
2
1
0
1
0
0
0
1
1
0
1
2
2
0
0
0
2
0
1
1
0
1
1
0
0
0
1
1
0
1
0
1
0
2
0
0
0
1
0
0
0
1
1
1
0
0
0
0
2
1
0
1
0
0
1
2
0
2
0
0
1
1
1
1
0
0
0
0
0
2
2
2
2
0
1
0
0
0
1
2
0
1
1
0
0
2
1
1
0
2
0
2
0
0
1
1
2
0
1
0
1
1
1
1
0
0
0
0
0
1
1
2
2
0
0
1
0
1
0
0
2
1
1
2
1
3
2
0
2
0
1
0
1
2
1
1
0
0
0
1
0
1
0
0
1
0
0
0
0
2
1
1
1
1
0
0
2
0
1
0
1
1
2
0
0
0
1
0
1
0
0
2
2
0
0
0
1
2
0
0
0
0
1
2
0
1
0
1
0
0
1
1
1
0
0
0
0
0
1
1
1
1
2
0
2
0
0
1
2
1
0
1
2
1
0
0
0
1
0
1
1
1
0
0
0
1
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
2
0
1
1
0
1
1
0
1
1
2
0
0
2
0
1
2
0
1
2
0
1
0
1
1
0
1
2
0
1
0
0
0
0
0
1
0
1
1
1
0
0
1
1
2
1
0
1
0
1
2
0
0
1
0
1
0
1
1
2
0
1
0
0
1
1
0
2
1
1
0
0
1
0
1
1
2
2
1
1
0
2
1
2
0
0
0
2
1
1
2
2
0
0
0
0
0
0
2
0
0
0
0
2
2
0
1
2
0
0
0
0
0
1
1
0
0
1
1
1
0
1
1
1
2
1
1
2
1
2
0
0
2
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
1
0
0
2
1
1
0
2
2
0
1
0
1
1
1
0
2
1
1
2
1
2
0
1
1
0
0
1
0
0
0
1
0
2
2
2
0
1
1
1
2
1
1
0
0
0
1
0
1
0
1
2
2
1
1
0
3
2
1
2
1
0
2
2
2
2
2
2
2
0
0
0
0
1
0
1
1
1
0
1
1
1
0
0
0
1
0
1
1
0
1
1
0
3
1
1
2
0
0
0
0
0
2
0
0
2
1
1
1
0
0
1
1
1
1
0
0
0
1
5
2
1
0
1
2
1
2
0
0
1
0
1
2
0
0
4
0
2
1
1
2
1
2
2
1
1
1
1
0
1
0
0
2
2
3
0
1
2
2
0
1
1
1
2
2
1
1
0
1
0
1
1
2
0
0
1
0
1
2
2
1
2
1
1
1
0
1
0
0
0
1
2
0
2
1
0
4
1
1
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
1
0
1
1
1
0
1
1
3
1
1
2
1
1
0
1
2
0
2
0
1
1
0
2
1
0
1
1
0
2
1
0
3
0
0
1
0
3
0
0
1
0
2
1
0
1
1
1
1
0
2
1
2
1
1
1
1
1
0
0
0
1
1
1
2
1
0
1
1
0
0
0
1
1
1
2
1
0
0
0
0
1
0
2
2
1
0
1
2
2
1
0
0
0
2
1
0
0
1
0
1
1
0
0
0
0
0
1
0
0
1
2
1
0
1
2
2
0
1
0
2
1
2
0
0
1
1
0
1
0
1
0
0
0
0
0
1
2
0
0
1
0
1
0
1
1
0
1
1
0
1
1
0
2
2
0
1
1
1
0
0
0
1
1
0
0
0
0
0
1
0
0
2
0
0
0
0
1
2
1
0
1
1
0
0
0
0
4
0
1
0
2
0
0
1
0
1
2
2
1
1
0
1
0
2
0
1
0
0
0
0
0
1
2
1
2
1
0
2
0
0
0
1
2
0
2
0
1
1
1
0
0
0
2
0
0
2
0
2
1
0
1
1
2
0
0
1
0
0
2
0
2
0
1
0
0
1
0
2
2
1
2
0
1
0
0
1
1
1
2
0
1
1
0
2
2
1
1
1
2
1
1
0
1
0
1
0
1
0
2
1
1
1
0
0
1
2
1
1
0
2
2
2
0
0
1
0
1
0
1
0
0
0
0
0
0
2
2
1
0
2
2
1
0
1
1
0
0
0
0
1
2
2
0
1
0
2
2
0
1
2
1
0
1
2
0
1
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
1
1
2
0
1
0
0
1
1
2
2
1
1
1
0
1
0
0
2
0
1
2
2
0
0
1
1
1
0
0
1
1
1
1
2
0
1
1
0
1
1
0
1
0
2
2
0
1
1
1
0
1
0
2
1
1
0
0
0
0
2
1
0
1
0
2
1
2
1
1
1
2
1
1
2
0
2
2
1
1
2
1
0
1
0
2
2
0
1
0
2
1
0
0
0
2
0
0
2
1
1
1
1
0
2
1
0
0
2
0
0
1
1
0
0
1
1
1
2
1
0
1
1
3
5
1
0
0
0
2
2
0
0
1
1
2
1
0
2
0
1
2
0
1
0
0
1
0
2
0
1
0
1
1
1
2
0
0
0
0
0
3
0
1
1
0
0
1
2
2
0
1
0
0
1
0
1
1
1
1
1
2
0
2
0
3
0
0
2
1
0
0
0
3
2
0
0
0
2
2
0
2
0
0
2
2
2
0
2
1
1
1
0
0
0
2
0
0
0
1
2
1
1
0
1
2
2
0
0
0
0
1
0
1
0
0
1
1
0
1
2
0
2
1
0
2
0
0
0
0
1
0
1
2
0
2
1
0
1
0
2
0
0
1
2
0
2
2
2
0
1
0
0
1
1
0
0
1
2
1
2
0
0
1
0
0
0
0
1
0
1
1
0
2
1
1
0
0
2
2
0
0
0
0
0
0
1
0
0
1
0
2
1
1
1
1
1
2
2
0
2
0
2
1
0
1
1
0
1
1
0
0
0
1
2
0
2
2
0
1
0
0
0
2
1
0
1
2
1
0
2
2
2
1
0
1
1
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
2
0
1
4
0
1
0
1
2
1
2
1
1
1
2
1
0
2
0
0
1
2
0
0
1
1
1
3
2
1
2
0
1
2
1
1
1
1
1
0
2
1
1
0
0
1
1
1
3
0
1
1
2
0
1
0
0
0
2
1
1
1
0
1
1
1
2
2
1
1
0
0
2
0
1
2
0
1
0
1
0
1
1
1
1
1
1
1
1
0
0
1
2
1
2
1
0
0
1
1
1
1
1
2
0
0
0
2
0
0
0
0
4
0
0
4
1
2
0
0
0
0
1
0
2
0
0
0
1
1
2
3
0
1
0
2
1
0
0
0
2
2
1
2
2
0
1
0
2
2
1
2
0
2
2
0
1
2
0
2
0
1
1
0
0
1
0
0
0
1
1
0
2
0
0
2
0
1
2
0
0
1
1
1
2
0
0
0
1
0
1
2
2
0
1
1
2
1
0
0
0
2
0
0
2
1
0
0
0
0
1
0
1
0
0
0
0
1
1
1
0
2
0
0
0
1
0
2
1
1
2
1
0
1
1
1
0
0
2
1
1
1
0
2
0
2
1
1
0
0
0
1
0
0
2
0
0
2
0
0
0
1
2
0
1
1
0
1
1
2
1
1
1
2
0
0
0
1
0
1
2
1
0
1
1
1
0
0
1
1
0
2
1
1
0
1
2
0
1
1
1
1
1
0
1
1
0
1
0
2
1
0
0
0
0
0
1
0
1
2
0
1
1
0
1
0
2
2
1
1
1
1
1
0
2
0
0
0
0
2
0
0
0
1
2
0
1
1
3
1
1
0
0
0
0
0
1
0
1
0
1
1
1
1
1
0
1
0
1
0
0
2
1
0
0
0
2
1
0
0
2
0
0
1
1
0
1
1
2
0
0
2
1
1
0
1
1
0
1
1
0
0
1
0
0
0
1
4
0
3
1
1
0
0
0
0
2
2
1
1
0
1
1
3
0
0
0
0
1
0
0
3
3
2
0
2
0
2
0
0
0
0
2
1
2
2
1
2
2
2
2
2
1
1
0
0
1
1
1
2
0
1
1
2
2
1
1
1
0
0
1
1
0
0
0
2
0
0
1
1
0
0
0
1
1
0
0
0
2
0
1
0
1
2
0
1
2
2
1
2
1
0
2
1
0
2
0
1
2
0
0
1
1
2
0
0
1
2
1
0
0
0
0
1
0
1
0
1
0
0
1
0
2
0
0
0
0
0
0
1
2
1
1
1
0
1
0
1
0
0
1
0
2
0
2
2
1
2
0
2
0
0
2
0
0
2
0
0
0
0
0
1
2
2
1
1
0
0
0
1
0
1
1
1
1
1
1
1
2
0
0
0
0
0
0
0
0
3
2
0
1
2
0
1
0
2
0
2
0
0
1
2
0
1
0
0
1
1
0
0
1
1
1
0
0
1
0
1
0
1
0
0
1
1
1
0
0
0
1
0
1
2
1
0
2
0
0
0
2
0
0
2
1
1
0
1
0
1
0
2
2
1
0
2
3
0
0
0
1
0
2
0
0
0
2
1
0
1
0
1
2
1
0
0
0
0
2
0
0
1
1
1
1
1
2
1
1
0
1
1
0
1
1
0
1
1
0
1
1
0
0
0
2
0
1
0
0
2
1
2
1
0
1
1
0
1
0
1
1
1
0
1
1
1
1
2
0
1
1
0
2
0
0
1
2
0
3
0
0
0
1
0
0
0
0
5
1
1
1
0
0
2
2
0
0
2
0
1
2
1
1
2
1
2
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
2
0
0
2
1
1
1
1
0
2
1
0
2
0
2
0
2
1
0
1
0
0
0
5
0
1
2
2
0
0
0
1
0
1
1
2
1
1
0
1
2
2
0
2
1
1
0
4
0
2
0
1
1
0
0
0
1
1
0
1
0
1
1
0
0
1
1
0
2
2
1
2
2
2
0
2
0
0
0
0
0
0
1
0
0
0
1
0
1
2
2
1
2
1
1
0
0
1
2
1
1
1
0
1
1
0
3
1
0
0
0
2
2
2
0
0
2
0
1
2
1
1
0
2
0
2
1
1
4
1
1
1
1
1
0
0
1
0
1
0
1
2
0
1
0
0
1
1
1
1
2
1
3
1
0
2
0
0
1
1
2
1
0
0
0
1
0
2
0
2
1
2
1
1
2
0
0
2
0
1
1
0
1
2
2
2
2
0
2
0
0
0
0
0
1
0
2
2
0
1
3
0
0
1
2
1
0
1
0
0
2
1
2
1
1
2
0
0
1
1
0
0
1
2
1
1
1
2
0
1
1
1
0
0
2
1
3
1
0
0
0
0
0
0
1
1
0
0
0
1
0
2
1
0
2
1
0
0
1
1
0
0
1
1
0
0
1
2
2
2
0
1
0
1
1
2
0
2
0
1
4
0
0
0
0
1
0
0
0
2
2
0
0
2
1
0
0
2
2
0
0
1
2
0
1
1
2
0
1
1
0
2
1
2
0
0
0
2
0
1
1
0
0
2
1
0
1
0
0
0
3
1
1
1
0
1
1
0
0
2
1
0
0
2
1
2
1
1
2
2
2
2
1
0
0
1
0
1
1
0
0
0
0
0
1
2
1
2
1
0
1
0
2
0
1
0
0
0
1
1
1
1
2
0
1
2
0
1
1
1
0
1
0
2
0
0
0
2
0
1
1
1
0
2
0
1
0
1
0
0
2
4
0
2
2
0
2
2
0
0
1
1
2
1
0
1
1
0
2
2
0
2
1
0
2
1
0
0
2
1
1
1
0
0
1
0
1
0
1
2
0
2
1
1
3
0
0
2
1
0
0
0
1
1
2
0
0
1
1
2
2
1
1
1
2
1
2
2
2
0
0
1
0
0
1
0
0
1
1
0
0
0
0
1
0
1
0
1
1
1
2
0
1
0
0
0
0
1
2
1
1
1
0
1
0
1
1
0
0
2
1
1
0
2
0
0
1
1
1
0
0
0
1
1
1
0
0
0
0
2
1
1
0
2
0
1
0
0
1
1
2
1
1
1
1
0
2
2
0
0
0
1
1
0
1
1
1
1
0
1
0
0
2
0
1
3
2
1
0
1
1
0
1
2
2
1
0
1
2
0
0
0
0
1
0
0
0
1
1
0
1
1
0
0
1
2
1
1
1
2
1
0
1
1
0
1
0
1
1
0
0
0
1
2
0
2
0
2
1
2
1
0
0
1
1
1
0
0
1
0
0
2
2
0
2
1
0
0
1
1
0
2
0
0
0
0
0
2
2
1
1
0
1
1
1
1
2
0
1
1
2
0
1
1
2
2
1
1
0
0
0
0
2
1
0
0
1
0
1
2
0
0
2
2
1
2
0
4
1
3
1
0
1
1
1
0
0
1
1
0
1
1
1
2
0
0
0
1
2
0
0
2
1
1
0
1
1
2
0
0
1
2
0
1
1
2
0
2
0
1
1
2
1
1
1
1
2
0
0
0
0
0
0
1
1
2
2
1
1
2
0
0
1
3
2
1
0
1
0
2
2
1
1
2
1
0
1
1
0
0
2
1
0
2
4
1
2
1
1
1
0
1
1
0
1
2
2
2
1
0
3
0
0
1
0
1
0
1
2
1
2
2
1
1
1
0
1
0
1
0
1
1
0
1
1
2
1
2
0
0
2
1
2
0
0
1
0
2
1
0
0
2
1
0
0
2
1
0
1
0
2
1
1
2
0
1
2
0
0
0
2
1
0
1
2
0
0
1
0
2
0
1
0
0
0
2
0
2
1
1
1
1
1
3
1
1
0
1
1
1
0
1
0
1
1
2
0
1
0
0
1
2
1
2
1
1
1
3
8
0
0
0
1
1
1
2
1
0
2
0
2
2
2
0
1
1
1
0
1
0
1
0
0
0
1
0
1
0
1
0
2
0
1
0
1
1
1
0
1
0
1
2
2
1
2
0
0
1
0
2
0
0
0
1
0
2
2
1
0
1
2
1
0
0
1
1
0
1
0
1
0
1
0
0
0
1
0
1
2
1
1
0
0
0
2
2
1
0
0
1
1
2
1
0
1
0
1
1
1
0
0
1
0
1
0
1
0
1
0
0
2
1
0
2
0
2
0
0
1
1
1
1
1
1
2
1
1
0
0
0
0
1
1
1
1
0
2
0
2
0
0
0
0
1
3
0
0
0
0
1
0
1
1
2
0
2
0
0
0
2
2
2
1
0
1
1
0
2
1
0
2
0
2
2
2
0
0
0
1
0
0
0
0
0
1
0
1
1
1
1
0
1
0
1
1
0
0
0
0
2
1
1
1
1
2
0
2
1
1
0
1
1
0
2
0
2
0
1
0
1
0
1
2
0
0
2
1
2
2
0
2
2
0
1
2
1
1
1
1
1
0
0
1
0
1
0
0
1
0
1
1
1
0
1
0
2
0
1
0
1
3
1
0
2
3
2
1
1
1
4
2
1
0
1
2
1
2
1
0
1
0
0
1
0
0
1
1
1
1
2
0
0
0
1
0
0
0
2
2
1
1
1
0
0
1
1
0
1
1
2
1
0
0
1
2
0
2
2
0
0
1
0
0
2
0
1
1
3
2
1
1
2
1
0
1
0
2
0
1
0
1
1
1
1
0
2
1
0
1
1
0
2
0
1
0
0
2
1
0
0
1
0
1
0
0
1
0
0
0
2
1
0
0
2
0
1
0
2
1
0
2
0
0
5
1
1
0
1
1
1
0
1
0
1
1
2
0
0
2
0
2
0
1
1
0
0
0
0
1
1
0
1
2
1
1
2
0
1
0
2
0
0
0
1
0
1
1
0
1
1
1
1
2
2
1
0
0
2
0
3
1
0
1
3
0
0
1
1
0
0
1
2
0
2
0
1
0
1
0
0
1
2
0
0
0
0
1
1
0
0
1
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
1
1
1
0
0
1
1
0
2
1
1
2
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
1
1
2
1
1
0
0
1
1
2
1
1
2
0
0
2
1
1
0
0
0
1
2
1
1
2
1
1
1
7
0
0
1
1
1
0
1
1
1
0
0
0
0
0
2
0
0
2
0
1
0
1
1
0
1
0
2
0
2
0
0
2
1
0
0
1
1
2
2
3
0
1
1
0
1
2
0
1
2
2
1
0
1
0
0
0
0
1
1
1
1
1
1
2
0
2
3
2
1
0
0
2
1
1
2
1
1
0
0
1
0
0
1
0
1
0
2
0
2
2
0
0
2
1
0
1
0
0
0
1
1
1
2
1
0
2
0
1
1
1
0
0
2
0
0
2
0
2
0
1
1
0
0
1
1
1
0
0
0
1
0
0
0
0
1
2
1
1
0
0
1
1
1
1
1
1
1
1
1
1
1
2
1
1
2
0
0
0
1
0
0
1
1
0
0
1
1
0
0
0
1
1
1
0
0
1
2
1
1
0
0
0
0
0
0
0
0
0
2
1
2
1
1
1
0
0
1
1
1
1
1
1
2
0
1
1
0
1
2
0
2
1
1
0
0
0
0
0
0
0
2
2
2
0
1
2
1
0
0
1
0
1
2
0
0
0
2
1
0
0
1
1
1
1
2
1
1
0
1
0
1
1
0
1
2
0
1
1
1
0
0
1
2
0
1
2
0
0
1
1
1
1
0
1
0
2
1
1
2
1
0
1
1
2
1
2
0
2
1
0
2
4
1
0
0
2
0
1
2
2
2
0
2
0
1
0
1
0
1
0
0
1
1
1
1
1
1
2
0
1
0
0
2
0
1
0
1
0
1
0
1
0
2
0
0
1
0
0
1
1
0
2
0
0
1
0
1
1
1
2
1
0
0
1
1
2
1
1
1
2
0
1
1
2
0
0
2
1
0
0
2
0
0
1
2
2
1
1
0
1
1
0
1
1
2
1
0
0
0
0
0
1
0
0
0
2
1
0
0
0
2
0
1
1
1
1
1
2
2
0
0
0
0
1
2
0
1
1
1
0
0
2
1
0
1
0
1
1
1
1
0
1
2
2
1
0
0
2
0
0
1
2
0
1
0
1
0
0
1
1
1
0
1
1
0
1
1
2
0
1
0
0
1
1
1
1
2
1
0
1
1
1
1
0
1
0
0
1
0
2
1
1
0
1
0
1
1
0
2
2
1
1
2
1
0
0
1
0
2
1
1
0
0
1
2
0
1
0
1
2
1
2
0
2
1
0
0
2
0
2
1
1
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
1
2
0
0
0
1
0
1
2
0
2
0
2
1
2
2
2
0
0
2
0
0
0
2
0
2
0
1
0
2
1
0
3
0
2
1
2
0
0
2
1
1
1
2
2
1
2
2
1
0
1
0
1
2
0
0
2
1
0
1
1
0
1
1
0
0
0
4
2
0
0
0
0
1
2
0
0
1
0
0
0
1
3
2
0
0
0
0
2
1
1
0
0
1
2
1
0
2
1
1
2
1
1
1
1
1
1
2
2
1
2
1
1
1
0
0
0
0
0
1
1
0
1
0
1
1
1
0
0
1
2
0
1
1
0
0
0
1
1
0
0
2
1
1
1
1
0
0
2
1
1
1
0
0
2
0
0
3
0
0
1
2
1
1
0
0
0
0
0
1
2
0
0
1
0
4
0
0
0
1
0
2
1
0
0
1
1
2
1
1
1
1
1
0
1
1
1
0
0
0
3
1
0
2
2
0
0
1
0
1
1
0
0
2
1
2
0
0
0
2
1
2
1
0
2
0
0
0
2
2
0
2
1
0
1
0
2
0
1
2
1
0
0
1
1
1
0
2
1
1
2
1
0
1
0
0
1
0
0
1
1
0
1
2
1
0
1
2
0
1
1
2
2
0
1
0
0
0
2
2
0
0
1
0
2
0
0
1
1
1
2
2
1
2
1
2
1
3
0
1
0
2
1
0
1
1
2
1
2
2
0
0
1
0
0
1
0
0
2
0
0
3
3
0
1
1
0
1
0
1
0
0
0
2
2
0
0
0
0
0
0
1
2
1
1
1
2
0
2
1
3
0
1
0
1
1
1
2
2
1
1
1
0
0
0
1
0
0
1
2
2
2
1
2
1
0
0
0
0
1
0
0
0
2
2
1
1
2
1
2
0
0
0
2
0
0
1
2
1
1
0
1
0
2
0
1
1
0
2
0
1
1
2
2
0
1
1
1
0
1
2
2
1
2
0
0
0
0
0
2
1
1
0
5
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
1
2
1
1
2
0
1
2
0
0
0
0
1
2
1
1
1
2
2
0
1
1
0
0
2
1
1
0
0
0
0
1
1
1
0
1
0
1
1
2
2
0
1
2
1
2
2
0
1
2
0
1
2
0
0
1
0
1
0
1
0
1
1
2
1
0
0
1
1
2
1
0
0
1
1
0
1
0
1
2
1
0
0
1
1
0
1
0
2
0
1
2
0
2
0
2
0
1
1
1
1
1
0
1
1
0
1
0
1
2
1
0
2
0
0
1
1
0
1
0
0
2
1
0
0
2
2
1
0
0
0
0
2
2
0
1
0
0
0
1
0
1
0
0
1
1
2
1
0
0
2
1
1
1
1
1
0
0
1
1
0
2
2
1
1
1
0
2
0
0
2
0
0
0
0
1
1
1
2
0
0
1
1
0
1
2
1
0
1
1
0
0
2
0
1
0
2
0
1
0
0
1
0
2
0
0
2
1
1
1
1
0
0
2
2
3
1
1
0
2
1
0
0
0
0
1
1
1
1
0
1
0
0
2
0
0
0
0
1
1
0
0
2
1
1
0
0
1
0
0
0
0
0
4
1
1
1
1
1
0
0
2
2
2
2
2
0
1
1
1
1
0
0
0
1
0
1
1
2
3
1
2
2
1
2
0
2
0
0
0
3
0
0
1
0
0
2
0
0
1
1
1
0
0
0
1
1
2
1
0
3
0
0
0
1
1
1
0
2
1
0
1
1
3
1
0
1
0
1
0
1
2
2
0
0
2
1
1
1
0
1
2
0
2
0
2
3
1
0
3
0
1
0
0
0
0
0
1
0
0
1
0
2
1
2
1
1
2
2
1
0
1
1
0
0
1
0
1
1
1
1
2
0
1
1
2
1
2
1
2
1
0
1
2
1
1
1
2
0
0
1
2
1
0
2
1
1
0
0
1
2
2
0
0
1
2
0
0
1
0
2
2
0
2
2
2
1
0
2
0
0
0
0
0
0
1
0
0
1
0
2
1
1
0
2
1
1
1
0
1
0
2
0
0
1
0
0
1
1
0
1
0
1
2
1
2
1
0
0
2
1
0
2
0
2
2
0
0
1
0
0
0
1
1
0
0
1
0
0
0
1
2
1
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
1
0
1
2
0
3
1
1
0
1
2
2
0
0
1
2
0
0
0
0
2
0
1
0
0
0
0
1
0
3
1
1
0
2
2
1
1
1
2
3
1
1
0
0
1
1
0
0
1
2
0
0
0
1
1
0
0
0
0
1
2
2
0
0
0
1
1
1
0
1
2
0
0
1
0
0
0
1
0
1
0
1
1
1
2
0
0
0
1
1
0
0
1
1
1
2
0
1
0
2
2
1
0
0
1
2
2
0
2
0
2
2
1
2
0
1
1
1
1
0
1
1
1
1
1
2
1
1
1
1
1
0
0
2
2
2
0
0
1
1
1
0
2
2
2
1
1
1
0
1
0
0
0
1
0
2
1
0
0
0
2
1
0
0
0
2
1
0
0
0
0
2
1
0
2
0
1
0
0
1
2
1
0
1
2
1
1
0
2
2
2
0
1
1
0
0
3
2
1
1
2
0
0
0
1
1
0
1
0
2
1
1
0
1
0
1
3
2
2
2
0
0
0
0
0
2
0
0
1
2
2
2
0
1
2
1
1
0
1
1
1
0
1
0
0
0
1
1
2
0
0
0
2
2
0
1
0
1
0
0
0
1
0
1
0
2
2
0
1
2
1
0
1
0
0
0
1
0
2
4
0
1
0
1
1
0
0
2
1
2
0
1
1
2
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
2
0
1
0
1
0
1
1
1
1
0
0
0
1
1
0
0
0
0
2
0
0
0
1
0
1
0
0
2
0
2
0
2
2
1
1
2
1
1
2
2
2
1
1
0
0
0
1
0
0
2
1
1
0
2
0
0
1
1
0
1
1
0
1
1
0
2
0
1
2
0
1
1
1
1
1
0
1
1
0
1
0
1
0
0
2
0
1
1
0
1
2
1
2
0
1
3
1
1
1
2
1
0
1
2
1
2
1
1
2
0
0
1
0
2
4
0
0
1
1
0
0
2
0
0
2
2
0
0
1
2
1
1
0
1
0
0
2
0
1
0
2
0
2
1
0
1
0
0
1
0
1
0
2
0
0
0
0
0
1
2
1
1
0
1
2
0
0
1
1
1
0
1
1
2
0
0
1
0
2
2
2
2
2
1
2
2
0
1
0
2
1
2
0
1
0
0
0
0
1
2
0
0
0
1
2
1
0
1
2
1
1
0
1
0
1
1
0
0
1
3
1
1
0
0
0
1
2
1
0
1
0
0
0
1
1
2
2
0
0
0
0
1
1
0
2
1
0
1
0
2
1
1
3
1
2
0
0
0
0
0
0
0
1
1
0
1
1
1
0
1
2
1
0
1
2
1
0
1
1
2
0
2
0
1
0
1
1
1
2
1
1
2
0
0
0
1
1
1
0
1
1
2
0
2
2
2
1
1
0
0
1
0
0
2
0
0
0
2
1
0
1
0
0
0
1
0
0
0
0
1
1
1
1
0
2
1
0
0
2
1
0
1
1
1
2
2
0
0
2
1
2
0
1
2
0
2
0
1
1
2
1
1
2
0
0
0
0
0
1
0
0
1
1
1
2
1
1
0
2
1
0
2
1
2
0
0
1
0
0
1
0
0
0
1
0
0
0
2
1
0
1
2
3
0
0
2
0
0
0
0
0
0
1
0
1
0
1
0
1
2
2
0
0
0
0
0
1
0
0
0
0
0
0
1
2
2
1
0
1
2
0
0
0
2
0
0
0
0
0
0
0
2
1
1
2
1
0
2
0
1
2
2
2
0
0
2
0
4
2
1
0
2
2
0
1
0
1
1
1
0
0
0
2
0
1
2
1
1
1
1
0
1
0
2
0
1
0
2
0
2
2
0
0
0
0
0
0
1
1
0
0
1
1
2
0
1
2
0
0
1
1
0
2
0
2
0
1
1
0
2
1
1
0
2
2
2
0
0
1
1
0
0
1
1
2
2
1
1
0
0
1
1
0
1
1
1
0
1
1
0
1
1
1
0
0
0
1
0
1
0
2
1
0
1
0
0
1
0
2
1
2
0
0
0
2
1
1
5
0
0
3
0
0
0
0
2
0
1
1
0
0
1
0
0
1
1
0
1
1
0
0
2
2
2
0
2
1
1
0
1
3
1
0
1
1
2
1
1
0
0
2
1
2
2
1
1
0
0
2
2
1
2
0
0
0
1
0
0
2
0
0
1
2
0
1
2
0
0
0
1
0
1
0
0
1
1
0
0
1
1
0
2
0
0
0
1
2
0
1
1
0
0
1
0
2
0
2
1
2
0
1
0
0
1
1
0
2
2
1
0
1
0
1
1
0
1
2
1
0
0
2
1
1
1
1
1
1
2
0
2
1
2
1
2
1
1
1
1
1
0
1
0
0
2
1
1
2
0
1
0
2
2
1
0
1
1
1
1
0
0
1
0
0
0
2
1
1
3
1
2
1
0
0
1
0
1
0
0
2
2
0
0
0
2
1
1
0
0
1
1
1
0
1
2
1
0
0
2
1
2
0
2
1
1
0
2
0
2
2
2
2
1
0
2
0
2
1
0
0
0
0
1
1
1
0
1
1
2
0
2
2
0
0
0
0
1
1
1
1
0
1
0
0
0
1
1
0
3
4
0
1
0
0
1
2
1
0
1
2
1
0
2
0
1
2
0
1
0
2
0
1
1
0
2
1
0
2
0
2
2
1
0
0
1
0
2
1
0
1
0
1
1
2
2
2
0
1
1
1
0
1
0
1
0
2
1
0
2
0
0
0
0
1
0
2
0
1
0
0
2
1
1
1
0
3
0
1
4
0
0
0
2
0
0
1
0
1
2
2
0
0
0
0
0
1
0
1
0
1
0
0
1
0
2
1
1
0
2
0
1
1
2
0
0
0
3
0
1
2
2
1
0
1
0
0
1
1
0
1
1
0
0
2
0
1
0
2
2
1
0
1
1
2
1
0
0
2
1
0
1
1
0
1
0
0
2
1
1
1
0
1
0
1
1
1
2
2
2
1
1
1
0
0
1
1
0
1
1
0
2
1
1
1
1
0
0
0
2
0
2
0
1
2
1
5
1
0
1
1
0
2
1
0
2
1
2
2
1
0
0
2
0
0
13
2
1
0
1
0
2
1
1
1
1
1
1
2
0
0
0
1
1
1
0
0
1
1
0
1
0
0
0
0
2
0
0
1
1
2
0
0
0
1
0
1
2
0
0
0
0
0
2
1
1
0
0
0
0
0
1
1
0
1
1
0
0
3
1
2
2
0
0
2
0
0
1
0
0
1
0
0
0
1
0
0
2
5
0
2
0
0
0
0
0
2
2
2
0
0
1
1
1
1
1
0
0
1
1
2
1
1
2
2
2
3
1
1
0
0
2
1
2
2
0
1
0
2
1
0
0
2
0
1
2
0
0
0
0
2
0
0
0
1
2
1
0
1
1
1
0
1
0
2
2
1
1
2
0
0
1
1
4
2
1
0
2
1
2
2
2
0
0
0
1
2
1
0
1
1
0
1
1
1
2
1
0
2
1
1
0
0
0
2
1
1
1
1
0
0
1
0
0
1
0
2
2
0
1
0
0
1
0
1
7
0
2
0
1
1
2
2
2
0
0
1
3
0
0
1
0
0
1
0
2
1
2
2
2
0
1
1
1
0
0
1
0
2
0
1
0
2
2
2
0
0
0
2
1
1
1
2
0
1
1
2
2
1
1
0
1
1
0
2
2
1
2
0
0
1
2
0
0
1
0
0
1
0
1
0
2
1
0
2
0
0
0
1
0
0
1
1
0
0
1
1
0
1
1
0
0
0
2
1
1
1
0
0
0
0
2
2
1
2
0
1
0
0
2
2
1
1
1
0
1
0
0
1
1
1
0
0
0
2
1
0
1
1
1
0
0
1
1
2
0
0
0
1
0
1
1
4
0
1
1
1
0
1
1
1
1
0
2
1
0
0
2
1
1
0
0
1
0
0
2
2
0
2
1
0
1
1
1
0
0
1
1
1
0
2
0
1
1
0
0
0
2
2
5
1
1
0
1
0
0
1
2
0
2
0
0
0
1
0
2
1
2
2
2
1
2
0
2
1
0
0
0
0
2
0
2
1
1
2
1
1
0
2
0
1
2
0
1
2
2
2
1
1
0
1
1
0
1
1
0
1
0
0
0
1
1
1
1
2
1
1
2
0
0
1
0
1
1
0
1
1
0
2
3
0
0
0
2
0
3
2
1
0
0
0
1
1
1
0
1
0
1
0
0
1
0
1
0
0
1
1
0
2
0
0
0
1
2
1
0
0
1
0
1
1
2
0
0
1
0
0
1
2
2
2
1
0
0
2
1
1
0
0
0
1
0
1
2
0
2
0
1
2
1
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
2
0
1
1
1
0
0
0
1
0
2
2
0
0
0
1
1
2
2
1
0
0
0
2
0
2
0
1
1
0
1
2
0
1
0
2
2
1
0
0
2
0
1
0
2
0
0
0
2
0
1
1
2
0
1
0
0
0
1
2
0
2
2
0
1
0
1
1
2
0
2
1
0
1
1
0
0
0
1
2
1
1
0
2
1
0
0
1
0
1
0
0
1
2
0
1
2
0
2
0
2
1
2
4
0
2
1
2
1
0
1
1
0
3
1
1
0
1
1
1
0
2
0
0
1
1
2
1
0
3
1
1
1
0
2
1
0
0
1
1
2
1
0
3
1
2
2
1
0
1
0
1
2
0
0
3
1
1
0
0
1
1
2
1
0
0
1
2
2
0
2
0
0
2
0
0
2
1
0
0
1
2
2
1
0
1
1
0
2
1
1
1
1
0
2
1
1
1
0
0
1
1
2
2
0
2
0
1
2
2
1
0
0
0
1
1
1
1
1
2
1
1
1
2
2
0
0
2
0
1
1
0
0
0
0
1
1
0
1
1
0
1
0
1
2
2
1
0
2
2
2
0
2
1
0
1
1
1
1
2
0
1
2
0
1
1
2
0
1
2
1
0
1
1
1
0
0
1
0
1
0
0
2
1
0
1
1
1
2
0
0
0
2
1
0
1
1
0
1
2
0
4
0
1
2
1
1
2
0
1
0
2
2
0
0
0
1
1
1
1
2
2
0
0
1
1
0
1
2
0
0
0
1
2
2
0
1
0
2
0
0
1
2
0
1
2
0
0
0
0
2
0
0
1
1
2
0
2
0
1
0
0
0
0
0
0
1
0
0
1
1
1
0
1
0
1
2
1
0
0
0
1
1
1
0
1
1
0
1
2
3
0
2
1
0
2
0
0
2
1
0
1
1
2
1
2
1
1
1
0
2
0
1
0
1
1
2
2
1
0
0
0
1
2
2
1
0
0
1
1
0
1
2
1
2
0
1
1
0
2
0
1
1
2
2
0
0
0
3
2
0
1
0
2
2
1
0
0
0
2
0
1
2
2
0
2
1
2
1
2
0
0
0
1
1
1
1
0
1
2
2
0
0
1
0
2
1
1
1
2
0
0
1
1
0
0
2
1
0
0
0
1
0
1
1
1
1
0
1
0
0
1
0
1
1
0
1
0
1
1
0
2
1
1
1
2
0
6
0
2
1
1
2
2
1
0
1
1
0
3
1
1
0
1
0
1
3
2
1
0
0
1
2
2
0
1
0
0
0
1
4
0
0
2
0
1
1
1
0
2
2
1
2
1
0
0
1
1
2
0
0
0
0
0
2
1
1
0
0
3
1
1
2
1
2
1
1
1
1
2
1
2
0
2
1
1
0
1
1
1
1
1
2
0
2
1
2
2
0
1
0
0
0
0
0
2
0
1
2
0
0
1
0
0
0
0
0
2
1
0
1
1
1
0
1
0
2
0
0
1
0
0
1
0
1
2
0
1
2
1
1
1
0
0
0
1
1
2
1
1
0
0
1
0
1
0
0
0
0
0
1
1
0
0
1
1
0
1
0
1
0
1
1
1
0
0
0
1
0
0
1
1
1
0
1
1
1
1
0
0
1
2
0
1
0
0
0
2
0
0
1
3
2
6
2
1
2
2
2
1
0
0
1
0
2
1
4
0
0
1
1
2
1
2
1
1
1
2
2
1
1
0
0
1
2
1
0
2
2
2
1
0
0
0
0
1
1
1
0
2
2
0
1
0
0
0
0
0
2
1
0
1
2
2
0
1
0
3
0
1
0
1
2
2
1
2
0
2
0
0
0
2
0
0
0
2
1
2
0
0
1
2
2
0
2
2
2
0
1
2
0
0
2
2
2
0
0
1
1
0
0
1
1
1
1
0
0
1
2
0
1
2
0
1
0
1
1
0
1
0
0
1
2
1
0
1
2
0
1
1
1
0
1
0
1
1
0
0
0
1
1
1
2
0
0
1
1
1
1
2
1
0
2
0
1
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
1
0
1
0
0
2
1
0
0
1
2
0
0
0
1
2
0
2
1
0
1
0
1
2
2
2
2
0
1
2
2
1
0
0
1
2
0
2
1
0
1
0
5
0
2
1
0
0
0
2
2
0
1
1
1
0
2
1
1
0
2
0
0
0
0
0
0
1
0
0
2
0
0
1
0
1
1
0
1
0
2
1
1
2
1
1
0
1
2
2
0
2
0
0
0
1
0
0
1
2
1
1
0
1
2
1
1
1
2
0
1
1
1
1
1
3
0
0
1
0
1
2
1
1
2
1
1
1
0
0
0
0
0
0
0
1
1
0
0
2
1
0
1
1
2
1
0
0
1
2
1
0
0
0
1
2
1
0
1
0
1
0
0
0
1
0
2
0
2
2
2
1
0
1
0
1
1
4
2
1
1
2
0
2
1
0
0
0
1
1
2
2
0
1
0
0
1
0
3
1
1
0
0
0
1
0
0
0
1
1
1
0
0
0
0
1
1
1
1
0
0
0
0
0
1
0
0
2
1
0
1
0
1
1
0
1
2
1
0
0
0
1
2
0
0
2
1
1
0
0
0
1
2
2
0
2
0
0
0
2
1
1
0
2
0
1
0
0
0
0
1
0
2
0
2
1
1
0
0
2
2
1
2
1
1
0
1
2
0
2
1
1
1
2
2
2
1
1
0
1
1
2
1
3
1
0
0
1
0
0
0
0
1
1
1
1
2
0
1
0
1
1
1
2
0
0
0
0
1
0
1
1
0
1
0
1
1
1
2
0
1
1
0
0
0
2
0
0
1
1
0
1
0
2
2
0
2
0
1
0
1
0
1
1
2
1
1
0
2
0
2
1
0
0
1
2
1
2
2
0
1
2
1
2
2
1
0
3
1
1
0
2
0
0
1
1
2
1
1
3
2
2
1
1
0
0
2
3
0
1
1
2
2
0
0
1
2
0
1
1
0
1
2
1
3
1
0
0
0
2
2
1
2
0
1
2
0
1
1
1
1
0
0
1
0
1
1
2
2
2
0
1
0
0
2
2
1
1
0
0
0
1
0
0
1
0
1
2
1
0
2
1
0
0
1
1
0
2
0
0
2
2
0
0
1
0
1
2
2
1
1
0
2
1
0
0
0
3
0
2
1
0
1
0
2
1
0
1
0
0
0
2
1
0
1
2
0
0
0
0
2
1
0
1
0
1
0
1
1
0
0
1
2
0
0
0
0
0
1
0
1
0
0
2
1
0
2
0
2
1
2
0
1
1
2
1
1
0
1
1
1
0
0
1
0
1
0
2
0
1
0
2
1
0
2
1
2
1
1
0
1
1
1
2
0
3
1
1
0
0
0
2
2
2
1
1
3
2
0
1
2
0
1
1
1
0
0
0
1
0
1
0
1
0
1
2
2
0
1
0
1
0
2
1
0
1
0
1
2
0
2
2
0
1
1
1
0
2
2
0
0
1
1
0
2
2
2
1
1
2
2
2
2
1
1
1
1
0
1
0
0
2
0
1
1
1
0
0
2
1
0
2
1
3
1
3
0
2
1
1
1
1
0
3
1
2
1
0
0
0
1
3
0
0
2
1
1
0
0
1
1
0
2
1
1
2
2
0
0
2
0
0
1
1
1
1
1
1
0
0
1
1
0
1
1
1
0
0
0
1
2
0
0
1
1
1
1
0
0
1
0
2
1
2
1
0
1
1
1
0
1
0
5
1
3
1
0
0
0
0
0
2
1
1
1
0
2
1
0
2
0
1
0
2
2
1
1
2
0
0
2
1
3
0
0
0
1
0
0
0
0
2
0
1
0
1
0
0
1
1
2
2
0
0
0
1
0
1
0
0
2
2
1
2
1
1
0
0
1
0
0
0
1
2
0
0
1
0
0
1
0
0
1
1
2
2
4
0
1
2
2
1
1
1
1
0
1
2
0
2
1
1
1
1
2
1
0
1
1
1
1
1
1
0
1
1
0
0
1
2
1
1
2
0
1
1
2
2
0
1
0
1
2
0
2
0
1
1
1
1
1
0
1
0
2
0
1
1
0
0
1
0
0
0
2
2
0
0
2
0
0
1
0
1
2
0
1
0
0
2
1
0
0
2
1
0
2
0
3
1
0
1
1
0
2
1
2
0
0
0
0
2
0
1
0
2
1
3
1
0
1
1
1
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
1
1
2
0
1
0
0
0
0
1
0
0
1
0
1
1
0
0
2
2
1
1
0
1
1
2
2
2
1
1
2
0
3
2
2
1
2
2
2
0
0
1
1
0
1
2
0
0
0
0
0
1
2
0
2
1
2
0
0
1
1
1
2
1
0
1
0
0
1
0
1
0
0
0
1
0
1
1
1
2
1
0
0
1
0
0
1
0
0
0
2
1
0
1
0
1
0
1
2
0
1
0
0
0
0
0
1
2
0
1
1
1
0
0
1
1
0
1
1
0
1
1
2
1
0
2
0
1
0
1
0
2
0
2
0
1
0
1
0
0
1
1
0
0
1
1
1
0
2
2
1
0
1
1
0
2
0
2
0
1
0
0
0
2
1
2
1
2
0
0
1
0
0
1
1
2
0
0
2
1
0
1
0
1
1
1
2
0
0
2
0
1
2
0
1
0
1
2
2
3
2
1
0
1
1
0
1
0
0
2
0
0
2
1
0
0
0
0
0
1
1
2
0
2
0
1
0
0
2
1
0
0
1
1
2
0
0
1
2
1
0
1
0
1
0
1
1
2
0
0
1
1
2
0
0
0
0
0
1
0
1
0
1
1
2
1
0
0
1
2
0
1
3
1
1
1
2
0
1
2
2
4
0
1
0
2
0
2
3
2
0
0
0
2
1
1
2
1
0
2
1
1
2
1
1
1
0
1
1
1
0
1
0
1
1
0
0
2
1
1
0
0
1
1
0
0
0
0
1
0
0
2
2
0
1
1
1
2
1
2
0
0
0
2
1
0
1
1
1
0
0
1
0
1
1
1
0
0
0
1
2
1
0
1
1
1
2
2
0
1
0
0
0
0
0
1
0
1
0
3
1
3
1
1
2
2
2
0
0
0
2
2
1
1
0
0
1
2
2
0
0
0
0
1
1
1
1
0
0
0
0
0
1
2
0
2
0
2
1
0
1
2
2
2
0
1
1
0
0
1
1
1
0
0
2
1
0
1
2
1
2
0
1
2
0
1
0
1
1
2
0
1
1
0
2
0
2
0
0
2
1
0
0
1
0
2
0
2
0
2
0
0
1
1
1
1
1
0
0
0
1
1
1
0
2
1
0
0
0
0
1
1
2
2
1
0
1
1
2
0
0
1
1
0
1
0
1
0
0
0
0
0
2
1
2
2
0
0
0
1
1
0
1
0
1
0
0
0
2
0
1
1
2
0
1
0
1
0
0
1
2
1
0
0
1
1
1
2
1
0
2
1
1
0
1
0
0
1
1
0
1
0
2
0
1
1
0
1
0
0
0
0
2
0
1
0
1
0
1
2
1
1
0
2
1
0
0
0
1
0
2
1
3
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
2
1
0
1
2
0
1
1
2
0
0
0
2
2
1
1
0
1
1
0
0
0
2
2
1
1
0
0
2
3
1
1
0
1
0
1
1
0
0
1
1
1
0
0
0
1
1
1
1
1
2
1
1
0
1
0
2
2
0
2
1
1
0
0
0
0
1
1
0
0
1
2
0
0
2
1
0
2
1
2
1
0
0
0
1
2
2
0
2
2
1
1
1
1
1
0
1
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
1
0
0
1
0
1
0
0
0
2
0
0
1
0
2
1
1
0
1
1
1
2
0
0
0
2
1
0
0
0
0
2
1
1
2
2
2
1
0
1
1
0
0
0
0
2
2
1
0
0
1
0
1
0
1
1
0
1
0
1
1
1
0
2
2
2
1
0
0
0
1
0
1
1
0
0
2
0
1
2
0
1
3
4
2
0
1
0
0
2
1
2
1
0
2
2
1
1
1
1
1
2
1
1
2
0
2
2
1
1
1
1
1
1
1
0
3
0
1
0
0
1
2
0
2
1
1
2
0
0
1
2
1
0
1
2
2
0
1
0
0
1
0
1
2
0
1
2
1
0
1
0
0
2
1
0
1
1
1
1
2
0
0
2
1
1
1
1
1
2
0
1
0
0
1
1
0
0
3
0
0
1
2
0
1
1
0
2
1
2
0
2
0
2
2
0
0
1
1
2
1
1
1
1
2
1
0
2
2
0
1
0
0
0
0
1
2
1
0
2
0
2
0
0
1
0
2
0
0
0
0
0
2
3
2
2
1
2
1
1
0
0
2
0
0
3
0
0
1
2
1
1
0
0
1
1
0
1
1
0
2
2
0
0
0
0
1
0
1
2
1
1
0
1
2
0
1
6
0
2
0
1
0
1
0
2
1
0
1
1
2
2
0
1
1
1
1
0
1
0
0
1
0
0
1
1
2
0
3
0
1
0
2
0
0
1
0
1
1
1
2
0
0
0
0
0
0
1
2
2
2
1
2
0
1
1
2
0
0
1
1
0
0
2
0
0
1
0
1
1
2
1
1
1
2
1
1
2
2
1
1
2
2
1
2
0
1
2
1
0
0
1
1
2
0
2
0
0
1
0
2
2
0
1
0
1
1
3
1
2
0
1
0
0
1
0
0
2
1
0
1
0
2
1
1
1
0
0
0
2
2
1
0
0
2
1
0
1
2
0
3
1
0
2
0
2
1
3
0
0
1
0
0
0
3
3
1
1
3
1
0
0
1
1
2
1
0
1
2
1
1
0
1
1
1
0
1
1
1
0
3
0
1
1
1
4
0
2
0
0
2
1
1
1
0
0
2
1
1
0
1
0
0
0
2
0
1
1
0
1
1
0
0
0
2
0
0
0
1
1
3
1
0
1
1
1
0
0
0
3
1
0
1
1
2
0
1
1
1
1
1
0
0
1
0
0
2
1
1
0
2
1
0
0
1
2
0
1
1
1
7
0
1
0
1
0
1
1
1
0
1
1
1
1
2
2
1
0
1
2
1
2
2
1
0
0
1
0
0
0
1
0
2
0
1
0
0
0
1
1
1
1
2
0
1
1
0
1
1
0
0
0
1
1
0
1
0
1
1
0
0
1
2
1
2
1
2
1
2
1
1
2
1
2
1
1
0
1
0
0
1
0
0
0
1
1
3
0
2
2
0
1
0
2
1
1
2
0
1
0
0
0
1
0
0
0
2
1
0
0
0
2
2
1
1
0
1
0
0
1
1
0
2
1
1
0
0
1
2
1
1
1
1
1
2
2
0
2
0
2
1
0
1
1
2
2
1
1
1
2
1
0
0
0
1
2
2
0
0
0
0
2
1
2
0
1
2
2
2
1
2
1
0
1
2
2
0
1
1
0
1
0
2
0
3
1
2
0
1
0
0
0
2
2
2
2
2
0
2
1
2
2
1
2
1
0
0
2
2
0
1
1
1
2
1
0
0
1
0
0
0
2
0
1
1
0
1
0
0
1
0
1
1
1
0
1
0
2
0
0
0
0
1
1
0
0
0
1
2
0
0
2
0
1
1
0
2
1
0
1
0
3
2
0
1
0
2
1
0
1
3
0
0
1
0
1
2
1
0
3
0
1
0
0
1
1
1
0
0
2
0
0
1
2
1
2
1
1
2
1
1
1
0
1
0
0
2
2
0
0
1
0
1
1
1
1
1
1
5
2
0
0
1
1
1
1
0
1
1
0
0
2
1
2
2
2
2
0
2
0
1
2
0
0
1
2
1
2
0
1
1
0
1
0
0
0
4
0
0
0
0
0
1
0
0
1
2
0
1
0
1
2
0
0
0
1
2
2
1
0
1
0
0
0
2
0
0
2
1
1
1
0
0
0
0
1
1
0
1
2
1
1
1
0
0
2
2
0
0
0
0
1
1
1
0
0
1
2
0
1
0
1
0
1
1
2
2
1
0
1
1
0
0
2
0
0
0
0
1
1
2
1
1
1
1
0
1
1
1
0
2
0
2
2
1
0
0
0
1
0
2
1
2
0
0
1
1
2
0
0
1
0
1
1
0
2
1
0
2
1
0
1
1
0
1
0
1
0
1
0
2
0
0
0
2
0
2
2
2
1
1
0
0
1
1
1
2
0
0
0
0
1
0
1
0
2
0
0
2
1
2
2
1
2
1
2
0
1
0
0
1
2
1
2
2
1
1
0
0
1
0
0
1
1
0
1
1
2
1
0
1
1
2
0
1
0
2
2
0
0
0
1
1
1
0
0
1
2
0
0
1
2
0
0
0
0
1
0
1
1
2
2
1
1
1
0
0
1
2
0
0
0
1
0
2
0
2
0
1
0
1
2
1
0
0
0
1
1
0
1
0
1
1
2
1
1
2
0
1
1
2
1
1
1
0
2
2
0
0
0
0
1
1
0
0
1
0
2
0
1
1
0
0
0
0
0
0
0
0
0
2
1
2
0
2
1
2
2
0
0
2
1
1
0
1
0
1
0
2
2
0
1
0
1
0
1
0
1
0
0
0
2
1
2
1
1
2
0
0
1
1
0
2
1
0
0
0
0
2
1
2
2
0
1
1
1
1
2
0
0
1
1
2
2
0
0
1
1
0
0
1
0
0
1
1
0
0
1
2
2
2
1
0
2
0
1
2
2
1
0
0
0
2
0
0
1
2
1
1
0
0
4
0
0
0
1
2
2
0
2
3
1
1
1
0
1
1
0
1
0
2
1
1
0
0
1
2
1
0
1
2
1
0
0
0
2
0
1
2
2
1
1
2
2
1
0
1
0
1
3
2
1
1
1
2
1
0
0
1
0
0
1
0
1
1
0
1
2
0
1
1
1
0
1
0
2
1
0
1
1
2
0
0
1
1
1
2
2
1
0
1
2
1
3
4
1
1
1
0
2
0
1
1
2
3
0
1
1
0
0
2
0
1
1
1
0
0
0
1
2
1
0
2
1
0
2
0
2
0
1
0
0
0
1
0
0
2
0
2
0
1
2
0
1
1
0
1
2
1
0
1
1
0
0
1
0
1
0
2
0
1
2
2
0
0
0
2
3
0
0
2
1
2
0
1
2
0
0
2
0
0
0
1
1
1
1
1
1
2
0
0
2
0
0
0
0
0
1
0
1
0
0
2
0
0
1
1
1
0
3
1
0
2
0
1
0
1
0
1
0
2
1
1
0
0
2
2
2
1
0
0
0
1
1
2
1
0
0
2
1
0
0
1
0
0
0
0
0
1
1
1
1
0
1
1
0
2
0
2
1
0
0
0
1
0
1
1
0
1
0
1
1
2
1
1
1
1
0
0
0
2
0
2
0
0
1
0
0
1
1
1
0
1
1
0
1
1
1
1
1
2
0
1
0
0
0
0
0
0
2
1
0
0
0
2
0
5
2
1
1
0
1
0
0
2
0
0
0
1
0
1
2
0
1
0
0
0
0
2
0
0
0
1
0
1
0
1
2
0
1
1
2
0
2
0
1
0
2
1
1
2
0
0
1
2
2
0
0
0
0
1
0
0
1
1
1
1
0
0
1
0
2
0
3
0
2
1
1
1
0
0
2
1
0
4
0
0
0
2
1
0
0
2
0
2
0
2
1
0
1
0
2
1
1
0
2
1
1
1
1
0
2
1
0
0
2
1
0
0
0
0
0
2
1
2
0
1
0
1
0
2
0
1
2
0
0
0
0
1
1
2
1
1
1
3
0
1
1
1
1
1
2
1
0
1
0
2
0
1
0
1
0
1
1
1
1
0
0
0
0
0
0
1
0
2
2
1
2
0
0
1
0
0
1
0
1
2
1
1
1
1
0
1
1
0
0
0
0
0
1
0
1
0
1
0
5
0
1
1
1
0
1
2
11
0
1
0
0
1
0
2
1
1
0
0
2
2
2
1
1
1
2
1
0
1
0
0
2
0
1
2
0
0
0
0
0
0
1
0
0
0
0
1
2
2
2
2
1
0
0
1
0
1
1
1
0
0
2
1
0
2
2
0
3
0
0
0
0
0
2
1
1
1
0
1
1
0
1
0
0
0
2
0
1
1
2
1
2
2
0
1
1
1
0
1
1
1
1
2
1
0
0
1
1
0
0
1
0
0
1
0
1
2
1
0
1
0
0
0
1
0
0
1
2
3
2
0
2
1
2
0
1
1
0
0
0
2
2
0
1
0
0
0
0
0
2
0
1
1
0
2
0
1
0
1
2
1
1
0
0
3
1
1
1
1
0
1
0
1
0
1
1
0
2
0
0
1
0
0
1
1
1
2
1
0
1
1
2
0
1
1
1
2
2
0
2
1
2
0
2
0
1
2
1
1
1
2
0
1
2
2
0
1
1
0
0
1
1
2
2
1
1
0
0
0
2
0
1
0
1
1
1
0
1
1
0
0
1
2
0
1
1
1
0
0
0
0
2
0
1
0
1
0
0
2
2
2
0
0
1
1
1
1
0
0
2
0
1
0
1
1
2
0
0
1
1
2
1
0
0
0
0
2
0
0
1
1
1
0
2
0
1
1
0
1
0
1
0
1
1
0
1
1
1
0
0
1
1
0
1
2
1
0
2
0
0
0
1
1
0
2
0
0
1
0
0
0
1
1
2
1
2
2
2
1
0
2
1
0
0
0
0
1
0
0
0
2
0
2
1
1
1
0
0
2
1
2
0
1
0
2
1
0
0
0
1
0
0
1
2
2
2
1
2
0
0
0
0
1
0
0
0
0
2
0
0
1
1
1
0
0
0
0
0
0
1
1
0
1
2
0
0
1
2
1
1
0
2
0
1
1
0
0
0
1
0
1
2
0
0
0
0
0
2
0
0
1
1
2
0
0
1
0
1
0
1
2
2
3
1
2
1
1
1
2
0
2
2
1
1
0
1
0
0
0
0
1
2
1
0
0
1
0
1
0
0
0
1
0
2
0
1
2
0
0
0
0
1
2
1
1
2
0
0
0
0
1
0
1
1
0
1
2
0
1
1
0
0
1
1
0
1
1
2
1
1
0
2
2
1
2
1
2
1
1
2
0
0
0
1
1
1
1
1
0
1
0
1
0
0
0
1
0
1
0
0
0
1
3
0
1
0
0
0
2
1
1
0
1
1
0
0
1
0
1
2
0
1
1
0
1
0
1
0
2
1
0
0
1
2
0
2
1
1
2
0
2
0
0
0
0
2
1
1
0
0
1
0
0
0
2
2
0
2
1
1
2
2
0
1
1
1
1
2
0
0
1
1
1
0
1
1
0
2
1
1
0
2
0
1
0
0
2
1
2
1
1
1
1
0
1
2
2
0
0
2
1
0
2
1
2
4
0
1
2
0
0
0
0
2
1
1
0
0
3
1
0
0
1
1
2
0
1
1
0
0
1
0
0
1
1
0
0
1
0
1
1
2
0
1
2
0
2
0
1
1
1
1
0
0
0
1
0
1
0
0
1
2
2
1
1
1
0
0
0
1
0
1
1
1
0
1
1
2
1
0
2
1
0
2
1
1
3
1
2
0
1
0
2
0
0
0
1
0
0
0
0
2
1
1
0
0
0
0
1
0
2
1
1
0
0
2
1
0
0
2
2
1
2
0
1
1
0
0
2
1
0
1
2
1
2
0
1
0
1
0
0
2
2
1
2
0
1
0
0
2
1
1
0
2
1
0
2
1
1
2
0
0
0
1
1
0
0
1
0
2
2
0
1
2
0
1
1
2
2
0
1
1
2
0
1
0
0
2
1
0
0
0
1
1
0
0
0
1
1
0
0
2
0
0
0
0
1
1
0
1
0
0
0
1
0
0
3
0
0
1
0
1
0
2
2
1
1
0
1
0
2
0
2
0
2
1
0
2
0
3
0
1
0
0
0
1
1
0
0
0
2
0
1
2
2
0
1
1
1
0
1
0
2
1
3
1
0
0
0
1
2
2
2
2
2
0
0
0
1
0
1
0
1
2
1
1
0
0
1
1
1
1
2
0
0
1
0
0
2
1
0
1
1
0
1
2
0
0
2
1
0
2
1
0
0
3
1
1
0
0
1
1
0
1
1
1
0
0
2
2
4
1
2
1
2
0
0
0
1
0
1
0
0
1
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
1
1
0
1
2
2
2
0
2
0
0
1
0
0
1
0
1
1
1
2
1
1
1
2
1
1
2
0
1
1
1
0
2
4
1
1
2
2
2
0
1
0
1
1
0
0
1
0
0
0
1
1
0
1
1
0
1
0
2
0
2
4
1
1
0
0
0
3
0
1
2
0
1
0
1
2
0
2
1
0
2
1
2
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
2
2
0
1
0
0
0
0
1
2
0
0
0
1
2
0
0
1
0
2
0
0
0
2
1
1
0
2
1
0
1
2
0
0
1
1
0
0
0
1
0
1
1
2
2
0
1
0
1
1
1
1
1
1
0
1
0
0
2
1
1
1
0
2
0
0
1
1
1
1
1
0
0
0
2
2
0
0
0
2
0
1
2
1
1
2
0
1
1
0
0
1
0
1
1
1
2
1
1
2
0
0
0
2
1
0
2
0
0
1
0
2
1
2
0
0
1
1
0
0
2
2
1
1
0
3
1
1
2
0
0
0
1
0
0
0
1
1
2
1
1
1
1
1
0
1
0
0
1
2
1
1
1
1
2
0
2
1
2
1
1
0
0
2
0
2
1
0
0
0
2
1
1
1
0
2
0
3
1
1
3
0
1
1
0
2
0
1
1
2
1
1
2
0
1
1
1
1
1
0
1
1
0
0
0
1
1
0
1
1
1
1
1
1
2
2
1
0
0
1
1
2
1
0
1
0
1
1
2
0
4
1
2
3
0
0
1
2
1
2
1
2
2
0
0
0
0
0
1
2
0
2
1
2
0
2
1
0
2
1
2
1
2
0
2
0
1
1
0
2
0
1
1
0
1
1
0
0
1
1
0
1
0
1
1
1
1
2
1
2
0
3
0
1
1
0
2
2
0
0
1
1
0
1
2
0
2
0
0
1
0
0
0
0
0
1
1
1
1
0
0
0
2
1
1
2
1
0
1
2
0
0
1
0
2
1
0
1
0
0
1
2
2
1
0
0
1
1
0
2
2
0
0
0
2
1
3
0
1
2
1
0
0
1
1
0
0
0
0
2
1
0
1
0
1
1
1
2
0
0
2
1
1
1
2
3
1
1
0
2
0
1
3
1
1
0
2
0
1
2
1
1
0
1
0
1
1
1
0
1
0
2
0
2
0
1
2
0
0
0
1
2
0
0
2
1
1
1
1
2
0
1
1
2
2
1
1
1
0
1
2
1
2
5
0
1
1
1
0
0
2
1
2
2
0
0
0
0
2
2
2
2
0
1
1
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
2
1
0
2
1
0
0
2
1
1
2
1
0
0
0
0
0
0
1
2
0
1
1
0
0
1
1
1
2
1
0
1
0
0
1
2
0
1
1
1
1
0
1
0
1
1
1
0
1
1
0
0
0
0
0
0
2
2
0
3
0
2
0
0
0
1
2
1
1
0
1
2
1
1
1
0
1
0
1
2
0
2
1
2
1
0
1
0
2
1
2
0
1
1
1
1
2
1
1
0
0
2
0
0
0
0
0
2
0
2
1
0
1
1
3
0
0
1
1
0
0
2
1
1
1
2
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
1
0
0
1
2
1
1
0
2
0
2
0
1
0
2
0
0
1
1
1
1
0
0
1
1
1
0
0
1
1
2
0
1
1
0
1
2
1
0
1
1
0
0
1
0
1
0
0
0
0
0
1
2
2
1
0
0
1
1
0
0
1
1
0
1
0
0
0
0
1
0
1
0
2
0
0
1
2
2
1
2
1
1
0
0
2
0
0
2
0
0
2
1
0
1
2
0
0
2
2
1
0
0
0
1
1
1
2
1
1
2
1
1
1
0
0
0
1
1
0
1
3
0
2
0
1
0
2
0
0
0
0
1
2
0
1
0
0
1
0
1
1
1
1
0
0
0
3
0
1
3
1
2
1
0
1
1
0
0
2
1
0
0
0
0
1
1
2
1
1
0
2
0
1
1
0
0
3
0
2
0
0
0
0
0
0
0
1
0
1
0
2
0
0
1
2
0
1
1
2
2
0
0
0
2
0
2
0
0
1
1
0
0
1
0
1
1
1
0
1
0
1
2
2
2
1
0
2
0
0
1
0
1
0
1
0
1
1
1
0
1
2
0
0
1
0
0
2
1
1
1
0
1
3
4
0
0
0
1
1
0
2
0
1
1
1
0
0
2
0
0
1
1
1
2
0
1
1
1
1
1
1
1
1
0
0
1
0
1
1
1
1
2
0
1
1
0
0
0
1
0
0
2
1
1
1
2
1
1
0
1
0
0
1
0
1
1
2
0
0
0
1
0
0
1
0
1
0
0
0
1
1
0
0
1
0
2
1
2
0
0
1
0
0
1
0
1
1
0
0
0
2
0
2
2
0
1
1
2
0
2
0
0
1
1
0
1
1
2
0
0
2
1
0
0
1
1
2
0
0
2
0
1
0
1
0
0
1
1
1
1
0
4
1
1
1
1
0
1
0
1
1
1
1
2
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
2
1
2
1
1
0
1
0
1
1
0
2
0
1
0
1
1
1
0
0
2
1
0
1
2
0
1
1
0
0
1
0
0
0
1
2
2
1
0
2
0
0
1
0
1
2
0
0
2
1
0
1
1
1
5
1
1
2
0
0
1
2
0
2
0
2
0
0
3
0
1
0
1
1
0
1
1
0
2
2
3
0
0
2
0
2
1
0
2
1
0
0
0
2
2
1
1
0
1
0
0
1
2
1
1
1
1
2
0
0
0
1
2
1
0
0
3
0
2
0
0
0
1
1
0
0
0
0
1
2
2
1
1
1
2
0
9
2
2
0
3
0
1
1
0
2
0
0
1
1
2
0
1
0
0
1
2
1
0
3
2
0
1
0
0
0
0
1
1
1
0
0
1
2
2
0
2
2
0
2
1
1
0
0
0
0
1
2
0
2
0
1
0
2
1
1
1
2
0
0
0
2
1
0
2
1
0
0
1
0
1
0
2
0
2
0
0
2
1
2
2
0
1
0
0
0
0
0
2
1
2
0
1
1
2
0
2
1
0
1
2
0
0
2
1
1
2
1
0
2
1
2
2
0
1
1
0
0
0
2
0
1
2
2
2
2
2
1
0
1
2
2
3
1
1
0
2
0
0
1
2
0
0
1
0
1
1
1
2
0
1
2
1
0
0
1
1
1
2
1
2
2
0
0
0
0
2
2
0
0
2
1
2
3
2
1
1
1
1
2
0
0
1
2
1
1
0
1
0
1
1
0
3
1
2
1
1
0
0
0
1
1
2
2
0
0
2
0
1
1
1
0
0
2
1
0
2
0
1
1
2
0
0
0
0
2
0
1
1
0
1
0
4
0
2
0
1
0
1
2
1
2
1
0
0
2
1
1
0
1
0
1
2
1
3
1
0
1
0
2
0
2
1
2
2
2
1
1
1
2
1
2
1
2
1
0
0
1
3
1
2
2
2
0
0
0
0
2
1
2
1
2
2
0
1
0
1
1
0
0
1
0
1
2
2
0
1
2
1
0
2
0
0
1
0
1
1
0
0
1
0
2
1
0
1
1
0
2
1
2
0
1
1
0
5
1
0
0
1
2
1
0
0
2
2
0
2
2
0
2
3
2
0
2
0
0
1
0
1
2
1
0
0
1
2
0
1
2
1
1
1
0
1
1
0
2
0
0
0
1
0
1
1
1
0
1
0
2
1
0
0
2
1
2
0
0
0
0
0
2
0
0
1
1
0
1
0
2
0
1
2
0
3
2
0
3
1
2
0
0
0
0
2
1
2
1
0
1
0
2
1
2
1
1
1
1
0
1
0
0
2
0
1
0
1
1
0
1
0
0
1
1
0
2
0
0
3
2
2
0
0
0
0
1
0
0
3
1
0
0
1
0
2
1
0
0
0
2
2
2
2
0
1
1
2
0
0
2
1
0
2
2
0
0
2
0
1
0
1
0
2
0
0
1
1
0
1
2
1
1
0
0
1
1
0
0
1
0
2
1
0
0
0
1
1
0
1
0
1
2
1
0
1
1
2
0
0
3
1
2
0
0
1
0
0
1
1
2
1
1
1
1
1
1
1
2
1
1
0
0
2
1
1
1
0
1
0
1
2
2
0
2
3
1
2
1
0
2
0
1
0
1
2
2
0
0
2
2
0
0
1
0
0
0
0
0
0
0
1
2
2
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
3
1
0
0
2
0
1
1
0
2
0
1
1
2
0
0
1
0
0
0
1
1
0
1
1
2
1
1
2
1
0
0
0
1
0
2
1
0
1
0
1
2
1
0
1
0
0
1
0
0
0
1
1
0
1
1
0
2
1
0
2
0
0
1
0
1
1
0
0
2
2
2
0
1
1
1
0
2
2
2
1
0
1
0
0
1
2
0
2
0
0
2
2
1
0
0
1
2
1
1
2
0
0
1
0
0
1
0
0
1
0
0
2
1
0
1
0
0
1
1
2
2
0
1
2
0
0
1
1
0
1
1
0
1
0
0
0
0
1
0
2
0
2
1
2
1
1
0
1
0
1
0
1
2
1
1
1
0
0
0
2
0
2
2
2
2
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
1
1
1
1
0
2
0
2
1
1
2
1
0
0
1
0
2
2
0
1
0
1
1
2
0
2
0
1
0
1
1
0
0
0
1
1
2
1
1
1
0
0
1
0
0
1
2
1
1
0
2
4
1
1
1
1
0
1
0
1
2
1
0
1
1
2
0
0
1
0
2
1
0
0
2
1
2
2
0
3
1
1
0
3
2
0
1
2
2
0
1
0
2
0
0
0
3
1
1
0
0
2
0
2
1
1
0
0
0
1
1
0
1
2
1
2
0
0
0
0
0
0
2
0
0
0
1
1
0
0
1
1
1
0
0
1
0
0
0
0
0
1
1
2
1
1
0
2
1
2
2
1
1
0
1
0
0
0
1
0
0
0
0
1
0
1
2
0
2
2
2
1
2
0
0
0
0
1
1
3
2
1
0
0
0
0
1
0
2
0
1
2
1
0
1
0
1
2
1
1
0
0
2
1
2
1
1
0
0
0
1
1
2
1
1
2
0
1
0
1
1
1
1
0
2
0
2
2
0
2
0
1
0
0
0
1
1
0
2
0
0
1
0
1
2
1
1
0
0
1
0
2
0
1
1
0
2
0
1
0
2
1
0
1
0
1
0
2
1
0
0
2
0
1
0
0
3
0
0
2
1
2
1
0
1
3
1
0
1
0
0
0
1
0
0
1
1
2
0
0
0
1
2
2
0
1
1
1
0
1
0
2
2
0
3
0
0
0
1
2
2
2
0
0
2
0
0
1
0
0
0
3
2
1
1
2
2
0
1
2
1
1
3
1
0
1
2
1
0
0
2
3
0
1
0
1
3
1
2
0
0
0
2
2
0
0
1
2
2
1
1
1
1
1
0
0
0
1
0
1
1
0
1
2
1
1
1
0
1
0
1
0
0
2
0
0
1
0
2
3
0
2
0
0
0
2
1
2
1
0
1
0
1
0
1
2
1
2
1
0
2
1
0
0
1
1
1
1
1
1
0
1
1
2
1
0
0
2
1
0
0
0
0
1
1
2
0
0
1
0
0
0
0
1
0
0
1
1
1
1
0
1
1
2
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
1
2
0
2
1
1
1
1
0
1
1
1
0
1
2
0
2
0
1
2
1
1
2
0
1
1
2
2
1
0
0
0
0
1
1
1
1
2
0
1
2
1
1
0
0
0
0
2
1
1
1
0
0
0
1
0
2
0
0
1
0
0
2
1
1
1
0
1
2
1
1
1
1
2
1
0
0
0
2
1
0
1
1
0
1
2
2
0
0
5
0
0
0
0
0
1
2
0
0
0
1
0
1
1
1
0
0
2
1
0
2
2
0
1
0
1
2
1
0
2
1
1
2
1
0
0
0
1
1
1
1
1
2
0
1
1
0
1
2
0
1
2
0
0
2
2
1
0
0
1
0
1
0
0
1
1
0
0
0
1
0
1
1
1
1
1
1
2
0
0
1
1
1
0
0
1
2
1
0
1
0
1
1
0
0
1
2
1
0
1
0
2
1
0
2
1
2
0
1
1
1
2
1
1
2
3
2
0
1
2
0
3
1
0
0
0
1
1
1
1
1
0
0
0
2
1
2
1
0
1
1
1
2
1
0
0
2
1
0
1
2
0
1
0
0
1
2
0
0
0
0
1
0
1
0
2
1
1
2
1
0
0
2
0
1
1
0
2
0
2
0
2
0
2
0
3
0
0
1
1
0
1
0
2
0
0
2
0
2
0
0
1
0
0
0
2
0
1
0
1
1
1
1
1
0
1
1
1
0
2
1
1
1
2
1
0
1
1
0
0
1
2
2
2
1
0
0
2
1
1
2
3
2
1
1
0
0
0
0
3
1
0
2
1
1
0
1
1
0
1
0
0
0
11
0
2
1
1
0
1
1
1
1
0
0
1
0
1
1
1
1
0
1
2
1
2
2
0
0
0
1
1
2
2
0
1
2
1
3
0
0
1
0
0
0
0
3
0
0
1
2
0
2
0
1
0
1
0
1
1
2
0
2
1
1
1
2
2
0
1
0
0
0
1
1
2
1
1
0
2
0
0
1
0
2
0
0
0
0
0
0
1
2
1
1
2
1
1
1
1
1
0
0
0
0
1
1
0
1
0
1
2
1
1
0
1
0
1
0
1
0
1
0
1
0
0
1
1
2
0
1
0
0
1
2
0
1
0
2
1
1
0
1
1
1
2
1
0
0
0
0
1
0
0
1
1
1
2
0
0
1
1
1
0
0
3
2
0
1
1
0
2
3
0
1
1
1
0
1
1
1
2
0
1
1
1
0
2
0
0
1
1
0
1
2
0
0
0
0
0
2
1
2
0
1
0
1
1
1
0
0
0
0
2
2
0
0
2
0
1
0
1
1
1
2
0
0
1
1
0
0
2
1
0
0
2
3
0
0
0
1
0
0
1
0
0
1
2
1
0
2
1
2
1
1
0
3
2
2
1
2
1
0
1
0
1
2
0
0
1
1
0
0
0
3
2
1
2
1
2
1
0
1
2
1
0
1
1
0
0
2
0
2
1
0
0
0
1
0
0
1
0
0
1
0
0
1
2
0
2
2
2
2
2
1
2
0
0
1
1
1
0
0
2
0
1
0
0
1
2
0
2
2
0
2
2
1
2
2
1
1
0
2
0
0
1
1
0
1
0
2
1
0
2
0
1
0
1
1
0
2
1
0
1
2
2
1
1
1
1
0
4
2
1
1
0
2
1
1
0
0
1
0
1
0
4
0
1
3
1
0
1
2
1
1
0
0
0
1
0
2
2
2
1
0
0
0
0
0
1
1
1
1
1
1
0
0
2
0
1
2
0
1
0
0
1
0
1
2
0
0
1
1
2
2
2
0
1
2
1
0
1
1
0
0
1
0
1
2
1
2
1
1
1
1
1
0
0
0
2
0
0
1
1
2
1
0
1
0
1
1
0
1
0
1
0
0
2
1
2
1
1
1
0
1
2
0
2
1
3
0
0
1
0
1
2
2
2
2
0
0
0
2
0
0
1
2
0
0
1
0
1
1
2
0
0
0
2
1
0
2
2
0
2
1
1
0
1
1
1
1
1
2
0
1
0
0
1
2
0
1
0
0
0
1
1
4
0
1
2
1
0
1
0
1
2
0
2
1
0
2
1
0
3
0
0
0
1
0
2
1
1
1
0
1
0
2
0
1
0
0
0
1
1
0
0
0
0
1
2
2
0
2
0
0
0
0
1
2
2
6
1
0
0
0
0
0
2
1
2
0
0
1
1
1
0
2
1
2
0
0
0
2
0
0
1
0
0
1
0
2
2
0
2
0
1
0
1
1
1
2
2
0
1
1
1
0
1
1
1
1
0
0
0
0
2
0
0
1
0
2
2
0
2
0
1
0
1
1
1
0
1
0
0
1
1
1
1
1
1
1
1
1
1
0
1
2
0
0
0
0
1
1
2
1
2
2
0
1
1
0
2
2
1
1
1
1
2
1
0
1
1
2
2
0
0
1
0
1
2
1
0
0
1
2
1
2
1
0
0
1
2
0
2
1
1
0
1
2
0
0
0
0
0
0
1
1
1
0
2
3
0
1
1
2
0
0
1
0
0
0
2
2
0
1
1
2
1
2
1
1
0
1
0
0
1
2
0
1
2
2
1
1
0
0
2
0
0
0
1
1
3
2
1
0
1
0
0
2
0
2
2
0
1
2
1
0
1
1
0
2
2
2
0
1
0
2
1
1
2
0
2
0
1
0
1
2
0
0
0
2
1
1
0
1
1
2
0
0
0
0
1
1
0
0
0
0
2
0
1
1
1
2
2
1
2
2
2
1
1
0
0
2
2
2
0
2
2
1
0
0
1
0
2
1
0
0
2
0
0
1
1
2
1
2
0
0
0
1
0
0
0
1
1
0
1
1
2
1
2
4
0
0
1
1
0
1
0
1
2
0
0
2
0
2
3
0
1
0
0
1
1
2
0
2
1
0
1
1
1
1
0
1
2
1
0
2
1
0
0
0
0
1
0
1
1
1
0
1
1
0
2
0
0
1
0
0
2
0
1
2
2
2
0
1
2
0
2
0
0
1
0
2
0
0
1
0
2
0
2
1
0
1
1
0
0
1
1
2
0
1
1
3
1
2
2
0
1
1
3
1
1
1
1
1
2
0
0
0
1
1
0
1
0
0
0
3
2
1
0
2
1
2
0
0
0
0
2
0
2
1
1
0
1
0
1
0
0
0
0
1
2
1
0
0
3
1
1
0
3
0
1
0
1
0
2
1
2
0
0
0
0
1
1
0
1
0
2
0
3
0
0
0
2
0
1
0
2
0
0
0
1
0
0
2
1
0
2
1
0
2
1
1
0
1
2
1
0
3
2
3
0
0
0
0
0
0
2
0
3
0
1
1
0
0
0
0
1
2
0
2
0
2
2
0
0
0
0
0
0
2
0
1
1
0
0
2
0
0
2
2
0
1
1
0
1
1
1
1
1
0
2
0
1
0
0
1
0
0
1
1
1
2
1
2
2
0
0
2
1
2
2
2
1
0
2
0
1
0
2
0
1
1
2
1
0
1
0
0
1
1
1
0
1
1
2
2
0
1
2
1
2
0
0
0
0
0
0
1
1
0
1
2
0
1
1
0
2
1
2
2
0
2
1
0
1
1
2
2
2
0
1
1
0
1
1
0
2
0
2
1
1
1
2
1
0
0
2
1
2
1
0
0
1
1
0
0
1
1
0
0
2
1
0
2
1
0
0
0
2
1
1
1
0
1
2
0
1
1
0
0
0
1
0
0
0
0
2
1
0
0
1
1
1
2
0
1
0
1
0
1
0
0
3
0
2
1
0
1
1
0
0
1
0
1
0
0
1
0
1
0
1
1
1
1
0
1
1
0
1
0
1
2
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
1
2
0
1
1
2
1
2
0
1
1
2
2
0
0
2
0
1
0
2
2
1
1
0
2
1
1
1
0
2
0
2
1
2
0
1
1
0
2
0
1
2
1
0
1
0
1
1
2
1
0
1
1
0
0
0
2
1
2
2
0
1
1
3
1
2
2
1
2
2
0
2
1
0
0
1
0
1
0
1
2
1
0
0
2
0
1
1
0
0
0
0
0
0
0
1
0
1
2
0
1
2
1
0
2
0
3
1
1
0
0
1
1
1
1
2
1
0
0
1
0
1
1
1
0
0
0
1
1
2
0
2
1
0
1
2
1
1
0
1
0
1
1
2
1
2
0
0
1
1
2
1
2
1
0
1
2
0
1
1
0
0
1
2
1
0
0
2
1
0
0
0
1
0
0
0
2
1
1
1
2
0
0
1
0
1
0
1
0
2
1
2
0
2
2
1
2
0
1
0
0
2
1
1
1
1
0
0
0
0
0
0
1
2
0
0
0
0
2
2
1
1
0
1
2
1
0
1
1
1
0
0
1
0
1
1
2
0
0
1
1
1
0
0
0
0
2
3
1
0
0
1
1
1
1
1
2
1
2
2
1
0
1
1
0
1
0
1
2
2
0
1
1
0
1
1
1
0
0
1
1
2
1
1
0
1
1
2
1
1
0
1
0
2
1
0
1
1
2
0
1
1
0
2
0
0
1
1
1
0
2
1
0
0
0
2
1
1
0
1
0
0
0
2
0
2
2
1
0
1
1
1
1
1
0
1
0
1
2
1
2
1
0
1
1
0
1
2
1
0
0
0
0
0
1
1
1
0
0
0
0
1
1
1
1
2
1
1
2
0
2
0
1
1
1
1
1
1
1
0
2
2
0
2
0
0
1
0
1
1
0
1
2
0
0
0
2
1
2
2
0
1
2
0
0
0
0
1
0
1
1
1
2
0
1
0
1
1
1
0
0
0
1
1
1
2
2
4
2
2
2
1
2
1
2
2
0
1
0
0
0
1
0
2
0
1
0
1
0
1
1
2
1
0
1
0
2
1
0
1
1
1
1
2
1
0
0
1
2
1
0
2
1
0
2
1
2
1
2
3
0
0
2
0
0
1
1
0
0
2
2
1
0
0
1
0
0
0
1
1
1
0
1
2
2
1
2
0
1
1
0
0
1
0
0
1
2
1
2
1
0
0
1
2
1
0
2
0
0
1
0
0
1
1
2
2
1
1
0
1
0
2
2
0
1
1
1
2
2
1
1
1
1
1
2
0
3
0
1
1
2
1
0
2
0
0
1
1
1
1
2
1
2
0
2
1
1
1
0
2
0
1
0
1
1
2
1
0
2
1
0
1
3
2
0
0
0
0
0
1
0
1
2
1
1
1
0
0
0
1
0
2
2
2
0
1
1
0
1
2
1
1
0
1
0
1
0
1
0
6
2
2
0
1
1
1
0
0
0
0
0
1
0
2
0
1
0
1
0
0
0
2
2
1
0
0
1
1
1
0
3
2
0
2
19
2
1
1
2
0
0
1
0
1
3
0
2
1
0
0
0
2
1
0
2
1
0
0
2
2
1
1
1
1
1
2
1
0
0
0
0
0
1
0
0
2
1
0
0
3
2
2
1
0
1
1
1
0
1
1
1
1
1
0
1
1
2
0
0
0
0
2
0
0
0
2
1
1
1
2
0
0
1
0
1
0
0
0
2
1
1
0
1
0
2
2
1
1
1
0
0
2
0
1
0
0
2
0
1
1
1
0
1
2
0
1
2
1
1
2
1
3
0
1
1
3
1
3
2
1
1
1
0
0
1
0
0
2
1
0
2
1
2
1
0
0
0
1
1
1
0
0
1
1
2
6
2
0
0
1
2
0
1
2
0
1
2
1
0
1
0
0
1
2
0
0
1
0
1
0
0
0
2
2
0
2
1
2
1
1
1
0
1
1
0
1
1
2
0
0
0
1
0
1
2
1
1
1
2
1
1
0
0
0
0
0
0
1
0
0
1
1
1
0
1
2
1
0
0
1
0
1
0
5
1
0
1
0
0
2
1
0
1
0
3
1
1
0
0
1
0
0
1
1
0
1
0
1
0
2
1
0
0
0
0
0
1
0
1
0
1
1
3
1
1
1
0
2
0
3
0
1
0
0
2
1
0
1
0
1
0
0
2
3
0
0
0
2
1
1
0
0
1
0
1
0
1
0
0
1
2
1
2
0
1
0
0
1
0
1
0
0
2
0
1
2
0
0
2
1
0
2
0
1
0
2
0
2
4
0
0
0
1
1
2
2
2
1
2
0
2
1
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
2
0
0
1
1
1
1
1
1
1
0
0
1
0
1
1
0
1
0
2
2
2
1
1
2
1
0
0
0
0
1
0
0
0
0
2
0
2
2
0
0
0
0
0
2
0
1
1
1
1
0
1
1
1
2
0
0
2
2
0
1
2
4
1
2
2
2
1
2
1
2
2
0
2
0
0
2
0
0
1
0
1
2
2
1
2
2
1
0
1
1
0
0
2
0
0
2
0
0
0
2
0
0
1
0
0
0
0
2
1
0
2
1
1
2
1
0
2
1
0
1
1
0
0
2
0
0
0
0
1
1
0
2
1
0
0
1
2
0
1
1
0
1
1
2
2
2
1
1
1
1
1
0
1
2
0
1
0
0
0
1
0
2
0
1
2
6
2
2
2
1
1
1
0
0
1
1
0
1
1
0
1
2
0
1
0
1
0
1
1
1
1
2
0
1
0
1
1
1
0
0
1
1
0
0
0
1
1
2
2
2
1
2
2
0
2
1
0
2
0
1
0
1
2
6
0
0
0
1
2
0
1
1
0
1
2
0
1
1
0
0
1
0
0
1
1
2
0
0
2
2
0
1
2
1
2
2
1
1
1
2
0
0
2
0
0
0
1
1
2
1
1
2
0
1
0
2
1
2
2
0
1
0
1
0
1
1
1
0
1
1
0
1
0
0
1
1
0
2
0
1
8
1
2
1
1
1
0
1
2
1
1
0
0
0
0
1
2
0
0
0
1
0
1
0
2
1
2
0
1
1
1
4
1
1
1
1
2
2
1
2
0
0
0
0
2
1
3
0
0
1
3
1
1
0
1
1
2
1
2
1
1
2
2
0
0
2
0
2
1
1
1
0
0
0
1
2
0
0
1
1
0
2
1
1
0
1
1
0
1
1
1
0
0
1
2
0
0
1
0
0
0
5
0
1
1
1
2
1
1
1
3
1
1
2
0
0
0
0
0
1
1
0
1
0
1
0
0
0
1
0
1
1
0
0
1
1
1
1
1
0
2
2
1
0
1
2
1
0
2
0
2
2
1
1
1
2
0
1
2
0
1
1
0
2
0
0
2
1
2
1
2
2
1
2
1
2
0
2
2
1
2
0
2
1
1
2
0
2
1
3
0
2
1
0
0
1
1
0
0
2
1
1
2
0
0
1
1
0
0
0
0
1
2
0
0
0
1
0
0
0
0
2
0
0
0
0
1
1
1
0
0
2
2
0
2
1
1
1
0
0
1
0
0
0
2
1
1
3
0
0
1
1
1
1
1
1
1
0
0
0
1
2
0
2
1
0
0
0
1
1
0
1
1
2
0
1
1
2
0
0
1
0
2
2
0
0
0
0
1
2
0
1
0
1
2
0
0
0
0
0
2
0
0
1
1
1
0
1
0
1
0
1
0
2
1
0
0
3
1
2
1
0
0
0
2
2
0
0
1
0
1
2
0
0
2
1
2
1
0
0
2
0
1
1
0
2
0
1
1
0
0
2
2
1
0
1
1
1
0
2
1
0
1
2
2
2
1
0
0
1
1
0
0
1
1
1
0
1
0
1
2
2
1
1
2
1
1
0
0
3
1
1
1
1
2
1
1
0
0
0
0
1
1
1
0
0
0
1
0
1
0
2
2
0
0
1
0
0
1
0
2
0
0
0
0
2
1
2
1
2
0
0
0
0
1
3
0
2
1
0
1
0
1
0
1
0
1
1
1
1
1
0
1
1
1
1
2
1
2
1
1
0
2
0
1
0
1
1
0
1
0
0
1
0
0
1
2
1
0
1
1
2
1
1
1
0
0
2
1
0
0
0
1
0
0
2
1
0
0
1
0
2
1
0
1
0
0
0
0
1
1
0
0
1
2
0
0
0
1
2
1
1
1
1
0
1
0
0
2
1
8
1
0
2
0
0
1
1
1
0
0
0
0
0
1
2
2
1
0
0
1
2
2
1
1
0
2
0
2
2
3
0
2
1
0
1
1
1
1
0
0
0
1
0
1
2
0
2
0
0
1
0
2
1
1
0
1
0
0
0
2
0
1
1
1
0
0
2
1
1
2
0
1
1
1
2
1
0
1
2
2
0
0
0
1
0
1
0
2
1
1
1
2
0
2
1
2
1
2
1
2
2
2
2
2
0
1
2
0
1
0
1
1
0
2
0
2
0
0
2
0
1
2
2
0
1
0
0
1
1
0
0
1
1
1
2
1
0
1
1
0
0
2
1
0
2
1
0
1
0
0
0
1
0
0
2
1
1
0
1
1
2
2
0
0
1
0
4
0
1
1
0
0
1
0
1
0
0
1
0
2
1
1
2
0
2
0
1
0
0
0
1
0
2
1
0
1
0
2
1
2
1
1
0
0
0
0
1
1
1
0
2
2
0
0
0
0
1
1
1
2
0
2
0
0
0
2
2
0
0
1
0
1
1
1
0
1
1
0
0
0
3
1
0
1
2
1
0
0
0
3
0
0
1
1
0
2
1
1
1
0
0
0
1
2
0
1
1
0
1
2
0
0
2
0
1
0
1
2
2
2
0
0
1
1
2
0
0
2
2
0
1
0
1
1
0
4
0
1
0
0
1
0
1
2
3
2
2
3
1
2
0
2
1
2
0
0
0
1
0
0
0
0
2
1
1
2
0
1
1
0
0
2
1
0
2
2
1
0
1
1
2
0
2
0
1
0
0
1
0
0
1
1
2
0
0
0
1
0
1
0
2
0
0
0
0
0
1
0
2
0
0
1
2
1
1
1
0
0
2
0
0
0
2
2
0
0
0
2
1
2
1
0
0
1
0
1
0
0
1
0
1
2
1
1
3
1
1
0
1
0
0
1
0
1
1
0
0
2
2
2
0
0
0
1
0
1
0
2
2
1
1
0
0
1
2
0
1
0
1
0
0
0
0
0
1
1
2
1
3
1
1
1
0
2
1
1
2
0
0
0
1
0
0
1
1
0
1
1
1
2
2
0
0
2
1
2
1
1
0
1
2
2
0
1
1
0
2
2
2
0
0
2
0
2
0
0
1
1
0
0
2
1
1
2
0
2
0
0
2
1
0
1
0
2
2
2
2
0
1
1
2
0
0
1
1
2
0
0
2
1
1
0
2
0
1
2
0
0
1
0
1
0
1
2
2
0
1
0
2
0
0
1
2
2
0
1
0
0
0
1
0
0
0
1
0
2
0
1
1
0
2
0
0
0
1
0
2
1
2
1
0
1
1
0
1
1
0
0
2
0
2
1
2
1
1
1
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
2
1
0
0
1
1
1
0
0
2
1
0
1
0
1
2
1
2
1
1
1
1
1
3
0
1
0
0
2
1
1
1
0
1
1
2
2
1
2
2
1
1
0
0
1
0
0
0
0
1
1
0
1
2
1
2
0
1
0
2
0
1
0
0
1
1
0
0
1
2
2
1
0
0
0
1
0
0
1
0
1
0
1
2
0
1
2
1
2
1
0
1
0
0
0
4
0
1
0
1
1
2
2
2
1
1
1
1
1
2
1
1
0
0
0
0
2
1
1
1
0
1
2
0
0
2
1
0
1
1
1
1
1
2
1
1
0
1
1
0
1
1
1
1
0
2
1
1
0
1
1
1
1
1
2
1
2
1
0
1
1
0
1
2
1
0
0
1
1
1
0
0
0
0
2
0
1
5
2
2
0
2
2
0
0
1
2
0
0
0
0
1
0
1
2
2
2
1
0
0
3
2
0
2
1
2
1
0
1
0
1
2
1
0
1
1
1
0
0
1
1
1
1
0
0
1
1
1
0
2
0
1
0
0
3
1
2
0
1
2
2
1
0
1
0
2
2
1
2
1
0
1
2
0
0
1
1
0
0
0
0
2
0
2
0
1
0
0
1
0
1
0
1
1
1
1
1
0
0
0
2
0
0
2
2
1
2
0
1
1
0
1
1
0
0
0
1
0
0
0
1
0
1
1
1
0
2
2
1
1
0
0
1
1
0
1
1
2
1
0
0
2
1
2
1
1
1
0
1
0
1
1
1
0
2
1
0
0
0
2
0
1
0
2
1
1
2
0
0
0
1
0
0
0
1
1
2
0
1
0
1
0
0
1
0
1
0
1
1
0
1
0
1
2
1
0
3
0
0
2
0
2
2
1
1
1
0
0
0
0
1
1
1
2
2
2
1
0
0
0
1
1
0
1
1
3
2
0
1
0
1
0
0
0
2
2
1
2
0
0
0
1
1
2
2
1
1
0
1
1
0
1
2
0
0
0
0
0
0
0
1
1
2
0
0
1
1
1
0
1
0
2
1
0
1
0
1
0
2
0
2
1
0
2
1
1
0
2
1
2
2
1
0
1
0
0
1
2
1
1
0
2
0
1
1
1
0
2
0
0
0
2
0
1
2
2
0
0
2
1
0
0
2
0
2
1
0
1
2
2
1
2
0
0
1
2
2
2
2
1
1
1
0
0
1
1
1
0
0
0
1
0
3
2
2
2
2
1
1
0
0
1
2
0
2
1
0
0
1
1
1
2
0
1
1
2
1
0
1
0
1
0
0
0
0
3
0
2
0
1
0
1
1
1
1
1
2
0
0
0
0
5
1
1
2
0
0
1
1
1
0
1
1
1
1
1
0
2
1
0
0
1
0
0
2
1
1
2
2
1
2
0
2
1
1
0
0
1
1
1
1
1
1
0
0
0
0
1
1
1
1
1
2
0
1
0
1
0
2
0
1
0
1
2
0
1
1
2
1
1
2
2
1
2
2
3
2
2
0
2
1
1
2
2
0
0
0
3
1
2
1
1
1
2
2
0
0
0
0
3
1
2
0
0
1
2
0
0
1
1
1
1
1
2
0
0
0
1
1
2
1
1
0
2
1
2
0
0
0
2
5
0
2
2
0
2
1
1
1
2
2
2
0
0
1
1
0
1
1
0
0
0
4
1
2
1
0
2
0
0
0
1
0
1
1
2
1
0
0
1
0
1
0
0
2
0
0
0
1
0
2
2
0
1
0
0
1
1
1
1
0
0
0
3
2
1
0
1
4
3
1
1
2
1
0
0
0
1
2
0
2
2
1
1
0
1
1
2
1
2
0
2
0
0
2
0
0
2
1
1
0
2
1
0
1
0
0
2
0
0
0
1
0
2
0
0
2
0
0
1
1
1
0
1
0
2
2
0
1
1
0
1
0
0
1
0
2
0
0
2
0
1
1
0
0
0
1
1
2
1
0
1
1
2
2
0
2
0
2
1
1
1
1
0
0
1
1
1
1
1
1
0
1
0
2
0
2
0
2
1
1
0
1
0
2
1
1
1
0
0
0
2
2
2
0
2
2
1
0
0
2
1
1
0
1
1
0
0
2
1
1
1
1
0
1
1
0
2
3
0
1
1
0
0
1
0
0
0
2
0
1
0
0
1
0
2
1
0
2
1
1
0
0
0
1
1
1
1
0
1
0
0
0
0
0
0
2
2
2
2
0
0
0
0
1
2
0
2
0
1
1
2
2
1
2
1
2
0
1
0
2
0
0
1
0
0
1
0
2
2
0
0
2
1
2
2
3
0
1
0
0
0
2
2
0
1
0
2
0
2
0
0
1
0
2
0
2
0
2
0
0
2
0
1
0
0
0
1
3
2
0
0
1
0
1
1
0
0
2
2
2
1
0
1
1
0
1
0
0
0
1
0
1
1
0
1
1
0
2
0
1
1
0
0
0
1
1
2
0
0
0
0
1
2
1
2
0
0
1
0
1
0
2
1
1
2
1
5
1
1
1
0
1
1
1
0
0
1
0
2
4
0
1
1
0
0
1
0
2
1
0
2
0
0
0
2
0
1
1
0
0
1
0
0
2
1
3
2
2
0
2
2
3
1
1
2
0
0
0
2
0
0
2
0
1
0
0
1
1
2
1
0
1
2
2
0
1
0
1
0
0
0
0
1
0
1
2
1
0
1
1
1
1
2
2
1
0
1
0
0
0
1
0
1
0
1
1
1
2
0
1
2
1
0
0
1
2
1
2
0
1
1
1
0
1
1
2
0
1
2
0
0
1
0
1
2
0
2
1
0
1
1
0
1
0
2
1
1
1
1
0
0
1
1
1
0
0
0
2
0
0
0
1
2
1
2
2
1
1
1
0
1
1
1
0
1
1
1
0
1
1
1
0
1
1
0
3
1
2
1
1
0
1
0
0
1
1
0
0
2
2
0
0
1
0
0
1
2
0
0
1
0
0
2
1
2
0
1
1
1
1
1
2
1
0
1
0
0
0
0
0
0
1
0
2
1
1
2
0
0
0
0
1
2
1
2
2
1
1
1
1
0
1
2
1
1
0
1
0
2
0
0
2
2
2
1
0
3
0
1
0
1
0
1
2
1
1
0
1
0
1
0
1
2
0
1
0
1
1
1
0
1
1
2
1
0
0
0
1
1
1
0
1
0
2
0
2
2
0
1
1
2
1
0
1
1
0
1
1
0
1
2
0
1
0
1
2
0
0
2
0
2
0
0
2
1
1
2
0
0
1
0
1
2
1
2
0
0
0
3
0
1
1
0
1
1
0
1
0
0
1
1
1
0
0
0
1
1
1
0
0
2
1
1
0
1
2
1
0
2
2
0
0
0
2
2
0
1
0
0
2
1
0
0
0
1
0
2
0
0
0
0
1
0
0
1
0
0
1
0
0
1
1
2
0
1
0
0
1
0
2
0
1
1
0
0
2
0
0
2
2
1
0
2
2
1
0
2
0
0
0
1
0
0
0
0
0
1
2
0
3
0
0
1
0
1
1
2
2
2
1
0
0
0
2
0
2
3
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
2
1
1
1
1
2
1
2
1
1
1
1
0
0
1
1
0
2
0
1
0
1
0
1
0
0
0
0
2
0
1
0
0
1
1
1
0
0
1
1
1
0
1
0
1
1
1
0
0
1
2
2
2
0
0
1
1
0
1
0
1
0
0
2
1
0
0
3
1
0
0
1
1
0
1
2
1
1
0
1
0
2
2
2
1
1
1
0
0
0
1
0
1
0
1
1
0
0
2
1
0
0
1
1
0
0
1
0
1
2
0
0
2
1
0
0
0
1
1
1
1
2
2
0
2
0
1
1
1
0
1
1
2
0
1
0
0
1
1
0
1
3
0
2
2
3
1
1
0
1
0
2
1
2
0
2
2
1
0
0
1
0
1
1
2
1
2
0
0
0
0
0
2
2
2
0
0
1
1
0
3
0
1
0
2
1
3
1
0
1
0
0
1
0
1
2
0
2
2
1
0
2
0
1
1
0
0
2
0
2
0
2
1
0
2
2
1
2
2
1
1
0
0
1
0
1
2
1
0
4
1
1
3
1
1
1
0
0
0
2
0
2
0
1
0
2
2
0
0
1
0
1
0
0
0
0
1
1
2
0
0
1
1
1
0
0
0
0
1
1
0
0
1
2
1
0
0
1
0
1
2
1
0
0
1
1
0
2
1
0
1
0
1
2
2
1
1
0
0
3
0
1
1
1
1
0
0
0
1
0
0
0
2
0
0
0
1
0
0
1
0
2
0
2
0
0
2
1
0
1
0
1
1
1
2
0
1
4
1
0
0
0
2
2
0
1
3
1
0
2
0
0
0
1
2
1
2
1
0
1
1
1
1
1
0
1
2
0
0
2
0
1
1
2
2
0
2
0
1
1
1
1
1
0
2
1
0
2
1
2
2
1
1
2
1
0
1
0
2
1
2
1
1
3
0
2
0
2
1
1
0
1
1
0
1
0
1
1
0
0
1
0
0
1
0
0
1
4
1
1
2
3
1
1
2
0
1
2
0
0
2
1
1
1
0
2
0
0
2
1
0
1
0
2
1
2
1
1
0
1
1
0
1
1
2
1
0
0
1
0
1
2
1
0
0
0
0
1
0
1
1
0
0
1
0
1
0
2
1
1
0
0
1
1
0
0
0
1
0
2
1
0
1
2
0
0
2
1
1
0
2
0
2
1
0
1
1
1
1
1
0
1
0
1
1
1
0
1
0
0
1
0
0
2
0
1
0
2
1
0
1
2
2
0
0
1
0
1
2
0
0
0
2
0
0
0
1
1
2
2
0
0
0
1
0
2
0
1
2
3
1
0
0
0
2
1
0
1
1
1
1
2
0
1
1
0
1
1
0
2
2
0
0
0
0
0
1
1
0
0
1
0
0
2
0
0
1
0
2
1
1
0
2
1
2
0
1
0
1
1
1
1
1
1
3
0
2
0
2
1
1
0
1
2
0
1
1
0
1
1
2
1
0
1
0
0
1
2
1
0
0
3
1
0
1
0
2
0
0
1
1
2
0
1
2
0
1
1
1
0
1
0
2
1
1
1
0
0
1
1
2
1
0
1
2
0
0
0
0
1
2
0
0
3
0
0
1
0
2
1
0
2
2
2
1
0
0
0
0
2
2
0
1
1
0
2
1
3
0
0
0
2
1
1
2
0
2
1
2
0
0
0
0
0
0
1
2
1
0
1
0
2
1
1
1
0
2
0
0
2
0
1
0
4
1
1
2
2
0
1
1
1
0
1
0
0
2
2
1
0
0
1
0
0
1
0
2
1
1
0
1
1
2
1
2
1
1
0
1
0
0
1
0
2
2
1
1
0
2
0
1
0
0
0
0
0
0
2
2
1
0
1
0
0
0
2
1
2
0
3
0
0
2
0
0
1
0
0
2
1
0
0
1
1
1
0
0
0
0
1
0
1
0
1
0
0
1
1
3
2
0
2
2
0
0
1
2
1
1
1
0
0
1
1
2
0
1
2
1
0
0
0
0
0
1
1
2
0
0
1
1
1
2
1
0
1
0
0
1
2
0
2
0
2
1
0
1
1
1
1
0
0
1
0
0
0
1
1
0
2
0
3
1
0
1
0
2
1
2
1
1
1
1
1
1
0
0
2
1
1
1
1
0
0
0
2
0
1
0
0
1
1
0
2
2
0
2
2
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
2
0
1
2
1
0
1
1
1
1
1
0
0
0
1
2
1
2
0
0
0
1
1
2
1
1
0
1
1
1
2
1
0
0
1
0
1
3
1
1
2
0
2
0
1
0
0
0
0
0
0
0
0
1
1
1
1
0
0
1
1
0
2
0
2
0
2
0
2
2
1
1
0
2
0
2
0
2
0
0
1
0
0
1
0
2
1
2
1
0
1
2
0
0
1
0
2
2
2
1
0
0
2
0
1
0
1
0
2
1
2
2
1
0
1
2
0
1
2
1
0
3
0
2
2
2
0
1
0
2
2
1
1
1
0
1
1
1
1
0
1
1
1
1
2
1
0
1
0
1
1
0
0
2
0
0
2
0
0
0
0
1
0
1
0
1
1
1
1
1
0
0
1
2
1
1
1
1
2
0
0
1
1
0
0
1
1
0
0
2
0
0
1
0
2
2
2
0
0
1
1
0
2
4
0
2
1
0
2
1
0
1
1
1
2
0
2
1
0
1
1
1
1
1
2
1
2
0
0
2
2
0
2
0
0
1
0
1
0
2
1
0
1
1
0
0
0
0
1
3
0
1
0
2
1
1
1
0
1
0
1
1
0
0
0
0
0
0
1
0
3
0
0
1
0
0
2
1
0
2
1
1
1
1
0
0
1
1
1
0
2
0
2
0
1
2
0
1
1
0
2
1
1
2
0
1
1
0
0
1
1
1
0
2
1
1
2
1
0
2
0
1
0
1
2
0
0
0
0
2
0
0
1
1
0
1
0
0
2
0
0
1
0
2
1
1
1
1
1
1
1
1
0
1
0
1
0
0
2
2
2
0
2
2
0
0
2
0
0
1
1
2
1
2
2
2
0
2
1
0
0
1
2
1
1
2
0
1
1
2
0
2
1
1
1
1
2
0
1
2
1
1
2
2
1
0
1
0
1
2
0
2
1
0
1
0
1
1
1
1
0
0
0
2
1
0
2
1
3
1
0
1
1
0
1
1
1
0
0
2
0
0
0
1
1
1
0
0
0
1
0
2
0
0
0
1
0
2
0
2
0
0
1
0
0
0
1
1
1
1
1
2
0
0
2
0
1
0
0
0
2
1
2
1
2
1
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
1
1
2
1
0
2
0
0
0
0
2
2
0
2
3
1
0
1
2
1
0
2
1
2
1
1
0
3
1
2
1
1
0
0
1
2
2
1
0
1
0
2
1
1
0
3
1
1
0
1
2
0
0
1
1
0
1
1
0
1
1
2
0
1
0
0
1
2
0
1
1
1
1
1
1
0
0
1
1
1
1
2
2
1
2
1
2
0
0
0
0
0
1
1
0
2
1
1
1
0
0
1
0
2
0
1
1
3
1
1
2
2
2
1
1
1
0
1
2
0
0
2
1
1
1
0
0
0
1
1
0
2
0
2
1
0
3
1
1
0
0
0
2
0
1
0
1
1
1
2
0
0
2
0
0
2
0
1
0
1
2
2
2
0
2
0
1
2
0
1
0
0
0
2
0
0
0
0
1
1
1
3
1
2
0
2
1
0
1
0
0
2
0
2
2
1
2
2
2
1
0
2
2
0
0
0
2
1
0
2
0
1
0
0
2
2
1
2
1
1
1
1
1
1
0
0
1
0
0
2
1
0
2
2
0
0
0
1
1
0
0
0
1
2
1
2
0
1
1
1
0
1
0
1
2
1
1
2
0
1
1
0
1
3
2
1
1
2
1
1
1
0
1
1
0
0
2
1
2
0
1
1
0
0
0
1
0
1
1
2
1
0
1
1
1
0
0
1
1
0
1
2
2
0
2
0
1
0
1
0
1
1
1
0
0
0
0
2
2
1
0
1
1
0
2
0
1
0
0
1
1
0
2
0
2
2
0
0
2
2
2
0
1
1
1
2
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
4
1
1
1
0
0
0
1
0
1
1
0
2
0
1
1
2
0
1
3
0
1
0
0
2
1
0
1
1
2
1
2
2
0
1
0
1
1
1
0
1
0
0
1
0
0
0
0
1
1
1
0
2
1
0
1
0
1
1
1
1
1
0
1
1
0
0
1
1
1
1
1
1
0
2
0
1
1
0
1
1
0
0
1
1
0
0
1
1
1
1
0
1
2
0
0
2
0
0
1
0
0
0
1
1
1
1
0
0
0
2
2
2
1
1
0
1
0
0
0
1
1
1
2
2
0
0
2
1
2
1
1
2
3
0
0
0
0
1
1
1
0
3
1
0
1
1
1
1
1
0
1
0
0
1
2
0
0
2
1
2
0
0
1
2
0
1
1
0
0
1
0
1
2
0
2
1
0
2
0
0
1
0
1
0
1
1
1
0
2
0
1
1
0
1
2
0
1
1
0
0
2
1
0
0
2
0
1
3
0
0
1
4
1
0
0
0
1
0
0
1
0
1
1
0
2
2
0
0
1
1
0
0
1
2
0
2
0
1
0
0
1
2
1
1
0
0
2
0
1
1
4
0
0
0
1
2
1
1
2
1
0
0
3
1
0
2
1
1
1
0
0
0
2
1
2
2
0
2
0
1
0
2
0
1
1
0
0
0
0
2
0
2
2
1
1
0
1
0
3
0
0
0
1
1
1
0
1
0
1
0
1
1
1
0
0
0
1
2
0
1
1
0
0
1
0
2
2
2
0
2
1
2
1
0
0
0
0
1
1
0
0
1
0
0
1
1
2
1
0
0
0
1
0
1
0
1
1
1
1
1
0
3
0
2
1
1
3
0
2
0
0
0
2
1
2
2
0
0
0
0
1
1
1
1
1
0
0
2
0
0
2
0
0
1
2
1
0
0
2
0
1
2
0
2
1
1
1
1
0
1
2
0
1
1
0
0
1
1
1
1
2
0
3
2
1
0
0
1
0
2
2
0
2
2
1
3
2
0
2
2
1
0
0
0
1
0
1
2
0
0
1
1
1
0
1
1
2
2
2
1
2
1
0
1
0
1
3
0
1
1
0
0
0
1
0
1
1
1
1
1
1
0
2
0
2
1
1
1
2
0
1
0
1
1
2
0
2
1
2
1
3
0
0
1
1
0
2
0
0
1
2
0
1
2
2
0
0
0
2
0
3
0
1
1
2
1
1
1
2
1
2
0
0
2
0
0
1
2
0
0
1
1
0
0
2
1
2
2
0
1
0
0
0
1
2
0
0
2
0
0
3
0
1
2
2
0
0
0
0
0
2
1
0
0
1
1
2
1
0
0
2
1
0
1
1
1
0
2
0
0
2
1
1
1
0
1
0
2
1
2
2
1
0
1
1
2
0
0
0
0
1
1
2
0
1
0
1
0
1
1
0
0
0
1
0
0
2
0
0
1
1
0
0
0
1
2
2
0
1
2
1
0
1
0
1
0
2
0
2
0
1
2
0
1
1
0
1
1
1
0
0
0
3
1
1
1
0
1
2
2
0
3
1
0
0
2
1
0
1
2
2
1
1
0
2
1
2
0
0
1
1
0
1
1
1
0
0
1
1
2
0
0
0
2
2
0
0
0
2
1
1
0
3
0
0
2
0
1
2
2
1
2
1
1
3
0
2
1
2
1
2
0
1
0
0
2
0
0
1
1
2
1
0
0
2
2
2
0
1
1
0
2
2
0
0
0
1
0
1
0
1
0
1
0
3
1
0
1
0
0
2
0
1
0
2
1
0
1
1
1
1
0
1
1
1
2
2
1
0
2
0
1
0
0
1
0
0
0
0
1
0
2
0
0
0
1
0
0
0
1
0
2
1
2
2
0
0
1
0
0
1
0
0
1
0
1
0
2
0
0
1
0
0
0
1
2
0
2
0
1
0
0
0
1
2
0
0
2
1
0
0
0
1
0
0
2
2
0
0
0
3
0
1
1
1
2
2
1
2
0
2
0
0
1
1
0
1
1
1
0
1
0
2
1
2
0
0
0
0
1
0
1
2
0
0
1
2
2
0
0
1
0
0
1
0
0
0
0
2
0
3
0
0
1
0
1
0
1
0
0
0
2
1
0
0
0
0
4
2
1
0
1
0
0
1
0
1
0
0
1
2
0
0
1
2
0
1
1
1
1
1
0
1
1
1
0
1
0
1
2
1
2
2
1
3
1
1
0
1
1
6
1
1
0
2
1
0
1
1
1
2
1
0
0
0
2
0
2
1
0
0
0
0
4
1
1
1
0
2
3
3
1
0
1
0
1
2
2
1
1
1
0
1
1
2
0
0
2
1
1
0
1
1
1
0
1
1
0
0
0
0
1
1
1
0
1
1
0
0
1
1
2
0
1
0
2
1
1
0
1
0
1
1
2
2
0
0
2
1
0
1
0
3
0
1
0
0
1
1
1
0
0
1
0
1
0
0
0
0
2
2
0
2
1
0
1
1
0
0
0
2
4
0
1
2
1
1
0
5
1
4
1
0
1
0
1
0
0
1
1
0
2
1
0
2
2
0
2
0
0
3
3
0
2
0
0
1
2
1
0
0
1
0
2
1
0
2
1
1
0
1
0
2
0
1
2
1
5
0
1
2
1
0
1
1
0
2
0
1
1
1
2
0
0
0
0
0
2
1
1
0
0
1
0
1
2
0
1
0
1
1
0
1
0
1
1
2
2
1
0
1
0
1
1
1
0
1
1
0
0
0
1
0
0
2
0
0
2
1
1
1
2
1
1
0
2
1
1
0
0
2
2
1
0
1
0
1
1
0
1
0
0
1
0
1
2
2
1
2
0
0
1
2
1
0
0
0
2
2
1
1
0
0
1
0
0
1
2
1
2
0
2
0
2
1
0
0
0
0
1
1
1
0
2
1
0
0
1
2
2
0
3
2
1
3
0
0
1
0
1
1
2
1
1
0
2
1
1
2
1
0
2
0
0
1
2
3
2
1
0
1
2
0
0
0
1
2
0
0
1
1
2
0
1
0
0
1
1
2
1
1
2
0
0
2
2
0
1
0
0
0
0
2
1
0
0
0
2
1
0
0
2
0
1
1
0
0
0
1
2
1
1
1
1
1
1
1
1
2
0
1
0
0
0
0
1
2
1
2
0
1
0
0
2
1
0
0
0
0
0
0
0
1
0
2
0
0
1
1
0
2
1
0
3
2
0
1
0
1
1
0
0
1
2
2
1
0
1
1
2
1
0
1
1
1
1
0
1
5
1
2
1
2
0
1
3
1
0
1
1
1
0
2
1
0
2
0
0
0
1
1
1
1
1
0
2
0
1
0
1
1
2
0
1
0
0
1
1
2
0
1
2
0
1
0
0
2
1
1
0
2
2
0
0
1
0
1
3
1
1
1
1
0
2
3
0
0
0
1
0
1
1
2
0
0
1
0
4
2
1
1
0
1
1
1
0
0
1
2
2
1
1
0
1
0
2
0
1
0
1
2
0
0
0
2
0
2
0
0
2
0
0
1
0
1
1
1
2
0
2
1
1
2
1
1
0
1
0
0
0
1
1
0
0
1
0
1
0
0
1
2
1
0
1
2
0
1
0
1
2
2
0
1
2
0
0
1
0
2
0
3
0
1
1
1
0
0
0
1
2
1
0
0
0
2
0
0
1
1
0
3
1
0
0
0
1
0
0
0
2
0
0
1
0
1
0
2
7
0
1
2
0
2
2
0
0
0
1
0
2
2
1
0
2
1
2
0
1
0
1
2
0
2
0
2
1
2
1
1
0
1
0
0
1
0
3
0
3
0
2
0
1
2
0
0
1
2
0
1
0
1
1
2
1
2
1
0
0
1
1
1
0
0
2
0
2
0
2
2
0
0
2
1
1
2
1
2
0
0
0
1
0
1
0
0
0
1
1
1
0
1
2
1
1
0
0
1
0
0
0
1
1
1
0
2
0
0
1
1
1
1
1
0
0
0
2
2
1
0
0
2
1
0
0
0
0
0
1
0
1
1
1
1
0
0
2
2
0
1
1
0
1
0
0
4
1
1
2
1
2
1
0
0
0
2
0
0
0
1
0
1
1
0
3
0
0
0
2
1
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
1
1
1
2
2
1
2
1
3
0
1
0
3
0
2
1
0
0
3
2
1
0
1
0
2
0
0
0
1
1
1
1
0
0
2
1
1
1
0
0
2
2
0
0
0
1
1
1
0
2
0
1
0
0
1
1
1
0
1
0
1
0
1
1
0
2
1
1
2
0
1
1
1
0
1
1
0
0
2
0
0
0
1
2
2
0
2
1
1
1
1
0
1
1
1
0
2
0
1
2
3
1
1
1
0
0
0
0
1
1
0
1
0
1
0
1
1
1
0
0
1
2
0
2
1
1
0
1
1
0
0
4
1
2
1
1
3
0
0
0
0
0
2
1
0
0
1
0
0
0
2
2
1
0
0
2
0
1
2
2
1
0
2
0
1
0
1
2
0
0
2
0
1
1
1
2
2
1
0
2
2
1
1
2
0
1
0
0
1
0
1
3
2
0
0
0
0
2
0
0
0
1
2
2
1
2
2
0
1
2
1
0
2
0
1
0
0
3
0
1
0
1
0
1
0
0
0
0
0
1
2
0
2
0
0
2
2
0
0
0
0
2
0
0
1
1
0
2
0
0
0
0
0
1
0
0
2
1
2
1
1
2
1
1
1
1
0
1
1
1
2
2
1
1
0
1
1
0
0
1
2
0
0
0
2
0
1
0
2
1
0
1
1
1
4
0
1
1
2
1
0
0
0
0
0
1
2
1
2
0
2
1
0
1
0
0
0
0
0
0
0
2
0
0
1
0
1
2
1
0
0
1
0
1
3
0
0
0
1
0
1
2
1
1
1
1
1
1
0
2
0
0
2
1
1
0
2
0
1
1
0
0
0
2
2
1
2
2
1
0
0
0
0
0
2
0
1
1
1
0
1
0
2
0
1
1
0
0
0
1
1
1
2
2
0
0
0
3
2
1
2
0
0
0
0
2
2
1
2
2
1
1
2
1
1
2
0
1
2
0
2
2
0
2
2
1
0
0
1
2
0
0
2
2
1
0
1
0
2
0
1
1
0
0
2
2
1
0
2
2
1
2
0
0
1
0
2
2
0
0
2
1
0
0
0
2
1
0
1
0
1
1
1
0
0
0
1
1
0
1
2
1
1
1
0
0
7
2
2
1
3
1
1
0
0
2
2
0
0
0
0
0
1
0
0
2
0
1
2
2
1
0
2
2
1
1
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
1
0
1
0
1
2
2
0
1
0
1
1
1
0
0
2
0
1
1
2
2
0
2
0
1
2
0
0
0
1
0
1
1
0
0
0
0
1
0
1
1
1
0
0
1
1
1
0
1
0
2
0
0
0
0
1
2
1
0
0
0
0
2
2
0
0
1
0
1
0
1
1
0
0
0
1
0
1
1
1
1
2
0
2
1
2
1
0
2
2
1
1
0
2
2
1
1
0
1
2
1
1
1
0
1
0
0
2
0
0
0
0
0
0
1
0
0
2
0
1
1
1
2
0
0
1
1
1
0
0
0
1
2
1
1
2
0
2
0
1
2
1
1
0
1
1
1
0
2
2
1
0
2
2
0
0
0
1
0
0
1
2
4
1
1
1
3
0
1
1
1
0
0
2
0
2
0
2
0
2
2
1
0
0
0
0
0
2
0
0
0
2
0
0
1
2
1
2
1
0
1
0
1
2
1
1
1
0
0
1
0
1
1
1
0
0
2
2
1
1
0
0
0
1
2
1
2
0
1
1
0
2
1
1
1
1
2
0
1
0
0
0
2
0
2
1
0
0
2
2
1
1
1
0
0
0
0
0
0
1
0
0
1
1
2
0
0
0
2
0
0
1
0
2
0
1
1
1
0
0
0
1
1
0
1
2
0
2
2
1
2
0
0
1
0
1
1
1
1
1
0
0
1
2
0
2
1
1
1
0
2
1
1
0
0
1
0
0
1
2
1
0
0
0
2
1
1
1
0
1
0
2
0
0
1
1
2
2
1
2
2
0
2
3
1
1
1
0
0
0
0
1
1
0
2
1
1
2
0
0
0
1
2
1
0
1
1
0
1
1
0
1
2
1
0
0
0
2
2
2
1
0
2
1
0
2
0
1
2
2
1
3
1
0
0
1
1
2
1
0
1
1
0
2
2
1
1
0
2
1
2
0
1
1
0
0
2
1
0
1
0
0
1
2
0
2
0
0
0
2
1
0
1
1
0
2
0
1
0
0
1
0
2
0
2
0
0
1
1
0
1
0
0
0
0
1
0
2
1
1
0
1
0
0
1
2
1
0
0
1
1
1
1
5
2
0
1
2
1
1
0
0
0
0
1
0
1
2
0
0
1
1
1
1
0
1
1
0
0
1
0
1
0
0
0
1
2
1
1
2
1
1
2
1
1
1
1
0
2
1
0
0
0
0
1
0
2
1
1
2
0
0
2
0
1
0
0
0
0
2
1
0
0
0
1
1
0
1
1
1
0
1
0
1
0
5
1
0
0
1
0
0
1
0
2
0
2
0
2
0
0
0
2
1
0
1
2
1
2
0
0
1
2
0
1
2
0
1
0
1
2
0
1
0
2
2
0
1
0
0
0
0
3
0
1
1
0
1
1
1
2
1
0
0
0
0
0
1
1
1
0
0
0
0
1
1
1
0
1
1
1
0
1
4
2
0
1
0
0
0
0
0
2
2
0
0
1
1
0
2
0
2
0
2
0
0
0
2
2
0
1
0
0
1
2
1
2
2
1
0
1
0
0
1
0
2
1
1
1
1
2
1
1
0
2
0
0
1
0
2
1
2
1
0
1
0
1
0
0
2
0
1
0
0
1
1
0
0
2
0
2
1
0
1
0
2
1
0
2
2
1
1
1
0
1
0
2
0
0
0
1
0
1
0
0
1
2
2
0
2
0
0
0
1
1
1
0
0
1
0
0
0
0
2
3
3
2
1
1
0
1
0
2
0
0
0
0
2
1
1
1
2
1
0
0
1
0
0
1
0
0
0
1
0
1
1
0
0
1
2
0
2
1
0
1
2
0
2
1
0
2
0
1
2
2
1
0
2
0
2
2
1
2
2
0
2
2
1
0
1
1
0
0
1
0
0
0
0
1
0
2
0
2
0
3
0
0
0
1
2
1
3
0
2
1
1
1
1
1
1
0
2
1
2
2
0
0
1
1
0
0
2
1
1
0
2
2
0
1
1
0
1
1
2
2
1
0
0
2
0
2
2
0
0
0
2
1
2
1
1
1
0
1
1
0
2
0
2
0
0
0
0
1
2
0
0
2
0
0
0
0
1
1
0
0
0
0
0
2
4
0
2
0
1
0
0
2
1
1
0
0
1
1
0
0
1
1
3
0
2
1
1
2
0
1
2
0
2
0
0
0
2
3
1
0
1
2
1
0
0
0
0
1
2
0
0
2
2
2
1
2
0
1
0
0
0
0
2
1
0
1
2
1
0
0
2
2
1
1
1
0
1
0
0
0
0
1
0
2
2
1
1
1
1
0
1
2
0
2
1
1
0
0
0
1
0
2
1
0
0
1
1
1
2
2
2
2
0
0
1
0
0
1
1
2
2
0
1
0
1
0
2
0
0
1
0
1
1
1
0
1
0
0
0
0
0
2
0
1
2
1
0
10
0
0
1
0
1
0
2
0
1
0
2
0
0
1
1
1
0
1
0
1
1
0
1
2
0
1
1
1
1
1
0
0
2
4
1
1
0
0
0
0
1
2
1
1
2
1
0
1
2
1
0
0
1
0
1
1
1
1
1
0
0
1
1
0
0
1
0
2
0
2
0
2
0
0
1
0
2
0
0
2
1
1
0
2
1
0
1
0
0
0
0
0
0
1
2
2
1
1
0
1
1
1
1
1
0
1
1
2
2
0
0
1
1
0
0
0
1
0
1
2
1
0
1
1
0
0
0
0
0
0
0
2
0
0
0
2
2
0
1
0
0
1
0
0
1
0
1
0
1
0
0
2
1
0
0
1
0
2
0
2
0
0
0
1
1
1
0
0
0
1
1
2
1
1
1
0
1
1
0
1
3
1
0
0
1
1
2
4
2
1
1
0
0
2
1
1
2
0
0
0
1
0
1
0
2
0
1
2
2
0
1
2
1
0
0
2
2
1
1
1
0
2
1
0
0
1
1
1
2
1
1
1
1
1
1
0
1
1
1
2
1
0
2
2
2
1
0
2
2
1
0
0
2
1
1
2
1
2
1
2
0
0
1
0
1
0
0
1
1
0
0
0
2
0
0
1
0
0
0
2
0
1
0
0
1
2
2
1
1
0
0
1
0
1
1
1
2
0
2
1
0
0
2
0
1
0
1
0
1
0
1
1
1
1
2
1
1
0
0
3
1
0
2
1
0
0
0
2
2
0
1
2
1
2
0
1
2
0
2
1
2
1
1
1
1
0
0
1
1
2
2
3
1
2
0
1
1
2
2
0
2
0
0
1
2
0
1
0
0
1
0
0
1
0
0
1
1
1
1
0
2
3
2
1
2
1
0
1
0
1
0
1
0
2
0
2
0
0
1
0
0
1
2
1
1
0
1
1
1
2
2
0
0
0
0
1
0
1
1
2
0
0
0
0
1
1
1
2
1
2
0
0
0
1
0
1
2
0
2
1
1
0
1
2
0
0
0
0
0
1
1
1
2
2
2
1
0
2
2
0
0
0
0
0
0
1
1
1
1
0
0
1
0
1
1
1
2
0
2
0
0
0
0
0
1
2
2
2
0
0
0
0
1
0
1
1
2
1
2
0
0
0
1
1
0
0
2
0
1
0
0
0
2
1
1
3
1
0
1
1
1
1
1
1
0
0
0
1
1
2
0
0
2
0
0
1
1
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
1
0
1
1
2
0
2
2
2
2
1
1
0
0
1
1
0
0
1
1
2
0
1
3
2
2
0
1
1
1
1
2
1
0
2
2
1
0
0
2
0
1
2
1
1
1
0
1
0
2
0
1
0
1
0
2
1
0
1
1
0
1
0
1
1
1
2
0
0
3
0
1
1
0
2
1
0
1
0
1
1
1
0
0
0
1
0
0
1
0
0
0
2
0
1
0
1
2
0
2
2
0
1
0
0
0
0
0
1
1
0
0
0
2
2
2
1
2
1
2
0
0
1
3
0
2
0
0
0
0
1
2
1
2
0
2
2
0
1
0
1
0
0
0
0
1
0
1
1
1
1
0
2
0
1
0
0
0
0
1
0
1
1
2
1
1
1
1
0
2
1
0
0
0
0
0
1
0
2
1
1
2
1
2
0
3
0
0
0
1
0
0
0
0
2
0
0
0
1
1
1
2
0
2
1
2
0
2
0
0
1
0
0
0
1
0
2
0
2
0
1
2
1
0
1
1
0
1
0
0
2
2
0
1
1
1
1
1
2
1
1
0
0
0
2
1
2
2
0
2
2
2
2
0
1
2
1
0
1
0
0
0
0
1
0
1
0
1
0
2
2
1
2
2
0
2
2
0
0
1
0
2
0
0
1
1
0
0
1
1
1
2
3
1
0
0
0
2
1
0
0
2
0
2
1
2
0
1
2
4
0
2
0
1
2
0
2
1
1
0
0
2
1
0
0
1
0
2
0
0
0
0
0
1
1
2
2
0
1
2
2
0
1
0
0
1
0
1
1
0
1
2
1
0
0
0
1
1
0
1
2
0
1
2
0
1
0
1
0
1
2
0
0
1
1
0
0
0
0
1
1
0
0
1
2
2
0
0
0
2
2
0
0
2
1
2
1
0
1
1
0
0
0
2
0
0
0
0
2
0
1
1
1
0
2
0
2
1
0
0
1
0
1
1
0
1
1
0
0
0
1
0
0
0
0
0
1
2
0
1
1
0
2
1
2
1
3
3
0
0
0
0
0
2
1
1
2
0
0
1
1
2
1
0
1
0
1
0
1
1
1
1
2
0
1
0
1
2
0
0
0
2
0
0
1
2
0
0
2
0
2
0
0
1
1
1
1
2
2
1
0
1
0
0
1
0
1
1
0
1
0
2
1
2
0
2
2
1
1
2
0
1
1
0
1
1
2
0
0
0
0
1
2
2
1
2
0
2
2
1
2
0
1
2
0
0
0
0
1
1
0
0
2
1
1
2
1
0
1
1
0
0
0
2
0
0
1
3
0
0
0
2
1
0
2
1
2
1
2
0
0
0
2
0
0
2
1
2
1
2
0
1
1
0
1
2
0
1
0
0
0
0
0
2
1
0
0
1
1
0
0
0
1
0
1
0
1
0
0
0
1
1
1
1
1
2
1
0
2
0
1
0
0
0
0
2
0
0
0
1
0
1
0
0
0
2
1
2
2
1
1
1
2
0
1
2
0
1
2
1
2
2
1
1
2
0
1
0
1
0
2
0
1
1
1
1
2
2
0
1
0
1
1
1
1
0
0
2
0
1
0
1
1
3
2
0
1
3
1
2
1
1
2
3
0
0
0
1
1
0
2
2
0
0
1
0
1
0
1
2
1
2
1
1
0
0
0
0
0
1
0
0
1
2
2
1
1
0
1
2
2
0
1
2
0
0
2
1
1
2
1
0
1
1
0
0
1
1
2
1
2
0
1
0
1
2
0
0
0
1
2
0
1
0
2
0
0
1
0
0
2
1
0
0
0
2
1
1
0
0
0
1
2
0
0
0
1
0
0
0
0
3
0
1
0
0
0
2
1
0
2
1
0
0
4
0
2
1
2
0
2
0
2
0
0
0
1
0
0
1
1
1
0
0
2
3
2
2
0
0
1
0
1
0
1
0
1
2
0
0
1
1
2
1
2
0
1
1
0
0
2
1
3
0
0
2
0
0
0
2
0
2
0
1
2
2
0
0
0
0
0
2
3
0
2
1
1
1
1
0
0
2
0
0
2
3
0
1
0
0
2
1
2
0
1
2
1
1
1
0
0
1
1
0
0
0
1
1
2
0
0
2
1
0
1
2
0
0
1
0
2
0
3
0
0
2
0
1
0
1
0
1
2
1
0
2
2
0
1
0
0
0
0
0
2
0
0
1
0
2
0
2
2
1
1
0
1
1
0
1
1
0
0
1
0
1
0
3
2
1
1
2
1
2
0
0
2
2
1
1
1
3
1
1
0
1
2
1
0
2
1
2
1
0
1
0
1
1
2
2
0
0
0
0
0
0
0
2
1
1
1
0
1
1
0
0
1
0
0
2
1
0
1
0
3
0
1
1
1
1
1
0
1
0
0
0
2
0
0
1
0
2
0
0
2
0
0
0
1
0
1
0
0
0
0
0
2
1
0
1
0
1
0
0
1
2
2
3
0
2
2
2
1
1
0
1
2
1
0
0
0
0
2
1
1
0
0
1
1
0
0
1
1
0
0
1
2
1
2
1
1
1
0
1
1
0
0
0
1
0
1
0
1
0
0
1
1
0
1
0
0
1
2
1
0
2
1
0
1
2
1
1
1
0
2
2
1
1
0
2
0
1
1
0
2
0
1
1
1
0
1
2
1
2
0
1
0
2
0
1
2
1
1
3
1
0
1
1
0
2
0
1
0
0
1
0
0
0
1
0
2
2
1
0
0
0
2
0
1
1
0
0
2
0
2
0
0
1
0
0
2
0
1
0
0
0
0
0
0
1
0
2
2
1
0
0
2
0
1
0
1
1
0
0
0
1
3
2
2
1
1
0
0
1
1
2
0
1
0
1
0
1
2
0
1
0
1
2
0
0
0
0
0
0
0
1
0
2
1
1
1
2
1
0
1
0
0
1
0
0
0
2
0
1
0
0
2
0
0
2
1
1
1
1
2
0
4
3
0
1
2
0
0
2
0
1
1
0
0
1
0
0
0
0
2
0
2
1
0
2
1
0
1
2
1
0
1
2
2
2
2
1
1
2
0
2
1
0
1
1
1
1
0
1
4
0
2
2
2
2
2
1
1
2
1
1
0
2
1
1
2
1
1
0
2
0
1
2
1
1
1
2
2
0
1
2
1
0
0
1
1
2
0
0
0
0
2
1
1
1
0
1
2
2
1
1
0
1
0
1
1
2
0
0
1
1
2
0
2
0
1
2
0
0
0
0
1
2
1
1
2
2
1
1
1
2
0
1
0
0
2
0
1
1
1
0
0
0
0
1
0
1
2
0
2
1
0
2
1
0
0
0
0
0
1
0
0
1
2
1
2
2
1
2
1
2
0
0
0
0
1
1
1
1
0
0
0
0
1
0
0
1
2
0
0
0
0
2
2
2
0
1
2
1
2
2
2
0
0
0
0
1
0
2
2
1
2
0
1
0
1
1
2
2
0
0
2
1
0
2
2
0
1
1
1
1
2
1
1
1
0
2
0
0
0
0
0
0
3
0
3
0
0
0
1
0
0
1
0
1
1
1
0
1
0
0
0
1
1
0
1
2
0
0
1
1
1
1
0
2
0
2
1
0
1
0
1
1
2
1
2
0
2
0
0
1
0
1
0
0
1
0
0
2
0
0
0
0
2
0
0
1
1
1
2
2
0
0
0
1
3
0
1
1
2
2
1
2
1
0
1
0
3
2
2
2
0
1
0
1
0
1
1
2
2
2
0
0
2
2
0
1
0
1
1
0
2
2
0
0
2
0
1
1
0
0
0
0
2
1
2
1
0
3
0
1
0
2
0
1
1
0
1
0
3
0
2
1
1
0
0
0
0
2
1
2
0
2
0
2
2
2
1
0
2
0
2
1
2
1
1
1
0
0
0
0
0
0
1
1
1
1
2
1
0
0
1
0
1
1
0
0
0
0
1
2
0
0
1
1
1
0
0
0
2
1
1
2
2
2
0
0
0
1
1
2
0
5
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
2
0
2
1
2
1
0
1
0
0
2
0
1
3
1
0
3
1
0
2
0
2
2
1
2
0
1
0
2
1
2
1
1
1
1
1
0
1
0
1
0
1
0
0
1
2
0
1
1
0
0
1
0
1
1
1
0
2
1
1
0
0
0
1
2
1
0
0
2
1
0
0
0
1
1
0
2
0
0
1
0
0
2
2
1
2
1
0
0
0
0
1
0
2
1
0
0
1
0
1
2
1
0
1
2
2
2
3
1
1
1
0
0
1
0
1
1
2
0
0
1
1
0
0
2
0
0
2
1
2
0
0
1
0
0
0
1
2
0
0
1
0
2
1
1
0
0
0
0
1
0
0
0
2
1
2
0
1
1
1
0
0
0
0
0
1
2
0
0
1
0
0
1
0
0
0
0
1
1
2
1
0
0
2
0
1
0
0
1
0
2
1
0
1
2
0
0
2
0
0
1
2
1
0
0
2
1
0
2
0
0
2
0
0
2
1
1
0
0
1
1
1
1
0
0
0
0
0
2
2
0
1
2
0
1
0
2
1
0
0
2
1
0
2
1
2
2
1
0
0
0
2
1
1
2
2
0
0
0
0
0
0
0
1
2
1
1
1
1
2
1
0
1
1
1
1
2
1
2
0
1
0
1
2
1
0
0
1
1
0
2
0
0
1
0
2
0
1
2
0
0
1
0
1
0
0
0
0
0
2
2
0
1
0
0
1
2
2
2
1
1
1
0
1
2
1
2
2
0
2
0
0
2
0
2
0
0
0
0
1
1
0
1
0
1
0
0
2
0
1
0
1
0
0
1
0
0
0
2
1
0
1
0
0
3
0
0
0
0
2
0
0
0
0
2
0
0
1
1
2
2
2
2
1
2
1
0
0
0
1
1
2
2
1
0
1
1
2
1
0
1
0
2
0
2
2
1
1
1
2
0
0
0
0
0
2
2
0
1
0
1
0
0
0
0
2
2
1
1
0
1
1
1
2
1
0
1
3
2
0
0
1
0
2
0
1
0
1
2
0
0
2
1
0
0
1
1
1
2
2
2
0
1
0
2
0
0
1
1
0
1
2
2
2
0
1
2
0
1
2
2
1
1
1
0
1
1
0
0
2
2
1
2
0
1
1
2
1
0
0
0
1
1
2
1
0
0
2
0
0
0
0
1
0
1
0
1
2
0
2
2
1
1
1
2
1
2
1
0
1
6
2
0
0
1
3
2
0
1
1
2
1
2
1
0
0
1
0
0
1
2
0
0
1
0
2
0
2
0
1
1
2
1
0
0
1
0
1
0
1
1
1
0
1
2
1
1
1
2
0
2
0
0
1
0
1
2
0
1
2
1
0
0
1
0
0
0
0
0
0
0
0
2
1
0
1
0
2
2
2
1
2
2
2
0
1
1
0
1
0
0
1
2
0
1
0
0
2
2
0
2
0
2
1
2
2
1
1
1
0
2
1
1
0
2
2
2
2
0
1
1
1
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
1
1
2
0
2
0
2
2
1
0
1
0
0
1
0
2
2
1
1
1
0
0
0
1
2
1
1
1
0
0
0
0
0
1
1
1
2
1
0
2
1
1
3
0
0
2
0
1
1
2
1
2
0
0
1
2
0
1
0
0
0
0
2
1
0
1
1
1
1
1
0
2
0
1
3
2
2
1
0
0
2
3
1
2
1
1
0
1
1
0
1
2
1
0
2
1
1
2
1
0
0
1
0
0
0
1
0
2
0
0
0
2
1
0
0
1
2
1
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
2
1
1
1
1
1
1
2
1
1
0
0
2
2
2
1
0
1
2
2
0
0
1
2
2
2
0
1
1
0
2
0
0
0
1
2
1
2
1
0
1
0
2
3
0
0
1
2
0
0
0
2
1
1
1
0
1
1
2
0
0
0
1
1
2
0
1
1
2
2
0
0
0
1
0
1
2
3
1
0
0
0
1
1
1
0
1
0
1
2
1
0
0
1
1
0
2
3
0
2
0
0
2
1
0
0
3
0
1
0
0
0
0
1
0
1
1
3
0
0
0
0
1
0
0
1
0
1
0
1
2
1
1
2
2
2
0
0
1
0
1
2
1
1
1
0
2
0
1
1
0
1
1
1
0
1
1
1
1
0
0
1
3
0
0
0
1
1
1
1
1
2
0
1
2
1
1
0
0
0
0
0
2
0
1
1
1
2
1
1
0
0
1
1
0
1
1
2
1
0
0
0
0
2
0
0
1
4
0
0
0
0
2
0
0
2
0
2
2
2
1
0
1
3
1
2
0
1
0
0
0
1
2
1
0
0
1
0
1
0
2
1
0
0
0
0
0
0
2
0
1
2
1
0
1
2
1
0
1
1
2
0
0
1
1
1
0
0
0
2
1
1
0
0
2
2
0
1
2
2
0
0
0
2
1
1
0
0
0
1
0
2
2
2
1
1
1
2
1
1
1
0
2
1
0
0
0
2
0
0
1
0
1
1
2
1
1
2
1
1
0
0
0
0
0
2
3
1
1
1
2
0
3
0
2
0
1
1
0
1
1
0
1
1
0
1
1
0
2
2
1
1
2
0
0
0
0
1
0
0
1
1
2
0
2
2
0
1
2
0
2
0
1
1
1
1
1
1
0
1
2
2
0
1
1
0
0
1
0
1
1
2
1
0
2
3
0
1
0
0
0
0
1
2
0
0
0
1
2
2
1
2
0
3
0
0
0
3
0
1
0
1
1
1
1
3
0
0
2
1
1
1
1
0
1
0
2
0
1
1
0
0
1
1
1
0
0
1
0
1
0
0
0
0
2
1
0
1
0
0
1
1
2
1
0
0
1
1
1
2
1
0
1
0
2
0
1
0
0
3
1
2
0
0
0
0
0
0
0
1
2
1
1
1
0
1
1
2
1
0
0
1
1
1
1
2
0
0
0
0
0
2
0
2
0
0
1
1
1
0
0
3
0
2
2
1
0
0
0
0
2
3
0
0
1
1
1
1
0
2
1
0
2
1
0
0
1
0
0
1
0
1
1
0
0
2
2
0
2
1
0
0
1
0
0
4
0
1
0
0
1
0
2
0
2
1
2
0
1
2
2
0
0
1
0
0
0
1
1
0
1
0
1
2
0
2
2
2
0
1
2
1
0
0
2
2
3
0
2
0
0
2
1
1
1
2
0
0
0
1
0
2
1
0
1
2
2
0
0
0
2
2
0
2
0
1
1
0
0
0
0
0
0
0
2
0
0
0
2
1
0
1
0
0
0
1
0
0
1
1
0
1
0
0
1
0
0
2
1
0
1
0
0
1
1
1
0
0
2
0
0
2
1
1
0
2
1
1
0
3
1
1
0
0
1
1
1
2
1
2
0
0
1
0
1
2
1
0
2
2
0
0
1
0
0
1
0
1
1
1
0
1
1
0
0
1
0
0
0
1
2
2
0
2
1
1
0
1
0
0
1
0
0
0
0
1
0
2
2
0
1
1
0
1
1
1
2
0
0
1
1
0
1
1
1
1
0
1
0
0
0
2
0
0
1
1
1
0
2
0
0
0
0
1
2
1
0
0
0
2
1
1
0
0
2
3
0
0
2
0
2
0
0
2
1
2
1
1
0
0
1
1
1
1
0
2
1
0
1
0
0
1
2
0
0
1
1
0
2
2
0
1
0
0
1
0
1
0
0
1
0
2
2
1
1
0
0
1
0
3
1
0
2
2
1
0
0
1
1
0
1
1
1
0
0
1
1
0
1
0
0
0
2
0
2
0
2
2
0
0
0
1
1
1
0
0
2
0
2
0
1
1
1
0
2
0
0
1
2
0
1
1
0
2
1
2
0
0
1
2
1
0
0
1
0
0
0
2
0
0
1
0
1
1
0
0
0
4
1
1
0
1
2
0
2
1
1
1
1
0
0
1
0
2
1
2
2
1
0
0
1
0
0
1
0
2
2
1
0
1
1
1
2
1
0
2
0
1
0
0
2
0
0
0
0
0
1
1
0
2
0
1
1
0
1
1
2
1
2
1
0
1
2
0
0
0
0
1
2
0
0
4
1
1
2
0
1
0
0
2
0
0
0
2
0
0
2
0
1
1
0
0
0
3
2
2
0
0
1
0
2
1
1
2
0
0
1
0
1
1
1
0
1
0
0
1
1
0
1
2
0
2
0
0
2
1
1
1
0
0
1
0
0
1
0
1
2
0
0
2
0
1
0
1
0
0
2
0
0
0
1
1
1
0
0
1
0
2
1
1
2
1
0
0
2
0
0
1
2
0
0
0
1
2
0
0
1
2
0
1
1
1
1
0
2
0
1
2
0
1
0
0
1
2
1
0
0
0
0
0
1
0
0
2
1
1
1
0
2
1
1
0
0
0
4
0
1
0
1
0
0
1
0
2
0
0
0
1
1
1
0
0
0
0
2
0
1
0
1
1
0
0
2
0
1
0
2
2
0
2
0
0
0
2
0
1
1
1
1
0
2
0
0
2
0
3
2
0
2
2
2
1
0
0
0
2
1
1
2
1
0
2
1
0
0
0
2
1
1
1
0
1
0
2
0
0
1
0
0
0
0
0
1
0
1
2
0
0
1
2
1
1
0
0
1
1
0
1
1
1
2
0
0
0
1
1
2
2
0
1
0
1
2
1
0
0
0
0
1
1
0
0
0
1
1
0
0
1
0
0
1
0
2
1
1
1
1
0
0
1
0
1
0
0
2
0
1
2
1
0
2
1
2
1
1
0
0
1
1
1
1
1
3
1
0
1
2
0
0
1
0
0
0
1
1
0
1
1
2
0
1
2
0
0
0
0
1
0
0
1
0
0
1
2
1
1
0
1
0
1
0
0
0
1
1
1
2
1
0
0
2
1
1
0
2
1
0
0
1
0
1
0
0
0
2
1
1
1
0
1
0
1
0
0
0
0
0
1
0
0
2
1
1
0
0
2
2
1
1
1
1
1
2
1
1
1
2
2
0
0
1
0
1
1
1
0
1
1
0
1
1
2
1
0
0
1
0
0
1
0
1
1
1
1
2
1
1
0
2
1
0
2
2
2
1
0
1
4
1
0
0
1
1
0
1
1
0
2
1
0
0
0
0
2
1
1
0
0
1
0
0
0
0
1
1
1
0
0
0
2
2
0
0
0
1
1
1
1
1
0
2
1
0
1
1
0
0
0
0
1
0
0
2
0
1
1
2
1
0
2
0
0
0
1
0
1
1
1
2
0
2
1
1
1
2
0
2
0
1
0
1
1
1
1
3
2
0
1
1
0
0
1
1
0
1
0
1
0
0
0
2
0
0
1
0
1
1
0
1
1
0
0
2
1
0
3
1
1
1
0
1
1
3
0
1
2
2
1
2
2
0
1
2
0
2
0
0
0
1
1
0
3
0
2
0
0
1
2
0
1
3
1
1
2
1
2
1
2
1
2
1
1
0
0
0
1
0
1
0
1
0
1
0
0
1
0
1
1
0
1
2
1
0
2
3
1
0
1
0
1
1
2
2
1
1
0
0
0
2
1
1
0
0
0
1
7
1
0
2
2
0
0
1
0
1
1
2
0
0
1
3
1
1
0
0
0
1
0
0
0
0
2
0
1
0
0
1
2
0
1
1
1
0
2
0
0
1
1
2
1
0
0
0
0
2
0
1
1
1
1
0
2
1
1
2
2
0
0
1
0
1
1
1
0
1
0
2
2
2
0
1
2
0
1
1
1
0
0
0
2
0
1
1
1
1
0
1
0
1
1
2
2
0
0
1
0
1
1
2
1
1
1
0
0
0
1
1
5
1
2
2
2
2
0
1
0
0
2
0
0
0
2
0
1
1
2
0
0
0
0
1
0
0
1
2
1
0
1
0
3
1
0
0
2
1
2
0
1
1
1
0
2
0
0
0
3
1
0
2
1
0
1
0
1
1
1
2
0
1
1
2
0
0
1
0
1
0
1
0
0
2
1
1
0
0
0
2
0
2
0
1
0
2
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
2
1
0
1
1
0
0
0
0
0
0
0
0
1
1
1
2
1
0
2
2
0
0
0
0
1
0
0
1
1
1
1
0
0
2
0
1
0
2
1
0
0
0
1
0
1
1
2
1
1
1
0
0
1
0
1
1
0
1
2
2
4
2
2
0
0
1
0
1
0
0
0
0
0
1
1
0
2
0
1
0
2
0
0
2
0
0
3
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
2
0
2
2
0
0
0
0
1
1
0
0
1
1
1
1
2
1
1
1
1
1
1
0
1
1
0
1
2
0
0
2
1
0
0
1
0
1
1
2
0
2
0
0
1
0
1
2
0
0
2
0
1
0
2
0
1
1
0
1
1
0
1
1
1
2
1
0
0
0
0
0
3
0
2
2
0
1
2
2
1
0
2
0
0
1
1
1
2
1
1
0
0
0
2
0
1
0
0
1
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
1
2
1
0
1
2
1
0
0
1
1
0
2
1
0
0
0
0
0
1
2
1
3
1
1
1
1
1
1
1
0
0
1
0
1
2
0
0
0
1
1
0
1
2
2
2
0
0
1
1
0
1
2
0
2
1
0
2
1
2
1
0
1
0
2
2
0
0
2
0
0
1
0
1
1
1
0
0
1
1
2
1
1
1
1
1
1
2
1
2
1
1
0
1
0
1
1
1
0
0
1
2
0
0
0
0
0
0
0
1
1
2
1
1
0
2
0
1
1
1
1
1
1
0
0
0
1
1
1
0
0
2
0
0
1
1
1
0
0
1
0
0
1
0
1
1
2
2
0
0
2
0
0
0
2
1
1
1
1
0
0
0
2
1
1
1
1
2
1
0
1
0
1
0
0
1
0
1
0
2
1
0
2
0
1
1
0
1
1
1
0
1
1
2
2
1
1
2
0
0
0
2
0
2
0
0
6
1
0
0
1
1
1
0
0
1
1
1
1
0
0
0
2
0
0
2
0
1
0
1
2
2
1
1
0
2
0
1
2
1
1
0
2
1
1
0
1
0
0
1
1
1
1
1
0
1
2
1
1
0
2
2
2
1
0
2
1
0
2
0
1
2
0
1
0
0
1
0
0
0
1
6
1
4
0
2
2
0
1
0
0
0
0
2
0
2
2
1
1
0
1
1
1
0
1
1
1
2
1
1
1
0
1
1
0
0
0
0
1
0
1
0
0
0
0
2
0
1
2
0
1
0
0
2
1
1
0
2
1
0
1
0
2
1
1
1
1
1
1
2
1
1
2
0
0
1
2
1
1
1
1
0
0
2
1
1
1
0
1
1
1
0
1
0
1
1
1
0
0
2
1
1
2
0
0
2
1
2
2
2
1
0
0
1
0
0
1
0
2
2
2
0
0
1
1
0
0
3
1
1
3
1
0
1
0
2
0
0
0
0
1
1
0
0
0
0
2
0
0
1
0
2
0
2
0
1
0
0
0
0
3
1
1
1
2
1
0
0
1
4
0
1
2
1
3
1
1
1
0
2
1
0
1
2
0
1
0
2
0
1
1
0
2
0
1
0
0
1
0
0
0
1
2
2
1
2
1
0
0
2
0
0
2
0
2
0
0
1
0
1
0
1
2
0
0
0
0
1
1
2
2
0
0
1
1
2
1
1
2
2
2
0
1
0
0
1
2
3
0
2
1
1
0
0
2
1
0
0
1
2
0
0
0
8
0
0
2
1
2
1
1
1
1
0
2
0
1
1
0
1
1
0
0
0
0
0
0
2
1
1
0
0
0
0
1
1
1
2
1
1
1
0
0
0
0
2
1
1
1
2
1
0
2
1
1
1
0
0
1
1
1
1
0
1
0
1
0
2
0
2
1
1
0
0
1
1
1
0
1
0
0
1
0
1
1
1
3
1
1
0
1
0
1
1
2
1
0
0
0
0
1
1
2
0
0
2
0
0
2
0
1
1
0
1
1
0
1
1
2
2
1
1
2
0
2
1
1
2
0
1
2
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
1
2
0
0
0
1
2
3
1
0
0
2
1
0
0
2
2
0
1
1
0
1
0
1
0
1
0
0
1
1
0
2
2
2
0
2
0
1
0
1
1
2
0
0
1
0
2
1
0
0
2
1
0
2
6
1
0
1
2
0
0
0
0
2
0
1
1
1
0
1
2
2
0
0
0
0
0
1
1
0
0
0
2
1
0
0
0
2
0
2
0
0
2
0
0
1
0
1
1
1
1
0
0
2
2
1
0
2
1
0
0
0
1
2
2
0
0
2
1
0
1
1
0
1
0
2
0
0
1
0
2
0
1
1
0
2
1
2
1
2
1
0
0
1
0
0
1
1
1
2
1
1
1
0
0
1
0
0
0
0
0
0
2
2
2
0
1
0
1
0
1
1
1
2
2
0
0
1
2
1
2
2
2
2
2
0
0
1
1
1
0
0
1
2
0
0
3
2
0
1
1
2
1
0
0
0
1
1
0
1
1
2
1
1
2
0
1
1
1
1
2
0
0
1
1
1
1
0
0
1
0
1
3
0
1
1
0
1
0
0
1
0
1
1
2
0
0
0
1
0
1
1
1
1
2
1
1
1
0
0
1
2
0
0
1
1
1
0
0
2
1
0
1
1
0
2
1
1
0
0
0
1
0
0
1
0
0
0
1
1
0
1
0
1
1
0
2
0
1
1
1
1
2
1
0
2
0
0
0
2
2
2
1
0
0
2
1
2
2
2
1
0
2
2
0
1
0
1
1
0
4
1
0
0
1
1
2
0
1
2
0
1
0
0
1
0
1
0
0
2
0
1
1
0
2
1
0
0
0
0
0
0
2
0
2
0
2
1
0
0
0
2
0
1
2
1
0
0
1
1
1
0
1
0
1
0
0
2
0
0
1
1
1
0
0
0
0
2
1
1
1
1
0
1
2
0
2
1
1
1
0
2
2
1
1
1
0
0
1
0
2
1
1
0
0
1
1
1
0
0
0
1
1
0
1
1
2
0
0
1
1
2
2
1
1
1
0
0
2
3
1
1
1
1
0
0
0
0
0
0
1
1
0
1
0
1
1
0
1
0
1
0
2
0
1
0
1
1
2
1
0
1
0
0
0
0
1
2
2
1
0
0
1
1
1
2
0
1
1
0
2
0
1
0
0
0
1
0
1
1
2
2
1
0
0
0
1
0
0
2
0
0
0
1
2
1
0
0
2
0
0
2
1
1
0
1
1
2
1
2
2
2
0
0
0
0
1
1
0
0
1
3
0
1
1
2
1
1
1
1
1
1
1
1
0
0
2
1
0
2
0
1
0
1
1
1
0
0
0
1
2
2
0
1
0
0
0
0
2
1
0
2
0
0
1
1
0
0
0
2
1
0
1
2
1
0
0
0
1
0
0
0
2
0
2
0
1
1
0
1
3
0
0
1
1
0
2
1
1
2
1
0
0
0
0
1
0
1
1
0
3
0
0
2
2
2
1
1
2
0
1
1
0
0
0
1
1
0
2
1
0
0
0
0
3
0
3
0
0
1
0
1
1
0
0
1
0
2
0
1
0
2
2
0
1
1
0
1
0
3
1
1
1
0
1
1
0
0
1
0
0
0
2
0
1
0
1
1
2
0
2
1
0
2
0
1
1
1
1
0
1
1
0
0
2
0
1
1
2
0
2
0
1
0
1
0
0
2
0
0
1
0
0
2
0
1
2
0
1
0
1
0
2
1
0
1
1
1
0
1
2
1
2
2
1
1
1
1
0
0
1
1
0
2
0
0
1
0
1
1
2
0
0
2
0
0
0
1
1
1
0
1
2
0
1
1
0
2
1
0
0
1
1
1
2
2
2
11
1
1
1
2
1
0
0
1
0
5
2
3
0
2
2
1
0
0
0
2
0
1
1
1
0
1
0
2
0
0
0
1
0
1
2
0
0
1
1
1
2
1
1
1
0
2
0
2
0
0
0
0
1
0
2
1
0
1
0
0
3
0
2
1
1
1
0
1
2
2
2
0
3
2
0
2
1
2
1
0
1
2
0
2
1
0
1
1
0
2
0
2
0
0
1
1
2
0
0
2
0
0
2
1
1
1
1
1
0
1
2
2
1
1
0
1
0
2
1
1
0
2
1
2
2
0
1
2
1
1
1
2
1
1
1
0
1
0
2
1
0
0
0
0
2
0
1
2
1
1
1
1
0
0
3
2
0
1
1
1
0
2
1
0
0
1
1
0
0
2
1
4
1
0
0
1
0
0
0
0
0
0
2
1
2
1
0
2
1
1
1
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
2
1
1
1
1
2
2
0
1
1
0
1
0
1
0
1
1
0
0
0
2
1
1
0
2
0
0
1
0
2
0
2
0
1
0
3
1
1
1
1
1
0
0
1
2
0
2
1
0
1
2
2
1
2
1
0
1
0
2
2
1
0
1
2
1
0
1
0
1
0
0
2
0
0
0
1
0
1
1
0
0
1
0
0
1
1
1
1
0
2
0
2
0
2
2
2
0
0
1
0
0
0
0
1
2
0
1
2
0
1
1
2
0
1
2
1
1
1
2
2
0
1
1
0
0
1
2
0
1
0
0
2
0
1
1
1
0
3
0
0
0
0
2
1
0
0
2
0
1
0
1
2
2
1
2
1
2
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
2
1
0
0
1
0
1
2
3
1
0
0
2
2
3
0
3
1
0
2
0
0
1
0
1
1
0
1
2
3
0
1
0
0
0
1
1
0
2
1
0
2
0
0
1
0
2
1
0
0
0
2
1
1
1
0
1
0
2
2
0
1
0
0
0
0
2
0
1
0
2
0
3
1
0
2
0
1
1
1
2
3
1
1
0
0
0
1
0
2
0
2
0
1
0
0
0
2
1
0
0
1
0
1
1
2
0
0
0
2
0
0
1
2
1
2
0
4
1
0
1
0
0
1
0
1
1
1
1
1
1
2
2
0
2
0
0
0
0
1
0
0
1
0
2
0
1
2
0
0
0
1
1
0
2
0
1
1
1
2
1
1
0
2
1
1
1
2
1
0
0
0
3
2
1
2
0
2
1
0
1
2
0
3
0
1
2
1
0
1
2
0
1
0
2
0
0
0
0
1
0
0
0
0
2
1
1
0
1
1
1
0
1
1
1
0
0
2
0
1
2
1
1
1
2
1
0
0
0
1
0
0
0
1
1
1
2
1
2
1
0
1
0
0
2
0
1
0
0
1
0
1
2
0
2
0
0
0
1
4
0
1
0
1
1
0
0
1
1
0
1
1
2
1
1
0
2
0
1
0
0
1
0
1
0
0
2
0
1
0
0
0
2
2
2
2
0
2
0
1
2
2
0
0
1
0
1
2
1
0
1
0
0
0
2
1
1
1
0
0
0
0
1
2
0
0
0
0
1
2
0
0
1
1
1
1
0
2
2
0
2
2
1
0
1
3
2
2
0
1
0
1
0
2
1
0
1
1
0
1
1
2
2
0
1
1
1
1
0
2
0
2
1
0
0
1
0
0
0
2
2
1
2
0
0
1
2
1
1
1
0
0
0
2
1
0
1
1
2
0
1
0
1
2
2
1
0
0
1
0
1
0
0
2
1
1
1
0
2
0
0
1
1
1
0
1
0
1
1
2
0
2
0
0
1
2
0
1
2
1
1
0
0
1
1
1
2
1
0
1
0
0
0
0
0
1
0
0
2
1
0
0
0
1
1
2
0
3
1
2
0
1
0
2
2
0
0
1
0
2
0
0
0
0
0
1
1
1
1
1
1
0
2
1
3
1
1
0
4
0
0
1
2
0
0
0
2
2
2
1
2
0
1
0
2
0
0
1
1
1
2
2
2
0
1
1
1
2
0
1
2
0
0
1
1
0
2
0
0
0
0
1
1
0
0
1
0
0
2
0
0
0
0
0
0
2
1
0
1
1
2
0
0
0
0
1
0
2
0
1
1
1
1
0
1
0
0
1
0
1
0
1
0
0
1
2
1
2
1
0
0
0
2
0
2
1
1
0
2
1
2
1
1
1
0
0
0
1
2
0
2
1
1
1
0
2
1
2
1
1
1
0
2
1
0
1
0
1
1
1
2
0
0
2
2
0
2
2
2
1
0
2
1
0
1
0
0
0
2
0
0
1
1
0
0
2
2
2
2
1
1
0
0
0
0
1
0
2
2
1
0
0
1
0
1
0
0
0
2
1
0
1
2
0
1
0
0
1
3
0
2
1
2
4
0
2
0
2
2
2
1
1
0
1
2
0
2
1
0
1
0
2
0
1
0
1
1
0
0
0
3
0
2
1
0
0
0
2
0
1
2
1
0
2
0
2
2
0
1
0
1
0
1
0
0
0
2
0
2
2
1
1
2
2
1
0
0
0
0
1
0
2
2
1
1
0
0
1
0
1
1
3
0
0
0
0
1
1
0
2
1
1
1
1
1
1
1
1
0
0
2
1
0
1
0
0
1
1
0
0
2
2
0
2
0
1
2
2
1
1
2
0
2
0
2
0
2
0
1
0
2
1
2
2
0
1
0
1
1
2
1
0
0
2
1
0
1
0
0
0
2
1
1
0
1
2
1
1
0
1
1
0
0
1
0
1
0
0
1
1
0
0
3
0
2
1
1
0
1
1
0
0
0
2
0
0
1
0
2
0
0
1
1
0
2
0
2
2
1
1
0
1
0
0
0
2
0
0
2
0
0
0
1
1
1
0
1
1
1
1
2
0
0
3
0
0
1
0
0
1
1
1
1
1
2
2
0
0
1
0
1
1
1
1
0
2
0
0
0
1
1
1
2
1
1
1
0
1
1
0
0
0
0
2
0
0
2
0
2
0
1
2
0
3
1
0
0
0
1
1
0
1
0
0
0
0
0
2
1
0
0
2
2
1
3
1
1
0
1
1
0
2
0
2
0
0
1
0
1
2
0
1
2
0
0
1
0
0
1
0
0
0
1
0
0
0
2
0
2
1
0
0
1
0
1
0
1
2
0
0
1
0
0
1
1
0
1
2
0
2
2
0
1
1
2
1
0
1
2
1
2
1
1
2
0
1
2
0
0
1
1
1
1
1
0
2
0
1
0
0
1
0
0
2
0
1
2
1
0
0
0
0
2
1
0
2
0
1
1
1
0
0
0
0
1
1
0
0
2
0
0
1
1
1
1
0
1
1
1
1
0
2
0
1
2
2
1
0
3
3
1
0
0
0
2
0
1
0
1
1
1
2
1
2
2
2
1
1
1
0
1
1
1
1
1
0
2
1
1
1
2
1
2
2
1
1
0
0
1
1
3
1
0
1
1
1
1
1
1
1
2
0
1
0
1
1
2
1
0
1
1
0
2
0
1
2
1
1
1
0
1
1
0
0
1
0
1
0
1
2
0
0
0
0
0
1
2
0
1
1
0
2
1
0
0
0
0
0
3
0
1
0
0
0
0
0
0
2
1
0
2
0
2
2
0
0
1
2
2
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
1
0
1
0
1
0
1
1
1
0
2
0
0
1
0
1
0
0
1
0
0
1
1
1
2
0
1
1
1
2
2
0
0
1
0
0
0
0
1
0
0
0
0
0
2
1
2
0
0
0
0
2
0
0
2
0
0
2
2
1
1
0
0
2
1
2
0
0
3
0
0
1
2
1
0
1
1
1
2
2
1
1
0
1
1
1
1
0
0
0
1
2
1
1
4
1
0
1
1
1
1
1
1
0
0
3
0
1
2
0
1
0
0
0
1
0
2
0
1
0
2
0
1
0
2
1
0
2
1
1
1
1
0
0
0
1
1
0
2
1
1
0
2
2
2
0
1
1
0
2
1
3
0
0
2
2
0
2
0
2
1
1
2
1
0
1
0
0
0
2
1
0
2
2
0
2
0
1
2
0
0
1
0
0
1
1
1
1
2
2
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
2
0
0
2
0
3
1
1
0
0
1
0
0
1
1
0
1
2
2
1
0
0
2
0
0
3
1
1
1
0
2
2
1
1
0
1
1
2
0
1
0
2
2
0
1
2
3
0
0
0
0
1
1
0
1
0
0
0
0
3
1
1
2
0
1
2
0
0
2
0
0
2
0
2
2
1
0
0
1
0
1
1
2
1
0
0
1
0
1
0
0
0
1
0
0
1
2
2
0
1
2
1
1
0
1
0
2
2
1
0
0
2
0
1
0
1
0
1
2
2
1
1
2
1
1
2
1
1
0
0
0
1
1
1
2
0
1
0
2
1
0
1
2
1
1
1
1
1
1
2
2
0
2
3
1
2
0
1
1
1
2
0
1
0
0
1
1
0
1
1
1
2
0
2
1
0
2
1
1
2
2
0
0
2
1
1
1
0
1
2
2
0
0
1
0
2
2
1
2
1
0
0
0
1
0
1
1
0
2
0
0
1
0
1
0
1
2
1
0
1
2
1
2
2
1
1
1
0
0
0
0
2
1
1
0
0
1
0
3
1
3
2
0
2
0
1
0
0
1
3
1
0
2
2
1
0
1
1
1
1
3
2
0
2
1
1
2
1
2
1
0
0
0
1
2
0
1
2
1
2
0
0
2
1
0
1
2
1
0
0
1
2
2
0
2
0
2
0
1
1
3
2
1
1
0
2
0
2
2
1
0
2
0
0
1
2
0
0
2
0
1
0
1
0
1
0
0
1
0
3
1
1
0
1
0
0
1
1
0
0
1
1
1
2
0
1
0
2
2
2
1
0
0
0
2
0
0
0
0
1
2
2
0
1
0
0
1
0
2
1
1
1
0
1
0
0
1
0
1
0
1
1
1
1
2
0
0
2
2
1
0
0
1
0
0
1
2
0
2
2
2
1
0
2
2
0
1
2
2
1
1
0
1
1
0
0
0
1
0
2
0
0
1
0
0
0
2
0
0
0
0
1
0
1
2
1
1
0
2
1
1
0
0
2
1
2
1
1
1
0
2
0
0
2
2
0
0
2
0
2
0
0
1
2
0
2
0
0
1
0
3
1
0
2
1
0
0
0
0
2
1
0
1
0
0
1
0
1
1
1
0
1
1
0
1
1
2
1
1
0
1
0
0
1
0
2
0
0
2
2
0
0
0
0
0
2
1
1
2
1
0
2
0
2
1
1
0
2
2
0
0
1
0
0
1
0
1
1
0
1
0
1
1
0
0
1
0
0
1
2
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
1
2
1
0
0
1
0
1
1
1
0
0
0
1
1
0
1
1
0
1
0
0
0
1
0
1
1
0
1
0
0
0
1
2
1
1
2
1
1
0
1
0
0
1
1
2
1
0
1
2
2
2
1
0
2
1
2
1
0
1
1
2
1
1
1
1
1
1
1
0
2
1
1
2
0
2
0
2
0
1
0
2
1
1
2
2
1
1
0
1
1
1
1
2
0
0
0
0
2
1
0
0
1
0
0
1
2
0
1
0
2
0
0
2
0
2
0
0
1
2
4
1
2
1
0
0
0
2
1
2
0
1
1
0
1
1
1
0
0
1
2
1
1
1
0
0
2
1
0
0
1
2
0
0
1
0
2
1
0
0
0
0
0
0
2
4
1
0
1
2
1
2
2
1
0
1
1
0
0
1
0
0
0
1
0
1
0
1
2
2
0
1
1
2
1
0
0
1
1
2
1
1
1
1
1
1
1
1
0
0
1
0
2
0
1
2
0
0
2
1
1
0
1
1
1
1
1
0
3
0
0
2
0
1
0
0
0
2
0
2
0
1
0
2
2
0
1
0
1
2
1
1
1
0
1
1
0
2
1
1
1
0
2
1
0
1
1
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
1
0
1
1
0
1
1
0
0
0
1
0
3
0
3
1
1
2
0
1
0
0
1
1
0
1
1
2
1
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
1
0
1
0
1
2
1
0
2
0
0
0
1
0
1
1
0
0
1
2
1
0
0
1
1
1
1
0
3
0
1
0
0
2
0
0
0
0
0
2
1
2
1
0
0
0
2
0
2
0
1
4
1
0
0
2
0
2
0
0
3
0
2
0
0
1
1
1
8
0
2
2
2
0
1
0
0
0
1
1
0
1
0
1
0
1
1
1
0
1
1
1
2
1
0
0
0
2
1
0
1
1
1
0
2
0
1
0
1
2
1
3
1
0
3
2
0
0
0
0
2
2
1
0
1
0
2
0
0
1
2
0
0
0
0
1
0
0
1
0
1
1
0
0
1
1
0
1
2
0
1
0
0
3
1
0
1
1
1
0
0
1
0
1
1
0
0
0
1
1
1
1
1
0
1
2
2
0
0
0
0
0
1
1
1
1
0
0
1
2
2
1
1
1
0
0
1
0
0
1
1
2
0
1
1
2
0
0
5
1
0
1
2
1
0
1
2
1
0
0
1
2
0
1
0
0
1
1
2
2
1
0
0
0
0
0
0
0
1
0
2
2
0
1
0
0
0
1
1
2
0
2
0
1
0
0
1
1
2
1
1
0
0
1
1
1
2
1
1
0
1
2
1
0
3
0
2
1
3
1
1
0
1
1
1
1
2
0
1
1
0
1
1
1
2
2
0
2
2
1
1
1
1
0
1
0
1
0
2
1
0
0
2
1
0
1
1
0
2
2
1
2
1
2
0
0
5
1
0
1
2
1
2
2
1
0
2
0
1
2
0
2
0
0
1
1
1
0
1
0
0
1
1
1
1
0
1
0
0
2
1
2
1
1
1
0
0
0
1
0
1
1
1
0
2
0
1
1
2
0
6
2
1
1
1
0
1
1
1
0
0
1
0
0
0
2
2
0
0
2
2
1
1
0
1
2
1
1
1
1
1
0
1
2
1
0
0
0
0
1
1
0
0
1
1
0
0
0
1
1
0
2
0
0
0
0
1
2
3
2
1
1
0
2
1
1
1
2
0
1
0
0
2
0
1
1
0
0
0
1
2
1
1
1
1
1
1
2
1
2
0
2
1
2
1
1
0
1
0
0
0
1
1
1
2
0
0
0
1
1
0
0
2
2
1
1
2
2
0
2
2
2
1
3
2
0
2
0
1
2
1
2
2
1
1
2
1
0
0
0
0
2
0
1
1
0
0
1
1
2
1
0
1
2
2
1
1
0
0
1
0
2
1
0
2
1
0
1
0
1
0
1
1
1
1
2
2
0
1
2
0
0
0
0
2
0
0
0
1
2
1
3
0
0
2
0
0
0
1
1
1
2
2
1
1
0
0
1
1
0
0
0
1
1
2
1
0
0
0
2
2
1
1
1
1
2
2
1
1
0
0
1
1
1
1
1
0
2
0
0
1
0
1
0
0
2
1
0
3
2
1
0
1
2
1
0
1
0
0
1
0
2
3
2
0
2
0
0
1
0
0
0
0
2
1
0
0
2
2
0
1
0
0
2
0
1
1
0
1
2
1
0
0
0
2
1
0
0
0
2
2
0
2
1
0
2
0
2
0
0
2
0
0
1
1
2
1
0
0
1
2
1
2
2
0
2
0
2
0
0
2
1
0
1
1
1
1
0
1
0
0
0
0
1
1
1
0
1
2
0
0
1
0
0
1
0
1
2
0
0
2
2
0
0
0
1
1
0
2
1
0
4
0
2
2
0
1
0
2
1
0
1
2
1
1
1
1
1
1
1
2
0
1
0
0
0
0
0
2
0
1
0
2
0
2
0
2
0
1
0
1
0
2
0
2
0
0
0
0
0
1
1
0
0
0
1
0
1
0
2
1
0
0
0
0
2
2
0
0
0
0
1
0
1
2
1
1
0
1
2
2
1
2
0
0
0
0
1
1
1
1
0
0
0
0
1
2
0
1
0
1
1
1
1
1
2
0
2
0
1
0
1
1
0
1
1
1
0
1
0
2
0
2
0
2
0
3
1
0
1
1
1
1
0
2
1
0
2
1
0
1
1
1
0
1
0
1
0
0
3
2
1
1
1
2
0
1
1
0
0
1
2
2
0
0
1
0
0
0
0
1
1
1
2
1
1
2
0
0
1
0
1
0
1
2
0
0
1
0
2
1
1
1
0
1
0
0
1
1
1
0
1
1
0
1
0
1
0
0
1
1
3
2
1
1
2
2
1
0
1
0
0
2
1
2
0
1
0
2
1
0
2
0
1
2
1
2
0
0
0
4
0
1
1
0
0
0
1
1
0
1
0
2
1
1
0
0
0
0
1
0
0
2
1
1
2
1
0
0
1
1
0
2
0
2
1
1
0
1
0
2
0
0
0
1
0
0
2
0
2
0
0
1
1
0
0
3
0
1
1
0
2
1
1
0
0
1
1
0
2
0
2
0
0
2
2
1
1
0
3
0
0
2
1
1
1
1
0
1
0
0
0
1
1
2
3
3
0
0
0
0
1
2
1
1
2
1
2
2
0
2
2
1
1
1
0
1
2
0
0
1
1
1
2
1
1
1
0
0
1
0
1
2
1
1
2
1
0
1
0
0
0
1
0
0
0
2
1
0
1
0
1
0
0
0
0
1
0
1
0
0
2
0
1
2
0
1
1
0
0
0
1
1
0
0
1
2
0
1
2
1
2
1
2
1
0
0
0
0
1
2
2
0
0
0
0
0
0
2
1
0
1
1
0
0
0
1
0
1
0
1
3
1
0
0
0
1
1
2
0
1
0
0
2
2
1
1
0
1
1
2
0
1
0
1
1
0
2
1
0
1
0
2
0
2
0
1
0
2
2
0
0
2
1
0
0
0
0
0
0
2
1
1
2
1
0
1
2
0
0
2
0
1
2
5
0
1
0
1
0
0
1
2
0
1
2
1
2
1
1
2
0
0
2
1
0
1
1
1
1
2
0
0
1
0
0
0
3
2
0
1
0
2
4
0
1
0
0
0
0
0
2
0
2
2
1
1
0
1
4
0
2
1
0
0
0
1
0
0
1
0
0
1
2
0
1
1
0
1
0
1
2
1
1
0
0
1
0
1
1
0
0
2
1
1
1
0
1
1
1
2
0
1
0
0
1
1
1
2
0
1
1
0
0
1
0
0
1
2
2
0
0
1
1
1
1
1
1
1
0
1
0
0
0
1
2
0
1
1
0
1
0
1
1
1
2
0
1
0
2
0
0
0
0
1
1
2
1
2
1
2
1
0
0
1
0
1
0
0
0
0
0
1
2
2
0
2
1
1
0
0
0
0
0
1
1
0
1
2
1
0
2
1
0
2
2
2
1
1
1
1
0
0
1
1
1
0
0
2
0
0
1
1
1
1
2
2
1
1
1
1
1
1
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
2
1
2
0
0
1
1
2
1
0
2
0
2
1
0
1
2
1
0
0
0
2
2
0
2
1
1
1
0
0
0
0
0
1
0
2
0
2
1
1
2
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
1
1
1
0
0
0
2
1
0
2
1
1
1
1
0
1
1
0
0
2
1
2
1
0
0
2
1
0
1
2
0
0
0
2
0
0
2
1
1
2
1
1
0
0
0
0
0
0
1
1
1
1
1
1
0
1
0
1
1
0
2
0
0
0
1
0
3
0
1
2
0
0
0
2
1
2
1
0
0
1
2
1
1
2
1
0
1
0
0
1
0
1
2
2
1
1
1
1
0
0
2
2
1
1
0
1
0
0
0
1
1
1
1
0
1
0
1
0
0
1
2
1
1
1
0
1
0
1
1
2
0
1
2
1
0
0
2
1
0
0
1
2
0
1
1
1
0
2
0
3
2
2
0
2
1
0
0
3
2
1
1
2
1
2
0
1
1
0
1
0
1
0
1
1
0
1
2
1
1
1
1
2
0
2
1
1
1
2
1
1
1
1
0
0
0
1
1
2
0
0
1
0
0
0
1
0
2
2
1
0
1
1
0
2
2
2
1
0
2
0
2
0
2
2
1
0
2
1
1
0
2
1
1
2
1
0
0
1
1
0
0
2
3
0
0
0
1
1
1
0
0
2
0
2
0
0
0
2
0
0
1
1
0
2
1
2
1
0
0
2
1
1
1
1
0
0
0
1
0
1
1
1
1
0
1
1
2
2
1
2
2
2
2
1
1
1
0
2
0
1
2
2
0
0
1
1
0
2
0
1
2
0
0
0
0
0
3
1
0
1
1
2
0
1
0
0
1
0
0
0
0
1
2
1
0
1
2
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
1
2
1
0
0
0
1
1
0
2
0
0
0
1
2
1
2
1
1
1
0
1
0
2
0
2
1
0
2
1
0
2
1
1
0
0
0
1
0
1
0
0
1
2
1
2
0
1
2
2
0
1
0
1
1
1
2
0
1
0
1
0
0
2
1
1
0
1
0
2
1
0
1
2
0
0
0
1
2
0
2
1
0
0
2
1
1
1
0
1
0
1
0
2
0
1
0
0
1
0
1
2
0
2
0
2
2
1
0
0
0
0
0
1
1
2
3
0
0
1
0
3
1
0
1
0
1
1
2
0
2
1
1
1
2
2
1
1
1
1
1
2
1
2
0
1
2
0
0
1
0
2
0
0
0
1
0
2
1
2
0
1
1
0
1
1
0
1
0
0
2
0
1
1
1
0
2
1
0
2
1
1
0
1
0
0
1
0
1
0
1
2
2
0
1
2
0
2
1
0
6
1
1
2
1
1
1
1
0
0
0
1
1
1
2
1
0
1
2
1
0
1
0
2
0
2
1
0
0
1
0
0
1
1
2
0
0
0
1
0
0
0
1
2
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
1
1
0
1
0
1
1
2
1
1
2
0
1
0
1
0
1
1
0
3
1
0
0
0
0
1
0
1
2
0
0
1
2
1
0
1
3
0
0
2
0
1
1
1
0
5
1
0
6
1
1
1
0
2
1
2
0
0
1
1
0
2
1
2
0
0
8
2
2
0
1
1
1
0
0
0
1
0
0
1
2
0
1
0
2
1
1
2
0
2
0
0
1
1
0
0
1
0
0
1
0
1
2
0
0
2
0
0
2
1
0
0
2
0
0
0
0
2
1
2
0
0
1
1
0
1
1
1
0
1
1
0
1
1
0
2
1
2
0
1
0
1
0
1
0
2
1
0
1
0
1
2
0
0
0
2
0
0
0
1
2
0
0
2
2
1
2
1
1
2
0
1
1
1
0
1
1
2
0
2
1
1
2
1
2
0
1
0
0
0
1
0
2
0
0
0
1
0
2
0
1
1
1
1
0
0
0
1
2
2
1
0
0
2
0
1
1
1
2
1
3
0
2
0
1
1
2
1
1
1
1
1
1
0
2
1
0
0
0
0
2
1
1
2
1
0
1
0
0
1
0
1
2
1
0
0
1
1
1
1
1
1
1
2
0
0
1
2
1
1
1
1
1
2
1
1
0
2
1
2
1
1
0
0
1
1
0
1
2
0
0
1
2
2
2
1
1
1
0
1
1
1
1
0
1
0
2
0
0
2
1
0
0
1
1
0
1
0
1
2
1
3
1
0
1
2
0
0
0
1
0
0
0
0
1
1
0
0
1
0
1
0
0
0
1
0
2
2
1
0
2
1
0
1
1
1
0
0
1
2
2
1
0
1
2
1
1
0
0
0
0
1
2
1
0
1
0
1
1
0
0
1
1
1
0
1
0
1
2
0
0
0
0
0
2
1
0
0
1
1
1
1
1
1
1
1
1
2
0
0
2
2
1
0
1
1
2
1
0
0
2
0
2
0
1
1
2
2
1
2
0
0
2
0
0
6
0
0
0
0
1
1
1
1
2
2
3
1
1
2
1
0
0
0
1
1
0
0
1
2
1
2
0
1
2
2
0
1
2
0
0
2
1
0
2
1
1
0
1
0
0
0
0
0
2
1
1
0
0
2
1
0
0
1
0
1
0
0
0
1
2
1
1
0
4
1
1
2
0
1
1
0
2
2
0
0
0
0
0
0
1
3
1
0
3
0
1
0
1
0
0
2
0
0
0
2
1
1
0
1
1
2
0
0
2
1
0
2
2
1
0
0
1
0
0
0
0
1
0
0
1
0
1
1
1
3
0
1
2
1
0
1
0
0
1
2
1
0
1
2
1
0
1
1
0
1
2
2
0
0
0
2
0
0
1
0
1
1
1
2
2
2
0
0
1
0
0
1
0
0
1
0
2
0
1
0
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
2
0
1
1
0
2
1
0
2
2
1
1
2
1
0
1
0
0
0
1
1
1
0
1
0
0
1
2
2
1
0
0
2
1
2
0
0
0
2
1
2
0
0
0
0
2
1
0
1
0
1
0
0
0
2
1
0
1
1
1
2
3
0
0
2
0
0
2
0
2
0
1
0
1
0
2
0
1
2
0
0
0
0
2
2
1
1
0
0
2
2
0
0
0
0
0
0
1
2
1
0
2
1
2
1
2
1
0
1
1
0
2
0
0
2
1
0
1
0
2
0
0
0
1
2
1
2
0
1
0
0
2
0
2
0
0
0
1
0
0
2
0
1
2
1
1
0
2
2
1
2
2
2
0
0
2
0
2
0
2
0
2
0
0
2
1
3
0
2
1
1
2
2
2
1
0
2
1
2
2
1
1
0
0
0
1
1
0
0
0
0
1
0
2
1
0
1
1
1
2
0
0
1
1
0
1
1
0
1
1
0
1
0
0
0
1
0
1
0
2
2
1
2
0
0
0
0
0
2
0
2
2
1
1
2
0
1
1
2
2
0
1
0
1
0
2
3
0
1
0
0
1
1
1
2
1
3
3
0
1
0
0
2
1
1
0
0
2
1
2
0
1
1
1
1
1
1
1
0
0
1
1
1
0
1
1
1
2
0
2
1
2
1
0
0
0
0
0
1
1
1
1
0
1
0
1
1
0
2
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
1
2
0
0
1
0
0
0
1
2
1
0
2
2
0
2
0
0
0
0
0
2
2
1
2
5
1
2
1
1
0
0
0
2
2
0
1
2
2
0
0
0
2
0
2
2
2
0
1
2
0
0
1
0
1
1
0
1
0
0
2
2
1
1
0
1
0
0
0
0
1
0
0
1
1
1
1
0
0
0
1
0
0
0
1
0
1
0
1
1
0
1
2
2
1
2
0
2
0
2
0
1
1
0
1
1
1
1
1
1
2
1
0
1
0
0
0
2
0
1
1
0
2
2
1
0
0
1
0
2
0
1
0
0
0
0
3
1
2
0
1
2
0
2
1
1
1
4
0
1
1
1
1
0
1
0
1
0
1
0
2
2
1
0
1
1
2
1
1
1
1
1
0
1
0
2
2
0
0
0
1
2
0
2
2
2
3
0
0
0
2
0
1
1
0
2
1
0
0
0
0
2
3
0
2
2
0
1
0
1
0
0
0
2
1
1
1
2
1
1
0
1
0
0
2
2
0
2
1
0
1
2
0
0
0
0
0
2
0
0
1
1
1
0
1
0
0
2
0
0
0
0
1
2
0
1
1
2
0
1
1
1
1
0
0
1
0
1
1
0
0
0
0
1
1
2
0
2
0
0
1
1
1
0
0
0
0
2
1
1
1
1
1
0
0
2
1
1
0
0
0
0
1
2
0
2
1
1
2
2
0
1
0
1
0
1
1
2
1
2
1
2
1
3
0
2
0
1
0
1
0
0
0
1
1
0
0
0
2
1
0
0
1
0
0
1
1
2
2
0
0
3
0
1
2
0
0
0
1
1
1
0
1
1
0
3
1
1
2
0
0
2
2
1
1
1
2
1
2
2
2
2
1
1
0
0
2
0
1
0
2
2
1
2
2
0
1
2
2
0
1
0
1
1
2
1
1
0
0
0
2
1
1
1
0
0
2
0
2
2
2
0
1
0
2
0
2
0
2
2
1
1
0
0
2
1
0
0
2
0
1
3
1
2
2
2
0
0
0
1
2
0
2
1
1
1
1
1
2
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
2
0
1
0
0
0
0
0
1
1
0
0
1
1
0
0
0
2
0
2
1
2
0
1
0
1
0
1
1
1
0
0
1
1
0
2
1
1
1
0
1
2
2
0
0
1
1
2
0
0
0
0
2
1
0
0
1
1
2
1
1
2
0
2
0
0
3
0
0
1
1
2
0
0
1
1
0
0
0
1
1
1
0
1
1
2
1
0
1
0
1
2
0
2
0
2
2
2
1
0
0
2
1
0
0
2
2
0
0
1
1
2
2
0
2
0
0
1
1
0
1
1
1
1
1
2
0
1
0
1
1
1
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
1
1
0
2
1
0
1
2
0
1
0
1
0
1
1
0
0
1
1
1
0
0
1
2
0
2
1
1
0
2
0
2
0
0
1
0
1
1
0
1
1
1
2
1
0
0
1
0
0
1
0
0
2
2
0
0
1
0
0
0
1
1
2
0
0
0
0
1
1
1
1
1
1
2
2
0
1
0
1
1
1
1
1
1
0
0
0
2
0
2
1
2
3
0
1
1
0
0
0
2
0
1
1
2
1
1
1
1
1
0
0
1
1
0
0
1
1
1
0
0
1
0
0
0
0
0
2
1
0
1
1
1
1
1
1
2
2
0
2
0
2
1
0
0
0
0
0
1
1
2
0
0
1
1
0
1
2
1
0
1
1
0
0
2
0
0
2
0
0
3
0
1
0
0
0
0
1
2
1
2
0
0
0
1
0
3
0
0
0
1
2
1
0
0
1
0
2
0
0
1
1
2
0
2
0
1
1
2
0
1
1
1
0
0
2
1
1
2
0
0
1
0
1
1
0
1
2
2
1
0
0
1
0
6
0
2
0
2
1
1
2
2
0
1
0
1
0
1
1
2
0
1
0
0
0
3
1
2
1
2
0
0
0
2
1
0
0
1
1
0
0
2
1
1
0
1
2
2
1
0
2
3
0
0
1
1
2
2
0
1
1
1
0
1
2
2
0
0
2
1
1
1
0
1
2
2
1
0
0
1
1
0
1
0
0
2
0
2
0
2
0
0
2
0
0
2
3
0
0
1
1
2
0
2
1
1
2
0
2
1
0
0
1
0
2
1
0
1
0
2
1
1
0
1
0
1
1
2
3
1
1
2
2
0
0
1
3
0
2
0
1
0
0
0
1
4
0
0
0
0
0
0
2
0
0
2
0
2
0
2
0
0
1
0
1
1
0
0
1
0
0
0
0
1
2
1
0
0
1
0
0
0
2
1
1
2
1
0
0
1
0
1
1
0
2
0
1
1
0
1
0
1
0
0
2
1
2
0
0
1
2
0
1
0
0
0
1
2
1
1
2
2
1
1
1
1
0
0
0
0
2
0
0
1
0
1
0
0
0
0
1
0
0
0
1
2
1
0
1
0
1
0
0
2
1
1
1
1
0
2
1
1
1
2
1
1
1
1
2
0
1
1
0
1
1
0
0
1
2
0
1
1
0
0
0
2
0
0
0
1
2
0
2
1
1
0
1
1
1
1
0
2
2
1
0
1
2
1
1
0
0
1
2
2
1
2
0
0
1
1
1
2
2
1
0
0
0
1
2
1
0
0
2
0
2
0
1
2
2
3
1
2
3
0
1
0
0
1
1
1
1
1
1
1
2
2
0
0
0
1
2
2
2
1
0
1
2
1
1
1
1
1
0
0
1
1
1
2
1
1
1
2
2
2
1
1
0
0
0
2
2
2
2
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
1
1
0
1
1
0
1
2
0
2
1
0
0
1
0
2
1
1
2
1
1
0
1
1
1
1
0
1
1
2
1
2
1
0
0
1
1
0
0
2
0
1
1
0
0
1
1
1
0
2
2
0
1
0
1
2
1
1
0
0
1
0
2
1
0
2
0
1
0
1
1
0
1
1
2
0
2
0
2
1
2
1
0
1
0
2
0
1
2
0
1
1
0
0
0
2
1
3
1
0
0
0
0
1
3
0
2
0
1
1
1
0
1
3
0
1
2
1
2
0
0
1
2
1
0
0
1
1
0
0
0
1
1
1
0
2
0
3
0
2
0
0
1
2
1
0
1
0
2
0
0
0
2
2
1
1
1
2
1
1
2
0
0
1
1
0
1
1
1
3
2
1
1
2
1
1
0
1
1
1
0
0
0
0
1
1
0
1
2
1
2
1
2
1
0
1
2
0
0
0
2
2
2
2
0
0
1
5
0
2
0
2
0
1
2
1
2
1
0
1
1
1
0
1
1
2
1
0
1
1
0
0
0
1
3
0
1
1
0
0
1
1
0
1
0
2
0
0
1
1
1
1
2
1
2
1
2
3
0
2
2
0
0
0
2
1
1
0
0
0
0
0
1
0
0
0
2
1
2
2
0
0
0
0
2
0
1
1
0
1
2
0
1
0
1
0
2
0
0
0
1
0
0
1
0
1
2
1
1
1
1
0
3
0
1
0
1
1
0
0
2
2
1
2
2
1
2
2
0
0
1
1
0
0
0
1
1
2
0
0
1
0
2
1
0
1
0
1
1
1
1
1
2
2
1
1
0
0
2
1
0
1
1
0
1
1
0
1
0
3
1
1
1
1
2
1
0
0
0
1
0
0
2
1
0
0
0
0
1
2
0
0
1
2
2
0
1
0
0
1
0
1
1
1
2
0
1
2
2
0
1
0
0
1
0
0
0
0
2
0
1
1
0
1
1
1
0
1
0
0
0
1
0
0
1
1
2
0
1
2
1
0
0
2
0
2
1
0
0
2
0
1
1
2
1
2
1
1
1
1
1
0
0
0
1
2
1
0
0
2
2
2
0
1
2
1
0
1
1
2
1
2
0
0
0
0
1
1
1
1
1
2
2
2
2
0
1
0
0
1
0
2
0
3
0
1
3
1
0
0
1
1
0
3
1
2
0
1
2
1
2
0
1
0
2
1
1
1
2
2
0
5
1
0
1
0
1
0
1
0
0
1
0
0
1
0
0
1
0
1
1
1
2
2
1
2
1
2
2
0
0
2
2
0
1
0
1
2
1
1
0
0
0
0
2
0
2
0
1
1
1
0
0
0
1
1
1
1
0
0
0
2
2
2
0
0
1
1
0
0
0
2
0
1
1
0
0
1
0
2
1
1
0
1
2
2
1
1
2
2
0
1
1
1
0
0
1
0
1
1
0
1
1
3
1
1
0
1
2
1
1
1
0
1
0
2
1
1
2
0
2
1
0
2
1
2
1
2
0
2
1
1
0
1
1
1
1
0
0
2
1
1
0
1
0
0
1
2
0
0
0
2
2
2
2
1
0
0
1
0
1
2
1
0
0
0
2
0
1
1
0
1
1
0
0
0
1
0
0
2
1
2
0
2
1
0
1
0
0
0
2
1
2
2
2
0
1
1
0
1
0
0
0
1
1
0
0
1
0
1
0
0
2
1
2
0
1
1
1
1
1
0
0
0
1
1
1
1
0
0
1
1
2
1
2
0
1
1
1
2
2
0
0
0
0
2
0
0
0
0
1
1
2
1
2
1
0
2
1
1
0
0
1
0
2
0
0
1
1
1
1
1
0
0
1
2
1
1
2
2
1
1
1
1
0
2
1
0
0
0
0
0
1
1
1
2
1
1
2
3
1
0
0
1
1
1
1
1
0
1
0
2
0
1
1
0
1
0
1
0
2
0
2
0
2
1
2
0
0
0
1
2
0
1
0
1
1
0
0
2
0
2
0
1
0
1
2
0
0
1
0
0
0
1
0
0
0
0
1
1
2
0
0
0
0
1
1
1
1
0
0
0
0
1
0
0
1
0
1
2
1
0
1
0
0
0
1
0
1
0
1
0
2
1
2
0
0
0
1
0
2
2
0
3
0
1
0
0
0
1
0
0
0
0
1
1
3
2
2
2
0
2
0
0
0
2
1
0
2
1
2
2
0
2
0
2
2
0
0
0
0
1
1
1
0
1
1
0
2
2
1
1
1
2
1
0
1
0
1
0
0
2
0
1
0
0
1
2
1
0
0
0
0
0
1
0
2
2
1
0
2
0
0
2
1
4
0
1
1
0
2
0
1
1
0
0
2
1
1
0
0
1
1
0
1
2
1
2
0
1
0
1
0
2
2
2
1
0
2
2
1
1
1
0
0
0
1
2
0
1
0
2
1
0
0
0
0
0
0
0
1
1
0
1
0
0
1
1
0
1
1
0
0
1
0
0
0
0
0
0
4
1
0
1
0
1
1
1
1
0
2
1
0
0
0
1
0
0
1
2
1
1
1
0
2
0
1
2
2
1
0
2
2
2
2
0
1
1
0
1
1
2
0
2
0
2
1
0
0
0
2
2
1
2
0
1
0
0
0
0
0
0
2
2
7
0
2
1
1
3
2
2
0
1
0
1
1
2
1
0
1
0
0
0
0
0
1
0
1
0
0
0
1
1
2
0
1
0
0
0
0
1
0
1
2
2
0
0
0
1
1
2
1
0
1
0
1
1
0
0
1
0
0
1
0
1
2
1
2
1
0
1
0
2
1
1
0
0
1
2
1
0
0
0
1
1
2
0
1
0
1
0
1
0
1
0
0
0
2
2
1
0
0
0
1
1
0
0
0
0
0
0
2
2
1
1
2
0
1
0
2
0
1
0
1
0
2
0
1
0
0
0
0
1
1
0
2
1
0
1
0
0
1
1
1
1
1
1
2
2
2
0
0
0
1
2
0
0
0
1
0
0
1
2
0
1
0
1
2
1
1
0
0
1
1
0
0
0
1
1
2
0
1
2
1
2
1
0
0
1
2
0
1
0
2
1
1
1
2
0
0
2
2
2
0
0
2
0
2
2
2
2
0
0
2
0
1
1
1
1
0
12
1
1
2
0
0
2
2
1
1
1
2
1
0
0
1
1
0
0
0
2
0
1
0
0
0
1
0
0
1
1
1
2
1
0
0
0
2
1
1
1
1
1
2
0
1
1
0
1
0
2
0
1
2
0
0
0
0
0
2
2
0
2
2
0
0
1
1
1
0
2
0
0
0
2
1
1
1
0
1
1
0
1
0
0
1
1
0
1
0
1
2
2
2
1
0
0
0
0
1
1
0
0
0
1
1
0
1
0
1
0
1
1
0
0
1
0
0
0
1
1
1
2
0
1
0
1
0
0
1
2
0
2
1
0
2
1
1
2
2
0
0
0
0
1
1
1
1
0
0
1
0
0
0
1
1
1
2
0
1
0
0
2
0
0
0
0
0
0
0
1
2
2
0
0
0
0
1
1
1
1
0
0
1
0
2
2
0
1
1
1
1
1
0
2
1
1
2
1
0
1
0
1
0
2
0
0
0
2
0
0
1
0
0
0
5
1
0
1
2
1
2
1
0
0
0
2
2
1
0
0
1
0
0
0
1
1
1
0
1
2
3
0
0
0
0
0
1
1
2
0
2
1
0
1
2
0
1
2
1
1
2
0
1
0
1
1
1
2
1
2
1
0
1
1
0
0
1
0
2
0
0
0
0
2
1
1
0
1
2
1
1
1
1
0
0
0
2
2
0
1
1
0
0
1
2
2
1
0
0
0
0
0
0
0
0
1
1
2
0
0
0
1
2
0
1
1
1
1
1
1
1
2
0
2
2
1
0
0
1
0
0
2
0
0
0
0
2
3
1
0
0
0
1
0
1
1
0
0
0
1
2
0
1
1
0
0
2
0
1
0
0
1
1
1
0
1
1
0
0
1
1
0
1
0
0
1
1
1
2
1
0
1
0
4
0
1
2
1
1
1
0
2
1
1
2
0
0
0
2
2
1
0
0
0
2
0
2
2
0
1
2
2
0
2
2
0
1
0
1
0
0
0
0
0
2
0
2
0
1
0
1
2
0
2
2
0
0
2
1
1
1
1
1
1
0
1
2
2
1
0
2
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
2
0
1
0
1
0
2
0
2
1
1
1
0
1
0
0
2
0
1
1
1
2
1
2
1
1
0
1
1
2
1
0
0
2
2
0
1
1
0
0
1
1
0
0
0
0
1
0
1
1
0
0
0
1
1
1
0
2
2
0
2
0
0
0
0
2
1
0
0
1
1
0
2
0
1
1
2
1
1
0
0
0
1
2
1
1
1
2
1
0
2
2
2
1
0
1
1
0
1
1
0
0
1
0
2
1
0
1
0
1
1
1
1
0
2
1
0
3
0
1
0
0
0
0
0
1
0
2
2
0
0
0
0
0
1
0
0
2
0
4
0
1
2
1
1
0
1
2
1
2
1
0
0
2
1
1
1
1
3
2
0
0
1
2
0
1
0
0
0
2
2
0
3
0
1
0
1
2
2
0
2
1
2
2
0
0
2
1
0
1
1
1
2
0
0
0
1
2
1
2
0
0
2
0
0
0
1
1
1
1
0
2
2
1
0
0
1
1
0
2
0
2
0
0
0
2
4
1
0
1
1
0
1
3
0
2
2
1
0
1
1
1
2
0
2
0
0
0
1
0
1
0
2
0
2
1
2
1
0
0
2
0
1
0
2
0
0
2
0
1
1
0
1
1
0
2
1
0
0
1
2
0
0
0
0
2
1
1
1
0
2
1
1
2
1
0
0
1
0
0
1
0
1
1
0
0
0
1
0
1
2
2
2
1
2
0
0
2
0
1
0
1
0
1
1
0
0
1
2
1
1
1
0
1
1
0
0
2
1
0
2
0
1
2
0
1
1
0
1
0
1
0
0
1
2
0
0
1
2
2
1
2
1
1
1
1
0
0
0
1
0
2
2
0
0
2
3
0
0
1
1
2
0
0
1
1
0
2
0
1
2
0
2
0
3
0
0
1
0
2
0
0
2
0
0
0
0
0
1
0
1
0
1
0
2
0
1
0
2
1
0
0
3
2
2
0
2
1
2
1
2
2
0
1
0
1
2
0
0
1
2
0
1
1
0
0
0
1
1
2
0
2
0
1
2
1
1
1
2
1
0
0
1
2
0
0
0
1
1
0
0
0
1
0
1
0
0
1
2
0
2
0
0
0
0
2
0
1
2
1
2
2
0
0
2
2
1
1
0
0
1
0
1
2
0
0
1
5
2
1
1
0
1
2
0
0
0
0
1
1
0
2
2
0
2
2
2
1
1
0
0
0
2
0
0
0
0
1
0
1
1
1
0
1
1
3
1
2
3
0
0
1
1
1
1
2
1
1
1
1
0
3
2
1
2
0
1
0
1
0
1
1
0
2
0
0
0
1
0
0
2
1
0
2
0
0
1
1
0
1
1
0
0
0
1
0
2
1
1
1
1
1
0
1
0
1
2
1
0
1
1
1
0
0
4
2
0
0
1
2
0
0
2
0
1
2
1
0
1
2
0
3
1
1
0
2
1
2
0
1
0
0
1
1
0
2
1
0
0
0
0
1
1
0
1
2
0
1
2
0
0
3
2
0
1
0
0
1
1
2
2
2
1
0
0
1
0
0
0
0
0
0
3
1
1
1
1
1
1
1
1
0
0
0
0
0
1
2
1
2
0
0
0
0
2
2
0
1
1
0
0
0
2
0
2
0
2
1
0
1
1
2
0
0
1
0
0
3
0
1
4
1
0
0
0
1
1
1
1
2
1
2
2
0
0
0
1
1
1
0
1
0
1
2
1
0
1
1
0
0
2
1
0
1
1
2
0
1
0
2
1
0
2
0
0
1
1
1
0
0
1
0
0
2
1
1
2
3
1
2
0
1
2
2
0
0
2
1
1
0
0
0
0
1
1
2
3
0
0
0
0
0
0
0
2
2
2
1
0
1
1
1
1
1
0
1
0
1
0
0
0
0
2
2
2
0
1
0
1
1
1
1
0
1
2
1
2
1
0
0
1
2
0
2
0
0
0
0
0
2
0
0
2
1
0
2
0
0
0
0
0
0
2
1
0
0
0
2
2
0
2
1
2
1
1
0
0
1
0
1
0
1
1
2
1
1
0
1
1
1
0
1
0
2
2
0
0
0
0
1
0
0
0
0
0
0
2
0
1
2
0
2
1
0
0
1
1
1
0
1
3
1
0
1
0
1
1
1
2
0
1
0
1
1
0
0
1
1
1
2
1
2
1
0
0
0
1
0
0
1
2
0
1
1
1
0
2
2
1
1
2
0
2
0
0
0
1
1
1
1
0
0
1
2
2
1
1
1
0
1
1
0
1
1
0
1
2
2
0
2
1
0
0
0
2
0
0
0
1
0
0
0
0
0
1
3
0
2
0
1
0
0
0
1
1
1
0
1
2
0
1
0
2
2
1
2
2
1
1
1
0
0
2
2
0
2
0
0
1
0
0
2
1
1
0
1
0
1
1
0
1
0
0
1
0
0
0
2
1
3
1
0
0
2
2
1
0
0
2
1
2
0
1
0
0
1
1
1
1
1
0
1
0
0
0
1
0
0
1
2
2
0
2
1
0
0
1
1
2
2
2
1
0
0
1
2
2
1
2
0
0
1
1
0
0
1
2
1
3
2
1
0
1
0
2
2
0
2
2
1
2
2
1
1
1
1
1
2
2
0
1
1
0
0
2
1
1
0
0
1
0
0
1
0
0
2
2
1
0
1
0
2
2
0
2
0
0
2
1
3
0
0
0
1
0
0
0
0
1
1
0
0
0
0
2
2
1
2
1
1
1
0
2
1
4
0
0
0
1
0
1
2
1
0
2
2
1
1
1
0
0
2
1
1
1
2
0
1
0
0
1
0
2
2
0
1
0
2
2
2
2
0
2
1
1
2
0
0
2
1
0
1
1
0
1
1
0
2
1
1
2
0
0
2
0
1
0
1
1
0
2
1
0
0
1
0
0
0
0
0
2
1
0
0
1
0
0
1
0
3
1
0
1
2
0
1
0
1
2
0
0
1
0
1
0
0
2
1
0
1
0
1
1
2
1
1
2
1
0
0
0
2
2
0
0
1
0
2
2
2
0
1
2
0
1
2
1
1
1
0
0
0
1
0
1
0
0
2
0
0
2
1
1
0
1
1
0
0
1
2
1
0
0
0
2
2
1
0
0
1
1
1
1
1
2
2
2
0
1
1
1
0
1
2
0
2
0
0
0
1
1
2
0
2
0
1
1
0
1
1
1
0
1
0
2
0
1
1
2
1
1
1
1
1
2
0
0
1
1
0
0
0
0
2
0
1
2
0
1
0
2
2
1
1
0
0
2
1
0
0
2
1
1
1
0
0
3
1
0
0
0
0
0
0
0
0
0
1
1
2
2
2
1
1
0
2
1
0
1
2
1
1
0
0
2
2
0
0
2
1
2
0
0
1
1
3
0
1
0
1
0
0
2
0
1
0
1
0
0
1
2
0
1
0
0
1
4
0
0
0
0
0
1
1
0
0
0
1
0
1
1
0
1
1
1
0
2
1
1
0
2
0
0
1
1
0
1
0
0
2
2
0
1
1
0
0
1
0
0
2
2
0
0
1
2
0
0
0
1
0
0
1
1
1
0
0
0
1
0
2
1
0
1
1
0
1
1
1
1
0
0
1
2
1
2
2
0
0
3
1
0
1
0
1
0
0
1
1
1
1
2
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
1
0
1
0
0
1
0
0
0
2
2
1
1
0
1
2
2
2
0
1
0
0
1
2
0
1
1
3
1
0
1
1
1
0
0
1
1
1
0
1
0
1
0
0
2
0
2
1
1
2
0
2
0
0
0
1
0
1
1
1
1
0
1
0
0
0
0
0
1
1
1
0
0
0
1
2
1
1
2
2
0
0
2
1
2
1
0
3
1
0
2
2
1
2
0
0
0
0
0
0
1
1
1
0
0
1
0
2
0
1
0
1
2
0
2
1
0
1
0
1
0
0
0
2
1
0
0
0
0
1
1
1
0
2
1
2
2
2
1
3
1
1
0
1
1
0
0
0
0
0
1
1
1
2
1
0
0
1
1
1
1
1
1
0
2
0
1
2
1
1
1
1
1
1
2
1
2
1
0
1
1
1
0
1
2
2
2
1
1
2
0
1
2
1
1
1
0
0
0
0
0
2
1
2
2
2
0
0
2
1
2
2
0
2
0
1
1
1
0
0
0
2
1
2
1
0
0
1
0
1
1
0
1
0
1
0
0
0
1
1
2
2
2
0
1
1
0
0
0
0
1
1
1
2
0
2
2
2
2
0
0
2
1
0
1
0
1
0
1
0
2
1
0
0
0
0
1
0
2
1
1
1
2
1
2
1
0
1
1
2
0
1
0
1
0
0
1
1
0
1
0
2
1
0
2
1
0
1
1
0
2
2
2
1
1
1
2
0
0
1
1
1
0
0
0
0
1
1
0
0
0
2
3
1
1
3
2
2
0
2
1
0
0
3
2
0
1
0
0
2
1
0
0
0
4
1
2
1
0
0
1
2
0
1
0
1
3
0
0
0
2
3
2
0
0
1
0
2
0
1
1
1
2
2
0
1
0
0
0
0
0
0
0
2
2
1
0
0
1
2
1
0
0
1
0
2
0
1
2
1
3
2
0
1
2
0
2
0
1
1
0
1
0
1
1
3
0
0
4
2
2
2
1
0
2
2
0
1
1
1
0
0
3
0
0
0
2
1
1
1
2
0
1
0
0
1
2
1
1
1
0
3
0
1
2
1
0
1
1
0
0
0
0
0
1
1
1
1
1
2
0
1
1
0
2
2
1
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
1
2
1
1
0
0
2
2
0
2
3
1
1
1
1
1
2
1
2
0
2
0
2
0
1
1
0
0
0
1
1
2
1
1
1
2
0
1
0
0
2
0
1
0
1
0
1
0
0
0
2
0
2
2
0
0
2
1
1
0
0
0
0
2
1
2
0
0
2
1
0
2
0
1
2
0
1
0
2
0
1
0
1
2
0
0
0
0
0
1
1
1
0
0
1
0
0
2
0
2
1
1
0
0
0
2
0
2
1
1
2
0
1
0
0
2
1
0
2
0
1
2
2
0
1
2
1
0
0
0
0
0
0
2
2
0
2
0
2
1
0
2
0
1
0
1
0
0
1
1
0
1
0
0
1
2
0
2
0
0
1
1
2
1
2
1
1
1
1
1
0
2
1
2
0
2
0
0
0
0
0
0
2
1
0
1
2
1
0
2
0
0
1
0
57
0
0
2
0
2
0
0
0
1
0
2
1
0
0
2
0
0
0
2
0
2
0
2
1
0
1
2
0
2
0
1
0
1
0
3
0
2
1
2
1
1
1
2
0
1
0
0
1
2
0
4
0
0
0
0
2
1
0
1
2
1
0
0
1
0
1
1
2
1
1
0
2
1
1
0
0
0
1
2
2
1
0
1
0
1
0
1
2
2
0
0
2
0
1
0
2
1
2
0
1
0
0
1
0
2
2
0
1
0
0
0
2
0
0
1
1
1
2
1
3
1
1
0
2
2
0
1
0
2
1
1
0
1
0
1
2
0
1
2
2
0
2
2
1
1
1
0
0
0
1
0
0
0
0
1
2
1
0
0
2
0
1
2
0
1
0
0
0
1
2
1
2
0
1
0
1
0
1
0
0
1
0
1
1
1
2
0
2
1
0
1
0
0
2
2
0
1
1
0
2
0
1
0
0
2
2
0
2
1
0
1
0
1
2
1
0
0
0
1
0
2
0
1
2
0
0
0
1
0
1
2
2
0
0
0
2
0
1
0
0
2
0
0
2
0
1
1
0
0
3
0
0
3
0
1
2
1
0
1
0
1
1
0
0
0
2
0
2
0
0
0
0
1
2
0
1
0
0
0
1
0
0
1
0
1
1
0
1
2
0
1
0
0
0
2
2
0
2
1
1
2
0
2
1
0
0
2
0
1
0
1
0
0
0
1
2
1
0
0
1
0
1
0
0
0
0
1
2
2
3
0
0
2
2
2
0
0
1
0
0
1
0
1
1
0
1
0
1
2
2
0
1
2
0
0
1
0
2
2
0
0
0
0
0
2
1
3
1
1
0
2
2
0
0
2
1
1
1
0
0
1
2
1
0
0
0
0
1
1
1
1
3
1
0
1
0
1
2
1
1
0
1
2
2
2
0
0
0
0
1
0
0
0
1
2
0
1
3
2
1
1
1
2
1
0
2
2
0
1
0
1
2
0
1
0
2
1
0
3
0
1
2
2
2
1
2
0
2
0
2
1
1
1
1
0
2
2
2
0
1
2
1
0
0
0
2
2
1
0
1
0
1
2
0
0
0
0
1
2
2
1
0
0
2
0
0
2
0
0
0
2
1
1
0
2
1
1
2
1
1
0
2
0
2
1
2
1
2
2
1
0
1
1
1
0
0
0
0
1
0
2
1
1
1
1
1
1
1
1
0
2
2
0
1
2
2
1
0
0
1
2
0
2
0
2
0
1
0
0
1
0
2
0
1
1
2
1
1
0
0
0
0
0
2
1
1
2
0
1
0
2
2
2
2
2
0
2
2
1
1
1
1
0
0
2
0
0
1
0
0
1
0
2
0
1
2
0
0
1
1
0
1
1
0
1
1
0
1
1
3
1
0
2
1
1
2
0
0
0
1
2
0
1
2
2
0
1
0
0
2
1
1
1
0
1
0
0
0
2
2
1
0
1
1
1
0
2
1
0
1
1
0
1
1
2
2
1
1
2
0
0
1
2
1
1
2
0
0
0
0
1
0
0
1
0
2
0
2
1
0
2
1
0
2
1
3
2
0
0
1
1
1
1
1
2
2
0
1
0
0
0
2
0
1
0
3
1
0
0
1
1
0
1
0
1
1
0
1
1
1
2
1
2
1
1
0
2
0
2
1
2
0
2
0
0
0
1
2
0
0
0
1
0
2
1
0
1
2
1
0
2
2
1
1
1
1
0
0
1
2
1
0
2
1
2
0
2
1
1
0
1
0
0
1
1
1
0
0
2
0
2
0
0
2
2
1
1
1
1
1
0
0
0
1
2
0
0
1
2
0
1
0
1
1
1
1
0
2
2
2
1
0
0
2
1
1
0
1
2
0
2
1
0
1
0
1
1
0
1
1
0
0
2
0
2
0
1
1
0
0
0
0
3
1
2
1
0
0
1
0
1
0
2
0
2
1
0
1
1
0
1
2
2
1
2
1
1
2
1
2
1
1
1
0
0
1
0
1
1
1
1
1
2
0
1
0
0
0
1
0
2
1
0
0
1
0
1
1
0
1
0
0
1
1
0
0
1
1
0
1
0
0
2
2
1
3
0
0
0
1
1
2
0
2
0
0
0
0
0
2
2
1
1
1
1
0
0
2
2
0
1
1
1
0
0
1
1
0
0
1
2
0
1
1
1
1
2
1
2
1
2
0
2
2
1
1
1
0
1
1
2
0
1
1
1
0
1
2
1
1
2
1
1
0
2
0
0
0
1
0
1
1
0
0
0
0
0
2
2
0
2
1
0
2
0
1
0
1
0
1
0
1
1
1
0
0
0
1
2
1
1
2
1
1
1
0
2
2
1
0
1
0
1
2
5
1
0
0
1
6
1
0
1
2
0
1
0
2
1
1
2
0
0
0
1
1
1
1
0
0
0
2
0
0
1
1
1
1
0
1
0
0
2
1
2
1
0
1
2
1
0
1
1
1
0
0
0
1
1
1
0
1
1
2
0
1
0
1
0
2
1
1
1
0
0
0
1
0
1
1
0
0
2
0
2
0
0
1
0
1
1
2
0
0
1
1
2
1
0
0
0
1
1
0
0
2
0
1
0
2
0
0
1
2
1
0
1
2
1
1
1
0
0
1
0
0
0
3
0
1
1
1
2
1
0
1
1
2
1
3
0
1
0
2
1
0
1
2
0
1
1
1
2
0
0
0
2
1
1
0
1
0
2
0
1
3
0
1
0
2
0
0
0
2
1
2
1
0
1
1
2
1
0
1
3
2
2
0
0
1
0
0
1
1
0
0
1
0
0
0
0
1
0
1
1
2
0
0
0
1
0
2
0
0
1
1
0
2
1
2
1
0
0
0
2
2
0
0
2
0
1
0
1
1
1
1
0
1
0
0
0
1
1
1
0
1
2
2
0
1
3
1
0
1
0
2
1
0
0
0
0
2
0
4
0
1
2
1
1
1
1
0
1
1
1
0
0
1
1
0
0
1
2
0
0
1
2
1
1
0
1
0
0
0
0
2
2
0
1
0
1
0
2
1
4
1
1
1
0
2
2
1
1
2
2
0
0
0
0
0
0
1
2
0
1
1
0
2
2
1
2
2
2
1
0
1
2
0
0
2
1
0
0
1
0
0
0
0
0
1
2
1
1
1
1
1
2
2
1
0
2
0
0
0
2
0
0
0
2
0
0
3
2
0
1
2
1
0
2
2
0
2
0
2
2
1
2
0
3
0
2
2
0
0
0
0
0
0
1
0
0
1
1
1
1
0
1
1
1
0
3
1
1
0
1
1
1
1
0
0
1
2
1
2
2
1
0
1
0
0
2
0
2
0
1
0
2
0
1
1
0
0
0
0
1
1
0
1
2
1
0
2
2
2
0
1
1
1
2
2
0
2
1
1
1
1
0
0
0
0
2
1
0
0
0
1
2
0
1
0
0
1
0
1
2
1
1
0
2
1
4
0
0
0
0
1
0
0
3
0
2
2
1
1
0
0
0
1
0
1
0
1
0
0
2
1
1
1
1
0
0
0
0
0
0
1
0
1
0
2
0
2
2
1
2
2
0
0
1
0
3
1
1
1
1
3
0
1
0
0
1
0
0
1
0
2
1
0
1
0
2
1
2
1
0
0
2
0
1
0
2
0
5
0
2
2
0
0
1
1
1
1
1
0
0
1
2
1
1
1
0
1
1
1
0
2
2
1
0
3
1
1
1
2
1
1
0
0
1
0
0
2
2
2
1
0
1
3
0
0
2
1
1
0
1
0
0
1
2
1
1
3
0
2
0
1
0
0
1
1
1
2
1
0
1
1
2
0
0
0
1
1
1
1
0
0
1
1
2
0
0
0
2
0
0
1
0
1
1
1
0
0
1
1
2
1
0
1
2
2
1
1
1
0
2
0
0
2
0
1
0
2
1
1
0
1
0
0
1
2
0
0
0
1
1
1
0
1
1
0
1
1
1
2
2
1
1
2
0
1
0
0
1
0
0
2
0
4
1
2
2
0
0
0
0
1
0
0
2
0
0
1
2
0
1
1
0
0
0
1
1
2
1
0
0
1
1
0
0
2
0
0
1
1
1
1
1
1
0
2
0
0
1
0
1
1
0
1
1
1
1
1
0
2
2
0
1
1
0
0
1
1
2
2
0
1
1
1
1
1
0
1
2
0
1
0
0
1
1
0
2
0
2
1
2
1
1
0
1
0
1
1
0
1
0
2
1
1
1
1
0
0
2
2
0
1
2
1
1
2
0
2
2
0
1
2
0
2
0
0
1
1
3
1
0
1
1
1
1
2
1
0
0
0
0
0
0
1
1
2
1
2
1
1
0
0
1
1
0
1
2
0
0
0
1
5
0
2
1
1
1
1
1
1
0
0
1
1
0
0
1
0
1
2
1
0
1
0
0
0
1
1
0
0
0
0
1
1
2
2
1
0
0
1
1
0
0
2
0
2
2
1
0
0
0
0
1
1
2
7
0
0
2
2
0
1
1
1
2
0
0
2
1
0
1
1
0
2
2
1
0
2
1
0
1
0
2
0
2
0
2
0
0
0
2
0
1
0
0
0
1
0
2
1
0
0
0
2
0
1
1
0
2
1
2
1
1
0
0
1
1
1
0
2
1
0
1
0
1
0
1
2
1
1
1
3
0
1
2
1
2
2
0
1
2
2
1
0
0
0
2
0
1
1
0
0
0
1
1
0
1
0
0
0
0
1
0
0
2
2
0
0
1
1
0
2
1
0
0
0
0
0
1
2
1
2
2
1
0
1
1
1
0
1
1
1
0
2
1
2
0
0
0
2
1
2
3
1
2
0
1
2
1
2
2
0
1
0
2
6
0
2
0
1
0
2
0
0
2
1
1
0
1
0
1
1
0
0
1
2
2
1
0
2
1
0
0
1
0
1
1
2
1
0
0
1
2
0
0
1
0
2
0
0
0
7
0
2
0
0
2
0
0
3
0
0
1
1
2
2
0
1
0
0
2
2
0
2
2
1
0
0
2
0
2
1
1
2
0
2
1
0
1
0
0
2
1
0
2
2
1
1
0
0
0
0
1
0
1
0
0
1
0
1
0
1
0
1
2
1
2
2
0
2
2
0
0
1
1
2
0
1
0
2
1
1
1
1
3
0
2
1
2
0
2
2
2
0
1
1
1
2
2
1
2
1
3
0
0
1
1
1
0
2
3
1
2
0
0
0
1
2
1
1
1
2
0
0
2
2
0
0
0
0
0
0
3
2
0
0
0
1
1
2
0
0
1
1
0
1
1
2
2
1
0
2
0
1
0
0
0
2
1
3
0
2
1
2
2
2
1
0
0
2
0
1
1
1
1
0
0
2
0
1
2
0
0
2
0
1
3
1
0
1
1
1
2
1
2
0
1
0
1
1
0
0
2
1
0
2
1
0
2
2
0
0
0
0
1
1
1
0
0
1
1
0
0
1
1
0
0
1
2
2
1
0
3
6
2
0
0
0
1
0
0
2
1
0
1
0
2
2
1
0
0
2
0
1
2
1
0
0
1
0
2
0
1
0
0
1
2
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
1
1
0
0
1
2
0
1
0
0
1
0
1
0
1
2
2
1
3
1
1
1
0
0
0
1
1
1
0
2
0
2
0
1
2
0
2
1
2
0
1
1
0
2
0
2
1
2
2
1
1
0
0
1
0
0
1
0
1
1
0
1
1
2
1
0
0
2
1
0
1
2
1
0
1
2
1
0
0
0
2
1
0
0
0
1
0
0
0
2
1
0
1
1
1
2
0
0
0
1
0
0
1
1
1
1
1
1
0
1
2
1
1
1
1
2
1
2
1
0
0
0
0
1
0
1
1
0
1
1
1
0
1
2
1
1
0
2
3
0
1
1
2
0
1
0
1
0
1
2
1
2
2
1
1
2
0
0
0
1
2
1
2
0
1
1
1
0
0
0
2
0
0
1
1
0
0
1
1
0
0
0
2
0
0
0
1
1
0
1
1
0
2
0
0
2
1
0
2
1
1
0
1
0
0
0
1
0
2
0
1
2
3
3
1
1
1
0
1
1
2
1
3
1
2
0
1
0
1
2
0
0
0
2
1
1
2
0
1
1
2
0
0
1
0
0
2
1
1
0
0
2
2
1
0
2
0
2
0
0
1
2
2
1
0
0
3
1
1
0
0
1
1
0
1
1
0
2
0
1
1
2
0
0
1
1
0
0
0
1
0
5
0
1
0
0
1
1
1
1
0
0
2
1
0
2
0
1
0
2
1
1
2
2
1
0
1
1
0
2
0
0
1
0
0
0
0
0
0
2
0
1
2
0
0
2
1
0
2
1
1
0
1
2
0
2
0
0
1
0
2
0
1
1
0
0
1
2
1
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
1
0
0
1
1
0
1
1
1
2
1
1
0
0
0
1
2
1
1
1
1
0
1
0
1
0
0
2
1
0
0
1
1
1
2
2
0
0
2
2
0
1
0
0
0
2
1
1
0
3
1
1
0
2
1
1
1
1
0
2
2
1
1
0
0
0
0
0
1
2
0
0
2
1
1
0
1
0
2
0
1
1
0
0
1
2
0
0
1
1
0
0
1
0
1
0
0
2
2
0
2
1
0
0
1
1
2
0
1
1
0
1
1
1
1
0
1
2
0
0
1
0
2
1
1
1
1
1
0
0
2
2
0
1
0
2
0
3
0
0
0
1
3
0
0
0
0
0
1
0
0
3
0
1
2
2
0
1
0
0
0
1
0
1
1
1
2
0
2
0
1
0
1
1
0
2
2
0
0
2
1
1
0
0
2
1
1
2
1
0
1
0
1
2
1
0
0
1
1
1
1
2
0
1
0
0
0
2
0
0
0
1
1
0
1
0
2
2
0
0
0
0
0
0
0
0
2
1
0
0
0
2
1
1
2
1
2
2
1
0
1
2
0
0
2
0
1
1
2
1
1
2
1
0
2
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
1
2
1
0
0
1
5
0
1
0
1
0
2
1
0
2
1
1
0
1
1
2
0
1
1
0
1
2
1
1
0
0
0
0
0
1
2
0
2
1
1
0
0
1
1
0
0
1
1
2
0
0
2
1
0
1
2
0
0
1
0
0
1
1
0
0
2
2
0
0
0
2
0
1
1
0
2
0
1
2
0
1
0
0
2
0
2
2
1
2
1
1
1
0
1
0
0
2
0
1
2
2
1
2
0
2
0
0
0
2
0
2
0
1
0
2
0
1
0
0
2
2
2
0
0
0
0
0
1
0
2
0
2
0
1
1
2
1
1
1
0
0
2
0
0
0
0
0
0
2
1
1
0
1
2
0
0
0
1
2
1
2
0
1
0
1
2
0
0
2
1
1
0
0
1
1
1
1
2
0
1
1
2
1
1
1
1
1
1
2
0
1
1
0
1
0
1
0
0
0
1
1
0
2
1
0
0
2
1
1
0
3
0
3
1
1
0
0
3
0
1
1
0
0
0
1
3
1
1
1
2
1
0
0
0
1
1
0
2
0
1
1
2
2
0
1
0
1
0
0
1
0
2
1
3
2
2
1
3
0
0
0
2
2
0
1
2
2
0
0
1
1
1
1
0
0
0
1
0
0
0
0
0
2
0
1
1
1
2
0
0
0
1
0
1
1
0
0
0
1
2
2
1
1
0
0
2
2
2
0
1
0
0
0
2
0
0
1
2
2
0
0
0
1
1
0
2
2
1
2
1
2
2
2
0
1
1
0
0
1
2
0
1
2
2
2
2
0
0
1
2
0
0
2
1
2
1
2
0
1
2
2
1
0
1
1
1
0
0
1
0
2
2
0
1
0
1
0
2
0
0
1
0
0
0
2
2
0
1
0
2
2
0
1
0
1
2
1
1
1
0
2
1
0
0
2
0
0
0
2
0
0
1
0
0
1
1
0
2
1
1
0
1
0
0
0
0
0
0
0
0
0
1
2
0
1
1
0
1
2
0
0
0
1
0
1
2
0
1
0
1
1
2
1
1
2
2
0
1
0
0
0
0
1
0
2
1
0
0
2
0
1
2
1
1
0
1
2
5
1
1
2
1
2
1
5
1
0
0
1
1
1
0
0
0
1
1
0
0
2
1
0
0
1
0
0
1
0
1
0
1
1
0
0
1
0
0
0
0
0
1
1
0
0
0
1
2
2
1
1
0
0
2
0
0
2
1
0
0
1
0
1
2
3
1
2
4
0
1
2
1
0
0
1
1
1
0
1
0
0
0
2
0
0
0
0
1
1
0
3
0
1
0
1
0
0
1
0
2
1
0
2
1
1
2
0
0
0
0
0
0
0
1
0
2
0
0
1
1
1
0
0
2
1
2
2
0
1
0
2
1
0
0
1
0
2
1
1
2
1
1
2
0
2
2
2
0
0
0
0
1
1
1
1
2
1
2
0
1
0
1
0
0
1
0
1
0
0
0
2
0
0
1
0
0
2
0
2
2
0
0
2
2
0
1
2
0
2
0
1
1
3
1
2
0
0
1
1
1
0
1
0
1
0
1
0
2
1
0
1
2
1
0
2
2
1
0
1
1
2
0
1
1
0
1
0
0
2
0
1
1
2
1
2
2
1
1
1
1
1
1
2
1
0
0
0
2
1
2
0
2
0
0
0
0
2
0
0
1
1
0
1
0
0
2
2
0
1
2
0
0
1
0
0
1
1
2
1
1
2
1
1
1
0
1
0
1
0
1
2
1
0
1
0
1
1
0
0
2
0
0
1
0
0
0
0
2
3
1
1
1
0
0
0
0
2
1
1
0
2
1
0
2
1
1
0
1
1
0
1
2
1
0
2
0
0
2
2
1
1
0
1
2
2
0
0
2
2
1
2
0
0
0
1
0
1
1
0
0
2
0
1
1
2
1
2
0
1
1
0
1
0
0
0
0
1
2
2
2
0
1
0
0
4
1
1
0
0
0
0
0
2
1
0
0
0
0
1
2
0
1
1
1
2
1
1
0
1
0
2
1
1
0
3
0
2
0
1
1
2
1
0
1
2
1
0
3
0
1
2
1
0
0
2
0
1
0
0
1
0
0
0
0
1
2
0
0
0
0
0
1
2
1
0
0
0
0
0
1
0
0
0
1
2
0
0
1
2
0
0
2
2
0
0
1
1
0
0
1
0
2
1
0
2
1
0
1
2
2
2
2
0
1
1
1
1
0
0
2
2
0
0
1
0
2
0
1
0
6
0
1
0
0
1
1
2
1
0
0
0
0
1
0
0
1
3
1
0
2
2
0
1
0
0
1
2
2
1
1
0
0
0
1
1
0
1
0
0
1
1
2
2
2
2
1
2
1
0
0
0
1
3
1
0
1
1
1
0
0
1
2
1
0
1
1
2
2
2
0
1
0
0
0
0
0
1
1
0
3
2
1
2
0
1
1
0
1
0
0
1
1
0
1
1
0
0
2
2
1
1
1
0
0
2
1
2
2
1
1
2
2
1
0
1
2
1
1
0
2
1
2
1
2
0
0
0
0
1
0
1
2
0
0
0
2
0
2
0
1
2
2
0
1
0
2
0
0
0
1
1
0
2
0
0
0
1
5
2
0
0
1
1
1
1
0
2
1
0
0
1
0
1
2
2
1
0
0
1
1
1
0
1
0
0
1
2
0
0
2
2
1
0
1
1
0
1
1
0
2
1
2
0
1
0
0
2
1
3
0
0
1
1
2
0
2
0
1
2
1
2
2
1
1
0
1
2
0
1
0
1
1
0
0
0
1
1
0
0
1
0
1
1
1
1
0
1
1
0
0
1
2
1
2
0
1
0
0
3
0
0
0
0
1
1
2
0
0
1
2
0
1
1
1
0
0
0
0
1
2
1
1
0
0
1
1
0
0
0
0
0
0
2
0
2
0
2
2
0
0
1
1
0
0
0
1
1
1
0
1
0
1
0
0
1
1
1
1
1
0
1
0
2
1
0
2
0
0
2
1
2
1
1
1
1
1
1
0
1
1
0
1
2
0
0
0
0
1
0
1
0
2
0
0
1
0
0
1
0
2
2
2
2
1
0
1
0
2
1
1
0
1
1
0
2
0
0
1
0
0
1
4
1
0
1
1
0
0
2
1
1
0
0
1
1
1
0
0
0
0
0
2
2
1
2
1
1
2
1
0
1
0
0
0
0
0
0
2
1
0
0
0
1
1
2
1
0
0
0
1
1
1
0
0
1
0
2
1
0
2
0
0
1
0
3
1
0
1
0
1
2
1
1
2
1
1
1
2
0
2
1
0
2
1
2
2
1
0
0
0
0
1
2
0
0
2
0
1
2
2
0
1
0
1
1
2
0
2
1
0
0
2
1
2
0
0
2
0
2
0
1
0
0
0
2
0
2
0
1
1
2
2
2
0
2
1
0
1
1
0
1
1
4
1
0
0
0
1
1
1
0
1
0
0
2
0
0
1
2
0
0
2
1
1
1
1
1
1
3
2
0
0
1
2
0
2
2
2
2
1
0
0
0
0
0
0
1
0
0
1
1
1
2
0
1
1
0
2
0
0
0
0
0
0
1
1
0
2
1
2
2
0
0
0
0
0
0
2
0
2
0
1
2
2
0
0
0
1
1
0
1
1
2
0
0
1
1
0
0
1
2
1
0
1
1
0
0
0
1
1
2
0
2
1
1
0
2
2
1
0
1
0
0
0
1
0
0
0
1
2
2
0
2
3
0
0
0
0
1
1
2
0
0
2
1
1
0
0
1
3
0
0
0
2
1
1
0
0
0
0
1
0
2
0
2
0
2
0
2
1
1
1
1
2
0
0
1
2
0
0
1
0
1
1
2
0
4
2
0
0
2
2
1
1
1
1
1
1
1
0
0
1
0
1
2
0
1
2
2
0
0
1
0
0
4
1
2
1
1
2
0
1
1
0
1
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
1
1
0
1
2
2
0
0
0
0
0
1
2
0
0
1
2
2
0
0
1
1
0
1
0
0
1
0
1
0
1
1
0
0
1
0
1
4
1
0
2
1
0
1
2
0
2
1
2
0
0
2
0
1
0
0
0
1
1
0
0
0
0
1
0
0
2
0
2
1
1
0
1
1
2
0
0
0
2
2
0
0
1
1
2
1
1
0
0
1
0
1
0
1
0
2
0
1
0
1
0
2
0
1
1
2
0
0
0
0
1
2
0
1
0
2
1
0
0
0
0
2
0
0
1
0
0
2
1
1
0
1
1
0
2
0
1
1
1
0
1
1
0
1
1
1
2
2
2
0
0
2
1
0
2
0
1
3
1
0
0
1
1
1
1
0
2
1
1
1
1
1
1
0
0
2
0
2
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
1
1
1
0
0
1
1
2
1
1
2
0
0
2
2
1
1
2
2
2
1
1
0
0
1
0
1
1
1
0
0
2
2
2
1
0
0
0
0
0
1
2
0
2
0
0
0
1
1
1
0
2
2
0
2
1
1
1
2
2
0
0
0
1
0
0
1
0
2
2
0
0
0
0
2
1
1
1
0
1
0
0
2
1
1
0
1
0
0
1
1
2
1
0
0
0
0
1
1
1
1
1
2
1
0
0
0
1
1
1
1
0
2
0
1
1
0
0
1
2
2
1
0
1
1
4
1
0
0
1
1
2
2
1
0
1
1
0
0
0
2
1
1
1
2
1
0
0
2
0
0
1
1
1
0
0
1
0
1
0
0
1
0
2
1
1
1
1
2
2
1
1
0
0
2
1
1
1
2
0
2
2
0
0
3
2
1
0
1
0
1
2
1
1
0
2
0
1
1
0
1
1
1
1
0
2
1
1
1
1
0
1
1
0
1
2
0
2
2
0
0
0
0
1
3
2
2
0
0
1
2
1
0
1
0
0
1
1
0
0
0
1
1
1
2
0
0
2
0
2
0
0
4
5
0
2
2
0
0
1
0
0
2
0
1
1
0
2
0
1
0
1
0
0
0
1
0
1
1
1
2
0
2
1
2
1
0
2
0
1
0
2
2
1
1
1
0
0
1
2
1
1
1
1
2
1
0
2
1
2
1
1
1
0
2
1
1
1
1
1
1
0
2
1
0
0
1
1
1
1
0
0
3
1
2
1
1
0
2
1
1
0
1
0
1
0
0
0
0
0
1
1
1
1
1
2
2
2
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
1
1
0
0
0
0
0
1
0
0
2
0
0
2
2
1
1
0
0
0
1
1
0
0
1
0
0
3
1
1
1
0
0
0
2
1
0
0
2
0
0
0
2
0
2
0
0
1
1
1
1
1
0
0
2
1
1
1
2
2
0
0
0
2
0
0
1
2
0
1
0
2
1
1
2
1
1
1
2
1
1
2
1
1
0
1
1
0
0
1
0
0
0
1
0
0
2
0
2
0
2
2
0
0
2
0
2
0
1
1
1
0
2
1
2
2
2
0
0
0
0
0
1
0
2
0
2
2
2
0
0
0
0
0
2
2
1
1
2
0
0
0
0
1
0
1
0
2
0
0
1
2
0
0
1
2
2
1
1
2
0
0
0
2
1
0
1
0
2
0
0
1
0
1
2
1
0
1
1
2
0
0
0
0
0
0
2
2
1
3
2
2
1
2
1
0
1
1
0
2
1
0
0
0
0
0
0
0
2
0
0
2
1
0
2
1
0
3
1
0
0
1
0
0
1
0
0
1
1
0
1
0
2
1
1
1
2
2
1
2
1
0
1
0
0
0
1
2
0
0
2
2
1
1
2
1
0
0
0
0
1
0
2
1
1
0
0
2
1
0
1
0
1
2
0
1
2
0
0
1
0
2
0
2
0
0
2
1
0
2
1
0
1
1
0
1
2
1
0
0
1
1
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
2
0
1
2
2
0
0
0
0
0
1
1
2
0
1
1
0
0
4
1
1
0
1
0
0
0
2
2
0
1
1
2
0
2
2
3
1
1
1
2
1
1
1
2
1
1
1
0
1
0
0
0
0
1
2
0
0
0
2
1
3
1
1
2
0
2
0
1
1
2
0
0
1
2
0
2
1
0
2
0
2
3
0
0
1
1
1
0
0
0
1
0
2
0
1
0
1
1
1
0
0
1
1
0
0
0
2
0
1
1
1
1
1
1
0
1
2
1
0
1
1
0
0
1
1
1
0
2
0
0
2
1
1
2
1
0
0
1
0
1
0
4
3
0
1
0
1
2
1
0
1
1
0
2
1
0
0
1
2
0
2
1
1
4
2
1
0
2
0
2
0
1
0
2
1
0
0
2
1
1
0
2
0
2
1
0
0
1
3
1
0
2
0
3
0
0
0
1
0
1
1
0
2
0
1
1
1
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
2
1
1
2
0
4
1
2
0
1
2
0
0
1
1
0
1
0
1
2
1
0
1
3
1
2
2
1
0
1
0
0
1
1
0
0
2
2
3
1
0
0
0
2
0
2
1
1
2
2
2
0
2
0
0
1
1
0
1
0
0
0
1
1
1
0
1
0
0
1
0
3
0
1
1
0
0
2
0
0
1
0
0
0
1
1
0
2
0
0
2
1
1
0
0
0
1
0
1
1
0
3
2
0
1
1
1
0
1
0
0
0
0
0
1
2
1
1
1
1
1
0
1
1
0
1
0
1
2
1
0
2
0
1
1
0
0
1
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
5
1
0
2
1
3
1
2
2
2
1
0
1
1
2
0
0
1
0
1
1
2
1
3
2
0
1
1
2
0
2
0
1
1
0
0
1
0
0
1
0
0
2
1
0
0
0
1
0
0
1
2
0
0
0
0
0
1
0
1
1
2
1
0
0
0
0
2
1
0
1
0
1
0
1
2
1
1
0
0
2
3
0
0
2
1
1
2
1
1
1
2
1
2
0
1
2
1
0
0
2
1
2
1
2
0
1
1
0
1
1
0
3
3
0
0
0
1
1
0
1
0
0
0
0
1
0
1
2
0
1
2
1
1
0
1
2
1
1
1
2
1
1
0
0
3
1
2
2
0
0
0
0
1
1
1
2
1
0
0
0
0
2
2
1
0
0
1
0
1
0
1
0
2
1
1
0
1
0
2
0
0
0
2
0
0
0
2
0
2
2
1
1
0
2
0
0
1
0
0
0
2
1
0
1
0
0
2
1
1
1
0
1
1
2
3
2
2
2
0
0
0
2
0
2
1
1
1
1
0
0
2
1
2
2
0
0
1
0
0
1
0
1
1
0
0
2
1
2
1
0
2
0
2
0
0
0
0
0
2
1
1
0
0
1
0
0
2
2
0
0
1
0
1
0
0
0
1
3
1
1
2
0
1
1
0
1
1
0
0
1
0
2
0
0
1
2
0
0
0
0
0
1
2
1
1
0
1
1
2
1
0
1
0
2
2
1
0
1
1
1
2
0
0
1
3
2
0
1
0
1
1
1
1
1
0
0
1
2
2
0
2
0
2
0
0
0
2
1
2
0
1
0
0
0
2
0
0
1
0
1
0
0
1
2
0
0
1
0
1
2
3
1
0
0
0
2
0
1
2
0
0
2
0
1
2
2
0
2
0
2
0
2
1
2
0
0
0
1
0
1
2
2
1
1
1
2
1
1
1
1
2
1
2
0
1
1
0
4
0
0
2
1
1
0
1
1
1
2
0
1
2
2
0
1
1
2
1
0
1
0
1
1
1
0
1
1
1
0
1
0
2
0
1
1
2
0
1
0
0
1
0
0
0
0
0
1
0
0
3
0
0
0
0
1
2
0
0
2
0
1
0
2
0
1
2
0
0
2
1
0
2
0
2
1
2
1
0
1
2
1
0
0
1
1
2
0
1
1
0
0
2
0
1
0
1
1
2
0
0
1
1
2
2
0
1
2
0
2
0
1
0
1
0
2
0
0
0
0
1
2
1
1
2
0
1
0
1
1
1
0
0
1
0
1
1
2
0
0
1
1
1
0
1
0
1
2
2
1
0
2
2
0
0
2
0
0
1
1
2
1
2
1
1
0
1
2
1
2
2
2
1
1
1
1
2
1
0
0
0
2
1
1
0
0
2
0
1
0
0
0
0
0
1
1
0
0
2
1
2
0
2
0
2
2
1
0
1
1
0
3
1
0
1
1
0
0
0
1
0
2
2
1
0
1
1
0
2
1
1
1
1
0
2
0
0
0
1
3
1
1
1
0
1
2
1
2
1
1
1
2
0
0
1
2
1
1
1
0
1
2
2
2
0
0
2
2
0
0
1
2
0
1
0
0
0
1
1
0
0
2
2
1
2
1
0
1
0
1
0
0
1
1
1
1
1
0
1
0
0
1
1
0
1
0
0
1
0
1
1
0
0
1
2
2
0
0
0
1
1
1
2
1
2
0
0
1
0
1
1
1
1
1
1
0
0
0
0
0
2
0
1
1
0
2
0
1
0
2
2
0
2
0
1
1
1
0
2
1
0
1
0
0
1
1
1
2
0
1
0
0
1
0
2
2
0
1
0
0
1
1
0
0
2
1
0
2
1
1
0
0
0
1
0
0
0
0
0
0
0
2
1
3
0
0
0
1
0
0
0
1
0
1
0
1
1
1
1
0
1
1
0
1
0
2
0
1
0
1
1
0
4
1
1
0
2
0
1
2
1
0
1
2
2
0
0
0
2
0
1
1
1
0
0
0
0
0
2
0
1
2
1
0
1
0
1
0
1
0
0
1
0
2
1
0
0
0
1
0
0
0
2
1
1
0
2
1
1
0
2
1
0
0
1
0
0
1
1
1
1
0
1
0
1
1
0
0
2
0
0
2
0
2
1
1
0
1
1
1
2
1
1
2
0
2
1
2
0
2
0
1
1
1
0
2
1
1
2
0
2
1
1
0
1
0
3
2
0
0
0
4
0
1
0
0
1
2
2
2
0
0
1
2
0
2
2
0
2
0
0
0
2
0
0
1
4
0
2
0
1
1
1
0
0
2
1
0
0
0
1
2
1
2
0
0
1
0
0
1
1
1
1
0
1
1
0
0
1
0
0
0
1
2
0
1
0
0
0
2
2
1
1
1
2
2
2
0
1
0
2
1
1
0
1
0
0
1
0
0
0
0
0
1
0
2
0
0
2
1
1
1
0
0
2
0
2
1
1
2
0
1
1
2
1
0
1
1
1
0
1
0
2
0
2
1
2
2
2
0
0
1
0
0
1
1
0
1
0
0
0
2
2
0
1
2
1
0
1
0
1
0
1
0
0
1
1
0
0
1
1
0
0
0
0
1
0
1
0
1
0
1
2
2
0
0
0
0
1
0
1
0
1
1
2
0
2
1
0
1
0
2
0
0
0
0
0
1
1
1
0
1
2
1
2
0
1
1
0
2
2
0
0
2
3
0
1
1
4
1
2
1
0
3
2
0
1
0
0
1
1
0
1
0
1
1
1
0
0
0
1
2
1
1
1
0
1
0
0
0
0
1
2
2
0
0
0
0
1
1
2
1
2
0
2
3
2
1
1
1
0
0
0
1
2
0
1
2
0
0
1
2
1
3
2
1
1
1
0
1
1
2
4
0
1
1
1
0
1
1
2
0
1
2
1
1
1
1
2
0
0
0
0
1
2
0
0
0
1
1
0
1
0
1
2
10
2
1
1
1
0
1
0
0
2
2
1
0
0
2
0
1
0
1
1
0
2
3
1
2
2
0
2
1
0
0
0
2
0
3
1
1
2
1
0
0
0
1
2
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
1
1
2
1
2
1
2
0
1
2
1
1
1
2
1
1
0
0
0
1
0
2
2
1
1
1
0
1
0
2
0
0
3
1
0
0
0
2
0
1
2
5
1
0
2
0
0
2
2
2
2
1
2
0
1
2
0
2
1
0
0
2
2
2
0
0
0
1
1
1
0
0
0
0
1
1
2
1
0
1
1
0
1
1
1
1
1
0
0
0
0
0
1
0
0
1
1
1
2
1
0
0
1
0
1
1
0
0
0
2
1
0
1
0
0
2
1
0
0
2
2
2
1
0
1
1
1
2
2
1
0
0
1
0
0
1
1
0
1
3
2
1
0
0
0
0
0
1
0
2
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
1
0
1
1
0
0
1
0
0
0
1
1
0
2
1
1
1
1
2
2
0
0
1
0
0
0
0
0
2
2
0
0
1
0
2
1
0
0
2
2
0
2
2
0
2
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
2
1
0
2
2
1
0
1
0
0
0
2
0
1
1
1
0
0
1
2
1
0
2
0
0
0
2
2
2
0
1
0
0
1
0
2
2
0
2
0
2
0
2
0
2
1
1
1
2
0
1
2
0
1
1
2
1
1
0
2
2
0
2
0
2
1
0
2
0
0
2
0
1
0
2
1
0
2
0
0
0
0
0
0
0
1
0
0
1
2
0
1
0
0
1
1
2
2
1
1
0
0
1
0
1
1
0
1
3
0
0
1
2
1
1
1
1
1
2
0
1
2
0
1
0
1
1
0
3
1
0
0
1
1
1
2
1
0
1
2
1
0
1
2
1
2
2
2
0
2
2
0
0
0
0
2
1
0
1
2
0
1
1
0
1
1
1
0
0
0
2
0
0
1
0
0
1
1
0
2
2
0
1
1
1
1
1
1
0
0
0
0
0
2
1
2
1
0
1
2
1
0
0
0
0
0
1
1
1
0
0
1
0
1
1
0
1
0
1
0
2
2
1
2
1
0
2
0
0
2
1
0
0
0
1
1
1
0
2
0
0
1
1
0
1
2
0
1
2
0
1
0
0
1
0
2
0
1
2
0
2
1
1
1
1
0
1
2
0
0
0
0
1
0
2
1
1
1
2
1
0
0
1
1
1
2
2
1
1
1
0
2
2
2
0
1
0
2
1
0
0
2
1
0
1
0
1
0
1
1
1
0
0
2
1
1
0
0
1
0
0
1
0
1
0
0
2
1
1
0
0
2
0
0
0
1
1
0
1
1
0
2
1
1
0
1
0
1
1
2
0
0
1
1
0
2
1
1
0
0
0
0
0
3
0
2
1
1
3
1
0
0
0
0
0
0
0
1
0
0
1
1
3
1
0
2
0
1
0
1
1
0
2
0
1
0
0
0
1
3
0
1
0
0
1
0
0
1
1
1
2
2
1
0
1
0
0
0
0
0
1
0
0
1
0
1
0
2
0
1
0
1
0
0
0
0
1
1
0
0
1
0
0
2
0
1
0
0
1
2
0
1
0
1
1
0
0
0
1
2
1
1
0
2
1
1
1
0
0
1
0
1
1
2
1
0
0
0
1
1
0
0
0
1
1
1
2
0
0
0
2
1
0
1
0
2
1
4
3
0
0
2
2
1
1
2
1
0
0
1
2
0
1
1
1
0
1
0
1
1
0
0
1
1
0
2
1
0
0
0
0
0
0
0
2
1
2
2
1
0
1
0
0
1
1
1
2
0
0
0
1
0
1
1
0
1
2
2
0
1
2
1
1
0
0
1
1
1
0
1
0
2
2
1
0
2
1
0
0
2
0
1
1
0
2
1
0
1
0
0
2
2
2
0
0
0
1
1
0
2
1
1
1
1
1
0
1
0
1
0
1
1
1
0
1
0
0
1
2
0
2
1
0
4
2
0
1
2
0
1
0
0
1
2
1
0
2
0
1
0
0
0
2
1
1
2
0
2
2
1
0
1
1
0
2
1
2
0
1
0
3
2
0
2
0
1
0
0
0
2
1
1
1
0
0
2
2
2
2
0
2
0
1
0
2
1
1
1
1
1
1
1
2
1
0
1
3
1
1
2
1
1
1
0
0
1
0
1
3
0
1
2
0
0
1
2
1
2
1
0
0
1
1
0
2
1
2
0
2
0
1
1
1
0
1
1
2
1
0
1
0
0
0
1
0
2
2
0
1
1
1
0
2
0
2
1
0
1
1
1
0
2
1
0
0
2
1
0
0
0
0
2
1
2
0
0
1
0
0
0
1
0
2
0
0
0
0
2
2
1
1
1
0
1
2
0
3
2
0
2
0
1
0
0
0
2
1
0
1
2
1
0
1
0
0
3
0
1
1
2
0
2
1
1
1
1
2
0
0
0
0
0
0
2
1
0
0
1
0
1
2
1
3
1
0
0
0
1
2
1
1
1
1
1
0
2
0
0
1
0
1
1
0
1
1
2
1
1
0
1
2
2
1
0
1
0
2
2
0
1
1
1
0
0
0
1
2
1
1
1
1
1
1
2
0
1
2
0
1
0
0
1
0
2
1
1
0
1
1
2
2
1
0
0
2
0
0
2
0
1
0
2
1
2
1
1
0
1
2
0
0
2
1
0
1
2
2
0
1
2
0
2
0
1
1
1
0
0
2
0
0
0
2
1
0
0
2
0
2
2
0
1
1
0
0
0
2
0
1
1
0
2
1
0
1
2
2
2
0
1
1
1
0
0
2
1
1
5
1
0
0
1
0
1
1
0
1
0
0
1
2
1
1
0
2
0
2
0
2
1
1
1
2
1
1
1
1
1
2
1
1
0
2
1
1
2
0
0
1
1
2
1
2
0
1
2
1
0
0
0
2
0
0
1
1
2
1
0
0
2
1
1
0
0
0
2
1
1
0
2
0
2
1
2
0
0
0
3
2
0
1
1
0
2
1
2
0
0
1
0
1
0
0
1
2
0
1
1
1
0
2
1
0
2
0
2
1
0
0
0
1
3
1
0
0
0
1
0
1
1
2
0
2
0
0
1
1
0
1
1
0
4
0
0
0
0
1
0
0
2
1
1
0
1
1
0
1
1
2
0
1
0
0
2
1
2
0
2
1
1
0
0
0
2
0
1
1
1
0
1
1
1
0
0
2
0
2
0
2
0
0
2
2
0
2
1
1
1
2
1
2
0
0
1
2
1
1
1
2
2
0
1
1
0
1
0
0
0
1
2
0
0
0
2
0
2
1
0
1
1
1
2
1
0
1
1
1
1
0
1
1
2
1
0
1
2
3
0
0
2
1
1
1
1
0
0
0
0
2
0
0
0
1
2
2
1
0
2
1
0
1
0
1
0
0
0
0
2
1
2
0
2
1
0
1
1
2
1
1
2
0
2
1
2
0
2
1
1
0
1
0
2
0
1
0
0
1
0
1
1
0
2
0
0
1
1
2
2
0
0
2
0
1
1
0
2
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
1
2
1
1
1
0
1
0
2
2
1
2
1
1
0
0
1
0
1
0
0
1
0
2
0
0
1
2
2
1
0
0
0
1
1
2
2
0
2
1
1
0
0
0
0
0
0
1
1
2
1
2
0
0
1
0
2
1
1
1
2
1
2
0
1
1
1
1
0
1
2
2
1
2
3
1
1
1
0
1
1
1
0
1
2
2
1
1
0
0
0
1
0
1
2
0
0
1
2
1
0
1
2
7
1
1
1
0
2
2
1
1
0
0
3
6
2
0
0
1
2
1
2
0
1
0
0
1
2
0
0
1
1
1
0
1
2
0
1
0
2
0
2
1
0
2
1
2
1
1
0
1
1
2
1
0
1
1
1
0
0
2
1
2
2
1
0
0
2
0
0
0
1
0
0
0
0
1
2
2
0
1
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
1
0
1
1
3
0
1
1
1
2
1
0
0
0
1
0
2
0
0
2
0
0
1
0
2
0
1
0
1
1
2
2
1
1
0
1
2
1
1
2
1
0
0
1
1
1
0
1
2
0
1
1
1
2
0
2
0
0
2
2
0
2
0
1
1
0
0
2
0
1
1
0
1
2
1
2
0
0
0
2
0
1
0
1
0
1
1
1
1
1
0
0
2
0
0
1
0
0
2
0
2
0
0
1
1
0
1
0
1
1
2
2
1
1
0
1
1
1
2
0
1
1
0
0
0
1
1
1
3
0
1
2
1
2
1
0
1
0
1
0
0
0
1
1
2
0
0
1
2
1
1
1
0
2
0
1
0
0
2
0
1
0
2
0
1
2
1
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
1
1
0
1
1
1
0
2
1
0
0
2
1
1
0
1
0
0
1
1
0
2
1
1
2
0
1
0
1
1
2
0
0
0
0
1
0
1
0
1
0
0
2
0
2
0
2
1
2
1
2
0
1
1
0
0
1
0
0
0
1
1
2
2
1
0
0
0
0
0
1
1
0
1
0
1
0
2
2
0
2
1
1
0
2
0
0
1
2
1
0
0
1
2
1
2
2
2
1
2
0
1
1
1
1
0
1
0
2
0
1
1
0
1
2
1
0
0
0
1
1
1
1
1
2
0
0
1
2
0
0
0
1
0
1
1
0
1
0
0
0
1
2
1
1
0
2
1
0
2
1
1
1
0
2
2
1
2
0
0
2
0
0
1
1
0
0
1
0
0
0
0
1
0
0
1
1
0
1
1
0
0
0
0
2
2
2
1
2
1
0
1
1
1
0
2
2
0
1
1
0
2
1
0
1
2
0
1
1
0
0
1
1
2
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
1
1
2
0
1
2
0
0
1
0
1
0
1
0
0
1
2
1
0
0
0
1
2
2
0
0
1
0
1
0
1
0
1
4
1
0
0
0
1
2
1
0
0
0
0
1
2
2
0
0
1
1
1
0
1
1
1
0
2
2
0
2
1
1
2
0
1
1
2
1
0
2
0
2
0
1
0
2
1
1
1
0
2
0
0
1
2
0
2
1
1
1
0
2
2
1
2
0
0
1
2
0
0
0
1
0
2
1
2
2
1
1
1
2
0
0
1
1
1
0
1
1
2
1
0
6
1
0
0
0
1
0
0
0
1
3
1
1
2
2
2
0
1
0
1
1
1
1
0
0
2
1
0
0
0
2
0
2
2
2
0
1
1
1
0
0
2
2
1
1
0
0
2
1
2
0
0
0
1
0
1
1
0
1
0
1
0
0
1
0
0
1
0
1
0
0
2
0
0
0
0
0
0
2
1
1
0
0
1
1
0
1
0
0
2
2
0
0
1
2
0
2
1
0
1
1
2
2
0
0
0
2
0
1
0
0
1
1
2
2
2
2
1
2
1
2
1
0
2
0
1
0
1
1
1
1
0
1
0
2
1
1
1
1
0
2
0
1
1
1
0
1
0
1
1
1
2
0
2
2
0
1
0
2
0
0
2
1
1
2
1
0
2
1
1
0
0
0
2
3
4
1
1
2
2
1
0
0
1
1
1
1
2
3
0
1
0
0
0
0
2
2
0
1
1
1
0
2
2
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
1
0
1
2
0
0
0
0
1
1
0
0
2
0
1
0
1
0
0
2
2
1
2
1
0
1
0
0
1
1
1
0
0
1
3
0
2
2
1
0
1
2
1
2
1
1
2
1
1
1
2
1
0
1
0
1
1
2
2
2
1
0
0
2
0
3
0
0
1
0
1
0
0
1
1
0
0
1
2
1
0
0
1
0
1
0
0
0
0
0
0
0
1
2
0
4
1
2
0
1
0
2
2
2
2
1
2
3
0
2
0
1
0
1
1
2
0
0
0
1
1
1
0
0
1
2
0
1
1
1
0
1
1
0
2
0
2
0
1
0
0
2
1
1
0
2
0
1
1
1
0
2
2
2
2
0
0
1
0
1
1
1
1
1
2
0
2
1
2
1
1
0
0
0
0
1
1
1
0
0
1
2
3
2
2
0
1
0
0
0
0
3
2
1
0
2
0
1
0
0
1
0
2
0
1
1
1
0
2
1
1
2
2
0
3
1
0
2
2
1
2
0
1
2
1
2
0
0
1
0
2
1
0
1
2
1
1
0
2
1
4
0
0
0
2
0
1
0
0
1
2
1
0
0
0
1
1
2
1
0
0
4
1
0
2
0
2
0
2
1
1
0
0
2
2
1
0
0
1
0
3
0
0
0
1
1
1
1
2
0
1
2
1
1
2
2
1
0
0
2
1
2
0
0
0
1
2
0
1
2
2
2
0
0
1
1
0
2
1
0
2
0
2
1
1
2
0
2
2
1
0
0
0
2
1
0
0
0
1
0
2
0
1
0
0
1
1
0
0
0
1
0
0
0
2
1
1
0
0
1
0
1
0
2
1
0
0
1
0
0
1
0
2
0
1
1
2
0
3
1
0
1
0
1
0
1
1
1
1
0
0
1
0
2
1
2
2
2
4
2
1
2
0
2
1
1
2
2
1
0
2
1
2
1
0
2
1
2
1
1
0
2
2
1
0
0
1
1
1
0
0
2
0
0
1
2
0
1
2
1
2
2
0
0
2
2
1
2
1
0
1
1
2
0
0
1
0
2
1
1
2
0
1
0
2
2
1
1
0
0
1
0
0
0
0
1
2
1
2
0
1
1
1
0
3
1
1
0
1
0
0
1
2
2
1
2
0
2
2
1
0
0
1
0
0
1
0
0
3
1
0
2
0
1
2
0
2
0
0
1
2
0
0
1
0
0
1
0
1
0
1
0
2
0
1
1
0
1
0
2
0
0
1
0
1
2
1
0
2
1
2
1
0
0
0
1
1
1
0
1
2
1
2
1
1
1
1
1
1
2
0
0
0
2
1
1
1
1
2
0
0
0
1
1
0
0
1
0
0
2
0
2
1
0
2
0
0
0
0
0
2
2
0
1
0
1
0
3
0
1
0
1
1
1
1
2
0
1
0
1
0
2
2
2
0
1
1
2
0
1
1
2
0
0
1
1
2
1
2
2
0
0
0
0
0
2
1
1
0
0
0
1
1
1
0
1
0
0
1
0
1
1
0
0
2
1
2
0
0
0
0
0
2
1
2
3
0
0
2
0
0
0
1
0
1
1
3
1
0
0
0
1
1
0
1
1
0
1
0
0
1
2
2
1
0
0
1
0
1
2
1
1
0
1
1
0
0
0
0
0
1
0
6
0
0
2
0
0
1
0
2
1
1
1
2
0
0
0
0
0
0
0
1
0
2
1
0
0
0
2
0
2
1
2
1
2
0
0
2
0
0
1
1
0
2
1
2
0
0
1
2
0
0
0
1
1
1
0
0
1
3
1
1
0
2
1
2
3
0
2
1
0
2
0
2
1
0
0
1
0
0
2
1
2
0
1
1
1
0
0
1
0
1
2
0
0
0
1
1
0
2
1
2
1
0
0
0
2
1
0
0
2
2
2
2
1
0
2
1
0
0
0
2
2
1
2
1
0
0
0
1
2
0
0
0
1
1
0
1
1
1
0
1
2
0
1
1
2
1
1
1
1
0
1
0
0
0
2
2
1
0
2
0
0
0
1
0
0
0
0
1
2
0
2
1
1
0
0
0
1
2
1
0
0
1
2
0
2
5
0
0
0
2
1
0
2
2
0
0
1
0
1
0
0
0
1
1
1
1
2
0
0
1
1
0
0
1
0
1
0
0
1
0
0
2
0
1
0
1
0
0
2
0
1
1
0
2
3
0
0
2
0
0
1
2
1
0
0
0
0
0
0
2
0
1
0
2
1
0
1
0
0
1
0
0
3
0
0
1
1
2
1
1
1
2
2
0
1
0
1
2
1
1
2
0
0
0
2
1
0
1
0
2
0
1
1
1
1
0
1
0
0
1
2
2
1
0
0
1
2
0
1
0
1
1
0
0
1
1
1
2
1
1
1
0
2
2
1
1
0
1
1
0
1
0
1
1
0
1
0
2
1
0
1
0
2
1
0
1
1
1
1
0
2
2
0
0
0
1
0
0
1
1
1
1
2
1
1
0
1
0
0
0
0
0
2
1
0
0
1
2
0
2
1
0
1
1
1
0
1
0
0
0
2
1
0
2
0
0
3
0
1
1
0
0
0
1
0
0
0
1
0
1
0
0
0
2
0
0
2
1
0
1
0
1
0
2
1
0
3
0
1
0
1
4
1
2
0
0
1
0
2
1
1
1
1
1
1
1
0
0
1
2
0
2
2
1
1
0
1
0
0
1
2
0
1
0
0
0
0
1
0
1
0
2
0
1
2
0
0
0
3
0
1
0
1
1
2
0
0
1
0
0
0
0
0
2
2
2
0
2
2
0
2
0
1
0
2
2
0
0
0
0
1
0
0
1
0
1
1
2
1
0
2
2
1
1
1
0
0
2
4
2
0
1
0
1
0
1
2
1
1
1
1
0
0
1
0
0
0
2
1
0
2
2
1
0
1
0
2
2
1
1
0
2
0
2
0
0
0
1
0
0
0
2
0
0
2
1
1
0
1
0
1
0
0
1
0
1
2
0
1
2
1
0
2
2
1
1
0
2
2
0
1
0
1
0
0
1
0
1
2
0
2
0
2
0
0
0
2
2
1
1
1
1
0
0
1
2
0
2
1
1
3
1
1
0
2
1
0
1
2
2
1
0
1
2
2
1
0
0
1
2
0
0
2
1
0
1
0
0
0
1
0
0
2
1
1
2
2
0
0
0
1
2
3
0
2
0
2
1
1
1
1
0
1
3
0
0
1
1
0
1
2
1
1
1
0
2
0
0
1
1
0
1
2
2
0
0
1
0
0
0
1
0
0
1
1
1
2
2
0
1
0
0
1
1
2
0
0
0
1
2
1
2
2
1
2
0
0
0
1
2
0
1
0
1
1
3
0
1
0
2
0
0
0
1
0
1
0
1
0
0
1
0
1
1
1
0
0
1
2
0
1
0
1
0
2
0
1
1
2
0
0
0
0
2
1
0
1
0
0
0
1
1
0
1
1
0
0
1
1
1
0
2
2
0
1
0
0
1
0
0
0
1
0
3
0
0
0
3
1
1
0
1
0
0
0
0
2
1
0
1
1
1
0
0
1
0
2
0
2
1
0
0
1
1
2
1
0
0
0
0
1
0
0
1
2
1
0
1
1
1
2
0
1
1
2
1
1
0
0
1
0
0
1
0
0
2
1
1
0
1
0
0
0
1
1
2
0
1
2
2
0
0
1
0
1
0
0
1
0
1
2
0
2
1
1
2
0
0
0
0
1
2
0
0
1
0
1
0
2
0
0
2
1
0
1
2
1
1
1
1
0
0
0
1
1
2
2
1
1
2
0
0
1
0
0
0
2
0
1
1
0
0
0
2
2
0
1
1
1
1
0
2
2
1
2
1
1
2
1
0
0
0
2
2
1
0
1
2
1
0
0
1
0
2
0
2
1
2
0
2
0
1
2
0
1
0
0
2
0
0
0
0
0
2
0
1
0
1
1
0
1
0
1
2
0
0
1
0
2
2
2
0
1
0
0
1
0
2
2
0
0
2
1
1
0
2
1
0
1
0
0
0
1
1
0
2
1
2
0
0
1
0
2
0
0
0
0
0
0
0
1
1
2
0
1
0
0
0
0
1
0
1
0
0
2
1
1
1
2
2
0
1
1
1
0
2
1
1
1
0
1
1
0
1
0
0
0
1
0
0
0
0
1
1
2
0
0
1
1
1
1
1
0
2
1
1
4
0
1
0
1
2
1
0
1
1
1
0
1
0
1
2
2
1
2
0
2
2
0
0
1
1
1
1
1
0
0
2
1
2
1
0
0
2
0
1
1
2
0
2
1
2
0
1
1
1
1
1
1
2
0
1
1
0
0
1
1
1
2
0
3
1
1
1
0
1
0
1
1
0
1
1
0
1
2
2
1
1
0
1
0
1
2
1
0
0
2
0
0
2
2
0
1
3
0
0
1
0
0
0
0
0
0
0
2
2
2
2
1
0
2
0
0
1
1
0
0
0
0
0
1
0
0
1
0
1
0
0
2
0
1
1
2
1
1
1
2
0
1
1
0
2
1
0
0
1
1
0
2
0
2
0
0
1
1
1
1
1
1
0
2
1
0
2
0
0
0
1
1
0
0
0
1
1
2
0
0
0
0
1
1
1
2
1
3
1
0
0
1
2
0
0
0
0
1
0
0
2
1
1
2
1
0
0
3
2
1
2
2
0
0
1
2
2
2
1
2
0
1
2
0
0
1
0
2
0
2
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
2
1
0
0
1
1
1
0
0
1
1
2
0
0
1
1
0
0
1
0
0
2
1
1
0
1
2
0
0
0
2
1
1
1
2
2
0
0
0
0
2
2
1
0
0
0
2
0
2
1
0
0
1
1
0
0
1
0
1
0
0
1
0
0
2
0
2
1
1
1
2
1
1
1
2
1
0
1
2
1
1
2
1
2
1
1
2
0
1
1
0
1
1
1
1
0
0
1
2
0
0
0
1
2
0
1
1
0
0
0
0
0
2
1
0
0
0
1
1
1
1
1
1
0
0
1
2
1
2
0
0
2
0
0
0
0
2
2
0
1
2
0
2
0
3
1
0
1
1
0
1
1
1
0
1
3
1
0
1
1
1
2
1
1
2
0
1
1
0
1
1
1
1
2
1
1
0
1
2
1
0
0
1
2
0
1
0
0
2
1
1
1
1
1
0
1
0
0
1
0
0
1
0
2
1
1
0
2
3
0
0
0
2
1
2
1
0
0
0
1
1
1
0
2
0
1
0
1
2
0
1
0
1
1
0
1
1
0
0
2
0
1
1
0
1
1
0
2
1
2
0
0
2
2
3
1
1
0
1
0
0
1
0
0
0
0
0
1
2
0
0
1
0
1
0
0
2
1
1
0
0
0
2
0
2
0
0
2
0
0
2
0
2
0
1
1
0
3
0
0
0
1
0
1
2
0
1
2
0
0
0
0
2
2
1
1
0
0
1
1
1
0
0
1
1
0
0
0
1
1
2
2
1
1
0
0
1
0
1
1
0
1
2
2
2
1
0
0
1
1
0
1
0
1
0
1
1
0
0
1
1
0
1
0
1
2
2
0
2
0
1
1
0
1
0
2
0
0
0
0
1
1
1
0
1
0
0
0
3
0
0
1
1
1
0
1
2
1
2
1
1
1
1
1
0
0
0
1
1
0
3
1
0
0
0
0
0
1
0
0
3
0
2
1
0
1
2
1
1
0
0
0
0
0
0
2
0
1
0
0
2
2
0
1
2
0
2
1
2
0
0
0
0
0
1
0
0
0
2
1
1
1
0
5
1
2
2
1
0
1
0
1
1
0
2
2
1
1
1
1
1
0
1
2
0
0
0
1
2
1
2
0
1
0
0
1
1
1
1
0
0
0
1
1
1
2
2
1
1
0
2
0
0
1
0
2
0
1
0
1
0
0
2
2
0
0
2
1
2
2
1
0
1
2
0
1
0
3
1
1
0
0
0
0
2
1
0
1
0
1
2
0
1
0
1
2
0
0
1
1
0
0
0
2
0
0
2
0
0
1
0
0
0
1
2
1
1
0
0
3
1
2
1
0
0
1
2
0
2
1
1
0
0
1
1
4
2
1
0
1
0
0
0
0
0
0
2
0
1
0
2
2
0
1
1
1
1
0
2
0
0
0
0
1
1
0
1
1
1
0
1
1
1
1
1
1
0
0
2
1
0
0
0
2
0
0
0
2
0
0
0
2
2
1
0
0
1
0
1
1
2
0
2
1
1
0
2
0
0
1
1
0
0
0
0
0
0
0
0
1
2
2
2
2
0
0
0
1
1
1
1
0
1
1
0
1
0
1
1
0
1
2
1
1
1
2
0
2
0
0
0
0
0
1
1
1
2
2
2
1
0
0
1
0
2
1
1
0
1
0
1
0
1
0
2
0
0
2
0
2
0
0
1
1
2
0
1
0
0
0
0
3
5
0
1
0
1
0
1
1
1
0
1
0
0
2
0
1
0
0
0
1
2
1
2
1
1
0
0
2
1
3
0
0
2
0
0
0
2
1
1
2
0
1
2
0
1
1
0
0
0
0
1
0
2
1
0
1
0
2
1
2
2
2
1
2
2
1
2
0
4
0
2
1
2
0
2
1
1
2
0
1
0
1
1
1
0
2
0
2
0
1
0
0
0
0
2
0
0
2
2
0
0
1
0
1
0
0
1
0
2
0
2
0
0
0
0
0
0
1
1
2
0
0
0
0
2
1
2
2
0
0
1
0
0
0
2
2
0
1
1
1
1
2
2
2
0
1
1
0
0
2
1
0
1
0
2
2
1
0
0
0
0
3
0
0
0
0
1
1
4
1
1
1
2
1
1
0
0
1
1
0
2
0
0
0
2
1
2
1
0
0
1
2
0
1
1
1
1
1
1
2
0
1
0
0
1
0
0
0
0
0
1
0
0
2
0
1
1
2
0
0
0
0
2
0
1
0
2
0
1
1
1
2
2
0
0
2
0
3
1
0
1
0
0
2
1
0
0
1
0
1
1
0
0
1
2
2
0
1
2
0
0
0
2
1
2
2
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
2
2
0
1
1
1
0
1
1
1
1
1
1
1
2
0
0
0
1
2
2
0
2
0
0
1
1
1
1
1
0
0
1
0
2
0
1
0
0
0
1
2
0
0
0
1
1
1
0
1
1
0
0
1
2
2
2
0
1
0
0
0
0
1
0
2
1
1
0
1
1
0
1
1
2
0
2
2
0
1
0
1
1
2
0
0
1
0
0
0
0
0
0
2
2
0
2
0
2
1
0
1
2
1
1
1
1
0
0
1
0
1
1
1
2
1
0
1
0
2
0
1
0
0
1
1
0
0
1
0
3
1
1
0
0
1
1
2
1
1
1
1
1
0
1
1
0
0
0
1
1
0
0
0
1
2
0
0
2
1
1
2
1
2
0
0
0
0
0
0
0
0
3
0
0
2
0
0
1
1
1
2
0
0
2
1
1
2
0
1
1
0
1
1
0
2
1
1
1
1
1
0
1
2
1
1
1
0
2
1
0
1
1
2
0
2
1
0
1
1
1
1
0
0
2
0
1
2
1
0
0
1
2
0
0
2
1
0
0
1
0
1
0
1
2
1
2
0
0
1
0
0
2
1
2
1
0
1
0
1
0
1
0
0
1
2
1
0
0
2
1
1
2
1
0
2
0
0
2
0
0
1
1
2
1
1
0
2
2
0
2
1
1
2
1
0
0
0
2
0
1
0
0
2
2
2
1
2
0
0
0
0
1
0
0
1
1
0
0
1
0
3
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
1
1
0
0
2
1
0
1
0
1
0
1
1
1
0
1
1
0
0
1
2
2
0
1
1
1
1
1
0
0
1
1
1
0
1
1
2
0
0
0
0
1
1
1
0
0
1
0
0
0
1
1
2
1
1
0
1
1
1
1
1
2
0
2
2
1
0
0
1
0
0
1
1
2
0
3
0
0
2
0
0
2
2
0
1
0
1
0
0
0
1
2
2
2
1
0
2
2
1
0
2
0
1
1
1
1
2
1
1
1
1
3
0
1
0
0
2
2
2
1
1
0
1
1
0
0
0
0
1
1
1
2
2
0
4
1
0
1
1
0
2
2
0
1
1
2
1
1
0
1
1
0
1
0
1
1
3
1
1
0
0
2
1
0
1
1
2
3
1
3
2
0
0
0
0
1
2
0
0
1
1
1
0
2
0
0
0
0
2
0
2
2
1
2
1
1
2
0
0
1
0
0
0
1
0
1
0
1
2
1
1
2
2
0
0
2
1
0
0
1
0
1
0
1
1
1
1
0
0
0
0
0
2
1
0
1
0
1
1
0
0
2
0
1
2
1
1
2
2
1
2
0
2
1
1
1
0
3
0
1
0
2
1
2
2
0
2
0
0
1
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
1
1
1
2
1
0
0
2
0
1
1
0
3
1
0
0
0
0
0
0
1
0
2
0
0
1
2
0
2
0
2
0
1
1
0
1
0
1
0
0
2
2
0
0
0
0
0
2
1
1
0
1
1
0
0
1
1
0
0
1
0
0
1
1
0
0
2
1
0
0
1
0
2
2
0
0
1
1
0
0
1
0
0
0
1
1
0
0
0
0
2
0
1
2
1
2
2
1
1
0
1
0
0
2
0
0
1
1
0
0
1
0
0
0
2
0
2
1
2
1
0
0
2
0
2
1
2
0
0
0
2
0
1
1
1
1
2
0
0
2
0
0
2
2
1
0
1
1
2
0
2
2
2
1
0
0
0
0
1
2
0
2
1
0
2
0
1
2
0
2
2
1
0
1
0
0
1
0
2
0
1
1
1
0
2
0
1
0
1
0
2
0
1
1
1
2
2
0
1
3
0
1
1
2
2
1
2
1
0
0
3
1
2
1
0
0
1
2
1
1
0
1
1
0
2
2
1
0
1
1
0
2
1
1
1
0
0
0
0
0
0
0
1
0
0
1
1
2
0
1
0
0
2
0
2
1
1
2
0
0
1
2
0
2
0
1
0
0
1
0
1
0
0
2
0
0
0
1
0
0
0
1
1
2
1
0
0
2
1
0
0
1
1
2
1
1
0
1
2
3
2
0
1
1
1
3
1
2
1
1
0
1
2
0
0
2
1
2
1
2
0
0
2
0
0
0
0
1
0
1
0
0
0
1
2
1
1
2
2
0
0
0
1
1
2
1
0
1
2
0
0
3
0
2
2
1
1
0
1
2
2
0
0
1
0
1
0
2
1
0
0
0
0
0
0
0
1
0
1
0
1
0
1
1
1
1
2
2
1
0
0
0
0
1
0
3
0
0
0
0
0
1
1
0
0
1
2
1
1
1
1
1
1
1
1
1
0
1
1
0
0
1
1
0
0
1
2
1
0
2
0
1
8
0
2
0
0
0
1
2
2
0
0
2
0
0
1
1
0
2
0
0
1
0
0
0
0
0
0
2
0
1
0
0
1
2
0
1
2
0
1
1
1
0
2
1
0
2
1
1
0
0
1
0
2
0
1
2
1
1
1
1
1
2
0
0
1
2
1
1
1
1
0
2
1
0
2
2
1
0
1
1
2
0
2
1
1
0
0
0
0
1
1
1
0
1
0
2
2
1
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
1
1
1
1
1
0
0
2
0
1
1
0
2
0
0
1
1
0
1
0
3
1
2
1
1
2
1
0
1
1
0
0
1
2
1
0
1
0
3
0
0
2
1
1
0
1
1
0
1
0
2
0
1
0
0
2
1
0
0
2
1
1
0
1
1
1
1
2
0
1
3
0
2
2
0
0
0
1
1
1
1
2
0
1
0
0
0
2
1
0
0
0
2
1
1
1
2
1
2
2
1
0
0
0
0
1
1
0
1
0
0
0
1
2
1
2
0
1
0
1
0
2
0
1
2
2
1
1
2
0
0
0
0
1
1
0
1
2
2
2
0
1
1
0
2
1
0
0
6
0
2
0
1
2
1
1
0
3
0
0
0
0
1
1
2
1
0
0
2
0
1
1
0
0
0
0
1
1
0
0
0
2
0
0
0
2
0
0
2
0
1
2
2
1
2
2
1
0
2
2
1
1
1
1
1
0
1
0
1
1
2
5
1
1
0
1
0
2
0
1
1
5
0
0
0
0
2
2
0
0
0
0
1
1
2
0
0
1
1
1
0
0
2
0
0
1
1
1
1
0
0
1
1
1
0
2
0
0
2
0
0
1
1
1
0
1
1
1
0
1
0
1
2
0
0
1
0
2
1
2
0
0
0
0
2
2
1
0
1
2
0
2
0
1
1
0
1
0
1
0
0
0
1
1
1
1
2
1
0
2
1
0
0
0
0
1
1
1
0
1
1
0
0
1
2
2
2
0
0
1
0
1
0
1
1
0
1
1
1
0
0
1
0
1
1
0
1
2
0
0
0
0
0
1
0
1
1
2
0
1
1
0
2
2
1
2
1
0
2
0
0
0
0
1
0
1
1
0
0
1
0
1
1
1
0
2
1
1
2
0
1
1
1
1
1
1
0
1
0
2
2
1
1
0
1
0
1
2
0
1
1
0
2
0
1
0
2
0
0
0
0
1
2
1
2
2
0
0
1
2
0
1
2
0
1
2
1
0
0
0
0
2
1
2
2
0
2
1
0
0
1
1
1
2
0
2
1
0
0
0
1
2
2
0
2
1
1
1
2
0
2
0
0
0
1
0
1
2
0
0
0
0
0
1
0
2
0
2
1
0
1
0
1
0
1
1
1
1
1
0
2
1
2
0
2
2
0
0
0
1
1
0
1
1
0
0
1
2
2
1
1
0
1
1
1
1
1
0
0
0
1
0
1
0
1
0
0
0
2
1
1
0
2
0
0
0
1
0
0
1
1
2
2
0
0
0
0
0
0
0
3
1
0
0
0
1
0
2
2
2
0
0
0
2
0
0
0
1
2
2
2
0
1
0
0
1
2
0
0
0
0
0
0
2
2
3
1
2
1
1
2
2
0
0
2
1
0
1
2
0
1
1
1
0
0
0
2
0
0
0
1
0
1
3
1
1
2
0
2
1
0
0
1
1
0
0
2
1
1
0
2
4
0
1
2
0
2
2
1
2
2
1
0
0
0
2
0
1
1
2
1
0
2
1
0
6
2
0
0
1
1
1
1
1
2
0
2
1
1
2
0
2
0
2
0
1
0
0
0
2
1
0
2
1
1
1
1
2
0
2
2
0
0
0
0
2
1
0
0
0
0
1
2
1
0
1
3
0
0
2
2
2
0
1
1
1
1
0
0
0
1
0
2
1
1
2
1
1
0
1
1
1
1
0
1
0
1
1
1
0
0
0
1
1
0
2
1
1
0
1
0
0
1
2
0
0
0
1
0
1
0
2
0
0
0
0
1
2
1
0
1
0
0
2
1
0
0
1
0
1
1
0
0
1
0
2
0
0
0
0
1
1
0
0
1
0
2
0
3
0
2
2
1
2
1
0
0
0
1
0
1
0
1
1
1
1
0
1
0
1
1
1
0
2
2
1
1
2
0
1
1
2
0
2
0
0
0
0
0
0
2
2
1
0
1
0
0
2
0
0
2
1
2
1
1
2
0
2
1
2
2
2
0
0
2
2
2
1
2
0
2
3
2
0
0
0
0
1
1
2
0
2
0
2
0
0
0
0
2
2
2
1
0
0
0
0
0
0
1
2
2
2
1
1
1
2
1
0
1
1
1
0
1
1
0
0
1
0
1
1
0
0
0
1
0
1
0
1
1
1
0
0
1
1
0
1
0
2
0
0
1
0
2
1
2
2
1
0
1
2
0
0
1
2
2
0
1
0
0
1
1
2
2
0
0
1
2
1
2
2
1
2
1
1
0
1
0
1
1
1
0
0
0
0
0
1
2
0
1
1
1
0
1
1
0
0
0
1
1
0
0
0
1
2
0
0
0
0
3
0
0
1
1
0
1
2
0
0
0
0
2
2
0
0
0
2
1
1
0
0
0
1
2
0
2
0
1
0
1
2
0
2
1
1
0
0
2
1
1
1
1
0
1
0
0
1
2
0
0
1
1
1
2
0
1
0
2
1
0
0
0
1
0
0
1
0
1
1
1
0
1
0
2
1
2
1
2
1
0
0
0
1
1
2
0
1
0
0
1
1
0
2
1
2
1
0
0
0
2
1
1
1
1
0
2
1
0
1
1
2
0
0
0
1
0
2
1
1
0
0
0
1
3
1
0
1
2
0
2
0
2
1
0
0
0
0
0
0
2
1
1
0
1
2
1
0
2
0
2
1
2
1
0
0
0
2
1
0
1
0
1
0
1
0
1
0
1
0
1
3
2
2
2
2
0
0
2
0
0
0
0
1
1
1
0
1
0
1
4
1
1
2
2
2
1
1
1
0
2
1
0
1
1
2
1
2
1
1
2
0
1
1
1
0
1
1
0
1
1
0
1
0
1
2
1
1
1
1
0
0
0
1
0
2
0
2
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
1
2
1
2
0
0
0
0
0
1
1
3
1
1
0
1
1
0
2
0
2
1
3
1
1
2
0
1
0
0
2
1
1
0
0
2
0
0
1
2
0
0
1
1
0
1
0
0
1
1
0
0
0
0
1
0
0
1
1
0
1
0
0
1
0
1
0
0
1
0
1
1
0
0
1
3
1
2
0
0
0
1
1
0
1
0
1
0
2
1
0
0
1
1
2
1
1
0
1
1
2
2
1
0
1
1
0
2
2
2
1
0
0
2
2
1
0
0
1
0
2
0
3
0
1
2
0
2
0
0
1
1
1
2
1
1
0
0
2
1
1
3
0
1
0
0
0
0
0
0
0
0
2
0
1
1
2
2
1
2
0
2
0
0
1
2
1
0
2
0
1
2
1
1
2
1
1
1
0
0
0
2
1
2
1
0
1
0
2
1
1
2
1
1
0
0
1
0
2
2
2
1
1
1
0
1
1
0
1
2
1
1
2
0
1
1
1
2
1
0
0
2
0
0
0
0
0
1
0
1
0
0
2
1
1
1
0
1
0
8
0
2
2
2
1
0
1
1
1
0
2
1
0
0
2
1
0
2
0
1
1
1
3
1
2
0
0
0
1
0
1
0
1
0
1
0
0
2
1
0
2
2
0
1
2
1
2
1
1
1
2
0
2
0
1
2
1
1
0
2
1
2
1
1
2
2
0
1
0
2
0
1
0
1
1
1
1
0
0
1
2
2
1
0
1
0
1
0
0
0
2
1
2
0
0
0
1
1
1
0
0
0
0
1
1
2
0
1
2
0
0
0
1
0
2
1
1
1
1
1
1
0
2
2
2
0
1
0
0
1
2
0
2
1
1
0
0
1
1
1
0
1
2
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
1
0
0
0
0
0
1
0
2
1
0
0
1
2
2
1
1
1
1
2
1
0
3
0
0
0
0
0
0
1
1
1
2
2
1
0
0
1
0
1
2
0
1
0
2
1
0
0
1
0
1
0
1
1
2
2
0
0
3
0
2
0
0
2
1
2
2
1
2
0
0
0
0
1
3
0
0
1
1
2
0
1
0
0
0
0
2
0
1
0
0
0
1
0
0
2
0
0
0
0
1
0
0
1
1
1
1
2
0
2
1
1
1
2
0
2
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
3
1
2
1
2
2
1
0
1
0
2
1
1
1
1
1
1
0
0
2
1
2
2
1
1
1
0
1
1
0
1
0
0
1
0
1
1
1
2
1
2
0
2
1
2
0
0
1
1
1
1
0
1
0
0
1
2
1
1
1
0
0
1
1
0
1
0
0
2
0
2
0
0
1
1
1
0
0
0
2
2
1
1
2
2
1
1
1
1
2
2
0
2
2
1
0
1
0
0
3
1
1
1
2
1
1
1
0
1
2
1
0
1
1
0
0
1
2
1
0
0
2
1
2
1
1
0
0
0
1
0
0
1
2
2
1
1
1
0
2
2
0
2
0
2
1
0
0
0
0
1
3
1
0
1
0
2
0
1
0
1
0
1
0
2
1
1
1
0
2
0
1
1
1
1
1
1
0
0
0
1
2
2
0
1
2
2
1
0
2
2
1
0
1
2
0
1
0
1
0
0
1
1
0
1
1
1
1
0
0
1
2
2
1
3
0
1
0
1
2
1
0
0
2
2
0
2
1
0
2
0
0
1
0
1
0
2
0
1
1
1
1
2
0
1
1
1
2
1
1
0
2
1
2
2
1
0
0
1
1
0
2
1
0
2
2
0
1
1
1
1
2
0
2
0
1
0
0
0
1
1
0
0
0
1
1
2
0
1
1
0
1
0
2
1
2
2
1
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
1
4
1
2
0
0
1
0
2
0
2
2
0
2
1
2
1
1
0
2
2
1
0
1
1
2
0
1
0
0
0
1
1
0
0
1
1
4
0
0
1
1
1
2
1
0
2
0
0
0
1
0
1
0
0
2
0
1
1
2
1
1
0
2
1
0
2
2
0
2
0
0
0
1
1
2
1
0
1
0
1
2
1
0
1
0
3
0
2
1
0
2
0
3
2
2
1
2
0
0
1
2
2
0
0
0
0
0
2
1
0
2
1
0
2
1
1
1
1
2
1
1
0
3
0
2
1
2
0
2
1
1
0
2
2
2
1
0
1
1
2
1
0
1
2
0
2
0
1
2
2
0
0
0
1
2
0
0
2
1
0
0
1
0
0
2
0
0
3
2
2
0
1
1
1
0
2
0
2
0
1
2
1
0
0
1
1
0
1
0
1
0
0
0
2
0
0
1
0
0
2
0
1
2
1
0
0
2
0
0
2
0
1
1
0
1
1
1
0
2
0
0
0
2
1
0
0
0
2
1
1
1
2
1
0
0
1
0
2
0
1
2
0
2
2
0
1
0
1
1
0
0
1
1
2
0
2
1
0
1
0
0
0
0
2
0
0
2
1
1
2
1
0
2
0
2
1
2
1
0
1
1
0
0
0
0
1
2
1
3
0
2
2
0
0
2
1
0
0
0
1
2
2
1
1
1
0
0
3
2
0
2
1
0
2
0
1
3
0
2
1
0
1
1
11
0
0
2
0
0
0
1
2
1
2
2
2
2
1
0
1
0
0
0
2
1
1
2
1
2
1
0
2
1
0
1
1
2
1
1
1
0
1
0
0
2
2
0
1
2
0
1
1
2
0
1
2
2
1
1
0
2
0
1
0
1
1
2
0
1
0
2
0
0
0
0
2
0
1
0
2
1
2
0
1
0
1
0
0
1
1
1
1
2
1
1
3
0
0
1
0
1
1
0
0
1
2
0
0
1
2
0
0
1
1
0
2
0
1
2
2
0
0
1
0
1
0
0
2
1
0
0
0
0
1
1
1
1
1
0
2
1
1
0
0
0
2
0
2
1
1
0
2
1
0
1
0
0
2
1
0
1
0
0
0
2
1
1
0
1
1
0
2
1
1
0
2
0
0
0
0
0
0
0
0
0
2
1
2
0
2
1
1
0
3
1
1
1
2
1
0
1
0
0
2
0
0
2
1
0
1
0
0
2
0
1
2
2
2
2
0
1
0
0
0
0
1
2
0
1
1
2
1
1
0
2
0
1
1
1
2
0
0
2
2
1
1
0
2
0
1
0
1
1
0
0
2
1
2
3
0
1
2
0
0
1
0
0
1
2
0
0
1
1
1
0
1
0
0
1
1
1
0
2
0
1
1
3
2
0
1
0
1
0
0
1
0
2
2
2
1
1
0
2
0
2
0
1
2
0
0
0
2
0
1
2
2
0
1
0
0
1
1
2
0
0
0
0
2
1
1
1
1
0
1
0
2
2
4
0
2
0
0
2
1
2
1
1
1
0
1
2
1
4
0
0
0
1
0
0
0
2
0
0
0
0
1
1
2
1
2
1
1
1
1
0
0
0
0
2
2
1
2
2
1
0
2
1
0
0
0
0
1
2
0
1
0
1
0
2
0
1
1
1
0
1
0
1
0
0
0
0
1
1
0
1
0
1
2
2
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
2
1
0
2
1
2
0
1
1
1
1
1
0
0
2
2
1
0
1
2
2
0
1
1
1
0
1
1
2
2
0
0
0
0
1
2
0
0
2
1
0
0
1
0
1
0
0
0
2
0
2
1
2
1
1
0
0
0
1
0
1
1
0
1
0
0
2
0
0
2
1
2
0
1
1
0
2
1
1
0
2
1
0
2
1
0
2
1
1
2
1
0
1
0
1
0
2
0
0
0
1
0
0
1
1
1
0
0
1
1
2
0
1
0
2
0
0
1
0
0
2
0
0
1
2
1
0
0
1
1
0
1
1
0
1
1
2
1
0
0
2
3
1
0
0
2
1
1
0
0
0
1
0
0
1
0
0
3
1
0
1
0
1
0
0
0
0
1
1
0
0
0
0
2
0
1
0
0
1
2
1
0
2
0
1
1
1
1
0
0
0
0
2
0
0
0
0
2
0
0
0
1
2
0
1
2
1
0
2
2
1
1
0
0
1
0
1
1
1
1
1
1
0
1
0
0
1
1
1
1
1
0
0
2
2
1
2
0
2
0
3
1
2
1
1
0
1
2
0
0
1
1
0
0
0
1
1
1
2
0
1
0
1
2
1
1
2
2
1
2
0
0
1
1
2
2
0
0
1
1
0
0
2
2
0
2
2
0
1
1
1
0
2
0
1
0
0
2
1
1
1
1
1
2
0
1
1
0
1
1
1
0
0
1
0
2
2
1
0
2
0
0
0
1
0
0
0
0
0
1
0
2
1
1
0
1
1
0
2
1
1
0
2
1
0
2
0
1
0
3
2
0
2
1
1
1
1
1
1
2
1
2
0
1
2
2
0
2
2
1
1
1
2
1
0
0
0
0
0
0
1
0
2
1
0
1
0
0
0
2
0
0
1
2
1
0
0
1
1
1
1
1
2
1
2
1
1
2
1
0
0
1
2
2
1
1
0
2
1
0
1
1
3
1
0
0
0
1
0
1
0
1
1
2
0
0
0
1
0
1
1
0
2
1
1
1
1
1
0
0
2
0
0
0
0
0
1
1
2
2
1
2
0
1
0
0
0
0
0
0
2
0
1
0
1
1
1
0
2
2
0
0
1
1
1
0
2
1
1
0
0
0
1
0
1
1
1
1
0
0
1
0
2
0
0
2
0
0
0
1
0
0
1
1
0
0
0
2
1
0
2
1
0
0
0
0
1
0
1
0
1
1
1
0
0
0
1
0
1
0
3
2
0
2
0
0
3
0
2
0
2
1
0
1
2
1
0
0
1
0
1
1
1
0
2
1
0
7
0
1
2
0
2
0
2
2
0
0
2
0
2
0
0
2
0
1
1
2
1
1
0
0
0
0
0
2
1
0
0
0
0
2
1
1
2
0
0
0
0
1
0
0
1
0
2
1
2
0
0
1
1
2
1
1
0
2
1
0
1
1
1
1
0
2
0
0
2
1
2
1
2
1
1
1
2
1
0
2
1
0
1
0
0
0
0
1
2
0
0
1
0
2
2
1
0
1
0
1
0
1
1
0
1
1
0
0
1
2
0
3
0
1
1
0
0
0
1
0
0
2
0
1
2
0
1
2
1
1
2
0
1
0
2
1
2
0
1
3
1
1
2
1
0
2
0
0
1
0
2
1
2
1
2
1
2
1
1
0
0
1
0
1
1
2
2
1
1
0
0
1
1
1
1
2
2
1
2
1
2
0
2
0
1
2
1
3
0
1
1
0
1
1
1
0
1
0
0
0
1
1
2
0
0
0
0
1
2
1
2
1
1
2
1
1
1
1
0
1
0
1
1
0
0
2
2
0
0
0
1
2
1
1
2
1
0
0
0
0
1
2
1
1
0
2
1
0
1
1
1
1
0
1
0
1
2
0
1
0
1
0
1
1
0
0
2
0
2
0
0
0
2
0
2
2
1
1
0
0
1
0
2
1
1
0
2
0
1
1
0
0
0
1
0
1
0
1
1
2
1
0
2
2
0
1
1
1
0
1
1
0
0
0
1
2
2
1
0
1
1
0
2
2
2
1
1
2
1
0
0
0
1
2
1
1
0
0
0
1
0
0
2
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
3
0
2
1
1
0
2
0
0
2
2
0
1
1
1
2
0
1
2
0
0
0
2
1
2
0
2
0
1
1
1
2
0
0
0
2
0
0
0
2
0
1
0
1
0
2
1
2
2
1
0
2
2
1
1
2
1
0
1
2
1
0
1
0
0
1
0
0
1
1
0
0
2
0
0
1
1
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
2
0
1
1
0
0
1
2
0
2
1
0
1
0
1
1
2
2
0
0
1
0
1
1
1
1
1
1
0
0
1
0
2
2
0
0
2
1
1
0
13
2
0
1
0
0
2
0
2
0
1
2
1
0
1
2
2
0
0
0
1
1
0
0
1
1
1
0
1
0
0
0
0
1
2
1
1
0
1
0
2
0
2
1
0
1
2
1
1
1
1
1
0
2
1
1
0
2
0
1
1
0
1
1
3
1
2
2
0
0
2
1
0
1
1
1
0
1
1
0
2
1
0
0
1
3
1
1
1
0
1
0
1
0
1
0
1
0
0
0
1
2
1
0
1
2
1
1
1
1
0
0
0
2
1
0
0
0
0
0
0
0
0
1
1
0
2
0
0
1
0
2
1
1
0
1
1
0
0
2
1
0
0
1
2
1
0
0
2
0
2
1
0
0
0
0
1
0
2
0
0
1
1
2
0
0
0
0
2
3
0
1
2
2
1
0
0
2
2
1
1
1
0
0
1
2
2
0
1
1
1
1
1
0
1
2
1
0
1
0
0
0
1
1
0
2
2
2
0
1
0
2
0
2
0
0
0
2
0
1
1
3
2
2
0
2
2
0
2
2
2
0
1
1
1
4
1
1
0
1
1
0
1
1
3
0
1
1
0
2
2
0
1
1
0
0
4
2
1
1
1
2
0
1
1
2
1
2
0
0
1
0
0
1
0
1
0
0
1
0
1
1
1
1
0
0
0
2
0
2
0
1
0
0
1
2
1
2
0
0
2
1
1
0
1
0
0
1
0
0
0
0
1
0
1
1
2
0
0
1
0
0
2
0
1
1
0
3
1
1
1
1
2
0
2
1
0
1
1
0
1
2
0
1
0
1
1
0
2
0
0
2
0
0
0
1
0
0
0
1
0
1
0
0
2
1
0
1
0
0
0
1
1
1
1
1
0
1
2
0
2
2
0
2
0
2
1
0
1
0
1
2
2
0
1
1
0
2
0
0
0
1
0
1
1
1
0
1
2
1
0
0
1
2
0
0
0
0
0
0
0
0
1
1
1
2
1
0
0
0
0
0
1
2
0
1
0
0
0
1
0
2
0
0
1
0
0
0
1
0
1
4
1
3
2
0
0
1
2
2
0
0
1
0
1
0
0
1
2
0
0
0
1
0
0
0
2
1
1
2
0
1
0
0
1
0
0
1
0
1
2
2
0
0
1
2
0
1
2
0
1
1
1
1
1
0
0
0
0
0
1
1
1
0
0
0
2
0
0
3
1
1
0
0
0
1
1
2
0
0
1
0
1
0
0
0
1
1
1
0
0
1
2
0
1
0
1
1
1
1
2
1
0
2
0
1
0
2
0
3
1
2
2
2
1
1
0
0
1
2
1
0
1
1
2
0
0
1
0
1
1
0
1
2
1
1
1
2
0
2
0
0
1
1
0
1
0
1
2
1
1
2
1
0
0
0
1
1
1
1
7
0
2
0
0
1
0
2
1
1
0
1
1
2
2
0
0
2
1
1
0
2
0
0
0
0
1
0
0
2
1
0
1
1
2
0
0
0
2
1
1
0
0
0
2
0
0
0
2
0
0
2
1
0
2
1
1
1
0
0
3
0
1
0
0
1
0
1
1
2
2
0
1
1
2
4
0
1
0
2
1
2
0
2
1
0
0
0
0
0
1
0
1
0
0
0
2
1
1
1
1
1
1
0
0
0
2
1
0
2
1
2
1
2
0
0
1
2
1
0
0
0
0
2
4
1
0
1
0
0
0
2
0
2
0
0
4
1
2
2
0
1
0
0
2
1
0
2
1
2
0
2
0
2
2
2
0
2
0
2
0
0
0
1
0
1
0
1
1
2
0
1
0
0
0
1
1
1
1
0
0
8
1
1
0
0
1
0
0
1
1
1
0
2
3
1
2
1
0
0
2
0
1
0
1
0
0
0
0
1
1
1
1
2
1
0
0
1
0
3
1
0
0
1
0
2
0
0
2
0
1
1
0
0
1
0
1
0
1
1
0
1
2
1
0
0
0
2
1
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
2
1
2
0
3
2
1
0
2
2
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
2
0
1
0
2
0
0
0
1
2
3
1
2
1
0
0
2
2
1
1
0
0
1
0
1
0
0
0
2
0
1
0
1
1
0
0
1
1
1
0
0
4
0
1
1
2
1
0
0
1
2
0
0
0
0
1
0
0
2
0
0
0
1
0
0
2
0
1
2
2
1
0
0
2
1
2
0
1
0
0
0
1
0
0
1
1
1
1
0
0
1
1
0
2
0
1
0
0
0
0
1
0
1
0
2
0
0
2
1
1
0
0
0
1
1
1
0
0
1
1
0
1
0
1
0
1
0
1
0
0
0
1
1
1
1
1
1
1
1
1
1
2
0
3
0
0
1
2
1
2
0
2
2
0
0
0
2
0
1
0
1
0
1
0
1
0
0
2
0
2
0
1
2
1
1
0
0
1
2
1
3
0
1
3
1
1
2
2
1
0
0
1
0
2
0
3
0
0
1
1
1
1
1
1
1
2
1
1
2
2
0
0
1
1
2
2
0
2
0
0
1
0
2
0
1
2
1
1
0
0
0
0
2
2
0
1
1
1
1
0
0
2
1
0
2
0
0
1
2
0
1
2
2
1
0
0
0
1
1
1
0
1
2
2
0
0
1
0
0
1
0
0
1
2
2
0
1
1
0
1
2
0
2
2
2
1
0
0
1
0
0
1
2
2
1
0
1
2
2
0
1
2
0
1
1
1
0
1
1
0
2
0
1
0
1
0
2
1
2
1
0
1
0
2
0
0
0
2
0
0
2
0
1
0
1
0
0
2
1
0
0
1
1
0
2
1
2
0
1
1
1
4
1
0
2
1
0
1
0
0
0
2
1
0
1
0
1
0
0
1
1
0
1
0
2
1
0
0
3
0
2
1
0
1
0
0
2
0
1
1
2
0
0
2
1
0
1
0
0
0
2
1
1
1
1
1
0
0
0
1
0
0
0
2
2
1
1
1
3
0
0
1
0
0
1
0
0
2
2
0
0
0
0
1
0
1
1
0
1
0
0
2
1
0
0
0
0
1
1
2
1
0
0
0
2
1
1
1
2
0
0
2
2
1
1
1
0
2
0
0
1
0
0
2
1
1
0
1
1
0
0
0
1
0
2
0
2
0
1
0
0
1
1
2
0
3
0
0
1
0
2
2
1
2
2
0
1
0
0
1
2
2
0
0
2
0
0
1
2
0
1
2
0
1
1
1
2
0
0
2
2
1
1
2
0
2
2
1
0
0
1
0
1
1
0
0
0
1
0
0
2
0
0
1
0
1
1
0
1
1
1
0
2
0
0
2
0
0
0
2
2
2
2
0
1
1
1
2
1
0
2
1
0
0
1
2
0
1
1
0
1
0
0
1
2
2
0
2
0
1
0
0
0
2
1
1
0
0
1
0
0
1
1
1
0
0
1
0
4
2
0
0
2
0
1
0
1
0
1
0
0
0
1
0
2
0
1
0
1
2
1
1
1
1
1
2
1
2
1
1
2
0
0
0
1
0
1
1
3
2
0
3
2
1
1
0
1
1
0
2
0
1
1
1
1
1
1
0
1
0
2
1
2
0
0
1
0
1
0
0
3
2
2
2
2
1
1
2
2
2
0
0
0
2
1
0
2
0
2
1
1
0
2
1
1
2
0
1
0
1
0
0
0
1
3
1
0
0
1
1
1
2
2
0
0
2
1
1
1
2
0
1
0
0
0
0
2
0
0
2
1
1
0
1
2
2
0
2
2
0
1
1
1
1
1
1
0
1
1
0
0
2
0
2
1
2
0
0
0
0
1
0
1
0
1
0
2
3
0
1
0
0
0
2
1
0
1
0
0
1
2
1
2
0
0
1
3
0
0
0
0
3
0
1
0
1
2
2
0
0
0
0
3
2
0
1
1
4
1
0
3
1
2
1
1
2
1
2
2
2
1
1
2
2
0
2
2
0
2
0
0
1
1
1
2
1
1
0
2
2
2
1
0
1
0
0
0
1
1
0
1
1
0
0
1
1
2
1
0
2
0
2
1
2
2
0
0
1
0
1
1
0
2
2
0
2
1
0
2
1
2
0
0
0
2
3
0
2
1
2
0
0
0
1
2
2
0
2
1
1
2
2
0
1
2
2
0
2
0
1
0
1
3
0
3
0
1
1
2
1
0
0
1
0
2
1
2
1
2
1
0
2
1
0
1
1
2
2
1
1
1
1
0
2
1
0
2
2
0
0
1
2
1
1
0
2
3
1
2
1
0
0
1
2
1
0
2
1
1
0
2
2
0
1
0
0
1
0
2
2
2
1
2
0
2
1
1
0
0
2
0
0
3
0
2
0
0
1
0
0
0
0
1
1
0
2
0
0
1
1
2
0
0
1
2
1
2
0
0
1
0
0
1
1
1
0
0
0
2
0
0
2
0
0
2
2
0
2
1
0
0
0
0
0
1
0
2
1
0
1
0
1
0
1
0
0
0
2
1
0
2
0
0
2
1
1
0
1
0
2
1
2
1
1
2
1
0
0
2
2
0
2
2
2
2
0
1
0
0
0
0
2
1
2
2
3
2
1
0
0
3
2
0
0
1
1
0
0
2
0
1
1
2
1
1
0
0
0
1
2
1
0
0
2
0
0
1
0
0
1
0
1
0
0
0
0
2
1
0
1
1
2
1
1
0
2
0
0
1
2
2
0
1
0
1
1
1
1
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
2
0
1
2
1
2
0
2
2
1
0
1
1
0
0
2
1
1
0
1
1
0
1
0
0
0
1
2
1
1
1
1
2
1
0
1
0
1
0
1
1
1
2
1
1
1
2
0
1
3
0
2
1
2
0
2
2
0
1
1
0
1
1
2
0
0
0
1
0
0
0
1
0
1
1
1
1
0
0
1
1
0
1
1
0
1
0
0
0
0
0
0
1
1
0
0
2
1
1
0
2
2
0
0
0
1
0
2
0
2
0
2
0
2
0
1
0
1
5
0
0
1
2
1
1
1
1
1
0
1
2
0
1
0
0
1
2
1
0
1
0
1
0
1
0
1
2
0
0
1
2
0
1
1
0
1
2
0
1
0
2
2
0
0
0
0
0
1
1
0
0
1
0
2
2
0
1
1
1
0
0
2
1
1
0
1
0
1
2
0
1
0
2
2
0
0
0
1
1
2
0
1
0
1
1
1
1
0
0
2
2
0
1
0
2
0
1
4
0
0
2
1
2
1
1
1
1
1
0
1
2
1
0
2
0
1
2
0
0
0
1
1
0
1
1
2
1
0
1
1
0
0
0
0
0
2
1
0
0
1
0
2
0
0
0
1
0
0
2
1
0
0
0
0
0
0
1
0
0
0
1
2
2
0
0
0
0
0
1
2
1
0
1
1
4
0
0
0
0
1
0
3
1
0
0
2
1
2
0
0
0
0
1
1
0
0
1
1
0
0
2
0
1
0
0
0
1
0
0
0
2
1
0
2
0
2
1
0
0
0
2
1
0
1
0
1
1
2
0
0
0
0
2
0
1
0
0
1
2
0
2
0
2
1
0
0
1
0
1
2
1
0
1
0
2
2
0
1
2
2
1
1
2
1
0
1
0
0
0
0
1
1
1
0
0
2
0
0
0
1
0
0
2
0
2
1
1
0
0
2
2
2
0
0
0
0
0
1
0
0
1
1
1
2
2
0
1
2
0
1
1
0
0
1
0
2
0
0
0
1
1
0
0
2
0
1
0
0
1
2
1
1
0
0
0
1
2
0
1
1
1
3
1
2
1
1
2
0
1
1
0
2
1
0
2
1
0
1
1
0
0
0
1
2
1
2
0
1
2
0
1
1
1
0
1
0
0
2
1
0
0
2
0
0
1
2
1
2
1
0
0
1
0
2
1
2
2
0
0
2
1
2
3
0
2
5
0
0
1
0
2
1
0
2
1
1
0
1
1
0
1
2
1
2
0
2
1
1
0
0
2
0
0
1
0
1
0
0
2
2
2
1
0
1
0
1
1
0
2
1
0
1
1
0
1
0
0
1
0
0
2
0
2
0
2
1
1
1
2
0
0
0
0
1
2
0
2
3
1
0
0
2
0
0
0
0
1
0
0
0
0
1
1
0
2
2
2
2
0
0
0
6
0
1
2
2
0
1
2
1
0
1
2
2
0
0
1
1
0
0
0
1
2
0
2
1
1
1
1
2
1
1
1
1
1
0
2
1
2
2
1
0
0
1
0
0
2
0
1
2
2
1
0
3
3
1
1
2
2
0
1
2
0
1
1
1
1
2
1
0
1
1
1
0
1
1
1
2
0
2
1
1
0
0
0
1
1
1
0
2
0
1
1
2
1
1
2
0
0
0
0
2
1
0
0
1
1
0
0
1
2
2
0
1
1
1
0
0
1
0
0
1
1
0
2
1
0
0
2
0
1
2
2
0
2
2
2
1
1
1
0
0
2
0
0
1
0
1
3
1
2
2
0
1
2
1
1
1
2
1
1
1
1
2
1
1
1
2
0
1
1
0
1
0
2
1
1
0
0
0
1
1
1
1
1
1
0
2
2
0
1
1
2
2
0
1
0
2
0
2
2
0
0
1
1
0
2
2
1
2
2
0
0
0
1
1
0
2
1
1
0
0
1
0
1
0
2
1
2
2
0
1
0
1
0
2
3
2
1
0
1
0
0
0
1
2
0
3
0
1
0
0
0
1
2
1
0
0
6
0
0
0
0
2
1
2
1
0
0
2
0
0
0
0
1
1
1
2
2
1
0
0
2
0
0
2
0
0
1
1
1
1
1
1
2
1
0
1
2
2
2
2
1
3
2
0
1
0
1
0
2
1
0
0
0
0
2
1
1
0
2
1
0
2
1
0
1
1
1
0
1
1
2
1
2
2
2
0
1
1
0
1
2
1
1
0
0
1
2
1
1
1
0
1
2
2
1
0
0
0
2
2
1
1
1
0
1
1
0
2
1
0
0
2
2
0
2
0
1
1
1
1
2
1
1
1
1
0
1
0
2
0
2
2
1
0
1
0
1
0
0
0
0
1
0
1
1
0
1
0
3
1
2
2
2
1
1
0
0
1
0
0
2
0
2
2
0
2
0
1
1
2
0
2
1
0
1
0
1
1
0
1
1
0
1
0
2
1
2
2
1
0
0
2
1
1
0
1
0
1
0
1
0
0
0
0
0
2
1
2
0
0
2
1
1
2
2
2
1
0
0
2
0
1
1
0
1
1
1
1
2
0
0
0
1
0
1
0
0
0
2
0
0
0
2
2
0
1
0
0
2
0
0
1
0
0
0
2
0
0
1
0
1
1
1
0
0
0
2
1
0
0
1
0
1
1
1
0
0
0
0
0
0
1
2
1
2
0
1
0
2
2
1
2
1
0
3
1
2
2
0
1
0
2
1
0
1
1
1
1
1
1
0
0
1
0
1
2
1
0
0
0
1
1
0
0
2
2
0
2
0
1
0
0
0
1
0
1
1
0
0
1
1
2
1
1
2
1
1
0
0
0
1
0
0
2
0
1
1
0
1
2
1
2
1
0
2
0
1
1
2
1
1
2
2
1
0
2
2
1
3
0
0
0
0
1
1
1
1
0
1
1
3
1
1
0
0
1
0
1
1
1
0
1
1
1
2
0
0
1
1
1
1
0
0
2
0
0
0
1
1
0
1
0
0
1
0
0
0
1
1
0
0
1
0
1
1
0
1
0
1
0
0
2
0
1
0
1
1
0
0
1
1
1
0
0
0
1
1
0
2
4
0
1
0
0
2
1
2
0
0
0
0
2
2
0
1
0
2
0
0
2
0
1
1
0
2
2
1
2
0
0
2
2
2
2
2
0
1
1
1
1
1
0
5
1
1
1
2
0
2
0
1
0
1
3
2
2
0
2
2
0
0
1
0
2
1
1
0
0
1
0
2
3
0
1
1
2
1
0
0
0
1
2
1
0
1
0
1
2
1
1
0
1
1
0
0
2
2
1
2
2
0
0
1
1
1
1
1
2
2
2
1
2
1
2
2
0
1
0
2
0
2
1
1
1
0
1
0
2
0
1
2
1
1
0
0
0
0
0
0
0
1
0
2
2
0
2
0
0
0
0
1
1
0
1
1
0
1
0
2
1
0
1
3
1
0
0
0
5
0
0
0
0
0
1
0
0
0
1
0
0
2
1
2
0
1
0
1
0
1
1
0
3
2
2
0
1
3
1
0
2
1
0
0
0
0
2
2
0
1
0
0
0
1
1
0
0
1
0
2
0
0
0
0
2
1
2
1
1
0
0
2
0
2
0
2
2
1
1
1
1
0
3
1
0
1
1
0
1
0
1
1
2
2
0
2
2
2
2
1
1
2
0
1
1
1
0
1
0
1
2
1
0
1
2
0
0
1
1
1
1
2
1
0
0
0
1
0
0
1
0
1
2
1
1
0
2
0
1
1
2
2
1
1
1
0
1
0
1
2
0
0
1
1
0
1
0
1
1
1
0
1
0
0
0
1
1
0
1
1
0
2
0
0
2
2
1
2
3
1
0
0
2
0
1
2
1
1
1
1
0
2
1
0
2
2
0
0
0
1
1
1
1
1
0
0
2
2
0
1
0
1
1
2
1
1
0
1
1
0
1
0
0
0
0
0
0
1
1
0
1
0
1
0
1
1
0
1
3
1
1
0
1
0
0
2
2
2
1
0
2
2
0
1
1
1
1
1
1
1
1
2
0
2
1
1
0
0
0
0
1
0
1
0
2
2
0
0
2
1
2
0
0
0
1
0
0
1
0
1
2
1
2
1
2
2
0
0
2
0
2
1
0
0
1
2
2
0
1
1
1
1
0
2
1
2
1
1
1
3
1
2
1
2
0
1
2
2
1
0
0
1
0
1
2
1
0
0
0
0
0
2
2
1
0
1
2
0
0
0
0
1
0
1
2
0
1
1
0
1
4
1
0
0
0
0
0
0
1
1
1
1
2
2
1
1
1
2
2
1
0
1
0
2
0
1
0
1
2
1
0
0
1
1
1
0
0
2
2
1
1
2
2
2
0
1
0
0
0
1
2
0
1
0
1
0
1
0
1
1
2
0
0
0
0
1
2
0
1
1
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
3
0
2
0
0
0
0
1
1
1
1
1
1
0
2
2
1
1
1
1
0
1
1
1
0
0
1
1
1
1
0
2
0
0
0
1
0
0
1
1
2
0
0
1
0
0
1
0
0
0
0
0
2
1
1
1
2
1
1
1
0
1
2
0
1
2
2
0
1
1
1
0
0
0
3
0
0
1
0
1
1
0
1
1
1
1
1
1
0
0
1
1
1
0
1
2
0
2
0
0
2
0
1
1
0
1
0
1
0
1
1
0
0
1
0
1
2
0
0
0
1
0
2
0
1
0
0
1
1
0
2
1
2
1
1
2
2
0
1
2
0
1
2
1
1
2
2
0
2
0
0
0
0
2
0
2
2
1
1
1
1
1
1
0
0
0
2
3
2
0
0
0
0
4
2
0
0
1
0
1
0
0
0
0
1
1
2
2
0
0
0
3
0
0
0
2
1
0
0
1
1
1
2
0
0
1
2
1
0
1
1
2
1
0
1
2
1
0
0
0
0
2
0
3
0
0
1
0
0
1
1
2
1
0
0
2
0
0
2
2
0
0
1
0
1
2
0
1
1
1
1
2
1
0
1
2
0
1
0
0
0
1
1
0
0
0
1
0
2
1
0
1
0
1
0
1
2
1
0
2
0
0
1
1
1
1
2
0
1
0
2
1
1
1
1
2
0
0
1
0
0
0
2
2
1
0
1
1
0
0
0
2
1
0
2
1
1
0
0
0
1
2
2
2
2
1
0
1
0
1
0
0
0
1
0
0
1
2
1
1
1
3
1
3
0
1
0
0
1
0
2
1
2
0
0
0
2
1
1
1
1
0
2
1
1
1
0
0
2
2
0
1
0
0
1
1
0
1
2
1
1
0
1
0
1
1
0
0
1
1
0
0
0
1
1
0
2
1
2
1
0
0
2
2
0
1
2
1
0
1
1
0
0
1
0
1
2
0
2
2
2
2
2
1
0
1
2
1
2
2
1
1
2
1
3
1
1
0
0
0
0
1
1
0
2
0
1
0
1
2
1
1
1
0
0
0
0
1
2
2
2
3
0
1
0
2
2
1
0
2
2
1
0
1
0
2
1
3
1
2
1
1
0
0
0
2
1
1
1
0
2
1
0
1
0
1
2
2
1
0
1
1
1
1
0
1
1
0
2
0
1
1
1
0
0
1
1
1
1
0
0
2
0
1
0
1
2
0
2
1
0
1
1
0
1
1
0
2
1
1
0
0
0
1
1
0
1
0
1
0
1
1
0
0
1
0
1
0
2
0
0
0
1
1
1
2
2
0
1
2
0
0
2
0
0
1
0
0
2
2
2
2
2
0
1
0
0
0
0
1
0
1
1
3
1
0
0
0
0
1
0
0
0
1
2
0
1
0
5
0
1
0
1
2
2
0
2
0
2
2
0
0
0
0
0
0
0
0
1
2
0
0
1
1
0
2
2
0
0
2
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
1
3
0
1
1
3
2
0
1
2
2
1
0
2
2
0
1
1
0
1
1
0
0
0
1
1
0
2
0
2
1
0
0
2
1
0
0
0
0
0
1
2
1
1
1
0
0
1
1
1
1
0
2
0
2
0
0
2
2
0
0
0
0
1
1
1
0
2
1
2
1
0
1
2
0
0
2
1
2
1
0
2
2
2
2
0
1
0
1
0
1
0
2
1
0
0
0
1
0
2
2
2
1
2
1
1
0
1
2
0
1
2
3
1
1
0
1
0
1
0
1
1
1
0
0
2
1
2
2
1
1
1
1
1
1
1
1
0
2
2
1
2
1
1
0
1
0
0
0
1
0
0
1
0
0
1
1
1
2
1
2
0
1
0
2
0
0
0
2
2
0
0
1
0
3
1
1
1
0
0
1
1
2
1
0
1
0
0
1
1
1
2
1
2
2
0
0
0
0
1
0
0
1
1
0
0
2
0
1
1
0
0
1
0
2
0
2
0
0
2
0
2
2
0
0
2
1
2
0
0
1
0
0
0
1
1
0
1
1
1
1
0
0
1
2
1
0
0
0
0
1
1
1
0
0
0
0
0
2
2
0
0
0
0
2
1
1
2
2
0
2
1
2
1
1
0
0
1
1
1
0
0
2
1
0
0
2
0
0
2
2
0
0
0
2
0
0
0
1
2
1
2
0
1
1
0
0
2
2
0
1
0
0
0
1
0
3
0
2
0
1
1
2
1
1
0
2
2
0
1
2
0
1
0
2
1
2
2
1
1
0
3
0
1
0
1
2
1
2
0
1
1
2
1
1
1
1
3
3
0
0
0
0
1
0
0
0
1
0
2
1
0
1
0
0
0
0
1
1
2
0
0
0
1
0
0
1
0
1
0
2
0
1
1
0
0
0
2
0
1
1
0
1
2
0
0
0
2
0
0
0
1
0
1
0
1
0
2
0
0
2
0
2
1
0
0
0
2
0
0
1
0
1
2
1
0
0
0
0
2
1
0
0
0
0
2
1
2
2
0
0
0
1
1
0
1
1
1
2
0
1
2
0
0
0
0
1
0
0
2
1
0
2
2
2
0
1
0
0
0
2
1
0
0
1
0
2
0
0
1
2
1
1
1
0
1
1
0
2
2
0
1
1
0
0
1
2
0
1
1
0
0
0
0
0
2
1
0
2
2
2
0
0
2
2
0
0
1
0
0
2
1
2
1
2
0
0
0
2
0
1
5
0
0
1
0
0
2
2
0
2
2
1
2
0
1
2
2
1
1
0
0
0
0
1
0
1
3
1
1
0
0
0
0
2
1
0
1
1
2
0
0
2
0
1
1
2
1
0
0
0
1
1
1
2
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
2
1
0
2
1
2
2
1
2
0
1
2
0
0
0
2
2
0
0
0
1
2
1
1
1
0
0
2
0
1
2
1
0
1
2
0
1
0
1
2
1
1
0
1
0
0
0
1
1
1
2
1
0
2
1
0
0
0
1
2
1
1
1
0
0
0
1
1
2
1
1
1
1
1
0
0
0
1
2
0
0
1
1
1
2
2
2
0
1
0
1
2
0
1
1
1
0
2
2
2
0
0
0
0
2
0
2
0
0
0
1
1
1
2
1
1
1
0
2
1
1
2
0
1
1
2
1
0
0
1
1
0
1
1
1
2
1
0
1
2
0
1
0
2
0
3
0
1
0
1
1
1
0
1
0
0
0
0
2
2
0
1
1
2
0
2
1
2
2
1
0
1
2
1
2
0
1
1
2
1
0
0
0
2
1
0
0
0
0
0
0
1
2
0
2
0
0
1
2
1
2
0
1
0
0
1
0
1
0
1
3
1
1
0
0
2
1
2
1
1
2
0
0
0
1
1
0
0
1
1
1
1
1
1
2
0
0
1
2
0
1
2
0
0
0
1
1
0
1
0
1
2
1
1
1
2
0
0
0
2
0
0
2
0
0
0
1
0
1
1
0
1
1
1
1
0
0
1
2
0
2
0
0
0
0
1
2
2
2
1
1
0
0
0
1
0
0
2
1
1
0
0
1
0
0
0
1
1
1
0
1
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
2
1
2
2
1
1
1
2
0
0
1
2
0
1
1
0
0
1
1
1
2
0
1
0
1
2
2
1
0
1
2
0
0
0
3
2
1
2
0
1
0
2
0
1
0
0
2
1
1
0
0
1
0
1
0
2
1
0
0
1
0
1
2
0
0
0
2
1
1
3
2
0
0
0
2
1
0
0
2
0
1
1
1
2
0
0
2
2
2
2
2
2
0
0
2
0
1
1
1
0
2
0
2
0
0
0
2
0
1
0
0
1
1
1
2
1
1
1
1
0
1
1
0
2
1
0
1
2
2
0
1
1
1
0
0
1
1
1
0
0
1
2
2
0
1
2
4
0
0
2
1
0
0
0
0
0
1
0
8
1
1
0
0
0
1
0
1
1
0
0
2
2
2
1
0
4
0
2
0
1
0
1
0
1
2
0
2
0
1
2
0
0
0
0
0
0
0
2
1
2
0
0
0
1
1
0
1
1
1
1
1
0
0
1
0
4
1
0
1
0
1
0
2
0
0
0
1
1
1
0
0
1
1
0
2
0
0
1
0
0
2
1
0
0
0
1
2
1
1
0
0
0
0
1
0
0
0
2
0
0
2
0
1
1
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
1
0
2
1
1
2
1
1
0
1
0
0
0
2
0
2
0
1
3
0
1
0
1
2
2
1
2
1
0
0
2
2
1
0
0
0
0
2
1
2
2
3
0
0
0
0
2
2
0
1
1
0
1
0
1
0
0
0
1
1
2
1
1
0
0
1
0
0
1
1
2
1
1
1
0
0
0
0
1
2
0
1
0
1
1
0
1
1
1
0
1
0
1
1
0
2
1
1
1
0
2
0
1
2
1
0
1
1
2
1
1
3
0
0
0
0
0
0
1
2
0
6
0
0
0
0
2
1
1
1
0
0
0
1
0
2
0
0
0
0
2
0
0
0
1
2
0
1
0
0
1
1
1
1
1
0
2
0
1
2
0
2
1
2
1
0
1
1
2
0
0
0
1
0
1
1
0
0
1
1
0
0
1
0
0
1
2
0
0
3
1
0
0
0
1
1
0
0
0
3
2
0
0
2
0
0
0
0
1
1
0
0
1
0
0
2
0
0
1
1
1
2
2
2
1
1
0
0
1
1
1
2
0
2
2
0
2
2
0
1
0
2
2
0
0
2
1
0
2
2
1
0
0
1
1
1
2
0
3
0
1
1
0
1
3
1
0
2
1
0
0
2
1
0
1
2
0
0
2
2
0
0
0
1
2
1
2
1
2
0
0
1
2
0
1
1
0
1
2
2
0
1
0
1
1
2
1
0
0
1
1
0
0
2
0
1
0
0
1
2
1
0
2
1
0
1
2
2
1
1
0
1
1
0
0
0
2
1
1
0
0
1
1
1
0
1
1
3
2
1
0
1
2
0
0
0
1
1
0
1
0
0
1
1
1
0
1
0
0
1
1
2
1
0
0
2
1
2
0
2
1
2
0
0
2
0
2
0
2
0
0
1
1
2
2
0
2
0
1
0
1
0
0
0
0
1
1
0
2
1
0
0
1
0
2
1
1
0
0
1
1
0
2
1
2
2
1
1
0
3
1
0
2
1
1
0
2
1
1
0
0
1
1
2
0
1
2
2
0
2
0
1
1
1
0
0
2
1
0
2
2
0
0
0
2
0
0
1
1
1
0
0
0
3
1
1
0
2
2
0
0
0
1
1
2
1
0
2
1
0
0
0
1
0
0
1
0
0
0
1
1
0
1
2
0
0
0
1
2
2
0
0
2
2
0
2
0
2
2
1
0
2
0
1
2
1
1
0
2
0
1
10
2
0
2
0
1
1
1
0
0
1
1
0
1
0
0
1
0
1
1
1
1
1
0
0
0
2
3
0
0
1
1
0
1
2
1
1
2
0
0
0
0
1
0
1
1
0
1
0
2
1
0
0
0
1
1
1
2
0
0
1
1
2
1
0
0
0
2
0
0
0
2
0
0
1
2
1
0
1
2
1
1
0
4
2
1
0
0
1
0
1
2
0
1
2
0
1
1
2
1
1
1
3
0
0
0
0
1
1
0
0
0
0
1
1
1
2
0
2
1
0
1
1
2
1
0
2
0
1
0
1
0
1
1
3
2
0
0
0
2
0
0
0
0
1
1
0
1
2
1
1
1
2
0
1
1
2
1
1
1
1
4
0
0
1
1
2
2
1
1
1
1
1
0
0
1
0
2
0
0
1
2
0
0
0
1
1
2
0
2
1
1
0
0
0
0
1
0
2
0
0
2
0
2
0
0
1
2
1
0
3
2
0
1
0
0
1
0
1
0
0
1
0
1
0
1
1
1
0
2
0
1
2
3
0
1
2
1
1
1
2
2
0
0
1
0
0
0
0
1
0
0
2
1
2
2
2
0
0
1
2
2
0
1
0
2
1
0
0
1
2
0
0
0
0
2
4
2
0
0
1
1
0
2
0
1
0
2
0
3
0
0
0
1
2
1
2
0
1
1
1
0
0
0
2
2
1
1
0
0
2
2
2
1
0
0
2
0
0
0
1
0
0
0
2
2
1
0
1
2
1
0
0
1
2
2
0
2
1
2
1
2
1
0
0
1
1
0
0
0
0
0
0
1
0
2
0
0
0
2
0
1
1
1
2
1
2
0
1
0
2
1
1
1
0
0
2
0
0
0
2
1
1
1
0
1
0
1
1
1
0
2
1
0
2
0
1
2
1
1
1
0
0
2
2
2
2
1
0
0
0
2
1
0
1
2
1
0
1
2
0
0
2
2
1
0
1
2
1
0
1
0
2
1
2
0
0
1
0
0
0
1
2
1
0
1
0
1
1
0
0
1
2
0
1
0
1
1
1
1
0
1
0
2
0
0
0
0
2
1
1
1
1
1
1
0
1
0
2
1
2
0
0
0
0
1
1
1
2
2
3
0
0
0
0
0
2
0
2
1
1
0
1
1
1
0
1
1
2
1
0
2
0
0
1
0
0
0
2
0
0
1
0
2
1
2
1
1
1
0
1
2
1
0
2
1
0
2
0
1
1
1
1
2
0
1
1
0
0
0
2
2
1
1
1
0
1
0
0
0
1
0
0
2
1
1
2
2
1
2
0
1
1
0
1
0
2
1
2
1
0
0
0
1
0
0
1
0
1
0
1
1
2
0
0
1
0
1
2
0
1
0
1
0
1
1
0
0
1
1
1
0
0
0
0
1
2
0
1
1
1
1
0
1
2
2
1
2
0
1
0
0
1
1
1
2
0
2
0
1
2
0
2
2
0
0
0
0
2
1
0
0
0
0
0
0
3
2
0
1
0
1
1
1
0
0
1
1
2
0
2
0
0
1
1
1
1
0
0
1
2
1
1
0
1
1
2
0
0
0
0
3
1
2
0
0
0
0
2
1
0
2
1
0
1
0
0
0
1
2
1
0
0
1
0
1
0
2
1
0
1
0
0
0
1
0
0
0
1
0
0
3
2
2
0
0
1
2
1
0
0
0
0
2
0
1
1
2
1
0
0
1
0
0
2
0
2
0
1
0
0
1
0
1
1
2
0
2
2
0
2
1
0
1
1
1
0
0
2
0
0
2
2
2
1
0
0
0
1
2
1
1
0
0
1
1
0
1
0
1
0
0
0
0
1
1
1
0
0
1
1
0
1
0
1
2
0
2
2
1
2
1
0
1
2
0
1
0
0
0
0
1
1
2
2
0
0
2
0
1
0
2
1
2
1
1
1
2
1
0
2
0
0
1
0
2
2
0
1
3
1
1
2
0
1
0
0
0
0
2
0
2
0
0
0
0
1
0
2
1
1
1
0
2
0
1
1
1
2
0
0
0
0
3
2
1
0
1
0
2
0
0
2
0
0
1
1
0
1
1
2
1
1
0
0
0
1
0
1
0
2
1
2
1
0
0
0
10
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
2
2
2
2
0
1
2
2
1
1
2
4
1
1
1
1
0
0
1
0
0
1
0
0
0
1
2
1
1
0
2
2
0
1
0
1
1
0
0
0
0
1
2
0
1
0
1
2
2
1
1
0
2
0
0
0
2
2
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
1
1
0
2
2
0
1
2
1
2
1
2
1
0
1
2
0
2
4
0
0
2
2
2
1
0
0
1
0
1
0
1
1
1
0
0
0
1
1
1
1
1
1
0
0
1
0
0
1
2
0
1
0
0
1
0
0
1
0
1
1
0
0
0
2
1
2
0
2
1
0
0
2
0
0
0
2
0
1
1
0
2
2
1
2
1
2
0
0
1
0
2
0
1
1
2
2
2
2
1
1
0
0
0
2
0
0
1
1
1
0
2
0
1
0
0
2
1
2
2
2
0
2
1
1
1
1
1
0
1
1
1
0
0
0
2
0
0
0
0
1
2
2
0
2
0
1
0
2
1
0
0
1
0
0
0
1
0
1
0
2
2
2
0
0
0
2
0
0
0
0
1
0
2
2
1
2
0
0
1
0
0
1
2
2
2
1
0
1
7
0
1
1
0
0
0
2
0
1
1
1
2
0
2
3
1
0
0
2
1
1
0
2
0
1
2
3
2
1
0
1
2
0
1
0
0
2
1
0
1
0
0
0
0
0
1
0
1
0
2
1
0
2
0
2
1
1
1
0
1
0
1
0
0
0
1
1
0
0
0
2
2
1
0
2
2
0
0
1
2
0
0
1
2
2
1
0
0
2
0
2
0
1
0
0
1
2
0
0
1
0
2
1
0
0
2
0
0
2
0
0
0
0
0
1
0
2
2
2
0
2
2
2
1
2
0
0
1
1
2
1
3
0
1
1
0
2
0
1
0
1
0
2
1
1
1
1
1
0
1
2
2
1
2
0
0
1
0
0
0
0
3
0
0
1
2
2
0
1
2
0
1
1
1
1
2
1
1
1
0
1
0
2
1
1
1
0
0
2
0
1
1
0
1
2
2
0
2
0
1
1
1
1
0
0
2
0
0
1
0
1
0
0
1
1
2
0
1
1
0
1
0
1
1
2
3
0
1
0
0
1
2
0
0
1
1
1
0
0
0
0
2
0
1
2
0
1
0
0
0
2
2
3
2
0
1
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
1
0
0
0
1
0
2
2
0
1
0
0
1
0
2
1
1
1
2
0
1
1
0
2
2
0
1
0
0
1
1
1
1
0
0
0
0
2
0
1
0
1
0
2
2
0
0
0
1
0
0
0
0
0
0
0
1
1
2
0
2
0
0
0
2
0
0
1
0
2
0
1
1
0
0
1
0
0
0
2
0
1
2
1
1
1
2
1
2
0
1
0
1
0
2
0
0
2
1
2
0
0
2
1
2
1
1
0
0
2
0
1
0
1
0
1
0
1
2
1
2
0
2
1
1
1
2
1
0
1
1
2
1
1
2
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
2
2
2
0
1
0
0
0
1
0
1
0
1
0
1
1
1
1
1
0
0
0
1
1
2
0
2
0
0
2
1
0
0
1
1
0
2
1
0
0
0
1
1
1
0
1
2
0
0
1
1
1
1
1
1
0
1
1
2
0
1
0
0
2
0
0
0
0
2
0
2
0
1
1
2
2
0
1
0
0
1
0
1
0
1
1
1
0
1
2
1
2
1
1
0
1
2
2
1
2
1
0
1
1
0
1
0
1
1
0
1
2
2
1
1
0
1
2
1
0
0
1
1
2
1
1
0
0
2
0
2
2
1
0
0
1
0
1
0
1
0
0
1
0
1
2
0
1
0
0
1
1
1
2
0
2
1
0
1
1
1
0
1
1
1
0
0
1
0
0
2
1
0
0
1
0
1
2
0
3
0
2
0
0
0
1
1
1
1
1
1
1
0
1
0
2
1
2
1
0
0
1
0
1
1
1
1
0
0
1
2
2
0
0
2
0
0
1
6
0
2
2
1
0
0
0
0
1
2
0
1
0
0
1
0
1
0
1
0
1
0
1
1
3
1
1
0
1
1
0
1
0
0
0
1
0
1
1
0
2
0
1
1
0
0
1
0
1
1
0
1
1
1
2
0
0
0
0
2
0
2
0
1
1
1
1
0
0
1
0
0
0
0
1
2
1
0
1
0
0
2
1
1
1
1
0
2
1
0
0
1
2
0
2
1
0
1
0
1
1
2
2
0
1
1
2
0
0
0
0
2
1
2
2
1
1
0
1
0
0
2
2
2
0
1
2
1
0
0
6
0
2
2
0
1
0
0
2
0
0
1
0
1
1
0
1
0
2
0
2
2
1
2
2
0
0
1
1
2
0
2
2
1
1
1
1
0
2
1
0
0
3
0
1
2
1
2
2
3
0
0
1
1
2
2
0
1
0
0
2
1
1
1
0
1
2
1
2
1
0
0
1
2
2
0
2
0
0
0
2
0
1
0
1
1
1
1
2
3
1
2
0
1
2
1
2
1
1
0
2
0
2
0
2
1
2
0
2
0
0
0
0
2
0
1
1
1
1
1
0
2
0
2
0
0
2
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
1
1
0
0
1
0
1
0
0
0
0
1
1
0
0
1
2
1
0
1
2
1
1
1
1
0
0
1
0
0
1
2
0
2
0
1
1
2
0
3
0
2
2
0
0
2
1
0
2
1
0
0
1
0
1
1
0
0
2
0
1
1
0
0
1
0
0
1
0
1
1
1
2
0
0
0
0
0
0
2
2
1
2
0
2
2
0
0
0
0
0
0
1
2
0
2
0
0
0
0
1
0
0
2
0
0
2
0
1
1
0
1
0
0
1
0
0
2
2
1
1
1
0
1
1
0
0
2
0
0
0
1
3
1
0
1
1
0
2
1
2
2
1
1
0
0
1
1
0
1
1
1
0
1
1
1
2
1
0
0
0
2
0
2
0
1
2
0
0
0
0
0
1
1
0
0
1
1
0
1
1
1
1
1
0
0
1
1
0
1
2
0
1
0
1
2
1
0
2
1
0
1
2
1
0
0
0
0
3
0
1
0
1
1
1
0
0
0
0
1
2
1
1
0
1
0
1
0
1
1
0
2
2
1
0
0
1
0
1
0
0
0
0
1
0
0
2
1
1
1
0
0
1
0
1
2
2
2
0
2
0
0
1
0
0
1
0
0
0
1
0
0
1
4
0
1
0
0
1
0
1
1
0
0
1
4
1
2
2
1
0
0
1
2
2
0
1
1
0
1
1
0
0
1
0
2
1
0
3
0
0
1
1
0
2
0
1
0
2
1
1
2
1
1
1
0
0
0
1
2
0
1
2
0
0
1
1
3
1
2
1
1
0
0
0
0
2
0
2
2
1
0
0
0
1
2
0
2
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
2
2
2
1
0
0
1
0
0
1
0
1
1
2
2
0
0
0
2
1
0
0
1
1
3
1
0
2
0
2
1
0
2
1
1
1
2
0
2
0
0
2
0
0
1
2
2
0
0
2
0
2
0
2
0
1
1
0
1
1
1
1
1
0
1
0
2
1
2
0
0
0
2
0
1
1
2
2
1
1
1
1
0
2
1
0
1
1
1
0
1
2
1
1
0
2
1
0
1
1
2
0
1
1
0
2
1
1
2
0
1
1
1
1
1
1
0
2
1
1
0
0
1
1
1
2
0
1
2
0
1
0
2
1
0
0
1
2
0
0
1
2
1
0
2
0
6
1
2
0
1
1
0
0
1
2
2
1
2
1
0
1
1
2
2
3
0
1
0
0
0
0
0
0
2
2
0
1
0
1
2
2
1
2
1
1
2
1
1
0
1
1
0
1
1
0
1
2
1
0
0
1
1
0
1
0
2
3
0
0
1
1
0
1
0
1
2
1
3
1
2
1
0
0
1
1
0
0
0
1
0
0
1
1
2
1
0
0
2
1
1
0
1
0
0
0
0
1
2
0
0
3
0
2
1
1
1
2
1
0
0
0
1
2
2
1
1
0
1
1
1
0
2
0
2
1
1
0
1
0
0
0
1
1
1
0
0
0
0
0
1
1
0
1
1
2
0
2
1
2
0
0
1
1
0
1
3
0
1
1
1
0
1
1
3
0
0
0
2
2
1
3
0
2
1
0
1
0
0
0
1
0
1
2
1
0
1
1
0
1
2
1
0
1
1
1
4
1
0
2
0
0
1
1
1
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
1
0
0
2
0
0
2
2
1
1
0
0
1
2
0
0
1
0
1
1
2
2
1
1
0
1
0
2
0
1
1
2
1
1
2
1
2
1
2
0
0
2
1
0
2
4
2
0
1
1
1
1
1
1
2
1
0
2
2
0
0
0
0
2
0
1
1
2
1
0
0
2
0
1
1
1
0
1
1
1
0
1
0
1
2
2
1
2
0
1
2
0
0
1
0
1
2
0
0
0
0
1
1
0
2
2
1
2
1
0
1
0
0
1
0
1
0
0
0
0
1
1
0
2
0
1
0
1
1
0
1
0
2
1
2
1
1
2
1
2
0
1
1
2
1
1
1
0
2
2
0
1
1
1
0
1
1
1
1
0
1
0
1
1
0
0
0
1
0
0
0
1
1
1
1
1
2
2
1
0
1
1
0
2
1
1
0
2
0
1
2
1
2
2
2
2
1
2
1
2
2
2
0
0
0
0
2
0
0
0
1
1
2
1
1
1
2
0
0
0
0
1
0
0
0
2
1
0
0
1
0
0
2
0
2
0
1
0
2
0
2
1
0
2
2
1
1
0
1
1
0
0
0
0
1
1
1
1
2
0
1
2
0
0
2
1
1
0
1
0
0
1
2
2
1
0
2
1
0
1
1
0
2
1
1
2
0
1
3
0
2
1
0
1
2
0
1
0
1
2
2
0
0
2
0
0
0
0
0
0
2
0
1
0
0
1
1
0
2
0
0
2
2
1
0
0
0
0
1
2
1
1
0
0
0
0
1
1
1
0
1
1
1
0
3
1
2
1
1
0
0
1
0
1
1
0
1
8
0
2
2
2
0
0
2
0
2
0
0
1
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
2
1
2
1
0
0
0
2
0
1
1
1
0
0
1
0
1
0
0
0
0
1
1
0
1
1
1
1
1
1
0
1
2
1
0
2
0
2
1
1
0
1
2
0
3
0
1
2
2
0
1
1
1
1
1
0
1
3
0
2
0
2
1
1
3
1
0
1
2
0
0
0
0
1
0
2
0
2
0
2
1
0
0
1
0
1
1
1
2
0
0
0
1
1
0
0
0
0
0
0
1
1
0
2
0
0
1
0
1
0
0
0
1
1
2
2
2
1
0
1
0
0
1
0
0
1
0
2
1
1
1
0
0
1
1
0
1
1
2
0
1
0
0
0
1
0
1
1
0
0
0
0
0
2
2
1
0
0
2
1
0
1
1
1
2
0
1
1
2
2
2
0
1
0
0
0
0
1
1
1
0
0
2
2
0
1
0
3
1
0
0
0
2
1
2
0
1
1
0
0
1
2
2
1
0
0
1
2
0
2
1
1
0
2
1
1
1
1
1
2
1
2
1
0
1
2
2
2
1
0
1
0
0
1
1
0
0
0
0
1
0
1
1
0
1
3
0
0
1
0
0
0
2
1
2
0
0
0
0
1
1
1
2
0
0
1
0
1
1
2
0
1
3
2
1
1
0
2
0
2
1
0
2
2
1
0
1
1
0
1
2
0
0
0
1
0
2
0
0
2
1
2
1
1
0
2
2
1
0
0
2
1
1
0
1
0
1
0
1
1
1
2
0
2
0
2
0
0
1
1
0
0
1
0
4
0
0
1
3
0
0
2
0
0
0
0
0
1
0
2
2
1
1
2
1
2
1
1
1
1
1
1
0
0
1
1
1
0
1
0
0
1
0
2
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
1
0
1
1
1
1
1
2
0
0
0
1
1
2
0
2
2
1
0
1
2
0
0
2
2
0
1
0
0
0
0
0
1
0
2
1
2
2
0
0
0
2
1
1
0
1
2
2
0
1
1
2
1
1
0
0
0
2
0
1
2
1
1
1
0
1
1
1
2
1
0
0
0
1
2
1
1
2
1
0
0
2
1
0
2
1
0
0
0
0
1
0
0
0
1
0
2
0
0
0
1
2
1
1
1
1
1
1
1
0
0
0
2
2
0
2
2
2
0
2
2
0
2
2
1
1
0
3
1
2
2
1
2
0
2
1
2
0
2
2
0
1
0
1
1
2
1
2
1
0
1
0
0
0
0
1
1
1
1
2
0
0
0
0
1
0
0
1
0
1
1
2
0
1
1
2
0
0
2
0
1
1
2
0
0
0
0
0
1
0
2
0
2
0
0
1
1
1
2
0
0
1
1
1
2
1
0
2
1
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
1
1
1
0
0
0
0
1
0
0
0
0
1
0
2
1
2
0
1
1
1
1
0
1
2
2
0
0
1
2
2
2
2
1
0
0
1
0
1
1
0
1
1
0
2
0
0
2
0
0
0
0
0
0
0
2
1
1
2
1
0
2
0
0
0
0
2
1
1
1
1
0
1
0
0
1
1
0
1
1
2
1
1
2
2
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
1
1
1
2
1
1
1
1
1
0
1
0
0
2
0
2
2
1
0
0
0
2
1
0
3
2
1
2
1
3
2
0
0
1
1
1
2
1
1
2
3
1
0
0
1
1
0
0
1
0
1
1
1
0
1
0
1
2
1
0
0
0
0
1
2
0
0
0
1
0
1
0
0
0
1
0
0
1
2
1
0
0
1
2
2
1
2
1
1
1
1
2
1
2
1
1
0
0
0
0
0
1
0
0
2
1
1
0
1
2
0
1
0
1
0
1
0
1
0
1
1
1
1
0
2
0
0
1
2
1
1
0
2
0
0
2
0
0
0
0
0
2
1
0
2
2
1
2
0
1
0
0
0
0
2
1
0
0
0
0
1
1
0
2
0
0
3
0
1
0
2
0
0
2
3
1
0
0
0
0
0
1
0
1
2
2
1
0
0
1
0
0
1
1
1
2
0
2
0
1
0
2
0
0
0
0
1
1
0
0
0
1
1
1
0
0
2
0
1
1
1
1
2
0
2
1
1
1
0
2
0
1
1
0
1
1
1
0
1
1
1
1
0
1
0
2
2
0
1
1
0
0
0
0
0
1
2
4
0
1
0
0
2
1
1
2
1
1
0
0
1
1
4
1
1
1
1
2
1
1
1
1
0
1
1
2
0
0
2
2
0
1
0
0
0
1
2
0
0
2
1
0
2
2
0
0
2
0
1
3
1
0
0
0
1
0
1
2
0
1
1
0
0
2
0
1
2
1
2
1
0
0
0
1
0
0
1
2
0
0
1
2
1
2
0
1
0
1
0
0
1
0
1
0
0
2
1
0
0
1
1
0
1
0
0
2
2
2
0
1
0
0
1
1
0
0
2
0
2
0
0
2
2
1
0
0
0
0
2
2
1
1
2
0
1
0
2
2
1
0
1
0
1
0
0
1
0
0
1
0
2
2
1
0
1
2
0
4
0
2
0
1
1
2
1
0
0
2
0
1
0
0
0
2
2
0
1
0
2
0
0
2
0
1
1
1
2
0
1
1
0
0
0
1
0
1
0
1
1
0
0
2
0
1
0
1
1
0
1
1
0
0
0
2
1
0
1
2
2
0
0
0
2
1
0
1
0
2
1
2
2
0
1
0
2
0
0
0
2
0
2
0
1
4
1
1
0
0
0
0
1
0
0
4
1
2
1
1
2
2
1
0
0
1
1
1
1
0
1
1
0
0
2
0
2
0
0
0
2
0
0
0
0
0
2
0
0
1
0
3
2
0
0
1
0
1
0
2
0
1
1
1
1
2
0
0
2
2
1
1
0
2
2
0
0
1
1
1
1
2
0
0
1
1
0
1
2
1
1
0
1
0
0
0
2
0
0
2
2
0
1
0
0
2
1
1
1
0
1
0
1
1
1
2
2
0
1
0
1
0
1
0
0
1
1
2
2
1
1
1
0
1
0
1
0
1
3
1
2
2
2
0
0
0
2
0
2
4
1
1
2
1
1
0
0
2
2
1
1
1
0
0
1
0
1
1
0
1
1
1
0
0
1
1
2
0
1
1
1
0
2
0
2
0
0
0
2
0
2
2
1
3
2
0
1
0
0
1
1
2
2
2
2
1
0
1
0
1
1
0
1
1
1
0
1
1
0
0
1
1
2
0
1
0
1
1
0
0
1
1
2
0
0
0
0
1
2
1
1
0
0
2
1
2
0
2
1
0
0
1
1
0
0
2
2
1
0
1
0
0
0
0
1
1
2
1
1
2
0
2
1
1
0
1
0
1
1
1
0
0
0
1
0
1
2
1
0
0
0
2
0
1
0
3
0
0
1
0
2
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
2
1
0
1
0
2
1
1
1
0
2
1
0
2
0
1
1
1
0
2
0
0
0
1
2
0
3
1
2
0
0
1
1
1
1
0
0
1
0
1
2
0
0
2
0
0
0
0
0
2
0
1
0
1
2
1
2
0
1
0
2
0
1
0
0
0
2
0
1
1
1
0
0
1
0
2
2
2
1
0
1
0
1
0
0
0
0
1
0
0
1
1
2
0
2
1
1
1
2
1
2
0
1
0
0
0
1
0
0
2
0
1
0
0
0
0
2
0
1
2
0
0
2
1
0
0
0
0
0
0
0
1
0
2
0
1
1
0
0
2
2
0
2
2
0
0
1
0
2
2
1
0
2
2
2
3
0
2
1
0
1
0
0
1
2
2
1
0
0
1
3
0
2
2
0
3
1
0
2
0
1
1
1
2
0
0
0
0
6
0
0
1
2
0
4
1
0
0
2
1
1
1
2
1
2
0
2
0
1
0
2
0
1
0
2
0
1
0
0
1
0
1
0
0
0
1
1
0
1
0
0
2
1
0
1
0
1
1
0
0
0
1
1
1
1
0
2
2
0
1
0
0
1
0
1
2
2
0
1
0
0
2
1
0
1
0
1
0
0
1
0
0
0
0
1
2
0
1
0
2
1
3
2
1
2
1
2
2
0
0
2
0
0
1
2
1
1
1
0
0
0
1
2
9
0
1
1
2
1
2
0
2
0
1
1
3
0
1
0
0
1
2
0
1
0
1
0
1
2
0
0
1
2
1
2
3
3
0
2
0
0
3
0
1
1
0
0
2
0
1
0
1
2
2
1
0
0
1
7
1
0
2
1
1
2
1
0
0
0
0
2
1
2
0
3
1
0
0
0
1
0
1
2
0
0
1
0
1
1
0
1
0
0
1
0
1
2
2
0
1
2
0
1
0
0
1
1
0
0
0
2
1
0
0
1
0
2
2
1
0
0
2
2
2
0
0
0
1
1
0
0
2
2
1
1
0
2
0
1
2
1
2
0
2
0
1
2
1
1
1
1
2
1
1
2
2
1
0
1
2
2
1
2
0
2
0
1
1
2
0
2
2
1
1
2
1
1
1
2
0
0
2
1
0
1
0
0
1
0
0
0
0
0
2
3
0
1
1
1
0
0
1
0
1
1
1
1
0
2
2
0
0
0
1
0
0
0
0
2
1
1
1
2
0
2
1
3
2
0
1
1
1
5
2
0
3
1
1
1
2
0
0
1
0
2
2
1
0
2
2
0
0
0
1
1
0
0
0
0
1
1
0
1
2
1
1
2
2
1
0
1
0
1
0
0
1
2
1
0
0
1
0
0
0
0
0
1
1
1
0
0
1
2
0
2
0
0
1
2
0
1
2
0
0
0
0
2
1
0
2
2
1
0
2
1
1
2
1
0
0
0
1
0
2
0
0
0
0
0
0
0
1
1
1
1
0
1
1
1
1
1
2
2
0
2
0
1
0
2
0
1
0
2
1
1
2
0
0
1
1
1
2
2
0
1
0
0
0
0
1
0
0
2
3
1
2
2
0
2
2
2
0
0
1
1
1
0
0
0
0
2
0
0
2
1
1
0
0
0
0
1
0
2
1
0
1
0
0
2
0
0
0
1
0
1
0
0
2
0
1
0
0
2
2
2
1
1
1
1
0
1
0
2
0
1
0
0
0
0
1
1
0
0
1
2
1
2
1
0
1
1
1
0
2
0
2
0
2
0
0
1
2
0
1
1
0
2
1
1
1
1
2
0
1
2
0
1
1
1
0
2
0
1
0
0
1
0
2
1
1
1
1
2
0
1
1
0
1
2
0
2
1
0
1
0
1
0
1
1
0
2
0
0
2
2
0
2
1
1
1
2
0
1
1
1
1
1
3
1
1
0
2
1
0
0
1
0
1
0
1
0
0
0
2
1
0
1
0
0
1
0
1
1
1
0
0
2
0
1
0
2
2
0
0
1
1
0
0
3
0
1
2
0
0
2
2
2
1
1
0
2
1
0
2
1
1
0
1
0
1
0
0
2
1
1
1
0
1
1
2
1
1
1
0
0
1
0
1
1
1
2
2
1
0
1
2
1
2
0
1
1
0
0
1
2
1
1
1
1
0
0
1
1
1
0
1
0
0
2
1
0
2
2
3
0
0
1
0
0
0
1
0
1
1
0
1
0
0
1
1
6
1
3
1
1
1
0
2
1
1
0
1
0
1
0
0
0
1
2
0
1
0
3
1
2
1
2
0
1
1
1
1
0
2
0
2
0
2
0
1
1
0
1
2
1
1
2
1
1
1
0
0
1
0
1
0
2
0
0
2
1
1
2
1
0
1
1
0
0
1
2
0
1
1
1
0
0
2
2
1
1
1
0
1
2
0
0
2
0
0
2
2
1
0
1
2
0
2
0
1
2
2
1
0
1
0
1
0
2
1
0
0
0
2
1
0
2
2
1
6
1
1
0
0
1
0
1
1
0
2
2
1
1
0
1
1
1
0
2
0
1
0
1
2
1
1
0
1
2
1
2
1
0
2
0
0
0
1
1
0
0
2
0
0
0
2
1
0
2
2
0
2
2
0
0
1
1
1
1
4
0
1
0
2
1
2
0
2
2
1
1
1
1
0
2
1
0
1
0
0
0
0
0
0
1
1
1
0
1
2
1
1
0
3
1
1
0
1
1
0
0
0
1
1
2
1
0
1
1
0
1
0
0
0
0
0
1
2
2
1
1
0
0
2
0
1
1
2
1
0
1
0
0
1
2
2
0
2
1
2
0
2
1
1
1
0
1
1
0
1
0
0
0
0
0
1
0
0
2
0
1
1
0
0
2
0
2
1
0
2
2
0
0
2
0
1
1
1
0
1
1
1
0
1
1
0
2
0
1
2
2
1
0
1
2
1
2
1
0
0
1
1
1
1
2
1
0
0
0
1
0
0
2
2
0
0
0
1
2
3
1
1
2
1
0
1
0
1
0
0
1
0
2
1
1
0
1
1
0
2
2
2
1
0
0
2
0
2
2
1
0
1
0
1
0
0
1
1
2
0
0
1
1
2
0
2
1
2
1
2
2
2
2
2
1
0
2
1
1
0
0
1
0
0
1
1
1
1
0
0
2
0
0
1
1
2
2
0
0
0
1
2
2
0
1
1
0
0
0
0
1
0
2
0
0
1
2
1
1
1
2
1
0
0
0
0
0
0
2
4
0
0
1
1
0
0
2
0
0
1
1
2
1
2
1
1
2
2
1
1
2
0
1
1
0
1
0
0
0
0
1
1
2
3
0
1
2
0
2
1
1
0
1
2
0
1
1
1
2
0
2
0
1
1
0
1
1
0
0
2
2
1
0
2
0
2
1
0
0
0
2
0
1
0
3
0
0
1
0
0
2
2
0
3
2
2
0
1
1
1
1
1
1
2
0
0
2
2
2
1
1
2
0
0
0
0
0
2
0
1
0
1
0
1
1
0
1
1
1
2
0
0
1
2
2
2
2
1
2
0
0
2
1
1
0
1
2
1
1
1
0
1
1
2
1
0
0
1
0
1
1
1
0
1
0
1
0
1
0
0
2
3
1
0
0
0
0
0
0
0
2
1
1
0
0
0
1
2
0
0
0
0
1
1
1
2
1
1
2
0
2
0
1
2
1
1
2
1
1
1
0
1
0
0
0
0
2
0
1
0
1
2
0
0
1
2
0
1
2
0
0
1
1
0
0
0
3
0
1
2
0
0
0
2
0
2
0
0
2
2
3
1
2
1
2
1
0
2
1
2
1
1
0
1
2
0
0
0
0
0
0
2
0
2
0
2
0
2
0
1
0
2
0
0
2
0
1
0
0
1
0
1
0
0
2
1
0
1
0
1
2
0
1
1
1
1
2
0
1
2
0
0
0
0
2
0
1
2
0
2
0
2
2
1
2
2
0
0
0
1
3
2
0
1
1
1
1
0
0
0
1
0
0
0
0
1
1
1
0
0
1
1
2
1
1
1
1
2
0
0
0
0
0
1
0
0
0
2
1
0
1
1
0
1
1
0
1
1
1
0
0
1
2
1
0
1
1
0
2
0
0
0
0
1
0
1
1
1
2
0
1
1
1
0
1
0
0
1
3
0
1
2
2
0
2
2
0
1
0
1
0
0
0
0
1
0
1
2
0
0
0
2
1
1
2
0
2
0
0
0
1
0
0
1
1
0
1
0
1
1
1
0
1
0
1
2
0
2
0
1
1
0
0
1
1
1
4
1
0
0
1
0
2
1
1
1
0
0
2
2
1
1
0
0
0
1
2
2
2
0
2
0
0
2
1
2
3
0
1
1
0
1
1
0
0
1
2
1
1
1
1
0
0
1
1
0
0
0
2
0
2
0
1
0
2
0
0
0
0
0
1
0
1
5
1
1
1
1
0
0
1
1
0
1
0
1
0
0
0
2
0
1
1
1
0
1
0
2
0
2
0
3
0
1
0
1
1
0
1
0
1
2
1
0
0
1
1
2
1
0
1
1
0
1
2
2
0
2
2
0
0
0
2
2
1
0
1
2
1
1
0
2
1
1
1
1
2
1
1
1
1
2
1
1
0
0
0
1
0
2
3
0
1
0
1
0
2
0
2
2
0
2
0
2
0
0
0
1
0
0
1
0
2
0
2
0
1
1
1
1
0
0
2
1
0
0
0
0
0
0
2
1
0
1
0
1
1
0
0
0
1
0
1
0
0
0
0
1
2
2
2
1
2
1
2
2
0
1
1
2
1
2
3
0
1
0
0
1
1
0
0
0
0
1
2
2
1
0
1
1
0
0
2
1
0
0
1
1
2
0
0
2
1
2
1
1
1
0
2
3
0
1
1
1
1
0
1
1
0
2
1
0
0
1
2
0
2
1
1
1
0
0
0
0
2
1
0
1
1
0
1
0
0
1
0
0
0
2
0
0
0
0
0
1
1
1
1
0
1
1
0
0
0
0
2
2
1
2
0
1
0
0
0
1
0
1
0
1
1
0
1
2
2
0
2
2
3
2
1
1
1
1
2
0
0
2
1
0
0
2
0
2
0
1
1
1
1
1
0
1
2
2
1
0
0
2
1
1
1
1
0
1
0
1
1
1
1
0
1
0
0
2
1
0
1
0
0
0
0
2
2
0
1
0
1
0
1
1
0
1
1
0
1
0
3
0
0
0
1
1
0
1
0
0
0
1
0
1
0
1
0
0
2
0
0
1
2
0
1
2
0
0
1
1
2
0
0
2
1
2
0
2
0
1
1
1
0
0
0
2
0
0
0
1
1
0
0
0
2
2
2
2
1
1
0
1
0
1
1
2
0
0
0
1
2
0
0
2
0
1
0
1
0
0
0
0
1
4
1
1
0
0
2
0
2
0
2
1
0
2
1
0
0
2
1
1
0
1
1
0
1
0
2
0
1
0
1
2
0
0
2
1
2
0
1
1
1
2
1
1
2
2
2
1
1
1
0
1
1
0
0
1
1
2
0
2
0
2
1
1
2
0
2
1
0
0
2
0
0
0
1
0
1
1
0
0
1
1
0
0
0
1
1
1
0
2
1
0
1
1
0
1
1
0
1
0
2
2
0
1
2
2
0
1
1
1
1
1
3
1
0
0
0
1
1
2
1
0
1
1
1
1
0
1
1
0
0
1
1
2
1
0
0
2
0
1
2
0
2
0
0
0
0
0
2
1
1
0
1
1
0
0
3
0
0
2
0
1
2
0
1
2
0
0
1
0
1
1
1
0
0
0
1
0
0
0
1
2
0
2
3
0
1
2
0
0
0
1
2
1
1
1
1
2
0
0
0
1
1
2
0
2
0
1
1
0
0
0
0
0
2
1
2
0
2
0
0
1
0
1
0
1
0
1
0
0
0
2
0
0
0
0
2
1
2
1
2
2
2
0
2
0
0
2
0
0
1
0
1
1
0
0
2
1
0
0
1
0
1
0
1
0
1
1
3
6
1
0
0
2
2
0
1
1
2
0
2
1
2
1
1
1
1
0
1
0
1
0
1
2
0
2
2
0
1
0
1
2
0
0
1
1
1
2
2
1
2
2
1
0
1
0
2
1
1
0
1
1
2
1
0
2
2
1
2
2
0
1
1
0
2
2
0
0
2
2
2
1
1
1
0
0
0
0
0
2
2
0
1
0
2
1
0
0
0
0
0
2
1
2
1
1
1
0
0
0
1
0
2
1
0
3
1
1
2
0
1
1
0
1
0
0
2
0
1
0
0
2
1
2
1
2
0
0
1
2
1
1
1
0
1
0
2
0
1
0
0
0
2
0
1
2
0
1
2
1
0
1
1
0
5
0
0
1
1
0
0
2
2
0
2
0
0
0
1
0
2
1
2
1
0
0
2
0
1
2
0
1
0
0
2
1
1
0
1
0
1
2
2
1
0
2
0
0
0
2
1
3
1
1
1
0
1
0
0
2
0
1
1
0
0
0
0
0
3
2
0
0
1
0
0
1
0
2
1
0
1
0
0
2
0
0
0
1
0
0
1
1
0
2
1
1
2
1
0
1
0
1
0
1
1
0
1
1
1
0
0
0
2
0
0
1
1
0
0
2
1
2
0
2
1
1
1
1
0
1
2
0
1
1
0
1
0
0
0
0
2
1
2
0
1
1
0
2
0
1
1
0
1
0
1
0
1
0
2
0
2
0
0
0
0
1
1
1
0
1
1
0
1
0
2
0
0
0
1
1
1
1
0
0
2
0
1
1
2
2
2
0
0
1
1
2
1
0
2
2
2
0
0
2
0
0
2
1
1
1
2
1
1
1
3
1
0
0
1
1
0
2
1
1
2
2
1
10
0
0
3
1
2
0
0
1
0
2
1
2
1
1
0
0
1
1
2
2
0
0
1
1
1
2
0
0
2
0
1
1
0
1
1
1
2
0
1
2
1
0
2
1
0
1
0
0
0
1
0
1
0
2
0
0
1
0
0
0
2
1
0
0
0
0
0
1
0
0
0
2
0
2
0
1
1
2
2
2
2
2
1
0
2
2
0
3
1
1
2
2
1
0
0
0
0
0
2
1
2
0
2
2
2
0
0
1
0
0
1
0
1
0
1
0
1
2
1
2
1
1
1
0
0
0
1
0
1
0
1
1
0
0
0
0
1
0
0
1
0
0
2
1
0
2
1
1
3
2
2
0
0
1
1
2
0
1
1
2
0
2
1
2
4
0
0
1
1
2
0
1
0
2
1
2
0
0
0
1
0
1
0
0
2
0
0
2
0
1
1
0
1
2
2
0
0
2
1
0
0
0
1
0
0
1
1
0
2
0
1
1
0
2
2
1
0
1
1
1
1
1
2
0
2
0
1
1
0
1
2
0
2
0
2
0
2
1
1
1
1
1
1
2
2
0
1
1
0
0
0
2
0
0
2
2
1
0
1
2
1
0
0
1
1
0
0
0
1
2
1
0
1
2
0
0
0
2
0
1
1
0
1
0
1
1
0
2
0
2
0
2
1
2
2
0
1
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
1
1
0
2
2
0
1
0
1
0
0
2
1
2
1
1
0
2
1
0
1
1
1
0
2
1
0
0
0
0
0
0
2
1
0
1
0
1
0
0
2
0
0
0
2
1
1
1
0
0
2
0
1
0
2
1
0
0
1
1
0
0
1
0
1
1
1
1
0
1
1
0
1
1
0
2
2
0
0
2
1
0
0
0
1
0
1
0
1
0
0
2
1
1
1
1
1
0
0
0
0
0
0
0
4
0
2
1
0
1
1
0
0
0
0
1
1
1
1
2
1
1
1
2
0
0
1
2
0
1
2
0
0
0
1
0
0
0
1
0
0
1
1
0
2
2
2
1
0
0
0
0
2
0
0
0
1
0
2
0
1
0
1
0
2
0
2
1
0
2
2
0
1
1
1
1
0
2
0
0
0
1
2
0
1
1
1
2
1
0
2
0
1
1
1
1
1
0
1
0
2
0
2
0
2
1
0
0
0
0
1
0
0
0
2
0
0
2
0
1
0
0
0
1
0
0
0
1
0
2
0
1
0
1
1
0
2
2
1
0
0
1
2
0
0
0
0
0
1
2
0
1
3
0
0
0
2
0
1
1
1
0
1
1
0
2
0
2
0
2
1
0
2
0
1
0
0
1
2
2
0
1
1
0
0
1
1
0
1
1
0
2
0
1
2
1
1
1
0
2
0
1
1
0
1
0
0
2
0
1
0
0
1
1
1
0
1
0
1
0
1
1
0
1
2
0
1
0
1
1
0
0
2
1
1
0
2
1
2
2
1
1
0
1
2
2
1
0
0
0
1
0
0
0
2
0
1
3
2
0
1
0
0
1
1
0
2
0
0
2
0
0
1
1
1
1
1
0
0
2
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
2
0
0
2
1
0
0
1
0
1
1
0
1
0
1
2
1
1
1
1
2
1
1
0
0
1
2
0
1
1
1
0
0
2
2
1
1
0
0
0
2
1
1
0
1
0
1
2
2
1
1
1
0
2
2
2
2
0
2
0
0
1
2
2
0
1
0
1
2
0
2
0
0
1
1
2
0
0
1
0
0
2
2
5
2
1
0
1
2
2
0
1
2
0
0
0
0
1
1
2
1
0
1
0
0
0
1
0
2
1
1
0
1
0
1
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
2
1
2
2
1
0
1
2
2
1
0
1
1
2
0
0
1
0
2
1
2
1
2
2
1
0
1
0
1
4
0
0
1
1
1
0
0
2
3
1
1
2
2
1
2
1
2
1
1
0
1
1
0
1
1
1
1
0
1
2
1
1
0
2
2
0
0
2
1
0
0
0
1
2
1
0
2
0
0
2
0
1
0
1
1
2
3
0
0
1
0
0
0
1
0
1
2
0
0
1
1
2
0
1
0
1
0
2
1
2
0
1
1
2
1
0
0
2
1
1
0
0
0
1
2
2
0
0
1
3
2
1
0
0
1
1
0
0
2
0
1
1
1
2
1
1
2
0
0
2
2
0
1
1
1
1
0
1
1
1
1
0
2
0
0
2
0
0
0
0
1
2
2
0
0
0
2
0
0
0
2
0
1
0
1
2
2
1
0
0
1
2
2
1
2
0
1
0
1
1
1
1
2
2
1
1
1
0
0
0
1
1
3
0
0
1
0
0
0
1
1
0
1
1
0
1
1
0
0
0
0
0
0
1
0
1
1
3
1
0
2
2
0
0
0
1
2
0
2
0
2
1
1
0
1
2
0
0
0
1
0
0
1
0
1
0
1
0
0
0
1
1
1
0
0
2
0
1
0
1
1
0
0
1
2
0
2
1
2
0
1
0
1
1
1
1
0
1
1
0
0
1
2
2
0
1
0
1
0
1
2
1
1
0
2
1
1
0
0
0
0
1
1
1
1
0
0
1
2
2
0
1
0
0
2
2
0
0
2
2
2
0
1
0
2
1
2
0
1
1
0
1
1
1
0
2
2
0
1
0
1
0
1
1
0
2
2
2
0
0
1
2
1
0
0
1
2
2
0
0
1
1
1
0
1
2
2
1
2
0
2
3
0
2
0
0
1
1
2
1
1
0
0
1
0
1
0
2
0
0
0
0
2
2
0
0
0
1
0
1
1
0
2
1
0
1
1
0
0
0
0
0
0
2
0
1
1
6
2
1
1
0
0
1
1
2
2
1
1
0
1
2
0
0
0
1
1
0
2
1
2
2
0
1
0
0
0
2
2
0
1
2
2
2
0
0
0
1
2
2
2
1
0
0
0
0
2
2
0
3
0
0
1
0
0
1
1
0
2
1
1
1
0
2
0
0
1
0
1
2
0
0
1
1
1
1
2
2
1
0
0
2
2
1
1
0
2
0
2
0
0
1
0
1
0
2
2
1
1
0
2
2
1
2
0
0
2
1
1
0
1
1
1
2
0
1
0
0
1
0
1
0
1
0
0
0
0
2
0
0
1
1
2
1
2
0
2
2
2
1
1
1
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
2
1
2
1
1
0
1
2
0
1
2
1
2
0
0
1
0
2
1
0
1
2
1
0
0
0
0
0
0
1
0
0
1
1
0
1
0
1
0
0
3
2
1
1
1
1
1
0
0
2
1
2
1
0
1
0
1
0
1
0
0
0
0
2
0
0
1
2
1
0
1
0
1
0
1
0
2
1
1
0
0
0
1
2
0
0
0
0
1
2
2
0
2
1
0
1
2
2
0
2
0
1
0
1
1
1
1
1
2
0
1
2
0
2
1
0
0
1
1
0
0
1
0
2
0
1
2
1
0
1
1
3
2
1
1
0
1
0
1
1
0
0
1
1
1
2
0
0
0
1
1
0
0
0
2
0
1
1
0
0
1
1
1
2
0
1
0
1
2
1
1
0
2
1
1
1
0
1
0
0
2
0
1
0
1
0
0
2
1
0
1
1
0
1
0
2
2
1
0
1
2
1
0
0
1
1
2
1
1
1
0
1
1
1
1
0
1
1
1
2
1
2
2
1
1
1
0
0
1
1
1
0
1
0
0
2
1
1
0
1
2
0
1
1
0
0
2
1
1
2
0
0
2
1
1
0
0
2
1
1
0
0
0
1
2
1
1
2
1
1
0
0
0
1
0
1
0
1
2
2
1
1
1
1
1
0
8
1
0
0
2
0
0
0
2
0
2
1
1
2
0
2
0
2
1
0
2
0
0
0
1
0
0
1
0
0
0
1
1
2
0
1
1
0
2
1
0
0
0
1
1
1
0
0
1
1
0
1
1
0
1
0
1
3
1
1
0
1
1
1
0
0
1
2
1
0
0
0
3
1
1
2
1
0
2
0
0
0
0
2
0
1
0
0
2
2
2
1
0
1
1
0
2
1
1
0
1
2
0
2
0
0
2
1
0
2
1
0
2
0
1
1
1
1
2
0
1
1
1
1
1
2
0
2
2
1
1
1
2
1
0
1
0
0
0
4
0
1
0
0
1
1
1
0
1
1
0
1
3
0
2
0
1
2
2
0
0
2
0
0
0
2
1
1
0
1
0
1
0
0
2
0
0
1
1
0
2
1
0
0
1
2
2
0
0
0
2
0
1
1
2
0
0
2
0
0
2
0
2
1
0
0
1
3
4
3
1
0
0
1
1
0
1
0
0
1
0
1
1
0
0
0
1
0
1
1
0
0
1
0
2
1
1
1
0
2
0
0
1
0
2
1
5
1
0
1
1
2
2
2
1
2
0
1
0
0
1
3
1
0
1
1
0
1
1
1
0
2
0
0
1
0
1
0
2
2
2
1
1
0
1
1
1
1
2
1
1
1
0
0
0
1
1
2
1
0
0
0
0
1
0
2
0
2
0
2
0
0
2
0
0
1
0
0
2
0
1
2
1
1
1
1
2
1
1
0
2
0
1
1
1
0
2
0
2
0
2
1
0
0
1
0
0
1
0
2
1
0
2
0
1
0
1
0
1
1
1
1
0
1
0
0
0
2
2
1
2
1
0
0
0
0
1
1
0
2
2
0
2
0
1
0
1
0
2
1
0
1
1
1
0
0
0
1
1
0
0
1
1
0
0
1
0
0
0
2
0
0
1
1
0
2
1
1
1
1
1
1
0
1
1
1
1
2
0
0
0
1
2
2
3
2
1
2
0
1
0
1
1
0
1
1
1
2
1
0
0
0
0
1
1
2
1
0
1
1
0
0
0
1
2
2
0
0
0
2
0
2
2
0
0
1
1
1
1
2
1
2
1
2
1
2
0
1
0
1
1
1
0
0
1
0
1
1
2
0
2
1
0
1
1
0
1
2
1
0
0
0
1
2
0
1
0
1
2
1
0
0
0
0
0
0
0
2
0
2
0
1
1
0
2
1
1
0
1
0
2
0
1
2
1
0
0
1
0
2
0
1
0
1
1
1
0
1
1
2
1
0
2
1
0
1
1
1
1
2
0
1
0
1
0
1
1
1
2
0
1
2
2
0
1
2
0
1
1
0
1
1
0
0
0
1
0
2
1
1
2
2
2
0
1
0
0
1
2
1
1
1
1
2
0
1
0
0
2
0
1
1
0
1
1
1
1
1
2
0
1
1
0
1
1
2
0
0
0
1
1
0
0
1
1
0
0
1
0
1
1
2
2
0
1
0
0
1
1
0
1
1
0
0
1
0
2
0
1
1
0
0
0
2
1
0
1
1
1
1
1
0
1
2
1
0
1
0
1
1
2
0
1
0
2
1
0
1
0
0
0
2
1
1
0
2
0
1
0
1
0
1
2
2
1
2
2
0
0
0
0
1
0
2
2
1
1
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
2
0
1
0
1
0
0
1
0
1
2
1
0
1
0
3
2
0
2
0
0
1
0
0
0
0
2
8
2
0
0
0
0
0
2
0
1
1
1
1
0
1
2
2
0
2
1
0
2
1
0
2
1
0
2
2
0
1
1
2
1
1
0
0
1
2
0
0
0
1
1
0
0
2
1
0
0
0
0
0
0
0
1
3
1
0
1
0
2
0
2
2
0
0
2
0
1
0
0
0
0
0
2
0
1
0
0
2
1
0
0
0
1
1
2
1
1
2
0
1
1
3
1
2
2
2
2
0
0
1
1
0
0
2
2
0
1
2
1
1
1
2
0
0
0
1
1
0
0
0
1
0
2
1
2
1
2
2
1
0
3
1
2
0
0
1
0
1
1
2
0
0
1
1
1
1
2
0
0
0
1
0
1
2
2
1
0
1
1
1
1
0
0
1
0
0
1
1
0
2
0
1
1
1
0
2
1
0
1
0
1
2
1
0
2
0
2
0
1
3
0
1
2
1
1
0
2
1
0
2
1
0
0
0
1
1
1
0
0
1
0
2
0
1
1
1
1
0
1
0
1
0
0
0
0
2
0
0
0
2
0
1
1
2
1
2
0
3
0
0
1
2
1
1
1
2
0
1
1
1
1
0
0
0
1
0
2
2
0
0
1
0
0
0
0
0
0
0
0
3
1
1
1
4
1
0
1
1
0
1
2
0
1
1
2
1
0
1
2
0
0
0
1
2
0
1
1
1
2
0
1
2
1
1
1
0
0
1
2
0
2
0
2
1
0
1
2
4
0
0
1
1
0
0
2
2
1
0
0
2
0
0
1
1
0
0
2
2
1
0
0
1
0
2
2
0
1
0
0
0
1
1
0
1
1
0
0
0
0
1
1
1
1
1
0
0
0
0
1
1
1
1
0
1
0
1
0
2
1
1
1
1
1
0
0
0
2
2
0
0
0
2
0
1
0
2
2
1
2
2
0
0
1
0
0
0
0
0
2
1
0
2
0
0
0
2
0
1
2
0
2
2
0
2
0
0
1
1
3
1
1
0
1
0
0
0
0
2
0
0
2
1
0
0
1
1
1
0
1
2
0
2
0
1
0
0
1
1
0
1
0
0
0
2
2
2
2
1
1
0
1
0
0
0
0
1
0
2
0
1
1
0
2
2
0
1
1
2
0
2
0
0
1
2
0
0
2
1
0
2
1
0
0
1
1
2
0
0
2
0
7
1
1
1
0
2
1
0
0
2
0
1
0
2
0
2
2
1
1
1
0
1
2
3
1
0
2
2
0
2
1
1
0
0
1
2
0
0
0
1
0
2
2
1
0
2
0
2
1
2
2
0
1
0
1
0
0
2
0
0
2
0
0
0
0
0
1
2
0
2
2
2
1
2
1
0
2
2
1
1
2
1
1
1
0
0
1
1
0
1
2
0
1
0
2
0
1
0
1
3
3
0
0
1
0
2
1
0
1
0
0
1
1
0
0
2
0
1
0
1
2
2
1
2
1
1
2
0
1
0
4
0
1
1
0
2
2
1
1
1
0
2
0
0
0
1
2
2
0
2
0
0
2
1
1
2
0
0
0
0
2
0
0
2
1
0
0
1
0
1
1
1
0
1
2
0
0
1
2
0
0
0
1
0
0
0
0
0
0
1
1
2
0
2
0
0
2
0
1
2
0
0
1
1
2
0
3
1
2
0
1
0
1
2
0
2
2
1
1
0
1
1
0
2
0
2
1
2
0
0
2
2
1
0
1
0
0
0
2
0
0
1
1
0
0
0
2
3
1
2
0
1
0
2
0
0
2
1
2
0
2
0
1
0
1
1
0
0
0
1
1
1
2
0
0
1
2
0
0
1
2
1
2
1
1
0
4
0
0
1
1
1
1
0
0
0
0
1
0
0
1
0
1
2
0
2
1
2
0
2
1
2
0
1
0
0
2
1
2
0
1
0
0
0
1
2
0
0
2
1
2
0
0
2
2
1
2
0
1
0
0
0
1
1
1
0
2
1
1
2
2
1
0
0
1
3
0
0
0
1
2
0
1
1
2
0
2
0
0
1
1
0
2
1
0
0
1
0
0
0
2
1
0
0
0
4
1
1
0
1
0
1
0
1
1
0
0
1
1
1
2
1
1
2
1
1
0
1
0
1
1
0
0
1
1
2
0
1
1
0
1
0
0
1
1
1
0
1
2
0
0
1
0
2
0
2
1
0
2
1
1
0
1
0
0
1
0
1
0
0
0
0
0
0
1
1
2
0
2
1
1
1
1
2
0
2
0
0
1
1
1
2
1
1
3
1
1
0
0
0
0
0
1
2
0
1
0
1
0
2
2
0
1
1
0
0
1
2
1
1
0
0
0
0
2
0
3
0
0
1
2
0
1
0
2
2
1
0
0
0
2
1
0
2
1
1
1
2
1
2
1
0
0
0
0
1
1
1
0
0
1
0
0
0
0
1
1
1
1
1
0
3
2
0
0
0
2
2
2
0
2
1
2
2
2
1
2
2
2
1
1
2
1
2
0
2
0
1
1
2
0
1
1
0
0
0
0
1
1
0
1
2
2
1
1
1
1
0
1
1
1
0
2
0
1
0
2
0
0
1
0
2
1
0
1
1
2
1
0
0
1
0
1
1
0
2
1
1
1
0
0
1
2
2
0
4
1
2
1
1
0
1
0
1
0
0
1
0
0
2
0
1
1
1
0
0
0
0
0
0
2
0
2
1
1
1
1
2
2
1
0
2
0
1
1
0
0
0
1
2
0
0
0
0
0
0
2
0
1
2
0
1
1
0
0
1
0
4
2
1
0
1
0
0
3
1
1
0
1
0
0
1
0
4
0
0
1
0
3
2
5
0
0
0
1
1
1
1
2
1
0
1
0
2
1
1
0
1
1
0
0
1
0
2
1
0
0
2
0
0
1
1
1
0
2
0
2
2
1
1
2
2
0
0
0
2
0
1
1
1
2
0
1
1
1
1
1
1
0
1
1
0
0
2
0
2
0
2
1
2
2
0
0
2
0
1
1
0
2
0
0
1
1
0
0
0
0
1
0
0
0
2
1
5
0
0
1
2
1
2
1
0
1
0
0
0
2
1
0
1
1
1
1
4
0
0
2
2
0
1
1
1
1
2
0
1
0
0
2
1
1
1
1
0
1
1
0
0
1
1
0
0
2
0
4
0
2
1
0
0
2
1
2
2
1
0
2
2
0
0
2
0
0
2
0
2
1
0
0
1
0
2
1
1
0
1
0
0
2
1
2
1
0
2
0
0
0
1
0
0
0
0
0
1
2
1
4
0
0
1
1
1
1
0
0
2
2
1
2
3
1
1
2
1
0
1
1
1
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
1
2
2
1
1
1
0
0
0
2
0
2
2
2
2
0
0
2
0
0
0
1
0
2
0
0
2
0
2
1
0
1
2
0
1
2
0
0
1
1
1
1
1
2
2
1
1
1
0
1
1
1
1
2
0
0
1
2
0
2
1
0
0
1
0
0
0
1
0
2
2
0
0
0
1
0
0
0
1
0
0
2
0
1
0
2
1
0
0
2
3
0
1
1
2
0
1
1
1
0
1
1
5
1
0
2
0
0
0
2
1
3
1
1
0
1
1
1
0
2
2
0
2
1
0
1
0
1
1
1
0
0
1
2
0
0
2
1
1
2
2
0
2
3
2
2
0
1
0
1
0
1
0
1
0
0
2
2
1
0
1
0
0
0
2
0
2
0
1
0
1
2
2
1
1
2
2
0
0
0
1
1
0
1
1
1
1
2
1
0
1
0
0
1
0
0
1
2
1
0
2
1
1
1
2
1
1
1
1
0
0
0
1
1
0
0
0
2
2
1
0
1
0
0
0
0
0
0
0
0
1
1
0
2
1
2
0
1
0
2
2
1
1
1
1
1
0
1
1
0
1
1
1
2
2
1
1
1
0
0
1
0
2
2
0
0
1
1
2
1
0
1
0
0
0
0
2
0
0
1
2
0
2
1
1
0
0
1
1
0
0
2
0
0
2
0
0
1
0
2
0
1
0
0
3
1
0
0
1
1
1
1
1
0
0
2
2
0
0
0
1
1
1
0
0
1
1
0
0
0
0
0
1
1
0
0
1
1
1
0
1
1
1
2
0
1
2
0
2
1
0
0
0
2
0
0
2
1
1
1
0
0
0
2
2
2
2
1
1
0
1
1
2
2
0
0
0
2
1
1
2
1
1
1
1
1
0
1
0
0
1
0
2
0
0
2
0
0
2
0
1
2
4
2
2
0
0
0
1
2
0
1
0
2
0
2
1
0
0
1
0
0
2
0
1
1
0
0
1
3
2
1
0
0
2
1
2
1
0
1
0
3
0
2
1
0
1
1
0
2
1
2
1
2
0
0
2
2
2
1
1
1
1
0
0
2
0
0
1
1
0
2
0
2
0
0
2
0
1
0
1
0
0
1
0
2
2
1
1
2
1
1
2
0
1
0
1
0
2
2
0
2
2
0
1
1
1
0
2
0
2
1
1
2
0
2
1
1
0
0
1
1
1
0
2
2
0
0
0
0
0
1
2
0
0
0
0
1
1
1
2
0
0
2
0
0
1
0
2
0
1
2
1
2
0
0
1
2
2
2
1
0
0
2
0
2
0
1
1
1
0
2
0
0
2
0
0
1
0
1
1
1
0
0
2
0
1
3
0
0
1
2
1
1
0
1
6
2
1
0
0
0
2
0
1
0
2
0
1
0
0
0
1
1
1
2
0
0
0
0
1
0
2
2
0
0
2
1
1
0
2
1
3
0
1
1
1
1
2
2
2
2
0
2
3
1
0
1
0
2
1
0
0
1
1
0
1
1
1
1
2
3
1
0
2
2
0
1
0
1
0
0
0
0
0
1
2
0
0
1
1
0
1
1
1
0
2
0
2
2
1
0
2
0
2
2
1
0
3
0
1
0
1
0
0
1
1
1
2
0
1
0
0
2
0
0
1
1
1
2
3
2
3
0
1
1
0
0
2
0
0
0
1
0
1
1
0
0
0
2
1
0
2
1
1
0
0
1
0
1
0
0
2
0
0
1
2
0
0
1
0
2
0
0
0
0
0
2
0
0
1
4
1
2
0
2
1
0
0
1
1
0
0
0
0
1
0
0
1
1
1
0
1
1
0
1
1
0
2
2
1
0
2
2
0
0
0
2
1
0
1
4
3
0
0
0
0
0
1
1
0
2
1
0
1
1
2
1
2
0
1
1
0
0
2
1
2
2
1
1
0
1
1
0
1
2
1
1
1
1
1
1
1
1
2
0
0
1
2
1
1
1
1
0
2
1
2
2
0
1
2
1
0
0
1
1
1
2
0
0
2
1
0
0
0
2
0
0
0
1
0
2
1
0
1
0
1
1
0
0
1
1
0
0
1
1
2
1
2
0
1
0
1
0
0
0
0
0
1
2
1
2
1
0
1
1
1
0
0
0
0
2
0
0
2
1
1
0
2
1
1
0
2
1
2
1
0
2
0
2
1
0
0
0
2
1
1
1
1
2
1
0
0
0
0
2
1
0
2
0
0
2
0
2
0
2
1
0
1
1
1
1
2
1
1
1
2
1
0
0
2
1
1
0
1
1
0
0
1
0
2
1
2
1
0
0
0
0
0
0
0
1
0
1
1
2
1
1
0
1
1
1
0
2
0
1
0
2
0
0
2
0
0
2
1
0
1
0
0
0
0
0
0
1
0
4
0
0
0
1
2
1
2
1
1
1
3
1
1
0
1
0
1
2
1
2
0
1
2
0
2
2
2
2
3
0
0
1
0
1
0
2
1
0
0
2
0
4
2
1
1
1
2
0
1
0
1
1
0
0
1
1
2
2
2
0
0
0
0
0
1
2
2
0
1
1
0
0
1
0
1
2
2
2
2
1
1
2
1
0
0
2
1
0
3
1
1
1
1
2
1
1
2
1
1
2
0
1
1
1
1
1
2
0
0
2
0
1
2
0
0
0
1
0
2
2
1
0
0
0
1
3
0
1
0
2
1
1
0
0
1
2
1
2
0
0
2
1
1
2
0
2
2
1
1
0
0
0
0
0
2
4
1
0
1
0
1
1
1
0
0
1
1
2
0
1
1
1
1
0
0
1
2
2
1
1
2
1
0
2
2
0
0
0
0
1
2
0
2
0
0
1
1
1
2
0
1
2
0
0
1
0
2
1
0
0
1
2
0
1
0
0
1
2
1
1
2
0
0
2
0
2
0
2
0
0
1
0
0
0
0
0
0
1
2
0
0
1
1
1
0
1
1
0
2
1
0
2
0
0
0
0
2
1
0
1
1
0
0
0
1
2
0
1
2
1
1
0
0
1
0
0
1
0
1
1
2
2
1
3
2
0
0
1
0
0
2
2
0
2
0
4
2
2
1
0
0
3
2
0
2
2
1
0
0
1
1
1
0
2
0
0
2
0
2
2
1
0
0
0
0
0
1
1
2
0
1
2
1
2
2
2
2
2
1
1
1
1
0
0
0
0
1
0
1
0
1
2
0
0
0
1
0
1
1
2
0
0
1
2
2
0
1
1
1
1
2
0
0
0
1
2
1
2
0
1
2
1
0
2
0
0
1
1
0
1
0
0
0
1
1
2
0
2
1
0
2
1
0
2
1
0
1
0
0
0
1
1
1
1
1
0
1
1
0
1
0
1
0
0
1
1
0
6
2
2
0
0
1
1
1
0
0
1
0
0
0
2
2
0
2
0
0
1
2
0
0
1
1
2
0
0
0
0
1
1
0
1
1
2
0
0
1
1
0
2
0
0
1
1
1
1
2
1
0
1
1
2
0
0
2
1
1
0
1
0
0
0
2
0
1
0
2
2
1
0
1
2
0
1
1
1
1
0
1
0
1
0
0
0
4
1
1
0
0
0
3
0
0
0
0
1
2
0
1
2
0
2
2
1
0
1
1
0
1
1
1
0
1
0
0
2
1
2
1
1
0
1
1
1
1
2
2
0
1
2
1
0
1
1
1
0
1
2
1
1
4
1
2
0
0
2
1
1
2
0
1
2
0
1
1
2
2
0
3
0
0
2
2
0
1
1
0
0
0
0
0
0
0
1
0
2
0
1
1
0
1
0
2
0
0
1
0
0
0
2
0
0
0
2
2
0
1
2
0
1
1
0
0
2
1
0
1
0
0
1
0
0
0
1
2
0
1
2
0
0
1
1
0
0
1
1
1
0
2
0
0
2
2
0
1
2
1
1
0
1
0
0
1
2
0
0
0
0
0
0
0
0
2
1
1
0
0
1
1
1
1
0
0
2
0
0
2
2
1
2
0
1
0
1
0
1
0
1
0
0
0
1
1
0
1
1
0
1
1
0
1
0
1
0
1
1
1
0
2
1
0
0
0
1
1
2
0
1
1
2
1
0
1
0
2
0
1
2
2
1
1
0
1
0
1
1
1
1
2
0
0
1
1
1
2
0
0
1
0
2
1
3
0
0
1
3
0
1
0
1
1
1
2
0
1
0
0
0
0
1
0
0
1
1
0
0
2
0
2
0
1
1
0
2
1
1
2
0
1
0
2
1
0
1
1
1
0
0
0
0
0
0
1
0
2
1
2
1
0
1
1
2
1
1
2
0
1
1
0
2
2
0
1
0
1
0
3
2
0
1
1
1
1
1
0
2
0
0
0
0
1
0
1
0
0
1
0
1
0
0
1
1
1
0
1
1
1
0
0
1
2
1
0
0
0
0
0
1
0
1
2
1
0
0
0
2
1
1
0
1
1
0
1
0
1
0
1
2
0
2
1
1
1
0
1
1
2
0
1
1
2
0
0
0
0
2
2
2
2
0
0
0
1
1
0
1
1
0
2
0
1
0
1
1
2
0
0
0
0
0
0
1
2
1
0
0
0
2
1
1
1
1
1
2
2
1
1
2
3
2
2
0
0
0
2
0
0
0
1
1
1
2
2
0
0
2
0
2
0
0
2
0
2
1
1
1
0
2
1
0
2
0
1
0
1
0
1
1
0
1
2
0
2
0
2
0
0
1
1
0
0
0
2
0
0
0
0
1
0
0
0
0
1
2
1
1
3
0
0
0
2
1
0
2
1
1
0
0
1
2
1
0
1
0
3
0
1
1
1
1
3
1
1
1
0
1
0
0
1
0
1
0
0
1
0
1
0
2
2
2
1
0
0
1
2
0
0
0
0
1
1
0
0
0
1
0
1
1
1
0
0
2
1
0
2
1
1
0
1
1
1
1
2
0
0
1
0
2
0
0
1
0
1
0
0
1
3
2
1
1
0
1
1
2
1
1
2
0
0
0
1
1
0
0
0
1
0
0
1
1
2
2
1
0
0
1
1
0
1
1
1
1
1
1
0
2
0
1
1
2
2
1
1
2
3
2
0
0
1
0
2
1
2
1
0
1
0
0
1
3
0
0
2
2
0
1
1
0
0
1
1
2
2
0
0
1
0
1
0
0
0
0
1
0
0
2
0
2
1
0
1
0
1
0
2
2
1
1
1
1
0
0
2
0
1
0
0
2
0
1
1
0
2
0
2
0
2
0
1
0
1
1
0
1
1
1
1
1
2
1
1
0
1
1
1
0
3
1
1
0
1
0
1
0
0
1
0
0
1
2
0
0
0
1
2
1
0
0
1
1
2
0
2
1
0
0
1
1
3
0
0
1
0
1
1
1
1
0
0
0
0
2
1
1
0
2
0
0
2
3
0
1
4
0
2
0
2
2
1
0
2
1
1
0
1
2
0
0
0
1
0
1
2
0
1
0
1
1
1
0
0
1
0
0
0
0
0
1
1
1
0
1
0
0
0
1
2
0
1
1
1
1
0
0
2
0
0
0
0
2
0
1
3
0
0
2
0
1
0
0
1
0
1
2
3
0
0
0
2
1
1
2
0
0
0
1
0
0
0
1
1
1
1
1
2
1
0
1
1
2
0
1
1
2
1
0
2
1
1
0
2
1
1
0
0
2
1
0
3
0
0
2
0
0
1
2
0
0
1
1
0
1
2
0
0
1
2
1
0
0
2
2
1
2
1
2
0
0
0
0
0
1
2
2
1
0
1
0
1
0
1
0
0
1
2
1
0
1
2
3
0
0
0
2
1
0
1
0
1
0
1
2
1
0
0
2
1
1
0
2
2
1
1
2
0
0
0
2
2
1
1
0
0
0
0
2
1
1
1
0
0
1
0
0
1
2
0
2
0
2
0
1
1
0
2
0
1
0
1
1
0
2
2
1
1
1
2
1
0
1
1
0
1
0
0
1
0
1
2
0
0
2
0
0
0
0
2
1
0
0
1
1
0
1
0
1
0
1
0
1
1
1
2
0
1
2
2
1
0
0
0
0
0
1
1
1
0
2
2
2
1
0
1
1
2
0
2
2
1
1
0
0
0
0
0
1
0
0
1
1
0
2
1
1
1
0
0
0
1
0
1
1
1
0
0
0
0
0
0
1
0
0
1
0
2
2
1
0
1
0
2
2
0
4
1
1
0
0
0
0
2
2
0
0
0
0
0
1
0
0
2
1
1
0
0
0
1
1
0
2
0
1
0
0
2
1
2
0
0
2
1
1
1
0
0
1
1
0
2
0
1
1
2
2
1
2
1
0
0
2
1
1
0
0
1
1
0
0
0
2
0
0
0
1
1
0
0
1
1
1
3
2
0
2
0
1
0
1
1
0
1
0
2
1
1
0
1
1
2
2
1
1
0
0
1
0
2
1
2
0
1
2
2
0
0
0
2
2
0
1
1
1
1
3
0
0
1
1
1
1
1
0
0
0
0
1
0
0
1
2
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
1
0
1
0
2
1
1
1
0
0
1
1
0
2
0
0
0
1
1
1
0
0
2
1
2
1
1
2
0
1
1
1
1
1
9
2
1
1
2
1
1
2
0
0
2
1
1
0
0
0
0
0
0
1
0
0
1
1
0
1
1
1
2
0
2
0
0
1
2
1
0
1
2
1
4
1
1
1
2
2
1
1
1
2
2
2
1
0
0
1
0
2
0
1
0
0
0
1
2
1
1
1
0
0
0
0
2
1
1
0
1
2
0
2
1
0
2
0
0
0
1
0
0
0
0
1
1
1
2
0
0
0
0
2
5
1
1
0
1
2
1
1
1
0
0
2
2
2
1
0
0
1
1
1
2
0
2
2
1
1
1
1
1
0
2
0
0
0
0
1
1
0
1
1
0
1
0
0
1
0
2
3
0
1
0
0
0
1
0
1
0
0
0
2
2
1
1
2
2
1
2
0
0
1
1
0
1
1
1
1
0
0
1
0
0
2
1
0
1
0
1
1
1
0
0
0
0
0
1
0
0
0
1
1
0
2
2
2
2
2
0
0
2
1
0
1
2
1
1
1
1
1
0
0
2
0
2
0
1
2
0
0
1
1
1
0
0
0
0
1
2
0
1
1
0
2
1
1
2
0
0
2
2
1
1
2
1
2
0
0
1
2
1
0
0
1
0
1
1
2
1
1
0
2
1
1
0
2
0
2
0
2
1
0
2
1
2
0
0
0
1
0
0
0
1
1
1
1
1
0
1
0
0
1
2
0
1
2
1
2
1
0
0
0
0
1
0
0
0
2
2
1
1
2
0
0
0
1
1
0
0
1
0
1
2
2
0
1
2
1
0
1
1
0
0
1
1
1
1
2
1
2
0
2
3
0
0
2
1
0
0
2
1
0
0
1
2
1
2
1
1
1
0
0
0
0
1
2
0
1
1
0
0
1
0
0
1
2
2
2
0
0
0
1
2
1
1
0
0
2
2
2
2
0
0
2
0
0
1
2
1
2
1
0
0
1
1
0
0
2
1
0
0
0
1
0
1
1
2
1
1
2
0
0
8
1
0
0
1
0
1
2
2
1
0
0
0
1
1
1
0
2
0
0
0
1
2
1
0
1
1
1
1
0
0
1
0
2
2
2
2
0
0
2
1
2
1
0
0
1
0
0
0
2
0
1
1
0
1
1
0
2
2
2
0
1
0
1
1
0
1
0
1
1
1
0
1
1
1
1
1
2
0
0
0
1
1
0
1
1
1
2
1
0
0
1
0
0
2
0
0
2
2
1
2
2
0
0
0
1
2
2
1
2
1
0
1
1
2
0
2
0
0
0
2
0
1
0
0
1
1
1
1
1
1
1
1
0
1
0
1
0
0
0
1
1
0
1
0
2
0
1
0
0
0
1
1
0
0
0
1
0
1
0
0
1
0
0
1
0
2
0
2
1
2
2
2
1
0
0
1
1
0
1
1
0
0
0
2
1
0
0
0
2
2
0
0
1
0
0
2
0
1
1
1
0
0
1
0
2
1
1
2
1
2
1
0
3
2
0
2
1
0
1
2
0
0
0
1
1
1
0
2
2
1
2
0
1
1
2
0
2
0
0
0
0
0
0
3
2
0
2
2
0
0
0
2
0
2
0
0
1
1
0
2
1
0
0
2
0
2
0
0
0
1
0
0
1
2
0
0
1
0
0
1
0
0
0
0
1
0
1
1
0
2
2
1
0
0
0
1
0
1
0
2
1
1
0
1
1
0
0
2
3
1
1
2
1
0
1
0
2
0
0
1
1
0
1
1
2
0
1
4
0
1
0
0
2
0
1
2
1
1
0
2
10
0
2
0
0
1
1
2
0
0
1
2
2
0
0
2
0
2
0
1
0
0
1
0
1
0
2
0
2
2
0
1
0
0
0
3
1
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
1
2
2
1
0
2
1
1
1
0
2
1
1
0
1
2
0
1
0
2
0
1
1
1
2
2
0
2
2
1
0
3
0
0
1
2
2
0
1
1
0
0
0
1
2
2
0
0
0
2
0
2
1
0
1
0
1
0
1
1
2
1
0
1
2
1
1
1
0
2
3
1
1
3
1
0
1
1
0
1
2
1
0
0
0
1
1
0
1
0
0
2
0
0
1
2
1
1
0
0
0
2
1
1
0
2
1
1
1
0
1
0
0
0
1
1
2
1
1
0
0
0
1
1
0
0
2
2
0
2
1
1
1
1
0
0
0
0
0
0
1
0
2
1
2
0
0
0
2
1
1
2
1
1
1
1
2
2
0
0
1
1
1
1
1
3
0
0
1
2
2
1
1
2
0
1
0
1
1
1
2
0
0
1
0
1
1
0
1
1
1
0
2
1
1
0
0
1
0
1
0
1
2
0
1
1
0
2
0
1
1
2
0
1
1
3
0
2
0
1
0
0
1
0
1
2
0
1
3
1
1
1
2
0
1
2
2
0
0
0
2
0
0
0
1
1
1
1
2
0
0
0
1
0
2
1
1
0
1
0
2
0
2
1
0
1
0
0
2
1
2
0
2
1
2
2
0
1
2
1
0
1
2
0
0
0
1
1
2
1
2
1
1
1
1
0
1
0
0
0
1
0
0
0
1
0
1
0
1
1
0
1
1
0
2
1
2
0
1
0
0
2
1
0
1
0
0
0
1
0
1
1
0
2
0
0
0
1
0
0
4
0
1
1
0
0
1
1
0
0
1
2
1
1
0
1
0
1
5
3
1
2
0
1
2
1
0
2
2
2
1
0
1
1
0
1
0
1
0
0
0
1
3
1
1
1
2
0
1
1
0
1
0
1
2
1
2
2
0
1
1
2
1
0
1
0
1
0
0
1
1
0
1
0
2
2
2
2
0
0
0
1
0
1
0
0
0
0
0
1
0
1
1
0
0
0
1
2
0
2
0
1
1
0
0
0
0
2
1
2
2
1
2
0
1
1
0
0
0
1
0
0
0
2
2
2
1
0
0
2
0
2
1
1
0
1
0
2
1
1
0
0
1
0
2
2
0
1
0
1
1
2
1
0
1
2
1
1
1
0
1
1
1
1
1
0
0
1
1
1
0
0
2
0
0
0
0
2
1
0
1
2
1
1
0
0
1
0
3
1
0
1
1
1
1
1
2
0
0
3
1
2
1
0
0
1
2
2
1
1
1
1
1
1
2
1
0
1
2
0
0
0
1
0
2
1
0
1
2
0
0
2
0
1
1
0
1
1
0
0
0
2
2
1
1
2
2
0
2
0
0
1
0
1
1
0
2
0
1
0
1
2
0
2
3
0
0
1
0
0
1
0
0
1
2
1
1
1
0
1
0
1
0
0
0
0
0
2
2
0
2
1
1
0
1
0
0
0
0
1
0
0
0
1
0
2
0
0
1
0
2
0
0
0
1
0
1
2
1
2
1
2
2
0
1
0
0
2
0
0
1
1
1
1
0
1
0
1
0
0
1
0
0
1
0
1
1
2
2
1
1
1
1
2
0
0
1
0
1
1
0
0
1
0
2
0
0
1
1
1
0
0
0
0
2
1
0
1
0
2
0
0
0
0
0
0
0
1
2
2
1
2
2
0
0
0
1
2
1
0
1
1
0
0
0
1
1
1
1
1
0
0
5
1
0
0
2
1
2
1
2
1
0
0
2
0
3
1
0
1
1
2
1
1
1
0
0
2
0
0
0
1
1
0
2
0
0
2
0
2
0
1
1
1
0
2
1
1
1
0
2
2
2
1
1
0
2
1
0
0
2
2
0
1
0
2
0
0
0
2
1
0
0
1
0
1
1
5
1
2
1
2
0
0
0
0
1
0
0
0
2
2
0
1
0
0
1
0
0
2
1
0
2
1
2
1
0
0
0
0
1
2
1
2
0
0
1
0
1
1
1
0
2
2
1
1
0
0
0
1
1
1
0
2
2
2
2
0
1
2
2
2
2
0
0
1
0
0
2
1
2
1
1
0
1
1
0
0
2
1
1
0
2
0
1
0
1
0
0
2
0
2
2
1
2
2
0
1
2
2
1
0
1
0
1
2
0
2
0
2
0
1
0
1
1
2
2
2
0
1
0
0
2
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
2
2
0
1
2
0
2
2
1
2
1
0
2
0
0
1
1
2
1
2
1
1
1
1
1
1
2
1
0
0
0
0
1
0
1
0
0
0
2
0
2
0
0
2
2
0
0
0
1
2
0
0
0
1
0
0
2
2
1
1
1
2
1
0
2
2
0
1
1
0
2
0
2
3
0
0
0
1
1
1
0
1
1
2
1
1
2
1
0
1
1
1
1
0
2
1
1
0
1
0
1
1
0
1
0
0
1
1
0
1
0
2
2
0
2
1
0
1
2
1
0
2
1
0
1
1
0
0
1
2
0
0
2
2
0
2
3
0
0
2
1
0
0
0
1
1
1
1
2
0
1
0
1
0
2
1
1
2
1
2
0
0
2
0
1
1
0
0
1
1
2
2
0
0
2
0
1
1
0
1
1
0
0
0
1
1
2
0
1
0
1
2
0
2
0
0
1
0
1
1
0
2
0
0
0
1
2
3
2
0
1
1
1
0
0
3
0
1
0
2
0
1
2
0
0
1
0
2
1
1
1
0
0
0
1
0
2
1
0
1
0
0
2
2
0
2
2
0
1
0
0
1
1
2
1
1
2
2
2
2
2
1
0
0
0
0
0
1
1
1
0
1
0
2
2
0
2
1
0
1
0
0
1
1
2
0
0
1
2
1
0
1
0
1
0
1
2
1
0
0
0
0
1
1
1
0
0
0
1
0
0
0
1
0
2
2
1
1
1
1
0
1
1
1
2
0
1
1
2
0
1
0
0
0
0
2
0
0
1
0
0
1
0
2
0
1
0
0
1
1
0
0
0
2
0
1
0
0
0
1
1
1
1
0
2
1
0
2
1
0
0
1
0
1
1
1
0
2
2
0
1
0
0
1
1
1
0
1
0
0
0
2
1
2
2
0
1
0
1
2
1
1
2
0
1
1
0
0
0
2
2
0
0
0
5
0
0
0
0
0
0
2
0
0
2
1
1
1
0
0
0
0
2
1
1
0
1
0
2
0
1
2
1
0
0
2
0
0
0
2
1
2
2
2
0
0
2
0
0
0
0
0
2
1
1
0
2
3
0
1
0
1
1
0
2
2
1
2
2
1
1
1
1
2
1
1
0
1
2
2
0
0
1
1
0
0
0
7
0
0
0
0
0
1
0
1
0
0
0
0
0
2
1
1
0
1
1
1
1
0
0
1
1
2
0
2
3
0
1
0
1
0
0
0
1
1
2
0
0
1
0
0
1
1
4
1
1
0
0
0
1
0
0
0
2
0
2
0
0
1
2
1
0
1
0
1
0
0
0
0
2
0
2
2
0
0
1
0
1
0
1
1
0
1
2
1
0
1
2
0
0
1
4
2
0
1
1
1
0
1
0
1
3
0
0
2
1
1
0
1
1
1
2
0
0
0
1
1
0
2
1
2
0
0
1
2
0
0
1
0
0
0
0
1
0
0
1
0
1
1
1
0
0
1
2
0
0
1
0
1
0
1
2
2
0
0
2
0
1
1
0
1
2
2
1
0
0
0
3
1
1
1
1
1
0
1
1
0
1
0
2
0
0
1
1
1
1
2
0
1
2
2
0
1
2
1
1
1
1
2
0
1
0
0
2
2
1
0
0
2
0
1
0
1
1
0
2
0
1
2
2
0
0
0
1
0
1
0
0
3
2
0
1
0
2
0
0
1
0
2
0
0
2
1
2
0
1
0
0
0
1
0
0
3
1
2
0
1
0
1
2
1
0
2
0
0
1
0
0
3
0
2
0
2
0
0
1
0
2
0
1
2
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
4
0
0
1
2
1
0
1
0
1
2
1
1
0
1
2
0
2
1
1
1
1
1
0
3
1
3
0
1
1
0
2
0
1
2
1
0
0
1
0
2
1
0
0
1
1
0
0
2
2
0
0
1
5
1
0
1
1
1
1
1
1
1
1
1
0
3
0
2
1
1
0
0
2
1
2
2
0
1
2
0
2
2
0
0
1
2
0
1
0
2
0
1
2
0
1
0
1
1
1
0
1
1
0
0
2
2
1
1
0
1
0
1
1
0
0
0
3
0
0
0
1
1
1
0
0
0
0
1
0
1
1
2
1
2
2
2
2
0
0
1
0
1
0
0
1
1
2
0
2
0
1
1
0
1
0
2
1
1
3
2
0
1
1
1
0
1
0
1
2
2
0
2
0
1
2
1
2
2
1
0
0
1
1
0
0
1
0
1
1
1
2
1
1
2
2
1
2
2
0
0
0
1
0
1
1
1
1
1
2
1
0
1
1
2
0
2
0
2
1
0
2
0
1
0
0
2
0
2
2
2
0
1
1
2
2
2
1
0
0
0
1
0
0
0
0
0
0
0
0
2
1
2
1
0
0
2
2
0
0
1
2
0
0
2
0
1
2
1
0
0
0
0
2
2
1
0
1
0
0
0
0
0
0
2
1
0
2
0
0
1
0
0
1
0
2
2
1
1
1
0
1
1
0
0
1
0
0
0
0
2
1
0
1
1
2
2
1
0
1
1
1
0
0
1
1
1
0
3
2
1
2
1
0
2
1
1
0
0
1
0
0
0
2
1
0
2
2
2
0
2
0
0
2
0
0
0
0
0
2
1
1
0
1
1
2
1
2
2
0
0
1
1
1
0
0
0
0
1
0
0
1
0
1
0
1
1
2
1
1
0
1
1
0
0
1
1
1
0
1
0
2
1
0
1
0
4
1
0
0
2
0
0
1
1
1
2
0
1
0
1
1
0
1
0
0
0
0
1
0
0
1
2
2
2
0
2
2
0
2
0
0
2
0
0
0
2
0
0
2
1
2
0
0
2
0
1
2
2
1
2
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
2
1
2
2
0
0
1
0
1
0
0
1
2
1
0
0
1
2
1
2
2
0
2
0
0
0
0
1
2
1
0
5
1
2
0
1
1
1
0
2
0
0
1
0
1
2
1
0
1
2
1
1
0
0
0
2
2
0
1
1
0
0
1
1
0
0
2
0
0
0
2
0
0
2
0
0
1
1
1
1
1
2
1
2
1
0
1
1
0
1
2
2
0
0
0
0
0
0
1
1
1
0
1
0
0
2
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
2
0
3
0
0
2
0
1
0
1
1
0
2
0
2
2
1
2
0
0
0
1
1
0
1
0
1
1
2
0
0
1
1
1
1
0
1
1
1
1
0
0
0
2
1
0
3
0
0
0
1
1
1
1
2
1
1
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
2
0
1
0
2
0
1
0
0
0
0
0
1
0
1
1
2
1
1
0
1
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
2
0
1
0
0
0
2
1
1
0
2
0
1
1
1
0
1
0
1
1
0
0
1
1
1
1
0
1
0
1
0
0
1
0
1
0
0
2
0
1
0
0
0
0
0
1
0
2
2
2
0
0
1
0
0
0
2
0
0
1
0
1
1
2
0
0
0
1
2
1
0
3
1
0
1
0
2
2
1
1
2
0
0
2
1
0
1
0
2
1
1
1
2
0
0
0
0
1
0
0
1
0
2
1
1
0
1
2
1
0
0
2
0
1
0
2
0
0
2
1
2
0
2
2
2
2
2
0
1
0
2
1
2
1
0
3
2
0
1
0
0
0
2
2
1
0
1
0
0
0
0
0
1
2
1
1
2
2
2
2
0
1
1
0
0
1
0
1
2
1
0
0
1
1
0
1
0
2
0
1
1
1
0
1
0
2
0
1
2
0
0
3
2
0
1
2
2
2
1
0
0
1
1
0
0
0
1
1
2
0
1
1
0
2
0
0
1
0
0
2
1
0
1
0
2
0
0
0
1
2
1
0
0
2
2
0
0
1
2
0
1
1
1
0
2
0
0
0
2
1
0
0
0
1
2
2
0
1
1
2
1
1
1
1
0
1
0
2
2
2
0
3
1
0
0
2
2
2
0
1
1
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
1
2
0
1
0
1
0
2
1
4
2
0
0
1
1
0
1
0
0
0
1
1
0
2
0
2
1
0
0
0
2
2
2
1
1
1
2
2
0
2
0
0
0
1
0
1
0
2
0
1
0
0
1
1
0
2
0
4
1
0
1
0
1
2
2
0
0
0
5
0
3
1
0
3
1
0
1
0
0
1
1
0
1
2
2
2
2
0
0
2
2
3
0
1
1
0
0
0
0
0
1
2
0
1
0
2
0
0
0
0
0
0
1
0
0
1
0
2
1
0
0
1
1
2
0
0
0
1
0
1
1
1
1
1
2
0
0
2
1
1
1
1
1
1
1
0
1
4
0
0
2
1
0
1
2
1
1
2
2
1
1
2
1
1
0
1
0
2
0
0
0
0
0
1
1
2
0
2
1
0
0
1
1
2
2
0
0
2
1
0
1
1
0
0
0
2
1
0
1
0
1
0
0
1
1
2
1
0
0
1
1
1
1
1
1
1
0
1
1
0
2
0
1
0
0
1
2
1
0
0
2
0
1
0
0
1
1
1
1
1
0
0
0
0
0
0
2
1
1
0
0
0
2
0
0
0
0
0
0
1
1
2
0
0
0
1
1
2
0
2
0
0
1
0
1
0
2
0
1
1
1
1
2
1
1
0
0
1
2
2
2
0
3
0
0
1
0
2
0
1
1
1
1
0
0
1
0
2
2
1
0
0
0
2
0
0
1
2
0
1
0
5
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
2
1
1
1
0
2
0
0
0
2
0
0
2
0
0
1
0
0
0
1
1
1
0
0
2
1
0
1
2
1
1
0
2
2
0
0
1
1
2
1
1
0
1
2
1
0
3
1
0
0
2
0
1
1
1
0
0
0
0
0
1
0
1
1
0
1
1
0
1
1
1
0
0
1
1
1
1
0
0
0
1
0
2
0
0
0
2
0
0
1
1
1
0
1
1
0
1
1
2
2
0
0
0
2
1
1
0
1
2
1
2
0
1
1
1
2
0
0
3
1
0
1
1
1
0
2
0
1
1
7
2
0
0
0
0
1
1
1
1
0
2
2
0
0
2
0
1
0
1
0
1
2
0
0
1
0
0
0
2
1
0
1
0
3
0
2
2
1
1
0
4
2
1
0
1
0
2
0
1
1
0
0
1
1
0
1
2
0
0
1
0
0
1
1
0
0
1
1
1
0
0
0
1
2
0
2
1
0
1
1
0
1
1
0
2
2
0
0
0
1
1
1
0
1
0
2
2
1
2
2
0
1
2
0
0
1
2
2
1
2
2
2
0
1
0
2
0
0
2
1
0
1
0
1
0
2
0
2
2
1
3
0
0
1
0
0
2
1
0
0
0
0
0
0
1
2
2
2
3
0
0
0
0
0
1
1
0
1
0
0
1
2
2
1
1
0
0
2
2
0
0
0
1
2
0
0
3
0
0
0
1
1
0
0
1
0
0
0
2
1
2
0
1
0
1
0
3
2
1
0
1
1
1
1
2
0
0
2
0
2
1
0
2
1
0
1
0
2
1
2
0
0
0
1
2
2
1
0
1
2
1
2
1
2
1
2
0
1
2
1
0
3
0
0
1
1
1
1
0
1
0
1
0
1
0
1
1
0
2
0
0
0
0
0
2
2
0
0
2
1
0
0
1
1
1
1
0
0
1
2
2
0
0
1
1
1
3
0
0
1
1
1
0
0
1
0
0
1
1
0
1
0
0
0
2
0
1
0
0
2
0
1
1
0
0
0
0
0
0
2
2
0
0
1
2
0
0
0
0
1
1
2
1
0
1
2
1
2
0
2
1
1
2
2
0
0
1
0
1
0
0
0
0
1
2
2
1
0
0
1
0
0
0
1
0
0
0
0
1
3
0
1
1
0
2
2
0
1
2
2
2
0
0
0
0
1
0
0
2
1
1
2
1
1
0
2
2
1
1
0
2
1
3
2
1
0
1
0
0
2
1
0
0
1
1
0
1
1
0
1
0
0
0
0
0
1
1
1
1
0
1
1
0
2
1
1
2
2
1
2
0
0
2
2
0
1
0
0
2
0
1
2
1
0
0
0
2
1
2
1
0
2
1
1
2
0
0
1
1
2
2
1
0
0
2
1
1
1
1
2
0
1
0
0
2
1
2
2
0
1
2
0
1
0
1
2
0
0
2
1
1
0
2
0
1
1
2
1
1
1
2
1
0
1
2
2
1
0
0
0
0
1
1
0
2
0
0
0
0
0
2
0
0
1
0
1
0
1
0
1
1
2
0
2
0
2
2
1
0
2
0
0
0
0
0
2
0
0
0
1
1
0
1
1
2
1
0
3
1
1
1
1
2
2
0
1
1
1
0
0
3
0
1
0
0
1
0
0
2
0
1
1
0
1
0
1
0
1
0
1
1
0
1
1
1
1
0
0
2
2
0
2
2
0
1
2
0
2
1
1
0
0
1
0
1
2
0
3
1
2
2
1
0
2
0
0
2
2
1
0
0
0
1
0
0
2
1
0
0
0
1
1
1
0
1
1
1
2
1
0
1
0
2
0
1
1
1
2
0
2
0
0
0
0
1
1
1
1
2
2
0
1
0
1
1
1
0
1
0
0
0
1
0
2
1
2
2
1
0
0
0
0
1
0
2
1
0
0
1
1
1
1
0
1
2
2
2
2
0
1
0
1
2
0
1
1
0
1
0
2
1
1
0
0
0
0
2
2
0
0
0
1
0
0
0
3
1
0
1
0
1
0
1
0
1
1
1
1
1
1
1
1
0
3
0
0
1
0
1
1
2
0
1
2
1
2
0
0
0
1
1
1
0
1
0
0
1
1
1
0
1
2
0
1
0
2
1
0
0
2
1
2
1
0
0
0
1
1
1
1
2
0
2
0
0
0
2
1
1
1
0
0
0
2
0
1
2
0
0
1
0
0
0
1
2
1
0
0
1
1
0
1
1
1
1
1
2
0
1
1
1
3
2
2
0
0
0
0
0
1
1
0
1
1
2
2
2
0
2
1
0
1
0
1
1
1
0
1
1
0
0
0
1
2
1
0
0
1
2
1
1
2
0
1
0
0
0
1
2
1
1
0
0
1
2
1
1
1
1
0
1
1
2
0
2
0
0
0
0
0
0
0
0
3
1
0
0
3
0
0
2
2
1
1
0
0
3
1
1
0
2
2
0
0
0
0
0
0
1
1
1
1
2
0
0
1
2
4
2
0
1
0
1
0
1
0
1
0
2
0
2
0
1
4
2
0
1
1
1
0
0
0
1
0
0
2
0
2
2
1
1
2
1
1
0
2
0
0
0
1
1
0
2
0
2
2
0
2
0
0
1
2
0
2
0
0
1
2
0
0
0
0
1
1
1
0
0
1
1
1
1
2
2
0
2
0
0
1
0
0
2
0
1
1
0
1
2
0
1
2
0
0
0
0
1
1
1
0
2
0
1
1
0
1
1
1
2
6
1
1
0
0
0
1
2
1
0
1
1
0
0
3
0
0
0
1
0
0
0
1
1
1
1
1
2
0
1
1
0
0
2
1
2
1
1
1
0
0
0
2
0
3
0
0
1
0
1
1
1
1
2
2
1
1
2
0
0
0
0
1
1
0
1
1
0
0
0
0
1
0
1
2
0
1
0
1
2
1
0
0
1
2
0
0
0
1
1
0
0
2
0
0
1
1
2
2
0
0
0
1
0
1
1
1
1
1
0
2
0
0
2
0
0
0
2
2
1
0
3
1
1
1
1
1
1
0
1
0
0
1
1
0
0
0
0
1
1
0
2
1
0
0
1
1
2
1
0
1
0
1
1
0
2
0
0
1
1
0
1
1
0
2
2
2
0
0
0
1
1
1
1
1
1
0
1
1
1
1
0
1
0
0
0
2
0
0
0
0
0
3
0
0
1
0
0
0
1
0
0
0
0
1
1
1
2
2
1
0
0
2
1
1
0
1
0
0
0
0
2
1
1
1
0
0
0
2
0
2
0
1
0
0
0
0
1
2
1
0
0
2
3
1
0
0
2
0
0
0
0
1
2
2
1
2
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
1
1
2
1
0
2
1
1
1
1
0
2
0
1
0
2
0
2
1
0
1
1
2
2
2
0
0
1
2
1
1
1
0
0
1
1
0
1
2
0
0
2
0
2
1
1
0
1
0
1
1
2
0
0
2
1
2
2
1
0
2
0
2
0
0
1
0
2
0
1
0
0
1
0
1
1
5
1
1
2
1
1
1
1
0
1
0
3
0
1
1
1
3
2
0
1
1
1
0
0
0
1
1
0
0
4
0
0
2
0
0
0
2
2
0
1
1
1
1
0
2
0
1
1
1
1
1
0
1
1
1
0
2
0
0
0
1
1
1
1
0
2
2
1
0
0
0
2
1
1
2
0
0
2
2
1
2
0
0
2
0
0
2
1
0
1
0
1
1
2
0
2
0
4
0
0
1
0
0
2
0
0
0
1
2
2
0
2
2
2
2
0
1
0
0
0
1
0
0
2
5
2
1
2
1
2
2
1
2
1
0
0
2
2
1
1
2
2
2
0
0
0
1
0
1
2
0
0
0
1
1
0
0
0
1
0
0
2
0
1
4
0
2
2
2
0
1
1
0
1
1
0
1
0
1
2
0
1
0
1
0
1
2
0
1
0
0
1
1
1
0
0
1
0
0
2
0
1
0
0
0
1
1
1
2
1
0
0
0
2
0
1
0
1
0
0
2
2
0
0
2
0
2
2
1
1
2
0
0
2
1
0
2
2
1
1
0
0
0
1
4
0
1
2
1
2
2
0
1
2
2
0
0
1
1
1
0
1
0
1
1
1
0
1
0
1
1
2
0
1
2
2
0
2
0
0
1
0
0
0
2
2
1
2
1
0
0
1
1
0
1
0
0
0
0
0
2
1
1
2
1
2
2
0
1
2
1
1
0
1
0
0
1
0
1
1
1
0
0
0
0
0
1
1
1
2
0
0
0
2
0
0
1
0
2
1
0
1
0
1
2
1
0
1
0
0
1
0
2
1
1
1
1
0
2
0
1
2
1
1
1
1
0
2
1
0
2
0
2
1
0
0
2
0
0
1
1
0
2
1
0
2
1
1
2
0
1
0
2
1
0
0
0
0
0
0
2
0
0
0
2
2
0
1
1
1
0
0
0
1
1
2
1
0
1
2
1
1
1
0
0
0
0
1
2
2
0
2
0
2
1
1
1
1
0
0
0
1
0
2
1
2
2
0
0
1
0
1
1
1
2
1
0
0
0
0
0
0
0
1
0
0
1
2
1
1
2
1
0
1
2
1
0
1
1
1
1
1
0
0
0
1
2
0
0
2
0
0
1
0
0
0
1
0
3
0
1
0
0
2
1
3
0
0
0
1
1
2
0
0
1
1
1
2
0
2
0
0
1
2
1
0
2
2
1
0
1
1
1
0
2
1
0
0
1
1
0
0
1
1
0
0
0
1
1
0
0
1
2
1
1
0
1
2
1
0
0
2
1
2
0
1
1
1
0
1
1
1
2
0
2
1
1
0
0
1
3
0
0
1
2
1
1
1
1
2
1
0
2
0
2
0
1
2
2
2
0
2
1
2
0
1
2
0
0
2
3
0
0
1
1
0
1
2
0
1
1
0
2
0
2
0
0
0
1
0
2
0
0
2
0
0
1
1
1
0
0
1
2
0
0
1
1
2
1
2
1
0
1
0
0
1
2
2
1
2
0
1
1
0
1
2
2
0
1
2
1
2
2
2
0
1
1
1
0
0
0
2
2
1
2
0
0
1
0
0
1
0
1
0
0
1
2
2
1
0
1
1
1
0
1
0
2
1
2
2
0
0
0
2
2
1
2
0
2
1
1
1
0
0
0
1
0
2
2
0
2
0
0
1
1
1
2
1
2
1
0
2
0
0
0
0
0
1
2
1
7
0
0
0
1
0
0
0
1
1
0
2
0
0
2
0
1
0
1
1
3
2
0
1
0
0
0
1
0
0
1
1
2
0
0
1
1
0
0
2
0
3
0
2
0
0
0
0
2
1
2
1
1
0
0
1
2
1
2
2
1
0
2
1
2
2
1
2
0
0
0
2
0
0
1
0
2
2
0
0
1
2
0
2
2
1
0
2
1
1
0
0
0
1
0
2
1
1
2
0
0
1
1
1
1
2
2
1
1
0
3
1
1
0
1
1
2
1
2
0
1
1
2
1
1
1
1
0
1
1
2
1
1
1
2
1
2
1
0
0
1
0
0
2
1
1
1
1
1
0
0
1
0
0
0
0
2
2
1
1
0
1
0
2
2
0
1
2
2
1
0
1
1
2
1
1
1
0
2
0
0
2
1
2
2
1
0
1
2
0
0
1
0
2
0
0
0
2
0
1
1
1
2
1
0
1
1
2
1
1
1
0
1
1
0
0
2
0
1
0
0
1
2
0
1
1
1
0
0
0
0
2
1
2
0
2
1
0
1
0
0
2
3
1
0
2
0
0
0
0
1
1
0
0
0
0
0
2
1
1
0
0
1
1
0
0
1
0
2
0
1
1
0
1
2
2
0
1
0
0
2
2
1
0
2
4
1
2
0
0
2
0
0
1
0
2
0
0
1
0
2
1
0
1
0
3
0
0
0
0
2
1
0
1
1
1
1
0
0
0
0
0
1
1
0
0
1
1
1
1
1
1
2
0
0
1
0
1
2
1
0
2
1
1
0
2
2
0
0
1
1
0
1
1
0
2
1
3
0
0
0
2
1
2
3
1
0
1
1
0
1
1
0
2
0
1
1
0
1
2
1
1
2
1
1
1
1
0
2
0
1
0
0
0
0
1
0
0
1
1
1
0
0
1
1
2
2
2
0
2
2
2
0
1
0
1
1
2
0
0
0
0
1
1
0
1
1
1
0
1
0
1
0
2
1
0
0
1
1
0
0
1
0
1
0
0
1
2
1
1
0
1
1
1
2
0
0
1
0
0
1
1
1
0
2
0
1
2
2
1
1
1
0
2
2
1
2
0
1
1
1
1
0
0
2
0
0
1
0
2
2
2
0
2
0
0
1
1
0
1
1
0
0
0
0
1
0
1
2
0
1
1
0
1
0
2
0
2
0
0
2
1
0
2
2
1
1
1
1
0
1
0
1
0
0
0
1
2
0
1
0
2
0
0
1
0
0
0
1
1
1
2
0
2
0
1
1
1
1
1
0
1
2
1
0
0
0
0
0
1
1
0
1
0
0
1
1
0
0
0
0
1
1
0
0
1
2
0
0
0
3
0
2
0
1
2
0
1
2
1
0
1
2
0
0
1
0
0
2
2
1
2
0
1
1
1
0
0
2
0
1
0
0
2
1
1
1
2
0
1
0
2
2
2
1
2
0
0
0
0
0
1
0
5
2
1
2
0
0
1
1
0
1
1
2
0
1
1
0
0
2
2
0
0
2
2
2
0
2
0
1
1
0
0
1
2
0
1
0
0
0
1
0
1
0
0
0
0
2
1
0
1
0
1
0
1
0
0
0
0
0
0
0
3
2
0
2
1
2
2
1
0
2
2
1
1
1
1
0
1
1
1
2
0
1
1
1
2
1
1
2
0
1
2
0
1
1
2
0
0
0
1
1
0
1
2
0
2
1
2
1
0
0
0
1
0
0
0
2
1
1
2
0
4
0
1
1
1
1
1
0
0
1
1
2
0
0
0
0
1
0
0
2
0
1
0
0
0
2
1
0
0
1
1
1
1
1
0
0
0
1
2
0
2
1
0
2
1
0
0
1
1
0
1
1
0
1
0
2
0
1
0
1
0
1
1
1
0
1
0
1
1
0
1
2
1
0
1
1
2
2
1
1
3
1
2
0
1
0
0
0
0
2
2
0
1
0
1
0
2
0
0
1
2
0
2
1
0
0
0
2
0
2
1
0
0
1
0
1
2
1
2
2
1
0
0
0
2
0
2
2
1
2
1
0
0
1
0
0
0
2
0
0
1
1
1
0
1
0
0
0
0
0
2
0
1
1
1
1
0
1
0
0
0
1
2
0
2
1
1
1
2
1
0
0
0
1
2
0
1
1
0
1
1
1
0
0
1
1
2
2
0
2
2
1
0
0
1
1
2
0
1
2
0
2
1
1
1
0
1
0
0
0
0
2
1
0
0
0
2
0
0
0
1
0
1
0
0
0
2
2
0
2
0
0
1
1
0
0
1
0
0
0
1
2
1
1
0
1
0
0
1
1
1
0
0
2
0
1
0
2
2
1
1
0
2
0
0
1
1
1
0
1
0
2
2
1
1
0
0
2
2
1
1
1
0
1
1
0
0
0
3
1
0
1
2
1
1
1
0
0
0
1
1
2
0
0
0
1
0
1
0
1
0
0
1
1
1
0
0
0
0
0
1
1
1
1
2
0
2
1
0
0
1
2
0
0
1
1
1
0
1
2
0
1
0
0
0
1
1
1
0
0
2
1
0
0
3
2
1
2
1
2
0
3
1
0
2
0
2
1
0
2
0
0
2
1
0
2
0
1
1
2
0
0
1
2
0
1
2
3
1
0
1
1
1
1
1
0
1
1
0
2
1
2
0
2
1
1
0
0
0
0
1
2
1
1
1
2
1
0
0
1
1
0
0
2
0
1
0
2
0
0
1
1
2
2
0
2
1
1
0
1
2
0
0
0
0
2
1
0
0
0
1
3
1
0
0
5
1
2
0
0
1
2
0
1
1
0
0
0
0
0
0
0
1
2
0
0
2
0
1
0
0
0
0
2
0
2
0
1
2
2
1
2
1
0
1
1
1
1
0
1
2
0
1
0
0
1
1
1
0
2
2
1
1
1
0
0
1
2
1
2
1
2
3
1
2
2
0
0
2
0
0
1
1
3
1
0
0
1
2
0
0
0
2
1
1
0
0
0
0
0
1
2
2
0
0
0
0
0
0
1
1
1
1
1
2
0
0
0
1
1
1
0
2
1
1
0
1
1
0
1
1
1
2
0
0
1
1
0
0
0
2
0
0
2
1
1
0
0
0
0
0
1
1
1
0
1
1
2
0
2
1
0
2
1
1
0
0
1
0
1
0
1
1
1
0
0
0
0
1
0
0
2
1
0
2
1
1
1
0
1
0
2
0
0
2
0
0
0
2
1
0
1
0
0
0
0
0
1
0
1
0
2
1
0
2
1
1
0
0
1
1
1
0
2
2
1
0
1
0
0
1
2
1
0
1
1
0
1
0
1
0
0
1
0
2
0
0
1
0
0
1
0
0
2
2
1
0
3
0
1
1
0
0
1
1
1
2
1
1
1
1
1
0
0
0
1
0
0
2
2
1
0
0
0
0
1
0
1
0
0
0
2
1
0
0
0
1
2
0
1
2
0
2
1
1
1
0
0
0
1
1
2
0
2
0
1
1
0
1
2
0
2
1
1
2
0
0
1
1
0
1
2
2
0
1
1
1
2
1
2
2
1
0
1
0
2
2
1
0
0
0
1
2
1
1
2
0
0
0
0
0
1
2
0
1
0
0
0
1
0
0
1
0
0
0
2
2
0
0
0
1
1
0
1
0
1
0
0
1
2
0
0
1
0
0
1
1
1
0
0
1
2
2
0
1
1
2
1
0
2
2
0
1
1
0
1
0
1
1
1
0
0
2
0
1
1
0
0
0
1
0
0
1
0
1
1
1
1
1
1
1
2
0
0
0
1
2
0
1
1
1
0
0
0
0
1
0
1
0
1
2
0
2
0
2
2
2
0
0
1
2
1
0
1
0
0
2
0
1
0
2
2
0
1
3
1
1
0
2
0
1
0
0
2
1
0
0
1
0
1
2
2
0
2
2
2
1
0
2
1
1
0
0
0
2
1
1
2
0
0
0
1
0
0
0
0
1
1
0
1
1
2
1
1
0
2
0
1
1
0
1
2
1
0
0
1
1
0
2
0
2
0
1
2
2
0
1
0
1
0
0
0
2
0
1
2
0
0
1
1
0
0
2
2
0
0
2
1
1
1
1
0
1
1
0
1
2
1
1
1
0
2
0
2
2
0
1
0
1
1
0
2
0
0
0
0
1
0
1
0
2
1
2
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
1
2
0
0
1
1
2
1
1
2
0
0
1
0
2
0
2
1
1
2
0
0
0
2
0
2
2
1
1
1
2
1
0
1
1
1
0
1
1
0
0
2
2
1
0
1
1
1
1
2
1
0
1
1
0
3
1
0
1
0
1
1
0
2
0
1
0
0
1
1
2
0
0
2
1
1
0
1
0
1
1
0
1
1
1
1
2
1
0
0
1
0
1
0
0
2
0
2
2
1
1
0
2
1
2
0
0
1
1
0
1
1
1
2
0
0
1
2
0
0
2
1
0
2
1
0
2
4
0
2
2
0
1
1
1
0
1
1
0
0
0
2
2
0
0
1
2
0
0
1
1
0
0
2
2
1
0
0
1
1
2
0
1
1
0
0
2
0
1
1
1
1
0
1
1
2
0
0
0
2
1
0
2
1
1
1
1
2
0
0
0
1
1
1
0
0
0
0
0
2
0
0
1
1
0
0
3
1
1
1
0
3
1
1
0
0
0
0
1
0
0
0
0
1
1
1
0
2
1
0
2
1
0
0
0
1
1
2
1
1
2
0
1
0
0
1
2
0
0
0
1
1
0
2
1
0
2
0
1
0
1
1
1
0
0
1
2
2
2
1
8
0
0
2
1
1
1
6
1
0
1
1
0
2
0
0
0
2
0
1
0
1
0
1
1
2
0
2
3
1
1
0
0
2
1
2
1
1
0
1
2
1
1
0
1
2
0
1
1
1
2
1
0
1
2
0
1
1
0
1
1
2
0
1
2
0
1
1
1
2
1
2
2
1
1
1
1
0
1
1
1
0
1
0
1
0
5
0
0
1
1
0
2
1
1
0
0
1
1
0
0
0
2
0
0
0
1
2
2
1
1
1
1
1
0
0
0
0
1
2
1
1
1
0
1
1
1
2
0
0
0
0
1
1
1
2
2
1
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
1
1
2
1
1
1
1
2
1
0
0
0
0
0
0
0
2
0
1
0
1
1
0
0
1
0
1
2
0
1
1
0
2
0
0
2
2
0
0
2
1
2
0
0
1
0
0
1
0
0
0
2
0
0
2
0
0
0
2
2
2
0
0
2
1
1
1
1
0
0
1
1
1
0
0
2
1
0
0
0
1
1
0
1
0
0
1
0
0
1
1
0
0
1
1
0
0
1
0
2
2
1
0
0
0
0
0
1
0
0
1
1
0
0
0
1
2
1
1
0
2
1
2
0
1
1
0
1
2
1
1
2
1
2
1
0
1
1
1
1
1
0
1
1
1
0
1
2
0
1
1
1
2
1
0
1
0
0
2
0
2
0
0
0
1
1
0
1
0
0
0
1
1
1
1
0
0
1
1
2
1
1
0
1
2
2
0
2
1
1
2
0
1
0
0
2
1
0
1
1
2
1
0
0
0
0
1
0
0
2
1
1
0
2
0
0
1
0
0
0
1
1
1
0
1
2
1
0
2
0
2
1
0
0
1
1
2
1
1
0
2
1
1
2
1
0
1
2
1
0
2
1
2
0
1
2
1
2
2
1
1
0
1
0
1
1
0
1
2
0
2
1
0
0
1
0
2
1
1
2
1
0
0
1
1
0
2
0
0
2
2
1
2
0
2
4
1
1
0
1
1
0
0
0
1
0
1
0
2
0
0
0
0
1
0
1
2
1
1
1
0
0
1
0
1
1
2
0
1
0
0
1
1
1
2
0
0
0
2
2
1
1
0
2
0
0
3
0
1
0
1
0
1
0
2
1
0
2
0
1
2
1
1
2
2
0
0
0
1
0
1
0
2
2
2
2
0
2
1
1
0
0
2
2
0
0
4
0
1
1
0
1
1
2
2
1
2
2
2
0
0
1
0
2
2
1
1
2
2
3
0
1
1
3
2
1
0
1
0
0
2
1
1
1
2
1
0
1
0
0
2
0
2
0
1
2
1
0
1
0
1
0
2
0
0
1
0
1
0
2
0
0
1
2
1
1
0
0
1
1
0
0
0
1
1
0
0
0
1
2
0
1
0
1
2
0
2
0
0
1
0
0
0
0
0
2
0
2
1
0
1
0
0
1
0
2
2
0
2
1
0
1
1
1
0
2
1
1
2
1
0
1
4
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
2
0
1
0
1
0
0
1
1
0
2
0
1
1
1
0
1
0
2
1
1
1
1
0
0
0
0
1
0
0
2
2
1
0
2
4
2
1
2
0
0
0
1
1
2
0
1
1
1
0
1
0
0
1
0
0
0
0
1
1
0
2
2
2
0
0
1
1
0
2
0
2
0
1
2
0
0
0
0
3
1
1
2
2
0
2
0
0
2
1
0
0
0
1
2
0
0
1
0
0
1
0
1
1
1
1
1
0
1
0
1
0
1
0
1
0
1
0
0
1
1
1
0
0
0
1
0
1
0
0
1
0
0
2
0
0
2
0
0
1
0
2
1
1
0
0
0
2
1
1
1
1
0
0
1
0
1
1
0
1
1
1
2
1
1
1
1
1
1
2
2
2
0
1
0
1
2
1
3
1
0
1
1
1
1
2
1
1
2
2
2
0
0
2
2
0
0
2
1
0
0
1
2
1
2
1
0
0
2
2
0
1
1
0
2
1
0
1
1
1
0
1
2
0
1
1
2
1
2
2
2
0
1
2
1
1
1
0
1
2
0
0
1
0
0
0
0
0
2
1
0
0
1
1
2
1
0
0
2
2
1
0
0
1
0
0
2
0
0
0
2
2
2
1
2
2
0
0
0
1
0
1
0
1
1
1
2
0
2
0
0
2
2
1
1
2
1
0
2
1
1
0
0
0
0
0
0
1
1
1
0
2
1
0
1
0
2
0
2
2
1
2
0
0
1
0
1
2
1
0
1
0
2
2
0
1
1
1
1
1
0
1
0
1
0
0
2
0
1
1
2
3
0
0
0
1
1
1
1
3
3
0
0
1
1
1
1
2
3
0
1
0
0
1
1
0
0
2
0
0
0
0
0
1
0
2
0
1
1
1
1
0
0
2
2
0
0
0
0
2
2
1
2
0
1
0
0
0
2
1
1
2
1
0
2
1
2
1
2
2
0
2
1
0
0
1
1
2
0
2
0
0
0
0
1
0
0
2
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
2
0
2
2
2
2
0
1
1
0
1
0
1
0
0
1
0
1
1
1
1
1
1
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
2
1
0
2
0
1
0
2
1
0
0
1
0
1
0
1
0
0
0
1
1
0
1
2
0
0
1
2
2
1
1
1
0
0
1
0
0
0
1
1
3
1
0
1
0
0
1
0
1
1
2
1
0
2
1
1
0
0
1
1
2
0
0
2
0
0
0
1
0
1
0
0
1
0
2
0
1
2
1
2
0
0
0
2
1
0
0
0
2
1
0
1
1
0
2
1
2
0
1
0
2
0
1
0
0
0
1
1
0
1
1
0
0
0
0
0
2
1
0
1
0
0
1
0
0
0
2
0
1
1
0
1
2
2
0
0
1
1
1
1
2
0
1
0
2
2
2
0
1
2
2
2
1
2
1
0
1
0
2
1
0
0
2
0
0
0
0
0
1
1
1
0
0
0
1
1
2
0
0
0
1
1
0
2
1
0
1
1
0
1
0
0
2
2
0
0
0
1
1
0
2
2
1
1
0
0
1
0
1
1
2
0
1
0
3
0
1
0
0
2
2
0
2
0
1
0
0
0
0
1
1
0
0
1
2
1
1
0
1
0
0
1
1
1
0
3
0
0
2
1
0
0
2
6
2
0
1
1
0
1
1
0
2
1
0
1
0
1
1
1
0
2
0
1
1
2
0
2
2
1
2
1
2
0
0
1
0
0
2
1
0
1
1
1
0
2
0
0
0
1
2
0
2
0
1
0
2
2
0
1
1
1
1
0
2
2
0
0
1
1
0
0
0
1
0
0
0
0
2
0
2
0
0
0
2
0
1
2
0
1
2
0
0
2
0
0
2
1
0
0
1
1
1
0
0
0
0
0
2
0
0
0
2
2
2
0
0
3
1
0
0
1
1
0
1
0
2
1
1
1
0
1
0
2
2
2
0
0
0
2
3
2
2
1
1
2
0
2
0
2
0
0
0
1
0
0
1
0
1
1
0
0
2
0
0
2
0
0
1
0
2
1
0
2
0
1
1
3
0
2
2
0
1
0
0
0
2
1
1
1
2
0
1
0
0
1
0
0
1
1
1
1
0
1
0
2
1
0
2
1
1
0
2
1
0
2
1
0
0
0
2
1
2
0
0
0
2
2
1
1
0
0
2
2
0
0
0
0
0
0
2
1
0
0
2
0
0
1
1
0
2
1
1
0
2
1
0
0
2
0
0
0
2
0
1
0
2
2
0
0
1
1
0
2
1
2
0
1
1
0
1
1
2
2
0
0
1
2
1
0
1
1
0
1
1
1
2
0
1
2
0
1
2
0
2
0
1
1
1
1
0
0
0
0
1
1
2
0
1
0
2
2
0
0
2
0
0
2
0
1
1
1
2
0
0
0
1
0
1
2
1
1
0
1
0
0
1
2
1
1
2
1
1
0
2
0
1
2
0
1
1
0
1
0
0
1
0
0
0
1
1
1
1
0
0
1
0
1
2
0
1
0
0
1
1
1
0
0
2
2
0
1
2
0
0
1
1
1
0
0
2
0
0
2
0
1
1
0
1
0
1
1
0
0
0
0
1
0
1
2
1
1
1
2
0
0
1
2
1
0
2
2
0
2
0
0
1
1
1
1
0
0
1
1
2
0
0
0
1
2
2
0
1
0
1
1
0
0
0
0
2
0
2
1
0
1
1
2
2
0
1
2
1
1
2
2
1
1
0
2
0
1
1
1
1
0
1
1
1
1
2
2
2
1
0
1
0
0
2
2
0
0
1
1
2
0
0
2
0
1
0
1
0
0
0
1
1
1
2
2
1
0
1
1
0
0
0
2
1
0
0
0
0
1
2
2
1
2
1
1
2
1
0
1
0
2
1
2
0
1
0
1
0
1
2
1
0
1
1
2
1
2
1
2
1
1
2
1
0
0
1
0
1
0
0
2
0
0
0
1
0
0
2
1
1
0
0
1
1
1
1
0
1
1
0
2
0
1
2
0
1
1
0
1
1
2
1
1
0
0
1
1
1
0
0
0
0
0
0
0
1
2
1
0
0
1
1
0
0
2
2
1
1
1
0
3
1
1
2
0
0
1
0
1
1
2
0
0
1
1
0
1
0
2
0
0
2
0
2
1
1
1
0
1
0
1
0
2
0
1
0
1
1
2
0
1
1
1
1
0
0
1
0
2
2
2
0
1
0
1
1
0
0
0
2
0
1
2
2
1
2
2
0
1
0
2
2
2
0
0
0
0
0
2
0
1
1
1
0
1
2
2
1
1
1
2
0
0
1
1
1
1
1
1
6
2
0
1
2
0
1
0
1
1
0
0
1
0
2
0
1
1
1
0
0
0
2
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
2
2
0
0
1
2
0
0
3
1
1
2
1
1
0
0
0
1
0
0
2
0
1
1
1
3
0
0
0
0
2
2
2
1
2
0
0
0
0
1
1
0
0
1
1
0
0
0
1
0
1
0
2
1
1
0
0
1
0
0
1
0
0
2
0
0
1
2
3
2
1
2
1
1
3
1
0
1
1
1
2
2
1
0
2
2
1
1
0
1
1
0
2
2
0
0
0
1
0
0
0
2
1
1
1
0
2
1
1
2
0
0
0
0
1
1
2
0
1
0
0
0
1
1
2
2
0
0
2
0
1
2
1
1
1
1
2
1
2
0
1
1
0
1
2
0
0
2
2
2
1
1
2
1
0
1
0
0
0
1
0
0
0
0
0
0
2
2
0
0
1
0
2
1
0
2
1
2
0
2
2
1
1
2
1
2
2
2
2
1
0
2
0
0
0
0
0
1
1
1
0
0
2
0
1
0
0
1
0
0
2
2
0
0
2
0
0
2
0
1
2
1
2
1
0
1
2
1
1
1
1
2
1
1
0
2
1
0
0
0
2
2
1
0
3
2
0
1
1
1
1
0
1
2
2
1
0
1
1
0
2
1
2
1
0
2
0
2
2
1
1
0
1
2
1
0
0
1
2
1
0
2
1
0
1
0
2
2
1
2
1
2
2
3
1
2
1
1
2
2
0
1
0
0
0
0
0
0
0
0
0
0
2
1
1
0
2
1
0
1
1
1
2
1
0
1
2
0
1
1
0
0
1
1
0
0
1
1
1
1
0
2
2
0
0
2
0
1
1
2
0
1
1
0
1
1
2
0
1
0
1
0
0
1
1
1
2
6
0
0
0
3
0
1
2
0
0
0
0
0
1
0
1
2
0
0
1
0
1
1
1
1
2
1
0
0
0
1
1
1
0
0
0
2
1
2
2
4
2
1
0
1
1
0
1
1
0
2
0
1
1
1
0
1
1
0
0
0
1
0
0
2
1
1
0
0
2
1
1
1
0
3
1
1
0
1
0
1
2
1
0
1
0
1
0
1
1
1
2
1
1
2
1
1
0
0
1
1
1
2
3
0
0
1
2
1
0
1
0
0
0
0
1
1
3
1
1
1
0
0
1
2
1
2
0
0
0
0
1
0
0
0
1
2
2
1
0
0
2
1
2
1
1
1
0
2
1
1
1
1
2
1
0
0
0
0
2
2
1
0
2
0
1
0
1
0
1
0
1
0
2
3
2
0
1
0
0
0
1
1
0
1
1
0
0
1
1
1
0
0
1
2
2
1
1
1
0
0
1
0
2
0
0
1
1
0
0
2
1
1
0
0
1
0
0
0
0
1
0
2
1
2
2
1
1
0
1
1
1
2
0
0
0
0
2
0
1
0
0
1
1
3
1
0
1
0
0
0
1
3
1
0
1
2
0
0
2
0
1
1
1
0
1
1
2
0
0
2
1
2
0
2
2
0
1
2
3
0
1
1
2
1
1
2
0
1
0
1
0
1
1
2
1
0
0
0
1
1
2
0
1
1
2
0
0
1
2
0
1
1
0
0
0
1
0
2
0
1
0
2
2
0
1
1
2
0
0
1
2
0
1
1
0
2
0
1
0
1
2
2
1
2
0
2
1
0
1
1
1
1
2
1
1
0
2
1
2
0
1
0
2
1
0
0
2
2
2
0
3
1
1
0
0
1
1
2
1
1
0
0
1
1
2
2
0
2
0
1
1
1
1
1
1
0
0
2
1
0
1
2
0
2
0
0
1
0
1
0
0
2
1
0
1
1
0
2
0
3
1
1
1
0
1
0
2
0
0
5
0
2
1
1
0
1
0
1
2
0
0
1
1
0
0
1
0
0
0
2
2
0
0
2
0
0
2
1
0
0
2
1
1
3
2
0
1
0
1
0
1
1
0
2
0
1
3
0
1
1
2
0
0
0
1
1
1
1
2
1
1
0
0
0
0
0
1
0
0
1
2
0
0
2
0
2
3
0
1
2
0
1
1
0
4
0
1
0
0
2
2
1
0
0
0
0
2
0
1
0
0
0
1
1
1
0
1
2
1
0
1
0
0
1
2
1
2
0
1
2
1
1
1
2
1
1
1
1
0
2
0
2
1
1
2
1
4
1
2
0
0
1
0
2
2
0
1
1
1
0
2
0
3
4
0
0
0
4
0
0
1
1
2
1
1
1
1
1
1
1
1
0
0
0
1
0
0
2
1
2
1
0
1
1
1
1
2
2
1
2
0
0
2
0
0
1
0
2
2
1
2
0
1
1
0
0
2
0
1
2
1
2
1
1
1
2
0
1
0
0
2
1
1
3
2
0
0
0
2
0
1
2
0
1
0
1
0
3
0
1
1
0
2
0
1
1
0
0
0
0
0
0
0
2
2
2
0
1
1
2
2
0
1
0
1
0
1
1
1
2
1
2
1
0
2
0
1
0
0
1
2
0
1
1
2
1
1
1
2
1
1
1
0
2
0
1
0
0
0
0
0
1
0
1
2
2
0
0
0
1
2
0
0
1
0
0
0
1
2
0
2
2
0
0
0
1
0
0
2
0
1
1
0
0
0
1
0
1
0
1
0
2
1
1
0
0
0
2
0
0
1
0
1
2
0
2
0
1
1
0
0
2
0
1
0
0
0
0
0
1
1
0
0
0
1
0
2
1
0
0
1
0
0
2
1
1
0
0
2
1
1
1
0
2
0
2
0
1
0
1
0
0
0
2
1
1
2
2
2
0
0
2
2
1
1
0
0
0
2
0
1
2
1
0
1
1
2
0
2
1
2
0
1
0
2
0
1
2
0
0
1
0
0
1
0
2
2
0
0
1
1
1
1
2
0
0
2
1
0
1
0
2
0
2
2
0
1
1
2
1
1
6
0
0
0
1
1
0
1
2
1
2
0
0
2
1
0
0
1
1
0
0
0
2
1
1
0
1
1
2
2
2
1
1
0
2
1
2
0
0
0
1
0
2
0
0
0
1
1
2
6
0
1
1
0
2
0
0
0
0
0
1
2
1
1
1
0
2
0
1
0
0
0
0
2
1
1
2
1
2
2
1
1
0
2
0
2
2
1
0
1
1
1
1
1
0
0
1
2
0
1
1
0
0
0
2
0
2
0
0
1
1
2
0
1
1
3
0
1
2
0
1
2
2
1
2
0
1
0
1
2
1
1
2
2
0
0
2
1
1
1
1
0
1
0
0
1
1
0
2
1
0
2
2
1
0
2
1
1
0
1
3
0
0
0
0
1
0
1
1
0
0
0
0
1
1
2
0
1
0
1
1
2
0
1
0
0
1
2
1
1
1
2
2
0
2
2
0
2
0
1
0
0
1
0
0
0
0
0
0
1
2
0
0
0
2
0
2
0
2
0
1
0
2
1
1
0
2
1
0
2
1
1
0
0
0
0
0
0
2
1
0
0
0
1
3
0
1
1
0
1
0
2
1
0
1
0
2
0
2
0
2
1
2
0
1
0
1
1
0
2
2
0
2
1
2
0
1
0
2
1
0
1
1
1
0
0
2
1
2
2
1
0
1
0
0
0
1
0
0
2
1
0
1
0
0
0
2
2
0
2
3
0
1
0
1
0
2
2
0
1
1
0
0
1
2
0
0
1
0
1
1
0
0
2
0
0
2
2
1
0
1
0
0
2
2
2
1
1
0
0
1
1
1
0
2
0
0
0
0
0
2
1
0
2
2
1
0
1
0
2
0
0
2
1
0
1
1
1
1
0
0
1
0
1
2
0
0
0
2
0
0
1
0
1
1
1
2
2
0
0
0
1
1
0
1
2
2
0
2
0
0
1
0
2
2
1
1
1
0
1
1
1
2
0
2
2
2
0
1
0
0
2
2
2
0
1
2
0
0
2
0
0
0
1
1
1
0
1
1
2
2
2
0
2
1
2
0
0
2
1
2
1
1
0
0
1
1
0
2
1
0
2
2
4
0
3
2
0
0
0
0
2
2
0
0
0
2
1
0
1
2
0
2
1
1
1
3
1
0
1
1
1
1
0
0
0
3
0
1
0
1
1
0
1
0
1
0
0
2
0
2
0
2
2
1
0
2
0
1
2
0
1
1
2
2
1
1
1
2
0
1
1
0
2
0
1
0
1
1
1
0
0
0
0
2
1
1
1
2
2
0
2
2
0
1
1
0
0
2
1
3
2
0
1
3
2
2
0
0
2
2
0
5
0
0
2
1
0
0
1
1
0
0
1
1
0
0
2
0
1
0
0
0
0
0
1
0
1
0
2
1
1
1
2
0
1
1
1
1
0
1
2
1
2
0
1
0
1
0
0
4
2
1
1
0
2
2
0
1
0
0
0
2
0
2
0
0
0
1
1
2
1
0
1
1
2
0
1
0
1
0
1
0
0
0
1
0
0
0
1
2
0
1
1
2
0
1
1
0
1
2
0
0
1
1
0
0
1
1
2
2
2
1
0
0
1
1
1
0
0
1
0
2
1
2
0
1
2
2
0
0
1
0
0
3
1
0
1
0
2
3
1
2
2
2
1
0
1
0
0
0
0
0
1
0
2
0
1
0
1
0
2
1
0
1
0
0
2
1
0
0
1
2
1
0
1
0
1
1
1
0
1
3
2
1
2
0
1
0
0
2
2
0
1
0
1
0
0
0
0
2
2
0
2
0
1
0
2
2
1
0
0
1
1
1
1
0
2
0
1
3
1
0
0
1
1
2
1
0
0
0
0
0
0
3
0
0
1
1
0
1
1
0
2
1
0
1
4
0
0
0
1
1
1
4
0
0
0
0
2
1
0
2
2
1
2
0
1
0
0
0
0
6
0
1
2
2
0
0
0
1
0
1
2
0
2
1
0
0
1
2
2
2
0
1
0
0
4
1
0
1
1
2
0
2
1
0
1
0
0
0
0
1
1
0
0
2
1
1
1
1
1
2
3
1
2
2
1
2
0
0
1
0
2
2
2
2
0
0
0
2
2
0
0
0
0
0
2
0
0
1
2
1
0
2
2
0
3
0
0
0
2
1
2
1
0
1
2
0
1
2
1
1
1
0
2
1
0
2
0
0
0
1
2
1
1
0
1
1
0
0
1
0
0
0
2
2
1
1
1
2
1
2
3
2
1
2
0
2
0
1
0
0
1
0
2
0
0
1
1
0
0
1
0
0
0
2
0
0
2
0
0
1
1
0
1
5
3
3
3
1
0
1
1
0
1
1
0
2
1
1
1
2
0
1
2
1
0
1
1
0
1
1
0
2
0
1
1
1
0
2
1
0
0
0
1
1
0
1
2
1
0
0
1
1
2
2
0
0
1
0
1
0
2
0
0
1
2
1
0
0
1
2
1
2
0
1
2
0
0
1
2
0
2
0
0
0
0
2
0
1
1
0
0
2
0
0
2
1
0
0
0
0
1
0
0
1
1
1
2
0
1
0
2
2
1
1
0
1
0
0
0
1
0
0
0
2
0
0
1
1
1
2
2
2
0
2
0
2
2
1
1
1
1
1
2
0
1
0
2
2
0
0
1
0
1
1
0
0
1
0
0
1
1
0
0
1
2
1
0
0
2
1
2
1
0
0
1
0
1
2
0
0
0
5
1
1
2
0
0
1
1
2
0
2
0
1
1
0
1
0
1
2
0
0
0
1
1
1
0
0
0
2
1
2
2
1
1
1
0
2
0
0
2
0
0
2
2
2
0
1
0
1
0
0
0
0
2
0
1
0
1
0
2
0
6
2
0
2
0
1
1
0
2
1
1
0
1
0
1
2
0
0
2
2
2
0
2
1
2
0
1
2
0
0
0
2
2
1
1
1
0
0
1
0
1
1
1
0
1
2
0
0
0
0
2
1
1
0
2
0
1
0
0
0
1
0
0
1
1
1
2
0
2
0
1
1
1
1
0
1
1
1
1
1
0
0
2
0
2
0
1
2
0
2
1
2
0
0
0
1
0
0
1
0
2
2
3
0
0
0
1
0
0
2
0
0
1
2
1
0
1
1
1
0
0
0
1
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
2
0
0
0
2
1
1
2
0
2
1
2
1
1
1
0
1
0
2
0
1
2
1
0
1
1
0
0
1
0
2
0
0
1
3
1
2
2
2
0
0
1
1
1
0
2
2
1
0
2
1
0
0
0
0
0
1
2
3
1
0
1
0
2
1
0
1
0
0
0
2
1
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
1
2
1
0
0
0
0
1
2
0
1
2
0
0
0
1
0
0
1
0
2
2
2
1
3
0
1
0
1
0
1
0
0
0
0
1
1
0
1
2
1
1
1
1
1
0
0
2
1
2
1
1
1
0
2
0
1
1
0
0
1
1
1
0
2
1
1
1
2
0
1
1
0
1
0
2
0
2
0
1
1
2
1
0
0
1
1
0
2
0
2
0
0
1
1
0
0
0
2
2
0
1
2
1
1
1
2
0
1
1
2
0
0
1
0
1
2
0
2
1
0
0
0
1
1
1
0
0
1
0
0
1
2
1
1
0
2
1
0
2
1
0
0
2
0
3
1
0
1
1
0
1
0
0
1
2
0
0
0
0
0
0
2
0
2
1
1
1
0
1
1
0
0
1
0
2
1
1
2
1
1
0
1
1
1
0
1
0
3
1
0
0
0
1
0
2
1
1
0
1
0
2
0
0
1
1
0
0
0
2
0
0
1
0
2
0
1
1
2
1
1
1
1
0
2
0
1
2
2
1
1
0
1
0
1
0
0
0
2
2
1
1
0
2
0
1
0
0
1
0
1
0
2
0
2
2
1
1
1
2
2
0
1
3
0
0
1
1
1
1
1
1
0
0
1
1
1
0
0
2
0
2
1
0
1
0
1
2
1
1
0
2
0
1
0
0
0
0
2
1
1
0
0
0
1
0
0
2
0
2
0
1
2
1
1
0
1
0
0
0
0
0
0
1
2
0
1
0
1
1
0
0
0
1
2
0
0
0
1
0
1
0
0
1
1
0
2
2
0
0
1
1
1
2
0
0
1
0
0
1
2
0
0
1
3
1
1
1
2
1
1
0
1
2
1
0
2
0
0
2
0
0
0
0
1
0
2
1
2
3
2
0
1
0
1
0
2
1
0
1
1
0
1
0
1
2
1
0
1
1
2
1
1
1
0
0
0
2
2
2
2
1
1
0
2
1
0
1
1
2
1
1
0
1
0
1
2
0
2
2
1
1
1
2
0
0
2
2
1
0
0
0
2
0
0
1
1
2
1
2
1
0
0
1
1
2
0
1
0
0
0
0
1
2
2
0
1
0
1
1
1
2
2
1
1
2
0
0
1
1
1
0
0
0
1
1
0
0
0
1
0
2
0
1
2
0
1
0
1
0
1
0
2
1
0
0
0
0
0
1
1
0
1
2
2
1
1
1
2
0
1
0
2
1
1
0
0
0
1
2
1
0
0
2
2
1
1
0
0
1
1
2
2
2
0
1
0
2
2
0
1
1
2
2
0
0
0
0
0
2
1
0
0
1
1
1
1
0
1
1
0
1
2
0
1
1
0
1
4
1
2
0
1
0
0
0
0
0
0
2
1
0
3
1
0
2
0
0
0
1
0
1
1
0
0
0
1
0
2
1
2
0
0
2
2
0
1
0
1
0
1
1
0
0
1
2
0
0
2
1
2
0
1
0
1
2
1
1
1
0
2
2
0
1
0
0
2
0
2
2
0
1
2
0
0
2
1
2
0
1
0
1
2
1
0
0
1
1
2
0
0
2
1
2
1
0
0
0
1
2
2
1
1
2
0
1
1
0
0
2
2
0
0
3
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
2
1
1
0
0
1
1
0
1
1
0
0
1
0
0
0
2
2
3
1
2
1
0
1
2
1
0
2
0
1
2
2
0
0
1
1
2
1
0
1
1
1
0
2
1
0
0
0
0
2
0
1
1
1
0
0
2
0
0
1
2
0
0
0
1
1
0
1
1
0
0
0
1
1
2
2
0
1
1
1
5
0
2
4
2
0
0
2
0
1
1
0
2
1
2
1
0
2
0
1
0
0
1
1
0
2
1
1
2
0
1
1
1
0
0
1
1
2
0
0
1
0
0
0
1
1
0
0
0
2
1
0
1
1
0
1
1
0
1
2
2
2
0
1
1
1
0
0
2
2
0
1
0
1
0
1
0
1
2
1
2
1
2
2
1
2
1
2
1
1
0
0
2
0
0
0
0
1
0
0
2
1
1
2
1
2
2
1
1
0
0
1
1
2
2
1
0
0
0
0
0
1
0
1
0
1
0
2
2
0
0
1
0
0
1
0
2
2
1
1
1
0
1
0
0
1
1
2
2
1
0
1
0
2
1
1
1
1
1
0
0
1
0
3
1
0
0
1
1
1
0
0
1
1
2
3
1
0
0
2
2
1
1
0
0
0
0
1
2
0
0
1
0
1
1
2
1
1
0
0
2
2
0
0
2
0
1
1
0
2
1
1
0
1
1
1
0
0
1
0
0
1
1
2
4
2
0
0
1
2
2
2
1
0
0
1
0
2
0
0
0
0
1
2
2
1
1
0
0
0
0
1
1
0
1
1
0
1
1
1
2
0
0
0
1
1
1
0
0
0
0
1
0
0
2
0
1
1
2
0
0
0
2
2
0
0
1
0
2
1
0
2
0
1
0
0
1
0
2
1
0
3
0
1
1
1
2
1
0
1
2
0
2
1
0
0
1
1
1
0
1
3
2
1
1
1
1
2
1
0
0
6
0
1
2
0
2
1
0
2
1
1
1
0
1
0
0
2
1
1
1
2
0
2
0
1
0
1
0
2
0
0
0
1
1
1
0
1
2
2
1
3
1
0
1
0
0
1
1
0
2
0
2
0
2
0
0
0
1
0
1
1
0
2
0
2
2
1
0
1
0
1
0
1
0
1
2
1
0
1
0
0
1
1
0
1
1
2
1
0
0
2
2
0
2
2
0
2
1
2
0
0
0
0
0
0
2
0
1
2
0
1
0
1
0
1
1
2
1
2
0
1
0
3
0
0
0
0
1
2
2
2
3
0
1
2
0
2
1
1
1
2
2
0
0
1
0
2
0
1
2
0
1
1
2
2
0
1
0
2
0
0
0
0
0
1
1
1
0
1
1
1
0
0
1
0
1
1
1
0
1
1
0
0
0
0
1
1
1
2
2
2
3
1
0
0
0
1
1
0
0
0
1
1
2
2
0
0
2
1
1
2
0
0
1
1
0
4
1
0
0
0
0
0
0
1
0
0
1
0
0
2
2
0
1
0
1
0
1
2
1
0
1
1
0
1
1
0
2
0
1
1
1
1
2
2
1
0
1
1
0
0
0
1
1
0
1
1
0
1
0
1
1
0
2
0
0
1
1
2
0
1
0
1
1
1
1
1
2
0
0
1
2
2
1
1
1
2
0
0
0
0
2
2
0
0
1
0
1
0
1
0
1
1
1
1
0
1
0
0
0
0
0
2
0
0
1
0
0
1
2
0
1
1
2
0
2
1
0
1
1
2
1
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
2
0
0
2
2
1
0
1
0
1
1
1
0
1
1
1
0
2
3
0
0
1
2
2
1
2
0
1
2
0
0
2
0
2
0
0
2
1
0
2
0
1
2
2
1
2
0
0
0
3
0
0
1
0
2
1
1
1
0
0
1
1
0
1
2
0
1
1
0
0
2
1
1
1
0
1
1
1
2
2
2
1
0
1
1
1
0
0
1
0
0
1
0
0
1
2
2
2
2
2
1
1
0
0
0
0
1
1
1
2
2
2
0
0
3
1
1
0
0
1
0
2
0
0
0
0
1
0
0
2
0
2
1
1
2
0
3
0
1
2
0
1
0
0
0
0
1
3
2
1
1
0
0
1
1
0
1
1
0
2
1
1
2
1
2
1
1
0
1
1
2
2
0
2
1
1
0
1
1
1
1
1
0
1
0
1
1
1
1
2
1
1
1
0
1
0
0
0
0
1
2
1
0
0
1
0
2
1
0
0
2
1
2
1
0
0
0
0
1
0
2
0
0
0
0
1
1
0
0
2
2
1
1
2
0
1
1
2
0
1
0
2
3
1
0
2
2
0
2
1
2
0
0
2
1
0
1
1
0
1
0
2
0
0
0
0
0
0
1
1
1
0
2
0
1
1
0
1
1
1
1
0
0
0
1
2
1
1
0
2
0
0
0
1
0
2
0
2
2
1
1
1
1
1
1
1
1
3
0
1
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
2
1
0
1
2
1
0
0
1
0
0
1
1
0
0
1
1
0
0
1
0
1
0
1
1
0
2
1
2
0
0
1
0
0
1
1
1
1
0
1
1
3
1
1
1
1
0
2
2
2
1
3
0
2
2
0
1
1
0
1
1
0
1
0
1
0
2
1
0
1
0
1
2
0
0
0
0
1
0
1
1
0
0
2
0
1
1
2
0
1
2
1
1
0
1
1
1
1
0
1
1
5
0
1
0
1
2
0
0
0
1
2
0
0
1
1
2
2
0
0
0
0
1
1
2
0
0
0
0
0
1
0
0
0
0
1
0
2
1
2
0
2
0
0
0
0
0
0
0
1
0
0
0
1
1
2
1
0
0
1
2
1
0
2
1
0
1
0
0
0
2
2
0
0
2
1
2
0
0
1
0
0
2
1
1
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
1
0
0
1
2
0
0
1
1
2
0
1
1
0
2
1
2
2
1
0
0
1
1
0
2
0
0
2
2
2
4
2
1
2
1
0
2
0
0
2
1
1
1
0
1
0
1
1
1
0
1
0
0
0
0
0
2
1
1
1
1
0
0
2
0
0
1
0
2
0
1
0
1
0
2
2
1
0
3
1
2
1
1
2
2
0
1
0
0
0
1
2
0
1
0
1
1
1
1
1
2
0
2
0
1
2
0
0
0
1
0
0
1
0
1
2
0
0
0
1
0
1
2
0
0
0
2
0
3
0
1
0
0
0
1
0
1
1
0
1
1
0
1
0
1
1
1
2
0
1
1
1
0
0
1
2
1
0
0
0
1
1
1
1
0
0
2
1
2
0
2
1
0
2
0
2
2
1
0
0
0
0
0
1
1
1
0
0
1
0
0
1
1
1
0
0
1
0
1
1
2
0
0
0
0
1
0
1
1
1
3
0
0
0
1
1
1
1
0
0
0
0
2
2
1
1
1
2
1
2
2
2
2
0
0
3
0
1
0
0
0
0
1
2
0
2
0
1
2
0
1
1
0
1
1
1
1
1
0
1
0
2
1
2
0
1
0
0
0
1
0
0
0
2
1
2
1
0
0
0
1
2
0
0
1
0
1
1
1
0
0
1
0
0
1
1
1
1
2
1
2
1
1
0
0
0
0
0
1
1
1
0
1
2
2
0
1
0
0
0
2
1
1
1
1
1
0
1
1
0
0
1
0
2
1
1
1
0
0
1
2
0
1
2
0
0
2
1
1
0
0
1
1
0
1
0
0
1
0
1
0
0
0
2
1
1
2
0
1
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
1
3
1
1
2
0
0
0
0
2
0
1
3
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
2
1
0
0
1
1
1
1
4
1
0
0
0
0
0
0
1
1
1
0
1
0
1
1
0
1
2
2
2
0
0
1
1
2
1
2
2
0
0
1
0
0
0
0
0
0
2
0
2
0
2
1
1
0
1
0
0
2
2
0
2
1
2
1
1
1
3
1
0
2
1
3
0
1
2
1
0
0
1
0
0
0
1
1
1
2
5
1
0
2
0
1
3
1
0
0
0
1
2
1
0
0
0
0
0
0
0
0
1
0
1
1
2
0
0
0
0
2
1
2
0
2
0
0
2
0
1
0
1
0
0
1
2
0
1
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
1
2
2
2
2
3
2
0
1
0
1
1
1
2
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
2
1
0
1
0
0
1
1
0
1
1
2
0
2
0
1
2
0
0
1
0
1
1
1
1
1
1
1
1
1
0
0
0
1
0
2
0
1
1
2
1
1
2
0
2
2
1
2
2
0
1
0
1
0
1
0
0
1
1
0
0
2
1
1
2
1
1
0
1
1
0
1
1
2
3
1
2
0
1
2
1
1
1
1
0
1
2
0
0
2
0
2
0
1
1
1
0
2
1
2
1
0
0
1
1
0
0
1
2
2
0
1
1
1
0
1
0
1
2
1
2
0
1
1
1
0
0
2
1
1
2
2
2
0
0
2
1
0
0
0
1
1
1
0
1
0
0
1
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
2
1
0
0
0
0
1
0
0
0
1
1
0
0
1
0
3
1
0
1
1
1
0
2
0
1
2
1
0
1
2
0
0
0
0
0
1
0
1
1
1
0
1
2
0
2
1
0
2
0
0
2
0
1
0
0
0
1
0
0
2
0
2
0
0
1
0
0
2
1
1
0
1
0
0
1
1
1
1
1
1
0
1
2
1
0
2
1
1
2
2
0
2
0
0
0
0
0
0
2
2
2
0
0
1
2
0
2
1
0
1
1
0
1
1
0
2
2
2
1
0
0
2
2
0
0
2
2
1
1
1
2
2
0
0
1
0
1
0
0
1
0
2
0
0
4
0
1
0
1
0
0
1
0
2
1
1
1
2
0
0
1
2
2
1
1
0
0
1
0
0
0
0
2
1
1
3
0
2
1
1
0
1
2
0
0
1
2
1
0
1
0
2
1
0
0
0
1
0
0
4
0
1
1
1
1
2
0
1
1
0
0
0
1
0
1
0
1
0
0
1
0
0
0
1
1
1
2
0
1
2
2
1
1
1
1
2
1
2
1
0
0
1
0
0
1
1
1
0
1
0
1
1
0
0
0
2
0
0
0
1
0
0
1
2
2
2
0
0
1
2
0
1
1
1
1
1
1
1
0
1
1
0
1
2
1
1
0
0
0
1
0
1
0
1
0
1
0
2
1
1
1
3
1
2
2
1
2
0
1
1
0
3
0
0
1
1
0
2
2
0
0
0
0
2
1
1
1
0
0
0
1
0
1
1
1
0
1
2
3
1
2
0
1
0
1
1
1
0
0
1
0
1
2
2
1
1
0
2
2
1
1
0
0
0
1
3
0
1
3
0
1
1
1
1
1
1
4
1
4
1
0
0
1
0
1
2
1
1
1
0
1
1
1
0
1
0
2
0
1
0
2
0
1
0
0
1
0
1
1
2
1
0
0
0
1
2
2
2
1
1
0
0
0
2
2
2
0
0
0
1
1
1
2
0
0
2
1
0
1
1
0
1
1
0
0
2
0
1
0
1
3
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
1
1
1
0
0
0
0
0
2
1
0
1
0
2
1
2
1
1
0
1
0
1
3
0
1
0
1
0
0
2
2
1
2
1
2
0
0
0
0
1
0
0
2
0
1
1
1
1
0
0
1
1
0
0
1
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
2
0
0
1
1
0
2
0
0
2
2
0
0
1
1
0
1
0
1
0
0
0
0
5
1
2
1
2
2
0
0
1
0
3
2
0
0
0
0
2
0
0
0
3
1
1
1
1
2
0
1
0
0
0
2
0
1
0
1
1
2
1
1
1
1
0
1
2
2
0
1
2
1
2
2
1
0
1
3
1
0
2
0
0
1
0
2
1
1
1
0
0
0
1
2
0
0
1
2
0
0
1
0
1
3
0
2
2
0
1
0
1
2
2
2
0
1
0
1
0
0
0
0
1
0
2
2
1
0
1
4
0
0
1
2
0
1
1
1
0
0
1
2
0
0
1
0
2
0
1
0
2
0
0
1
1
1
1
0
2
1
2
1
0
0
1
1
0
0
1
0
0
0
1
0
0
3
2
1
1
2
0
2
0
1
3
0
0
0
0
1
2
1
0
0
1
1
1
0
1
1
2
2
2
2
1
1
2
2
1
0
1
0
0
1
1
0
1
2
0
0
0
0
0
2
1
0
0
1
1
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
2
0
0
1
0
1
0
1
0
2
2
0
2
0
0
0
0
1
1
0
2
1
0
0
0
1
0
0
1
2
2
0
1
1
2
0
2
0
2
2
0
2
0
0
0
2
1
0
2
2
1
1
1
2
2
0
3
0
0
3
1
0
0
0
1
1
1
1
0
1
1
2
0
0
0
0
1
0
1
0
1
2
2
0
2
0
0
0
1
1
0
0
0
0
1
0
0
2
1
1
1
0
0
1
1
0
2
2
2
1
1
2
0
1
1
0
0
1
0
1
1
0
0
1
0
1
1
1
0
1
1
0
0
0
1
0
2
1
0
1
3
2
0
1
2
1
2
3
0
1
0
0
1
1
1
0
1
0
2
1
1
0
1
1
2
0
0
1
1
0
0
1
0
2
0
0
2
0
0
1
0
0
0
1
0
3
2
0
2
1
0
0
0
0
1
0
4
1
2
0
0
0
1
1
0
2
0
1
2
0
1
2
1
0
0
2
0
2
0
1
1
0
2
2
0
1
0
1
1
1
0
0
1
1
2
0
1
2
0
1
1
0
0
0
0
0
1
0
1
0
0
1
1
1
0
2
0
0
1
1
1
2
0
1
1
2
0
0
0
0
1
2
2
4
0
0
2
1
0
0
3
2
0
2
0
0
1
2
0
1
0
0
1
0
2
2
3
0
0
1
2
0
1
0
0
0
1
0
1
0
0
0
1
1
1
1
1
1
0
1
1
0
0
0
0
0
1
2
1
2
1
2
1
0
1
1
0
0
0
2
1
2
1
1
0
0
2
2
1
1
1
1
2
0
1
2
1
1
2
1
1
0
0
2
0
1
2
2
0
0
1
0
1
2
1
2
0
1
0
1
1
0
0
0
1
0
1
2
0
1
1
1
1
0
3
1
1
1
0
2
1
0
1
0
0
1
0
0
0
1
2
1
2
1
0
0
2
1
1
1
0
0
2
0
1
1
0
1
1
0
0
0
1
1
1
1
2
1
1
0
1
0
1
1
2
2
2
2
0
0
2
0
1
2
0
3
1
1
1
1
0
2
0
0
0
2
0
1
0
1
2
1
1
1
0
1
1
1
0
1
1
1
0
0
0
2
0
0
0
0
1
1
1
1
1
1
1
2
0
2
1
1
1
1
0
0
1
1
1
2
1
1
1
0
2
1
0
2
0
1
1
0
1
2
1
0
1
3
2
2
0
0
1
1
1
0
1
0
1
0
1
1
2
1
2
2
1
2
1
1
0
1
0
0
0
0
2
1
1
1
1
1
0
0
0
1
0
0
1
0
2
1
0
1
3
1
0
0
1
1
1
0
0
0
2
1
0
1
2
1
1
0
0
2
1
2
1
1
0
2
0
1
2
1
2
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
1
1
0
1
0
2
0
0
1
1
0
2
0
2
0
1
2
2
2
1
1
1
2
2
2
0
0
0
0
1
1
1
0
2
1
2
1
0
1
0
1
0
0
1
1
1
1
0
1
1
1
0
0
0
1
1
2
2
0
0
2
3
0
0
0
0
2
1
1
0
0
0
1
1
2
2
0
0
1
0
2
0
3
0
2
2
2
0
0
1
2
1
2
1
0
1
0
0
0
1
1
0
2
5
0
0
1
0
1
0
1
1
2
0
1
1
1
2
0
2
1
1
1
0
2
1
2
0
0
1
0
1
0
1
1
0
1
0
0
1
1
0
1
1
2
1
0
0
1
1
0
1
0
1
0
1
1
0
0
2
0
1
1
2
1
2
2
1
2
1
1
0
0
2
0
2
1
1
0
0
0
2
0
1
1
4
1
0
2
1
0
0
0
2
0
1
0
2
0
0
2
0
0
2
0
0
0
1
2
2
0
1
2
0
0
2
0
1
0
0
0
1
1
1
0
0
1
0
3
0
0
1
0
1
0
1
1
0
1
0
2
0
0
0
2
0
1
0
0
0
0
1
0
2
1
1
0
2
0
1
1
1
1
1
4
0
0
2
1
1
0
1
2
2
1
2
2
0
2
2
2
0
1
2
1
0
2
0
2
1
2
1
0
1
1
2
1
0
0
0
1
0
0
2
0
0
2
2
0
1
2
1
2
2
2
1
0
2
2
2
2
1
2
1
1
0
0
1
0
0
0
2
2
1
0
0
1
1
0
1
1
0
0
1
0
3
0
1
1
0
0
0
0
1
2
0
1
0
1
2
2
0
2
0
0
0
2
1
0
1
0
0
2
0
1
0
1
1
1
2
0
0
0
0
0
0
2
2
0
1
1
0
1
0
1
1
1
1
1
1
0
2
2
0
1
0
0
2
0
2
2
1
2
0
1
5
2
0
0
1
2
0
0
0
0
1
2
0
2
0
1
1
1
1
2
2
1
0
0
0
1
2
1
1
2
1
0
1
0
2
2
2
1
1
1
1
0
2
1
0
1
0
0
2
2
1
0
2
1
1
2
0
0
2
0
2
0
1
1
0
2
1
0
2
1
1
2
0
0
0
0
1
1
1
0
0
2
0
1
1
1
0
1
2
0
0
0
1
1
1
0
1
1
1
2
0
1
1
2
1
2
2
1
1
1
1
1
0
1
0
1
1
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
1
0
0
1
1
0
0
2
2
0
2
1
1
1
2
1
0
0
2
0
0
2
0
0
2
0
1
2
1
0
0
2
0
2
0
1
0
2
2
1
2
0
0
1
1
0
1
1
0
1
1
2
0
1
1
2
1
0
0
0
2
1
0
1
1
2
0
0
2
0
0
1
2
0
0
1
1
1
2
1
0
0
0
2
2
2
0
2
1
1
1
2
3
2
1
0
1
1
1
0
2
0
0
0
0
2
2
1
2
1
0
1
1
1
2
1
1
1
1
0
0
2
0
0
2
1
0
2
1
0
1
0
2
1
2
0
1
0
0
1
2
1
0
1
1
2
0
2
0
0
1
0
1
3
1
1
0
2
2
1
2
0
0
0
1
1
2
2
1
1
1
1
1
0
0
0
0
1
0
0
0
1
1
2
0
2
1
0
2
1
2
0
0
1
0
1
1
1
0
2
0
2
1
0
0
0
0
1
2
0
1
1
0
1
1
0
1
0
1
1
0
1
0
1
2
0
0
2
0
0
0
0
2
0
2
0
3
0
0
0
1
0
0
2
0
0
1
1
1
1
0
0
1
0
1
2
0
2
0
0
1
1
0
0
0
1
2
0
1
0
2
2
0
2
1
1
2
1
2
2
0
1
0
0
1
0
0
1
2
0
2
0
1
1
1
0
0
0
1
1
2
1
0
0
2
2
1
1
0
0
2
3
2
0
0
0
2
1
0
1
2
1
1
0
0
0
2
1
1
0
2
0
1
1
1
0
2
1
3
1
1
0
1
2
0
0
1
0
1
0
2
1
0
1
1
1
0
2
0
0
0
1
1
0
2
1
0
0
0
0
2
2
0
1
0
0
2
1
1
4
1
2
0
1
0
1
1
1
1
0
0
0
1
2
1
0
0
0
0
1
2
2
2
2
0
2
0
1
1
1
2
1
0
0
0
0
0
2
0
0
3
1
0
0
1
1
0
1
2
1
1
1
0
1
2
2
0
1
0
1
0
0
0
0
1
1
0
2
0
1
1
1
0
2
0
0
0
2
1
0
0
1
1
0
0
1
2
0
2
2
1
0
0
2
0
1
0
1
1
2
1
1
2
0
1
1
1
0
2
2
2
0
2
1
0
0
1
1
2
1
2
1
1
1
1
0
0
2
0
1
2
0
0
2
1
0
0
0
4
1
0
1
0
2
0
1
1
2
1
0
0
0
1
0
3
1
0
0
1
2
2
0
1
1
1
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
2
2
2
0
2
0
1
1
1
0
2
0
2
3
1
0
2
0
0
1
2
1
1
0
1
1
1
2
1
1
2
1
1
1
2
0
0
0
1
1
1
2
0
2
0
2
0
1
1
0
0
1
1
0
0
2
0
0
1
0
2
2
3
2
2
0
1
0
2
2
1
0
0
2
0
2
1
2
2
1
2
0
1
0
0
2
1
1
1
1
0
1
0
1
1
0
0
0
1
0
3
1
0
0
0
1
0
0
0
1
0
1
1
2
0
1
0
0
0
0
0
1
2
2
1
0
2
2
0
2
1
0
2
1
1
1
1
1
1
0
1
2
0
0
0
1
0
1
1
0
2
1
0
2
1
1
1
2
0
0
1
1
0
0
2
1
0
0
1
0
3
0
1
0
1
2
1
1
1
0
1
0
1
2
2
0
0
1
0
0
4
1
2
1
1
2
2
1
1
0
1
0
2
1
1
1
0
2
1
2
0
3
0
1
1
0
1
2
2
1
1
0
1
1
0
3
0
0
1
1
0
0
0
1
1
2
2
0
0
2
0
1
4
0
0
1
2
1
0
0
0
1
1
2
0
0
0
0
2
1
1
0
0
1
0
1
1
1
2
2
2
0
1
1
0
0
0
2
0
1
0
0
0
1
1
1
2
0
1
1
0
1
1
1
0
2
2
1
0
0
0
0
0
1
2
0
0
1
0
2
0
1
2
0
0
1
1
2
0
2
0
0
0
2
1
2
1
1
0
2
0
0
1
1
0
1
0
2
0
0
1
1
1
0
1
1
2
1
0
1
0
1
0
0
0
0
0
1
0
2
0
0
2
0
2
2
1
1
2
0
0
1
1
0
0
1
1
1
1
2
2
2
1
1
2
2
3
1
0
0
0
0
1
1
1
1
1
1
1
0
1
2
0
0
0
2
0
1
0
1
1
0
0
0
0
0
2
1
0
0
2
2
0
2
2
0
0
0
2
0
1
0
0
0
1
1
1
0
1
1
0
1
1
0
2
0
0
0
2
2
1
2
1
2
2
2
1
2
2
1
0
0
0
2
0
1
1
0
0
0
2
2
2
1
2
0
0
2
2
2
1
2
0
1
2
0
2
2
3
1
1
1
0
2
1
0
0
0
2
0
1
1
1
0
0
1
1
1
2
1
1
0
0
2
2
0
0
1
1
0
0
1
0
1
1
1
1
0
2
0
1
1
0
1
1
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
1
1
4
1
1
0
2
1
1
0
0
0
2
0
3
0
0
0
0
1
2
2
0
3
2
1
0
2
2
2
0
2
0
1
0
2
0
0
3
0
0
2
2
1
3
0
1
1
2
1
1
2
2
2
2
1
2
0
0
0
0
0
0
2
0
1
2
0
1
0
2
0
2
0
0
0
0
0
1
0
2
1
1
1
2
1
1
0
0
0
1
0
1
1
1
1
3
2
0
2
1
1
1
0
1
2
1
2
1
1
0
2
1
0
2
0
2
2
0
2
2
2
3
2
2
1
1
1
0
0
0
1
0
0
0
3
2
0
1
0
0
2
2
0
0
1
1
1
1
2
1
0
2
1
1
2
1
0
2
1
1
0
0
0
1
0
0
0
2
1
1
0
1
2
0
0
1
0
2
1
2
0
0
1
1
1
3
1
1
0
0
0
1
0
0
0
0
0
1
0
1
1
2
0
3
1
0
1
1
2
0
1
0
0
2
1
0
1
0
0
1
1
0
2
1
2
1
1
1
2
1
0
1
1
1
0
1
0
1
0
1
1
0
1
0
1
1
2
0
0
1
0
0
1
0
0
0
0
0
1
2
3
0
0
1
0
2
1
0
1
2
0
0
0
0
0
1
5
1
0
0
0
0
2
1
0
2
1
0
1
1
0
2
1
0
1
1
0
1
2
3
1
1
2
2
0
2
2
1
2
2
2
0
0
0
2
2
1
2
2
0
1
1
0
0
0
1
2
0
0
0
0
1
0
2
1
1
0
1
0
0
0
0
1
0
0
1
2
0
0
0
0
0
1
2
2
1
1
0
0
0
0
3
1
2
0
0
1
1
1
0
1
2
1
2
0
0
2
2
1
2
1
2
1
1
0
1
0
0
2
0
2
0
1
0
2
2
1
0
2
1
2
0
1
1
0
0
3
2
0
1
1
1
0
0
0
0
0
1
0
1
0
1
1
2
0
2
2
0
1
0
2
0
1
0
0
1
1
0
0
1
1
0
0
1
0
1
2
2
0
0
0
0
2
0
0
0
2
0
1
0
2
0
2
1
0
2
0
1
0
0
2
2
1
2
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
2
0
1
2
0
2
2
1
0
0
1
1
4
1
1
0
0
2
0
0
0
0
0
0
1
3
0
1
1
0
2
1
2
1
0
2
0
1
0
2
0
0
1
0
4
2
0
2
0
0
0
1
0
0
0
2
1
0
1
1
0
0
0
0
2
1
1
1
0
1
1
0
0
2
0
1
0
0
0
0
2
0
1
0
1
0
0
2
0
3
0
1
1
2
0
0
2
0
0
1
2
0
0
0
0
0
2
1
0
2
1
0
1
2
2
2
0
0
2
0
2
4
0
1
1
2
1
0
0
1
1
0
0
2
1
0
0
2
0
1
0
1
2
0
2
1
0
2
0
1
0
1
0
0
3
1
1
0
1
0
1
1
0
0
1
0
0
0
0
2
0
1
0
0
1
1
0
2
2
2
1
0
1
1
1
0
1
0
0
0
0
0
0
0
1
0
1
2
1
3
0
2
0
1
0
0
2
0
2
1
0
0
1
0
0
1
1
1
0
0
2
1
0
0
0
0
1
2
0
0
2
2
2
0
2
0
1
0
0
1
1
2
1
1
1
2
0
1
1
1
4
2
3
1
0
0
1
0
1
0
0
0
1
0
1
2
1
1
2
0
3
0
0
1
0
0
1
0
1
1
1
0
2
0
0
1
0
0
1
0
0
0
1
1
1
2
0
1
2
1
2
1
0
1
0
0
2
2
1
0
0
1
0
0
1
4
1
1
0
0
2
1
1
1
0
0
1
2
3
1
2
0
0
1
0
2
0
2
0
1
1
0
0
0
1
0
0
0
0
2
1
1
1
0
1
1
2
0
0
2
1
2
0
0
1
2
2
0
0
1
0
1
1
1
1
2
1
0
3
0
1
0
0
2
2
1
0
2
0
1
0
2
0
0
1
0
1
1
1
1
1
0
2
1
1
0
1
0
1
1
0
0
0
0
0
0
2
0
2
0
1
2
1
1
1
0
2
2
1
2
0
1
1
1
1
2
0
0
0
3
2
1
0
1
0
0
0
1
1
0
0
1
0
1
0
0
1
0
1
0
1
2
0
0
1
1
1
2
1
1
2
0
0
0
1
1
1
2
0
2
2
0
3
2
1
0
0
0
0
0
3
2
2
2
1
2
0
0
0
1
0
1
0
2
2
0
0
0
0
0
1
1
0
1
1
1
0
1
2
2
1
2
0
2
2
0
0
0
0
0
2
1
2
0
0
1
0
0
1
0
0
0
0
1
1
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
1
1
2
0
0
0
0
2
2
1
1
2
0
1
1
0
1
1
0
0
0
2
1
0
1
2
0
2
0
1
0
0
0
1
1
1
0
1
1
2
1
2
1
0
0
0
1
0
1
0
0
2
1
1
0
0
2
0
1
1
0
1
1
2
2
2
0
0
2
2
0
0
2
0
2
3
0
1
1
1
0
2
2
0
1
0
0
0
2
1
0
1
0
1
2
0
1
0
1
2
0
1
0
1
1
1
0
1
2
0
1
0
1
0
1
0
1
0
2
1
0
2
0
1
1
2
1
1
0
1
2
3
1
2
1
0
1
0
1
1
1
2
0
1
1
0
2
0
0
0
0
0
1
0
1
0
2
4
0
1
2
0
0
1
1
1
2
1
0
2
0
2
1
1
1
0
2
0
2
2
2
1
1
2
2
1
1
2
0
1
1
0
2
1
0
2
0
0
0
0
0
0
0
1
0
1
0
1
0
2
2
0
1
0
0
1
0
2
1
0
0
0
1
2
2
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
1
1
1
1
0
1
2
2
2
2
1
2
1
0
1
0
1
0
0
0
1
0
0
1
1
1
0
1
0
0
0
0
0
0
0
1
1
0
1
1
0
2
2
2
0
1
0
0
2
0
0
2
0
0
2
0
0
1
2
0
0
0
1
1
0
0
0
1
1
3
0
0
1
0
0
0
0
0
0
0
0
1
1
2
0
1
2
2
0
1
0
0
0
2
2
0
2
3
0
0
2
0
0
2
1
1
2
0
0
1
1
0
1
1
2
3
1
0
2
0
1
0
4
2
1
1
0
1
2
2
0
0
2
2
0
1
0
2
2
0
0
0
0
1
0
1
1
2
1
0
1
2
1
0
1
0
0
0
1
2
1
1
0
2
0
1
2
0
1
1
2
1
0
0
0
0
2
2
2
2
0
0
0
0
0
1
0
0
0
3
0
2
1
0
2
0
1
2
2
1
0
1
1
2
0
0
1
0
1
0
2
1
1
0
1
0
0
0
0
1
0
1
0
1
1
2
0
1
1
0
0
0
2
0
1
1
2
0
2
0
1
0
0
2
0
0
1
0
1
1
1
1
0
0
0
1
0
0
2
2
0
0
1
0
2
1
1
0
1
1
1
2
0
0
0
0
3
1
1
0
3
0
1
0
0
0
2
1
0
2
2
1
0
2
2
1
2
0
2
0
0
0
0
2
1
2
0
2
1
2
0
1
1
1
0
1
0
0
1
0
0
0
1
1
1
0
1
0
1
1
0
1
2
2
1
0
0
2
0
0
1
1
1
1
0
1
2
2
1
0
0
0
2
1
1
2
0
0
2
0
1
0
0
0
2
1
0
0
1
1
2
1
0
1
0
1
0
2
3
1
0
1
0
0
2
2
1
1
1
0
1
2
1
0
2
1
0
0
1
1
1
1
2
0
0
0
2
1
1
1
1
0
2
1
0
0
1
0
0
2
1
1
0
2
2
2
1
0
0
1
2
2
3
0
1
0
0
1
0
1
2
2
1
1
2
1
0
1
0
1
2
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
1
2
1
0
0
2
0
1
1
0
2
1
0
0
0
2
1
0
2
1
1
0
0
1
2
0
0
1
3
1
2
1
0
3
0
0
2
3
2
0
0
0
2
2
1
1
2
1
1
2
0
0
1
2
0
1
1
2
1
0
2
0
0
0
0
1
1
0
1
2
1
1
1
1
1
2
0
2
1
0
0
0
2
1
1
1
0
0
0
0
0
1
1
0
1
0
1
1
2
2
0
2
0
1
2
1
0
2
0
1
0
1
1
1
1
2
0
0
1
2
0
0
0
1
1
0
1
2
1
1
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
2
0
0
4
1
0
0
0
0
0
0
0
3
0
0
1
1
0
0
0
2
2
2
1
0
2
0
2
0
1
1
0
0
3
0
0
0
1
2
0
1
0
2
0
0
1
3
1
0
1
2
1
0
0
2
0
0
0
2
0
1
1
0
0
1
0
2
1
1
1
1
0
1
2
2
1
0
1
1
1
1
0
1
2
1
0
0
0
2
1
1
3
2
0
1
2
1
1
2
0
0
2
1
0
0
0
2
0
1
1
0
2
2
1
2
0
2
2
0
1
1
1
3
0
2
1
2
2
0
2
0
0
2
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
1
2
2
1
1
0
1
0
1
0
1
1
2
2
0
1
0
1
1
1
1
0
2
1
0
1
0
0
0
0
2
2
1
1
0
1
0
1
0
1
2
2
1
1
2
0
0
2
3
1
1
1
1
2
2
0
1
1
0
1
1
0
2
0
1
1
0
1
2
2
2
1
1
0
0
0
1
1
0
1
2
1
0
1
0
1
2
0
0
0
0
2
0
1
0
2
1
0
1
1
1
1
2
2
0
0
0
2
1
1
1
2
1
0
1
0
0
0
0
0
0
0
1
0
2
1
0
0
2
1
1
1
1
1
0
2
2
0
1
1
0
1
0
1
0
0
0
0
0
0
2
0
0
2
1
0
1
2
2
0
0
0
0
1
0
0
3
0
0
0
0
1
2
0
2
0
3
2
0
1
1
0
2
2
0
1
2
1
1
2
2
3
2
0
1
1
2
0
0
0
1
0
0
1
1
1
0
2
1
0
1
0
0
0
2
1
0
0
0
3
0
0
3
5
2
1
0
0
0
1
1
2
0
1
1
2
2
0
0
0
2
2
1
2
3
1
2
1
0
0
1
0
1
1
2
0
2
0
0
0
1
1
0
1
1
0
1
0
0
2
1
0
0
1
2
1
0
2
0
2
0
1
0
2
1
2
0
2
1
1
1
1
1
0
1
0
2
1
0
1
0
0
0
1
0
0
0
1
2
1
0
1
0
2
1
1
0
2
1
2
0
0
0
1
0
2
2
1
2
1
0
0
1
0
0
0
0
0
1
1
2
2
0
0
3
2
1
2
0
2
0
1
2
1
0
1
1
1
0
1
0
0
2
1
1
0
1
2
1
2
1
0
1
0
1
0
1
0
0
1
1
2
1
1
2
0
0
1
2
0
2
0
1
1
0
0
0
1
1
1
0
2
3
1
1
1
0
2
0
0
2
0
1
2
1
0
2
0
2
1
0
0
0
0
1
0
0
0
0
2
1
0
1
1
0
1
1
0
0
2
2
0
0
0
0
2
1
0
0
0
0
1
3
1
1
0
1
0
2
0
0
1
1
0
2
0
0
0
0
1
0
1
1
2
1
0
0
0
0
1
4
0
0
0
1
2
2
1
0
4
2
0
0
1
1
1
2
0
1
3
1
0
1
0
2
2
2
2
3
1
2
3
2
0
1
0
1
1
1
2
0
1
1
0
0
1
1
0
2
2
0
1
1
2
1
0
0
2
1
0
0
0
1
1
1
2
2
0
1
0
0
0
0
1
1
1
0
1
1
1
0
1
0
1
0
1
2
0
0
0
0
1
1
1
1
0
0
1
1
0
0
0
0
1
0
2
3
0
0
2
5
0
0
1
2
0
0
0
1
0
0
2
1
1
0
0
2
2
0
1
1
1
1
1
4
1
1
0
0
1
0
1
2
1
2
0
0
0
1
0
1
1
2
0
1
0
2
2
1
1
0
2
2
0
0
0
0
1
0
2
0
2
0
2
2
0
0
0
1
0
0
0
1
1
1
2
2
0
2
0
2
0
2
0
2
1
0
1
2
0
0
0
0
0
0
0
1
0
2
1
0
1
0
1
0
1
0
3
0
1
0
1
1
1
0
1
0
0
0
2
0
1
0
0
1
0
1
1
1
0
1
0
0
2
0
1
1
0
0
0
0
2
1
0
1
0
0
1
1
1
0
0
0
1
0
1
0
1
2
0
2
1
0
0
3
1
1
1
0
0
3
1
0
1
0
1
0
1
1
2
0
0
0
1
1
2
1
1
1
0
1
1
1
1
0
0
0
1
1
0
0
1
1
1
2
0
1
1
0
2
1
0
2
2
2
0
0
2
0
2
0
1
1
1
1
1
1
1
0
0
1
1
0
2
1
1
0
0
0
2
1
1
1
2
2
1
1
0
4
1
3
0
1
2
0
1
1
1
1
0
0
1
0
1
2
0
1
0
0
1
0
1
2
1
0
0
3
1
2
2
1
0
0
1
0
0
1
2
2
1
1
1
1
2
1
0
2
2
3
1
0
1
2
0
1
1
1
2
0
0
1
0
1
0
0
1
1
2
2
2
0
0
1
0
2
2
1
2
1
1
1
0
1
1
2
1
1
1
0
2
0
1
0
0
0
0
1
0
1
1
0
0
0
1
1
1
1
1
1
1
1
0
1
0
1
1
0
1
1
1
1
0
1
2
1
1
0
0
0
0
1
0
1
1
0
1
1
1
1
1
1
0
1
1
0
0
3
0
1
1
1
1
1
0
1
1
0
0
1
0
0
0
0
1
0
1
0
2
2
1
0
0
1
0
0
0
2
1
0
2
0
0
0
2
2
1
1
0
0
1
1
0
1
1
1
0
1
2
0
1
0
0
1
0
0
1
2
0
0
1
2
1
3
2
2
1
2
1
1
1
2
1
1
0
3
1
1
0
0
2
1
2
0
0
0
0
4
1
1
0
2
0
0
1
0
2
1
1
1
0
1
0
0
1
1
1
0
0
1
0
1
0
1
1
2
0
0
0
0
1
0
0
1
1
2
2
0
2
1
1
0
1
1
1
1
0
0
0
0
1
1
1
2
0
1
2
0
0
1
2
1
1
1
0
0
0
0
0
0
1
0
0
1
1
0
0
1
2
0
0
2
1
1
1
2
4
1
0
1
2
0
2
0
1
1
0
1
2
1
1
2
1
1
1
1
1
2
0
2
2
0
2
1
2
1
1
2
0
0
1
0
0
0
0
0
1
0
0
1
2
2
2
1
0
0
2
1
1
1
2
1
0
1
2
0
0
2
1
1
2
1
0
0
1
0
2
1
0
0
1
0
2
0
0
2
1
1
0
2
2
2
1
2
1
0
1
0
0
1
0
1
0
0
0
0
1
2
0
1
0
0
1
0
1
2
0
0
1
1
0
1
1
0
2
2
1
0
0
0
2
1
1
0
2
0
2
2
0
1
0
0
0
1
1
0
0
0
1
0
1
0
1
1
1
0
0
0
0
0
0
1
0
1
1
0
2
0
3
0
2
1
2
2
1
0
1
0
0
0
0
0
0
1
1
2
0
1
0
2
1
2
1
0
1
0
1
3
0
0
1
1
2
2
2
1
1
0
2
1
1
2
1
1
0
0
0
2
0
1
1
0
0
0
1
1
0
1
1
1
0
0
1
0
2
2
1
0
1
1
2
0
0
1
1
2
0
0
2
0
1
1
1
2
2
0
0
1
2
0
0
0
1
0
2
0
2
1
1
1
0
2
1
0
1
1
0
2
1
1
1
1
1
2
1
0
1
0
1
2
0
1
1
2
0
1
1
1
1
2
2
0
0
1
0
4
1
0
0
1
0
1
1
0
0
1
1
0
1
0
0
1
1
0
1
1
1
1
1
1
1
0
0
2
0
1
2
0
0
2
0
0
2
0
0
1
1
2
0
0
2
1
1
2
2
1
1
1
0
1
2
0
1
1
1
1
0
1
1
0
0
1
0
0
1
2
5
2
1
0
0
1
1
0
1
0
1
0
0
1
0
2
0
0
1
0
0
2
2
1
2
0
2
1
1
1
0
0
0
1
2
0
0
2
0
0
2
2
0
1
0
0
0
2
0
2
2
1
0
1
1
2
0
1
0
1
1
0
0
0
0
0
0
3
0
1
0
0
2
0
0
0
1
0
2
0
0
1
1
1
2
1
1
0
1
0
1
1
1
1
1
0
1
0
1
2
0
2
1
0
0
0
0
0
2
1
0
6
1
2
0
2
0
0
0
0
0
0
1
0
2
0
1
1
2
1
0
1
2
0
1
0
1
0
1
2
0
0
2
1
1
2
0
2
1
2
1
0
1
0
0
2
0
0
0
2
1
0
0
0
1
2
0
1
1
0
1
0
0
0
1
2
0
0
0
3
0
3
2
2
0
0
0
0
0
1
0
1
0
2
2
2
0
0
2
1
1
2
1
2
0
3
1
0
0
1
0
2
0
0
0
2
1
0
1
0
1
1
1
2
0
0
0
0
0
2
0
2
1
3
1
1
1
1
1
1
1
2
1
0
1
1
2
1
0
1
1
2
1
1
3
0
0
2
2
0
2
1
2
0
1
2
1
0
1
0
2
1
0
0
2
2
2
2
1
1
0
1
0
0
2
1
2
2
0
2
1
1
0
2
2
0
2
0
1
0
0
2
0
2
1
0
1
1
1
0
2
0
1
2
0
0
2
2
1
2
0
0
0
0
0
0
0
0
0
1
0
1
2
1
0
1
3
0
1
0
1
1
1
1
0
0
2
0
2
0
0
1
2
0
0
0
2
1
1
0
0
2
0
2
2
0
2
0
1
0
1
2
2
1
1
0
0
2
1
1
2
0
0
2
1
0
0
0
2
1
0
0
0
2
0
0
2
1
1
2
1
2
1
0
0
1
1
1
1
0
0
1
1
0
1
0
0
0
0
1
1
0
2
1
0
1
0
0
2
0
1
1
0
0
2
1
0
2
1
2
1
1
0
2
1
1
0
1
1
2
1
0
0
0
1
0
0
0
1
0
0
2
1
0
0
0
1
0
1
0
2
0
2
2
1
1
1
2
0
0
0
0
0
2
1
3
2
1
1
1
2
2
1
1
1
0
0
2
2
0
0
0
0
1
0
2
0
1
0
1
1
2
1
0
2
0
1
1
1
1
0
0
0
1
2
0
1
1
2
0
0
0
2
2
0
0
1
0
1
2
1
0
0
2
0
0
1
0
2
0
2
9
0
2
1
0
2
0
0
1
1
0
1
0
1
0
0
1
4
2
1
1
0
1
3
1
0
0
0
1
0
1
1
1
0
0
1
2
2
2
0
0
1
2
1
0
1
1
0
2
2
2
2
3
0
0
1
2
1
1
2
1
1
2
1
0
1
1
1
1
1
1
1
1
0
2
1
3
1
1
0
0
1
0
0
1
0
1
0
2
1
2
1
1
2
0
1
1
0
0
0
0
1
1
0
0
1
1
1
1
1
2
2
1
0
1
1
0
2
1
1
0
2
0
1
3
1
1
1
1
0
2
1
0
0
0
1
0
2
1
1
2
0
0
0
0
0
2
0
2
0
2
1
2
0
0
1
1
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
2
1
0
1
1
1
0
0
1
0
2
1
1
2
0
1
0
2
0
0
1
0
0
1
1
0
0
2
1
0
0
1
1
1
1
1
0
0
1
0
0
0
0
2
0
0
3
0
2
2
1
0
0
1
0
0
0
1
2
0
1
1
0
1
0
0
1
2
0
0
0
1
1
0
1
1
1
0
1
1
1
0
0
0
0
1
2
0
1
8
0
0
0
0
1
0
1
2
2
1
1
0
1
1
1
1
1
1
2
0
0
1
0
0
2
0
1
1
2
0
1
0
1
0
2
2
0
2
0
1
2
1
0
2
0
1
0
2
0
0
0
0
2
0
1
2
0
2
2
0
0
2
2
2
1
0
1
3
1
1
0
0
0
1
2
0
1
2
1
0
2
1
1
0
0
0
2
1
1
0
0
1
1
1
0
1
0
2
1
0
1
2
0
0
1
1
0
1
0
0
3
0
1
0
0
1
1
0
2
0
2
1
0
1
0
0
0
0
1
0
1
1
1
0
1
0
1
2
2
0
2
0
2
3
0
2
2
3
1
0
1
2
1
0
0
1
0
1
2
0
2
2
2
2
1
2
2
0
1
1
1
1
0
1
0
1
0
1
0
1
1
1
0
0
2
0
0
1
1
0
1
1
0
2
0
1
0
0
0
0
1
0
1
0
2
1
0
0
0
0
0
2
0
0
4
2
0
1
1
1
1
0
0
1
2
2
3
0
2
2
0
1
0
0
1
0
1
1
1
2
3
0
2
2
0
0
1
2
1
1
1
1
1
1
3
1
0
1
1
1
0
1
2
2
1
1
1
1
2
0
0
0
0
1
1
1
0
1
1
1
0
2
1
0
0
1
1
0
1
0
0
1
0
1
1
2
0
0
0
2
1
2
1
0
1
1
2
0
0
1
0
1
0
1
0
1
0
1
2
1
6
0
2
1
1
0
0
0
2
0
0
0
0
2
0
1
0
1
1
1
0
2
0
0
2
0
0
0
1
1
3
1
2
2
1
0
1
1
0
0
2
2
0
0
0
2
1
0
1
0
2
1
2
0
0
0
2
0
1
1
0
1
0
0
1
0
2
1
0
0
2
0
3
1
2
1
0
0
1
0
0
0
3
1
0
2
1
0
2
1
1
1
0
0
2
1
1
1
0
1
0
1
1
1
0
2
1
3
0
1
1
1
0
0
1
0
2
0
2
2
1
2
4
0
0
2
0
2
1
1
0
0
0
1
0
0
1
1
1
2
0
1
2
1
1
1
0
2
2
2
0
1
0
1
0
0
1
1
1
0
1
2
0
0
2
0
0
0
0
0
1
2
2
2
1
0
2
1
2
2
0
1
1
1
2
2
0
1
2
0
1
1
0
2
1
0
0
0
1
2
2
1
1
1
0
1
0
1
0
0
0
0
1
0
0
2
0
2
2
0
0
0
2
2
0
0
2
1
0
0
1
1
1
2
0
0
1
1
2
2
1
0
0
1
1
2
0
2
0
0
1
2
2
2
0
1
1
1
0
2
1
0
1
0
0
1
6
1
0
0
0
0
2
1
2
2
1
0
0
2
0
2
3
2
1
0
1
0
0
0
0
2
1
0
1
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
2
1
0
1
1
0
0
2
1
2
0
0
0
1
1
2
1
0
2
1
2
0
0
1
3
1
1
1
1
0
0
2
0
0
2
0
1
1
0
0
0
0
1
0
0
0
2
2
0
1
1
0
1
2
2
2
0
1
2
0
1
0
1
0
2
2
0
2
2
0
1
0
2
0
1
2
0
2
1
1
2
2
0
2
1
1
0
0
0
0
0
1
3
2
0
0
2
2
0
1
0
0
1
2
1
2
2
1
1
1
0
2
2
1
2
2
0
0
1
1
1
1
0
1
1
1
0
0
1
1
0
2
0
1
0
0
2
1
1
0
2
1
2
2
1
0
0
0
2
1
0
0
0
0
2
0
0
1
0
0
1
2
1
2
0
0
1
0
1
1
3
1
1
0
2
0
0
0
2
0
1
1
1
1
3
0
1
2
2
1
1
1
0
1
1
1
2
1
1
0
2
0
0
1
0
1
0
0
2
1
0
0
2
2
2
0
1
1
1
0
1
1
1
0
1
1
1
0
1
2
0
0
1
0
0
0
0
0
1
1
1
0
2
1
2
0
1
0
0
0
0
0
0
1
1
0
0
2
4
1
1
1
0
1
1
1
2
2
2
0
1
1
0
1
1
0
2
1
2
0
0
1
1
2
0
1
0
2
1
1
1
1
1
0
1
1
1
2
0
2
1
0
1
0
0
2
0
0
0
1
0
0
2
0
1
1
1
0
1
1
1
2
1
2
1
4
1
1
0
0
0
0
1
2
0
0
3
1
0
0
0
0
1
0
0
2
1
0
1
1
1
0
1
0
1
2
2
1
1
0
1
2
1
1
2
1
1
1
1
0
1
1
2
0
2
0
2
1
1
0
1
0
1
2
1
2
2
2
3
0
0
0
2
2
2
2
0
1
0
0
2
0
0
0
0
0
0
0
1
0
2
1
2
0
0
1
0
1
0
2
0
1
2
0
2
0
1
1
2
2
0
0
0
2
0
1
1
1
1
2
0
0
0
0
0
1
1
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
2
0
1
1
0
1
2
1
2
0
1
1
0
0
1
1
0
1
1
2
1
1
2
2
0
2
2
0
0
1
1
0
1
1
1
2
1
1
2
0
1
2
0
2
1
0
0
2
0
1
1
0
0
0
0
3
1
1
2
0
1
0
1
0
0
1
1
0
0
2
1
2
0
0
0
1
0
0
1
0
2
1
1
0
2
2
3
0
1
2
0
2
0
1
1
1
0
1
0
0
0
2
0
0
0
0
0
1
2
0
0
0
2
2
0
2
2
1
2
0
0
1
0
0
0
1
0
1
0
2
0
0
1
0
2
0
0
0
2
1
0
2
0
2
2
2
2
0
1
0
2
2
1
2
1
3
1
2
1
2
0
0
1
0
0
1
0
1
0
2
0
2
0
1
2
0
1
0
2
1
1
4
2
2
0
1
1
2
2
0
2
1
2
0
2
1
0
0
0
2
2
2
0
0
2
3
0
1
1
1
0
2
1
1
1
2
2
0
2
1
1
0
0
1
0
0
0
1
0
1
2
1
0
0
2
2
1
2
0
2
2
2
1
0
2
1
1
1
0
1
1
1
2
0
1
1
1
1
1
2
0
1
0
1
0
0
0
1
3
0
2
0
1
1
1
0
1
1
2
0
0
2
1
0
0
0
2
2
0
2
1
0
1
1
0
1
1
1
1
1
0
2
2
2
1
2
0
1
1
1
1
2
1
1
1
2
1
0
2
0
1
3
0
1
0
2
1
2
0
1
0
0
0
1
2
0
0
2
0
1
0
1
0
1
1
0
2
1
1
0
1
0
2
1
0
0
1
0
2
1
2
0
0
1
0
0
2
2
2
0
1
2
1
1
0
1
0
2
2
1
0
1
0
2
1
0
0
1
0
0
0
1
0
2
2
0
0
0
1
2
1
1
0
0
0
0
1
1
0
2
0
1
1
1
2
2
1
1
1
1
1
2
0
2
1
2
3
0
1
3
0
2
1
1
1
1
1
1
0
1
2
1
2
0
0
3
2
1
0
0
0
1
0
1
2
1
0
0
1
1
1
2
0
1
1
0
0
2
0
0
0
0
1
2
1
1
0
1
0
1
2
4
1
0
1
1
0
2
2
0
1
1
1
1
1
0
1
0
2
0
0
0
0
2
0
1
1
2
0
0
2
1
0
0
2
1
1
1
2
1
0
2
1
1
2
1
1
0
0
0
0
1
2
2
1
1
0
1
0
0
0
1
1
0
2
2
1
0
0
0
2
0
2
0
2
0
0
0
1
0
1
2
0
1
1
2
0
0
1
0
0
0
1
0
0
0
1
0
0
2
1
1
1
0
0
2
0
1
1
2
2
0
0
1
0
2
1
1
0
1
1
2
0
1
1
1
1
1
1
1
1
0
1
0
1
2
1
1
0
0
0
0
0
0
0
1
1
0
1
2
2
0
1
0
0
2
0
0
1
0
2
1
1
2
2
1
0
0
0
0
1
1
0
1
0
0
0
1
0
0
1
0
1
1
1
1
1
0
0
0
1
1
1
0
0
1
1
0
0
1
2
1
0
2
0
0
1
2
0
2
2
0
1
1
1
1
1
0
1
0
0
1
1
1
0
1
2
0
3
0
0
0
2
1
1
1
1
0
1
1
2
1
1
2
0
0
1
0
1
0
1
4
1
2
0
1
1
0
1
0
0
0
0
2
1
0
1
1
0
0
2
3
0
0
1
1
2
1
1
1
0
0
0
1
0
1
0
1
1
2
0
1
0
2
1
0
2
2
2
0
2
0
1
0
1
1
2
0
2
1
0
0
0
2
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
1
1
1
1
0
1
1
2
0
2
0
0
4
2
1
1
1
1
1
1
1
3
0
0
1
0
0
1
1
0
0
0
0
0
1
2
2
0
2
0
0
1
2
1
0
0
0
1
1
2
1
2
0
1
0
1
1
1
1
1
0
2
0
1
2
1
1
2
0
1
0
0
0
0
2
1
1
1
0
0
2
0
1
0
1
2
3
2
1
3
0
0
0
1
2
1
2
2
0
0
0
1
1
0
1
0
0
1
0
0
2
0
0
0
0
0
0
1
0
1
1
0
0
0
1
1
1
1
1
0
2
0
0
1
0
1
0
0
0
1
0
0
2
1
1
0
1
3
0
0
0
2
2
1
1
1
1
1
0
1
0
2
0
0
0
1
0
1
0
1
2
0
1
1
0
1
1
2
2
2
2
0
0
1
2
0
1
1
2
0
0
2
0
0
1
0
1
0
0
1
1
0
2
2
1
2
0
0
3
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
2
0
0
1
1
2
1
1
2
1
1
1
1
1
3
0
2
2
1
1
0
2
0
2
0
2
2
0
2
0
2
0
1
2
2
0
2
1
1
3
1
1
2
0
2
1
0
0
2
1
2
0
0
0
1
1
1
0
1
2
0
0
0
2
2
0
2
0
0
2
1
1
2
0
2
2
0
1
1
0
0
1
2
2
0
0
0
2
0
0
0
0
2
1
0
0
0
1
0
2
0
1
0
1
2
0
2
0
0
0
2
1
1
0
1
0
0
1
0
2
0
2
2
0
0
2
1
1
2
1
1
1
1
1
0
0
1
2
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
2
2
0
1
1
0
0
1
0
2
1
0
0
0
1
0
0
1
1
0
0
1
1
2
1
1
2
1
0
1
1
1
1
2
0
0
0
2
2
0
0
0
0
0
1
1
1
0
1
2
1
2
0
1
2
0
0
0
0
0
1
0
0
0
0
1
0
0
2
1
0
2
2
1
2
2
1
1
2
0
1
1
1
0
0
0
0
2
1
2
1
0
1
1
0
0
0
1
0
3
1
1
0
2
1
1
1
0
0
1
0
1
2
0
2
2
0
2
3
2
1
1
2
0
0
1
0
1
2
1
0
1
0
2
0
0
1
0
1
1
1
0
0
2
1
0
2
0
2
1
0
1
1
1
1
1
0
0
1
2
1
2
1
1
0
0
1
0
0
2
0
0
1
1
1
1
0
1
0
1
1
2
1
0
2
2
4
1
1
1
0
0
1
0
1
1
2
1
2
2
1
2
0
0
0
1
1
0
1
0
1
2
0
1
2
1
1
2
2
1
0
1
1
1
1
0
2
2
0
0
1
1
1
0
0
1
0
1
1
1
1
1
1
1
2
2
1
1
0
1
2
0
1
0
0
0
2
2
2
0
2
1
1
0
0
3
1
1
1
1
1
0
0
0
0
1
1
2
1
0
1
2
1
0
2
2
1
0
1
2
1
2
0
0
0
0
0
2
1
1
0
0
2
0
0
1
1
0
2
0
2
0
1
0
0
1
1
0
1
2
1
0
1
0
1
0
0
0
2
2
1
1
0
0
1
0
1
0
0
1
1
1
0
0
0
0
2
0
1
1
2
0
0
1
1
1
0
0
0
0
2
1
0
1
2
0
2
1
0
0
1
0
1
2
2
0
1
2
0
0
2
0
2
2
0
1
1
0
2
1
1
1
2
0
0
1
0
1
2
1
2
2
2
0
0
0
2
1
2
1
0
1
0
1
1
0
0
1
0
0
3
0
1
0
1
1
1
0
0
1
1
0
1
0
1
2
0
1
0
0
1
2
2
0
1
3
0
1
0
2
1
1
1
0
2
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
2
0
1
1
2
1
0
0
1
0
0
2
1
2
2
1
1
0
1
1
1
1
1
2
1
1
1
0
0
1
2
1
1
0
0
1
0
1
0
0
1
2
1
2
1
1
0
2
0
1
0
1
0
0
1
0
2
1
0
0
2
0
1
2
1
1
1
0
1
0
1
0
1
2
1
2
1
1
1
0
2
1
0
2
1
1
0
0
3
2
0
1
2
1
0
2
1
0
2
1
0
1
1
0
1
1
0
0
0
1
1
1
1
1
0
1
0
2
1
1
1
0
2
0
0
0
0
1
0
2
1
0
1
0
1
1
2
0
0
1
1
0
0
2
0
0
1
0
1
1
0
0
0
1
0
1
1
0
1
1
2
1
2
0
0
0
2
2
0
1
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
2
0
1
2
1
0
2
2
0
0
0
0
0
0
0
0
0
1
0
1
2
2
0
1
1
2
0
1
1
0
0
1
0
1
1
1
1
2
2
0
2
2
2
1
1
0
2
2
0
1
2
2
2
0
1
2
0
0
1
0
1
1
2
0
2
2
2
2
1
0
0
0
2
0
0
0
0
2
2
1
0
2
1
2
0
1
1
2
0
1
0
0
1
1
1
0
1
2
2
1
1
0
0
2
2
1
0
0
1
0
1
1
1
1
1
0
0
0
1
2
2
0
0
0
2
0
2
0
2
0
1
2
1
0
0
1
0
1
1
0
1
2
1
1
0
1
2
0
0
0
2
1
1
2
0
1
1
2
0
1
0
1
0
2
0
0
1
1
0
1
2
1
0
2
0
0
0
2
2
1
0
1
0
0
1
0
2
0
0
2
0
1
1
0
2
2
2
2
0
2
0
2
2
1
0
1
1
1
2
2
0
2
1
1
1
1
2
1
0
1
2
0
1
3
1
1
0
1
0
0
1
2
2
1
0
0
1
0
0
2
1
0
0
1
0
0
1
0
2
1
0
3
1
0
1
0
0
1
0
2
1
1
1
1
1
0
1
2
0
1
0
1
1
2
2
0
1
0
2
0
0
0
0
1
0
0
0
1
0
3
1
0
0
0
0
0
1
1
1
0
0
0
2
1
0
0
1
0
1
0
0
4
0
1
0
0
1
2
0
2
1
1
0
1
1
1
1
1
0
0
4
1
1
0
2
0
1
2
0
2
0
2
0
1
1
0
2
1
0
1
2
1
1
0
0
1
0
1
1
1
2
0
1
2
2
0
0
3
2
1
0
1
2
2
1
1
0
1
1
1
0
1
0
0
2
1
2
1
2
2
0
0
0
0
3
2
1
2
0
0
0
0
1
2
0
2
0
0
2
1
2
1
1
0
1
0
2
1
0
0
0
2
0
1
1
2
1
1
1
0
2
2
0
0
1
2
0
2
0
1
2
0
1
1
0
1
1
1
0
0
0
1
0
1
2
0
1
1
0
1
0
1
2
1
1
1
0
1
0
0
0
1
1
0
0
1
2
0
0
0
0
0
1
1
1
1
1
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
2
0
2
0
1
0
1
1
0
1
0
1
1
0
0
0
0
2
1
2
0
1
1
1
1
0
0
2
0
0
1
1
1
0
2
1
0
0
0
1
1
0
2
0
0
2
1
2
2
2
0
2
1
0
0
2
1
1
0
1
1
1
2
0
0
2
1
0
2
0
0
0
0
1
1
0
2
0
1
0
1
0
1
0
0
0
0
2
0
0
2
1
0
1
2
2
1
1
1
0
0
1
0
0
0
2
2
1
0
1
2
1
1
1
1
0
0
1
0
2
0
2
0
0
1
1
0
0
0
1
2
2
3
0
2
0
1
0
1
0
0
2
2
2
0
0
0
0
0
1
1
1
1
0
0
2
2
0
0
0
1
0
1
1
0
1
1
1
0
1
1
0
1
1
0
0
1
1
0
2
1
1
0
2
0
2
2
0
1
0
1
0
1
1
2
2
3
1
0
2
1
2
1
1
0
1
1
0
0
0
0
1
1
0
0
0
0
1
2
1
2
0
2
0
0
1
0
0
0
1
2
0
1
2
1
1
0
1
1
1
2
0
1
2
0
2
0
0
2
2
1
2
2
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
2
0
1
0
0
1
1
2
2
2
0
1
1
2
1
2
0
1
1
1
1
0
0
1
0
2
1
0
2
2
1
1
2
1
0
1
0
0
0
2
1
0
0
0
1
1
2
0
0
1
0
0
1
1
2
0
1
2
0
1
0
1
0
0
0
1
1
1
1
1
0
0
1
0
2
1
1
0
0
2
0
0
2
0
1
1
0
0
1
1
0
3
1
0
0
1
3
1
0
0
2
1
0
0
1
2
0
0
1
2
2
0
0
1
2
0
1
1
1
1
1
0
2
1
0
0
1
0
1
0
0
1
0
0
0
2
2
1
3
1
2
0
3
0
1
0
1
0
1
1
0
0
2
1
1
0
2
0
0
0
2
0
1
1
0
0
0
0
1
0
0
2
2
0
2
0
0
0
1
2
0
1
0
1
1
0
0
2
1
2
1
0
1
0
0
2
1
1
1
0
0
0
1
2
2
1
2
0
0
0
0
1
0
1
2
0
0
0
0
0
2
1
0
0
2
1
1
0
0
1
1
2
1
2
1
1
1
2
2
0
1
1
1
0
0
2
0
1
2
1
0
0
0
0
0
1
2
2
2
2
0
0
1
0
1
2
2
2
0
2
0
2
1
0
1
0
0
1
1
1
0
0
0
1
0
0
1
1
1
0
0
1
1
0
0
1
0
0
1
1
0
1
1
1
1
1
1
1
0
1
2
1
0
1
1
0
2
2
0
0
0
1
2
0
3
2
1
1
0
0
2
0
1
1
1
0
1
2
0
1
3
1
0
2
1
0
1
1
0
2
0
0
0
0
1
0
0
2
0
0
1
0
2
1
1
1
0
0
1
1
0
1
2
0
0
1
0
0
1
1
1
2
1
0
0
1
0
0
0
0
1
0
1
1
1
1
1
1
0
1
2
1
1
0
0
0
1
1
1
0
0
2
1
0
0
3
2
2
0
0
1
0
1
0
2
1
1
2
1
2
0
1
2
1
0
0
0
0
2
1
0
0
2
1
0
3
0
2
1
0
1
0
0
1
2
0
1
0
1
0
0
0
0
1
1
0
0
1
0
1
2
2
0
3
0
0
1
1
2
1
0
2
0
1
1
0
0
1
1
1
0
2
0
0
1
0
1
1
1
1
1
1
2
1
1
0
0
1
0
1
1
1
1
1
1
0
0
2
0
2
1
0
1
0
2
0
1
0
1
1
0
2
2
0
2
1
1
0
2
0
0
1
1
0
1
0
2
2
1
1
0
0
1
1
0
0
0
0
0
0
1
1
0
2
1
1
2
1
0
2
0
2
1
0
0
2
0
1
0
2
0
0
2
0
2
2
1
1
1
1
0
1
0
1
0
1
0
2
1
1
0
0
1
0
1
1
2
0
2
0
1
1
0
0
2
0
1
0
0
0
1
1
0
0
0
1
0
1
0
2
0
2
1
1
0
2
0
0
1
1
0
0
0
0
0
0
0
2
0
1
0
0
2
0
2
2
1
1
0
0
0
0
1
0
0
1
1
2
2
2
0
2
1
3
0
0
0
0
1
0
2
2
0
0
0
2
0
1
2
0
2
2
2
0
1
1
1
0
0
0
1
0
0
2
0
1
0
2
0
0
1
0
1
1
1
1
1
1
2
0
0
0
1
1
0
1
0
0
0
2
0
0
2
0
0
0
2
1
0
1
1
0
1
0
1
1
1
1
0
1
0
1
1
0
0
0
0
0
0
0
0
2
1
0
1
0
2
2
1
1
1
0
0
2
1
1
0
0
0
2
2
1
2
1
1
2
1
0
1
0
1
1
0
0
0
2
0
0
2
2
0
1
1
1
1
1
1
2
0
0
2
1
1
2
1
0
2
1
2
1
0
1
1
1
0
1
1
0
2
3
2
2
1
0
1
2
1
1
1
1
0
2
0
0
0
0
0
0
1
0
0
0
2
0
1
1
1
0
1
1
3
1
0
1
0
1
1
0
1
0
1
1
0
0
0
0
1
0
2
1
1
0
2
0
0
1
3
1
0
0
0
0
0
0
2
0
1
0
0
0
2
1
0
1
2
0
1
2
1
0
2
2
0
0
0
2
0
0
2
0
2
0
0
0
0
2
2
2
4
1
2
1
0
2
0
0
1
0
1
1
2
2
0
0
1
0
0
1
1
1
1
1
0
0
0
1
2
1
0
0
0
0
0
2
1
2
2
0
0
1
1
0
1
1
1
1
0
0
1
0
1
1
0
2
0
2
1
1
0
1
0
0
1
1
2
0
0
1
1
2
1
2
0
0
0
0
2
3
2
0
0
1
3
1
0
1
1
1
0
0
1
0
2
2
2
0
0
2
0
1
0
1
1
0
0
1
0
2
0
0
1
2
2
0
2
1
1
0
0
0
0
0
2
0
0
0
0
2
0
0
1
2
0
2
1
0
1
0
2
1
2
2
0
1
0
0
0
1
1
1
1
1
0
1
2
0
0
0
1
2
1
0
0
1
0
2
0
1
1
1
0
1
2
1
0
0
2
1
0
1
5
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
2
1
2
2
1
0
2
0
0
1
0
0
1
2
2
0
1
1
0
2
0
0
1
1
0
1
2
1
0
2
0
1
0
0
0
0
1
0
0
1
0
1
2
0
0
0
0
3
1
1
0
2
0
2
1
1
1
1
0
1
0
0
0
1
1
1
2
1
1
1
2
2
1
0
1
1
3
1
1
0
0
0
0
2
2
0
1
0
1
1
1
0
1
0
0
2
0
0
0
2
1
1
0
1
0
2
1
1
0
1
0
2
1
1
1
2
0
0
0
1
1
1
1
0
2
1
0
1
0
0
1
1
2
0
0
0
1
1
0
0
2
0
2
1
1
2
1
2
2
1
2
0
2
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
2
2
2
0
1
0
0
1
0
0
2
0
2
1
0
2
0
1
1
0
2
1
1
0
0
0
2
1
2
0
0
2
2
2
1
0
2
0
3
1
2
1
1
0
2
2
0
2
1
0
0
0
2
1
0
0
2
0
1
0
0
2
0
0
4
1
2
1
0
0
0
0
0
0
1
2
1
0
2
1
0
2
1
0
1
0
0
0
0
1
1
0
0
0
0
0
2
1
1
0
2
0
2
2
0
0
1
1
1
2
0
1
0
0
0
2
0
0
1
2
1
0
0
1
0
2
2
1
2
0
1
0
0
3
1
1
2
1
1
0
1
0
0
2
0
0
0
3
0
1
2
1
0
1
0
1
1
2
0
1
1
1
0
1
0
1
0
0
0
2
0
1
1
2
2
3
0
0
0
2
0
1
1
0
2
0
1
1
0
1
0
1
0
2
3
1
1
0
0
1
2
0
0
4
1
1
2
1
1
1
1
2
0
1
0
1
0
0
0
1
2
0
1
0
2
2
1
0
0
1
0
0
0
0
1
2
1
0
2
2
1
2
0
1
0
2
2
1
0
0
1
1
2
0
1
1
0
0
1
0
1
0
1
0
1
1
1
1
0
1
2
1
0
1
1
0
2
1
0
0
0
0
1
0
1
0
0
0
1
0
0
1
2
0
0
2
0
0
1
1
2
1
0
1
1
0
1
1
2
2
0
2
0
2
1
2
0
0
1
0
1
2
0
1
1
1
0
0
3
1
1
1
0
0
0
1
1
0
2
2
0
0
1
0
2
0
1
0
1
1
0
1
0
0
0
1
0
1
1
0
1
0
1
0
2
1
0
2
2
2
0
1
0
1
1
0
0
1
1
0
0
2
0
1
0
0
1
0
0
1
1
0
1
0
1
2
2
0
0
2
0
0
1
0
1
1
1
0
2
1
1
2
1
0
0
2
0
1
2
1
2
1
1
3
1
0
1
0
1
0
1
0
0
2
0
2
0
0
1
0
1
1
1
0
2
2
0
1
2
0
2
2
1
1
0
0
0
1
0
0
2
0
0
2
0
0
1
2
0
1
0
1
0
1
2
0
2
0
0
1
0
0
0
1
2
1
0
0
0
0
1
1
0
0
1
1
2
2
0
0
2
0
0
1
1
2
1
0
0
1
0
0
1
2
0
0
2
1
1
0
0
0
0
0
2
2
1
2
2
2
1
2
1
0
1
0
1
1
0
2
4
0
0
2
1
1
0
0
0
0
0
1
2
1
2
1
1
2
1
2
0
1
0
1
1
0
0
1
0
1
1
0
1
1
2
0
0
1
1
1
1
1
0
2
3
0
1
2
2
2
1
0
1
2
2
0
1
0
1
2
0
0
2
1
2
1
0
0
1
1
1
0
0
0
0
2
1
2
0
1
1
0
1
2
1
2
2
0
0
0
1
1
0
1
1
2
1
0
2
0
1
0
0
1
1
3
0
1
0
0
2
0
0
0
1
1
0
0
0
0
1
1
2
1
1
0
0
1
0
0
0
1
2
0
1
1
1
1
3
1
0
0
0
2
1
0
0
2
0
2
1
1
0
2
2
1
1
0
2
0
1
1
1
0
1
1
1
1
0
0
0
0
0
1
0
0
0
2
0
1
0
0
1
0
1
3
2
2
0
2
0
1
1
1
0
1
2
0
2
0
0
0
1
2
0
0
1
2
0
1
2
2
1
2
2
0
1
1
0
2
2
2
1
0
1
1
2
0
3
1
0
0
0
1
0
2
1
0
0
1
0
0
0
2
1
2
0
1
1
1
1
1
0
2
0
2
2
0
1
1
1
0
2
0
2
0
0
2
2
1
0
0
1
1
2
5
0
1
2
0
1
1
0
0
1
1
1
2
2
0
1
2
2
0
0
0
1
1
3
0
1
2
0
0
1
1
0
0
1
1
0
2
1
2
0
0
0
0
0
1
0
0
0
0
1
1
2
2
2
2
1
0
2
1
1
2
2
0
2
0
0
1
2
2
1
1
1
1
0
2
0
0
2
2
0
0
2
2
1
0
0
2
2
1
0
1
0
0
0
1
2
0
1
0
0
0
1
0
0
2
1
2
2
0
2
3
0
1
2
0
2
0
1
2
0
2
1
1
0
2
0
2
1
2
1
0
1
1
1
0
1
0
2
2
2
0
0
1
0
0
2
2
1
0
0
3
0
0
0
1
0
1
1
1
0
0
2
0
2
0
1
0
0
2
2
0
1
1
1
1
0
1
0
0
0
2
0
2
2
1
3
2
1
0
3
1
2
0
1
0
0
0
2
2
1
1
1
2
2
0
1
0
2
1
0
1
0
1
0
0
3
0
1
1
2
0
1
1
0
0
1
1
1
2
1
0
0
1
2
0
0
1
0
2
1
1
0
2
1
0
0
0
1
1
0
1
1
0
0
1
1
2
0
2
1
2
1
1
0
2
2
0
1
0
1
0
1
1
0
0
1
0
1
0
2
1
0
2
2
1
1
1
0
1
0
2
2
0
2
0
0
1
1
0
3
1
3
2
0
1
0
4
1
0
1
1
2
0
2
0
0
0
2
1
0
2
0
2
0
1
1
1
2
0
0
2
2
1
1
1
1
2
0
2
1
2
0
0
1
1
0
0
2
1
2
1
0
1
0
0
0
0
4
1
1
2
0
2
1
1
1
1
1
2
0
0
0
0
1
1
1
1
0
0
1
0
0
0
0
1
1
1
1
2
2
1
1
3
1
0
1
0
0
0
0
1
0
1
1
1
1
1
1
0
2
0
0
2
0
1
0
0
0
0
1
0
2
1
1
0
2
0
0
2
1
2
1
0
2
2
0
0
2
1
1
0
1
2
0
1
0
2
2
1
2
1
2
2
1
2
0
0
1
2
0
0
1
1
2
0
0
0
1
2
0
2
0
1
2
1
0
1
0
3
0
1
1
1
0
0
0
0
3
1
0
0
1
1
1
1
2
1
0
0
0
0
0
2
1
1
0
2
1
2
0
0
1
2
0
2
0
2
0
0
1
1
1
0
0
2
0
0
0
0
0
0
0
1
1
3
1
1
1
0
0
1
1
0
0
1
2
0
2
2
0
1
2
1
1
0
1
0
1
1
0
2
1
0
1
1
0
0
3
0
1
0
1
1
1
0
1
0
2
2
0
0
0
0
0
1
0
1
0
1
2
0
0
1
1
0
0
0
1
1
2
1
1
1
1
2
1
0
1
0
0
2
2
2
0
0
1
1
2
1
0
5
1
0
0
2
1
1
0
0
0
0
0
1
0
1
0
1
0
2
2
3
0
0
0
2
1
0
2
0
0
1
2
0
0
0
1
0
1
0
1
1
2
0
1
2
2
1
0
2
0
2
0
1
0
0
1
1
0
2
3
0
0
1
0
1
1
1
0
0
0
0
0
1
0
2
0
3
0
1
1
2
1
0
2
1
0
0
0
1
2
0
1
2
1
1
1
1
0
2
1
1
0
1
1
4
1
2
1
0
0
0
2
0
0
1
2
1
1
0
2
0
0
2
1
2
0
2
2
1
1
0
1
2
0
0
0
2
2
0
2
0
1
2
0
1
1
0
1
1
2
2
2
0
0
0
0
0
2
0
2
0
1
0
0
1
0
1
0
0
0
1
2
1
0
0
0
0
0
2
0
2
0
1
0
1
0
1
0
2
1
2
1
0
0
1
2
0
2
0
1
0
2
0
0
1
0
2
1
0
1
0
1
0
1
1
1
1
1
2
2
1
1
1
1
2
0
3
0
2
1
0
0
2
0
2
1
1
0
1
2
0
0
2
1
0
1
1
2
2
1
0
2
0
0
1
2
0
0
1
1
0
2
3
2
2
1
1
1
0
2
1
1
1
0
0
0
1
1
0
0
0
0
1
1
1
0
1
2
2
0
1
1
2
2
1
1
0
0
1
2
1
1
2
1
0
0
2
2
1
1
0
2
1
1
1
1
1
0
0
1
0
1
1
0
1
2
0
0
0
0
0
1
2
2
1
0
0
0
1
0
0
0
2
1
2
1
1
2
1
0
0
1
1
2
0
0
0
1
1
1
1
2
0
0
1
0
1
3
0
2
0
2
0
2
0
1
0
0
0
1
0
1
1
1
2
0
0
0
0
0
0
1
2
1
0
1
0
2
0
1
1
0
0
0
2
0
0
1
0
1
1
0
0
0
0
0
1
1
1
2
0
1
1
1
0
0
1
0
1
1
2
1
1
0
0
1
1
1
1
0
1
0
0
1
1
0
0
3
2
2
0
0
0
0
0
0
1
1
2
0
0
1
1
1
0
3
2
1
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
2
2
0
0
0
2
2
1
0
2
0
1
1
0
2
0
2
1
0
0
0
1
2
1
0
0
0
2
1
0
0
3
2
0
0
0
0
1
0
2
1
2
0
2
2
0
2
0
0
0
2
0
0
1
0
0
0
0
2
1
2
1
0
2
0
0
1
1
2
1
2
2
1
1
2
2
0
0
0
1
0
1
0
1
1
1
1
2
2
1
0
2
0
1
2
2
1
2
1
2
0
0
0
1
0
0
0
0
0
0
2
2
1
2
2
2
2
2
0
0
1
1
0
1
2
2
1
0
2
1
1
1
1
0
0
0
0
1
0
0
2
2
1
1
0
0
1
0
0
0
0
1
2
0
1
1
2
0
1
2
1
1
1
1
2
1
0
0
0
0
0
0
1
0
0
1
2
1
0
1
2
0
0
2
0
0
1
0
0
1
0
0
1
0
0
1
1
0
1
1
0
0
1
0
1
0
0
2
1
0
0
1
0
1
1
1
1
0
1
1
0
0
0
1
1
3
2
1
2
1
1
0
0
0
2
1
2
0
1
1
1
0
2
1
1
0
0
2
0
0
1
1
0
2
2
0
1
1
0
0
1
1
0
1
0
2
0
2
2
2
1
0
0
0
0
0
1
2
1
0
1
0
1
1
1
1
2
0
0
2
1
0
1
0
2
2
2
1
0
2
1
1
0
0
1
0
1
0
0
1
0
0
2
1
5
2
1
0
0
1
0
0
0
0
0
1
1
1
0
2
0
0
0
0
0
0
0
2
0
2
0
2
2
0
0
1
1
1
1
1
0
0
0
1
2
1
2
1
1
0
1
0
1
0
2
0
0
1
1
0
2
1
2
2
0
0
1
2
1
0
2
0
1
3
1
0
0
2
1
1
2
2
1
2
1
0
0
1
0
1
0
1
1
2
1
0
0
1
1
1
1
0
2
0
2
1
1
0
0
0
2
1
0
1
2
1
1
1
0
0
0
0
1
1
1
2
0
2
2
0
0
1
2
0
1
2
1
1
1
2
1
1
0
1
0
1
0
1
0
0
2
0
0
0
0
2
1
0
0
0
1
2
2
0
1
0
0
0
1
0
2
1
1
1
3
0
1
0
1
1
1
1
1
1
1
1
1
1
0
1
0
0
1
0
0
1
2
0
3
0
0
2
0
1
1
0
0
0
0
2
2
1
0
0
1
1
3
1
2
2
1
0
0
0
1
0
2
1
0
1
1
0
1
0
1
1
0
0
1
0
2
1
1
0
1
0
0
1
0
1
2
0
2
0
0
2
2
1
1
1
1
0
1
2
2
1
0
0
0
2
1
2
3
2
2
1
2
0
1
0
0
2
1
1
0
1
0
0
2
1
0
0
2
1
0
2
1
0
1
1
0
0
2
1
0
1
2
0
1
2
1
2
2
0
1
1
2
2
2
0
0
2
0
0
0
1
0
0
0
0
1
2
0
0
1
2
2
1
1
1
2
0
0
0
2
1
0
0
0
0
1
2
2
1
1
1
1
0
0
0
1
2
0
1
0
0
0
0
1
0
0
1
0
2
1
1
0
1
2
1
0
1
0
1
1
1
0
1
1
0
2
0
0
1
1
2
1
2
0
0
0
1
1
0
1
1
1
2
2
2
0
2
1
2
2
0
1
0
0
2
0
0
0
1
1
2
0
0
1
0
0
0
1
1
0
1
3
0
1
0
1
2
2
1
2
2
2
1
2
1
1
0
0
1
1
3
0
0
2
0
0
2
1
1
1
0
1
1
0
1
0
2
2
0
2
1
1
0
0
2
0
1
0
1
0
3
0
0
0
0
1
1
1
2
1
2
1
1
0
0
1
0
1
1
0
1
2
0
1
2
0
1
1
0
0
1
1
2
0
1
2
2
0
1
0
2
0
2
0
0
1
1
1
0
0
1
1
0
0
0
1
0
0
1
0
1
0
2
0
2
1
2
1
1
1
1
0
0
2
0
2
0
1
2
0
1
0
2
1
1
1
0
1
0
0
2
0
2
0
0
1
0
0
2
0
2
2
1
0
1
1
0
1
1
1
0
0
0
1
1
1
0
0
1
1
1
1
4
3
0
0
2
0
1
2
0
1
1
2
1
1
1
0
0
2
1
0
1
1
1
2
2
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
2
2
2
1
0
0
2
1
0
2
1
1
1
1
0
0
0
2
2
2
0
0
0
3
3
1
2
2
1
0
1
2
2
0
0
1
0
1
0
1
0
0
3
0
2
1
1
0
0
1
0
0
1
0
1
0
1
0
2
1
0
0
2
1
2
0
2
2
0
1
0
2
0
0
1
0
0
2
2
1
1
1
1
0
0
1
1
0
0
0
0
0
2
1
0
1
2
0
1
0
1
0
2
0
2
1
2
1
1
2
0
1
1
1
1
1
1
1
1
0
2
1
0
2
2
0
1
0
2
0
2
0
0
0
2
0
1
0
0
0
0
1
1
1
2
0
1
2
0
2
1
2
0
1
0
1
1
2
1
1
2
1
2
1
1
1
0
0
1
1
1
0
0
1
0
0
0
1
1
0
0
0
0
1
1
0
1
1
0
2
2
2
1
0
0
0
0
2
2
1
0
1
2
0
1
0
1
1
0
0
1
0
4
2
1
3
0
1
1
1
1
0
0
1
2
1
0
2
2
3
0
1
0
0
2
0
1
2
1
2
1
2
0
3
1
1
1
0
2
3
0
1
1
0
0
0
1
2
1
1
1
1
2
0
0
0
0
1
1
1
0
2
2
0
0
0
0
1
2
0
1
2
2
1
1
1
2
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
2
1
2
0
0
1
1
1
1
1
2
0
1
0
1
2
2
2
0
1
0
2
2
0
0
3
1
0
1
2
0
1
1
0
0
0
1
1
1
0
0
0
0
1
0
2
0
0
0
0
1
0
2
0
2
0
0
1
2
0
2
0
1
2
0
1
0
1
1
0
1
0
0
1
1
1
1
1
1
1
1
2
1
0
0
2
0
1
1
1
0
1
2
2
0
3
1
2
0
2
0
0
0
2
2
0
1
1
0
2
2
1
1
1
0
1
1
2
0
0
1
0
1
1
1
0
0
1
1
0
0
0
1
1
2
0
2
2
0
1
1
2
0
1
2
0
0
1
1
0
2
0
0
1
1
1
0
2
1
0
2
0
0
2
1
0
1
2
2
0
0
2
0
1
2
2
0
1
1
1
1
0
0
0
2
1
0
0
1
1
0
1
0
1
0
1
0
1
2
1
2
0
2
1
1
0
2
0
1
0
0
0
1
0
2
1
0
6
1
1
2
2
1
1
1
0
0
2
0
2
0
1
0
1
2
1
1
3
0
2
0
2
0
1
2
0
0
2
1
0
1
1
0
1
0
0
0
0
1
1
0
1
2
1
1
0
2
0
1
1
0
0
0
2
0
1
0
1
1
0
1
1
0
0
2
0
2
0
0
0
0
0
1
1
0
1
0
0
1
2
0
0
0
2
2
0
2
1
2
0
1
0
0
0
1
2
2
0
0
0
2
0
2
2
2
2
0
0
0
1
1
1
0
3
1
1
0
2
1
2
0
1
0
0
3
1
1
0
1
0
1
0
0
0
1
0
1
1
0
0
2
1
1
0
1
1
2
0
1
0
1
0
0
0
0
2
2
2
0
2
1
2
0
0
2
0
0
1
0
0
0
2
2
0
0
0
1
0
0
0
1
1
2
1
0
1
0
0
1
0
0
2
1
1
0
0
0
1
0
1
2
0
0
0
1
1
0
0
1
2
2
2
0
0
1
0
1
1
0
1
2
0
0
0
0
2
1
1
0
1
2
0
1
1
0
0
0
0
2
0
2
1
0
2
1
1
1
1
0
0
0
0
0
1
2
0
1
2
2
1
2
1
1
1
2
0
0
0
0
1
0
0
0
1
0
0
0
1
2
2
0
0
0
0
1
1
0
0
0
1
0
0
2
2
0
1
1
2
1
2
1
1
0
1
2
1
0
1
2
0
1
0
1
1
2
2
1
1
2
2
0
2
1
0
1
0
1
1
1
2
2
0
0
0
1
0
0
0
1
1
2
1
1
0
1
0
0
1
0
0
0
0
0
2
1
1
0
1
0
1
1
1
0
0
1
0
0
0
2
0
1
0
1
2
1
1
1
0
1
1
1
0
1
1
1
0
1
0
1
0
1
2
2
0
1
0
2
2
0
1
2
0
2
5
0
1
1
2
0
0
1
1
2
0
0
1
2
0
0
0
2
0
1
0
0
0
1
1
0
1
1
1
2
0
2
1
2
1
0
3
0
0
1
0
2
1
1
2
0
1
2
2
0
4
0
0
1
0
2
1
1
1
0
1
2
2
0
0
0
4
0
1
1
3
1
1
0
0
1
1
2
1
0
0
1
0
1
1
1
0
0
2
1
0
2
1
0
1
5
0
2
0
0
2
1
0
2
0
0
1
1
2
2
2
2
0
0
2
2
2
0
1
2
0
1
0
0
2
1
1
0
2
0
0
1
1
0
1
1
2
1
1
2
0
1
0
0
0
1
2
1
1
0
0
1
1
1
1
1
0
0
1
0
0
2
1
2
3
0
1
2
0
2
0
1
1
2
1
1
0
1
0
0
0
2
0
2
1
1
2
1
0
0
2
1
0
0
0
0
0
1
2
1
1
2
2
1
0
0
2
1
0
0
1
2
0
0
0
0
1
2
1
1
1
1
2
0
0
1
4
1
0
4
0
1
1
2
0
0
1
2
2
0
0
1
2
3
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
2
1
0
1
1
1
1
0
0
1
2
1
2
1
1
0
1
0
1
1
0
0
2
1
0
1
0
0
0
1
1
0
2
0
1
0
1
0
1
1
0
0
0
0
2
1
0
2
0
1
1
2
2
0
0
1
1
0
1
1
0
1
1
1
0
2
1
1
1
0
0
1
0
1
0
1
1
1
1
2
0
1
1
1
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
2
1
1
0
0
0
0
1
1
0
0
2
0
2
1
1
1
1
1
0
1
1
0
0
1
0
1
3
0
2
1
0
1
0
2
0
1
0
0
2
0
2
2
1
1
2
0
0
0
1
1
2
1
1
1
0
1
0
2
2
1
1
1
0
1
0
2
0
2
1
2
0
1
0
2
0
2
1
1
0
3
1
1
0
0
2
0
2
0
0
1
2
1
0
0
1
0
1
1
0
1
2
1
1
2
0
1
0
1
0
2
2
0
0
1
2
1
0
0
0
1
1
1
1
2
2
1
2
1
0
0
0
2
0
1
0
0
2
2
1
2
0
0
2
0
0
0
1
0
0
0
1
0
0
0
2
0
1
1
0
1
0
1
0
1
2
0
2
0
0
1
0
1
0
2
0
0
1
0
2
2
2
1
2
2
0
0
2
0
3
1
1
1
1
1
2
2
0
2
2
0
0
2
0
1
6
0
2
1
0
0
0
2
2
0
1
3
0
0
2
0
1
1
0
1
2
0
0
0
1
0
2
2
1
2
0
1
0
0
1
0
2
0
1
1
0
2
1
0
1
0
0
2
1
1
0
0
1
1
0
1
0
0
1
0
3
2
1
0
1
0
0
0
0
2
1
1
1
0
1
2
0
0
1
0
0
0
0
0
2
0
0
0
2
2
0
0
1
0
1
1
2
0
0
2
0
0
0
0
1
1
0
2
1
0
1
0
1
1
1
2
1
1
1
1
2
0
3
0
0
1
0
1
1
1
2
1
0
1
1
0
0
0
1
0
1
1
1
2
2
1
0
0
0
1
0
1
1
1
0
1
1
1
0
1
0
1
0
0
2
0
1
1
2
0
0
2
1
2
1
3
0
0
1
1
1
0
0
0
1
0
2
0
0
0
2
2
0
2
1
2
0
2
1
2
2
3
1
1
0
1
0
0
1
2
1
2
1
0
1
0
0
0
0
1
1
2
0
2
1
0
0
3
1
1
2
0
1
1
1
0
1
0
0
1
2
1
2
1
1
1
1
1
1
2
1
1
0
2
1
0
0
1
1
0
2
2
0
0
0
1
1
1
2
0
2
0
0
0
2
0
1
0
2
0
0
1
3
0
0
0
2
0
1
2
2
1
1
1
0
0
0
0
1
1
0
0
0
0
0
1
1
1
0
0
1
1
1
1
0
1
1
0
2
0
0
2
0
2
0
1
1
0
5
0
0
2
0
1
5
0
1
0
1
2
2
1
2
1
0
0
2
2
2
1
1
1
1
0
0
0
0
0
1
0
2
1
0
1
0
1
1
2
2
0
2
0
0
0
0
1
1
2
0
0
2
1
2
2
0
1
1
1
1
0
1
2
1
1
0
2
1
1
2
2
2
1
2
0
0
0
0
1
0
0
2
0
0
1
0
1
0
2
2
0
0
2
0
1
0
1
0
1
0
0
0
2
0
1
1
1
1
1
0
1
0
1
2
0
1
1
3
1
1
1
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
1
2
4
0
1
0
2
2
1
1
0
1
1
0
0
0
1
1
0
0
1
2
3
1
0
0
1
1
1
1
1
0
2
0
1
0
0
1
1
1
1
0
1
1
1
1
1
2
1
0
1
0
0
1
0
1
0
2
0
0
2
3
0
1
1
1
2
0
3
0
0
2
0
0
0
1
0
2
0
2
1
0
0
1
0
1
0
0
0
2
2
1
0
1
1
0
2
1
0
1
1
2
0
0
0
0
1
0
1
1
1
0
0
1
1
0
2
1
1
2
0
0
1
1
1
1
0
0
1
2
0
1
1
1
1
0
0
0
0
0
0
2
2
2
2
0
0
0
1
2
0
1
2
1
1
2
1
2
1
0
1
2
1
0
0
2
0
0
0
0
2
0
0
1
0
1
1
0
0
1
1
2
2
1
0
0
1
2
0
1
0
0
0
0
0
0
2
0
1
1
0
2
1
2
2
1
1
1
2
0
2
2
1
0
1
1
1
1
2
0
2
2
0
0
1
1
0
2
0
0
0
3
2
0
2
0
0
1
0
0
0
1
1
0
1
0
0
2
1
0
0
3
1
0
1
0
1
0
1
0
1
1
0
0
0
2
0
0
0
0
0
1
1
1
2
0
1
2
3
0
0
1
1
0
0
1
2
1
0
1
0
1
0
0
1
1
1
2
1
0
1
0
1
1
1
0
0
0
1
1
0
2
1
0
0
2
3
1
2
0
0
1
2
1
0
1
1
0
1
1
1
0
0
1
0
2
1
1
1
2
0
2
1
0
2
0
2
1
2
0
1
2
0
2
0
1
2
0
1
0
3
1
0
1
1
0
1
0
1
1
1
0
0
2
0
1
1
2
0
0
2
0
1
1
1
2
1
0
0
1
2
1
2
2
1
0
0
1
0
2
0
0
1
0
0
0
2
0
1
0
2
1
2
1
1
1
0
0
1
2
0
2
1
1
1
0
2
0
1
0
1
1
2
1
2
0
0
0
2
2
0
1
1
0
1
1
0
0
0
1
1
1
0
1
1
2
1
2
0
0
1
0
0
1
2
0
1
0
1
0
0
1
0
2
0
1
0
1
0
0
1
0
0
0
1
0
1
0
0
0
2
0
1
0
0
0
2
0
1
1
2
2
2
0
1
1
0
4
0
0
1
1
0
1
1
1
0
1
1
1
0
1
0
2
2
0
1
2
0
0
0
0
0
2
1
0
1
1
1
0
1
2
1
0
1
2
2
0
1
0
2
1
1
1
0
0
1
1
2
0
0
0
0
0
1
1
1
0
2
3
0
1
2
1
0
1
1
1
0
2
1
0
0
0
2
2
2
2
1
0
2
0
2
1
0
0
0
2
0
1
1
1
1
0
2
0
1
4
0
2
1
2
1
0
1
0
0
1
0
2
0
1
0
0
0
0
1
2
0
2
1
0
1
2
2
1
1
0
1
0
1
0
0
2
2
0
0
2
1
0
0
1
2
2
1
1
1
1
0
1
1
0
0
0
0
0
1
2
0
1
0
0
1
1
0
1
1
0
2
1
1
2
1
1
1
1
2
0
0
0
2
2
2
1
0
2
0
0
1
0
1
0
2
2
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
2
1
0
0
0
2
2
2
1
0
2
0
0
1
0
2
0
0
1
1
1
2
0
0
1
2
1
0
1
1
1
0
0
1
2
1
1
2
2
1
1
0
2
1
0
1
0
0
1
0
2
1
1
1
1
0
2
2
0
0
0
0
1
1
3
0
2
2
2
1
1
2
3
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
1
1
1
0
0
0
0
1
0
2
2
2
0
1
1
1
1
1
0
0
1
2
0
1
0
1
0
0
1
1
0
1
1
0
2
1
0
1
0
1
1
1
0
2
0
1
0
2
0
1
0
0
2
2
0
2
1
1
1
1
0
0
2
0
2
1
0
0
0
1
1
0
0
0
0
2
1
1
0
0
1
1
1
2
2
1
0
2
0
0
2
2
0
0
2
2
2
2
0
0
0
1
1
1
1
2
1
0
1
2
0
1
0
1
0
0
0
0
1
1
0
0
0
1
0
0
1
1
1
0
1
0
0
1
1
3
0
2
2
1
0
0
1
0
0
0
0
2
1
2
0
0
1
0
0
3
0
1
0
0
0
0
1
0
0
0
2
3
0
0
0
2
1
0
0
2
1
0
0
0
1
1
0
0
0
0
1
2
1
0
0
1
1
1
0
0
0
0
2
1
0
2
2
0
1
2
0
2
0
1
2
2
2
1
1
0
1
1
0
0
0
1
1
1
0
2
1
0
2
2
2
0
0
1
1
0
0
1
0
0
2
1
1
0
0
0
0
2
0
0
0
0
0
2
2
0
3
2
0
0
1
1
0
0
0
0
1
0
1
0
1
1
1
2
1
0
1
1
2
0
2
1
1
1
2
1
0
2
0
0
2
1
1
0
4
0
0
0
0
0
1
0
2
1
2
0
2
0
2
1
0
0
1
0
0
0
1
1
0
1
2
1
0
1
1
1
2
1
1
0
2
2
2
0
0
0
1
1
0
1
1
0
0
1
0
2
0
0
0
1
2
1
0
1
1
0
1
0
0
2
0
2
2
0
0
0
1
0
0
1
1
2
2
1
1
0
1
0
0
1
0
0
0
0
0
1
0
1
0
2
1
1
0
0
1
2
0
0
1
2
1
0
0
1
0
2
1
0
0
0
1
2
2
0
0
0
0
0
1
1
2
2
0
4
1
1
0
2
2
1
1
0
2
1
1
1
1
0
1
1
0
1
0
1
1
0
2
0
0
1
0
2
0
1
2
1
1
0
0
1
0
1
1
1
0
0
0
2
0
0
0
0
0
1
0
2
1
2
2
1
1
0
1
1
0
2
0
1
0
1
1
1
0
0
1
1
1
0
1
2
0
2
2
2
2
1
1
0
2
0
0
0
0
2
0
2
2
1
0
1
1
0
0
0
0
1
1
2
2
1
2
2
1
0
1
2
2
2
1
0
0
1
1
1
0
1
1
0
2
2
1
2
0
0
2
1
0
0
0
1
0
0
0
0
1
2
0
0
0
1
0
0
3
1
1
0
0
2
0
0
3
0
0
0
0
0
1
2
1
1
1
1
0
2
1
2
2
0
0
2
1
0
1
0
0
0
1
1
0
1
2
2
0
0
0
0
0
1
1
1
1
2
0
0
0
2
1
1
0
0
0
2
0
0
1
1
1
0
0
0
2
0
1
1
1
1
0
2
2
2
2
2
2
0
0
2
0
2
0
0
1
2
0
2
1
0
0
2
0
1
0
1
0
1
2
0
0
0
2
1
0
1
0
2
0
0
1
1
0
0
0
0
2
1
0
3
1
0
0
0
0
0
1
2
0
2
1
0
1
0
0
1
0
0
1
1
1
0
0
1
1
1
0
1
0
2
2
0
0
2
1
1
2
0
0
0
1
0
0
2
1
2
3
0
1
0
0
2
0
0
2
1
0
2
0
0
2
1
0
0
1
0
1
2
2
1
2
2
0
0
1
0
0
0
1
3
1
0
1
0
0
1
1
0
1
1
0
0
0
0
1
0
1
0
0
1
1
1
1
1
1
1
2
2
1
1
0
0
2
0
0
1
1
0
1
0
0
1
2
2
1
1
2
0
0
0
1
0
1
0
0
0
3
1
0
0
1
0
0
0
1
2
1
0
0
0
1
2
0
2
0
1
1
2
0
0
0
2
1
1
1
1
2
1
0
0
3
0
0
0
1
1
2
2
1
1
0
1
0
2
0
1
2
0
1
1
1
0
0
1
0
0
0
2
2
0
1
0
2
1
0
2
1
2
0
2
2
2
2
1
1
1
3
1
1
0
0
1
0
1
0
1
0
0
1
1
0
0
0
1
2
0
0
0
1
2
0
0
2
0
0
2
1
2
0
2
0
1
1
2
1
1
2
1
4
1
2
2
2
0
0
0
1
0
0
0
2
0
2
1
2
0
2
1
2
2
1
0
0
1
0
1
0
1
1
0
1
1
1
0
0
1
0
1
1
0
0
1
1
0
1
2
0
0
0
0
0
1
0
1
2
2
0
1
1
0
1
2
0
0
1
1
1
1
0
0
0
2
1
1
2
0
0
1
1
0
1
2
0
2
1
1
2
0
0
1
1
1
0
2
0
0
0
2
0
2
0
1
0
2
2
0
1
0
2
0
1
1
1
0
1
2
0
1
0
1
1
1
1
2
2
2
0
0
1
1
1
1
1
0
0
0
2
0
0
0
0
1
2
1
0
0
1
0
0
2
0
0
1
0
2
1
0
0
1
1
2
1
5
2
0
0
0
0
0
1
0
1
3
0
1
1
0
1
0
0
1
1
0
0
2
0
0
0
2
2
0
1
1
0
2
0
0
2
2
1
0
0
0
0
0
0
1
1
0
2
0
0
1
1
1
2
1
2
0
1
1
0
1
0
1
1
0
0
1
0
1
2
0
1
0
1
1
1
2
2
1
0
2
0
0
1
0
1
0
0
2
0
3
1
2
0
1
0
0
4
2
2
2
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
1
1
0
1
1
2
1
2
0
0
1
1
0
1
0
0
0
1
1
0
1
2
1
1
0
2
0
1
1
2
1
0
1
1
0
2
0
1
2
1
0
1
2
0
1
1
2
2
1
0
0
0
0
2
1
1
1
2
0
2
0
0
0
2
2
0
1
0
3
2
0
0
1
0
0
2
0
0
1
0
0
0
1
1
0
0
3
1
1
0
0
0
3
0
0
0
1
2
0
0
0
0
4
2
1
1
1
0
0
0
0
0
1
2
3
1
2
1
1
2
0
1
0
0
0
2
0
2
0
1
0
1
3
0
0
2
3
0
1
1
1
1
2
3
0
2
1
1
1
1
2
0
1
0
1
0
1
2
1
0
0
0
1
0
2
0
1
0
2
2
1
2
1
1
0
2
1
2
0
1
3
1
2
0
1
0
0
1
8
0
1
0
0
1
1
2
0
1
0
1
1
0
0
2
2
0
2
2
0
2
1
0
0
1
0
2
1
1
2
1
0
1
0
0
1
1
2
4
1
1
0
1
2
1
1
0
1
1
1
2
1
2
0
2
1
1
2
1
0
1
1
1
1
2
2
0
2
1
2
1
0
1
0
0
0
0
1
0
0
2
1
1
1
0
1
1
2
0
1
0
2
1
2
1
0
1
1
1
0
0
0
0
0
0
0
1
1
1
0
1
0
1
1
0
1
1
1
2
2
0
0
0
0
2
2
2
1
2
0
1
0
3
1
0
1
1
0
0
0
0
1
1
2
2
0
0
0
1
2
2
2
0
2
1
0
2
2
1
0
0
0
2
0
1
1
1
1
1
0
0
0
2
0
1
0
0
0
1
1
3
1
2
0
1
1
0
2
1
2
0
0
0
0
1
0
1
1
0
0
1
1
2
2
1
1
2
0
1
0
1
0
3
1
2
2
0
2
0
1
0
0
0
1
2
2
0
2
0
1
1
0
2
2
0
1
2
1
2
1
2
0
0
1
1
2
1
0
1
2
0
1
2
1
0
1
1
1
1
0
2
0
1
1
2
0
0
1
2
0
0
0
2
1
0
2
1
2
1
0
1
1
1
1
0
0
1
0
1
0
1
1
1
2
0
1
0
0
1
1
1
0
0
0
2
0
0
2
0
0
0
1
0
1
0
0
0
0
2
1
1
1
1
0
2
0
0
0
0
0
0
1
1
0
1
1
0
3
2
0
0
2
1
0
1
1
1
2
1
0
1
2
0
1
0
2
0
0
1
1
0
0
0
2
0
2
0
0
2
0
2
1
0
1
1
2
0
1
1
0
0
0
0
0
1
1
1
2
2
2
0
0
3
0
0
0
0
1
1
0
1
2
0
1
1
1
1
1
1
1
0
0
0
0
0
1
1
1
0
1
0
1
1
0
2
0
0
1
2
0
2
1
0
2
1
1
0
1
2
0
0
3
0
0
1
2
1
0
0
0
2
1
1
2
2
0
1
0
2
2
2
1
2
1
1
0
1
1
2
0
1
0
0
1
0
0
1
0
0
2
2
0
2
1
1
1
1
1
0
0
0
0
0
0
0
1
1
2
1
2
0
2
0
2
1
1
1
1
1
0
2
1
1
1
3
0
1
3
0
2
0
1
1
1
1
0
2
0
0
0
2
0
1
0
1
0
1
1
2
0
1
1
0
1
1
2
0
1
0
1
0
1
1
2
0
3
1
0
2
2
2
2
1
1
1
0
1
1
1
2
1
0
0
1
2
1
2
0
0
0
1
1
0
2
2
2
1
0
1
0
1
1
0
1
2
0
1
1
1
1
2
1
0
1
2
0
0
2
1
4
2
2
0
0
0
1
0
1
1
0
0
2
2
2
0
0
2
1
0
1
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
1
1
3
0
1
1
0
1
0
1
1
0
2
0
1
0
0
0
1
1
2
1
2
0
1
1
0
2
1
1
1
1
2
1
1
0
2
0
5
0
0
0
1
1
0
0
1
2
0
1
0
1
0
1
1
0
0
1
0
0
0
1
0
1
1
2
1
0
1
2
1
0
1
0
0
0
1
0
1
0
1
2
0
0
0
2
0
0
1
0
1
1
1
1
0
0
1
1
2
0
1
2
0
2
0
1
1
0
0
1
1
0
0
2
1
0
1
0
0
2
1
1
0
0
0
2
0
1
2
0
0
0
0
0
1
1
1
0
1
0
1
1
0
1
2
1
0
1
1
1
0
3
2
1
0
2
2
1
1
2
1
2
1
0
1
0
0
1
2
0
0
1
2
3
1
2
0
1
2
1
0
0
2
0
1
0
2
1
1
2
2
2
0
0
1
0
1
1
2
0
0
0
1
0
3
2
0
0
1
2
2
0
1
1
0
3
0
1
1
1
1
0
0
4
2
0
1
2
1
0
1
1
0
0
1
0
0
1
1
1
1
1
2
1
1
1
0
1
0
0
1
0
0
0
1
0
0
1
1
0
0
1
2
0
0
0
0
0
2
0
0
1
0
1
2
0
1
0
1
0
1
2
0
0
0
1
0
2
0
1
0
1
2
1
0
0
1
0
1
1
1
0
1
1
0
0
1
2
0
1
2
0
1
2
0
1
2
0
1
0
0
1
3
0
1
0
0
1
0
0
2
0
0
0
2
1
1
2
0
2
2
2
1
2
0
0
0
2
1
2
0
0
0
0
1
1
2
6
1
0
0
2
2
1
1
0
1
0
0
1
0
0
2
0
0
1
1
2
2
1
0
1
0
1
0
0
1
1
0
1
2
0
1
2
1
0
2
1
0
0
1
0
2
1
0
0
0
0
0
0
1
2
0
1
0
0
2
1
1
1
2
1
0
1
0
0
1
0
1
1
1
0
1
2
1
2
2
1
0
0
0
1
1
1
2
0
0
0
0
1
1
1
1
0
0
2
0
0
0
1
2
1
2
0
0
1
1
0
0
0
1
1
0
1
1
0
1
0
0
2
0
1
1
1
0
0
1
0
1
1
1
2
2
0
0
2
1
0
2
1
0
0
1
1
1
2
2
0
0
1
2
1
0
2
1
1
0
1
0
1
2
1
1
0
1
2
0
0
1
0
1
1
1
0
2
0
0
0
0
1
2
1
0
0
1
0
0
2
1
1
1
1
3
2
1
1
1
2
1
2
1
1
2
0
1
0
1
0
1
0
0
1
1
2
2
1
1
1
2
0
1
1
1
4
0
0
1
2
0
0
1
1
0
1
1
0
0
1
1
2
0
1
0
0
0
1
1
1
0
2
1
1
0
0
0
1
1
1
0
2
2
1
0
1
0
0
1
1
1
0
0
0
0
1
1
0
1
0
2
1
1
0
2
2
1
0
1
0
2
0
1
0
2
1
0
0
0
0
0
0
0
1
1
2
2
0
1
0
0
0
1
1
0
1
0
0
0
1
0
2
0
1
1
1
0
0
0
0
1
0
1
2
0
2
0
1
1
0
0
0
0
0
0
1
0
1
1
1
1
0
0
0
1
2
0
2
0
0
0
0
2
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
1
1
0
1
1
1
1
0
2
0
1
1
0
0
1
0
1
2
1
0
0
0
0
0
2
1
2
0
1
1
0
1
1
0
2
1
0
1
0
1
2
2
2
1
1
1
2
0
1
1
2
0
1
1
0
1
0
0
2
0
0
0
1
1
0
1
1
0
0
3
2
0
2
1
0
1
0
0
0
0
1
1
0
0
1
1
1
2
1
1
0
0
0
0
1
1
2
1
0
0
0
1
0
1
2
1
1
1
2
2
0
1
1
0
0
1
2
1
0
0
1
0
3
0
1
0
0
2
1
2
1
0
2
2
2
0
1
2
0
0
0
1
0
1
0
1
2
1
0
2
0
0
2
0
0
1
0
1
2
1
1
0
1
1
1
0
0
1
0
0
2
1
1
0
2
0
0
1
1
0
1
0
0
1
2
2
1
1
1
2
2
1
2
1
0
0
1
1
1
0
1
0
1
1
3
2
1
0
2
2
1
2
1
1
0
1
2
2
1
2
0
0
0
2
0
2
0
0
0
1
0
1
0
2
2
2
0
0
1
2
2
2
0
0
2
2
0
1
0
0
0
4
0
3
1
1
0
2
1
0
0
1
2
0
1
3
1
1
1
3
1
0
1
2
1
1
2
0
1
1
1
0
1
0
0
1
1
1
1
0
0
1
1
2
0
1
0
1
0
1
0
2
0
1
1
1
2
1
2
2
0
3
1
1
2
2
1
2
0
0
1
1
0
1
0
0
0
1
0
0
2
1
0
0
0
0
1
1
0
2
0
2
0
1
2
0
2
1
1
1
1
0
2
0
2
0
2
2
1
0
0
2
0
2
0
1
2
0
1
1
0
2
2
1
1
1
0
0
2
3
1
0
2
1
0
1
1
0
1
1
0
0
0
1
2
1
0
0
0
1
1
1
0
2
0
0
2
0
0
2
2
2
2
0
0
1
0
1
1
1
0
1
0
1
0
0
1
1
1
0
1
0
1
0
2
2
2
1
0
2
1
0
1
0
1
0
1
1
0
2
2
0
0
1
1
1
0
0
1
0
0
1
1
1
0
1
1
0
1
0
1
0
1
0
1
1
0
1
1
2
0
2
0
0
0
2
0
1
1
0
1
1
0
1
1
0
2
0
1
0
1
1
0
0
1
0
2
0
0
2
1
0
0
1
1
1
0
1
1
2
0
1
1
0
1
0
0
1
1
0
0
1
2
2
0
1
0
1
1
1
0
1
0
2
0
0
1
2
0
4
1
0
1
1
1
2
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
1
0
0
1
1
1
0
1
1
2
0
2
1
1
1
0
1
2
1
0
1
1
1
1
1
1
1
0
1
1
0
0
1
0
1
0
1
1
1
2
1
1
1
0
2
0
0
0
1
1
2
0
0
0
1
0
2
3
0
2
1
0
0
1
2
0
0
2
1
0
0
1
2
1
1
2
0
0
0
0
0
0
2
2
1
0
1
1
1
1
2
0
1
2
2
0
1
0
0
0
1
0
1
1
0
1
2
2
0
0
2
3
1
1
0
1
0
0
1
0
1
2
3
1
0
1
1
1
3
0
0
1
2
1
0
1
1
2
2
4
1
0
2
0
1
0
1
0
2
2
0
0
2
1
0
5
0
0
1
0
0
0
1
1
0
1
0
0
0
1
0
1
0
1
1
0
0
3
1
0
1
1
2
2
3
0
0
2
0
2
1
0
1
8
0
0
2
1
1
2
0
1
0
0
1
1
2
2
2
0
0
2
0
1
1
0
1
0
1
2
1
1
0
2
0
0
0
0
0
0
1
1
0
0
1
0
0
0
2
0
0
1
0
1
0
2
1
2
0
2
0
0
0
1
2
1
0
0
0
2
2
1
1
0
1
1
1
1
1
2
2
0
0
2
0
1
1
0
0
0
1
2
0
0
0
1
2
1
0
1
1
1
1
3
0
0
0
2
0
0
0
1
0
0
2
1
1
0
1
0
2
0
0
0
0
0
1
1
0
1
1
0
1
2
2
1
0
2
1
0
2
1
0
1
0
1
0
2
1
2
0
2
2
2
0
1
2
3
1
0
1
0
1
1
2
0
0
0
0
0
1
0
0
0
0
2
2
0
2
1
0
0
0
1
1
2
0
0
2
1
0
1
0
0
1
0
1
1
0
0
1
0
1
1
2
2
1
0
2
0
1
1
0
2
0
3
1
1
0
0
1
2
0
2
1
0
2
1
0
0
0
2
0
0
2
1
1
2
0
2
0
0
0
0
0
1
2
1
0
0
2
1
1
0
1
0
1
2
0
0
0
0
1
0
0
1
1
0
2
1
1
1
0
0
0
0
0
0
2
0
2
1
1
0
1
0
2
0
0
0
0
1
0
2
1
2
0
1
0
1
0
0
3
0
0
1
3
1
1
2
0
2
1
1
0
0
1
3
0
0
0
1
2
0
2
0
2
1
0
0
0
0
0
1
1
1
0
0
2
0
0
1
0
0
1
0
1
1
0
0
1
2
2
0
0
1
2
2
2
1
0
1
1
2
2
2
1
1
0
2
2
1
0
2
1
0
0
0
0
2
2
1
0
1
1
0
1
2
0
1
2
0
2
2
0
1
2
1
0
1
1
0
0
0
1
2
0
2
0
0
0
1
1
3
0
1
1
0
0
0
1
2
2
0
0
1
2
0
1
0
0
0
0
0
4
1
2
1
2
0
2
0
0
0
1
1
0
2
2
0
0
2
1
1
0
1
0
2
0
0
1
2
0
1
1
0
1
2
2
1
1
1
2
2
1
0
2
1
1
0
1
0
0
1
2
1
0
2
1
0
2
1
1
0
0
0
0
1
1
2
0
0
2
2
0
1
1
1
0
2
1
1
0
0
1
0
6
1
0
1
0
0
1
1
0
0
0
2
2
2
0
1
2
0
0
0
1
2
3
1
1
0
1
2
2
0
1
1
0
0
2
0
2
0
0
1
1
0
0
0
1
2
1
2
1
2
0
2
1
1
0
1
1
0
1
1
0
3
0
0
0
1
0
1
1
0
1
0
1
1
1
0
1
2
1
2
2
1
2
1
0
1
0
0
0
0
0
1
2
1
1
1
0
1
1
1
0
0
1
0
0
1
2
0
1
2
1
0
2
1
1
1
0
2
2
2
2
1
1
0
1
0
1
2
0
2
0
1
1
1
1
0
0
0
1
2
0
2
0
0
0
2
0
1
0
1
0
1
0
0
1
2
1
1
2
1
1
1
0
1
0
0
2
2
2
2
2
2
2
2
1
0
2
1
0
0
1
1
2
2
0
1
2
1
0
2
1
3
0
1
0
0
1
0
0
0
1
0
2
0
0
0
1
1
0
2
0
2
2
0
2
1
3
1
1
1
2
1
0
2
1
1
1
0
2
2
1
1
1
0
1
2
0
0
0
1
1
1
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
1
2
0
0
0
1
1
0
0
2
0
1
1
0
1
3
2
0
2
1
0
5
1
1
0
0
0
0
0
1
1
0
2
2
0
0
0
3
0
0
1
1
1
0
0
1
2
1
0
0
2
1
0
0
0
1
2
2
0
0
2
2
0
1
0
1
2
1
1
0
2
0
2
1
2
0
2
0
0
0
2
1
0
0
2
0
1
2
1
0
1
0
2
1
0
2
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
1
2
2
2
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
1
3
0
0
0
2
1
0
0
1
1
2
1
0
0
0
0
1
0
1
2
0
1
2
0
0
1
2
0
0
0
1
0
0
0
0
2
0
1
0
0
2
0
2
0
0
2
0
1
3
1
0
1
2
0
0
1
0
2
0
0
2
1
2
0
1
0
1
1
1
0
1
0
0
1
0
0
2
1
1
0
1
0
1
1
1
2
0
1
2
1
0
2
1
0
1
0
1
0
1
1
0
1
1
1
0
0
1
0
2
2
1
0
2
0
0
2
1
0
1
2
1
0
1
1
0
0
1
0
2
0
2
0
0
0
0
1
0
0
0
0
2
1
2
0
2
2
1
1
1
0
1
2
2
0
0
1
0
1
1
2
1
0
0
2
2
0
2
2
1
0
0
1
2
0
2
0
0
0
2
1
2
1
1
1
1
0
1
0
0
1
1
0
0
0
0
3
2
0
0
2
0
1
0
0
1
2
0
0
0
0
2
2
0
2
0
2
1
0
0
1
0
1
1
0
0
1
1
2
1
0
0
1
0
2
1
0
1
0
0
0
0
1
1
0
1
1
0
0
0
1
0
0
1
0
1
2
1
0
2
0
0
1
2
0
0
1
1
0
1
2
2
2
0
2
2
1
0
0
1
0
2
0
3
0
0
0
2
0
1
1
2
1
0
2
1
0
1
0
0
0
2
0
0
1
2
0
0
1
1
1
1
2
0
2
2
0
0
2
1
1
1
0
2
1
1
1
0
1
1
0
2
1
1
0
0
2
0
1
0
2
2
1
0
2
2
1
2
0
0
2
1
1
0
2
0
2
1
2
0
1
2
0
2
2
0
0
1
0
1
0
0
0
1
0
3
1
1
0
0
0
1
3
1
0
0
0
0
1
0
1
5
1
0
1
0
0
2
0
1
1
2
1
0
0
0
2
0
0
0
0
1
1
1
1
0
0
0
0
0
2
0
1
1
0
1
2
2
2
0
2
3
2
1
1
2
0
2
1
1
1
0
0
1
1
2
0
1
0
0
2
0
4
0
1
1
1
0
1
1
3
1
1
1
2
1
0
0
0
0
0
2
0
1
0
0
0
2
0
0
1
2
0
0
1
0
0
2
1
1
1
1
1
0
1
0
1
1
1
2
0
0
0
0
0
1
2
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
1
1
1
1
1
1
1
0
1
3
0
0
0
1
1
0
1
1
0
1
0
0
0
1
0
0
1
1
1
2
0
1
0
0
0
0
1
2
2
1
1
2
2
1
1
1
2
2
0
2
1
1
2
1
1
0
0
2
0
0
1
2
1
0
1
0
0
0
0
1
1
1
0
0
2
0
0
0
0
2
0
0
1
1
0
0
1
2
0
2
1
2
2
2
0
1
0
2
0
4
2
2
2
0
4
0
0
0
2
0
0
2
0
1
1
1
1
1
0
0
0
0
1
1
0
1
2
0
0
0
0
0
1
0
1
0
1
0
1
0
2
1
0
1
2
2
0
0
0
0
2
0
0
0
1
0
0
1
0
0
2
2
1
0
0
1
2
0
2
2
2
0
1
3
0
1
0
0
0
0
2
2
0
1
1
1
1
1
0
0
0
0
0
1
1
1
0
1
0
2
1
0
1
0
1
1
1
1
2
1
1
1
1
1
0
0
2
0
0
0
1
0
1
1
0
1
1
1
1
0
1
2
3
1
1
1
0
1
1
1
1
0
1
0
0
0
0
0
1
1
0
0
1
0
0
2
1
1
0
1
0
0
0
0
1
1
0
5
0
0
1
1
0
2
0
2
2
2
2
0
1
0
2
2
2
2
1
1
2
0
0
0
0
1
2
1
0
0
1
0
0
0
2
0
1
1
1
1
0
1
2
0
0
0
0
2
2
1
0
1
2
1
2
1
2
0
0
1
1
0
1
0
0
0
1
1
2
0
0
0
1
0
0
2
1
1
0
0
1
0
1
0
1
0
1
0
0
2
1
0
2
0
0
1
1
2
1
0
1
0
2
0
0
1
2
0
0
2
1
0
0
1
0
2
0
0
2
0
0
2
2
3
1
1
1
0
0
0
0
1
0
0
0
0
2
2
2
0
0
1
2
2
0
1
1
0
1
0
2
1
0
0
1
1
1
1
2
0
1
2
0
0
1
2
2
0
1
0
1
1
1
0
0
0
0
1
0
2
1
0
1
1
0
2
0
0
2
1
1
1
2
0
2
2
1
1
0
0
0
2
0
1
1
0
2
2
1
2
1
1
1
0
1
1
1
1
1
0
0
2
3
0
1
0
0
2
1
0
3
1
0
2
0
2
0
0
4
0
1
1
2
0
1
0
1
0
0
0
2
1
0
1
0
1
1
0
0
1
1
0
2
1
0
2
1
0
2
2
1
0
2
2
0
1
1
1
0
2
0
1
1
0
0
1
2
1
0
2
2
0
0
0
0
0
1
2
1
0
1
2
0
1
0
2
1
0
1
3
1
0
2
1
0
1
1
2
2
1
2
0
0
1
1
1
1
2
1
2
2
0
0
0
2
0
1
1
0
1
1
0
1
2
1
1
0
1
2
1
3
0
0
1
1
2
2
1
2
0
1
0
2
1
1
2
1
1
2
2
0
1
1
0
0
0
1
1
0
0
1
2
2
5
0
2
2
0
1
1
0
1
0
2
1
2
2
1
0
0
0
0
0
0
1
0
0
2
0
1
2
0
0
0
1
1
1
1
2
1
0
1
0
1
0
1
1
2
0
0
0
2
0
1
1
0
2
0
1
1
1
0
0
2
2
2
0
2
1
0
0
2
1
1
0
1
0
2
1
1
2
1
1
1
1
0
0
2
0
0
1
0
1
2
1
0
1
1
0
1
0
0
2
2
0
0
3
0
0
0
0
1
3
2
1
1
0
0
0
1
1
1
1
1
0
0
1
0
0
0
1
1
1
2
0
1
2
0
0
0
2
1
2
2
1
1
2
0
0
2
0
1
1
0
0
1
0
2
1
1
1
0
0
1
2
1
1
2
0
1
0
1
2
2
0
1
1
1
2
1
1
0
0
1
1
1
2
1
0
0
0
1
1
0
0
0
2
1
1
0
2
0
2
1
0
1
1
1
0
0
1
0
0
0
0
1
1
1
0
0
0
2
0
0
0
2
0
2
2
0
0
1
0
1
3
2
0
0
1
0
1
0
0
2
1
1
0
1
1
2
0
0
0
1
0
1
0
0
2
0
0
3
1
0
0
1
2
0
1
1
3
0
0
1
1
0
0
0
0
0
0
2
0
0
1
1
0
0
0
1
1
0
1
1
1
0
1
0
1
1
2
1
0
0
0
1
1
2
0
2
0
0
1
0
0
2
2
2
2
1
0
0
1
0
1
1
1
2
1
0
1
2
1
2
1
0
1
3
1
1
2
0
2
0
1
2
0
1
2
1
2
1
0
0
1
0
0
1
0
1
0
1
1
1
2
2
1
0
0
0
1
1
0
1
0
1
1
1
1
2
0
2
0
1
1
2
0
1
0
0
2
1
0
1
0
1
1
1
0
0
1
1
1
1
0
3
0
1
0
0
1
2
1
2
0
1
2
2
1
1
0
0
0
2
0
0
1
3
3
0
1
0
0
0
1
0
0
0
2
0
1
1
1
0
0
1
1
1
0
1
2
0
0
1
2
1
0
0
1
1
0
0
1
0
1
2
0
2
2
1
1
1
1
2
1
2
1
0
0
1
0
0
0
0
1
2
0
1
0
1
1
3
2
1
1
1
1
0
1
0
0
1
0
2
0
0
0
0
2
0
0
1
1
0
0
2
0
1
1
0
0
0
2
0
0
0
0
0
1
2
0
0
2
1
0
0
0
1
1
0
1
1
2
0
0
2
1
2
1
2
0
1
3
0
0
1
2
0
2
0
2
2
0
0
0
1
0
1
1
0
0
1
0
1
1
0
0
0
1
1
0
0
1
2
0
2
0
1
0
2
1
0
0
1
1
0
2
0
0
1
0
0
2
0
1
1
1
0
0
0
1
2
1
2
0
3
1
0
0
0
1
1
1
0
1
0
4
1
1
0
1
2
2
0
0
0
2
1
0
1
2
0
1
0
0
0
2
1
2
2
1
0
2
0
1
0
1
1
1
1
1
0
2
1
0
1
0
1
2
2
0
0
1
0
2
0
0
0
0
0
1
1
0
1
0
1
0
0
0
2
2
1
1
0
0
0
1
2
1
1
0
0
0
2
1
1
2
1
0
0
1
0
0
2
1
0
0
0
1
0
0
0
1
1
0
0
0
1
1
2
1
1
0
1
1
2
0
0
1
1
0
2
1
1
3
0
0
1
0
0
0
2
1
0
2
0
1
0
2
0
0
4
0
0
1
1
3
1
0
2
1
2
1
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
1
2
0
0
0
2
2
2
1
0
0
0
0
1
2
1
1
0
2
0
1
2
0
0
2
2
0
2
1
0
0
0
2
0
0
2
1
1
0
2
0
1
0
3
2
2
0
0
1
1
2
1
0
3
1
2
0
0
1
0
0
2
0
0
3
1
2
0
0
0
1
0
0
1
0
0
0
0
0
2
2
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
2
1
0
0
1
2
1
1
0
0
1
1
0
2
2
1
1
0
2
0
0
0
0
1
1
1
0
0
1
2
1
2
2
1
1
0
2
1
0
1
0
0
0
2
1
0
1
1
1
2
0
0
1
0
0
1
0
0
0
1
2
2
0
1
0
0
1
1
1
1
0
1
1
1
0
2
1
2
0
0
0
1
0
0
1
0
1
1
0
0
1
0
1
0
1
2
0
1
2
0
0
1
0
1
1
0
1
1
0
1
2
0
1
0
0
1
1
3
0
2
1
1
0
2
0
0
1
0
4
0
1
1
1
0
1
0
2
1
0
1
0
0
0
2
2
2
2
0
1
1
1
1
1
0
1
0
0
2
1
0
0
0
2
0
2
0
1
2
0
1
1
0
1
1
1
0
1
0
0
1
2
1
2
1
1
0
2
1
1
1
2
0
1
0
1
1
1
0
0
2
0
1
0
0
0
1
0
2
3
0
0
0
2
0
0
2
1
0
0
2
2
1
2
0
0
1
1
0
0
0
1
0
1
0
0
0
0
1
2
0
0
0
2
0
1
1
2
0
1
0
0
1
0
0
1
2
1
0
0
2
1
2
1
1
2
2
0
1
0
1
2
2
0
0
2
1
0
0
1
0
1
1
0
0
1
0
0
2
0
0
0
0
0
3
1
1
0
2
0
0
0
2
1
0
1
0
0
1
0
0
0
0
1
0
1
0
1
2
0
0
1
1
1
1
0
3
0
2
0
0
1
0
1
2
0
2
0
0
2
1
0
0
0
0
0
2
3
1
1
1
1
1
2
0
2
1
0
1
0
2
0
1
0
0
1
1
0
0
2
0
1
0
1
2
1
0
2
0
2
0
0
1
1
1
1
0
1
0
0
2
0
0
1
1
0
2
2
0
0
0
2
1
0
1
2
3
2
0
2
1
4
1
2
1
2
2
1
2
0
2
0
2
1
2
1
1
1
1
0
1
0
0
0
0
2
0
1
0
0
0
0
1
1
0
0
0
1
1
0
1
0
0
1
1
2
1
0
1
1
2
0
1
2
0
2
1
0
1
0
1
1
1
1
0
2
0
0
0
0
0
0
1
2
0
1
1
0
1
1
1
0
1
2
0
2
0
1
0
0
2
0
0
1
1
1
2
2
1
0
1
0
0
0
1
0
2
0
0
2
1
0
2
0
1
1
2
1
1
1
1
1
1
1
0
1
0
0
0
0
0
1
2
0
0
2
2
0
0
0
1
2
0
2
2
2
1
1
0
1
0
0
1
1
0
1
0
0
0
3
0
2
0
0
1
0
0
1
2
1
0
2
2
0
0
1
2
1
0
0
1
2
0
0
0
2
0
1
1
3
1
2
1
1
1
0
2
0
1
1
1
1
0
1
0
0
1
3
0
2
1
1
1
0
0
2
0
1
1
2
1
1
1
1
1
0
1
1
0
7
2
1
0
0
0
0
1
0
2
0
2
0
1
0
0
0
0
2
2
2
0
0
1
1
0
1
1
0
0
0
0
0
1
1
0
0
0
4
0
1
2
0
2
0
1
1
0
1
2
1
0
0
2
0
1
2
2
0
2
0
1
0
2
1
2
1
1
1
0
1
1
4
2
2
0
0
1
2
0
2
1
2
1
0
1
2
1
0
2
1
0
1
0
1
2
0
1
0
1
1
1
1
1
0
1
0
1
2
2
2
1
2
1
2
1
0
1
0
0
0
2
1
1
0
1
2
1
1
0
0
0
2
2
0
1
1
1
0
0
0
0
2
0
0
2
0
1
0
3
1
2
2
1
1
2
1
1
2
0
1
0
0
1
0
2
0
1
1
1
1
1
1
1
4
2
2
0
1
0
0
2
3
0
1
2
1
1
2
0
0
0
1
1
0
0
1
1
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
2
2
1
1
2
0
1
2
0
0
0
0
2
1
0
0
0
1
1
1
2
1
1
1
1
0
1
0
0
1
1
1
0
0
1
0
1
1
2
0
0
0
0
1
2
1
1
2
0
1
0
1
0
3
0
1
2
1
0
0
0
4
1
0
1
1
0
0
0
0
1
0
1
1
0
2
0
1
0
0
0
1
0
2
1
1
2
1
1
0
0
0
1
0
2
3
2
2
0
2
1
0
0
1
0
0
1
0
0
1
0
0
1
1
0
1
1
2
0
1
0
2
2
0
1
0
1
0
1
2
0
0
1
1
2
1
1
2
0
0
1
2
0
2
1
1
3
1
0
1
0
0
1
1
0
1
0
0
1
1
2
0
2
1
0
1
2
0
2
1
1
2
1
1
1
0
2
2
1
1
0
0
1
1
0
0
1
0
0
1
0
0
1
2
2
0
0
1
2
0
2
1
0
0
2
1
1
2
0
1
1
0
1
0
1
1
1
0
2
0
3
2
0
0
2
2
1
1
0
0
0
0
0
1
0
1
2
4
1
1
1
0
2
0
0
0
0
1
0
2
2
0
0
1
2
2
0
2
1
2
1
1
1
1
2
1
2
2
2
1
0
0
1
0
1
1
0
2
1
1
1
1
4
0
1
1
0
1
0
2
0
0
1
2
0
2
1
2
0
2
1
0
0
1
2
0
1
1
2
2
1
1
0
2
3
0
1
0
0
2
0
0
1
0
1
1
0
0
0
1
1
0
1
0
2
0
0
2
2
0
0
1
1
1
2
0
2
2
0
1
0
0
0
1
0
1
2
2
1
1
1
1
1
0
0
0
3
2
0
2
0
2
0
1
2
1
0
0
2
2
0
0
1
0
1
0
1
1
1
0
1
2
2
2
2
0
2
1
1
1
2
1
2
0
0
1
0
0
0
1
2
0
1
2
0
1
0
1
1
2
0
2
1
2
1
2
0
1
1
1
0
0
0
0
0
0
0
0
2
3
1
0
0
1
1
0
2
2
1
1
1
0
1
1
0
1
0
1
2
1
0
1
0
0
1
0
1
0
1
1
1
0
1
1
1
2
0
1
0
0
1
0
0
0
3
0
2
1
0
0
0
0
1
0
1
0
0
0
1
2
0
0
1
1
1
1
0
1
0
0
1
2
1
0
1
2
1
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
1
2
0
0
2
0
1
0
2
2
1
0
2
1
2
0
3
2
1
1
1
1
2
0
2
0
0
0
0
2
4
0
1
1
2
2
1
0
2
3
1
2
1
2
5
0
0
1
2
0
0
0
1
0
0
0
1
2
2
2
0
1
1
0
1
0
2
0
1
1
0
2
0
2
0
2
2
0
1
1
0
1
1
1
2
0
2
0
2
0
2
0
0
0
2
0
0
0
1
0
0
0
0
1
0
2
0
1
0
0
0
3
0
2
0
1
0
1
0
0
2
0
0
0
2
1
1
0
1
2
1
2
1
2
1
0
0
0
2
1
2
1
0
2
2
1
0
2
0
1
1
0
1
0
2
1
0
0
1
1
1
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
1
0
1
2
1
0
1
2
1
0
1
0
0
2
1
1
3
0
1
0
1
2
1
0
0
1
1
0
0
0
1
0
1
1
0
0
2
0
0
1
1
1
2
1
1
2
0
0
0
0
0
1
3
1
1
2
0
0
2
1
0
0
2
2
1
0
1
0
1
1
2
2
1
1
1
0
0
1
1
0
0
1
0
0
1
2
0
0
0
1
1
0
1
0
2
2
0
2
0
1
1
0
2
0
1
0
1
0
0
1
0
1
0
1
2
2
3
0
2
1
2
0
0
0
0
0
2
1
0
0
0
1
0
2
1
0
0
1
1
2
0
1
1
2
0
3
2
1
1
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
1
3
1
0
0
0
1
2
0
1
1
1
1
0
2
1
1
1
0
0
1
0
2
1
2
1
2
2
0
0
0
1
0
0
0
0
0
2
1
1
0
1
1
2
1
2
0
2
1
0
0
1
1
1
2
1
2
0
0
2
2
2
0
2
0
0
1
1
0
0
4
0
0
2
0
0
0
2
2
1
0
1
0
1
2
0
1
0
0
1
0
2
0
0
0
0
2
1
0
2
0
1
1
0
0
0
0
0
0
1
3
0
0
1
1
1
1
1
1
2
0
2
0
1
2
0
1
2
1
0
1
0
2
0
1
0
2
0
1
0
0
1
1
2
4
2
1
0
0
0
0
1
0
1
0
1
2
0
1
1
1
1
2
0
3
0
0
1
1
2
0
0
2
1
0
1
2
1
3
2
2
0
1
0
0
2
3
1
1
1
1
1
0
0
0
0
1
0
0
1
0
1
0
0
1
2
0
0
1
0
0
1
2
0
0
1
0
1
0
1
0
1
0
2
1
0
0
2
2
3
0
2
0
1
1
1
0
0
1
2
0
0
0
2
2
1
0
0
1
2
0
3
1
1
0
0
1
0
2
0
0
1
1
2
2
0
0
2
2
2
0
1
0
1
1
1
2
0
1
0
2
0
1
0
0
2
1
2
1
2
0
1
0
1
0
0
0
0
0
2
1
1
2
1
0
0
2
0
2
0
1
1
1
1
2
1
2
1
1
0
2
1
0
1
1
1
2
1
1
0
2
2
1
1
3
0
0
1
0
2
2
2
1
0
0
0
0
0
0
0
1
0
2
2
1
3
0
0
0
1
3
0
2
2
2
0
1
0
0
0
0
1
1
0
0
0
0
1
0
2
0
0
2
4
3
2
0
0
0
1
0
1
0
0
0
0
1
2
1
1
0
1
1
0
2
0
0
2
1
1
0
1
1
1
1
0
0
0
1
2
2
0
0
1
2
1
2
0
2
1
1
0
0
0
2
2
1
0
0
0
0
1
0
0
2
1
2
1
2
1
2
1
2
0
0
0
2
1
0
1
0
1
0
2
2
0
0
1
1
0
0
1
0
0
1
0
1
0
4
0
2
0
0
0
0
0
0
1
2
1
0
3
1
0
1
1
1
0
2
0
2
0
1
1
0
2
0
1
2
0
0
1
1
1
0
1
0
0
1
0
0
1
0
3
0
0
2
0
1
0
0
1
2
1
0
0
0
0
0
1
0
1
0
0
1
1
0
2
1
1
0
0
2
0
0
0
0
1
0
0
0
1
1
0
2
0
1
0
0
1
0
2
1
1
1
1
1
2
1
1
1
0
2
0
1
2
0
1
1
0
1
0
0
0
1
0
1
2
1
0
2
1
0
2
2
2
0
2
1
2
0
1
2
2
2
1
0
2
2
0
2
1
1
0
1
1
0
1
1
0
1
1
0
2
1
1
1
1
0
1
0
0
2
1
1
1
0
0
1
0
2
2
0
2
3
0
0
1
1
1
0
2
0
1
1
1
1
1
1
0
0
0
0
2
2
1
0
1
1
1
2
1
1
1
0
1
0
1
1
2
0
0
2
2
0
0
0
0
0
1
0
0
0
1
1
1
1
2
0
1
1
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
2
0
1
2
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
2
1
0
1
1
0
1
1
0
0
0
2
1
0
0
1
1
1
0
0
1
0
3
2
0
0
0
2
2
1
2
1
1
2
1
0
2
2
1
1
1
0
0
0
1
0
1
0
1
0
1
0
0
1
2
0
0
2
1
2
0
2
1
2
2
1
1
0
2
1
0
1
2
1
0
1
1
3
1
0
2
2
1
2
2
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
1
1
1
0
0
1
1
1
1
1
2
1
2
0
1
0
0
0
0
2
0
1
0
2
1
2
0
2
1
2
1
2
1
0
0
1
1
2
0
1
0
1
1
0
2
0
1
1
0
1
1
1
2
0
0
0
2
1
0
2
1
1
0
0
0
1
1
1
0
1
3
0
0
0
0
1
2
1
1
1
0
0
1
1
3
1
0
0
0
0
1
0
0
0
1
0
2
2
1
2
2
0
0
1
0
2
0
0
1
1
1
1
1
0
1
0
1
1
2
0
1
1
0
2
1
1
2
0
2
1
1
2
1
4
2
1
1
0
2
0
0
1
0
0
0
1
0
1
1
0
1
0
1
1
0
0
2
0
1
0
2
1
0
2
2
1
2
1
2
0
2
2
0
1
1
0
0
1
0
1
1
0
2
0
1
1
0
0
0
1
0
4
1
0
2
2
0
0
1
1
1
2
0
1
2
0
0
2
1
1
1
1
1
2
1
0
2
2
1
1
0
0
1
0
2
1
0
2
0
0
1
0
1
3
0
1
1
0
0
0
0
0
2
0
1
0
1
0
1
1
1
1
1
1
1
1
2
0
0
0
1
1
1
0
1
2
1
0
0
1
1
1
0
1
2
0
1
0
7
1
2
1
2
2
0
1
0
2
0
0
0
0
2
0
0
0
1
0
2
3
1
0
0
0
1
1
0
2
0
1
2
2
1
1
1
1
0
2
3
0
1
1
1
0
2
0
2
1
0
0
1
0
1
2
0
2
1
1
0
1
3
0
0
0
1
0
0
1
1
1
0
1
0
0
0
1
0
1
2
3
1
2
1
0
2
0
1
1
0
1
1
1
0
1
2
0
2
0
1
1
1
1
1
2
1
0
0
0
2
0
1
1
2
2
0
1
0
2
3
2
0
0
1
0
0
2
2
2
0
0
0
1
0
0
0
1
1
1
2
2
1
0
1
1
1
0
1
0
2
1
1
1
0
0
1
0
1
2
0
1
0
0
0
0
1
3
0
0
0
2
1
1
1
2
1
1
0
1
0
0
2
0
0
1
0
0
2
0
2
0
0
2
2
0
0
2
0
1
1
0
1
0
0
2
0
3
0
0
2
0
0
2
1
0
1
1
1
0
0
2
0
1
0
2
0
0
0
1
0
0
1
0
3
0
0
0
2
0
2
2
0
0
1
2
0
2
0
1
0
0
1
4
1
0
0
2
0
2
1
0
1
2
1
1
2
0
2
2
0
0
0
2
1
1
2
1
2
0
1
3
2
0
2
3
1
2
0
2
1
2
2
0
0
1
1
0
1
0
2
0
1
0
0
1
0
1
0
2
0
0
1
2
1
0
0
1
1
2
0
1
1
0
1
2
1
1
0
0
1
1
1
0
1
2
0
1
0
2
1
1
0
0
1
2
1
0
0
0
3
0
0
1
2
2
1
0
2
1
0
1
2
0
1
2
0
2
3
1
2
0
0
0
0
1
1
0
1
1
0
0
1
2
1
2
1
3
1
0
1
1
2
3
0
1
1
1
2
0
0
1
1
1
0
0
1
0
1
2
0
2
1
0
0
2
1
2
1
0
0
1
1
2
1
2
2
0
1
2
0
1
1
0
1
1
0
3
0
1
0
0
0
0
1
3
0
0
1
2
2
0
1
1
1
0
1
2
0
3
1
1
0
0
2
2
2
1
1
1
1
1
0
0
2
0
1
2
0
0
0
0
0
1
1
2
2
0
0
0
1
0
2
0
0
1
2
2
0
0
1
1
0
1
1
2
1
2
0
0
0
2
2
1
2
0
0
0
0
2
0
1
1
0
0
0
0
1
0
0
0
1
1
0
0
1
1
2
0
0
0
2
0
3
0
2
0
1
0
2
2
0
0
1
0
1
0
0
0
1
0
1
1
1
2
1
2
1
0
0
2
1
0
2
1
2
1
0
1
1
0
1
2
0
2
3
2
1
1
0
0
0
1
1
1
2
0
3
2
0
0
1
3
1
2
1
0
2
0
0
0
1
2
1
0
0
1
0
1
0
2
0
0
1
1
0
0
0
1
1
2
0
1
2
0
0
0
0
0
3
1
0
2
1
2
0
1
1
0
0
1
0
1
3
0
0
0
2
0
2
0
2
0
1
2
1
1
1
0
0
0
1
0
0
1
0
1
1
0
1
0
1
1
0
1
1
2
0
1
1
2
0
0
2
0
1
4
0
0
1
0
1
0
1
2
1
2
0
1
0
1
0
1
1
0
1
0
2
1
0
1
0
0
1
0
2
0
1
1
0
0
2
3
0
0
0
1
0
0
0
0
2
2
2
2
1
0
0
1
1
1
2
1
1
2
2
0
1
1
0
2
0
0
0
1
0
1
1
0
1
0
0
2
2
0
1
2
1
1
1
2
0
2
1
2
1
0
2
0
1
2
0
0
0
1
0
0
0
1
1
2
1
0
1
1
1
2
1
0
0
2
0
0
1
2
1
2
0
0
2
0
0
0
3
1
3
2
0
0
0
0
1
0
0
1
2
2
1
1
0
0
0
0
0
2
0
1
2
1
2
1
0
0
0
1
0
1
0
1
0
1
1
0
1
2
1
1
1
0
1
1
0
2
0
0
0
0
0
0
1
0
1
1
1
1
0
1
0
2
0
0
1
1
1
2
0
2
1
1
0
0
1
0
0
1
1
0
0
1
0
0
1
0
0
1
1
0
0
2
0
1
0
0
0
0
0
0
1
0
0
1
1
2
0
1
2
0
1
0
0
0
0
1
1
2
2
0
0
0
2
0
1
1
2
1
1
0
0
2
2
1
0
1
1
0
0
2
0
1
0
2
0
1
0
1
0
1
1
0
2
0
0
0
1
1
1
1
0
0
1
0
0
0
2
1
1
1
0
0
0
1
0
0
0
2
0
1
1
1
2
1
0
1
1
1
1
1
1
0
2
0
0
0
1
1
1
0
2
0
0
1
1
0
2
2
1
0
0
2
2
0
1
0
2
1
2
0
0
0
3
2
0
0
0
0
1
4
2
0
0
2
0
0
1
1
0
1
1
4
0
0
1
2
2
0
1
2
0
1
1
1
1
2
1
2
1
2
0
2
1
1
2
1
0
0
0
0
1
2
2
0
1
1
2
2
2
2
0
0
2
0
2
0
0
2
0
0
1
0
0
1
0
1
1
2
2
0
1
1
1
0
1
1
0
1
1
0
2
0
1
2
0
0
0
0
2
2
0
0
1
0
1
1
1
1
1
2
0
0
0
0
1
0
2
2
3
0
0
0
0
1
0
0
1
0
0
2
1
1
0
0
0
2
2
2
2
1
2
0
1
1
2
1
1
0
2
0
0
0
1
1
0
0
2
0
1
1
0
2
0
1
2
0
0
0
2
0
1
1
1
0
0
1
2
1
1
2
1
0
1
2
2
0
1
1
0
0
0
1
0
1
0
1
1
2
0
1
0
0
1
1
1
0
0
1
1
1
2
0
0
0
2
0
2
2
1
0
0
1
0
0
1
0
2
0
2
0
1
2
0
0
1
1
1
2
4
1
0
2
1
0
1
0
1
2
1
2
1
0
2
0
1
0
0
0
2
0
0
0
1
0
1
2
0
2
0
1
1
1
1
1
2
1
1
0
0
0
0
1
0
2
0
0
0
0
2
1
0
1
2
2
0
0
0
2
0
0
0
1
0
0
2
1
1
1
0
1
1
0
1
2
1
1
0
2
0
0
0
0
0
2
0
1
2
1
2
0
1
0
0
0
1
0
0
0
2
2
1
0
2
1
1
1
0
1
2
0
1
2
2
2
2
1
2
0
1
2
1
1
0
2
0
1
2
0
2
0
0
0
1
1
0
1
0
0
0
1
0
2
0
1
0
0
1
0
0
0
1
1
1
1
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
1
0
2
2
1
0
0
1
1
1
0
1
0
0
2
1
1
2
2
0
1
0
0
1
0
0
1
0
0
2
1
1
2
2
1
1
0
0
1
2
1
2
0
1
0
2
0
1
1
0
1
0
0
2
0
0
0
2
1
0
0
0
0
2
2
0
0
1
0
1
0
1
0
0
1
0
2
1
0
1
1
2
0
1
0
1
1
1
2
2
1
0
2
0
2
0
0
0
0
1
1
0
0
0
1
0
1
2
1
0
3
0
1
2
1
1
0
1
0
0
1
1
0
0
1
1
2
1
2
2
0
0
0
0
1
1
1
2
0
1
0
0
0
2
0
0
2
2
1
0
1
0
1
1
2
0
1
1
0
0
1
1
1
0
1
2
0
1
1
0
1
0
2
1
1
1
2
0
0
0
1
1
1
2
1
0
0
0
2
2
2
0
0
1
2
1
1
1
2
2
1
2
0
2
2
1
0
1
0
0
1
0
1
0
1
0
0
1
1
1
0
2
1
0
0
0
1
1
1
2
1
3
1
1
0
3
1
0
1
0
0
2
4
0
2
0
0
1
0
2
2
0
1
0
0
1
1
0
0
0
0
0
1
0
2
2
1
1
2
1
0
2
1
1
1
2
0
2
1
0
2
2
2
3
2
0
1
1
1
0
2
1
0
1
0
0
0
1
2
0
0
2
1
0
0
0
1
0
1
1
0
1
0
0
2
2
3
1
0
0
2
0
0
2
1
3
0
0
0
0
0
0
1
0
1
2
1
0
1
1
1
1
0
0
0
0
0
2
2
0
1
1
0
0
2
3
1
0
0
0
0
2
1
1
1
0
3
0
0
1
1
0
0
2
2
1
0
0
0
0
1
2
0
0
1
1
1
0
1
2
0
1
2
0
0
0
0
1
2
1
0
1
0
0
0
1
2
1
0
0
1
0
0
2
2
0
1
2
1
1
1
0
1
0
1
1
0
0
2
0
0
0
0
1
2
3
0
0
1
1
1
1
2
0
1
1
1
1
2
1
1
2
0
1
0
0
0
0
0
1
0
2
2
1
1
2
1
1
1
1
2
0
0
0
0
0
0
1
2
1
0
0
0
1
1
1
2
2
0
0
2
0
1
1
0
1
0
1
1
0
2
0
1
1
0
1
1
0
0
2
1
2
0
1
1
1
2
4
1
1
0
1
1
2
1
1
2
0
2
0
0
1
0
0
0
0
3
2
1
1
1
1
0
2
0
1
0
1
2
0
1
0
1
1
1
1
0
2
0
1
1
1
1
1
0
2
1
1
6
2
1
0
0
3
2
2
0
1
0
0
0
0
2
0
0
0
0
2
0
1
2
1
0
0
0
0
2
2
0
4
1
2
3
1
0
2
1
2
0
4
0
0
2
0
0
0
1
0
0
1
2
2
0
0
0
1
0
1
2
1
1
0
1
1
0
1
0
1
0
1
1
1
0
1
0
0
2
0
2
1
3
0
0
1
0
1
1
2
1
1
1
0
2
0
1
1
0
0
1
2
0
0
1
0
2
0
1
0
0
0
0
1
0
0
0
2
0
1
0
1
0
2
0
2
3
1
2
1
0
2
2
1
0
0
1
1
0
0
1
1
2
2
1
0
0
1
1
2
0
0
0
1
0
1
0
2
0
0
1
2
1
1
1
1
1
0
2
0
0
1
0
1
0
2
0
1
3
0
1
1
3
1
0
1
0
0
2
1
0
2
0
1
0
1
1
1
0
1
0
0
0
2
0
1
1
0
1
2
1
0
0
2
0
1
0
0
0
0
0
1
1
2
1
1
2
0
1
1
1
1
2
1
1
3
2
0
3
2
0
0
1
1
0
1
0
1
0
1
0
0
1
0
2
2
0
3
2
0
0
2
1
1
2
0
1
0
0
2
1
2
1
0
1
1
1
0
2
1
0
2
1
1
0
2
0
5
0
1
0
2
0
0
1
2
4
1
1
2
1
1
0
1
1
2
0
1
2
2
0
2
1
1
2
1
2
1
0
1
1
1
1
1
1
0
1
0
0
0
2
1
0
3
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
2
0
0
0
1
2
1
0
2
1
0
1
0
1
2
0
0
0
2
0
1
1
0
0
1
1
1
2
0
2
2
0
1
2
0
1
2
2
0
0
0
1
0
1
1
0
1
0
2
2
1
0
0
2
2
1
0
1
0
1
1
0
1
1
1
1
1
0
0
1
0
3
1
1
0
0
0
1
0
0
0
0
1
2
0
0
1
0
0
1
1
2
0
1
1
2
1
0
2
0
0
0
1
0
0
3
2
0
2
1
0
1
0
0
1
0
0
1
2
0
0
1
0
1
0
2
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
2
2
1
1
0
0
0
1
1
4
1
2
1
1
2
0
1
0
2
1
1
0
1
2
0
0
1
0
1
1
2
0
0
1
0
2
1
1
0
1
2
0
2
1
0
2
2
0
1
0
0
1
0
0
1
1
0
2
0
0
0
2
0
0
2
1
0
0
1
0
1
0
0
2
0
0
3
2
0
0
0
0
1
1
0
1
0
0
1
1
2
1
0
2
0
0
0
1
2
3
0
2
1
0
2
0
2
0
1
2
1
0
0
1
0
0
0
2
0
2
1
1
1
1
1
0
0
0
0
0
1
1
0
0
0
2
1
0
2
0
1
0
0
0
2
1
0
1
1
1
0
0
0
0
1
1
1
0
0
1
1
0
0
0
1
1
0
2
0
2
1
1
0
1
2
3
0
1
1
1
0
0
0
1
1
1
1
0
3
0
1
0
2
0
0
1
1
2
2
1
1
1
0
1
2
2
0
0
2
0
0
0
0
1
1
1
3
1
0
0
2
0
0
1
0
0
0
0
1
0
0
0
2
1
3
1
2
3
2
1
2
1
1
1
0
1
1
1
2
0
2
0
2
1
0
2
2
0
1
1
0
1
1
0
0
0
1
0
2
1
0
0
0
0
0
0
0
2
1
0
0
1
0
0
1
1
1
2
0
0
1
0
2
0
0
0
1
1
1
0
1
2
1
0
0
1
0
1
2
0
0
1
0
0
1
0
0
0
1
1
2
0
2
0
2
0
0
0
0
1
1
1
1
0
0
1
3
2
1
0
1
0
1
0
0
1
1
0
2
1
0
0
2
0
4
0
1
1
0
0
3
2
1
2
0
0
0
1
0
0
1
1
0
2
2
2
2
1
0
1
1
0
0
1
1
1
1
0
1
0
1
1
2
0
2
0
0
1
0
2
2
1
1
2
1
0
2
2
1
0
0
2
2
3
0
1
2
0
2
2
1
2
1
0
2
0
1
0
1
2
0
1
1
1
1
1
1
0
1
1
0
1
1
0
0
1
2
0
1
0
2
0
2
0
2
0
0
1
2
2
0
2
1
0
0
1
8
1
2
1
0
0
1
1
0
0
0
0
1
0
1
0
0
2
0
1
2
2
0
1
0
0
0
0
2
0
1
0
1
4
0
0
2
1
0
1
0
1
1
2
0
0
2
0
0
0
1
0
1
0
0
0
2
2
1
0
0
2
0
1
2
0
2
0
0
1
1
0
0
0
0
1
0
0
0
0
0
4
0
0
0
1
1
0
2
1
0
1
1
1
0
0
0
0
1
0
2
1
0
1
2
0
2
2
1
1
2
0
0
0
0
1
0
0
0
0
1
1
1
0
2
0
0
2
0
1
2
0
0
2
2
1
0
0
0
1
0
1
0
0
1
1
0
1
1
1
1
0
0
1
0
0
0
0
2
1
1
2
0
0
0
1
0
1
0
0
0
2
1
0
2
2
0
1
1
0
1
2
2
0
0
0
3
0
0
0
0
1
0
1
2
2
0
2
1
0
0
0
1
0
1
0
1
1
0
1
1
1
2
2
0
1
0
1
1
1
2
1
1
0
1
0
2
0
1
2
1
2
1
0
0
0
0
1
2
1
0
1
0
0
1
1
2
0
1
0
0
0
2
0
3
0
0
0
1
2
1
0
2
1
1
0
1
1
0
0
0
1
0
1
0
1
1
1
0
1
2
1
0
0
1
2
0
0
0
2
0
1
0
0
0
2
1
0
2
1
1
1
0
2
1
0
0
1
1
2
1
0
0
0
1
0
2
2
0
0
4
1
0
1
1
2
0
0
1
1
1
1
0
2
1
0
0
1
0
1
1
0
0
2
1
0
1
0
1
1
1
2
2
1
0
1
2
2
0
3
2
0
1
0
0
1
2
2
0
3
0
0
1
0
2
0
0
0
1
2
1
0
0
0
1
1
0
0
0
1
2
1
1
0
1
0
1
0
2
1
3
0
2
2
0
0
0
0
1
1
0
2
0
0
0
0
1
0
1
0
0
1
2
1
1
0
0
1
1
0
1
0
0
0
0
0
1
2
0
0
2
2
1
0
1
0
0
2
0
0
1
0
0
3
1
2
0
0
0
0
1
3
1
0
0
0
0
1
0
1
0
2
1
1
0
0
2
1
2
0
0
2
1
0
0
0
1
2
1
1
1
0
2
1
3
2
0
0
2
0
2
2
2
1
0
0
2
2
1
1
0
1
0
1
0
1
1
2
1
1
2
2
1
0
0
0
2
0
1
0
0
2
2
2
1
4
2
1
0
1
0
1
0
1
0
0
0
2
1
0
1
1
2
0
0
1
0
2
0
1
0
0
1
0
2
1
2
1
1
1
2
1
0
1
1
2
0
0
1
1
2
2
1
0
1
0
0
1
0
1
1
0
1
1
2
0
1
1
1
0
1
1
0
0
2
0
1
1
2
0
1
2
1
0
2
2
2
1
0
2
1
1
2
0
0
1
1
2
0
0
0
1
1
0
2
1
1
0
2
0
1
0
2
0
1
2
0
0
1
2
1
1
1
0
0
0
2
1
1
0
2
0
0
2
0
0
2
0
0
0
2
0
0
2
1
0
0
0
3
0
4
0
1
0
1
1
2
0
2
0
0
1
1
0
0
0
0
0
0
0
2
0
1
2
2
1
1
0
1
0
0
2
0
4
0
1
2
0
1
3
1
1
0
1
1
0
1
0
1
1
0
2
1
2
2
1
0
0
0
1
0
1
1
1
1
1
0
1
1
0
2
0
0
0
0
0
0
2
1
0
0
0
0
1
3
0
1
2
0
1
0
2
1
2
0
2
0
1
0
0
0
2
0
0
2
0
0
0
0
1
1
0
1
0
0
1
2
2
0
1
0
2
0
1
2
2
0
0
1
1
0
1
0
0
1
1
1
2
2
0
1
0
1
1
1
2
0
2
3
0
0
0
1
1
1
0
0
1
1
1
2
2
1
0
0
0
0
1
1
1
1
2
1
2
0
2
1
0
2
1
0
1
1
1
0
0
0
2
2
0
1
2
0
0
1
0
0
0
2
2
1
3
2
0
1
2
0
0
1
1
1
0
0
2
1
0
1
0
2
0
0
1
0
0
1
0
0
1
1
1
0
0
0
1
0
1
1
0
0
0
0
0
0
2
1
0
2
0
0
1
0
2
0
1
2
0
1
0
1
0
1
0
0
2
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
2
1
1
0
1
1
1
1
0
1
0
1
0
0
0
0
1
1
0
1
2
1
1
0
0
1
1
1
0
0
1
1
1
0
1
2
2
0
2
1
1
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
1
1
1
0
1
1
1
1
4
1
1
2
0
1
0
0
0
2
0
0
0
1
0
2
1
0
2
0
0
2
0
0
2
2
0
0
0
1
0
1
0
0
0
1
0
0
2
0
2
0
1
2
0
0
3
1
0
0
1
2
0
0
0
1
1
2
1
1
0
0
1
4
0
0
2
1
0
0
0
0
0
0
2
2
0
0
2
1
0
0
0
0
1
2
0
2
1
1
0
1
0
0
1
0
1
1
1
0
1
2
1
1
0
1
2
1
0
1
2
7
0
1
1
0
1
0
2
1
1
0
0
1
1
0
0
0
0
2
1
2
1
0
2
0
2
2
2
2
2
3
2
2
0
2
0
1
2
1
2
0
0
1
1
1
0
3
0
1
2
1
1
0
2
2
0
2
0
3
2
1
1
0
1
2
0
0
1
1
1
0
1
2
1
1
2
1
1
0
1
0
0
2
0
0
2
0
1
0
1
2
1
1
0
2
0
1
1
2
1
1
1
1
1
2
1
1
1
0
0
0
0
2
0
0
2
1
0
0
0
2
1
2
0
1
1
1
0
0
1
2
1
0
1
1
0
0
1
1
2
0
2
2
0
0
0
2
0
0
1
1
0
1
2
1
4
0
0
0
0
0
1
0
0
0
0
0
2
1
2
1
7
0
2
2
0
0
1
1
0
0
0
2
1
1
0
2
0
0
0
0
2
1
2
1
0
0
0
0
0
0
0
1
1
1
0
2
0
0
1
0
1
0
1
1
1
0
0
1
0
0
0
2
1
0
2
0
1
2
1
2
0
0
1
1
0
1
1
0
2
0
0
0
0
1
1
0
1
2
0
0
1
0
2
0
0
5
0
0
1
0
2
0
1
1
0
1
2
1
2
3
1
0
2
1
1
0
2
0
0
1
0
2
1
0
2
2
0
1
0
0
0
0
1
1
1
0
0
2
1
1
0
0
1
0
0
2
1
2
1
1
0
0
1
1
1
0
1
1
0
1
2
1
1
1
1
0
2
1
0
0
1
0
1
1
3
1
1
1
0
0
2
1
0
0
3
2
2
2
0
1
1
1
0
0
1
2
0
0
1
0
0
2
2
0
0
1
3
1
1
0
1
2
0
8
0
1
0
0
0
0
1
1
0
0
0
2
0
1
0
2
2
0
0
1
0
0
0
1
2
0
0
1
0
2
1
0
1
4
0
2
1
0
0
2
0
0
2
0
0
1
0
0
2
0
3
0
1
1
1
2
0
1
1
2
0
1
2
2
2
0
0
1
0
1
1
0
0
1
0
0
0
2
0
2
1
1
0
2
1
1
0
1
2
0
0
0
1
0
1
1
2
0
0
0
0
1
2
0
0
0
1
0
1
1
1
0
2
1
0
0
2
1
1
1
1
2
2
1
1
0
0
0
0
1
0
1
2
0
1
2
1
2
1
0
0
2
1
1
2
0
0
0
2
0
2
0
1
0
1
0
1
0
0
2
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
2
0
1
1
2
1
0
0
0
0
2
2
1
1
0
0
2
0
0
0
1
1
0
1
4
3
1
0
2
0
1
0
2
0
1
2
0
0
1
1
2
0
2
2
1
0
1
1
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
1
1
0
2
0
2
0
2
2
2
0
1
0
0
0
1
2
0
0
2
1
1
0
0
2
0
0
0
0
1
0
1
2
0
1
1
0
1
1
0
1
0
1
1
1
2
1
0
2
2
0
0
0
2
0
1
1
0
1
1
2
2
0
1
1
1
0
2
0
0
1
0
1
1
0
1
0
0
0
0
1
2
2
0
0
2
0
1
0
0
2
0
2
1
1
1
1
0
0
1
2
2
1
1
0
0
0
0
2
0
1
2
0
1
1
1
1
1
0
1
0
1
1
1
0
0
0
1
1
2
0
0
1
0
0
1
1
1
0
0
1
3
2
2
1
0
1
1
1
0
1
0
2
0
1
2
0
0
1
0
1
2
0
2
1
0
1
1
1
0
2
0
0
0
2
1
3
0
0
0
0
0
0
1
1
0
2
1
2
2
0
0
0
0
0
2
2
0
2
1
2
1
1
2
0
3
0
0
1
2
2
1
0
1
2
1
1
0
0
2
1
1
0
2
2
1
1
1
0
0
2
0
2
1
0
0
2
1
1
2
1
0
0
2
1
0
0
1
1
0
2
0
2
0
2
1
0
1
2
0
2
1
2
0
0
0
0
1
0
0
0
1
0
1
2
1
0
1
3
0
1
2
1
1
1
0
1
0
1
0
2
0
2
1
1
1
2
1
0
0
1
0
0
1
1
0
1
0
2
0
1
0
0
0
1
1
0
0
0
0
1
1
0
1
0
1
1
0
5
1
0
2
1
2
2
1
1
1
0
1
2
1
1
1
2
1
0
0
0
0
1
1
0
0
2
1
1
0
0
1
1
1
0
2
0
2
0
0
1
1
1
0
2
0
1
1
0
5
3
2
4
1
0
2
1
2
0
1
1
2
1
0
0
2
2
2
1
1
0
0
1
1
2
1
1
1
0
2
2
0
2
0
1
0
1
0
2
1
0
0
1
1
2
2
0
0
0
1
1
0
0
0
1
1
0
0
0
0
2
0
1
0
2
1
1
0
0
0
1
1
1
0
1
0
1
0
1
0
1
1
0
0
1
1
2
0
1
0
0
2
2
1
1
1
1
2
1
0
2
0
0
0
1
2
0
1
0
0
2
4
1
1
1
1
1
0
2
0
0
1
0
1
0
1
0
1
2
0
0
0
1
1
0
0
0
1
1
0
1
0
2
0
1
0
1
0
2
1
2
0
1
0
0
1
2
2
0
1
2
0
2
2
2
0
2
0
0
1
0
2
0
0
0
2
0
0
0
0
0
1
0
0
2
0
2
1
0
1
0
0
0
0
0
1
1
0
2
2
1
0
5
0
1
0
0
1
2
0
0
0
1
1
2
0
0
2
0
2
0
1
0
0
0
2
1
2
0
0
1
0
1
1
1
0
0
2
1
1
0
2
0
2
2
1
1
1
2
0
0
2
0
0
0
1
2
1
1
0
0
2
2
2
0
2
1
0
1
1
0
2
0
0
0
1
1
1
0
1
2
1
1
0
1
2
3
3
2
0
3
2
2
0
0
1
0
1
1
1
0
0
1
3
1
0
0
1
2
0
0
1
2
1
0
0
0
0
0
2
2
1
1
0
1
1
0
0
0
0
2
1
0
1
2
1
0
0
1
1
1
0
2
1
0
1
2
1
2
0
1
2
2
0
0
1
2
2
1
0
2
2
2
1
0
1
0
1
1
0
0
0
4
0
0
1
1
1
0
2
1
0
1
2
0
2
0
0
2
0
1
1
2
0
1
2
1
2
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
2
0
0
2
2
1
1
2
2
2
2
0
0
2
1
2
0
0
2
0
1
2
1
0
2
0
2
1
2
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
1
0
1
2
2
1
2
1
0
1
0
1
2
1
1
2
2
0
2
1
0
2
1
0
0
1
2
0
0
0
0
2
0
2
0
3
3
1
1
0
1
0
0
0
0
2
0
0
0
1
0
1
1
1
0
0
0
0
0
0
1
0
0
1
1
1
0
0
1
1
0
1
2
0
2
0
0
0
2
2
0
1
2
0
2
0
1
0
2
2
0
0
2
1
0
2
1
0
1
0
0
1
0
0
2
2
1
1
1
0
0
1
2
1
0
1
2
2
0
0
0
1
0
0
1
0
0
0
1
0
1
2
1
1
0
1
1
1
0
0
0
0
0
0
0
1
1
2
0
1
2
1
1
0
0
2
1
2
2
1
0
0
1
1
2
0
0
0
0
0
1
1
2
1
0
0
2
1
0
0
1
0
0
1
0
0
1
0
1
2
0
2
1
2
1
0
0
1
2
0
1
0
1
1
1
1
2
2
2
0
2
0
1
1
2
2
1
0
2
1
2
0
1
1
0
0
2
0
0
1
0
2
1
1
1
2
1
0
2
2
0
1
0
1
2
0
0
2
0
0
1
0
2
0
1
0
1
0
1
0
0
1
2
0
1
0
1
1
2
1
0
1
0
1
0
4
1
0
1
1
1
0
2
0
1
1
1
2
2
2
1
0
1
1
1
2
1
1
0
1
1
1
0
1
2
0
1
1
0
1
0
0
2
0
0
0
0
1
1
2
2
0
2
1
2
1
2
0
1
0
0
1
2
2
0
1
1
0
2
0
2
0
0
0
1
0
0
0
0
0
0
1
2
0
2
0
2
1
1
1
0
1
1
2
0
2
1
0
0
1
1
2
2
2
0
1
1
0
2
2
1
1
0
0
0
1
1
2
1
1
1
0
1
0
0
2
0
0
1
1
2
0
2
0
0
0
0
0
0
1
1
1
1
0
0
1
2
0
0
1
1
2
1
1
1
1
1
1
2
1
0
2
0
0
0
1
2
1
1
2
0
0
2
1
1
1
1
1
0
1
1
2
1
0
0
0
1
2
1
2
1
2
1
1
1
1
1
2
0
2
1
2
1
0
2
0
2
0
1
1
1
0
0
2
0
0
0
1
0
1
0
0
2
2
1
0
2
0
2
0
0
1
1
1
1
0
2
0
0
1
2
1
1
1
0
0
1
2
2
2
1
1
0
1
1
2
1
0
0
0
1
1
0
1
0
0
2
1
2
0
1
2
1
2
1
0
0
1
4
0
2
0
0
0
1
2
0
3
0
1
0
0
0
1
0
1
2
0
1
1
0
1
0
0
3
1
2
0
1
1
2
2
1
1
1
1
0
0
0
2
0
1
2
0
2
0
0
1
2
2
2
0
1
0
0
0
2
0
0
1
0
2
1
0
1
1
2
0
2
1
1
0
1
1
0
0
1
2
1
1
1
0
1
1
2
0
1
0
0
1
1
2
0
2
0
0
1
2
2
1
0
3
2
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
1
0
2
0
1
2
1
1
0
0
0
0
4
1
1
2
0
2
2
2
1
0
1
1
2
0
2
0
1
0
1
2
0
0
2
1
2
2
0
1
0
0
0
2
2
0
1
0
0
0
2
0
0
0
0
0
1
1
0
2
0
0
1
1
0
0
1
1
1
0
0
0
2
1
0
0
0
0
0
0
1
0
2
3
2
1
0
0
0
0
0
2
0
2
2
0
1
0
0
2
0
1
1
2
1
0
2
0
2
0
0
1
1
0
0
1
2
1
1
1
0
2
2
0
0
0
1
2
2
1
0
1
1
0
2
2
2
1
2
2
0
1
1
0
2
0
1
0
1
0
2
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
2
2
1
0
1
0
1
0
0
0
2
1
1
0
0
1
0
1
2
0
0
0
1
2
1
0
2
0
2
0
2
1
1
1
0
1
0
0
1
1
0
1
1
2
2
1
1
0
1
1
0
0
0
0
1
0
2
2
0
0
0
0
2
1
0
1
1
0
0
1
0
3
1
1
1
2
0
3
0
0
0
0
0
0
2
1
0
1
1
0
1
0
0
2
0
0
1
0
1
2
0
0
1
1
1
0
0
1
1
0
1
0
2
0
2
0
0
1
2
1
2
0
2
1
1
0
0
0
0
1
0
1
0
1
0
0
1
0
2
0
2
2
0
0
2
1
0
1
1
1
2
0
0
1
1
2
0
0
2
0
2
2
1
2
0
0
2
1
0
1
1
2
1
0
2
1
1
0
1
2
0
0
1
0
1
0
0
2
0
1
0
0
0
1
0
0
0
1
2
1
1
0
0
0
0
1
0
0
0
1
0
0
1
1
1
1
0
0
1
1
1
2
1
2
1
2
2
2
1
4
1
0
0
0
0
1
1
0
0
1
0
1
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
2
2
1
0
0
1
0
0
0
1
1
0
0
1
2
0
0
0
0
0
1
0
0
2
0
2
0
2
2
0
2
1
0
0
2
1
2
0
0
0
2
0
1
2
1
1
0
1
3
0
0
2
1
0
0
0
2
0
1
0
1
0
2
1
0
1
1
1
0
0
1
2
0
2
0
0
1
1
1
0
0
0
0
1
0
0
0
0
2
1
2
0
2
1
1
1
0
5
0
0
2
1
0
0
1
2
1
0
1
0
0
1
1
2
1
3
1
6
1
0
0
3
0
1
0
0
1
1
2
1
1
0
1
0
0
0
1
0
0
1
0
1
2
1
1
1
1
1
2
2
1
2
0
1
0
0
1
0
2
0
1
0
1
0
2
1
1
2
1
0
0
0
1
3
1
2
0
1
1
2
1
1
2
0
0
3
0
2
1
0
0
0
1
2
1
1
2
0
1
0
2
0
0
0
0
1
2
2
1
0
1
1
0
0
0
1
0
0
1
1
2
1
2
0
2
1
1
1
1
0
0
0
2
2
1
1
0
1
0
2
2
1
1
0
0
1
1
0
1
1
1
1
0
1
0
0
0
2
1
1
2
2
1
1
0
1
1
2
0
1
1
0
1
3
1
0
0
1
0
1
0
0
2
0
1
1
0
0
0
1
0
1
0
0
1
1
0
3
0
0
1
1
0
0
1
1
0
3
1
1
1
3
0
0
0
1
1
2
0
2
1
2
0
3
0
0
0
1
0
0
1
0
0
0
0
0
2
1
1
1
0
0
0
0
2
2
0
1
2
0
1
1
1
0
2
0
1
1
1
1
1
2
0
3
0
0
0
0
1
0
1
0
0
1
1
1
2
0
1
0
0
3
0
0
0
0
2
1
0
1
0
1
0
0
0
0
1
2
2
0
2
0
1
0
1
1
0
1
1
0
2
1
0
0
1
1
0
1
1
2
1
1
0
0
2
0
0
0
0
2
1
2
0
2
0
2
2
0
1
0
1
1
2
0
0
0
2
1
1
2
0
2
0
2
0
0
2
0
0
0
0
0
0
3
3
1
2
0
1
0
1
0
0
2
0
0
0
5
1
0
0
1
1
0
0
2
2
0
2
2
1
2
0
0
1
1
0
2
1
1
0
1
0
1
2
1
1
1
2
0
1
3
2
0
0
1
0
0
0
1
0
1
0
1
1
1
0
0
1
1
0
1
1
2
2
0
2
2
1
1
3
1
0
0
0
0
0
1
1
0
0
2
0
2
2
1
0
2
1
0
0
2
1
8
0
0
0
1
1
0
0
2
1
0
2
0
2
0
1
2
0
2
0
1
0
1
0
0
0
2
0
1
0
0
5
0
0
2
1
1
2
1
0
0
2
1
0
2
1
0
1
0
1
0
0
1
1
2
0
0
0
1
0
1
1
1
0
1
3
2
0
2
0
1
1
0
0
0
1
2
2
2
1
0
0
0
1
1
1
1
0
1
0
1
0
0
2
0
0
2
1
1
2
0
0
1
2
1
1
0
0
1
4
0
2
0
0
0
2
1
1
1
0
0
1
1
2
1
0
2
2
0
1
1
0
0
1
1
0
1
0
1
1
1
1
0
0
0
1
1
1
0
1
1
1
1
2
0
0
1
0
0
1
1
0
0
2
0
1
2
1
0
0
2
1
1
1
0
2
0
1
1
1
0
2
1
1
1
0
0
1
2
1
1
0
0
0
0
2
0
1
1
1
1
0
1
1
2
0
1
1
1
1
0
1
2
0
0
1
0
1
1
0
0
1
1
1
0
4
0
0
0
1
1
1
1
1
1
1
0
0
2
0
0
0
1
1
2
2
2
0
1
0
0
1
1
1
2
1
0
0
0
0
2
1
0
0
1
1
0
0
1
0
0
0
1
3
0
1
0
0
1
1
0
1
0
2
0
0
1
0
0
0
0
0
0
2
1
1
0
0
3
2
0
3
2
0
0
0
2
2
1
1
1
1
1
1
2
1
0
1
1
1
1
0
0
2
0
1
1
2
1
0
1
0
1
2
0
0
1
2
0
0
0
0
1
1
1
2
0
1
0
0
2
2
1
2
0
1
0
1
0
1
1
1
0
0
0
3
0
0
0
1
1
0
2
1
0
1
0
2
2
1
1
1
1
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
3
1
1
0
0
1
1
1
0
1
1
1
2
1
1
1
1
2
0
1
1
2
0
0
0
0
2
1
2
1
2
0
0
0
0
0
1
0
2
0
1
0
2
0
1
0
0
2
0
0
2
0
0
2
0
1
0
0
1
0
2
2
1
0
1
0
2
2
0
1
1
1
3
0
1
0
1
1
0
0
2
0
0
0
0
0
0
1
1
5
0
0
0
0
0
0
0
2
2
1
0
1
0
0
0
0
2
2
0
0
1
0
0
0
0
1
1
0
0
2
1
2
0
0
0
0
2
0
0
2
1
2
0
1
1
2
0
2
1
2
1
1
0
0
2
0
1
1
1
0
0
1
2
1
2
1
1
0
2
1
1
1
2
1
2
2
0
1
0
0
1
2
0
1
1
0
0
0
0
0
2
0
2
1
2
2
4
1
0
0
1
0
0
2
2
0
0
0
2
0
0
0
1
0
0
0
1
1
0
0
0
2
1
0
0
0
0
1
0
1
0
0
2
1
1
2
0
2
0
0
1
1
0
1
0
0
2
2
2
1
0
2
0
0
1
1
1
2
0
0
2
0
2
0
1
2
1
1
1
0
0
0
1
2
0
0
0
2
0
1
0
1
1
0
2
0
2
1
0
2
1
2
1
2
0
1
0
1
1
0
2
1
2
0
1
0
1
0
0
1
0
1
0
1
1
0
0
1
1
2
2
1
1
0
0
2
0
1
2
0
1
1
2
0
0
2
2
0
3
1
1
2
2
1
2
0
0
0
2
1
2
0
1
2
1
0
1
0
0
1
2
1
0
1
0
2
1
0
0
0
0
2
0
2
1
0
0
0
2
1
0
2
0
0
2
0
1
0
2
0
1
0
1
2
2
2
1
2
1
0
1
2
0
0
1
0
2
1
2
1
0
0
1
0
1
0
0
2
0
0
1
2
0
0
0
1
1
2
0
0
1
0
2
2
0
0
0
2
0
0
1
0
2
2
1
1
0
0
0
0
1
2
2
1
1
0
0
1
1
1
2
0
0
1
0
2
0
0
0
1
0
1
0
0
1
1
0
2
1
0
0
1
2
0
2
1
1
1
3
2
1
0
2
2
2
1
2
2
2
1
0
0
1
1
1
0
2
1
1
1
1
0
0
1
1
2
0
0
0
0
1
2
0
2
1
0
1
1
0
0
2
1
2
1
2
0
0
1
1
0
0
0
1
0
1
0
1
1
1
1
1
0
1
1
0
1
0
1
1
1
2
0
1
0
0
0
1
1
0
1
0
1
0
0
1
2
0
0
1
1
1
2
0
0
0
1
0
0
1
2
0
1
0
0
1
0
0
0
1
2
0
1
0
2
1
1
2
2
0
0
1
2
2
0
1
1
0
2
0
0
0
1
1
2
0
2
2
1
1
0
1
1
1
2
1
1
2
1
1
2
1
0
2
0
1
0
1
1
0
1
1
2
1
0
2
1
2
1
1
0
1
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
1
1
0
0
1
0
0
1
2
1
0
0
0
0
0
1
0
2
0
0
1
1
1
2
0
2
1
1
0
0
1
0
1
0
0
1
0
1
0
2
0
0
2
0
1
0
1
2
0
1
2
0
1
0
2
1
1
1
1
1
0
2
2
0
0
1
0
2
0
0
0
2
0
2
0
1
1
2
2
0
1
1
2
1
2
2
1
2
1
0
0
1
1
1
2
0
0
1
1
0
1
0
0
0
0
2
0
1
0
1
0
1
1
1
1
2
1
0
0
0
1
1
1
0
0
0
2
1
1
1
1
0
1
0
1
1
0
0
1
0
2
1
0
1
0
1
1
0
2
0
0
1
2
0
0
2
2
1
0
0
0
0
0
1
1
1
1
0
0
0
2
1
0
1
7
0
0
2
1
0
2
1
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
2
1
1
1
0
1
1
0
0
0
0
1
0
0
2
2
1
0
1
1
2
0
1
2
0
2
0
1
0
0
0
0
1
1
2
0
1
2
2
0
0
0
0
2
2
1
1
0
0
2
1
0
1
1
1
3
2
1
0
0
0
0
1
0
1
2
2
1
1
1
5
1
1
0
0
1
1
2
0
2
1
1
1
1
0
1
0
2
2
1
2
0
0
0
0
0
0
2
1
0
0
1
1
2
2
0
1
2
2
2
2
1
0
1
0
0
1
1
2
1
1
1
0
0
0
0
3
2
1
0
0
1
0
1
2
1
1
2
1
0
2
1
0
0
0
0
0
1
1
0
1
2
1
1
1
0
2
1
1
0
1
1
0
0
0
0
0
1
0
2
0
1
0
2
0
0
1
1
2
0
0
0
0
0
0
0
0
2
0
1
0
1
1
2
2
0
2
0
2
1
0
0
1
2
1
0
1
0
2
0
1
0
0
1
1
2
1
2
1
0
2
1
1
1
0
0
0
2
1
0
1
0
0
1
1
1
0
0
0
1
2
1
2
0
0
2
1
1
0
1
1
0
2
0
1
2
1
0
1
1
1
2
0
1
0
1
9
1
1
1
0
1
0
0
2
0
0
0
1
0
2
2
2
0
1
1
0
1
0
2
0
0
1
2
0
2
0
1
0
1
1
1
0
1
0
0
2
0
2
0
0
0
0
1
0
0
0
2
1
0
0
0
0
1
2
1
1
2
1
0
1
2
1
2
0
2
1
0
0
0
1
1
1
0
1
1
0
0
2
1
0
1
0
1
1
0
0
0
0
1
1
1
0
0
0
0
1
2
0
2
0
0
1
1
0
0
2
1
1
1
0
0
0
2
0
2
2
1
1
1
2
0
1
1
1
1
1
1
1
1
2
0
2
0
1
1
0
1
2
1
2
1
2
1
0
1
1
1
2
0
1
0
1
0
2
1
1
1
0
1
1
0
1
0
1
0
2
0
1
0
0
1
1
3
0
1
1
0
0
1
0
0
0
2
0
1
0
0
1
2
0
1
1
1
1
1
1
2
2
0
2
1
1
0
1
0
0
0
0
0
1
1
0
0
1
0
1
0
2
2
0
1
0
2
1
1
2
0
2
0
0
1
0
1
0
0
1
0
2
0
0
1
7
1
0
1
1
1
1
0
0
2
2
0
0
1
4
2
1
0
2
2
0
0
0
4
2
1
1
1
0
0
1
0
1
1
0
0
0
1
2
0
1
1
1
3
2
0
1
0
0
0
2
0
0
0
1
0
2
2
1
2
1
2
0
0
0
2
2
1
1
0
2
0
0
1
1
0
0
1
0
1
1
2
1
1
2
0
0
0
0
2
1
0
1
3
0
2
1
1
0
0
1
2
2
1
0
1
0
0
2
2
0
0
1
1
2
1
1
1
1
1
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
2
0
1
0
1
2
1
1
2
0
2
2
0
1
1
0
0
2
1
0
0
1
0
0
0
1
1
1
0
0
2
0
0
1
2
0
2
2
1
0
1
0
0
2
1
0
2
0
1
1
0
0
2
1
1
0
0
1
1
0
1
0
1
0
1
1
2
2
2
0
2
1
1
1
2
2
2
0
1
1
1
1
0
1
1
1
2
0
0
1
0
0
2
1
0
2
0
1
1
2
0
2
1
2
0
2
1
1
0
0
1
2
1
1
1
0
0
2
1
0
0
1
1
1
1
1
0
1
1
2
0
2
0
1
1
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
2
1
0
5
1
1
0
2
1
1
0
1
0
0
2
2
2
0
1
2
0
1
0
2
1
1
2
0
1
0
2
1
0
1
0
1
0
0
1
0
0
0
2
1
0
2
1
2
3
2
0
0
0
2
1
0
1
1
2
0
2
0
2
1
0
1
1
2
1
1
1
0
1
2
1
0
2
0
1
1
0
0
0
1
0
1
1
1
2
0
2
1
2
2
0
1
2
1
0
2
0
0
0
1
1
1
0
2
1
0
1
0
0
0
0
0
1
1
1
1
1
1
0
0
1
2
0
2
1
0
1
1
1
0
0
1
0
1
0
1
0
2
0
0
1
0
1
1
2
0
1
0
0
0
0
1
2
1
1
2
0
1
2
0
3
1
1
0
2
0
1
0
1
2
1
1
0
2
1
0
2
0
1
1
1
1
1
2
0
0
2
1
0
1
1
2
0
3
1
1
0
1
1
1
1
0
1
2
1
0
0
1
0
2
1
1
1
1
0
2
1
1
1
2
0
0
0
1
2
0
0
0
0
2
2
2
2
4
1
1
1
0
1
2
2
2
1
0
1
1
0
1
1
0
1
1
1
0
0
2
0
3
1
0
0
0
0
0
2
2
1
1
0
0
1
1
2
1
2
2
0
0
0
2
1
2
0
0
2
0
2
1
2
1
1
0
1
0
1
1
0
2
1
1
1
0
1
0
2
0
0
0
0
1
2
0
1
1
0
1
1
1
1
0
2
0
0
0
2
1
2
0
0
0
1
0
0
1
0
2
1
1
1
2
2
0
1
0
1
0
2
1
1
1
1
0
1
2
1
0
1
2
0
1
0
0
1
1
0
1
1
0
0
0
1
0
0
2
2
1
1
2
2
0
2
2
2
2
1
1
1
0
0
2
1
0
1
2
0
1
1
0
2
0
1
1
1
0
2
1
0
1
0
1
4
1
1
2
0
0
0
1
0
0
0
3
2
0
1
0
0
1
1
0
0
1
1
0
2
0
0
1
2
0
2
1
0
2
0
1
0
0
0
3
2
1
0
2
1
0
1
2
0
1
1
2
1
1
2
2
0
0
0
2
0
2
2
0
2
0
0
2
0
0
2
0
0
1
0
0
2
2
0
2
1
1
0
0
0
0
0
2
1
0
1
2
1
1
2
0
1
1
0
0
0
1
2
1
1
0
1
2
0
1
1
0
0
2
2
0
1
0
0
0
2
1
1
0
1
2
0
0
2
1
0
1
0
1
0
1
2
1
0
1
0
2
1
1
1
1
0
0
0
0
1
0
2
0
0
0
0
0
2
1
0
0
0
1
2
0
0
2
1
0
1
0
0
0
0
2
0
0
1
1
0
0
0
2
0
1
1
1
0
0
2
1
0
1
3
1
1
1
0
0
2
1
1
0
0
0
2
0
0
1
0
1
0
0
0
0
1
1
0
4
0
0
2
1
1
0
1
0
1
1
1
0
0
0
0
2
2
0
3
1
1
0
0
0
2
0
1
1
1
0
0
0
3
2
0
1
1
0
0
0
2
1
0
1
3
0
0
0
1
2
1
1
2
1
1
1
1
0
2
2
0
2
1
0
0
1
0
1
0
1
0
2
1
2
1
1
0
0
1
0
0
1
2
2
1
0
0
0
0
0
1
1
0
1
1
2
2
0
0
2
0
2
2
0
0
0
1
2
0
1
1
0
1
0
1
2
0
0
1
0
2
1
1
1
0
2
2
1
0
0
0
0
3
0
0
1
0
0
2
0
2
1
1
0
1
2
2
2
2
2
0
0
0
1
1
2
0
1
2
0
1
0
0
1
2
1
1
0
0
1
3
0
0
0
0
1
2
4
1
1
1
2
0
0
0
0
2
0
1
2
1
2
2
2
1
3
0
0
1
2
2
1
3
1
2
2
1
0
2
0
2
1
2
1
1
0
0
0
0
0
0
1
1
0
1
2
1
3
1
0
1
1
0
1
2
3
0
0
1
0
0
0
0
0
0
1
1
0
1
0
1
1
0
1
0
1
0
1
2
1
0
0
2
1
1
1
2
2
0
1
2
1
0
0
0
1
1
2
2
2
1
1
2
0
1
1
0
0
1
1
1
1
2
1
1
2
0
0
1
2
0
0
1
1
0
0
1
0
1
1
1
0
1
2
1
1
2
2
1
0
0
1
0
0
1
1
1
2
1
1
1
0
0
0
0
2
1
2
2
0
1
1
0
1
1
0
1
0
1
0
1
1
0
2
2
0
0
1
1
1
1
2
0
1
2
1
0
2
2
1
0
0
2
1
1
0
0
1
2
1
0
0
1
0
0
0
1
2
0
2
1
1
1
1
0
1
0
2
1
1
2
2
1
1
0
1
0
0
0
0
1
0
0
1
0
0
2
1
0
1
1
2
0
0
1
1
0
2
2
3
0
1
0
2
0
1
1
2
0
2
2
2
2
1
2
0
1
1
1
2
0
1
1
1
0
1
1
0
0
0
0
0
2
0
1
0
2
1
0
2
1
1
0
2
2
1
0
0
2
0
1
2
0
2
0
1
2
2
2
0
3
1
0
1
1
0
1
2
0
1
0
0
1
1
0
0
0
0
1
0
0
1
0
2
0
2
1
1
1
1
0
0
2
1
0
1
1
0
2
0
1
1
0
0
0
0
2
1
1
0
2
2
1
2
0
2
0
1
0
0
1
0
2
1
0
0
0
1
1
0
0
0
2
1
1
1
0
1
0
3
2
1
1
0
1
2
2
1
0
2
2
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
1
1
2
0
2
2
0
0
1
0
1
2
1
1
0
2
0
1
1
1
1
1
0
0
1
4
0
0
0
2
0
1
1
0
1
0
1
2
2
0
0
0
0
0
1
0
1
2
0
1
1
1
0
1
0
2
0
2
1
2
0
0
0
2
2
1
1
1
0
2
1
1
0
0
0
0
1
2
1
0
2
0
0
1
0
0
0
1
1
1
1
0
1
1
1
0
0
1
0
0
1
1
2
1
0
0
0
0
1
1
0
2
0
0
1
0
0
0
0
1
1
1
1
1
0
2
1
0
0
1
0
0
1
0
0
2
0
0
1
2
1
1
0
0
2
3
0
0
0
0
2
3
1
1
0
2
2
0
0
1
0
2
1
1
1
1
2
0
0
0
0
1
1
0
1
0
1
1
0
1
2
2
1
1
1
1
2
0
1
0
1
1
0
0
1
0
2
0
0
1
2
1
0
2
1
1
1
0
2
0
0
2
0
0
1
0
1
2
2
1
1
3
2
0
1
2
1
0
0
1
1
2
0
0
0
1
2
2
0
1
0
1
0
1
2
0
2
0
2
1
0
0
1
1
2
0
2
0
0
0
1
0
0
0
0
0
0
1
1
1
1
2
0
1
1
0
0
0
2
1
1
0
2
2
1
0
0
2
1
1
1
2
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
2
2
0
2
0
1
0
0
2
2
0
2
1
1
1
0
0
0
1
1
0
1
0
1
0
0
0
1
1
1
1
0
3
1
3
1
2
0
2
0
1
0
3
0
0
1
0
1
2
1
1
2
0
1
0
2
1
0
1
2
0
0
0
2
1
0
0
0
1
2
2
0
1
2
1
2
0
0
2
1
0
1
0
1
0
4
0
0
1
1
0
1
1
0
1
0
0
0
0
2
1
2
2
2
0
4
0
1
0
1
1
2
2
0
2
1
3
0
0
1
0
1
0
0
2
2
1
0
2
1
0
1
0
3
2
0
0
5
0
1
2
0
1
1
2
1
2
1
1
0
0
0
1
0
1
0
2
2
2
2
1
1
0
0
0
0
1
1
0
1
2
2
1
3
0
0
0
0
0
1
0
0
1
0
0
2
2
1
1
0
0
1
1
0
0
0
0
1
0
0
0
0
2
2
1
2
0
2
1
0
1
1
2
1
1
1
1
1
0
2
0
0
0
0
1
0
0
1
2
0
0
2
2
0
2
0
1
1
1
1
1
2
0
0
1
1
1
0
0
3
0
0
2
0
2
1
0
0
0
1
0
1
4
0
0
0
0
1
2
1
1
1
1
2
1
1
2
1
2
0
2
1
1
0
1
1
0
1
0
0
0
2
0
0
0
0
2
2
1
0
0
0
0
0
1
2
1
0
2
0
0
1
1
1
0
0
2
0
0
0
2
1
0
0
2
1
1
2
1
0
0
0
2
1
1
0
0
0
1
0
2
2
2
0
1
0
0
0
1
1
1
3
0
0
0
1
1
2
2
0
1
1
0
1
0
1
0
2
1
1
0
1
0
1
0
1
1
1
0
1
2
0
1
1
1
0
1
0
0
0
0
0
1
2
0
2
0
0
2
0
0
0
2
0
0
1
0
1
0
0
1
2
1
1
1
2
0
0
1
2
2
2
0
0
0
0
1
1
0
1
2
1
0
0
2
2
1
1
0
1
1
1
2
0
1
0
0
1
0
1
1
0
0
1
0
0
1
0
2
0
2
1
0
0
1
1
0
2
2
0
1
2
1
0
0
0
1
2
1
0
1
2
2
2
1
0
1
0
1
1
1
0
1
1
2
1
0
0
1
2
1
0
3
2
0
0
0
0
3
2
2
1
0
0
0
1
2
0
1
1
0
0
1
0
0
0
1
2
1
0
0
0
1
1
2
2
1
0
2
0
0
1
1
0
0
1
1
0
0
2
2
1
1
1
0
0
0
1
1
1
0
0
0
1
1
0
1
0
1
1
2
1
0
1
2
0
4
0
1
2
1
2
2
1
1
1
1
1
1
0
0
2
0
2
2
0
0
0
2
0
0
1
2
1
0
2
0
1
1
2
1
2
1
0
1
1
1
0
1
2
1
1
1
0
0
2
1
0
0
2
1
1
2
1
1
0
0
1
0
0
1
1
0
2
1
0
0
0
1
2
0
1
1
0
1
0
1
0
0
1
1
0
2
0
0
0
0
1
0
0
1
0
0
1
2
2
1
2
0
0
2
1
0
0
2
0
1
1
0
0
1
0
1
0
2
0
2
0
1
2
2
1
1
0
1
0
2
2
1
0
0
0
2
0
0
1
0
1
0
1
3
0
2
1
1
1
1
2
2
1
0
2
0
2
0
2
1
0
1
0
1
0
0
2
0
2
0
2
1
0
1
1
1
1
1
1
0
0
2
0
3
1
1
1
2
1
1
2
0
0
3
0
1
1
1
1
0
2
0
0
0
0
1
0
1
0
1
0
0
1
1
0
1
2
1
0
0
1
0
0
0
2
0
0
1
1
1
1
1
0
0
1
1
0
1
2
1
1
1
3
0
0
0
0
0
2
0
0
2
0
0
0
2
1
0
0
2
2
2
1
2
0
0
0
1
1
0
0
1
1
1
0
0
0
2
1
0
0
0
0
2
2
0
0
1
0
1
1
0
0
2
4
0
1
1
0
0
0
0
1
2
0
1
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
1
1
0
1
0
1
0
1
2
2
0
0
1
0
0
1
0
0
2
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
2
1
1
2
2
1
0
1
2
1
1
1
2
0
0
2
0
2
1
0
1
1
1
1
0
1
0
1
1
1
1
0
1
2
0
2
2
0
3
2
3
0
3
0
0
0
1
1
1
1
1
0
3
1
1
0
3
0
0
0
1
2
0
0
2
2
1
0
1
0
0
2
3
1
0
0
0
1
0
0
2
2
0
0
0
1
0
0
0
2
1
0
0
0
2
1
0
0
0
1
2
0
0
1
0
0
0
1
0
0
2
0
0
1
1
0
0
0
0
1
2
0
2
0
2
0
2
0
0
0
1
0
0
1
0
0
0
2
0
1
0
0
0
2
0
2
0
2
1
1
1
0
1
0
0
2
0
1
2
0
1
2
1
2
1
0
2
0
0
6
1
0
0
2
1
0
0
1
0
2
0
1
0
0
2
1
0
0
0
0
1
0
0
3
0
0
0
1
2
0
0
1
1
1
0
0
2
0
1
2
1
0
1
1
0
0
1
3
0
1
0
1
0
2
0
1
0
2
1
1
1
1
1
0
1
1
1
1
1
0
2
0
0
2
1
1
1
1
0
0
0
2
0
2
1
0
2
2
1
1
0
1
1
0
2
3
0
1
0
0
0
0
0
2
2
1
0
1
1
1
0
1
2
0
2
0
1
2
1
0
1
1
0
2
0
0
2
1
1
0
0
0
0
2
0
0
2
1
0
1
0
1
1
1
1
1
0
2
0
2
0
1
1
2
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
3
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
2
1
0
0
2
2
1
0
0
0
2
0
1
2
0
2
0
0
2
0
1
1
0
1
1
0
1
2
1
1
0
0
0
1
1
1
1
0
1
1
1
1
0
1
0
1
1
1
1
1
0
0
0
1
1
2
0
1
2
0
0
0
0
1
0
2
0
0
0
2
2
2
1
2
0
1
0
1
0
2
1
1
0
0
0
1
0
0
2
1
0
1
1
1
0
1
1
0
1
0
1
2
2
0
2
1
1
2
1
2
2
2
1
1
0
2
2
0
1
1
0
1
1
0
1
1
0
0
1
1
1
0
1
1
1
0
1
0
0
0
1
1
1
0
0
0
1
2
0
2
2
1
2
2
0
1
0
1
0
0
1
0
1
1
1
1
0
2
1
1
1
0
0
0
0
2
2
3
0
1
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
1
2
2
1
2
0
0
0
0
0
0
0
1
1
1
1
1
0
1
0
2
0
0
2
0
2
1
1
0
2
2
1
0
0
0
1
1
0
0
0
1
2
0
2
0
1
0
0
1
0
1
1
1
1
2
1
2
0
2
0
1
0
0
0
1
0
0
2
2
0
2
1
1
1
1
1
2
1
1
0
0
1
0
0
2
1
1
1
0
0
1
1
1
0
0
0
2
1
0
0
1
0
1
1
0
2
2
2
1
0
1
2
0
1
0
1
1
1
0
0
1
0
1
0
1
2
1
0
2
2
1
0
2
2
2
0
2
2
0
0
0
1
2
2
1
1
0
1
1
0
0
2
0
1
1
0
0
1
1
0
0
0
0
1
0
1
1
1
3
1
0
0
1
2
1
2
2
2
0
2
1
1
2
1
1
2
2
0
1
0
1
1
1
2
2
1
1
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
1
2
1
0
0
1
2
1
1
2
1
0
1
0
0
2
1
0
0
0
0
1
2
0
1
0
0
2
1
1
1
2
2
0
0
0
2
1
0
0
1
2
0
2
0
2
2
2
0
0
0
0
0
2
1
0
0
2
0
1
0
1
0
2
0
0
1
1
0
0
0
1
1
0
0
1
1
2
1
1
3
0
0
0
0
0
0
1
1
1
1
0
0
0
1
1
0
2
1
0
1
0
1
2
0
1
0
0
0
1
1
1
0
0
1
0
0
0
0
1
1
2
2
1
0
0
0
2
1
1
2
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
2
0
0
2
0
0
1
0
2
0
2
0
0
1
1
0
2
1
0
0
2
2
1
1
2
0
1
1
0
1
2
2
1
1
1
2
1
0
0
1
4
0
2
0
0
0
2
0
2
0
3
0
0
1
1
0
2
1
0
2
1
0
0
1
0
0
0
0
0
1
1
2
2
1
2
0
1
2
2
0
0
0
0
2
0
0
0
0
2
1
2
0
1
2
0
1
0
2
2
1
2
0
1
1
0
0
1
1
0
2
1
2
1
2
0
2
1
2
2
1
2
2
2
0
2
7
1
1
1
2
1
4
1
1
0
3
0
1
2
1
1
1
0
0
2
1
1
0
1
1
2
0
1
1
0
2
0
0
0
1
2
1
1
2
2
2
6
1
0
2
0
0
2
0
1
1
1
2
0
1
2
1
1
0
1
1
0
1
2
0
1
1
1
0
1
2
0
0
2
0
2
1
0
1
0
2
2
1
0
1
0
0
1
0
1
0
0
1
1
0
0
0
0
1
1
1
1
2
2
0
0
0
1
1
0
0
0
0
0
0
2
1
1
1
0
1
1
0
0
0
1
1
0
0
0
1
1
1
0
0
1
0
2
0
2
0
1
0
1
0
1
1
2
2
1
2
0
1
0
2
0
1
0
0
2
1
0
2
0
2
0
1
2
0
0
1
1
2
1
0
1
0
0
2
2
0
1
1
1
1
1
1
2
1
0
1
0
0
4
1
1
1
1
2
0
0
1
0
0
0
1
0
1
0
2
1
0
0
2
0
2
2
2
1
1
0
0
0
2
1
2
0
0
0
2
1
0
2
1
0
1
0
2
0
0
2
1
1
2
1
1
1
1
3
1
2
2
0
0
1
1
0
2
0
1
1
1
0
0
0
1
1
1
0
0
0
0
2
0
1
2
1
0
0
0
1
1
2
2
2
0
1
0
2
0
1
0
0
0
2
0
0
0
2
1
0
1
2
0
1
0
0
0
0
0
2
1
2
0
0
2
0
1
0
1
1
0
0
2
1
0
0
1
2
0
0
0
0
0
0
0
0
1
3
1
1
0
1
2
1
0
1
0
2
1
1
4
2
0
2
2
0
1
2
1
0
0
0
2
0
2
2
1
0
2
0
1
0
1
0
1
2
0
1
2
0
0
0
1
2
0
0
2
0
1
2
2
2
2
0
1
2
1
0
0
1
1
2
1
0
1
0
0
1
2
2
0
2
2
0
1
2
1
0
1
0
0
1
0
1
1
2
0
0
0
0
0
1
1
0
1
1
1
1
1
0
1
2
2
1
2
0
0
2
2
1
3
1
1
0
0
2
2
1
0
0
1
0
1
1
2
1
1
0
1
2
0
0
2
0
0
0
0
1
2
1
3
0
0
2
0
0
0
2
1
1
1
0
0
0
1
0
2
0
3
2
1
0
1
2
0
0
1
0
0
1
1
0
2
2
1
2
1
2
0
2
1
1
0
1
1
0
0
0
1
0
1
1
1
0
0
1
0
1
1
0
0
2
1
0
1
0
2
2
0
1
1
1
2
2
1
1
1
0
0
0
1
0
2
1
0
0
2
0
0
1
2
0
1
0
0
2
1
0
0
1
0
0
1
2
1
1
0
0
0
1
1
1
1
0
1
1
0
0
0
0
0
0
0
2
2
1
1
1
1
2
1
0
1
1
2
2
0
0
0
0
1
1
1
1
2
0
0
0
2
2
2
1
0
1
2
0
1
2
1
0
1
0
0
1
0
1
1
0
1
1
1
0
0
1
1
1
1
2
0
1
1
2
0
0
0
2
1
0
1
0
0
2
0
0
1
2
1
0
0
1
0
1
0
0
0
1
1
1
1
0
0
0
3
1
0
1
0
0
1
0
0
2
0
0
2
0
1
0
2
1
1
1
0
2
1
1
0
0
0
0
1
1
0
1
0
2
0
1
2
0
1
0
2
0
2
0
1
1
2
1
0
0
1
1
0
1
0
2
0
0
0
0
0
1
3
2
0
1
0
1
0
0
3
0
0
1
0
0
2
0
1
0
1
1
0
0
0
2
1
2
0
1
0
1
0
0
0
0
1
1
1
1
1
0
2
1
1
3
1
1
0
1
0
1
2
0
1
1
2
2
0
0
1
0
3
1
0
2
0
0
0
2
2
2
1
1
1
1
1
1
1
1
0
2
0
0
2
2
1
3
3
2
0
1
1
0
1
0
0
1
2
0
0
0
1
0
0
0
1
2
0
2
0
0
0
0
0
2
0
0
2
1
0
0
3
0
2
2
0
0
0
0
1
1
0
2
1
0
0
1
0
2
0
1
2
2
0
2
1
0
0
1
0
1
0
1
0
2
1
1
1
1
2
1
0
1
1
1
0
2
2
0
2
1
0
1
2
1
0
2
2
2
0
0
0
2
1
1
1
0
1
1
1
0
1
0
0
1
1
1
1
0
1
0
1
0
2
2
1
1
0
0
2
0
0
1
0
0
0
1
0
0
2
2
1
1
0
1
2
2
0
2
1
2
0
1
0
0
1
1
2
2
0
0
1
1
1
1
1
2
1
2
2
0
2
3
1
1
2
1
2
2
0
0
3
0
2
1
2
0
0
2
0
1
1
1
1
1
1
2
1
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
1
0
0
0
1
0
1
1
1
1
1
1
1
0
0
0
2
1
0
2
2
0
1
0
0
1
1
1
0
0
0
1
0
0
0
1
1
1
2
0
1
2
0
1
1
0
1
1
1
1
0
1
0
0
0
0
2
1
1
0
0
1
0
1
0
2
1
1
1
0
2
0
2
1
1
1
1
1
0
0
2
1
2
1
0
1
0
0
0
1
1
1
1
2
2
1
1
1
1
0
1
0
0
1
1
0
1
0
0
2
2
1
2
0
0
2
0
1
0
2
0
0
0
0
2
2
2
0
8
0
0
2
2
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
2
1
0
1
1
0
1
2
2
0
0
2
0
0
2
1
2
0
1
0
1
0
1
0
1
0
1
2
0
2
3
1
1
1
1
0
0
1
2
1
0
0
2
0
2
0
0
0
1
0
0
2
1
2
0
1
0
1
1
1
0
0
1
0
1
2
0
1
2
1
2
0
4
0
1
1
1
0
1
1
2
2
2
1
0
0
2
1
1
0
0
0
0
1
0
0
1
2
1
1
1
0
2
0
0
1
1
2
0
0
1
0
0
1
2
1
2
2
0
2
0
1
0
0
2
2
2
0
2
1
0
2
0
2
0
0
1
0
1
0
4
1
0
0
1
1
2
1
1
0
0
0
1
1
1
0
0
1
2
2
0
0
0
1
0
0
2
1
1
0
0
1
2
0
0
0
1
1
1
2
0
0
0
2
1
0
0
2
0
2
1
2
0
0
2
2
1
2
1
1
2
0
0
1
1
0
2
1
2
1
0
2
1
3
0
2
0
1
2
2
1
0
0
1
0
0
1
1
2
1
0
0
0
1
0
1
0
0
0
0
0
1
0
3
1
0
0
1
0
1
1
1
0
1
0
1
0
1
0
0
11
1
1
0
0
0
2
1
2
0
1
0
0
1
0
0
0
0
1
1
1
0
0
0
2
1
2
1
2
0
1
0
1
0
1
2
2
1
2
0
0
0
1
0
0
0
1
0
0
0
0
1
2
1
0
0
0
0
0
0
1
1
1
0
2
0
1
0
0
2
1
1
0
1
2
2
2
0
0
0
2
0
0
1
2
0
2
0
2
0
1
0
1
0
2
0
0
1
1
1
0
2
0
0
0
0
2
1
0
1
0
0
1
0
1
0
1
0
2
1
0
1
0
2
1
0
1
2
2
1
1
0
0
2
0
2
0
1
0
0
1
0
1
4
0
1
0
0
2
1
1
1
2
0
1
1
2
0
1
0
1
1
1
1
1
1
2
1
1
1
1
0
2
2
1
2
2
1
0
1
2
0
1
0
0
1
2
0
2
1
0
1
0
1
2
1
1
1
1
0
0
1
0
2
1
1
0
3
2
0
1
2
1
1
1
1
1
0
0
2
2
3
1
1
0
0
1
1
1
0
0
2
1
0
1
0
1
2
0
0
1
2
0
0
1
1
1
0
0
0
2
1
0
2
0
0
0
0
1
1
1
0
0
1
2
0
4
1
3
1
1
0
0
0
2
0
1
1
1
0
0
1
0
2
0
0
2
2
1
0
1
1
0
1
0
2
2
2
2
0
1
1
1
2
1
2
2
0
0
2
2
1
2
0
0
2
0
0
0
0
2
1
1
0
2
1
1
0
0
2
0
0
0
2
0
0
0
2
1
2
1
0
2
1
1
1
0
1
0
0
0
0
0
1
1
0
1
2
1
1
2
1
5
0
0
1
2
0
0
0
1
0
0
2
2
0
0
1
1
0
0
2
0
1
0
1
1
0
1
1
0
2
0
1
0
0
1
1
0
1
1
1
0
2
0
2
0
1
2
1
1
2
1
2
0
1
0
1
1
1
0
1
0
1
2
1
1
0
1
0
0
1
0
0
1
1
2
2
0
1
1
1
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
2
1
0
1
0
1
0
0
0
1
2
0
2
1
0
0
1
1
1
1
0
2
3
2
3
0
0
0
1
0
0
1
1
1
0
1
1
0
1
0
0
1
1
0
1
0
0
0
2
2
0
0
1
1
0
1
0
1
2
2
1
2
2
1
0
0
0
0
2
0
1
0
1
2
1
1
1
1
1
0
1
1
1
1
0
1
1
2
2
1
0
2
2
1
1
0
0
0
1
2
1
2
1
1
0
1
0
1
2
1
1
1
0
1
0
1
1
2
1
2
1
1
1
0
1
2
1
2
0
0
2
1
0
1
0
1
1
0
2
0
0
1
2
0
0
1
0
1
1
1
0
0
0
0
1
0
2
0
1
1
0
0
0
0
1
1
0
2
0
0
1
1
0
0
1
2
0
1
1
0
1
0
0
1
0
2
1
0
1
1
1
1
1
2
2
1
0
0
0
3
0
1
1
2
0
3
0
2
1
2
2
0
0
2
0
0
2
0
2
2
1
0
0
2
1
1
0
0
1
1
1
3
2
1
1
1
0
0
0
0
0
2
0
0
1
1
0
1
2
0
0
1
2
0
0
1
1
0
2
0
1
2
1
2
1
1
1
1
0
0
2
2
2
0
0
0
1
0
0
2
1
2
1
1
1
2
0
1
0
2
2
1
1
2
1
2
2
0
1
0
0
0
2
1
1
2
0
0
1
0
2
2
1
0
3
1
2
1
1
2
0
0
0
1
0
1
1
0
1
0
1
1
0
0
0
0
0
0
0
0
1
1
1
0
0
2
0
1
1
1
0
1
1
0
1
2
2
0
3
0
3
0
0
0
1
3
0
2
0
1
2
0
2
0
0
2
1
2
1
0
0
0
1
1
0
1
2
1
1
1
2
1
1
2
0
0
1
0
0
0
2
1
1
1
1
1
0
1
1
1
1
1
1
1
2
1
0
1
0
1
1
1
2
0
1
0
1
1
0
1
1
1
1
1
1
2
1
0
0
1
0
0
0
1
2
0
0
0
2
1
1
0
1
0
1
1
1
3
0
2
2
0
0
1
1
0
2
0
0
1
1
2
0
1
2
2
0
0
0
2
1
1
0
0
0
1
0
0
0
2
1
0
0
0
2
1
1
0
0
2
2
0
0
1
0
0
1
2
1
1
0
0
1
1
0
0
1
0
1
3
0
2
1
0
1
0
0
2
0
1
1
2
1
1
1
0
2
2
0
1
1
0
1
0
0
1
1
2
0
1
0
0
0
1
0
1
1
1
1
0
0
1
1
1
2
2
0
0
1
0
2
1
2
2
1
0
0
0
1
0
1
1
0
1
0
2
1
0
0
1
0
1
0
1
1
1
1
0
2
0
1
1
0
0
1
1
0
1
1
0
0
1
2
1
0
0
2
0
0
0
4
1
1
2
0
2
0
0
1
0
1
2
2
2
0
2
1
2
2
1
3
1
2
1
1
1
0
0
1
1
2
1
0
2
1
2
1
0
1
0
0
1
0
2
1
0
1
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
2
0
2
2
0
0
1
1
0
0
0
1
3
2
1
1
2
1
1
1
0
2
0
0
1
2
2
1
0
1
0
0
2
1
1
1
0
0
0
0
2
2
0
1
1
0
1
1
2
3
0
2
0
0
0
0
0
0
2
0
1
1
2
0
0
2
1
1
1
0
2
3
1
0
0
1
0
3
0
0
1
2
0
0
1
1
0
0
2
0
2
0
0
1
2
1
0
0
1
2
0
1
0
1
1
2
2
2
1
0
0
1
1
0
2
0
2
2
0
1
0
2
0
0
1
0
2
1
0
0
1
0
0
1
1
2
1
2
2
0
0
1
1
0
1
1
1
0
1
1
2
4
2
0
0
0
2
1
0
0
2
0
1
2
0
2
2
1
0
0
1
1
0
2
2
1
2
0
0
1
1
0
0
2
2
1
1
2
0
0
2
1
1
1
2
0
1
0
1
2
0
1
2
2
1
2
0
0
0
1
1
1
0
1
0
1
0
0
0
2
2
1
0
0
1
1
1
1
0
0
0
0
0
1
1
1
0
2
0
2
0
1
2
2
0
0
0
0
2
2
0
0
2
2
0
0
3
1
1
0
1
1
2
1
0
0
0
1
0
0
1
3
2
1
8
1
0
2
0
1
2
1
1
2
1
0
2
0
1
0
1
0
2
0
1
0
0
1
0
0
2
0
1
1
0
0
0
2
0
0
1
2
2
1
0
1
2
0
1
0
2
1
2
2
3
0
1
0
0
2
0
1
0
1
0
0
2
2
1
0
1
5
1
2
0
1
1
1
0
1
0
1
0
0
0
1
1
0
0
2
1
0
0
2
0
0
1
1
0
1
0
0
0
1
2
0
0
1
0
0
1
1
1
1
0
1
2
2
0
0
1
0
1
0
2
0
1
0
0
1
0
2
2
1
0
1
0
0
1
1
0
1
0
1
0
1
2
0
0
0
0
1
0
1
2
1
0
1
0
2
2
1
1
2
0
0
1
2
1
0
0
0
1
2
1
0
2
1
0
1
0
0
0
0
2
1
2
0
1
2
0
1
2
0
1
2
1
2
0
0
1
2
0
0
0
2
0
2
1
0
0
0
3
2
0
0
0
0
0
1
2
1
2
0
1
0
1
1
0
2
1
1
1
2
0
1
1
0
0
0
0
0
1
2
0
0
2
0
2
1
0
1
0
1
2
2
2
0
2
0
1
0
0
1
0
2
1
0
0
0
0
1
1
0
0
3
2
0
2
0
1
0
1
0
2
1
2
0
1
0
0
1
0
0
0
0
1
0
0
2
2
1
1
1
3
1
1
1
2
2
0
0
1
1
0
1
1
1
1
0
0
2
2
0
0
0
1
0
0
0
2
0
0
1
2
0
0
1
0
0
2
1
2
1
0
1
0
2
0
1
0
1
1
0
1
1
2
2
2
0
1
2
2
1
1
0
1
0
0
1
0
0
0
2
1
0
1
1
2
1
0
1
0
0
2
0
1
1
0
1
1
0
1
1
1
1
0
1
2
2
0
2
0
1
0
2
0
1
0
2
0
1
2
2
1
2
2
0
1
0
2
1
1
0
1
2
0
1
0
2
0
2
0
1
0
2
0
1
0
2
0
2
0
0
2
0
2
2
1
0
1
0
1
0
1
0
2
0
0
0
0
0
2
1
2
0
0
1
1
0
0
1
0
2
2
1
0
1
1
1
0
2
1
1
1
0
1
2
2
1
1
0
0
1
0
0
0
2
0
0
0
0
0
0
1
2
0
0
1
1
1
0
2
1
3
1
0
2
0
2
2
1
0
1
1
0
1
1
1
2
0
2
1
1
0
2
0
0
0
1
1
0
0
0
1
0
2
0
2
0
2
2
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
2
2
1
2
0
0
0
1
1
1
1
0
1
2
0
1
1
1
2
0
2
1
1
0
0
0
1
0
1
0
1
1
0
0
1
2
1
1
2
2
0
1
0
2
1
0
1
2
0
0
2
2
0
1
2
2
2
0
0
1
0
2
0
1
2
1
0
0
2
2
0
2
0
1
2
1
0
1
14
0
0
0
1
0
1
0
2
0
2
2
0
0
0
1
0
2
1
0
2
1
0
0
0
0
0
0
1
1
0
0
0
1
1
1
2
0
0
1
0
1
0
1
0
1
2
0
1
0
2
1
0
0
0
1
1
0
1
0
0
2
1
2
0
0
0
1
0
0
0
2
1
1
0
1
0
2
2
0
1
2
0
0
0
2
0
2
1
1
2
0
2
0
0
0
1
2
1
2
0
1
0
2
1
1
1
1
0
2
0
0
2
0
1
1
2
1
1
0
0
0
2
0
1
0
1
1
0
2
0
2
1
0
1
1
1
1
1
1
2
1
0
0
1
2
0
0
2
0
0
0
1
2
3
0
0
2
0
2
1
1
2
2
1
1
1
0
1
0
2
1
1
1
0
1
2
3
0
0
0
0
0
0
1
0
2
2
1
1
0
1
3
0
0
2
0
0
1
2
0
2
1
2
2
2
0
1
1
1
0
0
1
1
1
0
0
0
1
0
0
0
0
1
2
2
0
0
0
0
1
0
1
1
1
0
1
1
1
1
2
1
1
1
2
1
0
1
1
1
0
1
1
2
1
1
0
0
2
0
1
3
2
2
0
2
2
1
1
0
1
0
1
0
0
0
2
0
0
2
0
0
2
0
1
1
1
0
2
1
1
0
1
1
2
0
0
0
2
1
1
0
2
0
1
2
2
1
0
2
2
0
1
1
3
1
1
2
0
0
0
1
0
2
1
0
1
0
0
2
1
0
0
0
1
0
2
1
0
1
1
1
2
1
2
1
1
1
1
0
1
2
0
0
1
2
1
1
1
2
2
1
1
1
1
0
2
1
1
2
0
0
0
1
0
2
2
1
2
0
1
2
0
1
1
1
0
1
1
1
2
2
0
0
0
0
2
2
2
2
0
0
2
1
0
2
2
1
2
0
0
2
0
2
1
1
0
3
3
2
1
0
0
0
0
0
1
0
1
2
0
1
1
1
1
2
0
1
0
1
2
2
2
0
1
1
2
0
1
0
0
2
7
1
0
0
2
0
2
2
0
2
2
1
1
2
0
2
1
0
0
2
0
0
0
0
0
0
1
1
0
1
2
2
1
0
1
1
1
0
2
2
0
2
0
2
0
1
0
0
0
2
1
0
1
0
0
1
2
1
0
0
0
1
1
0
0
2
1
2
0
0
0
2
1
2
1
1
0
2
0
0
1
2
2
0
0
0
1
1
0
1
2
0
1
1
1
2
0
1
0
1
1
2
2
1
1
0
0
1
0
0
0
2
1
1
1
2
0
0
0
1
0
1
1
0
1
1
2
0
0
1
2
0
2
0
0
0
1
2
0
1
1
1
0
1
1
1
0
0
0
0
1
1
0
0
0
0
0
1
2
0
1
2
2
1
0
0
2
1
0
1
2
0
1
0
2
1
2
0
1
0
0
1
1
1
0
0
2
1
0
3
1
0
0
1
1
1
1
2
1
0
0
1
0
0
0
1
0
1
0
0
0
2
1
0
2
0
1
2
0
1
2
0
2
0
1
1
2
2
1
1
1
1
1
0
0
2
0
1
2
0
1
2
0
0
0
2
0
0
2
1
0
1
2
0
0
0
0
1
0
3
1
2
0
0
1
2
1
6
2
1
1
0
1
0
1
0
2
0
0
2
1
1
0
0
1
1
3
1
2
1
1
0
0
0
1
1
0
2
0
1
2
2
2
2
1
2
0
0
2
2
1
1
1
2
0
1
0
0
2
3
0
1
1
1
0
1
2
0
1
0
0
2
1
0
0
0
2
0
1
2
0
0
0
0
1
0
0
1
1
2
2
1
2
0
0
1
0
0
0
0
2
2
1
0
0
0
1
0
0
0
1
2
2
0
1
1
0
0
1
1
2
0
0
2
0
1
0
0
0
0
1
2
2
0
1
1
1
1
0
4
0
0
1
0
2
0
1
1
1
1
0
1
0
2
3
0
2
0
0
1
0
1
0
1
1
1
2
1
2
0
0
1
1
1
2
0
0
1
1
0
2
1
0
1
0
0
0
2
1
1
1
0
1
2
0
3
1
1
0
0
0
2
1
1
0
1
0
1
1
0
1
2
1
1
1
1
3
1
1
2
0
0
2
2
1
0
1
1
0
1
0
1
0
1
0
0
2
0
1
0
0
2
0
1
0
0
0
1
1
0
1
1
0
1
0
0
1
1
0
0
0
0
1
0
0
2
1
2
1
0
2
0
2
0
0
1
2
2
1
0
0
2
0
2
2
0
1
2
0
1
0
0
0
2
1
1
2
1
1
0
2
0
0
0
2
1
1
0
0
1
0
2
1
2
1
1
0
2
1
0
0
0
2
2
0
0
0
0
2
2
1
2
1
0
2
1
0
3
0
0
0
2
0
0
2
1
0
2
2
2
0
0
0
1
1
0
2
1
2
2
0
0
0
0
1
0
1
0
1
0
1
0
1
2
1
2
0
1
0
0
0
0
1
0
0
0
0
1
1
1
1
0
0
1
0
0
1
2
1
0
0
2
0
0
0
2
0
0
2
6
0
1
0
1
0
0
0
1
3
0
2
1
0
0
0
0
1
0
2
1
0
2
2
2
2
1
1
0
1
0
2
0
0
0
0
1
2
2
0
1
2
0
2
0
1
1
1
0
2
2
7
0
0
0
1
1
2
1
2
1
0
2
1
0
2
0
0
0
0
0
1
2
1
1
0
0
0
1
1
1
0
1
2
1
2
0
0
0
0
0
0
2
1
0
1
0
1
1
0
0
1
0
3
1
1
1
2
1
1
0
2
2
1
0
1
1
1
1
2
0
1
1
1
1
1
2
0
1
1
0
0
2
1
1
1
0
1
0
1
1
0
1
0
1
2
3
0
1
1
0
1
4
1
2
1
0
0
0
0
1
1
0
0
1
0
0
0
2
1
0
2
0
0
0
2
0
2
0
0
1
0
2
0
2
2
0
2
2
0
1
0
1
0
0
2
0
1
1
1
0
2
0
1
2
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
1
2
1
1
1
1
2
0
1
1
0
0
0
2
2
2
0
0
2
0
3
0
0
2
0
1
2
0
1
1
0
1
1
1
0
0
0
2
1
2
1
2
0
1
0
6
1
1
2
0
2
1
2
1
2
0
2
1
1
2
1
0
0
1
1
1
1
0
1
2
1
0
0
2
0
1
2
0
0
0
2
2
0
0
0
0
1
0
0
0
2
1
1
1
0
0
1
1
0
0
1
0
2
0
1
0
2
1
1
0
0
0
1
0
2
2
0
0
2
2
0
1
0
0
0
2
0
1
1
1
1
2
1
2
0
2
0
0
5
0
1
1
0
2
0
1
1
1
0
1
1
0
2
0
2
1
2
0
1
1
1
2
1
2
0
0
2
0
2
1
2
2
1
1
1
0
2
2
2
2
1
1
1
1
1
0
2
0
1
0
2
0
1
1
0
1
0
0
0
1
0
0
1
0
1
0
2
2
0
0
0
1
1
1
1
0
2
1
0
1
1
0
2
0
1
1
0
1
0
2
0
1
2
0
0
2
1
1
0
0
1
0
0
0
1
1
1
2
2
1
1
2
0
1
0
0
1
2
2
1
0
1
0
0
2
1
0
0
0
1
0
1
1
1
0
3
1
3
1
0
0
1
1
0
0
0
0
0
1
0
2
0
2
0
0
1
0
1
2
0
1
1
1
0
1
1
0
1
1
0
2
2
2
2
0
2
1
0
1
0
1
0
1
1
1
1
2
1
1
1
3
1
0
0
1
0
0
0
0
0
1
0
1
2
0
1
0
1
0
2
0
0
0
1
1
0
0
1
2
2
2
1
0
0
0
2
1
2
0
0
1
2
0
1
2
2
0
3
1
0
1
0
0
0
2
1
0
1
1
1
1
2
2
2
1
1
0
1
0
0
0
0
0
2
1
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
1
2
0
0
3
1
1
1
0
1
0
1
0
0
1
1
0
1
1
2
2
1
0
1
1
1
0
1
1
0
1
2
0
1
1
1
0
0
1
0
1
0
1
1
0
0
0
1
0
0
2
0
1
1
0
0
0
1
1
0
0
0
2
0
1
1
0
0
0
0
0
2
1
2
1
0
0
0
0
1
0
0
1
2
2
1
0
0
0
0
0
0
1
2
2
0
0
0
1
0
1
2
0
0
0
0
1
0
1
1
1
2
2
0
1
1
2
0
1
1
0
0
1
0
0
0
0
2
1
0
2
2
1
0
2
1
0
1
0
2
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
1
1
2
1
2
1
2
0
0
2
0
0
2
0
1
1
1
1
1
2
1
0
1
0
1
2
0
0
1
1
0
2
2
1
2
1
1
0
1
2
0
1
1
4
0
1
1
2
1
0
0
1
0
1
1
1
2
1
1
2
0
1
1
0
0
2
1
0
0
2
1
1
2
2
0
0
0
0
1
2
1
0
3
2
3
1
1
2
0
3
0
3
0
1
2
2
0
2
1
0
0
1
1
3
1
0
1
1
0
0
3
1
0
2
1
1
0
1
1
1
1
1
0
2
3
1
2
0
1
0
0
1
1
2
0
1
2
0
1
0
0
0
2
1
1
1
1
0
0
2
1
1
1
0
1
2
2
2
1
1
1
0
1
0
2
1
1
1
0
0
0
0
2
3
0
0
1
1
0
2
1
1
0
1
0
0
1
1
1
0
0
1
1
1
2
0
1
2
2
0
2
1
2
1
1
0
0
0
0
0
0
1
2
1
0
1
1
0
1
2
0
1
1
0
1
0
1
1
1
1
1
0
0
0
0
1
1
1
1
0
2
1
1
1
0
1
1
0
2
0
1
1
2
1
0
2
1
1
0
0
1
0
1
0
0
1
0
2
1
0
1
1
0
0
0
1
0
0
0
2
0
0
1
0
1
0
1
2
0
0
1
0
0
2
1
0
2
1
2
2
1
1
0
2
0
0
1
0
0
0
2
1
2
0
1
1
1
2
0
0
0
1
0
0
1
1
1
0
0
0
2
0
3
1
1
2
0
0
1
0
2
0
0
0
1
2
1
0
0
0
0
1
0
2
0
0
4
0
1
0
2
0
0
0
1
2
1
0
1
0
0
2
2
0
1
0
0
1
0
0
0
2
0
1
1
2
0
1
0
2
1
2
3
0
1
1
0
1
0
1
0
1
1
2
0
2
1
0
2
0
0
1
0
1
1
0
1
2
0
1
0
0
1
1
0
1
0
0
1
3
0
1
2
0
0
0
0
0
0
2
1
1
1
0
1
1
0
1
0
0
0
1
2
1
1
2
0
0
1
1
0
0
0
2
1
0
0
1
1
0
1
1
1
1
0
1
0
0
1
1
3
0
0
1
1
2
0
0
0
2
2
2
0
1
1
1
1
0
0
1
0
2
0
1
0
3
1
2
2
0
2
0
0
0
0
2
1
1
2
2
0
0
0
0
2
0
1
2
8
0
1
0
1
0
2
1
0
0
2
1
1
1
2
1
1
0
0
0
0
0
0
1
1
0
1
0
2
0
0
1
1
1
2
0
1
1
2
1
1
0
2
1
0
1
0
2
1
2
2
0
0
2
1
1
0
1
1
2
0
0
1
1
1
2
1
0
2
1
0
11
0
1
2
0
1
1
1
1
0
1
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
1
1
0
0
0
1
1
0
2
1
2
1
2
0
0
1
3
2
0
0
0
1
0
3
0
2
1
2
1
2
1
2
2
2
2
0
0
1
0
1
2
1
1
0
1
0
1
1
0
1
2
1
1
0
2
1
2
1
2
1
1
1
1
0
1
2
0
0
1
1
0
1
0
1
1
1
0
2
0
1
0
0
0
0
1
0
0
1
0
0
1
2
2
0
2
0
0
1
1
0
1
2
2
2
2
0
0
1
1
1
4
0
0
1
0
0
1
1
0
1
0
0
0
0
2
1
0
1
1
2
0
0
1
2
1
2
1
1
1
1
0
1
2
2
1
2
0
0
1
0
2
0
1
2
0
0
0
0
2
1
0
1
1
1
2
1
0
6
1
2
0
0
0
0
0
1
0
2
1
0
0
1
0
0
2
0
0
2
2
2
0
1
1
1
0
0
1
0
0
0
1
0
0
1
0
1
1
0
0
1
2
0
1
3
2
0
2
1
1
0
2
0
0
1
0
1
1
2
0
0
0
0
0
0
0
2
1
0
2
1
1
2
1
0
1
0
0
1
2
0
2
2
3
0
0
0
1
2
1
1
1
1
1
3
1
0
1
0
1
1
0
1
1
2
1
0
2
0
0
1
0
2
1
1
2
1
0
0
0
1
2
1
2
2
1
0
1
2
1
0
2
1
2
1
1
0
0
1
0
1
0
0
2
1
0
0
2
1
0
1
1
0
1
0
2
2
0
0
1
2
0
2
1
1
0
2
4
1
0
0
1
1
1
0
0
0
1
0
0
1
0
1
0
0
0
2
0
2
2
2
1
2
1
0
0
2
0
1
1
1
1
1
2
1
2
0
1
2
2
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
1
1
1
1
2
1
2
1
0
2
1
0
2
2
0
0
1
0
2
0
0
1
0
1
2
1
2
1
0
0
2
2
0
1
1
0
0
1
0
1
0
0
0
1
0
0
2
2
0
0
1
1
0
1
1
2
1
2
0
2
0
0
1
2
0
2
0
2
2
1
0
1
1
1
2
2
0
1
1
2
0
1
2
1
0
1
0
1
0
1
1
1
1
0
1
0
1
0
1
1
0
0
2
1
2
1
0
0
1
2
0
0
1
1
0
1
2
3
1
0
0
1
0
0
0
2
1
0
0
1
1
1
0
0
0
2
0
1
1
0
0
0
1
1
0
0
0
0
1
1
2
0
0
1
2
0
0
1
0
0
0
2
0
0
2
0
0
1
0
0
0
0
1
0
1
1
0
2
1
1
0
2
1
0
1
0
1
0
0
0
0
1
0
1
1
1
0
0
1
2
0
0
0
0
0
0
0
1
2
0
1
1
0
1
2
1
0
1
0
1
1
1
0
2
1
1
1
1
0
2
0
1
1
1
0
0
0
0
1
2
2
2
0
2
1
1
1
0
0
0
1
0
0
1
2
0
0
2
0
1
1
1
1
1
1
2
2
1
1
1
0
0
0
2
2
0
1
0
0
1
0
0
2
2
1
0
0
0
1
1
0
0
0
0
1
1
0
1
0
2
0
1
0
1
1
0
2
0
0
0
1
1
2
1
0
1
2
1
1
0
1
1
0
2
1
1
0
0
0
0
0
1
2
1
2
0
2
1
1
0
1
2
1
0
0
1
0
1
2
2
1
2
0
1
1
1
0
0
0
0
2
1
2
0
0
0
3
0
1
0
0
0
0
1
1
0
0
1
1
0
0
0
0
2
1
1
0
1
0
0
0
1
0
2
0
1
0
0
1
1
1
1
1
2
0
0
1
1
1
1
0
1
0
2
1
0
0
2
2
2
0
2
2
0
0
1
1
1
1
0
0
0
2
2
0
2
1
2
0
2
1
1
0
1
1
0
1
0
2
2
1
1
0
1
1
1
0
2
2
2
1
1
2
1
0
2
0
1
0
2
0
2
1
1
0
0
1
1
2
0
0
2
1
0
1
1
2
0
1
2
1
2
0
2
1
1
1
0
0
1
0
1
2
1
0
2
0
0
0
0
0
0
1
2
2
1
0
1
0
1
2
1
0
2
5
0
0
0
0
3
0
2
0
0
0
0
1
0
1
1
3
0
0
1
1
1
0
0
0
2
0
1
1
1
2
1
0
0
1
1
1
0
1
0
1
1
0
1
1
0
1
1
4
0
2
1
0
1
1
2
1
0
0
0
1
0
1
1
2
2
0
0
1
1
1
1
2
1
1
0
0
0
0
0
1
0
1
0
0
1
1
1
3
2
2
0
0
0
2
0
7
1
0
2
1
0
0
0
0
1
0
0
1
0
0
2
1
0
1
3
1
1
1
0
1
1
1
0
0
1
0
1
2
1
2
0
1
1
2
0
0
0
2
1
1
0
2
3
0
0
1
1
2
0
0
1
1
1
1
2
0
0
0
0
0
0
1
1
1
0
0
1
2
0
0
0
1
0
3
0
2
0
1
0
0
0
0
1
0
1
1
1
0
0
0
0
2
0
4
0
1
0
0
1
2
1
0
0
1
0
2
2
2
2
1
1
2
0
2
0
2
2
2
1
2
2
1
1
1
1
2
1
0
1
2
0
0
0
1
1
0
0
0
0
1
0
2
2
0
1
1
1
2
0
1
1
1
0
0
2
1
1
1
1
2
1
1
1
0
0
1
1
0
2
0
2
0
2
0
0
0
3
0
1
0
1
0
0
1
2
0
0
0
0
0
1
0
0
2
2
0
1
0
1
1
0
1
0
0
2
1
1
1
0
2
3
1
3
0
0
2
2
2
0
0
1
1
0
1
0
0
0
2
0
1
0
0
0
0
0
2
2
0
1
0
1
0
2
0
1
1
0
0
0
2
1
1
1
1
2
0
2
2
0
0
1
0
1
0
0
0
2
0
0
2
2
2
1
1
2
0
0
0
3
0
0
0
0
0
0
0
2
0
0
1
2
2
0
0
0
0
2
1
1
2
0
1
1
1
0
2
1
1
1
1
2
2
0
2
0
2
1
1
0
2
1
1
1
2
1
1
1
0
0
1
1
1
0
1
1
0
3
1
2
1
0
0
1
0
0
0
1
1
1
1
0
2
0
1
0
0
1
1
1
1
0
0
2
1
1
0
0
0
1
2
0
1
2
1
2
0
0
0
1
0
0
2
0
1
0
0
1
2
1
1
1
2
1
0
1
1
0
0
0
1
2
1
1
1
2
1
2
0
0
0
1
1
2
0
1
2
1
1
1
0
1
3
1
1
1
2
1
4
0
2
1
1
0
1
0
1
2
0
2
1
1
2
1
0
0
0
1
0
2
0
1
0
0
2
2
1
1
1
0
1
1
2
1
0
1
2
0
1
1
0
2
1
0
0
0
0
1
0
1
1
0
1
3
0
4
2
0
1
0
0
1
0
1
0
0
0
0
0
1
1
0
2
0
0
2
0
2
0
0
1
0
1
1
1
1
1
2
1
1
1
0
0
1
0
1
1
0
0
4
0
1
2
0
0
1
1
1
0
3
2
2
1
0
1
0
0
2
1
0
0
0
0
2
1
1
1
1
1
0
2
0
1
1
0
1
2
1
1
0
1
0
2
0
1
0
2
2
2
0
1
2
2
1
0
0
1
0
0
2
1
0
0
2
0
1
2
0
1
0
1
0
1
0
0
2
0
0
1
1
1
1
1
2
1
1
1
2
0
1
0
0
1
0
2
0
0
1
1
0
0
1
1
1
1
0
1
2
1
1
2
0
1
0
2
1
1
0
0
2
0
1
1
2
1
0
0
1
1
0
0
0
1
2
3
2
0
1
1
0
2
2
0
0
0
0
0
1
0
1
1
1
1
1
0
2
0
0
2
2
0
0
1
2
1
0
2
0
1
1
0
2
2
1
1
2
1
2
0
1
3
0
2
1
0
1
0
0
1
1
0
3
1
1
0
2
2
0
0
2
2
0
0
0
4
0
0
2
0
0
1
1
0
1
1
0
2
2
0
1
2
2
0
2
0
2
0
1
0
0
1
1
2
1
0
1
1
0
2
1
2
1
1
1
2
0
1
0
2
1
2
1
2
1
0
0
1
1
1
0
2
0
1
0
0
1
1
0
1
2
2
0
0
0
2
0
1
1
0
1
1
0
2
1
1
1
1
0
0
0
2
0
0
0
0
1
0
0
0
1
1
1
1
4
0
1
1
0
0
2
1
0
0
1
1
1
1
0
2
0
2
1
1
2
1
1
0
1
1
1
1
1
0
0
0
0
1
1
0
0
0
1
1
0
2
0
0
0
2
1
1
0
1
0
1
3
0
0
1
0
2
2
0
0
0
0
0
1
1
0
1
2
1
1
0
0
1
1
3
0
0
1
1
0
2
0
1
2
1
1
1
0
0
1
1
3
0
2
2
0
0
1
1
1
2
1
0
1
2
0
2
0
1
0
2
0
0
0
0
0
2
2
0
0
0
0
1
1
1
2
1
0
5
1
0
0
1
1
1
2
0
0
1
2
1
1
0
2
1
2
1
2
2
2
3
0
0
1
0
0
1
1
1
2
2
0
0
0
1
0
0
0
3
1
2
1
1
0
2
0
0
1
0
0
1
1
3
1
2
0
0
0
0
1
1
1
0
0
1
0
1
2
0
0
1
2
0
2
2
1
0
2
0
1
0
0
1
2
0
0
0
2
1
2
1
1
0
0
0
0
2
2
1
2
1
2
1
2
0
0
1
0
0
2
2
2
1
0
0
3
2
1
0
0
1
1
1
0
2
1
0
1
0
0
1
0
1
0
1
0
0
0
1
0
0
0
2
1
1
1
2
0
2
2
1
0
2
1
1
0
2
1
0
0
1
0
0
1
0
0
1
1
0
1
1
2
1
1
1
1
1
0
1
1
0
1
2
1
0
0
1
1
0
1
0
1
0
0
1
1
0
1
1
1
0
2
0
2
1
0
2
0
1
0
1
2
1
0
2
2
1
2
1
1
0
0
1
0
1
2
0
1
1
0
0
0
0
2
2
0
2
1
2
1
2
2
0
1
1
0
0
2
0
0
0
0
0
0
2
0
0
1
1
2
0
2
0
1
2
2
0
1
0
2
0
2
2
0
0
0
1
2
2
0
1
1
1
0
2
1
1
0
0
1
0
1
1
0
0
1
1
0
1
0
0
0
1
1
1
0
1
5
2
0
0
2
1
0
1
0
2
0
0
0
0
2
1
0
1
1
1
2
0
6
0
0
0
1
0
1
0
0
1
0
2
0
0
0
1
0
1
0
1
1
2
1
1
1
2
1
2
0
0
1
1
0
1
1
0
1
0
0
1
1
2
2
4
0
0
0
0
3
0
0
1
0
1
1
0
2
1
2
1
2
0
0
1
1
0
0
0
0
1
1
1
0
0
2
0
0
1
0
2
1
1
1
2
3
0
0
0
0
1
1
1
1
2
2
1
1
2
2
0
0
1
0
0
1
1
0
1
0
0
1
0
0
2
0
2
2
0
0
0
2
0
0
1
2
0
1
1
2
1
2
8
1
0
0
0
0
1
2
1
2
1
1
0
2
0
1
0
0
0
0
0
2
0
2
0
0
0
2
0
2
0
1
0
0
1
1
0
0
1
2
0
4
2
1
1
0
0
0
1
0
3
0
0
0
1
1
1
1
1
0
1
0
1
2
2
2
1
2
3
1
2
1
2
1
0
0
0
0
0
2
1
1
1
1
1
1
0
0
1
0
0
1
1
2
1
0
0
0
0
0
0
2
1
1
1
1
0
0
0
1
2
0
0
0
2
0
2
2
0
4
1
0
0
2
0
0
0
2
2
0
1
0
2
1
0
1
1
2
1
0
1
1
1
0
1
2
1
0
0
0
1
2
2
1
0
2
1
0
1
0
1
0
0
0
1
2
0
1
1
2
2
2
0
0
0
1
0
0
0
1
1
0
1
1
0
0
1
1
1
0
1
1
2
2
0
1
0
1
0
0
0
1
0
0
1
2
0
2
2
1
0
0
2
2
1
0
0
0
1
2
0
0
1
2
0
1
2
2
1
1
1
1
0
1
0
2
0
1
2
0
0
2
1
1
1
0
2
1
0
0
1
0
1
1
0
2
1
0
1
1
0
1
0
1
2
0
1
0
0
2
1
1
1
1
2
1
0
1
1
0
1
1
2
2
1
0
1
1
1
1
1
3
0
2
1
1
0
2
1
1
0
2
0
0
0
0
0
0
0
1
1
2
1
0
0
0
1
0
0
0
0
0
1
1
2
0
0
2
0
1
2
0
1
2
0
0
1
0
1
0
1
1
1
1
0
1
2
2
2
1
2
2
0
0
1
4
1
1
1
0
0
0
0
1
2
0
1
1
1
0
1
0
2
0
1
1
0
1
2
0
1
1
1
2
1
2
0
2
1
0
0
1
0
2
2
0
0
2
1
2
0
0
3
2
0
2
0
0
1
1
0
1
1
1
1
1
2
0
1
2
2
0
2
1
1
0
2
0
0
0
0
1
0
2
1
0
1
0
0
1
0
1
2
0
2
1
0
3
1
0
1
2
2
0
0
0
1
1
1
1
1
1
0
1
2
1
1
2
0
2
1
0
1
1
1
0
1
2
0
0
0
1
0
0
0
0
2
2
1
2
0
2
2
1
0
1
1
1
0
2
1
2
0
2
2
1
1
1
0
6
0
0
2
1
0
0
2
1
0
0
0
1
1
1
2
2
2
1
2
2
1
1
0
0
0
2
2
0
2
1
1
0
1
1
0
0
1
0
0
1
1
2
1
2
1
2
0
2
2
1
1
2
2
1
2
0
0
0
1
0
1
0
2
2
0
0
0
2
1
0
0
2
1
1
0
2
2
2
1
0
0
3
0
1
0
2
0
0
1
1
0
1
1
1
1
1
0
0
2
1
2
1
2
2
0
1
1
2
1
2
0
0
1
2
1
2
2
1
0
1
1
1
0
0
1
3
0
1
0
2
0
1
0
1
1
1
2
0
0
2
2
0
1
0
0
2
1
1
1
0
1
1
1
0
1
1
1
0
1
0
0
1
0
2
2
0
3
0
0
1
0
1
0
0
1
1
0
0
1
0
1
2
1
1
2
1
2
0
2
1
2
0
1
1
1
1
2
1
1
0
0
0
2
3
1
0
2
1
1
1
1
1
1
2
0
1
0
0
2
1
2
0
1
1
2
2
1
1
2
1
1
4
0
2
0
1
1
0
2
0
0
2
0
0
0
1
1
0
2
1
0
2
1
1
2
0
0
1
1
1
1
1
0
1
0
0
2
2
2
1
2
2
2
0
1
0
1
0
1
0
0
0
1
1
0
2
2
2
2
1
2
0
0
2
0
1
2
1
1
0
2
0
0
1
2
1
0
0
0
2
2
0
1
0
1
2
1
0
0
0
0
0
0
1
1
0
0
1
2
1
0
0
1
0
2
0
0
2
2
0
0
1
0
0
2
1
1
1
0
1
1
0
1
2
0
2
2
1
0
1
2
2
0
0
2
3
0
0
1
0
0
4
0
2
1
0
2
4
0
0
0
1
0
1
0
0
1
0
1
2
2
1
0
0
1
0
5
2
2
1
2
0
1
1
3
0
1
1
0
2
0
0
0
1
1
1
0
0
1
1
0
0
1
0
1
1
0
1
1
1
0
1
0
0
0
2
1
0
0
1
0
1
2
1
0
0
0
0
0
1
1
2
0
2
0
1
2
1
2
1
1
2
1
0
0
0
0
2
1
2
0
2
1
1
2
12
0
1
1
0
2
0
1
0
2
2
0
1
0
0
0
0
0
2
0
1
1
2
0
0
1
0
1
0
1
2
1
0
2
3
1
0
1
1
0
0
0
0
2
1
1
0
1
2
0
1
0
5
2
1
0
0
1
0
0
1
0
0
1
1
0
0
2
0
0
1
0
0
3
0
4
2
2
1
2
2
0
1
0
1
0
1
2
0
2
2
0
0
0
0
0
0
3
0
1
1
2
0
0
0
1
1
1
2
1
2
0
1
1
0
0
0
1
1
0
0
0
2
2
1
1
2
2
1
2
1
2
2
0
0
2
0
2
2
1
1
0
0
1
2
2
1
0
0
0
1
0
0
1
3
0
1
0
0
1
2
3
0
1
0
1
0
0
1
0
1
2
0
0
0
1
1
1
2
1
0
3
1
0
1
1
2
2
0
0
0
1
1
1
0
0
0
0
1
1
1
2
0
0
2
0
1
1
0
1
1
0
1
0
1
0
0
1
2
0
0
1
1
0
0
1
0
0
0
2
0
0
2
1
1
0
3
0
1
1
1
0
0
0
2
0
1
2
1
0
2
0
0
0
0
2
0
1
1
0
1
0
1
0
0
0
0
0
2
1
0
1
1
0
0
2
0
0
2
1
3
1
0
2
0
1
2
0
2
0
2
2
0
0
2
0
1
1
0
1
1
0
3
0
1
1
0
0
2
1
1
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
2
2
0
0
1
0
1
1
0
0
1
0
0
0
0
2
0
1
0
1
1
2
0
1
2
0
2
0
1
1
1
1
0
2
2
1
1
0
0
1
0
3
1
1
2
0
0
4
0
0
0
1
0
0
1
1
1
1
2
0
0
0
1
0
0
2
1
0
0
1
1
1
1
0
1
1
2
1
0
1
1
1
0
0
2
1
1
1
1
2
0
0
1
0
2
1
2
0
0
1
0
0
2
1
0
1
2
1
0
0
0
0
1
1
2
2
1
1
0
1
0
1
0
0
0
0
0
1
2
1
1
0
1
1
0
1
0
0
1
1
1
1
1
1
0
0
2
1
1
0
0
0
0
0
2
0
0
0
1
0
0
1
1
0
0
1
0
1
1
0
0
1
1
0
1
2
0
0
1
0
1
0
1
1
0
1
2
1
0
2
0
0
1
0
0
0
1
0
1
0
0
0
1
1
0
1
1
0
2
1
1
1
1
1
0
0
0
1
1
0
0
1
1
1
1
1
2
0
1
1
2
0
1
3
0
2
1
1
1
1
0
2
1
1
0
0
0
2
0
0
1
0
0
0
1
0
2
0
0
1
0
2
1
2
1
3
2
1
1
1
0
1
1
0
0
0
0
1
0
0
1
2
2
1
1
1
0
0
1
0
1
0
2
1
1
1
0
1
1
2
1
1
0
0
2
2
0
0
0
1
1
1
1
0
0
1
1
1
1
0
2
0
1
0
0
0
2
0
0
1
1
0
1
2
2
1
0
0
1
0
1
0
0
1
0
0
1
1
1
0
0
0
0
2
1
0
1
1
1
0
0
1
2
1
0
1
0
0
1
2
1
0
1
0
1
0
1
0
0
0
2
1
0
2
0
0
1
0
0
1
2
2
0
1
0
2
1
0
1
0
1
0
0
0
0
0
2
1
1
1
1
1
2
0
1
1
1
1
0
0
2
1
1
0
3
1
0
0
2
0
1
3
2
0
0
2
1
1
2
1
2
2
1
0
1
1
2
0
1
1
1
1
1
2
1
0
1
0
0
2
1
2
0
0
1
2
1
0
2
1
2
0
0
0
2
2
1
2
0
0
1
2
1
1
2
0
0
0
1
0
2
0
1
1
1
2
0
1
0
0
0
1
0
2
0
0
0
1
0
1
0
2
0
0
2
0
0
0
1
0
0
0
1
2
0
1
3
0
2
1
1
0
2
0
5
0
0
1
0
2
1
0
0
0
0
1
0
2
2
0
2
0
0
2
1
2
0
0
2
1
0
1
1
0
1
2
0
0
2
0
0
0
0
1
1
2
0
0
0
2
0
2
0
0
0
0
0
1
1
0
1
1
2
0
0
0
1
1
2
2
2
1
0
0
1
2
0
0
0
0
3
0
2
0
2
1
1
1
0
0
0
0
0
1
0
1
0
0
2
0
2
1
1
0
1
2
1
0
1
1
0
1
1
0
0
1
0
0
1
1
0
0
0
1
1
0
0
1
1
0
1
0
1
1
2
1
0
1
2
0
0
2
0
3
1
2
1
1
2
0
0
1
1
0
0
0
1
2
1
1
0
2
1
0
0
0
1
2
1
0
2
1
1
0
2
2
1
2
1
1
2
2
1
0
0
0
1
2
0
0
1
0
1
1
2
1
2
3
1
0
2
1
0
0
0
0
0
2
2
2
0
1
0
3
1
1
0
0
1
3
1
0
3
0
0
1
1
1
1
0
2
0
0
2
2
0
1
0
2
0
0
0
0
1
1
1
0
1
1
2
2
2
0
0
1
1
0
1
0
2
1
0
0
0
1
3
0
1
1
2
2
2
3
0
2
1
1
0
0
0
0
1
0
1
1
1
1
2
0
1
0
1
5
0
0
1
1
1
1
1
0
1
0
0
0
0
0
1
1
0
0
2
0
0
0
1
1
0
1
0
0
1
1
0
0
2
0
1
0
1
0
1
1
1
0
2
1
1
1
0
0
1
2
1
1
0
1
0
0
1
0
1
0
0
1
1
0
0
1
0
1
1
1
0
0
0
2
1
0
1
0
1
0
0
0
1
1
0
1
1
0
1
1
0
0
0
1
0
0
2
1
1
0
1
0
2
0
1
1
2
0
1
2
1
0
1
1
3
0
1
0
0
1
0
2
2
2
0
0
1
2
1
1
0
3
0
1
1
0
1
0
0
1
2
2
1
2
1
1
0
2
2
1
0
0
0
0
2
1
1
2
1
1
0
1
2
1
0
1
1
0
1
1
3
1
1
0
1
2
2
1
1
0
1
0
2
1
0
1
1
1
2
1
2
2
0
1
2
1
2
2
2
1
0
1
0
1
1
1
2
1
0
1
0
1
0
1
2
0
2
0
1
2
1
1
0
2
0
2
1
0
0
0
1
1
2
2
1
2
0
0
1
0
1
0
0
2
0
1
1
1
2
2
2
1
1
0
2
0
0
1
2
2
1
1
1
2
0
2
1
0
1
1
2
0
0
2
2
1
0
1
2
1
1
0
1
1
1
0
1
2
0
0
1
1
2
0
2
1
1
0
3
1
1
0
0
1
0
0
2
0
2
1
1
1
1
2
0
0
1
0
1
0
2
1
1
4
1
0
2
0
1
2
1
1
0
2
0
1
2
1
0
0
0
0
1
1
2
1
2
0
2
1
0
0
0
2
0
0
0
0
0
1
1
1
1
0
2
0
0
1
1
2
1
1
3
2
1
1
1
2
0
1
0
0
0
1
2
2
4
0
1
1
1
0
0
1
2
2
2
1
3
1
1
0
0
1
1
1
0
0
1
2
2
2
0
0
1
2
1
2
1
1
0
0
1
1
0
0
1
0
1
0
1
0
1
3
0
2
1
0
1
0
0
1
0
1
0
1
0
1
1
1
0
1
1
1
0
1
1
2
1
2
1
3
0
0
0
0
0
2
0
1
2
2
0
0
0
1
0
1
2
1
1
0
3
1
2
1
0
0
0
2
2
1
0
0
0
2
0
2
0
0
1
0
0
0
0
0
1
1
1
1
0
0
2
0
0
2
1
1
2
2
1
2
1
1
0
1
1
2
1
2
0
0
2
0
0
2
2
0
2
0
0
1
0
0
2
2
1
0
2
1
0
2
0
0
0
1
3
0
0
2
0
2
0
1
0
0
1
1
0
1
1
2
0
1
1
1
1
2
0
0
0
1
1
0
0
1
1
0
1
2
1
2
0
0
0
0
2
2
1
1
0
2
1
1
1
1
0
1
2
1
0
0
0
0
1
1
1
2
0
0
2
0
1
0
0
0
1
0
1
0
3
1
0
0
0
0
2
0
1
1
1
1
0
2
0
1
1
0
2
0
1
1
2
0
0
1
2
2
0
0
0
0
0
0
1
1
1
1
0
1
2
2
0
0
1
0
0
0
0
0
0
1
2
1
2
2
1
0
1
0
1
0
1
2
1
0
3
1
2
2
1
2
0
2
1
1
0
0
1
0
1
0
0
1
0
1
1
1
2
0
1
0
1
0
0
0
0
1
0
0
0
0
1
1
1
1
0
1
0
1
1
2
1
1
2
0
1
2
1
0
1
0
2
0
2
2
0
0
1
0
0
2
0
0
0
1
0
2
1
1
1
1
1
0
0
0
2
1
1
1
1
0
0
0
1
1
1
1
1
0
1
0
0
2
0
1
1
1
0
2
0
0
2
0
0
2
0
0
0
1
1
1
1
2
0
1
2
0
0
1
0
0
2
0
0
0
1
0
1
1
0
0
4
1
2
1
1
0
1
1
2
0
1
1
1
1
1
3
1
2
1
3
2
2
1
2
1
0
0
2
0
1
1
0
1
1
1
1
1
1
0
1
1
0
1
0
2
1
1
1
2
0
1
1
1
1
0
2
0
0
1
0
1
2
1
0
1
1
0
0
1
0
1
2
2
0
2
0
1
1
1
0
0
0
0
2
2
0
1
0
0
1
0
0
2
0
1
0
0
1
0
0
0
0
0
1
2
1
0
1
2
0
0
2
1
0
0
1
0
2
0
1
1
1
0
1
0
2
0
0
1
3
1
0
0
2
0
1
0
1
0
1
0
2
3
1
1
1
2
0
1
1
0
1
2
1
0
0
1
1
1
0
0
0
0
2
0
2
0
0
1
1
0
2
2
2
1
2
1
0
0
0
0
0
1
2
0
0
1
3
0
1
0
0
0
1
0
2
2
1
0
1
0
2
1
2
0
0
0
1
0
0
1
0
2
1
0
1
0
0
1
0
2
1
1
2
0
0
0
0
1
0
1
2
2
0
0
2
1
0
0
1
0
1
1
0
1
2
2
2
0
1
1
0
0
0
0
1
0
0
0
2
1
0
1
0
0
1
0
2
1
1
1
0
1
0
1
0
1
0
1
2
0
1
1
0
2
1
2
1
0
0
0
3
2
1
0
1
1
2
1
1
2
0
0
2
1
0
0
0
2
1
1
1
1
3
0
1
1
0
3
0
0
0
0
0
0
0
1
0
0
0
1
2
1
1
0
1
0
1
2
2
1
1
1
2
1
0
2
1
0
3
1
1
2
1
0
0
0
2
0
0
1
0
2
1
2
0
1
1
1
0
2
2
0
1
2
2
0
1
1
1
0
1
2
0
1
0
0
0
0
2
2
0
2
2
2
2
1
2
2
0
1
2
0
2
2
1
1
2
0
1
2
0
1
2
0
2
1
0
0
0
1
0
1
1
0
0
1
1
2
0
2
1
2
0
1
1
1
0
0
0
1
0
0
1
2
0
1
2
1
1
2
1
0
2
0
1
1
2
0
0
0
1
1
0
0
0
0
2
2
1
0
0
2
3
1
2
0
0
0
0
0
1
2
0
0
1
0
1
1
0
1
2
2
0
1
2
1
0
0
0
2
0
1
0
2
0
0
1
1
0
1
0
1
1
1
2
2
0
1
3
0
1
0
2
0
0
0
0
1
0
2
0
1
2
1
1
1
0
0
0
2
2
0
1
0
1
1
1
0
0
1
1
0
1
0
0
0
2
1
0
1
2
0
0
2
1
0
0
0
0
1
2
0
1
2
0
0
2
1
1
2
0
1
1
1
0
2
1
1
0
1
1
1
2
2
0
1
0
1
0
0
0
2
0
1
2
1
0
2
1
0
0
0
2
1
1
2
1
0
0
1
0
2
0
0
2
0
0
1
0
0
2
2
1
1
1
0
1
0
1
0
1
1
2
1
0
0
0
1
0
0
1
0
1
2
1
2
0
1
0
0
1
1
2
0
0
1
0
1
1
1
1
2
0
0
0
0
2
0
0
0
0
2
0
1
0
1
2
1
1
1
1
2
0
1
0
0
1
1
1
2
2
0
0
1
0
0
0
0
1
1
2
1
0
0
2
1
1
2
0
1
2
3
1
1
0
2
2
0
2
0
0
1
0
0
1
0
1
0
1
0
0
1
2
0
0
0
2
1
0
2
2
0
0
2
1
2
1
2
2
0
0
1
1
2
2
0
0
0
0
1
2
1
2
1
2
0
1
1
2
0
1
2
1
1
0
1
2
1
2
0
2
1
0
0
2
2
1
1
1
1
1
0
0
1
0
0
1
0
1
0
0
0
2
0
0
0
1
1
2
0
0
0
1
0
0
1
0
0
2
2
1
1
1
0
0
0
0
1
0
1
0
1
0
0
2
0
2
1
0
1
2
0
2
0
3
1
2
0
1
0
1
0
0
2
2
2
2
2
0
1
0
0
0
1
0
1
2
0
2
2
3
2
0
0
0
1
2
0
1
1
2
1
2
1
1
1
0
2
1
2
0
0
1
1
0
2
2
1
0
1
3
0
2
0
2
0
0
0
2
1
2
1
1
1
0
2
3
2
1
2
0
1
0
1
2
0
2
1
1
2
1
2
1
0
1
1
1
0
0
2
2
0
1
2
2
1
1
1
0
0
1
1
1
2
1
0
0
2
1
1
0
0
0
1
2
0
1
1
0
3
0
1
0
1
1
0
0
0
2
2
0
1
0
1
1
1
0
1
1
0
1
0
0
0
1
0
1
2
2
1
2
2
1
0
0
0
1
1
2
1
1
0
0
1
2
1
0
0
0
0
0
0
1
1
2
1
0
1
0
2
1
1
1
0
0
0
2
0
1
1
0
2
0
0
0
0
1
0
0
1
3
0
0
0
0
1
2
0
1
1
3
3
0
2
3
1
1
0
0
1
0
0
0
1
1
0
0
1
0
2
1
0
1
2
1
2
0
3
1
0
3
1
1
0
2
0
1
0
0
3
0
1
0
0
2
1
2
0
1
0
2
0
1
0
0
0
1
1
4
1
1
0
1
1
2
2
1
0
1
0
1
2
0
1
0
0
2
1
0
1
1
2
0
0
2
0
0
1
1
11
0
0
2
0
1
2
0
0
0
1
1
1
1
0
0
0
0
0
0
0
2
1
3
1
0
0
0
1
0
1
0
3
0
1
0
0
2
1
1
1
0
2
1
0
1
2
0
1
3
0
1
0
0
0
1
1
0
2
1
2
0
0
1
0
0
1
1
1
2
1
1
0
0
1
0
0
0
1
0
1
1
0
0
2
0
0
1
2
0
0
2
0
2
4
0
0
0
0
1
0
1
2
0
2
2
0
1
1
2
0
1
1
2
1
1
1
0
0
0
2
0
0
0
2
3
2
0
1
2
0
0
0
0
0
0
1
1
1
0
0
1
1
2
0
0
1
2
1
2
0
2
2
1
2
5
2
1
0
1
0
1
2
1
0
1
0
1
1
0
1
0
2
1
0
0
1
2
0
2
0
0
2
0
1
0
0
2
2
1
0
1
0
1
1
0
0
1
0
0
0
0
0
2
0
1
1
4
0
0
0
1
2
0
0
1
1
0
0
2
0
0
1
0
2
2
2
1
1
0
0
0
0
2
0
2
1
1
1
1
2
1
1
0
1
2
0
0
0
2
1
1
1
1
2
1
1
0
0
2
0
2
2
1
0
1
0
1
1
0
0
1
2
1
0
2
1
1
1
1
1
0
0
1
2
0
2
0
0
5
0
2
3
0
1
2
0
0
1
0
0
1
0
1
0
1
1
0
1
1
0
1
1
2
0
1
0
0
1
0
1
0
1
0
1
0
1
1
1
1
1
0
1
0
0
1
0
0
0
0
1
0
1
1
2
0
0
3
1
1
1
0
1
0
0
1
2
1
1
2
0
2
0
2
0
2
0
1
0
0
2
2
0
1
0
1
1
1
0
0
2
0
1
2
0
2
2
2
1
0
1
0
0
0
0
1
1
0
0
2
1
0
2
0
1
2
2
0
0
2
1
0
2
0
4
1
0
1
0
1
1
0
2
0
1
1
1
0
2
1
1
2
2
1
0
2
1
0
1
1
0
1
1
1
1
2
0
1
0
1
0
0
2
0
1
1
1
2
1
2
2
0
0
1
1
0
1
1
3
1
0
0
3
2
0
0
0
0
1
1
1
2
2
1
0
0
0
0
2
1
0
0
2
1
1
1
0
2
0
1
0
2
2
2
0
0
2
0
1
0
0
1
1
1
1
2
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
10
2
0
1
0
0
0
2
0
0
0
2
0
0
0
1
1
1
1
1
1
2
2
2
0
1
2
0
0
0
1
0
0
1
2
1
1
2
0
1
0
1
1
0
0
1
0
1
1
1
0
0
1
0
1
1
2
1
1
1
2
1
1
1
0
0
2
2
0
0
1
1
0
0
1
0
1
1
1
2
0
1
0
2
4
1
2
3
2
0
2
1
0
2
1
2
1
1
0
2
0
1
1
1
0
0
2
1
1
2
2
0
2
0
1
0
2
1
1
0
2
2
1
0
1
0
1
1
1
0
1
0
0
1
1
0
3
1
0
2
1
0
0
1
3
1
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
1
2
1
2
1
1
0
0
1
0
2
1
1
1
0
0
0
0
0
1
1
2
1
2
0
0
0
1
0
1
0
0
0
2
0
0
2
0
2
1
1
0
1
0
2
1
2
1
0
0
0
2
0
1
0
2
1
1
0
0
1
1
1
2
0
2
0
0
0
1
0
1
0
1
1
0
0
2
0
2
0
0
0
1
1
1
1
1
1
2
0
0
0
0
1
1
0
2
0
0
1
2
1
2
0
1
1
0
0
0
0
0
0
0
2
2
0
1
2
0
2
1
0
0
0
0
0
0
0
1
0
0
1
0
1
3
1
2
2
2
2
1
1
1
1
0
0
2
2
2
1
1
0
1
1
0
1
0
0
2
1
1
3
1
0
0
0
0
1
1
0
1
0
0
2
2
1
0
1
0
0
2
0
0
2
0
0
1
2
1
1
1
0
1
1
1
0
0
0
0
1
3
0
2
1
2
2
2
1
1
0
2
0
1
0
1
0
0
1
0
0
0
2
1
0
1
1
2
0
0
0
0
0
1
0
1
1
1
0
1
2
0
1
3
2
1
1
2
1
2
0
0
0
0
0
0
0
2
1
1
0
1
0
2
0
0
1
0
0
3
0
2
2
2
0
2
0
1
0
2
1
1
1
0
2
1
1
0
1
0
2
1
1
1
1
0
1
1
0
1
1
0
1
2
2
1
1
1
1
1
1
1
1
0
1
0
2
1
2
0
0
2
0
1
2
1
1
2
0
1
1
0
1
2
1
1
0
0
2
0
2
0
2
0
1
1
0
2
0
0
0
2
0
0
2
1
1
0
0
0
2
1
1
1
1
0
1
0
0
1
1
1
0
1
0
0
1
1
1
1
0
2
1
0
0
0
0
1
1
1
0
0
2
4
0
0
1
2
0
0
0
1
0
0
0
2
0
0
0
2
0
1
1
1
1
2
3
0
1
2
1
2
0
1
1
0
0
0
0
0
1
0
2
2
0
1
1
0
0
0
0
0
0
0
1
2
0
2
0
0
1
0
2
1
2
1
2
0
2
2
0
0
1
0
1
0
1
1
1
0
1
2
1
1
0
2
1
0
1
1
2
0
2
1
0
1
0
2
1
0
0
0
0
2
0
1
1
2
1
0
0
1
1
1
1
0
2
0
0
2
2
0
2
0
0
1
2
2
0
0
1
1
0
0
1
2
1
1
1
0
0
1
3
1
1
0
0
1
2
0
0
0
1
0
1
1
0
0
1
0
2
1
1
2
0
2
0
0
0
1
0
0
1
0
0
0
1
2
1
2
2
2
3
0
0
1
1
0
2
0
2
2
0
2
1
0
0
1
0
2
0
0
0
0
0
1
0
0
0
1
1
0
1
0
1
0
0
2
2
0
0
1
0
0
1
1
0
1
1
1
0
1
0
2
2
1
1
0
1
0
0
0
0
1
1
0
0
2
1
1
1
0
3
0
0
0
0
1
2
2
2
2
0
0
2
1
0
1
2
1
1
1
2
2
0
2
1
2
0
2
0
0
0
1
1
0
1
2
1
1
2
1
1
0
2
0
1
1
1
1
1
0
2
1
1
0
1
1
2
1
2
3
0
0
1
2
0
1
0
0
0
0
2
1
0
1
2
1
0
2
1
2
2
1
1
1
1
3
1
1
1
0
2
0
0
0
2
1
2
3
0
1
1
1
1
1
2
0
2
0
1
0
1
1
0
1
1
1
1
2
0
0
3
1
2
2
1
2
2
1
2
0
0
0
1
0
2
1
2
0
1
2
0
1
0
0
0
3
1
0
0
2
1
2
0
0
2
2
0
1
1
0
2
0
0
1
0
0
0
0
2
0
0
1
0
0
1
0
1
1
1
0
1
1
1
0
0
2
1
2
1
2
1
0
1
0
1
1
2
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
1
1
2
2
1
1
1
0
1
1
1
1
0
1
0
0
2
2
1
1
1
0
1
1
0
1
0
1
0
0
0
1
0
1
0
0
1
1
1
1
0
1
1
0
0
0
0
0
1
0
0
0
1
1
0
1
0
3
1
0
1
0
0
0
2
1
0
0
0
1
2
1
2
0
0
0
0
0
1
1
0
2
0
1
0
0
2
1
1
2
1
1
0
2
2
0
4
2
2
0
2
0
0
1
0
1
0
2
1
1
1
1
0
2
1
1
0
0
2
0
3
1
0
0
0
0
1
1
1
2
0
1
2
0
2
1
0
0
1
0
1
2
0
1
0
1
0
1
2
1
0
0
0
0
1
0
2
6
2
0
1
1
3
0
2
1
2
0
0
2
1
1
1
1
0
2
0
1
0
0
1
0
0
0
2
0
1
1
1
1
1
0
1
0
2
1
0
1
1
0
1
2
1
2
2
0
1
2
0
0
0
0
0
2
0
2
1
1
1
1
0
0
1
0
1
0
1
1
1
0
1
1
0
2
0
0
0
0
1
2
2
0
0
0
1
0
1
0
0
2
0
1
0
0
0
1
1
1
0
1
1
1
0
2
0
1
1
3
0
0
0
1
2
1
1
1
0
1
1
2
0
1
0
2
1
0
0
0
4
0
1
0
0
2
1
0
2
1
0
2
2
1
0
0
0
0
3
2
0
1
1
0
3
4
0
0
0
0
2
0
2
1
0
1
1
0
1
0
1
2
0
1
1
1
2
1
2
2
0
1
3
0
0
1
1
2
1
1
0
0
1
1
1
1
1
0
0
2
1
0
0
1
1
0
0
2
1
1
0
1
0
0
1
1
1
1
2
1
0
1
1
1
4
0
1
0
1
0
1
1
0
0
0
1
1
0
1
0
0
0
0
2
0
2
0
0
1
2
0
2
0
1
0
0
2
0
0
0
0
0
2
0
0
1
1
0
0
0
2
1
1
1
0
0
0
0
0
1
2
2
0
2
1
0
3
1
0
2
1
0
0
0
2
1
2
2
1
0
1
0
1
0
1
1
2
1
1
1
0
2
0
1
2
0
0
1
1
2
1
1
0
1
1
1
2
1
0
2
1
1
2
1
1
1
0
2
1
1
2
0
0
1
0
0
1
2
2
0
0
0
1
0
1
0
2
1
0
0
1
3
0
0
2
1
0
0
0
1
1
2
1
0
1
0
0
0
2
1
0
0
1
1
2
2
2
2
0
0
0
1
1
0
0
0
1
0
0
0
0
2
1
1
0
1
0
1
0
1
2
2
0
0
1
0
1
0
0
0
3
0
0
1
1
2
1
1
1
0
2
1
1
1
2
2
2
1
0
0
0
0
2
1
0
0
1
1
1
2
1
0
0
2
0
2
1
0
2
0
0
2
1
2
0
0
0
1
1
2
1
2
1
0
0
1
0
0
1
2
2
1
1
0
2
2
1
0
1
1
2
0
2
2
0
1
2
1
2
2
2
1
2
0
1
1
0
2
2
0
2
0
1
0
0
1
1
0
0
1
1
0
1
0
1
0
0
1
2
1
2
2
1
2
1
0
1
1
1
1
1
0
0
0
0
0
0
0
1
0
2
1
0
1
1
1
0
1
2
2
1
1
0
0
0
0
0
1
0
1
4
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
2
0
2
1
1
0
2
0
1
0
0
0
0
0
1
1
0
0
1
1
0
1
1
0
1
3
2
0
2
0
2
1
0
0
0
0
1
2
0
0
0
0
0
0
0
1
1
2
0
1
1
0
2
2
0
0
0
1
0
1
2
1
2
0
2
0
1
2
1
0
0
0
2
1
2
0
0
1
2
0
1
2
1
2
1
1
0
0
0
0
0
1
1
1
1
0
0
0
1
2
1
2
1
0
0
1
0
1
1
1
0
2
0
2
0
0
0
0
1
1
2
1
0
1
0
0
2
1
0
1
1
1
0
0
1
0
0
1
0
3
3
0
1
1
2
1
0
0
0
1
0
1
0
0
0
2
2
1
1
0
0
1
0
1
2
1
0
2
1
1
0
0
0
1
0
1
1
2
0
2
0
2
0
0
1
1
2
1
0
0
2
0
1
1
0
0
1
2
0
2
0
2
0
0
2
0
0
2
2
5
0
2
0
1
1
0
0
0
1
0
1
2
1
0
2
0
0
2
1
0
0
2
2
0
0
0
1
2
1
1
0
0
0
1
0
2
0
0
0
0
3
1
0
1
1
1
4
0
0
0
0
1
2
1
0
0
0
1
1
1
0
1
1
2
2
1
0
1
1
2
0
0
1
1
0
0
2
2
0
2
1
0
2
0
1
1
1
0
2
1
2
0
0
2
1
0
1
1
0
0
0
2
0
1
2
0
2
0
1
2
1
2
1
1
2
1
1
2
0
3
1
2
2
1
1
0
1
2
1
0
2
1
1
0
1
1
0
1
1
0
2
0
1
0
0
1
1
2
2
0
1
1
0
2
1
0
1
0
2
2
1
2
0
1
1
2
1
0
0
0
1
1
0
0
1
1
0
2
1
1
1
0
0
1
1
1
0
0
0
0
1
1
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
2
2
0
1
2
1
0
1
1
2
1
0
1
2
0
5
0
0
0
1
0
1
0
1
2
1
3
0
2
0
0
1
0
0
1
2
0
1
0
2
0
0
1
1
1
1
0
0
1
1
1
2
0
1
0
2
0
0
0
2
1
0
2
0
0
3
0
0
1
1
0
2
1
1
0
1
2
0
2
1
0
0
2
0
0
2
2
2
2
0
1
3
1
2
0
0
2
1
1
0
0
1
1
1
0
0
1
0
1
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
2
1
1
0
2
0
0
0
1
1
2
1
2
3
1
0
2
1
1
0
0
1
1
2
0
1
0
0
1
2
0
1
0
0
0
1
2
1
1
0
1
1
2
0
0
1
1
1
1
0
2
0
1
1
2
2
0
0
2
2
4
0
1
1
1
1
0
1
1
0
3
2
0
1
1
1
0
0
1
1
0
2
2
1
0
1
0
1
1
1
1
0
1
1
0
0
0
0
0
0
1
0
1
0
0
2
2
1
0
0
1
1
1
2
2
2
1
0
0
2
0
0
0
0
0
0
1
1
0
0
2
2
4
0
0
1
1
0
0
2
0
1
2
0
1
2
0
1
2
0
1
0
0
0
0
0
1
0
1
0
1
1
2
0
1
1
0
2
0
1
1
2
0
0
2
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
2
2
2
1
1
0
0
1
1
1
1
1
2
0
1
1
2
0
0
1
1
2
0
1
0
0
2
0
0
0
0
0
2
0
1
2
3
1
2
0
0
1
0
1
0
0
1
0
2
2
2
1
0
0
1
0
0
0
2
1
0
0
1
0
1
1
2
1
2
1
1
1
1
1
0
1
2
1
0
1
0
3
2
1
2
1
2
1
1
3
0
0
2
0
0
1
0
0
1
2
0
0
1
0
0
2
1
1
0
0
0
1
1
0
1
2
0
1
0
0
0
1
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
2
2
1
0
1
0
1
1
1
0
2
2
0
2
1
2
0
2
1
0
0
0
1
0
1
1
0
1
0
1
1
2
2
0
0
0
1
0
1
1
1
0
0
1
0
0
0
1
1
1
0
0
0
1
0
1
0
1
0
1
2
0
1
1
0
0
0
2
0
1
1
0
1
0
1
1
1
1
2
0
1
3
1
0
0
1
0
0
3
0
0
1
0
2
0
1
0
2
0
1
2
2
2
0
0
0
1
1
0
0
2
0
1
1
0
2
0
3
1
1
1
0
0
0
1
1
0
0
1
0
1
0
1
1
0
2
2
2
1
1
0
2
2
2
0
0
1
0
1
1
1
1
0
1
0
0
2
1
0
1
1
0
2
1
0
1
1
0
1
1
0
2
1
0
2
1
2
0
0
2
0
2
2
0
2
0
1
1
2
1
2
2
0
1
0
1
0
1
2
0
1
1
1
3
2
1
5
0
0
0
2
1
1
3
2
2
1
1
1
2
1
0
0
2
1
2
1
1
0
2
2
1
1
2
1
0
1
1
3
2
1
0
0
1
2
0
1
1
2
0
1
0
1
0
1
1
2
2
0
1
2
1
2
1
1
1
2
0
1
2
1
0
1
1
0
0
1
1
0
0
0
0
0
0
0
2
1
0
0
1
0
2
1
2
0
1
1
1
2
1
0
1
2
1
1
1
0
0
0
1
1
0
1
1
1
0
0
2
0
0
2
1
1
0
1
2
0
1
2
2
1
1
1
2
0
2
0
0
1
0
1
0
2
2
1
0
1
2
1
0
1
0
0
1
0
1
2
2
1
1
1
1
0
1
2
2
1
1
1
1
2
1
0
1
0
2
1
1
1
1
0
2
2
2
2
0
1
2
0
1
2
1
1
1
2
0
0
0
0
1
0
1
0
0
2
0
1
1
0
1
1
0
2
0
2
2
1
0
0
0
1
3
1
2
0
2
2
2
2
0
1
1
1
2
2
1
0
2
1
2
2
0
1
0
1
1
2
1
1
1
2
1
0
0
1
0
2
0
1
0
0
0
1
0
2
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
1
2
3
0
0
2
0
0
0
0
0
2
0
2
0
1
2
0
1
0
1
1
2
1
0
2
1
0
0
2
1
1
1
0
0
0
3
1
0
2
1
2
0
0
2
2
0
0
0
0
0
2
1
1
1
1
0
0
0
1
0
0
2
0
1
0
1
1
0
1
2
1
1
2
0
1
2
0
1
1
2
1
0
0
1
2
1
0
0
1
2
0
0
0
1
1
1
1
0
2
0
0
2
1
1
0
0
0
2
0
1
1
2
1
1
1
0
1
2
1
4
2
2
1
1
3
1
2
1
1
1
1
1
1
0
0
1
0
2
0
0
2
3
0
2
0
1
1
1
1
0
2
1
0
1
2
0
1
0
1
1
0
0
1
0
0
1
0
0
1
2
1
0
0
0
1
1
2
2
1
2
1
1
0
2
1
0
0
0
0
0
1
0
0
1
1
2
0
0
2
1
0
2
1
0
1
0
1
1
1
1
2
0
0
0
2
1
0
2
2
2
0
0
0
2
3
0
0
0
0
0
0
0
0
2
1
0
1
0
1
0
2
1
0
0
0
1
0
1
0
0
2
2
2
0
2
1
1
2
0
1
0
0
0
2
1
0
2
1
0
0
1
2
0
0
1
1
2
0
2
1
0
0
1
0
1
1
1
1
0
1
1
2
2
2
3
1
1
1
0
2
2
1
1
1
2
1
1
0
0
0
1
1
0
2
0
0
0
0
1
0
1
0
1
0
1
0
1
2
0
2
2
2
0
1
0
1
0
1
1
0
0
2
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
2
1
2
1
1
1
2
1
0
2
2
0
1
2
1
1
1
2
0
1
2
2
1
0
0
2
0
2
0
1
2
0
0
0
0
0
1
0
2
1
0
1
1
1
2
0
0
1
1
1
0
0
1
1
2
0
0
0
0
2
1
0
2
2
1
1
1
0
0
2
1
0
1
1
0
0
0
1
0
1
0
0
1
1
1
1
0
0
0
1
1
0
1
2
0
2
3
1
0
2
1
0
0
2
2
2
0
1
0
1
2
1
1
1
1
0
1
1
6
1
2
0
0
1
1
2
0
1
2
0
1
1
2
0
0
0
0
0
1
0
0
1
3
0
5
2
2
2
0
0
0
0
1
2
2
0
1
0
0
2
1
2
0
0
1
1
1
2
0
1
1
0
2
1
2
1
1
0
0
2
2
0
0
1
0
0
0
2
0
0
0
1
1
0
2
1
1
2
2
0
0
2
2
0
1
0
0
2
2
3
0
2
0
0
1
0
1
0
2
0
2
1
1
0
1
1
0
0
0
2
1
2
2
1
0
1
0
0
1
1
1
1
1
1
2
2
0
0
0
0
0
0
1
2
0
0
1
1
0
1
0
1
2
2
2
2
1
0
0
0
3
1
0
1
1
2
2
1
2
2
1
0
0
0
2
2
0
0
2
1
1
2
2
1
1
2
0
1
0
0
0
0
1
1
1
0
0
0
0
1
2
1
0
2
0
1
2
2
0
2
1
0
0
0
1
1
0
0
0
1
0
1
2
1
0
0
0
2
0
1
2
0
2
2
2
1
2
1
0
0
0
0
0
0
0
0
0
2
1
1
0
1
1
2
2
0
0
0
2
2
1
0
1
1
0
0
0
2
1
7
0
2
0
1
2
0
0
1
0
2
1
1
1
2
2
0
0
1
1
1
1
1
0
0
1
1
2
0
0
0
1
2
1
0
0
0
0
1
2
0
1
0
0
1
1
5
3
0
2
0
1
1
1
0
1
2
0
1
0
1
0
1
2
2
1
0
2
1
1
1
0
1
0
0
0
2
0
1
0
1
0
1
1
0
0
0
1
2
0
0
2
0
0
1
0
0
0
0
0
1
0
0
1
2
1
0
0
1
0
1
1
0
0
1
2
0
0
0
1
1
0
2
1
0
1
1
0
0
1
0
0
1
0
0
1
5
2
1
0
0
1
0
0
1
1
2
0
1
1
1
0
2
1
1
0
0
1
1
1
1
2
1
1
0
1
1
2
2
1
2
2
2
0
1
3
2
0
1
0
1
0
0
2
1
0
2
2
0
1
1
0
0
0
2
1
0
1
1
0
0
0
0
0
2
0
0
1
0
2
1
1
1
1
1
0
0
0
2
0
1
0
0
0
1
1
2
1
2
2
2
1
1
1
2
0
1
1
1
1
2
0
0
2
1
1
1
2
5
1
2
0
1
0
1
6
1
2
1
1
1
0
2
1
2
1
1
1
1
2
1
2
2
0
0
2
1
1
1
2
0
0
1
1
1
2
0
1
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
1
1
1
2
2
2
0
2
2
0
0
0
1
0
2
1
1
0
0
2
1
0
0
1
1
1
2
0
0
0
1
0
0
0
2
0
0
1
0
1
1
2
1
1
2
0
0
1
1
0
2
0
0
0
2
0
2
0
0
0
2
0
0
0
2
1
0
2
1
2
2
1
3
0
0
0
1
2
0
0
1
1
0
0
0
1
1
0
0
0
0
2
0
2
2
1
2
2
1
0
2
1
2
0
0
0
1
1
1
2
1
2
2
0
1
1
1
2
0
1
1
7
0
1
1
1
0
0
2
1
0
2
1
0
1
2
3
1
1
1
0
0
1
2
1
1
0
1
0
1
1
0
0
1
1
0
2
1
1
0
0
0
0
1
0
2
0
0
0
0
0
1
0
3
0
0
1
1
1
0
1
1
2
0
0
1
2
1
1
2
1
1
0
1
0
1
2
0
0
0
0
0
0
2
1
1
1
0
2
1
0
1
1
1
0
1
1
0
0
2
1
1
2
0
1
2
0
0
0
2
0
0
2
0
0
0
1
1
1
1
2
1
2
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
1
2
2
0
2
0
0
1
0
0
4
0
0
2
1
0
0
0
1
0
0
2
1
0
1
2
1
0
2
0
1
1
1
1
3
0
0
1
1
0
0
1
1
2
0
1
1
1
1
2
1
0
0
2
2
1
0
0
1
0
2
1
2
0
2
2
1
1
0
0
1
1
0
1
0
0
1
1
0
1
0
0
1
1
1
0
5
1
2
0
2
1
1
0
0
2
1
1
0
1
0
2
2
0
1
1
2
2
2
1
1
1
1
2
0
1
1
0
2
2
0
1
0
1
0
2
0
1
1
1
1
2
1
2
2
0
0
0
2
0
0
0
1
0
0
0
1
1
0
1
1
1
2
1
1
0
0
1
0
1
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
1
2
2
2
2
2
1
1
2
0
0
0
1
1
1
2
0
1
0
0
0
0
2
2
1
0
2
1
1
1
0
2
1
0
2
0
0
1
0
0
1
2
0
2
0
0
0
1
0
0
0
2
1
0
1
0
0
0
0
0
1
1
1
1
1
1
2
1
2
2
1
1
0
0
1
2
0
0
0
1
1
0
1
1
2
2
1
1
0
2
1
0
1
1
2
0
2
1
0
1
0
2
2
1
1
2
1
0
1
0
2
0
1
0
2
0
0
1
1
0
2
1
1
0
0
1
1
0
2
1
1
0
0
1
0
1
0
1
0
1
0
1
2
0
1
0
1
1
0
0
1
1
0
0
1
0
1
0
1
1
0
2
0
0
0
1
0
0
0
1
0
1
0
1
0
3
2
0
0
1
2
2
0
0
1
0
1
0
0
0
1
0
0
1
0
0
2
0
1
0
0
1
2
0
1
2
0
2
0
1
1
1
3
0
0
0
0
2
1
0
1
0
2
0
1
1
0
0
2
0
2
0
0
0
1
0
0
1
0
0
0
1
2
0
0
0
2
1
0
1
2
0
2
1
1
0
0
1
1
1
1
2
0
0
1
0
2
2
0
1
2
1
1
2
0
1
1
0
1
0
2
0
1
0
0
0
0
1
0
2
1
0
1
1
5
0
2
1
0
0
0
0
0
0
2
1
0
2
0
1
0
2
0
1
2
0
2
2
0
1
0
0
0
0
4
0
2
0
0
2
0
1
1
0
0
1
0
1
0
2
1
0
2
2
0
2
0
1
1
2
0
1
2
0
1
2
0
0
0
2
1
1
2
0
1
1
1
1
0
0
0
0
2
0
0
2
0
0
1
0
2
1
2
2
1
1
0
2
1
2
0
0
1
0
0
0
2
0
0
1
2
2
1
1
1
1
2
1
0
2
2
1
0
0
1
0
0
2
2
0
1
2
0
0
2
0
1
0
2
2
1
0
0
1
0
0
0
0
0
0
1
0
0
2
0
1
2
0
1
0
1
0
1
1
1
3
1
0
0
1
1
1
1
0
0
3
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
1
1
0
1
0
0
0
1
2
2
2
0
1
1
3
2
1
2
1
0
2
0
2
1
0
4
0
2
0
1
2
2
1
0
1
0
0
0
2
1
1
1
1
1
1
0
0
0
1
1
1
1
0
0
0
0
0
2
1
1
1
0
2
5
1
0
0
0
1
0
1
0
1
2
1
1
1
0
1
2
1
0
1
0
2
1
1
1
1
4
0
1
2
1
2
1
1
0
0
1
2
0
1
1
2
1
0
0
0
0
1
0
0
0
2
0
2
2
1
0
1
2
1
0
0
0
1
0
1
6
0
0
1
0
2
2
0
0
2
2
1
1
0
3
1
0
1
1
2
1
2
0
1
0
1
0
0
1
0
0
0
0
1
0
1
2
0
1
0
2
0
1
1
0
1
3
0
1
0
1
0
2
1
2
1
0
1
2
1
1
0
2
0
0
1
1
1
1
2
2
2
0
0
1
0
0
2
1
0
1
2
1
0
0
0
1
0
1
1
1
2
3
0
1
2
0
0
0
2
0
0
2
0
0
0
1
2
1
0
1
2
2
0
0
0
1
2
0
1
1
2
2
1
0
0
1
2
2
0
1
1
0
1
0
0
2
1
1
1
1
2
0
1
1
1
1
1
4
0
1
2
0
0
1
2
1
2
2
1
2
0
1
2
0
1
1
0
1
0
1
1
0
0
1
1
2
0
1
1
3
1
1
0
2
0
0
2
1
0
2
2
2
1
0
1
0
1
0
1
1
1
2
1
1
0
2
2
0
0
1
0
1
2
0
2
1
0
1
1
2
3
1
2
1
1
1
0
0
0
2
0
0
0
1
1
0
0
2
0
1
0
1
0
0
1
0
2
3
1
0
0
1
2
1
0
0
2
1
1
0
0
1
0
2
1
3
0
0
1
2
2
1
1
0
0
0
1
0
2
1
0
0
0
0
0
1
2
0
0
0
1
0
0
1
1
0
2
1
1
1
1
1
0
1
1
1
0
0
0
0
0
1
0
0
2
5
1
0
0
1
1
0
0
1
0
2
1
1
1
1
0
0
1
1
1
0
1
1
2
1
0
2
2
4
1
0
0
2
1
0
0
2
0
2
2
4
1
2
2
0
1
2
2
1
2
0
1
0
2
0
1
2
0
1
0
0
1
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
1
1
1
2
0
1
0
0
0
1
1
1
0
1
1
0
0
1
1
0
1
0
0
0
0
0
1
2
0
0
1
0
0
1
1
1
1
0
1
1
1
1
0
1
2
1
2
1
1
2
0
0
2
1
0
1
0
2
1
2
1
0
0
0
2
1
0
0
0
1
0
2
0
2
1
0
2
0
2
2
1
0
1
0
2
0
1
0
1
2
0
5
1
0
1
0
0
0
0
2
0
0
2
0
2
1
1
0
0
0
1
0
2
0
0
0
2
0
0
1
0
0
0
1
1
1
3
0
2
2
0
0
0
1
0
1
0
0
0
2
2
0
0
1
1
0
0
1
0
1
0
0
3
1
0
0
1
1
2
2
0
2
1
2
1
0
0
1
0
0
0
2
2
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
2
0
1
1
1
2
0
1
0
0
1
0
0
1
0
0
2
1
1
2
1
0
0
2
0
1
2
2
0
1
0
0
1
0
2
2
0
3
1
0
2
2
0
2
0
1
1
0
1
1
1
1
1
2
0
8
1
2
0
1
0
2
2
0
3
1
2
1
1
1
0
1
0
3
1
1
0
0
0
2
0
2
0
1
0
0
1
0
0
2
0
1
2
0
1
1
1
2
0
1
2
1
2
0
0
0
2
1
0
1
1
1
0
0
2
1
1
0
0
1
0
1
0
0
2
0
1
1
1
0
0
3
2
0
0
0
0
0
0
2
0
0
0
0
1
2
1
1
1
1
0
1
1
1
1
1
0
1
1
1
2
1
2
0
0
2
1
1
1
2
1
2
0
2
1
1
0
1
0
0
1
1
1
0
0
1
1
1
1
0
1
2
0
0
1
1
0
0
0
1
0
1
0
0
0
1
0
2
1
0
2
0
2
3
1
2
2
0
2
0
0
0
1
1
0
1
2
0
0
2
0
1
1
0
2
0
0
2
0
2
1
2
1
0
1
0
0
2
1
0
0
2
1
0
2
0
1
0
1
0
2
2
2
1
3
2
0
1
0
0
1
1
2
0
1
2
0
0
0
0
2
0
1
0
0
1
1
1
0
2
0
0
0
1
2
0
2
1
0
0
1
0
2
0
0
0
0
0
0
1
0
0
1
2
1
1
0
1
0
0
3
0
0
1
0
0
0
0
0
1
1
2
2
0
1
1
1
2
1
0
1
2
2
0
0
1
1
2
0
0
1
1
1
1
0
0
0
1
2
0
0
0
0
1
0
0
0
2
0
2
1
1
2
1
0
0
0
2
0
1
1
0
1
0
0
1
0
1
0
2
0
0
1
0
0
2
0
3
2
2
1
1
0
2
1
0
1
0
0
2
0
2
2
0
2
1
2
0
2
0
1
1
0
0
0
2
2
0
2
2
1
1
1
0
0
0
0
0
0
1
1
0
1
1
1
2
3
0
0
0
0
1
1
1
0
1
1
1
2
1
1
1
0
1
2
1
1
1
1
1
2
0
0
2
0
2
0
1
0
1
2
2
2
1
1
1
2
1
1
1
0
2
0
0
1
2
0
0
0
1
0
0
0
0
3
2
2
0
2
0
0
1
0
2
0
0
1
2
1
0
2
1
0
0
1
0
0
0
1
0
2
2
2
0
1
2
2
0
0
2
0
0
0
1
0
1
1
2
0
1
0
2
1
2
1
1
1
1
1
0
0
2
3
0
0
1
2
0
0
2
0
0
1
0
0
1
1
1
1
2
2
1
0
2
0
1
2
0
0
0
2
1
1
0
1
1
0
0
0
0
0
1
0
0
1
2
2
0
1
1
1
1
1
2
0
1
1
0
0
0
0
1
0
0
1
1
0
0
1
2
1
0
1
0
1
0
1
1
0
1
2
1
2
0
0
0
1
2
1
0
2
2
0
1
2
1
1
0
1
0
2
0
1
0
2
0
2
1
2
1
2
0
0
0
0
1
0
1
1
1
3
1
0
0
0
0
1
0
2
2
0
0
1
0
1
0
0
0
0
2
2
0
2
0
0
0
2
2
1
2
5
0
1
1
1
2
2
1
2
2
0
1
0
1
2
0
1
0
1
0
0
0
0
0
0
2
1
0
0
0
1
2
0
0
1
0
2
3
1
0
0
1
1
1
1
1
0
0
0
0
1
2
0
2
1
2
0
0
0
1
0
0
0
1
0
1
2
3
1
2
0
2
1
0
2
1
2
0
2
0
1
1
0
1
2
1
1
0
2
0
1
0
1
1
0
0
1
1
0
1
0
0
2
1
0
1
1
1
1
0
0
1
3
0
1
2
0
3
0
0
0
1
1
0
0
0
0
0
0
2
1
0
2
0
1
0
2
1
1
0
1
1
0
0
2
1
0
3
2
0
1
2
0
1
0
1
1
1
0
1
0
0
0
1
0
1
0
2
0
1
1
1
0
0
0
0
1
3
1
1
2
0
1
1
2
1
1
0
0
0
0
1
0
2
0
0
1
1
1
1
2
0
2
1
3
1
1
2
2
0
0
2
1
1
1
0
2
1
2
0
0
3
0
0
0
0
1
0
2
0
0
2
2
1
1
1
1
2
0
2
0
0
0
2
0
0
0
1
1
1
1
0
2
0
0
1
2
2
0
0
2
2
0
2
2
0
2
0
1
0
1
1
2
1
2
0
0
2
2
0
2
2
2
0
0
3
1
1
3
1
0
1
2
1
1
1
2
0
1
0
3
2
1
0
1
3
1
1
2
1
2
1
0
0
0
2
0
1
1
2
0
0
1
1
0
0
1
0
1
0
0
2
1
0
2
0
1
1
2
1
1
0
1
1
0
0
0
1
0
1
0
0
1
0
2
0
2
3
1
0
1
0
1
1
1
1
0
0
1
0
1
1
1
0
1
0
0
2
0
2
2
0
1
0
0
0
0
0
1
2
0
0
2
1
0
1
1
1
1
1
2
0
1
0
1
1
1
2
2
1
0
1
3
0
1
1
0
1
1
1
1
0
5
1
0
1
1
0
0
2
2
1
1
0
1
2
0
0
1
1
1
2
3
0
1
1
1
0
1
2
2
0
0
2
1
0
2
2
6
0
0
1
0
1
1
0
2
1
1
2
2
1
1
2
1
2
2
0
0
2
0
1
1
1
0
3
0
0
2
2
0
0
1
1
0
0
1
0
1
0
1
0
0
0
0
2
2
1
0
2
1
0
0
0
0
0
2
1
0
1
0
0
1
2
1
1
0
2
0
2
0
1
1
0
2
1
1
1
0
0
1
2
0
1
1
2
1
0
0
0
1
2
1
0
1
1
2
2
1
2
0
1
1
2
0
1
0
0
0
0
0
2
1
0
2
1
1
1
1
1
2
1
1
0
0
1
0
1
0
1
1
3
1
0
1
1
0
0
1
1
1
0
0
0
0
1
0
1
2
2
0
2
1
2
2
2
0
1
1
1
0
3
1
1
1
1
0
0
0
2
0
1
1
0
1
0
1
0
0
1
2
2
0
0
2
0
1
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
2
0
0
1
0
1
2
1
0
0
0
0
1
2
0
1
0
2
0
1
1
1
1
2
0
1
1
1
0
1
0
0
0
2
1
1
1
0
0
0
2
0
2
1
0
0
1
2
0
0
0
1
0
0
0
1
1
0
1
2
2
1
1
2
0
0
0
0
1
1
0
2
1
0
0
0
2
0
1
0
0
1
0
0
2
2
0
0
2
1
0
0
0
3
1
1
2
0
4
0
1
2
2
1
1
1
0
0
2
1
1
1
2
0
1
2
1
0
0
1
0
0
2
3
0
1
0
0
0
1
0
0
1
0
1
1
0
0
0
1
0
1
1
2
2
1
1
1
1
0
1
2
0
1
3
0
0
1
0
1
2
0
2
2
0
0
0
0
1
0
0
1
1
1
1
2
0
0
2
2
1
0
0
2
1
0
0
0
0
1
1
0
1
1
1
0
0
1
1
2
2
0
2
1
1
0
0
0
1
1
1
1
2
1
1
0
1
1
1
1
0
1
0
0
2
0
0
1
0
4
0
1
1
0
3
1
2
2
0
0
1
0
2
0
3
1
0
1
0
0
2
0
1
0
0
0
0
2
0
0
1
0
0
0
0
1
2
1
0
3
0
0
1
1
0
1
0
1
0
1
0
1
3
1
1
0
0
2
1
1
1
0
0
1
1
0
2
1
0
0
0
1
1
1
0
0
1
2
1
1
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
2
2
1
2
0
2
0
2
1
0
2
0
0
3
1
1
2
1
1
2
0
0
2
0
2
1
0
2
2
0
0
1
0
1
0
1
1
1
2
0
0
2
1
0
1
0
1
1
1
2
0
0
1
2
1
0
2
0
2
0
0
0
0
1
1
1
0
0
0
1
0
0
1
2
1
0
2
1
0
2
1
0
0
1
1
0
2
0
0
1
1
0
1
0
1
0
0
0
1
0
2
0
0
2
0
1
0
2
1
1
1
0
0
1
0
0
2
0
1
0
1
1
0
0
0
0
1
2
2
2
0
2
1
0
2
0
0
0
0
1
2
2
0
0
0
1
0
0
0
2
0
0
0
0
1
0
1
0
0
2
1
2
0
1
1
0
0
1
1
0
1
0
2
0
2
1
0
0
2
1
1
0
0
1
1
0
0
2
0
0
0
0
1
0
1
2
2
0
1
1
1
0
13
0
1
1
0
0
1
0
1
1
0
0
0
1
0
1
0
2
2
2
1
2
1
2
0
0
0
0
0
2
1
0
1
0
2
1
2
2
0
0
2
0
1
1
1
2
0
2
1
1
1
2
1
0
1
1
1
3
0
0
0
1
1
1
1
2
0
1
2
1
2
0
2
0
0
2
0
0
2
2
1
1
0
1
1
0
0
2
2
0
1
1
1
2
1
2
1
0
1
0
1
0
7
1
0
0
3
0
1
0
0
1
1
3
2
1
2
3
0
0
0
0
2
1
0
0
1
2
2
1
3
1
0
1
2
2
0
0
0
1
1
1
2
0
0
2
0
0
2
0
0
0
0
1
0
1
1
1
1
2
1
2
7
1
2
0
2
0
1
2
1
0
2
2
0
0
2
0
1
1
1
0
0
1
1
1
1
0
0
0
0
0
1
2
0
0
1
1
2
0
1
2
2
0
1
1
2
1
2
2
0
0
0
0
2
2
0
0
0
1
2
1
0
0
2
0
0
2
1
2
0
2
3
5
0
0
1
0
1
0
1
1
1
0
2
1
2
2
0
1
2
0
1
1
0
0
1
1
0
4
0
2
0
2
1
0
0
1
0
1
0
1
3
0
0
2
0
1
1
0
1
1
0
0
1
1
1
1
1
1
0
2
0
0
0
1
2
1
2
0
0
0
0
2
0
2
0
0
1
0
2
0
0
1
1
1
2
0
1
0
2
0
0
2
2
1
0
2
0
0
0
2
0
1
1
0
1
0
0
1
2
1
0
1
2
2
0
0
2
0
1
2
2
2
1
0
1
2
1
1
0
2
1
1
0
1
0
1
1
0
1
1
0
1
1
1
1
2
0
1
0
2
0
0
2
2
1
1
1
1
1
2
0
3
1
0
1
1
0
0
0
1
2
0
1
0
1
2
0
0
1
0
1
0
0
1
0
1
0
1
0
0
1
1
0
2
1
0
0
2
0
0
2
1
2
1
1
0
2
1
1
0
0
1
0
2
0
0
0
1
1
1
0
0
0
1
0
2
1
0
0
0
0
0
1
0
0
0
0
2
1
0
2
0
0
1
0
1
3
2
1
1
2
1
2
0
0
1
0
1
1
1
0
1
0
1
0
0
0
1
1
2
0
1
1
1
0
1
2
1
1
1
0
0
2
0
1
0
1
2
1
0
1
1
0
1
1
0
0
0
2
2
1
1
1
2
1
2
2
1
0
2
1
1
2
0
1
1
0
0
0
1
1
0
2
0
0
2
2
0
2
0
0
1
2
0
1
1
1
0
0
0
1
2
2
0
0
0
2
0
1
2
4
1
0
2
0
1
0
0
2
1
0
3
1
0
0
0
1
2
1
0
0
2
0
2
1
1
0
0
0
0
1
1
0
1
1
2
2
2
0
1
2
0
1
2
0
2
0
1
0
1
0
1
1
0
0
0
0
0
1
0
1
1
1
2
1
1
1
0
2
0
1
2
1
0
0
1
2
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
2
0
0
0
1
0
1
1
1
2
0
1
1
0
1
8
0
0
1
0
0
1
2
2
0
0
1
1
1
0
0
1
0
0
1
1
2
0
0
0
0
0
2
0
1
5
0
2
1
0
0
2
0
0
1
2
2
0
2
1
0
2
0
1
0
0
2
1
0
2
0
1
0
1
2
1
0
0
2
2
1
2
2
2
1
3
2
0
0
1
0
0
1
2
0
0
2
0
0
2
0
0
0
0
1
2
3
1
0
0
0
1
0
2
2
0
0
0
0
1
0
0
1
0
2
0
0
1
1
0
1
3
1
0
2
1
0
1
1
1
1
0
0
0
1
1
2
0
1
1
2
1
2
0
0
0
0
0
1
0
0
0
2
1
2
0
1
2
0
1
1
0
1
0
0
0
0
2
2
1
0
1
1
1
0
1
1
0
0
2
0
0
2
0
1
1
1
2
0
2
0
0
0
0
0
3
1
0
0
1
1
1
0
0
1
0
0
1
1
2
2
2
0
0
1
0
0
2
2
1
1
2
0
1
1
1
0
0
1
2
0
0
2
2
0
2
1
1
0
2
2
0
3
0
1
1
1
1
0
1
1
2
1
2
0
0
2
1
1
0
0
1
0
0
1
0
0
0
0
2
1
0
2
0
2
1
1
0
2
1
1
0
0
2
1
0
1
2
0
0
0
1
0
1
2
1
1
1
0
0
0
1
1
2
0
1
0
1
0
0
1
0
1
1
0
0
1
1
2
0
1
1
0
1
0
2
0
1
1
0
2
2
0
0
0
1
0
0
0
2
0
0
1
2
2
1
0
2
0
1
0
0
1
1
0
0
2
0
2
1
2
2
0
2
1
0
1
1
1
1
2
0
0
2
2
2
0
0
0
2
1
1
1
2
1
2
3
1
1
2
3
2
0
0
1
0
1
1
0
1
0
1
0
0
1
0
2
1
0
0
1
1
1
1
1
0
2
1
1
0
2
1
1
0
1
2
0
0
1
1
1
0
1
0
0
0
1
3
1
1
0
1
1
0
0
1
0
0
0
4
0
0
2
1
0
1
1
0
0
2
0
0
0
0
0
1
0
1
0
0
2
1
0
1
2
2
0
2
1
2
3
0
1
1
0
0
0
0
1
1
1
2
0
0
1
2
0
2
3
0
0
0
0
1
1
0
1
0
2
0
0
0
0
4
0
1
2
2
1
1
0
1
0
0
1
0
1
1
0
0
1
1
1
2
1
2
0
0
2
1
1
1
0
0
0
0
2
1
2
1
0
1
2
0
0
0
0
1
0
2
1
0
0
1
1
2
2
0
0
2
2
2
1
1
0
2
1
0
2
1
4
2
0
0
1
1
1
0
2
0
0
1
2
1
1
2
1
0
0
1
0
0
0
0
1
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
2
1
1
1
3
2
1
1
1
2
2
0
2
1
1
1
0
0
0
0
0
0
1
0
5
2
1
2
0
1
1
0
0
2
0
0
0
0
0
2
1
1
1
2
1
0
2
1
0
0
2
1
1
0
0
0
0
1
0
1
1
0
2
1
0
1
0
0
1
2
2
0
1
1
0
2
1
0
2
1
1
1
0
0
0
0
1
1
1
2
0
0
1
1
1
0
1
0
1
1
1
0
1
0
1
1
1
0
1
0
2
1
1
1
0
1
2
0
0
1
1
0
0
0
0
1
2
1
0
1
0
0
0
1
1
0
0
1
1
0
2
2
1
1
2
1
0
0
0
0
0
2
1
1
0
2
1
0
0
3
0
0
1
1
0
0
1
1
0
0
0
0
2
2
0
1
1
0
0
0
1
1
1
1
1
0
3
0
1
1
2
0
1
1
0
2
1
2
2
0
0
1
1
1
1
0
0
2
1
2
1
2
1
0
0
1
1
2
1
0
1
0
0
2
0
0
0
2
1
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
1
1
0
1
0
1
2
1
3
0
0
0
1
0
2
2
2
2
2
2
1
1
1
1
2
1
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
1
1
1
1
1
0
0
1
1
1
1
1
0
1
2
1
0
0
0
1
0
0
0
0
1
1
1
0
1
1
1
1
0
0
2
1
1
1
0
0
1
0
0
2
1
0
0
0
1
1
0
2
0
1
1
0
2
1
1
1
2
0
1
1
2
0
1
0
2
0
0
1
0
0
0
2
1
1
2
0
0
2
1
0
2
0
1
0
0
2
0
0
0
1
2
2
0
0
2
1
0
2
0
0
2
1
0
0
1
1
1
0
1
1
1
0
1
0
1
2
1
2
0
0
1
0
0
0
0
2
0
0
1
1
0
2
2
1
1
1
1
2
1
0
2
0
1
0
1
0
0
0
1
1
2
2
2
0
2
2
0
1
0
1
0
2
2
0
2
0
0
1
0
0
1
0
0
0
0
0
1
2
2
0
1
1
0
0
1
2
0
0
0
1
2
1
0
1
0
2
0
0
0
0
0
2
2
0
0
0
0
2
2
1
0
0
1
0
1
0
2
0
1
2
1
2
0
0
0
0
1
0
1
0
1
1
1
0
1
0
0
0
2
0
0
0
1
3
0
1
1
2
0
3
1
1
0
1
0
2
0
0
0
2
3
0
0
1
0
1
2
0
3
0
0
0
1
2
1
2
0
2
0
1
0
1
1
1
1
0
0
2
1
0
0
0
1
1
2
1
1
0
0
0
1
0
0
0
0
0
0
1
1
0
1
2
1
1
0
1
1
0
1
1
1
0
0
0
0
0
0
0
1
0
2
1
0
1
1
1
1
0
2
0
1
2
1
0
0
0
1
0
0
0
0
1
1
1
0
2
0
2
0
1
0
0
1
0
0
0
1
2
0
1
0
1
1
0
0
1
2
0
1
0
1
0
2
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
2
2
2
2
2
1
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
1
4
0
1
2
1
1
1
2
4
2
2
1
0
2
0
1
0
0
3
0
1
0
0
0
0
0
1
0
1
1
1
2
0
1
0
0
2
2
1
1
0
0
1
3
0
0
0
2
1
2
0
0
0
0
1
2
2
1
0
0
2
0
1
0
2
0
0
2
2
0
2
0
0
1
1
2
0
0
1
0
0
2
0
0
0
2
0
0
2
0
1
2
0
1
2
0
0
0
0
1
2
0
0
1
1
0
2
3
2
0
1
0
1
0
0
1
0
2
0
0
2
0
1
1
0
1
2
2
2
0
1
2
0
0
0
0
2
0
0
0
1
1
0
0
0
1
0
0
2
2
0
0
2
1
1
1
2
2
1
0
3
0
1
2
1
2
1
2
2
0
1
0
2
0
0
3
2
1
0
0
1
2
0
2
2
1
1
2
2
1
1
3
0
0
1
0
0
3
1
2
0
1
1
1
1
0
1
1
0
2
1
0
1
0
0
0
0
3
1
0
1
0
1
0
0
2
0
1
1
0
1
0
2
0
0
0
0
0
1
0
1
2
0
2
0
1
2
0
1
0
1
0
1
1
0
2
0
0
0
3
1
1
1
1
1
0
1
1
1
1
0
1
1
1
0
1
0
0
0
2
2
3
0
2
1
0
1
0
0
0
2
1
0
1
0
0
0
0
0
2
0
0
0
1
1
1
2
0
1
1
1
1
0
0
0
2
0
0
1
0
0
1
0
0
1
0
3
2
2
0
3
2
1
2
0
1
1
0
0
1
1
1
1
2
1
1
3
0
2
0
0
0
1
3
0
2
0
0
0
0
2
1
1
0
0
1
1
0
0
0
1
0
0
2
0
1
0
0
2
0
2
0
0
1
0
0
1
0
2
2
0
2
0
1
0
1
0
0
2
1
1
1
1
0
0
0
0
0
1
1
0
0
1
2
1
1
2
0
0
2
0
0
0
2
2
2
1
0
0
0
2
2
0
2
0
0
0
1
2
0
1
1
1
1
2
2
0
1
2
2
1
1
2
2
0
2
0
2
0
1
1
2
0
0
2
0
1
1
1
2
0
1
1
2
0
0
0
0
1
2
2
1
1
2
2
1
2
4
1
2
0
2
0
0
0
1
2
1
2
1
1
0
1
2
1
2
1
0
1
0
0
0
2
1
0
1
0
1
1
1
0
0
0
1
1
0
0
1
1
1
0
0
0
0
2
1
0
1
0
1
2
1
1
1
1
1
0
2
0
0
0
0
0
0
0
2
2
0
1
1
2
2
1
0
1
0
2
0
2
2
2
0
0
0
0
0
0
0
0
0
0
2
0
1
1
1
1
2
2
0
3
0
1
0
0
0
2
2
1
0
0
2
0
1
1
2
0
0
0
1
2
1
2
2
0
0
0
1
0
4
2
2
0
1
0
1
2
0
0
2
1
2
2
0
2
2
2
1
0
2
1
2
2
2
0
1
2
0
0
2
0
0
1
1
1
0
0
1
1
2
1
1
0
1
2
0
2
0
0
1
1
0
1
1
0
0
0
1
0
0
1
2
0
1
1
0
0
1
1
2
0
1
1
0
0
0
2
0
1
1
0
2
0
0
1
0
0
0
1
1
0
0
0
0
2
2
2
1
0
3
0
1
1
0
0
0
2
2
0
1
1
2
1
0
2
2
1
2
1
1
2
1
0
0
1
0
2
1
0
1
0
0
1
0
1
1
0
0
0
0
0
0
1
0
2
2
0
1
0
1
1
1
0
0
0
1
2
2
2
2
2
1
0
0
0
0
2
1
0
2
1
0
0
1
1
1
0
0
0
0
0
1
2
1
2
0
1
0
1
0
2
0
0
0
0
4
0
2
1
0
0
0
2
1
0
1
3
2
3
2
0
3
1
1
1
2
0
0
1
1
0
0
2
1
0
0
0
1
1
2
0
1
1
0
2
1
0
1
2
1
2
1
2
2
1
1
1
1
1
1
2
0
1
0
1
1
1
0
0
2
1
2
2
2
1
0
2
0
1
1
0
0
1
1
1
2
0
1
0
0
1
0
1
0
0
2
1
0
1
0
2
1
0
2
1
3
2
0
2
2
8
0
0
0
2
0
0
0
2
0
0
1
0
2
0
2
0
2
0
1
1
0
0
1
0
1
1
1
0
0
1
1
1
1
1
0
1
1
2
0
0
0
0
1
1
1
0
0
2
0
1
1
0
0
0
0
0
0
0
0
1
1
1
2
0
2
2
1
2
1
0
0
0
0
0
0
0
0
2
0
2
1
0
2
1
1
0
2
0
1
0
2
0
1
0
2
1
1
0
0
0
1
1
1
0
1
2
0
0
0
1
0
1
0
0
1
1
3
0
1
2
2
1
0
1
1
1
2
2
1
0
0
0
0
0
1
0
0
1
2
1
0
2
1
1
1
1
1
0
2
0
0
2
2
0
3
1
0
1
0
0
0
0
0
0
1
0
1
1
1
0
0
1
1
1
2
0
0
1
1
1
0
0
0
5
0
0
1
1
1
0
1
1
1
0
2
1
1
0
0
0
2
0
1
2
1
2
2
2
1
2
2
0
0
0
1
0
0
0
1
0
0
2
0
1
1
0
1
0
1
0
2
1
2
1
3
1
2
1
0
2
2
2
0
1
0
1
0
2
1
3
0
3
4
0
1
1
0
2
1
1
0
2
2
0
1
0
2
1
0
0
0
0
2
1
1
1
2
2
1
1
3
0
1
0
5
0
1
2
2
0
0
1
2
2
1
1
0
0
0
1
1
0
1
0
0
0
1
2
0
0
0
1
0
0
0
1
0
1
2
0
2
3
1
0
0
0
0
2
0
0
2
0
1
0
0
0
0
1
0
1
0
2
0
0
2
0
1
0
1
0
0
0
1
2
1
1
2
0
0
2
1
1
0
0
1
0
1
0
1
1
0
2
1
0
1
0
1
2
2
1
0
2
0
2
0
1
1
0
0
1
1
2
0
0
1
0
2
0
1
1
1
1
2
0
0
1
0
1
0
0
2
0
1
1
1
2
0
1
1
1
2
2
0
0
2
0
0
1
0
2
0
1
1
0
0
1
2
2
2
0
0
1
0
2
1
1
0
0
2
2
0
0
0
1
1
0
2
0
1
0
0
0
3
1
0
1
1
0
0
2
2
0
0
0
1
1
2
0
0
0
0
1
1
0
0
1
0
2
0
0
1
2
0
0
2
1
7
0
1
0
0
2
0
0
3
1
2
0
1
0
0
2
1
0
2
0
1
2
0
0
1
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
1
0
2
1
0
2
0
0
1
0
1
0
1
2
0
2
1
2
1
1
2
0
1
0
2
1
0
1
2
2
2
1
2
1
1
1
0
2
1
0
2
1
0
2
2
0
0
2
0
0
2
6
0
2
1
2
2
1
0
0
1
1
1
0
3
1
2
1
0
0
1
0
0
1
2
2
1
1
0
2
1
2
0
0
0
2
1
2
2
0
2
2
0
1
1
1
0
1
0
2
0
0
2
0
2
0
1
2
0
2
1
0
1
0
0
0
2
1
0
2
0
1
0
1
0
0
2
1
2
4
0
2
0
1
0
1
0
0
0
0
0
1
1
0
1
0
0
1
0
1
2
0
0
2
0
0
0
1
0
0
1
0
2
1
1
0
0
1
3
0
1
0
0
0
2
0
0
1
2
1
1
0
1
1
0
0
0
2
2
1
0
2
2
2
1
1
0
0
2
1
1
2
1
0
1
0
0
0
0
1
1
0
1
2
0
1
0
0
0
0
0
1
2
1
0
1
1
0
2
2
2
1
1
1
2
1
0
0
1
0
2
0
1
1
1
2
0
0
2
2
0
0
1
3
1
0
0
0
0
0
1
0
0
2
0
1
0
1
0
0
0
0
1
1
2
1
3
1
1
1
0
0
0
1
1
0
0
0
0
1
0
2
0
0
1
0
0
0
1
0
1
0
0
0
1
1
2
2
0
1
0
1
0
1
2
0
1
2
1
0
0
0
2
1
2
0
0
0
2
0
0
1
1
0
1
2
1
1
0
1
0
2
1
2
2
0
1
2
1
1
1
0
0
1
1
2
1
0
1
0
1
2
1
1
0
1
1
0
0
2
1
2
0
0
1
1
1
1
2
1
0
1
0
0
1
0
1
2
0
2
4
0
0
0
0
1
1
1
1
0
0
0
1
1
1
0
2
2
1
2
0
0
0
0
0
0
2
2
1
1
2
2
0
2
0
2
0
1
1
2
0
1
3
0
1
0
1
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
2
2
0
1
1
2
0
1
0
2
1
0
2
0
0
0
0
0
1
0
1
1
0
1
1
0
2
2
2
0
1
2
1
0
1
0
2
1
0
1
1
0
0
1
3
0
2
1
0
0
0
1
0
2
1
2
0
1
0
2
1
1
0
2
0
1
0
2
1
0
1
1
2
1
1
1
0
1
0
1
1
1
2
0
1
0
1
1
0
1
0
0
0
0
1
2
1
1
0
2
0
0
0
1
0
0
0
0
1
2
2
0
1
1
1
2
0
2
0
1
0
1
0
1
0
0
0
0
0
3
0
0
2
2
0
4
0
2
2
0
1
2
0
1
1
1
1
1
1
1
0
0
1
2
1
1
1
1
1
0
0
0
1
0
0
0
2
1
0
0
1
0
1
0
1
0
2
1
0
1
1
0
2
1
0
3
0
1
2
2
0
1
3
1
0
0
0
2
1
2
2
2
0
0
1
1
0
1
0
3
1
1
0
0
1
1
0
1
1
0
2
1
6
1
2
2
1
0
1
1
1
0
0
1
0
2
0
0
1
0
1
0
0
0
1
1
0
1
1
0
1
1
0
0
1
1
1
0
2
1
0
1
1
1
2
1
1
1
0
2
2
1
1
0
1
3
0
0
0
1
2
1
1
0
1
0
2
0
0
0
0
1
0
0
1
0
1
2
0
2
1
2
0
1
1
0
2
0
0
0
1
0
0
0
1
0
2
0
1
1
1
2
0
2
0
0
0
0
1
2
0
1
1
2
2
1
0
0
2
0
0
0
0
5
2
1
0
0
1
1
3
0
0
1
0
1
0
2
2
2
0
1
2
0
2
0
0
1
1
0
2
1
0
2
2
3
1
0
2
2
0
1
2
2
1
0
0
1
0
1
2
0
2
1
0
1
1
1
0
3
0
2
1
0
2
1
1
0
1
3
1
0
0
0
0
2
0
0
0
0
1
1
1
1
1
0
0
1
0
0
0
0
1
0
1
1
1
0
2
1
0
1
0
1
1
2
0
1
1
1
2
2
0
0
1
2
2
1
2
1
1
0
1
2
1
0
0
1
1
1
1
1
1
1
1
2
0
1
1
1
1
2
0
1
2
0
3
1
0
0
0
0
1
1
1
0
0
2
2
0
0
0
0
2
1
1
0
1
2
0
2
2
0
1
2
0
2
0
0
0
1
1
0
1
0
1
2
2
2
2
0
0
2
2
2
2
0
0
1
0
1
0
2
0
1
0
0
2
2
1
2
1
1
1
1
2
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
2
2
1
0
0
2
2
0
0
1
1
1
1
0
2
1
0
1
1
1
0
1
2
0
0
2
2
2
0
2
0
2
2
0
0
1
0
0
1
0
1
1
1
1
2
1
0
2
2
2
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
2
0
1
0
1
1
2
0
1
0
1
0
2
1
0
1
2
1
0
0
2
0
1
0
2
0
0
0
0
0
2
0
1
1
2
1
0
1
0
1
0
2
1
2
0
0
2
0
2
1
1
2
1
0
0
1
0
0
1
1
1
0
1
2
3
3
1
0
0
0
1
2
0
4
2
0
1
2
0
0
0
1
0
1
1
1
1
0
1
2
2
2
2
2
0
0
1
0
0
0
0
3
1
0
1
0
2
1
2
0
2
2
0
0
1
0
1
2
1
2
0
2
1
1
1
3
2
0
0
0
1
0
2
0
1
2
1
1
0
0
1
1
1
2
1
0
1
0
0
0
0
0
2
0
1
0
0
2
2
2
0
0
2
0
0
1
1
0
0
1
0
1
2
1
0
0
0
1
1
0
2
0
1
2
0
1
2
2
0
1
1
2
1
1
0
1
1
2
0
0
1
0
1
1
1
0
0
0
1
2
1
1
2
0
1
2
2
1
2
1
1
0
2
1
1
0
1
1
2
0
0
0
1
0
1
0
0
1
0
1
1
0
1
0
2
0
1
1
1
0
0
2
2
1
1
0
0
1
0
1
0
1
0
0
0
3
1
1
0
0
0
0
1
0
1
0
1
0
1
2
0
2
0
0
1
0
0
0
2
1
2
1
2
0
1
2
1
0
2
1
1
1
3
1
0
1
0
0
2
2
2
2
2
2
0
0
2
0
1
2
1
1
2
2
1
1
1
0
1
1
0
0
0
2
1
1
1
2
2
2
0
0
1
0
1
1
2
1
1
2
2
1
1
2
2
2
1
0
1
1
0
1
1
2
1
3
2
0
0
1
0
0
1
3
1
1
1
1
0
0
1
0
2
0
0
0
0
1
0
0
0
2
1
2
1
0
2
1
2
0
0
1
0
0
1
1
2
0
0
0
0
1
1
0
0
0
0
0
0
2
1
0
0
1
0
3
1
0
1
0
2
0
1
2
0
0
1
2
1
1
1
1
1
1
0
0
0
0
0
1
1
0
1
2
2
0
1
0
0
1
1
0
2
1
1
1
1
0
0
1
1
0
1
1
2
0
0
2
0
0
0
3
1
0
1
5
0
0
0
1
0
0
2
1
2
1
1
2
0
1
0
1
0
2
0
1
1
1
2
1
0
1
0
2
1
1
1
1
0
2
0
0
0
2
2
1
0
0
1
2
0
0
0
0
0
2
1
0
1
0
1
2
0
0
0
2
0
2
2
1
1
0
1
2
0
0
1
1
0
1
1
0
0
2
1
0
0
0
1
1
1
1
1
1
1
0
1
0
2
0
1
2
0
0
2
0
1
0
1
2
2
0
0
0
0
1
2
2
2
1
0
0
0
2
1
1
0
0
0
2
0
0
0
1
0
1
0
1
0
0
0
0
2
0
1
1
1
0
0
1
0
1
0
1
0
2
2
0
0
2
1
2
0
1
0
1
1
0
0
1
0
2
1
0
0
0
1
2
0
1
1
1
0
1
1
0
1
2
2
1
1
1
0
0
2
1
2
2
0
0
1
0
1
1
0
0
0
0
0
0
0
0
2
1
0
1
1
0
0
0
0
0
0
1
0
2
0
2
0
2
2
2
0
2
1
2
2
1
1
0
2
0
0
1
1
2
2
1
1
0
1
0
2
1
1
3
2
1
0
2
1
2
2
0
2
2
2
2
2
1
1
2
3
0
0
2
0
2
1
1
1
0
1
1
2
1
0
0
1
0
0
0
1
1
0
2
0
0
2
1
1
0
1
2
1
0
1
0
1
2
0
2
1
3
0
1
1
0
1
0
1
0
1
0
2
0
0
0
1
0
1
2
1
0
1
2
0
1
0
1
1
0
1
4
1
2
2
0
0
2
1
1
0
2
0
0
0
2
1
0
0
0
0
0
2
5
3
1
0
0
2
0
1
0
1
1
2
1
1
0
2
0
1
2
1
0
2
0
1
1
0
0
0
0
1
1
2
1
1
1
0
0
0
0
0
0
2
1
1
0
0
1
1
1
0
0
1
0
0
1
1
2
1
2
0
1
0
0
0
2
1
0
2
1
1
2
0
0
2
0
2
0
1
1
0
1
0
0
0
2
2
0
2
2
1
1
0
2
0
2
0
2
1
1
0
2
0
0
1
2
2
2
0
0
1
2
0
1
0
0
0
0
2
1
1
1
1
2
0
0
0
2
1
1
0
1
2
2
0
1
0
2
0
2
2
1
0
1
2
0
0
0
0
0
7
0
0
1
0
1
2
0
1
1
1
1
1
1
2
0
0
1
1
0
1
1
1
2
0
1
1
0
0
2
1
1
1
0
0
0
0
0
0
1
2
2
2
2
0
2
1
0
0
1
0
1
1
0
2
2
1
1
2
0
1
0
2
0
2
1
2
2
0
2
1
2
2
2
1
0
1
0
0
2
1
0
1
2
1
2
1
1
2
0
2
1
2
0
0
1
0
0
0
0
0
2
0
0
0
1
1
0
1
0
1
2
0
1
0
1
0
0
2
1
0
2
1
1
0
1
0
1
0
2
1
1
2
1
0
0
0
0
3
0
2
1
2
1
1
1
1
1
1
1
0
1
0
2
1
0
1
1
1
0
2
2
2
1
0
2
0
1
2
1
0
0
2
0
1
1
1
1
0
2
2
1
0
0
2
0
1
1
1
0
1
1
1
2
1
1
1
0
2
0
2
1
2
0
0
1
1
0
2
2
0
2
1
1
0
1
0
1
0
1
1
0
0
0
0
1
0
0
1
1
0
1
1
2
2
1
1
2
0
2
1
0
0
1
0
0
2
2
2
0
1
0
0
1
0
1
2
1
1
1
2
0
2
0
3
2
1
0
1
2
0
0
2
6
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
2
1
2
1
0
2
0
2
1
2
2
2
1
1
0
1
0
1
0
0
0
2
2
1
1
1
0
2
2
2
2
0
0
0
1
1
1
2
0
0
1
1
0
1
1
1
0
0
1
0
1
3
0
2
1
1
0
1
1
1
0
0
1
0
3
2
2
1
0
1
0
1
0
0
2
0
0
2
1
3
0
0
1
0
1
1
1
0
1
3
3
1
0
2
1
2
0
1
1
0
2
0
1
0
0
1
0
1
0
1
2
1
0
1
1
0
0
0
0
2
1
0
0
0
0
0
0
4
0
0
0
1
1
0
0
2
0
0
1
0
0
0
0
0
1
1
2
0
1
1
1
1
0
0
2
1
2
1
2
2
0
1
0
0
0
2
0
0
1
0
1
1
0
1
0
1
1
1
2
0
0
0
2
0
1
3
1
2
0
2
0
1
0
2
2
2
2
2
3
1
2
0
1
1
0
1
1
0
0
0
0
1
0
2
2
0
2
2
0
0
0
2
0
1
2
2
1
2
2
2
1
0
1
1
0
2
2
0
1
1
2
1
2
0
2
2
1
0
0
0
2
1
2
0
2
2
0
8
0
1
0
0
2
0
0
0
0
2
0
4
0
0
0
2
1
0
0
0
1
0
1
0
0
2
0
0
0
0
1
1
0
0
0
2
0
0
2
0
1
0
0
0
1
1
1
1
0
1
0
0
0
0
0
1
0
2
0
2
0
1
2
0
1
2
0
1
0
3
0
1
1
1
0
3
0
0
2
2
0
2
2
0
2
0
0
0
0
0
3
1
0
0
2
1
1
1
0
0
1
1
2
0
0
1
0
1
0
0
2
1
0
2
0
1
1
0
2
0
0
0
0
0
0
1
0
0
2
1
1
1
0
1
2
1
2
0
2
0
0
0
1
2
6
0
1
0
0
1
1
0
0
2
1
0
1
0
1
2
0
0
0
0
2
1
1
1
1
2
1
1
0
1
2
1
1
0
2
1
2
0
0
0
0
2
1
1
1
1
1
0
1
0
2
2
0
1
2
0
1
0
2
1
1
1
0
0
0
2
0
2
0
1
0
0
0
0
0
0
3
0
0
1
1
0
0
1
2
1
1
1
0
0
0
0
1
0
0
2
1
1
0
2
0
1
0
0
0
1
2
1
0
0
2
1
1
0
1
1
2
2
1
1
0
0
1
0
2
1
0
2
1
1
0
0
3
2
2
0
0
1
1
1
2
0
3
1
1
0
1
1
2
1
0
1
1
0
1
1
1
0
1
0
0
0
0
1
0
0
1
2
0
2
1
1
0
0
2
3
1
0
1
3
1
2
1
2
1
1
0
0
1
1
1
0
1
1
2
0
0
2
2
2
2
2
2
3
2
1
0
2
1
0
1
2
0
1
0
0
1
1
0
1
0
0
1
0
2
1
1
0
1
0
0
0
0
2
0
1
0
0
0
0
2
1
0
1
0
1
2
0
0
2
2
2
1
4
0
1
0
0
1
0
0
0
2
0
0
1
1
1
0
1
2
1
0
0
5
0
0
1
2
0
0
2
2
0
0
2
1
1
1
0
1
2
1
1
1
0
0
1
1
2
0
2
0
0
1
0
2
1
1
0
2
1
0
1
2
2
0
2
2
2
0
1
0
0
1
1
1
1
0
1
2
1
0
2
0
1
0
0
2
0
0
1
2
1
2
1
2
1
0
1
0
2
1
2
2
0
1
0
0
1
1
0
3
0
0
0
2
0
0
2
2
0
1
0
0
0
1
1
2
1
1
1
1
1
2
0
1
1
1
0
2
0
1
0
0
1
1
0
0
1
1
0
0
1
0
0
2
0
2
0
0
0
1
2
2
0
1
1
0
0
1
1
2
1
1
3
1
1
1
1
0
0
1
2
0
0
0
1
1
1
2
1
1
2
2
0
1
1
0
0
0
2
0
1
1
1
0
0
0
1
0
2
2
2
0
1
1
1
1
0
0
1
1
1
1
1
2
0
0
1
0
0
2
2
0
0
0
0
2
2
0
0
0
0
1
0
1
0
0
1
2
1
1
2
0
0
1
2
0
1
2
2
2
2
1
0
1
1
0
1
7
0
1
0
2
1
2
0
1
1
0
2
1
1
2
1
3
1
0
2
1
2
0
0
1
1
0
0
1
1
0
2
0
0
2
0
1
1
1
0
2
1
1
0
0
2
1
2
1
2
0
1
2
1
1
0
1
1
1
1
1
1
0
0
2
0
2
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
2
2
1
0
1
1
0
0
0
1
0
2
0
2
0
1
2
2
1
0
2
0
0
3
1
1
1
2
0
1
1
1
2
0
1
1
1
1
2
1
0
0
1
1
1
1
1
0
2
1
1
1
1
1
1
0
0
1
1
0
0
1
2
0
0
0
1
1
0
1
1
1
0
0
2
0
0
1
1
0
1
2
0
1
1
2
1
24
3
1
0
2
4
1
0
0
0
0
0
1
0
1
1
1
1
0
0
1
0
0
0
2
1
1
0
0
0
1
2
0
1
0
0
1
1
1
2
0
2
0
0
2
1
0
0
1
0
0
0
0
0
2
0
1
0
2
2
0
4
2
1
0
1
2
1
3
1
1
1
1
0
1
2
2
0
1
0
1
0
1
2
1
1
0
1
1
1
1
0
0
1
0
1
1
1
2
1
1
1
1
0
1
0
0
2
3
2
2
1
1
0
0
0
0
0
1
0
0
2
1
2
1
1
2
2
2
1
1
1
1
0
1
0
1
2
1
1
1
1
2
2
0
1
1
1
0
0
0
0
2
3
2
0
1
2
0
1
0
2
0
1
0
0
0
0
0
2
0
0
1
0
1
1
0
0
0
0
0
2
1
0
1
1
1
0
0
0
1
0
0
1
2
1
0
2
0
2
0
0
1
0
2
1
2
0
0
1
0
0
2
0
0
1
2
0
0
2
1
2
0
0
1
1
2
0
1
0
0
1
0
1
0
1
0
2
1
1
0
0
1
1
1
1
2
0
2
0
0
1
0
1
4
1
1
0
1
1
2
0
1
2
0
0
1
0
0
1
0
2
1
1
1
0
1
1
0
1
1
1
2
1
1
1
0
0
1
2
2
0
1
0
2
0
1
1
0
2
1
2
0
0
0
2
1
0
2
1
2
2
1
1
2
1
1
2
0
0
2
2
1
2
3
0
0
0
1
0
2
2
1
1
1
1
0
0
0
1
0
1
0
0
2
0
1
1
2
1
0
0
0
0
0
0
1
0
0
2
1
2
0
1
0
0
1
1
1
0
1
2
1
2
0
1
1
1
3
1
1
1
0
0
1
1
1
0
2
1
1
0
0
2
1
0
1
2
1
2
2
2
2
1
0
1
1
2
0
1
2
0
0
0
1
0
2
0
1
2
1
0
1
0
1
0
2
1
1
0
0
0
2
1
2
0
0
3
0
1
0
0
2
1
0
1
0
0
1
0
0
2
1
0
1
0
2
0
0
1
0
0
0
0
0
0
2
0
0
2
2
1
0
2
1
0
0
2
0
2
2
2
0
4
1
2
1
1
0
1
0
2
1
1
0
2
0
0
0
1
0
0
0
1
0
2
0
1
0
1
0
1
1
2
0
2
1
1
2
1
0
2
0
2
1
0
2
0
1
0
2
2
0
0
0
1
1
2
0
1
2
1
1
0
0
2
1
1
1
0
0
0
1
0
1
1
1
0
2
0
2
4
0
0
1
0
0
0
0
2
0
0
2
1
3
0
0
1
1
0
0
1
0
1
2
2
0
2
1
0
1
1
0
0
1
0
0
1
0
0
0
2
0
1
2
0
0
0
0
1
1
2
1
1
2
0
0
1
2
1
2
1
1
1
1
0
0
3
0
2
0
0
3
2
1
1
0
1
1
0
2
1
1
0
1
0
1
1
2
0
1
0
1
0
1
0
0
1
1
0
2
1
2
3
1
0
0
2
2
0
0
1
2
5
0
1
0
0
0
0
1
0
0
0
0
1
2
1
0
1
1
0
2
1
1
2
0
2
1
0
1
1
2
0
2
0
0
0
1
2
2
0
1
0
2
2
1
0
0
1
0
0
0
0
2
0
2
2
2
1
1
0
0
0
1
0
0
1
2
0
2
0
2
2
2
1
1
0
1
0
0
0
0
2
0
0
2
1
0
0
2
1
0
0
1
0
0
2
0
1
0
0
0
1
1
2
1
2
1
0
1
0
1
1
1
2
0
0
0
0
1
2
4
0
0
2
1
1
1
1
1
0
0
1
0
2
1
1
0
0
1
0
1
1
0
2
1
0
0
0
1
2
0
0
0
0
2
2
1
0
4
2
2
0
0
0
1
1
1
0
1
0
1
2
0
1
0
2
1
0
0
0
2
2
0
0
0
1
0
1
1
1
0
2
1
0
2
2
0
2
0
0
0
2
1
2
1
1
1
1
1
0
0
0
1
0
2
0
1
1
2
0
2
0
0
2
1
0
1
1
4
2
1
0
1
1
1
1
2
1
0
2
0
1
0
1
1
0
0
0
2
1
1
0
2
0
0
1
1
1
0
0
0
1
1
1
1
1
1
2
2
1
1
1
0
0
0
1
1
0
2
0
2
0
0
0
0
3
0
0
1
0
0
2
2
1
3
0
0
0
0
1
2
0
4
0
2
1
1
1
0
1
0
0
1
1
1
0
1
0
0
0
1
2
1
1
0
0
1
1
2
1
2
1
1
2
0
1
0
1
3
0
2
2
1
0
2
2
1
2
0
1
0
0
0
0
2
1
2
2
1
1
0
2
2
0
0
0
1
0
0
0
1
3
2
1
0
1
0
0
1
2
1
0
1
0
0
0
1
2
0
1
1
1
0
0
0
2
0
0
0
0
0
1
1
2
1
1
0
2
0
1
1
1
1
0
0
2
1
0
0
2
1
2
1
1
1
0
1
0
1
2
0
3
2
2
2
0
1
2
2
2
0
1
0
0
0
2
0
0
1
1
1
1
1
1
0
0
0
1
1
2
1
0
2
0
0
1
0
0
1
0
1
1
0
1
0
2
1
1
1
1
2
1
0
1
0
2
1
1
1
1
0
1
0
2
2
1
1
1
1
1
1
0
1
2
2
3
0
1
0
0
0
1
1
0
1
0
1
1
1
1
1
1
0
1
0
0
1
0
1
0
0
1
0
1
0
1
1
1
2
0
3
2
0
1
1
1
1
2
0
0
1
0
0
1
0
0
1
0
0
1
2
0
2
3
1
0
1
0
0
0
1
0
1
2
0
0
1
1
0
1
1
0
1
1
0
0
3
0
1
0
2
1
1
2
0
3
5
1
2
1
1
1
0
2
2
1
1
1
1
1
2
0
2
0
0
0
1
1
2
0
0
0
1
1
2
0
0
1
2
2
1
1
0
0
0
2
0
1
2
0
1
0
0
0
1
0
0
2
0
0
1
2
2
2
1
1
0
3
0
2
2
0
0
1
0
2
1
0
0
0
1
0
3
0
0
3
1
1
1
0
1
0
0
1
0
1
1
0
0
1
1
0
0
1
1
2
1
2
1
2
1
5
0
0
0
1
3
1
1
0
0
0
2
2
2
2
1
2
0
0
1
0
0
0
1
0
2
1
1
1
3
0
0
1
1
1
0
1
2
0
0
1
0
0
1
0
0
2
0
1
0
1
1
2
0
2
1
0
1
0
0
0
2
0
0
1
2
2
2
1
1
1
1
1
0
0
0
1
0
0
1
1
0
2
2
1
0
1
0
0
1
1
1
0
1
1
3
0
4
2
0
0
0
1
1
0
1
0
0
0
2
1
2
2
1
0
1
1
0
1
1
1
1
1
1
1
0
2
3
3
0
1
0
1
1
0
0
0
1
1
1
0
0
2
0
0
1
1
2
1
0
0
0
1
2
1
0
1
0
0
0
3
0
2
1
1
2
0
2
2
1
2
0
0
2
0
2
0
1
0
0
2
0
1
0
1
0
0
2
1
2
0
0
0
2
2
2
1
1
1
2
2
1
1
1
0
0
0
1
0
0
2
2
2
0
1
0
2
2
2
0
1
1
2
1
2
1
2
2
3
2
1
0
1
1
1
0
1
0
1
0
0
0
1
0
1
1
0
1
0
1
1
2
0
2
0
1
1
1
0
0
2
2
2
1
1
1
2
0
1
0
1
0
1
1
2
1
0
1
2
0
2
2
0
1
2
0
1
1
1
2
0
2
2
1
3
0
1
2
0
0
1
2
0
2
1
1
1
1
1
0
2
0
1
0
0
1
0
1
2
0
1
0
0
0
0
0
0
0
0
0
2
1
1
1
1
6
2
1
2
0
2
0
2
1
0
1
0
1
0
0
1
0
2
2
0
0
0
1
0
0
0
1
0
1
2
1
1
3
1
1
2
1
0
1
2
2
1
1
2
2
1
1
1
0
0
0
1
2
0
1
2
0
0
2
1
1
2
0
0
0
2
0
0
2
1
1
2
1
0
2
0
1
1
1
1
2
2
2
1
1
0
1
1
1
2
0
0
1
0
1
0
0
0
0
0
2
0
0
0
1
2
0
2
0
3
1
1
2
2
0
1
0
0
0
1
1
2
1
0
0
1
2
1
1
2
2
1
1
2
0
1
0
1
0
0
0
2
0
0
1
1
1
0
1
0
0
1
0
0
1
1
1
1
0
0
2
0
1
1
1
0
0
0
1
1
1
0
1
0
1
0
0
0
0
0
1
1
1
0
2
1
2
1
2
1
2
2
0
0
2
0
0
2
2
1
2
1
2
0
1
1
1
0
1
1
0
1
1
2
0
1
2
0
0
0
0
0
2
0
1
4
0
2
0
0
2
2
2
1
0
1
0
1
1
1
2
1
1
0
1
0
2
1
1
0
0
1
1
1
0
2
0
0
0
2
0
1
1
2
0
2
1
2
1
0
2
1
0
0
0
2
2
0
0
1
1
1
0
1
1
1
1
1
0
0
0
0
1
1
1
1
1
2
0
0
1
0
0
2
1
0
2
1
2
0
1
0
2
0
1
1
0
0
2
1
1
2
2
1
0
0
2
0
1
1
2
1
0
0
0
1
2
0
3
2
1
1
0
0
2
0
1
0
0
1
0
0
2
1
0
1
0
1
0
2
6
1
1
0
2
0
1
1
0
2
4
1
1
2
2
2
2
2
2
1
1
1
0
2
1
1
0
0
1
0
1
0
2
1
0
0
1
1
2
1
2
0
0
1
0
2
1
1
1
1
1
0
1
0
0
1
2
0
0
1
0
1
0
0
1
1
1
1
0
2
2
0
0
0
0
0
5
0
1
2
0
1
0
1
2
2
2
0
0
1
2
1
1
2
1
1
0
0
1
1
0
0
0
0
0
0
0
0
2
2
0
2
0
0
1
2
1
0
0
0
0
0
2
0
2
0
1
1
1
0
1
0
0
2
2
0
0
0
1
2
1
1
0
1
0
0
1
1
0
0
1
0
2
2
2
0
3
2
0
0
1
0
1
0
1
2
1
2
1
0
1
0
0
1
0
2
0
0
1
0
0
0
0
0
2
1
2
1
1
0
0
0
2
2
1
0
2
1
1
0
0
1
0
2
1
0
0
0
0
0
1
1
1
0
1
1
1
0
1
2
0
1
1
1
0
1
2
0
0
0
1
1
1
0
1
2
0
0
1
1
2
0
2
1
1
0
2
0
0
1
2
0
1
0
2
2
0
1
0
1
0
2
2
0
0
0
1
1
1
1
2
1
0
1
0
0
1
2
1
2
1
2
1
1
0
1
1
0
1
0
0
0
0
0
1
1
1
1
2
0
1
2
2
0
2
1
1
2
0
1
1
1
0
0
1
0
1
1
2
1
0
0
2
2
0
2
0
0
2
0
0
2
1
1
1
1
1
3
2
1
0
1
2
1
1
0
0
0
0
1
2
1
1
2
0
2
0
0
1
0
2
0
1
1
1
1
1
0
1
1
1
1
1
0
2
1
2
0
1
1
0
2
2
1
1
0
2
0
1
0
0
2
1
2
0
1
1
0
1
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
1
2
1
1
0
0
1
2
0
1
2
1
0
1
0
2
2
0
1
3
1
0
2
1
1
0
0
1
1
1
0
1
1
1
1
2
1
3
0
1
1
2
0
2
0
0
1
0
1
2
0
1
0
1
0
0
1
3
1
1
2
2
2
1
2
0
1
1
0
1
0
0
0
0
0
0
0
2
1
0
2
0
2
2
2
1
0
1
2
0
1
1
0
0
0
0
0
0
0
1
2
0
0
1
0
1
2
0
0
0
1
1
0
0
0
9
2
0
2
0
1
0
1
0
1
0
1
0
0
2
0
1
0
0
0
1
0
1
0
2
2
0
0
0
0
2
0
0
2
0
1
1
0
0
1
1
1
0
2
0
0
0
0
1
1
2
2
1
1
0
3
2
0
2
3
1
1
2
0
0
1
2
0
0
0
0
0
0
2
0
1
0
1
0
0
2
2
0
0
1
0
1
0
1
0
1
1
0
0
1
2
2
0
2
1
1
1
0
1
0
1
1
1
0
0
0
0
0
1
1
0
1
0
1
0
0
0
1
1
1
0
1
0
0
1
0
2
0
0
1
0
0
4
0
1
3
0
0
0
1
2
0
2
2
1
0
1
2
2
0
0
0
0
1
1
0
1
1
0
2
0
0
1
2
2
1
1
0
0
1
1
0
0
0
0
0
1
0
1
2
0
2
1
0
1
2
2
0
0
1
1
0
1
1
0
1
0
0
0
0
0
1
0
1
0
2
0
2
1
0
0
2
2
1
2
1
1
1
0
0
1
2
0
0
1
1
1
2
1
0
1
1
0
1
1
1
0
1
1
1
0
2
1
1
1
0
2
1
1
2
0
2
2
1
0
1
1
1
2
0
0
1
2
1
1
1
0
0
0
0
2
0
0
1
1
1
0
0
1
1
1
0
3
1
1
0
1
0
2
2
2
1
0
1
1
0
1
3
1
0
0
0
2
1
2
2
1
1
1
3
0
0
0
1
0
2
1
2
1
0
0
1
1
1
1
0
2
2
0
1
1
1
1
1
1
2
2
0
1
1
1
3
0
1
0
1
1
2
2
0
2
0
1
2
0
2
0
0
0
2
1
1
2
0
1
0
1
0
0
1
0
1
1
0
2
0
1
1
1
0
1
0
1
0
1
0
0
1
1
1
0
1
2
1
0
1
1
1
2
1
0
1
2
0
2
0
2
0
1
2
0
0
0
0
1
2
3
0
0
1
0
0
2
3
0
1
0
0
2
0
0
0
1
0
1
1
3
0
0
0
0
0
1
1
2
0
0
1
1
1
0
1
0
2
0
0
0
1
1
0
1
1
1
1
0
1
0
2
0
1
0
1
0
0
1
2
1
0
0
1
2
1
2
0
2
1
0
1
1
2
1
0
1
1
0
2
2
0
1
2
1
1
1
1
1
0
0
1
0
1
0
2
2
1
0
1
1
0
2
1
0
0
1
1
1
1
0
1
3
1
1
0
2
0
0
0
2
0
0
0
1
2
2
1
0
1
3
1
0
1
2
0
0
0
2
0
2
1
1
0
0
1
1
1
0
0
0
0
2
1
1
1
0
0
1
0
1
0
3
0
1
3
2
0
1
0
0
2
2
1
1
1
1
0
1
0
3
1
1
2
0
0
1
2
2
1
0
0
1
0
3
2
0
2
0
0
0
2
1
0
1
1
0
0
1
0
0
0
1
1
0
1
0
2
2
0
3
2
1
1
0
2
0
0
1
1
1
2
0
2
0
0
0
2
2
1
1
1
1
1
0
0
0
0
1
2
0
1
1
0
0
1
3
0
1
0
2
0
0
1
2
1
1
0
2
0
1
0
2
1
1
0
1
1
0
1
0
1
2
1
1
0
1
0
0
0
0
1
0
0
1
1
1
1
2
1
0
1
2
1
1
1
0
2
1
0
0
0
0
0
0
1
0
1
0
1
0
2
0
0
2
0
0
0
1
0
2
3
0
1
2
1
1
1
1
2
0
2
2
2
0
0
2
0
0
2
1
1
0
1
0
0
0
1
0
1
0
0
0
1
2
1
0
1
1
0
0
0
0
0
1
1
2
1
1
0
0
2
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
2
0
1
2
1
1
2
2
2
2
0
2
0
1
1
1
1
2
1
3
1
1
0
1
0
0
0
1
0
0
0
0
2
1
0
0
1
1
0
0
0
0
1
0
1
2
2
1
2
1
0
0
0
2
2
1
0
0
0
0
1
1
2
0
0
0
0
0
0
1
1
1
2
1
1
1
1
0
1
1
0
2
1
1
1
0
0
0
1
0
0
2
2
2
1
1
1
0
2
2
0
0
0
2
1
0
0
1
2
2
1
0
0
0
1
2
1
2
2
0
1
1
1
0
1
2
1
1
2
0
0
1
1
0
1
0
1
0
0
1
2
1
1
0
1
0
1
2
2
1
2
2
2
0
0
1
1
1
0
2
2
0
1
0
0
1
1
2
1
3
1
2
0
0
0
0
2
0
2
2
1
1
2
1
0
1
0
1
0
1
1
0
0
1
0
2
2
0
1
0
0
1
0
1
1
0
1
1
2
1
1
2
1
1
3
1
0
1
1
0
1
1
2
2
2
0
0
3
1
1
2
0
0
1
1
3
2
0
0
1
0
1
2
0
0
0
0
1
1
0
2
1
2
0
1
2
1
1
0
1
1
1
0
1
1
1
0
1
1
0
1
0
1
0
2
2
2
1
1
1
1
2
0
1
0
0
1
0
0
0
0
1
3
1
0
1
1
1
0
0
0
1
0
0
3
1
0
1
0
1
0
0
2
1
2
0
0
1
2
0
2
0
0
2
0
1
0
0
2
0
1
1
0
0
1
0
2
1
1
0
0
1
0
0
1
1
0
1
1
1
1
0
0
1
0
1
1
1
2
1
0
0
0
0
2
1
1
1
1
2
1
0
0
0
1
1
0
2
0
3
2
2
0
0
1
2
1
0
0
1
1
0
3
0
1
1
2
1
2
2
0
0
0
1
0
0
0
0
1
0
0
2
1
0
1
1
1
1
0
0
2
1
1
0
1
0
0
2
0
1
0
2
0
1
0
0
0
1
1
0
2
2
2
1
1
0
0
2
0
2
0
0
2
1
0
2
2
0
1
2
2
2
1
1
1
2
1
0
1
2
0
2
1
2
1
0
1
2
0
1
0
0
2
0
2
0
1
1
1
1
0
0
0
2
0
1
1
0
0
1
1
0
0
1
0
1
0
1
1
0
0
0
2
0
0
1
0
1
1
2
0
2
0
2
1
3
2
2
0
1
1
1
2
2
1
0
0
0
2
0
0
1
0
0
1
0
1
2
0
1
2
2
1
0
1
1
1
1
1
2
0
1
0
0
0
2
1
0
0
0
1
1
0
0
0
2
0
1
1
1
3
1
0
1
2
0
0
0
3
0
0
4
1
0
0
1
2
0
1
0
0
2
0
0
1
0
1
2
0
1
0
2
1
2
0
0
1
1
1
0
1
0
0
0
1
1
3
1
2
2
1
0
0
0
2
1
0
1
2
1
0
0
1
1
0
0
0
0
0
1
1
0
2
1
0
0
0
0
2
1
1
1
1
0
0
1
1
0
1
1
0
2
1
2
1
2
2
2
2
1
2
1
1
0
1
0
1
0
1
2
1
2
0
0
1
0
0
0
0
2
1
0
1
2
0
0
1
2
1
2
1
1
1
2
0
0
1
0
1
0
0
2
1
0
1
1
0
1
2
0
2
0
1
3
0
1
1
0
0
0
0
1
2
1
1
2
0
1
1
1
3
0
0
1
0
2
0
1
2
1
1
2
2
3
0
0
5
0
1
2
2
1
0
0
2
1
2
2
0
2
0
0
0
1
2
2
0
2
1
1
1
2
2
0
2
2
0
1
2
0
1
1
2
0
1
1
1
0
0
0
0
0
2
1
1
0
0
1
1
1
2
0
0
0
1
1
1
0
0
0
0
0
1
0
0
2
1
2
1
2
1
0
1
2
0
0
1
0
1
0
1
1
1
2
0
1
2
0
1
0
1
0
1
2
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
2
0
0
0
1
0
1
0
1
1
0
0
0
1
0
0
2
0
0
0
0
1
2
2
0
1
1
1
2
2
0
0
1
0
1
0
1
1
1
1
0
0
3
0
2
1
1
1
2
0
1
2
0
0
2
2
1
2
0
2
0
1
1
0
1
1
0
1
0
0
1
1
1
2
2
0
0
0
0
0
1
0
1
0
0
1
1
0
0
2
2
0
0
0
0
0
2
0
2
1
0
0
1
2
3
2
1
2
0
0
2
1
0
2
0
1
1
0
2
0
0
2
0
1
0
1
1
0
0
0
1
1
2
0
0
1
1
2
3
1
1
1
2
0
2
2
1
1
0
0
2
1
2
0
1
2
0
2
1
1
1
2
1
0
1
0
0
1
0
1
0
1
0
1
1
0
2
2
0
1
0
2
1
1
2
0
1
1
1
1
1
0
0
0
0
0
1
1
1
2
1
1
1
1
1
0
0
0
1
0
0
0
0
2
1
0
1
1
1
0
1
2
1
1
0
0
2
2
1
0
1
1
0
1
1
1
0
0
1
0
0
0
1
2
1
2
2
0
1
0
1
0
2
0
0
0
0
6
0
1
2
1
1
0
0
1
0
0
0
0
0
2
1
1
1
1
0
0
2
2
2
0
0
1
0
0
2
1
2
0
1
1
2
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
2
1
0
1
0
0
3
1
1
0
1
1
0
2
1
2
0
0
1
1
1
1
0
1
1
2
2
2
1
1
1
2
1
1
0
0
1
1
0
0
1
1
2
1
0
0
0
1
1
1
2
2
0
1
2
1
0
1
2
2
2
1
0
0
0
0
2
1
0
1
1
0
0
1
1
2
0
0
0
1
0
2
3
2
0
0
2
1
1
1
0
0
1
1
0
2
1
1
1
1
1
1
1
1
1
0
1
2
1
0
1
2
2
2
1
1
0
2
0
1
0
1
0
1
0
1
1
1
2
0
1
1
0
2
1
0
0
0
0
1
1
0
1
0
1
1
0
0
1
0
0
1
1
2
2
0
1
2
1
0
1
1
0
0
1
2
0
1
0
0
0
1
0
2
0
1
2
1
2
0
0
1
0
0
2
0
2
1
1
1
0
2
1
2
1
0
1
2
1
2
1
0
1
2
0
0
1
1
0
0
0
0
2
1
1
0
2
0
1
2
0
2
1
1
1
0
2
2
0
0
1
0
0
1
1
0
1
1
0
2
1
2
0
2
2
1
2
0
1
0
1
1
0
2
0
2
0
1
1
0
1
0
2
0
0
1
2
0
0
1
0
0
0
1
1
2
0
1
1
0
1
1
0
0
0
0
1
1
1
2
0
0
0
1
1
0
2
1
1
0
2
3
0
0
0
0
1
2
0
0
1
1
3
0
1
0
2
1
1
0
0
1
2
0
1
2
0
1
1
1
0
3
1
0
0
1
0
1
2
0
0
1
0
1
2
1
0
0
1
2
2
0
1
0
2
2
2
1
0
1
0
2
1
1
2
0
0
1
0
0
2
2
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
1
2
1
0
0
0
0
0
2
2
1
1
0
1
1
1
2
0
0
0
1
0
2
1
1
0
1
0
1
0
0
1
1
0
0
1
0
1
1
0
0
0
0
1
0
0
0
2
2
1
0
0
1
0
0
2
1
3
0
2
0
1
1
1
2
2
1
1
1
0
1
2
2
3
2
0
2
2
1
0
1
0
0
2
0
1
1
1
0
1
2
0
1
0
0
2
0
2
0
0
1
0
1
2
1
1
1
0
3
0
1
0
0
0
2
1
1
0
2
1
0
0
1
0
0
0
0
1
2
0
0
0
0
0
2
0
1
0
2
2
1
0
0
0
2
1
0
0
0
1
1
2
2
1
0
0
1
1
0
1
2
2
0
0
0
0
0
2
2
1
1
3
2
0
1
1
0
1
0
1
1
2
0
1
1
0
0
0
1
0
0
0
1
0
0
1
1
0
1
2
1
0
0
1
1
0
0
1
2
2
1
1
1
0
0
2
0
1
0
1
0
0
1
1
0
2
0
1
1
2
0
0
0
0
0
1
1
1
1
1
0
2
0
4
1
1
0
0
1
1
0
1
0
2
1
2
2
0
1
0
2
0
0
1
3
1
0
2
0
1
0
0
1
2
2
1
0
1
1
1
1
1
0
1
1
1
1
2
1
1
0
0
0
1
0
2
1
0
1
0
1
1
2
0
2
2
0
1
0
0
1
1
0
2
0
2
1
1
2
0
0
0
1
0
1
0
2
1
1
0
1
0
0
2
1
1
0
0
1
2
1
2
1
4
2
3
0
2
2
1
0
0
3
0
2
2
0
0
0
2
1
1
1
2
1
0
0
0
1
1
1
1
2
0
1
2
0
1
0
0
2
0
1
0
1
0
1
0
0
1
0
2
0
2
1
0
0
1
1
0
0
1
2
1
0
1
1
1
0
2
2
2
1
1
1
1
2
1
1
0
2
1
1
2
1
1
1
1
1
2
0
2
2
0
0
2
0
2
0
0
2
1
2
1
2
1
0
0
0
1
2
0
2
0
2
0
1
1
2
0
3
1
2
1
1
0
1
0
1
0
2
0
1
2
2
1
2
1
1
1
1
0
0
1
2
0
1
0
2
0
0
0
1
1
1
0
0
0
1
2
0
1
0
2
1
0
1
0
1
1
0
0
0
0
1
0
0
1
0
2
1
0
1
2
0
0
0
2
2
2
2
1
2
0
1
2
3
0
1
0
0
0
0
3
1
2
2
1
0
2
0
1
1
0
0
3
1
0
0
1
0
0
1
2
1
2
1
0
1
1
2
1
0
2
1
0
1
1
1
0
0
0
0
1
1
0
1
0
1
0
1
0
0
0
0
1
2
2
2
2
2
2
1
0
0
2
0
0
0
2
1
0
1
2
0
1
1
0
1
0
0
0
0
1
0
2
0
2
0
0
1
1
2
1
3
1
1
2
0
0
1
1
2
0
0
1
2
0
1
1
2
0
0
0
2
2
0
0
2
1
1
1
1
0
0
1
0
2
2
2
1
1
0
0
2
0
2
0
0
0
1
1
2
0
0
0
0
1
0
2
0
2
0
2
0
0
1
1
0
0
0
0
1
1
0
1
1
0
0
0
1
0
0
0
1
0
1
1
0
0
0
2
2
0
2
1
1
1
1
1
1
0
2
0
0
0
0
0
1
2
2
0
2
1
2
0
1
1
2
2
0
1
0
0
0
1
1
1
2
0
1
2
0
1
1
3
2
0
0
1
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
2
1
0
0
2
2
1
0
1
0
1
0
2
2
0
0
1
2
0
1
0
1
0
0
2
2
1
1
0
0
2
1
0
0
0
1
0
0
0
1
3
0
0
0
0
1
2
0
0
1
0
1
1
2
0
1
0
2
0
0
2
1
2
0
0
0
2
0
1
1
0
0
0
0
0
0
2
0
1
1
0
1
0
2
1
2
0
2
1
0
1
1
2
0
0
2
1
0
1
1
1
0
0
1
0
0
0
1
0
2
0
1
2
1
1
1
1
0
0
1
3
0
0
0
0
1
2
0
0
1
0
2
1
2
0
1
1
0
1
1
0
0
1
0
1
0
1
1
0
1
3
0
0
2
1
0
0
2
0
2
1
1
0
1
2
1
0
1
1
2
0
0
0
1
1
0
0
1
0
2
0
2
2
0
0
0
1
2
0
0
0
1
3
3
1
2
0
2
2
0
2
2
2
1
0
0
1
0
1
2
1
2
2
0
0
0
0
1
1
2
0
0
2
0
1
0
0
0
0
2
0
2
0
0
1
0
1
0
1
0
1
2
1
0
0
2
0
0
0
1
2
1
1
1
0
0
0
2
1
2
0
1
0
0
2
0
2
0
1
2
0
0
2
1
1
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
1
1
1
1
0
0
1
0
0
1
2
1
0
1
2
0
3
0
2
0
2
2
0
0
2
0
2
1
0
1
2
1
1
1
0
0
0
1
0
0
0
0
0
2
1
0
0
1
2
0
0
2
0
0
4
1
1
2
0
2
1
1
1
1
1
0
2
1
0
2
2
1
1
0
1
2
1
1
1
0
1
0
0
1
1
0
1
0
2
0
2
0
3
2
0
0
0
0
0
2
0
0
2
1
0
1
0
1
0
1
0
0
1
2
1
0
1
1
2
0
1
1
2
0
1
1
1
0
2
1
1
1
0
0
2
1
0
2
0
1
0
1
1
0
2
1
1
2
1
0
0
1
2
1
1
0
0
1
1
0
0
1
2
2
2
2
2
0
0
0
0
1
0
0
0
1
0
2
0
0
0
2
0
2
2
2
2
0
2
1
0
3
0
1
2
1
0
1
0
1
3
2
0
0
0
1
0
2
2
0
0
1
1
0
0
0
1
1
1
1
0
1
0
1
1
1
1
0
0
1
0
0
0
1
1
0
0
0
1
2
2
2
1
0
1
0
1
1
2
0
0
0
1
1
0
0
0
2
0
1
0
0
1
2
2
1
0
1
0
0
0
0
1
0
0
2
2
2
0
1
0
1
2
1
0
2
2
1
1
0
1
2
1
0
1
0
1
2
0
1
1
1
0
1
1
0
4
1
2
0
0
0
1
0
0
1
2
0
0
0
0
0
0
2
0
1
10
0
1
1
1
0
0
0
1
1
0
2
0
0
0
0
2
0
2
0
0
0
1
0
2
1
0
2
0
1
1
2
0
2
0
0
1
1
0
1
1
1
1
0
1
0
1
0
0
1
1
2
0
1
1
0
1
0
1
1
1
2
2
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
1
1
0
0
2
2
1
1
2
1
0
0
0
2
1
1
0
1
1
1
1
1
2
1
0
2
2
1
1
2
0
1
0
1
1
2
1
0
1
2
3
0
0
1
0
2
1
0
0
1
0
0
1
0
0
0
0
0
0
2
2
1
2
0
2
0
2
0
2
2
2
1
0
0
0
2
1
0
1
0
0
1
0
0
1
0
1
0
1
0
2
0
1
0
1
0
0
0
1
0
0
0
1
1
0
0
2
1
0
2
2
2
1
0
0
1
3
3
2
0
1
1
2
2
0
0
2
0
0
1
1
0
0
3
1
0
0
0
1
1
0
1
2
2
1
2
1
0
1
0
2
0
1
2
2
1
1
1
1
1
1
0
1
2
0
0
1
0
1
0
0
1
2
0
2
1
2
0
2
0
2
0
1
0
0
0
0
2
1
0
1
1
0
0
1
1
0
0
1
2
1
1
2
1
0
1
1
0
6
2
1
1
0
2
0
3
2
2
0
0
2
1
1
2
0
0
0
0
0
2
0
1
2
0
0
2
2
0
2
1
1
2
1
1
1
0
2
1
1
1
0
2
0
1
1
1
1
1
0
2
2
1
1
1
1
2
1
3
1
0
0
1
1
1
0
0
2
0
0
0
1
1
2
2
1
0
1
0
0
0
1
0
0
0
1
2
1
1
2
1
0
0
2
0
0
2
0
0
0
3
1
1
1
2
0
1
0
1
1
1
0
1
0
1
0
0
1
2
1
0
0
4
0
0
1
1
0
0
1
0
0
0
2
0
0
0
1
2
1
1
0
1
0
1
1
1
0
0
4
1
2
1
1
0
0
2
1
2
0
2
0
0
0
2
2
1
2
0
2
0
0
0
0
1
0
0
1
2
0
2
1
0
1
1
1
2
2
0
0
2
0
0
2
2
2
2
0
0
1
2
0
4
0
2
0
2
1
2
2
2
1
0
1
1
0
1
1
0
0
2
1
0
2
1
3
0
2
0
1
2
1
2
2
0
0
0
2
0
1
0
0
1
2
0
1
0
0
1
1
0
0
2
2
0
0
1
0
1
0
0
0
1
1
0
1
1
2
1
2
1
0
1
1
0
0
1
0
1
1
2
0
1
2
1
2
1
0
1
2
0
1
0
0
0
0
1
1
2
1
0
0
0
1
1
0
2
1
3
2
2
1
0
2
0
1
0
0
2
1
0
2
0
2
1
0
2
1
0
0
0
1
1
1
2
0
0
0
2
2
3
1
0
0
0
2
0
1
1
0
2
0
1
0
1
1
1
2
1
1
1
0
0
0
0
0
1
2
1
1
0
2
2
0
0
1
1
1
2
2
1
1
1
2
1
1
1
2
0
0
1
1
1
0
2
0
0
0
0
0
0
1
1
1
1
1
0
2
1
0
1
0
0
0
2
0
3
0
3
1
1
0
2
1
2
0
1
0
1
0
2
0
1
0
2
0
1
2
0
2
1
2
2
0
1
1
2
1
1
0
0
1
1
2
2
1
0
0
0
0
1
1
0
0
1
1
0
0
0
1
3
0
2
0
1
2
0
0
1
1
1
2
0
2
1
1
1
1
0
1
2
0
2
2
0
0
1
2
1
0
0
1
1
0
1
0
0
1
2
1
2
1
0
2
0
1
1
0
2
0
0
0
0
0
2
1
2
1
1
0
2
0
2
1
0
0
0
1
1
1
1
0
2
1
1
2
2
2
1
0
0
2
0
2
1
1
0
1
1
1
0
1
0
0
1
0
0
1
2
0
1
1
1
0
1
0
0
0
0
1
0
0
0
2
0
1
1
1
0
0
0
1
0
1
1
1
1
1
1
2
0
1
1
0
2
1
0
0
1
2
1
1
1
0
1
1
1
0
1
0
1
0
0
0
0
0
2
3
0
3
2
1
1
2
2
0
4
0
0
0
0
1
1
1
1
0
0
2
2
0
2
0
1
1
0
2
0
1
2
1
1
0
1
0
1
0
1
2
0
1
2
0
2
2
2
0
0
2
0
1
1
0
0
0
1
0
1
1
1
0
0
0
2
0
0
1
0
2
0
1
2
0
1
2
1
0
1
1
2
0
2
2
2
0
1
0
0
3
1
0
1
0
0
1
1
2
1
1
2
0
0
0
1
0
0
0
2
1
1
0
1
1
0
1
0
0
1
0
1
0
0
1
0
2
1
2
1
1
1
1
0
2
2
0
0
0
0
0
2
0
0
0
0
2
2
2
0
1
0
1
2
0
1
0
0
2
1
2
2
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
1
1
2
1
1
0
1
0
1
1
2
1
1
1
0
0
1
2
0
0
0
0
4
2
0
0
0
2
0
1
0
1
0
2
1
1
1
0
2
1
1
0
0
1
2
2
2
1
1
0
0
2
1
2
2
0
1
1
0
1
0
0
0
1
3
0
0
1
0
0
1
1
1
1
0
0
2
1
0
0
1
0
1
1
2
2
2
2
0
1
0
2
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
2
0
2
2
2
0
1
1
1
1
0
0
1
1
1
2
0
1
1
0
2
0
0
1
2
0
0
1
0
0
0
2
1
1
0
0
2
0
0
0
0
0
1
2
0
1
2
0
0
0
0
1
0
0
2
0
1
0
1
1
0
2
0
1
1
0
2
1
1
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
1
1
0
1
0
1
0
1
1
1
0
1
0
2
0
0
2
1
0
0
1
2
0
1
1
0
0
5
0
0
2
1
1
1
1
1
0
2
0
2
1
0
1
1
1
0
2
2
2
1
1
1
1
1
0
0
1
0
1
0
1
1
1
0
2
1
0
0
1
0
1
0
0
1
1
1
2
1
1
3
1
2
1
1
0
0
0
2
1
2
2
0
0
1
0
1
0
1
1
0
0
1
1
0
1
2
0
0
1
1
0
0
3
0
0
1
1
1
1
0
2
0
2
1
3
0
1
0
2
2
0
2
2
1
0
0
0
1
1
0
0
0
1
1
2
1
0
0
4
0
0
0
1
2
0
2
2
0
1
0
1
1
2
1
0
0
3
0
0
1
2
0
1
0
0
0
2
0
1
0
1
1
2
1
2
1
0
0
1
0
0
1
0
2
0
2
1
0
2
0
1
2
2
0
0
1
2
0
0
1
1
0
2
1
0
0
2
0
0
1
1
1
0
0
3
2
0
1
0
0
0
0
2
0
0
2
0
1
1
1
0
1
1
0
0
0
0
1
1
1
1
0
1
1
0
1
1
2
0
0
0
1
1
1
1
0
0
2
1
2
2
2
0
0
0
1
0
0
2
0
0
1
0
1
1
2
0
1
0
1
1
2
0
0
0
0
1
1
1
0
0
0
2
0
1
2
2
0
0
2
1
0
2
1
1
1
0
0
1
1
1
1
1
0
0
1
0
2
2
2
0
0
1
1
0
0
2
0
1
1
0
0
1
1
1
0
0
0
0
1
1
1
0
0
0
0
1
1
0
2
0
2
0
2
1
1
1
0
1
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
2
0
0
1
0
2
0
0
1
2
1
1
1
0
1
2
1
0
1
1
0
0
3
0
1
0
1
0
0
0
2
0
1
2
3
2
1
0
1
3
3
2
1
1
0
1
0
1
1
0
0
0
1
0
2
0
0
1
1
2
2
0
1
2
0
1
0
1
1
1
1
1
1
0
0
1
0
2
2
0
1
0
2
0
0
2
0
1
0
0
1
1
1
2
2
0
0
0
1
1
0
1
0
1
2
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
1
3
1
1
1
0
0
0
1
1
1
1
1
2
0
0
0
1
0
1
2
2
0
0
4
1
1
0
1
1
1
2
1
0
2
2
1
0
0
1
0
1
1
0
0
0
0
1
1
1
2
0
1
1
0
1
2
0
0
2
2
0
0
0
0
1
1
1
1
0
2
1
2
2
2
0
1
1
1
2
1
1
0
2
1
2
1
0
1
1
0
1
2
3
1
1
1
0
0
2
1
2
2
1
2
0
0
2
0
2
0
0
1
1
1
0
1
0
0
0
2
1
0
1
0
0
1
1
0
1
1
0
2
2
0
2
0
1
2
0
1
2
2
2
1
0
0
1
2
2
2
2
1
2
1
0
0
2
0
2
1
1
0
1
1
0
0
0
0
2
0
1
1
1
2
1
1
0
1
0
0
1
1
1
1
0
0
0
1
0
1
0
0
0
1
2
1
1
1
2
1
3
0
2
0
1
0
1
2
1
0
1
0
0
0
1
0
0
2
1
1
0
2
2
2
2
1
1
1
2
2
1
2
0
0
0
2
1
1
0
1
0
1
2
0
1
2
1
2
0
0
0
0
2
0
0
0
1
2
2
1
1
1
2
0
2
1
1
2
1
0
1
1
1
2
1
2
0
1
1
2
1
1
0
2
1
2
0
2
1
0
2
0
0
1
1
2
0
1
0
2
3
2
1
0
1
1
1
0
3
2
1
1
0
0
1
3
2
1
0
0
0
1
0
0
0
1
0
0
2
1
0
0
0
0
1
1
0
1
0
0
2
1
1
0
2
1
0
0
0
1
0
1
0
0
2
1
0
1
2
1
1
1
0
0
2
1
3
2
1
0
1
1
2
0
0
0
0
0
0
1
3
3
0
1
0
0
1
1
1
1
0
0
2
1
0
0
1
0
0
2
2
0
0
2
1
1
0
2
2
1
1
0
1
0
1
1
1
0
0
0
1
0
2
0
1
1
0
2
0
2
1
1
1
2
0
3
0
0
0
1
0
0
4
1
0
1
2
0
1
1
1
2
0
2
2
1
1
1
1
2
1
2
2
2
0
1
1
0
2
0
0
2
0
1
2
0
0
0
0
0
0
1
3
1
1
2
0
2
0
1
1
0
0
1
0
0
1
0
2
3
0
1
0
0
0
2
0
2
1
0
1
1
2
1
1
1
1
2
1
2
2
0
1
0
1
2
0
0
2
0
0
2
2
1
0
1
0
1
0
2
1
3
1
0
2
1
1
2
0
0
2
1
0
0
0
0
0
0
1
0
2
0
0
1
2
4
1
3
0
2
0
1
2
2
1
1
0
2
1
0
0
1
1
0
1
4
0
1
1
0
0
0
2
1
2
1
2
1
2
0
1
0
0
1
2
0
0
2
1
0
0
2
0
1
3
0
0
0
2
0
1
0
1
1
1
2
1
0
1
0
0
0
0
1
1
2
1
2
1
0
0
0
1
0
0
0
2
0
0
0
0
2
0
2
2
0
2
2
0
1
0
2
1
0
0
1
2
0
2
0
0
1
1
1
0
0
0
1
2
1
1
2
1
2
1
0
2
0
2
1
0
2
0
0
1
0
0
2
1
0
1
1
0
0
1
0
2
2
0
0
1
0
0
0
0
1
2
1
1
0
2
1
0
1
0
0
2
1
0
0
2
0
1
0
0
2
2
0
0
0
1
0
1
1
2
2
2
2
1
0
1
0
0
0
0
1
0
2
1
0
0
0
2
1
0
0
1
0
3
1
0
2
2
0
1
2
1
0
1
0
0
1
1
1
1
0
2
1
2
2
1
0
1
0
2
0
2
2
2
1
1
0
1
0
2
2
2
0
2
2
1
2
2
0
0
2
1
0
1
3
0
1
2
2
1
2
1
1
0
0
2
0
0
0
2
2
2
0
1
0
0
0
0
1
1
0
2
1
0
2
0
0
1
1
0
1
1
2
0
1
2
0
2
1
0
0
1
0
0
0
2
0
0
2
1
0
1
1
1
1
1
0
1
0
2
0
2
0
1
0
2
3
0
0
2
2
0
0
4
1
0
2
0
1
2
1
2
0
2
0
0
1
2
0
2
0
1
1
0
0
0
1
0
0
0
2
1
1
0
0
1
1
1
1
1
2
0
1
2
0
0
1
0
1
1
0
0
1
1
0
3
1
0
0
1
3
2
0
0
0
2
1
1
0
1
0
1
0
0
0
2
2
2
1
0
0
1
0
0
2
1
0
1
1
2
2
0
1
3
1
2
0
0
0
0
0
1
0
1
1
0
0
0
0
2
0
1
2
1
2
2
1
1
0
1
2
1
2
0
1
2
1
0
2
2
1
2
0
0
0
1
0
1
1
0
0
0
0
2
1
2
1
0
2
1
0
0
0
1
0
1
1
0
1
0
3
0
1
0
0
2
2
0
2
2
1
0
1
0
1
1
0
2
1
0
0
1
0
1
1
1
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
2
0
1
2
1
0
0
0
0
1
1
2
1
0
1
1
1
0
0
0
2
1
1
0
0
1
0
1
1
2
0
2
1
1
0
0
1
0
0
0
2
0
0
0
0
2
1
1
0
1
0
0
2
0
0
0
1
0
0
0
0
0
1
1
1
1
2
1
0
2
0
1
0
1
2
1
1
1
2
2
1
0
1
1
0
2
2
1
2
1
0
2
2
1
0
1
0
2
0
3
1
0
1
1
0
0
0
0
0
0
1
1
1
1
1
1
1
0
0
0
2
0
2
1
1
1
1
0
0
0
2
1
0
2
0
1
0
0
0
2
0
1
0
1
0
1
1
0
1
0
0
1
0
2
1
0
0
1
0
0
0
0
0
1
2
1
3
0
1
1
1
0
0
1
2
1
0
2
0
1
2
1
1
2
0
2
0
1
1
1
2
0
1
0
1
1
0
2
0
2
1
0
0
0
0
2
1
0
1
2
0
2
2
0
0
2
0
0
3
1
1
0
1
0
2
2
0
1
1
0
1
0
0
0
0
1
2
0
1
2
2
0
2
0
2
0
2
1
2
0
1
0
1
0
0
8
1
0
0
1
1
1
1
2
0
1
2
0
1
0
2
2
1
1
0
0
0
1
0
1
1
0
0
2
2
3
1
2
2
2
1
1
2
0
2
2
0
0
1
0
1
0
2
1
0
0
2
1
1
1
1
2
1
1
1
1
1
0
1
2
0
0
1
1
0
0
1
2
0
0
0
2
2
0
2
1
1
2
1
1
1
2
1
0
0
0
1
2
1
2
0
0
1
1
0
1
0
0
2
0
0
1
0
0
2
0
1
0
1
1
1
0
2
0
0
1
0
0
1
2
0
2
0
1
1
2
0
0
0
2
2
1
1
2
0
0
0
1
0
2
0
2
2
1
1
1
1
1
0
0
2
0
1
1
0
1
0
0
0
1
1
1
2
1
0
1
0
1
1
0
1
1
1
0
0
1
1
2
0
2
0
1
2
0
0
1
1
0
1
0
0
1
0
1
0
0
1
2
1
0
0
0
4
0
0
1
0
1
1
0
1
1
0
1
0
1
0
0
0
1
1
1
1
2
0
0
1
0
0
1
0
1
1
1
1
1
0
0
1
0
2
1
0
2
0
1
0
2
0
1
2
0
2
1
1
0
0
1
0
2
0
0
1
2
0
1
0
1
1
0
0
0
0
0
0
2
1
0
1
0
0
0
2
0
1
0
2
0
0
1
1
2
0
0
0
1
0
0
2
0
0
1
0
1
1
1
1
0
0
1
0
2
0
2
1
0
1
1
0
0
1
0
0
1
1
0
1
0
0
0
1
1
0
0
2
0
0
1
1
1
0
1
1
0
2
0
2
0
0
0
0
0
1
2
1
1
1
2
2
0
2
0
0
1
1
2
0
2
1
0
0
0
0
0
2
2
0
2
0
3
0
0
1
1
0
0
2
1
2
0
0
2
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
4
0
1
1
0
1
1
1
2
0
1
2
1
1
2
1
0
1
0
1
0
0
0
0
2
0
1
0
1
1
1
1
1
2
0
1
0
1
1
2
1
2
1
1
1
2
1
0
1
1
2
0
1
1
1
1
0
1
1
2
0
0
2
0
0
0
1
0
2
0
2
0
1
1
1
1
0
1
2
1
0
2
0
1
2
2
1
1
0
2
1
2
2
2
2
1
1
0
0
1
0
2
0
0
1
0
2
0
1
0
1
0
1
0
2
5
0
1
1
0
1
2
0
2
0
2
2
2
2
0
1
0
1
0
0
2
0
0
0
1
0
1
1
0
0
1
0
2
1
0
0
2
0
0
1
0
0
0
1
2
0
2
0
1
0
1
1
2
0
1
0
0
2
2
2
1
2
0
0
0
1
0
0
0
1
3
0
0
1
2
2
1
1
1
2
1
0
1
2
2
1
0
0
0
0
2
1
0
0
1
0
0
2
5
1
0
2
0
0
0
1
0
1
1
0
2
1
1
0
1
1
2
3
2
0
2
1
1
0
0
1
1
1
0
0
1
1
0
1
1
2
2
0
2
2
1
1
2
0
2
0
0
1
2
0
0
0
0
0
2
0
1
0
2
1
0
1
0
0
0
1
2
1
0
1
0
0
2
0
1
2
1
0
0
1
0
1
1
2
0
1
0
0
2
1
2
1
1
1
0
2
1
0
2
0
0
0
2
2
7
2
2
1
2
0
0
1
1
1
1
2
1
0
0
1
2
0
0
1
0
0
1
0
1
0
2
0
2
2
0
0
1
1
1
3
1
2
0
1
2
2
1
1
0
1
1
4
1
1
0
2
1
0
2
0
2
0
0
2
1
2
2
1
0
1
0
1
1
1
2
1
0
1
0
1
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
1
0
2
1
1
0
2
0
0
2
0
0
2
1
0
0
1
2
2
0
0
1
1
1
2
0
2
0
0
1
0
1
1
1
1
1
1
1
1
0
0
2
0
2
2
0
1
0
2
2
0
0
2
1
0
0
1
1
1
2
1
1
0
1
0
0
1
2
1
1
1
2
1
2
0
1
0
0
0
1
2
1
2
1
2
1
0
0
2
0
2
1
0
2
1
1
0
0
1
0
0
1
1
0
0
1
1
0
0
0
2
0
0
3
0
1
0
1
1
1
1
0
2
0
2
0
0
0
0
0
2
2
0
2
0
1
0
1
1
0
0
0
0
2
2
1
0
0
0
0
0
2
1
0
0
0
0
2
1
0
2
1
2
1
1
0
1
0
0
1
1
2
1
0
1
0
2
0
0
2
0
1
1
0
0
0
1
0
1
1
2
1
0
3
0
0
0
1
0
1
1
0
1
1
1
1
1
0
2
0
1
2
0
0
2
0
0
0
2
1
0
2
2
0
1
0
0
0
1
2
1
2
2
0
2
0
2
1
2
1
2
1
2
0
0
0
0
0
0
1
3
2
1
0
2
1
1
1
0
0
3
2
1
2
2
2
0
0
1
0
1
1
0
2
1
0
0
1
0
0
2
0
2
0
3
0
2
0
0
1
0
0
0
2
2
0
1
1
0
0
2
0
0
0
1
1
0
1
0
0
0
2
0
1
0
3
0
0
0
1
1
2
1
0
2
0
0
2
1
2
2
1
1
1
1
1
1
2
0
0
1
2
0
1
0
2
1
0
0
0
2
0
0
1
1
0
0
1
0
0
0
0
2
0
0
2
1
1
2
0
3
0
0
1
0
2
0
0
0
2
1
1
2
0
0
1
2
2
0
1
0
1
0
1
2
0
0
1
1
1
2
1
1
1
2
0
0
0
0
1
1
1
0
1
1
1
1
0
0
1
1
0
1
0
0
0
1
0
1
3
2
2
0
1
1
0
0
1
1
0
2
0
0
1
1
1
0
0
0
1
0
1
1
1
1
0
2
0
1
1
2
0
2
1
0
0
2
1
2
1
2
2
1
0
0
2
2
1
0
0
0
1
0
0
0
0
1
0
1
0
0
1
1
0
2
0
1
3
1
0
0
2
1
3
0
2
0
2
0
0
2
0
2
0
0
0
1
0
1
0
1
2
0
0
2
1
1
0
1
0
2
1
1
1
2
0
1
0
0
0
2
1
1
2
2
0
2
2
0
1
1
0
2
0
1
1
2
0
1
2
1
1
0
0
2
0
2
0
0
2
0
0
0
1
2
0
0
2
1
2
2
0
0
0
0
0
1
1
2
1
1
3
0
0
2
2
0
2
1
1
1
0
2
2
0
1
2
0
1
1
1
2
1
1
1
1
1
0
0
1
0
2
0
1
0
0
1
0
2
1
2
1
0
0
1
1
0
3
1
2
0
1
1
1
2
1
1
1
1
0
0
2
3
0
0
1
2
1
0
1
1
1
0
0
1
1
2
2
0
1
1
2
1
1
1
0
1
0
1
2
2
1
2
1
1
2
0
2
0
1
1
1
2
1
2
1
0
0
1
0
0
1
1
1
2
1
0
2
0
1
0
1
0
1
1
0
1
2
0
1
0
1
2
1
2
0
0
1
1
1
0
0
1
1
1
1
0
1
0
0
2
1
0
0
0
2
2
2
1
0
0
2
0
1
1
0
1
2
1
1
3
0
2
1
0
0
1
1
1
0
2
0
1
1
0
1
2
0
1
0
0
1
0
2
0
0
2
2
0
0
0
2
0
1
0
1
0
2
0
0
1
0
1
1
0
0
0
0
1
1
2
0
3
1
0
2
0
0
1
1
1
2
1
1
3
2
1
1
1
2
1
0
0
0
2
0
0
0
1
1
3
0
2
0
2
0
2
1
0
1
0
0
1
0
2
1
0
1
1
1
0
0
2
1
1
2
1
2
2
0
0
0
1
0
0
1
2
1
0
1
0
1
2
1
0
0
0
1
2
0
0
2
1
1
1
0
1
0
2
2
2
1
1
2
1
2
0
1
1
0
2
1
0
0
2
0
1
1
2
0
1
0
2
1
1
0
0
0
1
0
1
2
2
1
0
1
0
0
2
0
0
0
0
0
1
1
0
1
2
1
0
0
0
1
0
0
1
0
0
0
0
0
1
2
0
2
0
1
2
0
0
2
1
0
1
0
1
1
2
1
1
0
2
2
0
2
0
0
0
0
2
1
0
1
0
2
1
1
1
1
0
0
1
1
1
2
1
1
1
1
3
1
0
2
0
0
0
1
0
1
1
2
2
2
0
0
1
1
0
0
0
0
1
1
0
2
1
1
0
1
1
0
0
1
0
1
1
0
1
0
1
0
0
0
2
2
0
1
2
1
0
0
0
2
2
0
1
0
0
0
1
1
1
1
1
1
1
1
2
1
0
1
2
0
0
1
0
1
0
0
1
1
0
0
2
1
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
1
0
2
1
2
2
0
1
1
0
2
1
2
1
1
1
0
0
2
1
0
0
1
1
1
1
2
1
0
0
1
1
2
0
0
1
1
1
1
5
2
1
0
0
1
0
0
1
1
1
1
0
0
0
1
1
0
1
1
0
2
2
0
0
1
1
2
1
1
1
0
1
1
0
0
1
1
0
0
0
1
0
1
1
0
2
1
0
0
0
1
0
2
1
1
2
0
1
1
1
0
1
0
0
3
1
1
1
2
2
1
0
2
0
0
0
0
0
0
1
0
0
1
1
1
0
1
1
2
1
1
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
2
1
2
1
0
1
1
1
1
0
2
0
2
1
0
0
0
1
0
2
1
1
0
2
1
1
0
2
2
0
2
0
0
0
2
2
1
0
1
0
0
0
1
2
0
2
2
0
2
1
1
1
3
1
0
2
1
1
0
0
1
0
0
0
1
1
0
0
2
2
0
1
2
2
0
1
1
2
1
1
2
0
0
1
0
0
2
3
0
2
0
1
1
1
0
2
0
1
1
0
1
0
1
2
1
2
1
1
1
0
0
2
1
0
1
0
1
2
2
2
2
0
1
0
1
0
1
1
2
1
2
0
0
3
0
1
1
1
2
1
1
1
0
1
0
1
0
0
2
0
0
0
0
2
0
0
0
0
1
3
0
0
0
0
1
2
1
1
0
0
0
1
2
1
1
2
0
0
1
2
3
1
0
0
2
2
0
1
1
2
0
1
1
0
1
2
1
0
0
0
2
2
2
0
1
0
2
0
2
0
2
1
3
3
1
2
1
0
1
2
1
1
0
0
2
0
0
1
2
1
0
2
0
0
1
2
1
1
0
0
0
2
0
0
0
0
1
0
1
2
2
0
0
2
2
0
1
2
0
1
1
0
1
1
1
1
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
1
1
1
0
0
0
2
2
0
0
0
1
2
0
1
0
1
0
1
1
1
0
0
1
0
0
1
1
0
1
1
0
1
3
2
1
2
0
1
0
0
1
0
1
0
1
0
0
1
1
2
2
5
0
0
2
0
3
0
2
2
0
0
0
2
0
0
2
1
0
1
0
1
0
0
2
1
2
0
0
1
0
2
0
1
0
1
0
1
0
1
0
0
1
1
0
1
0
1
1
1
0
0
1
0
0
0
1
1
0
1
0
0
0
0
1
2
2
0
1
1
1
1
2
1
1
0
0
0
0
2
0
1
0
1
1
0
1
0
0
1
1
0
2
1
0
0
2
0
0
1
0
0
2
0
1
1
0
1
0
0
1
0
0
0
0
1
0
1
0
1
2
1
2
0
0
0
1
0
2
2
1
1
0
1
1
2
1
2
1
2
2
1
0
2
2
1
0
0
0
0
1
1
1
1
0
2
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
2
0
2
1
2
0
1
0
2
2
0
0
1
2
1
1
1
1
0
1
1
1
0
0
2
0
0
1
2
0
2
2
0
1
0
0
1
1
0
2
1
0
0
0
1
0
1
1
1
5
2
0
2
0
1
0
1
0
1
1
1
0
2
0
0
1
0
0
0
1
0
0
0
1
0
1
0
1
0
2
2
0
0
0
0
0
1
1
1
0
0
0
2
2
1
0
0
1
0
0
1
0
0
2
1
2
0
1
0
0
1
0
2
1
1
2
2
1
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
1
0
1
0
1
1
0
1
1
0
0
0
1
1
0
0
0
1
0
0
0
1
1
0
1
0
0
3
1
0
0
0
2
1
0
2
1
2
1
2
2
0
0
1
0
2
0
0
1
0
2
2
1
2
0
1
2
0
1
1
0
0
1
0
1
0
1
2
0
1
2
1
2
0
1
1
1
0
0
2
0
1
0
1
0
0
1
1
1
0
0
2
1
2
2
0
0
0
0
2
1
0
0
0
0
2
1
1
1
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
2
1
1
2
0
2
0
1
1
0
2
0
2
0
0
1
2
1
4
0
1
2
1
0
1
0
1
0
0
0
2
1
0
2
1
1
1
1
0
0
1
0
2
2
1
1
1
1
1
2
1
1
0
1
2
0
2
1
1
1
0
0
2
2
0
1
1
2
0
2
2
2
0
0
1
0
0
1
2
0
1
1
1
2
0
0
0
1
2
0
1
1
1
2
1
0
0
1
2
0
1
1
1
0
1
1
2
0
2
2
1
1
2
0
0
0
0
2
2
0
1
2
2
0
1
0
0
0
2
2
1
3
2
2
0
0
1
1
2
2
1
0
0
0
1
1
0
0
2
2
0
1
0
0
1
0
0
1
2
0
1
0
0
1
0
2
2
0
1
0
2
0
0
0
1
0
0
1
0
1
2
3
1
0
1
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
2
0
2
2
1
1
2
0
1
0
1
0
1
1
0
0
0
0
0
1
0
0
1
0
2
0
1
0
0
1
2
1
1
1
2
1
1
1
0
2
0
0
1
0
1
0
2
1
1
0
0
0
0
2
2
1
1
1
2
2
0
0
2
1
1
0
1
0
0
0
0
1
1
0
0
1
0
1
0
1
1
1
0
1
0
2
0
1
1
0
1
2
2
0
0
1
0
0
1
1
1
0
1
1
0
1
0
1
2
2
1
1
1
0
2
1
0
0
1
1
2
0
1
0
0
0
2
0
2
0
2
1
1
1
1
1
2
0
1
1
0
0
0
1
0
0
0
0
1
1
1
1
1
0
1
1
0
0
2
1
1
0
4
0
2
0
0
2
0
1
1
2
0
0
0
1
0
2
0
0
1
0
0
1
0
0
1
1
0
0
1
0
0
1
1
0
1
0
1
0
1
1
1
0
1
0
0
0
1
1
1
0
1
1
1
0
0
2
0
1
1
1
1
1
0
1
0
1
2
0
1
0
2
0
0
1
0
0
0
2
1
0
0
2
0
2
0
0
1
1
0
0
1
2
2
2
0
0
2
1
0
1
2
0
0
1
2
0
0
2
0
2
0
0
2
2
1
0
1
0
0
1
1
1
0
0
1
0
0
1
2
2
1
0
0
0
0
0
2
2
1
2
0
1
0
0
0
2
0
0
1
0
1
1
0
2
0
0
0
1
0
0
1
1
1
1
0
0
0
1
1
3
1
2
0
0
2
0
0
0
0
2
1
1
2
2
0
0
1
1
0
0
0
0
4
0
0
2
0
0
0
0
1
1
0
0
0
0
2
1
1
0
0
0
0
1
2
2
1
0
0
0
1
1
0
0
1
4
0
2
1
1
0
2
0
2
1
0
1
2
0
2
0
0
1
2
2
2
1
0
0
1
2
2
1
0
1
1
1
0
0
1
1
1
0
0
0
1
1
1
0
0
2
1
0
1
1
1
2
0
0
0
0
0
0
0
0
2
2
0
1
0
1
0
0
1
0
0
2
1
1
3
0
0
2
1
4
1
0
1
2
1
1
0
0
1
0
0
1
1
2
2
0
1
2
1
2
2
1
1
1
0
2
1
0
2
0
3
1
1
1
0
1
0
0
2
0
0
0
2
1
2
0
0
0
0
2
1
2
2
0
1
0
0
1
2
0
2
0
2
0
1
0
1
1
1
1
1
0
1
1
2
2
1
0
2
2
2
1
1
0
1
2
1
1
1
0
0
0
0
1
2
1
2
2
0
3
1
2
0
1
2
1
0
1
0
1
2
1
0
2
2
1
1
1
2
1
0
0
1
1
2
0
0
2
2
0
0
0
0
0
2
1
2
0
0
1
1
0
1
0
0
0
0
3
2
0
2
2
0
0
0
2
0
0
0
0
0
0
2
0
2
0
1
1
0
1
0
1
1
0
1
0
1
1
1
0
0
1
1
1
2
2
2
0
2
1
0
0
1
0
2
2
0
0
1
2
1
0
1
1
0
1
3
1
1
1
1
1
1
1
0
1
1
0
2
0
2
0
0
2
0
2
0
1
2
2
2
1
1
2
0
0
1
2
0
2
1
1
0
0
1
0
2
2
0
1
1
1
0
0
0
0
0
1
0
1
2
1
0
0
0
0
0
1
2
1
0
0
1
0
2
1
2
0
1
0
2
1
0
1
0
0
1
2
0
0
2
1
1
0
1
1
2
0
0
1
0
0
2
0
2
1
1
1
1
1
0
0
0
2
0
0
1
2
0
0
2
2
1
2
0
1
1
2
1
0
1
0
1
1
1
3
0
0
0
0
2
0
2
0
1
1
0
1
1
1
0
2
0
2
0
0
0
2
0
1
1
0
0
2
0
0
2
0
2
1
0
3
2
1
0
0
2
0
2
0
0
0
0
0
0
1
1
0
1
1
2
1
3
1
0
2
1
0
2
0
2
2
1
2
1
1
0
1
1
0
1
1
0
1
1
0
0
2
0
1
1
2
1
1
2
0
0
1
2
1
1
0
0
0
0
0
0
0
2
1
1
0
1
0
0
0
2
0
1
1
0
0
0
3
1
1
0
1
0
0
1
2
0
1
2
2
1
2
0
0
2
1
2
0
1
2
2
1
1
0
0
2
0
0
1
0
0
1
1
0
0
1
2
1
0
1
1
0
1
1
0
2
1
1
0
2
0
0
1
0
2
0
0
0
1
1
2
0
2
1
1
1
0
1
1
0
1
2
1
2
1
3
1
1
2
1
1
0
0
2
0
0
1
0
2
2
1
0
2
0
1
1
1
2
1
0
0
0
0
0
0
0
1
0
1
2
2
1
0
0
2
1
1
0
2
0
2
2
0
0
1
0
1
1
1
2
3
0
0
0
1
1
0
0
1
1
2
0
2
0
1
1
2
1
1
2
0
0
2
1
0
0
1
2
0
1
0
0
1
1
0
1
2
2
0
2
2
2
1
1
0
2
0
0
1
0
2
1
1
0
1
0
0
2
2
0
0
0
0
0
1
2
0
2
1
0
1
2
1
0
0
0
2
2
3
0
1
0
2
1
6
0
2
0
2
1
0
1
0
2
0
1
1
1
1
1
0
2
2
0
0
0
0
2
0
0
1
0
0
2
0
2
1
2
0
0
0
0
2
0
0
3
0
2
0
0
1
1
0
1
2
1
1
1
0
1
0
0
0
1
0
0
1
1
0
0
2
2
0
1
0
1
2
0
1
1
2
0
0
2
1
0
2
0
1
2
1
1
1
2
1
0
0
0
2
2
0
1
1
0
1
1
1
1
0
1
2
0
2
2
0
0
0
0
0
0
1
1
1
1
1
2
2
1
0
4
0
1
1
0
0
0
0
1
1
1
1
1
0
1
1
1
2
0
1
1
2
1
0
0
0
1
1
0
1
1
0
1
0
0
2
1
1
1
1
1
0
0
0
0
0
1
2
0
0
1
2
2
1
0
1
1
4
1
0
3
2
0
1
0
0
1
0
2
1
0
3
0
0
0
0
1
2
0
2
1
1
0
1
0
1
0
0
1
1
0
1
1
2
1
1
0
1
1
2
0
2
0
0
1
2
1
1
1
1
0
1
0
1
1
2
1
1
0
0
0
1
1
0
1
1
0
1
1
1
0
1
1
1
0
1
2
1
1
1
2
0
1
2
1
0
0
1
0
0
2
0
2
2
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
2
0
0
2
1
2
0
0
1
2
1
0
0
0
2
1
0
1
0
0
1
2
1
2
2
0
1
1
0
0
1
0
0
1
1
4
0
0
1
1
0
1
0
0
2
0
1
0
2
2
0
0
1
1
1
2
0
0
1
2
1
0
0
2
2
1
2
1
0
1
1
2
0
0
1
1
2
0
1
0
1
0
0
0
2
1
1
1
1
1
2
2
0
2
0
0
0
0
1
2
2
0
1
1
0
2
1
1
1
0
0
0
1
0
1
0
2
1
2
0
0
2
2
1
0
1
0
0
0
0
1
1
1
0
0
1
0
0
1
0
1
1
0
0
0
2
2
0
1
1
0
0
1
0
0
1
1
2
0
0
0
1
1
2
1
1
0
0
2
2
0
1
2
0
1
1
0
0
1
1
0
0
1
0
0
0
1
2
0
0
0
1
2
1
1
3
1
0
2
2
0
0
0
0
0
1
0
0
0
0
0
1
1
0
2
0
1
0
1
1
0
1
1
1
0
1
0
0
0
1
2
2
1
1
0
1
0
2
2
2
0
1
0
1
0
0
0
1
2
0
2
0
0
2
0
2
1
1
0
1
1
1
0
0
1
0
4
1
1
1
2
1
1
2
0
2
0
0
1
1
2
2
0
1
0
0
0
0
0
0
1
1
1
0
0
1
0
1
2
0
0
0
1
0
1
2
2
2
2
1
0
0
0
2
0
0
0
1
1
2
2
0
0
1
0
3
0
2
0
2
0
0
0
2
2
2
0
0
0
1
0
1
0
1
0
1
0
0
1
0
3
0
0
1
0
0
1
2
1
0
2
2
2
1
0
0
2
0
0
2
2
0
1
2
2
1
2
1
1
0
0
0
0
2
1
0
0
1
0
0
0
2
1
2
2
3
1
2
0
0
1
1
2
0
2
0
1
0
1
2
0
0
2
2
2
0
0
1
1
0
1
1
0
1
0
0
1
1
1
0
2
1
0
0
1
1
0
0
2
2
0
1
0
1
1
1
0
0
0
0
1
1
1
3
2
2
0
0
0
1
2
0
1
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
1
1
0
1
2
2
2
0
0
1
1
0
1
2
0
1
2
0
0
2
2
0
0
0
2
2
0
3
0
1
1
0
1
0
1
1
0
1
0
0
1
2
2
2
0
1
1
0
1
2
0
0
2
1
2
0
1
1
0
1
1
2
0
1
1
0
2
2
1
0
0
2
3
0
0
0
2
0
0
2
0
0
1
2
2
2
1
0
2
2
1
2
0
0
1
1
0
1
2
0
0
0
1
0
1
1
1
2
1
0
0
0
0
1
2
0
2
1
2
0
1
0
2
0
1
0
0
0
1
0
0
1
0
2
2
1
0
0
2
2
1
0
0
0
0
0
0
0
2
0
0
4
0
2
1
1
2
1
0
0
2
2
1
2
1
2
2
2
1
1
1
0
1
1
2
0
0
1
2
1
2
1
2
0
0
0
0
1
1
0
1
2
1
0
1
0
2
1
2
2
2
0
2
1
1
1
1
1
2
0
1
2
2
0
2
2
1
2
0
1
2
1
0
0
0
0
0
1
1
0
1
1
0
1
2
0
0
0
1
1
1
1
0
1
0
1
0
0
0
0
0
1
0
0
2
0
1
0
0
1
1
1
2
1
2
2
0
0
0
0
1
1
0
1
1
2
2
1
0
0
0
1
0
1
1
0
0
2
2
0
0
1
1
0
0
1
0
2
2
2
1
1
2
1
1
2
0
0
0
0
0
2
0
0
2
0
0
0
0
1
2
0
2
0
1
1
0
0
1
0
0
1
0
0
0
1
1
1
1
2
1
1
0
2
0
1
0
0
2
2
2
1
1
2
1
0
1
2
0
2
1
2
1
1
1
1
0
0
0
1
0
1
1
1
2
1
1
2
0
1
1
0
0
1
1
1
1
0
1
1
1
1
0
0
0
0
0
1
1
0
2
1
0
1
0
1
1
0
0
1
0
0
0
2
0
1
1
1
0
1
1
0
1
2
1
2
1
0
0
2
0
0
1
0
0
2
2
0
0
1
2
0
1
3
1
1
0
0
0
0
0
1
1
0
1
0
2
0
0
0
0
1
0
2
1
0
3
2
0
3
0
1
1
0
0
0
1
0
0
1
1
1
0
0
0
0
1
1
0
0
0
12
1
0
2
0
0
2
1
2
2
1
1
1
1
0
0
2
0
2
2
2
0
1
0
0
2
1
2
1
0
1
1
2
0
1
0
1
1
0
0
2
0
1
2
2
1
1
1
0
2
1
1
2
1
1
0
0
1
0
0
0
2
2
1
0
1
1
2
2
2
0
0
0
0
0
1
0
2
1
1
5
2
0
0
0
1
1
0
0
1
2
0
1
2
0
2
1
0
0
1
1
2
0
2
0
0
2
3
1
2
1
0
0
1
0
1
2
1
1
0
2
0
0
2
0
4
2
1
1
0
0
1
0
1
1
0
2
1
2
0
0
0
2
0
1
0
0
0
3
0
1
2
0
1
0
1
0
2
0
0
2
2
1
0
2
1
1
1
0
0
0
0
2
0
0
0
0
3
1
2
1
1
1
0
1
0
0
1
1
1
0
0
2
0
0
0
1
1
0
1
1
2
1
0
2
0
0
1
0
1
2
0
2
2
0
1
2
0
1
1
1
1
1
1
1
1
1
1
1
1
0
2
0
2
1
0
2
2
1
0
0
2
0
0
0
0
3
0
0
0
1
3
2
0
3
0
0
0
2
0
0
2
0
1
0
2
1
0
1
1
2
3
1
0
1
0
1
2
1
2
0
1
2
2
2
1
0
1
0
0
1
1
1
1
2
0
2
0
2
0
1
0
2
0
0
0
0
0
0
0
2
1
0
1
0
1
2
1
2
2
1
0
0
2
1
1
1
0
2
2
0
0
0
0
2
1
0
3
1
2
0
1
0
0
0
1
0
0
2
1
1
2
2
1
0
2
0
1
0
2
0
0
0
0
1
0
0
1
2
0
0
0
0
2
1
0
0
2
0
2
2
0
1
1
2
0
2
1
0
1
2
2
2
1
2
2
2
0
1
0
0
0
1
1
0
1
0
2
0
0
0
0
1
0
0
0
1
1
2
0
0
0
1
2
0
0
1
0
1
1
1
0
1
1
1
1
1
0
2
1
0
2
1
1
2
2
0
2
2
1
1
0
0
2
0
0
2
2
2
0
1
1
1
2
0
0
1
1
0
1
1
0
1
2
0
2
1
1
2
0
1
2
0
0
0
1
0
0
0
1
2
0
1
1
1
0
2
0
0
1
0
0
1
2
1
2
1
1
1
0
1
1
0
2
3
2
0
1
2
1
2
1
1
0
0
1
0
2
0
1
0
1
0
1
1
1
1
0
1
2
1
0
1
0
1
1
0
1
2
2
0
3
0
0
0
1
0
1
0
0
0
0
2
1
1
1
1
2
2
1
2
2
0
1
2
2
0
1
0
0
0
0
1
1
1
0
1
1
0
0
1
0
0
1
1
0
1
0
0
0
0
2
0
1
0
0
1
1
2
0
1
2
0
0
0
0
1
2
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
1
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
1
0
1
2
2
0
2
1
1
1
0
2
1
1
0
1
2
0
0
2
0
0
0
0
1
0
0
0
1
2
2
1
1
0
0
0
0
0
2
2
0
0
2
0
1
1
1
1
1
2
2
0
1
0
1
0
2
0
0
0
2
1
0
1
0
2
1
1
1
0
1
0
0
0
1
0
0
1
1
2
0
1
2
2
1
1
2
2
1
1
2
0
1
0
2
2
1
1
2
0
0
1
0
1
0
0
2
2
1
1
1
1
0
2
1
0
2
1
0
0
1
0
1
0
0
0
1
2
1
0
0
1
1
0
0
2
1
2
1
2
2
1
2
1
2
1
0
1
0
1
2
0
2
0
1
0
2
1
1
0
0
0
2
0
0
1
1
1
0
0
1
0
2
1
1
0
2
1
1
2
1
1
0
1
1
1
0
0
0
0
0
1
0
2
3
1
1
0
0
0
0
1
0
0
2
1
1
2
0
2
2
0
2
2
0
1
2
0
2
2
0
0
0
2
0
1
0
0
0
1
1
1
0
0
1
1
1
0
0
0
1
1
0
2
1
0
0
0
1
1
1
1
1
0
1
0
2
0
2
0
3
2
2
0
2
2
0
2
0
0
0
2
0
2
0
1
0
0
0
0
0
1
0
1
0
0
1
0
2
1
1
2
1
1
1
1
0
0
2
1
1
0
1
0
1
1
0
0
2
2
0
1
0
0
1
1
0
2
1
2
0
0
3
0
0
0
1
0
2
0
2
1
2
1
0
2
1
2
1
0
0
1
0
0
0
0
0
0
2
0
1
0
1
1
0
1
0
0
0
0
1
0
3
1
0
1
0
1
0
1
0
1
0
1
0
1
0
2
1
1
0
1
0
0
0
0
1
0
0
3
1
0
2
2
1
0
1
1
2
0
0
0
1
0
0
0
1
1
1
0
0
1
2
1
0
1
0
2
2
0
1
2
1
4
0
0
0
2
1
2
1
0
1
1
2
1
1
2
1
0
0
1
1
1
0
1
0
0
1
1
0
2
2
1
0
0
1
0
2
0
0
1
2
1
0
1
0
0
1
1
0
1
1
2
0
0
2
1
0
2
1
0
0
0
1
1
2
1
1
0
1
1
0
2
2
1
1
1
1
1
1
1
2
1
1
1
0
1
0
0
1
0
2
0
2
0
1
2
0
2
1
1
1
1
0
2
1
0
0
1
1
0
1
1
0
2
2
0
0
1
0
1
1
1
1
0
2
0
1
1
1
0
2
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
2
1
0
3
0
0
1
1
1
0
2
0
1
1
2
0
1
2
0
0
0
0
0
1
0
1
1
0
0
0
1
1
0
0
1
0
1
0
1
2
1
0
1
1
2
0
1
1
0
1
0
1
2
0
1
1
0
0
1
1
1
2
2
1
2
1
0
1
0
0
1
1
2
1
1
0
0
1
0
0
0
1
1
0
0
1
1
2
0
2
2
0
2
1
0
1
0
2
0
1
0
2
2
1
2
0
2
2
2
0
3
0
1
0
1
1
1
0
0
2
1
2
2
0
0
0
1
1
0
1
1
1
2
0
0
0
0
2
0
1
1
0
1
0
1
0
0
2
1
0
2
0
1
0
0
2
0
2
0
0
2
0
1
1
1
1
0
1
2
0
2
0
1
2
0
1
1
1
0
1
0
0
1
1
1
1
1
0
2
0
0
1
2
1
0
1
0
1
1
1
0
0
1
0
1
2
2
2
0
1
1
0
0
0
2
1
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
2
1
0
2
1
1
6
1
1
2
0
2
0
0
0
1
0
0
0
0
2
1
1
2
1
0
1
0
0
1
0
1
0
2
2
2
1
0
2
1
0
1
2
0
1
1
0
2
0
0
1
1
2
0
1
1
0
0
2
0
0
0
0
0
1
2
1
0
1
1
1
0
2
2
0
1
1
1
1
1
1
2
2
0
1
0
2
0
0
1
1
0
0
0
0
0
0
0
1
2
1
1
0
0
0
0
1
1
2
0
0
0
1
0
1
0
0
2
1
0
0
1
0
0
1
0
0
2
2
0
0
0
1
0
1
1
0
0
1
0
2
0
0
2
1
1
0
2
0
2
0
0
0
2
1
2
1
0
2
2
0
1
1
1
2
0
2
1
0
0
1
0
1
1
0
2
0
0
0
0
1
1
1
0
0
0
1
2
2
1
0
0
1
1
0
1
2
1
2
1
0
0
1
0
2
1
0
2
2
0
0
1
2
2
0
3
2
0
1
0
2
1
2
0
1
0
0
0
0
0
2
0
0
1
2
1
2
1
1
1
1
1
1
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
1
1
1
0
0
1
3
0
0
2
2
2
1
0
0
3
1
0
0
0
0
1
2
1
0
0
0
1
0
0
0
1
0
0
0
1
1
3
0
1
0
1
1
3
0
1
1
1
1
4
2
0
1
0
0
0
2
1
0
0
0
1
1
1
2
1
0
0
1
0
0
1
1
1
1
0
0
0
0
0
0
1
0
1
1
1
1
0
1
0
0
0
0
1
2
1
0
1
0
1
1
1
1
1
0
1
2
1
1
1
0
1
0
2
1
2
0
1
1
0
0
1
1
1
0
1
1
2
1
1
0
2
1
0
0
0
1
0
0
0
1
2
1
1
2
2
2
0
1
1
0
1
0
1
1
1
0
0
2
0
0
2
1
2
2
1
1
1
1
1
1
1
0
2
0
0
1
0
1
0
0
0
1
1
2
2
1
2
2
1
3
0
1
2
2
0
1
0
1
2
0
1
0
1
1
2
1
1
0
0
2
0
1
2
0
0
2
2
0
0
0
0
1
1
0
1
1
0
1
1
3
1
2
1
1
2
1
1
1
0
0
0
2
0
1
0
0
1
2
1
1
1
0
0
0
0
2
0
0
1
0
0
1
1
1
2
1
0
1
2
0
1
1
1
0
0
2
1
0
2
0
0
1
1
0
1
0
1
0
0
0
1
0
0
1
1
0
2
2
2
1
2
1
1
2
0
1
2
0
0
0
0
0
0
0
2
2
0
0
1
1
0
1
2
0
1
2
0
2
1
1
2
0
1
1
1
2
0
0
0
1
0
2
0
0
3
1
0
2
2
0
1
0
0
1
2
1
1
0
2
0
1
0
0
2
0
1
1
0
0
3
0
1
0
0
1
0
1
0
1
2
1
1
1
0
2
0
1
1
0
2
2
0
3
0
0
1
2
1
2
0
0
0
0
0
1
1
1
2
1
2
0
1
2
1
1
1
1
0
2
1
3
1
1
0
2
0
0
2
1
2
1
0
1
0
0
2
1
0
0
0
0
1
1
0
1
0
1
0
1
0
1
0
0
1
0
1
0
1
1
2
0
1
0
0
1
1
1
0
0
0
1
2
2
1
2
0
0
0
0
1
1
1
0
2
1
3
0
2
1
0
2
1
0
0
2
0
2
2
2
1
2
0
0
0
0
1
1
0
1
2
1
2
1
2
1
1
0
0
0
0
1
2
2
0
0
1
0
2
2
2
1
1
2
0
2
1
0
2
2
2
1
2
0
1
0
2
1
0
1
2
2
2
2
2
0
0
1
0
1
3
0
0
0
1
2
0
0
1
1
0
0
1
1
1
0
0
1
0
2
1
2
0
1
1
0
0
0
2
2
0
0
1
2
2
0
1
1
1
1
0
0
1
0
1
2
0
2
2
1
0
0
0
1
1
0
2
0
1
1
0
2
2
1
0
0
1
1
2
0
0
1
2
0
0
0
1
1
2
0
1
2
1
0
0
0
0
0
0
1
0
3
0
1
0
1
0
0
0
0
0
0
3
2
1
0
0
1
2
0
0
1
2
1
3
1
1
2
0
2
2
1
0
0
0
0
1
1
0
1
1
1
1
1
1
0
1
2
2
1
0
2
3
2
1
0
0
2
2
2
0
0
3
2
2
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
2
1
1
2
1
0
1
0
1
1
0
0
0
0
0
0
1
0
0
2
0
0
1
2
0
0
1
1
1
1
1
0
0
1
1
0
0
2
1
1
0
0
0
0
2
0
1
0
1
1
1
0
3
1
1
1
1
0
1
1
2
2
2
2
1
0
0
0
0
1
1
2
0
0
2
0
1
0
1
0
1
0
0
0
0
2
0
0
0
1
0
2
1
1
1
5
1
2
0
0
0
2
1
1
2
1
4
1
7
2
0
0
1
1
1
0
1
0
2
1
0
0
0
1
0
0
0
1
1
0
1
0
1
1
0
0
0
1
0
2
1
1
1
0
2
2
0
0
1
1
1
0
0
1
1
0
0
1
2
0
2
0
0
0
1
2
0
0
1
1
0
0
0
1
0
2
2
1
1
1
1
0
0
1
1
0
0
0
1
0
14
0
1
2
1
1
2
1
0
0
0
0
0
2
0
1
1
2
2
1
0
0
1
0
0
2
0
1
0
0
2
0
1
1
1
0
2
0
0
1
2
0
1
1
0
0
1
1
0
0
0
2
0
0
1
0
0
1
1
1
1
3
2
1
1
1
1
0
1
0
1
1
1
0
1
0
2
1
0
0
2
0
0
2
1
0
1
2
2
0
1
0
0
0
1
2
0
1
0
2
2
0
0
1
1
2
1
1
0
1
0
1
0
1
1
0
0
1
2
0
1
0
0
0
1
0
1
2
0
0
1
2
1
1
1
2
1
0
0
0
1
1
2
1
0
3
2
1
2
0
1
0
0
0
2
1
0
0
0
1
2
2
2
2
1
0
0
0
1
1
2
0
0
0
1
0
0
1
1
2
0
0
0
1
0
0
0
1
0
1
0
1
0
3
0
0
0
2
0
0
1
1
0
1
0
1
0
2
0
1
1
0
0
1
1
0
0
0
1
0
0
1
1
0
1
1
1
0
0
1
0
0
0
1
0
1
0
2
1
0
2
1
0
0
0
1
0
0
0
2
0
0
1
0
0
2
1
2
0
1
0
0
1
0
1
2
2
0
0
0
1
1
0
1
2
0
0
2
1
2
2
2
0
0
0
0
2
1
0
0
1
1
1
1
1
0
2
2
0
1
1
1
1
1
0
0
1
0
1
0
2
2
1
1
1
0
2
1
1
2
0
0
2
1
0
2
0
0
0
1
2
1
0
2
1
2
0
2
0
1
0
2
1
0
1
2
1
2
0
1
1
1
2
0
0
1
1
1
2
0
2
0
1
0
1
1
0
1
2
0
1
1
2
0
0
0
1
1
0
0
0
1
1
2
0
1
1
1
0
1
0
0
0
0
1
2
0
3
1
0
2
1
0
1
2
1
2
1
2
0
0
0
0
0
0
1
0
2
2
1
0
1
0
2
0
1
2
1
0
0
1
0
1
0
1
3
1
2
2
2
0
1
0
0
0
2
0
2
1
0
1
2
1
0
0
2
0
0
0
2
1
2
1
1
0
1
2
0
1
0
0
3
1
0
2
0
0
1
0
1
2
2
0
3
3
2
0
2
0
1
2
2
1
0
0
0
2
1
1
0
2
2
2
2
0
0
0
0
0
0
1
0
2
0
1
0
1
0
4
1
0
2
1
1
2
2
0
0
0
2
0
1
2
1
1
1
0
1
0
1
0
0
2
2
0
2
1
1
0
1
0
0
1
0
1
0
2
0
1
0
2
0
0
0
1
2
1
0
0
0
2
0
0
1
0
0
2
1
0
0
0
2
0
1
2
2
0
0
2
1
0
1
1
0
0
0
2
0
0
0
1
1
0
0
1
0
0
1
0
1
0
0
0
1
1
2
0
0
2
1
2
0
0
1
2
1
1
2
0
1
2
0
1
0
0
0
0
0
2
1
1
0
1
1
2
0
0
0
1
1
1
2
1
0
0
1
1
2
0
1
3
1
2
0
1
2
0
0
0
1
2
0
2
0
0
0
2
0
1
1
1
0
0
0
0
2
1
1
1
0
0
0
0
1
0
0
2
1
0
0
1
1
0
1
0
0
0
2
1
0
1
1
1
1
0
0
0
1
2
1
0
2
1
0
2
4
1
1
0
2
0
0
3
1
0
0
0
1
0
0
4
2
1
1
1
1
1
1
0
1
0
4
1
2
0
0
0
2
2
0
0
2
0
2
2
0
2
1
0
0
1
2
0
1
2
1
0
3
1
1
1
2
1
0
0
2
1
2
0
0
0
2
0
0
0
0
1
1
1
2
0
0
0
1
0
0
0
0
0
0
2
1
1
1
2
0
0
0
2
1
0
0
1
2
1
1
0
1
0
0
2
0
0
0
0
0
2
2
0
2
0
2
0
1
1
2
0
1
1
1
1
0
0
0
1
2
0
2
0
2
1
1
2
0
1
0
2
2
1
2
1
1
0
2
0
1
1
2
0
0
1
0
1
0
2
1
0
2
0
1
1
2
0
2
0
1
1
1
2
1
0
0
0
1
2
2
2
0
0
1
1
1
0
0
0
2
1
2
0
2
0
0
1
1
1
3
1
2
0
0
1
0
2
2
0
1
0
1
1
0
1
1
2
1
0
2
1
0
1
2
0
2
2
2
1
1
2
0
2
1
0
0
1
1
0
0
0
0
1
2
3
0
1
1
0
0
2
0
0
1
0
1
2
0
1
1
0
1
1
0
1
0
1
1
0
0
0
0
0
2
0
2
2
1
0
0
2
0
2
1
0
2
1
2
1
2
1
2
2
0
2
0
0
1
0
0
1
0
0
2
2
0
2
0
0
3
2
2
0
0
0
0
2
0
1
2
2
2
0
2
2
1
2
1
2
1
1
1
0
0
0
1
0
0
1
2
1
2
1
0
1
0
0
2
0
0
1
0
1
2
1
1
2
2
0
0
0
0
1
1
0
0
0
1
1
0
0
2
0
2
2
2
0
2
1
2
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
2
1
2
1
0
1
0
2
1
0
1
1
0
0
1
2
2
0
0
1
0
0
3
2
0
1
2
1
0
1
1
0
1
0
0
1
0
2
1
1
1
0
0
1
0
1
1
0
1
0
0
0
0
1
1
0
0
0
1
2
0
0
0
1
3
0
0
1
0
1
2
0
0
0
0
0
1
1
2
1
1
1
1
1
0
1
1
0
1
0
1
2
0
0
1
1
0
0
0
0
0
0
1
2
1
2
0
1
0
2
0
1
0
3
2
0
0
1
0
1
2
0
0
1
1
0
1
1
3
0
1
0
1
1
0
0
0
2
1
2
2
2
0
0
3
0
0
2
1
2
2
2
2
0
1
0
0
1
1
1
1
0
1
1
0
0
2
2
2
1
1
0
1
1
1
0
0
1
1
0
0
1
2
1
1
0
0
1
0
0
0
2
2
0
1
1
0
0
2
0
0
2
1
0
1
2
0
1
0
0
1
0
2
0
0
0
1
2
0
3
0
1
1
0
0
0
0
0
0
1
2
1
0
1
0
0
1
2
1
1
2
2
2
0
0
1
0
0
2
0
2
1
2
1
0
0
2
1
0
0
1
0
1
1
0
1
0
1
1
0
1
0
1
2
1
1
0
1
1
2
0
2
1
2
1
2
0
1
0
2
0
2
0
0
0
0
0
1
1
0
1
2
0
0
2
0
0
0
0
1
1
0
0
2
0
2
0
1
0
1
5
0
0
1
0
0
2
0
0
0
2
0
0
1
1
1
0
1
3
1
1
1
0
2
0
1
0
3
1
1
1
2
1
0
1
0
0
0
0
1
0
1
2
1
1
2
2
0
2
2
1
0
1
0
2
1
2
2
2
0
2
1
0
2
0
0
1
0
1
0
0
2
0
2
0
1
0
0
2
1
2
1
2
1
1
0
0
1
0
0
0
0
0
0
0
1
1
1
2
0
2
2
2
1
1
1
2
2
2
2
0
1
1
1
0
2
1
0
1
2
2
2
1
1
1
2
0
0
2
1
0
0
0
1
0
0
1
0
1
0
1
1
0
2
0
0
2
2
0
1
2
0
0
0
3
2
0
2
1
1
0
0
0
2
0
1
2
2
2
2
1
1
1
0
0
0
0
1
2
1
0
0
2
2
2
1
2
0
1
1
2
0
1
0
0
1
0
1
1
0
0
0
2
2
1
1
0
0
0
0
2
1
1
3
2
0
2
0
1
0
0
1
0
0
1
2
2
1
0
0
1
1
0
2
2
1
2
0
0
2
8
1
1
0
0
2
0
0
0
3
1
0
1
0
0
1
1
1
0
0
0
0
1
1
0
2
1
2
1
0
1
0
0
2
1
0
0
0
2
0
2
0
0
0
0
0
2
2
0
1
0
2
0
1
0
1
1
1
1
1
3
1
0
0
0
0
1
1
1
0
0
1
1
0
1
0
0
1
0
0
2
1
0
0
0
1
3
2
0
2
1
0
2
0
0
1
0
0
0
0
1
3
0
1
1
2
1
0
1
2
1
0
2
1
0
2
1
1
0
0
1
1
0
0
2
1
1
2
1
1
2
0
0
3
1
1
0
0
0
0
0
1
1
0
1
0
3
0
1
2
1
1
2
0
0
1
1
0
1
3
0
0
1
0
2
1
0
0
0
0
1
1
2
0
0
0
2
1
2
0
1
1
1
2
0
1
1
0
1
1
1
1
1
0
2
2
0
1
2
0
1
0
2
0
2
0
0
2
2
2
0
1
1
0
0
0
1
2
1
0
2
1
0
1
1
0
0
1
0
1
2
2
1
2
1
1
0
1
0
2
0
0
0
1
0
2
0
0
1
2
1
1
1
2
1
1
0
0
0
0
0
2
1
2
2
2
1
0
0
2
1
0
1
1
0
0
3
1
0
1
1
0
0
1
0
2
0
1
1
0
0
0
0
0
1
1
0
0
2
0
0
1
2
1
1
2
0
1
2
3
3
1
1
0
1
0
0
0
2
0
1
0
0
0
1
0
3
2
0
1
1
2
1
0
0
4
0
1
2
0
0
0
0
1
2
1
1
2
0
2
0
1
1
0
0
2
0
0
0
1
0
1
2
2
0
2
2
2
0
1
1
2
0
0
1
0
1
1
1
1
0
0
1
3
2
0
0
0
0
0
1
1
2
0
0
1
0
2
2
2
0
1
2
0
1
0
1
2
0
0
0
1
1
1
0
0
1
0
2
1
1
2
1
1
0
2
0
1
2
1
0
0
3
1
0
1
1
2
0
2
0
1
0
1
2
0
0
3
2
1
0
3
0
0
1
1
0
0
1
1
1
1
0
1
1
1
1
0
0
0
3
0
1
0
0
2
1
1
1
0
1
0
0
0
1
0
0
0
0
1
1
0
0
1
1
0
0
1
1
0
1
1
1
0
0
0
0
1
0
1
0
0
0
2
0
1
0
2
0
0
2
0
2
1
1
1
1
1
1
0
1
2
1
1
2
1
1
2
0
1
0
1
0
1
0
1
2
0
1
0
0
0
0
2
0
1
0
2
1
2
1
0
1
1
0
0
2
0
1
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
2
0
2
1
0
0
1
0
2
1
1
2
0
2
0
3
1
1
0
2
2
0
0
1
1
0
1
1
5
1
0
0
0
1
1
2
0
0
2
1
0
1
0
1
0
2
0
0
1
1
0
0
0
1
0
2
0
0
0
0
1
2
1
2
0
1
1
0
2
1
0
0
1
0
0
0
1
2
2
1
2
1
1
0
0
0
1
1
0
0
2
3
0
2
0
0
0
0
2
2
0
2
0
0
0
1
0
1
2
0
1
0
1
2
1
1
2
2
2
0
1
0
3
0
1
1
2
1
0
1
1
2
1
0
3
1
0
2
1
1
2
0
0
2
1
0
1
0
1
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
2
1
0
0
1
2
0
1
0
2
1
0
1
1
2
2
1
1
2
0
2
0
0
1
0
0
2
6
0
1
0
1
0
1
0
0
1
2
0
0
1
1
2
0
2
0
0
0
0
1
0
0
0
2
1
0
1
1
1
1
1
0
1
1
1
2
0
2
0
0
2
1
1
2
1
0
0
1
0
2
2
2
2
3
1
0
1
2
1
1
1
2
2
2
2
1
1
0
1
0
0
0
0
0
1
2
2
0
2
1
2
0
2
1
2
2
1
3
0
1
2
1
0
0
2
0
2
1
1
1
2
2
0
2
1
0
1
0
1
0
1
0
0
1
0
2
0
2
1
3
0
0
0
0
0
2
0
1
2
1
0
2
1
1
0
0
1
2
0
0
0
1
0
1
3
0
2
0
2
0
0
1
2
2
1
0
2
0
2
1
3
0
2
0
1
1
0
2
1
0
2
0
1
0
0
2
1
1
0
0
0
1
2
0
2
0
1
2
2
1
2
0
2
2
1
0
0
0
1
0
1
0
0
1
0
0
2
0
5
1
2
0
1
0
1
1
0
0
0
2
1
1
1
2
2
1
1
2
1
0
2
1
0
0
1
1
0
1
2
0
1
0
0
2
0
1
0
2
1
0
0
0
0
2
1
2
0
0
0
1
2
1
2
0
0
0
1
0
0
2
0
1
0
1
0
1
0
2
1
1
1
1
1
1
1
0
1
0
2
0
0
1
1
2
1
0
0
1
0
0
2
2
1
0
1
1
1
1
0
0
0
2
1
3
0
2
1
0
2
0
0
0
2
1
2
1
1
0
2
1
1
0
2
0
2
2
2
0
1
0
1
0
2
1
1
1
0
0
0
2
0
2
2
0
1
1
2
1
1
1
1
2
1
1
0
1
2
1
0
0
1
0
1
1
0
1
1
0
0
0
1
1
1
2
0
0
1
0
1
1
2
1
1
2
1
2
2
1
0
0
0
2
1
0
1
2
0
2
1
2
0
0
0
0
2
4
1
1
1
0
0
0
1
0
0
1
0
0
1
1
2
2
2
0
0
2
1
1
0
0
0
1
1
0
0
1
1
0
2
1
0
1
0
0
1
0
1
0
0
1
0
1
0
1
1
0
1
0
2
0
1
0
1
0
2
0
0
0
2
0
1
1
1
1
0
0
0
0
2
0
1
1
1
0
0
2
0
1
1
0
2
1
0
2
0
0
0
0
1
2
0
2
0
2
2
2
1
2
0
2
1
0
1
1
0
1
0
0
1
0
2
0
0
1
0
0
1
1
2
0
0
1
0
0
0
2
0
0
2
1
2
0
2
2
2
2
2
0
2
0
1
1
1
3
1
0
0
1
1
0
0
0
1
2
0
0
1
0
0
0
1
0
1
1
0
1
2
0
0
2
2
0
0
0
0
2
1
2
2
1
1
0
0
1
0
1
1
2
1
0
1
1
1
1
0
0
0
0
0
0
1
0
0
1
1
1
1
1
2
0
1
1
0
0
0
1
2
0
2
2
0
1
1
1
1
0
0
0
2
0
1
0
1
2
1
0
1
3
2
3
2
2
0
1
0
0
1
1
2
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
1
2
1
0
0
1
2
1
0
1
4
0
0
3
0
1
2
1
1
1
0
1
0
1
0
2
2
0
2
1
2
2
2
2
0
1
1
1
2
2
2
2
1
0
1
0
3
0
2
2
1
0
1
1
1
0
2
0
0
0
0
0
0
0
1
1
1
1
2
1
1
1
0
0
1
0
1
2
0
0
1
0
1
0
2
0
2
0
2
0
0
0
1
1
1
0
0
0
1
0
1
1
1
1
0
0
1
1
1
0
0
0
1
1
0
1
2
1
2
1
0
2
2
1
0
1
1
0
1
2
0
0
0
0
1
1
1
1
1
1
0
2
1
0
0
2
0
0
0
2
0
0
0
2
1
0
0
1
2
1
0
0
1
2
1
2
0
0
0
0
0
0
0
0
1
0
0
1
1
1
1
2
0
1
0
2
1
0
1
0
1
0
2
1
0
1
1
0
2
0
2
1
0
1
0
0
0
1
1
1
2
0
0
1
0
1
1
1
0
1
0
0
1
0
1
1
1
1
0
2
0
2
1
1
0
0
1
0
2
2
1
2
0
1
1
0
0
2
2
1
1
0
2
1
1
1
0
1
0
0
2
0
1
0
0
2
0
2
0
0
1
2
0
2
0
0
0
1
2
1
0
0
2
0
0
1
1
2
2
0
2
1
1
0
0
0
1
1
1
0
1
0
0
0
2
0
1
0
0
0
1
1
2
2
1
2
1
1
2
1
3
1
0
1
1
0
2
1
0
0
1
0
1
2
3
2
1
0
1
1
2
2
2
2
0
0
0
0
0
2
2
0
2
0
0
2
4
1
0
2
2
0
0
2
1
1
2
1
2
0
1
1
1
1
0
2
0
1
1
0
2
2
2
1
2
0
1
3
0
0
1
0
1
0
0
1
0
1
0
1
1
0
0
0
1
1
0
0
0
0
1
1
4
4
2
1
2
0
1
1
0
1
0
1
1
2
1
1
1
1
0
2
1
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
1
1
1
2
0
0
2
1
2
0
0
0
1
1
1
2
1
0
2
1
0
0
0
1
0
1
0
0
0
0
1
0
1
0
2
0
1
2
0
0
1
0
0
0
0
1
2
1
1
0
0
0
1
0
2
2
0
0
0
0
2
1
0
1
1
2
2
1
2
1
0
0
0
0
1
2
1
3
1
0
2
2
1
0
1
1
1
1
0
2
0
1
1
0
1
1
0
1
1
0
0
0
1
2
1
0
2
1
0
1
0
2
0
1
2
0
1
1
0
1
1
0
0
0
2
0
0
1
1
1
1
0
1
0
1
1
0
0
1
0
0
3
0
2
0
2
0
1
0
1
0
1
1
1
1
0
2
0
0
1
0
2
1
1
2
2
0
0
1
0
1
0
0
0
1
0
1
0
1
1
2
2
0
0
0
0
1
0
1
1
3
0
0
2
2
2
0
1
0
0
1
0
0
0
0
0
0
2
2
1
0
2
1
1
0
2
0
2
0
0
2
0
1
0
2
1
1
2
0
1
1
2
2
0
0
0
1
0
1
2
0
2
0
1
0
0
0
2
0
0
1
0
1
1
0
2
1
0
0
0
0
1
0
0
2
0
1
1
2
2
1
0
0
0
2
0
0
1
1
0
0
1
1
0
2
1
0
0
2
0
0
1
0
1
1
1
0
2
2
1
1
1
2
1
1
2
1
0
0
0
0
0
0
1
1
2
2
2
1
3
0
0
1
0
4
0
2
0
0
1
1
1
1
1
0
1
1
0
1
2
0
1
0
2
1
1
0
1
1
2
0
1
0
0
1
1
2
3
0
0
2
0
0
0
1
1
1
0
2
1
1
2
0
2
1
1
0
0
1
0
1
0
1
0
0
1
0
1
0
1
1
0
2
0
0
0
1
2
0
1
0
1
2
1
0
2
2
0
1
1
1
2
1
0
0
0
0
2
0
0
2
2
2
1
0
0
2
0
0
0
0
0
1
1
0
1
1
2
0
2
0
0
1
0
0
0
1
0
0
2
0
0
1
2
2
0
0
1
1
1
1
0
0
1
2
2
1
0
1
1
0
0
0
0
2
1
7
1
1
0
1
0
2
1
0
0
2
0
0
1
2
0
1
0
0
0
0
1
0
0
0
1
0
0
2
2
0
2
1
2
1
1
1
2
1
0
2
0
2
0
0
2
0
0
1
0
1
1
0
0
2
0
1
0
0
1
0
0
2
0
0
0
0
2
1
0
0
2
0
0
1
0
0
1
1
1
0
0
1
2
2
0
0
1
1
1
2
1
2
1
1
2
1
0
0
1
0
1
1
1
1
0
2
1
0
0
0
1
2
1
0
1
2
2
1
0
1
1
1
0
1
2
1
1
0
0
0
2
0
2
0
2
0
1
2
2
0
2
1
1
0
0
1
1
1
0
2
0
0
0
0
1
1
0
1
0
1
2
1
1
2
0
1
0
0
1
1
2
0
0
0
1
2
2
1
2
0
1
1
0
0
2
0
0
0
1
0
0
1
2
1
2
1
1
0
0
1
1
2
0
1
1
0
1
1
2
2
0
0
1
1
1
0
1
0
0
0
0
1
2
0
0
1
2
0
1
0
1
1
2
2
1
1
1
1
1
0
0
2
2
0
2
1
0
2
0
1
0
0
2
2
0
1
0
1
0
2
0
0
0
1
0
0
1
1
0
1
0
1
0
0
1
0
2
2
2
1
1
1
0
2
1
0
1
2
0
1
2
2
2
0
2
0
3
0
3
2
0
0
1
0
1
0
0
1
0
2
2
1
1
0
2
1
1
0
1
0
2
0
1
0
0
0
2
0
0
0
1
0
1
1
1
1
1
1
2
0
1
0
3
1
1
0
0
2
2
1
0
0
0
1
0
1
3
0
0
2
2
0
1
0
0
2
1
1
2
0
0
1
2
1
1
1
1
1
0
0
2
1
1
1
0
2
2
2
2
1
1
1
0
0
1
1
0
1
0
2
0
2
2
1
0
0
0
1
3
1
1
1
2
1
1
0
1
1
0
0
1
1
1
1
2
1
1
1
1
0
0
1
0
0
0
2
1
1
0
1
0
1
2
0
1
1
0
0
0
1
2
2
0
1
0
2
0
2
0
1
2
0
1
1
1
2
2
1
1
0
0
1
0
1
0
1
1
1
0
1
1
0
0
2
1
1
2
0
2
1
2
1
0
1
1
2
2
0
1
1
0
0
0
2
1
1
0
1
1
1
1
1
1
1
1
0
1
0
2
0
1
1
1
1
1
0
0
1
0
2
3
1
0
0
2
0
0
1
0
1
2
0
1
0
1
1
0
1
0
0
1
1
1
2
2
0
0
1
2
1
1
1
1
1
1
0
0
2
2
2
1
1
3
1
3
0
2
0
1
0
1
0
1
1
1
1
2
3
0
1
1
0
1
1
2
1
0
0
1
0
1
1
1
1
0
2
0
2
2
1
2
0
1
1
1
0
3
1
0
1
1
1
0
0
0
0
0
0
1
1
0
1
1
0
0
1
2
0
1
2
2
0
2
2
1
2
0
2
1
0
0
1
2
1
1
2
1
0
1
0
2
1
2
0
1
1
2
1
0
1
0
2
0
2
0
1
1
2
1
2
1
3
1
0
1
2
1
0
1
1
2
0
1
2
1
1
0
1
0
1
2
1
1
1
1
1
0
0
0
0
0
2
1
1
1
0
0
1
2
1
0
0
1
2
0
0
2
1
1
1
0
0
1
2
2
2
1
1
1
1
0
1
0
0
0
0
2
2
0
2
1
0
0
1
1
0
0
1
0
0
0
0
1
1
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
1
1
0
1
0
2
1
1
0
1
0
3
2
0
1
0
1
0
0
1
1
2
2
2
1
0
0
0
2
0
1
0
0
2
0
0
0
0
2
0
1
1
0
1
2
0
0
0
1
0
0
4
1
0
0
0
1
0
2
0
0
0
2
1
1
0
0
0
2
2
1
2
1
0
2
1
0
0
0
0
1
0
3
2
1
0
0
0
2
0
2
1
1
1
0
0
2
0
1
0
2
1
2
1
0
7
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
2
1
0
2
0
1
0
2
1
1
2
0
0
1
0
1
0
2
2
2
2
1
0
0
0
1
1
1
1
1
0
2
0
1
0
1
0
0
0
1
2
0
0
0
1
3
1
0
1
1
0
2
1
0
1
1
2
0
0
2
0
0
0
1
1
0
1
0
0
0
1
0
1
0
2
0
1
0
1
0
1
1
0
2
1
2
0
1
0
0
0
0
1
2
1
1
0
2
0
0
2
0
0
0
0
1
1
0
0
0
2
0
1
1
0
2
1
0
2
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
1
1
1
2
0
0
0
3
2
4
1
2
0
0
1
0
2
0
1
1
1
0
1
0
0
2
3
0
2
0
0
3
2
0
0
0
1
1
2
1
0
2
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
1
1
0
2
0
0
1
0
0
1
1
1
0
0
3
0
1
0
0
0
2
1
0
0
2
1
0
1
0
1
2
1
0
0
0
0
1
1
0
0
2
1
0
6
2
1
1
1
2
0
0
1
1
0
1
1
1
0
0
0
2
0
0
0
2
0
1
1
0
2
1
2
1
0
2
3
0
0
1
2
2
0
0
0
0
0
0
1
3
0
2
1
2
0
1
0
1
1
2
0
1
0
0
0
1
1
0
0
2
2
2
0
2
0
1
2
2
0
1
2
1
2
0
0
1
1
2
2
0
1
0
1
3
1
0
0
0
2
0
0
1
0
2
0
6
0
1
1
2
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
2
1
2
0
0
0
2
0
0
1
2
1
1
0
1
2
0
0
1
2
1
3
1
1
1
0
0
1
0
2
0
1
1
0
1
1
1
0
1
0
0
1
0
1
0
1
0
1
1
1
0
1
2
1
1
0
1
0
0
3
0
2
0
1
0
0
0
0
2
2
1
0
2
0
2
2
0
2
0
0
2
0
1
0
1
1
2
1
1
0
2
0
0
0
1
1
0
0
0
0
1
0
1
0
0
1
2
2
1
2
0
0
0
0
1
0
0
1
1
0
0
0
1
2
2
0
2
1
1
1
0
2
0
0
1
0
0
1
1
1
2
1
0
0
1
1
0
0
0
1
1
2
0
0
1
1
0
1
1
1
1
3
0
1
0
0
1
1
1
1
0
1
3
1
0
1
0
0
0
2
2
1
0
1
0
2
2
2
0
1
1
1
2
0
2
2
0
0
1
2
0
2
0
1
2
1
0
1
0
3
1
1
0
0
0
1
0
1
2
0
1
0
0
2
2
1
0
0
1
1
1
1
0
1
1
0
1
2
1
0
3
1
2
1
0
0
1
1
3
2
0
2
1
0
1
0
0
1
0
0
0
0
0
1
0
1
1
1
2
0
0
2
2
1
1
0
1
2
1
0
0
2
1
0
1
1
0
2
1
2
1
0
1
2
2
1
1
1
0
0
2
0
1
2
2
1
2
0
0
1
2
0
0
0
0
0
2
0
0
1
2
0
0
2
1
0
1
0
1
1
0
0
0
1
1
1
1
2
1
0
1
1
1
0
0
2
0
0
0
0
1
1
0
1
1
0
2
2
2
3
1
0
2
2
0
0
1
1
1
0
0
1
0
2
2
1
1
0
1
0
0
1
0
0
0
2
2
0
1
0
1
0
1
0
1
1
0
2
2
1
1
1
1
1
1
0
0
1
1
2
1
2
0
1
1
1
1
1
2
0
0
1
0
2
0
1
1
1
2
0
2
2
0
0
0
0
1
1
2
1
0
0
1
0
0
1
0
1
1
0
2
1
1
1
2
2
1
2
1
1
2
2
0
0
1
0
0
1
1
0
0
1
2
0
1
1
0
1
1
0
1
2
7
1
1
2
0
0
1
2
0
0
1
2
0
1
0
2
1
2
1
1
2
2
1
1
1
0
2
1
2
2
0
1
1
1
1
2
1
1
0
0
2
2
0
2
1
0
2
2
1
1
3
2
0
0
0
0
2
0
2
0
1
0
4
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
1
1
0
0
2
1
1
1
2
0
1
1
0
2
0
2
2
0
0
0
1
0
1
0
1
1
2
2
2
0
2
2
0
1
1
0
0
2
0
1
2
1
1
1
0
0
1
2
0
0
1
0
1
1
0
0
2
0
0
0
2
3
0
0
2
1
1
1
1
1
1
2
0
2
1
0
0
1
1
1
0
0
2
0
1
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
2
0
0
1
2
0
0
0
0
2
1
1
0
0
1
0
1
1
1
2
0
2
0
2
0
0
0
0
1
0
1
0
1
0
1
0
2
2
0
1
1
0
1
2
0
1
2
1
1
1
1
0
2
0
1
1
0
1
0
0
0
1
0
1
0
2
0
2
0
2
0
2
1
2
2
2
0
1
2
1
2
1
1
1
0
0
0
1
1
0
1
2
0
1
0
1
0
0
0
0
0
1
0
0
1
0
2
0
2
1
1
1
0
0
0
1
0
1
2
0
2
1
1
1
0
2
0
1
0
0
1
1
0
1
0
1
0
0
0
2
0
2
0
2
2
0
1
0
1
2
0
1
1
0
1
1
1
1
0
0
3
1
0
0
1
1
1
2
0
0
1
1
0
2
0
1
1
1
0
1
1
0
0
1
1
0
2
0
1
0
0
0
1
2
1
2
0
1
1
0
2
0
0
1
1
1
1
0
1
2
1
2
1
1
0
1
0
0
0
0
2
0
2
1
1
2
0
1
1
1
1
0
1
0
2
1
1
0
1
1
0
2
0
1
0
0
1
0
2
2
0
0
1
1
2
2
0
1
1
0
2
2
1
0
0
0
0
2
0
2
1
2
1
2
0
1
0
0
1
2
0
1
0
2
1
0
1
0
1
0
1
2
1
2
2
1
1
1
2
0
3
1
1
1
1
1
0
1
0
1
1
1
1
0
0
2
1
1
0
1
2
0
1
0
1
0
1
1
2
0
0
1
0
0
1
4
1
1
0
0
0
0
1
1
1
0
2
0
0
1
0
1
0
0
1
2
0
5
2
1
1
2
0
0
1
1
1
0
1
0
2
1
5
0
0
0
1
1
2
1
0
1
1
1
1
0
1
1
0
1
2
1
2
1
0
1
1
1
2
1
0
0
0
1
2
2
0
2
1
1
0
1
1
0
3
0
1
0
2
0
0
1
1
0
1
1
0
2
0
1
0
1
1
1
0
0
1
1
1
1
1
0
0
2
0
0
1
1
2
0
0
0
3
1
0
0
1
2
0
2
1
2
2
1
0
1
0
0
0
1
0
2
0
2
0
0
1
1
1
0
0
0
0
0
0
1
1
0
0
3
0
2
0
1
1
0
1
1
0
1
1
0
1
1
2
0
0
0
0
1
0
0
2
0
0
1
1
1
0
1
1
1
0
1
0
0
1
1
2
0
0
2
1
1
0
0
1
0
0
0
0
1
2
0
1
1
0
1
1
0
1
0
2
0
2
1
0
1
0
0
0
0
2
0
0
1
0
2
0
2
1
2
0
0
0
2
2
0
0
2
0
1
1
0
0
1
0
0
1
0
0
0
0
1
0
2
1
1
1
0
1
1
1
0
1
0
0
2
0
0
1
0
0
2
0
0
2
0
1
0
1
0
1
1
1
1
1
0
0
1
1
1
1
0
1
0
0
1
1
0
0
0
0
1
0
2
2
0
0
1
1
0
2
1
0
0
2
0
1
0
0
1
1
0
2
1
2
0
0
0
1
0
1
1
0
0
0
2
0
2
1
1
2
1
2
1
2
0
0
7
0
1
0
1
0
0
0
2
1
1
2
1
13
1
1
0
1
2
0
1
0
0
1
0
1
1
1
1
2
1
0
0
0
1
0
1
0
1
1
0
2
2
2
0
1
1
1
0
0
2
0
1
2
0
1
3
0
1
0
2
2
1
0
1
0
3
0
1
0
0
1
1
2
0
2
1
1
0
0
1
1
0
1
0
1
0
0
0
0
0
1
0
1
0
1
1
0
1
1
1
1
2
1
1
0
1
0
1
0
0
2
1
1
1
1
0
2
0
2
0
2
0
0
2
1
2
1
0
1
1
0
2
2
0
1
2
2
1
2
2
1
2
0
1
0
0
0
2
1
2
3
1
1
1
2
1
2
3
0
0
1
1
1
1
0
2
0
0
0
1
0
3
0
2
1
1
1
2
2
0
2
2
1
0
0
0
2
1
1
1
0
2
0
0
0
0
0
0
0
2
0
1
0
1
0
2
0
0
0
1
0
1
1
0
1
0
0
1
1
1
0
1
1
1
1
2
1
2
1
1
1
2
1
0
2
1
1
1
1
0
3
0
2
0
2
1
0
0
1
0
0
1
0
0
1
0
0
0
2
0
1
1
0
1
1
0
1
0
1
2
1
1
2
0
0
2
2
1
0
2
2
1
0
0
2
1
1
0
1
0
0
2
1
0
0
1
2
0
0
0
2
0
2
0
2
0
4
1
2
0
2
1
0
0
2
0
4
0
1
1
1
0
0
0
1
1
1
1
1
0
1
2
0
0
2
2
1
0
2
1
0
1
1
1
1
1
0
0
1
2
0
1
2
2
0
1
1
1
1
2
0
2
1
0
0
1
0
1
0
0
1
0
0
1
2
0
0
2
2
2
1
2
1
1
1
2
0
0
0
1
0
0
1
1
0
0
2
0
0
2
2
1
2
1
1
2
0
1
0
1
1
0
2
1
1
0
0
0
1
0
2
0
2
1
1
0
0
0
1
3
0
0
1
0
2
0
2
0
0
2
1
2
0
0
1
0
1
1
1
3
0
2
2
1
2
1
2
1
0
0
1
1
1
1
1
1
2
1
0
1
1
2
0
1
0
2
1
1
0
1
0
0
1
2
2
0
0
1
0
0
1
1
2
0
2
1
0
0
2
1
0
2
0
1
1
1
1
2
0
0
0
0
0
3
1
1
0
1
1
1
1
0
1
0
1
0
1
1
0
0
1
0
2
1
2
1
1
1
0
0
0
0
0
0
0
2
0
0
1
1
0
0
1
1
1
2
2
0
2
0
0
2
0
1
1
2
0
1
1
1
1
1
0
0
2
3
0
1
1
0
1
1
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
1
2
0
0
1
1
1
1
0
0
0
1
1
1
3
0
0
2
2
1
1
1
1
1
0
0
0
0
1
0
0
1
1
1
2
2
2
2
2
1
1
0
4
0
1
0
2
0
1
2
2
0
0
1
2
1
1
0
0
0
2
1
0
2
1
0
2
0
0
2
0
0
1
0
1
2
0
0
1
0
1
1
0
0
0
2
1
0
0
0
1
0
2
1
1
1
1
0
0
0
0
0
2
2
2
0
0
0
2
0
0
0
0
0
1
2
1
0
0
0
0
0
2
0
1
1
1
1
2
1
2
3
1
0
0
1
2
2
0
0
2
1
0
1
0
1
1
1
2
0
0
1
1
0
6
3
1
2
1
0
1
1
2
2
3
1
0
6
1
2
1
1
1
0
1
0
0
0
1
0
0
2
2
0
2
0
0
0
0
1
0
1
2
0
0
2
2
0
0
1
1
0
0
3
2
1
1
0
1
1
0
0
1
1
0
0
2
2
0
0
0
0
0
1
2
1
0
0
0
1
1
2
2
0
0
0
0
0
0
0
1
2
1
2
1
0
2
0
1
2
2
1
2
2
2
1
1
0
1
0
0
1
1
4
2
0
1
3
0
1
0
1
1
0
0
1
0
1
2
2
0
0
0
1
0
2
1
1
1
0
1
1
1
1
0
1
0
1
0
1
1
2
1
2
0
0
1
0
0
1
1
1
0
0
0
1
1
0
2
0
1
2
0
1
0
2
2
2
2
1
0
1
0
1
0
1
1
2
0
0
1
0
2
1
1
0
2
0
2
0
0
1
0
1
2
0
3
0
1
2
2
0
0
0
1
1
0
0
1
0
2
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
2
0
0
1
0
1
1
2
2
1
1
2
2
2
0
1
1
1
2
0
0
2
0
0
1
1
1
0
1
0
0
0
0
0
2
1
2
0
1
4
0
1
1
0
0
2
1
1
2
0
0
1
0
1
2
1
2
0
0
1
2
1
2
1
1
0
1
1
3
1
0
1
3
0
1
0
1
1
1
2
2
0
2
1
2
2
0
0
0
0
1
0
0
1
1
1
1
1
1
0
2
2
1
1
1
1
2
0
1
1
2
0
0
2
0
1
2
0
0
0
1
1
2
0
0
1
0
2
0
1
0
0
0
1
1
2
0
1
2
2
0
1
0
1
0
2
1
1
0
1
1
0
1
0
1
1
0
1
0
2
0
0
0
2
1
2
0
2
0
0
0
0
1
0
0
0
2
1
1
1
0
2
1
0
2
1
0
2
1
0
0
0
1
0
0
2
1
0
1
2
2
0
1
1
0
2
1
1
0
0
1
0
1
0
2
2
1
1
0
3
0
1
1
1
2
0
0
1
1
2
2
1
1
1
2
2
0
2
0
0
1
2
2
1
0
2
1
0
1
1
0
0
1
1
1
0
1
0
0
0
0
1
0
1
0
0
1
2
1
2
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
1
1
0
0
2
1
1
0
0
1
0
0
0
1
1
2
0
0
0
3
0
0
0
1
0
2
0
0
1
0
0
2
1
0
0
1
1
0
1
1
1
0
1
0
2
0
2
1
3
0
1
1
0
1
1
0
0
0
1
1
2
0
0
2
2
0
1
1
1
1
0
2
0
1
2
1
2
2
1
0
4
1
1
0
0
0
0
0
0
1
0
1
1
2
0
2
1
1
0
0
0
1
0
1
2
2
2
1
0
0
2
0
0
1
0
0
1
1
1
1
2
1
1
0
1
0
2
1
0
0
0
2
0
0
1
1
0
0
0
2
0
2
3
0
0
0
0
2
2
2
0
1
1
0
0
1
1
1
0
2
2
1
1
1
1
0
1
0
1
1
0
0
1
2
1
1
0
2
2
1
0
0
0
0
0
1
2
1
2
1
2
1
4
2
0
0
0
1
1
1
0
1
1
0
0
3
0
2
1
2
0
1
1
1
2
0
1
1
2
1
0
1
1
1
0
1
0
1
2
2
1
1
2
0
2
0
2
1
0
0
1
0
0
2
0
0
1
1
1
1
2
2
1
1
0
1
1
2
3
0
5
1
2
0
0
10
1
1
1
0
1
1
0
0
1
1
2
0
0
0
1
1
1
1
2
0
2
1
0
0
2
0
1
1
0
0
0
0
1
0
2
1
0
2
0
0
0
0
0
1
2
2
1
3
1
1
0
0
2
1
1
1
0
1
0
0
1
0
0
0
0
1
1
0
0
1
0
0
1
1
0
0
0
0
0
1
2
2
0
1
0
1
0
1
1
0
1
1
0
2
0
2
1
0
2
1
1
1
1
1
2
2
1
1
0
0
0
2
0
0
0
2
2
1
0
1
0
1
0
1
0
2
2
1
1
0
1
4
0
2
0
0
1
2
3
1
0
0
0
0
1
2
1
1
0
1
1
0
1
2
0
1
2
0
1
1
2
0
0
0
1
0
1
1
1
0
2
0
0
0
1
1
4
0
0
0
1
0
2
1
1
0
2
1
2
1
3
1
0
0
2
0
1
1
1
0
1
1
0
1
0
1
1
0
0
1
0
0
2
0
1
1
0
0
0
0
2
1
2
0
0
0
1
1
1
0
1
0
0
1
2
0
0
1
1
1
1
2
1
1
1
1
1
0
0
2
1
2
0
2
1
0
2
2
0
0
0
0
0
2
0
0
1
1
2
0
1
1
0
0
2
0
1
2
0
0
2
1
0
0
2
0
1
2
2
0
0
2
1
3
1
0
1
0
1
0
0
0
0
1
2
2
0
1
1
2
2
1
1
1
1
2
0
0
1
0
2
2
2
0
0
0
1
1
0
1
0
0
0
0
2
0
0
1
0
1
2
0
0
1
0
0
1
0
0
0
2
0
2
0
1
1
0
0
2
0
0
2
2
0
0
0
3
4
1
1
0
2
2
1
1
0
1
0
0
1
1
1
1
0
0
0
2
2
0
1
2
0
1
0
0
1
2
1
0
0
0
0
0
1
0
2
0
0
0
0
0
1
2
0
2
2
1
1
2
2
2
0
1
2
2
0
0
1
0
0
1
0
1
2
1
0
1
2
0
2
2
0
3
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
1
0
1
0
0
1
1
0
0
1
0
0
2
1
1
0
1
0
1
0
0
1
0
0
0
2
2
0
1
0
1
1
0
0
1
2
2
0
0
1
0
0
1
1
1
0
0
2
0
2
4
0
1
2
0
0
0
2
0
1
2
2
2
2
1
1
1
2
0
0
0
2
1
1
2
1
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
1
2
1
0
1
1
2
1
0
0
0
2
0
1
1
1
1
0
2
0
2
1
1
0
1
1
2
0
2
2
2
0
2
2
0
1
2
0
0
1
1
0
2
1
1
0
2
1
0
0
2
1
0
0
2
0
1
3
1
2
1
1
1
1
0
0
0
1
1
0
2
2
1
1
2
1
0
1
0
1
2
1
0
1
2
1
2
1
1
2
1
1
2
1
1
2
0
0
1
2
0
0
0
0
0
1
0
1
0
2
0
1
1
2
2
1
0
2
2
2
0
0
0
2
0
1
0
0
0
1
0
2
0
1
0
0
0
0
1
0
2
0
0
0
0
1
1
0
0
1
2
1
0
0
2
0
0
0
1
1
0
1
0
1
0
0
0
1
1
0
1
1
0
2
2
0
1
0
4
0
1
2
0
1
1
1
1
0
2
0
1
2
0
1
3
1
2
0
0
2
2
2
0
0
0
0
0
1
1
1
0
0
0
2
2
0
0
1
1
0
2
1
0
2
0
0
0
1
0
0
1
0
1
2
0
0
0
1
1
1
0
2
2
0
1
0
2
1
1
2
2
0
0
0
3
2
1
1
2
0
1
1
0
1
0
2
0
1
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
1
1
2
1
1
1
2
2
0
2
1
1
0
1
0
0
1
2
2
1
2
1
2
0
0
0
2
0
0
0
0
1
0
1
1
1
1
0
0
1
0
2
1
0
0
1
1
0
2
0
1
1
2
0
1
2
0
0
2
1
1
2
1
0
0
0
2
1
0
1
1
1
1
1
1
1
0
0
0
2
1
2
0
1
1
0
0
0
2
0
1
2
1
1
1
0
0
1
0
1
1
1
2
1
2
0
1
0
2
0
0
0
0
1
2
0
2
0
0
0
0
0
2
1
0
1
1
2
2
1
1
1
1
1
0
2
0
1
1
0
0
1
1
0
2
2
2
0
0
0
0
1
0
3
2
1
1
2
0
2
1
0
0
2
1
0
0
0
1
1
1
1
1
2
0
2
0
1
0
1
0
0
0
1
2
0
0
0
0
2
2
1
2
1
1
0
1
3
1
0
0
0
2
1
0
1
1
0
0
2
0
0
0
0
0
0
1
3
2
0
1
0
2
2
0
1
1
0
1
0
1
0
2
2
0
2
2
0
1
2
1
1
2
1
0
2
0
2
0
1
0
1
0
0
1
2
1
1
2
0
1
1
3
1
0
1
0
1
1
0
1
1
0
1
0
1
0
4
0
1
1
0
0
1
1
1
2
1
1
1
0
1
0
1
3
2
1
1
0
2
0
0
0
1
3
2
0
1
0
2
1
0
1
1
2
1
2
1
0
0
0
1
0
2
0
1
0
2
0
0
1
2
0
2
2
0
2
0
2
1
2
0
0
1
0
0
1
1
0
0
1
1
2
1
1
0
1
0
1
0
2
0
0
0
1
0
0
2
0
1
2
2
0
0
0
0
0
0
1
2
1
0
1
0
0
0
2
0
2
0
1
0
0
1
0
1
0
2
1
1
1
0
0
0
3
1
1
1
2
2
0
1
0
0
1
2
0
0
1
2
1
1
2
1
1
0
0
2
0
0
0
0
2
2
1
2
2
0
2
1
2
0
1
0
0
0
1
1
2
0
0
0
0
1
0
1
0
1
1
2
0
0
1
1
1
2
0
1
1
0
1
4
1
1
0
0
0
0
1
0
1
0
1
0
2
0
1
0
0
1
0
2
2
2
0
0
2
2
0
0
2
0
2
2
0
2
0
0
0
1
2
0
1
1
2
0
2
0
0
0
1
0
1
1
0
0
1
0
0
0
0
1
2
1
0
0
2
0
0
2
0
0
1
2
1
1
2
0
0
0
0
1
2
2
0
1
1
2
3
0
1
1
1
1
0
2
0
2
3
1
2
1
1
2
2
1
1
1
1
0
1
0
2
0
1
2
2
0
1
2
2
0
1
2
0
1
1
0
0
1
1
0
0
1
2
1
0
1
1
1
1
2
1
1
0
0
1
2
0
0
1
0
0
0
4
0
0
0
0
1
0
2
1
1
2
1
2
2
1
1
0
2
0
1
0
1
0
1
1
0
1
0
3
2
1
0
0
1
0
2
2
1
0
0
2
1
2
1
2
1
0
1
1
1
0
1
0
2
0
2
1
2
1
0
0
1
0
1
0
2
1
0
1
0
0
1
1
0
2
1
2
0
0
0
1
2
0
0
1
1
2
0
1
0
0
1
0
0
1
0
1
1
1
1
1
1
0
1
2
0
0
0
1
0
1
2
1
1
0
0
2
1
1
1
1
0
0
0
0
0
0
2
2
0
1
0
0
2
1
1
2
1
0
0
2
1
1
0
0
1
1
1
1
0
0
3
2
0
1
1
0
0
1
1
0
2
2
1
2
1
1
0
1
0
0
0
1
1
2
1
1
0
0
1
2
2
1
0
0
1
0
2
0
1
2
3
1
1
1
0
1
0
2
0
1
2
1
0
0
0
0
2
0
0
1
0
0
0
2
0
2
0
1
1
0
1
1
1
2
0
2
0
1
1
2
0
0
4
0
1
0
0
1
1
0
1
0
2
1
0
1
0
2
2
0
0
0
0
1
1
1
2
0
3
3
0
1
0
1
0
2
0
1
0
0
0
2
0
1
1
1
0
2
0
1
1
0
0
0
1
0
1
0
1
0
0
0
0
1
0
1
1
0
2
0
0
2
1
0
1
2
2
0
1
0
1
1
1
1
1
1
1
0
1
1
0
0
1
2
0
1
0
0
1
1
1
2
2
0
3
1
0
1
2
1
1
1
0
0
0
2
0
9
1
2
3
1
2
0
2
0
2
1
1
1
0
0
0
2
2
0
0
1
0
0
0
1
1
2
0
0
2
1
2
1
0
0
0
1
1
0
1
2
1
2
1
0
1
1
1
1
1
2
0
1
1
2
0
1
1
0
2
0
0
1
1
0
1
0
1
1
1
1
1
1
1
0
2
0
2
2
2
1
2
5
1
1
0
0
1
2
1
2
0
0
1
0
0
0
0
1
0
1
1
0
0
0
2
1
0
1
0
2
0
1
1
1
0
3
0
2
2
2
0
3
0
2
2
0
1
3
1
0
0
0
0
0
2
1
1
1
0
0
0
0
1
1
1
1
1
1
1
2
0
2
1
0
1
0
0
1
1
1
1
0
0
1
0
1
1
2
0
0
1
2
0
2
0
0
1
2
4
1
0
1
1
1
2
0
2
2
1
0
0
0
2
1
2
0
0
0
0
0
0
3
0
1
2
0
0
1
1
0
2
1
0
0
1
2
1
1
1
0
0
0
1
1
2
2
1
0
0
0
0
2
1
0
2
2
0
0
0
0
0
0
0
1
3
0
0
0
2
0
1
0
0
1
2
1
0
0
1
2
0
0
2
1
2
1
0
1
0
0
1
2
1
1
0
1
0
1
0
0
2
1
0
0
1
1
1
0
1
0
0
1
0
1
1
1
0
0
0
1
0
1
0
0
1
0
1
1
1
0
0
0
0
0
1
2
1
0
1
1
1
2
1
0
1
1
1
1
1
0
0
1
2
2
1
1
0
2
2
0
2
0
0
0
1
1
0
0
0
2
0
0
0
2
1
0
0
0
0
0
1
2
2
0
1
1
1
2
2
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
2
1
1
2
1
0
0
0
0
1
2
0
0
2
0
2
0
1
2
1
0
1
1
0
0
0
0
0
2
0
2
0
1
0
2
1
2
0
1
2
1
0
0
2
1
0
0
2
1
1
0
0
1
0
0
0
0
0
1
0
2
0
0
1
2
1
1
2
1
0
1
1
1
0
0
0
1
2
2
2
0
0
0
0
0
2
0
2
2
1
1
1
1
0
1
0
0
0
2
2
1
1
0
2
1
0
1
0
0
1
2
1
2
1
2
1
1
2
1
1
0
1
2
1
0
2
1
2
1
0
0
0
1
0
1
1
1
1
0
1
1
2
1
1
0
1
0
0
1
0
0
0
2
0
1
1
1
0
0
2
1
0
1
0
1
0
0
1
2
0
1
0
2
0
1
0
1
0
0
1
0
0
0
1
1
1
2
0
2
1
0
1
0
2
2
1
0
1
1
1
1
2
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
2
0
3
0
0
1
2
0
2
0
0
1
1
0
2
0
1
0
2
0
2
2
2
1
2
1
1
0
0
0
2
0
1
0
1
2
1
1
2
6
1
1
1
0
2
0
0
0
2
1
0
1
0
1
0
1
0
1
3
0
1
2
1
1
0
0
2
1
1
0
0
2
1
1
1
0
2
0
0
2
0
1
2
2
1
1
0
1
2
2
1
0
2
0
1
2
0
0
2
1
1
0
1
0
0
0
0
2
1
1
2
0
1
1
2
2
1
0
2
1
2
0
1
0
0
0
1
0
0
0
0
2
0
0
0
2
1
0
2
0
2
0
2
2
2
0
0
2
0
1
1
0
2
1
0
1
1
1
0
0
2
1
1
0
0
2
1
1
2
2
2
2
1
1
0
2
0
1
0
1
2
0
1
2
0
0
1
0
1
4
1
0
1
5
0
1
0
2
0
0
2
0
1
2
1
1
0
0
0
2
0
2
0
3
0
2
2
1
1
0
0
2
1
0
1
0
1
1
1
2
0
1
0
1
1
2
2
0
0
1
1
1
0
1
0
2
0
1
0
2
1
2
2
1
1
0
0
2
0
1
1
0
2
0
0
0
2
0
2
1
2
0
1
0
2
0
1
0
0
0
2
0
1
1
0
1
0
0
1
0
1
2
0
1
0
0
0
0
0
1
2
1
0
0
3
2
0
3
1
1
0
0
0
1
2
0
0
1
0
2
1
1
2
2
0
2
1
0
0
2
2
2
0
1
0
0
0
2
1
1
0
0
1
2
0
0
0
1
0
2
0
0
1
0
0
1
1
2
1
0
0
1
3
1
0
1
0
1
0
3
0
0
2
2
0
2
1
1
0
3
1
0
1
1
0
2
0
0
2
0
1
0
0
2
0
1
0
0
0
2
1
1
3
2
1
0
2
0
0
1
2
1
0
1
0
1
0
1
2
2
0
0
0
1
1
0
0
1
1
0
2
2
1
0
1
0
2
0
2
2
0
1
1
2
0
3
0
2
0
2
1
1
1
1
2
0
1
1
0
0
1
1
2
1
2
2
0
0
1
0
1
0
1
0
0
0
0
1
2
1
0
1
0
0
1
1
2
0
0
0
1
0
0
0
0
1
1
1
2
1
0
0
0
2
2
1
1
2
0
1
1
2
0
0
1
1
1
1
0
2
0
2
2
0
1
0
2
2
1
3
2
1
0
1
0
1
2
0
1
1
1
0
2
1
0
1
2
1
0
1
2
1
1
2
1
1
1
1
1
1
0
1
0
1
5
2
0
2
0
0
1
0
0
1
0
1
0
0
2
0
0
1
1
2
1
0
1
3
0
2
1
0
0
0
0
0
0
0
0
0
1
0
1
2
2
2
2
1
2
0
0
1
2
2
1
1
1
0
0
2
1
2
0
1
1
2
1
1
1
1
1
1
1
0
2
0
1
0
0
1
1
2
0
0
2
1
1
0
1
4
1
1
1
1
1
2
1
1
1
2
0
2
0
0
1
0
2
1
1
1
1
1
1
0
0
0
0
0
1
1
0
1
2
1
2
2
1
1
0
0
2
0
1
1
1
1
0
1
0
1
2
2
1
1
1
0
1
0
1
2
0
0
0
1
2
1
1
0
0
0
0
1
0
0
0
1
2
1
0
2
0
3
0
0
2
0
1
0
0
0
0
0
1
1
1
0
3
0
1
0
2
1
1
0
1
3
0
0
1
2
1
1
0
2
2
0
0
0
1
0
1
0
3
1
0
1
1
0
1
1
0
1
0
2
2
0
1
0
0
1
1
1
2
0
0
0
1
1
1
0
0
0
2
0
0
1
0
2
2
4
1
1
1
2
2
3
0
1
1
0
0
0
2
2
2
0
1
0
0
2
0
0
1
0
2
1
0
1
0
0
2
1
1
0
1
0
2
2
0
1
1
2
5
0
2
3
2
0
0
1
0
0
1
2
0
0
0
0
0
2
2
1
1
0
0
0
0
0
1
2
1
1
0
1
0
2
1
2
1
0
1
1
1
0
0
0
1
0
2
1
1
0
0
0
0
2
1
2
2
2
1
1
0
0
0
2
1
2
2
0
1
0
0
2
1
0
2
0
1
1
1
0
0
0
0
0
0
3
0
0
2
0
0
0
1
3
2
1
0
2
0
1
2
0
1
1
2
0
2
2
1
3
0
1
0
2
1
2
1
2
0
0
1
0
1
1
1
2
1
2
0
0
1
0
2
0
0
2
1
0
0
0
0
1
1
0
2
0
1
1
2
2
1
2
1
1
0
0
0
0
2
1
1
0
1
0
1
0
2
2
2
2
0
1
0
1
0
0
0
1
0
0
1
0
0
2
0
2
1
0
1
0
1
1
0
0
0
1
1
1
0
2
0
2
2
0
1
2
1
0
0
1
0
0
1
1
2
0
0
1
2
0
1
1
0
0
2
0
1
0
2
2
0
1
1
0
0
3
1
0
1
1
0
1
0
0
3
2
0
2
1
1
0
2
0
0
1
2
0
0
1
1
1
0
0
1
0
2
0
2
0
1
1
2
0
2
2
1
2
1
0
0
2
0
0
1
0
0
1
0
0
1
0
1
1
0
1
0
0
0
2
1
0
0
1
0
0
5
2
0
2
1
0
0
0
0
2
0
1
0
2
1
0
2
0
2
2
1
1
0
2
1
1
0
0
2
0
0
1
1
1
0
1
1
0
2
1
2
1
0
0
0
3
1
0
0
1
2
0
0
0
1
1
1
0
0
2
2
1
2
0
1
2
0
1
0
3
2
1
1
1
1
2
1
1
1
2
0
0
0
2
0
1
1
0
2
1
1
1
1
0
2
1
1
0
0
1
2
0
1
1
2
0
0
2
1
0
0
1
0
1
2
0
0
0
0
2
0
0
1
0
0
0
1
0
0
1
2
1
0
0
2
0
2
0
1
2
0
0
1
2
1
2
1
2
2
1
0
2
0
2
0
4
1
1
2
1
1
1
0
1
1
0
0
1
1
0
0
1
2
1
0
0
0
3
1
2
1
0
1
2
0
2
2
0
0
2
3
0
1
0
1
2
1
0
1
0
1
0
0
0
0
1
2
1
2
2
2
2
1
2
1
0
0
0
0
0
0
1
1
1
0
1
1
1
0
1
1
1
2
1
0
2
0
1
0
1
0
0
0
0
0
1
0
1
0
1
1
0
1
0
1
0
2
1
0
1
1
0
1
1
2
1
0
2
0
1
2
1
1
0
2
1
2
0
0
0
1
0
0
3
1
0
2
2
1
2
1
0
1
0
0
1
0
1
0
0
0
0
2
0
3
1
1
1
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
1
1
2
0
0
2
0
0
0
0
1
0
2
0
1
2
1
1
1
0
1
0
0
1
1
2
1
2
0
1
1
1
1
2
2
1
3
0
1
0
0
0
0
0
0
2
0
2
1
0
1
1
0
0
0
1
0
0
0
1
1
0
1
2
1
2
1
0
0
1
0
0
2
0
0
1
3
0
0
0
0
2
1
2
1
0
2
2
1
2
2
0
0
0
0
1
1
0
2
1
0
0
0
0
0
1
0
1
1
0
2
2
0
1
0
1
0
1
0
1
0
1
2
1
0
2
2
2
1
1
1
0
1
1
1
2
0
2
0
0
0
0
0
0
1
2
0
0
2
1
1
0
1
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
2
2
0
1
1
1
1
0
0
2
0
0
1
2
0
1
1
1
1
2
0
1
0
0
0
0
0
2
0
2
0
2
1
0
0
1
0
1
0
0
0
1
0
1
1
2
0
0
2
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
4
1
1
2
2
2
0
0
2
0
1
1
2
1
0
0
1
0
2
0
0
2
0
0
1
0
0
0
1
0
1
0
2
4
1
0
0
0
0
0
2
1
1
0
1
2
1
1
1
0
1
2
1
0
0
2
1
0
2
0
1
0
1
2
0
1
0
2
2
0
2
1
0
0
0
1
1
1
1
0
0
1
1
0
1
0
1
1
0
0
2
0
0
1
1
1
0
0
1
1
1
0
2
2
1
2
0
0
0
0
1
0
6
0
0
0
0
1
0
0
1
1
1
1
1
1
1
2
1
0
1
1
0
0
0
1
2
2
0
0
0
0
0
0
0
2
1
2
0
2
0
0
1
0
0
2
1
0
1
1
2
0
0
1
0
0
2
2
1
1
0
1
2
2
0
0
1
0
1
0
1
0
0
2
2
0
0
0
0
2
0
2
1
0
0
0
1
2
1
0
2
0
1
1
0
0
1
1
2
0
0
0
0
0
2
2
1
0
2
1
2
1
2
0
0
0
0
2
0
0
1
2
1
0
0
0
0
1
1
0
0
0
2
2
1
2
0
2
1
0
0
1
1
1
0
0
2
2
1
2
1
1
0
0
1
0
0
2
2
0
2
2
0
1
1
2
0
2
0
0
2
0
1
0
2
0
0
0
0
1
1
1
0
0
2
1
1
8
3
1
1
1
1
1
0
2
1
2
0
2
1
1
0
1
2
0
1
0
1
2
1
1
0
1
0
0
2
1
1
1
1
0
2
2
2
1
2
2
1
0
1
0
1
1
1
2
1
0
0
0
0
2
1
1
1
1
1
1
1
0
1
2
1
1
0
0
0
1
1
1
1
0
2
1
1
1
0
0
0
0
2
0
1
0
0
0
1
2
0
0
2
0
1
1
0
1
1
1
0
1
1
3
1
1
1
0
2
0
0
0
0
2
0
2
0
0
0
1
0
1
1
1
2
0
0
0
1
1
0
1
0
1
1
0
1
0
0
1
0
3
1
1
1
0
1
0
1
0
0
0
2
2
1
1
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
2
2
3
0
1
2
2
0
1
2
0
2
1
0
0
2
0
0
2
2
2
0
0
1
1
2
0
1
0
2
0
0
0
2
0
1
1
2
0
1
1
0
0
1
0
1
0
1
0
0
0
0
2
0
1
1
1
1
1
1
0
1
1
1
1
2
2
1
2
1
0
1
2
1
2
0
3
0
2
2
1
0
0
2
0
0
2
0
0
0
0
1
2
0
0
0
2
0
0
1
1
1
2
1
2
1
1
0
0
1
0
1
2
1
2
0
1
0
2
1
2
1
1
2
1
2
0
1
0
0
0
0
2
1
1
6
0
0
1
0
0
1
2
0
0
1
2
1
0
2
1
0
1
2
2
1
2
0
1
2
2
0
1
0
1
0
0
1
0
0
0
1
0
0
1
0
2
0
1
0
1
0
1
0
0
2
1
1
1
1
1
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
1
0
2
0
0
1
1
1
0
1
0
0
1
1
0
1
1
1
1
2
1
0
2
1
0
0
0
1
1
1
0
0
0
1
1
1
2
1
0
0
2
0
0
3
2
1
0
2
1
0
0
1
0
2
1
0
1
1
2
2
1
0
0
0
0
0
0
0
1
0
0
1
2
0
1
1
0
0
1
1
2
0
2
1
2
0
0
1
0
1
0
1
0
1
1
2
0
0
2
0
1
0
0
1
1
0
0
0
1
2
0
1
0
2
2
2
0
1
14
0
2
0
2
1
1
2
1
1
2
1
1
0
1
1
0
0
0
1
2
2
2
1
1
0
0
0
1
0
0
1
2
0
0
2
2
0
2
2
1
0
0
1
1
2
0
0
0
0
0
1
0
0
0
2
1
0
1
0
0
2
0
0
3
0
1
1
0
2
2
0
0
2
3
1
1
0
2
2
0
2
1
0
1
1
0
0
3
0
1
0
0
0
2
1
1
0
0
0
0
1
0
0
2
0
2
0
1
0
1
1
0
0
2
1
1
1
1
0
0
2
0
2
0
2
0
0
0
0
0
2
0
0
1
1
0
1
1
1
0
0
0
0
2
1
1
2
0
1
2
1
2
1
2
1
1
0
1
1
1
0
0
0
0
0
0
1
1
0
0
0
0
2
1
2
1
1
0
2
0
0
1
1
1
0
2
0
1
2
0
0
0
2
0
1
1
0
0
0
0
1
1
1
0
2
1
1
0
0
4
1
1
2
1
1
0
2
0
0
1
0
0
2
0
2
1
1
1
2
1
0
2
1
0
2
2
0
1
1
2
1
2
2
1
2
2
1
0
0
2
0
0
0
1
0
2
0
0
1
1
1
2
1
1
0
1
0
1
2
0
1
2
0
2
0
2
1
1
1
1
1
2
0
0
0
1
1
0
2
1
1
1
0
0
0
1
0
1
1
1
0
1
0
0
0
1
1
0
1
1
0
3
1
0
2
1
10
2
1
1
0
1
0
1
1
1
1
2
2
0
1
0
1
2
1
0
2
1
1
1
0
1
2
1
0
2
1
1
0
0
2
1
2
0
0
1
2
1
0
1
0
2
0
0
1
0
0
1
1
2
0
0
0
2
0
1
1
2
1
1
0
0
2
0
1
1
0
0
2
0
1
1
2
0
1
1
1
1
1
0
2
3
1
4
1
2
0
2
1
2
2
0
0
0
2
1
1
0
1
0
0
0
0
1
1
1
0
0
2
1
0
2
0
1
0
2
1
0
0
1
1
1
1
0
0
0
1
0
1
0
1
1
1
1
0
1
2
0
0
0
1
0
1
0
1
2
2
1
2
0
0
0
0
0
2
1
0
0
2
0
1
2
0
0
1
1
0
0
2
1
1
1
1
1
0
0
0
1
0
1
0
0
3
0
1
2
1
2
0
1
0
2
0
1
1
0
1
1
2
0
1
1
0
1
1
4
1
0
1
2
0
0
2
2
2
0
2
1
1
0
1
0
2
1
1
1
0
1
1
0
2
0
0
0
1
2
1
1
1
0
2
2
1
1
2
2
2
2
1
1
2
1
1
1
3
1
2
0
1
0
1
1
0
1
2
2
2
2
0
2
1
0
2
2
1
0
2
0
0
1
2
0
0
0
1
2
1
0
0
1
0
0
0
0
1
0
0
0
1
2
0
1
0
0
0
1
0
0
0
0
1
0
1
0
2
0
1
0
1
1
1
2
0
0
2
0
0
1
3
1
2
0
1
0
1
1
0
0
0
1
1
1
1
0
0
1
1
0
3
2
1
1
0
3
2
3
2
0
0
0
0
1
0
2
1
1
0
2
0
0
2
0
2
1
2
0
0
2
2
1
0
0
0
2
0
1
0
2
0
2
2
0
0
3
0
1
1
0
3
0
0
2
2
2
2
2
1
0
1
0
2
1
0
1
1
0
1
1
0
1
0
0
1
0
0
1
1
2
1
1
1
0
2
0
3
0
0
0
2
1
2
0
0
2
2
0
0
2
0
1
1
2
0
1
2
1
0
0
1
1
0
1
0
0
0
1
1
2
1
0
0
0
0
1
0
2
0
1
1
1
0
1
1
1
1
0
1
0
1
0
2
0
2
0
3
1
1
2
1
0
0
0
1
2
0
0
0
2
1
0
0
0
1
1
1
2
1
1
1
2
2
1
0
2
1
2
1
1
1
2
2
2
1
1
0
0
0
0
1
1
1
1
2
1
1
1
1
0
0
1
2
1
0
2
0
0
2
1
2
1
1
0
1
1
0
2
0
1
2
1
1
0
0
1
2
1
0
1
0
1
0
2
0
0
0
0
2
1
1
0
2
0
2
0
1
1
0
0
0
1
1
1
0
0
1
0
2
2
0
1
1
2
1
2
1
1
1
0
1
1
0
0
2
0
1
1
2
0
2
1
0
1
2
0
1
0
0
0
1
2
0
1
2
2
1
1
0
0
1
1
0
0
1
0
1
1
2
0
1
1
0
1
2
1
1
0
1
2
3
0
2
1
1
1
1
2
0
1
1
0
2
1
1
1
1
1
1
0
2
1
1
0
2
1
1
1
1
2
0
1
1
1
0
2
0
0
0
1
0
2
0
2
2
2
1
0
0
0
0
1
0
1
1
1
0
0
1
0
1
1
2
1
1
1
1
0
2
0
0
2
1
2
0
0
1
0
3
0
0
1
2
3
0
0
0
1
2
1
1
0
0
1
0
0
2
1
1
1
2
2
1
2
2
1
0
0
2
1
1
1
2
0
0
0
2
2
0
2
0
2
0
2
0
1
2
0
0
0
0
0
1
2
0
2
1
0
1
0
0
3
1
1
1
1
1
1
0
0
1
0
0
1
2
1
0
0
0
1
0
2
1
0
0
0
0
0
2
0
0
0
3
0
0
2
0
1
0
0
2
1
0
0
1
1
0
1
2
0
1
1
0
1
1
1
0
3
2
2
0
2
2
2
2
1
1
2
0
2
0
0
1
0
0
2
0
0
0
2
0
3
1
1
1
0
0
2
0
1
2
2
2
0
0
0
2
0
0
2
2
0
2
0
2
1
1
1
0
2
1
2
0
0
1
1
0
1
0
1
0
0
1
0
2
2
2
0
1
2
1
2
0
1
0
1
1
1
2
2
0
2
0
0
0
1
1
1
1
1
0
0
0
0
1
2
2
0
0
1
2
0
1
0
0
1
1
0
0
0
2
2
1
1
1
1
0
0
2
1
2
2
1
0
1
1
9
0
1
2
2
0
0
0
0
1
1
2
0
1
1
2
0
0
2
0
2
0
0
0
0
0
3
0
1
1
1
0
1
2
1
0
2
2
2
0
1
1
1
1
0
1
1
0
1
1
1
1
0
1
0
1
0
1
2
0
2
0
0
0
2
3
2
0
2
2
0
1
2
0
0
1
1
1
2
1
1
0
2
1
0
0
1
2
1
0
0
2
0
2
0
0
1
1
0
2
2
1
2
1
0
0
1
1
1
1
1
0
1
0
0
0
0
1
0
1
0
1
2
2
1
1
0
1
1
0
2
3
1
2
0
1
1
4
0
1
1
0
2
5
0
1
1
1
1
1
0
2
1
2
0
2
1
0
2
1
0
1
0
2
2
1
2
0
0
1
1
0
0
2
1
0
1
0
0
1
1
1
2
0
1
1
0
1
1
0
0
0
1
0
2
1
2
0
1
0
2
0
0
0
0
1
1
0
1
0
2
1
0
0
0
0
0
1
1
0
2
0
1
0
0
3
1
0
2
2
0
1
0
0
0
0
1
2
0
0
1
1
1
0
1
0
0
0
1
0
1
0
0
0
0
1
0
2
0
1
1
1
0
0
2
0
2
1
2
1
1
0
1
1
3
0
1
2
2
0
2
1
0
1
0
1
0
1
1
2
3
2
2
1
1
1
0
0
1
1
1
0
1
0
0
1
0
2
1
0
0
3
1
2
0
1
1
2
1
0
2
0
0
2
1
0
2
1
0
1
0
1
1
1
0
2
0
0
0
1
0
2
0
1
1
1
2
1
2
1
1
1
1
1
0
0
0
0
1
2
0
0
0
2
2
1
2
0
1
0
1
1
1
2
0
1
2
0
0
0
0
0
0
1
2
0
0
1
1
0
0
0
2
1
0
1
2
1
0
1
0
1
2
0
0
0
0
0
0
1
1
1
2
0
2
1
1
2
0
3
0
2
0
2
1
2
0
1
0
0
0
0
1
1
1
0
1
1
1
1
0
0
0
1
1
2
1
1
1
0
2
1
1
0
1
0
1
0
0
0
0
1
2
0
7
1
2
1
0
1
0
1
1
1
0
0
0
1
2
0
1
1
2
0
2
1
0
0
0
2
2
1
0
0
1
1
0
1
2
0
2
1
0
0
2
0
2
0
1
0
0
0
0
0
1
1
1
0
2
0
1
0
1
2
1
0
2
0
0
2
2
0
0
0
1
0
1
1
2
1
1
1
0
0
1
1
0
1
1
0
1
0
2
2
1
0
0
1
0
0
1
2
1
1
4
0
2
0
2
1
0
1
0
0
2
1
1
1
2
0
2
0
1
0
1
1
0
2
0
1
1
0
0
0
2
1
1
0
0
0
1
2
0
1
1
0
0
2
1
3
1
1
1
1
0
1
0
1
3
3
1
1
2
0
2
1
0
0
1
0
1
0
1
2
0
1
0
1
2
0
2
1
1
1
0
1
0
2
1
1
0
1
2
2
2
2
1
2
1
1
1
0
1
0
1
1
2
0
0
0
0
1
2
1
0
0
1
1
1
1
1
2
0
0
3
0
0
1
1
1
1
0
1
2
0
1
1
1
2
1
1
0
2
1
1
2
0
1
0
0
0
0
2
1
1
0
1
0
0
0
1
0
2
0
0
1
0
2
1
1
0
0
2
2
0
0
0
2
0
0
1
1
0
5
0
0
0
1
1
0
1
0
2
0
0
0
0
0
1
2
2
1
2
0
1
0
0
2
1
0
1
2
0
0
0
2
2
0
2
0
0
2
0
1
2
1
0
2
2
1
0
0
0
1
1
0
0
2
0
1
1
1
0
0
1
1
0
1
2
0
1
2
1
0
0
0
2
2
0
0
1
2
1
0
0
2
0
1
1
2
2
0
0
0
0
2
2
1
2
0
1
1
0
0
1
0
0
0
1
0
0
1
0
1
0
2
1
2
0
2
0
1
0
2
1
0
2
0
2
0
0
2
1
0
1
2
0
0
1
4
2
0
1
1
1
0
0
0
2
0
2
2
1
0
0
1
2
1
2
0
2
1
2
0
1
0
0
2
1
2
1
1
1
1
0
0
1
1
0
2
0
0
0
1
0
1
0
0
0
2
3
0
0
1
2
2
1
0
0
1
2
1
2
0
1
0
0
1
0
0
1
0
2
1
0
0
0
1
2
2
2
0
0
0
1
0
2
1
0
2
1
0
1
0
0
1
0
1
1
0
1
2
0
0
0
1
0
2
1
0
0
4
0
0
1
0
2
1
1
1
1
1
0
2
3
0
1
1
1
0
0
1
0
1
2
1
0
0
1
1
1
0
0
0
1
1
0
1
2
0
1
1
0
2
1
1
0
2
1
1
1
1
1
0
1
2
1
2
2
1
1
1
1
1
0
2
0
0
1
0
1
1
2
1
0
1
2
1
1
0
2
2
0
2
2
1
1
2
1
0
1
1
0
0
2
3
0
0
0
2
1
2
1
3
1
0
1
2
1
0
1
1
2
0
1
0
2
0
2
1
0
0
0
0
1
2
1
2
1
1
1
0
0
2
2
0
1
1
2
0
0
0
1
0
2
1
0
1
0
1
1
0
2
1
1
2
1
1
1
0
2
2
0
3
0
0
1
1
0
0
1
2
0
1
0
0
0
1
0
0
2
0
2
0
2
1
2
1
1
1
0
0
1
2
2
2
0
2
2
0
0
2
1
1
0
2
1
1
2
2
0
1
1
1
1
0
1
1
2
1
1
0
1
0
1
0
0
0
1
0
1
0
0
1
1
0
0
1
2
0
0
1
1
2
1
2
0
2
0
0
2
0
0
0
0
1
2
2
0
0
0
0
0
2
1
1
1
2
0
1
0
0
0
1
0
2
0
1
0
0
2
1
0
1
0
0
0
1
1
1
0
0
0
0
0
0
2
0
0
1
1
1
0
0
0
1
0
0
2
1
2
1
0
0
1
1
1
1
2
0
0
1
0
3
1
1
1
1
2
2
1
0
3
0
1
1
0
0
1
1
0
1
2
1
1
1
0
1
1
1
1
1
0
1
0
0
0
1
1
1
2
0
0
0
2
0
0
0
2
1
1
2
2
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
2
2
1
1
1
0
2
1
0
1
1
0
0
3
1
0
1
2
0
1
0
0
0
2
0
1
2
2
1
2
1
0
2
0
1
2
0
0
0
0
2
2
2
1
1
0
1
0
1
2
0
2
2
0
0
1
0
0
1
0
1
0
1
0
1
7
0
0
0
0
1
1
0
0
0
0
2
1
0
2
2
0
1
1
2
0
0
0
1
0
1
0
0
1
2
0
1
1
0
0
2
2
1
1
1
0
2
1
0
0
2
1
0
0
0
0
0
0
1
0
2
0
0
1
1
0
0
0
0
0
0
2
2
2
1
1
1
1
0
2
1
1
2
1
0
1
0
1
0
0
0
1
1
2
1
1
1
2
1
0
1
2
0
1
1
1
2
1
0
5
1
1
1
2
1
1
2
1
2
0
0
2
1
2
1
1
0
0
2
0
0
1
2
2
2
0
0
0
0
1
1
1
0
1
0
1
2
1
1
1
2
0
0
0
0
1
2
0
2
1
2
4
0
0
0
0
0
2
0
2
1
0
0
0
0
3
1
0
2
1
2
1
0
1
1
1
1
1
0
2
0
0
0
0
0
1
1
2
1
1
0
1
0
1
2
1
0
0
2
2
0
1
1
0
1
1
1
2
0
0
0
1
0
3
0
1
0
1
1
1
2
2
0
0
0
1
1
1
1
0
1
0
1
0
0
0
2
0
2
3
1
1
0
1
0
0
1
2
1
0
0
0
2
1
1
0
1
0
1
1
0
0
1
0
1
1
1
0
1
1
1
0
0
1
0
2
0
0
1
1
0
2
1
1
0
0
0
0
0
2
0
1
1
2
0
0
2
1
0
2
1
0
0
2
1
1
0
0
1
0
0
0
1
2
1
0
1
1
0
1
2
0
1
1
0
0
2
1
0
0
1
0
0
0
2
4
1
2
1
1
0
1
0
0
1
1
0
2
0
2
0
0
2
1
2
0
1
0
2
2
1
2
0
0
2
1
0
1
0
0
0
2
2
1
2
1
2
1
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
2
1
0
0
1
2
3
2
1
0
2
0
0
0
0
2
1
1
0
1
1
0
0
0
3
0
2
2
0
2
2
1
1
0
0
0
3
1
1
0
1
0
0
1
0
1
1
1
0
2
0
0
2
0
2
1
1
1
0
0
0
2
0
0
4
0
0
1
2
1
3
2
0
0
2
1
0
0
0
2
0
0
0
3
0
0
0
1
0
2
1
2
1
0
0
1
0
1
0
1
1
1
0
1
0
2
1
0
1
2
1
0
1
0
1
0
0
0
0
2
2
2
1
0
1
0
1
0
0
1
2
1
2
2
1
1
0
1
1
0
2
0
0
1
1
1
0
1
0
1
1
2
1
1
1
1
1
1
0
2
1
1
0
0
0
2
2
1
0
0
0
0
1
0
2
1
1
0
0
0
1
0
1
2
0
1
0
0
1
0
0
1
0
2
1
2
0
1
1
1
0
2
1
0
1
2
1
0
0
1
1
1
1
0
2
1
1
2
0
1
0
0
0
0
1
0
0
2
1
0
2
1
1
0
2
2
0
0
1
0
2
0
0
1
1
1
0
0
2
0
1
0
2
1
1
1
2
1
1
1
2
0
2
2
1
0
0
0
0
0
0
0
2
1
2
1
1
2
1
2
2
0
0
0
0
0
2
0
2
1
0
2
1
0
0
0
1
0
1
2
0
0
0
2
1
0
0
1
0
0
1
1
1
0
1
1
0
1
0
1
1
1
0
0
0
1
2
1
2
2
1
1
0
1
1
0
1
0
1
1
0
0
2
0
2
1
0
2
1
1
2
2
0
1
2
1
0
1
0
2
1
1
0
2
0
1
0
0
0
2
1
1
0
0
0
0
0
1
1
1
0
1
2
0
0
3
0
1
1
0
2
2
1
2
0
2
0
2
1
1
0
0
0
1
2
1
2
1
0
2
0
0
2
2
0
1
0
1
2
1
0
1
2
0
0
0
0
0
0
1
2
0
0
1
1
0
1
1
2
0
0
1
0
1
0
2
1
2
2
0
0
0
1
1
1
1
0
1
1
0
0
0
1
0
1
0
0
0
0
1
0
2
2
0
1
0
2
1
0
0
0
2
0
0
1
0
2
1
1
0
1
0
0
0
2
1
0
1
1
1
1
1
1
0
1
2
0
0
1
2
3
0
0
1
1
0
0
0
0
2
1
1
0
0
1
1
2
1
0
0
0
0
0
2
0
1
0
1
0
0
0
2
0
2
0
0
0
2
1
0
1
0
0
1
1
0
0
2
1
3
1
2
0
0
1
0
1
2
0
1
1
0
1
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
2
1
0
0
0
2
1
1
0
0
0
2
1
1
0
1
2
2
1
1
0
2
2
1
0
0
2
0
1
1
1
2
1
0
2
0
0
2
0
0
0
1
2
0
0
1
1
0
1
1
0
1
0
0
0
1
2
2
0
0
0
1
1
1
2
1
2
1
2
0
0
0
0
2
0
1
2
0
2
0
0
1
1
1
1
0
0
0
0
1
1
1
0
2
1
0
2
0
1
2
0
1
0
2
0
2
1
0
0
0
1
0
2
2
1
0
0
2
0
1
1
0
0
0
1
2
0
1
0
2
1
2
1
0
2
2
1
0
0
0
0
2
1
2
1
2
0
1
0
1
2
0
0
0
1
2
1
0
0
1
0
0
0
1
1
1
1
0
0
2
0
2
0
0
0
0
1
3
2
1
3
3
2
1
1
1
0
2
1
3
1
0
0
0
1
1
1
0
2
0
2
0
1
1
1
0
0
2
0
0
0
1
0
0
1
1
0
2
0
2
0
1
0
0
0
1
0
0
1
1
1
1
2
0
0
1
4
0
2
1
2
0
2
0
0
0
0
2
2
0
2
0
0
2
0
1
0
0
2
1
1
2
1
0
1
0
2
1
1
0
1
0
0
1
0
2
0
0
1
0
1
2
0
0
0
0
0
1
2
2
2
1
2
2
0
1
0
0
0
0
2
0
1
1
1
1
0
1
1
2
0
2
1
0
0
1
3
1
2
2
1
0
1
0
1
2
2
2
1
1
0
1
1
1
2
2
1
1
0
2
1
0
0
0
1
0
1
1
1
0
0
0
2
1
2
1
0
0
2
1
1
0
0
0
0
0
2
1
0
2
2
1
1
1
0
0
2
0
2
0
0
1
0
0
2
0
0
0
1
1
0
1
2
0
0
0
1
2
0
2
1
0
0
1
1
0
1
0
0
0
0
0
2
0
2
0
1
0
1
2
1
1
0
1
1
0
0
0
0
2
2
0
2
0
3
1
1
2
0
0
2
0
0
1
0
0
0
0
0
1
1
0
1
1
1
1
0
0
0
2
1
1
1
0
1
2
0
1
1
2
1
0
0
0
1
1
0
1
0
1
1
1
1
1
1
0
0
1
1
0
1
1
1
0
0
0
0
0
0
1
0
2
0
2
1
0
0
1
0
0
1
1
1
2
2
2
0
1
0
0
2
1
1
2
0
2
2
3
1
0
2
0
1
0
0
0
1
2
1
2
1
1
0
0
1
1
2
1
1
5
3
1
0
2
0
2
2
2
1
1
0
2
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
1
0
0
0
1
0
2
0
2
0
2
0
0
0
1
1
1
1
5
1
2
1
0
2
1
0
1
0
1
1
1
0
1
0
0
0
0
1
0
1
2
2
1
2
3
0
1
0
2
2
1
0
1
1
0
1
2
1
2
0
0
0
3
0
0
2
1
0
1
2
0
0
1
1
1
2
0
0
1
0
1
0
2
2
0
1
2
0
2
1
1
0
0
1
1
0
1
0
1
2
0
0
0
0
0
0
1
0
0
0
1
2
0
1
1
1
0
3
1
0
1
0
0
1
1
1
2
1
1
1
0
0
0
1
1
2
1
2
1
0
1
1
2
0
0
0
1
1
0
0
1
1
0
1
0
2
0
0
0
1
2
0
1
0
2
0
1
1
1
0
0
1
1
1
2
0
0
1
0
1
2
0
0
2
2
1
1
1
1
0
0
1
1
0
2
0
0
2
4
2
0
1
2
0
0
1
0
2
2
0
0
1
3
0
1
1
2
1
2
1
0
0
0
2
1
0
1
2
1
1
2
0
2
0
0
0
1
2
0
0
2
1
1
0
1
1
1
1
1
0
0
0
1
0
0
0
2
1
1
0
0
1
0
0
2
1
0
0
0
2
0
1
1
0
0
0
1
1
1
1
1
1
0
2
0
2
1
2
2
0
2
1
2
1
0
0
0
0
0
0
0
0
1
0
1
2
2
1
0
0
2
0
0
0
0
2
1
2
0
1
1
0
0
0
1
0
2
0
1
0
2
2
0
0
0
0
0
2
1
3
1
1
1
1
1
0
0
2
1
1
0
3
2
0
0
0
0
1
1
1
0
0
0
0
0
1
3
1
0
0
1
1
0
2
1
2
1
0
0
1
0
0
2
0
2
2
0
0
0
1
2
0
1
0
0
2
0
2
0
1
1
0
0
0
1
0
2
0
0
0
0
1
2
2
0
0
1
1
1
1
1
1
0
1
1
0
0
0
0
1
1
3
0
2
1
1
1
1
1
1
1
2
0
0
0
1
1
0
0
0
0
2
2
1
0
0
2
1
0
1
1
2
1
1
1
2
1
1
0
0
0
0
1
0
2
0
0
0
1
1
0
0
1
0
0
0
2
0
2
1
0
0
0
1
1
0
1
1
2
2
1
1
1
1
2
0
2
0
2
1
2
1
2
1
2
1
3
2
1
1
0
0
0
1
0
0
1
1
0
0
1
0
1
1
0
0
2
1
0
1
0
1
0
1
0
1
2
2
1
0
1
1
2
0
1
0
1
2
0
1
0
1
1
1
2
1
1
0
2
2
0
0
2
0
0
0
1
0
1
0
0
0
1
2
1
2
0
0
0
1
2
2
0
0
0
1
1
1
2
0
2
2
0
0
0
0
1
1
0
0
0
1
1
0
0
1
2
0
1
0
0
1
1
2
2
0
0
1
2
1
1
1
1
1
0
2
0
0
0
0
0
1
0
1
0
1
1
0
1
2
2
1
2
1
0
0
2
1
1
2
1
2
0
2
0
1
0
0
1
0
2
0
1
2
1
0
1
0
1
0
0
1
1
2
0
2
1
0
0
0
0
1
0
1
1
0
1
2
2
2
1
2
1
2
0
0
0
2
1
0
0
2
0
0
0
1
0
1
1
2
1
0
2
0
0
1
0
2
0
1
1
0
1
1
1
2
2
2
0
1
0
1
0
2
1
1
2
0
0
0
1
0
0
1
1
0
2
0
2
2
0
0
1
2
2
0
2
0
1
0
0
1
1
1
0
1
2
0
0
0
1
0
1
1
0
1
1
1
0
1
1
0
2
0
1
2
2
2
1
1
0
1
0
0
2
0
2
2
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
2
0
1
0
1
1
0
1
1
1
0
0
0
2
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
2
0
0
1
0
2
1
3
0
1
2
0
0
2
1
1
1
1
0
0
1
1
0
0
1
1
0
2
0
1
0
0
1
2
0
0
0
1
2
1
0
1
0
0
0
0
1
0
3
0
0
1
0
1
0
0
0
2
1
1
1
0
2
0
0
1
1
2
0
1
1
0
2
1
2
0
2
0
3
0
0
0
0
1
0
2
0
0
2
1
0
0
2
0
1
1
0
2
2
0
2
0
1
0
0
0
0
0
0
0
0
1
1
1
0
1
0
1
0
0
1
0
1
0
0
1
3
2
2
2
0
0
0
1
1
5
0
1
1
0
0
1
1
2
0
0
2
1
1
1
0
2
1
0
2
2
1
1
0
2
2
0
1
2
0
1
0
2
0
0
0
0
1
0
1
2
2
0
1
0
2
0
0
2
0
1
0
1
0
0
0
1
2
0
0
0
0
2
1
2
2
0
0
1
0
0
0
2
1
0
2
0
1
1
0
1
2
1
0
2
1
0
0
2
0
1
2
0
0
2
0
1
3
0
1
1
0
1
0
0
0
1
1
2
0
1
1
1
0
0
1
1
1
0
0
1
0
0
1
0
0
1
2
1
1
0
1
2
1
1
1
1
0
3
0
0
2
0
2
1
2
3
1
0
1
2
1
1
0
1
6
2
1
3
0
1
1
1
1
0
0
2
0
1
1
0
0
1
1
0
1
2
1
0
0
0
0
0
0
1
0
0
1
0
1
2
0
0
1
1
0
0
1
0
1
1
2
1
0
1
2
0
1
2
1
0
2
2
1
2
1
0
1
0
2
2
1
2
1
0
1
1
1
0
0
2
2
2
0
0
2
1
0
0
2
2
2
0
1
1
1
1
2
0
0
1
2
0
1
1
0
0
0
2
0
2
1
1
1
1
0
0
0
2
0
0
0
1
0
1
1
0
0
0
2
0
2
0
0
1
1
0
0
2
0
0
0
0
1
0
1
0
1
0
0
4
0
2
0
1
0
2
0
1
0
0
2
0
0
1
0
1
0
2
2
0
3
2
0
2
1
2
2
0
2
2
0
2
0
0
2
0
0
0
2
0
0
0
1
0
2
0
0
1
0
1
2
1
0
0
1
0
0
0
1
0
2
2
0
1
0
1
1
1
2
0
0
2
1
1
2
0
0
1
1
0
0
0
2
0
1
1
0
1
1
0
1
0
2
2
0
0
1
0
2
1
1
8
1
0
3
1
1
2
1
0
2
2
0
0
1
3
0
1
0
0
0
0
2
6
1
0
0
0
0
2
1
0
0
1
2
0
1
2
1
0
2
0
0
0
2
2
2
1
2
0
1
1
1
2
0
1
0
0
0
1
2
2
2
2
1
0
0
1
2
0
0
3
0
1
2
1
2
1
1
1
0
0
1
0
1
0
1
1
1
0
0
0
2
0
1
1
1
1
1
2
1
1
1
0
1
2
0
1
1
1
1
2
1
1
1
2
1
0
0
1
1
0
0
0
0
2
2
0
1
3
1
1
1
1
0
1
0
2
0
0
0
2
0
1
0
0
2
0
0
1
1
2
0
0
0
1
0
1
1
1
1
0
0
0
3
0
0
0
1
0
2
0
0
0
2
0
2
1
0
1
2
0
2
2
1
2
1
0
2
1
1
0
0
0
0
0
1
0
1
0
0
0
1
0
2
1
0
2
0
2
0
0
0
2
1
1
0
0
0
1
2
0
1
6
2
3
0
2
2
0
0
1
1
0
2
2
1
0
0
0
4
2
2
0
1
0
2
0
1
1
0
2
2
1
1
1
2
0
1
0
1
2
0
2
1
1
1
2
0
0
0
0
1
1
1
1
0
1
0
0
0
1
1
2
0
0
0
0
0
1
1
1
1
0
1
2
1
1
0
2
2
3
0
1
0
1
0
0
2
0
1
0
0
0
0
2
0
0
0
1
2
1
1
5
0
0
0
1
0
0
0
0
0
0
1
2
2
0
0
2
1
2
2
0
0
0
1
1
2
0
1
0
0
2
3
1
0
2
1
0
2
0
2
2
1
1
1
0
0
0
3
2
0
0
2
0
2
1
0
0
2
2
1
0
2
0
2
0
1
1
1
0
2
0
2
1
2
1
1
2
0
2
1
1
2
1
0
0
1
1
2
1
1
1
0
2
0
0
0
1
0
0
0
2
1
2
1
0
1
0
1
2
0
0
1
0
0
0
0
2
2
1
2
1
2
1
0
2
2
1
1
1
1
1
1
2
0
1
3
1
1
0
1
1
0
2
0
1
1
1
0
0
0
0
2
1
0
2
2
2
0
1
1
1
1
0
2
2
0
2
0
2
1
0
0
2
0
0
0
0
0
1
2
2
1
0
0
0
1
0
1
2
2
1
2
0
0
1
0
3
0
1
1
1
2
4
0
1
0
0
0
1
0
1
1
1
1
1
2
2
2
0
1
0
3
2
2
2
0
2
2
3
0
1
1
0
0
1
2
2
2
1
2
2
3
1
1
2
2
0
0
0
0
1
0
0
1
1
0
1
0
0
1
0
2
0
1
2
0
1
1
4
1
2
1
2
0
1
0
2
0
1
0
1
1
1
0
1
0
0
2
0
2
1
2
0
0
1
0
0
0
0
2
1
1
2
1
0
0
0
1
1
2
0
3
1
0
0
1
0
1
0
1
0
1
2
1
0
0
1
0
1
1
0
1
1
0
1
2
0
0
0
2
1
0
1
0
1
0
0
0
2
0
1
0
0
0
1
1
1
0
1
0
2
1
0
0
0
2
0
1
2
0
0
0
1
1
1
2
0
2
0
0
1
2
0
0
1
0
2
0
1
0
0
1
2
2
2
1
0
1
1
0
1
0
1
0
1
0
1
0
1
0
0
1
0
1
2
0
1
0
0
2
2
2
1
2
1
0
0
1
1
0
0
0
0
0
0
1
0
1
0
1
1
1
0
2
1
0
0
1
0
2
0
2
2
1
1
0
1
0
1
1
2
0
2
2
2
1
2
1
1
1
2
1
1
1
2
0
2
0
0
0
0
1
1
0
0
1
0
1
0
0
0
2
0
0
1
0
0
1
0
1
0
2
0
0
1
0
1
2
2
1
3
2
0
1
0
2
0
0
0
0
0
0
0
0
0
2
1
4
1
0
1
0
2
1
2
0
2
3
2
0
1
0
1
0
1
0
0
2
1
1
0
1
3
1
2
1
1
3
0
1
0
0
0
0
2
0
1
1
0
1
0
1
1
1
0
2
1
0
0
0
2
0
2
0
0
2
1
0
0
0
2
2
1
1
2
1
2
0
2
1
1
1
2
2
2
1
0
3
0
1
0
0
1
0
1
2
1
1
2
2
1
0
2
2
0
1
0
1
0
2
0
1
1
0
2
1
1
1
2
0
1
2
1
0
1
0
1
0
0
1
1
1
0
0
2
0
2
1
1
2
1
1
1
0
0
2
2
0
1
1
1
0
0
0
0
2
3
0
1
0
0
2
1
0
1
0
0
1
1
2
0
1
2
0
0
1
1
1
0
0
0
1
2
0
2
0
0
0
1
0
0
0
2
2
1
0
0
1
1
1
2
1
2
0
1
4
1
0
0
2
1
1
0
1
1
3
0
0
0
1
0
0
2
2
0
0
2
5
0
1
1
2
0
0
0
2
0
1
1
0
1
1
2
1
0
0
0
0
0
0
1
0
0
0
1
2
1
1
1
0
1
0
1
1
0
1
2
1
0
0
0
0
1
0
0
0
0
2
0
1
0
1
1
1
1
0
0
1
0
2
1
0
0
3
1
0
1
1
1
3
0
0
1
1
0
0
0
1
2
1
0
0
2
1
0
1
1
0
1
0
2
1
2
0
1
2
1
0
1
2
1
1
2
0
1
0
1
2
1
1
0
0
0
1
1
0
0
1
0
0
0
1
1
1
1
0
0
2
2
1
1
0
1
1
0
1
1
1
2
1
0
0
0
1
1
0
2
0
0
1
1
1
0
1
1
1
2
2
0
0
2
0
0
1
2
1
2
0
2
2
0
1
1
1
0
1
0
2
1
1
0
0
1
0
1
0
1
1
2
0
0
1
1
1
0
1
1
1
1
1
0
1
1
0
1
0
0
1
0
2
1
1
0
2
0
2
0
0
2
0
1
1
0
1
2
2
2
2
2
0
0
1
2
2
5
4
0
0
0
0
0
2
1
1
1
1
2
0
1
0
0
2
0
4
0
2
0
1
0
1
0
2
1
2
0
1
0
0
1
2
0
1
2
0
1
2
1
2
0
2
0
2
0
0
0
1
0
2
2
0
3
0
0
0
0
1
0
0
1
0
1
1
1
0
1
0
0
1
1
2
0
1
3
1
3
1
0
2
1
0
1
1
2
2
2
0
2
1
0
2
1
2
2
0
2
0
1
1
0
0
0
2
0
1
1
0
1
1
2
1
0
1
1
0
0
2
0
1
0
2
0
1
2
0
0
0
0
0
0
1
0
0
1
0
1
0
0
2
0
0
2
0
0
1
0
2
2
1
0
2
2
2
0
1
2
1
0
2
2
2
2
0
2
1
2
1
1
2
1
1
2
1
1
1
1
1
2
2
2
3
1
1
0
1
0
1
1
0
1
2
1
2
0
0
2
0
0
0
2
2
1
0
0
2
0
1
0
0
1
2
0
0
0
0
1
0
0
1
1
1
0
2
0
0
1
2
1
1
0
1
0
0
1
1
1
2
1
1
0
0
0
1
0
2
1
1
1
0
1
0
1
1
0
0
1
0
0
1
1
1
0
0
1
1
1
2
2
0
0
0
2
1
0
2
2
0
0
1
2
2
0
0
0
1
0
0
1
2
2
0
2
0
1
2
1
2
0
1
1
0
1
2
1
0
0
1
0
1
0
1
0
0
0
1
0
2
0
1
0
1
0
0
2
0
2
0
1
1
2
1
1
2
0
0
0
1
1
2
0
2
1
0
2
2
0
2
1
2
0
1
1
1
0
1
0
0
2
0
0
2
0
3
1
1
1
0
2
2
0
1
2
0
0
2
0
1
0
0
2
1
1
1
0
0
0
1
1
1
0
1
1
0
0
2
0
1
0
2
0
0
1
2
1
0
0
2
1
1
1
0
2
0
0
1
0
1
1
0
0
1
1
1
2
0
0
2
1
0
2
1
1
1
0
1
0
2
1
0
2
2
2
1
0
1
2
2
1
2
0
0
1
0
1
2
0
0
0
0
1
1
0
0
0
1
0
1
5
1
0
0
0
1
2
0
1
2
0
1
1
0
0
0
2
2
0
2
1
2
0
0
0
1
1
0
0
2
0
2
1
0
0
0
1
0
1
1
1
2
0
0
1
0
1
0
1
2
0
0
2
0
1
1
0
1
1
1
1
1
1
0
2
0
0
1
2
0
1
1
2
2
3
1
2
0
0
0
0
0
1
0
1
2
0
0
0
0
2
0
2
0
2
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
1
0
1
2
0
3
2
1
1
0
0
2
0
1
0
0
1
2
0
0
1
1
2
1
2
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
1
2
0
2
1
1
1
0
1
2
1
2
1
2
0
0
1
0
0
2
1
0
0
3
0
2
0
2
2
0
0
3
0
2
2
1
2
0
1
2
0
0
5
2
0
0
0
0
0
1
2
0
1
1
2
2
1
0
1
0
2
0
0
0
1
1
0
2
0
0
1
0
2
0
0
0
1
1
2
2
2
0
1
1
1
1
0
1
0
1
1
1
0
0
0
1
0
1
1
1
2
1
2
1
2
1
2
1
1
1
1
0
1
1
1
2
0
1
1
2
0
0
1
1
0
1
0
2
2
0
2
1
1
1
2
1
1
0
0
0
0
2
2
1
2
1
0
0
1
2
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
1
0
2
0
1
1
1
2
1
0
2
1
0
1
0
1
1
0
0
1
0
2
1
2
2
2
0
0
0
1
1
2
0
0
2
1
1
0
1
1
0
2
0
1
1
0
1
2
1
0
0
1
1
0
0
1
2
0
1
1
1
1
1
2
1
0
2
1
0
2
2
1
1
0
2
1
1
0
1
1
0
1
1
0
5
2
0
1
0
0
1
0
0
1
0
1
0
1
0
1
0
0
0
0
0
2
1
0
2
0
2
1
0
1
1
1
2
2
1
1
1
1
1
1
0
1
2
0
2
0
0
1
0
1
1
6
0
1
1
1
0
1
0
2
0
1
1
1
1
1
2
0
1
0
2
1
0
0
1
1
0
1
0
2
0
2
1
0
1
0
0
0
1
1
1
0
0
1
2
0
0
2
1
1
1
2
0
0
0
0
1
2
2
1
0
0
0
1
0
0
1
6
0
2
0
1
1
0
0
0
2
2
1
1
1
0
1
1
0
1
1
0
0
0
0
1
2
0
0
1
0
2
0
0
0
0
1
1
1
0
0
1
0
0
1
0
1
2
1
1
0
0
0
2
1
0
0
0
1
0
1
0
8
0
1
0
0
0
0
0
1
1
2
0
0
3
1
1
1
1
1
0
1
2
0
0
0
1
2
1
0
1
0
2
1
1
0
3
0
0
1
0
0
1
0
0
1
1
0
0
1
1
1
1
1
0
1
2
0
0
1
0
0
2
0
1
1
0
3
2
1
1
2
0
2
1
0
3
2
1
0
2
0
0
1
0
1
0
1
0
1
1
1
1
0
2
0
1
0
0
0
1
0
2
2
0
0
2
0
0
1
1
1
0
1
2
1
0
0
1
0
0
0
2
2
1
0
0
1
2
0
0
0
2
0
2
2
2
1
1
0
0
1
0
1
0
1
2
1
2
1
1
2
2
1
0
1
2
0
0
1
0
0
2
1
2
1
1
1
1
2
1
3
0
0
1
0
1
0
2
2
1
0
0
0
0
0
0
0
0
2
2
0
0
1
2
2
2
1
1
1
0
1
1
1
0
0
0
0
0
1
2
1
1
0
2
2
0
1
0
0
0
0
1
2
2
1
0
1
2
0
0
2
0
0
2
0
2
2
2
0
1
2
0
0
0
1
2
0
1
2
0
0
0
0
0
1
0
0
0
0
2
2
0
2
0
2
1
1
0
2
1
1
1
0
2
0
0
1
0
1
0
0
0
1
1
1
1
0
0
2
0
1
1
2
0
1
0
1
2
2
0
0
0
0
1
1
2
2
0
0
0
1
1
2
0
0
1
1
2
0
1
0
2
1
0
1
1
1
0
1
0
1
3
0
0
1
1
1
1
1
1
1
1
0
1
0
2
2
2
0
0
0
0
0
2
0
1
1
1
2
1
1
0
1
0
2
0
2
2
0
0
2
0
0
0
2
0
0
0
0
1
2
0
1
2
0
1
2
1
1
1
2
0
0
1
0
2
0
0
0
0
0
1
0
2
2
1
0
1
0
1
0
0
2
2
0
2
0
1
1
0
2
0
2
2
1
0
1
1
0
1
0
0
2
2
0
0
1
1
1
1
1
1
0
0
1
0
0
2
2
1
1
0
1
1
2
2
1
1
2
2
1
1
2
2
1
0
0
0
1
0
1
0
0
0
2
1
0
0
3
0
2
1
1
2
0
2
0
2
2
0
2
2
0
2
0
0
0
0
1
2
1
2
2
1
0
2
1
1
1
0
2
2
1
0
2
2
3
1
1
1
0
2
1
1
0
0
0
2
1
0
1
0
2
2
0
2
0
0
1
2
0
0
1
0
0
1
2
1
1
2
2
1
0
2
1
1
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
2
1
0
1
1
0
1
2
1
1
0
0
1
0
0
1
0
0
1
1
1
2
2
0
0
2
1
0
1
1
0
0
0
1
0
1
1
2
2
0
2
1
0
3
2
0
1
1
2
2
1
0
2
0
1
1
1
1
1
1
2
0
1
2
1
2
1
0
1
0
0
1
0
0
0
1
1
1
2
0
1
2
1
2
0
1
1
1
0
2
0
2
2
0
0
0
1
0
0
1
0
0
0
2
0
3
1
1
0
0
0
1
0
2
1
1
0
1
0
0
0
2
0
2
1
0
0
0
0
0
0
0
1
0
1
0
2
0
0
2
0
1
1
0
1
2
2
0
1
0
0
1
0
1
0
2
0
0
1
1
2
2
1
1
0
2
0
0
0
0
0
1
1
0
0
0
2
0
1
1
0
2
2
0
1
0
1
2
0
2
1
0
1
1
3
1
0
0
0
1
0
1
1
2
0
0
1
1
0
3
0
2
2
1
0
0
1
0
2
2
1
1
2
1
3
0
1
1
0
0
2
0
1
1
1
1
0
0
0
0
0
1
1
0
2
0
1
0
1
2
1
0
1
3
0
0
1
1
1
0
2
2
1
0
0
1
2
2
2
0
1
2
0
1
1
1
1
1
1
1
0
1
1
0
0
0
1
0
2
0
0
0
1
0
1
0
0
2
1
2
1
1
1
1
1
1
0
2
1
0
3
0
2
1
1
0
1
3
0
1
0
1
1
0
1
1
0
0
0
1
1
1
0
1
2
2
0
2
0
1
2
0
2
0
0
1
2
1
1
2
0
0
1
1
0
0
0
1
5
2
1
1
1
2
2
2
2
0
1
0
2
0
0
0
1
0
0
3
2
0
0
1
0
2
2
0
0
0
1
0
0
2
0
2
2
2
0
1
0
0
2
2
1
1
0
1
0
2
2
1
2
1
0
0
2
2
1
0
0
1
0
0
2
0
1
2
0
2
0
1
0
2
0
0
0
1
1
1
2
1
0
0
2
1
3
2
1
0
1
2
2
1
0
1
0
1
1
0
0
0
0
0
0
2
0
2
1
0
3
2
1
0
1
2
0
1
2
0
0
2
0
0
9
2
0
0
1
1
2
1
1
2
0
2
0
2
1
0
0
1
2
0
2
2
1
0
1
0
1
0
0
1
0
0
0
0
0
1
2
0
2
0
2
0
0
1
2
0
0
1
1
1
0
0
0
0
2
2
2
1
2
0
1
0
0
2
1
0
0
0
2
0
1
1
1
0
1
2
1
2
1
0
2
1
1
1
1
0
1
1
1
3
2
1
1
1
0
2
1
2
2
1
0
1
0
0
0
0
1
2
0
3
1
1
2
0
1
2
0
0
2
1
1
0
1
0
1
0
1
1
1
1
1
1
1
1
1
0
1
1
0
1
2
2
1
0
1
0
0
9
2
0
1
1
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
2
0
1
1
1
2
0
1
1
1
1
1
0
0
0
1
1
1
1
2
0
1
2
0
2
1
0
0
0
0
1
1
2
1
2
1
1
0
0
1
2
1
0
0
0
2
1
0
1
2
1
0
1
1
1
2
0
1
1
1
0
3
2
1
0
1
1
0
0
0
1
0
0
0
1
0
0
3
1
1
2
2
0
1
0
2
1
1
0
0
0
0
2
1
1
2
1
2
0
1
0
2
1
1
2
0
1
3
1
1
0
2
0
0
1
1
1
2
2
2
0
1
1
0
1
3
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
1
0
2
0
0
0
0
0
2
0
0
1
1
0
1
0
1
0
0
2
1
1
1
2
0
0
0
0
1
0
1
0
2
0
1
2
2
0
5
2
1
0
1
0
2
2
0
0
1
1
0
0
2
2
0
0
0
3
2
0
1
1
0
1
2
2
0
2
2
1
2
2
2
1
0
0
0
2
1
1
1
2
1
1
1
0
1
1
0
2
2
1
1
0
1
0
2
1
1
2
2
0
2
0
1
2
3
1
1
1
0
0
2
0
0
0
1
1
2
1
0
0
1
2
1
1
2
0
1
2
0
2
2
0
2
1
1
1
1
0
1
1
0
2
1
1
1
0
0
1
1
0
2
2
0
1
0
0
0
0
2
1
1
2
1
1
0
1
2
0
2
0
1
0
1
2
1
1
1
1
1
0
0
1
1
1
4
2
1
1
2
1
1
2
0
1
0
2
0
1
0
1
0
1
1
1
1
0
1
1
2
1
3
0
2
1
0
2
1
1
0
0
0
0
0
1
0
2
0
2
2
0
1
1
1
2
2
0
0
0
0
1
2
1
1
1
0
0
1
2
2
0
0
0
0
2
0
1
2
1
1
1
0
1
3
0
2
1
0
0
0
2
0
0
0
0
0
2
1
2
1
0
0
2
1
1
3
1
1
2
0
1
0
1
1
0
1
0
0
0
0
1
0
0
1
1
1
1
1
1
2
0
2
0
0
2
0
1
1
0
1
2
1
0
1
0
0
2
1
0
0
2
0
0
2
1
0
2
2
0
1
0
2
2
1
1
0
1
0
2
1
2
0
2
1
0
0
1
2
0
2
1
0
1
0
1
0
1
0
1
0
1
0
0
1
0
1
1
0
2
0
1
1
2
0
1
0
0
1
2
1
2
1
1
1
0
1
0
1
1
0
1
2
1
2
0
0
0
1
2
0
0
3
1
0
0
0
1
1
0
1
1
0
0
0
0
0
2
1
1
1
0
1
1
1
3
0
0
1
0
0
0
2
1
0
1
2
1
0
1
1
1
1
0
2
0
2
2
1
1
0
1
2
1
0
0
1
2
0
0
0
1
1
0
1
2
1
2
1
1
1
1
1
0
2
2
1
2
0
0
0
1
1
2
0
1
0
0
1
1
1
1
2
1
2
0
0
1
3
0
1
1
0
1
2
2
1
1
0
2
0
0
1
2
1
2
2
0
0
1
4
2
1
0
0
0
1
0
0
1
0
0
0
0
0
2
0
1
1
0
0
2
0
1
0
2
2
1
1
0
1
2
2
2
0
0
1
1
0
0
0
2
1
1
0
1
0
0
1
0
2
0
2
0
0
0
0
0
1
1
1
0
0
1
0
0
1
2
1
0
0
0
0
0
1
1
0
2
1
2
0
0
1
1
1
1
0
1
1
0
0
0
1
0
0
1
1
2
0
1
0
3
1
1
0
0
1
0
1
0
0
0
0
2
0
0
0
0
2
0
1
0
2
0
1
1
1
3
0
0
2
1
1
0
0
2
0
0
1
1
0
2
0
3
1
2
0
1
0
1
0
0
1
1
0
1
0
1
1
0
1
1
0
1
0
0
1
2
0
2
2
1
0
0
0
1
1
0
2
1
0
4
2
2
2
1
0
2
0
0
1
0
2
2
1
1
0
0
2
2
1
0
0
2
2
1
1
0
1
0
0
0
1
0
1
2
0
1
0
0
1
0
0
1
0
1
0
1
0
0
0
1
0
0
2
0
1
2
2
1
1
0
1
0
1
0
0
1
1
0
0
2
1
2
0
1
2
0
1
1
0
1
0
0
0
1
0
1
1
1
0
1
0
1
1
2
1
2
0
1
1
0
1
2
1
0
0
1
2
1
0
2
1
0
0
0
1
0
2
0
1
1
1
0
1
0
2
0
0
0
0
1
1
0
2
0
0
1
1
2
0
2
1
1
0
1
1
1
1
1
1
1
3
0
3
1
2
0
0
2
1
1
1
2
1
0
2
1
1
1
0
0
0
2
1
0
1
1
1
0
2
1
3
1
0
2
1
2
1
0
1
1
1
1
0
0
2
0
2
0
1
1
1
2
0
0
1
2
1
0
2
0
1
0
2
1
1
0
0
1
0
1
0
1
0
1
1
0
0
2
0
2
0
0
1
0
0
0
1
1
1
0
0
1
2
1
0
1
1
1
0
1
0
2
0
0
2
0
2
0
1
0
2
1
2
1
0
0
0
1
0
1
1
0
2
2
0
1
2
1
0
1
1
2
0
0
2
1
0
0
1
0
2
0
0
1
1
0
0
1
2
1
0
1
1
4
0
0
1
1
2
2
0
1
3
2
1
2
1
2
1
2
3
0
2
0
0
1
2
1
1
1
1
0
0
1
1
0
0
0
2
1
1
0
2
1
0
2
1
1
1
1
0
2
1
1
0
1
0
2
2
0
1
1
0
2
1
1
1
1
2
1
0
2
0
0
2
1
0
1
0
0
1
2
0
0
0
0
0
1
0
2
1
0
0
0
1
1
0
0
1
0
2
1
1
0
1
1
1
1
1
0
0
1
1
0
0
2
0
0
0
2
0
0
0
3
0
0
0
0
0
2
0
0
1
0
1
1
1
1
1
1
1
2
1
0
0
1
2
0
3
1
1
0
0
1
1
4
2
0
1
0
0
0
0
1
1
1
1
0
0
0
0
0
0
2
1
1
1
0
0
1
1
1
0
0
0
1
1
2
0
2
0
2
2
1
2
0
2
2
1
2
0
1
2
1
1
1
2
0
2
0
1
2
1
3
1
1
0
1
2
0
0
0
2
2
1
0
1
0
1
1
1
1
1
1
2
2
1
1
1
0
0
0
1
1
0
0
0
2
0
1
0
1
0
1
0
0
0
0
0
0
1
1
2
2
1
0
0
2
2
1
0
0
1
1
1
0
1
0
1
0
0
0
1
1
1
1
2
2
0
1
2
1
0
1
0
2
1
0
1
0
2
0
0
2
1
1
4
0
1
0
1
0
0
0
2
0
0
2
0
0
0
0
2
1
2
0
0
1
0
1
0
0
1
2
0
1
0
0
0
3
0
2
2
0
1
0
0
1
2
0
0
1
0
0
0
2
1
0
1
1
2
0
0
0
0
0
2
0
2
1
0
0
1
0
1
2
1
0
0
0
1
0
0
1
2
1
1
0
2
1
1
2
0
1
0
1
0
0
2
1
0
1
2
2
1
0
2
1
0
0
2
1
2
0
1
1
1
0
0
0
0
0
1
1
2
1
3
1
2
0
2
2
0
2
0
1
2
1
1
0
0
2
2
1
1
2
1
0
0
0
1
0
0
0
1
2
2
0
0
1
0
2
1
0
1
0
0
0
1
1
1
0
0
0
0
0
1
0
0
1
2
2
1
1
1
1
0
3
0
1
2
0
0
2
1
1
2
1
1
1
1
2
0
2
1
2
2
0
1
0
1
0
2
0
0
1
0
0
1
0
2
1
0
0
1
1
2
0
1
1
1
1
1
2
1
2
0
0
0
2
0
0
1
1
0
1
1
0
1
1
2
1
1
0
0
0
0
1
1
2
1
0
1
0
2
1
0
0
2
1
1
1
0
1
1
0
0
2
1
1
1
0
1
0
0
1
1
0
1
0
0
1
0
2
0
0
0
2
0
0
1
0
1
0
4
0
1
2
0
1
0
0
1
1
0
0
1
2
2
0
0
1
0
0
0
0
1
2
2
0
1
1
1
1
1
0
0
0
1
0
0
2
1
0
0
1
2
1
1
1
0
2
1
1
1
1
1
0
1
0
1
2
1
0
1
1
1
1
1
2
1
0
1
0
2
1
0
1
0
0
1
0
0
1
0
2
0
0
0
1
4
1
0
0
0
0
1
0
1
1
1
0
1
1
0
2
0
0
0
0
2
2
0
2
1
1
0
0
0
0
0
0
1
0
0
1
1
0
1
1
1
5
0
0
1
1
2
1
1
0
1
0
0
0
0
0
2
2
1
1
2
0
3
1
2
1
0
1
0
2
1
1
0
0
1
2
2
0
1
0
1
1
1
1
0
1
0
0
1
0
0
1
0
1
1
0
2
0
1
0
0
1
1
1
1
2
2
1
1
2
2
0
1
2
1
0
0
0
0
0
2
0
1
1
1
0
2
2
2
1
0
1
0
0
2
0
2
2
1
0
0
0
0
1
0
1
1
0
0
0
1
2
1
0
0
3
0
2
1
0
1
0
1
1
2
1
2
1
0
2
1
1
0
0
2
2
2
0
1
0
2
0
2
0
1
1
0
1
0
1
0
0
1
1
0
1
1
1
2
0
2
0
0
0
1
1
1
0
0
1
1
0
0
1
0
2
0
2
1
1
0
1
0
1
1
0
1
0
0
2
1
0
2
0
2
0
0
2
0
1
2
0
0
0
2
1
0
1
2
0
2
2
0
1
0
0
0
0
1
1
1
0
1
0
0
1
1
0
1
2
0
0
0
0
2
0
1
2
2
2
0
0
2
0
1
1
2
0
0
1
2
1
0
0
0
1
2
0
0
0
1
0
1
1
0
0
1
2
2
2
3
0
1
0
0
1
0
1
0
1
1
1
1
1
1
0
0
1
1
0
1
0
2
0
0
1
2
1
0
0
1
2
0
1
2
1
0
1
1
0
0
0
1
2
1
0
1
1
0
1
0
0
0
1
0
1
0
0
0
1
2
0
0
0
1
0
0
0
1
1
1
0
2
1
0
2
2
0
1
1
1
0
1
1
0
2
1
2
0
2
1
0
2
0
0
0
1
1
0
1
3
1
2
0
2
2
1
1
2
1
0
0
0
0
2
0
0
1
1
2
0
0
0
2
0
0
1
1
1
0
1
0
0
0
1
2
2
1
1
1
0
1
1
0
0
0
1
2
2
2
0
2
2
1
1
0
2
1
1
0
2
0
0
0
1
0
0
0
0
2
0
1
0
0
0
1
0
0
2
1
1
0
1
0
1
1
0
0
2
0
1
2
0
0
2
1
0
0
2
1
1
1
2
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
1
0
2
1
0
1
2
1
2
0
0
1
1
0
0
0
0
1
0
2
0
1
1
1
1
2
0
0
2
0
0
0
0
1
2
1
0
1
0
1
1
2
2
1
1
1
1
2
1
0
0
0
0
1
0
0
1
0
2
2
1
0
2
0
1
2
1
0
2
0
0
0
0
0
2
1
0
0
1
0
1
1
0
0
0
2
1
0
1
1
1
2
1
1
1
0
0
1
1
2
0
0
0
0
2
0
0
0
1
1
1
0
0
1
1
1
0
0
0
2
1
0
0
2
1
1
0
0
0
2
1
0
2
1
0
1
1
2
0
1
1
0
2
3
0
0
2
0
1
2
0
1
4
0
1
1
1
3
1
1
2
1
1
1
0
1
1
1
2
2
0
2
0
1
1
0
0
0
1
0
2
0
0
0
1
1
0
0
1
0
1
1
0
0
0
0
0
1
2
0
0
0
3
1
2
0
0
1
0
1
1
1
1
0
1
1
1
2
1
0
1
0
1
0
0
0
1
1
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
2
0
0
1
0
2
0
1
0
0
0
1
0
0
0
2
0
1
1
0
1
0
0
2
1
1
0
2
0
2
2
3
0
1
0
1
0
2
1
1
2
1
0
1
0
0
2
2
0
1
1
3
0
0
0
1
1
2
0
1
0
2
1
2
0
0
1
0
1
0
0
2
1
1
0
1
0
0
0
2
1
0
1
1
2
0
2
2
1
0
2
0
1
0
0
0
1
0
2
1
1
0
0
1
0
0
1
0
0
0
0
2
1
1
1
2
0
0
0
1
0
0
0
0
0
3
0
0
0
1
1
2
0
0
2
0
1
0
2
2
0
0
0
2
0
0
0
2
1
1
2
0
0
0
1
0
1
1
0
2
1
0
0
1
0
2
0
0
1
1
1
2
0
0
1
0
1
0
0
0
1
0
0
0
1
1
1
2
2
2
1
1
0
2
1
0
2
2
2
0
2
1
0
0
1
0
1
1
1
0
1
2
1
2
1
1
1
0
0
1
0
1
1
0
2
0
2
0
0
1
0
2
2
0
0
0
2
0
0
0
2
0
2
2
1
2
1
1
1
2
1
1
1
2
2
1
0
0
3
1
1
0
0
2
0
0
0
0
1
1
0
1
0
3
0
0
0
0
1
0
2
1
1
1
0
0
0
1
0
0
0
2
1
1
1
2
1
1
0
0
1
0
0
0
1
1
0
2
2
2
1
1
3
1
2
1
0
0
2
1
2
1
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
3
2
2
1
1
1
1
2
2
1
0
2
1
0
0
1
4
1
1
1
1
0
0
0
1
2
0
2
3
1
1
0
1
2
2
1
0
0
0
2
1
1
0
1
2
0
0
1
1
2
0
0
0
0
3
1
0
0
1
0
2
1
0
1
2
0
1
1
1
1
1
2
0
1
0
0
1
2
2
0
2
2
1
0
1
2
1
0
1
1
0
0
3
1
2
0
0
2
1
0
2
0
0
0
0
1
0
0
2
1
1
1
1
2
0
1
0
2
0
0
1
0
0
0
2
2
0
3
2
1
1
1
1
2
1
2
2
0
2
1
1
0
1
0
1
0
0
2
1
0
0
1
1
1
0
2
0
1
0
0
2
0
2
0
2
1
1
1
0
2
2
1
1
0
1
1
1
0
1
1
0
0
0
0
2
2
1
0
2
1
0
1
2
0
1
1
1
1
1
2
1
0
0
2
2
1
1
2
1
0
0
1
1
0
0
0
1
3
1
0
0
3
2
0
2
0
0
0
0
2
0
2
1
1
0
1
0
0
0
2
1
0
0
2
2
0
1
1
0
1
0
1
2
1
0
0
0
1
0
0
0
1
1
0
0
2
1
1
2
1
0
0
0
1
0
1
0
1
1
0
1
1
2
0
2
1
1
2
2
1
0
2
1
2
0
0
1
1
1
2
1
0
2
0
0
0
1
1
2
0
0
2
1
2
1
0
1
1
1
2
0
0
0
0
2
0
0
1
0
1
0
0
2
3
0
0
2
1
0
0
0
0
2
1
2
0
0
0
0
0
0
2
1
1
1
1
1
1
2
1
0
2
2
0
0
1
1
1
0
0
0
0
2
1
1
0
1
1
1
0
1
3
1
1
1
2
2
0
0
0
2
1
1
0
0
1
2
2
0
1
0
2
2
1
1
0
0
1
1
2
2
2
0
0
0
2
0
0
1
0
0
0
1
1
0
1
0
1
0
1
1
2
0
0
1
0
0
0
1
0
1
0
4
2
0
1
0
1
2
2
1
3
0
1
0
2
0
1
1
0
0
2
0
2
1
1
0
2
0
0
0
2
0
0
0
1
3
0
0
1
1
2
1
1
0
1
0
0
1
1
1
0
1
2
1
0
0
1
2
1
2
1
0
0
0
0
2
2
2
0
2
2
0
1
0
0
2
0
3
0
0
0
0
0
0
0
1
2
1
0
1
2
1
1
1
0
3
1
0
1
1
2
1
1
1
0
0
1
0
1
1
0
1
1
0
0
2
0
0
0
3
0
1
0
0
1
1
0
0
1
1
2
0
2
0
0
0
2
0
1
1
2
0
0
0
1
0
1
2
0
0
0
0
3
1
4
1
1
0
2
0
1
2
0
1
0
1
1
1
0
2
2
0
1
1
0
0
0
2
0
0
0
1
0
0
0
0
1
0
1
1
0
2
0
1
2
0
1
1
1
0
0
1
0
0
0
0
1
0
2
1
0
0
0
0
2
2
0
0
0
1
2
2
4
0
0
1
2
0
0
2
0
1
1
1
2
1
0
1
0
1
2
0
0
2
1
2
2
1
1
1
0
0
0
0
1
0
2
1
0
0
2
2
1
0
0
1
0
0
2
1
2
1
0
0
2
0
1
1
0
1
2
1
0
1
1
0
0
0
2
4
0
3
2
0
2
0
0
0
2
0
1
2
0
1
1
0
0
1
1
0
0
2
1
1
1
2
1
0
1
2
2
0
1
0
2
2
2
0
2
1
0
2
3
2
2
2
1
2
0
1
3
0
0
4
0
1
1
1
2
2
1
2
0
0
1
2
0
0
1
2
0
0
2
2
1
1
1
1
2
1
1
1
1
1
0
1
2
2
1
2
0
2
1
2
0
0
1
0
2
1
2
0
2
0
0
2
0
0
0
1
1
1
2
2
0
0
0
0
0
0
2
0
0
0
2
2
0
0
2
0
0
0
2
1
2
1
0
0
0
1
1
0
0
0
3
2
2
0
0
0
2
2
0
0
0
1
2
1
0
0
1
1
0
0
0
1
0
0
0
1
1
0
1
1
1
0
1
1
2
1
1
0
0
0
0
0
1
1
1
2
0
0
0
0
2
2
0
2
0
2
1
0
1
2
1
0
1
2
1
1
1
2
2
0
2
2
1
1
0
2
0
0
2
1
0
1
2
0
2
0
1
1
0
0
0
1
2
2
0
2
1
1
0
1
0
2
2
0
0
0
1
1
1
2
1
1
2
0
1
1
2
0
2
2
1
1
1
1
1
1
0
2
0
1
2
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
2
1
1
1
2
0
1
0
0
2
0
0
2
0
1
1
1
1
0
0
1
1
0
2
0
1
3
3
1
1
0
0
0
0
1
0
0
1
0
0
1
0
1
2
0
0
3
0
2
1
1
1
0
0
0
2
1
1
1
2
0
1
0
0
0
1
3
0
2
2
1
0
0
1
2
2
1
0
0
1
0
1
1
2
2
2
2
0
0
0
0
1
0
1
3
0
1
1
1
0
1
0
2
0
0
0
2
0
1
2
1
1
0
2
0
0
0
0
0
1
1
1
0
0
0
0
2
0
1
2
1
2
1
0
2
0
0
0
0
1
3
0
1
0
2
0
2
0
0
1
0
2
2
1
0
0
2
2
0
2
1
1
1
2
1
1
0
1
1
2
0
2
1
0
1
1
0
1
1
1
1
0
0
1
0
0
0
0
0
1
2
0
0
0
2
2
1
0
0
0
0
1
1
0
1
0
1
0
1
1
0
1
2
0
1
1
1
0
2
2
0
0
0
1
1
0
2
1
0
0
0
2
1
0
0
2
1
0
2
0
1
2
0
2
0
1
2
0
1
1
1
1
2
1
2
0
1
2
1
2
0
1
0
1
0
0
0
2
2
4
0
1
1
1
1
1
0
1
2
2
0
1
0
2
0
0
1
1
0
0
1
1
1
0
0
0
1
0
0
0
0
2
1
1
0
0
0
0
1
3
0
1
1
2
2
0
2
1
1
0
0
0
1
2
1
1
1
2
1
2
0
1
1
0
0
4
0
1
2
1
0
0
1
0
1
1
1
0
2
1
1
0
0
4
1
1
2
1
1
0
2
2
0
0
0
0
1
1
2
2
1
0
2
2
0
1
0
0
0
0
1
2
0
4
0
2
0
1
0
2
1
0
1
2
1
0
0
0
0
1
0
2
0
0
1
2
1
2
0
0
1
1
1
0
0
2
0
2
0
1
0
2
0
1
2
1
0
0
1
0
1
2
2
2
2
0
0
2
2
2
1
2
1
2
1
1
0
1
2
0
0
0
0
1
1
1
0
1
0
1
2
0
1
2
0
1
1
0
1
1
2
1
1
0
0
0
0
1
1
1
1
2
0
1
0
0
1
0
0
1
5
1
0
2
2
1
1
2
1
1
0
1
0
0
2
0
1
0
1
2
1
1
1
1
1
0
1
1
1
2
1
1
0
0
2
2
0
1
1
1
1
0
0
0
1
2
2
2
0
1
0
2
0
0
1
1
1
1
0
0
1
1
0
0
0
1
1
1
1
0
0
1
0
0
1
2
0
0
2
0
0
0
0
0
1
0
1
0
1
0
2
1
2
0
0
0
0
1
1
2
1
1
1
2
1
0
2
0
1
1
7
1
0
1
1
0
2
0
0
1
1
0
0
1
0
2
1
1
0
0
0
1
2
0
0
2
0
0
2
1
0
0
2
2
3
1
1
2
1
0
0
0
0
0
0
1
0
1
2
1
2
2
2
1
0
0
0
0
0
0
2
0
1
1
1
0
3
0
1
2
2
1
2
1
2
0
0
2
1
1
0
1
1
1
2
1
2
0
1
1
2
1
0
1
0
0
2
1
1
1
3
0
0
1
1
1
0
1
2
1
1
2
0
0
1
1
0
0
0
1
0
0
0
1
1
2
0
0
0
0
0
0
0
2
1
0
2
2
0
0
0
0
0
0
0
2
2
1
2
0
2
0
0
1
1
0
1
1
1
0
0
2
0
0
0
2
2
1
2
1
0
1
0
2
0
2
0
1
0
0
0
0
1
0
1
2
0
2
1
0
1
0
0
1
0
2
0
1
1
0
0
0
2
2
0
0
1
1
6
1
1
2
1
1
2
0
1
0
0
2
0
0
0
1
0
1
0
1
0
3
0
0
2
0
1
1
1
0
1
2
1
1
0
0
1
2
0
1
0
0
0
1
1
0
0
1
2
1
0
1
2
0
0
0
2
1
1
1
1
1
2
0
1
0
1
1
1
0
1
1
0
2
2
2
2
2
2
2
0
1
0
0
1
2
0
1
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
1
0
1
0
2
0
0
2
2
1
0
0
2
0
2
0
0
0
2
0
2
1
1
2
0
0
0
2
1
1
2
0
0
0
2
0
0
0
0
1
0
2
2
0
0
1
2
0
0
1
1
0
1
2
0
1
0
0
0
0
0
0
0
0
1
0
1
1
1
1
2
1
1
0
1
2
1
0
1
1
2
1
1
0
2
1
2
0
1
2
0
1
0
1
0
1
0
0
2
0
0
0
0
1
0
1
0
1
1
0
2
0
0
0
0
0
0
1
2
0
0
0
2
1
0
2
1
1
1
2
0
4
0
1
0
1
0
1
1
0
0
1
0
0
2
2
0
0
0
2
1
2
2
1
1
1
2
1
0
1
0
0
0
0
2
2
2
1
1
1
1
1
0
2
1
1
0
0
2
0
0
1
2
1
0
0
1
0
0
1
0
1
0
0
1
1
1
2
0
0
0
0
0
0
4
0
1
1
1
1
1
0
2
2
1
1
1
0
0
1
1
0
2
1
1
0
0
0
1
1
1
3
1
1
1
1
0
0
0
0
1
0
2
0
0
0
1
0
0
1
2
1
0
0
2
0
2
1
3
1
1
1
2
0
0
0
0
0
1
2
1
0
0
0
2
2
1
0
2
1
0
0
0
0
0
0
7
2
1
3
2
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
2
0
2
0
2
0
1
0
0
1
1
1
0
1
1
0
1
1
0
1
1
1
0
1
0
0
1
0
0
1
0
0
2
0
0
0
2
1
1
3
1
1
2
1
2
0
1
1
2
0
2
1
2
1
0
0
0
2
2
1
0
2
1
2
0
2
0
1
2
2
0
0
1
1
0
1
1
0
2
0
0
1
2
0
1
1
0
1
0
1
0
1
1
0
2
2
1
0
1
2
4
1
2
1
1
0
0
2
0
0
0
0
0
3
1
0
2
1
1
1
1
0
0
1
0
0
2
0
0
0
2
1
1
2
0
2
0
1
0
0
0
1
0
1
0
2
2
2
2
0
1
1
0
1
1
0
1
2
0
0
0
0
1
2
1
0
0
0
0
2
0
0
0
0
0
2
1
1
1
0
1
1
1
2
1
0
2
3
1
0
2
0
2
2
0
1
1
1
2
0
0
0
0
0
0
0
1
1
2
1
2
0
0
0
0
0
1
1
2
0
1
0
1
0
0
2
2
1
2
1
2
1
1
0
1
0
4
0
2
1
2
0
0
0
2
2
0
0
0
1
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
5
1
1
1
1
1
1
1
0
0
0
1
1
1
0
0
1
0
0
1
0
1
0
0
2
0
0
0
0
2
0
0
1
0
1
0
1
0
0
0
1
2
1
2
0
0
2
0
1
1
2
1
1
0
2
1
1
1
1
1
1
2
1
1
1
2
0
0
2
3
0
0
1
1
2
2
1
0
2
0
0
0
0
1
0
2
2
2
0
0
0
1
1
1
1
1
0
1
3
0
1
0
0
3
2
0
2
1
2
0
1
0
3
0
1
1
1
1
1
1
2
1
0
2
0
2
2
1
2
2
2
0
0
2
1
2
1
1
3
1
1
0
0
1
1
0
2
0
1
0
1
0
0
0
0
0
1
2
0
2
1
0
1
1
0
1
0
2
2
0
0
1
0
1
4
0
0
1
2
3
0
0
1
1
2
0
4
0
1
1
2
0
1
1
1
0
0
1
1
1
2
1
0
1
1
2
1
4
2
0
3
0
2
1
1
1
1
0
0
2
0
1
1
1
1
2
0
0
2
2
0
0
2
0
1
0
1
2
2
0
1
0
2
1
0
0
1
2
0
1
0
0
1
1
1
0
2
1
0
0
2
1
1
1
0
1
2
0
1
1
1
0
1
2
0
0
1
1
0
0
1
2
0
0
1
2
1
3
1
1
0
0
0
2
2
1
0
0
1
1
1
2
0
2
2
1
2
0
0
0
1
0
0
2
0
2
0
0
1
1
0
0
0
2
0
0
0
0
2
0
1
0
1
1
0
2
1
1
2
2
0
0
2
0
0
0
0
2
1
1
1
1
2
2
0
0
2
1
0
1
1
1
1
0
0
0
1
1
2
1
2
1
0
2
1
2
0
1
0
1
1
2
1
2
2
1
0
0
1
0
1
0
2
2
0
2
1
0
0
1
1
2
1
0
0
0
1
0
0
1
0
0
2
0
0
1
0
1
0
0
1
0
1
1
0
2
1
1
1
0
0
0
0
1
1
4
0
1
0
2
1
1
2
0
0
0
1
0
2
1
1
0
1
2
3
0
3
0
0
1
0
0
0
0
2
0
2
0
1
0
1
0
5
2
2
0
0
1
0
2
0
0
1
2
1
1
1
0
1
2
1
0
0
1
0
0
0
2
0
1
1
1
1
1
1
1
1
0
0
0
2
1
2
1
1
0
0
0
0
1
1
1
0
2
0
1
1
2
1
1
1
0
2
2
1
2
0
0
0
1
0
2
2
2
0
0
2
1
2
1
0
1
2
1
1
2
0
0
1
0
4
2
2
1
2
0
0
0
0
1
0
0
3
1
0
0
0
0
0
0
1
1
1
0
0
0
17
0
1
0
1
1
2
1
1
1
3
1
0
0
1
2
1
0
1
2
1
0
0
1
0
1
1
4
0
2
0
1
2
1
1
2
1
1
1
0
2
1
0
1
1
1
1
3
0
1
1
2
0
0
0
1
1
2
0
2
0
0
2
1
1
0
0
2
0
0
2
1
1
2
0
1
1
0
1
2
1
1
0
0
2
1
1
2
0
0
3
0
1
0
1
2
1
0
0
1
1
0
1
2
1
0
0
0
9
2
0
0
0
0
0
0
2
0
2
0
0
0
0
2
1
1
2
1
2
1
1
3
0
2
0
1
0
2
0
2
0
2
1
1
1
0
1
1
0
1
0
0
1
0
2
0
1
1
2
2
5
0
0
0
0
1
1
0
0
1
2
1
0
0
0
2
1
2
2
0
1
1
0
0
0
1
1
1
0
2
2
2
0
0
0
1
2
0
1
0
0
0
0
1
0
1
0
1
0
1
1
1
2
0
0
1
2
0
1
2
0
0
0
1
1
0
1
2
0
0
2
0
1
1
2
2
1
0
0
0
0
1
2
0
1
0
0
1
1
1
1
1
2
0
0
0
2
1
2
1
0
0
2
1
4
1
0
1
0
0
0
1
0
1
0
2
2
2
0
1
0
0
0
0
0
2
0
1
1
0
1
2
3
1
0
0
0
1
0
1
0
0
0
1
2
2
0
0
0
1
0
1
1
1
0
0
1
0
1
0
2
1
2
2
0
2
1
1
2
1
1
1
2
0
2
0
0
2
2
2
2
1
1
0
0
0
2
0
1
1
1
0
0
1
1
1
1
0
0
0
0
2
1
0
2
0
2
0
1
0
2
1
0
0
2
1
0
2
1
0
1
0
0
1
1
1
0
0
2
2
2
1
2
1
1
1
1
1
1
1
1
0
0
2
0
1
1
1
2
2
0
0
1
0
1
0
1
3
2
0
0
1
0
0
0
0
2
2
0
1
0
0
1
1
2
0
2
0
1
1
0
2
0
1
2
2
0
1
0
0
0
0
2
1
0
0
1
1
0
1
2
1
1
0
0
1
1
0
0
2
2
1
2
2
0
0
1
0
2
0
0
1
0
1
2
0
1
2
0
2
1
0
0
1
2
1
1
0
1
0
2
2
0
0
0
0
0
2
2
0
2
2
0
0
1
1
1
0
0
1
3
2
2
0
0
0
0
2
1
1
2
1
2
1
2
1
1
0
0
1
1
2
1
1
0
1
0
0
1
2
1
2
1
0
1
0
1
1
0
1
0
0
1
0
1
1
1
0
1
1
0
2
2
0
0
0
0
0
1
1
1
2
0
0
1
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
1
1
2
1
1
2
2
1
0
1
2
0
0
0
1
0
0
0
0
2
1
1
0
2
1
2
0
2
0
1
2
0
1
1
0
1
0
2
0
0
1
2
2
0
2
0
0
1
0
0
1
1
2
0
0
1
1
0
1
2
0
0
1
0
0
2
0
0
2
2
2
0
1
0
0
0
1
0
0
0
1
2
2
1
0
0
2
1
2
1
1
3
0
1
2
0
0
0
1
0
1
2
0
0
0
0
1
0
1
2
1
1
0
0
0
2
0
0
2
0
1
2
1
1
0
1
1
0
1
0
0
1
1
1
0
2
1
1
2
0
1
3
0
0
0
1
1
3
1
1
0
0
0
1
1
0
1
0
0
0
0
1
1
0
1
0
0
0
1
1
3
0
0
0
0
2
1
0
1
0
1
2
1
1
1
3
0
1
0
0
1
4
0
2
1
0
1
1
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
1
1
0
6
1
0
0
2
1
1
0
0
1
2
0
1
0
2
0
0
1
1
0
1
2
2
2
0
0
0
1
0
2
2
1
2
0
0
1
2
0
1
0
1
2
0
2
0
1
1
1
3
0
2
0
2
2
0
0
2
1
1
0
2
2
0
2
1
0
2
2
2
0
1
1
0
1
1
0
1
2
0
1
0
1
0
0
1
1
0
1
2
1
2
2
1
0
2
2
1
1
2
0
1
2
2
1
1
1
1
1
0
0
4
0
2
1
0
0
1
0
1
1
0
2
1
1
0
1
0
2
1
0
0
1
0
2
0
0
1
1
1
3
2
2
2
1
0
0
0
1
1
2
1
1
1
0
1
0
0
0
2
2
0
2
1
1
1
0
0
1
0
0
1
1
1
0
0
0
0
0
2
0
2
1
0
2
0
2
2
2
0
2
1
2
0
2
0
0
0
2
1
1
1
2
0
0
1
0
0
0
0
1
0
0
2
1
1
1
0
0
2
0
0
0
1
2
1
0
1
1
0
1
0
1
1
1
1
0
0
3
1
0
0
1
0
2
0
2
0
1
1
2
1
1
1
0
1
1
2
0
1
3
0
2
2
1
1
0
2
0
1
2
0
2
1
0
0
2
0
1
2
2
1
2
1
2
2
1
1
1
0
0
0
2
2
0
1
1
0
0
1
0
0
1
0
2
0
0
0
0
1
1
0
1
0
0
0
1
0
1
1
2
1
0
2
0
0
1
0
0
2
2
1
1
1
1
1
0
2
1
0
0
1
2
1
1
0
1
1
1
0
0
1
2
2
0
0
0
0
0
1
1
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
2
1
0
3
2
1
1
2
0
1
1
2
1
0
0
0
1
0
1
1
0
0
0
1
2
1
0
0
0
1
1
1
1
0
1
0
1
1
2
1
2
2
1
2
0
1
1
1
0
0
0
2
1
0
2
0
0
1
0
1
1
0
1
1
1
0
2
1
1
2
0
2
0
2
0
0
1
2
0
0
1
1
0
0
0
1
4
1
1
1
2
0
1
1
0
1
1
0
1
0
1
0
0
0
1
1
0
2
0
0
0
0
1
1
1
2
0
1
2
1
0
2
0
0
0
2
0
0
2
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
1
2
2
0
0
0
1
0
0
1
0
1
1
1
2
0
2
1
0
0
1
0
1
1
0
0
2
0
1
0
1
1
1
1
1
0
0
1
0
1
1
0
1
0
2
1
0
0
2
0
0
1
0
1
1
0
2
1
0
0
0
2
2
0
1
3
0
0
1
0
2
0
1
2
1
1
1
1
0
2
1
2
1
1
0
0
0
2
0
0
2
0
2
2
1
2
0
0
0
0
0
2
2
0
1
1
1
2
2
2
1
0
2
0
2
0
0
1
1
0
2
1
1
0
2
0
0
0
2
1
2
1
0
2
0
1
2
0
0
0
1
1
0
1
0
2
0
1
2
1
1
1
0
0
3
0
2
1
0
0
1
0
2
0
1
2
1
2
0
1
2
2
1
2
0
1
1
0
1
0
1
1
0
0
2
0
0
2
0
0
2
1
2
2
2
1
1
1
2
2
2
1
1
0
2
0
1
1
2
0
1
1
2
1
2
0
1
0
2
1
1
1
2
1
2
1
1
2
0
1
2
0
2
0
0
2
1
0
1
0
1
1
0
0
0
0
2
2
0
2
0
2
2
2
1
1
0
0
2
1
1
1
1
0
1
3
1
2
2
0
2
0
2
1
0
0
0
0
0
0
1
1
1
0
0
1
0
1
1
1
1
0
1
2
0
1
2
2
0
1
0
3
0
1
2
2
0
1
1
0
0
2
2
1
1
0
1
1
1
1
2
0
1
0
0
0
1
0
1
1
0
1
1
2
0
1
0
2
2
1
0
1
0
1
0
0
2
0
1
0
1
2
1
2
0
2
1
0
2
0
2
2
2
0
0
1
0
0
1
2
0
1
1
2
4
0
2
1
1
0
0
1
2
0
0
1
1
0
1
2
0
0
0
0
1
2
1
0
0
2
0
1
1
0
2
0
1
1
1
0
0
1
1
1
1
1
1
2
4
2
0
0
1
1
2
1
2
0
2
1
2
0
0
2
0
1
1
0
2
2
2
1
1
0
0
1
0
0
1
2
0
1
1
0
0
0
1
2
0
2
0
1
1
1
0
1
2
0
1
0
0
0
1
2
1
0
2
0
0
0
2
1
1
2
1
3
1
1
1
0
0
1
0
0
1
0
1
0
0
1
1
2
1
0
2
2
1
1
2
0
0
1
1
3
1
0
0
6
0
0
0
2
0
2
1
1
0
2
2
0
1
1
1
2
1
1
0
0
1
0
3
1
0
2
0
0
1
0
0
0
0
2
1
0
1
1
1
0
1
1
1
0
1
0
0
2
2
0
1
1
1
0
2
0
0
0
0
0
1
0
1
1
0
0
2
2
1
1
1
0
1
2
2
2
0
0
1
1
0
1
1
0
0
1
1
2
1
1
0
1
0
0
1
0
1
0
1
0
0
0
0
2
2
1
3
1
1
0
1
0
0
2
0
0
1
0
1
1
0
1
0
1
1
2
2
2
0
2
0
1
0
0
2
0
2
0
2
0
0
1
0
0
0
2
2
0
0
0
0
1
0
2
2
0
2
0
0
0
1
2
1
0
0
4
0
1
1
2
2
0
1
0
0
1
0
1
1
0
2
1
0
0
0
2
2
1
1
0
2
1
2
0
0
2
1
1
1
1
1
0
1
2
0
0
1
1
0
0
2
2
0
0
1
0
1
1
3
0
1
1
1
0
1
2
0
2
1
1
0
1
2
0
0
0
1
0
2
2
3
0
0
1
1
1
2
2
1
0
0
2
2
0
0
2
0
0
0
1
0
0
1
0
1
2
2
1
2
1
0
0
0
2
0
0
0
1
1
0
1
1
1
1
0
0
0
2
0
0
0
2
1
1
0
0
1
0
2
0
2
1
0
0
2
1
0
0
0
0
0
2
0
1
1
1
0
2
0
0
0
0
4
0
2
0
0
1
0
1
1
0
0
1
2
1
0
1
0
2
1
0
1
0
0
0
2
1
1
2
2
1
1
1
1
0
1
0
2
0
1
0
0
0
0
1
0
0
1
0
0
0
0
2
0
1
1
2
1
0
0
0
2
1
1
0
0
0
0
1
1
1
1
0
1
2
0
0
1
1
0
0
0
1
1
1
0
0
1
0
1
1
1
1
1
0
1
1
2
1
2
1
0
1
0
1
1
1
1
2
2
0
1
0
2
2
2
0
0
0
1
2
0
0
1
2
2
0
1
0
0
2
2
0
0
1
0
1
1
0
0
0
1
1
0
0
2
1
0
2
1
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
1
0
1
1
2
0
0
0
0
0
0
0
1
2
2
2
1
2
0
0
2
0
0
1
0
0
0
1
0
1
2
2
0
0
0
0
1
1
1
1
1
0
0
0
1
0
0
1
1
0
1
0
2
1
0
2
0
0
2
0
0
1
0
0
0
1
0
1
1
0
0
2
1
0
0
0
1
0
1
0
1
1
1
1
1
1
2
1
0
1
0
1
0
1
0
2
0
1
0
1
2
0
0
1
1
1
1
1
1
2
2
1
0
3
0
2
0
2
2
0
2
0
0
1
1
0
1
1
1
1
0
1
0
1
1
1
2
0
0
1
3
1
0
1
1
2
0
0
1
0
1
1
1
3
1
1
0
1
1
1
2
0
1
1
2
1
2
1
1
0
2
0
1
0
1
2
1
2
1
0
0
0
1
0
1
0
2
2
1
2
0
0
0
1
1
0
1
1
1
0
1
0
2
0
0
2
2
0
2
1
0
1
2
1
0
1
1
1
1
0
0
1
3
0
1
1
0
0
0
0
0
1
1
1
2
0
0
2
0
0
0
2
1
1
1
1
1
1
2
0
1
0
1
0
0
1
3
0
2
1
1
2
0
1
0
0
1
0
0
0
1
0
2
1
1
2
1
0
0
1
1
2
0
2
0
1
2
0
4
1
1
1
0
2
0
0
2
1
0
0
0
0
1
1
0
0
0
0
0
2
1
2
0
1
1
1
1
2
1
1
1
1
1
2
1
1
2
2
0
1
0
0
1
1
2
1
2
1
0
1
0
0
0
0
0
2
0
0
0
1
2
0
1
1
1
1
2
1
2
0
1
1
1
1
0
0
0
2
1
0
0
0
2
2
1
2
0
0
0
0
0
2
1
0
2
1
2
1
2
0
0
0
0
0
1
2
2
2
4
0
2
1
1
2
1
0
0
0
1
1
0
2
2
0
2
2
2
1
1
2
1
0
1
0
0
1
2
0
1
2
2
1
1
0
0
1
2
1
1
0
1
3
1
0
0
2
2
0
1
2
0
2
1
0
1
0
2
1
0
0
0
0
0
0
1
1
0
2
1
0
1
0
0
1
1
0
1
1
2
1
0
1
5
2
2
0
3
0
1
1
1
0
1
0
2
0
0
0
3
0
0
1
1
0
0
0
0
0
2
1
1
0
2
2
0
1
2
3
0
1
1
0
2
1
1
2
0
2
0
0
0
1
0
0
1
0
0
0
2
0
2
0
1
0
1
1
2
0
0
1
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
2
1
1
0
2
0
1
0
1
2
2
0
0
1
2
1
0
1
0
0
1
0
0
2
0
0
1
1
2
1
0
0
0
0
1
2
1
0
2
0
0
2
0
2
0
0
1
1
2
0
0
0
1
0
0
1
2
1
1
1
2
1
1
2
2
0
1
2
0
0
0
0
0
2
0
1
0
0
1
0
2
1
0
2
0
0
0
1
1
2
0
0
0
2
3
1
1
1
0
0
0
2
1
1
1
0
1
1
0
1
0
5
2
0
1
1
2
0
2
1
0
3
1
2
0
1
1
1
1
0
0
0
0
0
0
0
2
1
0
0
1
1
0
1
0
1
2
1
0
0
1
0
0
2
2
0
1
0
1
0
0
1
1
0
0
0
0
0
0
1
1
0
1
1
1
2
1
2
1
1
0
1
0
0
1
1
0
1
0
0
2
0
1
1
0
0
1
0
1
0
0
1
1
1
0
1
1
2
1
1
1
0
2
0
0
0
2
0
1
1
1
1
0
0
1
0
1
1
1
2
1
0
0
0
1
0
0
0
0
2
1
0
2
1
0
1
1
0
0
2
0
0
2
2
1
1
0
1
2
1
1
3
1
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
1
1
1
0
0
1
1
0
0
0
0
1
2
0
1
0
0
2
0
2
1
0
1
0
0
0
0
1
1
0
2
0
0
0
2
0
0
1
0
0
0
1
0
0
1
1
0
1
2
0
2
0
1
1
1
1
2
1
0
2
2
0
0
1
0
1
0
0
1
0
1
0
0
1
0
0
0
2
0
0
2
0
0
0
1
0
1
0
1
2
0
1
1
1
0
0
1
0
0
1
0
2
0
0
0
1
0
2
0
2
0
2
0
2
0
1
2
0
0
1
0
0
1
2
0
0
1
0
0
0
0
3
0
2
1
0
2
1
0
1
0
1
0
2
0
1
1
0
1
2
1
2
0
0
0
0
0
2
0
2
0
2
2
0
1
2
0
1
0
2
2
1
0
2
1
1
0
2
0
1
1
0
2
2
2
1
0
0
0
1
0
0
2
1
2
1
2
0
1
0
0
2
2
0
0
2
0
0
0
0
2
0
2
1
1
2
1
1
2
1
1
1
2
1
0
0
0
2
1
2
1
2
1
1
0
1
1
1
1
1
1
1
2
1
0
1
1
0
1
0
1
1
0
0
0
0
0
0
2
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
2
1
1
1
0
1
1
0
0
1
1
0
0
1
1
0
0
1
0
0
1
1
0
0
0
0
0
0
1
1
1
0
0
0
1
0
1
1
0
0
1
1
1
0
1
1
0
2
0
0
1
0
1
1
0
1
1
1
1
0
2
1
0
1
2
1
1
2
0
2
0
0
2
1
0
0
1
0
1
1
2
0
0
2
0
1
1
1
1
1
3
0
1
1
1
1
1
2
0
1
4
1
2
0
2
0
1
1
2
1
1
2
0
0
1
0
1
0
1
0
1
2
1
1
0
1
0
0
0
2
1
0
0
0
1
1
1
1
0
1
0
1
1
0
2
1
2
0
1
0
1
0
0
1
2
0
1
2
0
2
1
2
2
0
0
2
0
2
1
2
0
2
0
1
0
0
1
1
0
0
0
0
0
1
1
0
2
2
1
1
2
0
1
2
0
0
2
1
1
0
0
1
2
2
2
0
0
0
0
1
1
2
0
0
0
0
0
0
1
3
0
0
0
0
1
0
0
2
0
0
0
1
1
2
1
2
2
2
1
0
1
1
0
2
1
1
0
1
1
0
1
0
2
2
0
1
0
2
2
1
2
0
0
0
0
1
2
0
0
0
0
1
2
0
1
0
0
2
1
0
0
1
1
0
0
0
0
1
0
0
1
1
0
0
1
1
2
2
0
2
2
0
2
2
1
1
1
1
1
0
0
2
2
2
1
2
2
1
1
0
1
0
0
2
0
0
1
2
3
1
2
0
2
0
2
1
1
2
1
0
1
0
1
0
1
0
0
0
0
0
1
1
1
2
1
0
1
0
3
0
2
0
1
1
1
0
0
0
0
0
0
2
1
2
2
0
0
0
1
1
2
1
0
1
2
2
1
0
1
1
0
2
1
0
0
1
2
2
2
1
1
1
2
1
0
0
0
3
0
0
0
0
1
0
1
2
0
0
0
2
0
2
2
0
0
0
2
1
0
0
1
0
1
0
0
1
0
0
0
0
2
1
0
1
1
0
1
1
1
0
0
1
1
0
1
2
0
2
2
0
0
0
1
0
2
0
2
0
2
1
0
0
2
1
1
1
2
0
0
2
2
2
1
0
1
1
1
0
1
1
1
0
1
0
1
2
0
2
1
1
8
0
0
2
0
0
1
0
2
0
0
0
1
1
0
2
0
2
0
1
0
1
0
2
0
1
1
2
2
0
0
2
1
1
0
1
0
2
1
0
0
1
2
2
1
0
1
0
0
3
1
0
0
0
0
0
2
0
0
1
2
0
4
2
2
2
1
1
0
0
1
1
0
2
1
0
0
0
1
0
2
0
2
0
1
1
2
1
0
0
1
1
0
2
1
3
0
0
0
0
1
0
1
0
0
2
1
2
1
0
1
2
0
1
1
1
1
1
0
2
1
0
1
0
1
2
2
0
0
1
0
0
1
1
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
1
0
1
0
2
0
1
2
0
0
0
0
1
0
0
1
0
2
3
0
3
0
1
1
2
0
1
3
0
0
2
1
0
0
0
1
1
0
1
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
1
0
2
0
0
1
1
2
1
0
2
0
2
0
0
0
1
0
0
2
1
3
0
1
1
2
2
1
0
3
0
0
0
1
1
0
0
0
0
0
0
2
1
2
0
0
1
0
0
2
1
2
2
1
0
2
2
2
1
1
1
0
0
1
1
3
2
1
0
0
0
0
2
4
1
1
0
0
2
1
0
1
1
1
1
1
2
1
2
0
2
0
1
3
0
2
1
1
2
0
1
1
0
0
0
0
1
1
1
1
0
1
0
2
1
0
0
2
0
1
2
1
2
0
0
0
1
2
2
2
2
1
2
0
0
1
0
1
0
0
0
1
0
1
2
1
2
0
0
2
0
2
1
1
0
2
0
0
2
1
2
0
0
0
1
1
1
0
0
1
1
0
0
0
1
0
1
2
0
0
2
0
1
0
1
0
2
1
1
0
0
1
1
1
1
0
1
1
1
2
0
1
2
2
1
1
1
0
1
0
2
2
1
1
0
0
0
1
1
0
0
0
1
0
2
0
1
2
0
2
1
1
0
1
0
0
1
0
2
1
0
2
0
0
0
0
1
2
1
2
1
0
1
0
0
1
0
1
0
0
0
0
1
1
0
1
1
1
0
0
0
0
1
1
0
0
0
1
1
1
0
1
1
1
2
0
1
0
2
2
0
0
1
0
0
0
2
2
2
2
1
1
4
2
2
1
1
1
1
1
0
2
1
2
0
0
0
1
2
1
1
2
0
1
2
2
2
0
0
2
0
1
0
0
0
1
1
1
2
1
0
0
2
1
1
0
1
1
3
1
0
1
1
1
1
2
1
1
0
0
0
2
2
0
1
2
0
0
0
0
0
1
0
0
0
1
2
0
1
2
2
0
0
2
0
1
0
1
0
2
2
2
1
0
0
0
0
2
2
1
2
2
0
0
2
3
1
1
0
1
0
1
0
2
2
0
1
1
0
1
1
2
0
1
1
0
0
1
0
2
1
0
2
0
1
2
2
2
0
1
0
2
1
2
2
3
1
1
1
1
0
0
0
2
1
2
1
1
0
1
5
0
0
2
1
2
3
0
0
2
0
0
0
2
0
0
0
2
0
1
1
0
1
2
0
0
2
2
1
0
0
1
1
2
2
0
0
0
0
1
2
2
0
1
1
0
1
1
1
0
5
1
1
1
2
0
3
2
0
1
2
1
0
1
1
0
1
8
2
1
1
0
2
1
1
1
0
0
1
2
0
2
2
2
2
1
0
1
1
1
0
0
2
2
1
1
2
2
0
1
1
1
1
1
1
0
1
0
0
2
2
1
1
0
1
1
0
1
1
0
2
1
0
2
2
1
1
1
0
2
0
0
0
0
0
1
1
2
0
1
0
2
1
1
2
0
0
1
0
1
0
0
2
1
0
0
1
0
2
0
1
0
1
0
1
1
1
1
1
2
2
1
2
0
0
0
1
0
2
0
0
1
1
1
2
0
1
2
0
0
1
1
1
0
1
0
2
3
0
2
2
0
1
2
3
0
0
1
1
2
2
2
2
1
0
0
0
1
0
0
1
2
0
0
1
2
2
0
0
0
1
1
1
2
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
1
0
12
0
0
0
1
0
2
0
1
0
0
0
0
1
2
1
0
0
0
1
3
1
1
0
3
0
0
1
2
0
2
0
0
0
0
0
0
1
1
2
0
2
0
2
0
1
0
0
0
2
0
0
2
1
1
2
1
1
1
2
1
0
1
0
2
1
2
1
0
1
2
0
1
2
0
2
2
0
1
2
0
0
0
1
2
0
2
1
2
0
0
0
1
0
2
0
2
1
1
1
0
0
1
0
0
0
1
1
0
2
1
1
2
0
1
1
0
2
1
1
0
0
0
1
1
0
0
1
1
0
1
1
1
0
1
0
1
2
0
1
0
1
1
0
0
2
2
1
0
0
2
0
0
0
0
0
0
1
0
2
2
0
2
1
1
1
2
0
1
1
2
1
2
1
0
1
0
1
0
2
0
1
2
1
0
1
2
0
1
0
1
1
1
1
1
0
1
0
0
2
1
0
0
2
1
2
1
0
0
0
0
0
2
0
0
1
3
0
1
0
0
1
0
0
0
0
1
1
2
0
1
2
2
2
2
1
0
2
1
2
3
0
1
0
1
1
1
1
2
0
2
1
0
1
0
1
0
1
1
1
2
0
1
1
1
0
3
0
1
1
0
1
1
2
0
0
0
1
1
0
1
0
0
2
0
1
0
1
2
1
0
1
1
0
1
1
0
1
0
1
2
1
0
2
2
0
0
0
2
0
0
0
2
0
0
4
1
1
1
2
2
2
2
0
0
0
0
1
1
0
0
2
0
0
1
1
1
1
1
1
0
2
1
1
1
2
0
2
1
1
0
0
0
2
1
1
1
0
0
1
2
0
0
2
1
2
0
1
0
0
0
2
0
1
1
1
0
0
1
1
0
1
0
0
0
2
0
0
2
0
1
2
1
1
0
2
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
1
2
1
2
1
3
0
1
0
0
0
0
0
1
1
1
1
0
1
0
0
2
1
2
2
1
2
1
0
0
2
2
1
2
0
0
2
0
1
0
2
0
1
0
2
0
1
0
3
1
1
0
0
0
2
1
0
2
1
1
1
2
0
0
2
0
0
1
1
1
1
0
0
0
0
0
2
0
2
0
1
0
0
0
2
1
0
1
2
2
1
1
0
0
1
0
2
0
0
1
1
1
0
1
1
1
0
1
1
0
2
0
0
2
0
1
2
1
0
2
1
2
1
3
1
1
0
1
0
0
0
1
1
0
0
0
0
1
1
1
0
1
0
1
2
1
0
0
0
2
2
1
0
2
2
2
0
0
1
2
1
1
0
1
1
0
0
0
0
3
0
0
0
0
2
0
0
1
1
0
1
0
0
1
0
0
0
0
1
1
0
0
0
1
2
0
0
0
0
1
1
0
1
0
0
0
1
2
0
2
1
0
1
1
0
0
1
0
1
0
0
1
0
1
0
1
2
0
2
4
1
0
0
0
0
0
0
1
0
1
1
1
0
0
1
1
1
2
0
1
2
3
2
1
0
1
0
0
0
0
2
0
0
0
1
0
2
2
2
0
1
1
2
2
1
0
1
2
2
0
1
1
2
0
0
1
1
1
0
1
3
0
1
0
2
0
1
1
0
1
0
2
0
1
0
2
2
0
0
1
1
1
0
1
2
0
0
0
0
1
0
0
1
2
1
2
2
0
1
0
1
0
1
2
0
1
0
1
2
1
1
3
1
0
3
1
1
0
0
1
1
2
1
0
0
0
1
1
0
2
1
0
1
0
0
2
1
1
0
0
1
1
2
1
1
2
0
2
1
1
0
1
1
0
0
0
2
1
0
1
2
0
0
4
1
0
0
2
0
1
1
2
1
0
0
2
0
0
1
1
1
2
2
0
1
2
1
0
0
1
0
1
0
2
2
2
0
1
2
1
1
0
0
2
0
1
0
0
0
1
1
0
0
0
1
0
1
1
0
0
1
0
0
0
1
1
0
1
1
2
0
2
0
2
0
0
0
1
1
4
0
1
0
1
0
0
1
0
1
0
0
2
2
0
0
1
2
1
1
0
0
1
0
0
2
0
2
0
0
2
1
1
2
0
1
0
0
1
0
1
0
0
0
0
0
2
1
0
2
0
2
0
0
0
1
0
0
1
0
0
1
2
1
1
0
0
2
0
0
1
1
1
3
1
0
2
2
0
1
0
1
1
0
2
1
3
2
1
2
1
0
0
0
2
0
0
0
2
1
2
0
2
1
0
0
2
1
2
2
0
2
1
2
1
0
0
1
1
2
0
0
1
1
1
0
2
2
1
0
0
2
1
0
0
2
0
0
1
1
0
0
0
2
1
1
0
1
0
2
2
1
0
1
2
1
2
1
0
0
0
2
1
0
0
0
0
0
0
1
0
2
0
3
2
1
0
1
0
1
2
2
0
0
1
2
3
1
0
1
0
0
2
0
1
0
0
2
0
2
1
1
0
1
2
1
1
1
1
1
2
0
1
0
0
0
1
0
1
1
0
2
1
1
0
0
0
3
2
1
0
1
0
1
0
3
0
1
0
1
1
0
2
1
1
0
1
1
0
1
1
2
0
0
1
0
3
0
2
1
1
1
2
1
0
0
1
2
1
1
2
0
0
2
0
1
1
0
2
0
0
0
1
0
1
2
1
0
0
1
1
0
1
1
0
1
1
1
1
0
2
1
2
1
0
1
0
2
1
0
0
0
0
0
0
1
0
1
0
2
1
1
2
1
1
1
1
1
0
0
1
1
2
2
0
1
0
2
1
0
1
1
0
0
1
2
0
0
0
1
0
1
2
1
5
1
2
1
1
1
1
1
2
0
1
0
0
0
0
2
1
1
0
1
2
2
1
0
1
0
0
0
1
1
1
1
1
0
0
0
1
0
1
2
0
2
1
2
1
1
2
1
1
2
2
0
1
2
2
0
0
0
0
1
0
1
1
0
2
1
0
1
2
2
0
0
1
0
0
1
0
1
1
0
1
1
0
1
1
0
1
2
3
2
0
2
1
0
2
0
1
0
0
1
1
0
2
1
1
0
0
1
1
0
2
1
1
0
0
0
2
2
2
0
2
0
2
2
1
0
4
1
0
1
2
2
0
1
0
1
0
0
1
2
1
1
2
1
0
0
1
1
1
0
0
2
1
1
2
0
1
1
0
0
0
1
0
1
1
3
0
1
0
0
2
0
0
0
0
1
2
2
0
0
2
1
0
1
0
0
1
0
0
0
1
0
0
1
0
2
2
0
1
0
2
3
0
2
2
0
0
1
2
1
0
1
0
0
1
2
1
1
1
0
0
1
0
2
2
0
1
2
1
1
0
1
1
2
2
2
2
0
1
0
0
0
1
1
2
0
0
0
1
0
2
0
1
2
1
0
1
0
0
0
0
0
2
1
0
1
1
1
1
1
2
1
0
1
2
1
0
1
1
2
1
0
0
0
0
0
0
1
0
2
0
2
0
2
1
0
0
2
0
2
1
2
1
0
0
0
1
2
1
1
0
0
1
1
0
0
0
1
0
1
0
0
0
0
1
0
1
1
0
1
1
2
0
2
1
0
0
1
1
1
0
0
2
0
4
1
0
1
0
0
0
1
1
0
0
1
1
2
6
0
2
0
0
0
2
2
0
2
2
1
2
0
1
0
2
1
0
1
0
2
1
3
1
0
1
2
2
0
2
1
1
0
1
2
2
0
0
0
1
0
0
0
0
1
0
1
1
0
0
1
1
0
1
0
0
4
0
0
2
0
0
2
0
1
0
2
0
2
1
0
0
1
1
0
0
1
0
0
2
0
1
1
2
2
0
1
1
0
0
0
1
2
0
1
2
2
2
0
0
2
0
0
1
0
1
2
0
1
0
0
0
0
1
2
2
1
0
2
1
1
0
0
0
0
0
1
3
1
0
2
0
1
0
0
0
2
0
0
1
2
0
1
1
2
1
2
0
0
2
0
1
1
1
0
0
1
1
2
0
2
2
0
1
1
1
0
2
1
1
0
2
1
0
0
0
1
0
0
0
2
2
0
0
0
1
0
0
1
1
1
1
2
0
1
0
0
0
0
2
5
1
3
0
0
1
1
0
1
2
1
2
0
0
0
1
0
1
1
2
0
0
2
1
1
1
1
0
2
1
0
1
0
1
3
0
0
2
0
1
1
0
1
0
1
1
0
2
0
2
2
0
0
0
0
2
0
0
0
0
1
2
1
1
1
1
1
2
0
2
2
0
1
1
0
2
0
1
0
1
2
1
1
0
1
0
1
1
0
0
0
0
2
1
0
0
0
1
1
1
1
2
1
0
2
1
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
1
0
1
0
2
2
0
1
1
0
0
2
0
1
2
2
0
0
0
1
0
2
0
1
0
0
0
1
0
3
1
2
1
0
3
0
0
1
1
0
0
0
1
0
2
0
1
1
1
1
2
2
0
0
1
0
0
2
0
0
0
2
1
0
2
0
2
1
1
2
1
1
1
1
2
0
2
0
0
1
1
0
2
2
0
2
0
1
1
1
0
2
0
0
0
0
0
1
2
0
0
0
1
0
0
2
0
2
0
2
2
2
2
0
2
0
0
0
1
0
0
2
3
1
2
0
0
0
0
1
0
2
0
1
1
0
2
2
1
1
2
0
0
0
0
2
0
1
2
2
0
1
2
0
2
0
0
3
0
2
1
1
2
1
1
1
0
2
0
0
0
0
1
1
1
1
0
1
0
1
0
2
1
0
2
1
1
1
2
1
0
0
2
2
1
1
2
0
1
1
2
0
0
0
1
2
2
0
1
0
0
1
1
1
2
1
2
0
0
1
1
2
0
0
1
1
0
2
1
1
2
0
0
1
1
5
3
1
2
0
1
0
0
1
2
1
1
1
0
3
1
0
0
1
0
0
3
2
1
1
1
0
0
1
1
1
1
1
0
0
0
0
2
0
1
3
1
0
0
2
1
2
0
1
0
0
2
1
0
0
1
0
4
2
0
1
1
2
1
0
0
0
3
1
1
0
2
1
1
0
0
0
0
2
1
2
2
2
1
0
2
1
0
4
0
3
0
1
1
0
1
2
1
0
1
0
1
3
2
1
0
1
1
1
0
2
0
0
1
0
3
0
0
0
2
1
0
0
0
2
3
1
0
1
0
1
1
3
1
2
1
2
0
1
0
1
1
0
1
3
1
1
0
1
1
1
0
0
2
1
1
1
2
2
0
0
1
0
2
1
1
1
1
1
2
1
2
1
1
0
0
0
0
2
1
0
1
0
2
2
1
0
0
0
0
1
0
1
1
1
1
0
4
0
1
1
1
2
2
1
1
0
2
2
2
0
2
1
0
0
0
1
2
1
1
1
0
0
2
0
1
2
1
2
1
0
1
2
2
0
1
0
0
1
0
0
1
2
1
0
1
1
0
1
1
0
1
1
0
0
1
1
3
0
1
1
2
0
1
0
1
2
0
1
2
2
1
0
0
0
1
2
1
1
0
1
0
0
0
0
0
0
1
2
2
2
1
1
0
2
0
1
2
0
1
0
1
0
2
0
1
1
0
0
0
1
0
2
2
0
1
0
0
0
0
1
1
2
1
1
1
0
1
0
0
0
1
1
2
0
2
0
1
1
0
0
0
1
1
0
4
1
1
0
2
0
1
0
1
1
1
0
0
0
0
0
1
1
0
1
1
1
0
0
1
0
1
0
1
0
1
1
0
2
0
0
0
0
2
1
0
1
1
1
3
1
2
1
1
2
0
0
0
0
0
1
1
1
0
0
0
2
0
2
2
0
1
0
2
1
1
1
1
3
0
1
0
2
1
0
0
0
0
1
0
1
1
2
0
0
2
1
0
0
2
1
1
0
0
0
0
3
1
2
3
0
2
0
1
2
1
1
0
2
0
0
1
0
2
0
1
1
0
2
1
1
1
0
1
0
1
0
1
0
0
2
0
0
2
0
0
1
0
0
0
1
0
1
1
3
1
0
0
0
0
0
0
0
2
1
0
0
1
1
0
1
0
0
0
0
1
0
2
2
2
0
2
0
0
2
0
1
1
0
0
0
0
2
2
2
0
1
0
1
0
2
0
1
0
1
2
0
0
0
0
2
0
1
0
1
0
0
1
0
2
2
1
0
2
2
0
1
0
1
0
1
2
1
1
0
1
1
2
0
1
0
2
1
2
2
1
2
0
1
2
0
0
0
3
1
0
0
0
0
0
1
0
0
0
2
2
2
1
0
0
0
0
0
0
1
0
2
1
0
1
0
0
1
1
2
0
1
2
0
0
0
0
2
1
0
0
2
1
1
2
2
1
2
2
0
1
1
0
1
1
0
0
0
0
2
1
0
0
1
1
0
1
0
1
1
1
1
1
0
0
1
1
2
2
2
2
0
0
2
1
2
1
1
1
2
1
1
1
1
2
0
1
1
0
1
2
0
1
1
1
0
0
0
0
1
0
1
0
0
0
1
2
0
2
4
1
2
0
2
0
0
1
1
2
0
0
2
0
0
2
0
2
0
2
0
1
1
2
0
1
1
0
0
0
0
0
1
0
0
1
0
0
1
2
0
0
0
1
0
0
2
0
0
0
2
1
1
0
1
2
0
2
0
0
1
1
0
1
0
0
0
0
1
2
0
0
1
1
1
1
1
1
0
0
1
1
2
0
1
1
0
0
1
0
2
1
0
0
0
1
1
0
0
2
0
0
0
2
0
1
1
1
2
2
1
0
1
1
0
1
0
1
1
0
1
1
1
2
0
0
2
2
0
0
0
0
1
2
1
0
2
2
1
0
0
1
1
0
0
0
2
2
1
1
0
0
0
2
1
0
1
0
0
2
1
2
0
1
2
1
1
0
0
0
0
2
1
2
2
2
0
0
0
3
1
0
1
0
1
1
1
1
0
1
1
0
0
2
0
2
0
0
0
1
0
2
1
0
0
1
1
1
0
1
0
0
1
0
1
0
2
1
0
2
0
1
2
1
1
2
1
1
1
2
2
1
0
1
1
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
3
1
2
1
2
0
0
1
4
0
1
0
0
0
0
2
1
0
0
1
0
2
0
0
0
0
1
0
0
2
2
1
2
0
1
1
0
0
0
0
0
0
1
0
1
1
2
1
0
0
1
1
0
0
1
2
1
2
0
2
2
0
0
0
0
0
1
4
1
1
0
2
2
0
1
0
1
0
2
0
0
0
0
0
0
2
0
0
2
1
0
1
1
0
0
1
1
2
0
1
0
1
0
1
1
2
0
0
0
1
1
0
1
0
0
2
0
0
2
0
0
2
2
1
1
0
0
2
1
0
2
1
1
0
1
0
1
1
1
1
1
0
1
1
1
2
1
1
0
0
0
0
2
0
2
0
0
1
1
1
1
0
0
1
0
1
1
0
0
2
1
0
0
0
0
0
1
1
1
0
0
2
2
0
1
0
1
2
0
0
0
1
1
0
2
0
0
0
2
0
1
0
0
1
1
2
0
0
0
1
1
0
2
0
1
1
2
2
0
0
0
0
0
1
1
0
0
1
1
0
3
0
1
2
1
2
1
2
1
0
0
0
1
2
1
0
0
4
1
1
0
0
0
2
2
1
0
0
1
0
2
1
1
2
2
1
3
0
1
2
2
2
2
0
1
1
1
1
0
0
0
0
1
0
1
2
1
0
2
2
1
1
1
0
2
1
1
0
0
2
0
0
2
1
1
2
0
0
0
1
0
1
0
2
2
2
2
1
1
0
0
1
4
2
1
0
1
0
0
3
0
1
1
0
1
0
1
0
0
0
1
0
0
0
1
0
0
1
2
1
2
1
1
1
0
0
1
2
1
1
1
2
0
1
2
2
1
0
0
0
1
0
2
1
1
2
0
0
0
3
0
0
2
1
0
1
2
0
1
0
0
0
0
0
1
0
0
1
1
1
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
2
0
0
0
1
0
2
1
1
0
1
1
0
2
1
1
1
2
0
0
2
0
1
0
1
2
0
1
2
0
1
0
1
1
0
2
0
2
0
1
0
0
1
0
2
1
2
0
1
2
0
1
0
0
1
0
2
0
2
1
0
0
1
3
1
2
1
0
2
1
1
0
0
0
0
2
1
0
1
0
0
1
2
0
1
1
0
0
1
2
2
1
2
0
2
1
2
1
1
0
0
1
1
2
1
0
2
1
1
0
1
2
1
0
1
2
1
0
1
2
0
2
2
0
1
1
2
2
1
2
2
0
1
1
0
1
2
1
0
0
0
1
2
0
1
2
1
0
0
2
1
0
0
0
2
0
1
0
0
1
0
0
1
0
1
0
1
0
2
2
1
0
2
1
1
0
1
2
1
0
0
0
2
2
1
1
1
1
0
2
1
0
1
1
1
1
0
0
0
0
0
2
0
2
0
1
0
1
1
2
0
1
0
0
1
1
0
0
0
1
1
0
1
1
2
1
0
1
0
0
0
2
1
2
0
2
1
0
1
1
1
1
1
0
0
0
1
2
1
1
1
2
1
0
0
0
2
2
2
0
1
0
2
2
0
0
0
0
1
0
0
0
2
0
4
2
0
1
2
0
1
1
1
1
1
1
0
1
0
0
1
1
0
0
1
1
0
1
1
2
0
0
0
1
0
2
0
1
0
2
1
0
0
0
0
0
2
0
2
2
0
2
0
1
2
1
0
0
0
1
2
1
0
2
7
2
0
0
1
0
0
2
1
2
2
0
0
0
1
1
0
2
0
1
1
1
0
1
1
1
2
1
2
0
1
2
0
1
1
1
0
0
1
2
0
2
0
1
2
0
1
0
0
1
1
0
1
0
1
2
2
0
0
0
0
2
1
2
1
1
1
1
0
2
1
0
2
0
2
1
0
1
2
2
3
1
3
1
1
1
1
0
0
0
1
2
1
1
1
1
2
1
0
2
1
3
0
0
3
0
1
1
0
1
2
1
1
1
0
1
0
2
0
1
1
1
0
1
0
1
1
1
1
1
2
2
0
1
0
0
1
0
0
1
0
1
2
1
2
0
0
2
1
1
0
0
0
0
0
0
2
1
1
0
2
2
0
0
0
0
1
0
1
1
0
0
1
0
0
1
0
1
0
0
1
1
2
0
1
2
1
1
0
1
0
1
1
0
0
0
2
0
1
0
0
2
0
0
0
2
1
2
1
1
2
2
1
3
3
0
2
1
1
0
2
0
0
1
1
0
2
3
0
0
1
1
1
1
2
2
2
0
0
1
0
1
1
3
0
0
1
0
1
0
0
0
1
1
1
0
1
0
0
0
0
1
0
0
1
0
2
2
0
0
1
0
1
1
0
1
1
1
0
2
0
0
2
2
1
1
2
0
1
0
0
2
2
0
1
0
2
0
0
1
0
1
1
1
1
1
0
1
0
0
0
0
2
0
1
3
2
0
2
0
0
0
1
0
1
2
2
0
0
1
1
0
0
2
0
0
0
1
0
2
2
2
1
0
1
2
2
1
1
0
0
0
1
2
0
2
0
2
0
2
1
4
2
0
1
0
0
0
1
1
2
2
0
0
0
0
1
0
0
3
2
1
1
0
1
1
0
0
0
3
1
1
1
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
1
1
1
2
0
1
0
9
0
0
2
0
0
1
0
2
4
2
0
1
0
1
0
2
2
1
0
0
0
1
0
0
1
0
0
0
2
1
0
2
0
1
0
0
0
0
0
1
2
1
0
2
0
2
1
2
3
2
0
0
0
0
2
0
2
2
0
0
1
0
0
1
1
1
0
2
0
2
0
1
1
0
0
0
0
1
0
1
1
0
0
2
2
1
0
0
1
2
1
1
1
2
2
2
0
0
0
0
1
1
1
1
0
2
1
1
0
1
0
1
1
0
2
1
2
0
1
0
0
2
0
3
0
1
0
2
0
1
0
1
0
1
2
0
1
1
1
0
0
0
1
2
1
0
1
5
1
0
1
2
2
1
0
0
2
3
1
0
1
0
0
1
0
1
1
0
0
1
2
1
1
0
1
1
1
1
1
0
0
0
0
2
0
0
0
2
0
0
2
0
1
3
0
1
0
0
0
1
0
1
2
2
1
0
1
3
0
1
1
2
0
0
0
2
2
2
1
0
2
0
2
0
1
1
1
0
1
0
3
0
2
1
2
2
2
2
1
0
1
1
1
1
0
2
0
1
0
1
1
2
2
0
1
1
0
0
0
0
0
1
0
2
1
0
1
2
0
0
3
1
1
0
1
0
1
2
2
2
1
2
2
0
1
2
2
1
0
0
1
1
0
2
2
0
0
1
0
1
1
0
0
1
0
1
1
1
0
2
0
0
1
1
0
1
0
1
0
0
0
0
1
0
2
3
1
1
0
2
0
2
1
1
1
2
0
1
2
0
0
0
2
1
1
1
0
1
1
2
1
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
1
1
2
0
1
1
1
0
1
1
0
2
1
2
1
0
0
0
1
3
0
0
2
1
1
1
1
0
0
0
1
0
2
1
0
0
0
1
2
0
1
0
2
1
3
1
0
2
1
1
0
0
0
0
4
1
1
2
0
1
0
2
2
0
1
1
2
1
0
0
1
0
1
1
1
1
0
1
1
2
0
3
0
0
0
0
4
1
1
2
0
3
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
1
1
0
1
0
1
1
0
3
0
2
0
0
0
1
2
1
2
0
2
1
1
0
2
0
1
1
2
0
1
2
0
0
0
2
0
1
1
0
1
0
2
1
0
0
1
1
1
2
0
2
0
2
1
1
0
2
1
1
1
1
0
0
0
0
1
1
2
0
2
0
1
1
1
2
2
0
2
0
0
0
0
1
2
0
2
0
1
0
1
0
0
1
1
1
1
1
0
1
2
0
1
0
0
2
1
1
1
0
2
1
0
0
1
2
1
1
1
2
1
0
2
2
0
1
0
0
0
0
0
1
2
2
0
1
0
0
2
0
2
0
2
1
0
2
2
0
1
0
1
1
0
0
0
2
0
1
0
1
1
0
1
0
1
2
0
2
0
0
1
2
0
1
2
1
2
1
1
1
1
0
1
0
2
0
0
0
0
2
0
1
2
0
1
1
2
5
2
0
2
0
0
2
2
0
2
1
2
0
1
1
2
0
0
2
1
1
0
1
1
0
0
2
0
0
1
2
1
1
1
2
0
2
0
0
0
1
1
2
0
0
0
1
1
2
2
1
3
0
2
0
1
0
1
0
2
1
2
0
1
0
2
0
3
0
1
0
1
0
2
2
2
0
0
1
1
1
0
0
0
2
2
0
2
0
1
0
2
0
2
0
0
0
2
0
2
0
0
4
1
0
1
2
0
2
0
1
0
1
1
0
3
0
2
0
0
0
0
1
3
1
0
0
0
0
2
1
2
1
0
2
1
2
1
0
1
3
1
1
2
1
0
1
1
0
0
2
0
0
1
0
1
2
2
0
0
1
1
0
0
0
1
0
0
2
0
0
0
1
0
1
0
0
0
0
1
0
2
2
0
2
0
0
1
0
2
0
0
2
2
0
1
1
0
1
0
1
1
1
1
1
1
1
2
1
1
0
0
0
1
1
0
0
1
2
0
0
0
3
0
1
0
0
2
2
0
0
0
2
1
2
1
0
0
0
0
2
2
0
0
1
1
2
0
0
1
1
1
1
2
0
1
0
0
1
0
2
2
0
1
1
1
1
2
0
2
0
1
0
0
1
0
2
1
0
1
0
1
0
0
1
0
0
1
0
2
2
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
2
1
0
1
2
2
1
2
0
1
1
0
0
1
0
2
1
0
1
0
0
0
1
0
0
0
0
0
1
1
1
1
1
0
1
1
0
1
2
1
0
2
0
2
2
1
1
3
1
0
0
1
0
0
2
1
2
2
1
0
1
0
2
3
0
0
2
1
0
0
2
0
0
0
1
1
0
1
1
0
2
1
0
1
1
1
3
1
0
0
0
1
2
0
1
1
1
2
3
1
1
1
1
2
1
0
1
2
1
0
0
0
0
1
2
0
2
1
0
0
2
2
0
0
1
1
0
0
1
1
0
2
0
2
1
2
2
1
1
2
2
0
0
1
0
1
0
0
0
1
0
2
1
0
2
1
1
0
0
0
1
2
2
0
1
2
2
2
1
1
1
4
0
2
1
1
0
0
0
1
1
1
0
0
2
0
0
0
0
0
1
0
1
1
2
2
0
1
2
1
1
2
2
0
0
0
1
0
1
1
1
2
1
0
1
1
0
0
1
0
1
1
0
1
1
0
2
2
0
2
1
0
1
1
1
2
0
3
1
2
0
1
3
1
1
0
2
0
2
2
1
0
0
0
1
1
1
1
1
0
0
2
2
0
2
0
0
1
2
2
2
1
1
1
0
2
2
0
0
1
0
0
2
1
1
1
1
0
1
0
1
1
2
0
2
1
2
1
1
0
1
2
1
2
1
2
1
2
0
3
0
1
2
2
1
0
0
2
1
1
1
0
1
2
0
2
2
0
0
0
1
0
0
1
1
2
0
0
0
3
2
2
0
2
0
0
0
4
2
1
2
0
1
0
1
0
2
0
0
0
0
0
2
0
0
2
0
1
0
1
0
1
0
1
1
2
2
1
0
1
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
2
1
0
1
0
2
0
1
1
0
1
0
0
0
1
2
2
1
1
0
0
1
1
2
1
2
0
0
0
0
0
0
1
0
2
2
2
0
2
1
2
0
0
1
1
0
2
3
1
0
0
1
0
1
2
1
1
1
1
1
0
1
0
1
2
0
0
1
2
2
2
0
0
0
0
1
1
0
1
0
0
1
0
0
2
1
1
1
1
0
1
0
0
1
0
0
1
0
0
2
1
2
0
1
0
1
1
1
0
1
0
0
0
2
1
1
0
2
0
0
1
0
1
1
1
1
0
2
1
0
2
1
0
0
2
0
2
2
0
1
1
0
1
0
0
0
0
2
2
0
0
1
2
0
1
0
2
1
2
1
0
0
0
1
0
2
0
0
2
1
0
0
0
1
0
0
0
1
0
2
1
0
1
1
1
0
2
1
1
0
1
1
1
1
1
0
0
2
1
0
1
0
2
1
1
0
0
2
1
0
1
0
1
0
2
0
0
0
2
2
0
0
2
0
1
0
1
0
2
0
1
2
1
2
0
0
2
0
1
0
2
2
2
1
0
1
1
0
1
0
1
1
0
1
0
1
1
1
2
1
0
0
0
1
1
0
2
0
0
2
2
2
1
2
1
1
0
1
2
0
1
0
1
2
2
2
1
0
2
1
1
0
2
0
2
2
0
0
1
0
2
1
1
1
2
0
1
0
1
2
1
0
2
1
2
1
0
2
2
1
0
0
0
1
1
0
0
2
0
1
0
1
0
0
2
2
0
1
0
1
1
1
1
1
0
1
0
2
2
2
0
2
2
3
0
2
0
1
2
2
3
0
2
2
2
1
0
1
1
0
0
2
0
2
0
1
0
2
0
2
0
0
1
0
2
1
0
0
0
0
1
0
0
2
0
1
0
0
0
1
1
1
0
0
2
1
0
2
1
0
0
2
1
1
0
1
0
0
2
0
1
1
1
0
1
0
1
11
2
1
1
1
0
1
0
2
0
1
0
1
1
4
0
0
1
2
1
1
0
0
2
2
1
2
1
0
1
2
1
1
1
1
1
0
0
1
1
0
0
1
0
1
0
0
1
1
0
2
2
0
0
0
0
1
0
2
2
2
1
0
0
0
0
2
2
1
2
0
1
2
0
1
1
2
1
0
2
2
2
2
1
0
2
1
0
2
0
2
0
1
0
1
0
2
0
1
0
1
3
1
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
2
0
0
0
1
0
0
1
1
0
0
1
0
1
2
2
2
2
0
0
1
1
0
0
1
0
1
0
0
0
0
0
1
1
3
1
1
0
0
1
1
0
2
0
1
0
0
1
1
0
2
0
1
4
1
1
2
2
0
2
2
0
1
1
0
2
0
1
1
2
1
1
0
0
0
2
1
1
1
2
1
2
1
1
1
1
2
0
1
1
1
0
2
1
0
0
0
0
0
0
0
1
0
1
2
1
0
0
0
1
0
0
0
1
0
1
0
0
1
1
0
2
0
0
0
1
1
2
0
2
0
0
0
2
0
1
1
1
2
2
0
2
0
0
1
0
5
0
0
0
0
1
0
2
1
0
0
0
2
1
1
0
0
0
1
0
1
1
1
1
1
0
1
2
2
0
0
0
1
1
1
0
1
2
1
1
2
0
0
2
0
0
1
1
1
1
1
1
2
2
0
1
1
0
0
1
0
1
2
1
0
1
2
3
1
0
1
1
2
0
1
0
0
1
2
0
1
2
1
0
0
2
0
0
2
2
0
1
1
0
1
0
1
2
1
1
0
1
1
0
1
3
2
2
1
1
0
2
0
1
0
1
1
1
1
1
0
1
0
0
0
1
0
1
0
1
0
2
1
1
0
1
1
1
1
0
0
2
1
0
0
1
0
1
0
0
2
1
2
1
0
1
1
1
2
2
0
2
0
0
1
1
0
0
0
2
0
1
0
2
0
1
1
2
1
1
0
1
2
3
2
1
1
1
0
1
1
1
0
2
2
2
0
1
0
2
2
0
1
1
1
2
1
1
0
2
1
0
0
0
0
2
0
2
1
1
2
1
0
1
0
1
1
1
0
0
1
3
0
1
2
1
0
1
2
1
2
0
2
0
0
0
0
0
2
1
1
0
0
0
2
1
0
1
1
1
0
0
2
1
1
0
0
0
2
1
0
0
2
0
3
0
1
0
0
1
0
2
0
1
2
0
0
2
1
1
1
1
1
1
1
0
1
2
1
0
0
1
1
1
0
2
2
2
1
0
1
1
1
2
0
1
0
2
0
0
2
0
1
1
0
0
0
0
0
1
1
0
2
1
1
2
1
0
1
2
0
1
2
0
0
2
1
0
1
0
2
0
1
2
3
0
1
0
0
0
1
0
0
0
2
1
1
0
1
0
1
2
2
1
0
0
0
2
0
1
2
1
1
2
2
2
0
2
1
0
2
0
0
0
2
0
2
1
1
2
0
1
0
1
0
2
1
1
0
0
1
0
1
1
0
0
2
2
2
1
2
2
2
0
1
1
1
1
0
1
1
1
1
0
0
4
0
0
1
1
0
0
0
0
2
0
1
1
1
0
1
2
0
1
0
0
2
2
0
0
0
1
2
0
1
2
3
1
1
0
1
2
1
0
0
2
1
1
2
0
0
2
1
0
0
0
2
0
0
0
0
2
2
2
0
0
2
0
1
0
0
1
1
2
2
0
1
0
1
2
2
3
0
1
0
0
2
0
0
0
2
1
0
2
1
2
1
2
0
0
0
0
1
0
0
1
0
2
0
1
0
1
1
1
0
1
3
2
11
1
0
2
1
0
2
1
0
7
0
1
0
1
0
2
0
1
1
2
1
1
1
0
1
2
1
0
1
2
1
0
0
0
0
0
0
1
0
1
2
1
2
2
1
0
1
0
0
2
2
0
1
2
0
1
1
1
1
0
1
1
1
2
1
1
2
1
2
1
1
0
1
0
2
0
1
1
2
0
1
2
0
0
2
0
1
1
0
2
1
1
2
1
1
1
1
2
2
0
1
0
2
0
1
2
2
1
0
0
2
2
0
1
2
0
1
2
2
0
1
2
2
0
0
1
0
0
0
1
1
2
1
1
1
1
1
2
0
0
2
1
0
0
2
2
0
1
0
0
0
3
1
1
0
0
2
0
1
1
0
3
0
2
1
0
1
1
1
1
1
1
1
0
1
2
1
2
0
1
2
0
0
1
1
1
0
0
1
0
0
0
2
0
0
1
2
1
0
0
1
0
1
0
0
2
2
1
0
0
1
2
0
2
0
2
2
0
1
0
1
0
1
1
1
2
2
2
0
1
2
0
0
2
1
1
1
0
2
0
1
0
0
2
1
1
1
1
2
2
0
0
0
1
0
3
0
1
1
1
0
2
1
0
3
1
2
0
0
0
1
0
1
0
0
1
1
0
2
0
2
0
2
1
0
0
0
1
1
0
0
0
2
0
1
2
1
1
1
0
0
3
1
1
0
0
0
0
0
1
1
1
0
1
0
0
2
1
1
1
3
0
1
0
0
1
1
0
1
1
0
0
0
1
0
1
0
1
1
1
0
0
0
0
1
0
1
1
0
0
0
1
0
1
1
2
1
1
1
0
1
1
3
0
2
0
1
1
0
2
1
0
0
2
2
0
2
0
0
1
1
0
0
1
1
0
0
0
1
1
0
2
0
0
2
1
1
1
0
0
1
2
0
2
2
0
1
1
1
1
1
0
1
0
1
1
0
1
0
0
0
2
0
0
0
1
1
0
1
0
1
0
2
0
0
0
1
0
1
2
0
1
0
0
0
0
0
0
1
0
2
1
0
1
0
0
0
1
1
1
0
2
1
0
1
0
0
1
1
1
0
0
0
0
0
1
1
0
0
0
1
1
2
0
2
1
0
1
3
0
2
0
2
2
2
1
0
0
3
2
0
1
1
1
0
2
3
7
0
0
2
0
0
0
0
1
1
1
0
0
1
0
1
0
0
1
1
0
1
1
0
0
0
0
1
2
1
1
1
0
2
0
1
0
0
1
1
1
1
2
1
1
1
2
0
1
2
0
1
2
0
2
2
2
1
1
1
2
0
1
0
2
1
1
0
0
1
0
1
1
2
1
0
1
0
1
0
1
0
2
1
0
3
0
0
1
1
2
2
0
0
2
0
1
1
0
1
2
0
1
0
0
1
0
1
2
1
0
0
0
1
0
0
1
0
1
2
2
2
0
0
0
0
0
0
0
1
0
0
0
0
2
1
2
2
1
0
1
2
1
0
0
3
2
2
1
1
0
1
0
0
0
1
1
1
2
1
0
0
1
2
0
0
1
1
1
0
1
2
0
2
0
2
0
2
2
1
1
2
2
3
0
1
0
0
1
0
0
2
1
3
1
1
2
1
1
1
2
1
0
0
1
2
1
0
0
2
0
1
0
1
1
0
1
0
1
1
1
2
1
2
1
0
0
0
1
1
0
0
1
0
0
1
1
0
0
2
0
0
0
1
1
1
1
1
1
0
1
6
0
1
2
1
0
2
0
0
0
0
2
0
1
0
0
1
1
2
1
1
1
1
0
1
2
1
0
1
2
2
0
0
2
1
0
1
1
0
3
2
1
1
0
0
1
1
1
1
1
1
1
2
2
1
2
2
0
0
0
1
4
1
3
1
0
2
1
1
0
0
0
1
0
0
0
1
1
1
0
2
0
1
1
2
2
2
0
0
0
0
1
1
1
0
1
0
0
0
1
0
0
0
2
0
0
0
1
1
1
2
1
0
0
0
2
1
2
1
2
2
1
0
2
3
0
2
0
1
0
0
1
0
0
0
1
0
2
2
1
2
0
1
1
2
1
0
2
0
1
1
1
0
1
1
2
0
1
2
0
0
0
1
0
1
2
1
2
2
0
0
0
0
1
0
1
0
0
0
2
1
1
0
3
0
0
1
0
1
1
0
1
1
1
0
2
1
0
0
1
1
0
0
1
0
1
2
0
1
0
0
0
2
2
0
1
2
0
0
1
0
0
0
1
0
0
1
2
1
0
0
0
2
1
0
1
0
1
0
1
0
0
2
1
0
0
0
1
0
0
0
2
0
2
1
2
1
1
2
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
2
0
0
1
1
0
0
1
0
0
1
0
0
0
2
2
1
0
1
1
1
0
3
0
3
0
1
1
0
0
0
1
2
0
1
2
1
2
0
2
1
1
0
1
0
1
0
0
1
0
1
0
2
0
2
2
2
1
1
0
2
1
1
1
2
0
2
0
0
1
1
1
1
1
2
0
1
0
1
1
2
1
1
0
2
1
1
1
0
1
1
2
2
0
0
1
1
0
1
1
1
1
0
2
2
0
0
2
0
0
2
1
0
0
3
0
0
1
1
0
0
1
3
0
1
0
0
0
1
1
1
0
0
1
0
0
1
1
0
0
0
1
1
1
0
0
2
0
0
1
0
1
0
1
0
0
2
0
2
1
2
0
0
0
1
1
0
0
2
1
1
1
0
2
1
2
0
1
0
2
0
0
0
0
1
0
1
1
0
1
0
0
1
0
1
2
0
2
0
0
0
1
0
0
1
0
1
1
0
0
2
0
1
2
1
0
0
0
1
1
1
0
1
1
0
1
1
1
0
1
1
0
1
1
1
1
0
0
0
2
2
0
2
1
0
2
0
1
0
0
0
1
1
1
1
2
1
1
1
1
1
0
3
0
1
1
0
1
2
1
0
0
0
1
2
0
0
1
0
2
0
0
1
1
1
0
1
0
0
1
2
2
0
1
0
0
0
1
2
2
2
0
0
1
0
1
1
0
2
2
0
0
2
2
0
0
1
2
0
1
2
0
1
0
0
1
0
0
0
0
0
0
1
0
2
1
2
0
1
0
2
1
1
2
1
1
0
0
0
0
0
1
0
5
2
2
1
0
0
0
0
0
1
1
1
0
1
1
1
0
1
1
0
0
2
1
2
0
1
0
2
0
1
1
1
2
1
1
1
1
1
1
0
2
0
1
2
3
1
0
1
1
2
0
1
1
0
1
2
2
0
0
0
2
0
2
2
0
0
0
0
1
0
1
2
1
2
0
0
2
0
0
0
0
1
1
0
2
0
1
0
1
0
0
2
0
1
1
0
3
0
1
4
0
1
0
0
0
0
1
1
0
3
0
0
0
1
2
1
1
2
0
0
1
0
2
0
2
0
0
0
2
0
0
1
0
1
1
1
0
1
0
0
1
2
1
2
1
0
0
1
0
0
0
0
1
1
2
0
1
1
2
0
0
0
1
0
2
1
1
0
0
0
1
0
1
0
1
1
0
2
1
0
1
1
2
0
0
0
0
0
2
0
0
0
1
1
1
0
0
0
1
2
2
2
0
2
1
1
1
1
2
0
3
2
0
0
1
1
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
1
1
1
0
1
1
2
0
3
2
0
1
0
0
1
1
1
0
1
1
0
0
0
0
1
0
1
2
2
2
0
1
1
0
2
2
1
0
1
1
1
1
0
1
1
2
1
1
2
1
0
0
1
1
1
2
0
0
1
4
1
2
0
0
0
2
0
0
0
1
2
1
1
1
1
2
0
0
0
1
0
1
3
1
0
0
1
1
2
1
2
0
1
1
1
1
0
3
0
0
1
2
1
2
0
0
0
0
1
0
2
0
2
1
0
1
1
2
0
2
0
1
1
0
0
0
0
1
0
2
0
1
2
1
1
0
1
0
0
1
1
1
1
0
1
0
2
2
0
0
1
1
2
0
0
0
0
0
0
0
2
0
0
2
3
0
2
1
1
0
0
1
1
2
1
0
1
1
0
0
0
0
1
1
2
1
1
2
1
2
0
0
0
0
0
0
1
1
1
1
0
2
1
0
0
2
1
0
1
0
2
0
0
1
1
0
2
0
0
1
1
1
2
0
0
0
1
2
0
0
0
1
3
0
0
2
0
1
2
0
1
2
2
0
2
0
1
2
2
0
2
1
1
1
0
3
1
2
2
2
0
0
1
1
0
2
0
0
0
2
2
1
2
1
1
1
1
2
0
0
0
1
0
1
1
0
0
2
0
1
1
0
1
1
2
0
3
3
1
0
0
3
2
1
0
1
1
0
0
0
0
1
0
2
0
1
1
2
1
2
1
2
0
0
1
0
1
1
1
0
0
0
1
2
1
3
1
1
0
1
0
1
1
0
2
0
0
0
2
1
2
0
1
1
1
0
0
2
3
0
1
0
1
2
1
1
0
1
1
1
1
0
2
1
2
0
0
0
0
2
0
0
1
0
0
2
2
0
1
0
1
2
2
2
0
0
1
0
0
0
2
0
1
4
1
1
1
0
1
1
1
0
0
1
1
1
0
1
0
2
0
1
1
2
3
1
2
0
1
2
1
0
1
0
1
0
0
2
0
0
1
0
0
2
0
1
1
0
0
1
0
0
1
1
2
2
0
0
0
2
1
0
1
1
2
1
1
0
1
2
2
0
0
5
0
1
1
1
1
14
2
0
0
0
1
0
1
0
1
0
0
1
0
2
1
0
0
1
0
0
2
2
1
1
1
0
0
1
1
1
2
1
0
1
1
2
2
0
1
1
1
1
1
0
0
2
1
2
1
0
0
1
1
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
2
2
2
1
0
0
0
1
0
0
1
2
0
1
1
2
2
2
1
1
0
0
1
1
0
0
0
2
0
0
3
2
0
3
0
0
2
1
1
2
1
3
0
2
0
0
2
1
2
1
0
0
2
0
2
0
0
0
0
1
1
3
1
0
2
1
1
0
1
1
4
0
1
1
0
2
0
0
0
2
0
1
0
1
0
2
1
1
1
2
0
1
0
1
1
0
1
2
1
0
1
0
3
2
2
0
2
2
0
0
1
0
1
1
1
3
1
0
0
0
1
3
1
1
1
0
1
2
0
1
1
0
2
0
1
1
0
0
0
1
1
0
0
2
0
1
0
0
0
0
2
2
0
0
0
1
0
1
1
0
1
0
1
0
0
1
2
0
0
1
2
0
0
0
3
2
0
0
2
0
1
1
2
0
0
0
0
0
2
1
1
0
0
2
1
1
2
2
0
1
1
0
1
1
1
0
1
2
0
1
0
2
1
2
2
1
0
0
2
1
2
0
0
1
0
1
1
2
0
2
0
1
0
0
0
1
1
0
0
1
0
2
2
2
0
0
1
0
0
2
2
1
1
0
1
0
0
2
0
0
2
1
0
1
0
0
0
1
2
2
1
2
0
0
4
1
1
0
0
2
2
0
0
0
1
1
2
1
2
1
2
2
0
2
2
0
1
3
1
1
0
1
0
0
0
1
0
2
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
1
2
1
1
1
0
0
0
0
1
1
2
2
1
2
4
2
1
1
1
0
0
0
0
0
1
1
1
0
0
0
2
1
0
1
2
1
1
0
0
2
1
1
1
1
0
0
0
2
2
1
0
2
0
0
2
0
0
2
0
0
1
2
2
2
0
0
2
1
1
0
2
1
0
0
1
1
0
1
0
1
1
0
2
2
0
0
0
1
0
1
0
0
0
1
1
0
1
1
1
1
0
0
0
1
3
0
1
1
2
2
2
0
1
1
0
2
0
0
2
0
0
0
1
2
0
0
1
1
2
0
0
1
1
1
0
1
1
0
1
0
3
3
1
2
1
0
1
2
2
0
2
1
0
0
0
0
1
1
2
1
1
0
0
1
1
1
2
1
1
0
0
2
1
0
1
0
0
0
0
1
0
0
2
2
0
9
0
2
0
1
1
1
0
1
0
1
2
0
2
0
0
1
0
0
0
1
2
1
0
0
1
1
3
0
0
1
0
2
0
1
2
0
1
0
0
0
1
1
2
0
0
2
0
0
2
0
2
2
0
0
0
1
0
1
1
1
2
2
0
0
0
0
0
0
1
2
1
0
1
1
4
1
1
2
0
1
2
2
0
1
2
0
2
2
0
1
1
0
2
2
0
1
1
0
2
0
1
0
0
0
1
1
2
0
2
0
2
1
1
0
2
0
1
2
0
0
0
0
0
1
0
1
2
0
0
1
8
1
2
1
0
0
1
2
1
1
0
1
1
0
1
0
2
0
0
0
1
1
0
0
1
0
1
1
0
0
0
0
1
2
0
0
2
1
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
2
2
1
0
1
2
0
1
2
0
1
0
1
0
1
1
2
0
1
2
0
2
1
0
0
1
0
0
2
0
0
0
1
0
2
2
0
2
1
1
2
0
1
2
2
0
0
1
0
0
2
1
0
0
1
1
2
1
1
0
0
1
2
1
1
2
1
0
0
0
1
2
2
1
0
2
4
2
0
0
0
1
0
0
0
3
0
1
0
0
1
1
0
0
0
1
0
0
2
2
0
0
1
0
2
2
0
1
1
1
0
1
1
2
1
1
0
0
0
1
0
2
1
0
1
0
0
0
0
2
1
0
1
1
0
0
1
0
1
1
0
0
0
0
2
0
1
1
1
1
2
1
1
1
1
1
0
2
1
1
1
2
2
1
2
0
0
1
2
1
1
0
1
0
0
1
2
0
1
0
0
1
0
3
2
2
0
0
2
0
0
1
0
1
2
0
0
0
1
0
0
2
0
0
2
1
2
0
2
0
2
1
1
2
2
1
1
0
0
1
0
2
0
0
1
2
1
0
0
1
0
1
1
0
0
1
1
2
1
2
2
1
1
2
0
0
0
1
0
0
0
1
1
0
0
0
2
1
1
2
0
1
2
1
1
0
2
0
0
0
0
2
0
0
1
1
0
1
1
1
0
2
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
2
1
1
2
0
0
1
0
1
1
0
0
1
1
2
0
0
0
1
1
1
1
0
1
1
0
0
0
0
2
0
2
1
1
1
0
0
2
0
2
1
1
2
1
1
0
1
1
1
2
1
1
0
1
2
2
1
0
0
0
1
0
1
0
1
1
1
1
0
0
1
0
1
0
1
0
0
0
0
6
2
0
1
1
1
0
0
1
0
1
0
2
0
2
2
2
1
2
2
3
1
0
1
0
1
2
0
0
1
1
1
1
1
1
0
3
0
4
0
1
0
1
0
1
1
0
2
1
1
2
0
1
1
1
0
0
2
1
2
0
1
2
1
3
1
0
1
0
1
0
2
1
0
0
0
1
1
0
0
0
1
0
0
1
2
1
2
1
2
0
2
1
1
1
1
0
0
0
2
0
1
1
1
1
0
1
0
0
0
2
2
0
2
1
0
1
1
1
0
0
1
0
1
0
0
1
0
2
2
2
1
1
1
0
0
0
2
0
0
1
0
1
0
0
0
0
0
2
0
2
2
0
1
1
0
1
0
0
1
1
1
1
1
0
0
0
0
2
1
0
1
2
1
0
1
0
1
6
1
0
0
0
1
1
1
0
1
0
1
1
0
0
0
2
0
0
0
2
1
1
1
1
2
0
0
1
2
1
1
0
1
0
0
2
1
0
1
0
1
1
1
1
0
0
2
4
0
2
1
0
1
0
1
0
2
1
0
3
0
1
2
0
0
2
0
2
0
2
2
1
0
0
1
2
0
0
0
2
0
0
1
0
1
1
0
0
1
2
1
1
1
1
0
2
1
2
1
2
1
3
0
2
1
1
3
0
1
0
0
0
0
1
4
0
0
0
0
2
0
0
0
4
2
1
0
0
0
0
2
2
0
0
2
2
1
1
1
0
1
2
2
1
1
0
1
1
0
2
1
0
1
1
0
1
0
0
2
0
0
1
1
1
0
2
1
1
1
0
0
0
0
0
1
1
1
2
0
0
0
1
0
0
2
2
0
2
2
0
1
1
2
0
1
0
0
0
0
2
0
2
2
1
2
0
0
0
1
2
2
0
1
1
1
0
0
0
0
1
1
1
2
0
1
1
2
0
0
2
1
6
0
0
1
0
1
1
2
0
1
0
1
0
0
0
1
0
2
2
1
1
2
2
0
0
1
1
0
1
1
1
0
0
1
0
2
0
1
0
0
0
2
1
1
0
1
1
1
1
1
1
0
1
0
1
1
1
1
0
0
1
0
2
0
2
1
2
0
0
0
2
1
2
0
2
2
1
0
1
1
0
0
1
0
1
1
0
3
2
1
0
1
0
2
1
0
0
0
1
0
0
0
1
1
0
1
0
2
0
0
0
1
1
0
0
2
0
2
1
1
0
1
2
0
0
0
0
0
2
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
1
1
3
0
0
6
0
1
2
0
0
1
0
0
0
0
2
2
2
0
1
1
0
0
0
1
0
2
1
2
2
0
1
1
0
1
1
1
1
0
2
0
2
0
0
0
0
1
2
0
1
3
0
0
1
1
1
0
1
1
0
0
0
1
1
2
0
0
3
2
0
3
2
0
0
1
0
0
0
0
1
0
0
1
0
0
2
1
0
1
1
0
0
1
2
0
1
1
0
2
2
0
0
0
0
2
0
1
0
1
0
0
0
1
1
1
1
2
0
1
2
1
0
2
2
1
0
0
0
0
0
2
2
1
1
0
1
0
0
0
2
1
1
0
0
1
1
1
0
1
1
2
0
0
1
1
1
3
0
2
0
0
1
1
1
0
0
0
0
1
0
0
1
0
1
0
1
0
2
2
0
2
2
0
1
2
1
0
0
3
0
0
1
2
0
2
0
0
3
1
0
1
1
2
2
0
0
0
4
1
2
2
1
1
0
0
2
0
0
0
1
1
1
0
1
2
0
0
1
1
1
0
0
1
1
2
1
0
0
1
1
2
2
2
1
0
0
0
0
0
0
1
2
0
0
1
0
0
2
0
1
1
1
1
1
0
1
0
0
1
2
0
1
6
0
0
2
0
1
1
2
1
1
0
1
2
0
1
0
1
1
2
2
0
1
0
1
0
2
0
2
0
0
0
3
0
3
0
1
0
2
1
0
0
0
1
0
0
2
0
1
0
0
1
1
0
0
1
1
0
1
0
0
1
2
2
0
1
0
1
2
0
0
0
1
0
0
1
1
0
0
1
1
2
1
0
1
1
2
0
0
1
0
1
2
0
2
2
0
0
2
1
0
0
1
1
2
2
0
0
0
0
1
2
0
0
1
0
1
0
2
0
1
1
1
2
0
3
0
1
1
1
1
1
0
1
1
1
1
1
1
1
0
2
0
1
2
0
0
1
0
1
2
1
1
2
1
1
1
1
1
1
1
0
1
2
2
2
1
0
0
0
1
1
0
1
1
1
1
0
1
1
0
1
1
1
1
0
0
1
0
1
0
1
0
1
1
0
0
1
3
1
1
2
0
0
2
0
1
2
0
1
0
0
1
2
1
0
1
0
1
1
0
1
1
0
0
0
0
2
0
0
0
1
0
2
0
0
1
1
0
0
1
1
2
0
2
1
0
1
2
1
0
0
1
1
0
0
1
1
2
1
0
1
0
0
1
3
1
1
2
0
2
1
1
0
0
1
1
2
1
0
1
1
1
1
1
0
2
2
0
0
0
1
2
1
2
0
0
0
0
1
0
1
2
0
1
2
1
2
1
1
0
1
0
0
1
0
2
2
0
2
0
2
1
1
0
2
1
1
1
0
1
0
2
0
2
2
3
1
0
0
2
1
2
2
0
1
2
1
1
0
0
1
2
1
1
1
0
0
1
0
0
0
0
0
1
1
1
2
1
1
1
0
2
0
1
1
1
1
2
0
2
1
1
1
1
2
0
0
0
0
0
0
0
1
2
0
1
0
1
0
1
2
3
1
0
2
1
1
0
0
0
0
0
0
0
1
0
3
1
2
0
1
1
1
0
2
2
0
0
0
0
1
1
3
1
0
0
1
2
2
1
2
0
0
0
0
0
1
0
0
2
0
0
1
0
0
1
2
0
0
0
1
1
1
1
1
0
0
2
1
1
1
1
0
3
1
0
0
2
1
2
0
0
1
1
1
0
0
0
0
0
1
1
0
2
0
1
0
1
1
0
0
1
0
2
1
1
0
2
0
0
0
2
2
0
0
1
0
1
1
2
0
1
0
2
0
1
0
0
0
0
0
2
2
1
0
0
1
0
3
0
2
0
0
0
0
0
0
1
1
0
1
0
2
0
2
2
0
0
1
0
3
2
0
0
1
2
1
2
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
1
1
1
0
1
1
1
0
1
1
1
2
2
0
2
2
1
1
0
2
1
0
1
0
2
1
0
1
0
0
2
0
0
1
0
0
1
0
1
0
0
1
0
1
2
1
2
1
1
0
0
1
2
1
0
1
0
1
0
2
1
2
0
0
1
0
0
1
0
0
0
1
0
0
1
0
1
1
0
1
1
1
1
1
0
1
0
1
0
0
0
1
1
1
1
1
1
0
1
0
1
0
1
0
1
1
1
0
2
1
2
0
2
1
2
0
0
1
0
1
1
1
1
2
0
0
2
2
1
0
1
0
2
0
0
1
0
2
2
0
0
2
1
1
0
0
1
1
1
0
0
0
0
2
0
0
1
0
1
1
1
1
2
2
2
0
0
0
2
0
1
2
1
0
0
1
0
1
1
1
0
0
0
1
0
1
0
1
2
0
1
0
2
1
0
1
0
0
1
1
2
1
0
0
0
1
0
0
1
2
1
0
0
1
1
0
0
1
1
1
1
0
1
0
0
1
2
0
2
1
0
0
1
0
1
0
2
0
0
1
0
1
0
0
1
0
1
1
3
0
0
2
1
1
0
0
1
0
2
1
2
2
1
0
0
0
0
1
0
0
0
2
2
0
0
0
2
2
1
0
1
0
0
0
2
0
2
1
0
0
0
0
0
0
1
2
0
0
1
2
2
2
0
1
1
1
1
0
2
1
1
2
0
1
2
0
0
0
0
1
2
0
2
0
1
0
2
2
1
0
0
2
0
0
2
0
1
1
1
1
1
0
0
0
0
0
1
1
2
0
1
2
1
1
1
1
1
1
1
2
2
1
1
0
0
2
1
1
2
2
2
0
0
2
1
1
0
1
0
2
1
0
1
1
0
1
2
1
0
0
1
1
1
1
2
0
0
0
1
2
3
1
1
0
0
1
0
1
0
1
0
0
1
0
1
0
0
1
0
0
1
0
0
2
1
1
2
0
1
2
2
1
1
1
2
4
2
2
2
1
0
1
0
0
1
1
0
0
2
1
0
1
0
0
1
0
0
2
1
2
1
1
0
0
0
2
2
2
0
0
1
2
2
2
1
0
0
1
0
0
2
0
1
1
0
1
0
1
0
1
0
0
1
1
2
1
1
5
2
0
0
0
2
0
1
2
2
0
2
0
1
1
0
0
0
0
2
0
1
1
2
2
0
0
1
0
0
0
2
0
0
1
0
2
0
1
1
0
2
1
0
2
0
0
1
0
1
1
1
2
2
0
1
0
0
0
0
1
0
0
0
0
0
1
2
1
1
1
0
0
1
0
0
0
2
1
0
0
0
2
0
0
1
1
0
1
2
0
0
2
0
1
0
1
0
0
2
0
2
0
1
0
0
0
0
0
1
0
1
2
2
0
1
0
2
1
1
0
1
1
0
0
0
1
0
0
1
1
2
0
1
1
1
0
1
2
0
1
0
2
0
0
0
0
1
1
1
2
1
1
0
1
0
1
0
0
1
0
0
1
3
1
1
2
2
2
2
1
2
1
1
0
0
0
1
0
0
0
0
3
0
0
2
0
1
1
1
2
1
2
2
2
0
0
0
1
0
0
2
0
0
0
2
1
1
0
0
0
0
2
1
2
2
1
0
2
0
0
0
0
2
1
0
0
0
1
0
0
1
1
1
2
0
0
0
0
0
1
0
0
0
2
0
0
1
2
0
0
1
2
2
2
0
0
1
0
2
1
2
1
1
0
1
0
1
2
0
2
0
2
1
2
0
2
0
2
2
0
0
1
0
0
1
1
0
4
0
1
1
1
0
1
2
1
1
2
2
1
0
1
0
1
2
1
2
4
2
0
1
2
1
2
0
1
0
1
1
1
2
1
0
1
1
1
1
0
0
0
1
1
0
1
1
1
2
5
1
0
1
0
1
1
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
1
2
0
0
0
0
2
2
2
0
0
2
2
1
0
0
2
0
2
0
1
1
2
1
0
0
0
1
2
0
1
1
1
0
2
1
1
0
1
0
2
2
2
0
2
0
0
0
0
0
0
2
1
1
0
0
0
2
0
1
1
0
2
1
1
2
1
0
2
2
0
0
0
1
0
0
0
0
0
0
1
2
1
0
1
0
3
2
1
1
0
0
0
0
0
2
0
0
2
1
2
0
1
0
0
1
1
1
0
2
2
0
2
1
0
1
0
1
1
2
8
0
0
0
0
1
0
1
1
2
1
0
0
0
1
1
1
0
2
0
1
1
1
0
0
1
2
2
0
1
2
1
1
2
0
0
1
0
2
0
1
2
2
2
0
0
1
1
0
2
1
0
0
1
0
0
0
1
1
0
1
0
0
0
1
1
0
0
0
0
3
0
2
2
1
1
2
1
2
0
0
1
2
0
1
1
1
1
1
1
0
0
1
3
0
1
0
0
0
0
0
2
0
0
1
1
2
1
2
1
1
2
0
0
0
0
0
2
0
1
0
0
0
2
1
0
0
0
1
0
2
0
0
1
1
1
2
1
1
0
0
2
0
0
0
1
2
0
1
1
2
1
0
0
1
1
2
0
0
2
1
2
0
2
1
0
0
2
0
0
1
1
0
0
0
0
2
0
0
0
1
2
1
2
0
2
1
0
2
0
0
1
0
0
1
0
1
0
0
1
2
0
1
0
1
0
0
0
0
0
2
1
0
1
2
0
0
1
0
1
0
2
1
0
0
0
0
1
0
2
1
1
1
0
1
1
1
0
3
2
0
0
1
0
2
0
1
2
1
1
1
1
0
2
0
1
1
0
1
1
1
2
0
0
2
0
0
1
1
1
2
0
1
0
0
1
2
0
0
2
1
1
1
1
3
0
2
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
1
2
1
0
0
1
2
1
0
1
0
0
2
0
1
2
0
0
1
2
0
1
0
1
0
0
0
2
2
0
0
0
1
1
0
0
1
0
1
1
2
1
1
0
2
1
1
1
0
0
2
0
0
1
1
0
0
2
2
1
0
1
0
2
0
1
0
0
1
1
0
0
1
1
0
2
1
2
0
0
2
1
1
1
1
1
1
0
1
0
0
1
0
1
0
1
1
2
0
0
2
1
0
0
0
0
2
1
0
0
0
2
2
0
0
0
1
0
0
2
1
2
1
1
0
1
0
1
1
0
0
1
0
0
2
0
1
0
2
0
0
1
1
1
2
1
2
0
0
0
1
2
2
2
0
0
1
0
2
1
0
1
1
1
0
0
0
0
0
0
1
2
0
1
1
1
1
1
0
0
1
1
2
2
1
0
1
1
1
0
1
2
0
0
1
0
1
2
0
2
0
1
2
0
2
2
0
0
0
1
1
2
0
0
0
1
1
1
0
1
0
2
2
0
2
2
1
1
0
0
3
1
2
1
0
0
0
1
0
1
0
0
0
2
2
1
1
0
0
0
0
1
2
2
1
2
2
2
0
1
1
0
1
0
0
0
0
1
3
0
0
0
0
1
2
0
1
0
1
1
4
1
1
2
2
0
0
1
2
1
2
2
0
0
2
1
1
0
0
0
2
2
1
2
2
1
0
2
1
0
1
2
1
0
0
0
0
2
0
1
2
2
1
0
0
0
0
0
1
0
0
1
0
1
1
2
0
0
0
0
2
0
2
1
0
2
4
1
0
0
0
1
0
1
1
0
0
0
1
0
2
2
1
0
1
2
0
0
2
2
0
0
1
1
1
1
1
1
0
0
1
1
0
0
0
1
1
2
1
1
0
1
0
0
1
0
0
0
2
0
0
0
2
1
2
0
0
0
0
1
1
0
1
1
1
1
2
3
2
1
1
1
2
1
2
0
0
1
0
0
2
1
0
1
2
0
0
1
0
0
1
0
0
0
1
0
1
0
0
1
2
0
1
2
1
0
1
0
2
1
0
0
0
2
1
2
1
1
2
3
0
2
0
0
1
1
2
0
1
0
2
2
0
0
2
0
1
1
1
2
2
1
2
1
0
1
2
2
0
2
1
0
0
0
0
1
1
1
0
0
0
2
0
1
0
2
0
0
1
1
1
1
0
2
2
1
1
0
1
1
0
0
0
1
2
0
1
1
2
1
3
0
1
0
0
1
0
1
2
1
0
2
1
0
1
2
1
1
1
2
1
1
0
0
0
1
2
1
0
1
0
0
0
2
0
1
1
2
0
1
2
0
1
1
3
2
1
2
0
0
0
1
0
1
0
1
2
0
1
0
0
1
1
0
1
0
2
2
1
1
0
1
0
1
0
1
0
1
1
2
1
1
2
0
0
0
0
0
1
2
1
2
0
1
0
1
1
2
2
0
2
0
0
0
0
1
0
1
0
1
1
1
0
0
0
0
1
1
1
2
1
1
0
1
2
0
2
0
1
0
1
1
0
0
1
1
4
1
0
1
0
0
0
1
0
1
2
1
2
0
1
1
1
0
3
2
1
1
0
0
0
1
1
2
0
1
0
0
0
0
2
1
2
2
2
0
0
0
2
1
2
1
1
0
2
1
2
0
2
1
1
1
0
0
0
2
0
2
1
1
0
1
2
0
0
2
1
1
1
0
1
0
0
1
0
0
2
0
0
0
1
0
0
0
0
2
0
2
0
1
0
1
0
2
5
2
0
2
2
2
1
0
0
0
1
0
1
1
2
2
2
1
2
2
0
1
0
0
1
0
1
0
2
2
0
2
1
0
1
0
1
1
1
2
2
0
0
0
0
1
0
0
1
1
0
2
1
0
1
0
0
2
0
2
0
1
2
2
1
2
6
1
0
0
1
0
1
1
0
0
2
0
1
0
0
1
0
0
2
0
1
0
2
2
3
0
0
0
0
1
1
2
1
2
4
2
0
2
1
0
1
0
1
2
2
2
0
1
1
0
0
0
0
0
1
1
0
2
0
2
0
0
2
1
1
0
0
1
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
2
1
2
1
0
0
0
0
1
2
0
1
1
0
2
1
1
1
0
2
1
2
2
0
0
1
0
0
1
0
1
0
0
0
0
2
1
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
1
1
1
1
0
0
0
0
1
0
2
2
0
0
2
0
0
0
0
2
0
1
0
2
1
1
2
0
1
1
0
2
1
1
2
0
0
1
1
0
0
3
0
0
1
0
2
0
0
0
1
0
1
0
1
0
1
1
1
0
1
1
2
2
0
1
0
0
0
1
1
2
0
2
0
2
1
0
1
0
1
0
0
2
0
0
1
0
2
0
0
0
1
1
0
2
2
2
0
2
0
1
1
1
0
0
1
0
1
0
1
2
3
1
1
0
0
0
1
1
1
0
0
0
1
1
0
1
1
0
2
0
0
0
0
0
0
0
1
0
1
0
1
2
0
0
0
0
1
0
0
0
2
0
0
2
1
0
2
0
0
1
2
0
2
2
1
0
0
2
0
0
1
0
0
0
0
0
1
1
1
1
0
2
2
2
0
0
0
1
2
1
2
1
2
1
2
0
2
0
1
1
2
0
0
0
0
0
1
1
1
1
0
1
1
0
1
0
0
1
0
0
1
0
2
2
0
0
0
1
2
0
0
0
1
0
2
2
1
0
1
0
1
0
1
0
0
1
0
1
2
0
0
0
0
1
4
1
2
0
1
0
1
1
0
2
1
1
0
2
0
0
2
1
0
0
1
1
1
1
0
0
0
2
1
1
2
0
1
0
0
0
1
2
0
2
1
1
1
0
1
1
3
1
2
0
1
2
0
0
1
0
1
2
0
0
4
0
2
1
2
0
0
0
1
1
0
1
1
2
1
2
0
0
1
1
2
2
0
0
0
2
1
0
2
0
2
1
0
2
1
0
2
2
1
2
1
0
0
2
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
2
1
0
0
2
0
1
2
3
0
0
1
1
2
2
3
1
2
0
0
2
0
1
0
0
2
1
1
0
0
1
2
1
0
1
0
1
1
0
0
1
0
0
1
0
2
1
3
0
1
1
0
0
0
1
1
1
1
0
1
0
0
2
0
1
1
0
1
0
1
0
0
0
1
0
1
2
0
0
0
0
0
1
1
0
0
1
0
2
0
2
2
1
0
1
0
0
0
0
1
2
1
1
0
0
2
2
2
1
1
0
0
2
3
0
1
1
0
0
0
0
2
2
0
0
1
0
0
1
2
2
0
1
2
0
0
0
2
1
1
0
0
2
1
1
0
0
0
1
0
0
2
0
2
1
2
2
1
0
1
0
0
1
1
1
1
1
0
1
1
0
1
0
0
1
0
0
2
2
0
0
1
1
2
1
0
0
1
1
0
0
1
2
2
0
0
0
0
0
0
0
1
0
0
0
1
2
1
0
0
0
2
1
1
0
0
1
2
2
1
1
2
1
1
1
1
0
1
0
2
0
0
0
2
2
2
0
0
0
1
2
0
0
2
0
0
0
2
4
0
0
1
0
2
0
1
1
0
0
1
1
0
1
0
2
1
0
0
0
2
2
1
1
1
0
2
2
0
1
0
1
0
0
1
0
0
0
1
0
0
1
1
0
2
2
0
1
0
1
0
2
0
0
0
1
3
1
2
0
0
0
2
1
0
0
2
0
0
0
1
1
0
0
0
1
0
1
3
0
1
1
0
2
1
1
0
2
1
1
2
1
0
1
1
2
2
3
0
1
1
1
2
0
1
1
1
0
0
1
2
1
1
1
0
1
2
0
0
0
1
1
0
0
0
0
2
0
1
0
1
1
0
0
0
1
0
0
0
1
0
2
1
0
0
0
0
2
2
2
2
0
0
2
0
0
1
0
2
1
0
2
0
2
3
0
2
0
1
0
1
1
0
4
0
0
0
0
1
0
1
1
2
1
2
1
0
0
0
1
2
1
2
1
0
2
1
2
0
0
1
2
1
4
0
1
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
1
1
0
1
1
1
2
0
1
2
1
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
2
0
2
0
1
1
0
1
2
0
0
0
2
1
0
0
2
2
2
1
0
0
2
1
0
0
0
1
1
1
1
1
1
0
2
0
0
0
0
0
1
0
1
2
1
0
2
0
0
0
0
2
2
0
2
0
1
0
2
1
1
2
2
1
1
1
0
1
1
1
0
1
0
1
0
2
2
1
0
0
0
2
0
1
2
0
1
0
0
2
1
0
2
0
0
1
0
1
0
2
1
1
1
0
2
1
1
1
0
0
0
0
2
0
0
0
0
2
0
0
1
1
0
2
0
0
1
2
1
1
1
0
0
1
0
2
1
2
1
2
1
1
1
0
1
1
0
0
1
1
0
0
2
0
1
1
1
2
0
1
1
1
1
1
0
0
1
0
1
1
0
0
2
0
1
2
2
1
0
0
1
2
1
0
0
1
1
1
0
2
2
1
1
0
0
0
0
1
1
0
0
2
2
0
0
0
2
2
0
0
0
0
2
0
2
1
1
2
2
0
0
0
0
0
1
0
0
0
2
1
1
0
0
0
0
2
1
1
0
0
0
0
0
1
1
0
1
2
0
0
1
1
0
2
0
1
1
2
1
1
0
1
1
1
1
1
0
0
2
0
0
2
0
2
1
1
0
0
1
0
1
2
1
1
2
0
0
0
0
0
1
0
0
0
1
0
2
1
1
1
2
0
0
0
0
0
2
1
1
2
1
1
0
0
0
2
3
1
0
1
1
0
0
1
0
1
2
2
2
1
0
1
0
2
1
0
2
1
2
1
1
0
0
0
2
0
2
1
2
1
0
2
2
1
0
1
0
2
1
0
0
2
1
3
1
2
0
0
1
0
0
0
2
0
0
1
0
0
0
0
1
1
1
1
1
1
1
0
1
1
1
0
0
2
0
0
1
0
0
2
0
3
1
0
2
0
0
2
1
2
0
1
0
1
1
0
0
0
0
0
1
0
0
1
1
2
2
2
2
1
1
0
0
0
1
1
1
0
0
0
1
1
2
1
0
0
0
0
0
0
1
0
2
1
1
2
2
0
1
1
1
0
1
1
2
1
1
0
0
0
0
0
4
1
1
1
0
0
1
0
1
1
2
0
2
1
0
0
1
0
2
0
1
1
0
0
2
2
0
2
1
1
0
0
0
0
2
2
0
0
2
0
0
1
2
0
2
1
0
1
0
1
1
2
0
2
2
1
2
2
1
2
0
3
0
1
0
1
1
1
1
1
0
1
0
3
0
0
0
1
0
0
2
1
1
0
0
0
2
2
1
0
0
1
1
0
0
0
2
1
1
0
0
1
2
1
0
0
2
0
0
1
0
0
0
1
0
0
0
2
0
0
0
2
2
1
1
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
1
1
1
1
0
0
1
1
2
1
1
2
0
0
1
2
2
1
2
1
0
0
1
0
0
1
1
1
0
2
0
1
2
1
1
0
1
0
0
1
0
0
0
0
1
1
0
2
0
2
0
0
1
2
2
0
0
1
0
1
0
2
0
2
2
1
1
1
2
0
1
0
1
1
0
0
1
2
2
2
2
0
0
1
0
0
0
0
1
1
0
1
0
2
0
1
0
0
0
1
1
0
0
1
1
0
1
1
1
1
1
0
0
0
0
2
2
0
3
1
0
0
1
0
2
1
1
1
1
0
1
0
1
1
1
0
0
2
1
0
4
1
0
0
0
0
0
1
0
2
0
2
0
0
2
1
1
1
2
1
2
0
2
2
3
2
2
1
0
1
0
1
1
1
0
1
0
0
1
1
2
0
2
0
2
0
0
1
0
2
0
0
1
0
2
0
0
0
0
1
2
0
0
2
1
0
0
0
0
0
1
1
0
3
0
0
0
0
0
1
2
3
1
1
1
2
1
1
0
1
1
1
2
1
1
1
0
0
1
0
4
2
3
0
0
0
1
0
2
1
0
0
0
0
1
0
0
1
0
1
0
0
2
1
0
1
2
1
1
3
0
0
1
1
0
0
0
0
1
2
2
2
0
2
1
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
2
3
0
0
0
2
1
1
0
1
1
0
1
0
0
0
0
1
1
1
2
3
0
2
2
1
1
1
0
0
0
2
2
1
0
0
2
2
1
0
0
2
1
0
0
1
2
1
1
1
2
0
0
1
2
0
2
1
1
0
2
1
2
1
0
1
2
0
0
1
1
1
0
0
0
1
2
1
1
1
2
2
0
1
0
0
0
0
0
1
0
1
2
2
2
1
0
1
1
2
1
0
0
0
2
0
1
0
0
1
1
0
0
1
2
1
1
2
0
0
1
0
0
2
0
1
1
1
2
0
0
2
0
1
1
0
0
0
2
0
0
0
1
0
0
2
0
2
0
1
0
1
0
2
0
3
2
0
2
0
1
2
1
0
2
2
1
0
0
1
1
0
0
0
2
1
0
0
2
1
0
0
0
0
2
1
0
2
1
1
0
1
3
2
0
2
0
1
1
1
1
0
0
2
0
0
2
0
0
3
0
1
0
1
1
1
1
1
0
0
2
0
2
0
2
0
2
2
0
0
0
1
2
1
0
1
1
0
0
0
1
1
1
1
1
2
2
1
0
2
1
0
0
1
0
1
1
1
2
1
1
0
1
1
0
1
0
0
1
0
1
2
1
1
0
0
1
1
0
2
1
0
1
2
2
0
2
2
0
1
0
1
1
0
1
2
1
1
0
0
2
1
0
1
0
1
2
1
0
4
1
1
1
1
1
0
1
2
0
1
3
0
1
1
2
2
0
0
2
1
1
0
0
0
2
0
0
1
2
2
1
2
1
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
1
2
1
2
1
1
0
0
1
2
3
1
1
1
0
2
0
1
0
0
1
1
0
1
1
1
0
1
0
1
1
0
1
2
0
2
2
1
1
2
1
1
1
1
0
1
2
0
1
1
0
1
1
2
2
0
0
2
0
1
0
0
1
1
2
2
0
0
0
0
1
1
0
0
1
1
2
0
1
1
1
0
1
2
1
1
0
1
1
1
0
0
0
1
0
1
1
0
0
1
0
0
2
1
1
0
0
0
2
2
1
1
1
1
1
0
0
1
1
0
0
0
0
0
0
2
0
2
1
0
1
0
2
1
0
1
1
0
1
2
0
1
2
2
2
0
2
1
1
1
0
0
0
1
0
0
0
2
2
0
0
2
2
0
0
0
2
1
0
2
0
0
1
1
0
0
1
0
2
1
1
1
1
2
0
0
0
1
1
0
1
1
1
1
0
2
2
0
0
0
2
1
1
0
0
0
2
1
2
1
0
1
0
0
1
0
0
1
1
2
2
0
0
0
1
0
2
2
2
2
2
0
0
0
1
0
1
1
0
0
1
1
2
1
0
0
1
0
0
1
0
1
1
0
0
1
0
2
1
1
2
1
0
1
2
2
1
0
2
0
0
1
1
1
2
1
1
0
1
0
0
1
0
0
0
0
1
1
1
1
1
0
1
0
1
0
1
0
0
2
0
3
0
0
1
2
1
1
1
1
1
2
1
0
1
1
0
1
0
2
0
0
1
0
1
0
2
1
1
2
2
0
1
0
1
2
1
2
1
0
0
0
1
1
1
0
0
0
2
1
1
1
0
0
0
2
1
0
1
1
0
0
1
1
0
2
1
0
0
0
0
0
1
1
0
2
2
1
1
0
1
0
0
0
1
0
0
2
1
0
1
2
0
0
2
0
0
1
0
2
2
0
0
1
1
2
1
2
1
0
0
1
3
4
1
2
0
1
2
2
0
0
2
1
0
0
0
1
0
0
0
2
0
1
2
0
1
1
2
1
1
0
2
2
1
0
1
1
0
1
2
2
0
0
0
1
0
1
1
0
0
2
0
0
1
0
0
1
2
0
0
0
1
1
2
2
2
0
1
0
0
0
1
1
2
0
3
1
0
0
1
1
1
2
0
0
2
2
1
1
1
1
0
0
1
1
0
2
1
2
1
2
0
2
1
2
0
0
0
2
0
0
1
1
1
1
1
1
1
0
0
0
5
1
2
6
1
2
0
1
0
0
1
1
3
0
2
2
2
2
0
2
2
2
1
0
0
1
1
0
1
2
0
1
1
1
0
1
1
0
0
0
0
0
1
1
0
1
0
0
0
1
0
2
0
2
3
1
1
1
1
2
3
1
2
0
0
0
0
0
1
0
0
0
2
1
2
2
1
0
0
1
1
1
0
2
0
1
0
0
0
0
1
1
0
0
2
2
1
0
1
1
0
0
1
2
2
1
1
1
2
0
2
0
0
0
1
0
1
2
0
0
1
0
2
1
0
1
2
1
1
0
1
0
0
1
2
3
2
1
1
1
1
0
2
1
2
1
0
1
0
1
2
2
0
1
0
0
0
0
0
1
0
0
1
2
2
2
2
1
0
1
0
1
2
1
2
0
1
1
1
2
0
0
1
0
1
0
2
0
1
2
0
2
2
0
2
2
0
1
2
0
1
0
1
0
0
1
0
0
1
1
1
1
0
0
1
0
0
1
1
1
1
0
1
0
0
1
0
0
1
0
1
1
1
2
0
2
1
3
0
0
0
1
1
0
2
1
1
1
2
1
2
1
2
0
0
0
0
1
2
2
1
1
0
2
2
1
1
1
2
3
0
1
2
1
2
0
0
1
0
1
0
1
0
0
0
0
0
1
1
0
1
1
2
0
1
2
1
2
0
1
1
1
0
2
0
1
2
0
0
2
0
0
1
1
1
0
1
2
1
2
0
1
0
0
0
1
0
0
0
0
0
2
1
1
0
0
1
0
1
0
2
0
0
0
1
0
1
0
2
0
1
1
1
2
2
0
0
2
2
2
2
1
1
2
1
2
1
2
0
2
0
0
0
0
2
1
1
2
0
1
1
0
0
1
1
0
0
2
2
2
2
1
0
0
1
1
0
1
0
2
1
1
2
0
1
0
1
1
1
1
0
3
2
1
4
0
0
0
2
0
1
1
2
2
1
0
1
0
0
1
1
0
0
2
1
0
2
1
3
0
0
1
0
0
0
1
2
0
0
1
2
0
0
1
2
1
0
0
0
1
1
1
0
2
1
1
2
0
0
1
2
0
0
1
0
1
1
1
0
2
1
1
1
0
1
0
0
0
1
0
1
1
2
2
1
1
0
0
0
1
1
0
1
0
0
1
0
0
1
2
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
1
1
0
2
0
2
0
2
2
0
0
0
0
0
1
2
1
1
1
2
1
2
1
1
2
2
0
1
0
1
2
1
0
0
1
1
2
1
1
1
0
1
0
1
0
2
0
0
0
0
2
2
1
2
1
0
2
0
1
1
1
0
2
2
2
1
1
2
1
1
1
0
1
1
1
1
1
1
2
1
2
0
1
1
0
1
0
0
1
0
2
1
0
0
0
1
2
0
0
0
1
0
0
0
2
2
1
1
1
0
0
1
1
1
1
0
2
0
1
0
1
0
1
0
0
1
2
1
0
1
1
1
2
0
2
0
1
0
0
1
2
0
1
1
2
1
0
0
2
1
0
1
1
2
0
1
1
0
1
1
0
0
2
0
1
0
0
0
2
2
0
0
1
0
1
2
1
1
2
0
0
0
0
2
0
1
1
2
0
0
1
1
0
0
2
2
1
1
1
0
1
1
1
0
1
1
2
3
0
2
1
0
0
1
1
2
2
0
0
0
0
1
1
1
0
0
0
0
0
1
1
0
1
0
0
0
1
0
1
0
0
0
1
0
1
2
1
0
2
0
1
2
0
0
0
0
1
2
0
5
1
1
2
1
2
1
3
0
0
0
0
0
1
2
1
2
2
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
1
1
0
1
1
0
1
0
1
0
0
2
2
0
0
0
2
1
2
0
1
1
0
2
0
0
1
2
0
2
0
0
0
1
1
0
1
2
1
1
1
0
1
1
0
1
1
1
1
1
0
1
1
0
0
0
1
2
1
2
1
1
2
0
0
0
1
0
2
0
0
2
0
0
1
1
1
1
0
0
2
0
0
1
1
0
3
1
0
1
1
1
1
0
2
2
0
2
1
1
0
1
0
2
1
1
1
0
0
0
0
1
2
1
1
0
2
1
0
2
1
0
1
0
1
1
0
1
1
1
1
1
1
0
2
1
1
1
2
1
0
1
2
1
0
1
1
1
0
2
0
2
2
0
0
1
2
0
2
0
0
0
2
0
0
2
1
1
1
1
0
1
0
1
1
0
0
0
1
2
1
1
1
0
0
0
0
2
0
0
1
1
0
0
1
0
0
0
1
2
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
1
1
0
2
1
0
2
1
0
0
0
2
0
2
0
1
0
1
1
1
0
0
1
0
2
2
2
1
0
1
1
0
1
2
2
0
0
0
1
2
1
0
0
1
1
2
1
0
0
0
0
0
1
1
2
2
1
0
2
1
0
1
0
0
0
0
2
0
0
1
2
0
1
2
2
0
1
1
1
0
1
1
2
1
1
0
0
1
0
0
0
1
1
0
0
0
3
0
1
0
0
1
0
1
0
0
2
2
1
1
0
0
2
1
1
1
1
1
0
0
2
3
1
0
1
3
1
2
1
0
0
1
1
0
2
1
2
2
0
0
0
0
2
1
0
0
1
0
1
1
0
0
0
1
1
0
2
0
0
1
2
0
0
2
0
1
1
2
0
1
0
2
1
2
2
1
2
2
2
1
0
1
1
1
1
2
0
0
1
0
1
1
0
2
0
1
2
2
1
0
0
1
1
0
0
0
0
0
0
2
1
2
0
2
2
0
2
0
1
0
1
0
0
2
1
0
1
1
0
0
1
3
0
3
1
2
1
2
1
0
0
0
0
0
0
1
0
1
0
2
1
1
3
1
1
2
2
0
0
0
1
2
0
1
0
0
1
1
1
0
1
3
0
1
1
0
3
2
0
8
0
0
0
2
1
1
1
0
1
0
2
2
1
1
1
0
0
0
0
1
2
2
0
0
2
0
0
0
2
0
1
1
0
0
1
0
0
1
2
0
0
1
1
1
1
0
0
1
0
0
0
0
0
2
0
2
0
1
2
2
0
0
0
1
1
0
0
1
1
0
1
0
1
0
0
0
0
0
1
1
0
3
2
0
2
0
0
2
2
0
0
0
0
2
1
0
1
1
2
0
2
0
3
1
2
2
0
0
0
0
0
0
1
1
0
2
0
1
1
1
1
1
0
0
1
2
2
0
0
0
1
0
1
0
0
2
2
1
2
0
1
0
2
2
1
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
1
1
1
2
1
0
1
2
2
0
1
0
0
1
1
1
0
1
1
0
0
3
0
2
0
1
1
2
0
2
0
2
0
0
1
1
1
1
1
0
1
1
0
1
5
2
1
0
0
3
0
2
1
0
0
1
0
1
1
0
3
2
1
2
0
1
1
0
0
2
1
2
1
0
2
2
0
1
1
0
1
2
1
0
1
1
2
1
0
2
1
0
1
0
0
1
0
1
0
1
1
0
1
1
0
0
1
2
0
2
1
0
2
1
0
0
1
0
0
0
0
2
3
0
2
0
2
1
0
2
1
0
1
1
0
0
0
1
2
3
0
0
0
0
0
0
0
0
2
0
1
2
0
0
1
2
2
0
1
1
0
0
0
2
2
0
0
1
0
2
1
0
1
0
0
3
0
0
0
0
0
1
0
0
1
2
2
2
2
2
1
0
0
2
0
0
0
0
2
0
1
0
0
2
1
1
2
0
0
0
0
2
0
1
1
1
1
1
1
1
1
1
0
0
1
1
1
2
0
0
1
1
0
0
1
0
2
1
0
0
2
0
0
3
2
2
0
1
0
1
0
2
1
2
0
2
2
0
2
1
0
4
1
1
0
2
0
0
1
2
0
0
2
1
1
2
2
0
1
2
1
0
1
2
1
1
0
1
1
0
0
1
2
1
1
0
1
0
1
0
1
0
2
1
2
0
1
2
0
0
1
1
1
0
1
0
1
0
0
2
2
0
0
0
0
3
1
0
1
2
2
1
2
2
0
0
0
1
1
0
0
0
0
0
1
0
0
2
0
0
0
0
2
1
0
1
0
2
2
0
1
0
1
0
0
2
2
0
0
1
2
0
1
0
0
1
0
1
2
0
2
2
0
2
0
0
1
2
1
0
0
1
1
0
0
1
0
0
1
1
0
2
0
1
1
1
4
0
2
1
0
0
1
1
2
1
1
0
0
2
1
0
0
0
0
1
1
2
0
1
2
0
2
2
1
1
0
0
2
0
0
1
2
1
1
1
0
0
2
2
1
0
2
0
0
1
1
1
0
2
0
0
0
2
2
0
1
1
2
0
2
3
0
0
1
1
0
1
0
0
1
0
0
1
2
2
0
0
0
1
3
0
1
0
2
0
2
0
1
1
0
0
2
1
1
2
1
0
1
2
2
0
0
0
1
0
0
0
2
2
0
3
0
0
2
2
1
1
0
0
0
1
0
1
2
2
0
1
0
0
0
0
2
0
1
0
0
0
2
1
2
0
1
0
2
3
2
0
1
2
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
2
1
1
1
2
0
1
2
0
1
0
1
0
1
0
0
2
3
0
2
0
2
2
1
0
1
2
2
2
0
2
2
2
2
1
1
0
2
1
5
0
0
1
0
0
2
0
0
2
1
1
2
2
1
1
0
2
2
0
1
2
1
2
2
0
1
0
0
2
2
0
1
0
2
1
0
1
3
0
2
3
0
1
2
1
0
0
1
1
2
1
0
1
0
0
1
0
1
0
0
0
0
1
0
1
1
1
0
0
0
1
2
1
2
2
1
0
0
1
1
1
0
1
0
2
0
0
1
2
1
0
0
1
1
0
2
2
0
0
0
0
2
1
1
2
1
0
0
0
0
1
2
1
0
0
0
0
1
2
2
0
1
1
0
0
0
0
1
0
0
0
2
1
1
1
0
0
0
1
1
2
1
1
0
0
2
0
0
1
1
1
1
0
0
1
0
1
1
1
1
1
0
0
0
0
0
2
3
0
1
2
1
1
1
2
0
0
1
1
0
1
1
2
1
0
1
1
0
1
0
0
0
1
1
0
1
0
2
0
1
0
0
0
1
1
0
0
0
2
0
2
0
1
1
0
1
2
2
1
1
2
1
2
0
1
1
1
0
0
0
1
1
0
0
1
1
2
1
2
0
0
0
0
0
0
2
2
1
1
0
1
0
0
0
0
0
1
0
1
0
0
2
0
0
2
2
0
0
0
1
1
2
1
2
2
0
1
1
5
0
2
1
0
0
3
2
0
1
1
0
0
0
0
2
2
2
1
2
2
0
0
0
2
2
2
2
2
1
2
1
0
0
2
0
0
0
1
0
1
0
0
2
1
0
0
0
2
2
2
0
2
4
9
0
1
2
0
1
1
0
0
1
2
0
2
0
1
1
0
0
2
1
0
1
0
1
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
2
1
3
0
1
0
2
0
1
0
2
2
1
0
1
2
0
4
0
0
0
1
0
1
0
0
0
0
0
1
0
2
1
2
2
0
2
1
0
0
0
0
1
0
0
2
1
1
0
0
1
1
0
2
0
1
0
0
0
0
0
1
0
2
0
1
0
1
1
0
0
1
1
0
0
0
0
0
1
0
1
2
1
0
1
2
2
2
2
1
0
0
0
1
0
2
1
2
2
0
2
1
1
0
2
2
3
2
1
2
0
0
1
2
1
2
0
1
1
2
1
2
0
2
1
1
0
0
2
2
0
0
2
0
0
0
0
1
0
0
2
0
1
2
0
1
2
0
2
0
1
0
1
1
1
1
1
1
1
1
2
2
1
2
0
0
1
2
0
0
0
1
2
2
0
0
1
0
1
0
2
2
3
1
2
1
0
1
4
1
1
1
0
0
1
0
1
1
2
4
1
1
1
2
1
1
1
2
1
2
0
1
1
1
0
2
2
0
0
1
0
1
1
0
1
0
0
2
0
0
2
2
1
1
2
2
0
0
1
1
1
1
1
0
1
0
1
1
0
0
3
2
0
0
1
1
2
1
1
1
1
0
0
1
1
2
2
0
2
1
0
0
1
1
1
2
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
2
0
0
0
1
2
0
1
1
0
1
0
2
1
2
0
1
1
2
0
1
1
0
0
0
0
1
0
2
1
2
2
2
1
1
1
0
0
0
1
1
2
1
0
0
0
2
1
0
2
0
0
0
0
1
0
0
2
3
0
0
2
2
0
0
0
0
1
2
2
0
0
2
2
0
1
2
0
1
0
1
0
0
0
0
0
5
0
2
0
0
2
0
0
1
0
1
1
0
1
2
1
1
2
0
0
0
1
1
1
0
0
0
1
1
0
0
0
0
2
0
1
1
0
0
2
1
2
2
1
2
1
3
1
1
1
0
2
0
4
0
0
2
1
1
2
0
0
0
0
2
0
0
2
1
0
0
0
0
0
1
0
0
0
0
1
2
0
5
4
1
1
0
0
0
1
0
2
0
1
1
1
0
0
0
2
0
0
1
0
2
0
2
0
0
1
1
0
2
2
1
0
0
2
0
0
0
1
2
0
0
0
0
2
1
0
2
0
0
1
1
1
0
1
0
1
2
0
2
1
2
0
1
0
0
1
0
1
0
1
0
0
2
1
1
2
2
0
1
1
2
0
0
0
0
0
1
0
0
0
2
1
0
0
0
1
0
0
0
1
2
1
2
2
1
0
0
0
1
0
2
0
0
0
3
1
1
0
1
1
0
0
1
1
0
1
2
2
1
1
1
0
1
1
0
1
0
0
0
0
0
1
1
2
1
0
2
1
0
1
0
0
0
1
0
2
2
2
0
0
1
0
0
0
2
1
2
0
2
2
2
1
0
0
1
1
0
0
2
0
0
0
1
0
1
1
0
1
0
1
1
2
0
0
1
0
0
0
2
1
0
0
1
1
3
2
0
0
0
0
0
1
2
0
0
0
1
0
1
0
0
0
0
0
0
2
2
2
1
1
0
0
2
0
1
1
2
0
1
1
0
2
1
1
1
0
1
1
0
3
2
3
1
0
0
0
1
0
2
1
0
0
0
2
0
1
3
0
1
1
1
0
0
0
1
1
0
0
0
0
2
2
2
0
0
1
0
2
0
1
1
1
1
2
3
0
0
0
0
1
2
2
0
1
1
0
1
2
1
2
0
2
0
2
0
1
0
2
1
1
1
0
0
1
0
1
2
2
0
0
1
2
2
0
0
0
1
0
2
0
0
2
1
0
1
1
0
0
0
0
1
1
0
0
1
0
1
2
0
0
0
0
2
1
0
0
1
0
0
1
3
2
0
0
1
1
0
2
2
1
1
1
1
2
1
0
0
1
0
1
0
1
2
1
0
1
0
0
1
1
1
0
1
0
0
2
0
1
0
2
2
0
1
2
1
0
0
1
0
1
0
0
2
3
0
0
1
1
1
1
0
2
2
0
1
0
2
1
0
0
0
1
0
0
0
0
1
1
0
0
2
0
1
1
1
0
1
2
2
2
1
2
0
1
1
3
2
0
1
0
2
2
0
1
0
1
2
0
1
2
2
2
2
0
0
0
0
0
1
4
0
0
1
0
1
1
1
0
2
1
2
2
0
2
0
2
1
1
0
1
1
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
1
3
1
0
1
1
1
1
2
2
0
1
1
0
0
0
1
1
1
0
0
1
1
2
1
1
1
2
1
1
2
1
2
0
2
1
0
2
1
0
2
0
1
2
1
2
1
2
0
2
1
2
2
2
0
1
2
2
0
1
2
0
2
2
1
1
0
1
0
0
2
2
0
2
0
2
0
1
1
1
2
0
1
0
2
2
0
0
0
0
0
1
1
2
1
0
1
1
0
2
2
0
1
0
2
0
0
1
0
0
0
0
0
2
0
2
1
1
2
0
0
1
2
1
0
2
0
0
1
1
0
1
1
0
0
1
0
1
2
1
1
2
0
0
0
0
0
1
0
1
1
2
0
2
0
1
0
1
2
1
0
1
0
1
0
2
0
1
2
0
0
4
1
2
2
0
1
2
0
0
1
1
0
0
3
2
1
1
3
0
1
1
2
0
0
0
1
2
0
0
1
1
2
0
0
1
0
3
3
1
0
2
0
0
0
1
0
2
1
1
0
0
1
0
1
0
0
1
2
0
1
2
2
2
0
2
1
0
0
1
1
0
1
2
0
0
1
1
0
0
1
0
1
0
1
1
1
1
1
0
1
0
0
0
0
0
1
0
1
1
1
2
0
2
0
2
1
1
0
0
2
2
0
1
0
1
0
0
2
5
2
0
1
0
1
2
0
2
2
0
2
0
2
0
0
0
1
2
2
1
0
3
1
1
0
2
1
2
2
1
0
1
0
2
0
0
2
0
1
2
1
2
0
2
0
0
1
1
1
2
1
2
1
1
1
1
0
1
0
2
0
1
0
0
0
1
1
1
2
0
2
3
2
0
1
0
0
1
2
1
3
1
1
1
0
1
2
0
1
0
1
1
0
1
1
0
1
0
0
0
1
0
0
1
0
1
2
0
0
2
1
1
0
0
0
1
0
0
0
1
0
0
2
2
0
1
0
1
1
2
2
2
2
0
0
0
2
0
2
1
0
1
0
0
1
0
0
1
1
2
1
0
1
0
2
2
2
0
0
0
0
0
1
0
1
2
0
1
2
0
1
1
0
0
0
1
2
1
0
0
0
0
2
1
2
0
2
1
0
0
0
1
0
2
2
2
3
0
0
0
0
1
1
3
0
0
0
2
1
1
1
2
2
1
1
0
2
2
0
0
1
0
1
0
0
0
1
0
2
2
0
0
2
0
0
0
0
2
1
0
2
2
0
0
1
0
0
2
2
0
0
0
0
0
3
0
1
1
0
1
2
0
0
0
0
1
1
0
0
2
1
0
1
2
0
0
0
2
0
1
1
2
0
3
0
0
1
0
1
0
1
0
1
1
0
2
2
1
0
0
0
1
0
2
0
1
0
1
1
1
1
0
1
0
0
1
2
2
0
1
2
0
2
1
2
1
0
1
1
1
1
2
0
1
0
1
0
1
2
1
0
2
1
1
2
0
0
1
0
1
1
1
2
1
1
0
0
2
4
2
2
0
1
1
2
2
1
2
2
0
0
2
1
1
0
0
2
0
2
0
0
2
1
0
0
2
0
0
2
0
0
0
1
2
2
0
1
1
0
1
0
1
0
0
0
0
1
2
0
1
0
2
0
0
1
0
0
2
0
0
1
1
0
0
0
1
1
1
0
0
1
0
1
2
0
2
0
0
0
1
2
2
0
6
0
0
1
1
2
0
1
1
0
0
1
1
2
0
1
0
0
1
2
2
0
0
1
0
0
1
3
0
1
2
1
0
0
2
1
0
0
0
1
0
1
0
0
0
1
1
1
1
2
1
2
0
1
1
1
0
0
2
0
1
0
0
0
1
1
0
0
0
2
1
3
2
1
2
2
0
0
2
0
0
0
1
1
0
0
1
0
7
1
0
0
0
1
2
0
1
1
0
1
0
2
2
1
0
0
2
1
1
0
0
0
0
1
3
1
1
1
1
1
2
0
0
0
1
0
0
0
4
0
1
1
1
0
2
2
0
0
0
1
1
0
0
1
1
0
4
0
0
1
0
1
0
0
2
1
1
2
0
0
1
1
1
1
0
1
2
0
1
1
0
0
2
0
2
1
0
2
0
0
2
0
0
0
0
1
1
2
1
2
0
1
1
1
1
1
0
0
0
0
0
1
2
0
2
1
0
1
2
0
1
1
1
1
0
1
1
1
0
1
2
0
1
2
0
1
1
1
0
1
0
1
1
1
0
1
1
0
0
0
2
2
0
0
2
2
0
2
1
0
1
1
1
1
0
1
0
1
0
0
0
2
2
0
2
1
0
0
0
2
0
2
2
0
1
0
0
2
1
0
1
1
0
0
1
0
0
1
2
0
0
2
0
2
1
0
2
2
0
0
1
2
1
0
1
0
0
0
2
0
0
1
0
0
2
0
1
1
1
0
2
1
0
1
0
1
0
1
1
0
1
0
2
1
2
0
2
2
0
0
2
2
1
0
1
1
0
1
0
0
2
0
0
1
0
1
1
0
0
1
1
2
0
0
0
1
1
1
1
1
3
0
0
0
2
2
2
0
1
0
0
2
1
2
0
1
0
0
0
2
2
0
1
0
0
2
2
0
0
2
0
2
1
0
2
2
3
1
0
2
1
0
1
1
0
1
1
0
1
1
1
1
0
0
1
1
0
0
0
0
1
2
0
1
0
2
0
1
1
1
1
0
1
1
0
0
1
0
1
1
0
0
1
0
1
1
0
0
0
0
1
2
1
0
0
1
1
1
2
0
0
1
0
0
2
0
1
0
2
0
2
0
1
0
1
0
1
2
1
0
0
1
0
2
1
2
1
3
0
0
0
1
0
2
0
1
0
1
1
0
0
0
2
0
1
0
0
2
1
0
3
0
0
0
2
0
2
0
0
0
2
1
1
0
1
0
1
1
0
2
1
1
1
2
0
1
2
1
0
2
0
0
2
0
0
2
1
0
1
1
0
0
2
2
0
0
0
0
1
1
0
2
1
2
1
0
1
2
0
0
0
0
2
1
1
1
0
2
1
1
1
2
2
1
1
2
0
0
0
0
1
0
0
0
1
0
1
0
2
2
0
1
1
0
0
0
0
1
2
0
1
0
0
1
1
1
1
1
2
2
0
1
2
0
0
1
0
1
0
2
2
0
1
0
1
2
1
0
0
0
1
0
2
0
2
2
0
0
2
0
0
1
2
1
0
1
0
1
1
0
1
1
2
1
1
0
1
0
2
1
0
0
1
0
0
1
0
0
0
0
0
0
2
0
2
0
2
2
1
0
1
1
0
0
2
1
0
0
0
1
0
2
2
0
2
1
0
1
1
2
1
1
2
0
1
1
2
1
0
1
0
1
1
0
0
1
0
2
0
1
0
2
1
0
0
1
2
2
0
0
1
0
2
0
1
1
2
0
3
1
0
0
2
0
1
0
2
1
0
0
0
1
2
0
0
0
0
0
1
1
3
2
0
0
1
1
2
1
2
0
0
2
2
3
1
0
0
1
2
3
0
3
3
1
0
0
1
0
0
0
0
1
1
1
2
1
1
0
2
1
2
0
1
0
1
1
0
1
1
0
0
1
2
2
0
1
0
0
2
1
0
1
1
1
0
0
1
1
0
2
2
1
0
0
2
0
2
0
0
0
1
0
0
0
2
0
0
0
1
1
2
1
2
1
0
1
2
1
0
0
1
2
2
1
2
0
0
1
2
1
0
0
0
0
0
1
1
2
0
1
2
0
1
0
0
0
2
0
1
0
1
0
2
0
1
2
2
2
1
3
1
2
1
1
0
1
2
1
1
1
2
0
0
0
0
0
1
0
1
2
1
0
1
0
0
0
1
2
0
1
2
1
2
1
0
1
3
1
1
2
0
0
1
2
0
3
1
1
0
1
1
1
2
1
0
2
0
1
1
1
0
0
0
3
1
2
2
1
0
1
2
2
0
1
1
1
1
0
0
2
0
0
1
0
0
0
0
1
1
2
0
1
0
2
1
0
1
1
2
0
1
1
0
0
1
2
2
1
0
0
2
1
0
2
1
1
0
3
1
0
1
1
1
1
2
0
1
1
1
1
1
0
2
0
1
1
4
1
0
1
1
0
0
1
1
0
0
1
2
2
0
1
1
1
0
0
1
1
1
0
2
0
0
0
0
1
2
2
0
0
2
0
1
1
0
0
1
2
0
1
0
1
0
1
2
1
1
0
1
0
0
1
0
1
2
0
1
1
0
0
1
0
1
2
0
0
1
0
0
2
0
1
1
2
1
0
1
1
2
1
1
2
0
0
2
2
1
1
0
0
0
1
1
1
1
1
0
0
1
1
0
1
1
1
1
2
0
0
0
0
0
0
2
1
0
1
1
0
0
1
0
2
0
0
0
1
2
0
0
0
1
0
1
0
1
1
0
0
0
1
2
2
1
1
0
0
0
0
1
2
2
0
0
1
1
0
1
1
1
0
1
0
0
0
1
0
2
2
1
0
0
0
0
0
0
2
0
0
1
1
2
2
1
0
0
2
1
2
1
1
1
0
1
2
0
0
2
1
0
0
0
2
1
0
0
0
2
0
1
1
1
2
2
0
0
1
1
1
2
2
0
2
2
2
1
1
1
0
2
0
0
0
2
1
0
1
0
0
2
0
1
1
1
0
2
1
0
1
0
2
1
1
0
1
0
0
0
1
0
1
0
0
1
0
1
2
2
1
1
0
1
1
4
0
2
0
2
1
0
1
1
1
0
2
2
1
0
1
3
0
2
1
1
1
0
1
1
0
1
0
0
0
2
0
0
0
1
0
2
2
1
2
0
1
3
0
1
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
2
1
1
2
1
1
0
1
1
1
0
0
2
0
2
0
2
0
0
0
1
1
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
2
2
2
1
2
1
0
0
1
0
0
1
2
0
2
0
0
1
1
0
2
2
1
0
2
2
0
0
2
0
1
0
0
0
1
1
0
2
1
1
1
4
0
0
0
1
0
0
0
2
0
0
2
2
0
1
0
1
0
0
0
0
1
1
2
1
1
1
0
2
0
1
1
2
0
0
2
2
1
2
1
2
1
0
1
1
0
0
1
1
0
2
0
0
0
0
1
0
2
0
3
0
1
0
0
1
2
1
0
1
0
0
0
0
1
1
1
2
1
1
0
0
1
1
1
0
2
0
0
1
1
0
2
0
1
2
0
1
1
1
1
1
1
1
2
1
1
0
1
1
1
1
0
1
1
2
0
0
0
2
1
2
2
2
0
1
1
2
0
1
1
1
1
0
1
0
1
0
0
2
2
1
1
2
0
0
0
0
0
0
2
1
0
1
0
1
0
0
1
1
0
1
1
1
0
1
2
1
1
0
0
0
1
1
0
1
1
2
2
2
0
2
0
2
0
0
0
0
1
0
1
2
0
1
1
2
2
2
2
1
0
0
2
1
0
1
1
0
1
1
0
2
1
1
0
2
1
2
2
1
0
0
1
0
0
0
2
0
1
0
0
1
1
2
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
2
0
0
2
1
0
0
2
0
0
2
1
1
1
1
0
2
2
0
0
1
0
0
0
1
0
0
2
1
1
0
0
0
2
0
0
2
2
1
1
0
0
1
1
2
1
1
2
1
0
0
2
2
0
0
2
1
1
4
0
1
0
1
0
2
1
1
2
2
1
0
2
0
0
2
2
2
0
0
1
2
0
1
0
1
1
1
1
1
1
1
2
2
1
0
0
2
1
0
1
2
1
2
1
0
1
0
0
0
1
0
0
1
0
0
1
3
0
0
1
1
0
2
1
2
0
1
0
1
0
1
0
0
0
1
2
2
0
1
0
0
1
1
1
1
0
0
0
1
2
2
2
1
1
0
0
1
0
0
0
0
1
2
1
2
0
0
0
0
1
1
2
0
2
0
0
1
1
1
0
1
2
0
2
0
0
0
0
1
1
1
1
1
0
0
1
1
3
1
2
0
1
0
1
1
0
0
1
0
1
0
2
0
2
0
2
2
0
1
0
1
1
0
2
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
1
0
2
2
2
1
0
2
0
0
1
0
2
0
0
1
2
1
0
0
1
1
0
0
2
2
0
2
0
0
2
2
1
1
2
2
0
0
2
1
1
0
1
0
1
0
1
2
0
0
1
1
0
2
0
0
1
0
1
2
2
1
1
0
2
1
0
0
2
0
2
1
0
1
0
0
2
1
1
2
1
1
2
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
1
2
0
0
2
0
0
2
0
0
0
2
1
2
1
1
1
1
2
2
1
0
0
2
0
1
1
1
1
2
0
1
0
3
1
1
0
1
0
2
2
0
1
1
0
2
1
1
0
0
2
2
0
1
2
1
1
2
1
0
1
2
1
0
2
0
0
0
2
0
0
1
0
1
0
1
1
2
1
1
1
0
0
2
1
0
1
0
1
2
0
1
1
1
1
0
2
2
1
1
1
1
1
1
2
2
0
0
1
0
1
2
2
1
0
1
1
1
1
0
2
1
0
1
2
1
1
0
0
1
1
2
1
0
0
1
2
2
1
0
0
1
0
2
0
1
2
1
1
1
0
2
1
2
2
0
1
1
0
1
2
2
2
2
1
0
1
2
0
0
1
2
0
2
0
2
2
0
0
1
0
3
0
0
0
0
1
0
2
2
1
0
2
0
1
1
0
0
0
2
0
0
1
0
0
1
2
1
0
1
1
2
0
2
1
2
1
0
2
0
1
1
1
1
2
2
0
0
2
0
0
1
1
2
0
1
1
0
2
0
1
0
0
2
0
0
1
1
1
1
1
0
0
1
0
0
0
1
0
0
2
2
1
0
1
1
0
0
2
3
2
1
2
0
0
0
1
0
2
0
0
2
2
0
0
0
0
1
0
2
0
0
0
2
1
2
2
2
2
0
0
0
1
1
1
1
0
1
1
2
0
0
0
1
0
1
0
0
0
2
0
2
2
0
1
1
0
0
1
2
2
2
2
0
0
0
1
0
1
2
2
2
0
0
1
0
1
2
1
2
0
0
1
2
1
0
2
0
0
0
1
2
2
2
1
2
1
0
0
1
1
0
2
0
0
1
1
2
0
2
1
0
2
0
0
1
1
0
0
0
0
0
2
0
1
1
1
1
2
2
1
2
2
0
0
0
1
2
0
1
1
1
3
1
2
0
1
2
0
0
1
0
0
0
0
1
1
0
0
0
0
1
1
0
1
1
0
1
0
0
0
2
0
0
0
0
1
0
0
0
1
1
0
2
2
1
0
2
1
0
0
1
2
2
1
1
1
0
1
1
3
2
1
0
1
2
1
0
1
2
0
1
2
0
0
1
0
0
1
1
2
1
0
0
2
1
2
1
0
1
2
2
2
2
1
1
0
1
1
1
1
0
1
2
1
1
1
1
0
0
0
1
2
0
1
1
0
0
0
0
0
1
0
0
2
1
1
1
1
0
0
0
1
1
1
2
0
2
0
2
2
2
1
2
0
1
1
0
0
0
2
0
1
0
3
1
2
0
0
1
2
1
2
0
0
2
0
0
1
0
0
1
0
1
1
0
0
1
0
1
1
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
1
2
0
4
0
1
1
0
3
2
0
1
1
1
1
2
2
0
0
0
1
1
0
2
0
0
1
3
0
0
1
0
0
1
1
0
0
2
5
0
1
0
0
0
0
1
2
2
0
1
0
1
1
0
1
0
0
0
2
2
0
1
0
0
2
1
0
0
0
2
1
0
0
1
0
0
1
0
0
0
2
0
0
1
1
0
1
1
1
0
0
1
1
2
2
0
6
2
2
1
1
1
2
2
2
1
3
0
0
1
0
1
0
0
1
1
1
4
0
1
0
2
0
2
0
0
0
0
0
0
2
1
0
2
0
0
0
2
1
1
0
2
0
2
1
0
0
0
1
2
2
1
1
2
0
2
2
2
0
1
0
2
0
2
1
0
1
2
1
1
0
0
2
1
1
0
0
0
1
2
2
1
0
0
0
0
0
0
0
2
1
0
2
2
0
1
1
0
0
0
0
0
0
1
0
0
1
1
0
1
1
5
0
1
0
0
0
0
1
1
2
0
0
1
1
1
0
1
2
1
1
2
1
0
2
0
2
1
0
1
1
1
0
1
3
1
0
2
1
2
1
0
0
0
0
0
1
2
0
2
0
2
0
0
2
0
0
1
0
1
0
0
1
0
0
0
2
1
2
0
2
0
1
1
1
0
1
0
2
0
2
2
0
0
2
1
2
2
1
1
0
1
1
1
1
0
0
1
0
0
0
1
1
1
0
3
2
0
1
1
2
1
1
0
1
1
2
1
0
0
0
4
2
1
0
1
1
2
0
0
1
2
1
0
0
0
1
1
0
0
2
0
1
1
2
1
0
0
0
1
1
2
0
2
0
1
1
0
0
0
1
1
2
0
0
0
0
0
1
1
1
0
2
0
1
0
0
1
1
0
0
0
2
2
2
0
0
0
1
2
1
0
0
1
0
2
0
3
1
2
1
0
0
2
12
0
2
0
1
1
0
0
1
2
1
0
0
2
2
1
0
0
1
0
0
0
0
1
2
2
2
2
1
0
0
0
1
0
1
0
1
1
1
0
0
0
1
1
1
1
0
1
1
0
0
0
0
0
2
2
2
0
0
1
1
0
1
2
2
0
1
0
1
2
1
0
0
0
1
1
0
0
1
0
2
0
2
0
1
1
1
0
0
0
2
0
1
1
2
2
0
2
0
1
1
3
0
0
1
1
2
0
0
2
0
0
1
0
0
2
0
2
1
1
1
0
1
1
2
2
2
0
0
0
1
1
0
1
4
1
1
0
2
0
1
0
0
1
0
0
0
2
0
4
0
0
1
0
0
1
0
1
0
1
0
0
0
1
0
0
1
2
0
0
0
1
0
1
0
1
2
0
0
1
0
0
0
1
1
2
0
0
2
1
2
1
2
2
0
2
1
1
0
2
2
0
2
1
0
2
2
0
0
1
1
2
0
1
1
2
2
2
0
0
1
1
2
2
1
0
0
0
1
2
2
0
0
1
0
1
0
1
1
1
2
1
0
1
0
0
1
1
0
0
2
1
0
0
2
3
3
2
2
0
1
2
1
0
2
1
1
0
0
0
1
0
1
0
2
2
0
0
1
0
0
0
0
2
0
1
2
2
0
1
1
2
1
0
1
1
2
1
1
2
0
1
2
1
2
0
1
2
1
0
0
0
0
1
0
1
1
2
0
1
1
2
3
2
0
2
0
1
0
2
1
0
0
0
1
1
1
0
0
2
2
1
3
2
1
0
1
3
0
1
0
0
1
0
0
0
0
2
1
1
2
0
1
0
0
1
1
2
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
2
1
1
1
3
0
2
1
2
2
1
1
0
0
2
1
1
1
0
1
0
1
1
0
0
1
1
0
4
2
0
0
2
2
1
0
2
1
4
0
1
1
0
0
1
1
0
0
0
1
2
0
2
1
0
0
0
1
1
0
1
2
2
0
0
0
0
1
1
0
0
2
1
1
0
1
1
0
1
2
3
0
1
0
3
2
1
0
0
1
0
2
1
0
1
1
1
0
2
0
1
1
0
3
2
0
3
0
2
2
2
0
2
0
1
0
1
1
0
2
0
1
1
1
2
1
1
0
2
0
1
1
0
0
0
2
2
2
0
0
0
0
0
0
2
1
2
0
1
1
3
2
1
0
0
1
1
1
0
2
1
0
1
0
1
0
0
0
0
1
0
0
2
0
1
1
0
1
1
2
0
1
0
1
0
0
0
0
0
0
2
0
1
1
0
0
2
1
3
2
0
2
0
0
0
1
2
1
1
0
0
0
0
1
0
1
0
2
0
0
2
2
0
0
2
2
0
0
1
0
1
0
0
0
0
0
2
0
2
1
0
1
2
0
0
0
2
1
0
1
0
1
2
1
0
0
1
1
0
0
1
1
0
3
0
1
2
2
0
2
0
2
0
1
2
2
1
2
0
1
1
1
0
1
0
2
0
1
2
0
0
0
0
2
0
1
1
0
0
2
0
1
2
0
0
1
0
1
1
0
1
1
0
0
1
2
1
0
0
0
1
2
0
1
1
1
1
1
0
1
2
1
1
1
0
0
1
0
1
1
0
2
0
2
1
2
0
0
0
0
2
0
1
0
1
0
1
0
1
1
1
0
1
0
0
2
2
1
4
1
0
1
0
2
1
1
0
2
2
0
1
2
1
0
0
0
0
1
2
1
0
0
1
1
2
0
2
0
0
1
1
0
1
0
1
3
3
1
2
0
0
0
2
0
0
1
1
0
0
0
2
0
1
0
2
0
0
0
1
2
1
0
2
0
0
0
1
0
0
1
0
1
1
0
0
1
1
0
1
0
0
1
2
1
1
2
0
1
0
0
1
0
0
1
0
0
1
0
1
1
0
0
2
0
1
1
0
1
2
0
1
2
0
2
2
1
1
1
1
0
2
1
0
0
0
2
0
0
0
1
1
1
1
0
1
1
0
1
1
2
1
2
2
0
0
0
0
2
0
2
0
5
1
0
0
0
0
2
0
2
0
1
0
0
0
0
2
1
0
2
1
0
0
1
0
0
0
1
1
1
1
4
0
0
0
0
0
1
0
1
1
3
2
0
2
0
2
1
0
0
0
1
0
0
1
2
1
0
1
0
2
0
2
1
2
2
0
0
0
0
1
0
2
1
1
0
0
1
0
2
1
1
1
0
1
0
2
0
0
1
0
1
0
2
0
1
2
0
1
2
2
0
0
0
0
1
0
0
1
0
1
0
0
1
2
0
1
1
1
0
0
1
2
0
0
0
0
1
1
2
1
0
1
1
2
2
1
4
0
2
0
0
2
1
0
1
1
0
1
2
0
2
0
1
2
1
1
2
0
0
0
2
0
1
2
0
2
1
0
0
0
0
1
2
0
1
0
0
1
1
0
0
1
0
0
0
2
1
2
1
2
0
1
1
0
1
2
1
0
0
0
2
0
0
2
1
0
1
2
0
0
0
0
1
2
1
1
1
2
1
0
2
1
0
0
3
0
0
0
1
1
0
1
1
0
0
0
0
1
1
1
1
2
1
2
1
1
1
2
0
2
1
0
0
0
2
1
1
1
1
0
0
2
2
1
0
1
1
2
0
0
0
1
2
0
2
0
2
2
2
2
0
3
0
0
1
1
0
0
0
2
0
0
0
2
0
2
2
2
0
1
0
1
0
1
1
0
1
0
1
1
2
1
0
1
2
0
1
0
1
0
1
1
0
0
2
0
0
0
1
1
0
1
1
1
2
0
0
0
0
1
2
0
1
0
1
1
1
0
2
0
1
1
2
0
0
0
1
0
0
2
0
0
2
1
1
0
0
2
1
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
1
1
2
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
1
1
1
0
1
0
2
0
0
2
1
0
2
1
0
1
0
2
1
0
0
1
0
0
0
2
0
1
1
0
12
2
2
1
1
0
0
2
0
1
1
1
0
2
0
0
2
1
1
2
1
1
0
0
1
2
0
0
0
2
3
0
2
0
0
1
2
0
0
1
1
1
2
2
1
0
1
1
2
0
2
0
1
0
0
0
0
0
0
0
2
1
1
1
0
1
0
1
1
1
0
5
0
1
2
0
1
1
2
0
1
2
2
1
0
1
0
0
1
0
1
0
1
2
2
0
1
0
0
2
1
2
0
1
1
2
2
1
0
2
2
0
2
2
1
2
1
2
1
2
0
1
1
1
0
0
2
1
2
0
0
1
0
2
2
0
0
0
1
1
1
1
1
0
0
0
2
1
1
0
2
0
2
0
0
0
0
0
4
2
1
1
1
2
0
1
0
0
0
1
0
0
1
1
2
0
3
1
2
0
0
0
0
1
2
0
0
1
2
2
1
1
0
1
0
1
0
0
2
0
1
0
0
1
0
0
1
2
1
1
1
3
1
0
1
0
2
1
0
0
1
0
1
1
1
0
2
0
2
0
0
0
3
2
1
1
0
1
1
2
2
0
0
0
0
2
1
1
1
1
0
1
1
0
0
2
1
0
0
1
1
1
0
0
1
0
1
1
3
0
0
2
2
1
1
0
1
1
1
0
0
1
3
0
2
0
0
1
0
0
2
1
2
0
2
0
3
1
2
1
1
0
2
2
0
3
2
1
2
0
1
0
0
0
1
1
1
0
1
0
2
0
1
2
0
1
2
2
1
1
2
1
2
2
1
1
0
1
1
0
0
2
0
0
1
2
1
1
2
1
1
1
1
0
0
2
1
1
0
0
1
0
0
0
1
0
2
1
0
2
2
3
0
0
0
1
1
0
0
1
1
0
1
0
0
1
2
2
2
2
0
1
1
3
0
1
1
1
0
1
0
1
0
0
0
1
1
1
2
0
1
0
2
1
0
0
0
0
1
0
0
0
0
0
1
3
1
1
1
1
1
0
0
2
0
0
0
2
1
1
1
0
0
1
1
1
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
1
1
0
0
1
2
0
2
2
0
2
0
1
0
0
1
2
2
0
2
2
1
0
1
1
0
1
0
1
1
0
1
2
0
0
1
0
2
3
1
0
1
0
0
1
0
2
1
0
3
0
1
0
3
2
0
1
0
2
2
0
1
2
2
0
3
1
1
0
2
1
0
2
1
2
1
0
0
1
1
0
0
1
0
0
0
2
1
1
1
0
1
1
1
0
1
1
2
1
1
2
2
1
0
1
1
2
2
1
0
0
2
1
2
3
1
0
3
0
1
0
0
1
2
2
0
1
2
2
0
0
0
1
0
1
0
2
1
0
0
1
2
1
1
2
1
1
0
1
0
0
0
2
0
2
2
2
0
0
1
0
0
1
1
0
0
1
0
0
2
2
0
0
2
1
2
0
1
0
0
2
2
0
1
0
0
1
2
1
0
1
0
1
0
1
1
2
1
0
0
1
0
0
0
0
0
2
1
1
0
2
0
0
0
0
1
2
1
0
2
1
1
2
1
0
1
0
0
0
0
0
1
0
0
1
1
0
0
1
1
1
0
2
0
1
0
1
2
2
2
1
1
1
0
2
2
1
0
1
1
0
1
2
1
0
0
1
0
2
3
1
0
0
1
1
1
0
3
0
1
2
0
1
0
0
1
1
1
0
1
1
1
0
1
1
3
2
0
1
1
1
0
1
0
0
0
1
0
0
2
1
2
0
0
2
1
0
2
2
0
2
0
1
1
0
2
0
0
2
2
0
2
1
0
4
0
1
0
2
1
1
0
3
0
1
2
0
2
0
0
1
2
1
0
1
1
1
1
1
1
0
0
1
0
0
0
0
2
2
1
0
0
0
0
1
0
0
1
2
0
1
2
0
0
0
1
1
2
0
1
2
2
2
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
2
0
1
2
0
1
0
0
2
0
1
0
1
1
0
0
2
1
0
2
0
0
1
2
1
1
0
2
1
0
1
1
2
0
2
1
1
2
0
0
0
2
1
1
2
1
1
0
1
2
0
2
0
0
1
2
0
1
2
2
2
2
0
1
1
1
1
2
1
0
2
1
0
3
2
0
1
1
2
1
1
0
1
0
0
1
0
0
1
0
0
0
1
0
0
2
1
1
0
0
0
0
0
1
1
0
0
1
0
0
1
0
1
0
0
1
1
1
2
2
1
0
1
1
1
1
0
0
0
0
1
0
1
1
2
0
0
1
2
0
2
1
0
1
0
1
0
2
0
2
2
1
0
3
2
1
1
0
2
1
1
1
0
1
1
0
1
1
0
0
0
1
1
0
0
1
1
0
0
2
1
0
0
0
0
1
1
0
0
1
2
2
0
0
1
2
0
1
0
0
0
0
1
1
1
2
2
0
0
1
1
0
1
4
2
1
1
0
0
0
1
1
1
0
0
0
2
0
0
0
0
0
1
0
1
0
0
1
1
1
1
0
0
0
0
0
0
1
1
0
1
1
2
2
0
2
0
1
0
0
1
0
1
0
0
0
0
0
0
1
1
0
2
1
1
2
1
1
2
0
0
0
0
0
1
2
0
0
1
4
0
2
1
0
0
0
1
0
0
2
0
1
1
1
0
0
2
0
1
0
1
0
1
0
2
0
0
2
2
0
2
1
1
0
1
0
0
1
0
0
0
1
1
0
0
0
2
0
0
1
2
2
2
0
0
0
0
0
0
1
1
1
1
0
0
1
0
0
0
0
2
0
0
1
0
0
2
1
0
1
0
1
0
0
1
0
1
0
0
2
0
0
2
2
0
0
1
1
1
2
1
0
0
0
2
2
1
2
0
1
0
0
0
0
0
0
0
1
0
1
0
1
2
2
0
0
1
2
1
1
0
2
0
1
0
0
1
0
0
0
0
1
2
0
0
1
2
1
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
2
2
2
0
1
1
2
1
0
1
0
0
0
1
1
0
2
1
1
1
1
1
0
0
0
0
1
0
1
2
0
1
0
2
0
1
2
1
0
1
1
2
0
0
0
2
1
2
2
0
1
0
2
0
2
2
1
0
0
1
2
2
1
2
0
1
2
0
0
1
0
2
1
1
1
2
0
0
1
1
1
1
0
9
1
2
0
2
1
2
1
1
1
2
0
0
1
2
1
1
1
2
0
1
1
0
0
2
0
0
1
2
2
1
0
0
0
0
1
0
0
1
1
1
1
3
1
1
0
0
1
2
0
1
1
2
0
1
2
0
1
0
0
0
1
2
1
0
0
1
1
1
1
1
0
1
0
1
0
1
1
1
1
2
0
2
1
0
0
1
0
2
1
0
0
0
1
0
0
0
0
1
2
0
0
1
1
0
0
0
1
2
0
1
0
1
0
2
1
1
0
0
0
2
0
0
0
1
0
0
1
0
0
0
2
0
0
2
0
1
1
1
0
0
0
2
1
0
0
2
0
0
2
2
1
0
0
0
1
0
0
1
0
0
0
2
0
2
0
0
1
1
0
1
0
2
1
0
0
1
0
2
0
1
1
1
2
0
2
2
0
0
1
0
0
1
1
1
0
0
2
2
0
0
0
0
2
1
0
0
0
0
2
0
2
1
0
2
2
1
0
1
0
0
0
1
1
0
0
1
0
1
0
2
0
1
1
2
1
0
0
0
1
1
2
2
0
0
1
0
0
0
0
0
1
1
1
2
0
1
1
0
1
1
0
0
1
1
0
1
2
1
1
0
2
0
0
2
2
1
1
1
1
2
0
1
0
0
0
2
1
0
1
0
0
0
2
0
1
0
2
0
1
1
2
1
1
1
2
0
1
1
2
1
1
1
1
2
2
1
1
2
1
0
0
0
1
1
0
0
2
0
1
0
1
0
0
1
2
2
1
1
1
2
0
1
0
0
0
2
0
1
1
2
0
1
2
0
2
0
0
0
1
2
0
2
1
0
2
1
1
0
0
1
0
0
0
6
1
0
1
3
0
0
1
1
0
0
1
2
0
1
0
1
0
1
1
0
0
1
1
2
0
1
1
1
0
0
2
0
0
0
0
0
1
2
1
1
2
1
2
3
2
0
2
2
2
0
1
1
2
0
1
1
1
0
0
1
2
0
0
1
2
2
1
0
0
2
2
1
2
2
2
2
2
0
1
1
0
0
2
2
0
2
0
1
0
1
2
1
0
2
0
2
1
1
1
1
2
1
0
2
0
2
1
1
0
2
0
1
1
1
0
1
0
2
1
1
0
0
0
1
0
0
0
1
1
0
0
1
1
1
1
1
0
0
0
2
0
0
0
0
1
0
0
0
2
0
1
0
1
3
2
1
0
0
2
0
1
0
0
1
0
0
0
0
1
2
0
2
2
0
1
2
0
2
1
2
0
2
1
2
2
0
2
2
1
2
0
2
2
0
2
0
2
1
1
1
0
0
0
2
2
1
0
2
2
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
1
2
1
1
2
0
2
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
1
1
1
0
1
2
1
0
1
2
1
1
0
0
1
0
0
0
1
1
1
0
1
0
1
1
0
0
2
1
0
1
0
0
0
1
4
1
1
0
1
0
1
1
2
0
0
0
0
0
0
1
2
1
1
1
1
0
0
2
0
0
0
1
0
2
1
2
0
1
0
2
0
1
0
0
1
1
2
1
1
1
1
1
0
1
0
2
0
0
0
3
0
2
0
1
0
1
1
2
0
0
1
0
2
2
2
0
1
1
1
1
0
0
3
2
0
2
1
0
0
1
1
0
1
1
0
0
1
0
2
2
0
0
0
1
0
1
0
1
1
2
1
1
0
1
0
1
1
2
1
0
1
1
1
0
0
1
0
0
0
0
0
0
2
1
0
1
2
0
0
1
0
0
1
1
0
0
2
0
1
1
0
1
0
1
1
1
1
1
1
0
0
1
0
1
2
1
0
2
1
1
2
2
1
1
0
1
0
1
2
1
2
0
1
0
1
2
1
2
1
0
0
2
0
1
1
0
1
3
0
1
1
1
1
0
1
0
1
0
0
2
1
0
2
0
1
0
0
1
0
1
2
0
0
1
0
0
0
1
1
2
2
2
2
1
1
0
0
1
0
2
0
1
0
2
0
0
0
2
0
0
1
0
1
2
1
2
1
2
0
0
0
0
2
2
2
0
1
0
1
0
0
2
2
0
0
0
0
2
2
0
2
2
1
2
1
0
0
1
1
1
0
2
0
0
1
2
2
1
0
0
1
2
1
0
1
0
2
2
1
2
2
1
2
0
1
1
2
0
2
0
1
0
1
1
1
1
1
0
2
1
0
1
0
1
0
2
0
8
0
0
1
0
1
2
1
2
0
0
1
2
2
1
2
0
1
1
0
0
0
0
2
1
1
1
1
1
0
2
0
0
0
2
0
1
0
0
1
1
0
1
1
1
1
1
0
2
0
0
0
1
1
2
0
2
0
0
0
1
1
2
1
0
2
0
0
1
0
2
1
1
2
3
0
0
1
0
0
0
1
2
0
0
0
1
0
1
1
0
0
2
1
2
2
1
1
1
0
2
3
0
1
1
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
2
1
2
0
2
2
0
2
1
2
2
0
2
1
1
0
3
1
2
1
2
1
0
0
0
1
1
0
1
0
0
1
0
0
1
1
0
0
0
2
2
1
0
1
1
1
2
0
0
1
2
1
0
2
0
0
2
0
0
2
1
0
0
0
2
1
1
0
1
1
1
0
0
0
2
1
0
0
2
1
0
1
2
0
0
0
0
0
2
1
0
0
0
0
2
1
0
0
2
1
0
0
2
1
2
0
0
0
1
0
0
1
2
0
1
2
0
1
2
1
0
2
2
2
0
1
0
1
0
1
1
1
2
1
3
1
1
1
0
0
0
0
2
0
2
1
1
1
1
1
0
0
0
1
0
0
0
2
2
1
2
1
0
0
1
0
1
0
0
0
1
1
0
0
1
0
2
0
1
0
1
0
2
1
1
1
0
2
2
0
1
0
0
2
1
0
2
0
2
0
2
1
0
0
0
2
0
0
0
0
2
1
0
2
0
0
0
0
1
0
2
2
1
1
0
2
0
0
1
1
1
1
1
0
3
0
0
2
0
1
1
0
2
1
1
0
2
1
0
2
2
1
2
1
1
0
0
1
0
1
2
1
0
1
1
1
1
2
1
0
0
0
0
1
1
0
1
2
1
0
1
2
1
1
0
0
1
1
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
2
0
1
1
0
0
1
0
2
0
0
0
0
1
1
1
1
2
2
2
1
0
1
1
0
0
0
0
0
2
1
2
0
2
1
1
0
2
1
1
1
1
1
0
0
0
2
0
0
1
1
0
0
0
2
2
1
0
0
1
2
1
1
0
0
2
0
2
0
0
2
1
1
1
0
1
1
2
0
1
0
2
1
0
1
2
1
2
0
1
2
2
0
0
2
0
1
0
1
1
0
1
1
0
2
0
4
2
2
1
0
1
0
2
2
4
4
2
1
1
0
0
1
1
1
1
2
1
0
1
1
2
1
1
0
2
0
0
1
0
1
1
0
5
0
1
0
1
0
1
2
1
1
1
0
0
0
0
0
1
0
1
0
0
1
0
1
0
2
3
0
2
0
0
2
2
1
1
2
0
2
0
0
1
1
1
1
1
0
1
0
1
2
1
0
1
2
2
1
0
0
1
2
0
1
1
1
0
2
1
0
3
2
0
3
0
0
2
0
2
0
0
0
2
2
2
0
1
2
0
2
0
1
0
0
0
0
4
0
0
1
0
0
0
1
0
1
1
0
1
0
0
0
1
1
1
0
1
1
0
0
0
0
0
0
2
1
1
0
0
0
4
1
1
1
0
0
2
0
0
0
0
2
0
2
0
1
1
0
2
2
0
1
0
0
2
2
1
2
2
1
2
0
1
2
2
0
0
2
2
1
0
0
2
0
1
0
2
1
0
2
0
0
1
0
1
1
0
2
0
2
1
1
2
1
0
0
2
0
0
1
1
1
1
2
2
0
2
1
2
1
2
1
2
0
2
0
1
1
1
2
0
0
0
0
0
1
0
2
0
1
3
0
1
3
0
1
1
1
1
0
0
2
1
2
0
1
1
0
2
1
0
0
0
1
2
0
1
1
0
1
1
1
1
0
0
0
0
2
0
2
0
1
1
4
1
0
2
0
1
2
0
2
1
1
2
0
1
1
0
2
2
0
0
0
0
1
2
1
0
1
1
1
0
0
0
1
0
0
1
1
0
2
1
0
1
1
1
0
2
1
0
1
0
0
1
1
2
0
0
1
1
2
1
0
0
1
0
2
1
1
1
0
1
0
1
0
1
2
1
2
0
0
1
0
0
0
2
0
0
2
0
0
1
0
2
0
0
0
1
2
0
2
2
0
2
0
0
2
0
1
0
0
0
1
1
1
1
2
2
0
0
0
2
1
0
0
0
0
1
0
1
2
0
0
0
0
1
2
1
2
0
0
0
1
1
1
0
0
2
0
1
1
1
0
1
1
2
2
0
1
2
2
2
0
0
0
1
1
1
2
1
0
1
0
2
0
0
0
0
0
0
0
1
2
0
0
0
2
0
2
0
0
1
0
1
1
0
1
2
0
0
1
0
1
1
0
0
0
0
0
0
2
2
1
2
1
2
0
0
0
1
0
3
1
0
1
1
1
0
0
1
0
0
2
1
1
2
0
2
0
0
2
1
0
2
0
0
1
0
0
0
0
0
2
1
3
2
2
0
0
1
2
1
2
0
2
0
0
0
0
0
2
1
1
0
0
1
0
0
0
0
1
0
2
0
0
0
2
1
0
0
1
2
2
0
1
2
1
0
0
1
1
2
0
1
0
0
0
1
1
0
1
0
0
1
0
0
0
1
2
0
0
0
1
8
1
1
1
0
2
0
0
1
1
0
0
2
1
2
0
0
1
3
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
1
1
1
2
0
1
0
1
1
0
0
1
1
1
0
0
0
1
0
2
0
1
2
0
1
1
0
2
1
1
0
2
0
0
1
1
2
1
0
0
1
1
1
2
1
0
0
0
3
1
1
1
1
1
0
1
1
0
2
0
1
0
2
2
2
1
0
1
2
2
0
1
0
0
2
0
0
1
2
2
1
0
0
0
1
1
1
2
0
2
2
0
1
1
1
1
0
0
0
1
1
0
2
0
1
1
1
1
0
1
1
0
1
0
1
1
2
0
1
8
1
1
1
0
0
1
1
0
1
1
1
1
0
0
0
0
0
0
0
1
2
1
2
0
1
0
0
0
0
1
1
0
1
1
2
1
0
1
2
1
0
0
1
1
0
2
0
0
0
0
1
1
1
1
1
1
1
1
2
1
1
0
2
0
0
0
0
2
1
1
1
1
0
1
1
0
1
0
0
3
1
1
0
1
1
2
1
1
0
2
1
0
1
1
1
1
2
0
2
0
0
0
1
1
2
1
1
1
2
1
1
0
0
1
0
0
2
0
2
2
0
2
0
1
3
1
1
2
1
0
1
0
1
0
1
0
1
1
1
0
0
0
2
2
1
2
0
2
1
0
0
2
0
2
1
1
2
0
2
0
0
2
1
0
1
0
1
1
1
1
2
0
0
1
1
1
0
0
0
0
1
2
0
1
3
0
0
0
2
1
0
0
1
1
0
1
2
0
0
0
0
0
1
0
1
2
2
0
0
0
1
1
0
2
0
0
1
0
0
1
1
0
0
2
0
3
1
0
4
1
2
2
2
1
0
0
1
1
0
0
0
2
2
3
1
1
1
0
1
1
0
0
2
0
1
1
0
2
2
2
0
1
0
2
0
0
1
1
1
1
0
0
3
1
1
2
2
2
1
1
2
0
1
0
1
2
0
2
0
2
1
0
2
0
1
0
2
2
1
1
0
2
0
1
2
2
0
0
0
0
0
0
0
0
0
1
0
2
1
1
1
1
1
0
1
2
0
0
2
0
1
1
2
0
1
1
0
1
1
0
1
1
1
0
0
0
1
3
0
4
2
1
0
0
0
0
0
1
1
0
1
4
0
1
0
1
0
1
0
0
1
0
0
1
2
1
0
0
1
1
2
1
1
1
1
2
2
2
1
1
1
0
1
2
1
0
1
2
1
1
0
1
1
1
1
0
0
0
0
2
0
0
0
1
0
0
1
0
2
1
1
1
0
0
1
0
0
1
1
0
0
0
0
1
0
1
2
0
2
2
0
0
0
2
0
0
0
0
1
1
0
0
1
0
0
1
0
1
0
0
1
0
0
0
1
0
0
2
1
1
1
0
0
0
0
0
0
0
0
1
0
0
1
2
3
0
1
1
2
2
1
0
0
0
0
3
2
1
1
1
2
2
1
1
1
1
1
0
1
1
2
1
1
1
0
1
0
1
2
1
2
0
0
2
1
1
0
0
1
0
0
1
0
1
0
2
0
0
0
0
0
0
1
2
2
0
1
0
0
0
1
1
0
2
2
1
0
1
0
1
1
1
1
0
1
0
0
2
0
0
0
1
2
1
0
2
1
0
0
1
1
0
2
0
0
0
0
0
0
0
1
2
0
1
0
0
0
1
1
0
1
1
0
0
2
0
0
0
1
1
1
0
0
0
2
1
2
2
0
0
1
1
2
1
0
2
1
1
0
2
0
0
0
0
1
0
1
1
1
1
1
2
0
0
0
2
0
2
0
1
1
1
1
0
1
1
0
1
0
2
0
2
1
0
0
0
0
0
2
0
1
3
0
1
0
1
1
2
2
2
1
0
1
0
1
0
1
1
0
1
1
1
2
0
2
0
1
0
0
1
1
0
0
1
0
0
1
0
0
1
0
1
2
0
1
1
1
0
0
0
1
2
0
1
1
0
1
2
1
1
1
2
0
1
0
2
3
1
2
2
2
1
1
0
1
0
0
0
2
0
0
1
1
1
2
0
1
0
2
1
0
2
0
1
3
0
0
2
0
0
0
1
0
1
2
1
0
4
1
0
0
2
1
1
1
0
1
0
2
1
0
2
0
0
1
2
0
0
1
1
0
1
0
1
1
1
1
1
1
2
0
1
0
2
1
2
0
0
2
1
0
2
0
0
1
0
1
3
0
1
1
0
1
1
3
1
1
0
2
0
0
1
1
0
0
1
0
2
2
1
0
0
2
1
2
1
1
2
2
0
1
1
0
0
0
0
1
1
2
0
1
2
0
1
1
1
0
0
1
0
0
2
2
0
0
2
0
1
2
1
1
2
0
1
0
0
1
0
1
1
2
1
2
0
0
1
0
1
1
1
2
1
1
1
0
0
4
1
0
1
2
1
1
2
1
0
0
0
1
0
2
0
2
0
0
2
0
0
2
1
0
0
0
1
0
0
0
1
0
0
0
1
1
1
0
0
0
1
0
1
1
2
2
1
0
0
1
1
0
0
1
0
1
1
1
1
0
1
1
1
2
1
1
1
0
0
0
0
0
2
1
0
0
0
1
0
0
2
1
0
2
0
0
1
0
4
1
0
0
0
1
1
1
1
1
0
2
1
0
1
0
0
0
0
1
0
0
0
2
0
0
2
1
2
2
0
0
2
1
0
0
0
0
2
0
1
1
1
2
1
0
0
0
1
2
0
2
0
0
0
0
2
1
1
1
0
1
2
3
2
2
0
0
4
1
2
1
2
1
0
0
0
0
1
0
0
0
0
2
0
2
0
1
1
1
0
2
2
0
0
1
2
0
2
0
1
3
1
0
1
2
1
1
1
1
0
0
1
0
1
1
0
0
0
0
0
0
1
1
0
0
0
2
1
1
1
0
2
2
0
1
0
1
1
0
2
1
2
0
1
0
0
1
0
1
1
0
1
1
1
0
1
0
1
0
1
2
2
0
0
1
1
1
2
0
2
1
1
2
1
0
2
0
2
2
1
1
1
1
0
0
1
0
1
2
1
2
0
1
1
1
0
0
1
1
0
1
0
1
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
2
6
1
3
0
1
2
0
1
0
1
0
1
1
2
0
1
1
2
1
0
1
0
2
1
2
0
2
0
2
1
1
1
1
0
0
1
3
0
0
2
2
0
0
2
0
2
2
1
2
0
1
0
1
0
0
0
2
1
0
0
0
1
0
1
1
0
0
2
1
0
10
1
1
0
1
1
0
1
2
2
1
1
2
0
0
0
1
1
2
1
2
0
2
2
2
1
0
0
0
0
0
2
0
2
1
1
0
2
0
1
1
0
0
1
1
1
0
0
0
0
1
0
0
1
1
2
1
1
2
1
2
0
1
1
3
0
1
2
1
0
0
1
0
1
0
1
1
1
1
2
0
2
1
0
2
0
0
2
2
0
1
1
0
0
0
0
0
0
2
0
2
1
2
0
2
1
1
2
1
1
0
0
0
0
2
1
1
0
1
1
0
2
0
0
1
1
1
1
1
2
0
0
2
0
1
0
1
1
0
1
2
1
0
2
2
1
1
2
0
1
0
0
0
0
0
0
0
0
0
1
2
1
0
0
1
0
0
0
1
0
2
1
1
1
1
2
0
2
0
1
2
0
0
1
1
1
2
0
1
1
1
0
0
1
0
1
1
0
1
1
1
1
0
1
0
0
1
0
0
0
2
1
1
1
2
0
0
1
2
1
0
0
0
1
1
7
1
0
1
1
1
1
3
1
1
1
0
2
0
0
1
0
0
0
1
1
0
0
2
0
0
2
0
0
0
2
0
2
0
2
2
0
1
0
0
0
1
0
0
1
2
0
0
2
1
0
0
1
2
0
0
1
0
0
2
1
1
2
1
2
0
0
0
0
1
2
1
1
1
1
0
0
1
0
0
1
0
1
2
1
0
0
1
1
0
1
0
2
1
0
1
4
0
0
0
1
0
1
2
2
1
1
0
1
0
0
0
2
1
1
0
0
0
1
2
2
2
2
0
1
1
2
0
1
1
0
1
1
1
0
2
1
1
0
2
1
0
1
0
1
0
2
0
2
0
1
0
2
0
0
2
2
3
1
0
1
1
2
0
0
0
1
2
0
1
0
0
2
2
1
0
0
1
0
1
0
3
0
0
2
1
0
0
2
1
2
1
0
2
0
0
0
0
1
0
1
0
0
0
1
1
0
2
2
0
0
1
0
0
1
1
1
2
0
1
2
0
0
0
1
0
1
1
1
0
1
1
0
2
3
0
1
1
2
2
0
0
0
1
0
2
0
0
0
0
0
2
0
0
1
1
0
1
0
1
0
1
1
2
1
0
1
1
1
1
0
0
1
0
1
0
1
1
2
0
2
2
0
0
0
0
1
2
1
1
1
0
1
0
0
1
2
1
1
1
2
1
1
0
1
1
0
1
1
0
0
0
2
3
2
1
0
0
0
1
1
0
0
0
0
1
2
1
2
2
2
0
0
0
0
2
0
0
2
1
0
0
0
1
0
1
0
1
0
0
1
3
1
0
1
2
0
0
0
2
3
0
0
1
1
1
0
2
0
0
0
1
1
0
1
1
1
1
2
0
0
2
0
0
2
0
1
0
0
2
1
1
0
1
0
1
0
1
0
0
0
1
1
1
0
0
0
0
2
1
1
1
0
0
2
1
2
1
0
0
0
0
1
0
1
2
1
0
1
1
0
0
0
1
0
2
0
2
0
1
0
1
0
2
1
1
2
0
2
0
0
0
2
0
1
2
3
2
0
0
1
2
2
1
0
1
2
0
1
0
2
0
0
0
2
1
2
0
1
1
0
2
1
0
0
0
2
2
2
1
1
0
1
1
0
1
0
1
1
0
1
2
0
0
1
1
2
2
2
0
0
2
0
1
1
1
0
0
2
2
0
2
2
2
1
0
0
0
1
2
1
1
2
0
0
2
1
0
1
8
0
1
0
0
0
0
2
2
0
0
1
1
0
0
1
1
1
0
2
0
0
0
2
0
1
1
2
2
0
0
1
1
2
0
2
0
2
1
1
1
1
0
2
0
0
0
0
1
1
0
0
0
1
0
2
1
0
1
2
0
2
0
1
1
0
0
2
1
1
1
2
0
2
1
0
0
2
1
1
0
0
1
0
1
2
0
0
2
2
0
1
0
1
2
0
3
1
0
1
0
1
0
2
2
0
0
2
2
0
1
0
1
2
2
2
0
2
2
2
1
0
1
1
1
0
1
1
0
1
0
0
1
2
0
1
2
0
1
4
0
0
1
0
0
0
0
0
0
1
1
1
1
2
0
0
0
2
0
1
2
1
3
2
2
0
1
0
1
1
2
0
0
1
1
1
0
1
2
1
1
1
1
0
0
0
1
1
2
0
2
2
1
2
2
0
0
1
1
0
0
1
1
2
2
0
1
1
0
2
3
2
1
2
2
0
1
0
1
1
1
0
0
1
0
1
1
0
1
0
2
1
3
0
0
2
0
1
0
1
0
2
0
1
2
0
0
1
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
2
0
2
4
0
1
0
1
0
1
0
0
0
0
2
0
2
0
1
0
1
1
1
0
1
1
1
1
1
1
0
1
0
1
1
1
0
0
2
2
2
0
2
3
0
0
0
0
0
2
1
2
1
0
2
0
4
0
0
0
2
0
1
2
3
0
2
1
2
3
2
0
3
0
2
0
0
0
0
0
2
1
2
1
1
0
1
0
2
0
1
1
0
1
2
0
2
0
1
2
1
1
1
0
2
0
2
3
2
1
1
1
0
1
0
1
1
2
1
1
2
0
1
0
0
1
0
2
0
0
1
0
1
3
2
0
2
0
1
0
2
1
2
0
0
2
1
1
1
3
2
0
1
0
1
1
0
1
1
1
0
2
1
0
1
1
0
0
0
2
0
2
0
0
0
0
0
1
1
1
1
0
0
0
2
1
0
0
0
1
0
1
0
0
2
0
1
0
0
1
0
2
0
2
0
0
0
0
0
1
5
1
0
2
1
0
0
1
1
1
0
0
1
0
0
0
2
0
2
2
1
1
1
1
1
1
2
1
0
2
1
1
0
1
0
2
4
1
1
1
1
1
1
1
2
0
2
2
1
0
1
0
0
1
2
2
0
2
0
0
0
0
1
1
1
1
0
0
0
2
0
2
4
0
2
0
0
1
0
2
0
0
1
0
0
1
0
0
3
0
0
1
0
0
1
0
2
1
0
2
0
2
2
0
1
1
1
2
0
1
2
2
0
1
1
3
0
1
1
0
0
0
1
2
0
0
2
1
2
1
1
2
0
2
0
8
0
0
0
0
1
0
0
2
1
0
2
1
1
0
1
1
1
0
1
0
0
1
0
0
1
1
1
1
1
4
1
1
2
2
3
0
0
0
0
1
2
0
0
0
3
0
2
1
1
0
0
0
0
0
0
0
0
2
1
2
2
1
0
3
0
2
2
0
0
1
2
0
0
1
0
2
1
0
0
2
1
1
0
0
0
1
2
2
0
2
0
1
1
1
2
0
0
1
0
1
0
0
0
1
0
0
1
0
1
0
1
1
0
0
2
0
0
2
1
1
2
2
2
0
0
2
0
2
2
1
0
0
1
0
1
0
0
0
1
0
2
1
1
0
0
0
0
1
1
1
1
0
2
0
0
0
0
0
1
1
1
2
3
2
0
3
0
0
1
1
0
0
0
2
2
2
0
0
1
2
2
1
1
1
0
2
0
0
1
0
0
1
1
0
2
1
0
1
2
1
2
2
0
2
1
1
0
0
1
2
1
0
0
0
2
1
2
0
1
1
0
0
2
2
0
0
0
0
0
2
1
0
2
3
1
0
2
0
1
0
1
0
0
0
1
0
1
1
0
0
3
2
0
0
0
0
1
0
2
0
0
0
1
1
0
1
2
0
0
0
2
1
0
0
0
1
2
1
0
2
0
1
2
0
0
0
1
0
1
0
2
0
1
1
0
1
0
0
0
0
4
0
0
1
0
2
0
1
0
0
0
0
2
0
0
0
2
2
0
0
1
2
0
0
1
1
0
0
2
0
0
1
2
0
1
0
0
1
2
0
1
1
0
0
1
0
0
0
0
1
0
1
1
1
0
2
1
0
1
1
0
0
1
0
0
0
1
1
0
1
2
2
0
0
0
0
0
2
1
0
0
1
1
1
1
0
2
2
0
0
0
0
1
2
2
0
1
1
0
0
0
0
0
0
1
1
3
2
1
1
0
1
0
0
2
4
0
0
0
0
0
0
1
1
1
1
1
0
0
0
1
1
2
0
0
0
1
0
0
0
1
2
1
0
1
2
0
0
1
1
2
1
1
1
0
2
0
2
1
0
0
0
0
1
2
0
0
2
1
0
0
0
0
1
1
2
1
0
1
2
1
1
0
0
2
3
2
1
0
0
0
2
2
1
0
0
1
0
0
2
0
2
0
0
0
2
0
0
2
0
0
3
1
1
1
2
0
1
3
0
0
1
2
0
2
2
0
0
2
0
1
0
1
0
1
2
2
0
0
1
0
1
0
1
0
0
0
0
2
1
1
1
0
0
2
0
3
2
0
2
0
0
1
0
0
0
3
1
0
2
0
1
0
0
2
1
0
1
2
1
0
1
1
1
1
2
1
0
0
0
0
0
2
0
1
0
0
1
2
1
0
1
1
1
0
2
1
2
0
2
0
0
0
0
0
2
1
1
2
1
2
0
1
0
1
1
0
1
2
2
1
1
1
1
0
1
0
2
0
0
1
1
1
0
1
1
1
3
0
2
1
1
0
0
0
1
1
1
0
1
0
1
1
0
0
1
0
0
1
0
0
1
1
4
0
1
1
1
0
0
0
0
2
0
1
1
2
0
0
0
0
2
0
0
1
1
1
0
0
1
0
1
1
0
1
0
1
2
1
1
0
0
0
0
0
1
1
0
1
1
0
2
0
2
1
2
1
0
0
2
0
2
2
0
1
0
1
0
0
1
1
0
1
1
2
1
0
1
2
0
1
1
0
1
2
0
2
1
0
1
1
2
2
0
1
1
0
0
2
1
0
0
1
0
1
0
2
1
0
0
0
0
0
1
2
1
1
2
2
0
0
2
1
2
2
0
1
1
1
0
1
0
0
2
0
0
1
1
0
0
2
0
1
1
1
0
0
0
0
1
0
1
1
0
1
1
2
0
0
1
1
1
0
1
1
0
0
0
1
0
0
2
0
0
1
2
1
1
3
1
0
1
0
0
1
2
0
1
0
1
0
0
0
0
1
2
0
1
0
1
0
1
1
2
0
1
1
0
2
1
2
1
3
1
0
1
1
0
2
1
2
0
0
0
2
1
1
1
0
1
1
0
0
0
1
1
0
0
2
0
0
1
4
2
1
2
1
0
1
2
2
0
1
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
1
1
1
1
1
1
0
0
2
0
2
0
0
1
0
1
2
1
1
0
0
2
2
0
1
1
1
0
2
0
1
1
0
2
0
2
1
0
0
0
1
1
2
2
0
1
1
1
0
1
1
1
0
0
2
1
1
0
1
0
2
0
5
2
0
0
0
1
0
0
2
1
2
1
2
2
1
1
0
1
0
0
1
0
0
3
0
1
0
1
1
1
1
1
1
0
0
1
2
0
0
1
1
1
0
0
0
0
1
1
2
0
0
1
2
0
1
0
1
1
0
0
0
0
0
2
2
2
2
1
0
1
1
1
2
1
0
0
0
0
2
2
0
2
2
1
0
0
1
0
2
0
0
1
0
0
0
1
0
1
1
1
1
0
0
1
1
1
1
0
1
0
0
1
0
0
2
1
0
0
0
0
1
0
0
1
1
1
2
1
0
1
1
0
0
1
0
0
1
0
0
2
0
1
0
0
1
2
2
1
0
2
0
0
1
1
0
2
1
2
1
1
0
1
2
2
0
2
0
0
1
0
2
0
0
2
2
1
0
1
1
0
1
0
0
1
2
0
0
0
0
0
0
2
1
1
2
2
1
1
0
1
1
0
0
0
0
2
1
0
0
1
0
1
2
1
0
2
2
0
2
2
1
1
1
0
1
2
1
1
0
0
1
0
1
0
1
1
0
1
0
2
0
1
2
0
0
1
1
2
1
0
1
2
0
0
1
0
1
1
1
0
0
1
1
0
1
1
0
2
2
0
0
0
1
0
2
2
0
0
1
1
0
0
0
0
0
0
2
1
0
1
1
0
3
1
0
1
2
3
0
1
0
1
3
0
2
2
2
1
1
3
0
0
0
0
0
2
1
0
1
2
2
2
2
2
2
0
0
1
2
0
0
1
0
2
1
0
0
2
1
0
2
1
2
0
2
1
1
1
0
1
1
0
0
1
0
3
0
2
0
0
0
0
1
0
1
1
1
0
2
1
1
0
2
2
1
0
2
0
0
1
1
0
1
0
1
0
1
1
2
0
0
0
2
1
2
0
1
0
0
0
2
2
2
2
1
1
1
2
1
1
0
0
1
0
2
1
1
0
2
3
1
1
1
1
2
0
1
0
0
1
0
2
1
1
3
1
0
2
1
2
1
0
0
1
0
0
1
1
1
2
0
0
0
0
0
0
0
0
1
2
0
2
0
1
0
0
1
0
0
1
1
0
1
1
0
2
2
2
1
1
0
0
2
0
1
1
0
0
1
0
0
1
0
0
2
1
0
1
0
1
0
2
1
0
0
1
0
1
0
2
1
2
1
0
2
1
0
0
0
0
1
0
0
0
1
2
0
1
0
2
2
1
0
0
0
0
0
2
2
1
0
3
4
0
2
0
1
2
2
1
1
0
1
2
0
2
1
2
1
1
0
0
0
1
3
1
1
1
1
1
2
0
0
0
0
1
0
0
2
1
0
1
1
0
0
0
0
1
2
0
1
3
0
0
1
2
2
1
1
0
2
1
1
2
1
0
1
0
2
1
0
1
0
2
0
2
2
0
0
0
1
0
1
0
0
1
1
1
0
0
0
0
0
2
0
1
2
1
1
1
2
1
2
0
2
1
2
1
1
2
0
1
0
1
0
0
0
1
2
1
0
1
1
1
2
0
0
1
0
0
0
2
0
0
0
1
0
0
2
0
0
2
1
2
0
2
1
0
0
0
2
2
1
0
1
2
1
0
0
0
1
0
0
0
2
1
0
0
2
0
1
1
2
0
0
0
2
0
0
1
0
0
0
2
0
0
1
0
0
1
2
1
2
2
0
1
0
0
0
0
1
0
0
0
2
1
0
0
0
0
2
1
0
1
1
0
0
1
1
0
2
0
1
2
0
0
0
1
0
2
2
1
0
0
2
0
2
1
2
0
0
0
1
1
2
2
0
0
0
2
2
0
0
1
2
1
2
1
0
2
0
2
2
2
2
0
2
1
0
1
0
0
0
1
1
1
1
1
2
1
0
1
2
1
0
2
0
0
1
1
0
0
2
1
0
3
2
0
2
2
1
1
0
0
2
2
1
2
0
0
2
0
2
0
0
0
2
0
0
2
1
1
0
0
0
1
0
2
0
0
0
1
1
1
2
0
1
1
0
0
1
2
0
0
0
0
0
1
1
0
0
0
0
1
1
0
1
0
0
1
1
1
0
2
0
2
2
0
0
1
2
1
1
0
0
1
1
1
2
1
0
2
1
1
2
1
2
0
1
0
0
2
0
3
0
0
0
2
1
2
0
0
0
0
0
2
1
0
1
0
0
2
2
0
2
0
3
1
2
2
2
1
1
2
0
1
2
1
0
1
2
1
0
2
0
1
1
1
0
2
0
0
2
2
0
1
0
1
0
1
2
1
1
1
0
2
0
1
2
1
0
1
1
1
7
0
1
0
0
0
2
0
2
0
0
1
1
2
0
1
0
0
0
1
0
0
2
1
2
1
0
1
1
2
0
0
1
0
1
1
0
1
0
2
2
2
0
1
2
2
0
2
0
2
0
0
1
1
0
0
1
1
1
1
1
0
0
1
0
0
1
1
1
2
1
0
0
2
1
0
0
0
2
2
1
0
0
0
1
0
1
2
0
2
1
2
0
0
2
0
1
0
1
1
0
1
1
0
1
2
1
1
0
1
0
3
1
4
2
0
2
0
1
1
0
0
1
1
0
2
0
1
1
0
3
1
1
0
0
2
0
2
1
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
2
0
1
1
1
0
1
2
1
2
1
0
0
2
1
0
2
2
0
2
1
1
0
0
1
0
2
1
0
0
0
1
1
0
2
0
1
2
1
0
0
1
2
1
1
0
0
1
0
0
0
0
0
2
2
1
2
1
0
1
1
2
1
0
2
0
1
0
2
0
1
0
1
0
0
0
2
0
0
1
0
1
1
2
2
2
0
0
2
1
1
2
2
0
2
1
2
0
0
1
0
1
1
1
2
2
1
0
0
1
1
2
1
2
1
1
0
0
1
1
1
2
0
2
1
1
2
0
0
0
1
1
0
1
3
0
1
1
0
0
1
0
0
2
2
0
1
1
0
1
1
0
0
1
2
0
1
2
1
1
2
1
0
2
0
2
1
0
0
1
1
1
0
0
0
1
2
2
1
0
1
0
0
0
0
1
0
0
1
0
0
1
0
3
2
1
0
0
1
0
0
1
1
2
0
2
1
2
0
0
1
0
0
2
3
1
0
1
0
1
1
1
0
1
1
1
1
1
2
0
0
0
0
0
2
1
1
1
0
1
0
1
0
2
0
1
0
2
1
0
2
1
1
1
2
0
0
1
1
2
0
1
0
2
0
1
1
0
2
1
1
0
1
0
0
0
1
0
0
1
0
1
2
1
1
1
1
1
2
2
1
0
1
0
2
0
2
2
2
2
0
1
0
1
1
0
2
2
0
0
0
0
1
1
0
0
1
1
0
0
0
1
1
0
3
1
2
0
0
2
0
1
1
0
1
1
2
0
1
3
0
0
1
1
3
0
0
0
1
0
2
1
2
2
0
1
1
2
2
1
0
1
0
0
1
1
0
2
2
2
0
0
1
1
0
1
1
0
0
4
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
2
1
0
0
0
2
2
0
2
1
1
1
2
1
1
1
2
0
0
0
0
0
2
1
0
1
2
1
0
1
0
2
0
2
1
1
0
2
1
1
1
0
2
2
1
1
1
0
2
2
1
0
1
2
0
1
0
1
0
2
1
0
0
2
0
1
0
1
0
0
2
0
1
0
1
2
1
1
0
0
0
1
1
1
1
1
1
0
1
0
0
2
0
1
1
2
2
2
0
0
2
0
2
2
2
1
0
0
1
1
3
0
2
0
0
1
2
0
2
0
1
2
0
1
2
1
2
0
1
0
0
0
0
1
1
4
2
1
2
0
1
2
2
1
0
1
0
0
0
1
1
2
0
0
1
1
0
0
0
2
0
0
0
1
0
3
0
1
2
2
1
1
0
0
0
0
1
0
0
1
1
1
0
1
2
2
2
1
1
0
0
1
0
0
1
0
0
1
0
0
1
0
0
1
0
0
2
0
1
2
1
1
1
1
1
1
1
0
1
2
2
2
1
1
3
2
0
0
2
0
1
1
1
3
2
0
0
2
0
0
0
2
0
1
1
0
1
0
1
1
0
3
5
1
1
0
2
1
1
1
0
0
3
0
1
0
2
0
2
2
2
1
0
0
0
0
0
0
0
1
2
1
0
2
1
2
1
1
1
1
0
0
1
0
0
0
1
0
0
1
1
2
0
0
2
2
1
0
0
1
0
1
0
0
0
0
0
0
1
1
1
3
0
1
0
0
0
0
1
0
0
0
0
0
1
2
1
0
2
0
1
2
0
1
0
2
0
0
0
0
2
0
1
2
0
1
0
2
0
0
1
1
0
0
4
0
0
2
0
0
0
2
1
0
1
0
2
1
0
0
1
4
2
0
3
0
0
0
0
0
1
0
0
1
1
2
1
1
1
0
1
2
2
0
2
2
1
2
2
0
2
1
0
0
2
1
0
1
1
1
1
2
1
2
2
1
0
0
0
0
0
0
1
1
0
0
2
3
0
1
1
0
1
2
1
1
0
0
0
1
1
0
1
1
1
1
0
0
2
2
2
2
0
1
2
0
0
0
2
0
0
1
0
0
1
0
1
2
1
1
0
0
1
0
0
0
0
0
0
1
0
1
2
1
1
1
0
1
0
0
2
0
2
1
1
1
1
0
1
0
2
0
1
1
1
0
0
0
0
0
1
0
0
0
0
2
1
6
1
2
2
1
0
3
2
2
2
2
0
2
1
0
0
0
0
0
1
1
2
1
0
0
1
0
0
1
2
0
0
2
1
1
0
2
0
2
1
0
0
1
1
1
1
0
0
0
2
0
0
1
0
2
0
1
0
2
0
2
1
1
0
1
0
0
0
1
1
0
1
1
3
0
0
0
0
2
0
1
2
2
0
2
2
0
0
3
0
0
0
1
1
2
0
0
0
0
1
0
0
1
2
1
0
0
0
0
0
0
3
0
1
1
2
1
0
3
0
2
0
1
0
2
2
0
1
0
1
0
0
1
0
2
0
0
0
1
0
0
1
1
0
1
1
1
1
1
1
2
0
0
1
1
0
0
2
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
1
1
0
1
2
1
0
0
1
2
1
0
1
0
0
1
2
0
1
0
1
2
0
1
0
0
1
0
0
2
1
1
0
1
1
1
2
0
0
0
2
1
1
2
1
0
1
0
0
1
0
0
0
0
2
1
0
0
1
0
0
0
0
1
1
1
1
0
1
2
1
0
1
0
1
2
1
1
2
0
5
0
1
2
2
0
2
2
0
0
1
0
0
1
2
1
1
1
0
1
0
2
1
1
1
0
0
2
0
1
0
1
0
0
1
1
1
2
1
0
1
0
0
0
1
0
0
2
0
1
0
0
1
0
1
2
6
1
2
0
0
0
0
1
1
0
0
1
1
0
0
1
2
1
1
1
0
2
2
0
1
1
0
1
1
0
0
0
1
0
1
0
0
1
1
0
0
1
1
2
0
0
2
2
1
0
1
0
0
1
0
1
0
4
2
0
1
0
0
0
1
0
0
0
1
1
1
1
1
1
1
1
0
1
1
0
2
2
0
2
0
0
1
1
1
0
2
0
0
2
1
1
0
2
0
1
1
0
0
0
2
0
2
1
1
1
2
0
2
2
0
0
0
0
0
0
0
0
1
1
1
2
1
0
0
1
0
1
0
2
0
1
0
2
0
1
0
0
0
2
1
2
0
0
1
0
2
0
0
0
0
0
1
1
2
0
0
2
0
1
0
0
0
0
0
1
2
0
2
0
0
1
1
1
1
2
1
1
2
1
2
2
1
2
0
1
1
0
0
2
1
2
0
0
1
3
0
1
0
2
0
1
1
0
1
2
1
2
0
2
2
0
0
0
1
2
0
2
1
1
0
0
3
2
0
1
1
1
0
1
1
0
2
0
2
1
1
0
0
1
1
0
1
0
1
0
1
0
1
1
0
1
0
2
1
0
1
0
1
1
1
1
2
2
0
1
2
0
0
1
0
0
0
1
0
2
3
1
0
1
1
1
1
1
2
0
0
1
0
1
1
1
0
0
2
0
1
2
2
1
1
1
1
1
0
1
0
0
1
1
0
2
0
2
0
0
1
1
1
1
0
2
1
0
1
0
0
1
1
0
2
2
1
1
0
1
0
1
0
1
1
1
0
0
2
1
0
2
1
2
2
1
0
1
2
1
2
2
0
0
1
2
1
0
2
1
0
1
2
2
1
3
1
0
2
4
2
0
0
2
1
0
1
0
0
0
1
0
1
2
0
0
0
1
0
0
2
2
1
0
0
2
1
0
0
2
0
1
1
0
1
0
2
2
2
2
2
0
0
1
0
0
0
1
0
3
1
0
0
3
1
2
0
0
0
2
1
1
1
0
1
2
1
2
1
0
1
1
0
1
2
0
1
0
1
1
2
2
2
0
2
0
0
0
0
1
1
1
2
1
0
3
2
0
2
1
2
2
0
1
1
0
0
2
6
1
2
0
0
1
0
0
1
2
0
0
1
1
1
0
1
1
1
1
0
2
0
0
1
1
0
0
1
1
0
1
0
0
1
2
0
0
0
0
2
1
0
1
0
2
0
0
1
1
1
0
0
1
1
2
2
2
1
2
1
1
0
1
1
0
0
1
0
1
0
1
0
2
0
2
0
3
0
2
0
1
2
2
1
1
1
1
2
0
2
0
1
0
2
1
0
1
1
0
0
0
0
2
2
1
0
1
0
1
0
0
1
0
0
2
0
0
1
1
1
1
0
0
1
0
0
0
1
1
2
0
1
2
1
0
1
0
0
1
2
1
1
0
1
0
3
0
0
1
0
0
1
0
0
2
2
0
0
0
0
0
0
2
0
1
1
1
0
0
0
2
2
0
1
1
1
1
2
2
3
1
0
1
0
1
1
0
1
0
1
0
1
1
1
2
4
0
0
1
1
1
0
1
2
1
1
2
1
0
1
0
1
1
0
2
0
0
0
2
1
1
0
1
1
0
1
1
2
1
3
0
0
1
0
1
2
2
0
2
0
0
1
2
0
0
1
2
1
2
0
2
1
0
2
1
1
0
1
1
0
1
1
1
0
0
2
1
1
2
0
1
1
0
0
2
1
1
0
1
0
0
2
2
2
1
0
1
2
2
0
2
1
0
1
2
0
0
1
1
0
0
0
1
1
0
0
0
1
0
0
1
2
1
0
1
1
0
0
1
1
0
0
0
2
2
1
2
2
0
2
0
1
0
1
1
0
1
2
2
1
0
0
0
0
1
1
2
1
0
1
0
1
0
0
2
1
1
2
2
0
0
1
0
0
2
0
2
0
0
0
2
1
1
0
1
1
0
0
0
2
1
0
1
0
0
1
1
1
0
2
1
0
1
0
1
0
3
0
1
2
0
0
0
2
1
2
0
2
2
1
0
1
0
0
2
0
2
2
0
0
1
1
1
1
0
2
0
0
0
2
1
1
1
0
1
1
1
0
1
1
2
1
1
1
2
0
1
0
2
0
0
2
1
1
0
1
2
0
2
0
2
0
1
1
1
0
1
0
0
2
0
2
2
1
1
1
0
0
1
0
0
0
0
1
0
1
1
1
2
0
0
0
1
0
1
0
0
1
0
1
1
2
1
1
0
0
1
2
0
1
1
1
0
0
0
0
2
1
1
2
2
1
1
1
2
1
1
0
0
2
1
1
2
1
1
1
0
0
2
2
1
0
0
0
3
0
1
1
0
2
0
1
1
0
0
1
1
3
2
1
0
0
0
2
1
2
0
0
1
2
0
2
0
1
0
2
1
2
0
0
0
0
0
0
0
0
2
1
2
2
2
2
3
0
0
1
1
2
2
0
2
0
0
1
4
1
1
0
1
0
0
1
0
1
1
0
1
0
0
1
3
1
0
1
0
0
1
0
1
0
1
1
1
0
0
0
1
2
0
1
2
1
0
1
0
0
1
0
0
0
2
2
0
0
1
1
0
0
1
0
0
1
0
0
1
0
0
2
1
1
0
0
1
1
1
0
1
1
1
3
1
1
0
0
1
2
0
1
2
2
1
1
0
2
0
0
0
1
0
1
0
0
0
1
0
1
2
1
3
1
0
2
1
1
0
0
0
1
2
0
0
2
0
0
0
1
1
0
1
0
6
2
0
1
1
1
1
0
1
0
0
0
1
1
1
2
2
1
2
0
1
1
1
1
0
0
0
0
2
0
0
0
2
0
0
0
0
2
2
2
2
1
0
1
0
2
1
2
2
1
0
1
0
1
0
1
0
1
2
1
1
0
2
1
0
0
2
1
2
0
1
0
0
0
1
1
0
1
1
1
0
1
0
1
2
1
1
2
0
1
0
0
1
2
2
0
1
0
0
1
0
1
0
0
0
5
2
0
0
0
2
0
0
2
0
0
1
1
2
2
2
1
1
2
0
1
0
2
1
0
0
0
0
0
0
2
0
1
0
1
0
2
1
1
0
1
0
1
0
1
1
2
1
2
0
1
2
1
0
2
2
1
1
0
2
2
0
1
1
0
0
0
1
0
1
2
0
1
0
0
2
0
1
0
1
0
0
2
0
2
2
2
0
1
0
2
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
4
0
0
2
0
1
0
1
2
2
0
1
3
1
0
1
1
1
2
1
0
1
3
1
2
0
0
1
0
0
2
0
1
0
1
0
0
0
1
1
1
2
0
1
1
1
1
0
2
2
0
0
1
0
0
0
1
2
2
0
1
2
0
2
0
2
1
1
1
1
0
1
0
0
1
0
2
3
2
0
0
1
1
1
0
0
0
0
1
0
1
2
1
2
2
3
2
1
1
1
0
0
0
0
1
2
3
2
0
0
0
0
0
2
1
2
1
2
1
2
0
0
2
1
0
1
0
0
1
0
1
0
1
0
2
0
2
2
0
2
0
1
0
1
2
2
0
1
1
0
0
1
0
1
1
1
2
1
1
0
0
0
0
1
0
0
2
4
0
0
1
1
0
0
0
0
1
0
1
1
0
1
2
0
0
0
0
0
1
1
2
0
0
1
0
0
0
2
0
1
0
2
1
0
1
0
0
1
0
1
1
2
1
0
0
0
0
1
0
0
0
1
1
2
1
0
1
1
1
2
0
1
1
0
1
1
2
1
0
0
0
2
0
2
2
1
2
3
1
0
0
0
3
0
0
2
0
2
5
0
2
0
0
0
2
1
1
1
1
0
1
0
0
0
0
0
0
0
2
0
1
0
1
1
1
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
1
1
2
0
0
0
2
2
1
0
2
0
0
0
1
0
0
2
0
1
0
1
1
1
0
1
0
0
0
2
0
3
2
1
0
1
0
0
1
2
1
0
0
0
1
1
0
0
0
2
0
1
2
1
0
1
2
2
1
1
2
1
2
2
2
2
0
0
1
2
0
1
0
2
2
1
1
0
0
1
1
0
0
2
0
1
1
1
0
0
1
2
0
1
2
1
1
1
1
2
1
0
0
0
1
1
1
1
1
1
1
0
2
0
0
2
1
0
0
2
1
2
1
1
0
1
3
0
0
0
2
1
0
2
1
0
0
0
2
1
1
0
0
2
2
1
1
0
0
0
0
1
0
1
0
0
2
0
0
1
1
0
2
0
0
1
1
1
2
2
1
2
1
2
2
1
1
2
0
1
2
1
1
1
0
0
1
0
3
1
1
0
2
0
2
0
0
0
2
1
0
1
1
2
2
0
0
2
1
1
1
2
1
1
2
1
1
0
0
1
0
0
0
0
0
1
0
2
0
1
1
1
0
2
1
1
0
2
1
0
1
0
1
1
1
1
1
0
1
2
1
0
1
1
0
1
1
1
2
1
0
2
0
1
3
0
1
0
1
0
0
2
1
2
1
0
2
1
0
0
1
1
0
0
0
1
0
2
0
1
0
0
0
0
1
2
1
0
2
0
1
0
1
2
1
1
0
1
0
0
1
1
0
1
2
0
0
0
2
0
0
2
0
1
1
2
0
2
1
0
1
2
1
1
0
0
1
0
0
2
0
0
2
0
1
1
2
2
0
0
1
0
2
0
0
0
2
0
1
2
0
2
1
1
2
1
1
2
0
0
1
2
2
2
1
0
1
2
0
0
0
0
0
1
2
1
1
0
2
1
1
2
1
1
2
2
1
1
0
1
2
1
2
2
0
0
1
0
1
1
0
2
2
1
1
0
0
0
1
0
2
0
0
2
0
0
1
1
0
1
2
0
0
0
1
1
1
1
1
1
2
1
0
0
0
2
0
1
1
0
1
1
1
1
4
0
2
1
1
0
2
1
0
2
0
0
2
1
0
3
1
1
0
0
1
0
2
1
0
0
1
2
0
0
2
0
2
2
1
2
0
1
0
2
0
0
0
0
0
1
0
2
0
0
0
1
0
0
2
1
0
2
0
0
0
0
1
0
1
2
1
1
3
2
0
0
1
3
2
0
2
2
1
1
1
1
0
1
0
2
1
1
0
0
1
1
0
0
1
2
1
2
0
1
1
1
0
2
0
1
2
2
0
2
0
0
0
2
2
2
0
2
2
0
2
1
0
1
2
1
2
1
2
2
0
1
1
0
2
2
0
0
1
0
1
1
0
0
2
1
0
2
0
0
0
0
0
0
0
2
0
2
0
2
0
0
1
0
0
0
0
1
1
1
1
0
1
1
1
1
0
0
0
0
2
1
0
0
1
0
1
1
0
0
0
1
1
1
0
1
1
1
2
0
1
2
1
1
0
2
0
1
2
1
1
0
1
3
0
0
0
2
1
2
0
0
1
0
0
1
2
0
1
2
1
1
2
0
0
3
1
2
1
0
2
0
1
1
1
1
2
0
2
0
2
1
0
1
0
2
0
0
2
2
0
1
2
1
1
0
0
0
0
0
1
2
1
2
0
0
0
0
0
2
0
1
0
1
1
0
1
1
2
0
0
0
0
2
1
0
0
0
1
0
3
1
2
1
0
1
0
1
1
1
0
0
2
0
2
0
2
1
2
0
2
1
1
1
1
0
2
0
1
0
1
1
0
1
2
0
1
2
1
1
0
0
0
0
2
1
1
1
0
0
1
1
1
0
2
1
2
1
2
0
2
0
2
0
1
2
1
2
1
0
0
0
2
0
2
2
1
0
2
1
2
2
1
1
1
0
0
1
1
0
1
1
1
0
0
2
2
2
2
1
2
0
0
1
1
1
2
0
2
2
1
0
1
1
0
1
0
0
2
0
0
1
1
3
1
0
1
0
0
1
1
1
0
1
0
0
0
0
1
7
0
1
0
1
2
2
2
0
1
0
2
0
1
4
2
1
0
1
0
1
0
1
0
1
2
1
0
1
1
0
1
0
0
0
1
1
1
0
0
0
1
1
1
0
1
0
2
2
1
0
1
2
1
2
2
0
0
0
1
0
2
0
0
1
1
1
0
0
2
0
0
1
0
2
0
1
0
3
0
1
2
2
0
1
0
3
0
1
1
3
0
0
1
1
0
2
1
2
0
2
3
0
1
0
2
1
2
0
0
0
0
2
1
2
0
1
0
1
0
1
1
0
1
1
1
1
1
0
2
3
0
0
2
2
3
0
1
1
1
2
1
1
0
0
1
1
0
0
1
1
0
0
0
1
0
0
0
0
1
2
0
1
2
0
0
0
1
0
2
1
1
1
0
1
2
2
2
0
1
1
2
1
0
0
0
1
0
0
1
1
1
0
2
2
1
1
2
1
0
1
0
1
2
0
0
2
2
0
0
2
0
1
1
2
1
1
0
0
1
2
2
2
3
0
1
2
0
1
1
0
1
2
0
2
1
0
0
0
0
0
6
0
2
0
0
1
2
1
1
1
2
1
1
0
0
0
1
1
1
2
1
1
1
2
0
2
0
0
0
1
0
0
0
2
1
0
2
1
2
1
1
0
1
2
2
2
0
1
0
0
1
2
0
1
1
0
1
0
0
2
2
0
2
2
0
2
3
1
1
1
1
1
0
0
0
1
0
0
1
0
0
0
0
0
1
1
1
2
1
0
0
0
1
0
0
1
0
0
1
2
1
1
0
0
1
1
1
0
0
1
2
0
0
2
0
2
1
0
0
2
0
0
0
1
1
2
0
2
0
2
1
1
0
0
0
1
0
0
2
0
1
1
1
2
0
0
1
0
0
0
0
0
0
1
2
1
0
1
0
0
2
2
2
1
1
0
0
0
2
2
1
0
2
2
0
0
2
0
1
0
1
2
2
2
0
0
0
2
1
0
0
0
0
1
1
0
0
1
0
1
0
1
0
1
0
0
1
2
0
1
2
0
0
2
2
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
1
3
0
0
2
1
0
0
0
0
0
1
0
0
2
1
1
1
1
0
0
2
1
1
2
0
1
0
0
0
1
0
1
0
1
1
2
0
1
2
1
1
0
0
1
1
0
1
0
1
1
0
0
0
1
2
1
2
1
0
2
0
2
1
0
0
0
1
0
2
1
0
0
0
1
1
2
1
1
0
1
2
0
0
1
1
1
0
0
0
1
0
1
1
2
2
1
2
1
1
0
0
3
0
1
1
2
1
1
0
2
0
1
0
1
0
1
0
2
2
0
1
0
2
2
1
0
1
2
1
1
3
0
0
2
1
0
0
0
1
0
2
1
0
1
0
1
1
0
1
0
1
1
1
2
0
1
1
0
0
2
0
0
1
2
0
0
2
0
1
1
1
2
1
0
2
0
0
1
1
0
1
1
0
1
0
2
1
0
0
0
3
2
0
2
1
1
0
0
1
0
0
1
2
1
1
2
1
1
0
2
1
0
1
1
1
1
0
0
1
2
1
1
0
0
0
1
1
2
1
2
2
1
2
1
1
1
2
0
0
0
2
0
0
0
0
1
2
1
1
0
0
1
1
0
2
1
1
3
0
0
1
0
2
0
0
0
1
0
0
2
0
2
2
0
2
1
1
1
2
0
1
0
0
2
0
1
1
1
1
0
1
1
0
0
1
1
2
1
1
0
2
1
0
0
1
0
1
0
0
2
1
2
0
0
2
2
2
0
1
1
0
1
0
0
1
0
1
2
2
1
0
2
0
1
0
2
1
0
0
0
2
1
1
1
1
1
0
0
0
1
0
1
0
2
1
1
1
1
0
3
2
0
2
0
0
0
0
0
2
2
2
3
0
1
0
1
0
0
1
1
1
0
1
1
3
1
1
2
1
0
0
1
1
1
1
0
1
1
0
2
0
1
2
0
0
0
2
0
1
1
1
0
2
2
0
2
2
1
1
1
1
1
1
1
2
2
2
0
0
1
0
3
0
1
0
2
2
0
0
0
1
0
2
0
1
2
1
1
0
2
0
0
1
0
1
2
2
0
1
2
1
1
0
2
0
0
2
1
1
1
0
2
0
0
0
0
1
0
2
0
2
0
0
1
0
0
1
2
0
1
1
0
1
0
0
1
2
2
2
1
0
1
0
2
1
0
2
1
0
1
0
2
1
0
2
1
1
0
1
0
1
0
2
0
0
1
0
1
1
2
2
1
1
1
1
0
1
0
1
1
1
0
1
1
1
0
1
1
1
0
1
2
1
1
1
1
0
0
2
0
1
1
0
2
0
0
2
1
0
1
0
1
0
0
0
0
1
1
1
0
0
1
2
0
0
1
1
2
1
1
0
2
1
0
0
1
2
2
2
0
0
2
0
0
0
1
1
0
0
1
0
1
1
0
2
2
0
2
1
1
1
1
2
0
1
0
2
2
0
0
0
1
1
1
0
0
1
2
0
2
2
0
1
2
0
0
3
1
3
0
1
1
2
0
0
1
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
3
1
1
0
1
1
1
0
1
1
2
2
1
1
1
1
2
0
1
1
1
1
1
0
1
0
1
0
1
1
0
0
0
1
0
1
2
6
1
1
1
2
2
2
0
0
0
2
0
3
1
1
0
0
0
1
2
2
1
1
2
0
0
0
0
1
0
0
1
0
2
1
3
0
0
2
1
0
1
2
1
1
1
0
1
1
1
0
1
0
0
1
0
0
0
2
1
2
0
2
1
0
1
1
1
0
1
0
0
1
2
2
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
2
0
0
2
2
0
1
1
0
0
1
1
1
0
2
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
1
1
0
1
1
0
2
3
0
2
0
0
0
0
1
0
0
0
1
1
0
0
1
0
1
1
0
1
0
0
2
0
0
1
1
1
2
0
1
0
0
1
2
2
0
1
2
0
1
1
1
0
2
0
1
1
0
1
1
1
1
1
1
0
1
1
1
0
1
0
2
0
0
0
1
0
1
1
1
3
0
0
1
1
2
1
0
2
0
1
1
1
0
0
0
1
0
1
2
0
2
0
0
2
0
1
0
0
1
1
2
1
0
2
0
0
0
2
1
2
1
0
0
1
1
0
2
2
0
0
3
1
0
1
2
0
1
2
1
0
0
0
1
1
0
0
1
0
1
0
1
0
1
0
1
0
0
0
1
0
0
1
2
1
0
2
0
0
1
1
2
0
1
0
1
1
1
0
2
1
0
2
2
0
2
0
1
1
1
2
0
0
1
1
0
1
0
0
1
1
0
0
1
0
1
2
1
0
2
0
0
0
0
2
0
0
1
0
0
1
0
0
1
2
2
1
1
2
1
1
1
0
0
0
0
1
2
0
1
1
2
0
0
1
2
2
0
0
2
0
0
2
0
0
1
0
3
1
1
1
1
2
0
1
0
1
2
0
1
1
1
1
3
0
0
1
0
1
0
2
1
1
0
0
0
0
1
1
0
0
2
0
0
0
0
1
0
1
1
0
1
2
1
1
1
1
0
2
1
0
0
1
1
0
2
1
1
1
2
3
2
0
0
2
2
0
0
0
2
0
0
0
2
2
2
1
0
0
1
2
1
0
0
2
0
2
0
0
2
1
0
1
0
0
2
0
0
1
2
2
1
0
0
2
1
2
0
0
0
1
1
1
1
0
1
0
1
1
1
1
0
1
1
1
1
2
2
0
1
0
0
0
1
0
1
2
2
0
1
0
1
0
0
2
0
0
0
2
2
2
0
1
1
0
0
2
0
0
1
0
0
1
0
0
1
0
2
0
0
2
0
0
0
1
1
0
1
2
1
2
1
1
1
1
1
0
1
2
2
2
0
0
2
2
1
1
1
1
0
1
0
0
2
1
0
0
1
0
2
2
0
0
0
2
0
1
0
0
1
1
0
1
2
2
1
2
1
0
0
1
1
0
1
1
0
0
0
0
0
1
0
0
2
1
0
1
0
0
1
1
1
0
1
1
1
0
1
2
1
0
1
0
0
0
5
1
0
1
1
0
2
1
1
0
0
0
1
0
0
0
0
0
0
0
0
2
1
1
1
1
0
0
1
2
0
1
2
1
2
1
2
0
0
2
1
0
3
0
1
0
2
1
2
0
0
0
1
2
1
1
2
0
1
1
1
1
0
1
2
1
0
2
0
0
0
1
0
0
1
2
1
1
0
0
0
0
1
1
0
1
0
0
1
0
1
2
1
3
1
2
0
0
2
1
2
2
0
2
1
1
0
2
2
1
0
2
1
0
0
1
1
2
1
1
1
0
0
0
1
1
8
1
0
0
2
2
0
1
1
2
1
0
2
2
2
0
0
0
0
3
1
0
3
3
1
0
0
2
0
2
0
1
0
0
0
0
1
2
0
4
0
3
7
0
0
0
0
0
0
0
2
0
0
0
2
0
4
1
4
0
0
0
0
2
1
1
0
0
1
1
1
2
0
0
1
2
0
0
1
2
0
0
0
1
0
0
1
1
2
1
1
0
2
0
3
1
0
2
1
1
1
1
3
0
0
1
0
0
0
1
1
1
3
0
1
2
0
0
1
0
0
2
3
2
0
1
0
1
1
1
1
1
0
1
1
2
1
0
0
0
0
1
2
1
0
0
2
0
0
1
1
0
0
2
0
1
1
2
0
0
2
0
1
0
1
0
1
2
6
1
1
2
2
0
0
0
2
1
2
0
1
1
0
0
2
0
1
2
0
1
1
0
0
2
1
0
0
1
1
0
0
2
0
0
0
0
0
1
0
1
2
2
1
2
0
0
0
0
3
1
0
0
2
0
0
0
2
0
1
0
0
2
0
0
0
1
1
1
1
2
0
1
0
1
0
2
0
1
0
1
0
2
1
1
1
0
0
0
1
0
1
0
1
2
1
1
1
1
1
1
1
1
1
1
1
0
1
4
2
0
1
0
0
0
1
1
2
1
0
0
1
0
1
1
0
1
1
2
0
0
1
0
1
1
0
1
1
0
2
1
0
1
2
0
1
2
2
0
0
0
0
0
1
1
1
1
2
0
0
1
1
0
0
2
2
0
1
0
0
3
0
0
1
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
1
1
0
1
0
1
1
0
0
2
0
1
0
1
2
2
2
0
1
1
2
2
1
0
1
1
1
2
0
0
2
1
0
2
2
2
0
0
1
0
2
2
1
0
1
2
2
0
1
1
0
1
1
2
0
0
1
1
1
1
0
0
1
1
2
1
1
1
1
1
2
0
1
1
2
1
1
1
1
0
2
1
1
0
2
2
0
0
0
0
0
1
2
1
0
2
1
0
0
0
1
1
2
1
1
1
2
2
2
0
0
0
0
1
2
0
0
1
0
0
1
0
0
1
1
0
1
1
1
0
1
1
2
2
2
0
2
0
1
1
0
2
1
0
2
1
1
0
0
1
2
1
0
1
2
2
1
0
0
2
1
0
1
2
0
2
0
2
1
1
1
1
2
2
1
3
0
0
1
1
2
1
0
0
0
0
1
2
0
0
0
0
0
0
1
0
2
2
2
2
0
2
1
0
1
0
3
0
0
1
0
0
0
2
2
0
0
0
3
0
0
2
1
1
0
0
0
3
0
0
0
10
1
1
0
1
1
1
1
2
1
0
1
1
1
2
2
1
0
1
0
2
0
1
4
1
2
0
0
0
1
1
2
1
0
1
0
0
1
0
1
2
0
2
2
0
2
0
1
0
0
0
2
1
0
2
1
0
1
2
0
1
0
0
1
0
2
2
1
2
1
2
1
0
1
0
2
1
1
0
1
1
0
1
1
1
1
2
0
1
0
2
1
0
1
2
1
1
1
3
1
0
1
0
2
0
2
1
0
1
1
0
0
1
0
0
1
2
0
0
1
1
1
2
2
1
0
2
0
0
1
2
1
0
2
1
1
0
1
0
2
1
1
2
2
0
1
0
2
1
0
0
0
0
2
2
0
1
1
0
0
2
0
2
1
0
1
1
0
0
0
0
1
1
0
1
0
2
2
1
4
2
0
0
0
2
0
0
5
0
1
1
0
1
2
0
2
0
1
1
1
0
0
0
0
0
1
0
1
0
1
2
2
1
1
1
0
3
0
0
0
0
2
4
3
1
2
2
0
0
2
1
0
0
0
0
0
1
0
2
0
2
1
1
1
1
0
0
1
0
0
2
1
0
2
0
2
0
0
1
1
1
2
0
0
1
1
0
1
0
0
1
1
2
1
0
2
3
1
0
0
2
0
0
1
0
0
0
2
3
0
1
1
1
1
1
1
0
0
2
0
0
1
0
1
1
1
0
1
1
2
0
0
0
1
0
0
2
1
1
1
0
2
2
1
1
1
2
0
0
0
0
0
2
2
1
0
1
2
0
0
0
1
2
1
2
1
2
0
0
1
0
1
0
2
0
0
0
2
1
0
2
1
0
1
1
1
0
2
0
1
1
1
1
1
2
0
0
2
0
0
1
1
0
1
2
2
0
1
0
1
1
1
0
0
1
0
0
1
0
1
0
2
0
0
0
0
1
0
1
2
1
1
0
0
2
2
0
2
1
0
2
1
1
1
2
1
0
2
1
1
0
1
1
1
1
0
0
1
2
0
0
0
2
0
1
0
0
2
0
0
1
1
0
1
0
2
1
1
3
1
0
0
1
1
1
1
1
0
2
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
2
0
1
0
1
2
2
0
1
0
0
0
1
0
0
2
0
2
0
0
1
0
0
2
2
2
2
0
2
0
1
1
2
0
0
2
0
2
0
0
0
0
0
0
1
1
1
0
2
0
1
1
0
0
0
0
1
2
1
2
0
2
0
0
3
2
0
0
0
1
1
0
0
0
0
2
0
2
1
0
2
0
1
0
1
0
0
0
1
2
1
1
1
2
1
0
2
1
0
2
0
1
0
1
0
1
2
0
1
2
0
1
0
1
2
1
1
0
0
1
0
1
0
0
1
0
1
1
2
2
0
2
2
2
0
2
1
1
0
0
1
1
1
1
1
2
1
2
0
1
0
1
2
0
0
0
2
1
6
0
0
0
1
2
2
0
1
1
1
1
1
1
1
1
2
0
2
0
2
2
1
0
1
0
1
1
0
0
0
2
0
1
0
1
2
2
0
1
1
1
1
0
1
1
2
0
1
0
2
0
1
0
3
1
1
0
0
1
1
0
1
2
0
1
1
1
0
0
2
0
2
2
2
2
0
1
1
0
1
2
0
0
0
0
1
0
0
1
1
0
3
2
1
0
0
0
0
1
1
2
0
1
0
2
0
2
2
1
0
0
0
2
1
0
1
2
0
1
1
0
1
0
2
0
1
0
2
2
2
0
1
1
0
1
0
0
0
1
1
0
0
1
0
1
1
0
0
1
0
0
0
1
0
1
1
0
0
2
0
2
1
1
0
0
1
0
1
0
2
1
0
2
0
0
0
0
0
0
1
2
0
0
2
2
0
0
0
1
2
0
4
1
0
0
1
0
0
2
0
0
2
1
2
2
1
0
2
3
0
1
2
2
2
0
1
0
1
1
0
0
1
1
1
0
0
0
1
0
1
0
0
0
2
0
0
1
1
0
1
2
1
2
3
1
0
1
1
0
1
0
0
0
2
2
1
2
0
1
1
0
1
0
0
1
3
0
2
0
2
1
1
1
0
2
0
1
1
0
2
0
0
0
0
0
0
2
1
0
0
1
2
1
1
2
0
1
0
1
1
2
2
0
1
0
0
2
0
2
2
0
1
0
1
0
1
1
0
0
1
0
1
2
1
1
1
2
1
2
2
1
0
0
0
0
0
0
1
1
3
0
0
1
1
0
1
0
0
1
1
1
0
1
0
0
0
2
1
1
2
1
2
1
0
0
0
0
1
1
0
2
0
2
1
1
0
1
2
1
0
0
2
0
1
1
1
1
0
1
0
2
2
2
0
2
1
2
2
1
0
1
1
0
1
1
1
2
2
0
1
0
0
1
0
0
2
0
0
1
0
2
1
0
0
2
1
0
1
0
1
0
1
0
0
0
1
1
1
0
1
2
0
0
1
1
1
1
0
0
0
0
0
0
0
1
1
2
1
1
0
1
2
2
0
0
1
2
1
1
0
0
0
0
1
1
2
1
1
1
1
2
2
1
0
2
0
1
1
0
1
1
1
1
0
0
0
1
1
2
2
1
0
2
0
1
0
0
0
1
1
2
0
1
1
2
0
1
1
1
0
1
1
1
4
0
0
0
2
2
2
0
0
1
0
1
1
1
1
2
0
0
2
1
0
1
0
0
0
1
2
2
0
0
1
0
0
1
1
0
1
2
3
1
0
1
0
0
1
0
1
2
1
2
1
0
1
1
2
2
1
2
1
2
1
1
1
2
1
1
0
2
0
3
2
4
1
0
0
0
1
1
2
8
0
1
1
2
0
2
1
1
1
1
0
0
1
0
0
1
2
1
1
2
1
2
0
1
1
0
0
0
1
1
1
0
1
0
2
2
3
0
1
0
0
1
2
1
2
0
1
2
0
1
0
2
2
0
1
1
2
2
3
1
0
1
0
1
0
0
1
0
1
1
2
0
1
0
0
0
0
1
0
2
1
1
1
0
0
0
0
0
1
0
1
1
1
1
0
1
2
1
2
2
0
0
0
2
0
0
0
0
2
1
0
0
0
0
1
0
1
0
0
2
1
2
1
1
1
1
0
1
1
1
1
0
1
2
1
1
0
0
0
1
1
2
1
1
1
1
1
1
1
0
1
0
1
0
2
0
1
1
1
2
0
2
1
0
0
1
1
0
2
1
0
1
1
2
2
1
0
0
0
4
2
0
1
1
0
0
1
0
2
0
0
1
1
1
1
2
0
1
1
1
1
0
1
1
0
1
1
0
2
2
1
2
0
0
1
0
0
1
0
1
0
1
0
1
0
0
0
1
1
2
0
0
0
0
2
1
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
2
1
2
1
0
1
1
2
0
2
2
0
1
2
1
1
2
0
0
1
1
1
1
0
1
1
0
0
0
2
1
1
0
1
0
1
1
0
2
2
0
0
1
2
1
1
0
1
0
2
0
0
0
2
2
1
1
0
1
0
0
0
3
0
0
0
1
1
0
0
0
2
0
2
1
2
0
0
0
2
2
0
0
1
0
1
0
2
2
0
1
0
0
0
0
0
2
1
0
0
2
0
1
0
0
1
0
0
1
0
2
0
0
0
1
0
1
2
2
0
0
1
1
2
2
1
0
0
2
2
1
3
0
0
1
0
1
0
0
0
0
1
1
1
1
0
0
1
1
1
2
1
2
1
0
1
0
0
2
0
1
2
0
0
1
1
0
0
0
1
0
1
0
2
2
1
0
1
2
0
1
3
1
0
0
1
0
2
4
0
0
0
1
0
1
1
0
0
1
1
1
2
1
0
1
2
1
1
1
1
0
1
0
1
1
1
0
0
2
0
1
1
1
1
1
0
0
2
0
0
1
0
2
2
0
1
2
0
0
0
1
0
1
1
2
1
0
2
1
1
2
1
2
1
0
1
2
1
1
2
1
0
0
1
2
0
0
0
2
0
0
0
1
2
0
3
0
1
1
0
0
2
0
2
1
0
0
0
1
0
2
0
0
2
1
1
0
1
0
3
1
1
0
1
1
2
0
1
0
0
1
0
2
1
0
2
2
1
1
1
0
0
2
2
2
3
2
0
1
0
0
0
1
0
2
0
1
0
0
0
1
3
0
1
2
1
2
1
0
0
1
0
1
0
0
2
1
2
0
0
2
0
0
1
2
1
1
2
2
1
2
0
0
1
2
0
2
1
1
1
2
2
0
2
0
0
2
1
0
0
2
1
2
1
2
0
1
1
0
1
2
0
1
0
2
0
0
2
1
1
1
0
1
2
1
2
2
1
0
0
1
0
1
1
0
0
0
2
2
0
2
2
0
1
1
1
2
1
1
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
2
2
1
1
2
2
2
1
2
0
2
2
2
2
0
2
1
1
0
1
1
0
0
1
0
0
0
1
2
1
0
0
1
2
0
0
1
1
1
0
1
1
1
1
1
0
1
0
0
1
0
0
2
1
1
0
1
0
0
0
0
1
4
2
0
4
1
1
1
1
1
1
0
1
1
0
1
0
1
1
1
2
2
0
0
2
2
0
0
1
0
1
0
1
2
1
1
0
0
0
1
0
0
0
0
0
1
1
0
1
0
1
0
1
1
1
0
0
1
0
0
0
1
1
2
0
2
1
1
2
1
0
0
0
2
0
1
0
1
0
0
2
0
0
0
2
0
2
0
0
1
0
0
0
0
0
1
1
1
2
0
0
0
1
0
0
1
0
2
1
0
1
1
1
2
0
2
1
0
0
0
0
1
0
1
0
0
2
1
2
1
3
0
2
0
0
0
2
0
1
1
1
0
1
0
1
0
0
3
1
2
1
0
2
1
0
1
0
1
1
1
2
1
0
1
2
2
1
1
2
2
1
0
0
0
2
2
0
0
1
1
1
1
0
1
0
1
0
2
1
0
1
1
1
1
2
1
0
1
0
1
0
2
1
2
0
0
1
0
1
2
1
0
2
2
2
1
2
2
1
1
2
0
2
0
1
2
1
1
0
1
1
1
1
2
0
1
0
0
1
0
1
0
2
2
0
0
0
0
2
0
0
1
0
1
1
2
0
2
1
1
1
1
1
1
0
2
1
1
1
0
1
2
0
0
1
0
2
1
0
2
0
0
0
2
0
1
1
0
0
0
0
1
2
0
2
0
0
1
2
1
2
0
1
1
0
1
2
0
0
1
2
1
0
1
0
2
2
0
0
0
0
2
1
1
0
1
0
1
2
2
0
3
1
0
1
2
0
1
1
1
1
0
1
2
0
0
0
2
1
2
0
0
0
0
0
2
1
0
1
0
1
1
1
1
1
0
0
1
0
0
1
1
0
1
0
1
2
0
2
2
2
3
2
0
1
0
2
2
1
0
0
1
2
0
1
1
1
3
2
1
1
2
1
1
2
1
1
2
2
0
1
2
0
0
0
1
0
1
0
0
1
1
0
0
2
0
1
1
0
0
1
0
0
2
0
2
1
0
0
0
1
0
0
1
0
0
0
1
1
2
1
0
1
0
0
0
1
1
1
4
0
0
1
0
0
1
1
1
0
1
2
2
2
1
2
0
0
0
0
0
2
0
0
1
2
0
1
2
0
1
1
0
0
0
0
1
0
0
2
2
0
0
2
2
1
1
0
1
2
1
0
0
2
2
0
1
1
0
1
0
2
1
0
1
0
1
1
0
0
1
1
1
0
1
0
2
1
1
1
0
2
2
0
0
0
1
2
1
0
0
1
0
0
0
0
1
3
0
1
1
0
1
0
1
0
1
0
0
1
0
1
2
1
0
0
0
0
1
2
2
1
1
1
1
1
1
1
1
2
1
0
1
1
0
0
0
4
0
2
1
1
0
1
3
0
1
2
2
1
2
2
0
0
0
0
0
0
2
0
2
0
1
2
2
0
1
0
1
0
0
0
1
0
0
1
0
0
0
2
0
0
1
1
0
0
0
0
0
1
1
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
2
3
2
0
2
3
1
0
0
0
2
0
0
1
1
1
1
1
0
1
1
1
0
2
0
1
2
2
1
0
1
0
1
2
1
1
0
0
2
1
0
0
1
1
2
2
2
0
0
0
0
0
2
2
1
1
1
1
2
0
0
1
1
0
0
0
0
1
1
1
0
0
2
0
2
2
1
1
0
2
1
0
0
1
0
1
0
0
2
0
3
1
2
0
1
1
0
0
1
0
1
1
1
2
1
1
1
1
1
2
0
0
0
0
1
0
0
3
2
0
0
1
1
1
1
0
2
0
1
0
0
0
0
0
0
1
0
2
0
2
2
0
0
2
1
0
2
1
0
0
1
1
0
1
0
0
2
2
1
1
2
0
1
2
0
0
0
1
1
1
0
0
0
1
0
1
0
0
1
2
1
1
1
0
1
0
0
1
1
0
1
0
1
2
1
0
0
2
0
2
1
1
0
1
0
0
1
0
0
5
2
0
0
1
0
1
0
0
0
0
2
0
2
2
2
0
0
0
1
1
1
1
1
1
2
1
0
3
1
3
2
3
0
1
1
0
1
1
1
1
1
1
1
1
2
1
2
0
2
0
2
0
0
0
2
0
2
0
0
1
0
1
0
1
2
1
1
2
0
0
2
0
1
2
0
1
1
2
0
1
0
1
1
0
1
2
0
1
0
1
2
2
2
1
1
1
0
2
0
2
1
2
0
1
0
1
0
2
0
0
1
0
1
1
1
4
0
0
2
0
0
2
0
0
1
0
2
0
0
2
1
2
1
2
1
1
0
2
0
0
1
0
1
0
0
2
1
1
0
0
0
1
0
0
1
0
1
3
2
0
2
2
1
0
1
2
0
0
1
0
0
0
0
2
2
0
0
2
0
0
0
0
2
2
2
0
1
0
1
1
2
0
2
0
0
0
0
1
0
0
1
2
0
1
0
3
3
1
0
0
2
1
2
0
0
1
2
0
2
1
0
0
0
1
1
0
1
1
1
0
0
0
0
1
1
2
1
0
0
0
0
2
1
2
0
2
0
1
2
0
0
2
0
1
2
1
0
1
0
3
0
2
0
1
1
2
0
0
0
2
2
1
0
1
2
1
1
0
0
1
1
0
2
2
2
2
1
1
1
0
0
1
1
3
1
1
0
1
0
0
1
0
0
0
1
1
0
1
1
0
2
1
0
1
2
0
2
3
2
1
0
2
0
0
1
1
1
0
1
0
2
1
0
1
1
1
1
0
2
1
0
1
0
1
2
0
0
0
1
0
2
1
1
1
1
0
2
0
0
1
0
1
2
0
0
1
0
0
0
2
1
0
1
1
0
0
1
2
1
2
1
1
1
0
0
2
0
0
0
0
1
2
2
2
1
0
0
3
2
0
2
1
0
2
0
0
0
1
0
2
1
0
0
2
2
0
1
1
1
2
0
0
1
0
2
2
0
0
0
1
0
1
1
1
1
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
1
2
0
0
0
0
1
0
0
1
4
1
0
1
0
0
2
0
0
1
2
0
0
1
1
2
2
0
0
0
0
0
0
0
1
0
2
0
2
2
1
0
0
0
1
0
0
0
0
0
1
0
0
2
1
2
0
1
0
0
0
2
0
0
1
0
1
2
0
0
1
1
0
0
0
2
0
0
2
1
0
0
2
2
0
0
0
1
0
0
1
1
0
1
1
2
5
1
1
1
0
2
0
1
1
2
2
1
0
1
1
1
1
0
0
2
0
1
0
0
1
0
2
1
2
0
3
2
1
0
0
1
1
1
0
0
0
1
1
1
2
0
1
2
2
0
1
1
1
2
0
0
2
0
1
1
1
0
2
1
1
2
0
1
1
2
1
0
0
1
1
2
1
1
2
0
0
1
0
2
1
2
2
2
2
0
2
0
0
0
2
1
0
0
0
1
0
0
0
1
2
1
1
0
0
0
0
0
0
1
1
0
1
3
0
0
1
2
0
0
0
0
3
2
0
0
1
0
0
1
1
0
1
0
4
1
4
0
0
0
0
0
2
1
0
1
2
1
1
0
1
2
1
1
1
0
1
2
0
1
1
1
1
2
1
0
0
2
1
2
2
1
1
0
0
0
2
1
0
1
2
1
0
1
0
1
0
0
1
0
0
2
2
0
0
1
0
2
1
0
0
2
0
1
1
0
1
0
1
0
0
1
2
1
2
2
1
1
1
1
1
0
2
1
0
0
2
1
0
1
2
0
0
1
2
0
1
0
1
0
2
1
0
1
0
0
0
1
2
1
1
1
0
4
1
0
2
1
0
2
0
0
2
1
2
2
0
1
0
1
0
0
1
0
1
0
1
2
1
1
0
1
1
1
1
1
2
2
0
0
1
0
1
0
0
0
0
4
2
0
0
0
1
2
0
1
2
0
0
0
0
1
1
0
0
1
1
1
0
0
1
0
0
2
1
2
1
2
0
1
1
0
0
0
2
2
1
0
2
0
1
1
1
0
0
2
0
1
1
0
0
0
1
0
1
0
0
1
1
0
2
2
0
1
2
0
0
0
2
1
1
1
2
0
0
0
0
2
1
1
2
0
0
2
1
1
1
0
2
0
0
1
1
2
0
0
1
0
1
1
0
0
4
2
0
1
0
0
1
0
0
2
0
0
0
1
0
0
0
2
1
1
1
1
0
1
0
1
1
1
2
0
0
1
0
1
1
0
4
1
2
1
0
2
0
1
1
2
0
1
1
0
2
0
0
1
0
0
0
0
3
0
0
1
0
2
1
0
0
1
2
0
0
0
0
1
2
0
2
1
1
1
1
1
0
0
1
0
0
0
0
0
2
0
0
0
1
0
2
2
0
1
1
1
0
2
0
0
0
2
0
2
0
2
2
0
1
1
2
1
1
2
0
0
2
1
1
2
0
0
1
0
2
0
0
1
1
1
0
1
1
2
0
2
0
1
1
0
0
0
1
1
1
1
0
0
2
2
1
2
1
1
1
1
1
0
1
0
0
0
2
0
1
1
2
1
1
1
0
1
0
3
2
1
1
1
1
0
0
0
0
2
2
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
1
0
1
0
0
0
1
0
1
0
1
0
0
2
1
0
1
1
0
0
0
2
0
0
1
2
0
0
1
2
0
1
1
1
2
1
0
2
2
1
0
0
1
2
1
1
2
1
0
0
2
0
2
3
0
2
1
0
2
0
2
0
1
2
0
2
0
1
0
2
0
0
1
0
1
0
1
0
2
1
0
2
0
0
0
0
0
1
2
1
0
3
0
0
0
1
0
1
1
1
0
2
2
0
0
1
0
0
2
1
2
0
1
2
0
1
1
1
2
1
2
1
1
2
0
2
1
0
0
0
1
0
0
0
1
2
1
0
2
2
0
0
3
1
1
1
0
0
0
1
0
1
1
2
2
2
2
0
2
2
0
2
1
2
1
1
2
1
1
0
0
1
1
1
1
1
4
2
2
1
2
2
0
1
0
1
2
0
2
0
1
0
2
0
1
1
1
1
0
0
1
1
1
0
1
0
0
1
1
1
1
1
1
0
1
2
0
0
2
0
0
1
1
2
1
2
0
2
1
2
0
0
0
2
1
0
0
1
0
0
0
1
0
0
1
0
1
2
0
0
1
1
0
0
1
2
0
1
0
4
0
1
1
2
1
0
1
3
0
2
2
0
1
0
0
2
1
2
1
0
2
0
0
0
0
1
0
1
0
1
0
0
0
0
2
1
1
2
2
1
1
0
0
1
0
1
0
0
1
0
1
0
0
0
1
0
1
0
2
2
1
1
2
0
0
0
2
0
1
1
0
3
1
2
1
1
3
1
0
2
0
1
1
1
0
0
1
1
1
0
0
0
2
2
0
1
1
1
1
0
1
0
0
0
2
0
2
1
0
3
0
0
0
2
0
0
0
0
1
1
0
2
1
0
0
1
0
0
1
0
1
0
1
2
0
1
0
0
0
0
1
2
0
1
2
1
1
0
0
3
1
1
2
2
3
0
2
1
1
2
2
4
2
1
2
0
1
0
0
0
1
0
1
0
1
0
1
2
1
1
0
0
2
0
0
2
2
0
0
0
1
1
0
1
0
0
0
2
0
0
1
0
2
0
0
1
0
0
0
0
1
1
0
0
1
1
0
2
2
0
2
1
0
2
0
0
0
2
2
1
1
1
0
1
0
0
0
1
2
2
0
0
0
0
0
1
1
0
1
1
0
0
1
0
0
2
0
1
0
0
2
0
0
1
3
2
0
2
2
2
1
0
2
1
1
0
0
2
2
1
1
0
0
0
1
1
2
1
2
0
0
1
1
1
1
0
2
3
1
1
0
1
1
1
1
0
2
0
1
1
2
0
1
1
2
1
0
0
0
0
2
0
2
2
0
2
2
1
2
0
2
0
0
0
0
0
0
1
3
0
1
1
1
1
2
2
2
1
0
1
0
1
2
1
0
1
0
1
0
1
0
2
0
1
1
1
0
0
1
0
2
0
1
0
2
0
0
0
0
0
1
2
1
2
1
2
2
0
1
2
1
0
2
0
2
0
0
0
2
2
0
1
0
0
0
0
2
1
0
2
0
0
1
0
0
1
2
2
1
2
0
0
1
0
1
1
2
0
1
1
1
1
0
1
1
1
1
1
1
1
2
0
1
1
2
3
0
0
1
2
1
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
1
1
2
0
0
1
2
2
2
2
0
1
1
2
0
0
0
1
2
2
1
2
0
0
2
0
1
0
2
1
0
0
1
0
0
0
0
0
1
0
2
0
0
0
2
1
0
0
0
0
1
1
0
1
1
1
1
1
2
0
0
0
1
1
1
1
1
1
1
0
0
2
0
0
0
0
2
1
1
2
1
1
2
1
1
2
0
0
3
2
1
1
0
1
1
1
1
0
0
2
1
3
1
2
0
1
0
1
0
3
1
0
1
0
0
1
0
0
2
0
1
0
2
2
0
0
0
0
1
2
2
1
0
2
0
0
1
0
1
3
1
1
2
0
2
0
0
0
1
1
0
1
1
1
1
0
0
1
1
3
2
0
0
0
0
1
0
1
1
1
1
0
1
2
0
0
0
2
2
2
0
1
1
1
0
1
0
1
1
2
0
1
1
2
1
1
2
0
1
2
1
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
1
1
2
1
0
2
3
1
0
1
1
9
1
1
0
1
0
1
0
0
1
0
2
1
0
1
2
0
2
0
1
1
0
2
1
1
0
0
0
0
0
0
0
1
0
0
1
1
2
0
0
1
0
0
2
1
1
2
0
0
0
1
0
1
0
0
1
0
0
2
0
2
0
1
1
0
1
2
0
1
0
0
1
1
2
2
0
0
2
0
2
1
2
0
1
0
0
0
2
2
1
1
0
1
0
2
0
0
0
0
1
2
0
0
2
1
1
2
1
1
0
0
1
0
0
1
2
2
0
1
0
1
0
0
0
1
0
0
1
2
0
0
2
2
0
2
1
0
0
0
2
1
0
0
0
0
0
0
1
1
0
0
0
3
0
1
1
2
0
1
0
0
0
0
0
2
1
2
2
0
0
2
1
2
2
1
0
0
2
1
0
2
1
0
1
0
0
1
1
1
1
1
1
4
0
0
1
2
1
1
2
1
1
0
1
1
0
0
0
0
1
0
1
0
1
0
0
0
2
1
0
2
0
2
0
2
0
1
2
0
0
0
2
1
1
1
2
1
1
0
2
2
2
0
2
1
0
0
1
0
1
0
1
0
1
1
0
3
0
0
0
2
2
1
2
1
0
0
0
1
1
1
0
0
1
1
1
2
0
0
0
2
0
1
1
2
0
0
0
1
1
0
0
2
1
1
1
2
0
0
2
0
1
0
0
1
1
1
0
1
0
0
1
0
0
0
1
2
1
2
1
1
1
1
2
1
1
0
2
0
2
2
0
0
0
0
0
0
1
0
2
1
0
0
0
1
1
1
1
0
0
1
0
2
2
2
0
1
0
2
1
1
0
1
0
2
1
1
0
0
0
1
2
0
1
2
0
0
1
0
0
1
1
1
0
1
0
0
2
1
0
1
0
0
1
0
3
0
0
1
1
2
1
1
0
0
1
1
1
0
1
0
1
2
0
1
1
0
1
2
2
0
2
0
2
0
2
1
0
1
1
1
0
1
0
2
2
0
1
2
2
1
1
1
1
0
2
2
1
2
2
2
0
0
0
1
1
1
2
2
1
0
1
0
0
1
2
0
1
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
3
0
0
1
0
1
2
2
0
0
0
1
0
0
2
0
1
0
0
0
2
0
2
0
2
0
1
2
2
1
1
1
0
0
2
0
1
0
0
0
1
0
1
0
1
1
0
0
1
0
0
1
0
1
0
0
2
1
0
2
0
0
0
0
1
0
3
2
0
1
1
1
0
1
0
1
1
1
1
1
0
0
0
0
1
2
2
0
2
1
1
0
1
0
1
1
1
2
1
2
0
0
1
2
0
1
0
2
1
1
1
2
1
3
0
0
1
0
0
1
0
0
1
0
2
1
0
2
2
1
0
0
2
2
1
1
0
2
1
0
1
1
1
2
3
1
1
0
1
2
4
0
2
1
1
0
1
1
2
0
1
0
1
2
2
2
1
0
0
0
0
1
1
0
1
1
1
0
1
1
0
0
0
1
1
0
0
0
0
1
2
0
1
1
0
1
1
0
1
0
1
0
1
1
1
0
1
0
2
0
1
0
1
2
1
1
0
0
2
0
0
0
1
2
0
1
2
0
1
0
0
1
1
0
0
0
1
1
0
0
2
1
0
1
0
1
2
0
1
4
0
2
0
1
1
0
0
0
2
0
1
0
0
2
1
1
0
1
1
1
0
0
2
2
0
1
1
1
1
2
0
1
0
2
1
0
1
2
0
2
1
0
1
0
2
2
0
2
0
0
1
0
1
0
1
1
1
2
0
0
1
2
0
1
0
0
0
1
0
0
0
1
0
1
0
0
1
0
2
1
3
0
1
0
1
0
0
2
0
0
0
0
1
0
0
0
0
2
2
0
1
0
0
0
1
0
0
2
1
1
1
1
2
1
1
0
1
0
1
1
1
0
0
1
0
0
1
0
1
1
1
1
0
2
2
1
2
0
0
0
0
3
1
1
1
0
1
1
0
1
1
1
3
1
0
0
1
0
2
0
0
1
0
0
2
1
1
1
1
2
2
0
0
0
0
0
1
1
0
2
0
0
2
1
2
0
1
0
1
1
0
0
1
3
0
0
1
0
0
1
2
0
2
0
2
2
1
1
2
1
0
0
1
0
1
0
0
0
2
2
2
2
0
0
2
0
0
0
2
0
2
1
1
2
2
1
1
0
1
2
1
0
1
0
2
0
2
0
0
2
0
0
0
1
1
1
0
1
1
1
2
2
2
0
2
1
0
0
2
0
0
1
2
1
1
0
0
0
0
1
1
0
0
2
0
2
0
1
1
0
0
0
1
1
1
1
2
1
1
0
0
2
0
0
0
0
2
2
0
0
2
2
1
1
1
3
1
1
1
0
1
0
2
0
0
1
0
2
0
1
1
2
0
0
1
0
2
1
3
0
2
0
0
0
2
4
0
1
1
0
2
2
0
0
0
0
1
1
1
0
1
0
0
2
0
1
1
1
0
1
0
0
0
0
1
2
0
0
1
2
0
1
0
1
1
1
0
0
1
1
2
0
1
1
0
1
1
1
1
0
1
2
2
1
1
0
0
0
0
1
2
0
1
1
1
2
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
3
0
2
0
0
1
0
2
1
2
0
2
0
1
2
3
2
1
0
0
2
0
0
0
0
0
1
1
0
0
1
0
2
0
1
1
1
0
1
1
0
0
1
0
2
0
0
0
0
3
1
1
0
2
2
1
1
0
1
2
0
1
0
2
1
2
0
0
0
0
1
1
0
0
2
0
1
0
0
1
0
0
4
1
0
0
2
0
2
1
0
0
2
1
0
1
2
0
0
2
2
0
1
2
2
1
0
1
1
2
2
0
0
2
0
0
1
1
0
1
1
2
0
2
1
2
0
0
0
2
0
0
1
2
0
0
0
1
0
0
0
2
1
1
0
0
0
0
2
1
0
0
0
2
0
2
2
1
0
0
0
0
0
0
1
1
0
0
0
1
1
0
1
0
1
1
0
0
2
0
1
0
0
0
0
1
2
0
0
0
0
0
1
1
0
0
1
2
0
1
2
2
0
0
0
0
2
0
0
0
0
0
1
1
0
1
1
2
1
2
1
0
1
1
0
1
1
1
2
1
1
3
0
0
1
0
2
0
0
1
1
0
0
0
2
0
0
0
0
2
0
0
1
0
1
3
1
2
1
0
0
0
0
2
0
1
0
1
1
0
0
2
0
0
2
1
0
1
2
0
0
0
0
2
0
1
2
1
1
1
1
0
0
0
0
2
0
1
0
1
0
0
2
1
1
1
0
0
0
0
0
2
0
2
1
1
0
1
0
0
0
1
0
1
1
0
1
2
2
1
2
0
1
1
0
2
3
1
0
0
2
0
1
2
1
2
1
1
2
0
4
0
2
1
1
0
1
1
2
1
0
2
2
1
1
2
0
1
1
0
2
1
0
2
0
1
0
1
0
1
2
2
2
0
0
1
3
1
1
0
0
2
2
0
1
0
0
2
1
2
1
0
0
0
0
1
1
2
1
1
0
0
1
1
1
0
0
1
0
0
0
1
2
0
0
0
0
2
0
1
0
0
0
2
0
0
1
2
1
0
1
1
1
1
0
2
1
0
2
0
1
1
0
1
0
0
0
1
1
1
1
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
1
2
0
0
0
0
1
1
0
0
2
1
0
1
0
1
0
0
2
0
0
0
1
1
1
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
2
2
1
2
0
0
0
1
0
1
0
0
0
2
0
0
1
2
0
2
2
1
0
0
2
1
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
2
2
0
1
2
0
1
1
1
1
2
1
1
1
0
0
2
0
0
1
2
0
3
1
0
0
1
1
0
1
0
2
0
3
0
0
1
1
1
3
2
2
0
0
1
2
0
2
1
2
2
1
2
0
1
1
1
0
2
2
2
0
2
1
0
0
1
0
3
2
2
1
0
1
0
0
2
0
1
1
0
0
0
0
2
1
1
1
0
2
2
0
1
0
2
1
0
0
2
2
0
0
1
2
2
1
2
0
0
1
1
1
1
0
1
0
1
0
1
1
0
1
0
0
0
2
0
0
0
1
2
0
0
1
0
1
0
0
1
1
2
0
0
1
2
2
0
0
1
0
0
2
2
0
1
1
1
0
0
1
0
1
0
0
0
0
1
1
1
0
1
0
2
1
0
1
0
0
0
0
0
0
0
0
1
1
0
1
1
1
0
0
0
2
0
0
0
0
0
1
1
1
1
1
2
0
0
0
1
1
1
0
2
1
0
1
1
1
0
0
1
1
2
0
2
0
1
2
0
1
1
2
2
1
0
1
0
0
1
1
1
2
0
2
2
1
0
0
2
0
0
2
0
2
1
0
1
0
1
0
0
0
2
1
2
0
0
0
0
2
1
0
1
0
0
0
0
0
0
1
0
0
2
1
1
0
1
0
2
0
0
1
2
1
2
0
0
2
0
2
1
1
0
0
2
1
0
2
0
1
0
3
0
1
1
1
2
1
0
0
2
2
2
0
1
1
1
1
0
1
0
0
1
1
0
2
2
3
0
1
1
1
0
0
2
1
1
2
2
0
1
1
0
0
1
2
2
1
1
0
0
0
2
2
1
2
0
0
1
2
0
1
3
2
2
2
2
2
1
0
1
1
0
1
0
1
2
1
0
1
1
1
1
0
0
0
0
2
0
0
0
0
1
2
2
1
1
1
1
1
1
0
1
0
0
1
0
1
1
0
0
0
2
0
1
0
0
2
1
2
1
0
0
0
0
0
1
0
1
2
1
1
1
1
1
0
1
1
0
2
2
1
1
1
1
3
2
0
0
0
1
1
0
1
1
1
0
2
0
1
0
0
0
0
0
2
1
1
0
0
0
2
0
2
1
1
1
0
0
2
0
1
0
1
1
1
0
0
1
2
1
0
1
2
1
0
0
1
0
1
0
0
0
2
1
0
1
0
2
1
1
0
0
0
0
0
1
1
1
0
2
0
1
0
2
0
2
2
0
0
1
0
0
0
0
0
1
1
1
2
0
0
0
0
2
1
1
1
0
2
1
1
2
0
0
1
2
1
1
1
0
1
1
1
2
1
0
0
1
1
2
0
2
1
1
1
2
0
0
2
1
0
0
0
0
0
2
0
0
0
2
2
0
3
1
2
2
0
2
1
1
2
1
0
0
1
2
1
1
1
1
0
0
1
1
1
2
0
1
0
1
0
2
1
1
1
0
1
1
0
1
0
0
4
2
2
0
0
2
2
1
1
1
2
2
0
0
2
2
1
2
1
1
1
2
1
1
0
0
0
0
2
2
1
2
0
1
1
2
2
2
0
1
0
0
0
2
2
3
0
1
1
1
1
1
0
0
0
2
0
1
0
1
0
1
0
0
1
0
0
1
1
2
1
0
0
2
2
1
2
0
0
2
2
0
3
2
0
2
0
1
0
0
0
1
2
0
2
1
0
1
1
0
1
1
1
2
0
1
2
1
2
2
1
0
1
1
2
1
2
1
1
0
1
0
1
0
1
1
0
1
2
0
1
0
0
1
1
0
2
1
0
0
2
0
2
1
2
2
2
0
1
2
2
2
0
0
2
2
0
0
1
1
0
1
0
2
1
0
1
2
1
1
0
2
0
1
0
0
1
1
2
0
1
1
1
1
0
0
1
0
2
0
1
1
2
0
0
1
0
0
0
1
0
2
1
1
0
1
0
1
1
2
1
2
1
0
2
3
2
1
0
1
0
1
2
2
2
1
1
0
0
2
1
0
1
1
2
0
1
1
1
1
1
0
1
1
2
1
2
1
0
3
0
1
2
0
2
1
1
3
1
2
0
1
1
1
0
0
0
0
0
1
1
1
2
0
0
0
0
0
2
0
0
2
0
1
1
0
2
1
0
1
1
1
1
0
0
0
2
0
1
1
1
1
1
1
0
0
0
2
0
0
0
1
1
0
1
0
0
0
0
1
1
1
1
0
1
1
1
0
0
1
1
2
0
0
2
1
1
0
2
0
0
3
1
0
0
0
0
0
1
1
2
1
0
2
0
0
0
0
0
1
0
0
1
1
0
0
1
2
1
1
1
1
0
0
1
0
0
2
0
0
1
0
2
0
1
0
0
0
1
0
0
2
1
1
1
0
0
0
1
1
2
0
1
2
1
2
0
1
0
2
0
0
1
0
1
1
1
0
1
2
1
0
1
1
0
1
0
0
1
0
0
2
0
0
1
0
0
0
2
0
2
1
2
1
0
1
1
1
1
2
0
2
2
1
1
1
0
0
1
1
2
0
0
4
0
0
0
2
0
0
0
0
2
0
2
0
0
1
3
0
1
1
1
1
1
1
1
0
2
0
1
2
1
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
1
1
1
1
1
1
0
1
1
1
2
0
1
2
2
1
1
0
0
0
1
1
1
0
1
1
0
0
0
2
0
0
0
0
2
2
0
0
1
0
1
0
1
2
3
1
0
0
2
0
1
0
0
0
2
2
1
0
0
1
1
0
2
1
1
2
0
1
2
0
0
1
1
0
0
1
0
1
0
0
0
1
2
3
2
0
2
1
1
0
0
1
0
1
2
2
1
1
1
1
0
1
1
2
0
2
2
0
0
1
0
2
0
1
1
2
2
1
1
2
0
0
0
0
2
2
1
1
1
0
0
0
0
0
0
0
2
2
1
0
0
0
0
1
0
0
2
1
1
0
1
2
1
1
0
0
0
1
0
2
0
0
1
1
0
0
1
2
1
1
3
0
0
1
0
2
1
0
0
1
1
1
0
1
1
1
1
2
2
2
1
0
1
2
0
0
1
1
1
1
1
2
0
0
1
0
0
0
1
1
0
0
2
0
1
2
2
1
0
0
2
2
1
0
0
1
0
0
0
0
1
3
2
1
0
2
0
1
0
0
0
1
1
0
0
0
1
0
0
2
1
0
1
1
0
2
0
0
1
1
0
1
3
2
0
2
1
0
3
0
1
2
1
0
2
2
0
0
0
0
0
0
0
0
2
0
1
0
1
2
1
0
1
2
1
0
2
0
2
2
1
1
1
1
1
1
1
0
0
1
0
1
0
0
1
0
1
0
0
2
0
2
2
1
0
1
1
1
0
1
2
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
2
0
1
1
2
1
0
2
1
0
1
0
2
0
0
0
0
2
0
0
1
2
0
1
1
2
1
3
0
1
1
0
0
1
1
0
1
2
0
0
0
0
0
1
2
3
1
1
0
0
2
2
0
0
0
0
1
1
0
1
0
0
1
0
0
2
1
0
0
0
0
0
2
2
2
1
2
0
0
0
2
0
3
0
2
1
0
1
0
1
2
2
0
1
2
0
1
0
1
0
1
1
1
3
1
0
1
1
0
1
0
0
1
1
0
1
0
1
0
0
2
0
0
1
0
0
2
0
1
0
1
2
2
2
0
1
0
0
0
0
1
0
1
3
0
1
1
0
0
1
0
2
1
0
2
0
2
2
1
1
0
0
1
0
1
3
0
1
1
2
0
0
0
1
2
1
2
0
1
1
2
0
0
1
0
0
0
1
0
2
0
1
2
2
0
2
1
1
3
1
0
1
2
0
1
0
2
2
0
2
2
2
0
1
1
0
1
1
0
2
2
0
2
2
1
0
0
1
0
0
0
2
0
0
0
2
1
1
2
3
2
0
0
0
0
0
1
0
1
0
2
2
0
2
0
0
2
1
1
2
2
0
2
0
0
0
0
1
0
2
1
0
1
0
2
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
1
1
1
2
1
2
0
0
2
2
1
0
2
0
1
1
1
2
2
1
2
1
1
0
0
1
1
1
3
0
0
0
0
2
2
2
0
7
0
0
2
2
2
3
1
1
1
2
2
1
1
1
1
0
1
0
1
0
1
1
1
1
2
0
0
1
1
0
2
2
1
0
1
0
0
0
2
2
2
0
0
0
1
1
2
0
1
1
1
0
0
2
0
0
1
1
0
0
2
0
0
0
2
0
0
1
0
1
2
0
1
2
2
0
4
0
0
2
1
1
1
0
1
2
1
1
0
0
1
0
0
2
2
0
1
1
1
0
1
0
0
0
1
0
1
2
2
2
0
0
0
0
1
2
2
2
2
0
0
0
0
3
1
2
1
2
0
0
0
2
1
1
0
0
0
0
1
2
1
1
3
1
1
0
0
0
1
2
2
0
0
0
0
2
0
1
3
2
1
2
0
1
0
2
2
1
2
0
2
2
0
1
2
0
1
1
1
0
0
1
2
2
0
1
0
2
1
2
1
1
0
2
0
0
0
0
1
2
0
1
2
1
0
1
0
1
1
1
0
2
1
1
1
0
2
2
1
0
0
2
1
1
2
0
2
1
1
0
1
0
0
0
0
2
0
1
1
1
1
0
0
2
1
0
2
2
0
2
0
2
1
0
0
2
0
1
4
1
0
0
0
2
1
2
1
1
1
1
2
0
0
0
2
0
2
0
1
1
0
1
1
1
0
0
1
0
0
0
2
4
1
2
1
2
1
0
2
0
1
2
1
1
1
2
1
1
2
0
2
1
2
0
1
1
0
0
0
0
0
2
1
2
0
0
1
1
1
1
2
0
1
1
0
1
4
0
0
1
2
0
2
1
2
1
0
0
1
1
0
1
1
2
2
1
0
1
3
1
0
1
1
1
1
1
0
1
1
0
1
1
0
1
1
2
2
0
2
0
0
1
0
0
0
2
0
1
0
1
0
1
1
0
2
2
0
2
2
2
1
1
0
1
1
0
2
2
1
2
2
0
0
2
1
0
2
2
1
2
0
0
0
0
0
1
1
1
1
0
1
0
0
1
2
1
1
2
0
1
0
1
1
2
1
6
0
1
1
2
0
1
0
1
0
1
0
0
0
0
1
0
1
1
2
3
2
2
1
2
2
0
0
0
2
1
0
0
0
0
1
1
1
0
0
0
0
2
0
1
1
0
1
2
2
0
0
1
2
1
2
1
0
1
0
1
2
2
0
1
1
1
1
1
0
0
0
0
0
1
1
0
0
3
0
2
0
1
1
2
0
1
2
0
2
1
0
1
2
1
3
1
0
2
1
1
0
1
0
0
2
0
0
1
0
1
1
0
0
0
2
0
0
0
2
1
0
2
0
1
0
0
0
0
0
0
0
1
0
2
1
1
2
3
1
1
0
0
2
0
0
0
1
2
0
2
4
1
0
2
2
1
0
1
1
0
1
1
0
0
1
1
1
1
1
1
1
1
2
0
1
0
0
0
1
0
0
2
1
0
0
1
0
1
1
2
0
0
1
0
0
0
1
1
0
2
2
3
1
0
0
1
1
0
0
0
1
2
1
2
0
1
1
0
1
0
1
2
1
1
2
0
1
1
0
0
0
0
2
1
2
0
0
0
2
1
2
2
0
0
2
0
1
2
1
1
2
1
1
1
1
0
0
1
0
1
1
0
1
2
1
0
2
0
2
2
0
1
1
1
1
3
0
2
0
2
1
1
1
2
0
0
2
0
2
0
0
2
3
0
1
2
0
0
1
1
1
0
0
1
1
0
2
0
1
1
0
0
1
0
0
0
2
1
1
0
0
0
2
0
0
1
0
0
2
1
0
2
0
1
1
1
1
0
1
2
1
1
1
0
0
0
1
0
1
0
0
1
2
0
0
2
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
1
2
1
0
1
1
0
0
1
0
1
0
0
0
1
2
0
0
2
1
2
0
0
0
1
0
2
0
0
2
1
0
0
1
1
1
2
2
1
1
1
2
1
0
2
0
1
2
1
2
0
0
1
0
0
0
1
1
1
0
1
0
3
0
2
1
2
0
2
2
1
2
0
1
1
0
0
0
1
1
6
2
2
1
0
1
0
2
0
1
0
1
1
1
0
2
0
1
1
2
3
0
0
1
0
1
1
1
2
0
0
1
2
2
2
1
0
1
0
2
0
0
0
2
0
2
0
0
2
2
2
0
1
1
1
0
2
0
0
2
1
2
2
1
3
0
1
0
0
0
1
2
1
1
0
1
0
0
0
0
1
1
2
1
1
2
0
1
0
0
2
1
1
2
2
0
1
2
0
2
2
0
1
1
1
1
0
2
0
0
1
0
2
0
2
1
1
0
0
1
1
1
1
0
0
0
1
1
1
1
1
1
0
0
0
0
1
1
1
2
2
1
1
0
0
2
0
0
1
1
0
0
1
2
0
0
0
1
0
1
0
0
2
2
2
0
2
0
0
1
2
0
2
2
0
1
0
0
1
0
1
2
1
0
2
1
2
2
1
2
1
2
0
0
1
1
2
5
0
0
2
0
1
1
2
0
0
0
1
2
2
1
0
1
0
1
1
0
1
1
1
1
2
1
1
2
2
0
2
1
1
0
1
1
1
0
0
0
0
1
0
2
1
1
2
0
1
0
0
1
1
1
1
0
0
2
0
2
2
0
2
2
1
1
1
1
0
1
0
2
1
2
1
0
0
0
1
0
0
0
1
1
0
1
0
0
2
1
0
0
1
0
0
2
0
0
0
0
2
1
2
0
1
1
0
0
0
1
0
3
0
2
1
0
0
1
0
0
2
1
2
0
1
0
0
0
0
0
0
0
2
1
0
0
1
1
2
1
0
1
1
2
2
1
0
0
3
0
1
1
0
1
10
2
2
2
0
0
0
2
0
3
1
0
1
2
0
1
1
1
1
0
0
0
0
0
0
0
2
1
1
1
1
0
0
0
2
2
2
1
2
0
1
0
0
0
1
2
0
2
1
0
1
2
0
2
0
0
1
2
0
2
0
1
0
1
1
2
0
0
0
1
0
0
1
0
1
1
0
1
0
2
0
1
2
0
0
3
1
1
2
0
2
0
2
1
0
1
2
1
0
1
1
0
1
1
0
2
1
1
2
1
2
0
0
0
0
0
0
2
0
0
0
1
0
2
1
1
0
2
0
0
0
1
2
2
1
1
0
1
2
2
2
1
0
1
1
0
3
2
2
1
1
1
0
0
1
1
1
1
2
1
2
2
0
1
1
2
1
1
1
0
0
0
0
2
1
1
2
0
1
0
2
0
1
1
0
1
2
1
1
1
1
0
0
1
1
0
0
1
0
0
2
1
2
2
1
2
1
1
3
1
1
1
0
1
1
1
1
1
2
1
1
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
2
0
1
0
0
1
0
0
1
0
0
0
2
1
2
1
1
1
2
0
2
1
2
2
1
1
1
1
1
2
0
2
0
0
2
1
0
2
2
2
0
1
1
1
0
0
2
0
1
0
1
0
0
0
1
6
0
0
1
1
1
2
1
1
1
1
2
2
2
1
0
1
1
1
0
0
0
0
1
0
3
1
2
0
1
0
1
1
1
1
0
2
0
1
0
1
1
1
0
0
3
1
1
0
0
1
0
0
1
1
2
0
0
1
0
0
1
1
0
1
0
1
0
0
1
1
2
1
1
0
2
2
1
0
1
0
3
0
0
0
0
0
0
0
3
4
0
1
0
0
0
0
0
2
1
0
2
2
0
2
1
1
1
1
2
2
0
0
2
1
0
0
2
0
1
2
0
2
1
0
0
1
0
2
2
0
0
1
0
1
1
1
0
1
0
1
0
0
0
0
0
1
1
2
1
1
3
1
0
0
1
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
2
0
1
1
2
2
1
0
1
2
2
1
0
1
1
1
1
1
2
0
2
1
2
1
0
1
0
1
0
2
2
0
2
1
0
2
3
2
4
1
1
2
0
1
0
2
0
1
2
1
1
0
0
1
0
0
1
0
0
1
1
1
0
1
2
2
0
2
1
1
0
0
2
1
0
0
0
0
1
2
0
0
1
2
1
0
2
2
1
1
2
1
0
1
0
2
0
0
1
0
1
2
1
1
2
0
2
1
1
0
1
1
0
2
0
0
0
2
0
2
1
2
2
2
0
2
0
2
2
0
3
1
1
0
1
0
2
1
1
1
2
2
0
2
1
2
1
0
1
0
0
1
0
2
1
0
0
0
0
0
2
0
2
1
0
1
1
0
1
0
2
1
2
0
1
0
0
0
0
0
0
0
1
1
0
0
0
2
0
1
1
0
0
0
0
2
0
1
2
2
2
2
1
0
2
2
1
0
0
2
1
1
0
1
0
1
2
1
0
1
0
0
1
0
0
1
0
1
0
0
2
0
0
2
0
1
2
1
0
2
0
0
1
0
0
0
1
0
1
1
1
0
0
0
2
1
0
2
0
2
0
1
3
0
1
1
1
0
1
0
0
0
0
0
1
0
1
2
1
2
0
0
2
0
0
0
1
1
2
1
2
1
0
2
0
0
2
1
2
1
1
0
0
0
0
1
1
1
1
0
0
0
2
1
0
0
7
0
2
1
2
1
0
0
0
1
0
1
0
0
1
2
2
1
2
1
2
0
1
1
1
1
1
0
0
2
0
0
1
0
1
2
0
0
0
1
2
2
2
0
1
0
1
1
2
1
0
1
1
2
0
1
1
3
2
2
0
1
0
0
1
0
0
1
0
1
0
1
0
1
0
0
2
0
1
0
2
0
0
1
3
1
0
0
1
1
2
0
1
1
1
2
1
0
1
2
2
2
0
0
0
1
0
0
0
0
0
2
2
2
0
1
0
0
0
0
2
1
0
2
1
0
0
2
1
1
2
0
0
1
0
2
1
1
1
1
1
0
0
0
1
0
1
0
0
1
3
1
0
2
3
1
1
0
0
2
1
1
0
1
1
2
0
0
0
2
1
2
0
0
0
0
0
1
1
1
1
1
0
1
1
1
1
0
1
2
1
1
2
3
1
0
2
0
0
2
2
1
0
0
0
1
1
0
1
0
0
2
1
1
2
2
1
1
0
4
0
1
0
0
2
0
0
1
3
2
3
0
0
1
1
1
2
0
2
1
1
0
1
1
1
1
2
1
1
0
0
2
1
0
1
0
1
1
0
0
1
1
1
0
0
3
2
0
1
0
0
0
1
2
3
0
1
2
2
0
0
1
2
0
1
1
2
0
1
0
0
0
2
0
0
0
1
0
2
2
1
2
1
2
0
2
0
1
2
1
1
1
1
0
0
1
0
0
2
1
1
2
2
2
2
2
1
0
0
1
1
0
0
2
2
2
0
1
2
1
2
0
0
0
0
0
1
2
2
0
1
2
0
0
1
0
0
0
1
0
0
2
1
0
0
0
0
2
1
0
1
1
1
1
0
2
2
0
0
2
1
1
0
0
2
1
3
1
2
0
0
0
0
1
0
1
2
1
2
1
0
1
1
0
1
2
0
0
0
1
0
0
2
1
1
0
0
0
1
0
2
2
0
1
2
0
1
0
0
1
1
1
1
1
0
0
1
0
0
1
0
0
0
2
1
0
1
0
1
0
2
2
0
0
4
0
0
2
0
0
0
2
1
0
1
0
0
0
0
1
2
2
1
0
0
1
2
0
4
1
1
0
0
0
0
0
1
2
0
1
0
0
0
2
2
2
1
0
1
2
1
0
0
1
0
1
2
0
1
1
0
0
0
1
0
2
0
1
3
1
0
1
1
2
1
0
0
1
1
2
0
0
0
0
0
1
1
0
1
0
1
0
0
0
2
1
0
1
1
1
0
1
0
0
0
0
1
0
0
0
1
1
2
1
1
1
2
0
1
0
0
3
0
2
1
0
0
0
1
2
1
2
0
2
2
0
1
1
0
0
2
1
0
1
2
0
0
0
0
0
0
2
1
1
0
0
1
2
2
1
1
0
0
1
1
4
1
1
1
2
0
3
1
0
0
1
1
0
1
0
2
1
0
0
0
2
1
0
1
0
1
1
0
0
2
0
1
1
1
2
1
1
2
0
2
0
1
0
1
0
0
2
1
1
0
0
0
2
1
0
1
0
2
0
1
2
0
1
0
2
2
2
3
1
0
1
0
0
1
0
0
1
1
2
1
0
2
2
1
2
2
0
0
1
2
1
1
0
1
0
1
1
0
0
0
0
0
0
0
1
2
1
2
0
0
0
1
0
2
2
1
0
2
1
1
2
1
5
0
0
2
0
1
0
2
1
0
1
0
2
0
0
0
1
0
2
0
2
1
2
1
0
1
0
0
0
1
1
0
1
0
1
0
2
1
0
0
2
0
1
0
1
0
0
1
0
2
1
2
2
1
1
1
2
1
0
0
0
1
2
3
1
0
1
1
1
1
1
2
0
1
0
0
0
0
1
0
0
0
0
1
1
2
0
1
1
0
0
1
0
0
2
1
1
0
1
2
1
1
2
2
0
1
2
1
1
0
0
1
0
1
0
1
1
1
1
0
0
0
2
2
0
2
1
5
2
1
0
2
1
1
1
2
1
0
0
1
0
0
0
3
1
1
0
0
1
1
0
3
0
1
1
0
1
1
0
1
0
0
0
0
0
2
0
1
0
0
1
2
1
1
1
0
1
1
0
0
2
0
1
0
1
2
2
0
3
1
1
0
1
0
0
1
1
1
1
1
2
2
0
1
0
1
0
1
0
0
0
1
0
2
2
1
0
1
1
0
2
0
2
1
0
2
0
2
0
0
0
0
2
0
2
0
2
1
0
0
2
0
1
2
2
1
0
0
0
1
1
2
1
2
0
2
0
0
2
1
0
0
1
2
0
0
1
2
0
0
0
0
0
1
2
0
2
0
1
0
2
0
2
1
2
0
0
0
2
0
1
0
2
2
1
1
1
0
1
0
0
2
0
0
2
1
1
0
0
0
1
0
0
1
1
0
1
0
0
1
1
0
2
1
0
0
0
0
0
0
2
1
2
3
1
1
2
1
1
0
2
1
0
1
1
0
0
1
2
2
0
1
0
1
0
2
2
1
2
0
0
2
2
1
2
2
2
1
1
0
2
0
0
1
1
0
0
0
0
4
0
0
1
1
1
1
1
2
2
2
1
1
1
1
0
1
2
1
0
1
1
0
0
0
1
1
1
0
2
2
0
1
2
0
0
1
0
1
0
0
1
2
2
1
0
1
0
1
0
0
0
2
0
1
0
2
0
0
0
0
3
1
0
2
0
1
1
0
0
0
2
0
0
0
4
1
3
2
0
1
2
1
1
1
0
0
1
2
0
0
1
0
1
0
0
0
0
1
0
1
0
0
2
1
0
1
1
0
0
0
1
2
1
2
1
2
0
1
0
1
0
2
0
1
0
0
2
1
0
0
4
2
2
0
1
0
2
2
2
0
0
2
1
1
0
0
0
0
0
1
2
2
0
1
1
0
1
0
1
0
1
1
0
1
1
0
2
1
0
0
3
2
0
2
0
1
2
0
0
0
0
1
1
0
1
2
0
1
0
2
0
1
0
2
1
2
1
0
0
1
1
2
0
1
0
1
2
2
1
1
2
2
1
0
1
0
1
1
1
3
0
1
0
0
0
0
1
1
2
1
1
1
2
2
0
2
1
1
1
2
1
2
1
2
1
1
2
0
1
2
1
0
2
1
0
1
1
2
1
0
1
1
1
0
1
0
0
0
1
0
1
0
0
2
1
2
1
0
2
2
0
1
0
0
2
0
1
1
0
1
0
1
0
0
0
1
2
1
0
1
1
2
2
0
2
1
0
2
0
0
1
1
1
0
0
1
0
0
0
0
2
2
0
0
1
1
1
0
0
2
1
1
2
0
0
0
1
1
2
1
1
0
0
1
0
1
1
2
1
1
1
0
2
2
0
2
0
0
2
1
2
0
1
0
1
0
1
1
2
0
0
1
0
0
0
0
0
0
1
0
0
1
2
1
0
2
1
0
1
1
2
2
1
0
1
1
1
1
0
0
0
0
1
1
0
2
0
0
1
2
0
1
0
0
1
1
0
2
1
2
1
0
1
2
2
0
3
0
1
1
2
1
2
0
2
0
0
0
2
1
1
1
1
0
1
0
1
1
2
1
2
0
0
2
1
1
1
1
1
0
0
0
0
0
1
0
1
1
0
0
1
0
2
0
0
0
1
3
2
1
0
0
0
2
2
0
0
2
0
2
4
1
2
2
3
1
0
1
1
0
1
0
2
2
1
0
0
0
2
0
0
2
0
1
0
2
0
1
2
1
2
1
1
0
1
2
0
2
2
2
1
2
2
1
0
1
2
0
0
1
2
0
1
0
1
0
0
0
2
2
2
1
2
1
1
1
5
0
1
0
1
1
0
1
1
0
1
1
1
0
1
0
2
1
1
1
4
0
2
0
0
1
0
0
0
2
0
1
0
2
1
0
0
1
0
0
1
1
3
2
0
0
0
0
2
1
0
2
1
1
2
2
1
0
1
1
2
0
2
2
0
0
1
2
2
1
1
1
0
0
2
0
0
1
0
2
0
0
1
1
0
1
0
1
0
1
1
0
1
1
1
1
1
2
0
0
0
0
1
1
0
0
2
1
1
2
0
0
2
2
1
2
1
1
0
0
1
2
1
1
0
1
1
0
0
2
0
0
0
0
1
2
0
0
3
1
1
1
0
1
0
1
2
5
0
2
0
2
1
0
2
2
1
1
0
2
1
0
0
1
1
0
0
1
1
0
1
2
0
0
1
0
0
1
1
1
1
0
2
0
1
0
0
1
0
0
1
2
2
0
0
1
1
1
1
1
2
1
1
2
3
0
0
0
1
1
1
0
1
1
0
2
1
0
0
0
3
1
0
1
0
1
1
0
1
2
1
0
0
1
1
0
1
1
0
0
0
1
0
2
1
1
2
0
0
1
2
0
0
0
1
1
0
1
0
1
2
2
0
0
0
0
1
1
1
0
2
1
2
1
2
0
2
0
1
0
1
2
1
2
0
2
2
2
1
0
2
1
0
1
0
2
0
0
0
2
1
1
1
1
0
2
0
0
1
0
0
1
8
1
0
1
0
0
2
0
0
0
1
1
1
0
1
0
2
1
1
1
2
0
1
0
0
0
0
0
1
1
0
1
1
1
1
1
0
2
2
1
1
4
1
0
0
0
1
2
0
2
1
2
0
1
2
2
1
1
1
2
1
1
1
0
0
0
0
1
1
1
2
0
0
1
1
1
0
1
1
0
1
1
1
1
2
2
0
1
1
1
1
1
0
0
2
1
1
1
0
0
1
0
2
1
2
0
0
2
0
0
0
1
0
2
1
0
1
1
0
0
1
0
1
2
0
0
1
1
0
1
1
3
0
0
0
0
0
1
1
0
1
0
2
0
1
2
0
2
1
0
0
1
0
1
0
1
2
0
0
0
1
0
1
2
1
0
2
1
1
2
2
1
0
2
0
1
0
0
1
1
1
1
2
0
0
2
0
0
2
1
0
2
2
0
2
0
1
0
0
0
0
0
1
0
1
0
2
2
2
1
1
1
2
0
4
2
0
1
0
0
2
1
1
1
0
2
0
2
1
1
2
1
2
0
2
1
1
0
2
2
0
0
1
1
0
2
1
0
0
1
1
0
0
0
1
0
2
0
0
1
0
0
0
0
2
1
1
1
0
2
0
2
1
0
2
0
1
1
0
0
0
1
0
1
1
0
0
0
1
1
0
1
0
0
3
0
0
2
3
0
0
2
2
0
0
2
3
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
1
0
2
0
1
2
0
2
2
1
0
2
1
1
0
1
1
0
0
1
1
0
1
0
0
1
1
2
1
0
0
2
2
0
0
2
1
1
2
0
0
3
2
2
1
0
0
0
1
2
1
2
0
1
0
1
1
2
1
0
0
0
2
2
0
1
1
0
0
0
1
0
1
0
1
1
0
0
1
0
2
1
0
0
0
0
1
2
1
1
2
0
1
0
2
0
0
1
1
0
1
1
0
0
2
0
0
0
2
0
2
1
1
2
0
0
2
0
0
1
1
0
0
0
2
2
0
1
2
1
1
1
1
1
0
1
0
0
2
0
0
0
2
2
0
0
0
0
0
1
0
2
2
0
2
1
1
0
1
0
1
0
2
1
0
0
2
1
1
0
0
1
0
1
0
1
0
1
0
1
1
2
1
0
2
0
1
2
0
1
1
1
1
1
2
0
1
1
1
1
1
0
1
0
0
0
1
2
0
0
0
1
1
1
2
1
2
0
1
2
0
1
0
0
1
1
1
0
2
2
3
2
3
1
2
2
2
0
0
1
0
2
0
1
0
0
0
1
0
0
0
2
2
0
1
0
1
1
0
0
1
0
1
0
1
1
1
0
0
1
0
1
0
0
2
1
1
0
0
2
2
0
1
2
1
2
1
2
0
2
0
0
2
2
0
1
1
1
1
0
0
2
1
1
1
2
0
1
1
1
1
1
2
0
0
0
2
0
1
0
2
0
1
1
2
0
0
2
0
1
1
0
2
0
2
1
1
0
0
0
1
0
1
0
1
1
0
2
2
3
1
1
0
0
1
1
2
0
2
1
0
0
0
1
1
2
0
0
2
0
0
0
2
1
1
1
2
1
0
2
0
2
0
0
1
0
1
1
0
1
1
0
0
0
2
0
2
0
2
2
0
0
0
0
0
1
1
1
0
1
1
1
0
1
0
1
1
1
0
0
1
2
1
0
1
0
1
1
1
1
0
0
1
1
0
0
1
2
1
2
2
0
0
0
1
1
1
0
2
2
1
2
0
1
0
0
0
2
0
1
2
1
2
0
0
0
2
0
0
1
1
0
1
0
1
0
0
0
1
1
0
2
1
0
0
2
0
1
0
2
1
0
2
0
0
2
0
2
1
1
2
2
1
0
0
2
2
0
2
2
0
1
1
0
1
0
0
1
1
1
1
1
1
3
0
0
0
1
1
0
0
0
1
0
0
2
1
2
1
0
1
0
0
0
2
1
0
0
0
0
2
0
0
1
2
2
2
1
2
1
1
0
0
2
0
0
2
0
1
1
0
1
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
2
1
1
0
2
1
1
1
0
1
0
0
1
0
1
1
1
1
1
0
1
0
1
0
0
1
2
1
2
0
1
1
0
0
2
0
1
0
0
2
0
0
0
0
0
2
1
1
2
0
1
0
1
2
2
0
1
2
1
1
1
2
0
0
0
0
1
0
0
1
1
1
1
0
2
1
0
0
0
0
2
1
2
1
1
0
2
0
2
1
2
1
1
1
0
0
1
0
0
0
0
2
4
2
2
2
1
1
1
0
0
2
0
2
3
0
2
1
0
0
0
1
0
1
0
0
2
1
1
1
1
1
0
0
1
2
2
1
0
1
2
1
1
1
1
1
2
0
2
1
0
1
2
0
2
1
1
0
0
0
0
0
0
1
0
1
1
0
1
1
0
0
2
2
0
0
1
1
0
0
1
1
0
0
0
1
3
2
1
0
1
0
2
1
0
2
4
0
2
1
0
1
1
2
1
1
1
1
0
1
1
2
0
2
0
1
0
0
1
1
2
0
0
1
2
0
0
1
1
0
1
2
1
0
1
1
1
2
0
0
0
0
1
0
0
3
0
1
0
3
0
0
1
0
0
2
1
1
2
2
2
0
1
0
0
0
1
1
0
1
0
2
1
0
0
2
2
1
1
1
3
2
1
2
6
2
0
1
0
2
2
1
0
2
1
0
2
0
1
1
1
0
0
0
0
0
0
0
0
1
0
1
5
1
0
1
0
0
0
2
2
0
2
2
1
0
1
0
0
2
2
0
0
0
1
1
1
1
0
1
2
1
0
1
1
0
0
0
0
1
2
0
2
2
2
0
0
0
1
1
1
0
4
1
0
1
0
0
1
2
0
1
0
0
1
0
1
0
0
0
0
1
2
2
2
0
0
2
2
2
1
1
1
1
0
2
0
1
1
0
0
0
1
1
0
1
0
1
2
1
0
1
1
1
2
0
0
2
0
2
0
2
1
1
3
1
0
0
1
4
0
1
1
0
0
0
2
0
1
1
1
1
1
1
2
1
0
2
2
0
2
0
2
0
2
0
2
0
0
2
0
0
0
3
0
0
1
2
1
2
1
1
0
1
1
1
1
2
0
0
0
0
1
1
1
1
1
1
0
0
1
0
1
1
0
1
1
2
2
0
1
0
1
2
0
0
0
0
0
2
1
1
2
1
1
1
0
0
1
0
1
1
2
1
0
1
2
1
0
0
1
0
0
2
2
1
1
0
0
3
1
1
1
0
2
0
0
2
0
1
0
1
1
1
2
0
0
1
0
2
1
2
1
1
2
0
1
0
0
0
1
0
1
2
0
2
0
1
1
1
1
1
0
1
1
2
0
0
0
0
2
2
0
0
0
1
2
0
2
1
2
2
2
1
0
1
1
0
2
1
0
0
0
1
0
0
1
1
0
0
0
2
1
0
0
1
0
1
2
0
0
2
2
0
2
0
0
1
0
2
0
0
0
0
0
2
0
1
0
1
0
2
0
0
0
2
1
1
1
0
0
2
0
1
1
1
0
0
0
1
0
2
0
1
1
1
0
2
2
0
1
1
1
0
2
1
0
0
0
0
0
2
0
1
2
1
2
1
0
2
0
0
1
2
1
0
0
1
1
3
1
1
2
1
1
0
1
1
2
1
2
0
1
0
0
2
0
1
2
0
0
0
0
1
0
2
0
0
0
0
0
1
2
0
1
1
0
0
1
1
2
1
0
2
2
1
1
0
0
0
0
1
1
2
1
0
0
0
1
1
1
0
0
0
0
2
0
1
0
1
1
2
1
0
1
1
1
1
0
1
2
0
1
0
0
0
2
1
1
1
1
1
0
0
1
1
0
2
0
1
2
0
1
0
0
0
0
1
0
1
0
0
2
0
0
0
1
2
0
2
0
0
1
1
0
0
2
1
1
0
1
1
1
2
1
0
2
2
0
0
0
1
1
2
0
0
2
1
0
1
0
2
1
1
0
0
2
1
0
0
2
1
1
2
0
0
2
1
0
1
0
0
1
0
2
2
0
0
1
1
1
2
0
2
2
0
2
0
1
1
2
1
0
1
2
1
1
1
1
1
1
0
1
0
0
2
0
0
0
2
0
2
1
2
1
1
1
1
2
1
0
1
1
1
1
0
0
0
1
0
1
0
1
1
1
1
2
0
0
0
0
1
2
2
2
0
0
0
2
1
0
1
0
1
0
1
1
0
0
1
0
1
0
1
1
1
0
1
1
2
2
0
1
2
0
0
1
1
1
1
2
2
0
2
0
0
2
0
2
0
1
2
2
1
2
1
0
1
1
2
2
2
0
2
0
1
1
0
1
0
2
0
0
0
2
2
1
2
2
0
2
1
1
2
1
2
1
0
0
0
0
0
1
2
0
1
0
2
0
1
0
1
0
0
0
1
0
2
2
0
2
0
1
2
1
2
0
1
1
0
0
1
1
0
2
2
2
0
2
1
3
0
2
0
2
1
1
0
0
1
0
0
1
1
1
2
0
0
1
0
0
0
0
1
0
1
0
2
0
0
1
0
0
1
2
2
1
2
1
0
0
0
0
2
1
2
2
1
1
1
1
0
2
0
0
1
0
0
1
1
0
0
2
1
1
1
0
0
1
0
1
1
1
2
0
1
3
1
0
0
1
1
2
1
3
0
0
2
0
0
1
1
2
1
0
1
2
2
1
1
0
0
0
1
1
2
1
1
0
1
1
0
0
2
0
1
0
2
0
1
0
0
1
2
1
0
0
0
2
1
0
1
2
0
1
0
1
1
0
0
0
2
0
2
0
0
2
0
0
2
0
0
0
1
0
2
0
0
1
0
0
0
1
0
0
2
1
0
2
0
2
1
0
1
1
0
0
0
1
2
1
0
2
1
0
0
1
1
0
0
0
1
0
2
1
0
0
1
0
0
0
0
2
0
1
0
1
1
1
0
0
1
0
0
0
0
0
1
1
1
2
1
1
0
0
0
1
1
0
1
0
1
2
0
1
2
1
2
1
2
0
1
2
0
1
2
2
1
0
0
0
0
2
2
0
1
0
0
2
1
2
2
2
1
0
0
1
0
1
1
2
1
0
1
1
1
2
0
0
0
1
0
1
2
0
0
2
0
1
0
2
1
0
1
1
1
0
0
0
2
0
0
1
1
1
0
1
0
1
2
0
0
0
1
0
0
2
0
1
1
1
0
2
1
0
2
0
1
2
1
2
2
1
1
0
0
3
0
2
0
1
0
2
3
2
1
1
1
0
1
1
0
0
0
2
1
1
0
0
0
0
0
3
0
1
1
2
0
0
2
1
0
2
0
1
2
2
0
1
0
0
1
0
0
2
2
0
0
2
2
0
0
0
0
0
0
0
1
1
0
2
1
0
1
1
0
2
1
1
2
1
0
0
1
4
1
0
0
2
0
0
1
1
0
0
1
0
1
0
1
2
0
2
1
1
1
1
0
2
2
1
2
0
0
1
1
1
2
0
1
0
1
0
1
1
1
0
1
3
0
0
2
1
0
1
1
0
0
1
0
1
0
2
2
1
1
0
0
0
0
0
1
1
2
2
1
0
0
2
2
2
1
2
1
0
4
0
0
0
1
2
1
2
2
0
0
1
0
0
2
0
1
0
1
2
1
2
1
0
0
0
2
2
1
0
0
0
0
1
2
0
0
2
1
2
0
1
1
0
0
2
0
0
2
1
0
0
1
1
0
0
0
1
0
0
0
1
0
1
0
0
1
0
1
0
0
3
0
1
2
0
2
2
1
0
0
2
1
0
0
4
0
1
0
1
0
0
0
2
0
0
1
0
3
0
2
0
0
1
1
1
1
0
2
0
0
2
0
1
0
0
0
0
0
1
2
2
2
0
3
0
2
2
0
2
0
2
0
1
0
0
0
2
0
1
2
1
1
2
0
0
0
1
2
0
4
0
0
2
1
0
2
1
0
2
0
0
0
0
0
0
0
1
1
1
2
2
1
2
1
0
1
1
1
0
1
0
0
1
1
0
2
1
1
1
2
0
1
0
2
0
0
2
2
1
0
1
0
1
1
1
1
0
3
0
3
2
2
1
1
1
1
0
0
1
0
1
2
0
2
0
0
0
1
0
0
2
6
0
1
2
1
0
1
0
1
4
0
0
0
0
0
0
0
1
3
1
0
0
0
0
1
0
1
0
2
0
1
0
1
2
0
1
2
2
1
0
1
2
2
0
0
1
2
0
0
0
2
1
1
2
1
2
0
1
2
0
1
0
1
0
0
1
0
1
2
0
2
1
3
1
0
0
0
0
0
2
0
1
1
2
0
2
1
1
0
0
5
0
0
1
0
1
2
0
0
0
0
1
0
2
2
0
1
0
0
0
1
0
2
2
0
2
1
1
1
1
1
0
0
2
2
0
2
0
1
1
0
0
0
2
2
0
0
1
1
1
0
1
1
0
0
1
1
0
1
1
0
1
0
0
1
1
2
1
2
0
0
1
1
0
2
0
4
0
1
1
0
1
0
0
2
0
1
1
2
0
2
0
1
2
0
0
0
2
1
0
1
2
0
1
1
2
1
0
0
0
1
2
1
0
1
0
0
0
1
0
0
0
2
1
0
1
0
1
1
1
1
1
1
1
1
2
1
1
0
1
1
1
1
0
1
0
0
2
0
0
0
0
0
2
0
1
1
1
1
0
1
2
0
1
1
0
1
1
1
2
1
0
3
2
2
0
2
0
0
0
0
2
0
1
0
2
0
2
0
0
0
1
1
2
0
0
1
1
2
0
1
0
0
2
0
1
0
0
0
0
0
0
2
0
3
2
1
0
0
1
0
1
1
2
2
1
2
2
1
0
2
2
0
0
2
0
1
1
0
0
3
2
0
2
0
1
1
1
0
1
2
0
1
0
0
0
0
1
0
0
1
2
1
1
1
0
0
0
0
2
0
2
0
1
0
0
2
0
1
1
2
2
0
0
1
0
0
2
1
1
0
0
2
2
0
2
2
2
1
0
2
0
0
2
0
0
1
1
0
0
0
0
2
1
1
2
0
2
1
3
1
1
0
1
0
0
0
0
0
0
2
1
0
0
0
2
2
1
0
1
0
0
0
1
0
1
1
2
1
1
2
1
2
0
1
0
1
0
0
0
0
0
2
0
0
1
1
1
1
0
0
0
1
0
0
1
0
2
0
0
1
1
2
0
1
0
0
0
1
2
0
3
0
0
1
1
2
0
1
2
0
1
2
0
1
2
1
1
1
1
0
1
2
0
2
0
2
1
0
1
1
0
1
1
1
0
1
2
2
1
0
1
0
1
2
0
2
0
1
1
2
2
0
2
1
0
2
1
1
1
0
0
1
1
0
0
3
0
1
1
2
0
1
2
1
2
1
1
1
2
0
2
1
2
1
1
2
0
1
1
1
1
2
0
1
0
1
0
1
1
1
0
0
0
1
1
1
0
2
0
0
2
2
0
1
0
1
2
2
1
0
0
0
0
0
1
1
1
0
0
2
1
1
0
2
0
1
2
1
2
1
0
0
2
2
0
0
1
1
2
1
1
0
0
0
1
0
0
1
3
0
0
2
0
1
3
0
1
1
1
2
1
1
0
2
2
2
2
0
0
0
0
1
1
0
1
0
1
1
2
0
0
1
0
0
1
0
0
1
2
0
1
0
0
0
0
0
0
1
2
1
2
1
1
2
1
2
2
2
1
2
2
2
2
1
2
1
2
0
0
0
2
0
0
1
0
2
1
2
2
1
0
0
1
0
2
0
1
1
0
2
1
0
0
2
0
1
0
0
0
1
2
0
2
1
1
0
1
1
1
0
0
0
2
1
2
1
2
2
1
2
1
1
0
1
1
1
0
0
2
1
1
0
1
0
1
2
1
0
2
0
1
1
0
0
2
1
1
2
0
0
1
0
0
0
2
0
2
0
2
1
1
1
1
0
2
1
0
1
1
1
0
0
0
2
0
0
2
0
2
0
0
0
2
0
0
1
0
0
2
0
2
0
1
0
0
0
0
1
0
0
1
1
1
0
4
2
1
0
0
0
1
2
2
1
1
1
0
0
2
0
0
1
0
0
1
0
1
1
1
0
0
2
1
0
1
0
0
1
2
2
1
0
1
1
1
1
1
0
1
0
1
1
1
1
1
1
0
0
0
2
1
1
3
2
1
0
1
0
2
2
0
0
2
0
1
0
1
2
0
0
0
1
1
2
0
1
0
0
0
0
1
0
1
1
2
0
0
2
0
1
0
1
2
2
0
0
0
2
0
0
0
1
1
1
2
1
1
2
2
2
0
0
1
1
0
4
0
1
2
1
0
0
0
2
2
0
1
1
1
1
1
0
2
2
0
1
2
0
0
0
0
1
1
0
2
2
1
2
1
2
1
2
0
4
0
0
0
0
1
1
1
1
0
0
0
1
0
1
1
2
2
4
1
0
1
0
0
2
0
1
0
0
1
0
2
1
1
2
0
0
1
0
1
0
1
3
1
0
2
0
0
1
0
1
2
0
1
1
0
0
0
0
2
2
2
1
0
2
2
0
0
1
0
0
0
1
0
0
1
1
2
1
0
2
1
2
0
1
0
1
0
2
1
2
0
0
0
1
1
1
2
1
1
1
1
1
0
0
2
2
1
0
2
0
0
0
0
2
1
1
1
1
0
0
0
0
0
1
0
0
0
1
1
0
2
0
1
1
0
3
1
1
2
2
0
1
1
1
0
1
2
1
0
0
2
0
1
2
1
2
2
1
0
1
0
2
2
0
0
1
1
1
0
1
3
1
2
0
1
0
1
0
1
2
1
1
2
1
1
2
0
2
1
0
1
0
2
0
1
0
2
1
2
0
0
2
0
1
0
1
0
0
2
0
2
1
1
0
0
2
5
0
0
1
0
0
0
1
0
0
1
0
1
0
0
1
0
0
1
1
0
1
0
0
0
0
0
2
1
0
2
0
1
2
2
2
1
1
1
2
1
2
1
0
0
0
1
2
1
2
0
0
2
1
2
2
1
2
0
0
2
0
1
1
0
1
1
0
1
1
0
0
1
0
1
0
1
1
0
1
2
1
0
0
1
0
0
4
0
0
2
1
0
1
1
2
2
0
1
2
1
0
1
0
0
3
2
0
1
2
1
0
1
1
0
0
2
0
1
1
0
0
2
0
1
1
1
2
0
0
2
1
1
0
2
2
2
0
0
1
0
1
1
0
2
0
2
1
0
2
0
2
1
1
1
0
0
0
2
1
0
1
0
0
1
2
2
6
1
2
0
0
0
0
1
2
0
1
0
0
1
2
1
2
0
3
0
0
2
2
2
1
0
0
1
0
0
0
0
1
0
1
1
1
1
1
0
0
1
0
0
0
2
0
1
0
2
0
0
1
0
0
3
1
1
1
0
0
2
7
1
2
1
2
1
2
1
1
0
0
0
1
1
0
0
2
3
1
1
2
1
0
2
0
0
0
2
0
0
1
0
2
2
0
2
0
1
1
0
0
0
1
0
0
0
1
0
0
1
2
2
0
0
0
0
1
1
1
0
2
0
2
0
1
0
0
2
2
1
0
1
1
0
2
1
0
2
1
0
0
1
0
1
0
1
1
0
0
2
0
0
1
1
1
0
0
1
0
0
0
1
2
2
2
1
1
0
1
0
3
1
0
1
0
0
0
2
0
0
1
0
1
0
0
0
0
0
3
0
1
0
2
2
2
1
1
2
1
1
1
1
2
0
0
1
2
0
2
2
1
2
0
2
2
0
0
1
0
1
0
2
1
2
0
3
0
0
0
2
0
2
0
0
2
1
1
1
0
0
1
1
0
1
2
2
1
1
1
1
1
2
1
2
2
1
0
1
0
0
1
1
0
2
0
1
0
0
0
2
0
0
0
2
1
0
0
1
0
1
1
0
0
0
1
2
2
0
0
1
0
1
0
2
0
1
2
2
1
1
1
1
0
1
0
1
0
2
1
2
0
1
2
0
1
1
2
2
0
0
0
1
0
1
3
2
0
0
1
2
1
0
0
0
0
0
0
0
0
2
0
1
0
1
1
1
2
0
1
0
0
1
1
1
0
0
2
0
2
1
1
1
0
2
0
0
1
0
2
1
1
2
1
1
1
1
1
0
0
1
0
1
0
2
3
2
0
0
2
0
0
1
1
0
2
0
0
0
1
1
0
0
1
2
0
2
1
0
1
1
0
0
0
1
2
0
0
2
2
1
1
2
1
0
1
0
1
1
0
1
2
0
0
0
0
0
0
3
0
1
1
0
2
0
0
0
0
1
1
1
0
0
0
0
0
0
1
1
0
0
4
0
1
0
0
0
0
0
0
0
0
3
0
2
1
1
2
2
1
0
0
1
0
0
0
0
2
0
1
2
1
2
1
0
0
0
1
0
2
0
1
0
0
1
1
0
1
1
1
0
0
0
1
2
0
2
2
2
1
0
0
0
1
1
1
0
0
0
1
0
0
0
1
2
0
1
2
2
0
0
1
1
0
1
1
2
0
1
1
2
3
1
2
0
0
0
2
0
0
1
1
1
2
0
2
2
1
1
4
1
2
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
2
1
2
2
0
2
2
0
2
2
0
1
2
1
2
1
2
2
0
1
1
1
0
1
0
1
1
0
0
1
1
1
2
2
0
0
1
1
0
0
0
2
0
1
1
1
1
2
1
0
1
2
2
1
1
2
0
1
0
0
1
0
2
1
2
1
1
0
2
2
2
1
0
2
0
1
1
2
0
2
0
2
1
2
1
0
2
1
0
1
0
0
0
0
1
0
1
2
0
2
0
1
0
1
0
1
0
0
2
0
0
1
1
0
0
1
1
1
0
2
0
2
1
0
0
0
1
2
1
0
1
1
2
0
0
1
0
0
2
1
1
2
2
2
0
1
2
2
1
2
2
3
0
0
1
1
1
0
3
0
0
0
1
0
2
0
0
0
0
1
2
0
1
0
2
0
0
2
0
4
2
1
2
0
1
2
2
1
2
2
1
1
2
0
1
2
0
0
0
0
2
1
2
2
0
1
2
0
2
1
0
0
0
1
0
1
1
0
0
0
4
1
0
0
0
1
1
1
0
2
0
1
1
2
1
2
2
2
0
0
0
2
0
1
2
0
1
2
1
0
0
1
0
0
1
0
0
0
1
1
2
1
2
0
0
0
0
0
1
0
2
4
2
0
1
1
1
2
0
2
1
1
1
0
0
1
0
2
1
2
0
1
2
2
1
1
0
0
0
0
0
0
2
1
2
1
0
0
0
0
1
0
1
1
1
2
0
2
1
0
2
2
3
0
2
0
0
0
2
0
1
2
2
2
0
1
0
1
1
1
0
0
0
1
2
1
1
0
1
1
2
1
0
1
2
0
2
1
0
1
0
0
2
1
1
0
1
1
0
1
1
1
2
0
1
0
0
2
1
1
1
0
0
4
2
0
0
0
0
0
1
3
1
0
1
2
1
2
2
2
1
2
2
2
0
0
0
1
0
0
0
0
0
1
1
0
1
1
1
1
1
3
1
2
0
0
0
0
2
0
3
1
0
0
1
2
2
0
1
2
1
0
0
0
1
0
0
0
0
0
0
1
0
0
2
2
2
1
1
1
1
0
0
0
1
1
2
0
1
1
0
0
1
0
2
1
0
1
0
0
2
1
0
2
1
1
0
2
0
0
1
0
1
3
0
2
0
1
0
1
2
2
1
0
0
2
0
1
0
2
1
1
2
0
0
3
1
0
0
2
0
1
0
0
1
0
1
0
2
0
2
1
0
1
0
2
2
0
1
1
1
1
2
0
0
2
1
1
1
0
0
0
0
1
2
3
0
1
2
0
1
0
2
0
0
0
1
0
0
0
1
0
1
0
2
2
2
0
0
0
2
0
1
2
2
1
2
0
2
0
0
0
0
1
0
2
0
0
0
2
0
1
2
0
1
0
0
0
1
0
1
0
1
1
1
2
0
0
2
0
1
0
1
1
0
1
0
1
0
2
1
2
1
0
0
0
2
1
1
2
0
1
0
2
0
0
2
3
0
0
0
2
1
2
1
0
2
1
0
0
1
0
2
0
0
0
1
0
1
2
1
1
0
2
1
2
0
0
0
1
0
2
1
0
0
0
1
0
1
0
0
1
0
1
1
2
0
2
1
0
1
1
2
2
0
0
0
0
0
0
1
0
1
0
1
0
2
0
1
0
1
0
1
2
0
2
0
1
1
1
0
0
1
2
2
1
2
0
1
0
0
0
2
0
3
1
1
1
0
2
1
1
1
0
1
1
0
0
2
0
1
1
2
1
0
1
2
0
0
1
1
1
3
2
0
0
1
1
0
1
1
0
0
2
1
0
1
0
1
1
0
1
1
0
1
0
1
0
1
2
0
0
0
0
0
1
1
0
1
1
0
1
0
2
2
0
0
1
0
0
0
1
0
0
0
2
2
2
0
1
2
0
0
2
0
1
2
1
0
0
0
0
1
2
0
1
0
0
2
1
2
0
0
1
1
0
0
0
1
2
0
1
0
0
0
1
1
0
0
2
2
0
2
0
0
0
2
0
2
1
1
1
1
2
0
1
1
0
1
1
1
0
1
0
0
0
0
1
2
1
0
0
0
0
0
1
1
1
1
0
4
0
0
0
0
0
0
2
1
0
1
1
1
1
2
0
0
0
0
0
2
2
2
1
1
1
1
0
0
2
2
0
2
0
1
0
2
1
2
0
1
0
1
1
0
0
2
1
1
5
2
1
2
0
1
0
1
1
0
1
1
0
1
0
0
0
0
0
2
0
1
1
0
0
0
2
2
1
1
0
0
1
1
0
0
1
0
1
1
2
1
0
0
1
0
2
1
1
1
0
1
0
0
2
0
0
0
2
2
2
0
0
1
3
2
0
1
1
0
2
0
0
1
1
2
2
2
0
1
0
0
1
0
1
1
0
0
2
0
1
1
2
2
0
0
1
2
0
0
1
0
1
0
1
2
1
1
2
0
1
1
0
1
0
2
2
1
1
1
0
0
0
1
2
0
1
0
1
1
2
0
1
1
0
0
1
2
0
0
1
2
1
0
1
0
0
0
0
0
1
0
0
0
1
0
1
3
2
0
1
1
3
0
0
1
0
0
1
0
0
2
0
1
0
0
1
0
0
0
0
0
2
0
0
1
1
0
1
2
2
0
1
0
2
0
0
0
0
2
0
1
0
0
2
0
0
2
1
2
2
0
1
2
0
1
1
0
0
0
1
0
1
0
0
0
1
1
1
2
0
1
1
0
1
1
1
0
0
2
2
1
1
1
0
1
2
0
0
0
0
0
2
0
0
0
1
2
1
0
0
0
1
0
0
0
0
0
0
0
2
0
2
1
2
3
2
1
0
2
1
0
0
0
0
1
2
1
0
2
1
1
1
1
1
2
1
2
2
1
1
1
1
0
2
0
2
0
0
1
1
1
0
1
0
2
1
0
1
1
1
1
2
0
1
0
1
1
1
1
0
2
0
0
1
2
1
1
2
0
0
2
1
2
2
0
0
2
1
1
0
1
1
2
1
0
1
1
1
0
1
0
0
0
0
1
0
0
0
0
1
1
1
2
0
1
0
1
0
1
0
0
2
2
0
0
0
2
2
2
2
0
0
1
0
2
1
0
1
1
0
2
0
0
2
0
0
0
2
1
2
2
1
1
1
2
0
1
1
1
1
1
0
0
1
2
0
0
0
1
0
1
2
1
1
0
0
0
1
1
0
1
0
0
0
2
0
2
2
0
1
0
2
1
0
0
1
0
0
2
2
1
1
1
1
3
2
0
1
0
0
1
1
0
0
0
1
1
1
0
2
0
0
0
1
2
2
0
2
0
1
1
2
1
0
0
1
1
0
1
0
3
2
0
0
0
1
1
1
0
1
0
0
0
1
0
2
2
2
2
2
2
1
0
0
0
0
0
1
0
0
2
1
0
1
1
0
0
0
0
0
2
1
1
1
0
1
0
0
1
2
1
2
1
0
2
0
1
0
1
2
1
2
0
0
0
3
2
0
2
2
0
1
1
2
0
2
0
1
1
1
2
0
1
2
0
2
1
2
1
1
2
0
2
2
0
2
1
3
0
3
0
1
2
0
1
0
0
0
0
2
0
1
2
1
0
0
0
2
1
0
1
1
2
1
2
2
0
1
0
0
1
0
0
0
2
1
2
1
1
2
1
0
0
0
0
2
0
2
1
2
0
1
1
1
0
3
1
2
0
0
0
0
1
1
1
0
0
0
1
2
0
0
1
2
0
1
0
2
2
0
0
0
2
2
0
2
0
0
3
1
0
2
0
1
0
1
1
1
2
0
1
0
0
1
1
1
1
0
1
0
0
0
0
2
0
1
0
0
0
0
2
1
0
0
0
1
1
1
0
0
1
0
2
1
1
1
0
0
0
1
0
0
0
0
1
0
2
0
1
2
1
0
2
1
2
1
1
1
3
1
1
0
2
1
0
0
1
1
1
0
2
0
0
0
1
2
1
0
0
0
1
0
0
1
3
0
1
2
2
0
0
0
0
1
0
2
0
1
0
1
1
1
1
2
0
1
0
1
1
0
1
2
1
1
0
1
1
0
1
0
2
0
2
1
0
1
1
2
2
2
0
1
2
3
1
2
0
0
1
1
1
2
2
0
0
0
1
0
0
2
0
0
2
2
2
1
0
0
0
1
3
0
1
2
2
0
0
0
0
0
0
1
0
1
0
2
0
0
1
0
0
0
0
0
1
1
0
1
1
0
0
2
0
1
2
0
1
1
0
0
1
0
0
1
0
0
0
1
0
2
0
1
0
0
0
2
0
1
1
1
0
0
1
1
0
0
0
1
1
1
2
2
1
0
0
1
2
1
0
0
0
1
2
1
0
2
2
2
0
0
0
1
1
2
1
2
1
2
0
2
1
1
1
0
0
1
0
1
0
0
0
2
1
0
1
2
0
1
2
0
1
1
0
2
1
1
0
2
1
1
1
0
0
2
1
1
2
0
0
0
0
1
2
0
2
0
0
0
1
2
2
1
0
3
1
2
0
1
1
2
1
0
1
1
0
2
2
0
2
0
1
1
0
2
1
0
0
2
1
2
2
0
1
0
1
1
0
1
1
2
0
1
0
1
0
1
0
0
2
0
0
0
1
0
0
1
1
0
1
0
1
0
1
1
1
1
0
3
0
0
1
1
1
0
2
0
0
1
2
2
2
1
0
2
0
0
1
2
0
1
1
0
0
1
1
1
1
0
0
1
1
1
1
0
2
1
0
0
0
2
1
1
0
1
1
1
0
0
1
0
2
1
1
1
1
1
0
1
1
1
2
1
0
1
1
0
0
1
0
1
0
1
2
1
0
1
1
0
1
2
0
0
1
1
1
0
2
0
1
1
1
1
1
0
1
1
1
2
0
0
1
2
0
0
1
0
2
0
0
0
2
0
0
1
1
2
0
0
0
0
0
2
1
1
0
2
0
2
0
0
1
0
1
2
2
1
2
1
0
1
1
2
1
2
2
0
1
2
1
1
2
2
0
1
2
1
1
0
0
0
0
0
1
1
1
1
0
1
2
1
1
0
0
2
2
0
0
1
0
0
0
2
0
0
4
0
1
0
0
1
1
2
0
1
1
0
0
1
1
2
0
0
1
0
1
1
1
1
0
1
1
0
1
1
0
2
0
1
0
1
2
1
2
0
0
2
1
0
1
1
0
3
1
0
1
0
0
0
1
0
0
0
2
1
0
1
0
0
2
0
1
1
5
1
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
1
0
1
2
2
1
2
1
0
0
2
0
0
2
0
2
1
1
0
1
2
0
0
0
2
1
2
1
0
0
0
0
0
0
2
0
0
0
0
0
1
2
1
0
0
1
0
0
2
1
0
0
1
2
0
1
0
0
1
0
0
0
0
2
0
1
0
2
0
0
1
1
2
2
3
0
1
0
2
2
1
0
0
1
0
1
2
1
1
2
0
0
1
1
1
0
0
1
1
0
1
1
1
0
1
0
1
0
0
0
0
0
0
1
1
1
1
1
0
1
2
2
0
1
1
1
0
1
1
2
2
0
0
0
0
1
1
0
0
0
2
0
0
2
0
0
1
0
0
1
0
0
0
1
1
1
2
1
0
1
0
0
2
1
0
1
0
0
5
0
1
1
0
1
2
1
0
0
1
0
1
1
1
1
1
1
1
1
0
1
3
1
0
0
1
2
0
2
2
1
1
1
0
0
0
1
0
0
0
1
2
1
0
0
0
1
1
1
1
2
1
1
0
1
0
0
0
0
2
1
0
1
0
1
1
0
0
2
0
2
1
3
0
0
1
1
1
1
0
2
0
2
0
1
0
0
1
0
0
1
1
0
0
0
2
2
0
0
1
1
1
0
1
0
2
1
0
1
1
2
1
0
3
3
0
2
1
1
0
0
1
2
0
2
1
0
1
0
0
0
1
0
0
1
0
0
1
1
0
1
2
1
0
1
0
0
0
1
0
1
2
1
0
1
0
0
0
2
2
1
1
2
0
1
1
1
0
0
0
2
0
2
0
1
1
1
1
0
0
0
0
0
1
2
1
2
2
1
1
0
0
3
1
0
1
0
1
1
0
1
0
0
0
1
0
0
0
0
1
2
1
0
1
1
0
1
0
0
0
1
2
0
1
0
0
0
1
0
0
0
0
1
2
1
0
0
2
2
1
0
0
1
1
0
1
0
2
0
2
2
1
1
0
2
1
2
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
2
1
0
0
0
0
2
0
0
0
1
0
0
1
2
1
1
0
0
1
0
1
0
0
1
1
0
1
1
0
3
0
1
0
0
0
2
1
0
2
0
2
1
0
0
2
0
3
0
1
1
0
1
0
1
1
2
1
0
1
1
0
0
1
0
0
1
1
0
2
1
3
0
2
2
0
0
1
1
0
1
1
1
0
2
0
1
0
1
2
1
2
2
0
0
0
1
2
0
1
2
1
0
0
1
2
2
2
2
1
3
2
0
0
1
1
0
2
0
2
1
2
0
2
1
1
0
0
0
2
0
2
2
0
1
1
5
1
0
0
2
1
2
1
2
0
2
2
1
2
2
0
0
0
2
0
0
3
2
0
2
1
0
0
0
1
0
0
0
1
1
1
2
2
0
0
1
0
0
1
1
1
2
0
2
0
0
0
1
0
0
0
0
1
0
1
0
2
2
1
0
1
2
0
0
1
0
2
3
0
1
16
2
1
0
1
0
0
1
2
2
0
0
2
0
0
0
1
2
0
0
0
1
2
0
0
2
0
1
1
0
0
2
0
1
1
1
2
2
3
0
1
2
1
1
0
1
1
0
2
0
0
1
0
1
1
5
1
1
2
0
0
0
0
1
0
1
1
0
1
1
0
1
1
1
2
1
0
1
2
0
0
0
2
1
1
2
2
1
2
1
1
0
0
2
0
2
1
0
2
1
1
2
2
0
1
0
0
1
2
0
0
0
1
0
0
2
1
1
0
1
2
0
0
2
1
0
1
1
0
1
2
0
1
0
3
0
2
2
1
0
1
0
1
0
0
0
0
0
0
2
2
1
2
0
0
0
1
1
1
0
0
2
1
1
0
2
1
1
2
0
0
1
1
0
2
0
2
0
0
2
0
2
0
2
1
0
0
2
0
2
0
2
1
1
0
0
1
0
0
0
0
1
1
0
0
1
2
0
1
2
1
2
1
0
0
1
0
0
0
0
1
2
0
1
1
1
2
1
0
0
0
4
0
1
0
1
1
0
1
1
0
0
0
0
1
0
0
0
2
3
2
1
0
2
1
0
2
1
1
1
1
0
2
0
2
1
2
1
0
2
1
1
1
1
0
1
1
2
0
0
1
0
1
2
2
0
0
0
0
1
1
2
1
1
0
0
0
2
1
0
0
0
0
0
2
1
1
1
0
2
1
3
0
1
1
1
0
0
1
1
0
1
0
2
1
1
2
0
0
0
0
0
0
1
0
0
0
0
2
2
1
0
0
2
1
1
0
0
1
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
1
1
1
1
1
0
1
0
1
2
1
0
1
1
1
0
1
0
0
1
1
2
1
2
0
0
1
1
0
3
0
1
1
1
0
0
2
1
1
0
2
0
0
0
0
0
1
1
0
0
2
1
0
0
0
0
1
2
1
1
0
0
3
0
2
2
0
0
2
0
1
2
0
1
1
0
1
1
0
2
1
1
2
2
3
1
1
0
2
1
1
0
1
0
0
0
1
1
1
0
1
0
1
1
0
2
0
1
1
2
2
0
1
1
1
1
1
0
1
0
0
0
1
1
0
1
3
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
3
0
2
1
2
2
2
0
0
0
0
2
1
2
2
1
2
1
0
1
0
0
2
0
0
0
1
2
3
2
0
1
2
1
0
1
2
0
1
2
1
1
2
2
0
0
0
0
1
0
0
0
1
1
2
1
0
1
0
2
1
0
0
1
1
1
1
2
1
1
1
0
1
0
0
1
1
1
0
0
0
0
0
1
1
0
2
0
1
1
1
0
1
2
1
4
0
1
0
1
1
2
0
0
1
0
0
0
2
0
0
1
1
0
2
1
2
2
0
1
1
1
1
2
2
2
2
0
0
0
0
2
1
1
1
0
2
0
2
0
2
1
1
2
1
1
1
0
0
0
1
0
0
2
1
0
0
1
1
1
0
0
1
1
0
1
1
0
3
0
0
0
1
2
1
2
0
2
2
0
2
3
0
1
2
0
0
0
2
0
3
0
2
2
2
0
2
1
2
0
2
1
0
1
0
1
0
0
2
0
1
0
0
2
0
1
0
0
0
0
1
2
0
0
2
0
1
0
0
2
0
0
0
1
1
0
1
0
2
0
0
1
0
1
0
1
0
0
0
2
1
0
2
1
1
1
1
2
1
1
1
1
1
1
0
1
2
0
1
3
0
0
0
2
1
2
0
0
1
1
0
0
2
1
0
2
1
1
1
0
1
0
0
2
1
0
1
1
1
1
1
1
1
0
2
0
2
0
1
0
0
1
0
0
0
0
0
1
0
0
1
1
1
1
0
0
1
1
0
0
1
10
0
3
1
1
0
1
0
0
4
0
1
0
1
1
1
1
0
0
0
1
0
0
0
0
1
0
1
1
2
0
1
1
0
1
0
0
0
1
0
1
1
2
2
0
0
0
0
1
1
2
0
0
1
0
0
2
1
0
0
1
1
2
0
0
1
1
2
2
1
0
2
0
0
1
1
1
1
0
0
1
0
0
2
0
1
2
2
1
0
2
1
0
1
1
0
0
0
1
2
2
0
1
2
2
0
1
1
1
0
1
0
1
1
0
1
0
0
0
2
1
1
0
0
1
1
0
2
1
0
0
1
2
2
0
2
0
0
0
0
2
1
1
0
1
1
0
0
1
0
0
1
1
0
0
0
2
1
2
2
1
0
0
2
2
0
0
1
1
1
0
1
2
2
1
1
0
1
0
0
0
2
2
3
1
1
0
0
2
1
1
1
2
1
0
2
0
0
1
0
1
0
2
1
2
1
1
3
2
0
0
1
1
0
1
1
1
1
0
1
2
0
0
0
1
2
1
0
0
0
1
0
2
0
2
0
0
0
0
1
1
0
2
0
2
2
1
0
0
1
1
1
0
2
1
1
1
0
0
0
0
1
1
2
1
1
1
2
0
0
2
1
0
0
0
0
0
2
0
1
0
1
0
0
1
1
0
2
1
1
1
0
2
1
0
0
1
0
2
0
1
1
0
1
2
1
1
1
1
1
0
1
1
0
0
2
1
0
2
0
1
2
0
1
2
0
1
0
0
0
2
1
1
7
0
0
1
1
2
1
1
1
2
1
0
0
0
0
1
0
1
0
0
0
2
1
1
0
1
0
0
0
1
1
1
1
0
0
3
1
0
1
0
1
1
1
1
1
1
1
1
2
0
0
2
0
1
0
1
0
0
1
1
1
1
0
0
0
2
0
1
2
1
2
1
1
0
0
0
1
1
2
0
0
1
1
0
1
0
1
0
2
0
0
2
2
1
0
2
1
2
2
1
1
0
1
1
0
1
1
0
2
1
0
1
0
0
0
2
0
0
0
1
0
1
1
2
0
0
1
1
1
0
2
0
2
0
1
0
1
0
0
1
1
1
1
1
2
2
0
0
1
2
0
3
0
0
1
2
2
0
0
1
1
1
1
0
2
1
0
1
1
0
2
0
1
0
0
1
2
1
1
2
0
1
1
1
2
1
1
1
0
1
1
1
0
0
2
0
0
0
2
1
1
1
0
2
0
0
0
1
1
0
2
0
1
0
1
0
1
0
2
1
0
1
0
2
1
2
0
2
0
1
2
0
1
2
0
0
0
0
1
2
0
1
0
2
1
0
1
1
1
1
0
0
0
0
0
1
0
1
1
0
0
0
1
2
1
0
2
1
1
0
2
2
1
1
3
0
0
0
0
0
1
0
1
1
1
0
0
2
0
2
0
0
2
0
1
1
1
0
2
2
0
0
0
1
2
1
3
0
3
0
0
0
0
1
3
0
0
2
2
0
1
0
0
0
0
1
2
0
0
2
0
1
2
0
1
2
0
3
2
0
1
0
0
2
0
2
0
1
0
1
0
2
1
0
1
1
2
0
1
2
0
2
3
0
1
0
0
1
0
1
1
1
1
2
0
1
2
0
1
1
1
0
1
3
2
2
0
1
0
1
1
1
0
0
1
3
1
0
2
0
0
2
1
1
3
1
2
2
0
0
1
2
1
1
0
2
1
0
1
1
2
2
0
1
1
1
0
2
0
1
1
0
0
1
0
1
0
0
1
1
3
1
1
0
1
0
0
1
3
0
1
0
1
1
2
1
2
1
1
2
0
1
1
2
2
1
2
0
0
0
1
0
0
1
0
0
0
1
1
2
0
0
2
1
0
0
2
0
0
0
0
2
0
1
1
0
0
0
1
0
0
1
0
0
0
1
0
1
2
0
2
0
0
0
1
1
1
2
0
0
1
1
1
0
2
1
1
1
2
0
1
0
1
1
2
1
0
1
2
1
1
0
2
0
0
0
0
2
0
1
0
2
0
1
0
0
0
1
2
2
0
1
0
2
1
0
2
1
2
1
0
1
0
1
0
1
1
0
0
1
0
0
1
1
0
1
2
0
0
1
1
0
0
1
1
0
1
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
2
2
2
0
0
1
2
2
1
0
0
1
2
1
0
0
0
0
2
0
0
0
1
1
1
0
0
0
1
0
2
1
4
1
0
1
0
1
1
0
0
0
0
0
1
1
1
2
1
0
2
1
0
0
0
0
3
0
0
0
2
0
2
0
0
0
0
0
0
1
0
1
0
2
2
0
1
0
0
0
1
0
0
1
0
0
1
1
2
0
0
1
2
1
2
0
2
2
2
0
1
1
2
0
2
2
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
1
0
2
2
2
1
1
0
2
0
2
0
0
0
1
2
1
0
0
1
0
1
1
0
1
2
0
0
1
1
0
2
0
0
0
0
2
1
1
1
2
0
4
1
1
1
1
0
0
1
0
1
0
1
1
0
0
0
2
1
2
0
0
2
0
1
1
1
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
1
1
1
1
1
0
1
2
1
0
0
2
1
0
0
1
1
0
1
0
2
1
1
0
1
0
1
0
2
1
0
0
0
2
0
1
1
1
1
0
0
0
0
2
1
0
0
2
1
0
1
1
0
1
1
1
0
0
2
0
1
1
1
1
0
0
1
0
1
0
1
0
1
0
0
2
1
2
0
2
0
0
0
0
0
2
1
2
3
2
1
2
2
2
1
1
2
1
2
0
1
2
1
1
1
2
2
0
0
0
3
1
1
1
0
1
0
1
3
2
1
0
1
0
0
1
0
0
0
0
2
1
1
1
0
0
1
0
2
2
1
2
3
0
0
2
1
2
1
1
5
2
0
2
0
1
0
0
2
0
0
0
3
1
1
1
1
0
2
6
0
0
2
0
1
1
1
2
1
2
1
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
1
1
2
2
0
0
0
2
1
0
1
0
0
1
1
0
2
1
2
1
1
0
2
2
0
1
2
1
1
0
1
2
2
1
0
0
2
0
0
0
2
0
0
0
0
1
1
0
1
1
2
0
0
0
0
0
0
1
0
2
1
0
0
2
2
0
0
1
2
2
2
1
0
0
0
1
1
1
2
1
0
0
4
0
0
0
1
0
2
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
1
1
2
3
0
0
0
0
0
1
0
2
2
0
1
0
0
5
0
3
1
1
2
2
0
2
3
1
1
0
0
0
0
2
0
0
2
2
1
0
1
2
2
0
3
0
2
0
1
1
1
0
2
2
1
2
0
1
0
2
0
1
1
1
1
0
2
0
0
1
1
1
1
0
1
2
2
1
1
1
0
0
2
1
0
1
4
1
0
0
0
1
2
2
1
0
0
0
2
1
1
3
0
1
1
1
0
2
1
1
0
1
0
1
0
0
1
0
1
0
1
1
1
0
2
0
1
0
0
2
2
0
1
0
0
0
0
1
1
0
1
1
0
0
1
1
1
0
1
1
0
1
2
0
3
2
1
1
1
1
1
0
1
0
0
0
0
1
0
0
0
1
2
2
2
1
1
1
0
1
0
1
0
0
0
2
2
0
1
1
0
1
0
2
1
1
0
1
0
0
1
1
0
2
2
2
2
1
0
0
0
0
2
0
0
2
0
1
0
0
0
3
2
1
0
1
1
1
1
2
1
2
1
1
2
1
1
2
2
1
1
0
0
2
0
0
1
1
1
0
0
0
0
1
0
0
0
0
1
2
0
0
1
0
1
0
3
0
1
4
1
0
0
0
0
6
2
1
0
2
0
0
0
2
2
1
2
6
1
2
0
0
1
2
0
0
0
1
1
0
2
0
1
0
1
2
0
0
0
0
2
0
2
0
1
1
0
0
0
3
2
1
0
1
1
1
1
3
0
1
2
0
2
2
0
0
0
0
0
1
0
1
0
1
0
2
0
0
0
0
0
1
2
0
1
1
0
0
1
1
0
1
0
0
1
3
0
2
2
1
2
0
0
2
0
1
1
2
0
1
3
2
0
0
1
1
0
0
1
0
1
1
0
0
1
0
0
0
0
1
1
2
0
1
0
0
2
0
2
1
0
0
1
1
0
0
1
0
1
0
1
0
2
0
2
1
1
0
0
1
2
0
1
1
0
1
1
1
2
2
1
0
1
0
1
0
1
0
1
1
3
3
3
1
1
0
1
0
1
0
0
1
2
0
0
2
2
0
0
2
0
0
0
1
5
2
2
0
1
1
1
0
0
0
1
0
1
1
1
0
1
1
0
1
1
0
2
0
2
2
1
1
0
1
2
0
2
0
1
1
2
0
1
0
2
2
0
2
3
1
2
1
0
2
2
1
0
0
0
0
0
1
0
1
1
0
0
2
2
1
0
1
2
2
1
1
0
0
1
0
1
0
1
2
0
1
2
2
0
1
1
1
0
0
2
0
1
1
0
0
2
1
2
0
1
2
0
0
1
0
0
0
1
0
0
0
1
0
2
1
1
2
0
1
0
1
0
0
2
0
2
0
0
1
1
0
1
0
0
0
1
1
2
0
0
0
0
0
0
2
0
4
2
1
1
4
1
3
1
2
1
0
2
0
1
2
0
1
2
3
3
0
2
1
2
2
0
0
0
1
0
2
0
0
0
1
2
1
0
0
2
1
1
0
1
2
2
1
2
1
0
2
2
2
2
1
0
1
1
0
1
1
2
1
0
1
1
0
1
0
1
0
0
0
0
1
2
2
0
1
0
0
1
0
0
1
1
0
2
1
0
1
0
0
1
1
0
0
0
1
2
0
1
0
2
1
0
2
0
0
2
2
0
0
1
1
0
1
2
1
1
0
0
2
0
1
0
0
0
1
0
2
0
1
0
1
0
1
2
2
0
0
1
0
2
0
2
2
1
1
0
1
1
0
0
2
1
0
0
1
1
0
0
1
2
0
1
1
2
0
1
1
2
3
0
1
1
0
0
1
1
2
2
0
2
1
0
1
2
1
0
0
0
0
0
0
2
2
0
2
0
0
1
1
0
1
0
0
2
1
1
0
2
0
1
1
2
0
2
0
0
0
0
0
1
0
0
0
0
1
0
2
1
0
1
0
0
0
2
1
1
0
0
0
0
1
0
3
1
1
0
0
0
0
0
1
0
2
2
1
0
0
0
2
0
1
2
0
0
0
2
0
0
2
1
1
1
1
2
0
2
1
2
0
1
1
0
2
2
2
0
1
1
1
0
1
1
0
1
0
0
0
1
1
1
0
1
1
1
0
1
2
2
0
0
0
1
8
2
1
1
1
0
0
0
0
1
2
0
0
0
0
2
2
0
0
0
0
0
1
0
1
1
1
0
1
0
0
0
0
1
1
2
1
1
1
0
1
0
0
5
4
1
1
0
2
1
2
0
2
0
1
1
1
1
0
1
1
0
2
2
1
1
2
2
0
1
2
2
0
1
3
2
0
0
1
2
1
0
0
0
0
0
0
0
1
1
1
2
1
1
0
0
0
0
1
0
2
1
0
0
1
1
0
2
1
1
0
1
2
0
0
0
0
4
2
0
0
1
1
1
0
0
2
2
0
2
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
2
1
1
0
2
2
1
3
0
1
2
0
1
2
0
0
0
0
1
0
1
2
1
2
1
0
0
0
0
0
2
0
1
1
2
0
0
0
1
0
0
0
1
1
0
2
0
2
2
1
1
2
0
0
2
0
1
0
2
0
2
1
0
2
3
0
0
1
3
2
0
1
0
2
1
2
2
0
2
0
0
1
1
1
0
1
0
1
1
2
0
1
2
2
1
0
0
2
1
3
2
0
1
1
1
2
2
2
3
0
0
2
1
1
2
0
2
0
2
1
1
2
0
0
0
1
0
0
1
1
0
1
0
1
1
0
2
1
2
1
0
0
1
1
0
1
0
1
0
1
1
0
0
3
1
1
2
1
0
1
1
1
1
0
0
0
1
2
1
1
0
1
0
2
1
0
1
1
0
1
1
0
0
0
1
0
1
0
3
1
0
1
0
1
1
0
0
2
0
0
2
1
0
0
0
0
1
0
0
1
1
1
1
0
2
0
0
0
1
2
0
3
4
1
0
2
0
1
1
1
2
2
0
0
1
0
0
0
1
1
1
0
0
1
0
0
1
0
0
0
1
1
2
2
2
2
1
0
0
0
1
2
1
0
0
0
2
1
1
2
0
1
0
0
1
1
1
1
1
0
1
1
1
0
2
1
1
1
0
0
0
1
1
1
0
1
0
1
1
0
1
1
1
2
2
0
0
1
0
0
1
0
0
3
1
0
1
1
1
0
1
0
0
1
2
0
0
0
0
0
1
1
1
2
2
0
2
1
0
1
0
0
1
2
1
1
1
1
1
0
0
1
1
0
1
1
1
2
0
2
0
1
0
0
0
2
0
1
1
1
0
0
2
0
2
1
0
0
0
1
0
1
1
1
2
1
0
1
0
0
2
2
0
1
0
1
0
0
1
0
1
1
2
1
1
1
2
2
2
2
0
0
3
1
1
0
1
1
4
1
0
0
1
1
0
0
0
2
0
0
0
2
0
0
0
0
0
1
1
0
0
1
0
1
0
1
1
1
2
0
0
2
1
0
0
0
3
1
0
0
2
1
1
0
0
1
2
1
2
0
2
2
1
1
2
1
0
2
0
0
0
2
2
1
1
1
1
0
1
0
2
3
0
1
2
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
1
0
0
2
0
2
0
0
1
0
0
1
1
1
0
0
2
0
0
1
2
0
2
0
1
1
0
1
0
2
1
2
0
0
0
1
0
2
0
0
0
0
0
1
1
2
0
0
0
1
1
1
0
0
0
0
0
0
1
1
0
1
1
1
2
2
1
1
0
1
0
1
1
2
3
2
1
1
0
2
2
0
2
2
0
1
1
1
0
2
0
1
1
0
2
1
0
1
0
2
1
0
1
1
0
1
0
1
2
1
1
1
1
0
0
2
1
0
2
2
1
0
0
1
0
1
1
1
1
1
2
1
1
0
0
0
9
2
0
1
1
0
0
1
0
1
1
1
1
0
0
0
2
0
0
2
1
0
1
1
0
1
1
1
0
1
5
1
0
0
0
2
2
1
1
1
0
1
1
2
2
0
1
1
0
0
0
2
2
1
2
0
2
1
1
0
3
1
0
1
5
2
1
2
1
1
1
0
1
0
4
0
0
1
1
1
1
1
1
2
0
0
0
1
0
0
0
1
0
2
2
1
1
2
0
0
1
0
1
0
0
0
0
2
0
0
0
2
2
2
0
1
0
2
0
2
0
0
2
0
0
1
1
2
2
0
0
1
2
0
1
2
1
2
2
0
1
0
0
2
2
1
0
1
1
0
0
2
1
0
1
0
1
0
1
2
2
0
1
1
1
2
2
0
0
1
2
0
2
1
1
0
2
1
1
0
2
1
1
3
1
1
3
0
2
1
0
2
0
1
3
1
2
2
1
0
2
1
0
1
0
0
1
0
0
0
0
2
0
1
0
0
0
4
1
0
0
1
0
1
1
0
2
1
1
0
1
2
1
1
0
0
2
0
0
1
1
1
0
0
1
2
0
1
1
2
0
0
0
2
0
2
0
1
0
1
1
0
2
1
2
1
0
5
2
0
0
2
2
2
0
2
0
2
1
0
1
2
1
0
0
0
0
1
1
2
0
0
2
1
0
2
0
2
2
4
0
2
0
2
0
0
0
0
1
0
1
0
0
1
1
1
0
0
0
2
1
1
1
2
0
1
2
2
2
1
2
0
2
1
2
0
1
1
1
0
1
1
0
1
4
0
2
2
1
0
1
0
2
0
0
2
2
0
0
1
2
0
0
1
2
1
0
1
1
1
1
0
0
0
2
0
0
0
0
0
0
1
0
0
1
2
2
2
0
0
1
2
0
0
1
1
1
0
1
1
2
1
2
0
3
0
2
1
2
1
1
1
0
0
0
0
2
2
2
0
0
0
2
1
2
1
0
1
2
1
1
1
2
2
1
2
1
2
0
0
1
1
2
0
0
1
1
3
0
2
0
0
1
0
3
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
1
2
0
1
1
1
0
1
1
2
1
0
1
0
2
2
1
1
1
1
0
0
0
0
0
1
2
0
2
1
1
0
1
1
1
1
0
1
2
0
1
2
1
0
0
0
1
0
0
0
1
0
4
1
0
0
0
0
1
1
1
2
1
1
1
2
2
1
1
1
0
2
2
3
1
0
0
2
0
2
1
0
2
0
1
2
1
1
0
1
0
2
0
1
0
0
2
2
1
0
1
0
1
0
0
0
0
1
2
0
0
1
1
1
0
1
0
1
0
0
2
1
1
0
1
1
2
0
0
2
1
2
1
2
2
2
1
1
1
0
2
0
1
2
2
2
0
0
0
1
0
1
0
0
0
1
1
2
0
0
1
1
2
0
1
1
0
1
1
1
2
0
1
0
1
0
0
0
0
0
1
1
1
0
0
1
1
1
0
1
0
0
1
2
2
1
0
1
0
2
0
0
1
0
0
0
0
2
0
1
0
3
3
0
0
1
2
1
1
0
1
2
2
0
2
1
0
0
2
0
1
1
1
0
1
1
2
0
0
0
0
2
0
0
1
1
0
0
0
1
1
2
0
0
1
2
1
0
0
0
0
0
2
1
0
2
2
1
0
1
0
1
1
0
0
0
1
0
0
1
0
0
1
0
1
1
1
0
0
1
2
1
0
2
2
1
1
0
1
1
1
0
0
1
0
0
1
0
0
2
2
0
0
1
1
1
0
1
0
0
1
1
2
0
1
0
0
2
1
2
1
1
1
0
0
2
0
2
1
0
1
1
0
2
1
1
1
0
0
1
2
1
1
0
2
0
1
2
2
1
0
0
0
1
1
0
2
2
0
0
0
0
1
1
0
1
1
0
0
0
0
1
0
1
2
0
2
0
1
2
1
2
0
1
0
0
0
1
0
3
1
0
0
0
1
0
1
2
0
1
2
2
3
0
0
0
1
1
0
1
2
0
0
0
0
0
2
0
1
1
2
1
0
2
2
1
2
2
0
1
0
0
0
1
0
1
3
1
2
1
0
0
0
0
2
0
1
1
0
1
1
0
1
1
1
0
0
1
1
2
2
1
0
0
3
0
1
1
0
0
1
0
0
1
0
1
0
1
2
1
1
0
0
1
2
1
1
0
0
0
1
1
1
0
2
0
1
0
0
1
2
0
0
0
0
2
1
1
1
0
2
1
2
1
3
0
1
0
1
0
0
1
0
2
1
0
1
1
0
1
1
2
0
0
1
1
1
0
1
1
3
0
1
2
1
2
2
0
0
1
1
0
0
1
0
2
0
1
2
0
0
1
0
0
0
0
1
0
0
0
0
2
0
1
0
1
3
2
2
1
0
2
1
1
0
1
3
1
0
1
1
2
1
0
1
0
2
0
1
2
1
0
0
1
2
2
0
0
0
2
0
1
1
1
0
0
1
1
0
2
1
1
1
0
1
0
1
1
0
2
0
2
0
0
0
1
0
0
1
2
2
0
0
0
1
0
0
0
1
1
1
2
1
1
0
2
0
0
1
0
1
0
1
0
2
2
0
1
0
1
2
2
2
2
2
0
1
0
1
0
0
1
0
1
0
0
1
1
0
1
2
1
0
1
2
0
2
3
1
0
1
1
0
1
0
0
2
0
2
5
0
0
0
1
2
1
1
0
0
1
0
0
2
1
2
0
1
1
2
0
1
1
1
2
0
1
0
1
0
2
1
1
1
1
1
1
4
1
0
1
1
1
2
2
0
2
0
2
3
1
1
0
0
3
1
0
2
0
2
1
2
1
1
0
1
0
0
0
2
2
0
0
0
0
1
2
0
1
1
1
0
1
0
2
1
1
2
0
0
1
2
0
0
1
0
0
0
1
0
0
2
2
2
1
2
2
0
1
1
0
0
0
0
0
3
0
2
0
1
1
0
0
0
0
0
2
0
0
2
0
2
2
2
0
2
1
0
0
0
0
0
1
0
0
0
1
1
0
1
2
1
2
1
1
1
1
2
0
3
1
2
1
0
2
1
0
1
0
2
1
0
1
1
0
2
0
2
0
1
0
1
2
1
1
2
0
0
0
2
0
0
0
2
2
1
0
1
1
0
1
1
0
0
1
0
0
0
0
1
0
0
0
1
1
1
0
1
0
2
0
1
1
0
1
1
0
0
1
1
1
0
0
1
3
1
1
0
2
3
0
0
2
2
2
2
3
1
0
0
0
1
0
0
2
2
1
1
2
2
0
0
0
1
1
2
1
0
0
0
0
1
1
2
2
0
1
2
0
1
1
0
0
1
1
0
1
0
1
0
0
0
1
1
2
1
1
0
0
0
1
2
2
1
0
0
2
1
1
0
0
0
0
2
2
0
1
1
0
1
0
0
0
2
3
0
1
1
1
0
0
2
1
0
0
1
1
1
1
0
2
1
0
0
1
0
0
0
2
1
2
1
0
2
1
0
1
0
2
0
1
1
1
1
2
1
2
0
2
2
1
2
2
0
0
1
0
2
1
2
2
1
2
1
0
0
0
0
1
1
0
2
2
0
1
0
1
1
1
0
0
1
2
1
0
1
1
0
1
2
1
1
0
1
0
1
3
2
0
2
0
0
2
1
0
1
0
2
0
3
0
0
0
2
2
0
0
1
2
0
0
1
0
1
0
2
1
0
0
0
3
0
0
1
0
0
0
3
1
0
0
2
0
2
0
2
1
1
1
2
1
1
1
1
0
0
0
1
0
0
1
7
0
0
1
1
0
1
2
0
1
2
1
0
1
3
2
1
0
2
0
0
0
0
1
0
1
1
1
2
1
2
1
1
0
1
1
1
2
0
1
1
2
2
1
1
4
2
2
1
1
0
1
1
1
0
0
1
0
1
0
1
1
1
1
0
0
1
2
2
1
1
1
0
0
2
0
1
1
7
1
0
0
0
1
2
0
2
1
0
1
0
2
2
1
0
1
0
0
0
1
1
0
0
1
0
2
0
0
0
2
1
3
2
1
2
1
1
1
2
0
1
0
1
0
1
0
2
1
2
2
0
1
0
1
2
0
2
0
1
1
3
1
0
2
2
2
1
1
2
1
0
1
1
0
1
2
1
0
0
2
1
0
0
0
1
0
0
2
0
2
0
0
1
2
2
1
2
2
1
1
0
0
1
0
0
2
1
0
0
0
1
1
1
2
0
0
0
1
0
0
0
0
0
0
2
1
1
0
0
1
2
2
0
1
2
1
2
0
1
1
0
2
0
2
0
0
0
1
0
0
1
1
1
1
2
2
0
1
0
2
1
1
0
0
0
2
2
1
2
0
0
3
2
2
1
0
2
1
0
2
0
0
0
1
1
1
1
0
1
0
1
2
0
1
1
0
2
1
1
0
1
1
0
0
0
1
0
0
0
1
2
0
1
1
0
1
0
1
0
2
0
0
1
0
0
0
2
1
1
0
0
2
1
1
1
1
0
2
1
0
0
1
1
0
0
2
0
1
0
0
0
1
0
2
1
1
0
1
0
0
2
2
0
0
1
0
0
1
2
0
0
0
2
0
2
1
1
0
0
1
1
1
1
2
0
0
2
0
2
0
1
0
0
0
2
1
2
1
1
2
0
5
0
0
2
0
1
1
3
0
1
1
0
2
0
1
1
1
2
0
1
1
1
0
1
2
0
1
0
1
1
0
0
1
0
2
2
0
1
0
1
0
0
0
0
0
3
3
1
1
1
0
2
1
2
1
0
0
0
0
1
0
1
1
1
1
0
0
2
1
0
0
1
0
2
1
0
0
1
1
1
0
2
1
0
2
0
0
0
2
1
1
0
1
4
0
1
0
2
0
0
0
0
0
1
0
1
0
1
0
0
0
0
2
0
0
0
2
1
0
0
0
2
0
0
1
1
0
2
0
1
1
0
0
1
0
1
1
1
2
2
0
0
0
1
0
0
1
1
1
1
1
0
1
0
0
0
1
0
1
1
0
0
1
1
1
0
1
0
0
1
2
3
1
2
0
0
2
2
0
2
0
1
0
1
1
2
1
0
1
1
2
2
0
0
1
2
2
2
1
1
0
2
0
0
1
2
1
1
1
0
0
2
0
2
0
1
2
2
2
1
1
0
0
2
1
0
1
1
0
2
1
0
0
1
2
2
0
1
0
1
2
0
0
0
1
1
0
2
0
1
0
2
1
1
0
1
1
0
0
1
1
2
1
1
0
2
1
2
0
2
1
5
1
0
2
2
1
1
1
3
1
0
1
1
2
0
0
1
1
0
0
1
1
2
1
2
1
2
1
2
0
5
0
1
2
0
0
2
1
2
1
1
1
2
1
1
0
0
1
0
0
1
2
1
0
0
2
1
0
1
1
1
1
0
1
1
1
1
1
0
2
2
2
2
2
2
0
3
0
2
2
1
2
0
1
0
1
1
2
2
2
1
0
0
0
3
0
2
1
0
0
1
0
1
0
1
1
1
1
0
1
1
0
0
0
0
0
0
1
1
1
0
0
1
0
1
1
1
2
0
0
0
0
2
2
0
0
1
1
0
0
0
0
1
2
2
0
1
1
1
0
0
3
2
0
2
0
1
0
0
0
1
1
0
0
1
1
0
0
1
1
0
1
0
0
1
1
1
1
0
1
0
0
0
2
0
2
1
0
1
2
0
0
1
0
2
1
2
0
0
2
2
1
1
1
0
1
1
3
0
2
1
2
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
2
2
2
1
2
1
2
0
0
1
0
2
1
1
0
0
2
2
0
0
0
0
2
0
1
0
1
0
1
0
1
0
0
0
0
1
1
0
0
1
0
1
2
1
0
0
2
2
0
0
0
0
2
1
0
0
0
0
1
0
0
0
1
0
2
1
2
0
2
1
2
2
0
2
0
0
0
2
4
2
1
1
2
0
0
1
1
0
1
2
0
2
2
1
2
0
1
1
1
1
1
2
0
1
1
1
2
0
0
0
2
0
0
1
1
3
1
2
2
1
0
1
2
1
1
0
0
1
1
3
0
0
1
1
2
0
1
0
1
0
0
0
0
0
1
0
0
1
0
2
2
1
0
1
1
0
1
0
2
0
0
3
0
0
0
0
2
0
3
1
1
2
0
2
0
2
2
2
0
0
0
0
0
1
0
1
1
0
0
0
0
1
1
1
0
0
0
1
2
0
1
0
0
1
2
0
1
0
2
2
2
0
0
1
0
0
0
0
1
1
0
2
0
0
2
1
0
0
1
1
2
0
1
1
2
2
0
1
2
0
1
0
1
1
0
1
2
0
1
2
0
0
0
0
1
1
1
0
0
0
1
0
0
1
1
2
1
2
2
2
0
2
1
2
0
0
1
5
0
2
0
1
0
1
0
0
1
0
1
0
1
1
0
2
0
1
1
1
1
0
0
2
0
1
0
0
1
0
3
0
1
0
1
0
0
1
2
0
1
2
0
0
1
2
2
2
2
0
0
0
2
0
1
0
3
1
2
0
1
1
1
1
0
1
1
0
0
1
1
0
1
0
1
1
0
0
1
1
2
1
2
2
1
0
1
0
0
0
2
0
2
0
2
2
2
1
1
1
1
0
0
0
1
0
0
2
0
2
0
0
0
0
1
0
1
0
2
1
0
0
0
0
0
2
1
0
1
2
1
1
2
1
0
0
2
1
1
0
0
0
1
0
1
1
0
2
1
2
1
0
1
0
1
0
1
0
1
0
2
1
1
1
0
1
0
1
2
0
1
1
0
0
1
3
0
0
2
1
1
1
0
0
1
0
0
1
1
2
0
2
0
0
1
1
1
2
0
1
1
0
0
1
0
2
1
0
1
1
0
0
0
1
2
0
2
0
0
2
0
0
0
1
0
0
0
1
1
0
0
1
1
0
0
1
1
0
1
1
0
2
1
0
0
1
0
3
2
0
0
0
0
1
2
0
1
0
0
0
0
4
2
1
0
1
1
0
0
1
0
3
1
0
1
0
1
0
0
2
1
2
2
0
1
6
0
0
1
0
2
2
1
1
2
2
0
1
2
0
1
0
2
0
1
2
2
1
1
0
1
1
0
1
1
1
0
0
0
2
2
3
0
1
0
0
1
1
2
1
0
0
2
2
1
1
1
0
1
1
1
0
0
1
0
1
1
0
1
0
9
2
0
1
0
1
0
0
1
0
2
0
0
0
0
0
0
2
1
1
1
2
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
2
0
2
3
0
1
2
1
2
0
1
0
1
0
0
0
1
3
2
1
0
1
2
1
2
2
0
0
2
0
2
1
0
3
0
1
0
1
1
0
1
2
0
0
1
2
2
1
0
0
0
0
2
2
1
0
1
0
1
1
1
0
0
2
1
2
1
0
0
1
1
0
0
2
0
0
0
0
0
0
1
2
2
1
1
0
0
1
2
1
0
0
1
0
1
0
0
1
0
1
0
0
1
1
0
0
3
2
3
1
1
2
1
0
0
0
0
0
0
2
0
0
1
0
1
2
0
1
2
2
2
0
1
0
1
2
1
1
0
0
0
0
1
2
1
2
0
0
0
2
1
1
0
0
0
0
1
0
1
0
1
0
2
0
1
1
1
0
0
0
2
0
0
0
1
2
1
1
1
0
0
0
1
1
0
1
1
0
1
1
0
2
0
0
0
1
0
0
0
0
2
0
1
1
0
1
1
1
0
1
1
5
0
1
1
2
0
1
0
1
2
1
0
0
0
1
0
0
0
1
1
0
3
1
4
0
1
0
1
0
0
0
1
2
0
0
2
2
1
2
1
0
1
0
0
0
1
2
1
0
1
0
0
0
0
2
2
0
1
0
0
1
2
1
2
0
1
1
0
0
1
1
0
1
0
2
0
0
1
2
2
2
2
0
0
0
1
1
0
0
1
2
0
0
0
2
2
0
0
0
0
1
1
1
2
0
0
0
0
0
1
0
0
1
1
1
2
0
1
2
0
1
0
1
1
0
0
0
0
0
1
1
2
1
0
0
1
2
0
0
7
1
0
2
3
1
1
0
4
2
0
2
0
2
1
1
1
2
2
2
1
0
1
0
2
0
2
1
2
0
0
1
0
2
1
1
0
2
2
1
0
1
0
0
1
0
2
1
1
0
2
0
2
1
2
1
2
1
2
0
1
1
0
0
0
0
0
0
2
0
0
2
0
1
1
2
1
2
1
1
0
1
2
0
0
1
1
0
0
1
1
2
0
1
0
1
1
2
1
2
0
0
0
1
2
0
0
0
0
0
0
1
0
1
0
2
1
0
1
0
1
0
3
0
0
0
0
0
1
2
0
0
0
0
1
1
0
2
0
2
1
1
4
2
0
1
0
0
0
2
0
1
1
2
0
0
1
1
0
1
2
1
2
2
0
0
1
1
1
0
0
0
0
0
0
2
0
2
2
0
1
0
2
0
2
0
0
1
2
0
2
0
1
0
0
1
1
1
0
0
0
0
0
1
2
0
0
1
0
1
0
1
1
1
0
1
1
0
0
1
1
2
0
0
0
2
0
0
1
0
2
2
2
0
0
1
1
0
1
1
0
2
0
1
0
2
3
2
0
0
0
2
0
1
0
1
0
1
1
1
1
2
2
1
1
2
1
1
0
2
0
1
0
2
2
0
1
1
1
2
1
0
0
0
0
1
1
2
2
0
1
0
0
0
1
2
1
1
0
1
2
2
2
2
1
1
1
2
0
1
0
1
1
0
0
0
1
0
0
0
2
1
0
0
0
2
0
0
1
1
1
0
1
1
0
1
2
0
0
0
0
2
1
0
0
1
0
1
2
0
2
1
2
2
1
1
1
0
0
0
0
1
1
0
2
0
0
1
5
1
1
0
0
2
1
2
1
1
0
1
2
0
1
1
0
0
1
1
0
0
0
1
1
1
0
0
2
1
1
1
0
2
1
1
2
0
0
0
1
1
1
0
1
1
2
1
1
1
1
2
0
1
1
1
2
1
0
0
0
2
2
2
0
1
0
0
1
1
0
1
0
0
0
0
2
0
0
0
2
1
0
0
1
0
1
2
0
0
2
0
0
2
3
0
2
0
2
0
2
1
0
2
2
1
1
0
1
1
1
1
2
0
0
1
1
1
2
0
1
0
1
2
1
1
0
2
1
0
0
1
1
0
0
2
2
0
1
0
1
0
1
1
1
0
0
0
0
1
0
0
1
1
1
1
1
1
2
0
1
1
2
2
1
0
0
1
0
0
0
1
1
2
1
2
2
1
0
2
0
1
2
1
2
2
0
1
2
2
0
0
2
1
1
2
0
1
0
0
2
1
1
0
2
1
0
0
2
1
1
1
1
2
0
1
0
1
0
0
0
1
1
1
2
2
1
0
2
0
1
2
1
1
2
0
2
1
0
1
0
2
0
2
0
0
0
1
1
1
0
0
0
1
1
1
1
3
2
0
0
2
1
0
0
0
0
2
2
0
0
1
0
0
0
2
2
0
2
0
2
0
1
0
0
2
2
2
0
1
1
0
0
0
0
2
2
0
0
0
0
1
1
0
1
3
0
0
3
1
0
1
1
0
0
1
0
0
0
1
0
2
0
1
0
1
1
0
2
0
3
0
0
1
1
0
0
1
2
1
1
0
1
0
1
0
4
1
1
3
1
1
0
0
2
0
0
0
1
2
1
1
1
0
0
0
1
0
0
0
1
1
1
0
0
1
1
1
0
0
1
2
0
0
0
0
2
1
1
1
0
1
0
1
2
1
1
1
2
0
2
1
1
0
0
1
0
3
2
0
0
1
2
2
0
0
0
1
1
1
1
0
1
1
0
2
0
1
0
0
0
1
2
1
1
0
1
1
1
0
2
0
2
1
1
1
1
1
1
1
2
0
2
1
0
1
0
0
2
1
0
0
0
2
1
0
1
1
0
0
2
1
2
0
1
2
2
0
0
2
1
0
2
2
1
0
2
0
1
1
0
0
0
1
0
0
2
0
0
1
2
1
3
1
1
1
0
0
1
0
1
2
0
3
2
2
2
0
0
2
0
0
0
1
0
1
2
0
1
0
0
0
1
0
2
2
0
2
0
1
1
1
1
0
0
1
1
0
0
0
1
2
0
0
2
1
1
1
2
0
0
0
0
1
1
1
1
0
1
2
1
0
0
1
2
2
1
1
1
0
4
1
1
0
1
1
0
1
0
0
1
1
0
1
2
1
1
0
2
0
0
2
1
0
2
0
0
1
1
0
0
2
2
1
1
0
2
2
2
0
0
1
2
2
0
0
1
0
0
1
0
0
0
0
0
1
1
2
0
1
2
0
0
1
1
1
2
1
0
2
1
0
2
0
1
0
1
0
1
1
1
1
0
1
0
1
0
2
0
1
1
1
3
1
0
2
0
2
2
1
3
0
2
1
1
1
0
2
0
0
2
2
2
2
2
2
2
1
2
1
1
1
2
2
0
1
0
0
1
2
1
1
0
1
2
2
2
0
0
0
1
0
1
1
0
0
0
1
1
2
1
1
2
0
1
1
0
1
1
0
1
0
2
1
2
0
1
0
0
0
0
0
0
2
0
0
3
0
0
0
1
0
0
0
0
1
1
1
0
1
1
1
0
1
1
2
0
0
0
0
2
1
1
0
2
0
0
1
1
1
2
1
1
1
1
1
1
1
0
2
1
0
1
1
0
2
0
1
1
3
0
1
1
1
0
1
1
0
1
0
1
2
0
2
2
0
1
0
1
2
1
1
1
2
0
0
2
0
2
0
2
2
2
1
0
0
0
1
1
0
0
0
0
2
1
2
2
0
0
1
1
2
1
0
0
0
1
2
0
1
2
2
0
0
2
1
0
1
1
1
0
1
1
0
2
1
1
0
2
1
2
1
2
0
0
2
0
1
1
0
2
1
1
0
0
1
0
0
3
2
3
1
0
0
2
1
1
1
0
2
1
0
1
0
0
2
0
2
2
2
0
0
1
0
1
2
0
1
2
1
0
0
0
0
0
0
1
2
2
2
0
0
0
1
1
0
0
2
0
1
0
1
1
0
0
0
0
0
0
0
0
2
0
0
2
0
1
1
0
1
1
0
0
0
1
1
0
0
0
1
1
0
1
0
2
0
0
1
1
2
0
0
1
1
0
2
0
1
0
0
0
0
0
1
1
2
1
1
1
2
0
1
1
2
1
2
1
1
2
0
2
1
1
1
0
0
1
2
0
0
1
0
1
1
3
0
2
2
2
0
2
0
0
1
0
2
0
2
0
0
1
0
0
0
1
0
2
1
1
1
0
0
0
0
1
3
1
1
1
1
2
0
2
0
1
2
0
0
0
1
0
0
0
1
1
0
1
0
0
0
1
0
0
0
1
1
1
0
0
2
1
0
1
2
1
1
2
1
0
2
0
0
1
0
1
1
1
3
1
1
0
2
1
3
0
0
3
2
1
2
1
0
1
1
2
1
1
2
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
1
1
0
1
0
0
1
0
2
2
2
0
2
0
1
0
0
2
0
0
2
0
2
1
0
0
2
0
0
2
0
1
0
0
0
1
0
0
0
0
1
1
2
0
1
0
0
1
0
2
2
2
1
4
1
1
1
2
1
2
1
2
1
1
1
2
1
2
2
0
1
0
1
1
0
0
1
1
0
2
0
0
4
0
0
2
2
0
0
0
0
0
1
2
0
1
1
0
1
0
2
1
0
0
0
1
0
2
0
0
0
1
2
0
0
0
1
0
0
1
1
0
0
1
2
0
0
1
0
0
0
1
0
1
1
1
0
0
1
1
2
1
2
1
2
1
0
2
2
2
0
1
2
1
3
1
1
1
1
0
0
0
0
0
2
2
0
0
1
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
1
1
1
0
0
1
0
0
1
1
2
0
0
0
0
1
0
0
0
2
0
3
0
0
0
1
0
2
2
2
1
1
0
0
2
1
0
0
1
1
0
1
2
0
0
1
1
1
0
2
2
1
2
0
2
2
0
0
0
5
1
0
1
1
2
1
1
2
1
0
0
0
0
0
1
0
0
1
2
1
0
1
1
0
0
0
1
1
1
0
2
1
1
1
1
0
2
1
0
1
0
1
0
0
1
1
2
0
2
1
1
0
0
1
2
0
2
1
0
1
1
1
0
2
2
1
0
2
0
0
0
1
3
0
0
0
1
0
0
2
0
2
0
1
1
0
1
0
2
0
0
0
2
0
0
0
1
1
0
1
1
0
0
1
0
0
0
0
0
2
0
1
2
1
0
0
1
1
0
0
0
4
0
0
1
0
2
2
1
0
0
2
0
1
1
0
1
1
0
0
1
1
0
1
0
3
0
0
1
0
0
1
1
1
1
0
1
2
0
1
0
0
0
0
3
2
1
0
1
1
0
1
0
3
1
0
0
2
1
0
2
0
0
2
0
2
2
0
2
2
2
2
1
0
0
2
3
2
0
1
0
0
1
0
2
1
0
2
0
1
0
2
0
0
0
0
2
1
0
0
1
0
0
0
0
1
2
0
1
0
0
1
1
0
1
1
1
1
0
5
1
0
0
0
0
1
0
0
2
2
2
2
1
1
1
0
0
1
0
1
0
2
0
1
0
2
1
1
0
2
3
1
0
1
1
1
0
0
0
0
1
0
1
1
1
0
1
1
1
1
1
1
1
0
0
2
0
0
0
1
2
1
0
1
0
0
0
1
1
0
0
2
3
0
1
0
2
0
0
0
2
1
0
0
0
2
1
1
2
0
2
0
0
1
0
0
0
2
1
1
0
1
0
1
1
1
0
2
1
1
3
0
0
2
0
2
1
1
0
1
0
3
1
0
0
0
0
0
0
1
1
1
0
1
0
2
0
2
2
1
1
1
1
0
1
0
1
1
1
1
0
0
2
1
1
0
0
2
1
0
1
0
1
1
1
0
1
1
0
2
1
1
0
1
1
0
2
0
2
3
1
0
1
0
0
2
1
1
1
2
0
2
0
0
0
1
1
1
1
1
0
1
0
0
1
1
0
0
0
1
1
0
1
2
0
0
1
0
0
0
0
2
0
1
0
0
1
1
1
0
0
0
0
2
0
0
0
1
0
2
0
1
1
1
1
0
2
1
1
1
2
0
0
2
0
0
3
1
2
0
0
1
1
0
2
0
1
0
1
0
0
0
1
0
2
2
0
2
0
0
0
1
0
0
2
0
0
0
2
0
1
1
1
1
1
2
1
0
1
0
1
0
0
1
1
2
2
1
1
0
0
0
0
1
0
0
1
0
0
2
0
2
2
0
0
0
1
2
0
0
1
2
0
1
1
0
0
1
0
1
0
2
3
2
0
2
5
0
0
0
1
0
0
1
0
2
2
2
1
2
1
2
0
1
0
0
2
1
0
2
0
2
2
0
0
1
1
0
2
1
0
1
1
0
1
0
1
1
0
1
2
2
1
0
2
0
0
0
2
0
0
1
2
1
1
2
2
1
1
1
0
3
1
2
1
2
1
0
1
1
1
2
0
1
1
1
0
0
1
2
1
0
2
2
1
1
0
1
0
2
1
0
2
0
1
0
2
1
0
2
1
1
0
0
1
0
0
2
1
1
1
2
0
1
0
1
1
3
1
1
0
2
1
0
2
0
0
1
1
1
0
0
1
3
0
0
2
1
1
1
0
2
1
1
1
1
1
1
1
0
0
1
1
0
1
3
0
0
1
0
2
0
0
0
0
2
1
0
0
1
1
1
2
1
1
5
0
1
0
2
1
2
2
2
3
1
1
0
1
2
0
0
0
1
1
1
0
1
0
1
0
1
0
1
2
0
0
0
0
0
0
0
1
2
2
1
0
0
1
1
0
1
0
1
0
1
3
2
0
0
2
1
0
1
2
0
1
1
2
0
1
2
1
1
0
1
2
3
1
1
1
1
1
1
1
2
1
2
0
0
0
1
1
0
1
0
0
0
2
0
0
2
0
1
0
0
0
1
1
2
2
2
1
1
0
2
1
1
1
1
0
1
1
1
1
1
0
1
0
0
1
1
0
0
0
1
0
1
0
0
1
0
0
1
0
1
1
0
2
0
1
1
1
4
1
2
0
0
0
2
1
0
2
0
0
0
0
1
2
1
0
1
0
2
1
0
0
0
0
2
1
0
0
2
1
2
1
0
1
0
2
0
2
0
0
1
0
0
1
1
0
0
1
0
0
0
1
0
2
0
0
1
1
0
1
1
0
1
1
0
1
0
2
1
1
0
0
2
1
1
1
1
0
1
1
1
0
0
1
1
0
1
1
0
2
1
2
0
0
2
2
2
0
1
0
1
1
1
1
1
1
0
0
0
1
2
1
1
1
0
2
3
0
1
2
0
1
0
0
1
1
0
0
1
0
2
2
2
1
0
1
0
1
0
1
0
1
0
1
0
2
2
1
0
1
0
0
0
0
0
1
0
2
4
2
0
0
0
0
0
1
0
2
1
1
1
0
0
1
1
4
1
1
0
1
0
0
1
1
1
1
0
1
0
0
0
0
1
0
2
0
0
2
0
0
1
0
2
0
2
2
0
1
1
2
0
0
2
1
1
1
1
2
2
1
0
1
1
0
0
0
1
0
0
0
0
2
0
0
2
3
2
1
1
1
1
2
0
1
0
1
0
0
0
2
0
0
1
3
0
0
0
1
2
1
0
2
0
0
0
1
2
2
0
0
0
1
0
3
0
1
2
0
0
0
2
1
2
2
0
0
1
3
0
2
2
2
1
0
1
1
2
1
0
1
0
0
0
0
1
1
1
1
1
1
0
1
0
1
0
1
1
2
1
1
2
2
0
1
0
1
1
1
0
1
0
1
1
1
0
1
0
0
2
1
2
2
0
0
1
4
0
1
0
0
1
0
0
1
0
1
0
0
1
1
2
1
0
0
1
0
2
0
0
1
2
1
0
2
1
0
1
0
0
0
1
0
1
1
0
0
1
0
2
2
0
1
0
0
0
0
0
0
1
2
1
2
0
0
1
2
0
1
0
3
0
0
1
1
1
3
1
2
1
1
0
2
0
0
1
0
0
2
1
2
2
2
0
0
0
2
0
2
0
1
2
1
1
1
0
2
1
0
1
0
1
1
0
2
0
2
3
0
0
0
3
2
0
0
0
1
1
0
1
1
0
0
0
1
0
1
0
1
1
2
1
1
1
0
0
1
1
1
1
0
2
1
0
1
0
0
2
0
1
0
2
1
5
1
2
0
1
0
2
2
1
2
0
1
0
1
1
3
0
1
0
0
0
0
2
1
0
1
1
0
0
0
0
0
0
2
1
1
1
0
2
0
0
0
0
1
2
0
1
0
1
0
2
1
0
0
1
0
1
0
1
2
0
1
1
1
0
1
2
0
0
2
0
1
0
1
2
0
1
1
0
2
2
1
1
1
0
0
1
1
0
0
0
3
1
2
1
0
0
0
0
0
2
0
1
0
2
1
1
1
1
0
0
0
0
1
0
2
0
0
1
1
1
1
0
1
2
1
1
2
0
1
0
1
1
0
2
0
0
0
0
2
0
0
0
0
0
1
0
1
1
2
0
1
0
1
0
0
2
1
0
0
2
2
2
2
2
0
2
0
2
0
1
0
0
1
1
0
1
0
1
0
2
0
0
0
1
2
2
1
1
1
2
0
1
2
2
1
1
1
1
1
1
1
1
0
2
2
0
0
1
0
0
0
0
0
0
1
1
3
1
0
1
2
0
2
0
0
0
0
1
1
0
1
1
0
0
0
2
2
0
2
1
3
2
1
0
0
2
2
0
0
2
1
0
0
2
0
1
0
0
0
0
0
2
0
0
2
2
0
2
1
1
0
1
0
2
0
0
1
0
1
0
2
0
0
2
1
1
1
2
1
1
0
1
1
0
2
0
1
2
0
0
1
1
2
1
1
0
2
1
2
2
0
0
1
0
0
0
2
0
2
1
1
0
2
1
0
1
0
1
2
1
0
0
2
0
0
0
1
0
1
1
1
2
1
0
2
2
2
3
0
0
0
2
0
1
0
1
1
0
1
0
1
2
1
1
1
1
1
0
2
0
2
0
1
1
1
0
0
0
1
0
1
0
1
2
0
1
1
0
1
1
0
1
0
1
2
0
2
0
1
2
0
1
0
0
1
0
0
2
1
1
1
1
0
2
2
0
1
1
0
1
2
1
1
1
0
1
0
1
1
0
0
0
0
0
1
1
1
2
1
2
1
1
2
0
1
1
1
1
2
0
0
0
1
0
1
1
1
1
0
2
0
1
1
2
1
1
0
2
2
0
2
0
1
0
0
1
0
0
0
1
2
1
0
1
0
2
1
0
1
0
0
2
0
2
0
1
0
0
1
0
0
2
0
2
2
2
1
1
0
3
0
1
1
1
2
2
0
1
1
1
0
0
1
0
1
0
0
1
0
0
1
0
1
1
2
1
0
0
1
0
2
2
0
0
1
0
0
0
0
1
2
2
2
0
1
0
1
1
0
1
0
0
1
0
0
0
2
0
2
1
2
0
1
1
0
2
1
2
1
1
0
1
2
2
0
1
0
2
0
0
0
1
1
0
2
0
0
0
0
1
1
1
0
0
0
1
3
0
2
0
2
1
0
3
0
2
2
1
1
0
1
1
0
0
2
0
2
0
0
1
0
0
1
0
2
1
1
1
1
1
0
1
2
0
2
0
2
0
1
1
0
0
0
1
2
0
1
1
2
0
2
1
0
1
1
1
0
0
0
0
0
1
0
2
1
1
1
1
0
0
2
0
0
0
0
0
1
1
0
2
1
1
1
0
2
0
2
1
1
0
0
0
2
1
2
1
0
2
1
1
0
2
1
0
2
1
0
0
2
2
0
0
0
0
0
1
1
1
2
0
0
1
0
1
1
1
1
2
0
1
0
0
2
1
2
0
0
1
1
0
1
0
1
0
0
0
0
1
0
2
1
1
2
2
0
0
1
0
1
0
1
1
0
0
4
1
1
2
1
0
2
2
0
2
0
0
0
2
0
0
1
0
0
2
0
1
2
0
2
1
1
0
2
2
2
0
2
0
1
0
0
2
2
0
1
1
1
1
2
1
1
1
0
1
0
0
1
1
1
0
0
1
1
0
1
3
0
2
0
0
0
1
1
2
1
0
1
2
2
1
0
2
1
0
0
0
1
0
1
1
0
0
2
1
2
0
1
0
1
0
0
2
2
0
0
0
0
3
0
2
2
0
2
1
0
1
2
2
0
0
0
0
1
0
1
1
0
1
0
1
1
2
1
0
1
0
2
2
2
2
1
1
1
1
0
1
1
1
0
2
2
2
0
1
0
1
0
1
1
1
0
1
1
1
2
2
1
0
1
1
2
0
2
2
0
0
0
1
2
1
1
0
1
0
2
0
1
1
1
0
1
1
2
1
1
0
0
2
1
1
1
1
0
1
1
1
1
2
0
1
2
0
2
0
0
1
2
0
0
0
2
1
0
0
2
1
2
0
0
3
0
0
0
0
0
1
1
2
1
0
1
0
1
2
1
2
1
1
0
0
0
1
0
0
0
1
2
3
1
1
0
1
1
2
0
2
0
1
2
0
1
1
1
1
0
2
1
0
0
0
2
2
1
2
1
2
1
1
2
0
0
2
1
0
1
1
0
1
1
2
0
0
0
1
0
1
0
0
0
0
1
2
1
0
0
0
0
2
0
2
1
0
0
0
1
2
1
0
0
0
1
0
0
0
0
2
1
2
2
1
1
0
0
1
0
0
0
1
2
1
2
2
0
1
0
0
0
1
0
2
2
1
1
1
1
2
1
2
0
2
0
1
0
0
1
0
2
0
0
0
2
2
1
0
2
1
0
2
0
2
0
1
0
0
2
2
0
1
0
2
1
1
0
0
2
0
0
1
0
0
0
0
0
0
1
1
0
0
1
1
0
1
0
0
1
2
0
2
1
1
1
1
2
2
0
2
2
1
1
1
2
0
0
0
0
2
0
0
1
1
0
1
0
2
0
1
2
0
1
0
0
1
1
0
0
2
0
2
2
2
0
1
1
1
0
0
0
1
2
0
0
0
0
2
2
1
0
0
1
2
2
1
0
0
0
0
1
0
0
0
1
2
1
2
0
2
1
0
0
1
2
1
1
0
0
0
0
4
2
0
1
1
0
0
2
1
1
0
0
0
1
1
1
2
2
2
0
1
0
0
0
0
0
1
1
0
0
1
0
2
0
1
1
1
1
0
2
2
0
3
1
0
1
0
0
0
0
1
0
0
0
0
1
1
2
2
2
0
2
2
0
0
2
2
0
2
2
2
2
2
0
0
0
0
1
3
0
0
2
2
0
2
0
1
0
0
2
0
2
1
0
1
2
0
1
0
0
1
1
2
1
1
1
0
0
0
2
0
0
1
1
1
2
0
1
0
0
1
2
2
0
1
0
1
0
0
0
0
2
0
1
1
0
1
0
1
0
0
1
1
1
0
0
1
1
1
1
0
1
0
1
2
0
0
0
0
1
1
0
1
2
0
0
2
1
1
2
0
0
1
0
2
2
0
0
2
1
0
1
1
2
0
2
2
0
8
0
1
1
2
0
2
0
1
0
1
1
2
1
0
2
2
2
5
1
2
1
2
2
0
2
2
0
0
0
1
2
1
0
2
2
2
1
1
3
2
1
1
1
1
2
0
0
0
1
1
1
1
0
0
0
0
2
0
1
1
2
2
0
0
0
2
1
0
1
0
1
1
1
0
1
1
0
0
1
1
1
2
0
1
0
1
2
2
2
0
3
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
2
0
2
0
1
0
1
0
1
1
2
2
1
1
1
0
1
0
2
0
0
0
1
1
0
0
1
1
0
1
1
2
2
0
2
1
2
1
2
1
3
1
0
0
0
0
0
0
0
2
0
1
2
0
2
1
0
1
0
2
0
0
1
1
0
0
0
0
2
1
0
1
1
2
1
1
0
0
2
0
1
1
0
2
3
2
1
2
0
1
2
2
0
0
2
0
0
0
1
1
0
2
2
0
0
2
1
0
0
0
1
1
2
2
0
0
1
3
2
1
2
0
1
1
1
2
0
2
1
0
2
2
0
1
0
0
1
0
2
0
0
2
0
0
1
0
1
1
2
0
1
2
2
0
2
0
0
0
1
1
0
0
0
1
2
1
0
0
1
1
1
0
1
0
2
0
0
0
1
1
1
1
1
0
1
0
0
1
0
1
1
0
0
0
2
1
0
0
2
1
0
0
0
0
1
1
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
2
1
0
1
2
1
0
1
1
0
0
0
1
2
0
2
0
0
1
1
1
2
0
1
0
2
0
1
0
1
2
1
1
0
2
1
0
2
1
2
0
1
2
2
0
1
1
0
0
1
0
1
1
1
1
0
2
4
0
0
2
1
0
0
3
0
0
0
1
1
2
0
2
2
0
1
2
1
1
2
1
0
1
0
4
0
2
2
0
0
1
0
1
0
0
0
1
1
2
0
1
0
0
0
1
1
1
0
0
3
1
0
1
0
0
0
0
0
1
1
1
2
0
0
1
2
1
0
1
2
2
1
2
1
1
0
0
0
0
0
1
0
0
2
0
0
2
1
3
0
0
1
1
2
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
3
1
0
2
1
1
2
0
0
0
2
1
1
0
0
0
0
1
1
0
0
0
0
1
1
1
2
0
4
1
0
1
2
0
1
1
1
0
2
0
1
0
0
1
2
0
0
1
0
1
0
1
0
0
1
1
1
1
2
1
2
0
1
1
0
2
0
1
0
1
0
0
0
2
1
0
1
1
0
2
1
0
2
2
0
0
0
1
2
0
0
1
2
1
1
2
0
3
1
0
1
2
1
0
2
1
1
2
4
0
1
1
2
0
1
0
1
0
0
0
0
1
0
1
0
1
2
0
0
2
1
0
0
0
0
2
0
4
2
2
0
2
2
1
1
1
0
2
2
1
2
1
2
2
0
0
0
0
0
0
1
0
1
2
0
1
0
1
0
0
3
0
1
0
2
1
1
0
0
1
0
2
2
0
0
1
1
1
1
0
0
1
1
0
0
0
0
0
2
0
0
0
1
1
1
1
0
3
3
0
0
1
1
1
2
0
1
1
0
0
1
0
0
0
0
1
0
2
1
1
1
0
2
0
0
1
0
2
0
0
0
2
0
2
0
0
0
2
1
0
2
1
0
0
1
0
1
0
2
0
1
1
1
0
0
0
2
1
0
1
2
0
0
1
0
0
0
0
0
0
0
2
1
1
1
0
1
1
0
1
0
2
1
2
2
1
2
1
0
1
1
1
0
2
1
1
1
0
3
0
1
1
1
1
1
2
1
2
1
1
0
2
0
1
1
0
0
2
0
1
0
1
0
0
2
0
0
0
2
0
1
0
1
0
2
0
4
2
0
0
1
0
2
2
0
0
1
1
1
1
1
1
0
2
1
1
1
1
0
0
1
0
0
1
2
0
0
0
2
1
0
1
1
0
0
0
2
2
0
2
1
0
1
6
0
2
2
2
1
1
1
0
0
0
0
1
0
1
1
0
0
1
0
1
1
1
0
3
0
1
0
2
2
1
1
0
0
1
2
0
1
0
0
0
2
1
0
0
0
1
1
0
1
0
1
1
1
0
0
1
2
2
0
1
2
0
0
2
1
1
0
0
0
0
0
1
0
1
0
0
2
0
1
1
0
1
0
5
1
0
2
1
1
0
2
2
1
0
1
0
0
2
0
1
2
1
1
0
2
1
0
1
2
0
1
2
0
2
0
0
2
0
1
1
0
0
1
2
1
0
0
2
0
2
1
0
0
2
0
2
0
1
2
0
0
3
0
0
2
0
0
2
0
1
1
0
0
1
1
0
4
0
0
3
1
2
0
3
1
1
0
0
0
1
2
3
0
0
1
0
0
0
2
1
2
1
0
0
1
2
1
0
0
1
2
1
2
0
1
0
2
2
0
0
1
1
2
0
1
1
1
1
0
0
1
2
1
0
2
2
0
0
1
2
0
0
1
0
1
0
0
0
1
1
1
0
1
1
0
0
0
0
1
1
1
0
0
1
0
0
0
1
2
2
3
1
1
0
1
0
1
0
0
1
2
1
0
1
1
2
1
1
0
2
0
1
0
0
1
0
1
2
0
0
1
0
0
0
0
1
2
1
0
1
0
1
2
2
1
0
0
2
2
1
1
2
2
1
1
0
1
0
0
0
1
0
2
1
0
1
0
0
1
1
1
2
0
2
2
0
1
0
0
1
0
0
0
2
3
2
2
0
0
0
1
2
0
1
1
0
0
1
1
0
1
0
1
1
1
0
2
0
2
0
0
2
0
1
1
1
0
1
2
0
1
0
1
0
2
0
0
0
0
2
0
0
0
1
2
1
0
0
0
2
0
2
1
0
0
1
0
1
1
0
0
1
0
1
1
1
1
1
1
0
0
1
0
2
1
0
2
2
0
1
0
2
2
0
1
0
0
1
0
1
1
0
0
2
0
2
0
0
1
1
1
0
2
1
0
0
1
2
0
0
2
0
1
0
2
1
0
0
0
1
0
1
0
2
1
1
0
1
2
1
0
0
0
0
0
0
1
0
2
0
1
2
1
0
2
2
0
1
2
1
0
1
0
0
1
0
0
1
2
2
2
1
1
1
1
1
0
1
1
2
1
0
0
0
1
1
0
0
0
0
1
0
1
1
0
0
0
0
2
0
3
0
0
0
0
1
0
1
2
1
0
0
2
0
1
1
2
0
1
0
0
1
0
1
2
0
1
1
0
2
1
1
1
0
0
3
0
2
0
2
1
1
0
1
0
0
1
2
2
1
0
2
0
1
2
0
0
2
1
1
0
0
0
2
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
2
0
2
2
0
2
0
2
0
1
1
0
1
0
0
0
0
1
0
1
1
0
1
2
0
2
0
0
0
1
0
0
0
2
0
0
1
1
0
1
2
0
0
0
1
0
1
1
0
1
1
1
1
0
1
1
1
2
1
1
0
10
2
0
3
2
0
1
1
3
1
1
1
1
0
0
1
0
0
1
4
0
2
1
2
1
1
0
0
2
1
1
2
0
1
0
2
0
0
1
0
2
1
1
1
1
2
0
0
0
0
0
1
1
1
1
1
3
0
1
2
2
0
0
2
0
0
0
0
2
1
0
1
1
1
0
1
0
1
0
1
0
2
2
1
0
0
0
0
0
0
2
0
0
3
0
0
2
1
0
1
1
0
0
1
0
0
1
0
0
2
0
1
0
1
0
0
1
0
2
1
0
1
0
0
0
1
2
0
1
0
0
1
0
1
0
0
0
0
1
1
0
2
1
1
1
1
0
1
1
1
2
1
0
0
0
1
0
2
1
1
0
1
0
1
2
0
1
1
0
0
0
1
1
0
0
1
1
1
0
0
0
1
1
1
1
2
0
0
0
3
2
1
2
1
2
2
0
2
1
0
0
0
0
0
0
1
2
0
0
0
0
1
0
2
1
2
1
1
2
1
4
1
0
0
0
0
0
0
5
1
0
1
2
0
2
1
0
0
1
1
0
2
0
0
1
0
2
0
2
0
1
0
1
0
1
0
0
0
2
1
1
1
0
0
0
0
0
1
1
1
0
1
2
2
0
1
1
0
2
1
1
1
2
0
0
1
2
0
0
0
0
0
1
1
2
2
1
0
1
0
6
1
1
1
0
2
0
1
3
1
0
2
2
0
1
1
0
2
0
0
2
1
1
3
0
0
0
1
0
1
0
0
1
1
1
1
0
1
2
4
0
0
0
2
0
2
0
1
0
0
1
1
1
2
2
0
1
0
2
0
2
2
0
0
2
1
2
1
2
2
0
0
1
1
1
1
1
0
2
2
1
1
0
0
0
2
1
1
2
3
0
0
1
1
0
2
0
0
1
0
2
0
0
1
2
0
0
1
0
1
0
0
0
1
2
0
1
1
0
0
1
1
2
0
0
2
0
0
2
0
0
2
0
2
1
0
0
0
0
0
1
0
1
2
1
2
0
1
2
1
1
0
0
0
0
0
2
4
0
0
0
0
0
0
1
1
2
1
0
1
1
0
3
0
1
1
0
0
0
1
1
1
1
1
0
2
0
0
1
1
1
1
1
0
0
0
2
1
3
1
1
0
0
0
1
1
2
1
1
0
1
0
2
4
2
2
0
2
0
2
0
2
1
2
2
0
0
2
1
0
0
2
2
1
1
1
0
0
2
0
0
0
2
2
0
1
1
2
2
1
1
1
1
0
1
0
1
2
1
2
1
2
0
4
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
1
0
0
1
0
2
0
0
2
0
2
0
0
2
2
2
0
0
2
2
0
0
1
0
1
0
1
1
2
2
0
0
2
0
0
0
1
2
2
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
2
0
1
2
0
1
0
0
1
0
0
0
1
0
1
1
1
1
2
0
1
2
1
1
1
0
1
1
0
0
0
0
1
2
2
2
1
0
2
0
1
0
1
0
0
1
1
1
0
1
2
2
0
0
1
1
1
1
0
2
1
0
2
0
2
0
0
1
0
0
1
0
1
0
1
1
0
1
1
1
1
0
1
0
2
2
0
0
0
1
1
0
1
0
2
1
2
1
0
0
1
1
1
2
1
0
1
2
1
1
0
0
0
1
4
1
0
1
2
2
0
0
2
1
1
1
0
1
2
5
1
2
1
1
0
1
1
3
1
0
0
1
0
1
1
0
0
1
2
0
2
1
0
3
1
0
0
0
1
0
0
1
0
0
0
0
2
1
0
0
0
2
1
0
1
2
0
2
0
2
0
0
1
0
0
0
1
1
2
0
2
0
0
2
1
2
0
1
1
2
1
2
1
1
1
1
1
2
2
2
0
0
1
2
0
1
0
1
1
0
2
1
1
2
0
2
2
1
1
0
0
0
0
2
2
0
0
1
0
1
2
1
1
1
0
0
1
0
0
1
0
2
2
1
1
3
1
0
2
0
1
0
1
0
1
2
0
0
2
1
0
1
1
1
1
1
0
2
1
0
1
0
2
1
0
1
0
0
1
1
0
1
0
2
0
0
1
0
0
0
0
2
0
1
0
1
1
0
0
1
1
2
2
0
2
2
0
2
0
1
1
1
0
1
0
0
0
2
0
2
1
0
5
1
1
0
0
1
0
2
2
0
1
1
1
2
1
1
2
0
1
1
0
0
1
0
1
0
1
0
1
1
1
0
1
0
1
2
1
2
2
2
0
0
2
2
0
0
2
0
0
0
0
2
2
1
1
0
1
0
0
3
0
0
0
0
1
2
0
1
1
0
0
0
0
0
1
1
2
0
0
0
1
0
2
0
2
1
1
1
0
1
1
0
0
1
0
0
1
2
1
2
2
2
0
0
1
0
1
2
0
2
1
0
0
2
1
1
2
0
1
2
0
1
1
1
0
0
0
1
1
2
1
1
1
2
1
1
1
0
2
2
2
3
0
1
0
0
0
2
0
0
0
2
0
0
1
0
1
1
2
0
1
3
2
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
1
0
2
2
2
0
1
0
0
1
1
1
1
0
0
2
3
0
1
1
1
2
2
1
2
0
1
2
2
1
0
0
1
0
1
2
2
0
2
2
1
0
1
0
0
1
2
0
1
0
2
2
0
1
1
0
1
1
1
0
0
1
0
0
1
0
1
1
2
0
1
0
0
2
1
1
1
0
0
0
2
0
1
2
0
1
0
0
0
2
0
0
2
1
0
0
0
2
0
2
1
0
0
0
0
0
1
1
1
2
0
0
1
1
1
1
1
0
1
0
1
2
0
2
2
0
1
2
0
1
0
0
1
1
0
0
0
1
1
0
2
1
0
3
0
1
1
2
1
1
2
0
0
1
1
0
0
1
1
0
0
1
3
2
1
0
0
2
1
1
0
2
1
2
2
0
1
1
1
0
1
1
1
0
1
1
2
1
1
4
0
2
3
2
0
3
0
1
2
3
2
3
5
0
1
0
0
0
0
0
0
0
0
1
0
2
2
1
2
2
2
1
2
2
2
0
1
0
2
1
2
0
1
0
0
1
0
0
0
1
2
0
1
2
1
1
1
0
2
1
1
0
0
1
1
0
1
1
1
1
1
0
0
2
2
0
0
0
0
2
0
0
0
2
0
1
0
0
1
1
1
1
2
0
1
1
2
3
0
2
0
1
1
3
2
0
1
1
3
0
0
0
2
0
0
1
0
0
1
2
0
0
2
0
1
2
1
0
0
1
0
0
0
0
2
1
1
2
1
0
0
0
0
0
0
0
2
2
0
1
0
0
1
1
0
1
1
0
1
0
1
1
0
1
2
1
1
1
1
0
1
1
2
0
0
0
0
0
5
3
2
1
2
0
2
0
2
1
0
2
1
2
2
0
1
0
0
2
1
0
1
0
0
2
1
3
1
2
1
4
0
0
1
1
0
1
0
0
0
1
0
1
0
2
0
2
0
2
0
1
0
2
2
0
2
3
0
1
1
0
1
2
0
2
0
0
1
0
1
1
2
1
1
1
2
1
0
0
1
2
3
0
1
0
2
1
0
0
1
1
0
1
0
0
0
2
0
1
0
1
0
1
1
0
1
0
4
0
1
2
1
0
0
1
1
0
1
0
0
2
1
0
0
0
2
0
0
1
1
0
2
0
0
1
1
0
2
0
2
2
1
0
1
0
0
0
0
0
0
0
0
0
0
2
1
1
1
0
0
0
0
1
0
0
2
1
1
0
0
0
1
2
2
1
2
0
2
1
1
0
1
0
2
1
1
1
1
0
1
1
0
0
0
2
1
2
0
1
2
1
1
0
1
0
0
2
0
0
0
0
3
0
0
0
0
0
1
2
0
2
1
0
0
0
0
0
0
2
2
1
0
1
1
0
1
0
1
0
1
2
2
0
1
0
0
1
2
2
0
2
0
0
5
0
1
2
0
0
0
0
2
2
1
0
0
0
0
1
2
1
0
2
1
2
2
0
2
0
0
2
0
0
2
1
0
0
2
1
1
3
0
2
0
0
2
2
1
0
1
0
1
2
1
0
0
0
0
1
3
2
0
0
2
1
1
0
1
0
0
0
0
1
1
1
1
0
2
1
1
2
1
0
0
0
0
1
0
0
0
0
1
2
1
0
1
1
0
0
0
0
0
1
1
2
2
0
0
1
0
0
1
2
2
0
1
1
1
1
0
1
1
0
2
0
1
1
2
0
1
1
0
0
0
2
0
2
1
0
1
0
0
0
2
1
0
0
2
0
0
0
0
1
0
0
2
0
3
0
2
1
1
2
1
0
1
0
0
0
1
2
2
0
2
0
0
1
2
2
1
2
2
2
0
0
0
0
0
1
1
0
2
1
1
0
2
1
0
2
0
0
0
0
2
1
1
1
0
2
0
0
2
0
3
1
2
0
0
0
1
1
2
1
3
0
2
0
0
0
0
1
1
0
0
0
1
0
2
1
0
0
0
1
0
1
0
0
0
0
0
1
2
0
2
2
0
2
0
1
1
1
1
4
1
1
0
0
0
0
0
1
0
0
1
2
0
1
2
1
2
1
0
0
2
2
0
0
2
2
2
0
1
1
2
1
0
0
1
0
0
0
0
2
1
0
1
0
0
1
1
0
1
0
2
0
0
0
0
1
2
1
1
0
1
1
1
0
0
2
0
0
1
0
0
0
1
0
1
1
2
0
0
1
0
1
1
2
0
1
0
0
0
1
2
0
0
2
0
1
0
2
1
1
0
2
1
0
1
1
1
2
2
1
0
0
2
1
0
1
1
1
0
2
0
1
0
0
1
0
1
1
1
0
2
0
2
1
0
2
1
0
1
0
0
0
1
0
2
1
1
1
0
0
1
2
0
2
1
1
0
1
2
0
2
0
0
0
0
0
1
0
2
1
0
0
1
1
1
2
0
1
0
0
0
0
2
1
2
1
1
1
0
2
2
1
0
0
0
0
0
2
2
1
0
2
0
1
2
1
0
0
0
2
1
2
0
1
1
0
0
2
1
0
1
1
0
1
1
0
2
1
0
0
0
0
2
4
0
1
0
0
0
0
1
2
0
0
1
0
2
0
0
0
0
0
1
2
0
0
0
2
0
2
2
1
1
0
2
1
1
0
2
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
1
2
1
0
1
1
0
1
2
1
0
0
2
1
0
1
1
1
2
2
2
1
0
0
2
1
0
2
1
1
1
1
1
2
2
1
0
0
1
2
0
0
2
0
1
0
0
1
2
0
2
1
2
2
0
0
1
2
0
0
1
1
1
0
0
0
2
2
0
1
1
0
0
1
2
2
0
2
2
0
0
0
0
0
2
0
0
1
0
0
5
0
0
1
0
2
1
1
0
1
1
0
0
1
1
0
1
1
1
0
2
1
3
0
1
0
1
2
0
0
1
0
2
0
1
0
2
0
1
0
0
3
2
0
1
1
1
0
1
0
0
0
1
1
0
0
4
2
1
0
2
0
1
0
0
2
1
1
0
1
1
2
2
1
0
1
0
0
1
1
2
1
1
0
2
1
0
3
0
1
1
1
1
2
1
0
2
0
0
0
1
0
1
1
1
1
2
2
2
1
0
1
1
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
1
0
0
2
0
2
0
0
0
0
1
1
1
1
0
1
2
3
1
2
0
1
3
0
2
2
0
0
0
0
0
0
2
1
2
2
0
0
1
0
0
0
1
1
1
1
1
1
0
2
0
0
1
1
1
1
0
2
1
0
2
2
1
0
0
2
2
0
0
0
1
0
1
1
1
0
0
0
2
0
2
1
0
2
0
0
1
1
0
2
2
0
0
1
2
2
1
0
0
0
2
2
0
2
1
2
0
1
0
0
0
1
1
1
1
1
1
2
0
0
2
0
0
1
2
1
2
1
1
0
0
0
0
0
1
2
1
0
2
0
1
1
1
1
2
0
0
0
1
0
0
1
1
1
0
2
2
1
2
1
0
0
1
2
2
1
0
2
2
2
0
0
1
2
1
1
0
1
0
0
2
0
2
0
2
0
1
1
1
0
1
2
1
0
1
1
1
0
1
0
1
0
1
0
1
2
0
1
1
0
0
2
0
2
0
2
1
0
0
1
1
1
0
1
0
0
0
0
1
1
0
2
0
1
1
0
0
1
2
2
1
1
0
0
1
0
2
0
1
0
1
0
0
1
1
2
2
0
1
1
0
1
1
0
0
2
1
2
0
1
1
0
0
1
2
1
1
2
0
0
1
2
0
1
0
0
0
1
0
1
2
0
0
1
0
0
0
0
1
3
1
2
0
1
0
1
1
0
0
0
3
1
1
2
0
0
1
0
0
2
1
1
0
3
1
1
0
1
0
0
0
0
0
0
2
1
0
1
0
1
1
1
1
1
1
0
1
0
2
1
0
2
1
1
2
0
0
1
0
1
0
0
0
1
2
0
2
0
0
2
0
0
0
0
0
0
2
0
1
0
2
0
0
1
0
0
1
0
0
1
0
1
1
0
0
0
1
2
0
0
2
1
0
0
2
1
0
1
0
1
2
1
2
1
0
1
1
0
2
2
2
2
1
2
0
0
2
0
2
2
0
2
0
1
1
0
0
0
1
1
2
0
0
0
0
0
0
2
0
1
2
0
2
0
1
1
1
1
0
2
0
0
1
2
1
2
1
1
0
0
1
0
1
1
2
0
0
1
0
1
0
0
0
1
1
3
0
1
0
3
1
2
1
1
1
2
1
0
0
1
0
3
0
0
0
0
1
0
1
0
1
0
1
0
1
1
0
0
1
1
1
0
0
0
1
1
2
0
0
1
1
3
0
0
0
0
1
1
2
0
1
4
0
0
0
0
0
0
0
2
0
1
1
1
0
2
0
0
0
1
1
1
1
0
0
1
1
1
2
3
1
0
1
2
2
1
1
1
0
0
1
0
0
1
2
0
0
1
0
0
0
0
2
0
4
0
1
1
0
1
2
0
0
1
2
2
0
0
1
2
0
1
1
1
0
0
0
2
1
0
0
1
2
2
0
1
0
0
0
2
0
0
1
0
2
0
1
2
2
0
2
0
3
2
2
2
2
2
1
0
2
0
0
0
1
1
0
0
1
2
2
1
1
1
0
3
0
1
0
0
1
8
1
1
1
1
2
1
1
0
1
0
2
2
0
1
0
0
0
0
0
1
0
1
1
2
1
1
0
0
1
0
1
0
0
2
0
1
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
2
4
0
1
2
0
1
1
2
2
0
1
0
0
0
2
1
1
1
0
0
0
0
1
1
1
0
1
1
1
2
1
1
1
0
2
4
0
3
2
0
1
1
2
1
1
2
0
0
1
0
1
1
1
1
1
1
2
0
0
0
0
1
0
0
0
0
2
1
0
0
0
1
0
2
1
2
0
0
2
0
2
0
1
1
0
1
0
1
5
1
1
0
0
1
1
2
0
0
1
0
2
2
0
0
1
2
0
2
0
0
1
0
1
0
1
2
0
1
0
0
1
0
1
1
1
1
1
0
1
1
1
0
1
0
0
1
1
0
2
5
2
0
1
1
0
0
0
0
0
1
0
2
0
1
0
2
0
2
1
0
0
2
2
1
1
0
2
0
0
1
0
2
1
1
0
1
2
0
1
0
1
0
2
2
2
2
0
0
1
1
0
0
0
0
1
1
2
2
1
1
0
1
1
0
1
1
1
1
2
2
0
0
2
0
2
2
1
1
0
0
0
1
0
2
1
0
0
1
1
1
0
2
2
0
0
1
2
1
0
2
2
0
0
2
2
1
1
1
0
1
0
0
0
0
1
0
1
0
1
2
2
0
0
0
0
1
2
1
1
1
1
0
1
2
0
0
1
0
2
2
1
0
2
1
1
1
0
1
0
1
2
0
1
0
0
2
1
0
1
0
0
0
1
2
2
0
0
0
0
1
0
0
0
0
1
1
2
0
1
1
2
0
0
0
0
0
0
1
2
1
0
2
0
2
1
1
2
1
2
2
1
1
0
1
0
0
0
1
1
1
1
1
0
1
1
2
0
0
1
1
2
2
0
1
2
1
0
0
0
1
0
0
1
1
2
1
1
0
1
0
0
1
0
1
0
0
2
0
1
0
0
2
0
2
1
0
1
0
0
2
2
2
1
0
0
2
0
2
2
1
1
0
0
3
0
1
2
0
1
0
1
0
1
1
2
2
0
1
2
0
2
1
1
0
1
0
2
1
2
0
2
0
1
1
0
1
1
0
2
2
1
0
1
1
1
1
1
0
0
2
1
0
2
0
4
1
2
1
0
1
2
1
0
4
0
0
1
0
1
1
1
0
0
3
1
0
1
0
3
1
2
0
1
2
2
1
0
1
2
1
0
2
0
0
0
0
1
2
0
0
2
2
1
2
0
0
1
0
1
0
1
1
0
0
0
1
0
0
0
2
1
1
2
0
2
0
0
1
1
1
1
1
0
0
0
2
0
0
2
2
2
1
2
1
0
2
0
0
1
1
0
0
0
0
0
2
1
1
0
1
0
1
2
2
2
0
1
0
2
0
1
0
0
1
0
1
0
0
1
0
1
0
2
0
1
0
1
2
2
0
0
0
0
1
1
1
2
0
1
1
0
0
1
3
0
0
0
0
2
2
2
1
1
0
0
1
2
2
1
0
1
0
0
0
1
0
0
3
1
1
0
0
2
0
2
2
1
0
1
0
0
0
1
2
2
3
1
0
2
2
1
0
0
0
2
1
0
1
1
2
1
0
0
1
0
2
1
1
0
1
1
0
1
0
0
0
0
0
0
2
2
2
0
1
2
0
1
3
0
1
1
2
1
1
1
1
1
0
0
2
0
1
1
1
0
0
0
0
1
0
0
2
0
1
2
0
0
0
1
2
0
1
0
1
1
0
2
0
1
0
0
0
3
2
0
2
1
2
0
2
1
2
2
1
1
1
0
0
2
0
0
2
0
1
0
0
0
0
1
4
0
0
1
0
1
1
0
1
1
1
1
0
0
0
0
2
0
1
0
1
0
0
2
0
1
1
0
0
1
1
0
2
5
0
0
0
1
2
1
0
0
0
1
1
2
0
2
1
1
0
0
0
0
2
1
1
0
1
0
0
0
1
0
2
2
0
0
0
1
0
0
0
0
2
2
1
1
0
1
0
1
0
0
1
1
0
1
2
1
2
2
0
2
2
0
0
0
1
2
0
0
0
1
0
0
0
1
0
1
2
0
1
0
1
1
0
1
1
2
0
1
0
1
0
1
0
1
2
1
0
1
1
0
0
0
0
0
2
1
0
0
0
2
0
0
0
2
0
0
1
1
0
1
2
0
1
0
2
0
2
0
1
2
1
2
0
1
1
0
1
1
1
2
1
0
1
1
1
1
2
0
1
0
0
1
0
1
0
2
0
2
1
1
1
2
1
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
2
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
1
2
1
0
0
0
0
2
2
1
0
0
0
0
0
1
0
0
3
0
1
2
2
0
1
0
2
1
3
0
0
2
0
1
1
1
1
1
1
1
0
0
0
1
1
1
1
3
2
0
0
1
2
0
1
0
1
2
0
0
1
0
0
1
1
2
0
0
0
0
0
0
0
0
2
1
2
1
2
2
1
0
0
0
2
1
0
1
0
0
1
0
0
0
2
2
0
0
1
2
1
2
2
0
1
1
1
1
0
1
2
0
2
1
2
2
0
1
0
0
1
0
2
0
2
0
0
1
2
1
0
0
2
1
2
1
0
1
1
1
0
2
0
1
1
1
1
1
0
1
1
1
3
0
2
3
2
1
1
2
1
1
0
0
0
2
0
1
0
0
0
0
0
3
1
0
0
1
0
1
1
2
2
0
0
0
0
0
2
4
0
1
1
0
2
0
0
1
2
0
2
0
2
2
0
1
2
2
0
0
2
1
0
2
1
0
1
0
0
2
0
1
1
1
1
2
0
1
2
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
2
2
1
0
2
0
2
1
0
0
1
0
0
0
0
2
0
1
2
0
0
1
1
1
0
3
1
2
0
0
1
1
1
0
1
1
1
2
0
0
2
0
1
0
1
3
0
2
0
2
1
0
0
0
1
0
1
2
0
2
1
1
2
2
0
1
1
1
1
0
0
2
2
0
1
2
0
1
1
2
1
0
0
1
0
0
2
0
1
1
1
0
2
1
2
0
0
1
1
1
1
0
2
2
1
0
1
0
0
2
1
1
1
2
0
0
1
1
0
0
1
0
0
0
2
2
1
1
0
2
1
1
1
0
3
2
0
0
2
2
1
2
1
0
1
0
0
0
3
0
1
2
0
1
0
1
2
0
1
1
2
0
0
0
0
2
0
1
0
1
2
0
1
1
1
2
0
1
0
4
2
0
1
0
0
0
1
2
3
0
1
2
1
2
0
1
1
1
0
0
3
3
0
1
2
0
2
1
0
0
0
0
2
2
0
0
1
2
0
0
3
1
1
0
1
1
1
2
0
2
2
0
2
0
1
0
0
1
1
0
2
1
0
0
1
4
0
1
0
1
0
0
0
1
1
1
1
0
1
0
0
0
3
1
2
1
1
1
1
1
0
2
2
1
2
2
1
0
1
2
1
1
0
2
0
1
1
0
2
0
2
0
2
1
0
3
0
0
1
0
1
0
0
2
2
2
1
2
1
1
1
1
0
2
0
0
0
0
0
0
2
0
0
1
2
2
1
1
0
0
0
0
2
0
3
0
0
0
0
1
0
0
3
0
1
2
1
3
0
1
1
1
0
1
0
0
0
2
0
2
0
1
1
3
0
2
2
2
1
0
1
0
2
1
0
0
1
2
2
0
0
0
1
1
0
0
0
0
0
2
2
1
1
1
1
2
1
2
2
4
1
2
0
1
0
0
0
1
0
0
2
0
1
2
2
0
2
1
1
3
1
0
0
1
0
0
0
1
0
2
2
0
1
0
2
1
1
0
0
1
1
1
1
0
0
1
0
1
2
3
0
1
1
2
0
1
0
0
0
3
0
0
1
0
0
2
0
0
1
2
2
2
0
0
0
2
2
2
1
2
0
0
0
2
1
0
2
0
0
0
1
0
1
1
1
0
0
0
1
2
0
1
1
0
0
0
0
0
0
0
1
1
2
2
0
2
2
1
0
1
2
2
0
0
0
0
0
2
0
1
2
0
2
0
0
1
1
2
2
2
2
2
0
1
1
0
0
0
0
1
2
2
1
0
1
1
2
1
2
1
2
1
1
0
0
0
3
3
2
2
1
2
2
1
0
0
1
2
1
2
0
2
0
0
0
1
0
0
0
3
2
0
1
0
0
1
0
3
2
2
1
2
1
0
2
1
1
2
1
2
1
2
1
1
0
2
2
2
0
0
1
1
0
1
1
0
1
2
1
0
1
1
1
1
2
2
2
2
2
0
2
1
1
1
0
1
0
0
1
0
0
3
1
2
1
1
0
0
2
0
2
1
0
2
2
2
1
1
2
2
1
0
2
2
1
1
0
1
2
2
2
0
1
1
1
2
1
0
0
0
0
0
1
0
1
1
2
3
0
0
2
2
0
1
2
2
0
2
0
1
0
1
1
0
1
0
2
0
0
1
0
2
0
1
2
1
1
2
1
0
1
0
1
0
2
4
0
0
1
2
1
2
1
1
2
2
0
0
0
1
0
1
2
2
0
0
2
1
0
0
1
0
0
1
0
1
1
2
0
0
3
1
0
2
1
1
0
0
2
1
1
0
0
1
1
0
0
0
0
1
0
4
0
1
0
2
0
1
2
0
2
2
1
0
0
1
1
0
0
3
1
0
0
1
0
0
0
1
0
2
1
2
1
1
1
1
2
0
0
0
0
2
1
0
1
1
0
0
1
1
0
0
0
1
0
0
2
1
0
1
1
0
0
2
0
0
1
0
0
0
0
0
0
2
1
1
3
0
1
1
0
0
1
2
1
0
0
0
2
0
1
0
0
0
0
0
2
1
1
1
0
0
1
0
1
1
0
2
1
1
1
1
2
2
1
1
0
0
2
0
0
2
1
2
1
0
0
0
2
1
0
2
1
2
1
1
1
1
2
0
0
0
0
0
1
0
1
3
1
1
0
2
0
2
1
1
1
0
1
0
1
2
0
0
0
0
0
2
0
2
1
1
4
1
0
1
0
1
1
1
2
0
1
0
0
1
1
2
0
0
0
1
0
2
0
2
2
0
1
0
1
0
3
0
0
0
0
1
1
2
2
2
1
0
1
1
0
0
1
2
1
3
1
1
0
1
0
1
0
2
0
2
2
0
0
0
0
0
0
0
0
1
0
0
2
2
1
0
2
1
1
2
1
0
1
0
0
0
1
0
0
0
0
0
1
0
1
1
2
1
1
0
1
1
2
0
0
1
0
1
1
0
2
2
0
2
0
1
2
0
0
0
0
2
0
1
0
1
1
0
0
1
2
2
2
0
3
0
1
1
1
0
1
0
1
1
0
0
0
2
1
0
0
1
0
0
1
0
1
1
1
1
2
0
1
0
0
1
2
1
0
0
0
0
0
0
4
0
0
1
1
2
2
0
0
0
1
0
2
2
1
0
3
1
1
0
0
0
2
0
0
1
1
1
2
1
0
1
0
1
1
0
2
1
0
0
1
1
2
0
2
1
0
1
0
2
2
0
2
1
1
1
2
0
0
0
0
0
3
0
1
0
0
1
1
4
0
0
1
2
1
0
0
0
0
0
0
2
2
2
0
0
3
0
1
0
2
1
1
0
2
0
2
1
0
0
1
1
0
1
2
2
1
1
2
0
1
1
1
3
0
1
1
2
0
2
0
0
0
2
2
0
1
2
0
1
0
0
0
0
0
0
2
0
2
0
1
1
1
1
1
1
0
2
2
1
0
4
1
1
1
0
2
1
1
2
1
0
0
2
1
1
1
0
1
0
1
1
1
2
0
2
3
0
1
0
1
0
1
1
0
0
0
0
2
1
1
0
0
1
0
1
2
1
2
0
1
2
1
1
2
0
2
0
2
0
0
0
1
0
2
0
2
2
1
2
2
1
1
1
0
0
1
2
0
0
2
2
0
1
1
1
2
1
1
3
3
2
0
2
0
2
2
2
0
1
0
2
0
1
0
2
1
2
0
0
0
2
0
2
0
0
0
1
1
2
2
2
1
0
2
1
1
0
1
0
1
1
0
0
1
2
1
0
1
1
0
1
1
1
0
1
0
1
0
0
1
1
1
2
1
1
1
0
1
0
0
1
2
2
2
2
1
0
0
1
0
0
0
1
1
3
0
0
1
1
0
0
0
2
0
0
0
0
1
1
2
0
0
2
2
0
0
0
1
1
2
2
1
0
0
1
0
2
1
1
0
1
2
0
1
1
0
0
0
0
2
1
0
0
1
1
0
0
1
1
0
1
0
2
0
0
0
2
0
0
1
0
2
1
2
1
0
2
0
0
1
0
0
0
0
1
1
0
0
1
2
0
1
2
1
2
1
2
0
1
1
1
2
0
0
0
0
0
0
2
0
2
0
2
1
1
0
1
0
2
0
0
1
0
0
1
0
2
2
2
0
2
0
0
0
1
1
0
1
0
1
2
0
0
2
0
0
1
0
2
2
1
0
1
1
2
1
0
2
1
0
2
1
0
0
0
1
2
1
0
1
0
2
1
0
2
0
0
1
1
0
1
1
0
2
1
0
0
0
0
2
0
1
0
0
1
2
1
1
1
0
2
1
2
0
0
1
1
2
1
1
1
2
0
2
0
0
2
0
1
2
0
1
1
2
2
0
0
0
1
1
0
1
2
1
0
1
2
2
2
0
1
1
2
0
0
2
2
1
2
0
0
2
0
1
2
1
1
0
0
0
2
0
2
1
0
0
0
0
0
2
1
0
0
0
1
2
1
1
0
1
1
1
2
0
0
0
0
0
1
1
0
0
0
0
0
1
1
1
0
0
0
0
2
1
0
1
0
0
2
2
0
1
2
0
0
1
2
1
2
2
2
1
0
0
0
0
1
0
1
2
0
1
1
0
0
0
0
0
0
0
1
2
0
0
2
1
1
0
0
1
0
2
0
0
0
0
1
0
0
0
1
2
1
0
2
0
0
0
1
0
3
0
0
3
1
2
0
0
0
1
0
0
1
0
0
1
0
1
0
1
0
2
0
0
0
2
1
0
1
0
2
1
0
1
0
1
1
1
0
3
0
1
2
0
1
0
1
0
2
2
1
2
0
1
0
0
1
2
0
0
1
1
2
0
1
1
1
0
0
1
1
0
1
0
0
1
2
2
1
2
1
2
1
2
0
0
0
0
1
0
2
0
1
1
0
0
0
1
0
2
0
1
1
1
0
2
0
1
1
0
1
0
1
0
0
0
1
1
1
1
0
0
2
0
0
0
1
2
1
0
0
2
0
0
0
0
1
2
1
0
0
2
0
2
0
1
0
0
1
1
1
2
1
0
0
0
0
0
2
0
2
1
2
1
1
2
0
0
0
0
1
1
1
0
1
0
0
2
0
0
1
2
0
1
1
1
1
0
2
0
1
2
0
0
0
0
1
1
0
2
1
1
1
1
1
0
1
0
1
0
2
2
1
1
2
1
1
0
2
1
1
0
0
1
0
2
0
0
1
0
0
0
0
2
0
0
2
1
2
0
0
0
1
2
0
0
2
1
1
0
1
2
1
1
0
0
1
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
1
1
2
1
2
0
1
1
0
0
1
1
1
2
0
0
0
0
2
2
0
0
1
1
1
0
0
2
2
1
0
1
0
0
1
0
0
0
2
1
1
2
0
0
2
1
2
1
0
1
2
0
2
1
2
0
0
1
0
0
2
2
0
0
1
0
2
0
2
0
0
0
0
1
3
0
1
0
1
1
0
0
1
0
1
1
2
0
2
2
1
0
0
1
0
0
2
1
2
2
0
2
2
0
0
2
2
1
0
0
2
1
1
1
0
2
0
1
0
1
2
0
0
1
0
0
1
0
0
2
0
1
0
1
0
1
1
0
1
0
0
1
0
0
0
0
1
1
2
1
1
1
3
1
0
0
0
2
1
0
2
2
1
1
1
1
2
2
2
3
0
0
2
0
0
1
0
1
1
1
1
0
0
0
0
1
2
0
1
0
0
0
0
0
3
2
2
0
0
1
0
0
0
0
1
2
1
1
1
1
0
0
0
1
0
2
2
3
2
0
0
1
1
1
0
0
1
3
0
0
0
1
0
1
0
2
0
1
0
0
2
2
0
0
1
0
2
0
2
1
2
0
0
1
2
3
3
1
2
2
1
0
1
1
0
1
0
0
0
2
0
0
2
2
2
0
1
1
1
2
0
1
2
0
0
0
2
0
1
1
0
0
0
1
2
0
0
1
0
0
0
1
0
1
0
3
0
2
1
2
2
0
1
0
2
1
0
0
0
2
1
2
0
0
0
0
2
1
0
2
2
0
1
0
0
1
1
1
0
0
0
1
1
0
1
2
0
3
1
0
1
0
0
0
1
1
0
1
0
1
0
1
1
2
1
0
1
3
1
0
1
2
1
0
1
0
1
2
1
2
1
0
1
0
1
2
0
1
1
1
1
1
1
2
0
2
0
0
2
0
1
0
2
1
0
2
1
0
0
1
2
0
2
1
0
2
0
0
1
2
0
2
1
1
0
0
0
0
1
0
0
1
0
0
1
0
1
1
1
1
1
0
0
0
2
2
2
1
0
1
2
2
0
1
2
1
2
0
2
1
1
2
1
0
1
0
0
0
1
1
1
1
0
1
2
2
0
1
0
1
1
0
0
0
0
2
0
1
0
1
1
2
1
2
0
0
1
1
0
0
2
0
0
0
0
2
0
1
0
2
1
1
1
1
1
0
1
2
2
0
1
1
0
0
0
1
0
1
0
1
0
1
1
2
1
0
0
1
2
2
4
1
0
2
1
1
1
1
1
1
0
1
1
0
1
0
0
2
2
0
0
0
2
0
0
0
0
0
2
1
2
2
0
1
0
1
0
0
2
2
0
0
0
0
0
4
0
1
1
1
0
0
1
0
1
0
0
1
0
0
0
0
0
1
2
0
1
2
1
1
1
0
0
1
1
1
0
1
0
1
0
1
1
1
0
2
1
1
0
2
2
0
0
1
0
0
0
1
2
1
2
0
0
2
1
0
0
0
0
2
2
2
1
0
0
0
1
0
2
1
1
0
1
0
0
2
0
0
1
1
2
1
0
1
0
1
1
1
1
1
2
2
1
0
1
0
0
0
1
1
1
0
1
1
1
0
0
0
0
1
1
2
1
2
0
1
0
0
1
1
1
2
1
0
1
0
0
2
1
0
1
2
0
0
2
0
2
2
1
0
0
0
0
0
0
1
0
1
2
2
1
1
0
2
1
0
1
0
0
1
0
2
1
2
0
2
1
0
2
0
1
0
0
0
1
1
0
1
1
1
0
0
0
2
1
2
1
0
0
2
2
1
2
0
2
1
1
0
1
0
1
0
2
1
2
0
2
0
0
0
1
1
0
2
0
0
1
3
1
0
0
1
1
2
3
0
0
1
1
0
0
0
0
1
1
2
2
1
2
1
0
1
0
0
2
0
1
1
2
0
1
1
1
1
0
1
0
0
2
2
0
0
2
0
0
2
1
0
2
1
0
1
2
1
0
1
1
0
2
1
1
1
0
0
1
2
0
0
2
0
0
1
0
0
0
1
0
3
0
0
1
2
1
0
0
1
1
1
1
1
0
2
0
1
1
2
2
1
2
1
0
0
2
0
0
0
2
1
2
2
0
0
1
0
1
1
1
1
1
0
1
2
1
0
0
1
2
1
0
0
0
1
1
1
3
0
0
0
2
2
0
1
2
0
0
1
0
1
0
0
0
0
0
1
0
2
0
0
2
1
1
0
1
0
0
1
2
1
2
1
1
1
2
0
1
2
2
2
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
1
1
0
0
0
1
1
2
1
1
0
0
1
1
0
0
2
1
1
0
1
0
0
1
0
1
2
0
1
0
1
1
1
0
1
0
1
0
1
0
1
1
1
0
0
2
2
0
0
0
0
2
0
0
2
3
0
0
0
1
0
0
1
2
2
1
2
1
2
0
0
0
1
0
0
1
2
0
0
0
1
0
2
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
1
0
1
0
2
0
0
2
0
1
2
1
2
1
2
0
0
0
1
2
1
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
2
2
0
1
2
2
1
2
1
0
1
1
2
1
1
0
4
0
0
2
2
0
1
0
0
0
1
1
1
0
0
1
1
0
0
1
0
0
2
0
0
2
0
0
0
1
1
0
4
2
2
1
1
2
1
0
1
0
2
1
1
2
0
0
0
0
2
0
1
1
2
1
0
1
0
0
2
0
1
2
0
2
0
1
1
0
1
1
2
1
0
0
0
1
0
1
0
2
1
1
1
0
1
0
0
1
1
0
1
2
0
0
0
0
1
1
1
2
1
1
2
2
0
0
2
1
1
0
1
1
1
1
0
1
0
0
2
0
1
0
1
1
1
2
0
1
1
0
1
2
1
1
1
0
0
1
0
1
1
0
1
0
0
0
1
0
1
0
0
1
0
1
0
1
1
0
1
2
2
2
0
1
1
1
0
1
0
1
0
1
2
0
0
1
0
0
1
0
0
1
0
1
2
1
2
2
1
2
2
0
0
2
2
1
1
1
1
1
1
2
0
2
1
1
1
1
0
1
0
2
1
1
0
3
1
2
1
2
0
1
1
0
0
0
0
0
1
2
0
0
1
1
0
0
0
2
0
0
1
0
1
0
1
1
1
1
2
0
2
0
0
1
1
1
0
0
1
1
1
2
1
0
1
0
0
0
2
1
0
0
0
1
1
1
0
0
0
0
1
0
1
0
0
0
0
1
2
1
2
2
0
3
0
1
0
1
2
0
2
0
2
0
0
0
0
0
1
0
0
0
2
1
0
0
3
0
1
0
0
0
2
1
0
1
0
1
0
1
1
1
1
1
2
1
1
0
0
2
2
0
1
0
0
0
0
0
0
3
1
1
0
0
0
0
0
1
1
1
0
2
2
0
0
1
1
0
2
1
1
1
2
1
1
0
0
2
1
1
0
0
0
2
0
0
2
1
1
0
0
1
0
1
1
3
0
1
2
1
0
1
0
0
0
1
0
1
2
2
1
0
0
2
1
1
0
0
0
0
3
0
0
2
2
0
1
2
1
1
2
1
0
0
2
2
0
1
1
0
1
1
0
2
1
1
2
0
0
1
1
0
0
0
1
15
0
2
1
1
0
2
1
1
1
1
0
2
0
1
1
1
0
1
1
0
0
0
1
0
1
2
1
0
0
2
0
1
0
2
2
0
2
2
0
1
0
1
2
0
0
1
2
0
2
0
0
1
1
1
0
0
2
0
0
0
1
0
0
2
2
0
0
0
2
0
2
1
0
1
1
0
2
0
0
0
1
2
1
0
1
2
1
1
0
2
2
0
0
0
0
1
1
1
1
0
0
1
1
2
1
2
2
2
2
0
0
1
0
0
0
0
1
1
1
0
0
1
1
0
2
1
0
1
0
2
0
2
1
1
0
2
0
0
2
1
1
0
1
2
0
0
0
0
0
1
0
0
1
2
1
0
0
0
2
2
1
0
1
3
1
0
1
1
2
2
0
2
2
2
1
0
0
1
0
2
1
2
2
1
2
1
1
1
1
1
2
1
1
2
3
2
0
2
2
1
1
1
1
1
0
0
0
0
0
0
0
2
0
1
1
0
0
1
1
0
0
1
0
2
2
5
1
2
1
1
1
1
2
0
1
1
1
1
0
0
0
0
2
1
0
2
2
2
1
0
0
0
4
0
1
2
0
1
0
0
2
1
1
0
1
1
1
0
1
1
0
1
0
1
2
0
2
2
0
1
2
1
2
0
2
0
1
0
1
1
0
0
2
0
1
3
0
0
2
2
2
1
0
1
0
0
2
1
1
2
1
0
1
1
0
0
0
0
1
0
0
2
4
1
2
0
2
1
1
2
0
2
0
1
0
1
2
2
1
0
2
0
1
0
1
0
1
1
1
1
0
0
1
1
0
1
0
1
2
0
2
1
0
1
0
1
0
0
0
0
0
1
0
2
0
0
2
0
0
0
1
0
2
1
0
1
0
0
2
0
2
0
0
1
0
0
0
2
0
1
0
0
0
1
1
0
0
2
0
1
0
0
3
0
1
2
2
2
2
2
0
0
3
0
2
1
1
0
2
0
0
0
1
2
1
0
0
0
1
1
1
0
1
1
0
0
0
0
2
1
0
2
0
2
1
1
1
0
0
0
0
1
2
0
0
0
2
2
2
0
1
1
2
0
2
1
2
1
0
2
0
0
0
2
1
0
2
2
2
0
2
1
1
0
2
1
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
2
1
1
2
2
0
1
1
2
1
0
0
1
0
1
1
0
1
1
0
0
0
0
0
1
0
0
0
2
1
1
1
2
0
0
0
0
1
1
1
0
0
3
0
0
2
0
0
0
2
1
0
1
2
0
0
1
2
2
0
0
0
0
1
1
2
0
2
1
2
0
0
1
1
1
0
2
0
0
0
1
2
1
0
1
2
0
0
0
1
0
0
0
1
0
1
0
1
0
2
0
1
1
0
0
0
0
2
0
2
1
0
2
1
0
1
2
0
0
1
1
0
0
2
2
1
1
1
1
2
1
0
0
1
1
2
2
0
1
0
0
1
1
1
0
1
1
0
1
0
1
2
0
0
1
1
2
0
0
2
0
0
0
0
0
2
1
2
0
2
1
1
1
2
1
1
2
0
2
1
0
2
1
1
0
0
0
1
0
2
2
1
1
2
0
1
0
0
2
0
0
1
0
0
1
0
1
2
1
0
1
0
0
1
0
0
0
0
1
2
0
1
2
1
1
0
0
1
0
1
1
2
2
1
1
1
1
4
0
1
1
1
1
1
1
0
1
0
2
0
1
2
0
1
1
1
0
1
2
1
1
2
1
3
1
0
2
0
0
0
2
0
2
2
1
0
0
2
2
1
2
1
1
2
1
1
1
1
0
0
1
0
1
2
0
0
2
2
0
0
1
1
0
1
0
2
1
0
2
1
0
0
2
0
2
1
0
1
1
0
0
1
1
2
1
1
0
2
0
1
1
2
1
2
0
0
2
0
1
2
1
0
0
2
1
2
1
0
1
1
0
0
2
0
0
1
2
1
1
2
3
0
2
0
0
2
0
1
4
0
4
0
0
2
1
1
1
1
0
0
0
0
0
1
0
0
1
0
1
3
0
0
1
1
1
1
0
2
2
1
0
1
0
0
1
1
0
1
2
2
2
2
2
0
1
2
1
0
0
0
0
0
1
0
2
0
0
0
0
2
0
2
1
0
1
2
1
0
1
1
1
0
0
1
2
0
2
1
0
1
1
1
1
0
1
0
0
0
0
0
2
0
1
0
1
0
2
2
0
0
0
1
2
2
2
0
0
1
1
0
1
0
1
2
1
1
1
2
1
0
0
2
2
1
0
2
2
0
0
2
0
1
1
0
0
0
0
0
2
0
1
1
4
1
1
0
2
1
2
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
3
0
2
1
0
1
0
0
0
0
1
1
0
0
0
2
0
0
1
1
1
1
1
2
0
2
1
2
0
0
0
1
1
2
0
2
1
0
0
1
1
1
0
0
0
1
0
1
0
2
2
0
2
0
1
0
0
2
2
2
1
2
1
0
0
1
1
0
0
0
0
1
0
0
0
2
0
3
0
1
0
1
0
2
0
0
1
0
0
2
0
1
0
0
0
0
0
1
0
0
1
0
1
1
2
2
1
0
1
1
1
0
0
1
2
1
0
0
0
1
2
0
2
0
0
1
0
0
4
0
1
0
0
0
0
0
1
2
0
1
1
1
1
0
1
2
0
1
1
1
0
1
0
1
2
0
1
0
1
0
1
2
1
0
2
1
1
1
1
1
1
1
2
0
1
0
1
2
1
0
0
1
1
1
1
0
2
2
1
0
1
0
1
3
0
0
1
0
1
1
0
1
1
2
0
0
0
1
1
1
0
0
0
3
2
1
1
1
1
3
0
1
1
0
1
2
0
0
1
2
0
1
1
0
0
1
1
4
1
2
1
1
1
0
0
1
0
0
1
1
1
1
0
1
1
3
0
2
0
2
1
0
0
1
0
0
2
1
0
2
2
2
0
1
0
1
2
0
0
0
1
0
2
0
1
2
0
0
0
1
2
0
0
1
0
1
2
0
0
0
1
0
0
0
0
2
2
3
2
0
1
1
1
0
1
2
1
2
1
2
2
0
0
1
2
1
0
0
1
0
0
0
1
1
2
1
0
0
2
0
0
2
2
0
0
1
2
0
2
3
0
0
1
2
1
1
1
0
2
1
1
0
2
2
1
0
5
2
0
1
1
2
2
0
0
1
0
0
0
1
1
3
1
1
2
0
0
1
0
2
2
1
2
0
1
0
0
3
0
0
0
0
1
1
1
1
0
0
1
2
2
0
0
0
2
5
2
1
0
0
0
1
0
2
1
1
0
2
1
2
0
0
2
0
1
0
0
0
1
0
0
2
0
3
2
0
0
0
2
2
2
0
3
2
0
1
1
1
0
0
0
0
1
1
0
1
2
1
1
1
0
1
2
1
1
0
2
0
0
0
1
6
0
0
1
2
0
1
0
0
0
1
1
0
0
2
2
1
1
1
2
1
1
1
1
0
1
0
1
2
1
1
2
0
2
0
0
1
2
1
2
0
2
1
0
1
1
0
2
2
0
2
1
2
0
0
0
0
0
0
1
0
1
1
0
1
0
2
1
1
2
0
1
1
0
3
0
3
2
0
0
1
1
1
0
0
2
1
0
1
0
0
2
0
1
0
0
0
2
2
2
0
0
0
2
0
0
2
0
2
0
0
0
3
0
1
0
0
1
0
1
0
5
1
0
0
1
1
0
1
0
0
1
1
1
0
0
1
0
1
0
1
2
1
0
2
3
0
0
2
1
2
0
1
1
0
2
1
3
0
0
2
0
0
2
1
0
0
1
1
2
1
2
0
1
1
1
0
2
1
2
0
0
1
1
0
2
1
1
2
1
1
0
0
0
1
1
3
2
0
1
2
2
0
0
1
2
1
0
0
2
0
1
1
1
0
0
0
0
1
1
1
3
2
1
1
0
1
0
0
0
0
1
1
0
3
0
0
1
0
0
1
1
2
1
0
1
0
1
0
0
2
1
2
0
1
1
1
1
2
0
1
0
0
0
4
2
2
2
1
0
0
7
1
0
3
0
3
1
0
0
1
0
0
0
0
1
0
0
1
2
0
2
0
0
1
1
0
2
0
0
1
0
0
1
2
0
0
0
1
1
0
1
0
2
0
1
0
0
0
0
1
0
2
0
0
1
0
0
1
0
0
1
0
0
3
0
1
0
1
0
0
0
1
1
1
1
0
3
1
1
1
1
0
2
1
0
1
0
2
1
0
1
2
0
2
0
1
0
0
1
1
0
2
1
2
0
0
2
2
2
0
1
2
0
1
1
0
1
6
1
0
0
0
0
1
2
1
1
0
0
0
0
0
1
0
1
0
0
0
1
1
1
1
0
0
0
0
2
0
1
0
0
2
2
1
1
0
0
0
2
1
2
1
0
0
2
2
0
2
2
0
0
0
1
0
0
1
0
1
1
0
1
1
3
0
1
3
0
0
1
1
0
2
1
0
0
1
1
2
0
0
1
1
1
2
1
1
1
0
0
2
0
1
1
2
1
1
2
0
0
0
0
0
1
0
2
2
1
2
1
3
1
2
1
1
0
2
0
2
2
2
0
2
1
0
1
0
1
0
1
0
0
0
1
0
0
0
1
2
0
0
2
0
0
1
1
1
1
1
0
0
2
1
0
1
0
2
0
0
0
0
1
1
1
0
1
0
2
1
1
1
0
0
0
0
0
1
3
1
1
0
0
2
1
1
1
1
1
1
1
0
0
0
0
1
0
1
1
0
1
1
0
3
1
0
1
0
2
0
1
0
1
0
1
2
0
0
0
0
0
0
1
0
2
2
1
1
0
1
1
1
0
1
0
0
1
2
1
0
1
2
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
3
1
2
2
0
1
0
2
1
1
1
2
0
0
1
2
0
1
2
0
1
1
1
2
1
7
0
0
1
2
1
1
0
2
0
0
0
2
0
0
2
0
1
2
2
0
1
1
1
0
2
2
1
2
0
1
1
1
1
1
1
2
1
0
1
0
1
1
1
1
1
0
2
1
1
1
0
0
0
1
2
2
0
0
0
1
1
0
0
2
2
1
0
1
1
0
2
1
2
2
1
0
0
0
1
0
0
0
0
1
1
2
2
2
0
3
0
0
1
1
2
0
1
0
1
0
1
1
1
1
0
1
0
2
1
1
0
0
2
2
1
2
3
0
2
1
0
1
0
1
1
2
2
1
0
1
2
2
2
1
0
0
1
3
1
2
0
0
1
1
0
2
1
1
2
2
1
1
1
1
0
0
0
0
0
0
1
0
2
1
0
0
0
1
0
0
0
2
0
1
2
1
1
1
1
0
0
0
1
0
0
1
1
1
1
0
2
0
1
2
1
0
2
0
1
1
2
1
0
0
3
0
2
0
2
0
2
0
2
2
0
0
1
1
1
3
1
2
0
1
0
1
0
0
0
1
3
0
1
2
2
2
0
1
0
1
2
0
0
1
0
1
0
1
2
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
1
1
2
1
0
2
1
1
0
1
1
1
1
1
2
0
1
2
2
1
2
0
0
1
1
0
1
2
0
0
1
1
1
0
1
0
1
1
0
2
1
1
2
4
0
1
1
0
2
1
2
0
0
2
1
2
2
1
0
0
0
1
0
0
2
0
2
1
0
1
0
1
0
0
2
0
1
0
3
2
1
1
1
1
1
1
1
1
2
1
2
0
1
0
0
2
1
1
1
0
0
0
1
0
0
2
1
3
1
1
0
2
1
2
1
0
0
1
2
2
0
2
2
1
1
0
1
1
0
1
0
1
2
2
0
2
0
1
0
2
1
1
0
0
1
1
1
2
1
1
0
1
1
2
2
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
2
1
0
1
0
1
2
0
0
2
0
2
0
1
1
1
1
0
0
0
0
0
1
1
0
0
0
2
0
2
1
0
0
1
0
1
0
0
1
0
1
0
2
0
1
0
1
1
0
1
6
1
1
1
0
3
0
0
0
0
1
2
0
2
1
2
0
1
0
0
1
1
1
1
2
0
0
0
0
0
0
2
2
1
0
0
1
1
1
1
0
0
2
0
1
0
1
1
0
0
2
0
1
1
0
0
1
2
0
1
1
1
0
0
0
0
0
0
2
0
0
1
1
0
0
2
0
1
2
0
0
1
1
1
1
0
1
0
1
0
1
0
0
2
1
0
2
1
0
1
2
1
0
2
2
0
0
1
0
0
1
2
1
2
2
2
0
0
1
4
1
1
1
0
2
0
2
0
0
2
2
2
0
2
2
0
2
0
1
1
2
1
0
0
0
1
1
0
0
1
2
0
1
1
0
1
1
8
1
0
1
1
0
0
1
0
1
0
0
0
0
2
0
1
1
0
2
1
0
0
0
2
0
1
1
0
1
0
0
0
2
0
0
1
2
1
1
2
0
1
1
2
0
0
0
1
0
2
0
1
0
2
0
1
1
2
0
1
2
1
3
0
2
2
1
0
0
2
0
2
0
2
1
0
0
2
1
0
1
0
0
2
0
1
1
1
1
2
0
1
0
0
1
1
1
0
0
0
2
1
1
0
1
1
1
0
1
1
1
0
1
2
1
0
0
0
0
0
2
0
0
2
2
1
0
0
0
2
5
2
2
2
1
2
0
1
0
1
1
5
2
0
0
1
0
0
0
0
0
1
2
0
1
0
0
1
0
0
0
1
1
0
0
1
2
0
0
0
2
1
2
1
2
2
1
1
0
1
2
1
0
0
1
1
0
2
0
1
1
0
0
2
1
1
0
1
2
1
2
1
2
0
1
2
1
1
1
2
1
1
0
1
0
0
2
0
0
1
0
2
0
0
2
0
1
0
0
2
0
2
2
2
3
0
0
2
0
2
4
1
0
0
1
0
3
2
2
2
1
1
0
0
0
1
2
0
0
0
0
0
1
0
2
1
2
0
0
0
0
0
1
0
1
2
0
0
1
1
1
1
0
1
0
0
1
1
0
0
2
1
0
2
2
2
0
0
0
0
0
1
0
1
0
1
1
0
1
2
1
1
0
1
0
0
2
1
0
0
0
1
1
1
1
1
0
0
0
2
0
0
1
0
2
1
0
0
1
0
1
0
1
1
1
1
2
1
0
1
0
1
2
2
2
1
2
2
1
0
1
1
1
0
0
4
1
5
1
0
1
1
1
1
1
1
0
2
0
1
0
0
1
0
1
1
1
0
0
0
0
1
1
0
1
0
1
0
2
1
1
1
2
0
0
2
1
2
0
1
0
2
1
0
2
1
2
0
1
1
0
0
0
0
1
2
0
0
0
1
1
2
1
1
0
2
1
1
1
1
1
0
1
0
0
2
2
1
0
1
2
1
2
0
1
1
0
0
0
2
0
0
0
1
1
1
1
1
0
1
1
2
1
2
0
2
0
0
2
0
1
1
0
1
0
1
2
1
0
2
2
1
0
0
1
4
2
1
1
1
1
2
0
0
1
2
0
0
0
0
0
0
1
0
1
1
0
2
2
2
0
1
0
1
2
1
1
1
1
0
0
1
1
0
0
1
0
2
0
1
1
0
0
0
2
2
1
0
3
0
2
1
0
2
2
1
0
0
0
1
0
0
1
0
0
0
2
1
2
1
0
0
0
2
0
1
2
0
3
2
1
0
1
1
1
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
1
1
1
1
1
0
1
1
1
1
1
0
1
1
0
1
1
1
1
1
0
2
0
1
0
0
0
0
0
1
1
1
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
3
1
2
2
0
2
2
2
0
0
5
0
1
0
0
0
0
1
1
2
0
0
0
1
0
1
1
1
0
1
0
2
0
0
1
1
2
1
2
0
1
1
2
0
1
2
0
1
1
0
0
0
1
0
1
1
2
0
2
0
1
1
0
2
1
1
1
1
0
3
0
1
3
2
1
1
1
1
0
1
0
1
0
2
0
0
0
0
0
1
0
0
1
0
1
2
0
1
2
2
1
0
1
0
0
2
2
1
0
0
1
2
1
0
0
1
0
0
1
0
0
0
1
0
1
0
2
0
0
2
0
0
1
0
1
0
0
1
1
1
1
0
1
1
1
2
1
2
1
1
1
0
0
1
1
2
1
1
0
2
0
1
0
1
1
1
1
1
0
0
2
1
1
0
2
0
1
2
0
0
2
1
2
2
2
0
1
0
0
1
1
0
2
2
2
1
0
0
2
0
0
0
1
0
2
2
1
1
1
2
0
2
0
1
1
2
0
1
0
2
2
0
2
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
1
1
2
0
2
0
1
0
0
1
0
2
1
2
1
0
1
0
0
0
1
0
1
0
1
1
0
2
2
0
1
1
1
1
1
0
2
0
2
1
0
1
0
0
1
1
2
1
1
0
0
1
1
0
1
2
0
0
1
1
2
1
0
1
2
0
2
0
1
1
1
2
0
4
0
1
0
0
0
0
0
0
1
0
1
0
4
0
0
1
1
1
1
1
0
1
0
1
1
2
0
1
0
0
2
2
2
0
1
1
5
6
0
0
1
2
1
0
1
0
0
1
1
0
3
0
0
1
1
0
0
3
1
1
0
0
0
1
0
0
2
1
1
2
0
1
2
1
0
0
0
0
2
1
2
0
0
3
0
0
1
0
1
0
2
2
1
2
2
0
1
2
1
0
1
0
1
1
2
0
1
0
0
0
0
1
0
0
0
2
0
1
0
1
2
0
2
1
0
0
1
0
1
1
2
1
2
0
1
2
0
0
2
1
1
2
0
1
0
0
0
1
2
0
1
2
0
2
0
0
0
0
2
2
1
1
2
0
0
0
2
0
1
1
1
1
2
0
1
1
1
0
0
0
0
1
2
1
2
0
0
0
1
3
1
1
0
1
0
2
2
0
1
0
1
2
2
1
1
2
2
2
0
0
0
1
2
2
0
0
2
2
0
2
1
1
0
0
0
2
0
0
2
0
1
0
1
2
0
1
0
1
0
3
1
0
2
1
0
1
0
2
1
0
1
3
1
1
0
0
0
0
0
0
2
1
2
2
0
2
1
0
1
0
0
2
0
2
0
1
1
1
0
0
1
0
3
0
1
2
1
2
0
1
4
2
2
0
2
2
1
1
0
0
0
0
0
2
0
1
0
1
1
1
0
0
1
2
0
2
2
0
0
1
1
2
1
1
2
1
0
1
1
2
0
0
0
0
2
1
2
3
0
2
1
2
1
0
1
0
0
1
1
2
2
0
1
0
1
1
1
0
1
0
1
0
0
0
0
0
2
0
1
1
2
1
2
1
0
0
0
1
1
1
0
0
1
0
0
0
2
1
1
2
1
0
0
1
1
1
0
2
1
0
1
2
1
1
0
0
1
1
0
0
0
1
1
1
0
1
0
0
1
1
2
0
0
0
2
0
1
2
0
1
1
0
1
1
0
0
1
0
1
2
1
0
0
1
2
2
3
1
2
0
1
1
2
0
0
0
0
0
1
2
3
0
1
1
2
2
1
0
1
0
1
0
2
1
2
0
1
2
1
0
2
0
1
2
2
0
2
1
1
0
0
1
0
1
1
0
0
0
0
0
2
1
0
1
1
0
1
0
1
1
1
0
0
0
0
2
2
2
2
0
1
0
1
1
0
0
0
1
1
0
0
0
0
0
0
2
0
0
1
1
1
0
1
2
1
0
2
1
2
2
1
1
2
0
0
1
1
1
1
2
0
2
1
1
1
2
0
1
0
2
1
10
0
2
1
1
1
1
2
2
1
1
1
1
0
1
0
0
1
0
4
0
2
1
2
0
2
0
2
0
0
2
1
2
0
0
2
2
2
1
0
0
0
0
0
2
1
4
0
0
0
1
0
1
0
0
0
0
1
2
1
0
1
1
1
0
0
1
1
1
1
1
1
0
0
2
1
1
0
0
0
2
0
0
0
1
0
1
0
1
0
0
0
1
1
0
0
0
0
2
0
0
1
0
1
1
1
1
0
0
2
1
0
0
2
1
2
0
0
1
1
0
1
0
0
1
0
2
1
0
0
1
0
0
2
1
1
1
1
2
0
1
3
0
2
0
1
0
0
2
0
0
0
0
1
0
1
1
2
0
2
1
2
0
2
0
0
0
0
3
0
0
4
0
0
0
5
0
3
0
1
0
2
2
2
2
2
0
1
0
1
0
0
0
0
2
1
2
0
0
1
0
1
0
0
0
1
0
2
1
0
1
0
1
1
0
1
1
2
0
1
1
1
0
0
1
1
0
1
1
1
0
0
1
1
1
1
0
2
0
1
1
0
0
0
0
2
0
2
1
2
1
3
1
2
2
0
0
0
1
1
0
2
1
2
1
0
0
0
1
2
0
4
1
1
2
0
0
1
0
0
1
1
2
0
2
0
2
1
2
1
1
0
1
0
0
4
1
2
0
1
0
1
1
0
0
0
2
1
0
0
1
0
1
1
1
2
1
1
0
2
1
1
0
2
0
0
1
1
0
0
2
0
2
2
1
0
0
2
1
1
0
0
0
2
1
0
0
2
1
0
1
1
0
0
2
0
1
0
0
1
1
0
0
0
2
0
0
1
0
0
1
1
0
0
3
1
1
1
0
1
1
2
0
0
1
0
2
1
0
1
0
2
0
1
1
1
1
1
0
0
2
2
0
0
0
1
2
0
2
0
2
2
0
1
2
1
1
2
0
0
1
1
2
1
0
0
1
2
1
1
1
0
0
0
1
2
0
0
0
0
0
0
3
1
1
2
0
2
1
0
0
2
0
0
1
0
2
1
0
0
2
2
0
1
1
1
1
0
1
2
0
0
0
2
1
0
0
0
0
0
0
0
2
0
2
1
0
0
2
0
0
2
2
2
0
2
2
1
0
0
2
1
0
0
1
2
2
1
0
0
2
0
2
1
1
0
1
0
2
2
2
0
1
0
0
1
2
1
2
1
1
2
1
1
2
0
1
1
1
0
2
0
1
1
1
0
0
0
0
2
2
2
0
2
1
0
5
1
0
1
2
1
1
1
0
1
1
0
7
0
1
1
0
1
0
1
1
0
0
2
1
0
0
2
1
0
0
0
0
2
1
0
0
0
0
2
1
1
1
0
0
2
0
1
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
2
2
2
1
0
2
1
0
1
1
1
1
2
0
2
1
1
2
2
0
0
0
2
1
0
1
2
0
0
1
1
1
0
2
0
0
1
2
0
0
2
1
1
0
2
0
1
1
1
0
0
0
0
0
2
1
1
0
0
1
0
0
0
1
1
0
0
0
0
3
0
0
0
0
3
1
1
2
0
2
0
2
0
0
0
1
1
0
0
1
2
0
1
0
1
1
0
0
1
2
2
1
2
1
1
0
2
1
2
1
1
0
1
0
0
1
1
2
2
0
2
1
2
0
1
0
1
1
5
1
0
0
2
0
1
1
1
0
1
0
1
1
1
2
0
0
2
0
0
0
3
0
1
0
1
2
1
1
0
2
0
0
2
0
1
1
1
0
1
2
1
1
1
1
1
0
0
1
2
0
1
0
1
2
1
0
0
1
0
0
1
2
0
0
0
1
1
2
0
1
2
1
1
0
1
0
1
2
2
0
0
1
2
0
1
0
0
0
2
0
0
0
2
0
0
0
2
0
1
1
1
2
0
0
1
1
0
1
2
1
2
0
1
1
1
0
1
0
0
3
1
1
1
1
2
0
0
0
0
2
0
2
1
1
1
2
0
1
0
0
2
1
2
0
2
0
1
0
1
0
2
3
0
1
1
2
1
1
0
1
1
3
3
0
0
0
0
0
2
0
1
1
1
0
1
2
1
1
0
0
2
0
0
2
1
2
2
1
1
2
1
0
1
0
0
1
2
0
2
0
1
1
1
0
1
1
0
0
0
0
1
1
0
2
0
1
1
1
1
2
2
2
2
1
0
2
1
0
1
1
2
2
0
0
2
1
1
1
2
1
0
2
0
0
0
3
0
1
1
0
0
0
0
1
1
1
2
3
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
2
1
1
0
2
1
0
1
0
1
0
0
1
0
0
0
1
0
0
0
1
0
2
0
0
1
1
1
1
0
0
1
1
1
0
0
0
2
1
1
1
1
2
1
1
1
1
0
0
2
0
0
0
1
1
2
1
0
1
2
1
0
3
1
0
1
2
1
0
1
2
2
1
1
0
0
2
0
0
2
2
2
1
0
2
6
0
0
1
0
1
3
0
1
1
0
1
0
2
0
1
0
0
0
1
2
0
0
2
1
2
1
0
0
0
1
2
0
1
2
0
0
0
1
1
2
1
0
1
0
0
1
2
0
2
2
1
2
0
1
3
0
3
0
2
2
0
1
2
0
0
0
5
0
1
1
1
0
2
0
1
2
1
1
1
1
0
1
0
0
0
1
2
0
0
1
1
0
1
0
1
1
1
0
0
0
2
0
0
2
1
0
1
0
0
0
0
0
0
1
1
1
1
1
0
2
1
0
1
1
0
0
1
0
0
1
1
0
1
0
0
0
0
2
1
0
0
1
1
0
1
1
0
1
1
1
2
1
1
1
2
0
1
0
3
1
2
1
1
0
1
2
3
1
0
1
0
1
2
0
1
1
0
0
0
0
2
1
1
2
0
2
2
0
1
2
1
2
0
0
0
0
0
2
1
0
0
2
1
0
0
1
0
1
0
3
2
0
1
0
0
1
1
0
0
1
0
3
1
0
1
2
1
0
1
1
0
0
2
1
0
0
1
1
1
2
2
2
0
0
1
2
2
1
0
2
0
0
1
1
1
2
1
2
2
1
2
2
1
0
0
0
1
0
0
0
2
0
0
1
2
2
0
0
1
1
0
2
1
1
1
0
0
1
1
0
0
0
0
1
1
0
1
1
1
0
1
2
0
1
2
1
1
1
0
0
3
1
0
0
1
0
1
0
0
0
0
1
0
0
2
1
1
0
0
1
2
1
2
0
1
2
0
0
1
2
1
0
0
1
0
1
1
0
0
0
0
0
1
0
1
1
1
0
2
1
0
1
1
2
1
2
0
0
1
0
2
0
1
0
1
0
2
0
0
2
0
1
1
2
2
1
2
1
0
1
0
0
2
0
1
0
0
1
2
0
0
1
2
2
1
0
0
0
0
1
2
0
1
2
0
2
0
1
0
2
2
0
1
1
2
0
1
0
2
0
0
0
2
1
0
0
2
0
1
0
2
0
1
1
0
0
2
0
1
2
0
1
0
0
1
0
0
0
2
0
1
0
0
1
1
0
2
1
0
2
1
1
3
1
2
0
0
1
1
2
1
0
0
0
1
0
0
0
0
1
1
2
1
2
0
2
2
2
1
1
0
1
0
0
0
0
0
1
0
0
1
2
3
1
2
0
1
1
0
2
2
0
0
0
1
0
0
0
1
1
1
1
2
0
1
1
2
0
2
0
0
1
1
2
1
1
0
2
0
5
2
0
2
1
1
0
1
0
1
0
2
1
0
0
0
0
2
0
1
0
2
0
0
2
1
1
2
0
2
1
0
1
1
1
0
2
1
1
1
1
2
1
0
2
1
0
2
5
0
1
0
0
1
1
0
0
0
0
0
2
2
1
3
1
0
1
2
1
1
0
1
1
2
1
0
1
1
2
2
1
0
2
0
0
1
2
2
1
2
1
2
2
0
1
1
1
1
1
1
1
0
0
1
2
2
0
2
2
2
1
2
2
2
1
2
0
0
1
1
0
0
0
1
1
1
2
1
0
0
2
1
2
1
1
1
0
1
0
0
0
0
0
1
1
0
0
0
0
1
1
1
2
1
2
1
2
0
0
1
1
2
1
2
0
0
1
0
0
2
1
1
0
1
1
0
0
2
1
2
1
0
0
2
1
0
0
0
2
2
0
1
0
2
0
0
1
1
2
2
2
2
0
0
1
0
2
2
0
0
2
1
2
2
1
1
0
2
3
1
0
1
0
1
1
1
0
2
1
0
0
2
1
0
1
1
1
1
0
0
0
0
1
1
0
2
1
2
2
1
2
1
0
0
1
2
1
1
1
0
1
0
0
1
1
1
2
1
1
0
1
1
2
1
1
0
0
0
0
1
1
2
1
1
0
0
1
1
0
1
1
1
0
2
2
1
2
0
0
0
0
0
2
0
0
1
2
2
0
2
2
2
1
0
0
1
2
0
1
0
0
2
0
2
1
1
0
2
1
1
1
0
1
0
0
2
1
1
2
1
0
1
0
0
1
1
1
2
0
0
0
3
0
0
1
0
0
1
0
2
1
1
0
1
2
1
0
0
2
0
2
1
2
1
1
1
2
1
0
0
0
2
3
1
1
1
1
0
0
1
1
0
0
2
0
0
1
1
0
0
1
1
0
0
0
2
1
1
0
1
0
2
0
0
1
2
1
1
1
0
0
0
2
1
1
0
0
3
1
0
2
1
1
0
2
0
2
1
0
2
0
0
1
0
0
2
1
2
0
0
1
1
1
0
1
0
1
0
1
2
0
0
0
1
1
0
0
1
2
1
0
0
2
0
1
0
1
2
0
2
0
0
0
0
1
0
1
0
1
0
1
1
0
0
0
0
0
1
0
0
1
1
1
1
0
1
2
0
0
4
0
1
1
0
0
1
0
2
0
1
1
0
1
1
1
0
0
1
0
1
2
2
2
1
0
2
1
0
1
1
0
1
0
0
2
0
2
1
2
2
0
1
0
0
0
0
0
1
1
1
0
2
1
0
0
1
0
0
0
2
0
1
2
0
0
1
0
0
2
0
0
1
0
0
0
2
2
0
2
0
1
2
0
0
1
1
1
2
1
2
0
0
2
1
0
1
0
2
0
0
1
0
0
0
1
2
0
0
1
0
0
2
1
1
0
0
2
0
0
2
0
1
0
0
1
0
1
0
1
0
2
1
1
0
2
2
0
2
0
1
2
0
1
0
0
1
1
0
0
2
1
1
0
0
0
0
0
0
1
1
2
2
0
1
1
1
2
1
2
1
1
1
0
1
2
1
1
1
1
1
1
1
3
1
1
2
0
2
1
1
0
0
0
1
2
0
1
0
1
1
0
1
0
1
1
1
0
2
0
1
0
0
0
1
1
0
2
3
1
0
2
2
2
2
2
2
0
1
1
1
1
2
0
0
1
0
0
2
1
1
1
0
0
0
0
2
1
0
0
2
0
1
0
0
0
0
1
2
1
1
0
1
2
1
1
0
0
1
1
0
0
2
0
2
0
0
0
1
1
2
0
1
1
0
1
0
1
0
0
0
1
1
1
2
1
1
1
0
0
1
2
0
0
0
1
1
2
2
0
1
0
1
0
1
0
0
0
1
2
1
1
0
0
1
2
1
1
1
1
0
1
2
1
1
2
0
1
1
2
1
1
0
2
1
1
0
0
0
1
2
2
1
1
2
0
0
0
1
1
1
0
0
0
2
0
1
1
0
2
1
0
0
2
6
2
0
0
3
4
0
0
0
1
0
0
0
0
2
0
2
0
2
2
1
0
2
0
1
0
0
0
0
1
2
0
1
0
0
2
1
1
0
2
2
2
1
1
1
1
1
0
1
1
0
1
1
1
1
0
1
1
1
0
2
0
0
1
2
1
0
0
1
2
0
0
0
2
0
1
0
0
0
0
0
0
1
2
1
0
1
1
1
2
0
0
1
2
0
0
0
2
1
0
0
0
0
1
2
1
1
1
0
2
1
1
1
1
1
1
2
1
2
1
1
1
1
0
2
0
1
0
2
1
1
1
1
0
1
2
0
0
1
0
0
1
1
0
1
2
1
0
1
0
2
0
0
0
1
1
2
1
1
1
0
2
1
1
0
1
1
0
2
0
2
1
1
0
1
1
0
0
0
1
1
1
1
0
0
2
0
0
0
0
2
0
0
1
1
1
0
2
0
1
0
2
2
1
2
1
0
1
1
2
1
1
0
0
1
0
1
2
0
0
1
2
0
0
2
0
0
0
0
2
0
1
1
1
0
1
0
1
0
1
2
1
2
1
0
0
0
0
2
0
3
1
0
0
1
1
0
1
2
0
2
0
2
1
0
0
0
2
0
2
2
2
2
2
1
0
0
1
1
0
2
2
1
1
0
1
1
0
0
1
0
0
0
0
2
0
1
0
2
0
1
1
1
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
3
1
2
0
2
2
0
0
0
0
0
0
2
3
0
0
1
1
2
0
1
2
2
0
1
2
1
2
3
1
0
1
2
0
1
1
1
0
0
1
0
1
1
0
0
0
0
2
0
0
0
0
0
1
1
1
0
0
1
0
1
0
1
1
0
0
0
0
0
4
0
1
1
0
0
1
0
2
0
0
0
2
0
0
2
0
1
0
5
1
0
2
1
1
1
1
2
1
1
0
1
1
0
0
1
0
1
2
1
2
1
0
2
0
0
0
2
0
4
1
0
0
1
0
1
3
2
1
2
0
1
1
0
1
0
0
1
1
0
1
1
1
2
1
0
2
2
1
1
2
2
1
0
1
1
2
1
0
0
1
1
0
0
0
2
2
0
3
0
1
2
1
0
0
2
1
0
0
2
1
0
2
0
0
2
0
2
1
2
1
0
1
0
0
1
3
0
0
1
1
1
0
0
2
0
1
2
0
2
0
2
1
1
1
1
1
0
1
2
1
0
2
0
1
0
0
0
1
1
0
0
0
0
2
1
1
1
1
2
1
2
0
2
2
1
1
0
1
0
0
1
0
2
1
0
0
2
1
2
0
2
0
2
1
1
0
0
1
2
0
0
1
0
0
1
1
1
2
0
2
2
2
2
0
2
1
0
1
1
0
2
1
1
0
1
0
0
2
1
1
0
2
1
1
1
1
0
2
1
0
1
4
0
0
0
2
0
1
2
0
0
1
0
1
0
2
2
0
1
1
2
1
1
1
0
0
1
1
0
3
1
1
0
0
1
0
2
0
2
0
0
0
0
0
2
1
1
1
2
0
1
1
0
0
1
1
1
0
1
0
0
1
2
1
0
2
0
1
0
1
0
1
0
1
2
1
2
0
0
1
1
0
0
2
0
0
0
2
0
0
0
2
1
2
0
2
0
0
0
1
0
2
0
0
0
0
0
0
1
1
1
0
2
0
0
2
0
0
0
2
0
1
1
1
0
2
1
1
0
0
2
0
3
2
1
0
3
1
2
2
0
1
1
1
1
0
1
1
2
0
2
1
3
0
1
0
2
2
1
0
0
2
1
2
0
2
0
1
0
1
0
1
2
1
3
0
0
3
1
2
2
1
0
1
1
0
3
0
1
1
0
2
0
1
1
0
0
1
0
1
0
0
2
2
2
0
0
1
1
0
1
2
0
0
2
0
0
1
1
2
1
1
2
2
1
0
0
0
2
1
0
1
0
0
1
0
1
2
0
0
1
0
0
1
0
1
2
1
2
0
1
1
1
2
1
1
2
1
0
0
1
1
1
0
2
0
0
1
1
0
1
1
1
0
1
0
2
1
2
0
1
2
1
0
2
0
0
0
1
0
0
1
0
2
0
1
0
0
1
2
0
1
0
0
0
1
0
1
0
1
1
1
0
0
0
2
0
0
2
0
1
0
1
1
1
1
2
0
1
2
1
1
0
0
0
0
2
0
1
0
0
1
0
0
1
0
2
1
0
1
0
1
2
0
0
2
0
2
0
0
1
0
0
0
2
0
1
0
2
1
0
2
0
2
2
1
0
0
0
1
2
1
1
2
0
2
2
0
0
0
1
1
0
1
2
1
0
1
0
0
0
1
0
2
1
0
2
0
1
2
1
1
1
0
0
1
0
0
1
2
1
0
1
0
1
1
1
2
0
1
5
0
0
0
2
0
3
0
2
0
0
1
0
0
0
0
0
2
0
1
1
0
1
2
1
0
1
0
0
0
0
1
0
2
1
2
0
1
1
0
0
2
0
1
0
0
1
2
1
0
1
1
1
0
1
1
1
1
1
2
1
2
2
1
0
1
0
0
1
1
0
0
1
1
2
2
1
1
0
1
0
2
0
0
1
2
0
0
3
0
0
0
2
2
0
0
1
0
1
1
0
0
2
2
1
0
0
2
1
0
1
1
0
2
0
1
0
1
1
0
1
1
0
0
0
1
1
1
2
0
0
2
0
0
0
2
1
1
0
1
2
1
0
1
1
0
2
1
0
2
0
1
0
0
0
1
0
2
1
0
2
1
2
0
0
0
1
2
0
1
0
2
1
2
1
0
0
2
2
0
0
2
0
1
0
0
0
1
1
2
0
0
3
1
0
0
2
2
2
1
1
0
1
0
2
1
1
0
1
2
1
0
0
1
0
0
1
0
2
0
0
2
0
2
1
1
0
0
0
2
0
1
1
0
0
0
1
2
1
0
2
0
1
1
0
0
2
0
1
1
0
1
1
2
2
0
2
2
1
1
0
1
0
0
0
2
2
0
1
1
0
0
1
1
1
0
0
1
1
0
0
2
0
0
0
1
1
1
0
0
2
1
1
1
2
2
1
1
2
1
2
0
0
1
0
2
0
0
1
0
1
1
1
1
0
1
1
1
0
0
3
0
0
0
2
0
0
1
0
0
1
1
0
2
0
0
1
0
1
0
1
1
1
1
0
1
1
0
0
0
1
2
0
0
1
0
1
0
0
1
1
0
0
1
0
0
0
1
0
1
1
1
0
1
0
2
1
2
0
3
1
0
1
2
0
0
1
0
0
1
1
1
1
1
0
1
1
2
0
0
2
1
1
2
0
0
1
0
1
1
1
2
1
2
2
0
0
0
2
0
0
0
0
0
3
2
0
1
1
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
2
2
1
1
0
1
0
0
2
1
1
1
1
1
2
1
1
1
1
1
2
0
2
0
2
1
1
0
0
1
1
1
1
1
0
0
2
2
1
0
0
0
0
0
0
1
1
1
0
2
1
0
0
0
1
1
0
0
1
1
0
0
0
0
1
0
1
2
0
0
0
2
1
0
0
0
1
1
1
0
0
8
2
0
1
1
1
0
1
0
0
1
2
2
0
0
5
2
1
2
0
0
0
2
0
0
1
1
0
1
0
2
0
1
1
2
3
1
0
1
0
1
1
0
1
1
1
1
0
1
0
0
2
1
0
0
1
2
1
2
0
1
3
0
0
0
2
1
1
0
1
0
0
2
0
1
2
2
0
1
1
2
0
0
0
1
1
0
1
2
3
2
1
1
1
0
0
1
0
0
1
0
2
0
2
0
0
1
2
1
2
1
1
1
2
0
1
5
2
2
1
0
1
2
1
1
2
0
3
1
1
2
0
0
0
1
0
1
1
2
2
1
2
3
0
3
0
2
1
1
0
2
0
0
0
0
0
1
0
1
1
3
2
1
1
2
2
2
0
1
1
2
0
2
2
1
2
0
1
2
0
1
0
0
0
0
2
0
2
0
1
2
1
2
1
1
0
1
1
1
1
0
2
0
1
2
0
1
2
0
2
2
2
2
2
4
1
0
2
0
1
0
0
2
0
1
0
1
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
1
1
0
1
1
1
2
0
0
0
1
2
1
2
0
0
2
0
0
0
1
2
2
0
1
0
0
0
0
3
0
2
0
2
2
2
1
1
0
1
0
2
0
0
0
0
0
1
0
0
1
0
0
0
2
2
2
1
0
0
1
2
0
1
1
2
0
2
1
0
1
3
0
0
1
0
2
0
0
2
0
2
1
1
0
2
1
2
1
1
0
0
0
1
1
0
1
1
0
0
0
2
1
0
1
0
1
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
1
0
0
1
1
0
1
2
0
1
0
1
1
1
0
0
1
0
1
1
1
2
0
2
1
0
1
1
0
0
1
0
1
0
1
0
1
2
0
2
2
2
0
0
1
1
0
0
0
1
1
1
1
0
1
1
2
0
1
2
0
0
0
0
0
0
1
0
1
0
1
0
2
0
1
0
0
0
0
0
2
3
2
0
2
0
0
0
1
1
1
2
2
1
0
1
0
1
2
3
1
0
0
1
0
0
0
2
2
0
0
1
2
2
0
0
1
1
1
0
1
0
2
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
2
1
1
1
0
2
2
2
0
1
2
1
1
1
2
1
2
0
2
0
1
0
0
0
2
0
0
0
1
0
0
2
1
2
1
2
0
0
0
2
0
0
5
1
0
1
0
1
0
1
0
2
0
0
0
1
2
0
1
1
0
1
0
2
0
2
1
0
0
1
0
0
1
2
0
0
2
0
1
2
2
0
2
2
2
1
0
1
0
1
0
0
1
1
1
3
3
0
0
0
2
1
1
0
1
0
0
0
0
1
0
2
0
2
1
1
1
2
1
0
2
0
1
0
1
2
1
0
0
0
0
1
0
1
1
3
1
2
1
2
1
0
2
2
2
1
2
0
0
0
2
1
0
2
0
0
0
0
1
2
0
1
0
1
1
1
0
1
0
0
2
2
1
1
1
1
3
0
1
1
2
1
0
0
1
2
1
1
0
2
1
2
0
2
1
0
2
0
1
2
1
2
2
2
0
1
1
0
0
0
1
2
0
2
1
1
1
1
1
1
2
2
0
0
0
3
1
3
2
1
2
2
0
2
1
0
2
2
2
0
1
0
1
1
0
2
1
0
1
2
0
1
1
1
1
1
1
2
1
0
0
0
1
1
1
0
1
0
2
1
1
1
0
0
1
0
1
0
2
1
0
0
1
2
0
0
2
0
2
2
0
0
2
0
0
2
0
1
1
0
0
1
0
1
0
0
1
2
0
0
1
2
1
0
1
0
2
0
2
1
2
2
4
1
2
0
1
0
2
1
1
2
1
1
2
0
1
0
0
1
1
1
0
1
2
1
1
1
1
0
1
1
0
1
2
2
0
0
1
1
1
0
0
0
1
1
1
0
1
0
1
2
1
3
0
1
2
0
0
1
2
0
2
0
2
0
2
0
2
0
1
0
0
2
0
1
0
1
2
0
1
0
2
1
2
1
2
1
1
1
1
2
0
1
1
0
2
0
1
2
1
1
0
0
0
0
2
0
1
2
0
2
0
0
2
0
0
0
0
0
0
0
1
2
1
0
1
1
0
0
1
0
1
0
1
0
1
1
1
0
1
0
0
3
1
1
0
0
1
0
2
0
1
2
1
1
2
0
0
1
1
0
0
2
0
1
0
2
0
1
2
2
1
0
1
0
0
1
0
0
0
1
0
1
1
2
2
1
2
2
2
2
0
0
1
2
1
1
1
1
0
0
0
2
2
1
2
0
1
1
1
2
0
1
0
1
1
2
1
0
1
0
0
1
2
0
1
1
1
1
0
1
1
0
1
0
0
1
1
0
0
0
2
0
0
2
1
1
1
1
1
3
1
1
0
1
1
1
0
2
1
0
2
2
0
2
2
0
1
1
2
1
0
0
2
1
1
1
1
3
0
1
0
1
1
2
0
0
0
1
2
1
1
1
2
0
1
2
2
1
2
2
0
2
2
0
0
1
1
2
0
0
2
0
0
2
1
0
0
0
1
1
1
2
3
0
0
0
0
1
2
0
2
1
2
6
1
1
2
1
2
1
0
1
1
1
1
0
0
1
0
2
0
0
1
0
0
1
0
1
0
0
1
1
0
0
2
0
1
1
0
0
1
0
0
1
1
0
0
0
1
2
0
1
2
0
2
0
1
1
1
2
2
0
1
1
1
1
1
2
1
0
0
0
0
0
1
0
2
1
2
2
1
1
2
0
0
0
1
0
1
0
0
0
1
2
1
2
2
1
0
0
0
0
1
0
0
0
1
0
2
3
0
2
1
0
0
1
1
0
0
2
1
1
2
2
1
0
0
1
3
0
0
0
0
2
0
0
1
1
2
1
0
0
0
1
1
0
2
2
1
1
0
3
1
0
0
0
0
0
0
0
1
1
0
2
0
0
1
0
1
1
0
1
0
1
0
2
1
0
7
0
1
1
0
1
0
1
1
2
2
2
0
0
1
0
2
0
2
0
0
2
0
0
0
0
0
1
1
2
1
0
0
1
1
1
0
3
0
0
0
1
1
0
0
2
2
1
1
1
0
0
2
0
0
0
0
1
2
1
0
1
1
0
1
0
0
2
0
1
1
0
1
0
1
0
0
1
0
0
2
5
1
2
0
0
1
0
2
1
1
1
0
1
2
1
2
1
2
1
2
2
0
0
2
1
0
2
1
1
1
2
1
0
1
2
0
2
1
1
3
1
1
0
0
0
2
1
1
0
1
3
1
0
0
0
0
1
0
0
1
1
1
2
0
1
1
2
0
0
1
0
1
0
2
1
0
0
2
1
0
0
1
1
2
0
1
2
1
0
0
2
0
1
0
1
2
0
0
1
0
0
1
0
0
2
1
2
2
1
0
0
0
1
1
1
0
0
1
1
1
1
1
0
0
0
2
1
0
0
0
0
0
1
1
0
1
1
1
1
2
0
0
0
1
0
0
0
1
1
2
0
0
0
1
1
1
0
2
1
0
0
0
0
0
1
0
2
1
0
1
1
2
0
1
1
1
1
0
2
0
0
2
0
0
1
2
0
0
0
0
1
0
0
2
1
0
0
0
2
0
1
2
1
2
1
0
0
2
0
0
1
1
0
1
1
2
1
2
1
0
2
2
0
0
2
0
0
1
3
0
0
0
1
0
0
1
1
2
1
1
0
0
2
0
1
0
2
2
0
0
1
1
0
1
2
2
1
2
2
1
0
0
1
2
2
1
0
2
0
0
1
0
2
0
0
0
0
0
1
0
0
2
0
1
2
2
0
1
0
2
0
2
0
0
2
0
1
2
2
1
0
1
1
0
2
1
4
3
2
1
1
1
0
1
0
1
0
1
1
2
0
2
1
2
0
2
1
2
1
0
2
0
0
2
1
1
0
0
2
1
0
0
0
1
1
2
1
1
1
1
2
1
2
1
2
2
1
0
1
1
0
2
0
1
2
0
0
2
2
1
1
2
1
1
0
0
2
1
1
1
1
0
0
1
0
0
0
0
2
1
0
1
1
0
1
1
0
1
1
1
0
1
1
0
0
1
1
1
0
1
2
0
0
1
1
1
2
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
1
2
0
0
0
1
0
1
1
0
0
1
0
0
1
1
2
2
1
1
0
0
1
1
0
0
1
2
1
1
2
0
0
0
1
0
2
0
1
2
0
0
0
2
0
0
1
2
1
3
0
2
2
0
0
1
0
0
1
1
2
0
0
1
1
2
3
1
0
0
0
0
2
0
0
0
0
0
2
2
1
1
1
1
0
1
3
0
0
1
1
0
1
1
1
1
0
2
1
3
0
1
1
1
1
2
0
1
0
1
2
0
2
1
0
0
1
0
1
0
0
0
2
1
0
2
0
2
0
1
0
0
2
0
0
2
1
1
0
1
2
2
1
1
0
1
1
2
1
0
0
1
0
0
2
0
2
2
0
1
0
0
0
1
1
1
0
0
1
0
0
1
1
0
2
0
2
4
4
1
0
0
0
1
1
1
2
1
2
0
0
1
0
1
1
2
2
0
0
2
0
0
2
0
1
1
1
0
0
1
1
1
2
0
1
0
1
0
0
2
1
1
2
1
0
1
1
0
1
1
0
0
1
0
1
1
0
0
0
1
2
1
1
0
0
1
1
0
3
1
1
1
2
0
2
1
0
0
0
1
1
2
1
0
0
0
0
0
0
0
1
2
0
1
1
1
0
1
0
0
0
2
0
2
0
1
2
0
1
0
2
1
3
2
1
0
2
0
1
2
1
2
1
0
0
2
2
2
0
0
2
0
1
0
2
0
0
0
1
1
1
1
1
0
0
1
2
0
2
0
0
0
0
2
2
1
1
0
0
2
1
1
1
2
3
1
2
0
1
1
2
1
0
1
0
0
2
0
0
2
0
1
0
0
1
0
0
0
0
1
0
1
0
0
1
1
1
1
1
1
2
0
0
1
1
0
2
0
2
0
0
0
2
2
0
2
0
0
2
1
1
0
1
1
1
2
1
0
1
1
0
0
3
0
1
1
2
1
0
1
1
0
0
0
1
0
2
1
1
1
0
2
0
1
1
1
0
1
0
0
1
1
1
0
1
0
1
1
0
2
2
0
2
3
2
0
0
0
1
1
0
1
1
0
0
0
0
0
0
2
0
0
1
0
0
1
0
1
1
1
0
1
1
0
0
1
0
0
1
0
1
0
0
0
0
1
1
0
0
1
0
1
1
0
1
0
1
2
1
1
0
0
2
0
1
1
1
1
0
0
2
2
1
0
0
1
1
1
1
2
1
2
0
0
0
1
2
2
2
1
1
1
2
0
2
1
0
2
1
0
1
1
1
1
1
0
1
0
1
2
0
0
1
1
0
0
0
0
2
0
0
0
1
1
1
0
0
0
1
1
1
0
0
1
1
2
0
1
0
0
0
1
0
0
2
1
0
0
1
1
0
1
1
1
0
1
2
0
2
0
1
2
2
0
0
0
2
2
2
2
0
0
1
2
1
1
1
1
0
1
0
1
0
2
1
2
1
1
0
0
1
0
3
1
2
0
0
0
1
1
2
1
0
0
0
1
1
1
0
1
0
1
0
1
1
0
0
0
1
0
1
2
1
0
0
1
2
1
2
1
2
0
0
2
1
1
1
0
0
1
0
1
1
0
2
0
1
0
0
1
0
0
1
0
0
0
0
2
2
0
1
0
1
1
1
0
0
0
0
3
0
0
1
3
1
0
0
0
0
0
1
1
0
1
0
1
0
0
2
0
2
1
0
0
2
2
3
1
2
1
0
1
1
1
0
2
1
2
2
0
1
1
0
2
1
0
1
0
0
2
0
0
2
0
1
0
0
1
2
1
0
0
1
0
1
0
0
0
1
1
0
1
0
1
0
1
0
1
2
1
2
1
2
2
0
1
1
0
3
0
2
2
1
0
2
0
0
1
1
2
2
1
0
1
2
1
0
0
0
1
0
0
0
1
1
0
0
2
2
0
0
2
2
1
0
1
0
2
1
1
0
1
1
0
0
0
0
0
0
0
0
2
1
1
0
0
0
1
1
0
1
0
1
0
2
2
3
0
2
2
2
0
0
0
0
1
0
0
2
0
0
1
2
2
1
1
0
0
0
1
1
1
1
0
1
0
0
0
0
0
1
0
1
2
1
1
1
1
0
2
0
1
1
0
3
2
0
2
1
0
1
1
2
1
0
0
0
0
1
1
2
0
1
1
1
1
0
1
1
0
1
0
2
1
1
0
1
1
0
0
0
0
2
0
0
0
1
0
0
0
1
2
1
1
0
0
1
0
1
0
1
1
1
0
0
2
1
0
2
0
1
1
0
1
0
0
2
1
1
0
2
0
0
0
2
1
0
1
0
0
0
1
1
1
1
4
2
1
1
0
1
2
0
1
0
0
0
0
0
2
0
1
2
1
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
2
0
2
1
0
2
2
0
0
1
0
0
0
0
0
0
1
0
0
1
1
1
2
1
2
2
0
0
2
2
2
1
2
0
1
0
0
1
2
0
2
2
0
2
0
2
0
1
1
0
1
2
1
1
1
0
2
1
0
1
0
2
1
0
0
2
0
1
1
0
2
0
2
0
0
0
2
2
2
0
1
0
2
0
0
1
1
1
0
2
1
0
0
1
1
1
1
2
0
0
0
1
2
0
0
2
2
0
0
0
0
0
1
2
1
0
2
1
1
1
1
0
1
1
1
0
1
1
0
0
2
0
0
2
1
0
1
0
1
0
0
0
2
0
0
0
0
1
0
0
2
2
0
2
0
1
2
0
2
1
1
0
0
0
2
1
0
1
2
1
1
2
2
0
0
1
0
0
1
0
0
2
1
0
1
2
0
0
1
0
1
0
1
1
2
0
2
0
4
0
1
0
2
1
2
2
0
0
1
0
1
0
0
3
0
0
0
2
0
1
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
2
2
0
2
0
1
2
0
1
0
0
1
1
0
2
2
2
0
0
1
1
0
1
2
2
1
0
1
0
1
2
2
1
0
0
0
0
2
1
2
2
0
3
0
1
0
2
1
1
1
0
0
2
0
0
2
1
1
0
1
1
0
0
1
1
1
1
2
0
2
0
0
0
0
0
0
1
1
0
0
1
2
0
0
0
0
2
1
3
1
0
2
2
2
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
1
2
0
0
0
2
2
1
1
0
0
0
0
2
0
1
2
0
2
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
2
1
0
2
2
2
0
2
2
1
0
1
0
0
0
2
0
0
2
0
2
2
0
0
0
1
0
1
1
1
1
0
0
0
2
0
0
1
2
2
1
0
2
1
0
2
0
0
0
1
0
0
1
0
1
0
2
1
1
1
2
0
0
1
1
1
0
0
0
0
1
1
0
1
2
0
0
3
1
0
1
0
2
0
2
1
1
2
0
2
1
0
1
1
0
0
2
0
2
1
1
0
0
2
2
2
2
1
2
1
1
2
2
1
0
0
1
1
2
1
2
2
0
0
1
1
0
0
2
0
0
0
1
1
0
2
1
0
1
0
0
3
0
0
1
2
0
0
2
0
1
1
0
0
0
2
1
0
2
0
5
0
0
1
1
1
1
0
0
0
0
1
0
3
0
2
0
0
1
0
1
0
0
1
1
1
0
1
0
1
0
1
0
0
2
0
0
0
0
1
0
0
1
1
1
1
1
2
1
1
1
2
0
1
0
0
1
1
0
3
2
0
1
2
0
1
0
2
1
0
1
0
0
1
1
0
0
0
1
0
0
0
1
0
1
0
2
0
1
1
1
0
0
1
1
2
1
2
0
1
0
2
2
0
2
1
1
0
1
0
1
0
2
1
2
2
1
0
2
0
0
0
2
1
2
0
2
0
1
3
0
2
0
0
0
1
1
0
0
2
2
1
0
1
0
0
1
2
2
2
0
1
2
0
0
1
0
2
0
0
2
1
2
2
0
0
1
1
3
0
5
0
1
1
3
0
3
0
1
3
0
2
0
2
0
1
1
2
1
0
0
1
0
2
2
1
0
1
0
2
0
2
0
0
0
1
1
1
2
1
0
0
2
0
1
0
2
2
0
1
2
0
2
1
0
1
0
1
0
0
0
3
0
0
2
1
0
0
2
1
2
1
1
0
0
1
1
0
1
1
0
1
0
0
2
1
0
2
1
1
0
0
1
2
1
0
0
1
1
0
2
2
2
1
0
0
1
0
2
0
2
2
0
1
1
0
1
0
2
0
0
2
2
0
0
0
2
1
3
0
1
1
0
0
0
0
1
0
2
0
1
1
1
2
1
0
0
2
1
1
0
0
0
1
0
0
2
0
2
1
0
1
1
2
0
1
1
0
0
0
1
2
1
0
0
0
0
2
1
0
0
2
2
1
1
1
0
0
0
1
0
0
1
0
2
1
1
2
2
0
0
1
1
0
0
0
2
1
1
1
1
1
2
1
1
0
5
1
0
1
1
3
0
0
0
1
0
1
0
1
2
2
2
1
0
1
0
0
0
2
1
2
0
1
0
0
2
1
0
2
0
2
1
1
0
0
1
0
2
2
1
0
2
0
1
1
0
0
2
1
1
2
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
2
2
0
1
0
1
0
2
1
0
1
0
0
1
1
1
1
1
2
0
1
3
0
0
2
1
0
1
1
0
1
0
2
1
2
0
1
1
2
0
2
2
0
0
0
0
0
2
0
0
1
0
2
2
1
0
0
0
1
0
0
2
0
2
0
2
0
2
0
0
1
1
0
2
2
1
0
2
2
1
0
0
1
1
2
2
0
2
1
2
0
0
2
2
1
1
1
2
2
2
0
1
1
0
1
1
0
2
2
1
0
0
1
1
2
1
1
1
3
0
1
1
2
0
0
2
1
2
2
0
0
0
1
2
0
2
3
0
1
1
2
1
0
1
2
0
2
1
2
1
0
2
1
0
0
0
0
1
1
0
2
1
0
0
1
0
0
2
1
2
1
1
0
1
0
0
2
0
1
0
0
3
1
0
0
2
0
0
1
0
0
0
1
1
1
0
0
0
1
1
1
1
1
0
0
0
0
0
0
3
0
2
1
0
0
0
0
1
1
0
0
0
1
0
0
1
0
1
1
1
2
1
0
1
0
0
0
1
1
0
0
0
0
0
2
0
1
0
0
1
1
2
0
0
1
0
0
0
1
1
1
0
1
1
0
2
1
1
0
1
1
1
0
0
0
2
1
2
0
0
0
0
0
0
0
1
2
0
2
0
0
0
1
1
0
1
0
0
0
0
0
1
0
2
2
2
0
0
0
1
2
0
2
2
1
1
0
0
2
0
0
1
0
2
1
0
1
2
1
1
1
1
1
0
1
0
1
1
0
0
1
2
1
0
0
2
2
0
2
2
1
1
0
2
0
2
0
2
1
0
2
0
0
1
0
2
0
0
2
1
1
2
0
1
1
0
1
1
2
2
1
2
1
0
2
0
2
1
1
0
0
0
2
0
2
2
1
3
0
0
0
0
1
0
1
1
0
2
0
1
1
2
0
1
2
1
0
1
2
0
1
0
2
1
2
1
1
0
1
0
1
0
0
2
0
1
0
1
1
0
1
2
1
2
0
0
3
1
1
1
0
0
2
2
1
0
2
2
1
0
0
0
0
0
1
0
0
1
2
2
2
1
0
0
1
2
0
1
0
0
2
0
1
1
0
1
1
0
0
0
1
0
1
1
2
2
1
1
1
1
0
2
0
1
1
1
0
1
1
1
0
0
2
2
0
0
1
2
0
1
1
0
1
0
1
0
1
0
1
2
2
2
0
2
0
0
1
0
0
2
0
0
0
0
1
2
1
1
1
1
0
0
0
1
1
1
0
2
1
0
0
2
0
1
0
0
1
0
1
0
2
4
1
1
2
1
1
1
1
2
1
0
0
1
1
1
0
1
1
0
1
0
0
0
0
2
2
1
1
2
1
2
0
2
0
2
0
0
1
1
1
1
2
2
0
1
2
0
2
1
0
2
1
1
0
2
1
2
0
1
2
0
1
0
0
0
0
0
0
0
1
1
2
2
1
1
0
1
1
1
2
1
2
0
0
0
1
1
0
1
0
0
1
2
2
0
1
0
0
0
0
2
2
1
2
0
2
1
1
0
0
0
0
0
0
1
1
0
2
1
1
2
1
1
1
1
2
1
1
0
1
2
1
1
0
1
2
0
1
2
1
0
0
1
2
2
0
0
1
1
1
0
1
1
0
1
0
2
0
0
2
2
1
0
1
2
2
0
1
1
2
0
2
0
1
2
0
0
1
3
1
2
0
0
1
2
1
0
0
0
0
0
0
0
1
1
0
1
1
2
1
1
0
1
1
0
2
0
0
1
2
2
1
1
0
0
1
0
1
0
0
0
0
2
2
2
1
1
1
2
0
1
0
0
0
0
1
0
0
0
0
0
1
1
2
0
1
0
0
0
1
1
1
0
0
1
1
2
0
1
1
2
2
0
2
2
2
0
0
0
1
1
0
0
1
1
0
1
0
0
2
1
1
1
1
0
1
1
0
0
2
2
1
0
1
2
2
1
0
3
1
1
0
1
2
1
0
0
1
0
0
1
0
2
6
0
0
3
0
0
1
2
2
1
0
0
2
0
0
0
0
1
0
0
1
0
2
1
1
2
0
2
0
1
1
1
1
0
1
0
0
0
1
1
2
0
0
0
1
1
0
0
2
0
0
0
1
0
0
2
2
2
0
3
1
1
0
0
0
2
1
0
0
0
2
0
2
1
1
0
1
0
0
0
0
0
0
1
0
0
2
1
0
2
1
0
0
1
0
0
0
1
1
1
0
0
1
2
1
2
1
1
2
1
2
0
1
1
2
1
1
0
1
1
0
0
1
0
1
0
0
2
0
1
1
0
0
2
0
0
0
2
1
0
1
0
1
0
1
2
2
0
1
1
3
2
2
1
0
1
1
1
1
2
2
2
2
1
2
0
0
1
0
2
0
0
0
2
2
1
0
2
0
0
0
1
2
1
1
3
2
0
1
2
0
1
1
1
1
1
0
2
1
1
0
0
0
2
0
2
1
1
1
1
1
1
0
1
0
1
2
0
1
1
0
2
2
0
1
1
1
0
2
1
1
1
1
1
1
0
0
0
1
0
1
2
0
1
4
1
1
1
2
0
2
3
0
0
1
0
1
1
2
0
2
2
0
0
1
0
2
0
0
0
0
0
0
1
2
1
1
0
2
2
0
0
3
0
1
0
0
2
1
1
0
1
2
1
1
0
1
1
2
2
2
0
0
1
0
1
1
0
0
0
2
0
2
4
2
1
0
0
2
1
0
2
1
1
1
1
1
2
0
1
2
2
2
1
1
1
2
1
2
3
1
0
0
0
1
1
2
1
2
1
1
2
0
1
2
1
0
2
1
2
2
0
0
2
0
1
0
0
1
1
1
2
1
0
2
1
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
1
1
2
0
0
1
0
1
2
1
0
1
1
0
2
1
0
1
0
0
0
1
2
2
0
0
0
1
5
2
0
0
2
2
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
2
0
3
1
1
1
2
0
1
1
2
0
0
0
0
2
1
2
0
1
3
1
1
0
1
3
1
1
0
0
3
1
0
0
2
1
0
1
1
0
2
1
0
1
0
2
1
0
0
1
1
0
1
0
1
2
0
2
1
2
1
0
1
0
1
1
1
5
3
2
1
1
1
1
3
0
1
0
0
1
0
2
2
0
0
2
4
2
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
1
1
2
1
1
2
0
2
0
1
0
0
2
0
0
1
2
0
0
2
2
0
1
1
1
1
2
0
0
0
1
1
0
0
1
1
1
2
0
0
1
2
0
0
1
1
1
0
0
2
0
1
0
0
1
2
2
2
2
0
1
0
0
2
2
1
1
2
3
1
1
0
0
2
2
1
0
0
1
2
0
0
0
2
2
0
0
2
1
1
0
1
0
2
1
2
0
0
2
1
1
1
0
1
1
2
1
0
1
0
0
1
0
1
2
2
2
1
2
0
0
1
0
0
1
0
1
0
0
0
0
0
2
2
2
3
2
2
2
0
1
0
0
0
0
2
1
2
1
0
0
1
0
2
0
0
1
0
1
1
0
2
1
2
0
0
1
0
0
1
1
0
1
0
0
1
1
0
1
1
0
0
1
0
0
0
0
1
1
1
0
2
0
0
3
2
0
1
1
0
0
0
0
1
0
3
1
2
1
2
0
0
2
0
1
2
1
0
1
2
2
0
2
1
1
0
2
0
0
2
1
0
0
0
0
2
1
0
2
0
0
2
0
1
1
0
1
2
2
0
0
0
0
1
1
0
0
2
0
0
1
0
5
1
2
2
1
0
1
1
1
2
3
0
0
0
0
2
1
4
0
1
1
2
1
0
0
1
2
0
1
1
0
2
1
0
0
2
0
0
1
2
0
1
0
1
2
0
0
0
2
0
2
1
2
1
0
1
2
2
1
0
0
0
2
1
1
2
1
1
0
0
1
2
1
2
1
2
1
2
0
0
0
0
0
1
0
1
1
1
0
0
1
2
1
0
0
0
0
1
1
1
1
0
0
0
0
1
0
0
1
1
1
2
0
2
2
0
1
2
1
0
1
0
1
0
1
1
2
0
3
1
1
1
2
1
0
1
1
0
0
0
2
1
1
1
0
0
0
2
1
0
1
0
0
1
0
1
2
2
0
0
2
0
0
2
2
0
0
1
4
0
1
2
2
0
0
1
2
1
2
1
0
1
2
0
2
2
0
0
1
0
2
0
2
2
0
0
2
2
0
0
1
0
2
0
0
1
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
1
0
2
0
1
0
0
1
1
1
0
0
1
0
0
0
2
0
0
1
2
1
0
0
2
0
1
0
1
1
1
0
0
0
1
0
1
0
1
0
2
1
0
2
1
0
0
0
1
0
0
2
1
1
2
0
1
0
0
1
0
2
2
0
0
2
1
1
3
1
2
1
0
0
0
1
0
1
1
0
1
4
0
1
0
1
0
1
2
0
1
0
0
1
1
0
2
2
2
1
0
0
0
0
0
1
2
0
0
0
0
1
1
0
2
1
0
0
0
1
0
0
1
0
1
2
1
1
2
3
1
1
0
0
2
2
0
1
1
0
1
0
1
0
0
0
1
1
0
0
1
2
2
0
1
0
0
0
0
0
0
0
4
1
0
0
2
2
0
0
2
0
0
1
1
0
1
3
0
0
0
2
0
1
0
2
1
1
1
1
1
1
1
1
1
0
1
0
0
2
0
1
2
1
2
1
1
0
0
0
0
0
0
1
0
0
1
0
1
0
2
0
2
2
0
2
2
1
0
0
2
0
3
2
0
0
2
1
0
0
0
0
0
1
0
2
1
0
0
0
1
0
1
0
1
0
0
2
1
1
2
1
1
1
0
0
0
0
0
0
1
0
2
0
0
1
0
1
1
0
2
0
0
0
0
2
0
1
0
0
0
1
1
0
1
0
1
1
0
1
0
1
1
1
0
1
0
1
1
1
0
2
0
0
2
0
0
1
0
1
0
0
0
0
2
0
1
1
1
1
0
2
0
0
1
2
0
0
2
0
0
2
0
2
1
0
0
0
0
0
0
2
0
1
0
2
1
1
1
1
0
0
1
0
0
2
0
0
1
0
0
1
0
1
1
1
0
0
0
1
2
0
2
0
0
1
0
0
0
0
1
0
2
1
0
0
2
1
0
0
2
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
1
2
0
0
0
2
0
1
1
1
1
0
2
0
1
0
0
2
1
1
0
0
1
1
0
0
0
0
0
0
1
1
1
2
0
0
0
0
1
1
0
2
2
4
1
2
2
1
0
1
0
1
2
0
2
2
0
1
0
2
0
1
0
1
0
1
2
1
1
1
0
1
0
2
1
0
2
0
1
0
0
0
1
0
2
1
0
1
0
0
0
0
0
1
1
1
2
1
0
1
1
1
1
1
1
0
1
0
0
0
0
0
1
0
1
1
0
1
1
1
0
0
1
0
1
1
0
0
2
1
0
1
0
1
0
1
2
1
1
0
1
0
1
2
0
0
0
1
0
0
2
0
0
1
2
0
2
2
1
0
1
1
1
0
1
1
2
1
1
2
3
0
1
1
1
2
1
0
1
1
1
0
1
1
1
1
1
0
1
1
2
0
0
1
2
0
1
1
0
1
0
1
1
1
0
2
2
0
0
1
2
1
0
0
0
0
0
2
1
2
0
1
2
0
0
1
0
1
1
1
2
0
1
0
1
1
2
0
0
2
0
1
0
2
2
1
0
0
1
0
1
0
0
0
1
1
0
0
0
2
1
1
0
1
0
1
1
0
2
0
0
2
0
1
1
0
2
0
0
1
2
0
2
0
1
0
1
1
0
1
0
0
1
0
1
2
13
0
0
0
3
1
2
1
1
1
1
1
0
1
1
0
0
0
0
1
1
1
0
0
1
0
0
1
2
2
0
0
0
1
0
1
1
0
0
1
1
0
0
0
1
1
0
1
0
0
0
2
1
3
0
2
0
0
1
0
2
0
1
0
1
0
0
2
0
0
0
2
0
2
0
0
0
0
1
1
1
0
1
1
2
0
0
1
1
1
1
1
1
1
1
2
0
2
1
1
2
0
0
2
0
1
0
1
1
1
1
1
2
1
1
0
1
0
2
0
1
1
2
2
1
2
1
0
0
1
1
0
2
0
0
0
0
0
0
0
1
1
1
0
1
2
3
1
0
1
1
0
0
1
1
2
4
1
0
1
1
1
1
2
0
1
1
0
0
0
1
3
0
1
0
1
0
1
0
0
0
1
1
1
0
1
2
2
1
0
1
1
0
2
1
0
1
0
1
0
2
1
1
2
1
0
2
2
0
0
0
1
0
0
0
0
2
2
0
1
1
0
2
0
0
0
1
0
1
1
1
1
0
0
0
0
0
1
2
1
0
1
0
1
0
1
1
1
0
0
2
0
0
1
0
1
0
1
2
1
0
1
0
1
0
1
1
1
1
1
1
2
2
1
0
2
0
1
2
1
0
1
0
1
0
2
2
3
0
0
2
0
1
0
2
0
2
0
1
0
1
0
1
0
1
2
2
0
2
1
1
2
0
3
0
1
0
0
0
1
0
1
2
0
0
1
0
1
0
0
0
1
1
0
1
1
2
1
0
0
0
0
1
0
0
1
0
0
1
0
0
1
3
1
0
0
1
2
0
1
3
0
0
0
0
1
0
0
2
0
0
1
0
1
1
1
2
0
0
0
1
1
1
0
0
0
1
2
0
1
2
0
1
1
1
0
1
0
1
0
1
2
0
2
1
1
2
0
2
0
0
1
1
1
1
2
0
1
2
2
3
1
2
2
1
1
2
0
0
1
1
1
2
0
1
2
1
0
0
0
2
3
1
1
1
1
1
2
0
1
1
1
1
0
0
2
2
1
1
1
2
2
2
2
0
1
1
0
2
0
2
0
0
0
1
0
2
1
1
0
1
2
0
1
0
0
2
1
2
1
0
0
0
1
1
1
0
0
0
1
2
2
0
2
0
2
1
0
0
1
2
1
1
0
1
2
1
1
2
0
1
1
1
2
0
1
0
1
1
1
0
1
1
0
0
0
1
1
2
0
1
0
1
0
0
0
0
1
1
3
1
0
1
0
0
0
0
1
0
0
0
2
1
2
0
2
2
1
0
0
2
2
0
0
1
0
1
0
0
1
3
0
1
2
1
0
0
0
0
1
0
0
0
1
2
0
1
1
0
0
2
1
1
2
0
1
0
1
1
0
0
2
2
0
1
0
0
1
1
3
1
4
0
2
0
0
1
1
1
2
0
2
1
0
2
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
2
1
2
0
1
0
1
1
1
2
1
2
0
0
2
0
2
0
0
0
1
1
0
1
1
2
1
0
1
0
0
0
1
0
0
1
0
0
0
0
2
1
1
1
0
0
1
2
1
2
1
0
0
0
0
1
0
2
1
0
1
2
1
1
0
1
1
0
2
0
1
0
2
1
1
0
0
1
1
1
1
2
1
1
2
0
1
2
0
1
0
0
2
0
0
1
2
1
1
2
1
0
1
0
0
0
0
0
1
1
1
1
0
0
2
1
1
1
2
1
1
0
1
1
2
2
2
1
1
1
2
2
1
0
0
1
0
1
0
1
0
1
0
0
0
1
2
0
0
2
0
2
0
0
3
0
1
0
1
0
1
1
2
0
1
0
0
2
2
1
0
1
2
0
0
2
1
2
1
1
2
1
0
0
0
1
0
0
1
3
0
2
1
2
0
0
0
1
0
1
1
0
0
0
0
2
0
1
0
0
0
1
2
2
1
1
1
1
1
0
1
0
0
2
0
0
0
0
1
1
0
2
2
0
1
0
2
0
2
0
1
0
1
0
0
0
2
0
0
1
0
1
1
2
2
0
0
1
1
1
0
3
1
0
0
1
2
1
1
2
1
0
0
1
1
3
1
0
2
0
1
1
0
1
0
1
2
0
2
2
1
0
1
1
2
1
1
1
5
0
0
0
1
2
2
0
3
2
0
0
0
0
1
2
1
0
0
0
0
1
2
2
2
1
1
1
2
0
0
13
1
0
1
0
0
2
1
0
0
0
0
1
1
1
0
0
1
0
0
0
2
0
0
1
2
0
0
0
2
1
0
0
2
1
1
1
0
0
4
3
1
2
0
1
1
1
0
0
0
3
1
1
2
2
2
2
3
0
1
2
2
0
2
0
1
0
1
1
0
1
1
1
1
1
1
1
1
0
2
0
0
0
0
0
2
0
0
1
1
1
1
0
1
0
0
2
0
1
2
0
2
0
0
0
0
3
1
0
1
0
0
2
1
0
1
1
2
1
2
0
1
1
1
1
0
0
0
1
0
1
0
0
1
1
1
0
1
0
1
0
0
2
0
2
0
0
1
1
2
2
0
0
1
2
0
0
0
0
2
2
0
0
1
2
2
2
0
2
1
1
1
0
1
0
1
0
3
2
0
1
3
0
0
2
1
0
2
2
1
2
0
1
0
2
1
0
1
2
3
1
0
0
2
1
1
1
2
2
1
1
2
2
1
0
1
0
0
2
1
2
2
2
1
0
2
1
1
0
0
0
2
1
1
0
0
2
2
0
0
0
1
1
2
0
1
1
0
2
0
1
0
0
1
0
0
2
0
2
0
2
1
0
2
0
1
1
0
2
2
0
1
0
1
2
0
1
2
0
0
0
1
0
1
0
2
2
0
1
0
2
1
1
0
2
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
2
0
2
0
0
1
0
2
0
2
2
0
2
0
0
2
0
0
1
0
0
1
3
2
2
0
0
0
0
0
0
0
1
0
2
0
2
0
2
1
1
1
1
0
1
2
0
2
1
1
1
0
0
0
1
2
0
1
2
0
0
0
0
0
1
0
2
2
0
0
2
1
0
0
0
1
0
1
2
0
0
1
2
1
2
1
0
1
0
1
1
0
0
0
1
1
2
0
1
1
0
0
1
1
0
0
0
2
0
1
0
2
1
0
0
1
0
0
0
0
2
0
1
1
3
0
1
2
2
0
1
2
0
2
1
0
2
1
1
0
1
0
0
0
1
0
1
0
2
2
1
0
1
2
0
0
2
0
2
1
1
1
0
1
0
1
2
2
2
1
1
0
1
0
2
0
0
1
1
0
0
0
0
0
3
0
0
0
0
1
2
0
0
1
1
1
1
0
1
0
0
0
1
2
2
2
1
1
1
1
0
0
1
0
1
1
2
1
0
0
2
1
2
3
2
0
0
2
1
0
3
1
2
1
0
1
0
1
0
2
2
1
1
1
1
0
0
3
0
0
0
0
1
0
0
0
1
1
2
0
2
0
1
2
0
0
0
0
0
0
0
0
1
2
2
0
1
0
1
1
2
2
0
1
0
0
0
1
1
0
1
0
0
0
1
2
0
0
2
0
1
0
2
0
2
1
0
0
0
0
0
0
2
0
2
1
0
0
1
1
2
0
0
0
1
1
0
1
0
2
0
0
0
0
1
1
1
0
2
2
1
1
0
0
2
0
1
0
3
1
0
0
2
2
0
2
1
1
0
0
2
1
0
1
1
1
2
1
0
2
0
2
0
1
1
2
1
0
0
0
0
3
1
0
1
0
0
0
0
1
0
1
0
0
2
1
2
0
0
0
1
1
0
0
0
2
0
0
1
0
0
2
0
1
1
0
1
0
0
1
1
1
0
0
1
0
1
1
1
0
0
1
2
2
2
1
1
1
1
2
1
0
1
0
0
1
1
1
1
2
3
0
2
1
0
0
2
1
1
0
0
0
1
0
0
1
1
0
2
0
1
0
1
1
1
2
1
0
0
0
1
1
1
2
1
1
0
0
1
1
1
1
0
0
3
2
2
5
1
2
2
2
1
0
1
0
0
0
1
0
0
0
2
1
1
1
2
1
2
1
2
0
1
0
1
0
0
1
1
1
1
2
1
2
1
2
1
0
1
1
0
1
0
2
1
1
1
1
0
1
1
0
0
1
0
1
1
0
0
2
1
0
0
1
1
1
1
0
0
0
1
1
1
0
2
0
0
0
0
0
1
0
2
1
2
1
0
2
2
0
1
1
0
0
0
0
1
2
2
2
0
1
0
0
0
1
0
0
1
1
0
1
1
0
1
0
0
0
0
0
0
0
2
0
1
2
1
1
1
1
2
0
2
1
2
1
2
0
1
0
1
1
2
0
1
0
2
1
1
2
0
1
0
0
1
1
0
0
0
1
0
0
0
2
0
2
2
0
2
1
1
1
0
3
0
1
2
0
1
0
1
0
1
0
1
2
1
2
1
2
0
1
2
2
0
0
1
1
1
2
2
1
1
1
0
2
2
1
0
2
0
1
0
1
1
1
0
0
0
0
0
2
0
2
2
1
1
1
0
0
1
1
1
0
0
1
2
1
0
1
2
1
1
2
2
1
1
0
2
1
0
0
1
0
2
1
1
0
1
2
0
0
2
0
2
1
0
1
0
0
0
1
1
2
1
1
0
1
2
1
2
1
0
1
0
2
1
1
0
0
2
1
1
1
0
0
2
0
1
2
1
1
0
2
0
2
0
1
2
1
1
2
2
1
2
2
0
1
1
0
1
1
0
1
1
1
2
0
0
0
0
1
0
0
2
2
2
1
0
2
2
0
0
0
1
0
1
0
1
0
2
2
2
1
1
0
0
0
0
1
1
0
2
0
0
0
2
2
0
1
0
0
2
1
0
0
0
0
1
1
1
2
0
2
1
3
2
0
0
0
1
0
1
1
0
1
2
1
1
0
0
0
0
1
2
0
0
0
0
1
0
0
2
2
1
0
2
0
2
1
0
1
1
2
0
1
0
1
1
1
1
2
0
1
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
2
1
0
1
1
0
0
1
1
1
0
0
2
0
0
1
0
0
0
0
0
0
1
3
0
2
0
1
0
0
0
0
1
0
1
0
1
2
2
0
1
2
0
2
0
1
1
2
1
1
1
3
1
0
0
1
0
0
2
0
1
0
0
1
0
0
1
2
0
1
0
0
1
1
0
1
0
0
1
0
0
1
0
2
2
1
1
0
0
2
0
2
0
1
1
0
0
1
0
0
0
0
0
1
0
1
0
2
0
0
1
1
0
0
2
0
0
1
1
1
2
1
0
2
1
0
1
1
2
0
0
0
1
1
0
1
0
0
2
2
0
2
2
2
1
1
0
0
0
0
1
2
0
0
0
0
1
0
0
0
1
2
0
1
2
0
0
1
0
0
0
1
0
2
2
0
0
1
0
1
0
1
0
2
0
0
1
0
0
2
2
0
1
1
0
1
0
1
1
2
0
0
2
0
0
1
0
1
0
1
1
0
0
1
1
1
0
2
1
2
2
0
3
2
1
1
2
0
1
0
0
2
0
1
0
2
1
2
2
0
0
0
1
1
1
0
0
1
0
2
0
2
2
1
1
1
1
0
0
1
0
0
1
1
1
0
0
2
2
0
2
1
2
0
2
2
2
1
2
0
0
0
0
1
0
0
1
1
0
1
1
0
0
0
0
2
0
1
0
0
0
2
0
0
0
2
0
0
0
3
0
2
1
1
2
1
0
3
0
2
3
1
1
0
0
1
0
0
2
0
0
0
2
2
2
1
2
0
2
0
1
1
1
2
0
0
2
1
1
0
0
1
3
1
0
1
0
0
1
1
1
0
0
1
0
1
2
1
0
1
1
2
0
1
1
2
1
1
0
0
0
0
0
2
0
1
0
0
1
1
1
0
2
1
0
0
1
0
1
3
0
0
0
2
0
2
2
1
0
2
2
1
1
1
0
1
0
2
1
0
0
2
0
1
1
1
2
1
0
1
1
2
0
1
1
0
0
0
1
2
2
2
0
1
2
3
0
1
0
0
2
1
0
2
1
1
0
0
1
0
2
1
2
2
1
1
1
0
0
1
0
1
0
2
0
0
1
1
1
1
0
0
0
1
1
1
2
1
0
2
3
1
0
2
1
0
1
1
2
0
0
2
1
1
1
1
1
1
0
1
3
0
0
2
0
2
1
1
2
0
2
0
2
1
0
0
1
1
0
1
1
0
1
0
0
0
2
0
1
1
0
0
0
2
2
0
1
0
0
0
2
1
2
0
1
0
1
0
1
1
0
2
1
0
1
0
1
0
0
2
0
0
1
0
0
1
0
0
2
2
1
2
2
1
2
1
0
2
0
2
0
2
1
1
1
1
2
1
0
0
2
1
1
1
1
1
1
0
0
2
1
1
0
2
0
1
0
2
1
1
0
1
1
0
2
0
0
0
2
0
0
1
0
1
3
1
0
0
1
1
1
0
0
1
1
2
0
1
1
2
0
0
1
1
1
0
0
1
2
1
0
0
0
0
0
2
0
1
1
1
2
1
1
1
0
2
0
2
0
1
1
1
0
0
0
0
0
0
1
2
1
1
1
2
0
2
0
0
0
0
0
1
1
0
0
2
1
1
1
1
2
2
3
1
0
1
1
1
0
0
1
2
1
2
2
2
0
1
1
1
1
0
0
2
2
0
0
2
1
1
2
0
0
1
1
1
0
3
2
0
1
2
2
0
1
0
2
2
0
2
2
1
1
2
0
0
0
0
0
0
1
2
1
1
1
0
1
2
0
1
1
1
2
0
2
1
1
1
2
0
0
0
2
1
0
2
1
1
0
0
1
2
0
0
1
0
2
0
1
0
1
0
0
1
0
0
0
0
0
2
0
1
2
0
1
1
0
1
1
1
1
0
0
2
2
0
0
2
1
0
0
0
1
0
1
2
1
2
2
1
0
0
1
2
2
0
2
2
2
1
1
0
4
0
0
2
0
0
0
1
1
0
2
2
0
1
1
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
2
1
2
0
0
2
0
1
2
0
0
0
0
0
1
1
0
0
1
1
1
2
1
0
0
0
1
0
1
1
3
0
0
0
0
1
1
1
0
2
0
0
1
1
1
0
0
2
0
0
0
1
2
1
1
1
2
1
1
1
0
1
1
0
0
2
2
0
1
0
2
0
2
1
2
0
1
2
1
2
1
1
3
0
0
0
1
0
2
1
1
0
1
1
0
2
0
1
2
1
3
2
2
1
1
1
1
1
1
0
0
1
2
2
0
1
0
1
1
0
1
0
0
1
0
1
0
0
0
0
1
2
2
1
1
1
0
1
2
0
1
0
1
0
0
0
0
2
2
0
0
0
1
0
2
0
1
1
0
1
1
0
1
2
1
0
0
1
0
1
1
0
2
0
1
1
1
2
0
0
1
2
2
0
0
1
1
1
1
0
0
0
0
1
2
0
2
1
0
0
1
1
0
0
0
1
0
1
1
0
1
0
0
0
1
0
1
0
1
1
0
2
0
2
1
0
1
0
0
0
0
0
1
1
2
2
0
3
2
1
0
0
1
1
1
1
2
1
2
0
2
1
1
2
1
0
1
1
1
0
1
0
0
1
1
2
2
0
1
0
0
1
1
1
0
0
0
1
1
2
1
1
0
2
1
2
1
0
1
0
0
1
1
1
2
1
0
0
1
0
0
1
1
0
1
0
0
1
0
1
1
0
1
0
1
2
1
0
2
0
1
1
1
2
1
1
0
0
1
0
1
1
0
0
1
0
1
0
0
1
0
1
1
0
0
0
0
2
0
0
1
0
0
2
0
0
1
0
1
0
0
1
1
0
1
2
1
2
0
0
0
0
2
0
1
1
0
1
0
1
1
0
2
2
2
1
1
0
2
2
2
1
1
1
0
2
0
1
2
2
2
0
0
0
0
1
1
2
2
1
1
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
2
1
0
1
1
2
0
0
1
0
1
2
1
1
2
0
1
1
1
0
1
0
0
1
2
1
1
0
2
1
1
1
0
1
0
0
0
2
2
2
1
2
1
1
0
0
0
0
1
1
0
0
0
0
0
0
1
2
2
0
0
1
1
1
1
3
2
2
0
2
1
0
2
1
2
2
0
0
1
2
0
0
0
0
2
0
1
0
1
0
2
2
1
1
0
0
0
0
1
0
1
1
1
0
0
0
1
2
1
0
0
1
0
0
2
0
1
0
2
3
0
0
1
2
0
0
2
1
2
2
1
0
1
2
0
1
0
0
1
0
2
0
0
2
0
1
0
0
0
1
0
0
1
0
2
2
0
0
1
2
1
1
1
0
2
1
1
0
1
0
1
1
2
2
0
0
1
1
1
1
0
2
1
1
1
1
0
0
0
0
2
1
2
1
1
0
0
0
2
3
2
0
0
2
2
0
1
0
2
1
0
0
0
0
1
0
1
2
0
1
1
2
0
2
0
1
1
1
0
0
1
0
1
0
0
2
1
0
0
1
2
0
1
0
0
1
2
6
0
2
0
0
1
1
2
2
0
0
1
0
1
1
1
0
1
2
0
1
0
0
0
1
0
1
2
0
2
2
2
0
0
0
1
0
0
1
1
1
1
0
3
1
1
1
0
1
2
0
1
0
0
0
2
0
1
1
2
0
0
0
1
0
0
0
2
2
1
1
0
1
1
0
2
0
0
0
1
1
2
0
0
0
1
2
1
0
1
1
2
2
0
1
1
1
1
1
2
1
1
2
0
0
1
1
1
0
0
0
3
0
0
1
1
1
0
2
0
1
1
0
1
0
1
1
1
0
1
0
0
0
0
2
2
0
0
0
0
1
1
0
0
1
0
1
0
1
1
0
2
0
1
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
2
0
0
0
1
0
1
2
1
0
1
1
0
0
2
3
1
1
2
1
1
2
2
1
0
2
1
1
0
1
0
2
0
0
0
0
1
1
0
1
2
0
0
0
0
0
0
0
2
2
0
0
0
2
1
0
0
0
0
2
1
1
0
0
1
0
0
1
1
0
2
1
1
0
1
2
0
0
2
0
1
2
1
2
0
0
0
2
0
2
1
1
1
0
2
0
2
0
0
2
1
1
0
0
1
1
0
1
1
2
1
0
0
0
0
2
0
2
1
2
1
0
0
1
0
1
0
0
2
1
1
0
0
2
0
2
3
2
0
1
0
1
2
1
1
1
1
2
1
2
0
0
2
1
0
0
1
1
1
2
0
1
2
1
2
1
1
0
2
2
1
2
0
1
2
1
1
1
2
1
0
1
0
0
1
0
1
1
1
1
0
0
0
2
2
1
1
1
0
2
0
1
0
2
1
1
1
1
1
0
0
1
1
1
1
2
1
1
0
0
0
2
1
1
0
2
0
1
2
0
1
1
2
1
0
0
0
2
2
1
1
1
1
1
0
2
1
3
0
2
0
1
1
0
0
0
0
2
1
1
2
1
2
2
2
2
0
0
1
1
2
1
1
2
2
1
0
0
0
0
1
1
0
0
2
2
0
0
2
2
0
0
1
4
1
2
2
0
2
1
2
0
1
2
0
0
1
1
3
2
0
1
1
2
1
0
2
2
0
0
2
1
1
0
2
0
2
0
1
1
1
0
1
4
0
0
1
0
0
0
0
0
1
2
0
2
1
1
0
0
0
1
1
0
0
0
1
0
0
1
1
0
2
0
2
2
0
1
0
0
1
0
2
0
1
1
0
1
0
1
0
0
0
1
0
0
2
0
1
0
2
1
0
2
0
1
1
0
0
0
0
2
0
2
1
0
1
1
2
0
0
1
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
1
0
2
2
0
0
1
1
0
0
0
0
2
1
2
0
1
1
1
0
0
1
1
1
1
2
1
1
1
0
0
1
1
0
3
3
1
1
1
0
1
1
1
2
1
2
2
1
0
1
0
1
0
0
0
0
1
0
0
2
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
1
3
2
1
0
0
0
0
2
0
0
2
2
1
2
1
1
2
1
0
0
0
0
1
1
0
0
1
2
0
1
1
1
0
0
1
0
0
0
0
0
0
1
0
0
2
1
1
0
1
0
2
0
0
0
2
0
0
0
0
1
0
0
1
1
0
0
1
1
1
0
0
1
1
2
1
2
0
0
2
1
0
2
1
1
0
1
2
0
2
2
1
0
0
3
1
1
0
1
1
1
0
2
1
1
1
1
1
2
0
1
1
0
1
2
0
1
0
2
0
1
1
0
0
0
2
0
0
2
1
1
0
2
1
0
2
0
0
1
1
1
0
1
0
1
1
1
2
0
1
0
1
0
2
0
0
1
0
2
0
1
0
1
1
1
0
1
1
1
2
0
0
2
0
3
0
1
1
0
0
0
0
0
1
2
2
2
0
2
2
2
1
0
1
1
1
1
0
0
0
0
2
1
1
0
0
0
0
1
2
0
4
0
0
1
2
1
0
0
1
2
2
0
1
1
1
2
3
0
1
0
0
1
2
1
0
0
0
1
2
0
0
0
2
1
0
1
2
0
0
1
0
1
2
0
2
0
1
1
2
1
2
1
0
0
1
1
0
2
0
2
0
2
2
0
1
1
2
2
2
2
1
1
0
0
1
0
1
1
0
1
0
0
2
0
0
1
0
0
1
1
0
1
2
2
2
1
2
2
2
1
0
0
0
0
1
1
0
1
1
2
2
0
1
2
1
2
1
0
0
3
2
0
1
0
0
1
1
0
1
1
1
2
2
0
1
1
0
2
1
2
0
0
3
0
1
0
0
0
1
0
1
0
1
1
2
0
2
0
0
0
1
0
1
0
1
1
2
0
1
2
1
0
0
0
0
1
0
1
1
0
0
2
1
1
2
0
0
2
1
1
0
1
0
0
1
2
0
0
1
0
1
1
0
0
1
1
1
3
0
3
1
1
0
1
2
1
0
0
1
1
1
0
0
1
0
1
0
1
4
1
0
0
2
0
1
4
1
1
2
0
0
2
2
2
0
2
2
1
2
1
1
0
2
0
0
2
0
1
0
0
2
1
0
1
1
0
0
1
0
1
0
0
2
1
1
1
1
0
1
0
0
2
3
0
2
0
1
0
0
2
0
2
0
2
0
1
1
0
1
1
0
0
0
0
2
0
1
1
0
0
0
1
0
2
1
0
0
0
1
0
2
0
0
1
1
2
0
2
0
2
0
2
1
0
2
1
0
0
1
1
0
1
0
0
0
0
2
0
0
0
1
2
0
0
1
0
1
1
0
0
0
1
1
2
0
3
0
2
2
0
1
0
1
0
0
1
0
0
2
2
1
1
0
0
0
0
1
0
2
0
1
0
2
0
1
2
3
1
2
2
1
1
2
1
8
2
0
0
0
0
0
1
0
2
1
2
1
2
0
1
3
1
0
0
1
2
1
2
0
1
0
1
0
0
0
0
2
1
0
2
0
0
0
0
0
2
2
0
1
2
0
2
0
0
0
1
2
0
0
0
1
0
0
2
1
0
1
0
1
1
2
1
0
1
0
1
1
1
0
2
2
1
2
1
0
1
0
1
0
2
2
0
0
0
0
1
1
2
1
2
0
2
1
0
1
0
1
1
2
0
1
0
0
2
0
0
0
0
0
1
0
1
1
0
2
1
0
0
1
0
0
5
2
1
0
0
2
0
1
1
0
0
1
2
1
2
1
0
1
1
0
0
0
1
0
0
2
0
1
2
0
0
1
1
2
0
0
1
0
0
0
2
1
0
3
0
1
0
0
1
1
0
0
1
1
2
2
2
1
1
0
0
0
0
1
2
2
1
1
2
0
1
2
2
2
0
2
1
0
0
1
1
2
0
1
1
0
0
0
2
2
0
0
0
1
1
1
2
0
1
0
2
0
2
0
1
1
2
0
1
0
2
0
2
1
2
1
2
1
1
0
0
0
1
3
1
1
0
1
1
0
1
1
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
1
0
0
1
2
0
1
1
2
2
1
2
0
0
1
1
2
1
2
1
0
2
1
0
0
1
0
0
0
2
0
1
1
3
1
2
1
0
0
0
1
0
1
0
1
1
0
0
2
1
1
2
1
0
1
1
0
1
0
0
0
0
0
1
0
2
0
2
3
0
0
0
0
2
1
1
0
0
0
2
0
0
1
0
0
1
1
0
2
0
1
1
0
1
2
1
0
1
2
2
2
1
0
1
0
2
0
0
2
0
0
1
2
1
0
0
0
0
1
0
0
0
0
2
1
1
0
1
2
2
2
0
0
1
0
1
0
0
0
0
0
0
1
2
0
0
1
1
1
2
1
0
0
0
2
0
1
2
2
2
2
0
0
0
2
0
4
2
0
2
1
1
2
1
0
0
1
1
0
2
0
0
0
0
1
1
0
1
2
2
2
0
2
0
1
1
2
1
2
0
1
0
3
2
0
2
2
1
0
2
0
0
1
0
1
2
3
0
2
0
0
1
1
1
1
1
0
2
0
1
1
1
1
0
2
2
0
0
0
2
1
2
2
1
0
0
0
0
0
2
1
0
0
5
0
1
0
0
1
1
2
1
0
2
1
1
0
2
0
1
2
1
2
0
0
1
1
2
2
0
0
1
1
0
0
1
1
0
0
1
1
0
1
0
1
2
1
0
0
0
1
0
0
2
0
1
0
1
2
1
1
0
1
1
0
1
0
0
1
1
1
0
2
1
0
1
0
1
2
0
0
1
2
2
0
1
2
0
1
0
1
0
1
1
0
0
2
1
0
0
1
2
2
0
0
0
0
0
1
0
0
0
1
0
0
1
1
3
0
0
1
2
0
1
0
0
1
1
1
2
2
0
1
1
1
1
0
1
0
0
3
0
0
1
0
1
1
1
2
0
1
0
1
0
1
2
1
1
0
0
0
0
0
0
1
3
0
0
1
0
0
1
1
2
2
0
1
1
1
0
1
1
2
0
1
0
2
0
1
0
0
1
2
2
2
0
1
2
2
1
2
1
0
0
0
1
1
1
0
0
2
2
2
1
0
1
1
1
0
1
2
0
2
0
1
0
2
0
2
2
0
0
1
0
2
1
1
0
1
0
1
0
1
2
2
1
2
0
1
1
0
0
0
2
0
1
2
0
1
1
1
0
2
0
1
2
0
2
0
2
1
0
0
2
2
1
0
1
0
1
1
0
0
0
1
0
1
1
0
1
0
0
2
0
2
0
1
0
1
2
2
0
0
1
1
0
1
1
1
0
0
1
0
0
0
1
0
1
0
1
1
2
0
0
0
2
0
1
0
1
1
1
1
2
1
0
0
2
0
0
2
1
0
0
1
1
0
0
1
0
0
1
0
0
1
2
1
0
0
0
3
0
1
1
0
2
1
2
1
0
0
0
1
1
0
2
1
0
1
2
1
1
0
0
2
0
0
1
2
1
0
1
1
0
0
1
0
2
2
0
0
0
0
0
1
2
0
1
0
2
2
1
0
2
2
1
1
0
0
0
3
0
2
1
1
6
0
2
0
0
0
2
1
0
1
0
0
1
0
1
0
1
2
2
1
0
0
1
0
1
1
2
2
2
1
2
1
2
1
0
0
1
1
2
0
1
0
1
0
0
2
2
0
0
1
1
0
0
1
0
1
0
0
0
2
1
0
0
1
2
10
1
2
2
1
0
0
0
1
2
1
2
1
1
1
1
3
0
1
2
1
2
1
0
1
0
1
0
0
0
0
0
6
3
1
0
0
1
1
2
2
0
0
0
2
0
0
0
0
2
2
1
1
0
2
0
1
0
1
0
1
0
0
0
1
1
0
2
0
1
1
1
1
2
1
2
0
2
0
1
2
2
0
2
1
0
1
1
1
1
0
1
2
0
0
0
1
2
2
1
0
0
1
0
0
0
0
1
1
1
0
1
2
0
0
1
1
2
1
0
0
1
0
1
10
1
2
0
2
0
0
1
0
1
1
0
2
1
1
2
1
2
0
2
2
1
1
0
2
1
1
1
2
1
0
1
1
1
2
2
1
1
2
2
0
1
1
0
1
2
1
1
0
0
2
1
0
1
0
0
0
0
1
1
0
1
0
0
0
1
0
1
1
0
2
2
0
1
1
1
2
1
1
1
2
1
2
2
1
0
0
1
2
1
1
0
1
1
1
2
1
0
0
0
1
1
1
0
1
0
1
0
0
2
1
2
0
2
2
1
0
0
0
1
0
1
2
2
0
1
0
0
1
2
0
1
0
0
1
0
2
1
0
2
0
0
2
2
1
1
0
1
2
1
2
2
2
0
2
1
1
1
1
0
1
0
0
0
0
1
1
1
1
2
0
1
1
0
0
1
1
1
0
0
0
0
1
1
0
0
2
0
1
0
1
0
0
1
1
0
0
1
0
0
0
2
2
0
0
1
0
0
0
2
0
1
1
1
2
1
1
0
0
0
2
0
0
2
1
1
0
2
1
1
1
0
1
0
2
0
1
0
1
0
0
1
0
0
0
2
0
1
1
0
1
1
0
0
1
1
2
0
0
2
0
1
0
1
0
2
2
2
0
1
0
0
0
1
0
3
0
0
1
0
1
0
3
2
1
1
1
0
0
0
2
1
0
1
1
1
0
2
0
1
1
2
0
0
0
1
2
1
1
0
1
2
0
2
0
0
1
0
1
0
0
1
1
0
0
0
2
0
2
2
4
0
1
0
1
2
0
1
1
0
0
1
1
1
0
2
1
0
0
2
0
1
2
0
0
1
1
0
1
2
1
0
1
0
0
0
1
0
0
2
1
0
1
0
0
1
1
1
1
0
0
0
2
0
2
1
0
1
0
0
0
0
2
1
2
2
2
1
2
2
3
1
0
1
0
2
2
1
0
1
2
1
0
1
0
2
0
1
1
1
0
2
0
1
1
0
1
2
1
1
0
2
1
0
0
2
0
2
1
1
0
1
1
1
0
0
1
1
0
2
1
3
1
1
0
0
0
0
1
0
1
2
3
1
1
0
1
1
1
0
1
0
1
1
0
2
1
0
1
1
2
1
0
0
1
0
1
0
0
1
0
1
1
0
1
1
2
1
1
1
0
0
0
1
1
2
1
1
2
1
0
0
1
2
0
0
0
1
1
0
1
0
1
1
2
2
2
0
0
0
0
1
0
1
2
0
0
2
2
1
1
0
0
2
0
1
1
0
1
0
1
0
2
1
1
0
1
1
0
0
2
0
2
2
2
1
0
0
2
0
0
1
2
0
2
3
1
1
1
0
2
2
0
0
0
0
1
0
0
1
0
1
0
1
1
1
0
0
0
1
0
1
1
2
4
1
0
1
2
1
0
0
1
2
1
1
0
0
2
0
2
2
1
2
1
0
0
2
0
1
0
0
2
1
0
1
0
0
0
4
2
1
1
0
1
1
2
0
0
2
0
1
1
1
2
0
0
1
0
1
1
0
1
0
1
1
1
1
0
2
0
1
0
1
1
0
3
0
1
0
2
1
0
0
2
0
0
1
1
1
1
0
0
1
2
1
2
0
0
0
2
0
2
1
3
1
2
0
0
2
0
1
0
0
0
0
3
1
0
0
1
1
0
0
2
0
1
0
0
1
2
1
0
0
1
2
0
1
0
0
0
1
1
0
2
0
3
1
1
1
0
0
1
0
1
1
0
0
1
1
2
1
2
1
0
1
0
0
2
2
0
2
0
0
0
1
2
2
0
0
0
2
1
0
2
2
1
0
0
1
0
0
1
0
0
1
1
1
3
2
0
0
0
3
2
0
1
0
1
1
0
1
0
0
0
0
2
2
1
1
0
2
1
0
1
1
2
1
1
2
2
0
2
1
1
0
0
1
0
0
2
0
1
0
1
2
2
1
1
2
1
0
1
0
1
0
1
1
0
1
1
0
0
3
0
1
0
0
0
0
0
0
1
2
2
0
1
1
1
0
0
0
1
0
0
0
2
3
1
0
1
1
1
0
0
0
1
1
0
1
0
2
0
2
0
2
0
2
1
0
1
1
2
1
1
0
2
2
1
1
0
1
1
0
1
0
2
0
1
0
0
1
0
3
0
0
2
0
0
0
0
0
0
1
0
2
0
1
0
0
0
1
3
1
0
0
0
2
0
1
0
1
0
0
2
0
1
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
3
1
1
1
0
0
0
0
0
2
1
2
1
1
2
1
1
0
2
1
2
2
1
1
0
1
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
2
1
1
2
2
1
0
0
0
0
1
0
1
0
1
0
2
0
2
0
0
1
1
1
1
1
0
0
0
1
1
0
3
1
1
1
2
2
1
0
4
2
1
0
0
1
0
2
2
1
0
0
0
0
2
1
0
0
1
0
0
0
1
1
0
1
0
1
0
1
0
1
0
2
0
1
2
1
1
1
2
1
2
0
0
1
0
2
2
1
0
1
1
1
1
0
0
1
2
2
0
1
0
2
0
2
1
1
0
1
1
2
2
1
0
0
2
0
2
0
0
0
0
2
2
2
0
1
2
2
0
1
1
2
0
1
2
2
2
1
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
2
0
0
1
1
0
0
0
1
2
2
2
0
2
1
2
0
0
0
0
0
0
1
3
2
2
3
1
0
1
2
0
1
1
1
1
2
1
1
1
0
0
2
1
1
1
1
0
1
0
2
2
0
1
0
0
0
0
1
1
0
1
0
1
1
1
1
0
1
1
0
0
2
2
0
0
1
0
0
1
2
2
0
0
0
0
0
0
0
2
1
1
0
0
2
0
0
0
0
1
0
1
0
0
2
0
2
0
2
2
2
0
1
2
0
1
0
2
0
2
0
0
2
0
1
0
1
1
1
0
1
2
1
0
1
1
1
1
1
0
0
0
1
1
0
1
2
0
2
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
2
1
0
0
1
3
0
2
2
1
0
2
2
0
0
2
2
2
2
2
1
0
0
1
1
1
2
0
1
1
0
0
0
1
0
1
1
2
1
1
2
2
1
2
1
0
0
1
0
0
0
2
0
3
2
2
1
2
0
0
0
1
0
0
1
2
0
1
0
0
2
1
0
1
1
1
1
0
1
1
0
0
0
2
0
0
3
1
0
0
0
1
2
1
2
2
2
1
2
0
0
0
2
1
0
1
0
1
1
2
2
0
0
2
4
2
1
0
1
1
0
1
1
0
0
2
0
2
2
1
1
0
0
0
2
0
2
1
0
1
1
1
2
2
2
0
2
0
1
0
0
1
1
2
1
2
1
0
0
0
0
1
0
0
0
1
1
1
0
2
1
1
0
0
0
1
0
2
0
2
2
0
2
0
0
0
0
2
2
2
2
2
2
2
0
0
0
2
0
0
1
2
1
2
1
0
2
2
0
2
2
0
1
0
1
0
0
0
2
0
2
1
0
1
1
1
2
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
1
2
0
2
1
0
1
2
0
1
1
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
1
2
0
4
1
0
0
1
1
2
0
0
0
0
1
1
0
0
1
1
0
0
2
0
0
0
0
2
2
0
0
0
0
1
0
1
0
1
1
1
1
0
1
0
1
1
1
0
1
1
2
1
0
0
2
1
2
0
0
0
1
1
0
0
1
1
1
1
1
0
1
0
0
0
2
1
0
0
0
0
0
1
1
1
1
1
0
1
0
0
1
0
1
1
1
1
0
1
2
0
0
0
1
0
1
1
0
3
0
1
0
2
2
0
1
1
2
2
0
2
1
0
2
1
2
0
2
1
3
0
2
0
0
0
0
0
2
0
2
0
2
2
0
0
1
0
1
1
0
1
2
0
0
0
1
0
0
2
1
1
1
1
0
2
0
2
1
1
0
0
1
0
0
2
2
2
0
0
1
0
1
1
1
1
1
1
1
2
2
1
1
0
0
1
1
1
1
0
0
1
2
0
1
0
0
1
1
0
0
0
2
1
1
1
0
1
3
3
2
1
1
0
1
0
3
1
1
1
2
0
1
1
1
2
2
0
0
0
4
3
2
1
2
0
1
0
0
1
1
0
1
2
0
0
2
1
0
2
0
2
0
2
0
1
2
2
1
0
0
0
8
0
2
0
2
3
0
1
0
0
0
2
0
2
0
1
0
0
2
1
0
0
2
1
2
1
1
0
0
0
2
2
1
1
1
1
2
1
0
0
1
0
1
2
1
2
1
1
1
0
1
1
1
0
1
1
2
0
1
0
0
0
1
0
1
3
1
1
0
1
1
2
2
1
0
0
0
0
1
0
2
1
3
2
1
1
2
1
0
0
1
0
2
0
1
1
0
0
2
2
1
0
0
2
1
2
0
0
1
1
1
0
1
0
2
0
0
0
2
0
0
2
1
2
0
0
1
0
0
1
0
2
0
2
1
2
2
0
0
0
0
0
0
2
0
2
1
6
0
0
0
1
0
2
1
0
0
1
0
2
0
0
0
2
0
1
2
2
1
1
2
0
1
2
3
0
1
1
1
1
0
0
2
0
0
0
3
0
2
1
1
0
2
0
2
0
0
0
2
3
0
0
0
0
1
0
0
0
1
0
1
1
2
0
1
1
0
0
2
0
2
1
1
1
0
0
0
1
0
1
0
2
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
1
0
2
0
1
2
1
1
0
1
2
0
0
0
0
3
0
0
0
1
2
1
0
0
0
1
2
0
0
3
1
0
0
0
0
0
1
2
0
1
1
0
0
0
0
0
1
1
2
2
0
2
1
0
2
0
1
1
1
0
2
0
1
0
0
0
1
0
2
2
0
0
0
1
0
2
0
2
0
1
0
1
0
0
2
1
1
0
0
2
0
1
2
1
2
0
1
0
0
0
0
0
2
0
4
0
1
1
0
0
0
0
2
2
0
1
1
1
0
1
2
2
0
1
0
1
2
0
0
0
1
0
2
1
2
1
0
1
2
1
2
2
2
2
1
1
0
0
0
1
2
1
1
2
0
0
1
1
2
0
0
1
1
2
0
1
2
1
0
2
0
1
0
1
0
0
1
1
0
0
1
1
2
1
2
0
1
0
1
2
1
2
2
1
0
0
2
0
0
0
0
0
1
0
2
0
0
1
0
0
1
0
1
2
0
1
3
1
3
2
0
0
1
2
0
0
0
0
1
1
0
0
1
2
3
0
1
1
2
0
1
1
0
0
2
2
1
1
1
1
1
0
3
1
0
1
0
0
0
2
1
1
1
0
1
2
0
0
1
0
0
4
2
0
0
1
0
0
2
2
2
2
2
1
0
2
0
0
2
0
1
0
0
2
0
2
1
0
1
2
2
0
1
1
0
1
0
0
1
2
1
2
2
1
2
0
1
2
2
0
1
0
2
1
2
1
0
1
2
2
0
1
0
0
1
1
0
0
0
2
2
2
0
0
0
1
2
0
1
0
1
2
0
1
0
0
0
2
0
2
1
0
1
2
2
2
0
0
0
0
1
0
0
0
0
1
0
0
1
1
2
2
0
1
2
0
1
1
0
1
0
1
1
3
2
0
0
1
0
2
0
0
1
2
0
1
2
0
1
0
1
1
0
0
2
1
0
0
0
1
0
0
2
0
2
0
0
0
0
1
1
0
0
0
0
1
3
1
1
1
1
1
0
2
1
1
2
0
2
0
1
2
0
0
0
3
0
0
1
2
1
1
2
1
2
0
1
1
0
0
1
1
1
0
0
2
0
2
0
2
2
2
0
0
0
1
0
0
1
0
1
1
2
0
1
2
0
2
2
2
1
2
2
0
0
1
0
0
2
0
0
0
0
0
0
1
4
2
1
2
0
0
2
0
1
0
0
1
0
1
0
0
1
2
0
1
1
0
2
0
0
1
0
1
2
1
0
1
0
0
1
0
1
0
1
1
0
1
0
2
0
0
1
0
0
2
0
0
2
1
1
0
2
3
2
0
0
0
1
0
2
2
0
0
2
0
2
1
1
1
0
2
2
0
2
0
1
0
1
2
0
2
0
1
2
1
2
1
1
0
0
0
0
0
0
0
0
3
1
0
2
1
2
3
0
1
1
0
0
0
0
2
0
2
1
0
1
1
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
2
1
0
1
1
2
1
0
3
2
0
1
0
0
0
1
1
0
0
1
0
0
1
2
2
1
0
0
2
1
1
0
0
3
0
1
1
0
1
0
0
2
2
1
2
1
1
1
0
2
1
2
1
2
2
2
0
1
1
0
1
0
1
0
0
1
0
0
2
1
0
2
0
2
0
2
0
2
1
2
0
0
1
0
1
0
2
1
2
2
1
0
1
1
2
2
1
1
0
1
0
1
1
1
0
0
1
0
1
1
0
0
2
1
1
1
1
1
0
1
2
0
1
1
1
0
1
0
1
1
0
2
1
1
0
0
0
0
1
0
0
2
2
1
0
1
0
2
2
3
1
2
1
0
1
2
1
0
2
0
1
0
2
0
0
0
2
1
1
1
1
1
1
2
1
0
1
0
1
2
1
0
0
2
0
1
2
1
0
0
1
1
0
0
1
0
0
1
0
1
0
0
1
1
0
1
1
1
0
2
0
0
0
0
0
0
2
0
2
0
0
1
0
0
4
1
2
1
0
0
0
2
0
1
0
1
2
0
0
1
1
0
1
2
0
2
2
2
0
1
0
1
0
2
0
0
1
1
1
1
2
0
0
0
0
2
0
0
2
2
0
1
1
1
0
0
0
1
0
1
2
1
0
2
0
1
2
1
0
1
1
0
0
2
1
0
1
1
0
2
1
1
0
0
3
2
2
2
0
1
1
1
1
2
1
1
0
1
2
0
2
0
1
0
0
1
0
2
1
1
0
0
0
1
0
2
2
1
0
1
1
0
2
2
1
1
0
0
0
1
1
1
2
0
0
0
0
1
0
0
2
0
1
1
0
1
2
1
0
1
2
0
1
0
0
1
2
0
1
0
2
2
0
2
9
0
0
1
2
0
2
0
2
1
0
1
1
0
2
2
0
4
0
1
1
0
0
2
2
1
1
2
0
1
0
2
2
0
2
0
1
0
2
0
0
2
1
1
1
0
1
0
1
0
1
2
1
2
1
2
1
0
1
1
1
0
2
0
1
0
0
2
2
0
1
0
0
0
0
0
1
2
0
1
1
0
1
1
1
0
0
0
2
1
0
0
0
0
1
0
1
2
1
1
0
1
1
0
0
1
2
1
0
1
0
1
0
3
1
3
1
1
1
0
1
1
1
2
0
1
0
1
0
1
0
0
1
1
1
0
1
2
1
0
2
2
1
1
1
0
0
2
3
1
1
0
0
0
1
2
0
0
2
1
2
1
2
0
0
1
0
0
2
2
1
2
0
1
0
0
1
0
1
0
1
0
1
0
1
2
1
1
0
1
1
0
1
0
2
1
0
1
0
2
0
1
1
1
2
1
1
1
2
0
3
0
1
0
0
1
0
2
2
0
2
0
2
1
0
1
0
1
1
1
1
2
1
0
1
2
1
1
1
1
2
1
0
1
0
0
1
2
2
1
1
1
0
0
1
0
0
1
0
2
0
1
1
2
2
1
2
0
1
3
2
1
0
2
1
0
2
1
0
1
0
1
1
0
1
1
0
0
0
1
0
1
1
1
1
1
1
1
0
2
2
1
1
2
0
0
0
1
0
2
1
0
1
2
2
0
1
0
0
0
2
0
1
0
0
2
2
0
1
0
0
1
0
1
1
0
0
0
0
1
0
1
1
0
0
0
2
0
0
2
0
0
0
2
1
1
0
0
1
0
2
0
1
3
2
0
1
0
0
1
0
0
2
0
1
1
2
0
0
1
0
1
0
0
2
1
1
0
1
0
1
0
0
0
0
1
2
0
0
0
1
1
2
0
1
1
2
0
2
2
1
0
0
0
0
0
2
0
0
0
1
0
2
0
1
0
2
2
2
2
1
0
1
0
1
1
1
1
2
2
1
0
2
2
1
1
1
2
2
1
0
0
2
0
1
1
3
0
0
1
2
0
1
0
2
1
1
2
1
0
1
1
2
2
0
0
0
2
0
2
1
1
2
2
2
0
1
1
2
1
1
0
1
1
0
0
2
1
1
1
0
0
0
1
2
2
2
1
1
0
0
0
0
0
0
1
2
0
0
2
0
2
2
0
0
0
0
1
1
1
0
1
0
2
0
1
0
0
0
2
0
0
2
0
2
0
2
0
1
1
1
1
1
2
0
0
0
2
0
1
1
0
1
0
1
0
0
1
0
2
1
1
1
0
0
2
0
0
0
1
0
2
0
1
0
1
1
1
2
0
1
1
2
0
0
0
0
2
1
0
3
1
2
0
0
2
1
0
0
2
0
0
0
0
0
1
0
0
2
1
1
0
2
1
0
1
1
0
0
1
2
2
1
1
1
0
0
0
2
2
1
0
2
1
2
0
0
2
2
0
1
0
1
0
1
1
0
1
1
1
2
0
2
1
2
2
0
1
1
0
1
2
1
1
2
0
0
1
2
1
0
1
0
0
1
1
1
2
0
1
1
1
1
2
1
0
0
0
0
1
0
1
2
1
1
1
2
0
0
1
0
1
2
3
0
0
0
2
0
0
0
0
1
2
1
2
2
2
1
0
1
2
1
0
1
1
1
2
0
1
1
0
2
1
1
1
1
2
1
1
2
1
0
0
1
1
0
0
2
2
1
1
2
1
1
2
1
0
1
1
0
0
0
0
0
0
1
2
1
1
2
2
1
0
0
0
2
0
1
1
1
0
0
0
1
0
0
0
1
2
1
1
0
1
0
0
2
1
2
1
1
0
0
0
1
1
0
1
1
2
0
1
2
1
0
1
0
0
1
2
2
0
0
0
2
0
0
1
1
0
0
0
1
0
1
0
0
0
1
0
2
2
1
0
0
2
0
2
2
0
1
0
2
1
1
0
0
0
0
0
2
1
2
2
0
1
0
1
1
2
0
0
1
0
0
0
0
2
0
0
0
0
1
0
2
1
1
1
1
1
3
1
0
1
2
1
2
2
0
0
0
0
1
0
2
2
2
0
1
0
0
0
2
0
1
1
3
0
2
0
1
0
0
1
1
1
2
0
0
5
1
0
1
1
1
2
2
0
0
1
1
1
1
1
2
0
1
1
0
1
0
2
1
0
0
0
1
1
0
1
0
1
2
0
1
1
0
3
0
1
0
2
1
0
1
0
1
1
1
2
1
0
1
2
0
1
0
1
1
0
0
1
2
1
2
0
2
1
1
0
1
1
0
3
0
0
1
1
0
1
2
0
1
0
0
0
0
1
2
0
0
1
1
1
2
2
0
0
2
2
1
1
2
2
1
0
1
2
1
0
0
1
0
1
0
2
1
0
0
1
3
1
1
0
1
0
0
0
0
2
1
0
1
0
2
2
1
0
0
0
0
0
1
1
1
0
0
0
0
1
1
1
1
1
1
1
0
1
0
0
0
1
1
2
0
2
2
0
0
1
0
2
0
1
0
0
0
0
1
1
0
0
0
1
1
0
1
1
2
0
0
1
0
0
2
0
2
1
2
0
2
0
2
1
1
2
1
1
0
2
3
1
2
0
1
1
2
1
1
1
1
2
0
0
0
0
2
1
1
0
3
1
2
0
0
0
1
1
0
2
2
1
0
2
2
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
1
1
0
1
0
0
1
2
2
1
0
2
0
0
0
0
3
0
1
2
2
1
2
1
1
2
2
2
1
2
0
6
2
0
2
0
0
0
0
0
0
1
2
0
2
2
1
2
2
0
0
1
1
1
1
1
1
1
2
0
0
0
2
2
2
1
0
2
2
2
2
0
1
4
2
1
2
0
0
0
1
1
0
0
0
1
2
0
1
3
1
1
1
2
0
0
0
0
0
1
1
0
1
0
0
7
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
2
1
1
1
0
1
0
0
1
2
0
2
2
1
1
1
0
1
2
1
2
1
2
0
0
0
0
1
2
0
1
1
0
0
1
1
0
2
1
2
2
0
0
2
1
0
2
0
0
3
0
2
2
0
1
3
1
0
2
2
1
0
0
1
0
1
2
0
2
1
6
1
0
0
0
0
2
1
2
2
0
1
1
0
0
1
0
0
0
2
1
1
1
1
0
0
2
1
1
1
1
1
0
0
1
1
0
0
2
0
0
0
1
0
3
1
0
0
2
0
0
1
1
0
0
1
2
0
0
1
0
0
0
2
1
0
0
3
1
1
2
1
1
2
0
1
2
1
0
1
1
0
2
1
1
2
1
1
1
0
0
1
0
1
1
3
0
1
0
1
0
1
0
0
0
2
0
1
1
0
0
3
2
1
0
2
0
0
2
0
1
0
1
0
2
3
0
1
1
1
1
0
0
0
0
1
2
2
2
0
1
1
0
2
1
0
1
1
0
0
0
1
1
0
2
1
2
1
0
1
0
1
1
0
1
0
0
0
2
0
0
1
0
0
2
1
1
1
2
2
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
1
0
1
1
0
1
0
0
1
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
2
1
2
2
0
1
1
0
0
1
1
1
1
1
1
0
0
2
1
3
2
0
2
1
1
0
0
0
2
2
0
1
0
1
1
1
1
0
2
2
1
0
1
1
0
2
2
1
2
1
1
1
2
1
1
0
0
2
0
2
0
0
1
1
0
0
1
2
1
0
2
0
0
1
2
0
2
1
1
0
2
1
1
0
1
0
0
2
0
0
0
1
2
2
0
1
1
0
2
1
1
0
1
1
0
2
1
0
2
0
0
0
1
2
0
2
0
2
0
2
1
0
1
1
2
1
0
1
0
0
1
1
2
0
1
2
0
2
0
2
0
0
1
2
1
0
0
2
0
0
0
0
1
1
0
1
2
3
1
0
2
1
1
1
0
0
1
1
0
1
0
2
0
1
1
1
0
0
1
0
0
1
1
2
1
2
1
0
2
0
0
0
1
1
1
0
2
1
0
2
3
2
0
2
2
1
3
0
0
0
2
0
0
1
0
1
0
1
0
2
2
1
2
2
1
0
1
0
2
0
1
0
0
2
0
0
1
0
1
2
1
1
3
0
0
0
1
0
0
0
2
1
1
0
2
0
3
1
0
0
0
1
0
1
1
0
0
1
1
1
1
2
0
1
0
0
2
0
0
1
1
1
0
1
0
1
1
0
1
0
2
0
1
0
0
0
0
0
0
1
0
1
1
1
0
0
1
1
1
1
1
0
2
0
2
0
0
5
1
1
2
2
1
1
0
0
1
0
1
1
0
2
2
0
0
0
1
0
0
0
2
0
1
0
0
2
1
1
0
1
1
1
2
0
0
0
0
1
0
0
1
1
1
0
0
0
2
2
0
0
0
0
0
1
0
2
2
0
0
1
0
1
0
0
2
0
2
1
0
0
1
0
2
0
0
2
1
1
0
0
1
0
1
0
0
1
2
1
1
2
1
0
0
2
0
0
1
0
0
1
1
1
1
0
2
0
1
0
0
1
0
0
1
0
0
1
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
1
1
0
0
0
1
2
2
0
1
1
2
0
1
0
1
1
0
0
0
1
0
1
5
0
0
0
1
1
0
1
0
2
2
1
1
0
0
3
3
1
2
1
2
1
2
2
1
0
0
1
0
0
1
0
1
2
0
0
1
2
1
2
0
0
0
0
0
2
3
1
2
0
0
1
0
0
1
1
3
0
2
1
1
1
1
0
2
0
0
0
0
2
1
0
0
1
1
0
1
1
1
0
1
0
0
0
3
2
0
0
2
0
0
2
2
2
0
2
1
1
0
0
1
0
0
0
1
0
0
0
1
1
0
1
0
1
1
0
2
1
0
0
2
1
0
1
0
2
1
0
2
0
1
1
2
1
1
0
2
1
2
1
2
0
0
0
0
0
0
0
1
0
0
2
3
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
2
2
1
0
1
1
0
1
2
0
1
0
0
0
2
0
0
0
0
2
1
1
0
0
0
1
1
1
0
1
0
2
3
1
0
1
1
1
2
1
2
1
1
1
1
0
1
0
2
1
1
1
0
0
1
1
1
1
1
2
2
0
0
1
1
2
0
2
2
3
1
1
1
0
0
1
1
1
2
1
2
0
1
0
1
2
1
1
0
1
2
0
1
2
0
0
2
2
1
0
1
1
1
1
0
1
0
2
2
1
2
0
1
0
0
2
2
0
1
0
2
0
0
0
0
0
2
2
0
1
2
1
2
0
0
0
0
2
0
2
2
0
1
0
1
1
1
1
2
0
2
0
1
0
0
2
0
0
0
0
1
0
1
2
1
0
0
0
0
1
0
2
0
0
1
1
2
2
2
0
0
1
2
0
0
0
1
1
1
0
0
0
1
1
2
1
0
1
2
0
1
0
0
0
1
0
0
2
1
0
1
0
2
1
1
0
1
2
0
2
0
2
1
2
0
1
0
2
3
1
0
2
1
2
1
0
1
1
0
2
0
1
0
2
2
0
0
1
2
1
1
0
0
0
1
0
0
1
2
2
0
1
2
1
0
1
2
0
1
1
2
0
0
2
1
2
0
0
1
1
0
2
0
0
0
0
1
1
1
0
2
0
2
2
1
2
1
0
1
0
0
1
0
2
1
2
0
2
0
0
0
1
0
2
1
1
2
0
2
2
1
0
1
1
1
1
2
1
0
2
1
1
0
1
0
0
0
1
1
1
0
0
0
2
1
0
0
1
1
2
2
0
0
0
1
0
0
0
0
0
2
1
1
0
1
0
1
0
0
1
0
1
0
0
0
0
2
2
1
0
0
0
2
1
0
2
2
0
1
2
0
1
1
1
0
1
0
1
1
4
0
0
0
0
0
0
2
1
1
2
1
1
0
1
2
0
0
1
0
1
0
0
0
1
0
2
1
1
0
0
1
1
1
1
0
0
0
0
0
0
2
2
0
0
0
0
4
1
0
0
1
0
1
1
2
0
1
0
1
0
0
2
1
0
1
2
3
1
1
0
1
0
0
0
1
1
0
1
1
0
0
1
0
1
0
0
0
1
0
3
1
3
0
0
1
0
0
0
0
1
4
1
2
0
0
0
1
1
1
0
1
0
2
0
1
2
2
2
3
0
2
0
0
4
0
2
2
0
1
0
0
0
0
0
1
0
2
0
1
2
1
0
1
0
0
0
2
0
0
1
1
0
0
0
0
1
0
0
2
2
1
2
1
0
1
0
0
1
0
0
0
1
1
0
1
1
2
1
1
2
1
1
1
0
0
1
0
2
1
1
1
0
1
1
0
1
1
1
0
2
4
1
1
0
1
3
0
2
0
1
2
2
3
2
1
1
1
1
0
1
2
1
1
0
1
1
1
0
2
1
0
0
0
0
5
2
2
0
0
2
0
1
0
0
0
0
0
1
0
1
0
0
0
2
0
1
1
1
0
1
2
2
2
0
0
0
1
0
1
1
0
1
0
0
0
0
1
1
1
1
3
1
0
1
0
1
0
0
0
2
1
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
3
0
0
0
3
1
1
1
0
0
0
0
0
0
1
1
0
1
0
0
0
2
1
3
0
1
1
2
1
0
0
2
2
1
1
2
0
1
2
0
0
1
0
2
0
0
0
0
0
2
2
0
1
2
1
1
1
1
2
0
0
1
1
0
2
2
0
0
1
1
1
1
0
0
0
2
2
2
1
0
0
3
0
0
1
1
0
0
0
0
0
4
0
1
1
0
0
2
2
1
2
1
2
0
1
1
0
0
1
0
0
0
1
1
1
0
1
1
1
1
1
0
1
2
3
1
2
2
0
2
1
1
2
1
0
0
1
0
0
0
2
1
0
2
1
1
0
2
0
0
0
0
0
1
0
1
2
1
0
2
1
0
0
0
3
1
0
1
1
1
2
1
0
1
5
0
1
1
0
2
1
1
1
0
0
1
1
1
0
0
0
1
2
0
0
2
2
1
1
1
0
1
1
0
2
1
0
0
1
0
2
1
1
2
0
1
1
1
0
0
1
1
0
0
0
1
0
1
0
1
0
2
2
0
0
1
0
0
1
1
2
1
1
0
2
1
2
2
0
0
1
2
2
2
0
0
1
1
1
0
1
0
2
2
2
0
1
0
0
2
1
2
1
2
0
0
0
1
0
0
0
0
1
1
0
0
1
2
0
0
0
1
0
2
1
1
1
1
1
0
1
1
3
0
1
0
0
0
1
0
0
1
1
2
0
1
0
1
1
0
0
3
1
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
2
0
0
2
0
0
1
1
0
1
2
2
0
0
0
0
2
2
0
1
1
0
1
0
1
0
2
1
0
0
1
1
1
0
1
1
0
1
0
0
0
0
1
0
2
1
2
1
2
1
2
0
2
0
0
0
0
1
2
0
0
1
0
0
0
0
0
1
1
1
0
1
1
0
1
2
1
0
0
0
1
1
0
0
0
2
1
1
1
0
4
1
1
2
2
1
1
1
7
1
2
0
0
2
1
1
0
0
2
0
0
1
1
1
0
1
0
0
0
0
0
2
0
0
1
2
0
1
1
2
1
3
2
2
0
0
0
0
1
0
0
1
2
1
1
0
2
2
1
2
0
0
0
0
0
2
3
2
1
2
1
0
1
1
0
1
0
2
0
1
1
0
0
1
2
2
2
1
0
0
0
0
1
0
1
0
0
0
1
2
0
0
2
0
1
1
0
2
1
2
3
0
0
0
2
0
2
2
1
1
1
1
2
0
1
0
0
0
0
1
2
1
1
0
0
2
1
2
1
0
1
0
1
0
0
1
1
1
1
0
0
2
2
2
1
0
0
2
2
0
1
1
1
2
0
0
0
2
1
0
2
1
1
2
1
2
2
1
0
1
0
0
2
0
2
3
1
0
2
0
1
0
2
0
0
2
0
2
0
2
0
0
1
1
1
0
1
0
2
1
2
1
1
0
1
0
1
0
0
1
0
0
2
0
2
1
0
0
1
1
2
2
3
1
1
0
1
0
2
2
1
1
0
2
0
1
0
1
1
0
1
0
0
0
2
1
1
1
1
2
1
0
0
1
0
2
0
0
0
0
1
1
1
2
0
0
0
0
1
1
1
1
0
2
0
2
2
2
2
1
0
1
2
0
1
1
2
1
0
2
1
1
2
2
2
0
3
0
1
2
0
1
2
2
1
2
2
0
2
2
2
1
0
2
0
0
1
0
1
2
0
0
1
1
1
2
1
2
0
2
0
3
0
1
1
0
1
1
1
2
0
0
1
0
2
1
0
1
1
1
1
6
0
0
0
0
0
2
0
1
2
1
1
0
1
0
1
0
0
2
1
2
2
1
1
1
0
1
0
2
0
0
1
0
0
1
0
0
1
2
0
0
0
0
0
1
0
0
0
2
1
1
2
1
0
0
0
2
1
1
1
1
1
0
1
2
2
0
0
0
2
1
0
2
0
1
1
2
1
3
3
1
0
0
4
0
0
0
0
0
2
0
1
0
1
1
1
0
1
0
1
1
1
2
2
1
1
0
0
0
0
2
2
0
1
0
0
0
0
1
1
1
2
2
0
1
0
2
0
1
0
0
0
0
1
2
0
2
0
0
1
2
2
0
0
0
0
2
2
0
2
0
0
1
2
0
1
1
2
1
0
0
1
0
0
0
1
2
3
0
0
0
2
0
6
1
2
0
2
1
2
0
2
1
0
0
1
1
1
0
1
1
0
1
0
0
3
2
0
1
0
1
2
0
2
1
2
2
0
1
0
1
0
1
3
0
7
0
0
0
0
1
2
2
2
2
1
0
2
0
0
0
0
1
0
1
0
2
1
1
0
1
0
1
0
1
1
0
1
0
0
0
1
0
0
0
0
2
2
0
1
1
2
0
0
0
2
2
0
0
0
1
1
2
0
0
0
1
1
1
3
0
1
1
4
1
1
1
3
0
1
0
1
0
1
0
1
0
1
2
2
0
1
1
0
0
2
2
0
0
1
0
0
0
1
0
0
0
0
2
1
1
0
1
1
0
2
1
1
1
1
0
0
1
1
1
1
0
1
0
1
0
2
0
2
0
1
0
2
2
0
1
0
0
0
2
1
1
0
2
0
0
1
2
0
1
1
0
0
0
0
1
0
1
1
1
0
1
0
0
2
0
0
2
0
2
0
0
0
0
1
2
1
0
1
1
0
0
1
0
0
0
2
0
0
1
2
2
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
1
1
1
2
1
1
0
0
1
0
0
1
1
2
2
1
1
2
1
1
2
1
2
0
0
0
0
0
1
0
0
1
1
3
0
2
0
0
1
0
1
0
2
0
2
0
2
1
0
2
0
1
1
2
1
0
0
0
0
1
0
2
0
0
0
0
1
1
2
1
0
0
0
0
2
0
2
1
2
0
0
0
2
1
0
1
0
0
2
0
1
2
0
0
1
0
0
0
1
0
0
0
1
0
2
0
0
0
1
1
1
2
2
1
0
1
0
0
1
0
2
0
2
0
0
0
2
0
3
1
1
0
0
3
2
0
1
1
0
1
1
1
0
0
0
2
1
0
2
0
0
1
2
1
1
0
1
1
2
1
1
1
2
1
2
0
1
0
1
0
0
2
0
2
2
2
1
1
1
1
1
0
0
0
0
1
0
2
1
1
0
2
0
1
2
0
2
0
1
2
3
0
1
2
0
0
2
1
0
1
0
1
0
0
0
1
0
2
1
0
1
0
0
0
1
0
1
2
1
2
0
0
0
1
2
0
1
2
1
1
1
1
0
0
2
0
1
0
1
1
1
2
1
0
1
1
1
1
0
1
0
1
0
1
0
1
0
1
0
1
0
2
2
2
0
1
3
0
0
2
0
1
1
0
1
1
0
0
1
0
0
1
0
2
0
1
1
1
2
2
0
2
0
0
0
1
1
1
0
1
0
0
0
0
2
1
0
2
0
0
2
0
2
1
1
0
0
3
1
1
0
1
1
1
0
0
1
0
1
2
0
0
3
0
2
2
1
1
0
1
2
1
2
0
1
0
0
2
1
1
1
0
0
0
1
0
1
0
1
0
1
0
0
0
0
2
2
0
1
2
0
2
1
2
1
2
1
0
1
0
1
1
1
0
1
0
1
0
0
0
2
2
1
2
1
1
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
1
0
1
0
0
2
1
1
1
2
1
2
2
2
1
2
0
1
0
1
0
0
2
0
2
2
0
1
2
0
2
2
0
1
2
2
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
1
1
0
0
0
0
0
1
1
1
0
1
0
0
0
0
1
2
0
0
0
0
1
2
0
1
4
0
0
0
3
2
2
2
2
0
2
1
0
1
1
1
1
1
0
0
0
0
2
1
0
1
2
1
0
0
0
1
2
0
1
0
1
2
2
3
1
0
0
1
1
0
1
1
0
1
0
1
0
2
1
1
0
1
0
0
0
0
2
2
1
2
1
0
0
0
0
1
0
0
1
1
2
2
1
2
1
2
2
0
0
1
0
0
0
0
0
2
0
0
0
1
2
0
2
0
0
1
1
1
1
0
0
0
2
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
3
2
1
1
1
0
0
1
2
1
1
1
2
1
0
1
1
1
0
0
0
0
1
0
2
2
0
1
1
2
2
0
1
1
2
1
0
1
2
0
1
0
0
1
0
1
0
0
1
0
0
1
0
1
1
1
0
0
1
0
0
2
0
0
0
0
2
0
2
2
1
0
2
2
1
2
2
1
2
0
0
2
0
2
1
0
1
0
1
0
0
1
0
0
1
1
1
1
1
0
3
0
0
0
1
0
1
0
1
1
1
1
0
1
1
0
1
1
2
0
0
0
1
2
2
0
1
2
0
1
1
1
1
1
1
0
2
1
2
1
1
0
1
0
0
0
0
0
1
0
2
0
1
0
2
1
0
1
1
2
1
2
1
2
0
2
0
2
0
0
0
2
1
3
1
0
0
0
0
0
1
0
0
1
1
1
2
1
0
0
1
2
0
0
2
0
0
0
0
0
4
0
2
0
2
1
2
0
0
2
1
1
0
0
0
2
0
2
2
2
0
0
0
0
0
1
2
1
0
0
0
0
1
1
1
0
2
0
0
2
0
0
1
1
0
2
0
0
0
0
1
0
0
1
0
1
0
2
0
2
3
0
1
0
1
3
0
2
0
0
0
2
0
2
0
0
1
1
2
0
1
2
1
0
0
0
0
1
0
0
2
0
0
1
0
0
0
4
1
0
0
0
1
1
1
3
1
1
0
1
0
1
1
1
0
1
1
2
0
2
2
1
0
0
1
3
0
0
2
1
1
0
1
1
2
0
2
1
1
3
2
1
1
0
1
0
0
2
0
2
2
1
1
1
0
0
0
1
1
1
1
2
0
1
0
0
0
1
2
0
0
1
1
0
1
0
1
2
1
1
2
0
0
1
1
1
1
0
1
0
2
2
0
0
1
1
1
1
0
1
1
1
0
1
1
0
0
2
1
1
1
1
1
0
0
0
2
0
1
2
0
2
0
2
2
1
0
1
1
1
1
1
0
1
1
0
0
1
0
1
0
2
2
1
0
1
0
2
1
1
1
1
1
1
2
2
2
0
0
1
0
1
1
0
2
0
0
0
0
4
1
0
2
0
0
2
1
0
0
0
1
1
0
7
1
2
1
1
0
0
9
0
1
1
1
1
0
4
1
1
1
0
0
0
2
0
1
1
0
1
0
0
1
0
0
2
1
0
2
1
1
1
0
1
0
0
0
4
1
0
2
2
1
1
0
0
1
1
4
2
0
0
2
0
1
1
0
1
1
0
0
0
1
0
0
1
1
1
0
1
2
1
1
1
0
1
0
3
2
0
0
2
0
1
0
1
0
0
0
3
1
1
0
1
0
1
2
0
2
0
1
0
0
1
2
0
0
1
1
1
0
1
2
0
0
0
0
1
0
0
0
2
0
0
1
0
2
2
0
2
1
0
0
0
1
0
1
1
0
0
2
0
1
1
0
1
2
1
2
0
2
1
0
1
1
1
2
1
0
0
0
0
2
1
2
1
0
0
2
0
3
6
0
0
0
1
1
1
0
2
1
2
2
2
2
0
1
0
0
0
1
1
0
2
1
0
0
0
2
1
2
1
1
0
0
1
0
0
2
1
1
1
1
1
0
2
1
0
2
1
1
2
0
1
0
1
1
1
0
0
0
1
0
2
0
0
0
3
0
2
2
1
0
2
1
1
1
1
0
0
0
1
0
1
2
0
2
1
2
0
0
3
0
1
1
1
2
0
0
1
0
0
1
2
1
0
2
0
0
0
2
0
1
2
0
1
0
0
1
0
1
0
0
2
0
2
0
3
0
0
0
1
0
1
0
1
0
0
1
2
1
0
0
1
0
0
2
0
0
0
0
2
2
0
0
0
2
1
1
1
0
2
2
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
2
0
0
2
1
1
0
0
0
0
0
0
1
1
0
0
2
2
0
2
0
2
2
2
2
0
1
1
2
0
1
0
1
1
2
0
2
1
0
0
0
0
1
1
2
1
2
1
2
0
1
1
2
1
0
0
2
0
0
0
2
2
0
0
0
0
0
2
0
1
1
0
0
3
1
0
1
0
4
2
0
2
0
2
2
1
1
1
1
0
1
2
0
0
0
0
2
0
2
0
0
3
1
1
0
1
0
1
0
1
2
0
1
0
0
1
2
0
0
0
0
0
1
0
1
0
1
0
0
1
2
2
1
1
1
3
3
1
0
0
1
3
1
0
1
1
2
0
0
2
0
0
0
2
2
0
1
2
1
4
0
0
1
2
0
1
0
1
0
1
1
0
0
2
1
0
0
0
1
0
0
1
1
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
2
0
0
1
0
1
2
0
0
1
0
0
2
2
1
0
1
0
0
3
1
0
0
1
0
0
1
0
0
1
1
2
2
0
0
0
1
1
0
0
1
0
13
1
1
0
1
2
0
1
0
3
0
1
0
2
0
1
1
1
1
0
0
0
0
0
2
0
0
2
1
1
0
1
0
1
0
2
1
0
1
0
1
1
2
1
1
2
2
0
2
1
0
0
0
2
0
1
0
1
1
0
1
0
1
0
1
0
0
0
0
2
2
0
0
1
1
3
0
2
0
1
2
0
1
0
1
1
0
1
0
1
1
0
1
2
1
2
0
1
0
1
0
2
1
0
2
0
0
2
2
2
2
2
0
2
1
0
1
0
2
2
2
0
0
1
2
2
0
1
0
2
2
1
0
2
1
0
2
2
1
0
0
1
2
0
0
0
1
0
1
1
0
1
2
1
1
1
0
2
2
0
1
2
0
0
0
0
1
2
1
0
0
0
1
2
0
1
2
0
2
1
0
1
1
1
1
1
1
2
1
1
2
0
1
1
0
1
0
1
0
0
0
1
1
2
2
0
0
2
1
0
0
0
0
1
1
2
2
0
1
1
2
0
2
0
1
0
2
0
0
1
2
0
1
1
0
2
0
1
1
1
0
1
1
0
1
0
0
2
1
3
2
2
0
2
2
1
0
0
2
2
1
2
0
2
2
3
2
0
2
1
0
2
0
1
1
0
0
0
1
1
1
2
1
2
1
0
0
0
1
2
1
1
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
1
1
0
0
2
2
1
0
0
0
2
2
0
1
2
1
1
1
1
1
2
0
1
0
1
0
0
0
1
0
1
0
0
0
1
2
0
0
1
1
0
2
3
2
1
0
2
1
4
1
0
0
2
0
0
1
1
2
2
0
2
2
0
2
2
0
2
2
2
1
1
2
0
2
2
2
0
0
2
1
1
0
0
1
2
2
2
0
0
0
1
1
0
1
0
1
2
0
1
0
0
0
0
2
1
0
0
0
0
1
1
1
0
0
1
1
1
0
1
0
0
1
0
1
1
0
1
0
0
2
0
0
0
2
1
1
0
0
1
1
2
0
2
1
1
0
1
0
1
2
0
0
2
2
1
2
1
0
1
0
0
0
0
1
1
2
0
2
2
1
1
0
0
2
0
0
1
3
1
1
1
1
0
1
0
2
0
0
0
0
1
2
1
1
2
2
1
0
2
0
2
1
0
1
2
1
1
1
0
0
2
2
1
1
1
2
2
0
0
1
2
2
0
0
3
1
1
1
0
2
2
1
1
1
0
0
0
1
1
1
1
1
3
0
1
1
0
0
0
1
1
0
0
0
1
0
1
0
1
2
1
0
0
0
1
1
0
1
0
0
0
0
1
1
3
0
1
1
0
2
0
2
0
0
1
1
1
2
1
0
2
0
0
1
0
2
1
2
0
1
1
0
2
0
2
1
0
0
0
1
0
1
0
0
2
0
2
1
1
0
0
0
0
2
1
1
1
0
2
0
0
2
0
2
2
0
1
0
0
2
0
0
0
1
1
1
3
2
2
1
2
1
1
1
0
1
1
0
1
0
0
0
2
1
0
0
0
1
1
1
1
0
1
1
0
2
0
0
1
1
0
2
0
1
2
0
0
2
1
0
1
0
0
1
0
1
1
2
1
1
1
1
0
1
0
1
1
0
1
1
2
3
1
1
1
0
0
2
0
1
0
0
2
2
1
0
1
0
0
1
3
1
2
1
1
1
2
0
0
0
2
1
1
0
0
0
0
0
0
1
1
0
0
0
1
1
1
0
0
0
2
0
4
1
1
0
0
0
1
0
0
2
2
0
2
0
0
1
1
1
0
2
0
2
0
1
0
3
0
2
1
2
1
1
0
0
0
1
1
0
0
2
0
0
1
0
0
0
2
1
0
1
1
0
0
1
0
2
2
2
1
0
0
0
2
0
0
0
0
2
1
0
0
0
1
0
0
1
0
0
1
0
0
0
3
0
0
2
0
0
0
0
2
2
1
1
2
1
2
0
2
0
0
1
1
2
1
0
1
1
0
1
0
0
0
1
0
0
0
1
1
0
2
2
2
1
0
2
2
0
0
0
1
1
1
2
1
0
1
0
1
0
2
0
0
0
0
2
0
0
1
2
1
0
0
0
0
1
0
2
0
2
1
1
0
0
1
2
1
0
1
1
0
3
0
1
2
0
1
0
1
0
0
2
1
0
1
0
1
1
0
1
0
2
1
0
1
2
2
1
1
1
2
0
1
1
0
1
1
1
1
0
0
3
3
0
1
1
1
1
1
1
0
0
1
2
0
0
2
1
1
1
3
2
1
0
0
1
1
0
2
2
0
1
1
1
2
0
2
1
2
0
0
2
2
2
2
1
1
1
0
0
0
3
1
0
0
0
0
1
1
2
1
0
1
0
0
1
1
2
1
2
0
0
0
0
2
0
1
2
1
1
2
1
0
2
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
1
2
2
0
1
1
0
0
0
0
0
2
1
1
0
0
0
1
1
0
0
1
2
2
0
2
1
1
2
1
0
3
0
1
0
1
2
0
0
0
0
1
1
0
2
0
0
1
0
0
0
0
1
2
0
1
0
0
0
0
0
0
1
2
0
1
1
0
3
1
2
0
0
1
0
0
2
1
2
1
2
0
1
0
0
2
1
0
1
1
0
2
1
1
1
0
0
2
1
0
2
0
0
0
1
1
1
1
0
0
1
0
1
3
0
2
1
0
2
0
1
0
0
3
0
0
2
0
1
0
2
0
1
0
2
0
0
1
0
0
2
0
2
2
0
0
1
1
1
1
2
0
0
1
0
0
2
0
2
0
2
2
1
0
1
2
2
2
1
0
0
1
1
1
1
2
1
1
1
2
0
2
2
1
0
1
1
0
0
0
0
2
0
0
2
2
0
0
1
1
0
0
2
0
1
0
0
2
0
1
0
0
0
2
0
1
2
1
1
1
2
0
0
0
1
0
2
1
1
1
0
0
1
0
2
0
0
0
2
1
1
3
0
1
1
0
5
2
0
0
1
1
0
0
2
0
0
2
0
1
1
0
1
1
0
0
0
1
3
1
1
0
0
0
1
1
1
3
1
1
1
2
2
1
1
2
0
0
0
2
0
0
2
2
0
1
1
0
1
1
0
1
1
0
2
4
0
2
2
0
0
1
2
1
1
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
2
2
2
0
0
0
3
2
1
0
2
0
1
0
1
2
0
3
0
2
2
0
0
2
1
2
1
0
0
1
1
0
1
0
0
0
0
1
2
2
0
0
1
1
2
0
0
1
0
0
0
1
0
1
0
1
1
0
1
1
1
1
0
1
1
0
1
1
0
0
2
2
2
0
2
1
0
0
1
2
2
1
2
1
1
2
0
2
1
0
2
1
0
1
1
2
0
0
2
1
0
0
0
1
1
1
0
1
3
0
0
2
1
1
1
1
1
0
0
2
1
1
0
0
1
1
2
3
2
2
1
0
1
2
1
0
1
1
1
1
2
0
0
0
1
1
0
0
0
1
2
0
2
2
0
1
0
0
0
0
1
0
1
0
1
0
3
1
2
1
0
2
0
2
2
0
2
1
3
1
0
1
2
0
0
0
1
2
0
0
1
2
2
0
1
1
0
1
1
0
0
1
2
0
1
1
1
2
1
1
0
1
1
1
2
0
0
1
1
2
0
2
2
0
0
2
0
2
2
1
0
1
1
2
1
2
0
1
0
1
0
0
1
0
1
2
1
1
0
0
1
2
0
0
2
0
2
0
0
0
0
0
1
2
2
0
1
0
0
0
0
0
1
0
2
0
0
0
1
0
2
0
2
0
0
1
0
0
1
1
0
0
0
1
2
0
0
1
0
2
2
0
0
2
2
0
1
0
0
2
0
0
0
1
1
0
1
1
0
0
0
1
2
2
3
0
0
0
1
2
1
1
0
1
0
1
1
0
2
2
2
0
1
0
0
1
0
0
0
1
2
1
0
0
1
0
0
1
0
2
0
1
0
1
0
1
0
0
1
0
1
0
1
2
1
1
1
0
3
0
0
0
0
2
0
2
1
0
0
0
2
1
1
0
1
2
1
0
0
0
2
1
0
1
0
1
1
0
0
2
2
0
3
1
1
2
1
0
0
0
0
0
0
5
2
1
1
0
0
1
0
1
0
0
2
2
1
0
0
0
2
2
1
0
2
1
2
0
1
0
0
0
0
1
0
3
1
0
1
0
0
0
0
1
1
0
1
1
1
2
2
1
0
2
2
0
0
1
2
2
0
0
3
0
1
0
2
0
0
1
0
2
0
1
0
0
1
0
1
2
0
0
0
0
0
0
1
0
0
2
1
1
0
1
1
2
0
1
1
2
2
2
1
0
2
2
0
0
2
0
0
0
0
0
2
2
2
0
2
0
0
2
2
1
0
2
0
0
1
1
0
0
1
0
1
1
1
0
1
1
2
0
1
1
0
2
1
0
0
1
1
0
0
1
0
0
0
1
0
0
1
2
0
2
0
2
0
1
1
1
2
2
0
2
1
0
1
1
0
1
1
1
1
0
1
0
3
1
3
1
1
2
1
0
1
2
0
1
2
1
0
0
0
2
0
1
1
0
1
0
1
0
2
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
2
2
1
0
0
0
2
0
1
1
2
0
2
0
2
1
1
1
1
0
0
1
0
1
1
0
0
2
1
0
0
2
0
1
3
2
2
1
0
0
2
0
1
1
1
2
1
0
1
0
0
1
0
1
1
0
0
2
0
2
2
2
1
1
2
1
1
2
0
0
2
0
0
0
0
0
0
0
1
0
0
1
2
1
1
0
0
0
1
0
0
1
1
0
2
0
0
1
1
1
1
0
1
0
0
2
2
0
2
1
0
0
2
2
2
1
1
0
0
2
1
0
2
1
1
2
0
1
2
0
2
1
1
1
2
0
1
1
1
0
2
1
0
1
2
1
2
1
1
1
1
4
2
2
0
2
0
0
0
1
0
0
0
2
1
2
0
0
0
2
3
1
0
0
1
0
2
2
2
0
0
0
0
0
0
0
1
2
1
0
1
0
0
2
0
0
0
0
0
1
0
1
0
0
1
0
1
2
1
2
1
1
0
1
2
1
0
2
0
1
1
1
2
2
0
0
1
0
0
1
0
0
0
0
1
1
1
0
1
2
0
1
1
1
0
1
0
0
0
2
1
1
2
1
0
0
2
2
0
2
1
3
0
0
0
0
0
1
0
1
1
0
3
1
1
0
2
1
1
0
1
1
1
0
0
1
0
0
1
14
0
0
0
1
0
1
0
1
0
1
2
0
0
1
1
1
2
0
0
0
0
0
0
0
1
1
0
0
0
1
1
2
2
0
1
1
0
2
1
1
0
2
1
0
2
0
0
1
1
0
0
2
0
2
3
0
0
2
2
1
0
0
1
2
2
0
0
1
2
1
2
0
0
0
0
1
0
0
0
0
1
3
1
0
2
1
0
1
0
2
2
1
0
1
1
0
1
2
2
0
2
0
0
0
1
1
0
1
0
0
0
2
1
0
2
2
0
0
2
1
0
0
1
0
1
0
1
1
0
1
0
1
0
0
2
0
0
0
1
2
0
1
0
2
1
0
0
1
0
2
1
0
0
0
2
0
0
1
0
0
0
1
1
0
0
2
0
0
0
1
1
2
1
0
0
0
0
2
1
1
0
1
1
1
2
0
0
0
0
0
1
1
2
2
2
1
1
1
2
2
0
1
0
0
1
0
0
0
3
2
2
1
0
2
0
1
2
2
0
1
0
2
0
1
2
0
2
0
2
0
1
2
2
2
3
0
1
2
0
1
0
1
0
1
0
1
1
0
0
0
1
2
2
2
2
2
0
2
1
3
1
1
1
2
1
1
1
2
2
1
2
0
1
1
0
2
1
1
0
0
0
1
2
2
1
0
0
1
3
2
0
0
0
1
3
0
1
0
0
1
0
1
0
1
1
2
2
0
3
1
0
1
1
0
1
1
0
2
0
0
1
1
0
1
0
2
2
1
0
0
0
2
1
0
0
0
4
1
1
1
0
1
0
2
2
1
0
0
1
0
1
2
0
0
0
4
2
2
1
0
2
1
0
3
1
0
0
1
0
2
0
1
1
0
2
3
0
1
0
1
1
1
0
2
0
0
2
0
1
2
1
0
2
0
2
0
1
0
0
0
1
0
0
1
0
0
1
3
3
1
0
2
0
2
0
2
0
2
1
0
1
0
1
2
1
1
1
2
2
1
0
1
0
0
1
0
1
3
1
0
0
1
0
0
1
2
2
1
2
1
0
1
0
2
0
0
1
0
1
0
0
1
1
1
0
1
1
0
1
2
0
0
0
1
1
1
1
0
1
2
2
0
0
1
0
2
1
0
0
2
0
1
0
0
0
0
0
0
1
0
2
0
1
0
1
2
1
0
2
0
0
0
2
0
0
1
1
2
2
1
2
1
1
1
2
1
1
0
0
1
0
1
1
2
0
0
0
0
1
1
0
0
1
0
1
3
0
2
0
1
0
0
0
2
3
2
2
2
0
2
0
0
1
0
1
1
1
0
1
0
0
2
1
0
2
1
0
2
1
2
1
1
1
1
0
3
0
0
0
0
0
1
0
1
0
0
2
2
0
6
0
1
1
1
1
0
2
0
1
0
2
0
1
1
0
0
1
0
0
1
0
0
0
2
0
1
1
1
2
0
3
0
1
1
1
0
2
1
1
1
1
0
0
0
2
1
0
2
0
0
0
1
2
0
2
1
1
0
2
0
1
1
2
0
1
1
0
0
1
1
1
1
0
0
0
0
1
2
0
0
0
0
1
0
0
1
1
0
1
0
2
1
1
2
1
1
0
1
0
1
2
1
0
1
0
3
0
1
0
0
1
0
1
1
0
1
2
0
1
1
3
1
1
0
3
0
1
0
0
0
1
1
0
1
1
0
0
1
2
2
1
0
1
0
3
0
2
0
1
0
2
1
0
0
0
0
1
2
0
1
1
1
0
1
0
0
0
1
2
0
0
1
0
1
1
0
0
0
2
2
0
2
2
1
0
0
2
0
0
2
1
2
0
2
0
0
0
0
1
2
0
0
2
0
1
1
0
1
2
1
1
1
1
0
0
1
1
1
2
2
1
0
1
2
2
2
0
1
0
2
0
2
0
0
2
1
0
2
0
1
1
0
1
1
1
0
1
0
0
1
1
1
0
1
1
1
0
2
1
1
0
0
1
2
1
0
0
0
0
0
0
1
0
2
0
1
1
2
0
1
2
0
0
1
1
1
0
2
0
2
0
0
2
0
0
0
2
0
0
1
0
1
1
3
2
0
1
0
0
1
1
0
0
1
2
0
2
2
1
0
0
1
2
0
1
0
0
0
1
0
0
0
0
2
0
0
0
1
2
0
0
0
0
1
0
1
0
0
0
0
0
2
1
1
1
1
1
1
1
2
0
0
1
0
0
1
1
0
0
1
1
2
0
2
0
0
1
0
1
0
1
0
0
0
1
0
0
0
1
1
1
1
1
1
0
1
0
0
1
0
1
0
0
2
2
1
0
1
1
2
1
1
1
0
1
0
0
0
1
2
0
2
1
2
0
0
0
0
0
0
2
2
0
0
1
1
1
2
2
1
1
0
0
1
0
2
0
1
2
1
0
1
1
1
0
1
1
2
1
0
2
0
1
0
2
0
0
1
0
0
0
0
0
2
0
0
5
0
0
1
2
0
0
0
1
1
0
0
0
2
1
2
0
0
1
1
2
0
2
0
2
1
2
2
2
1
0
0
2
0
0
0
1
1
0
0
1
0
0
1
2
1
1
1
1
2
1
1
2
0
0
0
1
1
1
1
0
0
0
2
2
1
1
0
1
2
2
1
0
1
2
2
1
0
0
0
1
2
0
3
1
0
0
0
1
0
0
0
2
1
0
2
0
1
1
1
2
3
0
0
2
1
1
1
0
0
1
1
1
0
0
2
2
0
2
0
1
0
2
2
0
1
0
1
1
1
0
1
3
1
1
0
0
0
0
1
0
1
0
0
2
1
1
0
0
0
2
1
0
0
0
1
0
0
0
2
1
2
3
2
3
0
1
2
0
1
0
1
0
2
1
0
2
2
0
0
0
1
0
1
1
1
0
2
1
0
1
2
0
0
0
1
4
2
2
1
0
2
1
0
2
1
2
0
0
0
4
0
1
1
1
1
1
1
0
1
0
1
1
0
1
0
2
0
2
0
1
1
2
2
2
0
1
1
1
1
0
0
0
2
1
2
1
1
2
0
0
1
2
2
0
1
1
1
0
1
2
1
1
0
1
1
0
1
1
0
0
0
1
2
1
0
2
1
1
1
1
2
3
2
1
0
2
0
2
0
0
1
2
0
1
0
1
0
0
0
0
2
2
1
1
1
0
0
0
0
2
1
1
1
1
0
0
3
1
2
1
0
1
1
0
2
1
2
0
2
0
0
1
1
0
1
0
0
2
1
0
0
0
2
0
1
1
1
2
1
1
0
0
0
0
1
0
1
0
1
1
1
0
2
0
1
2
2
1
0
2
1
2
2
1
1
0
0
1
0
1
1
1
0
1
2
2
1
0
0
0
0
0
1
1
0
1
2
0
0
1
1
1
1
0
0
1
0
1
3
1
1
2
2
0
1
0
1
0
0
1
0
2
1
1
2
1
2
2
0
2
0
2
0
1
0
2
1
1
1
0
0
0
0
0
0
1
1
1
0
2
1
0
2
0
1
0
0
1
0
0
0
2
1
0
0
0
0
1
1
0
0
0
2
2
0
1
0
1
2
2
1
3
1
1
0
1
0
0
0
2
1
0
2
2
0
0
0
1
1
0
0
0
0
2
0
1
1
0
0
1
0
2
1
2
2
0
0
0
1
1
0
1
0
1
2
0
2
0
1
1
0
1
1
0
0
1
0
2
2
1
0
0
0
0
0
2
1
0
1
2
1
0
0
0
0
1
0
2
2
1
2
2
1
1
0
1
2
1
2
0
3
2
0
1
0
1
2
1
2
4
1
1
0
0
0
2
1
2
2
1
1
0
0
1
1
1
2
0
0
0
4
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
1
1
2
1
0
1
2
1
0
0
0
0
2
0
1
0
1
1
2
0
0
0
1
0
2
0
1
1
2
1
2
1
0
1
2
2
1
1
2
1
1
2
1
0
0
2
0
1
1
1
0
0
0
2
1
2
0
1
2
1
1
2
1
1
1
2
1
1
0
0
0
2
1
0
0
1
1
0
1
1
0
0
1
0
1
1
0
0
0
0
1
1
3
1
0
0
4
1
1
2
1
2
0
0
3
1
0
0
0
0
1
1
0
0
0
0
1
0
1
2
0
1
1
0
0
1
1
0
0
1
1
0
0
2
0
0
0
2
1
2
0
1
3
1
0
0
2
1
0
0
0
2
1
1
2
2
2
2
2
1
1
1
0
1
2
0
1
2
0
0
0
0
2
0
0
0
0
0
1
0
2
2
2
1
0
0
0
0
1
0
2
5
0
0
2
0
0
0
0
1
1
0
1
3
0
0
2
2
1
1
3
1
0
1
0
2
0
2
0
2
0
0
1
1
1
2
1
1
0
2
2
2
2
0
1
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
2
1
0
1
1
2
0
1
2
2
1
2
3
0
1
1
2
0
1
2
0
0
2
1
0
1
0
0
1
0
1
0
1
2
0
2
0
1
0
0
2
1
1
3
2
2
0
2
0
2
0
1
2
2
0
0
2
2
1
2
0
0
1
1
1
0
1
1
1
0
0
1
2
1
0
1
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
1
1
2
2
2
0
1
0
1
1
2
1
2
2
1
0
2
1
0
2
2
1
1
1
0
1
1
0
1
2
0
2
1
0
1
0
2
0
0
2
0
0
0
1
1
1
1
2
1
2
2
1
0
0
0
0
0
3
2
1
0
1
2
2
0
2
1
1
1
2
0
0
2
2
1
0
0
2
2
0
2
2
1
1
0
1
0
2
2
0
4
2
2
0
0
1
0
0
2
1
0
0
2
0
2
2
0
0
0
2
0
0
2
2
1
1
2
1
2
1
0
0
1
0
0
2
1
0
1
1
0
1
1
0
2
1
0
0
0
0
0
1
0
0
3
2
2
1
3
2
1
1
1
2
1
1
1
2
2
0
1
1
0
1
1
1
2
1
1
0
0
0
0
0
0
0
1
1
1
1
0
4
0
0
2
0
2
1
0
0
2
2
1
1
1
0
0
2
3
0
1
0
0
2
0
0
1
0
1
0
0
0
2
2
1
0
0
0
1
1
1
1
1
0
0
1
0
1
0
2
2
2
1
0
0
2
1
0
0
1
0
0
1
0
0
0
0
1
2
2
0
2
1
3
1
0
0
0
0
1
0
1
1
0
0
0
2
1
0
1
1
4
1
1
1
0
2
1
1
2
0
0
1
0
0
1
0
0
2
1
1
2
1
0
1
2
1
4
1
0
2
0
0
2
0
1
4
2
2
0
0
1
0
1
0
1
1
1
2
0
0
2
2
0
0
1
0
1
0
0
2
1
0
1
2
0
2
2
1
0
0
0
2
1
0
0
0
0
0
0
0
1
1
1
1
0
1
0
0
0
1
0
1
2
0
1
1
0
1
0
1
1
3
0
1
1
0
0
1
2
0
0
3
1
2
1
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
2
1
1
1
0
0
2
2
1
0
1
0
2
1
1
2
1
2
0
2
2
1
0
0
0
1
0
0
1
0
1
0
0
0
1
0
1
1
0
2
1
1
1
0
1
2
1
0
0
1
0
0
0
1
1
1
0
0
0
2
2
0
2
2
0
2
1
0
1
1
0
1
0
1
1
0
2
0
1
0
3
2
2
1
0
0
0
2
0
1
0
0
1
1
0
0
0
1
2
0
2
0
1
0
0
0
0
2
1
0
2
1
0
1
0
1
0
1
1
2
1
0
1
2
1
2
2
1
2
0
0
0
1
0
1
1
0
1
0
0
0
0
1
1
1
0
1
0
0
1
2
1
0
1
1
2
0
2
1
0
0
1
2
1
0
0
1
0
0
2
1
2
0
1
0
1
1
1
0
0
2
2
0
0
1
1
1
0
2
0
0
2
2
0
1
2
2
1
0
0
2
1
0
2
2
0
0
0
1
0
0
0
0
2
0
1
0
0
0
2
0
0
1
2
1
0
1
0
1
1
0
1
3
1
0
0
1
1
1
0
0
0
2
1
0
0
1
0
1
1
0
0
1
1
0
1
1
0
1
0
1
2
0
0
0
1
0
0
1
1
1
0
0
0
2
0
2
1
1
0
2
0
2
1
0
1
0
0
1
1
0
2
0
1
2
2
2
2
0
1
1
2
1
2
0
0
2
0
0
1
2
1
1
0
1
1
0
2
1
0
0
0
0
3
2
0
0
1
0
3
0
1
1
0
0
2
1
1
2
1
0
0
0
1
0
1
0
2
0
1
2
0
2
2
2
1
0
2
2
1
2
1
1
0
0
0
1
0
0
1
1
2
0
1
0
0
1
2
0
0
0
0
1
0
0
0
1
2
1
2
1
2
2
1
1
2
0
1
0
2
1
1
0
1
2
0
2
0
2
1
1
0
1
2
1
2
2
2
1
0
0
4
2
1
0
1
0
0
0
0
1
1
0
2
1
0
1
2
1
1
0
2
1
1
1
1
2
1
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
2
2
1
2
2
2
2
1
0
1
1
1
0
1
0
1
2
1
0
3
1
1
0
2
2
1
0
2
0
0
0
1
0
0
2
1
1
2
0
0
0
2
2
1
0
2
2
2
1
2
0
2
2
1
1
1
0
0
0
0
0
1
2
0
1
1
0
2
0
0
0
1
0
1
2
0
2
2
1
2
0
1
0
0
0
0
1
0
2
0
2
1
1
0
0
0
0
1
0
0
1
1
4
1
0
2
0
1
0
0
2
2
0
1
1
2
0
1
1
0
1
0
2
1
0
0
2
0
0
2
2
0
2
1
2
0
3
0
0
1
2
0
1
2
1
2
2
0
1
1
1
0
0
2
1
0
0
2
1
0
0
1
1
2
0
1
0
1
1
1
0
2
0
0
0
0
0
0
3
1
0
0
2
0
0
2
0
0
0
2
1
1
1
0
0
2
0
0
1
1
0
1
1
0
1
1
1
2
2
1
0
1
1
1
1
1
0
2
0
1
0
2
0
2
2
1
1
0
0
0
1
0
1
1
2
1
2
2
1
0
0
0
1
0
1
1
0
0
0
0
1
2
2
2
1
0
0
1
1
1
2
0
1
1
0
0
2
0
1
2
1
2
1
1
1
2
1
1
1
1
2
0
2
1
0
0
2
2
1
1
1
0
2
1
1
1
0
0
2
3
0
0
2
1
0
0
1
0
0
0
2
0
0
2
1
1
0
0
0
1
1
0
1
0
0
1
0
2
0
0
0
2
0
0
1
0
1
0
0
1
1
0
2
1
0
0
2
1
2
1
1
1
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
1
1
1
1
0
2
3
0
1
0
0
1
0
1
0
1
3
0
1
0
0
1
2
1
2
0
0
0
0
1
1
1
2
0
0
0
0
0
0
1
0
1
2
0
1
2
0
0
0
0
1
0
2
2
0
0
9
1
2
1
1
0
0
0
2
0
0
1
0
2
1
1
2
0
0
1
0
1
0
1
1
1
1
0
0
1
2
2
1
1
0
2
2
0
0
0
1
0
0
2
0
1
3
2
0
1
1
1
0
1
0
0
1
2
0
0
0
2
1
0
1
2
0
1
0
0
1
1
0
1
0
0
1
2
1
2
2
1
0
0
0
0
0
2
2
1
0
0
2
0
1
0
1
0
0
0
0
1
2
2
1
2
0
0
0
0
0
1
1
0
0
1
0
0
0
2
1
1
1
0
1
0
0
0
2
0
0
2
1
0
0
1
0
0
0
2
2
1
2
0
1
1
1
0
0
1
1
1
1
1
2
1
2
0
1
1
1
0
0
0
0
0
0
0
2
1
1
0
2
2
0
1
1
1
1
1
2
2
0
1
1
1
0
1
1
1
1
2
0
1
0
0
0
0
1
1
1
1
0
0
1
1
1
0
0
1
1
0
1
0
1
1
1
1
0
0
2
0
1
0
0
3
0
1
1
1
0
1
1
2
1
0
1
1
1
1
1
0
1
0
0
1
0
2
1
0
2
3
0
0
0
2
1
2
1
0
1
2
1
1
0
1
1
1
1
0
1
1
1
0
0
1
2
0
2
1
0
0
0
1
2
1
0
0
1
1
1
1
0
0
1
0
1
2
1
0
0
0
1
1
2
3
1
1
0
1
2
1
0
1
1
0
0
2
1
1
1
2
1
1
0
0
2
0
0
1
1
0
0
0
0
0
2
1
1
1
1
0
1
0
1
2
0
0
0
2
0
0
1
0
0
1
1
1
0
0
0
0
0
0
1
0
0
2
1
0
1
1
2
0
1
1
1
2
0
1
1
3
1
0
1
0
2
0
0
0
0
0
2
0
1
2
0
1
3
2
0
0
0
2
2
1
0
0
1
2
1
2
1
1
1
1
2
0
1
4
0
2
0
1
0
1
2
2
0
1
2
2
2
0
1
0
2
2
0
1
2
0
0
1
0
0
0
0
0
0
1
2
1
0
2
0
0
0
1
1
0
0
2
1
1
2
1
2
2
1
2
0
0
1
1
1
0
0
2
1
0
1
0
2
2
0
1
0
2
1
1
1
1
0
2
2
1
1
1
2
2
2
1
1
1
1
2
1
0
1
1
1
0
1
0
0
2
0
1
0
0
1
0
2
3
1
1
1
1
0
2
1
1
1
1
1
0
1
1
0
0
0
0
1
0
1
0
0
1
2
0
0
1
0
2
1
3
0
2
0
1
1
0
1
0
1
0
0
2
1
1
1
1
0
2
2
0
1
0
1
1
0
1
0
1
2
1
0
0
0
1
1
1
0
1
1
1
1
1
0
2
0
0
0
0
1
0
3
1
0
0
2
0
0
1
2
1
0
1
0
1
1
0
0
0
0
1
1
0
0
0
1
1
0
1
0
3
2
0
0
1
1
2
2
0
1
1
1
1
1
0
0
0
0
0
0
1
1
0
1
0
1
0
2
0
1
0
0
0
0
2
2
1
1
1
2
0
0
0
0
0
0
2
1
2
0
0
1
1
1
0
1
0
1
0
2
0
0
2
1
0
1
1
2
0
2
0
1
0
0
1
1
0
0
1
2
0
0
1
2
1
2
2
0
1
2
0
0
0
0
2
2
0
0
2
1
0
0
0
0
1
1
0
1
2
0
2
1
1
2
1
0
0
1
1
0
0
1
0
2
1
2
2
0
1
1
0
2
0
1
2
2
0
0
1
0
0
1
1
3
0
0
2
2
2
0
1
2
1
0
2
1
0
0
0
2
0
1
1
0
1
2
0
1
0
0
0
2
0
0
0
1
0
0
0
1
0
0
2
0
2
1
1
1
0
0
2
0
0
1
2
1
0
0
0
0
1
1
1
1
2
1
0
1
0
0
2
3
1
1
1
0
0
0
2
1
0
1
0
0
1
1
0
1
1
2
1
0
1
1
1
0
3
0
1
0
0
1
0
0
0
1
1
2
0
1
0
0
1
1
0
1
2
0
0
0
1
0
1
0
1
1
1
2
0
2
0
1
0
0
1
1
2
1
2
2
1
0
0
1
1
0
0
0
2
0
2
1
0
1
2
1
0
1
0
1
0
2
1
0
0
1
2
1
2
1
1
0
1
0
1
1
2
0
1
2
2
1
1
1
0
0
0
1
1
0
2
1
2
0
2
1
0
0
2
2
0
1
1
1
1
0
0
1
0
0
0
0
3
1
2
0
0
0
0
1
1
2
0
0
5
0
1
2
1
2
0
1
2
4
2
1
0
0
1
0
2
0
1
2
0
2
1
1
0
2
1
1
2
2
1
0
1
0
1
1
1
1
0
1
1
0
1
1
2
0
0
0
0
0
1
0
0
2
1
0
0
2
1
1
1
0
0
0
0
0
2
1
0
0
1
1
2
1
0
1
2
2
0
2
1
2
3
0
2
2
1
1
0
2
1
1
0
0
1
0
2
0
0
0
1
3
1
0
0
1
0
1
0
0
0
1
2
0
2
0
3
1
0
1
0
2
3
1
1
2
0
0
0
0
0
1
1
2
0
1
1
1
0
1
3
1
1
0
1
2
2
0
0
2
0
1
1
1
0
0
0
4
1
1
1
0
1
0
1
2
2
0
0
0
2
1
1
1
2
0
0
0
1
1
0
0
2
2
1
0
0
0
2
0
0
2
0
2
3
2
0
3
0
0
0
1
0
2
3
0
0
0
0
1
0
0
0
1
0
0
1
1
0
1
0
2
1
0
1
0
0
0
0
2
1
0
2
1
0
0
2
2
2
1
0
3
0
1
1
3
2
0
0
1
2
1
0
0
1
0
2
0
2
1
1
2
0
2
2
1
1
0
0
3
1
1
1
1
1
2
0
1
0
2
0
0
0
0
0
0
1
2
0
1
0
2
0
0
1
1
1
0
0
2
1
2
1
1
0
0
0
0
0
1
0
0
0
1
1
2
0
1
1
0
2
1
0
0
1
0
1
2
0
1
1
0
2
0
0
0
2
1
1
2
1
2
0
0
1
0
2
2
2
0
1
0
0
2
0
2
1
0
1
0
1
0
3
0
0
1
1
0
1
2
2
1
1
0
1
1
1
1
0
1
0
3
1
0
1
0
1
0
0
0
1
0
1
1
0
0
0
1
2
0
0
2
1
2
0
0
1
0
0
1
0
1
2
1
1
1
0
0
1
0
2
1
0
0
3
0
0
2
0
1
0
0
0
0
1
1
0
0
0
1
1
0
1
2
1
0
1
0
2
2
2
1
1
0
1
0
0
1
1
1
0
2
0
1
1
1
0
1
1
1
0
0
1
1
1
2
0
1
0
0
1
0
0
1
1
0
1
0
2
1
0
0
0
2
0
1
0
1
2
2
0
1
0
2
1
1
0
0
0
1
0
0
2
1
0
0
0
0
1
1
0
0
0
1
0
2
1
0
0
0
1
1
0
1
0
4
1
0
1
2
0
0
1
0
0
0
2
1
2
0
1
1
1
0
2
1
2
0
0
0
0
1
1
0
0
0
0
2
1
0
1
1
0
0
0
2
0
1
0
1
1
1
1
1
1
0
0
0
1
0
0
0
0
0
1
0
1
0
2
1
4
2
3
0
2
0
0
1
1
2
1
0
0
2
0
0
1
0
0
2
2
1
1
0
0
1
1
1
0
2
0
1
0
2
0
0
1
1
2
1
1
2
0
0
3
0
1
0
1
1
2
2
0
0
0
1
0
0
1
2
0
2
2
2
0
2
0
2
1
1
2
1
0
1
1
1
0
0
0
0
0
0
2
1
2
1
2
1
1
0
1
0
0
1
2
0
2
0
2
0
0
2
0
0
1
2
2
0
1
0
1
0
3
0
1
1
2
0
1
0
0
1
1
2
1
0
2
0
0
0
2
0
2
2
0
2
0
2
1
0
1
0
0
0
1
1
1
1
1
1
0
0
1
1
0
1
2
0
2
0
0
0
1
0
0
2
1
2
0
2
1
2
0
0
1
0
1
1
1
0
0
0
2
2
0
1
0
0
0
1
0
2
0
1
0
1
0
0
1
0
0
0
2
2
1
0
0
2
1
2
0
2
0
2
0
2
0
0
0
0
1
0
1
0
0
0
3
1
1
1
1
0
2
0
1
1
2
0
1
1
1
0
0
0
0
1
1
0
2
0
1
2
0
0
0
1
0
2
0
2
1
1
1
1
2
1
1
0
0
1
2
2
1
2
0
1
2
1
0
0
0
2
2
0
0
0
2
1
0
1
2
0
0
0
2
1
0
1
0
1
0
1
1
1
0
1
0
2
0
2
1
0
0
1
2
0
1
1
2
2
1
0
1
0
0
0
1
0
0
2
1
0
1
1
0
0
2
1
2
1
0
0
1
0
2
0
3
0
1
1
2
0
2
2
0
1
0
0
1
1
0
1
1
0
1
1
2
1
1
0
0
0
0
2
0
0
1
0
1
0
1
0
2
2
1
1
0
0
4
0
0
1
0
0
1
0
1
0
0
1
0
1
2
4
1
2
0
2
0
1
2
0
1
2
0
2
2
1
0
2
2
0
2
1
0
1
0
2
1
2
1
2
0
0
0
0
1
0
0
0
0
1
0
0
0
2
1
1
0
1
1
2
0
1
1
2
1
1
1
1
2
0
1
0
1
2
0
1
1
1
1
1
1
1
1
0
2
0
1
0
1
0
0
1
1
0
0
0
0
2
0
1
2
0
0
0
0
0
1
1
0
0
2
0
1
2
2
2
1
1
0
2
0
0
0
0
1
2
0
1
0
0
1
1
0
0
0
0
2
0
0
0
2
0
0
1
3
1
2
1
1
1
0
0
0
1
0
0
2
1
1
2
1
0
0
1
3
0
1
2
2
1
1
0
0
1
2
2
2
0
0
1
0
1
1
0
0
2
1
1
2
1
1
2
0
0
2
2
0
1
0
0
0
0
1
0
1
1
0
0
0
2
2
2
1
3
0
1
0
4
0
1
2
1
0
1
2
0
1
1
1
1
0
2
1
1
0
0
1
2
0
1
2
0
0
2
1
2
2
0
2
0
0
2
0
3
0
2
1
1
0
1
0
1
2
1
2
0
2
0
1
2
2
1
1
0
1
1
0
1
0
2
0
1
0
0
2
1
0
0
0
1
1
1
2
0
0
1
1
0
1
1
1
1
0
0
1
0
1
1
0
0
1
2
1
0
1
0
1
1
3
1
1
0
1
0
2
1
0
2
1
1
0
1
0
1
0
3
1
0
1
0
0
1
2
1
0
3
1
1
1
2
2
2
0
0
0
1
3
2
1
1
0
2
1
0
0
0
1
0
0
2
0
1
0
1
0
1
2
0
2
1
0
1
1
1
1
2
0
1
0
1
0
1
0
1
0
2
2
0
1
0
1
1
0
1
1
1
0
0
7
0
2
2
2
0
0
2
2
0
0
2
1
0
1
0
0
2
0
1
2
0
1
1
1
0
1
0
1
0
0
1
0
1
0
0
1
0
1
2
0
2
0
1
0
1
2
0
1
0
0
1
1
2
1
0
0
2
2
1
0
1
1
1
0
2
2
2
0
1
1
0
0
0
0
0
2
1
2
1
0
1
0
1
0
0
0
0
0
2
2
2
0
0
1
1
1
2
0
0
1
2
0
0
2
2
1
0
0
1
0
0
1
0
1
0
0
0
0
0
1
1
0
0
1
1
0
1
0
0
2
0
1
0
0
0
1
2
1
0
2
1
1
0
1
1
0
1
0
1
2
1
1
0
1
1
2
2
2
1
0
2
2
0
1
1
1
1
2
0
1
1
2
1
1
1
0
0
0
0
0
1
0
0
0
2
0
2
1
0
0
1
2
1
0
1
0
0
1
0
1
0
0
1
2
0
3
1
0
1
0
0
1
1
2
1
0
0
0
0
2
0
0
1
1
0
1
0
2
2
0
0
0
3
0
1
0
1
1
1
0
0
2
0
0
1
0
0
1
2
0
1
2
2
1
2
0
1
0
1
1
1
0
1
2
0
2
0
1
0
2
2
0
2
2
1
2
0
1
1
1
1
0
1
1
0
0
1
0
2
1
1
1
1
0
0
2
0
1
1
2
0
0
0
2
2
2
0
0
0
2
1
1
0
2
2
0
1
1
1
0
0
1
1
1
0
0
1
0
2
1
1
0
0
1
0
0
0
1
1
1
2
2
0
0
0
0
0
1
0
1
2
0
1
0
2
0
0
2
0
0
0
1
0
3
0
0
1
0
1
0
0
0
1
2
0
1
1
0
2
1
2
0
1
0
3
1
0
0
2
0
2
0
0
0
0
2
0
1
0
2
0
1
1
1
1
2
1
0
1
0
0
1
1
0
1
0
1
0
0
1
0
2
1
1
0
2
0
0
1
2
2
0
0
1
0
0
0
0
2
0
0
1
1
0
0
1
0
0
1
1
1
1
2
0
1
0
2
0
1
1
1
2
1
2
1
0
2
0
2
1
1
2
2
1
0
0
1
1
0
0
0
1
0
2
2
1
2
1
2
2
2
1
0
0
0
2
0
1
1
1
1
3
0
0
2
0
2
0
0
0
0
3
3
0
0
1
1
2
0
1
0
0
2
2
0
2
2
0
0
1
0
0
0
0
1
0
0
0
0
0
1
2
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
2
2
1
1
2
1
2
0
2
0
0
1
2
0
1
2
0
2
4
2
0
2
1
2
0
2
0
2
0
0
1
0
0
0
1
1
1
2
2
0
1
0
2
0
0
2
0
1
1
2
2
0
2
0
1
0
1
2
0
2
1
0
1
2
0
0
0
0
0
1
1
2
0
2
1
0
1
1
2
0
2
1
0
2
1
1
1
2
0
2
2
1
2
0
2
0
1
0
2
0
0
1
0
0
0
0
2
2
1
1
1
2
0
0
0
1
2
2
1
1
0
0
0
1
0
2
2
1
0
2
0
0
2
0
1
0
2
0
1
2
0
0
1
1
0
2
1
1
1
0
1
0
0
0
1
1
0
2
1
0
0
2
0
0
1
2
0
0
0
1
1
2
0
1
0
0
1
1
1
1
2
1
1
0
0
1
1
0
0
0
1
0
1
2
1
0
0
1
0
3
2
0
1
0
1
0
3
0
0
0
0
0
0
2
0
0
0
3
0
0
1
0
1
0
1
0
0
0
1
0
1
2
0
0
1
2
2
2
0
1
0
1
2
2
0
2
2
0
1
2
0
2
1
1
0
2
0
1
2
1
0
0
0
0
0
1
0
1
0
0
0
1
2
1
0
0
0
0
0
0
2
0
1
0
0
2
1
1
0
0
0
0
0
1
0
0
1
1
0
2
1
2
0
1
0
0
1
0
1
1
0
1
1
1
1
1
0
2
0
2
0
0
0
1
0
1
2
1
1
2
0
0
1
0
0
0
0
0
2
0
0
1
1
3
0
0
0
2
2
2
1
1
2
2
3
0
0
0
2
1
2
1
4
0
1
0
0
2
1
0
1
1
2
0
2
0
0
3
1
1
1
0
1
0
0
0
2
2
1
1
2
1
0
0
1
0
1
2
0
1
0
1
1
0
1
0
0
1
0
0
0
1
2
1
1
0
1
0
2
0
0
0
1
0
1
0
2
0
1
0
2
1
0
4
0
0
1
0
1
1
0
0
0
1
1
2
0
1
0
0
2
1
0
1
0
1
0
0
0
2
1
1
1
2
0
0
0
1
0
0
1
1
0
0
0
0
1
2
0
2
0
0
2
1
0
0
2
1
2
0
2
0
0
0
3
1
1
2
0
1
0
0
0
0
1
1
1
0
1
0
0
2
1
1
3
2
1
0
0
0
2
1
0
0
0
1
2
1
0
1
2
1
1
1
0
1
1
2
0
1
0
0
0
1
1
2
2
0
2
0
0
1
2
0
2
0
2
0
0
2
0
0
0
0
0
2
2
0
1
1
1
0
0
1
0
0
1
0
2
0
0
0
0
2
1
0
1
0
2
1
2
1
0
1
0
2
1
1
1
0
1
0
0
1
0
1
1
2
0
0
2
0
1
0
1
1
0
1
1
3
1
2
0
1
1
1
1
0
0
0
2
1
0
0
0
0
2
1
2
0
1
1
0
1
1
0
0
0
1
0
1
0
1
0
0
0
1
1
0
1
1
0
1
0
1
1
1
0
0
1
0
0
0
2
1
1
2
2
2
0
1
0
2
1
0
1
0
0
0
2
0
1
0
1
0
0
0
0
0
1
0
2
0
1
1
2
1
0
1
1
7
1
0
2
1
0
1
2
1
2
1
1
0
2
2
1
2
2
2
0
0
1
0
0
1
1
0
1
0
2
1
2
1
2
1
0
2
1
1
2
1
1
2
0
1
0
0
0
2
3
1
2
0
0
2
0
2
0
1
1
1
0
1
0
0
1
0
1
1
2
0
1
0
0
2
0
0
0
0
1
2
0
3
2
0
6
0
0
3
2
2
1
0
0
0
11
2
0
1
1
2
0
1
0
1
1
2
1
0
0
2
0
2
1
0
0
5
1
0
1
0
0
0
1
1
0
2
2
2
1
1
0
1
0
0
2
0
0
1
0
2
1
0
0
1
1
1
2
1
1
1
1
0
0
0
0
0
1
0
1
1
1
0
0
2
1
0
1
0
0
1
1
1
1
1
1
1
0
2
0
0
0
0
1
1
5
0
0
0
0
0
0
0
1
2
1
0
0
2
0
1
3
0
1
0
1
0
1
0
0
1
0
1
1
1
0
1
1
0
1
0
1
0
2
2
2
0
0
2
0
1
0
1
1
3
2
1
2
0
2
2
1
1
0
0
2
2
0
1
0
1
0
0
0
3
2
0
2
1
0
0
2
1
2
0
0
0
1
0
1
0
0
1
0
2
1
0
0
2
0
2
1
1
0
0
0
3
1
2
2
1
1
2
1
1
0
1
1
0
0
0
0
2
1
2
1
2
0
0
0
1
0
1
0
0
1
1
0
2
1
1
0
1
0
0
1
0
0
2
2
2
0
1
0
2
1
1
0
0
1
1
0
1
2
2
0
2
1
1
2
2
2
0
0
1
0
0
1
1
2
1
0
1
0
2
0
2
0
0
1
2
1
2
2
0
0
1
2
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
2
1
3
0
0
1
1
2
1
3
1
1
1
2
0
1
0
5
1
0
2
1
0
0
1
1
0
0
1
1
2
2
1
1
2
2
0
1
2
0
0
0
0
0
1
0
1
2
1
1
0
1
0
0
0
2
0
0
1
1
1
2
2
2
0
0
1
2
1
0
1
0
0
1
1
1
2
0
0
1
1
2
1
2
0
0
2
1
1
2
0
0
0
0
1
1
2
2
3
2
1
2
0
0
0
0
1
1
2
2
2
0
3
2
0
2
2
2
2
0
2
1
0
0
2
1
0
0
5
4
0
1
1
0
1
0
1
1
1
1
0
0
0
1
2
1
2
0
1
0
1
0
1
0
0
1
1
1
1
0
0
0
0
0
2
0
0
0
2
1
0
2
1
2
0
0
4
1
0
0
2
0
1
0
0
1
0
1
1
0
2
1
0
0
0
1
1
1
0
1
1
0
2
0
0
0
0
0
1
1
0
1
0
2
1
2
1
0
0
1
0
0
1
0
1
1
2
0
0
2
1
1
1
1
0
2
0
1
2
2
3
0
0
0
0
1
1
0
1
2
2
1
0
0
2
0
0
0
1
0
1
1
1
0
0
1
2
2
2
0
1
0
2
0
1
0
1
0
0
2
2
2
1
0
0
2
1
0
0
0
2
1
2
0
0
2
1
18
2
1
2
2
0
2
0
2
1
0
0
0
1
0
2
1
2
1
2
1
0
2
1
1
2
1
0
2
0
1
1
1
0
1
2
2
0
0
2
0
1
5
1
1
2
2
1
2
2
0
0
1
2
0
0
1
1
1
2
0
0
0
2
0
0
0
2
1
0
0
2
1
2
1
1
0
0
0
0
0
0
0
2
0
1
2
2
0
1
0
0
1
1
0
0
1
0
2
2
0
0
1
0
1
0
1
3
1
1
0
1
0
1
1
1
0
2
2
1
0
1
2
1
1
0
1
2
0
1
1
0
0
1
1
2
1
0
0
2
2
2
1
1
1
2
1
1
0
0
1
0
2
0
1
1
1
3
0
1
2
2
1
1
1
1
0
2
1
3
1
1
0
2
0
2
1
2
2
0
1
0
1
1
0
0
0
1
0
1
2
1
1
1
2
1
1
0
1
0
1
2
1
2
0
2
0
0
2
1
1
2
1
1
0
1
0
2
2
2
0
0
0
2
0
0
0
0
0
1
1
0
1
1
1
1
0
1
1
1
2
0
1
0
1
1
1
1
0
1
2
0
2
1
1
0
1
0
0
1
0
0
0
0
1
2
1
0
0
1
1
0
1
1
0
0
0
0
0
1
0
0
1
0
1
2
2
0
0
1
0
0
0
0
1
0
2
1
2
1
1
1
3
1
0
1
0
0
2
1
0
1
0
0
1
0
1
1
0
0
2
0
0
1
0
1
0
0
0
0
2
0
0
2
0
1
0
1
0
0
0
2
2
0
1
1
2
0
1
0
0
1
1
0
0
1
1
0
1
0
1
1
2
0
2
0
0
2
2
2
0
0
0
2
1
2
0
0
1
0
0
2
1
1
1
2
0
0
0
0
0
1
1
1
2
0
1
0
0
2
1
0
0
0
1
1
0
1
0
1
1
0
2
1
3
1
0
1
2
2
1
0
1
1
2
0
0
0
0
1
0
2
2
1
0
3
1
1
0
0
0
2
2
0
1
1
0
1
0
0
1
0
1
1
2
1
2
1
0
1
0
0
1
1
1
0
1
0
0
0
1
1
1
0
1
1
2
1
1
0
1
0
2
2
2
2
2
0
0
0
1
1
2
1
0
1
1
2
1
1
0
1
1
2
0
1
0
1
0
1
0
1
1
0
2
0
1
0
2
0
0
1
1
0
2
1
1
2
0
0
1
1
0
1
0
1
1
1
1
1
2
0
1
1
1
0
1
1
1
1
0
0
0
0
0
0
2
2
1
2
1
1
3
1
1
1
1
2
2
2
2
0
2
1
2
1
1
1
0
2
1
0
1
0
0
2
0
0
1
1
0
1
0
1
0
0
0
0
1
1
1
2
0
0
0
1
1
0
0
2
2
3
0
1
0
0
1
2
0
2
0
1
0
1
1
1
0
2
0
0
1
0
2
1
1
1
1
1
1
0
1
1
0
2
1
1
2
1
0
1
0
1
2
2
1
2
2
0
1
0
1
1
0
0
1
2
0
2
1
2
0
1
1
2
1
0
0
0
0
1
2
2
0
0
1
2
0
1
1
2
0
0
2
0
0
3
0
2
0
0
0
0
1
2
0
0
1
1
0
0
1
0
0
1
2
1
0
1
1
1
0
2
0
1
2
0
2
1
2
1
0
0
0
0
1
0
2
0
1
1
0
0
0
0
1
1
2
0
0
0
0
0
1
1
2
0
0
1
2
2
0
2
0
0
1
1
1
1
2
0
0
2
3
2
2
1
1
1
0
1
1
1
2
2
0
0
2
2
2
2
2
1
1
1
0
1
1
0
1
1
0
0
0
0
1
0
0
1
0
2
0
2
0
1
1
2
0
0
2
1
0
2
1
1
0
1
1
1
2
1
2
2
0
1
1
0
2
1
0
0
1
0
1
2
0
0
1
1
4
0
0
1
0
2
0
1
2
1
2
1
0
1
2
1
0
0
2
1
2
0
0
1
1
1
1
0
2
0
1
1
1
1
0
1
1
0
0
2
0
1
1
0
2
1
1
2
2
0
1
2
0
1
1
2
1
0
2
0
2
0
2
3
2
2
1
0
0
0
0
2
1
0
0
1
2
0
0
1
0
1
1
1
1
0
0
1
0
0
0
0
0
1
0
0
1
0
1
1
1
0
0
1
1
2
2
0
1
0
1
2
2
0
2
2
2
0
0
0
0
1
0
1
1
1
0
2
2
0
2
1
2
1
1
2
1
0
0
0
0
2
0
0
2
1
1
0
2
1
1
0
1
0
0
2
1
0
1
1
0
2
1
0
2
2
2
0
1
2
1
1
0
0
2
1
1
1
0
0
0
0
0
2
0
1
1
1
0
0
2
0
0
0
1
0
1
1
2
0
0
2
3
0
3
0
0
1
2
1
0
0
1
2
1
1
0
1
1
2
2
1
1
1
0
2
2
2
1
1
0
0
0
0
0
0
2
0
0
0
0
1
1
1
0
0
1
2
4
1
2
0
3
0
0
0
0
2
0
2
0
1
2
1
0
2
2
0
0
3
2
1
0
1
2
0
3
1
1
2
1
0
1
0
1
0
0
2
1
1
0
0
0
0
0
2
1
2
2
2
1
0
0
1
0
1
0
1
2
1
1
0
2
2
0
2
1
0
5
0
2
0
0
3
0
0
0
0
1
1
0
1
1
1
1
2
0
1
1
0
2
2
0
0
0
2
0
0
1
1
2
1
2
1
1
1
0
1
0
1
2
2
0
1
2
0
2
1
0
0
1
2
1
2
0
2
2
2
0
0
0
0
0
1
0
0
0
2
1
0
0
1
1
1
1
0
1
1
0
0
1
1
1
0
1
1
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
1
0
1
1
2
1
1
1
1
1
0
2
2
0
1
2
2
1
1
0
0
2
2
1
0
0
0
1
1
1
1
0
2
1
2
0
0
2
0
2
0
0
1
2
2
1
1
0
1
0
1
1
0
1
2
1
2
0
1
0
0
1
1
0
1
2
2
0
0
0
1
1
2
0
0
2
1
0
0
2
1
1
1
0
0
0
0
0
1
1
1
0
1
0
1
1
2
1
0
2
2
1
2
0
0
1
0
0
1
0
2
0
0
0
0
2
0
0
1
1
0
0
1
2
1
1
1
0
2
0
0
1
1
0
2
0
0
2
0
1
0
0
1
1
1
0
1
1
2
1
0
0
0
1
2
0
0
1
2
1
0
0
0
0
0
0
1
2
1
2
2
1
0
4
1
0
0
1
0
2
2
0
2
1
2
0
0
1
1
1
0
0
0
1
1
0
0
0
2
2
1
0
2
0
0
1
1
2
2
1
1
2
0
1
1
0
1
0
1
2
2
0
1
0
1
0
1
0
2
0
1
1
0
0
0
0
3
0
0
1
0
1
1
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
2
2
2
0
2
2
2
1
0
0
1
2
4
1
2
0
0
0
0
0
0
2
0
1
1
1
2
0
2
1
1
0
2
1
0
0
1
0
0
1
1
8
2
0
0
2
0
1
1
0
0
0
1
1
1
0
1
2
1
0
1
0
0
0
1
0
0
1
0
0
2
0
1
0
2
2
0
1
1
2
2
3
0
1
0
2
2
1
1
1
1
0
1
0
1
0
1
1
1
0
0
1
0
2
0
1
1
0
1
0
2
1
0
2
0
1
1
0
1
1
0
2
1
0
0
1
2
2
2
2
0
1
0
2
1
0
2
1
1
1
1
0
1
0
0
1
1
0
2
2
1
1
1
1
1
0
0
1
1
0
2
1
0
0
1
0
2
1
0
0
2
1
0
1
0
0
0
0
1
0
1
1
1
1
0
0
0
1
1
2
0
2
1
0
2
0
1
1
0
2
0
3
1
0
1
0
1
0
0
0
1
0
0
2
0
1
0
1
0
2
0
0
2
1
1
0
0
0
0
1
0
0
2
0
1
0
1
1
2
0
0
1
1
0
1
1
1
1
3
1
0
2
1
2
0
1
1
0
1
2
1
0
2
1
1
2
0
1
2
2
2
2
2
1
1
1
2
0
1
0
1
2
0
1
1
2
0
1
2
2
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
2
0
2
1
1
2
1
1
1
3
2
2
0
1
0
0
1
1
2
1
0
1
1
1
1
1
0
0
2
1
0
1
2
0
1
0
0
2
1
1
1
2
1
1
2
0
1
1
0
1
0
0
0
0
1
1
1
2
0
0
1
0
0
2
2
0
0
1
1
1
1
2
1
0
1
0
9
2
0
2
1
0
3
1
0
0
1
0
1
0
0
1
0
0
2
0
1
0
1
1
2
1
2
0
0
0
0
0
0
0
1
1
0
1
0
2
2
0
0
1
2
3
1
1
0
0
0
0
0
1
0
2
1
2
0
3
2
0
0
2
2
0
0
0
0
2
1
0
1
0
1
0
1
0
2
2
0
0
2
1
1
2
1
0
0
0
1
1
0
0
1
0
1
1
0
0
0
2
1
0
1
1
1
0
2
1
1
2
2
1
0
1
0
1
0
1
1
1
2
2
1
0
1
1
1
0
0
0
2
0
0
3
1
0
1
2
0
1
1
0
1
0
1
0
0
0
0
1
2
1
0
1
1
0
0
1
0
0
1
0
0
0
2
0
2
2
0
1
2
1
0
2
1
0
1
2
1
1
1
1
0
1
1
2
2
0
2
1
1
2
0
1
2
0
2
1
1
0
0
0
0
1
1
1
0
2
1
1
1
1
1
1
1
0
3
1
1
0
1
1
0
1
1
0
0
2
0
0
0
2
1
1
0
0
1
1
0
0
1
0
0
2
2
1
0
0
2
1
0
1
0
1
0
2
2
0
0
0
0
1
3
0
0
1
0
2
1
2
1
0
1
1
0
0
0
2
1
1
2
0
0
2
2
1
1
2
2
0
1
0
1
2
2
0
2
0
0
0
2
0
3
1
0
1
0
0
2
0
0
1
0
1
1
1
1
0
1
1
0
0
1
1
2
0
0
2
0
0
0
1
1
1
1
1
1
1
1
1
0
1
0
2
0
0
0
1
2
1
0
0
1
0
1
0
1
0
0
0
0
0
1
1
0
1
0
3
1
2
1
1
0
1
1
0
1
2
0
2
0
0
1
1
0
1
1
0
0
0
1
1
2
1
2
2
2
1
1
0
0
0
0
0
2
0
1
1
1
2
1
0
2
0
2
0
0
0
0
0
2
1
0
2
0
2
1
1
0
5
2
0
1
1
2
1
1
0
0
2
0
2
0
4
0
0
0
3
0
0
2
2
0
0
1
2
1
0
1
1
2
0
2
2
0
1
1
0
2
1
0
0
0
2
1
2
2
1
1
0
1
2
1
1
0
0
2
2
1
2
1
0
2
1
0
1
2
0
1
1
1
0
0
1
1
0
1
0
2
1
1
0
0
0
1
0
1
1
0
2
0
0
2
2
1
0
1
2
3
0
0
2
1
1
1
1
0
2
2
0
2
2
1
0
2
5
0
2
1
0
1
1
1
0
1
1
1
1
1
1
1
5
0
2
0
1
1
2
2
1
0
1
0
0
1
2
0
0
2
2
2
1
1
1
1
1
2
1
1
1
1
2
1
0
0
2
2
0
1
0
0
1
1
0
0
1
1
1
2
0
0
2
0
0
1
1
1
3
2
2
1
0
1
2
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
2
1
0
0
1
2
0
2
2
0
1
0
0
0
0
0
2
1
0
0
1
0
2
1
0
1
0
0
1
1
0
1
2
0
2
1
0
1
1
1
0
0
0
0
0
1
0
0
1
2
0
0
1
0
0
0
0
0
0
1
1
0
1
2
0
1
0
2
1
1
2
1
2
2
0
0
2
1
2
0
0
1
1
1
1
0
2
0
2
0
1
0
2
0
1
1
1
1
0
1
0
0
2
0
1
0
1
0
1
1
1
1
1
1
1
0
0
1
1
0
1
1
0
0
0
0
1
0
2
0
2
0
0
0
0
2
2
1
0
0
0
0
0
0
0
1
2
1
1
1
1
1
0
1
2
0
0
1
0
0
0
1
1
6
0
0
0
1
2
1
1
2
1
1
2
1
1
1
0
1
0
2
1
0
3
0
1
1
2
0
1
0
1
1
1
2
1
0
0
0
2
2
1
1
1
2
0
0
0
1
0
0
0
0
1
0
2
0
0
1
0
1
0
1
2
0
2
2
0
1
0
0
0
0
1
1
1
1
0
1
1
1
2
3
1
2
1
0
0
1
0
1
1
1
0
1
2
1
0
1
1
2
2
1
1
2
0
0
1
1
1
2
1
2
2
0
0
0
0
1
0
4
0
0
1
2
0
2
1
0
0
1
1
2
0
0
0
0
0
1
1
0
1
0
0
0
1
2
2
0
0
0
0
1
1
2
2
3
2
0
2
2
2
2
0
1
1
0
0
0
1
3
1
1
2
1
0
0
0
0
2
0
0
0
1
0
0
0
2
2
0
2
0
2
1
2
2
1
0
0
0
1
2
3
0
0
1
2
0
0
0
0
1
0
1
0
1
0
1
1
1
0
1
2
1
1
0
1
1
0
0
0
0
2
2
0
0
1
4
2
1
2
0
0
0
1
0
0
1
0
3
0
2
1
0
0
0
0
0
1
0
1
0
1
1
1
0
1
0
1
1
0
0
2
1
2
1
0
1
0
0
0
1
0
0
1
0
2
1
2
2
1
1
1
0
2
0
0
1
0
0
0
0
1
0
2
0
0
2
1
0
0
0
1
1
1
2
2
0
1
0
0
2
2
2
0
0
1
0
2
1
1
0
0
0
0
2
2
0
1
0
2
2
1
2
0
0
0
1
2
1
0
1
0
1
1
0
1
1
0
1
2
0
0
1
0
1
1
0
0
0
0
1
1
0
1
0
1
0
2
1
1
0
2
0
2
0
1
0
2
1
0
1
1
0
0
0
1
2
1
0
0
1
2
0
1
0
1
1
0
0
1
0
2
1
2
2
0
2
1
3
1
1
1
0
1
0
1
0
0
1
0
1
0
1
2
0
2
2
5
0
1
1
0
2
2
0
1
0
1
0
0
2
1
2
2
0
1
1
1
1
1
2
1
0
0
0
1
2
0
0
0
0
0
1
0
2
2
2
1
0
1
0
0
2
0
2
2
1
0
0
1
0
0
0
0
0
0
1
1
1
2
2
2
2
1
1
1
0
0
1
1
0
0
1
0
0
0
1
1
0
0
1
3
1
0
0
0
0
1
0
1
0
0
1
1
0
0
0
1
1
0
0
0
1
2
0
1
2
1
0
1
0
0
2
1
2
0
1
0
0
1
2
0
2
2
1
0
1
0
1
0
0
0
2
0
0
1
2
0
1
0
0
2
0
2
1
1
1
2
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
2
0
1
0
1
1
1
1
1
1
1
0
1
2
0
1
0
1
1
1
0
1
2
1
0
0
1
0
2
1
2
1
1
0
0
0
2
2
0
1
1
1
1
1
2
0
0
0
0
0
1
1
0
0
1
2
0
0
2
0
0
0
1
1
2
3
0
0
0
0
0
2
1
1
0
1
0
2
1
0
1
0
2
0
2
0
2
2
1
1
1
1
0
1
0
1
2
2
1
1
0
1
1
2
2
0
0
2
1
2
0
0
2
1
1
1
1
2
2
5
0
0
0
2
0
0
0
1
2
2
0
1
2
0
0
1
2
1
0
2
0
0
1
0
1
0
2
0
2
0
0
2
1
2
2
2
1
1
2
0
0
0
0
1
2
2
1
0
0
1
2
0
0
1
1
2
0
0
2
0
1
3
1
0
0
2
2
2
1
0
0
0
1
1
2
0
0
0
2
2
2
0
1
0
1
0
2
1
1
1
0
0
0
1
1
0
0
2
0
0
1
0
3
1
0
0
0
1
0
1
0
2
1
1
1
0
1
1
0
0
1
1
1
2
1
0
1
0
1
0
0
2
1
2
1
1
0
1
0
0
1
0
1
0
0
2
2
1
0
1
0
0
0
0
2
1
0
1
2
0
0
0
0
1
1
2
1
0
1
1
2
1
1
0
0
0
1
0
1
0
0
0
2
1
1
2
3
0
1
0
0
1
2
1
3
2
0
1
0
1
3
0
0
0
1
0
0
1
2
0
3
0
2
2
2
1
1
1
0
0
0
1
0
2
0
1
2
0
0
0
0
0
1
1
2
1
1
2
0
1
0
0
1
0
0
0
0
2
1
1
0
2
2
2
2
0
2
0
0
2
0
0
0
0
0
0
1
3
2
0
2
1
1
1
2
1
1
2
0
0
0
2
0
0
1
1
0
1
2
1
0
0
2
0
0
1
1
0
2
1
0
0
0
0
0
2
0
0
1
0
0
1
1
0
1
2
0
0
1
0
0
1
0
0
1
1
0
0
2
0
0
1
1
1
0
0
0
1
0
2
1
1
0
1
2
0
1
1
2
0
1
1
1
0
0
0
2
0
0
2
0
0
1
0
1
0
0
1
1
1
0
1
0
1
0
2
0
1
0
1
1
1
0
0
0
2
0
1
2
0
1
1
1
0
0
0
0
0
1
0
2
0
1
1
1
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
2
2
1
0
0
0
1
1
1
2
0
0
1
1
2
2
0
1
0
1
2
1
0
1
0
1
0
0
1
0
2
0
2
2
1
1
1
3
2
1
2
2
1
0
0
0
2
1
0
1
0
0
0
1
0
0
0
2
0
1
0
1
2
0
0
2
1
2
1
0
1
0
3
0
1
2
1
0
0
0
0
1
0
0
0
1
2
0
1
0
0
2
0
0
1
1
1
2
0
1
0
0
0
2
1
1
0
1
1
2
5
0
1
2
0
0
2
0
0
2
0
0
1
2
1
1
0
0
0
0
1
0
2
1
0
0
0
0
0
1
1
0
1
1
0
1
0
0
2
1
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
2
2
0
0
1
1
0
2
0
2
1
0
2
0
0
0
1
1
2
1
1
2
0
2
0
0
0
1
2
2
1
2
1
1
2
1
0
2
0
0
0
3
1
0
0
2
1
1
1
0
0
2
2
2
0
0
0
0
0
1
1
0
0
0
0
2
1
0
1
0
0
1
0
2
0
0
0
3
0
0
1
0
0
0
0
1
0
2
0
0
0
2
3
1
1
0
1
2
0
0
1
0
2
1
0
0
2
0
2
2
1
0
1
0
0
0
1
0
0
1
2
1
0
1
0
0
1
1
2
1
1
0
1
0
1
0
2
0
2
0
1
2
0
1
3
1
1
2
2
0
0
1
2
0
0
0
1
1
1
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
1
0
2
0
0
2
1
1
2
0
1
0
0
1
0
2
2
0
0
0
1
0
1
1
0
0
0
2
1
0
1
0
1
1
1
2
0
1
1
2
0
0
2
2
1
0
1
1
0
0
1
2
3
2
3
0
0
0
1
2
0
0
4
1
0
1
2
1
0
1
0
1
1
0
1
0
2
0
0
0
1
2
2
0
2
1
3
1
0
1
1
0
2
2
1
2
1
0
1
1
1
1
1
1
0
3
0
0
2
0
2
1
0
1
2
2
0
0
1
2
2
0
0
0
1
1
2
2
0
0
1
0
2
2
2
0
1
2
0
1
0
1
0
0
2
2
0
0
1
1
0
2
0
0
2
1
1
2
1
1
0
0
1
2
0
0
0
1
1
1
0
0
0
1
1
1
1
2
2
1
0
1
1
2
1
1
0
2
0
1
1
1
0
2
1
2
0
1
1
0
3
1
2
3
1
1
0
0
1
2
1
2
0
1
0
0
1
0
2
1
0
1
0
0
0
0
1
0
0
1
2
0
3
2
2
0
2
0
2
1
2
0
0
1
0
2
0
0
0
1
2
0
1
2
3
0
0
0
0
0
0
2
0
1
1
1
2
0
1
1
2
3
1
1
0
3
1
1
0
0
0
0
0
0
1
0
0
0
2
1
0
1
1
1
2
0
0
1
1
0
3
1
1
2
0
1
0
1
0
0
0
3
2
1
1
1
1
1
1
0
0
0
1
1
0
4
0
1
1
2
0
2
0
0
2
2
0
1
1
2
1
0
2
1
2
1
1
1
2
0
0
0
0
0
0
2
0
2
0
0
0
2
2
1
0
1
1
0
1
0
0
0
0
1
0
0
0
2
1
0
0
0
1
1
1
2
2
1
1
1
0
0
0
1
1
0
0
2
1
0
0
2
1
1
0
0
3
1
1
1
1
1
0
0
1
0
2
0
2
1
0
0
1
0
2
1
1
0
1
1
0
0
3
0
1
1
0
0
2
0
0
1
0
1
0
0
2
2
0
1
1
0
0
2
1
2
1
0
0
1
0
1
0
0
0
1
3
0
2
1
0
1
2
0
0
2
0
0
0
0
2
2
0
0
0
0
0
3
1
3
1
0
2
0
1
2
0
1
3
1
0
0
0
0
0
0
1
1
0
0
1
2
0
1
0
0
2
1
2
1
2
0
1
0
3
2
1
1
1
0
1
1
3
0
1
0
1
0
2
1
2
1
3
0
1
1
1
2
2
0
0
0
1
1
0
0
2
2
1
0
1
0
0
2
1
1
0
0
0
0
1
0
1
0
0
0
0
0
1
2
0
2
1
0
0
1
0
0
2
2
1
0
1
0
0
1
0
1
2
2
0
0
2
1
0
0
0
1
2
0
1
2
0
1
2
1
1
1
3
1
1
2
2
0
1
1
2
0
0
2
2
2
0
0
2
1
0
2
1
1
0
2
2
0
0
0
1
0
1
1
1
0
2
2
0
1
5
0
1
2
0
0
2
1
1
1
0
1
1
1
2
1
1
0
0
2
1
1
2
0
2
1
1
2
1
1
0
2
0
1
0
1
2
0
1
1
1
0
0
0
0
1
2
0
1
2
1
0
0
0
1
1
0
0
0
0
0
0
2
0
2
1
1
1
2
0
1
1
1
0
0
2
1
0
1
1
2
1
0
0
1
1
2
0
0
0
0
2
1
0
1
2
0
0
0
1
1
1
2
0
1
0
0
0
0
0
2
3
0
0
3
1
0
1
0
1
1
3
2
0
0
0
1
2
0
1
1
4
1
1
2
1
1
0
2
1
1
0
2
1
0
1
1
0
1
0
1
2
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
2
2
0
0
2
0
2
1
1
0
0
0
0
1
1
0
1
0
1
0
0
2
2
1
1
1
1
0
0
2
0
1
2
0
0
1
2
2
0
0
1
0
2
1
0
2
1
1
1
0
1
2
1
1
1
1
0
1
0
1
0
2
1
0
0
0
1
1
1
2
1
0
1
1
1
0
0
0
1
2
1
0
1
4
0
0
0
0
2
1
0
1
3
0
0
2
1
1
2
1
1
0
0
0
2
0
0
4
1
0
0
1
1
2
1
1
1
0
1
0
0
0
5
0
0
0
1
1
0
0
0
1
1
1
0
0
0
0
0
2
0
2
2
2
1
2
1
0
2
1
0
1
1
2
0
2
1
1
0
1
0
1
1
1
0
1
2
0
2
2
1
2
1
0
0
0
1
1
2
0
0
1
1
2
1
1
1
0
0
1
3
0
1
0
1
0
2
0
1
1
2
0
1
0
1
0
1
0
0
7
2
1
2
0
1
0
0
1
1
1
3
0
1
0
1
1
0
1
0
0
0
1
0
0
2
1
1
1
1
1
0
0
0
1
2
0
0
1
2
0
2
0
1
1
2
0
1
2
2
2
1
1
1
0
1
1
1
2
1
1
0
0
0
1
1
0
2
0
0
2
1
0
1
1
2
2
0
0
2
1
0
1
1
1
0
2
1
1
2
2
2
0
1
0
1
0
1
0
3
1
1
0
1
2
0
0
0
1
0
2
1
0
0
1
0
0
0
1
0
0
1
2
1
1
0
0
0
0
0
1
2
2
1
0
2
2
0
0
0
0
0
1
1
1
0
0
1
1
1
0
0
2
0
2
0
1
0
1
1
0
0
0
0
0
0
1
0
2
1
1
0
1
0
2
0
1
2
1
1
2
1
1
1
0
0
0
0
1
0
2
2
0
1
0
0
2
1
2
2
0
0
1
1
2
0
1
0
1
0
0
1
0
2
0
0
1
0
0
0
0
1
0
0
0
2
2
1
2
1
1
1
2
0
1
0
1
0
0
2
1
0
0
0
1
0
2
1
1
2
1
1
1
0
1
1
0
2
1
0
0
0
2
1
0
2
2
0
0
1
0
1
0
1
2
1
2
2
0
0
0
2
1
1
2
0
1
0
0
0
1
0
0
1
0
1
0
1
1
1
2
2
1
1
0
0
1
1
0
2
2
0
1
0
2
0
1
0
0
1
2
1
1
0
1
1
0
2
0
1
0
1
1
1
0
1
0
2
0
1
0
2
0
0
1
1
2
2
1
2
1
3
0
2
2
0
2
1
0
0
2
0
0
2
1
1
0
0
1
0
0
0
0
0
0
2
1
2
0
2
0
1
3
1
0
2
1
2
2
1
0
1
0
1
2
0
0
1
0
1
1
1
2
0
1
0
1
1
1
0
1
1
0
0
1
1
2
2
0
0
1
0
0
1
2
1
1
0
1
1
2
1
1
1
2
2
0
0
0
0
1
0
2
0
5
0
0
2
1
1
3
0
0
2
0
0
2
0
1
0
0
0
0
2
2
0
3
2
2
1
1
0
0
0
1
1
1
0
2
1
0
2
0
0
0
2
0
0
2
1
2
1
1
1
0
0
1
1
1
0
1
1
0
0
2
0
1
1
2
1
2
0
1
0
2
0
1
1
1
2
1
1
0
1
0
1
0
2
0
1
1
0
2
0
2
0
0
0
1
1
0
0
1
1
2
0
3
1
2
0
1
1
1
0
1
2
1
1
1
2
0
0
1
1
1
0
0
1
1
1
1
2
1
2
1
0
0
0
2
1
2
2
0
2
0
2
0
2
0
1
1
5
1
0
3
2
1
0
2
2
0
0
1
3
0
2
0
1
1
1
1
1
1
3
1
2
0
0
0
2
0
1
0
2
0
1
2
0
0
1
1
0
2
2
1
0
0
1
0
1
0
1
2
2
0
1
1
0
2
0
1
1
1
0
0
0
0
1
1
0
3
1
0
0
0
2
2
2
1
0
1
0
2
0
1
1
0
2
0
0
1
2
0
0
1
0
1
1
0
0
1
0
2
0
2
0
1
0
0
0
2
0
2
1
0
1
0
0
0
1
0
1
1
0
1
2
1
0
1
1
1
2
2
1
1
1
2
1
1
2
0
1
2
1
2
0
0
2
0
0
1
0
0
0
1
0
1
1
0
1
1
2
2
0
1
2
0
2
0
2
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
1
1
1
0
1
0
1
0
1
0
1
1
1
2
2
0
0
1
2
0
0
1
1
0
2
1
1
1
0
1
1
1
1
0
0
2
0
1
0
1
0
0
5
0
0
4
1
2
1
0
0
0
1
0
0
2
0
0
2
0
0
1
0
1
0
0
1
1
0
2
1
0
1
0
1
0
2
2
1
0
2
1
0
0
0
1
1
1
0
0
1
0
2
0
0
0
0
0
0
1
0
1
2
2
0
2
2
2
0
1
0
1
0
0
2
1
1
0
0
0
2
0
0
1
0
1
2
1
1
0
2
1
0
0
1
0
1
0
1
0
0
2
0
0
0
0
2
1
0
2
0
1
1
2
0
0
1
0
0
1
0
0
1
0
1
1
1
1
1
1
2
1
0
1
0
2
4
0
0
2
0
1
1
1
4
1
1
1
1
1
1
1
1
1
1
2
1
2
1
0
0
1
1
1
1
0
0
1
1
1
1
1
1
2
2
0
2
0
2
2
2
0
0
0
2
1
2
0
2
2
0
3
0
0
1
0
0
0
3
1
0
0
1
1
0
0
0
1
1
0
0
2
1
0
0
1
0
2
0
1
1
0
1
0
2
0
1
0
0
1
3
0
2
0
2
1
1
3
1
0
2
1
0
2
1
0
0
2
0
2
1
1
2
1
2
0
1
1
2
2
1
0
0
2
1
0
1
1
0
1
1
0
1
1
2
1
1
0
0
2
0
1
0
1
1
0
0
0
2
0
0
0
0
0
2
1
0
0
0
2
2
1
0
1
1
0
0
0
1
0
0
1
0
2
1
1
2
2
1
0
0
0
0
1
0
2
0
1
1
2
1
0
0
2
1
0
1
1
2
0
1
2
1
0
0
2
1
1
1
1
2
0
0
0
1
1
0
0
0
1
2
0
2
1
1
0
0
1
1
1
0
0
1
1
0
1
1
0
0
0
1
2
0
0
0
0
1
0
0
0
2
1
2
2
1
0
2
0
2
0
0
1
0
1
0
2
1
1
0
1
1
1
2
1
1
1
1
3
0
2
1
1
1
0
0
1
1
0
2
2
2
0
0
0
2
2
1
0
1
0
0
0
3
0
0
2
0
0
1
1
0
2
1
0
0
4
1
0
2
2
1
0
1
0
1
1
0
0
1
1
0
1
1
0
2
0
1
0
2
0
1
0
0
0
1
0
1
2
1
0
0
1
0
1
0
2
0
0
1
1
1
0
1
1
0
2
1
0
0
1
2
2
0
1
2
1
0
0
2
1
0
1
0
1
0
1
1
1
1
0
0
0
0
0
2
0
1
0
0
2
0
0
1
0
1
0
1
1
0
2
0
0
0
1
2
0
2
0
0
2
1
1
2
1
2
1
2
2
0
0
0
2
1
0
1
0
1
0
1
1
0
0
0
0
1
1
0
2
2
2
2
1
1
2
0
1
0
0
1
0
1
0
1
2
2
0
2
1
2
0
1
1
1
1
1
0
1
2
1
2
0
0
0
0
1
1
1
0
0
0
2
0
2
0
2
2
0
2
2
1
2
2
2
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
3
2
0
0
1
1
1
1
0
1
1
0
1
2
0
3
0
0
1
0
1
1
0
1
2
1
1
0
0
1
0
2
1
1
0
0
2
2
1
0
2
0
1
1
1
0
1
0
1
0
1
0
1
1
0
2
0
1
0
0
2
0
0
0
1
0
1
0
0
0
2
0
0
2
1
2
0
0
0
1
2
0
2
0
0
0
1
1
2
1
0
1
1
4
1
0
2
2
0
2
0
3
2
1
0
0
0
2
2
0
0
0
1
1
5
1
1
0
2
0
0
1
2
2
1
0
3
1
0
0
3
0
0
2
1
0
1
1
1
2
1
2
0
0
1
2
1
1
2
0
0
2
2
0
1
0
1
2
1
1
2
0
2
0
2
0
4
0
0
0
2
1
1
0
0
0
3
2
0
2
0
0
0
1
2
1
2
1
3
0
1
0
1
1
2
2
1
0
0
0
0
2
2
0
0
1
2
0
0
0
2
1
0
1
1
2
0
0
0
1
1
1
1
1
0
0
1
1
1
2
1
0
1
2
1
1
1
2
2
0
1
0
2
0
2
2
0
2
2
0
0
0
1
0
1
0
0
2
1
1
0
0
0
2
1
0
2
1
1
1
1
1
1
1
0
0
2
1
1
0
0
3
1
1
0
0
0
1
2
0
2
1
0
1
2
2
1
0
2
0
1
0
3
0
2
0
0
1
1
1
1
1
1
1
1
1
0
1
0
0
0
0
1
1
2
0
1
1
1
0
1
0
0
3
0
2
0
1
0
1
2
0
0
1
1
0
0
1
1
1
1
0
0
0
0
0
0
1
2
0
2
0
0
0
1
1
1
0
0
2
1
1
2
0
0
2
0
1
2
2
0
1
1
2
2
1
0
1
2
1
1
1
2
1
1
3
2
0
1
2
0
0
1
1
2
0
1
0
0
0
0
0
2
2
11
1
1
1
1
1
0
1
2
0
0
2
0
0
2
0
1
0
1
0
1
2
1
2
1
2
0
1
2
2
2
2
0
0
2
1
0
1
1
0
1
0
3
0
2
1
0
2
0
0
0
0
2
2
0
1
0
0
0
1
0
1
2
0
2
0
0
0
0
0
0
0
1
0
1
2
1
0
2
1
0
0
2
1
1
0
2
2
2
1
1
1
1
0
0
1
1
2
1
2
2
1
0
1
1
0
0
2
1
0
0
0
0
1
0
0
0
0
1
2
1
1
0
0
1
0
0
1
1
2
0
0
0
0
1
0
1
1
0
0
1
0
1
0
0
1
2
0
0
1
0
0
2
2
0
0
2
0
2
0
2
1
0
1
0
1
0
0
0
1
2
0
3
2
2
0
1
2
0
1
1
2
0
1
0
0
2
0
0
3
0
1
0
0
2
0
0
0
0
0
1
0
0
1
1
1
3
0
1
0
1
0
0
2
3
0
3
1
2
2
0
2
0
0
0
1
0
0
1
0
1
1
1
1
0
1
0
0
1
0
0
0
0
1
0
0
1
0
2
0
1
1
1
2
2
2
0
1
0
1
1
1
1
0
1
0
2
0
2
0
0
1
2
0
1
0
2
1
2
0
0
1
2
2
0
0
0
2
1
0
1
0
0
0
0
0
2
0
1
1
1
1
1
2
0
1
1
1
0
0
1
2
1
0
1
2
2
0
1
0
0
0
2
1
1
0
0
0
0
1
1
0
1
2
1
2
1
0
0
1
2
1
0
1
1
2
2
1
1
0
1
1
1
0
2
0
1
2
0
2
2
3
2
1
0
1
2
1
2
1
0
0
0
3
0
0
1
1
1
1
0
1
1
0
2
0
0
1
1
1
0
0
0
0
2
0
2
3
1
2
1
2
0
0
0
0
1
2
0
2
1
1
0
0
2
1
0
1
1
0
0
0
2
1
0
1
1
1
1
2
1
1
1
2
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
2
1
2
1
0
2
0
1
1
0
1
0
2
0
2
2
1
0
1
1
1
2
2
2
0
0
0
2
1
2
0
2
1
2
1
1
1
0
0
1
0
0
0
0
1
0
1
0
1
0
2
0
1
2
2
0
2
0
2
2
2
0
0
1
0
2
1
0
0
1
1
0
1
1
1
0
1
1
1
2
0
1
1
2
0
0
3
1
0
0
2
2
0
0
4
0
1
1
0
0
1
1
0
2
0
0
1
1
1
2
0
2
2
1
0
1
1
1
0
3
1
0
2
0
0
1
1
0
0
0
2
2
1
0
0
0
1
1
0
2
0
1
1
1
1
2
0
0
0
1
0
0
0
1
0
1
0
1
2
0
2
2
0
0
1
1
1
0
1
0
0
2
2
0
0
1
0
1
2
1
0
0
2
0
1
2
0
0
0
0
2
2
1
1
1
0
0
0
1
0
1
2
0
1
0
0
0
0
0
2
1
0
2
0
1
2
1
2
2
0
0
2
0
1
0
2
1
0
0
3
0
2
0
0
2
2
1
0
1
2
1
0
1
0
1
0
1
0
2
1
0
2
2
0
0
0
1
1
0
1
0
2
1
0
2
1
0
1
1
0
1
1
0
1
0
0
0
1
2
2
0
2
0
0
0
1
2
0
0
1
0
2
0
1
0
0
0
0
0
1
0
1
0
1
1
1
0
2
0
1
0
0
0
2
10
0
0
0
2
0
0
1
2
2
0
1
0
0
1
1
1
1
1
0
1
1
2
3
0
0
0
0
0
1
2
2
3
1
2
1
1
2
2
1
0
1
0
2
2
0
0
1
1
0
0
0
2
0
1
0
2
2
0
1
0
0
0
1
0
1
0
2
0
2
1
2
1
0
1
0
0
2
0
2
0
0
0
1
2
0
2
0
1
1
2
2
1
2
2
1
0
1
1
1
0
0
2
1
1
1
1
2
1
0
1
1
0
1
0
0
0
1
2
2
1
2
0
1
1
1
0
1
0
2
1
2
0
0
0
0
0
1
2
2
2
0
0
0
3
0
1
0
2
1
0
0
1
0
2
0
2
1
2
0
0
1
0
1
1
2
1
0
0
2
0
1
2
2
2
0
2
2
0
0
1
1
0
2
0
2
0
0
1
0
1
1
2
0
0
1
3
1
1
1
0
0
0
1
1
2
1
2
0
2
0
0
4
1
1
0
1
1
1
2
1
1
1
1
1
0
1
0
2
1
2
0
0
1
2
0
2
0
1
1
0
2
1
1
0
1
0
1
2
0
1
0
1
0
1
2
0
0
2
1
1
0
2
2
0
0
2
1
1
1
1
0
0
2
0
2
0
2
0
1
0
0
0
0
1
0
1
2
0
0
3
1
2
0
2
1
1
0
1
0
2
1
1
2
2
1
1
1
0
2
2
1
1
2
1
2
2
1
2
0
2
0
0
1
0
0
1
1
1
0
0
0
1
1
1
3
0
0
0
1
2
0
0
0
0
1
1
0
0
0
1
1
0
1
0
3
0
0
1
0
1
2
0
1
1
1
0
1
1
1
0
0
1
1
1
0
0
1
0
1
1
2
1
1
1
0
1
1
3
1
0
1
0
1
0
2
0
0
2
1
0
0
1
1
0
1
1
1
0
0
0
1
1
1
1
0
2
0
2
1
1
0
1
2
1
1
0
2
1
0
1
1
0
1
1
0
0
1
1
0
0
2
0
2
2
0
0
1
1
0
0
1
0
0
0
2
1
2
2
5
3
2
2
3
0
1
1
1
2
1
0
1
2
1
1
2
1
1
2
0
2
1
0
0
1
0
0
0
2
2
0
1
2
3
1
0
1
1
0
0
1
0
1
1
2
0
1
0
0
0
0
1
0
1
1
2
0
1
0
1
1
0
0
0
2
1
0
1
0
0
1
2
2
1
2
1
1
1
2
0
1
1
1
0
0
1
2
0
0
0
1
4
0
0
0
0
0
1
2
1
0
0
2
2
0
0
1
0
0
1
0
0
0
0
2
1
1
1
1
0
0
1
1
1
0
1
0
2
0
1
0
1
1
0
0
0
2
0
1
2
0
2
0
0
2
1
1
1
0
0
0
1
1
0
1
0
0
1
2
1
1
4
2
0
0
2
2
1
1
1
1
2
4
1
0
0
1
0
0
1
0
2
0
0
0
0
2
0
1
1
1
1
0
0
1
0
1
0
0
3
1
2
1
0
1
2
1
0
2
1
2
2
5
1
1
7
1
1
1
0
2
1
2
0
0
1
0
1
1
2
1
0
1
0
1
1
0
0
1
0
0
1
0
1
0
1
1
2
0
1
0
2
0
2
1
2
1
1
0
1
1
0
0
1
0
0
0
2
0
0
1
0
1
0
1
1
1
2
2
1
1
0
0
1
1
0
0
0
0
0
0
1
1
1
0
4
1
0
0
0
0
1
1
2
1
1
1
1
1
2
0
0
0
1
1
0
0
0
1
0
0
2
0
2
6
0
0
0
1
0
2
1
1
0
0
0
1
1
2
0
0
1
0
2
1
0
2
1
1
0
0
4
0
1
0
0
1
0
0
0
0
0
2
0
1
0
1
0
0
2
2
0
2
1
1
0
0
0
2
1
1
1
2
0
1
2
0
1
2
3
0
2
0
1
1
2
0
1
0
0
2
0
1
1
3
0
0
0
1
1
0
1
0
2
0
0
1
0
2
1
2
0
1
0
2
1
2
1
0
1
0
2
1
1
0
0
2
2
1
0
2
1
2
1
2
1
1
0
2
0
1
0
1
0
0
0
0
1
0
2
2
2
1
0
2
1
0
1
0
2
1
2
0
0
0
1
1
2
1
1
0
0
1
2
1
0
1
1
1
2
1
1
1
0
0
0
1
0
2
1
1
0
0
3
0
0
0
0
2
1
0
0
1
0
2
0
0
2
2
2
2
2
0
1
0
0
1
0
0
1
1
2
0
2
2
1
0
2
0
1
0
2
0
1
2
1
2
0
1
0
2
1
1
1
2
0
2
1
0
1
2
1
0
0
1
2
1
0
2
0
2
4
2
2
0
2
0
1
1
0
1
0
1
0
0
1
0
0
0
2
2
2
0
0
0
0
0
1
1
1
0
2
1
1
0
2
1
1
1
0
0
0
1
1
1
1
2
0
0
0
2
0
1
3
1
0
2
0
0
1
2
0
1
1
1
0
1
2
0
1
0
2
3
0
1
1
0
1
1
1
0
1
0
0
1
0
0
0
2
0
1
1
0
2
1
0
0
1
0
0
1
0
2
0
1
1
1
0
2
0
0
1
1
1
2
0
0
0
0
0
1
1
1
0
0
1
1
1
0
0
0
0
0
0
2
1
0
2
1
2
0
0
0
0
0
0
0
1
2
1
2
0
0
2
0
0
1
0
0
2
1
0
1
1
0
2
1
0
0
1
2
0
2
0
0
0
2
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
1
2
1
0
0
3
0
2
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
2
1
0
1
0
0
0
0
1
0
2
0
1
0
1
0
2
0
2
0
0
0
1
1
2
2
0
1
0
0
0
1
0
1
0
0
0
1
1
1
1
1
1
2
1
0
2
0
0
1
0
0
0
0
0
0
0
2
4
0
0
0
0
2
0
2
0
0
2
0
1
0
0
0
0
1
1
0
0
1
1
1
0
1
2
1
0
0
0
2
1
1
0
1
0
1
1
1
1
0
3
1
0
2
1
0
1
1
0
0
0
0
0
1
0
0
0
1
2
2
1
1
0
1
0
0
1
0
1
2
1
1
1
0
1
1
4
1
0
3
1
1
1
0
1
0
1
2
0
1
0
2
0
1
0
0
1
1
1
0
0
0
1
0
0
0
0
2
0
1
2
1
0
1
1
0
0
1
0
2
0
1
1
0
0
0
0
1
1
0
0
0
1
0
1
1
1
1
1
0
0
0
0
2
1
2
2
1
2
2
0
0
0
0
1
0
3
1
0
0
0
0
2
1
2
0
1
1
0
0
0
1
1
2
1
1
0
0
1
0
2
0
0
1
0
1
1
1
2
2
2
2
0
0
1
2
0
1
2
1
2
1
2
1
0
0
1
0
0
0
0
0
1
0
0
2
0
0
1
0
1
0
0
0
0
4
1
1
1
2
0
2
0
0
0
1
1
0
0
2
0
0
0
2
0
1
1
1
1
1
0
1
2
1
1
0
1
1
0
2
2
2
0
1
1
2
0
0
1
0
0
1
2
1
2
0
2
0
1
0
1
0
2
2
1
1
0
2
0
2
1
2
1
2
2
3
2
2
0
1
0
0
0
0
0
0
0
2
0
2
1
1
0
1
1
3
0
0
2
2
1
2
1
1
1
1
1
0
0
2
2
2
0
2
0
0
0
1
0
1
1
2
2
1
2
1
1
0
0
2
0
0
0
1
2
1
0
2
1
0
1
0
1
2
1
0
1
2
1
1
2
1
1
0
1
2
1
0
0
1
1
0
2
1
0
1
1
0
1
2
0
0
2
2
0
2
2
0
0
1
2
0
0
0
2
2
2
0
1
0
0
1
1
0
0
0
0
0
1
1
0
0
2
2
1
2
1
1
0
0
2
1
1
1
1
2
1
1
4
0
2
2
0
1
0
0
0
0
0
0
2
0
2
2
1
0
1
1
2
0
0
2
1
1
2
1
0
1
2
1
0
2
1
0
0
2
1
2
0
0
2
0
0
0
2
0
2
0
1
1
2
1
1
0
1
2
2
1
0
1
0
2
0
0
1
2
2
0
1
1
0
0
0
0
1
2
1
0
0
1
0
0
0
0
1
1
0
2
0
0
1
1
1
2
2
1
1
1
1
0
1
1
2
1
1
1
2
0
0
0
4
0
0
0
0
1
0
0
1
0
1
1
0
1
2
1
0
1
1
3
0
0
2
1
2
0
1
0
1
1
1
1
1
0
2
1
0
0
1
1
1
2
0
2
0
2
1
0
1
0
1
1
0
0
0
2
3
1
0
0
0
2
2
2
0
3
0
1
2
1
1
1
0
0
1
0
2
2
0
1
0
1
2
1
0
1
1
1
1
1
0
1
0
2
1
0
0
2
0
0
0
2
2
2
1
2
1
1
1
2
2
2
2
1
2
2
2
1
0
1
1
1
1
2
0
0
0
2
1
0
0
1
3
1
0
0
1
0
0
0
0
1
1
0
1
0
1
0
0
2
1
0
0
1
1
1
0
0
0
0
2
0
0
0
1
0
2
1
0
1
0
1
1
0
1
2
0
1
0
0
2
1
0
2
0
1
1
2
2
1
1
2
1
0
2
0
1
1
3
0
2
1
0
1
0
1
2
1
1
0
2
1
1
1
1
1
0
2
1
0
0
0
2
1
1
0
3
0
1
1
1
1
1
1
0
1
1
0
1
0
1
1
0
1
1
1
1
1
2
0
0
1
0
0
0
1
0
0
1
2
1
2
0
1
0
2
0
1
1
2
1
0
0
0
1
1
2
2
3
1
1
1
1
1
0
1
2
1
2
0
1
1
0
2
2
0
0
1
0
0
2
1
0
2
1
0
1
1
0
2
1
0
0
0
0
1
1
1
0
2
1
0
1
1
2
1
0
0
1
2
2
0
1
0
0
0
0
1
1
0
1
3
0
0
0
0
1
1
2
0
1
0
0
0
1
0
1
2
1
1
0
2
0
1
5
1
0
0
1
0
0
3
0
2
2
1
1
1
0
0
0
2
0
2
1
0
1
0
0
0
0
0
4
2
1
1
1
0
0
0
0
2
2
0
0
1
1
0
1
0
1
0
0
0
0
0
0
3
0
1
1
1
2
0
2
2
1
2
1
1
1
2
0
1
0
0
1
0
0
2
0
0
1
2
0
0
1
0
0
0
2
0
1
0
2
1
1
1
2
1
0
2
1
0
2
1
0
0
1
1
0
0
1
0
0
1
0
0
3
1
1
1
0
0
0
0
0
0
2
0
1
0
2
3
0
0
2
2
0
0
0
1
0
1
0
2
0
1
0
0
1
2
0
1
2
1
0
1
1
2
1
1
1
0
1
0
2
0
2
0
1
0
2
1
0
2
2
1
1
2
1
0
1
1
1
1
2
1
1
1
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
1
1
2
0
1
0
2
2
1
1
3
2
2
1
1
0
1
0
1
1
0
0
2
1
0
2
0
0
1
1
0
5
2
1
1
0
0
1
0
2
1
1
0
0
0
1
2
1
0
1
0
0
0
0
0
2
0
0
1
0
1
5
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
2
0
0
0
2
0
1
1
0
2
1
0
1
2
1
2
0
1
0
1
1
0
1
0
0
3
2
0
1
0
0
2
0
0
2
0
1
0
1
0
1
1
1
0
1
0
1
2
1
2
0
2
2
1
1
2
1
0
1
0
0
2
1
2
0
0
1
0
1
0
0
2
2
2
1
2
2
0
2
0
0
0
1
0
1
0
1
1
0
0
0
1
0
1
1
0
2
0
0
1
1
2
1
0
0
1
0
1
1
2
1
0
0
0
0
0
1
0
0
1
0
0
0
1
3
1
2
1
0
2
0
1
0
2
0
2
1
1
1
0
2
1
0
0
0
3
0
2
1
2
1
0
1
1
0
2
2
1
4
0
2
1
0
1
0
1
0
1
1
1
2
0
0
2
0
0
1
2
2
1
2
1
1
1
2
2
0
2
2
0
1
1
1
1
1
0
0
0
0
1
1
0
0
1
1
1
0
1
2
0
0
0
1
2
1
1
2
0
1
1
1
0
1
0
0
0
0
0
2
0
2
0
2
0
1
1
0
2
2
1
0
2
2
2
1
0
1
0
2
2
0
0
1
0
0
2
3
1
0
0
0
1
0
1
1
1
1
2
0
1
0
2
1
0
0
0
0
1
0
0
0
1
0
2
0
0
1
1
0
1
0
0
0
0
0
2
0
2
1
0
2
1
1
2
2
2
0
0
2
2
1
2
1
1
0
2
1
0
2
1
1
2
2
2
2
1
0
2
1
1
1
1
1
2
1
0
2
2
0
0
0
0
1
0
3
0
0
0
0
2
0
0
0
0
1
0
2
2
1
0
1
0
0
0
1
0
1
3
0
2
4
0
0
0
2
1
2
0
1
1
1
1
1
1
0
1
0
1
1
0
1
0
2
1
0
1
2
0
1
0
1
0
3
2
1
0
1
1
1
2
0
1
1
2
2
0
0
0
0
0
0
0
1
2
2
2
0
0
0
0
1
0
0
0
0
2
2
0
1
1
0
0
1
0
0
0
1
1
1
0
2
0
2
0
1
2
1
2
0
1
0
1
2
0
2
1
1
0
2
1
0
1
0
1
0
1
0
2
1
1
0
1
0
0
0
0
0
1
0
0
1
0
0
1
2
0
0
2
0
0
0
0
2
1
3
0
0
0
2
2
0
2
0
3
0
0
1
1
1
1
0
0
0
1
2
0
0
0
0
1
1
1
0
3
0
0
1
0
1
1
0
1
0
1
0
0
0
0
0
0
0
2
1
0
1
1
0
1
0
0
0
1
2
2
1
1
0
0
2
2
1
2
0
1
0
1
1
1
0
0
1
1
3
0
1
2
0
1
0
1
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
4
2
1
1
0
0
0
1
0
0
1
1
2
2
0
2
1
0
1
0
1
0
1
1
0
0
0
1
0
1
2
1
0
1
1
0
2
1
1
0
2
2
1
2
1
1
0
1
0
1
0
2
2
2
1
1
1
1
2
2
3
0
1
1
6
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
2
0
1
2
0
0
2
0
0
2
0
1
0
1
1
0
0
0
1
0
0
0
0
1
0
2
2
1
1
0
2
1
1
0
0
1
1
3
0
0
1
0
1
1
1
0
2
0
0
0
1
2
1
2
2
3
0
2
1
1
2
2
0
0
1
0
0
1
2
2
1
1
0
0
2
0
2
0
2
1
2
2
0
0
0
1
0
2
1
2
0
1
1
0
1
0
1
0
1
1
1
2
2
0
1
1
0
1
2
1
0
1
1
0
0
2
0
4
0
1
0
1
1
0
2
0
0
1
0
1
0
0
3
1
0
0
0
1
0
0
1
2
0
1
0
0
1
1
0
0
0
0
2
1
1
1
1
1
2
0
1
1
1
1
0
1
0
0
1
1
2
0
1
1
1
1
2
1
0
1
1
0
0
1
1
1
0
0
1
1
1
1
2
1
1
2
0
1
0
0
0
2
1
2
0
2
1
0
5
1
1
0
0
1
2
1
1
2
0
3
0
2
1
2
0
0
1
0
2
2
0
1
0
1
0
0
1
0
0
0
1
0
0
2
0
1
1
2
0
0
2
0
2
1
0
0
0
2
1
0
1
0
0
1
0
0
2
0
1
1
1
0
2
0
1
2
3
1
0
0
0
2
0
2
1
2
1
2
2
0
1
0
0
1
1
2
0
1
1
0
0
1
1
0
1
0
0
1
2
1
0
0
0
2
1
0
0
0
2
0
0
0
2
1
0
2
0
0
0
0
0
1
1
1
1
1
2
0
0
0
2
1
2
0
0
1
1
0
1
0
1
2
1
2
0
1
0
2
0
0
1
2
2
1
0
1
1
1
1
1
0
0
0
2
0
0
1
0
1
1
1
0
2
2
3
2
1
0
1
0
1
2
0
0
0
1
0
2
0
3
1
2
2
0
1
1
1
0
1
0
0
1
0
1
0
2
0
1
0
1
2
2
0
2
0
0
1
2
1
1
0
2
0
1
2
0
0
0
1
1
0
2
3
1
0
0
2
1
0
1
2
0
1
1
0
1
0
1
2
0
0
1
1
2
1
2
1
2
0
1
0
1
0
1
0
0
1
1
2
0
2
0
1
1
0
1
0
1
0
1
3
0
1
0
2
0
1
1
2
0
1
0
1
1
2
1
0
0
1
0
1
1
1
2
1
0
0
1
0
0
2
0
2
1
1
2
0
2
1
1
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
2
1
1
1
0
1
0
0
2
1
1
2
0
1
2
1
1
0
0
1
2
2
0
0
1
2
1
1
1
1
2
0
2
0
0
0
2
1
1
1
1
0
1
2
0
0
0
0
0
0
0
2
0
1
0
0
2
2
0
1
0
0
0
2
0
0
0
0
2
0
2
0
0
1
1
2
1
0
0
0
1
2
0
0
0
2
0
2
0
0
0
0
1
0
0
1
1
1
2
0
1
2
2
1
0
1
1
0
0
1
0
1
2
1
1
0
1
1
0
0
0
0
2
6
0
2
1
1
1
2
0
1
1
0
0
2
2
0
0
0
2
1
1
0
0
1
1
0
1
0
0
2
1
0
2
0
0
1
1
1
1
0
0
0
1
0
2
0
1
0
1
0
0
0
1
1
2
2
1
0
1
1
0
0
0
0
0
1
0
2
1
0
2
0
0
0
2
0
0
0
1
1
0
1
1
1
1
1
1
1
1
0
1
1
2
0
0
0
0
3
2
0
0
1
0
2
2
0
2
1
0
2
1
1
1
0
1
0
0
1
2
1
1
0
1
0
2
2
0
0
0
0
1
1
2
2
0
1
1
1
1
0
1
0
0
0
1
3
0
0
0
0
0
0
2
2
0
1
1
1
1
0
2
0
2
1
1
1
1
0
0
1
2
0
0
2
1
0
2
1
1
0
0
1
0
0
2
0
1
1
0
0
0
1
1
1
0
0
2
0
0
0
1
1
1
1
0
1
1
2
2
2
2
2
2
0
0
1
1
0
1
2
1
1
0
0
0
0
1
0
1
0
0
2
0
1
0
0
0
0
1
1
0
2
2
0
0
0
0
1
0
2
1
2
0
2
2
4
0
2
1
0
1
1
0
2
2
2
2
0
1
2
1
2
1
0
2
1
2
0
0
1
2
2
1
2
1
1
2
2
2
0
1
2
1
0
1
0
1
0
1
1
1
1
1
0
1
0
1
1
0
0
0
2
1
1
2
1
1
1
1
1
0
0
1
2
0
1
2
1
1
0
0
2
1
1
0
0
0
1
0
0
0
0
0
1
0
1
1
1
1
0
0
1
1
0
0
2
2
1
0
1
1
0
1
1
2
0
0
0
3
1
2
0
2
0
2
1
2
2
1
0
1
0
0
1
1
0
1
0
1
2
2
0
1
1
1
1
1
1
0
1
0
0
0
0
1
1
2
0
2
1
1
2
0
0
0
0
1
1
0
0
2
0
1
0
0
0
0
1
0
2
2
0
0
2
1
0
0
1
0
1
0
2
2
2
0
1
0
0
0
0
0
1
1
0
2
0
0
0
0
0
2
0
4
1
0
0
1
1
0
1
1
0
0
0
0
0
2
0
0
0
2
2
1
0
1
2
2
1
2
1
0
1
2
1
1
0
0
0
4
2
1
2
2
2
2
0
1
2
1
1
0
0
1
0
1
0
1
2
2
1
2
0
0
1
1
0
2
0
0
1
2
0
1
2
0
2
2
2
1
1
0
2
0
0
1
1
1
0
0
2
1
0
2
1
0
1
1
0
1
0
0
0
2
0
0
1
0
1
0
1
0
2
0
0
1
1
0
1
1
2
1
1
1
1
0
1
0
0
0
0
2
1
0
0
0
2
1
2
1
0
0
0
1
0
0
2
0
0
0
1
2
1
2
0
0
0
0
2
0
1
2
1
1
1
1
0
0
2
0
0
2
1
0
1
3
1
1
1
2
1
0
0
0
2
1
1
0
1
1
0
0
0
0
2
1
0
1
1
1
0
0
0
0
1
1
0
2
0
0
0
2
0
2
2
1
0
0
1
1
0
0
1
0
3
2
0
2
1
1
0
1
0
1
1
1
2
1
1
1
1
1
1
0
3
0
2
2
1
1
2
0
0
0
1
0
1
0
2
2
2
0
2
1
2
1
0
2
2
0
0
0
1
0
0
0
2
0
0
1
1
0
0
1
0
0
0
1
2
0
2
0
0
0
2
1
2
1
2
2
1
2
0
0
0
0
0
0
0
1
1
0
0
2
1
0
0
0
0
1
1
0
0
2
0
1
0
0
1
2
2
0
1
0
0
1
1
1
1
0
2
1
2
0
1
2
2
2
3
0
2
1
1
1
0
2
0
0
2
0
2
2
0
0
0
1
0
0
0
1
0
0
0
1
2
1
2
2
1
2
2
2
0
3
1
0
0
0
1
0
1
1
2
1
1
2
2
0
2
2
1
0
1
2
2
1
2
0
3
0
1
0
1
1
0
1
0
0
0
1
1
1
2
1
0
2
1
2
1
1
1
0
2
0
1
1
1
0
1
1
0
1
0
1
0
2
2
0
1
1
1
1
1
2
0
2
1
1
1
2
0
1
0
1
2
1
0
0
1
2
1
2
2
2
1
0
1
1
1
0
1
0
0
1
3
1
0
1
0
0
1
2
1
0
0
0
0
0
1
1
1
2
0
0
1
0
1
1
0
0
1
2
0
1
2
1
2
0
1
1
0
2
0
0
0
2
0
1
0
0
0
1
0
0
1
0
0
0
2
1
0
0
1
1
1
1
2
0
2
2
1
1
2
3
3
3
1
0
0
1
0
0
0
0
1
0
0
1
2
0
1
2
2
1
0
1
1
0
1
0
0
0
1
2
2
0
3
2
0
2
0
0
0
0
1
0
1
1
1
1
1
0
0
1
1
1
0
0
1
0
1
0
1
1
1
1
0
1
1
1
1
0
1
1
1
1
1
2
0
1
2
0
1
2
0
2
1
1
0
1
1
1
0
2
2
1
0
1
0
0
0
1
1
0
2
0
1
0
0
0
1
1
1
2
1
1
1
0
1
0
1
1
2
0
0
0
1
1
0
0
3
0
2
2
2
0
1
1
2
1
1
1
0
0
0
0
2
1
1
1
1
1
1
4
0
0
2
0
1
1
1
0
1
0
0
2
0
0
1
1
3
0
2
0
0
0
0
0
1
0
1
1
2
0
2
2
0
0
1
0
1
1
1
0
0
2
2
1
1
1
1
0
2
0
0
1
2
1
2
2
2
0
1
0
0
1
0
2
1
1
1
0
1
1
0
0
1
0
0
0
0
0
2
0
0
1
1
0
0
0
2
2
1
2
0
1
1
1
0
0
1
1
1
0
2
0
2
1
0
1
2
1
2
1
0
2
1
1
1
0
0
1
2
2
2
0
2
1
1
0
2
5
1
1
1
0
1
1
1
0
1
0
0
2
0
1
1
3
1
0
0
0
1
1
0
1
0
1
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
2
0
0
2
0
1
2
1
1
2
0
2
0
0
1
2
2
2
3
0
1
1
0
2
1
0
1
0
0
0
0
0
1
0
0
1
1
0
0
2
0
2
2
0
0
2
0
2
1
1
0
5
1
1
0
0
0
1
0
0
0
1
1
2
1
2
0
2
3
1
0
0
0
0
1
0
0
1
0
2
0
1
1
1
0
0
2
0
0
2
0
2
1
1
0
2
0
1
0
1
2
0
0
1
0
2
1
0
1
1
2
2
1
1
0
2
0
2
0
2
0
1
0
1
1
0
1
0
1
0
1
0
1
1
2
2
0
2
2
0
1
1
2
0
2
1
2
2
1
2
0
0
0
1
2
1
0
1
0
1
0
1
2
1
1
0
1
0
0
1
1
0
1
1
2
1
0
1
0
0
0
0
1
0
0
2
2
1
1
2
0
2
0
0
1
0
1
2
0
0
2
1
1
1
0
0
0
1
0
0
2
2
0
0
0
1
0
0
0
0
1
0
0
3
1
1
2
2
1
0
2
1
0
0
1
1
1
0
0
1
1
1
1
3
1
1
0
1
0
1
1
0
0
2
2
1
0
2
2
0
1
1
4
1
0
2
2
0
1
1
0
0
0
1
1
0
1
2
1
1
1
2
1
1
0
0
2
2
0
1
1
0
0
0
2
2
0
1
0
0
1
0
0
1
2
1
1
0
1
2
1
2
1
0
1
1
2
1
2
1
2
0
0
0
0
0
0
3
1
1
0
1
0
0
2
2
2
2
0
0
0
0
1
0
1
0
0
1
0
2
2
1
1
1
0
2
1
0
1
2
0
2
0
2
2
0
1
1
2
0
0
1
1
1
0
1
3
2
0
0
2
1
0
1
0
0
1
0
2
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
1
0
0
3
1
2
1
1
0
0
0
0
1
0
0
1
1
1
0
2
3
0
2
1
0
0
7
0
1
0
0
1
0
2
0
1
0
1
0
0
0
1
3
1
0
1
1
1
1
1
1
1
1
1
2
0
1
0
1
1
1
0
0
0
2
0
0
2
2
2
0
1
0
0
1
0
1
1
0
0
0
0
1
0
1
1
2
0
1
0
1
0
2
0
1
1
0
2
0
0
1
2
1
0
0
1
1
2
0
0
1
2
2
0
1
1
1
1
2
0
0
2
0
1
2
2
0
1
0
0
1
2
2
0
0
1
0
2
1
1
0
0
1
0
0
1
1
0
1
1
2
1
0
0
1
0
0
0
0
3
2
0
0
0
0
1
1
1
1
1
0
1
1
0
2
1
0
2
1
0
2
0
0
1
1
0
0
1
0
0
2
2
1
2
0
0
1
2
1
2
1
1
2
1
1
3
0
1
2
1
0
1
2
1
2
0
0
0
2
0
1
3
1
0
0
1
1
1
0
0
0
2
1
1
0
1
2
1
2
0
1
1
0
1
0
1
1
0
2
0
3
1
1
1
1
1
1
1
0
2
2
0
0
1
0
0
3
0
0
1
1
0
0
1
2
0
1
0
0
1
1
0
1
1
2
0
2
0
1
0
2
1
1
2
0
2
0
2
2
1
0
0
1
6
1
1
2
1
2
1
3
1
2
0
1
0
1
0
0
1
1
1
2
2
0
1
1
1
2
0
1
0
2
0
2
2
1
1
0
1
2
2
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
1
2
0
1
2
2
0
1
2
1
0
1
0
1
0
1
0
1
1
0
0
0
1
2
0
0
0
0
1
1
1
2
0
0
2
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
1
4
2
2
1
1
2
0
1
0
1
0
1
0
0
2
2
2
0
0
0
0
2
2
0
1
0
1
1
1
1
1
2
2
0
0
0
2
0
1
1
0
0
1
1
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
2
1
0
2
1
0
1
2
2
2
1
1
0
0
1
0
1
3
0
0
1
1
2
0
0
2
0
0
1
0
0
0
2
1
0
0
2
1
1
0
1
1
1
1
1
0
1
1
2
1
0
1
0
2
2
1
0
0
1
0
1
1
2
1
2
1
1
0
1
1
0
2
1
0
0
1
0
1
0
2
2
0
1
0
1
0
0
1
1
0
1
1
2
1
2
0
0
0
2
2
1
1
1
1
2
1
1
0
0
2
1
0
2
0
1
1
2
0
2
0
1
1
0
1
0
2
1
0
0
0
1
0
1
2
2
2
1
2
0
0
0
0
1
1
1
1
0
1
1
1
1
0
1
0
0
0
0
0
0
0
1
0
1
0
1
2
1
0
1
0
2
0
0
0
1
1
1
1
0
0
0
0
0
1
2
1
1
2
0
0
1
1
2
0
0
2
1
0
0
2
0
1
1
0
1
1
0
0
1
0
0
0
0
0
3
1
1
2
1
1
0
0
0
2
0
0
0
0
1
1
0
0
1
2
1
0
1
2
1
2
0
0
0
0
2
2
0
0
0
1
0
1
1
0
1
0
2
1
1
0
0
2
1
1
1
0
0
0
0
1
1
0
1
1
0
2
2
1
0
1
2
1
2
1
1
1
0
1
1
2
1
2
0
1
0
2
2
0
1
1
2
0
1
0
0
0
2
1
3
2
0
0
0
0
1
1
2
0
1
1
1
1
1
1
1
0
2
2
2
0
0
0
0
0
0
2
0
0
0
1
1
1
2
0
0
2
1
1
0
0
1
2
1
4
1
4
2
2
2
1
1
1
1
2
2
0
0
0
2
1
1
3
0
0
1
0
1
2
0
2
0
2
0
0
1
0
1
0
2
2
2
1
2
0
2
0
0
1
0
0
1
0
0
0
0
1
0
2
0
2
2
0
0
0
2
1
0
1
2
1
0
4
2
1
1
2
0
0
0
2
1
0
0
0
0
0
2
1
0
2
0
1
0
0
1
1
0
1
0
0
1
1
0
0
0
0
1
1
2
2
0
2
2
2
2
1
0
1
0
2
1
1
1
2
0
1
0
1
1
0
0
1
1
1
1
2
0
0
0
2
0
0
0
0
2
0
2
2
1
0
0
1
1
0
1
1
1
0
2
0
1
0
1
2
0
1
0
1
2
2
0
2
2
2
1
1
2
1
0
2
1
1
0
1
2
2
1
0
0
1
1
0
0
0
0
1
0
1
2
0
2
0
0
1
0
0
1
1
0
2
0
0
1
1
0
0
0
1
0
0
0
0
1
2
1
1
0
2
0
1
0
1
0
0
0
1
1
0
1
0
1
0
0
1
0
2
2
2
0
0
0
2
2
0
1
0
1
0
0
2
1
0
1
0
1
1
0
1
1
0
1
0
1
2
4
1
2
0
1
1
0
1
1
0
0
0
0
1
2
2
1
1
0
1
1
1
0
0
0
0
0
1
0
1
1
1
1
1
0
0
2
3
0
1
0
0
0
1
2
2
1
1
1
0
1
1
1
0
0
2
0
1
0
0
1
1
0
0
2
1
1
1
1
2
1
1
2
0
0
0
1
2
1
0
1
1
0
0
2
1
0
1
1
1
1
1
2
0
1
1
1
0
0
1
1
0
1
1
2
1
1
1
1
0
2
2
1
2
0
2
1
1
2
0
0
1
1
2
2
1
1
2
2
1
1
0
0
2
0
1
2
1
0
1
1
0
0
1
2
0
0
0
0
0
2
1
1
0
0
2
1
0
2
0
2
0
1
1
0
1
0
0
1
0
1
2
0
0
1
0
2
2
0
0
0
0
4
0
2
0
2
0
1
0
0
1
1
1
1
0
2
0
0
0
2
1
1
0
0
2
0
2
2
1
0
1
1
1
0
2
2
2
0
0
0
1
1
0
1
0
0
2
0
2
1
1
0
1
1
2
0
0
1
0
1
1
0
1
2
2
2
2
1
0
0
1
8
1
1
1
2
1
2
1
0
0
1
0
1
1
0
0
2
1
0
0
0
1
2
0
0
2
0
1
0
1
1
0
1
0
0
0
2
1
0
1
0
1
0
1
0
1
1
1
2
0
1
0
0
0
1
2
0
0
0
2
0
2
1
1
1
0
2
0
0
2
2
0
1
0
2
1
0
1
0
0
2
1
1
1
1
0
0
1
1
1
0
0
1
0
2
0
0
1
1
2
0
0
2
0
2
0
1
0
0
0
3
0
1
2
1
1
0
1
1
2
0
0
0
0
1
1
0
1
0
2
0
0
2
0
0
1
1
0
1
2
2
1
1
1
1
1
1
1
0
0
0
0
1
1
0
1
0
1
0
0
0
2
0
0
0
0
1
1
1
3
0
3
1
0
0
0
0
0
1
2
1
1
1
0
0
1
0
2
0
1
1
1
1
0
1
0
3
1
0
1
1
0
2
2
2
1
0
2
0
1
1
1
1
2
0
2
2
0
1
1
0
0
0
0
0
1
0
0
0
2
0
3
0
2
0
1
1
2
0
1
0
0
2
2
0
1
2
0
0
0
2
2
2
2
1
3
1
2
1
2
2
1
0
0
1
0
0
0
0
1
1
1
4
2
2
1
1
1
0
0
0
0
3
2
1
1
1
1
3
0
1
2
1
0
2
0
1
1
0
0
1
1
1
0
0
1
0
0
3
1
0
0
1
0
0
0
0
2
2
1
0
0
0
1
0
1
0
2
0
1
0
1
1
1
1
1
1
0
0
1
1
0
0
1
1
1
0
0
2
0
2
0
2
0
0
1
0
1
0
0
0
0
2
3
1
1
2
0
0
2
0
2
1
2
1
1
1
1
0
2
2
0
0
2
0
1
1
1
0
2
1
0
1
0
3
1
1
2
0
1
0
0
1
1
1
2
0
0
0
1
0
1
5
3
1
0
1
0
0
1
1
1
1
0
1
0
1
0
0
0
2
1
0
0
1
0
1
0
2
0
0
0
1
2
1
0
0
1
1
6
0
1
1
0
0
0
0
0
0
1
2
1
0
2
1
2
0
0
1
0
2
0
0
0
4
0
0
0
2
1
1
1
1
2
0
1
1
2
1
2
1
2
1
2
2
0
0
0
1
1
1
1
1
0
0
1
0
0
1
1
2
0
0
0
2
0
2
1
0
0
0
0
1
0
1
0
0
2
0
1
1
1
0
0
1
0
2
1
1
0
1
2
3
0
0
0
0
0
0
0
1
1
2
2
0
0
2
1
0
2
0
0
0
0
0
0
0
1
0
1
0
0
3
2
2
0
2
1
2
0
1
1
1
0
0
0
1
1
0
2
2
1
0
0
2
2
0
0
0
1
2
1
0
1
2
1
0
0
0
1
0
2
1
1
2
0
0
1
0
2
1
0
2
1
0
0
0
0
1
0
1
1
1
0
1
0
0
1
1
0
0
1
1
1
2
2
2
1
0
2
1
1
2
2
0
1
1
0
1
3
1
2
1
0
2
2
0
1
1
1
2
0
0
1
1
0
2
0
1
2
1
0
0
1
1
2
2
1
2
0
2
1
1
1
0
2
2
0
0
0
1
2
1
0
1
0
1
0
1
1
1
0
1
1
1
2
1
1
1
1
0
0
0
0
0
0
0
1
0
1
1
0
2
1
1
0
2
0
0
2
0
0
0
1
2
2
0
0
2
0
0
2
1
0
2
0
0
1
2
1
0
0
2
2
0
2
1
2
0
2
1
1
2
2
0
0
0
1
0
0
0
0
0
1
1
0
0
0
2
1
2
1
1
1
2
1
1
2
2
1
1
1
2
2
2
1
0
0
2
0
0
1
1
1
2
1
0
1
1
0
0
2
0
1
1
5
0
0
0
2
0
0
1
0
0
2
0
2
2
3
1
2
2
2
0
1
0
1
1
0
2
0
0
2
1
0
1
0
0
0
0
0
0
1
2
0
1
2
0
0
2
1
1
0
0
0
1
2
2
2
1
0
1
1
1
2
2
1
1
1
0
0
0
1
0
3
1
0
0
1
0
0
0
2
2
2
1
2
0
0
2
2
0
0
0
0
1
1
0
1
1
1
1
0
0
2
0
2
1
2
0
1
0
1
1
0
1
0
1
1
1
0
1
0
0
0
0
0
0
2
2
0
0
0
1
1
0
1
0
0
0
1
1
1
2
1
0
0
0
0
1
0
2
0
0
1
0
2
0
1
2
0
0
2
1
1
1
0
1
0
0
0
0
1
0
1
0
0
0
0
2
2
1
0
2
0
2
0
1
2
0
0
0
4
1
0
2
1
0
1
0
0
1
1
1
0
1
0
1
1
2
1
0
0
1
1
0
1
0
0
1
0
0
1
0
0
2
1
2
1
0
2
0
0
0
0
1
0
0
1
1
1
1
0
0
1
1
1
1
0
0
0
0
2
2
0
1
0
0
2
1
1
0
1
0
1
0
0
2
0
2
1
0
1
2
2
1
1
0
2
2
0
1
0
1
1
0
0
1
1
1
3
1
2
1
0
1
0
0
1
2
2
0
2
1
2
2
2
1
1
0
3
1
1
0
0
2
0
0
0
2
1
1
0
0
1
0
1
1
1
0
0
0
2
1
1
1
2
1
0
1
0
1
2
2
0
1
2
2
0
1
0
0
1
0
0
0
1
0
2
0
1
1
0
1
0
2
1
1
0
0
0
1
0
1
0
1
1
2
2
0
2
1
0
0
0
1
0
1
2
0
0
0
0
1
1
3
2
2
2
1
0
0
1
1
0
1
1
2
0
1
1
0
0
0
1
1
1
2
2
2
0
0
0
1
1
0
2
1
0
0
0
0
0
0
2
1
2
1
1
0
0
1
2
2
1
0
1
1
1
0
1
0
0
1
1
1
1
0
0
0
1
2
1
2
1
0
0
0
0
2
0
0
1
1
1
1
1
2
0
1
1
2
1
0
1
0
0
0
1
0
0
0
0
0
1
1
1
0
1
1
0
1
7
0
1
2
2
1
1
0
0
1
1
1
0
1
0
0
2
0
0
1
2
2
2
1
3
1
0
0
0
2
0
0
1
0
0
0
1
1
4
0
0
0
2
1
0
2
0
0
1
1
2
2
2
1
0
0
0
0
0
2
0
1
1
0
2
2
0
0
1
2
1
2
0
2
0
0
1
0
1
1
0
1
2
1
2
1
0
0
0
1
2
0
2
0
1
2
1
2
0
2
1
1
0
0
0
1
1
1
0
1
3
1
1
1
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
2
0
2
1
1
1
0
0
0
0
0
0
1
2
0
2
0
0
2
0
1
1
2
1
2
1
0
1
1
2
0
1
1
0
0
1
0
0
1
1
2
2
2
0
1
0
1
0
1
1
0
1
1
0
0
0
0
0
0
0
0
1
1
0
1
2
0
2
1
1
2
0
0
0
0
1
0
1
2
0
1
1
1
5
2
3
0
1
3
2
0
1
0
0
1
1
1
1
1
2
1
0
2
1
1
1
2
1
0
0
0
0
0
1
1
1
0
0
1
1
0
0
0
0
1
1
0
2
0
0
1
0
2
1
1
0
0
0
1
1
1
0
1
1
0
0
1
1
2
1
1
1
1
0
2
0
0
1
1
0
0
2
2
1
0
1
1
2
2
0
2
0
2
1
1
2
2
1
1
0
1
0
2
0
0
1
0
1
0
0
1
2
1
2
0
0
1
1
1
0
0
1
0
0
2
2
1
0
0
0
1
0
0
0
0
0
2
1
0
1
1
0
1
1
0
1
1
1
1
0
0
1
0
0
1
2
0
1
0
2
0
1
0
0
2
2
1
0
1
0
1
1
1
2
0
0
1
1
2
0
2
2
1
0
2
0
0
0
0
2
1
0
0
2
0
1
0
1
0
3
0
1
0
0
0
2
1
2
0
1
2
0
0
0
1
0
2
0
1
1
1
2
0
1
3
1
0
1
0
1
1
1
0
0
1
0
1
1
0
0
2
2
1
1
1
0
0
0
1
1
1
1
0
2
1
1
0
1
0
1
0
2
0
1
0
0
0
1
1
0
0
1
0
0
0
0
2
1
2
2
1
2
0
0
0
2
1
2
0
2
2
1
1
0
0
1
0
2
1
0
1
0
1
0
0
2
2
1
0
2
2
0
0
0
0
2
1
0
0
1
0
0
0
1
2
0
1
0
2
3
1
0
0
0
2
2
1
0
2
1
0
0
0
0
0
2
0
0
1
1
0
1
0
0
0
1
10
1
0
1
0
0
0
2
0
0
1
0
2
1
1
1
0
0
0
2
2
0
2
1
1
2
1
1
0
1
0
2
2
2
1
1
1
1
0
0
1
1
0
1
0
0
0
0
0
2
1
0
0
0
1
1
2
1
0
0
2
0
0
0
1
2
1
1
1
0
2
2
1
0
0
2
0
0
2
3
0
2
1
1
2
0
1
0
1
2
0
1
0
1
2
0
0
2
2
1
0
1
1
0
1
0
0
2
0
0
2
0
0
0
1
2
0
1
1
1
1
2
0
0
0
1
1
0
0
0
1
1
0
0
0
2
2
2
0
1
2
1
2
1
1
0
0
2
0
0
0
1
0
1
0
2
1
0
1
1
1
2
0
0
0
1
2
1
2
0
1
0
1
0
2
0
1
1
0
0
0
0
0
0
2
0
0
2
2
2
0
0
0
0
2
2
0
1
0
2
1
0
0
1
1
0
2
3
1
1
0
0
3
1
1
0
0
2
1
2
1
0
1
0
0
0
0
0
0
0
2
2
0
0
1
1
2
0
0
2
2
0
1
0
0
0
0
0
0
0
0
1
1
1
1
0
0
2
0
0
2
2
1
0
0
1
1
0
0
2
2
1
2
1
0
2
1
1
1
0
0
0
1
0
2
2
1
1
0
0
0
1
1
1
0
0
0
1
0
0
0
1
1
1
1
1
0
0
1
0
0
2
2
1
2
2
2
2
0
0
1
2
0
1
1
1
0
3
0
4
3
0
0
1
2
1
2
0
0
0
2
0
1
1
0
1
2
2
2
3
0
1
0
2
0
0
0
1
1
2
2
2
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
3
0
2
0
0
1
2
1
0
1
0
1
1
1
0
0
2
1
1
1
1
0
0
2
2
1
0
1
0
0
1
0
0
0
1
0
0
1
1
0
1
2
0
0
1
5
2
2
0
0
0
1
1
2
1
0
1
0
1
2
1
1
2
9
1
1
2
0
2
0
0
0
0
0
2
2
1
1
1
0
0
0
0
0
0
3
0
1
0
0
1
0
2
1
0
1
0
1
1
1
0
0
1
1
2
0
1
2
0
2
1
0
0
0
0
1
0
2
0
1
0
1
1
0
0
1
1
0
1
2
0
0
0
1
1
1
0
0
0
1
1
2
1
0
2
2
1
1
0
1
0
1
1
0
2
1
0
0
2
1
0
2
0
0
1
2
2
0
3
0
1
2
1
0
1
0
1
0
0
1
0
2
1
0
2
2
3
0
2
0
1
0
2
0
0
1
2
0
1
0
1
0
0
0
0
0
1
0
0
3
0
2
2
2
1
0
0
1
0
1
0
1
2
0
1
0
1
0
1
0
0
1
1
1
0
2
1
2
1
1
2
0
0
1
2
1
0
1
1
1
1
1
0
1
2
0
0
1
2
2
2
1
0
0
1
2
0
1
0
0
0
2
2
0
2
0
0
1
1
1
1
2
1
0
2
0
1
1
0
2
0
2
2
1
2
2
1
2
2
2
1
0
1
0
0
0
1
2
1
1
0
1
1
0
2
2
0
0
1
0
2
2
2
1
2
1
1
1
1
1
1
0
1
0
0
1
1
1
0
0
1
0
0
2
2
1
1
0
0
0
2
2
1
0
0
1
0
1
1
1
0
0
2
1
0
2
0
1
0
2
0
3
0
0
0
0
1
2
1
2
2
0
1
2
1
1
1
0
1
2
2
2
2
2
1
0
2
0
0
0
0
1
2
0
0
0
0
1
3
0
1
1
0
0
0
1
1
0
0
1
2
2
2
0
1
1
0
0
2
0
0
7
1
1
2
0
0
0
2
0
0
0
1
1
1
2
1
5
2
1
1
2
0
0
1
0
0
2
0
0
2
2
0
2
1
0
1
0
1
1
1
1
0
0
0
1
2
1
2
1
0
0
0
0
0
2
2
2
1
0
1
1
2
0
0
0
0
1
1
1
1
1
2
0
3
0
1
0
0
0
0
1
0
0
1
2
1
1
2
0
0
2
0
0
2
2
0
1
2
2
1
1
1
1
1
1
1
5
0
1
0
1
1
3
0
0
0
1
2
1
1
0
1
0
1
0
0
2
0
0
0
0
1
0
2
1
0
2
1
1
0
1
1
0
0
0
1
2
0
1
0
0
1
1
0
0
2
1
2
0
0
1
1
1
0
0
0
2
0
0
1
0
0
1
2
2
0
2
0
0
2
0
1
1
2
1
0
2
0
0
1
2
1
1
1
2
1
0
1
1
1
0
1
2
0
0
0
2
0
1
0
1
0
0
0
1
2
2
2
0
1
2
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
1
2
0
1
0
2
2
1
2
0
1
3
0
1
2
2
0
1
0
2
1
2
0
1
1
1
1
0
0
0
1
1
0
0
0
0
1
0
1
0
1
0
0
1
1
1
1
0
1
2
0
0
0
0
0
0
1
1
0
2
0
0
1
0
1
2
1
0
2
1
0
0
0
1
0
0
0
2
1
1
0
1
0
1
0
1
0
2
0
2
0
0
2
1
1
0
3
0
2
0
0
3
2
1
0
1
1
1
0
0
0
0
1
3
2
0
1
1
1
1
1
2
0
0
1
0
1
3
1
0
0
2
0
0
1
0
0
1
0
1
2
2
0
0
1
0
2
0
1
0
2
1
0
1
1
0
1
1
2
2
2
2
1
0
0
2
0
1
1
1
1
1
0
1
2
2
0
1
0
0
0
2
0
2
2
0
1
1
2
1
1
1
0
1
0
0
0
1
1
0
0
0
1
0
0
0
1
1
0
0
1
0
0
2
1
2
0
1
1
0
0
2
2
2
0
0
0
0
2
0
1
0
3
0
2
1
1
0
0
0
1
2
1
1
1
1
3
0
0
1
0
0
0
0
0
0
0
2
2
2
1
0
0
0
3
1
1
2
1
1
0
2
1
2
0
1
0
1
1
4
2
1
0
0
0
1
0
2
0
1
0
1
1
0
1
2
2
0
2
2
0
2
0
0
0
1
1
1
2
0
1
1
0
1
1
2
0
0
0
1
0
0
0
0
2
0
0
0
1
0
2
2
2
0
1
1
2
0
1
0
0
1
2
2
1
0
1
0
1
1
0
0
0
2
0
0
0
1
0
2
2
2
1
0
0
0
0
0
0
1
2
0
0
1
0
0
1
2
0
1
0
2
0
2
1
0
2
1
3
2
0
1
0
1
1
2
2
1
1
1
1
2
0
1
0
3
3
0
1
1
2
0
0
1
0
0
0
1
1
2
0
0
0
1
1
1
0
1
0
2
0
0
0
0
2
0
0
0
1
0
1
3
0
0
0
1
1
1
1
1
1
2
2
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
1
2
0
1
2
2
1
1
0
0
1
0
0
0
0
0
2
1
1
0
0
1
1
4
2
1
0
0
2
0
0
0
1
1
1
0
2
1
0
1
0
1
2
0
0
0
2
0
1
0
2
1
0
1
0
0
2
1
0
0
6
1
0
1
2
3
0
1
0
1
1
2
0
0
0
0
1
0
0
0
0
1
0
1
2
1
1
0
0
1
0
2
1
1
1
2
0
1
0
2
0
0
1
2
1
0
1
0
1
1
0
1
0
2
1
0
0
3
1
2
1
0
0
1
2
1
2
0
1
0
1
2
0
0
1
0
1
0
1
0
0
0
2
0
1
2
2
1
5
0
1
0
0
0
0
0
1
0
2
1
0
2
1
2
0
1
1
1
0
1
2
0
1
0
1
0
1
0
1
2
1
0
0
0
2
1
2
1
2
0
0
1
1
0
0
2
0
1
2
1
0
0
0
0
0
1
0
1
0
2
1
0
0
0
0
1
0
1
2
0
0
0
2
1
1
2
0
1
1
0
2
0
0
0
0
0
1
0
0
0
1
1
2
2
2
1
0
2
0
1
1
2
2
2
0
1
0
0
1
1
0
1
2
2
2
0
0
1
0
1
1
2
0
2
0
1
0
1
1
2
0
2
2
0
0
0
2
1
2
0
2
0
0
1
1
0
1
2
0
0
0
1
0
1
0
0
1
0
4
2
0
3
0
0
0
0
3
0
1
1
1
1
0
1
2
1
2
1
2
2
0
1
0
1
0
1
0
2
1
1
1
0
0
2
1
1
2
0
0
0
2
2
2
0
0
1
0
1
1
1
2
0
3
1
0
1
1
0
1
0
2
1
0
1
0
2
2
2
1
0
0
4
1
0
1
0
0
0
0
1
0
1
0
2
0
1
0
0
1
0
0
0
0
0
1
2
0
0
1
0
0
2
0
0
0
1
0
2
1
1
1
1
0
0
0
0
0
1
0
1
0
1
2
2
0
2
0
0
0
1
0
0
2
2
0
0
0
0
1
0
2
1
3
1
1
1
1
0
0
1
1
2
0
0
1
1
0
0
1
1
0
1
3
0
0
0
1
1
1
2
0
0
1
2
0
1
1
1
2
0
0
1
0
0
2
1
0
1
0
2
1
1
1
0
1
0
1
1
1
0
2
0
1
0
0
1
1
1
0
1
0
2
1
1
1
0
0
2
1
0
1
2
0
1
2
0
0
1
1
2
1
2
1
1
0
2
0
1
1
0
1
0
2
2
0
2
0
0
2
1
2
1
0
2
0
1
2
0
3
1
0
0
1
1
1
0
0
2
1
2
0
0
2
2
1
0
1
0
0
0
0
1
0
2
1
1
1
1
1
1
1
1
1
0
1
2
0
1
2
2
0
0
1
0
1
1
2
0
0
1
0
0
1
0
2
1
2
0
1
1
1
3
3
0
2
0
2
0
1
0
0
0
1
1
1
1
1
0
2
3
0
1
2
1
0
0
1
1
0
1
0
0
0
0
1
1
0
2
4
0
2
2
0
1
1
0
2
1
0
0
0
0
2
2
0
2
0
0
0
1
0
1
0
0
4
1
1
1
0
2
0
0
1
0
2
0
1
0
1
2
0
1
0
1
1
0
2
2
2
1
0
2
0
2
0
0
0
0
2
2
2
0
0
0
2
2
1
0
1
1
0
1
1
1
2
2
2
1
1
1
0
2
0
2
0
1
3
0
1
0
0
0
0
2
0
1
0
0
0
1
0
1
0
0
0
0
0
1
1
3
7
2
1
1
1
2
1
2
1
2
1
0
0
0
1
0
1
1
0
0
0
0
0
2
2
0
0
1
0
0
1
1
1
0
1
0
2
2
1
1
0
1
0
1
0
1
1
0
0
1
1
0
1
2
1
0
0
2
0
0
0
0
2
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
1
2
2
2
1
1
0
2
0
2
2
1
0
1
1
0
1
1
1
0
2
0
1
0
0
0
2
0
0
1
0
1
1
0
0
1
0
0
1
0
1
0
1
1
0
0
0
0
1
1
0
1
1
0
2
0
1
0
2
2
0
0
0
0
1
0
0
0
1
1
0
1
1
1
1
0
0
1
1
0
0
1
2
1
0
0
0
2
1
0
1
1
0
1
0
2
2
1
2
1
1
1
0
1
2
0
0
2
0
1
2
1
1
2
0
0
0
0
2
2
0
2
2
2
2
1
2
0
0
0
1
0
0
1
2
0
0
1
1
0
3
1
1
2
0
0
2
0
1
0
2
0
2
0
1
1
2
0
1
0
0
3
2
2
2
1
0
0
2
0
1
1
0
2
0
0
1
1
0
1
1
2
0
1
1
0
1
0
0
1
0
0
0
1
0
1
2
0
0
1
2
0
1
2
1
0
0
1
1
2
0
0
2
2
1
1
0
2
1
1
1
2
0
2
2
2
1
1
0
1
0
1
0
2
1
2
2
1
1
0
1
0
0
1
1
1
1
0
1
3
1
0
0
2
1
1
0
1
0
1
2
0
2
0
0
2
0
1
0
2
2
0
0
0
0
0
2
1
0
1
1
1
0
2
2
1
1
1
1
1
1
2
2
1
1
1
0
1
1
2
0
0
1
0
1
0
0
0
2
0
0
1
0
0
2
1
1
1
1
0
1
1
1
0
2
0
0
0
2
0
1
2
0
0
2
2
1
1
1
0
1
1
1
1
1
2
1
1
0
0
1
0
0
0
2
1
0
1
1
2
0
2
0
1
0
1
0
4
2
2
0
0
0
0
1
2
1
0
1
1
0
0
1
0
0
2
1
2
0
0
1
0
2
2
1
4
0
1
1
1
0
0
0
0
3
0
0
1
1
0
0
1
1
0
1
1
2
1
0
0
2
0
1
0
1
1
2
1
1
0
1
0
1
0
1
1
1
0
0
2
0
1
0
0
1
1
2
2
1
0
1
0
1
1
1
1
2
0
1
0
0
4
0
0
2
0
0
2
0
0
0
0
0
2
1
0
1
2
1
0
0
1
0
0
0
0
1
0
0
0
2
0
1
0
2
2
2
0
2
0
1
1
1
1
1
2
0
0
1
2
0
1
2
0
2
2
0
0
0
1
1
3
3
1
0
0
0
2
1
2
1
0
0
2
1
3
1
0
2
2
0
1
1
0
1
0
1
1
0
0
0
1
2
1
1
2
0
0
0
0
1
2
1
1
0
0
2
2
1
0
1
1
1
1
2
2
0
2
0
0
0
0
2
2
1
0
0
2
0
0
0
0
0
1
0
1
1
2
1
1
0
0
2
0
2
1
2
0
0
0
0
2
1
1
0
1
1
0
1
2
0
2
1
1
1
1
0
0
2
1
1
2
2
1
1
0
1
0
1
1
2
0
0
2
1
0
1
2
0
3
2
1
1
1
0
1
0
0
1
1
1
1
0
2
1
3
1
1
1
1
2
0
2
1
0
3
1
0
0
1
0
1
0
1
0
2
2
1
1
0
0
1
0
0
0
2
2
0
0
1
1
2
1
3
0
0
1
0
2
1
0
2
1
1
0
0
0
0
2
0
2
0
0
0
1
0
1
1
0
1
1
0
0
1
1
2
1
2
1
1
0
0
1
2
1
1
0
2
0
1
1
0
0
0
0
0
2
1
0
1
0
1
2
1
0
0
2
1
0
0
0
2
3
2
1
2
6
1
1
0
1
2
0
2
0
2
0
1
0
0
1
1
2
1
1
2
1
0
0
0
0
1
0
2
3
1
1
0
0
1
1
2
0
0
2
1
0
1
1
4
0
0
0
2
0
0
0
2
1
1
2
1
0
0
1
0
1
1
1
0
2
1
0
0
0
0
0
0
0
0
1
2
1
1
0
1
1
2
0
0
1
1
0
1
0
3
3
0
1
0
0
0
2
1
0
0
1
0
0
1
0
2
0
2
0
2
0
1
0
1
0
0
1
1
0
0
0
1
1
2
0
0
1
0
0
1
1
2
0
1
0
2
1
0
0
0
1
1
0
1
0
1
0
1
1
0
0
2
0
0
0
0
2
2
1
1
1
1
1
1
0
2
1
0
0
1
2
0
2
1
1
2
1
0
1
0
0
0
2
0
2
0
0
1
1
2
2
0
1
0
2
1
0
0
0
2
1
1
2
1
0
0
1
0
2
0
1
0
1
1
2
1
1
0
1
2
1
1
2
1
0
0
0
1
0
2
0
0
0
1
2
0
1
1
2
1
0
1
2
0
1
1
0
1
1
0
0
1
1
1
2
0
1
0
1
0
1
0
1
0
1
1
1
2
0
0
1
1
0
0
0
1
1
0
0
2
1
2
1
0
0
0
0
1
0
2
8
1
2
2
0
0
1
1
0
0
1
0
0
0
0
2
0
1
2
3
0
2
1
2
1
0
1
1
0
0
2
0
1
2
1
1
0
3
0
0
2
0
1
2
0
1
0
1
1
1
1
2
1
0
1
1
0
1
1
0
0
0
1
0
2
0
0
1
1
1
0
1
0
3
0
2
2
1
1
3
1
2
1
1
1
0
1
2
0
1
1
1
1
0
1
0
1
2
0
0
0
0
2
0
0
2
2
1
1
2
1
1
2
0
1
1
0
1
1
2
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
2
1
1
0
1
0
2
0
0
2
0
2
1
1
0
1
1
1
1
0
0
0
2
0
0
1
0
0
1
0
1
0
1
0
2
1
0
0
0
2
1
0
1
0
3
2
0
0
0
1
1
1
0
1
0
0
1
0
0
2
1
0
1
3
0
1
2
0
1
1
1
1
0
2
0
1
1
0
1
2
1
2
7
1
2
0
1
0
0
0
1
2
2
2
2
1
0
0
0
0
0
1
0
3
1
1
0
0
0
2
0
2
0
2
2
1
1
2
1
1
1
2
0
0
1
0
2
2
4
6
0
0
2
2
0
1
1
0
0
0
1
0
0
0
0
0
0
1
1
2
0
0
1
0
0
0
0
0
0
0
0
0
3
0
2
0
0
1
1
1
0
0
1
1
1
1
0
1
1
1
2
0
0
1
2
1
3
1
0
0
0
0
1
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
2
1
1
1
1
0
1
0
0
1
0
2
0
1
2
0
1
1
1
0
2
0
2
2
0
0
1
0
0
2
0
0
1
1
1
0
1
1
0
2
1
0
0
1
0
0
2
2
5
1
1
0
2
0
0
0
0
0
0
0
2
2
0
1
1
1
0
0
0
2
2
2
2
1
0
1
2
1
2
0
0
0
0
0
1
2
1
1
2
1
0
1
1
2
0
2
0
1
0
2
0
0
1
1
2
0
2
1
1
1
0
2
0
1
0
1
2
1
2
1
0
1
2
1
0
0
1
1
2
2
0
0
2
0
1
2
2
0
0
1
0
2
0
0
1
0
2
1
0
2
0
0
0
0
1
1
2
1
0
1
0
2
1
1
0
0
0
0
0
0
2
1
0
2
0
2
1
0
1
1
1
0
0
0
1
1
0
1
1
0
1
1
1
2
1
1
1
0
1
0
3
3
0
2
1
0
1
2
1
1
1
0
1
2
1
1
1
0
0
1
1
0
1
1
0
0
1
0
1
0
0
1
0
2
0
1
2
2
1
1
2
1
1
1
2
1
0
2
0
0
1
2
0
1
1
4
1
0
1
0
0
2
0
0
3
2
1
0
2
1
1
1
1
1
0
1
0
0
0
2
1
2
1
1
1
1
0
1
1
1
0
2
3
1
0
1
2
2
0
2
2
0
0
0
2
1
0
2
0
1
0
0
0
2
2
2
2
1
1
1
2
0
0
1
1
0
0
2
0
1
2
2
1
2
0
1
1
2
2
0
1
1
1
1
1
1
0
1
0
1
1
1
1
0
2
0
0
0
0
2
1
2
0
0
1
0
0
2
2
1
0
1
0
0
0
2
2
0
0
1
0
0
0
0
0
0
2
2
1
0
1
1
1
0
0
1
1
1
0
2
0
0
0
1
1
0
0
1
2
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
2
0
0
0
1
1
0
2
3
5
0
0
0
2
0
0
1
2
1
0
3
2
1
1
2
1
0
0
1
1
1
1
0
0
0
0
2
2
1
0
0
0
1
1
0
0
0
0
1
1
1
1
0
2
1
2
0
0
1
2
2
0
0
0
1
0
0
2
0
0
1
1
0
0
2
0
0
2
1
1
1
0
1
0
0
1
2
2
1
0
0
0
1
2
0
0
0
0
0
1
0
1
1
0
2
0
3
0
1
0
0
0
2
0
2
1
0
0
0
0
0
1
1
1
0
0
1
1
2
0
1
0
1
0
0
2
2
0
0
0
2
0
0
1
2
1
2
1
2
0
0
0
2
2
0
1
0
1
1
2
1
1
2
0
1
1
1
4
3
0
0
0
2
1
1
0
0
2
0
1
1
0
2
2
0
0
0
0
0
0
1
1
0
1
0
2
0
0
1
0
3
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
1
2
0
2
0
0
0
3
0
2
1
1
0
0
0
0
1
2
1
0
2
0
1
1
0
1
0
0
0
2
0
2
1
3
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
2
1
0
0
1
2
1
0
0
0
0
2
0
0
4
1
2
1
1
2
1
1
0
2
1
0
1
0
0
1
2
0
0
1
0
2
0
1
0
1
0
1
0
1
1
0
0
1
0
0
1
0
0
0
2
2
0
2
2
1
1
2
1
0
2
2
1
1
0
1
1
0
0
0
0
1
0
0
1
1
1
2
0
0
2
0
0
0
1
0
1
0
0
0
1
1
1
1
1
0
2
0
0
3
2
1
1
0
2
2
1
0
1
2
0
0
0
1
0
1
1
1
1
1
0
0
2
1
2
1
0
2
1
0
2
1
1
0
0
2
2
0
2
0
2
1
1
0
0
1
0
1
0
1
0
1
0
2
1
1
0
1
1
1
0
2
0
0
1
2
1
0
0
1
2
0
1
2
0
1
1
0
0
2
1
2
1
0
0
2
0
0
2
1
2
0
1
1
0
0
0
0
2
0
0
0
1
1
1
0
0
1
2
1
1
0
0
1
2
0
1
0
0
0
0
0
3
0
0
1
0
1
2
0
0
0
2
2
2
0
0
1
0
1
0
0
0
0
1
0
2
0
1
0
2
2
1
0
1
1
1
0
0
0
1
0
2
2
0
0
1
0
0
1
0
1
1
1
0
0
0
2
0
0
1
1
1
0
1
1
0
1
1
1
0
2
1
0
0
2
2
1
2
1
1
0
1
1
1
1
1
2
0
0
1
1
1
0
1
1
1
1
2
0
1
1
2
1
1
1
0
0
0
0
1
1
2
0
0
1
1
1
1
0
0
1
1
2
2
4
1
2
0
0
0
0
0
1
0
0
3
0
0
1
0
1
0
1
0
1
2
1
2
1
0
0
1
0
0
0
1
1
2
2
0
0
1
0
1
2
0
1
1
2
2
1
0
2
0
0
1
1
1
1
0
1
0
1
2
2
1
0
0
2
1
1
2
0
0
1
0
1
0
0
1
0
0
1
0
2
2
0
0
1
0
0
0
2
1
0
0
2
2
0
1
0
2
0
0
2
0
0
1
0
0
2
1
2
2
0
0
1
0
0
1
1
0
2
0
0
2
0
2
0
0
0
1
1
1
0
1
2
2
0
1
2
0
0
0
1
0
1
0
1
0
0
1
2
2
1
1
2
0
0
1
0
0
0
0
1
0
0
0
1
1
2
0
1
0
0
0
2
0
1
1
0
1
0
2
2
2
0
0
0
0
2
1
1
0
1
0
0
0
0
1
0
1
1
0
0
0
1
2
0
0
0
1
1
0
4
1
0
0
0
0
1
0
0
1
0
1
1
1
1
0
1
2
1
1
0
2
2
1
2
0
0
2
2
0
1
0
0
1
0
0
2
1
1
1
1
0
4
0
1
2
2
1
1
1
0
1
0
2
2
0
0
0
0
1
1
0
1
2
0
1
2
1
0
2
1
0
0
1
0
1
0
3
1
1
0
0
1
1
2
2
1
0
1
0
0
1
1
0
1
1
0
0
1
3
0
1
0
0
0
1
0
2
0
0
0
0
1
0
0
1
1
0
4
1
1
1
2
0
1
0
0
0
1
1
0
2
0
2
2
2
1
1
0
0
0
1
0
0
0
1
1
1
0
2
1
2
0
1
0
1
2
0
1
0
1
1
0
2
0
0
1
0
1
0
0
1
0
0
1
1
1
0
1
0
0
0
2
1
0
0
3
1
0
0
2
0
1
1
0
2
0
2
0
0
1
2
1
1
0
0
1
2
1
0
4
2
1
0
1
0
0
0
1
1
0
2
2
0
0
0
2
0
2
1
0
1
2
2
1
0
0
2
0
2
0
1
2
1
0
0
0
0
0
0
1
1
2
4
0
1
0
1
1
1
1
2
2
1
0
2
0
0
1
0
3
0
0
0
0
1
0
1
0
1
1
2
0
0
1
1
2
0
0
0
2
2
0
0
0
0
1
1
1
1
0
0
0
1
0
0
1
0
0
3
1
1
1
1
2
1
1
0
1
0
0
0
0
2
2
1
0
0
2
1
2
2
0
0
1
0
0
1
0
2
0
0
0
1
1
1
0
0
2
1
1
1
0
2
2
1
1
1
0
0
0
1
1
1
0
0
2
1
0
1
1
0
2
2
1
2
0
0
0
1
0
1
0
0
1
0
1
1
0
0
0
1
1
0
1
0
1
0
1
2
0
1
1
0
0
1
1
1
0
0
2
2
1
0
2
0
0
1
2
0
1
0
0
2
0
1
1
0
1
1
0
0
0
0
2
1
2
1
1
0
1
2
0
2
1
0
0
0
2
0
1
1
1
1
2
2
1
0
2
1
1
2
0
1
1
0
0
2
2
2
0
0
0
0
0
1
0
0
0
1
1
1
0
2
0
1
1
0
1
2
1
0
1
0
1
1
0
0
1
1
0
0
0
0
1
0
0
2
0
1
2
1
1
1
1
0
3
0
0
2
0
0
0
0
0
0
2
2
0
0
0
2
0
3
0
1
2
1
0
0
1
1
2
0
2
0
2
0
1
2
0
1
1
0
1
2
1
0
0
1
1
2
0
1
1
3
1
0
0
0
0
0
1
2
1
0
0
2
1
2
0
1
2
3
1
0
0
1
1
1
1
1
1
0
0
1
1
1
2
0
1
0
1
0
1
2
1
0
0
2
0
2
0
0
0
2
0
0
2
0
1
2
0
2
1
2
0
2
1
0
0
7
0
1
1
1
1
0
1
2
0
0
2
0
2
1
2
1
0
1
1
1
1
2
0
2
0
0
1
1
1
1
0
1
2
0
2
0
0
0
2
2
1
0
2
0
1
2
1
0
1
1
0
1
0
1
2
0
1
0
1
2
1
1
0
2
1
0
1
0
0
0
0
2
0
1
0
1
1
0
2
0
1
1
0
2
0
0
0
0
0
0
0
1
2
1
1
0
0
0
1
0
0
1
0
0
2
0
2
0
1
0
0
1
1
0
1
1
2
0
2
2
0
0
1
1
0
1
1
1
0
0
1
1
0
1
1
0
1
1
0
2
2
1
0
1
2
0
2
1
0
1
0
1
0
2
0
1
0
3
0
1
2
1
1
1
1
3
0
0
1
2
0
1
0
0
1
2
2
1
0
1
2
1
1
0
0
2
1
0
0
1
1
1
1
1
0
0
0
0
1
0
1
0
0
1
0
1
0
2
1
1
2
1
0
0
1
2
1
2
0
0
1
0
0
0
2
1
2
1
0
1
1
1
0
2
0
2
0
2
2
0
1
1
0
0
2
0
1
0
1
1
1
1
1
2
2
0
2
2
0
2
2
2
0
0
0
0
1
0
0
0
0
1
3
0
0
1
0
0
1
0
1
0
0
1
1
1
0
0
0
0
0
0
0
1
2
1
2
0
2
0
1
1
2
1
0
0
0
0
0
0
0
0
0
1
0
0
2
2
2
2
1
1
1
0
0
2
2
0
0
1
1
1
0
2
0
0
0
1
0
1
2
1
2
1
0
0
1
0
0
2
0
2
1
2
1
0
1
0
1
1
1
1
0
3
0
1
0
1
0
1
1
0
0
1
1
0
2
1
0
1
0
0
1
0
1
1
0
0
0
0
2
0
1
0
2
0
1
1
0
0
0
2
0
0
1
0
1
0
2
2
1
0
0
3
2
0
0
3
0
0
1
2
1
2
0
0
0
0
0
1
2
2
1
1
1
1
0
0
0
1
1
2
1
0
0
1
0
1
2
1
0
2
1
0
2
1
0
2
1
0
1
1
0
1
0
1
0
2
1
1
2
1
0
1
0
2
0
1
0
1
1
0
1
1
2
1
1
1
2
1
0
1
0
3
0
1
1
0
1
0
2
1
2
1
0
0
1
0
1
0
0
0
1
0
1
2
0
0
0
0
2
0
0
1
1
0
2
1
1
0
0
8
0
0
0
2
1
0
0
1
0
1
2
0
0
0
0
1
0
0
1
0
1
1
1
0
2
1
1
2
1
2
1
0
2
0
2
2
1
0
1
1
1
0
2
2
0
2
0
2
0
2
2
2
1
0
1
1
1
0
2
2
1
2
0
0
1
0
1
1
1
2
0
2
0
1
1
0
0
2
0
2
2
0
2
1
1
0
1
0
2
0
0
0
2
1
0
1
0
0
0
1
1
1
0
0
1
1
3
1
0
0
2
0
0
0
0
0
0
0
1
0
3
0
0
1
1
1
1
1
2
0
0
0
2
0
0
1
0
1
1
1
0
1
0
0
0
0
1
0
2
2
2
1
1
2
2
0
2
0
1
0
1
0
1
1
0
0
1
0
1
1
1
0
1
0
1
0
1
2
0
1
2
0
0
2
0
0
2
1
1
2
1
1
1
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
2
1
2
2
1
0
0
5
1
0
0
0
1
1
0
2
1
2
2
1
1
2
1
1
0
0
0
0
1
2
0
2
0
0
1
2
2
0
0
2
2
0
0
1
1
0
0
3
0
1
2
0
0
1
2
3
1
0
2
1
1
0
2
2
0
2
2
1
1
0
0
1
1
1
0
1
0
1
1
0
0
1
1
0
2
1
0
1
1
1
1
1
2
2
2
2
2
0
9
1
2
1
1
1
0
0
1
0
0
0
0
2
3
3
2
0
0
0
0
1
1
1
1
2
1
1
0
2
1
2
0
2
1
1
0
2
1
1
0
1
1
0
0
0
1
1
0
0
2
0
2
0
1
0
1
2
2
0
0
1
0
2
3
0
0
0
1
0
1
0
1
1
0
2
0
0
0
2
1
3
0
2
0
1
1
0
0
2
0
1
2
2
2
4
0
0
0
1
0
0
2
0
0
2
1
1
1
1
0
1
1
0
0
1
0
1
2
2
2
1
2
1
2
0
1
0
0
3
1
1
2
1
0
0
2
1
0
1
1
0
1
1
1
2
1
1
2
1
2
0
0
0
0
0
2
1
1
0
0
1
2
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
2
0
1
2
0
2
1
1
2
1
1
2
0
0
1
1
1
1
0
1
1
0
0
1
2
0
1
1
0
1
2
1
0
1
0
0
1
0
0
1
1
3
0
0
0
2
2
1
0
1
0
0
1
1
0
0
1
0
0
2
1
2
0
1
0
0
0
1
1
2
0
2
0
0
0
0
1
2
2
1
1
2
1
0
1
3
0
0
2
2
0
1
0
1
2
1
2
0
1
0
2
0
1
1
1
2
1
2
3
0
0
1
1
2
1
2
1
0
0
0
1
0
0
1
2
0
1
0
2
2
1
0
0
0
1
1
0
1
1
2
1
1
0
1
2
1
1
0
0
0
1
1
0
2
1
0
2
1
2
0
0
0
2
1
1
0
1
0
1
0
1
1
2
2
1
1
0
1
2
2
0
1
0
2
0
0
0
0
1
1
0
2
2
0
0
0
0
0
1
1
2
0
0
1
1
0
2
0
0
1
0
1
1
0
2
0
1
0
0
1
2
0
0
0
0
0
1
1
1
2
0
1
0
0
1
1
0
1
0
0
1
1
0
0
0
2
1
0
2
0
1
0
1
1
2
0
0
1
0
0
1
0
1
1
1
2
0
0
2
0
2
0
1
1
1
0
2
1
0
0
0
1
0
1
0
2
0
0
2
0
1
0
0
0
0
0
2
1
2
0
0
2
1
0
1
0
0
0
1
2
0
1
0
0
1
2
1
0
2
1
0
1
1
0
0
0
0
0
1
2
2
0
1
0
1
1
0
0
0
1
0
1
3
1
0
1
2
0
0
1
1
0
1
2
0
0
0
0
1
1
0
1
0
0
1
1
1
0
2
1
0
0
2
0
1
0
1
0
0
1
1
3
1
1
0
2
2
0
0
2
1
0
2
1
2
0
0
1
0
0
0
1
0
1
0
1
0
1
0
1
1
2
1
2
0
1
2
1
1
0
1
0
1
0
1
1
1
0
1
0
0
0
0
1
0
1
1
0
0
0
2
0
1
1
0
1
0
1
2
0
0
2
1
1
1
0
1
1
0
1
0
2
0
0
1
1
0
0
2
1
1
2
0
0
0
0
0
0
0
2
0
0
0
1
2
1
1
0
0
1
1
1
0
1
1
0
1
0
0
0
0
1
0
2
0
0
0
0
1
2
0
1
0
1
2
0
0
1
0
0
0
0
0
1
1
0
0
1
1
0
0
1
1
0
0
0
0
0
1
2
0
2
0
1
0
2
0
1
0
1
2
0
1
0
1
0
2
3
1
0
0
1
0
0
0
1
0
0
0
0
1
1
0
2
2
0
0
0
2
1
1
2
0
1
0
0
0
1
0
2
1
0
1
1
0
1
1
0
1
1
0
1
2
0
0
1
0
2
1
2
0
1
1
0
2
2
0
1
2
2
1
2
0
1
0
1
0
1
0
0
0
2
0
1
0
1
0
2
1
1
1
1
0
3
0
0
1
1
0
0
2
0
1
7
0
1
0
0
2
1
0
0
2
1
0
3
1
1
1
0
0
0
1
1
0
2
2
1
1
0
0
0
1
0
1
2
0
1
0
0
0
2
0
1
1
0
0
1
0
2
1
0
0
2
0
0
2
1
1
0
2
1
0
0
2
1
2
1
2
0
0
0
1
0
0
1
1
0
0
1
0
1
1
2
3
2
0
0
2
0
1
0
1
0
2
0
2
1
0
0
1
1
0
1
0
1
0
1
0
1
0
1
1
0
0
0
1
1
0
3
0
0
1
1
0
1
0
2
1
0
1
1
0
0
0
3
1
1
0
0
0
2
2
1
1
0
2
1
1
0
1
0
2
0
1
0
2
0
2
0
1
2
1
0
0
0
1
2
0
0
0
0
1
0
0
0
2
3
0
1
1
1
0
0
2
0
0
2
1
1
2
1
2
0
0
0
0
2
1
1
1
2
0
0
2
2
2
2
2
1
0
1
1
1
1
1
1
0
1
3
0
1
0
1
2
1
0
2
0
0
0
0
0
2
1
1
0
1
0
0
1
0
0
2
1
1
2
0
2
0
1
3
0
1
2
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
1
0
2
1
1
0
0
2
0
1
1
0
1
1
0
1
1
2
2
2
1
0
1
1
0
1
0
0
0
0
1
2
0
1
0
1
0
1
2
0
0
0
0
1
2
0
2
0
1
1
0
1
0
1
1
1
0
0
0
1
2
2
1
0
0
0
2
0
0
1
0
2
0
0
0
1
1
0
2
0
2
1
0
1
0
1
1
0
0
1
1
0
1
1
2
1
1
0
0
1
0
2
2
1
1
0
1
0
2
0
1
0
1
0
0
1
0
1
0
1
0
0
2
2
0
0
0
1
1
0
2
0
1
0
2
1
2
2
2
0
1
1
1
1
0
0
2
1
0
0
0
1
2
0
2
2
1
0
0
0
1
1
2
1
0
0
0
0
3
1
0
0
0
1
0
3
0
1
0
1
2
1
0
0
2
0
2
1
1
0
1
0
0
1
1
0
0
0
1
1
0
1
1
0
1
0
2
0
1
0
0
0
0
0
0
2
0
0
0
3
1
2
0
0
0
0
1
0
2
0
1
0
2
2
1
2
2
0
1
0
0
1
1
2
1
0
1
1
2
0
0
0
0
0
0
0
2
0
2
1
1
2
1
0
0
2
1
0
1
1
0
1
1
2
0
0
2
1
0
1
0
2
1
2
0
4
0
0
1
1
1
1
0
2
2
1
1
0
0
0
1
0
1
1
0
0
2
1
0
0
0
0
0
1
1
1
0
1
1
2
1
2
1
1
1
1
1
0
1
1
3
1
0
0
2
0
1
1
0
0
1
1
1
0
0
1
0
0
0
0
2
1
1
3
1
0
1
1
1
0
1
2
1
0
0
1
0
0
2
1
0
1
1
2
2
0
1
0
0
0
0
0
0
0
0
3
1
3
1
2
0
1
0
1
2
3
0
0
3
0
2
2
0
1
0
0
2
2
1
2
2
3
0
1
0
0
1
0
0
0
1
2
1
0
2
0
1
0
1
1
1
0
1
1
2
0
0
2
1
2
1
0
1
1
0
2
2
2
1
1
1
2
0
1
0
0
0
0
1
0
2
2
0
2
0
0
0
1
1
2
0
0
1
2
0
0
1
0
1
0
2
1
0
1
0
0
1
0
1
0
1
1
1
0
0
0
1
1
0
0
2
1
0
2
0
2
0
0
1
0
0
1
2
0
1
0
2
0
1
2
0
2
1
1
0
0
0
0
2
1
0
0
8
2
0
2
2
2
1
1
2
0
2
0
3
0
0
1
2
0
0
2
0
0
0
1
1
2
1
1
0
1
0
0
0
0
0
1
0
0
2
1
1
2
1
0
1
2
2
0
1
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
1
0
0
2
0
1
2
1
2
1
0
1
1
2
2
0
0
1
1
0
1
0
2
0
0
3
0
0
2
2
2
0
2
1
0
1
0
3
0
0
1
2
1
0
2
2
1
1
1
1
1
1
1
1
1
2
0
0
1
0
1
0
2
0
0
0
2
0
0
2
0
0
0
2
0
0
1
0
0
1
0
0
1
0
0
0
0
1
2
0
1
0
0
2
1
1
1
1
1
2
0
1
1
1
0
0
0
0
0
1
0
0
1
2
2
2
1
1
2
1
0
0
2
0
0
1
0
0
0
0
0
2
0
2
1
1
0
0
2
0
1
1
2
1
2
1
1
0
1
1
0
5
2
1
0
0
1
1
1
0
1
0
1
1
3
0
1
0
0
1
0
1
1
0
0
2
0
0
1
0
1
1
0
2
1
2
1
1
2
0
0
1
1
0
0
1
0
3
1
1
1
2
1
1
1
1
0
0
1
0
1
1
2
0
1
2
0
0
0
0
0
1
0
1
0
1
0
0
2
1
0
3
3
2
3
0
1
0
2
1
0
0
1
0
1
0
0
0
0
2
1
1
0
0
0
1
1
2
1
0
1
0
0
0
0
1
1
0
1
1
0
0
4
1
1
1
1
1
1
0
2
1
2
1
2
2
1
1
0
0
1
1
0
2
0
1
0
0
1
1
1
0
0
2
1
1
0
0
2
2
0
1
1
2
0
0
0
0
2
1
1
1
0
0
0
1
0
0
1
0
0
0
1
2
2
2
0
1
1
2
1
1
0
1
0
2
2
1
0
2
4
0
1
0
2
2
0
1
0
1
0
1
1
1
1
2
2
2
0
2
2
1
0
1
1
1
0
2
2
2
1
1
1
2
1
2
1
1
1
1
2
2
0
1
0
1
0
0
0
0
0
2
1
1
2
2
1
0
1
1
0
0
1
1
1
0
0
0
2
2
0
0
2
0
1
2
0
0
2
2
1
1
0
0
0
0
0
1
0
0
2
1
0
1
1
1
2
0
0
0
2
0
0
0
2
0
2
2
1
2
1
0
0
2
0
2
0
2
2
0
2
1
1
1
0
1
0
1
3
2
0
1
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
1
0
2
1
1
0
2
0
1
0
0
1
2
1
0
2
2
0
1
0
0
1
0
2
0
2
2
0
1
1
3
1
2
2
1
0
0
0
4
2
1
0
0
0
2
0
0
0
2
0
0
1
1
1
0
1
0
0
0
0
0
2
1
1
1
1
0
0
0
0
0
0
0
0
1
1
1
0
1
0
1
0
0
0
1
2
1
3
2
1
1
0
0
0
0
0
1
1
0
0
3
0
0
2
0
2
0
1
1
1
0
0
0
0
0
2
0
1
0
1
1
1
1
1
0
1
2
0
0
2
1
3
1
0
1
0
2
0
0
0
1
0
2
1
1
1
1
1
1
0
1
2
2
1
0
0
2
0
2
1
1
0
0
1
2
0
0
2
0
0
0
0
1
1
0
2
1
0
2
2
2
1
1
1
0
1
1
1
1
2
0
0
0
1
0
2
1
1
2
1
0
1
0
0
1
0
0
2
2
0
0
1
1
0
1
2
2
0
2
0
1
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
2
0
2
1
2
1
1
1
1
0
2
0
0
2
0
0
0
1
0
0
0
2
1
0
0
1
0
2
2
1
0
0
1
1
0
0
2
0
1
1
1
2
0
0
1
2
2
2
0
0
0
1
1
2
1
2
1
0
2
1
1
0
0
1
0
0
1
1
2
1
2
1
0
1
2
0
1
1
0
1
0
2
0
0
2
0
0
1
1
2
0
0
1
0
1
0
0
3
2
1
1
1
1
0
0
0
1
2
2
1
1
2
0
0
0
0
1
1
2
0
2
0
0
0
2
0
0
1
0
2
0
0
2
1
0
2
2
1
2
1
1
0
0
0
1
0
0
1
0
2
2
0
3
1
1
2
1
0
1
0
0
1
1
1
3
1
0
2
0
0
1
0
2
1
2
1
0
1
0
0
2
1
0
1
0
0
0
1
1
0
0
1
0
0
1
0
2
2
0
1
2
0
3
2
2
2
3
0
1
2
1
2
1
2
1
1
2
1
0
0
1
0
3
1
1
0
0
2
1
0
0
0
1
0
2
0
0
4
0
0
2
0
0
2
1
0
1
1
1
0
0
1
0
0
1
1
0
1
1
0
2
2
0
2
1
1
0
2
2
1
0
2
1
0
0
0
0
2
0
2
2
1
1
1
2
0
0
1
0
2
1
1
1
1
0
1
1
0
2
1
1
0
1
2
0
0
0
1
0
1
1
0
2
2
1
0
0
0
1
0
2
0
1
1
1
1
0
1
1
2
2
0
0
1
1
1
1
4
2
1
0
0
1
0
2
0
0
0
1
0
1
0
1
2
0
2
2
1
1
1
0
2
0
2
0
2
2
0
0
0
0
1
0
0
0
0
2
0
1
1
0
1
1
1
1
0
1
0
1
1
1
0
2
3
1
1
2
0
1
1
0
1
1
1
0
2
0
0
2
0
1
0
0
1
1
2
1
1
0
1
0
1
1
1
2
1
1
0
1
1
1
0
2
0
0
1
1
1
2
0
0
1
1
0
1
0
2
2
1
0
0
0
2
1
0
0
3
0
0
0
1
0
1
2
0
2
3
0
0
1
1
2
1
2
0
2
0
1
1
2
0
0
7
0
1
0
2
0
0
1
2
1
0
1
3
0
2
0
0
1
1
2
1
1
1
1
0
0
0
2
0
0
0
0
2
1
2
1
1
0
1
1
2
1
0
1
1
2
0
0
1
1
3
0
2
2
0
2
1
1
2
0
2
1
2
1
2
0
0
2
2
2
0
1
0
2
1
0
0
0
1
0
0
1
1
1
1
0
1
0
1
2
1
0
1
0
0
0
1
1
0
1
1
0
1
0
2
3
0
0
2
0
0
2
2
0
0
0
0
2
0
2
2
1
0
0
0
1
1
0
0
1
2
0
0
2
0
2
0
1
0
0
0
1
0
0
0
1
0
1
2
0
0
0
0
1
1
2
1
1
2
1
0
1
1
2
1
0
0
1
1
0
0
0
1
1
2
0
1
0
0
1
2
1
1
0
2
1
0
0
0
0
2
0
1
1
0
2
0
0
1
0
0
2
1
1
1
1
0
1
2
0
1
2
2
1
1
0
2
1
0
0
2
0
0
1
2
1
0
0
0
1
1
0
0
1
0
0
0
3
1
0
1
0
0
0
1
2
0
0
0
0
2
0
0
1
1
1
1
1
1
1
1
0
1
0
0
1
0
0
0
2
2
2
1
1
1
0
0
2
1
0
1
1
1
0
1
1
1
1
0
1
0
1
2
1
0
0
0
2
1
0
0
1
1
0
2
1
0
0
1
1
0
0
0
1
0
1
0
0
1
2
0
0
1
0
1
1
1
2
2
1
2
0
1
2
0
0
0
1
0
2
0
0
2
0
1
1
0
1
0
1
0
1
1
1
0
0
0
2
2
1
1
1
1
2
0
1
2
1
1
2
2
0
1
0
1
1
0
1
1
1
0
0
1
1
1
0
1
0
0
3
0
2
1
1
0
1
2
1
0
2
1
0
1
1
5
2
1
1
2
2
1
1
0
1
0
0
1
2
1
0
1
1
1
0
2
1
1
0
0
0
0
1
1
0
0
1
2
1
2
2
0
1
1
2
1
3
0
1
2
1
0
1
2
0
1
1
0
0
0
0
1
2
1
1
1
0
0
2
2
1
1
3
2
1
0
0
1
2
1
0
1
2
0
0
0
0
1
2
0
0
0
0
2
2
1
1
2
1
0
1
1
0
2
0
2
1
0
0
0
0
0
2
0
1
0
2
1
0
0
1
1
0
2
1
2
1
0
2
0
2
0
2
1
2
1
0
0
1
0
0
0
1
0
1
1
2
2
0
0
1
1
0
1
2
0
1
1
0
0
2
2
0
0
1
0
1
2
1
1
1
0
0
1
0
1
0
0
0
2
1
2
0
1
0
0
0
2
1
2
0
1
0
2
1
0
1
0
0
0
0
1
1
2
0
1
1
1
1
2
1
1
1
2
0
0
2
0
0
2
0
1
1
1
0
1
0
0
0
0
1
1
1
0
1
1
2
2
2
2
0
0
1
1
0
1
2
0
0
1
0
1
1
1
0
2
2
2
0
2
0
0
1
0
1
1
0
2
1
1
1
1
2
0
1
2
0
0
0
2
1
0
1
2
2
1
1
1
2
0
1
1
1
1
1
0
1
1
0
0
0
0
0
2
3
0
0
1
1
1
0
1
0
1
1
0
1
0
2
0
1
1
2
1
1
2
0
0
0
1
0
1
0
0
0
1
2
1
2
1
1
2
0
0
1
1
0
5
1
0
0
0
1
0
2
0
0
0
0
0
0
0
2
2
0
0
2
0
2
1
2
1
0
1
0
0
1
0
0
2
2
2
0
0
0
2
1
3
0
0
0
0
2
0
0
0
2
2
2
0
1
1
2
0
2
1
1
2
1
1
1
1
1
0
2
1
1
0
0
1
0
1
1
2
1
0
1
1
1
1
0
2
1
0
0
1
1
0
0
1
0
0
0
1
0
1
1
0
1
1
1
2
0
2
1
2
0
2
0
1
2
0
5
1
1
1
0
0
1
0
0
0
0
0
1
0
1
0
1
0
1
0
2
1
0
2
1
1
0
0
0
0
0
0
1
0
2
0
0
2
1
0
1
1
2
1
0
1
1
2
1
0
1
0
0
0
1
2
1
2
1
1
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
1
0
0
1
2
0
1
1
0
1
2
0
0
0
0
1
1
0
2
2
0
0
1
0
2
0
1
2
0
3
3
0
3
0
1
1
0
2
0
1
1
2
0
2
1
2
0
0
1
0
1
0
1
0
1
0
0
0
0
1
0
2
0
2
1
1
0
4
0
0
0
0
0
3
0
0
0
1
1
2
0
0
1
1
0
0
2
1
4
0
0
2
1
0
0
0
0
0
0
0
2
1
0
0
0
2
2
1
0
1
1
1
1
1
1
0
1
1
2
1
2
2
0
0
0
0
0
0
1
0
0
1
2
1
0
0
0
1
2
1
0
0
0
1
0
2
0
1
1
0
1
2
1
1
0
0
1
1
0
2
2
2
0
1
1
1
1
0
0
1
0
2
0
1
0
0
0
2
0
3
0
2
1
1
2
0
0
3
0
0
1
2
1
1
2
0
4
0
1
1
2
2
1
0
2
2
3
1
1
2
0
1
0
0
0
2
0
0
1
1
1
1
0
0
1
1
0
1
2
2
0
2
2
1
0
0
1
4
0
0
2
7
2
1
0
0
0
2
0
1
0
0
2
0
2
1
1
1
1
0
2
2
1
0
0
0
2
0
0
1
2
0
2
2
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
2
1
2
1
0
0
0
0
2
0
0
1
0
2
0
0
3
2
0
2
0
0
1
0
0
2
1
0
0
0
2
0
1
0
2
1
0
2
2
0
0
2
1
0
0
0
0
0
2
0
1
1
1
1
1
1
1
1
1
2
0
0
2
2
1
0
1
0
1
2
1
2
1
2
0
1
0
2
1
2
1
0
0
0
1
2
1
2
0
1
0
1
2
2
0
0
0
2
2
1
2
0
0
2
0
0
1
3
2
0
0
0
2
1
0
1
3
0
0
0
1
0
1
2
2
0
0
1
1
2
1
0
0
1
2
1
0
1
2
2
1
0
2
1
0
0
1
0
0
1
1
0
0
0
0
2
0
1
2
1
1
1
0
0
3
1
2
0
0
2
0
1
0
0
2
2
1
1
3
1
0
2
2
0
0
1
1
1
0
1
2
0
1
0
1
0
0
1
0
1
0
1
3
0
0
1
0
2
0
0
0
2
1
0
0
0
0
1
0
0
2
1
0
0
0
1
2
5
0
2
0
0
1
1
2
0
1
0
1
0
0
0
0
0
2
1
0
2
0
1
1
0
2
1
2
0
0
0
1
1
0
0
2
2
1
0
1
0
0
1
1
0
2
0
1
0
0
2
0
3
1
2
0
1
1
0
0
1
1
0
0
1
2
0
1
1
1
0
1
1
2
0
1
2
2
0
1
0
1
0
1
1
0
0
2
1
1
1
1
1
1
0
0
2
1
0
1
0
1
1
1
1
2
0
2
1
0
0
1
0
0
0
1
3
0
1
0
1
1
1
3
1
0
0
1
0
1
0
0
0
1
2
2
0
1
2
0
1
1
2
1
1
1
0
2
2
1
2
2
1
1
0
1
1
1
1
0
0
0
1
0
0
3
0
1
0
1
0
2
0
0
0
0
0
2
2
0
2
0
1
1
0
1
1
2
0
0
2
0
1
2
2
1
0
0
0
0
1
1
2
0
2
1
1
0
1
1
1
2
2
0
0
1
2
0
0
0
0
0
2
1
0
2
2
1
4
2
0
0
2
1
1
0
0
2
1
0
1
0
1
0
1
0
1
1
0
0
1
2
1
2
0
0
0
2
0
0
2
1
0
1
0
0
2
0
0
0
0
0
1
0
2
2
1
1
0
0
2
0
0
1
1
0
0
0
7
1
0
1
1
0
0
1
2
1
4
1
0
1
0
0
1
1
0
2
0
2
1
1
0
2
2
0
0
1
0
1
0
1
0
1
0
1
1
2
0
2
0
2
1
1
0
0
1
2
2
2
1
0
0
0
2
2
0
1
1
0
1
1
0
2
2
1
1
1
1
0
0
0
1
1
0
1
0
0
1
1
0
0
0
2
1
1
2
0
1
1
1
2
1
1
1
1
2
3
0
0
2
0
1
1
0
1
2
1
2
1
1
0
1
0
2
0
1
1
2
1
1
0
2
0
0
0
0
0
0
1
2
2
0
2
0
2
1
0
0
0
1
1
0
0
0
1
0
0
2
1
0
1
2
3
0
0
2
0
0
2
2
2
1
0
2
0
2
0
0
1
1
3
0
0
2
2
1
1
2
1
0
0
1
2
1
0
0
2
0
2
1
1
0
2
2
0
0
0
1
0
2
0
0
1
1
2
1
3
0
1
0
0
2
1
0
1
1
0
0
0
0
1
1
0
2
1
2
1
0
1
2
1
0
2
2
0
0
1
1
0
1
0
2
1
0
2
0
0
2
1
1
2
2
1
1
0
2
1
1
0
1
0
1
1
0
1
1
0
0
0
0
0
2
0
0
0
2
1
0
0
1
0
1
3
0
0
1
1
0
1
0
1
0
0
0
0
1
2
0
3
2
0
0
2
0
0
0
1
5
0
0
0
0
0
0
2
2
0
2
1
0
2
0
1
1
1
1
1
3
2
1
0
0
4
1
0
0
1
2
1
1
0
1
1
2
0
2
0
1
2
2
2
1
0
2
1
1
0
1
1
2
0
0
1
1
0
1
0
0
0
1
0
0
0
2
2
2
0
1
2
1
0
1
0
0
2
0
1
0
0
3
0
1
2
0
1
1
1
2
2
1
0
1
0
2
1
1
1
1
2
0
2
0
1
0
0
1
2
0
0
1
1
1
1
1
1
2
0
0
0
0
1
1
1
0
0
0
1
0
1
1
0
1
2
2
0
0
0
2
1
0
1
0
1
2
1
1
1
1
1
0
0
1
1
0
3
1
0
2
0
1
1
1
0
1
1
1
0
1
1
1
0
0
0
2
0
0
1
1
0
1
0
1
1
1
0
1
1
1
0
1
1
2
1
1
0
0
2
1
1
0
0
0
0
0
2
1
0
2
1
1
0
1
1
0
0
1
0
3
1
0
0
1
2
1
2
0
0
1
0
0
0
1
0
2
1
0
0
2
1
0
1
1
1
0
0
0
1
0
0
0
1
0
1
0
0
1
1
2
2
2
1
2
0
0
1
0
0
0
0
1
0
0
1
1
0
2
1
0
1
1
0
2
1
1
0
1
0
0
0
2
0
1
2
2
1
2
0
1
1
0
2
1
1
1
1
0
1
1
1
1
0
1
1
0
1
1
0
2
1
2
2
2
2
0
1
1
1
0
1
0
0
0
2
1
4
0
1
0
1
0
1
0
1
1
1
0
4
1
2
0
1
1
2
0
0
2
0
1
1
1
2
0
0
0
1
2
1
1
0
1
1
1
2
0
1
1
2
0
0
2
0
0
0
1
0
0
0
1
1
0
0
1
0
1
0
0
1
1
1
2
1
1
1
0
1
2
2
0
2
0
1
0
1
0
1
0
2
0
0
3
2
0
1
2
0
1
1
1
0
1
2
1
0
0
0
2
1
1
1
0
2
2
2
2
0
0
1
1
0
0
1
1
0
0
0
1
0
0
1
0
0
1
1
1
2
2
2
1
1
0
1
0
2
1
1
1
2
1
0
1
0
1
0
1
1
0
1
1
1
2
0
0
0
0
0
0
1
2
0
1
0
0
0
1
1
0
2
0
1
2
1
2
0
2
0
0
0
0
2
1
0
1
1
0
1
0
0
1
1
0
0
1
2
0
0
2
2
1
2
0
1
1
1
0
2
2
0
1
1
2
0
1
1
1
1
0
1
0
0
2
1
0
1
1
0
3
0
1
0
0
0
1
0
0
1
0
2
0
0
2
2
2
0
1
0
0
0
1
0
0
1
0
1
2
2
1
2
0
2
1
0
2
2
1
2
0
0
2
0
2
1
0
1
1
0
0
2
0
1
2
0
1
1
1
2
0
2
1
1
1
0
0
0
1
0
1
1
2
2
2
0
0
2
2
0
0
0
0
0
0
0
1
0
1
0
3
2
0
1
2
0
0
0
1
0
0
1
2
0
0
0
1
2
0
0
0
2
1
0
2
1
1
0
0
0
1
0
1
1
0
2
1
1
1
0
0
0
1
1
0
0
2
0
2
0
0
1
1
0
1
2
2
1
1
1
1
0
0
0
1
0
1
0
2
0
1
1
2
0
1
0
1
1
0
1
1
1
0
1
1
1
1
2
2
2
0
0
1
1
0
2
2
1
2
2
1
2
1
2
0
2
1
1
0
0
0
0
0
1
1
1
1
1
1
2
1
0
0
0
1
1
0
0
1
0
2
1
2
1
2
1
0
0
0
0
2
0
0
0
1
2
2
1
2
1
2
0
2
0
1
1
2
0
1
1
1
1
0
2
0
1
1
0
0
1
0
1
1
1
1
0
2
0
1
2
0
0
0
1
2
1
0
0
1
0
2
0
2
2
0
0
2
2
0
0
2
0
0
1
2
0
1
1
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
2
2
2
1
1
2
1
0
2
1
0
2
0
1
0
2
0
1
2
0
0
1
0
1
1
1
1
1
2
0
1
0
2
0
0
2
0
0
1
0
2
0
2
1
0
0
1
2
1
2
0
0
1
0
1
0
0
2
1
1
0
0
2
0
1
2
2
0
0
0
0
2
0
2
1
0
1
1
2
1
2
0
1
1
1
0
1
1
1
0
0
1
0
0
0
1
1
2
0
2
1
0
0
0
2
1
2
0
1
2
0
2
0
1
0
1
0
0
0
1
1
0
2
0
1
0
0
0
0
0
0
1
0
1
1
1
1
0
2
0
1
1
0
0
0
2
0
1
0
0
1
0
0
2
1
0
2
1
0
2
3
1
2
0
3
1
1
1
0
2
0
2
0
0
1
1
0
2
1
0
0
0
0
4
1
0
2
1
1
2
0
0
1
0
1
0
0
1
1
1
0
2
0
0
1
2
0
1
1
0
0
1
0
2
0
1
0
1
1
0
2
1
2
0
1
2
1
3
1
0
1
2
0
0
2
0
1
1
0
0
1
2
2
0
0
0
1
0
2
3
1
0
2
1
0
1
0
0
1
0
0
1
1
2
1
0
1
2
0
0
3
2
1
0
1
0
1
2
0
1
2
2
0
2
0
1
1
0
0
2
1
2
0
1
1
0
1
0
1
1
1
0
0
2
0
2
1
0
0
1
2
1
1
2
0
1
0
1
1
1
1
2
0
2
1
1
1
2
0
1
1
1
2
1
1
1
0
2
2
0
1
1
2
2
0
1
0
2
0
2
1
1
0
3
0
0
1
1
0
1
1
0
1
0
1
0
1
0
1
3
0
0
0
0
1
0
0
0
1
2
0
2
0
0
3
3
0
0
2
0
1
1
1
2
0
0
0
1
1
0
2
0
1
1
1
1
0
2
2
0
0
2
0
2
2
2
1
1
1
0
1
2
1
0
0
1
1
1
3
1
0
0
1
1
1
0
0
0
0
2
2
0
0
1
0
0
1
0
2
0
1
1
0
1
0
1
1
1
1
0
1
2
2
0
2
1
0
1
0
0
0
1
2
1
0
1
0
1
2
0
1
0
0
0
2
1
0
2
1
2
2
1
0
2
0
2
0
2
0
1
2
0
0
0
0
0
1
2
3
2
1
0
0
0
1
2
0
1
0
1
2
2
0
2
0
0
0
1
1
1
2
1
2
1
0
2
2
0
2
0
1
1
1
2
3
0
2
0
0
0
1
0
1
1
0
0
1
1
0
2
1
0
0
1
0
2
0
2
1
1
0
2
0
0
0
0
0
0
1
0
0
2
0
1
2
1
0
2
2
2
3
1
1
0
2
1
1
3
1
0
0
0
0
2
1
1
0
2
0
0
0
0
2
0
3
0
1
0
0
1
0
1
2
2
2
0
0
0
2
0
2
1
2
3
1
0
2
1
0
1
2
0
0
1
0
0
2
0
1
1
1
1
0
0
0
0
0
0
1
1
1
2
1
1
2
1
0
0
2
2
0
2
0
2
1
0
1
2
0
0
1
2
0
0
0
0
0
2
0
1
2
0
0
2
2
1
0
0
0
1
0
0
2
0
2
3
0
0
0
2
0
0
1
2
1
0
1
1
1
1
0
0
0
1
0
0
0
0
0
0
1
1
0
2
0
1
2
0
1
1
1
1
0
0
0
0
1
0
0
1
1
2
1
2
1
1
2
1
0
0
1
0
0
1
0
0
0
1
2
0
2
1
0
0
2
0
0
1
1
0
0
0
0
1
2
0
0
1
0
0
1
0
1
1
0
0
1
0
1
0
2
2
3
0
1
0
0
0
1
0
2
0
0
2
2
1
2
1
0
1
1
0
0
1
2
0
1
1
2
1
0
0
1
1
2
1
0
0
3
1
1
1
1
0
1
1
0
1
1
0
1
0
2
2
1
0
2
2
1
2
0
2
1
0
0
1
1
0
1
1
1
2
0
2
0
0
1
2
1
2
0
2
0
1
1
0
1
2
3
2
2
0
0
2
0
0
1
0
1
2
1
0
0
0
0
0
1
0
2
1
0
0
0
0
0
2
1
2
1
0
2
0
0
1
0
2
1
3
0
1
1
0
1
0
1
0
1
1
1
0
2
0
0
0
2
0
2
2
1
0
1
0
1
0
0
0
0
0
1
1
0
1
1
2
0
0
1
0
1
0
0
1
1
2
1
0
2
0
0
0
2
0
0
1
2
1
2
0
1
1
1
1
2
0
1
1
0
2
1
2
0
1
2
0
0
1
2
2
0
0
1
1
2
0
0
0
3
1
2
0
2
1
0
0
2
0
1
2
0
1
1
0
0
0
1
0
1
1
0
1
0
1
0
0
1
0
1
0
1
2
0
2
1
0
0
0
2
1
3
1
1
2
0
0
0
0
0
0
2
0
2
0
1
2
0
0
0
3
0
0
0
0
2
0
0
2
1
2
1
0
0
2
1
1
0
0
0
0
1
0
2
1
0
0
1
0
0
2
2
2
1
1
0
1
0
1
0
1
0
1
1
1
0
2
2
0
0
0
0
0
0
2
3
0
1
0
0
0
0
1
0
2
1
1
2
2
1
2
0
2
2
1
1
2
0
0
2
0
0
1
0
0
2
0
2
1
1
0
1
1
0
1
1
0
0
0
1
0
0
1
0
1
1
0
1
0
0
1
0
1
2
2
1
2
0
2
0
2
0
2
2
1
1
1
0
1
2
0
0
1
0
0
0
1
2
1
0
1
1
1
0
1
0
2
2
0
0
1
1
2
0
2
0
0
1
0
2
2
0
0
2
0
0
0
1
0
0
1
0
1
1
2
1
2
0
1
0
1
0
0
0
2
0
1
4
2
2
2
1
0
1
0
1
1
0
1
0
1
1
0
0
0
0
0
1
1
2
0
1
2
2
0
1
3
1
2
1
0
0
0
0
1
1
1
0
1
0
1
0
0
1
0
1
1
0
2
1
0
2
1
2
0
0
0
0
0
0
1
0
0
2
0
1
2
2
2
1
0
1
0
0
0
1
1
2
1
1
2
2
2
0
0
1
0
1
2
0
1
1
1
0
1
2
1
2
0
1
0
0
0
7
1
0
0
1
2
0
2
0
0
2
0
1
0
0
1
1
2
0
0
0
0
0
0
0
0
1
2
1
0
2
0
1
1
2
0
1
0
0
0
1
0
0
2
1
1
0
0
1
0
1
0
0
1
2
0
1
2
1
2
1
0
0
1
2
2
0
2
2
1
0
2
2
0
0
1
1
0
1
2
0
1
2
0
2
3
1
0
1
0
1
0
1
2
1
1
1
0
1
1
3
2
1
0
0
0
1
1
0
1
0
0
2
0
2
2
2
0
2
1
0
2
1
0
2
1
0
0
1
0
0
0
0
0
1
0
2
1
1
2
1
2
1
1
0
0
1
0
0
1
2
1
1
2
0
2
2
0
0
2
2
0
1
1
2
0
1
2
2
2
0
1
1
1
0
2
0
0
2
2
1
1
0
2
3
0
0
1
0
0
1
2
0
2
2
1
0
0
0
1
0
1
1
0
0
0
1
2
1
0
1
0
0
1
0
1
1
1
1
1
2
0
1
1
2
1
0
0
1
2
1
2
1
3
5
2
0
0
0
0
0
1
0
0
1
2
2
1
0
0
0
0
0
0
1
1
0
0
0
2
1
2
0
0
2
1
2
0
1
0
1
1
0
1
0
0
0
2
2
0
1
1
2
0
2
0
1
1
1
1
1
2
1
2
1
2
1
1
1
0
1
1
1
0
3
1
1
1
1
2
0
0
1
0
0
0
2
0
2
1
0
2
2
1
0
1
2
0
2
0
1
2
0
1
0
2
0
1
2
0
0
0
0
0
1
1
3
2
0
0
1
2
1
0
1
0
0
2
2
1
1
1
1
0
2
0
0
1
0
2
0
2
0
0
0
0
0
2
2
0
0
0
1
1
0
0
1
1
0
0
1
0
1
1
1
0
0
0
1
1
0
1
1
1
0
1
0
0
1
1
0
1
0
1
1
0
2
0
0
0
1
1
0
0
1
0
0
2
0
1
1
1
0
1
2
1
1
1
0
1
1
0
1
0
2
2
2
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
1
2
1
0
0
1
1
2
2
2
1
0
1
2
2
1
0
0
1
1
2
0
1
0
0
2
2
0
1
1
1
0
0
1
1
3
0
0
0
1
0
0
1
0
0
1
2
0
2
1
0
0
1
1
0
1
0
1
2
2
0
1
0
0
0
1
1
0
1
1
5
1
2
1
1
1
1
1
0
0
2
1
4
1
1
2
0
1
0
0
0
1
0
2
0
1
1
1
0
1
1
0
0
0
1
2
0
0
1
1
1
0
0
1
2
1
1
0
0
2
1
2
1
0
0
0
0
2
1
2
0
0
0
0
0
1
0
1
0
1
0
0
0
2
2
2
2
0
0
1
1
0
2
2
0
0
1
2
2
1
0
1
0
0
1
0
0
2
1
1
2
2
0
2
2
0
1
0
2
2
2
0
1
2
1
0
1
0
1
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
1
0
2
1
0
2
0
1
0
1
2
0
2
1
1
2
0
1
2
0
1
2
1
2
0
0
0
0
2
1
0
0
0
1
0
0
1
1
2
1
0
1
0
1
1
0
1
2
1
1
0
1
0
1
1
0
1
0
1
1
0
3
0
1
2
1
1
2
0
1
1
0
0
0
2
2
2
0
2
0
1
1
0
2
1
0
2
0
0
0
0
0
1
1
2
1
1
0
0
1
0
2
1
1
1
1
1
1
2
0
1
1
1
0
2
0
1
2
0
0
0
2
1
0
0
2
1
1
0
1
1
0
1
0
1
0
1
2
1
1
2
1
0
0
0
2
0
0
4
0
1
0
1
0
1
1
0
2
0
1
0
1
1
2
1
0
0
0
2
0
0
0
0
0
1
2
2
0
1
0
0
1
0
2
1
1
0
0
0
0
0
0
0
1
0
1
0
1
2
1
0
0
0
2
1
0
1
2
0
0
0
2
0
2
0
3
1
0
1
1
1
0
1
0
2
0
2
2
2
2
2
0
0
0
1
0
0
1
1
0
0
1
0
0
1
0
0
2
2
1
1
1
2
2
0
0
0
0
1
0
0
2
0
1
1
0
1
1
2
0
0
1
1
2
0
2
1
0
0
2
1
0
2
1
2
0
1
0
1
0
1
0
2
1
0
0
2
0
0
1
0
2
0
0
0
0
0
2
0
0
0
1
1
0
0
0
1
0
1
2
0
1
2
1
0
1
1
2
0
0
2
0
0
2
1
0
0
1
1
1
1
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
1
2
1
1
0
0
1
2
2
1
1
2
1
0
0
1
2
2
1
0
1
0
0
0
2
2
1
0
2
2
0
1
1
0
1
0
2
0
0
1
1
0
0
1
2
0
0
0
0
0
1
1
0
0
1
1
1
1
0
2
2
1
0
0
2
2
0
0
1
0
0
2
0
1
0
0
0
2
1
0
0
2
0
0
1
2
0
1
1
1
2
0
0
0
0
0
1
0
3
1
0
2
2
1
2
2
2
1
1
1
0
2
0
1
1
0
0
1
1
1
0
0
1
0
3
0
0
0
2
1
2
1
0
0
1
0
1
1
0
0
1
2
0
0
1
0
1
0
1
1
2
0
0
0
2
0
1
1
2
0
0
0
0
0
0
0
1
0
2
0
2
0
1
0
0
1
2
0
0
1
3
1
0
2
1
1
1
1
0
1
0
1
1
1
0
2
1
1
1
0
1
1
2
0
2
1
1
1
2
1
1
0
1
2
2
1
0
2
0
0
1
0
0
0
0
0
0
0
2
1
2
0
0
0
0
2
1
0
0
2
3
0
1
0
0
0
2
1
1
1
1
0
2
0
0
0
0
1
0
2
0
0
2
0
1
2
0
0
0
2
0
1
0
0
1
1
1
1
1
0
1
2
0
0
0
1
0
1
1
1
0
2
1
0
0
1
0
0
1
0
1
1
0
3
0
2
2
0
0
0
2
2
0
0
1
1
0
1
1
2
2
2
1
0
1
0
1
1
1
0
0
1
0
0
1
2
1
0
2
0
1
0
2
0
0
0
2
1
0
1
1
1
0
1
1
1
1
2
0
0
1
1
1
0
3
1
0
0
0
0
0
0
1
1
1
0
1
1
0
2
0
0
0
0
1
1
1
2
4
0
0
2
0
2
0
2
0
2
0
0
2
2
0
0
1
1
1
2
0
0
1
0
1
0
1
0
1
1
2
1
1
0
2
0
2
3
0
2
0
0
0
1
1
1
1
0
2
1
2
1
1
1
1
0
1
0
1
0
0
2
2
0
2
2
0
0
1
4
1
2
2
1
2
0
0
1
1
0
0
2
0
2
1
1
1
1
1
2
2
2
1
2
0
2
1
0
0
1
2
0
0
0
2
1
1
1
0
2
2
1
1
0
2
2
0
0
0
0
1
0
0
0
1
2
0
1
0
1
0
0
1
2
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
2
0
1
2
0
4
0
2
1
1
1
0
0
0
0
1
2
2
2
2
1
2
1
2
1
0
0
0
0
0
0
0
1
1
0
1
0
1
2
0
1
1
1
1
0
0
2
1
1
2
0
1
0
2
2
2
0
1
2
2
0
1
1
1
2
2
0
0
0
0
0
1
1
0
3
1
2
2
1
1
3
2
1
2
1
1
0
2
0
2
0
2
3
1
2
1
1
0
2
2
2
2
2
1
0
2
1
1
2
1
0
1
0
1
2
1
1
1
2
2
0
1
1
0
0
0
0
0
0
1
0
0
1
1
0
1
2
2
0
0
0
0
2
1
0
2
0
0
0
0
1
0
1
2
0
2
1
1
2
0
0
2
0
1
0
1
1
2
0
1
1
0
1
1
1
1
0
1
2
0
0
1
2
0
0
0
0
0
0
1
2
0
1
0
0
1
2
2
0
0
1
1
0
0
1
0
1
1
0
0
1
1
0
2
1
1
1
1
2
1
0
1
0
0
1
1
1
0
1
2
0
2
2
1
2
1
3
1
1
0
0
0
1
1
0
1
1
1
3
0
0
1
0
0
0
1
1
1
1
1
1
0
2
2
0
2
2
1
1
2
0
1
1
1
1
2
1
1
1
2
0
0
0
0
2
1
0
0
1
2
4
0
2
0
0
0
0
1
0
1
0
1
1
1
0
0
2
2
1
2
2
2
1
0
1
2
1
1
0
0
0
0
0
2
2
0
1
1
2
2
0
1
1
1
1
0
2
0
1
1
1
1
3
1
1
2
0
1
0
0
1
0
0
2
0
1
2
1
1
2
0
1
1
2
1
0
0
2
1
2
1
1
2
2
2
0
3
0
0
0
2
0
1
2
0
2
1
0
0
1
0
0
1
2
1
0
2
2
0
1
0
0
1
0
0
0
0
0
0
0
2
0
1
2
0
0
2
0
1
0
1
1
0
1
1
0
0
1
0
1
2
2
0
0
1
0
1
0
1
0
1
0
1
2
0
0
1
0
1
2
0
2
0
2
0
1
0
0
1
0
0
1
0
0
0
2
2
0
2
1
1
0
1
1
1
0
0
0
0
0
1
0
2
0
1
1
2
1
0
1
2
2
1
0
0
0
1
0
1
1
0
0
1
1
0
1
1
1
0
1
1
2
1
2
2
2
2
0
1
1
1
2
1
0
0
0
0
1
0
1
0
1
0
1
0
1
1
2
2
0
0
0
1
0
0
0
0
1
0
1
1
1
2
0
0
1
2
1
0
0
1
0
0
1
1
1
0
2
0
0
2
1
0
2
1
1
0
1
0
2
2
1
0
2
2
0
0
0
0
2
2
0
0
0
0
1
0
1
1
2
2
1
0
1
2
1
2
0
1
2
0
0
2
1
0
0
1
1
1
2
1
2
0
0
0
2
1
1
0
1
2
0
0
0
1
1
1
1
2
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
3
2
0
0
2
2
0
0
0
0
1
1
1
0
1
0
2
0
2
0
2
1
0
0
0
1
0
2
2
0
0
1
2
1
1
2
0
1
0
1
1
0
1
2
0
0
1
2
0
1
0
1
1
1
0
1
2
1
0
0
1
1
0
2
0
0
0
0
2
0
1
3
0
1
1
0
1
1
1
1
2
1
0
1
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
2
0
2
2
0
1
0
0
5
0
1
2
1
0
1
2
2
0
0
2
1
1
1
1
0
1
1
0
1
1
0
0
0
1
0
2
2
2
0
1
1
2
0
1
0
1
0
0
1
1
2
0
0
2
0
0
0
2
1
1
1
0
0
2
1
0
1
1
1
1
0
2
0
0
2
1
2
0
0
2
3
1
2
1
1
1
0
1
1
3
1
1
1
1
1
0
2
2
1
1
2
1
2
0
2
0
0
3
1
1
1
1
1
0
0
1
1
0
0
1
0
1
1
2
0
1
0
0
2
1
1
0
2
1
2
0
0
1
1
1
0
1
0
2
0
0
2
0
0
1
0
0
9
1
1
2
2
1
1
1
0
1
0
1
0
0
1
0
2
0
0
1
1
1
3
1
1
1
1
1
0
1
0
3
0
0
1
0
0
2
0
2
2
1
1
1
0
2
0
2
1
0
1
0
0
1
5
1
0
1
2
0
1
1
1
1
2
1
1
2
0
1
1
1
0
1
0
1
0
1
0
1
1
0
2
0
1
0
1
0
0
0
3
2
1
2
0
0
1
2
2
0
2
0
0
0
1
1
2
0
2
1
0
2
2
1
1
2
2
0
0
0
1
1
0
2
2
2
0
2
2
1
0
2
1
2
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
4
2
1
1
1
1
2
2
0
0
2
1
0
0
0
0
0
2
1
2
2
2
1
1
1
1
0
2
0
1
1
0
0
2
2
0
0
3
0
0
1
1
2
1
2
1
1
0
1
2
1
0
1
0
1
0
0
2
1
0
0
1
1
1
2
0
3
0
0
2
2
2
0
0
1
0
1
0
1
1
2
0
1
2
0
1
1
0
0
2
0
1
0
0
0
2
1
1
1
0
0
2
4
0
1
0
1
1
1
0
1
1
2
0
0
0
1
2
1
0
2
1
1
1
2
0
0
0
0
5
0
2
0
2
0
2
1
1
1
1
2
2
1
0
0
0
0
1
0
0
1
1
1
0
1
0
0
1
2
0
0
0
2
0
1
2
1
1
1
0
0
1
2
0
0
0
1
0
0
0
0
2
1
1
1
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
2
0
2
0
1
1
0
1
0
0
1
0
2
0
1
1
0
0
1
0
1
1
2
0
1
1
0
1
0
0
0
1
1
0
0
0
1
0
1
0
0
1
2
1
2
2
0
0
0
0
1
1
0
1
2
1
2
0
0
1
2
1
1
0
0
1
2
1
1
0
2
1
0
0
1
2
0
1
0
1
1
0
2
2
2
0
0
2
1
0
0
0
1
2
2
0
0
1
1
0
1
0
0
0
0
0
0
0
2
1
2
0
0
0
1
2
2
1
0
2
2
1
2
1
1
1
0
0
1
1
0
1
0
2
1
0
0
1
0
0
0
0
1
0
0
2
2
1
1
2
2
1
2
0
0
2
1
1
0
0
0
2
1
0
1
2
1
1
1
0
1
1
1
1
1
2
0
2
0
1
7
0
1
2
1
4
1
0
1
2
1
0
1
1
1
0
0
0
1
1
3
1
1
0
1
0
5
0
2
2
0
0
0
2
2
1
1
2
2
2
0
0
1
1
1
2
2
0
1
0
0
0
2
1
2
2
0
0
0
1
1
1
1
0
2
1
2
2
1
1
0
0
2
0
0
0
1
1
2
0
0
1
0
1
0
0
1
1
1
0
1
2
0
0
0
1
1
0
1
2
2
0
1
0
2
1
0
1
1
1
1
0
0
1
1
1
0
1
0
1
0
2
2
2
0
0
0
1
1
2
0
0
2
2
3
1
0
0
0
1
0
0
0
0
1
1
0
0
2
0
3
0
2
1
0
1
0
0
0
1
0
1
1
0
0
2
1
0
0
0
0
0
0
0
1
3
1
0
2
0
2
1
0
1
2
1
0
0
1
2
0
0
2
1
0
2
2
1
0
0
2
0
2
1
0
0
1
0
1
1
1
3
0
0
1
0
1
0
0
1
0
1
0
1
0
0
1
0
2
2
1
1
0
0
3
1
0
0
0
0
2
0
0
1
2
0
0
1
1
2
0
2
2
0
1
1
1
0
0
1
1
0
0
0
1
1
2
0
0
1
0
1
0
1
0
2
0
1
3
0
1
0
1
0
2
0
1
2
1
0
2
0
1
0
1
1
3
0
0
2
2
1
0
1
0
0
1
1
0
1
0
0
2
1
0
1
1
2
2
2
1
1
0
2
0
1
1
1
1
0
0
1
0
1
1
1
3
0
1
1
1
0
0
0
1
0
0
1
0
3
0
0
2
2
0
0
1
2
1
1
0
1
2
1
2
2
0
1
1
1
2
1
1
0
1
0
1
1
0
1
2
0
0
0
0
0
0
1
0
1
0
2
0
0
1
0
2
0
1
0
0
0
0
1
1
0
0
1
1
1
0
0
2
2
1
0
1
1
1
0
0
0
0
2
3
1
0
0
1
1
2
1
0
0
1
0
1
2
0
1
0
0
1
0
1
0
1
0
1
0
2
1
2
2
1
2
0
0
0
2
0
1
1
0
0
1
1
0
1
0
1
1
0
2
0
0
2
0
2
0
0
2
0
1
1
0
1
0
0
0
0
1
1
1
1
0
1
1
1
2
0
0
0
0
1
0
1
0
0
1
1
0
1
1
0
0
1
0
2
1
0
1
2
1
0
5
0
0
0
2
0
0
1
1
2
0
0
2
0
0
2
2
0
1
0
1
0
2
0
1
2
1
0
1
2
0
0
0
1
2
0
1
0
2
1
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
2
1
0
1
2
3
0
0
0
0
2
2
0
1
1
2
0
0
0
0
0
0
1
1
0
2
0
2
1
1
0
3
0
0
0
1
1
2
4
1
0
1
1
0
0
2
1
2
0
0
1
2
1
0
1
0
2
0
1
1
2
0
2
3
0
1
1
2
0
1
0
1
0
2
1
0
2
0
0
2
0
0
0
0
2
2
1
1
2
1
1
0
1
0
0
0
1
2
0
2
2
0
0
0
2
0
1
0
2
0
0
2
0
2
1
0
0
1
0
0
0
0
0
1
2
0
0
1
2
1
0
1
0
1
2
0
1
2
0
1
1
0
1
2
1
1
0
2
2
0
0
1
1
0
1
1
1
2
0
0
0
0
2
2
2
1
1
1
2
0
1
1
1
2
0
1
1
0
1
0
1
2
2
0
5
1
2
1
1
1
1
1
2
0
2
1
1
0
0
0
0
0
0
1
0
0
1
1
0
2
4
2
0
0
0
0
0
0
1
0
2
0
1
0
0
0
1
0
0
1
1
0
0
1
0
1
0
3
1
0
1
0
1
1
0
0
0
2
3
0
1
1
1
1
1
2
0
0
2
1
1
0
0
0
1
2
2
0
0
0
0
2
0
3
2
0
0
1
0
1
2
0
0
0
1
0
1
0
1
1
1
1
0
1
1
1
1
0
0
2
0
0
0
1
0
2
0
0
2
0
1
1
1
0
4
0
2
0
1
1
1
1
0
1
0
1
1
2
1
0
2
1
1
2
1
0
2
3
0
0
0
1
3
2
0
0
1
2
1
1
0
1
2
1
0
1
0
2
2
2
0
0
0
1
1
0
0
1
2
1
0
4
2
1
0
0
2
0
2
2
2
2
1
1
2
0
2
0
1
0
2
1
1
0
2
0
0
1
0
0
0
2
1
1
0
1
0
1
1
0
1
2
2
1
2
1
1
0
2
0
0
2
0
1
1
0
2
1
2
2
0
2
1
2
3
0
2
0
1
2
0
0
1
1
1
1
0
2
2
0
0
2
1
1
1
2
0
0
1
1
2
0
0
0
0
1
2
0
2
0
0
2
0
0
1
1
0
0
2
2
0
2
2
0
1
1
0
1
1
0
1
0
2
0
0
3
1
2
0
1
1
2
0
1
0
2
2
1
2
0
1
0
0
1
2
2
1
1
0
2
1
1
0
1
1
1
1
2
0
0
0
0
0
0
1
2
1
2
1
1
3
1
0
1
0
2
0
1
0
0
1
0
0
2
2
0
1
1
1
0
0
0
1
1
0
0
1
1
1
2
0
1
0
0
0
1
0
2
1
1
0
0
0
2
0
2
2
0
0
2
1
0
1
0
1
2
0
1
2
2
2
4
2
0
1
0
2
2
1
0
2
1
2
0
1
0
0
1
1
0
0
1
2
1
3
2
1
2
1
0
0
0
1
2
2
2
0
0
1
0
2
1
1
0
1
1
1
2
0
0
3
1
2
1
0
2
1
0
2
1
0
2
1
0
1
0
2
2
1
0
2
1
2
0
2
2
1
2
2
1
0
0
0
1
0
1
1
2
2
0
0
2
0
0
0
1
1
0
2
1
1
1
1
2
1
1
0
0
0
2
1
1
0
1
0
0
1
0
1
0
3
0
2
0
0
0
1
1
0
0
0
0
0
1
0
0
1
1
1
1
1
1
1
1
1
0
0
1
0
1
2
1
0
1
2
0
1
1
1
1
0
0
1
1
0
0
2
0
1
1
0
0
2
1
1
2
2
0
2
2
1
0
0
2
1
0
1
0
1
0
0
2
1
1
2
0
0
0
0
0
1
0
1
1
1
2
1
0
0
1
0
1
2
0
1
0
0
1
0
1
1
1
0
0
0
0
1
1
0
1
0
1
0
0
2
1
0
0
1
1
1
1
2
1
1
1
0
2
3
0
2
1
1
0
1
0
2
0
2
2
2
1
2
0
1
1
0
0
0
0
0
0
1
0
2
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
5
1
0
0
2
2
0
0
1
0
2
1
0
2
1
2
1
1
0
0
0
2
2
0
0
1
1
0
0
1
0
0
0
1
1
1
2
0
1
0
0
0
1
0
1
0
1
2
1
1
1
0
0
1
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
2
0
0
3
2
1
0
0
2
0
2
0
0
1
2
0
0
1
1
1
1
2
0
0
0
1
1
1
0
2
1
1
2
2
2
1
2
2
1
0
0
0
3
0
2
0
2
2
0
1
2
1
0
0
2
2
0
0
1
2
1
1
0
0
0
1
2
2
1
1
2
1
1
0
3
2
0
0
0
0
0
0
2
1
0
1
0
1
0
0
2
1
1
1
0
2
0
1
0
2
0
2
1
0
1
1
1
0
0
2
0
0
0
0
0
1
0
2
0
2
2
0
2
0
1
2
0
2
2
0
1
2
1
0
1
1
0
1
2
0
0
2
1
1
0
0
3
0
2
1
0
0
2
2
0
2
0
1
1
0
2
1
1
0
2
0
0
1
1
0
0
1
0
2
1
0
0
1
0
0
0
1
0
2
1
0
1
1
1
0
0
1
2
0
2
1
1
1
0
1
1
1
1
0
2
1
1
0
0
0
1
2
2
2
2
0
1
0
0
0
2
0
3
0
0
2
2
0
2
0
1
0
0
1
0
2
1
1
0
0
2
2
1
0
2
2
1
0
2
0
3
0
0
1
0
0
0
2
1
1
0
2
2
0
2
0
0
2
1
0
0
2
1
2
1
0
1
0
0
1
1
1
0
2
1
0
0
0
0
1
0
1
0
2
1
1
0
0
0
0
0
1
2
2
1
0
1
2
1
1
0
2
0
1
0
2
0
0
1
1
0
1
1
2
0
2
1
1
0
2
0
0
1
1
2
0
0
1
3
1
0
0
0
1
2
2
1
1
0
2
2
2
2
0
2
2
2
0
1
2
0
1
0
2
4
0
1
2
0
2
0
1
0
0
0
0
0
0
0
1
2
0
2
0
0
2
0
0
1
0
0
0
1
0
1
1
0
0
1
0
2
2
1
1
0
2
1
1
1
1
2
1
0
1
0
0
0
0
2
2
0
1
2
0
1
0
0
0
1
2
0
0
1
2
1
1
1
1
1
1
2
0
0
0
2
1
0
2
1
1
0
0
1
1
1
0
0
1
1
0
0
1
0
0
2
1
0
0
0
1
1
0
0
2
1
1
0
0
1
1
1
0
1
1
2
0
0
1
0
0
1
0
2
0
2
1
1
0
4
2
0
0
1
1
2
1
1
1
0
1
0
1
0
0
1
2
0
0
4
2
2
2
1
0
1
0
1
0
1
2
0
0
1
1
1
1
2
0
1
1
2
2
1
0
1
1
2
2
0
0
1
2
0
0
1
2
0
1
2
1
0
0
0
1
2
3
0
0
0
0
1
0
1
0
0
1
1
3
0
0
1
2
0
1
0
0
0
1
0
2
0
1
2
0
1
1
2
1
1
0
0
1
1
0
0
1
0
1
2
0
1
1
0
1
0
0
1
1
0
1
2
0
0
1
2
1
0
0
2
0
1
0
1
1
2
2
0
2
0
1
1
1
3
1
2
0
0
2
0
2
1
0
1
0
2
0
0
1
0
1
1
0
0
2
2
1
0
1
0
0
0
2
1
0
2
0
2
0
1
1
2
0
19
0
1
0
0
0
2
0
2
3
2
1
2
1
1
2
0
1
0
3
2
1
0
0
0
0
1
0
1
0
0
1
0
1
0
2
1
1
0
2
0
0
1
1
0
0
2
0
0
1
0
1
0
0
0
0
1
1
1
0
1
1
2
1
0
0
0
1
0
0
0
2
0
0
1
0
1
0
0
1
1
0
1
0
1
0
2
1
0
0
0
0
1
1
0
2
2
3
2
2
1
2
0
0
0
0
0
3
0
1
0
5
0
0
0
0
0
1
2
2
0
0
1
2
0
2
2
2
1
0
1
1
1
1
1
2
0
0
0
0
0
1
0
2
0
1
2
0
0
1
0
0
0
0
2
1
1
0
2
1
0
1
1
0
0
0
1
3
2
0
1
1
0
0
1
2
2
1
1
0
1
0
0
0
0
0
2
2
1
1
0
3
0
1
0
0
0
0
1
1
1
2
0
1
1
2
1
0
0
0
1
0
1
0
0
0
0
1
0
2
2
0
0
1
0
1
0
0
1
0
2
1
1
0
2
2
0
0
0
2
1
0
2
0
0
2
2
0
0
4
1
0
2
3
1
2
1
1
0
0
1
2
1
2
2
0
1
0
1
0
2
1
0
2
0
1
0
0
0
0
2
1
0
2
1
1
0
2
0
1
1
0
1
1
0
0
0
0
1
0
0
1
2
1
0
0
1
2
1
0
1
1
1
0
1
0
2
1
1
1
0
2
1
0
0
2
1
1
1
0
2
0
2
1
1
1
0
0
0
0
1
1
0
2
0
0
0
1
2
0
2
1
1
0
1
1
0
0
2
1
1
1
3
2
1
1
0
0
0
0
0
2
0
1
1
1
0
1
0
1
0
1
0
2
0
1
2
0
1
1
0
0
1
0
0
0
2
0
1
1
0
1
2
1
0
0
1
0
1
0
1
0
1
0
1
0
2
1
0
0
0
0
2
1
2
0
0
0
1
2
0
0
1
0
2
0
3
2
0
1
1
1
0
0
2
0
2
1
1
1
0
0
0
2
1
1
1
0
1
2
2
0
0
1
1
1
1
1
1
0
0
0
0
1
0
0
2
2
0
1
0
0
2
2
0
1
0
1
0
1
0
0
0
1
2
0
0
0
0
0
1
2
1
0
1
1
2
2
1
1
1
2
0
0
1
1
0
0
2
0
2
0
1
0
0
1
2
0
1
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
2
2
0
1
2
0
0
0
2
3
0
0
1
0
1
1
1
0
2
1
2
1
1
1
1
1
0
0
2
0
1
0
1
0
1
1
0
0
2
0
1
2
1
0
2
2
0
0
2
0
2
0
1
0
0
0
0
0
2
0
2
0
1
0
2
0
0
1
0
1
0
2
0
0
0
0
2
1
1
2
0
1
1
1
1
1
1
0
1
1
0
0
0
0
1
1
2
0
0
0
0
0
2
0
1
0
1
0
2
1
1
1
0
1
2
0
1
0
0
0
1
2
2
1
2
1
2
0
0
2
2
1
1
4
0
0
2
1
0
0
1
2
1
0
0
1
0
1
2
1
0
0
1
1
0
1
0
0
1
0
0
1
1
0
2
0
0
2
2
0
0
1
0
1
0
2
1
2
0
0
2
1
0
0
0
0
0
2
1
1
0
3
0
0
1
1
1
2
1
1
0
0
1
0
2
0
1
0
0
1
0
1
0
0
0
0
0
1
0
1
0
2
0
0
0
0
1
2
0
0
2
1
2
0
0
0
0
0
0
1
0
1
3
1
1
0
0
0
0
2
2
2
1
0
1
0
0
1
0
1
1
1
2
1
0
2
0
1
3
1
0
1
0
1
1
0
0
3
1
0
0
3
0
1
2
2
1
2
0
1
1
2
0
2
3
1
0
0
0
1
1
1
1
0
0
1
2
0
1
0
1
0
1
3
0
1
1
1
0
4
1
0
1
2
1
1
2
1
0
0
1
0
1
0
1
0
1
0
0
0
2
2
1
2
0
2
2
0
0
0
0
1
0
0
1
2
0
1
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
1
6
0
1
2
0
0
0
2
3
0
0
1
1
0
1
0
2
0
0
1
1
1
0
0
1
0
1
0
0
0
0
1
0
0
2
0
1
1
1
2
0
0
1
1
0
0
0
1
2
1
2
0
2
2
0
2
0
1
1
1
2
0
0
0
1
1
1
1
1
2
2
2
2
1
1
0
0
1
0
0
1
0
0
0
0
0
0
1
5
0
2
1
0
1
0
2
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
2
0
0
1
0
0
0
1
1
1
0
1
1
2
1
0
0
0
0
0
0
1
0
1
1
0
2
1
0
0
0
0
0
2
1
1
0
0
1
0
0
2
0
1
1
2
1
2
1
0
0
1
1
2
2
1
1
1
0
0
1
1
0
2
1
0
0
2
1
0
1
0
0
0
1
1
0
0
1
2
0
0
1
1
2
2
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
2
1
0
0
0
0
0
0
2
1
1
0
4
0
0
2
2
2
2
2
0
1
2
2
0
0
2
0
0
0
1
1
0
0
2
2
0
2
1
1
1
3
0
3
1
1
1
0
0
1
2
1
0
2
0
1
0
1
2
1
0
4
0
1
0
1
2
1
0
2
0
2
0
1
1
0
2
0
0
0
0
0
0
0
0
1
0
1
0
1
2
2
2
2
2
2
0
1
5
0
0
0
2
0
2
0
0
1
0
1
0
1
1
1
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
2
2
0
1
0
0
0
0
1
1
3
1
2
0
6
2
1
1
0
1
0
1
0
1
0
0
0
0
2
2
1
1
1
2
2
2
1
0
1
0
1
2
1
1
0
2
1
0
0
1
2
0
1
0
0
2
0
2
1
0
0
2
1
2
0
0
0
1
0
1
1
1
0
1
1
1
1
2
0
0
1
0
1
0
2
1
0
1
2
1
1
0
0
1
3
2
2
0
0
2
0
2
1
0
2
0
1
0
0
2
1
0
0
1
1
0
0
1
1
2
0
1
1
1
1
2
1
2
2
1
0
0
0
1
1
1
1
0
1
0
0
0
0
0
1
1
2
1
1
0
0
1
1
1
2
0
1
1
1
0
0
2
0
1
1
1
1
1
1
0
1
1
1
0
0
1
0
2
1
0
1
2
1
1
0
0
0
0
2
1
3
1
1
1
2
0
1
2
1
2
0
0
1
2
2
1
0
0
0
0
0
2
0
0
0
0
1
1
2
1
0
1
1
1
0
3
0
2
0
2
2
2
0
0
1
0
0
0
0
2
0
0
2
3
0
1
0
2
0
0
1
1
0
2
3
1
1
0
2
0
0
0
1
2
1
2
2
0
2
2
1
0
0
0
0
0
1
0
0
1
2
0
1
0
0
0
0
2
2
0
0
2
1
1
2
0
1
0
0
1
2
0
0
2
1
0
0
2
0
0
1
0
0
0
1
2
0
2
0
1
1
2
1
0
0
2
0
0
0
0
1
1
0
2
0
0
0
1
1
0
1
1
0
2
2
0
1
1
1
1
1
0
1
1
0
0
1
0
2
1
0
0
2
1
0
0
1
1
0
2
1
1
2
1
1
2
0
0
1
0
0
1
2
1
2
0
0
2
0
0
0
1
1
0
1
0
0
1
2
0
1
2
2
0
2
2
2
0
2
0
0
1
0
0
2
0
0
2
0
3
0
2
2
0
0
1
2
2
2
1
2
0
1
1
0
0
0
0
0
2
1
1
2
0
0
2
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
2
0
1
1
0
0
0
2
2
0
1
0
1
1
1
0
0
0
0
2
0
0
1
1
1
0
1
1
1
1
0
1
0
1
1
0
0
0
0
0
0
2
0
2
0
2
0
1
2
0
0
0
1
0
0
0
1
1
1
2
2
2
0
0
0
0
0
0
1
0
1
2
0
1
0
1
4
1
2
2
0
0
0
1
0
1
1
1
0
0
1
0
1
0
1
0
0
2
0
2
2
0
1
2
1
2
0
1
0
1
1
1
0
2
2
0
0
2
1
1
2
0
0
0
0
2
1
0
2
0
0
2
1
0
0
1
0
0
0
0
0
0
2
1
2
0
2
0
1
1
1
2
3
0
2
1
2
1
0
0
2
0
0
0
5
1
2
0
1
0
1
2
0
0
0
0
0
1
0
1
0
1
0
1
2
1
3
1
1
2
1
0
0
0
0
0
0
3
0
0
1
0
1
2
1
0
0
0
2
0
0
1
2
1
1
1
2
1
3
4
1
1
0
0
0
0
1
1
1
0
2
1
0
0
2
0
0
1
1
1
0
0
2
0
0
1
1
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
2
0
0
1
2
1
1
0
2
1
0
1
1
0
1
1
0
0
1
1
2
1
1
2
0
0
0
1
0
0
0
0
0
0
0
2
1
1
2
1
0
2
0
1
1
0
2
1
1
2
0
2
1
0
0
0
1
0
0
0
2
0
1
1
1
2
0
0
0
1
0
1
1
1
0
0
0
0
2
0
1
1
2
2
2
2
1
0
1
2
0
2
0
0
0
1
0
1
0
1
0
0
1
1
0
1
0
0
0
0
0
2
0
0
0
2
1
0
2
2
0
2
2
0
0
1
0
1
0
2
2
0
1
0
2
1
1
2
2
0
1
0
1
0
1
2
0
0
1
1
1
0
0
1
2
1
0
0
0
0
0
0
1
0
0
1
1
0
1
0
2
1
2
2
0
0
1
0
0
1
0
0
0
1
0
1
1
1
1
0
3
0
0
0
0
0
0
1
0
1
0
2
2
0
0
1
0
2
1
0
0
0
1
0
2
0
1
1
2
0
1
1
0
3
1
0
0
0
1
0
0
0
2
2
0
1
1
1
1
0
2
2
0
1
0
1
1
2
0
2
1
0
0
0
0
1
1
0
1
0
2
1
1
2
0
0
0
2
1
0
0
1
0
2
0
0
0
0
2
1
0
0
0
0
1
1
0
1
2
2
1
0
0
0
2
2
0
1
2
0
1
1
2
0
1
1
0
1
0
0
2
2
0
0
0
0
0
1
0
0
0
2
1
3
1
1
0
0
2
0
0
0
1
2
0
0
0
1
0
0
1
1
1
2
0
0
0
1
0
0
0
1
1
0
2
0
1
2
1
0
2
1
0
1
1
0
2
0
0
0
0
1
2
2
0
2
1
1
2
0
2
0
0
1
0
1
0
2
2
0
2
2
0
0
0
0
1
0
0
0
0
1
0
0
1
0
2
0
1
1
2
2
0
1
1
1
1
3
2
0
0
0
0
0
2
2
0
0
1
1
0
2
0
2
4
0
4
0
1
3
1
2
1
0
2
1
0
4
1
1
0
1
1
1
0
1
0
0
1
1
0
1
1
1
0
2
1
0
2
1
2
1
0
0
2
0
0
0
1
1
1
0
1
0
0
0
0
1
1
1
0
1
2
1
1
1
1
1
0
1
0
1
0
0
1
0
2
1
1
2
0
0
0
0
0
1
2
0
0
1
1
1
0
1
0
2
1
1
0
0
0
0
0
0
1
2
2
0
0
2
0
0
0
2
0
2
1
1
2
2
0
2
0
1
0
0
0
0
0
2
4
1
0
1
0
2
1
2
0
1
1
0
0
0
2
0
2
1
2
0
0
0
0
0
1
1
2
0
1
1
0
1
2
0
0
1
4
1
0
1
1
0
2
0
1
1
2
0
1
2
1
1
1
0
1
0
0
0
1
0
2
0
0
3
2
1
2
2
2
1
2
2
0
1
2
0
0
1
2
0
1
0
2
1
1
1
1
0
0
1
2
1
0
0
0
1
1
1
1
0
0
1
0
2
1
2
0
1
2
2
2
0
1
2
1
0
1
0
0
2
2
2
2
0
2
1
0
0
0
0
1
0
1
0
2
0
1
0
1
0
1
1
1
0
1
2
0
2
1
0
0
1
0
2
0
0
1
2
2
0
0
0
4
1
2
1
1
1
0
1
0
0
0
0
1
1
2
0
0
1
0
1
0
0
0
1
0
1
0
2
0
2
0
0
0
1
1
0
1
2
0
3
0
0
0
0
1
1
0
1
2
2
0
0
0
2
0
2
0
2
1
2
1
1
0
3
1
0
2
2
1
1
2
2
0
0
2
2
2
0
2
1
0
0
4
2
1
0
1
1
1
0
0
1
0
1
1
2
1
2
0
0
0
2
0
0
1
0
1
0
1
0
1
0
0
1
0
3
0
0
1
0
1
1
1
0
1
2
1
0
0
1
0
0
0
2
2
0
1
2
1
0
2
1
0
1
2
0
1
0
0
0
0
1
1
0
0
0
0
2
1
0
1
0
0
0
2
1
0
2
0
0
2
1
1
1
0
0
0
2
0
2
1
2
0
0
0
2
0
1
1
1
1
1
1
0
1
0
1
1
1
1
1
1
1
0
0
2
0
0
2
0
1
1
1
1
0
0
0
0
1
1
1
0
1
1
1
1
1
2
1
0
0
0
1
0
3
0
2
1
0
1
0
1
1
1
2
1
0
2
2
1
1
0
1
2
0
0
0
1
1
0
0
1
1
1
1
1
0
2
2
2
0
0
3
3
0
0
2
1
0
0
0
1
0
1
0
1
1
1
0
1
0
1
0
0
0
0
0
1
2
1
1
1
0
0
0
2
0
0
2
0
0
0
1
1
1
3
1
0
0
1
2
0
2
0
0
1
0
0
0
1
0
1
1
1
1
1
1
0
0
1
0
1
1
0
2
1
2
1
0
2
0
1
2
2
0
0
1
1
0
0
0
1
1
2
1
0
1
1
1
2
0
1
1
2
1
1
2
0
2
0
0
1
2
0
2
2
2
0
2
2
2
0
2
1
1
0
0
0
0
0
0
0
1
2
1
0
1
1
0
1
2
1
0
2
0
2
1
1
0
1
0
0
1
0
0
0
1
1
0
1
0
1
0
0
0
0
0
1
2
1
0
0
0
0
1
0
0
0
1
1
2
0
1
0
0
3
1
1
2
1
1
0
1
0
0
0
1
1
0
2
0
1
0
1
0
0
1
1
1
2
2
1
0
1
2
1
1
0
2
0
1
0
0
2
2
0
2
0
1
0
0
0
1
0
1
1
0
1
0
1
1
1
2
0
0
1
1
1
0
0
2
2
0
1
0
1
0
2
0
0
2
0
0
0
0
0
0
2
1
1
1
1
2
0
1
0
1
0
2
2
1
0
1
0
1
0
2
0
1
0
2
1
0
0
1
0
0
2
2
0
1
1
0
2
3
1
0
0
0
0
2
0
0
0
2
2
0
2
1
2
0
1
0
1
0
2
2
2
2
0
1
0
0
1
1
1
3
1
2
0
0
1
2
0
1
2
2
1
1
1
1
0
1
0
0
0
0
1
1
1
0
1
2
1
0
1
0
1
2
0
0
2
1
2
2
2
1
0
0
0
0
1
1
0
1
0
2
0
2
2
1
1
2
1
0
1
0
2
2
0
1
1
2
0
1
0
0
0
0
1
0
1
0
0
2
0
0
0
1
0
0
1
5
1
2
2
0
1
0
0
1
1
1
0
2
0
0
0
1
1
0
1
0
1
0
0
2
2
0
0
1
1
2
0
1
1
0
0
2
1
1
1
1
2
1
0
1
2
2
2
1
2
0
0
1
0
1
1
1
1
2
0
0
0
0
0
1
0
1
0
1
0
1
0
1
0
0
0
1
1
2
1
2
0
0
1
2
0
0
2
0
0
1
2
2
2
0
0
0
0
0
0
1
2
1
2
2
1
2
1
0
2
0
0
0
2
0
0
1
0
1
3
0
1
0
0
0
0
1
2
1
1
0
1
0
0
0
1
2
1
0
1
0
1
1
0
1
0
1
0
0
1
1
1
1
0
2
1
2
0
2
0
1
2
1
0
1
2
2
1
3
2
3
1
2
0
0
2
0
0
0
1
0
2
2
1
0
2
0
0
0
1
0
1
2
2
3
2
2
1
1
0
0
3
1
0
1
2
0
1
0
2
2
0
0
0
0
0
0
0
1
3
0
1
2
1
1
0
1
0
0
1
1
1
0
0
0
2
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
2
0
1
0
2
0
1
0
2
2
0
1
1
0
0
0
0
1
0
0
0
1
0
1
1
1
0
2
2
0
0
2
1
0
1
0
0
0
0
0
1
0
2
0
0
1
0
0
1
1
0
0
1
0
0
1
1
0
0
0
1
1
2
0
0
0
0
0
0
2
0
2
0
0
1
1
2
1
1
2
0
1
1
0
2
0
2
0
0
0
2
0
2
1
0
1
2
2
0
2
2
0
0
1
0
1
0
1
2
1
0
0
2
0
1
2
3
2
1
1
0
0
0
2
0
0
2
0
2
1
1
0
1
1
1
1
2
2
1
2
1
2
1
1
1
2
2
1
0
0
0
2
1
0
2
1
2
0
0
2
1
1
2
2
2
2
1
2
0
1
0
0
1
2
1
1
0
0
1
1
1
1
1
0
1
1
1
2
2
0
2
0
0
0
1
1
3
0
0
1
0
2
1
0
2
1
0
0
1
1
2
3
0
1
1
1
1
1
1
2
0
5
2
0
1
1
2
0
0
1
1
1
1
1
0
0
2
1
0
0
1
0
1
0
1
2
0
1
1
1
0
1
0
0
1
1
0
0
2
1
1
0
0
0
0
0
0
2
3
0
0
1
0
2
0
6
2
1
2
2
2
0
0
1
1
0
2
1
1
0
1
1
0
0
2
1
0
1
0
1
0
0
2
1
1
0
2
1
0
2
0
0
0
1
0
1
1
1
2
0
0
0
0
0
0
0
0
2
0
2
0
2
2
1
2
1
1
0
1
0
0
0
1
0
1
2
2
0
0
2
0
0
2
1
0
1
0
2
0
1
0
1
0
2
0
0
0
1
0
1
0
1
0
0
1
1
2
0
1
1
2
0
0
1
2
1
0
2
1
0
2
0
0
1
1
1
2
0
1
2
1
0
0
1
1
1
0
1
0
4
1
0
1
1
0
1
2
3
0
0
0
1
0
0
0
1
1
0
2
0
1
1
0
2
0
2
0
0
1
0
0
0
2
0
0
1
1
1
0
2
0
2
2
0
2
0
0
2
1
2
1
1
2
0
1
1
0
2
0
1
0
1
2
1
2
1
0
1
3
0
1
0
0
2
0
1
1
1
0
3
1
1
0
0
0
0
2
1
0
0
1
1
0
1
1
2
2
0
1
2
1
1
0
3
1
0
1
1
1
2
2
0
1
1
0
1
0
0
2
2
0
1
2
0
1
1
1
0
2
1
2
1
2
1
0
2
1
1
0
1
0
1
2
3
0
0
0
0
1
0
2
0
1
0
0
2
2
1
0
0
1
0
0
2
1
2
0
0
0
0
1
2
0
1
0
0
0
2
0
0
0
1
0
1
1
1
0
1
2
1
0
1
1
2
0
0
2
0
0
0
0
0
2
1
0
1
3
0
1
2
2
1
2
2
0
0
2
1
2
0
0
2
0
1
0
2
0
2
2
0
2
1
0
0
2
2
2
2
1
0
0
0
1
2
2
0
2
1
0
1
1
2
2
3
2
3
1
1
2
0
1
2
0
0
0
1
0
1
1
1
1
1
1
0
2
1
0
0
0
0
0
0
0
0
2
1
0
1
2
1
1
0
0
0
1
0
1
2
1
2
2
0
1
2
0
1
2
1
0
0
1
0
0
0
1
1
1
0
1
0
2
1
2
1
3
0
0
2
0
1
0
0
0
0
2
1
0
0
1
0
1
1
0
0
2
0
1
0
0
0
0
1
1
2
2
1
2
1
0
0
0
0
0
2
0
1
1
2
0
2
1
3
1
0
3
0
0
0
1
1
0
1
1
2
1
1
0
0
2
2
0
2
2
1
0
0
1
0
2
1
3
1
2
0
0
2
1
1
2
2
2
0
1
2
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
2
2
0
1
1
0
1
0
2
2
2
1
1
1
2
0
1
2
0
1
1
0
0
0
0
0
1
1
1
0
0
1
1
0
1
1
1
1
0
2
2
0
1
1
1
0
0
2
2
0
0
1
1
0
0
1
1
0
2
0
1
1
1
0
0
1
0
0
0
1
1
1
1
2
2
2
0
1
1
1
1
0
1
0
1
0
1
0
0
1
0
0
1
0
1
2
2
0
0
0
0
2
2
1
0
0
0
0
0
0
0
2
0
0
2
0
0
3
1
1
2
0
1
2
0
1
0
1
0
0
1
1
1
1
0
0
0
0
0
1
2
1
0
1
2
0
1
0
2
0
1
2
0
1
0
1
0
0
1
1
1
2
1
0
0
1
1
1
0
0
0
2
0
1
2
0
2
1
1
2
1
1
0
2
0
2
0
0
2
0
0
0
0
0
0
2
2
0
1
1
1
0
1
0
2
0
1
1
2
0
0
1
0
0
0
2
0
2
1
0
0
0
2
1
0
0
2
1
0
0
1
2
1
0
0
1
0
1
0
0
0
2
0
0
1
1
1
1
0
2
1
0
1
0
0
1
2
1
1
0
0
1
0
0
0
0
0
0
1
0
2
0
1
1
0
0
0
0
1
1
0
0
0
1
0
0
2
2
2
0
0
1
1
0
2
1
1
2
1
2
0
2
2
3
0
1
1
0
1
1
2
2
0
1
0
0
1
0
0
2
1
0
0
2
0
0
0
0
0
2
0
1
1
1
2
2
1
0
0
0
1
2
0
0
2
0
3
2
0
0
1
0
1
0
2
7
1
0
1
1
6
0
0
1
1
0
1
0
0
0
0
0
2
0
2
2
2
1
0
1
1
1
1
0
2
0
0
0
0
2
1
0
1
2
1
1
1
1
1
1
1
0
0
1
0
2
1
1
1
0
1
2
1
1
1
2
1
2
1
1
2
0
0
0
2
0
1
2
0
0
1
1
0
3
3
0
1
1
0
0
1
0
0
2
0
2
1
0
1
0
1
1
1
1
0
2
1
2
0
1
0
0
2
1
0
0
0
2
1
1
3
0
0
1
1
2
0
1
1
2
2
2
0
1
0
0
2
2
2
1
0
1
0
2
0
0
1
0
1
1
1
1
2
0
1
0
1
1
1
0
0
0
0
0
1
0
0
1
1
1
0
1
0
1
0
1
2
1
0
2
2
2
1
2
0
0
2
0
1
2
0
0
0
2
0
1
2
2
2
2
0
2
0
0
2
1
2
0
1
0
0
0
0
2
1
1
0
1
0
0
0
2
1
0
1
3
0
0
0
1
1
0
0
1
0
0
0
0
2
2
0
1
1
0
0
1
0
0
0
0
1
0
2
1
2
0
2
1
0
1
0
0
1
2
1
2
2
1
0
1
2
0
0
1
2
2
0
1
1
0
0
0
1
0
1
0
3
1
1
0
0
1
2
0
0
2
2
1
1
0
2
0
1
1
0
0
2
2
2
0
1
0
1
0
0
0
1
3
2
2
0
1
0
1
0
0
0
0
1
2
1
1
0
1
0
1
2
1
1
2
2
1
0
2
2
1
0
2
0
1
1
2
1
0
2
0
1
0
1
0
2
0
2
2
1
0
1
1
0
2
2
0
1
0
1
0
0
0
1
1
1
0
0
2
1
1
1
0
0
1
1
0
0
1
1
1
2
0
1
1
0
2
1
0
1
1
1
0
0
1
0
0
0
0
2
1
1
0
1
1
0
0
0
0
0
0
0
0
4
0
0
1
1
0
1
0
0
2
0
1
1
0
0
2
0
1
0
2
0
0
0
2
2
2
2
2
0
0
0
2
1
1
0
1
1
1
2
4
2
0
0
1
2
0
0
0
2
0
2
0
2
0
1
1
2
0
2
0
0
1
2
1
2
2
1
0
0
1
2
1
1
1
0
2
0
0
0
0
0
0
0
2
0
0
2
0
1
1
2
1
0
0
1
0
2
0
0
2
0
0
0
0
0
0
1
2
2
2
1
0
2
0
2
0
0
1
2
2
1
1
1
1
0
0
0
1
0
1
0
2
1
2
0
0
0
2
0
2
1
1
0
0
1
1
0
0
3
2
2
0
1
1
1
1
0
1
1
0
0
2
1
1
0
2
1
0
0
2
1
0
0
0
1
1
1
0
2
0
0
2
0
1
2
0
2
0
2
2
1
1
3
1
3
2
1
0
2
0
1
1
1
0
0
1
3
1
0
1
1
1
1
1
2
1
1
1
0
2
2
2
0
1
2
1
1
2
1
2
0
2
0
1
0
0
1
0
0
1
1
0
2
2
1
0
0
0
1
0
1
0
0
1
2
0
0
0
2
1
1
2
1
2
1
0
1
1
0
0
1
2
1
0
1
1
0
5
1
1
0
0
0
2
1
1
0
0
2
0
0
1
0
0
2
2
0
0
1
2
0
0
0
1
2
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
2
1
0
2
0
1
2
0
2
0
0
2
2
0
1
0
1
1
1
0
0
0
1
2
1
0
1
1
2
0
0
2
0
0
2
1
1
0
1
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
11
2
0
0
3
1
0
1
0
0
2
2
1
0
3
2
0
0
2
1
2
0
0
1
0
1
2
0
0
1
2
0
0
2
0
0
0
0
1
1
1
1
0
0
2
1
1
0
1
0
0
0
1
2
1
0
2
0
0
1
1
1
2
1
1
0
0
2
0
0
2
0
1
0
2
0
2
2
0
2
1
0
1
0
0
1
0
0
0
0
2
1
1
2
0
1
2
0
2
1
0
0
0
1
2
0
0
2
1
1
1
1
0
2
0
1
1
0
0
2
2
2
0
0
1
0
2
0
2
1
0
1
1
1
1
0
0
0
0
1
1
1
0
0
0
2
2
1
1
0
0
1
1
2
0
2
1
1
1
1
3
3
2
0
0
1
0
1
1
0
0
2
0
1
0
0
2
2
1
1
2
1
1
2
2
2
1
1
1
1
0
1
0
2
3
1
0
1
0
2
0
1
1
1
2
0
0
0
1
0
2
0
0
1
1
2
0
1
1
2
1
1
1
3
1
0
0
0
0
1
1
2
2
0
0
1
2
0
0
0
0
2
0
1
2
2
1
2
0
2
0
1
0
0
0
2
0
0
1
0
1
0
0
2
3
0
2
1
1
0
0
1
0
0
1
0
0
0
1
2
0
0
1
0
1
0
1
0
1
2
2
0
3
0
0
0
0
1
1
2
1
2
0
1
1
2
0
0
0
4
2
1
0
2
0
0
0
1
0
1
2
0
1
2
2
1
2
0
2
2
1
1
1
1
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
1
1
0
1
0
1
1
0
0
0
0
2
2
1
4
0
0
0
2
0
1
2
1
0
1
1
0
0
0
1
2
2
1
0
0
1
0
2
0
1
0
2
2
0
0
1
2
0
2
0
0
0
1
1
0
2
1
0
1
1
0
2
0
2
0
1
0
0
2
0
2
1
2
0
0
1
0
2
1
0
2
0
1
1
3
0
1
0
1
0
0
1
2
0
2
1
0
2
1
0
0
1
1
0
0
1
0
1
1
0
1
1
1
2
0
0
2
1
2
0
0
4
2
0
2
2
1
1
0
1
1
0
0
1
0
1
1
0
2
0
2
1
1
0
0
1
0
3
2
3
0
0
1
0
1
2
0
0
1
1
1
2
1
1
1
2
2
1
1
2
0
1
1
0
0
1
2
0
1
1
0
3
0
1
0
2
1
3
1
0
0
0
2
0
1
4
1
1
0
1
0
1
0
1
1
0
2
0
0
1
2
1
1
1
1
0
0
0
1
2
0
0
1
0
2
1
1
2
0
1
1
1
0
1
1
2
1
1
5
0
0
2
1
1
1
2
2
0
2
0
1
0
0
1
0
0
0
1
1
1
0
1
0
0
0
0
0
1
2
2
1
0
0
1
2
0
1
0
0
2
1
1
2
0
2
2
1
0
0
2
0
1
1
0
0
0
0
2
1
0
1
1
2
0
0
0
1
2
2
1
0
0
2
3
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
2
2
1
0
0
1
1
2
0
1
0
0
2
0
0
0
0
0
2
1
2
1
0
1
2
2
1
0
0
0
1
0
1
2
1
1
1
0
1
1
1
0
0
0
1
0
1
1
1
2
1
0
2
1
0
1
2
0
0
0
0
1
2
0
1
1
0
1
2
0
1
1
0
1
2
0
1
0
1
1
2
0
0
1
0
0
0
2
1
1
2
0
0
0
0
2
0
3
1
0
1
2
0
1
0
0
1
0
1
0
1
2
2
1
0
0
1
0
0
0
1
1
2
0
0
2
0
2
2
2
1
0
0
0
0
1
0
1
0
0
1
2
0
1
0
0
2
0
2
0
1
2
0
2
1
1
1
0
0
1
0
1
0
1
2
2
1
2
0
1
2
0
1
1
2
0
1
1
1
0
0
1
0
2
0
2
1
0
0
0
2
0
1
3
2
1
2
2
1
0
1
0
1
2
0
1
0
0
2
0
0
2
1
1
2
0
1
0
2
0
0
0
1
0
2
1
0
0
2
0
0
2
2
0
8
0
1
0
1
1
0
0
3
1
0
0
0
1
1
2
1
1
2
2
1
0
0
0
0
2
1
1
1
0
1
1
0
1
0
0
1
1
0
0
2
0
1
1
0
0
0
1
0
2
0
0
1
0
1
1
2
1
2
1
0
0
1
2
0
0
2
2
0
0
2
2
0
0
1
1
1
1
0
1
0
1
1
0
0
1
1
1
0
0
0
0
0
1
2
1
0
1
0
1
0
2
0
0
2
0
0
0
0
0
1
0
0
1
1
1
2
0
1
0
0
1
1
0
1
3
0
1
2
1
2
1
0
0
1
1
1
2
0
1
1
0
2
2
1
0
1
1
2
1
2
0
0
0
2
0
0
3
1
0
1
1
0
0
2
0
2
1
2
0
1
0
1
0
2
2
0
1
0
0
2
1
1
0
0
2
0
1
0
0
1
0
1
1
1
1
1
2
2
1
0
1
1
1
1
1
0
0
0
0
2
0
1
2
0
2
1
0
1
0
2
0
0
1
1
1
1
1
1
1
0
0
0
1
0
1
1
3
2
1
2
1
1
0
1
0
0
2
1
0
1
2
0
1
2
1
1
1
0
2
1
0
1
1
2
0
1
0
1
1
2
2
1
1
0
0
0
0
2
0
2
0
0
0
0
2
2
0
0
1
2
3
1
1
0
1
0
0
0
0
0
2
0
1
1
1
0
0
0
1
1
0
0
0
1
2
1
1
0
0
1
1
0
2
2
2
1
0
0
1
2
0
0
0
2
2
1
1
1
0
1
1
1
1
0
1
0
1
1
1
1
0
1
1
1
1
2
1
1
2
6
1
0
1
0
1
0
0
0
1
0
2
1
0
2
1
0
0
2
1
1
2
0
1
1
2
0
0
1
2
2
1
2
0
0
1
0
2
1
2
1
0
1
1
1
1
1
0
0
1
0
0
0
0
2
1
1
1
0
0
0
0
1
1
0
0
0
2
0
0
1
0
1
2
1
0
1
1
0
0
1
0
0
0
0
1
2
1
0
0
1
1
2
1
1
0
2
2
0
0
0
1
2
1
1
0
1
0
1
0
0
0
0
1
0
0
1
1
1
2
1
2
2
0
0
0
2
1
0
1
1
0
1
0
1
1
1
0
1
2
0
1
1
1
1
1
0
2
0
1
2
0
0
1
1
1
0
1
0
1
1
0
1
0
0
1
0
2
0
0
2
2
0
0
1
2
4
2
1
1
0
0
0
1
0
0
2
1
1
1
1
1
1
1
0
0
2
0
2
0
2
0
0
0
0
0
1
0
1
1
0
0
1
1
1
1
1
2
2
0
2
1
1
0
1
1
1
1
1
1
1
1
1
1
0
0
2
1
0
0
0
0
1
1
0
0
2
1
1
1
2
2
1
1
2
0
2
1
0
0
0
0
0
2
1
2
1
1
1
0
0
1
2
0
0
0
0
0
1
0
1
0
0
2
2
1
0
2
1
1
1
0
2
2
0
2
2
0
2
1
0
0
1
1
2
0
0
1
0
1
0
1
2
0
0
1
2
0
0
0
2
1
2
0
0
1
2
0
1
0
0
1
0
1
0
1
0
1
1
1
0
1
0
1
1
1
2
0
3
0
1
1
1
0
0
1
1
1
0
1
1
0
0
0
0
1
1
1
2
0
1
0
1
0
1
2
1
1
1
2
1
0
0
2
1
1
2
1
0
0
1
1
0
0
2
0
0
1
0
0
2
0
0
1
2
0
0
2
0
1
2
0
2
0
0
0
2
0
1
1
1
0
0
1
2
0
1
0
2
0
2
0
0
2
1
1
0
0
0
1
1
1
0
2
1
0
0
0
1
1
1
1
0
2
2
0
2
0
1
1
0
2
0
0
2
0
0
1
1
0
0
0
2
0
1
2
2
2
0
2
2
1
2
1
2
1
1
1
1
0
0
0
0
2
2
0
0
2
1
1
1
1
1
0
1
0
1
0
1
2
2
0
0
0
2
0
1
1
1
0
1
1
1
0
2
2
0
1
2
1
1
2
2
0
1
2
0
0
0
2
0
1
2
0
0
0
1
3
1
3
0
1
1
1
2
0
1
1
0
1
0
11
1
2
1
0
1
0
2
1
0
1
0
0
0
1
1
2
0
1
0
1
2
0
1
1
1
1
1
1
2
1
0
2
0
1
2
1
0
0
1
0
0
2
0
0
2
1
0
0
0
0
0
1
1
2
0
1
0
1
1
0
2
1
1
1
0
0
1
2
4
0
1
2
1
1
0
0
2
0
1
0
1
2
1
1
0
1
1
0
1
1
1
1
1
0
1
1
0
0
2
2
0
0
0
0
2
0
0
0
2
0
1
1
2
1
0
1
1
1
2
1
0
0
0
0
0
0
0
1
2
0
1
0
1
1
2
2
2
0
0
1
0
2
1
1
1
0
0
1
1
0
0
0
1
1
0
2
5
1
0
1
2
1
1
1
0
0
2
2
2
1
0
2
1
1
2
1
0
0
1
2
1
2
1
1
0
1
0
0
0
0
1
1
1
0
2
0
0
0
2
1
0
0
0
1
1
0
2
0
0
0
1
0
0
1
1
2
0
0
1
2
0
0
2
1
0
1
1
0
2
2
0
0
1
1
0
0
1
2
1
1
1
0
1
0
1
1
0
0
1
0
2
0
2
1
0
1
0
1
1
0
2
1
2
2
1
2
0
1
2
3
2
0
1
0
0
1
0
1
2
1
1
1
2
1
0
2
0
1
0
0
1
0
1
1
2
2
0
0
0
0
0
1
0
5
1
1
2
0
2
0
1
0
2
2
0
0
2
1
0
1
1
1
2
0
0
2
2
0
2
2
0
0
2
2
1
2
0
1
1
1
0
1
0
0
0
0
1
1
0
0
0
1
2
0
2
2
1
0
2
1
1
0
2
2
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
2
1
0
0
0
1
0
0
1
0
1
0
3
0
1
0
1
0
1
0
0
1
1
2
2
0
0
2
0
2
0
1
2
1
0
1
1
3
1
0
0
0
0
2
1
1
0
0
2
1
1
0
1
1
0
0
2
0
0
1
0
2
1
1
3
0
0
2
2
0
2
1
0
1
2
3
2
1
1
0
0
1
2
0
0
1
2
1
3
0
0
1
0
0
0
2
1
0
0
2
1
0
1
0
0
3
1
1
2
1
1
1
1
0
1
2
2
1
1
2
1
0
0
2
1
1
0
2
1
0
2
0
1
0
2
0
1
0
1
2
0
1
2
2
1
0
1
0
2
2
2
2
0
0
0
1
0
0
2
1
2
1
2
0
1
2
2
0
1
0
0
1
1
3
0
0
0
1
1
1
0
1
1
1
1
2
0
0
0
0
1
1
0
1
1
1
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
2
0
1
1
0
0
1
0
1
0
1
1
4
0
0
0
3
0
0
1
0
0
0
0
2
10
0
0
0
0
1
1
1
1
0
0
0
0
1
0
0
0
0
1
2
0
0
1
0
0
0
2
1
1
0
1
1
0
0
0
1
2
2
1
0
0
1
2
0
1
2
0
2
0
0
0
0
2
0
1
0
1
0
0
1
2
0
2
0
2
0
1
0
1
0
1
0
1
0
0
1
0
0
0
2
1
1
0
0
1
0
0
0
0
1
0
0
0
2
2
0
2
1
0
0
0
2
0
0
1
1
2
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
1
0
1
0
0
0
1
0
0
0
1
2
0
1
0
0
1
0
1
0
0
2
2
0
2
1
1
1
2
1
2
1
0
1
0
0
1
1
0
0
0
1
1
0
0
0
1
2
1
1
0
1
0
2
1
0
2
1
0
0
2
1
0
0
0
0
0
0
0
0
2
2
1
0
2
0
0
1
1
0
1
0
1
1
0
1
0
1
2
1
0
0
1
0
1
2
0
1
0
0
0
1
0
2
0
0
0
1
1
2
0
2
0
2
2
0
0
1
1
1
0
2
0
2
0
0
1
0
0
1
1
1
2
2
0
1
0
2
0
1
0
0
1
0
3
0
1
0
1
1
2
0
0
1
2
0
1
0
2
1
0
0
2
1
1
0
0
0
1
0
0
0
2
1
0
1
0
0
0
2
0
0
2
0
0
2
0
0
0
0
1
2
2
1
0
1
2
2
0
2
1
0
0
1
1
0
1
1
1
1
1
2
2
0
0
1
0
2
3
1
0
1
0
1
1
0
0
1
0
1
0
2
0
2
0
0
0
1
0
0
1
1
0
1
0
2
0
1
0
1
0
1
0
1
1
2
0
2
1
1
2
2
2
0
1
0
1
0
0
1
2
2
1
2
1
6
2
0
0
0
3
0
0
0
1
0
1
1
1
1
0
1
0
1
1
1
1
0
1
0
0
0
2
0
2
1
0
0
0
0
0
1
0
1
1
2
2
1
2
0
0
0
1
1
0
0
1
0
0
0
0
1
0
1
1
0
2
3
1
1
0
0
3
1
1
0
2
1
1
0
0
2
1
1
2
1
2
0
1
2
1
1
1
0
2
0
1
0
0
1
1
0
0
1
1
0
1
1
0
0
0
1
1
2
0
0
1
2
2
1
1
0
1
0
0
1
1
0
1
0
1
0
0
1
2
0
0
2
0
1
1
0
5
1
1
0
0
0
1
0
1
0
0
0
0
1
2
1
2
0
0
0
1
1
2
1
0
0
0
1
0
0
2
1
1
2
0
0
1
2
0
0
1
3
1
0
0
1
1
1
0
1
0
0
2
0
0
2
1
0
0
0
2
1
0
0
0
3
1
1
0
1
1
2
0
1
1
2
0
0
0
0
0
1
1
0
1
2
2
1
0
2
0
2
1
0
1
2
1
0
0
2
0
0
0
2
2
0
1
1
2
0
0
1
0
2
0
1
0
1
0
1
0
1
0
0
0
0
3
3
1
1
1
0
2
2
2
2
0
1
0
2
1
2
0
1
0
0
0
1
1
2
0
2
0
1
1
0
0
2
1
0
2
1
0
0
0
3
0
1
0
0
1
2
0
0
1
1
1
0
1
2
1
0
0
0
0
1
2
0
1
1
1
1
0
0
0
1
0
1
0
1
1
0
2
1
1
0
0
1
0
1
0
1
0
1
0
1
0
1
2
0
0
0
2
1
1
1
0
1
2
1
2
0
1
0
1
0
1
1
1
0
1
1
0
0
0
0
1
0
0
0
2
2
0
3
0
0
3
1
0
2
2
0
0
0
0
1
0
1
0
0
2
1
0
0
1
0
1
0
1
1
1
0
1
1
0
0
0
1
0
1
2
0
3
0
0
1
2
0
1
0
1
0
4
0
0
0
1
1
0
0
0
1
0
0
2
1
2
1
1
0
2
0
1
1
3
0
2
2
1
0
0
1
1
0
0
0
1
1
1
0
0
0
2
1
0
2
0
1
0
1
0
0
2
1
0
2
0
1
0
2
1
0
1
1
1
1
1
1
3
2
0
1
0
0
1
1
2
1
1
0
0
1
0
1
1
2
1
2
0
1
2
2
1
0
1
0
0
1
1
1
1
1
0
0
0
2
0
2
1
2
0
2
0
1
2
1
0
2
1
0
1
0
0
2
0
2
1
1
0
0
0
2
1
1
1
0
2
1
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
2
0
0
1
2
0
1
2
0
2
2
1
1
1
2
1
0
2
1
1
1
3
1
1
1
2
0
2
1
1
1
1
0
1
1
2
0
0
1
0
0
1
2
2
1
0
1
1
0
2
0
0
0
2
0
1
1
1
0
0
1
2
1
0
1
0
1
0
2
1
0
1
1
2
0
1
0
1
0
0
2
0
1
2
0
0
0
0
2
0
2
1
2
2
2
0
1
1
2
0
1
0
2
2
0
0
1
0
0
0
1
0
0
1
1
1
2
0
2
0
0
0
0
2
0
1
0
1
1
0
0
1
0
2
0
0
0
0
1
0
0
1
1
1
1
0
0
0
0
1
2
0
1
1
2
0
0
1
1
2
1
1
0
3
0
0
2
0
2
1
2
2
1
2
0
0
0
0
0
3
0
0
2
3
2
0
2
1
0
1
2
1
0
2
1
1
0
0
0
1
0
1
0
1
0
0
1
1
1
1
0
1
1
0
0
0
0
1
1
1
1
1
1
2
0
2
0
1
1
0
1
1
0
4
0
1
3
0
1
0
0
0
0
0
0
1
0
1
1
2
1
0
0
0
0
2
1
0
0
1
0
0
0
2
0
2
2
1
1
1
0
1
1
2
1
2
0
0
0
0
2
1
0
3
1
2
1
2
0
2
0
2
1
0
1
0
1
0
0
1
1
1
2
0
1
0
0
2
0
1
0
0
0
2
1
2
2
0
1
1
2
1
1
2
1
0
1
0
0
2
1
0
1
1
1
1
0
1
2
0
2
0
1
0
2
0
0
2
1
0
0
1
2
1
0
1
1
1
0
2
1
1
0
0
0
0
1
0
1
0
2
2
0
1
0
1
0
1
1
0
3
0
1
0
0
0
0
1
2
1
1
2
1
1
1
1
1
0
0
0
2
0
0
1
2
2
2
1
1
1
0
1
1
0
1
2
0
2
2
1
0
1
2
0
0
2
0
0
2
0
0
0
0
1
1
2
0
2
0
1
2
0
2
0
0
2
1
0
1
0
0
0
3
0
1
1
3
1
1
0
1
1
0
0
0
0
1
0
1
0
1
0
1
1
2
2
0
0
2
0
1
0
1
1
0
0
1
1
1
0
0
0
1
0
1
0
0
4
1
0
1
0
0
2
1
1
8
1
1
1
1
0
1
2
1
1
1
2
1
0
2
0
1
2
1
1
1
0
1
1
2
0
1
1
1
0
0
2
2
1
1
0
1
1
2
0
0
0
2
2
0
1
1
1
0
0
1
2
0
0
0
1
1
1
2
2
2
0
0
1
1
0
2
0
2
0
1
0
1
0
0
2
2
1
1
1
0
2
0
0
0
1
0
0
1
0
2
0
0
0
1
1
2
1
1
1
1
1
1
1
1
1
0
0
0
1
0
1
1
2
2
0
0
0
0
1
2
1
0
0
0
0
1
1
0
1
1
2
2
2
2
0
2
2
0
2
0
0
2
1
0
1
2
0
1
1
1
2
2
0
2
2
0
1
0
1
1
2
2
0
2
2
0
1
1
0
2
2
1
0
1
1
1
0
2
0
0
0
1
1
0
0
1
0
0
3
0
0
1
0
2
1
1
1
1
0
1
2
3
1
0
2
0
1
3
0
1
0
0
2
2
1
2
0
2
0
2
1
3
0
1
1
1
2
8
0
0
0
1
0
0
2
2
1
2
1
2
0
1
1
0
0
0
0
2
1
3
1
0
1
1
0
2
1
0
0
1
0
2
1
1
1
0
1
1
0
0
2
0
0
1
1
1
1
2
0
0
0
2
1
4
0
1
0
1
2
1
0
2
1
0
0
1
0
0
0
0
1
1
1
2
0
0
2
1
2
2
1
1
2
1
0
0
1
1
1
0
0
1
0
1
1
0
1
1
1
0
1
2
1
0
1
0
1
1
1
0
0
1
0
4
0
0
0
0
3
1
1
0
0
0
1
0
0
1
0
1
2
0
0
1
0
1
1
1
0
1
0
0
0
1
2
0
1
0
0
0
2
1
2
1
0
1
3
0
1
0
0
0
0
0
0
1
2
1
0
0
1
0
1
0
1
1
1
2
0
0
0
2
0
1
1
1
0
3
1
0
0
0
0
2
1
1
0
0
1
0
2
1
2
0
0
0
2
1
0
1
1
2
0
0
0
0
2
1
0
2
0
0
1
1
0
0
3
1
0
0
0
1
1
2
2
1
1
1
0
3
2
0
0
1
0
0
1
1
1
0
0
2
1
0
0
0
1
0
2
1
2
0
2
1
1
1
0
0
0
2
0
4
2
0
2
0
1
0
1
2
0
2
0
0
1
2
0
1
1
1
2
0
0
1
0
0
2
0
1
2
1
1
2
0
1
0
1
1
1
1
1
2
1
0
3
1
2
2
2
0
0
0
2
0
0
0
0
0
2
0
3
0
2
0
0
0
1
0
0
2
0
2
0
0
3
2
2
0
0
4
1
3
1
0
0
1
0
0
0
0
0
1
2
3
1
2
1
0
0
0
0
0
2
0
1
1
1
2
2
2
2
1
1
2
1
0
1
0
0
0
0
1
2
1
2
0
2
0
2
1
1
2
1
0
2
0
0
1
0
0
1
0
1
0
0
2
0
0
0
1
0
0
2
1
0
0
3
1
0
0
1
0
1
1
0
0
1
0
0
1
0
1
0
0
1
4
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
2
1
0
1
0
0
1
3
1
1
2
1
0
0
0
1
1
0
1
2
0
2
0
1
2
1
0
0
2
2
1
0
1
1
0
0
1
1
0
0
1
1
1
0
1
0
0
0
0
2
0
1
1
0
2
1
0
2
0
1
0
0
0
0
1
0
1
2
0
1
1
1
0
0
1
0
0
0
1
1
2
0
0
0
2
0
0
2
1
2
1
1
4
1
0
11
0
2
0
2
0
1
2
2
2
0
2
0
1
0
1
0
2
0
2
0
1
1
0
0
1
0
0
2
0
0
2
1
1
2
2
1
1
1
0
0
1
1
0
1
2
1
1
2
1
0
1
2
0
0
2
2
0
0
0
1
0
0
1
3
2
1
0
3
3
1
0
1
2
2
3
0
0
0
2
0
2
1
1
2
1
1
1
1
1
1
1
1
0
1
1
0
2
3
0
0
0
1
1
1
1
0
0
4
2
0
2
2
0
0
0
1
1
1
0
0
1
1
0
0
0
2
0
0
0
1
1
0
1
1
0
1
0
0
0
1
2
1
0
0
1
0
0
2
0
0
1
0
0
2
2
0
2
0
1
0
2
2
0
1
2
0
0
1
0
1
4
2
0
0
0
3
0
2
0
1
0
1
0
2
0
2
0
1
1
2
1
1
2
1
1
1
0
1
2
0
0
0
0
0
0
1
1
1
0
2
2
1
2
0
2
1
1
1
2
2
1
0
2
0
2
3
1
1
1
1
0
1
2
0
0
2
0
0
2
0
1
0
1
2
0
1
1
2
0
0
0
1
1
0
0
0
1
0
2
0
0
0
2
2
0
2
0
0
0
1
1
2
0
1
2
0
1
1
1
0
1
0
1
0
1
2
0
0
2
2
0
2
0
0
1
1
1
0
3
1
0
1
2
2
2
1
0
0
2
0
2
0
0
0
2
2
1
0
2
1
0
3
0
0
0
0
1
1
0
0
1
1
2
1
2
2
0
0
0
1
1
0
0
4
0
2
0
0
2
0
0
0
1
0
1
1
0
0
1
0
0
2
0
1
1
0
1
1
1
1
2
1
0
2
1
0
1
0
1
2
1
1
1
1
0
0
0
0
2
3
1
2
0
0
2
1
1
0
0
1
1
1
0
1
2
0
1
0
0
0
0
1
1
1
1
2
0
2
0
1
0
0
2
0
0
0
1
1
0
2
0
2
0
2
1
1
2
0
3
0
1
1
0
2
1
0
2
0
3
0
1
1
0
1
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
1
0
1
1
1
0
2
0
2
5
0
2
1
1
1
0
0
0
1
2
2
1
0
2
2
2
1
1
1
1
0
1
2
0
1
0
0
0
1
0
1
0
0
2
0
1
1
0
2
1
2
2
0
0
1
0
1
1
0
0
1
0
0
0
1
0
1
1
0
0
0
0
1
0
0
1
1
1
2
0
2
0
0
1
0
1
0
1
1
0
0
0
1
0
1
1
1
1
0
0
2
0
2
1
1
1
1
2
1
2
0
2
0
1
2
1
0
1
1
1
0
2
0
0
1
3
1
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
2
2
1
0
0
0
1
0
2
2
1
0
1
0
1
0
0
0
0
0
2
2
0
0
0
1
0
0
1
2
0
0
1
1
0
0
2
2
2
3
2
1
0
1
1
1
2
1
1
2
0
1
2
2
1
0
0
1
0
0
0
1
2
0
0
2
0
0
0
2
2
1
1
0
0
0
2
1
2
0
0
1
0
0
0
1
1
1
1
1
0
2
0
3
0
0
2
0
0
0
2
1
0
1
1
2
0
0
1
1
2
1
1
0
0
0
0
1
1
0
2
0
0
2
1
2
2
1
0
0
0
1
2
0
1
2
0
0
0
1
0
2
1
1
0
1
1
0
0
1
0
1
2
0
0
2
2
2
0
0
0
1
0
1
1
1
2
2
2
1
0
0
1
0
0
2
0
0
1
0
1
1
0
0
3
2
0
0
1
1
2
1
2
1
1
2
1
1
3
1
0
4
1
2
2
1
1
0
0
1
0
1
2
1
1
0
0
0
0
0
0
1
2
2
1
2
2
3
0
0
1
2
2
2
0
0
0
1
1
1
1
1
0
0
1
0
0
2
1
2
0
0
2
1
1
1
0
2
0
0
2
1
2
0
1
1
1
0
0
1
0
2
2
2
2
2
0
1
1
0
2
0
0
1
0
0
1
1
0
0
0
0
2
0
2
0
1
0
2
2
0
0
1
0
0
0
1
0
0
0
0
1
2
2
1
2
2
0
2
1
1
1
1
0
0
1
2
1
0
0
1
0
3
1
2
0
2
0
0
0
0
0
0
0
2
1
2
2
0
0
2
2
0
3
0
0
0
0
0
0
0
1
1
2
0
0
4
2
0
2
1
2
1
0
0
0
0
1
0
0
0
1
2
0
2
1
1
1
0
0
0
1
0
1
0
2
0
0
0
0
1
0
0
2
1
0
2
0
1
0
0
0
1
2
2
1
0
1
1
2
1
1
0
1
3
0
0
0
0
1
0
0
0
0
1
2
0
2
1
1
0
0
0
0
0
0
1
2
1
1
1
1
2
2
2
1
0
1
0
1
0
0
2
0
1
0
0
1
0
1
1
1
1
0
1
0
1
0
1
2
0
0
0
0
1
0
1
2
0
0
2
0
1
1
2
0
1
0
0
0
1
1
2
0
0
0
0
0
1
1
2
3
2
1
0
0
1
2
0
1
1
0
1
1
1
2
3
0
0
2
0
0
0
0
0
0
1
0
1
1
1
0
0
1
0
1
2
0
0
1
1
0
1
0
0
1
1
1
0
0
0
0
1
0
1
0
2
1
0
2
1
2
0
0
1
3
0
0
2
0
0
0
0
0
0
2
0
1
0
0
1
0
1
1
1
0
1
1
0
0
0
0
2
1
1
1
0
1
0
0
0
0
0
0
2
0
0
1
0
0
1
2
0
1
0
0
1
0
0
1
2
0
0
1
0
0
0
0
2
0
0
0
0
0
1
1
0
2
2
0
1
0
1
1
0
0
0
2
1
2
2
1
1
2
0
1
1
1
0
0
0
0
0
0
0
0
1
1
0
1
0
2
0
0
2
0
0
0
0
2
1
1
0
0
2
1
2
0
1
0
1
1
2
0
0
2
0
2
0
0
2
1
1
1
0
1
1
1
1
2
0
0
0
2
1
0
0
0
1
2
2
0
0
0
0
1
1
0
0
0
0
1
1
2
0
0
1
0
1
0
0
0
0
0
0
2
1
0
2
0
1
2
1
3
2
1
0
1
1
0
1
0
0
0
0
0
2
0
0
1
0
2
1
0
0
1
1
0
0
0
1
0
1
1
1
1
0
0
0
2
0
0
1
1
1
0
1
0
1
1
0
0
2
2
0
0
0
0
1
1
2
1
1
1
0
0
1
1
1
1
2
2
1
0
1
2
2
1
0
1
0
0
0
0
0
0
2
0
0
1
1
0
0
0
2
0
1
2
0
0
0
2
2
1
0
2
2
1
0
1
0
1
0
1
1
1
1
0
4
2
0
2
0
0
1
2
0
0
1
1
0
0
2
1
0
1
0
2
2
2
2
1
2
1
0
1
0
0
1
1
0
0
1
0
0
0
0
1
2
1
2
2
1
1
2
2
0
0
0
0
2
2
1
1
1
1
1
1
1
1
2
1
0
2
2
2
1
2
0
1
0
1
1
0
0
0
1
1
1
0
1
0
1
0
1
1
0
0
1
0
1
2
1
2
0
0
2
0
0
0
0
0
1
1
1
2
1
0
0
2
1
0
0
0
2
1
0
0
0
2
0
1
1
3
1
1
1
1
0
1
0
2
1
1
0
0
0
1
0
0
1
2
1
0
2
1
0
0
0
2
2
0
1
0
4
0
2
2
0
0
2
1
2
2
0
0
1
0
0
2
0
2
1
0
0
0
0
0
1
1
0
1
1
0
0
0
2
0
1
3
1
0
0
0
1
0
0
2
0
1
1
2
1
0
2
0
2
0
2
1
3
1
2
1
2
1
0
0
2
2
0
2
0
1
0
2
1
2
0
1
0
2
1
1
1
1
1
0
2
1
0
1
2
2
1
0
2
1
1
0
0
0
2
1
1
0
0
1
0
1
0
0
0
1
1
2
0
2
0
0
2
1
0
1
0
2
0
1
0
2
1
2
2
0
1
1
0
0
1
0
1
2
0
1
2
1
1
0
0
0
1
1
0
0
0
0
0
2
0
0
0
2
1
2
0
0
0
0
0
0
2
1
1
2
1
0
0
0
2
2
1
0
0
1
0
0
0
2
2
2
0
0
1
1
2
0
2
2
2
1
0
1
1
1
0
0
2
0
0
1
0
0
2
1
2
2
1
0
0
2
0
2
0
1
1
0
1
0
1
0
0
2
1
1
0
1
0
0
0
0
0
0
1
0
2
1
2
0
2
1
2
1
1
0
1
1
0
0
0
0
2
0
1
0
0
0
0
0
0
1
2
0
2
1
0
0
0
1
0
0
1
2
1
2
0
0
0
1
0
1
1
2
2
0
1
0
1
2
0
2
0
3
2
0
0
2
0
0
0
1
1
0
0
0
1
1
0
0
2
1
0
1
2
1
2
0
0
0
0
0
0
4
1
1
0
0
0
0
0
0
1
1
2
0
1
0
1
1
0
0
0
1
1
1
0
0
0
1
0
1
1
2
2
2
0
1
1
1
2
1
0
0
2
1
0
0
1
0
2
0
0
2
0
1
0
0
0
1
2
1
1
1
1
0
0
2
1
0
1
1
1
0
0
2
1
0
2
0
1
0
0
1
0
1
0
2
0
1
1
2
0
1
0
0
1
0
0
1
0
1
0
1
0
0
1
0
0
0
1
2
0
1
0
0
3
0
0
1
2
3
1
1
2
0
1
0
2
1
2
1
2
1
2
2
1
0
1
1
4
2
0
1
1
1
1
0
2
3
1
2
0
1
1
2
2
1
1
0
0
0
0
1
1
0
0
1
2
1
2
1
0
0
0
2
0
0
2
1
1
0
2
0
1
1
1
1
0
1
2
1
2
1
0
2
0
2
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
2
2
0
1
2
0
1
1
0
2
0
0
1
1
0
2
1
1
1
0
1
1
0
0
0
1
0
0
0
2
0
2
0
0
0
1
0
0
0
1
0
1
1
2
0
0
0
0
2
0
1
2
1
0
0
1
0
2
1
1
0
0
2
1
0
0
0
0
1
0
1
0
0
0
2
1
1
2
1
0
1
0
1
0
1
0
2
0
2
2
1
1
2
0
2
1
0
1
2
0
1
0
0
0
2
0
0
1
1
1
0
1
0
0
1
2
1
1
0
1
0
2
1
1
1
1
2
0
0
2
3
0
0
0
2
0
2
1
2
0
2
0
1
2
1
1
0
0
1
1
1
0
0
0
2
1
1
2
0
0
2
0
1
3
2
1
2
2
1
1
0
1
0
2
0
0
2
0
2
2
1
0
2
0
2
1
1
0
1
0
0
1
0
0
0
0
0
1
0
1
2
0
2
0
1
1
0
0
0
0
1
0
1
1
0
0
1
1
1
0
2
0
1
0
0
0
1
2
0
0
0
0
0
1
1
1
0
0
0
1
1
0
2
0
0
0
0
0
2
2
0
1
2
0
1
0
0
1
1
0
1
1
0
2
1
0
0
0
0
1
1
0
0
1
1
1
2
1
3
1
1
1
0
0
2
0
0
1
0
1
0
2
1
2
0
1
2
0
0
3
2
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
1
2
0
0
1
0
1
4
2
2
0
2
2
1
2
1
0
0
2
2
2
1
2
2
0
1
2
2
2
0
1
0
1
2
1
1
1
0
0
0
1
0
1
1
1
0
2
0
0
2
0
0
0
0
1
2
0
0
1
0
0
0
0
1
1
0
2
0
0
0
0
0
0
2
2
1
0
1
0
2
1
1
0
1
1
0
1
0
2
1
0
1
1
2
0
0
1
1
0
0
0
2
0
3
1
3
1
1
0
1
0
1
0
0
2
2
0
0
0
0
1
0
2
1
0
0
2
0
2
1
0
1
2
0
1
2
2
1
1
1
0
0
1
0
2
1
1
1
0
0
0
1
0
0
1
1
0
0
1
2
1
1
0
0
0
0
0
1
0
0
0
1
0
0
3
2
0
0
2
0
0
1
0
0
0
1
0
2
2
0
2
1
0
0
0
1
1
2
0
1
1
2
2
1
0
1
0
1
1
0
1
0
0
2
1
1
1
1
0
1
1
1
0
0
1
3
0
1
1
0
2
0
1
2
2
1
2
1
2
0
0
1
2
1
2
1
1
0
0
1
2
0
0
0
2
0
0
1
1
0
1
0
0
2
1
0
2
2
5
1
1
2
1
1
1
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
2
1
1
2
2
1
1
0
2
1
1
1
0
2
1
1
2
1
0
1
0
2
1
0
1
2
0
2
1
2
3
2
0
0
2
0
1
0
2
1
1
2
0
0
1
0
1
1
1
0
0
0
2
0
0
0
5
0
2
3
1
1
2
0
1
1
1
1
3
0
1
0
2
0
1
1
0
1
0
0
2
0
0
1
1
0
0
1
1
2
0
1
0
1
0
1
1
1
2
1
0
1
1
1
2
0
2
0
0
1
2
3
1
0
0
0
2
0
1
0
0
0
1
1
0
2
0
1
1
1
0
1
0
0
0
0
1
0
2
2
1
0
1
1
1
2
1
2
2
1
2
2
0
0
0
0
2
1
1
1
1
0
2
0
1
0
0
2
0
0
0
0
1
0
0
1
2
0
2
1
0
1
0
0
0
1
1
0
0
1
0
2
0
0
0
2
0
2
0
0
1
2
1
0
2
1
1
0
0
0
1
5
1
1
1
0
0
1
1
0
0
0
0
0
2
8
1
1
0
0
1
1
0
0
0
2
0
1
2
2
0
0
1
0
2
0
2
0
0
1
0
0
0
1
0
1
1
1
0
0
3
1
1
1
0
1
1
1
0
2
0
0
0
0
0
0
0
2
1
1
0
2
0
0
0
1
1
0
0
0
0
2
1
1
0
0
2
0
1
0
0
1
0
0
0
1
0
2
1
0
0
0
1
3
0
1
0
0
0
2
0
2
1
0
0
1
1
0
0
0
0
0
0
0
1
1
0
1
1
1
1
0
1
0
0
1
0
0
0
1
1
1
1
2
1
1
0
1
2
1
0
0
3
1
0
2
0
0
0
0
1
1
1
0
0
1
2
2
1
0
0
0
2
0
0
0
0
0
2
1
2
0
0
0
1
1
1
0
0
1
0
1
1
1
0
1
1
2
1
0
2
0
0
1
1
2
0
2
2
0
1
0
1
0
0
1
1
1
2
2
1
1
0
3
0
0
1
2
0
2
0
0
0
2
0
0
2
0
1
0
0
2
2
0
0
0
0
2
2
1
0
2
1
1
1
0
1
1
0
0
1
1
0
0
1
0
1
1
2
0
0
2
2
0
0
2
0
1
0
0
1
0
2
0
0
1
1
1
2
0
0
0
1
2
1
0
1
0
1
0
0
0
2
0
0
0
0
0
2
0
0
1
1
0
2
0
1
0
0
1
0
0
2
1
0
1
1
0
1
1
0
0
2
0
0
0
0
1
0
1
0
1
1
2
0
0
0
1
0
2
0
2
0
1
1
1
0
2
0
1
1
0
0
1
0
0
2
0
0
0
0
0
0
2
0
1
1
3
2
0
0
2
1
2
2
0
1
2
0
0
0
1
1
2
0
1
0
1
0
0
0
1
0
0
0
2
1
1
1
0
2
0
0
1
0
0
1
0
0
3
1
1
1
0
0
0
1
0
0
0
1
1
2
0
1
2
0
0
2
0
0
1
0
1
1
1
0
0
1
0
0
1
0
1
1
1
0
2
2
0
3
1
1
1
2
0
0
2
0
1
1
0
0
2
2
0
1
0
1
1
1
1
2
0
0
0
1
2
2
1
2
0
1
2
0
1
0
0
2
1
1
1
1
2
0
0
2
0
0
1
1
0
0
0
0
0
0
1
0
2
2
3
1
0
2
0
1
1
1
2
2
2
1
0
1
1
0
0
1
0
0
1
0
1
0
0
1
2
2
1
0
1
1
1
0
1
4
2
1
2
1
2
1
2
0
1
2
1
1
2
0
0
1
0
1
0
1
2
0
0
0
0
2
1
0
0
1
1
1
1
0
0
2
1
0
1
1
0
0
1
1
0
1
1
0
1
1
0
0
1
2
2
0
0
1
1
4
0
0
2
2
2
0
0
0
0
0
0
0
2
0
2
1
2
0
1
2
0
2
0
1
3
0
1
0
0
2
1
0
0
2
2
0
0
2
2
0
0
0
1
1
0
0
0
2
1
2
0
2
1
0
1
1
1
1
1
0
0
2
0
0
0
1
2
1
0
2
0
1
1
0
2
2
2
0
2
0
1
1
0
0
2
0
1
0
1
0
1
0
0
0
0
1
0
0
1
0
0
2
1
0
0
0
1
1
1
0
0
2
0
2
0
0
1
1
2
1
1
0
1
1
0
1
2
2
0
2
0
2
2
1
2
2
1
0
1
1
2
0
1
0
0
2
2
2
0
0
1
0
1
1
0
2
2
0
0
0
1
1
2
1
0
1
2
0
0
0
0
0
2
2
1
0
1
1
1
0
0
1
0
0
1
2
1
2
1
1
0
1
1
1
0
1
3
0
2
0
0
1
0
2
2
0
2
3
1
0
1
0
0
1
0
0
1
0
0
0
0
2
0
2
1
1
0
2
2
1
0
0
1
0
0
0
0
1
0
1
2
2
1
1
2
0
1
0
2
2
1
2
2
1
1
1
1
0
2
2
0
0
2
0
1
0
1
0
2
1
0
1
1
1
1
2
1
0
0
0
2
2
2
2
0
1
1
1
1
1
0
0
1
0
1
1
2
1
0
2
3
1
1
1
1
0
0
1
2
0
0
1
0
2
4
2
1
1
2
1
2
2
0
0
1
2
1
0
1
0
0
0
1
1
2
0
1
7
0
0
1
0
1
1
1
0
0
2
1
1
0
0
0
1
0
2
0
2
1
1
0
0
0
2
0
0
1
2
0
0
0
2
0
1
2
1
1
1
0
0
0
1
2
2
1
0
3
0
1
2
2
0
2
0
2
1
2
1
1
1
1
2
0
2
2
1
2
2
1
0
1
2
1
0
0
0
0
1
0
0
0
1
0
1
2
1
1
2
0
1
1
2
1
1
1
1
0
0
1
0
2
1
0
2
1
1
0
1
2
0
1
0
1
0
1
1
2
0
1
0
1
2
1
3
1
2
2
1
1
1
0
1
0
0
2
0
2
1
0
2
0
1
2
0
0
0
1
0
0
1
0
2
0
2
2
1
1
2
0
1
0
0
0
0
0
2
0
2
0
2
1
0
2
1
0
1
1
2
1
1
1
0
0
1
2
0
0
0
1
2
0
1
0
1
2
0
0
1
1
0
1
0
0
2
1
2
0
1
0
0
0
0
0
0
0
0
1
0
2
2
1
2
1
1
1
0
0
0
0
1
0
0
1
0
1
0
2
0
0
1
1
2
0
1
0
1
0
0
0
2
2
2
1
1
1
0
1
1
1
0
0
0
0
0
0
1
1
0
1
2
0
0
1
1
1
0
0
2
2
2
0
1
1
0
0
1
1
2
0
1
1
1
0
1
0
0
1
0
1
1
1
1
1
0
1
2
2
0
1
1
0
0
0
1
0
0
2
0
1
0
0
0
0
2
0
0
2
1
0
1
0
2
0
0
1
1
0
0
1
1
2
1
1
1
0
1
1
1
1
0
0
0
1
0
0
1
2
1
0
0
1
1
0
0
0
1
2
2
1
2
3
0
0
0
2
0
1
1
0
0
0
1
1
1
0
0
0
0
1
0
1
2
1
0
1
1
1
2
1
0
2
1
0
0
2
0
2
0
1
0
0
1
0
0
0
1
0
0
1
1
0
1
1
0
0
0
2
1
1
3
1
0
0
1
1
1
0
3
2
0
1
1
1
1
2
0
2
2
2
2
1
0
1
2
1
1
2
1
0
1
2
0
1
0
1
0
3
1
0
2
1
0
1
2
1
0
0
1
0
0
1
2
2
0
1
0
2
0
0
1
3
2
0
1
2
1
1
0
1
0
0
2
0
2
1
1
1
0
0
0
1
2
2
2
1
1
1
1
1
0
3
0
1
0
0
0
1
0
1
0
0
0
2
0
0
1
2
0
1
2
1
0
0
0
1
1
2
0
2
0
0
3
0
0
5
0
1
0
0
1
0
1
2
1
2
2
2
1
0
0
0
1
1
0
1
1
1
1
2
0
1
1
1
0
0
1
1
2
0
1
0
1
0
1
0
1
1
0
1
1
1
2
1
2
1
0
0
0
0
1
2
0
2
0
1
0
0
2
0
0
2
2
0
2
2
2
1
1
2
0
2
2
0
0
1
2
1
1
0
0
1
0
1
0
0
1
0
1
2
1
2
1
0
0
2
1
0
1
0
0
0
2
0
1
2
2
2
0
0
0
2
3
1
1
0
0
1
0
0
1
0
0
0
0
2
0
2
0
1
0
0
1
0
0
1
0
1
2
0
0
0
0
0
2
0
0
1
2
2
1
1
2
0
2
0
1
2
1
0
1
0
2
1
1
2
0
1
2
2
0
1
0
1
1
0
1
2
0
0
1
1
1
2
0
2
0
1
1
1
1
0
0
1
0
2
0
1
1
0
2
2
1
0
2
2
1
2
1
1
1
2
1
0
1
0
0
1
1
0
1
0
1
1
1
2
0
0
1
0
1
1
2
0
0
1
2
0
1
0
0
1
1
0
2
2
1
0
1
1
0
1
1
0
1
2
0
1
1
0
2
1
1
2
1
2
0
0
1
2
1
1
0
0
0
1
1
0
0
0
0
1
1
0
1
0
2
2
0
0
0
1
2
0
0
2
0
0
1
0
0
0
2
0
1
1
2
2
0
0
1
0
0
0
1
2
0
0
0
1
0
2
0
1
1
6
1
0
2
1
1
1
0
0
1
0
2
1
2
2
0
1
2
1
3
0
2
0
0
1
2
0
2
2
2
1
2
1
0
0
0
1
1
0
1
0
0
2
1
0
2
0
2
1
1
0
1
0
0
2
2
1
0
0
1
1
0
0
0
1
0
0
0
1
0
1
0
1
1
1
4
0
0
2
1
1
0
0
0
0
0
2
2
0
0
0
0
0
2
1
1
2
2
1
0
1
0
2
1
0
0
2
1
0
0
0
1
1
2
1
1
1
3
0
0
2
0
1
2
0
1
0
1
2
2
0
3
1
2
0
1
1
1
0
0
1
0
0
1
1
0
1
0
1
0
1
0
0
2
1
2
1
1
0
2
1
1
0
1
0
0
1
2
7
0
0
2
1
1
2
1
0
2
1
0
1
2
0
2
1
1
1
0
0
4
1
2
0
0
0
1
2
1
1
0
1
1
2
0
2
2
1
0
1
1
0
0
0
2
0
1
0
0
0
0
1
1
1
1
1
1
2
1
1
2
0
3
1
0
1
1
2
1
0
0
0
1
0
1
1
1
2
0
0
0
2
0
0
0
0
0
1
1
0
0
2
1
0
2
1
1
2
0
1
1
0
2
0
2
1
0
2
1
2
2
1
0
2
1
1
0
1
2
0
0
1
0
0
1
0
0
2
0
1
1
0
2
0
0
0
0
0
0
0
0
2
0
0
1
1
0
2
1
2
1
1
1
1
0
3
0
0
1
1
2
1
0
0
1
0
1
0
1
0
3
0
0
2
2
1
1
1
0
0
0
0
0
0
1
0
1
0
0
1
2
2
1
2
1
2
2
0
2
2
1
1
2
0
1
0
0
1
1
1
0
0
0
1
1
0
1
0
1
1
1
1
1
2
0
0
2
1
1
2
3
0
2
1
2
0
1
1
2
1
1
1
1
1
2
0
0
1
2
1
0
0
0
0
2
1
0
0
2
1
0
1
1
1
1
0
3
1
2
3
0
0
1
0
1
1
1
1
0
1
0
1
2
0
0
1
1
2
0
0
0
0
0
0
0
2
0
0
1
1
0
1
0
2
0
0
0
1
0
1
1
2
1
0
0
1
0
2
2
0
0
1
0
0
0
2
1
0
1
0
1
2
2
2
1
0
1
2
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
1
1
0
0
1
1
0
1
1
0
0
1
2
0
0
0
0
0
1
1
1
1
2
2
1
1
2
1
1
2
2
1
1
0
1
0
0
2
0
2
1
1
1
5
2
1
1
0
1
1
0
1
0
1
0
0
0
0
1
3
1
0
1
0
1
2
2
1
1
2
0
0
1
1
0
1
0
0
2
1
1
0
0
0
0
1
0
2
2
0
0
0
1
0
2
0
0
1
2
3
2
2
1
0
0
1
0
0
0
2
0
0
0
2
4
0
2
2
0
1
1
0
2
1
0
0
0
0
0
0
0
1
0
1
1
2
1
0
0
1
2
1
0
1
1
2
1
0
1
0
1
0
0
1
0
0
2
0
0
1
2
2
0
2
0
0
2
1
2
1
2
1
1
0
0
0
0
0
1
2
1
2
1
1
1
2
0
0
0
3
0
1
5
0
0
0
2
2
1
0
0
0
0
2
0
2
2
0
0
1
2
1
1
1
2
1
0
0
0
1
1
0
1
1
1
0
0
5
2
1
0
0
1
1
1
1
1
0
1
1
1
1
2
0
0
1
0
2
1
0
1
0
3
0
0
1
0
0
2
0
1
0
0
0
0
0
0
1
0
0
2
1
1
0
1
0
2
1
2
2
1
0
3
0
2
0
0
2
1
1
1
0
1
0
1
0
0
1
1
0
0
0
0
1
0
1
0
1
2
2
0
0
1
0
0
0
1
1
1
1
0
0
0
0
0
1
2
0
1
0
0
1
1
1
1
0
0
1
1
1
1
0
2
1
1
0
1
0
0
1
1
0
1
1
0
1
2
0
0
0
1
0
1
2
0
0
0
2
0
0
0
1
1
1
2
1
0
0
1
0
0
0
0
0
1
1
0
1
0
0
1
1
1
2
0
1
1
2
2
1
0
2
0
1
2
2
1
0
1
1
1
0
0
1
2
1
0
2
2
0
0
1
2
0
0
1
1
2
0
1
0
0
0
1
1
0
0
0
1
0
1
1
2
0
2
1
1
1
1
0
0
1
3
2
0
0
1
2
1
0
1
0
0
1
2
2
2
1
0
2
1
2
0
0
0
0
0
1
0
2
0
0
1
1
0
0
1
1
0
1
2
0
1
1
2
0
0
0
1
3
2
1
1
1
0
0
0
1
0
1
1
1
1
2
2
1
0
0
0
1
2
2
0
2
0
0
0
2
1
0
0
0
2
0
0
0
0
1
0
2
0
0
1
1
1
0
0
1
2
1
1
0
1
0
1
0
0
0
2
0
0
0
0
0
1
2
0
0
0
1
0
0
2
0
0
1
2
0
0
0
2
0
1
1
1
0
1
0
0
0
1
2
0
1
0
0
0
0
1
0
0
1
0
1
2
0
2
0
1
0
0
0
1
1
2
1
1
1
0
1
0
0
1
1
2
1
1
1
0
1
0
1
0
0
0
1
1
0
2
2
0
0
1
0
1
0
1
0
1
1
0
2
2
1
2
0
0
1
0
0
0
1
1
1
4
0
1
1
0
0
1
0
0
1
2
1
0
2
1
0
1
0
1
0
0
1
0
2
0
1
0
1
1
0
2
0
0
1
0
2
1
1
2
0
2
1
2
3
0
2
1
0
2
0
2
1
0
2
0
0
2
1
0
0
2
1
0
2
1
0
1
1
2
0
1
1
1
0
0
1
2
0
1
2
1
1
0
0
1
0
2
0
1
0
0
0
0
0
1
2
3
0
2
2
1
0
1
1
0
0
0
3
0
0
1
0
0
0
0
0
0
1
0
0
2
0
2
0
1
0
5
2
0
0
1
1
2
1
2
2
0
2
2
2
2
2
0
0
0
0
1
0
1
0
2
0
0
0
0
1
1
0
0
2
1
3
1
0
0
0
2
1
1
0
1
0
2
1
0
1
0
1
0
0
1
0
0
1
2
0
3
2
1
1
2
1
0
3
2
2
0
2
0
1
0
1
0
0
0
0
0
0
1
0
1
12
0
2
1
1
1
1
1
1
1
1
0
0
0
0
2
1
0
0
2
2
0
1
0
2
2
0
2
1
0
2
1
1
0
1
0
0
1
1
2
0
0
2
1
2
0
1
0
0
0
1
0
1
0
1
1
0
2
0
0
1
2
0
1
1
2
1
2
1
2
1
2
0
1
0
1
0
0
0
1
0
0
0
2
2
1
0
0
0
2
2
3
1
0
0
0
0
0
1
0
0
0
2
0
1
1
1
1
2
1
0
0
0
2
0
0
0
0
0
0
2
1
0
1
1
0
1
2
2
1
0
0
2
1
0
1
1
0
2
1
2
0
2
2
0
0
1
2
1
0
0
0
3
0
1
0
2
0
0
0
2
1
3
1
0
0
1
0
1
1
0
0
1
1
0
0
0
1
2
0
1
0
2
0
1
1
0
1
0
0
0
2
1
0
0
1
0
2
1
1
2
0
1
1
0
2
2
0
2
0
1
0
0
1
0
1
0
0
1
1
2
0
3
0
0
0
0
0
2
0
2
0
1
0
2
1
1
2
2
1
1
0
1
2
1
1
0
1
1
0
0
0
0
0
1
0
0
0
0
1
1
2
0
1
1
0
1
0
0
1
0
0
1
2
0
1
3
1
0
1
0
1
2
0
0
0
1
0
0
1
0
1
2
0
1
0
3
1
1
0
2
0
0
0
0
3
0
0
3
1
0
0
2
0
1
0
1
1
0
2
1
0
1
0
1
2
0
1
0
1
0
2
0
1
1
2
1
2
1
0
1
1
0
1
0
1
1
2
1
0
0
1
0
0
0
2
0
2
0
0
1
1
1
1
1
1
1
2
0
1
0
1
2
1
0
2
0
1
2
1
0
2
2
0
2
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
1
1
0
3
0
2
0
0
2
0
0
2
2
1
0
0
2
0
0
0
1
1
1
1
1
2
0
2
1
0
1
1
1
1
1
0
0
0
0
1
0
0
0
1
1
1
1
0
0
0
0
0
1
2
2
2
0
0
2
1
1
1
0
2
2
1
1
1
1
1
2
1
1
1
1
0
2
1
0
1
1
2
0
0
0
0
2
2
0
1
0
1
0
0
0
0
2
2
2
0
1
0
0
2
2
0
0
2
1
0
1
0
0
2
1
2
0
2
0
2
2
1
2
1
1
0
0
1
0
0
0
1
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
1
0
2
5
1
1
2
1
1
1
1
1
1
0
4
1
0
1
0
0
1
0
1
0
0
1
1
1
0
0
0
0
1
0
2
2
0
1
0
1
2
1
1
2
2
0
2
1
1
2
2
0
1
0
2
0
1
1
0
0
0
1
2
0
0
0
0
0
1
1
0
2
0
0
1
1
0
1
1
0
0
2
1
1
0
4
0
0
2
0
1
1
1
2
0
0
2
1
0
0
0
2
1
2
2
0
0
1
0
0
0
0
0
0
0
1
1
1
0
1
1
0
1
1
1
1
0
0
0
1
0
1
0
0
2
0
1
1
2
0
0
0
2
0
2
0
1
1
0
1
0
1
1
1
1
0
1
0
0
1
0
2
0
0
1
0
0
2
1
0
1
0
0
2
2
1
0
0
0
1
2
0
0
1
0
1
0
1
4
0
0
0
0
1
1
1
0
1
1
0
1
0
1
0
1
2
0
2
1
0
0
0
0
0
4
0
2
0
2
2
1
0
1
0
0
1
1
0
0
2
0
0
0
0
1
2
1
0
0
0
1
1
1
1
1
1
1
0
1
2
2
0
0
2
0
1
0
1
1
2
0
1
1
0
2
1
2
0
1
1
0
1
2
1
1
0
1
0
1
0
1
1
2
2
0
1
2
0
2
0
0
1
0
0
1
0
0
0
0
2
0
2
1
0
0
0
2
0
0
1
0
2
0
2
0
1
1
0
1
0
0
0
1
0
0
2
1
2
2
0
1
0
0
2
2
0
0
0
0
0
1
1
0
1
2
2
2
0
1
1
0
0
0
0
2
0
0
1
1
2
0
0
2
2
1
1
1
3
1
2
0
1
2
1
1
6
1
1
0
1
2
1
0
2
1
2
2
0
2
0
0
0
0
2
0
1
0
0
0
1
0
1
1
1
0
0
2
2
2
0
0
0
2
1
2
0
2
2
1
0
1
0
0
1
2
2
0
2
0
0
1
0
2
1
0
1
1
2
0
0
1
1
1
0
0
0
1
2
1
2
2
1
0
0
1
1
0
0
0
1
2
2
1
0
0
1
1
1
0
1
1
1
2
0
0
0
0
3
0
0
2
1
1
1
0
2
0
2
0
1
2
0
1
2
1
2
2
0
1
0
0
0
1
1
1
0
1
1
1
1
0
1
0
1
1
0
0
2
0
0
1
0
1
0
1
2
0
0
1
0
0
2
2
1
0
0
1
0
0
1
0
0
1
0
0
1
0
0
1
0
1
1
1
0
0
0
0
0
0
1
1
1
1
2
1
0
0
2
0
0
0
2
1
0
2
1
0
0
1
2
1
2
1
1
2
2
2
2
1
1
0
0
1
4
0
3
2
0
0
0
1
0
2
0
1
2
1
2
1
1
0
2
0
0
0
0
2
1
0
1
0
0
1
0
0
1
1
0
1
0
2
2
0
2
1
0
0
2
0
0
0
2
2
1
0
0
1
2
2
0
1
1
0
1
1
2
0
0
0
1
0
3
0
2
1
0
0
0
0
2
0
0
1
1
2
0
0
0
0
0
1
2
0
0
0
3
0
1
0
1
0
1
2
2
0
0
2
2
0
0
0
0
0
2
2
0
1
0
1
2
0
1
0
2
1
1
0
0
0
1
0
0
2
0
3
1
1
2
2
0
0
0
0
2
0
2
2
1
0
0
2
2
2
0
0
0
0
1
0
0
0
1
0
1
2
1
0
0
0
1
1
2
2
0
1
2
0
2
2
1
0
0
0
1
1
0
2
0
0
1
0
0
2
2
1
0
0
1
0
1
2
2
1
1
1
1
1
2
1
2
0
2
0
2
1
0
2
0
1
0
0
2
2
2
0
0
1
0
1
1
0
1
1
0
0
2
1
0
0
1
0
2
1
1
1
1
0
0
2
0
1
0
0
2
0
1
2
0
1
1
1
0
2
1
0
1
1
1
1
0
2
2
0
0
0
1
2
1
2
0
0
0
0
2
2
1
0
1
2
1
1
1
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
2
1
0
1
2
2
1
0
0
1
2
0
0
0
1
0
1
1
0
2
3
1
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
1
2
0
0
1
0
1
1
1
0
1
0
0
0
0
1
2
1
1
0
2
0
2
0
0
0
1
0
1
2
0
1
0
2
1
2
0
0
0
0
1
0
1
1
2
0
1
0
2
0
1
0
2
1
2
1
1
1
0
0
1
2
1
0
0
0
1
0
0
0
1
0
1
1
0
1
2
1
0
0
0
1
1
2
0
2
0
1
1
0
3
1
0
1
1
4
0
0
1
0
0
0
0
1
2
2
0
0
0
3
1
1
1
1
0
2
0
1
1
1
1
2
2
2
1
1
3
2
0
0
1
1
2
2
2
1
1
0
4
2
0
0
1
1
2
0
2
0
1
1
2
1
1
2
1
0
1
1
1
0
2
1
2
2
0
0
0
1
2
1
3
2
1
0
1
0
1
1
1
1
1
2
3
1
2
0
0
2
1
0
1
3
2
0
1
0
2
0
2
2
2
0
0
0
0
2
2
0
0
1
0
0
1
0
1
1
1
0
2
4
0
0
0
0
0
1
0
2
2
1
2
2
1
2
1
1
2
1
0
1
1
0
1
1
2
0
1
0
1
2
0
1
1
1
2
1
3
0
0
0
1
1
0
1
1
2
0
2
0
1
1
1
0
0
1
1
0
1
2
0
1
0
2
0
0
1
1
0
2
0
2
1
0
5
3
2
0
2
0
2
2
0
0
1
1
2
0
1
0
1
2
2
0
0
2
0
0
1
1
0
5
2
0
2
0
0
0
0
0
1
0
0
0
1
1
0
1
2
1
1
0
2
2
0
1
2
1
1
2
1
0
0
0
0
0
0
0
2
0
0
1
0
0
1
3
2
1
0
0
1
1
3
1
1
2
0
2
1
2
0
0
1
2
2
0
2
1
2
0
1
0
1
1
0
1
0
0
1
0
0
3
0
1
1
2
2
1
1
2
0
1
1
0
0
1
2
0
1
1
1
2
1
2
0
1
2
0
2
0
0
2
0
2
1
1
1
3
1
1
1
0
1
0
0
0
2
0
2
0
2
2
0
0
2
1
2
0
1
1
1
0
1
1
0
0
0
0
0
1
0
0
0
1
2
0
0
0
1
1
2
0
0
1
0
1
0
0
1
3
1
2
0
0
1
0
1
0
1
1
2
0
1
1
0
0
0
0
0
1
0
0
0
1
1
1
1
0
2
1
1
0
0
0
1
0
0
1
0
2
0
0
2
1
2
0
1
0
1
0
2
0
0
1
1
0
1
0
1
1
1
0
0
0
1
1
2
1
1
0
0
2
1
2
1
1
0
0
2
1
2
1
0
0
0
0
2
0
0
0
0
1
2
2
1
0
1
0
3
0
1
2
2
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
2
0
1
0
1
0
0
0
0
2
0
1
1
2
1
0
2
1
1
2
0
2
0
1
1
0
1
0
1
2
0
1
0
0
1
2
0
1
2
0
2
1
0
1
2
0
2
1
0
0
1
0
0
0
3
1
1
1
0
1
0
2
0
1
0
1
2
3
0
0
0
2
4
1
0
2
2
1
2
0
0
1
1
0
0
0
1
2
1
0
0
0
0
2
0
2
2
2
0
0
1
1
0
0
2
0
0
2
0
1
0
1
1
1
2
0
1
1
0
0
2
1
2
1
0
0
2
0
1
2
1
0
0
0
0
0
1
0
1
2
4
0
0
1
1
0
1
0
0
2
2
0
1
0
2
0
2
2
2
0
2
0
0
0
2
1
1
2
2
2
2
0
2
0
0
0
1
0
1
0
1
2
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
1
2
0
1
2
0
0
1
2
2
0
1
0
0
1
0
3
0
0
1
3
0
1
3
1
1
0
1
0
2
0
2
0
0
1
1
1
1
0
0
1
0
2
0
2
1
0
1
0
0
2
1
0
1
1
1
1
1
0
0
1
1
1
1
0
2
0
0
2
1
0
1
0
2
2
2
0
1
2
1
0
1
2
0
0
0
0
3
2
0
0
1
2
0
0
0
2
0
1
0
0
2
0
0
2
2
2
2
2
2
0
1
0
2
1
0
1
0
0
0
0
1
2
2
0
2
1
0
1
2
2
1
1
0
2
2
0
5
1
2
0
1
0
0
0
2
1
3
1
1
1
0
2
0
2
2
1
1
1
0
1
0
1
1
0
0
0
1
0
2
2
0
0
2
0
0
1
1
2
1
0
1
2
4
0
1
1
0
0
0
2
0
1
1
1
0
1
1
1
0
0
1
0
2
5
1
1
4
2
1
0
0
2
0
0
0
2
0
1
0
1
2
0
0
2
2
1
1
0
0
1
1
2
0
2
0
1
1
0
2
1
0
1
2
0
0
0
0
0
2
0
0
1
0
1
1
0
0
0
2
1
0
2
1
1
2
0
0
2
0
0
0
1
0
2
1
0
1
1
0
2
0
0
0
0
0
1
1
1
1
0
1
0
2
0
2
0
1
0
1
0
1
0
0
2
0
3
2
0
0
3
2
0
1
0
0
1
2
1
2
2
2
0
1
1
0
2
0
0
1
1
0
0
2
2
2
1
1
0
1
1
1
7
2
0
1
0
2
0
2
1
2
2
0
2
0
3
1
0
1
1
2
1
1
0
0
1
2
0
0
0
0
3
0
1
0
1
1
0
0
0
1
2
2
0
0
2
1
0
2
1
2
2
0
1
0
2
2
0
2
0
0
0
1
1
0
0
0
1
0
2
1
1
3
0
0
0
1
1
0
0
1
0
0
0
0
2
2
0
2
1
0
1
3
0
1
1
3
2
2
0
0
0
1
2
1
1
1
2
0
0
0
0
0
0
1
1
0
1
0
2
1
1
1
2
0
1
0
2
0
1
1
0
2
0
1
0
1
0
0
1
1
0
0
0
0
1
2
2
2
0
0
1
0
0
0
1
1
0
2
2
0
1
2
0
1
1
0
0
1
2
0
1
0
0
2
2
2
1
1
1
0
1
1
0
2
2
0
0
2
1
1
2
0
1
1
0
1
1
0
2
0
3
0
1
0
0
0
0
0
1
2
1
1
2
2
0
0
2
0
1
2
1
1
0
1
1
0
1
0
2
4
0
1
2
1
2
1
1
1
1
1
0
1
1
0
1
1
1
0
1
0
6
1
1
0
0
0
0
1
0
0
0
1
1
2
0
0
0
0
1
1
0
1
0
1
0
1
1
0
1
0
1
1
1
2
1
1
1
1
0
0
0
2
1
0
0
1
0
1
1
0
0
2
1
2
2
0
2
1
0
0
0
1
0
1
1
0
0
2
0
1
1
0
1
0
0
0
0
1
2
0
1
1
0
0
2
0
0
1
0
1
1
0
1
0
1
1
1
0
2
0
1
1
1
1
1
2
0
0
2
0
0
1
1
2
1
2
2
1
1
0
0
0
1
1
1
0
1
0
0
1
2
0
2
0
1
1
2
0
1
0
1
0
2
1
0
0
2
2
2
2
0
0
1
1
0
0
0
2
0
0
1
0
0
1
0
0
1
2
0
1
2
0
0
1
0
1
1
0
0
1
0
2
0
1
2
1
1
2
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
1
1
0
0
0
0
2
1
0
0
0
0
1
2
0
1
1
1
2
1
1
0
2
1
2
0
1
0
0
1
1
0
1
1
1
0
1
1
1
0
1
0
1
0
1
2
2
0
2
0
2
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
1
1
0
2
1
1
2
0
0
0
0
1
2
1
1
1
0
1
0
0
2
0
0
0
2
2
0
0
2
1
1
2
0
0
0
1
1
1
0
2
1
1
2
2
0
1
0
0
0
0
0
1
1
0
0
2
2
0
0
1
1
0
1
1
0
0
1
1
0
0
0
0
2
1
1
1
1
1
0
4
0
1
0
1
0
1
2
2
1
1
4
0
1
1
0
0
1
2
0
0
2
2
0
1
0
0
2
1
2
1
3
1
0
0
1
0
0
0
0
0
2
0
2
1
0
2
1
1
2
1
1
2
0
0
1
1
1
0
1
0
0
1
1
0
2
0
2
0
1
0
0
1
0
0
0
2
1
0
1
0
1
0
0
0
2
0
3
0
2
0
1
1
1
2
0
2
1
2
0
0
1
0
1
0
2
1
0
0
0
0
1
2
1
0
2
1
1
2
0
0
2
2
1
1
2
1
2
0
1
0
2
1
0
0
0
0
0
0
2
1
2
2
1
0
2
2
2
0
0
3
1
1
1
1
1
0
0
1
1
0
1
0
1
1
0
2
1
1
1
0
0
1
0
1
0
2
2
1
0
1
0
1
1
1
0
2
2
1
1
1
2
1
1
0
1
0
1
2
0
2
1
0
1
2
2
0
1
3
0
2
2
2
1
1
0
0
2
1
0
0
0
1
0
1
0
5
1
1
1
0
1
1
1
2
1
0
0
1
1
0
1
1
2
1
1
0
0
0
2
0
1
0
1
1
0
0
1
0
1
0
1
0
0
1
1
1
0
2
0
1
0
0
1
1
1
0
0
0
0
1
0
0
0
1
0
0
1
1
0
1
1
0
1
0
1
2
1
0
2
1
1
0
1
0
2
0
2
1
0
0
1
0
0
0
1
0
0
0
0
2
0
2
2
2
2
1
3
1
1
0
1
1
0
2
0
0
1
1
2
1
1
2
0
1
0
0
1
0
2
2
0
2
1
0
1
4
1
1
2
1
1
1
2
1
0
2
1
2
2
2
3
1
0
1
0
1
1
1
0
0
1
0
1
0
0
1
1
2
1
2
0
1
1
1
2
1
1
0
2
0
0
3
1
5
0
0
1
0
0
1
0
0
2
0
2
0
1
1
1
0
0
0
0
3
2
1
1
2
1
0
1
2
0
1
1
0
0
1
1
1
0
0
0
0
1
1
0
0
0
1
1
1
0
0
0
2
0
1
1
2
1
0
0
0
1
0
2
1
1
0
2
0
1
0
2
2
3
1
0
2
0
0
0
0
2
2
0
1
0
2
0
1
1
1
0
1
0
0
1
0
0
0
0
1
2
2
0
0
0
1
1
1
1
0
0
0
0
0
1
2
0
0
0
0
0
1
1
2
0
0
0
0
0
1
0
2
0
0
2
1
2
1
1
1
0
0
1
0
1
1
1
1
0
0
1
0
1
0
0
1
1
0
0
0
1
1
0
2
0
2
0
0
0
1
1
2
1
0
10
4
1
1
0
1
0
1
0
0
0
2
1
0
1
0
1
0
1
2
1
2
0
0
0
0
1
2
0
0
1
2
1
0
0
2
0
0
1
0
0
2
2
0
1
1
2
1
0
1
2
1
1
0
2
1
2
2
1
0
1
0
0
0
0
0
1
0
2
3
0
2
0
0
1
1
0
1
0
1
2
1
2
2
2
0
2
0
0
2
2
1
0
1
0
0
0
1
2
0
1
0
0
3
0
0
0
2
1
2
1
0
1
0
1
1
2
0
1
1
0
1
0
0
1
0
0
2
2
2
2
0
2
0
0
0
0
0
0
0
0
1
1
2
2
2
2
2
1
1
0
0
1
2
0
0
1
1
0
1
0
0
0
0
1
0
1
0
2
2
2
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
1
2
1
0
0
0
2
0
0
0
0
1
0
2
3
2
0
2
0
2
2
1
0
0
0
1
1
0
2
0
2
1
1
2
0
0
0
2
1
0
1
1
0
1
2
1
1
0
4
2
0
1
3
1
0
0
0
1
0
1
0
0
0
2
2
0
0
0
1
1
2
1
0
0
0
0
1
0
0
2
1
0
1
0
1
1
1
1
1
1
1
0
1
0
1
1
2
0
1
2
0
0
1
1
2
0
1
0
3
0
0
1
1
0
1
1
0
2
3
2
0
1
2
1
2
1
0
0
1
1
0
1
2
0
1
2
0
1
2
1
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
1
2
1
2
1
2
1
1
2
1
2
2
2
2
0
1
0
0
0
2
0
0
1
1
2
2
1
0
0
0
0
3
1
1
0
2
2
2
2
0
0
0
0
0
1
0
1
1
1
3
1
1
0
0
0
0
1
1
1
2
2
2
0
0
1
1
1
0
0
2
1
1
1
0
0
1
0
0
1
0
1
1
3
0
0
0
2
1
0
0
2
2
0
0
0
2
2
2
1
2
2
0
1
1
0
3
0
0
0
1
1
1
1
2
0
0
0
2
2
2
1
1
1
1
1
1
1
1
2
0
1
1
0
1
0
2
2
0
1
0
1
0
2
1
0
0
0
1
0
0
0
1
0
0
0
2
2
2
0
2
2
0
0
3
1
0
0
1
2
0
1
1
1
1
1
2
2
1
2
0
0
1
1
1
1
2
2
0
1
0
1
0
0
0
2
1
1
1
0
2
1
0
2
2
2
0
1
2
0
0
0
1
0
0
1
3
1
0
1
1
1
1
2
0
2
0
2
1
1
1
0
2
2
1
2
2
1
3
1
0
1
0
0
1
1
0
0
1
0
3
0
1
0
0
2
1
1
2
0
1
1
0
0
3
2
0
0
1
2
0
0
0
2
0
0
2
1
0
1
2
1
2
1
1
0
0
1
0
1
2
0
0
2
2
2
1
1
1
1
0
1
1
2
0
1
0
1
2
1
0
1
0
0
2
0
1
2
1
1
0
1
1
1
1
0
0
2
1
0
7
1
1
2
2
1
0
0
1
3
0
0
0
2
0
0
0
1
2
1
2
1
2
2
1
2
1
2
1
0
1
1
0
0
0
0
0
1
2
0
0
6
0
1
1
0
2
1
0
2
0
0
1
2
0
1
2
1
1
2
0
2
0
1
0
1
0
1
0
1
2
0
2
2
0
1
0
0
1
1
0
0
0
2
0
0
0
1
2
0
1
0
0
0
0
2
1
0
1
0
1
2
3
2
0
2
1
0
0
2
2
0
0
0
1
0
2
1
1
0
0
0
0
2
0
2
2
1
0
0
1
2
1
1
1
0
0
0
0
1
2
1
0
1
1
1
1
0
0
2
0
0
0
1
0
1
1
0
2
1
1
1
0
0
2
0
2
2
2
0
0
2
1
1
1
0
2
0
0
0
1
6
1
0
0
1
1
0
0
1
0
1
1
1
1
1
1
0
1
0
2
0
0
0
1
0
2
1
0
1
1
4
0
1
1
0
0
0
1
1
2
1
1
2
0
2
0
1
0
1
1
0
0
2
0
0
2
0
1
1
1
0
1
1
1
0
0
1
1
0
0
1
1
2
1
1
1
1
1
2
2
2
1
0
3
2
0
1
0
0
1
1
1
2
1
2
1
1
0
1
1
1
1
1
0
0
0
0
1
3
0
1
0
1
0
1
1
2
0
1
0
1
1
0
0
0
1
0
2
1
1
0
0
0
0
2
1
2
1
0
0
0
1
1
0
0
1
0
2
2
0
1
1
0
1
2
0
1
1
0
1
2
1
0
0
1
0
1
0
1
1
0
0
0
1
2
0
2
0
1
0
0
0
0
1
1
0
1
0
1
2
1
0
1
0
0
0
1
2
0
1
0
1
1
2
0
2
2
2
1
0
1
0
1
0
2
0
0
0
2
0
0
1
1
1
0
0
1
1
1
2
0
0
2
0
0
2
0
0
0
0
1
1
1
0
2
2
2
0
0
2
0
1
2
0
0
1
4
0
1
0
0
1
0
2
0
0
1
2
2
2
0
1
2
0
1
2
0
1
0
0
5
0
1
0
0
0
0
1
2
1
2
0
1
0
1
2
0
2
0
1
2
1
2
0
2
0
0
0
2
1
1
0
2
2
2
0
1
0
0
2
2
1
0
2
1
0
1
2
0
1
1
0
2
2
2
1
2
0
0
0
1
1
0
3
1
0
2
1
0
1
1
1
2
0
2
0
1
1
0
2
0
1
0
0
0
0
0
1
0
1
2
2
1
0
0
2
0
1
1
1
2
0
0
1
1
2
1
1
2
1
2
0
1
1
2
1
0
2
1
0
2
0
0
1
1
2
0
0
0
0
1
1
2
0
0
2
0
2
0
0
1
1
0
0
2
0
0
2
2
1
2
0
0
0
1
1
0
0
1
1
0
0
0
0
0
2
1
0
0
0
1
1
1
1
0
1
2
1
0
0
1
2
1
1
1
2
0
2
0
0
1
2
2
1
0
0
1
0
0
2
1
0
1
1
2
1
0
0
2
1
2
2
0
2
0
2
2
0
2
1
1
2
4
0
1
2
0
0
1
1
0
0
0
2
2
0
0
1
0
1
2
2
1
0
0
1
0
0
2
2
0
0
4
0
2
2
0
2
1
3
1
1
2
1
3
1
0
2
2
0
1
1
2
1
0
0
3
0
1
0
0
2
1
2
0
0
1
2
0
1
1
1
0
0
1
2
0
0
1
2
2
1
1
2
1
0
0
1
0
1
1
2
1
2
2
0
0
1
1
0
1
1
0
0
0
1
1
1
0
0
2
1
1
0
1
0
1
1
0
0
1
1
1
0
2
1
2
2
2
1
1
0
0
0
2
0
2
0
0
0
0
1
0
1
1
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
2
1
1
1
0
0
0
0
2
0
3
2
2
2
0
2
2
0
1
1
1
0
0
0
0
2
0
1
0
0
0
1
0
1
3
1
1
0
2
0
2
0
0
0
2
1
0
0
0
1
0
1
1
1
0
2
1
2
2
1
1
2
1
0
2
0
0
2
1
0
1
1
3
0
0
0
1
0
1
1
1
1
1
2
0
0
0
2
0
0
2
0
0
2
0
2
1
0
0
1
2
2
2
1
0
0
1
1
2
1
1
1
0
2
1
0
1
1
0
2
1
1
2
0
1
1
1
1
0
0
2
2
3
0
2
1
0
1
0
1
0
1
0
0
1
0
2
0
0
0
1
1
0
0
2
1
2
0
1
0
1
1
2
0
1
0
0
2
0
1
0
1
1
2
1
1
0
1
1
1
0
1
1
1
0
0
0
2
1
0
0
1
1
0
0
0
1
0
2
1
0
1
1
1
2
0
2
0
2
1
0
2
1
0
1
0
0
1
1
1
0
1
1
0
0
0
0
0
0
0
0
2
1
1
1
2
2
1
1
0
1
0
2
1
0
1
0
1
1
2
0
2
1
1
0
0
1
1
1
2
0
1
0
0
0
0
1
1
2
2
2
2
2
2
2
0
2
0
0
0
2
0
2
0
0
0
0
0
0
2
2
0
1
2
1
1
0
2
1
1
1
0
0
1
2
1
0
1
0
1
0
0
1
1
0
1
1
1
2
2
2
0
0
0
0
2
1
2
1
1
0
1
1
0
1
1
1
1
0
0
2
1
2
1
1
2
0
0
1
0
1
0
1
0
1
1
1
0
0
2
0
0
2
1
1
0
2
0
0
2
2
0
1
1
4
0
1
1
2
2
1
1
1
0
0
1
2
0
0
1
0
2
0
2
0
2
0
1
0
0
0
1
1
1
1
0
2
2
0
2
2
0
1
0
0
2
4
0
0
2
0
2
2
2
1
0
1
1
0
2
0
1
1
0
0
0
0
2
0
1
1
0
0
2
0
0
1
0
2
0
1
0
0
1
1
4
0
0
1
0
0
2
2
0
0
0
2
1
0
1
0
1
0
2
0
0
0
1
1
2
1
1
1
0
1
0
2
0
1
0
2
2
2
1
0
1
0
2
2
1
3
0
0
1
2
1
2
0
0
0
0
2
0
0
2
2
2
0
0
0
1
1
0
2
2
0
0
0
4
0
0
1
0
2
1
0
1
4
0
0
1
0
1
2
1
2
0
2
1
0
1
0
2
0
1
1
0
0
0
0
0
2
1
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
2
1
1
1
1
1
1
1
0
0
2
0
2
1
2
2
1
1
1
0
1
0
1
1
1
2
0
1
0
1
0
1
1
0
1
1
3
1
1
3
2
1
0
1
0
2
2
1
1
1
0
2
1
1
2
0
2
0
1
1
2
0
6
0
1
2
2
0
2
0
1
0
0
1
2
2
0
0
1
1
0
1
0
2
1
0
1
0
1
0
0
2
1
0
2
0
0
0
2
1
2
2
1
0
1
0
1
1
1
0
1
0
1
2
1
0
0
1
1
2
1
0
0
0
1
0
0
0
2
2
0
0
0
0
1
0
1
0
0
2
0
2
2
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
2
2
0
0
1
0
0
2
0
1
0
0
0
1
0
1
0
2
1
0
1
0
1
0
0
0
1
0
0
2
1
1
1
2
1
0
2
1
1
2
2
0
1
0
0
1
0
0
0
2
1
2
1
0
0
1
2
1
1
0
2
0
1
1
0
0
0
0
0
0
1
0
0
2
1
1
1
1
0
1
0
1
0
1
1
1
1
1
0
1
1
0
1
1
2
1
2
1
1
1
0
1
1
1
3
1
0
0
1
2
1
2
0
0
0
1
0
1
1
0
0
0
0
1
0
1
0
1
1
0
1
1
0
1
2
1
2
1
0
1
0
1
1
0
1
4
2
1
0
0
1
0
1
3
0
0
0
0
1
0
0
1
1
1
1
0
0
0
1
0
1
0
0
2
1
0
0
2
0
0
0
1
2
1
2
1
2
1
0
0
1
1
2
0
0
0
1
1
2
2
0
2
0
0
0
0
1
2
2
0
1
0
2
1
1
0
2
2
1
2
0
1
2
0
0
0
2
1
2
1
0
2
0
0
2
1
3
1
1
0
1
1
2
0
0
0
0
0
0
2
0
0
1
0
0
1
0
2
0
1
0
1
0
0
0
1
1
0
1
0
0
1
1
2
3
2
1
1
1
0
0
0
2
1
4
0
0
1
0
0
0
1
0
1
0
0
0
0
1
3
0
0
0
1
2
0
1
1
1
0
1
1
1
1
0
2
0
1
0
2
0
1
0
0
1
0
0
0
0
2
4
1
2
0
2
2
0
0
2
0
1
4
0
1
2
0
2
1
2
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
1
1
1
1
2
1
1
1
1
1
1
1
2
0
0
0
0
1
2
1
0
0
1
0
1
1
2
0
0
1
1
0
0
1
0
0
0
1
1
0
2
1
0
2
1
2
0
0
2
0
1
0
2
1
1
0
1
2
1
0
1
0
0
2
1
0
0
1
3
2
0
0
0
1
2
1
1
1
1
1
2
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
1
1
0
3
1
1
0
0
1
1
0
0
1
0
1
0
0
1
0
0
1
0
2
2
1
0
0
1
0
2
0
2
1
0
1
0
0
1
2
1
0
1
1
0
1
1
1
1
0
0
0
1
2
1
1
0
0
0
0
1
1
3
1
0
0
1
1
0
1
2
0
1
0
0
2
0
0
1
2
1
0
2
1
1
1
1
1
0
0
0
2
0
1
2
0
1
1
1
0
0
1
1
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
1
0
0
1
2
1
1
0
1
2
0
1
1
2
2
1
1
1
1
1
0
1
1
2
1
2
1
1
0
2
2
2
0
2
0
0
0
0
0
1
0
1
1
1
1
0
1
2
0
2
1
1
1
1
1
1
1
0
2
0
1
0
0
0
1
0
0
1
5
0
1
1
0
2
1
0
2
0
1
2
0
2
0
0
2
1
0
0
0
1
2
0
2
1
0
0
2
1
1
2
0
0
0
0
2
0
0
0
0
1
0
0
1
0
1
0
1
1
1
2
0
0
0
1
0
1
1
1
1
0
1
1
0
0
2
2
1
1
1
1
1
0
0
1
1
0
1
0
1
0
0
0
0
1
0
1
0
1
1
1
0
2
2
1
0
2
0
1
2
1
1
1
2
1
0
0
0
1
2
1
1
1
0
1
2
0
0
2
1
0
0
0
1
0
1
1
2
0
1
0
2
1
1
0
0
0
1
0
3
0
0
1
1
2
1
0
0
1
0
1
0
0
2
0
0
2
1
0
0
1
2
2
1
0
2
0
1
2
2
0
0
0
0
2
1
2
1
2
0
0
0
0
2
1
0
0
0
1
0
1
0
1
2
0
1
1
0
0
0
1
0
1
0
1
0
0
0
0
0
1
1
2
2
0
3
2
1
0
0
1
1
1
0
0
1
1
1
0
1
1
4
0
0
1
0
0
0
1
3
0
2
2
2
1
1
0
0
1
1
1
2
0
0
1
1
1
0
1
2
1
0
1
0
2
1
1
0
0
0
0
0
0
0
1
0
1
1
0
2
0
0
1
2
0
1
1
2
0
0
0
0
0
2
0
0
2
1
0
1
1
2
0
1
2
2
1
0
0
1
1
1
3
2
0
2
0
0
0
1
0
1
0
1
1
1
2
0
0
0
1
0
0
1
2
0
2
0
1
2
3
1
0
0
0
2
1
2
3
2
1
0
0
0
1
1
0
0
0
2
0
0
1
1
0
2
1
0
1
2
1
1
2
0
1
0
0
2
1
0
2
0
1
0
1
1
0
0
2
1
2
0
1
0
0
1
2
0
0
0
1
1
0
0
0
0
1
1
0
0
0
1
1
0
1
0
0
1
1
0
2
0
2
0
1
0
2
0
1
2
2
1
2
0
0
0
0
0
0
0
1
2
1
1
1
1
1
1
0
2
1
3
2
0
0
1
1
0
0
0
2
1
1
0
1
0
0
1
1
1
1
0
1
1
1
0
2
1
0
0
2
0
0
0
0
1
2
0
0
1
6
2
1
0
0
0
0
0
0
0
2
1
0
1
1
0
0
2
0
1
2
0
1
0
0
1
2
0
2
2
2
2
1
0
0
0
0
3
1
0
0
0
0
1
1
2
1
1
1
1
0
1
2
0
1
1
0
0
2
1
4
1
0
1
1
0
2
0
2
1
0
1
1
1
0
1
1
2
1
0
1
0
0
1
1
1
0
2
0
0
2
1
0
1
2
1
0
0
0
2
0
0
0
1
1
1
2
0
0
1
2
1
1
0
0
0
1
2
0
1
1
2
0
1
0
2
2
0
1
0
0
1
2
1
1
1
0
0
1
0
2
1
1
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
1
1
1
0
0
1
2
2
1
0
1
1
0
1
0
2
2
1
0
1
2
2
0
1
2
2
1
1
1
1
0
2
1
0
1
2
1
0
0
1
2
0
0
0
0
0
1
1
1
2
0
1
1
2
0
2
1
1
0
0
1
2
0
0
2
1
2
1
1
0
0
2
2
1
1
0
0
1
0
3
1
1
0
0
1
1
0
1
0
0
0
0
1
0
2
0
0
2
0
2
0
1
0
0
1
2
1
1
0
2
3
2
1
2
0
1
2
1
1
0
1
2
1
2
0
0
2
2
1
2
0
0
0
1
1
0
1
0
0
0
1
2
0
1
0
0
0
0
1
0
1
0
0
1
3
1
0
1
0
0
0
0
1
1
2
1
1
0
1
1
0
1
1
2
0
1
2
1
1
0
1
1
0
2
0
0
1
0
1
1
1
0
1
0
0
0
2
2
1
2
1
0
2
1
0
1
2
1
0
0
2
1
0
2
2
0
2
1
2
0
1
1
1
0
3
0
2
0
2
1
1
1
0
0
1
1
0
2
0
0
0
2
1
0
0
1
1
0
1
1
2
0
0
0
1
0
0
1
0
2
0
0
0
2
2
0
0
0
0
1
0
1
2
0
0
0
1
2
2
0
1
0
0
0
0
1
0
1
2
0
1
1
1
2
0
0
1
2
0
2
0
1
0
2
1
0
0
0
1
0
0
0
0
0
0
0
1
2
1
1
0
0
0
1
1
1
1
1
2
1
1
1
1
0
1
1
1
0
0
1
0
1
1
0
0
0
2
0
1
1
0
1
0
2
0
1
0
1
0
0
1
1
1
1
0
0
0
0
1
1
1
2
2
0
0
0
0
0
1
2
2
1
1
1
0
2
0
2
0
0
1
0
0
0
2
1
0
0
0
0
1
2
0
2
1
2
0
2
1
2
0
2
2
2
1
0
1
0
2
2
2
0
2
0
1
1
0
9
2
1
2
2
1
0
1
1
1
0
0
1
0
1
0
4
1
2
2
2
0
0
1
1
3
1
0
5
1
0
1
1
2
1
0
2
0
1
2
2
0
0
1
2
0
2
0
0
0
0
1
0
0
1
1
1
2
1
0
1
0
0
0
0
1
1
1
0
1
0
1
3
1
1
1
1
2
1
1
1
1
0
0
2
0
0
0
0
0
0
2
0
2
0
2
1
1
0
0
0
2
2
2
1
0
2
0
0
0
0
2
0
2
0
0
0
1
2
0
2
2
0
2
0
2
1
1
2
0
1
1
1
2
1
0
2
0
0
0
0
0
0
0
0
2
2
1
1
0
0
2
1
1
1
0
0
1
1
0
2
0
1
1
1
0
0
3
2
2
1
2
7
0
4
2
0
1
1
1
0
0
0
1
1
2
2
1
1
2
0
0
0
2
0
1
0
0
1
1
0
0
2
0
0
1
0
2
1
1
2
1
0
2
0
2
1
0
1
2
0
0
1
0
1
1
1
2
1
1
1
1
1
2
1
2
0
1
0
0
2
4
0
1
1
0
3
1
2
0
0
1
0
2
1
0
2
0
1
2
0
1
2
1
1
1
0
2
0
0
0
1
0
0
1
0
1
0
1
2
2
0
1
0
0
0
1
0
1
1
2
1
0
1
1
2
0
1
0
0
0
1
0
2
2
1
1
0
2
0
0
0
1
2
0
2
2
1
0
1
1
0
0
1
0
2
2
2
0
2
0
1
0
1
0
1
10
2
1
0
2
2
0
0
1
0
0
0
1
1
1
2
0
0
0
0
0
2
2
0
0
0
0
0
2
1
1
0
3
0
1
0
1
0
0
0
0
0
0
1
0
2
0
2
0
2
0
0
1
1
3
0
1
0
0
2
2
2
0
1
1
2
0
1
1
0
0
1
1
0
0
1
0
0
1
2
1
3
1
0
0
0
2
0
0
0
1
1
0
1
0
0
2
1
1
2
0
2
2
2
0
0
1
1
0
2
0
0
2
0
2
1
2
0
3
0
1
0
2
1
1
2
0
0
0
2
1
0
0
0
0
0
0
2
2
0
0
0
0
2
0
3
2
2
0
0
0
2
0
1
1
0
1
0
0
1
1
1
2
1
2
0
1
2
0
2
0
0
1
0
1
0
0
1
2
0
1
0
1
1
1
0
0
2
0
1
1
1
2
0
1
1
0
0
0
0
1
0
0
0
0
0
2
1
0
2
0
0
0
1
2
1
0
0
1
0
2
1
1
1
1
0
2
0
0
1
2
0
1
0
1
0
1
0
1
1
0
1
0
0
0
2
2
1
1
1
1
0
1
0
0
0
0
1
1
1
1
0
2
0
0
0
2
0
2
1
1
0
0
3
1
1
0
2
1
0
1
1
0
1
2
1
0
1
0
1
0
3
2
1
1
1
0
0
1
1
3
0
1
1
1
3
2
0
1
2
1
0
1
1
0
2
1
1
0
1
1
1
0
0
1
0
0
0
0
2
2
0
1
1
0
0
0
2
0
0
1
1
2
1
0
0
1
1
0
1
1
0
1
0
0
0
2
1
2
0
1
0
1
2
1
2
0
2
1
1
2
0
1
2
1
2
1
2
0
1
0
0
0
1
0
0
0
1
0
1
0
0
2
0
0
0
1
2
1
0
3
0
1
0
0
0
0
1
0
2
0
0
3
0
1
0
1
1
2
2
2
0
0
0
2
0
2
0
0
1
0
0
1
2
1
2
0
0
0
0
2
0
1
0
0
0
2
3
1
1
1
0
1
0
0
5
2
2
3
1
1
0
1
1
2
1
2
1
1
0
1
0
0
0
0
1
1
0
2
0
0
0
0
2
1
1
0
2
0
2
1
1
0
2
1
2
1
1
0
4
0
1
0
2
2
2
0
4
2
2
0
0
2
2
1
1
1
0
2
2
2
2
2
0
2
0
1
0
2
1
0
2
0
2
0
0
1
2
1
1
1
0
0
1
2
1
0
0
0
1
0
0
0
0
2
1
0
1
1
2
2
2
0
0
1
1
1
0
0
0
2
2
0
0
0
0
1
1
1
2
0
2
1
0
0
0
1
2
0
0
0
0
0
0
2
1
1
0
0
0
1
0
0
2
2
2
1
0
0
2
0
1
1
0
0
1
0
1
0
1
1
0
3
2
1
1
1
0
1
3
0
1
1
0
2
0
1
0
1
0
2
1
1
2
0
1
0
0
0
1
0
0
1
2
0
0
1
0
0
2
0
2
1
1
1
1
0
2
2
1
2
0
2
0
1
1
0
2
0
0
2
1
0
0
2
2
0
2
1
0
1
2
1
0
0
0
0
0
2
1
0
1
0
2
0
1
2
0
0
2
0
2
1
0
0
1
0
2
2
1
5
0
1
2
2
0
2
2
0
0
0
2
0
0
1
0
0
0
2
0
1
2
0
0
0
2
1
0
1
2
0
0
0
1
0
0
0
4
1
0
0
2
0
2
1
1
1
1
3
0
1
0
2
2
1
0
1
1
0
0
1
0
0
0
0
1
0
0
0
1
0
1
2
1
1
1
2
2
0
1
2
0
1
1
1
1
0
2
1
1
1
1
1
1
2
2
0
1
0
0
1
0
0
0
1
1
0
0
1
0
2
1
0
1
2
2
1
2
2
1
1
0
0
0
2
0
1
1
0
0
1
1
0
1
2
1
1
2
2
1
4
2
0
1
0
1
1
0
1
0
2
0
2
1
0
1
0
2
0
2
1
1
0
0
0
1
2
0
0
0
2
2
0
1
0
1
1
1
1
1
2
0
1
0
0
1
1
1
1
1
0
1
2
1
0
2
1
1
1
0
0
1
0
2
1
2
0
0
2
0
0
0
2
2
0
0
1
1
0
1
0
0
0
0
3
1
1
1
0
0
0
0
1
2
0
0
1
2
0
1
0
0
2
0
1
1
0
1
1
1
0
0
0
1
0
0
1
1
0
1
1
1
2
1
2
1
1
1
1
0
4
0
1
0
1
1
0
0
1
1
2
0
2
0
1
0
0
2
1
1
0
0
1
1
0
2
0
1
1
1
0
2
1
4
1
0
1
0
0
0
0
2
0
2
1
0
0
0
0
1
1
2
2
2
0
0
0
0
1
0
1
2
0
0
1
0
0
0
0
0
1
1
2
2
3
0
0
0
1
0
2
0
0
0
0
2
2
2
0
2
0
1
1
2
1
1
1
2
1
0
0
0
0
2
1
1
1
2
0
1
0
1
0
1
1
1
0
2
0
1
1
2
1
1
1
1
0
2
0
0
1
1
2
1
0
1
1
1
1
0
1
0
1
0
2
1
0
1
0
0
1
0
0
0
0
2
1
0
0
0
1
2
0
0
1
1
2
0
0
1
0
2
2
0
1
0
0
0
0
0
2
2
0
2
0
0
2
0
0
0
0
1
1
0
2
0
2
0
1
0
0
0
0
1
0
2
0
2
0
0
1
2
2
1
0
0
0
0
0
2
1
1
1
2
2
0
2
0
1
0
1
1
0
1
2
5
1
0
0
0
0
1
1
2
0
2
2
0
1
1
0
1
1
1
0
0
0
0
1
0
2
1
2
1
2
1
2
0
0
2
2
1
0
0
1
0
2
0
0
0
2
0
0
1
0
0
1
0
1
2
2
0
0
2
0
2
1
0
2
1
0
0
0
0
1
0
0
0
1
0
1
0
1
1
2
1
0
0
2
0
3
0
0
2
1
2
2
2
1
0
1
1
2
0
1
1
0
1
2
0
2
1
1
1
2
0
0
0
1
1
0
0
0
0
3
2
1
1
0
2
2
1
1
0
0
2
1
2
0
2
0
1
0
0
1
2
2
1
1
1
0
2
0
1
1
1
2
0
1
1
0
1
0
1
0
0
0
1
1
0
1
0
0
2
0
1
0
0
1
1
0
0
2
1
0
1
0
1
1
0
2
1
1
0
1
1
0
1
1
1
0
1
0
0
1
0
0
0
0
1
1
2
0
1
3
0
2
2
0
1
1
1
0
1
2
2
1
1
1
0
0
1
0
2
2
0
0
1
1
1
2
0
1
2
0
1
1
0
0
1
0
0
1
0
1
1
2
0
2
2
0
0
2
1
2
0
2
0
0
0
0
1
0
1
1
1
1
0
1
1
0
4
1
0
1
1
0
0
0
2
1
3
1
1
0
0
2
2
3
0
0
0
0
0
1
0
0
1
0
2
2
0
1
0
1
0
1
0
1
1
1
0
0
0
0
2
1
1
0
2
0
1
2
2
1
3
0
2
0
1
0
0
1
0
0
1
2
0
2
2
0
1
0
0
2
2
2
0
2
0
1
1
2
0
0
3
0
0
1
0
0
0
2
0
0
1
1
2
1
1
2
2
2
2
0
1
0
0
0
0
0
2
1
2
2
1
0
0
1
0
0
0
1
0
1
0
0
1
1
0
1
1
2
1
1
1
2
0
2
1
1
0
1
2
0
1
0
1
1
1
0
0
0
1
1
2
0
2
0
4
1
0
0
2
2
1
0
0
1
1
1
0
0
0
1
1
2
1
0
2
0
1
0
0
1
1
3
0
1
0
2
0
0
1
0
0
0
3
1
0
0
2
0
1
0
0
1
1
1
1
0
1
0
2
2
2
1
1
1
1
2
0
1
2
1
1
2
0
0
1
1
1
1
0
2
1
0
1
2
0
0
0
0
0
0
1
0
0
0
2
1
0
2
0
3
1
2
0
1
1
1
0
2
2
0
0
0
1
1
0
0
1
1
0
0
2
1
0
0
2
1
0
0
1
2
0
1
0
2
0
1
0
0
2
1
1
1
1
3
2
2
0
1
2
0
0
0
1
1
0
1
2
1
2
0
3
2
1
0
1
2
1
0
0
2
0
0
1
2
1
1
2
0
0
1
1
0
0
2
1
0
0
2
2
0
1
1
2
0
0
2
1
2
0
1
0
0
1
2
2
0
2
0
0
0
2
1
1
2
0
0
0
0
1
0
1
2
0
2
1
1
0
0
1
0
2
1
0
0
2
0
1
2
2
1
0
2
1
1
1
0
1
0
0
2
0
1
0
0
0
0
1
1
1
0
0
1
0
2
0
0
2
2
2
1
1
1
1
0
0
1
0
0
1
1
1
2
1
0
2
1
2
0
2
1
0
1
0
1
1
0
1
2
0
0
0
0
0
0
0
2
1
0
0
0
1
1
1
0
0
0
0
0
1
0
0
1
0
0
2
0
1
0
0
1
0
1
4
0
1
1
1
1
1
0
0
0
1
2
0
1
0
1
2
1
0
2
2
2
2
2
0
0
2
1
2
0
0
0
0
0
2
0
2
0
1
1
0
0
0
0
0
0
0
2
0
0
0
1
2
0
1
3
0
2
1
1
0
1
0
0
0
1
2
2
0
2
0
0
1
0
0
1
0
0
1
0
0
1
0
1
0
1
0
0
0
1
0
2
0
2
0
2
2
1
0
0
0
2
0
2
0
0
1
2
0
2
8
0
1
1
1
1
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
1
2
0
1
0
3
1
1
2
0
1
0
3
0
2
2
0
1
1
2
0
1
0
0
0
0
2
1
3
2
1
0
1
1
1
0
2
2
0
2
2
0
1
2
2
0
2
1
1
0
2
1
1
1
1
1
1
3
0
0
0
1
1
0
2
2
0
0
0
0
0
1
2
0
2
2
0
2
3
0
2
2
0
1
1
1
0
1
0
2
2
0
1
0
2
0
2
0
0
1
1
2
0
2
1
1
0
1
0
0
1
0
2
1
1
0
2
1
1
0
0
0
1
0
2
1
2
0
2
1
1
1
0
1
2
2
1
2
1
1
1
1
0
0
2
2
2
1
0
0
0
0
0
2
0
0
1
0
0
1
0
1
1
1
2
0
3
2
0
0
1
2
0
1
0
0
2
1
1
0
0
1
1
0
1
1
1
0
0
2
2
1
1
2
0
2
2
1
3
2
2
1
0
0
0
1
1
2
0
2
2
0
0
1
0
1
1
0
1
0
1
0
0
0
2
0
1
3
0
4
2
0
0
0
2
0
0
0
0
0
2
0
1
0
1
2
0
0
2
5
1
0
0
0
0
0
1
2
1
0
0
1
0
2
1
3
1
1
0
0
1
0
0
0
1
1
0
1
0
1
0
1
1
0
2
0
1
2
1
2
2
1
1
1
1
0
0
1
1
2
1
3
1
2
1
0
0
0
1
0
0
0
1
0
1
0
0
0
2
0
0
1
1
1
1
1
0
2
0
1
0
2
1
0
0
0
2
1
0
0
0
1
1
0
1
2
1
1
0
2
2
1
0
1
1
2
0
2
0
0
0
1
0
2
1
2
1
1
0
0
1
2
1
0
0
0
2
1
2
1
0
1
0
0
1
0
0
1
0
0
0
0
1
1
2
2
2
1
2
0
0
2
2
0
0
1
1
1
0
0
1
1
0
1
1
0
0
2
1
2
0
2
2
1
1
0
1
1
1
0
1
0
0
2
1
0
1
0
0
1
1
1
1
1
2
2
0
0
2
1
0
0
1
0
2
0
2
1
0
3
0
1
2
0
1
0
0
1
0
0
0
0
0
2
1
0
2
0
3
0
1
0
2
0
2
0
2
1
1
0
2
0
0
0
1
0
2
2
0
0
0
0
1
1
0
1
0
0
0
0
0
1
1
0
1
1
1
2
0
1
0
1
0
1
2
0
1
0
1
0
0
1
2
2
1
0
0
0
0
1
2
1
0
0
0
0
0
1
2
1
2
1
1
0
0
0
0
2
1
0
0
1
0
1
0
0
0
2
0
0
0
1
2
1
1
1
1
0
1
2
1
1
0
0
3
2
0
0
1
0
2
3
1
0
2
0
1
0
3
0
0
2
3
0
1
1
2
0
1
0
1
2
0
1
0
1
2
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
1
0
0
1
0
1
1
2
0
2
1
1
2
0
0
0
2
1
2
2
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
1
0
1
0
0
0
1
2
1
0
0
0
1
2
0
1
1
0
0
2
0
1
0
1
0
2
2
0
0
0
1
1
2
2
5
2
0
0
0
0
0
2
1
0
1
1
0
0
2
1
0
0
1
1
0
2
2
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
2
0
1
0
1
2
0
2
0
1
0
0
1
2
1
2
0
1
0
0
2
1
0
2
0
0
0
0
2
2
2
2
0
0
2
0
0
0
0
2
0
0
0
2
2
2
2
2
1
1
1
2
0
2
0
0
2
1
1
2
0
1
1
2
1
2
0
0
0
0
0
1
2
1
2
0
1
1
2
1
3
0
0
1
0
2
2
0
0
0
0
3
0
1
0
0
2
2
2
0
1
0
1
0
0
0
1
2
2
2
0
0
1
1
1
0
1
0
1
0
1
0
2
0
1
2
0
1
1
2
2
0
1
2
0
1
1
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
1
0
2
0
2
0
0
2
0
1
1
0
0
1
1
0
0
0
0
1
2
0
1
0
0
0
0
0
0
2
0
2
0
0
1
2
1
0
2
2
1
0
0
2
1
0
1
2
0
0
0
0
0
1
2
1
1
0
0
1
0
1
2
2
4
2
2
0
2
1
2
0
1
2
2
0
1
2
1
1
3
2
1
0
0
0
2
1
0
2
1
2
1
2
0
0
0
0
0
0
1
0
0
0
0
1
1
1
2
1
1
0
1
1
1
1
1
0
0
0
0
0
0
2
1
0
0
2
0
0
0
1
0
1
1
1
2
0
0
0
0
1
0
0
0
2
1
0
0
0
1
1
0
0
2
1
0
0
0
0
0
1
1
1
1
0
1
0
0
1
0
1
1
1
1
0
1
1
0
1
3
1
0
0
2
0
0
1
0
0
0
1
0
0
3
1
0
0
0
2
0
1
1
0
0
1
2
1
1
1
2
0
1
2
1
0
0
0
3
0
2
0
1
0
0
0
0
0
1
1
1
2
0
1
1
1
1
0
1
0
0
2
2
1
1
0
0
1
0
1
2
1
0
1
0
1
1
2
2
2
1
0
0
0
0
0
0
0
0
1
1
1
0
0
2
1
1
0
0
0
2
0
2
0
1
0
0
0
1
1
2
0
0
1
2
0
0
2
0
1
0
2
1
0
1
0
1
2
0
2
0
1
0
0
1
0
0
0
1
0
1
0
1
2
2
0
1
0
2
0
1
1
1
2
1
1
2
0
1
1
0
1
1
1
0
1
0
0
1
1
0
1
1
1
0
0
2
0
1
2
0
0
0
0
1
0
1
1
2
1
1
0
0
0
1
2
0
2
1
1
1
0
1
2
0
0
0
0
1
1
0
2
1
0
2
0
0
1
1
0
2
1
0
2
0
0
0
2
0
2
1
1
1
0
0
0
1
0
1
1
0
1
0
0
1
2
0
1
1
2
0
0
0
0
0
1
0
0
0
2
0
0
1
0
1
0
2
3
0
0
0
2
0
2
1
0
2
0
0
2
0
0
0
0
1
0
1
1
0
1
0
2
2
2
1
0
1
0
1
1
2
0
0
1
0
0
2
1
1
1
0
2
0
2
0
2
1
0
2
1
1
2
1
2
2
2
2
0
1
0
0
0
1
0
1
1
2
1
0
1
0
0
0
1
0
0
0
1
1
1
0
1
1
0
0
0
1
0
0
1
2
1
0
1
1
0
1
2
1
0
3
2
1
2
1
0
2
2
1
1
0
0
2
0
2
0
1
1
0
0
0
1
0
2
1
0
0
0
1
2
1
0
2
2
0
0
0
1
2
1
1
0
0
1
2
0
0
1
1
0
1
2
0
1
2
0
0
2
1
2
0
1
0
1
1
0
0
0
0
1
1
1
0
0
2
2
2
1
2
2
1
1
2
2
1
0
2
3
0
1
1
1
0
0
0
2
0
1
0
0
1
1
2
2
1
1
0
1
0
0
0
0
1
2
1
0
0
1
0
2
1
1
2
1
2
0
0
0
0
0
0
1
1
1
2
0
2
2
0
0
2
0
0
2
1
2
0
0
0
2
1
1
0
0
1
0
2
1
1
0
1
1
2
0
2
0
0
1
2
2
1
2
0
0
0
0
1
0
1
0
0
0
0
0
2
1
0
2
2
1
0
1
0
2
1
2
1
2
0
2
1
0
0
2
2
2
1
0
0
0
2
0
0
0
1
1
2
0
2
0
1
1
0
2
2
0
1
0
0
1
2
2
0
0
2
1
2
2
0
0
1
1
1
0
0
2
1
2
1
0
0
1
1
0
0
4
0
0
3
1
1
2
1
2
1
1
0
0
1
3
0
0
1
1
0
0
3
1
1
0
0
0
0
0
0
2
0
1
0
0
2
1
2
1
1
2
0
0
0
0
2
0
0
0
1
1
0
0
1
0
2
1
0
0
1
0
1
2
0
0
3
2
1
0
0
1
1
1
0
0
1
0
1
1
1
0
0
1
2
0
0
1
2
2
1
3
2
2
2
1
2
2
1
0
3
1
0
1
0
0
0
0
0
1
0
0
0
1
1
2
0
2
1
1
2
2
0
0
2
2
0
0
0
1
1
2
1
0
0
2
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
1
1
0
0
2
0
0
2
0
0
1
1
1
0
1
0
0
2
1
0
0
0
1
1
0
0
2
1
0
1
0
0
1
1
0
0
0
2
3
1
2
2
1
1
0
1
1
2
1
0
0
1
0
1
3
2
3
0
0
0
0
1
1
0
1
1
0
2
0
0
0
0
1
0
1
2
0
1
0
2
0
2
1
0
0
0
1
2
0
2
0
0
0
2
2
0
2
1
0
0
2
0
1
1
0
2
1
0
2
0
1
1
0
0
2
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
1
1
0
0
0
2
2
2
2
2
0
0
0
1
1
0
2
0
0
0
1
0
0
1
1
2
1
0
1
3
1
1
0
0
0
0
0
0
0
1
1
2
0
0
0
0
2
0
1
0
0
1
0
1
1
0
0
1
0
1
2
0
1
2
0
0
0
2
2
0
2
0
1
0
1
0
0
0
1
1
0
2
0
0
1
2
0
0
0
2
0
2
0
1
1
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
2
0
0
1
1
0
1
0
1
0
1
0
1
1
0
0
2
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
1
3
0
0
0
0
1
1
1
0
1
2
1
2
1
2
1
0
1
0
1
0
2
2
0
6
0
0
0
0
2
1
1
0
1
3
2
0
0
0
0
0
1
1
0
1
2
1
1
2
0
0
1
0
1
0
1
0
0
0
1
2
1
2
0
2
1
0
2
1
0
0
0
0
1
1
2
0
2
1
0
3
1
1
0
0
0
2
0
0
0
1
1
0
2
0
1
1
0
0
0
0
0
0
0
1
1
3
2
2
2
1
1
1
0
1
2
0
2
1
1
0
2
2
2
1
0
0
1
1
1
1
2
0
1
0
1
0
1
1
0
0
2
0
1
2
1
2
2
0
1
2
2
0
2
0
0
2
2
1
1
2
0
0
0
0
0
2
3
1
1
0
1
2
1
0
1
2
1
0
2
0
1
1
0
1
0
0
0
1
0
0
0
1
2
1
1
1
0
1
0
0
2
2
1
3
0
2
2
2
1
0
1
0
0
0
1
1
0
0
0
0
1
0
2
1
0
0
1
1
1
0
0
1
0
1
0
1
1
0
2
2
1
2
1
0
0
2
0
0
2
1
0
0
0
1
0
0
0
0
3
2
1
0
1
4
0
0
0
1
0
1
0
1
1
2
0
1
0
0
1
1
2
0
0
1
1
0
1
0
0
1
2
1
0
0
2
0
0
0
0
0
1
2
2
0
1
0
0
0
1
1
0
0
0
2
1
0
3
0
2
2
0
0
2
2
1
2
0
0
2
0
1
1
0
0
2
0
0
0
0
1
1
0
1
2
0
4
1
0
1
0
0
1
0
0
1
0
0
0
1
2
0
2
1
1
0
2
0
0
0
1
2
0
0
1
1
0
0
0
2
1
0
1
1
0
0
2
0
2
1
2
0
0
0
0
0
0
1
1
0
2
2
1
0
0
3
1
1
0
0
1
1
1
2
1
0
2
0
2
1
1
2
0
0
1
0
1
0
1
0
1
0
1
3
2
2
3
1
1
1
1
2
1
2
1
1
0
0
0
1
0
1
1
1
0
1
0
0
0
1
1
1
0
1
2
0
0
0
0
0
1
1
1
1
1
1
0
0
2
1
0
0
0
1
0
1
0
2
0
1
0
0
2
1
2
1
0
1
1
2
0
2
2
0
1
1
2
1
1
2
2
0
0
0
2
1
1
1
0
0
2
0
1
1
2
1
0
1
0
0
1
0
1
1
0
0
1
2
0
0
1
0
0
1
0
1
0
2
0
0
2
2
1
0
1
2
0
2
2
1
0
0
2
0
3
4
0
2
2
0
0
2
2
0
2
0
2
4
0
1
0
1
0
2
1
0
0
0
2
0
1
2
2
2
1
0
2
2
0
2
0
0
1
1
0
1
0
1
0
1
1
2
0
0
0
0
0
0
2
0
2
0
1
0
0
0
2
0
0
1
0
1
2
1
1
1
1
1
0
0
1
1
0
1
1
1
0
0
2
2
0
1
0
2
0
0
2
0
2
2
0
2
2
0
1
1
2
1
0
0
2
0
0
2
1
1
2
0
0
0
2
0
0
2
2
1
0
1
1
0
1
0
1
0
0
0
0
2
2
1
2
1
0
2
2
2
3
1
0
1
1
2
0
1
0
0
0
1
1
1
0
1
1
1
1
0
1
1
2
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
1
2
0
0
1
0
0
2
0
0
0
0
1
1
2
2
2
2
2
0
2
1
1
0
0
1
1
1
1
0
1
0
1
1
0
0
2
1
1
0
2
0
0
0
0
1
2
0
0
0
1
0
0
2
1
2
3
0
1
0
0
0
2
0
0
1
1
0
1
1
0
0
0
0
1
0
2
0
1
1
0
1
0
1
1
1
2
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
8
1
3
0
2
0
0
0
0
1
0
2
2
1
2
1
0
1
1
0
0
2
0
2
1
0
2
1
0
1
1
1
0
1
0
0
0
0
2
1
0
1
1
1
2
2
1
0
3
0
1
1
0
1
0
1
0
1
1
1
1
3
1
2
1
2
2
0
1
1
0
0
1
0
0
0
0
0
1
1
1
0
0
1
1
1
2
1
0
0
0
0
0
1
0
0
0
1
2
2
0
0
0
1
1
1
0
1
2
1
0
0
0
0
0
0
2
1
2
1
2
0
0
2
1
1
0
0
2
0
0
1
0
0
0
1
1
0
1
0
0
0
0
1
1
2
0
1
0
1
1
1
1
2
1
0
1
0
0
1
1
3
2
1
0
2
0
2
2
1
1
1
1
1
0
1
0
2
0
1
0
0
2
1
2
0
1
1
0
0
2
0
1
3
2
0
0
0
1
1
0
0
0
2
1
0
1
1
1
2
1
1
0
1
1
1
0
1
0
2
1
0
0
2
1
2
0
1
0
2
1
1
0
0
1
0
0
0
0
1
0
1
2
0
0
0
0
1
0
1
0
0
2
1
1
1
1
1
0
1
0
0
0
1
0
0
0
2
1
0
0
2
1
1
2
0
0
0
2
0
0
0
0
0
0
2
0
2
1
1
1
0
0
0
0
1
0
0
0
1
2
0
0
1
1
0
0
1
1
1
1
1
1
2
1
1
0
1
1
1
1
1
1
1
1
2
2
1
1
1
2
0
1
2
0
1
0
0
0
1
0
0
0
2
0
0
1
0
1
0
0
2
2
0
1
0
0
0
2
1
1
1
1
0
0
0
1
1
0
0
0
1
1
1
1
0
2
1
1
0
0
0
2
2
0
0
1
1
0
2
1
1
3
2
1
1
2
1
0
2
0
1
0
1
1
2
0
1
0
0
0
1
0
3
0
1
0
1
2
2
2
0
0
2
0
0
3
1
0
2
1
2
0
2
0
1
1
0
2
2
0
1
1
1
1
0
0
0
1
0
1
1
0
0
0
0
2
0
1
2
0
1
0
0
0
0
1
1
0
0
0
2
0
1
2
3
0
0
1
1
0
2
1
1
1
2
1
0
0
1
1
1
1
2
1
1
0
0
1
2
2
0
1
2
0
1
0
3
1
1
0
0
2
0
0
0
0
1
1
1
0
0
0
2
1
2
1
0
1
0
1
0
0
2
3
0
1
0
1
0
0
0
1
1
1
0
0
2
2
0
0
1
1
1
2
2
2
2
1
0
0
1
0
1
0
1
1
0
0
2
1
0
0
2
0
1
1
0
1
1
0
2
1
1
0
1
1
1
0
1
2
0
1
3
1
2
1
0
1
1
1
1
0
1
1
8
2
0
0
0
1
0
3
1
2
0
2
1
0
1
0
0
0
1
1
1
2
1
2
0
1
1
2
2
0
2
1
0
2
1
1
1
1
0
0
0
0
0
2
3
2
1
0
0
0
1
2
1
0
0
0
0
1
2
2
0
0
0
0
1
2
1
0
1
2
1
1
0
0
1
1
2
1
1
2
1
0
0
0
0
2
0
0
1
0
1
0
2
0
1
0
1
1
0
2
1
0
2
0
0
0
0
0
1
0
2
1
0
0
0
2
2
0
1
0
0
1
1
1
0
0
1
0
0
1
1
1
2
0
0
1
0
2
0
0
1
1
0
0
0
1
2
0
0
0
0
1
1
0
2
0
0
0
2
1
0
2
1
2
1
0
1
1
1
1
1
0
2
1
2
2
1
0
2
0
0
0
0
0
0
0
0
2
1
3
2
2
2
0
2
0
0
2
0
3
0
1
1
2
0
0
1
1
1
0
0
0
1
0
0
0
0
0
2
1
2
0
2
2
0
1
1
0
1
1
1
1
0
0
0
0
3
0
2
2
1
2
0
0
1
0
1
0
0
0
0
0
2
1
0
1
1
1
0
0
1
2
3
0
2
0
1
0
0
1
0
1
1
1
0
1
1
1
1
2
2
2
1
0
2
0
2
1
2
1
0
0
0
1
0
1
0
2
2
0
0
0
1
0
0
2
0
2
1
2
0
1
0
0
1
2
1
0
0
1
0
0
0
0
1
2
1
0
2
0
1
0
1
0
0
2
0
0
1
0
1
0
0
2
2
0
1
1
1
1
2
2
0
0
0
0
0
0
0
2
0
1
1
0
0
1
0
0
2
2
3
0
1
0
1
0
1
2
1
2
1
1
0
0
0
1
0
0
0
0
1
2
0
1
1
1
0
0
2
2
1
1
0
0
0
1
1
0
0
0
0
3
0
0
2
0
1
0
1
0
1
2
0
0
0
2
0
1
2
1
2
1
0
0
1
0
0
1
1
0
0
0
1
1
2
1
1
0
2
2
1
1
2
2
0
1
1
2
2
0
2
0
0
0
1
0
2
1
1
0
0
0
0
0
0
2
0
2
0
2
2
0
0
0
2
0
0
1
0
0
0
0
2
2
1
1
1
1
2
0
0
0
1
0
1
0
1
1
0
1
0
0
0
0
1
0
2
0
1
1
0
0
2
2
0
0
1
0
2
1
0
0
0
0
2
0
1
0
0
1
2
0
0
1
2
1
0
0
0
1
2
0
0
0
0
0
0
0
1
1
1
1
1
0
1
0
2
2
2
0
1
4
0
0
1
1
0
0
1
0
2
0
0
1
3
0
1
1
1
1
0
0
1
0
0
1
0
1
2
0
0
0
2
2
1
1
0
2
0
2
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
2
0
0
1
1
0
0
0
1
1
1
1
1
0
0
1
0
2
3
1
0
0
1
0
1
1
1
2
0
1
0
1
1
2
1
1
1
2
2
0
0
1
0
2
1
2
0
1
0
2
2
2
1
1
1
2
1
1
1
0
0
0
1
2
0
0
1
1
2
0
0
1
0
0
1
0
0
1
2
1
1
2
1
0
0
1
1
1
0
3
2
1
1
1
2
1
2
2
2
1
2
0
1
1
0
2
1
0
0
0
0
1
0
1
0
0
0
1
0
0
5
1
0
0
1
0
1
1
1
2
1
0
0
1
1
0
1
1
1
1
0
1
0
0
0
2
0
0
0
0
0
3
0
2
2
2
0
1
2
0
0
1
1
0
0
2
2
1
0
2
0
1
0
0
1
1
1
1
2
0
1
0
0
0
2
2
2
0
1
1
1
0
2
2
0
0
1
0
0
1
1
0
1
2
2
2
0
0
1
0
0
1
1
0
0
1
0
0
1
0
2
0
0
1
2
1
0
1
1
0
1
1
0
1
1
0
0
0
1
0
1
1
0
0
2
0
2
2
0
0
1
1
1
1
2
0
0
1
2
1
0
1
1
1
0
0
0
0
1
0
0
1
2
1
1
2
0
1
4
1
0
0
1
1
1
2
1
0
2
0
0
0
1
1
2
0
1
2
1
2
2
0
0
2
1
1
3
0
2
2
1
0
0
1
0
0
1
0
2
2
0
0
1
0
0
1
2
1
1
2
0
2
1
0
1
2
2
2
2
0
1
0
2
0
2
0
0
2
1
0
0
2
2
0
0
1
2
0
0
0
0
0
2
0
0
0
0
2
1
0
1
0
1
2
0
1
2
0
1
1
0
0
0
0
2
1
2
1
1
1
0
1
4
0
1
2
0
0
1
0
1
0
0
1
0
1
0
1
0
0
1
0
1
0
2
2
0
1
0
1
0
2
1
2
1
2
1
0
1
1
0
1
1
0
1
2
2
1
0
1
2
0
0
3
1
1
1
2
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
1
1
3
1
0
1
1
1
0
0
1
3
1
0
2
0
0
2
1
0
0
1
0
1
0
0
1
0
0
2
2
2
2
1
1
0
0
2
4
0
2
1
1
1
1
1
2
0
1
0
0
0
2
1
0
1
2
1
2
3
1
0
0
1
0
0
1
0
0
4
2
0
0
0
0
0
0
1
0
0
2
0
1
1
0
0
1
1
2
1
0
0
0
0
0
0
2
1
1
1
0
2
1
1
2
2
2
2
1
1
0
1
0
3
0
0
2
0
2
1
0
2
0
1
2
0
2
3
1
0
1
0
1
1
2
0
1
1
0
2
2
1
1
2
0
0
1
1
0
1
0
0
0
1
1
2
1
0
0
1
0
2
0
0
0
2
2
1
1
2
0
1
2
0
2
1
2
0
1
0
0
2
0
0
0
0
0
3
2
1
0
0
0
2
2
1
0
2
0
0
2
2
0
1
0
0
2
0
1
1
0
0
2
1
1
0
0
0
1
0
1
0
1
3
1
2
0
2
0
0
0
3
1
2
0
0
0
0
0
0
0
1
2
0
1
0
0
2
1
0
1
0
2
0
2
0
0
1
2
1
0
0
1
10
2
2
2
1
1
0
2
2
1
2
1
0
0
1
0
1
0
1
0
0
0
2
1
1
2
2
2
0
1
2
1
2
0
1
0
1
0
1
1
0
1
2
0
2
1
0
0
1
0
1
1
0
0
0
1
2
1
2
0
1
0
3
1
2
1
1
2
0
1
0
0
0
2
0
0
1
1
0
0
1
2
0
1
1
1
0
0
1
1
0
1
2
1
1
2
1
0
2
1
0
0
0
0
1
0
1
2
0
1
1
0
0
0
0
1
1
0
0
0
1
0
1
2
2
0
0
1
1
1
0
0
5
1
0
1
1
1
0
0
1
1
0
0
2
0
0
1
2
0
0
0
0
1
1
2
1
0
0
1
1
1
0
0
1
2
1
1
2
2
2
2
1
0
0
0
0
1
1
1
1
1
0
1
0
0
0
0
1
0
0
0
1
0
2
2
2
1
1
1
0
2
0
2
0
1
0
0
0
0
1
2
0
2
1
2
0
0
2
0
1
1
2
1
1
1
1
0
0
0
0
2
1
3
0
0
0
2
0
2
2
0
0
2
1
1
0
0
0
1
2
2
0
0
0
1
0
0
1
0
1
1
2
1
2
1
1
0
1
1
2
1
2
2
0
1
1
1
0
1
2
1
3
2
1
0
1
0
1
0
0
1
0
3
2
2
0
2
0
1
2
2
0
1
0
1
0
0
2
1
1
0
0
2
0
2
2
0
1
0
2
0
2
3
1
1
0
0
0
1
2
0
1
2
1
2
1
0
2
2
2
1
0
1
2
1
0
0
0
0
0
1
0
2
0
1
0
1
1
0
1
1
2
0
1
1
1
0
0
0
1
2
2
0
1
0
1
1
1
4
1
0
0
2
0
2
0
0
2
1
0
5
1
0
1
0
2
2
1
1
1
0
2
1
0
1
0
0
0
2
2
3
0
0
1
2
1
2
2
2
2
2
2
1
0
1
2
0
2
0
1
1
1
1
1
2
0
1
0
1
0
1
1
0
0
0
2
2
0
1
0
1
1
0
0
1
1
0
3
0
1
1
2
0
1
1
1
0
1
1
1
0
0
1
1
2
1
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
1
2
1
2
2
0
0
1
1
2
2
1
2
1
0
0
1
0
1
2
1
1
1
1
1
2
2
1
0
2
0
1
0
1
1
0
2
0
2
2
0
2
0
0
0
0
0
1
1
1
0
0
0
0
2
4
0
1
2
1
2
0
2
1
0
2
0
0
0
1
1
0
1
1
0
1
0
1
1
0
0
0
0
1
1
2
0
1
0
1
0
2
1
1
2
3
1
0
1
0
1
1
0
0
2
0
2
0
1
1
0
0
2
1
1
2
1
0
0
2
1
2
1
2
1
1
2
1
0
0
0
1
0
1
1
2
0
0
1
0
2
0
0
1
0
1
1
0
2
0
0
2
1
2
1
0
1
1
0
4
0
2
1
1
1
1
1
0
1
1
1
4
0
1
0
1
0
0
1
0
0
0
0
1
3
1
0
2
2
1
3
0
1
0
2
1
1
0
1
1
0
0
0
0
0
1
2
1
1
0
0
0
0
0
2
1
1
1
0
2
1
0
0
0
2
2
2
1
1
0
0
2
1
1
0
2
2
2
1
2
1
0
1
1
0
1
4
1
0
2
2
1
1
2
0
2
2
2
1
0
1
0
2
0
1
0
1
0
0
0
2
0
2
1
0
1
0
0
0
2
1
2
3
3
2
1
0
0
0
1
2
0
2
0
2
1
1
1
0
1
0
2
0
1
0
0
1
1
0
1
2
1
2
1
1
2
0
1
2
0
2
1
1
0
1
1
0
0
1
0
0
0
0
1
0
0
1
0
0
2
0
2
0
2
1
2
1
1
2
0
1
2
1
1
0
1
1
0
0
1
0
2
1
2
2
2
1
0
0
2
2
0
1
1
0
0
2
1
1
0
1
2
0
1
2
0
0
1
3
0
0
0
2
0
0
1
0
1
0
1
1
0
0
1
3
0
1
0
2
0
1
0
1
1
0
0
1
2
1
0
1
0
1
2
0
0
2
1
1
2
0
0
1
2
1
1
0
0
3
0
0
2
1
1
0
0
0
0
1
1
3
1
2
0
2
0
2
1
1
2
2
2
1
1
1
2
0
0
1
2
0
3
2
2
1
2
0
1
0
0
1
2
0
1
0
1
1
2
0
1
1
0
0
0
0
0
1
0
1
2
2
2
1
0
1
1
1
0
0
0
0
2
1
0
0
2
1
0
2
2
1
1
2
0
1
1
1
1
1
2
1
0
1
0
2
2
0
2
0
2
0
0
2
1
0
2
0
0
1
0
1
2
0
2
2
0
2
3
0
2
0
0
0
1
0
0
0
0
0
2
0
0
1
1
1
0
2
0
1
0
1
1
0
1
1
1
0
0
0
1
1
0
0
0
1
0
1
0
1
0
1
2
0
2
0
0
1
0
0
1
0
1
1
1
2
0
0
1
2
1
2
0
1
0
0
0
0
0
0
0
0
2
1
0
4
2
1
2
0
0
0
0
1
2
1
1
0
1
0
0
0
2
0
0
0
0
0
0
1
0
2
1
2
2
0
1
2
2
0
2
2
0
0
0
0
1
0
0
1
0
0
2
1
0
1
2
0
0
2
1
1
0
1
1
1
1
0
0
1
1
0
1
1
0
0
1
1
0
2
0
1
0
2
1
1
2
2
1
2
2
0
2
1
0
0
0
0
1
0
3
1
1
1
1
1
0
2
2
0
2
2
2
1
0
2
2
1
0
1
1
0
0
1
1
2
1
0
0
0
2
0
2
0
1
1
0
2
0
2
2
0
0
2
1
1
0
0
0
2
1
2
1
0
0
0
0
1
1
0
2
1
1
2
1
0
0
0
2
1
0
1
0
2
2
1
1
2
0
2
0
2
0
0
0
0
0
2
1
1
1
3
0
1
1
1
2
1
0
2
1
1
1
0
1
3
1
1
1
1
0
0
1
1
1
0
1
0
0
1
0
0
0
1
4
0
0
0
1
1
0
1
2
0
2
1
1
0
1
1
2
1
0
0
1
2
2
0
2
0
1
1
0
2
0
2
0
0
0
1
1
1
0
2
0
0
0
1
1
2
1
0
1
1
2
1
0
0
0
1
1
0
0
1
2
1
1
1
0
0
1
0
1
1
1
1
0
2
0
1
1
1
0
0
2
1
1
1
0
1
1
0
2
1
0
1
2
0
3
1
2
2
0
1
2
0
0
2
2
2
0
0
0
0
6
1
0
2
0
2
0
2
1
0
1
1
1
2
1
0
0
0
2
1
1
0
0
1
0
1
2
2
1
0
2
1
0
0
0
2
0
1
0
0
2
0
1
0
2
2
2
4
0
2
2
0
0
0
0
0
0
0
1
0
1
1
1
1
0
1
0
2
0
1
0
1
3
0
0
1
1
0
0
1
1
1
1
1
0
1
0
1
1
2
1
0
0
0
0
1
2
0
1
1
1
1
0
1
2
1
2
1
0
0
0
2
2
0
0
1
1
2
0
2
0
2
0
0
0
1
0
0
0
0
2
1
2
2
1
0
2
1
0
0
1
1
0
0
1
0
0
1
1
1
1
0
2
0
0
0
1
2
0
0
1
0
1
0
2
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
1
0
1
1
0
3
1
1
2
1
0
1
0
0
2
0
1
0
0
1
1
0
2
0
2
0
1
0
2
1
2
0
1
1
1
0
2
0
0
2
2
1
0
1
2
0
0
1
0
0
2
1
0
1
2
3
1
2
1
1
1
0
0
1
2
2
0
1
0
0
1
0
2
2
0
1
0
1
3
2
0
1
0
1
0
3
1
2
1
0
0
0
1
0
2
0
2
1
0
0
0
0
2
1
0
1
0
0
1
1
2
1
0
0
1
1
1
0
0
0
3
0
2
0
0
1
1
1
0
0
0
3
3
0
0
0
0
0
6
0
1
1
1
2
2
0
1
1
0
0
0
0
2
1
2
1
0
0
1
0
1
1
0
0
2
0
1
2
0
0
0
1
1
0
0
0
0
0
2
0
1
0
0
1
1
0
0
0
1
0
1
2
2
2
1
1
0
0
1
1
2
1
0
0
1
1
1
0
0
1
1
1
0
0
1
1
2
2
0
2
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
2
1
1
2
1
1
0
2
2
0
2
0
1
1
2
2
0
0
0
0
0
0
0
2
1
0
1
0
2
1
2
0
1
0
0
1
0
0
0
0
0
1
0
0
4
1
2
0
2
0
0
1
0
1
0
2
1
2
0
2
1
0
0
2
0
0
3
1
0
1
0
1
2
1
1
1
3
0
1
1
1
0
1
0
0
2
3
0
2
0
1
0
3
0
0
0
2
1
1
1
1
0
0
0
2
0
1
0
1
1
0
1
1
0
2
0
0
0
0
0
1
0
1
0
0
2
0
0
2
0
0
1
2
3
1
1
1
1
1
3
1
1
0
1
2
0
2
1
0
1
0
2
1
1
1
1
0
0
0
0
1
1
0
1
1
0
2
0
2
0
2
0
0
1
0
2
2
1
7
0
1
2
1
0
0
0
1
1
0
0
1
0
0
1
0
0
1
1
0
1
1
0
1
1
2
0
1
1
1
1
2
0
1
0
0
1
0
0
0
0
0
0
0
2
2
0
0
2
0
1
2
1
1
2
1
1
1
0
0
0
2
0
2
1
0
0
1
2
1
1
0
0
2
2
0
1
2
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
1
0
1
1
0
1
0
1
1
2
1
0
0
1
2
1
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
1
0
0
2
0
1
2
1
0
1
0
1
1
0
0
0
0
0
0
2
2
1
1
0
0
0
0
1
1
1
0
1
9
1
0
1
0
0
1
2
2
1
0
0
1
0
0
1
0
1
0
1
3
1
0
2
1
0
0
2
0
0
2
1
0
3
1
0
2
1
1
1
1
0
0
0
3
1
2
1
0
3
0
0
1
0
2
0
0
0
1
2
2
0
2
1
0
1
0
2
0
0
0
0
0
2
0
1
1
0
0
2
0
0
1
2
0
0
1
0
3
2
2
2
0
0
1
0
2
0
0
1
1
0
1
1
1
1
2
2
2
0
2
0
1
1
1
0
1
0
1
2
0
1
2
2
0
1
1
1
1
1
1
2
0
0
0
0
0
1
1
2
1
0
1
2
0
0
1
0
0
1
1
2
0
3
0
1
2
2
0
0
1
0
0
1
1
0
1
1
0
1
2
1
0
1
1
1
0
0
2
0
0
0
0
0
1
0
0
2
2
1
1
0
1
2
1
1
0
2
1
1
0
2
0
0
0
0
1
1
0
2
0
1
0
1
1
2
0
0
1
0
0
0
0
0
0
1
1
1
1
1
1
2
0
1
0
0
0
0
2
1
1
0
1
1
0
0
3
0
0
2
2
0
1
1
1
0
2
2
1
1
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
2
0
0
0
2
0
0
0
1
0
0
2
3
0
2
0
1
0
0
1
2
1
2
0
0
2
0
0
0
1
0
2
1
1
1
2
0
1
1
0
2
1
1
2
1
0
0
2
0
0
0
1
1
0
2
0
1
0
2
0
0
0
0
1
0
2
1
1
0
1
0
1
1
0
1
2
2
2
1
1
1
1
1
0
0
1
1
1
0
1
2
0
0
0
0
1
1
0
2
1
1
2
1
0
0
0
0
1
2
0
0
1
2
0
1
2
1
1
1
0
3
0
1
1
2
0
0
1
1
0
1
2
1
0
1
0
0
1
2
1
0
1
1
1
0
1
0
0
2
0
0
1
0
0
0
2
1
0
1
0
2
0
0
0
1
1
0
2
2
0
0
2
2
1
1
0
0
2
0
0
0
1
0
0
0
0
2
2
0
1
2
1
1
1
2
0
1
1
2
2
0
1
0
0
0
2
0
0
2
2
1
2
0
0
0
0
0
2
0
1
0
0
1
1
0
1
0
0
0
1
0
1
0
0
1
1
0
1
0
0
1
1
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
1
1
2
0
1
0
0
2
2
1
1
0
2
1
2
0
1
0
0
1
0
0
1
1
1
1
0
1
1
2
2
1
2
0
1
1
1
1
0
1
0
0
1
1
1
1
2
3
0
2
0
1
0
2
0
0
0
0
0
1
0
1
0
0
0
2
1
2
0
0
0
1
0
1
0
1
2
2
0
1
0
1
0
1
3
0
1
2
0
1
1
2
0
2
0
1
0
0
2
0
1
0
3
1
0
0
1
2
0
1
1
0
0
3
0
0
0
2
1
2
0
1
0
2
0
1
0
2
1
2
0
2
1
0
2
0
0
0
0
1
0
3
0
2
0
0
2
1
1
1
2
1
0
2
1
0
1
1
0
0
0
1
1
7
1
0
0
1
2
0
0
0
1
1
2
0
0
0
0
0
2
1
0
0
1
0
2
0
0
0
2
0
1
1
1
1
1
0
1
2
1
0
0
0
1
1
2
2
0
2
0
1
2
1
0
0
1
0
0
0
3
1
0
0
2
0
0
3
1
0
1
1
2
0
1
1
1
1
2
1
0
0
2
1
1
1
0
2
0
1
0
1
1
2
2
0
1
1
0
0
1
0
0
2
1
0
0
1
1
0
0
2
0
0
2
1
1
0
1
2
1
0
0
0
1
1
0
2
1
1
1
0
1
0
0
0
0
1
1
2
0
0
0
3
0
0
0
2
0
2
1
0
0
1
0
0
0
1
0
2
0
4
1
0
0
1
0
0
1
0
0
0
0
1
1
1
1
0
1
0
1
2
2
0
1
0
0
1
2
0
2
3
0
2
1
0
0
1
1
2
2
1
0
0
1
0
0
0
0
0
2
2
1
0
0
1
0
0
0
1
0
2
3
1
0
2
2
1
0
0
0
2
1
2
0
2
2
1
0
1
2
0
1
1
0
0
2
0
2
1
0
2
1
1
0
0
1
1
2
2
2
0
0
1
1
2
2
2
0
1
0
1
2
0
1
0
1
1
1
1
1
0
0
1
0
0
0
1
1
0
1
0
2
0
2
0
1
2
1
0
2
2
0
0
0
1
0
0
0
0
1
2
0
1
1
1
2
1
1
0
1
1
1
2
0
0
0
2
0
0
2
0
1
2
2
1
0
1
0
1
2
2
2
0
0
2
0
2
2
3
0
2
1
1
0
2
1
1
0
0
0
1
2
0
0
1
1
1
0
1
0
0
1
1
1
0
2
1
2
1
1
1
0
1
0
0
0
1
0
2
0
0
1
2
1
1
0
1
1
1
0
1
1
0
1
1
0
2
0
0
0
0
3
3
0
0
1
1
1
0
1
1
1
0
1
1
1
2
0
2
0
0
2
2
2
0
1
0
1
1
0
2
0
1
0
2
0
1
2
1
2
0
0
0
0
1
0
2
1
0
2
1
0
0
2
0
1
0
1
0
1
0
1
0
0
1
0
1
0
1
2
0
1
1
1
0
0
0
1
0
1
0
1
1
2
1
2
0
1
0
1
2
0
1
3
1
0
0
0
0
0
0
1
1
2
0
0
0
0
0
1
0
1
1
1
2
0
0
4
0
0
0
1
1
1
2
1
0
1
0
1
2
1
1
3
1
1
0
1
1
1
0
1
2
2
1
0
2
1
0
0
1
1
1
1
1
1
1
3
0
2
0
0
1
1
1
0
1
2
1
2
1
0
1
0
0
1
2
3
0
0
0
0
1
1
1
2
0
2
0
1
1
1
0
1
0
1
0
1
0
2
0
2
0
0
1
3
0
0
1
1
0
2
2
0
1
1
0
1
2
0
0
2
2
1
0
0
0
0
1
0
1
1
0
2
0
0
0
2
1
0
1
0
0
2
1
0
1
0
0
0
0
1
0
0
0
1
1
0
0
1
1
1
1
0
1
0
0
1
2
2
0
0
0
0
2
2
2
1
1
1
2
2
1
0
0
0
2
0
0
0
1
2
0
0
0
1
1
2
2
0
2
0
0
0
0
0
0
1
1
1
1
0
0
0
0
1
1
1
0
2
1
0
0
0
0
0
1
1
1
1
0
3
2
2
0
0
0
1
1
1
2
2
0
0
2
0
2
1
1
1
0
0
0
1
0
0
1
0
2
1
1
0
2
2
1
1
1
0
1
0
2
1
0
0
1
0
0
2
1
1
0
1
1
1
0
0
0
2
1
1
1
0
1
0
0
0
1
1
1
1
0
2
0
1
2
0
1
1
2
0
1
1
0
2
1
1
0
1
0
1
0
2
2
0
2
1
2
0
0
1
1
1
1
0
0
3
0
0
0
1
1
0
1
0
2
0
0
0
0
1
2
0
1
0
0
1
2
0
1
2
1
0
2
0
0
1
0
1
0
0
0
1
1
1
0
2
1
2
1
0
0
0
2
2
0
0
0
2
0
1
0
0
0
1
2
2
0
0
2
2
3
1
0
2
1
1
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
2
2
1
2
0
0
0
2
1
1
0
1
1
2
0
0
0
0
0
0
0
0
0
1
0
2
2
1
1
1
0
3
1
0
1
1
2
1
0
2
1
2
0
1
1
2
2
1
1
1
0
2
1
1
1
0
0
1
2
1
1
0
0
0
0
2
0
1
1
0
1
0
1
2
1
1
0
0
0
3
0
0
0
2
0
1
1
0
2
0
2
2
0
2
2
0
1
0
2
0
0
0
1
1
1
0
1
1
2
1
0
2
0
1
1
1
2
0
2
0
1
0
0
1
1
0
0
1
0
1
0
0
0
0
2
0
1
2
0
2
0
0
0
2
2
2
0
1
1
1
0
2
0
2
1
0
1
0
1
0
1
2
0
1
1
2
0
2
0
1
0
1
2
0
1
0
2
1
2
2
0
0
2
1
1
0
0
0
0
0
1
0
1
2
2
1
0
2
0
1
2
2
0
2
1
0
1
0
1
0
0
1
0
3
0
2
2
2
2
1
1
1
2
3
1
0
0
0
0
0
1
0
1
2
1
0
0
2
1
1
1
0
1
1
2
2
1
0
1
1
0
0
1
0
1
0
3
2
0
1
2
0
0
1
0
2
1
2
0
1
2
1
1
0
1
2
1
2
0
0
1
2
0
1
0
0
1
0
1
0
0
0
1
2
0
1
0
0
1
1
0
0
2
1
1
2
1
0
1
0
0
1
1
1
0
1
0
2
0
1
0
1
0
2
1
0
1
1
3
0
0
0
2
0
1
1
2
0
0
0
2
1
0
1
1
0
0
0
2
0
1
2
1
1
2
0
1
2
0
1
0
1
1
1
2
0
1
2
0
1
2
0
1
0
0
0
0
1
0
0
0
1
3
0
2
0
1
1
0
0
1
2
0
2
2
2
0
1
0
0
0
2
3
0
2
1
0
1
1
0
2
0
0
0
0
0
2
3
0
0
2
1
0
1
0
2
0
1
0
1
0
1
0
1
0
1
0
0
0
2
0
2
0
2
2
0
1
0
2
2
2
0
1
0
0
1
1
0
0
1
0
2
1
1
0
1
1
0
0
2
1
0
1
0
0
2
2
1
1
1
0
0
0
2
2
0
0
0
0
2
0
1
0
0
2
1
0
3
0
0
1
1
0
2
1
1
1
2
2
2
2
0
1
1
0
2
1
0
2
2
2
1
0
2
1
1
0
1
2
0
0
1
1
0
0
0
0
0
2
0
1
0
1
0
2
1
0
0
0
1
0
0
1
1
0
0
2
1
1
2
0
2
0
2
0
0
0
2
2
1
1
0
0
2
1
1
1
2
1
0
1
1
0
2
1
1
1
1
1
0
0
1
2
0
1
2
2
0
0
0
0
2
1
2
0
0
0
0
0
0
3
1
1
0
2
2
0
0
0
0
3
1
1
1
2
0
0
0
1
1
0
0
1
2
0
0
0
2
0
2
1
2
0
2
1
1
0
0
0
1
0
0
0
0
0
0
0
1
2
0
1
0
0
2
0
0
1
0
0
0
1
2
1
2
1
1
0
1
0
2
0
0
1
1
1
1
1
1
0
2
2
1
0
0
0
1
1
1
0
0
3
0
0
1
0
2
0
0
2
1
1
1
2
1
0
1
2
0
1
2
2
1
0
1
0
1
0
0
0
0
0
1
0
2
2
1
1
0
1
2
1
0
1
0
0
1
2
1
1
1
1
0
1
0
1
0
1
2
0
0
1
1
2
0
0
1
2
2
2
2
0
0
1
1
1
0
0
2
0
1
1
0
0
0
0
2
1
0
0
1
2
0
2
0
0
1
1
0
1
2
1
2
0
1
1
0
2
3
0
0
1
0
0
2
0
3
0
0
0
0
3
0
2
0
1
0
3
1
1
1
0
0
1
1
1
0
0
1
2
0
1
0
0
0
1
2
2
0
0
1
0
0
2
1
1
2
1
2
2
2
0
1
1
1
1
1
0
0
1
0
0
1
2
1
1
1
0
1
1
0
0
1
0
1
2
1
1
0
0
0
1
1
0
0
0
1
0
0
0
4
0
0
2
0
0
2
2
0
1
3
1
1
0
1
0
2
0
0
1
0
2
1
0
2
1
0
2
0
1
1
2
0
0
2
1
2
1
0
0
4
0
0
0
2
1
0
1
0
0
1
0
0
2
2
2
0
0
0
2
0
1
2
0
1
1
0
1
1
2
1
0
4
1
1
0
2
0
0
2
0
0
1
0
1
1
0
0
0
1
1
1
1
0
2
1
1
0
1
2
0
2
1
2
0
1
0
0
0
2
0
0
0
2
0
2
0
1
1
0
1
2
0
0
0
0
1
0
1
0
1
2
0
0
0
1
1
2
1
1
0
0
2
0
1
1
1
0
0
1
1
2
0
0
1
0
0
2
1
0
0
1
2
1
1
1
1
0
2
0
0
0
1
1
2
0
1
1
0
0
2
0
2
2
1
1
1
2
3
0
0
1
1
1
2
0
0
2
1
0
1
1
0
1
0
0
3
1
0
1
0
2
0
0
0
3
1
2
0
2
0
1
1
0
2
1
1
0
0
1
0
1
1
1
0
1
1
0
1
0
0
1
0
0
1
0
0
0
0
2
2
1
0
2
1
1
0
0
1
0
0
2
0
2
0
1
0
2
1
1
0
0
2
1
1
1
2
4
1
0
0
0
1
2
0
2
0
1
0
2
0
0
2
0
2
2
0
2
2
1
2
0
2
1
0
0
2
1
0
0
2
0
1
1
2
1
0
2
1
1
0
0
0
1
1
2
0
0
1
0
1
0
2
0
1
1
3
1
0
1
0
1
2
1
1
0
0
0
0
1
1
0
0
0
2
2
2
1
1
1
0
0
0
0
0
1
0
0
2
0
2
1
2
2
1
2
1
0
1
0
0
0
0
0
0
0
0
2
1
0
2
0
1
0
0
0
0
1
1
2
0
0
0
1
0
1
1
1
0
1
0
2
1
0
0
1
0
0
0
2
2
1
0
0
1
2
0
0
2
0
0
1
2
2
2
2
0
0
0
2
0
0
0
2
2
1
0
2
0
2
1
0
3
2
2
0
1
2
2
1
0
0
1
0
1
1
1
1
2
1
2
1
1
0
0
1
1
3
2
0
1
1
1
1
0
1
0
0
0
2
2
2
1
1
0
0
1
1
0
2
0
1
2
1
0
1
1
0
2
0
0
0
1
1
0
1
2
0
0
0
0
1
0
2
1
0
0
0
0
0
1
0
0
0
2
1
2
1
2
0
1
0
0
1
0
0
0
0
0
1
1
0
0
2
1
0
1
0
0
1
1
1
0
1
1
0
1
0
0
0
1
1
4
1
1
0
1
1
0
0
0
0
1
1
0
2
2
2
1
0
0
1
2
0
1
0
0
1
2
1
0
2
1
1
0
0
2
2
2
0
1
1
1
3
1
0
1
1
0
0
1
0
1
2
1
0
0
1
1
1
0
2
1
0
1
2
1
2
1
2
2
5
0
0
2
0
1
0
0
5
0
0
0
1
0
0
2
1
1
1
1
0
0
4
0
1
0
1
0
1
2
1
0
2
1
1
1
0
1
2
1
1
0
0
0
1
0
2
1
0
1
1
2
1
1
2
1
2
0
1
1
0
1
1
0
0
3
2
3
2
0
0
1
2
0
2
0
1
1
1
1
0
0
0
1
0
0
2
0
1
1
1
1
3
1
1
0
1
1
0
1
1
0
1
0
0
1
0
1
0
0
1
2
0
0
0
2
2
0
0
2
2
1
1
0
0
1
0
1
0
0
1
1
2
3
1
0
0
2
1
0
0
0
1
0
1
0
2
1
1
0
2
1
0
3
0
1
2
1
1
0
0
0
1
1
0
2
1
2
1
1
1
0
0
1
1
2
2
2
2
2
0
1
0
2
1
1
2
0
0
2
2
0
1
0
2
1
0
1
0
1
0
2
1
0
0
0
2
0
0
1
0
2
1
0
0
0
1
2
2
0
1
1
0
0
0
2
0
2
2
1
0
1
0
0
1
1
0
0
0
1
1
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
2
1
2
0
0
2
0
0
0
2
1
0
2
2
2
1
0
0
2
0
0
2
1
0
1
2
2
1
1
1
2
2
0
1
0
1
0
0
0
0
2
0
3
0
1
0
2
1
2
0
1
0
2
3
0
2
0
0
1
1
2
1
1
1
2
2
1
0
2
1
2
2
0
0
2
2
1
2
0
1
1
1
1
0
2
1
5
1
0
0
1
0
1
0
0
1
0
2
3
2
0
1
1
2
0
1
1
1
1
2
0
1
2
1
0
1
0
1
1
0
1
3
1
1
0
2
0
2
2
0
1
0
1
0
1
0
0
2
2
1
0
1
2
2
0
0
1
0
0
0
0
2
5
1
2
2
0
0
0
2
2
1
1
2
1
1
1
2
2
2
0
1
0
0
0
1
1
3
0
2
1
1
2
0
0
2
0
0
0
0
1
0
1
6
0
1
1
2
3
0
1
0
0
1
1
1
0
0
1
2
1
0
1
2
1
1
0
1
0
1
1
1
0
1
2
2
1
0
0
0
0
2
0
1
1
0
0
0
1
4
1
1
1
0
2
1
1
2
1
1
1
0
2
0
0
1
1
1
0
1
0
0
1
2
1
1
0
2
1
0
1
0
0
2
2
0
0
0
1
0
1
0
0
0
1
0
1
2
0
0
0
0
2
0
0
0
0
2
2
2
0
0
2
1
1
1
0
1
2
0
2
1
0
1
0
1
2
1
0
0
0
2
2
1
0
0
0
0
2
2
1
0
0
2
2
2
2
2
0
0
0
0
2
2
1
2
0
2
0
0
2
2
1
1
2
0
0
2
0
0
3
1
0
0
0
2
2
1
0
0
2
0
0
1
1
1
2
0
0
0
2
2
1
0
1
3
2
2
0
0
1
0
0
0
1
1
1
2
0
0
0
2
2
0
1
2
0
2
1
0
0
2
1
1
1
0
0
0
2
0
1
1
0
1
1
1
0
2
0
0
1
2
0
0
0
0
1
0
2
0
0
0
0
0
1
2
1
2
2
1
1
0
0
2
1
0
0
0
1
0
0
0
1
0
1
1
2
0
0
0
0
0
2
2
1
1
0
0
1
0
0
0
0
1
0
1
2
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
1
1
1
1
1
2
1
0
0
2
0
2
1
6
1
1
0
1
1
1
1
1
0
2
1
2
1
0
1
1
0
2
1
1
0
1
2
0
0
0
1
2
0
1
1
1
0
2
0
0
1
0
1
0
0
3
2
2
2
0
1
1
1
2
1
1
1
2
0
2
1
1
1
2
2
2
1
0
1
1
0
0
0
1
0
0
0
3
2
0
1
0
2
0
0
0
0
0
0
1
1
0
2
2
0
1
1
2
2
0
2
0
2
0
1
1
0
1
1
1
1
0
0
0
0
1
1
1
2
0
1
1
0
0
1
0
0
0
1
0
0
0
2
0
2
2
2
0
0
1
0
1
1
0
2
1
0
2
1
1
0
0
0
0
2
1
1
1
0
0
1
0
1
0
1
1
0
0
0
1
1
1
0
1
0
2
1
2
1
1
2
0
1
0
0
1
0
2
0
1
0
0
1
2
0
1
1
1
1
1
0
0
4
0
0
0
1
1
2
2
0
1
0
0
0
4
1
0
1
0
1
1
1
2
0
1
0
1
0
0
1
0
3
0
1
0
2
1
2
2
1
0
4
0
0
0
0
0
0
2
0
0
2
0
1
1
3
0
1
1
0
1
0
1
1
1
1
2
2
0
1
0
1
1
0
0
1
0
1
0
2
2
3
1
1
0
2
1
1
0
1
1
1
0
2
0
1
1
1
0
0
1
0
1
1
2
2
5
1
2
1
0
0
2
0
1
0
1
1
2
1
0
0
2
1
0
1
1
2
2
1
2
0
0
1
0
1
0
0
0
2
2
0
0
4
0
1
0
1
1
1
0
0
1
1
1
2
0
1
0
1
0
0
2
1
0
3
1
1
0
1
0
1
0
0
0
2
1
2
0
1
0
0
1
1
0
0
0
0
1
0
1
1
0
0
0
1
1
0
0
1
0
1
0
0
1
0
3
2
0
0
0
0
0
0
2
1
1
0
4
2
1
2
0
0
1
2
0
1
1
0
1
2
1
0
0
2
0
0
0
0
0
1
2
1
0
0
1
0
0
2
1
1
0
0
1
0
0
1
2
0
1
1
2
1
2
0
0
1
2
0
0
0
0
0
0
2
1
0
1
1
1
0
0
0
1
0
0
1
0
2
0
1
1
2
3
0
1
1
1
0
0
0
1
0
0
1
1
1
2
2
0
0
0
1
0
4
0
0
0
0
0
1
1
2
0
0
0
1
2
0
0
0
2
1
0
0
0
0
0
0
2
1
0
0
1
1
1
0
1
0
2
0
1
3
2
1
1
2
1
1
0
0
0
2
1
3
0
1
2
2
0
1
0
1
0
0
0
0
1
1
1
1
1
0
1
2
0
0
1
2
1
2
1
0
0
2
0
0
1
1
0
0
2
0
2
1
2
1
1
1
0
2
0
2
0
0
0
0
0
1
0
0
2
1
0
0
0
1
1
0
1
0
0
2
2
1
0
1
1
0
1
0
0
0
2
1
1
1
0
0
0
1
0
0
2
2
0
0
0
2
1
2
2
0
0
0
1
0
0
0
1
1
4
1
0
3
0
1
0
2
1
1
1
0
0
1
2
1
1
2
2
0
1
1
1
0
1
2
0
0
1
2
0
0
0
1
2
2
2
1
0
3
0
1
1
2
0
1
1
0
1
1
0
2
1
0
1
1
1
1
0
0
0
2
1
0
1
0
0
0
2
0
1
0
0
2
1
0
2
2
1
2
2
0
0
0
0
0
1
2
0
0
1
3
1
1
0
1
1
2
1
2
1
0
0
0
0
0
0
0
1
0
1
0
2
1
1
1
2
0
0
2
0
2
1
1
2
0
0
0
0
1
0
0
0
0
1
0
0
1
2
1
2
2
0
0
0
1
1
2
0
0
2
0
0
0
0
2
0
0
1
1
0
2
2
0
0
0
2
1
1
2
2
0
1
0
0
2
2
1
1
1
1
2
1
2
0
0
2
2
0
0
2
1
0
1
0
0
1
1
0
0
2
1
0
2
1
2
1
1
1
0
1
3
0
4
1
0
1
2
3
2
1
2
1
1
0
2
0
0
0
0
2
0
1
2
1
1
2
2
0
1
0
1
0
0
1
0
1
1
0
2
0
2
1
0
1
0
2
1
1
1
0
2
1
2
2
0
1
0
0
1
2
1
0
0
0
0
2
0
0
0
0
2
0
0
1
1
2
2
0
1
0
0
0
1
0
1
1
0
0
1
1
0
1
2
0
0
0
0
1
2
1
1
0
1
2
0
0
0
0
1
1
0
1
0
0
1
2
0
1
1
0
0
2
0
2
2
1
0
0
0
0
1
0
0
0
0
1
2
2
2
0
0
0
0
3
2
0
0
0
0
2
0
0
2
1
0
0
1
0
0
0
1
1
1
0
0
2
1
1
2
0
1
1
1
0
2
2
0
2
0
0
2
1
0
0
0
1
1
1
0
0
0
0
1
0
0
2
2
1
1
1
0
0
1
0
2
1
1
1
3
0
0
1
1
0
1
0
1
1
2
0
2
0
1
0
1
1
2
0
0
2
3
0
1
1
0
0
1
1
1
0
0
1
0
1
1
1
1
0
1
2
2
0
0
0
0
0
2
2
0
2
2
1
1
1
2
1
0
1
1
1
1
1
1
2
0
1
0
0
2
0
2
4
0
0
0
2
1
1
0
0
1
0
1
1
1
0
2
2
3
2
2
0
0
1
0
2
1
0
0
0
2
1
0
1
2
0
2
0
3
2
0
1
1
0
0
1
1
1
2
2
1
2
2
0
0
2
1
1
0
1
1
0
0
0
2
1
1
2
1
2
0
0
0
1
0
2
2
1
2
0
1
0
1
0
2
2
0
1
0
1
0
1
0
2
0
0
2
1
2
0
1
0
0
0
0
2
0
0
2
0
1
0
1
1
0
0
2
0
0
1
1
0
0
0
1
0
1
0
0
1
0
0
2
0
2
1
0
4
1
0
0
2
1
0
1
1
0
0
2
1
2
3
0
0
0
0
0
2
1
1
1
1
0
0
2
1
3
1
1
2
2
0
2
1
0
0
1
1
0
1
1
1
2
0
0
1
0
2
0
0
1
1
1
1
2
3
1
2
1
0
0
1
1
0
1
1
1
0
0
1
1
2
2
0
0
1
1
1
1
0
0
1
0
0
2
0
1
1
1
0
2
0
2
1
0
1
0
1
1
0
2
2
0
1
1
2
0
1
1
1
0
0
0
0
0
1
1
1
1
2
1
0
2
0
2
0
3
2
0
0
3
0
0
1
2
1
1
0
1
0
2
2
3
0
0
1
1
2
0
0
4
0
0
0
2
1
1
2
0
1
2
2
0
1
2
0
0
1
1
0
0
0
2
1
0
1
1
1
0
0
1
1
0
1
0
2
0
2
1
2
1
0
3
1
1
2
0
1
2
0
0
0
1
0
0
1
0
0
0
0
2
0
0
1
0
2
0
0
2
0
0
1
2
2
1
2
0
0
1
1
0
0
1
0
0
1
0
1
0
1
1
0
0
1
0
1
0
0
2
0
2
0
1
1
2
2
1
1
0
1
2
2
2
0
0
1
1
1
1
1
1
0
2
0
1
0
0
0
0
2
1
1
1
0
1
0
0
1
1
0
1
0
1
0
1
1
0
0
0
1
0
0
1
1
2
0
0
0
0
0
1
2
1
1
0
1
0
1
0
1
0
1
1
0
0
2
1
0
2
2
2
0
0
0
0
2
1
2
1
0
0
2
0
1
0
1
1
1
1
0
0
0
0
1
0
0
1
2
0
0
1
0
3
2
0
2
1
0
2
1
2
1
0
0
0
2
0
0
0
0
2
0
0
2
0
1
1
0
2
0
1
1
1
0
0
0
0
1
1
0
0
0
0
0
2
2
0
1
0
0
0
0
0
1
2
2
0
0
1
0
0
0
2
2
0
1
0
0
1
0
2
1
1
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
2
1
1
0
1
1
0
2
0
1
1
0
0
2
2
0
0
0
2
1
0
2
0
0
0
1
2
2
2
0
0
2
2
1
2
1
0
0
1
0
1
3
1
0
0
3
0
2
0
1
10
2
2
1
0
1
0
2
0
0
0
1
2
0
0
0
0
0
1
0
0
0
2
1
1
1
0
2
0
1
1
2
0
1
0
0
2
1
1
0
0
0
0
2
0
1
1
1
1
1
0
0
0
0
0
3
2
0
1
2
1
1
2
1
0
0
0
1
0
2
0
0
0
0
1
1
1
2
0
0
2
0
1
2
1
0
2
2
0
1
0
0
1
0
1
0
2
0
0
2
2
1
2
0
1
0
1
1
0
0
0
1
1
1
1
0
2
0
2
0
0
2
0
5
1
1
2
2
2
1
1
2
1
0
0
1
2
1
0
1
0
0
2
2
1
0
0
2
0
0
2
0
1
0
3
0
0
1
1
3
0
0
1
0
0
0
0
2
2
2
1
3
0
0
2
0
2
0
0
0
1
0
2
2
2
1
2
1
1
1
0
1
0
1
2
0
0
0
2
0
0
0
2
2
1
1
1
3
1
1
0
0
1
0
2
0
1
1
3
0
0
0
0
0
1
1
1
0
0
0
2
1
0
0
0
0
0
1
1
0
1
0
2
0
2
1
0
0
0
2
2
0
1
0
0
1
1
2
0
0
0
0
1
1
0
2
0
0
1
1
1
0
2
1
1
1
0
2
0
1
0
2
0
0
0
2
0
1
1
1
1
2
0
0
2
0
0
0
1
0
0
1
0
2
2
1
0
0
0
0
2
1
0
1
0
1
1
0
0
0
1
2
0
1
0
0
0
2
0
0
1
1
1
0
0
1
1
0
0
2
1
1
1
0
1
1
0
2
1
0
1
0
0
1
2
2
0
1
1
0
0
0
1
1
2
0
1
2
1
0
1
0
2
1
0
2
2
2
2
1
2
2
0
1
2
0
1
1
0
2
1
2
2
2
2
0
1
1
2
2
2
1
0
0
0
5
1
1
0
1
1
1
1
0
2
0
0
0
2
2
1
0
1
0
0
0
0
0
0
2
1
1
2
0
0
1
0
1
2
0
2
1
0
0
0
2
2
0
0
0
2
1
1
0
1
0
1
1
0
2
2
0
0
0
0
0
1
1
1
2
2
0
2
2
1
1
2
0
0
1
2
4
0
1
0
1
2
0
0
1
0
1
0
0
1
1
0
1
1
0
0
0
1
0
2
0
1
0
2
0
0
1
2
2
0
0
1
1
0
0
1
1
1
1
0
1
0
1
0
1
0
0
1
0
0
2
2
1
1
2
0
0
1
1
0
0
2
0
2
0
1
2
0
0
1
2
1
2
0
1
1
0
0
1
0
2
2
1
3
0
1
1
0
1
2
1
0
2
1
2
1
1
2
2
1
1
0
0
2
1
0
1
2
2
1
1
2
2
2
0
0
0
0
0
0
0
0
0
0
1
2
0
1
2
1
0
1
1
1
0
0
0
1
1
2
1
2
1
0
1
1
0
0
0
1
0
1
0
2
1
2
2
0
1
4
1
0
1
1
0
0
1
1
2
1
0
2
2
1
0
0
2
1
1
1
1
1
0
0
0
1
2
0
2
0
0
1
2
0
2
0
2
0
2
1
1
1
0
1
0
0
0
1
0
2
1
1
3
1
0
0
0
2
0
0
0
2
1
0
2
1
1
1
0
1
1
1
1
0
0
4
2
2
2
2
0
0
2
0
2
0
1
0
2
0
0
2
1
1
4
2
0
1
1
0
1
0
1
0
1
1
0
0
0
1
0
2
1
1
1
2
0
0
2
0
2
0
1
1
0
1
0
0
2
2
1
1
1
0
2
4
0
1
0
0
0
1
0
2
0
0
0
0
1
1
0
1
0
2
1
1
2
0
2
1
0
1
0
0
0
0
0
0
1
2
1
2
0
0
0
2
1
2
2
1
2
1
1
1
2
2
0
1
2
0
3
0
1
1
0
2
0
1
0
0
0
0
2
0
1
0
1
0
0
3
0
1
0
2
2
0
0
1
0
0
2
0
0
2
1
0
1
0
0
0
2
0
1
0
0
0
2
1
1
0
1
0
1
0
1
1
1
1
1
1
1
0
1
2
0
0
2
1
0
0
2
2
0
2
1
2
1
0
1
1
0
1
0
2
0
2
1
2
0
1
0
1
0
0
1
0
1
1
0
2
1
2
0
1
0
0
0
2
1
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
1
1
0
0
1
1
0
0
1
0
1
0
2
1
1
1
1
0
2
0
1
2
0
0
1
0
0
1
1
0
1
0
0
2
0
1
0
0
1
0
0
0
1
1
0
2
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
2
1
1
1
0
1
1
1
1
0
0
0
2
1
1
0
2
0
0
0
1
1
0
0
1
2
0
1
2
0
0
1
2
2
0
1
2
0
2
0
1
2
0
1
0
1
0
2
0
1
1
0
0
0
0
0
0
2
0
1
2
2
1
1
1
0
0
1
1
1
1
0
1
0
0
2
2
2
0
1
1
1
2
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
2
2
1
0
0
0
1
0
1
0
1
1
2
0
1
0
0
1
1
0
1
4
0
1
1
0
0
2
2
0
0
0
1
0
0
0
1
0
2
0
2
2
3
0
1
1
0
0
2
1
2
2
1
1
1
0
2
0
1
0
1
0
1
2
2
0
1
2
1
1
0
2
2
1
0
1
0
1
2
2
2
2
1
0
2
1
4
0
0
2
1
0
0
1
0
1
1
1
0
0
0
0
0
4
1
1
0
2
0
0
2
0
0
0
2
2
0
1
0
1
0
0
2
0
2
0
2
1
1
0
2
0
1
0
0
2
0
0
0
0
2
0
1
0
0
0
1
2
0
0
2
0
0
0
0
1
0
2
2
0
0
0
1
2
5
0
1
0
0
0
2
0
2
0
2
0
0
0
1
1
3
0
1
0
1
2
1
2
0
2
1
4
0
0
2
1
1
0
1
0
1
0
0
2
1
2
2
1
0
0
2
1
1
0
0
2
0
1
1
1
0
1
0
1
1
0
1
0
2
1
2
1
0
0
2
0
0
2
2
0
0
0
0
0
1
2
0
1
2
1
0
0
1
0
0
0
2
1
0
2
2
0
2
0
1
0
1
1
2
0
1
1
1
1
1
2
1
0
0
1
2
0
1
0
1
0
2
0
2
1
0
1
1
0
1
1
2
1
0
0
1
0
1
1
2
2
0
2
2
2
2
0
2
1
0
0
0
0
1
2
2
0
0
0
0
2
1
0
0
1
1
1
1
0
1
1
1
2
2
0
0
1
1
0
1
1
1
0
1
1
1
1
1
1
0
2
1
1
1
2
2
1
1
0
0
0
0
1
1
1
0
0
0
1
2
1
0
1
0
0
1
2
1
2
2
0
1
0
2
2
2
0
1
0
1
0
0
2
0
2
0
0
0
1
0
0
2
0
3
0
1
1
1
0
1
1
1
0
0
1
1
1
1
2
1
2
1
2
0
1
0
0
2
0
0
1
2
0
2
0
1
2
0
1
2
1
0
2
1
0
1
0
2
1
1
1
1
0
1
0
1
1
0
2
1
0
1
0
0
2
2
0
0
2
1
0
2
2
0
1
2
0
1
2
0
2
2
0
1
1
0
1
0
2
0
1
0
0
0
2
2
0
2
1
1
0
2
0
0
1
2
1
1
2
0
0
0
1
1
0
1
0
0
0
1
1
1
1
2
2
1
2
0
1
0
0
1
0
2
2
0
0
2
1
2
2
4
0
2
0
1
1
1
2
0
1
0
1
0
2
0
2
2
1
0
0
2
0
0
2
2
0
1
2
0
0
0
0
1
0
2
1
2
0
2
1
1
0
1
0
0
0
0
1
0
0
2
0
1
1
1
0
0
2
0
2
1
1
0
0
2
1
0
2
1
1
2
0
1
3
0
1
0
0
0
1
2
3
1
1
0
2
0
2
2
2
0
0
2
1
0
1
1
1
1
1
2
2
2
0
1
1
2
0
2
0
0
0
0
1
1
2
1
0
0
1
0
0
2
0
1
3
1
1
0
0
1
3
2
0
0
2
2
1
0
0
2
2
2
1
2
0
0
0
2
2
2
0
1
1
1
0
0
0
0
0
1
1
1
1
0
2
2
2
0
0
0
1
0
0
0
0
0
0
2
2
1
0
1
2
1
1
0
2
2
0
0
1
0
2
1
2
1
3
1
1
1
0
1
0
1
0
1
1
0
1
1
2
1
2
0
1
1
2
0
1
0
0
0
0
3
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
1
1
1
1
0
0
1
1
0
2
2
1
0
0
1
0
0
0
0
0
0
0
1
1
2
0
0
2
1
0
1
0
0
2
0
0
0
1
2
0
0
1
2
1
2
0
0
0
1
2
1
1
0
0
0
0
1
1
0
1
2
1
1
0
0
2
0
2
0
1
0
2
1
0
0
1
1
1
0
1
0
1
1
2
2
0
0
2
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
3
1
2
0
0
0
0
0
2
1
0
0
1
2
1
1
2
2
1
1
1
0
0
1
2
0
2
0
0
4
1
3
1
0
0
1
2
1
3
0
2
1
0
2
3
1
0
0
1
0
2
2
1
0
0
2
0
2
1
0
2
1
1
1
0
1
1
2
0
1
1
1
0
0
2
2
0
0
0
1
0
0
2
2
1
1
2
2
0
1
2
2
1
1
1
2
1
0
1
1
0
2
1
2
2
0
0
1
2
0
0
0
0
1
0
1
1
0
2
2
1
0
1
1
1
0
0
0
2
2
1
2
0
1
1
2
0
0
2
0
1
2
1
2
0
2
0
2
1
0
2
1
2
0
0
2
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
1
0
1
2
1
1
2
1
0
4
1
1
1
0
0
1
1
0
0
0
1
1
2
2
0
1
1
0
2
0
1
0
1
1
1
0
0
1
0
0
2
0
0
2
4
0
0
1
2
2
0
1
4
1
1
1
1
0
2
2
0
1
1
1
0
0
0
0
1
2
0
0
2
1
1
1
0
0
0
1
2
2
2
2
1
1
0
2
0
0
2
1
1
0
1
0
0
0
0
0
1
2
1
0
2
1
0
0
1
0
0
2
0
2
2
0
0
2
0
1
0
0
2
0
2
0
0
1
2
1
1
1
5
2
1
0
1
1
0
0
2
0
1
2
0
4
0
2
2
0
0
2
2
0
0
1
0
0
0
0
1
2
0
0
0
0
0
2
1
0
2
0
2
1
0
1
0
2
0
0
0
2
2
1
0
0
0
2
0
1
1
0
2
1
1
0
0
1
0
1
2
1
0
1
2
1
2
1
2
1
0
1
0
1
1
2
1
0
1
0
1
1
0
0
1
2
1
0
1
1
0
0
0
0
1
1
1
0
0
0
0
1
2
0
1
1
1
1
1
0
3
0
0
1
0
1
1
0
0
0
2
0
0
1
0
1
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
2
0
0
0
1
0
1
2
0
2
1
0
2
1
0
0
1
2
0
1
1
0
1
2
1
1
1
1
0
0
2
2
2
1
0
1
0
0
0
1
0
0
0
2
1
0
0
1
1
0
1
0
0
0
1
2
0
0
0
0
0
1
2
1
0
1
1
0
1
2
1
2
0
1
2
0
0
2
1
0
1
2
1
1
2
1
2
0
1
1
1
0
0
1
0
1
2
2
0
0
0
1
1
2
0
0
0
0
2
0
0
2
0
0
2
1
2
2
1
0
0
1
0
1
0
0
0
1
0
0
2
0
0
0
0
2
1
0
1
1
1
1
1
2
1
0
0
1
1
1
0
1
1
1
2
0
0
0
0
0
1
0
0
1
1
1
0
1
0
1
0
1
0
2
2
0
0
1
1
1
0
0
0
0
0
1
0
3
0
1
2
0
1
0
1
1
0
2
0
1
1
1
0
1
1
2
1
0
2
0
0
1
1
1
2
1
0
0
0
2
0
1
0
2
1
0
0
0
1
2
0
1
0
0
0
3
0
1
2
0
0
0
1
2
0
0
0
0
3
2
0
0
2
2
0
0
0
0
1
0
2
5
1
1
0
2
1
0
2
2
5
0
2
1
1
0
1
0
1
2
1
1
0
0
2
0
0
1
0
0
0
0
1
1
4
1
0
0
0
0
1
1
0
1
1
2
0
0
0
1
1
3
0
1
0
0
2
0
0
2
1
5
2
1
1
0
2
0
0
0
0
1
0
1
2
1
2
0
1
0
0
0
1
0
0
1
0
0
1
2
2
1
0
0
0
2
0
0
2
1
0
2
2
0
1
1
0
2
0
1
2
0
2
2
2
1
0
0
2
0
1
1
2
0
2
0
1
1
1
0
0
2
3
2
1
1
0
1
0
0
2
1
0
0
0
0
0
0
1
1
0
2
2
0
1
1
0
0
0
2
2
1
0
1
0
2
0
0
1
1
0
0
2
2
0
2
1
1
0
1
0
1
0
2
2
2
0
2
2
1
0
2
0
1
1
2
1
1
0
0
1
0
1
1
1
0
1
1
2
1
1
0
1
0
0
0
0
1
2
0
1
0
0
1
1
0
0
2
0
1
1
0
1
1
1
1
1
2
2
0
0
1
1
0
1
2
0
2
2
0
0
1
0
0
1
1
1
1
0
0
1
1
1
0
2
2
0
0
1
0
1
2
0
2
0
1
0
2
3
1
1
0
0
0
1
2
1
1
2
1
0
1
0
1
0
1
0
1
1
1
0
0
1
0
2
0
2
0
1
1
0
1
2
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
2
0
1
0
0
0
1
2
1
1
2
1
1
3
1
1
0
2
1
2
0
1
1
0
0
1
1
2
1
1
1
0
2
0
2
1
1
1
0
1
0
0
1
1
0
0
1
2
1
2
1
1
0
1
1
2
2
2
0
0
0
0
2
2
0
2
2
0
1
3
3
0
0
1
1
0
0
0
1
0
0
0
1
1
0
0
2
0
1
1
0
0
0
1
2
0
0
0
0
1
1
0
2
1
0
0
1
1
1
1
0
2
2
1
0
1
2
0
2
0
0
0
0
2
0
0
0
1
0
0
1
0
0
1
1
0
0
0
1
0
3
0
0
0
2
2
1
0
0
0
2
1
0
1
2
1
0
0
0
0
0
0
2
1
2
1
0
1
1
1
0
0
0
2
0
1
1
0
2
1
0
0
1
0
2
2
2
2
0
1
2
2
3
0
1
2
0
2
2
1
0
0
1
0
0
0
0
0
2
1
0
1
1
0
2
1
2
0
0
4
1
1
2
0
1
0
0
2
1
1
0
0
1
2
0
1
0
2
1
0
1
0
0
0
0
1
2
1
0
0
1
0
1
0
2
0
2
1
0
0
0
0
1
0
0
2
0
1
0
0
0
1
2
0
0
0
2
0
0
2
1
1
2
1
1
2
1
1
2
0
2
1
2
0
0
1
2
1
0
0
0
1
2
0
1
1
1
1
0
1
0
0
2
1
0
1
2
0
2
1
2
1
0
1
1
1
0
2
2
2
5
1
1
2
2
0
0
2
1
1
1
0
0
1
0
2
2
1
0
2
1
0
2
0
2
1
0
1
0
1
0
0
0
0
1
0
1
1
0
0
1
1
0
2
2
2
2
1
2
1
0
1
1
1
0
0
0
2
0
0
0
2
1
1
0
0
0
0
0
1
2
0
2
0
1
1
0
0
4
2
0
0
1
0
1
0
0
0
1
2
1
0
1
1
1
0
1
2
0
3
1
0
1
0
0
1
1
0
0
1
0
0
1
0
0
2
3
1
1
0
2
0
0
2
0
0
1
0
1
0
2
0
0
1
0
1
1
2
0
0
0
1
1
1
0
1
1
2
0
1
2
0
0
0
1
0
1
1
0
0
2
1
0
1
2
1
0
1
0
1
1
2
0
1
2
1
1
2
2
2
1
1
1
0
1
2
0
1
0
0
1
2
1
0
2
1
0
0
0
0
1
1
2
2
0
0
0
2
1
0
2
1
1
0
0
1
2
2
2
2
0
1
1
2
1
0
0
0
1
0
0
1
1
0
1
0
1
1
0
2
0
0
0
0
0
0
0
1
0
1
2
2
1
2
0
0
2
1
0
0
0
0
0
1
1
1
0
1
1
1
0
2
1
0
1
0
1
2
1
2
1
1
2
1
0
0
0
0
0
1
2
2
1
1
2
4
1
1
0
0
0
1
1
1
2
0
0
2
2
2
1
0
0
2
1
1
0
2
0
0
1
1
0
0
2
0
0
0
1
1
1
0
2
2
0
0
0
0
1
10
1
2
1
1
0
1
2
0
1
1
0
1
1
0
2
1
1
0
0
3
0
1
0
1
0
1
2
1
1
0
0
1
1
0
1
2
0
2
1
2
0
2
0
1
3
0
2
1
1
0
0
2
4
0
1
1
2
0
0
0
1
0
2
1
0
0
2
1
0
1
1
1
0
0
4
0
0
1
0
0
2
0
0
1
0
0
1
2
2
1
1
0
1
1
1
2
1
0
0
1
1
1
0
1
1
0
1
1
1
0
1
1
0
2
2
0
0
1
0
1
10
0
0
0
0
0
0
0
0
2
1
1
1
0
3
1
0
2
3
0
2
0
0
2
0
1
1
0
0
0
0
2
1
2
1
2
2
0
0
1
0
2
0
0
1
1
1
2
0
0
1
0
1
0
0
1
2
2
1
0
1
1
1
1
1
0
1
1
1
1
0
0
2
2
2
0
0
1
1
0
0
0
2
1
2
0
1
2
2
0
2
0
0
2
0
1
1
1
5
2
1
0
1
1
2
0
1
2
1
1
1
1
2
2
1
0
1
0
1
0
0
1
1
2
2
3
1
1
0
1
1
1
1
0
0
1
1
1
0
2
0
0
0
0
1
2
0
2
0
2
0
3
1
0
1
0
2
5
1
0
0
1
2
1
0
1
2
2
1
1
1
2
1
1
2
0
0
0
1
2
2
0
1
1
0
2
1
1
2
1
0
0
0
1
0
0
0
2
0
0
2
0
1
1
1
0
0
2
2
2
2
1
1
0
0
1
0
1
0
0
0
2
1
1
1
1
1
0
1
0
1
0
0
2
0
1
3
1
1
0
0
0
2
0
0
2
2
0
0
1
0
0
0
1
0
1
0
1
0
1
1
0
3
3
2
2
2
3
1
0
2
0
1
0
2
0
0
2
0
2
1
0
2
1
0
1
0
2
2
0
2
2
2
1
1
0
2
2
1
2
1
2
0
1
3
0
1
1
0
1
2
2
2
1
1
1
1
1
2
1
0
0
0
1
2
1
0
1
1
2
1
0
0
2
2
1
0
0
1
0
1
3
0
1
2
1
1
2
0
0
2
0
0
1
0
0
0
1
0
0
2
2
1
1
0
1
0
1
0
0
0
0
1
0
0
1
2
2
0
0
1
2
1
0
0
1
2
2
0
0
0
2
0
1
1
0
1
1
0
0
1
0
1
1
0
0
2
3
0
2
0
1
2
0
2
0
1
1
2
1
0
0
0
1
0
1
0
1
1
1
0
1
0
0
1
0
0
1
2
2
1
0
1
2
2
0
1
1
1
1
2
0
4
1
0
5
1
1
2
1
0
1
1
0
1
2
2
1
0
0
2
1
0
0
1
1
1
1
1
1
1
0
0
1
1
2
2
2
1
1
0
1
2
2
1
1
0
0
0
2
0
1
1
0
2
1
1
0
0
1
2
1
2
0
0
1
2
1
0
0
2
0
0
0
0
1
2
0
0
1
2
2
2
1
0
0
0
1
2
1
0
1
1
0
2
0
1
0
2
2
0
0
0
2
1
2
0
1
0
1
2
0
1
2
0
2
1
2
2
2
0
0
0
1
1
1
0
0
2
2
1
2
1
0
0
0
0
1
1
0
1
1
0
0
1
1
2
1
1
0
1
0
2
1
1
0
0
0
0
1
3
0
0
0
0
0
2
0
2
0
0
2
1
2
0
0
0
3
1
2
1
0
0
1
2
0
0
0
1
1
0
0
0
0
0
0
0
3
1
2
0
0
0
0
0
0
1
2
1
1
1
0
0
0
0
1
1
1
2
1
0
1
1
1
1
2
0
0
1
0
1
2
1
2
0
0
2
1
0
0
1
2
2
1
2
2
1
0
0
1
0
2
0
3
2
1
1
1
0
2
1
3
0
1
1
0
0
2
1
0
0
0
1
0
0
0
0
2
2
1
2
0
0
0
0
1
1
1
0
0
1
0
2
0
1
1
0
2
0
2
1
1
0
1
0
2
1
1
1
0
0
0
0
0
0
2
1
2
1
1
0
1
0
2
0
0
0
0
0
2
2
2
3
0
2
1
0
1
0
0
0
1
2
1
0
1
0
2
0
1
0
0
2
0
2
2
0
1
1
0
0
1
1
2
2
0
2
1
2
0
2
2
2
0
0
1
0
0
1
0
1
0
1
0
0
2
0
0
1
1
2
1
0
0
1
0
1
1
1
2
0
1
3
1
1
2
1
1
0
2
1
0
1
1
0
1
0
0
0
1
0
1
1
0
1
1
2
0
2
1
0
1
2
0
1
0
0
0
0
0
0
2
3
0
1
1
1
0
1
0
0
0
2
1
1
0
0
0
1
0
1
1
0
1
0
0
2
3
2
0
1
0
0
2
2
1
0
1
0
1
1
1
1
0
1
0
2
0
0
1
0
0
1
1
2
0
1
1
1
1
0
1
2
0
0
0
0
1
1
0
1
1
2
1
1
2
0
0
1
1
0
1
0
0
1
2
1
0
0
1
2
0
1
1
0
3
2
0
1
1
1
1
1
1
1
0
1
1
2
1
1
1
1
1
0
0
0
2
0
2
0
2
0
1
3
1
1
0
1
2
0
0
0
2
0
0
0
0
1
0
2
1
2
1
0
0
2
1
1
1
1
0
1
1
0
0
2
1
0
1
0
1
2
0
0
0
0
1
1
0
0
0
1
3
2
0
0
1
2
2
2
0
0
1
0
2
1
0
0
0
1
0
0
0
1
1
0
2
0
2
2
1
0
1
2
1
0
0
1
2
0
2
0
0
0
0
2
0
1
1
1
0
0
0
2
0
1
0
2
0
0
1
0
0
1
0
0
1
0
2
1
2
1
0
2
1
1
0
1
1
0
0
0
1
2
0
0
1
2
1
1
1
2
0
0
0
2
2
2
1
1
3
0
2
2
1
2
2
0
1
0
0
2
1
0
0
1
0
2
1
1
0
1
1
1
0
1
1
1
1
0
1
1
0
2
2
0
1
2
0
2
2
0
1
2
1
2
0
2
0
2
0
0
1
1
1
1
0
0
0
0
2
1
2
2
1
1
1
0
2
0
2
0
2
0
2
0
1
0
0
2
0
2
2
1
1
2
0
0
1
1
0
1
1
1
1
1
2
1
2
1
0
1
2
0
0
2
0
2
0
0
2
2
2
2
1
1
1
0
1
0
1
2
2
0
0
1
1
2
0
1
1
0
1
0
1
3
1
0
6
0
1
0
0
2
0
0
1
1
1
1
0
0
0
2
0
2
0
1
0
1
2
0
0
0
0
2
1
1
0
0
2
0
0
0
3
1
1
1
0
2
2
2
0
2
1
1
0
0
0
0
1
2
1
2
0
1
1
2
1
1
1
2
0
2
0
2
1
2
1
2
0
0
1
1
0
0
4
0
0
1
0
0
1
1
2
0
1
2
1
0
0
0
0
1
0
0
0
0
1
0
1
2
2
0
0
0
2
1
2
1
0
2
2
1
1
2
0
0
2
2
0
2
1
1
0
1
0
0
2
0
1
0
2
0
1
3
0
0
0
0
1
2
2
0
0
0
1
4
1
0
0
2
1
0
0
1
1
0
1
0
0
1
1
2
3
0
0
0
0
2
1
0
1
1
2
0
0
1
1
0
2
1
0
1
0
0
2
0
1
2
0
1
0
1
2
1
0
0
1
6
2
1
1
1
0
1
2
0
0
0
6
0
0
2
0
3
0
1
1
1
1
0
1
0
0
1
1
0
0
1
2
0
0
1
1
2
0
1
2
0
1
0
1
0
0
2
0
1
1
0
2
1
0
1
1
0
1
1
0
0
2
1
1
0
1
0
1
0
1
0
1
0
2
1
0
1
0
4
2
2
2
1
0
3
0
2
1
0
1
2
1
1
1
0
1
2
2
2
0
1
0
1
1
1
1
2
0
0
0
1
0
1
0
0
0
0
1
2
0
1
3
2
0
0
0
2
1
1
2
1
1
1
2
0
2
0
0
3
0
0
1
3
1
0
2
0
0
2
0
1
0
1
2
2
0
0
1
0
0
0
0
0
0
2
0
1
2
2
0
0
0
2
0
1
0
0
0
1
2
0
1
0
0
2
0
0
0
1
1
0
2
1
0
1
1
0
1
2
1
1
0
2
1
1
0
1
0
2
0
2
2
0
4
1
1
0
1
1
1
1
1
0
1
2
0
1
0
0
0
1
0
2
0
0
0
1
0
0
0
2
1
2
0
0
2
1
2
0
1
1
0
0
2
0
1
1
3
1
2
1
1
0
1
1
1
1
0
2
0
0
0
1
0
0
0
1
0
2
1
0
1
0
0
2
2
2
0
1
1
0
0
0
1
0
0
0
2
0
1
0
0
0
0
1
2
1
2
1
0
0
0
1
1
2
1
0
2
1
0
1
1
2
1
2
1
1
0
1
2
0
0
0
1
1
1
0
0
2
1
1
2
0
0
2
2
0
1
0
0
0
1
0
1
1
1
1
1
2
1
0
1
1
1
0
0
1
0
1
0
0
0
1
1
1
0
0
0
3
1
1
0
2
0
2
0
0
1
2
0
1
0
0
0
0
2
2
0
1
0
0
0
0
0
2
0
1
0
0
2
0
1
0
2
1
0
2
2
1
0
0
2
0
1
0
1
1
0
1
0
2
0
0
0
2
0
0
0
2
0
1
0
1
1
2
2
0
1
0
0
2
0
0
0
0
0
1
0
0
1
2
0
0
1
0
1
0
2
0
1
0
0
1
0
2
0
1
0
0
2
0
2
1
0
2
0
2
1
2
1
2
0
1
0
1
0
0
2
0
1
0
0
2
2
0
1
1
0
0
0
0
3
1
2
0
0
1
0
0
0
1
0
1
1
0
2
1
2
0
0
2
1
1
2
0
2
1
0
2
0
1
0
0
1
1
1
0
1
1
2
1
1
0
2
1
2
1
1
0
2
0
2
1
0
0
0
2
0
1
0
0
1
1
2
1
1
1
0
0
0
1
0
0
0
1
1
2
0
2
1
1
1
1
1
1
0
0
0
1
2
0
0
1
0
0
0
0
1
0
0
0
0
3
1
2
0
1
0
2
0
0
0
1
1
0
1
2
1
2
0
1
0
1
0
0
1
0
1
0
1
0
2
0
1
1
1
2
1
0
0
0
0
1
1
2
0
1
1
1
1
0
3
1
2
1
0
0
0
0
0
0
1
1
0
1
0
2
1
0
1
1
1
1
1
2
1
1
0
1
1
0
0
1
0
1
2
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
2
0
2
1
1
1
2
1
2
2
2
1
3
1
2
2
1
0
2
0
1
1
1
0
0
1
1
0
1
2
0
1
1
0
1
2
1
2
2
0
0
2
0
1
2
0
1
1
2
1
1
1
1
1
1
0
0
0
1
1
0
2
3
1
0
0
0
0
1
2
0
0
0
1
0
0
1
1
2
0
1
0
0
1
1
0
1
1
2
0
2
1
1
0
0
0
1
2
1
2
1
1
0
1
2
1
0
0
2
0
1
0
0
0
1
2
0
1
0
1
0
2
3
1
0
0
0
2
0
2
0
2
0
0
0
0
1
2
3
1
0
1
1
0
0
0
1
1
0
0
1
0
2
2
2
1
0
1
1
2
1
1
0
0
2
2
0
1
1
1
2
3
1
0
1
0
1
0
1
1
2
2
2
2
1
1
0
0
0
0
1
4
1
1
0
2
1
1
1
1
2
1
0
0
2
2
0
0
2
1
0
3
1
0
2
1
2
0
0
0
1
1
1
1
0
1
0
1
1
1
5
0
2
1
0
0
1
0
0
0
1
0
0
1
2
0
1
0
0
0
2
1
0
1
2
2
1
0
0
0
1
2
2
0
2
1
0
0
0
1
2
1
1
1
0
0
1
0
1
0
2
0
0
0
2
1
1
0
0
0
1
1
0
1
0
0
0
0
1
1
0
1
0
0
1
0
1
1
0
2
1
2
2
0
0
0
0
1
2
2
2
1
0
1
1
1
0
2
1
0
1
0
1
0
0
1
0
0
1
0
1
0
0
2
2
2
1
0
0
0
2
0
0
2
1
1
2
1
0
0
2
2
1
1
1
0
1
1
0
2
1
0
0
1
0
0
0
1
2
2
1
2
1
1
2
0
0
2
2
2
2
1
1
2
1
2
0
2
0
2
2
0
0
0
1
1
0
0
2
0
2
2
0
0
0
1
1
2
0
2
0
0
0
2
0
0
4
2
1
1
2
0
1
0
0
1
2
0
0
2
2
0
0
0
1
2
0
1
0
2
1
0
1
0
0
1
1
1
3
1
0
0
0
0
1
0
0
1
0
0
1
2
0
0
0
0
1
1
2
0
0
0
2
1
0
3
0
1
1
0
1
2
1
1
1
1
2
0
1
0
0
0
0
0
0
2
1
1
2
1
1
0
1
1
2
1
1
1
1
1
0
2
1
1
2
0
1
1
0
2
2
2
0
0
0
0
0
0
0
2
0
0
0
2
1
2
1
1
0
0
1
1
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
2
1
1
2
0
0
0
1
0
2
2
1
1
0
0
0
3
0
0
1
0
1
2
0
2
1
1
1
1
0
0
2
0
6
0
1
0
0
2
1
1
0
1
2
1
1
1
0
1
0
1
0
0
2
1
2
3
2
0
1
0
0
1
0
2
2
1
0
1
1
0
1
0
0
0
1
1
2
1
0
0
0
1
2
2
1
1
0
1
1
2
0
0
2
2
1
0
0
2
0
0
1
0
1
2
1
2
4
2
0
1
0
1
2
1
1
2
3
1
0
0
1
0
2
2
2
1
0
2
1
0
1
2
1
2
1
1
1
1
0
0
1
0
1
1
0
0
0
0
1
1
1
0
1
0
0
0
2
1
0
1
0
0
0
0
0
1
0
0
2
0
1
2
1
1
2
1
1
2
0
1
0
1
1
2
0
0
0
0
1
2
0
2
0
1
1
1
1
0
0
0
0
0
1
2
1
0
1
1
0
2
1
2
0
2
1
0
0
2
1
0
0
1
0
0
2
1
1
1
2
0
0
0
0
2
1
0
0
1
0
1
0
2
2
0
0
1
0
1
1
0
1
0
2
0
0
0
2
2
1
2
1
4
1
1
0
3
2
1
0
2
0
0
0
0
2
2
0
1
1
1
2
2
0
0
2
0
1
0
1
2
1
2
0
0
1
0
1
1
2
1
1
2
1
1
1
0
1
0
1
0
0
1
1
0
1
2
5
0
2
0
0
1
0
0
0
2
0
1
2
2
2
2
1
0
0
1
1
0
0
0
1
1
2
1
1
1
0
2
1
2
0
1
2
0
1
0
1
2
0
0
2
2
0
1
2
2
1
0
2
0
0
2
2
0
0
0
2
1
0
1
1
1
0
2
0
0
1
2
1
1
0
1
0
1
0
0
0
0
0
1
1
0
0
2
1
0
2
1
2
2
1
1
0
0
2
2
0
1
1
0
1
0
0
2
3
0
0
2
0
0
2
1
0
0
1
0
1
0
0
1
0
1
4
0
1
0
0
0
0
1
0
3
1
1
0
0
1
1
2
0
0
0
0
1
2
3
0
2
1
1
0
1
0
0
1
0
2
2
2
1
0
0
0
2
2
1
0
0
0
1
2
1
0
0
0
7
0
0
1
1
1
0
0
1
0
0
2
0
0
1
1
1
2
2
1
2
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
3
2
0
0
0
0
3
2
0
0
2
0
0
1
0
1
1
1
2
1
1
2
2
2
1
1
0
1
1
0
0
1
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
3
1
0
1
0
1
0
0
2
0
0
1
2
2
0
1
1
0
1
0
1
0
4
1
1
0
1
0
1
1
0
0
0
0
0
2
0
0
1
2
0
1
0
0
0
2
1
0
2
0
1
0
0
1
1
1
1
1
0
2
0
0
0
0
2
2
1
1
0
0
0
1
1
0
3
1
0
2
0
2
2
0
2
1
1
2
1
2
1
0
1
2
1
1
0
1
2
1
2
1
1
1
0
0
0
2
2
0
1
2
2
1
0
0
2
1
0
2
1
1
2
2
0
1
0
0
1
0
1
0
0
1
2
1
1
1
0
0
1
2
1
0
0
0
0
2
1
1
2
0
0
1
0
1
0
0
1
1
1
0
0
1
0
0
0
1
1
0
0
1
1
0
1
0
1
2
1
0
2
0
1
1
1
1
1
0
2
2
2
1
1
1
0
0
0
0
0
1
1
0
1
1
1
0
1
2
1
0
1
0
1
1
2
1
1
2
0
2
0
2
2
1
0
2
0
1
0
0
1
1
1
1
1
1
0
2
1
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
2
2
0
1
2
1
0
0
2
1
1
1
0
1
0
0
0
0
0
1
0
0
0
1
0
2
0
0
2
2
1
2
2
1
0
2
0
0
0
1
2
0
1
0
1
0
0
1
0
0
1
1
0
0
0
1
0
0
1
0
0
0
2
2
0
0
0
0
2
0
0
2
0
1
2
2
0
1
0
0
0
0
0
2
1
1
2
2
0
0
1
1
1
0
0
1
0
0
0
2
0
1
0
1
3
0
1
2
0
0
1
0
1
2
2
2
1
1
1
0
2
0
1
2
0
1
1
1
0
0
0
2
0
0
0
1
0
0
1
0
2
0
0
0
1
0
2
1
6
3
0
2
2
0
2
2
0
1
0
2
1
1
0
1
1
0
1
1
0
0
0
0
1
0
2
0
0
1
1
0
0
1
0
0
1
1
0
0
2
2
1
0
2
0
0
2
2
2
1
1
1
0
1
1
0
2
2
2
0
1
0
0
0
1
1
1
1
0
1
2
0
2
1
2
1
0
2
0
1
0
2
0
0
0
0
1
0
0
0
1
2
0
0
1
0
0
0
1
0
0
0
0
2
2
1
1
1
0
1
1
2
0
0
2
1
0
1
1
1
1
2
1
1
1
0
1
0
0
1
0
1
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
2
0
1
2
0
0
1
0
2
1
0
2
0
0
2
0
3
1
1
1
1
0
0
2
1
1
1
2
2
0
1
1
0
2
0
2
1
0
0
0
2
0
0
1
2
1
2
2
1
0
0
0
2
2
0
0
1
0
0
1
2
0
0
1
0
0
0
0
0
1
0
0
1
1
1
1
0
2
0
1
2
1
0
0
1
2
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
2
1
1
1
0
2
2
1
0
0
1
1
1
0
1
1
0
1
2
1
2
2
0
0
0
1
0
1
0
0
0
1
0
1
1
2
1
1
2
0
0
0
0
2
1
0
1
0
0
1
2
1
0
2
0
0
0
2
2
0
1
0
0
1
0
1
0
1
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
1
1
0
0
1
1
2
1
1
0
0
1
2
0
1
0
2
2
1
1
0
2
0
2
0
0
1
0
1
2
2
0
2
1
3
0
0
1
0
1
0
0
1
0
0
0
2
0
0
0
0
0
1
0
1
0
1
0
2
2
1
0
0
0
0
0
1
0
0
0
2
1
1
1
0
1
0
2
0
2
3
2
0
0
0
1
2
0
0
1
1
1
1
0
1
0
0
0
1
0
2
0
1
0
1
1
0
2
1
2
1
0
0
1
2
0
1
0
0
1
0
0
1
0
0
1
0
2
1
0
0
1
1
0
1
0
2
1
1
0
0
2
1
1
1
1
2
0
0
0
2
0
1
0
1
0
1
2
2
0
1
1
2
3
1
0
0
0
0
1
2
0
0
2
0
0
1
0
1
0
1
1
1
1
0
1
0
0
0
2
1
0
1
1
1
1
0
2
2
0
0
0
2
0
1
0
2
2
0
1
0
0
0
1
1
1
2
1
0
2
0
0
1
0
2
1
3
2
0
1
1
1
1
1
0
1
0
0
0
0
0
0
0
1
1
0
5
2
2
1
1
0
2
2
1
0
0
1
0
0
1
1
0
1
2
0
0
1
1
0
5
0
1
3
2
0
1
0
0
0
1
1
2
1
2
0
1
1
0
0
2
0
0
2
2
2
1
0
2
0
0
2
1
0
2
6
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
4
1
1
0
2
1
1
0
1
1
1
1
0
3
2
1
0
1
0
0
0
0
2
0
1
2
2
1
1
2
0
0
3
0
0
0
0
2
0
2
0
1
0
0
1
2
0
2
1
0
2
1
0
0
1
2
0
0
2
0
0
1
0
0
0
2
2
2
1
0
1
0
1
1
0
0
2
0
1
2
1
2
1
0
0
0
0
1
1
2
2
0
2
1
2
2
1
0
2
1
1
0
1
0
0
1
1
1
2
2
0
0
0
0
0
0
0
1
2
0
1
1
2
0
1
1
2
1
1
1
1
1
0
2
0
2
2
2
0
0
0
2
2
2
0
2
0
3
0
1
1
1
2
1
1
3
0
0
1
2
0
0
0
2
1
1
2
1
0
0
1
2
2
0
0
0
0
1
1
0
0
1
0
1
0
2
2
1
1
0
1
0
0
0
1
0
0
2
1
0
0
0
2
0
0
0
1
0
2
1
1
2
1
0
0
1
1
0
0
0
1
4
1
0
0
2
0
2
0
0
0
0
0
0
2
2
0
2
1
0
1
1
0
1
0
1
0
2
0
2
0
1
0
1
1
2
1
0
2
0
1
2
2
0
1
0
1
0
1
0
0
0
0
1
2
0
0
1
1
0
1
1
2
0
1
0
1
0
2
2
0
0
0
0
0
0
1
0
0
2
2
2
0
0
0
1
2
0
0
0
0
0
0
0
0
1
1
1
2
1
1
1
1
0
2
0
1
3
1
0
1
0
2
0
0
1
1
0
0
0
2
2
0
1
1
0
1
2
0
2
1
1
0
0
0
0
2
0
1
0
1
0
1
1
0
1
0
1
2
1
0
0
0
0
2
1
0
2
1
1
1
1
0
0
0
1
1
2
2
1
1
0
1
2
0
1
1
1
1
1
2
0
1
1
1
1
2
1
1
0
1
1
0
0
1
1
2
1
0
2
0
1
1
1
1
0
0
0
0
2
2
2
2
2
0
0
2
1
0
0
1
2
1
0
1
1
2
1
2
1
1
2
0
0
2
4
1
2
1
0
0
0
2
0
0
0
1
0
2
0
1
1
1
0
1
1
1
1
1
2
0
3
0
1
0
1
0
1
2
0
0
1
0
0
2
1
1
2
2
2
1
0
1
0
0
0
2
1
0
1
1
0
1
2
0
1
0
0
0
1
1
2
0
0
0
2
1
0
1
1
1
2
0
1
0
0
1
0
1
0
2
2
1
1
0
0
1
2
2
1
0
1
0
0
0
1
0
0
1
0
1
1
0
1
0
0
1
0
2
1
2
0
2
1
0
1
0
2
2
1
0
2
0
2
1
2
2
1
1
2
1
0
2
2
0
0
0
1
0
1
3
1
3
0
1
2
1
0
1
0
3
0
0
2
0
1
1
1
1
0
0
2
1
2
2
1
0
0
1
0
0
1
1
1
1
1
1
2
0
0
1
0
0
1
2
2
1
1
1
0
0
2
0
1
2
1
1
0
1
0
0
0
0
0
1
1
1
0
0
1
2
1
1
1
0
0
1
0
1
1
0
0
0
1
2
0
2
1
1
2
0
0
1
1
0
1
0
2
1
0
3
2
1
1
0
0
0
1
1
0
1
1
2
0
2
0
1
1
0
1
2
0
1
1
1
2
0
0
0
3
0
0
2
0
0
1
4
0
2
1
0
0
1
0
1
0
2
1
0
1
1
1
0
1
1
1
1
0
2
0
1
0
1
0
0
0
2
1
1
2
2
2
0
0
1
0
1
0
1
0
0
2
2
2
1
0
0
0
0
0
1
0
2
0
0
0
0
1
0
1
1
0
0
1
1
3
1
0
3
2
2
2
1
1
0
0
0
0
2
0
1
2
2
0
1
1
0
1
0
1
1
1
0
1
0
0
1
0
2
0
0
2
0
0
1
1
1
0
0
0
1
2
1
0
0
2
0
2
1
1
2
0
1
1
1
1
1
0
2
0
1
0
0
1
0
2
0
2
1
0
0
1
2
1
2
2
0
0
0
2
1
0
1
2
2
1
1
1
1
2
1
0
2
0
0
0
1
1
2
1
0
2
1
1
1
2
0
2
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
2
0
1
1
2
0
0
0
0
0
0
1
2
1
0
1
0
1
1
2
0
0
0
0
0
0
0
1
2
1
1
1
2
2
1
1
0
1
0
0
0
0
1
1
2
0
1
2
6
2
0
0
2
0
1
2
0
0
2
1
0
0
0
1
0
1
1
2
0
0
3
0
2
0
2
1
1
0
0
1
1
0
0
0
0
0
0
1
3
2
2
0
0
1
1
0
0
1
0
0
0
1
2
1
0
0
1
2
5
1
0
1
2
1
0
1
0
1
0
1
0
1
0
0
0
1
1
1
0
1
0
2
2
1
1
2
1
1
0
1
2
1
1
1
2
0
1
1
0
2
2
0
3
0
2
0
0
0
1
2
0
1
0
0
0
1
1
1
1
1
1
4
1
2
1
2
0
2
1
2
0
0
0
0
2
2
1
0
0
1
0
1
0
2
0
2
0
1
0
1
2
0
0
3
0
1
0
1
1
0
0
2
1
1
0
0
1
0
0
1
0
1
0
2
1
0
1
1
1
0
2
2
1
2
1
0
2
0
1
0
0
2
0
1
2
0
0
0
1
2
2
3
2
1
2
1
0
1
0
0
2
1
1
1
0
0
1
1
0
1
1
1
0
0
1
0
0
0
2
1
1
1
1
2
1
1
0
0
1
1
1
1
0
2
2
0
1
0
1
0
0
0
1
1
1
0
2
1
0
1
2
0
1
1
0
1
0
0
2
0
1
0
1
1
0
1
1
2
2
0
0
0
2
1
2
3
0
0
0
0
1
0
2
1
0
0
1
0
1
0
0
0
0
1
1
0
1
1
0
0
0
1
0
0
1
1
0
0
1
1
0
2
1
0
1
1
1
1
0
2
1
0
0
0
0
1
2
0
2
2
2
0
1
0
0
1
0
2
0
1
0
0
1
1
2
1
0
0
0
0
1
1
1
3
2
1
2
6
0
0
0
0
0
0
0
1
0
0
2
0
1
0
1
0
0
0
2
2
0
0
0
0
1
0
2
0
1
2
2
1
2
1
0
0
0
0
1
0
0
1
2
0
1
0
0
0
1
0
0
1
0
1
1
1
1
0
1
2
0
0
1
0
0
0
2
1
0
1
1
0
1
0
0
0
0
0
2
2
0
1
1
1
0
0
0
1
1
2
2
1
1
2
1
0
0
1
2
0
2
0
2
0
1
2
0
1
2
1
0
0
1
0
0
0
0
2
2
0
0
0
0
0
2
2
1
2
1
2
2
0
2
2
0
1
0
2
0
0
1
2
0
0
0
0
2
2
2
0
2
1
0
2
1
2
2
1
0
0
0
0
0
1
0
2
2
1
1
1
0
0
1
2
2
1
1
0
0
0
0
1
1
1
0
0
2
2
3
1
2
0
1
1
0
0
0
1
4
1
0
1
1
1
0
0
1
0
1
1
3
0
1
2
0
1
1
1
0
1
0
2
2
0
0
0
1
1
1
2
0
1
1
2
2
0
2
1
0
2
1
0
1
0
1
2
1
0
1
2
0
1
0
2
0
1
0
2
0
0
0
1
2
0
0
0
0
2
0
2
2
0
0
0
0
1
1
1
1
1
1
1
0
2
0
1
0
1
0
2
0
0
0
1
2
0
2
1
1
1
0
0
0
2
2
0
1
1
1
0
2
0
0
1
1
1
1
1
1
1
0
0
1
0
0
1
0
0
1
1
0
1
0
2
0
2
1
2
2
2
1
0
1
0
0
0
2
1
1
1
2
1
1
1
0
1
0
0
2
0
1
2
1
0
1
2
0
1
0
1
2
0
1
0
1
1
0
4
0
0
0
0
2
1
0
2
1
2
0
1
0
2
0
2
0
1
2
1
2
0
0
0
1
2
2
1
0
0
0
0
0
0
0
1
1
0
0
1
0
1
1
0
2
1
3
1
2
1
0
0
3
1
0
1
4
0
0
0
0
0
2
1
0
1
1
1
0
2
1
0
3
1
0
1
0
1
1
3
2
0
1
0
0
0
0
0
1
1
1
0
0
1
0
0
2
2
2
2
1
1
1
0
0
0
1
0
0
0
1
2
1
0
1
1
2
0
0
2
1
1
0
2
1
0
0
0
0
0
1
0
0
2
2
1
0
0
1
2
2
0
0
2
2
2
4
1
0
2
1
1
0
0
2
2
2
1
1
0
1
3
1
1
2
1
2
2
0
2
2
0
0
1
0
2
0
2
0
0
0
0
0
2
0
0
0
1
0
2
1
1
1
1
1
2
1
2
2
0
0
0
0
1
1
2
2
0
1
1
0
1
1
1
2
0
0
2
0
0
1
0
2
0
1
1
1
0
0
0
1
0
1
1
1
0
0
1
0
0
1
2
0
0
1
2
1
1
2
0
2
1
1
2
1
0
0
1
1
0
0
1
2
1
0
0
1
2
1
1
0
0
1
1
0
0
0
0
1
2
1
1
2
0
1
0
0
1
0
1
1
1
0
2
1
2
0
1
2
0
0
0
0
0
1
1
2
2
1
1
0
1
2
1
0
2
0
1
2
2
0
1
2
2
0
0
1
0
0
2
0
0
1
1
0
1
1
3
2
1
2
1
1
0
3
1
0
2
0
2
0
2
2
0
0
2
1
0
2
2
1
1
2
2
2
0
2
1
1
1
1
1
0
0
1
2
2
1
0
1
0
2
1
0
0
0
1
2
1
0
1
0
1
0
2
1
1
2
0
1
1
0
1
1
0
2
1
0
1
2
0
1
0
0
1
2
1
1
1
0
0
1
1
0
2
1
1
0
1
1
0
0
0
1
0
0
1
0
0
0
2
1
0
0
1
1
0
0
0
0
1
0
1
0
0
0
2
1
1
2
0
1
1
0
1
0
0
1
3
0
0
1
0
2
2
0
1
1
0
0
0
1
0
2
2
0
1
0
1
2
2
0
1
0
2
1
1
1
2
1
1
1
2
0
0
2
0
1
1
1
0
0
2
0
1
1
1
3
1
2
1
1
0
2
2
0
1
1
1
0
2
0
2
0
2
0
0
1
1
1
0
0
2
1
1
1
0
1
3
1
1
1
2
0
0
0
0
0
0
1
1
4
0
2
0
0
0
2
0
0
0
1
1
2
2
0
0
2
0
0
1
1
0
0
1
1
1
0
0
0
0
1
0
0
3
1
1
1
1
0
0
1
0
2
0
2
1
1
1
0
0
0
1
1
0
0
0
1
0
1
1
0
3
0
1
0
2
1
1
2
0
0
0
0
2
1
0
0
0
0
2
1
0
2
0
2
1
1
2
2
2
2
0
1
1
2
1
2
1
0
0
1
0
1
1
0
1
0
0
1
1
1
1
0
1
0
2
3
2
0
2
0
1
1
2
1
0
2
1
1
1
1
1
0
2
0
1
0
2
2
0
2
0
1
2
0
2
2
0
0
1
2
1
0
0
0
2
0
0
0
0
2
1
1
2
2
2
0
2
0
0
0
0
3
1
1
2
2
0
0
1
0
0
2
2
1
0
1
1
0
0
1
1
1
1
0
1
1
1
1
1
0
0
0
0
1
1
1
0
0
2
0
0
1
2
2
0
0
0
0
2
2
2
1
2
0
1
0
0
0
2
1
0
0
1
0
1
0
1
0
0
1
0
1
0
0
1
2
2
0
1
0
0
1
0
1
0
2
0
1
0
2
2
1
2
0
1
0
1
1
2
1
0
0
2
1
0
1
0
0
0
0
2
0
0
2
2
5
0
1
0
0
1
0
0
1
1
0
2
2
2
2
0
0
0
0
0
0
0
1
1
2
1
2
2
1
1
1
1
1
1
2
0
1
2
2
0
2
0
0
2
1
0
0
1
0
0
0
0
1
0
2
0
1
0
0
1
0
1
1
0
1
1
0
2
1
2
3
1
1
1
1
0
1
1
1
0
0
0
0
1
0
2
0
2
2
0
1
1
0
2
1
2
0
0
0
1
2
3
1
1
2
1
0
1
0
1
0
2
0
2
0
0
0
0
1
0
1
0
1
1
0
0
1
0
0
1
2
0
1
2
1
1
1
2
2
3
1
0
2
2
0
0
0
2
1
0
3
0
1
0
0
0
0
1
1
1
1
1
0
0
0
0
1
0
1
0
1
1
0
1
0
0
0
2
1
0
0
2
0
2
0
2
2
0
0
1
2
1
3
2
0
2
1
1
1
1
0
2
2
0
1
0
0
1
1
0
0
2
0
0
2
1
2
2
1
0
1
2
0
1
0
1
2
1
2
1
0
2
0
1
3
0
1
2
0
0
0
0
0
1
0
2
1
0
0
0
2
2
2
2
0
2
1
0
1
3
0
1
1
1
1
0
2
2
2
1
0
2
1
2
1
0
2
1
1
0
2
1
0
0
2
2
1
1
1
0
2
0
0
1
0
0
1
0
1
1
0
0
1
0
3
1
1
1
3
0
1
0
1
0
1
0
2
0
1
0
2
0
1
1
1
0
0
1
1
1
0
1
0
1
2
0
0
0
2
0
0
0
0
0
1
0
0
1
2
1
0
0
0
0
1
1
0
1
2
1
0
1
1
2
1
0
0
0
0
1
2
0
2
0
1
0
0
0
1
0
2
0
0
0
0
2
0
1
2
1
1
1
1
0
2
1
0
1
1
0
0
0
0
1
0
1
1
1
0
1
1
0
1
0
0
1
2
1
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
2
0
1
0
1
1
0
4
2
1
0
0
0
1
1
0
0
0
2
0
1
0
1
2
1
1
1
0
0
1
0
2
3
0
1
0
0
2
0
0
0
2
2
2
1
1
0
0
1
1
0
1
0
0
1
0
1
1
2
1
0
1
1
1
2
1
1
0
1
2
2
2
0
2
0
1
1
2
1
2
1
1
0
0
2
3
1
1
1
2
0
3
1
1
0
0
2
1
0
0
1
1
3
0
1
2
0
0
1
1
1
2
1
2
0
0
1
1
2
0
2
1
1
1
2
1
0
1
0
1
2
1
0
0
1
2
1
0
3
2
0
1
1
0
2
1
2
2
1
0
2
1
0
0
0
2
1
0
0
0
0
0
1
1
2
0
1
1
0
0
0
0
0
0
0
1
0
1
2
1
0
4
2
1
2
0
1
0
1
0
2
1
0
1
1
0
2
2
1
1
2
0
1
1
1
1
0
1
2
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
2
1
2
0
0
0
0
1
1
1
0
0
2
1
0
0
0
1
1
0
2
1
3
1
1
1
1
0
2
3
0
2
2
0
2
1
0
0
1
0
0
0
1
1
3
0
1
0
1
0
0
1
0
0
1
1
0
1
1
0
1
0
1
1
0
2
0
0
0
0
1
2
1
0
1
1
2
0
0
2
2
0
0
1
1
2
0
2
1
1
2
0
2
2
0
1
0
1
0
2
1
0
1
1
1
0
2
2
1
0
0
4
1
2
2
0
2
0
0
1
0
0
0
0
2
1
1
0
1
1
1
0
0
0
1
0
0
2
0
0
1
2
0
0
1
0
1
0
0
0
0
0
2
0
1
1
1
1
1
0
2
0
0
0
0
0
2
0
1
1
1
1
2
0
0
0
0
1
1
2
0
2
0
1
2
1
0
1
3
1
0
1
1
0
0
2
1
0
0
0
0
0
0
1
0
1
0
1
2
0
0
0
2
1
0
1
1
0
2
1
1
1
1
0
1
0
0
0
0
0
0
1
2
0
0
0
0
1
2
9
0
1
2
0
2
0
2
1
1
2
0
1
1
0
0
2
2
0
2
2
0
1
0
0
0
2
1
0
0
0
1
0
0
1
0
1
0
1
1
0
2
1
1
1
1
0
0
0
1
1
3
3
1
0
2
1
2
0
2
2
0
0
0
1
0
1
1
1
0
1
0
0
1
1
0
2
0
0
1
0
2
1
2
0
1
1
0
2
0
1
0
0
1
1
2
0
0
0
0
0
1
0
1
2
0
1
0
0
2
1
0
2
2
1
0
0
0
0
0
0
0
0
0
0
3
0
0
1
1
1
0
0
0
1
0
0
1
1
0
0
0
0
1
1
2
0
0
2
2
1
0
0
0
0
1
0
0
2
1
1
3
2
2
2
1
2
0
2
0
1
0
1
0
0
2
0
0
1
1
0
2
0
0
1
0
0
1
2
1
2
0
0
1
1
0
2
1
0
0
1
1
0
0
0
4
1
0
2
0
2
0
1
0
0
0
2
0
0
2
2
0
0
0
0
2
3
1
0
2
2
0
0
4
1
0
1
0
0
0
1
1
0
1
1
1
1
0
1
0
0
2
0
0
2
2
0
0
1
2
0
0
2
0
0
1
0
0
1
2
0
1
0
1
1
0
0
2
0
1
0
0
1
1
1
0
1
1
0
1
1
2
0
1
2
0
0
0
1
2
0
1
0
1
1
0
1
0
1
2
0
0
0
0
0
1
1
1
0
1
0
0
2
0
0
0
0
2
1
1
2
0
0
2
0
2
3
1
0
2
1
1
0
0
0
1
0
2
0
1
0
1
1
1
1
0
0
3
0
1
2
0
1
1
1
2
1
1
1
1
1
0
0
1
1
0
1
1
0
0
2
0
0
0
1
2
0
1
0
1
1
1
2
0
0
0
0
0
0
0
0
1
0
1
0
1
1
1
2
0
2
2
0
1
0
2
1
1
0
1
2
2
1
0
1
0
0
1
1
0
0
0
0
1
1
0
1
0
2
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
5
0
0
2
0
0
1
1
1
2
1
1
0
0
0
0
0
0
1
2
1
2
1
2
0
1
2
0
0
1
1
1
1
0
1
2
2
1
0
2
2
0
2
0
2
1
1
6
2
2
0
0
0
0
1
1
0
0
1
1
0
1
0
2
2
0
1
0
1
0
0
0
1
1
1
2
1
1
0
0
0
1
1
2
0
1
0
0
0
0
2
0
0
2
1
1
1
0
0
0
1
0
0
2
0
1
2
1
0
1
0
1
1
1
0
3
0
1
0
0
1
0
2
1
0
1
2
1
1
2
1
0
0
0
2
0
1
1
0
1
1
1
1
0
0
0
0
0
1
0
0
0
2
0
1
2
1
1
1
0
1
0
0
1
2
0
1
0
0
0
2
1
0
0
0
0
1
1
0
2
0
1
1
1
0
1
0
0
1
1
2
1
1
0
0
0
1
0
2
0
0
1
1
0
1
0
4
0
1
1
1
1
1
2
2
0
2
0
0
1
1
1
2
0
0
3
1
0
1
0
0
1
1
0
0
0
0
1
0
0
0
3
1
0
0
2
1
0
0
1
0
1
2
1
1
1
4
0
0
0
0
2
2
0
1
1
0
1
0
1
2
0
2
1
1
0
0
0
0
0
0
0
1
0
1
0
0
1
2
0
2
2
1
0
0
1
1
2
1
2
0
0
0
0
0
0
0
0
1
1
1
1
1
0
0
2
1
1
1
0
0
0
1
1
1
0
2
2
2
0
2
1
0
1
0
2
1
0
0
2
1
2
2
0
0
0
2
0
0
3
2
2
2
2
1
2
2
1
0
2
2
1
1
0
2
1
0
0
0
2
1
0
0
0
1
1
1
0
0
0
0
0
0
0
1
1
0
0
0
1
1
2
1
0
2
2
2
2
2
0
1
0
0
0
0
2
0
1
0
1
0
0
2
1
2
1
1
2
2
0
1
0
0
0
0
1
1
2
0
1
1
0
2
0
0
1
1
1
2
0
1
0
1
0
0
0
0
0
1
0
1
0
1
0
0
2
0
1
0
1
3
1
0
1
0
1
2
0
1
0
0
0
1
2
1
0
1
0
2
2
0
0
0
0
2
0
1
0
2
0
2
1
1
0
2
0
1
2
0
0
2
0
2
1
2
1
2
0
0
0
0
1
1
1
0
2
1
0
2
1
2
0
2
1
0
0
1
0
1
1
0
1
0
0
0
1
0
1
1
1
1
0
0
2
2
1
0
0
1
0
0
2
1
2
1
1
0
0
0
1
2
0
2
0
0
1
1
0
2
2
1
2
2
0
0
0
0
2
0
0
0
0
0
0
1
0
1
1
1
1
0
0
0
1
1
2
2
0
0
1
0
2
0
1
1
0
0
2
0
4
1
0
0
0
2
2
2
0
0
0
1
1
1
0
1
0
1
1
0
1
2
2
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
2
1
0
1
2
1
1
2
0
0
1
1
0
1
1
0
0
1
2
0
0
0
1
0
0
0
2
0
0
0
0
0
1
1
1
1
1
3
0
0
0
0
1
2
1
0
0
1
1
0
1
2
1
2
1
1
1
2
0
1
0
1
2
1
0
0
1
2
1
2
1
0
1
0
1
1
2
0
0
0
1
0
0
1
1
1
0
0
0
0
2
1
2
1
0
1
2
1
0
1
1
1
0
0
0
2
1
0
0
0
1
0
0
0
1
0
2
2
0
1
0
0
1
2
0
1
1
0
1
0
2
1
6
1
1
1
2
1
2
2
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
1
2
1
0
1
0
0
2
0
0
1
0
2
0
1
1
0
0
0
0
1
1
1
1
0
2
2
1
0
2
2
0
1
0
0
1
1
1
0
1
0
0
0
1
0
2
0
1
2
2
1
2
2
1
1
0
0
2
0
0
0
1
0
0
1
0
0
1
0
1
2
1
0
1
0
0
0
1
0
1
0
0
1
1
2
0
0
0
2
2
1
3
0
0
2
1
2
0
0
0
0
0
1
1
1
2
2
0
1
0
1
2
0
2
2
0
1
0
1
1
0
1
0
0
0
0
0
0
0
1
2
0
0
0
2
2
0
0
0
0
0
0
1
2
0
1
1
1
0
0
0
1
0
0
2
0
0
1
2
1
0
1
1
0
0
0
1
1
0
0
1
1
0
0
0
2
0
0
2
1
0
0
2
0
1
1
1
0
1
0
1
2
0
2
1
0
0
0
1
3
0
0
0
3
1
0
0
1
1
1
0
1
1
2
1
0
1
2
0
2
0
2
0
0
1
2
1
2
0
0
2
0
0
0
0
0
1
1
1
0
0
2
0
1
0
0
0
2
1
1
0
1
1
1
0
2
0
1
2
0
2
1
1
2
1
0
1
0
0
0
1
0
1
1
0
1
1
2
0
0
0
2
0
0
2
1
0
0
0
0
1
0
0
0
2
1
0
1
1
2
1
0
0
1
1
2
1
0
0
1
0
1
1
1
1
0
0
0
1
0
0
0
0
2
0
0
1
1
0
1
0
1
2
1
0
1
0
0
1
1
0
0
0
1
0
0
2
0
0
0
0
2
0
0
2
2
2
0
1
2
0
1
0
3
2
1
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
2
3
2
1
0
1
1
0
1
0
1
0
2
1
2
1
2
0
1
1
1
2
2
0
2
1
0
1
2
0
0
0
1
1
1
1
1
0
3
2
1
1
0
0
0
2
0
0
1
2
0
1
0
2
0
0
3
0
0
1
1
1
1
1
0
0
0
0
0
1
0
0
1
2
1
0
1
0
0
0
0
3
0
0
1
0
2
1
0
2
0
1
1
1
0
1
0
1
1
2
0
0
0
0
1
0
1
1
2
0
2
0
1
0
0
2
0
2
0
0
1
1
1
0
0
1
1
0
2
1
0
0
1
1
0
1
2
2
0
2
1
0
1
0
1
0
1
0
0
1
2
1
1
0
2
1
1
0
1
2
0
2
0
0
0
1
1
2
2
1
1
0
1
0
0
1
0
0
1
2
0
1
0
0
1
2
0
1
0
2
1
1
2
0
0
0
2
1
0
1
1
0
1
1
0
0
2
2
2
1
0
0
1
0
1
2
0
0
0
0
0
0
1
2
2
2
4
1
0
1
0
2
0
2
0
0
0
1
0
0
0
2
0
3
1
3
0
1
0
0
0
0
0
2
1
1
0
0
0
0
0
0
2
0
0
2
0
1
2
1
0
0
1
1
0
2
0
3
0
0
0
1
0
0
1
1
0
1
0
0
0
1
2
0
2
0
2
1
0
1
2
0
0
1
0
2
1
0
2
1
0
0
0
2
2
2
0
2
0
2
0
2
1
0
0
0
0
0
2
0
0
1
0
0
1
2
1
0
0
1
0
0
0
0
1
0
0
0
1
1
1
2
1
2
0
0
2
1
3
2
0
2
1
1
2
0
1
1
2
0
0
0
0
0
2
0
1
0
0
1
1
2
1
1
0
5
1
0
2
1
1
0
0
2
0
0
0
0
2
0
1
1
0
1
2
1
0
2
2
3
0
1
2
2
0
0
2
1
1
0
2
0
2
1
1
2
0
0
2
1
1
0
0
0
1
1
0
2
1
2
1
0
1
1
0
1
2
1
2
2
1
2
0
2
0
0
1
0
2
2
2
2
0
0
0
0
0
1
3
2
1
2
3
1
0
1
1
2
0
2
2
2
1
1
0
2
1
0
2
1
0
0
1
1
0
0
1
0
0
0
0
2
0
1
2
0
2
2
0
1
1
1
1
1
1
1
1
1
0
2
0
0
1
1
1
0
1
0
1
1
4
2
0
1
0
1
1
0
0
1
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
1
0
1
0
1
0
1
2
0
2
2
0
0
1
0
1
1
1
2
2
0
1
2
0
2
0
0
1
0
1
2
1
0
0
0
1
0
1
5
1
1
1
0
1
0
2
1
0
2
0
1
0
0
1
0
1
1
0
1
0
0
0
1
1
0
2
1
2
1
0
0
1
0
2
4
1
0
2
0
1
1
1
0
2
1
0
2
0
2
0
0
2
0
0
1
1
0
0
1
1
0
0
0
0
0
0
1
0
1
2
0
3
2
2
0
1
0
0
1
1
2
1
0
0
0
1
0
2
1
2
2
0
0
2
1
0
1
2
2
1
0
2
2
2
1
1
0
1
1
0
1
0
2
0
0
0
0
0
0
1
0
0
1
2
1
0
0
0
1
0
0
0
1
0
3
0
0
1
1
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
1
2
2
0
0
1
0
0
0
0
3
1
0
0
1
0
2
2
0
1
1
0
2
0
1
1
0
1
2
0
2
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
1
2
0
0
1
1
0
0
1
0
1
2
1
2
0
0
1
0
0
1
0
0
3
1
3
1
0
0
1
1
2
2
0
0
0
0
2
0
0
0
2
0
0
2
0
2
1
1
0
1
0
0
1
2
1
2
2
1
0
0
0
1
0
0
0
2
2
0
1
2
1
3
2
0
0
0
0
1
0
0
2
2
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
2
0
0
2
0
0
0
2
0
2
1
1
0
1
0
1
0
0
2
1
0
0
0
1
0
0
0
0
0
1
1
1
1
0
0
1
2
0
1
0
1
0
1
0
0
1
2
1
0
0
2
0
0
0
0
2
1
2
0
2
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
1
2
2
2
0
0
0
1
1
0
0
0
0
0
2
1
0
0
0
0
1
0
1
1
1
0
0
1
1
1
1
2
1
3
0
0
0
1
0
0
0
0
0
0
1
0
0
1
2
0
1
1
0
0
1
1
2
0
2
2
1
1
0
2
0
2
2
1
0
1
1
0
2
0
2
0
0
3
0
1
2
1
2
2
2
1
0
0
1
3
2
1
1
0
1
0
0
1
1
2
0
1
1
1
1
0
0
1
1
1
0
2
0
0
1
0
0
2
0
0
0
0
1
1
0
1
0
0
1
2
1
0
3
0
1
0
0
0
2
1
0
0
0
1
0
2
0
2
0
2
0
0
1
0
0
1
0
1
1
1
0
1
1
0
2
1
1
0
1
1
0
1
0
1
1
0
2
1
1
0
0
2
1
0
0
2
0
2
3
0
1
1
2
1
0
1
0
1
0
1
2
2
0
1
1
2
1
0
1
1
0
1
2
0
0
2
1
0
0
0
3
0
1
0
1
0
1
1
2
0
1
0
1
1
1
0
2
0
0
0
0
1
3
0
2
1
2
0
2
0
0
2
0
0
2
1
0
0
1
0
0
0
0
1
0
1
1
1
1
1
1
2
0
0
2
1
0
0
0
0
0
0
0
2
1
1
0
0
0
0
1
1
0
1
0
3
1
0
0
2
1
0
1
0
3
0
1
2
0
0
0
0
2
0
2
2
1
2
1
0
2
2
0
1
4
2
1
1
0
0
1
2
1
2
0
1
1
0
0
1
1
0
2
1
2
1
1
1
0
0
0
1
0
2
2
1
1
0
2
0
0
0
0
0
2
0
1
2
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
3
0
1
1
1
0
1
1
0
1
2
1
3
1
1
2
1
2
1
0
0
0
4
1
0
1
0
0
0
2
3
1
1
0
0
0
0
2
1
0
1
2
1
2
2
0
0
1
1
1
1
0
0
2
2
3
1
2
0
1
0
1
2
0
0
1
1
1
2
0
0
0
2
1
1
0
0
0
0
1
0
0
0
1
1
2
1
0
1
0
0
2
2
1
0
2
0
1
0
1
1
1
2
1
1
0
1
1
1
0
0
1
1
3
0
0
1
0
2
1
0
2
0
1
0
2
2
1
0
1
0
0
0
1
0
2
1
0
2
2
0
2
1
1
0
0
2
1
0
1
1
0
0
0
0
1
1
0
2
0
2
1
1
0
1
1
2
1
0
2
1
2
1
0
1
1
0
0
0
0
1
0
0
1
0
0
2
1
1
0
0
2
2
1
0
0
1
2
1
0
1
2
1
2
0
2
0
1
0
0
0
1
1
0
0
0
0
1
1
0
0
2
1
0
0
5
1
0
1
1
2
1
2
1
0
2
2
0
2
0
1
0
0
2
0
2
0
2
2
0
0
1
1
2
2
0
1
2
0
1
0
0
1
0
1
0
0
1
4
0
2
1
4
2
0
1
1
2
2
2
1
1
1
1
0
1
0
0
2
1
1
0
4
0
2
2
1
0
0
0
2
1
2
0
1
1
2
2
0
1
0
1
3
0
1
0
1
0
0
1
2
1
0
2
0
1
0
0
0
0
2
1
1
0
1
0
0
1
1
1
0
0
0
1
2
1
2
2
0
2
0
0
1
2
1
0
0
1
0
1
2
0
0
1
2
0
0
2
1
1
1
1
1
0
0
1
1
0
2
1
0
1
0
0
0
0
1
0
0
1
0
0
2
0
1
1
0
1
1
1
1
1
0
1
2
0
2
0
2
2
1
1
0
0
2
1
2
2
0
0
0
0
1
0
1
0
0
0
1
0
1
0
2
0
0
0
1
0
2
1
0
1
0
2
0
1
2
1
1
1
1
1
1
0
1
1
1
2
1
0
1
2
1
0
1
1
0
2
0
0
0
0
1
0
0
1
2
0
0
0
1
2
0
1
2
2
1
1
1
1
1
1
0
0
1
0
1
1
1
0
1
1
1
0
4
1
1
2
1
1
1
2
1
2
1
0
0
0
1
1
0
2
0
0
2
0
2
0
0
3
1
1
0
1
1
0
1
0
0
1
1
2
1
2
0
0
2
1
0
2
0
1
0
0
1
0
1
0
1
1
0
2
1
2
0
1
0
1
2
1
1
0
1
0
0
2
0
0
0
0
2
2
2
0
0
1
0
3
0
0
0
0
0
0
1
0
1
1
0
1
2
2
0
1
1
0
0
4
0
1
1
1
2
0
1
1
1
0
1
0
0
0
1
2
1
0
0
0
1
1
1
2
0
2
0
0
2
0
2
2
1
2
2
0
0
0
2
0
3
0
1
1
1
2
1
0
1
0
1
1
0
1
1
4
0
1
1
0
2
0
1
0
2
1
0
1
0
1
1
1
0
0
0
0
1
0
0
1
2
2
0
0
2
2
0
2
1
0
1
0
1
1
2
1
0
1
0
0
2
4
1
1
2
0
0
1
2
1
2
1
2
1
2
0
2
0
2
0
3
1
1
1
1
0
0
0
0
2
1
0
0
0
0
1
1
1
0
0
2
1
0
1
0
2
1
0
2
2
0
1
1
2
1
0
1
2
0
0
1
0
1
1
1
1
1
0
0
0
1
1
3
0
1
2
2
0
0
0
0
1
2
0
0
0
0
0
1
0
1
2
1
2
2
2
1
0
1
0
0
1
1
1
0
2
1
0
2
0
0
0
1
2
3
1
0
0
2
0
0
0
1
0
0
4
0
0
0
0
1
1
1
1
2
2
2
0
1
0
1
0
2
0
0
1
0
1
1
0
0
1
1
0
1
0
0
4
0
2
1
0
0
0
1
1
0
1
1
1
1
1
0
1
2
2
1
0
1
1
0
1
0
1
0
1
2
0
1
1
2
2
0
0
0
0
0
0
2
2
3
0
0
0
0
1
2
1
1
2
1
0
0
2
2
0
0
2
0
0
1
0
0
1
1
2
2
2
2
0
1
1
1
4
0
0
1
1
1
0
1
0
0
1
0
2
2
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
2
1
0
0
0
0
0
0
1
1
1
1
2
1
2
1
2
0
0
2
1
0
1
1
2
0
2
0
1
2
0
1
0
1
0
1
0
1
1
1
0
2
1
2
1
1
1
0
0
1
1
1
0
2
0
0
0
2
0
2
0
1
0
1
0
0
2
1
1
1
1
0
0
0
0
2
0
0
1
0
2
0
2
1
0
1
1
1
1
0
2
0
2
2
0
1
2
0
0
0
2
0
0
0
2
0
0
1
2
1
1
0
0
0
0
0
0
1
0
0
1
2
1
0
2
0
2
0
2
1
0
2
0
0
1
1
1
0
1
0
1
2
1
0
0
0
0
1
1
2
0
1
0
2
0
2
2
2
1
0
2
0
0
1
1
1
1
2
1
0
2
1
2
1
2
2
2
1
1
1
0
0
2
0
0
0
2
0
1
1
0
1
0
0
1
0
0
1
1
2
3
1
0
1
1
0
2
1
0
1
1
0
1
0
0
1
0
1
1
0
0
2
1
1
2
1
1
2
2
1
0
0
1
0
1
0
1
0
0
0
1
0
2
2
1
0
0
0
2
2
2
0
1
1
2
1
1
1
0
1
0
1
0
0
0
1
2
1
0
1
0
0
0
0
1
0
1
2
0
2
0
0
2
1
2
1
1
1
0
3
2
1
0
0
0
0
0
1
1
1
2
2
2
0
1
2
2
1
1
0
1
0
0
2
0
1
0
0
0
0
1
2
0
2
1
0
2
0
2
1
0
1
0
0
1
1
0
2
0
0
2
0
0
0
1
1
0
0
2
2
2
1
1
0
0
2
1
2
3
1
0
0
0
1
0
2
0
0
0
2
1
1
1
1
1
0
1
0
1
0
1
0
0
0
1
1
0
1
0
2
1
1
0
0
2
0
0
0
0
0
1
0
1
2
1
0
1
0
1
1
0
1
1
1
1
0
0
1
0
0
2
0
1
0
1
2
0
0
1
2
0
0
0
1
2
0
0
2
1
0
2
1
1
0
2
0
2
2
0
0
1
1
2
0
0
1
1
0
2
0
1
0
0
0
2
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
3
2
0
0
0
0
2
2
0
0
1
1
3
0
2
3
0
0
0
1
1
1
1
2
1
0
2
0
1
1
0
0
1
0
7
1
1
0
1
2
1
2
2
2
0
0
1
2
6
0
0
2
1
0
0
1
0
1
2
1
1
1
1
1
0
1
2
2
1
1
2
0
0
2
2
2
1
2
0
0
2
1
2
1
2
0
1
1
2
0
1
1
1
1
1
1
1
2
1
0
2
1
0
0
1
1
0
1
0
0
0
0
0
1
0
0
2
1
0
2
1
0
1
0
0
2
0
2
0
0
0
2
0
1
0
0
1
0
1
2
1
0
1
2
0
0
2
1
0
1
1
0
1
1
2
0
1
1
1
0
2
0
2
1
1
0
2
1
0
0
0
2
0
0
2
1
2
0
0
0
1
0
0
0
0
2
1
0
1
1
2
2
1
0
1
1
0
2
0
0
0
1
1
2
2
0
0
0
2
1
2
0
1
1
1
1
1
0
2
1
1
0
0
1
2
0
1
0
1
1
1
1
1
1
2
2
0
0
0
2
1
1
1
1
2
0
1
1
2
0
0
2
1
0
1
2
0
2
2
2
1
1
2
1
2
1
0
2
1
0
1
0
0
1
0
0
0
0
1
0
1
2
0
1
2
0
1
0
1
1
0
0
0
1
2
1
2
1
1
0
0
2
2
2
0
1
0
4
0
0
1
0
1
1
1
2
2
0
0
0
2
0
2
2
1
0
1
1
0
1
0
2
2
2
1
0
1
1
2
0
0
0
2
0
0
0
2
1
0
1
0
1
1
1
2
0
0
0
1
0
0
0
0
0
0
2
0
1
0
1
2
2
1
0
0
0
2
0
0
1
2
1
2
0
2
0
2
1
1
1
1
1
1
0
1
0
1
1
2
1
3
2
0
1
2
0
1
0
2
2
2
0
3
0
0
0
0
2
0
0
2
0
0
0
0
0
1
1
0
1
1
0
2
0
0
0
0
1
2
1
2
1
0
1
0
0
2
1
1
0
3
1
2
2
2
0
0
0
2
0
0
0
0
0
1
0
1
2
1
0
2
1
1
2
2
0
2
3
0
1
1
1
0
2
1
0
1
1
2
2
0
1
0
1
1
1
1
2
0
1
2
1
2
3
0
1
0
3
1
1
2
0
0
0
0
2
1
1
0
0
1
0
0
2
1
0
0
0
0
0
2
0
0
0
3
0
0
0
1
0
0
2
0
1
2
2
1
0
1
1
0
1
0
0
1
0
0
1
2
0
0
0
2
1
2
2
2
0
1
0
0
0
2
1
1
2
1
0
1
0
0
0
1
3
0
0
1
0
1
1
0
0
0
0
0
1
2
0
2
1
0
1
1
0
1
2
0
1
0
2
2
1
0
1
2
0
0
1
0
2
1
1
1
1
2
2
0
2
1
2
2
0
2
1
0
0
2
1
0
2
1
0
2
0
1
0
2
1
1
1
1
0
0
2
0
1
0
0
0
2
1
0
1
1
1
2
2
1
1
0
2
0
1
0
1
0
1
1
0
1
1
0
0
0
2
1
2
0
0
2
1
1
2
2
1
1
0
0
1
0
1
0
2
1
2
0
0
1
1
2
1
2
1
1
1
0
0
1
0
0
1
0
2
1
0
2
2
0
1
1
0
0
0
1
0
2
1
0
1
0
2
2
0
0
1
0
0
1
1
2
2
0
2
0
1
1
0
0
0
0
1
0
0
2
0
2
1
1
0
1
2
2
1
2
2
0
2
0
2
0
0
0
0
0
0
0
0
2
1
1
0
0
0
2
3
1
1
1
2
2
0
0
2
1
1
1
0
1
1
1
0
3
0
0
0
0
0
2
0
1
1
0
1
0
1
0
1
0
2
2
1
0
1
1
0
0
0
0
0
0
0
1
1
2
0
0
1
1
0
0
1
0
2
1
0
2
1
2
1
2
0
0
0
2
2
1
0
2
0
1
0
0
4
0
1
1
0
1
1
2
0
0
1
0
0
1
1
1
0
1
0
0
1
1
1
1
3
0
2
2
0
0
0
1
0
2
0
2
3
0
2
0
0
2
0
2
0
0
0
0
1
1
1
1
2
0
0
1
1
0
0
1
2
1
0
0
2
1
0
1
2
0
2
4
2
2
2
0
2
1
2
2
1
1
1
1
2
2
0
1
0
0
0
0
0
1
1
1
0
2
1
2
1
1
0
0
1
1
0
2
3
0
0
0
1
2
1
0
0
0
0
1
2
2
1
0
2
2
0
0
0
1
0
2
2
0
0
1
0
0
0
1
1
1
1
1
0
0
0
0
0
0
2
0
0
1
0
0
0
1
1
1
1
1
1
1
2
2
1
0
0
2
0
1
0
2
0
1
2
1
2
1
1
0
1
1
2
1
2
1
0
0
1
1
0
0
0
0
1
0
2
0
0
0
2
1
2
1
0
1
0
2
2
2
1
3
0
0
5
2
2
0
0
1
1
2
0
1
1
0
2
0
1
2
1
0
2
0
1
0
0
0
1
2
1
0
0
2
1
2
2
1
0
2
1
0
0
0
0
1
0
2
1
2
1
1
1
1
0
1
0
0
2
0
0
0
0
2
2
0
0
1
2
0
1
1
2
1
0
1
0
1
2
1
1
0
0
0
0
0
0
0
0
1
0
2
3
2
0
2
0
2
2
1
0
2
2
1
0
0
0
0
2
0
0
2
1
1
0
2
1
1
0
2
1
0
2
0
0
1
1
0
1
2
0
1
1
1
1
1
0
1
3
1
0
0
0
0
0
2
1
0
0
1
1
0
1
2
0
1
1
2
1
1
2
0
1
0
1
0
0
0
0
0
2
0
1
2
0
1
0
1
0
1
0
1
2
2
1
0
0
2
0
2
0
0
1
1
1
0
0
1
0
0
0
1
0
1
2
0
0
0
0
2
1
2
1
0
2
1
2
1
1
1
1
0
0
0
0
1
0
0
0
1
0
1
2
1
1
0
1
1
2
1
0
1
2
2
1
2
0
2
0
0
2
1
1
0
2
0
1
1
1
1
0
2
0
2
1
1
0
0
1
0
1
2
1
1
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
1
2
1
0
1
1
1
0
0
3
2
1
2
1
1
0
0
1
2
1
0
2
0
1
1
1
0
0
0
1
0
0
1
3
1
0
0
0
0
1
1
1
0
0
1
1
0
1
2
1
0
0
0
0
0
0
1
1
0
1
2
1
0
0
1
0
2
1
1
0
1
1
0
1
1
3
0
1
0
2
1
1
2
0
2
0
1
1
0
2
0
1
0
1
2
1
0
2
1
1
1
1
0
1
1
0
1
1
1
0
0
2
0
2
0
1
0
0
1
0
1
3
1
0
0
0
2
1
1
0
1
0
0
0
1
1
0
0
1
0
1
2
2
0
1
1
1
0
0
2
2
1
1
1
3
0
1
0
1
3
0
1
0
0
2
2
2
1
0
1
2
0
1
1
1
2
0
0
0
1
1
2
0
2
0
1
0
1
2
2
0
1
1
0
0
1
1
1
0
0
0
0
1
2
2
0
2
1
1
0
0
2
1
1
0
0
0
1
1
0
0
2
0
0
1
0
1
1
1
0
0
1
0
0
0
1
2
1
2
0
2
2
0
1
1
1
0
1
2
4
0
0
1
0
1
2
1
2
0
1
0
2
0
1
1
1
1
0
1
1
1
0
0
2
0
0
0
0
1
2
0
2
1
0
1
0
0
2
0
0
0
1
2
0
2
0
1
0
1
1
1
2
0
0
3
1
0
0
1
0
1
0
0
2
0
1
2
0
1
0
0
0
0
2
1
1
1
0
0
2
0
1
0
2
1
0
0
0
1
0
5
0
1
0
0
0
1
1
0
2
2
3
0
1
0
2
0
2
0
2
0
1
0
1
0
1
2
2
1
1
2
2
1
0
1
0
1
1
1
0
1
1
0
1
1
2
1
2
0
0
1
2
0
1
0
0
1
1
0
3
0
3
1
1
1
0
0
0
2
0
1
1
1
1
1
1
0
1
2
0
0
3
1
2
0
2
1
0
0
1
2
0
0
1
1
0
1
0
0
0
2
0
0
2
0
1
2
0
0
2
1
0
1
2
1
2
2
0
1
0
0
0
0
1
0
1
0
0
0
2
1
1
1
1
0
1
2
2
0
0
1
0
0
0
1
2
2
0
2
1
2
0
0
2
0
0
1
0
1
2
0
0
1
0
1
2
1
1
1
1
0
2
0
0
1
0
1
3
1
2
2
0
1
0
1
2
1
2
1
2
4
1
2
1
1
2
1
1
0
0
0
0
2
1
0
0
0
1
1
1
1
1
0
1
2
2
0
1
0
1
0
2
2
2
0
0
0
2
0
1
0
1
0
1
0
1
0
0
1
1
0
1
2
1
2
0
0
1
2
1
0
1
1
2
1
0
1
2
0
1
2
1
1
1
0
0
0
2
2
1
0
1
0
0
2
1
2
1
1
0
0
2
2
1
1
0
1
2
0
0
2
0
2
0
1
0
1
0
0
0
1
1
0
1
1
0
0
0
2
0
1
0
2
1
1
0
1
1
0
0
2
1
0
0
1
0
2
1
0
1
1
0
1
0
1
1
3
2
0
0
0
1
0
1
2
0
0
0
1
0
0
0
0
1
0
1
1
0
0
2
0
1
3
0
1
1
1
1
0
0
1
0
1
0
0
1
0
1
2
1
2
0
0
0
0
1
1
0
0
0
0
1
0
1
0
1
2
1
0
0
1
1
0
1
1
0
0
1
1
0
0
0
2
0
2
2
1
1
1
1
2
1
1
1
0
0
2
0
2
0
0
1
0
1
0
0
2
2
1
0
0
1
0
2
0
1
0
0
2
1
1
0
2
1
0
1
0
2
1
1
2
0
0
1
0
0
3
2
2
0
0
0
0
0
1
1
1
0
0
0
0
1
2
2
1
1
2
0
1
0
0
0
0
0
1
0
1
0
1
0
0
2
0
0
2
0
3
2
0
1
0
0
0
1
1
1
0
1
2
2
0
2
0
1
2
0
1
2
1
0
1
2
2
0
1
0
3
1
2
0
2
1
1
2
1
2
1
1
0
1
0
2
2
0
1
2
2
1
2
0
1
2
1
0
1
2
0
0
2
0
1
2
2
0
3
0
0
0
1
0
0
0
0
1
1
0
1
3
0
0
2
0
0
0
1
2
2
2
0
1
1
2
2
1
2
1
2
1
1
2
2
0
0
1
0
1
0
0
0
2
0
1
7
2
1
0
0
1
1
0
0
1
1
1
1
0
0
1
1
0
2
1
1
0
0
0
0
0
0
0
0
2
1
1
1
1
0
2
2
1
0
1
0
0
2
0
0
0
2
0
2
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
1
1
2
0
1
1
2
0
0
0
1
2
0
1
1
2
0
1
1
1
2
3
1
2
1
0
0
0
0
0
0
0
1
1
2
0
0
0
2
1
1
0
1
1
2
1
1
1
0
1
1
1
1
0
1
1
1
0
2
0
0
1
1
2
0
0
0
0
1
2
1
0
0
1
2
0
1
0
0
0
1
0
2
0
1
1
1
0
1
2
1
2
1
0
0
0
1
0
1
1
1
0
2
0
1
0
1
0
0
0
0
1
1
0
1
0
2
1
0
0
1
0
0
2
2
0
0
0
2
1
0
2
0
1
3
0
0
2
2
1
2
0
1
1
1
0
2
2
1
1
3
1
1
0
0
2
1
0
2
0
1
2
0
0
3
0
0
1
0
0
1
0
1
2
0
0
0
2
0
1
1
1
2
1
0
1
0
1
0
0
2
2
1
2
0
0
2
1
1
0
1
2
0
1
0
0
0
1
1
0
3
0
2
1
2
0
1
1
0
1
1
2
1
1
1
0
1
1
1
2
0
1
0
2
0
1
2
0
1
0
1
2
1
1
0
0
1
2
0
0
1
2
0
0
2
1
1
1
1
0
3
2
1
3
2
1
1
0
0
0
0
0
1
0
0
1
1
0
0
0
2
0
0
0
0
2
0
1
0
0
2
0
0
1
1
2
0
2
1
1
1
0
2
0
0
2
1
0
2
2
0
0
1
0
2
2
0
0
1
0
2
2
0
1
1
0
1
0
1
1
1
1
0
1
0
1
1
1
0
0
0
0
1
2
2
0
2
1
1
2
0
1
2
1
0
0
0
0
1
2
0
0
1
1
1
1
0
1
2
1
2
0
1
1
1
0
0
1
1
0
0
2
0
2
1
0
0
0
0
1
1
1
2
3
0
1
1
1
1
1
0
0
0
0
0
1
0
1
0
0
0
0
2
1
2
1
0
0
0
1
0
1
1
1
0
2
2
1
1
0
1
0
1
0
1
0
0
2
1
1
0
0
0
1
0
0
0
2
0
1
0
1
0
1
0
0
0
1
0
0
1
0
2
0
1
2
0
0
0
1
0
1
0
4
2
1
0
0
0
1
0
0
2
1
1
1
0
1
2
1
1
2
2
0
0
0
1
1
0
1
1
0
0
0
0
1
2
0
3
2
2
1
0
2
0
1
1
0
1
2
0
2
1
2
1
0
1
1
2
0
1
0
0
1
1
1
0
1
2
1
0
0
0
0
0
0
0
2
0
2
0
1
1
1
0
1
2
1
1
2
2
1
0
1
0
0
1
0
0
1
1
1
0
2
0
1
1
0
1
2
1
1
0
1
2
1
0
2
1
1
0
1
0
0
0
0
1
1
2
0
2
0
1
2
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
2
0
1
1
0
0
2
0
0
1
0
2
1
1
1
0
0
0
0
1
1
0
1
2
2
0
0
1
0
2
0
2
0
0
0
2
1
0
2
2
2
0
1
2
1
1
0
0
1
0
1
0
2
0
1
2
2
1
0
0
2
2
2
1
2
1
0
1
2
0
2
2
0
0
1
0
1
2
1
0
1
1
1
1
0
0
1
2
0
2
1
2
0
0
1
2
1
0
2
0
0
0
0
1
0
1
1
0
1
1
2
0
0
2
4
1
0
0
1
0
0
1
2
0
0
1
3
1
0
1
0
1
0
2
2
0
0
0
1
0
1
2
1
0
0
1
1
1
2
1
0
1
1
2
0
2
0
0
1
0
0
0
0
2
1
0
1
1
1
2
2
1
0
0
0
1
2
2
1
1
2
1
0
0
1
2
0
0
0
1
2
1
0
1
0
0
1
2
0
0
1
2
0
1
0
1
1
0
0
2
0
2
1
1
2
2
0
0
1
0
2
2
0
2
1
0
1
2
1
0
1
0
0
1
1
1
1
0
1
0
2
0
0
0
0
0
1
1
0
1
2
1
0
0
1
0
1
1
0
2
0
2
2
0
0
0
2
1
2
0
2
0
0
2
1
0
0
1
1
0
0
2
1
0
1
0
1
1
0
1
1
1
0
1
0
0
1
2
1
1
0
0
0
0
0
0
0
0
1
1
1
1
1
1
2
2
0
1
0
3
0
2
2
2
1
1
2
2
1
1
0
0
1
0
1
1
2
0
1
1
1
0
0
1
2
0
1
0
0
2
0
0
1
2
1
0
0
0
0
1
1
0
1
0
0
0
2
2
2
2
0
0
0
1
1
1
1
1
0
1
2
1
2
0
0
0
0
0
0
0
1
1
1
1
1
0
0
1
1
0
1
1
0
2
0
2
1
0
0
1
0
2
2
0
1
2
2
0
0
2
2
0
4
0
0
0
1
1
0
1
0
0
0
0
1
1
1
1
0
1
2
1
2
0
0
1
1
2
1
0
2
0
0
0
0
1
0
1
1
1
2
1
1
0
2
0
0
0
2
1
0
0
0
2
2
0
1
0
0
1
0
1
0
0
1
1
1
1
0
1
1
0
1
0
1
1
1
2
2
1
0
1
2
2
0
1
2
1
0
2
0
1
0
2
1
1
0
0
1
0
2
2
1
0
2
1
0
2
2
1
0
0
0
0
0
0
2
1
1
0
0
1
2
0
0
0
1
1
1
1
0
0
0
1
1
1
1
1
0
1
2
2
1
2
1
1
0
0
2
2
1
1
0
0
2
1
1
1
1
1
0
1
1
1
0
0
0
2
1
2
1
1
0
0
2
0
2
0
1
1
0
1
0
1
0
0
1
0
1
2
1
0
2
2
1
0
1
0
1
3
2
0
2
0
1
2
1
1
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
1
0
0
1
1
0
1
1
0
1
0
1
1
1
2
2
1
1
0
2
1
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
2
1
0
1
0
0
1
0
0
2
0
0
1
0
0
1
0
0
2
0
1
1
2
0
0
0
1
2
0
2
0
0
1
2
1
1
0
2
1
0
1
0
2
0
1
0
2
0
2
1
2
0
0
0
0
1
1
2
0
0
1
0
2
0
0
1
1
1
0
0
0
2
0
2
1
1
7
0
1
1
0
1
1
2
1
0
1
0
4
0
1
1
1
0
0
1
2
0
1
2
0
0
0
4
1
0
2
1
0
1
1
1
0
0
1
0
0
1
0
1
1
0
2
1
1
1
1
1
1
1
0
0
0
1
0
1
0
0
0
0
0
0
1
2
0
0
2
0
3
2
0
0
1
0
1
1
1
2
1
1
0
2
2
0
3
0
2
0
0
1
1
1
2
0
2
2
1
0
1
0
1
2
2
0
2
2
0
0
0
2
1
2
1
1
0
2
2
2
1
4
1
0
0
0
0
1
1
2
1
0
1
1
0
2
1
2
2
2
0
2
1
0
1
0
1
0
1
1
1
1
0
1
0
1
0
2
1
0
1
0
1
0
2
0
1
1
1
0
1
0
0
0
0
0
0
1
0
2
0
1
1
1
0
0
0
4
0
0
2
1
0
0
2
2
1
3
1
1
0
2
0
0
0
0
2
0
0
2
1
2
1
2
0
0
1
0
1
1
2
1
1
2
0
0
2
1
1
2
1
0
0
1
1
0
0
1
0
0
1
0
2
0
0
0
3
1
1
0
2
0
1
1
0
1
0
1
1
0
1
0
1
1
2
2
0
1
0
0
2
2
0
0
0
2
0
0
2
0
2
0
1
0
0
1
0
0
1
0
1
3
2
1
0
1
2
1
1
0
2
2
1
1
1
2
0
0
0
1
1
0
0
1
0
1
2
1
1
0
1
0
0
2
1
2
0
1
1
0
0
0
2
0
0
1
1
0
1
1
2
1
1
0
2
2
0
0
1
0
0
1
0
1
1
2
2
0
0
0
0
1
0
2
1
0
1
1
2
2
0
1
1
0
1
1
1
2
0
2
1
1
0
1
1
1
2
1
0
0
4
0
1
1
0
1
2
1
0
0
0
1
2
1
1
1
0
1
1
0
2
3
0
0
1
1
0
0
0
1
0
0
0
2
0
0
2
0
2
2
1
2
0
1
2
0
2
0
0
1
0
0
0
0
1
0
1
1
3
1
0
1
2
1
2
0
1
0
2
0
0
0
0
1
2
0
1
1
1
1
0
0
1
2
0
2
0
2
0
0
2
0
1
1
0
0
0
1
1
0
0
1
0
0
2
0
0
1
2
1
1
0
1
1
1
0
1
2
2
0
1
1
0
0
1
0
2
1
1
2
2
1
0
0
1
0
2
0
2
2
1
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
1
1
2
1
0
0
0
4
1
2
1
0
1
0
1
2
2
0
0
2
1
0
0
1
2
0
1
2
1
0
1
1
1
1
0
0
0
0
0
0
0
2
2
1
2
2
0
0
0
1
0
0
0
0
1
0
2
1
0
1
0
0
1
1
2
1
0
2
7
0
1
0
1
2
0
0
0
2
0
0
2
1
0
2
0
1
2
2
2
2
0
1
0
0
2
0
1
1
0
2
0
1
1
0
0
0
2
2
1
1
1
0
1
0
1
0
0
1
2
2
1
0
0
0
0
0
0
2
0
2
1
0
2
0
0
2
0
2
0
2
0
1
0
0
0
0
1
1
0
0
1
0
1
2
1
2
0
2
2
2
1
1
1
0
1
1
0
1
1
1
1
0
2
0
1
2
1
0
0
2
0
0
2
0
1
0
2
0
0
1
0
0
2
0
0
0
0
2
0
0
1
1
0
1
2
1
0
0
1
0
1
1
0
2
1
0
1
0
1
0
0
0
0
1
2
0
1
0
2
0
2
0
1
2
0
1
0
0
2
1
0
1
0
1
1
1
0
0
0
0
2
2
1
1
0
0
0
0
1
2
1
1
0
1
0
0
0
0
1
2
0
1
0
2
2
1
0
2
2
1
2
1
1
1
0
0
1
1
0
1
1
2
1
0
1
1
0
0
0
0
1
0
1
1
1
0
1
0
0
1
0
0
2
1
1
2
3
3
0
0
0
0
0
2
1
2
0
0
0
0
1
1
0
0
2
1
1
1
2
1
0
0
0
2
0
0
0
1
1
0
1
0
0
0
2
1
0
1
0
0
2
1
0
1
0
1
0
0
1
0
1
1
2
2
1
1
0
1
0
1
2
0
0
0
1
1
0
0
2
0
0
0
0
1
0
0
0
0
0
1
1
0
1
2
1
0
0
1
0
1
0
0
0
0
1
2
0
0
2
1
0
0
1
0
1
0
1
2
0
1
0
1
1
1
1
2
0
0
2
2
2
2
2
0
1
0
1
0
0
2
2
0
1
1
1
1
0
0
1
0
2
1
0
2
1
2
1
0
1
0
1
0
2
0
0
0
2
1
1
1
1
2
4
0
0
0
1
1
2
2
1
1
1
0
1
1
1
0
1
1
3
0
0
1
1
1
0
1
1
0
0
1
1
2
1
0
0
0
1
2
0
2
0
1
2
0
0
2
1
1
0
1
2
0
0
0
1
1
1
1
1
0
1
2
1
0
0
1
2
1
0
2
2
2
3
1
2
0
1
1
1
0
2
0
0
1
1
2
0
0
2
1
2
1
0
1
2
0
1
0
0
2
0
0
2
0
2
0
2
2
2
0
0
1
0
0
1
2
1
0
1
2
1
1
1
0
0
1
2
2
2
1
2
0
0
1
1
2
1
0
0
1
1
1
0
0
0
1
1
0
0
0
0
2
1
0
2
0
1
2
1
2
0
1
0
0
0
0
1
0
0
0
1
1
0
0
1
2
1
1
0
0
0
1
2
0
0
0
1
1
1
2
0
1
0
0
0
0
3
1
3
1
1
0
1
0
0
0
2
2
2
0
0
2
0
1
1
2
6
0
1
1
2
0
1
1
0
0
2
1
1
0
0
2
1
1
0
0
1
1
1
1
0
1
1
0
1
2
1
0
1
2
1
0
1
0
1
0
0
1
1
1
2
1
1
1
0
0
2
0
0
1
0
1
0
0
0
1
0
0
1
2
1
0
2
0
1
1
2
1
1
1
1
1
1
2
0
0
0
0
0
2
0
0
0
1
1
0
2
2
2
2
1
1
1
0
1
1
0
0
0
2
2
0
3
0
0
0
1
1
2
0
1
0
2
1
2
3
1
0
2
2
1
0
2
1
1
0
0
1
0
2
0
0
1
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
2
16
1
1
0
0
1
0
0
0
0
2
0
1
0
0
1
0
0
1
1
0
1
0
3
1
1
1
0
0
1
1
0
1
0
2
1
2
0
0
1
1
0
2
0
2
2
0
1
0
0
1
0
2
1
1
1
1
0
0
2
1
0
1
2
1
1
0
1
1
1
1
1
2
1
0
0
0
2
1
0
0
0
0
2
2
1
0
0
0
0
1
2
1
0
1
1
2
0
1
2
0
1
2
1
1
0
2
1
1
0
1
0
0
1
0
1
2
0
2
0
1
0
1
2
3
1
1
0
2
1
2
0
2
2
1
2
0
0
0
1
2
1
1
2
0
1
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
1
1
2
1
1
0
2
0
2
0
1
1
0
1
0
0
1
2
0
1
1
0
2
1
0
2
2
1
1
1
0
1
1
1
1
1
0
1
1
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
2
0
0
0
0
1
1
0
1
0
1
0
1
1
0
2
2
2
1
1
0
0
2
3
2
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
2
1
0
1
1
0
1
2
3
1
1
0
1
0
1
0
0
0
2
0
1
1
0
0
2
0
1
2
1
1
2
0
2
2
1
2
1
1
0
1
0
0
0
2
0
0
0
1
1
0
2
1
0
0
3
1
1
0
0
1
0
0
1
1
1
1
0
1
0
0
0
0
0
1
0
2
0
0
0
1
0
0
1
1
1
1
2
0
2
0
0
2
2
0
2
0
0
0
2
1
0
0
0
1
0
1
0
1
0
1
0
1
0
0
2
0
2
0
2
0
2
0
1
0
0
1
0
0
1
1
1
2
2
0
1
1
1
0
2
1
0
0
1
0
0
0
0
1
0
2
2
1
1
1
5
0
1
3
0
1
0
1
1
1
1
0
0
0
1
2
2
1
1
2
1
0
0
1
0
0
0
2
1
0
0
2
0
1
1
0
0
1
0
1
2
0
0
1
0
0
1
0
2
2
1
1
2
0
1
0
4
0
1
0
2
1
1
0
1
0
1
0
2
0
0
1
0
0
0
1
2
0
1
1
0
0
0
2
0
0
2
1
2
1
0
1
2
1
0
0
0
1
1
2
0
0
2
1
0
0
2
0
1
1
2
0
2
1
0
1
1
0
2
1
2
1
1
0
0
1
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
2
0
0
1
0
1
2
1
2
1
0
0
1
0
2
0
0
0
0
1
0
1
1
1
0
1
2
0
0
0
1
2
1
1
0
1
0
1
3
0
2
1
0
0
0
0
0
0
0
2
0
1
1
1
2
0
0
1
0
0
3
3
0
0
1
0
0
2
1
0
1
0
0
2
0
1
1
0
1
0
1
0
1
0
1
0
2
2
2
1
0
1
0
1
1
0
0
1
1
2
0
0
9
1
0
2
0
0
2
1
0
1
0
2
0
1
2
0
2
1
1
2
3
5
0
0
2
0
0
2
1
2
0
0
2
1
1
0
0
0
2
0
0
1
0
2
1
2
0
0
0
1
1
2
2
0
1
1
2
1
0
0
1
1
1
2
0
1
1
0
2
4
2
2
0
0
0
0
0
1
0
2
2
1
1
2
0
2
1
0
1
0
0
2
1
0
2
0
0
0
1
2
2
0
1
2
0
0
0
2
0
2
0
0
0
2
2
2
0
2
2
2
2
1
1
1
0
0
3
2
0
1
1
0
2
0
1
3
1
1
0
0
1
0
0
1
0
0
2
2
1
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
1
1
1
1
1
0
0
0
0
2
0
1
1
1
1
2
1
0
0
0
1
1
0
1
0
2
1
1
0
0
2
1
2
1
2
1
1
1
0
0
1
0
0
1
2
0
0
1
0
1
0
2
1
1
1
1
1
0
0
1
0
1
0
1
2
0
2
2
1
0
1
1
2
0
0
0
1
1
0
0
1
1
0
1
0
1
1
1
0
1
2
1
2
2
2
0
0
1
2
1
1
2
0
1
0
1
1
1
0
0
1
0
0
0
0
2
0
1
1
1
2
1
2
2
2
0
0
0
0
1
1
0
3
0
1
1
0
1
1
0
0
1
1
1
0
0
1
0
3
0
0
0
0
1
0
3
0
0
0
0
1
2
1
1
2
0
2
1
2
0
0
2
1
2
1
2
1
0
0
1
2
2
1
1
0
1
1
2
1
0
1
0
2
0
0
1
2
1
0
1
0
1
2
0
0
1
0
2
1
0
0
0
1
0
1
1
0
0
0
2
2
1
0
0
1
0
0
2
1
0
1
0
0
0
0
0
0
1
1
0
1
0
1
0
1
0
2
1
0
1
0
3
2
0
0
0
2
1
1
0
1
0
2
1
0
1
2
1
1
2
1
1
0
1
2
3
1
2
2
2
0
2
2
1
0
2
1
1
0
2
1
2
0
0
1
1
1
1
1
0
0
2
1
0
0
2
0
1
1
1
2
1
1
1
0
0
2
3
0
0
1
1
2
0
0
1
0
0
1
2
1
1
0
1
0
1
0
2
0
2
1
0
2
2
1
0
1
0
1
1
1
1
0
2
1
1
1
1
0
0
2
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
1
0
0
1
3
2
0
0
1
1
2
1
2
2
1
0
0
0
2
0
0
0
1
0
0
2
2
2
1
1
4
1
0
2
0
1
2
1
0
1
2
1
1
0
0
2
1
2
0
1
0
1
2
2
2
2
1
1
2
1
0
0
2
0
2
2
1
0
1
0
0
1
0
0
1
1
0
2
1
0
1
2
0
1
2
2
0
1
0
2
0
0
1
2
0
2
0
0
0
1
0
5
1
1
0
0
1
1
1
2
1
0
1
1
0
0
1
1
2
1
3
0
1
1
2
0
1
0
1
0
0
1
1
1
1
1
1
0
2
1
2
2
2
0
2
2
0
0
1
2
0
1
2
0
0
2
0
2
1
0
2
2
0
0
1
0
0
0
1
0
1
1
0
2
0
2
1
1
2
2
2
0
1
0
0
0
0
1
1
1
1
2
0
0
0
1
0
1
1
0
4
0
2
2
1
0
0
0
0
1
0
2
1
0
0
0
1
0
0
1
0
1
0
2
1
0
0
2
0
0
2
1
0
1
0
1
1
0
0
2
2
0
2
0
2
0
1
1
0
0
2
2
2
0
0
2
2
0
0
2
1
1
0
0
0
1
2
0
1
0
0
2
0
2
2
0
2
1
2
1
2
0
1
0
1
1
1
1
0
1
0
3
0
0
1
0
0
1
0
0
0
0
0
0
1
0
2
2
1
2
1
2
1
1
1
0
2
1
1
1
1
0
1
1
0
0
2
0
1
0
0
0
0
1
0
1
0
2
0
2
0
2
0
0
0
0
0
1
1
1
0
1
0
0
0
1
2
1
2
2
2
2
2
1
3
0
1
0
1
1
0
0
1
0
2
1
1
0
0
0
2
1
1
1
1
0
1
1
0
2
0
0
0
0
2
0
1
0
1
0
2
0
2
2
0
0
0
0
1
1
0
0
1
0
0
2
1
2
0
0
1
2
1
0
2
2
0
2
0
0
0
1
1
1
0
1
0
1
1
0
0
0
0
1
2
2
3
2
0
0
1
2
1
0
0
1
0
2
0
1
2
1
0
1
1
0
1
2
0
0
2
0
0
2
1
0
1
0
2
0
2
1
1
0
0
3
0
0
4
0
2
1
0
0
2
1
0
0
1
2
1
1
1
1
2
2
0
1
0
2
2
1
1
1
0
2
1
0
0
0
1
0
1
1
0
1
1
0
0
0
2
2
1
1
1
2
0
2
1
2
1
0
1
0
0
1
2
0
0
0
1
1
1
2
0
1
1
0
1
1
0
2
0
0
0
0
1
0
0
0
2
0
0
1
0
2
0
1
0
0
0
0
1
0
0
1
0
2
0
2
3
0
0
1
2
1
1
0
1
1
1
0
2
0
1
2
0
1
1
2
2
1
0
0
2
0
1
0
0
0
1
0
2
0
1
2
1
0
0
1
0
0
0
1
2
0
1
0
2
0
0
0
1
0
0
1
2
0
1
1
1
2
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
2
1
0
0
2
0
1
2
0
1
1
0
0
0
1
1
3
1
1
1
2
0
1
1
1
1
1
1
1
1
1
0
0
1
1
2
0
0
2
1
2
1
0
0
1
1
1
0
3
0
0
2
1
1
0
2
0
2
1
1
0
0
2
0
0
0
2
0
0
0
1
0
1
0
0
0
2
2
0
0
0
1
1
0
2
0
1
1
2
2
0
2
1
0
1
0
1
0
3
1
0
1
0
0
1
0
1
0
1
0
1
0
2
2
1
2
0
1
2
1
0
0
1
0
0
0
2
0
2
2
0
0
1
0
4
2
1
2
2
1
0
0
3
0
1
1
0
0
0
0
0
0
2
2
0
0
0
2
2
1
2
1
2
0
1
2
2
0
0
1
0
1
1
0
1
0
0
1
0
1
0
0
2
1
1
1
1
1
0
1
0
0
2
0
0
0
1
1
1
2
0
1
0
1
0
0
0
0
0
0
1
0
2
0
1
0
0
2
0
0
1
1
2
1
0
0
1
0
0
0
2
0
1
0
1
0
0
0
1
2
1
1
0
0
1
1
0
2
0
0
1
0
0
1
0
0
2
0
2
0
1
0
0
0
0
0
1
1
0
0
2
1
0
0
0
1
2
0
0
2
0
0
0
0
0
0
1
0
1
1
1
2
1
1
1
0
1
1
1
2
2
1
0
0
1
1
0
1
2
0
2
0
2
0
0
1
2
0
0
0
0
0
1
2
1
1
1
0
0
0
1
2
1
2
0
0
0
1
2
0
3
0
0
1
2
1
2
1
2
0
1
2
1
1
0
2
2
1
0
2
2
0
0
1
2
1
0
4
2
1
2
1
2
1
2
0
0
1
0
2
1
1
1
0
1
0
0
0
2
0
0
1
1
1
0
1
0
0
0
0
0
0
1
1
0
2
0
0
2
1
2
2
2
0
0
1
1
0
1
2
0
2
0
2
0
2
1
0
2
2
0
0
0
2
3
0
1
0
2
0
0
0
1
1
1
1
1
1
1
2
0
1
1
2
1
2
1
0
2
0
1
2
2
0
1
0
1
1
2
0
1
1
1
1
0
1
1
1
0
0
1
1
0
0
0
1
0
0
2
3
4
4
0
3
2
0
1
1
1
0
1
0
1
2
2
0
2
0
0
2
1
0
2
0
1
0
0
0
1
2
2
2
1
0
0
1
2
0
2
1
2
4
2
1
0
1
0
1
1
0
0
2
1
1
0
0
1
1
0
0
0
0
1
1
1
0
0
1
0
2
0
1
1
2
0
0
0
0
2
2
3
1
2
1
1
1
2
1
0
1
0
1
1
0
2
1
0
2
1
0
0
1
0
2
1
1
1
0
1
0
2
0
1
2
0
1
0
0
1
1
0
0
1
1
0
1
0
1
1
1
1
0
0
0
1
1
1
1
0
0
2
0
1
1
0
0
1
0
1
0
1
1
1
0
1
0
0
1
2
2
0
1
0
0
1
2
1
2
0
2
0
0
0
0
1
1
0
1
0
1
0
3
1
1
1
0
1
2
1
4
1
0
1
0
1
2
1
0
1
0
0
2
1
1
1
2
1
2
1
0
4
2
2
0
2
2
0
0
1
2
2
1
2
1
0
2
0
1
1
0
0
0
0
1
2
1
2
0
1
1
0
0
2
2
1
1
0
2
0
1
0
0
0
0
1
2
2
0
1
1
0
1
0
2
0
0
0
0
0
1
2
2
2
2
0
0
1
0
1
0
0
2
0
0
1
2
3
0
1
2
0
0
0
0
1
1
0
1
1
0
0
1
1
2
0
0
1
0
1
0
1
0
1
2
1
0
0
1
1
0
1
1
0
0
1
0
1
0
1
0
2
1
0
0
1
0
0
0
0
0
1
2
0
1
0
3
1
1
2
0
0
2
0
1
1
1
1
1
1
1
0
2
0
0
0
1
2
2
0
0
0
0
2
0
2
1
1
0
0
1
1
0
1
2
1
0
1
2
0
0
2
1
1
1
0
1
1
0
2
2
1
0
0
2
1
0
0
0
1
3
0
1
2
1
1
2
2
0
3
2
1
2
2
1
2
1
0
0
0
0
0
0
0
1
2
1
0
0
2
2
2
1
0
2
1
0
0
2
1
2
1
2
0
2
1
0
2
0
1
0
0
5
2
0
0
1
1
2
1
0
0
0
1
0
1
0
2
2
0
0
0
2
0
1
1
0
1
0
0
0
2
2
0
2
0
1
0
0
0
0
0
2
0
1
1
0
0
0
6
0
0
2
2
1
0
0
2
1
1
1
1
0
2
0
0
1
1
0
2
0
1
1
0
1
0
0
1
1
0
0
0
0
1
0
0
1
1
1
1
1
0
2
1
1
1
1
1
1
0
0
1
0
0
2
2
1
2
1
0
0
0
1
0
0
2
0
0
2
1
1
0
0
2
0
1
1
1
1
1
0
3
2
1
1
1
2
1
0
0
1
1
0
0
0
0
1
2
1
1
0
0
2
0
2
1
0
0
2
1
1
0
0
1
0
1
2
1
1
2
1
1
1
3
2
1
0
0
1
1
2
1
0
0
0
1
0
1
2
2
1
0
0
2
0
1
1
0
0
0
0
1
2
1
0
0
0
1
2
1
0
0
1
1
1
2
0
0
0
1
1
0
1
1
0
0
0
0
0
1
1
0
0
1
0
0
2
1
0
1
1
0
2
0
2
1
2
0
2
1
3
0
2
0
1
0
1
0
1
1
0
0
1
1
1
2
0
0
0
2
1
2
0
0
1
2
0
2
1
2
0
0
0
0
0
0
0
1
0
1
2
1
1
0
1
0
0
1
1
2
2
1
2
1
1
1
1
0
1
1
1
0
2
1
1
0
1
2
2
1
0
2
1
1
0
1
1
1
1
0
0
1
0
0
0
0
1
3
2
2
0
0
1
1
1
0
0
0
0
0
0
2
0
1
0
0
2
0
0
3
0
0
0
1
0
2
1
0
1
0
0
2
0
2
0
2
0
0
1
0
1
1
2
0
2
0
1
0
1
0
1
0
0
3
2
0
0
2
1
1
1
0
1
1
2
0
1
0
1
1
0
0
1
0
0
2
2
0
0
0
1
0
0
0
1
2
2
0
0
1
1
0
0
1
0
1
1
0
0
1
0
1
0
1
0
2
0
0
4
2
2
2
0
0
1
0
1
0
0
1
0
1
0
1
1
0
0
0
2
2
1
0
2
0
2
0
0
1
1
1
0
1
2
1
0
1
0
2
2
0
1
0
0
0
2
0
0
1
2
2
1
2
2
0
0
0
0
1
1
1
0
1
1
1
0
0
1
0
2
0
0
0
0
2
2
2
0
1
0
2
0
0
2
0
0
0
0
2
1
0
2
0
1
0
0
2
1
1
1
3
0
1
1
0
0
0
0
0
0
0
1
0
0
1
1
1
0
2
2
0
1
3
0
2
0
0
0
1
0
0
1
1
1
0
1
0
1
1
0
2
2
0
0
2
1
1
0
2
0
3
2
0
1
2
1
1
1
1
3
0
0
0
1
0
1
1
0
1
0
0
0
0
1
0
0
1
1
1
1
0
0
1
0
1
1
0
0
0
0
0
0
1
1
0
1
1
1
0
0
0
2
0
0
1
1
3
0
0
1
0
2
1
1
1
1
1
0
3
0
0
2
0
0
0
1
2
0
0
1
1
1
2
1
0
0
1
2
0
1
1
1
2
0
1
0
0
0
0
0
2
1
3
1
0
0
0
0
2
0
2
2
0
2
1
2
2
0
1
1
2
1
0
2
2
0
2
0
1
0
0
0
0
2
1
1
2
1
1
1
2
1
1
0
1
1
1
1
1
1
0
2
2
0
1
0
2
0
0
1
4
1
0
1
1
0
2
0
1
3
0
1
0
2
1
2
1
0
1
2
2
0
0
1
0
0
0
2
1
1
0
2
1
1
1
2
0
1
2
0
1
1
2
1
2
0
1
0
0
0
2
1
0
2
1
1
1
0
0
1
0
1
1
0
0
0
0
0
0
1
2
0
0
2
1
0
0
0
1
0
1
0
2
0
2
0
1
0
2
1
2
0
1
2
1
0
1
0
0
0
2
0
0
2
1
0
1
1
0
0
2
0
0
0
2
0
0
0
0
1
0
2
0
2
2
1
0
0
0
1
1
2
1
1
2
0
1
0
1
0
2
1
0
1
0
0
0
2
1
1
1
1
0
0
0
2
0
2
0
2
2
0
1
0
2
0
0
1
0
0
1
2
0
2
0
0
0
0
0
0
0
0
1
2
0
2
1
1
1
1
0
0
1
1
1
1
1
0
0
2
1
1
0
2
1
0
0
1
1
0
0
0
2
0
1
2
0
0
0
1
0
0
0
2
2
2
2
0
1
0
1
0
0
1
0
1
1
1
0
1
0
0
0
1
2
2
0
2
0
0
2
1
1
2
0
0
2
1
0
3
2
0
0
0
0
1
2
2
0
1
1
3
1
0
0
1
2
1
0
2
2
0
0
0
2
2
0
2
0
1
2
1
1
1
0
0
2
2
0
2
2
1
2
0
0
1
1
0
2
2
1
0
1
1
1
1
1
0
1
1
0
1
0
0
0
2
0
0
1
2
2
1
0
0
0
0
1
0
1
0
0
0
0
0
1
2
0
1
0
0
0
0
0
1
2
1
1
3
0
1
1
0
1
1
1
2
0
0
0
2
1
1
0
0
1
1
0
0
1
1
1
0
0
0
2
2
0
2
2
2
0
1
0
1
1
0
2
0
1
1
2
0
2
1
0
0
0
1
1
0
0
2
2
1
0
0
2
1
0
0
1
1
2
0
0
0
0
0
1
0
0
0
0
0
2
0
1
1
1
0
1
1
0
0
0
2
1
0
0
0
0
0
2
2
3
2
0
1
0
2
1
0
0
0
0
0
0
1
2
1
1
1
1
2
2
2
0
1
0
0
0
1
3
1
2
1
0
0
1
0
0
1
0
0
1
0
1
0
1
3
0
0
1
0
2
0
0
0
2
2
1
2
0
2
1
1
1
2
1
1
0
1
0
2
0
0
0
0
0
1
8
0
0
3
2
2
1
1
0
2
0
0
1
0
1
3
2
2
0
0
0
0
1
1
1
0
1
0
0
0
2
1
1
0
0
0
0
1
1
1
0
1
0
2
0
2
2
1
0
1
1
0
1
0
1
1
0
1
0
0
0
0
0
0
2
1
0
0
1
2
1
0
0
1
2
1
0
1
2
1
1
2
1
0
1
1
1
1
2
0
2
2
1
2
0
0
1
1
0
0
0
0
1
1
1
3
0
0
0
1
1
0
0
2
1
0
2
0
0
2
0
1
2
1
2
3
2
1
0
0
1
0
2
2
1
2
0
1
2
0
0
0
0
0
0
1
1
2
0
2
1
1
1
0
1
2
1
1
0
1
0
1
0
1
0
0
1
2
1
0
1
3
0
0
1
2
0
0
2
2
1
0
0
0
4
2
0
1
0
1
1
1
0
1
0
1
0
1
0
1
0
0
2
2
0
2
0
0
0
1
0
1
2
0
0
0
1
0
2
0
0
0
0
1
0
0
2
1
0
1
2
1
1
1
1
0
1
0
1
1
2
1
1
2
0
1
1
2
0
0
0
1
0
0
0
2
1
2
0
0
0
1
2
0
0
0
1
1
1
1
2
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
2
1
2
0
0
1
1
0
5
0
1
0
0
3
0
0
0
2
2
1
1
1
0
0
1
0
0
0
2
1
1
0
0
1
1
0
1
0
0
2
0
2
1
0
1
0
0
0
1
0
2
0
0
2
2
1
2
1
1
0
3
1
0
3
2
1
2
1
0
0
0
1
2
1
2
0
0
1
1
2
1
0
1
1
1
0
0
0
1
0
2
2
0
0
1
2
1
2
0
2
1
1
0
2
1
1
2
1
1
0
0
2
0
1
2
0
1
1
1
0
0
0
0
2
1
1
1
0
1
0
0
1
1
0
0
0
0
1
0
3
0
2
0
0
1
0
1
1
2
1
1
2
1
0
1
1
0
1
2
0
1
0
2
0
0
2
1
0
2
0
0
0
2
1
2
0
0
2
1
7
2
1
1
2
0
1
1
2
2
2
2
0
0
2
1
2
1
0
2
0
0
0
2
0
0
1
0
2
1
1
0
0
1
1
2
0
0
0
1
0
0
3
1
1
0
0
1
0
0
2
1
0
2
1
2
0
2
0
1
0
0
0
1
0
1
2
1
1
0
3
2
0
0
1
0
1
0
1
1
1
2
0
2
2
0
1
2
0
2
0
0
2
2
2
1
0
0
0
2
1
0
0
1
0
0
2
1
0
1
0
2
0
1
2
2
0
0
0
2
0
1
2
0
2
0
0
0
1
0
0
0
0
1
1
1
0
0
1
2
0
2
0
1
1
0
2
0
0
0
0
1
0
0
2
2
1
1
1
2
1
1
0
0
2
1
0
0
0
1
1
3
1
1
1
1
0
1
0
0
0
1
0
0
1
0
0
2
2
0
1
0
1
2
1
1
0
0
1
0
1
1
2
0
1
0
0
2
3
1
2
0
0
1
2
1
2
1
0
0
1
0
0
2
2
1
0
2
0
0
1
1
2
0
0
0
0
0
0
1
0
1
1
1
2
0
1
0
1
0
2
2
1
0
1
0
0
0
0
2
1
1
1
0
0
1
1
0
0
0
3
0
1
0
0
1
2
0
2
2
0
0
1
1
0
0
2
1
1
2
1
0
0
1
0
2
0
0
1
0
0
0
2
1
2
0
1
0
2
1
1
0
1
0
0
0
1
0
0
0
1
1
0
2
1
2
1
0
0
0
1
5
1
1
2
1
1
1
1
0
2
0
1
1
0
0
1
1
0
0
1
1
0
1
0
1
1
1
1
2
0
1
1
1
1
1
0
0
1
0
2
2
2
2
0
1
2
1
1
0
1
0
0
1
1
1
0
0
2
0
1
0
2
2
0
1
0
0
0
0
2
0
1
1
2
0
2
0
1
0
0
2
1
1
1
0
0
0
0
1
2
1
1
0
0
1
0
1
0
1
1
1
1
0
0
1
1
2
1
0
1
1
2
0
1
0
2
2
0
2
0
1
1
0
1
1
1
0
1
3
0
0
1
1
0
2
1
0
0
1
2
1
2
2
1
0
0
1
0
0
1
2
0
2
0
2
1
2
1
1
0
1
0
1
1
0
2
0
1
0
2
2
2
2
2
2
0
2
0
0
2
1
1
0
0
0
3
1
0
0
0
1
2
2
1
1
2
2
0
0
0
0
0
1
1
0
1
1
1
0
1
1
1
3
0
0
2
1
0
2
0
1
0
2
1
2
0
2
0
2
1
1
2
0
0
0
0
0
0
0
3
1
1
2
0
0
1
0
2
1
0
0
0
0
0
1
0
2
2
0
0
1
2
0
0
2
1
0
0
2
1
1
1
0
1
0
2
1
1
0
0
2
3
2
1
1
1
1
0
1
0
0
2
2
2
1
0
0
1
0
0
1
2
2
0
2
0
0
0
1
1
0
1
1
1
1
1
2
1
0
0
1
0
2
0
1
0
0
2
1
1
2
1
1
0
1
1
1
1
2
1
1
0
0
0
2
2
0
0
1
0
0
0
0
0
2
1
1
2
1
0
0
1
2
0
1
6
0
0
0
2
0
1
1
1
2
1
2
0
0
2
1
0
0
1
2
1
0
1
2
0
2
1
1
1
1
1
0
1
1
0
1
1
1
2
0
0
2
1
2
0
0
0
0
0
0
1
1
1
1
0
1
1
0
1
1
0
1
1
1
0
1
1
2
0
0
1
1
0
0
0
0
1
0
0
0
1
2
2
1
2
0
1
1
1
2
2
2
1
1
1
1
2
2
2
0
1
0
0
1
0
0
0
2
2
3
2
2
1
0
1
1
0
2
0
0
0
0
0
0
1
1
2
4
1
2
1
0
1
2
0
1
1
1
0
1
2
3
0
2
2
1
2
0
1
0
2
1
0
0
1
0
1
2
1
1
0
0
0
1
0
1
2
0
0
2
0
0
2
2
0
1
1
0
1
2
1
4
1
2
1
2
0
0
2
0
2
1
1
0
0
1
2
0
0
0
2
2
0
0
2
2
2
0
0
0
2
0
1
0
1
0
0
1
1
2
0
1
0
4
2
1
2
1
1
1
1
0
0
1
2
0
1
1
0
1
0
0
1
1
0
0
0
2
2
1
1
1
0
0
0
0
0
2
1
2
1
2
0
1
0
2
1
0
2
0
2
0
0
0
0
1
1
0
2
0
3
0
2
0
1
0
1
2
0
0
1
1
2
0
1
0
2
1
1
1
2
2
0
2
1
1
0
2
0
0
0
0
0
3
0
1
1
0
2
2
0
2
2
0
1
2
0
0
2
0
2
1
2
0
1
0
2
1
2
1
1
1
1
0
1
0
1
0
0
0
2
2
2
1
3
1
0
2
1
0
0
0
0
0
1
1
2
2
1
2
1
2
2
2
0
2
0
1
0
0
1
1
0
0
0
0
0
1
1
2
2
0
0
0
1
0
2
2
0
0
1
2
1
1
2
0
1
2
0
1
1
2
0
1
0
2
1
0
0
0
0
1
1
0
3
0
1
0
1
1
0
2
1
1
0
1
2
1
2
0
2
1
0
0
0
0
1
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
1
2
1
0
1
2
0
0
1
0
1
0
1
1
1
2
1
1
0
0
2
0
0
0
5
0
1
0
0
0
1
2
0
0
2
0
0
0
0
1
2
0
1
0
1
1
1
2
1
0
0
1
2
0
1
0
2
0
0
0
1
1
0
0
0
0
2
0
0
1
2
2
0
1
1
2
1
2
1
4
1
0
0
0
0
1
2
1
0
1
0
1
0
2
0
1
2
0
0
1
0
0
2
2
1
1
0
2
1
0
0
2
2
1
0
2
0
0
1
0
0
0
0
1
0
0
1
2
0
0
2
1
1
1
1
2
1
1
2
1
0
1
0
0
1
0
0
0
2
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
2
0
0
1
0
2
1
1
1
1
1
0
1
0
0
3
1
1
0
1
1
1
1
1
2
0
1
2
2
0
0
0
1
0
2
1
0
1
4
2
2
0
1
0
1
1
0
0
0
0
0
1
0
1
1
1
0
2
1
0
2
0
1
1
0
0
0
2
1
1
2
0
0
0
0
1
1
1
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
2
1
0
0
1
1
1
1
1
1
0
1
1
1
2
1
0
2
2
1
0
0
0
2
1
2
2
0
1
1
0
1
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
1
0
2
0
5
0
0
1
0
0
0
0
1
1
2
2
0
1
1
1
1
2
0
1
1
2
2
0
2
1
1
0
0
0
2
2
0
0
1
0
3
0
0
0
0
1
2
0
0
1
2
0
1
0
1
1
1
0
0
0
0
1
0
0
1
0
1
0
2
1
1
0
2
1
1
0
0
1
1
1
1
2
1
2
1
0
1
0
0
1
1
1
2
0
2
1
2
1
3
1
1
0
1
2
2
1
1
0
0
2
1
0
2
0
0
0
1
1
1
2
0
0
0
0
0
1
0
1
0
1
1
0
0
0
1
1
0
0
1
0
0
1
0
1
2
0
2
1
1
0
2
0
1
1
0
1
0
1
1
0
0
0
0
0
1
1
1
0
1
2
0
1
0
1
1
1
2
1
2
1
2
2
0
0
0
0
1
0
0
2
0
0
1
0
1
1
0
2
0
1
2
2
2
1
0
2
2
1
2
1
0
0
0
2
1
1
2
1
2
1
0
2
2
0
3
2
1
2
1
1
5
1
0
0
1
1
1
1
2
2
2
0
1
1
0
2
0
2
1
0
0
2
0
0
1
0
0
1
0
1
0
0
0
0
1
0
2
0
1
2
0
0
3
0
2
1
1
1
2
0
0
1
0
2
2
0
0
1
1
2
2
2
1
1
1
0
1
1
1
2
0
1
2
0
1
0
1
1
0
0
1
1
2
1
1
1
1
1
1
0
0
1
0
2
1
4
0
0
0
0
0
0
2
0
1
1
0
0
1
1
0
1
0
0
0
2
0
0
0
0
1
2
0
0
1
0
1
0
0
1
2
0
0
1
0
1
0
0
0
1
1
1
1
1
0
2
1
1
0
1
0
1
0
1
1
1
0
1
0
1
0
1
0
0
0
1
0
0
2
0
2
0
1
0
0
1
1
0
1
0
1
0
0
2
1
1
1
0
1
0
0
1
2
0
2
0
0
1
2
2
1
0
1
0
2
1
2
2
0
1
0
1
0
0
2
2
1
2
1
1
0
0
0
0
1
2
2
2
1
2
0
2
0
0
3
0
1
0
0
0
2
2
2
1
1
2
0
2
0
0
0
1
0
2
0
1
2
0
1
0
0
2
0
2
0
2
2
1
0
0
0
1
0
0
2
0
0
0
2
0
0
2
2
0
1
1
1
2
0
1
1
1
0
0
1
1
1
1
0
0
1
0
2
0
2
1
0
1
0
0
1
0
0
0
2
1
1
2
1
1
0
2
2
1
1
2
0
1
0
1
1
0
1
0
1
1
2
1
1
1
0
1
0
1
2
2
2
0
0
0
1
2
1
0
2
1
1
0
0
0
0
2
0
0
0
0
2
1
0
0
2
1
1
1
0
1
0
0
0
0
1
0
1
5
1
0
0
1
1
0
0
2
0
0
2
1
1
0
2
1
0
0
2
2
0
0
1
1
0
0
1
2
2
2
0
2
0
0
0
0
0
0
1
0
1
2
1
1
2
2
2
0
1
2
0
0
1
2
0
0
1
1
0
0
0
2
0
2
0
0
2
0
1
2
0
1
0
1
0
0
0
0
0
0
0
2
2
1
0
1
2
2
0
1
0
1
0
1
1
1
1
1
0
2
4
2
2
0
2
1
1
1
1
0
1
2
0
2
0
1
0
2
0
0
0
0
1
0
1
1
0
0
1
1
2
2
3
0
0
2
0
1
1
2
1
0
0
1
2
0
0
0
1
0
0
0
0
2
1
0
1
2
1
0
2
2
0
0
6
1
2
0
0
0
0
0
0
0
2
1
1
0
1
2
0
0
1
1
1
0
0
2
0
0
1
1
0
1
3
1
0
1
1
1
0
4
1
2
2
1
1
2
0
0
0
1
1
1
1
0
0
1
0
0
2
0
1
0
1
1
1
0
0
0
1
3
1
0
0
1
1
2
0
0
0
0
0
1
0
1
2
0
1
1
1
1
0
0
0
1
1
0
1
1
1
1
1
1
1
0
1
1
0
1
0
1
1
0
1
0
1
2
2
2
0
0
1
1
2
2
0
1
0
0
1
0
2
2
1
1
1
0
2
0
0
0
0
1
0
0
2
0
4
1
0
2
0
0
2
0
1
0
0
0
0
0
1
0
1
1
0
2
0
1
1
2
0
2
3
0
1
1
2
1
1
0
1
0
2
2
2
1
0
0
1
1
0
1
2
0
2
0
2
1
1
1
1
1
1
0
2
1
2
0
0
1
1
0
0
1
2
0
1
1
2
1
0
2
2
2
2
1
0
0
1
1
1
2
1
6
0
1
1
0
1
0
2
2
2
1
0
1
2
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
2
2
0
1
0
0
2
0
1
2
0
1
2
1
1
3
0
0
0
0
0
1
0
2
0
0
2
3
0
1
1
1
0
0
1
2
0
0
1
1
1
0
0
1
1
1
0
0
1
1
0
1
0
2
0
0
0
2
1
1
1
0
2
0
2
1
1
0
1
0
0
1
0
0
1
1
2
0
1
0
4
0
1
1
1
1
0
0
1
1
2
1
2
1
1
0
0
0
2
1
1
2
0
0
0
2
2
1
0
0
1
0
1
0
2
2
1
0
0
0
2
0
1
0
0
0
2
1
0
1
0
3
0
2
0
0
0
0
2
0
0
0
0
1
0
2
2
0
1
0
0
0
2
1
0
0
0
2
0
0
0
1
0
2
1
2
2
0
1
0
0
3
0
0
1
2
1
1
2
0
1
0
0
1
1
2
1
1
0
0
2
1
1
0
0
0
0
1
2
2
3
2
0
2
1
2
2
0
0
2
0
0
2
1
2
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
2
0
1
2
0
0
1
0
2
1
0
1
0
0
0
1
2
1
2
0
0
0
0
2
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
1
0
1
2
0
1
0
2
2
1
0
1
0
1
0
0
0
1
0
2
2
0
0
0
0
2
2
3
2
2
0
0
1
0
1
1
1
1
2
0
0
0
1
1
0
0
0
2
0
0
3
1
2
1
1
0
2
0
0
0
0
2
1
2
1
0
1
0
1
1
1
0
2
0
1
2
1
1
1
1
2
2
1
1
0
0
0
0
0
0
0
2
2
0
2
1
1
0
0
1
0
0
1
0
0
0
0
2
1
1
2
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
2
1
0
0
2
1
1
0
2
1
1
2
2
1
0
0
0
0
0
1
2
0
1
2
0
1
0
2
0
1
0
1
2
0
0
1
2
0
1
0
1
2
2
2
0
2
0
1
3
2
0
0
0
2
0
2
0
1
1
0
2
1
1
0
0
0
0
0
1
2
0
1
1
2
1
1
0
0
1
3
0
2
2
0
0
0
2
1
0
1
0
2
0
0
1
0
2
0
2
2
1
0
2
0
1
2
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
2
2
0
1
0
1
1
3
2
2
2
0
0
0
0
0
2
2
1
2
0
1
2
0
2
2
1
1
1
0
2
0
1
0
2
0
1
0
2
0
0
0
2
0
0
2
2
3
0
2
2
1
0
1
0
0
0
0
0
1
1
1
0
0
2
2
2
0
0
1
0
1
2
0
1
2
1
1
0
2
3
1
0
1
1
0
1
1
0
1
0
1
1
2
1
1
2
0
0
2
0
1
0
2
1
1
0
2
2
1
0
1
0
1
1
2
1
0
0
1
0
1
0
1
1
0
1
0
1
0
2
0
2
1
1
0
2
0
0
3
2
0
1
0
2
2
1
2
1
0
0
2
0
1
2
0
1
2
2
1
0
0
0
2
1
1
0
0
1
1
3
1
1
2
0
0
1
2
0
2
0
0
0
0
2
2
0
1
2
0
0
1
1
0
1
1
0
1
1
2
0
0
2
2
1
2
2
0
0
0
0
2
0
0
2
2
1
0
3
0
0
1
2
1
0
0
0
1
0
2
2
0
0
3
1
0
0
0
1
1
2
0
1
2
1
2
1
0
1
0
0
1
0
1
1
0
2
2
0
1
0
1
2
1
0
0
2
2
1
2
0
2
0
1
1
0
1
0
0
0
0
1
1
2
2
2
2
2
1
1
0
0
1
1
0
0
0
2
1
1
0
2
0
0
0
0
2
0
0
0
0
2
0
1
2
0
0
2
1
1
0
0
0
0
2
0
2
0
0
1
1
2
2
2
0
2
1
1
0
1
2
2
1
2
0
1
0
2
1
1
1
2
2
1
0
2
0
0
2
2
1
0
3
1
0
0
0
0
2
2
2
0
0
0
2
1
1
1
2
2
5
1
0
0
2
1
2
2
1
2
0
0
1
1
0
0
0
2
0
0
1
1
2
1
0
3
1
0
0
0
0
0
1
1
2
1
2
1
2
0
1
0
0
1
4
1
2
2
1
0
2
2
0
0
0
0
0
2
1
0
0
1
1
1
1
1
0
0
1
2
0
2
0
0
2
2
0
1
1
0
2
1
1
1
3
0
0
3
0
0
2
2
1
1
1
0
1
2
2
0
2
2
0
1
1
1
1
3
0
0
2
1
0
2
0
2
0
0
0
0
0
1
2
1
0
0
1
2
0
0
0
0
0
3
0
0
1
0
0
2
2
1
0
0
0
0
2
1
0
0
1
1
0
2
1
0
1
2
1
0
0
0
1
2
3
1
0
0
2
0
2
0
2
1
0
1
0
1
1
0
1
0
1
1
0
0
0
1
0
2
2
1
1
1
2
1
1
1
2
1
0
2
0
1
0
1
1
0
0
0
2
0
0
1
0
2
0
2
0
1
1
1
1
1
4
1
0
0
2
0
0
0
0
1
0
1
1
0
1
0
0
2
1
0
3
0
0
1
0
1
0
1
2
0
1
1
0
0
1
2
2
0
0
1
2
2
2
0
2
0
1
0
1
1
0
1
0
0
2
0
0
1
2
1
0
2
0
0
2
0
2
0
1
1
1
2
0
1
2
0
0
2
1
1
0
0
0
1
1
1
0
2
2
2
1
0
0
2
0
2
1
0
2
0
2
1
0
0
2
2
0
1
0
0
1
0
1
1
2
1
2
0
0
1
1
0
2
0
2
1
0
0
2
1
1
0
0
0
1
0
0
1
2
0
2
1
0
1
0
0
1
1
1
2
1
0
1
1
0
0
2
0
2
1
1
0
0
0
1
2
0
0
2
1
0
1
2
2
2
2
0
2
2
1
1
1
1
2
0
3
1
0
2
0
1
1
0
0
1
0
0
0
1
1
1
0
2
2
2
3
1
1
2
1
0
1
0
0
0
1
1
1
2
2
2
0
1
0
0
2
2
1
0
0
0
0
1
2
1
0
2
0
1
2
2
2
2
0
1
2
0
0
0
0
0
0
2
0
1
2
1
1
2
1
1
0
0
1
1
1
0
0
0
1
2
1
0
1
2
0
0
0
1
1
0
1
1
0
0
0
2
1
0
0
1
1
0
0
1
0
2
0
1
2
0
1
0
0
0
0
1
0
1
1
1
1
1
2
1
2
0
1
1
2
0
0
0
2
1
2
1
0
0
1
0
0
1
0
1
2
0
0
1
0
1
1
1
0
0
0
0
2
1
2
0
2
1
0
0
2
0
1
2
1
1
1
0
0
1
1
3
0
1
2
0
1
1
3
0
0
1
1
2
0
1
0
2
1
1
1
0
2
0
0
1
0
3
0
0
0
0
0
1
0
0
1
1
2
0
1
1
1
0
0
2
1
1
1
0
1
2
1
0
1
2
1
0
1
2
0
1
0
1
1
2
0
0
1
0
2
0
2
0
1
2
0
0
1
2
1
1
1
1
2
0
1
1
1
3
1
0
0
0
0
1
1
0
2
0
0
0
0
0
0
1
2
1
1
2
2
0
2
2
1
0
0
2
0
1
1
2
2
2
1
1
2
1
0
0
1
2
0
1
0
1
1
1
0
2
0
1
0
0
0
1
0
1
2
0
0
1
0
1
0
1
0
0
1
2
1
2
2
1
1
2
2
1
0
1
2
0
2
0
2
0
0
0
1
0
0
2
2
0
1
2
0
2
1
0
1
1
0
0
2
0
1
1
1
1
1
0
1
0
0
2
0
0
1
0
0
0
0
1
1
1
0
0
1
0
0
0
1
0
0
1
1
2
3
1
0
1
1
0
0
0
0
1
1
1
1
0
0
0
0
1
0
1
1
1
1
1
0
0
1
0
0
1
1
0
0
1
2
1
2
0
2
0
1
1
0
0
1
1
1
0
0
0
0
1
0
2
1
0
0
2
2
1
0
0
0
1
0
2
1
2
0
0
1
2
1
0
2
1
0
1
0
2
0
0
0
0
2
2
0
1
0
2
1
0
1
2
0
0
0
0
0
2
0
1
1
1
2
0
1
0
1
0
0
0
0
1
0
2
0
0
2
0
0
0
2
2
0
0
2
0
1
0
0
0
2
0
0
0
1
2
0
0
0
2
2
1
0
0
0
1
1
1
0
0
1
0
2
1
1
0
0
1
1
1
0
1
1
2
1
1
0
0
7
2
2
0
1
0
0
0
0
1
2
1
0
0
1
2
1
2
2
0
0
0
0
0
2
2
0
2
3
0
2
2
2
0
1
2
1
0
1
0
0
0
0
1
1
0
0
1
0
1
0
0
0
1
1
2
2
1
0
1
0
0
0
2
1
0
1
2
0
1
2
0
2
2
1
0
2
0
1
1
1
0
1
0
0
2
1
1
1
1
2
0
1
1
1
1
1
1
1
2
0
0
1
1
0
0
0
0
0
1
0
1
1
0
0
2
0
2
1
0
1
2
0
0
2
1
0
1
1
0
1
0
1
0
0
1
0
0
1
0
2
1
1
0
0
0
2
2
0
1
0
1
0
2
0
1
0
0
1
0
1
0
0
2
0
1
2
1
0
0
0
2
0
0
0
1
1
1
2
0
0
1
0
0
0
1
2
0
2
0
0
1
3
1
1
1
0
2
0
1
1
1
1
0
0
0
0
2
1
1
1
2
1
0
1
1
1
2
1
2
1
3
0
2
2
3
1
2
0
1
2
0
1
2
0
2
1
0
0
1
0
0
2
0
0
1
2
0
0
0
0
1
2
2
1
0
0
0
2
3
0
1
0
0
1
1
1
0
1
0
0
2
1
2
1
0
0
1
2
2
2
0
0
1
2
0
1
0
1
1
0
0
1
3
1
2
0
3
1
1
0
0
1
1
0
1
0
0
1
0
1
0
0
1
2
2
2
2
0
0
0
0
0
0
0
1
0
0
1
2
1
1
1
1
2
0
0
1
0
0
2
2
0
2
2
2
0
0
0
1
1
0
1
1
0
0
1
1
0
1
2
0
0
0
1
0
2
2
0
2
1
0
1
0
1
1
0
1
2
1
0
1
1
1
1
1
1
2
1
0
2
0
0
0
1
0
0
0
0
1
0
0
1
2
2
2
0
2
0
1
0
1
0
0
0
2
0
1
2
1
2
2
1
1
1
1
0
0
2
0
1
0
2
2
1
1
0
1
1
2
1
1
0
0
1
1
1
1
0
1
2
0
0
0
0
0
0
0
0
1
0
1
1
1
0
3
0
2
1
0
0
2
1
2
0
1
1
2
1
0
0
0
1
2
0
0
0
0
0
3
2
1
2
1
2
2
0
0
0
0
0
3
1
2
1
0
1
2
2
1
0
2
2
1
0
1
0
2
1
0
2
1
2
1
0
0
0
1
0
0
0
0
0
2
0
1
0
0
1
2
0
2
1
0
1
0
1
2
0
1
4
0
0
1
0
1
1
2
2
0
1
0
0
1
1
0
1
1
2
1
0
1
2
0
1
0
2
1
1
1
0
0
0
0
0
0
1
1
0
1
0
2
0
2
0
2
0
0
3
0
0
1
0
2
0
1
1
0
2
0
2
1
2
0
2
0
1
0
0
3
2
0
0
0
0
1
1
0
1
0
1
1
0
0
1
0
0
1
0
1
0
2
1
2
0
1
2
0
0
1
0
0
0
2
0
1
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
2
1
0
0
0
1
3
1
0
0
0
0
1
0
0
1
1
0
1
3
0
2
0
1
1
2
0
1
1
1
0
1
1
0
0
0
1
1
1
0
0
2
0
0
4
1
2
1
2
1
0
0
0
0
0
1
0
1
0
2
1
0
0
2
0
0
1
0
1
0
1
1
1
1
0
0
2
0
0
1
1
1
0
0
0
3
0
1
1
0
1
1
1
2
2
0
1
0
0
1
0
0
1
1
1
1
0
0
0
0
0
0
1
0
2
2
0
1
1
1
2
0
0
7
0
2
0
1
1
0
0
0
0
0
2
0
0
1
0
0
1
2
0
2
1
0
1
0
1
0
1
0
2
0
1
0
0
0
1
0
0
0
1
1
1
0
1
1
0
0
1
0
0
0
1
1
1
1
0
0
2
0
1
2
1
0
1
1
2
0
0
0
0
1
1
1
1
1
0
2
0
1
1
1
0
0
0
2
2
1
0
0
0
2
2
0
0
1
0
1
2
0
1
1
2
0
2
0
1
0
2
2
1
1
2
4
1
0
0
1
1
1
0
0
2
0
1
0
0
1
0
2
1
1
1
1
1
1
1
0
2
0
1
0
0
0
0
0
2
0
1
0
1
1
0
1
1
0
0
0
0
0
1
1
1
0
2
1
1
0
2
1
0
1
0
1
1
0
1
2
0
2
0
0
0
2
0
2
1
0
2
0
1
0
0
0
1
1
0
3
1
0
0
1
2
2
2
0
0
1
2
0
0
0
0
0
0
2
2
1
1
1
0
0
0
2
0
2
1
0
2
0
0
1
1
0
0
1
1
1
2
2
0
2
0
0
1
1
1
1
0
0
0
0
0
1
1
0
2
2
1
0
0
1
0
0
1
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
1
1
1
0
1
3
1
3
1
0
1
1
0
0
2
0
1
0
0
8
2
1
1
2
0
0
2
1
0
0
0
1
0
0
1
2
0
2
1
2
0
0
0
0
2
2
1
0
1
1
1
0
1
0
0
2
1
1
0
1
0
0
0
1
1
0
2
0
0
0
1
1
1
0
1
1
0
1
1
2
3
2
2
0
0
1
2
2
0
0
3
0
2
0
3
2
1
2
2
0
2
1
0
2
0
1
1
0
1
1
0
1
0
0
2
2
1
2
0
2
0
0
1
2
2
2
2
0
0
2
1
1
0
1
3
0
2
2
0
0
1
3
1
0
0
3
0
2
1
2
0
0
3
2
0
0
1
1
2
1
2
2
1
1
2
1
2
1
1
1
1
1
1
1
1
1
0
1
1
1
1
2
0
1
1
2
2
0
2
2
0
1
0
0
1
1
1
1
1
1
0
1
0
1
2
0
2
2
0
0
0
1
0
1
2
1
1
1
1
1
0
0
0
2
1
1
1
0
0
0
0
2
0
1
2
1
0
1
1
1
0
0
1
2
1
0
0
0
1
1
0
0
1
0
0
2
2
2
0
1
1
0
1
2
0
2
0
0
1
2
2
1
1
1
2
1
1
2
1
1
5
0
1
2
2
0
0
0
1
2
1
0
3
1
0
0
1
1
0
1
1
2
0
2
2
1
1
0
2
3
1
1
0
0
2
1
1
1
1
2
0
0
1
1
1
0
1
0
0
0
0
0
0
0
2
2
1
1
2
0
1
0
1
1
2
1
1
1
1
0
1
2
1
0
1
0
2
0
0
2
0
1
2
1
0
2
0
0
1
1
1
1
1
0
0
0
1
1
0
2
0
0
2
1
0
2
2
0
0
0
1
1
1
1
2
0
2
2
2
0
1
1
0
2
2
0
2
0
0
2
2
0
1
1
0
0
0
0
2
0
0
1
0
2
0
1
0
0
2
0
2
2
0
1
0
1
1
1
1
1
0
0
0
0
2
0
1
1
0
1
1
2
3
1
0
2
0
2
1
0
0
0
2
1
0
2
1
2
2
1
0
2
0
2
0
0
0
1
1
1
2
2
1
1
0
1
4
1
0
1
2
1
0
1
0
0
1
2
2
1
1
2
0
0
1
0
2
1
1
1
1
2
2
0
0
0
0
0
1
2
1
1
1
1
2
0
1
1
0
1
0
0
2
0
1
2
2
0
1
1
1
1
1
1
2
0
0
0
0
0
0
0
2
1
0
0
0
1
1
0
0
0
0
0
1
0
2
2
2
1
2
0
2
0
1
1
1
0
0
0
0
2
1
2
1
3
0
1
0
3
2
0
0
3
0
2
1
1
0
1
2
1
0
2
0
1
0
1
0
0
0
2
4
1
3
2
1
1
0
0
0
1
2
0
0
1
0
2
2
1
0
1
1
0
0
1
1
2
1
0
2
0
0
1
2
1
0
0
0
1
1
2
3
2
2
0
1
0
3
0
2
0
0
0
1
0
0
0
0
0
0
1
0
2
1
2
2
3
0
0
1
2
2
0
0
0
2
1
0
0
0
1
1
1
1
2
2
1
0
1
0
0
1
0
0
0
0
2
1
2
2
1
0
0
1
2
1
1
1
1
2
0
0
1
0
2
0
0
0
0
0
0
1
0
0
3
1
0
1
1
2
0
2
1
2
0
0
0
1
1
2
0
1
0
0
2
2
0
3
2
1
2
0
2
1
2
0
1
0
1
1
1
0
2
0
2
0
0
1
0
1
1
0
2
0
0
0
0
1
2
1
0
0
2
1
0
1
1
0
2
2
1
0
2
0
1
1
0
0
0
0
0
0
0
2
2
2
1
1
0
1
2
1
1
1
0
0
0
1
0
2
0
0
1
0
1
1
1
0
1
2
1
1
0
0
1
0
2
0
0
0
3
0
1
0
1
1
1
0
0
1
1
0
1
0
0
1
0
0
2
0
0
0
2
2
2
1
0
0
0
0
2
1
2
1
1
0
1
0
1
0
1
5
0
0
2
0
0
0
2
1
1
1
0
0
1
0
0
0
0
1
0
1
1
0
1
0
0
1
0
0
0
1
1
0
2
0
0
3
0
0
2
2
1
1
2
0
1
0
3
1
0
1
1
1
0
1
2
0
1
1
0
2
0
2
0
1
1
1
0
0
1
0
0
0
0
0
0
2
1
1
1
2
3
0
0
0
2
0
2
1
1
1
0
0
2
1
0
1
1
1
0
0
0
0
0
2
0
0
2
1
1
1
4
0
0
0
0
1
0
1
0
0
0
2
0
0
3
0
1
1
1
2
0
0
2
0
1
0
0
2
1
0
2
1
2
0
2
1
0
2
0
0
2
1
0
2
1
1
0
1
0
2
2
1
1
2
0
1
0
2
1
0
0
1
2
1
1
1
1
1
2
0
0
1
2
1
0
0
0
1
1
1
0
0
0
0
0
1
0
1
0
1
1
2
2
1
0
2
1
2
1
1
2
2
0
0
2
2
1
0
2
0
2
2
0
0
0
2
0
0
1
0
1
0
0
1
1
1
1
2
3
0
1
0
1
0
1
0
1
1
0
1
0
0
0
1
0
1
0
2
1
1
0
0
1
1
0
2
0
0
0
1
0
2
0
2
0
1
0
1
2
0
1
0
2
2
0
1
1
1
0
0
1
0
1
1
0
0
0
2
3
1
0
0
0
2
1
1
1
0
2
1
0
0
0
1
4
1
0
1
0
1
0
0
0
2
0
0
0
1
1
1
1
0
1
2
1
1
1
0
0
2
0
0
1
2
1
2
1
2
0
1
2
0
1
1
1
2
0
0
1
1
1
0
0
1
0
0
0
1
1
0
0
1
0
0
2
3
0
1
1
0
1
0
0
1
0
0
0
0
2
0
1
2
0
1
0
2
0
0
0
1
0
0
0
1
2
1
0
2
0
1
2
0
1
2
0
2
1
1
0
1
1
2
0
0
0
0
1
1
0
0
2
0
0
2
2
2
3
1
1
2
1
0
0
0
0
0
1
2
1
2
0
0
0
2
1
0
1
0
0
1
0
0
1
0
0
1
2
2
1
0
0
2
0
0
1
1
2
0
1
2
0
0
1
1
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
2
1
0
0
2
2
1
2
0
0
0
2
1
1
0
1
0
0
0
2
0
2
1
0
1
1
0
2
0
1
2
1
0
0
0
1
0
0
1
0
0
2
3
1
0
2
0
2
1
0
0
1
2
2
1
2
0
0
1
0
1
0
0
1
1
0
1
0
0
2
1
0
1
2
1
0
0
1
1
1
2
0
1
2
1
0
1
0
0
1
2
0
0
0
0
1
0
0
1
1
1
2
1
0
1
1
1
1
0
1
0
0
0
1
1
1
0
0
0
1
0
0
0
2
0
2
2
2
1
2
0
0
1
0
0
0
2
2
2
0
0
2
1
1
1
0
3
2
1
1
0
0
1
0
1
1
0
0
0
0
1
1
2
4
1
2
0
0
2
0
0
0
1
1
0
0
2
1
0
0
2
2
0
0
1
1
0
0
2
2
1
2
1
0
2
1
0
0
1
2
0
0
1
2
2
1
2
0
1
1
2
0
0
1
1
0
0
1
0
2
2
1
1
2
2
1
0
0
0
2
0
2
1
0
0
1
1
1
0
2
0
1
1
0
1
2
0
0
0
2
0
1
1
2
1
0
0
0
0
1
2
1
1
0
2
2
0
0
0
1
0
2
1
1
0
1
1
0
0
0
0
1
2
2
0
2
0
1
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
3
1
0
2
0
2
1
0
0
2
0
1
2
2
2
0
1
1
0
1
1
0
1
1
0
1
1
2
0
0
0
1
1
2
1
2
0
2
0
1
0
0
1
0
2
1
0
1
0
1
0
1
3
0
0
0
0
2
0
1
3
1
0
2
1
0
2
2
0
0
0
0
0
0
0
1
4
0
1
2
1
1
1
0
0
0
1
3
0
2
0
1
1
0
1
0
1
0
0
0
0
0
0
1
0
1
2
1
1
1
1
0
0
0
0
1
2
1
0
1
1
1
1
0
0
2
1
0
0
1
0
0
2
0
2
0
0
2
0
0
2
1
1
0
0
2
2
2
0
2
0
1
0
0
1
1
1
2
0
0
1
0
2
2
1
0
1
0
2
0
1
0
0
2
1
1
2
0
0
0
1
2
0
2
1
0
0
1
0
1
1
0
0
2
1
0
0
2
0
0
2
1
0
0
2
0
0
0
0
1
1
1
0
0
1
1
1
1
0
2
1
0
0
1
0
2
1
2
1
0
2
0
0
2
0
1
0
0
1
1
1
0
0
1
2
2
1
1
0
0
1
2
1
1
2
1
1
0
2
3
0
0
1
2
0
0
1
0
0
2
2
1
1
2
1
0
0
2
1
0
0
0
1
2
0
3
1
1
0
2
0
1
1
0
1
2
0
1
1
0
0
3
1
0
0
1
0
1
2
0
0
0
0
0
4
2
1
0
0
1
1
2
1
0
1
1
1
2
4
0
2
0
6
2
2
0
0
0
0
1
2
0
0
0
2
0
1
0
2
1
4
1
0
0
2
1
0
1
1
1
2
2
0
1
0
0
0
3
1
0
0
0
0
1
3
1
1
2
1
1
2
1
0
2
1
0
2
1
1
0
0
0
1
0
0
2
1
0
2
1
0
0
1
1
0
2
0
1
0
0
2
1
0
1
1
1
0
2
0
0
0
2
0
1
2
2
1
1
0
0
1
0
1
0
2
1
0
2
0
0
0
2
1
1
1
1
2
2
0
0
2
1
0
1
0
1
0
2
0
1
1
0
0
0
0
2
1
1
2
1
0
1
0
0
0
0
2
0
0
1
0
0
1
0
3
2
0
1
2
0
1
1
3
0
0
0
1
0
0
0
2
0
2
0
1
0
2
2
0
1
1
2
0
1
2
1
1
2
0
0
2
1
2
1
0
2
2
0
0
0
0
0
1
1
1
0
0
1
1
0
0
2
1
0
1
0
2
0
1
0
0
1
1
1
2
3
0
1
1
1
0
0
0
2
0
0
1
0
2
1
2
1
0
0
0
1
0
1
4
1
0
2
2
0
0
3
2
0
0
2
0
2
2
1
1
0
1
0
1
2
0
1
1
1
1
0
1
1
1
0
1
0
2
2
0
3
0
0
1
0
0
0
1
1
2
2
2
2
0
1
2
0
0
1
1
1
1
0
0
0
1
2
0
0
1
1
2
1
0
1
1
0
1
1
0
0
1
2
0
0
0
1
0
2
1
1
1
2
0
1
0
0
2
1
0
0
0
0
1
0
1
1
1
0
0
1
2
2
0
1
0
0
2
0
0
1
1
0
2
1
1
0
1
0
0
1
0
0
1
3
2
0
1
0
0
0
1
1
2
0
2
0
2
1
0
0
0
1
0
0
0
1
0
2
0
2
0
1
0
2
1
2
0
0
1
0
0
2
1
1
2
1
1
0
0
2
0
1
1
2
0
0
0
1
0
0
2
0
0
2
0
1
0
2
1
1
1
1
2
1
1
0
1
2
1
2
1
1
0
1
1
1
0
2
1
0
1
1
3
0
0
2
3
1
1
0
0
0
1
1
0
2
0
3
2
2
1
1
0
2
0
2
0
0
1
0
2
1
0
0
0
0
0
1
2
0
0
0
2
2
1
1
2
2
1
0
0
0
2
2
0
3
0
0
0
1
0
1
2
2
0
0
0
0
1
0
1
2
1
0
1
1
0
1
0
0
0
1
2
0
2
0
0
2
0
2
2
2
0
2
0
1
1
0
1
2
1
0
1
2
0
1
0
0
2
0
0
0
0
0
0
8
1
0
2
0
0
0
0
1
0
1
0
0
0
0
2
0
2
2
2
0
0
2
2
1
1
1
1
3
1
0
2
0
0
0
1
1
2
0
0
2
1
1
0
0
0
1
1
0
0
1
1
0
2
0
1
2
0
0
0
2
0
2
3
2
0
0
2
1
2
0
2
1
2
0
0
2
0
0
2
0
0
0
1
1
1
0
1
1
2
1
0
0
0
0
1
0
0
1
0
0
0
2
2
1
0
1
0
1
1
1
1
2
1
2
2
0
2
1
0
2
0
1
1
0
0
0
0
0
1
2
2
2
2
1
0
2
0
1
0
0
1
0
1
0
1
0
2
1
1
0
1
0
2
0
0
0
2
0
0
0
2
0
0
1
0
0
0
2
0
0
1
2
0
0
2
2
0
2
1
2
0
0
0
2
0
1
0
0
1
3
0
0
0
0
0
1
0
2
2
1
0
1
1
0
0
0
1
2
1
1
1
0
2
1
1
1
0
2
2
1
1
2
0
2
1
2
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
3
0
0
2
0
1
0
0
1
1
1
2
2
1
0
1
1
0
0
1
1
0
3
0
1
0
1
0
0
2
0
0
2
1
0
1
0
0
1
0
0
0
1
2
1
0
0
0
1
2
0
0
1
0
0
1
0
1
0
0
0
0
4
2
1
1
0
0
0
0
2
0
0
0
1
1
0
1
2
0
0
0
1
0
2
0
1
0
0
0
2
0
0
1
2
0
2
1
1
0
1
1
2
0
0
1
1
3
1
2
1
0
0
1
1
0
0
1
0
1
3
1
1
0
1
0
1
0
0
1
0
1
2
2
0
0
0
0
1
0
0
1
5
1
0
2
2
1
4
1
0
0
0
1
0
1
1
0
0
0
2
1
2
0
1
1
0
1
0
3
0
1
1
0
0
2
0
1
1
2
1
1
2
0
0
1
0
2
0
1
0
1
0
1
0
0
1
2
0
2
0
0
1
2
1
2
0
1
0
0
0
1
1
1
0
1
1
0
0
0
0
3
0
0
1
0
1
0
1
0
1
1
1
1
1
1
1
1
1
1
2
0
0
0
0
1
0
0
0
2
0
2
1
2
0
1
0
1
0
1
0
1
1
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
2
2
1
0
1
2
2
1
1
1
2
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
1
2
0
0
0
1
0
0
2
1
0
0
1
2
1
0
1
0
0
2
0
2
1
0
0
0
0
0
0
1
1
2
0
0
0
1
1
2
0
1
2
1
2
2
1
0
0
1
2
2
0
1
1
0
1
0
0
1
2
1
0
0
0
0
0
1
2
0
6
2
0
0
2
2
2
1
1
1
0
3
2
1
2
1
1
2
2
0
1
0
1
0
2
1
1
2
0
1
2
2
0
1
2
0
1
1
2
0
2
0
0
2
1
1
1
0
1
1
0
2
0
1
1
1
2
2
2
0
2
2
2
0
2
1
0
2
0
0
1
0
0
2
2
0
2
0
1
0
2
0
2
1
0
2
0
0
2
0
1
0
1
2
0
1
1
0
0
1
1
2
1
1
2
2
0
0
0
1
2
0
1
0
0
0
0
0
2
3
2
0
2
0
0
0
1
0
1
1
2
0
0
1
3
0
0
0
1
0
2
2
0
1
0
0
2
0
0
1
0
2
0
0
0
2
1
0
0
1
0
1
0
1
0
1
1
1
1
2
1
2
1
0
1
0
0
1
0
0
0
4
0
1
1
0
0
1
0
1
1
0
2
0
2
0
0
0
1
1
0
1
2
0
0
2
1
2
0
1
0
0
1
3
1
1
2
1
0
0
2
0
2
2
1
0
1
2
0
0
1
2
0
1
2
1
0
1
1
1
0
2
1
1
2
1
0
0
2
0
0
2
0
0
0
1
1
2
0
2
0
1
0
0
2
1
0
0
0
0
0
0
0
1
0
1
2
4
0
1
1
1
0
0
0
0
0
2
2
0
2
1
0
1
1
1
2
0
0
2
1
1
0
1
1
1
0
0
0
1
1
1
0
1
0
1
2
2
2
0
1
2
0
1
0
2
2
0
0
0
1
0
0
1
0
1
0
1
1
2
1
0
0
1
0
2
2
2
0
1
0
0
0
0
0
0
0
2
0
1
0
1
1
1
1
0
0
0
0
0
2
0
2
1
0
0
1
0
0
1
0
0
1
2
0
0
0
2
1
2
1
1
1
2
1
1
0
1
2
1
0
1
2
1
2
0
1
0
1
1
1
1
2
1
0
0
0
1
0
1
1
0
2
0
0
1
0
1
0
1
0
1
0
0
1
0
1
1
1
0
0
1
2
2
2
2
0
0
1
0
1
2
1
0
1
2
0
0
2
2
0
2
1
1
0
2
2
1
2
0
1
0
1
1
0
0
0
2
0
0
2
1
0
0
0
0
1
2
0
0
0
1
2
2
1
1
1
0
1
1
2
1
1
0
0
0
0
1
1
2
0
1
0
2
0
2
0
0
2
1
0
1
1
0
0
1
2
0
0
1
0
0
1
1
1
0
2
0
0
0
2
1
0
1
1
1
0
0
1
1
1
1
2
2
2
1
2
0
1
2
0
2
0
2
1
0
0
0
1
1
0
3
0
2
0
0
0
0
2
0
1
1
2
1
1
1
2
2
1
0
0
1
2
2
0
2
0
2
2
0
1
2
0
1
0
1
1
1
2
2
1
2
2
0
1
1
2
0
0
0
0
1
1
0
0
2
3
1
0
1
1
2
1
2
0
1
2
6
0
1
1
0
1
0
0
1
0
0
0
1
2
0
0
0
0
1
1
1
1
0
0
2
2
0
1
0
1
0
1
0
0
1
2
0
1
0
1
0
0
1
1
1
1
0
0
1
2
0
2
0
0
2
0
1
1
0
1
1
0
0
2
0
3
0
0
0
2
1
2
0
1
0
0
2
1
1
1
2
2
1
0
2
0
0
1
2
0
1
0
1
2
0
0
1
0
2
0
0
0
0
1
1
0
1
0
0
0
2
1
1
2
0
1
3
0
1
1
0
1
0
1
0
1
2
1
0
1
1
0
0
1
1
1
1
1
1
0
0
0
1
2
1
2
2
0
2
2
0
0
1
0
0
0
1
2
0
1
1
2
1
2
1
0
2
2
1
1
0
2
0
0
2
0
0
0
0
2
1
0
0
0
0
1
2
2
0
1
0
0
0
0
1
1
0
2
0
1
0
0
0
0
0
0
2
1
0
1
2
1
1
0
2
1
1
0
1
2
0
0
1
0
1
0
1
0
0
0
1
1
0
0
1
2
0
0
0
2
1
3
2
0
0
0
1
1
2
1
3
1
0
4
2
2
0
1
0
1
0
0
0
1
1
0
0
1
0
0
1
0
0
1
0
0
2
0
1
0
1
1
1
0
0
1
2
2
1
0
1
1
1
0
0
1
0
0
1
0
0
2
0
0
1
1
0
2
0
1
0
0
0
1
2
2
1
1
0
1
0
1
0
2
0
0
0
0
0
0
1
1
0
1
1
0
1
1
2
1
1
1
0
0
1
0
0
2
2
1
2
2
1
0
1
2
0
2
0
2
1
1
1
1
1
0
0
1
0
0
2
3
0
1
0
0
2
1
0
0
2
0
2
0
0
1
1
0
0
3
0
1
0
1
1
1
1
2
2
1
1
1
1
0
0
1
2
2
2
0
0
2
0
1
2
1
0
0
1
0
0
0
2
2
0
2
0
2
0
0
0
1
1
2
0
1
2
0
1
1
0
0
0
0
1
0
1
1
1
1
2
1
0
1
0
2
2
0
0
2
0
0
1
1
2
1
1
0
2
0
1
2
0
1
0
0
0
0
0
0
1
2
1
1
0
2
1
0
1
1
0
0
1
0
0
1
0
0
1
0
1
0
0
1
1
0
2
2
2
1
0
1
3
1
1
1
1
1
0
0
0
0
0
2
0
1
1
0
0
1
0
2
1
0
1
2
1
0
0
3
2
2
0
2
0
0
0
2
0
0
1
0
1
0
6
0
0
2
1
0
0
0
1
3
2
0
1
0
1
1
0
0
3
0
0
0
0
2
0
2
1
0
0
0
1
1
2
6
2
0
0
2
1
1
2
0
1
0
1
0
0
0
1
0
2
1
0
2
0
0
2
1
0
0
0
1
0
4
0
0
1
0
2
1
2
1
0
1
0
0
1
0
0
2
1
1
2
1
0
1
1
2
0
1
0
2
0
0
0
2
2
0
1
0
1
1
2
0
0
0
0
2
1
0
0
1
1
1
2
2
1
0
0
1
1
1
2
1
2
0
0
1
1
1
1
0
0
0
2
4
0
1
1
1
0
0
2
0
0
2
1
0
2
2
2
1
2
2
0
1
2
2
0
1
2
0
2
0
2
0
0
2
0
0
0
0
1
2
0
0
1
1
0
1
1
1
1
1
0
1
1
2
2
1
0
2
0
0
0
2
0
1
2
0
0
1
2
2
1
2
0
0
1
1
1
0
0
2
0
2
2
1
0
2
1
0
1
0
1
1
0
4
0
1
1
1
2
0
0
1
1
1
0
2
2
0
0
1
1
0
1
1
2
0
1
0
0
1
0
0
0
1
2
1
0
0
1
0
0
1
0
2
1
0
3
0
1
2
0
3
0
0
0
0
0
1
2
0
0
1
1
0
1
0
0
2
0
0
1
0
0
1
2
1
0
1
0
1
1
1
0
1
0
2
0
1
0
1
0
2
2
2
1
1
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
2
0
1
1
3
1
1
1
1
2
2
0
1
1
0
0
1
0
1
1
1
0
0
2
2
1
1
0
0
1
2
1
2
1
0
0
1
1
1
0
2
1
1
0
1
2
0
2
1
0
1
0
2
1
2
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
2
0
0
1
0
1
1
0
2
0
2
0
0
2
1
0
0
1
1
0
1
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
2
0
0
0
1
1
1
2
1
2
1
1
0
0
2
1
0
0
2
1
0
2
0
0
1
0
1
1
2
1
0
0
1
1
0
0
0
2
0
0
1
0
0
0
1
0
2
1
2
0
0
0
1
0
0
0
1
2
0
0
3
0
0
0
0
0
1
1
0
1
1
0
0
0
3
0
1
2
1
0
2
0
1
1
3
2
2
1
1
0
0
1
1
0
0
0
0
2
1
0
0
2
2
0
2
0
2
2
0
2
1
3
2
0
2
0
1
0
2
0
1
1
0
2
3
2
0
0
1
1
0
2
1
1
1
2
0
0
1
1
0
0
8
2
0
1
0
2
0
1
2
1
0
0
2
2
2
0
1
0
0
1
1
0
0
2
0
1
0
1
2
0
1
0
0
2
2
0
0
0
1
0
1
0
0
1
1
1
0
1
1
2
0
1
0
0
0
0
0
0
2
0
1
1
1
2
1
0
2
0
2
0
2
1
0
0
2
0
0
1
1
1
1
2
1
0
2
1
2
0
1
0
0
0
0
1
2
2
1
0
0
0
0
0
1
0
2
1
3
0
1
2
1
0
1
2
0
1
1
2
3
2
1
0
1
0
1
0
0
1
0
0
0
2
0
1
1
1
0
4
1
1
0
1
0
1
0
1
1
1
1
0
0
2
0
0
0
1
0
0
1
1
0
2
0
3
1
2
1
2
0
0
0
2
1
0
2
0
2
0
0
1
0
1
2
1
2
2
0
0
1
0
1
1
0
1
0
1
0
0
2
1
0
0
0
1
1
0
2
1
2
1
2
1
2
2
0
2
1
0
1
2
0
0
1
2
1
0
1
0
0
1
0
0
0
1
1
0
3
2
2
2
2
1
0
1
2
0
0
2
0
0
3
1
1
1
2
2
1
1
0
1
0
2
0
0
0
0
1
0
1
1
0
0
0
0
2
1
0
1
0
0
1
0
1
0
1
2
0
3
1
0
1
2
1
1
1
0
2
2
0
1
0
0
2
1
0
2
3
2
0
1
0
2
0
1
2
0
2
1
1
2
0
2
0
0
0
0
1
0
0
1
2
0
2
0
0
1
1
1
1
1
1
0
1
0
2
1
2
0
2
2
0
0
0
1
0
0
2
0
2
1
2
1
2
2
2
2
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
1
0
1
1
1
0
0
1
2
2
1
0
1
0
2
0
1
0
1
2
0
0
2
0
0
2
1
1
0
1
2
0
1
0
1
1
2
1
1
1
2
0
1
2
0
0
2
1
1
0
1
3
2
1
1
2
0
0
1
0
0
0
1
1
1
0
1
2
2
0
0
0
1
0
1
0
0
0
2
0
2
1
1
1
1
2
1
0
2
2
2
0
0
1
1
0
0
0
1
2
0
0
1
0
1
1
1
0
0
0
1
1
0
1
1
1
1
2
2
1
0
1
0
0
2
0
2
2
1
4
1
1
0
0
0
2
0
2
1
1
3
0
1
0
1
0
0
3
0
1
1
2
1
1
0
0
1
0
0
0
1
1
2
2
0
1
0
0
2
0
0
0
0
1
0
1
0
3
0
0
0
2
2
2
2
0
2
0
2
2
0
0
2
0
1
0
0
0
4
0
0
0
0
2
1
0
0
0
2
1
1
0
0
1
3
1
4
1
2
1
1
1
0
2
0
3
1
0
1
1
0
0
2
1
0
0
1
1
1
1
1
4
2
0
0
1
1
1
1
0
0
0
2
1
0
1
0
0
0
0
0
1
1
0
1
0
0
0
1
2
0
0
2
0
0
0
0
2
0
1
2
0
0
0
0
2
2
0
0
1
0
1
1
2
0
1
2
0
3
1
2
1
1
2
0
1
0
1
0
2
0
3
1
0
0
2
1
0
1
2
2
1
0
0
1
1
0
2
1
1
1
1
0
0
0
2
1
0
1
0
3
0
0
0
0
2
1
0
0
2
2
1
0
2
2
1
1
1
1
0
2
2
1
0
0
0
2
0
1
1
0
2
1
0
0
2
1
1
1
1
1
0
0
1
0
1
1
1
0
1
2
0
2
1
2
0
0
0
1
1
1
1
1
2
2
1
1
0
0
0
0
1
1
2
2
1
0
2
1
0
1
0
0
0
2
0
0
0
1
0
1
0
1
1
1
0
2
0
0
1
0
1
0
0
2
1
1
1
1
1
3
1
0
2
2
2
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
1
1
2
0
0
0
0
0
1
0
0
2
2
0
2
1
0
0
1
3
1
1
2
1
2
0
2
1
0
2
0
2
0
1
1
2
2
0
0
2
1
2
0
1
1
0
0
1
0
0
1
0
1
1
0
2
2
0
2
0
2
0
0
0
0
2
1
1
2
0
0
2
0
2
1
2
2
1
0
2
0
3
1
0
0
0
0
0
2
2
0
1
1
1
0
1
1
1
0
1
1
0
2
1
0
0
2
2
0
1
1
0
0
1
0
2
0
1
0
3
2
0
0
0
1
1
0
2
0
1
1
1
0
1
2
0
1
1
0
1
1
1
0
2
0
1
5
0
2
2
1
2
1
0
2
2
3
2
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
2
2
0
1
0
1
0
1
2
1
0
0
1
2
1
0
0
0
0
2
2
2
0
2
0
1
1
0
1
2
0
1
0
0
1
2
2
2
0
0
0
0
1
2
0
0
1
1
2
0
0
1
2
2
1
2
0
2
0
0
1
0
1
0
3
0
0
1
2
2
1
2
0
1
1
2
0
2
0
1
1
1
0
1
0
2
0
0
0
1
0
0
0
1
1
0
1
0
0
0
2
1
1
0
1
0
2
1
0
2
0
0
2
1
1
0
1
0
0
0
2
0
1
0
0
0
0
1
1
1
0
2
0
0
1
0
0
0
0
0
0
0
2
0
1
1
0
1
0
1
2
2
0
0
0
1
0
2
0
0
0
2
1
1
0
2
2
1
0
1
1
0
0
0
0
0
1
1
0
0
0
2
1
0
1
0
3
2
2
0
2
2
0
0
1
3
0
1
0
2
1
1
1
1
1
2
1
2
1
1
0
0
1
0
0
0
1
2
2
2
0
0
1
1
0
0
1
0
0
1
1
0
0
0
0
0
3
1
1
0
1
0
0
0
2
1
1
1
0
0
2
0
2
0
2
0
1
0
2
1
1
1
1
0
0
1
2
0
1
1
0
2
0
1
1
0
2
0
1
0
1
0
0
0
0
1
2
1
0
1
0
2
0
1
1
1
0
2
4
1
2
1
2
0
2
1
1
1
1
1
2
2
2
2
1
2
0
0
0
0
1
3
1
2
0
0
1
1
2
0
0
0
2
1
1
0
2
1
0
1
1
0
1
0
0
1
2
1
0
0
0
0
2
0
0
1
2
2
0
0
2
2
0
0
1
1
1
1
1
0
2
1
0
0
1
1
2
2
1
1
1
0
1
0
0
0
1
1
0
1
1
0
1
0
0
0
2
0
0
1
0
0
2
1
1
0
0
0
0
1
0
0
1
0
0
0
1
1
1
0
0
2
0
0
2
2
0
0
0
1
0
0
1
1
1
1
1
0
1
1
0
2
2
1
4
1
4
2
1
0
1
2
1
0
0
1
1
0
0
0
1
0
0
1
0
0
3
3
2
0
0
1
2
1
3
1
0
0
0
1
0
0
5
0
0
2
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
2
0
1
1
0
2
1
0
2
0
1
1
1
0
1
2
1
1
2
1
0
1
1
0
0
2
1
0
0
0
1
0
1
1
1
1
0
0
1
0
0
1
0
0
1
0
0
2
1
0
0
1
0
3
0
2
0
1
0
1
1
0
3
1
2
1
0
1
1
0
1
0
0
1
1
1
1
1
1
0
0
0
1
0
1
0
0
0
1
2
0
1
0
0
0
0
2
0
0
0
0
2
1
0
2
2
0
1
1
2
1
1
2
0
0
0
1
1
1
1
0
1
1
0
0
0
1
1
0
1
1
1
1
0
1
0
0
2
0
0
1
0
2
0
4
0
1
0
0
0
0
1
3
0
0
1
1
0
0
0
0
2
0
2
0
0
0
1
1
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
1
0
1
0
2
1
1
1
2
1
0
1
1
0
2
0
1
2
1
0
1
0
1
1
0
0
2
1
0
1
2
0
0
1
1
0
0
0
2
1
2
3
3
1
2
1
0
1
1
0
2
2
0
0
0
1
2
0
2
1
0
1
2
0
0
2
0
0
2
0
0
2
2
1
2
1
1
1
0
0
2
0
0
1
1
2
1
2
1
0
1
1
1
1
1
0
0
2
0
0
0
0
1
1
1
1
0
1
0
2
0
0
1
1
1
0
0
1
2
1
1
1
0
0
1
1
0
1
1
2
1
0
2
0
2
0
0
0
2
0
2
0
0
0
1
1
1
0
6
0
0
2
1
1
0
0
2
1
0
0
0
1
2
1
0
1
0
1
1
1
0
1
2
2
0
0
0
1
2
1
0
0
2
0
1
1
0
1
0
1
0
0
1
0
0
0
1
0
0
0
1
2
0
0
0
3
2
0
1
1
0
1
1
1
0
0
1
0
1
1
1
2
1
1
1
0
0
0
0
3
2
0
1
3
1
1
0
1
0
1
0
2
2
0
1
1
1
0
0
1
1
2
0
1
2
2
0
1
0
1
1
2
1
0
0
2
0
0
2
2
0
0
1
0
0
2
2
0
0
2
1
2
1
1
2
1
1
1
0
1
1
0
0
1
0
2
2
0
2
0
1
1
0
0
0
1
0
1
2
2
0
0
0
3
1
0
0
1
1
2
2
0
1
2
2
2
0
1
0
2
0
1
1
0
0
2
2
2
2
1
2
2
0
0
1
0
2
1
2
2
0
1
0
0
2
2
2
2
0
0
1
2
0
1
0
1
1
3
2
0
0
0
1
1
0
0
1
1
0
1
1
1
1
1
1
1
2
1
2
0
1
0
2
0
2
0
2
0
0
0
0
2
0
0
0
0
0
1
0
1
1
1
1
0
0
1
1
2
1
2
1
1
1
1
0
0
1
1
0
1
0
2
0
0
0
0
2
1
3
1
0
0
0
0
3
1
1
0
0
1
0
2
1
1
0
0
0
0
0
5
0
1
2
0
2
1
1
0
2
2
2
0
0
0
0
2
1
0
0
2
2
0
1
0
2
1
1
1
0
2
1
0
0
2
1
1
2
0
1
0
2
0
0
0
0
0
0
1
1
1
2
0
0
1
2
0
0
1
1
2
0
1
1
1
2
2
0
1
1
1
0
1
0
0
1
2
1
0
0
1
0
2
0
0
0
1
1
2
1
2
1
0
1
0
0
0
1
0
2
0
0
4
2
1
0
2
2
0
2
1
2
0
3
0
0
0
1
1
1
1
0
1
0
1
1
2
2
1
1
0
0
0
0
2
1
2
2
0
1
0
0
1
1
0
2
1
0
2
3
1
0
0
1
1
0
1
1
0
1
0
0
2
2
0
0
0
1
1
2
1
1
1
1
1
0
1
1
1
0
0
0
2
2
1
2
2
0
2
1
1
0
2
1
0
1
2
0
1
0
1
1
1
0
0
0
1
0
1
1
1
2
1
1
2
1
0
1
1
1
0
1
1
1
0
1
1
2
0
1
2
0
1
1
2
1
1
1
0
0
1
0
2
1
0
0
0
1
0
0
0
0
1
0
0
2
2
1
2
1
1
0
0
0
1
1
1
1
1
0
2
0
0
1
2
0
0
2
1
0
0
2
0
1
2
0
0
1
1
0
0
1
0
0
0
0
2
0
1
1
1
2
1
0
0
1
2
1
0
0
0
2
1
1
0
0
0
1
0
0
1
1
0
1
1
1
0
0
2
0
1
1
2
0
1
2
2
1
1
0
0
1
1
1
0
0
0
1
1
2
1
1
0
0
2
1
1
0
1
2
0
0
0
0
1
0
2
0
0
1
1
0
1
1
2
0
0
0
2
0
0
0
0
0
1
1
0
2
0
0
0
1
0
1
1
2
0
2
0
1
0
2
0
0
1
0
2
0
0
3
0
2
1
2
1
2
0
2
0
0
0
2
2
0
0
1
1
0
0
1
1
0
1
2
1
2
0
1
1
1
0
0
1
0
0
0
2
0
0
0
1
0
0
1
0
1
1
1
0
0
1
0
0
0
1
2
0
1
2
2
2
1
2
0
2
0
1
0
0
1
1
1
0
0
2
1
1
1
0
1
0
0
0
0
0
2
1
0
2
0
3
0
1
1
2
2
1
0
2
1
1
1
2
0
0
2
1
2
1
0
0
1
2
0
0
1
0
0
1
1
1
1
1
1
1
1
1
1
0
1
2
0
0
1
0
0
0
2
0
2
0
0
0
0
2
2
0
1
0
0
1
1
1
1
1
0
2
1
1
2
1
0
1
0
1
0
0
1
0
0
1
0
0
1
0
0
1
2
0
1
0
2
0
3
0
0
0
0
0
1
0
0
2
0
1
0
2
1
0
1
0
1
0
1
0
0
0
2
1
0
0
2
0
0
0
0
0
0
1
0
2
1
1
1
1
1
1
0
1
0
2
1
1
1
0
0
2
0
1
0
0
0
1
0
2
1
1
0
1
0
1
2
1
0
1
0
0
2
0
2
1
0
0
1
0
0
0
1
0
0
2
2
1
0
2
0
1
1
0
2
0
0
0
2
0
1
0
1
0
0
2
0
1
2
0
2
0
0
0
0
1
2
1
1
2
1
0
1
2
0
0
0
0
2
0
1
0
2
0
2
2
0
1
1
2
1
0
1
1
0
0
2
0
0
0
1
1
0
1
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
2
0
1
2
0
1
0
1
2
0
2
1
2
1
0
1
1
2
2
0
1
0
0
0
0
2
2
0
0
1
0
1
1
1
1
1
1
1
0
0
0
0
2
0
0
0
2
2
0
0
2
0
0
0
0
2
1
2
1
0
2
0
1
1
1
1
1
1
0
0
0
2
0
0
0
2
1
0
1
1
1
2
1
0
1
2
1
2
0
0
1
1
3
1
0
2
1
0
1
0
2
1
2
0
2
0
2
1
0
0
1
2
0
2
2
2
0
2
0
1
1
0
0
1
2
1
0
0
0
0
0
2
1
1
1
1
0
0
2
2
1
2
1
2
0
0
2
1
1
1
2
1
0
1
2
0
1
0
0
0
0
1
1
2
1
1
0
0
1
0
1
0
2
2
1
0
1
1
0
0
1
0
1
1
0
0
1
0
2
1
2
0
2
0
2
1
1
0
0
0
0
1
1
2
0
1
0
0
0
0
0
1
1
2
1
1
0
0
0
1
2
1
1
2
0
2
1
1
1
0
0
2
0
1
0
2
0
1
0
1
0
2
1
0
0
0
1
1
1
0
1
1
0
0
1
1
0
1
1
0
0
2
1
1
2
0
0
2
2
2
0
1
2
1
2
0
1
0
0
2
1
0
0
2
2
2
2
1
4
2
0
1
1
0
1
0
1
2
0
0
1
1
0
0
0
1
2
2
2
1
0
0
2
0
2
0
0
0
2
0
0
0
1
1
2
0
1
0
0
2
0
3
0
0
0
1
1
2
0
1
0
0
1
1
1
1
0
0
0
1
1
2
0
2
1
1
0
1
1
1
0
1
1
0
0
1
0
0
0
2
0
2
2
4
2
0
1
1
2
1
0
2
1
0
1
2
0
0
2
1
0
0
0
0
2
1
0
1
0
0
0
2
1
1
0
4
1
2
2
2
1
0
0
0
0
2
0
1
2
1
2
1
1
1
0
1
0
0
0
1
0
2
2
0
1
1
1
2
2
2
0
1
0
1
1
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
1
1
0
1
1
0
0
1
1
1
1
1
1
1
0
2
1
0
1
1
1
1
0
1
0
5
1
0
1
0
1
1
0
0
0
1
0
1
0
1
0
2
0
2
2
0
0
4
0
0
0
0
2
0
0
2
0
0
1
2
0
0
1
0
1
1
2
1
0
2
0
2
0
1
1
1
2
0
4
1
2
1
1
1
1
2
1
1
0
0
2
0
2
2
1
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
1
0
1
0
1
0
2
1
0
1
2
1
0
1
0
2
2
1
0
0
1
0
1
1
0
1
0
1
2
1
1
1
0
1
1
1
2
3
1
0
1
0
2
1
0
0
1
1
2
1
0
1
0
1
2
1
1
0
0
1
0
2
0
0
2
1
0
0
2
0
2
1
1
0
0
2
1
1
0
1
0
1
0
2
4
0
1
0
1
0
0
2
0
2
2
3
1
1
1
0
1
1
2
0
1
2
1
1
0
2
2
2
0
1
0
0
1
0
2
0
0
0
3
1
0
1
0
0
2
0
1
1
2
0
0
0
1
0
0
2
2
0
2
1
1
0
2
0
0
0
0
0
0
1
2
1
1
1
0
1
3
0
1
2
0
0
0
0
2
3
0
2
0
1
1
1
0
0
1
2
0
1
2
2
0
2
0
2
1
0
1
0
2
3
0
2
0
1
0
1
1
0
3
1
0
1
1
0
1
1
1
0
0
1
0
0
1
0
1
0
2
1
0
1
0
0
1
0
1
1
2
0
2
1
1
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
2
1
2
1
1
0
1
1
0
0
0
0
0
1
1
2
0
0
1
1
0
1
1
0
0
0
0
0
1
2
1
0
1
0
2
1
0
1
4
0
1
0
1
1
0
2
4
0
1
1
2
0
0
0
0
0
1
2
2
0
1
0
1
0
1
2
1
0
2
0
2
0
1
0
2
1
1
1
1
0
2
1
1
1
0
0
2
1
1
1
1
2
1
0
1
0
2
0
2
2
2
1
0
0
1
0
0
2
0
1
2
2
2
0
2
0
2
1
1
0
1
1
2
0
1
0
2
0
0
0
1
2
0
1
1
0
1
0
1
0
1
0
1
1
2
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
1
0
2
0
1
0
0
2
0
0
0
2
1
1
1
2
1
1
1
2
0
0
1
1
1
0
0
0
0
1
0
2
1
1
0
1
2
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
1
1
1
0
1
0
0
0
1
0
0
0
1
1
1
1
0
0
0
1
2
0
0
2
1
0
2
2
0
0
1
1
0
2
2
1
1
1
0
1
1
2
1
3
2
0
2
0
2
2
1
1
1
0
1
0
1
1
1
0
1
0
1
0
4
0
1
2
1
1
2
0
2
2
2
1
2
0
0
2
0
1
1
1
0
0
1
2
1
1
1
0
0
0
0
1
0
0
2
2
0
0
1
1
0
1
0
0
0
0
1
1
0
2
1
1
1
0
1
2
1
0
1
0
2
0
1
0
0
2
2
0
0
1
2
2
1
1
0
1
1
0
0
1
1
2
2
1
1
0
0
0
0
0
0
1
0
1
2
1
0
1
0
0
0
0
1
0
0
0
0
1
1
2
1
1
0
0
1
0
2
0
2
0
0
0
2
1
2
1
0
6
0
2
1
0
0
1
2
0
1
0
2
2
2
2
1
0
2
0
1
0
1
0
0
0
1
1
0
0
0
1
1
2
0
1
0
0
0
1
1
0
1
2
0
0
1
0
2
0
0
2
1
0
1
0
1
0
1
1
1
0
0
0
1
0
1
0
1
2
0
2
2
1
0
2
1
0
0
0
1
2
1
0
1
0
1
1
1
2
1
0
1
0
1
2
0
0
0
0
0
0
2
1
1
1
0
1
0
0
0
0
0
2
0
1
2
1
2
0
2
1
0
1
0
2
0
0
0
0
2
1
0
2
2
1
5
2
0
1
2
0
2
0
1
1
0
1
1
0
1
2
0
1
1
1
1
1
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
2
0
1
0
1
0
2
2
1
1
0
2
2
1
0
0
0
0
2
1
2
1
1
2
0
0
0
0
0
2
5
0
0
0
0
2
4
1
1
1
1
0
2
1
1
0
1
2
0
2
1
0
0
0
0
1
0
0
1
1
0
1
1
1
1
0
2
1
0
1
0
1
0
1
2
0
0
1
0
0
0
0
0
0
1
2
1
0
0
2
0
0
0
2
2
1
0
1
2
0
1
0
1
0
0
1
0
1
0
2
0
1
2
1
0
0
2
0
1
0
1
0
2
2
0
0
0
0
1
1
2
0
1
1
1
0
0
1
2
0
0
1
2
1
1
3
0
0
0
2
2
1
1
0
0
0
1
2
1
1
1
0
0
0
1
1
0
2
0
0
0
2
0
1
0
0
0
0
0
2
0
1
1
2
1
0
1
1
0
0
1
0
2
0
1
2
1
0
1
1
2
0
1
0
0
0
2
0
0
0
1
1
2
0
2
0
0
2
0
1
1
0
2
2
2
2
2
2
0
1
2
2
0
0
0
1
1
0
1
1
0
0
2
0
1
2
2
2
0
2
0
1
2
1
0
2
0
1
0
0
1
0
0
1
2
1
0
0
1
0
2
1
0
0
1
0
0
2
2
3
0
0
0
1
1
0
2
2
1
1
0
1
0
0
0
1
1
2
1
1
2
0
0
0
2
0
2
1
2
0
2
0
0
1
2
0
2
0
1
2
2
0
0
1
0
2
0
0
0
2
2
0
3
1
1
1
13
1
1
1
1
1
0
1
1
2
1
2
2
0
3
0
0
1
0
0
1
0
1
1
2
1
1
0
0
1
1
1
1
0
2
0
1
2
2
1
3
1
2
1
1
2
0
0
1
1
2
2
2
1
0
0
1
1
2
2
0
0
0
0
0
1
2
0
2
0
2
1
2
2
1
0
2
1
1
2
0
0
0
1
0
1
1
1
2
0
2
0
1
1
2
1
0
0
2
0
1
0
1
1
0
0
2
0
1
1
0
1
1
0
2
0
2
1
2
2
0
0
0
0
1
0
1
2
1
0
2
0
2
2
0
0
2
1
2
0
1
1
0
0
0
1
2
0
1
1
1
1
1
0
0
1
2
1
2
2
1
2
0
2
2
2
2
0
0
0
0
0
1
0
0
2
0
2
0
0
0
3
0
1
0
0
1
0
0
1
2
2
1
1
0
1
1
0
0
1
1
0
0
0
1
1
1
2
1
2
0
1
1
2
0
1
2
0
1
1
1
0
0
0
0
0
0
0
1
1
0
1
0
0
3
1
0
2
0
1
1
2
2
1
3
0
1
0
1
1
2
0
1
2
1
2
2
2
0
1
1
0
0
0
0
1
2
2
0
2
2
1
1
1
2
0
1
0
2
0
0
1
0
1
1
1
2
0
0
0
0
1
0
1
2
0
1
0
0
1
3
0
0
2
1
0
0
0
0
0
1
1
1
0
0
0
0
2
1
1
1
0
2
2
1
1
0
1
1
0
0
3
1
2
2
1
1
0
0
0
2
0
0
1
1
1
2
1
2
0
0
0
0
2
1
0
0
2
2
0
0
0
0
1
1
1
1
1
0
0
1
1
1
0
1
1
0
1
0
0
0
0
2
1
0
1
2
0
2
2
1
0
1
2
0
0
1
2
0
2
0
1
1
2
1
1
0
0
0
1
0
2
0
0
2
0
0
0
1
1
1
0
1
0
0
2
0
0
0
0
1
1
0
1
0
1
1
0
1
0
1
0
1
0
2
1
2
0
0
0
0
1
1
0
0
0
2
1
1
0
0
2
1
0
1
1
0
1
1
0
0
1
1
0
2
0
2
0
1
2
0
1
1
3
1
0
1
1
0
1
1
2
1
1
1
0
1
0
1
0
1
0
0
2
1
0
0
2
1
2
0
0
3
1
0
0
1
7
0
2
1
0
2
1
2
1
0
0
0
0
1
0
0
2
1
1
1
2
0
1
2
0
0
0
0
1
0
0
1
2
1
1
0
1
2
1
3
0
2
0
0
2
0
1
0
2
1
2
0
1
1
0
1
0
0
2
1
2
2
0
0
0
2
2
2
0
0
1
2
0
0
2
0
2
1
2
2
0
1
0
0
0
1
3
2
1
1
0
1
0
0
2
1
0
0
1
0
0
1
1
1
1
0
1
0
0
1
0
1
0
0
0
0
0
2
1
0
2
1
1
2
0
1
3
1
0
2
0
0
1
1
1
0
1
0
2
0
1
0
1
0
2
0
0
0
2
1
0
1
0
0
0
2
0
0
0
0
0
1
1
0
2
0
1
0
0
2
1
0
0
0
1
0
1
1
0
1
1
0
3
1
2
1
0
1
1
1
0
0
0
3
0
0
0
1
1
2
2
0
1
1
2
2
0
1
2
1
0
0
1
2
1
0
0
1
0
0
1
1
0
1
1
1
2
0
1
0
0
0
2
1
0
1
0
2
1
1
0
0
0
0
2
1
0
1
0
7
1
0
0
1
2
0
2
1
0
2
0
0
2
0
1
1
1
1
1
1
2
0
0
0
1
1
1
2
1
0
1
0
1
0
1
0
2
1
1
1
1
0
0
1
0
0
0
1
0
0
2
2
0
3
1
1
0
1
1
1
0
1
1
0
0
0
1
2
1
1
2
2
2
0
1
1
0
0
2
1
2
0
1
0
0
2
1
1
0
0
2
0
1
0
1
2
1
0
1
0
0
0
1
0
2
0
1
2
0
2
0
0
1
1
1
1
0
0
3
0
1
0
0
1
1
0
1
1
0
3
2
0
0
0
1
0
2
0
1
1
0
2
1
1
0
1
2
2
2
0
0
2
0
0
0
1
0
0
1
1
0
1
2
0
3
0
0
0
1
2
1
0
1
1
1
0
0
0
0
1
2
1
0
2
2
2
2
2
1
1
1
0
0
2
0
0
1
1
1
1
0
1
2
0
1
0
0
2
2
2
2
2
2
2
1
2
2
1
0
1
2
1
0
0
1
1
0
1
2
2
1
0
0
2
0
2
1
0
1
0
0
1
1
3
0
2
0
0
2
0
1
0
0
0
2
0
0
1
2
1
0
0
1
3
1
0
1
1
0
0
0
0
1
2
1
1
2
1
2
0
1
0
0
0
1
0
0
2
0
1
0
1
0
1
1
2
1
2
0
1
2
0
0
1
1
0
2
1
2
2
1
1
1
0
2
0
1
0
1
1
0
0
0
1
0
2
2
0
0
1
0
1
0
1
0
0
0
0
2
0
2
1
0
0
1
1
2
1
0
2
0
3
2
2
0
0
2
1
1
1
1
2
1
1
1
2
0
0
0
0
2
0
1
0
0
0
1
1
0
0
0
2
1
0
1
0
2
1
0
0
1
0
0
0
1
2
1
1
0
0
1
2
1
0
0
0
2
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
1
0
1
1
1
1
0
1
0
0
0
0
0
1
0
1
0
0
1
1
0
1
0
2
2
1
0
0
2
2
0
0
0
0
2
0
1
6
0
1
2
0
2
1
0
0
0
0
1
2
0
1
1
1
0
0
1
0
0
1
2
0
0
1
0
1
1
0
0
0
0
2
1
4
0
2
0
0
0
1
1
3
2
1
0
2
0
0
1
2
0
0
0
1
0
0
0
0
4
0
0
1
0
1
2
1
0
1
0
1
1
0
0
0
3
1
0
0
0
0
1
0
1
2
0
0
1
1
0
0
0
0
1
1
1
0
1
0
2
1
2
0
2
1
0
1
1
0
0
1
1
1
0
0
1
1
2
0
1
2
0
0
0
2
1
1
3
1
1
0
1
1
0
1
0
2
0
0
0
2
1
0
0
2
0
2
0
1
1
0
0
0
1
0
0
0
2
0
0
2
1
0
2
0
0
2
0
2
2
0
1
2
0
2
1
1
0
1
1
2
1
2
1
0
1
1
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
1
2
2
0
0
0
0
0
0
0
3
1
1
1
1
1
0
0
0
1
0
2
0
1
1
1
1
2
2
2
0
0
1
0
0
0
0
0
0
2
0
1
1
0
0
0
1
2
0
2
1
0
0
1
1
0
1
0
2
1
1
0
0
0
3
2
1
1
2
0
0
0
0
1
1
1
1
0
1
1
1
0
0
2
1
3
1
2
2
2
1
2
0
0
2
0
1
0
2
1
2
1
0
1
1
0
0
1
0
1
3
1
0
0
2
0
1
0
0
2
0
1
0
1
1
2
0
0
1
2
2
0
1
1
1
0
1
0
1
0
0
1
1
1
0
1
2
1
2
2
0
1
0
0
2
2
1
0
0
1
2
0
1
1
2
1
0
1
0
1
1
1
0
1
0
5
0
0
0
2
0
0
0
0
0
0
0
1
2
1
0
2
0
0
1
1
1
1
0
1
1
1
2
1
1
2
0
2
0
0
0
2
1
0
2
2
1
0
1
1
2
0
1
0
1
2
2
1
1
2
2
2
0
1
1
1
0
0
1
1
0
0
0
0
2
0
0
1
0
0
1
0
1
0
1
0
2
0
3
2
1
2
0
1
0
3
0
0
2
1
0
1
1
0
1
1
0
0
6
1
0
2
2
2
0
1
0
0
0
0
1
0
0
0
0
1
0
0
3
2
0
1
2
2
0
1
2
1
1
0
2
0
0
0
0
1
1
0
1
0
0
0
1
1
2
0
1
0
2
0
1
3
0
0
2
2
0
0
1
0
0
0
1
0
1
0
0
0
0
0
2
0
0
1
3
0
0
1
2
0
0
0
2
0
1
3
0
1
2
0
0
2
2
1
0
0
0
0
2
1
1
0
2
0
2
1
1
0
0
1
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
2
0
0
1
0
1
0
1
1
1
1
0
0
1
2
2
2
0
2
1
0
0
1
2
0
0
2
0
0
0
1
1
0
1
2
0
0
2
2
2
0
0
0
1
1
0
1
1
0
2
2
3
1
1
0
1
0
2
2
3
0
0
1
0
1
0
0
2
0
1
2
0
2
2
2
1
0
0
2
1
0
1
2
0
1
2
2
1
0
2
1
0
2
1
0
0
0
0
3
0
1
1
1
0
1
0
1
0
1
0
0
1
2
2
0
1
0
0
1
1
1
0
1
0
1
2
0
1
0
0
0
0
0
0
1
0
0
0
1
0
2
2
1
0
1
0
1
1
0
2
2
0
0
0
1
1
1
0
0
0
1
1
0
0
1
2
0
1
0
0
1
2
2
0
1
1
1
2
0
0
0
1
0
0
0
0
2
0
0
1
2
0
0
2
1
0
1
2
0
1
0
1
0
2
2
0
1
0
0
0
2
1
2
0
0
1
0
0
2
0
0
1
0
1
2
0
0
0
0
0
1
0
0
1
0
0
1
1
1
2
1
2
1
1
0
1
1
1
0
0
0
1
2
2
0
1
0
1
2
1
0
0
0
2
2
1
1
0
1
0
2
0
0
0
2
0
1
0
0
1
0
0
0
0
0
1
2
1
1
2
2
0
2
1
1
0
2
2
9
1
1
1
0
1
0
2
2
1
1
2
1
1
0
0
2
2
1
1
2
1
0
0
1
0
1
0
1
2
0
0
1
0
0
2
1
0
0
0
1
0
2
2
1
1
0
2
2
0
0
1
1
0
0
2
0
0
1
1
0
2
0
2
0
0
1
2
1
0
1
2
0
1
0
1
2
0
2
0
0
0
1
0
2
2
0
1
1
2
0
1
0
1
2
0
0
0
2
1
1
1
0
1
0
0
0
1
0
0
0
2
0
0
0
1
0
0
1
0
1
0
2
0
0
0
0
0
1
0
0
2
0
1
2
2
1
2
0
0
1
1
0
0
0
1
1
0
1
0
0
0
0
1
2
1
1
0
2
0
0
2
4
0
0
1
0
0
1
0
0
1
3
1
1
0
1
1
1
0
0
1
0
0
2
0
1
1
0
0
2
0
0
0
2
1
0
0
0
1
2
2
1
0
0
1
1
0
2
1
1
1
1
0
0
0
0
0
0
0
1
2
0
1
2
1
1
0
2
0
1
2
2
0
2
2
2
1
0
0
0
0
1
2
0
0
0
2
1
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
1
2
0
1
1
1
2
1
1
1
1
0
1
1
0
0
1
3
1
0
0
1
0
2
0
2
1
0
0
1
0
2
1
0
1
0
1
0
1
0
0
0
1
0
1
7
1
1
0
1
1
1
2
0
0
0
0
2
0
2
1
2
2
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
1
1
0
1
2
0
3
0
0
2
1
0
1
0
0
1
1
1
1
1
0
1
0
0
0
0
1
2
2
0
0
0
1
0
0
2
2
2
1
2
1
0
0
0
0
0
2
2
0
0
0
0
1
0
1
0
0
2
0
1
0
2
0
1
0
1
2
1
0
1
0
0
0
0
1
2
0
0
1
0
1
0
2
2
2
3
2
2
1
0
1
1
1
0
1
1
2
0
0
1
0
3
1
1
2
0
1
1
0
0
0
1
1
1
0
0
2
2
3
0
1
2
1
2
1
0
1
0
1
2
2
1
1
3
1
0
1
1
0
0
1
0
0
0
0
0
2
0
0
2
0
2
2
2
1
0
0
2
0
0
0
0
0
1
0
0
0
0
3
2
0
0
0
0
1
1
1
0
1
2
0
0
0
2
1
2
0
0
1
1
1
1
0
0
0
2
0
1
2
0
1
1
0
0
1
0
0
2
1
0
0
1
2
0
0
2
2
2
1
1
2
1
0
0
2
0
2
0
2
2
0
1
0
1
0
0
0
0
0
1
1
0
2
1
1
0
0
1
2
1
2
0
0
1
1
2
0
1
0
1
0
1
3
1
0
0
2
1
0
1
0
2
2
1
1
0
1
0
0
1
1
2
0
0
0
0
1
0
0
1
0
1
0
1
2
0
1
1
0
1
1
1
1
0
1
1
1
0
1
0
0
2
1
1
0
0
1
1
2
0
0
0
1
1
0
0
0
0
0
0
0
2
2
0
0
1
2
0
2
0
1
2
1
2
0
0
0
0
1
0
0
1
1
0
2
1
1
0
3
0
1
2
0
0
2
2
1
0
1
2
0
0
1
1
0
2
0
0
1
1
1
0
2
0
1
0
0
0
1
2
0
2
0
1
0
4
1
0
1
3
0
1
1
2
2
2
1
2
0
0
1
0
1
0
0
2
0
0
0
0
0
2
2
0
0
1
0
2
0
0
0
2
1
0
0
0
2
1
2
1
0
0
0
1
1
1
1
0
2
0
0
0
2
0
0
1
1
0
0
1
1
1
1
1
1
0
1
2
0
1
0
0
2
3
1
0
1
0
2
1
2
1
2
2
2
0
1
0
0
1
1
2
0
1
1
1
1
0
0
1
0
0
0
0
2
2
1
0
0
0
0
1
1
0
1
0
1
2
0
1
0
2
1
1
0
0
0
1
1
0
0
0
0
1
0
0
2
2
2
1
1
1
0
0
1
4
0
0
2
0
1
2
0
2
0
0
0
1
0
0
3
0
0
1
0
2
1
1
0
0
1
2
2
0
0
0
1
2
1
1
1
0
0
0
2
1
1
0
2
2
1
0
1
2
0
0
1
0
0
0
0
0
2
1
2
1
1
0
2
0
1
2
0
0
0
0
1
1
1
1
0
0
0
0
2
2
0
2
0
1
0
0
1
2
1
0
2
0
1
1
1
1
3
0
0
2
1
0
0
0
1
0
4
0
1
3
1
1
0
0
1
1
1
2
0
1
1
1
2
1
1
0
0
0
0
2
0
0
0
1
2
0
0
0
2
0
0
1
1
0
2
1
2
1
0
1
1
0
3
2
2
0
2
0
1
1
0
0
1
3
0
1
0
1
0
2
0
1
1
2
2
1
0
0
1
2
1
2
0
0
2
2
1
0
0
0
0
2
1
1
1
2
1
0
2
1
0
1
1
1
1
2
0
2
2
0
0
0
1
0
0
2
0
1
1
2
0
0
1
1
2
0
1
0
1
1
0
0
0
0
0
0
1
2
0
0
1
1
1
1
2
0
1
1
0
2
0
0
0
1
0
0
1
1
2
2
1
1
1
1
0
0
2
1
1
2
1
0
1
0
2
1
0
1
0
0
1
1
0
1
0
0
2
1
2
3
0
1
0
0
0
1
0
0
2
0
0
0
1
1
1
2
0
0
1
0
0
1
1
2
0
1
1
1
2
0
1
0
2
0
1
1
0
1
0
1
2
0
2
0
0
0
0
0
2
1
0
2
1
1
0
0
0
0
2
1
1
0
0
1
1
1
1
2
1
0
0
1
0
0
1
0
2
0
0
0
1
0
2
0
2
1
1
1
0
1
0
0
0
0
1
1
2
1
1
0
0
0
0
1
0
1
0
0
2
0
1
0
0
1
0
0
2
1
0
0
0
2
2
0
0
0
0
2
0
2
0
0
2
1
1
0
1
1
0
2
0
1
2
0
1
1
8
0
0
1
1
0
0
1
2
1
2
0
1
1
0
0
0
0
1
0
1
0
2
0
1
0
2
1
2
0
0
3
0
7
0
0
1
0
1
2
1
1
0
1
0
1
2
0
4
1
1
1
0
0
0
1
1
1
0
1
1
0
0
1
1
0
2
2
1
0
1
1
0
1
2
0
1
0
1
0
1
1
1
1
1
0
0
1
0
1
3
0
1
1
2
2
0
0
0
1
1
0
0
0
0
3
2
0
0
1
2
1
0
1
2
0
0
1
1
1
0
2
3
1
0
1
1
1
2
1
0
0
1
1
1
2
2
1
1
1
0
0
1
3
0
0
0
2
2
2
0
2
2
2
2
2
0
1
1
1
4
1
1
0
2
0
0
1
0
0
2
0
1
1
1
0
0
1
2
0
0
1
2
0
1
1
2
2
2
0
1
1
0
2
0
3
2
0
0
2
1
0
1
1
1
1
1
0
1
0
1
0
0
0
1
1
2
2
2
2
0
0
2
2
1
2
1
2
0
0
2
0
0
1
0
1
1
2
0
0
0
1
2
0
0
0
1
0
1
1
1
0
2
0
2
2
1
2
2
2
0
1
2
0
0
1
2
2
1
0
0
1
0
1
2
1
0
0
1
2
0
2
0
1
0
0
0
2
1
0
2
2
1
0
0
0
2
0
0
0
2
0
1
1
1
1
2
0
1
0
2
1
0
0
2
2
0
0
0
1
2
1
1
2
2
2
1
1
1
0
2
1
1
2
2
2
2
1
2
1
2
1
0
1
0
1
1
1
0
1
0
0
2
1
0
0
1
1
1
2
2
0
0
0
1
0
0
2
2
0
2
1
1
1
0
2
1
0
0
0
0
5
0
1
2
1
2
0
0
1
1
0
1
0
1
0
2
1
2
1
1
0
0
0
0
2
3
0
0
0
0
0
2
1
0
1
0
0
0
2
1
0
0
1
1
1
0
2
0
0
0
0
1
3
0
2
0
2
0
1
1
0
1
0
1
1
1
0
2
2
1
1
0
0
1
1
0
2
1
2
0
0
2
0
2
1
1
2
2
1
1
1
0
0
0
2
0
2
1
0
0
0
2
2
1
1
1
0
0
0
0
0
1
0
2
2
2
1
1
1
0
2
1
0
1
2
2
0
0
0
1
0
1
2
1
0
1
1
0
0
1
1
0
0
0
2
1
1
0
0
1
2
1
0
1
0
1
2
2
0
1
0
0
1
1
1
0
0
2
1
1
0
1
1
1
0
1
1
0
0
0
0
1
2
1
1
0
0
2
0
0
0
2
0
2
0
0
1
0
1
2
0
0
1
1
0
0
1
1
2
1
0
1
1
1
0
1
1
0
0
5
0
0
1
0
0
2
2
1
1
2
2
0
2
1
2
1
0
0
0
2
2
0
1
2
2
2
1
2
0
0
1
0
0
0
2
1
1
1
1
0
1
1
2
1
1
0
0
0
0
2
0
1
0
2
1
1
0
2
1
0
4
1
1
1
2
1
1
3
0
2
2
1
1
0
2
0
0
0
0
0
1
0
1
1
2
2
0
0
0
2
0
1
0
2
2
2
1
0
0
1
1
0
2
2
1
0
0
0
2
1
1
0
2
1
2
0
0
0
0
2
1
1
0
2
0
1
2
4
0
0
1
2
1
1
0
0
1
0
3
1
0
1
1
2
0
1
0
2
0
2
1
0
0
1
0
2
2
0
1
0
1
2
0
0
0
0
2
0
0
2
1
1
0
2
0
2
2
0
1
2
1
1
1
1
2
1
0
0
1
1
1
1
1
0
1
0
2
1
0
2
0
2
0
1
0
0
3
0
0
1
1
0
2
0
0
2
2
0
3
1
2
0
0
0
1
1
0
1
1
1
0
1
2
1
1
1
0
0
1
0
0
1
1
0
2
0
1
0
1
1
0
2
0
1
2
1
0
1
2
1
0
0
0
1
2
1
2
0
0
0
0
2
0
0
0
1
1
1
2
0
1
0
1
0
2
0
1
2
2
1
1
2
1
2
0
0
2
0
2
2
1
0
1
1
0
0
1
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
1
2
0
1
0
2
1
1
1
1
1
1
2
0
0
2
1
0
1
2
0
1
0
1
0
0
1
0
1
1
0
0
1
1
1
0
1
0
1
0
2
2
1
2
0
0
1
0
1
0
0
0
0
0
0
0
2
0
3
0
0
0
1
2
1
0
0
1
2
1
2
2
0
1
0
0
1
0
0
1
2
0
0
1
2
0
1
2
0
0
0
1
1
1
1
0
0
1
1
1
0
0
0
0
2
2
2
2
1
1
0
0
0
1
0
4
2
0
1
0
2
2
0
1
1
0
1
1
0
0
1
2
2
0
0
1
1
0
0
1
0
0
1
1
1
0
0
3
1
1
1
0
0
1
1
0
2
1
0
0
0
0
1
0
1
2
2
0
2
2
0
0
2
2
0
0
0
1
0
1
1
0
2
2
0
0
2
1
1
1
0
2
0
1
2
1
1
2
0
0
0
2
0
1
1
1
0
1
0
1
0
0
0
0
0
2
2
0
1
0
1
0
0
0
1
2
1
0
2
1
2
1
0
1
0
1
0
0
1
1
2
1
0
1
1
1
2
0
0
0
0
2
0
2
0
0
3
2
0
0
0
0
0
0
0
1
2
1
0
1
2
1
0
1
1
1
1
0
0
0
2
1
0
2
0
0
0
1
3
2
0
0
2
1
0
1
0
0
1
0
1
0
3
1
1
1
0
0
2
0
1
1
1
0
0
1
0
1
1
0
1
2
1
2
2
1
0
1
1
0
1
0
0
1
0
0
1
0
2
0
0
0
1
1
2
1
1
1
1
1
1
0
0
2
2
1
0
1
0
1
0
0
2
1
0
1
2
0
0
1
1
1
1
1
2
2
0
0
0
2
1
0
2
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
2
0
2
2
1
1
0
2
0
0
0
0
1
0
1
1
3
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
1
2
1
0
0
1
2
1
0
0
1
1
2
0
0
0
0
3
2
0
0
1
2
0
1
2
2
1
1
2
1
2
0
0
1
2
0
1
1
1
2
2
2
0
2
2
0
1
0
2
1
2
0
0
0
1
1
1
0
0
0
1
0
1
1
0
1
2
1
0
2
2
0
0
0
0
1
0
2
0
0
1
0
1
1
1
0
0
0
2
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
1
0
2
2
1
1
1
2
1
0
0
0
1
0
0
1
0
0
0
2
1
0
1
1
2
1
1
1
1
1
1
1
1
0
0
1
0
2
0
0
0
2
2
4
1
0
3
1
1
1
0
1
1
0
2
0
0
3
0
1
3
1
0
0
3
2
1
0
0
0
2
0
0
3
0
1
0
2
2
1
1
2
0
2
1
2
1
0
0
1
0
1
1
2
1
0
0
2
0
3
0
1
2
1
0
0
1
0
1
0
2
1
1
0
0
1
1
0
0
1
0
2
1
0
0
0
1
0
0
1
1
1
0
1
1
0
2
2
1
1
0
1
1
2
1
2
0
1
0
1
0
1
2
1
0
2
0
1
0
1
0
0
0
1
0
2
1
1
3
0
0
1
0
0
1
1
1
1
0
1
1
0
0
0
0
2
0
0
2
1
1
2
0
2
2
0
1
0
2
2
0
1
0
2
0
1
0
2
0
1
0
1
0
3
0
0
1
0
2
1
0
1
3
2
1
0
0
0
1
1
0
1
0
2
0
0
2
2
2
0
1
0
2
0
1
0
0
0
1
2
2
0
2
3
0
0
0
1
1
2
0
1
0
1
1
0
0
2
0
0
2
2
0
0
1
0
1
0
0
2
2
1
1
0
0
1
0
1
1
2
1
1
1
1
0
0
0
0
0
2
1
0
0
1
0
1
2
0
0
0
1
1
0
1
0
0
0
0
0
1
2
0
2
0
2
1
2
0
0
0
1
1
0
1
1
1
2
0
1
2
1
0
0
1
2
0
3
2
1
0
1
0
0
2
1
1
0
0
0
0
0
2
1
0
0
3
0
2
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
1
2
1
3
2
0
2
0
2
1
0
2
2
0
2
1
0
0
2
0
1
1
1
0
1
2
2
1
1
0
2
2
2
1
2
1
1
0
0
0
1
1
0
1
0
0
1
1
0
0
1
0
2
1
2
1
2
0
1
0
2
0
1
0
0
2
0
1
0
0
0
1
2
0
3
0
1
1
0
1
0
0
2
1
1
1
2
0
1
3
2
1
0
0
0
1
2
1
0
1
1
1
1
0
0
0
0
3
1
2
0
1
1
2
1
1
2
1
0
0
2
0
1
3
1
2
2
2
0
1
2
0
2
0
2
0
0
2
0
0
1
0
1
2
0
1
2
2
0
0
1
2
0
2
0
0
1
0
0
1
2
0
1
0
0
0
0
1
0
2
0
0
1
2
0
2
1
1
0
1
1
2
1
0
0
0
0
1
1
0
1
2
1
1
2
2
0
0
0
1
0
0
1
0
1
0
0
0
0
2
0
0
0
0
3
0
0
2
0
1
0
1
0
0
0
1
1
0
2
0
1
2
1
0
0
0
0
0
0
2
1
2
1
1
3
1
1
2
2
2
2
2
1
0
1
0
1
0
1
2
0
0
0
2
1
0
0
2
1
1
0
0
1
2
2
0
0
1
0
0
0
2
3
0
0
2
1
0
0
2
0
0
2
0
0
0
0
0
0
4
0
2
1
1
0
2
1
1
0
0
2
1
0
0
1
0
1
1
2
1
1
2
0
0
0
0
2
0
0
2
0
0
0
1
2
1
1
1
1
1
0
0
0
0
0
1
1
0
0
2
2
2
1
2
0
1
1
1
0
0
0
1
2
0
0
1
2
0
1
2
0
2
0
0
0
0
1
1
0
1
1
0
2
1
0
1
0
2
0
1
1
0
0
1
0
0
0
0
2
0
1
0
0
3
2
1
0
2
0
0
2
1
0
1
0
0
0
2
1
1
1
0
2
1
0
0
1
1
2
2
1
0
1
1
2
1
1
0
1
2
0
0
1
2
2
2
0
1
1
2
2
1
2
0
1
2
2
1
1
0
0
0
2
0
0
1
0
0
1
0
1
0
1
1
1
0
1
0
0
0
0
1
0
2
2
2
0
0
2
1
2
0
0
0
1
0
2
1
1
1
1
0
2
0
0
0
2
1
0
0
0
2
0
0
1
0
2
1
1
2
0
0
1
1
1
2
0
1
0
3
1
1
1
0
1
0
0
2
2
1
1
0
3
1
0
0
1
1
0
1
1
0
0
1
0
0
2
1
2
0
1
1
0
0
2
0
1
0
1
0
1
1
1
0
1
1
0
0
2
0
1
2
0
1
1
0
1
2
2
2
0
1
0
1
1
0
0
1
0
1
0
0
1
2
0
0
1
1
0
1
0
0
1
0
0
1
1
2
1
2
0
1
1
1
1
0
1
1
0
1
0
2
1
1
1
1
1
2
0
1
1
1
1
0
1
0
0
0
2
2
1
3
2
1
1
2
0
1
3
1
2
0
1
2
1
0
0
2
0
1
1
0
1
0
2
0
1
0
0
0
0
0
1
2
1
0
0
2
2
0
0
0
1
0
0
1
1
1
1
1
0
2
0
1
1
0
1
1
0
1
1
0
1
1
0
2
0
0
0
2
1
1
0
1
0
0
0
1
1
1
0
0
0
2
1
2
0
2
1
0
0
1
0
1
1
1
0
1
0
0
2
1
1
0
1
1
0
0
0
0
0
2
0
0
1
0
1
1
0
0
1
1
2
2
1
1
1
5
1
1
1
0
0
1
1
0
0
2
1
0
0
1
2
3
1
1
2
1
2
2
0
0
2
0
0
2
1
0
2
1
0
0
1
2
1
2
0
1
1
1
2
0
1
0
0
0
0
0
1
2
0
2
1
0
0
2
0
0
1
2
1
1
2
0
0
0
2
0
1
1
1
1
2
0
0
1
1
1
1
2
0
0
1
0
0
0
1
0
1
0
1
0
1
0
0
2
0
1
0
0
0
0
0
1
0
1
1
2
1
2
3
0
0
0
0
2
0
0
1
1
1
0
0
1
2
0
1
1
1
2
0
1
2
0
1
0
2
0
3
0
2
1
1
0
0
0
0
1
0
0
2
1
0
0
2
0
0
2
2
2
2
2
1
1
2
0
1
1
0
1
1
2
0
3
0
2
0
0
1
2
1
0
0
0
0
0
1
2
0
2
0
2
2
2
2
1
3
0
1
0
2
2
2
0
0
2
1
0
0
1
1
0
1
0
1
1
2
2
1
1
0
0
0
1
2
0
0
1
2
0
1
0
2
1
0
1
1
0
0
1
0
0
1
1
2
0
1
0
0
0
0
2
0
0
0
0
2
1
0
0
0
1
0
0
0
0
1
0
0
1
1
1
1
0
1
0
2
2
0
1
2
2
0
0
0
0
2
2
1
1
2
0
0
0
1
0
0
2
3
1
0
1
0
1
2
0
0
2
0
0
1
2
0
2
1
0
0
0
2
0
0
1
1
1
2
2
0
0
2
0
2
0
2
0
0
0
0
0
0
1
1
1
1
0
1
0
1
1
1
2
0
1
1
0
1
1
1
0
1
2
0
2
0
2
2
0
0
1
1
0
1
0
0
0
0
0
2
1
1
1
0
2
0
1
0
0
1
0
2
0
1
0
2
0
2
0
2
0
2
1
1
0
1
0
0
0
0
0
1
0
1
1
0
0
1
1
0
0
1
0
2
0
0
1
1
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
1
0
1
0
0
0
3
0
2
0
0
1
0
0
2
1
2
0
0
1
0
1
0
2
1
1
2
0
0
0
0
0
1
0
1
0
1
1
2
0
0
1
2
0
0
1
0
0
0
1
2
1
0
0
1
0
0
1
1
1
3
0
0
0
1
1
0
1
0
0
1
0
1
0
1
2
1
1
2
0
0
1
0
0
0
1
2
0
0
1
2
1
2
1
2
1
2
1
1
2
0
2
0
1
0
0
2
0
0
2
1
1
0
0
2
0
1
0
0
0
2
0
1
0
2
2
1
2
1
1
2
0
1
0
2
0
0
1
1
2
1
0
0
0
0
0
0
0
2
2
0
1
1
2
2
3
0
2
0
0
0
0
0
0
1
0
1
0
0
1
0
1
1
1
0
0
1
1
1
1
0
0
0
2
2
2
1
2
1
1
2
6
1
2
0
0
1
3
0
0
1
1
0
0
1
3
2
1
1
1
1
0
2
0
0
1
2
1
0
0
0
1
0
2
2
1
1
0
1
1
0
0
0
0
1
1
0
0
0
1
2
0
1
1
1
0
2
0
0
0
2
0
2
0
1
0
0
1
2
1
2
2
1
0
3
2
0
1
2
1
2
2
1
0
0
1
1
0
2
0
0
1
1
2
0
1
1
0
2
0
2
1
1
0
1
1
2
1
0
1
0
0
1
0
2
0
1
1
0
0
0
1
0
2
2
0
0
1
0
0
2
0
1
2
0
1
0
0
1
1
2
1
1
0
0
1
1
0
0
0
1
0
2
2
0
0
0
0
2
2
1
1
1
0
0
2
1
1
1
0
2
1
0
0
0
2
1
1
1
2
0
0
1
0
0
0
2
0
1
1
2
0
1
0
0
0
2
1
2
0
1
0
2
1
1
0
1
1
2
0
0
1
2
1
0
1
1
2
0
1
0
0
0
1
1
2
2
2
2
0
11
0
0
0
2
0
2
2
0
0
1
1
1
1
1
1
0
0
0
0
1
1
2
0
1
0
0
1
1
1
0
0
2
2
1
0
1
1
1
0
2
0
0
2
0
2
2
1
0
0
0
1
0
2
1
0
0
1
0
0
0
2
2
1
1
1
0
1
1
0
0
0
2
1
0
1
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
1
1
1
0
1
2
1
2
1
3
1
1
0
1
1
0
1
3
2
2
2
0
0
1
0
1
1
2
1
0
4
0
0
5
1
0
1
1
0
0
0
1
2
2
0
1
2
1
0
0
1
2
0
1
0
1
2
1
1
1
1
0
1
0
2
2
1
2
2
1
0
0
2
0
0
2
0
0
1
1
0
1
1
1
0
0
2
0
1
1
1
0
0
2
0
2
1
0
1
1
1
0
1
1
0
1
1
1
0
2
1
1
0
1
1
1
2
1
3
0
2
2
1
2
0
0
2
0
1
2
2
2
2
0
1
1
0
0
0
1
1
0
2
0
1
0
1
2
2
2
2
0
2
1
1
1
0
0
1
0
1
0
2
1
1
0
0
2
1
0
3
0
0
0
0
1
0
0
0
1
0
0
0
1
0
2
2
0
0
2
0
0
0
1
1
1
1
0
1
0
0
0
0
0
0
0
0
2
1
0
2
1
0
0
0
2
0
1
1
1
0
0
0
1
5
1
1
0
0
0
0
3
1
0
0
1
1
0
2
2
1
0
0
0
1
1
0
0
0
1
0
0
2
0
1
0
1
1
0
2
1
1
0
1
1
0
1
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
1
2
1
2
0
1
2
0
1
0
0
1
0
1
2
1
1
0
0
1
0
0
4
0
1
0
2
2
2
1
1
1
0
0
2
1
0
1
0
0
0
0
0
2
2
1
1
0
0
0
1
1
0
1
1
0
1
0
2
2
2
0
0
0
1
2
0
1
1
1
1
1
0
1
1
2
0
0
2
0
1
1
1
1
1
1
0
0
0
0
0
1
1
0
1
1
2
0
0
0
0
1
0
2
0
1
1
1
1
1
0
0
1
0
2
0
0
0
0
0
1
0
0
1
2
2
1
2
1
0
2
1
1
0
3
1
1
1
1
2
0
2
1
0
2
0
0
0
2
0
0
0
0
1
2
0
3
3
1
2
1
2
2
2
1
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
1
1
0
0
1
1
2
0
0
0
0
0
2
0
0
2
2
2
0
0
1
0
0
0
0
0
1
1
1
1
0
0
0
0
0
1
0
2
2
1
0
1
0
2
0
2
1
2
1
1
0
0
1
1
2
0
1
2
1
1
2
1
2
2
0
0
0
1
0
0
1
1
2
0
2
0
0
0
2
2
1
1
0
0
1
0
2
2
0
0
1
1
1
0
0
0
0
1
1
1
1
1
1
2
0
1
0
0
2
1
1
0
2
2
1
0
0
0
0
2
0
1
0
0
1
0
1
1
2
1
1
0
0
2
1
1
0
0
0
1
0
1
2
1
1
2
0
2
0
0
1
2
0
0
0
0
1
2
2
0
2
0
1
2
1
1
0
2
2
1
1
0
1
1
1
0
0
1
1
1
0
0
1
0
0
0
0
1
0
1
1
0
0
0
1
1
1
1
1
0
0
1
1
1
2
3
0
1
1
0
0
0
1
1
0
2
2
0
0
0
2
2
1
1
1
0
1
0
0
1
2
0
0
2
1
0
0
0
1
0
0
2
0
0
2
0
1
1
0
1
1
2
0
2
0
2
0
0
0
0
0
2
0
0
3
0
0
2
0
0
1
0
0
2
0
1
1
1
0
1
2
1
0
2
0
2
1
0
1
2
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
2
2
0
2
0
4
1
2
0
1
0
0
0
1
2
0
1
1
1
0
2
1
2
0
1
1
0
0
1
1
0
1
2
2
0
1
1
2
2
2
0
1
0
2
0
0
1
1
1
2
2
1
0
1
3
1
1
2
1
2
1
0
0
1
1
1
2
0
2
2
1
0
0
1
1
0
0
1
1
1
1
0
1
2
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
2
1
0
1
2
0
2
0
0
1
0
2
1
1
0
2
0
2
0
0
0
0
2
0
0
0
2
2
1
0
0
0
0
0
0
1
0
1
0
0
1
0
1
1
1
0
1
0
1
1
0
1
0
2
0
1
0
1
0
1
2
2
1
0
0
2
0
1
2
0
2
1
1
1
0
1
2
0
1
1
0
0
0
2
2
2
1
6
2
0
2
0
1
1
1
1
1
1
1
1
0
0
1
0
0
0
1
0
1
2
1
1
1
1
1
0
0
0
1
0
0
0
0
2
0
0
0
1
1
0
2
1
0
1
0
1
2
1
1
0
0
1
1
1
0
2
1
0
0
1
0
0
0
1
3
0
0
2
0
1
0
0
1
1
0
0
2
2
0
0
0
2
1
2
1
0
0
0
1
0
1
0
1
1
1
0
2
2
1
1
0
1
1
1
2
1
0
0
1
1
0
0
0
0
2
0
2
2
3
0
2
0
0
1
0
0
2
0
1
0
2
0
0
2
0
0
0
0
1
2
0
0
2
1
1
2
0
0
1
0
1
0
0
2
2
1
2
1
2
0
2
1
0
0
2
1
0
2
1
2
0
1
0
1
1
2
0
1
2
1
0
1
1
1
0
1
0
1
2
1
1
1
0
1
0
0
0
0
0
1
0
0
0
2
1
0
0
3
2
0
1
1
0
2
0
1
1
0
2
1
0
0
0
0
2
2
0
0
1
1
0
1
1
1
0
0
0
2
1
2
2
2
1
1
0
1
0
0
0
1
0
0
2
1
0
0
2
1
2
0
0
0
1
0
0
1
0
0
0
0
0
1
2
0
1
0
1
1
1
0
0
1
1
0
0
0
1
0
0
1
1
0
1
0
0
0
0
1
1
1
4
1
0
1
0
1
2
2
0
3
2
1
2
1
0
1
1
1
0
0
2
2
0
1
1
1
0
2
1
0
2
0
2
0
0
0
2
2
2
1
2
2
0
1
1
1
1
1
0
0
0
2
0
0
0
0
1
2
0
0
0
0
2
2
2
0
0
0
0
0
2
0
0
0
1
2
1
1
2
0
0
1
0
1
1
0
0
0
0
1
1
1
1
2
0
0
0
1
0
0
2
1
2
0
0
0
0
1
0
0
0
0
1
3
1
1
1
0
0
2
0
1
0
1
1
0
1
1
1
0
0
2
0
0
1
0
2
1
0
2
0
0
1
1
1
1
1
1
0
0
2
0
2
0
1
3
0
2
0
0
0
0
0
0
1
1
2
2
2
4
2
1
0
0
0
0
1
1
2
1
0
2
0
0
0
0
1
0
0
1
1
0
2
3
0
2
0
1
0
1
0
0
0
2
0
0
1
0
1
2
1
1
2
1
2
0
2
0
0
2
0
1
1
0
0
1
2
1
0
0
1
2
0
2
1
0
4
2
2
0
1
2
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
1
1
2
0
0
0
0
1
3
0
0
0
0
1
1
1
0
2
0
1
0
1
1
2
1
0
0
0
0
1
0
1
0
3
0
1
1
0
0
0
0
0
1
0
1
1
0
1
0
0
1
0
2
0
0
2
1
1
0
1
0
0
1
0
0
0
0
1
1
2
0
0
1
2
1
3
1
2
0
0
2
2
2
0
1
0
0
1
0
2
1
1
0
0
0
1
0
0
2
0
1
0
1
1
0
1
2
2
2
0
0
1
1
1
0
2
1
1
0
1
0
1
2
0
1
2
1
2
0
2
2
0
1
2
1
2
0
1
0
1
0
0
1
2
1
2
0
0
1
0
1
2
0
0
0
2
0
0
3
1
1
1
1
0
1
0
1
0
0
1
1
0
1
0
2
1
0
1
0
1
0
0
0
2
2
2
0
1
0
1
0
0
1
1
2
0
1
1
1
1
2
0
5
2
0
2
0
1
0
0
0
0
0
1
1
0
1
0
3
2
2
0
1
1
1
1
1
1
0
2
2
0
0
1
2
1
0
1
1
0
3
1
2
0
0
2
3
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
2
2
1
0
1
0
2
2
2
1
1
2
2
2
0
0
2
1
1
2
1
0
0
8
2
1
0
2
0
0
2
0
1
1
2
1
1
2
0
1
1
0
1
1
0
1
0
0
1
0
1
1
2
1
2
1
0
0
0
1
1
0
2
0
0
1
0
0
4
2
1
1
0
2
0
1
0
2
0
0
1
1
1
0
1
1
1
0
1
0
0
1
0
2
1
2
2
1
3
3
0
1
0
0
1
0
1
0
0
0
0
1
1
2
2
1
1
2
0
0
0
1
0
2
0
1
0
1
1
0
0
0
0
1
1
0
0
1
2
2
2
1
0
1
0
0
0
2
1
4
0
2
1
0
1
0
0
0
1
0
1
1
1
0
1
1
1
1
1
1
0
1
1
0
1
0
0
0
2
0
0
0
2
0
1
0
1
0
0
0
3
0
0
0
0
0
0
0
2
1
0
1
2
2
2
0
2
0
2
0
2
1
0
0
1
2
1
1
2
2
2
1
1
1
2
1
0
0
1
0
0
1
2
2
2
1
0
1
0
1
0
2
0
0
2
2
0
0
0
1
0
0
0
0
1
2
0
0
1
1
0
1
0
0
0
1
1
0
1
1
4
0
2
2
0
1
2
0
2
1
2
3
1
1
1
2
0
1
1
1
2
1
1
1
2
1
0
1
0
0
0
1
0
1
0
0
0
1
1
0
1
0
0
0
1
4
0
2
3
1
1
3
0
1
1
1
1
0
0
1
6
1
5
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
3
1
1
1
0
2
1
2
0
0
0
1
1
0
1
1
0
2
1
1
3
0
1
1
1
1
0
0
2
2
0
1
0
1
1
1
0
0
1
1
2
0
2
0
0
0
1
2
0
0
0
2
0
2
2
0
2
1
1
1
0
1
2
2
1
1
0
0
1
0
2
1
1
0
2
2
0
0
2
0
2
0
1
0
1
1
0
3
0
0
0
1
1
0
1
1
2
0
1
0
1
0
0
1
0
1
0
0
3
1
0
0
1
0
1
0
0
0
1
2
2
1
0
2
2
1
0
0
1
2
0
1
1
1
1
1
1
0
0
1
0
1
1
1
2
2
1
0
2
1
2
2
0
2
0
0
1
2
0
1
1
0
0
0
1
0
1
2
1
0
0
2
2
0
1
0
0
2
0
0
0
1
2
0
2
1
0
2
0
1
2
0
2
0
0
2
0
1
0
2
1
0
0
0
1
0
0
2
2
1
1
0
0
2
1
0
0
0
0
1
1
0
2
0
0
2
1
1
1
0
1
0
0
0
1
2
1
0
0
2
1
1
0
0
1
2
2
1
1
1
0
0
1
0
1
2
1
1
1
1
1
0
0
0
2
3
2
1
0
0
0
2
0
2
0
0
0
1
0
2
0
0
0
1
1
0
2
1
0
0
1
1
2
2
2
2
1
0
2
0
0
1
1
1
2
1
0
1
2
1
1
0
0
1
0
4
0
0
0
0
1
0
2
3
1
0
0
1
1
1
0
0
0
0
1
0
0
1
1
0
2
1
0
0
1
1
0
1
1
0
0
0
0
0
0
2
1
2
2
1
1
2
0
1
0
0
0
2
0
1
1
2
0
0
0
0
2
2
1
1
1
0
1
0
1
2
2
0
0
0
0
1
0
1
1
0
1
0
2
1
1
1
0
2
0
0
0
3
0
1
0
1
2
1
1
1
0
3
1
0
1
0
1
0
1
0
0
2
1
0
0
0
0
0
1
2
1
2
0
1
0
0
0
0
0
0
1
1
0
0
1
1
2
1
0
0
0
0
1
0
1
0
0
0
1
0
2
1
1
1
2
2
0
0
1
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
1
1
1
1
1
0
1
0
1
0
0
0
2
1
0
0
0
0
0
0
2
0
1
0
0
2
2
0
1
1
0
1
2
0
0
2
1
1
2
1
2
1
0
0
2
0
0
0
0
0
1
1
2
1
2
0
0
0
0
2
0
0
1
1
0
0
0
1
1
0
0
0
1
3
0
0
0
1
0
0
1
0
2
1
0
1
0
1
0
2
2
0
0
1
0
2
0
0
0
2
1
0
0
0
0
2
1
0
0
0
0
2
2
1
2
1
1
0
0
1
1
0
0
0
2
1
0
1
0
0
0
1
1
0
2
2
1
2
1
1
0
1
0
1
1
2
2
1
3
1
1
0
2
2
0
0
0
1
0
0
2
1
0
0
0
1
0
2
2
1
2
1
0
0
2
1
0
0
2
0
2
1
1
2
1
1
0
0
1
1
0
0
0
0
2
0
2
2
1
2
0
1
1
1
1
2
0
0
1
0
0
0
0
1
0
0
0
1
0
2
1
0
0
0
1
0
1
1
0
1
2
2
0
0
0
1
1
4
2
0
1
1
1
1
1
0
0
0
1
2
1
1
0
1
0
2
2
1
2
1
0
0
2
0
0
0
0
2
1
2
0
1
1
1
0
1
1
1
3
1
2
0
0
0
1
1
0
1
1
0
1
1
0
1
1
1
2
1
0
1
2
0
1
1
0
1
0
0
1
2
1
2
1
1
1
1
0
1
1
1
0
0
2
0
1
3
0
0
2
2
0
0
1
3
0
2
1
1
1
0
0
0
1
2
2
2
1
0
0
0
1
2
1
0
0
1
0
0
1
0
2
1
0
1
2
0
0
1
0
1
1
0
0
2
1
0
1
0
1
0
0
0
1
0
1
2
1
0
0
1
1
1
0
0
1
1
0
0
1
2
2
2
1
4
0
0
0
0
2
1
1
1
1
2
1
0
1
2
0
1
0
1
1
0
1
1
0
2
2
0
0
3
0
0
1
1
1
0
0
2
0
0
0
1
1
1
0
2
0
0
0
1
0
0
0
2
1
1
0
2
2
0
2
1
0
2
0
1
1
2
4
0
0
0
0
2
2
0
0
0
0
1
1
1
0
0
1
1
0
0
3
1
0
2
0
2
2
3
0
2
1
0
2
0
2
0
0
0
0
1
1
1
1
0
0
1
1
0
0
0
2
2
2
1
0
1
0
0
1
0
0
1
0
1
1
1
1
1
2
1
1
1
0
2
0
1
1
1
0
1
1
0
0
1
0
0
0
1
2
0
1
2
1
2
2
0
1
0
1
0
1
1
3
1
1
0
2
0
0
2
0
1
0
1
0
2
0
2
2
0
1
0
0
0
1
2
0
1
0
1
2
1
0
0
1
0
0
1
2
2
0
0
0
2
0
1
0
2
1
0
0
2
0
1
1
1
1
1
2
0
0
0
0
1
0
0
1
2
0
1
0
0
2
0
0
1
1
0
1
2
2
0
1
0
0
1
0
1
1
1
1
0
1
0
0
0
1
2
2
0
0
1
3
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
2
0
2
1
0
2
2
0
1
1
0
1
1
1
1
2
1
0
1
0
6
1
2
0
1
2
0
2
0
1
1
0
0
2
2
2
1
0
0
1
1
1
1
1
2
1
2
1
1
0
0
1
2
2
2
0
0
0
1
0
1
0
0
0
0
0
2
0
3
2
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
2
0
0
1
2
0
1
1
0
0
0
2
0
2
0
0
2
2
0
0
0
0
2
0
1
2
0
0
1
2
0
0
2
0
2
0
2
0
0
0
2
2
0
1
1
1
1
0
0
0
0
3
1
0
0
0
0
1
0
0
2
0
0
0
1
0
3
1
0
2
2
0
1
0
1
0
0
0
1
2
3
0
0
0
1
0
0
0
2
2
0
0
0
1
1
2
0
2
0
0
0
0
1
1
4
0
0
0
0
2
1
0
0
1
1
2
0
1
0
0
0
0
0
2
0
2
1
0
1
0
2
2
1
2
1
0
0
1
2
2
0
2
0
0
0
0
2
0
0
2
1
1
0
1
2
2
1
2
1
0
0
0
0
1
0
0
2
1
1
0
2
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
2
1
0
0
0
2
0
5
0
2
1
1
1
0
0
0
0
0
1
1
0
1
2
0
1
0
0
2
1
0
0
2
0
1
0
1
0
0
1
0
0
2
1
2
0
2
0
1
0
1
0
0
1
2
1
2
1
1
0
0
0
0
1
2
0
0
1
0
1
0
2
0
0
1
1
0
0
1
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
2
1
1
2
0
0
1
1
0
3
0
1
1
1
1
2
0
1
1
2
2
2
1
1
0
1
0
2
1
1
1
0
1
2
2
2
1
0
0
1
1
5
0
0
0
0
1
0
2
2
0
0
1
2
0
0
0
2
0
2
0
2
2
0
0
1
1
0
0
0
0
1
0
0
2
0
0
0
0
3
2
0
1
1
1
0
0
1
0
2
0
2
0
1
0
1
2
0
2
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
2
1
0
0
0
1
1
2
1
0
2
0
0
0
0
1
1
1
1
1
0
1
0
1
1
0
1
0
0
0
2
2
1
0
1
0
0
1
2
2
0
0
0
0
1
1
1
0
1
2
2
0
1
0
0
1
1
0
3
0
0
2
1
1
1
0
1
2
0
0
2
2
0
1
0
0
2
1
2
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
2
0
0
2
1
1
0
0
0
0
2
2
0
2
1
1
1
1
2
1
2
2
1
0
1
1
2
2
0
0
1
0
0
2
0
1
2
1
1
0
2
1
2
1
2
0
0
2
1
0
1
1
1
3
3
1
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
2
0
1
2
0
2
2
0
2
2
0
1
1
2
2
0
1
0
1
0
0
1
1
0
0
0
0
2
0
0
0
0
2
0
0
1
0
1
2
0
1
1
2
0
0
0
0
1
0
0
1
0
1
2
2
1
2
0
1
0
0
2
2
1
0
0
2
1
1
3
2
0
1
0
1
4
0
2
1
1
2
2
0
0
1
1
0
0
0
0
1
1
0
3
0
0
2
1
1
1
0
1
1
1
0
0
0
0
2
2
0
0
0
1
2
0
2
3
1
0
2
2
1
1
2
0
0
0
2
4
1
1
0
0
0
0
2
2
1
2
1
0
2
1
0
0
1
0
2
1
0
2
0
0
1
1
0
1
0
0
2
2
0
1
1
1
1
2
0
2
2
0
0
2
0
2
1
0
2
0
1
1
0
1
0
1
2
0
3
0
0
0
1
2
2
0
0
2
1
2
2
0
0
2
1
0
1
2
0
0
1
1
1
0
1
0
2
0
0
0
1
1
1
1
0
1
1
2
0
0
1
1
0
0
1
1
0
2
0
0
1
1
2
0
2
1
1
1
1
0
0
1
0
2
0
0
0
1
1
0
0
0
2
1
0
1
2
2
0
0
2
1
1
0
1
1
2
0
1
2
1
1
1
1
1
0
0
1
2
2
1
1
2
7
0
2
1
1
2
1
1
1
1
0
1
0
0
0
1
1
1
1
1
1
1
5
1
1
0
0
1
1
1
1
1
0
0
0
0
2
1
0
0
1
2
1
1
0
1
2
2
0
0
0
0
0
0
0
2
0
0
1
1
2
1
1
1
1
1
4
2
0
0
1
0
0
2
1
2
1
3
1
0
0
2
0
2
0
1
1
1
1
0
0
2
0
1
1
1
2
1
0
1
0
1
1
0
1
1
1
2
2
1
0
0
2
2
0
0
0
1
0
1
1
2
1
2
2
2
0
0
2
2
0
1
0
1
0
2
2
1
2
1
1
1
1
0
1
1
0
1
1
0
2
1
0
0
0
2
1
2
0
0
1
0
2
2
0
2
0
0
1
0
1
1
1
0
0
1
0
1
0
0
1
1
0
0
2
1
1
1
2
0
1
1
0
1
0
0
1
1
2
1
2
1
0
0
1
0
0
2
0
0
2
1
0
0
1
0
0
1
1
0
1
0
0
0
1
1
0
0
0
0
2
2
10
1
1
0
2
0
0
1
0
0
2
0
1
2
0
2
0
1
2
0
0
0
0
2
0
1
0
0
1
1
1
2
3
1
0
3
2
1
1
1
2
0
2
2
0
0
1
0
0
1
0
1
1
0
1
0
0
1
1
1
2
3
0
0
1
2
1
1
1
1
2
0
0
0
1
0
2
2
1
1
1
1
0
1
0
2
2
1
3
0
2
1
2
1
0
1
0
0
1
2
2
1
0
1
0
1
1
0
0
1
0
0
0
0
1
0
1
1
0
0
1
1
0
1
0
0
1
0
1
0
0
2
0
2
1
2
0
1
1
0
1
1
1
0
2
0
1
0
2
2
1
1
2
1
1
1
1
1
0
0
0
1
2
0
0
2
1
0
0
1
0
1
1
3
2
1
2
0
2
1
2
1
0
0
1
0
0
1
0
1
1
1
0
1
1
2
1
1
0
2
0
0
1
2
1
1
0
0
0
0
2
2
2
0
0
1
2
1
0
0
2
2
0
2
1
1
0
1
2
1
0
2
0
0
1
2
0
3
2
1
0
1
1
1
2
1
0
0
1
2
0
0
1
1
2
1
0
0
1
1
2
0
3
4
0
0
0
0
1
0
1
1
1
1
1
1
2
1
0
0
2
0
1
1
0
0
0
0
1
0
2
0
1
2
0
1
0
1
1
2
0
0
2
1
1
1
0
0
2
0
0
0
1
1
0
2
3
1
0
1
2
2
0
0
2
0
0
2
1
1
0
2
0
0
2
2
3
0
0
0
0
1
1
2
2
2
2
2
0
0
0
0
0
0
2
2
1
1
0
1
0
1
1
0
0
0
1
1
0
0
2
1
2
1
1
0
1
0
1
1
1
2
0
1
0
0
0
0
0
1
0
0
1
0
2
0
1
0
0
2
1
0
2
0
0
1
0
0
0
0
0
1
1
0
2
2
0
0
0
2
2
1
0
0
0
1
1
2
0
0
0
0
2
2
1
1
2
1
1
1
0
0
1
1
0
0
2
0
2
0
0
0
1
0
1
2
0
0
0
0
1
1
2
0
0
1
0
1
0
0
1
2
2
0
0
0
0
1
0
1
0
2
0
0
0
1
0
1
1
2
2
0
1
2
0
1
1
1
3
0
0
0
1
0
0
0
2
0
0
0
1
0
2
2
0
0
2
3
1
2
2
1
1
0
0
0
1
0
1
2
1
2
0
0
0
1
1
0
2
1
0
2
0
2
1
2
1
0
1
2
0
1
1
0
0
0
0
0
1
3
2
1
0
2
6
0
1
0
0
0
1
0
1
2
0
2
1
0
2
0
0
0
2
0
1
0
0
2
1
1
2
0
2
0
0
0
2
1
1
1
1
2
1
1
1
1
1
2
2
2
0
0
0
0
0
0
0
0
0
1
0
2
1
1
0
1
1
1
1
0
2
0
1
0
0
1
2
0
0
2
1
2
0
1
1
0
2
0
0
1
0
0
1
0
2
1
0
1
2
1
1
0
2
2
0
1
0
0
3
0
0
1
1
2
0
1
0
1
0
0
0
1
2
2
0
1
1
0
1
0
2
1
0
2
2
0
2
0
1
1
2
1
2
1
1
1
2
1
2
3
0
1
2
2
2
0
1
0
2
0
2
2
1
0
0
1
0
1
2
0
2
0
1
0
1
1
0
0
0
0
0
0
1
2
1
0
1
0
1
1
0
0
1
0
0
0
0
2
0
0
0
2
1
1
0
0
1
0
1
2
0
1
0
1
1
1
2
1
0
0
1
2
1
2
1
3
1
0
0
1
0
2
0
0
0
1
0
0
0
1
0
1
2
1
0
2
0
0
2
0
1
0
0
0
1
0
1
1
2
1
0
2
0
0
0
2
2
2
0
0
0
1
1
2
1
2
1
1
0
1
2
1
1
2
1
2
2
1
0
0
3
0
0
0
0
0
1
2
0
1
1
1
0
1
1
2
0
2
0
0
1
0
0
0
1
2
1
1
1
2
0
0
1
0
0
2
2
0
0
0
2
1
0
1
2
0
1
1
1
2
1
2
1
0
0
0
1
0
1
0
2
1
0
1
1
3
1
0
1
0
0
2
2
0
0
0
0
0
1
1
0
1
0
2
1
0
0
0
1
0
1
2
0
0
1
1
1
1
2
2
0
2
0
0
0
0
0
1
1
0
2
1
2
0
2
1
0
1
1
1
2
0
0
1
0
2
1
0
0
0
0
1
2
1
0
0
1
0
1
1
1
0
1
1
2
1
0
0
0
2
1
0
0
0
2
0
1
0
0
1
0
0
0
0
0
1
0
0
2
0
2
0
0
1
1
0
1
0
0
0
0
1
2
0
0
3
2
2
0
1
1
2
3
0
0
2
1
0
2
2
0
0
1
1
1
0
3
1
1
1
0
0
0
1
2
1
2
0
4
0
2
2
0
0
1
2
0
2
0
0
1
0
0
2
0
7
0
2
0
0
1
0
0
0
1
2
0
0
1
0
0
0
0
1
1
2
0
1
1
0
1
0
1
1
2
0
4
2
3
1
1
0
2
0
2
0
0
2
0
2
1
1
2
1
2
1
0
2
1
0
1
2
1
0
1
0
0
0
1
4
0
0
1
2
2
1
1
1
1
1
1
2
0
2
2
0
0
1
1
1
0
2
2
0
0
0
1
3
2
0
0
0
2
1
0
1
1
1
0
0
1
2
2
2
0
3
1
0
1
0
0
1
0
0
0
0
2
1
2
1
1
0
2
0
0
1
0
0
1
2
0
2
2
2
0
0
1
0
1
2
0
0
2
0
1
1
0
0
0
1
0
0
0
2
1
1
0
1
0
1
0
1
2
2
0
3
1
1
0
0
0
2
1
0
1
0
0
0
2
0
1
2
1
2
1
0
1
0
1
0
0
1
2
0
2
1
0
1
2
2
2
0
0
0
0
1
0
0
1
2
1
1
2
0
2
1
1
0
0
0
1
0
2
2
0
0
1
2
0
0
0
0
2
0
0
0
1
0
0
0
1
1
0
1
1
2
1
1
1
1
3
0
0
0
1
1
0
0
1
0
1
0
1
2
0
2
1
1
2
1
0
2
0
1
0
0
2
1
1
0
0
1
1
0
2
2
0
0
1
1
0
1
1
2
0
1
0
0
0
2
0
0
0
2
1
2
0
2
1
2
0
0
1
0
2
1
2
1
1
0
0
1
0
1
2
2
2
1
1
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
1
1
1
1
1
2
2
1
2
1
1
2
0
1
2
2
0
0
1
0
0
0
1
0
2
0
1
1
1
0
3
2
1
2
0
0
2
0
1
6
2
2
1
0
3
0
4
0
1
2
0
1
2
2
0
0
1
2
0
1
0
1
1
1
1
1
0
0
0
1
0
2
0
2
1
0
1
1
1
0
1
0
4
1
1
1
2
4
0
0
1
2
2
0
0
1
0
0
1
0
0
0
0
1
0
0
1
1
1
1
0
2
2
2
0
0
0
3
1
3
2
1
0
0
2
1
0
0
0
1
1
0
1
0
2
0
0
2
2
0
2
1
0
2
0
2
2
1
1
2
1
0
1
0
1
1
0
2
1
1
1
0
1
1
0
0
2
1
0
2
1
1
0
2
2
1
1
0
2
0
1
0
1
2
1
1
1
1
1
1
2
0
0
0
1
0
1
2
1
0
1
2
1
0
1
3
1
0
0
1
0
0
2
0
2
0
1
0
2
0
0
2
1
0
2
0
1
1
2
0
1
0
1
0
0
1
0
2
0
1
0
2
0
0
1
2
2
1
2
1
1
1
0
2
1
0
1
0
0
0
2
1
0
1
0
0
0
2
0
0
0
0
2
0
1
0
1
1
0
1
0
0
0
2
2
0
2
1
0
2
2
2
2
0
0
2
0
0
1
0
1
0
2
0
2
3
1
0
0
0
2
0
1
2
2
2
1
1
1
1
0
0
1
2
0
0
0
1
1
1
0
2
1
0
0
0
2
0
0
1
0
1
0
0
0
1
1
2
1
2
1
3
2
1
2
1
1
1
0
2
0
1
1
0
1
1
0
1
1
1
1
1
1
1
0
1
1
2
3
3
0
2
0
2
0
0
1
2
0
2
0
1
0
2
1
1
2
1
2
1
0
0
2
0
2
1
2
2
2
0
0
0
1
0
0
0
2
2
0
1
2
0
0
1
0
2
1
2
0
0
2
1
1
0
2
0
0
0
0
1
2
0
1
0
2
1
0
2
0
0
2
1
0
0
1
2
2
0
0
0
0
0
0
0
1
0
2
1
2
0
1
0
0
0
2
1
1
2
0
0
2
0
1
3
2
0
1
0
2
2
0
1
0
2
2
1
0
0
2
2
1
1
0
1
0
1
1
0
1
0
0
0
0
0
1
1
0
2
0
1
1
0
1
1
3
1
0
0
0
0
1
2
0
0
0
0
0
1
2
1
1
0
0
2
1
0
0
0
1
1
3
1
1
2
1
1
0
0
2
0
2
0
2
0
1
1
0
0
2
1
0
2
0
1
0
2
2
2
0
1
2
0
0
1
2
0
2
0
0
0
2
1
2
1
1
0
0
0
0
1
1
0
0
2
2
1
0
1
2
1
1
1
0
2
0
0
0
2
1
1
1
1
1
1
1
0
1
2
2
0
0
0
1
2
2
1
0
0
1
1
0
0
2
0
1
0
0
2
2
0
2
0
2
1
0
2
0
0
0
0
1
1
0
1
1
0
1
2
0
0
0
0
0
0
0
0
4
0
2
2
1
1
0
0
1
0
0
1
0
0
2
0
1
1
2
1
1
1
1
0
1
0
0
0
0
2
1
1
2
2
0
0
0
0
1
0
1
0
1
0
0
0
1
2
0
1
0
2
2
0
0
1
1
0
0
0
1
2
3
1
0
0
1
3
0
0
1
0
1
1
1
2
0
1
1
0
0
0
2
0
2
1
1
0
2
1
1
2
2
0
3
2
1
1
3
2
0
0
0
0
2
2
0
1
2
1
0
0
1
0
0
2
0
1
0
1
0
2
1
1
1
1
1
0
0
0
1
2
1
2
0
2
0
0
0
0
2
0
1
0
0
0
0
2
1
0
1
0
2
1
0
0
1
0
1
1
0
1
1
1
1
1
1
2
2
1
1
1
0
0
2
0
1
1
0
2
0
0
2
1
0
1
1
2
1
0
1
1
0
0
0
0
2
2
0
1
0
1
2
1
1
1
0
1
1
2
0
0
1
1
1
0
1
0
0
0
1
1
1
2
2
1
0
2
1
0
1
0
0
2
1
0
0
3
0
1
0
1
0
0
1
0
0
0
0
1
0
2
0
2
1
2
1
0
0
0
1
1
2
1
2
0
1
1
0
2
2
0
0
1
0
1
1
0
1
2
1
2
0
0
2
0
0
2
0
2
0
0
0
0
1
1
1
2
2
2
2
1
0
1
0
1
2
0
2
1
1
0
1
1
2
0
1
0
0
0
2
2
1
2
4
0
2
0
0
2
0
1
1
0
1
2
1
1
2
1
2
0
0
1
0
0
1
1
0
1
2
1
0
0
1
1
0
1
1
1
0
0
0
1
0
0
2
2
0
2
0
1
0
1
0
2
0
0
0
2
1
0
1
1
0
1
0
0
1
0
0
2
1
0
1
1
2
3
1
0
1
1
0
2
1
2
1
0
0
1
0
1
0
0
1
0
1
1
0
2
1
1
2
2
0
0
1
1
2
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
2
1
2
1
0
0
0
0
1
1
5
0
0
1
3
2
2
1
2
2
0
1
0
2
0
1
1
2
2
2
2
2
1
0
0
2
3
1
0
3
0
1
2
0
1
2
1
1
0
2
1
2
1
0
0
0
0
1
2
0
2
0
0
1
0
1
0
0
1
1
1
3
3
0
1
0
0
1
1
2
0
2
0
1
1
2
0
2
1
0
0
0
0
0
1
0
2
1
0
2
2
0
0
2
0
2
0
3
2
0
1
2
2
2
1
0
0
1
0
0
0
0
2
1
0
0
1
1
0
0
0
1
0
2
1
1
1
2
1
1
1
0
2
1
3
1
0
1
0
1
0
3
0
2
0
0
0
1
0
0
0
1
1
2
2
0
2
1
1
2
0
1
2
1
0
0
2
0
1
0
1
0
0
1
0
1
0
1
2
0
0
1
1
1
1
1
0
0
1
2
1
2
1
2
0
1
0
0
0
2
2
1
0
1
0
0
2
2
0
2
0
2
1
0
2
2
1
2
3
1
0
1
1
1
1
0
0
0
0
0
0
1
2
1
2
1
0
1
0
0
3
0
1
0
0
1
1
1
2
0
0
0
0
1
1
2
0
1
0
1
1
1
2
0
0
1
0
2
1
2
0
0
1
0
1
1
0
0
0
1
0
0
1
1
0
1
0
2
2
3
2
1
2
0
1
0
1
0
1
2
1
2
0
0
0
1
0
0
0
1
2
0
0
0
2
0
2
0
2
0
2
0
2
2
1
1
1
0
0
0
1
2
2
2
3
1
1
1
0
0
2
0
0
0
2
0
1
2
0
2
2
0
2
2
2
1
0
0
1
2
1
5
0
1
2
2
0
0
0
2
1
1
2
2
1
2
0
0
1
0
0
0
1
1
0
1
0
1
1
1
1
2
0
0
0
1
1
0
2
0
2
0
2
1
2
0
0
0
1
0
0
1
0
0
1
1
2
1
2
2
1
0
1
0
0
1
0
1
1
0
0
0
1
2
0
0
1
0
0
0
1
0
2
2
0
0
3
0
0
1
1
0
1
2
0
0
1
0
0
0
0
1
0
2
1
0
1
0
0
0
0
2
1
0
1
0
0
1
1
1
0
1
0
0
0
2
1
1
0
0
2
0
1
0
1
1
0
2
1
0
0
0
1
0
1
0
2
2
0
1
1
1
0
1
1
0
0
1
2
0
1
0
0
0
1
1
1
0
1
1
2
1
1
2
1
0
1
0
0
0
1
2
1
1
0
1
2
1
1
1
1
1
0
1
2
5
0
3
0
1
0
1
1
1
0
0
1
0
0
0
0
0
0
1
2
0
1
0
2
1
2
0
0
0
2
1
0
1
0
1
0
0
1
2
2
1
0
1
1
1
0
0
0
1
0
0
2
1
1
1
1
2
1
1
1
0
1
0
1
2
2
0
2
0
0
0
0
1
1
1
2
2
0
0
0
2
4
0
2
1
0
0
0
2
0
0
0
0
1
0
0
0
1
0
2
0
0
2
0
2
0
0
2
1
0
1
0
1
1
0
0
1
0
0
1
0
2
0
1
1
0
1
1
0
1
0
1
2
0
0
2
1
1
0
3
0
0
2
0
1
1
0
1
1
0
0
0
1
0
2
0
0
1
2
1
1
0
1
0
2
1
1
0
1
0
0
0
3
2
0
0
1
0
0
0
0
2
1
2
1
4
1
0
1
0
1
2
1
0
2
1
1
1
2
0
0
3
0
2
0
0
0
1
3
1
0
3
2
2
2
1
1
0
0
1
1
2
0
0
0
2
0
1
0
1
0
0
0
1
1
0
1
0
0
0
1
0
1
1
2
1
0
0
1
1
3
0
2
1
0
2
1
0
0
2
1
0
2
1
0
1
1
2
2
0
0
2
1
0
1
0
0
0
1
1
1
1
1
1
0
0
0
0
1
2
2
2
1
0
2
2
2
0
2
1
1
0
0
1
0
0
0
0
1
0
2
0
0
1
1
2
1
0
0
2
0
1
2
0
1
1
0
1
0
0
0
1
0
1
1
0
1
3
0
3
1
3
0
1
2
1
2
0
1
1
1
0
0
0
2
2
1
0
1
0
0
1
0
0
2
0
1
0
0
1
0
0
2
0
2
0
1
0
1
0
0
2
1
0
2
2
1
1
0
2
0
1
1
0
2
2
0
2
1
2
2
0
2
0
1
1
1
0
0
2
1
0
0
2
1
0
0
1
1
0
2
0
0
0
0
1
0
0
1
1
0
1
0
2
2
0
1
2
1
2
3
1
1
0
1
1
1
2
0
0
1
0
1
2
3
0
2
1
1
0
1
0
0
0
2
0
1
2
2
0
0
0
4
0
0
0
0
2
0
0
1
0
2
0
0
1
2
0
0
0
0
1
0
1
1
1
2
1
3
0
1
1
0
2
2
1
0
2
1
1
1
1
0
0
0
0
1
1
0
1
0
0
0
0
0
1
2
0
2
0
1
0
3
1
0
1
2
0
2
0
0
0
2
1
1
1
4
0
0
1
1
1
0
1
0
1
1
0
2
0
2
2
1
1
1
1
1
0
1
0
2
1
1
0
2
1
0
1
2
0
1
1
1
0
0
0
2
2
0
1
1
1
1
0
1
0
1
1
0
2
0
0
1
0
0
0
0
1
1
0
2
1
0
0
1
1
0
4
0
0
1
2
2
1
0
0
1
1
2
0
1
1
1
1
2
1
2
2
0
2
0
0
2
1
0
0
0
1
0
0
0
0
0
0
2
1
1
0
0
0
0
0
1
0
1
1
0
1
0
1
3
2
0
0
0
0
1
0
0
0
2
1
0
1
2
0
0
0
1
1
1
2
3
1
2
1
0
0
0
0
0
0
2
0
1
2
0
2
2
0
1
2
0
1
0
0
0
2
1
0
1
1
0
1
1
1
1
2
0
0
0
2
0
0
1
1
0
1
1
2
1
0
2
0
1
2
2
0
2
0
2
3
1
0
2
2
1
1
0
0
1
0
2
0
1
0
0
1
1
2
0
0
0
1
0
2
1
0
0
0
1
1
2
1
0
0
1
1
2
1
1
2
0
0
0
1
0
0
2
2
1
1
2
2
0
0
0
1
0
0
2
0
1
2
0
1
1
2
1
0
1
1
1
0
1
1
0
0
2
1
0
1
0
1
0
1
2
1
0
0
0
2
1
2
2
0
2
0
1
0
0
1
2
2
1
2
2
6
1
0
1
0
2
1
3
0
0
2
1
2
0
1
0
0
0
2
1
1
1
1
0
0
4
0
1
0
0
1
0
2
1
3
1
2
0
0
2
2
1
0
1
0
1
0
1
1
1
0
0
2
0
1
1
0
0
0
0
0
1
0
3
2
1
1
1
0
1
1
0
2
0
0
1
0
1
0
1
0
0
0
1
2
0
0
0
0
2
1
1
1
2
1
1
1
0
0
1
1
0
0
2
2
0
0
0
0
0
2
1
1
0
0
0
0
0
0
1
0
0
1
1
1
2
0
2
0
1
1
0
1
0
1
2
0
2
1
1
0
0
1
0
0
0
0
1
1
0
1
0
0
1
2
1
0
0
2
0
0
1
0
1
1
0
1
1
1
1
1
1
2
2
0
0
0
1
0
0
1
2
1
0
1
0
2
0
0
0
2
2
0
2
0
0
2
3
2
0
2
1
1
1
0
1
0
1
0
1
2
1
3
1
0
0
1
5
1
2
0
1
2
2
1
1
0
0
0
0
1
1
0
2
1
2
1
0
1
3
1
0
1
1
2
0
5
0
1
0
1
1
1
2
2
0
1
0
2
0
1
2
2
0
2
2
0
2
0
2
13
0
2
1
0
1
1
0
1
0
0
0
0
2
1
1
1
0
2
1
0
0
0
2
2
0
2
1
1
1
0
2
1
0
0
1
2
0
1
3
0
1
1
1
2
1
2
0
0
0
0
2
1
1
1
2
0
1
0
0
0
0
1
2
1
0
1
1
1
0
0
0
0
0
1
1
1
0
1
2
1
0
2
1
0
0
2
0
2
1
2
1
2
1
1
0
2
2
1
0
1
0
0
1
2
0
0
0
0
2
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
2
1
1
1
2
0
2
0
2
3
1
1
0
1
1
1
2
1
0
0
0
1
0
2
0
0
1
0
0
1
1
0
0
0
1
0
2
0
0
1
0
0
0
0
1
2
0
2
0
1
0
0
1
0
2
0
1
0
0
0
1
0
1
0
2
2
2
1
0
1
1
1
2
0
2
1
1
1
2
1
1
1
2
2
0
1
2
1
1
0
0
0
2
1
1
0
1
0
0
1
1
2
0
2
1
1
1
2
0
1
2
0
2
0
1
1
2
1
1
0
2
0
0
0
0
1
0
0
0
1
1
1
2
1
0
0
1
0
1
0
2
2
1
0
0
0
2
1
0
1
0
1
0
1
0
2
2
2
0
1
3
2
1
0
1
2
0
2
1
1
0
0
0
1
1
0
1
1
2
0
1
0
0
0
0
2
1
0
0
2
1
0
2
1
2
1
0
0
2
1
2
0
0
2
2
0
3
0
0
1
1
1
2
2
0
1
1
2
2
1
2
0
2
0
0
1
2
0
0
1
0
0
1
1
1
0
2
0
0
0
0
0
0
1
1
2
0
1
1
0
1
1
0
2
1
0
0
1
2
2
0
1
0
1
0
1
1
1
1
1
1
2
2
0
0
2
0
1
0
0
0
0
1
2
0
0
0
1
0
2
1
1
0
0
1
0
1
2
2
0
0
1
2
0
1
1
0
1
2
2
0
0
2
2
0
1
0
1
0
0
1
1
0
0
0
1
1
1
2
2
0
0
1
2
1
2
0
0
1
0
1
0
0
1
0
1
1
0
0
1
1
0
0
1
0
2
1
0
0
0
4
2
0
1
0
0
0
0
0
1
0
0
1
0
0
1
2
0
0
2
0
1
2
0
1
1
1
1
1
1
0
0
2
0
1
1
0
1
1
1
1
0
0
2
0
0
1
0
1
0
0
2
0
1
1
1
0
0
2
1
0
2
0
0
0
1
0
1
0
0
2
2
0
0
2
1
0
2
0
1
2
0
0
1
0
0
1
1
2
0
2
1
1
0
1
0
1
0
1
0
1
2
0
1
3
1
1
2
2
1
2
0
0
1
1
1
0
1
0
1
2
1
0
3
1
1
0
1
1
1
1
0
1
1
1
0
0
0
1
2
2
0
2
1
1
1
0
2
2
2
2
1
2
0
0
2
1
1
1
0
1
1
0
2
2
1
2
0
2
0
2
2
2
1
2
0
1
0
0
1
2
0
0
1
0
0
2
1
3
2
0
1
2
1
0
1
1
2
1
1
1
2
0
1
2
0
1
0
2
0
2
1
1
2
0
2
0
2
0
1
1
0
0
2
1
1
1
0
0
0
1
1
2
0
0
2
2
1
0
0
0
1
1
1
2
0
0
1
1
0
0
2
0
1
0
1
1
0
2
0
0
2
1
2
1
1
0
0
0
1
1
1
2
1
1
0
1
1
2
2
1
2
2
2
1
0
1
0
1
6
2
0
1
1
1
0
2
5
0
2
2
2
2
2
1
0
0
2
1
0
0
1
2
0
1
0
2
1
0
0
0
0
1
2
0
0
0
0
1
1
0
1
1
0
0
2
0
0
1
0
0
0
1
0
2
2
2
2
0
0
0
0
1
0
1
2
0
0
3
0
2
0
0
1
0
0
0
1
1
1
0
2
0
0
2
0
3
0
0
1
1
1
0
2
2
0
2
2
1
0
2
0
1
1
3
1
1
1
1
1
0
0
0
0
1
1
1
0
1
0
1
2
0
0
1
0
0
1
1
0
1
2
0
2
1
0
0
2
0
1
0
1
1
1
2
0
0
0
2
0
0
0
1
0
1
0
2
1
2
0
0
2
1
0
1
2
1
0
1
0
2
2
0
0
0
3
0
0
0
3
0
0
0
0
2
0
0
1
0
1
1
0
0
1
1
0
0
1
0
2
1
0
0
0
1
2
1
1
1
1
0
2
2
0
0
1
0
2
1
0
2
1
0
2
2
1
2
1
0
2
0
0
0
1
0
2
1
0
1
1
0
0
0
0
1
1
0
2
0
2
1
1
1
1
3
2
0
0
1
2
0
0
1
0
0
2
2
0
0
0
1
0
1
2
1
0
1
0
0
0
0
2
0
1
0
2
1
0
2
1
0
2
1
2
2
0
0
0
1
2
1
0
1
2
2
0
0
1
0
4
0
1
0
1
0
2
0
0
0
0
1
1
2
0
0
1
2
0
0
0
2
0
2
0
2
1
0
0
0
2
0
1
1
1
0
1
0
1
1
0
0
0
2
0
2
1
0
1
2
0
3
1
2
0
0
1
0
1
2
5
2
0
0
0
2
1
1
0
0
2
0
0
0
0
1
0
1
1
0
0
1
0
0
1
0
2
0
1
2
0
0
1
1
1
2
1
1
1
0
1
0
2
2
0
1
2
0
0
2
0
2
2
1
2
1
0
1
0
2
2
1
0
1
0
0
0
2
1
1
1
0
0
2
1
0
2
1
1
2
1
0
0
0
1
0
2
2
1
2
1
1
1
0
0
2
1
0
1
0
2
0
3
1
0
0
2
3
1
0
0
0
1
1
0
2
0
1
0
2
0
2
0
0
0
1
2
2
1
0
0
1
0
1
1
0
1
2
0
1
2
0
1
0
1
0
1
0
0
2
2
4
1
0
0
0
2
1
2
0
2
0
1
1
2
1
2
1
1
1
0
0
0
2
0
1
2
2
1
1
1
0
1
0
0
1
1
0
2
1
1
2
1
2
3
2
1
2
1
3
2
0
1
1
2
2
0
0
1
1
1
0
1
1
0
0
1
1
1
0
2
0
2
1
1
2
0
1
0
1
1
0
1
2
0
0
0
1
1
1
0
0
1
0
0
1
2
1
1
0
0
0
0
1
0
2
2
0
1
1
0
1
1
2
0
2
0
0
2
2
1
0
2
0
0
0
0
1
0
0
0
0
2
0
1
2
0
1
2
1
2
1
3
0
1
0
2
2
0
2
0
2
1
0
1
0
0
2
0
0
0
0
2
2
1
0
0
1
0
2
1
0
2
0
0
1
2
1
1
0
0
2
2
1
1
2
0
0
1
1
2
2
0
0
0
1
0
1
2
1
0
0
2
0
0
3
2
0
0
3
1
0
2
0
1
1
2
1
0
2
0
2
2
0
1
2
2
1
7
0
2
0
1
0
0
0
0
2
1
2
1
2
2
1
1
1
1
1
0
0
2
0
0
0
1
0
0
1
0
0
0
1
0
2
0
2
1
2
0
2
2
1
0
0
3
1
1
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
1
1
2
2
1
4
1
0
2
1
0
1
0
0
1
1
0
3
2
0
2
2
1
0
0
0
0
0
0
0
1
2
1
1
1
0
1
0
0
2
1
0
2
0
0
0
0
0
0
2
0
1
2
2
2
1
0
1
0
0
1
0
0
0
2
1
0
0
1
0
2
0
0
2
2
1
0
0
0
1
1
0
0
2
0
1
0
1
1
1
0
1
1
1
1
0
1
1
0
0
1
2
1
1
1
0
0
1
1
1
1
0
0
2
1
1
0
0
2
0
0
2
1
0
0
1
1
0
0
2
0
1
0
2
0
1
2
0
1
0
0
1
0
0
1
0
1
1
0
0
1
0
1
0
2
2
1
0
1
0
1
1
2
0
0
1
2
1
0
0
1
0
0
0
0
1
0
1
2
1
2
0
0
1
2
0
0
0
1
1
0
2
0
0
1
0
1
0
1
0
1
0
1
1
2
0
0
0
1
1
1
0
0
0
0
0
1
3
1
1
3
1
2
0
1
1
0
0
1
2
0
1
2
2
0
2
0
1
2
0
3
0
2
0
0
0
1
0
1
0
1
1
1
0
0
0
0
0
0
2
0
2
1
0
0
2
1
0
1
0
0
0
0
1
1
2
0
2
1
0
0
0
1
2
0
2
1
0
1
1
0
1
1
0
2
2
0
1
2
2
0
1
0
1
0
2
1
1
1
0
0
1
2
1
0
1
0
0
2
1
0
0
2
0
0
2
1
1
0
0
2
1
0
0
1
0
2
2
1
0
0
3
3
0
0
1
0
1
0
0
2
2
1
0
0
2
0
2
0
0
0
0
0
0
2
1
1
0
0
1
1
0
0
0
1
0
0
1
0
1
1
2
0
1
1
0
0
0
0
0
0
0
0
1
0
2
2
1
0
0
3
0
0
2
2
0
1
0
2
1
1
0
0
2
0
0
1
1
0
0
0
0
0
2
0
2
1
1
0
0
2
0
1
2
0
2
0
1
2
2
1
2
0
1
2
1
2
1
0
0
0
2
0
0
0
0
0
1
1
1
0
2
1
0
0
1
0
0
0
1
2
1
1
2
0
2
0
0
1
0
1
0
1
1
1
0
0
1
0
1
1
0
1
1
0
2
1
1
0
1
0
0
0
2
2
0
1
0
0
2
0
1
0
1
0
0
1
1
2
2
2
1
1
1
0
1
0
0
0
0
2
0
2
0
0
0
0
1
1
0
0
2
0
2
0
1
2
2
0
1
2
1
2
0
0
0
3
0
1
1
0
0
0
0
2
0
1
2
1
0
0
1
3
0
2
1
0
1
2
1
1
0
1
0
0
1
0
1
2
0
0
0
1
0
3
2
0
2
0
0
0
4
1
2
0
1
2
0
1
0
0
1
0
2
1
1
1
1
1
0
0
0
0
0
2
0
0
1
2
1
2
0
1
0
1
2
0
2
2
0
1
0
0
0
0
0
1
2
1
4
0
2
0
1
2
1
1
1
0
4
1
1
2
0
1
1
0
0
3
3
1
0
1
2
0
2
2
1
0
0
0
2
0
0
4
0
2
0
2
1
0
1
0
1
0
0
0
0
1
1
0
1
2
0
1
1
0
3
2
0
0
0
1
0
0
0
0
2
1
1
0
0
0
1
0
2
0
0
0
0
2
2
1
1
0
1
0
1
0
1
0
0
2
2
1
1
0
0
0
2
0
2
2
0
0
0
0
0
0
0
1
0
1
1
1
0
0
1
0
1
1
0
1
1
1
2
0
1
0
0
2
0
0
0
0
1
1
0
1
1
1
2
2
0
2
1
1
1
0
0
0
1
1
1
2
0
1
2
2
0
2
0
1
1
0
1
1
1
1
1
2
1
0
0
0
0
0
1
0
1
1
1
0
0
0
2
0
2
0
1
0
0
0
2
0
0
0
0
1
1
2
0
2
2
1
0
0
0
1
0
2
2
0
2
1
0
0
2
2
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
1
0
0
1
1
0
2
0
2
1
0
0
0
1
0
0
2
4
1
1
0
1
2
0
0
0
1
0
1
1
0
0
1
2
0
0
2
0
0
5
0
2
1
3
0
0
1
0
0
2
1
0
0
2
0
1
2
1
2
1
0
0
1
1
0
2
1
1
2
0
3
1
2
0
1
0
2
1
2
0
2
1
2
0
2
0
0
1
5
0
0
3
2
1
2
0
0
0
0
1
0
2
0
0
1
0
2
0
0
1
0
0
1
2
1
0
0
1
1
1
0
0
1
0
0
0
2
0
2
2
0
2
0
2
1
0
2
1
1
2
0
0
0
0
0
0
2
1
1
0
0
0
0
2
0
1
1
0
0
0
1
0
2
2
2
0
1
1
1
0
1
1
1
0
1
1
0
1
0
2
0
0
0
0
2
1
0
0
1
3
1
2
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
2
1
1
0
0
2
2
0
1
0
1
0
0
0
1
1
1
0
0
2
0
1
0
0
0
0
1
3
0
1
1
1
0
1
1
2
0
1
1
1
0
2
1
1
1
2
0
1
0
1
1
0
2
1
0
1
0
0
0
1
1
1
0
1
0
0
1
2
2
0
1
0
1
0
2
2
1
1
1
2
0
0
0
2
2
0
0
1
0
1
0
0
1
3
0
1
1
2
1
0
0
1
0
1
1
0
0
0
1
0
1
3
1
0
1
0
2
0
0
0
1
1
0
2
0
1
3
2
0
0
1
1
0
2
0
0
0
0
1
0
0
1
0
0
0
1
0
2
1
1
1
2
1
2
0
2
1
0
2
0
1
0
0
3
1
1
2
1
2
0
1
2
2
2
1
1
0
1
0
0
2
1
2
0
0
2
2
1
1
2
0
1
0
1
1
1
1
2
1
0
1
1
0
0
0
0
0
1
2
1
0
2
1
2
2
3
1
0
2
1
0
2
0
0
0
0
2
0
0
0
2
1
2
0
1
0
1
0
1
3
0
1
2
0
1
1
0
1
0
0
0
1
0
0
1
1
1
2
2
1
0
1
0
1
1
1
2
0
1
0
3
0
0
2
0
0
2
0
2
1
0
0
0
0
2
0
2
0
0
1
0
0
1
0
1
1
1
1
1
2
2
0
2
0
0
0
2
1
0
1
0
0
2
1
0
1
1
0
1
0
0
1
1
1
0
0
0
1
1
0
0
1
0
0
0
2
1
1
1
1
1
2
2
0
1
2
0
0
0
0
0
2
2
0
1
0
0
0
0
1
0
0
0
0
2
2
2
0
0
1
2
1
1
1
1
0
2
2
0
0
0
2
1
1
1
1
2
0
1
2
1
0
2
0
1
3
0
0
0
0
2
2
1
0
0
2
2
1
0
0
2
2
2
1
1
2
1
1
0
1
1
0
0
2
2
1
0
2
1
2
2
0
1
1
1
1
0
0
2
2
0
1
0
0
1
1
2
0
1
2
0
1
1
0
2
0
1
2
0
2
2
2
1
1
1
0
0
0
0
0
0
1
2
0
0
2
2
0
1
0
1
2
1
2
2
0
0
0
1
0
1
2
1
1
1
0
1
0
0
1
0
1
0
0
0
1
1
0
0
0
2
1
2
1
1
1
1
0
1
1
0
1
3
0
2
0
0
2
1
2
0
0
0
0
0
0
1
1
0
1
1
1
1
0
1
0
0
0
1
0
1
0
1
0
2
1
0
0
2
0
1
1
1
0
0
1
2
1
1
0
0
0
1
3
1
0
1
2
1
0
1
2
0
0
0
1
0
0
1
1
2
0
1
0
0
0
0
1
0
1
2
2
2
0
2
1
1
0
0
2
0
2
0
0
2
2
1
0
2
2
0
0
1
0
2
0
0
0
1
0
2
1
1
0
1
1
3
0
1
0
1
2
0
1
2
0
2
1
1
0
0
0
2
1
2
1
0
0
0
1
2
0
0
0
1
1
0
3
0
0
1
1
1
0
0
1
0
2
0
1
1
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
1
0
1
1
0
2
0
2
1
0
2
2
2
2
1
0
1
2
1
1
1
0
2
0
2
1
1
0
1
0
2
0
1
0
1
2
0
1
1
1
0
1
0
1
1
1
0
0
1
0
1
0
2
1
2
2
0
1
1
1
1
1
1
0
2
1
0
0
0
0
0
1
0
1
3
0
0
0
2
2
1
0
2
2
0
1
0
2
1
0
0
0
2
2
0
0
0
2
0
1
2
1
1
0
3
2
0
2
1
1
1
0
2
1
1
0
2
2
2
1
2
2
1
2
0
0
1
1
1
2
0
0
0
0
0
0
1
2
2
1
0
2
1
0
1
0
1
0
1
2
1
1
2
0
1
0
2
1
0
0
1
2
0
0
2
0
1
2
1
0
0
1
0
1
1
0
1
1
1
2
2
2
0
2
1
0
2
0
0
3
0
1
1
1
1
2
2
0
1
2
1
0
0
2
0
2
1
2
1
0
0
0
1
1
0
1
0
0
0
2
0
0
0
1
1
1
1
1
0
2
0
0
1
2
1
1
0
0
0
1
2
0
0
1
0
0
1
0
1
0
0
1
0
3
1
0
1
0
0
0
0
2
2
0
0
1
1
0
2
1
0
1
2
1
1
2
0
1
2
0
0
1
2
0
1
2
1
2
1
0
2
0
0
2
0
2
1
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
2
0
1
2
2
2
0
0
0
0
1
0
0
0
2
1
1
2
0
1
1
1
0
0
0
1
2
0
0
1
0
0
1
2
1
2
2
2
3
1
1
4
0
0
2
1
1
1
0
0
1
1
0
1
4
0
1
2
2
2
0
3
0
1
2
0
2
3
1
0
0
1
0
2
1
0
0
1
1
0
2
0
1
1
1
0
0
1
1
0
1
0
1
2
1
1
0
0
2
1
1
1
1
0
1
1
1
1
0
0
1
1
1
0
1
0
0
2
1
2
0
1
0
1
0
0
1
0
1
0
1
1
1
0
0
2
0
8
1
1
1
0
0
2
1
0
0
1
0
1
0
1
0
0
1
1
1
1
0
0
1
0
0
0
2
1
0
0
0
2
4
0
0
0
0
0
0
2
2
1
1
1
1
1
1
0
1
2
0
0
0
1
1
0
0
0
0
2
0
1
2
1
1
0
1
2
0
1
0
1
2
1
1
0
0
0
0
0
1
2
0
0
1
1
0
1
0
0
0
0
1
1
1
0
2
1
0
0
1
0
1
2
1
1
1
0
1
1
1
1
1
0
0
0
0
0
1
1
2
2
1
1
1
1
0
1
1
0
0
2
0
0
1
1
0
0
0
0
2
0
0
0
1
2
0
1
1
0
1
3
1
1
1
0
2
1
1
0
2
2
0
0
1
0
0
0
0
2
2
3
0
0
0
1
1
0
0
0
0
1
1
0
2
1
1
1
2
1
1
1
0
0
0
1
1
1
1
0
1
0
2
1
0
1
1
0
0
0
0
1
1
0
1
2
0
2
0
2
1
0
1
0
1
1
1
2
0
1
0
0
0
2
0
0
0
0
0
0
0
2
1
0
2
2
2
2
1
1
1
0
1
0
0
0
1
1
0
0
0
1
0
1
1
0
0
0
1
0
1
2
1
2
1
1
1
0
5
0
2
2
2
0
2
1
2
2
2
1
1
0
0
2
1
1
1
1
1
1
0
0
1
1
1
0
1
1
0
1
1
0
0
0
1
0
2
1
0
1
0
2
0
0
2
0
1
3
0
1
1
0
0
0
2
2
0
1
2
2
1
2
2
0
0
1
0
0
0
2
0
2
2
2
0
1
1
1
1
1
1
2
0
0
0
0
1
2
0
0
0
0
2
1
0
2
0
0
1
0
1
0
1
1
1
2
0
0
1
0
0
1
0
2
1
2
1
1
0
0
0
0
0
0
0
1
0
1
0
2
2
2
0
1
1
1
1
2
0
2
2
0
2
1
0
0
2
1
2
0
0
0
2
1
2
0
0
0
0
0
1
1
0
2
0
1
1
0
5
2
1
1
2
0
1
0
2
0
0
0
2
0
0
0
1
1
0
0
2
0
0
0
0
2
1
1
1
0
3
1
1
2
0
2
2
1
1
0
2
1
1
0
0
0
1
0
1
0
0
0
0
1
0
1
1
1
0
0
1
0
2
0
1
0
1
0
2
0
0
0
0
1
0
0
1
1
1
0
1
1
2
2
0
2
0
2
1
0
0
2
1
0
0
1
0
2
1
1
1
0
0
1
0
1
2
0
0
3
1
0
1
0
0
1
0
0
2
0
1
3
0
0
0
0
2
0
0
2
2
2
0
0
1
0
1
0
2
0
1
0
0
1
0
0
2
0
1
0
1
0
1
0
2
0
0
1
2
3
3
2
0
2
2
0
1
3
2
1
3
1
0
1
0
2
1
2
1
1
1
2
2
2
0
0
2
1
0
0
0
2
1
2
0
0
1
0
1
1
1
2
1
0
1
2
2
1
1
6
3
1
0
1
0
1
0
2
0
0
1
1
0
0
1
0
2
0
1
0
2
1
1
0
2
0
0
2
0
1
0
1
1
1
2
1
0
0
0
1
1
0
0
0
1
0
2
0
0
2
0
0
2
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
1
0
2
1
0
2
0
1
0
4
2
1
2
0
0
0
1
1
1
1
1
0
0
0
0
0
1
0
1
0
1
2
1
0
0
0
0
2
1
0
1
1
0
2
1
1
0
0
0
0
1
1
2
0
1
0
1
0
2
0
1
1
1
0
0
2
0
1
1
1
1
0
2
1
0
1
0
2
1
1
0
0
1
0
0
0
2
2
0
0
0
2
0
0
3
1
0
0
0
2
2
1
0
0
0
1
2
0
0
1
2
0
1
0
0
1
2
1
0
1
1
1
2
0
3
1
1
0
0
0
0
2
1
2
2
1
1
0
0
1
1
1
0
0
2
0
1
0
0
1
1
1
0
0
0
0
1
1
0
1
0
1
0
0
1
0
2
1
2
0
1
1
2
1
0
1
0
5
0
0
1
0
0
0
1
0
1
1
2
2
0
2
2
1
1
0
0
1
1
0
0
2
1
0
0
0
1
0
1
2
0
0
0
2
0
0
0
0
2
0
1
0
2
0
1
0
3
0
0
0
0
2
2
2
1
0
1
1
0
1
1
1
0
0
0
0
0
2
2
1
1
2
1
0
0
0
0
1
0
1
0
1
1
2
2
0
0
1
1
0
0
0
0
0
2
0
1
0
0
1
0
2
1
1
2
1
0
1
2
0
1
0
0
0
0
2
0
0
1
0
1
1
0
2
2
1
2
0
2
1
1
1
0
1
0
0
1
0
0
1
1
0
2
2
0
1
0
1
1
0
0
0
1
0
1
0
0
1
0
2
1
1
0
0
1
0
1
2
0
0
1
0
0
0
1
1
0
0
0
1
4
0
0
0
1
2
0
0
0
0
2
2
0
1
2
0
1
1
2
2
1
0
1
2
1
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
1
0
1
1
0
0
0
0
0
3
2
1
0
1
1
1
0
0
0
0
2
1
0
0
0
0
2
2
1
2
2
2
0
1
2
0
1
0
0
2
1
2
0
1
0
1
1
0
3
1
0
2
2
1
1
2
1
0
0
1
1
1
1
0
0
1
1
0
1
0
2
1
1
0
1
0
2
0
1
2
0
0
1
0
0
2
1
1
0
1
1
0
2
1
1
0
0
2
0
0
1
2
1
1
0
1
1
1
1
1
0
0
1
0
0
0
1
1
0
0
0
1
1
1
2
2
0
1
0
2
0
1
0
0
2
0
0
2
0
1
0
0
0
1
2
1
0
0
1
1
1
0
1
2
0
1
2
0
2
1
0
0
2
2
1
1
0
0
0
1
0
0
0
1
0
0
2
0
0
0
2
0
1
0
1
1
0
2
0
1
2
0
1
0
1
1
1
0
2
2
1
2
0
0
0
1
1
1
1
2
0
0
0
0
0
1
2
1
1
0
3
0
2
0
1
0
1
1
2
0
1
2
0
0
2
2
0
0
1
1
0
1
1
4
2
0
0
2
1
1
0
1
0
0
0
0
0
0
0
0
0
1
2
0
2
0
1
1
2
2
0
2
1
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
2
1
1
2
2
0
0
1
0
0
0
2
1
2
0
1
0
0
2
0
1
1
0
1
0
1
1
1
0
1
2
1
1
1
1
1
1
0
1
2
0
1
1
1
0
1
0
2
1
2
1
0
2
1
1
0
3
0
1
0
1
2
1
0
0
1
4
1
0
1
0
0
0
2
0
1
0
0
2
0
1
1
1
0
1
0
2
0
1
1
0
2
3
1
1
2
1
1
2
2
1
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
1
1
2
1
1
0
5
0
0
0
0
1
1
0
1
0
0
0
1
2
0
1
0
2
0
0
1
0
1
2
0
1
2
0
1
2
0
1
0
2
0
2
0
1
1
1
0
1
1
0
1
0
2
0
1
0
0
1
1
1
5
2
1
2
1
1
1
1
0
0
1
0
2
1
0
1
1
0
0
0
1
2
1
1
2
2
1
1
1
0
0
0
0
2
2
1
1
2
0
1
0
2
1
0
1
0
3
1
0
3
0
1
1
1
0
0
2
2
0
1
1
0
1
2
1
0
0
2
0
1
0
0
1
1
0
0
0
0
0
1
1
0
0
0
1
1
1
0
1
1
2
1
1
0
0
3
2
1
1
0
0
0
0
2
0
1
0
1
0
0
0
1
0
1
0
2
2
1
0
0
2
1
0
0
1
1
0
1
0
1
2
0
2
0
1
0
0
4
0
0
1
0
2
0
1
0
0
1
1
1
1
1
2
0
1
2
1
0
0
2
0
2
0
1
1
2
2
1
0
0
2
1
1
0
2
2
1
2
0
0
1
1
1
0
1
0
1
3
1
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
1
0
0
1
1
0
0
0
0
2
0
2
1
0
0
1
1
2
0
1
2
0
1
0
1
0
0
1
1
2
2
0
1
0
2
1
0
0
2
2
0
1
0
0
0
0
1
0
2
1
0
0
1
0
0
2
1
0
0
0
2
0
1
1
2
0
6
2
2
0
1
0
0
0
2
0
1
2
1
0
2
2
2
1
1
1
0
0
1
1
2
0
1
1
0
0
2
0
2
1
1
0
0
0
1
1
0
0
1
1
1
0
0
0
1
0
1
2
2
2
1
2
0
0
0
0
2
2
2
2
2
2
1
3
1
0
2
1
0
1
0
1
2
2
0
0
2
2
2
2
1
0
0
1
1
0
0
1
0
0
2
1
0
0
0
0
0
2
0
1
0
0
1
3
0
2
2
2
2
0
1
0
1
1
0
1
0
0
1
1
1
0
0
1
0
1
2
1
0
0
1
2
0
1
0
0
0
1
2
0
0
0
0
1
0
1
1
1
0
1
2
4
2
0
0
1
0
2
2
1
1
2
0
1
1
2
1
0
0
0
1
0
0
0
0
0
1
2
1
2
1
2
2
0
0
0
1
0
2
0
0
2
0
1
1
1
0
1
1
1
0
2
1
1
0
1
0
0
0
1
1
0
0
2
2
1
1
2
0
1
0
0
0
1
2
2
0
2
1
1
0
2
1
2
0
1
0
0
1
0
0
0
0
0
0
2
0
0
2
2
1
0
0
0
0
0
2
0
1
0
2
1
0
2
1
1
2
1
0
1
2
0
0
0
2
0
1
2
1
0
2
0
0
2
1
0
3
2
1
1
0
1
0
0
1
0
0
4
2
1
2
0
0
0
0
1
1
2
1
0
0
1
2
1
1
0
0
0
0
0
0
0
2
2
1
2
0
0
1
1
0
0
1
0
0
0
0
0
0
1
1
2
1
1
2
2
0
2
0
1
1
1
0
0
0
2
1
0
3
2
2
0
1
0
1
1
1
0
1
1
2
0
0
1
0
0
2
2
0
1
1
1
0
0
0
1
0
1
0
0
1
0
0
0
1
2
0
1
2
0
1
0
0
0
1
0
0
2
1
1
2
0
1
0
1
0
0
0
1
2
1
0
0
0
1
1
0
0
1
0
0
0
0
1
0
1
2
2
0
2
0
2
0
0
0
0
0
1
1
1
0
2
2
0
0
2
0
0
0
0
1
3
0
0
2
1
1
0
0
1
0
1
1
0
1
1
1
1
0
2
1
0
2
1
1
1
0
1
0
1
1
0
0
2
1
1
0
1
0
0
0
0
0
1
0
2
1
1
0
1
1
1
1
1
1
0
0
2
1
1
1
0
0
0
0
1
2
2
1
0
2
0
1
1
0
3
0
1
0
2
1
2
2
1
1
2
1
2
2
2
1
1
2
0
0
1
1
0
2
2
1
0
0
1
0
0
2
1
1
2
2
0
1
0
2
1
1
0
2
0
0
3
1
2
1
0
1
1
1
1
0
0
1
1
2
1
0
0
0
1
2
1
1
3
2
2
0
1
0
2
1
1
2
1
1
0
0
1
1
1
0
1
0
1
0
1
2
0
0
2
2
0
0
0
5
0
1
2
0
2
0
1
0
0
0
0
0
1
0
0
0
1
1
1
0
1
0
1
1
2
2
1
0
2
1
2
2
0
1
1
0
2
1
1
2
1
1
1
1
0
0
0
1
0
2
2
1
1
1
2
0
2
1
0
0
2
1
0
1
0
0
0
1
1
1
3
0
1
2
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
1
2
0
0
0
0
2
2
2
1
2
0
0
1
1
0
1
2
2
2
0
0
0
1
0
0
0
0
1
0
2
0
0
0
1
0
0
2
0
1
1
2
1
0
1
1
2
0
0
1
0
1
1
0
0
1
2
0
0
0
0
1
2
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
1
2
1
0
0
0
0
1
0
0
1
1
0
1
2
1
1
2
1
2
1
0
0
0
2
2
2
1
0
0
2
0
1
1
0
1
1
2
1
0
1
0
0
0
0
1
1
2
0
2
3
2
1
1
0
1
0
0
1
0
0
0
3
0
0
0
0
1
1
1
1
1
0
0
1
1
1
0
2
0
0
1
0
2
0
1
0
1
1
3
1
0
1
0
1
1
1
0
1
3
1
1
2
0
2
0
0
2
0
2
1
0
0
1
1
1
2
2
0
1
0
1
0
1
1
0
2
3
0
2
1
2
0
1
0
2
0
0
0
1
0
1
1
0
1
0
0
1
0
2
2
0
2
0
0
0
2
2
1
0
1
0
0
1
0
1
1
0
0
1
0
1
2
1
0
1
2
2
2
1
1
0
1
0
0
0
1
2
0
2
0
2
0
0
0
1
1
1
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
1
0
1
1
1
0
1
1
1
3
1
0
0
2
2
0
2
0
1
2
0
3
0
0
0
0
0
0
1
0
1
0
0
1
2
1
1
1
1
3
2
0
0
0
1
1
2
0
2
0
0
0
0
1
1
2
2
0
3
1
3
0
0
1
2
1
2
0
1
3
2
1
1
0
0
2
0
2
0
0
2
0
1
1
0
1
1
0
0
2
0
0
0
0
2
2
1
0
1
2
2
0
0
0
0
1
2
2
1
2
2
0
2
1
2
0
0
0
0
2
1
1
2
0
0
2
1
2
2
1
0
1
0
0
2
0
0
1
0
0
0
0
1
1
2
1
0
0
1
1
0
0
1
1
1
0
0
2
0
2
1
0
0
0
2
2
1
1
1
1
0
2
0
1
0
0
2
0
0
1
0
1
0
0
1
2
1
0
0
0
2
2
1
1
0
1
0
2
2
0
2
0
2
0
2
1
1
0
1
0
1
1
1
0
1
1
2
0
0
2
0
2
1
2
1
1
0
0
1
2
0
0
1
2
0
1
2
0
0
2
1
1
0
1
1
1
1
1
0
0
0
2
2
0
0
1
0
0
2
0
1
1
0
1
2
1
1
2
1
1
0
0
0
0
1
0
0
1
0
0
1
1
0
0
1
0
0
0
0
1
0
1
2
1
1
1
0
1
1
1
0
0
0
0
2
0
0
0
1
0
1
2
0
0
0
2
3
2
1
0
1
1
1
2
1
2
0
0
1
0
1
0
0
0
1
0
2
0
1
1
1
1
2
0
1
0
1
0
2
0
1
0
2
0
0
2
3
0
2
1
2
2
0
1
0
0
1
0
0
2
1
2
1
1
0
0
1
0
0
0
0
1
2
2
0
1
0
1
0
0
0
1
0
0
1
0
1
1
0
3
1
1
0
0
2
3
3
1
2
2
0
0
2
0
0
0
2
2
1
1
2
0
1
1
2
0
1
2
0
0
2
0
0
1
1
2
1
1
1
0
0
0
0
0
0
1
2
1
1
1
2
0
2
2
0
2
0
0
1
1
1
1
0
0
1
2
1
0
1
1
2
2
0
0
0
0
0
1
1
1
1
1
1
0
1
0
0
1
1
2
2
0
1
1
0
1
0
1
2
2
1
2
0
1
1
3
0
0
2
2
1
0
0
1
2
1
2
1
1
0
2
2
0
2
1
1
0
1
1
2
1
2
2
1
1
0
1
0
1
1
1
0
1
0
1
0
0
0
0
0
1
0
0
1
1
2
0
1
0
0
1
0
0
0
1
1
0
0
1
2
1
2
0
0
0
0
1
1
2
0
3
1
0
1
4
0
0
1
1
0
0
2
2
0
1
1
2
1
0
1
0
0
1
1
1
2
4
1
2
1
0
1
1
1
0
1
0
0
1
0
1
0
0
1
5
1
0
1
0
0
1
0
1
0
1
2
0
2
0
2
2
0
1
2
0
0
1
0
1
1
0
2
2
1
0
2
1
0
1
1
0
0
1
1
0
0
0
1
1
1
1
1
0
0
0
0
0
0
0
0
2
1
2
2
2
1
1
2
0
0
0
2
1
0
2
2
0
0
0
0
1
2
1
1
0
2
0
1
0
1
2
0
0
2
2
0
1
1
2
0
1
0
1
1
0
1
1
1
2
1
1
1
2
4
1
1
1
1
1
0
2
0
2
0
1
1
0
2
1
2
1
1
0
1
0
0
0
0
2
0
0
0
0
0
1
1
0
1
0
2
0
1
0
1
0
0
0
0
0
1
0
0
1
2
2
0
2
2
1
1
0
1
1
1
1
0
0
0
2
2
0
2
0
1
0
0
0
1
0
0
1
2
1
0
2
2
0
1
0
3
2
0
5
1
0
1
1
2
0
1
0
2
2
0
0
1
0
1
1
1
0
2
1
2
1
1
0
0
0
0
2
2
0
0
1
0
1
1
1
2
3
0
1
1
0
1
2
0
1
2
0
2
1
0
0
2
1
2
0
0
1
0
0
0
2
0
1
0
1
0
0
0
0
0
2
1
1
2
1
0
0
0
0
1
0
1
2
1
0
0
0
0
1
0
0
3
3
2
2
1
0
0
1
0
2
1
2
0
1
1
2
0
0
1
1
0
0
1
0
0
0
0
2
0
1
1
0
3
1
3
1
0
0
0
2
2
2
2
0
1
1
1
0
0
0
1
1
0
1
0
1
0
1
0
1
1
2
1
1
1
2
0
1
1
0
0
0
1
1
1
1
2
0
0
0
0
0
0
2
0
1
0
1
1
1
2
1
1
2
4
1
0
0
0
0
0
0
1
0
0
2
2
0
1
0
1
1
1
0
0
0
0
4
0
1
1
0
0
1
0
0
2
0
0
1
1
0
1
1
0
1
2
2
1
0
1
1
1
0
3
0
2
1
1
1
1
0
0
1
2
1
0
0
0
1
0
1
3
0
2
0
0
1
0
1
1
1
1
1
2
1
0
0
1
2
1
1
1
1
0
1
1
1
1
3
0
2
2
0
2
1
0
1
2
0
1
1
0
1
0
1
1
0
0
0
0
2
0
1
0
1
0
1
3
2
2
1
1
2
0
2
1
2
2
1
2
2
1
1
2
0
1
1
0
0
0
2
2
1
1
0
0
1
1
1
1
2
0
0
1
0
0
0
1
2
1
3
0
0
1
1
0
1
0
2
2
1
1
1
1
0
0
2
2
0
0
0
1
1
2
1
0
1
1
1
0
2
1
1
2
0
2
1
1
0
1
0
1
0
2
1
1
0
2
2
1
0
2
1
0
0
2
1
0
1
1
1
1
0
0
0
1
1
1
1
1
0
0
1
2
1
0
0
2
2
1
1
1
0
0
1
0
2
0
1
0
1
0
1
1
0
2
1
1
2
0
2
2
2
2
0
0
0
2
3
0
1
0
0
2
0
0
0
0
2
3
1
2
0
0
1
0
0
1
2
1
0
0
0
2
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
1
0
0
1
0
2
1
1
1
1
0
2
1
1
0
1
2
1
2
2
1
1
0
2
0
2
1
2
1
2
0
1
0
0
0
2
1
0
2
0
0
0
1
0
2
3
0
1
0
1
2
2
0
1
1
1
0
0
1
2
1
2
1
1
0
1
1
1
1
1
0
0
1
2
1
0
1
2
0
1
1
0
1
0
2
1
0
1
1
1
1
1
2
1
0
0
0
2
0
0
0
1
1
0
3
0
1
0
0
2
0
0
1
1
1
3
1
1
0
0
1
0
2
0
1
0
1
1
1
2
1
0
0
0
0
0
0
1
0
1
2
0
2
0
1
1
0
1
0
0
0
1
1
1
0
2
2
0
1
0
0
1
0
2
0
1
1
0
1
1
2
2
0
0
0
1
1
3
1
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
3
0
1
1
1
2
1
1
0
2
1
1
2
0
1
0
0
0
2
2
0
1
0
1
1
2
1
0
0
0
1
0
0
0
0
1
0
2
1
2
2
1
1
3
1
0
0
0
2
2
2
2
0
0
1
3
3
0
0
0
1
1
2
0
3
1
0
0
0
1
1
1
1
1
0
0
0
0
1
1
2
0
2
1
0
1
1
1
1
0
1
2
1
1
0
0
1
0
2
1
1
1
0
2
0
1
0
0
0
0
0
1
0
1
1
1
2
2
0
0
0
0
2
0
1
0
1
0
1
2
1
2
0
0
0
1
4
2
2
0
0
1
0
1
1
1
0
1
2
2
2
1
0
2
1
0
0
0
2
1
0
1
0
1
0
1
1
0
0
1
1
0
0
0
1
0
1
0
0
0
0
2
1
0
1
1
0
0
0
1
1
1
0
3
2
1
4
1
0
2
2
0
2
0
0
2
1
0
0
0
1
0
1
4
0
0
1
1
2
0
2
1
0
2
2
0
1
0
0
0
0
1
0
1
0
1
0
2
0
0
0
4
2
0
1
1
1
2
0
0
0
0
1
1
2
0
1
1
1
1
1
0
1
0
0
0
2
2
1
2
1
0
0
1
1
0
1
1
2
2
0
1
1
1
0
0
0
1
0
2
1
1
0
1
2
1
0
0
1
1
1
2
2
0
0
0
2
0
2
0
0
0
2
0
1
0
0
1
2
1
0
0
2
0
0
0
0
1
2
0
0
0
1
0
1
1
0
0
0
1
1
2
0
2
1
0
1
0
2
1
1
2
1
0
1
2
0
2
0
2
0
0
1
2
2
0
2
1
1
0
2
0
1
1
1
2
0
0
1
0
1
1
0
0
0
0
1
1
2
2
0
1
2
1
0
2
1
0
2
0
0
0
1
0
1
1
0
1
2
0
0
0
2
1
0
1
0
1
1
1
2
0
1
2
0
0
2
0
1
1
0
1
0
2
0
1
2
0
1
0
0
1
0
1
0
1
3
1
1
0
0
2
0
2
1
1
2
1
0
1
0
1
0
1
1
0
2
3
1
1
0
0
2
2
0
1
1
0
0
2
0
3
2
0
0
0
1
1
2
2
0
0
2
2
0
2
0
0
1
0
1
0
2
0
0
0
2
1
1
0
0
2
1
2
0
0
1
0
1
1
0
2
0
1
3
2
1
1
2
1
1
1
1
2
1
2
2
1
1
0
0
0
0
2
1
0
2
0
1
0
1
1
1
0
0
0
1
2
2
2
0
1
2
1
0
0
0
2
1
0
1
0
1
0
2
0
1
0
3
0
0
0
0
0
0
0
1
0
2
0
0
2
2
3
1
1
0
0
0
0
1
0
0
1
0
1
2
2
0
0
1
2
0
2
1
1
1
2
1
0
1
1
0
0
2
0
1
1
3
0
1
2
2
0
2
0
0
0
0
0
0
1
2
1
1
0
1
0
2
0
2
0
1
2
1
0
0
0
2
0
2
0
0
0
2
1
0
0
0
0
0
1
1
1
0
1
0
0
0
0
1
0
1
2
2
1
0
1
0
0
0
0
2
0
0
2
0
0
0
3
2
0
1
0
0
1
2
2
0
0
1
0
2
0
2
2
0
0
0
1
0
0
0
1
2
1
0
2
0
0
1
1
1
0
2
0
1
2
1
0
0
1
6
2
0
0
1
0
0
1
0
0
0
0
1
0
1
0
1
0
0
2
2
1
0
1
1
0
2
0
2
1
2
2
2
0
1
0
2
1
0
1
1
1
0
2
0
0
1
2
0
1
2
1
2
1
0
1
1
0
1
2
0
1
1
2
2
0
1
0
1
1
1
0
0
0
1
2
0
2
0
2
0
2
1
2
0
1
1
1
1
2
1
2
0
1
0
1
2
2
1
0
0
1
0
1
0
0
1
0
0
2
1
1
0
2
0
1
0
1
2
0
1
3
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
2
1
1
1
1
1
0
0
1
0
1
0
0
0
0
1
1
0
0
0
2
0
0
1
0
0
0
2
1
1
0
0
1
0
2
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
3
2
0
1
0
0
0
0
1
2
1
2
2
1
2
2
1
1
2
6
2
1
0
1
0
0
1
2
1
0
0
2
0
1
1
0
2
1
0
0
0
0
0
0
1
2
1
0
0
1
1
1
1
2
1
0
1
0
0
0
2
2
0
0
2
1
0
1
0
0
2
1
1
1
1
0
1
0
0
0
1
1
1
0
0
0
0
2
2
2
1
0
1
0
1
2
2
1
2
0
1
0
0
1
1
0
1
2
0
2
1
0
0
1
0
1
2
1
1
0
0
1
0
0
1
2
0
1
1
2
2
0
1
1
1
1
0
0
0
0
1
0
0
0
1
0
0
2
2
2
0
0
0
1
1
0
2
0
1
0
0
1
1
1
0
3
1
1
1
2
1
0
0
0
1
1
0
2
1
0
1
0
0
1
2
1
0
0
1
0
0
0
0
1
1
1
1
0
2
1
2
2
2
0
0
0
2
0
0
0
2
0
1
1
2
0
0
2
0
0
0
0
0
1
1
0
0
2
0
2
1
1
1
1
2
1
0
1
1
1
2
2
0
0
2
1
0
2
0
1
2
2
0
1
0
1
0
0
0
2
0
0
2
0
2
2
0
1
0
2
0
4
1
0
1
2
0
1
0
2
2
1
2
0
1
0
0
2
1
0
0
1
0
1
1
0
1
1
0
0
2
2
1
0
0
2
0
3
0
0
0
0
2
1
2
2
0
1
2
0
1
1
1
1
1
2
1
1
1
0
0
2
0
1
1
1
2
0
1
1
2
0
1
0
0
2
1
0
1
1
2
2
2
0
1
0
0
2
1
0
0
1
1
1
1
0
2
1
3
1
0
0
0
0
0
0
1
1
0
1
2
0
0
0
1
2
0
1
2
2
1
0
0
1
2
0
0
2
0
2
1
1
1
0
3
0
2
0
0
1
0
2
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
1
1
1
0
0
0
2
2
1
2
0
1
1
2
2
2
0
0
1
0
0
0
0
1
1
2
2
2
1
0
1
1
2
0
0
1
0
0
0
0
2
1
0
1
0
0
2
0
2
2
1
1
1
1
1
1
0
1
0
1
0
2
1
1
1
0
2
1
0
0
1
2
0
0
2
0
0
1
2
1
1
1
3
0
2
2
0
0
0
1
2
0
0
0
1
1
1
0
1
0
2
2
0
1
0
0
1
1
1
0
2
2
0
2
0
2
0
1
1
1
3
1
0
1
1
1
0
1
2
3
1
0
1
0
2
2
2
0
1
0
0
1
1
1
1
1
0
2
2
2
0
0
0
1
0
1
0
1
2
0
0
1
1
0
1
0
0
0
0
0
1
1
2
0
0
2
2
1
1
0
1
1
1
0
1
1
0
1
2
0
0
1
2
1
0
2
0
0
0
0
1
1
1
0
0
0
2
1
0
2
0
2
1
0
0
0
1
0
0
2
2
1
0
0
0
1
0
2
2
2
0
2
0
0
1
0
2
1
0
1
0
1
1
1
0
0
0
0
1
0
2
0
0
1
0
2
1
2
1
0
0
1
0
0
0
1
2
0
0
1
0
1
1
2
0
0
1
0
3
0
0
0
2
1
0
0
1
1
1
2
1
2
0
0
2
1
1
1
2
0
2
2
2
0
0
1
2
1
0
1
1
2
0
2
0
0
0
0
0
1
0
1
1
1
2
1
0
0
1
1
0
0
0
2
2
1
1
0
0
0
0
0
1
1
1
1
0
1
0
0
2
1
2
1
0
1
2
0
0
1
2
2
2
2
1
0
0
0
0
2
1
1
3
2
0
0
1
0
2
2
1
0
0
0
1
0
0
0
1
1
2
0
1
1
2
0
1
0
1
0
2
0
0
0
1
0
0
0
2
1
0
1
0
1
2
0
0
2
0
1
0
1
0
1
0
2
0
1
0
1
3
0
0
1
0
0
1
2
0
0
0
1
0
0
1
0
0
0
0
1
1
1
0
0
0
0
2
1
2
0
1
2
1
1
2
2
1
0
0
0
1
1
0
2
0
2
2
0
0
1
0
0
0
0
0
1
0
1
1
3
0
2
0
0
2
0
1
2
1
0
0
0
1
0
2
1
1
2
2
1
1
0
1
1
2
1
1
1
0
2
2
1
1
2
0
1
0
1
2
1
1
2
2
0
0
1
0
3
1
0
0
0
0
1
2
0
1
2
1
1
0
1
0
2
0
1
0
0
1
0
1
0
0
1
2
0
0
2
1
1
0
2
2
0
1
0
1
1
2
0
2
0
1
0
2
3
0
1
1
0
0
1
0
2
0
1
1
0
0
0
0
0
1
3
2
2
0
0
1
0
1
0
1
1
2
2
1
1
0
0
0
1
0
0
0
0
1
0
1
0
1
0
1
2
1
0
0
1
1
1
0
0
1
1
2
0
0
1
0
1
1
0
2
2
1
0
0
0
2
1
1
2
1
1
1
0
0
0
1
0
2
2
1
0
2
1
2
0
2
2
0
1
2
0
0
1
1
1
1
1
1
1
0
1
1
0
2
0
1
1
3
2
0
2
1
2
0
0
0
0
1
0
2
0
0
1
1
1
1
0
1
0
1
2
2
0
0
0
1
2
0
0
2
0
1
0
0
2
1
0
1
2
0
0
2
0
2
0
0
2
0
2
1
0
0
1
2
1
1
0
2
2
0
2
1
2
0
0
0
1
2
0
0
1
1
0
2
1
1
1
1
2
1
0
0
0
0
1
1
0
2
0
1
2
0
2
1
1
2
0
0
0
0
0
2
0
0
2
1
0
1
2
1
0
1
0
0
2
2
1
0
2
1
1
0
1
2
0
0
0
0
1
0
1
2
2
0
0
0
1
1
2
1
1
1
1
2
1
0
1
2
0
1
2
0
3
0
0
1
1
0
0
0
2
1
0
2
1
1
1
1
0
0
0
0
0
1
0
2
1
1
0
0
0
0
2
1
2
1
2
2
1
0
1
4
1
6
0
0
0
0
2
1
0
2
1
1
1
1
1
2
1
0
1
0
0
1
0
2
1
1
1
2
1
2
1
0
1
1
0
2
2
1
0
1
1
0
2
2
2
0
0
0
2
2
0
1
1
1
1
1
1
0
1
0
0
0
0
1
1
1
1
0
1
0
0
0
1
2
0
2
1
1
1
0
0
0
0
0
1
0
0
0
1
2
0
0
0
1
2
0
0
2
1
0
1
0
0
0
1
2
0
0
0
0
1
2
1
0
2
2
1
3
0
0
1
1
1
1
0
1
0
0
0
1
2
2
0
1
2
0
0
1
0
1
0
1
0
0
0
1
2
0
0
1
0
0
0
1
0
1
1
1
1
2
2
1
0
1
0
0
1
1
0
2
1
0
1
0
5
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
1
0
1
1
1
1
2
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
2
0
1
0
1
0
0
2
0
3
0
0
1
1
0
0
0
2
1
1
2
0
1
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
2
3
1
1
1
0
2
0
2
2
1
2
3
1
0
2
0
0
0
1
1
1
0
0
1
1
2
0
0
0
0
1
1
1
1
2
0
0
0
1
0
1
0
1
0
0
1
1
1
1
2
1
2
2
1
0
2
0
1
1
2
1
1
0
1
2
1
0
1
0
0
2
1
0
0
2
0
0
0
0
1
2
0
1
1
0
1
0
1
0
1
0
1
0
2
0
1
1
1
2
2
0
2
1
1
1
0
1
2
3
0
0
0
1
0
1
0
0
0
0
0
2
1
1
1
2
0
1
1
1
0
0
0
1
0
1
0
0
2
0
2
2
0
0
1
0
2
0
1
0
0
2
2
1
2
1
1
0
1
1
1
1
2
2
0
2
2
1
1
0
1
2
0
1
1
1
1
1
1
1
0
0
2
1
2
3
0
0
2
2
0
1
0
0
1
0
1
1
2
0
1
0
2
2
1
2
1
1
1
2
1
0
0
0
1
0
1
1
0
0
0
2
0
1
0
1
1
2
0
1
1
1
0
1
1
0
1
1
0
0
2
1
0
1
1
1
1
0
1
0
2
0
1
2
0
1
1
1
0
2
1
1
0
0
0
0
1
0
2
0
1
0
1
1
1
0
2
0
1
1
0
0
1
1
2
0
0
0
0
3
1
0
1
0
0
0
0
0
1
2
3
1
0
2
1
1
1
1
2
1
0
2
2
1
0
0
0
2
2
2
1
0
1
2
2
0
2
0
1
1
0
1
0
1
2
0
0
2
0
1
0
2
1
0
0
1
2
1
0
0
2
0
0
0
0
0
1
0
1
1
0
0
0
2
2
2
1
0
2
2
0
1
0
0
0
1
1
2
2
1
0
0
1
2
2
0
3
1
2
1
1
0
0
0
1
0
0
0
2
0
0
0
1
1
0
1
1
0
0
1
0
2
2
0
1
1
2
1
2
0
1
2
1
0
1
2
0
1
0
2
2
0
1
0
2
0
2
2
1
1
1
0
0
0
0
1
0
1
0
0
0
1
0
0
2
0
1
1
0
1
1
1
0
1
1
2
0
1
1
0
2
0
2
0
1
2
2
1
0
1
1
0
1
2
2
2
0
1
2
2
1
0
0
1
0
1
2
1
0
0
1
3
1
2
0
0
1
0
1
0
0
0
0
1
1
2
0
1
1
0
2
2
2
0
2
1
0
0
2
1
0
1
1
0
1
9
2
1
0
1
1
0
2
1
2
0
1
3
2
0
2
2
1
2
0
1
2
0
1
0
0
2
2
0
1
2
2
1
0
0
0
3
0
1
1
2
1
0
1
0
2
0
0
0
2
0
2
0
0
1
2
0
0
0
1
2
0
1
0
0
1
1
2
2
0
0
2
0
3
0
0
0
2
3
1
2
0
1
0
0
1
1
1
0
1
2
1
1
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
1
0
2
1
1
1
0
1
1
0
2
1
0
1
0
1
0
2
2
2
1
2
0
0
1
1
0
0
2
2
0
0
0
0
2
0
0
1
1
2
0
2
0
0
1
1
1
1
1
1
1
0
0
1
0
1
0
2
0
0
0
0
1
1
1
1
1
2
0
2
0
0
1
1
0
2
1
0
2
0
1
1
2
0
1
1
0
2
0
0
1
2
0
0
2
1
1
2
1
2
0
1
0
2
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
2
1
2
0
5
2
0
2
1
1
0
1
2
2
0
2
2
0
2
1
0
1
0
1
0
1
0
2
1
1
0
0
0
0
0
0
2
1
2
0
0
0
0
0
2
2
1
0
2
0
0
1
2
0
1
0
0
2
0
1
0
0
0
1
2
1
0
1
1
0
1
0
3
0
0
0
0
1
2
0
0
2
2
1
1
2
0
2
0
1
1
2
0
2
2
1
0
2
0
2
0
0
0
2
2
0
2
2
1
1
1
0
1
2
2
2
2
0
1
0
1
0
0
0
0
1
2
0
1
1
1
2
0
1
0
0
1
2
0
1
0
0
0
0
0
1
0
2
1
0
0
0
0
2
0
0
1
1
0
0
1
0
0
0
0
0
1
1
2
2
0
0
0
0
2
1
1
1
0
2
1
2
0
0
1
0
1
0
0
2
0
0
0
1
0
0
1
0
1
0
0
0
1
1
1
2
0
0
2
1
2
0
0
1
1
0
0
2
1
1
1
2
1
0
1
1
0
2
0
0
1
2
2
0
0
1
0
0
2
0
1
2
0
0
0
1
0
0
2
2
2
0
0
0
1
2
0
1
1
0
0
1
1
1
0
1
0
1
1
0
1
0
0
0
0
1
0
1
0
0
1
2
1
1
0
0
0
2
2
0
0
0
1
0
1
0
1
1
2
0
0
0
0
1
0
0
0
2
0
1
0
2
1
1
0
0
1
1
0
1
0
0
1
0
1
2
0
0
2
2
3
1
0
8
1
1
0
1
0
2
0
1
1
1
0
2
0
0
0
1
1
0
0
0
1
1
1
1
1
1
0
2
2
1
0
0
2
1
3
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
1
0
0
0
0
1
1
2
0
0
1
1
0
0
2
2
2
1
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
2
1
0
0
0
1
0
2
1
0
2
1
2
1
0
0
1
0
1
2
0
0
0
1
0
2
0
1
0
1
0
2
2
0
1
1
0
2
0
1
0
3
1
0
1
0
0
1
0
1
0
2
1
2
1
1
1
0
0
2
2
0
1
0
0
1
2
0
2
2
0
0
1
0
3
0
2
0
0
0
0
0
2
1
2
0
2
1
2
0
1
2
3
1
0
0
2
1
0
2
0
0
1
0
2
1
0
2
5
0
2
0
2
0
2
2
2
0
0
0
3
0
2
0
2
0
0
0
1
0
2
0
2
0
0
1
0
0
0
1
0
1
0
2
0
0
0
2
0
0
1
2
2
0
1
0
1
1
2
1
0
0
0
0
1
1
0
1
2
2
1
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
1
1
1
0
2
0
0
0
1
2
0
1
0
1
1
0
0
1
1
2
1
1
1
1
0
0
0
0
0
0
2
1
1
0
0
1
1
1
2
2
1
1
1
0
1
0
0
0
1
2
2
2
0
0
2
1
0
1
1
1
0
2
1
1
0
1
1
2
1
0
1
0
0
2
2
0
1
2
0
0
0
1
2
8
0
1
0
0
0
1
2
1
1
0
0
1
2
1
0
1
1
0
1
1
2
0
1
1
0
0
1
2
1
0
2
0
0
0
0
1
1
0
1
0
0
2
0
0
0
0
0
2
1
0
0
0
1
0
2
0
2
1
0
2
0
1
0
0
1
2
0
0
0
0
2
1
0
0
0
1
2
2
2
2
0
1
0
0
0
1
1
0
0
0
1
0
2
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
1
0
1
0
1
2
0
1
2
0
1
3
0
1
1
0
1
1
0
0
0
0
2
0
0
0
2
1
0
2
0
1
0
0
1
1
2
0
0
1
1
1
0
2
1
1
1
0
3
2
0
0
0
0
0
1
1
0
2
1
0
6
1
0
0
2
1
1
0
2
0
0
0
0
1
2
1
1
1
1
1
1
0
1
0
2
2
0
1
0
0
0
1
0
1
0
1
3
0
0
2
2
0
0
0
2
0
1
0
0
0
0
2
0
1
0
0
1
0
0
2
0
0
2
0
0
0
0
1
0
2
1
1
1
1
1
2
1
2
0
1
0
2
0
2
0
1
0
1
1
1
0
0
3
1
1
3
0
1
1
2
0
0
0
1
1
0
0
2
2
0
2
0
0
0
0
0
2
1
2
0
0
3
0
0
2
2
0
1
0
0
0
2
2
0
0
0
0
2
2
0
1
1
0
0
2
0
0
1
0
0
0
2
0
1
0
1
2
2
2
2
0
1
2
0
1
1
0
0
0
0
0
1
0
2
2
0
0
2
1
1
2
1
1
0
0
0
0
0
0
1
1
1
0
2
0
1
0
2
1
0
0
0
0
0
1
2
0
0
1
2
0
0
0
2
1
2
0
0
2
2
2
1
1
0
0
0
0
0
2
0
2
1
0
1
0
2
1
1
2
2
0
0
1
0
0
2
1
0
1
2
0
0
1
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
1
1
0
0
0
0
2
3
1
2
0
2
1
0
2
0
1
1
0
0
2
2
0
1
0
1
1
0
2
2
0
1
1
0
0
1
0
1
1
1
1
1
2
0
1
1
0
2
1
1
1
0
0
1
2
1
0
0
0
1
2
0
2
2
0
2
0
1
1
2
0
2
0
1
0
0
0
0
4
1
0
1
0
2
2
1
4
1
0
0
0
0
1
0
1
0
0
0
1
1
1
0
1
2
2
1
2
0
0
2
0
0
0
0
0
1
1
1
1
1
2
1
0
2
2
2
1
0
2
2
2
1
1
0
0
0
0
0
1
1
0
2
0
2
1
2
0
2
0
0
2
2
1
0
0
1
1
0
1
1
2
0
1
0
1
1
1
1
0
0
1
1
0
1
0
2
8
1
1
0
0
1
0
0
0
1
1
2
1
0
0
0
1
1
2
0
0
2
1
0
0
0
2
2
1
0
1
0
0
0
0
2
0
0
1
1
1
0
2
2
2
2
0
2
2
1
1
0
0
0
0
1
0
1
2
1
0
2
2
0
0
1
0
1
1
1
2
0
2
1
0
0
0
0
0
1
0
2
0
0
1
1
0
0
0
1
1
0
0
0
1
1
0
0
3
1
0
1
0
1
2
1
0
0
0
1
2
1
0
1
1
1
0
2
0
2
1
0
0
1
0
0
1
2
0
0
1
2
0
0
0
2
1
0
2
0
0
0
1
0
2
1
1
4
1
1
0
0
2
1
2
2
1
2
1
0
0
0
0
1
0
2
1
1
1
0
1
0
1
2
0
2
2
2
2
0
0
0
1
1
0
2
0
2
1
0
0
2
2
0
2
2
0
0
0
0
0
2
1
1
0
1
1
2
0
0
1
2
1
1
0
0
0
2
2
1
0
0
0
1
0
0
1
0
1
2
0
1
2
1
0
0
2
2
1
2
2
1
2
1
1
0
1
0
1
2
0
1
0
2
0
1
0
0
2
0
0
0
3
1
1
0
0
1
1
0
0
0
2
2
0
0
0
1
0
0
2
1
2
0
2
0
0
1
0
1
0
2
1
2
3
2
0
2
2
0
0
2
0
1
0
0
0
1
2
1
0
1
0
0
0
0
2
1
0
1
2
1
0
0
1
0
1
0
0
0
0
2
1
0
1
1
0
1
1
2
1
1
0
2
0
0
2
0
1
0
2
2
0
1
0
0
1
0
2
0
1
0
2
1
0
0
0
2
0
1
3
0
0
1
0
2
0
0
0
2
1
0
0
0
1
0
2
0
1
1
0
0
1
1
1
0
2
0
0
2
2
0
1
0
1
2
1
0
0
0
2
0
1
2
0
1
0
0
1
0
0
2
2
0
2
0
0
0
2
3
1
0
0
1
0
0
1
0
0
3
1
0
1
0
1
0
0
2
0
1
1
2
0
1
0
1
1
0
0
0
1
0
2
2
0
1
0
2
0
0
1
2
1
0
0
1
0
0
0
1
0
1
0
1
1
0
1
1
2
4
0
1
1
0
1
0
1
0
2
0
0
0
0
0
1
1
0
0
0
2
1
1
1
0
1
0
1
0
1
0
1
5
1
0
2
1
1
1
1
0
2
0
2
0
2
0
0
0
0
2
0
1
1
1
1
0
1
0
0
1
2
0
2
1
1
1
1
2
1
1
1
1
1
0
1
1
1
1
2
2
1
0
1
0
1
0
1
2
0
0
1
2
0
0
0
0
1
0
0
2
0
0
0
1
2
0
0
0
2
1
2
0
1
2
0
1
0
0
0
1
0
0
1
0
2
2
0
1
2
1
2
0
1
0
2
1
1
0
2
2
0
0
1
0
0
1
0
0
1
0
1
2
0
0
0
1
1
2
1
0
0
2
0
0
2
1
0
2
2
1
2
1
1
0
0
2
1
1
1
0
0
2
0
1
0
1
0
0
0
1
1
0
2
1
0
1
0
1
0
0
2
1
2
0
4
1
2
2
1
0
2
2
1
1
1
1
0
1
1
2
0
0
1
1
1
2
1
0
1
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
2
1
2
1
0
1
0
1
0
0
1
1
1
0
2
0
1
1
0
2
2
1
0
0
0
1
1
1
1
0
0
0
1
1
2
2
1
2
1
2
1
2
2
1
2
1
0
0
1
1
0
0
2
1
0
2
0
2
1
0
0
0
0
1
1
1
0
1
2
0
1
0
2
0
1
0
1
0
0
0
0
1
1
0
2
1
0
1
0
0
1
0
1
0
1
1
0
0
0
2
2
0
0
0
1
0
0
0
1
2
0
2
0
2
0
0
1
1
0
1
1
2
0
1
0
0
0
1
1
0
0
2
0
0
1
0
3
0
0
0
2
6
0
2
0
2
0
2
0
1
0
1
2
1
2
2
0
0
0
0
0
1
0
1
2
1
0
1
3
1
1
1
0
2
0
0
1
0
0
0
2
0
0
2
0
1
2
0
0
0
0
0
1
0
0
2
0
0
2
2
1
2
1
0
0
0
0
3
2
2
0
0
1
2
0
0
2
1
1
0
1
2
0
1
0
0
0
1
2
1
1
0
0
2
0
2
1
1
0
0
1
0
1
0
0
0
0
0
3
1
1
0
1
0
2
0
1
0
1
1
0
0
1
1
0
1
0
0
2
1
2
2
1
0
0
3
2
2
1
0
0
0
1
0
0
2
0
0
0
1
1
0
0
0
1
0
0
1
0
0
1
0
0
0
3
0
1
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
3
1
1
0
2
1
1
1
0
1
1
2
0
0
1
1
1
1
0
2
1
0
2
1
4
0
0
1
1
0
2
0
0
1
0
0
0
0
2
2
1
0
0
0
0
2
0
2
0
0
2
0
1
1
1
3
1
1
1
0
0
0
1
1
0
1
1
0
1
1
1
0
1
0
0
0
1
1
0
2
2
2
1
2
2
0
0
1
1
0
1
0
1
2
1
2
2
0
1
1
0
0
3
1
1
0
1
0
2
1
0
2
1
1
1
2
1
1
0
0
0
0
0
0
3
0
1
2
1
0
1
0
0
1
0
0
0
1
2
1
0
0
0
1
1
1
0
2
0
0
2
1
1
1
0
1
1
1
0
1
1
1
0
1
0
0
0
0
2
0
0
0
0
1
0
0
2
0
1
0
0
0
0
1
0
1
0
2
2
0
2
1
1
0
0
1
1
1
0
1
2
1
1
0
2
0
0
1
1
0
1
1
0
1
0
1
1
0
0
2
1
0
1
1
1
1
0
0
2
2
0
0
2
1
2
1
0
1
1
0
1
0
0
2
2
1
0
2
1
1
2
1
1
1
0
1
1
1
1
1
1
0
2
2
2
0
1
0
2
1
1
0
0
0
1
1
0
0
0
1
2
1
1
2
1
0
2
2
0
1
1
2
0
1
1
2
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
3
3
1
2
1
1
1
2
0
0
0
0
0
1
0
0
2
1
2
1
1
0
0
0
0
0
1
0
1
1
1
1
0
2
1
2
2
0
0
2
1
1
0
2
1
0
0
0
0
0
1
0
2
1
0
1
1
0
0
0
2
1
1
1
0
1
1
2
0
0
0
1
2
2
0
0
0
1
1
0
2
0
1
1
2
1
2
1
0
1
0
1
2
1
0
0
0
2
0
0
0
1
1
1
1
1
1
1
2
2
0
2
2
0
0
0
2
1
0
0
0
1
0
1
2
2
0
2
1
1
1
1
1
0
1
2
1
1
2
2
0
0
1
0
0
1
1
1
0
0
1
0
1
2
1
0
0
0
0
2
2
1
0
1
0
0
1
1
0
1
0
1
1
1
1
1
1
2
1
1
1
1
0
1
0
0
0
2
1
2
2
0
0
1
2
0
2
0
0
0
2
0
0
1
0
0
0
2
0
0
1
1
1
1
2
0
2
0
2
2
1
2
0
0
2
0
0
0
1
1
0
1
1
2
0
2
1
0
1
2
2
0
0
3
1
2
0
0
1
1
1
1
1
2
0
0
1
2
2
1
1
2
0
0
2
2
2
1
0
0
0
2
0
0
1
1
0
0
2
2
0
1
1
1
1
2
1
2
0
0
2
1
0
1
1
2
0
1
2
1
0
2
1
0
1
0
2
0
2
0
2
1
1
0
2
0
0
0
0
0
0
0
0
3
0
2
1
2
0
0
0
2
1
0
1
0
0
2
0
0
2
1
1
0
0
0
0
0
0
0
2
2
2
1
1
1
1
0
1
0
0
0
0
0
0
1
0
2
0
2
0
0
1
0
1
0
1
0
1
0
2
0
1
0
0
1
2
0
1
0
1
1
0
2
2
2
0
0
1
0
1
0
0
1
1
0
1
2
0
1
0
0
2
0
1
1
1
2
0
0
1
1
0
2
2
1
2
0
0
1
3
0
0
0
2
1
0
0
1
0
0
0
1
1
0
0
2
0
0
0
0
1
0
0
0
1
1
0
1
0
1
2
0
0
2
1
1
1
0
0
0
2
0
0
3
0
1
0
1
2
2
0
1
1
0
0
0
1
2
2
0
0
1
1
2
1
2
0
0
1
0
0
0
0
2
0
1
1
1
1
1
2
0
2
0
0
0
0
1
2
0
2
0
2
1
1
0
0
0
2
0
1
0
2
1
0
0
0
2
1
0
2
2
1
0
0
2
0
0
0
1
0
0
0
1
2
1
0
2
0
1
3
1
2
1
0
2
0
1
1
0
0
1
1
2
0
0
1
0
0
1
1
1
0
1
2
0
1
1
0
1
1
0
0
1
1
1
0
3
2
2
0
0
2
1
0
1
2
0
3
1
1
0
1
1
2
0
3
1
1
1
0
1
0
0
1
0
2
0
1
0
4
0
0
1
0
0
1
1
0
1
0
0
2
0
0
0
2
0
0
0
2
1
1
2
1
1
1
1
0
0
2
0
2
0
1
0
0
2
2
0
1
1
2
1
0
0
0
0
0
1
1
1
0
1
0
2
2
0
1
3
0
1
2
1
0
1
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
1
2
1
0
0
1
1
1
2
1
0
0
1
1
2
1
1
2
1
2
1
2
0
0
1
0
0
1
0
0
0
2
0
0
1
0
1
1
0
2
2
2
2
1
2
2
0
0
0
1
0
1
1
1
0
1
1
0
1
1
1
1
1
1
2
2
0
0
2
1
2
2
2
1
1
0
0
0
1
1
0
1
1
1
2
0
0
0
1
2
2
0
0
0
1
2
0
0
1
0
0
1
0
0
2
2
0
1
2
1
2
0
0
1
1
2
0
0
0
1
0
1
0
0
1
1
0
0
1
0
0
1
0
1
0
0
0
1
1
0
0
2
0
0
1
0
1
2
0
2
0
2
0
1
2
2
1
1
1
0
0
0
1
0
0
0
1
0
2
0
0
0
3
1
1
0
0
1
2
0
2
1
2
1
2
0
0
1
2
0
0
2
0
0
1
0
0
1
1
0
0
0
2
5
0
1
1
2
0
0
0
0
1
1
1
0
2
0
1
1
2
2
1
0
1
0
1
2
1
1
2
0
1
1
0
2
0
2
1
2
2
2
1
2
0
1
2
0
1
0
2
1
0
1
2
0
2
1
0
0
0
2
2
1
0
1
0
1
0
0
1
0
1
0
0
2
1
0
1
0
0
1
2
0
1
0
0
0
1
2
1
2
0
0
1
0
0
0
5
1
1
1
0
0
2
0
0
0
1
1
3
0
0
0
1
1
0
2
1
1
0
1
1
0
1
2
0
1
2
1
1
1
0
1
1
2
1
1
0
0
2
1
1
1
1
0
0
1
0
1
2
0
1
3
1
0
0
2
2
0
2
0
2
1
2
1
0
0
0
0
1
0
2
0
1
0
0
2
1
0
1
1
1
2
0
2
1
0
1
2
2
0
0
0
0
0
1
0
0
1
1
1
0
0
2
1
0
0
0
0
2
1
2
0
1
1
0
1
2
1
2
1
0
0
1
0
0
1
0
1
2
2
0
1
0
0
1
1
0
0
2
0
0
1
0
0
1
2
0
2
1
1
2
0
1
2
2
0
0
0
0
3
1
0
0
2
1
0
0
1
2
2
1
0
0
0
0
2
2
1
1
0
2
0
0
0
0
0
2
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
2
3
0
2
0
0
0
1
0
2
1
1
2
1
2
1
2
0
1
1
2
1
3
2
2
0
0
0
5
2
1
0
0
0
1
0
0
1
0
0
3
0
1
2
2
1
2
1
2
0
0
1
0
1
1
0
2
1
1
0
2
2
0
2
0
1
1
0
0
1
0
3
3
0
1
0
0
1
1
1
1
1
1
0
2
1
0
2
1
0
1
3
1
1
2
0
0
0
1
2
1
0
2
0
1
1
0
1
2
1
1
0
1
2
2
0
2
2
0
1
2
0
1
2
1
1
1
0
1
1
1
1
0
1
1
1
1
1
0
0
0
0
0
1
1
2
0
2
2
1
2
1
2
1
1
0
2
0
1
1
1
0
1
1
1
0
0
3
1
1
0
2
2
0
2
0
1
1
1
0
0
3
1
3
1
1
2
0
0
1
1
1
0
2
0
0
1
0
2
1
1
0
1
2
1
2
1
0
2
1
1
2
1
1
1
2
0
1
0
2
0
2
0
1
0
0
0
0
1
1
1
1
0
0
0
2
1
1
0
0
0
0
1
0
0
0
2
0
1
0
1
0
2
2
1
0
1
0
0
0
2
0
1
2
0
0
0
1
2
1
0
0
0
2
0
0
1
1
0
0
0
2
1
1
1
1
1
1
0
1
2
3
0
0
0
0
2
2
1
1
0
1
0
0
0
0
2
2
2
1
1
0
2
1
0
2
1
1
2
0
0
0
2
1
3
1
1
0
1
0
2
0
0
0
2
1
2
1
2
1
2
2
2
2
1
2
0
2
0
0
1
0
0
0
2
1
2
1
1
0
2
3
1
1
2
0
2
1
0
1
1
0
0
1
0
0
0
0
0
0
1
0
1
1
1
0
0
1
0
3
1
0
0
0
0
1
0
1
2
1
0
2
0
2
3
2
0
1
2
2
2
3
1
1
0
1
1
0
0
0
0
1
3
2
3
1
4
2
1
1
0
1
0
1
1
2
0
2
0
0
0
2
0
0
2
2
2
1
1
2
1
0
2
1
1
1
0
1
0
0
1
2
0
2
0
1
0
2
2
0
2
1
2
0
1
1
1
3
2
2
1
0
0
0
2
2
1
2
2
0
1
1
0
1
0
0
0
1
1
2
0
2
2
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
1
0
1
3
0
2
0
1
0
1
2
1
0
2
1
0
2
3
1
1
1
0
0
1
2
0
0
1
0
1
0
0
0
2
2
2
0
1
0
3
1
0
0
0
1
1
0
1
2
0
0
2
1
2
1
1
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
1
0
1
2
1
0
2
0
0
0
1
0
1
2
1
1
0
2
0
2
1
0
1
1
0
2
0
0
0
0
1
2
2
1
0
0
2
2
1
0
1
0
1
2
1
1
1
0
1
0
2
2
1
0
0
0
2
0
0
1
1
0
0
2
0
0
2
1
0
2
0
1
0
1
5
0
1
1
1
0
0
2
0
0
0
0
1
2
1
1
0
1
0
0
2
2
1
0
0
2
2
1
0
3
0
0
2
1
1
0
0
0
1
0
2
1
1
1
1
0
2
1
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
1
4
2
3
0
3
0
0
0
0
1
0
1
2
1
2
1
3
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
1
1
0
4
2
2
1
2
0
1
1
0
0
2
2
0
2
0
0
1
1
2
2
0
1
0
0
1
0
2
2
1
0
2
0
0
0
1
1
3
0
0
1
1
0
1
3
1
1
0
2
0
2
1
1
2
2
1
1
0
2
0
0
0
1
1
0
1
2
0
1
0
1
1
1
0
1
1
1
0
1
2
1
0
0
1
2
1
0
0
0
0
2
2
1
0
1
0
0
0
0
0
0
1
1
0
0
2
2
2
2
0
1
0
1
2
1
2
1
0
1
2
0
0
1
0
0
2
2
0
0
1
0
1
0
0
0
1
1
0
2
0
1
0
0
0
2
1
0
0
0
1
0
3
0
2
2
2
0
0
1
0
0
2
2
1
0
1
1
2
1
1
1
2
0
0
1
2
0
2
0
0
1
0
1
0
1
1
3
2
1
0
1
0
0
0
1
3
0
2
0
1
0
0
1
0
1
0
1
1
1
1
1
0
0
0
1
0
0
1
0
0
3
1
1
0
1
2
1
0
0
1
0
1
0
2
1
2
0
1
2
0
0
2
0
2
1
1
0
2
0
0
1
0
1
1
2
0
2
2
0
1
0
2
1
0
1
2
0
1
1
0
1
0
1
0
1
0
2
0
0
0
0
1
1
2
3
1
0
0
0
0
2
0
2
2
3
1
0
0
1
2
2
1
0
0
0
0
1
1
0
0
2
0
0
0
1
0
2
0
0
1
0
0
2
1
0
2
2
2
0
0
0
1
2
0
3
1
1
0
1
1
1
0
0
1
0
0
0
0
0
2
0
0
1
2
0
2
1
2
2
1
1
2
0
0
0
0
1
1
2
1
1
1
1
1
1
1
1
0
0
2
1
0
2
2
0
0
3
0
0
1
1
1
1
0
0
1
0
1
1
0
1
0
1
0
1
1
1
2
0
1
0
0
0
2
1
0
2
0
1
0
1
0
0
2
0
1
1
0
1
0
1
0
2
1
1
0
2
0
2
1
0
1
1
0
1
0
2
1
1
0
2
1
2
2
2
0
1
1
1
2
1
0
0
1
1
1
2
0
1
1
0
0
1
0
0
1
1
0
1
0
2
1
0
1
0
1
2
0
0
2
1
1
1
1
0
0
0
1
0
0
0
1
2
0
2
0
2
1
0
0
0
2
0
2
1
2
0
0
0
0
0
0
0
0
1
0
1
0
1
2
1
0
1
1
1
1
1
2
0
2
0
0
2
0
0
0
0
0
0
1
0
1
1
0
0
1
1
1
1
0
2
2
1
1
1
1
2
1
1
0
2
0
2
1
0
2
1
0
1
2
0
0
1
2
1
2
0
3
0
0
1
0
0
2
0
0
1
0
1
0
1
1
1
0
0
0
0
1
2
0
1
1
1
1
0
2
0
1
0
0
0
0
1
0
2
0
0
0
1
0
1
3
0
2
1
0
0
3
2
1
1
1
2
1
0
0
0
0
0
1
1
0
1
0
0
2
1
3
6
2
0
1
2
0
0
1
1
2
0
1
1
0
1
0
0
0
0
2
1
1
1
1
0
0
0
0
0
1
0
1
0
2
0
1
0
0
2
0
0
0
2
2
0
1
2
1
1
0
0
2
2
1
2
2
0
0
0
0
0
1
1
1
0
0
0
2
0
0
0
1
1
1
2
0
2
0
1
1
2
1
2
1
1
0
0
0
0
1
2
0
0
2
1
0
1
2
1
1
0
1
0
0
2
0
0
2
0
0
2
1
0
2
1
0
0
0
1
1
0
2
2
0
0
0
1
2
0
0
1
2
1
1
2
1
0
1
2
1
1
0
0
1
2
0
0
0
1
0
0
1
1
0
0
1
1
0
0
1
2
0
0
0
2
0
1
0
0
2
3
1
1
1
0
0
0
0
0
1
0
0
1
2
0
0
0
2
1
0
1
0
2
0
1
1
2
1
0
2
0
3
0
2
2
0
2
1
0
0
1
0
1
0
1
0
1
1
1
0
1
0
0
0
0
2
0
0
2
0
1
2
1
1
0
1
1
0
2
2
2
1
1
0
1
0
1
1
0
0
0
2
2
1
1
1
0
1
0
0
3
1
1
0
0
1
2
0
1
2
2
2
1
0
1
2
1
1
0
2
2
0
1
1
3
1
1
1
0
1
1
0
1
1
0
1
1
1
0
1
1
0
0
1
0
2
1
0
0
1
2
1
1
3
2
0
2
1
1
1
1
1
2
1
2
1
0
0
2
1
0
1
0
1
2
2
1
2
0
0
0
0
0
2
0
1
3
0
2
0
2
0
1
1
2
1
0
0
1
1
2
0
0
2
0
2
0
1
1
1
0
1
1
1
0
0
2
1
1
0
0
0
1
0
2
0
2
0
0
1
2
0
0
1
2
2
1
1
1
0
0
2
2
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
1
0
2
0
0
0
1
0
0
0
0
0
0
2
2
0
1
1
1
0
1
0
1
0
0
1
2
0
2
0
0
0
2
0
2
0
0
0
0
2
0
1
0
1
7
1
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
2
0
1
0
1
0
1
1
1
0
0
2
0
2
0
1
0
0
0
0
1
1
0
0
0
2
1
1
1
0
0
1
1
0
2
1
1
0
1
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
2
1
0
0
0
0
0
1
3
0
0
1
0
0
2
0
2
0
2
0
0
0
1
1
1
0
1
0
1
1
1
1
0
0
1
1
0
0
2
1
1
1
0
1
0
2
0
0
0
0
1
1
2
1
0
1
0
1
0
1
1
3
3
0
0
0
1
2
0
0
1
1
0
1
0
1
1
1
0
2
1
2
0
0
2
0
1
1
2
1
0
0
0
1
0
0
2
1
1
2
1
1
2
1
2
1
0
0
1
2
1
0
1
1
1
2
0
0
1
0
0
0
2
0
1
2
0
0
1
0
2
1
1
2
1
0
3
0
1
0
2
0
1
2
0
1
0
2
2
0
0
0
3
1
1
1
2
2
1
0
0
1
1
2
0
0
3
2
0
1
0
1
0
2
1
0
0
0
1
1
2
0
1
0
4
1
1
1
0
0
1
1
1
2
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
1
0
0
1
1
0
0
0
2
1
2
1
0
2
2
1
1
2
1
1
0
0
1
0
0
2
2
0
0
1
2
1
2
1
0
2
1
1
0
0
0
0
1
0
0
0
0
1
0
1
1
1
1
1
2
0
1
0
2
0
2
0
0
1
0
1
1
1
1
0
3
1
0
0
0
2
0
2
0
1
0
0
2
1
0
2
0
1
0
2
0
0
2
0
0
0
0
2
0
0
1
2
1
1
0
0
1
1
0
2
2
2
1
0
1
2
1
1
1
2
0
0
2
1
1
2
0
2
1
0
1
1
3
0
1
2
1
0
3
2
0
0
1
0
1
2
1
2
0
2
1
0
2
1
1
0
1
2
1
1
2
1
1
0
0
0
0
0
0
0
2
0
2
3
0
0
0
0
0
0
0
1
2
1
1
1
2
0
0
1
2
1
1
0
0
1
0
0
0
0
0
0
1
0
2
0
0
1
1
1
0
2
0
0
0
2
0
1
1
1
1
1
1
0
0
1
2
0
2
1
1
0
1
0
1
1
0
1
2
1
0
0
1
0
0
2
1
0
0
0
2
1
2
1
0
1
1
2
2
0
3
1
0
1
1
0
0
0
0
1
0
2
1
1
2
0
0
1
2
2
0
2
2
0
0
2
0
1
1
1
1
1
2
2
1
2
2
0
0
0
0
0
2
0
0
3
0
0
2
0
1
1
1
1
1
0
1
0
0
1
1
4
1
1
0
1
0
0
2
1
0
1
0
0
1
1
2
2
2
2
0
1
2
0
0
1
0
0
1
1
1
0
1
0
2
1
1
1
1
2
2
1
0
1
0
3
0
0
1
1
1
2
2
0
0
1
2
2
2
1
0
0
1
0
1
2
0
0
2
1
0
1
0
1
1
0
0
0
0
1
0
0
1
1
1
1
1
1
0
0
0
0
2
0
1
1
1
1
0
0
0
1
0
0
1
1
1
1
0
0
1
0
0
2
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
2
0
1
2
0
2
2
0
0
0
1
2
1
1
1
0
1
0
0
1
0
0
0
2
2
0
1
1
0
0
2
1
1
2
0
0
0
0
0
0
0
0
2
1
0
1
0
2
2
2
1
2
1
1
0
1
2
1
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
2
0
0
0
0
1
1
2
0
1
2
1
0
0
1
1
2
0
1
0
0
0
2
2
2
0
0
0
0
1
0
0
2
0
1
1
1
2
1
0
1
1
0
1
0
0
1
0
1
1
1
0
0
1
2
1
1
1
1
0
2
0
0
0
0
1
1
1
0
2
1
1
0
0
1
1
1
2
0
2
0
1
4
0
1
1
1
0
0
1
2
1
1
0
2
0
0
0
1
2
0
0
2
1
0
0
2
2
0
2
0
2
1
1
2
0
1
2
1
0
0
0
3
1
0
2
3
1
0
1
1
1
0
0
0
0
3
2
0
0
1
2
2
0
0
2
2
0
2
1
0
0
1
0
2
0
1
0
1
0
1
2
0
1
0
1
1
1
0
1
1
0
1
0
2
0
1
1
0
1
0
0
0
0
0
0
0
1
1
0
2
0
1
0
0
2
1
2
1
0
0
0
0
0
0
1
3
0
0
0
1
1
2
0
1
0
0
0
2
1
0
3
2
1
2
2
0
1
0
0
0
2
2
2
2
0
0
0
1
2
0
0
0
0
1
1
0
1
0
2
1
0
0
1
0
1
0
2
0
1
1
0
0
2
1
1
2
1
0
3
0
1
0
1
0
0
0
0
2
2
1
0
0
1
2
2
1
0
1
2
2
0
0
0
0
1
0
1
0
0
1
0
0
2
1
2
0
1
1
2
1
0
0
0
1
1
1
0
0
1
2
1
5
1
0
1
1
3
1
1
1
0
0
2
1
0
1
0
0
1
2
1
0
2
0
1
1
1
0
0
2
0
0
0
0
1
0
0
1
2
1
0
1
2
1
2
1
0
0
0
1
1
0
1
0
0
0
2
3
1
1
1
0
0
0
0
1
1
0
0
0
1
2
6
1
1
2
1
2
0
0
0
0
0
2
1
1
0
1
0
1
0
0
2
1
1
0
0
1
1
2
1
0
1
0
0
1
0
1
1
0
2
2
0
2
0
3
0
1
0
0
0
0
0
2
0
2
1
0
1
0
0
0
1
1
0
1
1
2
0
1
2
3
0
0
0
1
2
1
2
1
0
1
1
0
0
1
2
1
0
2
0
2
0
1
0
0
0
2
0
1
0
0
1
1
1
0
0
0
1
0
0
0
1
1
1
0
0
1
0
1
1
2
0
1
2
2
0
2
0
1
2
2
1
0
1
2
0
0
2
1
1
0
0
1
3
3
1
1
1
1
0
0
1
0
2
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
2
1
0
0
0
0
0
0
2
0
3
0
1
2
0
0
1
3
1
0
0
2
2
1
2
0
2
2
0
0
0
1
2
1
1
1
0
1
1
1
0
0
0
1
1
2
0
0
1
0
0
2
2
0
1
1
0
2
3
0
0
0
2
3
0
0
2
0
0
0
1
0
1
0
1
1
2
2
2
1
1
1
0
2
0
0
1
0
0
0
2
0
1
2
0
1
2
2
0
1
2
2
1
0
1
1
1
1
0
2
3
0
1
0
0
0
2
0
2
1
2
1
0
1
0
0
2
0
2
1
0
0
0
0
1
0
0
0
0
8
0
1
1
0
0
0
1
0
1
0
1
0
0
0
1
0
3
0
1
1
1
1
1
2
0
2
0
0
0
0
0
0
0
1
0
2
1
2
1
1
1
0
0
1
0
2
2
2
1
2
2
2
2
1
1
0
1
1
2
1
0
0
0
1
0
1
1
0
1
0
1
1
1
2
0
1
0
0
2
0
1
0
2
1
1
0
0
1
0
1
0
2
0
1
0
1
0
2
0
2
0
1
0
0
2
2
1
1
2
0
1
0
0
1
0
1
0
2
2
0
0
0
1
1
0
2
0
1
2
0
1
2
1
2
1
1
1
1
1
1
2
2
2
1
0
1
0
2
0
0
1
1
2
1
1
1
1
7
1
1
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
1
0
1
0
0
0
1
0
0
0
0
0
1
1
1
1
1
2
2
3
0
0
1
0
0
1
0
0
1
0
1
0
0
2
0
1
0
2
1
1
0
0
1
1
1
2
2
0
1
2
1
1
1
0
2
1
1
2
2
0
3
1
1
0
1
2
0
1
1
0
0
0
1
0
3
2
0
0
1
1
0
0
3
1
0
3
2
2
1
1
0
0
1
1
0
0
4
0
0
0
0
0
0
1
1
0
1
1
0
1
1
1
0
1
0
1
0
0
1
1
0
0
0
0
2
0
0
2
1
0
1
2
0
2
0
0
0
1
0
2
1
1
0
0
1
1
2
2
1
1
1
0
2
2
1
1
2
1
0
0
1
1
0
0
2
0
5
1
2
0
0
1
2
1
2
0
0
0
1
1
0
0
2
1
1
1
0
1
1
1
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
2
0
1
0
0
0
1
2
1
2
0
0
1
0
1
2
0
1
1
2
1
0
2
0
1
1
1
0
0
1
0
2
0
0
1
0
0
1
2
1
1
2
1
0
0
2
2
0
2
1
1
2
0
0
0
2
1
0
2
2
1
1
0
2
1
1
3
2
1
2
0
1
0
0
2
1
0
1
2
2
2
2
1
1
2
2
0
0
0
2
1
0
0
1
2
2
1
1
1
4
1
0
0
1
1
1
0
1
0
1
0
0
1
2
2
2
1
0
0
2
2
2
0
0
1
0
0
0
0
1
2
3
2
0
2
1
2
1
0
1
1
2
1
0
1
1
2
0
0
0
1
0
0
1
1
1
1
0
2
2
0
2
2
2
0
1
2
1
0
0
0
0
1
0
2
1
1
0
0
2
1
1
5
2
2
1
0
1
0
2
0
0
0
1
1
0
2
1
1
1
0
0
1
1
0
0
2
1
0
0
1
2
1
1
1
0
0
0
1
3
1
2
0
0
1
0
2
0
1
2
0
3
1
2
2
1
1
0
2
0
0
0
0
1
0
2
1
0
2
0
1
2
0
0
0
0
1
1
0
1
1
1
1
1
0
0
3
2
1
1
1
1
1
0
1
1
0
1
0
0
2
0
2
0
1
2
1
0
2
1
0
0
1
2
0
1
0
0
2
1
0
0
1
1
2
1
0
1
0
0
0
1
2
0
2
0
0
1
1
1
0
1
0
0
0
1
0
1
1
2
0
0
0
1
0
0
0
1
2
1
2
0
6
0
0
0
0
1
2
2
1
1
1
0
1
1
0
1
1
1
1
0
1
1
0
1
0
0
1
2
0
0
1
0
0
0
2
1
2
2
0
1
0
0
1
0
0
2
0
0
2
1
1
0
1
1
0
1
0
0
0
2
0
0
2
2
1
2
1
2
1
2
1
0
2
2
0
0
2
1
0
0
0
1
0
1
1
1
2
2
1
0
2
1
2
0
1
0
0
0
2
2
2
0
0
2
1
0
0
0
0
0
0
0
2
0
2
1
0
1
0
1
0
1
0
0
1
0
1
0
2
1
0
0
0
2
0
0
1
1
1
0
0
0
0
2
1
0
2
0
0
1
1
0
2
0
0
0
1
2
0
2
0
2
0
0
1
0
0
0
1
1
1
1
0
2
2
0
0
1
0
1
0
0
0
1
1
1
1
1
1
1
2
1
0
2
1
1
0
1
1
1
0
0
0
2
0
0
0
0
1
0
0
1
1
0
2
0
1
1
1
0
0
0
2
1
0
0
0
0
0
0
0
2
1
1
6
0
5
0
0
1
1
0
2
2
1
1
2
1
0
1
2
4
0
0
1
1
1
0
1
2
3
2
0
1
0
1
1
0
0
0
0
1
0
0
0
1
2
0
2
1
1
0
0
0
1
0
0
0
1
0
2
1
1
0
0
1
1
1
1
1
0
0
0
0
3
0
1
0
1
2
1
1
0
2
0
1
0
1
0
2
2
0
0
1
1
2
0
1
0
2
1
1
1
1
0
2
2
1
2
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
1
1
1
0
1
0
1
1
1
1
0
1
0
0
0
0
0
2
0
0
0
0
2
2
1
1
0
2
1
0
1
0
0
0
1
1
1
0
0
1
1
1
2
0
1
1
1
1
0
1
2
1
0
0
2
1
2
0
1
0
1
1
0
2
1
1
0
1
2
1
1
0
1
0
1
1
0
2
1
1
0
1
0
1
1
0
1
1
2
1
0
0
0
0
0
0
0
0
0
1
3
1
0
0
0
1
1
0
1
1
1
0
0
1
0
0
0
1
0
2
1
2
1
0
0
1
0
1
2
1
0
0
1
0
0
1
1
0
2
1
0
0
0
1
0
2
1
2
1
1
0
3
1
2
1
1
0
0
0
2
0
0
2
0
2
2
0
0
1
0
2
1
2
2
1
1
0
1
1
1
1
1
1
1
1
1
2
2
1
0
1
2
0
0
0
0
2
1
1
0
1
0
0
1
1
1
1
2
0
0
0
0
1
2
2
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
2
1
1
0
1
0
1
0
1
0
0
0
2
0
0
1
0
1
1
2
1
2
2
0
2
0
2
0
1
1
0
2
0
0
2
0
0
0
1
2
0
0
0
1
2
0
2
1
2
2
1
2
0
1
0
1
0
1
1
2
0
1
2
1
0
1
9
0
1
1
0
1
0
0
1
2
0
2
0
1
2
0
1
0
2
1
0
1
1
1
0
1
0
0
1
2
0
0
3
1
0
0
1
0
0
1
1
0
1
0
1
0
2
2
1
0
2
0
2
0
0
0
1
0
0
2
1
0
0
1
1
0
0
0
0
1
2
2
1
0
2
1
0
2
1
0
2
1
2
1
2
2
1
0
0
2
1
0
1
0
2
1
0
0
0
2
1
1
1
1
0
0
0
1
0
1
0
1
1
0
1
2
2
1
0
0
2
0
3
1
0
0
2
1
0
0
0
2
0
2
0
0
0
0
1
1
2
0
0
0
1
2
0
0
2
0
7
1
2
0
0
1
1
1
1
1
0
1
0
1
2
0
0
1
0
1
1
2
0
1
1
0
2
1
1
1
0
1
1
1
0
1
1
1
0
2
2
2
0
2
2
2
0
0
1
0
2
0
1
1
0
0
0
2
0
1
1
2
0
1
1
2
3
1
1
2
0
0
2
1
1
1
1
2
1
1
0
0
0
0
0
0
1
2
2
1
0
1
1
1
1
2
0
0
1
0
1
0
1
1
0
1
1
0
0
0
1
2
2
2
0
0
1
1
1
0
0
1
1
0
1
0
2
2
2
0
0
3
1
1
0
2
1
1
2
1
1
1
0
2
1
0
1
0
1
0
0
1
1
1
1
0
1
0
0
0
4
1
0
1
1
0
1
0
2
2
1
2
0
1
1
0
2
0
1
2
1
1
0
1
1
2
1
2
2
0
1
2
2
0
1
0
3
2
0
1
0
1
1
1
0
1
0
0
1
0
0
2
1
0
0
0
0
0
2
1
0
2
1
1
2
1
0
0
0
1
0
1
0
1
2
0
2
0
0
1
0
0
1
1
1
1
1
2
0
0
0
3
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
1
2
0
1
0
1
1
0
0
1
0
0
0
1
1
0
0
2
1
0
0
1
1
1
1
1
1
0
1
0
1
2
0
0
1
0
1
1
0
1
2
0
1
1
1
2
0
0
3
1
1
0
2
1
1
0
1
0
0
1
0
0
0
0
1
1
0
1
0
2
0
1
4
1
3
1
1
2
0
2
0
2
0
3
0
0
3
0
0
1
1
0
0
0
1
1
0
2
2
0
0
0
1
0
0
0
2
0
1
5
0
0
1
0
1
0
1
2
1
2
0
1
0
0
0
1
3
1
0
0
1
0
0
1
0
0
0
1
0
1
1
1
1
1
1
0
1
0
0
0
0
0
0
0
1
0
1
1
0
1
0
1
0
0
1
0
0
2
0
0
2
1
1
0
0
1
0
2
1
0
2
1
1
3
0
0
0
0
1
1
1
0
1
2
2
1
1
1
0
0
2
1
0
1
0
0
0
2
2
3
0
1
0
0
1
2
1
0
1
0
1
2
1
0
0
0
0
1
0
0
3
1
0
0
0
3
2
0
0
2
2
0
0
0
1
0
1
0
0
0
0
1
1
2
0
0
0
2
1
0
0
2
1
0
0
0
0
2
1
0
0
3
2
0
1
1
2
2
2
0
1
2
2
1
1
1
0
1
0
1
1
0
1
1
1
2
0
0
0
1
0
2
1
1
1
0
1
0
0
0
1
2
0
0
3
0
0
1
0
1
0
1
1
0
0
0
1
1
0
2
0
0
1
1
0
0
1
1
2
0
1
1
1
0
0
0
0
0
0
2
0
0
1
0
1
0
0
1
2
2
2
0
1
1
0
2
1
0
1
0
1
0
0
1
0
1
0
0
1
0
2
0
1
2
2
0
0
1
1
0
0
0
1
0
0
0
0
1
0
2
1
0
2
1
0
0
1
1
2
2
3
0
2
1
6
1
0
1
1
0
2
0
2
0
0
1
1
1
0
1
1
0
0
0
1
2
2
1
0
0
1
0
1
0
0
0
1
0
2
0
2
2
0
2
1
0
0
0
1
1
1
1
0
0
1
1
1
2
0
0
1
1
2
0
0
0
1
1
1
2
2
0
1
0
0
0
0
0
2
0
1
1
1
2
0
0
2
3
1
1
2
0
2
2
0
1
1
1
1
1
1
1
1
2
0
1
1
0
1
0
0
0
0
1
1
1
0
1
0
0
1
1
2
0
0
0
0
1
1
0
1
1
1
2
0
1
1
2
2
0
0
0
3
1
1
1
0
1
4
0
1
0
2
3
0
2
1
1
0
1
1
1
1
1
0
2
0
0
2
0
2
1
0
0
1
1
0
0
0
1
1
1
0
0
1
2
1
1
3
1
1
0
0
1
1
2
0
0
0
1
1
0
1
0
0
0
0
2
1
0
0
2
2
1
0
1
0
0
2
0
0
1
1
2
2
0
1
0
1
2
2
1
1
1
2
0
0
0
0
2
0
0
1
0
1
1
2
0
0
0
0
2
2
1
2
2
1
0
1
0
2
0
1
2
2
0
0
2
2
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
3
0
0
2
2
0
1
1
2
2
1
1
1
1
0
0
0
1
0
1
1
0
0
2
0
2
2
1
0
0
1
1
0
2
1
2
2
0
2
1
0
0
0
1
0
2
1
1
2
0
1
1
1
1
0
0
0
1
0
0
0
1
1
2
1
1
1
0
1
1
1
2
0
2
1
0
0
2
1
2
0
1
0
2
0
1
2
0
1
0
1
0
0
2
1
0
2
2
0
0
0
1
1
0
2
0
0
1
1
0
2
2
0
0
0
1
0
0
3
1
1
1
0
0
2
2
1
0
0
0
0
0
1
1
0
1
1
0
2
1
0
3
1
1
2
0
1
0
0
1
0
1
2
0
0
1
1
1
1
0
7
1
0
1
0
0
0
1
1
1
2
0
0
0
2
1
1
1
1
0
0
0
0
1
0
0
2
1
0
1
0
2
2
0
0
0
1
2
1
1
0
1
0
0
2
1
1
2
0
0
1
2
1
1
0
2
1
0
0
1
0
0
1
0
0
0
2
0
1
1
0
0
1
1
3
0
0
3
1
0
1
0
0
2
1
1
1
0
1
0
0
2
2
1
0
0
1
0
0
1
1
2
5
1
1
1
0
0
2
2
1
1
1
2
1
1
0
2
1
2
0
1
1
0
1
2
1
2
0
1
0
2
3
2
2
0
0
3
1
0
1
1
0
1
0
0
2
1
0
2
0
1
1
1
2
0
0
1
2
2
2
1
0
1
0
1
0
0
0
0
1
1
2
1
1
1
2
0
1
0
2
1
1
1
1
2
1
1
2
1
0
2
1
0
1
2
2
0
0
0
2
1
1
0
1
0
0
0
0
1
1
0
0
2
0
1
1
2
0
1
3
1
0
1
0
0
2
2
0
0
0
0
0
1
2
1
0
0
1
1
0
0
0
1
0
0
2
0
1
0
2
1
0
0
2
1
1
1
2
0
2
1
0
0
2
1
1
1
2
0
1
2
0
0
1
0
1
2
0
0
1
0
2
2
0
0
0
0
0
0
1
2
1
1
1
0
0
2
0
2
1
1
1
1
2
0
0
0
2
1
1
0
0
2
2
2
0
0
1
3
2
1
2
0
2
0
0
1
0
0
0
1
2
0
2
1
3
1
1
1
2
0
0
0
2
1
2
2
1
1
1
0
2
0
0
0
0
2
0
0
2
1
1
0
1
0
0
0
1
2
0
1
0
1
0
1
1
1
2
1
0
0
1
1
2
1
0
0
1
1
1
0
2
1
0
1
0
0
0
0
1
0
2
0
0
0
2
1
0
0
1
2
0
1
1
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
2
0
1
0
1
0
0
0
0
1
0
1
0
0
1
2
0
2
2
0
0
1
2
0
2
2
1
2
0
1
1
1
0
2
0
1
3
0
1
0
1
2
2
0
0
2
2
1
1
0
0
2
0
0
2
0
0
0
0
0
1
1
0
2
2
2
0
1
1
0
1
0
0
2
2
0
0
1
2
1
0
1
2
0
0
0
1
1
1
0
0
2
1
1
1
2
1
1
1
2
0
2
0
2
0
2
2
0
0
1
2
0
0
1
1
0
0
0
2
1
1
1
2
0
1
2
0
1
2
1
2
2
1
1
1
2
2
1
0
0
2
0
0
0
0
0
0
1
0
4
1
2
1
2
0
2
1
0
1
2
1
0
2
1
0
2
0
0
0
0
0
1
0
0
0
1
0
0
2
1
0
2
0
0
2
2
1
2
1
2
1
1
0
0
1
2
1
1
0
1
0
1
0
0
0
0
0
0
1
2
4
2
0
2
0
0
2
1
0
0
1
1
0
0
0
0
0
2
0
0
0
0
6
1
1
0
0
2
2
1
0
2
1
3
0
0
2
0
0
0
0
1
1
1
0
0
3
1
0
0
0
2
1
0
0
1
2
2
0
1
0
2
0
1
0
0
2
3
2
1
2
1
0
1
1
0
0
0
2
1
0
0
0
2
1
1
0
0
1
1
0
1
0
1
0
0
1
2
2
2
1
1
2
1
0
0
0
3
1
1
0
0
1
2
0
2
1
0
2
1
2
1
0
0
2
1
1
0
1
1
1
0
0
0
1
0
0
2
2
0
0
2
0
0
2
1
2
0
2
1
0
0
1
0
1
0
0
0
0
1
0
1
1
1
0
0
1
2
1
0
1
0
1
1
1
0
1
0
1
1
2
1
1
0
1
1
1
1
0
0
0
1
0
1
2
3
1
1
2
1
0
1
0
0
0
1
1
1
0
2
1
5
0
1
1
2
0
1
1
1
1
1
0
0
0
0
1
0
2
2
0
0
0
0
0
0
1
1
0
0
2
2
0
0
1
1
2
2
0
1
1
1
0
0
2
1
2
0
0
0
1
1
0
2
1
0
0
1
0
0
0
2
1
0
2
1
0
0
2
0
1
1
0
0
0
0
1
1
0
1
3
2
0
1
2
0
0
0
0
2
1
1
2
0
0
0
2
0
0
1
2
3
1
0
0
1
0
0
4
2
0
0
1
1
1
1
2
1
0
1
1
1
0
1
1
1
1
1
0
1
0
2
1
2
1
1
2
0
0
1
2
2
0
1
0
0
1
0
0
1
2
0
5
0
1
1
1
1
0
0
1
2
0
0
2
0
1
2
0
0
0
0
1
0
2
0
1
0
0
1
1
1
0
0
2
1
1
1
0
0
0
2
1
0
0
0
1
0
1
2
0
0
1
0
1
1
2
1
0
0
2
1
2
1
0
1
2
1
0
2
1
1
4
0
0
1
0
0
0
0
0
1
0
2
2
1
0
1
0
1
1
1
0
0
0
2
0
0
0
0
0
1
2
1
1
1
2
0
0
0
0
0
0
1
1
0
0
2
1
2
0
0
1
2
0
2
0
1
1
2
2
0
0
0
0
1
1
0
1
0
0
1
2
1
1
3
0
2
1
1
0
0
0
1
0
2
1
2
1
2
0
0
1
1
0
0
0
2
2
0
0
1
2
1
3
0
1
1
0
1
3
0
0
2
1
3
2
2
1
0
2
0
2
2
2
1
0
0
0
0
0
0
2
2
2
0
1
0
0
0
0
1
2
2
2
0
0
0
2
2
0
0
0
1
0
0
0
0
1
1
1
0
0
1
0
2
4
1
0
1
1
1
0
0
0
2
1
0
0
1
1
1
1
0
0
0
0
0
1
1
0
1
1
2
1
0
1
0
1
1
1
0
0
0
0
1
2
2
1
2
0
1
1
2
1
1
1
0
2
0
1
1
1
0
1
2
1
1
0
0
2
2
3
0
2
0
1
2
0
0
0
0
2
2
1
0
1
0
3
0
0
0
0
0
1
1
0
0
0
1
0
0
0
2
2
0
0
2
0
1
0
0
1
8
1
0
0
2
0
0
0
0
2
1
0
1
1
1
0
1
0
1
0
2
0
1
0
2
2
0
1
0
1
0
1
1
0
0
2
2
0
0
1
1
1
1
0
2
1
0
0
1
1
2
2
2
2
0
0
0
2
2
0
0
0
2
0
2
1
0
1
0
1
2
1
1
1
1
0
1
2
0
1
2
0
2
0
0
0
2
0
1
0
0
0
1
0
0
2
2
1
0
3
2
2
1
2
0
2
1
2
2
2
0
2
1
0
1
2
0
1
2
1
1
2
0
0
0
2
1
2
1
0
1
0
1
1
0
1
1
2
1
2
2
0
2
0
1
1
0
1
2
0
1
1
0
0
0
0
1
2
2
0
2
2
0
0
0
0
1
1
2
1
0
2
1
2
0
1
0
0
2
3
1
2
0
0
0
2
0
1
1
1
1
1
0
0
0
0
1
2
0
2
2
0
0
1
0
0
1
2
0
1
0
4
1
0
1
2
1
1
1
1
0
0
2
1
1
0
1
0
0
0
1
2
0
1
0
1
0
1
2
0
1
2
0
1
0
1
0
0
1
0
0
1
1
0
0
0
1
2
2
1
0
1
1
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
1
1
2
0
1
0
0
1
1
1
1
0
1
3
2
0
3
1
1
2
0
2
0
1
1
0
0
0
1
0
1
0
0
2
2
0
1
1
0
0
0
1
0
3
0
0
0
0
0
1
0
0
0
1
0
1
0
1
1
2
0
1
1
1
0
2
0
1
2
0
0
0
0
0
1
2
1
1
2
0
1
0
0
1
2
2
1
0
1
0
0
2
1
0
0
1
1
0
2
1
0
1
2
2
0
1
2
0
0
2
0
0
2
2
1
2
1
1
1
1
2
0
1
1
1
1
1
0
1
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
2
2
0
3
0
1
1
0
0
1
1
0
0
0
0
2
1
0
0
1
1
0
0
0
0
0
1
2
0
0
1
0
0
0
1
1
1
1
0
0
0
2
2
1
0
0
1
0
1
1
1
0
0
2
1
1
1
1
0
0
0
0
1
0
0
1
1
2
1
1
1
0
0
3
1
0
0
0
1
0
0
0
0
1
0
1
2
2
0
1
2
0
1
0
0
0
0
2
0
0
2
1
1
0
0
0
0
2
1
1
0
0
1
0
1
2
0
1
0
0
1
1
1
2
2
0
0
1
0
2
1
1
1
0
2
1
0
0
1
1
1
0
1
0
0
1
0
0
3
2
0
1
0
1
1
0
3
0
2
1
1
1
1
0
2
1
2
1
1
0
0
1
1
1
1
0
0
0
1
0
0
0
1
0
0
0
2
0
1
1
1
0
1
2
0
2
0
1
0
0
2
0
2
0
1
0
0
1
0
0
1
2
1
2
2
0
2
0
1
0
2
1
1
1
1
1
0
1
0
0
2
1
1
0
0
0
0
0
2
3
2
1
0
0
2
2
0
0
0
2
0
1
2
1
2
0
0
1
1
2
2
1
0
2
1
0
1
2
0
0
2
2
0
2
0
2
0
0
0
0
0
2
0
0
0
0
1
2
2
0
0
0
2
0
0
1
2
0
0
1
1
0
1
1
1
2
1
2
0
0
1
0
1
2
2
2
2
1
1
0
2
0
2
0
0
0
0
1
0
1
0
1
0
0
0
1
2
0
1
2
0
1
0
2
1
0
2
1
1
1
1
0
2
1
2
0
0
4
2
1
0
0
2
0
0
0
2
2
0
0
0
1
2
0
3
1
1
0
0
1
2
2
0
2
1
1
2
1
0
1
1
1
0
0
0
0
1
0
1
0
0
1
1
1
0
0
1
2
2
2
0
2
0
1
0
1
1
0
0
1
1
0
1
1
0
0
2
0
2
2
2
1
2
3
1
0
1
0
1
0
1
1
0
1
1
3
0
0
0
4
0
0
1
0
0
0
0
0
0
0
1
1
1
1
3
2
2
0
0
0
0
2
0
2
0
1
2
1
0
1
0
1
1
1
2
0
1
1
1
1
0
2
0
1
0
0
2
1
0
1
0
0
0
1
2
2
0
0
2
0
1
1
0
0
1
0
0
2
1
1
0
1
2
2
2
0
1
0
2
2
0
0
1
0
2
1
0
0
2
0
0
0
0
0
0
1
1
1
0
0
1
0
1
2
1
1
0
0
0
0
0
1
2
2
0
1
2
2
0
0
0
4
0
1
1
2
0
0
2
1
1
2
0
1
0
0
1
1
2
0
1
1
0
1
1
1
0
0
2
1
2
0
0
0
0
0
0
2
1
0
1
1
0
0
2
2
0
0
1
0
1
1
0
0
2
1
1
0
2
0
1
0
0
1
0
0
1
1
0
1
1
2
1
0
1
0
1
0
0
0
2
0
0
1
1
0
0
0
0
1
0
2
0
0
2
2
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
1
1
1
1
2
2
3
2
0
0
2
1
1
1
0
2
0
1
3
0
1
1
1
2
0
2
0
2
2
3
0
1
0
0
1
1
1
1
1
1
1
2
1
1
0
0
1
0
0
2
0
0
0
0
1
1
0
2
2
0
1
0
1
1
0
1
1
2
1
2
0
0
1
0
1
1
2
1
1
0
0
1
2
0
0
1
0
1
0
2
0
1
0
2
0
2
0
1
2
3
1
1
2
2
0
2
1
1
1
0
2
0
0
0
2
0
0
2
0
0
1
0
2
1
0
0
0
2
2
0
2
2
1
1
2
0
0
0
1
0
0
1
1
1
0
0
3
0
2
1
0
1
1
1
1
1
0
2
1
0
2
0
1
3
0
1
0
0
1
1
1
1
2
0
1
1
2
1
0
2
1
0
0
2
1
0
2
0
0
0
0
2
0
1
0
1
2
0
1
1
1
0
0
1
1
1
2
0
1
2
1
1
3
0
1
0
0
0
1
2
1
1
2
1
0
2
1
1
1
1
1
1
1
0
1
2
1
0
0
1
2
1
1
2
2
0
1
0
1
0
1
1
2
0
1
1
2
2
2
1
0
0
3
1
2
2
2
2
0
1
1
2
1
0
2
2
1
1
2
2
1
0
2
0
2
0
1
1
1
0
0
1
0
2
0
1
1
2
0
1
0
1
1
0
2
0
0
1
1
0
0
2
2
1
1
3
0
0
0
0
0
0
1
0
1
0
2
1
1
1
1
2
0
1
0
0
0
1
0
1
1
0
2
1
0
2
0
0
1
1
1
2
1
0
0
1
1
1
2
0
0
1
0
0
3
0
2
2
1
2
1
2
2
1
0
1
0
1
0
0
0
1
0
1
1
1
0
0
1
1
0
0
2
1
0
0
0
2
1
0
1
0
2
2
0
1
0
0
2
0
1
0
3
1
2
0
1
0
1
0
1
2
1
0
1
1
0
2
2
1
1
2
0
0
0
0
1
1
0
0
0
1
0
1
2
0
0
0
0
1
0
1
1
0
1
1
2
1
2
0
0
1
2
2
0
0
2
0
1
0
2
0
0
0
1
1
0
0
2
0
1
0
0
1
1
0
1
2
2
0
2
1
0
0
0
1
1
0
0
1
1
0
0
0
0
1
0
0
0
2
0
2
1
1
2
0
0
1
1
0
0
1
1
1
1
1
0
0
0
1
1
2
0
0
1
0
2
2
7
0
1
1
0
2
0
1
0
0
1
2
3
1
0
0
1
0
0
2
0
0
2
1
1
0
1
0
1
1
1
0
1
0
0
1
1
0
2
1
3
1
1
0
1
2
0
2
0
1
0
3
1
2
2
1
0
1
0
0
1
1
0
0
1
1
1
0
0
1
2
1
0
1
1
2
0
1
1
2
0
0
1
2
2
0
2
2
1
0
1
2
1
0
1
0
0
1
0
0
1
0
1
0
3
2
1
0
2
1
2
0
2
1
2
1
1
1
0
0
0
7
0
0
1
2
0
1
1
1
1
2
2
0
0
0
0
1
2
0
1
1
0
0
0
0
0
2
1
0
2
0
0
2
2
1
0
0
1
0
0
2
0
0
2
0
0
2
1
2
1
1
2
1
0
1
1
0
2
0
0
2
0
0
0
0
0
2
0
2
0
1
0
0
2
0
1
0
1
1
0
0
0
1
0
2
0
0
1
1
3
2
1
1
1
2
0
0
0
3
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
3
0
2
0
1
0
1
1
2
1
1
2
1
1
1
0
2
2
1
2
0
2
0
0
0
2
2
2
1
0
1
0
0
0
0
2
0
2
3
0
0
0
2
0
0
0
0
1
4
1
0
2
2
2
0
0
0
0
0
0
0
2
1
1
0
0
1
1
0
0
0
0
2
0
0
1
0
3
1
0
2
0
2
1
1
0
1
0
2
0
2
1
2
1
0
0
2
0
0
3
3
1
0
1
0
2
0
3
2
0
1
0
1
1
0
2
2
1
0
1
2
0
0
1
0
0
0
0
0
2
2
4
0
0
0
2
1
1
0
0
0
0
2
1
0
0
1
0
0
2
0
0
1
0
0
0
2
2
0
0
0
1
1
1
1
1
3
2
0
2
1
0
1
0
0
0
2
0
1
3
0
2
0
1
0
1
1
1
0
1
3
2
1
0
2
2
0
0
0
0
1
1
2
0
1
0
1
2
0
1
0
2
1
1
0
2
1
0
0
0
1
0
1
2
0
1
1
1
0
0
0
0
2
1
2
2
2
2
1
0
1
1
1
0
0
2
0
2
2
1
2
0
0
0
1
2
1
0
0
0
0
1
2
1
2
1
2
2
0
0
1
0
0
1
2
0
1
2
0
0
2
0
0
0
1
1
1
2
1
0
2
1
0
0
0
0
2
0
2
1
0
1
1
0
1
2
0
0
2
2
0
2
1
2
1
2
1
0
0
1
1
2
1
0
1
0
1
0
1
0
0
0
0
1
1
0
1
1
0
1
0
2
2
2
0
2
1
3
0
0
1
0
0
0
1
2
1
2
1
0
0
2
0
1
1
0
1
1
1
1
2
0
0
2
2
1
1
2
1
0
2
0
0
1
1
0
0
0
0
0
0
2
1
2
2
0
1
0
1
0
2
1
0
0
0
0
0
1
2
1
0
0
2
0
0
1
0
0
2
1
1
2
0
1
1
2
2
1
2
0
2
2
2
0
2
0
0
0
2
0
2
0
0
2
0
1
0
0
0
1
0
2
1
0
0
1
0
2
0
1
1
1
1
2
1
2
3
2
1
2
1
0
0
0
0
0
2
1
2
0
1
2
1
1
1
1
1
0
2
0
3
0
0
1
1
1
1
1
1
1
1
3
1
2
5
2
0
1
0
0
0
2
1
2
0
1
0
1
0
0
0
1
1
0
0
1
1
0
1
0
1
1
0
0
2
1
1
3
0
0
1
0
0
0
0
1
2
2
1
1
1
0
2
1
0
2
1
1
1
0
1
0
1
0
0
0
0
2
2
0
1
0
2
0
2
2
0
0
1
3
0
1
2
1
1
0
0
1
0
0
0
2
2
1
0
3
1
2
0
1
0
2
0
0
1
1
0
1
2
0
0
2
1
2
0
0
1
1
1
1
2
0
1
1
1
0
1
0
4
0
0
3
2
4
2
1
1
0
0
0
0
0
1
3
1
1
0
2
0
0
0
1
1
1
1
1
1
0
2
2
0
1
1
1
1
1
2
0
0
0
1
1
0
0
0
2
0
0
2
0
0
1
1
0
5
2
1
0
0
0
1
0
0
1
1
0
1
2
0
1
0
0
0
0
2
1
0
0
1
1
0
0
0
0
1
1
1
1
1
0
0
0
0
2
0
0
2
2
1
3
0
0
3
0
1
2
0
1
1
2
0
0
1
1
0
1
1
1
0
0
2
1
1
1
1
1
2
0
0
1
1
2
0
0
2
1
0
0
1
1
2
0
1
1
2
0
2
0
1
0
0
1
0
0
2
1
0
0
1
0
0
0
0
1
2
1
2
0
1
0
1
1
2
1
2
1
2
0
0
2
2
1
1
0
1
0
1
0
0
0
1
0
1
2
1
0
1
1
1
1
0
0
2
2
0
0
1
1
0
0
1
0
0
2
2
1
2
2
0
2
0
2
1
0
0
1
2
2
0
0
1
1
0
1
0
1
1
1
1
0
1
2
1
0
0
1
0
1
1
0
1
0
2
2
0
0
0
1
0
1
2
1
0
2
0
0
0
0
0
0
3
1
1
2
0
2
0
0
2
0
0
0
0
2
0
0
2
0
0
2
0
0
0
3
1
1
1
1
0
0
1
0
1
2
0
0
0
1
1
1
2
1
0
1
1
0
1
0
1
1
0
3
0
1
0
1
1
2
0
1
0
1
0
0
1
0
1
1
3
0
1
0
2
1
1
0
2
2
0
2
0
0
1
2
1
2
2
1
1
0
0
0
0
0
0
1
0
1
1
0
0
1
1
0
1
1
1
0
1
0
2
2
0
1
0
2
0
0
2
2
1
0
0
2
0
0
2
1
2
0
1
0
2
0
2
1
0
0
1
2
0
0
0
0
5
1
0
1
2
1
0
0
2
3
0
0
2
0
2
1
1
0
0
1
2
1
0
1
0
0
2
2
0
2
2
2
2
0
0
1
1
1
0
1
2
1
1
2
1
0
2
2
0
0
0
0
0
1
1
0
1
1
1
0
1
2
3
1
1
2
1
1
1
1
1
1
1
1
1
0
1
4
2
0
2
1
1
2
2
0
0
1
1
0
4
2
0
0
1
0
0
1
0
1
2
0
1
1
1
0
2
2
0
1
0
2
0
0
0
2
0
0
0
2
1
1
1
0
0
2
2
0
1
3
1
0
0
0
0
0
0
2
0
2
0
0
1
2
0
0
1
0
2
1
0
1
1
0
0
1
1
0
1
0
2
0
0
1
0
2
0
2
0
1
1
2
0
2
2
0
0
0
0
0
0
1
2
0
2
0
0
0
1
1
1
2
0
1
2
0
1
1
0
2
0
2
2
0
1
0
1
0
2
1
3
2
0
0
2
0
0
1
1
0
1
0
1
1
1
0
2
2
2
2
0
0
1
0
0
2
1
1
0
0
0
2
2
0
2
0
2
1
0
0
2
0
2
2
1
1
2
0
0
2
1
1
1
2
1
0
1
1
0
0
0
0
1
1
1
0
0
0
0
2
0
0
1
1
1
0
0
1
2
1
1
1
0
1
1
3
1
1
0
2
0
0
3
0
1
1
1
0
1
1
0
1
0
1
2
1
0
1
1
0
1
1
2
0
1
1
0
0
0
0
0
0
0
0
0
2
2
1
1
2
2
3
0
1
1
0
1
1
2
2
0
1
0
0
3
0
0
0
1
1
1
2
1
3
2
1
0
2
0
2
1
1
2
1
1
0
1
1
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
2
1
0
0
1
0
0
0
0
0
0
2
3
0
0
1
1
2
2
0
1
1
2
0
0
0
1
1
0
2
2
2
1
1
0
1
0
2
2
0
1
2
0
0
0
0
2
0
0
1
1
0
0
0
0
1
2
2
0
2
0
1
1
0
0
1
0
1
2
1
0
2
0
0
2
2
0
1
0
0
1
1
0
0
1
0
1
0
1
2
0
1
0
1
1
1
1
1
0
0
0
2
2
1
0
1
0
3
1
1
1
0
0
0
0
0
1
0
2
2
0
0
2
1
2
0
0
0
0
1
0
1
1
2
2
1
1
1
1
1
0
2
0
1
0
0
0
0
0
2
0
0
0
1
1
2
2
1
0
0
1
0
0
0
1
0
1
1
0
0
0
1
2
2
0
2
1
1
0
1
1
0
1
0
2
0
0
0
0
2
1
0
0
1
1
2
3
0
0
0
1
1
2
0
0
0
0
0
0
1
1
2
2
1
1
0
1
1
0
1
0
1
1
1
2
0
0
2
1
0
0
1
1
1
0
0
0
2
0
2
0
2
1
2
1
1
2
2
1
2
2
0
0
0
1
1
0
0
1
0
0
1
1
0
0
2
0
0
2
2
0
2
1
1
0
1
2
0
1
1
1
0
1
0
1
0
0
0
2
0
1
1
1
0
0
0
0
2
0
2
2
1
1
0
0
2
2
3
1
1
2
2
2
2
2
2
0
1
2
0
1
2
1
5
2
2
2
2
2
1
0
2
2
2
0
1
0
0
2
0
2
0
1
0
0
1
0
0
1
0
1
0
0
1
2
0
0
1
0
0
1
0
0
1
1
1
1
1
2
0
1
0
0
0
1
1
2
1
0
2
2
0
1
0
0
1
2
2
0
1
0
0
1
1
2
0
0
1
0
1
2
1
0
2
2
1
1
0
1
0
0
1
0
2
0
0
0
0
0
7
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
2
0
2
0
1
0
1
1
1
0
1
1
1
0
1
2
0
1
0
0
0
1
0
0
1
0
0
0
1
0
1
0
1
1
2
0
1
0
0
0
2
0
1
0
1
0
2
2
2
1
0
2
0
1
0
0
1
1
0
0
0
0
1
1
1
0
0
0
2
1
1
1
1
2
0
0
0
0
1
0
2
1
2
0
1
2
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
1
1
2
1
1
0
0
0
0
0
1
0
0
0
2
0
1
0
0
1
2
1
1
2
0
0
1
0
0
3
0
1
0
2
0
1
0
0
0
0
0
1
2
0
2
2
0
1
0
2
0
0
0
1
1
0
0
1
0
0
5
2
1
0
0
1
0
1
1
1
0
0
1
0
0
0
1
0
1
2
1
0
1
1
1
2
1
1
1
2
0
0
1
0
1
2
1
0
2
2
0
1
1
0
0
1
1
1
0
2
0
1
1
2
1
1
1
0
0
2
0
2
2
2
0
1
2
0
1
1
0
1
1
2
0
0
1
2
0
2
2
0
0
0
2
2
2
1
0
1
0
0
0
0
1
2
2
0
1
2
0
1
2
1
1
0
1
1
1
1
0
0
1
0
2
0
0
1
2
1
1
0
3
0
0
0
0
0
2
1
0
0
1
2
0
1
0
1
0
0
1
1
4
1
1
0
1
0
0
0
0
2
1
0
2
0
2
0
1
1
0
2
0
1
2
0
0
2
2
0
2
1
1
0
2
0
0
1
1
0
0
0
1
0
1
1
0
0
1
3
2
1
0
1
1
2
0
2
0
2
0
1
1
0
1
3
1
0
1
0
2
0
0
1
2
1
2
2
1
2
2
0
0
0
2
2
1
2
1
0
0
1
1
1
1
1
0
0
0
0
0
2
2
2
0
0
1
1
0
1
0
0
1
0
2
0
1
2
1
0
0
0
0
0
1
1
0
3
1
1
0
2
0
0
0
1
0
1
0
0
0
1
2
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
1
2
0
2
1
1
0
0
2
1
0
1
1
1
1
2
0
0
0
2
2
0
2
0
0
1
1
1
2
1
0
0
1
1
0
0
0
1
0
1
3
0
1
1
1
0
1
0
0
2
0
2
7
1
0
0
2
1
0
1
0
2
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
3
0
0
0
0
0
0
1
0
1
1
1
1
0
1
2
1
1
2
2
1
1
1
0
1
1
1
0
0
2
0
2
2
0
2
2
1
0
1
1
2
1
0
2
2
0
1
0
1
1
2
2
1
1
1
1
2
1
1
1
1
0
0
0
2
2
1
1
0
0
0
0
1
0
1
1
2
0
1
1
0
0
2
0
2
0
0
0
0
0
3
0
0
0
0
1
0
0
0
1
1
0
0
0
1
1
1
0
1
0
1
1
0
1
0
1
1
1
5
0
0
1
1
0
0
0
1
1
1
0
0
2
1
0
1
1
0
0
0
1
0
2
1
1
0
1
1
0
0
1
0
1
1
0
2
1
2
1
0
3
2
2
0
1
2
1
2
0
2
0
0
0
1
0
0
0
1
1
2
1
0
2
1
1
0
0
2
1
1
1
1
1
2
1
1
0
0
1
1
1
0
0
0
2
0
1
1
1
1
2
0
0
1
1
2
1
3
1
2
1
1
0
1
0
2
0
0
0
0
0
0
2
1
1
1
0
0
0
0
0
0
1
0
0
2
0
1
2
0
1
2
2
1
1
2
1
2
2
2
2
2
0
0
0
0
1
1
2
1
1
1
0
1
1
1
2
1
0
0
1
2
2
0
0
0
1
1
1
2
2
0
0
0
1
1
1
2
0
0
0
2
1
0
0
0
1
1
1
0
1
3
0
0
1
2
1
1
0
0
0
1
1
1
1
2
0
0
0
2
2
2
1
2
2
1
0
0
1
0
4
1
0
1
0
0
1
0
0
1
1
0
0
0
1
0
1
1
0
0
1
0
1
1
0
0
1
0
0
1
1
2
0
1
0
0
0
0
2
0
0
1
2
1
0
1
1
1
0
0
1
0
0
2
0
1
0
3
1
2
1
0
1
1
0
0
2
1
0
1
0
2
1
2
0
1
0
3
0
0
0
1
0
0
2
0
1
0
0
0
0
0
1
2
0
0
2
6
0
1
2
2
0
0
1
0
1
0
1
2
0
1
0
0
0
1
1
0
0
0
1
2
0
0
0
3
2
2
1
2
1
0
0
0
0
2
0
2
1
1
0
2
0
2
1
0
0
1
0
2
1
0
0
0
2
0
2
1
1
0
1
1
0
0
1
2
1
0
0
0
1
1
1
2
0
1
1
2
2
0
0
1
0
0
2
0
0
0
2
2
1
1
0
0
1
0
0
2
1
0
0
2
1
1
0
0
1
2
0
2
0
0
0
2
2
1
0
2
2
1
1
0
1
1
0
0
2
0
1
1
2
1
0
1
0
1
0
3
0
0
0
0
2
1
0
0
2
0
1
1
1
1
1
0
1
1
2
0
2
2
0
0
0
0
0
1
0
3
1
1
0
0
0
0
1
1
1
0
0
2
0
0
0
0
1
1
0
1
2
0
2
0
2
1
2
1
1
2
0
1
1
0
0
0
2
1
0
1
0
0
0
0
2
2
1
0
2
1
1
0
1
0
1
0
1
2
0
2
1
2
1
0
1
0
0
1
1
0
1
0
0
1
0
2
2
1
1
2
2
1
1
0
0
1
0
0
2
1
1
0
0
1
0
3
1
1
1
2
0
3
1
2
1
1
2
0
1
1
2
2
0
0
1
1
0
0
0
1
0
2
1
0
0
1
0
0
0
1
0
1
0
2
1
2
0
3
2
1
1
0
0
1
0
2
0
2
0
0
1
0
0
0
2
0
1
0
0
1
2
1
0
1
2
0
2
2
2
1
1
0
0
0
2
1
0
1
1
0
2
1
0
2
5
0
0
2
0
0
0
1
0
0
1
1
1
1
0
1
1
0
1
2
0
0
1
2
1
1
0
0
0
1
2
0
0
1
2
1
1
1
0
2
0
0
0
0
1
1
0
1
2
2
0
0
0
0
0
1
1
2
2
0
1
0
1
0
2
1
0
0
1
2
0
1
1
0
2
1
0
0
1
0
1
0
2
0
2
1
0
1
1
1
2
1
0
1
0
1
2
1
1
1
1
0
1
0
2
2
1
0
0
0
2
2
0
0
0
1
0
2
0
1
2
2
1
1
1
1
1
1
0
0
0
0
2
0
1
1
1
0
2
0
1
0
0
1
1
2
1
0
0
2
2
0
2
2
2
2
2
2
0
0
1
0
0
3
0
0
0
0
1
0
0
0
2
1
1
0
2
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
1
2
0
2
0
0
0
1
0
0
2
0
1
1
0
1
0
2
0
0
0
0
4
2
2
0
0
2
1
1
1
1
0
1
0
1
1
1
0
0
1
2
0
0
1
1
5
1
0
1
0
2
0
0
1
0
0
1
1
2
0
0
1
0
0
0
0
1
1
1
1
2
2
0
0
1
2
0
0
1
1
0
1
2
1
0
1
1
0
1
1
1
2
2
2
2
2
1
1
0
1
3
2
2
0
2
2
2
0
0
0
0
0
0
2
0
1
2
0
0
1
0
1
2
1
1
0
1
1
1
0
0
2
1
2
1
0
1
2
1
1
2
0
1
0
0
0
1
0
1
2
0
1
0
1
0
3
1
0
1
0
1
2
0
2
0
3
1
0
1
0
1
2
2
2
0
1
0
0
2
0
1
1
2
1
0
0
0
1
0
0
0
1
1
1
0
1
0
0
0
0
1
2
2
1
0
0
0
1
1
0
0
0
0
3
2
2
2
1
0
0
0
0
2
1
1
1
2
1
1
0
2
1
0
1
0
2
0
0
1
2
0
0
1
1
1
0
1
2
0
0
0
1
0
0
2
2
5
1
1
1
2
1
1
2
2
1
0
2
2
0
1
1
0
2
1
1
2
1
1
0
0
1
1
1
1
2
1
0
1
0
0
0
1
0
0
0
1
0
0
1
1
1
0
0
2
3
1
1
0
1
0
0
0
1
2
2
0
1
0
0
1
0
0
0
2
2
1
0
0
0
2
0
1
1
1
1
0
1
1
1
1
2
0
0
1
2
0
1
1
1
1
1
1
0
0
2
0
1
1
1
1
2
1
2
2
2
2
1
0
1
1
0
0
1
0
2
0
1
1
0
2
0
1
1
2
1
2
0
0
1
0
0
2
1
1
0
0
0
0
0
0
0
2
0
0
0
2
1
2
1
0
2
1
3
2
1
0
1
2
0
1
1
1
1
1
1
0
1
2
1
0
2
1
1
1
2
0
1
1
0
0
1
0
0
2
1
0
1
3
0
2
0
0
1
1
2
1
1
0
2
0
1
0
0
0
2
2
1
1
1
0
1
1
0
2
2
0
0
0
2
0
1
1
1
1
1
1
0
1
2
1
2
2
0
1
0
0
2
0
1
0
2
2
0
0
1
1
0
1
0
2
1
0
0
2
1
1
0
2
1
1
2
1
1
1
1
1
0
2
1
1
1
2
0
0
1
0
0
4
0
0
1
1
1
0
1
2
0
0
1
0
1
1
0
3
0
0
0
1
2
0
0
1
1
2
0
2
0
0
2
0
0
2
0
0
1
0
1
2
1
0
1
1
0
2
2
1
3
0
0
0
0
0
2
2
2
1
0
0
0
0
1
2
0
0
1
1
3
0
0
0
0
0
0
2
0
1
0
1
2
1
0
1
1
2
0
1
2
1
1
0
1
2
0
1
0
0
0
3
0
2
1
0
1
1
0
1
0
1
0
1
1
0
0
1
0
2
0
2
2
0
1
2
0
2
1
0
2
0
2
1
1
2
0
1
0
2
0
0
2
1
1
0
2
0
1
2
1
0
0
2
1
0
0
2
0
1
1
1
0
0
0
2
0
0
2
1
1
0
0
0
0
1
0
0
1
1
1
0
2
2
1
0
0
1
1
2
2
2
0
2
2
2
0
0
2
0
0
3
2
1
2
2
1
2
1
1
0
1
0
0
2
1
0
1
0
1
0
2
1
2
0
0
0
1
1
2
0
1
0
1
1
0
1
0
0
1
0
1
1
2
2
0
2
2
0
1
0
2
1
0
2
3
0
1
2
1
2
1
1
1
1
0
0
2
0
2
0
2
2
1
0
0
2
0
1
0
0
2
0
0
2
1
1
1
0
1
0
0
2
1
0
1
0
1
1
2
0
0
1
0
2
2
1
1
0
0
2
0
1
2
0
1
0
0
1
0
0
1
2
1
1
1
0
0
2
1
1
2
0
1
0
1
1
2
2
0
2
0
2
1
0
2
0
0
1
2
2
2
0
1
0
0
2
3
1
0
0
2
0
0
0
2
1
0
0
0
0
0
0
1
1
2
0
2
0
0
1
0
2
0
1
1
1
2
0
1
1
2
2
1
0
1
0
1
0
1
2
1
2
0
0
0
0
1
1
1
1
1
1
0
2
2
0
0
0
0
1
1
0
0
0
2
2
0
1
1
1
0
1
0
1
2
0
0
1
0
0
2
0
3
0
1
0
0
2
0
0
2
1
2
2
1
0
1
0
0
2
1
3
0
5
0
1
2
1
0
1
1
0
0
1
1
1
0
2
1
1
0
2
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
2
4
2
2
1
1
0
0
0
1
1
1
0
2
0
0
0
1
0
0
0
0
2
1
0
0
0
0
1
0
0
2
0
1
1
1
1
1
4
1
0
0
0
1
2
0
2
0
0
0
0
0
0
1
2
1
0
1
1
1
0
2
0
0
1
2
0
0
1
1
2
3
2
0
0
1
0
1
1
1
1
2
0
0
0
3
1
1
0
1
0
0
0
2
0
0
0
1
0
2
0
2
1
2
3
1
0
1
1
0
2
2
2
0
2
0
0
1
2
0
1
0
0
1
0
1
0
0
0
2
1
1
0
1
0
1
0
1
0
1
0
1
1
0
1
1
0
0
0
1
0
0
1
2
0
1
1
0
2
0
1
1
1
0
2
0
0
1
0
1
1
0
2
0
0
1
0
0
3
0
0
1
1
1
1
0
0
1
0
2
2
2
0
1
1
1
2
0
2
1
1
0
2
2
1
2
1
1
1
0
2
1
0
1
1
1
1
1
0
0
1
0
1
0
0
1
0
1
3
0
0
2
1
2
0
0
1
0
2
1
0
0
0
1
0
2
1
2
2
1
1
0
1
2
1
2
2
1
0
1
1
1
1
1
2
0
0
1
1
1
0
0
1
1
2
1
1
1
0
0
0
0
3
0
0
0
2
0
1
0
0
2
1
0
0
1
1
2
4
0
0
0
0
1
0
0
0
0
0
0
2
1
2
0
0
1
1
0
2
0
0
2
1
1
0
1
2
0
2
0
0
0
1
2
0
1
1
1
1
2
0
0
0
1
1
1
0
1
1
1
0
0
0
1
0
0
2
1
1
0
1
0
1
0
0
1
0
0
1
2
1
1
1
1
0
0
0
0
1
2
2
0
2
1
2
1
1
0
0
1
1
0
0
1
1
0
1
0
3
0
1
1
1
1
2
0
0
0
0
0
2
0
0
2
4
0
1
0
1
1
0
1
0
1
1
0
1
2
0
1
2
0
1
0
1
2
0
0
1
2
2
1
1
0
0
1
0
2
2
1
0
0
0
0
2
0
1
0
1
0
0
0
1
2
1
0
1
1
2
0
0
0
2
1
2
0
1
1
0
1
0
1
2
2
0
2
1
0
1
2
1
0
0
1
0
0
2
1
3
1
0
0
2
0
1
0
0
2
0
0
0
0
1
1
2
0
1
3
1
1
1
1
1
0
2
0
1
0
0
2
2
0
2
0
1
0
1
0
1
1
1
0
0
1
0
2
0
2
0
1
1
0
0
2
1
1
1
1
1
2
0
2
1
1
1
2
1
1
1
2
1
1
2
1
2
2
0
1
1
0
2
1
0
3
0
1
0
1
0
2
2
2
0
2
2
0
1
1
3
0
0
0
0
0
0
2
1
0
0
1
2
3
0
0
1
2
1
1
0
2
1
1
2
0
0
0
0
2
0
1
2
0
2
1
0
0
1
2
0
0
0
0
1
0
1
2
0
1
0
0
0
1
0
1
2
0
0
1
0
1
2
1
1
1
1
2
1
0
1
0
1
1
0
0
2
0
3
1
1
0
0
0
0
0
0
2
1
2
2
1
0
1
2
0
1
0
0
0
1
1
1
0
0
1
0
2
0
2
2
2
1
0
1
2
0
2
0
2
0
2
2
0
0
0
0
1
0
0
1
2
1
1
1
2
2
0
1
0
1
1
1
0
1
2
1
1
1
1
0
1
2
0
2
2
0
1
0
1
0
1
0
0
1
0
1
1
2
0
2
1
0
0
0
0
0
0
0
1
1
2
0
0
0
0
1
1
1
1
1
1
2
0
1
1
0
2
0
0
0
2
0
2
1
0
1
1
2
0
0
0
2
2
0
0
2
0
1
0
1
0
0
0
0
0
1
1
0
0
0
2
1
2
1
2
2
1
0
0
0
1
2
0
1
1
1
0
0
0
0
1
1
1
2
1
0
1
1
0
1
2
0
0
1
0
0
1
0
0
0
0
0
2
0
1
0
1
3
2
0
1
0
0
1
1
1
1
0
0
0
0
3
0
0
1
2
2
2
0
1
0
1
0
0
1
1
2
2
0
2
2
0
0
0
1
1
1
0
2
0
0
2
1
0
1
0
1
0
0
1
2
3
0
1
3
1
2
0
0
1
0
0
1
1
0
1
0
1
1
0
0
2
0
0
1
0
0
0
1
2
0
0
1
3
1
0
2
0
1
0
1
0
1
1
2
2
0
0
1
1
1
0
0
0
2
0
1
0
2
0
0
1
3
0
1
0
1
0
0
1
2
1
0
0
3
0
1
1
2
1
0
0
1
0
0
2
0
1
1
0
1
0
2
0
0
0
1
1
0
0
1
2
0
2
1
1
0
0
0
1
0
2
1
1
0
1
0
1
0
2
3
0
1
2
2
1
1
1
2
0
2
0
0
0
0
1
0
1
1
2
1
1
0
1
0
0
0
1
0
3
2
2
0
2
3
0
1
2
3
0
0
0
1
0
1
2
0
0
0
1
1
1
0
2
1
1
1
0
2
0
0
1
0
0
1
2
0
0
1
0
0
0
1
0
0
1
2
0
1
2
0
0
0
0
1
1
1
2
1
0
0
1
1
0
1
2
2
0
1
2
1
0
0
2
2
0
2
2
1
1
2
2
1
2
0
0
0
0
1
2
1
2
0
0
1
1
1
2
0
1
0
1
1
0
1
2
1
1
0
1
0
2
1
1
2
0
1
2
0
0
1
2
0
1
0
2
0
0
0
0
0
1
2
1
0
0
0
0
2
1
1
0
0
0
1
1
1
0
2
0
0
1
0
1
2
0
2
1
0
1
1
0
0
0
1
0
0
0
1
0
0
0
1
1
0
2
0
0
0
1
1
1
0
2
0
2
0
2
1
1
0
0
0
2
0
1
0
1
0
0
2
2
1
0
0
1
0
1
0
1
1
1
1
1
0
0
0
1
2
2
2
2
1
2
0
0
2
3
2
2
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
2
0
0
2
0
1
0
0
0
1
0
2
1
2
0
0
0
0
0
0
0
1
0
2
3
2
0
1
0
1
2
1
1
0
1
0
2
0
1
0
0
1
1
0
2
0
2
0
0
1
1
2
0
1
0
2
2
1
0
0
1
1
1
0
0
2
1
0
0
0
0
2
1
1
0
0
1
2
0
0
0
3
1
1
1
1
1
0
0
1
1
1
1
0
2
0
1
0
0
1
2
1
1
0
0
0
0
0
0
0
1
1
0
1
0
0
2
0
2
1
1
0
1
0
0
2
1
2
0
2
1
1
1
0
0
2
6
1
0
1
2
2
2
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
1
2
0
2
1
2
0
2
0
2
2
1
1
2
1
1
0
0
0
1
1
2
1
2
1
1
0
0
1
0
0
0
1
1
3
2
1
1
1
1
0
1
2
0
0
0
0
1
0
1
2
2
0
0
0
0
1
2
0
2
1
2
0
1
1
0
0
0
0
1
0
1
2
0
2
1
0
0
0
0
2
1
1
1
2
2
0
2
0
1
2
2
1
0
1
1
0
0
0
0
1
0
2
2
0
0
0
0
1
1
0
2
2
1
0
1
1
0
2
2
0
2
0
2
0
2
1
0
1
0
0
0
0
3
0
0
0
2
0
0
1
0
0
0
0
0
2
0
1
0
0
1
0
1
0
0
2
1
1
0
0
0
1
1
0
0
1
0
2
2
0
2
0
1
1
0
0
1
2
2
1
0
1
0
0
0
0
0
2
0
0
0
1
2
1
0
0
0
0
0
1
2
0
0
0
1
0
0
2
2
1
0
0
1
0
2
2
1
1
1
2
0
0
1
1
1
0
2
1
0
0
1
2
0
0
1
2
1
0
0
0
2
1
0
0
2
0
1
2
2
0
1
1
0
2
0
1
1
1
1
0
1
1
1
0
2
2
1
3
0
0
0
1
2
1
1
0
0
0
2
0
2
0
1
0
0
2
1
1
2
0
2
1
1
2
1
1
1
0
2
2
0
0
0
1
0
1
0
1
0
1
0
0
2
0
2
0
0
0
0
1
0
0
1
2
0
0
2
3
1
1
1
0
1
0
0
1
0
1
0
0
0
2
0
2
2
2
1
1
2
0
1
0
0
0
0
0
2
1
1
2
2
2
2
1
1
0
0
0
0
1
0
0
0
2
0
0
0
0
2
1
0
2
0
2
0
1
0
1
1
0
0
0
3
0
1
1
2
2
1
0
0
2
0
1
2
1
1
0
0
1
2
0
0
1
2
0
0
1
0
1
2
0
1
0
1
2
0
1
3
0
0
0
0
1
2
0
0
3
0
3
2
0
1
2
1
2
2
0
2
2
0
0
1
0
0
0
0
2
0
1
1
1
2
0
0
1
1
0
2
1
2
2
0
0
0
1
0
0
1
0
1
0
1
2
0
1
1
0
1
0
2
1
1
1
1
0
1
2
0
0
2
1
2
0
0
2
0
0
3
1
2
0
1
0
0
0
2
1
3
0
1
2
0
0
0
1
0
0
2
1
1
0
1
1
0
1
1
1
1
1
2
0
0
0
1
1
1
1
0
0
1
0
2
1
1
1
0
0
1
1
0
2
0
2
0
0
0
0
1
0
0
2
2
2
0
0
1
0
0
0
1
1
1
2
0
0
0
1
1
0
2
0
0
1
0
1
4
1
0
2
1
1
1
0
0
2
1
0
1
0
0
0
0
1
1
2
2
0
0
2
0
0
0
0
2
1
2
0
0
0
1
0
0
2
0
1
0
2
2
2
0
0
1
1
2
0
1
0
2
1
0
0
2
2
0
1
0
0
1
1
0
2
1
1
1
1
0
1
1
2
2
1
0
0
1
0
2
1
1
2
2
2
1
1
2
2
1
4
1
1
0
0
1
0
0
0
2
0
1
0
2
1
2
1
1
1
0
1
0
0
0
0
1
2
1
0
0
0
3
2
1
0
1
0
1
0
0
1
1
2
1
0
1
0
0
0
0
0
2
1
0
0
1
0
1
0
3
2
2
1
0
1
1
0
0
1
2
2
1
2
1
1
2
1
0
0
0
0
0
0
1
0
1
1
1
0
0
1
0
0
0
0
0
1
1
0
0
2
1
2
1
2
0
0
0
1
0
1
1
0
2
0
1
1
1
0
0
2
2
0
0
0
1
0
1
2
1
2
2
1
1
2
0
3
1
0
0
0
1
0
3
0
1
2
0
1
0
0
2
2
1
0
2
2
0
2
0
1
1
2
1
0
0
0
0
0
2
1
2
1
0
2
0
1
0
2
2
2
2
6
1
2
0
2
0
0
0
0
2
0
0
0
0
0
0
2
1
1
2
2
2
0
0
0
0
0
1
0
2
2
1
2
1
0
1
0
2
2
0
0
2
0
1
1
0
1
1
0
0
0
2
1
0
2
2
0
0
0
1
2
1
1
0
1
2
1
0
0
0
2
0
0
1
0
1
1
1
1
1
2
1
0
2
0
0
2
2
0
0
1
1
1
0
0
1
0
0
0
1
2
1
0
0
1
2
0
0
2
1
2
0
1
0
6
1
0
1
1
0
0
1
3
2
0
1
0
0
0
0
1
3
1
2
0
0
1
0
1
1
0
2
0
0
2
0
0
2
1
2
0
1
1
1
1
0
0
0
1
0
0
1
2
1
0
1
0
1
1
0
0
3
0
0
1
0
2
5
1
0
1
2
0
0
0
2
0
0
2
1
0
2
0
1
0
2
1
0
0
2
0
1
1
0
1
1
2
0
2
0
1
1
0
0
0
1
0
2
0
0
2
0
1
1
0
0
0
0
2
0
0
0
1
0
1
2
0
2
0
2
1
0
0
1
1
1
0
1
3
0
1
0
1
2
0
0
1
0
0
0
1
1
0
1
1
1
2
1
1
1
0
1
0
2
1
1
2
1
0
0
0
0
1
2
0
1
0
1
1
0
0
0
0
1
0
2
2
2
1
2
2
1
0
1
1
0
1
0
1
0
0
2
2
1
0
1
1
0
0
1
2
2
0
0
0
2
2
1
1
1
0
1
1
0
1
0
2
1
1
4
2
1
2
1
2
1
1
1
2
0
0
1
1
0
1
1
2
0
2
0
2
1
1
0
1
0
3
0
1
1
0
1
1
0
1
1
0
0
2
1
0
0
0
2
1
0
2
2
2
1
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
1
1
0
0
0
0
1
1
0
1
1
1
1
0
1
1
2
2
0
0
1
0
1
1
0
2
2
1
0
0
2
1
2
1
2
2
0
1
1
0
0
2
1
2
0
2
0
2
0
1
0
2
0
0
1
1
0
1
1
0
1
0
1
1
1
2
0
1
0
1
0
0
1
0
0
1
1
1
0
1
0
0
1
1
0
0
2
1
2
0
1
2
0
0
0
0
2
1
1
0
0
2
1
0
2
2
0
2
2
1
0
1
0
1
1
0
1
0
0
2
1
0
0
0
1
0
1
0
0
2
1
1
0
2
1
0
0
2
2
0
1
0
2
1
1
1
0
0
2
0
0
2
1
0
2
2
1
0
1
1
0
0
0
1
2
0
0
2
0
2
0
1
1
0
2
0
2
0
2
0
0
2
2
1
0
0
0
0
4
1
0
0
2
0
2
0
1
0
0
1
0
1
1
0
4
0
2
2
1
0
0
0
0
0
2
0
1
0
0
1
0
1
1
0
0
0
1
0
2
0
2
0
0
1
2
0
1
1
0
2
0
0
2
2
0
1
0
0
0
1
1
2
1
1
1
0
1
1
2
2
0
0
0
1
2
0
1
1
2
0
0
0
2
1
0
2
0
0
1
2
0
0
2
0
0
1
0
0
2
1
1
1
1
1
1
1
1
1
2
2
2
0
0
0
2
0
2
1
0
0
0
1
0
0
1
2
0
2
1
1
0
0
0
1
2
1
0
0
1
1
0
1
0
2
0
1
0
2
1
1
0
1
0
0
0
2
2
1
0
1
1
0
0
1
2
2
1
1
2
1
1
3
0
0
2
1
0
0
0
1
1
0
1
4
1
1
2
1
1
0
0
0
2
0
2
1
0
2
0
0
0
1
0
0
0
2
0
2
0
0
1
1
2
0
0
0
1
1
0
0
0
1
0
1
0
0
1
2
0
2
0
2
0
0
1
0
1
2
0
1
1
2
1
0
0
1
2
0
0
0
0
0
1
1
0
0
0
0
1
0
1
2
0
0
0
0
0
0
2
1
3
0
1
1
0
1
1
0
0
1
2
1
3
2
2
1
0
1
1
1
0
1
1
1
0
1
0
1
1
0
0
1
1
1
2
0
2
1
0
0
0
5
2
1
0
0
0
0
1
1
1
0
4
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
1
1
2
2
2
1
2
2
1
0
2
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
1
1
0
0
1
0
1
2
1
1
1
2
0
1
0
2
1
0
1
1
0
1
2
1
1
0
1
1
2
0
1
0
2
2
1
1
2
1
2
0
1
0
1
2
0
0
1
1
0
1
0
1
0
0
2
1
1
2
0
1
3
2
1
0
2
1
0
1
3
0
1
2
0
1
1
0
1
1
2
1
1
0
1
0
2
2
1
0
2
0
2
0
0
1
0
2
1
1
2
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
2
2
0
1
2
0
1
0
0
0
0
1
3
2
1
1
0
0
1
0
1
0
2
1
1
1
0
1
2
1
1
1
2
0
2
2
2
0
0
0
1
0
0
2
0
1
2
0
1
0
1
1
2
0
2
2
4
0
0
3
1
2
0
2
0
0
0
0
0
2
2
0
2
0
0
1
0
0
2
0
0
0
0
0
0
1
1
0
0
1
0
1
2
2
1
2
0
1
2
1
1
1
0
0
1
1
0
1
0
0
0
1
1
0
0
1
2
2
2
2
2
1
1
0
2
0
0
3
0
0
2
0
0
0
1
0
1
1
2
0
1
1
0
0
2
1
1
1
2
2
1
0
2
0
0
1
1
0
1
1
1
0
1
2
2
2
0
0
1
0
0
1
0
0
1
0
2
0
0
0
0
1
0
2
0
2
0
2
0
0
2
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
1
0
0
2
1
0
0
0
2
0
0
1
1
0
1
0
3
1
2
0
2
0
1
1
2
1
1
1
0
1
2
0
1
1
2
1
1
0
0
1
2
2
0
1
0
0
0
1
0
0
0
1
0
0
1
1
2
3
0
2
1
2
1
1
1
1
1
1
2
2
0
0
1
3
1
1
0
0
0
0
1
0
0
0
0
2
0
0
1
1
0
1
1
2
0
2
0
0
1
1
0
2
0
1
3
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
1
1
0
2
0
2
0
2
1
2
1
1
0
2
0
2
1
0
1
2
2
2
1
0
0
0
0
0
0
1
1
0
2
0
0
2
0
0
0
1
0
2
1
1
0
2
1
0
2
0
0
0
0
1
1
0
0
1
0
0
2
0
0
1
0
0
1
0
2
1
1
0
0
0
0
0
1
0
0
0
5
1
1
1
1
1
0
1
0
2
0
1
0
0
1
0
1
0
6
2
1
1
2
0
1
1
0
0
0
0
0
1
0
1
0
1
1
1
0
0
1
1
0
0
0
0
1
0
1
1
0
0
2
0
1
0
0
1
1
1
1
0
2
1
0
1
0
1
1
0
1
0
0
0
1
1
2
1
1
0
2
2
0
1
2
1
0
0
2
1
0
0
2
1
0
2
0
2
0
0
2
2
0
1
2
1
0
1
2
1
0
2
1
1
1
0
0
1
0
0
1
2
2
1
1
0
0
1
0
2
1
0
0
0
0
1
1
1
3
0
1
0
0
1
2
1
2
1
0
1
0
1
0
0
0
1
1
1
2
1
0
1
1
2
1
2
1
2
0
0
0
0
1
1
1
0
1
2
0
2
0
0
1
1
0
0
1
1
0
2
0
0
0
0
1
2
1
0
0
2
0
0
1
1
1
1
0
1
0
0
1
0
0
2
0
0
1
1
1
0
0
0
0
1
0
1
1
2
2
0
1
1
2
2
0
0
0
0
2
1
0
1
1
0
0
0
0
2
2
2
1
1
1
1
0
0
0
0
1
1
0
2
0
0
0
1
0
0
1
1
3
0
1
1
1
0
2
1
2
1
0
2
2
0
1
1
0
1
2
1
0
1
1
1
2
0
0
2
2
2
0
0
0
1
1
2
2
1
0
1
1
0
0
1
0
2
2
1
1
2
0
2
1
0
1
1
1
0
0
0
1
0
1
0
1
0
1
0
0
2
0
2
0
1
1
2
2
2
0
2
0
2
2
2
1
1
1
2
2
2
0
2
1
2
1
0
2
0
1
0
0
0
0
1
3
0
1
0
1
1
1
0
2
2
2
1
0
1
1
1
0
1
0
1
2
1
1
1
0
0
0
2
0
0
0
0
1
1
0
0
2
0
1
0
1
1
2
0
0
1
2
2
2
1
2
1
1
0
2
1
1
1
2
0
1
1
1
1
3
0
1
0
0
1
0
0
1
2
0
1
2
0
0
0
0
1
1
0
1
0
2
0
0
1
1
1
0
1
0
0
1
1
4
1
2
1
0
0
2
0
2
1
0
0
0
1
2
1
1
0
1
0
1
0
1
1
0
1
0
0
2
1
3
0
2
1
0
1
1
1
0
2
1
0
2
0
0
1
0
1
0
0
1
0
1
0
0
1
1
2
0
0
0
0
2
1
1
0
2
2
1
1
2
1
0
2
2
0
1
0
0
0
0
1
0
1
2
1
1
0
1
0
1
0
1
0
0
0
1
1
0
2
0
2
0
1
1
0
3
3
0
1
1
0
0
0
2
2
2
1
0
1
0
1
0
1
0
0
0
3
0
1
2
2
0
0
1
0
0
0
0
0
2
1
1
2
1
0
1
1
1
0
0
1
2
2
1
0
0
0
0
1
0
0
0
1
2
2
0
1
0
2
1
5
0
1
1
0
1
0
0
1
1
1
1
0
3
2
0
0
1
1
1
0
0
1
1
0
0
0
0
1
0
2
0
0
2
0
2
1
1
0
2
2
0
2
2
2
0
2
1
0
1
0
0
2
1
1
2
1
1
1
1
1
0
1
0
3
2
2
1
2
0
0
1
1
1
1
2
0
1
1
2
2
2
1
0
0
1
1
1
0
0
1
1
0
0
1
2
1
1
0
0
1
0
1
1
0
1
2
1
1
0
2
0
2
0
2
2
1
0
1
1
2
0
2
0
0
0
3
1
0
0
1
1
4
1
0
0
2
6
1
0
0
1
1
2
0
0
0
0
1
1
1
1
0
0
0
0
2
1
0
0
2
0
2
2
2
1
1
2
0
2
1
0
2
0
1
0
0
0
0
0
2
1
0
1
1
2
2
0
2
1
2
0
0
2
1
0
0
0
1
2
2
0
1
1
0
0
3
1
0
0
2
2
0
0
2
3
1
1
0
0
0
0
1
2
1
2
0
2
2
2
0
0
0
0
1
1
2
0
2
0
1
0
0
0
1
1
0
0
0
0
0
0
0
2
1
2
1
1
0
0
0
1
2
1
2
0
1
2
2
1
1
1
1
2
2
0
1
0
2
1
0
2
1
1
1
1
0
1
2
0
1
0
2
1
3
1
0
0
0
0
0
0
1
2
0
1
1
1
1
1
1
0
0
1
0
0
0
0
0
1
2
0
2
1
0
0
0
2
1
0
0
0
0
1
1
2
2
1
2
0
1
2
1
0
2
1
1
1
1
0
1
0
0
1
0
0
1
0
0
1
0
1
1
0
0
1
2
0
0
1
0
0
1
0
0
2
0
1
0
1
2
1
0
1
3
0
0
0
1
0
2
0
0
1
0
1
2
0
0
0
1
0
1
2
0
2
1
1
2
1
1
1
1
0
1
0
0
0
1
0
3
1
1
1
0
1
1
0
0
0
1
2
0
2
1
0
1
2
0
0
2
1
1
0
1
1
2
0
0
12
0
1
0
2
0
2
2
0
0
4
1
2
0
1
1
1
1
0
2
0
1
1
0
3
1
0
1
1
0
1
2
1
1
1
1
6
2
1
0
1
1
0
0
1
2
0
3
2
1
0
2
0
0
0
1
0
0
1
1
0
0
1
2
1
1
1
2
0
0
0
1
1
0
1
0
0
3
0
1
1
1
0
1
0
1
0
1
1
1
0
1
1
0
0
1
1
0
0
0
2
1
1
0
2
0
1
0
0
0
2
1
2
0
1
1
0
1
1
1
2
0
1
0
2
2
2
2
2
0
1
1
2
2
0
0
0
0
1
0
1
1
1
0
0
1
0
0
0
1
0
0
0
0
0
2
0
1
0
2
0
0
1
0
1
0
0
1
0
0
1
1
1
1
0
2
1
2
1
0
0
2
0
1
1
1
1
1
0
0
0
1
2
1
1
1
1
1
2
2
1
1
2
1
2
1
2
0
0
0
1
2
1
0
2
0
0
0
0
2
1
0
1
1
0
0
0
0
1
2
2
1
1
0
0
0
0
0
1
0
1
2
1
0
2
0
2
0
1
0
2
1
1
1
1
2
0
0
2
2
1
2
0
0
1
1
2
0
2
0
1
1
0
1
0
0
1
1
0
1
0
1
0
0
0
0
1
2
1
0
1
1
0
0
1
2
0
1
0
1
0
1
2
2
2
2
1
0
2
0
0
2
0
2
1
0
1
0
0
0
1
1
2
0
2
2
1
0
3
3
1
2
0
2
0
1
3
1
1
2
0
0
0
1
3
0
2
1
0
0
1
0
2
2
2
0
0
2
0
2
0
2
0
1
0
2
1
0
1
1
1
1
0
2
2
0
2
1
1
0
2
1
1
1
0
2
2
3
2
0
1
1
0
1
0
0
2
1
0
2
0
2
1
1
0
1
3
1
1
0
1
1
0
1
0
2
1
1
2
1
0
2
1
2
1
0
1
2
2
2
0
1
0
0
2
1
0
0
1
0
1
0
0
0
0
0
0
1
2
0
2
0
0
0
2
0
1
0
0
2
1
0
1
2
1
1
0
0
0
0
0
0
1
1
2
0
1
0
0
1
2
0
1
1
1
1
2
2
0
0
0
2
1
1
2
3
1
0
0
0
0
0
1
1
1
0
0
2
1
2
1
0
0
1
0
1
1
0
0
0
2
1
0
0
0
2
2
0
0
0
0
0
1
1
1
0
0
1
1
0
0
1
1
0
2
2
1
1
1
2
0
0
1
1
0
1
0
0
0
1
2
0
1
2
0
0
1
0
1
1
1
1
0
1
2
0
1
1
0
2
1
1
0
1
2
1
0
0
2
0
0
0
2
0
0
1
2
1
2
0
0
0
1
1
0
0
2
1
0
1
1
2
0
1
1
2
0
0
1
0
0
0
2
0
0
1
1
0
1
1
1
2
0
2
1
2
0
1
2
3
1
0
2
2
0
2
3
0
1
0
1
0
0
1
0
1
0
2
1
2
1
2
0
2
1
1
0
0
0
0
1
0
0
0
1
1
2
0
0
1
1
0
0
2
0
2
0
2
2
0
1
0
0
2
1
0
0
1
0
1
1
0
0
1
2
2
0
1
0
2
0
0
0
0
1
1
0
2
1
1
1
0
0
0
1
1
0
0
1
1
0
0
0
0
0
1
1
2
0
1
0
0
0
1
1
1
2
0
1
2
2
2
0
1
0
0
0
1
1
0
3
0
0
0
1
1
0
0
1
0
1
1
3
1
0
2
0
0
4
1
0
0
2
0
0
1
1
0
0
0
0
1
0
0
1
0
3
1
1
1
1
0
1
1
2
0
2
0
1
0
1
0
2
0
1
0
0
1
0
1
1
0
0
0
1
0
0
1
0
1
1
0
0
1
0
1
1
1
2
0
1
2
1
0
0
0
2
1
1
0
2
1
0
2
1
0
1
0
1
1
0
1
2
3
2
1
0
2
1
0
1
3
2
1
0
2
1
1
2
2
2
0
1
1
0
0
0
1
1
0
1
1
0
0
0
1
0
2
0
0
2
2
0
2
2
0
2
0
2
2
1
2
1
0
0
0
0
0
1
0
1
1
1
1
0
2
0
0
1
0
0
1
1
0
2
1
0
0
2
0
1
1
2
0
0
1
0
0
0
2
2
1
2
0
1
0
2
0
2
0
0
0
2
0
2
0
0
1
0
0
2
1
1
0
1
0
1
2
1
0
1
2
2
0
1
0
0
0
2
0
1
1
0
0
1
1
1
0
1
1
0
1
1
0
0
2
0
0
1
0
1
0
0
1
0
1
0
0
1
1
1
0
3
0
1
1
1
0
1
0
1
2
1
1
0
1
1
1
2
0
2
0
2
1
1
1
1
1
2
0
1
0
0
0
0
2
1
1
2
0
0
1
2
2
0
0
3
1
0
2
0
0
1
0
3
0
0
2
0
1
0
1
1
0
0
0
3
2
1
1
2
1
0
0
1
1
1
0
0
1
0
2
0
2
2
0
1
0
0
0
0
1
2
1
1
2
0
1
0
2
4
2
1
1
1
0
0
1
0
0
1
1
1
0
0
1
1
1
0
0
0
1
1
0
1
4
2
1
1
0
3
1
0
2
1
1
1
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
1
1
1
0
2
1
0
1
1
0
1
0
1
4
1
2
1
2
1
0
0
1
0
0
1
0
0
0
0
0
1
1
2
1
0
1
1
0
0
1
0
1
1
1
2
1
1
1
2
0
0
1
1
0
1
2
0
0
1
0
0
2
0
2
0
1
1
0
1
0
1
0
1
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
2
0
1
0
1
2
0
0
1
1
2
0
0
1
1
0
0
2
0
1
0
0
2
1
0
0
0
2
2
3
2
0
0
2
1
1
1
1
2
1
0
0
0
0
0
1
0
1
6
0
0
2
0
0
0
1
0
2
2
3
1
1
1
1
2
1
2
0
1
0
0
0
0
0
1
0
1
1
0
0
1
1
1
2
0
0
1
2
2
1
0
2
2
3
0
1
2
0
1
0
0
0
0
1
0
1
2
0
2
1
0
0
0
1
2
2
0
2
0
1
1
1
0
2
2
0
1
1
1
0
0
0
1
0
0
0
3
0
0
1
0
1
0
0
2
0
2
0
0
0
2
1
1
0
1
1
2
0
2
0
1
2
0
0
2
1
0
1
0
2
0
1
0
0
1
2
2
1
0
0
3
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
2
0
1
1
1
1
0
0
0
2
1
2
2
0
0
3
2
4
1
2
1
0
2
0
0
0
1
0
0
0
1
1
0
2
1
0
1
0
0
1
0
1
2
0
0
2
1
1
2
0
0
2
0
0
0
2
1
0
1
0
0
1
2
1
1
1
2
1
2
1
2
2
1
1
0
0
0
2
0
1
0
0
0
0
0
1
2
0
2
0
1
0
2
0
0
1
2
2
1
1
1
0
0
2
0
1
1
0
0
0
1
1
1
0
2
1
0
0
0
1
0
0
1
2
1
0
0
1
0
1
0
0
0
1
2
2
3
1
0
1
1
1
1
0
3
2
0
0
2
0
2
2
1
0
0
1
0
1
0
2
1
0
2
0
1
2
0
0
0
1
3
0
1
0
1
0
1
1
0
2
2
1
1
2
1
1
0
0
0
0
1
1
0
0
1
1
1
2
1
2
0
1
2
0
0
1
2
2
0
1
0
0
1
2
1
0
2
2
0
1
1
0
1
0
1
2
1
1
0
0
0
0
0
0
1
0
2
1
0
0
1
0
2
2
0
1
2
2
0
1
0
0
0
1
0
1
2
0
0
1
1
0
1
1
2
1
3
0
0
1
2
2
1
1
0
1
1
2
2
0
1
1
1
1
1
2
1
0
1
0
1
0
2
2
0
3
1
1
2
2
0
2
2
0
1
0
2
0
2
1
1
1
0
1
2
1
5
0
1
2
1
2
0
0
1
0
2
0
0
1
1
1
0
1
1
1
0
0
1
1
2
0
0
1
0
1
1
0
0
2
2
1
1
2
1
0
0
0
1
1
1
1
0
0
1
0
0
0
2
1
0
0
1
1
1
0
0
1
1
2
1
1
1
0
1
1
1
2
2
0
2
1
0
0
1
1
0
0
0
2
0
0
1
1
0
2
2
1
1
0
1
1
2
1
2
2
0
0
1
2
2
0
3
0
0
0
0
1
1
0
1
2
1
2
1
0
0
2
2
0
0
0
2
0
0
0
0
0
0
1
1
1
0
1
0
3
0
0
0
2
0
1
0
0
1
1
1
1
0
1
1
0
0
1
0
0
1
0
0
0
1
0
2
2
2
0
1
1
0
0
0
1
3
1
1
0
1
0
0
2
1
2
0
3
0
0
1
0
0
0
0
1
2
0
1
1
0
1
1
0
1
0
2
1
0
0
0
1
0
1
2
2
1
1
2
2
0
0
2
0
2
0
2
0
0
0
0
1
0
3
0
2
1
0
0
1
2
1
1
0
0
1
2
0
1
2
1
1
0
0
0
0
1
2
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
2
0
0
1
0
1
1
0
0
1
1
0
2
1
0
1
0
0
1
1
2
1
0
1
0
1
0
2
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
2
1
2
2
1
0
2
1
1
2
2
2
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
1
1
0
0
2
0
2
1
0
0
1
0
1
0
0
2
1
2
0
0
1
0
2
1
0
0
2
2
0
1
2
2
0
0
1
2
0
0
0
1
2
1
0
0
0
0
1
1
1
0
2
0
0
1
0
0
2
2
2
2
0
2
1
1
0
1
1
1
0
1
2
0
1
0
0
0
1
2
3
1
0
0
1
0
1
0
0
0
0
0
1
1
2
0
0
0
2
0
0
0
1
0
1
0
0
1
1
1
1
0
0
1
0
0
1
2
2
1
0
0
2
2
0
0
0
0
0
1
0
2
0
1
0
1
0
1
0
1
0
2
0
0
0
1
0
0
0
0
0
1
0
2
0
1
1
0
0
1
2
1
0
0
1
1
0
0
1
2
0
1
1
1
0
1
0
0
0
0
0
1
1
2
0
0
0
0
0
1
2
0
0
0
1
1
1
0
1
0
1
2
0
2
0
2
1
1
2
1
2
0
0
2
1
1
1
0
2
2
1
0
2
4
0
0
1
1
2
0
1
0
0
1
1
0
2
0
1
2
0
1
2
1
0
2
1
1
1
1
1
1
0
0
1
0
0
1
0
1
0
0
1
1
5
2
0
0
0
0
1
1
0
1
0
0
1
2
0
1
1
1
2
0
0
0
0
0
2
1
1
1
1
1
0
0
1
2
0
2
0
2
1
0
1
1
2
1
1
2
0
0
4
0
1
0
2
0
0
0
0
1
2
0
0
2
2
0
0
1
0
2
2
1
2
0
0
1
0
2
0
0
0
0
1
1
0
2
2
0
2
0
0
1
1
1
2
2
1
2
1
0
0
1
2
1
1
2
0
1
2
1
2
1
1
2
0
0
0
0
0
0
1
1
1
2
1
0
2
1
2
2
2
1
2
0
0
1
1
2
0
2
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
2
0
0
2
0
0
0
4
0
2
0
1
1
0
1
2
1
0
2
1
1
0
0
1
0
2
1
1
2
1
1
1
2
0
1
2
0
0
2
0
0
0
1
1
1
0
2
1
1
1
0
2
0
0
1
0
2
1
0
1
0
1
2
1
1
2
1
0
1
1
1
0
2
2
2
1
0
0
0
1
1
1
0
1
0
2
0
0
0
0
1
2
0
0
0
0
0
0
1
1
0
2
0
0
0
0
1
0
0
0
0
0
2
1
0
1
0
3
0
1
0
1
1
0
0
0
2
2
1
0
2
2
0
0
0
1
0
1
1
1
1
1
1
1
0
0
2
0
1
2
1
1
2
1
3
0
0
2
0
1
1
0
2
2
0
0
0
0
2
1
1
1
1
2
2
1
0
1
0
1
0
2
1
0
1
0
0
3
0
0
0
1
0
0
0
1
0
2
1
0
2
0
2
1
0
1
1
0
0
0
1
0
0
0
0
2
0
1
1
1
1
3
1
0
1
0
1
0
2
2
2
1
1
2
0
0
1
0
3
0
0
2
0
1
0
0
1
0
0
1
1
2
1
2
1
1
1
2
0
0
1
1
2
0
0
0
0
1
2
0
0
0
1
0
0
0
0
1
2
3
2
0
0
2
1
1
0
0
0
0
1
1
0
2
1
2
1
0
2
1
0
0
1
0
0
1
0
2
0
0
0
0
1
2
0
0
0
1
2
0
0
1
0
1
0
0
1
0
1
1
0
0
2
2
1
2
0
2
1
2
1
0
0
1
1
1
0
1
3
0
1
0
1
0
1
2
4
0
2
0
1
1
0
1
0
2
0
1
0
0
2
0
0
0
2
0
2
0
1
0
0
2
0
0
1
0
0
0
0
2
1
1
1
2
2
0
0
0
0
0
2
0
1
2
0
1
1
0
0
1
0
0
2
0
1
2
1
1
0
1
2
0
0
1
0
0
0
2
1
2
0
0
0
0
0
0
2
0
0
1
2
1
2
0
1
1
0
2
0
0
3
1
0
0
1
0
1
1
2
0
2
1
0
2
0
1
2
0
0
0
0
0
0
0
2
0
1
1
1
2
0
3
0
0
0
1
1
0
1
0
1
0
1
4
1
2
0
0
1
1
2
0
0
2
1
0
1
1
0
2
2
2
2
0
1
4
1
1
0
0
1
0
2
1
3
2
2
2
0
2
0
1
0
0
0
1
3
0
0
2
0
0
1
1
1
0
0
0
2
0
3
0
0
0
1
1
0
2
0
1
1
2
0
2
2
0
1
1
2
0
1
1
1
1
2
1
0
2
0
0
1
1
1
1
0
0
1
0
1
2
3
2
0
4
1
0
1
0
1
2
4
2
0
1
1
0
1
0
1
0
1
0
0
0
0
0
1
2
2
1
3
2
0
0
0
1
1
0
0
1
0
1
2
0
2
0
0
1
0
1
2
2
2
0
0
1
1
1
2
2
1
0
1
1
0
0
2
2
0
0
1
2
1
0
2
3
1
0
3
1
0
0
2
1
0
3
0
1
1
0
0
1
0
0
2
1
0
1
1
0
0
1
1
0
0
0
1
0
1
0
2
1
0
0
0
2
0
0
2
4
2
0
2
1
0
0
2
1
1
1
2
0
1
1
0
1
0
1
1
2
0
0
1
3
1
2
0
0
2
0
0
2
2
0
3
0
0
0
2
1
0
1
0
0
2
0
3
1
2
2
0
0
1
1
1
0
2
0
0
0
3
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
2
0
1
2
2
0
1
2
1
0
0
1
0
0
2
1
0
0
1
1
2
0
1
0
1
2
1
0
0
1
1
1
1
0
0
1
0
2
2
1
0
2
1
1
1
0
1
1
1
1
0
0
1
0
0
0
0
1
0
0
1
0
1
2
0
0
0
2
0
1
2
1
2
3
1
0
1
1
2
0
2
1
2
1
1
0
0
2
2
1
1
1
1
0
1
2
1
2
0
1
1
2
0
0
1
1
2
0
0
0
0
1
4
0
1
0
0
1
1
2
0
1
1
1
0
0
0
2
0
1
1
1
1
0
1
3
1
1
0
2
1
0
2
0
0
1
1
2
1
0
2
0
0
0
1
1
0
0
1
2
1
1
1
2
2
0
2
2
2
1
2
2
2
3
0
0
0
1
0
0
1
1
1
2
0
2
0
0
0
2
1
0
0
1
1
1
0
1
0
0
1
0
1
0
0
1
0
0
2
1
1
1
0
0
1
1
1
1
1
0
1
0
0
0
0
2
4
1
0
0
2
0
2
1
1
1
1
0
2
2
1
0
1
1
2
0
2
2
2
1
0
1
0
2
1
0
0
1
0
0
2
2
3
1
1
0
0
2
2
0
1
2
1
1
2
2
1
1
0
0
1
1
1
1
0
2
1
0
0
0
0
2
1
2
2
0
0
2
2
0
2
1
1
1
0
0
0
0
0
1
1
2
0
1
2
0
1
0
2
0
0
1
0
0
0
0
1
0
0
0
0
1
1
2
0
0
0
1
0
1
1
0
0
0
2
1
0
1
0
2
2
0
0
1
1
0
0
0
0
1
0
1
1
1
1
0
0
0
0
0
0
0
1
1
0
0
1
1
1
2
2
2
2
1
2
0
1
1
1
0
1
0
1
1
2
1
2
0
0
0
1
1
1
0
1
0
0
2
1
0
0
0
2
2
0
1
1
1
1
1
1
1
0
2
1
0
0
2
1
0
1
0
0
0
1
0
0
1
0
1
1
2
2
1
0
0
1
0
2
2
0
2
2
0
0
2
0
0
0
2
0
2
0
1
1
2
2
0
2
1
1
0
1
2
1
1
1
2
0
0
1
0
0
3
2
0
2
1
2
0
1
0
0
0
1
0
0
0
0
1
2
1
0
0
2
2
1
0
2
1
0
0
0
1
0
0
2
1
1
2
0
0
1
2
1
0
1
2
0
2
1
0
0
1
0
0
1
0
2
2
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
7
0
0
0
2
3
0
2
0
1
1
0
2
2
1
1
0
1
0
0
1
1
1
0
2
1
1
0
0
1
1
0
2
1
2
1
1
1
0
1
1
0
3
1
1
1
1
0
1
0
1
1
1
1
0
1
0
2
1
0
1
0
0
0
0
1
1
1
1
1
2
0
2
2
1
2
0
2
1
1
0
0
2
0
0
1
2
1
0
0
1
1
0
0
1
0
2
0
0
1
0
1
0
0
1
0
1
0
1
0
0
0
0
0
1
0
1
2
0
0
0
2
1
1
2
0
2
1
0
1
1
0
0
0
3
0
2
0
0
0
0
0
1
0
0
1
1
1
1
0
0
2
0
1
1
1
2
0
0
1
0
1
1
0
0
0
0
0
1
0
1
1
2
0
0
0
1
1
0
2
0
0
2
2
0
1
1
1
1
2
2
0
0
0
1
0
1
0
0
0
1
1
1
1
2
1
1
1
1
0
2
0
0
1
2
0
1
0
0
0
1
0
0
0
2
1
0
0
0
1
0
2
1
1
1
2
0
0
0
2
2
2
0
1
1
1
0
2
0
0
0
0
2
1
1
0
0
0
2
1
1
0
0
1
1
2
0
3
1
0
1
1
1
0
0
2
0
0
2
2
0
0
0
0
0
2
1
2
1
1
0
0
0
2
2
0
2
0
1
0
2
0
1
0
1
1
0
2
0
0
0
1
1
0
0
1
1
0
2
2
1
0
0
1
0
0
0
1
0
2
2
2
3
1
1
2
0
2
1
1
0
2
1
0
0
0
0
2
1
2
0
1
1
1
0
0
3
0
0
0
2
0
1
0
1
1
2
1
0
0
1
1
1
1
2
0
0
1
1
2
2
2
0
0
0
1
0
0
1
2
2
2
0
1
1
0
1
0
1
1
1
0
1
0
1
0
0
2
0
0
1
1
0
2
1
0
0
1
0
0
2
0
1
0
2
1
0
0
1
0
0
0
1
0
1
0
2
2
1
1
1
0
1
0
0
1
1
2
2
2
0
2
1
0
0
2
3
1
0
1
1
0
2
2
0
2
2
1
1
2
0
0
0
2
1
0
1
0
2
1
2
1
0
1
0
0
0
0
1
1
0
2
0
0
0
1
0
2
2
0
0
2
0
0
1
2
0
1
1
1
1
0
1
0
0
2
0
0
0
2
0
1
2
1
0
1
0
0
0
1
0
0
0
1
1
0
1
2
0
0
1
0
0
1
1
2
0
2
0
1
2
0
1
1
0
0
1
1
1
2
1
0
2
2
0
0
1
2
0
1
0
1
1
1
2
0
1
2
1
1
1
0
1
0
0
1
0
1
1
0
0
2
0
1
2
1
0
1
1
0
1
2
0
1
1
1
1
0
0
0
1
1
0
3
0
0
1
2
1
1
0
0
2
1
1
1
1
1
1
0
1
1
0
0
2
0
1
1
0
0
0
0
1
1
1
1
1
0
2
0
0
1
0
1
1
0
2
1
1
2
3
0
0
2
2
0
1
0
0
1
0
1
1
0
0
2
3
1
1
0
1
3
0
1
0
1
0
0
0
0
0
1
2
1
0
2
1
2
2
0
2
2
2
0
1
1
1
1
0
0
1
1
0
1
0
0
0
2
1
0
1
1
0
0
1
1
1
0
0
1
0
3
1
2
0
2
1
2
0
0
0
0
1
3
2
0
0
0
1
0
0
1
3
0
1
0
0
0
0
2
0
0
0
2
1
0
1
1
0
0
0
1
2
2
0
2
0
1
2
1
0
2
0
1
0
1
1
0
3
0
0
0
0
0
1
0
0
0
1
1
0
1
1
1
0
1
2
0
1
2
0
1
0
0
0
1
2
2
1
1
2
1
0
0
0
1
0
0
3
0
0
0
2
1
0
2
0
2
1
1
1
1
2
1
0
1
2
1
1
0
1
0
1
1
0
0
0
2
0
1
1
1
2
0
0
0
0
1
2
0
2
0
0
2
1
0
0
1
0
3
1
0
2
0
0
1
0
1
2
0
0
1
0
0
0
2
1
1
1
2
7
0
1
2
0
0
0
2
0
0
0
2
2
1
1
0
1
0
3
0
2
1
1
1
1
2
2
1
1
2
0
0
0
1
1
0
2
1
1
0
4
1
0
1
0
0
2
0
1
0
1
2
0
0
2
1
1
1
0
1
0
1
2
0
0
0
0
1
0
2
1
0
0
3
2
0
1
2
2
2
1
0
2
1
0
0
0
1
1
0
0
1
0
1
1
0
1
2
0
1
1
2
0
1
2
0
1
1
0
0
0
0
0
2
2
0
1
0
1
2
1
0
1
1
2
0
1
1
0
0
1
3
1
0
1
0
1
2
0
0
0
1
2
1
0
1
1
1
0
2
3
0
0
2
0
0
1
2
2
1
0
0
0
0
0
2
1
0
2
0
0
1
2
1
0
2
1
2
2
1
1
0
0
0
1
1
0
1
0
1
0
1
1
1
0
1
1
0
1
2
0
0
1
0
0
2
0
1
0
0
1
1
2
0
0
1
2
1
0
0
2
0
1
1
2
2
0
0
0
1
0
0
0
2
2
2
2
0
0
0
0
0
1
0
0
2
1
0
1
0
0
2
2
2
0
1
0
2
1
0
2
0
1
2
1
1
1
0
1
0
2
1
2
0
2
0
2
0
1
0
0
2
1
0
1
1
0
0
0
0
1
0
1
1
1
1
1
0
2
0
2
0
2
1
3
2
0
0
0
1
0
0
0
0
1
0
1
1
2
2
0
1
2
0
0
0
0
1
1
1
1
9
1
0
1
2
0
0
1
2
1
2
2
2
2
2
0
0
0
2
2
1
0
2
1
0
0
0
0
1
1
0
0
3
0
1
0
1
0
0
3
1
0
0
0
0
2
1
1
1
0
1
0
2
0
0
1
0
2
1
1
2
2
2
1
1
1
0
1
2
0
0
0
0
1
1
1
0
1
1
0
1
0
1
2
0
2
1
0
3
2
0
0
0
0
0
1
0
1
2
1
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
2
2
1
2
3
1
1
0
0
1
2
0
1
0
0
0
2
1
2
5
0
2
3
2
0
0
0
1
1
0
0
2
1
2
0
0
1
1
2
0
1
0
1
0
0
1
0
0
0
0
2
0
1
2
0
0
2
1
0
0
0
0
1
2
2
0
1
0
1
1
1
0
0
1
1
0
1
0
1
1
0
2
1
1
1
1
0
0
1
0
0
0
1
0
3
0
1
0
0
0
0
2
0
1
0
2
1
2
2
0
0
2
1
1
0
0
2
2
0
2
2
1
0
0
2
2
0
1
2
1
0
1
1
2
0
1
2
1
0
1
0
0
2
1
0
1
1
2
1
0
0
2
2
0
2
2
0
3
1
0
2
1
2
2
1
1
1
1
1
1
1
2
0
0
2
1
1
0
0
2
4
1
0
0
1
0
1
0
1
1
0
0
1
1
0
0
2
1
0
0
0
0
1
2
2
3
0
1
1
1
1
0
1
1
2
0
0
2
2
0
1
2
1
1
0
0
1
1
0
2
0
1
0
0
0
0
2
0
0
0
0
1
1
2
1
0
2
0
0
0
0
0
2
1
0
1
0
0
0
1
2
1
0
1
2
0
1
2
0
0
0
1
0
0
0
0
1
0
1
2
1
0
1
2
0
0
2
0
1
1
1
0
0
1
1
2
2
0
0
1
0
0
1
2
0
0
0
1
0
1
2
2
1
1
1
0
0
1
0
0
0
0
1
0
2
1
0
1
0
0
0
1
0
1
0
1
0
1
0
2
1
0
0
2
1
0
0
2
0
2
1
1
2
1
1
0
2
1
1
1
0
1
1
1
1
2
1
1
0
0
0
1
1
1
1
1
0
0
0
0
0
0
0
1
0
2
2
0
0
2
0
1
1
1
2
2
0
2
2
1
2
0
2
1
0
1
1
0
2
3
2
0
2
0
1
0
1
1
0
0
0
1
1
0
2
3
0
2
0
0
1
1
0
0
1
0
1
1
0
2
1
1
1
0
0
1
0
0
1
1
0
0
0
0
0
2
2
2
1
0
2
4
1
1
2
2
1
0
1
1
0
0
0
0
0
0
2
1
0
0
2
0
1
0
0
1
0
1
2
2
0
2
1
2
2
2
1
2
2
0
0
2
1
0
0
1
0
1
2
2
2
0
0
0
0
1
0
2
1
0
1
2
0
1
1
0
0
0
0
1
1
2
1
0
1
0
0
1
0
1
1
2
0
2
0
0
0
1
1
0
1
0
1
1
1
1
1
0
0
1
1
1
2
1
1
0
2
1
0
0
0
1
0
0
1
0
1
1
0
0
0
1
0
0
1
1
0
0
2
1
1
0
0
0
2
1
0
1
1
0
0
2
2
0
1
1
1
0
0
1
0
1
1
3
0
1
0
0
0
1
1
0
0
0
0
1
0
1
0
1
1
0
1
1
0
2
0
0
0
0
1
1
0
1
2
1
1
1
1
1
0
1
1
0
1
1
3
0
1
1
0
0
0
1
0
2
0
0
0
1
0
1
0
2
1
2
0
0
2
0
0
0
0
1
2
0
2
1
2
1
0
1
0
0
1
0
0
0
0
0
2
2
0
2
1
1
0
0
0
3
1
0
0
0
2
1
0
1
1
2
1
4
0
2
0
0
0
1
0
1
1
0
2
1
0
0
1
1
0
1
1
1
0
0
1
1
1
2
0
4
0
0
0
0
0
1
0
1
2
0
3
1
2
2
2
2
0
5
2
2
2
0
1
0
2
1
1
0
0
2
2
0
0
2
0
0
0
1
1
2
2
0
1
0
0
0
0
0
2
1
2
1
0
0
1
0
2
1
1
1
0
0
1
1
2
0
0
1
0
0
0
1
2
0
1
3
0
0
0
1
1
2
1
0
2
2
2
0
1
0
0
0
0
1
1
2
2
2
0
1
2
0
0
2
1
0
2
0
3
2
0
0
1
0
2
0
0
0
1
0
4
0
3
1
2
1
1
0
1
0
2
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
3
0
1
0
1
0
2
2
1
0
1
1
0
1
0
0
0
1
0
1
1
0
1
0
0
0
0
1
4
0
2
0
2
0
0
0
0
0
1
3
1
0
1
1
1
0
1
2
0
1
2
2
0
1
0
2
0
2
2
0
1
0
0
2
0
1
1
1
0
0
0
1
2
1
1
1
0
1
0
0
0
1
2
0
1
0
0
0
2
0
1
0
0
1
0
0
1
0
1
1
0
0
2
0
3
1
1
2
0
0
1
0
1
2
0
1
1
1
0
0
2
0
0
0
0
0
0
0
1
0
0
2
2
0
0
1
1
0
0
2
2
0
0
1
1
0
0
2
1
0
1
2
0
0
1
1
0
2
0
1
0
0
0
1
0
2
0
1
0
0
0
1
1
2
1
2
1
2
1
1
0
2
0
0
0
2
2
1
2
2
0
0
2
0
0
0
0
2
1
1
0
0
2
2
0
2
0
0
2
0
0
0
0
0
2
0
1
2
0
1
0
1
0
2
1
0
0
2
2
0
0
1
0
0
1
3
1
1
0
2
1
1
0
0
2
1
2
2
1
1
2
0
1
0
1
0
1
1
0
0
0
2
1
1
0
2
0
2
1
0
0
0
2
1
1
2
1
0
0
1
1
0
1
0
1
1
0
2
1
2
0
1
1
1
0
1
2
1
0
0
3
0
2
0
0
0
1
1
2
0
1
1
1
1
1
2
1
2
1
1
0
2
0
1
3
1
0
2
1
2
2
0
0
2
0
0
1
0
0
0
0
1
1
2
1
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
2
2
1
0
0
0
1
1
2
0
2
1
2
0
2
2
1
2
0
1
0
2
0
0
1
1
1
0
2
0
0
1
2
0
0
0
1
0
2
1
0
1
0
0
1
1
1
1
1
1
0
1
0
0
0
0
2
2
0
2
0
0
2
0
1
0
2
1
0
1
1
3
0
0
1
2
0
1
0
2
3
1
1
3
2
0
0
0
1
1
2
0
0
2
0
0
0
0
2
2
0
2
0
2
1
0
2
4
2
1
0
0
1
0
2
1
0
2
1
2
2
1
2
2
0
1
1
0
0
0
1
0
0
1
2
2
1
2
0
2
0
2
1
0
1
2
1
0
1
0
2
0
0
0
0
2
0
0
0
2
1
1
0
1
2
0
0
0
2
1
1
0
0
2
0
1
1
2
2
0
2
1
1
1
3
0
0
2
2
1
2
0
2
1
0
0
0
0
2
0
1
1
0
0
1
0
0
1
0
0
1
1
2
0
0
2
0
0
0
1
1
1
2
0
0
0
1
0
0
0
0
1
2
0
0
0
1
0
0
0
1
0
0
0
0
2
1
0
1
1
1
0
0
0
0
0
1
1
1
1
0
1
0
0
0
1
1
2
0
0
0
0
0
0
0
1
0
1
1
1
1
0
1
1
2
1
1
0
0
0
2
1
0
0
0
0
2
2
0
1
2
0
1
1
0
0
0
0
1
1
2
1
0
2
0
0
1
0
0
0
1
0
2
0
1
0
2
2
0
2
0
0
0
0
0
1
0
2
1
1
0
1
0
2
1
1
0
1
2
1
0
0
0
0
1
0
1
1
1
1
2
0
0
0
0
2
0
0
1
1
1
0
1
0
2
0
0
1
0
1
1
0
1
2
1
0
0
1
0
2
1
2
0
0
2
0
1
2
0
0
0
1
0
0
1
1
1
2
0
2
0
1
1
2
1
1
0
2
1
1
0
0
0
2
1
2
0
2
0
0
0
0
0
0
0
1
2
1
0
1
2
1
1
1
2
0
1
0
0
1
2
2
0
2
1
0
0
1
0
0
2
0
1
0
1
0
2
0
1
1
1
2
1
1
2
2
0
0
1
2
0
0
2
0
0
0
0
2
1
2
1
0
1
0
0
2
0
0
1
1
1
0
0
0
2
0
1
0
0
1
2
2
0
0
0
1
0
1
0
0
0
0
0
0
1
2
0
1
2
0
1
0
3
1
0
0
1
2
1
0
1
0
1
0
1
1
0
1
1
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
3
1
0
1
2
0
0
1
1
0
2
2
1
0
1
1
0
0
2
0
1
0
3
0
1
0
2
2
1
2
1
1
0
1
1
1
1
0
0
2
2
1
0
0
1
1
0
1
0
1
1
0
1
2
0
0
1
2
1
2
1
1
0
0
0
1
0
0
1
1
0
0
0
1
1
1
1
2
0
1
1
0
0
1
0
1
0
0
2
1
1
0
2
0
0
0
0
1
2
1
2
2
0
0
0
1
3
0
1
2
0
0
2
1
2
2
2
1
3
2
0
0
1
0
2
1
2
1
1
1
2
0
0
2
1
1
0
1
2
2
1
0
1
1
1
1
0
1
1
0
2
2
2
1
1
1
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
1
2
0
1
1
1
1
1
2
0
2
2
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
1
0
2
1
1
0
1
2
0
1
0
2
1
0
2
1
0
0
1
0
2
1
1
1
0
0
0
0
2
0
0
0
0
1
2
0
1
2
1
1
2
0
0
1
0
1
0
1
1
2
0
2
0
2
1
0
1
2
1
0
1
0
2
2
2
1
0
2
2
2
3
0
1
1
2
2
0
2
0
0
2
0
1
2
1
2
1
1
2
1
0
0
0
0
1
1
0
0
0
1
1
0
0
0
2
1
0
1
2
2
2
2
2
0
0
2
1
2
0
0
0
1
1
3
2
0
0
0
1
2
0
0
1
1
1
1
2
0
1
1
1
1
0
1
0
0
2
0
1
0
6
2
2
0
0
0
0
1
0
3
0
0
3
2
2
1
0
0
1
1
1
0
0
3
1
0
0
1
0
0
2
1
1
0
3
0
0
1
3
1
0
1
1
1
1
1
0
1
1
0
2
0
2
0
0
0
2
0
1
3
0
2
2
2
1
0
0
2
0
1
1
0
2
1
0
0
1
0
2
1
0
0
2
0
1
1
0
1
0
2
0
3
0
0
2
0
1
0
0
1
2
0
0
0
1
0
1
0
1
2
0
1
1
0
0
1
2
1
0
2
2
2
0
1
1
0
0
1
0
2
2
0
3
0
0
2
1
1
1
2
2
0
1
1
0
1
0
0
2
1
0
1
0
0
1
1
2
1
0
1
0
0
0
1
1
2
1
1
0
1
0
0
2
1
1
1
0
0
2
0
1
1
1
2
2
2
0
1
2
0
1
1
1
1
1
2
0
0
0
0
0
2
2
1
1
0
1
1
1
0
0
0
0
2
0
1
1
1
1
0
2
2
1
1
1
2
1
2
0
1
0
2
0
2
2
1
1
0
0
3
0
1
0
1
2
0
0
2
0
0
0
1
0
2
2
1
2
1
2
0
2
0
0
1
0
2
1
2
1
0
0
0
1
0
1
1
0
1
0
1
1
3
1
0
2
0
1
2
1
0
0
0
0
0
3
2
1
1
0
2
2
1
1
0
0
0
1
0
0
1
1
2
1
0
0
1
3
0
2
0
1
0
4
2
2
1
0
0
0
1
1
0
0
1
0
0
0
2
0
2
1
1
0
2
1
0
2
2
1
0
1
2
0
1
1
1
0
0
1
0
0
0
1
2
1
2
2
0
2
2
1
0
2
1
0
1
1
0
1
0
1
0
0
0
1
1
1
0
0
1
1
1
2
1
1
0
1
2
1
0
0
1
2
0
0
2
2
0
0
2
0
0
0
1
2
1
0
2
0
0
2
1
1
3
2
2
1
2
1
1
0
0
2
0
1
1
1
2
1
2
2
0
2
0
1
0
0
0
1
1
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
1
2
0
1
2
1
1
1
2
1
1
0
1
2
1
0
0
0
2
0
0
1
0
0
0
1
1
0
0
0
0
2
2
3
0
0
1
0
2
0
0
0
1
1
1
1
2
0
1
0
2
1
1
1
2
2
1
0
2
0
0
1
1
0
1
1
0
0
5
1
0
1
1
1
1
3
1
2
0
1
1
0
0
0
0
0
0
2
1
1
2
0
1
1
2
1
0
2
0
2
0
1
0
0
0
0
1
1
0
0
0
0
2
1
0
1
1
0
0
0
0
0
0
1
2
0
0
1
1
1
5
1
0
0
0
0
0
0
0
0
0
1
0
0
1
2
1
0
1
1
1
0
0
1
2
2
0
0
2
1
1
1
0
2
0
0
2
0
2
2
1
1
0
1
0
0
1
2
1
0
1
1
0
2
0
2
0
1
1
0
1
1
1
1
0
2
0
2
2
0
1
1
1
1
1
0
1
1
1
0
1
0
0
2
1
0
1
1
2
2
1
0
0
1
0
0
1
1
0
0
1
1
2
1
1
0
0
2
1
3
1
0
1
0
0
0
0
1
0
1
2
1
1
1
1
1
1
0
3
0
2
1
1
0
2
0
1
1
1
2
2
1
0
1
1
1
1
0
3
1
2
2
1
2
0
0
2
0
0
2
1
0
0
0
1
0
0
0
1
2
2
0
0
1
2
0
0
1
1
1
0
1
2
0
1
1
0
0
0
1
1
5
1
1
0
0
1
0
1
2
0
3
1
1
1
0
0
1
0
0
1
0
0
1
0
1
0
1
1
0
2
1
0
0
3
0
1
1
2
1
2
2
2
2
1
0
0
0
0
0
1
2
0
0
2
1
0
0
0
2
0
1
0
2
1
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
3
1
1
1
2
2
0
2
0
1
1
0
2
2
2
2
0
0
1
2
0
1
2
1
0
0
1
0
0
3
1
0
1
0
0
1
1
0
0
0
2
2
0
0
2
0
0
0
1
2
1
1
1
1
2
0
3
0
0
2
0
1
1
1
0
0
0
1
1
1
2
0
0
0
2
1
0
0
2
1
2
2
2
0
2
2
1
1
0
2
1
1
1
0
3
2
2
0
2
2
1
5
0
0
2
0
0
1
0
1
0
1
2
0
1
2
1
1
0
0
2
0
2
1
1
0
0
2
0
1
0
2
2
1
0
0
5
0
1
1
1
0
1
2
2
2
0
2
2
0
1
0
2
2
1
1
1
1
2
0
1
1
1
2
0
0
1
0
0
3
2
1
1
0
0
1
1
2
1
0
1
1
2
1
1
1
0
0
1
0
1
2
1
2
2
0
2
0
0
2
1
0
1
1
2
3
0
1
1
2
0
0
1
0
2
1
1
1
0
0
2
2
2
1
0
2
2
1
1
0
1
1
0
0
1
2
1
0
0
1
2
1
1
0
0
1
1
0
0
0
0
1
2
2
1
0
1
0
0
1
2
1
0
2
1
0
1
0
0
0
0
0
1
0
1
2
3
0
0
0
0
0
3
2
0
1
2
0
2
1
4
2
2
1
2
1
0
0
0
0
0
0
2
1
2
1
1
0
0
2
0
0
0
2
0
1
1
0
1
0
2
1
0
1
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
1
0
0
0
2
1
1
0
2
2
1
2
0
0
0
0
1
0
0
0
1
1
1
0
0
2
0
1
0
2
2
0
2
0
2
1
0
0
1
2
1
2
1
0
1
0
0
1
0
2
1
0
1
1
1
0
0
0
0
0
2
3
1
1
2
2
0
1
2
1
0
1
0
1
1
1
0
0
0
0
0
1
2
0
1
0
1
0
1
1
0
1
0
0
1
0
0
2
0
1
2
0
2
1
3
1
0
2
0
0
2
1
2
1
2
0
2
0
0
0
1
0
0
4
0
0
0
0
1
0
2
2
0
2
2
1
1
1
0
4
2
1
2
1
1
2
1
1
0
1
0
0
1
1
1
1
0
0
0
1
1
0
0
1
0
2
0
0
1
1
2
0
1
0
1
0
2
0
0
0
2
1
2
0
0
1
0
0
0
2
0
1
0
1
0
1
1
1
0
0
0
0
1
1
0
1
1
1
1
0
1
0
0
0
1
0
2
1
0
0
0
0
2
0
0
2
0
1
0
1
0
1
2
0
2
0
0
1
1
0
1
1
0
0
2
1
2
2
1
2
0
2
1
1
0
0
0
0
2
0
0
0
1
0
0
0
2
3
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
2
1
0
3
2
0
1
0
0
0
1
0
1
0
0
2
0
2
2
0
0
2
0
0
1
1
1
2
2
2
0
1
1
0
0
0
0
0
1
0
0
0
1
2
0
1
0
1
0
2
1
1
0
1
7
1
1
3
1
0
0
0
1
1
0
1
0
1
1
0
0
0
1
0
1
0
0
0
2
1
0
0
0
0
0
0
0
1
1
1
1
1
1
0
2
0
0
0
0
2
1
1
0
0
1
2
1
0
2
0
0
2
0
0
1
4
1
0
0
2
1
1
0
2
1
3
2
1
0
0
0
1
0
2
1
2
1
0
2
1
2
1
0
2
1
2
2
1
1
2
0
1
0
0
1
0
1
1
0
0
1
0
1
0
1
1
0
1
2
0
1
2
1
2
0
0
2
1
2
0
2
1
1
0
0
0
1
0
0
0
0
2
1
0
1
0
1
0
0
0
0
1
0
2
2
2
0
1
2
1
0
1
0
0
1
0
0
1
2
0
1
2
0
0
0
0
2
1
1
0
1
1
2
0
0
0
0
1
0
2
2
1
0
1
0
2
1
0
1
2
0
0
0
0
2
1
1
1
1
0
0
1
1
0
0
0
1
1
0
2
0
0
0
1
2
0
2
2
0
1
0
2
1
0
0
0
0
1
1
0
0
2
2
2
0
1
0
1
2
1
0
2
2
1
0
0
0
2
0
1
1
1
2
0
1
0
1
0
2
1
0
0
2
0
1
1
0
0
1
1
2
1
1
2
1
1
1
1
0
3
2
1
1
0
1
0
0
2
1
1
3
0
0
0
2
0
0
0
2
0
2
2
0
0
0
1
1
1
1
0
1
1
0
0
1
1
0
2
1
2
1
0
2
0
0
0
3
2
0
1
0
1
1
1
2
0
0
0
1
1
3
3
0
1
0
0
0
0
2
1
1
0
1
0
1
0
1
0
2
2
1
0
2
2
1
0
1
0
0
0
0
1
2
0
0
1
1
0
0
0
1
1
1
2
1
2
0
0
1
1
2
0
1
0
3
1
0
0
1
2
0
2
1
1
0
0
0
0
1
0
0
2
0
1
1
2
1
1
1
0
0
2
1
3
2
1
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
1
0
3
0
1
1
0
0
1
0
0
0
1
2
4
1
1
1
0
0
0
0
1
0
0
0
1
0
1
0
2
1
0
1
0
2
1
2
0
1
1
1
2
1
2
1
1
1
0
0
0
2
0
2
0
1
2
2
0
0
2
2
1
0
1
2
1
1
0
0
2
2
0
2
0
0
0
2
1
1
0
1
1
1
2
2
2
2
2
0
0
1
2
0
0
0
2
1
1
0
1
0
0
2
1
4
0
0
2
0
0
0
1
1
2
0
2
1
0
2
2
0
2
0
2
1
0
0
2
0
1
2
0
2
2
1
1
2
0
0
2
1
1
0
1
1
0
0
1
2
2
0
0
0
2
1
3
2
2
1
1
2
0
1
1
0
2
1
0
2
0
0
0
0
0
0
1
0
1
1
0
2
0
1
0
0
1
1
1
2
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
2
0
1
1
3
1
2
0
1
0
1
1
1
1
1
1
2
0
1
1
0
1
2
1
2
1
1
3
2
2
1
1
0
0
0
1
0
2
2
0
1
1
1
2
1
1
0
2
1
2
0
2
0
0
0
2
2
1
0
2
1
0
0
1
3
0
1
1
0
1
2
1
2
0
0
1
0
2
0
0
2
0
1
2
0
6
1
0
1
1
2
0
0
2
1
1
3
2
1
0
2
1
0
1
2
2
1
2
0
1
0
2
1
1
0
2
0
1
0
2
1
1
0
1
0
2
1
2
1
1
0
1
1
0
0
1
1
0
0
0
1
2
0
1
1
0
1
2
1
1
0
2
0
1
1
0
2
0
0
1
0
1
1
0
0
0
1
0
0
0
2
0
1
1
1
1
2
1
0
0
1
0
2
0
0
0
1
1
0
0
0
1
0
1
1
1
2
1
1
0
1
1
0
1
2
1
1
0
0
1
0
2
2
2
2
1
1
2
1
0
0
1
2
2
0
0
0
2
1
2
0
0
1
0
0
2
1
0
0
2
1
2
1
1
1
0
1
0
1
2
0
0
0
1
2
0
0
2
1
0
0
4
1
1
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
2
2
0
2
0
2
0
2
1
1
1
2
1
1
0
0
0
2
1
0
0
2
1
1
2
3
1
0
3
1
1
3
1
0
3
0
2
2
1
1
1
1
1
0
2
1
1
0
1
2
0
0
0
0
0
2
0
0
1
1
1
0
2
1
0
2
0
1
1
1
1
0
1
0
1
1
2
1
1
0
1
2
1
0
2
2
2
1
0
2
1
0
1
1
0
0
0
1
0
2
0
1
0
0
1
0
1
0
2
1
0
3
0
0
1
0
0
2
1
1
2
1
0
2
0
1
1
1
1
0
1
0
0
0
2
3
0
0
1
1
1
0
0
2
1
0
2
0
2
0
1
0
0
2
2
0
1
0
0
1
0
1
0
2
0
0
1
2
0
1
1
1
1
0
1
0
0
0
2
0
1
1
0
0
0
0
0
1
1
0
0
2
2
0
1
0
1
0
2
1
1
0
3
0
1
0
2
1
1
1
0
0
2
0
2
1
1
1
1
0
2
1
0
0
0
0
1
1
1
0
2
1
1
1
0
0
1
0
0
0
2
0
0
0
0
2
1
0
1
0
0
2
2
0
0
0
0
2
0
2
0
1
0
0
0
3
1
1
1
0
0
0
2
0
1
1
0
1
2
0
1
0
2
2
0
0
0
0
1
0
0
2
0
1
1
0
0
0
1
0
1
0
1
0
1
2
1
0
0
1
0
0
1
0
1
0
0
0
0
0
2
0
0
2
0
1
0
0
1
0
0
0
1
0
2
2
1
1
2
0
7
0
0
1
1
2
0
1
1
2
0
0
0
2
0
0
2
2
1
0
0
0
1
0
0
1
0
0
0
1
1
1
1
2
1
0
1
1
0
0
2
1
0
2
1
1
1
0
0
1
2
2
1
1
1
0
1
0
1
1
0
1
0
1
2
0
1
1
1
0
2
0
0
0
0
1
0
1
1
0
2
3
1
1
0
0
0
0
0
1
0
0
2
0
0
2
0
0
2
0
0
0
2
2
0
2
2
0
0
2
0
1
2
0
1
0
1
0
1
0
0
1
3
2
1
1
3
1
0
1
0
0
0
0
0
0
1
1
0
2
1
0
1
1
0
0
0
0
0
0
0
0
1
0
2
2
0
0
1
0
1
1
0
0
0
0
2
0
0
1
0
1
1
0
1
2
1
0
1
0
1
1
0
1
0
0
0
2
0
0
0
1
0
2
1
0
2
0
1
0
1
0
0
2
0
2
0
0
0
0
1
0
1
2
0
1
2
2
0
0
0
0
2
2
1
0
0
0
0
1
1
1
0
1
0
1
1
0
0
1
0
2
1
1
0
0
1
0
1
1
0
0
2
2
2
2
2
0
1
2
0
0
0
1
0
1
0
1
0
0
1
0
1
2
0
2
1
1
1
0
0
0
0
2
0
1
1
0
0
0
1
0
1
0
1
0
0
1
0
2
0
2
1
0
0
0
1
1
0
0
2
1
2
0
0
1
0
2
2
0
1
0
0
2
1
3
1
2
1
0
1
2
0
1
2
0
1
1
3
0
0
1
1
0
0
1
1
0
0
0
0
1
2
1
1
0
3
0
0
0
0
0
3
0
1
0
2
1
2
1
1
1
0
0
0
1
1
0
2
0
1
0
0
1
0
2
0
1
1
1
1
0
1
0
1
0
1
0
0
0
0
0
2
1
0
2
0
2
1
1
0
0
0
0
0
1
2
0
1
0
0
0
1
0
2
0
0
1
1
0
2
2
2
2
2
1
2
0
0
1
1
2
1
1
3
2
0
3
0
2
1
0
0
0
1
2
0
1
1
0
2
0
0
0
1
0
1
2
0
1
1
3
1
1
2
1
2
1
0
1
0
0
1
0
0
1
0
1
2
0
0
0
0
1
0
1
0
0
2
0
0
0
1
1
1
1
2
0
0
1
1
0
0
3
2
1
6
0
0
2
0
0
2
1
0
2
0
1
0
1
2
0
2
1
0
1
1
2
2
0
0
1
0
0
2
2
0
0
2
0
0
1
0
1
0
0
0
2
0
2
2
1
0
0
2
1
0
0
2
2
0
0
1
0
1
1
1
0
2
1
2
0
1
0
0
1
1
1
0
2
0
2
1
0
2
2
0
0
1
0
1
0
0
1
0
0
3
0
1
2
0
1
2
0
2
0
2
2
2
2
0
1
1
2
1
0
1
1
0
0
1
1
2
0
1
0
0
0
2
1
0
0
2
3
2
0
0
0
0
0
1
0
2
2
1
2
0
2
1
2
1
0
2
0
2
1
0
2
0
1
0
2
0
0
1
0
0
0
0
0
3
0
0
0
2
2
0
1
0
2
1
2
1
0
0
1
1
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
1
1
0
2
0
1
0
0
0
0
1
1
1
0
1
0
0
1
0
0
0
1
2
0
0
2
1
0
0
1
0
1
2
1
2
0
0
1
0
0
1
1
2
2
2
0
1
0
2
1
2
1
0
1
0
1
0
2
1
0
0
0
0
1
1
0
0
0
0
0
0
1
2
0
2
1
2
6
0
0
0
1
2
2
0
1
0
1
2
0
1
1
2
0
1
0
2
1
1
2
0
0
0
0
2
0
0
0
0
1
1
1
2
0
1
2
1
1
1
1
0
3
2
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
1
0
1
2
0
0
2
0
1
2
2
0
0
2
1
1
1
1
1
1
2
1
1
1
1
2
0
1
1
1
1
1
1
4
1
0
0
0
0
2
2
2
1
1
0
0
1
1
2
2
0
1
1
1
0
1
1
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
1
2
1
0
0
0
2
0
0
1
0
0
1
1
2
1
1
0
0
1
2
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
1
1
1
0
2
0
1
1
0
0
0
2
0
1
0
2
1
2
0
0
0
1
1
1
1
3
1
1
0
2
0
2
1
1
0
8
1
0
3
0
1
0
2
1
2
0
0
0
0
1
1
1
1
1
1
0
0
0
0
1
0
1
1
2
2
1
1
1
2
0
0
2
1
2
0
0
1
0
1
2
2
0
1
0
0
0
1
1
1
0
3
0
0
0
0
1
0
0
2
1
1
1
1
1
0
0
2
1
1
1
1
1
1
0
2
1
0
2
0
0
0
2
0
2
1
0
1
0
0
0
0
1
1
2
2
0
0
0
0
2
1
0
0
2
0
1
0
2
2
0
1
2
2
0
2
2
0
1
0
0
0
1
1
2
1
1
0
0
1
0
1
1
0
2
2
2
2
0
1
0
1
0
1
1
0
2
0
0
1
0
1
0
0
0
0
1
1
0
1
3
2
0
2
0
0
0
0
1
0
0
2
0
0
0
0
2
1
1
1
0
0
0
1
0
0
1
0
2
0
0
1
0
2
1
0
0
0
2
0
1
1
0
0
1
1
1
2
0
2
0
0
0
0
3
0
1
2
1
1
2
1
0
1
1
0
0
0
2
1
1
0
0
2
0
1
0
0
0
0
1
1
1
0
0
1
2
0
0
2
0
0
0
1
2
2
0
2
0
0
0
1
0
1
2
0
1
1
1
1
0
0
1
2
0
2
1
1
0
2
1
2
0
2
0
0
0
2
0
2
2
1
0
0
0
0
1
0
1
0
1
2
2
0
1
0
0
1
1
0
0
0
2
0
1
1
1
0
0
0
1
1
0
1
1
1
0
1
0
0
0
1
0
0
2
1
1
1
2
1
2
1
0
0
0
0
1
0
0
1
1
2
0
0
2
0
0
0
1
0
1
1
3
0
1
1
0
1
1
1
2
0
1
0
0
0
1
0
1
0
0
1
0
0
0
1
2
0
0
1
2
1
0
1
0
0
2
2
1
1
1
1
1
2
1
2
0
1
2
0
0
2
0
1
2
2
2
1
2
2
0
1
0
1
2
3
0
1
0
2
0
1
0
0
1
1
0
1
1
1
2
1
2
1
0
0
0
1
0
1
0
0
0
1
0
0
1
0
2
1
0
1
0
2
0
0
0
1
2
1
0
0
1
0
2
2
0
2
2
1
2
0
0
0
1
0
1
1
0
0
1
0
2
2
2
0
1
0
1
0
0
0
1
0
2
0
2
3
2
1
0
1
0
0
0
2
0
1
1
1
1
0
1
2
2
1
0
1
1
1
0
2
0
1
3
0
1
2
1
0
1
1
0
0
0
1
2
0
2
0
0
0
0
2
0
1
2
0
0
1
0
0
1
2
2
1
0
3
2
2
2
1
0
0
2
0
1
0
0
1
2
0
0
0
0
1
1
1
0
0
0
1
0
1
0
2
0
1
1
0
0
1
0
0
2
2
0
0
2
0
2
1
1
0
0
1
2
2
0
0
0
2
1
0
0
1
0
0
0
1
0
1
0
0
1
3
0
2
0
1
0
0
0
2
0
1
1
1
0
2
0
1
2
0
1
0
2
0
0
2
1
1
0
2
0
1
0
2
1
2
2
2
2
2
0
1
1
0
0
0
0
3
0
0
1
1
0
1
1
1
1
0
0
1
1
1
0
1
0
1
2
0
0
1
1
2
0
1
2
2
0
0
1
2
0
0
2
2
2
2
2
0
1
1
0
2
1
1
1
1
2
0
0
1
1
2
0
0
0
1
0
0
0
0
0
2
2
2
1
0
0
2
3
0
2
0
0
0
1
1
2
2
1
2
3
2
0
0
2
1
1
0
1
0
0
1
1
1
0
2
0
2
0
1
0
0
0
2
0
1
1
0
2
1
1
1
2
1
0
1
2
0
1
0
1
0
0
0
0
0
0
2
1
0
0
1
2
1
1
0
0
0
0
0
1
1
0
1
1
0
0
0
1
0
2
1
0
1
2
2
2
2
0
1
2
0
4
0
0
0
2
1
0
0
2
0
0
1
0
1
2
0
2
2
1
2
2
1
2
0
1
0
1
2
0
1
0
1
1
1
1
2
1
1
1
0
1
0
2
1
2
0
0
1
0
1
0
0
1
0
0
2
0
0
0
0
2
0
2
1
1
0
0
1
0
1
1
0
2
1
0
1
1
1
0
1
0
1
2
2
1
0
0
1
0
1
1
0
2
1
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
1
0
1
0
0
1
1
2
0
1
2
2
2
0
1
1
1
0
1
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
2
1
1
0
2
2
1
1
0
0
0
1
0
2
2
0
2
0
0
1
0
0
0
1
0
1
0
1
0
1
2
2
2
0
2
0
0
1
0
1
0
2
2
1
0
0
1
2
2
1
0
0
0
0
0
1
2
1
1
0
1
1
0
1
0
1
2
2
0
0
1
1
2
0
0
0
0
1
1
0
1
2
1
0
2
1
0
0
2
0
0
2
1
0
0
0
1
1
0
2
1
1
1
0
0
0
1
1
3
1
2
0
0
1
0
1
1
1
2
2
2
2
0
1
2
0
1
0
1
1
2
1
0
0
1
0
0
1
0
0
1
2
1
0
0
0
0
0
0
0
2
0
1
1
0
1
1
1
0
2
3
0
0
2
0
1
0
2
0
0
2
1
0
2
0
3
0
0
1
1
0
2
1
1
0
0
3
2
2
1
0
0
1
0
0
0
1
0
1
0
1
3
1
1
0
1
0
1
2
0
2
0
0
0
4
1
1
1
1
2
1
1
0
0
1
0
0
1
0
0
2
2
1
0
1
0
0
0
0
3
0
0
2
1
0
2
0
2
0
0
1
1
1
1
0
1
1
0
2
2
0
1
2
2
0
1
0
0
0
0
0
0
0
0
1
2
2
2
2
0
0
0
1
5
0
2
2
2
1
0
2
1
1
1
0
1
1
2
1
2
1
2
2
1
1
1
0
1
1
2
0
2
2
0
1
2
1
0
1
2
1
1
0
0
0
0
0
3
0
0
0
0
1
1
2
1
3
1
0
1
0
0
1
1
2
0
0
0
2
2
1
2
1
2
1
0
0
1
0
2
2
0
2
0
0
0
0
1
2
0
0
1
0
1
0
1
1
0
0
0
1
2
0
1
1
1
0
0
1
0
1
1
0
1
0
1
1
0
1
2
0
0
0
0
0
1
0
1
0
1
0
2
2
2
1
1
2
1
1
1
0
1
1
2
2
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
2
1
1
2
1
0
1
1
2
0
0
2
1
1
2
0
1
0
0
2
2
0
0
2
0
3
0
1
2
2
1
0
2
0
2
1
0
0
0
0
0
0
0
1
0
2
1
0
2
0
0
0
0
0
1
1
2
3
2
0
1
1
0
0
1
0
0
1
1
0
0
1
0
2
1
1
1
2
1
1
0
1
1
0
3
0
1
1
8
0
0
1
0
0
1
0
0
0
0
2
1
2
2
1
1
0
0
2
0
0
0
1
0
2
2
1
2
1
1
1
0
0
0
1
2
1
1
1
1
1
0
0
0
0
9
2
0
2
0
0
0
1
0
2
2
0
2
1
0
2
0
0
0
1
2
2
1
2
1
0
1
1
0
0
1
1
0
1
1
1
1
0
0
3
2
0
0
1
0
0
0
0
1
0
3
1
0
1
0
1
3
0
1
2
1
1
1
0
0
1
0
0
0
0
1
2
0
1
1
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
2
0
0
0
2
2
0
0
1
0
2
0
1
1
1
0
0
0
1
1
0
1
1
2
0
0
1
1
1
0
2
2
0
0
0
0
1
0
0
0
1
0
0
0
1
2
0
1
1
1
2
1
0
2
1
0
0
1
1
0
0
0
1
1
0
0
0
0
1
2
0
2
1
0
0
0
0
0
0
0
0
1
0
2
0
2
1
1
1
0
0
0
1
1
1
1
0
1
1
0
2
0
0
2
2
0
1
0
1
2
1
2
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
2
1
1
0
1
0
0
2
0
0
0
0
0
0
1
0
1
1
0
0
1
1
0
0
0
1
1
0
0
0
2
2
1
0
0
1
0
0
0
2
2
2
1
0
0
1
1
1
0
0
2
1
0
0
0
0
2
0
0
2
1
2
1
1
2
1
0
0
1
0
1
2
2
1
1
2
0
0
1
1
0
0
0
2
1
1
0
0
2
0
1
0
1
1
2
1
2
0
1
1
2
2
0
2
1
0
1
0
0
2
2
1
0
1
0
1
0
1
0
1
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
2
0
0
1
1
0
2
1
1
0
1
1
2
1
0
2
0
1
1
2
1
0
0
1
4
1
0
2
0
0
0
1
0
0
2
0
1
0
0
0
1
0
1
0
1
1
1
2
0
0
0
0
1
1
0
0
0
0
2
2
2
0
1
0
1
1
1
2
0
2
0
1
0
0
1
1
0
1
1
1
1
1
0
0
0
2
1
1
1
2
0
0
1
1
1
0
1
0
1
1
2
0
2
0
1
0
2
0
2
0
0
1
1
0
0
0
0
0
1
0
2
1
0
0
1
0
1
0
2
2
1
1
4
0
0
0
1
1
1
0
2
2
2
2
0
0
0
2
0
1
1
0
0
1
1
1
1
1
1
2
0
0
0
2
0
0
1
2
1
0
0
0
0
2
1
0
0
1
1
0
1
1
0
0
2
2
2
2
2
1
1
1
0
0
0
2
0
1
2
2
2
0
2
0
1
0
1
1
0
0
2
1
2
2
2
0
1
1
0
1
2
1
2
1
2
1
0
2
2
1
1
0
1
0
1
0
0
1
0
2
0
1
0
3
0
2
1
1
0
1
2
0
0
0
0
0
0
2
1
0
2
2
2
1
0
0
0
1
2
0
0
0
0
1
0
0
0
0
2
1
1
0
2
3
2
1
2
2
1
1
1
1
0
2
0
1
0
0
0
1
1
1
0
1
0
2
1
1
0
1
0
1
2
1
3
1
1
0
1
1
2
0
0
0
1
2
0
0
1
0
1
0
1
0
0
1
1
0
2
1
0
0
0
0
1
1
0
0
2
0
2
0
0
2
0
0
0
0
1
2
1
2
1
2
0
0
0
2
0
2
1
1
4
1
0
2
1
1
1
1
0
1
2
7
0
0
0
1
2
1
0
0
1
1
0
0
1
0
2
1
0
1
0
1
1
4
1
0
1
1
1
0
2
0
2
2
2
1
0
1
0
0
0
1
0
2
1
0
1
1
0
1
1
1
1
0
0
0
0
0
1
1
0
2
1
0
2
0
2
0
2
2
0
0
0
2
3
1
0
1
0
0
0
2
0
2
1
1
3
0
1
2
1
2
1
1
0
0
1
2
1
0
0
0
0
1
1
0
1
0
0
1
1
1
0
1
0
1
0
0
0
0
1
0
0
0
0
2
1
2
2
1
1
1
0
0
3
2
0
2
0
1
1
1
2
0
0
1
0
0
0
0
2
0
2
2
1
0
1
1
1
0
0
4
1
0
3
0
1
0
1
1
0
1
2
2
0
1
1
0
2
2
2
0
0
2
1
2
1
0
0
2
1
1
0
1
1
1
1
0
0
2
4
0
0
1
0
2
0
0
1
0
1
0
0
1
2
0
0
0
1
1
0
2
0
0
1
0
0
0
0
1
1
2
2
2
0
0
2
0
0
1
1
0
0
1
0
0
0
2
0
0
2
3
1
0
0
1
0
2
1
1
0
0
0
1
2
2
0
1
2
0
2
1
1
0
1
2
2
2
1
1
1
2
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
2
1
2
0
1
0
0
0
1
1
0
0
2
1
0
0
0
0
0
2
0
1
0
1
0
1
0
0
0
2
2
0
0
1
0
0
1
0
0
2
1
0
1
1
0
2
3
0
2
1
2
2
1
0
0
0
0
1
1
4
2
2
3
1
2
1
0
1
0
0
0
2
1
4
0
3
1
0
1
0
0
0
0
3
1
0
1
1
1
1
3
1
1
1
2
2
0
2
0
0
0
0
0
2
2
0
2
1
1
0
0
0
1
6
0
1
0
0
1
2
0
0
0
1
1
1
2
2
0
1
1
2
0
0
2
0
0
0
2
2
1
0
1
1
0
1
1
0
2
0
1
1
2
2
1
1
0
0
0
1
0
2
1
0
0
1
0
1
1
2
0
0
2
1
1
0
0
0
0
1
2
0
0
0
2
1
0
0
2
2
1
0
1
0
0
2
0
0
0
2
1
1
0
0
1
1
0
2
1
0
2
0
1
0
1
0
2
1
1
0
1
0
1
1
0
1
0
1
1
0
2
0
1
0
1
1
2
0
1
0
1
0
2
1
1
0
0
0
0
0
1
1
0
1
0
0
2
0
1
1
0
1
1
0
1
0
1
0
1
0
1
1
1
2
2
0
1
2
2
0
0
1
1
1
0
1
0
1
1
0
0
1
2
1
3
1
0
1
1
0
1
0
0
2
0
1
2
2
1
1
0
1
1
0
1
0
1
0
2
1
0
2
5
0
1
0
0
1
0
1
2
2
0
1
1
0
0
0
0
2
1
1
0
2
1
1
1
0
0
1
2
0
2
2
1
2
1
0
0
2
0
1
2
0
2
2
0
0
1
1
0
1
2
0
1
2
1
1
2
0
1
2
2
0
1
3
2
2
0
1
1
2
0
1
0
0
1
0
0
1
2
0
5
0
0
0
2
0
1
0
0
0
2
2
1
1
0
0
1
4
2
0
0
0
0
1
0
1
1
0
3
0
0
1
2
1
2
1
2
2
1
2
0
0
1
0
2
1
2
2
0
7
2
0
0
2
1
1
1
2
0
1
2
0
0
0
1
1
1
0
1
2
0
1
0
0
0
1
1
1
1
1
2
1
0
1
1
0
1
0
1
1
0
0
1
0
0
0
2
1
0
1
2
0
0
1
2
1
0
0
1
0
3
0
2
0
0
2
2
1
1
1
0
2
1
2
0
1
0
0
0
0
2
0
0
0
1
0
1
1
0
2
1
0
3
2
1
1
1
2
1
0
1
0
0
2
1
0
1
0
0
0
1
1
2
2
1
1
1
1
0
0
0
0
0
2
2
0
0
1
0
2
1
2
2
1
1
0
6
2
0
3
0
2
2
0
0
0
0
1
0
0
2
0
1
1
0
2
0
0
1
2
1
2
1
2
0
0
1
2
1
1
0
0
2
2
0
0
2
0
3
2
0
0
0
2
0
1
1
2
0
0
0
0
0
0
0
1
0
1
0
1
2
0
2
2
1
2
0
0
1
1
0
0
0
0
0
3
1
1
1
0
2
0
2
1
0
1
2
2
0
1
0
1
0
1
1
1
1
0
0
1
1
1
0
1
6
0
1
0
2
1
1
0
0
1
2
0
2
0
0
1
0
1
0
0
0
2
0
0
2
0
0
1
1
1
1
0
1
2
2
1
1
2
1
0
0
1
2
0
1
1
0
2
1
0
0
0
1
0
1
0
1
0
0
1
1
2
1
0
1
2
0
1
0
1
1
0
2
2
0
2
1
0
2
2
0
1
0
1
2
2
2
0
1
3
1
0
1
1
0
0
1
0
2
0
1
0
2
2
0
0
0
1
0
0
1
1
0
1
0
1
1
0
1
0
1
1
2
1
1
2
0
3
0
1
1
2
0
1
0
1
0
1
0
2
2
0
0
0
0
2
2
2
0
0
0
3
0
1
1
0
1
0
0
0
0
1
0
1
0
1
0
2
2
1
2
2
1
0
2
0
0
2
0
1
0
1
1
1
0
1
1
0
1
0
2
2
2
4
1
1
0
0
0
2
1
0
2
2
1
0
0
1
0
0
0
1
1
0
0
1
0
2
0
0
1
0
0
0
1
0
2
1
0
0
2
2
2
1
0
2
0
1
1
0
0
2
1
2
0
2
2
0
0
1
0
0
0
0
2
1
1
0
1
2
0
2
0
1
1
0
0
0
1
1
1
1
1
3
0
2
0
1
0
0
1
0
1
0
0
0
0
0
1
2
0
0
1
1
0
1
0
1
0
0
0
0
1
4
1
0
1
1
2
0
0
0
0
0
0
0
2
1
2
1
0
2
1
0
0
2
2
0
1
1
1
0
0
1
1
0
1
0
0
0
2
0
0
0
1
0
0
1
0
0
1
0
0
1
2
1
0
1
0
1
0
1
0
0
1
1
0
1
1
0
0
0
1
0
0
2
1
0
0
0
0
0
0
1
2
0
2
1
1
0
0
0
1
0
0
0
0
1
0
1
1
0
1
1
1
1
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
1
1
1
0
0
0
0
1
2
0
1
0
1
1
2
1
0
2
1
0
1
2
0
1
1
0
2
0
1
1
1
0
1
0
1
0
0
2
6
0
0
1
1
1
0
2
0
3
0
1
2
1
1
2
2
0
0
3
0
1
3
1
0
1
1
0
0
1
1
0
0
1
2
2
0
0
1
1
0
2
0
0
1
1
4
1
1
2
0
0
1
1
0
2
2
2
0
2
0
0
1
2
0
0
2
1
0
1
0
2
0
0
1
0
0
1
0
2
0
0
0
2
0
2
1
1
1
2
1
0
2
1
1
1
0
2
0
2
0
2
1
1
1
0
1
2
3
1
1
2
2
0
0
1
1
0
0
0
3
1
2
1
1
1
1
1
0
0
1
1
1
2
2
0
1
2
0
2
2
0
0
1
2
0
2
0
1
1
1
0
0
0
0
1
0
0
1
0
1
0
2
1
0
3
1
2
1
0
2
0
1
0
0
2
1
1
0
1
2
0
0
0
0
0
0
2
1
1
0
0
2
0
0
1
1
0
1
0
1
0
1
1
1
0
1
1
1
0
2
0
1
2
0
0
0
0
1
1
2
0
1
0
0
0
1
2
0
0
1
0
1
0
2
1
1
0
0
1
0
1
2
1
1
0
1
1
2
0
1
2
0
1
0
1
2
0
0
0
2
0
0
1
0
0
1
0
1
1
1
0
1
1
1
1
2
2
0
1
0
0
1
1
0
0
1
0
1
0
1
2
0
0
0
2
1
0
1
1
0
2
0
0
1
1
0
2
2
0
5
2
0
0
1
1
1
0
1
0
0
2
1
0
1
0
0
2
1
3
1
2
0
0
2
0
0
1
0
0
0
1
0
0
2
0
0
1
2
2
0
6
0
0
1
2
0
1
1
1
2
0
0
1
1
1
1
0
2
2
2
0
2
1
1
0
0
1
1
2
1
0
2
0
0
1
2
1
1
1
0
2
1
1
2
0
1
2
0
0
1
0
1
2
2
0
0
3
0
2
0
0
0
2
0
1
0
1
0
1
2
1
1
0
0
0
1
1
2
0
0
2
1
0
2
0
0
0
1
1
2
0
0
2
1
0
2
2
2
1
1
0
2
1
1
1
2
1
2
1
2
0
0
1
1
2
1
0
2
2
2
0
1
0
1
2
0
0
0
5
1
0
2
1
2
1
1
2
0
2
1
0
1
2
1
0
0
1
0
2
2
0
0
2
0
0
0
1
1
0
1
1
0
0
1
0
1
2
1
2
1
1
0
0
0
1
0
1
2
1
0
0
1
1
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
2
1
0
1
0
0
0
1
0
1
0
0
0
1
1
1
0
1
0
1
1
0
1
1
1
1
0
1
0
2
1
1
0
2
2
0
2
0
1
0
1
0
0
1
0
1
2
1
1
2
0
0
0
1
2
0
0
0
2
1
0
0
0
2
0
1
0
3
2
2
1
1
0
1
0
1
0
0
0
0
0
1
0
1
0
1
1
1
1
1
2
2
0
3
1
0
0
0
1
1
1
0
0
1
0
0
0
2
2
2
0
2
0
1
0
1
2
0
1
2
0
2
1
2
0
2
1
2
1
5
1
0
1
1
1
1
1
1
0
0
2
2
0
1
1
1
0
1
0
1
1
1
0
0
1
0
0
2
0
0
1
1
1
2
0
0
2
0
1
1
0
0
0
0
0
1
0
1
0
1
0
1
2
0
2
0
0
0
0
0
1
0
2
1
0
0
1
1
0
1
1
1
1
1
0
2
0
0
1
1
0
0
1
1
1
0
1
1
0
2
2
0
0
0
1
0
1
0
2
1
1
0
0
0
2
0
2
2
1
0
2
0
1
0
1
1
0
0
1
0
0
2
1
0
2
0
2
2
2
2
1
2
0
2
0
0
0
1
2
2
2
1
2
2
0
1
0
1
2
1
0
0
0
0
1
1
0
1
2
2
0
2
0
0
0
1
1
0
1
3
0
0
0
2
1
1
0
1
1
2
1
0
1
1
1
0
0
1
1
1
1
2
1
1
0
3
2
0
1
0
1
1
0
1
1
0
1
1
1
1
0
0
1
1
2
0
0
1
0
1
0
0
0
1
0
2
0
0
1
2
0
1
1
0
2
1
1
0
1
2
1
0
1
1
0
3
1
1
2
1
2
0
0
2
0
2
0
0
1
1
1
2
2
2
1
0
1
0
0
0
0
0
2
0
2
0
0
1
1
0
0
0
0
0
1
2
0
1
2
0
1
1
0
2
1
2
3
0
0
0
0
0
0
0
0
1
1
1
0
1
1
1
1
2
2
2
0
1
0
1
2
11
0
2
2
1
1
0
1
1
0
1
1
0
3
0
1
2
1
2
0
2
2
1
0
0
2
1
0
0
0
1
0
1
1
0
1
0
0
0
1
1
0
0
0
1
2
1
0
1
0
0
2
0
1
0
1
0
0
1
2
0
1
1
1
2
1
0
1
0
0
1
2
0
0
1
1
0
2
0
1
0
0
1
2
1
2
1
0
0
1
1
0
0
0
2
0
1
1
0
2
0
2
0
1
2
0
0
1
2
0
1
1
0
0
2
1
1
1
0
3
0
0
1
0
1
2
2
0
1
1
1
1
0
0
2
1
1
1
1
1
0
0
0
0
0
1
2
1
1
1
0
0
0
0
1
0
1
1
1
1
1
2
0
0
0
2
0
0
0
1
1
0
1
0
1
1
1
2
0
0
2
1
2
0
1
0
1
0
1
0
1
1
2
3
2
2
1
1
1
1
1
0
0
1
0
1
1
1
0
0
0
0
0
2
1
0
1
0
0
0
0
0
2
1
2
1
0
0
1
2
1
0
0
0
0
1
0
0
2
2
0
1
1
1
1
2
0
0
1
1
0
1
0
0
0
0
2
0
2
0
0
0
0
0
1
2
2
2
0
1
1
2
1
0
2
2
2
2
0
1
0
1
1
1
0
2
2
1
0
0
1
1
0
0
0
0
0
0
0
2
2
4
0
0
1
2
1
1
1
2
2
0
0
2
0
0
0
0
2
1
1
2
0
0
2
0
1
0
0
0
1
0
1
1
1
1
0
0
0
0
0
1
2
1
1
0
1
0
0
1
0
0
1
0
0
1
0
0
1
0
0
1
1
1
2
1
0
0
1
1
0
2
0
0
0
2
0
1
1
2
0
1
1
1
0
0
1
2
1
1
1
2
1
0
1
0
2
1
1
1
0
1
0
0
2
1
2
1
1
0
0
1
1
0
1
1
1
1
0
0
1
0
2
2
0
0
1
0
1
1
0
0
0
1
0
0
0
2
0
1
1
0
1
0
2
0
0
1
0
2
0
1
0
0
0
1
0
0
1
0
1
1
0
0
1
0
2
0
0
1
1
1
0
1
3
0
0
2
2
0
1
0
0
1
2
1
2
2
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
1
1
4
0
1
1
0
0
1
0
2
0
0
0
1
2
1
2
1
0
0
0
0
1
0
0
0
3
0
2
0
4
0
2
0
0
0
1
1
0
1
1
1
1
0
0
0
1
0
2
1
1
1
1
0
0
1
2
1
1
0
1
2
1
0
2
1
1
1
1
1
1
1
0
2
2
2
2
1
0
1
1
2
0
1
1
1
1
0
1
0
2
1
1
1
0
0
1
1
0
1
2
2
2
2
0
1
1
0
1
1
2
3
0
2
0
0
1
1
1
0
1
1
0
0
2
1
1
0
0
2
0
1
2
0
1
2
1
0
0
2
1
0
0
1
0
1
1
0
2
1
1
0
0
0
1
1
1
0
1
2
1
1
0
2
0
0
0
0
0
0
0
0
0
0
2
1
1
1
2
1
2
1
0
2
1
0
0
0
0
1
2
1
1
0
1
0
0
0
0
2
0
0
1
0
0
0
0
1
1
1
0
2
1
1
1
0
0
0
2
1
0
1
0
1
0
1
0
1
1
1
1
0
3
0
0
0
0
0
0
0
1
0
0
0
1
1
1
2
2
0
0
2
0
0
2
2
1
1
1
1
0
0
1
1
1
1
0
1
1
0
1
1
0
1
2
0
1
0
0
1
1
1
0
1
1
1
0
1
0
1
1
1
0
1
1
2
1
0
0
1
1
0
0
0
0
2
0
1
0
0
2
2
0
2
1
2
1
1
0
1
0
1
0
0
0
0
1
2
1
0
0
0
0
2
0
0
0
0
0
2
0
1
2
0
1
0
3
0
0
2
0
0
2
1
1
0
1
0
0
0
1
1
2
1
1
0
1
0
0
3
0
2
1
2
1
1
2
0
1
0
1
2
0
0
0
0
1
0
0
1
1
1
1
1
0
0
1
3
0
1
0
1
0
0
0
1
1
0
0
1
0
0
1
0
0
1
1
0
2
2
0
0
2
0
0
1
0
1
0
1
1
0
1
1
1
0
0
2
0
1
2
0
0
1
0
2
2
0
0
0
3
1
2
0
1
0
1
2
2
0
0
1
1
0
2
2
0
0
1
0
1
1
0
2
0
2
2
1
2
1
0
1
1
0
0
1
1
0
0
0
1
0
2
0
1
1
2
0
0
2
1
1
1
0
0
1
0
1
1
1
1
1
0
1
2
2
0
0
0
1
0
1
0
0
2
0
1
0
2
0
1
0
2
1
2
0
1
0
2
2
0
0
2
1
0
0
0
0
1
0
0
1
0
1
0
0
0
2
1
0
1
2
1
0
0
1
1
0
0
2
0
2
0
2
0
0
0
2
0
0
2
2
0
2
1
1
0
0
0
1
1
2
0
0
0
2
0
0
2
0
0
0
0
5
0
2
0
3
0
0
2
1
1
0
0
3
0
0
1
1
1
0
1
1
1
1
0
0
2
2
0
0
2
0
0
0
0
0
1
2
1
1
1
1
0
0
1
2
2
1
1
2
2
1
0
2
0
2
0
0
2
0
0
1
0
1
1
1
0
1
1
0
0
0
0
1
2
1
0
0
1
0
1
2
1
1
0
0
2
0
0
1
2
2
0
1
1
0
1
1
0
1
0
0
1
1
2
1
0
1
2
0
0
2
2
1
2
1
0
2
0
2
0
1
0
0
1
1
0
0
0
0
1
0
0
1
1
3
1
0
1
1
1
2
0
1
0
1
0
0
1
2
0
0
1
0
1
1
0
0
0
2
1
0
1
0
1
1
0
2
0
2
1
0
1
1
0
0
0
2
0
3
0
2
2
2
1
1
0
0
0
2
2
1
0
2
1
0
1
1
1
0
2
2
0
0
2
1
1
1
2
1
1
0
0
0
1
0
1
1
0
0
1
0
0
0
1
0
0
2
1
1
1
1
1
0
2
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
2
0
1
1
1
1
1
0
1
0
1
2
1
1
2
2
1
1
0
0
2
0
2
1
1
1
0
1
0
2
0
1
1
2
0
0
0
2
2
2
0
1
0
2
0
0
1
0
1
1
1
1
2
2
1
3
2
1
0
0
1
0
0
0
1
0
1
2
1
1
0
2
2
2
1
1
0
2
0
0
0
0
1
1
0
2
1
0
2
1
1
1
2
0
0
2
2
0
1
3
2
1
1
3
0
1
0
5
0
2
0
1
2
2
1
0
1
0
1
2
1
0
1
1
1
2
1
0
1
1
0
1
1
2
2
1
0
0
2
1
0
2
0
1
2
1
0
0
0
0
0
0
2
0
1
0
2
0
0
0
1
1
5
0
1
2
1
1
1
1
0
1
1
1
2
0
2
2
1
0
2
1
2
1
0
1
1
0
0
2
1
1
1
1
1
1
0
1
1
0
2
1
1
2
2
2
1
0
2
0
1
2
1
0
1
1
0
1
1
0
0
0
2
2
1
0
0
2
0
2
1
1
1
2
1
0
1
1
0
0
1
2
1
0
2
0
0
0
0
2
1
1
0
1
0
2
0
1
1
1
2
2
1
0
2
1
0
0
0
1
1
0
1
1
2
0
0
0
0
0
2
1
0
1
2
1
0
1
1
2
2
1
1
1
1
1
1
0
1
1
1
1
0
2
1
3
1
0
2
1
2
1
0
0
0
1
1
1
1
2
0
1
2
0
1
1
1
0
0
0
0
1
2
0
2
0
0
1
2
1
0
1
1
1
2
1
1
0
0
1
0
1
3
1
0
2
0
2
0
1
0
0
1
1
1
1
0
1
1
1
1
0
0
0
1
2
0
0
1
2
2
1
0
1
2
0
0
2
1
3
0
1
2
0
0
0
2
1
0
2
2
0
0
0
2
1
0
1
2
2
0
0
0
0
1
0
0
0
0
2
2
2
1
1
1
0
2
0
2
0
0
2
0
1
1
0
1
2
0
0
2
0
0
1
0
1
0
2
1
1
0
0
2
0
1
2
1
0
0
0
2
1
1
0
1
2
0
1
0
2
1
2
2
2
0
0
1
0
3
0
1
0
0
2
0
0
1
2
2
0
0
0
1
1
0
1
0
1
2
0
0
1
0
0
1
1
1
1
0
2
1
0
1
0
0
0
0
2
1
2
2
2
2
1
1
1
0
2
0
0
2
2
1
0
1
0
0
1
2
0
0
0
0
2
2
0
0
0
0
1
0
0
0
1
0
0
1
1
0
2
0
1
1
0
0
2
2
0
0
2
1
2
1
2
0
1
0
1
0
1
1
0
1
1
1
1
0
3
1
1
3
0
2
0
0
1
1
1
2
0
2
0
0
1
0
0
1
1
1
1
1
0
1
1
0
0
1
1
1
0
0
2
1
0
1
2
0
0
2
2
2
1
0
0
2
2
3
0
2
1
1
1
2
0
2
2
2
2
1
1
1
1
1
2
1
0
1
1
0
0
0
2
0
1
1
0
0
0
0
2
1
1
0
2
1
0
1
1
0
1
0
2
1
0
1
0
0
2
2
0
0
0
0
0
2
1
0
1
0
2
0
2
1
0
1
2
0
2
1
0
1
2
1
0
2
0
1
1
0
2
0
0
0
0
0
0
0
1
0
2
2
0
1
0
0
2
1
0
1
0
2
1
1
0
0
0
0
0
1
1
0
1
0
0
1
0
1
0
0
2
1
1
1
0
1
1
1
0
0
0
1
0
0
0
1
0
2
1
2
0
2
2
2
2
0
0
1
2
0
0
1
2
1
1
1
0
1
0
0
0
0
2
1
2
0
2
0
1
1
0
2
1
2
0
2
0
0
3
0
3
0
0
1
0
1
0
1
1
0
0
0
1
0
1
0
0
1
2
1
0
1
0
3
0
2
0
0
2
1
1
0
2
1
0
2
0
0
0
0
0
2
1
1
1
1
0
2
1
0
1
1
1
1
1
0
0
0
0
0
1
2
1
1
1
0
1
0
1
1
0
0
1
1
0
1
0
1
1
0
2
0
1
0
2
1
0
0
1
1
0
0
1
1
1
1
0
0
0
2
1
2
0
1
1
2
1
1
0
1
2
0
1
1
1
1
2
1
1
0
0
0
1
1
0
0
0
0
0
1
0
2
2
0
0
2
1
2
0
3
1
2
0
0
1
1
2
1
0
1
4
0
1
1
1
5
0
0
1
1
1
2
0
0
1
0
1
0
0
2
0
2
2
1
1
0
1
1
1
0
1
2
1
2
1
2
0
0
0
0
0
2
2
2
1
0
1
0
1
1
2
2
1
0
1
1
2
0
0
1
0
1
1
1
0
0
1
0
2
2
1
1
0
1
0
1
0
2
0
0
1
1
3
2
0
0
0
0
2
1
1
2
1
1
2
0
0
0
0
0
1
2
1
1
1
2
1
0
1
1
1
0
1
1
1
0
1
0
1
2
0
0
1
2
1
0
0
0
1
2
0
0
1
0
1
1
0
0
1
2
2
0
0
1
0
1
0
1
0
1
3
2
0
0
0
1
1
1
0
2
1
0
2
0
1
0
2
1
3
0
1
0
0
0
2
1
0
2
0
2
0
1
0
0
1
2
1
2
1
1
2
0
0
0
2
1
0
2
0
1
0
1
1
2
1
0
0
1
0
1
0
0
1
0
1
1
2
0
3
0
0
1
1
0
1
2
0
0
1
2
3
0
1
1
2
3
2
1
0
1
0
0
1
2
1
0
1
0
0
0
0
2
1
0
0
0
0
1
1
2
2
0
2
0
2
0
2
1
2
2
0
0
0
0
4
2
1
0
1
2
0
2
1
2
0
1
0
1
0
0
1
0
0
0
2
0
1
2
0
0
1
0
0
1
0
2
1
1
2
1
0
2
1
0
1
1
0
1
0
2
0
0
2
0
1
2
0
0
0
0
0
1
1
0
1
2
0
0
1
2
0
0
1
1
0
0
1
0
0
1
0
1
0
0
0
0
2
2
0
0
0
1
0
3
0
1
2
1
0
2
1
0
1
2
0
1
0
2
2
1
0
2
1
1
2
0
0
0
0
1
0
0
2
2
1
0
1
0
0
1
0
1
2
1
0
1
2
0
0
1
0
2
1
1
1
0
1
0
1
0
0
2
1
1
2
2
0
0
1
1
1
2
0
0
0
2
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
2
0
1
1
1
1
0
0
0
1
2
0
0
0
0
1
1
0
0
1
1
1
0
0
0
1
0
0
0
2
1
0
1
0
2
0
0
1
1
1
2
0
1
0
1
2
0
1
0
1
2
2
1
0
0
1
1
2
0
0
2
0
1
1
0
0
0
0
1
3
0
2
0
1
1
1
2
1
0
0
1
1
1
1
1
1
1
0
0
1
2
2
4
0
0
2
1
0
1
0
1
0
1
1
2
1
0
1
2
1
0
0
1
0
1
0
1
2
2
0
0
0
1
0
0
1
0
2
0
2
0
1
0
0
1
1
1
1
2
1
0
2
0
1
2
1
1
1
1
1
1
0
0
2
0
0
1
0
5
0
2
0
1
1
0
1
1
1
1
2
0
0
2
0
0
1
1
0
0
2
1
1
0
1
2
1
0
1
1
2
0
0
0
0
0
1
0
0
2
0
1
2
0
0
1
0
0
1
1
0
1
1
0
0
1
0
0
2
2
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
1
0
0
1
2
0
2
3
1
0
1
2
1
2
0
0
1
1
0
0
1
0
0
0
0
1
1
0
0
0
1
2
2
1
1
0
2
1
2
2
0
1
0
1
0
0
0
2
0
1
2
0
1
1
3
0
1
0
0
2
0
2
3
2
2
0
2
2
1
0
1
0
0
1
2
1
1
0
2
2
2
0
0
1
0
2
0
1
2
0
2
1
0
2
1
1
2
2
1
0
1
1
0
1
0
2
2
0
2
1
0
0
1
1
0
1
2
0
0
0
1
0
1
1
1
0
0
2
2
1
2
1
1
0
2
0
2
0
1
1
0
2
2
1
0
1
2
1
2
2
0
2
2
2
1
1
0
2
2
0
3
1
1
0
1
2
0
1
1
1
0
2
0
0
2
0
1
0
0
1
1
1
2
3
0
0
1
2
0
1
1
0
0
0
2
0
0
0
0
1
0
1
0
0
2
0
2
0
2
1
2
2
2
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
1
2
0
1
1
2
0
1
2
2
1
1
1
0
1
2
0
1
1
1
0
0
0
1
2
1
0
0
6
1
0
2
1
2
1
0
0
0
1
1
0
2
0
0
2
0
0
2
1
0
0
0
0
0
0
1
1
1
2
1
1
0
2
0
1
1
2
0
1
1
0
2
1
0
0
2
1
2
1
1
0
0
0
0
2
0
0
1
0
0
1
0
0
0
2
2
1
2
0
2
1
1
0
1
1
0
0
1
1
1
1
2
1
1
1
2
1
0
2
2
1
2
0
1
0
0
0
0
1
0
1
1
1
0
2
1
0
3
1
1
1
0
0
1
0
1
0
0
0
2
1
1
0
0
0
1
2
2
1
2
0
0
0
0
1
1
0
0
2
0
4
4
0
2
0
1
2
1
1
0
0
0
1
1
6
0
1
0
0
0
0
1
0
2
1
1
1
0
0
0
0
0
0
0
0
1
0
2
1
1
2
1
1
2
1
0
0
0
2
1
1
1
1
0
0
0
1
2
0
0
1
0
0
0
0
2
1
1
0
0
0
1
2
1
0
0
2
1
1
1
2
0
0
0
0
0
0
1
2
0
1
2
1
2
1
1
0
0
0
0
1
0
1
0
0
2
1
0
1
1
0
0
2
1
0
0
2
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
1
2
0
1
1
0
0
0
0
1
0
0
1
2
0
1
0
1
0
1
1
1
2
2
0
3
2
2
0
4
1
1
1
0
1
1
0
1
0
0
1
0
0
1
2
1
0
0
0
0
2
1
0
0
0
1
0
0
0
1
2
1
1
2
0
1
0
2
2
2
0
1
1
2
1
2
1
2
1
0
0
1
0
1
1
2
0
1
0
0
0
0
1
0
2
0
0
0
0
1
1
1
1
0
0
0
0
2
1
0
1
1
0
0
1
0
1
2
1
0
0
0
2
0
0
0
1
2
0
0
0
2
0
0
0
0
3
2
2
0
1
1
2
1
1
1
1
1
2
2
1
2
0
1
0
0
0
1
1
2
1
1
6
0
2
2
1
2
0
1
2
2
0
0
0
1
0
1
2
0
1
0
2
1
0
0
2
1
2
1
0
3
1
0
2
2
1
1
1
0
0
0
1
2
2
1
0
1
0
1
1
1
1
1
0
1
1
0
1
5
2
1
0
0
0
1
1
0
1
1
1
0
0
0
1
2
1
0
0
0
2
0
0
2
0
2
2
0
0
2
0
0
1
1
0
1
1
3
2
1
1
0
0
0
0
1
1
3
2
2
0
1
1
2
0
1
0
0
0
0
1
2
8
1
0
0
1
2
0
2
0
2
0
1
0
0
1
1
2
0
2
0
1
1
0
1
2
2
2
1
1
0
0
1
2
2
0
1
0
2
2
3
2
1
1
0
0
1
2
1
1
1
0
2
2
1
2
1
0
1
1
1
1
0
1
0
1
0
0
0
0
1
1
0
1
0
1
0
1
0
1
1
0
0
1
1
1
0
2
2
0
2
1
0
0
1
0
1
1
0
1
0
0
0
2
0
2
2
1
1
1
0
0
0
1
0
0
1
1
1
2
2
0
1
1
0
0
1
1
3
0
1
0
1
1
0
0
1
0
0
1
1
1
2
0
0
2
1
0
1
2
2
1
2
1
1
1
2
1
1
0
2
0
1
0
2
2
0
0
1
1
2
0
2
1
0
1
2
0
1
1
2
1
1
0
0
1
0
1
1
0
0
0
2
2
0
0
2
0
0
1
0
4
2
0
1
0
0
2
1
1
2
2
0
1
2
0
1
1
1
0
1
2
0
2
0
0
0
0
1
3
0
0
0
2
1
0
0
0
0
1
1
2
1
0
0
0
2
0
0
0
1
0
0
0
1
2
0
1
2
1
2
1
2
2
1
2
0
1
1
0
2
0
2
0
1
2
0
0
1
0
2
2
1
0
1
1
0
0
0
0
2
2
1
0
2
1
0
1
1
0
0
2
0
1
2
1
2
1
1
0
0
1
0
2
1
2
0
0
0
2
1
0
4
0
2
1
0
0
0
0
1
0
1
1
0
1
1
0
4
1
0
0
1
1
1
0
1
1
1
0
2
0
1
2
0
0
2
2
0
0
1
0
2
0
2
2
0
0
1
0
0
1
0
1
1
1
0
1
0
0
2
0
1
1
0
1
0
1
0
2
0
1
0
1
1
0
1
1
2
0
0
1
2
0
2
1
1
1
1
1
0
0
1
2
0
0
0
1
0
0
0
1
0
2
2
0
0
1
0
0
0
1
1
0
0
1
0
1
1
0
1
0
1
1
0
1
2
0
0
1
3
0
0
1
0
2
0
2
3
1
1
0
1
2
0
1
0
1
1
0
1
0
0
2
0
0
0
2
2
0
1
0
1
0
0
1
0
0
0
0
1
0
1
0
0
2
2
2
0
1
1
0
0
1
1
0
1
0
1
0
2
1
1
0
1
2
0
0
1
2
1
0
0
1
1
1
1
1
1
1
0
2
0
0
0
0
1
1
1
0
0
1
0
1
0
1
0
1
0
1
1
2
0
0
1
0
2
1
1
0
0
2
1
1
1
0
2
0
0
0
0
2
1
1
1
1
0
1
2
1
0
0
0
0
2
0
0
3
2
1
1
0
1
0
1
1
0
0
0
2
0
0
1
1
0
0
1
2
0
1
2
0
2
0
1
0
2
2
0
0
2
1
0
0
1
0
2
1
0
0
0
2
1
0
2
2
2
2
1
0
1
1
0
2
2
1
0
0
0
0
1
2
0
1
0
1
1
1
0
0
0
0
0
1
2
1
1
2
0
1
0
2
0
0
1
0
0
2
1
1
3
0
0
0
0
1
0
0
0
0
0
2
1
0
2
1
1
1
1
0
0
2
0
2
1
0
0
1
1
0
1
2
0
0
2
0
1
2
0
0
0
0
2
1
0
0
2
1
0
2
4
2
1
2
0
0
0
0
1
0
1
1
1
0
0
0
0
2
1
1
1
1
0
2
0
1
0
0
0
3
1
2
0
1
2
2
0
2
1
1
0
1
1
1
0
0
0
2
0
1
2
0
1
0
1
1
1
0
2
1
0
0
1
2
0
1
0
0
1
0
1
1
2
1
0
1
1
0
0
1
1
0
1
1
0
1
0
3
1
2
0
1
0
1
1
2
2
1
0
2
2
0
0
0
1
1
1
1
1
2
1
0
2
0
0
1
2
0
2
0
1
1
0
1
2
0
2
0
0
2
1
1
0
0
1
1
2
0
1
2
2
1
2
0
0
1
0
2
1
0
1
0
2
0
1
0
0
2
0
2
1
1
1
0
0
1
1
0
2
2
0
1
1
0
0
1
2
2
2
0
2
0
2
0
2
1
0
2
1
0
1
0
2
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
2
0
2
2
0
0
1
1
0
2
0
1
1
0
0
0
2
1
1
2
2
1
0
0
0
0
1
0
2
2
0
0
1
1
2
0
2
1
1
0
0
0
0
0
2
0
1
1
2
2
1
2
0
0
1
0
2
0
1
1
0
0
1
2
1
0
0
0
0
0
2
1
4
2
2
1
1
1
2
0
1
0
0
0
1
0
1
2
0
0
0
1
0
0
1
0
0
1
0
2
0
0
1
1
1
2
1
0
0
0
1
1
0
0
0
3
0
1
0
0
0
0
1
1
0
0
1
0
2
2
1
0
0
0
1
2
2
2
2
0
0
2
2
0
1
1
3
2
1
2
0
1
2
1
2
4
1
2
1
1
1
0
1
1
0
0
3
0
0
2
0
1
0
0
2
1
2
0
1
0
0
1
0
2
2
1
0
2
0
0
2
2
0
0
1
1
0
1
0
1
1
0
3
0
1
0
1
2
2
0
2
0
0
0
0
2
2
0
0
2
0
0
1
0
1
1
0
2
0
1
0
0
1
0
1
0
1
0
0
1
0
2
1
0
1
1
1
1
1
2
1
1
0
0
1
0
0
1
1
0
0
2
0
0
0
1
1
1
1
1
3
1
0
1
1
2
0
0
0
2
2
0
0
1
2
0
1
2
0
4
0
2
0
0
2
1
2
0
1
0
0
1
2
2
0
1
2
1
1
0
1
0
0
1
1
0
3
1
2
1
0
2
1
0
1
0
1
1
2
0
2
2
0
0
0
1
0
0
0
1
1
0
2
3
0
0
2
2
0
2
2
1
2
1
1
0
0
1
1
1
1
0
2
0
1
0
2
0
1
0
1
0
0
1
1
2
2
1
2
0
1
2
0
0
0
1
1
2
1
1
2
2
1
0
0
0
1
1
1
0
0
0
2
0
1
2
0
1
0
1
1
1
0
1
1
2
1
1
0
0
2
2
0
0
2
2
2
0
0
0
1
0
1
1
0
2
0
0
0
1
2
0
0
1
0
0
0
1
1
1
1
2
2
1
0
1
1
1
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
2
1
0
2
0
2
1
1
0
1
1
1
0
1
1
1
0
0
0
1
1
1
0
0
1
2
1
0
0
0
1
1
1
2
1
2
1
2
1
1
0
0
0
1
2
2
1
0
0
0
0
0
0
0
0
1
2
2
0
0
1
0
2
0
0
0
0
1
2
0
2
0
1
0
0
1
0
0
0
1
0
2
0
0
0
0
1
0
0
0
2
2
0
0
2
1
0
1
1
2
0
0
1
1
1
1
2
2
2
0
2
2
2
1
0
2
1
0
2
0
1
0
1
0
0
0
3
0
2
0
1
1
0
1
0
0
0
0
0
2
3
0
0
2
0
1
0
2
2
2
0
1
2
1
2
0
1
2
1
0
0
2
1
0
0
2
1
0
0
0
2
1
0
1
0
1
1
1
2
1
0
2
2
0
1
0
1
1
0
2
1
1
1
1
0
2
0
2
1
2
0
2
1
0
0
2
0
2
1
0
2
2
1
0
0
0
2
0
1
0
2
0
2
0
2
1
1
1
0
1
1
0
1
1
2
0
2
0
2
0
2
0
2
1
2
2
0
2
1
1
1
2
0
2
1
2
0
0
0
1
2
0
2
0
1
1
0
0
0
0
1
2
0
1
1
2
0
1
1
0
0
0
1
0
1
0
1
2
1
1
1
0
1
0
1
0
2
1
4
0
2
0
0
0
0
2
1
1
0
1
0
0
3
1
0
1
1
1
1
2
0
0
1
0
2
2
0
0
1
1
2
3
1
0
1
0
1
0
0
1
1
0
1
2
0
0
0
2
1
0
1
1
1
1
0
1
0
1
2
0
2
0
1
0
1
1
1
1
1
0
0
0
0
0
2
1
1
1
1
0
1
0
0
2
1
1
1
2
1
0
0
0
0
1
2
1
1
1
2
2
2
2
2
0
2
1
1
1
0
0
0
1
2
0
1
1
2
0
1
1
0
1
1
0
2
1
0
0
2
0
0
0
1
1
0
0
1
1
0
0
0
0
3
1
0
2
2
0
0
1
0
0
2
1
1
2
2
0
1
1
1
2
1
1
2
2
1
2
2
1
1
2
2
1
1
1
1
2
2
0
0
2
0
1
0
2
1
0
1
1
0
0
0
14
0
0
0
1
0
1
2
0
0
2
1
1
2
2
1
0
2
0
2
1
2
0
2
2
2
2
0
0
0
1
2
1
2
1
3
1
0
1
2
0
0
0
0
1
2
0
0
2
0
0
1
0
1
0
1
2
1
1
0
0
1
0
2
2
0
2
1
1
0
0
0
1
2
0
0
1
1
2
0
0
2
1
1
1
0
2
0
0
0
1
1
1
2
0
1
2
1
0
0
1
1
3
2
1
0
1
3
2
0
0
0
0
0
0
2
2
0
9
1
1
0
0
2
0
0
0
1
2
0
1
0
0
0
2
0
1
2
1
0
1
2
0
0
2
0
1
2
0
0
1
0
0
1
1
2
0
0
1
0
2
2
0
0
0
0
1
3
0
1
0
1
1
1
0
1
0
0
2
1
2
0
0
0
2
2
0
1
1
2
1
1
0
0
1
1
1
1
2
1
1
1
0
1
2
1
0
1
2
1
0
0
2
0
1
0
2
1
1
0
0
2
2
0
1
0
0
2
2
1
2
2
0
0
0
0
1
1
1
0
0
1
1
2
0
1
1
1
2
1
1
1
2
0
2
2
0
1
0
0
2
2
0
2
0
0
1
2
0
0
2
0
0
1
1
0
0
1
0
1
1
0
0
2
1
0
1
1
1
0
0
0
0
1
0
1
1
1
1
2
1
1
1
2
1
0
0
0
2
1
0
0
1
1
1
1
1
0
0
0
0
2
0
2
1
0
1
1
1
0
1
0
0
1
0
0
2
1
1
0
0
1
1
2
0
0
0
1
0
0
0
0
2
2
1
0
0
2
1
2
0
0
0
1
0
1
1
1
0
2
1
1
0
2
0
2
5
0
0
0
1
1
2
1
0
1
1
2
2
1
0
0
1
0
0
0
2
0
1
3
2
0
1
0
1
1
0
0
1
0
1
1
2
0
2
1
1
1
0
1
0
2
1
0
0
1
1
0
1
0
1
0
0
2
0
2
1
1
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
2
1
1
2
2
1
0
1
0
1
1
0
0
1
2
2
1
2
1
1
0
2
0
0
4
0
4
2
0
1
0
0
0
2
1
0
1
2
0
2
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
4
0
2
1
2
0
1
0
1
0
1
0
0
0
1
2
0
1
1
1
0
0
0
1
1
0
0
2
0
1
2
1
2
0
0
2
0
1
1
2
2
2
3
0
2
0
0
1
1
2
0
2
2
2
0
0
0
2
0
0
2
1
0
1
1
1
2
0
0
2
1
0
0
0
1
1
2
0
2
2
0
1
1
2
1
2
1
1
2
1
0
2
0
0
0
0
1
2
1
2
2
0
2
1
2
1
2
0
2
4
1
0
2
1
1
0
1
0
1
0
0
1
1
0
1
0
1
1
1
1
2
3
0
1
2
0
0
1
2
0
3
1
1
0
0
1
1
0
2
0
0
1
0
0
0
0
2
2
0
0
1
0
1
1
1
2
0
1
0
0
0
1
0
0
1
1
0
0
2
0
1
1
2
7
1
0
0
1
0
0
0
1
1
1
1
0
0
0
2
0
0
0
2
0
3
1
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
2
0
1
2
0
0
0
0
2
1
0
0
1
0
2
1
2
1
2
1
1
2
1
2
0
3
0
1
1
1
0
0
1
2
1
0
1
1
0
0
0
1
0
0
0
0
0
1
2
0
0
1
0
0
0
0
1
0
4
2
0
0
2
0
2
0
0
0
1
4
0
0
1
0
2
2
0
2
2
0
1
1
1
0
1
1
1
1
2
1
1
1
0
1
1
1
2
0
0
1
0
0
1
0
0
1
8
1
0
0
1
1
1
0
0
0
1
0
1
1
1
2
0
0
0
0
2
1
2
0
0
1
1
1
0
1
2
0
2
0
0
2
0
0
0
4
0
2
1
0
1
2
0
0
1
1
0
0
0
0
0
0
0
2
1
2
0
0
0
1
1
2
0
1
0
0
0
0
1
0
1
0
0
0
2
0
1
0
0
0
1
0
0
1
0
1
1
1
0
1
1
0
0
0
0
0
0
0
2
1
0
0
1
0
2
2
0
0
2
0
1
0
0
0
0
0
0
2
1
1
2
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
1
2
0
0
0
0
0
0
1
0
1
3
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
1
0
1
0
0
2
0
0
0
1
0
3
2
0
2
2
1
1
1
1
1
1
0
1
2
0
2
2
0
0
1
0
1
2
0
0
0
3
0
0
1
1
0
0
0
1
2
0
1
2
1
0
0
0
0
1
2
2
0
1
2
2
0
2
0
1
2
2
0
0
0
1
0
2
2
0
2
1
0
1
0
0
1
0
0
1
0
2
0
0
1
2
3
0
0
2
1
1
0
1
1
1
0
0
0
2
1
2
1
2
1
0
0
1
0
0
2
2
1
0
2
0
1
2
1
0
2
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
3
2
2
0
1
0
1
0
0
2
1
0
0
0
0
0
2
2
0
1
0
0
0
0
0
1
1
1
0
0
2
0
2
1
0
2
1
1
1
1
0
1
1
0
1
0
2
1
1
2
0
1
1
0
1
0
0
2
1
2
1
0
2
0
0
1
1
0
0
1
0
0
1
0
0
0
1
2
0
1
1
1
0
1
2
0
2
1
0
3
0
0
0
1
2
0
0
1
0
2
0
1
0
2
0
1
2
1
0
1
0
1
0
0
1
0
0
0
1
1
0
1
3
0
1
0
1
2
0
1
2
1
1
0
0
2
0
0
0
1
0
2
1
0
0
1
0
2
0
0
1
2
0
2
2
4
1
0
1
0
1
1
1
1
1
1
0
1
0
1
1
0
2
1
1
0
0
1
0
3
2
2
0
0
0
0
0
1
3
0
0
0
2
1
1
0
0
1
0
2
2
1
1
0
1
1
0
0
2
0
0
0
0
1
0
0
2
1
0
0
1
1
1
2
0
0
0
1
1
0
0
2
0
2
1
1
0
1
1
1
0
1
1
2
1
1
2
0
3
2
2
2
1
0
0
2
1
2
1
2
0
0
1
0
0
1
1
1
0
0
1
1
1
1
0
0
0
0
0
0
1
0
1
2
1
0
0
1
0
0
0
0
1
0
1
0
1
0
0
2
0
0
0
2
1
1
1
0
0
0
0
0
0
2
0
0
2
0
1
2
2
1
1
0
1
2
1
1
0
0
0
1
0
0
1
1
0
0
0
2
2
1
0
0
2
4
1
0
1
2
0
1
0
2
0
0
0
0
1
1
1
2
0
2
0
2
0
2
2
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
2
0
1
2
1
1
0
2
2
0
0
0
0
1
2
1
2
1
2
2
1
2
1
1
0
0
1
0
2
0
1
0
1
1
1
2
0
0
0
1
1
1
0
0
1
1
2
1
2
0
0
1
1
0
1
2
2
1
2
0
0
0
0
1
1
3
1
1
2
1
1
2
1
1
0
0
2
1
0
1
0
2
0
1
0
1
0
0
0
0
0
0
1
1
1
2
2
2
0
2
1
2
0
0
1
1
0
1
1
2
0
0
2
0
1
0
1
0
2
1
0
0
1
1
1
1
1
0
2
1
1
2
0
0
1
0
1
0
0
0
1
0
1
1
0
0
0
2
0
1
1
2
1
2
1
0
0
2
0
1
1
1
1
1
2
0
1
2
0
2
1
1
1
1
2
1
0
0
0
1
1
0
0
0
0
1
0
0
2
3
2
0
0
1
0
1
0
1
0
2
2
1
2
1
0
0
0
0
0
1
0
0
1
0
0
0
1
1
1
1
1
1
2
0
0
1
1
0
1
1
0
1
1
0
1
0
2
1
2
1
2
1
1
1
1
0
0
2
2
0
1
0
0
0
2
1
1
0
0
0
1
0
1
1
1
0
0
0
1
0
1
1
1
2
0
0
2
1
0
1
1
2
1
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
2
1
0
1
0
1
0
1
0
0
0
0
2
2
1
3
2
3
1
1
1
0
2
0
0
1
2
0
1
1
1
0
0
1
2
1
0
1
0
1
2
1
1
0
1
1
1
1
2
1
1
0
0
0
1
1
0
1
0
1
2
0
0
1
1
2
2
2
0
0
0
0
2
0
0
2
1
0
0
0
2
1
0
0
0
2
0
1
1
2
1
0
0
0
2
2
2
2
0
1
0
1
1
0
2
1
0
0
2
1
3
1
1
1
0
0
0
1
1
1
0
0
1
2
0
0
3
0
1
0
1
1
0
2
0
2
2
0
2
1
0
0
1
2
0
0
0
0
1
1
1
0
0
1
0
0
0
0
1
3
0
1
0
2
2
2
1
0
0
1
2
1
1
1
0
3
1
0
0
0
1
1
1
1
1
2
4
2
1
0
1
0
2
3
0
0
0
0
2
0
0
1
2
0
1
1
0
0
1
0
2
1
0
0
1
0
0
1
1
0
0
2
0
0
2
0
0
2
1
1
0
1
0
0
1
0
3
1
0
0
1
0
2
0
0
0
0
0
1
0
1
0
0
0
1
1
0
2
0
1
0
0
2
0
0
0
1
0
0
0
1
0
2
2
2
2
1
0
0
1
0
0
1
0
1
1
1
0
0
1
2
2
1
0
0
2
1
0
0
0
3
0
1
0
0
0
1
2
0
2
1
1
0
1
1
0
1
1
2
1
1
2
1
2
0
2
1
0
1
1
3
0
1
1
0
0
1
0
1
0
1
1
0
1
2
1
0
1
1
1
1
2
0
0
2
0
1
2
0
1
1
0
0
0
0
2
2
2
1
0
1
2
1
1
2
0
0
1
2
0
1
1
2
0
0
0
1
3
1
2
0
1
0
0
0
0
0
0
2
1
2
0
0
1
0
0
2
0
0
1
1
1
0
1
0
1
0
1
0
2
0
0
3
1
0
1
1
1
1
2
2
2
0
0
0
0
0
5
2
0
0
1
1
1
0
0
2
0
1
1
1
0
0
0
2
0
1
0
2
0
1
1
2
1
1
2
0
2
3
2
1
0
1
2
0
0
0
1
2
1
0
1
0
2
1
2
1
1
2
0
0
0
0
2
0
1
1
0
1
1
0
0
1
2
0
0
2
3
1
0
0
2
0
0
0
0
0
1
0
2
1
1
1
3
2
0
0
1
1
0
2
0
2
1
1
0
0
2
0
0
0
0
2
1
2
2
1
1
1
0
1
4
0
0
1
0
0
0
1
1
0
1
1
1
0
0
2
2
2
0
1
1
1
0
3
2
0
0
0
0
1
1
1
0
0
1
0
1
1
0
2
1
1
0
1
0
1
0
1
2
1
0
0
1
0
0
3
0
0
1
2
1
0
1
1
2
0
0
1
0
0
0
0
1
1
0
0
1
0
0
2
1
0
1
0
1
0
1
0
1
2
1
0
0
0
0
1
1
1
1
2
2
2
0
0
0
2
0
1
0
1
0
1
0
2
2
0
1
0
0
0
1
0
2
1
0
0
0
0
1
2
0
2
0
1
0
2
0
0
1
1
2
1
0
2
2
1
2
2
1
2
2
0
3
1
1
0
1
0
0
0
0
2
0
2
1
1
0
1
0
0
1
2
1
0
0
1
1
0
2
0
1
0
0
0
1
0
0
1
1
0
0
1
2
2
0
3
2
2
0
2
0
1
0
0
0
0
0
1
1
2
1
2
1
2
0
1
0
0
0
1
0
1
1
1
2
1
1
1
1
1
1
0
1
0
1
2
0
0
2
1
1
2
2
1
0
0
2
2
1
2
2
0
0
0
0
1
0
0
2
0
1
0
1
0
0
0
1
1
1
1
1
2
0
2
1
0
0
2
2
1
0
0
0
1
0
0
1
0
0
0
0
0
2
1
2
1
1
0
4
1
1
0
0
2
0
0
1
1
0
0
2
0
1
1
1
2
0
2
1
2
0
1
1
0
2
2
2
1
2
0
2
1
0
1
1
0
2
1
2
0
1
0
1
2
0
1
1
0
2
1
0
2
1
0
0
1
0
0
0
1
0
1
0
2
1
2
1
1
1
2
0
1
1
2
1
2
2
0
0
1
1
0
2
0
2
2
0
2
0
0
0
1
0
1
2
0
1
0
2
1
0
0
1
2
0
0
0
0
2
0
2
1
1
0
2
1
0
0
1
1
2
1
1
0
2
0
1
1
1
0
0
0
2
1
2
2
2
1
0
0
0
1
2
2
2
0
1
1
1
1
1
2
0
0
1
0
1
3
0
1
1
0
2
1
2
0
0
1
0
2
1
0
1
0
0
1
0
0
1
2
0
1
1
0
0
1
1
1
1
0
1
2
0
0
1
0
0
0
0
2
0
0
2
0
2
1
1
0
1
2
0
2
0
0
2
0
2
1
0
2
2
1
1
0
1
0
0
0
1
0
1
3
0
2
1
0
1
1
1
1
0
1
0
1
1
2
3
1
0
1
1
1
0
1
2
1
0
0
1
1
0
1
0
1
1
0
0
0
1
2
1
0
1
1
0
0
0
1
2
1
1
0
2
1
0
0
1
0
0
0
1
0
1
1
1
0
0
0
1
2
1
0
2
1
2
2
2
1
1
0
0
0
1
2
0
1
0
1
1
0
0
0
2
1
0
0
2
1
1
1
1
1
2
1
2
1
0
1
0
1
1
1
1
1
2
1
1
0
2
1
0
1
1
2
1
2
2
0
0
0
0
1
0
1
0
0
0
1
0
2
1
1
2
0
1
0
0
1
3
1
0
2
0
0
0
0
0
2
2
2
0
2
1
2
1
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
1
2
1
1
0
1
0
2
1
0
1
2
2
0
0
3
2
1
0
0
0
1
1
1
0
2
1
0
2
1
0
1
1
0
2
2
1
0
1
0
2
1
1
0
1
0
0
0
1
1
2
0
0
1
1
0
1
1
2
2
1
0
1
0
2
0
0
1
2
0
1
2
2
0
1
1
0
1
0
0
2
0
0
0
0
1
1
1
1
0
0
1
0
0
1
0
0
2
2
0
0
1
0
1
0
1
0
1
2
1
2
0
1
0
2
1
2
0
0
0
2
0
2
2
1
1
1
0
0
1
0
2
1
2
0
0
0
1
0
0
1
3
1
0
1
1
0
0
2
0
1
2
0
0
1
1
0
2
1
1
1
0
1
0
2
2
1
0
1
5
0
1
2
0
1
1
1
0
0
0
1
1
0
0
1
1
1
2
1
1
0
1
0
1
2
1
1
0
2
2
1
0
0
2
0
1
0
1
2
1
2
2
0
0
0
2
2
1
0
0
2
1
2
2
2
1
0
0
0
1
1
1
0
1
1
0
1
1
1
2
1
2
2
0
1
2
0
0
1
0
2
0
2
1
2
0
1
1
0
0
0
0
1
0
0
1
1
0
0
0
0
1
1
0
2
1
2
1
1
0
2
0
7
0
1
0
2
0
1
2
2
1
1
1
0
0
1
1
0
0
0
3
0
1
1
0
0
0
1
0
0
2
1
2
2
0
0
1
2
0
0
0
1
2
1
1
0
1
1
0
2
0
1
1
2
1
2
0
1
2
1
0
0
1
0
0
0
0
2
1
1
1
2
0
1
2
1
2
1
0
0
0
1
2
1
0
1
1
0
2
0
2
1
1
0
0
0
1
0
0
0
2
0
0
0
1
1
1
0
0
2
1
1
1
1
1
1
0
1
0
1
1
1
1
1
1
2
1
0
1
0
0
1
0
2
1
0
0
2
0
1
2
0
1
0
2
1
1
2
1
0
1
1
0
2
0
2
0
2
1
1
2
0
2
2
1
1
0
0
2
0
0
2
0
2
1
0
0
0
0
0
2
2
0
2
1
2
1
0
0
2
0
0
0
2
0
0
0
2
2
1
2
1
1
1
0
0
2
2
0
2
0
0
1
0
1
1
0
0
0
0
1
0
1
1
2
1
1
2
1
0
1
1
1
2
0
0
0
2
0
0
1
2
2
1
2
0
0
2
1
0
2
0
0
1
0
0
2
2
0
1
0
0
1
2
0
2
0
1
0
1
1
1
0
0
2
0
2
1
1
0
1
0
0
1
1
0
1
0
0
2
0
1
0
2
1
0
1
0
1
0
0
1
0
2
0
2
2
0
1
1
1
0
0
0
2
2
1
0
0
1
1
0
0
0
1
1
0
0
2
1
0
1
0
1
4
2
0
1
2
2
1
2
0
0
2
1
0
0
2
0
3
2
1
1
1
1
1
0
1
2
0
2
0
0
1
0
0
0
0
1
1
1
1
1
0
0
0
0
2
2
3
0
0
1
0
0
1
1
1
1
1
1
1
2
1
1
0
0
1
0
1
2
1
2
1
2
1
0
2
2
1
2
2
2
1
1
0
1
1
0
3
1
1
0
2
0
1
1
0
2
0
1
0
2
0
1
2
1
1
2
0
0
0
0
2
1
2
0
1
1
1
0
0
0
0
0
1
1
1
1
1
0
1
0
0
0
0
1
1
0
0
2
0
0
0
2
0
1
1
1
0
0
0
2
1
2
1
1
0
2
0
0
1
0
0
0
0
1
3
0
2
0
2
1
0
0
2
1
2
1
0
0
2
2
1
0
1
2
2
1
2
0
0
0
0
0
0
0
0
0
0
1
0
1
2
2
0
1
0
0
2
1
0
2
1
1
2
1
0
0
2
1
0
2
0
0
0
2
2
0
0
1
0
0
0
1
2
1
0
2
0
0
2
1
0
1
0
0
1
0
2
0
2
0
0
0
2
1
0
1
1
2
0
0
0
2
2
1
1
1
1
1
0
1
0
1
1
1
0
0
1
0
2
0
0
0
1
0
0
0
0
0
1
2
0
0
1
0
2
0
2
2
1
0
0
2
2
1
0
1
2
1
1
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
2
1
2
0
0
2
2
1
0
1
1
0
0
2
0
0
0
2
0
0
2
2
1
0
7
0
2
0
0
1
2
1
2
1
2
1
2
1
0
0
2
0
2
1
2
0
1
0
1
0
1
0
1
0
0
2
2
0
0
1
0
1
0
1
0
0
2
0
1
1
2
0
1
0
2
0
1
2
2
0
2
1
0
1
0
1
2
1
0
1
2
0
1
0
2
1
2
1
0
1
1
0
0
2
0
1
0
0
0
0
2
1
1
2
2
2
0
0
0
2
1
0
1
1
0
0
1
0
0
0
2
0
2
0
2
3
1
0
0
0
1
0
1
0
0
0
2
0
2
1
0
1
1
1
0
1
0
0
1
1
1
1
0
0
0
1
0
0
2
1
0
2
1
0
1
0
1
1
2
0
0
0
0
2
0
2
1
0
0
1
0
1
1
1
2
0
1
1
1
0
2
0
0
0
2
0
0
0
0
0
0
0
2
1
1
0
0
1
0
1
1
1
0
0
1
2
0
0
0
0
2
0
0
2
0
0
1
0
1
1
0
1
1
2
0
1
0
0
2
1
0
1
0
2
0
0
2
0
0
1
3
1
0
2
1
2
2
0
0
2
2
2
2
0
0
0
0
0
0
3
2
0
2
2
1
0
1
1
0
0
2
0
1
2
3
0
1
1
1
0
0
0
1
0
0
2
1
0
3
0
0
0
0
2
1
1
0
0
1
1
1
0
0
1
0
2
1
0
2
2
0
2
0
1
0
0
1
2
1
0
0
2
0
1
1
0
0
0
2
2
0
0
2
2
0
0
1
1
0
2
0
0
1
1
0
0
0
0
1
0
2
0
0
2
1
0
0
0
2
1
0
0
1
1
1
0
0
0
0
1
1
0
0
2
1
1
1
1
2
2
2
2
0
1
0
2
0
1
0
0
2
1
2
1
0
1
1
1
0
1
0
0
0
1
2
2
2
1
0
0
1
1
0
1
0
2
0
1
0
0
1
0
0
0
2
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
1
1
1
0
1
1
0
0
1
0
0
0
0
1
1
1
0
1
0
1
1
0
2
2
0
3
0
0
1
0
1
0
4
1
1
1
3
2
0
0
1
4
1
1
1
0
0
0
1
2
0
0
0
0
0
1
1
1
2
1
0
0
1
0
0
0
1
1
0
1
0
0
0
2
2
1
2
1
0
2
2
2
0
1
1
0
1
1
2
2
0
0
0
1
0
0
0
2
1
1
2
2
1
0
1
1
0
1
1
0
1
0
3
0
1
0
1
0
0
1
2
0
1
2
0
0
1
1
2
0
0
2
0
2
0
1
2
2
1
2
1
0
1
0
0
0
1
1
2
0
0
0
1
1
0
1
1
1
2
0
0
1
0
2
2
1
0
2
0
2
1
0
0
2
1
1
0
0
0
0
2
0
2
1
1
0
1
1
0
1
1
0
0
0
0
1
0
1
2
0
2
0
2
1
2
1
0
0
1
1
1
2
0
1
0
2
0
0
0
1
0
0
0
2
0
0
2
1
0
1
1
1
1
0
0
0
0
1
0
0
2
0
1
0
2
2
1
1
0
0
1
1
0
0
1
0
0
1
0
3
2
0
2
1
0
1
0
1
0
1
2
0
0
1
2
0
0
1
1
0
1
0
1
1
1
1
0
1
0
0
1
1
4
0
2
0
0
1
2
1
0
1
0
1
1
2
1
2
0
0
0
0
0
0
0
1
1
0
2
1
0
2
0
1
1
1
2
1
0
0
1
0
1
0
2
0
2
0
1
2
2
0
0
1
0
2
0
2
0
0
2
1
1
0
1
1
1
1
1
1
0
2
0
1
0
2
1
0
2
0
0
0
0
2
0
0
1
0
0
1
1
2
0
2
0
1
1
0
1
3
0
0
1
0
1
2
0
1
2
0
1
2
0
1
1
0
1
2
0
2
2
0
1
2
0
1
0
0
1
1
2
1
0
1
2
0
0
1
0
1
0
1
1
0
1
0
2
0
1
1
0
0
1
2
1
0
2
0
0
1
1
0
1
1
1
1
0
2
1
0
0
2
0
2
0
0
1
0
0
0
0
0
3
0
0
1
0
2
3
1
1
0
0
2
0
0
0
2
2
0
0
1
0
0
2
2
2
1
0
0
0
1
0
1
0
0
1
1
0
0
0
0
3
2
0
0
2
0
1
0
2
0
1
1
0
2
1
0
0
1
2
1
0
0
2
1
3
0
1
0
0
0
0
0
1
1
1
0
1
2
1
1
1
1
2
2
1
0
2
0
1
1
0
0
2
0
0
1
1
2
1
1
1
0
0
0
1
0
0
0
2
0
1
1
1
1
1
0
1
0
0
1
0
1
1
0
1
0
0
2
0
0
1
0
1
1
0
2
0
1
1
0
0
0
2
1
1
0
2
1
0
0
1
2
1
0
2
1
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
1
0
1
2
0
1
1
0
2
2
1
1
3
0
1
2
0
0
0
2
1
2
0
1
0
1
0
2
0
0
2
0
0
2
1
0
2
0
0
1
0
2
2
0
1
0
2
2
2
0
1
1
1
1
0
2
2
1
1
1
1
0
0
0
0
0
1
2
1
0
0
2
2
0
0
0
2
0
0
2
0
1
1
0
0
2
0
2
1
2
1
1
1
1
1
1
0
0
0
0
0
1
1
1
2
2
1
0
1
2
1
0
2
1
2
0
1
1
1
0
0
1
1
1
2
2
0
4
0
0
1
0
1
0
1
0
0
1
0
2
2
0
1
2
0
1
0
1
0
2
0
0
2
2
1
1
0
1
1
1
1
1
0
0
3
1
0
0
0
0
0
2
2
1
2
0
1
0
0
1
2
2
2
0
0
1
1
0
1
1
0
0
2
0
0
1
1
0
0
1
0
1
1
2
0
2
0
1
0
0
2
1
0
0
2
0
0
2
2
0
0
1
0
1
1
0
1
0
1
2
1
1
2
1
0
2
1
0
1
3
1
0
1
1
1
0
0
0
1
2
3
1
0
2
0
0
0
2
1
0
0
2
2
1
1
1
2
1
0
1
1
1
0
3
0
0
0
0
0
1
1
0
1
1
0
1
0
0
2
2
0
4
0
0
1
2
0
1
0
2
1
0
0
0
0
0
1
1
1
1
0
2
0
1
2
0
1
0
2
0
2
0
1
2
1
0
2
0
1
2
2
0
2
1
0
0
0
2
0
1
0
1
0
0
0
1
0
2
0
2
1
1
0
2
1
0
1
1
0
1
0
0
0
2
2
1
1
2
0
0
1
0
2
0
0
0
1
0
1
0
0
1
2
1
2
1
0
1
2
1
0
1
0
1
1
1
1
1
1
0
2
1
1
0
1
2
2
1
0
2
2
0
0
1
0
1
0
2
2
0
0
0
0
2
0
0
2
1
0
1
1
1
2
1
0
0
0
0
0
1
1
1
0
1
0
1
2
0
0
2
1
0
0
2
1
1
2
1
0
1
0
1
1
0
0
1
0
0
2
1
0
2
0
1
0
0
0
2
2
0
2
0
2
0
0
0
0
3
1
1
1
0
1
0
1
2
0
1
0
1
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
1
0
2
1
0
2
2
2
0
2
0
0
0
1
0
1
0
3
1
0
0
2
1
0
1
1
2
0
0
0
0
1
1
0
0
1
1
3
1
0
1
0
1
0
0
2
1
2
1
0
1
0
0
1
0
0
3
1
1
0
0
0
1
0
0
2
1
1
0
2
0
0
2
1
1
0
1
1
0
1
4
1
0
1
1
0
3
1
2
0
1
0
1
1
0
0
2
0
0
0
1
0
0
2
1
0
1
0
0
0
1
1
1
0
1
0
2
2
1
1
0
0
0
0
0
1
2
2
0
0
1
0
0
0
0
2
1
2
0
0
0
0
1
0
2
1
2
0
1
1
1
0
1
0
1
1
1
2
0
1
0
1
1
0
1
1
1
1
2
2
0
0
0
0
1
0
2
2
1
0
0
1
1
1
1
0
0
1
0
0
0
1
1
0
1
1
1
0
1
2
0
2
0
0
1
1
2
0
1
0
1
0
1
1
0
1
0
0
1
0
0
1
0
2
0
2
1
1
3
2
0
2
1
2
0
0
2
2
2
1
2
0
1
2
1
0
1
1
0
2
0
1
0
1
2
0
1
0
0
1
0
2
0
1
0
1
0
1
0
1
0
1
0
2
0
0
0
2
1
0
1
1
0
2
0
0
1
0
1
1
0
0
0
1
0
1
0
0
2
0
0
1
0
1
0
0
0
2
1
0
0
0
0
0
1
1
0
0
0
2
1
2
0
1
0
1
0
1
1
0
0
1
0
1
1
0
1
0
0
0
0
1
1
0
0
0
0
2
1
1
1
1
2
1
0
1
0
1
0
1
1
0
1
1
0
2
3
2
0
1
0
2
1
1
1
1
1
1
0
2
0
0
1
1
2
1
1
1
0
1
2
1
2
3
0
0
1
1
0
0
0
0
0
0
2
0
0
0
1
1
0
0
2
2
2
1
0
2
1
2
2
3
0
0
0
0
0
2
0
2
1
3
0
0
1
2
1
1
0
0
1
0
1
0
3
2
1
0
0
1
1
0
2
2
2
1
1
0
1
1
1
1
1
2
3
0
0
0
2
1
1
2
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
1
0
2
2
1
1
1
2
0
0
0
1
0
1
0
1
1
0
0
2
1
1
1
2
0
2
0
0
0
0
1
2
0
1
0
0
0
0
0
2
0
2
0
1
0
1
1
1
1
1
2
1
0
1
1
0
0
1
2
0
2
1
1
2
2
2
1
1
2
2
0
0
1
0
2
1
0
0
1
0
2
1
1
2
0
1
1
3
0
2
0
1
0
0
0
2
1
0
0
0
1
0
0
0
1
1
0
0
1
0
1
0
0
0
0
1
0
0
1
0
1
0
1
0
2
0
1
2
0
0
2
1
2
0
0
1
1
1
2
1
0
1
2
2
0
2
0
0
1
0
1
0
0
1
3
2
1
2
0
0
0
0
2
2
2
2
0
2
0
0
0
1
2
1
1
2
1
1
1
2
3
0
0
0
1
3
2
2
1
1
1
2
0
1
0
0
1
0
1
0
0
1
0
0
1
0
2
3
1
2
1
1
0
0
1
0
0
2
2
0
2
2
0
1
0
0
0
1
0
1
0
0
0
0
2
0
0
1
1
1
1
2
0
0
1
0
2
0
0
2
0
2
0
2
0
1
1
0
0
0
0
0
1
0
0
1
4
1
1
0
1
0
2
1
0
2
0
1
2
1
1
0
0
0
1
0
1
0
2
0
1
0
0
1
1
0
0
2
0
0
1
1
0
0
1
2
0
0
0
0
0
1
1
2
2
0
0
4
0
0
2
1
2
1
2
1
0
1
0
1
0
1
1
1
0
2
1
1
2
1
1
1
0
0
0
2
0
1
1
2
0
0
0
0
0
0
0
2
1
3
0
2
0
0
0
1
2
0
2
0
1
0
1
1
1
1
2
1
2
0
0
2
1
0
1
1
0
0
0
0
0
0
1
2
4
0
0
0
0
0
0
1
2
1
1
1
1
1
0
0
0
2
1
0
2
0
2
1
0
1
2
0
0
4
1
1
2
2
1
0
0
0
0
2
1
2
0
0
2
0
1
1
1
2
1
0
1
1
0
0
0
0
0
0
1
1
0
0
1
0
1
2
0
1
1
3
0
2
2
0
0
2
1
0
2
1
0
1
0
1
0
1
1
0
1
2
0
1
0
0
2
0
1
1
2
1
1
0
2
0
0
2
1
1
1
0
0
1
0
1
1
1
2
1
1
2
1
0
2
0
1
2
1
2
0
2
4
1
1
2
0
0
0
1
2
2
1
0
0
0
0
0
0
1
0
1
1
0
5
0
0
0
0
1
1
0
1
0
1
1
7
0
1
1
0
1
1
2
0
2
2
1
1
0
1
2
1
0
0
3
2
0
2
0
1
0
1
2
0
1
1
1
0
0
1
0
0
2
0
0
1
2
1
0
2
2
0
0
0
1
0
3
2
2
1
2
1
2
0
0
1
2
0
1
1
2
1
2
0
2
0
0
1
0
0
0
1
2
2
0
0
1
2
0
0
0
0
3
0
1
0
0
1
1
2
2
0
0
2
2
1
0
0
1
0
0
1
1
1
0
2
0
1
0
2
1
1
1
0
0
0
2
2
2
2
0
1
0
1
0
1
0
0
2
1
0
1
0
1
0
2
1
1
0
2
1
0
2
1
0
1
2
0
1
1
2
1
0
2
0
2
2
2
3
0
2
0
1
1
0
2
0
0
1
0
2
0
1
2
0
0
0
0
1
1
0
1
0
0
0
1
0
0
2
1
2
3
0
1
1
0
0
0
0
0
3
0
0
1
0
1
0
0
1
0
1
0
2
1
1
0
1
1
2
0
0
0
2
0
2
0
0
1
3
2
2
0
2
2
1
0
2
0
0
2
2
0
0
0
0
0
1
1
2
2
1
1
2
2
0
0
0
0
2
0
2
0
2
2
0
0
0
0
1
1
0
3
0
0
3
0
2
1
4
2
2
1
2
0
2
0
0
2
2
1
1
0
0
0
0
0
0
0
0
0
2
2
1
1
0
0
1
0
1
0
0
0
1
2
2
1
0
1
2
0
0
1
0
2
1
0
1
1
1
1
0
2
0
2
0
1
0
0
2
0
2
1
0
0
1
0
1
0
0
2
1
1
0
1
0
2
1
0
1
1
0
2
0
0
1
0
1
2
0
2
1
1
2
0
1
2
1
0
1
3
0
1
0
2
1
0
1
1
0
0
1
1
2
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
2
0
0
2
1
1
1
0
0
1
0
0
0
0
1
0
0
0
2
2
2
0
2
1
1
2
2
1
2
2
1
3
1
0
0
0
0
1
0
0
0
1
1
1
1
1
0
1
1
2
0
1
1
2
0
0
0
2
1
0
1
0
2
1
0
0
1
1
0
0
2
0
2
2
0
1
0
0
1
0
2
0
1
2
1
1
0
0
0
0
1
2
1
0
1
1
0
1
1
2
0
0
1
1
1
2
1
2
0
2
0
1
1
0
1
1
1
1
0
0
1
2
0
2
1
2
1
0
2
1
2
1
0
1
0
0
0
2
0
0
2
0
2
1
0
0
0
1
1
1
0
0
0
1
1
0
2
0
2
1
2
0
2
0
1
0
0
1
0
1
2
0
0
1
0
1
2
0
1
0
0
1
3
0
0
2
1
2
1
1
0
0
0
2
1
0
1
0
2
1
0
0
1
0
0
2
2
2
1
0
1
1
0
1
2
2
2
0
0
1
0
1
2
0
2
3
1
0
1
1
0
0
0
2
1
1
0
1
1
1
0
1
1
2
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
1
1
0
0
3
0
0
1
1
0
0
0
2
0
2
0
1
0
0
2
0
1
2
0
1
0
1
1
2
0
0
0
2
2
1
0
1
2
0
1
1
1
2
1
2
2
0
2
0
1
0
3
1
2
1
0
0
1
0
2
1
0
0
0
0
0
0
1
0
1
1
2
0
1
2
0
0
1
0
1
1
0
1
0
2
0
1
0
2
0
0
1
2
0
1
1
0
0
0
0
0
0
0
1
0
0
1
2
0
1
1
1
0
0
1
0
2
1
1
2
1
1
0
1
0
1
1
0
0
2
1
0
2
0
2
0
0
2
2
0
1
1
2
2
0
1
2
1
0
0
0
2
0
1
0
4
1
1
0
2
0
0
0
2
1
0
2
1
1
1
0
3
3
2
1
0
1
0
0
0
0
1
0
0
1
0
0
1
1
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
1
1
2
2
0
2
1
1
0
0
1
0
2
0
2
2
1
2
0
1
0
2
0
1
0
0
0
0
1
1
0
0
1
1
0
0
1
0
0
2
0
1
1
2
1
0
7
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
1
1
2
1
2
1
0
0
0
0
0
1
1
0
0
1
1
2
2
0
0
1
2
0
1
0
1
0
1
0
0
1
0
2
1
1
1
1
0
0
0
1
0
0
0
0
0
1
0
1
1
1
0
0
1
2
0
0
1
1
0
1
1
1
2
0
2
2
2
2
1
0
1
0
2
0
2
1
0
1
1
1
0
2
0
0
1
0
1
1
2
1
1
0
1
1
1
1
1
2
1
0
0
0
2
0
0
1
1
0
0
0
1
0
1
0
0
1
0
2
0
0
1
2
2
1
2
3
0
0
0
0
2
0
2
0
0
2
0
1
1
2
0
1
0
0
1
2
2
3
0
0
1
0
2
2
1
0
0
0
0
0
1
2
0
0
3
1
2
1
0
0
1
2
0
0
1
1
0
0
1
0
1
2
0
0
1
0
2
1
0
0
2
0
2
2
0
1
2
0
0
1
2
1
2
0
1
2
0
1
0
0
1
0
2
0
0
1
2
0
2
1
0
1
0
1
1
2
0
0
0
1
2
0
0
0
2
0
1
0
1
0
0
2
0
0
3
0
2
1
0
0
2
0
1
1
2
1
2
0
1
0
1
0
1
0
0
0
1
0
1
1
1
1
0
0
1
0
0
2
3
1
1
2
1
1
0
0
1
0
1
0
0
1
0
2
1
1
1
0
1
2
0
0
1
0
0
1
2
1
1
0
0
0
0
1
0
2
0
1
0
1
0
2
0
0
0
1
2
0
1
0
2
2
0
1
0
0
0
0
0
2
1
0
1
1
0
2
0
2
0
1
1
2
0
0
0
0
0
0
0
0
2
1
0
2
1
0
0
1
1
0
1
0
1
0
0
0
2
1
0
1
1
1
0
1
1
0
1
1
0
0
2
2
1
0
0
0
4
0
0
0
0
2
1
2
1
0
1
0
0
1
0
2
1
3
2
0
1
0
4
0
1
0
0
0
1
0
0
1
2
0
1
1
0
1
1
1
1
1
0
2
0
0
1
0
1
1
2
2
0
0
1
1
0
1
1
1
2
0
1
0
1
3
0
1
1
2
0
0
1
1
0
1
0
1
0
2
1
0
0
2
0
0
0
0
1
0
0
0
0
1
0
1
1
2
1
2
1
2
2
0
3
0
0
0
0
0
1
0
0
0
1
3
1
0
2
2
2
0
1
0
0
1
2
1
0
0
1
0
0
0
0
2
2
0
0
0
1
2
1
0
2
1
0
0
2
0
0
0
2
1
0
0
1
1
1
1
1
0
0
1
1
0
0
0
1
1
2
1
1
0
0
2
0
0
1
1
0
2
2
2
0
0
0
0
2
0
0
2
0
0
0
1
0
2
0
0
2
2
1
3
2
1
1
0
1
0
2
0
0
2
0
1
1
2
0
2
0
1
0
0
1
0
0
0
0
1
2
1
1
0
1
0
2
0
0
1
0
1
0
0
2
0
1
1
1
1
1
2
0
1
2
0
0
2
2
3
0
1
1
2
0
2
0
2
1
0
0
0
0
2
0
1
2
1
2
0
1
1
2
0
0
3
0
0
1
1
0
1
0
0
0
1
1
0
1
0
1
0
0
2
2
0
1
0
0
1
2
1
0
0
1
2
0
2
0
0
2
2
0
3
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
2
1
1
2
0
1
0
2
0
1
1
2
1
2
2
2
1
0
1
0
0
0
0
1
1
1
0
2
1
2
1
1
0
2
0
0
2
0
1
0
1
0
0
0
3
0
0
0
2
1
1
1
0
0
2
0
1
2
0
1
1
0
0
1
1
3
0
2
1
1
0
2
1
2
0
1
0
0
0
0
2
0
2
0
1
1
0
1
2
0
0
2
2
2
0
0
0
0
1
2
3
1
0
1
2
1
1
2
0
1
0
0
2
1
0
0
0
2
0
1
0
1
1
1
1
1
2
1
1
0
2
0
0
0
2
0
2
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
1
0
1
0
0
0
1
1
0
0
1
0
0
0
1
1
1
1
1
2
1
1
1
0
1
0
2
2
2
2
2
1
0
0
0
1
0
0
3
1
2
2
0
1
1
1
3
0
1
0
0
2
0
1
0
0
0
0
2
0
0
1
2
0
1
0
0
1
0
1
2
0
0
1
0
2
1
2
1
1
0
0
1
2
1
1
1
0
0
1
1
0
2
0
1
0
0
0
1
1
2
0
0
0
0
1
2
0
0
1
1
1
0
1
0
2
2
2
2
0
0
0
1
0
0
1
3
0
1
0
2
1
1
1
0
0
1
1
5
1
0
0
1
0
1
1
2
0
1
0
1
1
2
0
0
1
0
1
1
1
2
0
1
0
0
2
0
0
0
0
1
0
1
1
0
2
0
0
0
0
6
2
0
1
0
0
0
2
1
0
0
0
2
2
2
0
0
0
0
2
0
1
0
0
0
1
1
1
1
0
1
0
3
1
0
1
1
1
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
2
1
2
2
0
2
1
0
0
2
1
1
2
1
2
1
0
1
2
1
2
1
0
1
1
2
0
1
1
0
1
0
2
0
1
1
1
2
0
0
0
1
0
0
0
0
0
1
3
1
2
2
1
2
0
0
0
1
1
0
0
0
0
0
0
1
1
2
0
1
0
0
0
0
2
0
2
1
0
2
0
0
0
1
1
2
1
0
0
1
1
1
0
0
1
1
0
2
0
0
2
1
2
0
1
1
0
0
0
2
1
0
0
1
0
1
2
0
0
2
2
1
2
0
2
1
0
1
2
1
0
0
0
1
0
0
0
1
2
3
0
1
0
1
0
1
5
0
2
0
0
0
0
2
1
0
2
0
2
2
1
1
2
0
0
2
2
0
0
1
4
0
1
1
2
1
1
2
1
0
1
0
0
1
2
3
0
0
1
1
1
1
0
0
1
0
2
0
1
1
0
1
1
0
1
0
0
2
1
0
0
1
1
1
0
0
1
0
0
0
1
1
2
2
0
1
0
0
0
0
0
1
0
0
0
0
2
0
2
2
0
2
0
1
0
1
2
0
0
2
0
1
1
1
2
1
1
0
0
0
0
1
2
0
1
0
1
2
2
0
0
2
0
1
1
1
1
1
2
0
0
0
2
2
2
0
0
2
1
2
1
0
2
2
0
0
0
1
1
0
1
1
2
2
1
1
4
0
1
0
0
1
0
2
2
0
0
1
2
2
0
0
1
0
1
1
0
0
2
2
1
0
0
1
1
2
0
0
2
0
0
0
0
0
2
0
0
1
2
3
2
1
0
2
1
1
1
0
0
0
0
0
1
1
1
0
1
0
0
2
2
1
0
1
0
0
3
1
1
2
0
1
0
0
1
0
2
1
0
0
0
1
1
1
2
1
1
1
2
1
1
1
1
0
2
0
0
0
0
0
0
0
0
1
4
1
2
1
1
0
0
1
1
0
0
0
0
2
1
1
0
0
1
1
1
0
0
0
1
2
1
2
1
0
0
0
2
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
1
0
2
0
1
1
1
0
1
2
0
0
2
1
1
0
1
2
1
0
0
2
2
0
0
1
0
0
1
0
2
1
0
1
0
1
0
1
0
1
2
1
0
2
0
0
0
1
1
0
2
1
1
0
1
1
0
0
1
0
0
1
2
0
0
0
1
0
1
1
1
2
1
2
1
0
2
2
1
0
0
0
0
1
2
0
0
0
0
0
0
2
1
1
0
1
0
3
0
0
0
1
1
1
0
0
2
1
0
0
1
0
3
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
2
0
2
0
2
0
1
0
0
0
0
1
2
0
0
1
0
1
2
0
0
2
0
1
2
2
0
1
0
0
0
0
2
2
2
0
2
2
1
3
0
2
2
0
1
0
2
0
2
1
0
1
0
0
1
0
0
2
0
0
0
2
0
0
0
2
2
1
2
0
1
0
1
0
1
1
1
2
1
1
2
2
1
1
0
0
0
1
0
1
1
1
0
0
0
1
0
2
0
1
0
0
0
0
1
0
0
0
0
1
0
1
1
0
2
0
0
3
2
1
1
0
1
0
0
1
1
1
0
1
1
1
0
1
0
2
0
0
0
0
3
1
0
1
0
0
1
0
1
2
2
2
1
1
0
1
0
0
2
2
2
1
0
2
1
0
0
0
0
1
2
1
0
1
2
2
0
0
1
1
0
1
2
2
0
0
0
0
1
1
2
1
0
2
1
1
0
1
2
2
1
2
2
2
0
0
1
0
1
0
0
2
2
1
2
0
0
0
1
0
0
0
1
0
1
0
0
1
0
1
1
1
1
1
2
0
0
2
0
0
2
0
2
1
0
0
0
1
0
1
0
2
0
1
2
0
2
0
0
0
0
0
0
0
4
1
1
2
0
0
0
2
0
0
2
2
1
0
1
2
0
2
1
1
3
1
0
2
0
0
0
2
1
0
0
0
0
1
2
1
0
1
0
0
0
2
2
1
0
0
0
0
0
1
0
0
2
2
2
0
1
2
1
0
1
0
1
1
5
2
1
0
0
2
0
0
0
1
0
1
0
1
1
2
0
0
0
0
0
1
0
0
1
0
0
1
2
2
0
2
0
1
0
1
2
2
0
1
1
0
0
2
2
3
1
2
0
1
0
0
0
1
1
0
2
0
0
1
1
2
2
0
0
0
1
0
0
1
2
1
2
0
2
0
2
1
0
1
1
0
2
0
2
0
0
3
2
1
1
1
0
2
3
1
1
1
0
1
0
2
1
1
0
1
0
1
2
1
1
1
0
0
0
0
1
0
0
0
2
1
1
0
2
0
9
0
0
0
0
0
0
1
1
1
2
1
0
2
2
0
2
2
1
0
1
1
0
1
0
1
2
0
1
1
2
2
1
1
0
0
0
1
2
0
0
0
1
0
0
3
1
0
0
1
1
2
1
0
1
0
1
0
0
1
0
2
0
3
0
1
0
1
2
2
1
1
1
1
2
2
0
1
2
1
1
1
0
2
0
2
2
1
0
1
1
0
0
2
1
0
0
0
3
1
1
0
0
0
1
0
2
1
1
0
2
0
0
1
0
1
0
0
1
1
0
2
2
2
1
1
0
1
0
1
0
1
2
2
1
1
0
2
0
3
0
1
1
0
2
0
0
0
0
1
1
0
0
2
0
1
0
2
0
2
3
0
1
0
2
1
0
1
0
0
0
1
1
1
1
3
0
1
2
0
1
1
1
1
0
2
2
1
0
2
1
1
1
1
3
0
1
0
2
2
1
0
2
1
0
1
0
0
1
2
0
0
2
0
0
0
1
0
2
0
1
1
0
1
2
2
0
2
0
1
2
0
1
0
0
1
0
0
0
0
2
0
1
2
0
0
1
0
1
1
2
0
0
0
1
1
0
0
0
0
0
1
1
1
1
1
0
1
1
1
1
1
0
1
1
0
1
0
1
1
1
2
1
1
0
2
0
1
1
1
1
0
1
1
0
0
1
2
1
1
2
1
3
0
2
1
0
1
0
0
0
1
1
2
1
2
0
2
1
0
0
0
1
0
0
1
2
0
0
0
0
0
2
0
0
1
0
1
2
0
0
1
2
0
0
1
0
2
1
1
1
0
0
1
2
1
1
1
0
2
2
2
2
1
2
0
1
0
0
2
2
1
0
0
2
0
0
0
1
0
1
2
2
1
1
1
2
1
1
0
2
0
0
1
2
0
0
1
1
0
4
2
1
2
2
0
1
0
0
1
0
0
1
0
0
0
1
2
0
1
0
0
4
1
0
0
0
2
1
0
1
1
1
0
1
0
1
0
1
0
1
0
0
1
1
1
0
2
0
0
1
1
0
2
2
1
2
0
2
1
2
0
0
0
1
0
0
0
1
2
0
1
1
3
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
1
1
2
0
0
0
1
1
0
0
1
2
2
0
1
1
0
1
1
1
1
1
1
1
1
1
0
1
2
0
1
2
0
3
2
0
1
0
2
1
2
0
2
1
1
1
0
0
0
0
0
0
2
0
0
2
1
0
1
3
2
0
1
1
0
0
2
0
0
0
2
0
0
1
0
0
2
0
1
0
1
2
0
1
2
1
1
1
1
0
0
2
1
0
1
0
0
1
1
0
2
2
0
1
2
0
0
2
0
0
0
2
0
1
0
1
1
0
0
2
0
1
1
0
2
2
1
2
1
0
0
1
1
0
0
0
0
0
2
0
0
1
0
0
0
1
1
2
0
1
1
1
0
0
1
0
1
2
0
0
0
1
0
1
0
1
1
1
1
0
0
0
1
1
2
2
0
1
2
1
2
1
1
0
2
1
0
2
1
0
0
2
2
1
1
2
2
0
2
0
2
1
1
2
1
1
2
0
2
1
0
1
2
1
0
0
1
0
0
0
1
0
1
0
0
0
1
3
0
0
2
1
2
1
0
0
0
0
2
1
1
0
0
0
0
2
1
1
0
1
1
0
0
2
0
0
1
2
1
0
0
0
0
0
0
1
0
0
1
0
0
2
2
0
1
2
1
2
2
2
1
2
0
1
0
3
0
1
1
0
1
2
1
1
4
1
1
2
0
1
0
0
0
0
0
1
0
0
2
2
0
0
0
1
2
1
2
2
0
2
1
1
2
1
2
0
1
0
2
1
1
1
0
0
1
1
1
0
0
3
0
1
0
2
0
1
0
1
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
2
2
1
0
1
0
3
0
0
1
1
1
0
0
0
1
1
0
1
0
3
1
1
0
1
1
1
2
0
2
0
1
1
2
0
1
2
2
2
2
1
0
1
0
2
1
2
0
1
1
2
2
1
0
1
0
0
1
2
0
0
1
1
0
2
1
0
0
1
1
2
0
0
2
1
2
1
0
0
1
0
1
2
0
2
0
2
0
1
1
2
2
0
0
0
0
2
3
1
1
0
0
0
1
0
1
2
1
0
1
1
0
0
0
0
1
1
0
0
0
1
1
2
1
0
0
2
1
2
1
0
2
1
1
1
1
1
0
2
0
0
2
0
0
1
1
2
1
2
0
0
1
0
1
0
0
0
0
1
1
1
1
2
1
3
0
0
0
0
2
1
2
0
2
2
0
1
1
0
0
0
1
1
2
2
1
0
1
0
0
2
1
1
0
1
0
2
2
0
0
0
0
2
0
1
0
1
1
1
0
2
2
1
1
1
0
0
0
2
2
0
1
0
2
1
0
2
1
1
1
2
0
0
2
0
0
2
1
1
2
1
1
0
2
1
1
0
1
1
1
1
2
0
0
0
1
2
1
0
2
1
0
2
0
0
0
0
1
2
0
1
0
1
0
1
4
0
0
0
0
2
1
1
0
1
2
1
0
0
0
0
2
1
0
2
0
0
0
0
2
0
2
2
1
2
1
2
0
2
0
0
0
0
0
0
1
1
1
0
1
1
0
0
0
1
0
2
0
2
1
2
0
0
0
0
1
2
2
1
0
1
0
2
0
0
2
0
1
0
1
2
0
0
0
2
0
2
1
1
0
1
2
0
0
1
2
0
1
0
0
2
0
1
0
1
0
0
0
1
0
1
1
1
1
1
2
1
2
0
0
1
0
0
0
1
0
1
1
1
1
1
0
1
0
1
1
0
1
0
0
1
1
0
0
0
0
0
0
1
1
1
1
0
0
1
0
1
0
2
1
1
0
0
0
2
2
0
2
1
1
0
0
0
0
1
2
2
1
1
3
0
1
2
0
1
0
2
1
0
2
0
0
2
2
1
2
0
0
2
0
2
0
0
1
0
2
0
1
0
0
0
0
1
1
0
3
1
1
0
2
1
0
0
1
0
0
1
0
1
0
0
1
1
0
0
0
0
0
2
1
2
0
0
2
0
2
1
0
2
0
2
1
1
0
0
1
1
1
2
0
0
1
0
1
0
0
2
1
0
0
1
2
2
0
1
3
0
0
0
2
0
2
1
0
0
1
0
1
0
0
0
0
1
1
1
2
2
0
0
0
4
0
2
0
1
0
1
1
2
2
0
0
1
1
1
1
0
1
2
0
1
2
1
2
1
0
2
0
1
1
0
1
0
0
1
0
0
0
1
0
1
2
1
1
1
0
1
1
0
1
1
4
2
0
0
0
0
0
1
0
2
2
1
1
1
0
1
0
0
0
2
2
0
1
0
0
0
0
1
2
1
0
2
0
0
2
1
1
2
1
1
0
0
1
1
0
0
2
1
1
0
1
0
0
1
1
1
0
0
2
2
1
2
0
3
0
0
0
1
1
0
2
1
0
0
0
0
1
1
0
2
1
1
0
2
0
0
2
0
2
0
0
1
0
0
2
0
4
0
2
0
0
2
0
0
0
2
0
1
0
1
2
0
1
1
2
1
0
0
0
0
2
1
1
0
1
2
2
0
0
0
1
0
1
0
2
1
0
1
1
2
0
2
1
1
2
2
0
1
0
1
0
0
1
2
2
1
0
0
0
0
0
0
1
1
0
1
0
0
1
1
0
0
2
0
1
0
1
4
0
2
1
1
1
2
0
0
0
0
1
0
0
0
0
2
1
1
0
0
2
0
1
0
1
0
0
1
0
0
0
1
1
2
0
2
1
1
0
0
0
2
0
0
0
1
0
1
0
1
4
2
0
1
0
0
2
0
2
0
1
2
1
0
2
1
0
0
2
0
0
0
0
2
2
0
2
0
1
1
1
1
0
1
1
0
1
0
1
5
0
0
1
0
0
0
2
2
2
2
1
0
0
2
1
0
0
1
2
2
1
1
0
1
1
1
1
1
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
1
1
0
1
0
0
0
1
0
1
2
1
0
0
1
1
2
1
0
2
2
2
1
0
1
2
0
0
1
0
2
2
2
2
0
0
2
0
0
1
2
1
0
0
0
1
1
0
1
0
0
2
0
0
1
0
2
1
0
0
0
2
1
1
1
0
0
0
0
0
0
1
2
0
1
0
0
0
1
0
0
0
2
2
0
0
1
0
0
1
0
0
1
2
2
0
1
0
1
1
1
0
0
2
0
2
1
0
1
1
2
1
2
2
0
1
0
1
0
1
0
2
1
0
1
1
0
0
0
1
0
0
2
0
2
1
1
0
0
1
1
1
2
0
1
1
0
1
1
2
2
0
2
1
2
2
1
0
0
0
1
1
2
2
1
2
1
1
2
0
0
1
0
1
0
0
0
0
1
2
2
0
0
0
0
0
1
1
1
2
0
0
0
1
1
0
0
0
2
0
0
1
3
0
2
2
2
1
0
1
2
0
1
1
0
1
0
1
0
0
1
0
1
0
0
2
1
1
0
0
1
0
1
0
2
0
2
0
2
1
1
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
2
0
1
0
0
1
1
1
1
0
0
1
2
1
1
0
2
0
0
0
0
1
0
0
1
0
3
0
0
1
0
2
2
0
2
2
1
1
0
3
0
0
0
0
1
0
2
1
0
0
0
2
0
1
1
2
1
0
1
0
1
0
0
1
0
0
1
0
1
3
0
1
0
0
1
2
0
2
1
0
2
1
0
2
0
1
2
2
0
1
2
1
1
1
2
0
3
0
0
2
1
2
2
0
2
0
1
0
1
1
2
0
0
0
3
0
0
2
0
1
0
2
1
2
1
1
0
2
1
2
0
1
2
2
0
1
0
0
1
0
0
1
1
0
0
1
0
0
0
0
1
0
2
1
2
1
0
0
2
0
0
2
0
1
2
2
0
0
0
0
1
2
0
2
0
2
1
0
0
0
0
0
2
1
2
1
1
2
1
1
0
0
0
0
0
0
0
3
1
0
0
0
0
0
1
1
0
1
1
0
0
0
0
2
0
2
2
2
3
1
1
2
0
5
0
1
0
2
1
1
1
1
0
2
2
0
2
2
1
0
2
2
0
2
2
1
1
1
1
1
1
0
1
1
0
0
2
0
2
2
1
0
0
2
1
0
0
2
1
1
2
1
2
2
0
0
0
1
0
2
0
1
0
1
1
1
2
0
1
1
1
1
1
2
0
1
0
1
1
0
0
0
0
0
0
2
1
2
1
0
1
1
0
2
2
0
1
1
0
1
0
1
1
0
2
1
1
0
0
1
0
1
0
0
0
1
1
0
1
1
0
0
1
0
0
0
1
0
2
1
0
0
2
2
2
0
2
2
0
0
0
1
1
2
1
0
2
1
0
1
0
0
1
0
1
2
2
0
0
1
0
0
2
1
0
1
0
1
2
0
0
0
0
1
0
0
0
0
1
1
2
0
1
1
0
0
0
0
0
1
1
0
2
1
1
1
2
2
2
0
0
0
1
2
1
2
3
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
1
0
0
0
2
1
1
2
1
0
1
2
2
0
0
0
2
1
0
2
2
2
0
0
0
1
2
0
3
2
2
2
1
0
2
2
0
1
0
0
1
0
1
1
0
2
0
0
2
0
0
2
1
1
1
2
2
0
0
0
2
0
0
2
0
0
1
0
1
1
0
0
1
0
2
1
2
0
0
0
0
0
2
1
1
0
0
0
0
0
1
0
1
2
0
0
2
2
1
2
2
1
2
0
1
1
2
1
1
0
2
1
0
0
1
2
1
1
2
0
2
1
0
0
0
0
1
0
0
1
2
1
1
0
1
1
1
2
1
0
0
1
0
2
1
1
2
1
1
0
0
1
1
1
1
0
0
1
0
1
2
1
0
2
0
0
0
1
3
0
0
1
1
1
0
0
1
1
0
1
2
0
1
2
0
1
0
0
1
0
1
2
0
1
2
1
0
1
0
1
2
1
1
0
1
0
0
1
0
1
0
0
1
2
0
0
0
1
1
2
0
0
0
2
0
2
0
0
2
2
1
1
0
2
1
1
1
1
2
1
0
1
2
1
1
0
1
2
2
0
1
0
2
2
0
2
1
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
1
2
1
0
2
2
0
0
1
0
0
0
0
2
0
0
2
4
2
0
0
2
0
0
0
0
1
0
2
2
0
1
1
0
0
0
1
2
1
0
0
2
0
0
0
2
1
1
0
0
0
1
0
1
0
2
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
2
0
0
0
1
0
1
1
2
0
1
0
2
2
0
1
2
0
0
0
1
0
0
2
0
0
2
1
0
1
0
1
1
2
1
1
2
2
2
1
1
0
1
0
1
2
2
0
0
0
1
0
1
0
2
0
2
2
2
1
0
0
0
0
1
1
0
2
0
0
2
0
0
2
0
2
0
2
0
2
2
1
0
0
0
0
2
2
0
0
1
1
1
0
2
0
1
1
1
1
2
0
1
3
0
1
0
1
1
1
0
1
0
2
2
1
0
1
0
0
1
0
1
1
0
2
0
1
1
0
0
1
0
1
1
0
1
0
0
0
2
1
2
1
0
1
2
0
1
2
1
1
4
2
0
1
0
1
1
2
0
0
0
2
0
0
0
1
0
2
0
0
1
2
0
0
3
3
0
0
1
2
1
1
0
2
0
0
1
0
3
1
2
1
2
1
1
0
1
1
2
2
0
1
1
1
1
1
2
2
2
1
0
0
1
1
2
1
0
1
0
0
0
0
2
0
0
2
2
2
2
2
1
2
0
0
0
1
2
2
0
0
1
2
0
0
0
2
0
1
1
0
2
3
1
1
2
0
2
3
1
1
0
2
2
0
1
0
1
0
0
1
2
1
0
0
0
2
1
2
0
0
0
2
2
0
2
1
0
1
0
0
1
0
2
0
3
1
1
0
2
0
0
1
2
0
0
2
1
1
0
2
1
1
1
0
0
1
1
0
1
0
0
0
0
0
3
1
0
0
1
2
0
0
1
0
2
0
0
2
0
1
1
0
2
1
1
1
2
0
0
0
1
0
1
1
2
1
0
2
0
1
0
1
0
2
1
1
2
1
0
0
2
0
0
1
2
1
0
0
0
2
0
0
2
1
0
1
0
2
0
0
1
2
0
0
2
1
2
1
2
0
1
0
0
1
0
1
2
2
1
1
2
1
0
1
0
0
2
2
0
0
2
0
2
0
0
2
2
0
0
2
0
2
1
1
0
1
2
0
2
2
0
1
0
1
1
0
1
0
1
0
2
1
0
0
2
1
1
2
0
0
2
0
0
0
1
1
1
0
1
0
1
0
2
0
0
1
0
1
1
1
1
0
0
0
1
1
0
0
0
1
1
1
1
2
0
0
2
1
0
0
1
1
1
2
0
0
0
1
0
0
0
1
1
0
0
1
1
3
0
0
1
0
1
0
0
1
0
1
0
0
1
1
0
0
0
1
0
1
1
1
0
0
2
2
1
0
1
0
2
0
1
1
1
0
0
1
1
0
1
0
1
1
2
1
2
0
2
1
0
1
2
3
1
2
1
0
1
0
0
0
1
1
0
0
2
2
0
2
1
2
1
0
0
0
2
0
0
2
0
1
0
2
1
1
1
0
1
0
1
0
0
0
1
1
2
1
0
1
2
1
1
0
0
2
2
0
0
1
3
0
1
0
0
2
2
1
1
0
1
0
2
0
0
0
0
0
1
0
2
0
2
0
1
2
2
0
0
2
1
2
0
0
1
1
1
1
0
1
1
0
1
0
1
2
1
0
2
0
2
1
0
0
0
1
0
0
1
1
1
0
0
1
0
0
2
2
0
2
1
1
0
0
1
1
0
2
0
2
0
2
1
0
1
0
1
0
0
1
1
0
0
1
0
2
2
0
2
0
0
3
1
1
2
1
1
0
0
1
0
0
0
2
0
1
2
0
0
1
2
2
0
2
1
1
1
0
0
2
1
1
1
1
0
0
1
1
0
1
0
0
0
0
1
1
0
1
2
1
2
1
1
0
0
2
0
1
1
0
2
0
2
0
1
0
0
0
0
1
1
1
0
2
1
0
1
2
4
0
3
0
0
0
2
0
2
1
2
0
2
0
1
2
1
1
1
0
1
0
0
0
0
0
2
0
0
0
2
0
2
1
4
3
0
1
0
2
1
2
1
0
1
0
2
1
2
1
2
0
0
1
0
0
0
1
1
1
2
1
2
0
3
1
1
2
0
0
2
0
0
2
0
0
2
1
1
0
3
2
2
1
0
0
1
1
0
0
0
2
0
0
1
0
1
1
0
1
2
0
0
2
0
2
2
2
1
3
1
1
0
3
0
0
0
1
2
2
2
0
2
0
0
1
1
1
2
2
0
0
2
1
1
0
2
1
0
0
0
0
0
0
1
2
1
0
1
2
0
1
0
1
1
1
1
2
0
0
1
0
1
1
0
0
0
0
2
0
2
0
0
1
0
0
1
0
0
0
0
2
0
0
0
1
2
1
0
0
0
0
0
0
1
1
1
1
0
0
0
2
0
1
0
0
0
1
1
2
1
0
0
1
2
1
3
1
0
0
0
1
2
1
0
0
2
1
1
1
2
0
1
1
0
2
0
0
1
0
1
0
0
1
0
1
0
1
2
1
1
2
1
0
2
0
1
1
1
0
1
1
1
2
2
1
0
1
0
2
1
2
0
1
2
0
2
1
1
2
0
1
0
1
0
2
0
0
0
0
1
1
0
2
1
0
1
0
2
1
1
0
2
1
2
0
0
0
1
1
0
1
0
1
2
2
1
1
0
2
2
0
1
0
0
2
1
1
0
0
0
1
2
0
1
1
2
0
1
2
3
0
0
1
0
0
3
1
0
1
1
2
2
0
2
1
0
0
0
2
1
1
0
0
0
1
2
0
1
0
0
1
1
0
0
0
1
2
0
1
0
1
0
1
1
0
0
0
3
0
0
1
0
0
2
0
3
2
0
2
1
1
0
0
1
0
2
2
1
1
1
1
1
0
1
1
1
0
1
0
2
1
2
1
0
1
1
8
0
1
1
0
0
2
0
1
0
1
2
2
2
1
1
0
0
0
0
2
1
0
2
1
1
1
1
2
1
0
0
2
2
0
0
2
1
2
2
0
0
0
0
0
0
0
0
0
1
2
1
1
2
1
0
0
0
2
2
1
1
0
0
1
0
0
2
2
2
1
0
0
0
2
2
0
0
1
2
0
1
0
0
3
0
0
0
0
1
1
1
1
0
1
2
0
2
0
1
1
0
2
1
2
2
1
1
0
1
1
2
1
1
0
0
0
1
1
1
1
0
1
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
2
0
1
1
2
1
0
0
1
0
0
1
1
2
1
0
1
0
0
1
2
1
0
0
0
1
1
0
0
1
1
2
2
0
0
1
3
1
0
1
1
0
1
0
1
0
0
0
1
0
0
0
1
0
0
2
0
0
1
1
1
0
0
2
0
0
1
0
0
0
1
0
1
0
0
0
1
0
2
1
1
2
1
4
2
1
0
1
0
0
1
2
1
0
0
1
1
0
0
2
0
0
0
2
0
1
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
1
1
0
0
1
0
0
2
0
0
0
1
0
0
1
1
3
0
1
0
2
1
1
0
2
1
0
1
2
3
1
1
2
1
5
2
0
1
0
0
0
1
1
0
1
2
1
1
0
1
2
0
1
0
1
2
0
1
2
1
2
1
1
1
1
1
1
0
2
1
1
0
1
1
1
0
2
1
0
2
0
0
0
1
0
0
1
2
1
1
0
0
3
0
0
0
0
0
1
1
1
0
2
2
0
1
1
1
0
0
2
2
0
1
0
0
0
1
1
1
1
1
2
1
2
0
1
2
0
1
0
1
0
0
0
0
2
1
0
0
0
0
2
0
1
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
1
2
0
1
1
1
4
0
0
0
0
2
0
2
2
1
0
1
0
2
1
0
0
0
0
1
2
2
0
1
1
1
2
3
2
0
1
3
0
0
1
2
0
0
0
0
0
3
0
1
0
1
2
1
0
0
0
0
1
1
0
2
2
0
1
1
0
2
2
1
1
1
3
2
0
1
0
1
2
1
2
0
0
0
2
2
0
0
2
1
0
1
1
2
0
3
3
0
1
1
1
1
1
0
1
0
0
2
1
2
1
2
1
0
2
1
0
1
2
0
0
1
2
2
1
0
1
4
1
1
0
1
2
1
1
0
0
0
0
0
0
1
0
2
0
1
1
0
1
2
0
0
2
1
1
1
1
1
1
0
1
1
0
1
1
1
1
1
0
1
0
2
2
0
1
1
1
1
0
0
0
0
1
2
1
0
0
0
1
2
1
0
1
2
3
0
2
1
0
2
1
0
1
2
1
0
1
0
0
0
2
1
0
1
1
1
0
0
0
0
1
2
0
0
1
1
1
1
1
1
2
1
2
2
1
0
2
2
0
2
0
1
0
0
0
1
1
0
1
1
1
1
2
2
3
0
1
1
1
2
2
2
1
1
0
0
1
0
2
1
2
1
2
0
1
0
1
0
1
0
0
1
0
2
2
1
0
2
3
2
2
0
0
1
2
0
2
0
0
0
0
0
0
0
0
1
1
0
0
2
0
1
0
0
3
1
0
0
2
0
1
0
0
2
0
0
2
1
0
0
0
0
1
0
1
0
1
0
1
0
0
2
1
1
1
1
0
0
3
0
0
0
0
0
0
0
0
1
1
0
2
0
0
1
1
1
0
2
2
3
2
0
0
0
0
0
0
0
0
1
1
1
3
0
0
2
2
4
1
0
1
0
2
2
0
2
0
0
0
2
1
1
0
1
0
2
0
1
2
1
1
1
1
2
2
0
1
1
1
1
1
2
2
1
1
0
0
0
1
0
1
2
1
2
1
0
0
1
0
1
2
0
1
2
0
0
2
0
1
1
1
1
0
0
2
2
2
0
2
1
0
2
0
0
0
0
2
0
0
0
1
1
0
1
1
2
2
1
2
2
2
0
1
0
0
2
1
2
1
0
1
0
1
0
0
1
1
2
1
0
1
2
0
0
0
1
0
8
0
2
0
0
0
2
2
1
0
0
1
1
2
1
1
2
1
1
0
0
1
2
0
2
1
0
2
1
0
0
1
0
0
1
0
1
1
1
1
2
1
1
2
0
2
1
0
0
1
1
2
0
2
2
2
1
1
2
0
2
1
1
2
1
1
1
1
1
0
2
0
2
0
0
0
0
2
1
2
1
0
2
1
0
1
0
2
2
0
0
1
0
2
1
1
1
2
2
1
2
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
2
1
0
1
1
2
1
1
0
2
0
1
0
0
1
1
0
5
1
1
0
0
3
0
0
0
2
0
0
0
0
1
0
1
2
0
0
1
2
2
0
2
0
0
1
0
0
1
1
0
2
1
2
2
0
1
1
1
0
2
1
1
2
0
0
0
1
0
0
1
1
0
0
1
1
1
0
1
2
0
1
0
0
1
1
0
1
1
2
1
1
0
0
1
0
1
2
0
1
1
2
3
1
0
0
0
1
2
4
1
1
0
1
1
0
2
0
1
2
0
0
0
1
0
2
0
2
0
1
1
1
1
2
0
1
0
0
0
0
0
2
1
3
3
0
1
1
1
1
1
0
1
2
0
3
2
0
0
0
1
1
0
0
0
0
2
1
0
0
2
0
1
1
3
2
1
0
1
0
2
1
1
1
0
0
1
1
0
0
2
2
1
1
1
1
0
1
1
0
1
1
2
1
1
0
2
0
0
0
0
1
2
0
0
2
2
2
1
2
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
1
2
1
0
2
0
1
0
1
2
1
2
0
0
1
0
0
0
1
1
0
0
4
2
1
0
0
0
0
0
1
1
1
0
0
1
1
0
0
0
3
1
2
1
0
1
0
0
2
3
2
1
0
3
1
0
0
1
1
0
1
2
1
1
1
2
1
0
2
1
0
0
0
1
0
1
3
1
1
2
1
0
0
0
1
2
0
1
1
1
0
0
0
1
1
0
0
2
0
0
2
1
0
1
1
0
1
0
1
2
3
0
1
2
0
2
0
2
0
1
1
0
0
1
1
0
0
2
0
0
1
2
0
0
2
1
0
2
0
1
3
1
0
1
0
2
0
1
1
0
1
1
0
0
1
1
2
0
0
0
0
1
0
1
0
0
0
1
0
1
0
1
1
3
2
0
0
0
2
1
0
1
0
0
0
0
1
0
0
0
1
4
0
1
1
0
0
1
0
1
2
1
1
2
0
1
0
0
0
0
0
2
2
0
1
1
2
1
0
1
0
0
2
0
0
2
0
1
1
0
2
0
0
1
2
0
0
0
0
2
0
0
0
1
1
2
1
2
0
0
0
0
1
1
1
0
2
1
0
2
1
0
1
1
2
2
0
2
0
1
1
1
2
0
1
1
1
1
0
0
1
2
1
0
0
2
0
1
1
2
1
1
1
0
1
2
2
1
1
0
0
0
0
0
2
0
0
0
1
2
0
2
0
1
0
0
1
2
2
2
2
1
1
1
1
0
0
1
1
1
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
1
0
3
0
1
0
1
1
1
2
1
0
0
1
0
0
2
0
0
0
1
0
0
0
2
0
0
1
0
1
1
0
2
1
0
1
1
0
1
1
0
1
1
2
0
2
0
1
1
0
0
0
2
0
1
1
2
1
1
2
1
1
1
4
1
0
2
1
0
1
0
1
0
2
1
1
0
0
1
0
1
1
2
0
0
0
1
0
0
0
0
1
2
1
0
0
0
1
1
0
1
0
2
2
1
1
0
0
0
1
1
0
1
0
2
1
2
2
1
0
2
0
0
0
1
1
2
0
0
1
1
1
0
0
1
1
0
2
0
2
1
0
1
2
2
0
0
0
2
0
0
2
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
2
0
0
1
0
0
2
1
1
0
2
1
0
0
0
1
0
0
1
0
1
1
0
0
0
0
1
1
1
2
0
0
1
1
0
2
0
0
0
0
0
1
1
1
0
2
2
3
1
0
2
2
3
3
0
0
0
0
2
0
2
2
2
1
1
1
0
1
1
1
1
0
1
2
2
0
1
1
0
0
2
2
2
1
0
2
2
2
1
0
1
0
1
1
1
0
2
1
1
1
0
0
0
1
0
1
2
1
0
2
1
0
1
1
1
0
0
4
0
1
2
0
0
0
2
1
2
1
2
0
0
0
0
0
0
0
2
1
0
1
1
1
2
0
1
1
2
0
2
0
0
0
1
0
1
8
1
2
0
1
0
0
1
0
1
1
4
1
0
1
0
1
1
0
2
0
0
2
1
1
1
2
1
0
41
0
0
1
2
2
1
2
1
0
2
1
2
1
1
2
2
1
0
2
0
1
2
0
1
0
1
1
0
2
2
0
1
0
0
1
1
0
1
0
2
0
1
0
1
2
0
0
2
0
0
0
0
1
1
0
0
0
1
0
0
1
0
1
0
1
0
0
0
2
1
0
2
1
0
1
1
0
1
0
1
0
1
1
0
0
0
0
2
2
0
1
0
1
0
2
0
0
0
1
2
1
2
0
0
0
1
0
1
0
0
4
1
2
1
1
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
2
0
2
1
0
1
2
1
0
1
0
2
0
0
0
0
1
2
1
0
2
0
0
1
1
1
0
0
0
2
2
2
2
0
1
0
1
1
0
0
0
2
0
1
1
1
0
0
1
2
1
0
1
1
2
0
0
2
0
2
1
3
0
0
0
1
0
0
2
0
0
2
1
1
1
1
2
1
0
0
1
2
0
1
0
0
2
1
0
0
1
0
1
0
2
0
2
0
1
2
2
0
2
0
0
1
1
2
2
0
1
2
2
0
2
1
2
2
1
1
0
0
0
0
0
1
0
1
1
1
0
2
1
2
1
2
0
1
0
0
2
0
0
0
1
0
0
1
0
1
1
1
2
2
1
0
0
0
0
1
0
0
0
1
1
0
1
1
2
2
1
0
2
1
1
0
0
1
2
0
2
1
1
0
0
0
2
1
1
1
0
2
1
0
0
0
0
0
1
0
2
2
1
1
2
0
1
0
0
0
3
0
0
0
1
4
1
2
2
2
0
0
1
1
3
0
1
1
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
3
1
1
0
0
1
0
0
1
1
0
1
0
1
1
1
1
0
2
0
0
1
2
1
0
0
1
0
1
1
1
1
1
0
0
2
0
0
0
0
1
1
1
1
0
0
1
1
2
2
3
1
1
3
1
1
0
2
2
0
0
0
1
2
2
1
1
2
0
2
0
0
0
0
0
0
1
0
0
1
1
1
2
2
1
0
0
0
2
2
1
0
1
5
1
0
0
1
0
0
0
0
0
0
1
2
0
1
0
2
2
1
1
2
1
0
2
2
0
1
0
0
0
2
0
1
0
1
1
2
0
0
2
0
1
0
0
1
1
1
1
2
0
1
1
0
1
1
0
2
2
1
2
2
2
1
0
0
1
1
0
1
1
1
0
3
1
1
1
0
1
1
1
0
0
0
1
1
0
0
2
2
0
2
2
1
2
0
1
1
1
0
1
1
0
1
1
0
0
2
0
1
2
1
0
1
0
2
0
0
0
1
0
0
0
0
2
1
0
2
0
0
0
2
1
0
1
1
2
0
0
2
1
2
1
2
2
0
0
2
1
1
2
0
0
2
2
2
1
1
1
1
0
0
0
0
2
2
2
0
2
1
1
3
0
2
1
0
0
0
1
1
0
1
0
0
0
0
1
1
0
0
1
0
1
0
0
0
1
1
1
0
1
0
0
2
2
0
1
0
1
1
2
2
1
2
0
0
0
0
1
2
0
0
2
1
0
0
1
0
1
2
0
2
2
2
0
0
1
1
0
1
1
1
4
0
0
1
0
0
2
2
1
2
0
1
0
0
0
2
0
0
0
0
2
0
1
1
0
2
3
2
1
0
2
2
3
1
0
1
0
1
2
0
1
0
2
1
0
1
0
1
1
2
0
0
0
0
1
1
2
0
1
0
0
1
1
1
1
1
1
0
0
0
1
1
1
2
0
2
0
1
1
2
0
0
0
2
0
1
0
2
0
1
0
0
0
0
0
1
0
2
2
1
0
0
2
0
2
2
0
1
1
0
1
0
1
0
0
1
2
2
1
0
2
0
1
1
1
0
0
2
0
1
2
2
1
2
0
0
0
1
2
2
1
0
1
1
2
1
2
0
2
0
0
0
0
1
0
3
2
0
1
0
0
1
2
0
0
0
1
0
1
1
1
1
2
1
0
0
1
0
1
0
2
1
0
0
2
1
0
0
1
0
0
1
1
2
0
0
2
1
0
2
3
1
0
1
1
1
2
1
1
1
1
1
0
1
0
0
1
0
1
1
2
0
0
0
1
1
0
0
1
1
1
0
2
0
2
1
2
1
1
1
1
1
0
0
0
0
3
1
1
1
1
2
1
0
1
1
0
1
1
0
1
1
0
0
0
1
1
0
0
1
0
0
0
2
0
1
2
0
0
0
1
1
2
0
0
0
1
0
1
1
1
1
2
5
2
0
0
2
1
1
2
0
0
0
1
2
0
0
1
0
2
1
1
0
0
1
2
2
2
1
0
1
0
2
0
0
0
1
0
3
1
1
0
0
1
1
0
0
2
1
0
1
1
1
0
1
0
1
0
4
2
0
1
0
1
0
2
0
1
1
0
0
0
2
0
0
0
0
2
0
1
0
1
0
0
0
2
2
1
0
1
0
0
1
2
0
0
1
1
1
1
2
4
0
1
2
0
0
0
1
0
1
1
0
0
1
1
1
2
1
2
1
1
0
1
1
0
0
0
0
1
0
0
1
1
0
0
0
2
2
2
1
0
0
1
0
0
0
2
2
1
1
0
1
1
4
1
1
1
0
0
0
2
0
0
1
0
1
1
0
0
1
2
1
1
0
0
0
1
2
1
1
0
0
1
1
2
0
2
1
1
1
2
1
2
0
0
0
1
0
0
0
1
2
0
0
0
2
0
1
2
2
2
2
0
1
0
0
2
1
1
1
1
2
1
1
1
0
2
1
1
0
1
2
1
0
1
1
1
0
1
0
0
2
1
1
0
2
0
2
1
1
2
0
0
0
1
0
2
0
2
0
2
0
0
1
1
1
0
0
1
2
1
0
1
0
0
1
1
2
0
0
0
0
2
0
0
0
0
0
2
1
1
1
1
1
2
1
2
2
1
0
1
0
2
1
0
3
2
4
1
1
0
0
1
2
0
1
0
2
1
1
0
1
1
1
0
2
2
0
1
0
2
1
0
1
1
0
0
1
2
1
1
1
0
1
0
1
0
0
1
0
0
2
0
0
0
2
0
1
0
0
2
0
0
1
1
1
1
1
2
0
0
1
1
1
1
0
0
0
0
2
1
0
1
0
0
2
0
2
0
2
0
1
2
0
2
0
2
0
0
4
2
0
0
0
1
0
1
0
0
0
1
1
0
2
0
2
2
0
2
2
1
0
0
0
1
2
0
0
0
0
1
0
2
0
3
1
1
0
0
0
1
1
0
1
0
0
1
2
0
0
0
2
1
1
2
1
2
4
1
0
0
0
1
0
2
0
2
2
2
1
0
1
0
1
0
0
1
2
1
2
2
0
0
1
0
1
0
0
3
1
1
0
2
0
0
0
2
2
1
1
1
1
1
0
0
0
2
0
0
1
2
0
0
0
1
0
1
0
1
1
2
2
0
1
1
1
2
1
3
0
2
0
0
2
1
1
2
0
1
0
0
1
1
1
2
2
2
2
2
0
1
1
0
2
2
1
1
1
2
0
2
0
0
1
1
1
0
2
1
1
2
0
0
0
0
1
2
0
1
1
3
1
0
1
2
0
0
0
1
0
2
1
0
0
1
0
0
0
2
0
1
1
1
0
0
1
2
1
0
1
0
0
0
2
2
0
1
2
0
0
2
0
0
0
0
1
2
1
0
1
1
0
0
0
1
1
1
2
1
1
1
0
1
1
2
0
1
1
0
0
0
1
2
0
1
1
2
0
1
0
0
1
0
0
1
1
0
2
0
1
2
1
0
2
1
2
0
0
1
0
0
2
0
2
2
0
1
2
0
1
0
1
1
0
0
2
1
0
1
1
1
0
0
3
0
0
1
1
1
2
2
2
2
1
1
0
0
0
0
1
1
0
0
2
1
2
0
2
1
2
2
0
0
0
2
0
0
1
2
1
3
1
1
1
0
1
2
1
2
1
1
2
1
1
2
1
2
2
0
1
0
2
1
0
1
0
0
1
2
1
1
1
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
1
1
0
0
1
0
0
1
2
0
1
2
1
1
1
1
1
0
0
0
0
1
0
2
0
1
1
1
2
1
0
1
0
1
2
0
1
2
1
2
1
2
1
2
0
0
0
2
1
2
0
0
2
1
1
0
2
2
2
0
0
2
2
1
0
0
1
1
1
0
0
0
1
1
2
2
1
1
0
1
1
2
0
0
1
0
1
2
2
1
0
0
1
1
2
0
1
0
1
2
0
1
0
1
0
0
0
1
0
1
0
0
1
0
0
0
2
1
2
2
0
2
1
0
1
0
1
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
1
1
0
0
0
1
1
2
0
2
1
1
0
0
1
1
2
2
2
1
2
1
0
1
0
2
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
1
2
0
0
2
1
2
1
1
1
0
1
2
0
1
0
0
1
0
0
0
2
0
1
2
1
0
0
1
2
1
3
1
1
2
1
0
1
0
1
1
1
1
0
0
2
2
1
1
2
2
2
1
1
0
1
1
1
0
0
2
0
0
0
2
0
1
1
2
2
2
2
0
0
1
1
0
0
1
0
0
0
1
1
2
0
2
1
0
0
2
0
0
1
2
1
1
1
0
1
1
0
2
2
0
0
0
2
0
1
0
2
2
1
0
0
0
1
1
2
0
1
0
1
0
0
0
2
2
1
1
0
0
1
1
6
0
2
0
3
2
3
0
1
2
0
1
0
2
2
0
0
1
0
1
0
1
0
2
1
0
0
1
0
2
4
0
3
0
1
0
1
0
3
1
2
0
0
2
1
0
1
2
1
1
1
0
0
0
1
1
0
2
0
2
1
2
0
0
2
2
1
1
1
1
1
0
3
2
2
2
0
1
0
0
0
1
1
1
1
0
0
0
1
2
1
0
2
1
0
1
0
0
0
1
1
0
0
0
0
1
1
1
1
1
0
0
0
0
0
2
0
1
0
0
1
1
0
0
1
1
2
2
1
1
2
0
0
2
0
0
0
1
0
2
1
1
2
2
0
0
0
0
0
2
0
0
0
1
2
1
2
0
1
0
1
1
0
0
0
0
1
1
0
0
1
1
1
0
1
0
1
2
2
0
0
1
0
0
1
0
1
0
0
2
2
1
1
2
1
0
1
0
2
0
2
0
1
0
0
0
0
1
1
0
1
1
1
1
0
0
0
1
1
0
1
2
0
1
0
0
2
1
0
0
2
2
2
0
2
1
2
0
1
0
1
1
1
0
0
0
2
0
1
1
2
0
0
1
0
0
1
0
0
1
2
1
1
0
1
2
0
0
2
1
1
0
0
0
2
2
0
0
2
2
0
0
2
1
2
0
2
1
2
2
0
1
1
1
0
0
2
2
2
0
0
0
0
2
0
1
0
0
0
2
1
2
2
1
2
0
1
1
0
1
0
0
2
1
0
2
1
2
1
0
2
1
0
1
0
2
1
1
1
4
1
0
0
0
2
1
1
2
0
1
1
0
0
0
1
1
1
1
0
2
0
0
1
2
0
0
2
1
1
0
0
1
1
0
1
0
1
0
0
0
0
2
1
2
0
1
0
2
0
0
0
1
2
1
0
1
2
1
0
0
4
2
1
2
2
0
0
0
0
1
2
0
2
0
0
1
0
0
1
2
1
2
2
2
0
1
3
2
1
1
1
3
0
1
2
0
0
0
1
2
0
1
0
0
1
0
0
0
1
0
2
1
0
0
0
2
1
0
1
2
1
0
1
1
1
0
0
0
0
0
0
1
2
0
1
1
0
1
2
0
0
2
0
0
0
2
0
0
0
0
1
1
0
0
1
2
2
2
0
0
2
0
0
0
0
0
3
1
0
2
0
0
0
1
1
0
0
1
1
1
1
2
0
0
2
1
1
0
0
2
1
1
1
0
0
0
0
0
0
1
0
2
0
2
2
1
0
2
0
1
0
0
1
1
0
2
0
0
0
2
1
0
2
1
2
1
1
2
1
0
0
3
0
0
1
0
2
3
1
0
0
2
1
2
3
1
1
0
2
0
2
0
1
0
2
1
2
0
1
0
0
2
0
2
0
0
1
3
1
0
0
1
1
1
0
0
0
0
1
0
0
0
1
0
2
0
2
0
1
1
1
1
1
0
2
1
2
0
2
2
1
1
0
0
1
1
0
1
1
0
2
0
2
0
2
0
0
1
1
1
0
0
2
2
0
0
2
1
2
2
2
0
1
1
2
1
1
2
1
0
0
2
0
0
0
0
0
1
0
0
0
2
1
0
1
1
2
2
2
0
0
0
1
0
1
0
2
1
1
0
1
2
0
1
0
2
0
2
0
0
1
0
0
0
1
1
1
0
1
1
0
0
2
2
0
0
0
0
2
0
1
1
1
2
0
2
0
1
2
2
1
2
2
0
0
0
0
1
2
0
1
2
1
1
0
0
0
2
1
0
0
3
0
1
0
0
2
0
2
1
0
2
0
2
0
0
1
2
2
1
1
1
0
2
0
0
1
1
2
0
0
2
2
0
1
1
1
1
2
1
2
2
1
0
2
1
0
2
1
0
0
0
0
1
0
1
2
1
0
1
0
0
1
0
0
2
2
0
0
3
0
0
0
1
1
1
2
0
0
0
0
1
0
2
1
0
1
4
1
2
1
0
2
5
2
1
2
0
0
1
0
2
2
1
0
0
0
0
2
2
2
0
1
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
2
0
2
2
2
0
2
1
2
0
0
0
2
0
0
2
0
1
0
1
2
1
1
2
1
0
1
0
2
0
0
2
1
0
0
0
2
0
1
0
2
0
2
2
0
0
0
2
2
0
0
1
0
1
0
2
0
1
0
2
0
0
2
1
1
1
1
0
2
1
0
0
2
1
0
2
1
1
3
0
0
0
0
1
0
0
0
2
2
1
1
0
0
0
1
0
1
0
3
1
1
0
0
1
0
1
1
0
0
0
0
0
0
0
2
1
0
0
3
1
1
0
1
0
1
0
0
1
1
2
0
1
0
1
2
2
0
0
1
0
2
2
0
3
1
1
0
0
0
2
0
0
0
0
0
0
1
2
1
0
1
1
2
1
1
1
2
3
1
2
0
0
1
0
2
0
0
0
0
3
1
2
3
2
0
3
0
0
2
1
1
0
2
0
1
0
1
1
1
0
0
4
0
2
2
0
0
1
0
0
0
2
1
0
1
1
2
0
2
0
2
0
2
0
1
1
0
0
0
1
0
2
1
0
1
2
1
0
2
0
1
0
0
0
0
0
1
1
1
1
0
2
0
1
1
1
0
2
0
1
0
2
1
0
0
2
0
0
0
2
0
0
1
1
3
0
0
2
0
0
1
0
1
2
1
1
0
2
0
0
1
0
0
2
1
0
2
0
1
2
0
0
0
2
0
2
0
0
2
0
2
1
2
2
2
0
0
0
2
1
0
1
0
2
0
1
0
2
1
1
1
1
0
0
0
1
0
1
0
3
0
0
1
11
0
3
0
2
1
2
0
1
0
2
0
1
1
0
2
0
1
1
1
0
0
0
0
0
0
1
0
1
2
0
1
0
1
0
3
0
3
0
0
0
2
1
1
1
1
0
0
1
0
1
1
2
0
0
1
0
0
1
1
2
0
2
0
1
2
1
0
0
0
0
1
0
2
0
0
1
0
2
1
1
0
1
0
0
1
1
1
1
0
2
0
1
0
1
1
2
0
2
2
1
2
1
0
1
2
1
0
2
0
1
1
0
1
0
0
0
2
1
0
1
0
0
0
1
0
0
0
0
0
1
3
1
1
1
2
2
0
0
2
2
0
1
1
0
1
2
6
0
2
1
0
2
0
0
0
1
2
2
0
1
1
0
1
2
0
1
0
0
0
1
1
1
1
2
0
0
2
1
0
0
1
0
1
0
0
0
1
1
0
0
0
1
1
0
0
1
2
1
0
0
1
1
2
2
1
0
2
0
2
2
0
1
2
2
1
0
1
0
0
2
2
0
1
0
0
0
1
0
0
2
1
0
2
2
0
1
0
1
0
0
0
2
1
0
1
1
0
1
0
0
2
1
0
0
1
0
0
2
0
0
0
1
0
0
1
0
0
1
1
1
1
0
0
2
0
1
2
1
0
1
1
1
1
1
0
0
1
0
2
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
3
0
1
0
0
2
1
1
1
1
1
0
1
1
1
1
2
0
1
0
0
0
1
2
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
3
0
2
0
1
0
0
2
0
1
0
0
2
2
0
0
1
0
0
0
0
2
1
1
1
0
1
1
0
1
0
1
1
1
0
2
1
0
2
1
0
0
2
1
0
1
0
1
2
0
1
0
0
2
0
1
0
0
0
0
0
1
0
0
2
3
1
0
2
0
2
0
0
0
1
0
4
4
2
1
0
0
2
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
2
2
0
0
1
1
0
0
0
2
0
0
2
2
0
0
0
1
1
1
2
1
1
1
2
0
0
0
0
2
1
2
0
0
2
0
1
0
1
1
1
0
0
2
1
0
2
1
1
0
2
1
0
2
1
0
2
1
1
0
0
1
1
1
1
0
1
0
1
5
1
2
2
0
2
0
2
2
2
1
0
0
1
2
1
2
1
1
1
0
1
2
2
0
1
1
2
2
1
2
0
1
2
1
0
1
0
1
0
0
1
0
2
0
2
1
0
2
0
1
0
0
0
0
8
2
0
1
2
0
1
0
0
0
1
1
0
1
0
1
0
0
2
0
1
1
1
0
2
0
2
0
2
2
0
0
2
1
0
1
0
1
1
2
1
0
2
0
0
0
1
0
2
2
1
0
1
0
0
0
0
1
1
1
0
2
0
1
1
1
0
0
0
1
1
0
0
1
1
1
0
3
0
0
0
2
0
2
1
2
2
1
2
0
1
1
2
0
0
2
0
0
0
0
4
1
0
1
1
1
0
1
1
0
0
2
1
0
2
2
2
1
0
1
1
1
1
2
3
1
0
0
0
1
0
0
0
0
0
2
0
0
0
1
1
1
0
0
0
2
0
0
1
1
0
0
2
0
2
1
0
2
1
2
0
1
1
0
0
1
2
2
0
1
2
0
2
0
0
0
0
0
1
0
2
0
1
2
1
1
2
1
0
1
0
0
1
3
0
0
0
2
2
1
2
1
0
1
0
2
1
1
0
0
3
1
0
0
0
1
0
0
0
0
1
1
1
0
1
1
1
0
1
1
1
1
0
2
2
0
2
0
1
0
0
1
0
1
0
0
1
0
1
1
0
2
0
8
2
1
1
0
0
1
2
1
0
0
0
2
0
0
1
0
0
1
0
0
1
2
2
0
1
1
1
1
0
0
0
0
2
2
2
0
0
0
1
1
1
2
1
0
2
0
2
1
3
0
0
0
3
0
0
1
1
1
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
2
0
1
1
2
0
0
0
0
1
2
2
2
0
0
1
0
0
1
0
0
1
0
1
2
2
0
2
0
0
1
0
2
1
1
0
2
1
2
1
1
1
2
2
2
0
2
1
1
1
1
1
0
1
2
0
2
0
0
0
1
1
1
0
1
2
1
2
1
0
1
0
0
0
2
1
0
1
0
2
0
0
1
0
2
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
1
2
0
2
0
0
0
1
0
1
1
0
1
0
0
0
2
0
1
0
0
0
0
0
0
2
3
0
0
0
0
0
1
1
1
2
2
2
1
0
1
2
2
2
0
2
0
1
0
0
1
1
1
0
1
1
2
2
5
1
0
0
1
2
0
2
2
1
0
0
1
2
1
1
1
0
1
0
1
8
2
1
0
1
0
6
1
0
0
0
0
0
2
0
2
0
2
2
1
1
0
0
0
0
0
2
0
2
1
0
1
2
1
1
1
2
1
0
1
0
0
1
0
2
1
2
3
2
1
1
0
0
0
1
0
1
0
0
0
0
1
0
2
1
0
2
1
2
0
0
1
2
2
0
2
0
2
2
0
1
2
1
0
1
1
2
0
0
0
0
1
0
0
1
1
0
1
1
1
2
1
0
0
1
1
2
1
2
0
1
0
0
2
1
0
3
0
1
0
0
0
0
0
0
1
0
1
3
1
1
1
2
2
1
2
0
1
0
0
1
1
2
0
0
0
0
2
0
1
1
0
1
2
1
0
3
0
1
0
0
0
2
0
0
2
1
1
1
0
2
0
1
0
1
2
2
1
1
1
2
2
1
2
0
1
1
1
0
2
2
1
2
0
1
0
1
1
0
1
1
1
0
1
2
2
0
0
2
1
1
0
1
0
2
0
1
0
0
1
0
1
1
1
0
2
0
2
0
1
0
2
0
2
0
0
1
1
0
0
0
0
0
0
2
0
0
1
1
1
0
1
0
0
1
0
2
0
1
0
1
0
2
0
0
1
2
0
0
0
1
1
2
2
0
0
1
2
0
1
0
0
2
2
0
0
1
1
1
0
0
0
0
1
0
1
1
1
0
1
1
0
0
0
1
1
1
0
0
0
0
2
2
1
0
1
1
1
1
1
0
1
0
0
2
0
1
0
0
1
0
0
0
1
1
1
1
0
0
0
1
1
1
1
1
1
0
0
1
0
0
1
0
1
1
17
2
0
0
2
3
2
2
2
0
0
0
1
1
2
0
1
0
0
1
1
0
2
1
0
0
0
0
1
2
0
2
1
1
0
0
1
0
0
0
0
1
2
1
0
3
1
2
0
1
1
2
0
6
2
1
1
0
1
0
0
1
0
1
0
1
0
0
1
1
1
1
1
1
1
0
0
0
1
0
1
0
0
1
1
1
0
1
2
2
0
0
1
0
0
0
2
0
0
1
1
2
0
1
0
0
0
1
0
1
0
2
2
1
1
2
0
1
1
1
1
0
2
2
4
0
0
1
1
0
0
1
1
1
1
0
0
0
0
3
0
0
1
2
2
0
1
0
0
1
2
2
1
1
0
1
0
1
2
0
2
0
0
0
0
1
0
1
2
1
1
1
1
1
0
2
0
3
0
0
1
2
2
1
0
1
0
1
0
2
1
0
1
0
1
0
2
0
0
2
0
1
0
1
1
0
3
0
1
0
0
0
1
0
0
0
0
1
2
1
1
1
2
0
1
0
1
3
1
0
1
0
1
2
1
1
0
2
0
0
1
0
0
1
0
0
0
2
0
0
0
2
0
0
1
2
2
1
1
0
0
1
1
0
0
0
1
0
0
2
2
8
0
0
1
1
2
2
0
1
1
2
0
2
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
1
0
0
2
3
1
2
2
0
0
0
0
2
0
4
1
1
0
2
0
1
1
2
0
2
0
2
2
3
0
0
1
0
2
0
0
1
1
1
2
1
0
0
1
0
0
0
2
0
0
1
1
0
0
0
1
0
0
0
1
1
2
2
0
0
0
2
0
0
1
1
2
2
0
1
0
0
0
0
0
0
1
1
1
0
0
0
1
0
1
0
1
2
0
1
0
1
2
2
1
0
0
1
1
0
0
0
2
1
1
2
2
4
2
2
1
2
1
0
1
2
1
0
1
0
2
0
2
2
0
1
2
0
1
0
0
1
0
0
0
0
2
1
1
1
1
0
0
0
0
0
1
1
0
0
1
2
0
0
0
0
0
1
2
1
2
1
1
0
0
0
0
1
0
1
0
2
1
0
3
0
1
0
0
0
0
0
0
0
0
1
2
0
1
0
1
0
0
0
0
1
2
0
2
1
2
1
2
1
1
2
0
2
1
0
2
0
1
1
1
0
0
0
1
1
0
0
0
0
2
2
0
0
2
1
0
0
0
1
2
0
0
0
1
1
1
2
0
1
2
0
1
2
0
1
0
1
0
2
0
0
2
2
2
0
0
1
2
1
1
1
2
2
2
2
2
0
0
1
0
0
1
2
1
0
1
0
0
1
0
2
0
1
1
0
1
0
1
0
0
2
0
0
1
1
1
0
0
0
0
1
1
0
1
2
0
1
1
0
2
0
3
0
0
2
1
1
0
2
0
0
1
0
2
0
0
1
2
2
2
2
0
1
2
1
0
0
0
2
0
0
0
2
1
0
2
0
0
1
2
1
0
2
2
0
1
0
0
0
0
0
0
1
2
1
0
0
2
0
0
0
1
0
0
1
1
0
1
1
0
0
0
2
1
2
1
0
2
0
2
0
0
2
0
0
1
0
1
0
0
1
0
1
1
0
1
2
1
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
1
0
1
0
2
2
2
1
1
1
0
0
0
0
0
0
0
2
1
0
1
1
0
1
3
1
2
2
1
0
0
0
0
0
6
1
2
2
0
0
0
0
2
1
1
1
0
1
0
0
0
2
0
2
1
0
1
2
1
0
2
1
3
0
0
2
0
0
0
1
1
1
0
0
0
2
0
0
1
2
2
1
0
2
2
2
0
2
2
1
0
2
1
0
0
0
1
1
1
1
1
2
0
2
2
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
2
0
2
0
3
1
0
0
0
1
1
0
2
0
0
2
1
0
0
2
0
2
0
0
0
1
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
2
2
1
2
1
1
1
1
2
0
1
2
1
0
0
1
0
0
2
1
1
0
0
0
0
2
0
2
0
0
1
1
0
0
0
2
1
0
0
0
1
0
2
2
1
2
1
2
1
0
0
0
1
1
2
0
0
0
0
0
2
0
2
0
2
1
0
4
0
0
0
1
1
2
0
0
1
2
1
1
1
2
2
1
1
0
1
0
2
1
2
0
1
0
0
0
2
4
0
2
2
1
0
1
1
0
1
1
1
0
0
1
0
0
0
0
0
1
1
3
1
0
1
0
1
2
0
2
1
2
1
1
0
0
1
0
2
1
1
0
0
2
0
0
0
1
0
0
0
0
0
1
1
2
0
2
0
0
1
0
1
1
0
0
0
2
2
2
1
0
1
0
2
0
0
2
0
0
0
0
0
0
0
2
1
2
1
1
0
0
1
0
0
1
0
1
2
0
2
0
0
0
0
1
0
1
1
1
1
1
2
2
1
0
0
1
2
2
0
1
1
2
0
2
2
1
0
0
2
0
0
1
1
0
0
2
1
1
2
1
0
0
0
2
0
1
0
0
2
0
1
0
0
1
1
0
1
0
2
1
0
1
1
1
2
0
1
1
2
0
1
1
0
0
0
2
2
0
0
0
2
1
2
1
1
1
1
2
1
0
1
0
2
1
2
1
0
0
1
1
0
0
1
1
2
0
1
0
1
2
0
0
0
0
2
1
0
2
0
0
0
2
4
1
2
0
1
1
2
0
0
0
0
2
1
2
1
0
2
0
2
1
1
1
0
0
0
2
1
0
0
0
1
1
1
1
0
1
1
0
0
2
1
0
0
0
1
2
2
1
1
1
3
1
1
0
1
2
2
0
1
0
0
0
1
2
0
0
1
0
2
0
0
0
1
1
0
0
1
2
1
1
1
3
1
0
0
1
0
2
0
0
3
1
0
0
1
0
2
1
1
1
1
2
0
2
0
1
4
2
2
1
1
1
0
2
2
1
1
1
1
1
0
0
0
0
0
0
2
1
1
0
0
2
0
1
1
0
0
0
1
1
1
3
0
2
1
1
3
1
0
2
1
1
1
1
0
1
0
0
0
0
0
3
0
0
0
1
1
2
2
1
0
0
2
3
1
1
0
1
1
1
1
2
1
1
0
2
0
2
0
0
1
0
1
1
0
1
1
1
2
0
1
0
0
0
0
1
1
1
0
0
2
0
0
0
1
2
0
0
1
0
3
0
0
1
1
1
0
0
1
0
2
0
2
1
2
2
0
1
1
0
2
0
1
1
1
0
2
0
0
2
2
1
1
1
0
0
2
0
1
2
0
1
2
2
2
2
2
2
0
2
0
0
0
1
0
1
1
0
1
1
0
0
0
2
1
1
0
1
2
2
0
0
0
1
0
6
0
2
2
1
3
1
1
1
0
0
2
1
0
0
0
0
2
0
0
2
1
2
0
0
2
0
1
1
1
2
0
1
0
0
0
0
2
2
0
2
2
0
1
0
2
1
0
0
0
0
2
0
2
2
1
3
1
2
1
0
2
1
0
0
1
1
0
0
1
0
1
0
1
3
0
0
0
0
1
0
0
1
2
1
0
0
2
0
0
0
1
2
0
1
1
0
1
2
2
0
2
0
1
0
1
1
0
0
0
0
1
0
1
1
1
0
1
1
1
2
1
1
1
2
2
2
2
0
1
1
0
1
1
3
2
2
0
0
0
0
0
1
2
2
1
2
1
0
0
0
2
1
1
1
0
0
1
2
1
0
1
1
1
1
0
0
1
2
0
2
0
2
0
2
1
0
1
0
1
1
1
0
0
1
1
0
0
0
1
2
0
1
0
2
0
0
1
0
1
1
1
1
2
1
2
1
0
2
2
1
0
0
1
2
0
1
2
0
1
2
1
0
0
1
1
2
1
0
1
0
1
2
0
0
0
0
0
1
1
1
1
1
0
0
0
2
1
1
2
0
1
1
1
1
1
0
0
0
0
2
1
0
0
0
2
1
2
1
0
2
2
1
0
0
1
1
1
2
1
1
0
1
0
0
3
0
2
0
1
0
0
1
0
0
0
0
1
1
1
2
0
2
1
1
0
1
1
1
1
2
0
0
2
1
0
0
2
3
1
0
0
0
1
0
0
3
0
1
1
0
0
0
0
1
1
0
1
0
1
1
2
2
1
0
1
2
0
1
0
3
2
0
0
2
0
0
1
2
0
2
1
0
3
0
0
1
2
0
0
2
1
0
0
0
0
1
2
0
1
2
0
1
2
1
0
0
0
1
0
1
0
2
2
1
2
0
2
2
0
2
0
0
1
0
0
3
1
0
1
1
2
0
0
0
1
0
0
0
2
2
0
0
1
1
0
0
0
0
2
0
0
0
1
1
1
1
0
1
2
2
0
1
0
1
1
2
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
1
1
1
2
1
1
2
2
1
1
1
1
1
0
1
0
2
0
0
0
1
1
1
1
2
0
2
0
0
2
0
0
0
0
0
1
1
0
1
1
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
1
0
1
0
1
1
0
2
0
1
1
0
1
0
0
1
2
2
0
1
1
0
1
0
0
1
0
0
1
3
0
0
2
1
0
0
1
2
1
0
0
0
2
0
2
0
0
1
1
1
0
0
0
1
1
0
0
0
1
0
1
1
0
0
1
1
1
1
1
0
1
2
0
1
2
1
1
1
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
2
1
1
0
2
1
0
1
1
0
0
0
1
0
0
1
1
1
2
1
2
0
0
1
1
0
1
0
2
0
1
1
1
1
0
1
0
0
2
1
1
1
1
1
1
1
2
2
2
0
0
2
1
2
1
2
1
1
2
2
1
0
1
1
2
0
1
0
1
1
2
2
0
1
1
2
0
1
1
0
3
2
0
1
0
2
0
0
0
1
0
2
2
0
2
1
1
0
0
1
0
4
1
1
0
0
0
0
1
1
0
0
1
0
0
2
0
0
0
1
0
1
0
0
2
2
0
1
1
0
1
1
2
0
0
2
1
0
0
2
0
2
2
2
0
2
1
0
0
0
0
0
1
0
0
2
0
0
0
1
3
1
0
2
3
0
2
2
1
2
0
0
0
1
0
0
1
0
1
2
2
0
1
1
2
1
2
1
0
1
0
0
2
1
0
1
2
1
1
0
2
0
0
0
1
1
0
2
1
0
1
0
1
2
1
2
0
0
2
0
0
1
1
0
2
2
1
1
1
0
2
1
1
0
0
0
0
1
2
0
0
0
2
0
0
0
0
1
2
1
2
3
1
1
0
1
1
1
1
0
1
2
2
0
0
2
0
2
0
0
2
0
0
1
0
0
0
0
1
1
0
1
0
1
0
0
0
2
0
0
1
0
0
1
2
1
2
0
0
1
2
2
0
0
2
2
1
1
1
3
2
0
0
0
0
2
2
2
1
0
1
0
2
2
1
0
2
0
1
2
2
2
1
0
0
1
0
0
1
1
0
2
0
1
0
0
2
0
1
1
1
1
0
0
2
2
1
0
0
2
0
0
2
0
0
0
2
1
1
2
2
1
0
1
0
0
1
1
0
0
2
0
0
0
1
0
2
1
1
0
2
1
3
1
1
0
2
2
0
1
2
1
2
2
0
0
0
0
0
2
1
0
1
2
1
0
2
1
0
1
2
2
1
0
2
0
2
0
2
2
2
0
1
1
1
2
0
0
0
0
1
0
0
1
0
1
0
1
1
1
0
0
1
2
0
1
2
1
1
1
1
0
0
1
0
1
2
1
2
0
1
1
0
1
1
2
1
1
0
0
0
1
0
0
0
0
1
2
1
1
1
1
2
1
0
0
0
2
0
0
0
1
1
1
0
2
2
2
0
0
1
0
0
1
1
1
2
0
4
1
0
2
2
0
0
0
1
2
2
1
1
1
1
1
0
2
0
1
1
0
2
0
0
0
0
0
0
1
1
1
0
0
1
0
0
2
2
2
0
1
0
1
0
2
0
1
0
0
1
1
2
1
2
0
1
0
2
0
0
0
0
1
2
0
2
1
1
1
0
0
1
1
2
0
2
0
1
2
0
0
4
0
1
0
2
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
1
0
1
0
0
1
2
1
0
2
0
0
2
0
0
1
2
0
0
0
1
1
1
0
0
2
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
2
1
0
1
0
0
2
0
3
2
0
1
1
0
0
0
1
2
1
0
0
2
2
0
0
0
0
1
1
0
0
2
0
1
2
1
1
2
1
1
1
1
1
0
0
0
0
1
2
0
1
1
2
0
2
2
2
0
2
1
3
2
1
0
2
0
2
1
0
0
1
2
2
1
1
0
0
1
1
2
2
3
0
0
2
0
1
0
1
1
1
0
0
2
0
3
0
2
0
1
1
1
0
1
1
0
0
1
1
0
1
0
1
1
1
0
0
2
1
1
1
2
1
1
2
0
2
2
0
0
0
1
0
0
1
0
0
1
0
0
1
1
3
1
1
1
0
2
2
1
0
1
1
0
1
1
2
0
0
1
2
0
2
2
1
0
0
1
2
0
2
1
1
0
1
1
0
1
1
2
0
0
0
0
1
1
1
2
0
1
0
0
0
2
1
1
0
1
0
2
0
1
0
0
1
0
1
0
0
2
1
1
1
2
1
1
0
0
1
0
2
0
0
0
2
1
1
0
0
3
1
1
1
1
0
0
0
2
0
0
1
2
0
1
0
1
0
2
2
1
2
0
0
0
1
2
0
1
0
1
0
0
2
0
4
2
1
1
1
2
0
0
0
2
1
1
1
0
0
1
0
0
1
0
0
1
2
2
4
1
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
1
1
2
0
2
0
2
0
0
2
1
2
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
1
2
1
0
0
2
0
2
1
2
1
0
1
2
0
0
0
1
1
1
1
1
0
0
6
0
0
1
0
1
1
2
1
2
1
0
0
2
1
2
0
2
0
0
2
0
1
0
1
1
0
0
1
0
0
0
2
2
0
2
2
2
1
0
2
1
1
1
2
1
2
1
2
0
1
1
2
1
2
0
1
0
1
0
1
0
0
0
1
0
1
0
1
1
1
1
1
0
0
1
1
5
1
0
0
2
0
1
1
0
2
1
1
0
1
1
0
1
1
1
0
0
0
0
1
1
0
1
0
1
0
3
0
0
1
0
1
1
0
1
1
0
1
2
1
1
1
0
0
1
2
0
0
2
1
0
0
0
1
0
0
1
2
2
0
1
0
1
3
0
0
1
0
2
3
1
2
2
2
0
0
0
1
1
0
2
1
0
0
0
0
1
0
2
0
0
0
2
0
1
1
1
0
1
1
2
1
0
0
0
1
1
1
0
0
0
0
0
1
1
0
2
0
0
2
1
1
1
2
0
0
1
4
0
1
0
0
3
0
0
0
0
1
2
2
0
2
1
2
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
3
2
1
2
0
0
2
0
1
0
1
0
0
3
2
2
0
2
1
2
0
1
0
1
0
0
5
1
2
1
0
1
2
0
1
2
1
1
0
1
1
0
0
0
0
0
2
2
0
0
1
2
0
0
1
0
1
0
0
1
0
1
1
0
0
1
0
1
1
1
1
2
2
1
0
2
2
2
0
1
2
0
1
0
0
0
1
0
0
2
0
2
0
0
1
1
2
2
1
1
0
1
1
3
1
0
0
1
0
1
1
1
0
0
0
1
1
1
1
2
1
1
0
2
1
1
1
0
0
0
1
0
0
0
0
1
2
2
2
1
1
3
1
1
0
0
2
1
1
0
2
1
0
1
1
1
2
1
0
0
0
0
1
1
0
0
1
1
1
0
1
0
1
0
0
2
0
1
2
1
1
2
0
1
0
0
0
0
1
2
0
2
0
2
2
1
0
1
0
2
2
0
2
0
0
2
0
2
0
0
2
1
0
0
1
2
1
2
1
2
1
1
0
2
2
0
1
0
1
0
1
0
1
0
0
0
2
1
0
1
0
0
0
1
1
2
2
0
2
2
0
0
0
1
0
1
1
1
0
1
1
0
0
2
1
1
1
0
0
4
1
2
0
2
0
1
2
0
1
1
0
0
1
0
0
1
1
0
0
2
1
1
2
0
0
0
1
0
0
0
1
1
1
0
2
0
1
0
0
3
0
0
0
0
1
2
0
2
2
1
2
2
0
0
2
1
1
2
1
0
1
1
0
2
1
0
1
6
0
2
1
0
0
0
1
1
0
0
0
2
1
0
0
1
1
2
1
0
1
1
2
2
2
1
1
0
0
0
1
2
1
1
0
1
1
0
1
3
0
1
1
0
0
0
0
2
0
0
1
1
0
1
1
2
1
1
1
2
0
0
1
1
1
0
1
0
3
1
2
0
2
1
0
1
1
0
0
1
2
0
2
2
1
2
0
1
1
2
2
0
1
2
3
0
0
0
0
2
0
0
0
2
0
2
0
1
0
1
1
0
0
1
2
3
1
1
0
0
1
0
0
0
1
1
1
1
1
2
0
3
1
0
5
2
1
1
5
1
0
1
0
0
0
0
1
1
1
0
0
0
1
1
0
1
0
0
2
0
0
0
0
1
2
0
1
0
1
1
1
0
1
0
0
0
1
1
0
2
1
1
0
1
2
0
0
0
0
1
2
0
2
0
0
1
1
1
0
0
0
2
0
1
2
0
0
0
1
0
1
1
2
2
0
0
1
1
1
0
2
0
0
0
2
0
0
0
2
0
2
2
0
1
0
1
0
2
1
1
2
1
1
0
0
0
1
2
1
0
2
0
0
0
0
1
2
1
1
3
1
0
0
0
2
0
0
2
0
0
1
0
0
3
2
1
2
2
0
2
2
1
0
0
0
0
0
1
0
1
0
1
0
0
1
2
1
1
0
1
1
0
4
0
0
0
2
2
0
0
0
0
4
1
0
0
1
0
3
0
2
2
1
0
0
0
0
0
2
3
0
0
0
0
0
1
1
0
1
2
2
2
0
1
0
0
2
0
1
2
2
1
0
0
0
0
1
1
2
2
0
1
0
0
1
0
0
1
2
0
0
0
1
1
1
1
0
1
1
0
1
1
2
2
1
1
0
1
1
0
2
0
1
0
1
0
1
1
2
2
0
2
1
2
0
1
1
1
1
2
1
1
1
0
0
1
4
2
2
1
0
0
0
0
1
0
0
1
0
0
1
0
0
1
2
1
0
0
2
2
0
2
1
0
1
0
1
2
0
2
0
0
1
1
0
2
1
1
0
2
0
1
1
2
1
0
0
1
0
1
2
1
1
0
1
1
1
0
0
1
0
0
0
2
0
1
0
3
1
1
0
2
2
3
2
0
2
1
0
1
2
1
2
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
2
1
0
0
0
2
0
0
0
1
1
0
2
0
0
0
1
1
1
1
1
2
0
0
3
1
0
0
1
1
0
2
4
2
1
0
2
1
2
0
0
1
0
1
1
2
2
0
2
0
2
0
0
2
0
1
1
0
0
1
0
1
0
2
1
1
2
0
3
1
0
1
2
0
2
1
0
0
0
0
2
0
0
2
0
2
0
0
1
2
1
1
0
0
1
0
1
1
0
1
0
1
1
0
1
0
0
1
0
1
0
0
2
1
1
0
1
2
0
1
2
0
0
1
0
0
1
0
2
3
1
1
1
0
1
1
2
0
1
0
1
0
2
1
0
0
1
2
1
1
0
0
2
0
0
0
0
0
0
1
1
0
0
0
3
1
0
1
0
0
0
1
0
1
0
0
0
1
1
1
0
0
0
0
0
1
0
1
0
0
1
2
2
0
0
0
0
1
1
3
0
0
1
0
0
2
0
1
2
0
0
1
0
2
0
2
1
0
2
2
0
1
0
2
0
2
1
1
0
0
0
0
0
1
2
0
0
0
1
0
1
1
0
1
2
0
1
0
2
0
0
0
1
1
2
0
0
1
0
1
0
1
0
0
0
0
0
0
1
1
2
1
1
0
1
1
2
1
0
0
0
1
0
1
1
2
0
0
2
1
0
0
1
1
1
2
1
2
1
0
0
0
0
0
2
2
1
1
1
0
1
1
1
1
0
2
1
2
2
0
2
0
0
2
0
1
1
2
0
1
1
1
2
1
1
1
0
0
1
1
1
0
0
1
0
1
1
1
0
2
0
2
0
0
1
0
1
1
0
1
2
0
1
2
1
2
0
2
0
1
1
0
1
1
2
0
2
1
0
0
2
0
1
1
0
0
0
0
1
0
1
1
0
1
0
2
0
1
1
1
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
1
2
1
0
2
0
1
1
2
0
1
2
0
1
1
0
2
1
1
0
1
1
0
2
2
0
1
0
0
2
1
0
0
1
1
0
2
0
0
1
1
0
2
0
0
0
2
1
1
1
1
2
0
1
0
0
0
2
0
1
0
1
0
2
1
0
1
1
3
0
1
3
0
1
1
0
2
2
1
2
2
2
2
0
2
2
0
0
2
1
0
0
0
2
0
3
2
0
2
0
0
5
1
1
1
0
0
1
2
0
1
0
0
1
0
1
0
2
0
0
0
0
0
0
1
1
0
2
1
0
2
2
1
0
0
1
1
2
1
0
1
0
0
2
2
0
1
1
1
1
0
0
1
0
0
2
0
0
1
2
0
2
2
0
4
0
2
0
1
1
0
2
0
0
2
0
2
2
1
0
0
1
1
1
1
1
1
0
0
0
0
2
0
0
0
0
1
1
1
1
0
0
0
1
0
0
1
0
1
0
2
0
2
0
1
0
1
0
1
0
1
2
0
0
1
0
1
0
1
1
1
0
2
0
1
2
1
1
2
1
0
3
0
2
0
0
0
0
2
2
0
2
0
0
1
0
1
1
1
2
0
2
0
1
0
3
1
0
2
0
1
0
1
1
0
0
1
0
0
1
1
0
1
1
1
2
0
1
0
1
0
0
0
0
1
1
0
1
0
1
2
0
1
1
2
1
2
0
1
0
2
0
1
0
1
1
2
0
0
0
0
1
1
0
0
0
0
0
1
1
0
2
2
0
0
2
1
1
2
0
0
2
0
1
1
1
1
2
1
0
0
1
2
0
0
1
1
1
0
1
1
0
0
1
1
0
0
2
0
0
0
0
0
1
2
2
0
2
0
2
1
0
1
1
1
1
1
2
0
0
0
0
1
0
0
1
2
1
0
2
3
1
1
2
0
0
2
1
0
1
2
0
1
0
1
0
1
1
0
1
1
1
0
1
0
1
2
1
0
1
2
0
1
2
1
2
1
2
0
0
0
2
1
1
0
2
0
0
1
2
1
1
0
1
0
0
0
0
1
1
0
0
3
1
1
0
0
1
1
0
0
0
2
0
1
1
1
0
0
0
0
0
0
2
0
1
5
1
2
0
0
0
0
0
2
2
0
0
0
0
3
0
0
0
3
0
0
1
2
1
0
2
0
0
1
0
1
0
2
1
1
2
0
1
0
0
1
0
1
0
0
0
0
0
1
0
2
0
1
1
1
2
1
1
2
0
1
2
0
0
2
1
1
0
2
0
2
2
2
0
1
0
0
0
0
0
0
2
0
1
0
1
0
2
0
0
1
1
0
0
0
1
0
1
0
1
0
1
2
0
0
1
1
0
0
1
2
0
2
0
0
0
1
0
1
0
0
1
0
0
0
1
0
2
1
2
1
2
0
1
0
1
0
0
0
1
0
1
3
0
1
2
0
2
0
0
2
0
1
1
1
1
0
2
0
1
1
2
2
2
0
2
0
0
0
0
0
0
0
2
0
0
0
1
1
0
1
0
1
1
0
2
0
0
0
0
2
2
0
1
1
3
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
1
1
0
0
0
2
2
1
0
1
1
0
1
1
0
1
0
0
2
1
1
2
0
1
0
3
1
2
0
0
0
2
3
2
0
2
3
0
2
1
0
0
2
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
2
1
1
0
1
0
0
0
1
0
1
2
0
0
1
0
1
0
2
0
3
0
2
2
1
1
1
0
1
0
1
0
2
1
1
1
0
1
0
1
0
2
1
1
0
1
1
1
0
0
0
1
0
2
1
0
2
1
0
1
1
0
0
1
0
0
2
1
2
1
2
1
1
0
0
2
2
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
2
2
2
0
0
1
1
1
0
1
1
1
0
0
0
0
1
1
1
0
0
3
0
1
2
2
0
1
0
0
1
1
0
0
0
2
0
0
0
2
1
1
1
0
1
0
1
0
2
0
0
2
0
1
1
0
1
1
1
2
1
2
0
0
0
0
0
1
0
0
2
0
1
1
0
1
2
2
0
2
1
0
0
0
0
1
1
0
2
1
0
1
2
2
2
0
0
1
0
1
2
1
1
1
2
2
1
1
1
1
0
1
2
0
0
2
2
3
2
2
0
2
2
1
0
0
0
1
2
0
1
2
1
2
0
0
1
1
0
1
0
1
0
0
0
1
1
0
1
0
1
1
1
0
0
0
1
3
0
0
1
0
0
0
3
0
1
0
1
0
2
1
3
1
1
0
4
0
0
1
1
0
1
1
0
1
1
0
2
0
2
0
1
0
1
2
0
0
0
0
2
1
0
0
0
0
2
0
2
1
3
1
0
0
0
1
0
1
2
0
0
0
0
0
0
1
2
0
2
0
2
1
2
0
2
0
2
0
0
0
2
0
0
1
2
0
2
2
1
0
1
0
0
2
0
0
0
1
0
1
2
1
0
0
2
1
2
1
2
0
0
1
1
1
0
1
3
0
0
2
1
1
1
1
2
0
0
0
2
2
0
1
2
1
2
0
1
0
0
1
2
0
0
1
2
1
2
1
2
2
0
1
0
1
1
2
2
0
1
2
0
3
0
2
2
1
1
0
0
1
1
0
2
0
0
2
0
0
1
2
0
2
0
1
2
2
1
1
2
0
0
1
0
0
2
0
2
0
2
2
0
2
1
0
2
0
1
1
2
0
0
1
0
1
0
0
0
2
0
6
0
1
2
1
0
1
1
0
0
0
3
0
1
1
2
1
0
5
0
1
1
0
3
0
2
1
1
0
1
0
2
1
1
1
1
1
0
0
1
1
1
0
1
2
0
0
2
0
1
0
2
1
0
0
1
0
1
1
2
1
2
1
1
0
0
1
2
0
0
0
0
3
0
1
0
1
1
1
2
0
0
2
1
0
0
0
1
0
1
0
2
0
0
0
0
1
2
1
2
0
0
0
1
0
1
3
1
1
1
1
1
0
1
0
1
0
0
0
2
0
0
0
0
2
0
0
1
0
1
0
1
1
0
0
1
0
0
0
1
2
1
1
1
2
1
0
2
1
0
0
0
1
0
0
0
1
0
0
0
1
3
0
0
1
0
0
1
1
2
0
2
1
1
2
1
1
2
1
0
0
0
1
0
0
0
0
1
1
1
1
0
1
1
0
0
0
1
0
1
2
2
3
2
1
2
0
1
0
0
2
0
1
2
2
1
2
0
2
0
1
0
1
0
3
2
0
0
1
0
2
1
1
0
1
0
1
0
0
2
2
1
1
0
1
1
1
0
3
0
0
2
0
2
0
0
1
1
0
2
1
1
2
0
0
1
0
1
3
0
0
2
0
2
2
2
2
2
2
0
2
2
2
0
0
0
1
1
1
0
2
1
1
1
0
0
1
0
1
0
0
2
0
0
1
1
0
0
2
0
1
1
1
0
0
1
0
0
0
1
0
0
2
1
1
1
1
0
1
1
1
1
1
1
0
1
1
1
1
2
3
0
0
0
0
1
0
1
0
0
2
1
0
0
0
2
0
0
0
0
1
1
0
1
1
0
0
1
0
0
0
1
0
0
0
1
1
2
0
1
1
0
1
2
2
0
0
2
0
2
0
1
0
1
1
0
1
0
1
2
0
0
2
0
1
1
0
1
1
2
0
0
0
1
0
2
0
1
1
0
0
0
0
1
1
2
0
0
1
0
0
2
0
0
1
0
3
2
0
2
1
1
0
0
2
1
1
0
0
2
1
0
0
0
1
0
2
0
2
1
1
0
0
0
2
1
2
2
1
0
0
0
1
0
0
3
0
2
0
0
0
1
1
2
0
1
0
0
0
1
1
2
3
1
0
0
1
2
0
0
0
2
0
1
0
0
0
1
1
2
1
0
1
1
2
0
1
1
0
0
0
0
1
2
1
1
0
0
0
1
2
2
1
3
0
2
0
1
1
0
0
0
1
0
3
0
0
1
1
0
0
1
0
1
1
2
2
1
2
0
1
1
0
0
1
1
2
0
1
2
1
0
0
2
1
0
0
1
0
2
1
0
1
0
0
1
1
1
0
0
0
1
0
2
0
0
0
2
0
1
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
1
1
1
2
1
1
2
2
0
2
1
1
1
1
1
2
2
1
2
1
2
0
1
0
1
0
0
0
0
1
1
2
1
1
0
1
0
0
0
1
1
1
2
2
0
1
0
0
1
2
0
1
1
0
1
0
0
0
0
2
0
0
2
1
1
0
0
0
2
2
0
1
0
0
0
1
1
0
1
0
1
0
1
1
1
1
0
0
1
0
1
0
0
1
1
2
0
0
0
0
0
0
2
0
2
0
1
0
0
2
5
1
2
0
2
0
1
1
2
0
0
2
0
2
2
0
0
2
0
0
2
2
0
0
1
2
2
2
1
1
1
1
2
1
0
0
0
1
2
0
0
0
1
2
0
0
1
1
0
0
1
0
0
2
0
0
0
1
2
0
1
0
1
1
1
1
1
0
2
0
1
1
2
2
0
2
1
1
2
1
0
0
0
0
1
2
1
2
2
0
2
0
1
0
2
0
2
2
0
1
2
1
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
3
2
0
0
0
0
0
0
2
0
3
1
2
2
1
0
1
1
0
0
0
1
0
2
3
1
0
0
1
0
1
1
0
0
1
0
1
2
0
1
0
2
0
0
0
0
1
0
0
1
0
1
2
2
1
1
0
2
1
0
0
0
0
0
0
0
1
2
2
2
2
0
1
0
0
2
2
1
2
1
0
0
0
0
1
1
2
0
0
1
1
1
1
2
1
0
2
1
0
1
2
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
1
2
0
1
0
0
1
2
1
0
2
1
2
2
0
1
0
0
0
0
0
0
0
2
0
1
0
2
2
1
1
2
1
0
0
1
2
0
1
0
0
1
2
1
0
2
2
1
1
0
2
2
0
2
1
1
1
0
1
2
0
2
1
1
0
2
0
1
3
3
0
0
0
1
0
0
0
0
0
1
1
0
1
2
2
1
1
1
0
0
1
1
0
1
2
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
2
1
2
1
0
0
0
1
1
0
0
2
0
0
1
0
1
0
2
0
1
0
0
0
1
0
0
0
1
1
0
2
0
1
0
0
2
3
6
3
3
2
0
1
0
0
1
0
0
0
0
1
1
0
1
0
1
1
1
2
0
1
0
2
2
0
0
0
1
0
1
1
0
0
0
3
0
1
0
1
1
0
1
1
1
0
1
0
2
0
0
2
0
2
2
1
1
0
2
0
0
1
2
0
2
1
1
0
0
1
0
1
0
2
0
1
2
1
0
2
2
2
0
3
1
0
2
0
0
1
0
1
0
0
2
2
0
1
0
0
2
1
2
1
1
1
0
0
0
0
0
0
1
1
1
1
2
0
1
0
0
0
2
0
0
1
0
1
2
0
2
0
0
0
0
2
1
1
3
1
0
0
2
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
1
1
0
0
0
0
1
1
0
0
2
2
1
1
0
1
1
1
0
0
1
1
1
2
0
2
2
2
0
2
0
1
1
0
1
2
0
0
3
1
0
0
0
1
0
0
1
0
0
1
1
0
0
1
0
2
1
0
0
2
2
2
3
0
1
2
1
1
1
0
2
1
0
2
1
1
1
1
1
0
0
0
0
0
2
2
1
1
0
0
0
0
1
0
1
1
0
0
0
1
2
2
0
0
2
1
1
0
1
1
0
0
1
0
1
1
1
1
1
1
0
0
0
0
2
2
0
1
1
0
2
0
0
0
0
0
2
0
0
0
1
1
0
1
0
0
1
1
0
1
0
0
2
1
1
1
0
0
0
1
1
1
0
0
1
0
0
1
1
3
0
3
1
0
0
1
1
0
1
2
0
0
1
1
1
0
0
1
1
0
2
1
1
1
1
0
0
0
0
1
1
1
0
1
2
0
1
0
0
1
1
1
1
0
1
1
1
0
2
1
1
0
1
0
2
2
2
0
0
1
1
0
2
1
0
0
1
0
0
1
1
1
2
0
0
1
1
0
0
0
2
1
2
1
1
1
0
1
1
0
1
0
1
2
2
0
2
1
1
0
0
0
0
0
1
1
0
0
1
0
0
0
1
1
0
1
2
1
1
2
2
0
0
0
1
2
2
0
0
2
1
0
0
2
0
1
0
2
0
0
0
0
2
1
3
0
2
2
1
0
0
0
2
5
0
0
0
2
0
2
0
2
0
0
1
1
0
1
2
1
2
1
0
0
1
2
0
1
0
1
2
1
2
2
0
0
1
1
0
2
0
1
0
2
1
1
0
1
0
1
0
2
2
1
0
1
1
0
1
1
0
3
1
2
0
0
2
2
0
2
0
5
0
1
1
1
0
2
0
0
1
1
0
0
1
0
0
0
1
1
0
0
0
0
1
1
0
1
0
0
0
2
0
2
0
2
2
2
0
0
1
1
0
0
0
3
1
0
1
0
0
0
0
1
2
2
0
0
2
0
1
0
1
1
1
1
0
0
2
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
1
8
0
0
0
2
1
0
0
0
0
0
0
1
0
2
2
1
0
0
1
0
2
0
0
2
0
0
0
1
1
1
1
2
0
0
0
0
1
0
2
0
0
0
0
0
0
1
1
1
0
2
2
2
0
0
0
0
1
2
0
1
2
0
0
2
2
2
0
0
0
0
1
1
1
1
2
1
1
0
0
0
1
2
1
0
0
0
0
0
2
1
2
1
1
0
2
0
1
1
0
0
0
0
0
0
0
0
2
0
2
0
3
0
0
1
0
1
0
0
1
2
0
0
0
0
0
2
1
0
1
1
2
1
2
0
0
0
1
1
1
2
0
0
0
1
2
1
0
2
1
2
0
0
0
2
2
0
1
1
1
0
0
1
1
1
3
0
0
0
3
2
1
1
1
0
0
1
0
0
2
1
0
2
0
0
0
1
2
1
2
2
1
2
0
0
0
1
0
0
2
0
1
1
2
2
1
0
0
0
1
0
1
1
1
0
2
0
0
0
2
0
2
1
0
1
0
0
1
1
0
1
1
0
0
1
0
0
1
0
2
1
0
1
1
0
1
0
0
0
1
1
1
1
2
2
1
0
0
1
1
2
0
2
1
1
0
1
0
2
0
1
0
0
2
1
0
2
0
0
2
1
0
1
2
0
0
2
1
0
0
0
2
0
2
1
1
1
0
0
1
0
0
1
1
2
1
0
1
0
0
1
1
1
2
0
0
2
0
0
1
2
0
1
1
0
1
0
0
2
0
1
0
0
1
0
2
0
2
0
0
0
0
1
0
1
1
2
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
1
1
0
1
1
1
0
1
2
1
0
0
0
1
2
0
1
0
2
1
1
0
1
0
0
1
2
0
1
2
0
3
0
0
0
1
0
1
0
1
1
1
0
1
2
0
0
0
1
1
1
0
0
1
1
1
0
0
0
2
1
2
0
2
1
2
0
1
2
0
1
1
2
0
0
1
2
0
1
0
2
2
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
1
2
2
3
0
2
0
0
1
0
2
1
1
2
1
1
11
2
1
0
0
0
0
0
0
0
2
0
1
1
0
2
0
2
2
0
0
0
1
0
1
1
1
1
1
1
1
0
1
1
0
0
0
1
2
1
1
2
0
1
1
2
1
1
1
2
2
1
1
0
0
0
1
1
1
2
0
0
0
1
1
0
1
1
1
2
1
1
0
0
1
1
0
2
0
0
0
2
0
0
1
0
1
0
1
2
0
0
0
0
1
1
1
0
2
2
1
0
1
0
0
0
0
2
1
0
0
2
2
2
1
0
0
1
0
1
0
1
1
1
2
1
0
0
1
0
1
0
0
0
1
0
0
1
1
1
0
0
2
0
0
0
0
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
0
2
1
0
1
0
2
1
2
0
0
2
0
2
0
1
1
0
0
1
1
0
1
0
0
2
2
1
3
2
1
1
1
0
0
0
2
1
0
0
1
1
0
2
0
1
0
0
0
1
0
2
0
0
0
1
0
0
0
0
1
0
2
2
0
0
0
2
0
1
2
0
1
2
1
0
1
1
0
0
2
2
1
1
2
1
0
2
2
1
2
1
1
2
0
0
0
2
1
2
3
5
1
0
1
0
1
2
1
2
0
0
2
0
1
1
0
0
1
1
0
0
0
4
1
2
2
0
2
2
0
0
1
0
0
0
0
0
0
2
0
2
1
0
1
2
1
0
1
0
0
2
1
2
1
0
1
1
0
0
0
0
1
2
0
0
1
2
1
2
0
0
1
1
0
1
1
0
0
0
1
1
0
1
1
1
0
1
1
0
0
1
0
1
1
2
0
0
1
0
2
0
1
0
0
2
0
0
1
0
1
2
0
3
1
1
0
1
1
0
1
0
1
0
1
2
0
0
1
0
0
1
0
1
0
2
0
2
0
1
1
0
1
0
2
0
0
2
0
0
0
0
1
0
0
2
0
1
1
1
0
0
1
0
2
0
6
1
0
3
0
0
0
1
1
0
2
1
0
0
2
2
1
1
2
1
0
0
0
1
0
0
1
0
0
1
1
1
1
0
0
1
1
0
0
2
2
0
2
0
1
0
0
2
2
1
1
2
0
1
0
0
1
2
0
0
2
2
0
0
0
2
2
0
2
1
2
1
0
1
2
0
0
0
1
0
1
1
2
0
0
1
1
3
1
0
2
1
1
0
0
0
0
0
2
1
1
0
0
1
2
1
1
0
1
2
2
1
2
2
1
0
0
1
0
0
0
0
2
1
1
1
0
1
0
0
0
1
0
0
0
1
1
1
0
0
0
2
2
0
2
0
0
0
1
1
2
0
1
1
1
1
2
1
1
0
3
1
2
1
1
2
1
2
0
2
0
0
2
1
0
0
1
0
0
0
0
1
2
1
0
2
1
2
2
2
0
2
1
1
1
3
0
2
0
2
0
1
0
1
0
1
0
0
1
2
2
0
0
0
2
1
1
0
4
0
0
1
0
2
0
1
1
0
0
0
1
0
2
0
0
2
1
2
1
0
0
0
1
0
0
3
0
0
0
1
1
2
2
0
1
1
0
0
2
1
1
2
1
0
0
1
2
0
0
0
0
1
0
2
0
2
1
2
1
1
1
0
0
1
2
1
4
2
0
0
0
2
0
1
1
1
2
1
1
0
1
0
1
1
0
0
1
0
1
1
0
1
0
0
0
2
0
0
1
0
2
1
0
0
2
0
1
0
0
0
2
1
2
1
1
1
1
0
2
0
1
2
1
0
1
0
0
0
4
0
1
0
0
0
2
0
0
0
1
1
2
0
0
2
0
1
1
0
3
0
1
0
0
1
0
2
0
1
2
0
2
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
1
2
1
0
0
1
1
0
0
0
0
1
1
1
1
0
1
1
1
3
0
0
2
2
0
0
0
0
1
1
1
1
0
1
1
1
0
1
2
1
0
0
1
0
1
2
0
1
1
0
1
2
0
0
1
1
1
0
0
0
1
0
0
2
1
0
0
1
2
0
0
0
0
1
2
3
0
0
0
1
1
0
2
0
0
1
1
1
0
2
0
0
0
0
2
2
1
1
2
1
1
1
0
1
0
0
1
1
0
0
2
1
1
0
0
0
1
1
2
0
1
2
1
0
0
1
0
0
1
0
0
1
2
0
1
0
2
0
0
2
0
0
0
0
0
2
0
1
1
1
1
1
2
0
1
0
1
0
1
1
0
2
2
0
0
1
2
1
1
2
0
2
0
1
0
1
3
0
0
0
0
0
0
1
0
0
2
2
0
1
1
0
1
2
1
0
2
1
1
0
1
1
1
1
1
1
2
0
1
0
0
0
2
0
2
1
2
0
0
0
0
0
0
1
1
1
1
1
2
2
0
0
1
0
2
0
0
0
0
0
0
0
3
2
0
2
0
0
0
0
3
0
2
0
1
0
1
0
0
0
0
0
1
1
1
1
0
1
0
0
2
0
0
0
0
1
1
1
0
0
0
0
0
0
1
1
0
1
1
1
1
1
0
1
1
0
0
1
1
1
1
0
1
0
0
1
0
1
0
2
2
1
1
1
1
0
1
0
1
2
1
1
3
0
0
0
0
2
2
0
1
1
0
1
0
0
0
1
2
1
2
1
0
0
0
0
0
2
1
1
0
0
1
0
1
1
2
0
1
1
0
1
1
0
0
1
0
2
1
0
0
1
0
0
1
1
1
1
0
0
1
1
0
0
1
0
1
0
4
0
2
1
0
0
1
0
2
0
2
1
3
2
0
0
0
1
1
0
1
0
1
2
1
0
0
1
1
0
1
1
0
1
0
1
0
1
0
2
0
0
0
0
1
2
0
0
1
1
0
1
2
0
0
2
1
0
2
0
2
0
1
0
0
1
0
0
2
1
0
1
2
0
0
2
2
0
0
1
1
0
1
2
0
0
1
1
2
0
1
4
1
0
1
1
0
1
1
2
1
0
1
1
0
0
1
2
3
1
0
0
1
0
2
0
2
2
0
0
1
0
1
1
0
1
1
1
0
2
1
0
0
0
2
1
2
2
0
1
0
2
0
1
0
2
1
2
0
1
1
0
0
0
0
0
0
1
1
1
1
2
0
1
1
2
2
0
0
1
1
0
1
0
0
0
2
1
0
1
1
0
0
1
1
1
0
2
1
0
0
0
2
1
2
0
1
0
0
1
0
2
0
1
0
0
0
1
1
0
0
0
0
2
1
1
1
1
2
2
1
0
0
0
0
4
2
1
1
1
0
0
0
1
0
0
0
0
0
0
2
2
0
1
2
1
0
0
0
0
1
0
1
0
3
0
0
1
1
0
2
0
2
1
0
0
1
2
0
1
0
0
0
1
3
1
1
2
0
0
1
2
0
0
2
1
1
2
2
3
0
2
1
2
1
0
1
0
0
1
1
2
2
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
1
0
2
1
1
0
2
1
0
1
0
2
1
3
2
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
2
1
0
1
2
0
2
1
1
2
0
2
1
1
1
1
1
0
0
2
0
0
0
1
1
0
1
1
1
2
1
0
2
0
2
0
0
0
1
1
1
0
1
1
1
0
0
0
0
2
1
0
0
0
1
1
0
0
2
1
2
1
1
0
0
1
1
1
1
1
0
0
0
1
0
2
2
0
1
1
0
0
1
0
0
0
0
0
0
1
1
0
1
2
0
0
1
0
0
1
0
0
1
0
2
1
0
1
1
0
0
1
0
0
0
1
1
2
0
2
2
0
2
1
1
0
1
1
0
1
0
2
2
3
0
0
0
0
0
1
1
0
0
0
2
1
1
0
2
1
0
1
0
0
1
0
1
0
1
1
0
0
0
0
2
1
1
0
1
1
0
2
0
1
2
0
1
1
0
0
0
0
2
1
1
0
1
0
1
0
0
1
0
0
0
0
0
2
1
0
1
0
0
1
0
7
1
2
0
1
0
0
1
1
0
0
1
1
1
1
0
0
1
0
2
0
1
2
0
0
1
1
1
1
2
2
0
1
1
1
1
0
1
0
0
2
0
1
1
2
0
0
1
0
0
2
0
2
2
1
2
1
2
1
1
0
0
3
0
2
0
1
2
0
0
1
0
0
2
0
2
0
0
2
1
2
0
0
0
2
0
0
1
0
1
0
1
2
0
0
1
0
0
1
1
1
2
1
0
4
1
3
0
2
0
0
1
1
0
0
0
2
2
0
1
2
1
1
1
1
1
0
1
2
1
1
2
1
1
0
1
0
0
0
0
1
0
0
0
1
1
2
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
1
1
1
0
1
0
0
0
0
2
2
1
0
0
0
2
0
1
0
1
0
0
1
0
2
0
0
0
1
1
0
0
0
1
0
0
1
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
1
1
1
1
1
0
1
0
2
0
0
2
0
2
2
0
1
1
1
0
1
1
0
2
0
2
0
1
1
2
2
0
0
0
2
0
1
3
0
0
0
0
0
0
0
1
3
2
0
2
2
0
0
0
0
0
3
1
0
0
2
2
1
0
2
1
0
1
0
1
0
1
1
0
1
2
0
0
0
0
1
0
1
0
0
0
1
0
2
1
2
0
0
1
1
0
0
1
4
2
0
1
0
1
0
0
0
1
0
0
0
0
2
0
2
2
0
1
0
0
0
0
1
0
1
0
0
3
0
1
0
1
1
2
0
0
1
0
1
1
0
1
1
0
0
0
0
2
0
0
0
0
2
0
0
2
2
0
0
1
0
2
2
0
0
0
2
1
1
1
0
2
1
1
2
1
0
1
3
1
0
0
0
0
1
2
0
0
2
0
2
1
1
0
1
0
1
1
1
2
1
0
0
0
1
0
1
1
1
0
0
1
1
2
0
0
1
0
1
0
1
0
0
0
1
1
0
1
2
1
0
1
0
1
0
0
0
1
4
1
1
2
1
2
1
1
1
0
0
2
1
0
1
0
1
0
2
0
0
0
0
0
1
2
1
0
1
1
2
0
0
0
0
0
2
1
0
0
1
1
1
0
2
0
0
0
1
2
1
8
2
1
2
1
0
0
0
1
0
0
1
1
1
2
1
2
1
1
0
0
1
1
2
2
0
0
2
0
0
2
0
0
1
0
0
0
2
1
2
2
0
1
0
0
1
0
0
1
2
0
1
0
0
0
1
0
0
2
0
2
0
1
0
0
0
1
0
2
2
1
2
1
3
0
2
0
0
0
2
1
0
1
1
2
0
0
1
2
0
1
0
0
0
1
1
0
2
1
0
0
2
1
1
1
0
0
3
1
0
0
1
0
1
0
1
2
1
2
1
0
0
1
2
0
2
1
1
0
1
0
2
0
2
2
0
0
2
2
2
1
1
0
0
1
1
0
1
1
2
2
1
1
2
2
1
0
0
1
0
1
2
0
1
1
0
1
2
1
1
0
0
0
0
2
1
0
2
0
1
2
0
1
0
1
1
1
1
0
0
1
2
1
2
0
0
4
0
0
0
1
2
0
1
2
0
2
1
1
2
0
1
2
1
1
0
0
1
1
1
0
0
2
1
0
0
1
0
0
2
1
0
2
0
0
1
1
0
2
0
0
0
1
2
2
2
1
1
0
1
1
1
1
0
0
1
0
0
2
3
1
0
3
0
2
0
1
1
0
1
1
1
1
0
0
0
1
1
1
2
1
1
0
1
0
0
2
1
0
2
1
1
0
1
1
1
0
1
0
0
3
0
0
0
0
0
2
2
2
1
0
0
2
1
0
1
1
0
2
1
2
0
0
2
1
2
1
0
1
0
0
0
1
2
1
0
2
0
1
1
1
0
1
2
1
2
0
0
0
2
0
0
1
0
1
0
0
0
1
1
0
0
2
1
0
0
0
1
0
0
0
0
0
0
1
2
0
1
2
0
0
2
1
0
0
1
0
1
1
0
0
0
1
1
1
0
1
2
0
1
1
0
2
1
0
1
2
1
0
0
2
0
0
0
0
2
0
0
1
2
1
1
0
0
1
0
0
1
1
0
0
2
2
0
1
0
2
2
1
0
1
0
0
5
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
3
1
0
0
1
0
1
0
1
2
2
1
1
0
0
1
1
0
2
0
1
0
2
2
2
2
2
2
0
0
0
1
1
1
0
2
2
2
0
0
0
2
0
0
2
0
0
0
0
1
0
0
1
2
1
1
0
1
0
3
1
1
0
2
0
0
2
0
0
1
1
0
1
1
4
2
0
2
3
0
0
1
1
0
1
0
2
1
0
1
2
1
1
2
2
0
0
2
1
0
0
2
2
0
1
2
1
2
2
0
2
2
0
0
1
2
1
0
1
0
0
1
0
1
2
1
0
2
2
2
0
0
2
0
0
0
0
2
1
2
1
1
1
1
0
2
1
0
0
1
1
1
2
0
1
0
1
1
4
0
2
1
1
1
2
0
2
0
3
1
1
2
3
0
0
2
1
0
1
1
0
0
1
0
1
1
0
2
1
1
0
0
0
0
1
0
2
0
0
1
2
2
1
0
0
0
1
0
3
3
2
0
1
0
1
0
0
1
0
0
2
0
1
2
0
1
1
0
1
0
0
0
1
4
1
0
0
1
0
0
0
1
1
0
0
1
0
1
0
0
0
0
1
2
0
0
2
2
1
0
0
2
1
0
1
1
2
2
1
0
0
1
0
1
1
0
1
0
1
1
2
2
0
0
2
1
2
0
1
0
0
0
0
1
1
0
0
1
2
0
0
0
2
0
0
1
3
0
1
0
1
0
0
0
0
1
2
2
0
1
0
2
2
1
0
3
0
1
0
0
1
0
0
0
0
0
1
0
2
1
1
0
2
0
0
2
0
2
0
0
2
0
0
0
1
1
0
0
2
2
2
2
1
1
0
1
1
0
0
0
2
1
3
0
2
1
0
2
2
1
2
2
2
0
0
1
2
0
0
0
1
0
0
1
1
0
2
0
0
0
0
1
4
2
1
2
0
0
1
1
0
0
1
0
1
0
0
2
1
1
0
0
1
1
1
1
2
1
1
0
0
1
2
0
1
0
1
0
1
1
1
1
1
1
2
2
2
2
2
2
4
1
0
1
3
0
1
2
0
0
0
1
0
1
1
1
1
1
1
1
2
1
1
2
0
1
0
2
1
0
1
0
1
1
1
0
0
2
1
1
2
1
3
0
0
1
1
1
1
1
1
0
0
0
2
0
1
0
2
0
1
0
1
2
0
4
0
0
0
0
3
1
0
2
0
1
0
0
2
1
0
0
1
2
1
0
2
1
0
2
2
0
1
1
1
1
1
1
0
0
0
1
1
0
0
2
0
1
0
1
0
1
1
0
1
0
2
0
1
0
2
2
0
0
0
0
2
2
0
1
1
2
2
0
1
1
0
0
2
0
1
0
2
2
0
0
1
1
0
2
0
2
0
3
0
0
1
0
2
2
0
0
1
0
1
0
0
1
1
2
0
0
0
0
1
1
2
0
0
2
0
0
0
2
0
0
2
2
0
2
1
2
1
1
2
0
0
2
1
1
1
0
1
1
2
0
2
0
0
1
0
2
0
1
1
0
2
2
2
0
1
0
2
2
0
1
1
1
1
0
1
2
0
1
2
0
2
0
0
2
0
0
0
0
0
1
0
3
1
0
2
0
3
0
2
0
1
0
0
0
0
1
0
1
1
2
0
1
1
5
0
0
1
0
2
1
0
1
0
0
3
0
2
1
0
0
1
1
2
0
2
2
0
0
0
0
2
2
0
0
0
2
0
1
2
1
2
2
0
0
1
0
2
2
1
1
2
0
0
2
1
0
2
2
0
0
0
1
1
0
0
0
1
0
1
1
0
1
0
0
1
0
0
0
0
1
0
0
1
1
0
1
2
2
2
0
2
1
1
1
0
0
2
2
2
0
1
1
1
0
2
2
0
0
1
2
0
1
1
2
0
2
1
2
1
0
2
1
1
1
2
1
0
0
1
1
1
0
0
3
0
1
0
1
1
0
2
1
1
0
1
1
1
5
1
0
2
0
2
0
0
1
0
0
0
0
0
1
0
0
0
2
1
2
1
0
2
3
1
1
0
2
0
0
0
1
0
0
0
0
0
1
2
1
2
1
1
0
1
2
0
1
2
0
1
0
1
0
0
0
1
0
0
0
1
1
0
0
3
1
2
0
2
0
1
2
0
1
0
3
0
1
1
0
0
1
1
0
0
0
0
2
2
2
4
1
2
2
0
2
0
0
0
2
2
0
2
0
0
1
1
2
2
0
0
0
1
0
1
1
1
2
1
1
2
0
2
4
0
1
1
2
1
1
0
2
1
0
2
1
0
0
1
1
0
1
2
0
0
2
1
2
0
1
0
0
1
0
0
0
0
2
0
0
3
1
1
0
0
2
1
1
1
0
1
0
0
0
2
1
0
1
2
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
1
1
2
1
1
0
2
1
0
1
0
1
0
1
0
2
0
3
1
1
2
0
2
0
0
3
1
2
2
2
0
1
1
1
1
0
1
2
1
1
1
2
1
3
0
2
1
0
1
2
0
1
2
2
2
1
2
2
0
1
2
0
0
2
2
2
1
2
0
2
2
2
0
0
0
2
1
1
1
0
1
0
1
2
0
0
1
1
2
1
0
1
2
2
2
1
2
0
0
1
0
2
1
2
0
1
1
1
4
0
1
2
1
1
0
0
2
1
1
1
0
2
0
0
1
0
1
2
0
0
0
1
1
0
1
1
2
2
1
2
2
2
1
2
1
1
1
0
2
1
2
0
1
2
2
0
0
0
0
0
0
1
0
0
0
1
0
1
1
2
1
1
2
1
4
1
1
2
0
0
0
2
0
0
1
2
0
1
1
1
1
2
1
0
2
2
1
1
1
1
0
0
1
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
1
0
0
0
1
1
1
0
1
2
2
0
1
0
0
0
1
0
0
2
1
0
0
0
2
0
1
0
2
2
0
1
1
2
3
2
0
2
0
1
1
2
1
1
0
0
0
0
0
2
0
1
1
0
2
1
0
1
2
0
0
1
1
0
2
2
0
1
0
1
2
2
0
1
1
0
0
0
1
1
2
0
2
2
0
2
0
1
0
2
0
2
0
2
1
0
2
0
2
1
1
0
2
0
0
1
2
0
0
0
1
0
1
0
0
0
0
0
2
0
2
1
1
0
1
2
2
2
0
1
0
0
1
2
2
1
0
4
1
2
2
1
1
2
1
1
0
0
1
0
0
0
0
2
0
1
1
0
0
0
0
1
0
0
0
1
1
1
0
1
0
1
0
2
1
1
2
0
0
1
1
0
1
2
0
0
1
0
3
0
1
2
0
1
1
0
1
0
1
0
0
1
1
0
2
0
1
0
1
1
0
1
0
0
0
0
2
1
1
2
1
2
2
1
2
2
1
2
0
1
0
0
0
2
1
0
0
1
3
2
0
1
1
0
0
0
1
2
0
1
1
1
2
1
1
3
1
1
1
1
2
2
1
2
0
1
1
1
1
0
0
1
0
0
2
2
1
2
1
1
2
0
1
1
2
0
0
2
0
0
1
0
1
0
0
0
1
1
0
0
0
0
2
1
0
2
2
2
0
1
0
0
1
2
1
1
1
1
0
2
1
1
1
0
1
0
0
0
0
0
0
1
2
0
0
2
1
1
2
0
2
0
0
0
1
0
2
1
2
0
1
0
1
0
0
0
1
2
0
0
0
1
0
0
0
1
1
0
0
1
1
1
2
0
2
1
0
2
1
1
1
2
2
1
0
0
0
0
1
0
0
0
1
0
2
1
0
2
1
1
0
1
2
1
1
0
1
0
2
1
1
1
0
2
0
0
2
1
2
0
0
2
2
1
1
1
0
0
1
3
0
2
0
1
0
0
1
1
2
0
0
0
2
2
0
1
0
0
1
0
0
1
0
0
3
0
1
0
1
1
0
2
1
0
1
2
1
3
1
1
3
0
0
2
1
0
2
1
1
0
1
1
1
0
0
1
0
0
1
2
2
0
1
1
2
1
1
0
0
0
1
0
2
1
1
1
0
2
0
0
0
1
2
2
0
0
0
0
0
0
2
1
0
1
5
0
0
0
0
0
0
0
1
1
0
1
1
1
0
1
0
2
0
1
0
1
1
0
0
2
0
1
1
0
2
1
1
2
0
0
0
1
0
0
2
1
0
2
2
0
2
2
1
2
2
0
0
2
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
1
1
1
1
0
0
0
2
0
2
2
0
1
1
0
1
0
0
0
1
1
0
0
0
0
1
1
2
1
3
0
0
2
0
1
1
1
0
0
2
1
0
0
3
2
0
2
2
0
0
1
1
0
0
0
0
1
0
0
1
0
0
3
2
1
2
2
0
1
1
1
2
0
1
0
2
1
0
0
0
1
0
0
0
1
2
0
1
0
2
0
1
0
0
0
0
0
1
2
0
2
1
1
0
1
2
1
0
0
0
0
1
0
0
2
0
2
2
0
2
0
0
0
0
2
0
0
0
1
0
0
1
1
2
2
1
0
2
2
0
1
2
1
2
3
0
0
1
1
1
0
2
2
0
0
0
1
2
0
0
0
1
2
0
1
3
0
2
1
1
2
2
0
1
1
2
2
1
2
2
1
0
0
1
1
0
0
2
0
1
1
1
1
2
1
1
1
1
0
1
0
0
1
2
1
1
0
0
2
0
2
1
1
0
2
0
2
0
0
1
1
0
2
2
1
1
1
1
2
2
2
3
1
1
1
1
0
2
2
2
1
2
2
0
0
0
1
2
0
2
0
0
1
1
2
1
0
0
1
0
1
2
0
1
0
2
1
1
0
0
0
1
1
0
1
3
2
2
2
1
1
3
2
0
0
0
2
1
1
0
1
0
2
0
0
1
0
1
0
2
1
0
0
1
0
1
1
1
1
0
1
2
1
1
0
0
0
0
0
0
1
2
0
2
1
1
1
0
0
2
0
2
2
0
1
0
1
2
1
1
0
2
0
0
2
1
0
1
0
2
2
2
1
0
2
2
0
1
0
0
0
1
0
2
0
2
0
1
0
0
2
0
1
2
1
2
3
0
2
0
2
1
2
0
0
1
1
1
0
1
0
2
1
0
1
0
1
0
0
2
2
1
1
1
0
0
3
0
0
1
0
0
1
0
2
0
1
1
1
2
2
2
0
1
0
1
0
0
1
2
2
1
2
0
0
0
2
2
0
0
0
4
1
1
0
1
2
2
0
2
0
0
2
1
0
4
0
1
0
2
0
0
1
0
1
0
3
1
0
0
1
2
1
2
0
1
0
1
1
1
0
0
0
1
0
2
0
1
0
0
0
0
1
0
1
2
1
0
2
0
1
3
0
0
1
2
1
0
1
1
0
1
0
0
0
1
0
0
1
1
2
0
0
1
1
2
1
0
2
0
0
0
1
2
0
0
1
0
0
1
0
0
1
0
0
1
2
1
1
2
1
1
1
0
0
0
1
2
2
0
0
1
1
0
1
2
1
0
2
1
2
1
0
1
0
0
0
0
0
1
1
1
2
0
0
0
0
1
2
0
2
2
1
0
0
0
2
1
1
0
0
0
1
0
2
0
1
2
1
0
1
0
0
2
1
2
1
1
0
0
0
0
0
1
0
1
0
0
2
0
2
2
2
1
2
1
0
2
2
2
0
0
1
3
0
1
2
0
0
1
2
0
0
1
0
2
0
0
1
0
1
2
0
0
2
0
1
0
2
1
1
0
1
0
0
1
0
1
2
1
1
2
1
0
1
2
0
0
0
1
0
0
0
1
2
1
0
0
0
0
0
1
0
0
0
1
1
1
0
2
1
0
0
1
0
1
2
1
0
0
0
0
1
0
0
1
1
0
1
2
0
1
3
2
0
1
1
0
0
1
2
1
1
2
0
1
0
0
2
1
0
0
2
0
0
3
1
1
1
0
2
0
0
1
1
1
1
0
0
0
2
0
0
0
0
1
0
2
0
0
0
2
0
1
0
0
1
2
2
0
1
0
0
0
0
2
1
1
1
1
1
0
0
1
0
0
1
1
0
0
0
0
0
0
2
1
0
1
0
1
2
0
1
0
1
1
1
1
2
1
1
1
1
0
0
0
0
2
1
1
0
1
0
1
2
0
0
0
0
0
1
2
0
1
1
1
0
0
1
0
1
1
1
0
0
1
1
3
0
0
1
1
3
2
1
1
0
0
0
0
1
0
0
0
1
2
0
0
2
2
0
0
1
1
0
0
2
1
1
1
0
0
0
1
1
0
2
0
2
1
1
2
1
1
2
0
1
0
0
0
1
0
0
0
0
2
1
0
0
0
1
1
0
2
0
0
0
1
1
1
0
0
0
1
2
0
2
0
1
2
0
0
1
0
0
3
1
0
1
1
0
0
0
1
0
1
0
0
1
1
0
0
1
2
1
0
0
0
1
1
2
2
1
0
0
0
1
1
0
1
0
2
0
0
2
1
1
2
1
0
1
0
0
2
0
1
1
3
1
0
0
1
1
1
0
2
0
0
2
0
0
0
0
0
0
2
0
1
0
1
0
0
1
2
1
0
0
2
1
0
1
2
2
1
0
0
2
0
3
1
1
0
1
2
2
1
0
0
1
0
0
0
0
1
0
1
1
1
1
0
0
1
1
0
0
0
2
0
0
0
1
0
1
0
3
1
2
2
0
0
1
1
0
1
1
0
2
1
0
2
0
1
0
1
0
1
0
0
0
0
1
0
1
0
1
1
0
2
1
0
1
0
0
1
2
0
1
1
2
2
0
0
1
0
1
0
0
0
2
1
1
1
3
0
0
0
2
1
1
0
1
1
0
1
0
0
2
0
0
0
1
1
3
1
0
0
0
1
1
0
0
0
0
1
1
1
2
1
1
1
1
0
0
2
0
2
1
0
1
0
0
1
1
0
1
0
1
0
0
0
1
1
0
0
0
0
1
0
0
5
1
1
2
0
0
0
1
1
0
1
0
1
0
2
2
0
1
3
0
0
2
0
1
0
0
0
1
1
0
1
1
0
1
1
0
2
1
1
0
2
0
0
1
2
2
0
1
1
0
2
0
1
1
2
2
0
0
0
1
0
2
0
0
0
0
2
0
0
0
1
2
0
1
1
2
2
0
1
2
0
1
0
0
0
0
0
2
2
2
0
0
1
1
1
2
1
2
0
1
0
0
0
2
0
1
0
0
1
0
0
2
0
1
1
2
1
0
2
1
0
0
2
0
2
2
1
0
0
2
0
0
1
2
1
2
2
0
1
1
1
0
0
0
2
1
2
1
0
0
1
1
0
1
0
1
0
1
2
0
0
1
0
0
0
1
2
0
0
1
2
0
1
1
1
0
1
2
2
0
2
0
1
0
0
2
0
1
0
1
0
0
1
1
2
1
2
1
1
2
0
1
2
0
0
0
1
0
2
4
1
1
1
0
0
2
0
0
1
2
1
0
0
0
3
1
4
1
0
0
0
0
2
0
1
2
0
1
1
2
2
2
0
1
0
0
0
0
2
0
0
1
1
2
0
0
1
1
1
0
0
2
1
0
0
1
0
0
1
1
0
0
2
0
0
1
1
0
1
0
1
0
0
2
1
2
1
0
2
1
0
2
1
1
0
2
0
0
2
0
0
1
1
1
1
1
2
0
1
1
0
0
1
0
0
0
2
1
0
0
2
0
0
1
1
1
1
0
2
0
1
0
2
2
0
0
2
0
0
0
0
0
1
2
2
1
0
1
0
1
2
0
1
1
0
0
1
0
0
0
1
0
1
1
0
1
0
1
2
1
0
1
1
0
0
1
1
2
1
0
0
3
0
1
0
1
2
0
0
1
1
0
2
1
0
1
1
1
0
0
1
0
2
0
3
0
1
1
2
0
0
2
0
0
1
2
1
0
0
1
2
0
0
1
0
1
0
1
0
2
1
0
1
2
2
1
0
0
2
0
0
0
0
0
0
0
1
0
1
2
4
2
0
1
0
1
0
0
2
0
0
2
0
2
1
0
0
1
2
1
0
0
1
1
0
0
1
1
0
1
0
1
1
2
1
0
1
1
2
0
0
0
1
2
0
0
0
2
0
1
6
1
1
1
2
0
1
0
0
0
4
1
1
1
1
0
1
1
2
2
5
1
0
0
0
1
1
3
1
1
2
0
0
2
0
1
0
0
2
1
0
4
2
1
1
2
2
0
2
0
0
1
0
0
1
1
3
0
0
0
0
0
0
1
0
1
1
1
0
0
0
2
0
1
2
1
0
1
0
0
2
0
0
2
1
1
2
1
0
0
2
1
0
0
1
0
1
1
3
0
0
1
0
1
0
0
0
0
1
1
0
1
2
2
0
0
0
1
1
0
0
1
0
0
1
1
1
2
0
0
1
2
0
0
0
1
0
0
1
0
0
0
3
1
1
2
2
2
0
0
0
1
0
2
0
2
0
2
0
0
0
2
1
0
2
0
1
2
0
0
0
1
0
0
0
1
0
2
3
0
2
1
2
0
1
0
3
0
1
1
0
0
2
0
0
1
1
0
1
1
2
0
2
0
0
2
2
2
2
0
3
0
0
0
2
2
0
0
0
2
0
1
2
0
0
0
0
0
0
0
2
0
1
1
1
1
1
0
2
0
0
0
1
2
1
2
0
0
2
0
0
1
4
2
0
0
0
1
0
0
1
0
1
1
1
2
1
2
1
1
0
2
0
1
1
1
2
0
0
1
0
2
2
0
2
1
1
2
1
1
2
0
0
0
2
1
2
0
0
0
0
1
1
0
0
1
0
0
0
2
0
1
1
2
0
0
2
1
1
0
0
1
3
2
0
4
1
0
0
0
0
0
0
2
1
0
1
2
2
1
0
0
0
0
0
0
0
1
0
0
1
0
1
1
2
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
1
1
0
2
0
2
0
1
1
0
0
0
0
0
1
2
2
2
0
0
1
2
2
2
2
7
0
1
0
2
1
1
0
0
0
1
0
2
1
0
1
1
0
1
2
0
0
1
0
0
2
1
0
2
0
0
0
0
0
1
1
2
0
1
0
1
2
0
0
2
2
1
1
2
0
1
2
1
2
1
0
1
1
1
0
1
0
0
2
0
1
1
1
1
0
0
2
1
0
3
1
2
0
1
2
1
0
2
0
0
0
1
0
0
1
2
0
1
1
2
1
1
1
1
0
1
1
1
0
0
1
0
3
1
0
2
0
1
1
1
1
2
0
0
0
0
0
1
0
2
2
0
0
0
0
1
0
2
1
1
2
0
0
1
1
0
1
0
0
2
0
0
0
0
1
0
0
1
2
0
0
0
1
1
1
0
0
0
0
1
0
1
3
0
1
2
1
0
1
0
0
1
0
0
0
0
1
1
0
2
2
0
2
1
1
0
0
0
2
0
1
0
2
0
1
0
3
1
1
2
0
1
1
0
2
1
1
2
1
0
0
2
0
2
1
0
0
0
0
1
2
0
1
0
0
0
1
1
1
2
0
0
1
0
0
1
0
0
0
1
0
2
2
0
2
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
2
1
1
2
1
0
0
1
0
1
0
2
0
1
0
0
2
2
2
0
2
0
3
1
2
0
1
1
0
0
1
1
0
1
0
1
2
0
0
0
0
1
0
2
0
0
0
1
1
0
2
1
0
0
0
0
2
0
3
1
0
2
2
1
0
1
0
2
2
1
0
1
2
0
1
2
1
0
0
0
1
1
0
1
4
1
0
1
1
1
0
0
0
1
2
0
2
2
0
0
0
2
1
2
2
3
2
0
0
1
1
1
1
1
0
0
1
1
0
0
0
2
0
1
1
1
1
1
2
0
0
0
0
0
2
1
0
0
1
2
0
1
0
0
1
0
2
1
0
0
0
1
0
1
2
0
0
0
1
0
2
1
2
2
1
1
0
0
0
0
2
1
1
1
1
0
0
1
1
1
1
0
1
1
2
0
0
2
1
1
0
3
1
1
0
2
0
1
0
0
2
1
0
0
1
0
0
1
0
0
1
1
0
0
0
2
0
0
2
0
1
1
2
2
0
1
2
1
0
2
3
2
1
2
0
1
2
1
0
1
0
1
0
0
1
0
1
0
2
2
1
0
1
1
2
3
2
0
2
0
1
2
0
2
2
1
0
2
0
1
0
1
2
2
2
1
0
0
0
0
0
1
1
1
0
2
1
0
1
2
0
0
0
1
0
1
1
0
2
2
1
2
0
2
1
1
0
1
2
2
2
0
2
1
2
0
2
1
0
1
1
0
2
1
2
1
0
0
1
1
0
1
0
1
2
1
2
1
0
0
0
0
1
0
1
1
1
0
1
2
2
1
0
1
2
1
0
1
1
1
1
1
0
1
0
0
3
0
0
2
2
0
1
0
0
1
1
0
2
0
0
0
0
2
0
0
0
2
0
1
0
0
1
1
0
0
2
1
2
2
2
2
1
0
2
0
0
0
0
4
2
0
0
1
0
0
0
0
1
0
0
0
3
1
0
0
0
2
1
1
1
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
2
2
1
0
2
2
3
0
1
2
0
1
1
1
1
1
2
1
1
0
2
0
1
0
0
1
0
3
1
1
0
1
0
1
0
0
1
0
2
1
0
0
2
5
0
1
4
0
0
1
0
1
2
1
2
1
1
1
1
0
2
1
0
1
2
2
0
1
0
1
0
1
0
0
0
2
1
1
0
0
2
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
2
2
2
0
0
1
0
0
0
2
2
2
0
0
0
1
2
2
0
1
0
2
0
1
0
0
0
2
4
1
2
0
0
1
1
1
1
1
1
0
1
2
2
0
2
2
0
1
0
1
2
2
0
0
0
1
1
0
2
0
0
0
1
1
0
1
0
1
0
1
1
1
1
1
1
0
0
1
0
0
1
1
2
0
2
1
0
0
0
4
2
0
1
0
0
2
0
3
1
0
2
2
1
1
0
0
3
0
2
1
0
1
0
0
2
0
0
2
1
2
0
0
0
1
1
0
0
0
1
2
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
1
1
1
0
0
1
0
0
1
1
1
0
0
0
1
1
2
2
2
1
0
1
2
1
1
0
2
1
0
2
1
0
0
0
0
0
1
1
0
2
1
1
0
0
1
0
0
1
2
1
1
2
1
0
2
1
2
2
0
2
0
0
2
0
2
1
0
2
0
1
1
2
0
0
1
0
1
0
0
2
1
1
1
0
0
0
2
1
1
0
1
2
2
2
0
1
4
0
2
0
0
1
0
1
2
2
2
0
0
2
0
1
0
1
1
1
0
2
1
0
0
0
2
0
1
0
0
1
0
0
0
0
1
2
2
0
0
0
0
0
1
1
0
2
1
1
2
0
1
2
3
2
1
0
0
1
0
2
2
0
1
1
2
0
1
2
1
2
0
1
0
1
0
0
1
1
1
0
1
0
1
0
1
2
0
0
2
3
2
0
1
1
2
0
0
3
0
0
2
2
1
0
2
1
0
3
1
0
0
0
0
1
1
2
2
0
1
0
0
1
2
1
0
0
0
0
1
2
1
1
3
1
0
1
1
0
0
0
0
2
2
1
0
0
0
2
1
2
1
1
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
2
0
1
0
2
0
0
0
1
2
2
1
0
0
0
2
0
0
0
1
0
1
1
2
1
1
1
3
0
0
1
0
2
2
0
1
2
0
0
1
0
1
0
1
1
2
0
1
1
0
2
2
1
1
0
0
1
1
1
0
2
1
0
2
2
0
0
2
0
0
1
0
1
2
1
0
1
1
1
0
0
1
1
0
0
2
1
0
1
2
2
0
2
1
2
1
0
1
0
0
0
0
0
1
0
1
0
2
1
1
1
0
0
2
1
0
0
1
1
0
0
2
1
2
3
1
1
1
1
0
3
0
1
0
3
1
1
0
1
1
0
0
1
2
2
2
1
0
0
2
0
0
0
2
1
1
0
2
1
0
0
1
0
1
1
2
1
1
1
1
0
0
0
1
1
2
1
0
1
0
2
0
1
1
1
1
0
0
0
1
2
1
2
2
0
0
2
0
0
0
2
1
1
0
0
1
0
1
1
1
0
1
1
0
0
0
0
1
1
0
0
2
0
2
1
0
0
2
1
0
1
0
0
0
0
0
2
1
1
0
0
1
1
2
0
1
0
2
1
2
1
0
0
0
1
1
0
1
0
1
1
0
0
0
1
1
0
1
2
2
1
1
2
1
0
2
2
1
2
2
1
0
0
0
2
2
0
0
0
1
0
1
0
1
1
0
1
0
2
2
0
0
0
0
0
0
1
0
3
0
1
1
2
0
0
0
1
0
0
0
1
1
1
0
1
2
2
0
1
1
0
1
0
0
1
0
0
0
1
0
2
0
2
1
2
0
1
2
0
0
0
2
1
1
2
1
1
1
2
1
0
0
1
1
1
0
1
0
0
2
1
0
1
0
1
1
0
2
1
1
1
1
2
0
2
2
1
2
0
2
1
0
2
1
0
1
1
0
1
1
5
1
0
2
1
1
0
1
1
1
1
1
2
0
0
0
2
1
2
0
1
0
1
1
0
0
1
3
0
1
1
0
0
0
0
1
0
0
2
0
1
1
2
2
0
0
0
1
1
0
2
1
0
0
0
1
0
1
1
1
1
1
0
0
1
0
1
0
0
0
2
1
2
0
0
0
1
2
1
0
1
0
0
0
1
0
0
0
2
1
0
1
2
0
2
2
1
1
1
0
2
4
2
1
0
0
0
0
2
0
1
1
2
0
2
2
0
1
0
2
2
0
1
0
0
0
2
0
0
0
1
2
2
2
1
0
0
0
1
1
3
1
1
1
0
0
0
0
2
3
0
0
3
1
0
0
1
1
1
1
1
1
1
0
2
0
1
0
1
0
0
2
2
0
2
0
0
0
0
0
0
0
1
2
0
0
2
2
2
2
2
1
0
1
0
2
3
0
0
0
0
0
0
1
2
0
1
0
2
0
0
1
0
1
0
2
1
0
1
0
2
0
0
0
2
2
0
0
1
0
1
0
0
0
1
2
1
0
0
0
1
0
0
0
1
2
2
0
0
1
3
2
2
2
0
0
0
2
1
0
0
0
1
2
2
1
0
1
0
1
0
0
2
0
0
0
0
0
1
1
1
2
0
0
1
0
1
1
1
1
0
1
2
1
2
1
1
2
1
0
1
1
2
1
1
0
0
2
1
2
1
0
0
0
2
1
2
0
0
1
2
0
0
0
0
0
0
2
0
3
0
1
1
0
2
1
2
0
1
2
1
0
0
1
1
1
0
2
0
2
1
1
1
1
0
1
0
2
1
0
0
1
0
1
1
0
2
2
1
1
1
0
1
0
1
0
0
0
1
0
2
1
0
1
2
2
1
2
0
1
0
0
2
2
0
3
0
0
1
0
2
3
1
0
0
0
2
0
1
1
2
2
1
0
1
0
1
2
2
0
1
1
0
1
2
1
0
1
0
1
0
1
2
0
0
1
1
0
0
0
0
1
2
1
2
0
2
0
0
2
1
0
1
1
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
1
2
1
0
2
0
0
0
2
1
1
1
0
0
0
1
0
2
2
1
2
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
2
0
1
0
0
1
2
0
0
1
2
1
1
0
1
0
0
1
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
2
0
1
1
1
0
1
2
0
1
0
0
0
2
2
1
2
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
1
1
2
2
3
0
0
3
0
0
0
1
0
1
2
0
1
0
2
0
1
0
0
1
2
0
0
0
0
1
0
1
1
1
0
2
0
0
2
2
2
0
0
2
2
1
0
1
0
0
0
0
1
1
1
2
2
3
1
2
1
0
1
0
0
0
0
0
2
1
2
0
0
0
0
1
1
0
0
1
0
1
1
2
0
1
1
0
2
0
2
0
0
0
0
0
0
0
0
2
2
1
2
1
1
0
0
1
2
0
2
2
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
2
2
0
0
0
0
1
1
2
0
0
1
0
0
1
0
1
2
0
1
1
0
1
0
1
0
1
0
0
1
1
2
2
1
0
1
2
0
0
0
1
2
1
0
0
2
0
0
0
2
1
0
2
1
0
1
0
0
0
0
3
1
1
0
2
2
2
1
1
1
0
1
1
0
1
2
1
0
2
2
0
1
1
0
2
2
2
2
0
1
1
1
1
2
2
1
0
0
0
1
1
0
2
0
1
0
0
2
0
1
2
2
0
2
1
0
0
0
1
2
1
2
0
1
1
1
1
0
0
0
2
0
1
0
1
0
0
1
0
0
2
2
4
3
0
1
2
2
1
2
2
0
1
2
2
1
1
0
0
2
0
1
0
1
0
0
0
0
1
0
2
2
1
1
1
0
0
0
1
0
0
0
0
2
2
0
1
1
1
0
1
2
0
2
1
1
0
0
3
1
1
1
1
1
1
0
0
1
1
0
1
2
0
2
1
2
1
2
0
1
1
1
1
2
0
0
0
0
1
2
0
0
1
2
0
1
0
2
0
0
0
2
0
1
0
1
0
1
3
0
2
2
0
2
0
4
0
0
0
2
0
2
0
0
0
0
0
1
1
0
0
1
0
2
0
1
0
2
1
0
1
2
2
1
0
0
2
2
1
0
2
0
1
2
0
0
0
1
2
1
2
0
0
1
0
1
0
0
0
0
0
1
0
1
1
0
2
2
2
2
0
1
0
0
0
0
0
0
2
1
0
1
0
1
1
1
1
0
1
0
0
2
0
0
2
0
1
1
0
1
1
1
0
0
0
1
0
0
2
1
1
0
1
2
0
0
0
3
2
0
3
0
0
2
0
0
1
0
1
1
1
1
1
1
0
0
0
0
0
1
0
0
2
0
0
0
1
2
3
2
0
1
2
0
2
0
1
0
0
0
1
1
1
1
0
0
1
0
2
1
1
0
1
1
0
0
0
1
1
0
1
0
0
1
1
0
0
2
1
0
1
2
2
1
1
2
0
1
2
1
2
2
1
0
1
0
1
0
1
1
0
0
0
0
1
2
1
0
1
0
0
1
0
0
1
1
0
1
0
0
1
0
1
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
1
1
1
2
3
1
1
0
0
2
0
0
2
1
0
2
1
2
2
1
2
1
2
1
1
2
1
0
1
2
1
0
0
0
0
0
0
1
2
0
1
1
0
1
1
0
2
0
1
1
0
0
1
1
0
1
0
0
0
1
1
2
0
1
0
0
2
0
1
1
1
0
0
2
0
1
0
0
2
1
1
5
0
0
1
1
0
0
2
1
0
0
1
1
2
1
2
1
0
1
2
0
2
0
2
0
0
2
0
1
1
1
0
0
0
0
0
0
0
2
0
1
2
2
0
1
1
2
0
0
0
0
0
2
0
2
0
0
1
1
0
0
0
0
0
1
1
0
1
1
0
1
0
2
0
1
1
1
0
2
2
0
0
0
0
0
0
1
2
0
0
2
2
0
0
2
1
0
0
1
2
2
0
0
0
1
1
0
1
0
0
0
0
1
1
0
0
0
1
0
0
4
0
0
0
0
1
1
2
0
0
1
3
1
2
1
0
2
2
0
0
1
1
0
2
0
1
1
1
0
2
0
0
1
2
2
2
1
0
1
0
1
1
0
2
2
1
0
0
1
2
1
1
0
1
0
0
2
2
0
0
1
0
2
0
0
0
1
1
0
0
2
2
0
1
1
1
2
1
0
1
1
0
2
0
2
0
0
0
0
0
2
0
2
2
0
3
2
1
0
2
1
0
0
0
2
2
0
0
0
2
1
0
0
0
2
1
2
1
0
0
2
1
1
1
0
0
0
1
1
0
1
1
1
1
0
0
0
0
2
0
0
2
3
2
1
1
1
0
1
1
2
0
0
0
2
2
0
0
0
1
1
0
0
1
1
0
0
0
1
1
0
2
0
2
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
2
0
0
3
0
0
1
1
0
1
0
0
2
1
0
3
0
2
1
2
3
1
1
1
2
2
0
2
1
0
2
0
1
0
1
0
1
1
1
3
0
0
0
2
1
1
1
1
1
0
0
1
1
1
1
1
1
1
2
1
1
0
0
0
2
0
2
0
0
1
2
1
0
0
1
0
0
0
2
2
2
0
2
2
0
2
1
0
0
1
1
1
0
0
1
1
2
1
0
1
0
0
1
1
3
0
1
0
0
1
2
0
1
2
1
2
0
1
1
0
1
1
0
2
0
2
1
0
1
2
0
2
0
1
2
1
3
2
0
0
0
0
0
2
2
1
2
2
1
1
0
1
2
0
0
2
1
1
0
0
1
0
2
0
1
1
1
1
1
0
1
1
0
1
2
2
4
1
2
2
1
1
1
0
0
1
0
1
0
0
1
1
1
2
1
2
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
1
2
0
0
0
1
2
2
2
2
1
0
1
1
9
1
0
1
1
1
2
1
0
0
1
0
1
1
1
1
3
2
1
0
2
2
1
0
1
1
0
3
1
1
0
0
0
2
2
1
1
0
0
1
2
0
1
1
0
0
1
0
0
1
0
4
0
0
0
0
1
1
0
2
1
1
2
0
1
0
0
2
1
0
0
1
0
1
0
0
1
0
0
0
2
2
1
0
1
1
0
0
1
0
0
1
1
1
1
0
0
1
0
1
0
1
0
0
0
0
1
0
0
1
0
2
0
1
2
0
1
1
0
1
0
1
2
2
1
0
1
1
2
0
1
2
0
0
0
0
0
1
0
2
0
1
0
0
1
1
1
1
1
0
0
0
0
1
1
2
0
0
1
0
1
1
2
0
1
1
1
2
0
1
1
0
0
0
1
3
1
1
0
2
0
1
2
0
1
1
1
1
2
0
1
0
2
2
1
1
1
0
0
1
0
2
0
2
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
1
1
0
0
1
1
1
1
1
1
0
2
1
0
1
0
1
0
1
0
2
0
1
0
1
0
0
1
2
0
1
0
2
1
1
1
1
1
1
1
4
0
0
2
0
3
2
1
1
0
0
0
2
2
0
0
2
0
1
0
0
0
1
0
0
0
1
2
2
1
0
0
2
0
1
0
1
1
0
1
0
0
0
1
0
0
1
0
2
0
2
1
0
0
1
0
1
1
0
0
2
2
0
2
0
1
1
0
4
0
1
2
1
0
1
2
1
1
0
0
1
1
2
1
0
0
1
1
0
2
0
0
2
0
0
0
2
1
0
2
0
0
0
1
0
1
1
0
0
1
0
0
2
0
1
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
1
1
1
2
1
1
1
1
0
0
1
0
2
0
1
0
0
1
1
1
1
1
1
0
1
1
0
1
2
1
1
1
2
0
1
1
1
0
1
2
0
1
0
1
0
1
1
1
1
0
0
0
2
1
1
2
1
1
1
0
2
2
0
0
0
2
1
0
2
1
1
0
1
1
0
1
1
1
0
2
0
1
0
1
0
2
0
1
0
1
1
0
0
1
1
0
1
0
0
0
1
2
0
0
0
1
1
1
1
1
2
1
0
0
1
2
0
0
0
2
0
1
0
2
1
1
0
0
2
0
0
0
2
1
0
1
0
2
0
0
0
1
1
2
2
1
2
1
2
0
0
1
1
1
0
0
1
0
0
1
0
0
1
2
0
1
0
2
1
1
1
2
0
2
1
2
1
1
1
0
0
1
0
1
1
1
1
2
0
1
0
1
0
1
1
1
1
1
0
0
1
2
0
0
1
0
2
2
1
0
0
2
0
2
1
0
1
1
1
2
2
0
1
0
1
2
1
0
1
1
2
0
0
1
0
0
1
1
0
2
0
0
0
1
1
1
1
0
2
2
1
1
0
2
2
1
0
0
0
0
2
0
2
2
1
1
0
2
0
0
0
0
0
2
0
0
2
0
1
1
0
0
1
1
1
0
0
1
0
2
1
2
0
1
0
1
0
2
1
1
0
1
0
1
2
2
1
1
0
1
0
0
1
1
2
0
1
1
0
2
1
2
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
1
1
4
2
2
2
1
0
0
0
2
0
2
0
0
0
2
0
0
2
0
1
1
0
0
1
0
0
1
0
1
1
1
1
0
1
1
1
2
0
1
1
2
0
1
1
1
2
1
0
1
0
0
0
1
2
1
2
0
0
0
1
0
1
0
1
2
0
1
0
0
1
1
1
0
0
0
2
0
0
0
0
1
0
0
2
1
0
0
0
1
1
0
0
1
2
2
1
0
1
0
3
0
1
2
0
1
1
0
0
0
0
1
0
0
0
0
1
1
2
2
1
0
0
0
1
2
2
1
0
2
0
0
1
0
0
1
1
1
1
0
0
0
0
1
0
1
0
3
1
1
0
1
2
0
1
0
1
0
0
1
0
0
0
2
1
1
0
2
1
1
0
0
1
2
2
1
2
0
0
1
1
1
2
9
0
1
0
1
1
1
0
0
1
2
1
1
1
1
0
1
0
0
1
1
0
1
0
1
1
0
1
0
0
1
0
1
0
2
0
1
0
0
0
0
0
0
0
0
2
2
0
1
1
0
1
1
1
2
0
1
1
0
2
0
0
1
0
2
1
0
0
0
0
2
0
2
2
0
0
2
1
2
0
2
0
0
0
2
2
2
2
1
0
1
2
0
1
1
2
1
0
0
2
0
0
3
0
0
0
0
0
1
0
0
0
0
0
2
1
0
2
2
0
1
1
1
0
1
1
2
0
0
1
1
2
0
0
0
0
1
0
2
1
0
0
1
0
1
1
0
1
1
0
0
4
0
2
1
0
0
1
2
0
1
0
1
0
0
1
2
0
1
2
2
0
0
1
1
0
2
1
1
1
1
2
0
0
1
0
1
1
1
2
0
2
0
2
0
1
2
1
0
1
1
0
1
0
2
0
1
2
0
2
2
2
2
1
0
1
1
1
2
0
1
2
0
2
2
1
2
3
1
0
0
1
2
2
0
0
0
1
1
0
1
1
1
0
0
1
0
0
0
1
3
0
0
1
0
0
1
1
0
1
0
2
0
0
0
1
1
0
0
0
0
0
1
0
2
2
1
2
1
0
1
0
0
1
1
1
2
5
0
1
0
0
0
1
2
1
1
1
0
2
0
0
0
0
2
0
2
0
1
0
1
0
1
1
0
1
0
0
0
0
3
0
1
1
0
1
1
1
0
2
0
0
1
1
1
0
1
1
0
1
1
1
1
1
1
0
2
0
0
0
2
1
1
1
0
2
2
0
1
1
0
0
2
2
0
2
1
1
0
0
0
2
2
0
1
2
2
1
0
0
2
0
0
1
1
1
0
2
1
1
0
0
0
0
1
0
0
1
0
0
1
2
2
1
1
1
0
1
1
4
0
0
0
0
0
2
2
0
1
0
0
2
1
0
1
2
1
0
1
1
0
0
0
0
1
2
0
0
2
1
1
0
1
2
1
0
0
1
1
0
1
1
1
1
1
2
1
1
1
0
1
0
1
0
1
2
2
2
1
1
0
0
2
0
0
0
0
1
1
0
0
1
2
0
0
0
1
0
0
0
0
1
2
0
1
0
2
0
0
1
1
0
2
1
0
1
2
1
1
2
1
0
0
0
0
0
0
0
0
0
1
2
1
2
1
2
0
2
1
1
2
2
0
0
0
1
0
2
0
0
1
0
2
0
2
1
1
1
1
1
1
1
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
3
0
1
2
2
0
0
0
1
0
1
0
0
2
0
0
0
0
1
0
0
1
2
2
0
1
0
2
1
1
0
2
2
0
1
0
0
1
2
1
1
2
0
1
1
1
2
0
1
0
0
0
2
1
0
2
0
0
2
1
1
0
1
1
0
2
1
1
0
3
1
1
1
2
1
1
1
1
0
1
0
0
1
0
0
0
1
2
0
0
0
0
0
0
1
0
2
0
0
2
1
0
1
0
2
1
1
0
0
2
0
1
0
1
1
1
0
1
0
2
0
0
1
1
1
0
1
0
2
1
2
0
1
0
1
0
0
0
1
0
0
2
1
0
1
2
0
0
2
2
1
0
1
2
2
0
0
0
0
0
0
1
1
0
2
1
1
2
1
0
1
2
2
0
1
0
0
1
1
0
2
2
1
1
0
1
2
0
1
2
1
0
0
0
0
1
1
0
0
1
0
0
2
1
1
0
0
1
1
0
1
1
0
0
1
0
1
2
1
1
1
0
2
1
2
2
1
8
0
1
1
1
1
2
0
2
0
1
0
0
1
1
2
1
1
2
0
0
0
2
0
0
2
2
1
1
2
0
1
0
0
1
2
0
0
0
1
2
0
1
2
0
1
2
1
0
2
0
1
0
0
0
2
0
0
1
0
1
1
0
0
2
2
0
2
1
0
0
0
2
1
2
1
0
1
1
2
0
1
1
0
0
0
1
0
1
0
0
0
2
0
2
0
1
2
0
2
1
1
0
0
0
2
1
0
1
0
1
0
0
0
1
0
2
1
0
0
2
1
0
0
0
1
0
2
2
1
0
4
1
0
0
1
1
0
0
2
2
1
0
0
1
1
1
2
2
0
1
0
1
1
1
1
0
0
0
0
0
1
0
1
2
0
1
0
0
0
1
3
0
2
0
0
0
1
3
0
2
1
3
2
3
1
0
0
0
0
1
1
0
1
0
3
0
0
0
0
2
1
0
0
0
0
0
1
1
0
0
1
2
1
2
1
0
1
0
0
2
1
1
0
0
1
0
0
1
0
2
0
0
0
1
1
2
2
2
1
2
0
0
0
2
1
0
0
0
0
0
0
1
0
0
1
1
0
1
1
0
1
0
1
0
0
2
2
0
1
0
0
0
0
2
0
1
1
0
0
2
1
2
2
2
0
0
2
0
1
1
1
0
1
2
1
1
2
1
1
1
0
0
0
0
0
2
2
1
2
1
2
2
2
1
0
0
0
0
1
0
0
0
0
0
1
2
1
1
0
1
0
0
0
2
0
1
1
0
0
0
0
1
0
1
0
1
1
1
1
1
1
0
0
1
0
0
0
2
1
1
0
0
2
1
0
2
1
1
1
0
0
0
0
2
0
0
1
0
0
0
2
0
1
0
0
0
1
1
0
1
0
1
1
2
0
0
0
1
0
1
1
2
1
1
1
0
0
1
3
0
1
0
1
1
0
2
0
0
2
0
1
0
0
1
0
2
1
2
1
2
1
0
0
2
2
1
1
2
1
2
2
2
0
1
0
0
0
1
1
2
1
1
0
1
1
0
3
0
0
0
1
0
0
1
0
1
0
0
2
1
0
0
2
2
2
0
0
2
0
0
0
1
0
0
0
1
3
0
0
0
2
0
2
1
1
2
2
0
2
0
0
2
0
2
0
0
1
2
1
1
2
0
0
2
1
0
0
1
2
0
0
2
0
0
0
1
0
1
2
2
2
0
0
0
1
0
2
1
1
1
0
0
1
0
0
0
0
1
0
1
1
2
2
2
2
2
1
2
0
1
0
0
2
1
0
0
0
0
1
0
0
1
1
0
1
1
2
0
2
1
1
0
1
2
0
2
0
1
0
0
1
2
0
0
0
1
0
1
3
1
0
1
2
1
0
1
2
1
0
2
0
2
0
0
1
1
1
1
1
1
0
1
2
1
2
2
0
1
1
2
2
0
0
0
0
2
2
1
0
0
1
1
2
2
1
1
0
2
0
1
0
2
2
0
0
0
0
1
0
2
1
0
1
0
1
0
0
1
0
1
2
0
0
0
2
2
2
0
2
0
1
1
0
2
0
1
1
1
1
1
0
1
1
2
0
0
0
2
1
0
2
0
2
0
1
0
1
1
2
1
0
1
2
1
0
0
1
2
1
0
2
0
2
0
1
0
1
0
2
2
1
2
2
0
0
2
0
1
0
1
2
0
2
2
2
0
0
2
0
0
0
1
2
0
0
1
1
2
0
1
2
0
1
0
0
1
1
0
0
1
2
0
2
0
1
0
0
0
0
0
1
2
1
1
0
0
0
0
0
0
0
2
2
1
0
0
1
0
1
0
0
1
0
0
0
1
0
0
6
2
1
0
1
1
2
1
2
0
0
0
2
0
1
0
1
1
0
1
0
1
0
0
1
1
0
1
2
2
0
1
2
0
1
1
1
1
1
2
0
1
2
2
1
0
0
1
0
1
1
0
0
2
1
0
2
1
1
1
0
0
2
1
0
0
1
0
0
1
1
1
0
0
0
2
1
2
0
0
1
2
0
1
0
0
0
2
0
2
2
2
0
2
0
2
0
2
1
2
0
2
1
0
2
1
0
1
1
2
1
0
0
1
1
0
0
0
0
2
1
1
1
0
0
1
0
2
0
2
0
0
2
2
0
1
0
0
1
1
0
0
1
1
2
0
0
0
2
2
1
1
0
0
2
1
0
0
2
2
0
1
0
0
1
2
2
0
2
2
1
2
0
2
0
1
0
0
2
1
1
0
1
2
2
1
1
1
2
2
0
2
3
1
0
0
1
0
0
0
0
0
0
2
2
0
0
1
0
1
0
1
0
1
0
1
1
0
1
2
1
0
1
0
1
2
2
0
1
2
2
1
2
2
2
0
2
0
0
2
0
0
1
0
1
2
0
0
1
1
3
0
0
1
2
0
1
2
0
0
1
0
0
2
2
1
0
0
0
1
0
1
2
0
2
1
0
1
2
1
1
2
0
1
0
1
0
1
0
1
0
1
0
0
1
0
0
1
2
0
0
0
0
2
0
0
0
0
1
1
1
2
2
2
0
2
1
0
0
1
1
0
1
1
2
1
0
0
0
0
0
1
2
2
0
2
0
1
1
0
1
0
0
1
0
1
0
1
1
1
0
5
2
1
0
1
0
0
2
1
1
2
0
0
1
0
1
0
2
0
0
0
2
0
1
0
2
1
0
0
2
1
2
1
0
0
2
2
0
1
1
1
0
0
0
1
0
1
1
0
2
0
1
2
0
0
1
0
1
0
0
0
1
0
0
0
1
1
2
1
0
1
2
0
2
1
1
0
1
1
1
0
0
1
1
1
0
0
0
0
0
1
2
0
1
2
1
0
2
2
0
0
2
0
0
1
1
2
0
0
1
0
0
2
0
3
1
1
1
0
1
1
1
0
1
1
2
2
0
0
1
2
0
0
0
1
0
1
2
0
0
0
0
2
2
0
1
0
2
0
0
1
0
2
2
2
0
0
0
0
0
2
1
1
1
2
2
2
0
1
0
1
2
0
1
0
2
1
0
0
1
0
0
0
1
2
2
2
0
0
0
0
2
1
2
0
1
0
1
1
1
1
1
1
0
2
2
0
0
0
0
2
0
1
0
0
1
0
2
2
0
2
1
1
1
0
2
1
0
2
0
0
2
1
0
2
1
1
1
0
1
0
0
2
0
1
1
0
1
1
2
0
1
1
2
0
2
0
0
1
2
0
0
2
2
2
1
3
0
0
0
1
0
1
2
0
0
1
2
1
2
0
2
2
0
0
0
0
1
1
1
1
2
0
0
0
1
2
1
0
0
1
2
0
1
2
2
0
2
1
0
1
2
1
0
0
0
1
0
2
2
0
2
0
1
1
1
2
2
0
1
0
0
2
1
0
2
2
0
0
1
1
1
0
2
2
1
1
3
1
1
0
2
0
0
0
1
1
2
0
0
1
0
1
2
0
0
1
1
0
1
0
0
1
0
2
2
1
2
1
2
0
0
0
1
1
1
0
0
0
1
2
1
0
0
0
1
0
0
0
2
0
2
0
0
0
2
1
1
2
0
0
2
1
0
1
0
5
1
0
0
1
2
0
1
0
2
0
0
2
1
1
1
0
0
0
1
0
0
0
0
1
0
1
0
0
2
1
0
1
1
1
0
0
0
0
0
0
1
2
2
0
0
1
2
0
5
0
1
1
1
0
0
0
1
1
0
0
0
1
1
1
0
0
1
0
1
1
0
0
2
2
0
1
2
2
0
1
1
0
0
0
2
0
2
1
2
0
1
1
0
1
1
0
0
2
1
0
3
1
2
1
0
2
1
2
0
1
1
0
1
2
2
0
1
2
1
0
1
0
2
0
0
0
2
2
1
0
1
1
0
1
2
1
1
2
0
1
0
2
1
3
2
0
4
1
0
0
0
0
2
1
0
0
0
0
1
1
0
1
0
2
2
0
1
0
1
2
0
0
2
1
1
0
1
0
1
2
0
1
0
0
0
2
2
0
1
0
0
2
1
2
0
1
0
0
0
1
0
0
0
1
2
0
0
0
1
0
0
0
0
1
0
1
1
2
0
0
0
1
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
4
0
0
1
2
2
0
0
0
0
1
1
2
0
0
1
1
1
3
1
0
2
0
2
1
0
0
0
2
2
2
0
0
3
0
2
1
1
0
2
1
2
1
1
0
0
0
2
2
0
1
0
1
2
1
2
2
0
0
1
2
0
0
1
0
0
0
0
0
2
0
0
0
0
1
2
2
1
0
0
0
0
2
1
0
1
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
1
1
0
1
0
0
0
0
2
0
1
1
0
2
0
1
0
1
1
0
0
1
0
2
1
0
1
2
0
1
0
1
0
1
0
2
1
0
1
0
0
0
0
2
2
2
0
1
3
0
3
0
2
2
1
0
1
2
2
2
1
0
0
2
1
2
2
1
1
0
0
1
0
0
1
0
1
1
0
0
2
0
1
0
0
0
1
1
0
1
1
0
2
1
2
0
0
1
1
1
2
2
1
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
2
0
0
0
0
1
0
1
0
1
0
0
3
0
0
0
1
1
0
0
2
0
2
2
0
1
0
2
1
1
1
0
0
1
0
0
1
0
0
0
0
0
0
2
2
1
0
0
1
0
1
1
0
0
1
2
1
1
2
0
1
0
2
0
1
2
2
1
2
0
1
0
1
2
0
2
0
1
0
0
0
1
0
1
0
0
4
0
0
1
1
1
1
1
1
1
1
1
0
1
0
0
1
0
2
0
1
1
1
0
0
2
1
1
0
0
0
1
1
1
0
2
1
2
0
2
0
1
1
0
0
0
1
1
0
0
1
1
2
2
5
0
1
0
0
0
4
2
0
1
1
1
0
2
1
2
2
0
2
2
0
1
0
0
1
2
0
1
2
1
2
1
0
2
0
0
1
0
0
1
2
0
2
0
0
2
0
2
0
1
1
0
0
0
2
1
1
1
1
0
0
0
2
1
1
0
0
0
1
1
0
1
0
1
0
0
0
2
0
1
0
1
2
0
0
0
0
3
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
2
0
1
0
2
0
0
1
1
2
2
1
1
0
1
2
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
2
1
1
1
4
0
0
2
0
0
0
0
0
1
1
1
0
0
1
2
2
0
0
0
1
2
2
0
2
0
0
0
1
0
1
3
0
1
0
0
0
0
0
2
0
2
2
1
0
0
1
0
1
0
1
1
1
0
2
0
1
0
1
0
1
0
0
0
2
2
0
2
1
2
0
1
0
0
0
0
0
0
0
1
2
1
0
0
0
1
1
1
1
1
1
0
0
1
1
0
1
1
2
0
0
1
0
3
2
0
2
1
2
0
0
1
0
2
1
0
0
1
0
3
0
1
0
0
1
0
1
0
0
1
0
0
2
1
0
0
2
1
1
0
2
0
0
2
2
0
0
0
2
1
1
2
1
0
2
0
0
1
0
1
0
1
0
1
2
1
2
1
2
2
2
0
1
1
0
1
2
1
2
0
2
1
2
0
1
0
1
1
2
0
2
2
0
1
0
1
0
0
0
0
2
0
1
0
0
1
1
3
1
0
0
0
0
2
0
1
2
1
3
0
0
2
1
2
1
1
1
0
0
0
0
2
0
0
1
3
1
1
1
1
1
0
0
0
0
0
1
0
1
1
2
2
2
0
1
0
0
1
1
2
1
0
0
0
0
5
3
2
1
0
0
0
1
2
0
0
1
1
0
0
0
0
0
0
0
0
1
1
1
0
0
1
1
0
0
0
1
0
1
0
0
1
1
2
1
0
0
0
0
0
0
0
0
0
1
2
1
1
1
2
1
0
2
0
2
1
1
0
0
0
1
0
2
2
0
1
0
0
0
0
1
2
1
0
3
0
0
1
0
2
1
1
2
0
2
0
1
0
1
0
1
0
0
2
1
1
0
0
2
1
0
0
1
1
0
0
0
2
1
2
1
0
1
0
0
1
1
0
1
2
0
2
1
0
0
2
1
0
2
0
1
3
1
1
0
0
1
0
0
2
1
1
1
2
2
0
0
0
2
1
1
1
0
0
1
1
0
1
0
1
1
0
2
1
3
0
1
0
0
2
2
0
1
1
0
2
1
0
0
0
2
0
2
1
1
0
0
1
1
0
0
1
0
0
1
0
1
0
2
0
0
0
2
0
1
1
1
1
0
0
0
1
3
0
1
0
2
1
0
0
0
1
2
0
1
2
0
2
0
1
0
1
0
1
0
1
1
0
1
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
1
1
0
0
0
1
1
1
0
2
1
0
0
1
1
0
2
1
2
0
1
0
0
0
2
0
0
0
0
0
1
2
1
1
0
1
0
1
2
2
1
1
1
2
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
2
1
0
1
0
1
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
2
0
1
0
0
2
0
0
0
1
1
1
1
1
0
0
1
2
1
1
1
1
1
0
0
2
0
0
0
2
0
1
0
0
1
0
2
0
1
1
0
0
1
1
0
2
1
1
1
0
2
1
1
0
0
0
0
2
1
0
0
1
1
0
0
0
0
1
1
0
1
2
0
2
0
2
0
0
2
1
1
1
1
1
0
1
0
0
0
0
2
1
0
1
0
1
0
1
0
0
2
2
0
0
2
0
0
1
0
1
2
1
1
0
2
1
1
0
1
2
0
0
1
1
1
2
2
1
0
0
1
2
1
1
1
2
0
0
1
0
0
1
1
0
2
1
1
1
2
2
0
0
0
0
0
2
1
1
2
1
0
1
0
0
0
0
0
1
1
0
1
0
1
0
2
0
0
0
0
0
2
2
2
2
1
1
0
2
2
2
1
0
0
2
0
0
1
0
0
1
1
2
1
0
2
1
2
0
0
1
0
0
0
0
0
1
2
0
1
0
0
1
0
0
0
2
1
1
1
2
0
0
1
2
0
0
1
1
1
3
0
2
2
1
1
1
1
0
1
1
0
1
0
2
1
0
1
1
0
0
0
0
2
0
2
1
0
1
0
0
1
0
1
0
0
0
0
1
1
1
0
0
0
0
1
0
2
1
2
0
0
0
1
2
1
2
0
1
2
2
2
0
1
0
0
2
1
1
0
0
2
1
0
1
1
0
2
1
0
2
2
0
1
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
2
1
1
2
1
1
0
0
1
1
0
1
1
1
2
2
0
1
1
2
1
0
1
0
2
2
1
0
0
0
0
0
0
0
0
2
0
1
0
2
0
1
0
0
0
2
1
2
1
0
0
0
2
0
2
0
1
1
2
0
1
2
2
1
1
0
1
0
0
1
1
1
2
2
0
1
1
7
0
2
0
1
0
2
1
2
0
0
1
0
0
1
2
0
0
1
2
1
0
1
1
1
2
1
0
1
1
1
0
1
1
0
0
1
1
0
0
0
2
0
0
2
1
1
2
0
0
1
2
2
2
0
1
0
0
1
2
2
0
0
1
0
0
0
0
0
2
0
2
0
1
0
1
0
0
0
2
1
1
1
2
2
1
1
0
3
0
2
0
2
0
0
1
0
3
1
0
1
2
1
1
1
0
2
2
0
0
2
0
1
0
0
1
0
2
1
1
0
0
1
2
2
1
1
0
1
0
0
1
1
0
1
0
0
1
1
1
2
0
0
1
0
0
1
3
1
2
1
0
0
0
2
1
2
1
2
1
0
0
2
1
0
0
1
0
1
0
2
1
0
1
1
0
1
0
1
0
2
1
0
1
1
1
2
3
0
2
1
2
1
0
2
2
1
2
1
0
1
0
0
0
1
2
2
1
1
1
0
1
1
1
0
0
0
0
0
3
1
2
0
0
1
1
0
0
1
1
1
1
2
0
2
0
0
2
0
1
0
1
1
0
1
0
0
0
2
0
2
0
0
2
2
0
2
0
0
1
0
1
2
0
0
0
0
1
2
0
2
0
0
2
1
4
1
1
0
1
2
0
0
0
1
2
0
2
2
1
0
2
2
3
1
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
2
1
2
0
0
1
1
2
0
2
0
0
1
2
1
1
2
1
0
2
0
0
1
1
0
0
0
0
1
0
0
1
2
1
0
1
1
0
2
0
2
1
2
1
1
0
1
0
1
0
1
0
1
0
1
1
2
0
0
1
2
1
2
0
1
0
2
0
0
1
1
1
3
0
0
1
1
2
0
2
2
2
2
0
0
1
1
0
1
1
0
0
0
0
1
0
1
2
1
2
0
0
2
1
1
2
3
0
1
0
1
1
0
1
0
0
2
0
2
0
2
0
1
2
1
0
0
0
1
0
0
2
1
2
0
0
2
0
2
0
1
0
0
2
0
1
1
0
0
0
0
0
0
2
0
2
0
0
0
1
1
0
0
0
1
0
1
0
1
1
1
1
1
1
2
2
0
1
2
1
0
0
0
0
0
1
1
0
1
1
0
1
0
0
2
2
0
1
1
2
0
1
0
0
0
1
2
0
1
1
0
2
1
1
2
2
0
0
2
1
0
0
1
0
0
0
0
0
2
2
0
1
0
0
2
2
2
0
1
0
0
1
1
0
1
0
1
1
0
1
1
0
0
1
4
0
0
0
1
0
1
0
2
2
0
1
0
1
2
1
1
0
0
0
0
1
0
0
1
0
0
0
1
2
1
0
0
1
0
1
1
1
0
0
0
1
1
1
1
1
1
1
2
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
2
0
2
2
3
1
2
0
1
1
1
1
0
1
0
0
0
2
4
1
2
0
0
1
2
2
0
0
1
0
2
1
1
1
0
1
0
1
0
2
0
1
1
2
1
1
1
2
1
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
2
1
1
1
0
1
1
0
2
2
1
1
1
0
1
0
1
1
0
2
1
1
1
2
0
2
0
1
1
0
0
2
2
1
1
1
0
2
0
0
1
0
0
1
1
1
2
0
1
1
0
0
1
1
0
0
0
1
0
2
1
1
0
0
1
0
2
0
1
1
2
1
1
0
2
0
1
1
2
2
4
1
0
1
0
0
1
0
1
1
0
0
1
2
0
0
0
1
0
2
0
0
1
1
2
0
0
1
1
1
1
2
2
0
1
2
0
0
0
1
1
1
0
0
1
1
1
1
1
2
0
1
1
1
3
0
0
0
0
2
2
0
0
0
2
1
2
2
1
0
2
2
2
1
1
1
0
1
0
0
1
1
1
0
1
1
2
1
2
1
1
0
1
0
1
0
2
1
1
0
0
1
1
0
0
0
2
0
1
0
0
0
0
1
1
0
0
2
1
0
1
2
0
1
3
2
2
0
0
0
0
0
0
2
1
0
0
1
0
0
2
1
1
1
0
1
0
2
0
2
1
1
1
0
2
1
5
0
3
1
1
2
0
0
1
0
0
0
1
2
0
2
0
0
1
0
0
0
0
2
2
2
1
2
1
1
0
2
2
2
0
1
0
1
1
1
1
2
2
1
2
1
0
2
2
2
0
0
0
2
3
1
0
1
1
0
1
2
0
1
1
1
1
0
1
2
1
1
1
0
2
0
0
0
0
2
0
2
2
3
0
1
1
2
0
1
0
0
0
0
1
0
1
2
0
2
1
1
0
2
0
0
2
0
1
2
0
2
1
0
2
2
1
0
1
1
0
2
0
3
2
1
1
0
0
0
2
2
1
0
1
0
2
1
0
2
2
2
1
1
0
2
2
0
0
0
0
2
0
1
1
0
1
1
1
1
2
2
1
0
3
1
1
2
2
0
1
0
1
0
1
1
0
0
0
1
1
0
1
0
1
0
1
1
1
0
0
2
0
2
2
0
0
0
2
0
0
0
0
1
2
0
2
1
2
2
1
2
0
0
2
1
0
1
1
0
0
0
1
0
0
0
1
1
0
0
0
2
1
0
0
1
1
1
2
1
0
0
0
1
0
2
1
2
1
0
0
0
1
1
1
2
0
1
0
2
0
0
1
2
0
0
0
1
1
1
1
1
1
0
0
0
0
2
1
0
1
1
0
1
0
0
1
2
0
0
0
0
1
0
0
1
1
2
1
0
1
0
2
1
1
1
2
0
1
1
0
1
1
0
2
2
1
1
0
2
2
2
1
0
0
0
2
0
2
0
2
2
0
0
1
0
2
2
4
2
0
0
1
0
1
2
1
0
1
0
0
1
0
0
1
1
2
1
0
0
1
0
0
0
0
0
1
0
0
2
2
0
0
2
0
1
1
1
2
1
0
1
0
1
1
1
1
1
0
1
0
1
1
2
3
0
0
0
0
0
2
0
2
0
1
0
0
1
1
0
0
2
1
0
1
1
0
0
0
1
1
3
2
2
1
1
2
1
0
0
0
1
0
0
3
1
1
2
0
0
2
2
0
1
2
1
1
2
1
0
0
1
0
1
1
2
0
0
0
1
0
1
1
2
1
1
1
1
0
1
1
1
1
0
0
1
2
0
0
1
1
0
0
2
1
1
2
1
0
0
2
1
2
1
1
1
0
2
0
0
1
1
0
1
0
2
1
0
2
2
1
0
1
0
0
2
1
2
1
0
1
0
1
0
0
1
2
1
2
3
0
1
1
1
0
0
0
2
0
0
0
0
0
1
0
2
0
1
1
1
1
0
1
1
1
1
0
0
0
0
2
0
3
2
0
0
0
0
0
0
0
1
0
1
0
2
0
0
1
0
0
1
1
2
2
1
0
1
0
1
2
2
0
0
2
0
1
0
0
0
1
0
1
0
2
1
1
0
0
0
2
3
1
2
0
0
0
2
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
2
0
2
1
1
2
0
1
0
0
1
2
1
0
0
1
2
1
0
0
1
0
1
1
0
1
0
0
1
0
0
3
0
2
0
0
1
2
2
0
0
0
0
0
1
0
0
0
0
0
1
1
1
1
1
0
1
2
0
2
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
1
0
1
1
2
0
0
0
0
1
0
1
2
0
0
2
0
3
3
0
1
0
1
0
0
0
1
2
0
0
1
0
1
2
0
3
0
0
2
1
2
0
0
2
2
2
0
2
1
2
0
0
0
1
1
1
0
0
0
0
3
0
2
1
1
1
1
0
0
0
0
0
1
0
0
2
1
0
1
2
1
0
2
1
2
1
1
1
1
1
1
0
0
2
1
0
1
2
1
0
0
1
2
1
0
3
2
4
0
0
2
2
0
2
1
0
2
0
1
1
0
0
2
0
0
1
0
0
2
0
2
2
0
0
0
0
0
1
2
1
1
2
1
0
1
1
0
0
0
0
1
4
0
1
1
1
2
0
1
0
1
0
0
0
0
1
2
2
0
0
2
0
2
1
0
2
0
0
1
1
0
0
1
0
1
2
1
2
0
1
0
2
1
0
2
0
0
0
2
2
0
0
0
0
2
2
0
3
2
1
0
1
2
1
1
0
1
0
1
1
0
1
1
1
2
0
2
0
1
1
3
2
1
1
2
0
1
4
0
0
0
2
0
1
0
0
1
0
1
1
4
3
2
1
1
0
0
2
1
0
0
1
0
0
1
0
1
1
1
1
0
1
1
0
2
0
0
1
1
0
1
1
0
0
2
2
0
0
0
2
1
0
1
0
0
1
0
1
1
0
0
2
1
2
3
1
0
2
1
0
1
1
0
0
1
2
0
1
0
2
2
1
1
0
1
0
0
0
0
0
0
2
1
0
2
0
0
2
1
1
2
2
0
2
2
1
1
1
1
1
0
2
1
0
2
2
0
2
0
2
0
1
1
2
1
2
0
0
2
0
2
1
0
2
1
1
1
2
1
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
2
1
1
2
1
0
0
2
0
5
1
1
0
1
0
1
1
2
0
0
0
0
2
1
0
1
2
1
1
0
2
0
0
2
0
0
1
1
1
2
2
1
1
1
0
1
0
0
0
2
0
0
2
1
2
1
0
1
1
0
1
1
0
2
2
1
1
0
1
0
1
0
0
0
0
2
2
1
1
1
1
0
1
1
0
1
0
2
0
2
1
0
0
1
2
0
0
1
0
0
0
0
1
1
0
1
2
3
0
0
0
2
2
0
0
1
0
1
1
2
0
0
1
0
0
1
1
0
0
1
2
0
1
0
1
1
2
0
3
1
0
0
0
1
0
2
2
1
0
1
1
0
2
0
2
0
1
1
1
0
2
0
0
1
1
1
0
2
2
1
1
1
1
1
2
0
0
2
2
0
1
1
1
2
0
0
1
1
1
2
0
0
0
1
0
1
0
1
2
0
1
1
2
2
0
0
0
0
0
0
1
1
1
1
1
2
1
1
1
0
1
2
1
1
2
1
0
0
1
0
0
1
0
0
2
1
3
1
1
1
1
1
0
0
0
0
1
2
1
2
0
2
0
1
3
0
0
0
0
0
1
0
0
2
0
2
0
1
0
0
0
1
2
2
0
0
2
1
0
0
1
3
0
0
0
1
1
0
0
1
0
0
1
1
2
0
0
1
1
1
2
2
2
0
0
2
1
0
1
0
0
2
0
0
0
2
1
0
1
1
0
0
0
1
1
0
2
0
0
0
0
1
1
0
0
0
1
1
1
0
1
1
1
0
0
0
1
1
1
0
5
2
0
0
1
0
1
0
1
2
0
1
0
0
2
1
1
1
1
2
1
0
0
0
1
0
0
0
2
2
1
0
2
0
1
1
0
0
1
0
0
2
1
1
2
0
1
0
1
0
2
0
2
0
0
1
0
0
1
1
0
2
1
0
1
1
0
0
0
0
1
2
1
0
2
0
1
3
1
1
1
1
2
0
1
0
0
1
2
0
4
1
2
2
0
1
4
2
2
0
2
2
1
2
0
1
0
1
1
0
2
0
0
3
0
0
2
0
0
2
0
1
4
1
0
2
2
0
0
1
1
2
1
1
0
0
0
0
0
0
1
0
0
1
1
0
0
2
0
1
2
0
2
0
1
0
2
2
0
0
2
1
1
1
1
0
1
2
0
0
2
1
2
2
0
2
2
1
0
1
0
1
0
1
1
0
0
0
2
0
1
1
2
2
0
1
2
2
0
0
2
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
1
2
0
1
0
0
1
0
2
0
1
0
0
1
0
0
0
1
0
0
1
1
0
1
1
1
2
1
2
2
0
0
1
0
0
2
0
0
1
0
1
0
2
1
1
0
0
0
0
1
2
1
0
0
0
2
2
1
0
0
2
0
1
1
2
1
1
1
0
1
0
0
2
2
2
2
0
1
0
0
1
0
1
0
1
1
0
0
0
2
0
0
0
0
2
1
1
0
2
1
1
1
0
0
0
0
2
1
0
2
2
1
0
0
0
2
2
1
0
1
1
2
0
1
0
0
0
1
1
2
1
1
1
2
0
0
2
1
2
1
0
0
1
0
2
1
1
0
2
1
0
1
1
1
1
1
1
0
0
0
2
3
1
3
0
1
0
1
0
0
0
2
1
1
0
0
0
0
0
2
0
0
1
0
2
1
2
1
1
0
2
0
0
0
0
2
1
0
0
1
0
0
0
1
2
1
2
0
2
0
3
0
0
1
1
3
1
1
0
2
0
0
1
0
0
0
0
2
1
0
0
0
0
2
2
0
1
2
0
2
0
2
0
0
1
1
0
2
1
1
0
1
1
2
0
0
1
1
1
1
1
0
0
1
1
1
2
2
1
1
0
2
2
0
0
1
0
1
0
2
1
0
1
1
0
2
1
1
1
0
2
1
0
1
0
0
0
0
2
0
1
0
2
0
1
0
0
2
0
0
2
2
0
1
2
2
0
2
2
1
2
0
0
2
1
2
2
1
1
2
0
1
1
2
0
2
2
0
2
0
1
0
0
0
2
1
1
2
2
0
1
1
2
2
2
1
1
0
1
2
1
0
0
2
2
2
1
0
0
2
2
0
2
1
1
2
0
2
0
0
2
1
0
0
2
1
0
2
2
2
0
1
1
1
0
0
1
0
2
2
0
0
0
0
0
0
1
0
0
1
3
1
1
2
1
0
0
0
1
0
1
0
0
1
1
4
0
1
1
2
1
1
1
0
0
2
0
2
0
0
2
2
1
1
1
2
0
0
1
1
1
0
0
0
2
2
1
2
0
2
0
0
1
2
2
0
1
0
1
4
0
1
0
1
0
3
1
0
0
1
1
1
0
0
0
2
1
0
0
0
1
0
1
0
2
1
2
2
0
2
0
2
2
0
0
0
0
1
0
1
2
1
0
2
0
1
0
1
1
2
1
0
0
1
0
0
2
1
0
0
0
1
2
2
1
2
0
0
1
0
0
2
1
0
1
1
0
2
9
0
0
0
1
0
0
1
0
0
2
1
0
1
1
1
0
1
0
1
0
2
1
0
1
1
1
1
0
0
1
0
0
2
2
0
1
0
1
5
0
1
0
0
0
1
1
1
0
0
0
1
1
2
2
2
2
4
1
0
0
0
2
0
2
1
0
2
1
1
0
1
0
1
0
1
1
1
2
0
0
0
2
2
2
0
2
0
0
1
0
0
0
0
1
1
2
1
0
1
2
0
0
1
1
2
0
0
0
2
0
0
0
1
1
2
1
2
1
1
2
0
0
1
1
1
0
0
1
0
1
0
1
0
1
1
0
1
0
1
0
0
1
1
1
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
1
1
1
0
0
1
1
0
3
1
2
0
0
0
0
2
0
0
0
2
0
0
2
1
0
2
1
1
0
2
0
4
0
1
1
1
0
1
1
0
0
0
1
0
1
1
0
0
0
0
2
0
1
1
0
1
0
1
1
0
0
1
1
1
0
1
2
2
1
1
3
1
0
0
0
1
0
0
1
2
2
2
2
2
0
0
0
1
2
1
2
0
2
0
1
0
1
1
2
2
1
0
1
0
1
0
2
3
1
2
0
0
1
2
0
1
0
2
2
2
1
0
1
0
0
0
1
0
0
0
0
1
2
0
1
0
2
0
1
1
0
2
1
0
1
0
1
0
0
0
0
0
2
0
1
1
1
1
1
0
1
0
0
0
1
2
0
2
1
0
0
0
2
0
0
3
0
0
2
0
1
2
0
1
0
0
1
2
0
2
2
1
2
0
0
2
1
1
2
1
1
0
4
1
1
2
1
2
2
0
1
0
1
2
0
0
0
0
0
1
2
1
1
2
0
0
0
1
0
2
1
0
0
2
1
0
0
1
0
2
2
0
1
0
0
1
0
2
0
0
2
0
0
1
0
1
1
1
1
0
0
0
2
2
2
3
2
0
0
1
2
2
1
1
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
1
0
1
0
1
0
0
0
0
2
0
1
2
0
0
1
0
2
0
2
1
0
4
1
1
0
1
0
0
0
1
1
0
2
2
0
0
1
0
2
2
0
0
2
1
1
0
0
0
2
1
1
0
0
0
1
0
0
1
0
2
0
1
2
0
0
2
1
0
0
2
0
0
0
0
0
1
0
2
0
1
0
2
0
2
1
2
0
1
0
2
1
0
2
1
1
0
2
1
2
1
2
2
2
1
2
1
0
0
1
1
0
1
0
2
0
2
1
0
1
0
0
0
0
1
1
2
0
0
4
0
0
0
1
1
0
1
1
1
1
2
0
1
0
0
1
0
0
1
0
1
2
0
0
1
0
0
0
0
0
2
0
1
0
0
0
2
0
1
0
0
1
2
0
2
1
0
0
1
2
1
0
0
1
0
0
1
1
1
1
2
2
0
0
1
0
0
1
8
1
1
0
1
1
0
0
2
0
2
2
0
0
0
1
1
1
2
1
0
1
0
0
1
1
0
2
0
1
1
1
0
1
0
0
0
0
0
0
1
2
0
1
1
1
0
2
2
1
1
0
0
0
2
1
0
2
1
2
0
2
0
0
1
1
0
0
0
0
0
2
2
1
1
2
2
0
2
0
2
0
0
1
1
2
1
0
2
0
2
0
0
1
1
1
0
2
0
2
0
0
2
1
1
1
0
0
1
2
0
0
1
1
1
0
1
1
1
1
0
0
2
3
1
0
0
1
1
2
1
1
1
0
0
0
1
1
1
1
1
1
0
1
0
0
0
1
0
0
1
1
0
0
0
1
0
1
1
1
1
0
1
2
0
0
0
0
1
0
1
0
0
1
0
0
1
1
1
2
1
0
1
0
0
2
0
2
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
1
0
0
0
0
0
2
0
0
1
0
1
0
1
1
2
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
2
2
1
0
0
1
2
2
0
2
2
0
1
1
1
0
0
0
0
1
2
0
0
0
2
0
0
1
2
0
2
2
0
0
2
1
0
2
0
0
0
0
0
2
1
0
0
0
0
1
0
1
3
0
2
1
1
1
1
1
2
0
0
1
0
1
1
1
0
0
3
1
1
1
3
0
0
1
1
1
1
0
1
1
0
0
0
1
2
0
1
2
2
0
2
2
2
0
0
2
0
1
1
2
1
0
2
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
3
1
0
2
0
1
1
1
2
0
2
0
0
2
0
0
2
0
1
0
0
0
0
0
0
1
0
2
0
1
0
0
3
4
1
1
2
2
0
1
1
2
0
2
1
0
0
0
0
2
0
0
1
0
3
2
2
0
1
2
0
0
0
1
4
0
0
0
3
1
1
0
1
1
0
0
1
1
0
2
1
2
0
2
1
1
0
1
1
0
1
1
1
2
0
0
1
1
3
1
2
0
0
2
0
0
0
1
1
1
1
0
2
1
0
1
2
0
0
2
0
1
2
0
0
2
0
1
2
0
0
0
0
2
1
0
1
1
0
0
0
0
2
0
1
2
1
2
2
0
1
0
0
0
1
0
0
1
2
0
2
1
1
0
0
2
0
2
2
1
0
2
0
0
2
0
0
0
2
0
1
1
2
2
2
0
1
2
1
0
1
0
2
1
0
2
0
3
0
0
2
1
1
0
2
1
1
0
1
1
1
1
0
0
0
1
0
2
1
0
0
1
1
0
1
0
1
1
0
2
0
0
1
0
1
2
0
1
0
2
1
1
0
0
1
0
2
1
2
2
0
0
0
0
0
1
0
1
2
0
1
0
1
1
1
0
2
2
0
3
0
1
0
0
2
0
0
0
2
2
1
0
1
1
0
0
0
1
0
1
0
1
2
0
2
0
2
0
1
1
0
0
1
1
0
1
1
1
1
1
1
2
0
2
1
2
1
0
1
1
1
1
0
1
1
0
1
2
0
1
2
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
1
2
0
1
0
0
1
1
2
1
1
1
0
1
1
1
0
0
1
2
1
1
1
0
1
0
2
1
5
2
0
0
2
3
0
1
0
0
2
1
1
0
1
2
2
1
1
1
0
0
0
0
2
2
1
0
1
0
0
2
1
0
0
0
1
2
2
0
0
0
0
2
1
1
0
1
0
2
1
0
0
0
0
2
0
0
1
0
0
1
0
1
1
1
1
1
0
1
0
1
0
1
0
2
0
2
0
1
2
0
0
1
0
1
1
0
0
2
0
6
1
1
0
1
2
1
2
2
0
1
1
0
0
1
1
0
2
2
1
0
2
0
0
1
0
0
1
1
1
1
0
2
0
1
1
1
1
0
1
1
0
0
0
1
2
1
1
1
0
0
0
2
2
0
0
0
0
2
1
0
2
0
0
0
1
2
1
1
0
1
0
2
0
0
0
1
2
0
0
0
2
2
0
1
2
0
0
1
0
2
1
2
0
0
0
1
2
0
1
3
0
0
1
0
0
0
0
2
0
0
1
1
0
0
0
0
0
2
1
2
1
2
2
1
0
1
2
2
0
2
1
2
0
1
2
2
1
2
1
0
0
3
0
1
3
0
1
0
2
0
2
1
1
1
0
1
0
0
0
0
0
3
0
1
1
0
0
0
0
1
2
0
1
0
1
2
2
0
0
0
0
0
1
1
2
2
0
0
2
1
2
1
2
1
0
0
0
0
2
0
0
1
1
1
0
0
2
1
0
1
1
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
1
0
1
1
0
2
0
0
1
0
0
2
1
0
0
0
1
0
1
0
0
1
1
2
0
0
0
2
1
0
0
0
0
2
0
2
0
1
2
2
0
1
0
1
0
1
1
1
4
2
2
0
0
1
1
2
0
0
1
0
0
0
1
1
0
2
1
2
1
0
2
0
0
0
0
1
0
0
2
0
0
1
0
0
1
1
0
2
1
1
1
1
1
0
2
0
0
0
0
1
2
0
1
0
1
0
2
0
1
2
0
1
1
2
0
0
0
2
1
2
0
0
1
0
2
0
0
0
1
1
0
0
0
1
2
0
1
0
0
0
2
0
2
3
0
0
0
0
0
0
1
0
0
2
0
2
1
1
0
0
4
0
1
0
2
0
0
2
0
0
1
2
0
0
1
1
0
0
1
2
0
0
0
0
2
0
1
1
1
0
1
1
0
0
0
1
2
1
2
0
0
0
1
0
0
0
0
1
2
0
0
0
1
1
0
1
0
0
1
1
0
1
0
0
1
0
0
1
0
1
1
0
0
1
0
1
0
1
1
0
1
0
1
0
1
1
0
2
1
1
1
0
0
2
2
0
1
1
2
0
0
0
1
2
1
1
0
0
2
0
1
0
0
0
0
1
0
0
0
1
1
0
1
0
1
2
1
0
1
0
0
0
1
2
1
1
1
0
2
2
0
1
0
0
2
0
0
1
0
0
2
0
2
2
1
0
1
0
0
0
2
1
2
1
0
1
4
1
1
2
0
0
1
0
2
0
0
2
1
0
3
0
0
1
1
0
1
1
0
1
2
2
2
1
1
0
0
0
0
1
0
0
2
0
2
0
0
2
1
2
2
0
0
1
0
0
0
1
3
0
1
1
1
1
1
2
2
0
0
2
2
2
0
1
0
0
1
1
0
3
2
2
0
0
1
1
0
1
0
0
1
3
0
1
1
2
1
1
0
1
2
2
1
1
1
1
0
1
1
0
0
2
1
2
1
1
2
0
8
0
2
0
0
2
1
2
0
0
0
2
1
1
1
0
0
0
2
0
0
0
1
1
0
0
1
0
2
0
2
2
0
2
0
2
0
0
0
0
0
0
1
0
1
2
0
0
1
1
2
0
1
1
0
1
0
0
2
0
1
3
1
0
2
0
1
1
0
0
0
0
1
1
0
2
1
2
0
0
0
1
0
2
1
1
2
1
0
2
1
3
1
1
1
0
0
0
0
0
2
2
0
0
2
1
1
0
1
1
1
0
0
2
2
1
0
2
2
1
2
1
1
1
1
1
1
2
0
2
1
0
2
0
1
0
1
2
1
0
0
0
2
3
0
0
0
2
2
2
0
1
0
1
2
1
0
1
0
3
2
0
0
0
1
0
0
1
1
0
1
0
2
0
0
1
1
1
0
0
2
1
1
3
0
0
2
0
1
0
0
0
1
0
1
0
0
2
0
0
0
0
0
2
1
0
3
0
2
1
0
0
1
1
0
0
0
2
0
0
2
1
1
1
1
0
2
0
1
0
2
0
1
2
0
0
0
1
1
0
0
0
1
0
0
0
0
0
2
1
0
0
0
1
0
0
0
1
1
1
0
0
2
1
2
2
3
0
2
2
0
1
0
2
2
0
1
0
1
0
0
0
1
1
1
1
1
0
0
1
1
0
0
2
0
0
0
0
1
0
0
0
1
0
1
1
3
0
2
0
2
1
1
1
1
1
1
0
0
0
2
0
0
3
0
1
2
2
1
1
2
0
2
0
1
0
1
0
1
1
1
2
0
1
0
0
1
1
1
2
0
0
1
0
1
2
1
2
2
1
2
0
0
1
2
3
1
1
1
0
1
2
0
0
0
1
1
0
0
2
0
1
1
0
1
1
0
0
0
1
0
2
0
0
0
1
1
0
0
0
2
2
1
2
1
0
2
1
0
1
1
0
0
1
1
1
1
0
0
0
1
2
0
2
1
0
0
2
2
0
0
0
1
2
0
2
0
0
0
2
2
1
0
0
0
1
0
2
1
1
4
1
1
0
1
0
1
0
1
1
1
1
0
2
2
0
1
0
2
0
2
0
0
1
1
1
2
1
2
1
0
2
2
0
0
2
1
0
1
1
2
0
0
2
0
0
1
1
1
1
1
0
1
1
2
2
2
1
0
0
2
0
1
1
1
0
2
2
1
0
0
2
1
3
1
1
1
2
2
1
1
1
0
0
0
1
1
2
2
2
0
2
2
2
1
1
0
1
1
2
0
2
1
1
0
0
0
5
2
2
1
0
2
1
0
0
1
0
1
1
2
0
1
0
1
0
0
4
2
0
1
3
2
0
0
0
0
1
1
0
1
0
1
2
1
1
1
0
1
0
2
2
0
2
0
1
0
0
1
0
0
0
2
0
1
3
2
1
0
1
2
1
1
1
1
2
2
0
1
1
0
0
2
1
0
2
1
0
2
0
0
2
1
0
1
2
0
1
0
1
0
0
2
1
1
2
2
0
1
1
1
1
0
2
0
1
2
1
1
1
0
1
2
2
0
0
2
2
0
0
1
1
1
1
1
0
5
2
0
0
1
0
1
1
0
1
1
2
1
0
1
1
0
1
1
1
0
0
0
0
0
0
1
2
2
1
0
1
0
3
0
0
0
1
1
1
0
2
0
0
0
0
2
0
1
1
0
1
1
4
2
2
0
2
0
0
2
2
2
0
1
3
2
0
1
1
0
2
1
2
0
0
0
2
0
2
0
1
0
4
2
1
0
0
0
1
1
0
1
0
0
1
0
0
2
1
0
0
0
2
1
0
1
0
1
0
0
1
0
1
0
2
2
0
1
0
1
1
0
1
1
1
2
0
2
1
0
2
2
1
1
0
2
1
2
0
1
2
0
3
2
0
0
0
2
0
0
2
1
0
1
2
0
2
1
0
1
2
0
0
1
0
1
1
0
0
0
0
0
1
0
1
1
2
1
1
0
0
1
2
1
1
1
1
0
0
1
1
1
0
2
1
0
2
2
3
0
1
1
2
0
0
1
0
0
2
1
1
2
0
1
1
1
2
0
1
0
1
0
1
1
0
1
1
1
1
2
1
0
1
0
0
1
1
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
4
2
1
0
0
1
0
0
1
0
1
0
1
0
0
2
0
2
0
1
0
0
1
2
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
2
2
1
0
1
0
0
2
2
1
1
0
2
0
2
1
0
0
1
1
2
1
0
1
0
1
1
0
1
0
0
0
2
1
1
2
0
0
0
0
2
0
2
0
0
0
2
1
1
1
2
2
2
0
0
2
1
0
0
2
1
1
1
1
0
2
2
1
2
0
0
0
2
0
1
0
0
1
0
1
1
0
0
2
2
0
2
1
0
1
2
0
0
2
0
0
0
1
0
2
0
0
2
1
0
1
3
0
1
1
2
0
0
0
1
1
0
0
0
0
1
0
2
2
0
0
1
1
1
1
1
0
1
1
1
1
0
0
1
2
1
1
1
0
0
0
0
0
0
1
1
2
0
0
0
1
2
2
1
0
0
2
2
0
0
1
0
1
0
1
2
0
0
0
0
0
1
1
2
2
2
2
0
2
0
0
1
1
1
0
1
1
2
0
2
1
1
0
0
1
0
0
0
0
2
2
1
1
0
1
1
0
0
1
0
0
0
2
0
0
1
1
0
1
1
0
0
0
0
1
0
0
1
2
0
1
0
0
1
0
0
0
0
2
0
0
1
0
2
0
2
1
2
1
2
0
1
2
0
0
0
0
0
1
0
0
2
0
1
1
0
1
1
1
0
2
0
2
1
0
0
2
2
1
0
0
0
2
2
0
0
2
1
1
0
0
0
1
1
0
1
2
0
0
1
1
0
2
0
0
2
0
0
2
0
1
0
0
0
0
1
0
0
1
3
0
1
3
1
1
0
0
1
0
1
0
2
1
0
2
0
2
0
2
0
2
0
1
1
1
2
1
1
1
0
0
0
1
2
1
2
0
0
2
1
0
0
0
1
0
1
2
0
3
0
0
1
1
1
1
1
2
0
1
0
9
1
0
1
0
0
2
0
0
1
0
0
0
0
1
0
2
0
1
1
1
0
0
0
1
0
1
2
1
1
0
0
2
1
2
0
2
1
0
1
0
1
1
0
0
2
1
0
2
1
3
0
2
2
1
2
2
0
2
2
0
0
0
3
2
2
1
0
1
1
1
2
2
1
0
0
0
0
1
1
2
1
0
0
1
1
0
1
0
2
0
1
1
0
1
0
0
0
2
0
0
1
2
2
0
0
0
2
1
1
1
1
0
0
0
1
1
0
0
1
2
0
1
1
1
1
1
0
2
1
0
1
1
2
2
0
1
3
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
3
2
0
0
1
2
0
0
0
2
0
2
0
0
0
2
1
2
2
0
0
2
0
2
2
0
1
0
1
0
0
2
2
2
2
1
1
0
0
1
2
0
2
1
0
0
0
0
1
1
1
1
1
4
2
0
0
2
1
1
1
1
0
0
2
1
0
0
6
1
1
0
1
0
2
1
0
0
2
0
1
0
1
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
3
0
0
1
2
1
0
0
2
0
2
2
1
0
0
2
0
2
0
0
0
1
1
0
0
0
0
0
1
0
2
0
1
1
1
0
0
1
0
2
0
1
1
1
1
1
0
0
1
0
0
0
1
2
0
0
2
1
2
0
0
2
1
0
0
1
2
2
1
1
1
1
0
0
4
0
0
0
0
1
2
0
1
2
1
0
0
0
0
1
0
1
1
0
0
0
0
0
2
0
0
1
0
2
1
1
2
2
0
0
2
1
1
0
0
2
1
1
0
0
1
0
0
1
0
9
2
0
2
1
2
2
2
1
2
0
2
0
0
2
0
2
0
1
2
0
0
2
2
2
1
1
0
2
0
0
0
1
2
0
0
0
1
0
1
2
1
1
0
2
0
2
2
0
0
2
2
0
2
0
1
1
1
2
0
1
2
1
0
1
1
2
1
0
1
0
2
0
0
1
2
0
0
0
1
0
0
1
2
0
1
1
0
1
1
0
0
0
0
1
0
1
2
1
0
0
2
2
0
1
2
2
1
0
0
0
0
0
2
2
1
2
2
1
0
0
2
2
0
2
1
0
2
0
1
0
0
1
1
0
2
1
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
3
1
2
0
2
3
1
1
1
0
0
1
1
0
0
0
0
1
2
0
1
0
2
0
1
0
1
0
1
1
1
0
1
0
1
2
1
0
1
0
0
2
1
2
1
2
1
0
2
0
2
0
0
2
1
2
0
0
1
2
1
2
0
1
0
0
2
0
0
1
2
0
0
1
2
1
0
2
0
2
1
2
0
2
0
0
1
1
0
0
1
0
1
2
0
0
1
1
1
0
1
2
0
0
1
0
0
2
1
1
0
1
0
1
1
1
2
0
1
2
2
0
0
0
1
0
0
1
0
1
1
2
2
0
1
3
0
2
2
1
1
1
0
1
2
0
1
1
0
0
1
0
2
1
2
0
1
2
1
0
2
2
0
1
1
2
1
0
0
1
2
0
0
1
0
1
1
1
2
0
0
0
0
1
2
1
0
2
2
1
2
2
0
1
1
0
0
0
1
0
0
0
2
0
0
1
1
1
1
3
1
1
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
1
0
1
1
1
0
1
0
1
0
1
0
2
0
0
0
0
1
2
2
0
0
2
0
0
2
2
1
1
0
0
0
1
2
0
2
2
0
0
0
1
0
0
1
0
3
0
2
0
3
2
0
1
1
1
0
0
1
1
1
1
1
1
2
0
2
1
1
0
1
0
1
0
0
2
1
0
0
0
1
2
2
1
2
1
2
0
0
0
0
0
2
0
0
1
0
1
0
0
1
2
2
2
2
0
2
0
0
2
0
0
0
0
1
0
1
0
0
0
1
1
0
0
1
0
1
1
0
4
1
1
0
1
0
0
0
1
1
2
0
0
1
0
0
1
0
0
0
2
1
0
1
0
1
0
1
1
0
1
2
2
1
1
0
0
2
0
2
1
3
0
1
1
0
1
0
0
0
0
1
2
0
0
0
1
2
0
0
0
1
0
0
1
2
2
2
2
1
1
0
1
1
2
1
1
2
1
2
0
0
0
0
1
0
2
2
1
3
1
0
1
0
2
0
0
0
0
0
0
2
1
2
1
2
1
0
2
0
1
1
1
0
0
2
1
1
1
1
0
2
0
2
1
0
3
0
0
1
2
1
0
2
1
2
0
2
2
1
1
2
2
0
1
0
0
2
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
2
1
0
1
0
1
1
0
1
2
2
0
1
1
0
0
0
1
1
2
0
2
0
1
2
0
1
1
1
0
2
2
0
2
2
1
0
0
1
1
1
3
1
0
2
1
0
0
0
2
0
2
1
2
1
3
1
0
0
1
0
0
0
0
2
0
0
2
0
2
2
0
1
1
1
1
0
2
2
1
1
1
0
1
0
0
1
1
0
1
1
0
1
1
0
0
0
0
1
1
1
1
0
2
1
2
0
1
0
0
0
1
1
0
1
0
0
0
0
2
1
0
1
0
2
1
2
0
1
0
2
0
0
0
0
2
0
0
1
0
1
0
0
1
1
1
0
1
0
2
1
0
4
0
0
0
0
0
1
0
0
0
0
0
2
1
0
2
2
0
0
0
2
1
0
2
0
2
0
1
0
1
1
0
2
0
2
0
1
1
1
1
2
0
1
0
2
1
1
0
2
1
2
2
2
1
1
1
0
0
2
0
0
1
0
0
2
0
0
2
0
2
1
1
2
0
2
0
2
1
3
1
0
1
2
0
2
1
0
1
0
0
5
0
0
0
2
1
0
2
2
0
0
1
2
0
2
1
2
1
0
1
1
2
0
1
0
1
0
0
1
1
2
0
2
2
1
1
2
0
1
1
0
2
1
1
1
1
2
1
0
1
0
2
0
1
0
0
2
2
2
0
2
0
1
1
1
0
0
2
0
4
1
0
0
2
1
2
1
2
0
0
2
1
2
1
0
0
0
2
2
0
0
0
0
0
0
1
0
0
1
0
2
2
2
1
1
0
0
0
0
2
1
3
0
1
0
1
0
2
1
1
0
0
1
0
3
0
1
0
0
0
1
0
1
2
0
2
0
0
1
0
1
0
2
0
1
0
1
1
0
1
0
0
1
2
1
0
2
1
1
0
0
0
1
1
0
1
2
1
0
1
0
0
2
2
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
1
1
1
2
1
2
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
3
1
1
2
0
1
0
2
1
3
2
0
0
0
0
1
0
1
1
0
2
1
0
2
0
0
1
1
0
3
0
1
0
1
0
0
2
0
2
1
2
3
1
1
1
1
0
0
1
2
1
0
1
1
0
1
2
1
1
0
2
0
0
0
1
2
0
1
1
0
1
0
0
0
2
1
2
1
1
0
1
0
0
1
1
1
0
0
1
0
1
0
0
0
1
1
0
2
0
0
1
0
1
2
1
1
3
2
1
0
1
0
0
0
0
0
0
2
1
1
0
1
0
1
0
2
2
0
1
0
0
0
1
1
2
0
1
0
0
1
1
0
0
1
2
1
0
0
2
0
0
0
1
0
2
1
0
2
1
0
1
0
2
1
0
0
1
2
1
1
0
0
0
0
0
1
2
0
2
2
2
2
0
0
1
1
1
1
2
1
1
0
0
1
0
0
2
1
1
0
1
0
0
0
2
0
0
1
1
0
2
1
0
1
0
3
0
2
0
0
2
1
0
0
1
0
5
2
0
1
0
1
1
0
2
0
1
0
1
2
1
2
0
2
2
2
0
1
0
0
2
0
1
0
1
0
0
2
4
0
1
2
2
1
1
2
0
1
0
1
0
1
0
1
1
2
1
2
0
0
1
0
1
0
1
2
0
0
1
1
1
0
1
0
1
2
1
1
0
2
2
0
2
0
0
2
1
0
0
0
1
2
0
0
1
0
1
2
0
1
1
0
2
0
4
0
1
2
2
1
0
0
0
0
1
0
1
2
2
2
1
0
1
2
0
1
0
0
0
1
0
1
0
0
0
1
1
0
0
1
1
2
2
1
1
2
1
0
2
0
2
0
2
0
0
0
1
1
1
0
1
1
2
2
0
0
0
0
0
2
0
2
0
0
1
1
1
0
1
2
0
2
1
1
0
3
1
0
0
1
2
0
0
1
0
1
1
1
0
1
2
0
2
0
1
1
1
2
1
0
0
0
1
0
0
1
0
2
1
1
1
0
2
1
2
0
0
3
1
1
1
0
1
2
0
1
0
0
0
1
0
0
0
2
0
0
0
2
0
2
1
1
1
1
0
2
0
1
1
1
1
0
1
1
0
2
2
1
0
0
1
0
4
3
0
2
2
2
2
0
2
2
0
0
0
0
0
0
1
1
3
0
2
0
0
1
1
0
0
1
0
1
0
1
1
1
1
0
1
0
2
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
1
0
1
0
1
1
2
4
1
0
1
2
1
0
0
2
0
1
3
1
1
0
2
0
1
2
1
0
2
1
0
2
2
6
0
1
1
1
0
1
0
0
0
0
1
2
0
0
1
2
0
0
1
2
0
1
1
1
1
1
0
1
0
0
0
1
0
0
2
0
0
1
0
0
2
0
1
0
0
0
1
0
1
0
1
0
2
1
2
1
1
2
1
1
0
2
3
0
0
2
0
1
0
0
1
2
0
1
1
1
1
0
0
0
1
1
2
1
0
1
2
1
0
2
1
1
1
2
0
0
1
0
1
2
2
0
0
0
1
0
0
3
0
0
2
1
2
1
1
0
0
0
1
1
1
1
1
1
2
1
0
0
2
1
2
1
0
0
1
2
0
0
2
1
1
2
0
0
2
1
0
1
2
1
0
1
2
0
1
0
3
1
1
1
1
1
1
1
0
4
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
2
0
0
2
0
1
1
1
1
2
0
0
0
0
0
0
0
1
2
1
1
0
0
1
0
2
0
0
0
2
2
0
1
0
0
2
3
1
0
1
0
2
0
0
2
1
1
0
0
0
3
0
2
1
2
1
0
1
2
2
0
0
1
0
0
2
0
1
0
0
0
0
0
0
1
1
1
0
2
0
1
2
0
0
2
0
1
0
0
2
0
0
1
2
0
1
2
0
2
0
2
2
0
0
1
1
1
0
2
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
2
3
2
1
0
1
2
2
1
0
0
2
1
1
0
1
0
0
1
0
0
4
1
0
1
3
0
1
0
1
0
1
2
2
1
2
0
0
0
0
0
0
2
0
0
2
0
0
1
1
0
1
2
1
1
2
1
0
1
0
1
0
0
0
1
0
0
1
1
1
0
0
0
0
0
2
1
0
0
1
0
0
1
0
1
2
0
1
2
1
1
1
2
0
1
2
2
2
0
0
1
2
1
1
2
0
1
0
1
2
0
2
1
1
1
1
2
0
2
0
0
3
1
0
0
2
0
1
0
1
0
0
1
1
0
0
0
2
1
2
1
2
2
1
0
1
1
1
0
0
2
1
2
1
1
0
2
1
1
2
1
0
0
0
0
2
0
2
1
0
0
1
1
1
1
0
0
0
2
0
1
0
0
1
0
1
0
1
1
1
1
1
1
1
0
2
0
2
0
1
1
0
0
0
1
0
0
0
2
1
1
1
2
1
0
0
2
3
0
0
0
2
0
0
2
1
0
2
1
0
2
1
0
1
1
2
1
1
0
1
1
1
0
2
1
0
0
0
1
2
2
1
0
0
1
0
1
0
0
1
0
0
2
0
0
0
3
0
1
0
1
2
0
0
0
1
2
0
1
1
1
2
2
0
0
0
1
0
1
0
0
2
2
0
0
1
1
0
0
0
1
2
0
1
1
1
1
0
1
1
0
2
0
1
0
2
2
1
0
0
1
0
1
0
2
0
3
0
0
0
3
1
1
0
0
1
1
1
3
2
3
0
1
2
2
1
0
1
3
2
0
2
2
0
1
2
0
0
1
10
2
0
1
2
1
2
1
0
1
0
1
0
0
1
1
0
0
1
1
1
1
2
0
0
0
1
1
2
2
0
0
2
0
1
1
1
1
2
0
0
1
0
2
1
1
0
0
0
2
0
1
2
1
0
1
0
0
0
0
0
0
2
0
0
3
0
1
2
2
2
1
1
2
2
2
1
3
0
0
0
0
1
0
0
2
1
2
1
2
0
0
2
0
0
0
2
0
2
0
0
1
1
0
1
0
1
0
0
0
2
1
0
2
2
0
0
1
0
1
0
1
1
1
2
2
0
0
2
1
0
1
0
0
0
1
1
2
1
0
0
1
1
1
0
2
0
1
2
0
0
1
0
1
1
1
2
2
0
1
0
0
2
0
1
0
0
1
1
2
2
1
2
0
0
1
1
1
2
1
0
1
2
2
0
2
0
0
1
2
1
0
1
1
0
2
0
0
0
0
0
0
0
1
0
0
2
1
0
1
2
1
0
0
0
5
1
0
1
1
0
2
0
0
2
1
1
1
0
3
0
0
2
2
1
1
1
0
2
1
0
1
0
1
2
0
1
0
0
2
1
2
1
0
1
1
0
0
1
2
0
1
2
1
2
2
0
0
2
1
2
2
0
0
1
0
1
0
0
1
0
1
0
1
0
0
1
1
1
2
0
0
0
1
2
0
1
2
1
2
2
1
0
0
0
1
0
0
1
1
0
0
2
2
1
1
1
2
0
1
2
0
0
1
1
0
1
2
2
0
0
2
2
1
1
1
0
0
1
1
1
1
3
0
1
0
0
0
0
0
1
0
0
0
2
0
1
1
2
2
1
1
0
2
0
0
1
1
1
2
2
0
0
0
0
2
1
0
1
2
1
0
2
2
1
2
1
0
0
0
2
0
2
0
2
0
0
0
0
1
0
2
0
1
0
2
1
0
2
0
0
5
0
1
1
2
1
0
1
0
1
0
1
1
2
0
1
0
0
1
1
0
2
2
0
1
1
0
1
1
0
1
2
0
0
2
1
0
0
0
1
1
1
0
1
0
2
0
0
1
2
1
2
0
0
1
2
0
2
0
1
0
1
1
1
0
0
1
0
1
2
0
2
0
0
0
0
0
0
0
1
0
1
2
0
0
1
2
2
0
1
1
3
2
1
1
1
2
1
1
0
0
0
2
0
0
0
0
0
1
1
2
2
1
0
0
1
3
2
0
0
2
0
1
0
2
0
0
0
1
0
0
2
1
1
1
0
0
2
1
0
0
0
0
0
1
1
0
1
0
2
1
1
0
1
2
0
2
0
0
0
0
1
1
1
1
1
0
0
0
0
0
1
1
1
2
0
0
2
1
1
1
1
0
0
1
1
2
2
0
0
1
0
2
0
0
3
0
1
0
0
1
0
1
0
2
0
0
1
2
0
1
0
1
0
1
1
1
2
0
2
0
2
0
2
2
0
1
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
1
1
1
2
0
0
0
0
1
0
0
2
3
0
1
0
0
0
1
0
0
1
1
1
1
2
1
0
1
0
0
1
0
2
2
2
1
0
0
0
2
0
1
0
2
1
0
1
0
0
2
1
2
2
1
0
0
2
1
0
1
0
2
0
1
0
0
0
0
1
1
1
0
1
0
2
2
0
1
1
0
0
0
0
0
0
2
0
2
1
0
1
2
1
3
1
2
1
1
0
1
0
1
1
1
1
0
0
0
1
1
0
0
1
0
0
0
2
1
1
0
1
2
1
1
0
0
0
0
2
2
0
0
0
1
2
0
0
0
0
1
0
1
2
0
0
0
0
1
0
0
3
0
2
0
2
0
1
1
0
0
1
0
0
0
2
2
1
1
0
0
0
0
0
0
2
0
0
1
0
0
2
0
1
1
1
1
2
0
2
0
1
0
2
1
0
1
2
3
1
0
0
2
1
0
1
1
0
0
0
1
0
2
0
1
0
2
0
1
0
2
0
0
0
0
2
0
0
0
0
1
2
0
1
0
1
0
0
1
1
0
2
1
0
1
0
0
0
1
2
0
1
1
1
1
2
1
2
2
0
0
1
0
1
2
0
2
0
2
2
2
1
2
1
1
0
0
0
2
1
0
2
0
0
1
1
0
1
1
2
2
0
0
1
0
1
1
2
1
2
1
0
1
4
0
1
0
2
2
1
2
1
0
1
1
0
2
0
1
1
1
0
1
0
1
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
1
0
1
0
2
2
0
1
0
0
2
2
2
2
0
2
1
0
0
1
0
0
1
0
0
1
1
0
1
2
0
0
0
0
0
0
1
0
0
3
0
0
1
0
1
2
0
2
1
0
1
1
0
2
0
2
2
2
1
2
1
0
2
0
1
0
1
4
0
2
1
0
0
2
1
3
0
1
1
2
1
0
2
0
1
0
0
2
1
2
2
2
0
1
0
0
1
0
0
0
1
2
0
1
2
0
2
1
1
0
2
0
0
2
0
1
0
1
2
1
2
2
2
0
1
0
0
0
0
1
1
3
2
1
1
1
2
2
0
2
0
2
0
0
2
1
2
2
0
2
1
2
2
1
1
2
0
0
1
1
0
2
1
2
1
0
0
2
1
2
1
1
0
1
0
2
1
0
2
0
1
0
0
0
2
1
2
0
1
1
2
1
0
1
2
0
2
1
0
1
2
1
0
0
0
2
0
1
0
0
2
2
1
2
2
1
2
1
3
2
1
0
1
2
0
0
1
1
0
2
0
0
2
0
1
0
2
2
0
0
0
2
0
0
1
0
0
0
3
0
0
1
0
1
1
2
0
0
2
1
0
0
2
1
0
0
4
1
0
0
1
1
1
3
0
0
0
0
2
1
2
0
2
0
1
0
0
0
0
0
0
0
4
0
1
0
2
1
1
1
1
0
0
2
2
0
0
0
1
0
1
0
2
0
0
2
1
0
0
1
0
1
2
0
0
0
2
2
2
1
0
0
0
0
0
0
1
0
2
2
0
1
1
0
1
2
1
0
1
0
0
0
0
1
2
0
0
0
1
2
0
0
1
1
2
0
0
2
1
0
1
2
0
0
2
1
0
0
0
1
2
1
2
0
2
0
0
2
0
1
0
0
0
0
0
1
0
0
1
1
2
0
1
1
0
0
0
0
0
2
1
2
1
1
0
1
0
1
1
1
3
2
2
1
1
1
1
0
0
1
1
0
1
1
0
0
0
0
0
0
2
1
1
0
1
1
2
2
2
2
1
0
1
0
0
1
3
0
1
0
0
0
2
0
2
2
1
0
1
1
0
0
2
1
1
0
1
0
1
2
2
0
1
2
0
0
0
0
2
2
1
1
0
2
1
0
0
2
0
2
2
0
0
0
2
1
0
1
0
1
1
0
1
2
0
1
0
2
1
0
0
2
1
0
0
0
0
2
0
1
0
0
1
0
1
1
0
0
0
2
1
0
0
1
0
0
1
0
0
1
0
2
2
1
1
1
1
1
2
1
0
0
0
2
0
2
0
1
1
0
0
0
2
1
2
0
1
1
1
1
1
0
0
0
2
2
1
0
1
0
0
1
0
0
0
1
0
2
1
2
1
3
0
0
2
0
1
0
1
0
0
1
1
2
1
2
0
1
1
1
1
0
1
1
0
1
0
0
1
0
0
1
2
0
0
2
1
0
1
2
1
1
0
1
1
0
0
1
0
1
1
1
1
0
0
0
2
0
1
3
0
2
0
2
0
0
1
0
0
1
0
1
1
0
1
0
1
0
0
0
1
0
2
1
2
0
1
0
3
0
1
1
0
0
1
0
0
1
1
0
0
0
2
0
0
0
1
1
0
0
0
1
1
1
0
1
0
1
0
1
2
2
0
1
2
0
4
0
2
1
2
0
0
2
0
1
1
1
0
0
1
1
0
0
1
2
2
2
2
0
2
0
2
0
2
2
0
2
0
0
0
2
1
0
0
0
1
0
0
2
0
1
0
1
0
1
1
0
0
0
0
1
1
2
1
0
0
0
2
0
0
4
1
3
1
0
0
2
1
1
2
1
0
0
2
2
1
0
1
1
0
1
2
1
0
1
2
0
0
0
1
1
1
1
0
0
1
1
0
0
0
1
2
1
0
1
2
1
1
1
1
1
1
1
0
1
2
1
0
1
0
2
1
2
0
0
0
0
1
1
7
0
0
1
1
2
1
2
3
0
0
0
2
1
2
0
0
0
1
1
0
0
1
1
1
0
2
1
2
0
2
1
1
2
1
1
0
1
0
0
0
2
0
2
0
0
1
0
0
1
2
1
0
1
0
0
0
2
0
2
1
2
1
0
1
1
1
0
1
1
2
1
2
2
0
1
1
2
0
2
0
0
0
0
2
0
0
1
1
0
1
2
0
0
1
0
1
1
0
4
0
0
0
0
0
0
2
2
2
0
1
2
1
1
1
0
1
1
1
0
0
0
0
1
2
1
2
0
0
0
0
0
2
1
0
2
0
1
0
0
0
0
0
0
0
1
2
0
1
0
0
0
1
1
0
0
1
1
0
0
1
0
2
0
1
1
0
1
1
0
1
1
0
1
1
1
1
0
1
1
0
1
1
0
0
2
1
1
0
1
0
0
0
1
2
1
0
0
0
0
1
1
2
1
0
0
0
4
0
0
0
0
2
1
1
0
1
0
1
0
0
0
2
0
1
1
2
0
1
1
0
4
0
0
1
2
2
1
0
0
2
0
0
2
0
0
1
1
1
2
3
1
2
1
0
2
0
1
2
0
2
3
2
2
0
1
0
1
0
1
1
0
1
0
1
2
0
1
1
1
2
1
1
0
1
2
1
3
1
0
0
3
2
0
2
1
2
1
2
2
1
0
2
0
1
1
2
1
1
1
2
1
1
2
0
0
2
0
3
6
0
0
0
1
2
2
0
2
2
2
0
0
0
0
1
0
1
1
0
0
0
0
1
1
0
0
1
0
1
1
1
1
0
0
1
2
0
0
2
2
0
1
0
0
6
0
0
0
0
1
2
1
0
0
3
0
2
2
1
0
0
0
1
2
1
1
1
0
0
1
0
0
1
1
0
2
2
1
2
0
1
2
1
2
1
0
2
1
1
1
1
1
2
0
0
1
1
1
0
1
2
0
0
0
1
2
2
1
2
1
0
0
0
0
1
1
0
0
1
2
2
0
1
2
2
0
1
1
1
0
1
0
0
0
1
0
1
1
1
1
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
1
2
2
1
0
0
1
0
2
1
2
0
2
0
0
0
0
2
0
2
1
2
1
2
2
1
2
1
1
1
2
1
1
0
1
0
1
0
0
0
1
0
0
0
2
2
1
0
0
1
2
2
1
2
0
0
3
1
1
1
0
3
1
1
1
0
0
1
0
1
1
1
2
1
1
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
1
0
1
1
0
2
2
1
0
1
2
2
3
0
0
0
0
0
2
3
0
1
2
1
0
0
0
0
0
2
0
0
0
2
2
0
2
1
0
0
1
0
1
1
1
0
0
2
0
2
1
0
1
1
0
1
0
0
0
0
0
2
2
1
0
0
2
1
2
1
0
1
0
1
1
2
1
0
0
1
0
0
1
0
1
1
0
1
0
1
1
1
0
0
0
0
1
1
0
1
1
1
2
0
2
1
1
2
0
1
2
1
0
0
0
1
0
2
0
1
1
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
1
0
1
2
1
1
0
0
0
1
3
1
1
0
0
1
0
1
0
0
1
0
1
1
2
2
1
1
1
1
0
0
1
1
2
1
1
1
2
1
0
1
2
0
1
1
1
1
2
0
0
2
0
1
1
0
0
0
0
1
1
0
0
2
0
1
2
1
0
1
0
2
1
0
3
0
1
2
2
0
1
2
0
1
2
0
2
2
1
0
2
1
1
1
1
2
0
2
0
1
0
2
1
1
0
0
4
0
1
2
2
0
1
0
2
0
1
0
2
0
1
2
1
0
0
1
0
1
0
0
1
1
3
3
0
1
0
1
0
0
0
0
2
3
1
0
0
0
0
0
0
2
1
0
0
1
0
2
0
1
7
0
2
1
1
2
0
1
0
1
1
0
1
1
2
1
1
2
2
1
1
0
0
0
1
0
1
0
1
0
1
0
2
0
0
1
2
2
1
0
0
1
0
0
1
1
1
1
0
1
4
1
0
2
1
0
1
1
1
1
1
0
0
1
0
1
0
0
0
0
1
1
2
1
0
1
1
2
1
0
1
1
1
0
2
0
0
1
2
0
1
0
1
1
0
1
1
0
2
2
1
1
1
2
0
0
0
2
0
1
0
1
0
1
2
2
2
2
1
0
0
4
0
0
0
1
1
0
2
2
1
0
2
0
1
2
2
2
0
2
2
1
1
1
3
2
2
2
1
1
0
1
0
0
1
0
1
0
1
0
2
0
2
2
2
0
0
0
0
4
0
0
0
2
0
1
1
0
1
2
2
1
1
1
1
2
2
1
0
1
0
2
0
1
1
1
1
0
2
0
1
1
0
0
0
1
1
2
1
2
1
0
0
1
1
0
1
2
1
1
0
1
0
2
2
1
0
1
0
0
0
1
1
1
0
0
1
0
0
0
1
1
1
1
2
1
1
0
1
1
1
0
0
0
0
2
0
0
1
0
0
0
1
1
0
1
0
1
0
1
0
0
0
0
0
2
2
1
1
1
0
0
0
2
2
1
2
0
0
0
0
2
2
0
0
2
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
3
1
0
0
2
1
1
1
1
1
1
0
1
1
1
1
0
0
1
2
1
0
2
1
0
0
0
1
1
2
0
0
0
0
2
1
1
2
0
2
1
2
1
2
0
1
2
0
1
0
1
0
0
1
2
0
0
2
0
0
1
1
2
2
1
0
0
0
0
0
2
1
0
2
1
1
0
0
1
0
1
1
0
2
0
1
0
0
1
0
0
0
1
1
0
2
2
1
1
1
2
0
0
1
0
0
0
1
1
1
0
1
2
0
2
2
2
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
2
1
0
2
0
1
0
0
0
1
0
2
1
0
0
1
1
0
0
1
0
2
2
2
1
0
2
1
2
0
2
0
0
0
0
0
2
0
0
2
1
0
0
0
1
1
1
0
0
0
2
0
1
1
0
1
0
0
0
2
2
1
0
1
1
1
0
0
0
0
0
1
1
0
0
1
1
1
0
0
1
2
1
2
0
2
2
0
1
2
2
2
0
0
0
2
1
2
1
0
2
0
1
0
1
2
0
0
0
2
0
3
0
2
3
0
1
2
1
1
3
0
1
2
0
0
1
0
0
0
0
2
0
0
1
1
0
2
0
0
1
1
1
0
1
2
0
2
0
0
0
2
0
0
1
1
2
1
1
0
0
2
1
1
1
0
1
0
0
0
2
1
1
2
0
0
0
1
0
0
2
0
0
0
0
2
1
2
1
0
2
0
1
0
2
1
0
2
0
0
1
1
1
0
1
1
0
1
1
0
0
1
0
0
0
1
1
0
0
0
1
1
2
0
2
0
0
0
1
0
0
1
1
0
0
0
0
2
1
1
0
1
1
1
0
0
0
0
0
2
0
2
6
0
0
2
1
0
3
1
1
2
1
2
1
1
1
0
0
1
2
0
0
0
0
1
0
1
0
0
1
0
1
1
1
0
0
0
2
1
0
1
2
0
2
2
0
1
0
1
2
0
2
2
0
2
0
2
0
1
2
0
1
1
1
0
0
0
0
0
1
1
1
0
0
1
2
0
0
2
1
1
1
2
1
0
1
0
0
0
2
0
2
1
2
0
0
2
0
0
1
1
2
1
1
0
1
1
0
1
0
0
0
2
2
2
2
2
0
0
1
1
0
1
1
2
0
0
0
1
1
0
0
1
0
0
0
1
1
1
0
1
1
0
1
0
1
1
0
1
0
1
0
1
2
1
0
0
1
1
1
1
2
0
1
1
2
0
1
0
2
0
0
1
0
0
2
0
1
0
2
1
0
2
3
3
0
0
2
0
1
1
1
2
0
0
1
2
2
2
0
1
0
0
1
2
1
1
0
1
1
1
2
0
2
2
0
2
0
2
1
0
0
0
2
0
1
1
2
1
0
1
2
2
0
1
0
0
2
0
1
1
0
1
0
0
0
0
1
1
0
0
1
1
1
1
0
0
2
2
0
2
0
1
0
0
2
1
0
1
1
1
0
1
1
0
1
1
0
0
0
1
0
0
0
1
2
2
2
0
1
0
0
0
1
0
0
1
0
0
1
2
0
1
1
0
2
0
1
0
1
0
0
0
0
3
0
1
2
1
0
0
0
0
0
1
0
1
4
2
1
1
0
1
1
0
1
1
2
2
0
0
1
0
0
0
0
1
0
2
0
0
1
2
0
2
2
1
0
0
1
0
0
2
1
2
2
2
1
1
0
2
1
0
1
0
1
0
0
0
0
0
2
1
0
0
2
1
1
0
1
0
1
0
2
1
1
0
0
1
0
0
2
1
0
1
2
0
1
1
1
0
1
1
2
3
2
1
1
0
0
1
1
2
2
0
1
2
2
0
0
0
0
0
2
0
2
1
1
2
1
1
2
3
0
1
1
1
1
1
1
0
2
1
1
1
0
0
1
0
1
1
1
2
0
0
0
2
2
5
0
0
2
2
1
2
0
0
0
1
1
0
0
0
0
1
2
1
1
1
0
0
1
1
0
1
1
0
0
0
1
0
3
2
1
0
0
1
0
0
0
2
0
0
0
0
0
3
0
1
0
1
1
0
2
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
2
1
0
2
1
4
3
1
1
2
2
0
2
1
1
2
1
2
2
1
2
2
1
3
0
1
2
1
1
2
2
0
2
1
2
0
1
0
1
1
0
1
0
0
0
2
1
0
0
0
0
1
1
1
0
2
2
1
1
0
2
1
1
0
1
0
2
0
0
0
1
2
0
0
0
1
1
2
0
1
0
0
0
1
1
0
2
3
0
1
0
1
0
0
2
0
0
0
0
1
0
0
1
0
3
2
0
2
1
0
0
1
1
1
0
0
1
2
1
2
0
0
2
0
1
2
0
0
0
1
2
0
1
1
1
1
1
1
1
1
1
1
1
0
1
1
0
0
1
1
0
1
1
0
4
1
0
0
0
2
2
0
0
0
0
0
1
0
1
0
2
0
2
1
1
0
1
0
0
0
1
0
0
0
2
0
2
1
0
0
2
1
1
1
2
1
2
1
1
0
1
1
0
3
0
0
0
1
2
0
0
0
1
0
0
1
1
0
0
0
1
1
1
0
1
1
0
0
0
2
2
1
2
0
0
2
2
1
0
0
1
1
1
1
5
0
1
0
1
0
1
0
0
0
2
0
1
2
1
1
1
2
0
2
1
2
0
0
0
0
0
1
0
0
0
2
1
0
0
1
1
0
1
0
0
3
1
1
0
1
2
1
0
0
0
0
0
1
1
0
2
0
1
1
1
0
0
0
0
0
2
0
2
1
0
0
2
0
2
0
0
1
2
2
2
1
0
0
2
2
1
0
1
0
0
2
0
0
2
1
2
0
1
1
0
0
1
0
2
2
1
1
0
1
0
0
0
1
0
1
1
1
1
2
1
2
1
0
1
2
0
0
1
0
0
0
2
0
2
0
2
1
2
2
0
2
1
0
0
0
2
1
1
0
1
0
1
0
0
1
1
1
0
2
1
0
1
1
0
2
0
2
2
2
0
0
3
0
1
1
2
0
1
1
2
2
1
0
0
2
1
1
0
2
1
0
2
2
0
0
0
0
0
2
1
0
2
2
2
2
1
1
1
1
0
1
0
0
0
1
2
1
0
0
1
1
1
2
0
1
0
2
1
2
0
1
1
2
0
1
0
0
0
2
0
2
1
0
1
0
2
1
1
0
0
0
1
1
0
1
0
0
2
0
1
1
0
2
1
2
0
2
0
0
0
1
1
1
0
1
0
1
2
0
1
2
2
2
2
0
0
0
0
1
0
1
1
0
0
0
1
1
1
2
0
0
0
1
0
1
2
0
1
1
0
0
0
0
2
2
0
0
1
2
1
2
1
2
1
1
0
1
1
0
1
2
2
1
0
2
0
1
2
1
0
1
0
0
0
0
1
1
1
0
1
0
1
0
0
1
0
0
2
1
2
0
4
1
1
0
0
1
3
1
0
0
1
2
1
1
0
0
0
3
1
2
2
0
0
2
0
2
1
1
0
0
3
0
0
0
1
1
2
1
0
2
1
0
2
1
0
2
1
0
1
2
1
1
0
0
0
0
2
2
0
0
0
0
0
1
0
1
0
0
2
1
0
2
1
0
0
2
1
0
1
0
0
0
0
0
0
0
1
1
2
1
0
0
2
2
2
3
2
1
4
1
1
0
2
1
1
1
0
0
2
2
0
1
1
2
0
2
2
0
0
0
1
1
1
1
0
1
2
1
0
1
0
0
1
2
1
1
1
0
0
1
2
0
2
0
1
1
0
0
0
1
2
2
1
0
0
0
0
2
2
0
0
0
2
1
0
1
0
2
0
2
2
0
0
2
2
1
3
2
0
0
0
0
1
2
0
2
0
0
0
2
2
0
1
3
0
0
1
0
4
1
2
1
2
1
3
4
0
1
0
0
2
1
1
0
1
0
1
0
0
1
1
0
2
1
2
1
2
1
1
0
2
2
2
0
1
2
2
2
0
0
1
0
0
1
2
0
0
0
0
1
1
0
1
0
0
1
1
1
1
0
0
0
0
1
0
2
0
1
0
1
2
0
0
1
0
2
1
0
0
0
1
1
0
2
2
1
1
0
0
0
0
2
1
0
2
1
1
0
0
0
0
1
1
1
0
0
1
1
0
2
0
1
1
1
0
0
0
1
1
1
3
0
0
1
0
1
1
0
0
2
0
0
0
2
0
0
0
2
2
0
1
2
0
1
2
1
0
2
0
1
1
0
3
1
1
0
1
0
1
0
0
0
0
1
0
1
0
0
2
0
0
1
2
0
0
0
0
1
0
0
2
1
1
0
0
0
1
0
0
1
0
0
2
0
0
1
0
0
0
0
0
1
0
1
1
0
0
1
1
1
0
2
2
3
2
1
2
0
0
0
1
1
1
1
0
2
2
0
1
3
0
1
0
0
2
1
0
1
0
0
0
0
1
0
1
0
0
3
1
0
0
1
0
0
1
0
1
0
0
0
1
1
1
1
1
1
0
1
1
1
1
0
1
1
0
0
3
1
2
1
0
1
1
0
1
2
0
2
1
0
0
0
2
0
0
1
0
0
0
2
0
0
1
1
1
1
0
1
1
0
0
1
0
0
2
0
0
0
1
1
0
2
0
0
2
3
0
2
2
1
0
2
1
0
1
0
2
1
1
1
0
2
1
1
1
0
1
1
1
0
0
0
0
0
0
2
1
0
2
0
0
0
2
0
2
1
0
1
2
1
0
2
0
1
0
1
0
0
1
0
1
0
2
2
0
1
1
1
0
1
0
0
1
2
1
2
3
0
2
2
2
2
1
1
0
1
0
1
2
0
1
1
2
0
1
0
0
0
0
1
0
2
0
1
0
2
2
0
1
3
1
0
1
2
6
1
2
2
1
0
0
0
0
1
2
0
0
0
1
1
0
0
2
0
0
1
2
0
2
0
1
2
0
1
1
2
2
0
0
1
0
1
0
1
1
2
0
1
2
0
1
1
1
0
0
0
2
0
2
0
0
0
0
2
0
1
2
0
1
0
1
0
0
1
0
1
0
2
2
0
1
0
1
1
9
1
0
1
1
0
2
1
0
1
2
0
0
1
1
0
6
0
0
0
1
2
0
1
1
0
1
2
1
0
0
2
2
1
1
0
0
2
0
0
0
0
2
1
2
0
0
1
2
1
1
1
2
0
1
2
2
0
0
0
1
2
2
0
0
2
1
2
2
1
0
0
2
0
0
1
1
1
0
0
0
1
1
2
1
1
1
2
1
1
0
3
0
0
1
1
1
0
0
0
0
0
2
2
1
0
1
0
0
1
2
2
1
1
1
2
1
0
0
0
0
1
1
0
3
1
0
0
2
1
1
1
2
1
0
1
1
0
0
1
0
0
2
1
2
0
0
1
0
0
0
0
1
1
1
2
0
1
0
0
0
1
1
1
2
2
1
0
0
0
0
2
2
0
2
0
2
2
1
0
0
1
2
0
0
1
2
1
0
1
2
0
1
0
0
0
0
1
1
1
0
1
1
0
0
0
0
1
1
0
0
2
0
0
1
1
0
0
2
1
0
0
1
0
2
2
2
0
0
2
2
2
0
1
0
0
0
0
0
1
1
1
0
1
4
1
0
0
2
0
1
1
2
1
0
1
1
2
0
1
2
1
1
1
0
3
0
2
0
1
0
0
2
0
0
0
2
1
0
2
2
0
0
0
2
2
0
0
1
0
1
2
4
0
1
0
0
2
0
2
2
0
1
2
1
0
0
1
0
1
3
0
0
2
1
0
0
1
1
0
3
0
1
0
2
6
2
1
2
1
0
0
0
1
1
1
0
1
0
0
0
0
1
0
1
1
1
2
0
1
0
0
2
0
1
0
0
0
1
2
1
0
0
0
0
1
2
0
0
2
3
0
0
1
0
0
0
0
0
2
0
1
5
0
0
0
2
0
0
1
0
1
2
2
0
0
2
0
0
1
0
1
1
0
0
2
1
2
0
0
1
2
0
0
0
0
0
0
2
2
1
1
0
1
1
0
1
1
0
2
0
2
0
3
2
2
1
0
1
0
0
1
0
0
0
2
2
0
0
1
0
0
2
1
0
1
1
1
0
0
1
0
0
0
0
0
2
1
0
0
2
0
0
2
1
1
1
2
1
1
2
2
1
0
0
0
2
0
1
1
1
0
1
2
1
0
0
0
0
0
0
0
2
0
2
2
1
2
0
0
0
1
1
1
1
1
0
2
2
0
0
0
0
0
1
1
1
1
0
2
0
3
0
2
0
0
0
3
1
2
0
0
0
1
1
0
2
0
2
0
0
0
1
1
0
2
1
0
0
0
0
0
0
2
1
1
0
4
0
0
2
0
2
2
0
1
2
0
1
0
0
0
0
0
0
1
1
2
1
1
1
1
1
1
1
1
0
0
1
0
0
0
0
0
2
0
0
0
0
2
2
1
1
2
2
1
2
2
2
0
2
0
1
1
0
2
0
2
1
1
0
0
0
1
0
0
0
2
2
0
2
0
1
0
1
1
0
0
2
0
0
0
0
0
0
1
0
0
1
1
1
1
1
2
2
0
0
0
0
1
2
0
2
0
0
1
0
1
0
2
0
0
0
1
1
3
0
1
0
1
0
1
1
0
0
1
1
0
0
0
0
0
1
0
1
2
2
0
0
0
0
0
2
1
2
0
1
1
0
0
0
0
1
1
1
1
2
1
0
2
2
2
0
1
2
1
1
2
0
1
0
1
0
0
1
0
1
1
0
0
1
1
1
0
1
0
0
0
2
1
1
0
0
0
2
1
1
2
1
0
0
1
0
0
0
0
2
0
2
1
1
1
0
1
1
1
1
1
1
0
1
0
1
2
1
1
0
2
0
1
1
2
0
0
0
2
2
1
2
0
1
2
0
1
1
2
1
0
0
0
0
2
1
0
1
0
2
0
2
1
2
0
0
2
2
0
2
1
0
0
1
0
2
1
3
0
0
0
0
1
1
0
1
1
1
2
2
2
0
0
1
1
1
2
0
0
0
1
0
0
0
2
0
0
0
1
2
2
1
0
0
1
0
0
2
0
0
0
0
0
0
1
0
2
0
1
1
0
2
2
0
0
0
2
0
0
2
1
0
2
2
0
1
0
1
1
1
1
1
0
2
2
1
2
0
1
2
2
0
0
0
1
2
0
1
0
2
1
0
0
1
2
0
0
2
0
1
1
1
2
2
0
1
3
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
2
1
1
2
0
0
0
0
0
0
2
1
1
1
0
2
1
0
1
1
2
1
1
1
1
2
0
2
1
1
2
2
2
0
2
1
0
0
1
0
2
0
1
1
1
1
1
0
1
1
1
1
1
0
1
1
0
1
0
2
0
1
0
1
0
0
2
0
2
2
0
0
1
0
0
1
2
0
1
0
0
2
0
1
1
1
1
1
2
0
1
1
0
1
1
0
1
3
0
1
2
0
1
0
2
0
2
1
0
0
0
0
0
1
2
2
0
1
0
1
2
1
2
0
0
0
1
1
4
1
1
1
0
0
1
0
0
2
1
0
1
1
1
0
0
2
1
2
0
1
1
0
0
1
1
2
1
1
0
1
0
0
0
2
2
1
1
2
0
3
0
0
2
2
2
1
0
1
2
1
0
2
2
1
0
1
0
0
0
1
1
2
0
1
0
2
0
1
0
1
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
1
1
1
1
0
0
0
1
1
1
0
0
2
0
0
1
0
0
1
2
1
4
2
2
0
0
1
2
1
0
0
3
0
1
0
0
0
0
1
1
1
1
1
1
1
2
2
2
1
1
0
0
2
0
1
1
0
0
0
0
1
0
0
1
0
0
0
2
0
2
1
0
1
1
0
0
0
1
0
1
0
1
1
0
3
1
1
3
1
4
2
1
0
0
0
1
0
0
0
0
6
1
2
1
0
0
1
0
1
0
2
0
1
0
1
2
2
1
0
0
2
0
2
1
0
1
2
2
2
2
2
0
0
1
1
1
0
1
1
0
0
0
1
0
0
2
2
0
0
2
1
0
2
2
0
1
2
1
1
0
1
1
2
0
0
2
1
1
0
0
0
1
0
2
1
0
1
0
1
0
0
0
0
0
1
2
2
2
1
0
0
1
0
0
1
1
0
0
2
0
0
1
0
2
0
2
0
2
0
3
1
1
1
0
2
0
0
0
2
0
0
0
4
0
2
1
0
1
0
0
0
0
0
7
2
1
2
0
1
0
1
0
0
0
0
1
1
0
0
1
0
1
2
1
3
1
1
1
0
1
0
0
0
0
1
3
1
0
0
2
0
2
0
1
1
1
0
0
2
2
0
0
1
0
1
1
1
2
0
1
0
0
0
1
2
2
1
0
2
0
0
2
0
0
0
0
0
1
1
0
2
0
0
1
0
1
0
2
0
0
0
1
2
0
0
0
0
1
1
1
1
0
0
2
0
0
1
0
1
1
0
0
1
2
0
2
1
1
1
2
1
0
1
0
0
0
0
1
0
0
2
0
1
3
0
0
0
1
0
0
1
0
0
1
2
0
1
0
2
1
0
2
1
0
1
1
2
1
1
2
1
1
1
1
0
0
1
1
2
1
0
1
1
1
2
1
2
2
0
0
0
1
2
2
0
2
1
0
1
2
0
0
1
0
2
0
0
0
0
0
0
1
0
1
0
0
3
0
1
0
2
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
2
1
1
2
0
2
1
2
0
0
1
0
1
0
1
2
2
0
0
1
1
0
0
1
0
1
1
1
0
1
0
1
2
0
0
1
0
0
0
2
0
1
0
1
2
1
0
1
0
2
2
1
1
1
0
2
0
0
3
0
1
1
0
0
1
0
0
1
1
1
1
2
1
0
1
1
0
1
2
2
1
1
0
1
1
0
0
1
2
0
0
0
2
2
0
1
2
0
1
1
1
0
0
1
0
2
0
0
0
2
0
1
2
1
2
0
0
1
1
2
1
0
1
2
0
1
0
2
2
1
2
1
1
2
0
1
0
0
2
0
0
0
1
1
0
2
2
1
0
1
2
2
2
0
1
1
0
1
2
1
0
1
1
1
1
3
1
2
0
2
0
2
1
1
1
0
1
0
0
0
1
1
1
2
0
1
1
1
0
2
0
2
2
1
1
1
0
0
2
2
1
3
0
0
1
0
2
1
1
0
1
0
2
2
0
2
0
2
1
2
0
2
0
1
0
1
0
2
1
0
1
0
0
0
0
1
1
2
1
0
2
1
1
0
1
0
2
1
2
2
1
2
0
1
2
2
2
1
0
1
0
1
0
1
0
0
0
0
0
2
0
1
1
1
1
0
0
0
1
2
0
2
1
1
1
0
1
1
0
0
2
2
0
0
2
1
0
2
0
0
0
1
0
1
1
0
0
2
1
3
0
0
2
0
0
0
1
0
2
2
1
0
0
1
0
0
1
0
0
1
1
0
2
0
1
1
0
0
2
2
0
0
2
0
0
0
1
0
2
2
0
0
1
0
2
3
1
0
0
1
1
0
0
1
2
2
0
1
0
0
1
1
2
1
1
1
3
2
0
0
2
2
1
0
0
1
1
1
2
2
0
0
2
1
0
1
1
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
1
1
2
2
1
0
2
2
0
1
0
0
2
0
1
0
1
1
1
1
1
1
0
1
0
2
0
1
2
0
2
1
0
2
2
0
0
1
1
0
2
0
1
2
1
1
0
0
1
0
0
1
0
2
0
2
2
0
2
1
1
2
1
0
1
2
0
1
0
0
0
2
0
0
0
0
2
0
1
0
1
0
0
0
1
1
2
0
0
1
2
0
0
0
0
1
1
0
0
0
0
0
2
2
2
0
0
0
2
2
1
2
0
0
1
1
1
0
2
0
1
1
0
0
0
1
0
0
2
1
0
0
1
0
0
2
0
2
1
1
1
0
1
0
2
2
0
0
0
0
3
2
1
1
1
1
1
0
1
2
0
1
1
2
0
0
0
0
0
0
0
1
2
0
1
2
2
2
1
1
0
0
1
0
0
2
1
0
0
1
0
0
1
0
2
0
0
0
0
1
1
0
1
1
1
0
0
0
0
0
2
1
1
0
0
1
2
0
0
1
0
1
2
0
1
0
1
0
0
0
1
1
1
1
2
1
0
1
2
0
0
1
0
0
0
0
2
0
1
1
0
0
2
1
0
0
0
0
0
2
2
0
1
0
1
0
1
0
1
1
1
0
0
0
1
0
1
1
0
0
0
3
0
2
1
2
2
0
0
2
1
0
1
0
1
2
2
0
1
2
1
0
2
2
2
0
2
0
1
1
2
1
2
0
2
0
2
1
1
3
1
0
2
0
0
2
0
2
1
1
0
1
1
0
1
1
0
2
0
0
1
0
2
0
0
1
1
2
0
0
1
0
1
0
0
0
0
0
1
2
2
0
1
1
1
7
0
1
3
1
0
1
0
0
0
1
0
1
0
0
0
1
0
1
1
0
2
2
1
0
1
0
2
0
2
2
2
1
2
0
0
2
0
0
0
1
1
2
0
1
0
1
0
2
2
2
0
1
2
0
0
1
0
0
1
0
0
1
1
2
0
2
1
0
1
0
2
0
2
2
0
1
0
0
2
2
0
0
0
3
2
0
2
1
0
0
0
2
1
0
0
1
0
0
1
0
0
1
0
0
2
2
1
1
1
2
1
2
1
0
0
0
0
0
1
0
2
2
2
1
2
0
1
1
0
1
2
0
0
1
0
0
2
0
2
2
1
2
0
0
1
1
1
1
1
2
0
1
0
2
0
1
0
2
0
1
0
0
2
0
0
2
0
0
0
1
1
2
0
0
0
0
1
2
1
1
0
0
0
0
0
1
0
0
1
1
0
2
0
2
1
1
2
1
1
0
0
2
2
2
0
1
1
0
0
0
2
0
1
1
1
2
2
1
0
1
1
0
0
1
1
0
0
1
1
0
1
1
1
1
0
2
0
0
0
1
0
1
2
0
0
2
1
1
0
1
1
1
1
0
1
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
2
2
0
1
1
0
1
0
0
1
0
0
0
1
1
0
1
0
0
2
0
0
0
1
1
1
2
0
0
1
1
5
0
2
0
1
1
0
0
2
0
2
2
1
2
1
1
0
0
1
0
3
1
0
3
2
2
1
3
1
1
1
0
1
1
0
2
0
0
0
1
0
0
0
2
1
2
1
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
1
0
2
1
0
2
2
0
2
0
0
0
0
0
0
2
2
2
0
1
1
0
1
1
1
1
0
0
1
1
2
3
1
0
6
3
0
1
1
0
0
1
1
1
0
2
0
0
0
1
0
1
0
0
2
0
0
0
0
2
1
2
1
1
1
2
1
1
1
0
2
0
1
1
0
1
1
0
2
2
0
2
1
1
0
0
0
0
0
2
0
1
1
0
1
1
0
2
0
0
0
0
2
0
0
1
0
0
1
1
0
2
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
1
1
1
0
0
2
0
2
1
1
0
0
0
1
0
1
0
1
0
0
0
1
1
0
1
1
0
0
0
1
0
2
2
1
2
0
1
0
0
0
1
0
2
0
0
2
0
2
0
1
2
1
2
1
1
0
2
1
1
2
0
1
1
0
0
0
0
0
0
0
2
2
0
3
0
1
1
2
1
0
0
1
0
1
1
1
0
1
2
0
2
2
0
2
0
1
0
0
2
0
1
0
0
0
0
1
0
0
0
1
0
0
2
1
0
1
3
1
2
0
2
2
0
0
1
0
1
0
0
0
0
1
1
1
1
2
2
0
0
2
0
2
0
0
0
2
1
0
2
2
0
1
1
5
1
0
1
0
2
1
1
1
0
2
0
0
1
0
1
1
0
0
2
0
0
1
0
0
1
0
0
1
2
0
0
2
2
1
2
0
0
0
0
2
1
1
0
0
1
0
1
1
0
0
1
0
2
0
0
1
1
0
2
0
2
2
0
1
1
1
0
1
0
1
0
0
0
0
1
0
0
0
2
0
1
1
2
1
2
0
0
0
1
1
2
0
0
0
0
2
2
3
2
1
1
0
0
2
0
1
0
0
0
0
0
1
0
1
1
2
0
1
0
1
1
1
1
0
0
1
1
2
2
1
0
0
1
0
1
0
0
0
1
2
0
1
0
0
1
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
1
0
0
1
0
2
2
1
1
1
1
0
2
1
1
1
2
2
0
0
1
1
1
1
0
0
0
0
1
0
1
0
2
1
0
0
2
0
0
1
1
0
0
1
1
2
2
2
2
2
2
2
2
1
2
1
1
2
0
2
1
0
0
1
1
1
0
2
0
1
0
1
2
0
0
2
2
0
1
0
0
0
1
1
2
0
1
1
0
2
1
2
2
2
1
0
0
0
1
0
0
1
2
0
0
2
0
2
1
2
0
1
2
0
0
1
0
0
1
1
2
1
1
1
2
0
2
1
2
0
1
0
0
1
1
0
0
0
2
1
0
0
2
0
2
1
1
1
0
0
1
0
0
0
1
0
0
1
2
0
2
0
0
0
1
1
0
0
1
0
1
1
0
0
0
0
0
1
2
1
1
1
0
0
1
0
0
0
1
2
1
2
2
1
0
2
0
1
1
0
1
0
1
1
1
2
2
0
0
2
1
2
0
0
0
0
1
1
1
2
0
1
1
1
0
0
2
2
2
2
1
2
0
1
0
0
0
0
1
1
0
2
0
0
1
1
0
2
1
0
0
1
2
0
1
2
0
0
0
0
1
0
1
2
2
0
0
2
1
1
0
0
2
1
0
0
0
1
1
0
0
1
1
0
2
0
0
2
0
0
0
0
1
2
3
1
2
1
0
0
0
1
1
0
0
1
2
2
0
1
0
2
0
0
0
2
1
1
1
0
1
2
2
2
0
1
1
1
0
0
1
1
1
1
0
2
0
0
2
1
0
1
0
0
2
1
0
1
1
0
0
0
2
1
2
0
1
2
0
0
2
2
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
3
2
0
2
0
0
2
0
1
1
1
1
1
0
1
2
2
1
0
0
2
1
0
1
1
1
2
1
0
2
2
1
0
0
0
0
0
1
1
1
0
1
0
0
1
2
0
0
2
2
0
0
1
0
0
2
0
1
1
0
0
0
1
0
0
2
1
1
2
0
0
1
1
0
1
0
2
0
1
0
0
1
0
0
0
0
2
1
2
1
2
1
2
0
0
0
0
2
0
1
2
1
2
0
2
0
1
0
1
2
0
0
0
1
0
1
0
1
0
0
0
0
1
1
0
1
0
1
1
0
1
1
0
0
1
0
2
0
0
2
2
0
0
2
1
0
1
1
1
2
0
2
1
2
0
2
1
1
2
1
0
0
0
2
0
2
0
1
0
2
0
6
0
0
1
1
2
1
1
0
0
1
1
1
1
1
1
2
0
2
1
2
1
1
1
1
1
0
1
2
2
2
0
3
0
1
0
2
3
3
1
2
2
0
1
0
0
0
2
0
2
1
1
0
1
1
0
1
2
0
1
3
1
0
1
0
1
1
0
2
1
1
1
0
2
0
0
3
0
2
0
0
1
0
2
0
2
0
2
0
1
1
0
1
0
0
1
1
2
0
1
0
2
1
0
1
2
0
2
1
1
0
2
1
2
0
1
1
1
0
2
2
0
2
1
1
0
0
0
0
0
1
3
1
1
1
2
2
1
0
0
0
1
2
1
2
1
0
0
1
1
0
2
1
1
0
2
1
0
0
1
2
2
0
1
0
0
0
1
1
2
0
2
2
0
0
0
2
2
0
0
0
0
0
1
0
0
0
1
1
2
2
0
1
1
0
0
0
0
2
0
1
2
0
0
1
1
1
0
0
1
1
1
1
0
1
0
0
0
1
0
2
2
0
0
1
0
0
2
0
1
1
0
2
2
0
0
3
2
1
0
1
1
0
2
3
0
0
0
2
1
1
0
1
0
2
1
0
2
2
1
2
1
0
0
0
1
1
1
1
0
2
1
2
2
0
0
0
1
2
2
0
2
0
1
2
0
0
0
1
1
0
0
0
1
0
0
2
1
1
0
2
0
2
1
1
2
0
1
0
2
1
2
0
1
0
1
1
1
0
1
0
0
2
0
2
0
2
2
2
0
0
1
1
1
0
1
1
0
0
1
3
0
1
1
2
2
1
0
0
0
0
0
0
0
1
1
1
2
0
2
0
1
1
0
0
2
0
1
1
0
0
0
0
1
0
0
0
1
1
2
0
3
0
1
0
0
1
1
1
0
0
1
2
1
0
0
0
0
2
0
0
1
1
0
1
1
0
0
0
1
1
2
2
2
0
0
1
0
0
1
1
1
1
2
0
0
0
1
0
2
1
0
1
0
1
2
1
0
0
2
1
1
1
0
1
0
0
1
1
1
2
1
1
1
0
2
1
0
2
0
2
0
0
0
3
1
2
0
1
1
0
0
1
0
1
2
0
1
0
1
2
2
0
0
1
1
1
0
1
0
1
0
1
1
2
1
2
0
3
2
1
2
1
1
2
1
0
1
3
1
1
2
1
1
0
0
1
1
2
2
0
1
0
1
1
0
0
0
1
1
0
0
1
2
1
0
1
0
0
1
1
0
0
1
2
1
0
0
1
0
0
1
1
1
1
3
0
2
0
1
0
0
0
0
0
0
4
2
1
2
0
0
0
2
0
0
2
1
1
0
1
1
1
1
6
0
1
0
0
1
0
0
1
1
2
2
0
2
1
0
2
1
1
0
1
1
0
0
1
1
1
2
0
1
1
0
0
0
6
1
1
0
0
0
1
2
1
2
2
1
0
0
1
0
3
0
0
1
1
0
0
2
0
0
0
1
4
1
1
1
0
1
2
0
2
2
0
0
1
1
1
0
0
2
0
0
1
1
0
2
0
1
2
0
1
1
0
2
2
1
2
1
1
1
0
0
1
0
2
0
0
0
1
2
0
0
2
1
1
0
0
2
1
1
0
2
2
0
2
2
2
2
0
0
0
0
0
1
1
1
0
1
1
0
1
1
1
1
1
0
1
2
0
0
0
2
0
1
2
2
0
1
0
0
2
0
1
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
2
1
1
2
1
0
1
0
1
0
2
0
2
1
2
0
1
0
0
1
1
0
0
1
0
0
2
2
0
2
0
1
1
0
0
2
1
2
1
1
2
1
0
1
0
2
1
1
0
0
1
1
1
0
0
0
0
0
0
1
0
0
2
0
0
3
0
0
0
1
0
1
1
0
1
1
0
1
0
0
1
0
1
2
3
2
0
0
0
0
0
0
0
0
2
0
1
1
1
0
0
2
1
1
1
1
0
2
0
0
1
2
2
0
0
0
2
2
1
0
1
2
1
2
1
1
2
1
1
0
1
0
1
1
1
0
0
1
0
0
1
1
0
0
0
1
1
0
2
2
2
0
1
1
1
0
1
1
1
1
0
2
1
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
2
0
0
0
0
0
1
1
1
1
0
1
2
1
0
0
0
1
1
0
1
1
2
0
0
2
1
0
1
0
0
2
0
1
1
0
2
0
0
0
0
1
0
1
2
0
0
0
1
2
1
0
0
2
1
2
1
0
2
1
1
0
4
2
0
2
0
0
1
1
1
1
0
2
0
1
0
1
0
0
1
2
0
1
0
0
0
1
0
1
1
1
0
2
1
0
1
2
0
1
1
0
0
1
0
3
0
0
2
1
1
1
0
0
0
1
0
0
0
2
1
0
0
0
1
1
1
0
1
1
0
0
0
2
0
0
2
0
0
1
1
1
2
1
2
0
0
2
0
2
1
1
2
0
0
0
2
0
1
0
1
1
0
1
0
0
1
0
1
0
2
0
0
0
0
0
2
0
2
0
0
1
1
0
2
1
0
0
1
1
0
2
0
0
1
0
0
1
0
0
1
0
2
0
1
2
1
0
0
0
2
0
1
0
0
2
1
2
0
0
2
1
0
1
2
0
1
0
0
2
1
1
0
0
2
0
0
2
1
1
2
0
0
0
1
0
2
2
0
0
1
0
1
0
1
0
1
1
0
1
2
1
0
0
2
0
1
2
0
1
1
0
2
0
1
0
0
2
0
1
2
0
2
2
0
1
1
0
0
1
1
0
0
0
0
2
0
0
1
0
0
1
1
1
0
0
0
1
1
1
1
2
0
1
2
1
2
1
0
2
0
1
0
0
0
1
0
1
0
1
2
0
0
2
1
0
2
2
1
2
2
1
1
0
0
0
1
0
1
2
0
0
3
1
1
1
2
0
1
0
1
0
1
2
1
1
0
0
1
1
1
1
1
1
0
0
0
1
1
3
0
1
0
1
1
2
1
1
0
0
2
0
2
0
1
0
0
2
1
2
0
0
2
0
1
1
1
1
0
0
1
1
2
0
0
1
0
1
0
1
1
0
1
0
0
0
1
1
2
0
1
0
1
0
1
1
0
1
0
1
0
0
3
0
0
0
2
0
0
0
1
0
2
0
2
0
1
0
0
1
2
1
0
0
2
0
1
3
0
0
1
0
0
1
1
2
2
0
0
2
0
0
1
2
1
0
1
1
0
0
1
2
1
2
0
0
1
0
1
1
0
0
1
0
1
0
3
0
1
2
0
1
1
0
0
0
0
1
0
0
0
2
2
1
2
2
0
1
1
0
0
0
0
1
0
1
0
2
1
1
1
3
2
0
2
1
2
0
0
0
1
0
1
2
0
0
0
0
1
1
2
0
2
0
0
3
2
0
1
1
0
2
2
2
1
0
1
1
0
0
0
1
0
2
2
0
0
0
3
1
0
1
1
1
0
2
0
1
1
1
1
2
0
1
1
1
0
1
0
1
0
2
1
0
0
1
0
0
0
0
1
1
0
0
0
1
1
0
1
0
0
0
2
0
0
2
1
0
2
1
1
0
0
0
1
0
2
0
0
0
0
1
0
0
1
1
0
1
0
0
0
2
0
1
1
1
1
2
2
1
0
0
1
2
2
0
0
1
2
2
0
0
2
2
2
2
2
0
2
1
1
1
1
1
0
2
1
0
0
0
2
0
1
1
1
0
0
2
1
0
0
1
1
2
2
2
2
0
3
1
0
1
1
1
1
0
1
0
1
0
0
0
0
0
1
2
1
0
0
0
0
0
0
1
0
1
1
2
1
2
2
0
0
0
0
0
1
0
0
1
1
2
1
2
0
0
0
1
1
0
0
0
1
1
2
0
2
0
1
0
0
0
1
0
1
2
1
1
1
0
0
0
0
2
2
0
0
0
1
0
2
2
0
1
0
1
2
1
1
0
0
0
0
0
2
0
1
4
1
2
0
2
0
2
1
0
1
0
1
1
1
1
0
1
2
0
0
0
0
0
2
2
1
1
2
0
2
2
0
2
0
1
1
0
0
0
2
1
1
0
2
2
1
2
0
0
1
0
1
1
0
0
1
0
0
1
2
1
1
0
1
2
0
1
2
0
0
1
0
0
1
2
0
3
2
2
0
0
0
1
2
0
0
1
0
2
0
2
0
0
1
2
1
0
0
2
2
0
0
0
1
1
2
0
0
1
0
1
1
0
2
0
1
2
1
2
0
0
0
2
0
0
0
4
0
0
1
0
1
1
0
1
0
2
1
1
2
1
3
0
1
0
1
1
1
0
0
0
0
1
0
2
0
0
1
1
0
0
1
1
0
0
0
0
1
0
1
0
0
0
1
1
1
2
1
2
1
1
2
1
0
1
1
0
2
0
2
0
2
1
0
1
1
0
0
1
1
0
1
0
1
0
0
0
1
0
0
2
0
2
0
0
0
1
0
2
1
1
0
2
0
3
0
2
2
0
1
1
2
2
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
1
0
0
1
1
0
0
2
2
0
2
0
0
2
1
1
2
1
1
0
1
1
2
2
1
1
0
0
2
1
1
1
1
0
0
2
1
1
0
0
0
1
1
1
2
1
0
2
1
2
1
0
2
0
0
0
2
0
1
0
1
1
2
0
1
0
2
1
2
1
0
0
2
2
2
2
0
0
2
1
0
2
0
0
1
0
0
2
1
1
0
0
1
1
0
0
2
1
0
1
0
1
3
3
0
2
1
2
0
1
2
1
1
2
1
1
2
1
0
0
0
2
1
1
1
1
0
2
0
0
0
1
1
0
0
0
0
2
2
0
0
4
0
1
1
1
2
0
2
0
2
0
4
0
0
0
2
2
1
0
0
0
2
0
1
1
1
0
2
0
0
1
1
0
0
1
0
0
1
0
0
0
0
2
6
2
2
0
2
0
0
2
2
1
0
0
1
0
1
0
2
0
2
0
0
0
0
0
0
1
2
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
3
1
0
1
0
0
0
0
2
1
1
4
0
1
0
1
0
1
1
0
0
3
1
2
0
1
1
0
0
1
1
1
2
1
0
1
1
1
1
1
0
1
0
0
2
1
0
2
0
0
0
1
0
0
0
0
1
0
1
0
0
2
0
0
1
1
0
0
0
2
0
0
1
1
0
1
1
0
1
0
0
0
0
1
0
1
1
0
1
0
1
2
0
1
1
0
0
0
0
0
1
2
1
1
0
0
0
1
0
1
0
0
0
1
1
0
3
1
1
2
0
0
0
0
2
0
0
1
0
1
2
1
0
0
0
1
3
0
2
1
0
1
0
2
0
0
0
0
0
2
0
0
1
1
1
1
2
2
1
2
0
3
3
0
2
1
1
1
0
0
0
0
0
1
1
0
1
1
1
1
2
0
0
2
2
0
0
1
1
0
1
1
0
1
0
0
1
0
1
0
0
0
0
0
1
1
0
2
0
1
0
0
2
0
0
0
1
3
1
2
0
0
1
0
1
0
1
1
2
1
0
1
0
1
0
1
1
1
2
0
0
0
0
0
0
2
0
2
2
1
0
1
1
0
2
1
0
0
1
0
0
2
0
2
2
1
2
2
1
1
0
1
0
2
0
0
1
2
0
1
1
1
0
0
1
0
2
0
0
1
1
0
1
0
0
1
1
2
1
0
3
2
0
0
0
0
2
1
0
1
0
1
0
1
0
1
2
0
1
2
1
0
0
2
2
3
0
1
0
2
1
1
0
0
0
0
0
2
0
0
0
1
1
0
1
2
2
2
0
2
0
0
0
0
2
1
2
2
1
2
2
0
1
1
0
0
1
2
1
1
1
1
0
0
0
0
1
2
2
0
2
0
1
1
0
1
0
1
0
2
1
2
1
2
1
0
0
0
1
1
0
0
0
1
0
3
0
1
0
0
2
2
0
0
0
2
0
0
1
0
1
0
1
2
0
0
3
2
0
0
1
2
1
0
1
0
1
1
3
1
0
0
1
0
0
3
0
1
0
0
0
2
2
1
1
2
2
0
1
1
2
1
1
3
1
0
1
1
0
0
0
0
0
1
0
1
0
0
0
2
0
1
0
1
0
2
1
2
1
0
0
2
1
1
2
0
0
1
1
0
2
1
3
0
2
2
2
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
1
0
3
0
0
1
0
0
2
0
2
1
2
2
1
0
1
0
0
1
0
1
0
1
0
2
1
0
1
2
0
1
0
0
1
2
1
1
1
1
1
2
0
2
1
1
0
2
0
0
2
0
0
2
0
2
1
0
0
1
0
2
0
0
2
0
1
1
0
0
1
1
0
0
0
1
0
2
1
1
0
0
0
0
2
1
2
0
2
2
0
1
1
0
0
0
2
1
0
2
1
1
2
0
2
2
2
0
2
0
0
1
0
1
1
0
5
1
2
2
0
2
1
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
2
1
3
0
1
2
2
1
1
1
1
2
0
2
0
2
0
0
2
1
0
2
0
0
0
1
0
2
2
1
0
2
1
1
1
0
2
0
1
2
2
1
0
1
2
1
0
1
2
0
1
0
0
2
0
0
1
0
1
0
1
0
0
0
1
1
1
0
1
0
0
0
2
1
1
0
1
1
2
4
0
0
1
0
1
1
1
1
0
0
0
2
2
1
0
0
2
1
1
2
2
0
2
0
0
1
0
0
1
2
0
0
1
1
0
0
1
0
1
0
1
1
3
0
1
1
1
2
1
1
0
0
1
3
0
1
2
0
1
0
1
1
2
0
2
3
0
1
0
1
1
1
0
0
1
1
2
0
0
1
1
1
0
0
2
3
2
1
1
1
2
0
1
2
1
0
0
0
0
0
0
0
0
2
1
0
0
0
2
1
1
0
1
1
2
1
0
0
2
1
1
0
3
0
1
2
0
1
1
0
1
0
0
0
1
0
2
0
2
0
0
0
1
2
0
2
0
1
0
0
0
1
2
1
0
1
2
0
1
0
1
2
2
1
0
0
0
0
0
0
1
0
1
1
0
0
2
0
1
1
1
1
0
0
0
0
0
0
0
1
2
0
0
0
1
3
0
3
0
1
1
1
0
2
0
1
0
0
1
1
2
1
1
0
0
0
0
1
1
0
0
0
2
2
0
0
0
2
5
1
2
0
1
0
1
1
0
0
0
0
0
1
2
0
1
2
2
0
1
1
1
2
0
0
0
1
1
1
0
0
0
0
1
0
0
0
1
1
0
2
1
0
0
0
0
1
2
2
1
0
1
0
2
1
2
1
0
0
0
0
0
0
0
1
1
2
0
3
0
2
0
0
0
1
0
1
0
1
0
0
2
1
1
1
0
2
1
1
2
0
0
2
1
0
1
2
2
0
0
0
2
1
1
1
1
0
0
1
2
1
0
1
0
1
1
2
0
1
2
0
1
1
0
2
1
0
0
2
1
1
4
0
0
1
1
1
1
0
2
0
1
0
0
0
2
0
2
1
0
2
2
0
0
2
0
2
0
2
0
0
2
0
3
0
0
1
0
1
0
0
1
0
1
0
0
1
2
0
2
1
2
1
1
0
0
0
0
0
0
4
3
2
0
1
0
0
2
0
0
2
1
1
0
1
1
2
2
0
1
0
0
2
0
1
0
1
0
2
2
0
0
0
2
2
1
0
1
0
2
0
0
0
1
3
2
1
2
1
0
1
0
1
0
0
2
1
1
2
1
3
0
2
2
2
0
0
1
0
2
0
0
0
0
0
0
0
2
2
1
0
1
2
0
1
2
0
0
1
1
0
0
1
1
2
1
2
1
1
0
2
0
1
0
0
1
1
0
1
1
0
0
0
0
1
0
2
0
0
1
1
2
0
0
2
0
1
2
1
2
0
0
0
0
0
0
1
1
5
1
0
1
1
0
1
1
0
0
3
1
2
2
1
0
2
2
0
2
1
1
0
2
0
1
0
0
0
1
1
1
2
0
0
2
0
0
0
2
0
0
2
0
0
0
1
1
0
0
0
2
0
0
2
1
0
0
1
0
0
1
0
1
2
3
2
1
2
0
1
1
2
0
1
2
2
0
1
0
0
0
2
0
1
2
0
1
2
0
1
0
2
1
1
2
1
2
0
2
0
1
0
0
0
2
0
2
0
1
1
2
0
0
1
0
0
1
1
0
0
1
1
0
0
0
2
0
1
1
3
0
0
1
0
3
1
2
2
2
1
1
1
0
1
1
0
1
0
2
0
2
2
1
0
2
0
2
0
1
0
1
0
0
0
0
2
3
1
1
0
2
1
1
1
0
2
0
1
1
2
2
1
0
1
0
1
0
0
0
0
1
3
1
0
0
1
0
0
0
2
0
1
1
1
0
2
1
1
1
1
1
2
0
2
3
0
3
0
2
2
1
0
1
2
1
0
0
2
1
2
1
0
1
0
2
2
0
0
1
1
0
2
1
2
1
0
0
1
0
0
0
0
1
0
1
2
2
0
1
2
0
1
0
0
1
2
2
1
1
0
1
2
2
1
0
1
1
1
1
0
1
0
1
0
0
2
0
1
0
1
0
1
2
2
0
0
0
2
0
0
0
0
1
2
2
0
1
1
1
2
0
0
1
0
0
1
1
0
0
0
0
2
1
1
0
1
0
2
1
0
2
0
0
0
0
1
1
1
1
1
0
1
1
0
2
1
2
1
1
1
0
2
0
1
0
0
1
0
2
0
1
0
1
0
2
1
0
1
1
0
0
1
2
2
2
1
1
0
0
1
1
1
1
1
0
2
2
1
0
0
1
1
0
2
1
0
0
2
2
1
1
1
1
0
2
0
0
2
1
0
1
0
2
0
0
1
0
2
0
2
2
2
2
1
1
0
1
2
2
0
1
2
2
1
0
2
0
1
0
2
0
0
2
0
2
0
1
2
0
0
0
2
0
0
2
0
1
0
0
1
0
0
0
0
0
1
2
0
0
1
1
0
0
1
0
0
1
2
0
2
0
0
1
1
0
0
2
0
0
2
2
0
0
2
1
1
0
2
1
0
1
0
0
0
2
0
0
0
2
0
1
0
1
0
0
1
0
0
0
2
2
1
1
1
0
2
2
1
0
0
1
2
1
0
1
1
0
0
0
0
1
1
2
1
0
1
0
0
0
0
2
1
2
0
1
1
0
0
1
1
1
0
0
0
1
2
2
2
1
1
0
1
0
0
0
0
1
0
0
2
0
2
1
0
0
2
0
0
0
0
0
1
1
0
2
1
1
0
1
1
1
0
1
1
0
0
1
1
1
2
2
1
1
1
0
1
0
3
1
1
2
1
0
2
1
0
1
0
0
2
1
2
0
1
2
2
1
0
0
2
0
1
0
0
0
1
1
3
1
2
0
1
1
0
0
0
1
2
0
0
1
1
2
2
0
2
1
1
2
1
0
0
1
1
1
1
1
2
2
0
2
2
2
0
0
1
1
0
1
2
0
1
1
1
0
0
0
2
0
1
0
0
1
2
1
1
0
0
1
2
1
2
1
2
0
1
0
1
0
0
0
0
3
0
0
3
1
1
1
0
0
0
0
1
0
2
1
1
0
0
0
1
1
1
2
3
2
2
1
2
0
2
2
0
1
2
0
2
1
0
0
1
1
1
0
1
2
2
1
0
0
0
0
1
0
0
1
4
1
0
0
0
1
0
2
1
1
0
1
1
2
2
1
1
1
0
1
0
2
1
0
1
0
1
0
1
0
1
1
1
1
0
2
1
0
0
0
0
0
1
0
2
0
0
1
1
1
1
2
0
0
0
1
0
0
0
0
0
0
2
0
0
2
2
2
0
1
0
2
0
0
2
1
1
0
0
0
0
1
4
1
1
1
1
0
1
0
0
0
0
2
0
0
1
2
0
2
1
0
2
1
1
1
1
0
0
1
1
2
1
0
0
0
1
0
1
2
0
0
1
2
1
1
1
0
0
2
0
0
0
0
0
1
1
0
1
0
0
1
2
1
0
1
1
0
1
1
0
2
0
4
2
3
0
0
1
0
0
0
1
1
0
0
0
1
1
3
2
0
2
0
0
1
0
2
1
0
2
1
0
1
1
0
0
0
0
2
2
1
0
1
1
1
2
0
0
1
0
1
1
1
1
0
0
0
2
2
1
2
2
0
0
0
1
2
0
1
1
0
1
1
2
0
2
0
1
1
1
0
0
2
0
0
0
0
1
2
2
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
2
1
1
0
0
1
2
0
1
0
0
0
2
0
2
1
0
1
0
3
1
0
0
0
0
2
0
1
0
0
0
2
0
2
0
1
0
2
2
0
2
1
3
0
0
0
2
1
12
1
0
2
0
2
0
0
1
0
1
1
1
2
0
1
0
0
1
0
1
1
0
1
1
1
1
2
0
1
0
1
0
1
1
3
1
0
2
0
0
1
1
1
1
1
0
1
1
2
2
0
0
2
3
0
1
0
1
1
0
0
1
1
0
0
1
0
1
0
0
0
1
1
0
1
0
0
1
0
1
1
1
0
0
0
0
1
1
1
0
0
0
2
0
0
0
0
2
1
2
0
1
1
0
1
0
1
0
0
1
2
1
1
2
2
2
2
0
2
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
2
0
0
2
1
0
1
2
2
1
0
0
1
1
1
1
1
2
0
0
1
0
1
2
0
1
0
1
0
2
1
1
1
0
0
0
0
2
0
2
2
0
1
0
1
1
0
1
1
0
0
2
2
0
1
0
1
0
1
0
2
0
1
0
0
0
0
1
0
1
0
0
1
0
1
1
1
0
1
2
0
1
0
0
0
0
1
1
1
1
0
1
2
0
0
2
0
0
3
1
1
1
2
0
0
2
1
0
1
0
0
1
1
1
2
1
1
1
1
0
1
1
2
0
0
1
2
0
1
2
1
1
1
2
1
0
0
0
0
0
0
1
2
0
0
1
0
1
2
2
2
1
1
0
1
2
2
0
1
0
2
0
0
1
0
1
1
2
1
0
1
0
1
2
0
1
0
0
1
1
0
1
3
2
0
0
0
0
0
2
0
2
2
2
0
2
0
2
2
1
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
5
2
2
1
0
0
0
0
1
2
1
0
0
2
1
0
0
0
0
1
0
0
0
0
1
2
2
0
0
1
0
1
0
1
2
1
3
1
1
2
2
0
1
0
2
0
0
2
3
0
0
1
1
0
0
0
1
0
2
3
1
1
2
1
2
1
0
2
2
1
0
0
0
2
0
2
0
0
1
1
0
1
2
0
1
0
0
3
0
0
1
0
1
0
0
1
1
0
1
2
1
1
0
0
1
4
0
1
1
2
0
1
0
2
1
1
0
0
0
0
0
0
0
0
1
1
1
1
1
0
0
0
0
0
0
2
2
0
1
0
1
2
0
0
0
1
0
2
1
2
0
0
1
1
2
0
0
0
2
0
2
0
2
0
1
0
1
1
1
1
1
0
2
2
0
1
0
2
0
2
0
0
0
2
0
0
0
1
2
2
2
1
0
0
1
2
0
2
2
0
0
1
0
1
1
0
0
0
0
0
0
1
1
0
0
2
0
0
1
1
1
1
0
0
1
1
2
2
0
1
0
1
0
1
0
0
1
0
2
0
1
2
0
0
2
1
0
0
0
0
0
2
2
0
0
0
2
2
0
2
0
0
1
0
2
1
0
0
1
1
0
1
0
1
0
0
2
1
0
0
1
0
0
3
0
0
2
2
1
2
2
1
1
1
2
1
0
0
0
0
0
1
0
0
0
2
0
1
1
2
0
2
0
1
0
1
0
1
0
1
3
0
1
2
1
0
2
0
3
2
0
0
0
0
0
0
0
2
0
2
1
0
2
0
4
0
1
0
0
3
2
1
1
1
1
2
0
0
0
0
0
1
2
0
1
0
1
0
0
0
1
0
1
0
1
0
0
0
0
2
0
1
0
3
2
2
1
1
0
1
1
2
2
0
0
1
1
0
1
0
0
1
0
0
1
1
2
0
0
0
2
0
1
0
1
2
1
0
0
0
2
0
0
2
1
3
0
0
1
1
1
1
1
0
0
0
0
2
0
0
1
2
2
2
1
2
0
0
2
1
0
0
0
2
2
1
1
1
0
2
1
1
1
2
0
0
2
1
0
2
3
1
0
2
2
2
0
2
1
1
2
0
2
1
2
1
0
1
0
0
0
1
0
1
0
0
1
1
1
1
2
0
0
1
0
1
1
1
1
1
0
0
0
2
0
0
2
2
2
0
2
1
0
2
1
0
0
2
2
0
2
2
1
0
0
0
0
1
2
1
2
0
2
1
0
1
1
0
1
2
2
2
0
0
1
2
0
2
2
0
0
1
0
1
2
1
2
0
0
1
2
1
1
0
1
0
1
0
1
0
2
0
1
1
0
0
1
2
1
0
0
1
1
1
1
4
2
0
1
0
1
2
0
0
1
1
1
1
0
0
1
1
0
0
0
0
1
1
0
3
1
0
1
3
3
0
2
1
0
0
0
1
2
0
0
1
1
2
2
1
2
0
2
2
1
1
1
1
3
1
2
0
2
2
0
1
2
1
1
0
2
1
0
1
3
0
2
2
2
1
2
0
1
0
2
1
1
0
0
2
0
1
1
1
1
1
0
0
0
1
1
1
0
0
0
1
0
1
0
1
1
0
0
0
1
0
2
0
1
1
1
2
2
2
0
0
0
0
0
1
0
0
3
1
0
2
0
1
1
1
1
2
1
1
0
1
0
0
2
2
0
1
0
1
2
0
1
0
1
3
0
0
0
2
0
0
0
0
2
2
1
2
0
1
0
2
1
1
1
2
2
0
2
0
0
0
1
0
0
2
0
0
0
3
1
0
0
1
0
1
0
1
2
0
2
0
0
0
1
0
0
1
0
1
1
2
0
1
0
1
0
0
1
1
0
1
1
1
1
0
2
1
1
3
0
0
0
0
1
0
1
0
0
0
1
1
0
1
1
1
0
2
0
1
0
1
0
1
1
1
0
1
2
0
0
0
0
0
1
1
1
1
0
1
2
0
0
0
2
2
1
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
2
0
1
1
2
1
0
0
1
0
0
0
2
1
0
0
0
2
0
1
2
1
0
1
1
1
0
2
0
0
1
0
2
0
0
0
0
1
0
1
0
1
0
2
0
0
1
0
1
0
0
0
0
2
2
0
1
0
1
1
2
2
0
1
0
0
0
1
2
1
0
0
0
0
0
2
2
1
1
1
2
2
1
2
0
1
0
2
0
0
1
0
1
2
0
1
1
0
0
0
1
2
0
0
0
0
2
2
0
0
1
0
0
0
1
0
2
1
0
1
2
3
1
0
1
0
0
1
1
0
0
0
2
0
0
0
1
1
0
2
1
1
1
0
0
1
1
2
2
3
0
1
0
1
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
3
0
1
0
0
2
1
1
1
0
0
0
0
1
2
0
0
1
0
0
0
2
0
1
1
0
1
0
1
0
1
2
0
0
1
1
2
0
2
1
2
1
0
1
2
1
0
0
0
1
2
0
0
0
0
1
2
0
3
2
0
0
1
0
0
1
0
0
0
1
0
0
2
2
0
0
1
0
0
0
0
0
1
0
0
2
1
1
1
2
0
0
3
2
0
0
0
2
0
2
1
0
1
2
2
0
2
1
1
1
0
2
0
0
1
0
0
4
2
0
2
1
0
0
1
0
2
0
2
0
1
1
2
1
4
0
0
0
0
1
0
0
0
1
1
2
0
0
0
1
0
0
0
0
1
0
0
2
0
1
0
0
1
1
0
0
2
1
1
0
0
0
1
0
2
0
1
0
1
0
0
2
0
0
1
2
0
1
2
2
1
1
0
2
0
1
0
2
1
2
0
1
1
0
0
0
0
2
1
0
0
0
0
0
1
1
0
1
1
0
1
0
0
0
2
2
2
0
0
0
3
2
1
0
2
2
0
1
1
0
2
0
1
1
2
0
1
0
0
0
1
1
1
0
1
0
1
0
2
1
2
1
0
1
2
0
0
0
2
1
1
3
2
0
2
2
0
1
0
2
3
1
2
2
1
1
0
1
2
2
0
0
1
0
0
2
1
0
1
0
0
0
1
1
0
0
2
2
2
0
1
0
0
1
0
0
1
0
0
0
0
1
2
2
1
0
0
0
0
0
0
2
0
2
1
1
0
1
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
1
2
0
1
1
1
2
1
1
1
2
3
2
0
0
1
1
0
2
0
0
0
0
1
1
0
1
1
0
2
0
0
0
2
2
1
2
1
1
2
0
0
0
1
3
1
0
2
2
2
1
2
1
0
0
0
1
0
0
0
2
2
1
2
2
1
0
1
0
2
0
1
0
3
0
0
0
1
0
3
1
0
1
2
1
1
0
2
0
0
2
0
1
0
2
0
2
2
0
0
1
0
0
2
0
0
0
0
1
1
0
1
0
0
2
1
1
1
1
0
1
2
1
2
1
2
2
0
0
1
1
1
0
0
1
0
2
2
0
0
1
2
0
0
0
1
0
0
0
1
0
0
3
0
1
0
2
1
1
0
0
1
2
1
2
0
1
1
0
5
1
0
1
0
0
0
1
0
2
0
0
0
0
1
1
0
1
0
0
0
1
0
1
2
1
1
1
0
1
1
2
1
1
1
0
0
2
1
0
0
2
2
0
1
2
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
2
0
0
2
0
0
0
2
2
0
0
0
2
0
1
1
0
1
1
0
2
2
1
0
0
1
0
0
1
0
0
0
0
0
2
1
2
4
1
2
2
1
2
0
0
1
0
0
1
0
0
1
0
2
2
0
2
2
1
1
2
1
0
1
0
1
0
0
2
1
0
0
1
2
1
2
0
0
2
1
1
0
1
0
0
1
1
1
2
0
2
0
2
0
1
0
1
1
1
0
2
0
2
0
1
1
1
1
1
2
2
2
0
1
1
1
0
2
0
0
1
1
0
2
1
0
0
0
0
1
0
1
1
0
0
1
1
2
1
0
0
2
1
0
0
2
0
0
0
0
0
1
1
0
0
0
0
1
2
1
0
0
2
0
0
1
0
2
0
2
0
1
1
0
0
1
2
1
1
1
3
1
1
0
3
0
1
0
0
2
0
0
1
0
2
1
0
1
0
1
0
0
2
1
1
0
0
2
0
0
2
1
0
1
2
0
2
0
1
0
0
1
2
0
0
0
1
2
3
0
1
1
0
0
0
0
2
0
2
0
2
0
1
2
1
2
1
1
0
1
0
3
0
0
1
1
1
0
1
1
1
0
0
0
1
0
0
0
0
1
2
0
2
2
2
2
1
0
0
0
0
2
0
2
0
0
0
0
2
1
0
1
1
1
2
0
1
0
0
3
0
2
1
1
0
2
0
1
0
2
1
2
2
0
1
1
1
1
1
0
0
2
2
0
0
0
1
0
3
0
0
1
2
1
0
0
1
0
0
1
1
0
0
0
1
1
1
1
1
0
0
2
1
1
0
0
1
2
0
0
0
0
1
1
2
1
0
1
0
0
4
0
0
0
0
1
1
2
0
1
0
1
1
2
0
0
0
2
0
0
0
0
0
0
3
0
2
1
2
0
0
2
2
1
6
2
0
0
0
1
2
2
0
0
2
0
1
0
0
0
2
4
0
0
0
2
1
2
1
0
0
0
0
0
0
12
1
0
0
1
0
1
0
1
2
0
1
0
0
0
2
1
1
1
0
0
0
2
2
1
0
2
0
1
2
2
1
1
2
1
2
1
0
1
0
0
1
2
0
0
2
1
0
1
2
1
2
0
2
0
0
1
0
1
0
0
1
1
0
0
2
0
0
1
0
0
0
0
3
0
0
0
1
0
1
1
0
2
0
1
0
0
0
2
0
0
0
0
0
1
2
2
0
2
0
2
0
0
1
0
3
1
2
2
0
0
2
2
1
0
0
2
2
0
0
0
1
0
0
1
0
1
2
2
0
0
0
0
2
0
1
0
2
1
2
1
1
1
0
1
1
1
1
1
2
3
0
2
0
1
1
0
1
0
0
1
0
2
0
1
0
1
0
1
0
0
1
0
0
1
2
1
0
0
0
0
0
2
1
2
1
1
2
0
0
1
0
0
0
1
1
1
0
1
1
0
2
0
0
0
1
2
1
0
1
0
0
0
1
0
0
2
0
0
1
1
2
0
1
2
1
1
1
1
1
0
0
2
1
0
1
0
0
1
0
0
2
0
2
0
0
0
2
2
0
1
1
1
1
1
0
2
0
1
0
1
0
0
0
2
2
0
2
0
0
3
1
2
1
0
1
1
1
0
0
0
1
1
2
0
0
0
2
0
1
2
0
1
0
2
0
1
1
2
1
0
2
2
0
0
2
1
0
3
1
0
2
0
0
2
0
1
1
1
0
1
0
2
2
1
1
1
1
3
2
1
0
0
0
2
0
0
1
0
1
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
2
1
0
2
1
2
1
1
2
1
0
1
0
0
1
0
0
1
0
0
2
0
0
2
0
0
0
0
2
0
0
1
2
0
1
0
1
1
1
0
3
1
0
1
0
1
1
2
1
1
0
1
1
0
0
2
2
2
0
0
1
0
2
0
0
0
0
0
2
1
2
0
3
0
1
1
2
1
1
0
0
1
0
1
2
1
1
0
0
2
1
0
0
0
0
1
0
1
0
1
1
1
1
0
1
1
1
0
2
0
0
2
2
1
2
0
3
1
1
1
1
0
0
2
0
0
1
1
1
0
0
1
0
1
0
2
0
1
1
2
1
1
1
1
0
0
0
1
0
1
1
1
0
1
2
1
0
2
1
2
0
3
0
0
0
2
1
1
3
1
0
0
0
0
0
1
0
1
2
0
1
2
1
1
0
2
2
1
0
1
1
0
1
2
0
1
0
0
1
1
2
2
2
2
0
1
1
1
2
0
1
0
0
0
2
0
1
0
2
1
1
1
1
0
1
1
1
1
1
2
0
1
0
1
1
1
2
2
1
0
0
2
0
2
0
0
2
1
0
2
1
0
0
0
4
0
1
2
5
1
1
2
0
1
0
2
2
1
0
0
2
2
1
0
2
0
1
2
0
0
1
0
0
1
0
0
1
1
0
0
0
1
0
0
2
0
0
2
0
0
1
2
0
1
0
0
0
0
1
0
2
2
2
1
1
1
0
2
1
1
0
0
0
0
0
1
2
1
2
2
0
1
0
0
1
2
1
0
0
0
2
2
0
1
0
2
2
1
1
1
0
2
0
1
0
1
1
0
1
0
0
1
0
1
0
1
0
0
0
1
0
0
3
2
0
0
0
1
1
0
1
1
0
2
0
0
2
0
0
0
0
1
1
0
2
1
0
0
1
0
1
0
0
2
0
1
0
0
1
0
1
0
1
0
0
1
0
1
0
1
0
2
1
0
2
0
1
1
0
2
2
2
1
0
0
1
1
0
0
0
1
0
0
2
0
0
1
1
0
0
0
1
1
0
1
0
1
1
2
0
1
2
0
0
0
1
1
1
0
1
1
0
2
0
1
2
1
1
2
0
0
0
0
2
1
0
0
0
2
2
2
0
1
0
0
1
2
0
3
2
0
0
0
1
1
2
2
0
0
0
0
1
0
0
0
0
1
1
1
0
2
0
1
0
1
1
0
1
0
0
0
2
0
0
0
0
1
0
0
2
1
0
1
0
0
0
1
1
2
0
0
0
2
0
1
1
0
0
0
0
0
0
1
2
1
0
0
2
1
0
1
2
0
1
1
0
2
0
0
2
1
0
0
1
1
2
2
1
0
0
1
0
2
0
0
0
0
2
1
1
1
1
2
1
0
1
2
0
0
0
0
1
0
2
0
0
1
0
2
3
1
2
0
1
1
0
0
0
0
0
0
0
2
0
1
2
2
0
0
0
0
2
1
2
3
1
2
1
0
0
1
0
0
2
2
0
0
3
1
1
1
0
0
0
2
0
3
0
5
2
1
0
0
3
1
0
1
0
0
0
1
2
0
1
0
0
1
1
1
1
1
0
0
1
0
0
1
0
0
1
1
1
0
0
0
0
0
1
0
0
0
2
0
2
0
2
1
1
0
1
1
0
1
1
0
0
1
2
0
0
2
0
0
1
0
1
0
0
1
0
2
1
0
0
2
0
1
1
2
2
2
2
2
0
0
0
0
0
0
2
1
2
0
0
0
0
0
1
2
0
2
0
0
1
1
1
0
0
2
1
0
0
2
2
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
2
3
0
0
0
0
1
0
1
1
0
1
2
0
1
2
2
0
0
1
0
2
2
0
1
0
2
2
1
1
1
2
0
1
2
0
1
1
0
1
1
1
1
0
1
0
0
1
0
1
0
2
1
3
1
2
0
1
1
2
1
2
1
1
0
1
0
1
0
0
1
1
0
0
1
5
1
0
0
1
2
1
1
0
0
0
1
3
0
0
1
1
1
0
1
1
2
1
0
0
1
0
1
0
2
1
2
0
2
0
0
1
2
0
1
1
1
0
0
0
0
0
2
0
0
0
1
3
0
1
2
1
0
0
0
0
0
0
1
0
2
0
1
0
1
2
0
1
0
2
1
1
2
1
1
0
0
2
2
1
1
2
0
0
2
1
1
0
1
1
0
1
2
3
0
0
1
2
1
0
0
0
0
0
0
0
2
0
2
0
1
0
1
0
2
0
0
0
0
2
0
0
0
1
1
0
2
2
0
2
0
0
0
2
1
0
0
1
0
0
1
1
0
2
1
1
1
1
2
0
0
0
0
1
1
0
0
0
1
1
1
2
1
0
0
0
1
2
1
0
2
1
1
0
0
3
0
1
1
0
1
1
1
0
0
1
2
1
0
2
0
0
0
0
2
0
1
1
1
1
0
1
0
1
0
2
2
0
1
1
0
0
1
1
2
0
1
0
0
0
1
2
2
2
1
0
1
1
2
0
1
1
1
2
3
0
0
0
0
0
1
0
1
0
0
0
3
0
0
1
0
1
1
0
2
0
0
4
1
0
0
1
1
2
0
1
0
2
2
0
0
1
4
2
1
0
2
1
2
0
2
0
0
0
2
0
2
1
0
1
2
0
1
2
0
0
1
1
0
1
2
0
0
2
1
0
3
0
1
1
0
1
1
1
1
2
2
0
2
0
1
0
0
1
0
3
1
1
0
0
2
0
1
1
2
2
0
2
0
1
2
0
0
0
0
2
0
1
0
1
2
2
0
1
0
0
1
0
0
0
0
0
1
1
2
1
0
1
1
0
0
0
2
0
2
0
1
0
0
2
0
2
2
0
0
1
0
0
1
2
0
0
1
0
1
0
0
0
0
1
2
2
1
1
0
2
2
0
1
1
2
1
1
1
1
2
0
2
2
0
1
1
0
0
1
2
0
1
0
0
0
2
0
0
2
1
0
0
0
2
0
1
1
1
1
1
0
2
1
2
1
1
2
0
0
1
1
2
1
1
0
0
2
1
0
0
1
1
1
1
2
1
3
1
1
1
1
2
0
0
0
1
2
1
1
1
1
2
0
0
2
1
0
1
0
0
0
2
1
1
1
1
0
1
0
0
1
2
0
2
0
3
0
0
0
2
1
2
0
0
1
0
1
1
1
0
0
1
0
1
0
0
1
2
1
1
0
2
0
2
1
1
0
2
1
2
0
0
0
0
1
0
0
1
1
2
0
3
2
2
2
0
2
1
1
0
1
1
1
0
1
1
0
1
0
2
0
2
2
0
0
1
2
1
1
1
0
1
1
0
0
2
0
1
0
1
0
3
0
0
0
2
2
1
0
0
0
1
0
2
0
0
1
0
1
2
1
1
0
2
0
1
2
0
0
1
0
0
1
1
1
2
1
0
2
2
1
2
1
3
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
1
0
1
0
0
0
1
0
1
1
0
0
0
2
0
0
1
2
1
2
2
2
1
0
1
1
1
3
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
2
0
2
2
0
2
2
0
0
0
1
2
2
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
1
2
0
0
1
1
1
1
0
2
0
1
0
0
2
0
0
2
4
0
0
2
0
0
0
2
0
0
2
1
1
1
1
1
2
0
2
1
0
1
1
0
1
1
1
0
1
1
0
1
1
2
0
0
4
0
0
0
1
2
1
0
0
0
2
0
2
2
2
1
1
0
0
0
2
1
0
0
1
1
1
2
1
2
0
1
0
0
1
1
0
0
1
0
1
2
1
2
0
2
1
1
2
0
0
1
2
0
0
0
0
2
0
2
2
2
0
0
0
0
1
0
0
0
1
0
1
2
1
0
3
1
2
1
2
0
1
0
1
4
1
1
1
0
0
2
0
1
0
1
1
0
2
2
1
2
0
1
0
2
0
0
0
1
0
0
1
1
0
0
1
1
1
0
2
0
0
2
0
0
0
1
1
1
2
3
2
1
2
0
1
1
3
3
2
0
1
3
2
2
0
1
0
0
0
1
0
1
0
2
0
0
0
0
0
2
1
0
2
0
0
0
0
0
1
1
0
1
1
1
2
2
0
2
0
1
0
0
0
0
1
0
0
2
0
1
0
1
2
1
0
1
0
1
1
0
2
1
0
1
0
0
0
2
1
2
1
0
0
1
2
0
1
1
0
2
0
2
1
0
1
0
1
0
1
1
0
1
0
1
2
0
2
0
0
1
1
0
0
1
1
1
1
1
0
1
3
1
2
0
2
0
1
0
1
0
0
1
0
2
0
1
0
1
0
0
0
1
0
1
0
1
1
1
2
1
0
0
1
0
1
0
3
1
1
2
3
2
0
0
0
0
1
0
0
0
2
1
1
1
0
1
0
0
2
2
0
0
0
1
2
2
1
2
1
0
0
0
0
1
1
0
0
1
1
1
1
0
0
0
1
1
2
0
2
1
0
1
1
2
0
0
2
0
2
0
0
0
0
2
3
0
0
1
2
0
1
0
0
2
0
2
0
1
0
0
0
0
1
0
1
0
1
4
0
3
0
2
1
0
2
0
0
2
2
0
0
1
0
3
0
0
1
1
0
0
0
1
2
2
0
0
2
0
1
3
2
0
0
1
1
0
0
2
0
1
4
0
2
2
0
0
2
2
0
1
2
3
1
1
2
2
0
0
0
0
1
1
1
2
0
0
0
0
0
2
2
1
2
2
1
1
1
0
2
2
0
1
1
0
1
1
2
1
0
1
1
1
0
2
0
2
2
2
1
0
1
0
2
0
0
1
1
0
1
1
0
2
1
2
1
3
0
1
1
1
2
2
2
0
0
0
1
2
2
0
0
1
0
1
0
0
0
1
1
1
2
0
0
0
0
2
2
1
2
0
0
1
1
0
2
2
0
2
0
1
0
1
0
0
0
0
1
1
0
2
1
0
1
1
1
1
0
0
2
0
0
2
1
2
2
1
0
1
2
2
2
1
0
2
0
0
1
0
1
1
1
0
0
2
0
1
0
0
0
1
1
0
0
0
2
1
1
0
0
1
1
1
0
0
1
1
0
0
0
1
0
0
2
1
2
2
0
0
1
2
0
0
0
2
0
0
0
2
2
2
0
1
0
1
0
1
1
0
0
1
0
1
1
1
0
0
2
0
0
2
0
2
0
0
2
2
1
2
1
1
1
0
1
1
0
0
0
2
0
0
2
3
1
1
0
0
1
2
1
0
2
1
0
0
0
0
1
1
1
0
1
0
0
1
1
0
1
2
0
1
2
2
0
0
1
0
1
0
1
0
2
0
0
2
1
0
2
0
1
1
1
1
2
0
1
0
0
0
0
0
0
2
2
0
2
1
1
2
1
1
0
1
0
0
0
1
0
0
5
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
1
2
2
0
0
0
0
1
1
1
1
3
2
2
1
1
0
0
1
2
1
1
0
2
0
1
2
1
0
0
0
2
2
0
0
3
2
0
2
1
1
2
0
0
1
1
0
0
1
0
3
0
0
1
0
0
0
2
1
2
3
1
0
1
0
0
0
0
0
2
0
1
2
1
1
0
0
0
0
1
0
2
0
0
0
1
2
2
1
1
1
0
0
1
2
0
0
1
1
2
0
1
1
1
0
2
2
2
1
1
0
0
2
0
1
0
1
1
0
1
1
2
0
0
2
2
1
2
0
0
1
2
0
0
2
0
0
2
0
0
0
2
1
3
0
1
1
1
1
1
0
0
0
2
0
0
3
1
1
0
1
0
0
1
0
2
0
0
0
0
2
1
1
1
0
2
0
2
0
0
0
0
0
0
0
0
2
1
2
1
0
3
1
2
0
2
0
0
2
0
0
2
1
1
0
0
1
3
1
1
0
0
0
1
0
1
3
0
0
2
1
0
1
2
0
2
2
0
2
0
0
1
0
0
1
2
1
2
1
0
1
0
1
0
1
2
1
0
0
1
1
1
2
0
0
0
1
0
0
0
1
0
1
2
0
2
1
0
0
0
0
0
0
3
0
1
0
0
0
0
0
2
0
1
2
0
4
0
1
1
2
0
2
1
1
0
1
0
0
1
0
3
2
1
2
0
0
1
2
1
0
1
4
1
1
1
1
0
0
1
1
0
2
0
0
1
0
0
0
1
1
1
0
2
1
1
0
0
0
0
1
0
0
1
1
1
1
2
1
1
1
3
0
0
1
1
0
0
1
2
0
2
1
1
1
1
0
0
0
2
2
0
1
2
2
1
0
3
1
1
2
3
0
1
2
1
0
0
1
1
0
2
0
0
0
1
0
2
1
1
1
0
1
0
1
1
0
2
0
0
2
0
2
3
0
2
0
0
1
0
1
2
1
1
0
1
1
2
1
1
0
2
3
1
0
1
2
0
2
1
0
0
1
0
1
0
2
0
0
1
3
2
1
1
1
1
0
0
1
2
0
1
0
0
0
2
0
1
1
0
0
2
0
2
0
5
1
1
2
1
1
0
2
0
0
2
1
1
1
2
0
2
2
1
0
2
0
2
0
0
0
1
2
0
0
2
1
0
1
1
1
1
0
0
2
2
0
1
0
0
0
1
2
1
0
1
1
1
1
0
2
1
5
1
1
1
1
0
0
2
2
0
0
2
0
2
1
1
1
0
2
0
0
0
6
2
0
0
0
2
1
2
2
2
1
0
0
2
0
0
2
1
0
1
0
1
1
1
0
1
0
1
1
1
1
0
2
1
1
1
0
2
1
0
1
1
2
1
0
0
0
0
1
1
0
0
0
1
0
1
0
1
0
1
1
2
1
0
1
0
2
1
2
3
0
0
1
0
2
1
0
1
1
0
0
2
0
2
1
1
1
2
2
1
2
2
1
1
0
0
2
1
2
0
2
2
0
1
1
1
0
1
2
2
1
0
1
1
1
1
1
1
1
2
1
2
4
1
1
1
0
0
2
1
1
0
0
0
1
0
1
0
1
2
1
0
0
0
2
2
0
0
0
0
1
2
0
2
1
0
2
0
2
0
2
0
0
2
2
1
0
2
1
1
2
2
1
1
1
1
3
1
1
2
0
0
2
0
1
1
2
1
1
1
2
0
0
0
0
2
1
0
2
0
1
2
0
1
0
2
2
0
0
0
0
1
2
0
0
0
0
2
2
0
0
1
3
2
0
0
1
0
0
0
0
0
2
2
1
0
2
0
0
2
0
1
2
0
2
2
0
0
1
0
1
2
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
2
0
1
2
0
0
1
0
0
2
3
0
4
0
0
2
0
0
0
0
0
0
2
1
0
1
0
1
2
2
0
0
2
1
1
0
0
0
1
1
1
1
0
2
2
1
0
0
0
1
0
0
0
0
1
1
1
1
1
2
2
0
0
2
0
1
0
1
2
2
3
2
2
1
0
2
0
1
2
2
0
1
1
0
0
2
2
2
0
1
0
0
0
2
0
1
0
1
2
3
2
2
2
0
2
2
1
2
0
1
2
0
0
1
0
0
1
1
1
2
1
0
0
1
1
0
0
0
0
2
1
1
1
0
0
0
0
1
2
2
1
0
0
1
2
2
1
0
0
1
1
1
1
0
0
0
0
2
0
0
0
2
0
1
0
0
1
2
0
3
0
0
2
0
1
1
4
0
0
0
2
2
2
2
0
2
0
0
2
2
1
0
1
3
0
1
0
1
0
1
1
2
1
1
1
0
1
0
1
1
2
0
0
1
2
0
1
0
1
2
2
1
0
1
0
0
0
0
0
1
1
2
2
0
2
0
2
0
2
1
2
0
1
0
0
1
0
2
3
1
1
1
1
1
2
2
1
0
0
1
0
0
1
1
0
1
0
0
2
0
0
1
2
0
0
1
2
1
1
1
1
1
2
1
2
0
0
2
1
1
0
1
0
1
1
2
1
0
2
0
2
2
0
1
0
0
1
0
0
2
1
0
0
0
0
0
1
0
0
0
1
0
1
5
0
2
0
2
1
1
0
1
2
2
0
0
0
2
1
0
1
0
2
0
2
1
2
1
1
0
1
0
0
1
1
2
0
1
0
1
2
0
1
1
1
1
0
1
0
0
0
0
2
1
2
1
0
0
2
2
0
1
0
0
0
2
0
2
0
1
0
3
2
0
2
2
2
0
2
0
1
0
0
1
0
2
0
1
2
2
0
1
0
1
1
2
0
0
1
1
0
0
0
2
1
0
2
0
0
1
1
1
1
1
0
3
1
1
2
0
1
0
0
1
1
1
0
2
1
0
1
0
1
1
0
2
0
0
0
0
0
2
0
0
0
2
0
0
2
2
1
0
1
0
1
2
1
2
0
1
2
0
1
1
0
0
0
1
1
0
1
2
0
2
1
1
0
2
0
1
1
1
1
1
2
2
1
0
0
0
1
1
1
1
0
0
1
2
1
0
1
2
2
0
3
2
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
1
1
1
2
0
0
0
0
2
1
1
1
1
0
2
2
0
0
0
0
1
1
1
0
0
0
2
0
1
0
0
0
0
2
0
0
1
0
1
0
1
1
0
0
1
1
1
0
2
2
0
2
0
1
2
1
0
0
0
0
1
1
0
1
1
1
2
0
0
0
0
2
1
0
0
1
0
1
0
1
2
0
1
0
2
1
1
0
0
1
0
0
1
0
2
0
0
0
0
0
0
1
0
2
1
1
2
1
0
1
0
0
1
2
0
1
0
2
0
2
2
0
0
1
1
1
1
1
1
0
1
0
2
1
0
0
4
1
0
1
1
1
1
0
2
0
2
0
0
0
0
1
0
0
1
2
0
1
0
0
1
1
2
0
0
0
0
0
2
1
0
0
0
0
0
1
2
2
0
0
0
1
0
2
0
2
0
1
2
0
0
2
0
1
1
0
2
1
2
1
0
0
2
0
2
1
0
2
0
2
0
1
1
1
0
0
1
0
2
0
0
1
1
0
1
2
1
2
0
0
1
1
1
0
0
1
1
1
2
0
0
1
2
0
0
0
1
0
0
1
1
1
1
1
1
2
0
0
1
0
1
1
0
4
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
1
0
0
1
0
0
1
0
0
0
1
1
0
1
0
0
2
1
0
1
1
0
0
0
1
0
0
0
2
1
2
1
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
1
2
0
1
0
2
2
1
1
0
0
2
2
0
2
1
1
1
0
0
3
1
2
1
1
0
1
2
2
1
2
0
1
1
0
1
0
4
2
0
2
0
0
0
0
1
2
0
2
1
2
0
0
1
2
1
2
0
2
1
0
3
1
2
1
1
3
1
1
2
2
1
2
0
0
2
0
0
1
1
0
0
0
1
1
0
2
0
1
1
2
3
0
0
1
2
0
0
0
0
0
0
2
2
0
0
3
1
0
1
0
1
1
1
1
0
0
1
0
0
0
2
0
0
2
0
1
1
1
0
0
2
1
0
2
0
0
0
0
0
0
1
0
1
2
2
0
2
0
0
0
0
1
0
0
0
2
2
1
2
0
1
1
0
2
0
1
2
0
1
0
0
2
1
1
0
0
0
1
1
0
2
2
2
0
0
1
0
0
2
0
0
0
2
2
0
1
2
0
0
1
2
0
0
1
0
2
0
1
0
2
1
2
0
0
0
0
0
2
0
0
1
0
0
1
6
0
1
1
0
2
0
1
1
1
0
0
1
2
0
1
0
2
1
0
0
0
0
0
0
2
1
0
0
1
1
1
2
1
2
0
1
1
1
0
2
1
1
1
0
1
1
2
0
1
1
1
0
2
2
1
0
3
2
1
2
2
1
0
1
0
0
0
1
0
0
0
1
1
0
0
1
0
2
1
1
2
0
1
0
0
0
0
1
1
0
1
3
0
1
0
2
1
2
3
2
0
0
1
2
0
2
0
0
1
1
1
1
1
0
0
0
3
0
2
2
0
1
1
1
0
1
1
1
0
1
0
0
0
0
0
1
2
1
1
1
0
2
1
0
0
2
2
0
1
1
0
1
1
0
0
1
1
0
0
2
0
0
0
1
1
0
0
2
1
0
1
0
1
2
0
1
0
0
0
1
1
0
0
3
0
2
1
2
1
0
2
2
0
1
1
0
0
2
0
0
0
2
1
1
0
1
1
0
0
2
0
0
3
2
2
0
0
1
3
0
1
1
1
0
2
0
0
0
0
0
2
0
2
0
0
2
1
2
0
0
0
1
2
1
1
2
2
2
0
0
2
1
2
0
2
1
0
1
1
0
2
0
1
1
0
0
1
1
0
1
0
0
1
2
0
1
0
0
0
0
0
1
0
1
2
1
1
1
0
2
1
0
0
0
1
2
2
0
0
0
0
0
0
0
1
0
2
0
1
0
0
2
2
0
0
2
0
0
0
1
1
2
1
1
0
0
0
0
0
0
2
1
0
0
3
0
1
1
1
1
2
0
0
1
2
0
1
0
0
1
0
1
0
1
1
1
0
1
0
1
2
3
1
0
2
2
0
2
1
3
0
2
1
0
0
2
1
1
1
2
1
0
1
1
0
1
0
1
1
0
0
2
1
0
0
2
2
1
0
1
1
2
1
0
1
1
0
1
0
1
0
0
0
2
2
0
1
2
2
1
0
2
1
0
2
0
0
0
0
1
0
0
0
0
2
0
2
0
2
1
1
0
2
0
2
1
1
0
1
0
1
0
0
1
0
0
1
0
0
1
1
0
2
1
0
2
0
0
0
1
0
0
0
3
2
0
1
1
1
0
0
0
1
1
2
1
2
2
1
2
1
1
0
2
4
0
0
0
1
2
0
0
1
1
1
1
2
1
1
2
0
0
1
0
2
0
1
1
1
1
0
0
1
0
1
2
0
1
0
1
0
0
2
0
2
0
0
1
1
1
2
1
1
1
1
1
0
0
1
2
2
0
0
0
4
2
0
1
1
0
1
1
1
0
0
2
1
0
1
2
0
0
0
1
0
1
0
2
1
2
0
1
1
0
2
0
1
0
0
0
0
1
2
0
2
1
2
1
1
0
2
1
0
0
1
1
1
0
0
0
1
0
4
0
0
1
1
0
2
1
1
2
1
1
1
1
0
1
0
1
2
0
1
0
0
0
0
1
1
0
1
0
1
0
1
0
2
0
0
2
0
0
3
1
1
0
2
1
1
1
0
0
1
1
0
0
0
1
0
0
0
1
0
2
0
0
3
0
1
1
1
0
0
0
2
0
1
0
0
0
0
9
2
0
0
1
2
2
1
0
3
1
2
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
2
2
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
1
2
1
0
1
2
1
2
0
1
0
0
1
1
1
1
0
1
2
2
0
1
1
0
0
1
0
0
2
0
0
0
2
2
0
3
0
0
1
0
2
0
0
0
2
2
2
0
1
1
0
0
0
2
3
0
1
2
1
1
0
2
0
2
2
0
0
0
2
3
1
0
0
1
0
0
0
0
0
2
1
0
0
1
1
0
1
0
1
1
2
0
2
0
1
0
1
0
1
0
0
1
1
0
0
1
0
2
1
1
2
0
1
0
1
1
1
0
0
0
0
1
0
0
0
0
2
0
1
0
1
0
1
1
0
1
0
2
2
1
2
0
0
2
0
1
1
0
0
0
2
2
1
2
1
1
1
0
1
1
0
2
1
0
0
2
2
0
1
1
0
1
2
1
1
1
0
0
0
1
2
1
2
0
1
1
2
1
1
0
2
2
1
2
0
0
1
2
0
0
2
1
1
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
1
0
1
3
2
0
1
0
2
1
0
2
1
0
0
1
0
1
1
2
1
0
0
1
2
1
1
1
0
1
0
0
2
0
1
1
0
0
0
1
1
0
1
1
1
0
2
0
0
2
0
0
0
0
4
2
2
2
2
0
1
2
0
2
0
2
1
1
2
0
0
1
1
2
1
2
0
1
0
1
0
1
0
0
0
2
0
0
2
1
0
2
0
1
3
0
0
1
0
2
1
2
1
1
0
2
0
0
2
2
0
0
0
0
0
0
1
1
1
0
2
0
0
0
2
1
1
1
0
0
2
0
0
1
0
0
1
0
1
0
0
2
1
1
1
0
1
0
0
1
2
0
1
0
1
0
0
2
1
0
0
1
0
0
0
2
0
0
0
3
2
1
0
2
0
1
0
0
0
0
1
0
0
0
0
2
1
2
1
1
0
1
0
0
1
4
2
0
0
0
2
0
2
1
2
1
1
0
1
0
0
1
1
2
2
1
1
1
1
1
0
1
0
1
4
1
2
2
0
1
1
0
1
0
2
1
3
2
0
1
2
1
1
2
1
1
1
0
1
1
2
0
2
0
0
0
1
1
1
0
1
1
0
0
1
0
0
1
2
1
0
0
2
1
2
1
0
1
0
1
1
1
2
1
0
2
1
2
0
0
0
1
0
2
2
0
0
1
1
1
1
0
0
0
1
1
0
2
0
1
0
1
2
1
0
1
0
1
1
2
1
0
2
2
0
2
0
0
1
0
0
1
1
1
0
1
0
2
2
0
0
0
0
0
2
1
1
1
2
2
1
0
1
0
0
0
2
0
0
0
2
2
2
1
1
0
0
0
0
0
3
0
1
0
1
1
0
0
0
0
0
0
0
0
2
1
0
1
0
0
1
2
0
1
2
1
0
2
0
1
2
0
0
2
2
2
0
0
1
0
2
1
0
2
1
0
1
2
1
1
1
1
0
0
0
0
1
1
1
2
0
1
1
0
0
1
2
0
2
1
0
1
0
1
1
0
1
2
1
0
0
3
0
1
0
0
1
0
1
1
0
2
0
2
1
2
2
0
0
0
0
1
1
0
0
2
0
1
0
0
0
1
2
0
1
1
0
0
1
1
0
0
0
0
2
0
0
1
0
1
1
2
0
0
0
1
2
0
0
0
1
1
0
1
1
0
0
1
0
0
0
0
2
1
1
0
0
0
1
2
2
1
1
0
1
0
0
0
0
0
1
1
1
1
0
0
0
1
1
3
0
0
0
1
0
2
0
1
1
1
2
1
1
0
0
4
2
1
1
2
2
2
2
2
0
2
0
0
0
1
0
0
0
0
1
2
2
0
1
1
1
1
0
0
0
0
1
1
0
1
2
0
1
0
0
1
2
0
0
0
0
2
0
2
0
1
0
2
1
0
1
0
0
1
1
0
0
1
0
1
2
0
0
0
1
1
1
0
3
0
2
1
0
1
1
2
0
1
1
2
1
0
1
1
1
0
0
1
1
0
2
1
0
0
1
1
1
0
2
0
2
0
1
1
2
1
0
1
0
1
1
0
0
0
0
0
2
1
1
1
0
1
0
2
2
2
2
1
6
0
0
0
0
1
0
1
1
0
0
1
2
2
2
1
1
0
2
1
0
2
2
2
1
0
2
1
1
5
0
0
0
1
2
0
1
0
0
2
2
0
1
1
1
2
0
0
1
1
0
0
0
0
0
0
0
0
1
2
0
0
2
0
2
0
3
0
0
2
0
5
2
1
0
1
1
0
1
2
1
1
1
1
0
1
3
2
2
1
0
0
0
0
2
1
2
2
1
1
1
2
0
1
1
2
1
2
3
1
3
0
2
1
0
1
1
3
1
0
0
0
2
0
0
0
0
3
2
1
0
2
2
0
0
1
0
2
3
0
0
0
0
2
2
0
2
0
0
0
1
2
0
0
1
1
0
1
1
1
0
2
0
2
0
0
0
0
0
0
5
0
1
2
2
1
1
1
0
0
0
1
1
2
3
2
0
1
1
0
0
1
0
2
2
0
2
1
1
1
0
0
0
1
0
1
2
2
0
0
3
0
0
2
2
1
1
2
1
0
0
1
0
1
0
0
2
1
0
1
0
0
1
1
2
0
0
1
1
1
0
2
0
0
0
0
0
1
2
4
0
2
0
1
0
1
0
1
1
3
2
1
0
0
2
1
2
0
1
1
1
2
0
1
0
0
2
1
2
2
0
2
1
0
1
0
2
1
0
0
0
1
1
1
1
2
0
1
1
1
0
1
1
1
1
0
1
0
0
0
0
1
2
0
0
1
3
1
0
2
1
1
0
1
2
1
2
1
0
1
0
2
0
2
0
1
0
0
2
2
0
2
1
1
2
2
1
0
0
0
0
2
1
0
2
0
1
2
1
0
2
2
0
1
0
1
2
0
0
2
0
0
0
0
1
1
2
0
1
0
3
1
2
2
2
1
0
0
1
0
1
2
0
0
2
1
1
0
1
1
2
1
0
0
0
0
2
0
1
0
0
1
1
2
0
0
0
1
2
1
0
1
0
1
1
0
1
0
0
1
2
1
2
1
2
3
2
0
0
0
3
2
0
0
0
1
0
0
0
0
1
1
1
2
1
1
0
0
1
1
0
0
0
1
0
1
2
1
1
0
1
2
0
0
1
0
0
0
0
0
2
1
0
0
1
1
2
2
1
0
1
1
0
0
1
2
1
0
2
1
0
2
1
0
1
1
0
0
1
0
2
1
2
2
0
0
1
2
0
2
0
2
0
0
0
1
0
2
2
1
1
0
2
0
1
1
1
1
1
0
6
0
1
0
0
0
1
1
0
2
1
2
0
1
1
2
2
2
0
2
1
0
0
0
1
2
2
0
1
2
1
7
2
1
0
2
0
2
0
0
0
0
1
1
1
0
0
2
1
0
1
1
0
0
0
0
1
1
0
2
2
0
1
0
2
0
0
2
0
1
1
0
0
0
0
1
0
0
0
3
1
1
0
0
1
2
1
0
0
2
1
0
1
0
1
1
0
0
2
0
1
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
2
1
2
1
1
2
0
0
0
0
0
2
0
1
1
2
0
2
2
0
0
1
1
2
0
0
2
2
3
2
1
0
0
1
2
1
1
1
2
0
0
1
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
1
2
1
4
0
0
1
2
0
1
0
0
0
1
0
1
2
0
1
0
0
2
0
0
1
0
1
2
1
1
1
0
1
0
0
2
2
1
0
2
1
2
1
0
0
0
0
2
0
2
1
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
1
1
0
0
2
0
0
1
0
0
2
1
1
0
1
1
0
0
1
1
1
0
1
0
1
0
1
0
0
0
4
0
0
0
1
1
2
1
0
0
0
0
2
0
0
0
1
0
1
0
0
1
0
0
0
0
3
0
2
0
1
1
0
2
0
0
0
1
0
2
0
1
2
1
0
1
0
0
1
0
1
2
1
2
1
1
1
2
0
1
0
1
0
2
1
0
1
0
2
0
1
1
1
1
2
2
1
2
0
2
0
1
1
0
0
0
0
1
0
2
1
0
2
0
2
0
1
2
2
0
2
1
0
2
0
2
0
0
0
2
2
2
2
0
1
1
0
0
1
0
1
2
0
1
1
0
0
0
0
0
0
2
0
1
0
1
1
0
0
0
0
0
0
0
1
2
0
1
1
0
0
1
1
1
0
1
1
0
0
2
0
1
1
0
2
2
1
2
0
2
0
1
0
0
0
1
0
0
1
1
1
2
0
0
0
1
1
0
1
1
0
1
0
1
0
2
1
0
0
0
1
3
0
0
0
0
2
1
0
2
0
1
0
1
0
2
1
1
1
2
1
0
0
0
1
0
2
2
0
1
3
0
2
2
1
2
0
0
1
0
2
1
0
2
0
0
1
1
0
1
0
1
0
1
0
0
0
0
1
1
1
0
0
0
1
3
1
0
2
2
2
0
1
1
1
1
2
0
1
2
1
2
2
0
0
1
2
0
2
1
0
1
1
2
0
1
1
1
0
1
0
2
0
5
2
0
1
0
2
0
0
0
1
1
0
1
2
1
1
2
1
0
2
0
1
1
1
2
2
0
1
2
0
2
0
0
0
1
1
1
0
1
0
1
1
0
2
2
0
0
0
0
2
0
0
2
0
1
0
0
1
1
0
1
0
0
1
2
1
1
0
2
1
2
1
2
2
0
1
0
2
2
0
0
2
1
1
1
0
0
0
0
1
2
1
1
1
0
0
1
2
0
0
1
0
2
0
1
0
2
2
1
0
0
0
2
1
1
2
0
0
0
2
1
0
3
4
2
1
2
2
1
1
0
2
1
1
0
1
1
2
0
2
0
0
1
2
2
2
0
2
1
2
2
1
1
2
0
0
2
3
0
0
0
0
1
1
1
1
1
2
0
0
0
1
1
0
0
2
1
0
0
1
1
0
1
2
1
1
0
1
0
1
0
0
1
0
2
0
0
0
0
0
1
1
2
0
1
1
0
1
1
1
0
0
2
3
0
1
0
2
0
0
2
1
1
0
1
2
0
0
0
1
0
0
1
1
2
1
2
0
1
0
1
0
2
1
1
1
0
0
1
1
2
0
0
1
1
2
1
0
2
2
1
0
1
1
1
0
0
1
0
0
0
1
1
2
0
1
0
1
1
2
3
0
3
1
0
0
0
0
0
1
0
2
0
2
1
0
0
1
0
2
1
1
2
0
0
0
0
0
1
1
1
1
1
0
0
0
0
1
2
2
0
0
0
0
0
2
2
0
0
1
1
1
2
0
1
0
1
1
0
2
0
0
1
1
1
0
1
0
1
0
0
2
1
0
3
2
1
1
0
0
0
0
1
2
1
1
2
1
1
1
1
0
2
1
2
0
0
2
3
2
2
1
0
2
1
2
0
0
2
1
1
0
1
1
0
0
0
1
2
1
2
2
1
2
0
1
0
1
0
2
1
1
0
0
0
1
0
2
1
2
0
0
0
0
2
1
2
1
2
1
0
0
5
0
1
1
1
1
2
1
0
0
0
6
0
3
0
2
0
0
0
2
0
1
0
2
0
0
0
2
0
0
1
0
1
3
0
1
0
0
1
0
0
0
1
0
0
2
0
1
0
2
0
0
0
0
1
1
0
2
0
0
0
1
1
1
1
2
2
1
0
2
2
0
0
2
2
0
1
0
0
0
1
1
2
1
0
2
2
2
0
0
1
1
2
0
0
0
0
1
1
1
1
0
0
0
2
0
0
0
3
2
0
1
1
1
1
0
1
1
1
0
1
1
0
0
0
0
1
2
0
2
2
0
1
0
1
0
1
1
0
2
2
0
0
0
1
2
1
1
2
1
0
0
2
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
1
1
0
1
0
2
2
2
1
1
0
1
0
1
1
1
2
0
0
0
1
0
2
0
1
1
1
0
2
0
0
1
0
1
0
2
1
2
0
0
2
0
1
1
0
0
2
1
0
1
1
0
1
1
2
1
0
0
0
1
2
1
0
0
2
1
1
1
2
0
0
0
2
1
0
2
3
2
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
1
0
2
0
1
2
0
2
0
0
2
0
0
1
1
0
2
1
2
0
1
0
0
1
0
0
1
0
0
1
0
1
1
2
2
0
0
1
1
0
0
2
0
1
2
1
0
0
0
0
1
1
2
1
1
2
0
1
1
0
1
0
2
0
0
0
0
1
2
0
1
0
0
0
1
3
1
0
2
1
2
1
0
1
0
1
1
1
0
2
0
2
0
1
1
0
1
1
1
0
1
1
1
1
0
0
2
0
0
1
2
0
1
1
1
0
0
1
0
2
1
0
2
1
2
2
0
2
0
1
2
1
0
0
2
2
1
0
2
0
2
0
1
0
0
0
1
0
1
1
0
2
1
0
2
0
0
5
1
2
0
1
1
0
0
1
1
1
1
2
1
1
2
1
0
2
1
2
1
0
0
1
0
2
1
0
1
0
2
1
0
0
0
1
0
0
1
1
0
0
1
0
1
0
1
1
1
2
0
2
0
2
0
1
1
0
1
1
0
0
1
1
0
0
0
0
0
0
2
1
1
1
1
1
1
1
0
0
0
0
1
0
2
1
2
1
0
0
1
0
1
0
1
1
3
1
3
1
0
2
2
0
0
2
0
0
1
1
1
1
2
3
1
2
1
0
0
1
1
1
1
0
0
0
1
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
1
1
2
1
0
1
1
2
0
1
2
0
0
1
0
0
1
0
1
2
0
0
2
0
1
2
2
0
0
2
1
1
0
1
0
0
2
0
0
1
0
0
0
0
0
0
1
2
1
0
0
0
0
1
2
0
0
0
0
0
0
1
2
0
0
3
0
2
2
4
1
0
0
1
1
1
1
0
0
1
2
2
2
0
0
0
1
0
1
1
2
0
2
0
0
1
2
0
2
1
0
1
0
3
2
0
0
1
1
2
2
1
0
1
0
2
0
0
0
0
1
1
2
1
0
2
0
0
2
0
0
0
1
2
0
1
1
2
1
2
2
2
2
1
0
1
0
1
0
1
2
0
0
1
0
1
2
1
0
0
1
1
1
0
0
2
0
0
1
1
1
1
1
0
1
2
1
1
0
1
0
1
1
0
2
1
0
0
1
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
2
1
0
1
1
0
0
2
1
1
1
1
1
0
1
0
1
2
0
1
2
2
2
0
0
1
0
0
2
0
2
1
1
0
1
0
1
0
2
1
1
1
0
2
2
2
0
1
1
1
1
2
1
1
1
1
2
0
2
0
0
2
0
0
2
2
1
0
0
2
0
1
1
2
3
1
1
1
2
1
0
1
1
0
0
0
1
0
2
2
2
2
1
1
0
0
0
0
1
1
0
0
0
1
2
1
0
2
0
0
0
2
1
1
0
0
1
1
1
0
1
0
1
1
2
1
0
1
1
1
1
2
0
2
1
0
1
1
1
0
0
1
0
0
1
0
0
0
0
1
0
1
0
1
0
2
1
2
1
0
0
1
0
2
1
0
0
1
0
1
1
2
0
1
0
2
0
2
0
2
1
0
1
0
2
0
1
0
0
1
0
1
0
0
0
0
0
2
2
2
0
0
2
1
0
1
1
1
0
0
1
2
0
2
1
0
2
0
0
0
0
1
2
2
1
2
0
0
2
1
1
1
2
2
0
2
2
0
1
0
0
0
0
1
1
2
2
2
1
1
0
2
1
1
1
1
2
0
1
2
0
0
1
2
2
0
1
1
0
1
0
0
1
1
0
1
0
1
1
0
1
1
1
0
1
0
0
1
0
0
1
2
1
2
0
0
1
0
0
2
1
0
1
2
0
0
1
1
0
2
0
0
1
2
1
2
0
0
0
0
1
0
1
1
0
2
2
0
0
0
0
0
0
0
1
0
1
0
2
0
2
1
2
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
1
0
0
1
2
1
1
1
0
0
3
1
0
1
0
3
0
2
0
1
1
0
0
0
2
0
0
0
0
0
1
1
0
0
1
1
1
0
0
0
2
0
0
0
0
1
1
0
0
0
0
1
1
4
1
0
0
1
1
0
3
1
0
1
2
2
0
0
2
1
1
2
2
0
0
2
1
3
0
0
1
0
0
1
0
1
1
0
2
0
1
1
2
1
0
0
3
1
1
3
0
2
1
3
1
2
0
0
0
1
2
0
0
1
2
1
1
2
0
2
1
2
1
2
0
1
0
1
1
0
0
0
1
0
1
1
1
1
2
1
1
0
0
1
2
0
0
1
0
0
2
0
3
2
1
1
0
1
1
1
0
0
1
0
2
1
2
0
0
1
0
1
0
2
3
2
0
0
0
0
1
2
0
1
2
0
2
2
1
0
0
0
1
1
1
3
0
0
0
0
2
1
1
1
1
1
0
2
1
1
0
0
2
0
0
0
1
0
0
1
0
1
2
1
2
2
1
0
1
1
1
0
3
0
1
2
0
0
1
1
0
1
0
0
1
1
3
2
0
0
1
2
1
0
0
1
0
1
2
2
1
0
1
0
1
1
0
1
0
0
0
3
0
1
1
1
1
0
1
1
2
1
2
0
0
1
1
1
1
0
1
0
1
1
0
1
0
2
0
0
0
0
0
0
1
1
5
0
0
0
1
0
1
0
1
1
2
0
0
0
1
2
0
0
0
1
0
0
1
1
1
1
0
1
1
1
0
1
1
0
0
1
2
0
0
1
2
1
0
1
1
2
1
0
7
1
2
0
1
2
2
1
0
2
1
2
0
0
0
0
1
1
1
1
1
0
0
1
2
1
2
0
0
1
1
0
1
1
0
2
0
2
1
0
1
0
0
2
1
0
0
1
1
3
0
1
0
1
2
0
0
0
1
0
0
2
2
0
2
0
1
1
1
2
0
2
3
0
2
0
1
2
1
0
2
1
0
2
1
0
0
0
0
2
0
2
1
1
2
1
0
0
0
0
2
0
2
0
0
0
3
1
0
1
2
0
0
1
0
1
1
0
0
1
2
1
0
2
0
2
0
1
0
2
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
1
1
2
0
1
0
1
1
1
1
0
2
1
1
0
0
0
1
0
1
0
0
1
1
0
2
2
1
0
0
1
2
0
1
0
1
0
2
2
0
0
1
0
0
1
1
1
2
0
0
1
2
1
2
2
1
0
2
0
0
2
1
1
0
2
2
2
1
0
2
1
0
1
2
0
1
0
0
1
0
0
0
1
2
0
2
1
0
1
2
1
0
1
0
2
0
1
0
1
0
0
0
1
1
2
0
1
0
1
0
1
1
1
0
2
0
2
1
0
1
0
2
0
2
1
1
1
0
1
0
0
0
1
1
0
0
4
0
1
1
0
3
0
0
0
0
1
2
0
2
1
0
1
1
0
2
0
0
2
3
0
0
0
1
0
2
1
0
1
0
0
1
0
2
0
1
3
1
1
2
0
0
1
2
0
0
1
2
1
0
0
0
1
1
1
2
2
1
0
1
1
0
2
1
0
0
1
3
0
1
1
0
1
1
1
0
0
1
1
0
1
0
0
2
0
2
0
0
0
0
0
0
2
2
1
1
2
0
2
0
2
0
2
0
2
2
0
1
2
2
2
1
0
0
1
0
1
0
2
2
1
1
1
0
0
2
1
1
0
1
0
1
0
2
0
2
3
2
1
0
4
1
0
1
2
1
0
0
1
2
1
0
1
0
2
0
0
0
1
0
0
1
1
2
0
0
0
0
0
0
2
0
0
2
0
1
0
1
0
2
0
1
2
0
0
0
1
0
1
1
1
1
0
1
0
0
0
1
1
0
0
0
2
0
1
0
0
2
2
1
1
0
0
1
1
0
0
0
0
2
1
1
0
2
2
2
2
1
0
1
0
2
0
1
0
0
1
1
1
2
2
0
1
1
0
2
1
0
1
0
0
1
0
2
2
0
2
0
0
2
2
2
0
0
1
0
0
0
1
0
1
0
1
0
1
2
2
0
2
1
1
1
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
2
1
1
0
1
0
2
2
0
0
1
1
1
2
0
2
2
1
1
0
0
0
0
0
1
1
1
0
2
2
0
0
0
2
0
2
2
2
0
2
2
2
2
2
0
2
1
1
0
0
1
0
1
2
1
9
2
0
1
1
1
2
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
1
1
0
0
1
0
2
0
1
0
0
0
0
0
0
0
1
0
1
2
0
0
1
0
1
2
0
0
0
0
0
0
1
1
2
8
0
1
1
2
1
0
1
0
2
0
0
0
2
0
1
0
1
2
1
0
0
0
0
0
0
0
2
1
0
2
1
1
0
2
2
0
1
0
0
0
1
2
0
2
0
0
1
0
0
2
0
0
1
2
1
0
0
2
0
2
0
0
1
1
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
1
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
2
1
1
2
2
0
0
0
2
1
2
1
2
3
0
2
1
2
2
1
1
0
0
1
2
1
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
2
0
1
2
0
1
1
0
0
2
2
0
0
1
1
2
1
1
0
0
0
0
2
0
0
1
1
0
0
1
1
2
1
1
0
2
1
1
2
1
0
0
1
0
1
0
2
0
2
1
2
1
2
0
1
0
1
2
1
0
1
1
0
2
2
1
2
2
1
1
1
0
1
0
0
1
1
0
0
1
2
0
0
0
1
0
1
0
2
1
2
0
2
0
0
0
1
1
1
1
0
1
2
2
0
2
1
1
1
1
0
0
1
1
2
0
0
1
1
0
3
0
0
3
1
0
0
0
1
2
0
0
1
0
2
0
2
1
0
0
0
0
1
1
0
3
1
0
1
0
0
1
0
0
0
2
0
0
1
1
0
1
1
0
0
1
1
1
1
1
0
1
0
0
1
0
1
0
0
1
0
2
0
0
2
0
0
1
0
0
0
2
1
2
0
1
2
0
0
0
0
1
0
0
1
0
0
0
2
1
1
1
2
0
1
0
2
0
0
1
2
1
1
0
2
0
1
1
2
1
1
0
2
1
0
0
1
1
1
1
2
1
1
1
2
0
0
0
1
1
2
0
0
1
0
0
1
2
1
0
1
1
0
0
0
1
1
0
0
1
0
1
1
0
1
2
1
0
0
0
1
2
0
0
1
2
0
1
0
0
1
2
1
2
3
2
0
1
1
0
0
1
1
0
2
1
0
2
2
1
0
0
1
1
2
0
1
2
1
0
1
1
0
0
1
0
1
0
0
1
0
0
1
2
2
2
3
2
1
2
0
0
1
1
1
1
0
1
0
2
2
0
0
0
0
1
0
0
0
2
1
0
0
1
0
3
2
1
1
0
0
0
1
0
0
2
0
0
1
1
0
0
2
0
2
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
1
0
1
1
2
0
0
0
0
0
2
0
1
1
0
0
1
1
0
1
1
2
2
0
0
1
0
2
2
2
1
0
0
0
1
1
2
0
0
1
1
0
1
1
1
0
0
0
2
1
0
3
1
2
0
2
1
0
0
0
0
2
0
2
0
0
0
1
0
1
1
0
0
0
0
1
1
1
0
1
0
0
2
0
0
0
0
2
1
1
1
0
0
0
2
0
2
1
2
0
2
0
0
0
0
0
0
1
0
0
2
1
1
1
0
0
0
1
0
1
0
0
1
0
0
1
2
2
1
2
1
3
0
2
2
0
2
0
1
0
0
3
1
1
0
0
1
0
0
2
1
0
0
0
0
1
0
1
1
0
2
0
2
0
1
0
2
1
1
0
1
1
1
1
0
0
0
0
2
0
1
0
0
2
1
1
2
1
0
1
0
1
2
0
0
2
2
1
0
1
2
0
0
1
2
1
2
0
0
0
1
1
0
0
1
1
1
0
1
0
1
0
3
2
2
1
2
2
2
0
1
1
0
1
0
1
0
2
1
1
0
0
0
0
1
2
2
0
0
0
0
1
1
0
2
0
0
1
0
1
0
1
1
1
0
0
1
0
0
0
0
2
1
0
0
1
2
0
0
1
2
2
0
1
2
0
1
0
2
2
4
0
0
1
1
2
0
0
0
0
1
0
1
1
1
0
2
1
0
1
2
0
2
0
1
0
1
0
1
0
1
2
0
2
0
1
2
0
1
0
1
1
1
0
0
2
0
1
1
0
0
1
0
1
0
0
2
0
2
1
2
1
1
0
2
1
0
1
1
1
1
2
1
2
1
0
1
0
0
0
0
0
0
2
1
1
0
1
0
1
0
2
0
4
2
1
2
0
0
1
2
2
2
0
0
1
0
2
0
0
2
0
3
0
2
0
0
0
0
1
0
2
2
0
0
0
1
2
1
0
1
0
0
0
0
0
1
1
0
0
1
2
0
0
0
0
0
1
2
2
1
0
1
0
2
0
0
0
3
0
0
1
0
0
2
0
0
0
0
0
0
2
2
2
0
0
0
2
0
3
0
0
2
1
2
0
0
0
0
2
2
1
1
1
1
1
2
2
0
0
0
0
2
1
0
1
0
1
0
2
2
1
1
1
1
1
2
1
1
0
1
1
0
1
0
2
0
2
0
0
1
0
2
1
1
2
1
1
0
2
0
1
2
1
1
1
0
0
1
1
0
1
2
0
1
0
0
1
1
0
0
1
1
2
1
2
1
1
1
2
1
0
1
0
0
0
0
1
2
0
1
1
1
0
1
1
1
1
0
1
3
1
0
0
1
0
0
0
2
1
1
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
3
0
1
2
0
2
2
0
0
0
1
0
0
0
1
1
1
0
0
0
1
0
1
0
1
1
1
0
0
0
0
0
2
0
2
1
1
2
1
0
0
0
1
0
1
0
2
0
1
2
0
1
2
2
0
1
2
0
0
0
0
0
2
1
0
2
1
0
1
2
0
0
2
2
0
1
1
0
0
1
2
0
0
0
2
1
1
0
2
2
0
1
1
0
0
2
0
0
1
2
2
1
0
0
0
0
0
0
2
0
0
0
1
1
0
0
2
0
1
1
0
2
5
2
2
1
0
2
1
0
0
0
1
1
1
0
2
1
0
2
2
2
0
1
1
2
1
2
1
0
0
1
0
1
1
0
2
2
1
1
1
1
2
0
1
1
2
2
0
2
1
1
1
2
0
1
2
0
0
0
2
1
0
2
1
0
0
1
0
3
0
0
0
1
0
0
1
0
1
0
1
2
1
0
1
2
2
0
0
1
1
0
0
0
0
2
1
0
2
1
1
1
1
1
2
1
0
0
1
1
0
3
1
0
0
0
1
1
2
0
1
2
1
0
2
2
1
1
1
0
0
0
0
1
1
0
1
0
0
1
0
0
0
1
0
0
1
1
1
2
0
2
0
2
0
0
0
2
0
0
0
2
0
0
1
0
1
2
0
0
1
2
0
1
1
0
0
1
1
2
1
2
2
2
1
2
0
2
0
0
2
1
0
1
0
1
1
2
0
0
1
2
1
2
1
2
0
1
0
0
2
2
0
0
2
1
2
1
1
1
2
0
2
2
2
2
2
1
0
2
1
1
0
1
0
0
0
1
0
0
1
1
0
0
1
0
0
2
0
0
0
0
0
0
1
2
2
2
3
2
2
1
0
0
2
0
1
1
0
1
0
0
1
1
0
0
0
0
1
0
1
1
1
0
2
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
2
0
1
0
0
0
2
0
3
0
1
1
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
2
1
0
0
1
1
1
1
2
0
1
1
2
2
0
1
0
3
2
1
2
2
0
2
1
0
3
1
0
0
0
2
0
0
2
0
2
0
2
1
0
2
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
1
0
2
1
1
1
0
0
1
2
0
0
0
0
2
0
1
2
0
0
2
2
1
0
0
0
2
3
2
2
0
3
0
0
2
1
2
2
0
0
0
1
2
0
0
1
1
0
2
1
0
0
0
0
2
1
2
1
2
0
0
0
1
2
0
1
1
2
1
0
0
2
2
1
0
2
0
0
0
1
0
0
1
1
2
1
2
0
1
1
1
0
0
1
1
0
0
0
1
0
0
1
0
0
1
2
0
0
0
1
1
0
1
0
1
2
0
1
1
2
0
0
0
1
2
2
1
0
2
0
0
0
2
1
0
0
2
2
2
0
4
2
1
0
0
2
2
1
0
2
1
0
0
0
0
0
2
1
1
1
1
0
1
0
0
1
2
2
1
1
2
2
0
0
2
1
0
0
1
1
2
1
1
0
2
0
0
1
2
2
1
0
0
0
0
2
1
2
0
0
0
1
1
1
1
1
0
0
1
1
0
1
0
0
2
2
0
0
0
2
0
2
1
1
0
0
2
2
0
0
0
0
1
0
2
1
0
2
0
1
1
2
1
2
1
0
0
0
0
1
0
0
1
1
0
0
2
0
1
0
0
0
2
0
2
1
0
0
0
0
2
2
0
0
1
1
1
1
2
0
0
1
1
2
0
1
0
0
1
0
2
1
0
1
1
0
1
1
0
2
1
0
0
0
0
1
1
1
1
1
1
0
0
3
2
2
0
2
0
2
0
2
1
0
2
2
0
1
1
3
1
3
2
0
2
1
0
0
2
0
1
0
0
1
1
0
0
2
1
2
1
0
2
0
0
0
0
0
0
1
2
1
2
1
1
1
2
0
2
2
1
2
0
0
1
2
0
1
2
2
0
0
2
1
0
0
0
0
2
1
0
2
2
1
1
1
0
1
0
0
1
1
0
0
1
0
2
0
1
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
2
2
1
1
0
0
2
2
0
2
1
0
2
0
0
0
0
0
2
0
0
0
2
0
1
2
0
1
0
0
0
1
1
0
1
1
1
1
0
2
1
1
0
0
0
2
0
0
2
1
3
0
0
3
1
4
0
0
0
1
0
0
0
2
1
0
1
1
2
0
0
1
0
1
2
0
0
2
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
1
2
0
2
1
1
0
0
0
0
2
0
1
0
0
1
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
2
0
2
0
0
1
0
0
2
1
0
0
0
0
0
1
0
1
0
1
0
1
1
1
0
0
0
2
1
0
0
1
1
0
0
0
1
1
0
1
2
0
0
1
2
1
1
1
1
1
2
0
0
0
1
2
2
0
1
1
2
0
2
2
0
1
0
0
0
2
1
1
0
1
0
0
2
0
2
0
1
1
0
2
0
2
0
1
0
1
1
0
0
0
1
1
2
1
1
2
0
1
0
0
0
2
0
0
2
2
1
1
0
0
2
0
0
0
0
2
1
0
1
2
0
0
0
2
1
2
0
2
0
1
1
0
0
2
0
1
0
0
0
1
0
0
2
2
0
1
1
1
0
0
1
2
1
1
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
2
3
2
0
2
1
2
1
3
2
1
0
0
0
0
3
1
1
1
0
0
1
2
2
1
0
2
0
0
1
2
2
2
2
0
0
1
0
2
2
1
0
0
0
1
1
0
1
0
0
1
2
1
0
0
2
0
1
0
0
2
0
1
0
1
2
0
2
0
0
0
1
0
2
0
1
1
2
1
2
2
0
2
0
0
2
0
1
0
1
1
2
2
0
2
0
0
0
1
0
1
0
1
0
2
3
0
0
1
0
0
2
0
0
2
0
1
0
0
1
1
0
1
0
0
2
0
0
1
2
1
0
1
0
2
0
2
1
0
2
0
0
2
1
2
0
0
2
2
0
0
0
0
0
0
2
1
0
0
3
1
0
2
2
1
1
1
1
2
2
0
1
1
0
1
0
1
1
0
0
1
2
2
1
0
0
0
0
0
2
2
0
2
1
0
2
0
0
1
0
0
1
1
1
1
2
1
0
1
0
0
0
2
2
4
0
0
2
0
2
0
0
0
0
1
1
2
0
0
0
0
2
0
3
1
1
0
2
0
0
4
1
1
0
0
1
0
0
0
0
0
1
1
0
2
0
0
1
0
2
0
1
0
1
0
2
2
4
1
0
0
0
1
0
2
0
0
0
0
1
2
2
2
2
2
0
2
0
1
1
0
0
0
2
2
2
1
0
1
1
0
2
2
1
2
0
2
2
0
2
0
1
1
2
2
0
1
0
2
0
1
0
1
1
1
0
1
1
1
2
1
0
2
2
1
1
0
0
0
0
1
0
2
0
0
1
1
2
1
1
0
1
0
1
0
0
0
0
1
2
0
1
1
0
2
1
0
1
1
0
1
1
1
2
0
0
1
0
0
1
3
2
1
1
1
1
2
0
0
0
1
0
0
0
0
1
2
0
0
1
2
0
0
1
0
2
1
3
1
0
1
0
0
2
1
0
0
0
1
0
2
1
1
2
0
0
1
0
0
1
1
0
0
1
4
1
0
0
0
2
0
0
2
6
1
1
0
2
2
0
1
0
2
1
2
1
1
1
0
1
0
1
1
0
1
0
2
0
0
0
0
0
1
1
0
0
0
0
0
2
1
2
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
2
1
1
1
2
1
0
1
0
2
1
1
2
1
0
1
2
1
0
2
1
0
1
1
2
0
2
1
2
2
0
1
2
2
0
1
2
1
2
0
2
2
0
0
1
0
2
1
0
0
2
1
1
2
0
0
0
0
2
1
0
0
1
1
2
2
0
3
3
0
2
2
2
1
1
1
0
2
2
1
0
2
0
1
0
2
1
2
0
1
1
0
0
0
1
1
2
2
1
1
0
2
1
0
1
0
0
1
1
0
1
2
0
0
1
2
1
0
0
2
2
1
0
1
0
1
0
0
2
0
2
0
0
2
2
0
4
3
2
1
0
0
0
1
1
0
1
1
1
0
0
0
2
0
1
0
0
1
1
1
0
1
1
1
0
1
2
0
1
0
1
2
0
0
1
2
0
1
2
2
0
2
0
0
1
0
1
0
0
1
0
0
2
0
0
0
1
0
2
1
0
2
0
1
0
0
1
1
2
0
1
2
1
2
1
0
1
1
2
0
0
2
1
0
0
3
0
1
0
0
1
0
2
1
0
2
0
1
0
2
1
1
1
0
0
0
0
2
1
0
1
0
0
0
1
2
0
1
0
1
0
0
2
1
0
1
2
0
0
0
2
0
0
0
0
2
0
2
0
1
2
1
2
1
0
2
0
0
2
0
2
2
0
1
1
1
2
0
0
1
1
0
1
1
1
1
2
0
0
0
2
0
0
0
1
0
0
2
0
2
0
1
1
0
0
0
2
1
2
1
0
1
2
0
1
0
1
0
0
0
2
1
0
0
1
1
1
0
1
1
2
0
1
2
2
1
1
2
0
0
1
2
0
0
2
0
2
2
0
0
1
0
0
0
1
2
1
1
1
0
0
0
1
1
0
0
0
2
2
0
2
0
1
0
1
0
1
0
0
1
1
0
2
1
0
2
1
2
1
4
1
2
0
0
0
0
1
0
2
1
0
0
0
0
1
1
1
2
0
0
0
2
1
0
1
0
1
2
3
2
0
1
0
0
0
2
0
1
0
0
0
1
1
1
1
0
0
1
1
0
2
1
0
1
2
1
1
0
4
2
1
2
2
0
1
4
1
0
0
3
0
0
0
1
0
1
0
2
2
0
0
0
1
1
0
0
0
2
0
2
2
1
0
0
0
1
0
1
0
1
2
0
0
2
0
0
0
1
1
0
2
1
0
3
1
1
1
1
3
0
1
0
0
2
1
1
2
2
0
2
0
2
0
0
2
0
0
2
0
0
1
3
1
2
1
2
1
1
0
3
0
1
2
0
2
2
2
0
0
0
0
0
1
0
1
0
1
1
2
2
0
0
1
3
0
0
1
1
2
0
4
0
1
0
2
2
1
1
2
1
1
0
1
2
1
2
2
1
3
0
0
1
0
2
1
1
1
0
1
2
0
2
2
0
1
0
1
0
2
0
1
1
0
0
0
0
0
0
0
0
2
1
2
1
1
1
1
0
0
0
2
2
1
1
0
2
2
0
0
1
0
1
1
0
0
0
0
1
2
1
1
0
2
0
1
0
0
2
0
0
0
1
0
2
1
0
0
0
0
0
1
1
2
5
0
0
1
1
1
1
0
2
3
1
1
1
2
1
0
2
2
2
1
0
0
0
1
0
1
0
2
1
1
0
1
0
2
2
2
1
1
0
0
0
0
0
1
0
2
0
1
2
1
2
0
0
0
1
0
2
0
1
1
1
1
0
2
0
1
0
0
1
0
3
2
1
0
0
0
2
1
0
1
0
2
1
1
0
2
1
0
1
1
1
0
0
2
0
2
1
2
1
2
0
1
0
0
1
0
0
0
2
0
1
1
0
1
0
2
2
1
2
2
0
4
1
0
0
0
1
2
0
1
0
1
1
1
0
2
1
1
1
0
1
1
1
1
0
1
0
2
0
0
1
0
0
0
0
1
0
0
2
1
1
2
0
0
0
0
2
1
2
2
0
1
1
0
0
0
1
0
1
1
0
0
1
0
1
0
1
0
1
0
1
0
0
0
0
2
1
0
1
2
2
0
0
2
1
0
0
0
0
0
1
1
1
1
0
2
1
0
2
0
1
2
2
2
1
1
0
1
1
1
0
1
0
0
1
0
0
1
1
0
1
1
1
0
0
1
2
1
1
0
1
1
0
1
0
1
0
0
2
1
1
0
0
0
2
2
0
1
0
0
1
1
0
2
0
0
1
2
2
0
0
0
1
1
1
1
2
0
1
0
0
0
2
0
0
1
0
2
2
0
0
1
0
0
1
0
1
1
0
0
2
0
1
0
1
0
0
1
2
0
0
0
0
0
1
2
0
1
1
1
0
0
0
2
0
2
1
1
2
0
1
1
1
1
0
2
1
1
0
1
0
1
1
1
1
1
0
2
0
0
0
1
1
0
1
2
0
0
1
1
1
0
0
1
2
0
0
2
1
2
2
0
2
2
1
1
1
1
0
1
0
1
2
0
2
0
0
0
3
1
0
1
1
1
0
2
2
1
3
0
1
2
0
3
2
1
0
2
1
1
0
2
1
2
1
3
1
0
0
0
0
1
0
1
0
0
1
0
0
1
0
2
0
0
1
1
1
2
0
0
0
0
0
0
0
0
1
1
3
0
1
2
1
1
0
0
0
0
0
1
0
1
2
0
0
2
1
0
0
2
1
2
0
3
1
0
0
2
1
0
1
1
0
1
2
1
1
0
0
2
0
2
1
1
1
1
0
0
1
0
0
1
1
1
0
0
0
0
2
1
2
2
2
2
1
2
0
2
0
0
0
0
0
0
1
0
1
0
2
1
0
1
0
0
0
0
0
2
1
1
1
0
2
3
2
0
0
0
1
2
2
1
0
1
1
1
1
1
0
0
0
2
1
1
0
2
1
2
0
0
0
1
0
0
1
1
0
0
0
0
0
0
2
1
0
0
1
0
1
0
0
0
2
0
1
0
1
0
1
0
2
2
0
2
0
1
2
0
0
0
0
0
0
2
0
0
0
0
3
0
0
2
0
0
0
1
2
0
1
1
2
2
2
0
2
2
0
0
1
2
0
0
0
0
1
1
0
1
1
2
0
2
0
0
0
1
0
1
0
1
2
2
1
0
0
2
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
1
1
0
2
1
0
2
1
0
0
1
0
2
1
0
1
0
0
2
0
1
1
2
1
1
0
1
0
0
1
0
2
2
0
2
0
0
1
0
1
2
1
2
1
1
1
1
0
1
1
1
2
1
5
1
1
0
2
2
1
0
0
2
1
0
1
1
0
0
1
2
1
1
0
0
1
2
1
2
0
0
0
0
2
0
0
1
0
2
0
1
1
1
0
2
2
3
0
0
2
1
1
0
0
1
1
2
3
1
2
0
1
0
1
1
2
1
2
1
1
0
0
0
1
2
0
2
0
2
0
0
0
0
1
2
0
2
1
0
1
0
1
0
0
0
0
1
0
2
0
0
0
4
1
0
2
0
1
0
0
2
0
0
1
1
2
0
0
2
3
0
0
0
0
0
1
1
0
0
1
1
2
1
0
1
0
1
2
0
3
2
0
2
1
1
2
0
1
2
1
0
1
0
0
1
1
0
2
2
1
0
1
0
1
0
0
0
0
0
2
2
0
1
0
0
1
1
1
1
2
0
0
0
2
0
2
0
2
1
2
0
0
0
1
1
1
2
0
1
1
0
1
2
2
0
2
2
2
0
2
2
1
1
0
2
0
0
2
1
0
0
2
0
0
1
1
0
1
2
1
1
2
1
0
0
2
1
1
0
0
0
3
0
0
0
0
1
0
2
2
0
2
0
1
2
1
1
2
1
1
1
0
0
1
1
0
0
0
2
0
0
1
3
1
0
0
1
2
0
0
3
0
2
0
1
2
1
0
0
1
2
2
0
2
2
1
0
0
0
1
2
1
0
1
1
2
2
2
0
0
1
2
0
0
2
1
0
1
0
0
0
0
1
2
2
0
1
2
1
0
2
0
1
2
2
0
1
2
2
1
1
0
2
0
0
1
0
2
1
1
1
0
3
1
0
0
2
1
0
1
1
0
0
0
1
0
0
4
2
0
1
1
0
2
1
0
0
0
2
0
0
0
1
0
2
0
0
1
0
0
2
0
0
0
2
0
1
0
1
1
0
1
2
0
1
0
2
2
2
2
0
1
1
0
1
2
0
1
0
3
1
8
2
0
0
1
1
0
1
2
2
0
2
1
1
0
0
2
1
0
1
2
2
1
1
0
1
1
0
0
2
0
0
1
0
1
0
0
1
1
0
0
1
0
1
1
1
0
1
1
1
1
0
0
1
1
0
1
0
1
0
1
0
0
1
2
0
2
2
1
0
1
1
0
3
1
0
0
0
0
2
1
0
0
1
1
1
0
0
1
0
0
1
1
3
1
1
1
1
0
0
0
0
0
0
1
2
2
2
0
1
2
0
0
1
1
0
1
0
1
1
0
1
0
0
0
0
0
0
2
1
0
1
1
0
2
0
1
2
0
2
2
0
1
0
1
2
0
1
0
0
0
0
2
0
0
1
0
1
0
1
1
1
1
5
0
2
2
0
0
0
1
2
1
1
0
0
1
0
3
0
0
2
2
0
0
2
0
0
0
1
1
3
1
1
1
0
1
2
2
1
2
0
0
1
1
0
1
0
0
2
0
0
0
0
1
2
0
0
0
1
0
0
0
0
1
0
2
2
0
1
1
0
0
1
0
0
0
0
2
1
0
0
0
1
1
0
0
0
0
1
0
0
1
1
0
2
0
1
1
2
1
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
2
1
2
1
0
0
0
2
2
1
0
0
0
0
0
1
2
2
0
2
0
0
0
0
0
1
2
1
0
0
0
0
1
0
0
0
0
0
0
1
1
2
0
1
1
1
2
0
0
0
0
0
1
1
1
0
0
0
1
0
1
1
0
0
2
1
1
0
0
1
1
1
1
0
1
2
2
3
1
2
1
1
1
1
2
2
1
0
0
0
2
0
0
1
0
0
0
0
2
1
0
0
0
2
0
0
0
1
1
1
1
0
1
0
0
1
0
0
0
0
0
2
1
1
0
1
1
1
1
0
2
0
0
0
0
3
2
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
1
1
2
2
0
1
2
0
2
1
2
0
1
1
0
2
1
0
0
1
0
2
0
2
0
1
1
0
0
1
2
0
1
0
1
1
0
0
1
1
0
0
0
1
0
0
0
0
2
1
1
2
2
2
1
0
0
1
1
1
0
0
2
0
2
1
1
0
0
1
1
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
1
1
0
1
2
1
1
2
0
0
0
0
0
2
1
2
0
0
1
0
0
0
1
2
2
1
0
2
2
2
0
1
1
1
0
1
1
0
7
2
0
4
0
0
1
2
0
2
1
1
1
0
2
0
1
2
0
0
0
0
1
0
1
2
2
2
1
0
0
1
1
2
0
2
1
1
1
1
0
0
0
0
1
1
0
1
0
3
1
0
0
2
2
2
0
1
0
2
2
0
0
0
1
0
2
0
1
2
1
1
1
0
1
2
1
1
1
2
0
0
0
1
2
2
0
1
0
2
0
0
0
0
1
0
1
0
0
0
2
1
2
0
2
2
0
1
1
1
0
2
0
1
3
0
0
2
0
1
1
0
2
0
0
0
0
1
1
0
2
2
2
1
2
0
2
1
1
0
2
0
2
0
2
0
2
1
0
1
0
2
1
2
1
1
2
1
0
0
0
1
1
1
0
1
0
2
0
0
1
2
1
2
1
0
2
1
2
0
1
2
8
0
0
2
1
0
0
1
0
1
0
0
0
0
2
2
1
2
2
2
0
1
0
1
1
0
1
0
0
0
1
2
2
3
0
0
1
4
1
2
1
1
1
0
0
1
1
0
1
2
1
0
0
1
1
0
0
2
1
1
1
1
1
1
0
2
0
0
2
2
1
0
0
1
0
0
2
0
1
1
0
0
2
1
0
0
0
0
1
2
1
1
0
0
2
0
1
0
0
0
1
0
0
2
1
0
2
1
2
0
1
2
0
1
0
0
0
1
1
0
2
0
1
1
0
0
2
0
1
2
0
1
0
0
1
2
1
0
2
2
0
0
0
0
1
0
1
1
1
0
0
0
0
2
0
0
4
1
2
2
0
0
0
2
1
0
2
0
0
0
0
0
1
0
2
0
1
0
0
1
0
1
4
1
0
1
1
2
0
2
1
0
1
1
0
0
1
0
1
1
2
1
1
1
1
2
3
0
0
1
0
0
1
0
2
1
2
1
1
2
1
1
0
1
0
0
1
0
1
0
1
0
1
0
1
1
1
0
2
1
0
1
0
2
0
0
0
0
1
1
1
0
2
2
1
2
2
1
1
1
1
1
1
0
0
1
0
0
0
3
0
3
0
3
1
2
1
1
1
1
0
2
3
1
2
2
2
0
1
2
0
2
0
1
2
0
0
0
2
1
0
2
0
1
2
0
1
1
0
2
1
0
0
0
1
0
1
2
1
0
1
2
0
0
0
0
1
2
0
1
0
0
2
1
0
2
1
2
2
0
1
0
1
0
2
1
0
0
2
0
0
0
1
1
0
0
0
1
1
0
0
1
0
2
0
1
0
0
1
1
2
0
1
2
2
0
2
1
0
2
0
1
0
1
2
0
1
1
0
0
0
0
0
1
0
0
0
1
1
2
0
0
0
2
0
0
1
1
1
2
0
0
1
0
0
1
0
2
0
1
5
0
0
0
1
1
0
1
0
1
0
1
0
2
0
1
0
1
1
0
1
0
0
0
1
0
0
0
1
1
0
1
1
2
0
2
0
2
1
0
0
0
0
0
3
0
0
0
2
0
1
0
1
1
1
1
1
0
2
0
1
0
1
1
2
1
0
0
2
2
0
1
2
0
0
1
0
2
1
1
0
1
2
1
2
1
1
2
0
0
0
1
0
0
0
2
1
2
1
1
0
0
1
2
0
1
0
1
0
0
3
0
1
1
1
0
2
0
0
1
2
1
0
0
0
0
1
0
2
1
1
0
2
0
1
0
1
1
0
0
0
1
1
0
0
1
1
1
2
1
2
1
2
2
0
2
1
1
2
0
0
2
3
0
0
1
0
0
0
0
2
1
1
2
2
0
2
0
0
1
2
1
2
1
1
1
0
0
1
1
0
1
0
0
1
0
0
2
2
1
0
3
0
2
1
2
0
1
2
2
2
0
2
0
0
1
0
1
1
1
0
0
0
2
0
0
2
3
0
0
0
2
1
0
2
1
2
1
0
1
1
0
1
2
1
2
1
1
0
2
1
2
0
0
1
1
1
2
1
0
2
0
0
1
0
1
2
2
1
1
0
1
2
0
0
1
1
1
0
0
2
0
0
2
1
2
0
0
3
1
0
1
2
2
1
1
0
1
1
0
1
0
0
1
1
1
1
0
0
0
0
0
2
1
0
0
0
0
1
1
1
1
1
0
0
0
1
0
1
0
1
1
2
0
2
1
0
0
2
0
0
0
2
1
0
0
1
1
1
0
1
1
3
0
0
0
1
1
0
0
0
2
1
0
1
1
0
0
1
0
0
2
2
0
0
0
0
2
1
0
0
0
1
1
2
0
0
1
0
1
1
1
0
2
0
1
2
0
0
2
1
0
0
0
0
0
3
0
0
1
0
0
0
2
1
0
2
2
2
0
0
2
0
2
0
2
0
0
0
1
0
0
1
0
0
2
1
1
0
1
0
1
0
1
0
0
1
0
1
3
1
0
0
0
1
0
0
0
0
1
0
0
2
1
0
1
1
2
0
1
0
0
1
2
0
2
0
1
1
0
1
1
0
2
2
2
1
1
2
1
1
1
3
1
2
0
1
0
0
1
0
0
0
1
0
2
0
0
0
2
0
0
1
0
0
0
1
0
1
0
2
0
0
2
0
0
5
1
1
3
1
0
0
1
2
0
0
0
1
0
0
0
0
0
1
2
3
0
0
0
0
0
0
0
2
2
1
2
2
0
0
2
1
1
1
1
1
0
1
2
1
2
1
1
0
0
1
0
1
2
0
2
0
2
0
0
2
0
0
0
1
1
1
1
0
1
0
0
1
2
2
0
0
1
0
3
2
0
0
1
1
2
1
2
0
0
0
1
3
1
0
3
0
2
1
0
2
5
1
2
0
1
1
1
1
0
0
1
0
1
0
1
1
1
2
0
0
2
2
1
1
0
0
0
0
0
1
0
0
2
0
0
2
2
0
1
1
1
0
1
1
1
0
0
0
1
2
0
1
2
0
2
2
0
3
0
2
0
1
1
2
0
1
1
2
1
0
2
1
0
1
2
0
0
1
2
2
0
0
1
1
2
0
1
1
0
0
1
1
1
2
2
0
0
0
1
0
1
0
0
0
0
0
0
0
1
2
3
1
0
1
2
1
2
0
0
1
2
2
2
1
1
2
0
1
1
2
1
1
0
0
2
1
0
0
0
0
0
2
1
0
2
1
1
2
1
0
0
2
0
2
0
1
2
2
0
0
1
1
0
0
1
1
0
2
0
0
1
0
2
0
0
0
1
1
0
0
0
2
1
1
1
0
1
0
0
0
0
1
2
1
1
0
0
0
0
0
1
1
1
2
3
2
2
1
0
0
2
0
2
1
2
1
0
0
0
0
2
0
1
0
1
0
0
2
0
0
1
1
0
2
1
2
2
1
0
1
3
1
0
0
1
2
0
0
0
0
0
1
0
1
0
0
1
0
0
1
2
2
2
2
1
0
0
2
2
0
2
0
2
0
0
2
0
1
1
0
0
0
2
0
0
2
0
2
2
1
0
2
0
1
0
1
1
2
1
0
2
2
1
0
0
0
0
2
0
1
0
0
2
2
1
0
1
0
4
1
1
0
1
0
0
0
0
2
1
0
1
1
1
0
1
0
1
0
0
1
0
1
2
1
1
1
0
1
0
1
0
0
0
1
1
2
0
0
1
1
0
0
1
1
0
2
0
0
1
4
2
0
2
1
0
0
1
2
1
2
0
1
0
0
1
2
2
0
1
1
1
0
0
2
2
1
4
0
1
1
0
2
0
0
2
2
0
1
1
2
0
1
0
1
1
0
2
1
0
2
1
1
1
1
0
1
0
3
1
0
1
1
0
0
2
0
1
0
0
0
0
2
1
1
3
2
2
0
1
2
3
2
0
1
0
1
1
0
2
1
1
0
1
0
2
0
2
1
1
2
1
0
1
2
0
1
1
1
0
1
1
0
0
2
0
0
2
1
0
2
1
0
0
2
0
0
2
1
1
1
3
3
0
1
2
1
0
2
1
1
0
1
2
0
0
2
0
2
0
0
0
1
0
2
2
0
1
0
0
0
1
0
0
1
0
2
2
2
1
1
0
0
0
0
4
0
2
1
1
0
1
2
4
1
1
2
0
0
1
0
1
0
1
0
0
1
1
0
0
0
0
0
1
0
2
1
2
1
0
0
0
0
0
1
2
0
2
2
0
1
0
0
1
0
2
1
0
2
1
0
0
2
1
1
2
0
2
2
0
0
2
0
0
2
1
3
1
2
0
0
0
0
1
0
0
0
0
0
1
2
1
0
0
0
1
2
0
2
1
0
1
1
1
1
0
1
0
2
2
1
0
0
1
2
1
0
1
1
0
2
2
1
1
1
0
1
1
1
0
2
1
0
0
0
1
1
0
1
2
0
2
0
1
0
0
2
1
1
2
2
2
0
0
0
0
0
0
2
1
0
1
1
2
2
0
1
0
2
2
0
2
1
1
1
0
1
0
0
3
0
1
2
1
0
0
2
1
2
1
1
2
3
1
0
1
1
0
0
0
2
1
0
0
2
1
0
2
0
2
0
1
1
0
0
0
2
1
1
1
0
1
1
2
2
2
1
2
2
1
1
0
0
1
1
1
0
0
0
0
0
2
0
2
2
0
0
1
1
2
0
1
1
0
1
1
1
0
1
1
1
0
1
0
1
0
1
0
1
2
0
2
1
1
2
0
4
2
0
0
0
0
0
0
2
0
0
1
1
0
0
1
1
1
0
2
0
1
1
0
1
1
2
1
0
1
2
2
0
1
1
1
1
0
0
1
0
1
0
1
0
0
0
1
0
0
0
2
0
4
0
0
3
0
0
2
0
1
0
1
0
1
1
1
1
2
2
1
2
1
1
1
1
1
1
2
0
1
0
2
2
0
1
0
2
2
0
1
0
1
1
0
1
0
3
1
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
2
0
0
1
0
2
0
2
2
2
1
2
1
0
1
1
2
1
1
0
1
1
2
0
1
1
1
2
1
2
2
0
2
0
0
1
0
1
0
2
1
1
0
3
1
1
1
0
0
0
0
1
2
0
1
0
0
0
0
1
1
0
0
0
0
1
1
1
0
1
2
1
0
0
4
1
2
1
1
1
0
0
2
0
0
2
0
0
0
1
2
1
1
1
2
2
0
1
2
0
0
0
0
0
0
1
0
2
1
0
1
1
0
0
1
0
1
2
0
1
1
0
1
0
2
2
1
2
0
2
1
2
1
1
0
0
0
0
2
1
1
1
2
0
0
1
0
1
2
0
0
1
0
2
2
2
1
2
2
2
1
0
1
0
0
1
0
2
1
2
1
0
1
0
1
0
0
1
2
1
2
1
0
0
0
2
2
0
1
2
1
0
0
2
1
0
0
0
0
0
2
0
0
1
0
1
2
0
2
1
0
0
2
0
0
2
1
1
0
1
1
1
1
0
0
0
0
1
0
1
2
1
1
0
1
1
2
0
0
1
0
1
0
0
1
0
1
1
0
0
1
2
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
1
4
2
0
2
0
1
1
1
1
0
0
0
2
2
1
1
1
2
1
0
1
0
0
1
2
2
2
0
0
1
0
0
1
2
2
0
2
1
0
0
0
0
1
0
1
0
0
1
1
2
0
0
1
0
0
0
0
0
0
2
0
1
1
0
2
0
0
0
1
0
2
1
0
2
1
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
1
2
1
2
2
0
1
0
2
1
2
1
2
0
2
0
2
3
0
0
1
0
0
1
2
1
2
2
0
0
2
1
0
1
2
2
1
0
0
1
0
1
0
2
1
2
1
1
0
2
1
2
1
0
0
0
0
1
2
0
1
2
1
0
2
0
1
0
2
0
0
0
0
2
1
1
0
1
0
0
0
2
2
0
0
1
0
0
1
1
2
0
0
0
2
1
1
1
1
2
0
0
0
0
1
1
0
1
1
1
1
1
0
0
1
1
1
1
1
1
0
3
2
1
2
2
1
1
1
1
0
0
1
0
0
1
1
0
1
1
1
1
0
0
2
2
1
1
0
0
0
0
1
1
0
0
0
1
1
2
0
1
1
2
0
0
0
1
0
0
0
0
0
0
0
1
2
0
1
1
1
1
2
2
2
1
0
0
0
0
3
1
0
1
0
0
2
0
1
3
1
1
1
2
1
1
1
0
2
3
4
0
0
2
0
0
0
1
0
0
0
0
1
1
1
1
1
0
0
1
0
0
0
1
2
0
0
2
1
0
0
4
2
0
0
1
0
1
1
0
0
2
1
2
1
1
1
0
0
0
0
1
0
2
2
1
0
1
0
1
2
2
0
0
1
1
0
2
0
0
0
1
2
0
1
2
2
1
1
1
0
2
1
0
1
2
0
0
1
1
0
1
0
2
0
0
1
2
2
0
2
3
1
1
1
0
0
0
0
1
1
1
0
1
1
0
0
0
1
2
0
0
1
1
0
0
0
0
1
2
1
0
0
0
0
1
1
0
2
0
0
0
0
2
1
0
2
0
0
1
1
1
1
1
0
0
0
1
2
0
0
1
0
0
2
0
1
0
2
0
2
0
1
0
0
1
1
0
1
1
1
1
2
0
2
0
0
1
0
1
0
0
2
0
1
2
0
2
0
1
0
1
0
2
0
0
0
1
1
0
1
1
0
0
0
2
2
0
0
1
2
0
1
0
1
0
0
0
0
1
0
1
1
1
0
1
1
0
1
0
0
0
2
1
0
1
0
0
0
1
0
1
0
0
2
1
1
0
1
0
0
1
1
2
2
2
2
0
1
2
2
2
2
0
2
0
0
1
1
0
0
1
0
0
0
1
1
0
1
1
0
0
1
1
0
1
2
0
1
1
0
0
1
2
1
2
2
0
0
0
0
1
0
0
0
0
1
0
0
1
1
2
2
1
0
1
0
2
0
0
3
0
0
1
0
2
0
2
0
0
1
0
1
1
0
0
2
0
1
1
2
2
0
2
1
1
1
0
0
1
1
2
1
1
2
0
0
0
2
1
1
2
1
0
1
2
0
1
0
1
0
0
1
1
1
0
0
3
1
0
1
2
0
0
0
1
1
0
2
0
2
1
0
2
0
0
1
1
0
3
1
0
0
4
1
1
1
1
1
1
1
1
1
0
1
0
1
1
1
2
1
0
0
0
2
0
0
0
2
1
1
0
0
1
1
0
0
0
0
1
2
0
1
2
2
2
0
1
1
2
1
0
1
0
0
1
0
2
1
0
1
1
1
0
1
1
1
2
1
1
0
0
2
0
1
0
0
2
1
1
0
1
0
0
2
2
0
1
1
0
0
1
1
0
0
2
2
1
0
0
3
1
1
2
1
0
0
1
0
0
1
0
0
1
3
0
2
0
2
0
0
1
0
1
2
0
0
1
1
0
0
0
1
2
0
0
0
0
0
0
2
0
1
0
0
1
1
1
2
0
1
0
0
0
0
1
1
1
1
0
1
2
0
0
2
0
1
0
1
1
2
1
0
0
2
2
2
0
0
1
0
1
0
1
0
0
2
0
0
0
0
0
0
1
1
0
1
2
2
0
1
1
1
0
0
1
2
2
0
1
4
0
2
1
2
0
0
0
0
0
0
1
0
0
2
2
2
0
0
1
0
0
2
1
2
0
0
2
0
2
1
0
0
0
1
2
2
2
2
1
0
1
1
1
1
1
0
2
1
0
1
1
1
1
0
0
2
0
2
1
2
0
0
0
0
1
0
1
2
0
2
1
1
3
2
0
1
0
0
1
0
1
0
1
1
3
0
0
2
2
0
2
0
1
1
2
0
0
2
1
1
1
0
1
2
0
2
0
0
1
0
3
0
1
0
0
1
0
0
0
0
1
0
2
0
1
0
0
0
0
0
2
0
2
0
1
0
2
0
0
1
1
1
0
0
1
1
0
1
0
0
1
0
0
0
3
0
1
1
0
0
3
1
2
2
1
0
3
0
0
0
1
1
1
0
0
1
2
0
2
2
1
0
0
0
0
2
1
2
0
1
0
2
1
1
1
2
2
1
2
2
0
3
2
0
0
0
0
2
1
0
1
1
1
1
0
1
1
3
0
2
1
0
0
2
1
2
0
0
1
0
0
1
2
1
0
1
1
2
0
0
0
1
1
0
0
0
1
1
1
0
1
0
1
0
2
0
0
0
0
0
0
3
1
0
2
2
2
0
0
1
0
2
0
0
0
0
0
0
1
0
0
2
0
1
2
2
0
2
1
0
0
1
0
2
0
1
0
1
0
2
1
1
0
0
1
2
2
0
0
0
2
0
1
1
0
2
0
1
1
1
0
0
5
0
1
1
1
0
1
0
0
0
1
1
0
0
1
0
0
0
2
0
1
1
2
0
1
0
1
2
0
0
1
0
0
2
0
2
0
0
0
2
1
0
0
0
2
0
0
0
0
2
1
0
1
0
0
0
0
1
2
1
1
0
0
1
0
2
0
0
1
2
1
0
2
2
0
0
2
1
3
1
1
0
1
1
1
1
0
1
0
2
2
0
2
5
3
1
0
2
1
0
0
0
0
0
1
2
0
2
0
0
1
3
0
0
0
2
0
1
0
0
1
1
2
2
1
2
1
0
1
1
1
0
1
1
2
0
2
0
2
2
2
0
1
0
1
0
0
0
0
0
2
2
2
0
1
2
0
0
0
1
0
0
0
1
2
1
1
0
1
1
1
0
0
0
0
0
2
2
0
0
0
1
0
0
1
0
2
1
1
2
0
0
1
0
1
0
2
0
1
1
0
0
0
2
0
0
1
0
1
2
2
0
1
1
0
0
2
0
1
0
2
0
0
2
1
0
3
0
0
1
2
0
2
1
0
0
2
3
0
0
2
0
0
1
1
1
2
0
0
1
0
1
0
0
0
0
0
1
0
2
0
0
0
2
1
0
0
0
0
1
0
0
2
2
0
2
0
1
1
0
2
0
0
1
0
2
1
0
0
1
0
2
0
0
0
1
1
0
0
2
0
0
1
2
0
1
0
0
1
0
0
1
2
0
1
2
2
0
0
0
1
1
0
2
0
1
3
1
1
1
2
1
1
2
1
0
0
1
0
0
1
1
1
0
0
2
1
2
2
0
0
1
2
0
0
1
0
0
1
1
2
0
0
0
0
1
0
0
2
0
1
1
0
0
0
0
1
1
0
0
0
1
0
1
2
0
0
0
2
2
2
0
1
0
0
0
1
0
1
0
2
2
0
0
2
0
2
0
1
1
0
1
1
1
0
1
0
0
2
1
0
2
1
2
1
1
0
0
0
2
1
1
0
1
1
0
1
1
2
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
1
1
0
0
1
1
0
1
0
0
1
1
1
1
0
1
2
0
0
0
0
2
1
0
1
2
4
0
0
1
0
1
2
1
1
0
0
2
2
0
1
1
2
1
1
0
2
1
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
1
1
0
0
2
2
1
0
1
0
0
0
0
0
0
1
1
2
2
1
2
0
0
1
0
0
2
1
1
1
1
2
0
2
0
1
1
1
0
0
0
1
1
0
0
0
1
0
2
1
0
2
1
1
0
2
0
0
2
2
1
1
0
2
3
3
1
0
1
1
1
2
1
1
0
2
0
0
1
0
2
1
0
0
0
2
0
0
2
1
1
0
0
2
1
1
0
2
1
0
0
0
0
0
1
0
1
0
0
0
0
0
2
2
3
1
1
0
2
0
1
0
0
1
1
0
1
0
0
0
2
0
0
1
0
0
0
2
7
0
1
1
1
0
1
1
0
0
1
0
2
0
1
0
1
0
1
0
0
0
2
2
1
0
0
0
0
1
1
1
1
0
2
0
2
1
1
2
0
1
1
1
2
1
0
0
0
1
2
1
2
1
2
0
0
2
2
0
2
1
1
1
1
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
2
0
2
0
1
0
0
0
1
1
2
2
0
0
2
0
0
0
1
2
0
1
0
0
2
1
0
1
2
2
2
2
0
0
0
1
0
0
2
0
0
1
0
0
1
0
1
2
1
2
1
0
1
2
0
2
0
2
2
2
1
1
2
1
1
2
2
1
0
1
0
0
1
1
1
0
2
0
0
2
1
1
0
2
1
2
2
1
0
1
0
1
0
0
0
0
1
0
1
0
0
1
0
1
0
1
0
0
0
0
1
0
0
3
1
3
0
2
0
1
0
2
0
0
1
1
1
0
1
3
1
0
1
2
0
0
1
0
0
1
2
0
1
1
0
0
1
0
1
0
1
1
0
2
1
0
0
0
0
0
2
2
0
1
0
2
2
0
0
1
1
0
3
2
0
0
0
0
0
0
0
1
0
1
0
0
10
1
2
2
6
0
1
1
2
2
0
3
1
1
0
1
0
1
0
0
2
0
1
2
0
0
0
0
1
0
1
1
2
1
0
2
1
1
0
0
0
0
0
2
2
0
0
2
1
3
0
1
0
0
0
0
0
2
0
0
1
0
2
0
2
1
1
0
1
1
1
2
1
1
0
0
0
0
1
0
0
1
0
1
2
2
2
0
0
1
0
1
1
1
0
0
0
0
1
0
1
0
0
1
2
0
1
0
0
0
5
0
0
2
0
2
0
1
1
0
0
1
1
2
0
2
2
1
0
1
1
0
1
0
0
0
1
1
2
0
0
2
0
1
1
2
1
0
2
1
2
0
1
0
0
0
0
1
1
3
0
0
1
1
1
1
0
0
0
2
1
0
0
1
0
1
0
0
0
0
0
2
2
1
2
0
0
1
1
1
1
1
0
1
1
1
0
2
2
0
0
0
0
2
0
0
0
0
2
1
0
0
1
1
1
1
2
1
2
0
1
2
0
1
1
1
0
0
1
2
0
1
0
1
0
1
1
0
0
1
1
2
2
0
0
2
0
0
0
2
1
0
0
0
0
0
0
1
0
1
0
0
1
1
1
1
2
0
1
2
1
2
1
0
1
0
2
0
1
1
1
0
2
1
0
1
0
2
0
1
1
1
0
0
0
0
0
1
2
0
2
2
1
1
1
0
1
0
1
0
0
2
2
1
0
2
1
1
0
0
0
1
1
1
0
2
0
2
2
0
0
0
2
1
0
0
1
1
0
1
0
3
0
1
2
0
1
0
0
1
0
1
0
1
1
2
2
2
0
1
0
0
1
1
1
0
0
2
0
2
2
0
1
1
1
1
1
2
0
2
0
0
1
0
2
0
0
1
1
0
2
0
0
0
0
0
1
5
0
1
1
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
1
1
2
0
0
0
1
0
0
0
2
0
1
1
1
0
2
2
2
0
0
1
2
1
0
0
2
2
3
0
0
0
0
2
1
0
2
2
1
0
1
1
0
2
0
0
2
1
2
2
2
0
2
1
1
2
2
0
2
0
1
0
0
1
1
0
1
0
2
0
1
0
2
0
1
2
0
2
0
0
0
1
1
2
0
2
0
2
2
1
1
1
1
3
0
1
2
1
2
0
2
1
1
1
0
0
0
2
0
2
1
0
2
0
3
1
0
1
4
2
0
0
1
1
3
2
1
0
0
2
0
2
0
0
4
0
1
0
0
2
0
0
0
0
0
2
0
1
1
1
0
2
0
2
2
0
0
1
1
1
0
0
1
2
0
1
2
0
0
1
1
1
0
1
1
0
0
1
0
0
1
0
0
1
0
0
1
2
1
1
1
0
0
2
0
0
0
2
2
2
2
2
1
2
0
0
0
1
2
0
0
1
1
2
1
2
0
1
1
0
3
0
2
2
0
1
1
1
0
2
2
1
1
1
2
0
0
0
2
0
2
0
0
2
0
1
0
2
1
0
0
0
1
0
0
1
0
0
1
2
1
0
2
1
0
2
1
0
3
1
1
1
0
1
2
2
0
2
0
0
1
1
0
0
2
0
1
0
1
1
1
0
0
0
1
4
0
2
0
1
1
1
1
1
0
1
0
0
2
1
2
2
0
1
0
0
1
1
1
1
1
0
1
1
1
1
1
2
3
1
1
2
2
1
0
2
1
0
1
0
0
1
0
1
0
1
2
3
2
0
2
0
0
2
0
1
2
0
0
1
1
1
1
1
0
2
1
0
1
1
0
0
0
1
1
1
1
3
0
0
0
0
1
1
1
0
1
1
2
0
2
1
2
1
0
0
0
0
1
0
2
1
1
1
3
0
1
6
1
1
1
1
1
0
1
1
1
0
2
1
1
1
0
1
0
0
0
0
0
2
0
2
1
0
0
1
1
2
1
1
1
0
0
0
0
1
1
0
0
2
0
4
2
1
0
2
0
0
1
0
2
1
1
2
2
0
0
0
0
2
1
1
2
0
1
1
0
0
1
1
0
0
2
1
0
1
1
2
2
2
0
0
0
0
1
0
1
0
0
1
2
1
1
0
0
2
1
1
1
0
0
0
0
1
0
0
0
1
1
0
2
1
0
0
1
0
1
1
0
0
1
0
1
0
0
1
0
1
2
0
1
1
0
0
2
0
0
3
1
0
0
0
0
1
1
2
0
2
1
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
1
0
0
0
1
2
1
0
2
3
1
0
1
0
2
0
0
1
0
2
1
1
0
1
0
2
1
1
0
0
0
2
0
0
2
2
1
2
1
1
0
0
2
0
0
2
0
1
0
2
0
0
1
0
1
2
0
2
2
1
0
2
0
1
0
0
0
1
1
1
1
2
1
2
1
0
1
1
2
1
2
1
0
1
1
1
2
1
0
1
1
0
1
0
1
0
1
1
0
0
0
0
0
2
2
0
0
1
1
2
1
1
1
0
1
2
0
0
2
2
1
0
2
0
0
2
2
1
1
1
0
1
1
0
0
0
1
0
1
1
0
3
0
2
3
0
2
0
0
1
2
0
0
0
2
0
2
1
0
0
0
1
0
2
1
1
0
1
1
1
2
3
2
0
0
1
1
1
1
0
0
1
0
2
0
0
2
0
1
2
0
1
0
0
2
0
2
1
1
0
2
1
0
1
2
0
0
0
0
0
1
0
0
2
0
2
1
0
2
0
0
2
2
3
0
2
1
2
1
0
1
0
1
2
0
2
1
2
1
0
2
1
1
2
2
0
2
2
0
1
1
0
0
0
0
1
0
0
1
2
1
1
0
0
2
1
0
2
2
0
0
1
1
1
1
1
1
1
0
1
1
1
1
1
0
2
2
1
0
1
0
0
1
1
0
0
0
1
1
2
2
0
0
0
0
1
1
0
3
1
2
0
2
1
2
1
2
0
7
1
0
0
0
0
2
0
1
0
4
2
1
0
2
0
0
0
1
0
1
0
2
1
1
2
0
0
1
0
0
2
1
1
0
0
2
1
0
0
0
1
2
2
0
1
0
2
1
0
1
1
1
0
1
0
0
0
0
0
0
0
0
1
1
0
2
1
0
0
0
0
0
2
1
2
1
2
2
0
0
1
1
0
1
2
1
0
0
1
3
0
1
2
0
2
1
2
0
2
2
1
2
2
1
1
1
0
0
2
0
0
0
2
0
2
1
0
2
1
2
0
1
0
0
2
0
0
0
2
0
1
0
0
0
2
0
1
0
2
2
0
1
0
0
2
1
1
2
0
0
0
1
3
1
2
1
0
2
2
0
0
1
2
0
1
1
0
3
1
0
2
2
0
1
0
1
0
0
2
1
2
0
0
1
1
0
1
0
0
0
1
0
0
0
1
3
0
2
2
2
0
0
0
1
1
0
2
0
1
0
1
0
1
0
1
0
0
1
2
0
1
0
1
2
0
1
2
2
2
0
1
0
1
0
0
1
1
0
0
1
0
2
1
1
1
0
1
2
1
1
0
0
1
0
0
0
0
1
3
0
0
1
1
2
2
0
0
0
0
2
1
1
0
1
0
0
0
1
0
0
2
0
0
0
0
1
2
3
0
2
0
2
0
1
1
0
1
1
1
0
0
2
0
2
1
0
0
1
0
0
0
1
0
2
1
1
0
2
2
0
0
0
1
2
0
0
1
2
0
2
1
1
0
1
4
0
0
0
0
0
2
1
2
2
1
1
0
3
0
1
0
0
2
0
2
1
0
0
0
1
0
1
0
1
1
1
1
1
0
1
1
0
1
0
1
0
0
0
0
1
2
0
1
0
1
1
2
2
0
1
0
2
0
0
1
2
0
0
2
1
0
1
2
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
2
2
0
0
0
2
0
1
2
2
1
2
1
0
0
0
1
0
1
1
1
1
0
1
1
0
1
1
0
2
0
2
0
0
0
0
1
0
2
0
2
1
0
0
0
0
2
1
2
2
2
0
0
0
1
2
1
2
0
0
0
0
2
0
1
0
1
1
1
0
0
0
0
0
0
1
6
0
2
2
2
1
1
1
0
1
1
1
0
2
0
1
1
0
2
1
1
0
0
0
0
1
0
1
1
2
2
0
2
0
0
0
2
2
1
0
0
1
0
1
0
1
1
1
1
2
0
0
1
1
1
2
1
2
1
1
1
1
0
1
0
1
0
0
2
2
1
1
0
0
1
0
2
0
0
1
0
1
1
0
1
0
2
0
1
3
1
0
1
0
0
1
0
0
0
0
1
2
1
0
0
0
0
2
2
0
0
0
1
3
0
1
1
0
0
0
1
2
0
0
2
2
0
0
2
1
2
2
1
0
2
0
0
1
1
0
1
2
1
0
1
0
0
1
2
0
0
1
1
0
1
2
1
1
0
1
1
2
0
1
1
0
2
0
4
1
1
2
2
1
2
1
0
0
2
0
2
2
0
1
2
2
0
0
0
1
2
0
1
0
1
1
0
2
2
1
0
0
2
2
1
2
0
0
0
0
1
2
0
1
1
1
0
1
2
2
0
2
0
0
0
2
1
0
0
2
1
1
3
0
1
1
0
0
1
2
0
2
0
2
0
0
1
0
2
1
2
1
1
0
1
2
1
0
1
1
1
0
0
2
1
2
0
1
1
1
3
1
1
0
2
1
1
0
0
1
2
0
0
1
0
0
1
2
0
1
2
1
2
0
0
0
1
0
1
1
1
1
1
0
0
1
0
0
0
0
0
3
0
2
0
1
0
1
1
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
2
1
1
1
0
0
0
1
0
1
0
2
0
0
1
2
2
0
4
1
0
0
0
0
0
0
1
0
1
0
2
0
2
1
2
0
1
1
1
1
2
0
2
2
2
0
0
2
2
0
0
1
1
2
0
0
2
1
2
1
0
2
0
0
0
0
0
1
1
0
2
1
0
1
1
1
1
0
1
1
2
0
1
0
0
2
1
2
0
1
1
0
0
0
0
2
0
0
0
0
2
0
1
2
0
0
1
0
2
1
0
0
0
2
1
0
1
0
1
0
1
2
2
0
1
2
0
0
1
0
0
2
1
1
0
0
2
0
1
2
0
0
2
0
1
1
0
0
0
0
2
1
1
1
0
1
0
2
1
2
1
1
1
1
2
2
0
0
0
0
1
2
2
1
0
2
0
1
2
0
1
1
0
1
1
0
0
1
0
0
0
1
0
0
1
2
1
0
1
0
1
2
0
2
1
0
0
2
2
0
1
1
2
0
0
0
1
1
0
0
1
2
0
0
1
0
0
0
1
0
1
0
0
0
0
0
2
1
0
1
1
0
0
0
0
1
2
2
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
1
1
0
1
0
2
0
0
0
0
0
0
0
1
2
1
2
1
0
0
0
1
0
0
1
0
1
0
2
1
0
1
0
0
0
1
1
1
0
0
1
0
0
2
0
0
2
0
1
0
1
3
0
0
1
0
1
1
1
0
0
0
0
0
0
1
0
0
0
1
1
0
2
1
0
0
0
1
1
0
0
1
0
0
0
2
0
1
2
0
0
4
0
0
0
1
1
2
1
0
0
2
2
2
0
1
1
0
0
1
1
0
0
2
1
0
0
0
1
2
1
1
3
0
0
1
1
1
2
0
1
0
1
0
1
1
0
2
0
2
2
2
1
2
0
1
1
1
1
1
0
1
0
0
0
1
0
1
1
2
0
2
0
1
0
1
1
0
0
2
1
1
0
2
0
1
2
1
2
2
2
0
1
2
0
2
0
0
2
0
1
0
2
1
0
0
1
0
1
1
0
1
1
2
0
0
0
1
1
0
0
1
0
0
0
2
1
0
1
0
1
0
2
0
1
1
0
1
0
0
2
0
0
1
2
2
0
0
0
2
1
1
0
0
0
1
2
0
2
0
0
2
0
0
0
2
1
1
0
1
0
0
3
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
2
1
0
1
1
0
1
1
2
2
0
1
2
2
0
2
0
0
0
0
2
1
0
0
0
2
0
0
1
1
0
2
1
0
1
1
1
2
2
1
0
2
0
0
1
1
0
0
1
1
1
2
2
0
0
0
1
2
0
1
2
2
2
0
2
0
1
0
1
0
2
2
2
1
0
0
0
0
0
0
1
0
1
2
2
0
0
2
2
0
0
2
0
1
2
0
1
0
1
0
0
0
0
2
0
0
1
1
1
0
1
1
0
1
2
1
1
1
2
0
2
0
1
1
0
2
0
0
1
0
0
0
0
1
1
1
2
1
0
1
0
6
0
0
2
0
2
1
0
1
2
0
1
1
0
0
2
2
1
0
2
0
0
1
1
0
1
1
2
0
0
0
0
1
2
2
0
1
1
0
1
1
0
2
0
1
0
1
0
0
1
0
2
2
0
1
2
1
2
0
0
1
1
1
0
0
0
0
1
1
0
0
1
2
0
1
1
1
1
6
1
0
0
1
0
1
0
0
0
1
1
0
1
2
3
1
2
0
0
0
0
2
0
0
2
2
0
1
2
1
1
0
0
0
1
0
0
0
2
2
0
0
2
0
2
1
0
1
1
1
0
0
0
2
0
0
0
0
1
0
1
2
1
0
1
1
0
0
1
0
1
0
2
3
2
1
2
1
0
0
0
0
1
1
0
2
0
0
1
1
2
2
2
1
0
0
2
1
1
2
1
1
2
2
1
2
0
1
0
0
1
2
1
1
1
0
2
0
2
2
0
0
0
0
0
0
2
0
0
0
2
2
1
2
2
2
0
1
1
1
2
0
1
1
1
0
0
1
2
3
2
1
0
0
2
0
0
1
0
0
1
0
2
0
1
0
0
0
0
1
2
1
0
1
1
2
1
2
0
1
0
1
2
1
1
0
0
0
4
0
0
1
1
2
2
1
0
0
0
0
1
0
0
2
2
0
1
2
2
2
0
2
0
3
1
1
0
0
2
2
2
2
1
0
3
1
1
0
2
2
0
2
1
1
1
1
0
1
0
0
0
1
0
0
0
0
2
0
1
0
1
1
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
1
1
0
0
0
0
2
0
1
0
0
1
0
1
0
0
0
0
1
2
1
2
1
0
1
0
1
0
1
1
1
0
0
2
2
0
0
1
2
2
1
1
0
1
0
2
2
0
1
2
0
0
0
1
0
0
1
1
1
1
2
0
1
0
2
1
2
1
1
1
0
0
0
0
2
1
1
0
0
2
0
0
1
2
2
1
1
0
0
1
0
0
1
1
0
1
0
2
0
0
1
2
0
0
0
0
1
0
1
1
0
1
1
1
1
2
0
0
1
0
0
2
1
0
2
1
0
2
1
1
1
1
0
2
1
1
0
1
1
1
1
2
1
0
1
1
1
0
0
2
2
2
1
0
1
0
0
2
0
0
0
0
1
1
1
0
2
1
0
0
0
1
1
2
2
2
0
1
0
1
1
2
0
0
0
2
1
0
4
1
3
2
1
1
2
0
0
0
0
0
0
2
0
1
0
2
0
2
0
1
2
1
2
2
0
0
1
1
0
0
1
2
0
0
2
0
0
0
0
0
1
1
1
0
1
1
0
1
1
0
1
0
1
0
0
1
0
3
1
0
0
0
0
2
1
2
0
2
0
1
1
0
0
0
1
0
1
0
2
0
2
3
1
1
0
2
1
1
2
0
1
2
0
1
1
1
0
1
0
0
1
0
1
2
2
0
2
1
2
2
1
0
0
0
2
0
1
2
0
2
2
1
0
2
1
0
2
1
0
0
0
1
0
1
1
1
0
1
1
0
2
0
2
0
1
0
0
1
0
0
0
1
1
1
1
1
0
0
1
2
0
1
0
0
2
0
2
0
1
1
2
1
0
0
1
1
2
0
0
2
2
2
2
0
0
0
0
1
0
0
1
1
2
0
0
1
0
2
1
2
0
0
1
0
1
2
0
2
2
2
3
2
0
1
0
0
3
1
1
1
0
0
2
2
0
1
1
1
0
1
1
1
0
1
2
0
0
1
2
1
0
0
2
0
0
1
1
0
1
1
2
0
1
1
0
2
0
1
1
0
0
0
0
0
0
1
0
0
1
2
2
0
1
1
0
2
0
0
0
0
1
0
3
2
2
0
1
0
1
0
2
1
0
0
0
0
0
2
0
0
2
0
1
1
2
0
1
2
0
1
0
0
0
0
2
0
1
1
2
3
1
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
2
3
0
0
0
0
0
2
0
2
0
0
0
2
1
0
1
1
0
2
2
1
0
0
0
1
1
2
1
0
0
1
0
0
1
0
0
0
0
0
3
1
0
1
1
0
0
2
2
1
2
2
1
1
0
1
0
1
2
0
1
0
0
0
1
0
2
0
0
2
1
0
1
0
1
1
0
2
1
2
2
1
2
1
1
1
1
2
0
0
0
0
1
2
0
0
2
2
0
2
2
0
1
2
1
2
0
0
0
2
2
0
0
0
0
0
0
0
0
1
2
0
0
3
1
1
0
1
3
1
0
1
2
1
1
0
1
1
2
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
1
1
3
1
2
2
2
1
2
1
1
2
1
1
1
1
1
2
0
2
1
1
1
0
1
0
0
1
2
0
0
1
0
0
1
2
2
0
1
1
1
2
2
1
0
1
1
0
2
0
0
0
0
0
0
1
1
0
0
1
2
2
0
0
1
1
2
1
0
0
1
0
0
0
0
0
0
0
2
2
1
1
2
0
1
0
3
0
0
0
1
0
1
1
0
0
1
2
1
1
1
1
2
0
0
1
0
2
2
0
0
1
1
1
2
0
1
1
1
0
1
2
1
2
0
1
1
1
2
0
1
0
1
0
2
0
0
0
1
2
1
1
0
0
1
1
2
0
0
0
2
1
1
0
1
1
1
0
2
1
1
1
3
1
1
0
2
2
0
0
0
0
2
1
1
2
0
2
2
1
0
0
1
2
1
2
1
3
1
1
2
0
0
2
0
0
0
1
0
2
2
0
3
0
0
2
1
1
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
2
0
2
1
0
1
2
2
2
1
0
2
1
2
1
0
1
2
0
0
1
1
0
0
0
0
0
0
1
1
1
1
2
2
0
0
3
1
2
2
0
1
0
1
0
0
0
2
1
1
0
0
4
1
2
0
2
0
1
0
2
2
1
1
0
1
0
2
0
4
1
1
1
1
0
2
0
2
1
0
1
0
0
1
2
1
0
0
0
0
0
2
0
1
0
2
0
0
0
1
0
0
1
0
0
2
2
0
0
0
0
0
0
1
0
0
2
0
2
0
0
1
0
1
3
0
0
0
1
1
0
0
1
1
1
0
0
1
1
1
1
2
0
0
2
0
0
0
0
0
0
0
2
0
1
1
4
2
0
0
0
1
2
0
2
0
1
3
0
2
0
1
1
0
1
1
0
0
2
1
1
2
1
1
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
1
1
0
1
0
1
0
1
1
3
2
0
1
2
0
1
0
1
0
0
2
0
0
0
1
0
0
1
2
0
0
2
1
1
1
2
0
1
1
1
0
2
0
0
2
2
0
2
1
0
1
0
1
0
1
0
0
1
0
0
1
1
0
0
1
0
0
1
0
1
0
3
1
1
2
0
1
0
0
0
1
1
0
2
0
1
0
2
0
2
0
0
0
0
2
2
0
0
0
0
1
1
0
2
1
1
0
0
0
1
2
1
0
2
1
0
1
2
1
0
0
2
3
1
1
0
1
0
2
1
2
0
0
1
0
0
2
1
0
1
3
0
0
2
1
0
0
0
0
0
0
0
0
0
1
1
1
2
2
0
2
0
2
1
0
2
0
0
1
2
0
2
0
0
0
0
1
1
0
1
2
1
1
1
2
1
1
0
0
0
1
2
0
1
1
1
0
1
0
0
0
1
0
0
2
1
1
1
0
1
0
1
1
0
0
1
0
2
2
2
1
1
1
1
0
2
2
0
0
1
1
2
2
0
0
2
2
0
2
1
1
0
2
1
1
0
2
0
2
0
2
0
0
2
0
1
2
0
1
0
1
1
1
1
2
1
0
0
0
1
0
0
1
0
0
1
0
1
11
1
2
2
1
1
0
1
0
1
1
0
1
0
0
0
2
0
0
0
2
0
2
0
1
1
1
2
0
0
1
1
2
0
0
2
0
1
0
2
0
0
1
2
2
0
1
0
0
3
1
0
2
1
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
2
1
1
3
0
1
1
0
1
0
0
0
2
0
1
1
2
1
0
2
1
1
2
1
1
0
2
0
2
2
0
1
2
2
1
0
0
0
0
0
1
0
1
0
1
0
1
2
1
0
0
1
2
0
1
1
0
1
3
0
1
0
2
1
0
1
0
0
2
1
0
2
2
2
0
1
2
1
1
0
0
1
0
1
0
2
1
0
2
0
2
1
1
1
0
0
2
1
2
0
0
0
1
2
0
0
1
1
0
0
1
0
1
1
2
0
1
0
0
2
0
2
1
0
1
1
1
2
1
3
0
1
1
0
0
2
1
1
0
0
0
0
1
1
0
1
2
1
0
2
2
2
1
1
2
0
2
1
0
0
0
1
0
0
0
2
0
2
1
0
0
1
2
0
0
0
0
2
1
2
1
0
0
1
2
0
1
1
0
1
2
0
1
1
1
0
0
2
0
2
2
0
1
1
0
1
1
0
3
0
1
0
2
1
0
1
0
1
2
2
2
0
1
1
0
1
2
0
2
0
2
2
0
1
0
2
1
1
2
0
1
0
1
1
0
0
0
0
1
0
1
2
0
0
1
1
1
0
0
1
1
1
1
2
0
2
0
0
1
1
2
2
0
1
1
0
1
0
2
2
1
0
0
2
3
1
0
0
0
1
0
2
0
0
0
0
0
2
1
1
0
1
0
1
0
1
1
0
0
2
2
2
1
1
0
2
1
0
2
1
2
0
1
3
0
0
0
1
1
0
1
0
1
2
0
1
1
0
2
0
0
2
0
0
0
1
2
1
1
1
1
0
1
1
0
2
0
2
1
2
0
1
0
0
1
2
0
1
1
1
2
2
0
0
2
0
2
0
0
2
1
2
0
1
0
1
1
0
0
2
1
1
0
1
2
0
2
0
1
0
1
1
2
1
2
0
2
0
1
0
0
3
0
0
2
0
0
7
2
0
0
0
0
0
0
1
2
1
1
1
2
1
2
2
1
0
0
1
1
0
0
1
1
0
1
0
0
0
0
0
1
0
1
2
2
1
1
0
1
1
1
0
2
1
1
0
0
1
1
0
0
0
1
0
0
0
0
1
1
2
0
0
0
1
1
1
3
2
1
0
0
0
0
1
1
2
0
2
1
0
0
1
2
2
1
0
2
1
2
0
2
0
1
1
0
0
1
0
1
1
1
1
0
0
2
1
2
0
1
2
2
1
1
1
2
1
1
0
2
2
1
0
1
1
0
2
0
1
1
1
1
2
2
0
0
1
0
0
0
0
2
0
0
0
1
0
1
2
1
0
0
2
3
1
0
2
2
0
1
0
0
1
2
1
2
2
3
1
2
0
0
0
1
0
0
1
0
2
0
1
0
0
0
1
0
1
1
1
0
1
1
1
0
1
1
0
1
2
2
0
2
2
2
0
4
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
3
0
0
1
1
0
1
1
0
2
2
2
2
1
1
2
1
1
0
1
1
0
1
0
0
1
3
1
0
0
2
2
1
2
0
2
1
1
1
2
1
1
2
1
0
0
0
2
3
0
1
0
1
2
0
3
0
0
2
1
1
2
0
0
1
1
1
0
0
0
0
2
0
2
1
0
0
1
0
1
0
0
1
0
1
1
1
2
0
0
2
1
1
1
0
2
1
2
1
1
0
2
1
2
0
0
0
1
2
1
1
0
0
1
0
1
0
2
0
1
0
0
0
0
0
1
0
0
1
0
1
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
1
1
1
0
2
1
1
2
0
0
1
1
0
1
1
1
1
0
1
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
2
1
2
0
0
2
1
0
1
0
1
2
2
1
2
0
2
1
0
0
0
0
0
2
1
2
0
2
0
1
1
1
1
0
1
1
0
0
2
0
2
0
1
2
2
0
2
0
1
1
1
0
0
1
0
2
4
0
0
0
2
2
0
2
1
0
0
2
0
0
2
0
1
0
1
2
1
0
2
1
1
1
0
2
2
1
0
0
2
2
0
2
0
0
1
0
2
0
0
0
1
1
1
1
0
2
1
0
0
1
0
1
0
0
0
1
2
0
0
2
3
1
2
0
2
1
2
1
2
2
2
1
1
0
2
0
1
1
1
0
2
1
1
2
1
2
2
2
0
0
0
2
1
0
1
2
2
0
0
1
1
0
0
1
2
2
1
2
0
2
1
1
1
0
1
1
0
1
2
1
2
1
1
0
1
0
0
1
2
0
0
1
0
2
1
1
1
0
0
2
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
2
0
1
0
0
0
0
0
2
1
1
0
1
1
1
1
2
1
1
1
3
0
2
0
1
1
2
0
1
0
0
0
0
2
0
1
0
0
0
1
0
2
1
1
0
2
2
0
2
1
0
2
1
2
0
2
1
0
2
3
1
2
0
0
0
1
1
2
2
0
2
0
2
0
1
2
1
0
1
0
0
1
3
0
1
0
2
2
1
0
0
0
0
1
0
0
1
0
2
1
1
1
0
0
2
1
1
1
1
1
0
0
0
1
0
0
1
0
1
3
0
0
1
1
0
3
0
2
1
0
0
0
0
1
0
1
2
1
0
0
1
0
1
1
2
0
2
0
0
0
0
0
1
1
1
0
1
1
0
2
1
1
1
2
0
0
0
1
0
2
1
0
2
0
1
0
0
1
1
1
0
0
1
0
1
1
1
0
2
0
0
1
1
1
1
2
2
1
0
0
0
0
1
0
0
2
1
2
0
1
1
1
1
0
0
1
1
2
3
0
1
2
0
1
0
1
1
1
2
0
1
2
0
2
2
1
1
2
1
1
0
1
0
1
3
1
2
2
1
0
2
4
3
1
1
1
1
0
1
2
1
1
1
0
2
0
1
2
1
0
0
0
2
1
1
0
2
2
0
3
1
2
0
0
0
0
1
0
1
0
1
0
1
1
0
2
2
0
1
0
1
1
0
0
3
0
2
1
1
1
2
0
0
0
0
0
1
0
0
2
0
0
1
2
0
1
0
0
0
2
0
3
0
0
1
0
0
0
0
0
1
2
0
0
2
2
0
2
2
0
1
1
1
1
0
0
0
0
1
1
2
0
2
2
3
0
0
0
0
1
0
0
2
1
1
1
0
1
2
0
0
1
1
0
1
1
1
0
0
2
0
2
0
0
0
0
1
2
1
2
2
0
0
1
0
0
0
2
0
0
2
0
1
1
2
0
0
0
2
1
0
1
0
2
1
0
0
1
1
0
0
0
0
0
1
1
1
1
0
0
2
2
2
1
0
1
2
0
1
0
2
0
1
1
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
2
1
1
0
1
0
1
0
0
1
0
0
1
2
0
2
0
0
0
1
0
1
0
0
0
1
0
1
2
0
2
1
1
0
0
2
0
1
1
0
1
0
0
1
1
1
1
1
1
2
0
0
1
1
0
2
2
0
1
0
0
0
0
2
1
1
1
1
2
1
0
1
0
0
2
0
1
0
1
0
0
2
2
0
0
1
2
1
0
0
2
0
3
0
0
1
0
0
0
1
0
2
0
1
1
2
0
2
2
2
0
3
0
0
0
0
0
2
1
1
1
0
1
2
0
1
2
0
1
1
1
2
1
0
1
0
0
0
2
1
0
0
0
1
0
0
1
1
0
2
0
0
1
0
1
0
0
0
0
2
1
1
2
1
1
1
0
0
1
2
0
1
0
0
0
0
0
1
2
2
1
2
0
0
0
1
0
1
0
0
1
1
1
2
0
0
0
0
0
0
0
2
2
0
0
1
0
0
1
0
0
0
2
2
1
1
1
0
0
1
0
1
0
1
1
0
3
0
0
1
1
1
2
1
0
0
2
2
1
1
0
0
1
0
0
0
1
2
2
0
0
0
0
0
0
0
1
1
0
0
0
2
2
1
1
0
2
0
1
2
0
1
1
0
2
2
2
0
0
0
0
0
0
0
0
1
0
2
0
1
1
2
3
1
2
1
3
1
1
0
0
0
0
0
1
1
2
1
0
2
0
0
1
0
1
1
0
2
1
2
1
0
1
0
1
1
1
0
0
1
0
0
0
2
2
0
0
1
0
0
0
0
0
1
0
1
0
0
2
0
2
0
0
1
1
4
4
2
0
2
1
1
1
0
1
0
0
1
1
0
1
1
1
0
0
0
2
0
2
0
2
0
0
0
1
0
1
0
2
1
1
2
1
0
1
0
1
1
1
0
1
0
1
1
0
0
0
2
0
1
1
0
1
0
1
1
0
0
0
0
1
2
0
2
3
0
0
2
0
0
1
0
0
1
0
2
0
1
1
0
0
1
0
2
0
0
3
0
0
1
1
1
0
2
1
0
1
1
1
0
1
0
2
0
2
1
1
1
1
0
1
2
1
0
0
1
0
1
1
0
2
0
1
0
0
2
0
0
1
0
0
0
0
2
0
0
0
2
2
1
1
0
1
0
0
0
0
0
0
1
2
1
0
0
1
1
0
2
2
0
1
0
1
0
1
1
0
0
2
1
0
0
0
0
1
0
2
1
0
1
3
0
2
1
1
1
0
1
1
2
1
1
0
1
2
0
1
0
1
1
0
0
0
0
0
1
1
0
1
1
1
1
0
0
0
0
0
1
0
0
5
0
0
1
2
0
1
0
2
1
0
2
0
0
1
1
2
2
2
0
1
1
2
2
1
1
1
0
1
0
0
0
0
7
2
1
1
2
0
0
0
0
2
1
0
0
1
1
0
0
0
0
1
0
1
1
1
1
0
2
1
0
2
1
4
2
0
1
1
1
0
1
1
0
0
0
0
0
0
2
1
0
0
2
0
1
0
0
2
0
1
0
2
0
1
1
0
1
2
2
0
1
2
0
1
0
0
1
1
1
0
1
0
0
1
0
0
0
0
0
2
1
1
0
0
0
0
4
1
1
0
1
0
0
1
1
0
2
0
0
0
0
1
0
0
1
0
0
2
1
1
0
1
0
1
0
1
2
1
0
0
0
1
2
0
0
1
2
0
0
0
0
0
1
1
2
0
2
2
0
0
0
0
0
1
0
1
1
0
1
2
0
2
1
0
0
1
0
2
2
0
1
1
2
0
2
1
1
0
1
1
2
0
2
2
1
0
2
4
2
0
0
0
1
0
2
1
0
0
1
1
1
1
2
2
1
2
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
1
0
2
1
0
2
7
0
1
0
2
2
1
1
0
2
2
0
1
2
2
0
1
2
1
4
1
2
1
1
1
1
0
0
2
0
0
0
1
0
1
0
1
1
0
2
0
0
1
0
0
2
1
2
0
2
1
0
0
0
1
0
0
0
0
0
1
1
2
2
2
3
0
0
0
0
0
2
2
0
0
2
0
0
1
0
0
1
0
0
1
3
1
1
1
1
1
0
0
1
1
2
0
1
0
2
0
0
1
2
0
2
0
0
0
0
1
2
1
0
2
2
2
0
2
0
0
0
0
2
2
3
0
0
2
0
0
1
0
1
1
1
0
1
0
0
1
0
1
1
0
2
1
1
0
0
0
0
0
0
1
0
1
0
0
0
2
1
1
2
1
2
1
2
1
0
1
1
1
1
0
2
1
0
0
0
0
1
2
1
1
1
0
0
0
0
1
2
0
1
0
2
0
0
0
2
2
2
2
1
1
1
1
1
0
1
0
0
0
3
1
0
0
2
2
1
0
2
2
1
2
0
0
2
0
1
1
0
1
0
1
0
1
0
2
1
2
0
2
1
0
1
0
1
0
2
1
0
1
2
0
1
2
1
0
2
0
2
0
2
0
0
1
0
1
0
1
2
1
0
0
1
0
0
0
2
0
0
2
2
0
0
0
1
1
0
0
0
0
0
2
2
1
1
0
0
0
2
0
0
1
0
2
2
2
1
1
1
1
0
2
0
0
1
0
0
0
0
0
1
0
0
0
1
2
0
0
2
1
0
0
2
2
2
0
0
0
1
1
1
0
1
1
0
0
1
0
0
2
1
0
1
0
0
1
0
1
2
0
1
0
2
1
0
0
1
0
1
0
0
2
0
2
1
0
0
1
1
0
2
1
0
0
1
0
2
2
0
2
2
1
2
0
1
0
0
0
0
1
1
1
1
0
2
1
0
2
0
0
0
1
2
0
0
1
0
2
0
1
0
1
2
0
4
2
1
1
0
1
2
1
1
1
1
0
0
0
0
1
1
0
0
1
1
2
1
0
0
1
0
1
1
0
0
0
1
0
1
2
2
1
0
1
2
1
0
0
1
1
2
0
0
1
0
0
1
2
0
0
0
2
0
1
0
1
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
1
3
1
1
0
0
1
0
1
1
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
2
1
1
0
0
1
0
1
1
2
0
1
0
1
2
0
0
1
2
2
1
0
1
0
2
0
1
0
1
0
1
0
1
1
2
0
1
1
1
0
1
1
1
0
1
0
1
0
1
0
0
1
1
1
2
0
1
0
1
1
0
1
1
0
0
1
0
0
1
2
1
3
2
2
0
1
1
1
0
0
0
2
1
0
1
1
0
0
0
1
2
0
0
0
1
0
2
0
1
0
1
2
0
1
2
2
0
1
1
1
0
1
2
0
0
1
0
2
0
0
0
0
2
1
0
1
1
1
0
1
2
2
0
0
1
0
2
1
1
1
0
2
1
2
1
2
2
2
3
2
1
0
0
1
0
2
1
2
1
1
2
0
0
0
1
2
2
1
0
1
2
1
1
1
0
1
1
0
2
1
0
0
1
2
2
1
1
0
0
0
1
1
1
2
0
1
0
0
0
2
2
0
0
2
1
2
2
1
0
2
1
0
0
0
2
0
0
0
0
0
1
2
2
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
1
1
2
1
0
1
2
0
2
1
1
2
1
0
1
1
0
1
1
1
1
0
1
0
1
1
1
0
1
1
1
0
1
1
0
2
2
1
2
1
2
1
1
0
2
0
2
0
1
0
0
3
2
0
0
0
1
0
1
0
1
0
0
0
1
0
2
0
1
2
1
0
3
0
0
2
1
0
0
1
1
0
0
1
1
2
0
0
1
2
2
2
0
0
0
2
1
2
0
0
0
2
2
0
0
0
2
1
2
0
2
2
0
2
2
2
1
0
0
0
1
0
2
2
1
0
0
0
1
1
0
0
1
2
0
0
1
0
1
1
2
0
0
1
1
0
0
2
1
0
2
2
0
0
2
0
0
2
0
0
1
0
0
1
2
0
1
0
0
2
2
1
1
1
0
1
0
1
0
1
2
2
1
1
1
1
0
0
0
0
0
1
2
2
2
1
2
0
0
0
0
2
2
2
1
2
3
0
0
1
1
0
1
0
2
1
1
2
0
1
1
1
1
1
1
1
1
0
0
0
2
1
0
0
1
0
2
1
0
0
2
2
1
1
0
1
0
2
1
2
1
0
2
0
1
1
1
0
0
1
1
1
2
1
1
0
1
0
0
1
1
0
0
1
0
0
1
1
0
0
0
1
1
1
0
1
1
0
1
0
0
2
1
0
1
0
2
0
1
1
0
1
0
0
2
0
1
0
2
0
1
0
1
2
1
0
0
1
0
0
1
0
1
1
1
5
2
0
0
0
0
0
1
1
0
0
0
0
1
0
1
1
1
2
0
2
2
2
1
1
0
1
2
1
0
2
1
0
1
0
0
3
0
1
0
1
0
3
0
1
0
0
2
2
1
1
0
0
0
1
0
3
2
0
0
2
4
0
0
1
0
2
1
0
0
2
0
1
1
1
1
0
0
2
0
0
1
1
0
1
0
1
0
0
0
0
0
1
0
2
0
0
2
2
1
1
1
1
1
1
1
1
2
0
0
1
0
1
2
1
1
1
0
2
0
2
2
0
0
1
2
0
0
1
0
2
0
0
0
1
0
1
1
1
1
2
3
0
0
0
1
2
0
2
0
0
2
1
0
0
1
1
0
0
0
0
2
1
1
2
1
2
0
1
1
0
0
1
0
0
0
1
0
2
0
2
0
0
1
0
0
0
1
1
0
0
3
1
1
1
2
0
0
2
1
2
1
2
0
0
1
1
1
0
1
0
0
2
0
1
2
0
1
2
2
0
1
1
1
0
0
0
0
0
0
0
0
1
1
0
1
1
1
0
1
0
2
0
0
0
1
2
0
0
0
2
1
1
0
0
0
1
0
0
0
2
2
2
1
0
0
2
0
0
0
1
2
0
0
1
5
0
1
1
0
1
2
0
3
2
0
0
0
0
0
2
2
1
1
1
0
1
2
0
1
0
1
1
2
3
1
0
0
2
1
0
0
2
0
1
1
0
1
0
0
1
2
0
1
0
1
1
0
1
0
0
2
1
0
1
2
1
1
0
1
1
1
0
1
1
0
1
1
0
1
0
0
1
0
1
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
1
1
0
2
1
0
2
0
0
0
0
1
0
2
1
0
0
0
0
1
1
1
2
0
1
0
0
0
1
0
0
1
1
2
0
0
1
0
1
1
0
1
1
0
0
2
1
0
0
1
0
1
0
0
2
0
0
1
0
2
1
1
0
1
0
2
0
1
0
1
2
0
2
0
0
1
0
1
0
0
0
1
0
1
0
0
0
2
0
1
2
0
0
1
0
0
1
2
0
0
0
0
1
0
2
2
0
2
2
1
1
0
0
0
0
2
1
0
0
0
1
2
2
0
0
1
0
1
0
0
1
1
0
0
2
2
1
0
2
0
0
2
1
1
0
1
2
1
0
1
0
0
4
2
0
1
1
0
1
1
1
0
1
0
0
2
0
0
0
0
1
0
2
0
0
3
2
1
2
2
3
0
2
0
0
0
1
2
2
0
1
3
1
1
0
1
2
0
2
0
1
2
1
2
0
0
1
2
1
0
1
1
0
1
4
0
0
1
0
1
1
0
2
0
1
0
3
1
0
1
1
0
2
2
0
0
1
0
1
1
1
0
2
2
0
0
0
2
0
0
1
0
2
0
2
1
0
1
0
0
2
1
0
1
0
0
0
1
0
0
1
0
0
0
0
2
2
1
2
1
0
2
0
2
0
0
1
1
0
1
0
1
0
1
1
1
1
0
0
1
1
0
1
1
2
0
3
0
1
0
1
0
0
2
0
2
1
0
0
0
0
0
2
1
1
2
1
0
0
0
3
1
0
0
2
1
0
1
1
1
0
2
0
0
1
1
2
0
0
0
1
0
4
0
0
0
1
2
0
0
1
0
0
1
2
0
0
0
0
0
2
0
1
1
1
0
0
0
1
1
1
2
1
1
0
1
2
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
2
0
0
1
2
1
1
0
2
1
0
1
0
1
0
0
0
2
2
2
0
0
2
0
2
2
0
0
2
0
0
0
1
0
0
2
1
2
1
1
0
0
3
1
0
1
1
0
3
1
2
2
0
0
0
1
1
1
2
1
0
1
0
1
1
0
1
1
1
0
1
1
0
1
1
0
0
0
0
1
2
1
2
0
0
1
0
1
1
1
0
2
1
2
0
2
2
3
1
0
2
0
1
1
1
1
2
2
3
1
0
2
0
2
1
1
0
0
1
1
1
0
0
0
2
1
1
1
0
1
0
0
2
1
2
2
0
3
0
0
1
1
0
0
2
2
1
0
1
0
0
0
0
0
1
0
2
2
1
1
0
2
0
0
1
0
1
2
0
0
0
1
1
0
2
0
0
1
1
1
0
1
1
1
0
1
1
0
3
1
0
0
0
2
0
0
0
0
1
2
0
1
0
1
0
1
2
2
3
2
1
0
0
0
2
0
0
1
3
1
0
0
0
1
0
1
1
1
1
0
1
1
0
0
0
1
0
1
4
1
0
0
0
1
1
0
1
2
3
1
1
3
0
3
2
0
0
0
2
0
0
0
0
0
1
1
1
1
1
0
1
2
2
2
2
1
2
1
0
0
0
1
0
1
0
2
1
1
0
1
0
0
0
0
0
2
0
0
2
0
0
3
0
1
0
2
0
1
0
1
0
0
2
1
1
1
0
1
3
1
0
0
1
0
1
2
0
0
1
1
1
0
0
1
0
1
1
0
0
2
2
0
0
2
0
0
1
1
2
2
1
1
1
1
0
0
1
2
1
1
1
1
0
1
1
2
0
1
0
0
1
0
0
0
0
2
2
0
1
2
0
0
0
2
0
0
0
0
1
1
0
0
1
1
0
0
1
0
0
1
3
1
0
1
1
0
3
2
0
2
0
2
0
1
0
1
0
1
1
2
0
0
1
1
0
0
1
1
0
2
0
0
2
0
1
0
0
1
0
1
1
0
0
1
0
0
0
2
1
2
1
1
1
1
0
2
0
2
0
1
2
0
1
0
1
0
0
1
0
3
2
1
0
0
0
0
1
1
0
2
3
1
0
0
2
0
1
1
1
0
0
2
2
0
0
0
1
2
1
2
2
1
1
0
1
1
2
0
1
0
1
2
1
1
1
0
1
0
0
2
1
1
0
1
1
0
0
1
2
0
1
1
1
0
0
0
1
2
1
2
0
1
1
0
2
2
1
1
0
1
3
0
0
2
0
0
0
1
1
1
1
0
3
1
1
0
0
1
0
2
1
3
0
1
0
0
2
0
0
1
1
1
1
2
0
1
2
1
1
0
2
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
2
0
1
2
2
2
1
0
2
0
1
2
1
2
1
0
2
1
1
1
0
1
0
0
1
1
0
2
2
0
2
0
2
2
0
1
0
2
1
0
2
1
2
2
0
1
1
0
2
0
0
1
0
1
2
2
0
2
1
1
0
0
2
0
2
0
1
0
1
1
1
1
0
1
0
2
0
0
2
2
2
1
0
4
0
2
2
1
2
0
0
0
0
1
0
2
1
0
1
0
0
1
0
2
0
1
1
1
0
2
0
3
0
1
1
2
2
1
0
0
1
0
0
0
0
1
0
0
1
0
0
1
2
0
0
2
1
0
0
1
2
0
2
0
0
1
0
0
1
1
2
0
1
0
1
0
1
2
1
2
0
0
0
0
0
1
0
2
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
2
0
0
1
0
1
2
0
1
1
2
0
2
0
0
1
2
0
0
1
0
1
2
1
1
0
1
1
3
0
2
0
1
1
1
0
0
0
1
0
1
1
0
1
0
0
1
0
1
2
1
0
0
0
0
1
1
0
0
1
2
1
2
2
0
0
0
0
0
1
1
4
0
0
1
2
3
1
1
0
1
1
0
0
0
3
1
0
0
0
1
1
2
2
1
0
1
2
0
1
0
1
0
2
0
0
1
0
0
1
0
0
1
0
0
0
0
2
1
1
0
1
1
2
2
0
2
0
0
2
0
2
0
0
1
2
0
1
2
0
0
3
1
1
2
0
0
2
0
2
1
1
0
2
1
1
1
1
1
1
1
0
0
2
0
2
0
0
0
1
0
2
0
0
1
0
2
1
0
0
0
2
2
2
0
0
2
0
0
1
1
0
1
1
1
0
0
1
0
0
2
0
1
1
2
0
2
1
2
0
0
1
2
0
1
0
0
2
1
0
0
0
1
2
1
0
0
0
2
2
0
2
0
1
2
1
0
2
2
0
0
2
1
0
2
0
0
1
2
2
0
0
2
1
0
1
1
1
0
1
0
0
0
1
1
2
0
0
0
1
0
2
1
1
1
0
1
0
0
0
0
2
0
2
0
0
2
1
2
1
0
2
1
2
1
0
0
1
0
0
0
2
0
1
0
2
2
0
0
2
1
1
0
2
1
0
1
1
1
2
0
0
4
0
1
0
1
1
2
0
0
1
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
2
1
2
0
1
1
0
1
2
2
2
1
0
0
0
2
1
0
1
2
2
2
0
0
1
0
0
1
0
2
1
0
1
2
1
1
4
0
2
2
1
0
0
1
0
2
0
3
1
0
0
1
1
1
0
2
1
1
1
1
0
1
0
0
2
0
0
0
0
2
1
0
2
0
1
0
1
0
1
0
0
1
0
1
0
0
1
0
0
0
0
1
2
1
2
1
2
0
2
2
0
1
1
0
2
0
2
1
0
2
0
0
0
0
3
0
0
2
1
1
0
0
1
2
0
0
2
2
2
0
2
0
3
0
0
0
0
0
1
1
1
1
0
0
0
2
0
1
0
0
0
2
2
0
0
1
1
2
1
0
0
1
2
0
1
0
1
0
1
1
0
2
1
1
0
1
0
0
0
1
1
2
1
0
1
2
2
1
0
2
2
1
0
0
0
1
0
1
0
0
2
1
0
2
2
0
2
1
1
0
0
0
2
0
2
0
2
1
0
0
1
1
0
1
0
1
2
1
1
0
2
1
1
1
2
0
2
2
0
2
2
0
1
1
1
0
1
0
2
0
2
2
0
0
0
0
0
0
2
1
0
0
1
1
0
0
2
0
0
0
1
0
0
1
0
0
0
1
2
0
2
0
2
0
2
1
0
1
0
1
1
0
1
2
2
1
2
0
0
0
0
1
1
0
1
1
1
0
0
0
0
0
0
0
0
1
1
1
2
0
3
0
3
4
1
0
1
5
2
0
0
0
2
0
1
2
1
0
0
2
1
0
0
1
2
0
0
1
2
2
1
0
1
0
2
0
1
2
0
0
1
3
0
2
0
2
1
1
0
0
1
2
0
2
1
0
0
0
0
0
0
1
0
1
2
1
2
0
1
1
1
1
0
0
0
1
0
2
0
0
0
1
1
1
0
1
1
0
3
1
2
1
0
0
2
0
1
2
2
1
0
1
2
1
0
0
1
2
2
2
2
2
2
0
0
0
0
0
0
1
1
1
1
1
2
1
0
0
2
0
1
0
1
1
1
0
0
0
1
0
1
1
0
2
2
0
1
0
1
0
0
4
0
1
0
2
0
1
1
0
2
0
1
0
1
0
1
0
0
0
0
0
2
0
2
1
1
2
0
2
1
2
0
1
1
0
0
1
1
2
2
0
6
2
2
2
0
1
0
0
2
0
0
0
0
2
0
0
1
2
0
1
1
2
1
1
0
1
2
2
0
0
1
1
1
0
1
0
1
0
3
2
2
1
0
2
2
0
2
0
0
0
1
1
1
1
0
2
1
1
0
1
0
1
0
0
0
0
0
1
0
2
3
1
1
0
0
1
1
3
1
0
2
0
0
0
0
1
0
0
0
0
0
0
1
2
1
2
0
1
1
0
2
0
3
1
0
1
1
0
0
2
2
0
1
0
1
1
0
0
4
2
1
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
1
5
1
2
1
1
1
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
1
0
0
0
0
2
0
2
0
2
2
0
1
0
0
2
0
1
1
0
1
1
2
0
1
2
2
1
2
0
0
2
0
2
0
2
0
1
1
0
0
1
1
1
4
0
1
2
0
0
0
1
0
0
0
2
1
0
0
1
0
0
2
0
0
1
2
0
1
2
2
1
0
0
3
1
0
0
1
2
0
0
0
0
1
0
2
2
1
0
1
1
0
0
0
1
2
2
0
1
2
0
1
0
0
0
0
0
0
1
1
2
0
1
2
1
1
1
0
2
1
0
0
2
0
4
3
0
2
0
1
1
0
2
0
0
1
0
0
0
2
1
1
2
2
1
2
2
0
2
0
1
1
2
0
2
2
1
2
1
2
1
0
2
1
1
0
0
0
2
1
0
0
1
0
0
1
1
0
1
1
2
2
1
1
0
2
0
0
1
2
0
0
2
0
1
0
0
1
1
2
0
0
0
2
1
0
0
0
2
1
0
0
2
0
1
0
0
2
1
1
0
0
0
1
1
1
0
2
0
1
1
1
1
0
2
0
1
2
2
0
2
0
1
0
0
0
1
0
0
1
0
1
1
1
2
0
4
1
1
1
1
0
0
0
0
0
2
1
2
0
2
1
0
0
0
0
0
0
1
0
1
1
0
0
2
0
0
0
0
1
0
0
1
0
0
0
2
0
3
2
1
1
1
2
1
0
0
2
0
2
0
0
0
0
2
0
0
0
2
0
0
1
0
0
2
1
1
0
0
0
0
1
1
0
2
1
2
2
0
1
0
0
1
0
0
1
1
0
1
1
1
1
1
1
0
2
1
1
1
0
0
2
2
0
1
0
0
0
1
0
2
1
0
1
1
0
2
1
1
1
0
1
2
1
0
0
1
0
0
1
2
2
3
2
2
3
0
1
2
1
1
0
1
0
0
1
1
0
1
1
1
2
1
2
0
2
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
2
0
2
1
2
1
1
0
1
0
1
0
1
1
0
1
2
2
1
1
1
1
0
0
2
1
1
1
2
1
0
1
1
3
0
0
0
2
2
0
2
0
2
1
0
0
1
0
2
1
1
2
3
0
1
0
0
2
4
0
0
0
1
0
1
2
2
3
2
1
0
0
0
1
0
1
2
0
1
1
2
3
1
1
1
1
0
1
1
1
0
1
1
1
2
0
2
0
0
0
2
1
0
2
0
2
2
0
2
1
2
1
2
0
0
1
1
2
0
0
2
0
0
0
1
0
0
0
1
1
2
0
1
0
1
1
1
2
1
1
1
0
1
0
2
2
0
0
3
0
2
0
0
0
1
1
3
1
0
1
1
0
0
0
0
1
1
0
1
2
1
0
1
1
1
1
0
1
2
1
0
1
1
0
1
1
0
0
3
1
1
0
1
2
0
3
0
0
2
1
0
0
0
1
1
0
0
0
0
0
1
1
0
2
1
1
1
1
2
0
2
2
0
1
1
1
1
0
1
1
0
0
2
1
1
0
1
1
1
2
1
3
1
2
1
1
2
1
0
0
2
0
1
2
0
2
2
2
0
2
2
3
0
0
0
2
0
0
0
3
2
2
0
1
1
2
0
1
0
0
0
0
1
0
0
2
0
2
0
1
1
0
1
0
1
0
2
0
0
0
0
0
0
1
0
4
0
0
0
1
2
0
1
0
0
1
0
0
2
0
1
2
2
2
1
7
1
1
0
1
0
0
0
0
2
0
2
1
1
2
2
0
0
1
1
1
0
1
0
0
1
2
1
0
1
1
2
2
2
2
2
1
0
0
1
0
2
2
0
1
0
0
0
1
1
0
0
0
0
1
0
1
2
1
2
1
1
0
0
2
0
0
4
2
0
0
1
0
0
1
0
0
1
1
1
0
0
1
1
0
0
0
3
1
0
1
0
2
0
0
0
1
0
1
1
2
2
2
0
1
1
0
1
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
1
1
1
2
2
0
0
3
1
2
1
1
0
4
0
2
1
0
2
0
0
1
0
0
1
2
2
2
0
1
2
0
0
1
2
1
1
1
2
0
0
0
1
0
2
1
1
0
0
0
2
2
1
1
0
2
1
0
0
0
0
0
0
1
3
0
3
2
0
0
0
2
1
1
0
3
0
1
1
1
2
0
0
0
1
1
1
0
0
0
0
1
2
0
1
1
1
0
0
0
1
2
0
0
0
1
0
1
1
1
0
1
1
2
1
0
0
0
0
0
2
0
1
1
0
0
0
0
1
1
0
0
1
1
0
0
1
1
2
1
0
0
0
0
1
0
1
0
1
0
1
0
2
0
2
0
2
1
1
0
0
1
1
3
0
0
0
1
0
0
1
2
2
0
1
2
0
0
1
0
2
0
0
1
1
1
0
0
3
1
2
0
1
0
2
0
1
2
0
0
1
2
2
0
0
1
1
2
2
2
0
1
1
0
0
0
2
0
1
0
0
1
1
2
1
1
0
0
2
0
0
2
0
1
2
1
0
2
1
2
0
2
2
0
2
1
1
3
1
0
2
0
2
0
2
1
1
1
0
0
0
0
1
2
2
0
0
0
1
0
0
0
1
1
0
2
2
0
0
0
2
2
0
2
0
2
0
1
0
1
1
0
2
0
0
0
2
1
1
2
0
1
1
2
0
2
0
1
0
0
1
0
0
1
2
0
2
0
0
1
0
0
1
1
1
0
1
0
1
0
0
0
1
1
2
2
2
0
1
1
1
1
0
1
0
0
1
0
0
1
2
1
2
1
0
0
1
2
2
1
1
2
2
0
0
0
1
0
0
1
2
0
0
0
1
1
0
0
0
0
0
1
1
1
2
1
2
0
1
0
1
0
1
0
0
1
1
0
1
0
1
1
0
2
0
0
1
1
0
1
4
0
0
0
1
1
0
1
1
0
0
2
0
0
1
2
6
0
0
1
2
1
0
1
0
0
7
0
1
0
1
2
3
1
0
1
0
2
0
1
1
0
2
1
1
1
0
2
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
1
1
2
0
2
1
2
0
2
0
0
1
0
0
1
0
1
1
1
2
0
0
1
0
2
0
3
1
0
3
1
2
0
2
1
1
1
0
1
0
1
1
0
1
2
1
1
0
0
1
2
0
0
2
0
0
0
1
2
0
0
0
0
2
0
1
1
0
2
0
0
2
1
2
0
1
1
1
1
0
0
1
2
0
0
4
1
0
0
1
0
1
1
0
0
1
2
0
4
0
1
1
1
0
0
1
2
0
2
2
0
2
0
1
2
0
0
0
2
1
1
1
0
0
1
2
0
0
0
2
2
1
0
1
0
1
2
2
2
0
2
2
1
0
0
2
2
0
1
2
1
0
2
1
2
1
1
1
0
1
0
0
1
1
0
1
0
2
1
1
0
0
0
2
1
0
1
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
1
1
0
1
1
1
2
2
0
1
0
0
0
2
3
0
2
1
4
0
0
0
2
1
1
2
1
0
2
0
0
2
1
2
1
1
2
0
2
0
0
1
0
0
0
1
0
0
2
1
0
1
1
2
0
1
1
1
0
0
1
0
2
0
0
0
0
1
0
1
0
0
2
0
1
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
1
0
1
2
1
0
1
0
0
0
1
0
3
0
0
2
1
0
0
1
1
1
0
1
0
0
0
2
0
0
2
0
0
1
1
2
0
0
3
0
2
0
1
0
0
2
1
1
2
0
0
1
2
2
2
1
2
1
2
1
1
0
2
1
0
1
0
1
0
0
0
0
2
1
1
0
0
0
0
1
0
0
1
0
1
2
0
2
1
1
1
2
0
2
1
1
0
0
1
0
2
0
0
2
2
2
2
1
1
0
2
1
1
1
1
1
1
0
1
2
0
0
1
1
1
1
2
0
0
2
0
2
0
0
0
1
1
0
1
1
0
0
0
0
0
0
1
0
2
0
0
0
2
2
1
1
1
2
2
0
1
1
0
0
0
0
0
0
0
2
0
1
1
0
1
0
0
0
0
1
0
2
2
1
2
2
0
0
0
0
1
0
0
2
2
1
0
1
0
1
1
1
0
2
1
0
2
0
0
0
1
1
0
1
2
3
2
1
0
0
0
0
1
2
0
2
1
0
2
1
1
1
0
1
1
1
0
2
0
2
0
1
1
1
2
0
1
1
1
1
0
2
1
1
1
0
1
1
2
0
2
1
1
1
0
1
2
0
1
2
0
0
1
1
0
0
1
0
1
0
0
1
2
0
1
2
2
1
0
0
1
1
0
2
0
1
0
1
0
0
3
1
0
2
0
2
2
0
0
0
1
1
1
0
0
0
0
0
2
0
1
1
0
0
2
2
0
1
0
0
0
1
0
1
1
1
0
0
0
1
0
0
2
0
0
0
0
0
0
1
2
0
2
0
2
0
2
1
0
3
0
2
1
1
0
1
2
0
2
0
0
1
1
0
0
0
0
1
1
0
1
2
0
0
1
1
1
2
0
0
0
0
0
1
2
0
1
0
1
2
2
0
2
2
0
0
2
0
1
0
0
0
3
3
1
0
0
1
2
0
0
0
0
0
1
0
1
3
0
1
1
2
0
0
1
0
1
0
1
0
0
0
1
1
1
1
2
1
0
1
2
0
1
1
1
5
3
2
1
2
1
1
0
2
0
2
1
0
0
1
0
2
1
0
2
1
2
1
1
0
3
1
2
0
2
2
1
1
0
1
3
0
0
2
0
1
1
1
0
0
0
0
2
5
0
1
1
3
0
0
0
1
0
0
0
0
1
0
1
0
2
1
1
1
0
0
2
1
1
2
1
1
0
2
0
1
1
2
0
1
2
0
2
0
1
1
4
0
1
1
0
0
1
1
0
1
0
1
0
1
2
0
2
0
0
1
1
2
1
1
2
1
2
1
1
0
0
1
0
1
2
1
0
0
0
0
2
0
0
1
1
0
1
1
0
0
0
1
0
1
2
2
2
1
0
0
0
2
0
2
1
0
0
0
1
1
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
2
1
0
0
1
0
0
0
1
0
1
2
2
0
0
0
1
0
0
1
0
2
0
1
0
0
1
0
1
2
0
1
2
1
0
0
0
1
2
3
0
0
3
1
0
1
0
0
1
0
1
0
1
0
2
3
0
3
0
1
1
1
1
2
0
0
0
0
0
2
2
2
2
2
1
5
0
0
1
0
2
3
1
0
0
2
0
0
0
0
2
0
1
1
1
2
0
0
1
0
1
1
1
0
1
1
0
0
0
1
0
0
2
0
2
0
1
1
0
2
3
1
1
2
4
0
0
0
1
0
1
2
0
0
0
0
1
1
1
1
1
1
1
0
0
1
0
2
1
0
1
1
1
2
0
0
0
0
0
0
1
0
0
2
0
0
1
1
1
1
2
1
0
2
0
1
0
0
1
2
0
1
0
0
0
1
1
0
1
1
0
2
1
0
1
0
0
1
0
1
1
1
1
0
0
0
0
0
0
0
0
0
2
0
0
3
4
1
0
0
1
2
1
0
1
0
0
2
2
0
2
0
0
0
3
0
1
2
0
1
1
1
1
2
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
2
0
1
2
1
0
1
0
0
2
1
1
1
2
0
2
1
1
1
2
0
1
0
0
1
0
1
0
2
1
2
1
2
0
0
1
0
0
0
1
0
1
0
1
1
2
2
0
2
0
0
0
3
0
0
0
1
0
0
1
0
0
1
2
0
0
0
0
1
1
1
1
1
0
0
0
1
0
1
0
0
2
0
0
2
2
2
1
0
0
1
2
0
0
0
0
2
1
0
1
2
1
1
1
0
1
0
1
0
1
1
0
0
1
0
0
0
0
1
0
2
1
2
0
1
0
0
1
1
0
0
1
0
2
1
0
0
2
1
0
1
0
1
2
2
2
2
2
0
1
0
1
1
0
0
0
1
0
0
2
2
1
0
0
2
0
1
2
0
0
0
0
0
0
1
0
1
1
0
1
2
0
0
0
2
1
0
0
1
0
1
1
2
1
1
2
1
0
1
2
2
0
1
2
0
0
3
1
2
1
1
1
0
2
0
1
2
2
1
0
0
0
1
0
1
0
1
2
1
2
1
0
1
2
1
2
1
1
1
1
2
1
0
0
0
2
1
1
1
1
0
0
0
2
3
0
0
0
1
1
0
0
2
0
0
2
1
1
0
1
1
0
2
0
0
0
2
0
1
0
0
2
2
1
2
1
1
1
1
3
2
1
2
2
0
1
1
1
2
0
1
1
0
1
1
0
2
1
0
2
1
0
1
0
0
1
0
0
0
0
0
0
0
1
2
0
1
0
1
2
0
0
1
2
0
0
0
2
2
0
4
1
0
0
1
1
0
0
1
2
0
0
0
1
0
1
0
2
0
1
0
1
1
2
1
1
0
0
0
0
0
1
2
0
0
3
0
2
0
1
2
3
0
0
2
1
1
1
1
2
0
2
1
2
0
0
0
0
0
0
1
1
0
1
1
1
0
0
0
1
0
0
1
2
0
0
0
2
1
0
0
1
2
1
2
1
1
1
2
2
4
0
1
4
2
1
2
0
0
0
2
1
0
1
0
0
0
1
1
0
1
1
1
1
1
2
1
0
2
0
1
0
0
2
1
2
0
2
0
1
2
0
0
1
0
1
2
0
0
0
0
2
1
1
1
0
1
0
0
1
2
1
2
1
1
2
5
2
0
2
1
1
0
1
0
0
0
0
0
1
1
2
0
2
0
2
0
2
1
1
1
0
0
0
1
1
0
0
1
1
1
0
0
1
0
1
0
2
1
1
1
0
0
2
0
0
1
0
1
0
1
2
1
2
1
1
1
0
1
1
1
0
0
1
1
2
0
1
0
0
2
1
0
1
1
5
0
0
0
0
1
0
1
0
2
1
0
0
0
1
0
0
0
2
0
0
2
1
0
0
2
0
1
0
2
1
1
0
0
1
0
0
3
2
2
1
1
2
1
0
0
1
1
1
0
0
0
1
2
1
0
2
1
2
1
0
2
1
0
1
0
0
1
1
0
1
1
1
1
2
0
1
0
1
0
2
1
0
2
0
0
1
0
0
1
0
2
0
1
1
0
1
2
1
0
2
0
1
0
2
1
3
1
2
1
5
0
0
2
3
1
0
2
0
2
2
2
1
2
1
1
0
2
1
1
1
1
0
2
0
1
0
0
2
1
0
1
0
1
0
1
0
1
1
0
2
0
0
0
0
1
1
2
0
0
0
2
1
0
1
0
1
0
0
0
0
0
2
0
0
0
1
2
1
2
0
2
0
0
1
4
0
0
0
0
0
0
1
0
2
0
1
0
2
0
2
0
2
0
0
1
2
0
0
0
0
1
3
1
0
0
1
1
0
0
1
0
1
0
1
1
2
0
2
0
0
0
1
1
0
0
1
1
1
1
0
0
1
2
0
0
2
2
1
1
1
2
1
1
0
2
0
0
1
0
2
1
1
0
0
1
0
0
0
1
0
1
2
0
0
1
2
1
1
2
3
0
1
1
0
1
2
2
1
0
1
0
1
2
1
1
0
0
0
0
0
2
0
2
0
2
1
1
1
1
2
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
2
1
1
2
0
0
2
0
0
1
1
0
0
1
0
2
0
2
1
2
0
2
0
1
0
0
1
0
1
1
1
0
0
0
0
2
0
2
2
0
0
1
0
0
0
1
4
0
0
0
0
0
0
0
0
1
0
1
3
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
2
1
1
1
1
0
1
0
0
1
0
1
0
1
2
0
2
1
0
0
0
1
2
1
1
0
1
0
0
1
0
0
1
0
2
0
2
1
0
2
1
1
1
1
0
2
0
0
0
0
0
1
0
0
0
2
0
0
1
1
1
1
1
2
0
0
2
0
0
1
2
0
1
1
1
0
1
0
1
0
0
1
1
2
0
2
2
0
1
1
0
1
0
1
0
0
0
1
2
0
2
2
0
0
0
0
0
2
2
1
0
0
0
1
0
1
0
0
2
0
0
0
0
0
1
1
1
1
3
2
0
0
2
2
0
0
0
0
5
1
2
0
0
0
2
0
1
0
0
0
0
0
0
4
0
0
0
1
2
2
1
0
1
1
2
0
0
2
0
0
1
1
0
2
0
2
1
1
0
1
0
0
0
0
0
2
1
0
2
0
0
0
1
1
0
0
0
1
2
1
1
1
0
0
0
0
1
0
1
1
1
0
0
1
1
1
4
0
0
1
0
0
0
0
2
1
2
2
4
0
0
0
1
0
1
0
1
1
2
0
2
2
0
0
3
0
0
2
0
1
1
1
0
2
2
2
2
1
2
0
0
0
2
2
0
0
1
0
4
1
1
4
2
0
2
0
2
1
2
1
0
1
0
0
2
2
1
0
1
2
0
0
1
0
1
1
0
0
1
1
1
1
0
1
1
0
1
0
0
1
0
0
2
0
0
2
0
0
0
0
1
1
0
0
1
1
0
0
1
0
1
2
1
1
1
0
0
0
2
1
2
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
2
1
1
1
1
1
1
1
1
1
1
1
2
1
0
1
1
0
0
1
0
2
0
1
0
0
5
1
0
2
0
2
0
0
0
2
1
0
0
1
0
0
1
0
0
0
0
0
1
2
1
1
0
1
1
2
1
1
0
0
2
0
1
0
0
0
2
2
0
0
0
0
1
1
0
0
0
0
1
0
2
0
0
2
1
2
1
1
0
0
0
2
1
0
0
1
4
2
2
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
1
2
1
1
0
0
0
1
2
1
0
2
0
0
2
1
1
1
1
2
0
0
0
1
1
0
2
2
1
0
1
0
2
2
0
0
0
1
0
0
1
1
1
1
1
1
0
0
1
1
1
2
1
2
1
2
0
0
0
1
2
0
0
0
1
0
2
2
0
0
0
2
0
1
0
0
0
2
0
0
0
1
1
2
2
3
0
2
0
1
0
2
0
0
1
2
0
0
1
0
0
1
1
0
1
2
0
1
1
3
0
1
0
0
0
1
0
2
2
2
0
1
0
0
1
0
1
1
2
2
0
1
0
0
0
1
0
1
0
1
1
3
2
0
0
1
1
0
0
0
0
1
1
0
1
1
0
0
1
1
1
1
2
0
1
0
1
0
1
1
1
2
1
1
1
1
2
1
1
1
2
0
0
0
2
1
1
0
1
0
2
0
0
0
1
1
0
0
0
2
1
1
1
0
0
1
2
0
2
1
1
0
0
1
2
0
1
2
0
1
1
0
0
2
1
0
0
1
0
1
1
2
1
2
0
1
0
0
1
0
0
1
2
1
1
0
2
0
1
0
0
1
0
0
0
1
1
0
2
1
0
0
0
0
0
1
1
1
1
0
2
1
1
2
0
0
1
2
1
2
0
1
0
1
1
0
2
0
2
1
2
0
1
1
0
1
0
0
0
0
2
0
1
0
0
3
0
2
0
0
1
1
2
1
2
2
1
2
1
0
1
0
0
0
0
0
1
2
1
0
2
0
1
0
2
1
1
0
2
0
1
0
0
0
5
1
1
1
3
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
2
1
2
0
0
1
1
1
0
0
1
1
1
0
1
0
1
1
1
0
0
2
2
0
0
3
1
0
1
0
1
0
0
0
0
0
1
2
0
1
0
0
3
0
0
1
1
0
1
0
1
1
0
1
2
0
1
0
2
3
0
2
0
0
2
0
0
1
1
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
3
0
1
0
1
1
2
1
0
0
2
1
0
1
0
0
2
0
0
1
2
3
1
0
0
4
1
0
0
1
0
2
0
1
0
1
1
0
0
0
1
1
0
1
0
1
0
0
0
1
1
2
0
2
1
0
0
1
0
0
1
2
1
1
1
2
0
0
0
0
2
2
0
0
0
0
2
2
0
2
1
0
0
2
0
1
1
1
1
1
1
0
2
0
1
2
1
1
0
4
0
2
0
1
0
0
0
1
1
0
1
1
0
2
2
0
1
1
0
1
0
1
2
1
2
0
0
0
0
0
1
0
1
0
0
0
1
2
0
1
1
0
2
0
1
2
2
0
0
0
1
1
2
0
1
1
0
1
0
2
2
0
1
2
1
0
0
0
2
1
2
0
2
1
0
1
0
2
0
1
0
1
0
1
1
1
0
0
0
0
0
1
1
2
0
1
1
1
2
2
1
2
4
0
0
0
0
0
1
1
1
1
0
0
0
0
1
0
1
0
1
0
0
0
1
1
2
0
0
0
0
2
2
0
0
1
0
0
0
1
0
2
1
1
0
0
0
2
2
0
1
1
2
0
0
1
0
1
0
2
1
1
1
1
0
0
0
2
1
2
0
0
1
0
1
0
2
0
1
0
3
2
0
2
0
1
0
1
2
2
2
2
0
2
0
0
0
2
2
2
1
1
0
2
0
1
0
0
0
1
1
1
0
2
1
0
1
1
2
0
0
2
2
1
1
1
2
2
0
0
0
0
2
0
0
1
0
2
1
0
1
1
0
1
1
1
0
0
1
0
0
0
1
1
1
2
0
0
2
0
1
1
0
0
0
2
0
1
2
0
1
1
2
0
0
0
1
1
0
0
1
2
0
1
0
0
1
3
0
0
0
0
0
1
1
0
4
0
0
0
0
0
1
1
1
1
1
1
0
0
0
0
0
0
0
1
0
2
1
0
1
0
0
0
1
2
1
1
1
1
1
0
0
1
1
1
2
0
0
2
0
1
2
1
0
1
1
0
1
0
1
0
0
3
1
1
0
0
0
0
0
2
0
0
1
2
1
2
0
0
2
1
0
0
1
1
1
2
0
1
0
0
0
0
0
0
0
2
2
2
1
1
1
5
0
2
0
0
1
1
0
0
1
0
2
0
1
2
1
0
2
1
0
2
1
0
2
0
2
1
2
1
0
0
1
2
1
1
2
0
0
1
2
0
2
0
1
0
2
0
0
0
0
0
2
0
1
1
2
0
1
1
1
1
0
0
1
1
1
0
2
1
0
0
0
1
0
1
2
1
0
2
0
1
1
2
0
2
1
2
0
2
0
0
2
0
1
1
2
0
1
1
1
0
1
0
0
0
1
1
0
2
1
1
0
1
0
1
0
1
1
0
0
0
0
0
0
1
0
1
0
0
2
1
0
2
0
2
1
1
1
0
0
0
1
0
1
0
2
0
1
1
0
0
0
0
1
0
2
0
1
1
0
0
1
0
1
0
2
0
1
0
0
1
0
1
0
1
0
0
0
2
0
1
0
2
2
1
0
0
0
0
1
2
1
1
2
0
1
0
1
2
1
1
0
0
0
2
0
1
2
2
1
1
1
1
0
0
1
1
2
1
1
1
0
0
1
1
2
2
1
0
0
2
1
2
1
2
0
0
0
1
2
0
0
1
0
1
1
1
1
1
0
1
0
0
2
1
2
0
0
1
0
0
2
1
1
0
1
2
2
2
1
2
0
0
2
2
1
0
1
1
0
1
1
0
1
1
0
2
1
1
2
1
0
0
2
0
1
0
0
1
0
0
1
0
1
1
1
1
0
0
0
1
0
1
0
0
1
2
0
2
0
2
1
0
2
0
0
0
0
1
0
1
0
0
0
0
1
1
1
0
1
1
1
0
0
2
1
0
1
0
1
0
0
0
2
1
0
2
0
1
0
1
3
0
0
1
1
2
0
1
0
2
2
1
1
2
2
1
0
0
0
0
1
2
0
0
2
2
1
0
2
1
0
1
1
2
1
2
1
0
1
0
1
3
0
1
0
0
0
0
1
2
0
0
0
1
1
2
0
1
2
0
2
1
0
1
3
0
1
2
0
1
1
0
0
0
1
0
4
0
2
1
1
1
1
1
0
0
2
0
0
2
0
1
1
1
2
2
0
1
0
2
1
2
0
1
1
0
0
0
2
0
0
0
0
0
0
2
1
2
0
1
0
0
1
2
1
2
0
0
2
2
1
1
2
2
0
1
0
0
0
0
0
1
1
2
0
1
1
1
0
1
0
1
0
1
1
0
0
0
2
0
1
0
0
0
0
2
1
1
1
0
2
0
0
0
0
0
0
0
1
1
1
0
0
0
0
2
0
0
2
1
0
2
0
1
2
0
0
0
0
0
1
0
0
0
2
0
0
1
2
1
1
3
0
1
0
1
2
2
1
0
1
0
1
2
1
0
1
2
1
2
2
1
0
2
2
0
0
1
0
0
1
2
0
0
0
0
1
0
1
2
1
2
0
1
0
1
2
0
0
2
0
1
0
2
1
2
2
0
2
0
0
0
0
0
1
0
0
1
0
0
1
2
0
0
2
1
2
0
1
2
2
0
0
1
1
0
0
0
0
0
0
0
1
2
0
2
1
0
2
2
0
0
0
0
1
1
2
0
2
0
0
1
0
1
1
0
2
0
0
2
0
1
1
1
0
1
1
0
0
0
0
1
1
1
1
1
2
0
0
0
0
1
3
2
1
1
2
1
0
0
2
1
1
2
1
0
0
1
2
2
1
2
0
1
0
0
3
3
2
0
0
0
1
1
1
0
1
2
0
0
1
0
1
1
0
0
9
0
0
0
0
0
1
0
0
1
0
2
1
0
1
0
1
0
2
0
0
1
0
2
1
0
0
0
2
1
0
0
0
3
2
0
0
2
1
0
2
2
0
1
2
0
1
2
0
1
1
0
0
0
2
0
0
0
0
2
0
0
1
1
1
2
2
2
1
2
0
2
1
1
0
2
1
0
2
0
2
0
1
0
2
0
0
0
1
0
0
0
1
1
2
1
1
1
2
0
2
0
2
2
1
0
1
0
0
0
0
0
0
1
0
0
1
1
2
0
1
1
0
0
1
1
1
0
1
1
1
0
1
2
2
0
2
0
1
1
2
0
1
1
1
1
1
2
0
1
0
0
0
0
0
1
0
0
1
0
2
2
1
4
3
0
1
1
1
1
1
1
0
2
0
1
1
1
0
1
1
1
1
0
1
1
0
0
0
0
2
1
1
0
0
0
1
1
0
2
1
0
3
0
0
0
1
0
2
1
0
2
1
0
1
0
2
1
1
0
3
0
0
0
0
1
0
0
2
1
0
2
0
0
0
0
2
1
2
0
2
0
1
0
0
0
0
0
2
0
0
0
1
1
1
0
0
0
0
1
1
0
1
0
0
1
2
2
1
2
1
0
0
2
2
2
0
1
0
1
0
1
0
2
1
0
2
2
1
0
1
1
0
0
2
0
2
1
2
1
0
2
1
0
1
0
2
0
1
3
0
0
1
0
1
1
2
2
0
1
2
1
1
1
0
2
0
3
1
2
1
0
0
0
0
2
1
1
1
1
0
3
0
2
0
0
0
0
0
1
0
0
1
2
0
2
0
1
0
0
0
2
0
0
1
1
1
1
2
0
0
0
2
1
2
0
1
1
0
1
0
1
0
2
2
1
0
1
1
1
1
0
1
0
1
1
0
0
0
0
0
2
0
0
2
0
1
1
2
1
1
0
0
0
0
1
2
1
0
0
0
0
1
1
1
0
0
0
0
0
1
1
1
0
0
0
1
0
1
2
1
3
0
0
1
2
0
1
2
1
0
1
1
1
0
1
2
1
0
2
1
0
2
3
1
1
0
2
1
1
1
0
1
1
0
1
2
0
1
0
2
1
1
0
1
0
3
1
2
0
1
2
0
2
0
0
1
1
2
0
0
1
1
0
1
1
1
2
0
2
1
1
1
1
2
2
0
0
2
1
1
0
0
0
1
1
0
0
0
0
1
1
2
0
1
0
2
1
0
1
0
1
1
2
0
1
2
0
0
0
0
0
0
0
2
0
0
1
2
1
1
1
1
0
0
2
2
0
1
1
1
3
2
0
2
2
0
0
0
2
0
0
0
2
0
1
1
0
0
2
0
0
1
1
2
0
0
2
2
1
2
2
4
2
0
1
0
1
2
0
1
1
0
0
0
0
0
0
0
2
1
2
0
0
0
1
1
0
1
1
0
0
1
0
0
2
0
4
2
0
1
1
0
0
0
1
0
1
1
0
1
1
1
1
1
0
0
0
0
0
1
2
1
3
0
1
2
1
0
0
1
1
2
2
0
0
1
2
2
0
2
2
1
0
0
0
1
0
2
0
0
1
0
2
1
1
1
2
1
2
0
2
0
0
2
0
1
1
1
0
4
0
0
0
2
0
1
0
0
0
0
0
2
0
1
0
2
0
1
0
2
0
0
1
0
2
0
0
1
0
1
0
0
1
1
2
1
0
4
2
0
1
0
2
1
1
0
0
0
0
2
0
1
1
0
2
2
0
2
1
2
0
0
1
0
2
1
0
1
1
1
0
1
0
2
1
0
2
0
0
0
0
0
1
0
0
1
0
1
1
0
2
1
1
0
0
1
0
0
0
0
1
1
0
1
0
1
0
0
0
1
4
1
0
1
0
1
0
0
1
0
0
1
0
0
2
0
1
0
2
0
2
0
0
0
3
0
1
0
0
0
0
2
1
0
1
0
0
0
2
1
0
0
0
1
1
1
0
0
1
2
1
0
0
1
0
1
1
0
1
1
1
0
0
1
2
2
1
2
0
2
1
1
1
0
0
0
0
1
0
0
2
0
1
1
1
0
0
1
1
2
0
0
2
0
1
2
0
0
1
0
1
2
0
0
0
0
0
0
0
1
1
2
3
0
0
1
0
0
0
0
0
1
1
1
1
1
2
0
1
0
1
1
2
0
1
1
2
0
2
0
0
1
0
0
2
0
1
0
2
2
1
0
0
1
0
0
2
0
1
0
0
1
0
1
0
0
2
1
0
0
1
0
1
1
2
0
1
2
0
1
1
0
0
1
0
0
0
0
1
0
0
0
2
0
1
2
1
0
2
2
2
2
1
0
0
2
0
2
1
1
2
1
1
0
0
0
1
1
1
0
1
1
0
1
0
0
0
0
2
1
0
0
4
0
0
0
2
1
0
0
1
2
1
1
0
0
0
0
3
2
2
0
3
0
0
1
0
2
1
0
1
0
1
1
0
1
2
0
1
2
1
1
1
1
0
0
0
3
0
1
0
2
1
0
0
1
2
2
0
0
1
1
0
0
1
0
2
0
1
1
2
1
1
2
1
0
0
0
4
0
1
1
1
0
0
1
1
2
1
2
1
0
0
1
1
1
1
1
0
0
0
2
1
0
0
0
1
1
0
2
0
0
0
1
1
0
0
2
0
0
3
2
0
1
0
2
2
1
1
1
1
1
0
1
1
1
1
0
0
0
1
1
2
1
1
1
1
0
3
2
0
0
0
1
0
1
1
0
0
1
1
2
1
0
1
0
0
0
0
0
0
1
1
2
1
0
1
1
0
1
2
2
0
1
2
1
0
1
1
1
0
0
2
0
0
1
2
1
0
1
0
2
3
0
2
2
0
1
0
2
1
2
1
1
1
0
0
0
1
1
1
1
0
0
0
1
2
1
0
0
1
0
0
1
2
0
1
0
3
0
1
0
0
2
2
1
2
2
1
1
0
0
0
0
1
2
1
1
1
1
1
1
1
0
0
2
0
1
0
1
0
1
0
0
1
0
1
2
0
1
0
0
0
1
0
1
2
2
0
0
0
0
0
1
0
2
1
0
0
0
0
0
2
2
1
0
0
2
0
1
0
0
0
2
2
2
1
1
0
1
0
1
0
1
1
0
0
1
0
2
2
1
0
1
0
0
0
1
1
1
0
1
0
0
1
0
1
0
1
1
1
1
0
0
0
1
2
0
0
1
0
1
4
0
1
0
1
0
2
0
1
0
0
0
2
0
0
1
0
1
1
1
2
0
2
1
2
0
0
1
0
1
0
3
0
0
2
1
0
1
1
2
0
0
1
0
1
1
1
0
1
2
0
0
1
2
0
1
1
2
0
1
0
0
1
0
0
1
1
1
2
1
0
0
1
2
1
0
0
2
1
1
1
0
0
2
2
1
0
0
1
0
1
2
0
0
2
1
2
2
1
1
0
0
1
0
0
1
0
1
1
2
0
0
1
0
1
0
1
1
1
3
1
0
0
2
2
2
2
2
0
2
1
2
0
0
0
1
0
0
0
1
0
1
1
0
1
0
1
2
1
0
2
0
1
0
1
0
1
2
0
0
0
1
0
1
0
0
1
1
1
1
0
1
4
2
2
0
1
1
1
0
2
1
2
1
3
1
1
2
2
1
1
2
0
1
0
0
0
1
1
1
1
2
2
0
0
0
1
1
2
1
2
0
0
1
0
3
0
1
0
0
2
3
2
0
0
2
1
1
1
2
2
2
2
0
0
1
2
0
1
0
1
1
0
1
1
2
0
0
1
0
1
0
0
1
1
1
2
1
1
6
0
0
1
0
0
1
2
2
0
2
1
1
1
0
1
2
2
0
1
0
1
1
1
0
1
0
2
1
0
0
2
2
1
1
2
0
1
1
0
1
1
0
2
0
0
0
0
1
1
1
0
0
2
2
1
0
1
0
0
0
2
3
0
0
0
1
2
0
1
2
0
1
0
0
1
2
1
0
2
0
1
2
0
2
2
0
0
2
1
1
5
1
0
0
0
0
0
1
1
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
2
2
0
1
0
0
0
1
1
0
0
1
1
0
0
1
2
1
1
2
1
0
1
2
0
0
0
1
2
0
2
1
0
2
1
1
2
1
0
1
1
1
1
1
1
2
1
1
0
1
2
2
1
1
0
1
0
0
0
0
0
1
0
1
0
2
0
1
0
2
0
2
0
0
1
0
0
1
1
2
2
0
0
0
0
0
1
0
0
0
2
1
0
2
2
0
0
0
0
1
2
1
1
0
0
1
2
1
0
2
0
0
1
1
1
0
1
1
2
2
0
1
1
2
0
1
0
0
1
1
1
1
1
0
1
0
0
2
2
1
1
0
2
0
1
0
0
2
2
2
1
1
0
1
0
0
1
1
2
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
2
1
2
0
0
1
0
0
0
2
0
0
2
0
0
2
1
0
2
1
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
1
2
1
1
1
0
1
0
1
1
1
4
1
1
2
1
2
2
0
1
0
0
0
0
0
1
2
1
1
0
2
0
2
0
0
2
1
1
1
2
1
2
2
0
1
0
2
0
1
0
0
0
1
1
2
2
0
0
2
1
2
0
0
1
0
1
1
2
2
1
0
2
0
1
1
1
2
1
1
0
0
1
1
1
1
0
0
0
0
0
0
0
1
1
2
0
0
1
1
1
1
0
0
0
1
2
0
0
2
1
0
0
0
0
1
1
1
0
2
3
0
1
0
0
1
0
0
3
2
0
2
0
1
2
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
1
1
0
0
1
1
0
1
0
0
0
0
1
1
0
0
2
0
1
1
0
1
1
1
1
0
0
0
0
0
1
0
0
0
1
0
2
0
0
2
0
0
2
1
0
0
0
1
1
0
0
1
1
1
2
2
1
0
0
1
0
2
1
0
0
2
2
0
3
2
0
0
0
2
2
2
0
0
2
1
0
0
0
2
2
1
0
0
1
0
2
0
1
2
1
1
0
0
0
1
0
1
1
1
1
1
1
1
1
0
1
0
2
0
1
1
1
1
1
1
1
0
2
0
0
0
2
2
1
0
0
0
1
1
1
1
0
2
0
0
1
1
2
2
0
0
1
1
0
0
1
2
2
2
0
1
1
1
0
1
0
2
1
0
0
1
0
1
2
1
0
2
0
0
0
0
0
0
0
2
0
1
1
0
0
0
1
0
3
0
0
2
0
0
1
0
2
0
0
1
0
0
1
0
0
2
0
1
0
1
2
0
2
0
2
1
0
0
0
1
0
1
1
1
0
0
2
2
0
0
1
1
2
0
0
1
0
0
1
0
1
3
0
1
0
0
0
2
0
0
0
1
0
2
0
0
0
1
0
1
0
2
0
0
1
0
0
0
1
2
1
1
1
0
1
2
2
1
1
1
1
1
0
4
0
0
2
2
2
2
0
2
0
2
3
0
0
1
0
1
0
2
0
2
1
2
0
1
0
1
0
0
2
1
1
0
0
0
0
1
1
0
0
2
2
2
0
1
1
1
1
0
0
0
3
1
1
1
0
2
1
0
0
2
1
1
0
1
1
2
0
1
1
0
0
1
2
0
0
2
3
1
0
0
1
1
1
1
2
0
2
0
1
2
0
1
0
1
0
1
1
2
1
0
2
0
1
2
1
0
1
2
0
2
2
0
1
1
0
1
2
0
0
1
0
0
1
0
1
2
0
1
1
1
2
0
2
1
1
0
0
3
2
2
1
1
1
2
1
0
2
0
1
0
1
0
1
0
0
2
0
2
0
0
2
0
0
1
1
2
0
2
1
1
0
0
1
1
1
1
0
1
1
1
1
0
0
1
0
0
1
1
0
1
2
0
0
1
0
1
0
0
2
2
0
1
0
0
1
0
1
0
1
1
0
2
0
1
1
0
0
0
1
2
0
0
1
1
1
1
2
2
1
0
0
0
0
1
1
2
0
1
4
0
0
0
0
0
0
2
1
0
1
3
0
1
0
0
0
0
2
1
0
1
2
2
1
0
1
1
0
0
1
0
1
0
2
1
1
0
0
2
0
2
0
0
1
1
1
2
0
2
0
1
0
2
0
2
0
2
3
2
1
1
0
1
2
0
1
2
0
0
1
0
0
0
1
0
0
3
1
0
0
0
2
1
1
0
0
1
1
0
2
0
1
1
1
2
3
0
1
0
2
0
2
0
0
0
1
1
0
0
0
1
0
0
1
0
0
2
2
0
0
0
1
0
0
2
1
0
1
1
0
1
2
2
2
1
0
0
1
1
0
0
0
2
0
2
0
0
3
0
1
0
0
2
1
1
1
2
2
0
2
0
0
0
0
0
1
1
0
1
0
2
1
0
0
2
0
1
2
1
0
1
0
2
2
2
1
1
2
1
1
1
0
0
0
0
0
2
2
1
0
1
0
1
0
2
2
1
1
2
0
0
2
0
2
0
1
2
0
1
1
0
0
0
0
1
0
2
1
0
0
1
0
0
0
2
0
1
1
0
2
2
0
2
0
0
3
2
1
0
0
1
0
1
2
0
0
1
0
1
1
0
1
2
2
0
1
0
2
0
0
0
0
1
1
0
0
2
2
1
0
2
1
1
1
2
1
1
0
0
3
1
0
1
0
1
2
1
0
0
1
1
0
1
1
1
0
2
1
0
2
1
2
2
0
0
0
0
1
1
0
0
2
1
0
0
0
0
0
0
1
0
1
0
1
1
2
0
0
1
0
0
1
0
0
0
0
3
1
1
1
2
0
1
1
1
1
1
1
0
0
2
1
0
1
0
2
0
1
0
1
1
1
0
1
3
1
1
0
0
0
2
2
1
0
0
1
0
1
1
0
1
0
1
1
2
0
0
1
1
1
1
0
0
0
0
0
0
0
1
3
0
1
0
1
0
0
0
2
0
0
0
0
0
1
2
0
1
2
1
1
0
0
1
2
1
2
2
0
1
1
1
2
0
1
0
1
2
2
2
1
1
2
2
1
0
2
1
0
1
0
2
1
0
0
2
1
1
0
2
1
0
1
2
2
0
2
1
0
1
0
0
0
1
0
1
1
0
2
0
0
1
0
0
2
2
1
2
1
0
0
1
0
0
0
1
0
0
1
0
2
1
0
0
0
1
1
1
1
0
1
0
0
1
1
1
2
0
0
0
0
1
0
1
1
1
2
2
0
0
1
3
0
0
0
1
1
1
0
2
1
0
1
1
0
2
0
0
2
0
0
0
1
0
2
2
1
0
1
0
1
0
0
1
2
0
1
1
1
1
1
0
0
2
0
0
1
2
1
0
4
0
0
1
3
2
1
0
0
2
2
1
0
1
1
2
1
1
2
0
2
0
0
1
0
0
2
2
0
1
1
0
1
0
0
1
0
1
1
0
2
0
1
2
2
0
1
1
2
2
0
0
0
1
1
0
1
2
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
4
0
1
1
1
2
2
1
1
1
2
1
0
1
0
2
1
0
2
0
2
2
1
0
0
0
0
0
2
0
0
0
2
2
0
2
2
0
0
2
1
0
1
2
0
1
0
2
0
2
0
1
2
0
1
0
1
0
0
1
0
0
2
0
1
0
1
1
0
1
1
0
2
4
0
1
2
0
2
1
2
0
1
2
0
1
2
2
0
0
0
0
1
0
0
0
0
1
2
0
1
0
0
2
0
1
2
2
1
0
2
2
0
1
1
1
1
1
2
1
2
0
1
2
1
0
0
0
1
1
2
0
2
0
0
1
0
0
1
4
0
0
0
0
0
1
2
2
2
0
0
1
0
0
0
1
2
0
1
0
1
0
0
0
1
1
0
2
2
0
0
0
0
2
0
0
0
0
2
0
0
1
1
0
1
0
1
0
2
2
0
0
2
1
0
2
1
0
1
1
5
0
2
3
0
1
1
1
2
1
0
0
0
0
1
1
1
1
1
1
0
0
0
2
0
0
1
0
1
0
0
1
0
0
1
2
2
0
0
1
2
0
1
2
1
2
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
1
2
0
0
0
0
1
2
3
0
0
1
2
1
2
1
0
1
1
2
2
1
2
2
1
1
2
0
0
0
0
1
1
0
0
2
0
0
0
0
2
0
1
1
0
0
0
1
0
1
2
2
0
0
1
1
0
2
1
1
0
1
0
0
2
0
2
1
1
2
2
1
2
0
1
1
2
1
2
1
2
0
1
1
1
1
0
1
1
0
0
0
1
2
0
1
0
0
2
0
1
0
0
1
1
0
0
0
1
0
1
0
0
0
2
0
0
1
1
1
0
2
2
0
0
1
0
2
0
1
0
0
0
0
0
1
0
0
1
2
2
1
0
0
0
0
0
0
0
0
1
2
1
0
1
0
0
0
1
0
0
1
1
1
1
1
2
0
1
1
0
0
2
1
2
0
2
1
0
0
0
0
2
1
0
0
0
0
1
0
2
2
0
1
1
0
1
1
1
2
0
0
1
2
2
1
1
0
1
2
2
2
1
1
0
0
2
0
2
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
2
0
4
0
0
2
1
1
1
0
2
1
0
0
0
1
2
0
0
0
0
0
0
0
0
1
1
1
1
0
0
2
1
0
0
2
0
0
1
0
1
2
1
1
2
0
0
1
0
2
0
0
1
0
0
0
0
1
0
0
0
0
2
2
0
2
1
1
0
1
0
2
4
2
0
1
1
0
1
2
2
2
0
2
2
0
0
1
1
2
0
0
0
1
2
0
1
1
0
1
0
0
2
2
0
0
2
2
1
0
2
1
1
1
1
2
1
0
0
2
0
2
0
0
3
1
0
1
1
2
0
1
0
1
1
0
0
0
2
0
0
0
0
0
2
0
1
1
0
3
1
2
1
0
0
2
0
1
2
2
0
0
1
1
0
1
1
1
1
0
1
1
1
0
1
1
0
2
2
1
0
2
0
0
2
0
0
0
0
1
1
2
1
0
1
0
0
2
1
1
0
1
0
1
1
0
2
2
1
1
0
0
2
0
0
2
0
0
1
1
0
1
0
0
1
0
0
0
0
1
1
0
2
1
1
0
0
1
0
3
2
1
0
1
2
2
1
2
0
0
1
0
0
0
2
0
1
2
2
1
1
1
1
0
2
0
2
2
0
0
1
1
1
3
0
0
0
0
0
0
2
2
2
0
1
1
2
0
2
0
0
1
0
2
2
0
1
1
1
0
1
0
1
0
1
2
1
2
1
1
1
2
0
1
1
1
1
0
2
1
0
1
1
1
1
1
0
2
0
2
1
1
0
0
2
0
1
1
0
1
2
1
2
2
1
1
0
1
0
2
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
3
1
0
2
0
0
1
1
0
0
2
0
0
1
0
0
0
1
0
2
0
1
2
0
2
2
0
1
1
1
0
2
0
3
0
0
0
0
0
0
0
2
0
0
0
1
3
1
0
0
2
0
0
2
0
2
0
0
0
0
0
2
1
1
1
0
1
0
1
1
1
1
0
1
0
1
2
1
1
0
0
0
0
2
1
1
0
0
0
1
1
0
0
0
0
1
2
0
0
0
1
0
0
1
1
1
0
2
2
0
0
0
0
0
2
0
0
1
1
0
0
1
0
0
0
1
1
0
2
1
0
0
0
0
0
1
2
0
2
0
0
1
1
2
0
2
1
0
0
2
1
0
0
0
2
0
0
1
1
0
0
0
2
0
1
1
0
0
1
0
1
2
1
0
0
0
0
1
1
0
2
1
0
1
0
0
0
1
1
0
1
2
0
0
0
2
0
1
0
1
1
1
2
0
1
2
2
1
1
0
2
2
0
0
2
1
0
2
1
2
1
0
0
0
1
0
2
2
1
2
0
1
0
0
0
2
1
2
1
1
2
1
1
1
0
0
0
0
3
0
0
1
1
1
1
0
0
0
0
0
2
1
1
0
1
0
2
1
2
2
2
2
0
2
2
0
1
0
0
0
1
2
0
2
1
0
2
1
2
2
2
1
0
1
0
3
2
1
1
0
0
0
2
1
1
1
0
1
0
2
2
1
0
2
0
1
2
0
2
0
0
0
0
0
1
1
1
0
0
0
0
3
0
1
0
0
1
1
0
0
1
2
0
0
0
1
0
2
0
0
1
1
2
1
2
2
1
1
0
0
0
2
0
0
0
0
1
1
1
1
1
0
1
1
0
1
2
1
2
0
0
2
0
10
0
1
1
2
1
0
2
2
1
0
3
1
0
0
1
1
0
0
1
1
0
1
1
0
1
2
0
0
1
0
2
2
1
2
0
1
0
0
1
1
2
1
2
1
1
0
1
1
0
0
0
0
2
0
2
2
1
1
2
1
0
2
1
0
0
1
1
1
2
0
0
0
0
0
1
1
1
2
2
1
0
1
0
1
0
1
0
0
2
0
0
0
3
0
1
2
1
2
1
1
0
0
0
1
0
2
1
0
1
2
1
2
0
1
2
1
0
0
0
2
2
0
0
0
0
1
0
2
0
0
1
0
0
0
1
1
0
0
0
0
1
0
3
1
0
0
0
0
0
1
2
2
0
0
1
0
0
2
1
0
2
0
2
2
2
1
0
1
1
0
1
2
0
1
0
2
1
1
2
2
2
1
2
2
0
0
0
0
0
0
0
1
0
0
0
3
1
1
1
2
1
0
1
1
0
1
0
0
1
1
2
1
0
0
1
2
0
0
1
1
1
2
1
1
0
2
0
1
0
1
1
1
1
1
2
0
0
0
1
0
0
1
1
2
0
1
1
1
0
1
1
0
1
1
1
0
2
1
0
1
2
0
0
0
0
0
0
0
2
2
1
1
1
1
2
1
1
2
0
0
2
0
0
2
0
0
0
1
2
2
1
1
0
1
2
1
2
0
1
1
1
1
1
0
0
1
1
2
2
1
1
1
2
0
1
0
0
2
0
1
2
1
2
2
0
1
0
3
1
0
0
0
2
0
1
1
2
0
0
0
1
2
1
0
0
1
2
2
2
1
0
0
1
1
0
2
1
1
2
0
1
2
2
0
1
0
0
2
0
1
1
1
1
1
1
0
1
0
0
0
1
1
1
2
0
0
2
1
1
2
2
2
0
0
0
0
0
0
2
1
1
1
0
1
1
1
2
0
0
1
2
1
1
2
1
0
0
1
1
1
0
0
2
0
1
1
1
0
1
0
1
1
0
0
1
2
0
1
1
0
2
0
1
0
1
1
1
0
0
1
1
1
2
1
0
2
1
2
0
0
0
1
1
0
0
0
0
0
4
0
1
2
0
2
1
2
1
2
1
1
1
2
0
0
0
2
0
1
0
2
0
1
0
0
1
0
0
0
0
0
1
0
2
0
0
0
1
0
1
0
1
1
0
0
1
0
2
1
2
2
1
2
0
0
1
1
1
2
0
2
0
2
0
0
0
2
2
0
2
0
1
0
1
1
0
1
0
2
0
2
0
0
1
0
0
2
3
2
2
0
1
0
2
1
0
0
0
0
0
0
3
0
0
0
0
1
1
0
0
1
0
1
1
0
0
0
0
0
2
0
1
2
0
1
1
0
1
1
0
0
0
0
1
2
0
1
1
1
0
1
1
1
0
0
1
1
1
1
1
2
0
2
1
2
2
1
1
0
1
0
0
1
2
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
1
2
0
1
0
1
2
0
0
2
1
0
2
0
1
1
1
1
0
2
0
0
0
0
2
2
2
0
1
1
0
0
1
3
0
1
1
1
0
0
1
1
2
1
0
0
1
2
0
0
5
0
2
1
0
2
1
2
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
3
0
0
1
1
0
0
1
1
2
1
1
1
0
1
0
1
2
0
0
2
0
1
0
0
2
0
3
0
1
1
1
0
0
1
0
0
0
1
2
2
0
0
0
0
0
0
3
0
2
1
1
0
2
3
0
0
0
0
2
2
0
1
0
0
0
2
0
1
0
0
0
0
1
1
2
0
0
1
2
2
0
0
2
0
0
1
1
0
0
1
2
0
0
0
0
2
2
0
0
0
0
0
0
1
0
1
1
2
2
1
1
1
1
0
1
1
0
1
1
1
0
0
0
1
2
0
0
0
0
1
1
2
0
2
0
1
2
1
0
1
0
1
0
0
1
0
1
2
2
0
1
0
0
0
0
2
1
2
0
1
2
2
2
2
1
2
1
0
3
2
1
1
2
1
2
0
2
1
1
0
0
1
1
0
1
1
0
0
0
0
0
2
0
2
1
2
1
2
1
2
0
3
0
0
0
0
0
1
0
2
0
2
2
2
0
1
0
0
0
0
1
0
1
1
0
1
2
0
0
2
0
0
0
0
2
2
2
2
2
1
0
0
1
0
0
1
0
2
0
0
0
3
0
1
1
0
0
0
2
1
0
0
1
2
0
2
0
0
0
1
2
1
0
0
1
0
0
0
1
0
1
1
0
1
3
1
1
0
4
0
0
0
0
1
0
2
1
0
0
5
1
2
1
2
1
0
0
0
1
0
2
0
0
1
2
1
1
0
0
0
2
0
0
1
1
1
1
0
0
2
0
1
1
1
3
1
1
2
1
0
2
1
1
2
0
2
1
0
2
2
0
1
0
0
2
0
0
2
0
0
1
0
0
1
1
1
2
1
1
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
1
1
0
1
5
1
2
1
0
0
2
1
2
0
2
1
0
2
0
2
1
0
2
0
0
1
0
1
1
3
2
0
0
1
0
1
2
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
1
1
0
2
0
0
1
1
0
2
0
0
0
1
1
0
0
0
0
0
2
0
3
1
0
1
3
1
0
0
1
2
0
0
2
3
1
0
2
0
0
0
1
1
2
0
1
1
1
2
0
0
1
1
0
1
1
2
1
1
2
0
1
1
2
2
0
0
1
0
1
2
1
2
1
0
0
1
0
2
2
0
1
0
1
0
1
2
1
2
0
2
1
3
0
1
0
1
1
0
1
0
0
0
0
2
0
5
1
0
1
2
0
1
1
0
2
0
2
0
2
0
1
0
0
0
2
0
1
1
0
0
0
1
0
1
1
1
0
1
0
1
1
0
2
0
0
0
1
0
1
0
2
0
0
1
2
0
0
1
0
1
1
0
0
0
1
2
1
2
0
0
1
1
2
2
2
2
0
1
0
1
0
1
2
0
2
1
0
0
1
0
0
2
0
1
1
0
0
0
0
1
1
1
4
2
0
3
0
2
0
1
0
1
0
2
0
1
3
2
0
2
0
0
0
0
0
1
1
0
2
1
1
1
3
1
1
0
0
1
0
2
0
1
0
2
1
2
0
0
0
0
1
1
0
0
0
1
0
0
0
0
2
1
5
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
1
0
0
2
1
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
1
2
2
1
1
2
1
0
2
0
0
1
1
1
2
0
2
1
1
0
0
0
0
0
0
0
0
1
1
0
2
1
0
2
0
1
1
0
2
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
2
1
1
0
0
1
0
1
1
3
1
0
0
1
0
3
1
0
0
2
0
1
1
0
1
0
0
0
2
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
1
1
1
2
1
0
2
0
1
0
1
2
0
0
1
0
1
2
0
0
1
0
1
0
0
1
1
1
0
0
0
0
1
0
2
0
1
1
0
2
1
0
0
0
0
0
0
2
0
1
1
3
1
1
0
0
0
2
0
1
2
1
0
0
1
0
0
2
2
1
1
2
0
2
0
0
2
0
0
1
1
1
2
0
1
0
0
1
2
1
1
3
1
0
1
2
0
1
0
2
2
1
0
2
0
0
2
2
1
0
1
1
0
0
2
1
2
0
1
0
2
0
0
1
2
1
2
1
3
0
2
2
0
1
0
0
0
1
0
0
0
1
1
1
0
0
1
0
2
0
0
1
0
1
1
0
0
1
1
1
0
0
0
1
0
2
0
1
2
0
1
2
1
0
1
0
0
0
0
0
0
0
1
2
2
0
2
0
1
0
0
0
0
1
0
1
1
1
1
2
1
2
0
0
2
1
2
0
2
0
2
1
2
2
0
0
1
1
2
1
1
0
2
1
2
1
1
1
1
2
0
2
0
1
1
2
0
2
0
1
0
0
1
1
0
1
1
1
0
0
1
1
2
0
1
1
1
1
1
2
2
0
2
0
1
1
0
2
4
0
1
0
0
0
1
2
2
0
1
0
1
1
1
1
0
0
0
2
1
0
1
0
2
0
1
0
1
2
2
1
1
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
1
1
0
0
2
0
0
1
1
0
0
0
1
0
0
1
1
0
0
1
2
0
0
1
1
1
0
0
0
1
1
1
0
1
0
2
1
2
0
1
2
1
2
1
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
1
0
1
0
2
2
1
1
0
1
0
0
2
2
1
2
1
0
0
1
0
1
0
0
1
0
2
1
0
1
1
0
0
1
0
0
3
0
0
1
2
2
2
2
1
2
0
1
0
0
0
1
2
0
0
1
1
1
0
1
2
2
1
0
0
1
1
2
0
2
0
1
0
0
2
1
0
1
1
1
0
0
0
0
2
2
0
0
0
0
2
2
0
1
1
0
0
1
0
1
2
1
1
1
0
0
2
1
1
0
0
0
0
1
1
0
0
1
0
2
1
0
0
0
1
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
2
1
0
1
1
2
0
0
1
0
1
1
1
2
2
0
1
1
1
1
1
0
0
0
0
0
0
0
2
0
2
1
1
0
0
2
0
2
1
2
1
1
0
0
1
2
0
2
2
0
1
0
1
1
0
2
2
2
1
0
0
1
0
1
1
0
1
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
1
0
0
2
0
2
2
2
0
1
1
1
1
1
0
1
0
0
0
0
0
0
0
2
2
3
1
1
2
1
0
0
0
1
0
0
0
1
0
1
0
2
0
1
0
2
1
2
2
0
3
1
1
0
2
0
1
0
2
0
1
2
1
1
2
0
1
1
0
0
1
1
1
1
0
0
1
0
0
1
0
0
1
1
0
2
0
1
0
0
2
2
0
1
1
0
0
1
1
0
0
0
1
0
0
0
2
1
2
0
2
0
1
0
0
1
1
1
1
2
0
1
2
0
1
1
1
2
2
0
1
0
1
0
1
2
0
0
0
0
3
0
1
1
0
0
1
2
0
2
1
0
1
3
2
2
1
0
1
0
0
1
1
0
1
0
0
0
0
1
2
0
1
0
2
2
1
1
0
0
1
1
0
2
1
0
2
2
0
1
5
2
1
1
0
2
2
0
0
0
0
1
0
0
0
1
0
2
2
0
1
2
1
0
0
0
2
1
0
0
1
0
0
0
0
2
0
0
0
0
1
1
1
2
1
2
0
1
1
2
1
2
1
1
0
2
1
0
1
0
1
1
0
1
1
0
0
1
0
1
1
1
0
1
1
0
1
2
2
2
1
0
1
2
2
2
2
1
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
2
0
0
1
0
2
2
2
0
1
0
1
0
0
0
0
0
0
2
1
1
1
0
1
1
0
0
2
1
0
2
1
0
2
0
0
0
2
2
0
1
0
0
1
2
1
1
0
1
0
0
0
1
2
0
1
2
0
1
0
0
0
1
0
2
2
2
1
2
0
2
2
1
2
1
0
0
1
0
0
0
1
0
2
0
2
1
1
2
1
2
2
2
0
1
2
0
0
0
0
2
0
1
1
0
0
0
0
1
1
0
0
0
0
1
0
2
0
1
0
2
0
0
0
3
1
1
2
0
1
2
1
1
3
0
0
0
0
0
1
1
0
1
0
1
0
0
1
1
0
2
1
2
2
1
1
2
0
2
0
1
2
2
1
2
0
1
1
0
1
0
1
2
0
0
0
1
1
2
0
2
1
2
0
4
0
1
0
0
0
1
1
1
0
2
1
0
0
2
0
1
2
2
1
0
0
0
0
1
1
1
1
2
2
0
0
3
2
1
2
1
2
1
0
1
3
1
1
0
1
2
0
0
0
2
0
1
1
1
0
0
0
2
0
0
2
2
2
1
0
0
1
1
1
1
2
2
0
0
0
0
2
0
1
0
1
2
0
2
0
1
0
2
0
0
3
0
0
1
0
0
2
0
0
2
1
0
0
2
1
3
1
1
1
2
0
2
1
1
0
0
1
0
1
0
0
1
3
0
1
2
1
0
0
1
1
1
1
3
2
1
1
0
2
2
1
1
2
2
1
0
1
1
1
0
1
1
2
1
0
0
2
0
0
2
2
1
2
0
0
2
1
1
2
1
0
2
1
1
2
0
2
1
0
1
0
1
2
0
1
1
1
1
0
1
2
1
1
0
0
2
0
0
0
1
1
1
0
1
0
1
2
0
0
0
1
1
2
0
2
0
1
0
1
0
2
0
2
2
0
2
0
2
1
1
0
0
1
0
1
1
0
0
1
0
0
1
1
0
0
2
1
0
1
2
1
0
0
0
2
1
0
0
0
2
0
1
0
0
1
2
0
1
0
0
1
0
1
1
2
0
0
0
3
1
1
1
0
2
0
1
1
1
0
1
0
1
0
2
3
0
0
1
1
2
0
0
0
2
1
2
1
0
0
2
0
1
1
0
0
1
2
1
1
0
1
2
1
0
0
0
2
1
1
1
2
0
2
0
1
0
1
0
0
1
2
0
0
0
1
1
0
1
2
1
0
1
1
2
1
1
2
1
0
1
1
0
1
1
0
2
0
0
1
1
2
1
0
2
2
2
1
2
0
0
0
1
0
2
0
1
1
1
1
0
1
0
2
0
0
0
1
1
0
0
1
0
0
0
2
2
0
2
0
1
0
0
1
0
0
2
0
2
2
0
0
1
0
1
0
2
1
3
0
1
1
0
1
0
0
1
0
2
0
0
2
1
0
2
0
1
0
1
1
1
0
2
0
1
0
2
0
0
1
2
0
0
0
0
3
0
2
0
0
0
0
1
1
1
1
0
0
0
2
0
0
1
1
2
2
2
0
2
0
1
2
0
1
0
2
0
0
2
0
0
1
1
1
0
1
0
2
0
0
2
0
1
0
0
1
2
0
0
1
0
0
2
0
0
1
0
1
0
0
0
0
1
0
1
1
1
1
1
2
2
0
1
2
0
1
1
1
2
1
0
1
0
0
1
0
2
0
0
1
1
0
0
1
0
1
0
0
0
2
1
0
0
1
0
0
0
1
0
0
0
7
1
0
1
0
1
0
0
0
0
2
0
2
2
0
2
0
0
1
1
1
2
0
0
2
2
0
0
1
1
0
1
2
0
1
0
0
0
2
0
1
1
0
2
0
0
0
1
2
1
0
0
0
0
1
1
1
2
0
0
2
2
2
0
1
0
1
0
0
0
2
1
0
0
1
0
1
1
1
1
1
2
2
1
0
0
9
0
1
2
1
0
2
0
2
0
1
0
0
1
1
2
1
0
0
2
1
1
1
1
0
0
0
1
0
0
1
1
0
2
1
0
0
1
0
2
0
0
2
0
0
0
0
2
0
1
0
0
0
2
1
0
0
0
0
0
2
1
2
1
0
1
2
1
1
0
1
0
2
2
2
2
2
1
2
1
1
0
0
2
2
1
0
0
0
2
0
0
2
1
1
2
0
1
1
2
1
2
0
2
2
0
1
0
0
1
0
0
1
0
0
0
1
1
0
1
2
2
0
0
1
1
1
2
7
0
2
1
2
0
2
0
0
1
0
2
0
1
1
0
2
0
1
2
0
2
1
0
0
0
1
0
0
1
2
0
1
1
0
0
1
1
0
0
0
0
0
0
1
1
3
0
1
1
2
1
0
1
1
0
2
0
0
1
1
0
0
2
1
0
0
2
0
0
0
2
2
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
4
2
0
1
1
2
0
1
2
0
2
0
2
0
1
2
0
0
2
1
2
0
0
2
1
0
0
0
2
1
1
1
3
0
2
1
1
1
1
1
2
1
2
0
0
0
1
0
1
1
0
0
1
1
1
2
0
2
1
0
1
2
1
1
0
1
2
2
0
2
2
1
3
0
1
1
0
1
0
1
0
0
1
2
0
2
1
2
0
1
1
1
2
0
0
1
1
1
0
0
1
0
2
0
0
0
0
2
1
1
2
1
0
2
0
1
2
1
0
0
2
2
1
2
0
1
0
3
0
1
1
1
0
0
0
1
1
1
1
1
2
0
1
0
0
1
0
0
1
0
0
0
0
0
4
1
0
0
1
1
0
2
2
0
2
0
2
0
1
1
1
1
2
1
1
1
0
0
0
0
2
1
1
9
2
2
0
1
1
2
2
1
0
0
2
1
0
2
1
1
2
1
2
1
2
1
1
1
1
0
1
0
0
2
1
1
0
0
2
1
0
0
0
1
2
0
0
0
0
1
2
1
1
1
0
1
0
3
0
0
1
1
2
1
2
2
2
0
0
1
1
0
0
1
1
0
2
0
1
0
0
1
1
0
1
1
1
2
0
0
1
2
1
1
1
0
0
0
3
0
1
0
1
1
0
0
2
1
0
1
1
2
1
0
1
1
0
1
0
1
2
1
1
0
0
0
0
2
0
0
2
0
1
2
0
0
0
0
1
0
1
2
2
2
2
0
0
0
0
2
1
1
0
1
0
3
2
2
2
0
3
1
1
0
0
1
0
1
2
3
0
2
1
1
0
0
0
0
2
2
0
2
2
1
1
2
2
0
1
0
2
0
2
0
1
0
3
0
2
0
1
1
2
1
0
0
1
1
0
0
2
1
0
1
1
1
1
1
2
0
1
0
1
2
1
1
0
0
2
3
3
1
1
1
0
0
1
0
1
0
0
2
0
0
0
1
2
1
1
1
0
0
0
0
0
1
2
2
0
1
1
2
2
0
0
1
0
0
1
2
2
1
0
2
0
0
0
1
0
1
1
0
2
0
1
0
0
2
0
1
1
1
1
0
0
1
0
2
1
1
0
0
1
0
0
1
0
0
1
2
0
0
2
1
2
2
0
2
1
0
1
1
1
1
2
1
0
2
4
1
1
1
0
2
0
1
2
0
1
0
1
1
0
0
1
1
0
2
0
3
0
2
0
0
1
2
1
0
2
2
1
0
0
0
0
0
1
0
2
0
0
1
0
0
1
0
1
1
1
1
0
0
0
0
2
2
2
1
1
1
0
0
0
1
0
1
1
1
1
1
2
0
0
2
1
0
0
1
0
0
0
2
0
0
2
0
0
0
4
0
2
2
0
0
2
2
0
0
1
0
1
1
2
1
1
2
1
0
2
1
1
1
1
2
0
2
1
0
0
0
1
1
1
0
3
2
1
0
1
2
0
2
0
3
1
0
1
1
2
2
2
0
0
2
2
0
2
1
1
2
1
1
1
0
0
0
0
2
1
1
1
2
2
0
1
1
0
0
1
2
0
1
2
2
0
1
0
0
0
0
0
0
1
2
1
1
3
0
0
0
0
2
0
0
0
1
2
0
0
0
2
0
2
1
0
0
1
1
0
0
4
1
0
0
0
0
1
6
0
2
2
1
1
2
1
2
1
0
0
1
2
3
2
1
0
2
0
2
2
1
0
0
0
1
0
0
1
0
1
1
1
0
0
2
2
0
0
0
0
1
2
0
0
0
0
1
0
0
0
2
1
2
1
1
2
0
0
0
0
1
2
0
0
1
2
2
1
2
2
0
1
1
0
0
1
2
2
2
0
2
0
2
0
5
0
0
0
0
1
0
1
1
2
0
0
1
0
2
0
0
0
1
2
0
2
0
0
5
0
1
2
1
1
1
0
0
0
0
1
2
0
1
0
2
2
1
1
1
0
0
0
0
0
2
1
1
0
2
0
0
2
0
1
2
0
1
1
1
1
0
1
1
2
2
2
2
0
0
0
1
0
1
2
2
2
0
0
0
0
1
0
0
0
0
1
2
0
1
1
0
1
2
2
1
2
0
0
1
1
0
4
1
1
1
0
2
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
2
2
1
1
0
1
0
0
1
2
0
0
2
1
1
0
0
0
3
0
1
2
0
1
0
1
2
1
0
1
1
1
0
0
3
0
0
0
0
1
2
0
0
1
2
1
0
2
0
2
0
1
1
2
2
1
2
0
1
1
0
0
2
1
1
0
1
2
0
1
2
0
0
2
1
2
1
1
0
0
1
1
1
2
0
1
0
1
0
0
0
1
1
1
1
2
3
8
0
1
0
2
1
1
0
1
2
0
0
0
0
0
0
0
0
0
1
2
1
1
1
0
0
0
0
1
1
0
1
0
2
1
1
1
1
0
1
3
1
1
1
0
0
0
2
0
1
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
1
1
2
3
2
0
0
0
0
0
2
1
1
0
1
0
2
1
2
0
0
2
1
1
1
0
1
0
0
1
0
1
0
2
1
2
2
1
1
1
1
2
1
2
1
0
1
0
1
1
0
0
1
0
0
0
1
0
0
0
0
1
2
0
1
0
1
1
0
0
0
2
0
0
0
2
0
1
2
0
0
0
2
0
0
2
0
0
0
3
2
0
1
0
2
2
1
1
1
0
0
3
1
0
0
1
0
0
1
0
2
0
1
0
0
0
0
0
1
0
1
0
0
1
1
2
0
0
2
0
0
1
1
0
1
2
1
0
0
0
1
0
1
3
1
2
0
0
0
1
2
0
2
0
1
0
0
2
1
0
2
2
2
1
0
0
1
0
1
2
0
0
0
1
1
1
0
2
1
0
0
1
0
0
2
1
0
0
0
0
2
1
1
0
0
1
0
2
0
1
0
0
0
1
0
0
1
1
1
2
2
2
1
1
0
0
0
0
0
2
0
0
1
1
0
1
1
1
1
0
0
0
2
0
0
0
1
0
0
0
1
0
0
2
0
1
1
1
1
0
1
2
3
0
1
2
0
1
0
0
1
0
2
1
1
0
1
2
0
2
2
1
0
0
0
0
0
1
3
0
2
0
0
0
0
1
0
1
1
0
1
0
2
0
0
0
0
0
0
0
1
2
2
1
0
2
0
0
1
1
1
1
2
0
2
0
0
0
0
0
1
1
0
1
0
0
2
0
2
1
0
0
0
2
0
2
0
1
0
2
1
1
0
0
0
2
1
0
2
1
0
1
1
0
1
0
0
1
1
0
0
0
1
0
2
1
1
0
0
1
0
0
1
2
2
0
0
4
1
2
1
0
0
1
1
0
0
2
1
2
0
0
0
0
2
0
0
2
2
0
1
1
0
0
2
2
0
2
0
1
1
1
0
2
0
2
0
1
0
0
0
0
2
2
0
2
1
1
0
1
0
1
3
0
1
2
0
2
0
0
1
2
2
1
0
1
0
2
1
0
2
1
0
0
0
1
2
0
0
2
1
1
0
2
0
0
1
0
1
2
1
1
0
0
2
3
0
1
2
0
2
1
0
2
0
0
0
1
1
0
0
1
1
0
0
1
0
2
0
0
0
0
2
0
2
0
0
1
1
0
2
1
0
2
1
1
1
2
2
1
0
0
0
0
2
1
0
1
2
0
1
0
0
1
0
2
1
0
0
1
2
0
1
0
1
2
1
0
1
0
0
0
0
1
1
0
1
0
1
2
0
0
0
2
0
2
2
0
0
1
2
0
2
0
0
0
0
1
0
0
0
2
0
0
0
1
1
0
0
0
1
0
1
1
0
1
1
4
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
1
1
0
0
1
0
1
1
2
0
1
1
1
1
0
2
0
1
0
1
2
2
1
1
1
3
1
1
1
0
1
0
2
2
0
0
1
1
0
1
0
0
1
2
1
1
2
0
1
2
0
0
1
0
2
0
0
1
1
0
1
0
0
0
1
1
0
1
0
2
0
1
1
2
0
2
0
0
0
2
0
0
0
1
6
0
0
0
3
0
0
0
1
2
0
0
0
2
1
0
1
0
2
1
2
1
1
0
2
1
1
0
2
1
0
1
2
2
0
0
2
0
0
1
2
1
0
0
0
2
2
2
0
1
0
2
2
2
1
2
1
1
0
1
0
0
1
1
0
2
1
0
0
0
0
0
0
1
0
1
0
0
0
2
2
1
2
2
0
0
0
1
1
1
1
0
2
2
0
3
1
1
1
0
0
1
1
0
1
0
0
1
0
2
0
0
2
0
0
0
0
0
2
2
2
2
1
1
0
1
1
3
1
2
0
0
0
0
0
0
0
0
0
1
1
0
0
2
1
1
0
0
1
0
1
2
0
0
2
0
0
1
0
1
0
0
2
0
1
1
2
0
0
0
0
1
1
0
1
1
0
2
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
3
1
2
1
2
1
0
1
1
2
0
1
1
1
0
2
0
2
1
0
1
0
0
0
1
0
0
0
0
1
2
0
2
1
2
1
1
0
0
0
0
1
1
2
1
1
0
0
2
1
1
0
0
0
1
0
1
1
1
2
0
1
0
1
0
0
1
0
1
2
1
1
1
0
1
1
1
0
1
1
2
4
0
2
2
1
0
3
2
1
0
0
2
0
2
0
0
0
2
0
1
1
0
1
0
1
0
0
1
0
0
3
1
0
2
2
1
0
1
2
1
1
0
2
2
1
0
2
0
0
2
0
0
2
0
0
0
1
0
0
1
2
0
1
1
0
0
0
1
2
1
1
0
1
0
4
1
1
2
1
0
1
1
0
0
1
2
0
1
0
0
0
0
1
2
1
0
1
2
0
1
0
2
2
1
0
1
0
1
2
0
0
0
1
2
2
1
1
0
0
1
2
1
1
0
1
0
0
3
0
2
2
2
1
0
0
0
0
0
2
0
1
0
0
2
0
1
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
2
1
2
0
0
1
2
0
0
0
0
1
1
0
1
0
0
0
0
0
2
1
0
0
2
1
0
1
0
1
1
0
0
1
1
1
1
1
0
1
1
0
0
1
0
1
0
1
2
1
0
1
0
0
1
1
1
0
2
2
0
0
2
1
2
0
0
1
0
1
2
1
0
0
1
0
0
0
0
0
1
2
2
2
0
2
0
2
0
2
1
1
1
0
0
1
1
0
0
0
0
0
1
0
1
0
1
0
0
1
0
2
2
2
0
1
0
0
1
1
0
0
2
1
2
1
3
1
2
0
0
0
1
1
0
0
0
0
1
0
0
2
1
0
0
1
0
0
0
0
1
0
0
1
1
0
1
2
1
1
0
0
0
1
1
1
2
0
0
0
1
1
2
0
0
1
0
0
0
2
1
0
2
0
0
0
1
0
2
1
0
2
0
0
2
0
2
0
1
1
0
0
1
0
0
0
1
2
0
0
1
2
0
2
1
2
0
2
0
2
1
1
1
1
0
0
0
1
1
1
2
0
2
1
2
2
0
0
1
0
1
1
0
1
0
2
2
1
1
2
0
0
2
2
2
1
0
0
0
0
0
0
0
0
0
2
1
1
3
2
2
1
1
1
2
0
1
1
0
0
0
0
2
0
0
1
2
2
0
0
1
1
2
0
0
2
0
0
0
1
1
1
0
1
2
1
2
0
0
2
0
2
0
0
1
1
1
2
0
2
1
0
1
2
8
2
0
1
0
0
3
0
2
1
0
0
2
0
0
0
0
0
2
0
0
2
0
2
1
0
1
0
1
1
1
2
2
1
2
1
0
1
0
0
0
1
0
0
2
0
0
2
1
0
0
0
1
1
0
1
2
0
2
0
2
2
0
0
1
1
0
0
1
0
2
2
2
1
1
1
1
1
1
2
1
0
0
2
0
0
0
1
2
0
2
0
0
2
1
0
0
0
1
0
0
0
1
0
2
1
2
1
0
2
1
1
0
0
1
1
0
0
1
2
1
0
2
2
2
1
0
0
1
0
3
1
0
1
3
1
0
2
2
0
1
2
1
1
0
2
1
1
0
0
2
0
0
0
1
1
1
0
2
1
0
0
1
0
1
1
0
1
1
0
2
1
1
1
2
1
1
0
0
0
1
0
1
0
1
0
0
0
1
1
0
2
1
1
1
1
0
0
3
2
0
2
1
0
2
0
2
1
1
2
1
2
0
2
0
0
0
2
0
2
2
1
0
0
1
0
1
0
0
2
0
0
2
1
2
0
1
0
1
1
1
2
0
1
0
1
1
2
0
1
0
0
2
2
2
1
1
1
2
0
2
0
0
2
1
1
0
1
0
1
1
0
0
2
1
2
1
2
1
1
1
1
1
2
1
0
0
1
0
0
1
1
0
0
1
0
1
0
0
0
2
0
1
2
2
1
0
1
1
0
0
0
0
2
2
2
1
0
1
0
0
0
2
1
1
1
0
0
0
0
0
0
0
1
0
0
2
1
0
2
0
3
3
0
0
0
1
1
2
1
2
2
1
1
1
0
0
0
1
2
1
1
0
0
1
2
1
1
2
1
0
1
0
0
1
0
0
1
1
1
0
0
2
2
4
1
1
0
0
0
2
0
0
2
1
0
0
0
2
0
1
0
1
1
0
1
1
1
1
3
0
0
1
0
0
0
0
1
1
1
1
0
2
1
2
1
1
2
0
0
1
1
1
1
1
1
0
0
2
1
0
1
2
0
0
1
0
0
0
1
0
0
0
0
2
0
1
3
0
2
1
0
2
1
0
1
2
0
0
0
2
0
0
1
1
1
0
0
0
1
1
2
2
2
0
0
1
0
1
2
1
1
1
2
0
0
0
1
1
2
1
2
0
0
2
1
1
5
0
2
2
0
0
1
2
2
3
1
0
1
0
2
0
0
0
1
1
1
1
0
1
0
2
0
0
2
2
2
2
1
1
1
1
3
0
0
2
2
1
1
2
2
3
0
1
0
0
1
1
2
0
1
0
0
1
0
1
2
0
0
0
0
0
3
1
1
1
1
1
4
0
1
2
0
2
0
1
1
0
1
0
1
1
0
1
0
2
1
0
0
1
1
2
0
1
2
1
0
0
2
1
1
1
1
0
0
1
0
2
1
1
1
2
2
1
0
0
1
1
0
0
0
0
2
1
1
0
0
1
1
0
2
1
0
1
2
0
1
0
1
0
1
2
1
0
3
1
0
0
1
5
0
0
1
1
0
0
1
1
0
1
0
0
2
1
1
0
0
0
0
2
1
2
1
1
1
0
0
0
2
1
1
0
1
0
0
0
0
1
0
2
0
2
0
0
2
1
2
1
1
0
2
1
0
1
1
1
2
0
0
1
5
2
1
2
2
0
2
0
0
0
1
2
0
1
0
0
2
1
0
1
0
2
0
1
2
0
2
2
2
0
0
2
2
1
1
0
0
0
1
0
1
2
1
0
1
0
3
2
0
1
0
1
0
1
1
2
1
2
1
1
1
0
0
0
1
0
0
0
2
2
1
1
0
1
2
2
2
1
1
0
2
0
1
1
1
0
0
1
2
0
1
0
0
0
2
0
0
0
2
0
1
1
1
1
2
0
0
2
0
1
1
1
0
0
2
0
0
1
0
2
2
0
0
1
2
0
1
0
3
1
2
1
1
0
1
1
0
1
1
1
0
0
0
1
1
2
1
0
1
2
0
2
0
0
2
0
0
1
0
0
1
0
1
1
0
2
0
2
1
2
0
1
0
1
2
0
3
0
2
0
1
1
0
0
1
0
1
0
0
0
1
0
2
0
1
1
1
2
0
1
1
0
0
0
0
0
2
1
0
0
2
1
1
0
0
2
1
0
0
0
1
1
0
1
2
0
0
2
0
0
0
0
0
3
0
0
0
1
0
1
0
2
0
0
3
0
1
1
1
1
0
2
1
0
1
0
0
2
0
0
1
1
1
0
3
1
1
0
1
0
2
2
0
2
0
2
2
0
0
1
2
1
1
2
1
0
1
2
2
1
0
0
1
1
1
0
0
2
2
3
1
0
0
1
1
1
1
0
2
2
2
2
2
1
2
0
2
0
1
1
2
0
0
0
1
1
0
1
0
2
2
0
1
2
1
1
0
0
0
1
1
0
1
0
0
1
1
0
1
0
0
1
0
0
1
2
0
1
0
0
0
1
0
0
0
0
0
1
0
1
1
1
1
1
0
0
2
0
1
0
0
1
0
3
1
0
0
2
2
1
1
1
1
0
0
0
0
0
1
0
0
0
0
1
0
2
2
0
0
0
1
1
0
0
2
0
0
0
2
0
0
0
0
0
1
0
2
0
1
1
0
2
1
0
1
0
0
0
0
1
1
1
1
0
0
1
2
2
1
0
1
1
0
0
1
0
1
0
2
2
0
0
2
2
1
1
0
0
2
1
1
2
1
0
0
0
1
1
2
2
1
0
0
0
1
3
0
0
2
0
0
2
0
1
2
1
1
1
1
1
2
1
1
0
2
2
0
0
1
2
0
3
0
1
0
1
1
0
0
2
0
1
2
1
1
0
1
1
2
1
1
2
0
1
1
0
0
1
2
1
0
0
0
1
1
0
2
0
0
1
1
0
1
1
0
0
0
1
1
2
0
1
1
1
1
0
0
1
1
2
1
0
2
1
1
0
2
0
0
2
0
2
0
2
2
1
0
1
3
1
1
0
2
2
1
2
0
0
1
1
0
1
1
1
2
1
0
1
0
1
2
0
1
1
0
1
0
0
1
0
2
0
2
0
0
1
0
2
1
2
2
1
1
0
0
0
1
1
0
0
0
1
0
1
0
1
2
0
0
1
1
0
0
0
0
1
1
1
1
0
2
2
1
0
0
2
1
0
1
1
2
2
1
0
0
0
1
0
0
0
0
1
1
1
1
2
1
1
0
2
2
0
0
1
0
0
0
2
0
2
0
0
1
0
0
2
1
0
0
0
0
1
0
1
1
0
1
0
1
1
0
0
1
0
0
1
1
1
0
7
0
0
1
0
1
0
0
1
0
1
0
0
2
2
0
3
1
0
0
0
2
2
2
1
0
0
0
2
0
2
0
1
2
1
0
0
1
0
1
1
0
2
0
2
0
4
0
0
2
2
1
2
3
0
2
0
1
2
0
0
2
1
0
0
1
2
0
0
1
0
0
0
1
1
1
2
0
1
1
1
0
0
1
0
2
0
0
2
0
1
0
1
1
2
0
1
0
1
0
1
2
0
0
2
0
0
1
0
1
2
1
0
0
0
0
1
0
2
1
2
1
2
0
1
0
1
2
1
1
2
0
0
1
0
0
0
1
1
0
1
0
0
0
0
1
0
2
0
1
2
1
1
0
0
0
1
0
0
2
0
0
0
0
0
1
1
1
1
1
1
0
1
1
0
1
2
0
1
1
0
0
1
0
3
0
2
1
2
1
2
1
2
0
2
2
2
1
0
1
2
1
0
1
0
0
2
2
1
3
2
0
2
1
0
0
1
1
1
0
1
0
1
0
2
0
0
0
0
0
1
1
1
0
0
0
1
0
3
1
1
1
0
2
1
1
1
0
5
0
0
2
0
1
1
0
1
2
2
0
0
0
2
0
0
0
1
0
1
1
0
1
0
0
0
1
1
2
0
0
1
0
1
2
0
0
0
2
3
0
0
1
0
0
0
3
0
0
0
2
0
1
1
0
0
0
2
0
0
0
1
1
2
0
1
1
2
0
1
0
0
1
1
0
0
0
2
3
1
1
0
0
1
2
1
2
0
1
0
0
0
0
0
2
1
2
1
1
1
0
2
0
0
0
1
2
0
0
0
0
2
2
0
1
2
1
0
0
0
0
1
2
0
0
1
0
0
2
0
0
0
2
0
1
2
2
2
0
0
2
0
1
2
0
2
2
1
0
2
0
2
2
1
0
0
1
2
2
0
0
1
0
2
1
1
2
0
0
1
2
0
0
0
0
0
0
0
0
0
1
2
1
0
2
1
2
1
1
2
0
2
0
0
1
1
0
1
1
1
2
0
1
2
1
1
2
2
2
1
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
2
1
1
1
1
0
0
0
5
0
2
0
0
1
0
0
2
1
0
0
1
2
0
0
1
0
0
0
0
1
0
1
2
0
1
0
0
0
0
0
0
2
1
2
1
0
0
2
1
3
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
1
0
0
1
2
1
1
1
2
0
1
0
2
0
1
2
1
1
0
1
2
0
0
0
2
0
2
0
0
1
1
1
0
2
0
0
1
0
0
0
1
0
0
0
1
1
2
0
2
0
1
1
1
1
0
0
0
0
1
1
0
0
2
0
1
2
2
0
0
0
1
1
2
1
1
2
0
0
0
0
0
1
2
1
0
2
2
1
0
0
0
1
1
1
0
1
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
1
2
0
2
1
1
2
2
1
1
1
0
0
3
0
0
0
0
2
1
1
0
2
2
0
0
2
0
2
0
1
0
0
2
0
1
0
0
0
0
0
1
1
0
2
5
1
0
0
0
1
0
0
1
1
1
0
0
0
1
0
0
2
1
0
1
2
2
2
1
1
0
2
0
1
1
0
0
2
1
3
1
0
2
0
2
1
0
1
1
0
2
0
0
1
1
1
1
1
1
3
1
2
1
1
1
0
2
0
1
0
1
2
1
2
2
0
0
0
2
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
2
1
1
0
2
2
0
0
1
0
1
1
0
0
0
0
0
0
1
1
3
1
0
0
0
0
1
0
1
0
1
0
1
2
0
1
1
0
1
0
1
1
0
1
0
1
1
0
0
1
1
0
1
1
0
1
2
2
1
1
1
2
2
0
2
1
0
2
0
1
0
2
0
1
0
2
0
0
0
1
0
0
1
0
2
1
0
0
1
0
0
0
0
0
1
2
2
0
0
0
0
2
0
1
0
0
0
2
1
0
1
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
2
2
1
0
0
0
2
2
0
0
2
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
1
1
0
2
1
1
0
0
1
0
2
1
0
0
1
0
2
0
0
2
0
0
0
1
1
2
0
0
1
2
1
1
1
1
1
1
2
0
3
2
2
1
0
1
0
0
1
1
0
1
1
0
2
1
0
2
1
0
0
1
2
0
2
1
1
1
1
1
0
2
1
0
1
0
1
1
1
2
0
0
0
0
0
3
2
0
1
2
1
0
1
2
0
1
2
1
0
0
2
0
0
0
2
0
1
1
0
0
1
0
1
0
1
2
0
2
1
1
2
0
0
2
2
0
1
2
2
0
0
0
1
2
1
0
0
1
0
2
1
0
0
1
2
1
0
0
0
0
0
0
2
0
1
1
1
0
0
0
2
1
1
0
0
1
1
1
0
2
2
0
1
0
1
2
1
0
2
0
0
0
2
1
1
0
2
0
1
1
1
0
0
1
0
0
1
1
0
0
0
1
1
0
0
1
3
1
0
0
1
2
0
1
1
0
1
1
2
1
1
2
0
0
0
0
0
0
0
0
1
0
1
1
0
2
1
0
0
2
0
2
0
2
2
2
1
1
0
0
1
1
0
1
2
1
2
1
2
1
2
0
1
0
1
1
1
2
0
1
0
2
0
1
0
1
3
0
1
2
1
2
0
1
0
3
0
1
0
0
0
2
0
1
1
2
2
2
1
1
2
0
0
1
0
0
1
0
1
2
1
2
1
2
0
0
0
0
1
0
1
0
1
2
0
0
1
0
0
2
0
1
1
2
0
1
3
1
1
0
0
0
0
0
0
0
1
2
0
2
1
2
0
0
0
0
0
2
0
1
1
0
1
1
0
0
2
0
0
1
0
2
2
1
0
1
1
0
1
2
2
1
0
0
2
1
0
2
2
0
1
1
1
1
0
2
0
2
1
2
0
0
0
2
0
0
1
1
0
0
2
0
0
0
1
1
0
1
0
0
0
1
1
0
2
0
0
0
1
0
2
1
1
0
0
1
1
0
2
3
0
1
0
0
1
1
3
2
0
1
0
1
1
1
1
2
1
0
0
0
0
1
1
0
0
0
2
0
1
0
1
0
0
1
2
2
2
0
0
1
2
1
0
0
2
1
2
1
0
1
2
1
2
1
1
0
2
2
0
2
1
0
1
0
0
0
0
0
0
0
1
0
0
1
1
2
2
2
2
1
2
2
1
2
1
0
0
0
2
2
1
1
0
1
0
0
1
1
0
0
1
1
1
0
0
0
1
0
2
0
2
0
1
0
2
0
0
1
0
0
1
1
2
2
0
1
0
2
0
0
2
0
2
0
1
1
1
2
2
2
1
1
0
2
2
0
1
1
0
2
0
0
6
0
0
2
0
1
0
1
2
1
2
0
0
1
1
1
0
2
1
0
1
0
1
0
1
0
0
1
2
2
0
1
0
2
0
0
0
0
2
1
1
1
0
0
0
1
0
1
2
2
1
1
0
0
1
0
0
1
1
1
1
2
1
0
0
0
0
2
2
2
1
0
3
0
0
0
1
0
2
1
1
1
0
1
2
2
1
0
1
0
1
2
1
1
1
0
2
0
2
0
0
1
2
1
0
0
0
0
0
1
1
2
0
1
1
0
0
2
1
0
0
0
0
1
3
0
1
0
0
0
0
0
0
0
2
1
1
1
0
1
0
0
0
1
1
1
0
1
0
1
0
0
1
1
0
1
1
1
0
0
1
1
2
0
0
0
0
0
1
0
1
2
1
0
1
1
1
1
1
0
1
1
0
1
1
0
2
0
2
1
0
2
0
1
0
1
0
0
0
0
1
0
1
2
1
1
0
1
0
1
0
0
1
1
0
1
1
1
0
0
2
0
0
1
1
1
1
3
1
1
2
1
0
1
1
1
0
2
1
0
1
0
0
2
1
0
1
1
0
0
0
0
1
0
1
1
0
0
1
0
0
1
1
2
1
1
0
0
1
1
1
0
1
1
1
1
1
1
2
0
1
2
1
0
0
0
1
0
1
0
2
2
1
0
0
1
1
0
0
0
1
0
0
1
0
0
0
1
1
1
0
0
0
1
0
0
0
2
1
0
1
1
2
0
0
1
1
2
1
0
2
1
1
0
0
0
0
1
1
1
0
1
1
0
0
0
1
0
2
1
0
0
0
0
0
0
1
0
1
0
1
1
0
2
0
1
0
2
0
1
2
1
2
0
0
0
0
0
1
0
0
4
0
0
1
0
2
1
1
0
1
1
2
1
0
0
0
2
1
0
0
1
1
0
0
1
2
1
0
0
0
2
0
0
1
0
0
0
2
0
1
1
1
2
1
1
1
1
2
0
0
1
1
1
0
0
2
1
0
0
1
0
2
1
0
0
1
0
0
0
2
0
0
2
1
2
1
1
0
0
1
1
0
0
0
0
0
2
0
0
1
2
1
0
0
0
1
1
1
1
2
2
2
0
1
0
1
0
0
1
1
0
0
0
1
0
2
1
1
0
1
0
1
1
0
2
0
0
0
0
1
0
2
1
0
0
0
1
1
1
2
0
1
0
0
1
2
1
1
0
2
2
1
0
1
2
0
0
1
2
0
2
0
0
0
0
1
0
1
1
0
1
0
1
1
0
3
0
1
1
0
1
2
0
1
2
1
1
0
1
0
2
1
1
1
0
1
1
2
0
1
0
0
0
1
2
0
2
0
0
1
0
2
0
1
0
0
1
0
2
0
2
1
0
2
0
0
0
1
0
0
2
0
0
0
2
0
2
3
1
1
1
2
0
0
1
1
1
1
0
1
2
2
1
1
0
0
0
0
0
2
0
1
1
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
1
0
1
0
1
1
0
0
1
1
2
1
0
0
0
0
0
0
1
0
2
0
0
0
2
2
2
2
0
0
1
2
0
1
2
2
2
0
1
0
1
1
0
1
0
1
1
2
0
0
0
2
1
3
2
0
0
1
0
2
1
2
0
2
1
0
0
0
1
0
0
0
0
1
1
1
1
0
0
0
1
0
0
0
0
0
0
0
1
1
2
0
0
1
1
0
0
0
1
0
0
1
1
2
1
0
2
1
2
2
1
0
1
1
1
1
0
0
2
1
0
1
0
1
1
0
0
1
0
2
1
0
0
2
0
1
1
0
0
0
1
2
1
1
0
0
0
1
2
1
1
0
0
2
2
2
0
2
0
0
0
0
1
1
2
0
0
1
1
0
0
0
1
0
0
2
0
1
0
1
0
0
1
0
0
1
0
1
1
0
0
1
0
1
0
1
0
2
2
0
1
3
1
1
0
0
2
2
2
0
1
0
1
0
1
2
1
1
1
0
1
1
0
0
0
1
0
0
3
1
2
0
0
2
0
0
0
1
1
0
0
0
0
0
1
0
1
2
3
0
1
0
2
1
2
0
2
1
0
1
1
1
1
1
2
0
0
1
0
1
0
2
1
0
0
1
1
0
2
1
1
1
2
0
2
0
1
0
2
1
1
3
0
0
1
0
0
0
0
2
1
0
1
0
0
1
1
2
1
1
2
1
0
1
1
3
0
1
0
1
2
2
0
2
0
2
0
0
0
1
1
1
0
0
2
1
2
1
2
0
1
1
2
1
1
2
4
0
1
2
0
2
2
1
1
0
0
0
0
0
2
2
0
1
1
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
2
0
2
0
0
1
0
0
0
0
0
2
1
0
0
2
1
0
0
2
0
1
0
1
1
1
0
1
2
2
2
1
1
0
1
2
2
1
0
2
1
0
1
1
2
1
0
2
2
0
0
0
0
1
0
0
1
0
0
0
2
0
2
0
0
1
1
0
1
1
0
0
0
1
0
1
0
0
2
0
1
0
1
2
1
1
0
0
0
1
0
2
0
1
1
0
0
0
0
1
0
0
0
0
1
0
1
2
1
1
0
0
1
0
2
0
0
0
1
0
1
2
2
1
0
0
0
0
1
0
0
1
1
0
1
2
2
1
2
2
0
0
0
0
0
2
2
0
2
2
0
1
1
0
0
2
1
0
0
0
1
1
1
1
2
0
1
1
1
0
1
1
1
0
0
2
2
0
0
0
1
1
0
0
1
0
1
0
1
1
0
0
1
2
0
1
1
0
0
1
1
1
1
1
2
3
0
0
0
0
0
0
0
1
0
2
0
2
0
2
1
1
0
0
0
0
2
0
0
0
0
2
1
0
0
0
2
1
2
1
1
0
2
0
0
0
0
0
1
2
0
1
0
1
1
3
1
1
0
2
1
2
0
0
0
0
1
0
0
1
0
0
1
2
1
1
2
0
0
1
1
1
0
0
0
0
1
0
1
2
1
1
0
2
1
1
1
0
0
2
2
0
2
0
0
0
1
0
2
0
3
1
2
2
1
0
2
1
0
1
0
1
0
1
0
1
1
2
2
0
0
2
0
1
0
1
2
1
1
1
1
0
1
0
2
1
0
1
1
1
1
1
2
0
1
1
1
2
1
1
1
2
2
0
1
1
1
2
2
0
2
0
1
1
3
2
1
1
1
0
0
1
0
0
0
1
1
1
0
0
0
0
2
0
0
2
3
2
0
1
0
1
3
2
0
1
0
0
0
0
0
1
0
0
1
0
1
0
2
1
1
0
1
2
1
0
3
0
0
1
1
1
1
2
0
1
0
0
0
1
1
2
1
1
0
0
1
1
0
1
2
0
1
1
1
0
1
1
2
2
0
2
0
1
1
0
3
1
0
3
1
2
0
0
0
2
2
2
1
0
1
0
0
1
1
1
1
2
0
1
1
1
2
1
1
2
1
1
2
1
1
0
1
0
0
1
0
2
0
1
2
0
2
1
0
1
1
0
0
0
1
0
1
0
1
1
0
2
1
2
3
1
0
2
0
1
0
1
0
0
0
0
2
0
2
1
0
3
1
0
1
0
1
0
1
2
0
0
2
1
1
1
2
1
0
1
0
1
1
1
1
1
1
0
0
0
1
0
2
1
0
2
0
2
1
0
2
2
1
1
0
1
0
0
1
1
1
1
0
1
0
1
1
0
2
1
0
2
1
0
2
0
7
2
1
0
1
0
1
0
1
0
0
2
3
3
1
0
0
0
1
1
0
2
1
0
1
0
0
0
1
2
2
0
1
0
1
0
2
2
0
1
1
1
2
0
0
1
0
1
1
1
1
1
0
1
2
1
1
0
0
2
0
1
0
0
1
1
2
0
1
1
0
1
0
4
0
0
3
0
0
1
1
0
0
0
2
0
1
1
1
0
2
0
0
2
0
1
0
0
0
0
0
2
1
0
1
0
2
1
0
1
0
1
1
0
1
0
1
0
0
0
1
1
0
0
0
0
2
2
1
1
0
1
1
1
1
0
0
1
0
1
0
2
0
1
0
0
0
0
0
0
0
1
0
0
1
1
1
1
1
0
0
0
1
1
0
0
2
2
1
1
1
1
0
2
0
1
1
1
1
1
0
0
0
1
1
1
0
0
0
0
0
0
2
0
1
2
1
0
1
1
3
0
0
0
2
1
1
2
0
1
0
0
1
1
0
0
0
0
0
1
1
1
1
1
0
0
2
1
2
1
0
2
1
1
1
1
1
0
0
1
0
0
0
2
0
0
0
2
0
0
2
1
2
0
0
1
0
0
1
0
0
2
1
0
2
0
0
0
0
0
1
2
0
1
1
1
0
0
0
1
2
0
0
0
0
0
1
1
0
0
1
1
1
1
1
1
1
2
2
1
0
0
0
2
2
1
1
0
1
0
1
0
1
0
0
0
2
1
1
1
0
0
0
0
0
0
0
0
2
1
2
0
1
0
1
1
2
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
1
0
1
0
4
0
1
0
3
0
1
0
2
1
2
1
1
0
1
0
0
1
0
0
2
0
1
0
2
1
1
2
1
0
0
0
1
1
0
2
0
1
1
2
1
2
0
0
1
2
0
0
0
0
0
1
2
2
0
1
3
1
1
0
2
0
1
1
0
2
7
0
0
0
1
0
3
0
1
0
0
1
0
1
0
0
1
1
2
3
1
0
0
2
1
0
1
2
1
1
0
1
1
2
2
0
1
0
0
2
1
1
1
0
2
0
0
1
0
0
0
1
0
0
0
1
0
1
0
1
1
1
0
1
0
0
2
0
1
0
0
1
1
2
1
2
0
1
0
0
1
2
1
0
1
0
0
0
0
0
1
0
2
1
2
1
0
0
0
1
2
0
0
0
2
2
0
0
0
2
0
2
0
1
0
2
2
0
0
1
0
0
2
2
1
1
0
0
0
2
1
0
2
0
1
1
0
0
0
3
0
0
0
0
2
1
0
0
0
2
0
1
0
1
2
0
0
0
1
2
1
0
0
0
2
1
0
1
0
2
2
0
1
2
3
1
1
0
2
0
1
0
2
0
1
1
0
2
1
0
1
1
0
1
2
2
2
0
1
1
0
0
2
0
3
0
0
0
0
0
0
2
0
0
0
0
1
2
1
0
0
0
0
1
0
2
0
1
0
0
1
0
0
0
1
0
2
0
0
0
0
1
1
2
1
1
1
1
1
2
0
0
0
1
0
0
1
2
2
1
0
1
1
1
0
1
0
0
2
1
0
0
0
0
3
1
3
1
0
0
0
1
0
2
1
0
1
0
0
0
3
0
3
1
0
0
1
1
0
0
0
2
0
0
0
1
0
1
1
0
1
0
0
0
2
1
2
0
0
2
0
0
0
0
2
0
1
0
1
0
0
0
0
2
2
1
0
2
2
1
0
0
2
1
1
0
1
1
1
1
1
1
2
2
2
0
3
0
1
0
1
0
1
2
0
2
2
1
1
0
0
0
2
0
0
0
2
2
0
0
0
0
1
0
1
2
2
0
1
1
1
3
0
1
1
3
1
0
0
0
1
1
1
0
1
3
2
2
0
1
2
0
1
1
1
1
1
1
0
0
2
0
0
2
0
1
1
2
1
2
1
0
0
2
1
0
2
2
0
0
2
1
0
0
0
1
1
1
0
0
0
1
2
1
1
0
0
0
3
0
1
0
2
0
0
0
0
1
0
0
0
1
0
2
2
1
0
0
1
0
0
2
1
1
1
0
0
0
1
2
1
2
2
0
2
1
3
0
1
1
1
2
1
0
2
0
2
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
1
1
0
1
1
1
2
1
0
1
0
1
0
2
2
1
0
0
2
0
1
0
1
0
0
0
1
0
0
0
2
1
2
0
1
1
0
0
0
1
1
1
0
1
0
0
1
0
0
1
1
0
0
0
1
1
0
1
1
2
1
2
0
2
2
1
1
1
2
1
0
1
2
1
0
0
0
1
2
0
0
0
2
1
1
0
0
1
0
0
0
1
1
0
0
1
0
0
1
2
1
0
1
0
1
1
1
2
0
1
1
0
0
2
1
0
0
0
1
2
2
0
0
2
2
3
5
1
1
2
0
1
1
0
2
2
0
0
0
1
2
2
2
0
1
2
1
0
4
0
0
0
1
0
0
0
1
0
1
2
0
2
1
0
2
0
1
0
1
2
1
4
1
0
0
0
0
1
1
0
0
0
2
1
1
1
2
0
0
0
2
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
1
2
1
1
1
0
2
3
1
2
1
1
1
0
2
2
2
0
1
1
2
2
2
1
0
0
1
2
0
1
0
0
2
1
0
2
0
3
0
0
2
0
0
1
0
1
3
1
1
1
2
1
0
1
2
0
1
1
1
0
1
1
0
2
0
0
0
1
1
0
0
0
0
2
1
1
0
0
1
0
0
1
1
1
1
0
1
0
0
0
2
0
0
0
2
2
2
2
1
1
2
1
0
0
0
0
1
1
0
0
1
1
0
2
1
1
1
2
3
2
1
1
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
1
2
1
1
1
1
0
0
0
2
2
1
2
1
1
1
0
0
1
1
1
0
1
2
1
2
0
2
2
2
0
0
0
1
1
1
0
0
2
2
2
1
2
0
2
2
0
2
1
0
0
0
0
1
5
0
1
0
1
1
1
1
1
0
0
2
1
1
1
2
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
2
0
1
2
0
0
0
1
1
0
0
1
1
0
0
1
1
2
0
0
0
2
0
0
1
1
2
2
0
1
0
1
1
0
0
2
2
0
1
0
1
0
2
1
0
1
0
0
0
1
2
0
0
0
1
0
2
0
0
0
1
2
2
1
2
0
3
0
1
1
1
1
2
1
0
0
0
2
1
0
1
1
0
1
2
2
1
0
0
1
0
0
1
0
2
0
0
1
1
0
1
2
0
1
0
1
1
2
0
0
0
0
3
0
0
0
0
0
1
1
1
1
0
1
0
0
0
1
0
0
0
2
3
1
0
2
1
2
1
2
0
0
1
0
1
0
1
3
0
1
0
1
0
0
0
1
2
2
0
0
1
2
0
1
0
7
1
0
0
1
1
1
1
1
0
2
1
1
0
0
1
1
2
0
0
1
2
0
1
0
0
0
0
1
2
1
0
2
1
1
2
0
1
1
2
2
1
1
2
0
2
2
1
0
0
1
0
1
2
1
1
0
0
0
1
0
0
0
1
0
1
2
1
0
0
2
0
3
0
0
0
0
1
0
1
2
1
2
2
1
2
0
1
0
0
1
0
1
1
1
2
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
1
2
0
1
0
0
1
0
2
1
2
1
1
1
2
1
0
0
0
2
1
2
0
1
0
0
0
1
0
1
2
2
2
2
1
0
0
0
0
0
1
0
0
1
1
0
1
0
1
1
0
2
0
2
0
1
0
0
1
0
1
1
0
0
2
1
1
0
1
0
1
2
1
0
0
2
0
1
0
0
1
1
0
1
0
1
0
0
0
1
1
0
3
0
3
1
1
1
1
0
0
0
1
2
0
1
2
1
0
2
4
0
2
1
0
0
0
0
0
2
1
1
1
0
1
1
0
0
2
2
1
0
0
0
1
3
1
2
1
2
2
2
0
1
2
0
0
2
0
4
0
0
0
1
0
1
0
0
2
0
0
0
0
1
1
0
1
1
0
0
1
1
0
1
0
1
0
2
0
1
0
1
0
0
2
1
1
0
0
0
1
1
2
1
1
1
2
0
1
1
0
0
0
0
1
1
0
1
2
0
0
0
0
0
2
2
0
0
0
2
0
1
1
2
0
1
0
0
1
1
0
0
0
0
0
0
1
1
0
0
1
5
2
1
0
1
1
2
0
0
0
1
1
0
0
1
0
0
1
1
2
1
0
2
0
1
1
0
1
0
1
1
1
0
2
2
1
4
2
1
2
2
2
1
0
1
1
0
1
1
0
2
2
0
0
1
1
0
2
0
0
0
2
1
1
0
0
1
1
1
1
1
1
1
0
1
0
0
1
0
2
0
2
1
0
0
2
0
0
0
2
0
0
2
1
1
1
2
2
1
2
2
0
0
2
2
0
0
1
0
2
0
0
0
0
1
0
1
2
1
1
1
0
0
0
2
0
0
0
0
0
2
0
1
0
0
1
1
0
1
0
0
0
0
2
0
0
2
1
2
1
1
1
2
1
2
2
1
1
0
6
0
1
0
0
0
1
1
1
0
1
1
0
0
0
2
0
2
1
0
1
0
0
0
0
0
0
0
0
0
2
1
2
0
0
1
0
1
2
1
2
0
2
2
0
1
0
1
1
1
0
0
0
1
1
1
2
0
1
0
2
0
0
1
3
1
2
2
0
0
1
0
1
0
1
0
0
1
0
2
3
1
0
0
0
2
1
0
0
1
0
0
0
0
0
1
1
0
0
1
0
1
1
4
1
0
1
1
1
2
0
0
1
1
1
0
0
1
0
1
1
0
0
2
2
1
0
2
0
0
0
2
2
1
2
0
1
2
0
1
0
1
1
0
0
0
1
0
2
0
0
2
0
2
1
2
0
2
1
2
0
0
2
1
0
1
0
4
1
1
1
2
0
1
0
1
0
0
0
0
0
2
0
0
0
0
1
1
0
2
0
1
0
0
1
2
1
2
2
0
1
0
1
0
2
1
1
2
1
2
0
0
1
0
0
0
0
2
1
1
4
2
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
1
1
1
1
0
2
1
0
2
0
0
1
2
0
2
2
1
1
0
1
1
1
1
2
0
0
0
1
0
0
1
1
0
0
1
0
2
1
0
0
0
0
0
3
0
1
2
1
0
0
2
2
1
1
1
1
1
1
0
2
1
0
0
1
1
3
0
2
1
1
0
2
2
0
0
2
3
2
1
0
1
1
2
1
0
1
0
1
0
2
1
1
1
0
0
1
0
0
0
1
0
2
1
2
1
0
0
1
0
2
1
0
1
2
1
0
2
2
0
0
0
2
2
0
1
1
2
1
1
1
0
0
0
0
2
0
1
0
1
0
0
1
0
0
1
0
0
3
0
1
2
0
1
1
0
0
0
1
2
0
0
3
0
0
1
1
0
0
0
1
0
1
0
0
1
0
2
0
0
1
2
0
2
1
0
0
0
0
2
1
1
1
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
1
1
2
1
1
1
2
0
0
2
2
2
1
0
1
2
1
1
2
2
1
1
4
2
0
0
1
1
0
1
0
1
1
0
0
1
2
0
0
2
2
1
0
1
1
0
1
0
2
0
2
0
2
1
0
1
0
0
2
1
2
1
1
2
0
0
1
2
2
0
1
1
2
0
2
1
1
0
0
1
0
1
2
0
1
2
0
2
1
1
0
0
1
2
1
1
0
1
1
0
0
1
1
2
2
1
2
1
1
0
1
1
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
1
1
0
0
2
0
1
2
1
1
0
0
0
1
0
0
0
1
2
0
2
1
0
1
0
1
1
0
1
0
0
2
1
2
0
1
0
1
0
1
2
1
2
1
0
1
1
2
1
2
2
1
1
1
0
2
0
0
0
0
2
1
1
1
1
0
0
0
0
0
2
1
0
1
0
2
1
0
2
2
0
1
0
0
1
1
0
0
0
1
1
1
2
1
1
3
2
2
1
1
0
0
2
1
2
2
0
0
0
2
2
2
0
0
2
0
1
0
0
1
0
0
0
2
2
0
1
1
0
0
2
0
2
0
0
0
1
0
0
0
0
1
0
1
0
2
0
0
1
0
0
1
0
0
0
0
1
1
0
1
1
2
0
0
0
0
0
1
0
2
2
2
0
1
1
0
1
0
0
2
1
0
2
1
1
0
2
2
1
2
0
1
0
1
0
0
0
0
1
1
1
1
0
0
0
1
0
1
0
1
2
2
0
2
1
0
1
1
1
0
0
0
0
0
0
2
0
1
1
1
0
0
0
2
2
0
0
2
0
0
0
0
1
1
1
3
1
2
0
1
1
2
1
0
1
1
1
1
0
0
0
2
0
0
0
1
0
0
2
1
1
0
0
0
0
1
1
0
2
1
1
0
0
0
0
0
1
4
0
2
0
0
0
0
2
1
2
0
0
0
1
1
0
0
0
0
0
2
2
0
0
2
0
0
1
1
1
1
1
0
1
1
0
1
0
1
1
0
0
2
0
0
1
1
0
1
2
1
0
0
2
1
0
1
2
0
0
0
0
0
1
0
1
0
1
1
1
0
2
1
1
1
0
2
0
0
0
1
2
0
1
1
2
2
0
1
1
1
0
0
1
2
1
1
1
0
1
0
1
1
3
1
2
1
1
0
1
0
1
1
0
1
1
3
2
1
6
0
2
1
1
1
2
0
0
1
0
1
1
3
5
0
2
0
0
2
4
1
0
2
1
0
1
2
1
1
0
1
1
0
0
2
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
1
0
1
2
0
1
0
0
2
1
0
2
0
2
1
0
0
0
0
2
0
0
0
0
0
1
0
4
1
2
1
0
1
0
1
1
1
1
0
2
2
0
0
1
2
0
1
2
0
0
0
1
0
1
2
1
0
1
0
0
2
0
0
2
1
0
0
0
0
4
3
0
2
1
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
2
0
0
2
2
1
1
0
1
1
1
0
0
1
2
0
0
1
0
1
1
0
2
2
0
0
2
1
2
2
1
0
2
1
5
2
2
0
2
0
1
1
1
0
2
0
0
1
1
0
0
1
1
2
0
1
0
0
2
3
2
1
2
0
2
1
1
2
1
0
0
0
1
0
2
2
0
0
1
1
1
1
1
2
1
1
1
0
0
1
2
1
1
1
0
1
0
2
0
0
0
0
1
1
0
2
1
0
1
0
2
1
0
1
0
1
0
2
0
2
2
0
2
0
1
1
0
1
0
1
1
4
1
0
1
2
0
2
1
0
1
0
0
0
2
0
0
2
0
1
0
0
0
0
1
0
1
0
0
1
2
2
1
1
1
0
0
1
0
2
1
2
0
1
0
0
1
1
1
2
1
2
1
1
1
2
1
0
2
1
1
0
1
0
1
2
0
0
1
0
1
3
2
1
2
0
2
1
1
2
1
0
0
0
0
1
2
2
0
1
1
0
0
1
0
2
0
1
1
0
2
0
1
1
1
0
1
1
0
0
1
1
1
0
0
1
1
0
1
0
0
0
0
1
1
2
1
0
2
0
0
1
0
1
2
1
1
1
0
1
0
1
1
1
2
1
1
1
0
1
0
0
0
1
1
0
0
1
0
0
2
2
2
1
0
1
3
1
1
2
0
1
0
2
0
1
1
1
1
0
1
1
0
0
1
1
1
0
1
1
1
1
0
2
1
0
0
2
0
0
2
0
1
0
0
0
1
0
0
0
2
1
1
1
3
1
2
0
1
2
2
2
1
1
1
0
1
1
0
0
1
0
0
0
0
0
2
0
2
0
1
0
0
2
0
0
2
1
0
0
2
1
1
0
0
2
1
1
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
1
0
1
2
0
0
2
1
4
0
0
1
1
0
0
2
0
0
1
0
1
0
1
0
0
0
1
0
2
0
0
2
0
1
3
0
0
1
1
0
0
0
0
2
0
1
1
0
0
0
1
1
1
2
2
2
0
1
2
2
0
0
1
0
0
0
0
1
0
1
2
0
1
0
0
0
2
0
0
1
0
1
0
0
0
2
0
0
0
0
1
0
1
0
2
0
2
0
2
1
0
0
1
0
2
1
0
0
2
0
0
0
0
2
1
0
0
2
0
2
1
3
0
0
0
0
1
2
2
1
0
3
1
0
1
0
0
1
0
2
0
0
0
0
1
0
1
0
1
1
0
0
0
3
0
1
2
0
0
0
1
1
1
1
2
2
1
2
1
1
1
2
0
2
1
1
0
1
2
0
1
0
0
0
1
0
0
2
1
0
0
1
1
1
1
1
2
1
2
1
0
1
2
0
0
2
0
0
2
0
2
1
0
0
2
2
0
0
1
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
2
0
2
2
1
0
2
0
2
0
1
2
0
0
0
0
0
0
0
1
0
2
1
1
1
0
2
2
2
1
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
1
2
1
0
4
2
1
0
0
0
1
0
1
1
2
0
2
0
1
0
2
1
1
0
0
0
0
1
1
2
2
1
1
2
1
0
0
1
2
2
0
2
1
0
0
1
1
0
0
0
1
1
1
1
0
0
2
1
1
1
1
0
1
0
0
2
1
1
0
1
0
5
0
0
0
1
1
1
1
0
0
0
0
1
1
1
0
1
1
0
0
2
2
0
1
3
0
1
1
0
0
2
0
0
0
0
1
0
1
2
0
2
2
0
0
0
0
0
2
1
0
0
0
1
2
0
0
1
0
0
0
2
2
1
1
1
1
0
0
1
1
1
2
2
1
1
0
1
1
1
2
2
0
1
1
0
0
0
1
0
1
0
0
2
0
2
1
1
1
1
1
2
0
1
1
2
1
1
1
2
0
1
2
2
1
1
0
0
0
2
1
2
1
0
0
1
0
3
1
1
1
0
2
1
1
0
0
0
1
0
0
1
1
0
1
0
0
2
2
0
2
1
0
2
1
0
0
2
1
2
0
0
0
1
0
0
0
0
0
0
1
1
1
2
3
1
1
1
1
1
0
2
2
0
1
1
0
0
0
1
1
2
0
0
2
0
1
1
2
0
1
0
2
1
0
1
2
0
0
1
1
2
2
0
2
0
0
2
0
2
1
0
0
1
0
1
0
2
0
1
2
0
0
1
1
1
2
2
2
2
1
0
1
2
1
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
1
0
0
1
2
0
1
2
1
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
1
0
1
1
0
1
0
2
0
2
1
0
0
0
2
1
0
0
0
2
1
0
1
0
1
1
2
2
0
1
0
2
1
0
1
1
0
1
2
0
0
0
1
1
2
1
2
1
0
0
0
0
5
1
0
1
1
0
2
0
2
0
1
0
0
0
1
0
0
0
1
1
1
1
1
2
0
0
0
2
1
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
1
3
1
1
0
0
2
0
2
1
2
0
2
1
1
1
1
0
0
0
0
1
0
0
0
0
1
2
0
1
3
1
0
0
1
0
0
1
0
0
1
0
0
1
0
1
0
1
2
2
0
2
0
0
0
2
0
1
1
0
0
0
0
1
2
0
0
0
2
1
0
1
2
0
0
1
2
1
1
0
2
0
0
1
2
1
0
1
1
2
2
0
0
1
0
0
1
2
1
0
1
0
0
1
1
0
2
5
2
1
1
1
0
1
1
2
0
0
0
2
1
2
1
0
1
2
1
1
1
1
0
1
0
2
0
3
2
0
2
0
1
2
0
1
0
0
1
0
0
0
1
1
0
0
2
1
0
0
1
0
2
0
0
1
0
2
1
1
0
0
1
1
1
0
0
0
1
2
0
0
1
0
0
2
0
0
1
1
2
0
0
0
1
2
2
1
0
1
3
0
0
1
1
0
0
0
0
1
0
2
0
1
1
0
1
0
2
1
0
1
1
1
1
1
2
2
2
2
2
0
0
0
2
2
1
1
1
1
0
1
2
0
1
1
0
1
0
0
1
2
2
0
0
0
1
3
2
0
1
1
0
0
1
1
1
0
1
2
1
0
1
0
0
0
1
1
1
0
1
0
1
0
0
1
1
0
1
1
1
2
0
0
0
2
0
2
1
1
0
1
0
1
0
2
1
0
0
1
2
1
1
1
1
0
2
2
0
1
0
0
2
1
0
0
0
0
0
0
0
0
3
1
1
1
0
0
0
0
2
1
0
1
0
2
1
0
1
1
1
1
1
0
2
0
0
0
0
1
1
0
0
2
1
1
1
0
1
0
0
0
0
1
0
2
2
1
2
0
1
2
2
0
0
5
0
2
1
0
2
1
4
0
1
0
1
1
0
1
0
0
0
2
1
0
2
2
0
0
2
0
1
0
0
3
0
1
1
0
1
1
2
1
0
1
0
1
1
0
0
0
0
1
2
1
0
0
0
1
0
1
2
0
0
1
1
1
1
1
1
0
1
1
2
1
1
0
2
0
0
1
1
1
3
1
1
0
1
0
1
2
0
0
0
0
0
1
1
3
0
1
1
0
0
1
1
2
0
0
1
1
1
1
1
0
2
1
0
0
0
2
1
2
1
2
1
2
1
1
0
1
0
1
1
0
0
1
0
0
0
1
0
1
0
1
3
1
0
1
1
0
0
1
2
1
2
1
1
0
1
1
1
2
0
1
2
1
0
1
0
1
0
1
0
0
0
0
2
1
2
0
2
1
2
1
0
2
1
0
1
0
1
0
0
0
0
1
1
0
0
1
2
1
0
0
1
1
1
0
1
2
0
0
0
0
2
2
1
2
1
1
1
0
3
0
1
1
2
0
0
0
0
0
1
0
0
2
1
2
0
0
2
1
2
2
2
1
1
3
0
2
2
1
2
2
1
2
1
1
1
0
0
2
1
0
0
2
0
1
0
2
0
2
1
1
0
1
2
0
0
1
1
0
1
0
1
0
1
1
0
0
1
0
2
0
1
0
0
0
3
0
1
1
0
2
0
0
1
1
0
1
0
1
0
0
0
1
0
0
0
2
0
0
1
0
0
1
1
2
1
0
0
1
1
0
0
0
3
0
1
2
0
1
1
1
1
1
1
1
2
1
0
0
0
0
1
1
0
1
0
1
1
1
2
1
0
1
0
2
0
2
2
0
0
1
0
1
1
1
1
2
2
0
0
0
1
0
3
2
2
0
1
1
1
0
0
0
1
0
1
1
0
4
0
0
1
1
0
0
1
0
1
0
2
1
1
0
2
0
1
1
0
2
0
0
2
2
0
2
1
1
0
1
1
1
0
1
0
0
1
1
2
0
0
1
2
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
1
0
2
0
1
2
2
0
1
1
1
0
0
0
0
1
0
2
0
0
1
1
1
2
0
1
0
1
0
0
0
0
2
1
0
0
2
0
3
2
0
1
0
2
1
0
2
2
0
1
1
0
0
0
2
0
1
0
1
0
1
1
1
2
0
1
0
0
0
0
0
0
2
1
1
1
1
1
2
1
0
0
2
0
1
1
0
1
1
0
0
1
0
1
2
0
1
0
0
1
0
0
1
3
0
1
0
3
1
1
1
1
0
0
1
4
0
0
1
1
1
0
0
0
2
1
2
1
0
0
3
0
1
0
0
0
0
0
1
1
1
0
1
1
0
0
0
1
0
1
0
1
2
2
2
2
1
0
1
0
2
1
0
1
1
1
2
5
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
2
1
0
2
1
1
1
0
1
0
2
0
2
1
0
0
0
1
0
2
0
1
2
0
0
1
1
0
0
2
0
0
0
0
2
1
0
1
1
2
0
0
1
0
1
0
0
1
0
1
0
0
1
0
2
1
1
1
2
0
0
1
0
0
1
0
0
0
2
0
2
0
0
2
2
0
0
0
1
0
0
0
1
2
2
2
0
2
2
1
0
1
0
1
1
0
0
2
0
3
1
0
0
0
1
0
1
1
1
1
1
0
2
0
0
1
0
2
1
0
0
2
2
0
0
0
2
1
0
1
1
0
2
2
1
0
1
2
1
1
1
0
0
1
0
1
1
0
2
1
0
1
1
0
2
1
1
2
1
2
0
0
1
0
0
2
1
2
1
0
1
1
2
0
0
1
2
0
0
1
1
2
1
1
0
1
2
2
2
2
2
1
1
0
1
2
0
2
0
1
2
2
0
0
0
1
1
1
0
2
1
2
2
0
0
2
0
0
0
1
1
0
1
1
0
1
0
1
2
1
1
2
2
1
0
0
0
0
3
0
1
1
2
0
1
1
1
0
2
0
0
0
0
0
2
2
0
1
3
0
0
0
1
1
0
2
0
2
0
0
0
2
0
1
0
0
0
1
1
0
1
2
2
0
0
1
2
2
1
0
1
1
2
2
2
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
2
1
1
1
0
0
1
0
1
0
0
1
1
1
2
0
1
0
0
0
1
1
1
2
0
0
1
1
0
0
1
2
2
0
2
0
1
1
1
0
0
1
2
1
2
2
0
0
0
2
1
0
0
1
0
0
1
0
1
0
2
1
1
1
2
0
0
0
2
0
0
1
2
0
0
2
0
0
1
0
1
0
1
0
0
0
1
2
0
2
0
1
0
0
1
2
1
2
1
0
2
1
1
1
0
0
1
2
1
1
0
1
2
0
1
0
0
0
0
1
0
1
1
1
1
0
1
3
2
0
1
1
1
0
2
0
1
1
1
0
0
0
1
0
2
0
2
0
0
0
2
0
0
1
1
2
1
1
0
0
0
0
1
0
1
0
1
1
0
1
1
1
0
2
0
2
1
0
1
0
1
2
1
1
2
2
1
1
0
0
0
0
1
1
1
1
2
2
0
1
3
0
0
1
2
1
1
1
0
1
0
1
2
0
2
0
2
2
0
2
2
2
2
2
2
1
0
1
0
0
0
0
0
1
1
1
2
0
0
1
1
6
0
0
1
1
1
0
0
1
1
1
2
0
0
2
2
0
2
0
0
2
0
1
1
0
2
1
1
0
0
1
0
1
2
1
0
2
1
1
1
0
0
1
0
0
3
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
1
1
0
1
1
5
2
1
2
0
0
1
1
0
2
1
1
0
0
1
2
0
1
1
1
0
1
2
2
0
0
2
0
0
1
1
1
0
0
2
1
0
0
0
1
0
0
1
2
1
2
1
1
0
2
0
0
0
2
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
2
1
1
0
1
1
1
0
1
1
0
1
0
2
0
0
1
2
1
0
1
0
0
1
0
2
0
4
1
1
2
2
0
1
0
0
0
0
2
0
0
4
1
1
2
1
2
0
1
1
0
2
0
0
1
2
2
1
0
0
2
1
2
0
0
0
1
1
1
0
1
0
1
0
0
0
1
1
2
1
1
0
0
0
2
1
0
1
1
2
0
2
1
0
2
2
0
0
0
1
1
1
0
1
2
0
0
0
2
1
1
0
0
1
1
0
1
0
0
0
2
1
2
1
2
2
0
1
0
1
1
2
2
1
3
2
0
1
0
0
0
2
0
0
2
1
1
1
0
0
0
1
2
1
1
0
2
1
1
0
1
0
1
4
1
0
0
0
1
1
0
0
2
2
0
0
2
0
0
2
0
2
0
0
1
2
1
0
0
0
0
0
1
2
0
1
0
2
2
2
0
2
1
0
1
1
1
0
0
1
0
0
0
0
1
0
0
2
0
0
2
0
0
1
2
1
0
1
1
2
2
0
0
1
1
1
0
1
0
0
1
0
2
0
1
1
1
2
0
2
1
0
0
0
2
1
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
3
0
1
1
0
1
0
1
2
1
0
0
1
0
0
0
0
1
0
0
2
0
0
0
2
0
0
1
0
0
1
0
1
1
1
1
0
1
0
1
1
1
0
1
0
1
0
0
1
0
1
0
0
0
0
0
1
1
2
2
1
1
0
1
0
0
0
2
0
2
1
1
1
2
1
2
1
1
9
0
1
1
2
0
1
0
1
0
0
0
0
0
0
2
2
1
0
1
1
0
2
0
1
2
0
1
0
0
0
0
1
0
1
2
0
1
1
0
0
1
0
1
0
3
1
1
1
0
1
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
2
2
1
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
2
1
0
2
0
0
1
0
0
1
1
0
1
0
1
2
0
1
1
1
0
1
0
1
4
0
1
0
0
1
0
0
2
2
0
0
0
1
0
0
1
0
0
1
1
2
0
2
1
0
0
0
0
0
1
1
0
2
1
1
0
1
1
0
2
1
1
1
1
0
0
0
0
1
0
0
2
2
2
2
0
0
2
2
2
2
1
0
0
1
1
6
1
1
0
1
2
1
1
1
1
1
0
0
1
0
2
0
1
0
0
0
2
1
0
0
1
0
1
0
2
0
0
2
2
0
0
2
2
1
0
0
2
6
2
0
0
2
0
1
1
1
1
1
0
2
1
0
0
1
1
1
0
0
2
1
0
1
2
2
1
0
1
1
1
2
1
1
0
0
2
0
2
0
0
1
0
1
1
2
0
2
0
4
0
0
0
0
1
1
0
0
2
2
0
0
1
1
1
2
2
0
0
1
0
0
1
1
2
1
0
0
1
1
0
0
1
0
1
0
0
2
0
1
0
0
2
0
1
1
1
0
0
1
0
1
0
1
0
1
1
0
0
2
1
2
1
0
1
2
0
1
0
1
2
0
2
0
1
0
1
1
2
0
1
0
5
1
0
5
0
0
0
0
1
2
0
1
1
1
1
0
0
1
0
0
0
1
2
2
0
0
1
1
1
0
0
2
1
0
2
0
1
0
1
1
1
0
2
1
2
0
0
1
0
2
0
1
2
2
0
1
3
0
1
0
0
1
1
1
3
0
1
0
0
2
1
0
0
1
2
0
1
1
0
0
2
0
0
1
0
0
1
1
0
0
1
1
1
0
1
3
3
1
2
1
2
1
1
1
1
2
0
0
0
0
1
0
1
0
0
2
1
1
2
0
0
0
0
0
2
1
2
0
0
2
2
0
0
1
1
1
0
1
0
0
1
1
1
1
0
2
2
2
4
2
1
2
0
2
0
0
0
1
1
3
2
1
1
2
1
3
2
2
3
0
2
1
1
1
0
0
2
0
2
2
0
0
1
2
1
0
0
1
1
0
2
2
1
2
0
2
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
1
1
2
1
2
1
2
0
2
2
1
0
2
0
1
0
1
0
0
1
1
3
1
1
1
1
0
0
0
1
2
0
1
0
0
1
0
0
1
0
2
0
1
2
1
0
0
1
0
0
1
1
2
0
0
0
0
1
0
2
2
0
1
1
0
2
1
1
2
0
1
0
2
1
2
1
1
1
1
0
0
0
0
0
1
0
1
0
0
1
3
0
0
1
0
2
1
0
1
0
0
1
2
0
2
0
0
0
0
0
0
1
1
1
2
1
4
1
2
0
0
0
0
0
0
1
2
0
1
0
2
2
0
4
0
1
2
1
0
1
1
1
1
2
1
1
2
0
0
1
0
0
1
2
0
2
1
0
1
1
2
0
0
0
2
1
2
0
2
2
0
1
0
2
2
2
0
1
0
2
0
1
0
0
0
1
1
1
1
1
0
0
1
0
1
0
2
2
0
0
0
0
0
0
1
1
0
0
2
1
2
1
1
1
0
2
1
0
2
1
1
0
1
0
0
0
2
2
1
1
1
0
0
0
0
0
0
0
1
0
1
0
2
1
0
3
0
1
0
1
0
0
0
0
0
0
1
0
1
0
1
0
2
0
2
0
2
3
3
2
0
1
3
0
2
0
0
2
2
0
0
2
0
0
2
1
0
0
0
0
0
2
0
0
1
1
2
0
0
1
2
0
0
0
3
2
2
2
0
1
2
2
2
1
0
1
0
1
2
0
1
0
0
0
1
0
2
0
1
1
2
0
0
0
1
0
0
2
1
0
0
1
0
1
1
0
1
1
1
0
0
0
1
0
0
0
0
1
2
1
0
1
2
0
1
1
1
0
0
1
0
1
0
0
0
1
0
0
0
1
1
0
2
0
2
1
0
3
2
2
1
1
0
0
0
1
1
0
0
2
0
1
1
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
2
1
1
1
0
0
2
1
2
0
1
0
0
1
1
2
0
1
1
0
0
0
3
0
1
1
2
0
1
0
0
1
0
0
2
0
0
1
2
1
0
3
0
0
1
1
0
1
1
1
1
0
0
1
0
0
1
3
1
0
0
1
1
0
0
0
2
1
0
0
0
1
0
4
0
0
0
0
1
0
0
0
0
1
1
1
1
1
0
0
0
2
0
2
0
2
0
0
1
2
0
0
0
1
1
0
1
1
0
0
0
1
1
0
1
0
0
2
0
1
1
1
2
0
2
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
2
2
0
2
1
0
0
0
1
2
0
0
0
2
1
2
0
2
0
5
1
0
2
2
0
2
1
0
1
0
0
0
3
1
1
3
1
1
1
0
0
1
0
1
0
0
0
1
2
0
0
1
2
0
1
0
1
0
2
1
0
0
0
1
1
0
1
0
1
1
1
0
1
1
1
0
4
1
0
0
0
1
1
0
1
2
0
0
0
2
0
0
0
1
1
1
1
0
0
0
2
0
0
0
0
1
2
1
2
0
2
2
0
1
1
0
1
1
1
0
2
0
2
1
1
0
2
0
0
1
2
0
0
0
1
0
0
0
1
1
1
0
1
0
2
0
1
0
2
2
0
0
1
1
0
0
0
0
1
0
1
0
0
1
0
0
1
0
2
1
1
2
0
2
0
2
2
0
0
0
0
0
1
0
0
1
2
0
2
2
1
0
2
0
0
0
0
0
2
2
1
0
2
0
0
2
0
1
2
1
1
2
0
0
0
0
1
0
0
0
2
2
0
2
0
1
1
0
1
0
0
0
0
0
1
0
2
0
1
2
0
0
0
0
0
0
0
2
0
1
1
2
1
1
0
0
2
2
0
0
0
1
1
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
2
0
0
2
1
0
1
1
2
2
0
0
0
0
0
1
0
0
2
2
0
1
0
0
1
1
0
0
2
0
0
1
0
1
0
2
0
1
1
2
1
3
1
2
1
0
0
2
2
1
2
1
0
1
0
1
1
0
2
0
0
0
1
1
0
0
0
0
1
0
3
1
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
2
2
0
2
1
0
2
1
0
0
0
0
0
1
1
0
1
1
1
2
2
1
2
0
2
0
1
0
2
1
1
0
1
1
1
0
0
0
2
1
0
2
0
1
0
1
2
2
0
1
1
1
0
1
0
0
0
1
0
2
2
0
0
1
2
1
1
0
2
1
1
1
0
1
0
0
2
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
2
0
1
0
0
1
2
1
0
1
2
1
1
0
0
0
1
1
1
2
0
1
0
2
0
0
0
0
1
0
3
0
0
2
2
0
0
1
0
1
0
1
0
4
0
2
1
2
2
2
2
0
1
1
0
0
0
0
0
0
0
0
0
1
2
0
2
1
0
0
0
0
2
1
3
0
1
2
0
0
0
0
1
0
1
0
1
1
0
1
1
1
1
0
2
0
0
1
2
0
0
2
1
2
1
2
0
2
2
0
2
2
2
0
0
2
0
0
1
1
0
2
1
0
4
0
1
0
0
1
0
0
1
0
0
0
0
0
2
0
2
1
2
1
0
0
1
1
1
1
1
2
0
0
0
2
1
1
0
2
2
1
0
1
0
1
0
0
0
0
2
1
0
0
1
0
0
1
2
0
2
0
3
2
1
1
0
0
0
0
1
0
0
0
0
1
2
0
0
0
1
1
1
1
0
1
2
0
0
1
0
1
1
0
0
0
2
0
1
0
0
2
2
2
1
2
0
0
0
1
0
0
0
2
1
1
0
2
2
2
1
2
1
1
1
0
2
0
2
1
0
2
1
1
0
2
0
0
2
0
1
2
2
0
2
1
0
1
0
0
0
1
0
2
1
2
2
2
2
0
0
1
1
0
1
0
0
0
0
0
1
0
2
0
2
0
2
0
0
1
1
0
1
2
0
2
2
2
0
0
2
0
0
0
1
1
0
1
1
0
2
0
1
0
0
1
0
2
2
1
0
3
0
0
1
1
0
1
2
2
1
0
1
2
1
0
2
2
2
1
0
1
1
1
0
2
2
0
0
0
1
1
0
2
1
0
2
2
1
2
1
1
0
0
0
1
1
1
2
0
2
0
0
1
0
2
0
0
1
1
1
1
0
0
2
1
0
2
1
0
1
0
1
1
2
0
1
0
1
2
0
2
2
1
0
1
0
0
1
2
0
1
1
2
0
0
0
0
0
1
0
1
1
2
1
1
0
1
1
1
4
1
1
0
0
1
1
1
0
0
1
0
5
2
0
0
1
2
0
0
1
2
1
1
0
2
2
0
0
0
3
0
0
0
0
0
2
1
1
0
1
1
1
1
0
0
1
1
1
2
1
0
2
1
0
1
1
0
0
0
0
1
1
1
0
0
1
0
0
0
0
1
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
1
2
0
6
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
4
1
2
2
2
0
1
1
0
0
2
1
1
2
1
0
0
0
2
0
0
1
2
1
0
2
1
1
0
0
2
0
2
0
0
1
1
1
2
0
0
0
2
0
0
0
0
0
1
0
0
1
1
0
0
1
2
1
1
0
0
1
0
0
0
1
2
1
1
1
0
0
2
3
1
0
1
1
1
2
1
1
0
0
0
0
0
1
0
2
0
1
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
2
0
0
1
0
3
3
1
1
0
2
0
0
1
0
3
0
2
2
0
0
0
0
1
0
0
2
1
2
2
2
0
1
1
0
2
0
0
1
1
0
2
0
1
0
0
0
0
1
0
2
2
0
0
0
0
0
1
0
2
1
1
0
1
2
2
1
0
2
0
0
1
1
0
1
2
0
0
1
2
0
1
0
1
1
1
2
1
0
0
1
0
0
0
1
2
0
2
1
0
0
2
1
0
1
0
1
0
1
2
2
2
0
0
1
0
0
1
1
0
2
0
0
1
1
0
2
1
1
0
2
1
1
1
1
0
0
0
1
3
1
1
0
1
0
2
0
2
0
2
0
0
1
2
2
1
0
0
1
1
0
1
0
1
2
3
0
1
2
0
0
0
0
2
0
2
1
0
2
0
2
1
0
0
1
1
2
1
0
1
0
2
1
0
0
2
0
1
0
2
0
5
1
0
0
0
0
2
1
2
1
0
0
1
0
1
0
0
0
2
0
0
1
0
2
0
1
1
1
2
0
0
1
0
1
0
1
0
0
1
0
1
2
1
0
0
1
0
0
0
1
2
0
0
0
2
2
1
1
1
1
0
0
1
2
1
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
2
0
0
2
1
0
1
1
0
1
1
0
2
0
0
0
1
1
2
0
0
0
1
0
1
1
0
1
1
0
0
1
2
1
0
1
1
0
2
1
2
2
0
0
1
1
0
0
1
1
2
1
0
1
1
2
1
1
1
2
1
0
0
1
1
0
1
2
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
2
1
2
0
0
0
0
2
0
2
1
0
0
1
0
2
2
0
0
0
1
1
0
1
0
2
2
0
0
1
0
1
2
0
2
1
0
0
1
1
0
0
1
0
0
1
2
1
1
2
0
0
0
0
1
0
1
0
3
1
1
2
2
2
0
0
0
0
0
1
0
1
2
0
1
2
0
2
2
1
1
0
0
1
0
0
1
1
1
0
0
1
0
0
0
1
0
0
1
1
1
0
2
0
0
2
2
1
0
1
1
1
0
2
2
1
0
1
1
2
1
1
0
1
1
0
0
2
1
0
1
0
0
0
0
1
0
1
0
0
0
1
3
1
2
0
1
1
1
1
0
2
1
1
0
0
1
0
2
1
1
0
1
1
0
0
2
0
1
0
1
1
1
0
2
0
0
2
1
0
1
0
0
0
1
0
0
1
0
0
0
0
2
0
0
3
2
0
0
1
1
0
1
0
0
2
2
1
1
0
0
1
1
0
1
2
2
0
1
0
0
0
1
0
2
1
2
1
2
1
0
0
0
0
1
0
0
0
1
1
0
0
1
1
1
1
0
0
0
1
2
1
0
0
0
1
1
0
1
0
0
2
0
1
2
2
0
0
2
0
1
1
0
1
0
1
0
1
1
2
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
2
2
1
0
0
0
2
1
2
0
0
2
0
0
0
2
2
1
1
2
0
2
1
0
1
0
2
1
0
0
1
0
0
0
0
0
1
0
1
2
0
2
1
0
1
0
0
0
0
2
0
0
2
1
0
0
0
2
0
2
0
0
1
0
0
2
1
1
0
0
1
0
0
0
1
1
0
1
1
2
1
2
1
2
0
1
0
0
1
2
0
0
1
1
0
0
0
0
0
2
0
1
0
0
1
1
1
1
0
2
0
1
0
0
0
1
0
2
0
1
1
1
2
1
1
0
0
1
2
2
1
0
1
2
1
0
2
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
6
1
2
1
2
0
0
2
0
1
3
1
2
0
1
2
0
0
0
0
2
2
0
0
0
2
0
1
1
1
0
0
1
0
0
0
0
0
2
2
2
0
0
1
1
1
1
1
3
1
0
1
2
0
1
0
1
2
0
2
2
0
2
1
0
3
0
0
1
2
0
0
0
1
1
0
1
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
1
0
3
1
1
0
1
1
0
1
1
2
0
1
0
1
1
1
0
2
1
1
0
0
0
2
3
1
0
0
0
1
1
2
0
0
2
1
0
0
1
1
0
0
0
1
1
1
2
1
1
1
1
2
0
0
0
0
2
1
0
0
1
0
0
1
0
0
0
2
1
1
0
0
0
1
1
1
0
1
0
0
0
0
2
0
1
2
1
0
1
0
0
2
0
0
0
2
1
0
2
3
1
2
1
1
0
0
0
0
0
0
1
0
1
1
1
1
2
0
0
1
0
1
1
0
0
2
2
1
0
3
0
7
1
0
2
1
0
2
0
0
1
0
1
1
1
0
0
0
0
1
1
2
0
0
2
0
0
0
0
2
0
1
0
2
2
0
0
1
0
0
1
1
0
0
1
0
1
0
1
2
0
0
1
0
0
0
0
1
1
2
1
0
0
0
2
0
2
0
1
1
0
1
1
1
2
1
2
0
0
0
0
0
1
2
0
1
1
2
1
2
0
1
2
0
0
0
0
1
0
2
0
1
0
4
2
1
1
1
2
0
0
0
0
0
1
1
1
0
0
1
1
1
0
1
2
2
0
0
1
0
0
0
2
2
0
0
0
3
1
1
2
0
1
1
0
0
0
0
1
1
0
0
2
2
0
1
1
2
2
0
0
3
2
0
0
0
2
3
2
3
2
0
1
2
0
0
2
1
1
0
2
1
0
1
0
0
1
1
0
0
1
2
0
2
2
0
2
1
1
3
2
1
0
0
2
1
1
0
0
2
0
0
1
2
0
1
0
0
0
2
0
2
1
0
0
0
0
1
1
0
0
0
0
2
0
0
0
1
1
0
1
0
0
1
0
2
0
1
0
0
1
1
0
2
0
0
0
0
0
1
2
2
2
0
2
0
0
2
0
1
2
0
0
1
0
1
2
0
1
1
0
2
0
1
1
0
0
1
2
2
1
1
1
2
0
2
0
0
2
0
0
0
2
0
1
1
0
0
2
2
2
0
2
1
2
0
1
2
1
0
0
0
0
0
0
2
1
0
1
0
1
1
1
0
0
0
1
1
2
3
2
0
2
0
0
1
2
0
0
0
0
0
0
1
1
0
0
0
2
2
0
1
0
0
0
0
0
2
0
2
1
2
1
0
4
0
1
0
0
2
1
1
0
0
0
0
0
2
0
0
1
0
0
2
0
2
1
2
1
1
1
1
1
0
0
0
0
2
2
1
2
2
1
1
2
1
0
2
1
2
2
1
0
1
2
2
0
1
0
0
1
2
2
2
2
0
0
1
1
0
1
1
1
0
2
0
0
2
0
1
1
0
2
2
1
2
1
0
2
0
2
2
0
1
2
0
1
0
1
0
0
0
0
2
1
2
1
0
0
0
1
2
1
0
0
1
0
0
1
2
0
0
1
0
1
0
0
1
1
0
2
1
1
1
0
0
0
1
2
0
0
0
1
1
1
0
1
3
2
1
2
0
1
0
1
1
1
1
1
2
1
2
2
2
0
0
1
1
0
2
1
0
1
2
0
0
0
0
2
0
0
0
1
0
0
1
2
0
1
1
1
1
0
1
0
2
2
2
2
2
2
0
0
1
0
1
0
0
0
0
0
0
2
1
1
0
2
1
1
0
1
0
2
0
0
0
0
1
2
2
0
0
1
0
2
0
0
0
1
0
0
3
2
2
0
0
2
2
1
0
2
1
0
1
1
0
1
1
0
0
3
0
1
0
0
0
1
0
0
1
0
1
2
3
1
0
0
0
1
1
0
0
1
1
1
2
0
0
1
2
1
1
1
1
2
1
1
0
1
0
0
2
0
1
1
0
0
0
1
0
0
0
1
2
0
0
0
1
0
0
0
4
0
2
0
1
0
0
1
0
0
2
0
0
0
2
0
0
1
2
0
2
0
3
2
0
0
0
0
1
0
0
2
0
2
2
0
1
0
1
2
1
2
0
1
2
2
0
1
0
0
0
1
0
2
1
0
0
1
1
4
0
1
1
0
2
2
0
2
0
1
1
0
1
0
1
3
7
1
1
0
0
1
0
0
1
1
2
0
0
0
2
0
0
0
1
1
2
1
2
0
1
0
0
1
3
0
0
1
0
1
0
1
1
2
2
1
2
1
0
4
1
0
0
1
1
0
0
2
0
0
0
1
1
0
0
1
1
1
0
2
2
0
1
0
1
0
1
0
0
1
0
0
2
1
2
2
0
0
1
2
0
0
0
0
1
1
0
1
0
0
0
0
1
0
1
1
1
2
0
1
1
0
0
0
1
2
2
0
1
0
0
0
2
1
0
0
1
1
3
1
1
1
0
3
1
0
0
2
0
2
0
0
0
0
2
2
2
0
0
0
1
1
1
1
0
0
0
1
0
0
0
0
1
0
2
0
1
1
0
2
0
1
2
0
2
1
1
0
2
0
1
0
0
1
1
2
0
0
1
2
0
1
1
0
0
0
3
0
1
0
0
2
0
0
0
1
1
2
0
0
2
0
0
1
0
0
4
0
1
0
0
1
2
1
2
0
1
2
1
1
2
2
2
1
1
1
0
2
1
0
1
0
2
1
0
0
0
0
0
1
0
1
0
0
2
2
0
1
2
0
0
3
1
1
0
2
0
0
0
1
1
0
0
0
0
1
1
1
0
1
0
1
1
0
0
0
0
0
0
1
1
0
1
2
1
0
0
0
1
1
0
1
0
0
1
2
0
0
0
1
1
0
1
0
1
1
0
1
0
2
1
0
2
0
2
2
0
1
0
0
0
4
2
1
0
1
0
0
2
0
2
0
2
0
0
0
0
0
1
1
2
0
1
2
4
2
0
0
2
1
0
1
0
0
0
2
1
2
0
0
2
0
2
0
0
2
1
0
0
1
2
1
0
2
0
0
0
2
0
1
0
1
2
0
1
2
0
0
1
0
2
0
1
1
0
0
0
0
0
1
0
0
1
1
0
1
0
1
1
2
1
0
1
0
1
1
0
2
0
0
2
0
1
0
2
1
1
1
1
0
0
0
0
1
2
0
0
2
0
0
1
0
0
0
1
1
0
2
2
0
1
0
0
1
2
0
0
2
2
3
3
2
1
1
2
0
0
2
1
2
0
0
0
2
1
0
2
1
1
0
1
0
0
1
0
2
0
1
0
1
0
1
1
3
0
0
1
0
0
0
2
1
0
1
1
1
0
2
1
0
1
0
2
0
0
1
0
1
1
2
0
1
0
0
0
0
2
2
0
2
0
0
1
1
0
0
1
1
2
1
2
0
1
0
0
1
0
2
2
2
0
0
1
0
0
2
0
2
2
0
0
0
3
1
0
0
0
0
2
1
2
0
0
1
0
1
0
0
1
0
1
2
0
0
0
0
1
0
1
0
1
0
0
1
3
2
0
0
0
0
2
1
1
2
0
1
0
1
2
1
0
2
1
0
0
1
2
1
1
1
0
0
0
2
1
1
2
0
1
2
0
1
3
0
0
1
1
1
2
1
1
0
2
3
2
3
7
2
1
1
2
2
0
1
0
2
0
0
0
1
0
0
1
2
0
0
0
0
0
1
2
1
0
0
4
0
2
1
0
0
0
0
1
1
1
1
1
0
0
2
1
0
1
1
1
2
0
0
1
2
1
1
1
2
0
1
2
0
1
1
0
1
0
1
2
1
2
0
0
0
1
1
1
1
1
2
0
0
1
1
1
0
1
0
1
1
2
0
2
2
0
0
3
0
0
0
0
1
0
2
0
0
1
0
1
2
1
0
1
0
0
0
0
1
1
1
0
0
2
2
0
2
0
0
1
0
1
0
2
1
0
2
0
2
2
1
2
0
0
1
0
0
0
1
1
0
0
1
2
0
0
0
1
1
1
0
1
0
2
0
0
1
0
0
1
0
2
0
2
0
0
0
0
1
1
0
0
1
1
1
1
1
1
1
1
1
0
0
1
1
1
0
1
2
1
1
2
1
0
1
1
1
1
1
0
0
0
2
0
2
0
0
0
2
0
0
0
0
1
0
1
1
0
1
0
2
2
0
2
2
1
1
0
1
0
0
0
0
1
1
2
0
1
0
2
1
0
0
0
1
0
1
0
0
0
1
2
2
0
2
1
0
0
1
2
0
1
2
2
0
1
1
0
0
0
1
1
1
2
2
0
2
0
2
0
1
0
1
0
0
2
1
0
5
0
0
1
0
1
0
0
1
2
0
2
1
1
2
1
2
2
1
1
1
0
0
1
2
0
1
0
0
0
5
0
0
1
0
2
2
1
0
2
1
1
1
2
2
0
0
0
1
1
2
1
0
0
0
1
1
0
1
2
1
0
0
2
2
0
0
1
2
0
2
1
0
2
1
0
0
2
0
1
0
1
1
0
0
0
0
1
0
0
0
3
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
2
2
0
2
0
0
1
1
1
2
0
0
2
1
1
1
0
0
0
1
0
0
1
0
2
0
1
1
1
0
0
0
1
1
2
1
0
1
2
2
1
0
2
0
2
0
0
1
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
2
1
0
0
2
0
2
1
0
1
1
1
2
0
1
1
0
0
1
0
1
1
0
1
0
0
0
0
0
1
0
0
0
1
1
1
0
0
2
0
2
0
0
0
0
0
0
0
0
1
1
0
1
1
0
2
0
0
0
1
1
0
0
1
1
0
0
0
1
1
0
0
0
0
2
2
0
0
2
2
0
0
0
1
0
2
1
1
1
2
0
0
1
0
0
0
1
0
2
0
0
1
1
1
0
0
0
1
0
1
1
0
0
0
0
2
2
1
2
1
0
0
1
1
1
1
0
0
2
0
0
0
0
0
1
0
1
1
2
0
0
0
0
2
1
1
1
0
1
0
1
2
0
0
0
2
1
2
0
0
1
0
0
3
1
2
0
1
0
0
1
0
1
2
0
1
1
0
0
1
0
1
0
3
1
1
2
0
1
2
0
1
0
0
2
0
2
0
0
0
2
0
1
0
1
1
2
0
1
0
3
2
1
0
0
1
0
0
1
0
1
0
1
0
2
2
1
2
0
0
2
1
1
1
3
0
0
1
1
0
1
2
1
1
1
1
2
0
2
0
0
0
0
2
1
0
1
2
0
1
2
0
1
0
1
0
0
1
0
0
0
0
1
2
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
1
2
2
2
0
2
0
0
0
1
2
1
2
1
0
0
0
1
1
0
1
1
1
0
0
0
2
0
3
0
0
0
0
1
1
0
0
0
2
2
1
0
0
1
1
0
0
1
0
1
0
1
0
0
2
1
1
0
0
0
3
0
1
0
0
0
2
1
1
2
1
0
0
0
0
1
0
1
0
1
0
1
2
1
2
0
0
4
1
1
0
2
0
1
2
0
2
1
2
0
2
0
2
0
2
1
0
1
2
0
1
1
1
1
2
1
1
1
1
0
0
2
0
0
2
0
0
2
1
2
1
3
0
0
0
1
0
2
0
1
3
0
2
1
0
1
0
0
0
0
0
2
2
0
1
1
1
1
1
0
0
0
0
0
0
1
1
1
1
1
0
0
0
0
4
0
0
1
0
0
2
0
0
1
1
2
0
0
2
1
0
1
1
1
0
1
1
0
0
1
1
1
0
0
1
2
0
0
2
1
2
2
0
0
2
0
0
0
2
0
1
0
1
2
0
0
1
1
2
1
0
1
2
0
0
0
1
0
0
0
1
0
0
0
0
1
0
2
1
1
2
0
1
1
0
0
1
0
2
2
0
1
2
0
2
0
1
2
0
0
0
0
1
0
0
2
0
2
1
0
2
0
1
1
1
1
3
0
0
1
1
2
2
0
2
1
1
1
2
2
0
1
1
1
1
1
0
1
0
0
0
1
0
0
1
0
0
0
1
2
0
0
1
0
2
0
0
1
1
2
1
0
0
2
2
3
1
1
0
0
2
0
0
1
0
1
0
2
0
1
0
2
0
2
1
1
0
1
2
0
0
1
0
2
2
0
1
0
1
1
0
0
0
0
1
1
2
1
1
2
2
0
0
0
0
0
0
2
2
2
0
2
0
0
2
0
0
2
0
0
2
2
1
1
0
0
1
0
0
0
0
0
2
0
1
0
2
1
0
2
1
1
2
0
1
1
1
2
3
1
0
0
1
0
1
0
0
0
0
1
0
1
2
0
0
0
1
2
2
0
0
1
0
0
0
1
1
0
2
2
1
2
0
0
1
1
2
1
2
1
1
1
0
0
1
0
2
1
0
2
0
1
0
0
2
1
1
2
2
3
2
2
2
1
1
1
1
2
1
0
1
1
2
1
0
1
0
1
2
0
1
1
0
1
0
2
0
3
0
1
1
1
1
1
0
0
1
1
0
1
0
0
2
0
1
1
1
1
2
1
3
1
0
0
1
0
1
1
1
1
0
0
1
0
0
1
0
2
1
0
2
0
2
0
2
0
2
0
0
1
0
2
1
0
0
1
1
0
0
0
2
2
0
2
0
0
0
1
2
1
0
0
0
2
0
0
3
2
0
0
1
0
2
2
1
0
1
0
0
1
0
2
0
0
1
0
1
0
0
2
1
0
1
0
1
0
1
1
0
0
1
1
2
1
1
2
0
0
1
1
1
0
1
0
0
0
0
0
2
0
0
2
2
1
0
0
0
1
0
1
1
1
2
1
0
0
2
0
3
0
2
0
1
0
3
1
1
0
1
1
0
2
2
2
1
0
0
0
1
0
0
2
2
1
0
0
2
0
1
1
0
2
1
0
0
1
0
0
1
1
1
0
0
0
3
2
1
1
0
1
0
1
0
0
2
1
0
2
0
1
0
0
1
2
1
0
0
2
2
1
0
1
0
0
3
1
1
0
2
2
0
2
0
0
0
1
2
2
0
2
0
0
0
1
0
0
2
0
0
1
2
0
0
1
1
0
2
0
0
1
0
0
1
1
2
2
2
2
2
1
0
0
1
3
1
0
1
0
1
0
0
0
0
0
1
1
2
0
0
0
0
1
1
0
1
2
1
2
1
1
0
0
1
1
2
0
0
2
2
0
1
1
0
0
1
1
2
1
2
3
1
0
1
2
1
2
0
1
1
0
0
0
0
0
2
2
1
0
1
0
0
1
0
1
0
1
2
2
1
1
0
3
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
2
0
1
2
1
0
1
1
1
2
2
0
2
2
2
2
2
1
0
1
3
2
1
1
1
0
3
0
0
0
2
2
1
0
0
0
1
0
0
0
0
1
0
2
2
0
0
2
2
0
0
0
1
0
1
0
0
0
0
0
1
1
0
2
1
1
1
2
0
2
1
1
0
2
0
1
0
0
2
0
1
1
1
2
0
0
2
0
0
1
0
0
0
1
2
0
0
1
0
0
0
2
2
0
1
2
2
0
1
0
1
2
2
0
0
2
0
0
0
0
0
0
0
2
3
1
2
0
0
2
1
0
1
0
0
1
0
1
1
0
0
1
0
1
0
0
0
1
0
0
2
2
1
1
0
0
2
0
2
0
0
1
0
1
1
1
0
0
1
0
1
0
1
0
0
0
0
2
0
0
0
2
1
0
0
2
2
0
0
1
2
0
0
1
2
0
2
0
1
0
3
1
1
1
2
0
2
1
2
1
0
0
1
0
0
1
1
0
1
0
1
1
2
0
2
0
1
1
1
1
2
1
1
0
0
0
0
0
0
0
2
0
0
0
1
1
2
1
0
0
1
0
2
2
1
0
2
0
0
2
0
1
0
0
1
0
1
1
0
1
1
0
2
2
0
3
1
1
2
0
0
2
2
0
0
0
2
0
2
2
0
2
3
1
1
0
0
0
1
0
1
1
0
1
1
0
1
3
0
0
2
1
0
1
1
2
0
0
1
1
0
2
2
1
2
0
0
0
2
2
1
1
0
1
2
1
0
1
2
0
0
1
0
2
0
0
0
2
0
2
0
0
2
0
1
0
2
0
0
0
0
2
1
1
1
1
0
0
1
1
1
2
1
2
0
1
0
2
0
1
1
2
2
0
2
0
0
0
3
1
1
1
2
0
1
1
0
0
1
0
0
1
2
1
0
0
0
0
0
1
1
2
1
1
0
1
1
0
5
1
0
0
1
2
2
2
0
1
0
0
0
2
0
1
0
2
0
0
0
2
2
0
0
0
0
1
3
2
0
0
1
0
1
2
1
1
1
1
1
0
1
1
0
1
0
1
1
0
2
1
2
1
1
1
1
0
2
0
1
1
2
1
0
0
0
4
0
0
0
0
1
0
2
0
1
1
1
2
1
2
2
0
2
2
1
0
1
2
0
0
0
2
2
2
1
1
2
0
2
2
0
1
1
2
2
2
1
0
1
1
1
1
2
0
2
1
1
1
2
2
1
1
0
0
0
0
1
2
0
0
1
1
0
0
1
0
1
2
0
1
2
0
0
1
2
0
1
1
1
0
3
0
1
1
1
2
1
1
0
2
0
2
0
0
2
1
0
0
0
2
0
2
2
1
0
2
1
1
1
1
2
1
1
2
2
2
0
2
0
1
1
1
1
0
2
2
1
1
2
1
1
0
0
2
0
0
2
0
1
2
0
0
0
1
1
2
1
2
1
1
2
7
0
1
1
1
0
1
0
0
1
0
0
2
0
1
0
0
0
0
1
1
0
1
1
1
2
1
0
1
1
0
1
0
2
2
2
0
3
1
3
2
0
2
1
1
1
0
2
2
0
1
2
0
2
2
0
2
3
1
1
1
0
0
2
0
0
0
0
0
0
1
2
0
0
2
0
0
0
1
0
1
0
2
0
2
1
0
2
1
1
1
2
1
1
1
0
1
0
0
0
0
1
2
1
1
1
1
2
2
0
1
1
0
1
2
0
0
2
1
0
0
0
2
1
0
0
0
0
0
2
0
1
1
1
1
0
0
2
1
1
2
0
1
0
2
2
1
0
1
0
3
0
1
1
0
0
2
1
2
0
2
0
0
1
1
0
1
1
1
0
2
1
3
1
0
2
0
2
0
2
2
0
1
1
2
1
2
2
2
0
0
0
1
1
0
1
2
1
0
1
1
0
0
0
1
1
0
0
1
2
2
0
0
0
1
0
2
2
0
1
1
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
1
2
1
1
1
0
0
0
1
2
2
2
1
0
2
0
1
2
0
0
0
1
2
0
0
1
1
0
0
1
1
1
0
1
0
0
0
2
0
1
0
0
3
1
1
0
1
0
0
0
1
2
0
0
0
2
0
0
1
2
0
0
1
0
1
1
2
0
0
1
0
1
0
0
1
0
0
1
0
0
0
2
2
3
0
0
0
1
0
1
1
2
1
3
1
0
0
0
1
2
0
1
1
0
0
1
0
0
2
0
2
1
0
1
0
0
1
0
0
0
0
2
2
1
2
2
2
1
1
2
0
0
0
1
2
2
0
2
6
2
0
1
2
5
1
0
1
0
1
2
0
2
0
2
1
0
0
0
1
1
0
2
2
1
2
1
1
0
2
0
0
0
1
2
0
0
0
1
0
0
0
0
1
0
1
0
1
2
0
1
2
0
0
1
0
0
1
0
0
0
1
0
0
0
1
2
1
2
0
1
0
0
1
1
2
0
0
1
2
1
1
1
3
0
0
2
0
1
0
0
2
2
1
1
1
0
3
0
0
1
0
1
0
1
0
0
0
1
0
0
0
1
0
2
1
1
2
1
0
1
2
0
2
1
1
1
0
0
0
0
0
0
2
0
2
2
0
1
2
1
2
0
1
1
1
2
0
0
0
2
0
0
0
1
2
2
0
2
1
2
1
1
2
0
1
1
1
0
3
1
4
0
2
1
1
0
0
0
0
0
1
1
1
2
1
7
1
1
1
1
0
1
1
1
2
0
1
0
1
0
0
1
2
1
3
0
0
0
0
1
1
0
0
0
2
0
2
0
0
0
1
2
1
1
2
2
1
0
0
0
2
2
1
0
0
2
0
0
0
0
2
0
0
3
1
0
1
2
0
1
0
0
2
0
0
0
0
0
1
1
0
0
1
1
0
0
1
1
0
1
0
2
2
2
0
0
1
0
2
2
1
1
1
0
1
0
0
1
2
1
0
0
1
0
2
2
0
0
1
1
0
0
1
0
2
1
1
0
0
0
1
0
0
0
2
0
0
1
3
0
0
1
2
0
0
1
1
2
2
0
0
2
0
6
0
0
2
0
0
1
1
0
0
0
2
1
0
0
1
1
3
0
0
0
2
1
1
0
2
2
0
0
2
0
1
2
0
1
0
2
1
0
0
1
1
2
0
0
0
1
2
0
0
2
1
0
2
0
0
0
2
2
1
4
0
0
0
0
1
2
0
2
1
0
0
1
1
1
1
0
1
1
0
0
0
2
1
0
1
0
1
1
1
1
2
1
0
1
3
0
2
0
0
0
0
0
1
2
1
0
1
1
1
0
1
1
0
1
2
1
1
1
2
0
0
0
1
1
1
0
0
0
0
2
0
0
1
2
1
2
0
1
2
0
1
0
1
2
2
0
0
1
0
1
0
2
2
0
0
0
2
2
1
0
2
2
1
1
1
0
2
0
1
0
1
1
2
0
1
0
0
2
0
0
0
0
3
0
0
1
0
1
0
0
2
1
1
0
0
1
3
1
2
1
2
1
1
0
2
1
1
0
1
1
0
1
0
0
0
2
2
1
1
0
2
1
0
1
0
1
1
0
2
1
0
0
1
4
0
2
1
0
1
1
1
0
0
2
0
1
1
2
0
1
0
0
0
1
1
1
1
0
2
0
0
0
1
1
0
0
2
0
2
1
2
1
1
0
0
1
0
2
0
1
3
1
1
1
0
2
0
1
5
0
1
2
0
2
1
0
2
1
0
0
0
2
1
1
0
1
0
1
1
0
1
0
1
1
1
1
0
0
1
0
0
1
0
0
2
1
0
1
0
2
0
2
2
0
0
2
0
0
0
1
1
2
0
1
0
1
0
2
2
0
1
2
1
2
0
0
2
0
0
1
1
1
1
0
2
2
0
0
2
1
1
1
2
1
1
2
2
0
0
0
1
0
1
2
0
1
1
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
2
1
0
1
1
0
1
1
3
2
0
0
1
2
2
2
0
0
0
0
2
0
0
1
0
1
0
0
0
2
2
0
0
0
2
1
1
1
2
0
2
0
0
0
1
1
1
2
1
0
1
1
3
0
1
2
0
0
2
1
0
0
2
1
1
0
0
0
0
0
1
0
0
1
1
0
2
2
0
2
2
0
0
2
0
2
1
1
2
1
0
0
0
0
0
1
0
2
1
4
2
1
0
1
1
0
1
0
1
1
0
1
0
1
0
2
1
0
0
1
0
0
1
0
1
2
2
0
0
0
1
0
1
2
0
1
1
2
2
1
0
2
0
0
1
0
1
0
0
0
1
1
1
1
0
2
1
1
0
1
1
1
0
0
0
2
1
0
1
0
2
1
1
1
0
0
2
2
0
0
1
1
0
0
0
0
1
1
2
0
0
0
1
0
1
0
0
1
2
1
0
1
2
1
1
1
1
3
0
2
0
0
0
3
0
1
0
0
1
2
0
1
1
0
1
1
2
0
0
1
1
0
0
0
0
2
1
0
1
1
0
0
1
0
0
2
0
0
1
1
0
0
0
1
1
1
0
1
0
1
0
1
1
0
1
0
0
0
2
0
0
2
1
0
0
0
0
0
1
0
1
3
0
1
0
1
0
2
0
1
1
0
1
0
1
2
1
0
0
1
0
0
2
1
0
0
0
0
2
0
0
1
1
0
0
1
0
0
0
1
2
2
7
1
0
1
0
1
2
0
0
1
0
0
0
2
1
2
0
0
0
0
2
0
1
1
1
1
0
2
1
0
1
0
1
0
1
0
0
0
1
0
1
1
1
1
2
1
1
1
2
0
0
1
0
2
1
1
0
1
0
0
0
0
0
0
1
1
0
2
0
1
1
0
1
0
0
1
1
2
0
0
2
0
1
2
0
2
0
0
0
0
2
1
0
1
2
0
1
0
0
1
1
1
2
1
0
0
2
1
0
1
1
1
0
0
1
0
1
0
0
1
0
0
0
2
1
0
2
0
1
1
0
2
1
0
0
0
2
1
1
1
1
0
0
0
1
2
1
2
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
1
2
1
1
2
0
2
0
2
1
1
3
2
0
2
0
2
0
0
2
1
0
2
0
0
1
2
0
1
0
2
0
2
0
0
1
0
2
0
0
0
1
0
0
0
1
1
0
0
0
1
0
2
0
4
1
0
1
2
1
2
1
1
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
1
1
0
1
1
0
1
0
0
2
0
1
0
2
1
1
0
2
0
0
1
2
1
0
2
0
1
2
1
1
0
0
3
2
1
0
1
1
1
1
1
2
0
1
0
1
1
0
1
3
1
0
0
0
0
1
2
0
0
1
1
2
1
1
1
0
0
1
1
2
1
1
0
1
2
2
0
2
1
1
2
1
0
1
1
0
0
3
1
0
1
2
1
2
1
2
0
0
0
0
2
0
1
1
2
2
0
0
1
0
0
1
1
1
2
0
1
1
1
1
1
1
2
2
2
0
1
1
0
0
0
1
0
2
0
0
1
2
0
1
0
1
1
0
1
2
1
1
0
1
4
2
0
0
3
2
2
0
0
1
2
0
2
1
1
0
2
3
2
2
0
0
1
0
1
1
0
0
0
1
1
0
0
1
1
0
0
0
1
2
0
0
1
1
1
0
1
0
2
2
1
0
2
1
2
0
0
0
1
0
1
0
1
1
0
2
2
0
1
0
3
1
0
0
0
1
1
0
0
0
0
3
1
0
1
0
0
0
1
1
2
0
2
0
0
0
0
0
2
1
0
0
1
0
1
2
1
2
0
0
0
0
0
0
0
2
1
0
1
2
1
0
2
2
0
0
0
2
1
1
1
0
0
0
2
1
1
0
0
1
0
1
1
2
0
0
0
0
1
2
0
0
2
0
1
1
1
2
1
0
1
0
2
0
1
2
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
1
0
0
1
1
0
1
1
0
0
0
1
0
0
1
0
2
0
1
0
2
2
1
2
0
0
0
1
2
1
1
0
0
1
0
2
1
1
1
1
1
0
0
2
1
2
1
0
2
1
1
0
1
0
2
1
2
1
1
2
2
1
0
0
2
1
2
1
2
2
2
1
0
2
0
0
0
1
1
1
0
2
2
0
0
0
2
0
0
0
1
0
2
0
0
0
1
0
2
2
0
1
2
2
2
1
1
0
2
0
0
1
1
0
1
1
1
2
1
0
0
1
1
0
0
0
0
1
0
2
0
3
2
2
0
0
0
2
0
1
1
2
0
1
1
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
2
0
0
1
1
2
0
1
0
3
0
1
3
0
0
0
1
2
0
1
0
0
1
3
0
4
2
0
0
0
3
1
0
0
1
1
2
2
2
0
1
0
1
0
2
0
1
2
0
0
1
0
0
0
1
2
1
2
2
1
1
0
1
0
1
0
0
1
0
0
1
1
1
0
0
1
2
1
1
0
2
0
0
2
1
3
0
0
2
0
1
0
0
0
1
0
0
0
1
2
0
2
3
0
1
0
0
2
0
1
0
2
1
2
0
0
0
0
0
2
1
0
1
1
0
1
1
2
1
2
0
2
0
2
2
1
1
1
1
3
0
0
2
1
2
0
1
2
2
0
2
2
0
1
2
2
0
1
0
2
1
0
0
0
1
0
0
1
1
0
0
1
2
1
0
1
0
0
1
0
0
0
1
1
0
0
2
1
2
1
0
1
0
3
1
0
0
0
1
0
0
2
2
4
2
0
0
0
1
0
0
1
1
0
0
0
0
1
0
2
2
1
0
0
2
2
1
1
1
1
2
0
0
1
2
1
1
2
0
1
0
4
0
1
2
2
2
1
1
1
2
0
1
0
1
0
0
0
2
2
1
2
0
1
1
1
0
1
1
1
1
0
0
0
0
0
0
0
2
1
0
1
1
0
0
0
1
2
0
0
3
1
0
0
0
1
1
1
1
2
0
0
0
0
0
1
1
2
0
0
0
2
1
1
0
1
1
1
1
0
1
0
0
0
1
0
0
0
0
0
0
2
0
1
1
1
0
0
1
1
0
1
0
0
1
1
1
1
2
0
0
2
2
2
1
1
1
3
1
1
1
2
1
1
2
1
1
0
1
1
2
2
0
1
1
2
0
0
1
1
1
0
0
0
0
1
0
3
1
0
0
0
2
0
1
0
1
0
2
1
1
1
0
0
0
0
0
2
0
0
2
0
1
0
0
0
1
2
2
0
2
0
2
0
0
0
1
0
0
0
0
2
2
1
1
1
0
2
0
0
0
0
2
0
0
1
0
0
0
0
1
0
1
1
1
0
1
3
0
0
1
0
0
2
0
0
2
0
0
0
0
1
2
2
2
1
1
2
2
1
2
1
0
0
0
0
1
0
0
1
0
0
1
1
2
1
1
0
0
0
1
1
0
0
2
1
1
0
0
1
2
2
2
0
0
1
0
1
1
2
1
1
0
1
1
1
0
0
2
0
0
0
2
2
2
1
0
0
0
0
0
1
0
1
0
1
1
2
0
1
0
1
0
1
0
1
1
0
0
2
2
0
1
2
2
1
0
0
0
0
2
0
0
0
1
1
1
0
1
1
2
1
1
0
1
2
0
3
0
3
1
1
1
2
3
1
2
0
1
0
1
0
1
2
0
0
0
0
2
2
2
0
0
2
0
0
0
0
0
2
1
2
1
0
2
1
2
1
0
1
1
1
1
0
0
2
0
1
0
0
1
0
1
1
0
0
0
0
1
1
2
1
1
1
0
1
0
1
1
0
3
0
0
0
1
0
1
0
1
0
2
1
0
1
0
0
0
2
0
0
1
0
0
0
2
0
1
0
1
2
1
2
2
2
1
2
0
0
2
1
2
2
1
1
2
0
0
2
0
1
1
1
0
0
0
1
2
1
0
1
1
0
0
0
1
1
0
2
1
0
2
0
0
2
0
1
1
0
0
0
1
1
0
1
0
2
0
1
0
2
2
2
0
1
1
0
0
2
1
1
1
0
2
0
0
1
1
1
0
0
2
1
2
0
2
0
0
0
1
1
1
0
0
1
1
2
0
1
0
0
1
0
0
1
2
1
0
0
0
1
1
0
1
0
0
2
0
0
2
0
0
1
1
0
1
0
1
1
2
2
0
2
0
1
2
1
0
0
0
2
2
2
1
1
1
1
1
0
0
1
0
0
0
1
1
1
1
0
0
0
0
2
2
0
1
0
1
0
1
1
1
2
2
0
1
1
0
1
1
1
1
2
2
1
0
0
0
0
2
1
0
1
2
0
0
0
2
1
0
0
1
0
0
0
0
1
2
2
0
1
1
1
2
0
0
1
1
0
0
3
4
0
1
0
1
0
2
0
0
2
1
3
2
2
0
2
0
0
1
0
0
0
0
0
0
3
0
2
0
0
1
2
0
0
0
1
1
0
2
1
1
2
2
1
1
1
2
1
2
0
1
0
1
0
1
1
0
2
1
1
0
1
1
1
1
0
0
0
0
1
0
2
1
0
0
2
0
3
2
0
1
0
0
2
1
1
1
0
2
0
2
0
2
0
1
1
1
0
13
0
2
2
0
0
0
1
1
2
1
0
0
1
0
1
0
0
2
1
2
1
9
0
2
0
0
3
2
1
2
0
0
1
1
0
2
2
1
1
1
1
0
1
0
2
0
0
0
1
2
0
0
1
0
0
3
2
1
0
0
2
2
0
0
2
2
0
2
0
1
2
0
2
0
0
2
1
1
2
1
0
0
2
2
0
0
0
0
1
0
2
1
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
1
1
1
1
2
2
0
2
2
1
0
0
2
0
0
1
0
1
0
0
0
0
1
1
0
1
0
1
1
0
1
1
1
0
0
0
1
0
0
0
2
0
1
2
0
0
1
0
0
1
2
1
1
0
1
0
3
0
1
1
1
0
0
2
3
1
2
1
0
0
3
2
2
1
0
0
1
0
0
2
0
2
2
2
3
0
2
1
0
0
2
0
1
1
1
2
1
0
3
1
0
2
0
1
1
1
0
0
1
0
0
2
0
2
1
0
1
2
0
1
0
0
0
2
0
0
0
0
1
1
2
1
1
2
0
2
1
1
0
0
1
1
1
2
1
2
0
0
2
2
0
1
0
0
1
0
3
0
0
0
0
0
2
0
1
1
0
2
1
1
2
1
0
2
0
1
2
0
0
0
0
2
1
0
1
0
1
0
0
2
1
0
0
0
1
1
0
1
3
1
3
1
2
2
2
2
1
2
1
0
1
0
2
0
4
0
0
1
1
0
0
1
0
0
0
2
2
0
0
2
2
1
1
1
0
2
0
0
0
2
2
1
0
0
1
0
2
1
0
1
1
2
0
2
0
0
0
0
0
1
1
2
1
0
3
0
1
0
2
1
2
0
1
2
2
0
0
0
0
0
0
2
0
2
1
2
0
1
1
0
2
2
0
0
0
1
1
2
0
0
0
1
0
1
2
1
2
0
0
1
1
2
0
0
0
2
3
0
1
1
0
0
4
0
0
0
1
2
1
1
1
1
0
0
0
5
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
2
0
0
0
2
0
0
0
1
0
0
1
0
1
0
0
0
0
1
2
0
2
1
2
1
0
0
0
2
1
2
1
1
0
1
1
0
0
1
1
0
1
0
1
0
1
0
0
1
0
0
2
1
1
0
0
0
1
1
0
1
0
0
1
0
0
0
0
1
2
2
2
0
0
0
1
2
1
1
0
1
1
1
0
0
1
1
1
0
1
1
2
0
2
0
1
0
0
0
2
0
0
2
1
0
1
0
1
0
0
0
0
2
2
2
0
0
2
2
1
0
0
4
0
1
1
2
1
1
0
2
0
0
0
2
2
0
1
1
2
2
1
1
1
2
2
1
1
1
0
2
0
1
0
1
1
0
1
2
1
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
2
0
1
0
1
2
2
0
1
2
2
2
1
0
0
0
1
1
1
2
0
0
1
1
0
2
0
0
0
1
0
2
0
2
1
1
1
0
0
0
0
0
2
1
0
0
0
1
1
1
1
1
0
0
1
0
0
0
0
1
0
1
2
2
1
0
2
1
0
1
0
1
1
0
0
0
0
1
0
2
1
1
1
1
1
0
0
1
2
1
1
1
1
0
1
2
1
2
0
0
1
3
1
0
1
1
1
0
1
0
3
0
1
0
0
1
2
6
1
0
0
1
0
1
1
1
0
3
0
0
0
1
0
1
1
2
0
0
1
0
1
2
1
1
0
2
1
0
0
0
1
2
1
2
0
1
0
0
0
0
0
1
1
2
1
0
0
0
1
0
0
2
0
0
1
2
1
0
1
0
0
1
0
2
1
0
1
2
1
1
1
1
2
0
1
2
1
1
1
3
0
0
1
0
0
2
1
2
0
1
0
0
1
2
2
0
0
2
0
0
1
1
1
0
0
1
0
2
0
2
0
0
1
1
2
0
0
0
2
0
1
2
2
2
2
1
0
1
2
0
1
0
1
0
0
1
0
0
1
0
1
0
1
1
0
0
2
0
2
2
0
0
2
1
0
2
1
1
0
0
0
0
1
1
0
0
1
1
1
0
0
0
0
1
1
0
1
0
1
0
1
0
2
0
0
0
1
0
0
1
1
1
1
1
0
0
0
1
1
0
0
2
1
0
1
1
0
2
0
2
0
1
2
1
0
2
0
0
1
0
1
1
1
2
0
2
2
0
1
0
0
0
0
1
1
0
0
2
0
0
0
1
0
0
0
0
0
2
1
1
1
1
1
1
1
2
1
1
1
0
0
0
2
0
2
0
1
1
0
2
2
0
1
1
0
0
0
0
0
0
0
0
0
0
2
2
1
1
0
2
1
1
0
1
0
0
1
0
3
0
1
0
2
0
2
0
0
0
0
1
1
0
2
2
1
0
1
1
0
1
1
0
0
0
1
1
1
2
1
2
2
1
1
0
0
1
1
0
0
1
0
0
0
1
0
2
2
1
0
0
1
2
0
1
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
2
1
2
2
2
0
0
0
0
0
0
1
0
1
0
1
0
2
1
1
0
0
1
0
0
0
1
0
1
0
0
0
1
0
1
2
2
5
1
1
0
0
1
2
0
2
1
1
1
0
1
0
1
1
2
0
0
0
1
1
1
0
0
1
2
0
0
0
0
1
1
0
2
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
1
1
0
1
0
2
0
1
1
0
0
0
5
1
3
1
3
1
0
1
0
0
1
1
2
0
1
0
0
3
0
1
2
2
0
0
0
1
1
0
1
0
2
1
1
0
0
1
0
0
1
0
0
1
2
2
0
2
0
1
1
1
2
0
0
1
0
2
0
2
2
0
0
7
1
2
0
0
1
0
1
1
2
0
1
0
1
0
0
0
1
0
1
1
1
2
1
1
0
1
2
1
0
1
2
1
0
0
1
0
2
0
0
1
0
0
0
1
2
0
0
2
1
1
0
1
0
1
1
0
1
0
1
1
3
0
0
2
1
0
0
0
2
2
0
1
0
2
1
0
0
0
1
1
1
0
2
2
0
1
0
1
1
1
0
2
1
1
0
2
1
1
2
0
0
1
1
1
2
2
0
1
0
0
1
0
1
2
2
0
0
0
0
0
0
2
0
0
0
3
0
1
0
2
0
2
0
2
1
0
1
1
0
1
0
0
0
2
0
0
1
2
2
1
1
1
1
0
0
0
0
1
2
0
1
2
0
0
1
0
0
0
0
0
1
0
0
6
2
0
1
0
1
1
2
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
2
1
1
0
1
3
0
0
2
1
0
1
0
1
0
0
1
1
1
2
1
2
1
2
0
0
0
1
1
2
0
0
0
2
1
0
1
1
1
1
1
2
2
1
1
1
0
2
0
0
1
0
1
1
2
0
1
0
1
0
0
0
0
2
0
0
0
2
0
1
1
0
1
0
1
0
0
0
1
1
0
0
1
2
0
1
1
0
1
0
2
0
1
0
1
1
2
2
2
2
2
0
0
0
0
1
2
2
0
1
2
0
0
2
1
0
0
0
0
0
0
0
1
0
0
1
0
2
2
1
2
0
0
0
2
1
0
2
2
1
1
0
1
1
0
0
1
0
0
0
1
2
0
0
0
1
1
2
0
1
2
1
0
1
0
1
0
1
0
0
3
1
1
0
0
1
2
1
1
0
0
0
0
1
1
0
2
0
0
1
0
0
0
0
1
0
1
0
2
0
0
0
1
1
0
1
1
2
0
0
0
0
0
0
1
0
2
1
2
0
2
2
0
2
2
2
0
2
1
0
0
2
2
1
0
0
0
2
2
1
0
2
2
1
0
2
0
0
2
1
1
0
0
1
0
0
1
0
0
2
0
2
2
2
2
0
0
3
1
0
2
1
2
1
1
0
1
2
2
2
1
1
1
2
0
1
0
1
0
0
1
1
2
2
0
0
2
1
2
0
0
1
1
0
0
1
0
1
0
0
1
0
2
2
0
0
1
1
0
0
0
1
1
1
1
0
1
0
0
0
0
2
0
1
0
2
0
0
3
2
0
1
0
0
1
1
1
2
1
1
1
1
2
1
1
1
2
0
0
0
0
1
2
2
2
1
1
0
0
1
2
1
3
2
1
1
0
1
1
0
2
2
0
0
0
1
2
1
1
2
0
2
1
1
0
0
1
1
0
2
2
0
0
0
2
1
1
0
0
1
0
1
1
2
1
2
1
2
2
0
2
2
0
0
0
1
0
1
0
1
1
1
0
2
0
2
2
1
0
0
0
0
0
0
0
0
2
2
1
2
2
1
2
0
0
0
0
1
0
1
2
0
2
1
0
1
1
0
2
1
2
0
2
0
1
2
0
0
0
0
1
0
0
2
0
1
2
1
0
2
1
2
1
2
0
0
2
0
2
0
2
2
1
0
2
0
0
1
0
1
1
0
1
1
2
2
2
0
0
0
1
2
0
2
0
2
0
0
0
0
2
2
2
0
0
1
0
1
0
1
3
0
2
1
0
1
2
0
0
0
0
1
0
0
1
0
1
1
0
1
0
0
0
0
3
0
1
0
1
2
0
2
1
2
0
0
0
1
0
2
0
0
2
0
1
2
1
0
0
2
2
3
0
1
0
2
2
1
2
0
0
1
1
2
2
0
1
0
2
0
2
0
1
3
2
0
1
0
1
1
1
1
1
1
0
2
0
0
1
0
0
1
1
0
0
0
2
0
2
0
2
1
3
0
0
0
1
2
2
1
1
1
1
0
1
2
2
1
1
0
2
0
2
2
1
0
0
0
2
0
1
1
0
0
1
0
1
1
0
1
2
0
0
0
2
2
0
0
0
0
0
1
2
2
1
0
2
2
1
2
0
0
1
2
2
2
0
2
0
0
0
0
1
1
2
0
1
1
0
2
0
1
2
1
0
1
0
0
1
0
2
2
2
0
0
0
2
0
0
0
0
1
2
0
0
1
0
2
1
1
0
0
2
2
1
0
0
0
0
0
2
0
1
0
1
0
0
0
0
1
0
1
0
0
1
1
0
3
1
0
2
0
1
2
0
1
5
1
1
2
1
2
2
2
0
1
0
4
1
1
0
1
0
1
0
1
0
2
1
1
1
1
0
2
0
0
2
0
0
0
0
0
0
1
1
1
0
2
2
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
2
0
2
0
0
0
1
0
1
0
2
1
0
1
1
0
0
0
2
2
1
2
2
2
1
0
0
0
0
2
2
2
3
2
0
0
0
1
0
1
2
1
0
2
1
1
2
0
1
0
0
1
2
1
1
0
2
1
1
0
1
0
0
1
0
0
1
0
1
0
0
2
0
1
1
0
0
0
2
2
1
0
1
1
0
0
1
0
0
0
1
0
2
0
2
0
0
2
0
0
1
1
1
2
0
1
0
1
1
1
0
0
0
0
0
1
0
0
2
1
2
1
2
1
0
0
1
1
0
0
0
0
2
2
2
1
0
0
1
2
0
3
0
0
0
1
0
0
0
1
0
0
1
2
1
2
0
1
0
0
0
0
2
0
0
1
0
0
2
1
0
1
1
0
0
1
0
0
0
0
0
2
2
0
2
1
1
0
1
0
0
0
1
1
0
1
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
1
0
1
2
1
1
1
1
2
1
1
1
0
1
2
0
0
0
1
1
1
0
6
2
0
4
1
1
0
0
2
0
0
1
0
1
2
2
1
2
1
0
0
0
0
2
0
0
0
2
0
3
0
0
0
0
3
0
2
1
3
1
0
1
0
0
10
0
0
3
1
2
1
2
2
0
0
1
0
2
2
0
2
0
1
1
0
2
0
1
0
1
2
0
0
0
2
0
2
2
1
1
2
0
0
0
2
2
1
0
1
1
0
1
0
0
0
2
0
0
0
2
0
0
2
1
1
2
2
1
1
0
0
0
1
1
2
1
0
1
3
3
0
0
1
0
2
2
0
0
2
0
3
0
1
3
2
1
1
0
1
0
0
0
0
2
0
0
0
2
1
0
0
0
2
2
2
1
0
0
1
0
2
0
1
0
1
1
0
0
2
2
0
0
0
1
1
0
2
1
0
0
2
0
0
2
1
2
2
3
0
2
1
2
0
1
3
0
0
0
1
0
0
2
0
0
1
1
2
0
1
1
2
0
0
0
0
2
4
1
0
1
1
1
0
1
1
2
1
0
0
1
1
1
0
0
1
0
1
0
1
0
0
0
2
0
0
1
0
1
0
0
0
1
0
0
0
0
4
2
1
1
1
0
0
1
1
0
1
0
0
1
0
1
2
3
1
1
1
0
0
0
0
1
0
0
0
2
0
0
1
0
1
1
0
2
2
0
0
0
2
0
1
0
0
2
0
1
0
2
0
0
2
0
1
1
1
1
0
1
1
0
0
1
0
1
0
0
1
0
0
0
1
2
0
1
1
0
0
2
1
0
0
0
1
1
0
1
0
0
0
3
1
0
0
0
0
1
0
0
5
1
0
0
1
1
0
2
0
0
1
1
2
2
0
0
0
1
2
2
2
0
2
1
2
1
0
0
0
1
1
1
0
1
1
1
1
0
1
0
0
1
0
0
1
0
2
0
3
0
1
0
1
1
2
1
1
2
0
0
0
2
2
1
0
2
8
0
1
1
2
0
0
1
0
0
0
0
1
1
2
0
0
1
0
1
0
1
0
0
1
1
1
0
1
0
1
6
0
2
2
1
0
0
0
1
0
2
0
2
0
0
0
1
0
1
0
0
0
1
0
1
0
1
0
2
0
1
1
0
2
0
0
0
1
1
2
0
1
1
2
0
0
1
2
0
0
2
0
0
1
2
1
0
2
0
0
0
1
0
1
1
0
2
1
0
0
1
0
2
1
0
0
1
1
0
0
0
0
2
0
1
1
0
1
0
2
0
0
0
6
0
1
2
0
2
2
1
0
1
1
0
0
1
0
2
1
1
0
2
1
0
1
0
1
1
0
1
0
2
0
0
3
0
1
0
0
1
0
2
1
1
0
1
0
1
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
1
0
0
1
1
1
0
1
2
0
1
0
2
2
3
1
1
0
0
0
0
1
2
0
2
1
1
1
2
0
0
0
0
2
0
1
0
0
2
0
2
1
0
0
1
1
0
2
0
3
2
1
2
1
0
2
1
0
0
0
0
1
2
1
1
0
1
0
1
0
0
0
0
0
2
0
1
0
1
1
2
0
2
0
0
1
0
2
0
0
2
1
2
0
0
1
2
0
2
0
1
0
1
2
2
0
2
0
1
0
0
1
0
0
0
0
0
3
0
1
2
1
2
0
1
0
1
1
1
3
0
2
2
2
1
0
1
1
2
0
1
1
1
2
2
0
0
1
1
0
2
1
1
0
1
0
0
0
2
1
0
0
0
1
1
2
0
1
2
2
0
0
1
0
2
0
2
1
0
0
0
0
2
0
1
1
2
0
0
0
0
1
1
1
2
0
0
0
0
0
1
1
1
0
0
1
2
0
1
2
1
1
0
2
1
0
0
0
2
0
1
0
1
0
2
0
0
0
0
1
2
0
1
2
1
0
1
0
0
2
0
1
1
0
0
0
0
2
1
0
0
1
0
1
0
2
1
0
0
2
2
0
0
2
0
1
2
1
1
0
0
0
1
0
1
1
1
0
1
1
0
1
0
0
2
0
1
0
2
0
1
1
0
0
1
0
2
1
1
2
2
1
1
3
1
1
1
2
1
1
2
0
2
0
3
2
1
1
2
0
0
1
0
0
1
1
0
1
1
0
2
2
0
1
0
1
0
1
2
0
0
0
2
0
1
0
0
0
4
1
0
1
0
0
2
1
2
0
2
1
1
2
0
0
0
0
1
0
1
1
1
0
2
1
1
1
0
0
0
0
0
0
0
1
1
2
0
1
2
1
1
0
1
0
1
2
0
0
0
0
0
0
2
0
2
1
0
0
0
4
1
0
1
2
1
2
1
2
1
2
2
1
0
1
0
2
1
2
0
0
0
0
2
1
1
1
0
1
1
0
0
1
1
2
0
1
0
0
0
0
0
0
0
0
0
2
2
0
2
1
0
1
0
0
0
0
0
0
0
1
2
0
0
0
1
1
2
0
1
0
0
2
1
1
3
2
1
2
0
0
2
2
0
2
0
1
2
0
0
2
0
1
0
0
1
1
2
0
2
1
0
1
1
0
0
2
2
2
1
1
1
2
0
0
0
2
0
0
0
1
0
1
2
0
0
0
0
2
0
3
1
0
0
0
2
3
0
0
1
2
0
0
2
1
2
2
0
0
1
1
1
3
0
0
0
2
1
1
0
0
0
0
1
0
0
0
0
1
0
2
1
2
2
0
0
1
0
1
1
0
1
1
1
0
2
0
2
1
0
1
2
1
0
1
0
1
2
0
0
1
2
0
2
1
1
1
0
1
1
0
0
2
2
2
1
0
0
0
0
1
1
2
1
1
0
1
2
1
2
1
0
0
1
2
0
0
2
0
1
1
0
1
0
0
2
0
1
0
1
1
1
2
1
0
1
2
0
0
1
0
1
0
0
2
0
0
1
1
0
2
0
0
2
0
0
2
2
0
0
0
2
0
1
3
0
0
2
0
1
1
0
2
1
2
1
2
2
0
0
0
2
1
0
1
0
0
2
0
0
0
1
0
0
1
2
0
0
2
1
1
2
2
1
1
0
0
1
1
0
0
0
1
0
2
2
0
1
1
0
2
1
0
0
0
0
1
1
1
0
0
2
0
1
0
0
0
0
1
0
0
1
2
0
0
2
0
2
0
0
2
1
0
1
2
0
2
1
0
2
1
0
0
0
0
0
2
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
3
0
0
2
1
2
0
1
1
4
0
0
2
0
1
1
0
0
0
1
1
1
0
2
0
0
0
0
3
1
0
1
2
1
1
1
1
0
0
0
2
0
1
3
2
1
0
1
0
2
1
2
1
1
1
2
0
2
0
1
0
1
0
3
1
0
0
0
2
0
0
1
0
2
1
2
0
0
0
3
1
0
1
0
0
2
0
0
0
0
1
1
1
0
1
1
1
1
0
0
1
0
1
0
0
1
1
1
0
0
0
0
0
1
1
0
0
1
0
1
1
0
0
1
0
0
0
0
0
1
1
0
0
2
2
1
1
1
0
0
2
1
2
3
2
1
0
0
0
2
0
1
2
0
2
2
1
1
1
1
1
3
0
1
1
2
0
1
0
2
0
0
0
2
0
1
0
2
0
1
1
1
0
0
1
0
2
3
0
0
2
1
1
2
2
1
2
1
0
1
1
1
0
0
1
0
1
0
0
2
1
1
1
1
0
1
1
1
1
1
1
1
2
2
1
0
2
0
0
1
3
1
2
0
2
0
2
0
2
2
2
1
0
2
0
2
0
1
1
0
1
2
1
0
0
1
0
0
0
2
0
2
2
1
0
1
1
0
0
2
1
1
0
1
1
1
1
2
1
1
1
0
2
1
0
1
1
0
1
0
2
2
0
1
0
1
0
1
2
2
0
1
0
0
1
0
0
0
1
0
0
1
1
0
0
0
1
1
1
2
0
0
1
0
0
1
2
3
1
1
0
0
0
1
0
0
2
0
2
2
0
0
0
1
0
0
1
0
0
1
0
0
0
0
2
1
0
0
3
2
2
1
1
2
1
0
2
2
1
0
2
1
0
0
2
1
1
1
2
0
0
0
1
1
0
1
1
2
1
1
2
0
0
2
0
0
0
0
0
1
1
0
1
1
0
0
2
0
0
0
1
0
0
2
0
2
0
0
2
2
0
0
1
0
1
0
0
1
2
0
1
2
0
1
0
2
1
0
2
0
0
0
0
0
0
1
1
1
4
1
0
1
0
2
0
1
0
1
0
0
0
0
1
0
1
1
0
0
0
0
3
2
1
0
0
1
0
1
0
1
2
0
2
2
0
0
0
1
0
1
2
2
1
1
0
0
0
0
2
2
1
1
0
1
0
0
2
1
2
1
0
0
2
0
0
1
4
2
0
0
0
0
2
1
0
0
0
0
1
1
0
0
1
0
0
2
1
0
0
0
2
2
2
0
0
0
0
0
0
0
1
2
2
0
1
0
1
0
2
1
1
1
2
1
0
0
5
0
2
1
1
0
1
0
0
2
1
1
0
0
0
0
2
2
0
0
0
0
0
1
0
2
0
1
0
1
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
1
0
1
0
0
0
1
0
1
0
1
2
1
0
0
1
0
0
0
3
2
0
0
0
0
1
1
0
2
0
1
1
0
0
1
1
0
1
1
0
0
0
0
1
0
1
0
1
0
1
0
2
0
2
0
0
0
1
2
1
1
1
1
0
3
0
0
0
1
2
2
0
2
0
0
0
1
0
0
1
0
2
0
0
0
0
2
0
1
0
0
0
0
2
1
2
0
2
2
1
0
0
2
1
1
2
0
1
0
0
3
0
1
1
1
0
1
1
2
2
2
1
2
1
0
0
2
2
1
0
0
1
2
1
0
0
0
1
0
2
0
0
0
1
1
2
2
2
1
1
0
0
0
2
0
1
3
3
0
1
0
1
0
0
2
2
1
2
1
0
0
1
0
2
1
2
0
0
2
0
0
2
1
1
0
1
0
0
0
1
1
2
0
0
2
0
1
0
3
2
2
0
0
0
2
1
1
2
0
0
4
0
0
1
1
1
1
0
1
0
2
0
2
0
1
0
1
0
1
1
1
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
2
1
2
1
1
0
0
0
1
2
0
1
0
0
0
2
0
2
1
0
0
1
2
1
2
0
1
0
0
1
1
0
1
1
1
2
0
3
1
0
1
0
1
1
2
1
2
1
1
1
0
0
2
0
2
1
0
2
1
1
0
0
3
0
0
0
0
2
0
1
1
1
0
0
0
1
5
1
1
2
1
1
1
2
0
2
1
2
0
0
1
1
0
0
1
0
2
0
0
1
1
1
0
1
0
1
0
2
2
1
0
1
0
0
0
0
0
1
1
0
2
1
0
0
1
0
0
0
1
0
1
0
0
0
1
0
1
1
1
0
0
1
3
0
2
0
1
0
0
0
0
0
1
1
0
1
0
0
0
2
2
0
0
1
1
2
1
2
2
2
1
1
1
2
1
0
1
0
0
1
1
1
3
1
0
0
0
1
0
2
0
0
2
2
1
0
0
1
0
1
1
0
1
1
2
3
2
0
1
1
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
2
0
0
1
0
0
2
2
0
0
2
1
2
0
0
0
0
2
2
0
1
0
0
1
0
3
0
2
2
0
0
2
0
0
1
0
0
1
2
0
0
2
2
1
2
1
2
0
0
1
0
2
0
2
1
0
0
1
2
2
2
1
0
2
3
0
2
1
0
1
1
0
1
0
1
2
2
2
1
0
0
2
3
2
1
1
1
0
0
0
1
1
0
2
1
1
1
2
0
0
2
0
1
0
1
1
0
0
0
1
0
0
0
0
1
2
0
3
0
2
2
0
1
1
0
1
1
0
0
0
0
2
1
0
0
1
0
0
0
0
2
1
0
1
1
2
0
1
1
0
2
0
0
0
1
0
1
0
0
0
1
0
2
0
0
0
1
0
1
0
1
0
2
1
0
1
0
1
2
0
0
2
2
3
4
0
0
0
1
0
0
0
0
1
1
0
1
1
0
0
1
2
0
1
2
1
1
0
0
0
1
0
0
1
1
0
1
1
0
2
2
1
2
0
2
2
2
0
1
1
0
0
1
1
1
1
0
0
1
0
0
1
2
1
0
2
0
1
1
0
1
1
0
0
0
0
1
0
0
1
0
0
2
1
0
2
2
0
0
0
1
0
0
1
0
0
1
0
1
4
2
2
1
0
1
1
3
2
1
0
0
0
1
0
0
0
0
2
1
0
0
1
1
0
2
1
1
0
0
0
0
0
0
0
0
0
1
0
2
1
2
1
1
0
1
0
2
0
0
1
1
1
0
2
2
1
2
0
0
0
1
2
1
0
0
1
1
1
0
1
2
0
0
1
1
1
0
0
0
1
4
1
0
0
1
2
1
0
0
1
3
0
1
1
0
0
0
1
0
0
2
0
0
0
0
2
0
1
2
1
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
1
2
1
2
0
1
0
1
1
1
2
1
1
0
1
1
0
0
2
2
1
0
1
0
1
0
0
0
1
1
1
1
0
0
0
0
0
1
0
0
1
1
1
0
1
1
0
1
0
1
1
1
2
0
0
1
2
1
0
0
0
0
0
0
0
1
0
1
0
1
1
1
1
1
2
0
1
2
0
0
0
1
0
2
0
0
1
1
2
0
1
0
0
0
0
1
1
0
0
0
0
2
3
0
1
1
0
1
2
0
0
2
2
1
0
0
2
1
2
0
1
0
1
2
0
0
1
0
1
0
2
2
0
1
2
1
0
0
1
2
2
1
0
2
0
1
0
0
1
2
2
2
1
0
2
1
2
0
2
1
2
1
2
0
1
0
0
2
0
1
0
0
0
0
0
0
2
0
0
1
1
2
2
1
0
0
1
1
1
1
0
0
0
0
1
2
1
0
0
2
2
2
1
0
2
2
1
1
1
2
2
0
1
0
1
0
1
2
1
0
3
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
1
1
0
0
1
0
1
2
1
0
0
2
1
0
1
0
2
0
0
1
0
1
1
2
0
1
0
2
2
0
1
2
0
2
0
0
0
2
2
0
1
1
0
0
1
1
1
0
2
2
0
1
0
2
1
1
3
1
2
1
0
0
0
0
1
0
0
1
1
2
1
2
2
2
1
2
0
0
1
0
1
0
0
0
0
0
2
0
1
0
1
1
0
0
0
0
1
0
2
0
1
1
2
1
2
0
0
1
0
0
1
0
1
1
0
1
1
1
0
2
1
2
0
2
0
0
2
1
0
0
0
1
2
1
0
0
1
1
0
1
0
1
2
1
1
1
2
2
2
0
0
2
0
1
0
2
0
0
0
1
0
1
0
1
1
2
1
0
0
0
0
0
0
1
1
1
1
1
0
1
1
0
2
1
0
0
0
0
0
2
0
2
1
2
0
0
0
1
2
0
0
0
0
0
1
0
0
1
0
0
1
1
0
1
0
2
1
0
2
1
1
0
0
1
0
1
0
1
1
0
2
1
1
0
0
2
0
1
1
0
1
2
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
1
0
0
0
2
2
0
1
0
1
0
1
1
2
0
0
1
1
1
2
0
2
1
1
1
1
0
0
0
0
2
1
1
0
1
0
0
1
1
1
2
0
1
1
1
1
1
1
0
0
2
0
1
0
1
0
2
2
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
1
1
0
1
1
2
1
1
2
0
0
2
1
0
2
0
2
0
0
0
0
0
0
1
0
0
1
1
1
0
2
0
1
0
0
0
2
0
4
2
1
0
0
2
2
1
2
1
0
2
0
1
2
1
1
0
0
0
0
2
1
2
0
1
2
1
2
1
0
1
1
0
1
1
2
2
2
2
1
1
1
0
0
2
2
0
1
0
1
0
0
0
0
1
0
1
0
0
1
1
1
1
0
2
1
1
1
0
1
0
0
0
1
1
0
1
0
0
1
2
2
0
0
0
1
0
0
0
0
0
2
1
1
1
0
0
1
2
1
0
1
0
2
0
0
2
0
2
0
1
0
1
1
0
1
2
1
1
0
1
1
0
0
1
1
1
0
1
0
0
0
2
1
0
1
1
1
2
1
2
2
1
1
3
1
1
2
0
2
0
1
1
1
1
2
1
2
0
0
2
0
0
1
1
1
0
1
0
2
1
1
1
0
0
1
0
1
0
0
1
1
1
0
1
0
2
1
2
2
2
0
0
0
2
1
2
0
0
1
0
0
0
0
1
1
2
0
0
1
0
1
0
0
0
0
0
0
2
1
0
1
2
1
0
0
0
2
1
2
0
0
2
0
1
2
0
0
0
1
1
1
0
1
2
1
0
0
2
2
0
0
1
2
1
0
2
1
2
1
0
0
1
0
0
0
0
3
1
0
0
1
2
2
0
1
0
1
0
1
0
0
1
0
2
0
1
0
1
0
1
0
2
1
1
0
1
0
0
0
3
0
0
0
1
1
0
0
0
2
1
0
0
0
0
0
0
0
2
2
0
0
2
0
3
1
0
0
0
1
2
1
1
2
0
0
1
0
0
2
0
1
0
2
0
1
0
2
0
0
0
0
0
2
0
0
2
1
2
2
0
2
2
0
2
2
1
0
0
1
0
0
2
1
0
3
2
0
1
0
0
0
1
0
1
0
2
0
1
0
0
1
0
1
0
0
2
1
0
0
0
2
2
1
1
1
2
2
2
0
0
1
1
1
2
2
1
0
1
0
2
0
0
3
0
1
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
1
2
2
1
0
0
2
0
0
1
2
2
2
1
2
2
2
0
0
0
1
2
0
1
0
1
0
2
1
1
0
3
0
2
1
1
0
1
1
0
0
1
2
0
1
1
1
3
0
1
0
1
0
2
0
1
2
1
2
2
1
3
0
1
0
2
0
2
0
0
1
0
1
2
2
2
0
0
2
1
1
1
2
0
2
1
0
0
2
0
1
0
1
0
1
0
0
0
2
2
0
2
2
2
0
3
1
2
0
0
1
0
0
0
1
2
2
1
0
0
2
0
2
0
0
1
1
0
2
1
1
1
1
3
0
0
0
1
0
2
2
1
2
0
2
1
0
0
0
0
1
1
4
0
0
0
0
6
0
0
0
0
0
1
0
2
0
2
1
0
1
0
1
1
0
0
0
1
0
2
2
1
0
4
2
2
2
1
0
0
0
2
1
1
0
2
0
0
1
0
1
2
1
1
1
0
2
2
0
1
0
0
1
2
1
1
0
0
0
1
1
0
2
1
0
0
2
2
0
1
1
1
0
0
0
0
1
0
2
1
0
1
1
2
2
0
2
0
0
1
2
0
0
1
2
1
0
2
0
1
1
0
0
0
0
1
2
0
0
0
1
0
0
1
0
0
0
1
0
1
2
0
0
1
0
0
0
2
0
1
1
0
0
0
0
2
0
2
1
2
1
0
2
1
1
0
0
2
1
0
0
2
0
1
1
0
2
0
2
1
0
2
0
0
2
0
1
0
0
1
1
1
1
1
1
2
2
0
2
1
2
1
1
2
2
1
0
1
0
1
1
1
1
0
1
0
0
1
0
1
1
1
0
1
0
0
1
1
1
0
2
2
1
2
0
0
0
2
0
2
0
0
0
0
0
2
0
1
0
1
1
0
1
0
0
0
0
2
1
0
1
1
0
0
1
1
1
2
0
2
2
0
1
2
2
0
0
1
1
2
0
1
1
0
1
1
2
1
1
2
2
0
0
2
0
1
0
1
2
2
2
0
0
0
0
0
0
1
1
0
2
0
2
1
0
0
0
2
2
1
0
1
0
1
2
0
1
1
1
1
1
2
1
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
1
1
0
1
1
1
0
1
1
1
1
1
0
0
2
1
1
1
1
0
0
0
0
0
0
1
0
0
0
1
2
0
1
0
1
1
2
1
0
2
0
1
1
0
2
1
0
0
0
0
0
0
0
2
0
1
0
0
2
1
2
2
2
1
3
1
0
0
2
1
2
2
1
0
1
0
1
3
1
1
1
2
0
0
1
1
0
1
0
0
2
3
0
1
1
0
2
0
0
3
0
1
0
0
3
0
3
0
1
0
0
0
2
0
0
1
2
1
1
1
1
0
0
0
1
2
2
0
0
1
0
0
0
0
1
0
0
0
0
2
1
1
2
0
2
0
1
3
1
0
0
1
0
0
3
1
2
0
0
3
0
0
2
0
1
2
0
2
0
2
2
2
1
0
0
2
0
1
0
0
0
2
0
1
0
1
0
0
0
1
0
0
1
2
1
1
0
0
0
3
0
1
0
1
0
1
0
1
0
1
0
0
2
0
0
1
1
0
0
1
0
2
2
0
0
1
1
0
0
1
2
2
2
0
1
2
0
2
0
2
1
0
1
1
2
1
2
2
1
1
0
2
1
0
1
1
1
0
2
1
1
0
2
2
1
0
0
2
2
1
2
0
0
0
1
2
1
1
0
0
0
0
1
1
0
0
2
1
0
2
0
1
1
1
1
3
0
2
0
2
1
0
1
1
0
1
0
0
1
1
1
2
2
2
0
0
2
2
1
1
2
0
0
3
0
0
2
0
2
0
0
2
0
1
1
1
1
2
0
0
2
2
0
0
0
4
2
0
0
0
2
0
1
0
1
2
2
0
0
0
2
1
1
1
0
1
0
1
1
0
0
1
1
1
0
0
0
1
0
1
0
1
0
1
2
0
0
0
0
0
2
1
0
0
1
0
1
1
0
0
0
1
1
2
0
4
1
0
2
0
0
0
0
2
1
0
2
2
1
0
1
0
1
0
0
1
1
0
1
0
2
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
2
1
2
0
2
0
1
0
0
2
1
1
1
0
0
1
2
2
1
2
2
2
2
0
0
0
1
0
1
1
2
0
0
1
0
0
0
0
1
0
0
0
1
2
1
1
1
0
1
0
1
0
1
0
0
0
0
3
0
0
0
0
0
2
1
1
1
1
0
3
0
1
2
0
2
0
0
0
2
0
0
0
0
1
0
2
2
1
1
1
0
1
2
1
3
1
1
0
0
0
0
0
0
0
0
1
0
2
0
2
0
1
0
2
0
1
1
1
0
0
1
0
0
0
0
1
1
2
0
0
1
0
1
2
0
0
0
2
3
0
0
0
1
1
0
1
0
1
1
2
2
0
0
0
0
0
0
1
0
0
2
0
0
2
0
2
2
1
0
1
1
0
0
0
1
3
1
0
0
1
3
0
1
0
1
0
1
1
0
0
0
0
2
0
2
1
1
0
3
0
1
0
2
1
2
1
0
2
2
0
0
0
0
0
1
0
1
2
0
0
0
3
1
0
4
1
0
1
1
1
1
1
1
1
1
1
0
1
0
1
1
1
1
1
1
1
0
1
1
1
1
1
2
2
0
0
0
0
0
0
0
0
2
0
1
2
1
0
1
0
4
0
0
1
1
1
2
1
0
0
1
1
1
0
1
0
2
1
0
0
0
1
2
2
0
1
0
1
0
0
0
2
1
1
0
0
2
1
2
0
1
1
1
2
1
2
2
0
1
2
0
1
2
1
1
0
0
0
0
1
2
0
2
0
1
2
0
1
0
1
1
1
1
0
0
2
1
2
2
0
2
1
0
2
2
1
0
0
0
0
0
0
2
0
1
0
0
1
2
2
1
0
0
1
2
1
1
1
2
0
1
1
1
1
0
0
1
1
0
1
0
1
2
0
0
2
0
0
0
0
1
0
2
0
0
0
0
3
0
1
1
2
0
0
0
2
1
0
2
0
1
1
2
0
1
2
0
2
2
2
2
0
0
0
0
0
0
2
0
2
1
1
1
1
1
0
0
2
1
1
1
1
1
2
1
0
1
2
0
0
2
0
1
1
2
0
3
0
1
0
0
1
1
1
0
0
1
3
0
0
0
0
1
0
3
0
2
0
1
1
1
0
2
0
1
1
0
2
2
0
0
1
0
2
1
0
2
0
2
0
0
0
0
0
2
2
0
1
2
2
0
1
0
0
0
0
0
0
0
2
0
1
2
1
2
2
1
0
0
1
3
0
2
1
0
0
1
0
0
2
1
0
1
0
0
1
1
1
1
0
0
3
1
2
0
0
0
0
1
1
0
0
0
0
1
0
2
0
1
1
1
2
0
2
2
2
2
1
0
0
0
1
1
0
1
2
1
1
0
1
2
0
0
0
0
1
2
0
2
0
0
1
0
0
1
2
1
0
0
0
1
0
1
1
2
0
2
1
2
0
0
1
2
2
1
2
0
0
0
2
3
1
0
1
0
0
1
1
1
1
1
0
2
2
1
1
0
0
3
0
1
1
1
0
0
1
0
0
1
0
2
1
0
0
1
1
0
0
0
0
0
1
0
1
1
2
1
1
0
1
0
5
0
0
0
2
0
0
2
0
0
1
1
1
1
0
1
0
0
2
0
1
2
1
0
2
1
0
0
0
1
0
0
2
2
0
0
0
2
0
2
0
0
1
0
2
1
2
0
2
2
0
0
1
2
1
0
2
1
0
1
0
0
0
0
0
1
0
0
1
0
0
2
0
0
1
3
0
0
1
0
1
0
1
0
2
0
0
1
0
0
2
1
0
1
1
0
2
0
0
0
1
1
0
0
1
2
1
0
1
1
1
1
1
1
2
1
1
2
1
0
0
1
1
2
0
1
1
0
2
2
1
1
2
0
0
0
0
1
2
1
0
1
1
2
0
0
2
0
1
0
1
0
0
2
1
2
2
0
1
2
0
1
2
1
1
1
0
2
1
2
0
2
1
1
0
1
1
2
0
0
0
1
2
2
0
2
0
0
0
0
2
1
2
1
0
1
1
1
0
0
0
2
2
1
0
2
2
2
0
1
1
0
2
1
0
0
0
1
0
1
1
0
1
0
1
0
2
0
0
2
0
1
0
1
1
2
0
1
0
0
2
0
2
2
1
0
0
0
0
1
1
1
1
1
0
1
1
1
1
1
1
2
0
3
1
0
0
1
1
0
1
1
1
2
0
1
0
1
1
0
0
2
0
2
1
1
1
1
0
1
1
0
0
1
0
0
1
0
0
0
1
1
1
1
1
0
0
2
1
0
2
2
0
1
0
2
2
1
0
0
2
0
2
0
1
0
0
0
1
0
2
2
0
0
0
2
0
0
0
2
0
0
1
0
0
2
0
1
1
0
1
0
1
1
3
1
0
0
0
1
1
0
0
0
1
0
0
0
0
2
2
0
1
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
2
1
0
0
1
1
1
1
1
1
2
1
1
2
4
2
0
1
1
0
1
1
1
0
0
1
1
0
5
2
3
0
0
0
0
0
1
0
0
0
1
1
1
0
1
0
0
3
2
2
0
0
1
2
0
1
1
0
1
0
0
0
3
0
2
0
0
1
2
0
1
1
1
1
0
0
2
1
0
1
0
1
2
1
1
1
2
0
0
1
0
0
0
0
0
0
1
8
1
1
0
0
2
2
1
1
0
1
1
0
2
2
0
1
0
0
2
0
1
2
1
0
0
0
1
2
1
1
2
0
0
0
2
1
0
0
0
1
1
0
1
2
0
2
0
0
3
0
0
0
0
1
0
1
0
1
6
0
0
1
0
1
0
1
2
0
1
0
1
0
0
2
0
1
2
0
1
0
1
0
2
0
0
1
1
1
1
2
1
2
1
0
0
0
1
1
0
2
2
0
0
0
0
1
0
0
0
1
2
0
1
1
0
1
2
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
2
1
1
0
1
2
1
0
1
3
2
0
1
0
0
2
2
0
2
1
0
1
0
1
1
0
0
1
0
1
2
2
2
1
0
2
0
0
0
1
0
1
1
1
0
0
0
0
2
1
1
0
2
3
1
0
1
0
2
0
0
1
1
0
0
1
0
0
0
1
0
2
0
1
5
1
0
0
0
0
1
0
3
0
2
1
0
0
0
2
0
0
1
0
0
1
1
2
1
0
1
0
0
2
0
0
0
0
0
0
0
1
1
0
1
1
2
1
0
1
1
0
0
2
0
1
0
2
1
0
1
1
1
0
2
0
0
1
0
0
0
2
1
0
0
0
2
1
1
2
1
0
2
1
0
2
0
0
0
2
3
2
1
1
1
0
0
2
0
0
1
0
0
1
2
1
0
0
2
1
0
1
0
2
0
0
0
2
2
0
1
2
0
1
1
2
0
0
2
1
2
1
2
0
2
0
2
0
1
1
0
1
1
1
1
1
1
0
2
0
0
2
2
0
0
0
0
1
0
3
0
1
1
0
1
5
0
0
0
0
0
1
1
0
0
2
0
2
0
1
0
2
1
2
2
1
0
0
1
0
1
0
0
0
0
0
0
1
1
1
0
0
2
0
0
2
2
2
1
3
0
2
0
1
1
0
1
1
0
2
2
1
2
0
0
1
2
0
1
2
2
1
0
2
1
2
0
1
2
0
2
0
0
2
0
1
1
1
1
2
2
0
0
0
1
0
0
2
1
1
2
0
0
1
0
0
0
2
2
1
0
1
1
2
0
0
1
0
0
1
0
2
0
2
0
4
0
1
0
2
0
0
1
0
0
2
2
1
1
2
1
0
0
1
0
1
0
2
1
2
1
2
0
1
1
1
1
1
2
1
1
0
2
2
0
0
0
0
0
0
2
1
1
2
0
0
2
1
0
0
1
1
0
2
1
0
2
1
2
2
1
1
0
0
0
1
1
1
1
0
0
0
1
0
1
1
0
1
2
1
0
0
2
0
2
0
1
0
0
1
1
3
1
1
1
1
0
1
0
0
1
1
2
0
0
0
1
2
1
2
1
0
0
0
2
2
0
1
0
1
0
1
1
1
1
0
0
0
1
1
1
0
0
0
0
0
1
0
2
0
0
2
2
1
0
1
2
2
0
2
0
1
1
0
0
1
2
1
1
0
0
2
0
1
0
0
0
1
1
0
1
0
2
0
0
1
1
1
1
1
0
2
2
0
1
1
0
2
0
1
1
0
0
1
0
0
1
2
1
3
0
0
1
0
1
2
1
2
0
1
2
2
2
1
2
1
0
0
0
0
1
2
1
1
1
1
1
0
1
0
1
2
0
0
1
1
0
1
0
0
1
1
1
2
0
1
0
0
1
2
3
0
1
0
2
1
1
1
0
4
1
0
1
2
1
0
1
1
1
1
1
1
1
1
1
2
0
0
0
1
1
0
0
0
1
1
0
2
0
1
0
0
1
1
1
1
2
0
0
1
0
0
1
0
0
2
0
0
2
0
0
1
0
1
0
1
0
0
1
1
2
1
0
0
1
0
0
0
2
0
1
0
0
0
2
2
0
1
1
1
1
0
0
0
1
1
1
0
2
2
2
0
0
0
1
1
0
0
0
1
1
0
1
0
0
2
2
0
0
0
3
9
2
1
2
1
0
0
0
1
1
2
0
1
0
1
2
1
1
0
0
0
0
0
0
0
1
2
1
1
0
0
0
2
0
0
1
0
0
1
1
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
1
1
0
0
1
0
2
1
0
0
0
1
0
0
1
3
2
1
1
1
2
2
0
1
0
1
0
0
1
1
0
1
1
2
1
1
0
1
1
2
0
0
1
0
0
3
1
1
1
1
2
1
1
2
2
0
2
0
1
0
2
1
1
2
1
0
2
0
2
1
0
2
0
1
0
0
1
1
0
0
0
0
1
0
1
1
0
0
1
0
0
2
2
0
3
0
1
1
1
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
2
2
0
0
0
0
1
0
1
0
2
0
2
1
1
2
1
0
0
0
1
1
1
1
1
0
1
1
0
1
1
2
0
2
1
1
0
0
1
9
2
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
1
0
2
0
1
1
1
1
0
0
1
0
0
1
1
0
1
0
0
0
1
0
0
0
0
1
1
1
1
0
0
0
0
0
0
2
1
2
2
3
0
0
1
1
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
2
0
1
0
0
2
2
2
1
0
0
0
1
2
0
1
2
0
1
0
4
1
2
0
4
2
1
3
2
2
0
1
0
1
1
0
2
1
2
1
2
0
1
4
0
1
0
0
0
0
1
2
2
0
3
2
1
0
0
0
1
1
0
1
0
0
1
0
1
0
0
0
0
0
1
1
0
2
0
0
2
0
0
0
0
2
1
2
0
1
0
0
0
2
0
1
2
0
0
1
0
1
1
0
0
0
1
1
0
0
0
0
2
0
0
0
0
2
1
2
0
1
0
0
2
0
0
0
1
0
0
2
5
2
1
0
0
0
0
0
0
0
0
1
2
0
1
0
1
1
0
0
1
1
0
0
0
2
0
2
0
2
0
1
2
1
2
2
0
1
0
1
0
0
2
0
1
0
1
1
1
0
1
1
1
0
1
2
0
2
1
0
0
2
23
1
0
1
2
1
1
0
0
0
1
0
0
1
0
2
1
1
0
0
0
0
1
1
2
0
1
0
0
1
0
1
1
0
0
1
1
2
3
0
1
0
0
2
0
1
1
1
0
1
1
0
1
0
2
1
0
0
1
0
1
1
1
2
1
2
0
0
1
0
1
1
2
0
2
1
3
1
2
0
1
0
0
1
0
1
0
0
0
0
1
2
0
0
1
1
1
2
1
2
1
2
1
3
0
1
1
0
0
0
1
0
0
1
2
0
2
0
0
1
2
0
0
1
0
1
1
1
0
1
0
0
2
0
0
0
0
1
0
0
1
0
1
0
0
1
2
1
2
1
2
1
1
1
0
0
0
1
0
1
0
1
1
1
0
0
1
0
0
0
1
1
1
0
1
1
2
0
1
1
2
1
1
2
0
0
0
1
1
1
0
1
1
2
2
0
1
2
1
0
1
0
1
0
1
1
0
0
0
0
1
0
0
1
2
0
2
0
1
0
1
2
0
1
1
0
1
0
1
2
1
1
0
0
0
1
1
0
0
0
3
0
0
0
2
0
1
0
0
1
0
1
2
0
0
0
2
1
2
0
1
1
0
2
0
0
1
0
1
0
1
1
0
0
0
1
0
0
2
0
1
1
1
2
1
0
2
0
2
2
2
3
0
0
2
2
1
2
0
2
0
0
0
1
1
2
0
1
0
1
2
0
2
1
2
1
0
0
0
2
4
2
0
2
1
1
1
1
1
2
0
0
1
2
2
0
0
2
0
0
1
0
0
0
0
1
0
1
0
1
1
1
0
1
1
0
1
0
2
1
1
0
0
0
1
0
2
0
2
1
1
2
2
0
0
1
1
1
2
1
1
3
0
0
0
1
0
0
0
0
1
0
1
2
1
0
0
1
1
2
3
4
2
0
0
0
0
0
1
2
1
1
0
0
1
1
2
2
0
1
0
1
0
0
0
2
1
0
1
1
1
1
1
0
2
1
1
2
0
1
1
0
0
1
0
0
3
0
0
0
0
1
1
2
2
2
4
0
2
1
1
1
0
0
0
0
2
0
2
1
0
0
2
1
2
2
0
2
1
1
0
0
1
0
1
1
0
0
2
0
1
2
2
1
0
1
0
1
1
0
2
0
1
0
2
1
0
0
0
0
3
1
0
0
2
2
1
2
1
1
1
0
2
1
1
2
0
1
2
1
0
0
0
0
1
1
0
0
0
1
3
0
0
2
0
1
0
0
0
0
2
0
0
1
2
0
2
1
0
1
1
1
0
1
0
1
0
0
0
1
2
0
0
0
1
0
3
0
0
0
0
1
2
0
1
0
0
0
1
1
1
1
0
2
2
1
0
1
0
1
0
0
1
0
1
2
0
1
2
1
0
0
2
0
1
0
1
1
1
0
1
0
0
0
1
3
1
2
0
1
0
1
0
0
1
2
1
2
0
1
1
1
0
0
0
1
0
0
1
0
0
0
0
0
1
1
1
1
2
1
2
1
1
0
1
0
2
2
1
0
0
0
1
2
0
1
0
2
2
0
1
1
1
0
1
1
0
2
0
0
1
1
0
0
1
2
0
1
0
1
2
0
1
0
0
1
1
1
0
0
0
1
2
1
0
0
0
0
0
2
0
0
2
2
2
1
0
1
1
0
2
0
1
1
1
1
1
0
1
0
0
0
2
0
2
1
0
1
3
0
2
1
0
2
0
2
0
2
2
1
2
2
0
1
1
2
1
0
1
1
1
1
0
1
1
0
1
0
0
1
1
2
0
1
1
0
0
2
1
1
1
2
1
1
1
1
0
2
2
0
0
0
3
0
3
1
1
0
0
2
0
0
0
2
0
2
0
0
0
1
0
0
1
0
1
0
2
1
0
2
1
0
2
1
1
1
0
1
0
0
0
1
0
1
2
2
1
0
0
1
2
1
0
1
0
1
2
0
0
1
1
0
0
3
0
1
2
0
0
0
1
0
2
1
1
1
2
1
1
1
2
0
2
0
0
1
2
1
1
1
0
2
0
0
0
1
0
2
0
0
0
0
2
0
1
0
1
2
0
0
1
2
1
1
2
1
1
1
1
1
2
0
0
1
0
0
1
2
0
2
2
0
0
0
1
0
1
0
1
3
0
1
2
1
0
2
1
0
0
2
0
0
2
1
1
1
0
1
2
0
4
1
2
0
1
0
1
2
0
0
0
2
1
1
0
0
0
2
1
0
0
1
0
2
2
1
0
1
1
0
2
0
0
0
2
1
0
0
2
0
0
1
0
2
0
2
0
0
0
0
2
2
1
1
2
1
1
0
1
1
0
1
0
1
1
1
0
1
1
2
2
0
0
1
1
1
1
1
0
0
1
0
0
0
2
0
1
1
0
1
2
0
2
0
1
0
0
0
0
0
0
0
0
2
1
0
0
1
2
2
4
0
1
1
2
0
1
1
0
1
1
1
1
0
1
3
1
0
0
0
1
2
0
0
1
0
1
1
2
2
2
0
0
2
0
0
0
0
0
0
2
0
0
1
1
0
0
0
2
1
0
1
0
0
0
0
0
1
1
0
1
0
0
0
2
2
2
1
2
2
1
1
2
1
1
2
0
0
0
0
2
1
2
1
0
1
0
1
0
2
2
2
0
0
0
0
0
1
2
0
2
1
1
1
2
0
0
0
1
0
0
1
2
2
0
0
0
0
1
1
0
2
2
0
1
2
0
1
2
1
1
1
0
1
0
1
0
0
0
1
0
0
0
1
4
0
0
0
2
0
2
1
1
2
2
1
1
1
0
0
1
0
1
1
1
0
0
1
1
2
0
1
0
0
1
1
0
1
0
0
1
0
2
1
1
2
1
2
0
1
2
1
3
1
1
2
1
0
0
1
1
0
1
0
0
2
2
1
1
0
0
1
1
0
1
1
0
0
1
1
1
0
2
0
0
0
2
1
0
1
0
0
1
1
0
0
0
0
2
3
2
2
1
2
0
0
1
2
0
1
0
1
1
0
0
0
0
2
0
1
1
0
2
2
0
0
0
2
0
0
0
2
1
1
0
1
2
2
1
0
1
0
2
1
0
1
0
2
2
0
0
2
0
1
2
0
2
1
3
0
0
1
0
0
2
0
1
1
1
1
0
1
1
2
0
0
2
0
0
2
0
1
0
2
0
1
1
1
0
2
0
0
0
1
1
1
0
0
0
0
0
0
1
1
0
0
0
2
0
1
2
1
0
0
0
0
1
1
0
0
0
2
0
1
0
1
0
1
0
0
0
2
0
2
2
2
2
0
0
0
0
0
1
1
2
1
1
0
0
0
0
0
2
2
2
1
2
0
1
1
0
0
2
2
1
0
0
2
2
1
0
0
0
1
1
0
2
0
2
1
0
1
1
2
1
1
0
0
1
0
2
0
0
0
1
0
1
0
0
5
2
0
0
0
2
0
0
1
0
0
3
0
0
0
2
1
3
2
1
0
2
1
2
1
0
2
1
1
2
2
2
2
2
2
1
0
1
0
0
0
1
1
2
1
0
0
0
1
0
1
2
1
0
0
0
1
1
1
0
1
0
1
1
2
0
0
0
1
0
0
0
0
0
2
0
2
1
1
0
0
2
1
0
2
0
0
0
2
1
0
0
1
1
0
0
0
1
1
0
0
1
1
1
0
2
0
0
2
1
2
1
1
1
0
1
2
0
0
0
2
2
2
0
1
1
1
1
1
2
0
0
1
2
1
0
0
2
1
0
1
0
0
2
0
2
1
0
1
1
0
1
0
0
0
2
2
1
0
0
0
0
2
1
1
0
1
2
0
1
0
0
1
3
4
1
0
0
1
2
0
2
2
1
2
0
0
0
1
2
0
0
0
1
1
2
0
3
2
0
0
0
0
0
2
0
0
1
0
0
1
2
0
0
1
2
0
0
1
2
0
1
0
0
0
1
1
2
2
1
0
0
1
0
0
1
0
1
1
0
0
2
0
1
1
2
2
0
0
0
2
0
0
0
0
2
2
0
2
1
0
0
1
1
0
1
0
1
0
2
0
1
1
1
0
0
0
0
0
1
0
0
2
1
2
1
1
1
0
0
0
0
0
1
1
1
0
0
2
0
1
1
1
1
0
2
2
0
0
1
0
2
0
0
0
2
0
2
2
1
0
0
0
0
0
1
3
1
0
3
2
0
0
0
0
0
1
2
0
1
0
0
0
0
1
2
3
0
0
2
0
0
0
2
1
0
1
2
2
0
2
0
1
0
1
0
0
1
2
1
0
0
1
1
1
0
0
0
0
1
1
0
1
0
1
1
0
0
2
0
1
0
2
1
0
1
1
0
0
1
1
0
0
1
1
0
0
2
2
1
0
0
0
1
2
0
1
0
0
0
0
1
1
0
0
0
2
0
2
1
0
2
2
1
0
2
1
2
1
1
1
0
0
0
0
0
0
2
1
0
0
2
0
2
0
1
0
0
0
1
0
0
0
0
0
0
1
1
2
0
3
3
0
1
0
2
1
0
2
1
0
0
1
2
0
0
0
2
0
0
0
0
2
2
0
2
1
1
2
2
0
1
0
3
0
0
1
0
0
0
2
0
0
0
1
5
1
2
0
2
0
1
1
1
0
1
0
1
0
2
0
0
2
0
2
1
1
2
0
1
2
0
1
0
0
0
1
2
0
0
0
0
2
2
0
0
1
0
0
0
1
0
0
0
0
1
0
1
2
0
0
1
0
2
1
0
1
2
0
0
0
1
1
0
1
2
2
2
0
3
0
0
0
0
1
0
2
0
2
0
2
2
0
1
0
0
1
1
1
0
1
1
0
2
0
0
1
1
0
0
2
2
1
0
0
0
1
2
3
1
1
0
0
1
0
1
2
0
0
2
0
1
1
2
2
1
1
1
1
1
1
2
1
1
0
2
0
1
0
1
1
0
2
1
0
1
0
2
0
0
2
0
2
0
1
0
1
2
2
1
0
1
1
2
0
1
1
0
2
0
0
1
0
1
1
1
2
0
0
2
2
0
1
0
0
0
1
0
1
1
1
0
0
0
1
0
0
0
0
0
0
1
0
2
0
2
1
2
1
2
1
2
0
0
0
2
0
1
1
0
2
0
2
2
1
0
1
1
1
1
0
0
0
0
2
1
0
1
0
2
1
0
0
2
1
0
0
1
2
2
0
0
2
0
1
1
1
1
2
1
0
2
2
1
0
0
0
2
0
0
0
0
1
0
1
0
1
0
0
0
0
2
2
0
0
0
1
0
0
0
1
1
2
2
2
1
0
0
1
2
2
1
1
0
2
1
0
0
0
0
0
0
0
0
1
3
3
0
0
0
1
0
2
1
1
1
0
1
1
2
0
0
0
0
1
0
1
0
0
1
1
0
2
2
0
1
1
1
0
1
2
3
1
2
1
0
0
0
2
0
0
1
1
1
2
0
1
0
1
0
2
2
0
0
1
1
1
1
0
0
1
0
0
1
2
1
2
2
1
1
0
0
2
0
0
1
0
0
1
1
0
0
1
0
0
0
1
1
2
0
0
4
0
0
1
0
1
0
0
1
0
1
0
2
2
0
2
0
3
1
1
0
1
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
1
0
1
2
0
0
1
0
1
2
1
0
0
1
1
5
0
0
1
1
2
1
0
1
0
0
1
1
1
0
2
0
0
0
1
1
1
1
0
0
1
0
2
0
1
2
0
2
0
2
0
1
1
2
0
1
0
0
2
0
0
0
1
0
2
1
2
0
0
2
1
3
0
0
1
0
2
0
3
0
2
0
1
0
1
1
2
0
0
1
1
0
1
0
1
0
1
0
1
0
0
2
2
0
1
2
2
2
0
2
0
0
2
1
0
1
1
1
0
2
0
0
0
2
1
1
0
0
1
1
1
0
3
0
2
0
1
0
0
2
0
1
0
0
1
2
1
2
2
0
0
1
1
1
0
2
1
2
0
0
2
2
0
1
0
1
1
1
0
2
1
1
2
1
0
0
1
0
1
0
1
1
1
1
0
2
0
1
0
0
0
2
1
0
1
0
1
0
1
2
2
0
0
0
1
0
0
0
1
2
0
1
1
2
0
1
1
0
0
1
2
0
2
1
1
0
0
1
1
0
0
1
0
2
2
1
1
2
1
0
2
1
1
1
0
1
2
2
0
0
1
0
2
0
0
2
0
0
0
1
1
0
1
1
1
1
0
2
1
1
1
2
1
1
0
1
2
1
0
1
0
1
0
2
0
1
1
0
0
0
0
1
0
1
0
0
2
1
2
2
0
1
1
0
1
0
1
0
2
1
1
1
2
0
0
1
1
1
0
0
2
0
0
1
1
0
0
1
1
1
0
0
0
1
1
2
1
0
1
0
0
1
0
0
0
2
1
1
0
0
1
1
0
0
0
1
2
0
2
0
0
1
0
1
0
0
2
1
0
2
2
1
1
1
0
1
0
1
1
2
2
0
1
1
0
0
0
2
1
0
0
0
0
0
0
1
4
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
2
0
0
2
0
1
2
0
3
0
0
2
1
0
1
0
0
1
1
0
0
0
2
0
0
0
1
0
2
2
0
1
1
2
0
0
1
0
0
2
2
1
1
0
0
0
2
0
0
0
0
0
0
1
1
3
1
1
1
0
0
0
1
1
0
1
0
0
0
3
1
2
0
1
0
2
1
1
1
0
2
2
2
0
0
0
0
0
1
1
1
1
1
0
1
0
2
0
0
2
2
1
0
1
5
0
0
0
1
1
2
1
2
1
0
0
0
1
2
0
0
1
6
1
1
0
2
0
2
0
0
0
1
2
0
2
0
0
2
2
0
0
0
0
2
2
0
0
2
1
2
1
0
1
2
0
0
2
1
2
0
0
1
0
0
2
2
2
1
1
1
0
1
1
1
1
1
2
2
2
1
1
2
1
1
1
0
2
0
2
2
0
1
2
1
0
4
0
0
0
1
1
0
0
1
2
2
0
1
0
0
1
2
2
0
0
0
1
1
1
2
0
2
0
0
0
0
0
2
1
2
0
1
0
0
0
2
2
0
0
0
0
1
0
0
2
1
2
0
0
1
2
1
1
2
1
0
1
1
2
0
1
0
0
1
1
1
0
3
0
2
1
1
0
1
0
0
2
1
0
1
1
2
1
0
0
1
1
0
2
1
0
0
0
0
2
2
1
1
1
1
1
0
0
0
1
1
0
2
1
1
2
2
1
0
0
1
1
2
2
0
2
1
0
0
0
0
0
1
0
0
0
1
0
1
2
0
3
0
0
0
0
2
0
1
1
1
0
0
0
2
1
1
0
1
0
0
1
0
0
2
0
1
2
2
1
1
0
1
0
0
1
1
1
0
1
0
1
0
0
1
0
1
0
0
0
2
2
1
0
1
1
1
0
1
1
1
2
2
1
0
0
0
2
2
1
0
1
1
1
1
1
0
1
2
2
0
0
1
2
0
2
1
1
2
0
0
0
1
0
1
0
1
2
1
2
0
2
2
1
1
0
1
1
1
0
1
2
0
1
0
2
0
1
1
1
1
0
2
2
0
1
1
1
0
2
4
0
0
0
0
2
0
1
1
0
2
1
1
0
1
2
1
2
0
1
2
1
0
1
0
1
1
0
1
2
0
0
0
0
1
1
0
1
2
1
1
1
2
1
0
1
2
0
0
0
2
2
0
1
0
0
0
2
0
1
1
1
0
0
1
0
1
0
0
0
1
1
1
1
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
2
1
0
1
1
2
2
1
0
0
0
0
2
0
2
1
0
2
2
1
0
0
0
2
1
3
0
1
0
0
2
1
1
1
1
0
0
0
1
0
1
0
2
0
1
2
1
0
1
1
1
1
0
2
1
0
0
0
2
2
2
0
1
0
0
0
0
0
0
1
1
2
0
0
3
0
2
0
2
1
0
1
0
0
1
0
1
1
1
0
1
1
0
1
1
0
1
2
0
2
1
1
0
2
0
1
1
1
0
0
0
2
0
1
0
2
0
2
1
1
1
1
0
0
0
2
1
2
1
1
1
1
0
1
1
6
0
1
1
0
1
0
0
1
0
0
0
2
1
1
0
0
2
0
2
0
0
1
1
2
4
1
0
1
3
0
1
2
2
1
2
1
2
1
2
2
0
2
1
0
1
0
0
2
0
0
0
0
1
1
1
1
1
0
3
2
12
0
0
1
1
0
2
0
0
1
0
2
0
0
3
1
3
2
2
0
1
0
1
1
0
2
2
0
1
2
2
2
1
2
2
2
1
0
1
0
1
0
1
2
0
2
1
0
0
1
0
0
1
1
1
1
0
2
0
0
1
0
0
0
0
0
1
1
0
2
0
0
0
0
1
2
2
2
0
2
1
1
1
1
2
0
2
1
2
1
1
1
0
2
0
2
0
2
0
2
1
1
2
0
0
1
1
2
1
0
0
1
0
0
1
1
0
1
0
0
1
1
0
2
2
1
2
1
0
1
2
0
0
0
1
1
1
2
0
0
0
0
0
0
0
0
1
0
2
0
1
0
1
0
0
0
1
1
0
0
0
0
2
0
0
0
0
2
0
1
0
2
2
0
2
0
0
1
0
0
0
2
0
1
1
0
1
0
0
0
2
0
1
2
1
1
1
1
1
0
0
3
0
0
3
0
0
2
2
1
1
1
1
2
1
0
1
0
2
1
2
0
1
0
1
1
0
0
2
0
0
2
1
0
0
4
3
1
0
1
1
1
2
0
0
2
1
0
0
1
3
2
2
0
1
0
1
1
1
1
0
2
1
0
1
0
2
2
1
0
1
1
2
1
0
1
1
0
1
1
0
0
1
0
0
1
0
2
2
1
2
1
1
2
1
1
1
0
1
0
1
1
0
1
1
1
0
0
0
1
1
0
0
2
1
2
1
0
2
0
1
2
0
3
1
2
0
1
2
1
2
1
0
0
0
1
1
0
0
1
0
0
1
2
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
2
2
0
0
0
1
1
1
0
0
2
2
1
0
0
0
0
1
1
2
1
0
1
1
0
1
0
1
0
0
1
0
1
0
1
1
2
0
0
0
0
0
0
1
2
2
1
2
1
2
1
0
1
0
2
0
0
1
0
1
0
0
0
1
1
1
0
0
1
3
1
3
1
0
1
0
0
0
1
1
1
1
2
2
0
2
0
6
1
0
9
0
0
1
1
1
0
2
1
1
1
0
0
1
3
0
2
0
2
2
0
1
1
1
0
1
0
0
1
1
1
1
1
1
1
1
1
1
0
0
1
0
2
1
2
1
2
0
0
1
1
2
0
2
0
0
0
2
0
0
2
1
0
0
0
0
0
2
0
0
0
0
1
0
1
2
2
1
0
1
0
0
1
0
0
0
0
0
1
0
1
0
1
0
1
1
2
2
0
0
0
1
0
2
0
2
0
2
1
2
1
1
2
0
0
0
2
1
0
2
1
0
0
1
0
2
2
8
2
0
0
0
0
2
1
0
2
0
0
0
0
0
1
2
0
1
0
0
0
0
1
0
2
1
1
1
2
0
3
2
2
2
0
3
1
0
3
0
1
1
1
4
1
1
2
2
1
0
0
1
1
2
0
2
0
1
0
1
1
0
2
1
2
0
0
2
1
0
0
2
3
1
2
2
1
0
2
0
1
1
0
0
2
0
0
1
0
1
0
1
1
0
1
1
2
0
0
1
0
0
0
2
0
1
2
2
1
2
1
1
1
2
2
1
0
1
1
2
1
0
3
0
0
0
1
2
1
2
0
2
0
0
1
0
1
1
0
2
0
0
1
1
0
0
1
1
1
2
0
0
0
0
0
0
0
1
0
0
0
2
1
2
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
2
1
0
2
2
0
2
0
0
2
0
0
1
1
1
1
1
0
2
1
0
1
2
2
2
1
1
2
0
0
0
0
0
2
1
0
0
0
1
0
0
0
2
0
0
2
1
2
1
0
0
1
2
2
2
0
0
0
2
1
1
0
1
3
1
2
0
2
0
0
1
1
2
2
0
1
2
0
0
1
0
1
0
1
2
2
2
2
1
2
1
0
1
1
1
0
1
1
3
1
0
0
1
0
2
1
0
0
0
1
0
0
0
0
0
0
1
1
0
1
1
2
0
0
2
0
0
4
1
0
0
2
0
1
1
0
4
1
2
1
0
0
0
2
2
1
0
0
2
2
1
1
0
1
0
2
0
0
1
0
0
0
2
0
2
1
0
1
1
1
2
0
1
1
2
1
2
0
0
1
0
0
0
2
1
2
2
0
1
0
0
2
0
0
0
0
1
1
1
1
3
0
1
0
0
1
1
1
0
0
1
0
0
0
1
1
2
0
2
0
2
0
0
0
0
2
0
3
0
0
1
0
0
2
1
0
1
1
0
2
1
0
1
2
0
1
0
1
0
1
2
1
1
2
1
1
2
0
2
0
1
2
0
2
0
2
1
2
2
2
1
1
0
2
0
2
1
1
1
1
0
0
1
0
1
0
2
0
0
2
1
1
1
2
1
0
0
1
0
0
0
0
1
2
2
1
1
0
2
0
0
0
0
2
0
1
0
1
0
0
1
2
2
2
0
2
1
0
3
0
0
1
0
2
1
0
2
1
0
2
0
1
1
1
0
0
1
1
2
0
0
1
0
0
0
2
2
1
1
1
1
1
0
1
0
2
0
0
2
0
0
0
0
1
2
2
1
0
0
0
2
1
0
0
0
0
1
0
0
2
1
0
1
0
0
1
0
0
2
3
0
1
0
1
2
2
0
0
0
0
1
1
0
1
1
0
1
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
1
1
0
1
2
1
0
0
0
0
1
1
0
0
1
0
1
2
0
1
0
1
1
2
2
1
1
0
1
0
1
1
1
1
2
1
2
1
0
0
2
1
0
1
2
1
0
1
0
2
0
2
2
0
0
0
2
0
1
1
0
1
1
0
1
0
0
0
2
2
0
0
1
1
0
0
0
1
2
0
0
1
1
0
1
2
0
1
0
0
2
2
1
2
2
2
1
0
0
1
0
1
1
1
2
1
0
1
0
2
0
1
0
1
2
1
2
0
2
1
0
3
0
1
1
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
2
1
2
0
0
2
2
0
2
2
2
1
0
0
0
1
0
1
0
0
1
0
0
0
1
0
2
1
0
0
2
2
0
0
2
0
1
0
2
0
1
2
0
1
0
0
0
1
0
2
0
1
2
1
2
1
0
2
2
1
1
2
0
2
1
1
2
0
0
0
1
1
2
2
0
1
0
1
0
0
1
0
1
1
0
0
1
2
1
0
0
2
1
0
2
1
0
1
1
2
2
1
0
2
1
0
0
1
1
2
2
0
0
0
0
0
0
2
1
2
0
2
2
0
1
0
1
1
1
0
0
0
1
0
1
2
1
2
2
0
2
1
1
2
2
2
2
0
1
1
1
0
0
0
1
1
1
0
0
0
1
1
0
2
2
2
1
1
0
1
1
1
0
0
2
0
0
0
0
1
1
2
0
1
1
0
0
2
1
0
2
0
1
1
2
0
2
1
2
0
2
0
0
0
1
0
1
0
2
0
1
1
1
1
0
0
1
1
1
1
2
0
0
2
1
1
0
2
2
0
2
0
1
1
2
1
2
0
1
2
1
2
0
0
0
1
1
1
0
2
1
1
2
2
2
1
2
0
1
1
1
1
1
1
2
1
2
0
0
2
0
0
0
2
0
0
1
2
1
2
0
0
0
0
3
0
0
1
0
1
1
0
0
1
2
0
0
1
2
0
2
0
1
0
2
0
0
0
1
0
1
0
1
2
1
2
1
0
1
2
1
1
1
0
1
0
1
0
0
1
1
0
0
0
0
1
1
0
1
2
1
2
1
0
0
1
1
1
0
0
1
1
1
1
1
0
0
0
0
0
1
1
0
1
1
1
2
1
0
0
0
1
0
0
2
2
2
0
0
1
2
1
0
2
1
1
1
0
2
2
1
0
1
2
1
1
1
1
3
0
3
0
1
1
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
2
1
1
0
2
0
0
1
0
2
1
0
2
0
1
0
0
0
0
2
1
0
2
0
0
2
1
0
1
0
1
0
2
2
2
0
0
0
1
0
1
0
2
1
0
2
2
0
1
0
0
3
0
2
1
0
2
0
1
0
2
1
1
2
1
1
2
0
1
1
0
1
0
0
2
2
0
2
1
0
1
0
1
0
0
0
0
0
1
0
1
1
0
1
1
0
0
2
0
2
0
2
0
0
0
0
2
0
0
1
1
0
1
1
1
1
2
0
1
1
1
0
1
2
1
2
0
1
1
1
0
1
2
2
0
1
1
1
1
0
1
0
1
1
0
0
0
1
1
0
1
2
1
0
1
0
0
1
0
1
1
0
0
1
2
2
1
1
0
1
1
0
0
1
2
0
0
2
0
0
0
0
0
0
3
0
0
2
1
0
0
0
2
1
1
3
1
0
1
2
1
1
2
0
2
0
0
1
1
2
1
1
2
1
1
3
2
0
3
1
0
3
1
1
1
0
1
1
0
0
2
1
3
0
1
0
2
0
2
1
2
2
1
1
0
0
2
0
1
0
0
3
2
0
1
0
0
1
0
0
2
1
0
1
1
2
1
2
3
0
0
0
1
1
0
1
1
0
1
0
1
2
0
2
0
1
0
0
1
2
1
1
0
1
2
0
0
2
0
0
1
0
1
2
2
1
0
1
1
2
0
1
2
1
1
2
2
0
0
0
1
0
1
1
0
2
0
2
1
0
0
1
1
1
1
2
0
1
0
0
2
0
0
0
1
0
2
1
0
1
2
1
0
1
1
2
1
1
0
0
1
1
1
2
0
0
0
1
0
2
0
2
2
1
0
1
1
1
0
3
0
0
0
0
0
1
0
0
1
1
2
2
0
2
0
0
1
2
1
1
0
1
1
2
1
2
0
1
1
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
2
1
2
0
0
2
0
0
0
2
0
0
0
0
2
0
2
1
5
1
1
4
1
0
2
0
0
0
0
0
1
0
2
0
2
1
0
2
0
1
1
0
0
1
2
1
0
0
3
1
0
0
0
1
0
1
0
2
1
1
1
1
0
3
0
1
1
1
0
0
0
0
2
0
0
0
2
2
0
1
1
0
2
0
0
1
0
2
1
2
0
1
2
0
0
2
2
1
1
2
0
1
0
0
1
2
0
2
0
0
1
0
0
1
2
0
1
2
0
2
0
1
2
0
1
1
1
0
1
2
1
1
1
0
3
1
1
1
0
1
0
0
1
1
1
0
2
0
1
1
0
0
0
1
1
0
0
1
3
0
1
0
0
0
0
0
2
2
4
2
2
0
1
1
1
1
2
1
2
3
1
1
0
1
2
0
0
0
0
4
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
1
1
1
0
1
0
1
0
1
0
0
2
1
2
1
2
0
1
0
0
2
0
2
0
1
0
0
0
1
0
2
1
1
2
0
0
0
0
1
1
0
0
1
1
1
1
0
1
0
1
2
0
0
0
1
1
1
0
1
2
0
0
2
2
1
0
0
3
2
0
0
1
2
2
0
0
1
1
1
0
1
1
2
1
1
0
0
0
1
1
1
0
1
0
1
1
0
1
2
0
0
0
1
2
0
0
1
2
2
0
1
1
1
1
0
0
1
1
2
0
0
1
5
0
0
0
4
3
0
0
0
1
1
1
1
0
1
0
2
0
2
1
0
2
1
2
0
1
1
0
1
0
3
0
2
0
0
2
2
0
2
0
1
0
1
0
2
1
1
0
1
1
1
1
1
0
0
2
0
1
1
2
0
1
1
0
0
2
1
2
0
1
2
1
0
2
1
0
0
0
0
0
2
0
1
0
0
2
2
0
4
1
0
1
1
2
0
0
2
2
1
1
0
0
0
1
2
0
0
1
0
0
1
0
2
1
1
2
0
0
0
0
1
0
0
0
1
0
0
2
1
1
2
0
0
0
1
1
2
2
0
2
0
2
0
0
1
2
2
1
1
0
1
1
1
2
1
1
1
1
0
2
0
0
1
2
0
1
0
2
0
0
1
0
1
0
2
1
0
1
0
0
1
1
1
0
0
1
1
1
0
4
0
1
0
0
1
2
1
2
0
3
0
1
0
1
0
1
0
0
0
0
1
1
1
0
0
0
2
1
0
0
0
2
1
1
0
1
0
1
0
0
0
1
1
2
1
0
0
0
0
2
1
2
0
1
0
0
1
1
1
1
2
1
0
1
0
0
0
1
2
1
0
1
2
2
0
2
1
1
1
1
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
2
0
1
0
0
1
3
1
2
0
0
0
2
1
0
1
0
0
0
0
2
0
0
0
0
1
1
0
2
1
0
0
1
0
0
1
1
0
0
2
2
0
0
0
0
1
2
0
1
2
0
0
1
1
0
1
0
0
0
1
1
0
1
0
3
2
0
0
1
0
1
3
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
1
0
2
0
0
0
0
1
2
1
0
1
1
2
2
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
1
2
0
0
1
1
3
0
2
2
2
1
2
1
1
0
2
2
1
2
2
0
1
1
2
0
1
3
1
1
1
1
0
2
2
1
0
0
0
1
1
1
0
1
0
0
0
0
1
2
0
2
2
0
1
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
2
2
1
0
0
0
2
1
2
0
1
2
1
2
1
0
1
0
1
0
0
0
2
0
0
1
0
0
2
0
1
1
0
1
1
0
0
2
0
1
1
1
2
0
0
0
1
2
0
1
1
1
1
1
1
0
0
0
2
1
2
1
0
2
0
0
1
0
0
1
1
2
1
0
0
1
1
0
0
1
1
2
0
0
2
0
1
1
1
0
0
0
0
1
1
0
2
1
1
3
0
0
1
1
1
2
1
2
2
0
3
2
1
0
0
0
1
1
1
0
0
0
1
2
0
2
2
2
2
1
2
0
1
2
0
1
0
1
0
0
0
0
0
2
1
0
1
1
1
0
2
2
1
1
1
1
0
1
0
0
0
1
0
2
0
1
1
0
1
0
2
0
0
0
2
2
0
0
0
1
0
0
2
1
0
0
2
0
0
0
0
2
0
0
0
1
2
0
0
1
0
1
2
1
2
1
1
1
1
2
2
2
0
0
0
0
0
2
1
0
1
1
1
0
1
1
2
1
3
1
2
0
0
1
0
1
0
0
1
0
0
1
0
0
1
1
1
1
0
2
1
2
0
1
0
1
1
1
1
1
2
1
0
1
0
0
1
0
2
0
1
2
0
0
2
3
2
0
0
1
1
0
0
2
1
1
1
2
2
0
0
1
2
2
0
1
2
0
4
1
0
2
2
0
1
0
2
2
1
0
0
1
2
1
0
0
1
0
0
1
0
1
2
2
1
0
1
0
0
0
2
2
1
2
0
0
2
0
0
0
0
0
1
1
3
0
2
2
1
1
0
0
0
0
0
0
5
0
0
1
3
0
1
0
0
1
1
6
2
1
1
1
0
2
2
1
1
0
1
2
0
0
1
0
0
2
0
2
2
0
2
0
1
0
0
2
2
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
1
2
2
1
0
2
0
1
1
0
2
0
2
0
0
2
0
1
1
1
0
2
1
2
0
1
1
3
0
0
2
1
1
0
0
0
2
0
1
1
1
0
2
1
0
2
2
2
0
1
1
1
0
0
0
1
0
1
2
1
3
0
1
1
0
0
0
0
1
0
1
1
1
2
2
0
0
1
1
2
0
2
0
1
0
2
2
1
3
2
1
1
0
0
1
3
2
1
0
2
1
1
1
1
2
0
0
2
2
0
0
1
0
0
0
0
1
0
1
0
1
2
1
1
0
1
0
1
0
0
0
2
1
0
0
1
0
2
0
0
1
0
1
2
0
0
1
1
0
0
0
1
1
1
0
0
0
0
1
2
0
0
2
2
1
0
0
1
1
0
0
2
2
0
2
0
0
0
0
2
2
1
0
0
0
2
2
2
0
2
1
0
1
0
0
0
2
2
0
1
0
0
0
0
0
1
1
1
2
1
2
0
1
1
2
0
0
0
1
5
0
1
2
2
2
1
0
2
1
0
1
0
0
2
2
2
0
1
1
1
0
0
2
0
2
0
1
1
1
2
1
0
2
0
0
1
0
0
0
0
0
2
0
0
0
2
1
1
1
0
0
0
0
2
1
1
2
1
2
0
6
1
1
1
0
2
0
2
0
0
0
0
1
1
0
0
1
1
0
1
1
2
0
2
0
1
0
0
1
0
0
0
1
2
0
2
0
0
3
2
0
1
1
2
1
0
2
0
0
0
0
2
0
0
1
1
0
0
2
2
3
0
1
0
0
0
1
1
0
1
1
1
0
1
2
1
1
1
0
2
0
2
0
0
0
0
0
2
0
2
1
0
0
1
0
2
0
0
1
1
1
2
0
0
0
1
2
0
2
1
0
1
1
1
1
0
0
2
0
1
0
0
2
0
1
1
0
0
0
2
1
1
0
0
0
1
1
2
1
1
0
0
2
0
0
0
1
1
0
0
0
1
2
1
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
1
1
2
1
0
2
0
2
0
0
2
3
1
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
1
1
2
1
1
0
1
0
2
0
0
0
0
1
1
2
0
0
1
1
1
1
0
0
1
0
1
1
1
0
0
0
0
1
1
1
0
1
0
1
2
1
0
0
0
1
0
1
0
0
1
0
0
2
9
0
0
1
1
2
0
1
2
1
0
2
2
2
2
2
2
1
0
0
2
2
0
1
0
0
0
0
1
2
1
0
1
1
2
0
0
1
0
1
0
1
0
2
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
2
0
0
1
1
4
0
2
1
0
0
1
0
2
0
0
2
2
0
0
0
1
0
1
0
0
0
2
0
0
2
1
1
1
0
2
1
0
5
0
0
0
1
0
0
3
0
1
0
0
1
2
0
2
2
2
1
0
2
2
0
1
1
0
1
0
2
0
0
2
1
0
0
0
0
2
0
2
0
0
0
1
0
1
0
0
2
0
1
0
0
0
2
1
0
2
0
2
0
1
2
1
0
1
0
1
2
0
2
0
2
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
1
2
2
2
0
2
1
1
1
0
0
0
0
1
1
2
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
2
2
0
2
0
0
0
0
2
0
0
1
0
0
0
2
2
1
1
1
0
1
2
0
0
1
2
0
2
2
0
0
0
0
2
1
1
1
0
1
1
0
1
2
0
2
0
0
1
1
2
0
1
2
2
0
0
2
1
2
1
0
0
0
0
2
0
2
1
2
0
0
1
1
0
0
0
0
1
0
0
1
0
0
1
2
1
1
1
0
0
1
0
2
3
0
1
0
2
0
2
0
1
2
0
1
0
0
2
1
2
0
2
1
0
1
0
1
1
2
1
0
0
0
0
0
2
0
0
1
1
2
2
2
1
1
0
1
2
0
1
2
1
0
1
0
1
1
0
1
1
0
0
1
0
0
0
1
1
2
2
0
1
1
1
0
2
0
1
1
0
0
1
0
0
1
2
1
0
2
2
1
2
2
0
3
0
0
0
1
0
0
1
0
1
2
0
1
1
0
0
1
1
2
1
0
3
1
0
1
4
1
1
1
0
0
1
0
1
2
2
0
2
0
0
1
3
0
0
1
1
2
0
0
1
0
2
1
1
2
2
2
1
0
0
0
4
0
0
1
0
0
1
1
0
1
0
0
3
1
0
2
0
0
1
2
2
0
2
0
2
0
1
0
1
1
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
2
1
0
1
0
1
1
1
0
2
2
1
1
0
2
0
0
1
0
2
0
1
1
1
0
1
1
1
0
0
1
0
1
0
2
1
0
2
1
2
0
0
3
1
1
0
0
1
0
0
1
0
0
0
1
0
0
1
0
1
1
1
0
1
1
2
1
1
1
2
1
1
0
0
0
0
2
0
2
1
1
0
1
1
1
1
2
2
0
4
1
0
1
1
0
1
0
0
0
2
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
1
3
0
0
0
1
0
2
0
2
1
1
2
1
2
0
1
1
1
1
0
1
1
1
1
3
0
2
0
2
1
2
0
1
0
0
1
0
0
1
0
0
1
0
2
2
1
2
0
1
0
2
2
1
2
0
1
0
0
2
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
1
1
1
0
0
1
1
0
0
0
1
1
0
2
2
2
0
1
1
0
0
2
2
0
1
1
0
0
1
1
0
2
0
0
0
0
0
1
0
1
0
0
0
2
1
2
1
0
2
2
0
1
2
0
0
1
2
1
0
0
0
1
0
2
0
2
1
2
0
0
1
2
0
1
0
2
2
1
1
2
2
0
1
0
0
1
1
1
2
1
1
1
2
1
2
1
0
0
0
2
3
0
0
1
0
1
1
1
0
2
2
1
0
1
2
2
0
1
1
1
3
1
0
0
1
0
0
0
1
2
0
1
0
1
0
2
1
2
2
0
2
1
0
2
0
0
2
1
2
0
0
1
0
1
2
0
2
0
0
0
1
2
0
2
1
0
0
0
1
1
1
2
2
0
1
1
1
1
2
0
1
1
0
1
1
1
0
0
2
2
0
1
1
0
2
0
2
2
0
1
2
2
1
1
0
2
0
1
1
2
1
0
1
0
0
2
2
0
1
0
1
0
1
1
2
2
0
2
1
1
1
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
1
0
2
0
0
0
2
0
1
1
1
0
0
2
1
0
1
1
0
1
1
1
1
0
1
1
0
2
1
0
0
1
2
0
1
1
1
0
1
1
0
1
0
0
1
2
3
0
2
2
1
1
2
0
0
2
0
0
0
1
1
3
0
1
0
1
0
0
0
0
2
2
1
2
0
0
1
1
0
0
1
1
1
2
1
1
0
1
0
0
1
1
1
1
1
0
0
1
0
1
0
0
1
0
0
1
0
1
0
2
1
2
1
1
2
1
1
0
1
0
0
0
1
2
1
0
0
2
2
2
1
0
0
2
1
0
1
2
1
1
2
0
2
0
1
0
2
1
2
0
2
1
1
1
1
0
1
0
0
1
1
2
1
2
0
2
0
1
2
2
0
0
0
2
0
1
0
1
2
1
1
1
0
2
1
0
1
1
1
2
1
1
1
1
1
1
0
0
1
1
1
2
0
0
0
1
0
0
1
0
1
0
0
0
3
0
1
1
0
2
1
0
0
0
0
2
1
2
0
2
0
1
0
0
0
2
0
0
1
0
0
2
2
1
2
2
0
2
1
0
1
0
1
0
1
0
0
1
2
0
0
0
0
2
2
0
0
2
1
0
1
0
0
2
2
1
1
1
0
1
0
2
2
0
0
0
0
1
1
0
1
1
1
1
1
2
0
0
0
1
0
2
1
1
0
0
0
1
0
2
2
1
2
1
1
0
1
0
2
2
1
0
1
0
0
2
1
1
1
1
0
1
2
1
3
0
0
0
3
2
0
0
0
3
0
0
2
0
1
1
1
0
0
0
1
3
1
1
0
2
0
1
0
2
1
0
0
0
1
0
0
1
1
2
2
2
1
0
0
1
2
1
0
0
0
0
1
0
1
1
1
1
1
0
0
0
0
1
2
0
0
0
2
1
2
1
1
1
2
2
1
0
0
1
0
1
2
1
1
1
2
1
2
2
0
1
1
0
0
1
1
2
0
2
0
1
0
1
0
1
1
4
2
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
2
2
1
2
2
0
1
1
1
2
2
0
0
1
1
0
1
0
1
0
1
0
2
2
0
0
1
0
1
2
0
0
1
0
0
0
0
0
1
1
0
2
2
0
0
1
0
1
0
0
0
2
2
1
0
0
1
0
1
2
1
0
2
0
2
1
2
2
0
2
0
0
1
0
1
2
0
1
2
1
2
1
4
1
1
2
2
1
0
2
0
1
1
1
2
1
2
1
1
1
1
2
0
2
0
2
2
0
0
2
2
1
1
2
0
1
0
1
0
0
0
2
1
2
0
2
1
2
2
0
2
0
1
1
0
2
0
0
0
1
1
0
0
0
1
0
2
0
2
0
1
0
2
2
2
2
2
0
1
1
0
0
0
0
0
0
1
0
1
0
0
1
1
1
0
0
0
1
2
0
0
0
1
0
0
0
0
1
2
3
0
0
0
1
2
1
2
0
0
2
2
2
0
3
0
0
2
1
1
0
1
0
0
2
2
1
1
1
1
1
1
1
2
0
0
1
1
2
2
0
1
1
0
0
0
2
0
1
0
0
0
0
1
1
0
2
0
1
2
0
2
0
0
1
0
0
0
0
0
2
0
1
2
1
0
1
1
1
1
0
2
0
2
2
0
0
0
1
0
2
1
1
2
1
1
0
0
2
1
2
0
0
0
0
1
2
0
0
2
1
3
1
1
2
0
0
0
0
0
0
1
4
1
0
0
0
0
3
0
1
1
0
3
0
1
0
0
3
0
1
0
1
0
0
0
0
2
0
0
0
2
0
2
0
1
0
1
0
1
0
1
0
0
2
0
0
1
0
1
1
1
1
1
2
0
2
1
0
2
2
0
1
0
0
0
0
1
1
0
0
1
0
1
0
0
2
0
0
1
0
1
1
1
1
0
0
0
0
1
1
0
0
1
1
1
1
1
1
1
1
0
0
2
0
0
0
2
1
2
1
0
0
1
0
2
2
1
1
0
1
1
2
0
0
0
0
2
1
1
0
1
1
0
0
1
1
1
0
1
0
1
1
0
2
1
0
1
0
0
2
0
1
2
1
0
0
0
0
0
6
2
2
2
0
2
0
0
1
0
1
1
0
1
2
1
0
0
0
1
1
0
1
0
0
1
1
0
0
1
2
0
0
1
1
1
0
0
0
0
0
0
0
2
0
1
0
0
2
1
1
1
0
1
1
1
2
1
0
1
2
2
0
2
0
0
0
0
0
0
0
1
2
2
1
0
1
0
2
0
0
0
0
2
1
0
0
0
1
1
0
0
1
0
1
0
4
0
2
1
0
0
1
0
0
2
2
0
2
0
0
0
0
1
1
0
1
2
3
5
5
0
0
0
1
0
0
0
1
0
0
0
1
1
1
0
0
0
1
0
0
3
0
0
2
2
0
1
0
0
0
0
1
1
1
0
2
0
0
2
2
1
0
3
1
0
2
1
0
1
2
2
2
0
2
2
0
0
1
1
2
1
1
0
2
0
1
1
6
1
0
2
2
2
1
1
1
0
2
0
0
1
1
1
0
2
1
2
0
2
0
3
0
1
0
1
0
2
1
0
2
2
0
1
0
0
1
2
0
2
3
0
0
0
1
1
2
2
0
2
1
1
1
0
1
1
0
3
1
0
0
0
1
2
0
0
1
0
1
0
0
1
1
0
0
1
0
2
0
0
0
1
1
0
0
1
0
2
2
1
1
0
2
0
0
0
1
0
1
0
0
1
0
1
0
1
0
0
0
1
1
2
0
3
2
2
1
1
0
2
0
1
3
0
2
1
2
1
1
1
2
1
0
0
0
1
1
0
1
0
0
0
1
2
1
2
2
0
1
1
1
0
0
0
2
2
0
0
2
2
1
1
1
2
1
0
2
2
1
0
2
0
0
0
2
0
1
1
1
1
0
0
1
0
2
1
1
1
0
0
1
2
1
0
2
0
0
0
0
2
0
1
0
0
1
1
1
0
0
0
1
0
2
2
1
0
0
1
0
2
2
2
0
2
1
0
1
1
1
2
0
0
1
2
1
0
0
2
0
0
0
0
0
0
1
2
1
0
2
3
0
2
1
0
1
0
0
0
2
1
2
2
0
1
0
2
0
0
1
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
1
1
0
1
1
0
1
1
1
1
0
0
0
0
0
0
2
1
2
1
0
0
1
2
1
0
1
0
0
1
0
1
1
1
1
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
2
0
1
0
1
0
0
0
0
0
1
1
0
3
1
0
0
0
0
1
0
1
0
4
2
1
1
0
0
1
3
5
1
1
1
2
1
1
0
1
0
0
0
2
0
2
0
0
1
0
2
0
0
1
1
0
1
0
1
0
2
0
1
1
0
0
2
0
3
2
1
0
1
3
0
0
0
0
1
2
0
0
2
0
2
1
2
0
0
2
2
0
0
2
0
2
0
3
0
0
1
1
1
1
0
0
0
1
2
5
1
2
0
2
1
2
0
0
0
1
0
1
2
1
0
1
2
1
0
1
1
0
0
2
0
1
1
0
1
1
2
1
0
1
0
2
2
1
2
0
2
0
0
1
1
1
1
0
2
2
4
1
1
0
1
1
1
2
2
1
0
1
0
0
0
1
0
0
0
3
1
0
1
2
1
0
1
2
2
1
1
0
0
0
2
2
0
1
0
1
1
0
1
0
0
2
1
1
1
2
0
0
0
2
1
1
1
1
0
0
2
0
1
0
0
1
2
0
0
2
0
1
1
0
2
0
0
0
0
1
0
0
0
1
0
0
1
1
1
0
0
1
2
2
0
1
0
2
2
0
2
1
2
1
0
0
0
2
2
0
0
0
1
0
0
0
0
0
1
1
1
2
3
2
2
0
2
1
2
1
1
1
0
3
0
0
0
1
1
1
1
1
0
0
2
0
1
2
2
1
0
0
0
0
2
0
0
0
1
0
2
0
1
2
0
1
0
1
1
0
1
3
0
2
1
1
2
1
0
0
2
1
0
0
2
0
0
0
1
1
0
0
0
1
0
1
0
1
0
1
0
0
0
2
0
1
3
0
2
0
0
2
2
1
1
0
3
2
1
0
1
0
1
0
0
0
0
0
1
0
2
1
1
0
0
2
2
1
0
2
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
1
0
1
1
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
1
0
0
2
0
0
1
0
2
2
1
0
0
0
2
0
1
0
2
0
1
0
2
2
1
2
1
0
2
2
0
2
1
1
2
0
1
0
1
0
0
0
0
0
2
0
0
1
0
1
1
0
0
1
0
0
0
0
2
1
1
0
1
1
4
0
0
0
0
1
1
2
1
2
1
1
1
2
2
1
0
0
0
0
0
0
1
1
0
2
2
2
0
1
0
4
1
0
2
1
0
0
2
1
0
0
1
2
1
1
1
2
2
2
1
2
1
0
1
0
0
0
2
1
2
2
0
2
2
0
1
1
0
1
2
0
1
1
3
0
2
1
1
1
0
1
0
0
1
0
1
1
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
2
0
0
1
1
0
2
0
1
1
0
2
2
0
1
0
0
2
1
0
0
0
0
3
0
1
2
0
0
1
1
0
2
0
1
1
1
1
1
0
0
1
2
1
0
0
0
0
1
2
2
0
1
1
0
0
1
1
1
0
2
0
0
2
0
1
0
0
1
0
7
0
1
2
0
2
1
1
2
0
1
0
0
0
2
0
2
2
0
0
0
1
2
0
2
0
0
2
0
1
0
2
1
2
2
1
0
1
2
2
0
2
1
2
0
2
1
2
0
0
2
1
2
1
2
0
3
1
2
0
1
1
0
0
1
1
1
1
1
0
1
1
0
2
0
2
1
1
0
1
1
1
2
2
0
2
2
0
1
1
1
1
0
2
1
1
1
0
0
1
0
0
1
2
0
0
2
0
0
0
2
0
2
0
2
0
0
2
1
0
0
0
1
1
1
1
1
2
1
1
1
2
0
1
1
1
1
0
0
1
1
2
0
0
0
1
2
1
2
0
0
0
0
0
1
0
0
0
2
0
2
0
1
1
2
1
0
1
1
0
2
2
1
0
1
0
1
1
0
0
0
1
0
0
1
0
0
1
2
0
1
2
0
1
2
1
0
0
0
1
1
0
0
1
0
2
2
2
1
2
2
3
0
1
0
0
1
2
0
0
1
0
0
1
2
2
2
1
0
2
0
0
0
0
0
2
1
0
2
1
1
0
0
0
1
1
0
2
1
0
1
2
1
1
0
2
2
1
0
1
2
0
1
2
1
0
0
0
1
0
0
1
1
0
1
0
0
0
0
3
0
2
1
0
0
0
1
0
0
0
1
0
0
1
0
2
0
2
0
2
1
1
1
0
1
0
1
1
3
2
0
0
1
2
1
1
0
0
0
1
0
1
3
1
1
0
0
1
0
1
2
1
2
1
0
1
2
0
2
2
0
1
0
0
2
0
2
0
1
1
2
0
1
1
0
0
0
1
0
2
2
1
1
0
1
1
0
2
0
0
2
0
3
0
3
0
0
0
2
1
0
1
1
0
0
0
1
2
1
0
2
0
2
2
0
1
1
0
0
2
1
0
2
0
5
0
0
1
1
0
0
0
0
1
0
0
1
0
0
2
0
1
2
1
0
0
1
0
2
1
0
1
0
0
2
0
0
1
1
1
1
2
0
0
0
1
2
0
0
0
0
2
0
0
2
0
0
0
0
2
2
2
0
1
2
0
1
0
1
2
0
0
0
2
2
0
2
2
0
2
1
1
1
2
1
2
0
0
0
0
0
1
0
1
1
1
1
1
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
1
2
3
0
0
0
0
0
2
0
0
3
1
0
0
0
1
2
0
0
0
2
0
2
1
2
1
1
1
2
2
2
0
0
1
1
0
2
1
1
0
1
2
0
0
0
0
1
1
0
1
1
0
2
1
1
1
1
2
1
1
0
1
3
1
0
0
0
0
0
1
0
1
1
0
0
1
1
0
0
0
0
0
2
0
0
0
3
2
0
0
1
0
1
0
1
0
0
1
0
1
1
0
0
0
1
1
0
2
2
1
0
0
0
2
2
1
0
1
1
0
0
1
2
1
0
2
2
2
0
1
1
0
0
1
1
2
1
1
0
1
0
0
0
5
2
0
0
2
0
0
2
2
1
2
1
2
0
0
0
2
0
2
2
0
1
0
1
2
0
0
0
1
3
0
1
0
0
1
0
2
1
0
1
0
1
1
1
0
0
1
1
0
0
0
1
1
2
0
0
3
0
0
0
3
1
0
0
0
1
0
2
0
1
0
2
2
1
2
0
0
0
0
0
2
0
1
1
2
1
1
2
0
0
2
0
1
1
0
1
0
1
0
1
1
0
1
0
0
1
2
2
1
0
0
0
0
0
2
1
0
0
1
3
0
3
0
1
1
2
0
0
1
1
2
0
1
1
0
3
2
1
1
1
0
1
0
0
1
0
0
2
2
0
0
1
2
0
0
1
0
0
1
0
2
1
0
2
0
0
1
0
1
0
1
0
1
0
2
2
1
2
0
0
0
2
1
1
2
1
1
0
1
1
0
0
1
1
0
2
2
2
0
1
1
1
2
1
1
0
1
0
1
2
0
1
2
0
1
2
2
2
1
0
2
2
1
0
0
1
2
2
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
2
2
0
2
2
0
1
0
0
0
2
0
2
1
2
0
0
1
0
1
0
1
2
0
1
0
0
0
2
1
1
0
1
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
2
0
1
0
1
0
2
1
1
0
0
1
1
1
0
1
1
0
0
1
0
2
0
1
1
2
1
1
0
0
0
1
0
0
2
1
1
1
2
0
1
0
1
1
1
2
2
0
2
2
1
0
0
0
1
1
1
1
0
1
0
2
0
1
1
1
0
0
1
1
1
0
1
0
1
0
0
1
1
2
1
1
0
1
1
2
2
2
0
0
1
1
0
2
1
0
3
1
1
3
1
0
1
1
1
0
0
2
4
2
1
1
2
0
1
2
0
0
2
0
0
2
0
0
1
2
2
0
0
0
0
2
2
2
1
0
1
0
1
0
0
1
2
1
0
2
3
0
1
1
1
0
0
0
1
0
0
0
2
1
0
2
1
0
1
1
0
2
1
2
2
1
0
0
2
1
0
0
0
0
0
2
0
1
0
0
0
0
1
1
2
1
0
1
0
1
1
0
1
1
0
2
0
0
2
0
2
0
0
2
0
1
2
2
2
1
0
1
1
0
1
2
2
0
0
2
1
0
0
0
2
0
0
0
1
0
2
0
1
1
1
1
0
1
0
0
1
0
2
1
0
1
1
0
0
0
0
2
1
0
2
1
1
0
2
2
0
1
0
1
1
2
1
1
0
1
0
3
0
0
1
1
2
0
2
1
1
0
1
2
1
0
0
0
1
0
0
0
1
0
0
1
1
3
0
1
2
2
1
1
0
2
3
1
0
0
0
1
1
2
1
1
0
1
2
0
1
0
0
1
0
1
2
0
1
2
0
0
2
2
2
0
1
2
1
1
1
0
2
2
0
1
1
0
2
1
0
2
2
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
3
1
2
0
2
1
1
1
1
2
1
1
1
0
2
0
0
1
1
1
10
0
2
0
0
0
0
1
1
0
2
0
1
0
0
1
0
0
1
0
0
1
0
2
0
0
1
2
0
1
0
2
0
0
0
0
1
0
1
0
1
2
1
1
1
2
0
0
0
2
1
0
1
0
2
0
1
0
0
1
0
0
1
1
0
0
0
1
0
2
2
0
2
1
2
1
2
1
2
0
0
2
2
1
0
1
0
1
0
1
2
1
0
1
6
2
0
2
1
0
1
0
1
1
2
2
1
2
2
0
0
1
1
0
2
0
1
1
2
0
1
0
0
0
3
0
0
0
1
1
0
2
0
1
0
1
2
1
2
1
1
0
2
2
1
1
1
0
0
1
2
1
1
3
0
0
2
1
2
1
1
2
2
1
2
2
1
1
0
2
2
1
0
0
0
1
1
1
0
2
1
2
1
2
0
0
1
2
2
0
0
0
1
0
0
0
0
0
0
1
1
0
2
0
0
0
1
1
0
2
0
0
2
2
0
0
1
1
1
1
3
1
1
2
1
1
0
4
0
0
0
1
1
0
0
1
2
1
0
0
0
1
0
0
0
0
1
0
2
1
1
0
0
0
0
0
1
3
1
2
1
0
1
0
0
0
0
2
1
1
1
1
1
1
1
0
0
0
0
2
0
2
0
1
1
2
0
2
1
0
1
2
0
0
0
2
2
0
2
1
0
0
0
0
0
0
2
1
1
0
0
0
2
1
1
0
1
0
0
0
0
0
1
1
0
1
0
0
2
0
0
0
0
2
1
1
0
0
0
1
0
0
1
2
1
1
0
1
2
1
1
0
1
2
2
0
0
2
2
0
0
0
1
1
0
2
0
0
0
0
0
1
2
1
2
1
2
0
0
0
0
1
2
1
0
1
1
2
2
1
0
1
7
1
1
0
2
1
1
1
2
0
1
1
1
0
1
0
1
0
0
1
1
0
0
1
1
0
0
1
0
0
0
0
2
1
2
0
0
2
2
3
2
1
0
0
0
0
0
2
5
1
0
0
0
2
0
0
2
2
3
2
1
1
1
0
0
2
1
0
1
1
1
1
1
1
0
2
0
2
0
1
1
2
0
0
0
0
1
1
1
1
1
0
1
0
0
0
0
0
1
1
1
1
0
0
0
0
1
0
1
0
1
0
1
2
0
4
0
2
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
1
0
0
1
0
1
2
3
1
0
1
1
1
0
0
0
0
1
0
1
0
1
2
2
0
1
0
1
1
1
1
0
1
0
0
0
0
0
2
1
1
0
2
2
1
1
0
2
0
0
1
2
1
0
0
2
2
2
0
1
0
1
1
0
0
1
0
2
1
0
2
2
0
0
1
1
0
2
2
0
1
2
1
0
1
0
2
2
1
0
0
0
2
0
1
2
1
1
2
1
0
2
0
2
0
1
1
1
1
0
2
0
2
2
2
0
1
0
0
1
0
2
1
2
0
1
2
2
0
1
2
0
2
0
1
0
1
1
1
1
0
1
1
1
1
2
1
0
0
2
0
1
1
2
0
1
4
0
1
1
1
2
1
0
2
2
0
0
0
0
1
0
2
1
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
1
0
2
0
0
0
2
0
1
2
0
0
0
2
1
0
0
0
0
1
0
1
1
1
2
0
1
3
2
0
2
0
0
2
3
3
0
0
0
1
1
1
2
0
0
1
0
0
0
2
1
0
0
2
0
1
2
2
0
1
0
0
2
2
0
0
2
2
0
2
1
2
0
0
0
2
0
0
0
2
0
2
1
0
0
1
1
1
1
1
2
1
0
0
1
0
1
0
1
0
2
1
1
2
1
10
1
0
0
2
0
1
0
0
2
0
2
1
1
0
1
0
0
2
1
0
0
0
1
0
2
1
1
2
0
2
2
1
1
2
2
1
1
2
1
0
0
2
1
1
1
2
0
2
0
1
2
1
0
0
2
1
0
0
1
1
2
1
0
0
1
1
0
1
0
2
3
2
0
0
0
1
2
2
0
1
2
1
0
0
0
0
1
2
0
1
0
1
0
0
2
2
0
1
2
2
2
1
1
0
2
1
0
1
0
1
1
1
0
1
0
0
0
0
0
2
0
0
2
0
1
0
1
1
2
0
1
0
0
1
0
1
2
0
2
2
1
0
1
0
0
0
1
2
2
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
1
1
0
1
1
2
1
0
1
2
0
2
1
1
0
0
1
2
2
2
0
1
1
1
1
0
0
0
0
0
0
1
2
1
0
1
0
1
0
2
0
1
0
0
1
1
2
0
0
1
0
2
2
2
0
2
0
1
1
0
1
1
0
0
0
2
0
0
1
1
0
0
2
1
1
0
2
1
0
1
0
2
0
1
1
0
2
0
0
0
1
0
0
1
1
2
1
2
1
2
2
2
1
0
2
2
0
1
0
0
1
2
1
0
1
0
0
1
2
0
0
1
1
2
2
2
1
0
0
0
1
0
0
1
1
3
0
0
0
1
0
0
2
0
1
0
1
0
1
1
1
2
4
0
0
2
1
1
1
2
0
0
1
2
0
0
0
0
0
1
0
0
2
0
0
0
0
3
0
1
1
0
2
0
0
0
1
0
1
1
0
0
0
1
2
0
1
1
1
0
1
1
0
1
0
0
1
0
0
2
0
1
0
2
0
2
1
0
2
2
0
0
0
2
0
0
1
3
0
1
2
0
1
1
0
0
1
0
0
1
1
1
2
1
1
2
2
0
0
1
0
1
0
0
2
1
0
1
1
0
0
2
1
0
1
0
1
2
1
0
0
1
2
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
1
1
1
0
1
0
2
1
1
0
2
2
1
0
0
0
0
0
2
1
1
2
1
1
2
1
1
2
1
2
1
0
0
0
1
1
0
0
0
0
1
0
1
0
0
1
2
0
2
0
0
0
0
0
2
2
0
0
1
0
0
0
2
0
0
0
1
1
1
0
1
0
1
2
1
1
0
0
2
2
2
1
1
0
0
1
0
0
2
1
1
0
4
0
0
0
1
0
2
0
2
1
2
1
0
0
0
2
1
1
0
0
0
0
2
1
1
2
1
1
0
0
1
0
0
1
0
0
2
0
1
1
0
0
0
0
1
2
0
0
1
3
1
2
0
0
1
0
0
0
1
1
1
1
1
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
1
2
1
1
2
1
0
2
2
1
1
0
0
0
1
0
0
1
0
2
0
1
2
1
0
0
0
0
1
0
1
1
1
1
1
2
0
0
0
2
0
0
2
0
0
2
0
2
1
1
1
1
2
0
2
0
2
2
1
0
1
0
0
2
1
1
2
0
1
0
1
0
0
1
1
1
0
0
1
1
1
2
2
2
0
0
1
1
0
4
2
0
1
0
0
0
1
0
2
0
1
1
2
1
3
0
0
0
2
0
0
0
1
0
1
0
0
2
0
0
1
0
2
0
0
0
0
1
2
0
2
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
2
0
2
1
0
0
0
1
0
3
0
0
2
1
2
1
0
3
1
1
1
0
1
2
1
0
0
1
0
2
0
1
1
0
0
0
1
1
0
0
2
0
1
0
1
1
0
2
1
0
1
1
0
0
2
0
1
3
1
0
0
1
1
0
2
0
0
2
1
2
1
1
1
0
1
1
2
0
0
1
0
0
0
0
0
0
1
1
2
0
0
1
1
0
0
0
0
2
2
1
0
1
2
0
0
0
1
1
1
1
1
1
1
2
0
1
0
1
0
2
0
0
1
0
0
0
0
1
4
1
2
3
0
2
1
2
0
2
0
2
0
1
2
1
0
1
1
0
0
2
2
1
0
0
0
2
2
2
2
0
1
1
2
2
1
0
2
0
0
0
0
1
0
0
3
2
0
1
1
1
0
1
2
0
2
2
3
1
2
2
0
0
0
1
0
2
1
0
2
1
1
2
1
1
0
0
0
0
0
0
2
2
0
2
0
1
0
1
0
2
1
1
0
1
0
0
1
0
0
1
0
0
1
0
0
1
2
0
0
0
1
1
0
0
1
0
2
2
2
2
1
1
2
0
2
0
2
0
1
1
1
0
1
1
0
1
0
1
1
2
0
0
1
0
0
0
0
0
0
4
1
0
2
0
1
2
0
1
0
0
1
0
0
0
0
1
0
0
0
2
0
1
0
1
0
0
1
0
0
2
0
0
1
0
0
1
0
0
2
2
1
2
1
0
1
0
1
0
0
1
0
0
0
0
0
0
2
1
0
1
0
0
0
0
2
1
0
1
1
0
0
1
0
2
1
1
0
2
1
1
0
0
0
1
2
1
2
0
1
0
0
1
0
0
0
0
2
2
2
2
0
1
1
2
0
0
2
3
2
0
1
0
1
1
0
0
0
0
2
2
0
1
0
1
1
1
3
0
1
0
1
1
0
1
1
2
1
0
0
0
0
2
0
0
2
0
2
1
0
0
1
0
2
0
0
0
0
1
0
0
0
1
1
1
1
3
2
0
2
1
1
2
2
1
0
0
0
0
0
0
1
0
0
1
2
0
1
0
2
1
1
1
0
0
0
2
0
0
1
3
0
0
0
0
0
1
1
0
2
8
0
2
2
2
1
0
0
0
1
0
2
1
2
0
0
0
2
1
0
2
0
2
1
0
0
1
1
2
1
1
1
0
0
0
0
0
0
1
0
1
0
0
1
1
1
0
1
1
1
1
0
2
2
0
1
0
0
0
1
0
0
1
1
0
1
0
2
2
1
0
1
2
3
0
0
2
1
0
1
0
1
2
2
0
1
0
2
0
0
2
0
0
0
0
1
1
1
1
1
0
1
1
0
1
1
0
0
1
3
2
2
2
1
3
0
0
1
0
0
2
2
0
0
1
8
0
3
0
0
0
1
0
0
1
1
0
0
2
1
2
1
2
0
2
2
0
0
0
1
1
0
2
0
0
0
1
1
1
0
1
1
2
1
1
0
0
0
0
1
1
1
0
0
1
0
1
1
2
2
2
0
1
2
0
1
1
0
2
3
0
0
0
1
1
1
2
1
0
1
1
1
2
1
2
0
1
0
1
0
1
1
2
0
2
2
0
0
1
0
2
0
1
0
2
1
0
2
0
1
0
2
1
0
1
2
2
0
2
1
2
0
2
1
0
0
2
0
0
2
0
0
1
0
2
0
2
0
2
0
0
0
0
0
0
0
2
0
2
0
2
0
0
1
1
0
0
0
0
0
1
1
0
0
2
0
1
2
2
0
0
1
2
1
1
2
1
1
1
0
2
3
1
1
0
2
2
2
0
0
1
2
1
0
1
1
0
1
1
0
2
2
1
1
2
0
2
0
2
1
0
1
0
0
0
1
2
0
1
2
4
2
1
1
1
2
0
0
2
0
1
1
0
0
1
1
0
0
2
1
0
0
1
2
0
0
1
0
1
0
1
1
1
0
0
2
0
2
0
2
2
0
4
1
0
1
0
1
2
0
3
1
2
2
0
0
3
0
0
1
1
0
1
0
1
0
0
2
3
1
1
2
0
0
1
0
1
0
0
0
1
1
0
0
2
1
0
2
0
1
1
2
0
1
0
2
1
1
2
2
2
2
1
1
1
0
0
2
1
0
1
0
0
1
0
0
0
1
0
1
1
0
0
1
2
2
1
1
1
2
1
0
0
1
0
1
0
0
0
1
2
1
1
0
1
1
1
0
1
1
2
0
2
0
0
0
1
2
0
0
0
1
2
2
1
2
0
1
0
0
0
1
1
1
2
1
1
2
2
0
0
1
2
0
0
0
0
1
0
2
1
0
1
1
0
1
0
1
1
1
0
1
3
0
0
3
1
1
0
0
1
1
2
0
0
2
1
1
2
0
0
1
0
0
0
0
2
2
1
1
0
1
0
2
3
6
0
0
1
1
1
2
2
1
1
0
2
1
2
0
0
1
0
0
2
1
1
1
0
0
0
1
2
0
0
2
1
1
2
1
1
0
2
0
0
2
2
0
0
1
1
0
1
0
0
1
0
0
2
0
0
1
1
1
2
2
0
1
0
1
1
1
0
1
1
1
1
2
0
1
2
1
0
2
2
0
2
1
0
1
0
0
1
2
2
2
1
1
0
0
1
2
2
0
1
2
1
2
2
1
0
2
1
0
1
2
1
0
1
2
0
2
1
2
0
1
0
1
2
0
2
1
0
0
0
2
2
1
0
1
1
0
1
1
0
0
0
0
1
0
0
0
1
0
0
1
1
1
2
0
2
0
0
0
1
0
1
2
2
2
1
1
0
0
1
3
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
5
2
0
0
2
2
0
0
0
2
0
0
1
2
0
0
1
2
2
0
1
1
0
2
2
1
0
2
0
0
0
1
1
1
1
0
1
1
0
1
1
1
0
5
0
1
1
1
1
0
1
2
2
0
1
0
0
3
2
2
1
0
1
1
0
0
3
1
5
4
0
2
1
0
1
1
1
0
2
0
0
2
2
1
0
0
0
1
2
0
0
2
1
1
2
2
1
0
2
0
2
1
0
0
0
1
0
0
2
0
0
1
1
0
1
0
0
2
2
1
0
0
1
1
2
2
1
2
2
0
1
0
0
0
2
1
2
1
0
0
1
0
1
0
0
1
2
0
3
1
0
0
1
0
0
0
2
1
0
1
1
0
1
0
1
1
2
0
2
0
1
0
2
0
0
2
1
0
2
0
1
0
0
1
0
1
0
0
1
1
1
1
0
1
2
1
1
0
0
1
0
2
1
0
1
0
1
2
2
0
2
1
2
0
1
2
1
0
1
1
0
0
4
1
0
1
2
0
0
0
0
1
0
0
1
0
0
0
1
0
1
2
1
0
0
0
0
1
0
1
0
1
0
1
2
1
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
1
0
1
1
0
0
2
0
2
1
0
1
2
1
0
0
0
1
0
2
1
0
1
0
0
1
2
1
0
2
1
1
0
1
2
2
1
1
1
2
0
0
0
2
0
2
2
0
0
1
0
5
1
0
0
1
1
0
0
1
1
1
0
0
2
2
1
2
2
0
1
2
1
1
0
1
0
0
0
1
0
1
0
0
1
1
0
0
0
2
0
1
1
2
4
0
0
0
0
0
0
1
0
1
1
1
2
0
1
1
0
1
1
0
1
0
2
0
0
1
0
1
2
2
2
2
0
0
0
2
0
0
0
1
2
0
0
1
0
0
0
1
0
0
1
1
0
1
0
3
0
1
2
0
0
0
1
0
1
1
0
0
0
0
0
0
2
1
0
0
0
2
1
0
0
2
2
0
0
0
0
1
0
0
0
0
1
1
1
1
1
0
1
0
0
0
1
1
1
1
0
0
2
0
2
0
1
0
4
1
2
2
0
0
2
0
0
0
2
2
1
2
2
0
2
1
2
0
0
2
0
0
2
1
0
0
0
0
2
1
1
1
0
1
0
1
2
1
0
0
1
1
2
2
0
1
1
2
2
0
1
0
0
0
1
1
0
1
2
1
3
1
2
0
0
2
0
0
1
1
1
0
1
0
2
1
0
0
0
2
0
1
0
3
0
2
2
1
1
2
0
1
1
0
2
4
2
0
1
1
1
0
1
1
0
2
2
2
0
0
1
0
2
1
2
0
0
0
2
0
0
0
3
1
0
0
1
2
2
0
1
0
0
0
2
0
0
0
2
0
1
0
0
1
1
1
1
1
1
0
1
2
1
2
1
0
1
2
0
1
0
0
1
0
1
2
2
1
0
2
1
0
1
0
0
0
2
0
0
1
0
0
1
1
0
0
0
0
2
0
0
1
0
1
0
0
0
1
3
0
3
2
0
1
0
0
0
0
0
1
0
0
3
0
2
0
2
2
0
0
1
0
0
1
0
1
1
0
2
0
2
0
1
1
0
1
2
0
0
1
1
0
0
1
0
0
0
1
0
1
2
0
0
0
1
1
2
1
1
0
0
2
0
0
0
0
2
1
2
0
0
0
2
0
1
2
2
0
0
0
0
0
0
0
1
0
1
0
1
1
1
0
2
0
0
1
0
2
0
1
0
2
2
0
1
2
0
2
1
1
0
2
0
2
2
0
0
3
0
0
2
0
0
1
3
1
0
2
1
1
2
0
2
1
0
1
0
1
2
2
1
0
0
0
2
0
1
1
0
0
0
1
2
2
0
2
2
1
1
2
0
0
2
2
1
2
2
0
1
1
0
2
0
0
2
0
0
2
1
1
2
0
0
1
2
2
2
0
3
1
0
0
2
2
0
0
0
1
0
2
4
0
0
4
0
1
1
1
0
1
2
1
2
0
2
0
0
0
0
0
0
0
2
1
2
0
0
0
0
2
1
0
0
1
2
1
0
0
0
1
2
1
1
0
2
0
0
2
0
2
2
0
2
0
1
0
0
1
1
0
0
0
2
1
1
0
2
2
1
1
1
0
0
0
0
0
0
1
1
0
0
2
0
2
2
0
0
0
0
0
2
0
1
1
0
0
2
1
1
1
0
2
1
0
0
5
2
1
0
2
1
1
1
1
1
1
0
1
2
0
0
1
1
2
0
0
2
0
0
0
1
0
0
0
2
2
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
2
2
2
2
0
1
2
0
0
2
2
1
0
1
2
1
2
0
0
2
1
2
0
1
2
0
1
0
2
1
1
1
0
0
0
0
0
0
2
0
1
0
0
1
0
1
0
1
2
1
0
1
0
1
1
2
0
0
2
1
0
0
1
1
1
0
0
0
1
1
0
1
0
1
0
0
2
0
1
2
0
0
2
0
0
0
1
1
1
0
0
0
1
2
2
0
1
2
0
2
0
0
1
0
1
1
1
0
1
2
3
1
2
2
1
0
0
0
1
0
1
0
0
1
1
0
0
0
1
0
0
2
0
0
0
2
1
0
0
0
1
3
2
2
1
0
0
0
1
1
0
0
1
0
0
0
2
1
1
3
1
1
0
2
0
2
0
0
1
2
0
0
0
0
0
1
0
0
0
1
1
1
2
0
0
0
2
0
1
2
1
0
0
1
2
1
1
1
0
0
0
0
3
1
1
1
0
0
0
0
2
2
2
0
1
1
3
2
0
1
0
1
0
1
1
1
2
0
1
2
2
2
0
0
0
2
0
2
0
1
0
0
1
2
0
2
0
0
0
2
1
1
0
0
1
2
2
0
0
0
0
0
1
1
1
1
1
2
0
1
2
1
0
0
0
0
2
2
1
0
1
0
1
0
1
0
1
0
2
0
2
0
1
0
1
1
2
0
2
1
2
3
1
0
2
0
2
0
0
0
0
1
2
1
2
1
1
2
1
0
1
1
0
1
0
0
1
0
1
1
0
2
1
2
0
1
0
0
1
1
0
2
0
2
2
2
2
2
0
2
0
1
0
1
0
0
0
0
1
0
0
1
0
1
1
0
1
0
0
1
0
0
1
2
1
1
1
1
1
0
1
0
0
0
1
2
2
1
0
1
0
0
1
0
0
0
0
2
5
0
1
0
0
1
0
1
1
2
2
0
1
1
0
0
2
1
1
0
0
1
2
0
3
0
0
1
0
1
0
0
0
0
1
1
0
0
2
0
2
2
1
0
0
1
2
0
0
2
2
1
0
1
0
1
2
2
1
2
2
0
1
0
0
0
4
1
1
0
0
0
3
0
0
2
1
1
0
2
1
1
0
0
2
0
0
0
1
0
2
1
0
0
1
1
0
2
0
1
2
1
1
1
1
1
2
1
0
0
0
1
2
1
1
0
0
0
0
2
0
3
0
1
1
0
1
0
0
0
3
1
0
1
0
2
0
1
0
1
0
0
1
0
0
0
1
1
0
0
0
2
0
0
0
0
2
1
0
1
0
0
0
0
0
1
0
0
2
1
0
0
2
0
2
0
4
0
0
1
1
0
0
2
0
0
1
1
0
0
0
1
4
1
0
1
2
1
0
0
0
0
1
1
0
1
2
1
1
0
2
0
0
0
1
2
0
2
2
1
0
2
0
1
0
0
2
0
2
0
1
0
1
2
1
2
0
1
2
0
2
1
0
0
0
0
1
2
0
2
0
0
0
0
2
1
1
1
0
2
0
0
2
0
0
0
0
1
2
1
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
1
1
1
0
0
0
1
0
0
1
1
0
2
1
0
1
0
0
2
0
2
0
0
1
0
0
1
1
1
2
0
1
2
1
1
2
2
1
1
0
1
1
2
0
1
0
1
0
0
0
0
1
1
1
0
0
1
1
1
2
0
2
1
1
3
0
3
0
0
1
0
1
0
2
0
2
0
0
1
1
1
1
0
0
0
0
1
3
0
1
0
1
0
0
0
1
2
2
2
2
0
0
1
2
2
2
2
0
1
2
0
0
2
2
0
0
1
0
0
0
2
0
0
0
0
0
2
2
1
1
2
0
0
1
1
1
0
2
2
2
1
0
0
2
0
0
0
1
0
0
1
3
0
0
0
1
2
1
3
1
3
1
1
0
0
1
0
0
2
1
0
0
5
2
0
2
2
1
0
1
0
1
1
1
1
0
1
1
1
0
3
0
0
3
2
0
2
1
1
0
1
0
2
1
0
0
0
2
2
0
1
1
0
1
1
1
2
1
1
2
1
0
2
0
1
1
1
0
0
2
0
2
2
0
0
0
0
0
0
0
2
0
1
0
2
0
2
2
0
1
0
1
0
0
0
0
2
0
1
0
2
0
2
0
2
0
0
0
3
1
1
1
0
0
2
0
1
1
1
1
0
2
1
0
1
1
1
2
0
3
0
1
0
0
1
1
0
0
1
2
1
2
1
0
0
1
1
1
0
2
0
4
0
0
2
1
0
0
2
0
1
2
1
0
2
0
0
1
1
1
2
0
1
2
1
0
0
0
1
1
1
3
0
0
3
0
0
0
2
2
0
2
1
1
1
0
0
0
0
2
1
0
0
2
1
1
2
1
1
1
1
0
0
0
2
1
1
1
1
1
2
0
0
0
1
0
0
0
0
1
2
0
0
1
1
0
0
0
0
1
0
1
0
2
1
1
1
2
1
2
0
0
1
0
2
0
2
1
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
2
1
2
2
1
1
0
0
0
2
2
0
0
0
1
0
1
2
0
0
2
0
4
0
0
0
0
0
2
2
0
0
0
1
1
0
0
0
0
0
0
1
1
2
0
1
0
1
1
0
0
0
1
1
3
0
1
0
2
2
0
0
0
1
1
0
1
1
0
0
1
2
2
2
2
0
1
1
1
1
0
1
1
0
1
1
0
1
0
1
0
0
2
0
0
4
2
2
3
2
1
0
2
1
1
2
1
2
1
2
1
0
0
0
0
0
2
1
1
1
1
1
2
1
1
0
2
0
2
0
0
1
0
0
4
2
2
2
0
1
2
1
1
1
1
0
0
1
2
0
0
3
2
0
1
1
2
0
2
0
0
1
0
1
1
0
0
1
1
2
0
1
2
0
1
1
0
0
0
1
0
0
1
1
0
0
0
0
0
2
3
0
0
2
0
1
0
0
0
0
2
2
2
0
0
1
0
2
0
0
0
0
1
2
1
1
1
0
1
1
0
2
1
1
3
1
4
1
0
2
1
1
2
1
0
0
0
1
1
0
2
0
2
1
0
1
0
1
1
2
0
1
0
1
1
0
0
1
0
0
0
2
3
2
0
1
1
1
0
0
1
1
0
0
0
0
0
0
2
1
0
2
0
0
1
1
1
2
1
1
0
1
2
1
1
1
1
1
1
1
0
2
1
1
0
1
0
0
0
2
1
2
2
1
0
2
0
2
7
0
2
1
1
0
0
0
0
1
0
2
0
2
1
1
3
2
3
0
2
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
1
0
1
1
1
0
1
1
1
0
0
1
3
0
2
1
0
0
2
2
1
0
1
1
1
1
1
2
0
2
2
1
1
1
1
0
0
0
2
2
0
2
2
1
0
1
0
0
0
0
2
0
2
2
1
0
1
0
1
1
2
1
0
2
0
1
1
1
0
1
1
1
2
0
1
1
0
1
0
0
1
0
3
0
1
1
0
0
0
1
0
2
0
1
0
0
1
0
2
0
2
0
2
1
0
1
0
0
0
1
0
2
0
1
0
0
1
1
0
0
1
0
1
0
2
1
0
2
1
1
0
2
0
0
0
0
0
1
0
1
2
2
1
2
3
2
2
1
0
2
0
0
0
1
0
0
2
0
1
0
2
2
1
1
1
2
0
1
2
1
0
0
0
0
0
0
0
2
0
1
1
0
1
1
0
1
0
2
2
1
1
0
1
0
0
2
0
0
2
2
0
0
0
2
0
1
0
3
1
0
1
0
1
2
0
1
1
2
2
2
1
2
0
2
1
0
0
2
0
0
0
0
2
1
1
2
0
1
0
0
0
0
0
1
2
0
2
2
1
1
2
2
0
0
1
2
1
0
1
0
2
0
0
1
0
0
0
0
0
2
1
2
0
0
2
0
0
2
0
0
1
0
2
2
1
1
0
0
0
1
2
1
2
0
1
1
0
2
1
1
0
0
0
2
0
2
2
2
0
1
2
1
1
0
1
0
2
1
0
0
0
0
0
1
0
0
2
2
1
0
0
0
1
2
2
2
2
1
1
0
0
1
1
2
1
1
2
0
1
0
1
0
1
1
0
0
0
0
1
0
1
0
0
0
2
0
1
2
0
1
0
2
0
0
0
2
0
2
0
0
2
0
1
1
0
5
0
1
0
0
1
1
1
1
1
0
1
0
1
1
0
2
1
2
0
0
1
1
1
0
1
1
0
0
1
0
0
2
0
0
2
2
2
1
0
0
0
2
1
2
1
0
1
0
0
0
1
0
2
0
1
2
0
0
0
1
2
1
0
2
1
1
0
0
2
2
1
1
1
1
1
0
0
0
0
1
1
0
0
1
1
1
1
0
0
0
1
0
0
1
0
1
0
0
0
1
0
1
0
0
1
1
1
2
0
2
0
2
1
2
2
2
0
2
1
0
0
0
0
0
0
1
0
0
1
1
1
2
0
1
0
0
2
0
0
0
1
1
0
0
1
2
0
1
0
2
2
0
0
2
0
1
1
1
0
2
0
0
1
1
1
0
2
0
0
0
1
0
0
2
0
1
0
0
1
2
1
3
2
0
0
2
0
1
2
2
1
1
0
1
1
0
0
0
2
0
2
0
2
2
2
0
0
1
2
2
1
1
1
0
0
0
1
0
1
2
0
0
2
1
1
1
1
0
1
1
0
0
0
2
0
0
1
3
0
0
8
1
1
1
1
0
0
1
1
1
2
0
0
1
1
2
0
0
0
2
0
1
1
2
0
2
1
1
0
0
0
2
1
1
1
0
1
0
0
1
0
2
2
2
0
2
1
0
1
0
0
0
1
2
2
0
1
1
0
0
0
1
0
1
1
0
1
1
1
1
1
0
1
2
0
1
0
0
1
1
1
1
0
1
0
1
1
1
2
1
2
0
1
0
0
0
1
0
2
0
1
2
0
1
1
2
1
0
0
0
2
0
2
0
0
0
1
0
1
0
2
1
0
2
0
1
1
2
1
0
0
0
1
0
2
0
2
2
1
1
0
2
2
1
1
0
0
2
1
2
2
0
1
0
0
2
0
0
2
0
0
0
0
0
2
2
2
1
2
0
0
4
1
0
1
1
0
0
1
0
0
0
1
1
2
2
1
0
1
0
1
0
2
2
1
1
0
0
1
0
1
1
0
1
1
0
1
0
0
1
2
0
0
2
0
0
2
1
0
0
0
1
0
1
2
1
1
1
0
0
1
0
0
0
0
0
0
1
0
1
0
2
2
1
0
0
0
0
2
1
1
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
1
0
1
2
0
0
0
0
0
1
1
0
1
0
1
1
0
1
1
0
0
1
0
0
4
0
1
0
0
1
1
0
2
1
1
1
0
2
3
0
1
2
1
0
0
2
0
0
0
1
1
0
1
3
1
0
0
2
1
2
1
2
1
0
1
2
0
0
1
0
0
2
1
2
0
2
0
0
0
0
2
0
1
1
2
1
0
1
1
1
0
2
2
1
1
0
1
1
0
0
1
1
1
0
1
2
2
1
1
0
0
1
0
0
1
0
0
0
1
4
0
0
0
1
0
2
0
0
0
2
0
0
0
0
2
0
1
0
2
1
1
0
1
0
0
2
1
1
1
0
2
1
2
1
0
0
0
0
0
1
0
2
0
0
0
2
0
0
2
0
2
0
1
0
0
0
1
1
0
0
2
1
1
2
0
0
1
2
0
0
1
0
1
1
0
0
2
0
1
1
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
1
1
0
0
0
0
2
0
1
0
0
2
0
0
1
1
1
0
0
1
0
2
0
1
2
3
0
0
0
1
7
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
1
1
0
0
1
0
1
0
1
1
1
0
0
2
1
0
0
0
0
1
0
1
1
2
0
1
2
0
2
0
1
0
1
0
1
1
2
0
0
0
1
1
1
0
0
0
2
1
2
1
2
0
1
1
1
1
1
1
1
0
0
1
0
2
0
1
0
0
1
1
1
0
1
0
1
1
2
1
1
0
2
2
1
1
2
0
0
2
1
1
1
1
0
2
1
1
0
2
0
0
0
0
0
2
1
1
0
0
0
1
1
0
0
1
1
0
1
2
0
0
1
0
1
1
0
1
0
3
3
0
1
0
2
0
1
0
0
2
0
2
0
0
0
0
1
0
1
0
1
0
0
0
2
1
1
2
1
0
0
0
2
1
1
1
0
0
1
2
0
0
1
0
1
1
3
1
0
1
1
0
2
1
2
2
2
1
0
2
0
0
0
1
0
1
0
2
0
2
2
1
1
2
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
1
0
0
2
0
1
1
0
2
0
0
0
2
1
1
2
0
1
0
2
0
2
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
3
2
0
0
0
1
2
0
2
0
0
0
1
1
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
1
1
0
2
1
0
0
0
0
0
0
1
1
0
0
0
0
2
0
1
0
1
0
0
0
0
2
2
0
2
0
0
2
2
1
1
0
2
1
2
0
1
1
2
1
1
0
0
0
2
0
2
1
1
0
2
1
0
0
2
0
0
2
2
2
1
0
0
0
2
0
0
0
1
0
0
2
1
0
4
0
0
0
1
2
0
1
0
1
1
1
1
1
0
1
0
0
1
1
0
0
0
1
2
1
1
2
0
1
2
0
1
1
7
1
0
0
2
2
1
1
0
0
1
2
0
0
2
0
1
0
1
1
2
1
2
0
0
1
2
1
0
0
2
1
1
2
1
2
1
2
2
1
1
1
3
0
0
0
2
2
0
0
1
0
1
0
1
2
4
0
0
2
0
0
0
2
0
2
0
0
1
1
1
2
2
2
1
0
1
2
0
2
0
0
2
1
0
1
0
1
0
1
1
2
1
1
1
2
2
0
0
1
1
0
2
0
1
0
1
2
0
0
0
0
0
0
1
2
1
1
0
2
2
2
2
1
0
0
1
0
1
4
0
1
0
0
0
1
0
1
2
0
1
2
2
0
1
0
2
0
1
2
0
0
2
0
1
0
0
0
1
0
1
0
1
2
1
1
0
2
1
1
0
0
1
2
0
0
2
0
1
1
1
1
0
0
1
0
0
2
2
1
0
0
1
1
1
1
1
0
2
1
0
0
0
0
1
0
1
0
0
2
1
2
0
0
0
1
0
2
0
1
2
0
0
2
0
0
1
0
0
0
1
2
2
0
2
1
0
2
0
1
0
1
2
0
0
1
0
0
0
2
2
1
1
1
0
2
1
0
0
1
0
2
0
0
0
1
1
2
0
0
0
1
0
3
1
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
1
1
0
0
0
0
0
2
2
2
1
0
0
1
2
0
0
1
0
0
2
1
1
0
0
0
0
1
1
2
1
2
1
0
0
0
0
0
0
0
0
1
1
1
0
0
2
0
0
0
0
0
0
1
0
1
1
0
0
1
1
1
1
0
3
1
0
1
0
2
2
0
0
1
1
0
2
2
0
3
1
0
0
1
2
1
2
0
1
0
1
1
0
2
0
0
0
3
0
2
1
0
1
0
1
0
0
0
2
2
0
1
1
2
1
2
0
1
1
0
0
0
1
4
2
2
0
0
0
0
1
0
0
0
1
0
2
1
2
1
2
0
1
0
0
0
1
1
1
0
2
0
3
1
1
0
1
0
1
1
1
1
0
0
0
1
0
1
0
1
0
0
2
2
1
1
2
0
1
1
0
0
2
0
0
1
0
0
0
0
1
0
1
1
0
0
1
1
2
0
1
0
2
1
2
1
1
2
1
2
1
0
0
2
1
0
2
1
0
2
1
0
0
3
0
2
0
1
1
1
0
1
1
0
2
1
0
0
0
0
1
2
0
1
1
0
0
1
1
1
2
1
0
2
3
1
0
1
1
0
0
0
0
0
2
2
1
0
1
0
0
1
1
2
2
2
0
1
0
1
2
0
1
0
2
0
0
1
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
2
0
1
0
1
1
2
0
0
0
1
2
2
2
1
1
0
2
0
1
1
2
1
1
0
0
0
2
1
2
1
0
1
0
2
1
0
1
0
0
1
1
2
2
1
0
0
2
1
1
1
0
1
0
0
0
0
0
0
1
0
2
3
0
0
2
2
0
0
0
2
1
1
2
1
1
0
1
2
0
0
3
0
0
0
2
1
1
2
0
0
2
0
0
2
0
0
2
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
3
1
1
2
0
2
1
1
0
1
0
0
1
0
2
1
0
0
0
0
1
3
1
0
1
1
0
0
0
1
1
0
0
0
1
1
1
2
2
1
1
0
1
0
2
1
0
2
2
2
2
1
0
1
1
1
0
0
0
0
0
0
0
3
1
0
1
0
1
0
1
1
0
1
1
0
3
0
1
0
2
2
2
0
0
0
1
0
0
0
1
1
0
1
2
1
0
0
2
1
1
0
1
0
1
1
0
1
1
1
1
2
0
0
1
0
0
0
1
2
2
0
0
2
0
1
0
1
0
1
2
0
0
0
0
2
1
0
1
0
1
0
0
0
2
2
0
0
1
0
1
2
1
2
0
2
1
0
0
2
1
1
0
2
0
0
2
0
0
0
0
1
0
2
0
0
0
0
1
0
0
1
0
1
2
0
2
1
1
1
0
1
0
1
0
0
2
2
0
0
1
1
0
1
0
0
0
2
1
0
1
0
1
2
0
1
1
2
1
2
0
2
0
1
1
2
1
0
1
0
1
0
0
1
1
2
1
0
1
0
0
1
0
0
2
0
1
1
1
0
0
0
1
3
1
0
0
1
1
0
0
1
1
1
0
2
2
0
1
0
0
1
2
0
2
1
0
1
0
2
0
1
0
1
0
1
0
1
1
2
0
0
2
0
0
0
0
0
0
1
0
1
2
0
0
2
0
0
0
2
0
1
0
1
1
1
1
0
1
1
0
0
0
0
1
1
0
2
0
0
1
0
1
2
2
2
1
1
0
1
2
0
1
0
0
1
1
0
0
2
1
2
2
2
2
0
0
0
0
1
1
0
2
1
0
2
0
0
0
1
0
0
1
1
0
0
2
1
1
0
1
1
0
1
2
1
1
1
0
0
2
1
0
1
2
1
1
0
1
0
0
0
7
0
0
1
0
1
0
3
2
1
0
2
0
1
1
2
1
1
0
1
1
1
1
1
2
0
1
2
2
1
1
2
0
1
2
2
1
1
0
0
0
0
1
1
0
1
2
1
0
0
2
0
0
1
2
1
0
1
0
0
1
1
1
0
0
1
1
0
1
1
1
1
0
2
0
1
1
2
0
0
2
2
1
2
2
0
0
1
0
1
1
1
0
1
2
0
1
1
2
2
2
0
0
1
1
1
2
0
2
1
1
1
1
1
0
1
0
0
2
2
2
1
0
0
0
2
2
0
2
2
1
2
0
0
1
0
0
2
1
0
0
1
0
0
0
0
1
0
1
2
1
0
0
0
2
0
0
1
1
0
2
1
2
1
2
0
0
0
0
1
0
3
0
0
1
0
1
1
0
0
2
0
1
2
2
0
0
0
1
2
0
0
0
2
1
0
0
0
1
1
1
2
1
0
1
0
1
1
0
0
0
0
0
2
0
1
2
1
0
0
6
2
0
0
0
0
0
2
0
0
0
0
0
1
2
2
2
0
1
1
1
0
0
1
0
0
2
1
0
0
0
0
0
1
0
0
1
1
0
1
1
0
1
0
1
0
2
0
2
1
1
1
0
2
1
0
1
1
0
0
1
2
0
0
1
2
2
2
2
2
0
0
1
1
1
0
0
0
0
0
2
2
1
1
0
0
1
0
2
0
1
1
2
2
0
2
1
1
0
2
0
1
0
4
1
2
1
2
0
0
1
0
2
0
0
2
2
2
0
1
0
2
0
5
0
1
1
2
1
1
0
0
0
2
2
0
0
2
1
0
1
1
2
2
1
0
0
2
1
1
1
1
2
1
0
0
0
0
0
1
1
0
1
0
1
1
0
0
2
0
2
0
2
0
0
2
0
1
2
0
1
2
1
0
0
2
0
1
0
0
1
1
3
1
0
1
2
1
0
1
0
0
0
1
2
0
0
0
1
0
2
2
0
0
1
0
1
2
4
0
2
0
0
0
1
1
1
0
0
0
2
1
0
1
0
2
2
2
1
0
1
2
2
1
1
0
0
2
0
1
1
1
0
1
0
1
1
2
0
0
1
0
0
0
1
1
1
0
0
2
0
0
1
0
1
1
2
1
2
0
1
2
0
0
0
0
2
1
2
1
1
0
2
0
0
1
1
0
0
1
2
1
1
2
0
1
2
1
1
0
1
1
0
1
1
0
1
0
0
1
0
1
2
0
1
1
0
0
1
0
2
0
1
0
0
0
0
2
1
1
0
1
0
0
0
2
0
2
2
0
2
0
0
1
0
1
2
0
1
0
1
0
1
1
0
1
2
2
0
2
1
0
1
2
2
0
2
0
0
1
2
1
1
2
0
2
1
2
1
0
1
0
2
0
2
0
0
0
0
1
0
0
2
1
1
0
1
1
0
1
0
1
0
1
0
1
2
1
1
2
1
1
0
2
1
0
1
1
0
0
0
0
0
3
2
1
1
1
2
0
1
0
1
0
0
0
2
0
0
2
1
0
1
2
0
0
1
1
2
2
0
0
0
0
0
2
0
0
1
0
1
2
1
2
4
0
0
0
0
0
3
0
0
1
1
2
0
2
0
2
1
0
1
0
1
0
1
0
1
0
1
1
2
0
1
2
0
1
0
1
1
1
0
2
0
1
2
0
1
2
1
1
0
1
1
0
0
0
1
0
0
2
1
1
2
1
0
0
0
1
0
1
0
1
1
2
0
1
0
0
1
2
0
0
1
0
0
2
0
0
2
0
0
1
0
1
0
1
0
1
0
2
1
0
1
0
0
0
2
0
2
0
1
1
1
1
1
0
0
0
0
0
0
1
0
0
2
0
1
0
2
0
1
0
0
1
0
0
2
0
1
0
0
0
1
1
1
2
1
0
0
0
1
0
1
0
0
1
0
1
1
0
0
2
0
0
2
0
1
1
1
2
3
0
0
2
0
2
0
0
0
1
1
0
1
0
0
1
0
0
0
1
1
1
1
2
1
0
0
1
2
0
2
1
0
2
1
2
7
0
0
2
1
2
0
0
0
0
2
1
0
0
0
1
1
0
1
2
1
1
2
1
1
1
0
0
0
0
0
1
0
0
1
1
0
1
2
0
0
0
0
1
1
2
2
1
1
0
0
0
1
1
0
0
2
1
0
1
1
2
0
1
0
2
0
1
1
0
0
0
2
2
0
2
0
0
0
2
2
2
2
0
2
1
0
0
2
1
2
0
0
1
2
2
0
0
1
1
0
1
2
2
2
0
0
1
1
1
2
0
0
1
1
0
0
1
2
2
0
0
0
2
0
0
0
2
1
0
2
0
1
1
0
0
0
1
2
2
0
1
1
2
0
2
1
0
0
1
1
2
0
2
2
0
1
1
0
1
0
1
1
1
0
2
0
2
1
1
1
0
2
1
2
1
0
0
1
1
1
0
2
1
1
0
0
0
1
0
2
1
1
1
0
1
0
1
1
2
2
0
0
1
0
1
3
0
1
2
1
0
1
0
0
1
0
1
0
0
0
1
0
2
0
0
1
0
3
0
1
1
1
1
0
2
0
0
0
0
1
1
3
0
2
0
0
2
0
0
0
1
2
0
1
0
0
1
1
1
4
0
2
1
1
2
1
1
0
2
0
0
0
1
0
1
0
2
0
0
1
1
0
2
1
0
1
0
0
2
0
2
1
0
0
1
1
1
2
1
1
1
2
2
0
1
0
1
2
0
2
1
0
0
0
3
0
0
2
2
0
1
1
2
2
0
1
0
1
1
2
0
2
0
2
0
2
1
0
1
0
0
0
1
0
2
0
0
2
1
2
0
2
0
4
0
1
5
1
3
1
2
0
0
2
1
0
0
0
4
2
1
2
1
2
1
2
0
2
1
0
0
1
2
1
2
0
0
1
0
1
1
1
1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
2
2
2
0
0
2
0
1
0
0
1
0
1
0
1
1
0
1
0
1
0
1
1
3
0
0
2
0
0
2
0
1
1
2
0
2
1
2
0
0
1
0
2
2
0
0
1
1
3
0
0
1
2
0
1
1
2
0
1
0
0
2
0
0
0
0
1
2
1
2
0
0
1
0
0
1
0
2
0
0
2
0
0
1
2
1
0
0
2
0
1
1
1
0
2
3
2
2
0
0
2
2
0
2
0
1
1
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
2
0
1
0
4
0
0
1
2
1
2
0
0
0
1
0
2
2
0
2
1
0
1
1
0
1
1
2
0
0
1
1
2
2
0
2
5
2
1
1
1
1
2
2
3
0
0
1
1
0
1
1
0
1
1
2
2
1
3
0
0
0
0
1
2
2
0
2
0
1
1
1
1
2
2
1
0
2
1
0
2
0
0
2
0
1
1
1
1
0
0
1
1
0
1
0
0
0
0
1
0
2
1
0
1
2
1
0
0
0
2
1
1
1
0
2
0
1
1
1
2
1
1
2
1
0
1
0
0
2
1
2
2
0
0
3
2
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
2
2
1
1
1
0
1
2
1
2
1
2
0
0
0
2
1
2
2
2
0
0
1
4
1
0
0
1
0
1
0
2
1
1
0
0
1
0
1
2
2
0
1
0
2
1
1
0
2
0
1
0
1
1
1
0
0
2
2
0
0
1
1
0
1
1
0
0
1
0
1
1
0
2
0
0
1
2
2
0
0
2
0
0
0
0
0
1
0
1
1
0
1
1
1
0
2
2
1
0
1
1
1
2
0
0
1
1
1
0
2
2
1
0
3
0
2
0
0
1
1
2
0
0
0
2
2
2
0
1
1
2
0
2
0
2
0
0
1
0
0
0
2
0
0
1
0
2
1
2
1
0
1
1
0
0
2
1
2
1
0
0
0
0
2
0
0
0
0
0
2
2
0
0
1
0
2
2
1
0
2
2
0
0
0
0
1
1
1
1
0
1
0
2
1
0
0
2
0
2
1
4
0
1
1
2
0
0
1
2
2
0
0
0
0
0
0
0
2
0
1
2
1
0
1
0
1
0
1
2
0
0
1
1
0
1
0
3
1
2
0
3
1
2
1
2
0
0
1
0
0
1
0
0
1
1
2
2
2
2
0
0
1
2
0
1
0
2
0
0
1
1
2
1
1
0
2
2
1
0
1
0
0
4
1
1
0
1
1
0
0
1
0
0
0
0
2
0
2
2
2
2
0
0
0
0
0
1
0
1
1
0
0
1
0
1
0
2
2
1
1
1
1
1
0
1
0
1
1
1
1
0
0
5
1
0
2
1
0
0
0
0
1
1
0
1
2
1
1
1
0
2
1
1
2
1
0
1
1
2
0
2
1
0
1
0
5
0
2
2
1
1
0
0
2
1
2
1
0
1
0
1
2
1
0
0
1
2
1
0
2
2
2
1
1
2
0
0
1
1
0
1
3
1
2
1
1
2
0
0
0
0
1
0
0
0
2
0
0
0
0
2
1
1
0
0
3
0
1
1
0
1
1
0
1
0
0
1
2
1
1
1
0
0
0
0
1
1
0
0
2
1
0
1
1
0
1
1
2
1
0
1
0
0
1
0
1
2
1
2
1
0
2
2
0
2
0
1
0
1
0
2
2
1
2
1
2
0
1
1
2
0
2
0
0
0
2
0
0
0
1
2
2
1
0
2
0
0
1
1
0
2
2
0
1
2
2
0
0
0
0
0
1
1
3
0
3
0
0
0
1
0
0
1
0
0
0
0
2
0
0
1
1
0
0
1
1
2
0
0
1
0
2
2
4
2
0
0
1
0
2
1
1
1
1
2
0
2
2
2
1
0
0
1
2
1
1
0
2
0
1
0
2
2
1
0
2
0
0
0
1
1
1
1
1
2
0
0
2
1
2
2
0
0
0
0
0
1
0
2
0
2
2
0
2
0
0
3
3
1
1
1
1
0
0
0
0
1
1
0
0
0
0
3
0
1
0
0
0
2
0
0
0
1
0
3
2
0
0
0
1
0
0
0
2
0
1
0
0
0
2
0
1
0
0
1
1
1
0
2
0
2
1
0
0
0
0
1
0
2
0
0
0
0
0
1
2
3
0
2
2
0
1
1
1
0
0
0
1
2
0
2
0
0
0
1
0
5
0
0
0
0
2
0
2
2
1
2
0
0
0
0
0
1
0
1
3
1
2
1
1
0
2
1
0
1
0
1
0
0
1
3
0
0
0
1
0
2
0
2
0
2
1
1
2
1
1
1
1
1
0
2
0
2
0
1
1
0
0
1
1
0
1
0
2
1
0
1
0
0
0
1
1
1
2
2
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
3
0
0
1
1
1
1
1
0
1
0
2
1
0
0
2
1
0
1
2
0
0
2
0
1
2
0
1
1
1
1
0
1
1
2
1
0
0
1
0
1
0
1
0
0
2
0
1
1
1
1
0
0
1
0
0
1
0
2
0
1
1
0
2
1
1
0
2
0
1
2
0
0
2
1
0
0
0
2
1
2
0
2
0
1
0
1
0
0
1
0
3
1
0
1
0
0
0
2
0
2
0
1
1
2
1
1
0
2
0
0
1
1
0
2
1
0
2
0
0
0
1
0
2
2
2
0
0
0
2
1
2
2
0
0
0
2
1
1
0
1
1
2
0
0
1
0
0
1
1
0
1
2
1
0
0
0
1
2
0
0
2
1
1
2
0
0
1
1
1
0
0
1
1
0
0
2
0
0
3
0
2
0
1
1
0
1
2
1
0
0
0
1
0
0
2
1
0
1
1
1
0
3
1
0
0
2
1
0
0
0
0
0
0
1
1
0
1
1
1
1
1
0
1
0
1
0
1
1
0
0
0
2
1
0
0
0
1
1
0
1
1
1
0
2
0
1
2
0
2
0
0
0
1
1
2
0
1
3
0
2
0
0
0
1
3
0
0
0
0
2
0
0
0
1
0
2
1
0
1
1
1
2
0
2
0
1
1
1
0
1
2
1
0
1
1
1
2
0
1
0
0
1
2
2
1
1
1
0
0
2
1
0
0
1
2
0
1
0
0
0
0
0
0
2
3
1
1
0
1
0
0
0
1
2
0
0
1
0
0
0
0
0
2
1
2
1
2
2
0
1
2
1
0
0
2
2
1
0
2
1
0
0
2
1
2
1
0
1
1
0
1
0
1
0
1
2
2
0
0
0
1
2
0
1
0
1
1
2
0
2
1
2
2
0
0
2
1
2
1
2
1
2
2
1
0
0
0
0
2
1
0
1
0
1
0
0
0
1
3
1
0
0
2
0
1
1
0
0
0
0
2
0
0
0
0
2
0
1
0
1
0
1
0
0
0
1
3
1
0
2
0
0
2
1
2
2
1
0
0
1
2
1
2
1
0
2
0
1
2
0
2
0
0
1
0
0
2
2
2
1
2
2
1
0
1
2
0
0
0
0
1
1
1
0
2
1
1
0
1
0
0
1
1
0
2
1
1
0
1
3
1
2
0
1
2
0
0
0
0
0
1
0
0
1
2
0
1
1
1
0
1
0
0
1
2
1
2
2
0
0
1
1
0
1
1
0
0
0
3
2
0
1
2
0
2
2
4
2
0
2
1
0
2
0
2
1
4
0
0
2
0
0
0
1
1
0
2
1
1
0
2
0
1
0
0
2
1
0
0
0
1
0
1
0
0
0
0
2
0
1
0
2
2
2
1
1
1
0
1
2
1
0
2
2
1
1
0
1
1
2
2
1
1
2
1
0
0
0
2
0
0
1
2
0
0
0
1
0
1
2
2
0
2
0
0
1
0
0
2
0
0
1
1
0
0
1
2
1
2
0
4
2
0
1
2
1
2
1
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
2
1
1
2
2
0
1
0
1
2
1
1
1
0
2
0
2
1
1
2
0
0
2
0
0
0
0
0
0
0
0
1
1
0
1
1
1
0
1
0
2
1
2
0
1
2
1
0
1
1
1
0
2
1
2
2
2
0
2
1
2
1
0
1
2
1
1
2
2
1
1
0
1
4
0
2
0
1
2
1
0
0
1
0
1
0
2
2
1
1
1
0
2
0
1
1
0
0
1
0
0
0
0
1
0
0
1
1
0
2
2
0
2
2
1
0
2
0
2
0
0
0
0
1
0
2
0
2
1
1
1
0
1
0
0
0
2
0
0
0
0
1
1
0
2
0
1
1
0
1
0
0
0
1
2
1
0
0
1
1
0
0
0
2
2
1
2
2
1
1
2
0
4
0
1
0
0
1
3
0
1
2
2
1
0
1
1
0
0
2
0
0
0
2
1
1
0
1
1
0
2
0
1
1
1
0
0
0
0
0
0
1
0
2
1
0
1
0
1
1
0
0
0
1
2
0
0
0
3
2
0
0
2
1
1
0
0
1
0
1
0
2
2
2
0
1
2
0
0
0
0
0
0
0
2
2
0
1
1
0
2
0
0
0
0
2
0
1
1
1
0
0
2
2
0
0
1
0
1
0
1
1
1
0
0
0
0
0
2
2
0
0
1
3
0
0
2
1
3
0
2
2
1
1
1
0
1
2
1
1
1
0
0
2
0
1
1
0
1
2
2
2
2
2
0
0
0
1
1
1
0
2
0
0
2
0
0
0
0
0
0
1
1
2
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
2
0
2
0
1
0
0
0
0
9
2
0
0
1
0
0
0
0
1
1
0
1
0
2
1
0
0
0
1
2
2
0
0
0
2
2
2
1
1
1
1
1
0
1
1
1
0
0
2
0
1
0
1
0
0
1
0
0
0
0
0
3
1
0
0
1
1
0
0
0
0
2
0
0
1
0
0
0
3
0
1
2
1
1
1
0
1
1
0
0
0
2
1
1
0
1
0
0
0
0
2
1
0
2
0
1
1
0
1
0
0
0
2
1
1
2
1
0
1
1
1
2
2
0
3
0
1
1
1
0
1
2
0
1
0
0
0
0
0
1
1
0
0
0
0
1
1
1
0
0
0
1
0
1
0
0
1
3
1
1
1
1
0
2
2
0
1
0
0
1
2
1
2
2
1
0
0
2
0
1
1
1
0
1
2
2
2
0
1
1
0
1
0
0
1
0
1
1
1
2
0
1
1
0
0
0
0
0
1
2
0
1
2
1
1
1
2
1
1
0
1
3
2
1
2
2
1
1
0
1
2
2
1
1
0
1
1
1
0
0
2
2
1
1
2
1
2
2
2
1
0
1
0
0
2
1
1
0
0
1
2
1
1
0
0
0
0
1
2
1
1
0
0
1
0
1
0
1
1
2
0
0
2
0
1
0
1
1
3
0
1
1
1
2
0
1
1
1
0
0
0
2
0
2
1
0
0
0
1
0
0
0
0
1
1
2
1
1
0
0
1
0
0
3
0
2
0
2
0
0
3
1
1
1
1
1
1
1
1
0
0
2
2
0
2
0
1
1
0
1
1
2
1
2
0
0
0
1
2
1
2
0
1
0
1
2
2
0
1
1
1
0
2
2
0
1
0
1
1
1
1
1
2
0
0
0
0
1
2
0
0
2
1
1
0
2
2
1
1
1
0
0
0
0
1
0
2
1
0
1
1
1
1
1
0
0
3
1
0
0
0
2
0
1
0
0
2
0
2
2
2
0
0
0
0
0
1
3
1
0
0
0
2
5
1
0
0
2
2
0
0
0
0
0
1
0
1
0
1
0
0
2
1
2
1
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
2
2
0
3
0
1
0
1
0
1
2
1
1
1
1
0
1
2
1
1
1
1
0
1
0
1
0
1
2
1
1
1
1
0
1
0
0
0
0
2
0
0
0
2
0
2
0
0
2
1
0
1
1
0
0
0
0
0
0
0
1
1
0
0
2
1
0
0
0
0
2
1
0
0
1
2
2
0
0
0
0
1
0
2
0
1
0
0
0
2
1
2
0
3
0
1
2
0
0
1
0
0
0
2
0
0
3
1
2
1
2
1
0
2
0
2
0
1
1
0
0
2
0
2
1
0
1
2
2
0
1
0
0
1
0
0
1
2
1
1
0
0
2
2
0
1
0
1
1
0
0
2
0
1
0
0
1
0
1
3
0
0
3
2
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
2
1
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
1
2
2
1
1
1
1
0
1
0
2
3
0
0
0
1
0
1
1
1
3
0
2
2
3
1
1
1
1
0
1
2
1
1
0
0
0
2
2
0
0
0
2
0
1
0
1
1
2
0
0
0
2
1
0
1
0
0
1
1
0
1
0
1
2
0
0
0
0
0
0
0
0
2
0
2
1
0
2
2
1
1
0
1
2
0
0
0
1
1
0
0
1
0
0
0
0
1
2
0
0
6
1
2
1
0
2
0
2
1
1
2
0
0
2
1
0
2
0
2
1
0
1
0
0
3
1
0
1
0
0
2
0
0
1
0
0
1
0
2
0
1
1
0
1
0
2
0
1
0
0
1
2
0
2
1
2
0
0
1
1
0
0
0
2
1
0
2
2
0
1
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
1
1
0
0
1
1
0
0
3
0
0
1
2
1
2
3
2
2
1
2
0
1
2
3
0
0
1
0
0
1
0
1
6
0
1
1
0
0
0
0
0
1
0
1
2
2
0
2
2
0
0
0
0
0
1
2
1
0
0
1
0
2
0
1
1
0
0
0
0
0
0
1
0
1
1
1
1
0
0
0
0
1
2
0
1
0
0
0
2
1
0
0
2
1
0
2
0
1
1
2
0
0
1
1
1
0
1
2
1
1
2
2
1
1
0
1
0
9
1
1
1
2
0
0
0
0
2
1
1
0
0
1
0
1
1
0
0
0
1
0
0
0
2
1
2
3
0
0
1
2
0
0
0
0
2
0
1
1
2
1
1
2
0
1
0
0
2
1
2
0
1
0
0
0
1
0
1
0
1
1
1
1
2
0
2
1
2
0
0
0
0
2
1
0
1
1
0
1
1
0
0
2
0
0
0
1
2
0
0
1
0
2
0
0
1
1
2
1
2
0
2
1
0
0
1
1
1
0
2
2
0
0
3
1
0
0
0
1
0
1
0
0
1
2
2
2
1
1
1
1
1
1
0
1
0
0
0
1
2
2
0
0
1
0
0
1
1
1
2
0
1
1
0
0
0
0
0
2
0
0
0
1
1
1
1
2
0
1
0
0
2
0
0
1
0
0
1
1
0
1
0
0
1
0
1
0
1
2
0
1
1
1
2
0
0
1
0
0
1
1
0
1
0
1
1
0
2
1
0
0
0
2
2
0
0
1
1
1
2
0
0
1
0
1
1
1
0
0
1
0
2
2
0
0
1
0
1
0
1
2
0
1
0
1
1
2
0
1
1
2
1
0
1
0
1
1
0
0
1
0
0
1
1
1
0
0
1
1
0
0
0
1
2
2
2
1
1
0
0
1
1
0
1
0
1
1
2
0
2
0
2
0
0
0
1
2
0
2
1
1
0
2
1
1
0
0
1
1
1
3
0
0
2
0
2
1
1
0
2
0
0
0
0
0
0
1
1
0
0
1
0
2
2
0
1
1
0
2
1
0
2
0
2
0
2
0
1
0
0
1
0
0
1
1
0
0
0
1
1
0
0
2
2
2
2
1
0
1
1
1
1
0
0
1
1
0
2
1
0
2
2
2
2
0
1
1
0
1
0
0
1
0
0
0
0
1
0
1
2
2
2
2
1
0
0
2
2
0
1
0
1
2
0
1
1
0
1
2
2
1
0
0
1
1
2
0
2
1
2
0
2
0
1
0
1
0
0
1
2
0
0
0
3
2
0
0
0
1
0
2
0
0
0
0
1
2
0
2
1
0
1
2
0
2
2
0
0
1
1
2
2
0
0
0
1
0
2
0
2
2
0
0
1
0
0
2
1
0
1
2
0
0
0
2
1
2
2
1
1
1
0
0
0
1
1
1
1
0
2
0
0
2
0
2
0
0
0
1
1
0
2
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
1
1
1
1
0
0
0
2
1
0
0
0
1
2
3
0
0
0
2
0
2
1
0
0
1
0
0
0
2
4
0
0
1
0
0
2
1
0
2
1
1
1
0
1
1
0
1
1
0
2
0
0
1
2
0
1
0
0
2
0
0
4
0
1
0
0
0
2
0
0
1
1
2
0
0
2
1
1
0
1
0
0
0
2
1
1
2
0
2
1
1
0
1
1
0
1
1
1
20
0
0
2
0
0
2
2
0
2
2
0
0
0
0
1
1
1
0
1
0
2
2
0
0
0
1
1
1
1
1
1
2
0
0
2
0
1
1
2
0
0
2
0
4
0
2
1
0
0
1
0
0
1
0
5
2
0
0
1
1
0
0
0
0
0
2
0
1
0
1
2
1
0
0
0
2
1
0
0
0
0
1
0
2
0
2
0
1
1
2
1
0
2
2
2
2
0
0
1
0
1
1
1
2
1
1
1
1
0
0
1
2
1
0
1
0
1
1
2
1
1
1
3
0
0
2
1
0
0
0
1
1
2
0
1
0
0
3
2
2
0
0
1
2
0
0
1
2
0
1
1
1
0
0
0
2
2
1
2
1
0
0
2
1
1
1
0
2
1
7
2
1
1
0
0
1
0
1
2
2
1
0
0
0
2
2
0
1
0
0
1
0
1
3
2
2
2
1
1
0
1
2
2
0
0
2
1
1
0
2
0
1
1
0
1
0
1
2
0
2
0
1
0
0
0
0
2
2
0
0
0
1
1
1
0
0
0
0
2
1
0
2
2
1
0
3
0
0
2
1
1
0
2
0
1
0
0
1
2
1
1
2
0
0
2
0
1
2
2
0
0
0
1
0
0
0
2
0
2
1
2
1
1
1
2
1
0
1
0
1
0
0
0
0
0
1
2
0
2
0
1
0
2
1
0
1
3
1
2
1
1
1
1
0
1
1
1
0
1
2
1
0
0
1
0
1
2
1
1
0
1
1
0
2
0
0
0
0
1
1
0
0
2
0
0
1
2
1
0
0
1
2
0
0
0
0
1
0
0
1
0
0
0
1
1
1
1
3
0
1
0
2
0
1
2
0
2
1
2
0
0
0
1
0
0
1
0
0
1
0
0
0
1
1
0
0
2
2
0
0
0
0
1
0
1
1
1
2
2
0
0
0
0
0
1
1
0
0
0
1
0
2
1
0
1
0
1
0
0
1
1
0
0
0
0
1
1
0
1
0
0
0
1
0
2
0
0
2
1
1
1
0
0
0
1
1
2
1
1
2
0
1
0
2
0
2
2
0
1
1
1
2
0
0
2
0
0
2
2
1
2
1
0
2
1
0
1
3
0
0
2
1
1
2
2
1
1
1
0
2
2
0
0
0
2
0
0
0
2
0
1
0
4
2
0
0
0
0
0
1
1
0
0
2
0
0
2
0
2
2
0
0
0
2
1
0
2
0
0
1
0
1
0
0
0
0
0
0
2
6
2
2
2
0
1
2
0
3
0
2
1
0
0
0
1
2
2
1
2
0
1
0
0
2
2
1
0
2
0
2
0
0
0
1
0
2
2
2
0
0
2
0
0
0
0
0
1
0
2
2
1
0
2
0
0
2
2
2
2
0
2
0
1
2
2
0
1
0
1
1
0
0
0
0
2
0
0
1
1
0
0
0
1
2
0
0
0
0
0
0
0
0
1
2
1
0
1
1
0
1
1
1
0
0
1
1
1
0
1
1
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
1
1
1
2
0
1
0
0
0
2
0
1
2
0
2
0
0
2
2
0
2
2
1
2
0
0
1
0
2
0
1
2
1
3
0
2
0
0
0
2
0
1
0
1
0
0
0
0
0
2
1
1
0
2
0
1
0
1
1
0
1
0
1
0
0
0
0
1
0
1
0
0
2
1
3
1
0
2
0
0
0
0
1
0
0
2
1
0
1
0
2
1
0
0
1
1
0
0
1
0
2
0
0
0
2
0
2
0
1
2
1
0
0
0
1
0
2
1
0
0
3
2
2
0
0
1
1
2
2
0
0
0
2
1
1
1
0
0
0
0
1
0
2
2
1
1
0
1
0
0
1
1
1
1
1
0
2
2
0
2
2
1
1
2
1
0
0
0
1
1
7
1
1
0
2
0
0
2
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
1
1
1
1
4
0
2
1
0
0
1
3
8
2
1
1
1
1
1
2
0
0
0
0
0
0
1
2
1
0
2
1
0
1
2
0
0
1
1
0
0
0
2
1
0
0
0
0
1
0
2
1
2
0
1
1
0
1
1
1
0
1
1
2
1
0
0
0
1
2
1
2
1
1
1
2
1
2
1
0
2
2
2
1
1
0
2
0
0
2
0
0
1
2
1
1
1
0
1
1
1
1
2
0
0
0
0
2
2
0
0
0
1
0
0
1
0
0
1
0
0
1
0
1
0
1
0
0
3
0
1
0
0
0
2
0
0
0
2
0
0
1
2
1
0
0
0
0
0
1
0
0
0
2
4
0
1
2
2
0
0
0
2
0
1
0
2
0
0
2
1
0
0
2
1
1
1
1
3
0
0
0
2
0
2
0
0
4
0
0
0
0
1
1
2
2
0
1
1
1
2
0
2
1
0
0
1
0
0
0
0
1
2
1
0
1
1
1
2
0
1
0
3
0
2
0
2
1
1
2
0
0
2
1
0
0
0
3
0
1
1
0
0
0
2
1
0
0
1
2
2
0
1
3
1
2
1
0
1
1
0
0
1
1
1
1
1
0
1
0
0
1
0
0
1
2
2
0
2
1
2
1
0
2
0
0
0
0
1
1
1
2
2
2
0
0
0
0
2
2
1
0
2
2
0
1
0
0
0
0
0
2
0
0
2
2
0
0
1
1
0
1
2
0
0
1
0
0
0
2
0
1
1
1
0
1
1
2
1
2
1
0
1
1
1
0
2
1
2
1
1
0
1
1
0
1
1
0
2
0
2
0
0
2
0
1
1
0
1
0
2
2
0
0
1
0
0
0
1
0
1
1
0
2
2
0
1
1
1
0
1
2
0
0
0
0
0
1
0
1
0
0
0
1
2
1
2
1
0
0
2
1
2
1
0
1
0
0
1
0
1
0
0
2
0
2
0
0
0
2
2
1
0
1
0
0
1
0
2
0
1
1
0
2
0
1
0
1
2
1
1
0
0
0
0
0
0
0
1
1
2
0
1
2
2
1
0
0
0
4
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
1
0
0
0
0
2
0
0
1
0
2
1
0
1
2
0
2
0
1
2
1
0
2
0
0
3
0
1
2
1
2
1
0
0
0
1
1
2
1
0
1
0
0
2
2
0
0
0
0
2
0
1
3
0
0
1
0
0
2
1
2
0
2
1
0
2
0
1
2
2
3
0
1
0
0
0
1
2
0
0
2
0
0
2
1
2
0
0
2
1
0
0
2
0
1
0
0
3
2
2
2
0
0
0
0
1
1
0
3
2
1
0
0
1
1
0
1
0
1
0
0
2
0
2
1
0
1
1
0
0
0
1
2
0
0
1
1
1
0
2
0
1
0
2
2
2
0
1
1
2
0
0
1
0
0
2
0
2
2
0
1
1
2
2
0
2
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
2
2
2
0
0
0
0
2
0
1
0
2
2
1
0
2
1
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
1
2
2
1
2
0
1
0
2
0
0
2
0
0
0
0
0
0
1
2
0
1
2
2
0
0
0
0
1
0
2
0
1
1
0
1
2
0
0
0
2
0
1
0
0
0
0
0
2
1
0
0
1
2
1
1
1
2
1
0
0
0
0
2
0
2
0
0
2
0
0
0
0
1
2
0
0
1
1
2
0
2
0
1
2
0
1
2
1
1
2
4
0
1
2
2
1
0
0
0
2
3
0
0
2
1
1
0
0
0
2
0
2
1
1
0
0
0
1
0
0
1
0
0
1
0
1
2
0
0
0
1
0
1
2
0
0
0
3
0
0
1
0
1
0
2
2
1
2
1
2
1
2
1
1
2
0
1
0
0
2
0
2
2
0
1
0
0
1
2
2
0
2
1
0
1
1
0
1
0
1
1
0
2
0
1
1
1
1
0
1
0
1
1
1
1
2
2
2
1
0
1
0
2
0
1
1
0
0
2
2
1
0
1
0
1
0
0
1
0
1
2
1
0
0
0
1
1
0
0
3
1
1
1
2
1
2
2
0
1
1
2
2
0
0
0
2
0
0
1
1
0
0
0
0
0
1
1
0
0
0
3
1
1
1
1
0
2
0
2
1
0
0
2
2
1
0
1
0
0
0
0
0
0
2
0
0
0
1
1
0
0
1
1
0
2
0
1
2
0
0
2
1
0
0
2
2
2
0
0
0
1
0
0
1
1
0
0
1
2
1
0
2
0
2
1
2
1
1
0
2
0
2
2
0
2
3
0
0
1
1
1
0
0
2
0
1
0
0
1
2
0
1
1
1
0
0
0
0
1
1
0
1
1
1
2
0
1
0
1
1
1
2
1
0
1
0
1
0
0
2
0
0
4
2
2
2
1
2
1
0
0
0
1
2
1
2
1
0
2
0
0
1
0
2
0
0
0
2
2
0
3
1
1
0
0
1
0
1
0
1
1
1
0
0
1
0
0
1
1
0
2
1
0
1
0
0
1
0
0
0
0
0
1
1
0
0
1
0
1
2
1
0
1
2
1
0
0
1
0
2
2
1
0
2
1
1
1
2
1
2
0
1
1
2
3
0
0
2
0
1
0
1
1
2
1
0
0
1
0
3
1
2
1
1
2
1
1
0
0
1
2
1
0
0
2
2
1
0
2
1
1
0
0
1
0
0
0
1
0
1
2
1
1
1
0
0
0
1
1
0
0
1
1
0
0
0
2
1
1
2
1
2
1
1
1
2
1
1
2
0
4
2
0
1
2
1
1
0
1
1
0
0
0
2
2
1
2
0
0
1
1
0
1
0
0
1
1
1
0
0
0
0
1
3
0
0
0
2
0
0
1
1
1
0
0
1
1
2
2
1
1
2
1
2
2
1
0
0
0
1
2
0
0
0
1
1
0
2
1
1
1
1
0
1
1
1
0
0
2
0
3
0
2
1
1
0
3
3
0
0
0
1
2
0
1
1
2
0
3
0
0
0
1
0
2
0
1
1
0
3
2
2
0
0
1
0
1
1
0
0
2
0
1
0
1
0
0
0
0
0
1
1
0
0
1
2
0
0
1
2
2
1
1
2
0
1
2
0
0
0
1
1
1
0
4
0
1
0
0
1
2
0
0
1
0
1
1
1
1
0
0
1
0
1
2
1
0
0
0
1
0
0
0
0
1
0
0
1
0
1
3
0
0
1
1
2
1
1
0
0
0
0
0
1
1
0
2
0
0
0
2
0
0
2
2
2
1
0
1
0
2
0
0
2
1
0
2
0
0
2
0
3
0
0
2
2
1
2
0
0
1
2
2
1
0
1
0
0
0
2
2
1
1
2
2
1
2
0
0
1
2
0
0
1
2
1
1
2
3
0
2
1
1
1
2
2
0
1
1
2
2
0
0
1
1
1
1
0
0
1
2
0
2
0
2
0
1
1
2
0
1
1
0
2
2
2
0
0
1
1
0
2
1
0
0
1
0
1
2
1
2
1
0
2
1
2
2
0
0
2
2
1
0
1
0
1
2
1
0
0
1
2
0
2
1
3
0
0
1
0
1
0
1
0
1
1
0
1
1
1
0
0
0
0
1
1
1
0
0
1
2
1
0
0
1
1
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
1
1
1
0
0
3
0
2
1
1
1
0
2
2
2
0
2
0
1
1
0
0
1
0
1
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
1
0
1
0
2
1
1
0
0
1
2
1
1
1
1
0
0
0
0
1
0
2
1
1
0
1
1
1
1
2
1
1
1
1
0
1
0
0
0
1
0
0
0
2
0
1
1
0
0
2
1
1
0
0
1
0
0
1
2
0
2
1
0
0
1
1
1
0
0
1
0
0
1
2
0
0
0
1
2
0
2
1
1
2
0
1
1
1
1
1
2
1
0
0
2
2
2
1
1
0
5
0
0
0
0
2
0
1
0
1
0
1
0
1
0
1
2
1
1
1
1
2
2
1
1
1
1
0
2
1
0
1
0
0
1
0
0
1
0
0
0
0
2
0
2
1
1
0
1
0
0
1
1
0
1
0
1
0
0
1
2
1
2
1
0
0
0
0
0
1
2
1
0
0
0
0
2
0
1
1
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
1
1
6
1
0
1
0
0
0
1
0
0
1
2
1
1
0
0
0
2
1
1
1
1
2
0
0
2
1
2
1
1
2
1
0
2
0
0
1
1
1
2
0
0
1
0
1
1
0
2
1
2
2
1
0
0
0
0
2
1
0
1
0
0
1
1
0
0
1
0
2
2
2
2
1
0
0
2
1
1
0
0
1
1
0
1
0
0
1
0
0
0
1
0
1
1
0
2
0
1
1
1
2
0
1
3
2
0
0
0
0
0
5
1
1
0
1
0
0
0
0
0
0
0
2
0
1
1
0
2
1
2
0
0
0
0
1
0
1
2
1
0
1
1
0
0
1
2
2
0
0
1
0
0
0
2
1
0
2
1
1
1
2
1
1
1
1
4
1
1
1
1
0
1
1
1
0
0
0
0
0
1
1
1
1
1
0
2
1
1
2
0
1
0
1
0
1
2
0
1
0
1
0
0
1
0
0
2
0
0
1
0
1
1
2
1
0
0
7
0
0
2
0
1
0
0
0
1
1
0
0
1
0
0
0
1
1
1
2
2
0
1
1
0
0
3
0
1
1
1
0
0
1
1
0
0
2
2
0
0
2
2
0
0
0
2
1
1
0
0
0
0
2
0
0
1
0
0
1
2
2
3
0
0
2
1
2
0
0
2
0
0
0
0
0
0
0
0
1
0
1
2
1
0
0
0
2
2
0
0
0
2
1
0
2
0
1
1
0
1
0
0
0
0
1
0
0
2
0
2
2
0
0
2
1
0
0
2
0
1
0
1
4
0
2
0
2
0
2
2
2
1
0
1
0
0
2
1
0
0
0
1
0
2
1
1
1
1
1
0
1
0
2
1
0
0
0
0
2
1
1
2
3
1
0
0
1
0
1
1
1
2
0
0
0
2
0
1
1
1
0
0
0
2
2
1
2
0
1
0
1
2
1
1
1
1
0
0
2
1
2
0
0
2
0
0
1
2
2
1
1
2
1
1
0
2
0
0
0
0
0
1
2
1
0
0
0
0
1
1
1
0
0
2
0
0
0
0
2
2
2
0
2
2
1
1
1
0
0
0
1
1
0
0
0
1
2
0
1
2
1
0
0
2
2
2
1
0
0
2
0
1
0
1
0
1
1
1
0
0
0
1
1
1
1
0
0
1
2
0
1
2
2
0
1
0
0
1
0
0
0
0
2
1
0
0
2
2
1
0
0
0
0
1
1
0
1
0
0
2
0
1
1
2
2
0
1
1
0
1
2
2
2
1
2
2
1
3
0
0
0
2
1
1
1
0
1
0
1
0
0
0
0
1
2
1
1
0
0
2
1
1
0
1
0
0
0
2
0
2
1
0
2
0
1
4
2
1
0
0
0
0
0
0
2
1
2
1
0
0
1
1
1
0
2
2
1
2
1
0
1
0
0
1
0
0
1
4
3
1
0
1
2
1
2
0
0
0
1
0
1
0
0
0
1
1
2
1
0
1
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
1
0
2
1
0
0
0
0
0
1
0
1
1
0
0
0
0
1
2
1
1
0
1
0
1
0
1
2
2
0
0
0
0
1
2
3
2
1
0
2
2
1
0
0
1
1
1
1
0
0
0
2
1
2
0
0
0
0
1
0
0
0
1
2
1
0
0
1
1
2
2
0
0
0
1
1
2
1
0
1
1
0
0
0
1
1
0
1
0
1
3
0
0
0
2
1
1
1
1
0
0
1
1
1
0
0
0
0
1
0
1
1
0
0
1
2
2
1
1
1
0
1
0
2
0
1
0
0
1
2
0
1
0
1
1
0
0
2
0
1
2
0
0
0
2
2
1
2
1
1
3
0
1
1
2
2
0
1
1
0
2
0
0
2
2
2
1
1
0
2
0
0
1
1
1
2
2
0
1
2
0
0
1
1
0
2
6
1
1
2
0
1
1
2
2
0
2
0
0
0
0
0
1
1
0
6
0
0
1
1
2
0
1
1
1
2
0
0
2
0
2
6
2
2
1
0
2
2
0
0
2
0
2
1
2
1
0
2
0
1
1
0
1
2
1
2
0
0
1
1
2
0
0
0
0
0
0
2
0
2
0
2
0
2
0
1
0
0
1
2
1
1
0
0
0
1
0
1
2
0
0
1
2
0
3
1
0
1
1
0
0
0
1
1
0
1
1
0
1
0
1
0
1
0
0
1
1
1
0
2
0
0
0
1
0
0
0
2
0
2
2
2
1
2
2
0
0
1
0
0
1
0
0
2
2
0
0
2
1
1
1
0
0
0
1
2
1
2
1
0
0
1
1
2
0
1
6
2
3
0
0
2
0
1
1
1
0
0
1
1
1
1
2
1
1
3
1
1
6
1
0
2
1
0
1
1
0
1
0
1
0
0
1
0
2
1
2
0
0
0
2
2
0
0
0
0
2
1
1
1
1
0
1
1
1
1
1
0
0
1
3
0
0
0
1
1
1
0
1
1
0
1
2
2
1
1
2
0
1
0
1
2
0
2
0
1
1
1
0
2
1
0
0
1
1
2
0
1
2
1
0
0
1
0
1
0
0
0
1
1
0
0
0
1
0
0
1
0
1
1
0
1
1
2
1
3
0
0
1
1
1
0
1
0
0
1
2
2
0
0
0
0
0
0
2
1
0
0
2
1
0
1
0
3
2
1
0
0
0
3
2
0
2
0
1
0
0
1
0
0
1
0
0
0
3
1
0
0
0
0
0
1
0
0
0
0
1
1
1
0
1
0
0
1
2
3
0
2
1
3
2
1
0
0
1
2
1
0
2
0
1
1
2
2
0
0
1
0
1
0
0
0
0
1
1
0
0
1
0
2
0
0
0
0
2
0
1
0
0
2
0
2
0
2
1
1
2
0
0
2
0
1
1
0
0
2
0
0
1
1
0
0
0
4
1
1
0
0
2
2
1
0
3
1
0
0
0
2
0
1
0
2
1
0
0
0
4
0
0
0
1
1
2
0
1
0
0
0
0
0
2
0
1
1
1
1
2
1
0
1
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
2
0
1
0
1
0
0
2
3
0
1
2
2
1
2
2
2
0
0
1
0
0
2
3
1
1
1
0
0
1
2
1
0
3
2
3
0
0
0
0
0
0
1
1
0
0
1
1
0
0
2
3
2
2
4
0
1
1
1
0
0
0
1
1
0
0
0
1
2
0
0
0
0
2
0
1
1
0
1
1
1
0
1
0
3
0
0
2
0
0
2
2
2
0
1
0
0
2
0
0
0
2
0
1
2
1
2
2
1
1
2
1
0
0
1
1
1
1
0
2
2
1
1
2
0
0
0
2
0
0
1
0
0
0
0
2
1
0
1
0
0
0
1
0
0
0
0
2
2
0
0
0
1
0
0
1
0
0
1
1
0
2
0
2
2
1
0
0
0
2
0
1
0
1
0
1
1
0
0
0
1
2
2
0
0
2
2
1
0
1
0
2
0
1
0
0
2
0
3
1
2
0
0
0
0
2
0
1
2
1
0
0
1
2
0
2
2
1
0
2
0
0
0
2
0
1
2
2
3
1
0
3
0
1
0
0
2
1
1
2
1
0
2
2
2
0
0
0
1
0
0
0
0
0
2
1
0
0
1
1
1
1
1
0
1
1
1
1
1
0
1
1
0
1
0
1
1
0
0
0
1
0
1
4
1
0
1
2
2
0
2
0
1
0
1
0
1
1
1
1
0
2
1
1
2
1
0
0
0
1
1
1
0
0
1
0
0
2
2
2
1
0
1
0
1
1
0
0
2
0
0
1
0
1
2
0
1
1
0
0
1
0
0
0
2
0
1
1
0
2
0
0
0
3
1
0
0
0
2
0
1
1
0
2
1
0
1
0
1
0
0
0
0
2
1
1
1
2
0
1
0
0
2
0
0
0
0
0
0
1
2
1
1
1
2
0
1
0
1
2
0
0
0
0
2
0
5
2
2
0
2
1
1
2
1
0
0
2
1
1
0
1
0
0
3
1
1
2
1
1
0
0
2
0
0
1
1
0
1
1
0
0
0
1
1
0
0
2
1
0
0
0
0
1
1
2
1
0
0
2
0
0
1
1
1
0
1
0
2
0
1
1
1
0
2
1
1
0
3
0
0
0
2
1
1
0
0
0
1
1
0
1
1
0
0
2
1
0
0
2
1
0
0
0
1
0
0
0
2
1
0
0
0
1
1
1
2
1
0
0
1
0
2
0
1
0
1
1
0
0
0
1
0
2
0
1
0
0
2
2
0
2
1
2
1
1
2
2
0
0
2
0
2
1
1
0
2
2
0
1
0
0
0
2
1
0
2
2
0
1
1
2
1
0
1
0
1
0
0
1
0
3
0
1
0
0
0
2
1
0
0
2
1
1
2
0
0
0
0
0
2
2
0
0
1
1
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
2
2
2
0
1
0
1
0
1
0
1
2
1
0
1
1
0
0
0
0
0
0
1
3
2
2
0
1
0
1
1
2
0
2
0
0
1
2
1
0
1
0
0
0
0
1
2
0
0
3
1
0
0
1
1
1
0
2
2
0
0
2
1
2
0
0
1
2
1
0
1
2
1
1
2
1
2
0
0
2
1
1
0
2
2
0
0
0
0
2
0
0
0
1
2
0
1
1
0
0
0
0
1
2
0
0
0
1
2
0
0
0
0
1
1
1
0
2
2
0
2
0
0
0
1
0
0
2
0
0
2
2
2
1
0
0
1
0
2
1
2
0
2
1
0
0
0
1
1
2
1
0
0
1
0
0
1
0
0
0
3
0
1
1
0
0
2
1
1
1
1
0
0
2
0
1
0
1
2
0
1
0
0
0
0
2
0
0
0
1
1
0
0
1
1
2
0
2
0
0
1
0
0
0
1
0
1
2
0
0
0
0
1
0
0
2
1
2
1
2
0
1
1
1
0
1
1
0
0
0
0
0
2
0
1
2
0
0
0
0
0
2
0
2
1
1
1
0
1
0
0
2
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
1
0
1
0
0
1
0
2
0
0
1
0
0
1
0
0
1
1
0
0
0
1
2
2
2
2
0
1
1
0
1
2
2
0
1
1
1
0
0
1
0
2
2
1
2
0
2
4
0
0
2
1
3
0
0
0
0
1
0
0
0
0
1
1
1
0
2
0
0
1
0
3
0
0
1
0
1
0
1
0
0
1
0
1
2
0
1
0
1
2
1
0
0
2
0
1
0
1
1
0
0
0
0
1
0
1
1
1
0
1
0
1
1
0
0
0
0
1
2
2
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
1
2
0
0
1
0
0
1
1
0
0
2
0
0
1
2
2
4
1
1
3
0
1
0
1
0
1
0
1
0
2
1
1
0
1
1
0
0
1
2
2
0
1
0
1
1
0
0
0
0
0
2
0
1
1
0
1
1
1
0
1
2
2
1
1
0
2
0
0
1
1
1
1
2
1
1
0
0
1
1
2
0
0
0
0
2
1
1
1
2
1
1
2
0
1
0
2
1
1
2
2
0
0
1
1
0
1
2
0
0
1
0
0
0
3
0
0
2
0
0
0
1
0
1
0
0
0
1
1
0
1
2
0
1
2
1
1
1
0
2
0
1
2
0
0
0
0
0
2
0
2
1
1
0
0
0
0
1
0
1
0
0
1
0
2
0
0
0
1
2
2
0
2
1
0
1
1
0
0
2
1
2
0
1
2
0
0
0
1
1
0
0
1
1
2
1
0
0
0
0
0
2
0
0
1
2
0
2
1
0
2
1
2
0
0
0
1
1
0
1
2
1
0
1
0
0
0
0
1
0
0
0
4
0
1
1
1
1
0
1
2
2
0
0
2
2
0
2
1
2
2
1
3
0
1
1
2
0
0
0
1
0
0
1
2
1
0
2
1
1
1
1
1
0
2
0
0
2
1
0
1
1
1
2
2
0
1
2
0
0
0
0
0
1
0
1
0
1
2
1
2
1
1
1
1
0
0
1
2
0
2
2
5
0
0
0
0
0
2
0
0
1
0
1
1
0
0
1
0
2
0
1
1
1
1
3
0
1
0
1
0
0
0
0
0
1
0
4
0
1
4
1
0
3
1
0
2
1
2
1
1
0
2
0
1
0
1
0
6
2
0
2
0
0
0
2
1
2
3
0
1
1
1
4
1
2
2
0
2
1
2
2
0
5
1
1
1
2
1
1
1
0
1
1
0
0
0
1
1
1
0
0
0
1
1
1
2
0
1
1
2
1
3
3
1
0
0
0
1
1
1
2
2
2
0
1
1
2
1
1
0
1
0
1
1
0
2
2
0
0
2
0
0
1
1
1
1
3
0
1
0
0
1
1
0
1
6
0
3
1
2
1
2
0
2
2
2
1
2
0
0
1
2
1
1
1
2
2
2
0
2
2
0
2
0
1
1
1
1
2
2
0
0
1
2
1
1
2
0
0
1
0
0
0
2
0
1
2
0
0
1
0
0
0
1
0
2
0
1
1
0
0
2
1
0
1
0
0
0
1
1
2
0
2
2
0
1
1
0
1
2
0
1
0
1
1
0
0
0
1
2
2
2
2
0
0
0
1
1
2
0
2
0
0
2
1
0
0
0
2
2
1
1
0
2
2
0
0
1
0
0
1
0
0
0
0
2
0
1
2
0
0
1
0
0
0
0
1
0
0
2
1
2
2
0
2
0
0
0
1
0
1
0
0
1
0
1
0
1
0
2
0
2
2
1
2
1
1
2
0
1
1
0
1
0
1
0
0
0
0
1
2
0
2
0
1
2
2
0
1
2
1
1
1
2
0
2
0
0
1
1
1
0
0
0
1
0
3
0
0
2
2
1
1
0
2
0
0
0
1
2
0
2
2
1
1
0
0
0
0
1
0
2
0
1
1
2
0
1
0
0
1
3
0
0
0
0
0
1
0
0
2
0
1
0
0
2
1
0
0
1
0
0
0
1
1
1
1
0
1
0
2
0
0
0
0
0
1
0
0
0
3
4
0
0
2
2
0
2
0
0
1
0
0
1
2
2
2
1
0
1
1
1
0
0
0
2
1
1
1
0
1
1
0
0
3
1
0
1
2
1
2
0
0
0
0
0
0
0
0
0
1
1
0
2
2
0
0
1
2
0
0
1
1
1
0
1
0
0
1
0
1
0
0
1
2
1
2
1
0
2
1
1
2
1
3
2
0
1
2
2
0
0
0
2
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
2
3
0
0
1
1
0
0
1
0
0
3
0
2
1
1
0
1
1
0
0
1
1
0
0
0
1
0
0
1
0
0
0
2
2
0
1
2
1
0
1
1
2
0
0
1
0
2
0
2
1
0
1
0
1
1
0
1
2
0
1
0
0
2
1
0
0
1
1
0
1
1
0
0
2
0
0
0
1
1
0
2
1
1
0
0
1
2
1
0
2
0
0
1
1
1
1
0
0
0
1
0
1
1
1
0
0
0
0
0
1
2
2
1
1
0
0
0
0
1
1
1
1
2
2
1
1
10
2
0
0
0
2
0
1
1
1
0
1
0
2
2
1
2
2
3
0
1
1
0
0
1
0
1
1
2
0
0
0
2
1
1
0
2
0
0
0
0
0
1
2
1
0
0
1
1
0
0
1
2
1
0
0
0
0
1
1
0
1
0
1
1
2
0
1
1
0
2
0
0
1
2
2
1
1
0
3
1
1
0
1
0
1
0
2
0
0
0
3
0
1
2
0
2
0
1
0
0
0
0
1
1
0
3
2
0
1
2
0
1
2
2
0
1
0
0
0
0
0
1
0
1
2
2
2
2
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
1
2
2
1
1
1
1
0
2
1
0
2
1
0
1
0
0
0
2
0
0
1
0
0
1
0
1
1
1
0
0
0
1
0
0
0
1
0
1
1
1
0
0
1
1
1
2
0
0
0
0
1
0
1
0
0
0
2
0
1
1
0
0
1
1
2
0
2
2
1
0
1
0
1
1
0
0
2
2
2
0
1
0
2
2
0
0
1
0
1
0
1
1
1
0
0
1
0
1
0
1
1
2
1
0
2
1
0
0
1
1
1
1
2
1
0
1
1
0
1
0
2
0
2
0
1
0
1
0
3
1
0
0
1
1
1
0
0
2
1
1
1
0
0
0
0
1
0
0
1
2
1
1
1
0
1
1
2
0
0
1
2
0
0
2
0
0
2
1
2
0
1
1
0
0
0
2
0
2
1
0
0
1
1
0
0
0
2
1
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
2
0
1
0
1
0
0
0
0
2
1
0
1
0
1
1
0
0
0
1
2
1
1
1
0
1
1
2
2
0
2
1
1
1
0
1
2
1
1
1
0
1
1
0
0
1
1
0
0
0
1
1
0
1
0
0
1
2
1
1
2
0
0
2
2
0
1
0
0
1
0
2
1
0
1
0
0
0
0
1
1
1
2
0
2
2
0
0
0
1
2
0
0
1
1
2
0
2
0
1
0
2
2
1
1
0
0
0
0
1
2
0
0
0
1
1
2
0
1
1
0
0
1
0
0
1
1
0
0
1
0
0
1
2
1
2
1
0
1
2
0
0
0
1
1
0
1
0
1
1
0
1
0
0
0
0
2
0
1
0
0
0
0
1
1
0
2
0
2
1
0
2
2
0
0
1
1
2
0
0
1
0
0
1
0
0
1
0
1
2
1
0
0
1
0
2
2
2
0
1
0
0
0
0
1
0
0
5
1
1
1
0
0
0
2
0
1
0
0
4
1
0
2
0
3
0
0
1
1
0
2
0
2
1
0
2
1
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
2
0
0
2
1
2
2
0
1
1
1
0
2
1
1
1
0
0
1
2
0
0
1
1
0
1
0
0
1
0
1
1
1
0
0
1
0
2
2
1
0
1
1
1
0
2
1
1
0
1
0
2
0
2
0
2
2
0
0
0
0
0
1
1
0
2
0
3
0
1
0
2
2
2
0
0
0
0
0
1
0
2
2
1
0
2
1
1
0
1
1
2
1
0
0
0
1
0
1
1
1
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
1
0
1
0
0
2
1
0
0
1
2
1
1
2
0
1
1
0
0
0
2
0
1
0
3
0
1
1
1
0
2
1
0
1
1
1
0
0
0
0
2
0
1
0
0
0
1
0
0
1
0
1
0
1
1
1
1
1
2
1
2
0
2
0
0
1
0
1
1
1
3
0
0
1
1
0
1
0
1
1
1
1
2
2
0
2
0
0
2
2
2
1
1
0
0
0
0
1
0
1
1
0
2
1
0
1
0
0
1
2
2
2
1
0
0
1
2
1
0
0
2
3
2
0
1
1
2
0
2
1
1
2
1
0
0
1
0
1
2
1
1
0
2
0
1
0
0
0
0
2
0
2
0
1
2
0
0
0
0
1
0
0
2
1
0
2
1
0
1
1
2
0
2
1
0
0
0
0
1
1
2
1
1
0
1
0
1
0
0
0
1
2
2
1
1
1
1
0
2
1
0
3
1
0
2
1
1
1
1
0
0
0
1
1
0
1
0
2
1
2
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
2
1
0
0
0
1
0
0
1
1
1
2
0
1
0
0
1
1
0
0
1
1
0
0
2
0
1
0
1
1
1
0
0
1
0
0
1
1
0
2
1
0
1
3
1
0
0
2
0
2
0
0
0
1
0
1
0
2
1
0
0
2
1
0
2
1
1
1
0
0
2
2
0
0
2
0
0
0
0
2
1
0
1
0
0
0
0
0
2
1
1
0
0
1
0
1
0
1
0
1
1
1
0
1
1
0
0
2
0
1
0
1
0
0
1
0
0
0
2
1
1
1
1
0
3
0
1
0
0
1
2
1
0
0
1
1
1
1
0
0
2
1
2
0
0
1
3
1
0
1
0
1
0
0
1
3
1
0
0
1
0
1
1
2
2
0
1
2
0
0
0
0
0
0
2
1
1
1
0
2
0
0
2
0
2
0
1
0
2
0
2
1
0
2
0
2
0
1
1
1
2
0
1
2
2
0
1
0
0
0
2
1
2
2
0
1
0
1
1
0
2
0
0
1
0
2
1
0
2
2
2
1
0
0
0
1
3
1
0
0
0
2
0
1
1
2
0
1
0
1
1
0
0
1
2
0
1
1
0
0
0
2
0
1
1
1
0
0
2
1
1
1
0
0
0
1
0
1
0
1
0
1
1
0
0
1
1
0
1
0
1
1
1
0
0
0
2
0
0
1
2
2
0
0
1
0
1
1
1
1
1
2
1
2
1
0
2
1
1
0
0
0
1
0
1
0
1
2
0
1
0
0
1
1
1
0
1
0
0
1
0
0
1
0
2
1
0
0
1
0
1
0
1
1
0
0
2
2
0
0
0
0
1
0
1
0
1
1
0
0
1
2
1
0
1
0
1
1
0
1
0
0
0
0
0
1
0
2
0
1
0
0
1
1
1
3
2
1
0
2
0
0
1
0
0
2
1
0
0
0
0
3
2
1
1
0
0
0
1
1
1
0
2
1
1
2
0
1
1
0
1
2
1
0
0
2
0
0
2
0
1
0
0
1
0
1
2
0
0
1
0
2
2
0
0
0
1
2
1
1
1
0
0
0
0
2
1
1
0
2
0
0
0
2
0
0
1
1
1
1
1
1
0
2
0
1
1
0
0
1
0
2
3
2
0
1
0
0
0
0
1
0
0
0
0
2
0
0
1
1
1
1
1
2
0
1
1
0
2
2
2
1
0
1
0
0
1
1
0
2
1
2
1
1
1
1
0
1
0
1
0
2
4
2
2
2
0
2
1
1
2
3
2
0
2
0
3
2
3
2
0
1
2
0
0
2
1
0
2
1
0
1
2
0
0
0
2
0
0
0
1
1
0
1
0
2
1
0
2
1
0
2
1
0
1
2
1
0
0
1
0
1
0
0
1
1
1
0
2
0
0
1
0
0
1
1
2
2
2
0
2
0
0
0
0
2
1
0
1
2
0
0
0
0
2
0
0
1
2
1
1
0
1
0
0
0
1
1
0
1
0
0
2
2
0
0
0
1
2
1
0
1
2
0
1
2
0
0
4
1
0
0
2
0
1
1
1
1
1
2
0
1
1
1
3
0
0
1
2
0
0
0
0
0
2
0
1
2
0
2
1
0
2
0
1
0
1
2
0
0
2
0
1
0
0
0
0
1
0
2
1
0
1
1
0
0
1
1
1
1
1
0
2
0
1
1
2
0
2
1
1
2
2
2
0
0
0
0
1
1
1
1
2
1
1
2
0
0
2
0
1
2
0
1
1
0
0
0
0
2
1
0
1
0
0
1
0
1
4
1
2
2
2
2
0
0
2
2
0
1
0
1
2
1
0
1
1
0
1
3
1
0
0
0
1
2
1
0
2
0
1
2
2
1
0
1
0
2
0
0
1
1
1
2
0
2
1
1
0
2
1
0
0
2
2
0
1
0
1
2
1
1
0
2
0
1
1
2
1
1
0
2
1
3
1
1
2
2
0
0
2
1
1
0
2
1
0
1
1
1
1
1
0
2
0
0
2
0
0
0
1
0
3
0
2
0
0
2
2
0
0
0
2
1
0
0
1
1
0
1
1
1
2
1
2
0
0
0
1
2
1
1
1
0
2
0
2
0
1
0
0
0
0
0
0
0
1
1
2
1
0
0
1
2
2
0
1
0
2
0
0
1
2
0
0
2
0
0
0
0
1
2
0
0
1
2
2
2
0
0
0
0
0
1
3
2
1
2
2
1
1
2
1
1
0
2
0
0
1
2
0
1
0
1
1
1
0
0
1
0
0
0
0
2
0
1
1
0
2
0
2
0
0
0
0
1
1
0
0
0
1
2
2
1
0
0
1
0
1
1
0
1
0
2
0
0
1
1
0
0
2
0
0
2
2
2
0
2
2
2
0
1
0
1
1
0
2
0
1
1
6
1
2
0
2
0
1
1
1
2
1
0
0
0
0
2
2
2
2
1
1
1
1
2
0
1
1
2
1
0
2
0
1
1
0
2
0
0
1
0
2
3
0
1
1
2
1
0
2
1
1
2
1
1
2
0
0
0
1
0
0
0
2
1
1
2
0
2
1
2
0
0
0
0
2
0
1
2
1
0
2
0
0
1
0
0
0
0
1
2
0
1
2
1
2
0
1
0
0
1
1
2
1
0
0
0
2
0
2
0
0
0
1
0
0
1
0
2
0
2
0
1
2
1
0
2
2
1
0
0
1
1
1
0
0
0
0
0
1
0
0
0
1
2
1
0
0
1
0
2
1
2
1
1
0
0
1
0
1
3
0
1
1
0
0
2
0
2
2
0
0
1
1
1
1
0
1
0
4
1
1
1
0
0
2
1
1
0
1
1
1
1
0
0
0
2
0
1
0
2
0
1
0
2
0
0
2
0
2
0
1
1
0
2
2
0
2
0
1
2
1
2
1
2
1
0
1
2
0
1
0
2
1
2
0
0
1
0
2
0
1
1
0
0
0
2
2
1
1
0
0
1
1
1
2
0
0
0
2
0
2
0
0
0
1
2
0
1
2
2
0
1
0
0
1
0
0
6
0
0
0
1
0
0
1
0
0
2
0
0
1
0
1
1
2
2
2
0
0
1
1
0
1
0
0
0
2
2
1
1
0
0
0
0
0
0
0
1
1
1
1
1
1
1
2
2
1
0
0
1
2
0
1
2
2
1
1
0
0
0
0
2
1
2
1
0
0
0
0
0
2
0
1
1
1
1
0
2
0
0
1
1
0
0
2
0
0
1
0
0
1
2
1
0
1
2
0
0
1
0
1
1
0
1
0
0
0
0
1
1
2
0
1
0
1
1
2
1
2
1
1
0
0
2
0
2
1
0
2
0
0
1
0
1
2
1
0
1
2
1
2
0
1
0
2
0
0
0
0
2
0
1
0
2
0
2
0
1
1
0
0
0
0
1
1
1
1
1
0
0
1
1
0
0
1
2
1
0
0
1
0
0
1
0
0
0
2
1
1
1
1
0
0
0
1
2
0
2
0
0
1
0
2
2
1
0
2
0
1
2
0
1
0
1
2
1
2
0
1
1
0
0
0
1
0
0
1
1
2
0
1
2
2
0
1
3
0
2
1
2
1
0
0
0
1
0
2
0
0
0
0
0
0
1
2
1
1
0
0
1
0
2
0
0
2
0
0
2
0
0
2
1
0
2
0
1
2
1
1
0
2
1
1
0
0
1
1
0
0
2
2
0
1
0
1
2
0
0
1
1
0
2
1
0
2
0
1
2
0
2
4
2
0
2
2
0
0
1
2
0
2
2
1
2
1
1
1
2
0
1
0
0
2
0
2
0
0
1
1
0
1
1
0
1
0
0
2
0
0
1
1
1
1
0
1
1
0
1
1
0
1
2
2
2
0
2
1
0
0
0
1
0
1
1
1
0
1
2
2
0
1
1
0
1
0
1
0
0
0
1
0
0
1
0
0
1
1
0
0
0
2
2
0
0
0
0
0
0
0
2
1
2
2
1
0
0
0
0
2
0
1
0
2
1
1
0
0
1
0
0
0
2
0
0
2
2
2
0
1
1
1
0
2
0
1
2
2
0
2
0
0
0
1
0
7
0
0
0
2
1
2
1
2
2
0
0
0
1
0
2
1
0
1
1
0
0
1
3
0
1
0
0
1
1
0
2
0
2
0
1
1
0
0
1
0
1
0
2
1
2
3
0
2
1
0
0
2
2
0
0
0
2
0
1
0
0
0
1
2
0
1
0
1
2
1
0
1
0
1
0
0
1
0
2
0
2
0
0
1
0
1
1
0
0
1
1
2
0
3
0
1
1
0
1
0
2
2
2
1
0
2
0
0
2
0
0
2
1
0
0
2
1
2
1
1
1
0
2
0
1
0
0
1
0
1
0
0
1
0
2
1
0
1
1
1
1
0
1
2
0
0
2
1
0
1
2
0
0
1
0
0
0
0
0
0
2
2
1
0
0
1
0
1
0
2
2
1
3
0
2
1
0
2
0
0
0
0
1
1
0
0
1
2
0
1
0
0
0
1
0
2
0
0
1
1
1
2
0
2
1
0
2
0
2
0
1
2
2
1
0
1
0
0
1
1
2
0
7
0
1
0
0
1
2
1
0
0
2
0
0
2
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
1
0
2
0
1
1
1
1
2
1
2
0
2
0
2
0
2
1
1
0
0
0
0
2
2
0
0
0
0
1
1
1
1
0
1
0
1
0
1
1
2
1
0
0
1
2
0
1
0
2
2
2
0
0
1
2
0
1
2
0
1
0
0
0
0
1
1
2
2
0
2
0
1
0
1
2
0
0
1
2
2
0
1
2
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
2
1
1
2
1
0
2
0
0
1
1
0
0
2
0
0
0
2
0
1
2
1
1
1
0
1
1
0
1
0
0
0
2
1
0
2
0
0
1
1
0
2
2
3
1
3
1
0
1
1
0
0
0
2
0
0
1
2
0
1
1
1
0
0
1
0
0
0
0
1
0
2
0
1
0
2
0
0
0
1
0
0
0
1
1
1
2
0
1
0
1
1
0
0
0
0
2
1
0
0
0
0
0
1
1
0
0
1
0
1
0
3
0
2
0
1
0
2
0
0
1
1
1
0
1
0
3
0
0
0
1
1
2
0
0
0
0
1
1
2
2
0
1
0
0
0
1
0
2
0
0
2
0
2
0
1
0
3
0
1
1
0
0
1
1
0
2
1
1
0
1
0
0
2
1
2
2
0
1
0
2
1
0
1
0
0
0
3
1
2
0
1
1
0
0
1
2
1
1
3
0
0
0
1
4
2
1
1
2
4
0
0
2
1
1
0
0
0
0
0
0
2
2
2
1
0
1
1
2
0
1
2
0
0
1
1
1
2
0
1
0
0
0
0
2
0
2
0
0
1
1
0
0
1
2
0
0
0
2
0
0
1
1
2
1
0
1
0
1
3
1
2
1
0
0
2
2
0
2
2
1
0
1
1
0
1
0
0
3
0
0
1
1
2
0
0
1
2
2
2
0
0
0
0
1
1
0
2
1
1
2
0
3
1
1
0
2
0
2
0
2
0
0
1
0
0
0
2
2
3
2
0
0
2
0
0
1
0
1
0
0
0
1
0
1
1
1
1
1
0
0
1
0
1
2
0
0
0
0
0
1
0
0
1
1
1
0
2
1
0
2
1
1
1
2
2
0
1
0
0
0
2
0
0
1
0
1
0
0
0
0
1
1
0
2
0
1
1
0
0
2
0
1
2
0
0
0
0
0
1
0
1
1
0
2
0
0
2
2
0
2
1
0
3
1
0
0
0
1
1
0
1
0
1
2
2
0
0
0
2
0
1
1
0
0
0
2
0
0
1
0
1
1
0
1
0
0
1
1
1
0
3
0
1
0
0
0
2
0
0
1
1
0
2
0
2
0
1
1
1
0
2
1
2
1
0
1
2
2
0
3
1
0
1
2
0
0
0
1
2
1
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
1
0
1
1
0
0
0
0
0
2
1
0
0
0
0
0
0
1
2
0
0
0
1
1
2
0
1
1
2
1
1
0
1
1
1
0
1
2
0
1
0
0
1
1
0
2
0
0
0
2
1
1
0
0
0
2
1
1
0
2
2
0
0
0
0
2
0
0
1
0
1
0
2
2
1
0
0
2
1
2
2
2
0
0
0
0
1
0
0
2
0
0
1
1
0
0
0
0
2
0
1
2
1
0
0
0
0
1
2
0
1
1
0
2
0
0
0
1
1
0
1
2
1
0
2
1
0
2
1
0
0
0
0
2
1
0
0
0
2
1
0
0
0
0
1
2
1
0
2
0
0
0
1
2
0
0
3
0
2
1
2
2
0
2
2
0
1
0
1
0
2
1
1
0
0
1
0
1
0
0
0
2
1
1
2
1
0
0
0
2
1
0
0
1
2
1
0
0
2
1
1
0
2
0
0
0
1
0
0
1
2
1
1
1
0
1
2
0
2
2
1
0
0
0
1
0
0
0
1
2
1
0
0
1
1
0
0
0
2
2
2
3
0
2
0
1
0
1
1
0
0
1
0
1
2
1
2
2
1
1
0
0
2
0
1
1
0
0
1
0
0
3
0
1
0
2
0
2
0
1
1
1
1
1
2
1
0
2
2
1
0
0
2
0
0
0
0
0
1
0
1
1
1
0
0
1
1
2
0
0
0
0
1
2
1
1
1
1
0
0
0
2
0
2
1
0
1
1
0
0
0
1
1
0
1
1
0
0
2
2
0
2
1
1
1
0
0
1
0
0
0
3
1
1
0
0
1
2
0
1
0
2
1
1
2
0
0
2
0
0
0
0
2
0
0
1
1
0
2
0
1
1
0
0
1
1
0
1
1
1
1
1
1
0
2
2
0
0
0
1
0
0
0
1
0
0
2
0
0
1
1
1
0
2
0
0
2
0
2
0
1
0
1
0
0
1
1
0
2
0
1
0
1
0
2
0
0
2
0
0
2
1
0
1
0
0
2
2
0
0
2
1
1
2
0
0
1
1
0
0
1
1
1
2
2
2
0
0
0
0
1
0
0
0
1
2
3
1
1
0
0
1
0
1
0
0
2
1
2
0
0
1
0
1
1
1
0
0
2
0
0
2
1
0
1
1
0
2
0
0
0
2
2
1
2
0
0
1
0
0
3
0
2
1
0
0
1
2
1
0
2
1
2
0
0
0
0
0
1
2
0
1
2
2
0
0
0
2
0
0
1
0
1
0
0
1
3
1
2
0
1
0
0
2
2
2
2
2
1
1
0
0
0
0
0
2
2
2
1
1
1
0
0
0
3
2
1
1
1
1
0
0
0
0
2
0
1
1
1
0
1
1
1
1
0
0
1
0
1
0
1
1
1
1
2
2
0
1
2
0
0
0
2
0
0
1
0
0
0
2
1
0
1
0
1
1
2
2
0
2
1
1
1
2
0
1
1
0
0
0
0
6
0
2
0
0
1
1
1
1
1
1
2
1
0
0
2
2
0
0
0
0
0
0
1
1
2
0
1
2
0
2
2
0
2
1
0
2
1
1
2
0
1
3
0
2
1
0
2
1
0
0
0
1
2
2
2
1
0
1
2
0
0
1
0
1
0
2
0
0
1
1
0
2
1
2
1
0
1
2
2
0
1
2
0
1
0
0
0
2
0
1
0
0
1
1
0
1
0
1
0
0
0
2
0
2
0
1
2
0
0
1
3
1
1
0
1
2
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
2
4
0
0
2
0
1
0
0
0
1
0
1
0
2
1
1
0
0
1
0
2
2
2
1
2
0
0
1
0
0
1
0
2
0
0
2
1
0
0
2
1
0
0
1
1
0
1
1
2
1
0
0
0
1
1
0
0
3
1
0
0
2
0
0
1
2
0
0
0
0
1
1
2
0
1
0
1
0
0
0
0
1
1
0
1
0
0
0
2
0
0
1
1
1
2
1
0
2
0
0
1
0
0
1
0
1
2
0
0
4
0
0
2
1
1
1
0
0
1
4
1
0
0
2
1
0
0
1
0
0
1
0
0
0
1
1
0
1
2
1
1
1
0
1
0
1
1
2
2
0
1
2
1
0
0
0
0
2
1
0
1
0
0
2
1
0
1
0
2
0
0
0
1
0
2
1
0
0
3
2
2
0
0
2
0
2
2
1
2
1
0
0
1
0
2
1
1
0
0
1
0
0
1
2
2
1
2
2
1
1
2
0
1
0
2
1
0
2
2
0
0
1
0
1
0
1
0
2
0
0
1
0
0
2
0
0
1
0
2
1
2
1
0
0
1
1
1
1
2
0
0
0
0
1
1
0
2
2
0
0
0
0
2
0
1
0
1
0
0
0
1
1
0
1
0
0
0
0
2
0
0
1
0
0
1
0
0
1
0
1
1
0
1
2
0
1
2
1
2
0
0
0
1
0
2
0
1
1
1
0
0
2
1
0
0
0
1
2
2
1
1
0
0
2
2
0
0
0
2
0
1
1
0
1
2
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
2
0
0
1
1
1
1
0
2
1
1
0
0
0
2
1
2
2
1
0
0
0
2
2
0
2
1
6
2
1
2
1
0
1
0
0
1
0
2
1
0
0
1
1
0
1
1
0
2
1
0
0
2
0
1
0
1
1
0
0
0
0
0
0
1
1
0
1
0
3
0
1
1
0
2
0
0
1
1
0
1
0
1
0
2
0
2
1
0
1
1
1
0
0
0
2
0
1
2
2
2
0
0
1
0
1
1
1
2
1
0
2
0
0
1
0
0
2
1
2
0
0
1
0
0
2
0
0
1
2
0
0
0
1
0
2
0
0
4
2
2
1
0
0
2
0
0
2
0
2
0
0
0
3
1
2
1
1
0
0
1
1
1
0
0
0
2
1
0
1
2
1
0
2
2
0
0
2
1
0
2
0
1
1
2
2
1
2
2
0
1
1
0
0
0
0
2
1
0
0
1
2
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
3
1
1
1
0
0
0
3
0
0
0
0
0
1
0
1
1
0
0
0
1
0
1
1
2
0
1
0
3
1
0
2
1
1
2
1
2
0
0
1
0
2
4
0
0
1
2
2
1
0
0
1
2
2
0
1
0
2
2
1
0
0
1
0
1
0
1
0
0
0
0
0
0
3
0
0
2
1
0
0
2
1
2
1
1
2
0
1
1
1
1
0
0
2
0
0
0
0
0
2
0
2
0
1
0
1
0
1
2
1
1
1
1
2
0
0
0
0
1
1
1
0
0
0
1
1
0
1
1
0
2
1
0
1
1
1
1
0
0
1
2
0
2
2
1
0
0
1
2
2
0
1
0
0
1
0
1
1
0
2
2
1
0
0
0
0
1
0
3
2
0
2
0
1
0
1
2
0
0
0
1
2
0
2
2
0
1
1
1
2
0
0
1
0
1
0
2
2
2
1
0
2
3
1
1
1
1
0
0
2
3
0
1
0
2
0
0
0
0
1
1
1
1
1
2
2
0
0
1
0
0
0
1
1
2
1
1
0
1
1
0
1
2
2
0
0
1
1
1
1
0
0
0
1
1
0
1
1
0
1
2
1
0
0
0
1
0
0
0
2
0
1
1
1
0
0
0
3
0
2
1
1
0
2
2
1
2
0
1
0
0
1
0
1
1
1
2
1
1
2
0
5
0
0
2
1
0
1
0
2
0
1
0
1
2
2
0
0
0
2
1
0
1
1
0
1
1
1
0
0
2
1
1
1
2
1
2
0
2
2
1
1
1
1
2
2
1
2
2
0
3
1
0
1
1
1
2
0
1
0
0
2
2
0
0
2
0
1
1
1
1
0
0
0
2
2
0
1
1
2
0
2
1
0
0
0
2
0
2
1
0
0
0
1
0
0
1
0
1
2
1
2
0
0
0
1
2
2
0
2
0
0
0
0
0
0
0
2
1
0
0
1
1
2
2
1
1
1
0
1
0
1
0
1
1
0
1
0
0
1
0
1
0
2
1
1
0
0
1
1
1
0
2
0
1
1
0
0
0
0
2
1
2
0
1
1
0
0
0
0
1
2
2
2
0
2
0
1
2
2
0
2
1
0
2
0
2
0
1
1
1
0
1
2
0
0
1
0
2
2
1
0
1
1
1
1
1
2
2
0
1
0
1
0
0
0
0
2
1
1
0
0
0
1
0
0
0
2
0
1
1
0
0
1
0
0
2
0
2
2
1
0
2
2
1
2
0
1
2
1
4
1
0
0
1
1
0
1
2
1
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
2
1
0
1
0
1
1
2
0
1
0
0
0
0
2
2
0
2
1
0
0
0
1
0
0
1
3
3
0
1
0
0
1
0
1
0
2
2
0
1
1
3
0
2
0
0
2
1
1
1
0
0
0
2
0
0
0
0
1
1
2
1
0
1
2
0
1
0
0
0
0
0
1
1
0
2
0
0
2
0
1
0
0
1
1
1
0
1
1
1
1
2
0
1
1
0
1
1
0
0
0
0
1
1
0
2
1
0
2
0
0
1
0
1
0
3
2
1
2
1
0
0
0
1
1
0
2
1
0
2
0
4
8
2
1
2
0
1
1
0
0
2
1
0
3
1
0
1
0
0
0
0
1
1
0
1
2
0
2
1
0
1
2
0
1
1
0
1
2
2
0
0
2
0
1
1
2
1
0
0
0
1
0
1
3
1
2
1
1
1
2
0
1
1
2
0
1
2
0
1
1
0
1
2
1
0
2
1
0
0
1
1
1
0
0
0
1
0
2
1
1
2
0
1
0
2
0
2
0
1
0
4
0
0
2
2
1
0
1
2
1
0
1
0
0
0
1
0
1
0
0
0
0
0
1
2
0
0
0
0
1
0
1
0
0
1
0
2
2
2
0
1
0
0
1
2
1
1
0
2
2
2
1
1
2
0
0
2
2
1
1
0
1
2
0
1
0
2
2
0
1
2
3
1
0
1
0
1
2
2
0
0
0
0
0
0
1
1
2
1
1
0
1
1
2
0
0
1
0
2
2
0
0
2
0
0
0
2
2
1
1
0
0
1
2
0
0
0
2
0
0
1
1
0
2
1
0
1
3
0
2
0
1
0
0
2
2
0
0
0
0
0
0
0
1
1
0
0
1
0
0
2
2
1
2
1
1
1
0
2
0
0
5
1
1
0
0
0
0
0
1
2
1
1
0
3
0
1
0
2
4
1
2
0
0
1
2
0
0
1
0
0
0
2
0
0
1
0
1
1
1
2
2
2
1
1
1
0
1
0
0
0
0
1
2
0
1
1
0
1
1
2
1
1
0
1
1
2
0
1
1
1
1
1
1
2
0
0
3
1
2
0
2
2
1
1
0
2
2
2
0
0
0
0
0
1
1
1
0
0
2
0
0
0
1
0
0
1
0
1
2
1
1
0
1
0
0
0
0
0
1
0
1
0
0
0
2
1
0
0
0
0
0
0
2
2
0
1
1
0
0
1
1
1
2
1
1
0
3
0
1
2
1
2
1
1
1
0
2
2
0
0
2
0
1
0
1
1
0
2
0
2
2
2
1
0
0
2
0
2
1
1
0
0
1
2
0
0
2
1
1
0
1
0
0
1
0
2
0
0
1
0
1
2
0
1
0
0
2
0
2
0
0
1
1
0
0
2
8
0
1
1
1
1
0
0
0
0
2
0
0
0
2
0
2
1
1
0
0
5
2
3
0
0
5
2
2
2
0
0
0
0
1
0
0
1
0
0
0
1
1
0
2
0
0
2
2
0
1
2
0
1
1
0
0
1
2
2
2
0
0
0
0
0
1
1
0
2
0
0
0
2
0
0
0
0
1
2
1
0
1
1
0
2
1
2
1
0
0
1
0
1
0
0
0
1
0
0
0
2
1
0
0
0
0
0
2
0
1
1
0
1
1
0
2
0
3
2
0
0
0
2
1
0
1
2
1
1
0
1
2
2
0
1
2
1
0
2
0
2
0
1
0
2
1
1
1
0
2
0
1
1
1
0
1
0
2
1
2
1
0
2
4
1
0
6
1
0
0
2
2
1
1
0
0
0
1
0
0
0
0
0
2
2
1
0
0
1
2
3
0
2
0
0
2
0
0
1
2
0
0
0
0
1
1
0
0
0
0
1
0
2
0
1
1
1
1
1
1
0
1
1
1
3
1
0
0
2
1
1
0
0
2
0
2
1
1
1
0
2
1
2
1
1
0
0
2
2
0
1
0
0
0
0
0
2
0
3
0
0
2
1
0
1
1
2
1
2
0
2
0
0
1
0
0
1
0
0
1
1
2
1
0
1
2
1
1
0
2
0
1
0
0
0
0
0
0
2
0
2
0
0
0
2
2
1
1
2
2
0
0
1
2
1
1
1
2
0
2
1
1
0
3
1
3
1
1
0
1
0
1
1
2
0
0
1
1
0
1
0
0
1
0
0
0
2
1
0
1
1
2
0
1
1
0
1
2
1
2
1
0
9
0
0
1
0
0
2
1
1
1
0
1
1
1
0
0
1
0
0
1
0
1
0
1
2
2
2
0
0
2
0
2
1
0
0
0
0
0
1
1
1
0
2
0
2
2
1
1
0
2
0
1
2
0
1
1
1
0
2
1
1
0
0
2
1
0
1
1
1
0
1
0
0
0
0
0
1
0
0
0
2
1
0
0
0
1
0
2
2
2
2
2
2
0
2
1
0
0
2
0
2
0
0
1
1
0
1
0
0
0
1
0
1
2
2
1
1
1
0
0
1
1
1
0
2
2
0
2
0
0
0
2
2
2
1
2
1
0
1
2
3
0
0
0
1
0
0
0
2
0
0
1
2
0
1
2
0
1
1
1
0
1
1
1
0
2
2
2
2
0
2
2
0
1
3
2
0
0
2
1
1
0
0
2
1
0
0
2
1
0
0
1
0
0
1
2
0
0
0
2
1
0
0
1
2
0
2
0
2
0
1
0
2
2
0
1
1
1
2
1
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
2
1
0
2
0
1
1
1
1
2
1
2
0
0
1
2
2
2
1
1
0
1
1
1
1
1
0
1
1
0
1
1
1
1
0
1
1
0
0
0
0
1
0
1
1
0
1
0
1
1
1
0
0
0
2
1
2
0
0
2
0
2
2
0
1
2
4
1
2
2
0
1
0
0
1
0
2
1
1
0
2
1
0
0
2
1
0
2
0
1
1
0
1
2
1
0
1
0
1
0
2
1
2
0
7
0
1
2
2
0
0
2
1
1
0
0
2
0
0
1
0
0
1
1
1
4
0
0
2
0
2
2
2
0
0
0
1
0
3
0
1
1
0
0
1
3
2
0
0
0
2
0
0
0
1
1
2
0
0
1
0
2
1
0
2
2
2
0
0
2
0
2
2
2
7
0
1
2
0
0
0
0
1
0
0
1
2
0
2
1
1
1
2
1
0
0
0
0
2
0
0
1
2
2
1
1
0
1
1
0
2
1
1
1
2
0
2
0
0
0
1
1
1
0
0
0
1
0
3
1
2
0
0
1
1
0
0
0
2
2
0
0
1
2
1
2
0
1
2
1
1
1
1
1
0
0
5
1
0
0
2
0
2
0
0
2
0
1
1
1
0
1
1
2
1
4
0
2
1
0
0
1
1
1
0
1
1
1
1
1
0
0
2
0
1
0
1
0
0
0
1
2
0
2
0
0
1
0
1
0
0
1
0
0
0
2
0
0
1
0
0
0
0
1
2
1
0
1
2
1
0
0
0
0
1
0
2
1
3
2
0
1
1
0
0
3
2
2
0
1
0
1
0
1
2
1
1
3
0
0
1
2
1
0
3
0
0
2
0
0
2
0
2
2
1
0
1
1
1
2
2
0
1
0
0
1
0
0
2
0
0
1
1
1
0
2
0
0
2
0
0
0
2
2
1
1
2
0
2
2
1
2
1
0
2
0
1
1
1
1
1
2
0
0
0
2
2
1
2
0
2
1
1
0
0
0
0
4
2
0
2
0
1
2
1
2
1
0
1
0
2
2
2
1
1
1
0
1
1
0
0
0
1
0
1
0
0
0
1
0
0
2
1
0
0
0
1
2
1
0
2
0
0
2
2
0
0
1
1
1
0
2
1
1
0
2
0
0
0
1
2
1
1
1
1
2
1
0
3
2
1
1
0
1
1
0
2
3
0
0
1
1
1
3
0
0
1
1
0
0
2
3
1
2
1
0
1
0
1
0
0
1
0
0
2
1
2
0
1
1
0
0
2
0
0
0
2
0
2
0
1
1
0
1
1
0
0
2
1
1
2
2
1
2
1
0
0
1
2
0
0
0
0
2
0
0
1
0
2
1
0
1
2
1
0
2
2
2
1
0
1
0
0
1
0
2
2
2
0
0
1
3
2
1
1
0
1
1
1
1
0
1
1
2
2
2
0
0
2
0
1
1
2
0
1
1
0
0
2
2
2
5
1
0
1
0
1
0
1
2
1
1
0
0
0
0
1
0
0
0
2
2
1
0
1
2
0
0
2
1
0
0
0
1
0
0
2
2
0
0
1
1
0
2
1
0
0
2
2
2
0
1
1
1
1
2
0
0
0
0
0
0
0
1
1
0
2
0
1
1
0
0
0
0
1
0
0
1
2
1
2
0
2
1
1
0
0
1
1
0
0
0
1
1
1
2
0
0
0
1
1
2
1
1
0
1
1
0
1
1
1
1
0
0
0
1
1
0
0
1
1
2
2
1
0
5
0
1
1
1
0
1
0
0
2
0
0
1
0
0
1
0
0
0
0
1
2
2
1
2
0
1
0
0
2
1
0
1
1
0
2
0
1
2
1
0
1
2
1
0
1
0
2
2
0
2
0
3
1
1
1
1
0
1
2
1
0
0
0
0
1
0
1
1
0
0
0
2
2
1
2
1
0
2
0
0
0
0
0
0
2
2
2
2
0
0
2
0
2
0
0
3
0
2
1
1
1
0
2
0
2
0
1
2
1
0
1
1
1
0
1
0
0
0
1
1
0
0
0
1
0
0
1
2
2
0
0
1
1
1
1
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
2
0
0
1
1
0
1
0
1
0
0
2
0
2
1
2
1
1
0
0
1
0
1
1
2
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
1
1
1
2
2
0
2
0
1
0
0
0
2
0
0
0
0
2
2
1
0
0
2
0
1
2
1
0
0
0
0
0
1
1
0
0
0
1
1
1
0
0
1
2
0
2
3
0
1
0
0
2
0
0
0
2
0
1
2
2
1
0
2
0
0
0
0
0
0
0
0
2
1
0
1
0
1
0
0
1
0
0
0
2
0
0
1
1
0
0
1
1
0
0
1
0
1
1
2
1
2
0
1
0
0
1
1
0
0
0
2
2
0
1
0
0
2
2
0
1
0
0
0
2
5
2
2
2
0
0
0
0
1
0
0
1
0
0
0
0
1
0
2
1
1
0
0
1
1
1
0
2
0
1
1
0
2
2
1
2
2
0
2
0
2
2
1
2
1
0
0
0
2
1
1
0
1
0
1
0
2
2
2
1
0
1
1
2
0
0
0
2
1
1
1
1
1
2
1
1
1
2
2
0
0
0
1
0
2
0
1
0
0
0
1
0
0
1
1
0
0
1
2
0
1
0
0
0
0
2
1
0
0
0
2
1
1
0
0
1
0
1
0
2
0
0
3
0
0
0
2
0
0
2
0
0
0
1
1
0
0
2
0
2
1
2
0
2
0
0
0
0
1
2
0
1
0
1
0
1
1
0
0
0
2
2
0
1
0
2
0
0
0
0
2
2
2
2
0
2
2
0
1
1
2
1
2
2
1
0
1
1
1
1
1
1
1
0
2
0
0
0
0
2
0
0
1
4
2
1
0
1
1
1
2
2
2
1
1
1
0
1
1
3
1
0
2
0
2
1
0
1
3
0
1
2
0
2
0
1
0
2
0
0
0
0
1
3
1
0
2
2
1
1
2
0
0
1
0
2
2
2
1
2
0
1
0
0
1
2
1
0
0
0
2
1
1
2
1
1
1
1
0
0
0
0
0
1
1
0
1
1
1
1
2
0
1
1
0
1
1
0
1
1
0
2
1
1
1
2
0
1
1
1
0
0
0
2
2
0
0
1
1
0
1
1
0
1
0
0
2
0
2
2
1
0
2
0
2
1
0
1
3
0
2
1
2
1
1
0
0
0
0
0
1
2
0
1
1
1
3
0
1
0
2
1
1
0
0
1
0
1
0
1
1
0
1
2
2
1
0
2
0
3
1
1
2
2
0
1
2
3
0
0
1
1
0
2
1
1
0
1
0
1
2
1
0
2
1
1
3
0
1
2
0
2
0
1
0
1
1
0
0
1
2
2
2
1
0
0
0
0
0
1
0
1
2
0
0
1
0
2
1
0
0
1
1
0
0
1
0
0
1
2
0
0
0
0
0
1
0
2
2
0
0
0
0
2
1
1
1
1
1
1
0
2
1
1
0
0
0
0
0
2
0
3
0
0
1
1
1
0
2
0
0
1
1
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
1
0
1
0
0
2
0
2
0
1
1
1
2
2
0
0
0
2
3
1
0
0
0
0
1
0
1
2
1
2
2
1
0
2
1
2
2
2
2
0
1
0
1
1
0
0
1
2
2
0
0
2
0
0
1
1
0
0
0
0
2
0
1
1
1
0
0
3
1
0
0
0
1
2
2
0
1
1
0
1
1
0
1
0
0
1
2
0
1
0
2
1
0
0
0
0
2
1
1
1
2
0
2
0
0
1
0
0
0
0
0
0
2
2
0
1
2
0
0
1
2
2
0
1
1
0
0
1
0
0
0
0
2
0
0
1
1
2
1
2
0
0
1
0
0
0
0
2
2
1
1
0
0
0
0
2
1
0
2
0
0
0
2
2
0
1
2
1
1
0
0
0
0
3
1
0
2
0
1
0
0
1
0
1
1
0
0
0
1
2
1
1
2
0
1
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
1
0
1
2
1
0
3
1
0
0
0
0
1
1
2
0
2
3
0
2
1
2
2
1
0
1
0
3
2
1
0
0
0
0
0
1
1
1
0
1
1
0
1
1
0
1
0
0
1
2
2
0
2
1
0
0
0
0
2
2
0
1
2
0
0
0
0
0
1
0
0
2
1
1
0
0
1
0
1
0
1
1
2
0
1
2
1
1
1
2
2
1
0
1
0
1
1
1
2
0
2
1
0
1
1
0
0
2
1
0
0
2
1
1
2
0
3
1
1
0
0
3
0
2
1
0
2
1
0
1
1
0
0
1
0
1
1
0
1
2
1
0
1
0
0
2
0
0
0
1
0
0
0
1
2
0
2
0
1
2
3
0
0
0
2
0
1
3
0
2
0
0
2
0
1
2
0
0
1
0
1
0
1
0
1
0
0
0
1
0
1
2
0
1
2
2
0
0
2
0
0
1
0
0
2
0
2
1
2
2
1
0
2
0
0
0
1
2
1
1
0
0
1
0
0
1
3
2
1
2
0
0
1
1
1
0
0
0
1
1
0
0
0
0
1
2
0
2
0
1
3
0
1
2
1
0
0
0
1
2
1
1
0
1
0
0
0
1
0
4
2
2
2
2
1
2
0
2
2
2
0
0
2
0
0
0
2
0
1
2
0
0
0
2
2
0
0
0
4
0
1
0
2
0
1
2
1
0
1
1
1
0
0
1
3
0
0
0
2
2
1
2
1
1
1
0
0
2
1
2
2
0
0
1
0
2
1
0
0
1
1
1
0
0
8
0
2
1
0
0
0
1
1
1
0
0
0
1
0
0
0
1
2
0
0
2
0
1
0
0
0
0
0
0
0
1
2
0
0
2
1
1
0
1
0
0
0
0
0
1
1
0
2
2
2
1
1
1
0
1
0
0
2
1
0
2
2
0
0
1
0
1
1
0
1
0
0
0
2
0
1
0
1
1
2
2
0
3
1
0
2
0
0
0
0
2
2
0
1
0
1
2
2
2
2
1
0
1
0
1
0
1
1
1
0
1
2
0
0
1
1
3
2
0
1
2
0
0
0
3
0
0
2
0
0
2
2
2
1
0
1
1
2
0
2
0
1
2
0
1
4
0
2
0
1
2
1
1
1
2
1
0
0
0
0
1
1
0
0
2
0
0
1
0
0
0
2
1
1
1
1
1
2
0
0
1
1
0
1
0
1
0
0
0
1
0
1
0
0
0
0
1
0
2
1
0
2
3
1
2
2
0
4
0
0
0
1
0
0
1
0
2
2
0
0
2
0
1
1
0
1
0
0
2
1
0
1
0
2
0
0
2
0
0
1
1
0
1
2
0
1
1
2
0
2
0
1
8
1
1
2
0
0
0
1
2
0
0
2
0
2
2
0
1
0
2
1
2
2
3
0
0
0
1
1
1
0
0
1
1
2
2
0
1
0
1
0
0
2
0
2
0
0
0
2
1
0
1
0
1
0
1
0
1
1
3
1
0
1
1
0
0
1
2
0
1
0
2
1
0
2
1
2
2
0
1
0
0
2
0
1
1
2
2
1
2
0
0
1
1
0
0
0
0
0
1
0
1
1
0
2
0
2
0
1
0
1
2
0
1
0
0
1
1
2
1
1
1
0
0
2
0
0
0
1
0
1
1
1
0
0
2
3
1
3
2
0
0
2
0
1
0
1
0
0
1
0
2
1
1
1
0
0
0
2
1
1
5
1
1
1
0
1
1
1
0
2
1
0
1
0
0
0
1
0
0
0
1
1
1
0
1
0
1
1
0
0
0
1
2
0
1
0
3
2
1
0
0
1
2
0
1
1
2
1
2
2
0
0
0
1
1
1
1
2
2
0
1
0
0
3
0
0
1
2
2
0
1
1
0
2
0
0
0
0
1
1
2
2
1
2
0
0
1
2
1
0
2
1
0
0
0
2
0
0
1
2
2
1
2
0
0
0
0
0
0
2
0
0
1
0
0
0
2
2
2
1
2
1
1
2
2
1
2
0
2
1
0
0
1
1
0
1
1
0
0
1
2
1
0
0
0
1
2
1
0
2
0
0
1
0
1
0
0
1
2
1
1
0
0
0
0
1
2
2
2
0
2
1
1
0
0
1
0
0
0
2
2
2
0
0
0
0
2
2
1
0
1
2
1
0
1
1
1
1
1
0
1
1
0
2
4
0
0
0
1
1
1
1
1
0
0
0
1
2
2
1
1
0
1
0
6
2
2
1
0
1
2
2
0
0
0
2
2
2
0
1
0
2
0
0
1
2
2
1
0
2
1
0
1
0
1
0
0
0
0
1
0
0
2
0
1
2
0
1
0
1
1
0
0
2
2
2
2
2
1
0
0
0
1
1
0
0
1
2
0
0
1
2
0
0
0
1
0
2
1
0
0
2
2
2
0
2
1
2
0
0
0
2
2
1
2
2
0
0
0
0
2
2
1
0
0
0
0
2
0
0
1
0
1
0
1
2
1
0
0
1
2
0
1
0
1
1
0
2
1
1
1
0
1
0
0
0
1
1
1
2
0
1
0
0
1
1
0
2
1
1
2
1
0
1
1
0
1
1
0
1
2
0
0
1
0
0
2
0
0
0
0
1
1
0
1
1
1
2
0
0
1
0
0
0
1
0
2
0
2
1
1
1
1
2
1
0
1
0
2
0
1
0
0
2
0
2
0
0
0
1
1
1
1
1
0
0
1
0
3
1
0
1
0
1
0
0
1
2
0
0
1
0
1
1
1
0
1
0
0
2
1
1
1
0
2
0
2
0
1
0
0
0
0
0
0
0
1
1
2
1
0
1
2
1
1
2
1
0
1
1
2
0
1
1
0
0
2
1
0
0
0
0
1
0
0
1
1
0
0
0
1
0
1
2
0
0
0
1
1
1
2
1
1
0
0
1
1
0
1
1
1
1
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
1
1
0
1
1
0
0
0
0
2
1
0
2
1
0
0
1
0
0
1
2
2
2
2
1
0
2
1
0
0
2
1
1
0
0
1
1
2
1
1
0
0
0
0
0
1
0
2
1
2
0
0
0
0
2
0
2
0
8
0
2
0
2
1
2
1
1
0
0
0
2
0
1
1
0
0
1
0
1
0
0
0
2
0
2
1
0
2
2
1
1
0
0
1
1
2
0
0
2
1
2
0
2
0
1
0
1
2
1
1
2
1
1
1
0
0
1
2
2
1
2
2
1
1
1
2
0
0
0
0
1
1
2
0
2
1
2
1
1
2
1
1
2
0
1
0
4
0
1
1
1
1
0
0
2
1
2
2
1
1
2
0
0
1
0
2
0
0
2
2
0
0
1
2
0
0
0
0
1
1
2
2
0
1
0
0
0
0
2
0
1
0
2
1
0
0
0
2
1
1
1
1
0
1
1
0
1
2
1
0
0
0
0
0
0
2
1
0
2
0
0
1
0
2
0
1
1
1
2
1
3
0
0
2
0
2
1
0
0
0
1
1
0
2
1
1
2
1
0
0
1
0
2
0
0
2
0
0
0
2
2
2
2
0
0
1
0
1
0
1
2
1
0
2
2
0
0
1
2
3
0
0
0
2
1
2
1
0
0
1
0
0
0
2
2
0
1
0
2
0
0
2
1
0
0
1
0
1
2
0
0
2
2
0
0
0
1
0
0
2
1
1
1
1
1
2
2
0
0
0
1
2
0
1
1
1
1
2
2
1
0
2
0
1
1
2
1
1
0
1
1
1
1
0
0
1
0
0
0
2
2
0
1
0
0
1
1
1
0
0
0
1
1
0
2
0
0
2
1
1
0
1
0
2
0
0
2
0
0
0
0
1
0
1
0
1
1
0
0
0
2
0
0
0
0
0
2
1
0
1
1
0
2
0
0
0
2
1
1
0
0
1
3
0
1
0
1
1
0
1
1
0
1
0
0
0
1
2
1
1
0
1
0
1
0
1
1
0
1
0
2
0
0
1
2
0
0
0
2
0
0
0
0
1
1
2
1
0
1
3
2
2
2
0
2
0
0
0
2
0
1
2
1
0
3
0
0
2
0
0
0
2
2
1
0
1
3
2
1
1
0
0
0
0
2
0
1
2
1
2
2
1
0
1
1
1
0
1
1
0
0
0
0
0
2
1
0
0
0
1
2
0
0
0
0
0
0
1
1
1
1
2
1
1
1
0
1
1
1
0
0
0
1
2
2
0
2
0
1
1
0
0
1
2
1
0
0
1
1
0
2
0
0
0
1
1
0
0
1
0
2
0
0
0
1
0
0
0
2
0
0
0
3
1
0
1
1
0
0
0
2
2
2
0
0
1
2
1
2
0
8
1
1
1
0
1
0
0
0
1
1
0
0
0
0
1
0
1
2
1
0
1
0
0
1
1
0
1
2
1
2
0
0
1
1
2
1
0
0
1
2
1
0
1
0
2
1
0
1
0
1
2
0
0
0
1
0
1
0
1
2
0
0
1
0
0
0
1
2
1
0
0
2
1
1
2
0
0
2
0
2
0
0
0
0
1
1
0
2
0
0
1
1
0
1
2
1
0
1
1
0
0
0
1
2
0
1
0
0
1
0
1
3
0
2
0
1
0
0
2
0
1
1
1
0
0
0
1
1
0
1
0
2
1
2
0
0
1
0
2
0
0
0
0
1
0
1
2
2
0
0
2
2
1
0
2
0
2
1
0
1
0
0
1
0
2
1
1
0
0
1
1
2
2
1
0
1
2
0
0
3
1
1
0
1
1
0
0
1
0
2
0
2
0
2
2
2
1
1
0
0
0
2
0
1
2
2
0
0
0
3
0
0
2
0
1
0
0
1
2
0
1
1
0
0
2
0
1
0
0
1
1
0
1
1
1
0
0
0
0
0
1
0
0
1
1
3
1
0
0
2
1
2
1
0
1
2
4
0
0
1
0
1
1
0
0
0
2
2
2
3
1
1
0
2
0
0
1
0
3
0
0
1
0
0
0
4
2
1
0
0
0
2
2
2
0
0
0
1
0
0
0
0
0
0
2
2
0
1
0
0
0
0
1
1
0
1
0
1
1
1
0
1
1
1
1
0
0
0
0
0
0
1
1
0
0
0
2
0
1
1
0
1
1
0
2
2
0
2
1
1
1
1
0
2
2
0
2
2
0
1
1
1
0
2
0
0
0
0
0
2
2
0
0
0
1
0
1
0
1
0
0
0
0
0
2
0
0
0
2
1
0
1
1
0
0
2
0
0
1
0
1
2
1
0
0
0
2
0
0
0
1
2
1
0
0
0
0
1
2
1
2
1
1
1
0
1
0
0
0
2
2
1
0
1
0
1
0
1
1
0
2
0
0
0
0
0
1
0
1
1
2
0
2
1
0
0
0
1
0
0
1
1
2
1
0
0
1
2
1
2
1
1
0
0
0
0
0
2
1
0
0
1
0
0
1
0
0
2
0
1
0
0
1
0
0
1
0
0
0
1
2
1
1
0
0
2
0
1
2
2
1
1
1
0
2
1
2
0
2
1
1
0
0
0
0
2
3
0
0
0
1
0
0
2
1
1
1
3
0
1
1
2
0
0
1
0
0
1
0
1
2
1
1
0
1
2
1
2
0
0
1
0
1
0
1
0
0
2
2
1
0
1
2
1
1
1
0
0
2
0
1
1
0
2
0
1
1
0
0
2
0
0
1
1
0
0
1
1
0
2
1
1
0
0
2
0
0
1
1
2
1
1
1
2
2
0
0
1
1
1
0
0
2
0
0
2
1
1
0
0
1
0
2
1
1
0
2
1
0
2
1
2
2
0
1
0
0
0
4
3
1
0
0
0
1
1
2
0
1
0
0
1
2
1
0
0
0
0
1
2
0
0
3
0
1
0
2
1
1
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
1
1
0
1
0
0
1
2
1
3
2
0
2
2
0
1
1
1
0
1
0
1
1
1
0
1
1
2
1
0
1
0
2
0
1
1
0
0
1
0
1
0
0
0
1
2
0
1
1
2
2
0
0
0
2
0
2
1
0
0
2
1
1
0
0
1
1
1
1
3
0
1
1
0
2
2
1
1
2
0
2
1
0
1
0
2
0
1
1
2
0
0
0
1
0
1
2
0
0
2
0
1
1
1
0
0
0
1
3
2
1
0
2
1
0
0
1
2
1
0
2
0
0
0
1
1
0
0
3
1
2
0
0
2
2
1
0
2
0
1
1
1
2
0
0
0
2
0
0
0
1
2
2
2
0
0
2
2
1
2
0
1
0
0
2
1
1
2
1
1
1
0
2
2
0
0
0
0
1
1
2
0
0
0
0
1
0
1
0
0
1
0
1
0
1
0
0
2
0
2
2
0
1
0
1
0
1
0
1
2
1
2
2
1
1
1
2
0
0
0
0
1
0
1
0
0
0
3
2
1
0
1
0
0
0
0
2
1
0
1
1
2
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
2
0
1
2
1
1
1
2
0
1
0
0
0
2
2
1
1
1
0
0
0
0
2
4
0
0
1
2
2
2
0
1
1
0
1
1
1
2
1
0
0
0
1
1
1
4
1
0
2
0
1
0
1
0
0
1
2
0
1
0
1
1
2
1
0
0
2
1
1
0
0
0
0
2
2
1
0
0
0
2
1
1
0
3
0
0
0
0
3
2
1
1
0
1
1
2
0
2
0
0
0
0
1
1
0
1
0
0
1
1
1
0
0
1
1
2
0
0
2
0
0
3
1
0
1
2
0
1
1
0
0
0
0
1
2
2
1
1
3
0
0
1
0
2
2
0
1
2
1
1
0
0
2
0
1
0
0
0
1
2
0
2
0
0
2
0
0
2
1
1
0
1
1
0
1
0
1
1
0
2
0
1
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
1
1
1
0
2
1
3
0
2
0
2
0
2
0
2
0
1
1
0
1
0
2
1
2
0
0
1
0
0
1
1
2
2
2
0
2
0
1
0
2
1
0
1
1
0
2
0
0
0
2
1
0
2
1
1
1
0
0
0
0
0
0
1
0
2
1
1
0
0
0
2
1
2
2
2
0
2
0
2
2
1
0
0
1
1
1
2
0
0
0
0
2
0
2
2
0
1
0
0
0
0
0
1
0
0
0
0
2
1
2
1
1
0
2
0
0
1
2
1
0
0
2
1
0
1
0
0
0
0
0
0
2
0
0
0
1
1
1
1
2
2
0
1
0
2
0
1
0
2
0
1
1
1
1
0
0
0
1
1
0
0
2
0
1
1
1
2
0
1
0
0
1
0
2
0
1
2
1
0
0
0
1
1
1
1
0
0
0
1
2
1
1
1
0
2
1
0
2
1
0
1
1
0
1
2
0
1
2
1
1
0
0
1
1
1
0
0
0
0
0
1
0
1
0
0
0
1
1
1
0
1
0
0
1
1
0
0
0
1
1
0
0
1
2
1
0
0
0
1
0
0
0
2
0
0
2
1
1
2
0
2
2
1
1
2
2
2
0
2
1
0
2
0
1
0
1
1
1
0
0
1
1
1
1
0
0
0
2
0
2
1
1
1
0
1
0
1
2
0
3
1
1
0
0
1
0
1
0
0
0
0
2
1
4
0
0
0
1
0
2
2
0
0
2
1
1
1
0
0
2
0
0
2
2
0
0
0
2
0
0
1
1
2
1
1
0
0
0
0
3
0
2
0
2
1
0
1
1
0
1
0
2
0
2
1
0
0
2
1
0
0
0
2
1
0
0
0
0
1
1
1
0
1
0
2
0
2
0
0
3
1
0
0
1
1
0
0
1
1
1
2
0
0
0
0
2
1
2
0
1
0
0
1
2
2
0
0
0
1
1
0
1
1
0
0
2
0
0
0
1
0
0
1
0
0
2
0
1
0
0
0
0
0
1
1
3
0
0
0
2
0
0
1
1
2
0
2
2
2
0
2
1
0
1
1
0
0
2
0
1
1
2
0
1
0
3
1
2
0
1
2
1
2
0
0
0
0
1
0
0
0
2
1
1
1
0
1
1
1
2
1
0
0
1
0
1
1
0
0
0
2
0
2
1
0
1
0
0
0
0
1
0
0
0
0
1
1
0
2
2
1
1
0
0
0
1
0
1
1
1
2
1
2
1
2
0
1
1
0
1
0
0
1
2
0
0
2
2
1
0
1
2
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
2
0
1
2
0
1
2
2
1
2
1
0
0
0
0
2
2
0
0
2
1
1
2
0
1
0
0
0
2
1
2
0
1
0
0
0
0
0
1
0
1
1
2
1
1
0
2
0
1
2
2
2
0
0
0
1
0
0
2
2
2
1
0
0
3
1
0
2
2
2
1
0
2
0
1
2
1
0
0
0
0
0
0
3
1
0
1
1
1
2
0
1
1
0
0
0
0
2
1
2
0
1
1
0
1
0
0
0
1
0
0
2
2
0
1
3
0
1
0
1
0
2
0
0
0
0
0
0
0
0
1
0
4
0
2
0
0
1
1
2
0
1
0
1
1
1
1
1
0
2
0
1
0
1
1
2
0
2
0
0
0
1
0
1
0
1
1
1
0
1
2
0
2
1
0
2
1
0
0
0
3
0
1
2
1
1
1
1
1
0
3
1
1
0
1
0
2
2
0
1
1
1
2
2
2
1
1
0
0
1
1
0
0
2
1
0
1
1
1
0
0
1
1
1
1
1
2
2
1
2
0
2
0
0
0
1
2
0
1
2
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
1
2
1
1
1
1
0
2
0
0
0
2
0
1
2
0
1
0
2
1
0
0
1
1
1
1
0
1
0
0
1
0
1
0
1
2
0
0
0
1
0
1
2
1
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
1
2
0
1
0
0
2
2
0
2
0
0
1
1
0
0
1
3
1
0
2
0
1
0
0
0
1
2
1
0
0
2
0
0
0
2
1
0
2
0
2
0
0
0
0
1
0
3
1
1
1
0
0
2
0
1
0
2
1
1
2
0
0
3
1
2
0
2
0
0
0
2
1
0
1
0
1
1
1
0
0
0
0
0
1
1
2
0
0
0
1
1
4
2
0
2
0
0
1
1
2
1
1
1
0
2
2
1
1
1
0
1
0
0
1
1
2
0
1
1
0
0
2
0
0
1
0
1
0
0
0
0
0
1
1
0
0
1
3
0
2
2
2
1
1
0
2
0
0
1
2
0
1
1
0
1
1
1
0
2
0
1
0
1
0
0
0
1
0
1
2
3
2
0
1
2
2
0
0
0
0
0
0
2
1
1
0
1
1
0
2
1
1
1
0
1
2
0
2
0
1
1
0
1
0
0
1
2
1
2
0
0
1
2
2
0
0
0
0
0
0
0
0
2
1
0
0
2
2
0
1
0
2
2
0
1
1
1
1
0
1
1
1
0
0
1
1
0
1
0
1
1
0
0
1
0
0
3
0
0
1
2
1
0
2
1
1
2
0
1
0
0
2
0
0
1
2
0
0
0
1
0
0
1
0
0
0
1
0
1
1
1
1
0
0
0
0
0
1
1
0
0
1
0
0
0
2
2
2
1
1
2
0
0
1
0
0
6
1
1
2
0
0
0
1
1
0
0
1
1
0
1
1
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
2
1
0
1
0
2
2
0
3
1
1
0
1
0
2
2
0
0
1
1
0
0
1
1
2
2
1
1
1
0
1
0
1
0
0
0
2
0
2
0
1
2
1
0
0
0
2
3
0
0
0
0
0
0
1
0
1
0
0
2
0
2
2
2
0
0
0
1
2
0
2
1
0
0
0
1
0
0
0
0
0
2
2
0
0
1
0
0
0
0
2
0
2
0
0
0
0
1
0
3
0
1
2
0
2
0
2
0
1
0
0
0
2
0
1
1
0
1
0
1
0
1
3
2
0
1
0
1
1
0
0
0
2
0
1
2
0
0
0
1
2
0
0
1
2
0
0
0
0
2
0
2
0
1
2
0
0
2
0
2
0
0
0
2
0
1
3
2
2
1
1
0
2
0
0
0
1
0
2
0
0
2
0
0
0
1
2
0
2
2
0
2
0
2
1
1
1
0
0
0
1
2
0
1
2
0
0
0
0
0
2
1
0
0
0
2
1
0
0
1
0
0
0
0
2
2
0
5
1
2
0
0
0
0
1
1
1
0
0
0
1
0
0
0
1
0
2
2
0
0
1
1
2
0
1
1
1
1
4
2
0
1
1
2
0
0
2
0
0
0
1
0
0
0
1
1
0
1
3
1
1
1
1
1
1
0
1
1
0
0
1
1
2
1
0
1
1
0
0
0
1
0
0
0
1
1
0
0
1
1
1
1
0
1
1
0
2
0
2
0
2
1
0
0
1
1
0
1
0
0
0
1
1
0
0
0
1
2
0
0
2
1
0
0
1
0
1
2
2
0
0
1
0
0
0
0
1
0
1
0
0
0
1
2
1
0
1
1
0
2
0
0
1
2
0
0
1
2
0
0
1
1
1
1
5
0
1
0
0
5
0
1
0
0
1
0
2
0
1
0
0
0
0
0
1
0
0
0
2
0
2
0
2
0
0
0
2
0
2
0
0
0
0
3
0
0
1
0
2
0
1
1
0
1
0
0
1
0
1
0
0
0
0
0
1
0
2
1
0
0
1
2
1
2
0
0
1
0
3
1
0
0
1
2
1
1
1
1
1
0
2
0
0
1
2
0
0
0
0
2
2
1
0
0
0
2
0
1
2
1
0
0
2
2
2
1
0
0
0
1
1
0
0
1
0
0
2
0
0
2
0
0
0
0
1
1
0
2
0
1
3
1
0
0
2
1
0
1
0
1
0
0
2
1
2
0
1
1
0
0
0
2
0
0
0
1
4
0
2
0
0
0
2
0
0
0
0
2
1
1
0
1
1
0
0
1
0
0
0
1
0
0
1
2
0
1
1
1
2
0
0
0
0
0
0
2
2
0
1
0
0
0
2
1
0
0
2
1
2
2
2
0
0
1
1
1
1
0
0
0
0
1
0
1
1
1
0
0
1
3
1
0
0
1
0
2
1
0
0
0
1
1
0
0
2
2
0
0
1
2
0
0
1
1
0
2
0
1
1
1
0
1
0
1
1
0
1
1
2
1
0
2
2
0
0
0
1
2
1
1
2
1
2
2
1
0
1
0
1
1
1
0
1
1
1
1
1
0
2
0
0
2
0
2
0
1
2
0
1
1
0
1
1
2
0
1
2
0
2
0
1
1
0
1
0
2
3
1
1
2
0
2
0
2
1
0
0
0
0
0
0
0
2
2
2
0
0
1
2
0
0
1
1
0
1
0
0
1
2
1
3
2
1
1
0
0
0
2
1
2
2
1
2
2
0
2
1
0
1
1
0
0
0
2
1
0
0
2
1
1
1
2
1
0
0
0
1
2
2
0
2
1
0
0
0
0
2
1
0
1
0
0
2
0
0
2
1
2
2
0
1
0
2
2
0
0
0
1
2
1
1
2
0
0
0
2
1
2
0
0
4
0
2
0
2
0
0
1
0
1
1
2
0
1
0
0
1
1
0
0
2
0
0
2
0
2
1
1
2
0
1
1
0
1
1
0
0
0
0
0
0
0
1
5
0
0
0
0
0
1
1
1
0
0
1
1
0
1
1
1
0
1
1
0
0
0
1
0
1
0
1
0
2
2
1
0
1
0
1
2
2
0
0
0
1
0
1
0
0
2
0
2
2
0
1
0
0
1
0
1
0
2
1
1
1
0
2
0
1
0
0
1
1
1
0
0
2
0
0
1
0
0
0
1
2
2
0
1
0
1
0
1
1
0
0
1
2
0
1
0
2
1
2
0
1
0
2
2
1
0
0
1
0
0
0
2
2
0
1
0
2
1
0
0
0
0
0
1
0
0
2
2
0
1
0
2
1
1
0
0
1
1
1
0
0
0
1
0
1
0
0
1
1
1
2
0
0
1
1
2
2
1
0
0
0
2
2
1
0
0
1
2
1
1
1
2
0
1
1
0
0
2
2
5
0
0
1
2
2
2
0
0
0
1
0
1
1
2
0
0
1
1
0
2
0
2
0
2
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
4
0
0
0
1
2
2
0
2
0
1
0
0
3
0
1
1
1
0
1
2
2
1
0
0
0
1
0
1
2
0
3
1
0
0
0
1
2
1
2
1
0
1
1
0
0
2
1
2
0
3
1
1
1
1
1
0
2
0
2
2
0
1
0
0
0
2
2
3
1
0
1
1
0
1
1
0
0
2
0
0
2
1
1
2
1
0
1
1
2
1
1
1
1
1
1
0
0
3
0
2
0
2
0
0
2
0
0
1
0
2
2
1
0
0
0
1
3
1
1
2
2
0
1
3
0
0
0
0
1
1
0
0
0
0
2
2
0
0
0
2
0
0
0
0
1
3
0
1
1
1
1
0
0
1
0
0
1
1
1
1
1
0
0
0
1
1
0
1
2
0
2
1
1
1
1
0
2
0
0
1
0
1
1
0
1
0
2
1
1
3
0
2
0
1
1
2
2
0
0
1
0
0
0
0
1
0
0
0
1
1
1
2
1
1
1
0
0
0
0
1
0
0
0
1
0
1
2
0
0
0
1
0
0
0
0
0
1
0
2
0
0
1
1
1
0
0
0
1
1
2
0
1
1
2
1
0
0
0
0
0
2
2
0
0
2
0
2
2
1
0
1
2
1
0
0
1
0
1
2
1
0
0
0
2
1
0
0
0
0
0
1
0
0
2
2
0
2
0
1
0
1
1
2
1
0
0
0
0
0
1
0
0
1
1
1
0
1
0
0
1
2
0
0
0
0
2
2
1
0
2
1
3
0
2
0
2
0
0
1
0
0
2
1
0
0
1
1
2
0
1
1
2
1
1
0
2
1
0
0
1
3
0
0
0
1
1
0
0
0
2
0
1
2
2
0
0
2
1
0
2
1
2
1
2
0
1
1
0
0
2
1
0
0
2
1
0
2
2
0
0
0
0
1
0
0
0
1
1
1
1
0
0
1
0
2
0
2
1
1
1
0
2
2
0
0
0
1
1
1
0
0
1
1
1
1
2
0
0
0
0
0
0
1
1
1
2
1
2
2
1
0
1
2
0
1
2
1
0
1
1
0
0
1
0
1
2
0
0
1
0
0
0
1
0
1
0
1
1
1
2
0
0
0
1
0
0
0
2
2
0
0
1
0
2
2
0
0
0
0
1
0
1
0
3
1
1
0
2
3
0
0
2
2
1
2
1
2
2
1
0
0
2
0
3
2
3
2
0
0
2
1
0
0
2
1
1
0
1
0
0
0
0
2
0
0
2
0
0
2
0
0
0
1
2
0
0
0
0
2
1
1
0
0
0
2
1
0
2
0
2
1
0
1
2
0
0
0
0
0
0
2
1
2
0
0
2
1
1
1
1
1
0
2
0
1
2
2
3
1
1
0
2
0
1
1
1
1
2
2
1
0
0
1
0
2
0
0
0
0
0
2
2
1
2
0
1
0
2
1
1
0
1
3
1
2
2
2
1
0
0
0
1
2
0
0
0
0
0
2
1
0
0
0
0
1
0
1
1
0
0
0
2
1
0
0
0
2
0
1
2
0
0
2
1
1
0
0
1
0
0
1
0
1
0
0
0
0
2
0
0
0
2
0
2
0
2
1
0
0
0
1
1
0
0
0
2
0
0
2
1
1
0
2
1
0
0
2
2
2
0
1
0
2
2
0
2
1
0
0
0
1
0
2
0
0
2
2
1
2
1
1
2
0
1
0
0
1
0
2
0
0
1
1
1
2
1
2
2
2
1
0
0
0
1
1
0
0
2
1
0
0
0
2
1
1
0
2
2
0
0
0
1
0
2
2
0
0
0
0
0
0
2
1
0
0
1
0
1
2
2
1
0
0
1
1
1
0
1
1
2
0
2
2
2
0
1
2
1
1
0
2
1
2
1
1
1
0
1
1
2
0
0
1
1
1
1
1
1
1
0
0
1
1
1
0
0
1
1
0
0
2
0
0
3
0
1
0
1
0
1
0
0
1
1
0
2
1
0
2
1
3
3
0
0
0
2
0
1
0
0
0
2
0
2
0
0
2
1
0
2
1
2
1
1
1
0
2
1
0
1
2
1
0
2
0
0
0
0
1
2
1
0
1
0
0
1
1
0
2
0
2
2
0
0
2
0
2
2
0
1
0
2
0
0
1
0
0
1
1
1
1
0
0
0
1
0
2
2
0
2
1
0
0
0
1
1
1
0
0
1
1
1
1
2
0
0
1
1
1
0
2
1
0
2
0
0
2
1
1
0
0
0
0
1
0
1
2
0
0
2
2
0
1
1
0
1
1
1
1
0
1
2
0
0
2
0
0
2
0
0
1
0
2
0
1
0
0
0
2
0
0
0
2
0
2
0
0
1
0
2
0
0
2
0
0
2
1
0
0
2
1
2
0
1
0
1
0
0
1
1
1
2
1
0
0
2
1
0
0
0
0
0
0
0
0
2
2
0
1
1
1
1
1
2
0
2
2
0
3
1
1
0
0
1
0
0
2
1
2
0
1
1
3
0
1
2
0
0
2
1
1
0
2
0
0
0
0
0
0
1
1
0
1
0
2
0
1
2
0
1
0
2
0
0
1
1
0
0
1
0
1
0
2
1
3
0
1
1
0
1
0
2
0
2
2
2
1
2
1
2
2
1
1
0
0
2
0
0
0
0
0
0
1
2
2
0
0
0
0
2
1
1
0
1
3
2
2
1
2
2
0
1
2
1
0
0
0
1
1
0
2
0
1
1
2
2
1
0
0
0
0
1
1
1
0
1
0
0
3
2
1
2
2
0
1
1
0
0
0
1
2
0
0
3
0
1
2
2
0
2
0
0
0
1
0
2
1
2
2
1
1
2
0
2
0
0
0
0
7
2
1
0
1
0
0
1
0
1
1
0
1
1
1
0
2
1
1
2
2
0
2
1
1
0
0
2
1
0
0
1
2
0
0
1
1
2
1
1
1
2
3
0
0
2
1
0
1
0
1
0
0
1
3
1
1
1
0
2
0
0
2
2
0
1
0
1
2
1
0
0
1
0
1
0
0
1
2
1
0
1
0
1
2
1
2
1
0
0
0
0
1
2
0
1
0
1
1
1
2
1
1
2
0
0
0
0
0
2
1
2
0
1
0
0
2
1
0
0
1
1
0
1
1
1
1
1
0
0
1
1
0
0
0
1
3
2
0
0
1
1
0
2
0
0
1
2
0
0
2
2
0
1
1
0
0
1
0
0
2
1
0
2
1
1
1
1
0
3
0
2
1
0
2
0
1
0
0
1
2
0
1
0
1
1
1
1
0
1
1
0
0
2
1
2
1
1
0
2
0
1
0
0
0
2
0
2
1
2
2
1
0
0
1
2
2
0
2
1
2
2
2
1
1
0
2
2
0
1
2
0
1
2
0
1
0
0
2
0
1
1
2
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
3
0
1
0
0
0
1
0
0
1
1
0
0
1
1
1
0
1
3
1
2
0
2
1
1
1
0
2
0
2
0
1
1
2
0
0
0
0
1
0
0
1
0
0
1
2
1
0
1
0
0
0
1
0
0
1
0
1
1
0
2
0
0
0
0
0
1
1
1
1
0
0
1
0
0
0
0
2
0
1
1
0
1
0
0
0
2
1
1
0
0
0
0
0
0
1
1
1
0
1
0
1
0
2
0
1
0
2
0
0
1
0
2
0
0
2
0
0
0
0
1
1
1
2
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
2
0
0
1
0
1
0
1
0
2
0
0
0
0
1
2
1
1
2
0
0
0
0
2
1
2
0
0
0
2
1
0
0
1
1
1
1
0
0
2
2
0
0
1
1
0
0
2
0
0
1
1
0
0
1
0
0
0
1
0
0
2
1
2
5
0
2
1
1
0
1
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
2
1
1
0
1
1
1
0
0
0
0
2
0
0
2
0
1
1
0
1
1
1
1
0
2
1
2
1
0
1
0
2
1
0
2
2
0
1
1
2
1
1
1
2
2
1
1
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
2
0
0
0
2
1
0
2
0
0
1
1
1
1
0
2
1
2
0
0
0
1
1
1
1
2
0
2
0
0
2
0
1
1
1
1
0
1
2
0
1
0
0
0
0
1
0
2
0
0
3
0
2
0
1
2
1
0
2
2
2
2
0
1
1
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
2
1
1
0
2
2
1
0
0
0
0
1
2
0
2
1
2
0
0
0
2
0
1
0
1
0
0
0
2
0
2
0
1
2
0
0
0
2
2
2
0
0
0
0
1
0
0
1
0
2
1
0
0
1
0
2
1
1
0
0
1
0
0
1
1
1
2
1
0
1
1
1
1
2
1
0
1
1
1
2
1
0
1
0
1
0
0
2
2
0
0
2
2
0
0
0
0
2
1
1
0
0
3
0
0
2
1
3
0
0
3
0
0
1
1
1
0
1
0
1
0
0
0
1
1
0
2
1
1
0
2
0
1
0
0
1
2
1
0
1
0
0
0
0
1
0
1
1
2
2
0
2
1
0
3
0
1
1
0
1
1
0
0
0
1
1
2
1
0
2
2
2
2
0
1
0
2
0
1
0
0
2
0
0
1
3
1
1
0
0
2
0
0
2
0
1
2
1
1
0
2
2
2
2
0
0
0
1
2
1
2
0
0
0
2
0
0
1
1
2
0
0
2
1
0
1
1
1
0
2
0
1
0
2
1
2
0
0
0
2
2
0
0
0
2
2
2
2
0
2
2
1
4
1
0
1
2
1
0
1
0
0
0
1
1
0
0
2
3
2
0
1
0
2
1
1
2
2
0
1
2
0
0
0
2
1
2
1
0
0
1
1
0
1
1
2
3
1
0
2
0
0
2
0
1
1
2
0
2
0
1
0
1
0
0
2
0
1
1
1
0
0
2
0
1
0
1
0
0
2
1
0
0
0
1
2
1
1
1
2
0
0
1
1
1
0
1
0
0
1
1
0
1
1
2
1
2
1
2
0
0
0
0
2
1
2
2
2
0
2
1
1
0
1
1
0
2
0
1
1
2
1
0
0
0
1
0
0
1
0
1
1
2
2
0
0
1
1
0
2
0
1
0
0
0
1
1
0
6
4
1
0
1
1
0
0
0
0
0
0
1
0
1
0
1
2
0
1
1
1
1
1
0
1
0
0
1
0
1
2
0
2
0
0
2
1
1
0
0
1
1
1
1
0
1
0
0
2
1
1
0
0
1
0
0
0
0
0
0
2
2
0
0
2
0
0
1
4
1
1
2
0
2
0
2
1
1
0
0
1
1
1
1
2
1
2
1
0
1
1
1
2
0
0
1
1
1
0
1
2
0
0
0
0
0
0
1
5
0
0
1
2
0
1
2
0
1
0
0
1
0
0
2
0
0
1
2
1
0
1
0
2
0
0
0
0
1
1
0
0
2
0
1
1
1
1
1
1
0
0
0
2
1
0
1
1
1
2
1
4
0
0
0
1
2
2
1
0
1
0
1
2
2
1
1
0
1
1
0
1
0
0
2
0
0
0
0
0
1
1
0
0
2
2
0
0
0
1
0
0
1
1
2
1
1
4
1
2
0
0
1
2
2
1
0
0
0
1
1
0
0
1
0
1
0
0
2
0
1
0
1
1
1
2
2
0
2
0
0
0
0
2
1
0
2
2
1
2
1
2
1
2
0
0
1
1
0
1
0
0
1
2
0
0
1
1
2
1
0
0
0
1
1
4
0
0
0
0
2
0
0
2
2
2
1
2
1
0
2
0
0
0
1
1
1
2
2
1
1
0
1
0
2
2
0
3
0
1
0
1
0
2
1
0
2
0
0
2
0
2
2
0
0
1
0
1
0
0
1
1
0
1
1
1
1
0
0
1
0
0
0
1
1
0
0
1
1
1
0
0
0
0
0
1
5
2
2
0
0
0
0
1
0
2
0
1
2
2
2
0
0
2
0
1
0
1
1
2
2
1
1
1
0
1
0
2
1
0
2
2
1
2
1
0
0
2
0
1
2
1
0
1
1
0
1
0
1
0
0
1
0
0
0
2
0
2
1
1
2
2
2
1
0
2
2
0
2
0
1
1
2
1
0
1
1
0
0
2
0
0
1
1
1
0
1
2
2
0
1
1
0
2
2
1
2
0
2
0
0
2
0
1
4
2
0
0
1
1
0
0
0
2
1
0
1
1
0
0
0
1
0
0
0
2
1
2
1
0
0
0
1
2
0
1
1
0
1
0
0
1
0
0
1
2
0
2
0
1
1
1
0
1
1
2
1
0
1
0
1
0
0
0
2
1
1
2
0
2
0
1
4
1
0
0
0
1
1
0
1
0
1
2
0
0
0
0
1
1
0
1
2
2
0
1
0
1
0
0
1
1
2
0
0
0
1
0
0
0
1
2
0
0
1
2
0
2
2
1
1
1
0
0
0
0
0
1
1
1
0
1
0
0
2
1
1
1
2
2
1
0
2
1
1
1
2
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
2
1
1
0
1
1
2
0
2
0
0
1
1
3
0
0
0
2
0
2
0
1
2
1
1
0
2
0
0
1
1
0
0
4
0
1
0
2
0
0
1
0
0
0
2
0
2
1
1
0
1
1
1
0
0
2
2
1
2
0
0
0
2
1
2
0
0
2
0
0
0
1
0
0
0
2
0
1
2
0
1
0
0
2
2
0
0
0
0
1
0
2
1
2
1
1
1
1
1
0
0
2
2
0
0
2
1
0
1
2
2
1
0
1
0
0
0
1
1
1
1
0
0
1
1
1
2
2
1
0
0
0
2
2
0
1
0
0
1
0
2
2
0
0
1
2
0
1
1
1
0
0
0
2
1
0
0
1
1
2
2
0
0
0
2
1
1
2
0
0
1
1
1
0
1
0
0
0
0
0
0
1
0
1
2
0
1
0
0
2
1
0
1
0
1
0
1
0
12
0
1
0
0
1
2
1
1
0
0
1
2
1
1
1
1
1
0
1
0
1
0
0
1
2
0
4
0
0
1
1
0
0
3
0
0
1
0
2
1
0
0
1
0
1
0
1
0
2
2
0
0
1
1
2
1
1
0
1
1
1
1
1
0
0
2
0
1
1
1
0
2
2
0
2
2
0
0
3
0
0
0
1
1
0
1
0
0
2
2
2
0
1
1
2
1
0
0
0
0
0
1
2
1
0
2
0
0
2
0
2
0
1
2
1
0
0
1
0
1
2
2
1
1
2
0
1
0
1
2
2
2
0
1
0
1
0
0
0
1
2
0
0
1
0
1
0
1
0
0
0
2
1
2
1
2
0
1
0
0
0
0
0
2
1
2
0
1
1
1
0
2
2
0
0
0
1
1
1
0
4
0
1
2
1
0
2
1
1
2
1
0
0
3
0
0
1
1
1
2
1
0
0
2
1
1
2
1
0
1
0
1
1
0
2
1
0
1
0
0
1
0
3
0
2
0
2
2
1
2
0
0
0
1
1
0
2
0
0
0
2
1
1
1
1
1
1
0
0
1
0
3
0
2
1
1
1
0
0
1
0
2
1
1
0
1
3
1
1
2
0
2
2
0
0
1
0
2
2
0
2
1
0
0
1
1
0
1
2
1
1
1
1
3
2
0
0
0
0
2
0
2
2
9
0
2
0
0
0
0
2
0
0
0
1
5
1
0
1
1
0
1
0
1
3
1
1
0
0
0
0
1
0
1
0
1
0
0
0
1
0
1
0
0
0
0
1
1
2
2
0
1
0
2
0
1
2
1
0
0
2
1
1
0
1
0
0
2
0
0
2
2
0
0
1
0
2
0
1
0
0
1
0
0
0
4
1
0
0
1
1
0
0
2
0
1
1
0
1
2
1
2
0
1
1
2
1
2
1
1
0
0
0
0
2
3
0
2
1
1
0
0
1
3
0
2
1
0
0
0
1
2
1
2
0
0
1
1
1
0
0
2
2
2
0
0
1
1
0
2
0
2
1
2
0
0
0
1
1
2
2
2
1
0
0
1
0
1
1
0
0
1
0
0
0
1
0
0
1
1
0
0
1
0
0
2
0
1
2
1
0
1
0
0
0
1
0
0
1
1
1
1
0
0
1
0
1
2
0
1
1
1
0
0
0
1
1
1
0
0
0
0
0
0
1
1
1
0
0
2
0
0
0
1
0
1
1
0
2
1
0
1
0
0
0
1
0
0
0
0
1
1
2
0
1
0
0
1
0
0
0
2
1
0
2
0
1
2
2
0
0
0
1
2
1
1
1
0
1
1
1
1
0
1
2
2
3
1
1
1
2
0
1
0
0
0
1
1
0
0
0
0
2
0
1
1
2
0
1
0
1
0
0
0
1
1
2
1
0
0
2
1
2
0
2
1
0
2
2
0
0
0
1
0
1
2
1
1
0
0
0
0
2
1
1
2
2
0
1
0
0
0
0
0
2
0
0
0
2
1
0
1
1
1
1
0
1
0
2
0
0
1
0
1
1
0
2
3
1
0
1
1
2
1
1
0
2
1
0
2
1
0
0
1
2
0
0
0
2
1
1
1
1
0
0
1
0
0
0
1
2
0
0
0
0
2
1
0
2
0
2
0
0
1
1
0
1
2
0
4
2
1
1
0
0
1
3
0
0
0
0
2
0
0
0
1
0
0
1
1
1
0
0
0
5
0
1
1
1
0
1
1
0
1
1
1
0
0
2
3
1
2
2
0
2
0
2
1
0
2
0
1
0
2
0
2
0
1
2
0
1
1
1
1
1
2
1
0
0
0
1
0
1
1
0
0
2
0
1
1
0
2
0
0
1
1
1
0
0
1
2
1
1
2
1
0
0
1
0
0
2
0
1
0
0
0
0
2
1
1
0
2
0
0
1
1
1
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
1
0
0
0
0
1
0
0
2
0
0
0
2
0
1
0
1
0
0
2
0
1
2
1
1
2
0
2
0
2
1
0
0
0
1
2
0
0
1
1
0
0
2
2
0
0
2
0
0
0
2
0
0
2
2
1
0
2
1
2
0
2
0
1
1
3
1
1
1
0
1
0
0
2
2
3
0
1
0
1
1
1
1
1
0
2
1
2
0
0
2
1
0
0
1
1
0
1
1
0
1
1
0
0
1
0
0
0
0
2
1
1
0
0
0
0
2
1
0
0
0
1
1
1
2
1
0
2
2
0
0
0
0
1
0
1
1
2
2
1
2
1
2
1
0
1
1
0
1
0
1
0
1
1
3
0
2
1
2
0
2
0
0
0
0
0
0
1
1
1
0
1
0
2
2
0
1
2
1
0
0
0
1
1
1
0
2
2
0
1
2
2
1
0
0
0
0
1
1
1
1
1
1
1
0
1
0
1
2
1
0
0
1
2
1
0
0
1
2
0
2
0
0
2
3
1
2
1
0
2
1
0
1
2
0
0
1
0
1
1
0
2
1
1
0
2
2
1
0
2
1
2
0
3
0
0
2
1
0
0
2
0
0
0
0
0
1
2
2
2
0
1
3
2
3
0
1
2
0
1
2
0
0
0
1
0
2
1
1
1
1
2
0
0
2
0
0
1
0
1
0
0
2
1
2
0
0
1
0
0
0
0
0
1
2
2
2
1
1
1
0
1
0
0
1
0
0
2
2
0
2
0
1
1
0
0
1
1
2
0
2
2
0
0
1
0
2
0
1
0
1
1
2
0
2
1
0
2
1
0
0
0
0
1
1
0
1
1
1
1
0
2
1
0
2
0
2
0
1
0
0
1
2
1
0
0
1
2
0
2
1
0
2
2
2
2
0
1
1
0
0
0
1
1
0
2
0
1
1
0
4
0
0
0
2
0
1
0
0
1
0
0
1
1
1
1
2
0
1
0
1
0
1
1
0
1
1
0
0
0
0
1
1
0
2
0
2
1
2
0
0
2
1
1
1
1
0
1
1
0
1
2
1
1
1
2
1
0
0
1
2
2
0
0
1
0
0
0
1
2
0
0
0
0
1
1
0
0
0
2
0
0
1
3
2
0
0
0
2
1
0
0
2
0
2
0
6
1
2
1
2
1
2
1
1
1
0
1
1
1
0
2
2
1
2
2
1
2
0
0
1
1
1
1
0
2
0
0
1
2
0
0
0
2
1
0
0
2
0
0
2
1
2
0
0
0
1
0
1
0
0
4
0
1
1
2
2
1
1
0
0
2
0
0
2
0
0
1
0
1
2
2
0
0
0
2
1
0
2
0
1
1
2
1
3
0
1
2
1
0
1
0
2
2
0
1
1
2
2
1
1
1
1
0
1
1
1
0
1
1
1
0
0
1
1
1
0
1
1
0
1
0
1
1
0
3
0
2
0
0
2
1
1
0
1
0
0
0
0
1
1
1
1
2
1
0
1
1
1
1
2
0
1
1
0
2
2
2
3
1
1
1
2
1
1
4
0
0
2
0
2
0
0
0
1
1
0
0
1
2
0
1
0
4
2
0
0
2
0
2
1
1
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
1
2
2
0
1
1
1
1
0
0
2
0
0
0
0
2
1
0
0
2
0
1
1
1
1
2
2
0
0
0
1
1
0
0
1
0
2
0
0
0
1
1
2
0
0
0
2
1
1
0
1
2
0
1
1
0
1
0
0
1
2
1
0
0
2
2
1
0
0
0
2
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
1
0
0
1
2
0
2
1
1
2
1
0
2
2
0
1
0
0
0
1
0
0
2
2
1
0
2
0
1
1
0
2
0
2
2
0
0
0
2
2
0
0
1
1
2
0
1
2
1
1
0
0
1
1
1
0
1
0
0
0
0
1
1
2
1
0
1
1
0
0
0
1
1
0
0
0
0
0
1
1
1
2
0
1
0
0
2
0
1
0
0
1
1
0
0
2
0
0
1
1
0
0
1
0
0
2
0
0
0
0
1
0
1
0
0
1
0
0
3
0
1
1
0
0
2
2
0
0
0
1
0
1
0
0
2
1
0
2
0
0
0
0
1
1
4
2
0
1
0
1
1
4
2
0
1
1
0
2
0
0
1
2
1
1
1
0
0
0
1
1
2
2
0
1
2
0
0
0
0
1
1
0
0
0
0
2
0
0
0
2
0
0
2
2
0
2
2
2
0
0
0
1
1
0
1
0
2
2
1
0
2
1
0
1
2
0
1
0
1
1
1
0
0
0
2
0
1
1
0
0
1
0
0
1
0
1
0
0
0
0
0
1
1
3
0
1
2
0
0
2
2
0
0
0
1
1
0
1
1
0
1
0
2
0
2
2
0
0
2
1
2
1
3
0
1
2
2
2
0
0
1
1
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
3
2
1
2
0
1
2
3
0
0
1
0
1
0
1
0
2
0
1
1
0
1
0
2
1
0
2
1
0
1
0
1
1
0
0
0
1
3
0
0
0
1
2
0
1
0
0
2
0
0
0
4
0
1
1
1
1
0
0
0
0
0
1
0
1
0
2
1
0
0
0
1
1
1
2
0
0
0
2
0
2
1
2
4
0
2
0
0
1
0
0
0
0
0
1
0
1
0
2
0
0
0
2
0
0
2
1
3
2
0
1
1
0
0
2
1
4
0
0
0
0
1
0
0
0
2
2
1
1
2
0
2
0
2
0
1
1
0
1
1
0
2
1
1
0
0
0
1
0
0
0
0
2
0
1
1
0
0
2
0
0
0
1
1
1
0
0
2
1
0
1
0
0
1
3
1
1
0
0
0
0
1
1
2
3
1
0
0
1
1
2
2
1
0
0
0
0
1
2
0
2
0
0
2
1
2
2
1
1
1
2
1
2
2
2
2
0
0
0
0
0
0
1
2
1
2
1
2
0
2
1
0
0
0
0
1
0
1
1
2
1
0
3
1
1
0
1
0
0
1
1
1
1
0
0
2
0
0
0
1
1
0
0
4
1
1
1
1
0
2
0
0
2
2
2
1
1
2
1
1
1
0
2
0
0
1
1
0
2
1
1
2
1
0
0
1
0
2
1
2
1
1
1
0
0
1
2
1
1
0
0
2
1
0
2
1
3
0
1
0
2
1
1
1
2
0
1
0
2
0
1
0
0
2
0
1
0
0
0
0
1
2
0
1
1
1
0
0
0
0
1
1
0
0
0
0
0
2
0
0
2
1
2
1
1
1
0
2
0
1
1
2
0
1
1
1
1
1
0
0
2
1
2
0
0
0
2
0
0
0
2
0
0
0
1
1
0
0
0
0
1
1
0
1
1
1
0
1
0
1
0
0
1
0
2
1
1
1
1
2
1
1
0
1
0
1
1
1
0
0
0
2
0
1
2
3
0
2
0
0
1
1
2
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
2
0
1
1
1
1
2
1
1
1
2
1
1
1
0
0
0
1
0
2
1
1
0
0
1
1
0
1
1
3
0
0
2
1
2
0
2
1
1
0
1
0
0
0
2
2
1
0
1
1
2
2
0
1
0
2
0
0
0
1
0
1
1
1
1
0
2
0
1
0
0
2
2
0
1
1
0
1
0
0
2
1
0
0
0
1
0
2
0
0
2
0
1
0
1
0
1
0
0
0
0
1
2
1
2
0
0
0
0
0
0
1
0
0
2
1
2
0
1
1
1
0
1
1
0
0
0
0
1
1
0
0
1
0
1
2
1
0
2
1
1
0
2
2
0
2
0
2
0
0
1
1
0
0
0
1
0
0
2
0
2
0
0
4
0
2
0
1
1
1
0
0
0
1
0
0
2
0
0
1
2
3
0
1
0
0
0
1
1
1
0
1
1
1
4
0
0
0
1
2
0
0
0
0
0
1
0
2
2
2
1
1
0
0
2
0
2
0
2
2
2
1
0
0
1
0
0
0
0
0
0
1
0
1
0
1
1
1
1
1
1
2
0
0
2
0
1
0
1
0
1
1
2
1
1
0
2
0
1
2
2
1
0
0
0
0
0
1
1
0
0
1
0
1
2
2
0
1
0
2
0
1
1
1
0
2
1
0
0
1
0
1
1
0
1
0
2
0
0
1
1
0
1
1
1
0
0
0
1
1
2
1
1
1
0
0
0
1
3
0
2
1
0
1
0
0
2
0
0
0
2
2
0
0
2
1
2
0
1
0
1
2
0
2
1
0
2
2
0
1
0
1
0
0
2
2
0
1
2
0
2
0
0
2
1
1
2
2
0
0
2
0
1
2
1
0
1
2
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
1
1
1
0
0
0
1
3
0
0
1
0
0
0
1
0
1
2
1
1
0
0
0
1
0
1
0
2
2
1
0
1
1
1
0
1
1
2
0
1
3
0
1
1
2
2
3
2
0
0
1
1
2
1
1
2
0
1
0
0
1
2
1
1
1
1
2
1
0
3
0
3
1
2
2
0
2
0
0
1
0
0
0
0
2
1
0
0
1
1
0
2
0
0
2
0
2
0
0
1
0
0
1
1
2
1
0
2
0
0
2
0
0
0
2
2
2
1
1
1
0
2
1
2
2
0
0
0
2
2
0
2
2
3
1
2
0
0
0
1
0
0
0
1
0
2
2
1
1
2
1
0
0
0
1
1
1
0
0
0
2
1
1
1
0
1
1
1
1
1
1
1
1
0
0
2
1
0
0
0
1
1
0
2
1
0
0
0
2
0
1
1
2
0
1
2
3
0
2
1
0
1
0
0
1
0
0
1
3
0
0
2
2
2
1
1
0
2
0
0
1
2
0
0
0
1
2
2
0
0
2
0
0
1
2
0
1
2
0
0
0
1
4
2
1
1
0
2
0
0
3
1
1
0
2
2
1
2
0
0
2
1
2
1
0
1
0
1
0
1
1
2
0
0
1
0
1
0
0
0
1
2
1
2
1
0
0
2
1
0
0
0
2
1
0
0
1
1
1
1
1
1
1
0
1
0
2
1
0
0
1
1
1
1
1
2
0
1
2
0
0
1
0
0
0
1
2
1
1
0
0
0
1
0
1
0
0
1
1
0
0
0
1
2
1
0
2
1
0
2
0
1
0
0
2
1
2
0
1
2
0
1
1
1
0
1
1
0
0
1
1
1
1
0
1
2
0
0
3
0
2
1
0
1
0
1
1
0
0
0
0
0
1
0
0
0
1
1
1
2
1
2
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
1
1
1
1
0
1
2
0
2
0
2
0
0
2
0
1
0
0
0
1
0
0
0
2
0
1
0
2
0
2
0
1
0
1
2
0
1
2
0
0
2
1
0
0
1
2
2
0
1
0
0
1
1
0
1
1
1
0
1
0
1
0
2
1
2
0
0
0
0
0
0
1
4
1
0
2
2
1
0
1
0
1
0
0
2
0
0
0
1
1
0
0
0
2
3
0
1
1
0
1
3
0
1
2
1
0
2
1
0
0
2
1
0
1
1
1
0
1
3
1
2
2
2
1
1
0
1
1
0
1
2
0
3
0
2
0
0
0
1
1
1
1
2
2
0
3
0
0
2
0
0
2
0
2
0
2
1
0
1
0
2
0
0
1
1
0
1
1
1
0
0
1
2
1
2
0
2
1
0
1
1
1
1
1
1
0
0
1
0
2
2
1
1
0
1
1
2
9
1
0
1
2
2
1
1
0
0
2
0
0
2
1
2
2
0
2
0
0
0
2
1
0
1
2
1
0
0
0
1
2
2
0
1
0
2
0
2
0
1
0
2
0
1
0
0
1
1
0
0
1
0
2
1
0
2
0
1
0
2
2
0
1
1
2
2
1
0
0
2
0
1
0
0
0
0
0
0
0
0
1
1
1
0
2
0
2
2
1
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
1
1
0
0
1
0
1
2
0
1
0
0
2
1
2
2
1
2
1
2
1
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
2
2
0
1
3
1
0
0
1
0
2
0
0
2
1
0
1
1
0
2
2
1
0
0
0
1
1
0
0
1
1
0
1
0
0
0
1
0
1
0
0
0
0
2
0
0
0
2
1
0
1
1
1
0
1
1
0
2
1
0
0
0
1
1
1
0
0
0
2
3
1
1
0
1
0
1
0
2
0
1
2
1
0
1
0
0
2
2
0
1
0
0
2
0
1
1
0
2
0
0
0
0
1
1
2
1
0
2
0
1
0
0
0
1
1
0
0
1
0
0
2
0
2
1
2
1
3
0
0
2
0
1
1
1
1
0
0
0
0
0
1
0
0
0
2
0
0
2
0
1
1
0
1
0
2
1
2
0
1
2
1
1
0
1
2
2
1
2
0
2
0
2
0
5
0
2
2
1
0
0
1
0
0
0
2
1
3
0
0
0
0
1
1
0
1
0
1
1
0
1
0
2
1
0
3
1
0
2
0
0
0
0
1
0
0
0
0
0
2
2
1
2
0
0
1
2
1
1
0
1
0
0
2
0
2
2
0
0
0
1
0
2
1
0
0
0
2
0
2
2
1
0
0
1
2
1
1
0
0
0
0
0
0
2
2
2
0
0
0
0
0
1
1
2
1
3
0
1
0
0
1
2
1
1
0
1
0
1
1
1
0
0
2
0
4
0
0
0
0
0
0
0
1
1
0
0
4
1
1
0
0
1
1
2
0
2
0
0
2
0
1
1
0
1
1
0
0
1
0
1
0
1
2
0
2
2
1
0
1
0
1
2
0
1
1
2
0
0
0
0
2
2
1
0
1
0
0
0
0
0
3
1
1
1
1
2
0
1
2
0
0
0
1
0
2
0
2
0
2
1
0
1
1
0
0
0
0
2
2
0
2
0
0
1
1
1
0
0
1
1
1
1
0
1
1
1
2
0
0
1
1
0
0
0
0
0
0
0
1
1
1
1
1
0
0
1
2
1
0
2
0
0
1
0
0
2
1
0
1
0
1
0
0
1
2
0
0
2
2
1
1
0
0
0
1
2
2
1
1
1
0
0
0
0
0
1
0
0
0
0
1
1
2
0
1
1
1
2
0
1
1
0
0
1
1
2
0
2
0
0
1
0
1
0
0
1
2
1
1
1
0
2
2
1
2
0
1
2
1
0
0
2
0
0
1
0
0
1
2
0
1
0
0
1
0
0
1
2
1
1
0
0
0
1
0
2
0
0
0
3
1
3
2
2
2
2
1
1
3
1
0
1
1
1
0
1
1
0
3
0
1
0
0
0
0
1
0
1
0
1
2
0
2
1
1
0
0
0
1
0
1
3
1
2
0
1
1
0
2
0
2
0
1
0
1
0
1
0
1
0
1
2
1
0
2
1
1
0
1
0
2
1
2
0
0
0
1
0
1
2
2
0
0
0
2
1
2
1
0
1
0
1
0
1
0
0
1
1
2
3
2
0
0
1
1
1
0
1
0
0
3
1
1
3
0
0
0
1
0
2
2
0
1
1
0
2
3
2
1
2
2
0
0
2
1
0
2
1
1
0
1
1
1
1
2
2
0
1
0
0
0
0
0
1
3
2
1
1
0
1
1
0
0
0
1
0
0
1
1
0
0
1
0
1
1
0
0
2
2
0
0
1
0
1
1
2
0
1
1
0
1
1
1
0
0
2
0
2
0
0
0
1
0
1
2
0
0
0
0
1
1
0
0
1
1
1
1
0
1
2
0
2
0
1
2
2
0
2
0
2
0
1
0
0
2
0
1
0
0
0
2
0
0
0
2
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
2
2
2
1
2
0
2
2
1
0
1
2
1
2
1
1
0
1
2
1
0
2
0
0
1
2
1
0
0
0
1
2
0
1
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
1
0
1
1
1
1
0
0
1
0
0
0
0
0
2
1
2
2
1
2
0
0
0
0
1
1
2
0
2
1
0
0
0
0
2
1
0
2
0
0
0
2
2
0
0
1
0
1
1
1
0
0
0
0
1
2
2
1
1
1
0
0
2
0
2
0
0
1
0
0
1
1
1
2
1
0
0
0
0
1
0
0
1
0
0
0
0
1
2
1
0
0
1
0
0
0
1
2
1
2
1
0
0
1
1
0
2
0
1
2
0
2
0
2
0
2
1
0
0
0
1
2
0
2
0
2
0
2
2
1
1
0
0
4
1
2
1
0
1
2
0
1
2
1
1
1
0
0
0
1
2
0
0
1
2
0
0
1
0
1
2
1
0
0
0
0
1
0
0
2
0
0
1
1
0
5
1
1
2
0
1
2
0
2
0
0
0
1
1
0
0
0
2
0
1
0
0
0
2
0
0
0
1
0
0
1
0
1
1
2
1
0
0
1
0
0
1
2
1
1
1
0
1
0
1
1
2
1
0
2
1
0
0
0
3
1
0
1
1
0
2
0
0
2
0
2
1
0
0
1
1
0
0
2
2
0
0
2
0
0
0
0
0
1
1
0
0
1
1
1
1
0
3
0
1
1
1
0
0
1
0
0
1
1
1
1
1
0
2
1
1
2
2
2
0
2
2
2
1
1
1
2
0
0
2
2
0
1
2
2
2
2
0
0
1
1
1
0
2
0
0
0
1
2
0
0
0
1
1
2
3
2
1
0
0
3
1
2
1
2
1
0
0
2
0
0
0
0
2
0
1
0
1
2
2
1
2
0
2
1
0
0
0
1
0
1
0
1
0
0
0
0
1
2
2
0
1
1
0
0
1
1
2
0
2
0
3
0
0
1
0
0
0
1
0
0
0
0
1
0
1
1
1
1
4
0
0
0
0
1
0
0
0
1
0
0
0
1
1
2
0
0
1
0
0
0
2
0
0
2
2
1
0
0
0
1
1
1
1
0
1
0
0
3
2
0
2
0
2
0
2
1
0
0
3
1
0
2
0
2
2
2
0
0
0
1
0
1
2
0
0
0
0
1
2
1
1
1
0
1
1
1
3
1
0
1
1
1
1
1
0
1
2
0
1
1
2
2
0
0
1
1
0
1
1
1
2
0
1
1
2
1
0
0
0
1
0
1
0
4
0
1
1
0
1
0
1
0
2
1
3
0
1
2
1
2
1
2
2
1
2
2
0
1
1
2
1
1
1
2
2
0
0
1
0
0
0
0
0
1
1
0
0
2
0
0
0
0
1
2
1
0
1
1
0
0
0
2
0
0
1
0
0
0
2
0
2
0
1
0
1
2
1
1
3
2
0
1
1
0
0
0
1
0
0
2
0
0
2
0
0
1
2
1
0
2
3
0
0
2
1
0
1
0
1
0
2
1
0
0
2
1
0
0
2
2
1
0
0
0
0
0
0
2
1
1
1
0
1
0
0
0
2
0
0
0
2
2
0
1
2
0
0
0
1
0
1
0
0
2
0
0
2
1
1
0
0
0
0
1
0
0
2
0
0
1
2
0
0
0
2
0
1
0
2
1
1
1
1
2
0
1
1
0
1
0
1
5
2
0
0
1
0
2
0
0
0
0
1
0
1
0
2
1
0
0
1
1
0
2
2
0
0
0
1
0
1
1
0
0
1
0
0
2
0
1
0
0
2
0
1
0
1
0
0
2
1
1
1
0
2
0
1
1
1
0
0
3
0
0
2
0
0
1
2
2
0
0
0
2
1
0
0
2
2
0
0
0
1
1
2
1
1
0
0
2
1
0
0
1
0
2
0
1
10
2
2
1
0
1
2
1
0
0
2
0
0
1
0
0
1
0
2
1
1
0
0
0
0
1
0
0
0
2
0
2
3
1
0
2
1
1
2
2
2
0
0
0
0
0
1
2
1
1
2
1
0
1
0
1
0
0
1
1
0
0
0
1
1
0
2
2
1
1
2
0
1
0
0
2
1
0
0
2
1
1
0
1
0
0
2
0
1
1
1
1
2
3
2
1
0
0
0
1
0
2
1
1
1
0
1
0
1
0
0
1
1
0
2
3
0
0
0
0
0
2
1
0
0
0
0
2
1
1
1
2
2
2
2
1
2
0
1
1
0
0
2
0
1
1
3
0
2
0
1
0
1
1
0
0
2
0
0
0
2
0
0
2
1
0
0
1
1
0
1
1
1
2
0
2
1
2
0
2
3
0
0
0
2
1
0
0
2
0
0
1
1
1
0
0
0
2
0
1
0
1
1
1
1
0
1
0
1
0
1
1
2
0
0
1
1
1
1
0
1
0
0
0
0
0
0
0
0
0
2
3
1
0
1
1
0
1
0
1
0
2
1
1
0
0
2
1
0
0
0
0
0
1
2
1
0
1
2
2
2
0
1
1
0
0
1
1
0
1
0
0
0
1
1
0
1
0
1
1
1
1
0
2
1
0
1
0
1
1
1
1
0
4
1
1
2
0
0
0
0
1
1
0
0
1
2
0
0
0
0
1
1
1
1
2
0
0
0
1
0
0
0
0
1
1
1
0
0
3
2
2
1
1
1
2
1
1
0
0
1
1
0
2
1
0
0
0
1
1
2
1
0
2
0
0
1
1
0
0
0
0
0
4
0
0
1
2
0
2
2
1
1
2
1
1
2
2
1
2
0
1
0
1
2
0
0
1
1
3
2
1
2
2
0
2
1
2
0
2
1
2
0
0
0
0
0
0
1
0
1
1
0
0
2
1
2
2
0
0
1
0
0
2
0
0
0
1
1
0
2
2
0
2
0
0
1
2
1
1
0
1
1
0
0
0
0
1
2
1
0
2
1
1
2
2
2
1
1
1
0
1
0
0
1
0
0
2
0
1
0
0
0
1
0
0
0
2
0
0
1
3
1
1
0
1
2
1
0
0
0
0
2
0
1
0
0
0
0
1
1
0
2
0
0
1
2
2
0
1
0
0
2
2
2
1
0
1
1
0
0
0
0
0
1
0
0
2
0
1
1
0
1
4
0
0
0
0
0
0
0
1
0
2
0
1
0
1
2
2
1
2
0
0
0
1
0
0
4
1
2
0
1
3
2
2
1
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
1
0
0
1
0
0
0
1
0
1
0
0
1
0
1
2
1
0
0
0
0
0
1
0
3
0
0
0
2
0
1
1
1
2
0
1
0
0
0
1
1
1
1
1
1
3
1
0
1
2
2
2
2
1
0
2
2
2
0
1
0
0
3
1
1
0
1
2
1
0
0
0
0
2
1
1
0
2
0
2
0
0
1
1
1
1
2
0
1
1
2
0
2
1
1
0
1
0
2
1
2
0
1
2
0
0
1
1
2
2
1
2
1
0
0
2
0
1
0
0
0
0
1
1
1
1
0
2
2
0
1
1
0
0
0
1
1
0
2
2
1
0
1
0
0
2
0
1
2
1
1
2
0
0
0
0
0
3
2
1
1
2
2
2
0
2
0
0
1
1
1
2
2
1
1
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
1
0
2
0
1
1
1
3
1
3
2
1
0
1
1
1
1
1
3
0
0
1
2
1
0
0
3
0
2
0
1
0
0
2
0
0
0
2
1
0
0
0
0
1
1
0
2
1
1
1
1
1
2
0
2
2
0
0
0
0
0
2
2
1
1
2
2
2
0
0
0
1
3
0
1
2
2
1
0
1
2
1
2
0
0
0
0
1
0
1
0
0
0
1
0
0
2
2
1
0
0
1
0
2
1
0
0
2
0
0
1
1
0
1
1
0
0
2
3
1
1
1
1
0
1
1
1
1
1
1
0
2
2
1
2
2
0
1
1
0
0
0
1
1
1
1
0
0
0
1
1
1
2
1
2
0
2
2
0
1
1
1
0
0
1
1
1
2
1
0
2
2
2
0
1
0
2
0
2
2
1
1
0
1
0
1
1
2
2
2
0
2
0
1
0
0
1
1
1
0
1
0
1
0
0
0
1
0
1
0
0
0
2
0
2
0
1
2
2
0
1
1
0
0
0
2
0
0
0
1
0
0
0
2
1
2
3
0
0
2
0
2
0
0
2
2
1
1
1
4
0
0
2
0
5
0
2
1
2
0
1
1
0
0
0
2
0
1
2
2
1
1
0
2
2
0
1
0
0
1
0
0
2
0
1
0
0
1
2
1
0
0
0
2
2
0
2
0
0
2
1
0
2
1
0
2
0
1
1
1
1
2
0
0
1
1
0
2
0
0
0
0
1
2
0
1
1
1
0
0
2
1
0
0
1
1
0
0
1
2
0
1
0
1
2
0
2
1
0
1
1
1
0
0
2
1
0
1
0
1
0
0
1
0
1
0
1
0
1
1
2
0
2
0
1
1
0
1
0
0
4
1
1
1
1
0
1
0
1
2
0
2
1
0
0
0
1
1
0
1
1
1
0
0
0
0
0
0
2
1
0
0
0
0
2
1
1
1
2
1
1
1
1
0
0
0
0
0
2
0
0
0
1
1
0
2
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
2
1
1
2
0
0
2
0
1
1
1
1
0
1
1
0
0
2
1
1
1
0
2
1
1
1
2
0
0
0
2
1
0
0
2
2
0
2
2
1
1
2
0
0
0
1
1
1
0
0
1
2
0
1
0
0
0
1
2
1
2
0
0
1
1
1
1
0
1
0
0
0
0
0
1
2
1
0
1
0
2
0
0
0
2
1
1
0
0
0
1
1
2
1
0
1
1
0
1
1
1
1
1
1
2
0
0
0
2
1
0
0
0
1
2
2
2
1
0
0
1
0
1
2
0
0
0
1
2
1
0
1
1
0
1
1
2
1
2
0
2
1
2
2
0
1
0
0
2
0
0
0
1
0
1
1
1
1
0
1
0
2
2
0
1
0
0
0
0
0
0
0
1
2
0
1
2
0
1
2
0
0
0
0
0
1
1
0
0
0
1
0
0
0
2
0
1
0
1
1
1
1
1
0
2
0
2
1
0
1
1
0
1
1
0
0
0
2
0
0
1
1
1
1
2
1
0
0
3
0
0
1
1
1
1
0
1
1
2
1
1
2
7
1
2
0
0
1
2
0
0
1
2
1
1
1
1
0
0
2
0
1
1
2
0
1
2
0
1
1
1
4
2
2
3
2
2
1
0
0
0
1
0
2
2
2
0
0
1
1
0
0
1
3
2
0
0
2
1
1
0
1
1
3
0
1
0
0
0
0
1
0
0
0
0
1
0
2
0
1
0
0
1
1
0
1
1
0
1
1
1
1
1
0
0
0
2
1
0
2
1
0
0
0
1
0
0
0
0
1
0
1
0
1
1
1
0
1
1
1
2
0
2
1
2
1
1
0
1
3
0
2
2
2
0
0
1
0
2
1
0
1
3
1
1
0
0
0
1
0
2
1
0
2
0
0
0
0
0
2
0
0
0
1
2
0
0
1
0
2
1
1
0
2
0
1
2
0
2
0
2
2
1
2
1
0
0
1
0
1
1
1
1
0
1
1
2
0
2
0
0
1
2
0
0
0
0
2
1
0
0
0
1
0
1
0
0
1
1
1
1
2
0
2
0
1
1
1
0
2
1
3
0
1
2
2
0
2
1
1
2
2
0
2
2
1
0
1
0
0
0
2
0
1
2
1
2
1
0
2
0
2
2
0
0
1
0
1
0
1
0
1
1
0
1
2
0
1
1
0
0
0
0
2
2
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
2
3
2
0
0
2
0
2
1
1
2
2
1
0
2
0
0
0
1
1
0
1
0
1
1
0
1
0
1
1
2
1
3
2
0
0
2
0
2
1
2
0
1
3
0
2
0
1
1
1
1
1
0
1
0
0
0
0
0
0
0
1
1
0
2
1
1
2
0
0
0
2
1
0
2
1
2
0
0
1
0
0
1
2
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
1
1
1
0
0
2
2
2
2
0
0
0
1
2
1
1
0
0
0
1
0
1
2
2
2
2
0
0
0
1
0
2
0
1
0
1
1
1
2
0
0
1
0
0
2
1
0
1
0
0
0
1
0
1
0
0
1
0
1
0
1
3
0
1
0
0
2
1
0
1
1
1
0
1
0
1
1
0
0
1
0
1
0
1
2
1
2
2
2
2
1
2
1
0
1
1
0
2
0
2
0
0
1
2
0
2
0
0
0
2
2
1
1
0
2
1
0
1
1
0
0
1
0
2
0
1
0
1
1
1
1
1
1
2
2
3
0
0
1
0
2
1
1
0
0
1
1
2
0
0
0
0
0
1
0
2
2
2
3
0
1
1
0
0
1
0
0
1
0
1
0
0
0
1
0
2
1
0
0
0
6
0
1
0
1
0
1
2
0
0
0
1
0
0
0
1
1
1
2
0
0
0
0
1
0
0
1
0
0
0
2
1
0
0
3
2
1
0
1
0
0
1
1
1
0
1
0
0
0
1
1
2
1
1
1
1
0
1
2
0
0
1
1
0
0
2
1
0
2
2
1
0
0
0
0
0
2
2
1
0
0
2
0
0
1
0
1
2
0
1
0
0
1
2
2
0
1
2
0
0
1
0
1
1
2
0
2
1
3
1
1
2
3
0
1
1
2
2
7
0
0
0
1
0
1
0
2
0
2
0
0
1
2
2
0
0
0
0
1
1
0
1
1
1
1
2
0
1
0
1
1
0
0
0
0
1
0
1
0
0
1
0
1
0
2
0
1
0
0
1
0
1
0
0
0
1
1
0
0
1
1
2
2
0
1
2
0
1
1
0
0
2
0
1
2
2
2
0
1
2
0
0
2
0
0
1
1
0
0
1
1
2
2
1
0
0
0
1
0
2
0
2
0
1
1
1
1
0
2
2
1
0
0
2
0
2
0
0
0
0
0
1
1
0
1
0
0
0
0
1
1
0
1
1
2
1
1
1
0
0
0
1
0
0
2
1
3
1
2
0
1
2
2
1
1
2
0
0
0
2
0
2
0
2
0
1
2
0
1
1
1
1
2
1
1
0
0
1
0
2
0
0
1
0
0
0
1
0
2
0
0
1
1
0
1
2
0
0
0
2
2
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
2
2
0
1
0
0
0
0
2
0
1
1
0
0
0
0
0
0
2
0
1
1
0
0
1
2
0
0
1
1
0
0
1
1
1
2
0
2
0
1
3
2
1
0
2
2
1
2
2
2
2
0
0
0
0
1
0
1
0
0
2
0
2
0
1
1
1
1
0
2
1
2
0
0
0
1
1
1
2
0
0
0
1
1
1
0
0
5
0
0
1
1
1
0
2
0
1
0
1
2
1
0
0
0
0
1
2
0
1
1
1
1
1
0
0
0
0
0
2
2
0
1
1
1
1
0
0
0
1
1
0
0
2
0
0
2
0
0
1
1
0
0
0
1
1
0
0
0
1
0
0
2
0
1
0
2
1
2
0
0
0
1
0
1
1
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
2
1
1
0
0
0
1
1
2
2
0
0
1
0
0
1
2
1
1
0
0
2
1
1
1
0
1
0
1
0
1
2
0
1
1
0
2
1
1
0
0
0
1
0
0
1
0
1
0
2
0
2
0
0
0
0
1
0
0
2
0
1
0
0
0
0
1
1
0
2
2
0
1
1
0
1
1
0
0
1
1
1
0
2
1
1
2
1
0
1
2
2
0
1
0
0
1
0
0
0
0
1
0
0
0
2
1
1
1
0
0
0
0
2
2
0
1
2
0
2
0
1
0
1
1
1
0
2
1
0
0
0
0
1
0
0
2
1
0
0
2
0
2
0
0
0
0
1
1
0
0
0
1
1
1
0
2
1
1
0
0
0
0
1
0
3
0
0
0
0
2
0
1
1
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
2
2
2
0
0
2
0
1
2
1
0
1
0
0
0
2
1
3
0
4
0
1
0
0
0
1
1
0
0
1
2
0
1
1
1
0
1
0
0
0
0
2
1
2
0
0
0
2
0
1
0
1
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
1
1
1
0
1
0
1
0
0
0
2
1
2
0
2
0
2
0
1
1
0
0
1
1
0
1
0
0
0
0
2
0
0
2
2
2
1
0
1
1
1
0
0
0
0
1
0
0
2
2
5
1
0
1
2
0
2
0
0
0
0
0
2
0
0
1
2
0
1
2
0
1
0
1
1
1
1
0
0
2
0
2
0
2
2
0
3
1
2
0
1
0
1
1
0
1
0
2
1
2
2
0
1
0
1
0
2
2
0
0
2
1
1
2
0
0
0
0
0
2
0
0
1
0
2
2
0
1
2
2
1
2
0
2
2
2
1
1
0
1
1
2
0
1
1
2
2
0
2
0
2
1
0
2
0
1
0
0
0
2
0
2
0
2
0
0
2
2
2
1
0
1
1
0
0
1
0
0
1
2
1
1
1
1
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
2
1
0
2
2
1
0
0
1
0
1
0
0
0
2
2
0
0
2
0
0
2
1
1
1
1
0
2
1
1
0
0
2
0
0
1
1
0
2
0
0
0
1
1
0
2
0
2
1
1
2
1
0
0
1
0
0
2
0
0
1
1
1
2
0
0
1
0
2
2
0
2
1
0
1
1
2
3
1
1
0
0
2
0
1
1
0
2
2
0
0
3
1
2
0
3
1
1
2
1
0
1
0
0
0
1
0
0
1
1
0
0
0
1
1
0
1
0
0
0
2
2
1
1
0
3
2
1
1
0
0
1
0
0
0
1
0
1
0
0
1
0
2
0
1
1
1
2
0
0
1
2
2
1
1
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
1
0
1
0
0
1
1
2
1
1
2
0
2
1
1
2
1
1
0
2
1
2
0
0
4
0
1
1
0
0
0
0
0
0
1
1
2
0
1
2
1
0
0
0
1
2
1
0
0
1
1
1
2
1
1
0
0
0
1
0
1
0
1
1
2
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
1
1
0
2
2
1
0
0
0
1
0
0
0
0
0
0
0
0
2
2
1
2
0
0
0
0
1
1
1
0
0
0
1
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
2
0
2
2
0
0
0
0
2
0
0
0
1
1
0
0
2
1
1
0
1
0
1
1
0
1
0
2
2
0
0
0
0
0
0
1
2
0
1
2
1
1
1
0
1
0
2
2
1
0
1
1
0
2
1
0
1
1
1
1
2
2
1
0
2
0
1
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
2
2
1
1
1
1
0
0
0
0
2
0
0
0
0
0
0
1
0
1
1
1
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
2
0
1
0
2
2
1
1
2
1
0
0
1
0
1
1
1
0
2
1
2
1
0
1
1
2
0
0
1
0
1
0
1
0
2
0
1
0
1
0
2
0
0
3
1
1
2
2
1
0
0
0
0
0
1
1
1
2
0
0
0
0
0
0
2
2
1
1
2
0
2
0
0
0
0
2
1
2
0
0
0
0
2
1
0
0
1
2
1
0
0
0
0
0
2
2
0
0
1
1
0
3
2
0
1
1
2
1
0
1
1
0
0
1
0
2
0
0
0
0
1
1
3
0
1
2
1
1
1
1
2
0
1
0
1
1
0
2
0
0
0
2
0
0
1
1
1
1
0
0
0
0
0
0
0
2
2
2
2
1
0
0
1
0
0
0
1
0
1
0
0
0
1
1
1
0
1
0
1
1
1
1
1
0
2
2
1
1
0
2
1
1
1
0
0
1
0
1
1
0
2
1
0
1
1
0
1
0
0
0
0
3
0
0
1
1
2
2
0
1
0
1
0
1
1
2
1
2
1
0
2
0
0
0
1
2
0
1
2
0
1
0
1
5
0
0
1
0
1
1
0
1
0
0
1
1
0
2
0
0
0
0
0
0
1
0
0
2
0
1
2
1
0
2
0
1
3
1
0
1
0
1
0
2
0
0
1
2
1
2
1
0
0
0
0
0
1
0
2
0
1
2
1
2
1
1
1
1
0
0
1
2
1
0
0
2
1
2
0
2
0
2
1
2
2
0
0
1
2
2
0
0
2
0
1
2
0
0
0
0
1
1
2
2
0
0
0
0
2
2
2
0
0
0
0
2
1
2
1
1
2
1
1
0
2
0
0
2
2
0
1
0
0
2
0
1
0
2
0
2
2
1
2
0
0
1
1
1
2
1
1
1
2
0
0
1
0
2
0
0
0
0
0
3
0
0
0
1
4
0
1
2
2
0
0
1
0
2
2
0
1
2
0
0
1
0
2
2
0
1
2
2
0
0
1
0
0
2
1
2
1
1
2
1
0
1
2
0
1
2
0
0
1
0
0
2
1
4
1
1
0
2
1
1
1
2
1
1
0
2
1
0
0
1
0
0
0
2
5
0
1
0
0
0
0
2
1
0
0
1
2
0
1
1
1
0
0
2
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
3
0
0
1
1
2
0
1
1
0
0
3
0
0
1
1
0
0
1
1
2
0
0
0
1
0
2
0
1
0
1
0
0
0
1
0
0
1
1
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
1
1
2
1
0
1
1
1
2
1
1
2
0
2
0
0
1
0
2
0
0
1
0
0
0
0
0
1
1
1
0
0
1
2
1
0
2
0
0
1
0
1
7
0
0
1
0
1
1
0
2
0
1
2
0
0
0
0
0
2
1
0
0
1
2
0
0
1
2
0
1
1
0
2
1
1
0
1
1
1
0
0
1
1
0
0
1
0
0
0
0
1
0
1
1
2
2
0
1
1
1
1
1
0
0
0
1
0
0
1
1
1
1
0
1
0
0
0
2
1
0
1
2
2
0
0
1
1
1
0
0
0
0
1
1
1
1
3
1
0
1
0
2
0
1
2
0
2
0
2
2
1
0
0
2
2
1
0
0
0
0
1
1
0
0
0
1
2
1
0
0
1
2
0
2
2
0
1
0
0
2
1
0
2
2
0
1
1
1
1
0
0
2
0
0
1
2
0
0
0
1
2
2
0
0
0
1
0
1
0
1
0
1
1
0
2
0
0
2
2
0
0
2
0
0
0
0
2
0
2
1
1
0
0
1
0
0
0
0
2
0
0
1
0
1
1
0
0
1
2
2
1
1
1
2
0
0
0
0
1
1
1
0
0
0
0
0
2
0
0
2
0
0
1
0
0
2
1
0
1
0
1
2
1
0
1
0
0
1
1
1
1
0
0
1
0
0
0
0
1
0
1
1
0
1
0
0
0
2
0
0
3
0
0
0
2
2
0
0
1
1
0
0
0
2
0
2
1
1
1
0
1
0
2
0
0
1
0
2
1
1
4
2
0
2
0
0
0
1
0
0
1
1
2
0
0
0
1
1
1
1
2
0
1
1
0
1
2
1
1
2
1
2
0
0
1
0
0
0
1
0
2
0
0
2
0
1
1
0
0
1
1
1
2
0
0
0
2
1
1
1
0
0
2
1
0
2
2
0
2
1
2
0
2
0
0
1
0
0
0
0
0
1
2
1
0
1
0
0
0
0
1
1
0
1
1
1
2
1
0
1
0
0
0
0
2
1
0
0
3
1
0
0
0
0
0
0
6
1
1
1
2
0
1
0
0
0
0
0
1
1
2
2
0
1
0
1
1
0
0
1
0
0
0
0
0
1
2
0
0
0
1
1
0
0
0
1
1
1
0
0
0
0
1
1
2
1
1
2
0
1
2
0
2
1
1
1
0
1
1
0
0
2
0
3
2
1
2
2
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
2
0
0
2
1
1
0
1
0
1
1
2
1
0
0
0
0
3
2
0
0
1
0
1
0
1
0
0
1
1
0
1
0
1
2
0
2
0
1
1
1
1
0
1
1
0
0
0
2
1
1
0
0
1
1
0
6
0
0
1
0
1
2
0
1
0
0
2
0
1
2
0
1
0
0
0
0
0
0
0
0
2
0
1
0
1
1
0
3
2
0
0
0
2
1
0
1
0
0
0
1
0
0
0
1
2
0
0
1
2
0
1
2
1
1
0
1
1
2
1
0
0
0
1
4
1
2
1
1
2
0
1
0
1
1
0
0
0
1
0
2
0
2
1
0
2
1
0
1
1
1
0
0
1
0
0
1
1
0
0
0
0
1
2
1
0
1
0
0
0
0
1
0
0
2
2
0
2
2
1
1
0
2
1
0
2
1
0
0
0
2
0
0
1
0
0
2
0
2
1
1
0
1
0
0
2
0
1
2
1
1
0
1
2
1
0
0
0
0
2
1
3
0
0
1
5
1
2
0
1
1
0
0
0
1
0
2
1
1
0
0
2
1
1
2
1
1
2
2
1
1
0
1
1
1
0
0
0
2
1
2
0
1
0
0
1
2
2
0
0
2
0
2
1
0
0
2
1
2
1
0
0
2
0
0
2
1
2
1
1
0
0
1
0
0
0
0
0
1
2
0
0
0
2
1
1
2
0
0
2
0
1
2
1
0
0
0
1
0
0
1
1
0
0
2
0
1
1
1
0
0
1
0
1
2
1
1
0
2
0
2
2
0
0
0
1
0
1
1
0
0
2
1
0
1
0
1
2
2
0
3
1
0
2
1
0
0
0
1
0
3
1
1
2
0
2
0
0
1
0
2
0
1
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
1
0
2
0
1
4
0
1
2
1
0
2
1
1
1
1
1
0
1
0
0
0
1
1
1
0
2
1
2
0
0
0
1
1
2
0
1
0
1
2
0
0
0
1
1
2
1
1
0
1
1
1
1
1
0
1
1
2
0
0
0
0
1
2
1
2
0
2
0
1
1
0
0
2
4
1
1
2
0
1
2
1
0
0
0
0
0
0
0
1
2
0
1
2
0
0
0
0
0
1
0
3
1
1
0
0
2
1
0
0
1
1
0
2
0
1
2
0
2
2
0
0
0
0
0
1
1
0
0
1
0
0
1
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
2
1
2
0
0
2
0
0
1
0
0
2
2
1
1
0
1
1
0
0
2
0
0
0
1
0
1
0
6
1
0
0
0
1
0
5
2
0
0
0
0
1
1
0
1
1
1
0
2
1
2
0
1
0
4
1
1
0
1
1
3
0
0
0
0
1
3
2
2
0
1
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
2
0
0
2
1
0
2
1
1
0
0
0
1
0
0
2
1
1
0
1
1
0
2
2
0
0
0
2
1
0
0
1
0
2
0
2
1
0
0
0
3
2
1
2
1
0
1
1
1
0
0
0
2
1
2
0
1
2
1
1
0
1
3
0
1
1
0
2
1
0
1
0
1
1
1
0
1
2
2
2
0
0
0
0
0
2
1
2
0
2
1
2
0
2
0
1
0
2
1
0
0
1
0
2
1
3
0
0
0
1
1
0
2
0
0
1
0
1
0
1
0
0
1
2
1
0
0
0
1
1
1
1
2
0
1
0
0
1
1
0
1
1
2
2
2
0
0
2
1
1
2
0
1
1
1
1
0
0
2
0
2
0
0
0
1
1
2
0
2
0
0
0
1
0
1
2
1
1
0
0
1
2
1
1
1
1
2
0
2
1
0
0
1
1
2
1
1
0
1
0
1
0
2
2
0
1
2
0
2
2
1
0
0
1
1
0
1
2
0
3
2
0
1
0
1
1
2
2
0
0
1
1
1
1
0
0
1
1
0
0
1
0
0
2
1
0
0
1
2
1
0
2
2
2
0
0
0
1
0
3
2
1
0
1
1
2
2
1
0
1
0
0
0
1
0
1
2
1
0
2
1
0
0
1
0
1
0
0
1
2
0
0
0
0
1
0
1
2
0
0
2
0
0
0
1
0
1
0
0
1
2
2
0
2
1
0
2
1
0
2
2
1
0
0
0
1
2
0
3
0
0
1
1
0
0
1
0
2
0
1
2
0
0
1
0
2
1
0
0
1
0
1
2
1
0
0
0
0
0
2
1
0
0
0
1
0
0
1
0
0
2
2
1
0
0
0
0
0
0
0
0
1
1
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
1
1
1
1
0
1
1
0
2
0
1
0
1
1
2
3
0
0
1
2
0
1
0
0
1
0
0
0
1
2
0
1
2
2
2
1
1
0
0
0
0
0
0
1
1
2
0
1
2
1
0
2
0
1
1
3
0
2
0
2
2
2
0
1
0
1
0
2
0
0
0
1
2
0
0
0
1
1
0
1
0
0
2
0
1
0
0
1
0
1
0
1
2
0
0
0
0
0
8
2
0
0
0
0
1
1
0
2
2
0
0
0
0
0
1
0
1
1
1
1
0
1
0
2
2
0
0
2
2
0
1
0
1
1
0
0
0
1
0
3
0
0
0
0
1
1
1
0
0
0
1
2
0
0
0
0
2
0
0
0
1
0
1
0
1
1
1
0
1
0
2
2
2
0
0
2
0
0
1
1
0
2
0
1
0
0
1
0
0
2
1
0
0
0
2
1
0
2
0
0
1
2
1
0
1
1
1
1
2
1
1
2
0
0
1
2
0
0
0
1
2
0
2
0
0
2
2
2
0
0
2
1
1
1
0
2
2
0
0
1
2
0
1
1
0
0
2
0
2
2
0
2
0
0
1
2
1
1
1
0
0
0
1
1
1
0
1
0
1
0
0
0
1
0
1
1
1
0
1
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
2
1
2
0
0
1
1
0
0
3
1
0
0
0
0
1
3
0
0
0
2
1
0
2
2
0
0
0
1
2
0
2
1
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
1
1
2
1
1
0
0
1
0
1
2
0
1
0
0
1
2
1
1
0
0
2
1
0
0
0
0
2
0
1
2
1
2
0
1
7
2
0
0
0
0
0
3
1
0
0
0
0
0
0
0
2
1
1
1
1
0
1
1
2
0
0
0
2
0
0
0
0
2
1
0
0
1
1
2
1
0
0
0
2
0
0
1
0
1
0
1
0
1
2
1
0
3
0
0
1
2
0
0
1
0
1
0
0
1
1
1
1
1
1
0
1
0
1
0
1
0
1
2
3
2
1
2
1
1
1
1
0
0
1
1
1
0
2
0
0
0
1
0
1
1
0
0
2
0
1
1
0
1
1
1
2
0
0
3
0
1
1
0
1
1
0
0
0
0
0
0
0
0
1
1
0
2
2
0
0
1
0
2
2
2
1
0
1
1
0
1
2
0
1
1
3
1
1
0
0
1
1
0
0
1
1
2
2
0
0
1
0
1
2
2
0
2
0
2
0
1
2
1
1
0
2
0
1
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
2
0
1
0
1
0
1
0
0
1
4
1
0
0
2
1
0
2
2
1
0
1
0
0
1
0
2
1
1
1
1
1
1
0
1
0
2
0
1
1
0
1
2
1
0
4
0
1
1
2
2
1
1
1
0
1
0
2
1
0
0
2
1
0
0
1
1
0
0
1
1
2
2
2
0
1
0
3
1
0
0
1
0
0
0
0
2
2
2
0
0
1
0
1
1
0
0
0
0
2
2
1
1
0
0
1
1
0
1
0
0
1
0
1
2
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
2
1
3
1
1
0
1
3
0
1
1
2
0
3
1
1
1
2
1
1
2
1
1
0
0
2
0
2
0
0
1
0
1
0
0
1
1
0
1
2
0
2
1
1
2
1
1
0
1
2
0
0
1
1
0
1
1
1
0
0
0
0
0
1
2
0
0
0
0
2
0
3
3
1
0
2
0
0
1
0
0
1
2
1
1
1
2
0
2
0
0
1
0
0
1
2
0
1
1
1
0
2
0
2
1
0
0
0
2
2
0
0
0
1
0
0
0
0
1
0
0
1
0
0
2
0
0
0
1
0
1
0
0
1
1
1
2
0
0
0
1
2
0
0
0
2
1
0
1
1
1
0
2
0
2
1
1
1
1
0
0
0
0
0
1
0
2
1
0
0
1
0
1
0
0
2
1
2
3
0
0
0
1
0
0
0
2
0
1
1
0
1
2
1
0
1
1
1
2
1
2
0
2
2
0
0
1
2
1
0
0
0
1
2
1
2
0
2
0
1
1
1
0
2
1
1
0
0
1
2
1
1
2
0
1
1
2
2
1
1
0
1
1
0
1
0
1
2
0
0
2
1
1
1
0
5
0
1
2
1
2
2
2
0
0
0
0
0
0
0
2
1
1
0
1
1
0
0
0
2
0
0
1
0
0
2
2
2
1
2
0
0
1
0
0
1
1
1
0
0
1
1
2
1
1
2
1
2
0
0
1
0
2
1
1
0
1
1
0
2
1
0
2
1
1
0
0
0
1
1
1
0
2
0
1
1
2
1
1
0
1
0
1
1
3
2
1
1
0
1
0
1
0
2
0
0
1
1
1
0
1
0
0
2
2
1
2
1
2
3
1
0
2
1
0
0
0
2
2
1
0
2
0
2
0
0
0
1
2
0
2
1
1
1
0
1
0
0
0
1
2
0
1
2
0
0
1
2
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
2
0
0
0
0
3
0
1
0
2
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
2
0
1
0
1
0
0
2
0
0
1
2
0
0
0
1
2
1
2
0
0
0
0
1
0
0
2
1
1
0
0
1
0
0
0
0
2
1
1
1
1
1
1
2
2
1
0
0
1
0
1
1
0
2
2
0
1
1
2
1
0
1
0
1
1
1
2
2
0
2
0
2
0
0
0
0
0
1
2
1
1
1
1
0
1
0
1
0
1
0
1
1
0
1
0
1
2
2
2
0
0
1
0
0
0
0
0
0
2
2
1
0
0
1
0
2
1
1
2
2
2
0
0
0
0
0
2
1
1
1
0
0
0
0
1
2
2
2
1
0
2
0
0
1
2
1
1
0
0
0
0
1
0
1
0
0
0
1
0
1
1
0
0
0
1
2
0
1
2
1
0
0
0
0
1
0
2
1
1
1
1
0
0
2
1
1
1
1
3
1
2
2
1
2
1
1
0
0
2
0
2
1
2
1
1
3
1
0
1
1
0
1
0
0
2
2
2
1
1
0
0
1
0
2
1
0
1
1
1
0
1
1
0
2
2
0
0
1
2
2
0
0
0
1
2
0
0
3
0
0
0
0
1
0
2
0
1
0
0
1
0
0
0
0
0
0
1
0
3
0
0
2
1
1
0
0
1
1
0
1
0
1
0
1
1
1
0
1
0
1
2
1
0
1
0
0
0
1
2
2
2
1
0
0
0
0
1
1
1
2
0
1
0
0
1
1
1
2
1
2
2
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
2
1
2
1
0
1
1
2
0
2
1
1
0
0
2
1
0
0
1
1
0
1
1
2
1
0
2
0
0
1
2
1
0
0
0
0
1
2
0
0
1
0
1
0
1
0
1
0
2
1
1
1
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
1
0
0
1
1
1
1
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
1
2
2
1
1
2
1
0
0
2
2
1
2
1
0
2
0
0
0
1
1
2
1
2
1
1
1
2
1
1
1
2
2
0
1
1
0
0
0
1
2
0
1
0
0
2
2
0
0
0
1
1
0
2
2
1
0
2
2
2
1
0
2
2
1
0
0
2
0
2
0
1
0
1
1
0
0
2
0
1
1
1
2
0
1
0
2
0
0
0
0
0
0
2
1
2
2
0
1
1
0
2
0
2
1
0
0
1
0
0
0
0
1
1
2
0
0
2
0
0
2
0
1
0
2
0
2
0
2
0
1
0
1
0
1
1
0
0
2
1
1
0
1
1
1
0
0
0
0
0
0
0
1
2
1
0
0
0
1
0
1
0
0
0
0
2
0
0
0
2
0
1
1
1
0
0
2
1
1
2
0
1
1
1
0
0
0
0
1
2
1
1
2
1
0
0
0
0
1
2
0
0
1
0
0
2
1
0
2
1
2
0
1
0
1
0
1
2
0
0
0
1
3
0
1
2
0
1
0
0
2
1
1
2
2
0
0
3
1
2
2
2
2
1
1
0
1
1
1
0
1
3
1
0
0
1
1
0
0
1
2
1
0
2
1
0
0
0
0
0
1
2
2
0
0
2
2
1
0
0
0
1
3
0
0
2
0
0
0
1
0
1
1
0
2
0
2
1
0
0
0
0
1
1
2
0
1
0
0
2
1
0
0
1
2
0
2
2
2
0
0
0
0
1
0
0
0
2
0
0
0
0
1
1
0
1
1
0
1
0
0
3
1
2
0
2
0
0
1
0
1
0
0
3
0
0
0
2
0
2
1
1
1
3
0
2
1
0
1
0
2
1
2
1
0
0
0
2
0
1
1
0
0
1
0
1
0
0
1
0
0
0
1
2
2
1
0
0
3
1
0
1
2
1
3
2
0
2
0
1
1
1
0
0
0
0
0
0
0
3
1
0
0
0
0
0
2
2
2
3
1
1
0
0
0
0
2
0
0
1
1
0
0
1
0
0
1
2
0
2
1
2
1
1
1
0
1
0
0
0
1
1
2
1
1
1
0
0
0
0
2
2
4
2
1
1
0
0
0
2
0
0
1
0
0
2
0
1
0
0
1
1
1
2
1
1
1
0
0
1
2
1
1
1
2
1
0
1
1
0
0
0
2
0
0
1
2
0
2
2
1
1
1
0
0
1
0
2
1
1
1
0
0
2
1
1
2
0
3
2
0
0
1
1
1
0
2
1
0
1
2
1
0
0
1
1
0
1
1
1
0
0
2
0
1
3
1
0
3
1
1
1
1
0
0
2
0
1
0
0
2
0
2
1
4
1
0
0
0
2
4
1
0
0
2
1
1
2
1
1
1
2
1
1
0
0
1
2
0
0
0
2
0
3
2
1
1
1
1
1
3
0
2
0
1
0
1
0
2
1
1
1
0
0
1
0
2
1
2
1
0
0
2
0
2
1
0
2
1
0
0
2
1
1
1
1
2
1
0
0
0
0
0
0
1
2
1
2
0
1
0
3
0
0
0
2
0
1
0
2
1
1
1
2
0
0
0
0
1
2
2
0
1
1
2
2
2
0
2
0
0
0
1
1
1
0
1
1
0
2
1
0
2
1
0
0
0
0
1
2
2
0
1
0
2
1
1
0
1
0
0
2
0
1
1
2
2
2
1
0
1
0
0
0
0
2
0
2
1
1
0
2
0
1
1
1
1
2
2
2
1
2
0
0
0
0
1
1
1
2
0
0
2
2
0
1
1
0
1
0
2
1
2
0
1
0
1
0
1
1
0
1
2
2
0
0
0
2
1
2
2
2
2
0
2
1
2
1
2
0
0
0
0
0
1
1
0
1
2
0
0
2
0
1
1
0
0
2
1
0
0
1
2
0
0
2
0
4
0
2
0
1
0
0
0
0
1
0
0
1
0
1
2
2
0
1
2
1
0
0
3
2
1
0
0
0
0
0
0
0
0
0
3
0
0
2
2
0
1
0
0
0
1
0
0
1
1
0
0
1
0
0
0
2
1
0
2
0
2
0
1
0
0
1
0
0
2
0
0
1
0
0
0
0
1
1
0
1
0
2
0
0
2
2
0
2
0
0
1
0
1
6
0
1
0
1
1
1
0
2
1
0
2
1
2
2
0
1
0
1
0
0
0
1
1
0
2
1
0
0
0
0
4
0
1
2
1
0
0
0
0
0
1
2
0
2
1
2
1
0
1
2
1
1
0
0
1
0
2
1
2
0
1
1
0
0
1
0
1
0
1
0
0
2
1
1
1
0
1
0
0
0
0
2
0
0
0
1
0
1
1
1
0
0
2
0
1
0
0
1
0
0
2
0
1
1
1
2
0
0
1
0
0
1
0
2
0
0
2
1
0
0
1
1
2
3
0
0
1
0
3
1
0
1
0
0
1
1
1
0
2
0
0
1
0
0
1
2
1
1
2
0
0
0
1
1
0
0
1
0
0
0
2
1
1
1
0
1
0
1
2
2
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
2
2
0
1
2
0
0
2
0
1
0
1
0
0
2
0
1
0
2
0
1
0
0
1
2
2
2
2
0
0
3
0
0
1
0
1
0
0
2
2
0
2
0
0
0
0
0
1
2
0
0
0
0
2
0
2
0
2
2
0
2
1
0
1
0
0
1
1
0
2
0
1
0
1
0
1
0
0
2
1
0
0
0
1
2
0
0
1
0
0
0
1
0
1
0
1
0
0
2
0
0
0
2
0
1
0
0
1
0
1
2
1
1
1
0
2
1
2
0
2
0
1
0
1
0
2
1
0
0
2
2
0
0
3
1
1
0
1
0
1
2
1
2
0
0
0
0
2
0
0
0
0
1
0
1
2
1
1
0
0
1
1
1
1
1
1
1
0
1
1
1
0
0
0
0
1
1
0
0
1
0
1
1
3
0
1
0
2
1
2
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
1
1
0
0
2
2
0
0
1
1
1
0
1
0
1
1
0
1
3
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
1
0
0
1
1
2
0
1
1
0
0
0
2
2
2
3
1
2
0
2
1
2
1
0
2
2
1
2
0
1
1
0
0
0
1
1
0
1
2
0
1
0
1
0
0
1
2
1
1
0
0
0
0
1
4
2
0
0
1
1
0
0
1
1
0
1
0
1
0
1
0
1
0
1
0
2
1
1
2
1
1
0
0
1
0
2
0
0
2
0
2
1
1
1
0
0
2
1
0
0
0
2
0
2
0
0
0
0
0
1
0
4
0
0
0
1
1
2
1
0
1
0
1
2
0
1
0
1
2
1
0
0
0
1
1
1
1
0
1
0
0
1
0
0
0
1
1
0
1
1
2
1
1
0
1
1
1
0
1
0
1
2
0
1
1
0
0
2
0
2
1
0
1
2
0
2
0
1
0
1
2
2
0
0
2
1
1
0
1
0
0
0
0
0
0
1
0
1
2
1
0
1
0
0
2
1
0
1
1
0
0
0
2
0
1
1
0
0
0
0
3
2
2
1
0
0
0
1
0
0
0
1
2
2
1
0
2
0
1
1
0
0
0
1
0
0
2
0
0
0
1
0
1
2
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
1
1
1
0
0
1
0
2
0
1
2
1
0
0
2
0
2
1
0
1
0
0
2
0
0
0
0
1
1
2
1
2
0
1
0
1
0
2
0
0
2
1
2
1
0
1
0
1
1
0
1
1
0
1
2
2
1
1
2
0
1
2
0
0
0
1
1
0
1
0
0
1
1
0
0
0
2
3
1
2
2
1
2
1
0
2
2
2
1
2
1
0
0
0
1
1
1
1
1
0
4
1
0
0
1
2
0
0
2
1
2
2
1
0
4
1
2
0
0
2
1
2
2
1
0
0
1
2
0
0
1
0
2
0
2
1
0
0
0
0
2
0
1
1
2
0
3
0
0
0
1
1
0
0
1
1
0
1
0
1
0
1
2
1
2
1
1
0
0
2
0
1
0
1
0
1
0
1
1
0
0
0
0
0
1
1
2
1
0
0
0
1
2
2
0
0
2
1
1
2
0
0
0
0
0
1
1
1
0
2
2
0
1
3
2
0
1
0
0
2
1
1
1
0
0
0
1
1
2
1
1
2
1
0
2
1
0
0
0
3
0
0
0
0
2
2
1
3
1
2
0
2
0
0
0
1
1
1
2
0
0
1
0
1
2
0
1
1
0
0
1
0
1
1
0
3
1
1
0
2
1
1
1
1
1
2
2
1
3
0
1
0
2
2
0
0
2
1
0
1
0
0
0
1
2
0
1
1
0
2
0
2
1
1
1
0
0
2
0
0
0
1
0
0
2
0
0
2
0
0
1
2
0
1
0
0
0
0
0
2
1
1
0
1
0
1
0
0
0
1
2
0
3
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
2
0
2
0
1
1
0
2
1
1
0
0
0
1
1
1
2
1
2
1
1
1
0
0
0
0
1
1
2
3
0
0
2
1
0
2
2
0
0
1
1
1
0
2
0
0
0
0
1
1
0
1
1
2
1
3
0
2
0
0
0
1
1
2
2
1
0
1
2
2
0
1
1
3
0
1
0
1
0
1
2
1
2
0
0
6
1
0
0
0
1
0
0
2
0
1
0
1
2
2
1
0
2
1
0
2
1
0
1
0
2
0
0
2
1
1
0
0
0
2
1
1
2
0
0
1
2
1
2
0
2
1
1
1
1
2
0
1
2
1
2
1
2
0
1
0
0
0
2
0
1
1
0
0
1
1
0
0
2
2
0
2
0
0
1
0
2
0
0
1
1
0
0
2
0
1
3
0
2
0
2
2
1
1
2
2
1
1
0
0
0
1
1
0
1
0
1
0
0
0
1
0
2
0
0
1
0
2
0
0
1
0
1
0
0
1
0
2
1
1
1
1
1
0
0
0
2
3
1
2
0
0
2
1
1
1
0
0
1
1
1
0
0
1
0
1
1
0
0
1
1
0
0
2
0
0
1
0
0
1
0
2
1
2
0
1
0
0
1
1
2
2
1
0
0
0
1
0
3
0
1
0
0
0
0
1
1
2
1
0
0
1
2
1
1
0
2
2
0
0
1
0
1
1
2
1
0
2
0
0
2
0
1
2
0
0
0
1
0
0
0
1
1
2
1
1
0
2
0
0
1
2
2
0
1
1
0
1
2
1
1
1
0
2
1
0
0
1
0
0
0
0
0
1
0
2
0
1
1
1
1
1
1
1
1
1
0
0
1
1
2
3
2
0
0
0
0
1
0
0
2
0
2
0
2
3
0
1
1
2
1
0
0
0
1
1
0
1
2
0
0
2
0
0
0
1
0
0
1
0
0
2
0
1
1
0
0
2
2
2
2
0
0
1
2
0
2
2
1
0
0
0
2
0
1
2
0
0
0
2
0
2
0
0
1
0
0
1
0
0
0
0
2
0
2
2
2
0
0
0
0
1
1
1
0
1
1
1
0
0
0
0
0
3
0
1
0
2
0
2
1
2
0
2
0
0
2
1
0
5
0
1
0
0
3
0
1
1
0
0
0
1
2
0
1
2
1
0
1
0
2
0
0
0
0
0
0
1
1
2
0
1
0
0
0
0
1
0
1
2
2
0
1
0
0
1
0
0
2
0
2
0
0
0
2
0
2
1
0
2
1
2
2
2
2
1
1
2
1
2
1
1
0
2
2
0
2
0
1
0
2
0
1
1
2
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
1
0
1
2
2
0
2
0
1
1
2
0
1
0
1
2
0
1
1
0
0
0
2
1
1
2
1
0
0
2
1
1
0
0
0
2
2
1
0
0
1
1
2
0
0
0
0
2
0
0
0
1
1
2
1
1
0
1
1
0
2
0
0
0
0
0
1
0
0
1
1
2
1
3
1
1
1
1
2
0
0
0
0
0
1
0
0
1
1
0
0
1
1
2
0
0
2
2
2
2
2
0
2
1
0
0
0
1
1
0
1
0
0
0
0
0
0
2
0
2
2
2
2
1
1
2
0
0
2
1
0
0
1
0
2
0
3
2
1
1
0
1
1
1
0
3
0
2
2
0
0
1
2
0
0
0
0
1
0
0
1
0
1
0
0
1
0
2
1
1
0
1
2
0
1
0
0
1
0
1
1
1
0
1
0
0
1
1
0
0
0
1
2
1
0
0
0
0
1
0
0
0
0
1
0
0
1
1
1
0
0
1
2
2
0
1
1
0
0
2
1
1
0
1
2
0
1
1
1
0
1
0
3
2
2
0
0
0
2
0
2
0
2
0
1
0
2
1
2
2
0
2
1
0
1
1
0
0
2
0
0
0
1
1
1
0
2
0
1
1
0
1
1
1
2
0
1
0
0
0
0
1
0
0
4
1
2
1
0
2
1
1
0
2
2
1
1
0
1
2
1
1
1
1
1
0
0
2
2
0
1
0
0
0
1
0
1
0
1
2
0
1
0
2
2
0
1
1
1
2
1
1
0
0
1
0
2
2
0
0
0
0
0
0
4
0
1
2
1
1
1
2
1
2
2
1
1
2
1
0
0
0
0
0
0
1
0
0
1
0
1
1
1
2
1
2
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
2
1
2
1
0
1
1
0
1
0
1
1
0
0
0
1
2
1
2
1
2
2
1
0
2
0
0
1
0
0
0
0
1
1
2
1
0
0
1
1
1
0
0
0
0
1
1
1
0
0
1
1
0
0
2
2
0
0
0
1
2
0
1
2
0
1
0
0
1
1
0
0
2
1
1
2
1
1
4
0
0
0
2
0
0
1
1
1
0
0
1
1
2
0
0
0
1
0
1
2
1
1
0
2
1
2
0
0
0
1
0
0
0
1
2
1
0
1
1
1
1
0
1
1
0
1
3
0
0
0
0
1
0
0
0
0
0
1
2
1
0
1
0
0
3
1
1
1
0
1
0
2
1
0
1
1
2
0
1
2
2
1
0
2
1
1
0
0
1
0
0
2
1
0
0
0
1
2
1
0
2
0
1
0
0
0
0
0
1
3
0
1
1
0
0
0
0
0
2
2
2
2
0
0
2
3
1
1
2
0
1
0
2
2
0
0
0
0
0
1
0
0
2
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
1
0
2
1
1
0
1
0
2
1
2
1
1
0
0
0
1
2
0
1
1
1
0
0
1
1
0
2
1
1
1
1
1
3
2
1
1
0
1
0
0
1
0
0
0
1
2
1
1
2
2
2
2
0
1
1
1
0
2
1
0
1
1
2
0
2
0
0
0
2
2
1
1
1
1
1
2
0
3
2
1
1
0
1
1
0
0
2
2
0
2
0
0
2
2
0
0
1
0
0
0
0
0
1
2
0
2
1
0
0
2
2
1
0
2
1
1
1
1
1
2
2
1
0
1
0
0
1
1
0
2
1
0
1
2
0
1
0
0
0
3
0
1
0
2
1
1
0
0
0
0
0
0
2
0
1
0
0
1
2
1
0
2
0
1
0
2
0
2
1
2
2
0
0
2
0
0
0
3
0
0
0
2
1
0
1
0
1
1
1
0
1
0
0
0
2
0
0
1
0
0
2
1
0
1
1
0
0
0
0
1
0
0
1
2
0
2
1
1
0
1
0
1
0
1
2
1
0
1
1
1
0
1
1
0
0
1
0
0
1
2
0
0
0
0
2
2
1
0
2
0
0
0
2
0
1
1
0
1
1
1
2
2
2
1
2
0
0
1
3
0
0
1
1
1
2
1
0
1
0
0
1
0
1
2
0
0
0
1
0
0
1
2
0
2
1
1
0
1
0
1
1
0
2
1
1
0
2
0
1
2
2
0
2
1
2
0
1
0
2
0
0
2
2
0
2
0
2
1
1
1
1
1
1
1
2
1
2
1
0
2
1
1
0
0
2
2
2
2
0
0
0
0
0
1
1
0
1
1
1
2
1
0
0
1
0
0
1
1
1
1
1
2
2
1
2
0
0
0
0
0
2
1
0
0
1
2
1
0
1
1
0
1
2
1
0
2
1
1
0
1
2
0
0
0
0
0
2
0
1
2
1
4
1
1
1
2
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
2
2
1
0
2
1
0
1
0
0
1
2
0
1
0
2
0
0
0
1
1
0
0
1
0
0
1
0
0
0
1
0
1
0
1
2
0
1
1
0
2
1
2
2
1
1
2
0
1
1
1
1
1
1
0
1
0
1
2
0
0
0
1
0
0
0
1
2
1
0
0
0
0
0
1
0
0
2
0
1
1
0
2
1
2
0
1
0
1
0
1
1
2
1
0
0
1
1
1
3
0
0
0
1
0
0
0
0
1
1
1
2
0
1
2
1
2
2
0
0
2
1
0
1
1
2
0
1
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
2
0
1
0
0
1
2
0
0
1
0
1
1
2
1
0
1
4
1
2
0
1
2
1
0
1
0
0
1
0
1
0
1
0
0
2
2
1
0
0
1
0
2
0
0
0
1
0
0
0
1
1
0
1
1
1
2
0
0
1
2
1
2
0
0
1
1
0
2
0
1
1
2
2
0
0
0
1
1
1
0
0
1
1
0
0
1
0
0
0
0
1
0
1
1
3
0
0
0
2
0
0
0
1
1
1
0
0
0
1
0
1
0
0
0
1
2
1
1
1
2
1
1
1
0
0
0
4
1
1
0
0
0
0
2
0
0
0
0
2
0
2
2
2
2
0
2
0
0
1
0
0
2
2
0
1
0
2
0
0
3
1
0
1
1
0
1
2
1
0
0
1
1
2
0
0
0
1
2
1
0
1
3
3
2
1
0
0
1
1
1
0
1
1
0
2
1
1
0
0
0
0
0
2
3
0
2
0
2
0
1
2
0
1
0
1
0
2
1
0
1
1
1
0
0
1
2
1
0
0
1
0
2
0
0
0
2
3
0
1
1
3
1
1
0
2
1
2
0
0
0
1
0
1
0
1
2
2
0
0
2
1
0
2
1
0
0
0
0
1
1
1
2
2
1
1
0
2
0
0
2
1
0
2
0
2
0
1
0
0
2
1
0
2
2
0
0
2
1
0
0
0
1
0
0
1
1
0
1
2
0
0
0
1
1
1
0
1
0
0
2
2
0
0
1
2
0
0
1
2
0
0
0
2
1
0
0
2
1
1
1
1
1
0
0
0
1
0
0
2
1
0
2
1
0
1
0
1
0
0
2
2
0
0
1
0
0
0
0
1
0
0
0
2
0
2
0
0
2
0
1
0
0
0
0
0
0
1
2
0
1
2
1
3
1
1
0
0
0
0
1
1
1
1
2
0
0
0
2
0
2
2
0
1
1
0
2
1
1
2
1
1
1
0
1
2
1
0
0
2
1
1
1
2
2
0
0
0
0
2
0
0
2
1
0
1
3
1
0
0
0
2
0
0
1
2
1
2
0
0
0
0
0
0
1
1
1
1
2
0
0
0
0
0
0
1
1
0
0
0
0
0
2
1
1
2
0
2
0
2
0
0
1
2
1
0
1
1
1
1
0
0
1
1
1
1
2
0
0
2
1
0
2
0
0
0
3
1
0
0
2
2
1
2
0
0
0
1
0
0
0
2
0
2
0
2
0
0
0
0
1
1
1
0
1
1
0
1
0
1
2
0
2
2
0
2
1
0
0
1
1
2
1
1
0
0
0
2
0
0
2
2
0
0
1
0
2
1
0
1
0
2
2
1
10
0
2
1
2
1
0
0
1
0
0
1
0
0
1
0
2
0
1
1
1
1
0
1
2
1
0
2
0
1
0
2
1
0
8
1
0
2
0
3
0
1
1
1
2
0
0
0
0
0
0
0
1
1
2
1
1
0
2
0
0
0
0
0
1
0
2
0
0
1
1
1
2
1
0
0
0
0
0
1
0
2
2
1
1
0
0
0
0
2
5
1
0
1
0
0
2
2
1
2
2
2
1
0
0
1
0
0
0
2
2
1
0
4
1
0
0
1
0
1
2
0
1
0
2
1
2
0
2
2
1
1
1
2
1
0
0
0
0
1
0
0
0
1
2
1
0
0
0
1
0
1
1
1
2
1
8
0
2
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
2
0
2
2
2
1
2
1
1
0
1
1
2
1
2
1
3
2
1
0
0
0
1
0
0
0
0
0
1
2
1
2
1
0
0
1
2
0
1
0
0
0
0
0
1
2
1
2
1
2
2
0
0
0
0
2
1
1
0
1
0
1
0
1
1
0
0
0
1
0
0
0
1
0
0
1
0
2
1
0
0
0
0
1
2
0
1
0
0
0
0
0
1
0
1
2
0
2
1
0
0
0
0
1
0
1
2
1
2
0
1
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
2
2
1
0
2
0
0
0
1
0
0
1
1
1
2
1
0
1
0
0
0
0
16
2
1
0
1
0
1
1
0
2
0
1
0
0
1
2
1
0
0
0
1
3
0
0
0
2
0
0
1
1
1
0
1
1
0
1
1
0
2
1
2
1
2
0
0
1
1
0
2
1
0
0
0
4
0
1
0
2
1
1
0
2
0
0
0
0
2
3
3
0
2
2
2
1
1
2
0
1
2
1
1
0
2
2
0
2
0
1
1
0
0
2
2
1
0
0
0
0
0
0
2
0
1
0
1
0
1
1
0
1
1
1
0
0
1
0
2
0
1
2
0
1
1
1
0
0
1
0
2
0
2
1
1
0
3
0
5
0
0
0
1
0
0
1
1
1
0
1
0
2
0
0
1
2
0
2
0
1
1
2
0
0
1
2
0
2
0
0
0
1
0
1
2
2
0
1
0
1
1
0
0
0
0
0
0
0
1
1
0
0
2
1
0
0
0
1
0
0
0
0
1
1
2
0
1
1
0
1
1
2
1
0
2
1
0
2
0
2
2
1
1
1
1
0
1
2
2
0
0
2
1
1
2
1
1
0
0
2
0
0
2
1
1
2
2
0
0
1
1
1
2
0
0
2
0
0
2
1
1
0
1
0
0
0
1
0
1
0
0
2
2
0
0
0
2
0
0
0
0
2
0
1
1
2
0
1
0
1
3
2
1
1
1
0
1
0
1
1
1
1
0
0
0
0
0
1
0
3
1
0
0
1
0
0
0
1
1
1
2
1
0
2
0
1
1
0
0
1
1
1
3
1
1
0
0
2
1
2
1
1
1
2
0
1
0
0
0
2
0
2
0
2
2
0
0
1
1
1
1
2
2
1
0
1
0
0
2
0
0
1
0
0
2
0
1
4
0
1
0
1
0
1
0
0
1
0
0
0
2
0
2
0
1
0
0
0
0
0
2
0
1
2
2
1
0
2
1
0
1
0
1
0
2
1
2
2
1
0
1
2
0
0
0
2
0
0
2
2
0
0
1
2
0
1
0
2
0
2
0
1
2
0
0
1
0
1
0
0
1
2
0
1
0
0
1
0
1
3
0
3
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
1
2
2
1
0
0
1
1
0
2
0
0
1
0
1
1
0
0
2
1
1
0
0
1
2
2
0
0
1
1
1
0
2
0
0
1
0
1
2
2
0
1
1
0
0
0
1
0
1
1
0
0
0
1
1
1
0
0
2
2
0
0
0
0
2
2
2
0
2
0
2
0
0
0
2
0
0
0
1
1
3
0
0
0
0
0
1
2
2
0
0
1
2
1
1
1
0
0
1
1
0
0
0
0
0
1
1
2
1
0
1
0
0
0
1
2
1
0
0
1
0
1
1
2
0
2
0
1
1
1
1
0
0
2
1
0
2
0
2
0
1
0
0
1
1
1
0
0
0
0
0
1
0
2
0
1
0
1
1
0
2
2
2
0
0
1
0
0
0
0
1
0
0
0
2
2
2
1
2
0
0
0
2
2
1
2
3
1
0
2
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
1
2
1
0
0
0
0
1
1
1
2
3
0
0
0
2
0
1
2
0
2
0
0
0
2
0
0
0
0
1
0
2
2
1
0
2
1
0
0
1
0
2
1
0
1
2
0
0
1
0
0
4
1
0
0
1
0
0
1
0
2
2
1
0
0
0
3
1
0
1
0
2
4
0
2
0
0
1
0
0
2
2
0
2
1
2
0
0
2
1
1
0
2
0
1
0
0
2
0
2
2
1
0
0
0
1
0
1
1
0
3
2
1
1
0
1
0
1
0
0
1
0
0
0
2
2
0
0
1
0
0
0
3
1
0
2
1
1
0
0
1
1
0
2
0
2
0
0
2
2
1
0
3
2
1
0
0
0
0
1
0
0
0
1
0
0
2
0
0
2
0
0
0
1
5
0
2
1
1
0
2
2
0
0
1
0
2
1
1
1
0
1
1
0
0
0
0
1
0
0
0
0
1
2
0
2
1
0
2
0
1
0
0
1
2
1
1
0
1
0
0
4
1
1
0
2
0
2
2
2
0
0
0
1
0
2
1
0
0
1
0
0
0
1
2
2
1
0
0
0
0
1
2
2
0
0
2
0
0
1
1
0
0
2
0
1
1
0
0
0
0
0
0
0
1
2
2
0
1
0
0
0
0
0
2
0
0
1
1
0
0
1
0
0
0
2
0
0
0
0
2
0
2
1
0
1
0
0
0
0
0
0
1
2
0
0
2
0
1
1
0
1
2
0
1
2
1
1
0
0
0
0
1
0
1
0
0
0
1
1
1
2
1
0
1
0
1
1
2
0
0
0
0
2
3
2
1
1
2
1
2
1
1
0
0
1
1
1
1
0
1
1
1
3
2
0
0
3
2
1
0
0
0
1
2
1
1
0
0
0
0
1
0
2
1
1
0
0
1
0
0
2
1
2
2
1
1
1
1
1
0
0
0
2
1
1
0
0
0
2
1
0
1
1
0
0
1
0
0
2
0
0
0
0
0
1
1
2
0
1
3
1
0
1
0
1
1
1
1
1
2
0
0
0
2
1
2
2
0
0
0
2
1
0
3
1
1
1
0
0
2
1
1
2
0
1
1
1
1
0
0
1
0
0
1
0
1
0
0
1
2
0
1
1
0
2
0
2
1
0
0
1
1
0
2
1
1
0
1
2
2
1
0
0
1
0
2
2
1
0
0
0
2
1
1
4
2
1
0
1
1
0
5
0
1
0
0
1
0
3
0
1
1
2
0
1
1
0
0
1
0
0
2
0
0
2
2
1
1
1
0
0
1
0
0
1
0
0
0
1
2
0
1
0
2
0
0
1
2
1
2
0
0
1
2
0
2
0
1
1
0
0
0
1
2
1
0
0
1
4
3
2
0
0
2
0
0
1
1
2
2
3
1
2
0
2
0
2
1
2
0
1
0
0
1
1
1
0
2
1
2
1
0
1
2
0
1
0
1
1
0
0
0
2
0
0
1
0
1
2
1
2
0
0
1
1
2
0
1
1
1
1
2
0
0
2
0
0
0
2
1
1
0
0
0
0
1
2
0
0
2
0
0
1
1
2
2
0
2
0
2
1
1
2
0
0
1
2
0
0
0
2
0
0
2
0
2
0
1
0
1
1
1
2
0
0
1
2
0
2
1
1
0
0
0
2
2
2
4
0
0
0
0
0
1
0
0
1
0
0
2
1
1
0
0
1
0
0
1
0
0
1
1
1
1
1
0
1
0
0
1
0
0
2
2
0
0
0
1
0
0
1
1
0
0
0
1
1
0
0
0
1
0
0
0
1
1
0
1
0
2
1
0
0
2
2
1
0
0
2
1
0
2
0
1
1
0
1
1
2
1
0
3
1
1
0
1
1
2
0
0
2
2
0
1
0
0
1
0
1
1
2
2
0
0
0
0
0
0
1
1
0
0
1
2
1
2
0
0
2
1
1
0
2
2
0
2
0
2
0
1
1
1
1
0
0
0
1
2
1
2
1
2
2
2
0
0
1
0
1
1
2
1
0
0
1
1
1
0
0
1
0
2
1
0
1
0
0
0
1
0
1
1
0
1
0
1
3
2
0
1
2
0
0
1
1
1
0
1
0
2
1
1
0
1
1
1
4
0
0
1
1
2
0
1
0
1
0
1
0
1
1
2
0
0
1
2
2
0
0
1
0
2
1
0
1
0
0
1
0
3
0
0
1
0
1
1
1
0
0
2
2
1
1
0
1
1
1
0
0
0
1
0
2
2
2
0
1
0
0
0
2
0
0
1
1
0
0
1
2
1
1
1
1
2
1
2
0
2
2
0
1
0
0
2
1
1
2
0
0
2
2
0
1
1
1
1
1
1
2
2
1
1
1
1
1
0
0
0
2
1
2
0
2
1
2
1
0
0
0
0
1
0
0
1
0
0
2
0
0
1
1
1
0
1
3
1
1
0
1
1
2
0
1
1
0
2
1
0
0
2
0
2
0
0
0
1
0
0
0
1
0
0
2
2
1
2
0
1
0
2
0
1
0
0
2
0
0
1
1
0
0
1
1
0
0
0
1
2
2
2
2
1
0
0
0
0
0
2
1
1
0
0
1
5
1
1
0
2
0
2
1
0
4
0
0
0
1
1
0
0
0
1
2
1
2
0
0
1
1
0
0
0
0
0
1
0
1
2
1
2
2
2
2
0
0
1
0
0
2
2
0
0
1
0
1
0
0
2
0
2
0
1
0
0
0
2
0
1
2
0
1
2
1
0
0
0
0
0
1
0
2
0
0
0
0
0
1
1
1
1
0
0
1
2
1
0
0
1
2
2
1
0
0
1
1
1
0
0
1
1
1
1
1
1
2
0
0
0
5
0
1
0
1
1
1
2
0
0
1
2
1
0
2
3
0
0
1
1
0
0
1
1
1
1
0
2
2
0
0
1
1
2
1
1
0
0
0
0
1
2
0
0
0
2
2
0
0
1
0
2
2
0
2
1
0
2
0
1
1
0
0
1
2
0
2
2
2
0
2
0
2
0
0
2
0
0
1
0
2
1
0
0
0
0
2
1
2
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
2
1
3
2
2
0
0
2
0
1
0
0
3
1
0
0
1
0
0
1
0
1
2
2
0
0
1
2
1
2
0
0
0
0
1
1
0
1
1
2
2
0
0
0
2
0
0
1
0
2
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
2
1
1
3
1
0
2
2
0
1
0
1
0
0
1
0
2
0
0
0
1
0
1
2
1
0
0
2
1
1
0
1
1
1
1
0
1
0
0
0
0
0
1
2
0
0
1
0
1
1
2
1
2
0
1
1
2
0
0
2
0
1
0
0
0
2
2
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
1
1
0
0
0
2
0
0
4
0
0
2
0
2
1
1
0
1
0
0
1
3
2
0
0
0
2
2
2
2
0
0
0
1
0
0
1
1
0
0
0
1
1
0
0
2
1
0
0
1
3
0
2
2
2
2
0
0
0
1
0
2
2
2
0
0
1
1
0
2
2
2
1
0
0
0
1
0
2
0
0
0
1
1
0
0
1
0
1
1
0
1
0
0
0
0
1
1
1
1
0
1
1
2
1
1
2
2
1
1
1
2
1
0
1
1
1
0
1
2
0
1
0
1
1
3
0
0
0
1
7
0
0
1
1
1
2
2
0
0
1
0
0
0
1
1
1
1
0
1
3
0
1
1
0
1
0
2
1
1
0
1
1
0
0
1
1
0
1
1
0
1
0
2
0
0
0
0
1
1
0
0
1
1
2
1
1
0
0
0
1
0
0
0
0
1
0
2
0
1
2
1
0
0
0
1
1
0
0
1
0
2
1
1
2
2
2
1
1
1
0
0
2
0
2
2
0
0
0
1
0
1
2
0
0
0
1
1
0
2
1
1
0
0
1
0
1
1
1
1
2
0
0
1
1
0
2
1
1
0
0
0
1
0
0
0
0
1
0
0
1
2
2
2
0
1
0
2
0
2
2
0
0
1
0
0
1
1
1
0
2
2
0
0
0
1
1
0
0
1
3
0
0
1
1
2
0
0
0
0
1
0
0
0
0
1
2
0
2
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
1
1
0
2
0
0
1
1
2
1
1
2
1
2
1
0
1
1
0
0
0
1
1
2
2
0
2
0
0
0
0
0
0
0
0
2
3
1
0
0
0
1
0
1
2
0
0
1
0
0
0
0
1
0
0
1
0
1
1
2
2
1
0
1
1
0
2
2
1
1
1
0
6
0
0
3
2
1
0
0
1
2
0
0
1
0
1
1
2
2
0
1
2
1
1
2
1
3
0
0
2
0
0
2
0
2
2
0
0
1
1
2
0
0
0
1
1
1
1
0
2
0
2
2
2
0
1
2
0
0
0
0
0
0
1
0
2
0
1
1
0
0
0
2
0
1
0
1
2
2
1
0
0
1
2
0
1
2
0
7
2
2
2
4
0
1
0
1
1
0
2
0
0
1
1
3
1
1
2
0
0
1
0
1
2
0
1
1
0
0
1
0
2
1
2
1
0
0
2
0
0
2
1
0
0
2
1
1
0
2
0
1
0
0
0
0
1
2
2
1
1
0
2
0
0
2
1
0
1
1
1
0
1
1
1
0
2
0
1
2
0
1
1
0
0
0
0
2
1
0
1
2
0
0
2
1
2
1
1
0
1
0
1
0
0
0
1
1
0
1
2
0
1
2
1
1
0
1
0
1
1
3
0
1
1
0
0
1
2
0
1
1
2
1
0
0
0
2
2
0
1
0
0
0
0
0
1
0
0
0
1
1
2
0
2
0
1
1
1
1
1
0
0
1
1
1
0
1
1
2
0
1
1
0
1
1
0
0
1
0
1
0
1
0
2
0
1
2
0
2
0
1
0
1
0
2
0
0
0
2
0
1
0
0
1
2
2
2
1
1
2
0
1
1
1
1
1
0
2
0
0
1
0
1
0
1
1
2
2
2
2
1
0
1
2
1
0
1
0
3
0
0
1
0
1
1
0
0
1
1
0
0
1
2
1
1
1
0
2
1
2
0
2
1
1
1
1
1
2
0
0
1
2
1
0
2
1
1
2
0
4
1
0
1
1
0
0
1
2
1
1
0
2
2
1
1
2
0
2
0
2
0
2
0
0
2
1
0
1
1
0
0
1
0
1
0
0
1
1
0
1
1
0
2
0
1
1
1
0
0
0
2
0
0
0
0
0
0
0
2
1
2
2
0
0
2
0
2
0
0
1
0
0
0
0
1
0
0
2
0
1
0
2
2
1
1
1
0
0
0
1
0
1
0
2
2
2
0
2
1
0
1
2
0
0
1
0
1
1
0
0
0
2
1
0
0
0
1
0
1
2
1
3
0
1
1
2
1
0
0
2
0
2
1
2
2
2
2
1
2
1
0
0
0
1
1
2
0
1
0
0
0
0
1
0
0
0
2
2
0
1
0
2
0
0
0
0
1
2
0
0
0
0
1
1
2
1
1
1
1
0
0
1
0
1
1
1
2
0
1
0
4
0
0
1
1
2
0
1
1
0
2
1
1
2
0
0
0
0
0
1
0
0
1
0
0
0
0
2
1
0
0
2
2
1
0
0
1
1
2
0
2
2
2
1
2
1
2
1
1
2
0
0
0
2
0
0
1
0
1
1
2
4
1
1
0
2
0
0
0
2
1
0
0
1
1
0
0
2
1
1
1
0
0
0
0
1
0
1
0
2
0
2
0
0
1
1
1
0
0
2
0
1
0
0
0
1
0
0
0
2
0
1
0
1
1
1
0
0
1
0
0
2
0
2
0
0
0
1
2
1
0
1
1
0
1
0
1
2
1
0
0
1
0
0
1
1
0
1
2
0
1
1
2
1
0
1
0
0
0
0
1
1
1
1
1
2
0
2
1
2
0
0
0
0
0
2
1
2
2
0
0
0
1
1
2
2
1
0
0
1
1
0
0
0
0
1
0
0
2
0
0
1
0
0
1
0
0
1
1
1
2
1
0
0
1
1
0
0
2
1
1
0
0
1
2
1
6
2
0
0
2
1
2
1
0
0
0
1
1
1
0
0
1
1
1
0
0
0
1
2
0
0
0
1
1
1
1
2
0
0
1
1
2
1
0
2
1
2
1
0
2
2
0
1
1
2
1
0
0
1
2
1
0
0
0
1
2
2
2
2
0
0
0
2
1
0
0
1
0
0
0
2
0
1
1
0
0
1
1
2
2
0
2
1
1
1
0
1
0
0
2
2
1
1
0
0
0
0
2
2
1
2
1
1
0
0
0
0
0
1
0
1
0
0
1
0
0
2
2
0
1
1
1
1
2
0
0
0
1
0
0
0
1
0
1
1
2
0
1
1
0
1
1
1
0
1
0
0
1
0
2
0
0
0
0
0
1
2
1
2
0
1
1
0
1
2
0
0
2
0
1
0
0
2
2
1
1
0
2
0
0
0
0
2
1
2
1
1
0
2
1
2
0
0
2
0
0
0
0
1
0
0
1
1
2
2
0
1
1
0
2
1
0
1
0
0
0
2
1
2
0
3
1
2
1
2
2
2
2
2
1
1
0
0
1
2
2
1
0
2
0
1
0
0
2
0
0
0
0
0
2
2
2
0
0
0
0
0
1
0
0
2
0
1
0
1
2
1
1
0
0
2
2
1
1
1
0
0
2
0
2
2
1
1
2
0
1
1
0
2
1
0
1
2
2
0
2
0
0
0
1
3
1
0
0
1
2
0
0
1
2
0
0
2
1
0
1
0
2
0
2
1
1
0
1
0
0
1
0
1
2
2
1
1
1
2
1
0
1
1
2
1
0
0
1
0
1
0
1
0
1
1
0
1
1
2
0
2
1
1
0
1
0
2
0
0
2
1
1
0
2
1
2
1
2
1
1
1
2
0
0
1
2
0
1
1
2
1
1
2
0
0
2
2
2
0
1
0
1
1
0
1
1
0
0
1
0
0
0
0
2
1
0
2
1
0
1
0
0
2
0
0
2
0
0
1
1
1
1
0
0
0
0
2
1
1
0
1
0
0
0
0
1
1
3
0
2
0
2
0
0
0
2
1
1
1
0
0
1
0
3
0
1
4
1
1
1
1
2
2
0
0
2
1
1
0
2
1
1
0
0
2
0
0
0
2
0
1
0
2
0
0
0
0
0
1
0
0
1
1
2
1
1
0
0
3
0
1
2
1
2
1
0
0
2
2
0
1
1
2
2
2
1
0
0
2
1
0
1
0
1
1
0
1
2
0
1
0
0
0
2
0
0
0
0
1
2
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
2
0
1
1
0
1
0
0
0
3
0
0
2
2
0
1
1
0
0
1
1
1
0
0
2
1
1
1
0
0
0
0
1
0
0
4
0
3
1
2
0
1
1
0
0
1
0
2
1
2
2
1
1
1
2
1
2
0
1
1
1
0
0
0
1
2
1
1
2
0
1
0
1
0
1
0
0
0
0
2
1
0
0
2
1
2
0
1
0
0
0
1
1
0
1
0
0
1
0
2
0
0
2
1
2
2
0
0
0
2
1
1
2
0
0
0
0
0
1
1
0
0
2
2
1
1
1
1
1
1
0
1
0
0
1
2
2
2
0
1
2
2
1
2
2
0
1
2
2
2
0
1
2
1
0
0
2
2
2
1
0
0
2
0
2
1
1
2
1
3
1
2
2
3
0
2
1
0
0
2
1
1
0
1
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
1
1
0
0
1
2
1
0
2
1
2
0
2
1
1
2
2
0
0
2
0
1
2
0
0
0
1
0
0
0
1
2
0
0
1
1
0
0
2
2
1
2
2
0
1
2
1
0
2
0
1
0
0
0
2
0
2
0
2
0
0
2
4
2
0
0
0
0
1
0
0
1
0
3
1
2
2
0
0
0
2
1
1
1
1
0
0
0
3
0
3
0
0
0
1
0
1
0
1
1
1
0
2
1
0
0
2
0
3
2
0
1
1
0
2
2
1
1
2
0
1
0
1
0
0
1
2
1
1
1
2
0
1
0
2
2
0
0
1
0
0
0
1
1
0
1
2
2
1
2
2
2
1
2
2
0
0
1
1
1
0
0
2
0
2
2
0
0
2
0
1
0
1
1
0
1
2
0
1
2
0
0
2
1
1
0
2
0
1
2
0
1
1
0
2
1
1
0
2
0
0
1
2
0
1
1
1
2
0
0
1
0
1
0
2
0
2
1
0
1
2
1
0
1
1
0
0
1
2
1
0
2
0
2
0
0
2
1
2
1
0
1
1
2
1
0
1
1
1
3
1
1
1
2
1
0
0
3
1
0
0
0
1
0
2
1
1
0
0
2
1
0
0
0
1
1
1
3
0
4
2
0
0
1
1
1
0
1
3
1
0
2
0
1
2
0
0
1
0
0
0
1
0
1
2
1
0
0
1
1
2
2
0
0
1
0
1
0
0
2
0
2
2
1
1
0
1
2
0
1
0
0
1
2
1
1
1
1
0
0
0
1
0
3
0
1
0
0
2
0
0
3
0
1
0
1
2
0
2
0
1
2
2
0
2
1
0
0
0
0
0
0
3
2
2
2
1
0
2
0
1
0
1
1
0
1
1
3
0
0
0
0
0
2
0
0
2
1
1
1
0
2
0
0
0
1
1
1
0
1
1
0
1
1
0
0
1
1
0
0
1
1
0
1
1
0
0
1
2
0
0
2
0
0
1
1
1
0
1
1
1
0
1
2
3
0
1
1
1
1
1
2
1
1
0
3
2
0
2
2
0
0
0
3
0
2
1
0
0
1
0
2
1
1
0
0
0
0
1
2
0
1
1
1
0
3
1
2
2
0
2
1
2
4
2
0
1
1
0
2
0
1
0
0
0
2
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
1
2
1
1
0
2
0
1
1
1
0
1
0
3
1
0
1
0
2
0
0
0
1
2
0
1
0
2
2
0
2
0
1
0
1
1
0
2
0
1
2
0
0
2
3
2
0
1
0
0
1
2
1
2
0
1
1
2
1
0
0
1
2
2
2
0
1
1
2
0
0
1
0
1
2
1
1
3
2
0
3
2
0
0
0
1
2
2
0
1
1
2
1
1
1
0
1
1
0
2
0
0
1
1
1
1
0
0
2
1
0
1
4
2
1
0
2
1
0
2
1
1
0
1
1
0
1
1
1
1
2
0
0
0
1
1
1
2
2
1
0
2
0
2
0
2
1
0
1
2
0
0
0
0
1
2
1
0
2
2
2
0
0
0
0
1
0
2
1
2
0
2
2
1
1
1
0
0
3
1
0
0
1
1
1
1
2
0
1
0
0
0
0
0
2
2
0
1
0
1
1
0
0
1
1
2
2
2
4
1
1
1
0
5
1
0
0
2
0
0
0
2
0
1
2
1
0
1
1
0
2
0
0
1
4
0
0
0
3
0
1
1
0
2
0
2
1
1
0
1
0
1
2
0
0
2
0
0
2
8
2
1
0
0
1
1
0
2
0
2
1
0
2
0
1
3
0
0
1
1
2
2
0
0
1
1
2
2
0
0
1
0
0
1
0
0
2
2
3
0
0
0
0
1
0
1
0
0
0
0
1
1
1
0
1
2
1
0
1
2
2
0
0
0
0
1
1
2
0
0
1
2
3
0
2
0
0
0
0
1
0
2
0
2
0
0
1
0
0
0
1
0
0
2
0
0
2
0
0
0
1
1
1
1
0
0
1
0
0
0
0
1
0
0
0
1
0
1
2
0
0
1
1
0
1
2
1
2
1
0
0
1
1
1
2
1
0
0
0
0
0
2
1
2
0
0
1
0
1
2
1
0
0
0
1
1
0
4
0
1
1
1
2
0
2
1
1
2
0
0
1
0
0
1
0
0
2
1
1
1
2
1
2
1
1
0
1
0
1
2
0
0
1
3
1
1
0
2
0
2
2
1
0
0
1
1
2
1
1
0
1
1
0
3
2
1
1
2
1
0
0
3
2
2
1
1
1
0
2
0
1
1
0
0
2
1
2
1
0
0
0
0
2
0
0
1
1
0
3
2
0
1
1
0
0
1
0
1
0
2
0
1
1
0
2
2
1
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
2
0
0
2
1
0
0
1
0
1
1
1
0
0
0
0
0
0
0
2
0
1
0
1
1
1
0
0
0
2
1
0
0
2
1
0
1
1
1
0
0
1
1
1
1
0
1
2
2
0
0
0
2
1
0
0
0
1
2
1
1
0
2
1
1
1
0
0
1
4
1
0
1
1
2
1
2
2
0
0
0
0
0
0
1
1
2
0
2
0
1
1
0
2
0
1
1
2
2
1
2
1
0
2
1
0
0
2
1
2
0
2
0
0
2
2
2
0
1
2
0
2
0
1
0
2
1
2
0
2
0
0
3
2
1
2
1
1
1
1
0
1
1
0
0
1
0
1
1
0
0
0
0
1
0
0
0
2
2
1
1
2
0
1
1
0
2
2
0
1
2
0
1
1
1
1
1
0
0
2
1
1
1
1
1
0
2
2
2
0
1
1
0
1
0
1
0
2
0
0
0
0
1
1
0
2
1
1
0
0
2
0
2
0
1
0
0
0
6
0
1
0
0
0
0
0
0
3
0
0
0
1
1
0
0
0
0
0
2
0
1
0
0
1
1
1
3
1
1
2
0
0
2
1
2
2
0
0
1
1
1
0
0
1
0
1
0
2
1
0
2
1
0
1
3
0
2
0
0
0
1
2
1
0
2
1
0
0
3
1
0
1
0
2
0
0
1
0
1
0
1
0
0
2
0
0
1
1
0
1
0
0
1
0
0
0
0
0
2
2
0
1
2
0
2
1
0
0
0
0
0
0
1
0
1
1
1
1
0
0
3
2
0
1
0
2
0
2
0
3
1
0
0
1
0
0
1
0
0
0
0
1
0
0
1
1
2
1
1
1
0
0
1
0
1
0
0
1
2
0
3
0
0
0
2
2
0
0
2
0
1
0
0
1
0
1
0
0
2
3
1
1
0
1
2
0
0
0
0
0
1
0
2
0
1
0
2
0
1
1
3
1
2
0
0
0
0
2
0
1
0
0
3
1
0
0
0
0
0
1
0
2
0
1
1
1
0
2
0
1
0
0
2
2
0
3
3
1
1
2
0
0
0
0
1
1
0
1
1
1
2
1
1
2
0
0
1
0
1
0
0
1
1
0
2
0
0
5
0
1
0
1
0
1
0
1
1
2
0
0
0
4
2
1
1
1
1
1
1
0
1
2
2
0
1
2
0
0
0
1
1
2
1
0
0
0
0
1
1
0
1
2
0
1
0
1
0
0
0
1
2
0
0
2
0
0
0
0
2
0
0
2
1
1
1
1
1
1
2
0
0
0
0
1
1
0
2
0
5
1
1
0
0
1
1
0
0
0
2
1
0
1
2
0
0
0
1
2
1
0
2
0
1
1
1
1
0
0
0
0
2
2
1
2
0
0
0
2
0
1
1
0
1
1
1
2
2
1
2
2
0
1
1
2
0
1
0
1
1
0
0
1
0
2
0
1
1
0
0
1
0
0
0
0
1
3
2
1
0
2
0
0
2
0
1
0
0
0
0
2
1
1
3
1
0
2
0
2
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
2
1
1
2
0
3
1
1
1
0
0
0
0
1
1
2
0
1
1
2
2
1
2
0
0
0
2
1
2
1
1
0
0
2
1
0
1
1
0
2
1
1
1
1
0
0
0
0
0
1
0
0
1
1
2
1
2
0
1
0
0
0
1
0
1
0
0
1
2
1
0
1
0
2
0
1
0
0
0
0
2
0
0
1
2
3
0
0
0
0
2
1
2
1
1
0
1
0
0
1
1
2
1
0
0
0
0
0
2
0
2
2
1
0
1
1
2
2
1
2
1
0
3
2
0
1
2
0
2
2
5
0
1
2
0
1
0
0
0
1
1
1
0
1
1
1
2
0
5
1
0
1
0
2
0
2
1
0
2
0
2
2
0
1
1
1
2
0
0
0
0
1
1
1
0
1
2
0
0
0
2
1
0
0
1
1
2
1
0
0
0
1
0
2
0
0
1
0
0
1
2
1
3
1
1
1
3
1
2
1
2
1
0
2
0
0
0
0
0
1
0
0
1
1
1
1
2
0
2
0
1
1
2
0
0
0
1
0
0
1
1
0
0
2
0
2
1
1
1
0
0
0
2
2
0
1
2
0
1
0
1
4
1
0
0
1
0
2
1
1
0
2
0
0
1
1
0
0
2
0
0
2
1
0
0
1
0
0
2
0
1
1
2
1
0
1
2
0
0
1
1
0
0
2
1
0
2
1
1
1
1
0
0
2
1
2
1
0
0
1
0
1
0
1
0
0
0
2
1
4
1
2
2
0
1
2
2
0
0
1
1
0
1
1
1
0
0
0
0
2
0
0
2
2
2
1
1
2
1
1
2
2
2
2
1
2
2
1
1
2
2
1
0
1
1
0
0
0
1
0
2
0
1
1
1
0
0
1
0
1
1
0
2
2
1
0
0
0
2
2
0
0
2
1
2
0
0
0
0
2
3
0
1
0
2
2
1
0
0
2
1
0
1
1
1
0
0
0
1
0
0
0
2
0
0
1
1
1
2
3
0
0
0
0
2
2
1
2
0
0
2
0
1
2
1
0
0
0
1
0
0
1
0
0
2
1
1
2
1
1
0
1
0
1
2
0
0
1
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
1
1
0
1
0
0
1
2
0
1
0
1
1
1
0
1
0
2
1
1
0
3
0
1
1
0
2
0
0
0
2
0
2
0
0
4
0
0
0
0
1
0
0
0
1
2
1
0
0
1
0
1
0
1
0
0
0
2
2
0
2
0
1
0
0
1
1
1
1
2
0
0
1
0
1
0
0
0
0
1
1
0
1
1
0
1
1
1
1
1
0
0
1
0
0
0
0
0
0
1
1
0
1
0
1
1
1
1
0
0
2
0
2
0
2
1
1
0
0
0
0
0
1
0
1
1
1
1
0
1
2
2
0
0
2
0
0
0
0
2
2
1
0
2
2
0
1
1
0
3
2
0
2
2
0
0
0
1
0
0
3
0
0
0
0
0
1
2
1
2
2
2
0
0
0
0
0
2
4
1
0
0
0
4
1
2
2
0
1
1
1
0
0
1
1
2
0
2
0
0
0
1
0
1
1
4
1
1
0
1
1
0
0
0
1
0
1
1
1
2
1
2
0
0
1
1
2
0
1
3
1
0
3
2
0
2
1
1
1
1
1
2
2
1
1
0
1
0
2
2
0
0
2
0
1
1
1
1
0
0
2
1
0
0
2
2
1
1
2
0
0
1
0
2
0
0
0
2
2
2
1
1
1
0
2
0
2
1
0
0
0
1
0
0
1
2
1
0
0
0
0
1
0
0
1
2
0
0
2
0
1
0
0
1
1
1
2
0
2
0
2
0
2
2
1
0
2
0
0
2
1
2
1
1
2
0
1
0
3
0
1
0
4
0
2
1
2
1
0
0
1
1
0
3
0
0
1
1
0
0
2
0
1
1
0
0
2
2
0
0
0
0
1
1
0
1
2
0
0
0
0
1
0
0
1
0
0
1
0
0
2
0
0
1
2
0
0
0
1
0
4
0
1
1
0
2
2
1
2
1
1
1
1
1
0
1
1
2
0
2
0
0
1
0
0
2
0
0
1
2
1
0
0
0
0
1
1
1
0
1
1
0
0
3
1
2
1
1
2
2
0
0
2
0
0
1
0
0
0
1
1
0
1
2
0
0
1
0
0
1
0
1
2
2
2
0
0
2
0
0
2
3
2
2
0
0
2
0
3
1
0
0
1
2
0
2
2
1
1
1
0
0
1
0
1
1
2
1
0
0
0
1
0
2
0
0
0
0
1
5
1
0
0
0
1
2
0
1
1
1
0
2
1
1
3
1
1
1
1
1
0
0
2
0
1
0
0
0
2
0
0
0
2
0
0
0
1
1
0
1
1
0
1
3
1
3
0
0
1
2
1
0
0
2
1
1
0
1
1
1
1
0
2
0
2
1
3
1
0
1
0
1
2
1
0
2
1
0
0
3
2
0
1
0
1
0
2
0
2
2
0
3
0
0
0
1
0
0
0
1
2
0
2
0
1
0
2
0
2
2
2
2
0
0
0
0
2
1
0
0
1
1
2
0
0
0
0
0
0
0
0
2
0
1
1
0
2
0
1
2
0
0
0
1
2
0
2
0
1
0
1
0
1
0
1
0
0
0
0
1
1
0
0
1
2
1
2
1
0
2
2
0
1
2
0
0
0
0
0
0
2
2
0
0
0
0
2
1
0
0
0
1
0
2
2
2
0
1
0
0
1
0
0
0
1
0
1
0
0
0
1
2
0
1
2
0
1
1
2
1
1
0
0
1
2
0
1
2
1
0
1
0
2
1
1
0
0
0
2
1
1
2
0
1
1
1
0
1
1
2
1
0
1
3
0
2
0
0
0
0
1
0
0
2
0
2
1
2
0
0
0
0
0
1
0
2
0
1
0
0
2
1
2
1
0
0
0
1
1
1
2
0
0
1
2
0
1
0
0
0
2
1
1
0
1
0
0
0
0
1
0
2
1
2
0
0
1
0
2
0
2
1
1
0
0
1
1
0
0
0
0
2
0
1
1
0
1
0
1
1
1
0
2
1
1
1
0
1
0
1
1
0
0
0
1
2
1
0
1
2
1
1
1
2
0
2
2
1
0
0
2
2
0
2
1
1
0
1
1
0
0
0
1
1
2
2
1
2
0
1
2
0
0
0
2
1
1
2
1
2
1
0
0
2
2
0
0
0
1
1
1
0
0
1
2
2
0
1
0
2
0
0
2
0
2
2
1
2
1
0
0
1
0
1
0
0
1
2
1
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
1
0
1
1
1
2
1
0
0
1
0
0
0
1
1
1
0
0
0
1
0
1
0
1
0
0
0
2
2
2
1
2
2
0
0
2
1
0
3
2
0
1
2
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
1
0
0
1
0
1
2
2
0
1
0
1
1
1
0
0
0
0
1
2
1
1
1
1
1
0
0
2
1
0
0
2
2
0
2
0
1
0
1
2
2
1
0
2
0
1
2
0
0
0
1
1
1
1
0
3
1
2
0
2
1
0
2
0
0
0
1
2
0
2
2
2
1
1
0
1
0
1
0
1
1
0
0
1
1
0
0
2
2
1
0
0
0
1
2
3
0
0
1
2
2
1
1
2
1
2
0
0
0
1
0
1
0
1
0
2
2
0
2
2
1
0
1
1
0
2
0
2
0
0
0
1
1
0
0
0
0
0
1
1
2
1
0
1
1
0
1
1
1
0
1
0
2
0
0
1
0
2
1
1
1
0
1
0
0
0
1
1
1
1
0
1
0
0
1
1
2
0
0
0
0
1
0
2
0
0
0
0
2
0
1
1
0
0
1
0
0
1
2
2
1
0
2
1
0
2
1
0
1
1
1
1
1
2
1
1
1
1
1
0
1
0
0
0
1
1
1
0
2
1
0
1
0
0
1
1
1
2
0
0
1
1
2
0
0
1
0
0
1
0
1
0
2
2
2
1
0
2
1
1
1
0
0
0
0
3
1
2
0
0
1
0
1
0
0
0
0
2
3
0
3
1
1
1
0
0
0
0
2
0
0
0
0
0
0
1
3
2
0
0
2
0
0
2
0
1
0
2
2
2
1
0
1
1
0
1
0
1
0
0
1
0
2
2
2
0
1
2
0
1
0
1
1
0
2
2
0
0
2
2
0
0
0
2
1
0
3
0
2
0
0
0
2
1
0
1
0
2
1
1
1
0
0
1
0
2
0
1
0
1
1
0
0
2
0
2
2
0
0
0
0
0
1
2
0
0
1
0
1
0
1
0
2
0
0
1
1
0
0
1
0
0
2
0
0
0
1
0
0
1
1
1
2
0
1
0
0
0
1
0
2
0
0
1
1
2
2
0
1
3
0
0
1
1
0
0
0
1
0
1
0
1
4
1
1
1
2
0
0
1
0
1
2
0
0
0
0
0
1
1
0
2
1
0
0
1
0
1
0
3
1
0
0
1
2
2
0
0
1
0
0
0
2
0
0
1
0
0
1
1
0
1
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
2
1
0
0
2
1
1
0
1
0
1
0
0
1
0
1
1
0
2
0
0
0
0
0
0
0
0
0
1
1
0
1
2
0
2
0
1
2
1
1
2
0
2
0
1
0
2
1
0
1
1
1
2
0
1
1
0
0
1
2
0
0
1
0
2
2
1
0
0
1
0
1
0
1
1
1
0
0
1
2
1
1
2
1
2
1
1
1
0
1
2
2
0
0
0
2
0
0
0
1
0
1
0
1
0
3
1
0
0
1
1
1
1
1
2
0
1
0
0
0
0
2
1
0
1
0
1
1
0
0
2
0
2
0
2
1
0
2
1
1
2
2
2
2
1
1
0
2
0
3
0
2
0
1
1
0
0
0
1
0
1
0
2
1
0
0
2
1
0
0
0
0
0
0
1
0
4
2
1
0
0
0
1
2
1
0
0
0
2
0
1
1
0
2
0
0
1
0
0
1
2
0
2
0
1
0
0
0
0
2
0
0
1
1
1
1
1
0
0
1
1
1
1
2
1
0
2
1
0
0
0
0
7
2
0
0
2
0
1
1
0
1
1
1
0
1
0
1
1
1
2
0
0
1
1
1
0
2
0
0
0
0
0
2
0
2
2
0
0
2
1
0
1
2
1
1
0
0
0
1
2
0
2
0
0
0
0
1
0
2
0
1
1
0
1
0
1
2
0
1
0
1
0
0
0
2
0
1
1
0
0
0
2
1
0
2
1
0
0
0
2
0
2
0
2
1
1
2
1
0
0
2
0
2
2
1
1
1
1
1
1
1
1
1
0
0
0
2
1
0
2
0
0
1
1
1
0
0
0
2
2
1
0
2
0
0
1
1
2
1
0
1
0
2
0
1
1
2
0
1
0
1
1
0
0
1
0
2
0
1
0
1
0
0
1
0
0
0
2
2
0
2
1
2
0
1
1
1
0
1
1
0
2
1
1
2
1
0
0
0
0
1
0
0
1
1
2
0
0
0
0
1
0
1
0
0
1
7
0
0
1
1
1
0
1
0
0
0
1
1
4
1
0
0
1
0
1
1
0
0
1
1
0
1
0
1
0
2
2
0
0
0
1
1
2
0
2
2
2
2
1
1
1
0
3
0
0
1
1
3
2
1
2
0
0
1
1
1
0
1
2
1
0
1
1
0
0
2
1
0
1
2
0
2
2
0
2
1
0
1
3
0
0
2
0
2
2
1
0
2
1
1
1
0
0
0
3
1
1
2
0
2
0
1
0
2
0
2
1
1
1
1
0
0
0
2
1
1
0
2
1
3
0
0
0
1
0
1
2
0
1
0
0
0
0
0
1
1
2
0
3
2
1
2
1
1
2
2
2
0
1
0
1
1
0
2
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
1
1
0
0
1
0
1
2
0
0
1
0
1
0
0
1
0
0
1
2
2
1
0
1
1
0
1
8
2
0
0
1
2
0
1
1
1
1
1
1
0
1
0
2
2
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
7
1
0
1
2
0
0
0
0
2
1
2
2
0
0
1
1
1
2
2
0
0
0
0
0
0
5
0
1
2
2
0
0
2
1
0
1
0
0
1
1
1
0
1
0
0
2
1
1
0
1
1
0
0
2
0
1
1
1
0
2
0
1
1
0
0
0
0
0
2
1
1
0
0
2
0
0
0
0
2
1
1
0
1
0
1
0
0
2
1
0
2
3
1
0
0
2
1
0
0
2
2
2
1
0
0
2
2
0
0
2
2
2
1
1
1
2
0
2
0
1
0
1
1
1
2
2
0
1
2
1
2
1
0
1
1
1
1
0
0
1
0
0
0
0
0
2
1
0
3
0
2
1
1
1
1
0
0
0
0
2
0
2
0
1
2
1
0
0
0
1
1
2
2
0
0
0
1
1
0
0
0
2
0
1
1
0
0
0
2
1
0
1
1
0
0
0
1
1
0
1
1
0
2
0
1
0
1
1
0
1
1
0
1
1
1
0
0
0
1
1
0
2
0
0
2
1
0
6
0
2
2
1
1
0
2
0
1
1
1
0
0
1
1
0
0
0
6
0
0
2
2
0
1
1
1
1
0
0
2
2
0
2
2
1
0
0
1
1
0
1
2
0
2
1
2
2
0
1
0
1
2
0
1
0
1
3
0
0
0
2
1
0
0
1
1
1
1
2
0
0
6
1
1
1
2
0
0
1
0
0
1
2
2
0
1
1
0
0
0
1
1
1
2
0
1
2
2
0
1
1
1
0
0
2
2
0
0
0
2
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
1
1
2
2
0
2
1
3
0
0
0
0
0
2
0
2
1
2
2
0
0
0
1
0
2
0
3
1
0
0
2
1
0
0
3
1
0
1
1
0
0
2
0
1
0
0
0
2
1
0
0
2
0
2
2
0
2
0
0
2
0
1
0
0
1
1
1
1
0
0
0
2
1
1
0
2
2
0
0
1
2
1
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
2
0
0
0
2
1
0
0
1
0
2
0
0
0
0
0
2
0
0
1
0
0
0
2
1
0
1
0
1
1
2
2
1
0
1
0
2
0
0
2
1
0
0
2
0
0
0
1
1
1
1
1
2
1
1
0
2
0
0
0
0
0
1
1
0
1
0
1
1
4
0
1
0
1
1
0
1
1
0
0
1
1
0
1
3
0
1
1
0
1
0
0
1
0
0
2
0
2
0
1
1
2
2
0
0
1
0
2
0
0
0
0
1
1
1
1
0
1
2
0
0
0
1
0
2
1
4
3
2
0
0
0
2
1
0
0
0
0
1
0
0
0
1
1
0
1
2
0
0
1
0
2
0
0
1
0
1
0
1
0
0
2
2
0
1
0
2
1
1
0
1
0
1
0
0
0
0
0
2
2
0
0
1
0
2
0
1
1
0
0
1
1
0
0
2
2
1
2
1
0
0
0
0
1
1
1
0
0
2
0
2
1
2
0
2
2
1
0
0
2
0
0
1
0
1
1
1
0
2
0
0
0
0
1
0
0
1
2
0
2
0
1
0
1
1
2
2
0
0
0
2
1
1
1
2
0
2
2
0
0
1
2
1
1
2
1
0
2
1
0
0
0
1
1
0
1
1
1
1
0
0
1
1
0
0
0
1
2
1
1
0
0
2
0
0
0
2
1
2
1
0
0
1
1
1
1
0
0
2
1
0
0
2
0
0
2
1
0
0
1
0
0
2
1
1
2
3
1
0
2
0
2
1
1
1
0
0
0
2
2
0
0
2
0
2
1
1
1
1
1
1
0
2
0
1
0
7
1
0
2
0
0
0
2
0
0
2
2
0
2
1
2
0
1
1
0
0
0
1
0
0
2
1
2
0
1
1
1
1
1
2
0
0
0
2
3
0
1
1
0
0
0
0
0
1
0
1
1
0
0
0
2
0
2
2
1
1
1
0
0
0
2
2
0
3
1
0
1
2
1
0
1
1
1
0
1
0
1
0
2
2
0
0
1
1
1
1
0
1
1
1
2
1
0
1
1
0
0
1
0
1
2
0
0
2
2
1
1
2
0
1
2
0
0
1
0
0
1
1
1
1
1
0
2
0
0
2
2
1
1
0
0
0
2
1
2
0
3
0
0
0
2
0
0
0
1
1
3
2
1
0
2
2
0
2
1
0
1
2
0
1
2
2
0
0
0
1
0
2
0
0
2
2
2
0
0
0
0
1
1
1
2
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
2
2
1
0
1
0
1
1
1
0
0
1
0
0
2
0
1
0
0
1
2
0
0
2
1
1
1
0
0
0
0
0
0
1
0
0
0
2
0
1
2
0
2
0
0
1
2
0
0
0
1
0
0
0
0
0
0
2
0
1
1
1
0
0
2
0
0
0
0
3
3
0
2
0
0
0
2
0
0
0
0
2
5
0
0
0
0
1
1
1
0
1
2
1
1
1
1
1
0
1
0
0
2
2
2
1
1
2
1
0
2
0
0
0
2
1
2
1
2
1
4
1
0
0
0
0
2
1
0
0
1
0
0
2
1
0
0
0
1
0
2
0
0
1
1
2
2
1
1
1
2
1
1
2
0
0
0
1
1
0
1
1
1
2
1
0
0
0
0
1
0
1
0
1
0
0
1
0
1
1
0
0
0
1
0
1
0
1
0
1
1
1
1
2
0
0
2
0
1
1
0
0
0
2
0
0
0
0
2
2
1
1
2
0
0
1
0
2
2
1
0
2
1
1
0
0
2
1
0
2
8
0
0
1
1
1
0
0
1
2
4
0
0
0
2
0
0
0
1
0
0
2
2
1
0
1
1
0
1
1
0
0
0
0
2
2
1
3
0
1
1
0
0
0
0
1
1
0
2
0
0
1
0
2
0
0
1
0
2
1
1
2
0
0
1
0
1
1
3
0
2
2
2
1
2
1
0
1
2
1
1
1
1
0
0
0
2
1
0
2
0
1
0
2
0
2
2
1
1
3
1
1
2
0
1
2
1
1
1
1
0
0
1
1
0
1
0
0
0
0
0
2
1
1
1
0
1
0
1
2
1
2
0
2
1
2
0
1
1
1
2
0
1
0
2
2
1
0
1
2
1
0
0
0
2
1
0
2
1
2
0
1
0
0
1
0
0
0
1
1
0
2
0
0
0
2
0
0
5
0
2
2
1
0
1
2
1
1
3
0
0
2
1
0
2
0
1
1
0
1
0
0
0
1
1
0
1
0
0
1
1
0
0
2
0
1
0
1
2
1
2
0
2
0
2
0
1
0
1
1
0
0
0
0
1
2
2
0
0
1
1
2
2
0
0
2
1
2
0
0
0
0
2
0
2
2
2
1
0
3
2
0
2
1
1
1
1
1
2
0
0
0
1
1
0
1
1
0
0
1
1
0
1
0
0
1
1
1
0
1
2
1
1
2
0
4
0
1
2
0
0
2
0
0
2
2
0
2
0
3
1
0
0
0
1
0
1
1
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
2
0
2
0
3
1
0
2
0
2
0
1
2
0
1
2
2
0
2
1
1
1
1
2
0
1
0
1
0
0
2
0
0
2
0
1
0
0
1
0
0
2
0
0
0
0
0
1
1
1
0
2
0
0
0
0
1
0
2
0
1
0
2
0
0
1
2
1
2
0
1
1
0
1
0
2
0
2
0
1
0
1
2
2
0
1
3
0
1
0
2
0
2
1
1
4
1
1
2
1
1
1
1
2
1
0
0
1
0
1
0
1
1
1
1
1
0
2
2
1
0
1
0
0
2
0
2
0
2
2
0
1
0
1
1
1
2
2
0
0
2
0
1
2
0
2
0
1
1
0
0
2
0
2
1
1
0
1
1
1
0
0
0
2
1
2
1
1
0
0
1
0
1
1
0
0
1
0
2
0
1
2
3
0
2
1
0
0
2
2
0
0
3
2
0
0
0
0
4
0
0
0
1
1
0
0
1
2
0
0
1
1
1
1
1
0
2
1
2
2
2
1
0
1
4
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
1
0
2
1
1
0
0
0
2
1
0
0
1
0
0
2
1
0
0
0
2
0
0
0
1
0
2
2
0
2
1
0
0
0
2
0
0
0
0
2
0
1
0
1
2
0
0
1
1
0
0
1
0
0
0
0
1
0
0
1
2
0
0
1
0
0
0
1
1
1
1
1
0
1
0
1
0
0
1
2
0
1
0
0
1
1
0
0
0
2
1
2
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
1
1
2
0
1
1
1
1
2
0
1
0
0
0
0
0
1
1
0
1
0
0
4
0
2
0
0
0
1
1
0
3
0
0
0
0
1
1
0
1
0
0
0
0
1
1
0
0
0
1
0
1
1
9
1
0
0
1
1
0
0
2
2
2
1
0
2
0
0
1
0
1
1
0
1
1
0
0
0
0
2
1
0
1
1
2
0
2
0
1
1
2
0
1
1
0
2
0
1
2
0
0
0
0
1
0
2
1
1
2
2
1
1
0
0
1
0
1
1
1
0
0
0
0
0
0
1
0
1
1
1
2
5
1
2
1
1
0
1
0
1
0
0
0
0
1
0
0
1
1
2
1
1
0
0
0
3
1
0
1
0
1
0
0
1
0
0
0
1
1
0
2
0
0
0
0
0
1
0
1
0
1
0
1
0
2
1
0
0
0
3
1
2
2
0
0
2
1
0
1
1
0
2
1
1
2
2
2
0
0
0
0
0
2
0
0
0
2
0
0
1
0
2
1
0
1
1
1
0
2
0
1
0
0
0
1
2
1
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
2
0
0
0
0
1
1
2
2
0
0
2
2
0
1
2
0
1
2
1
0
0
1
0
1
0
1
1
0
0
2
2
2
0
0
0
3
2
2
2
1
0
0
1
1
0
1
0
0
0
0
1
0
1
0
0
1
1
5
0
0
2
0
0
0
1
1
0
1
2
1
1
1
0
1
0
0
1
0
0
3
0
1
0
1
1
0
3
0
0
0
1
0
1
2
1
1
2
2
1
0
1
0
0
0
1
2
0
0
1
0
1
1
0
0
0
0
1
0
2
0
3
0
0
2
1
0
0
0
0
1
1
1
0
0
1
0
1
0
0
3
1
0
0
0
0
2
2
0
1
2
2
1
0
1
0
1
0
0
0
1
0
2
2
2
0
0
2
0
1
1
3
1
1
0
0
1
1
1
1
0
1
2
1
3
1
1
0
0
1
0
0
1
2
1
0
0
0
0
2
0
1
0
2
1
1
2
1
1
2
0
0
0
1
1
1
2
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
1
2
0
1
2
1
0
1
0
1
0
2
2
1
0
0
0
1
1
0
2
2
0
2
0
1
1
2
1
1
0
2
1
1
0
0
0
2
0
2
0
2
0
1
0
0
0
2
0
1
1
1
0
1
0
2
1
0
0
0
0
0
0
1
1
0
0
0
3
0
0
0
0
0
0
1
1
1
1
1
0
1
2
1
0
0
4
0
0
0
0
1
3
0
2
0
0
0
1
1
1
1
0
0
2
1
0
0
2
0
0
2
1
2
0
0
0
1
2
0
0
1
0
2
0
0
1
1
0
0
0
1
2
1
0
0
0
0
1
1
0
0
0
1
0
0
2
2
0
1
5
0
2
0
1
1
2
1
2
2
0
0
2
2
0
0
0
1
0
0
1
1
0
0
1
0
2
1
1
0
0
2
0
0
2
1
1
1
2
0
1
0
0
1
1
0
1
1
0
2
1
1
2
2
2
0
2
1
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
1
0
1
1
2
0
0
2
0
0
0
0
0
1
2
1
0
0
0
2
0
4
1
2
1
1
0
0
0
0
0
0
0
0
1
2
1
1
1
0
1
0
0
0
2
0
0
1
2
1
2
0
0
1
0
0
1
1
0
2
3
0
0
2
1
0
0
0
0
1
1
1
0
1
2
0
1
0
0
1
1
2
0
1
1
0
1
1
0
0
0
2
0
1
1
1
0
1
2
1
0
0
0
0
2
1
0
1
1
1
2
0
0
0
1
1
1
0
1
1
0
1
1
0
5
1
2
2
0
2
0
0
0
2
2
0
1
0
0
0
3
1
1
1
0
0
0
0
1
1
1
0
1
2
0
2
0
2
0
2
1
1
1
1
0
0
0
0
1
0
1
0
1
0
0
1
1
0
3
0
1
1
1
1
1
0
1
0
0
1
1
1
0
1
0
0
0
2
1
0
2
1
0
1
1
0
2
1
0
1
1
2
1
2
0
0
0
2
1
1
2
0
2
1
0
1
0
0
0
0
1
0
0
0
2
0
0
1
1
0
1
0
1
0
0
1
2
1
1
0
2
1
0
0
0
2
0
2
0
2
1
1
2
0
0
1
0
2
1
0
0
0
1
0
1
0
0
1
0
0
2
1
0
1
2
0
1
0
2
2
1
0
1
2
2
0
1
0
0
1
1
1
0
0
2
0
0
0
0
2
0
0
0
1
2
0
2
1
2
1
0
0
0
2
0
0
2
2
3
1
1
1
1
0
0
0
1
1
2
0
0
1
2
0
0
1
2
0
0
0
0
0
2
1
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
1
2
1
0
1
0
3
0
1
2
1
1
1
1
1
1
1
1
1
1
0
2
0
0
2
0
1
0
2
1
0
2
2
1
1
0
2
0
1
1
0
1
2
1
1
1
0
0
0
0
0
0
0
1
2
1
0
2
2
1
2
1
2
1
0
1
0
1
0
0
2
0
2
0
0
0
1
2
0
0
1
0
1
0
2
2
0
0
0
0
2
1
1
1
1
1
2
0
2
0
0
1
0
1
1
1
0
0
0
0
1
2
0
1
0
0
1
0
1
1
2
3
1
2
0
0
0
2
1
2
1
0
2
2
2
2
2
0
0
0
0
0
1
1
0
1
1
1
2
1
2
2
2
0
2
1
0
3
2
0
0
1
1
0
1
0
0
2
0
1
3
1
1
0
1
0
0
0
0
1
0
1
1
1
1
0
0
1
1
2
0
0
0
1
0
0
1
2
1
2
0
0
0
0
0
0
1
1
0
0
0
1
0
1
1
1
2
2
1
1
0
0
0
1
0
0
2
1
1
2
2
0
1
3
0
0
0
0
2
2
0
1
0
1
0
1
2
0
1
2
2
0
1
1
0
0
0
2
0
0
0
3
0
1
1
0
1
1
1
1
1
0
2
0
1
0
0
0
2
0
3
2
0
0
1
0
0
1
0
0
1
4
0
1
5
0
0
0
1
1
1
1
0
1
2
4
0
1
2
1
0
0
0
1
1
2
2
1
0
0
0
1
1
1
1
2
0
0
1
3
0
2
0
1
1
1
0
2
1
1
2
1
1
0
0
1
0
0
1
3
1
0
0
0
2
1
0
1
2
1
2
2
2
1
0
2
0
0
0
0
0
0
2
0
2
0
2
0
0
1
0
1
0
1
1
0
1
1
1
0
2
0
2
1
0
0
0
0
2
0
1
0
2
1
0
1
0
2
0
2
0
2
0
1
0
2
0
0
2
0
0
0
0
0
0
0
1
2
0
1
0
2
0
2
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
2
0
0
1
1
1
1
1
0
0
0
0
1
2
1
0
0
1
0
1
0
0
0
1
1
1
1
0
1
1
0
0
1
2
0
0
0
0
1
0
0
1
1
1
0
1
0
0
0
0
0
2
2
0
1
1
1
1
0
1
0
1
2
2
0
0
2
2
0
2
2
0
1
0
1
0
0
1
0
0
0
2
2
0
0
0
0
2
0
1
1
2
0
0
2
1
1
0
2
1
2
0
1
0
4
0
0
0
0
0
0
0
2
2
1
1
1
1
2
2
0
0
2
1
0
1
0
1
1
0
0
0
0
2
2
3
2
0
0
0
0
1
2
0
2
1
0
0
0
1
0
0
1
1
0
2
1
1
0
2
0
0
0
0
1
0
2
0
1
0
1
0
0
0
0
1
0
0
1
0
1
1
0
0
3
2
2
1
2
1
0
2
1
0
0
0
2
2
1
1
1
0
1
0
1
2
1
2
1
1
0
3
0
0
0
2
1
0
0
0
2
2
1
0
0
0
1
2
1
2
1
1
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
2
1
1
2
2
0
0
2
1
2
0
1
0
0
0
0
0
0
1
0
1
2
0
1
0
0
0
1
0
1
0
1
2
2
1
0
0
1
2
0
0
2
1
0
1
2
3
1
1
2
0
2
1
0
0
1
1
0
0
0
1
1
2
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
1
1
2
0
0
0
0
2
1
1
0
1
1
0
1
1
2
1
0
0
1
0
0
0
1
0
2
2
0
0
1
1
1
0
0
0
2
2
0
0
0
2
0
2
2
0
1
0
2
0
1
0
1
2
0
1
3
1
0
0
1
0
1
0
1
2
1
2
2
0
2
0
1
0
0
0
2
1
0
2
0
0
0
0
2
1
0
0
1
2
0
1
1
1
1
0
0
1
1
0
0
1
1
0
1
0
2
0
3
0
2
1
0
1
2
1
1
0
2
0
1
0
0
2
1
1
5
2
0
1
1
1
0
1
2
0
0
1
1
1
1
1
1
1
0
0
0
0
1
0
1
0
2
1
2
1
1
2
0
0
0
0
1
0
2
0
1
2
6
0
0
0
0
2
2
0
0
2
0
0
1
2
0
0
0
0
1
0
0
0
0
0
2
0
2
0
2
0
0
0
0
1
2
1
0
0
0
1
2
0
2
1
0
0
2
1
1
0
0
1
0
1
0
1
0
0
1
0
2
2
0
0
0
0
0
1
2
1
1
1
2
0
1
0
0
0
0
0
0
2
1
0
1
1
2
2
0
0
0
1
0
2
0
1
0
0
1
1
0
0
0
0
0
0
2
1
1
0
1
0
2
2
1
0
1
0
1
2
1
0
2
0
0
1
0
2
1
1
1
0
0
2
1
1
2
0
1
0
0
1
1
0
0
1
0
2
1
0
1
2
1
0
2
1
1
0
1
1
0
0
0
0
1
0
2
0
0
0
0
0
1
1
1
0
1
2
0
1
0
0
0
1
0
2
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
3
0
2
0
1
1
0
0
0
0
1
1
2
1
1
1
1
0
0
0
1
1
0
3
1
1
0
0
1
1
0
0
0
0
3
2
0
1
0
2
0
1
0
1
0
1
0
1
2
1
2
0
1
0
1
1
0
0
0
0
2
1
2
2
5
4
0
1
1
2
2
0
0
0
2
0
0
3
1
2
0
1
0
1
0
0
0
1
1
0
2
1
1
2
0
2
1
1
2
0
2
1
1
0
2
2
1
2
0
0
2
1
2
2
0
1
0
1
2
1
0
0
1
0
0
2
1
1
0
2
0
2
0
0
1
1
2
0
2
2
0
2
2
0
2
2
0
2
0
0
0
1
0
1
0
1
1
1
1
1
0
0
2
2
2
0
1
2
0
0
0
0
1
0
0
0
0
0
1
3
0
1
0
1
2
0
0
2
1
1
0
1
2
0
1
1
0
1
0
1
1
1
0
0
0
1
0
0
1
0
0
0
0
0
1
1
2
0
1
0
0
0
0
1
0
1
1
2
0
1
1
0
0
1
0
0
1
2
2
2
0
3
1
0
1
1
2
1
2
1
0
0
0
2
0
1
2
2
1
2
0
1
1
1
2
0
1
2
0
1
1
0
1
0
1
1
1
1
1
0
1
0
0
1
0
1
0
2
1
1
1
1
1
2
0
0
1
0
0
0
0
1
0
0
0
2
1
0
0
1
2
3
2
1
1
1
2
0
0
2
1
0
0
1
0
2
0
0
1
1
2
1
1
0
1
2
1
0
1
0
1
0
1
1
1
0
2
2
2
3
0
0
0
1
1
1
1
0
0
2
0
0
2
0
2
1
2
0
0
0
1
1
1
1
2
0
0
0
0
2
2
1
0
1
0
1
2
2
1
1
1
0
2
0
1
1
1
0
1
0
0
0
1
0
1
1
0
0
2
0
3
0
0
0
3
1
2
0
0
0
1
0
1
1
1
0
2
0
1
1
0
1
2
0
0
0
0
0
1
0
3
0
2
0
1
2
1
2
1
1
1
2
0
1
2
2
0
1
1
0
2
0
1
2
0
0
1
0
0
0
0
1
0
1
0
1
1
1
2
2
1
1
0
1
1
0
1
1
2
0
0
0
1
0
0
0
1
0
0
1
2
0
0
0
0
1
0
0
1
1
0
1
0
2
1
1
0
1
0
1
2
0
0
2
2
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
1
2
0
1
2
2
3
0
1
0
0
1
1
1
1
0
1
0
1
2
3
0
0
0
0
0
1
2
1
2
2
0
1
1
1
2
3
0
2
0
0
0
2
2
0
0
0
0
0
0
1
0
2
1
2
2
1
2
0
1
0
0
0
1
1
2
1
0
0
0
2
0
0
0
0
0
1
0
1
1
0
1
4
0
3
1
1
0
1
1
0
0
0
2
2
0
3
1
2
2
1
0
2
1
1
1
0
0
0
0
0
0
0
2
2
1
0
1
1
0
0
1
1
0
0
2
0
1
2
0
2
0
3
1
0
0
2
1
0
1
0
1
3
0
2
2
0
0
0
0
0
2
0
1
0
0
1
2
2
2
1
1
0
0
0
1
1
1
1
2
1
0
2
1
0
0
0
1
1
0
1
1
2
2
0
0
0
1
2
0
0
1
2
1
0
1
2
1
3
0
0
0
2
2
1
0
0
0
1
1
1
1
1
1
0
0
0
2
0
0
3
0
1
0
0
1
2
2
0
1
0
1
0
0
1
1
1
1
1
0
0
1
2
2
2
0
0
2
0
1
0
1
0
0
0
0
1
0
1
2
0
2
2
2
0
1
2
1
0
1
0
0
2
1
0
0
0
1
1
0
2
0
0
1
0
1
0
1
1
2
0
2
1
1
2
1
0
0
0
0
0
0
1
0
1
0
1
0
2
2
0
0
1
0
0
0
1
0
2
0
2
1
0
2
0
1
0
0
0
1
0
2
1
2
0
0
2
2
0
2
0
1
0
2
1
2
0
1
2
1
0
3
0
1
1
1
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
1
1
0
1
0
1
0
0
2
1
2
0
3
2
0
0
0
1
0
1
0
2
2
0
0
1
0
2
2
0
2
1
0
0
1
0
2
1
1
1
1
1
2
2
0
0
1
2
1
1
1
1
1
1
0
2
0
0
0
1
0
0
1
0
1
2
1
0
1
0
0
1
2
2
2
1
2
2
0
0
3
1
0
1
1
1
1
0
2
0
2
1
0
0
2
0
1
0
2
0
1
1
0
1
1
2
0
0
0
0
0
1
2
1
0
0
1
2
0
0
2
1
0
4
0
2
1
1
1
0
0
1
0
1
2
2
2
2
3
1
1
2
1
0
2
0
1
0
0
0
2
0
0
0
1
0
0
1
0
2
2
0
0
1
0
0
1
1
0
0
1
0
1
0
0
1
1
2
0
2
0
1
0
0
0
2
1
0
1
0
2
1
2
0
1
1
0
0
0
2
0
0
0
0
1
2
1
1
1
2
0
0
0
0
0
0
1
2
0
2
0
2
0
0
0
0
0
0
1
1
0
0
0
1
1
3
1
0
0
0
0
0
0
2
0
1
2
1
0
0
0
0
2
0
1
0
0
0
1
1
0
0
1
0
0
0
1
0
2
1
1
1
2
1
0
2
1
0
2
0
0
0
1
1
0
1
2
0
1
2
1
1
0
0
1
0
1
0
1
2
0
1
1
1
0
1
0
1
1
2
2
1
3
1
2
0
0
0
0
1
2
4
0
2
0
0
3
0
1
0
0
0
1
0
0
0
1
1
1
2
1
0
0
2
2
0
0
1
1
2
1
0
1
1
1
0
0
1
1
2
2
0
1
1
2
0
1
1
0
0
1
2
1
0
0
1
1
1
1
2
4
0
0
0
1
2
0
1
2
0
0
0
0
0
0
1
0
1
1
0
1
1
5
0
1
0
1
0
0
0
0
2
1
0
0
2
0
1
0
1
0
0
1
2
0
2
2
1
0
1
0
1
1
0
0
2
0
0
1
1
2
2
0
2
1
2
0
1
2
2
0
0
1
1
0
1
0
0
1
1
2
0
2
1
1
1
0
0
1
2
1
0
0
2
1
2
0
0
2
2
0
2
0
1
1
2
0
2
1
1
0
0
1
1
2
2
2
0
1
1
1
1
1
2
1
1
1
0
0
2
1
1
0
0
2
0
0
0
0
1
1
1
0
0
0
0
0
0
2
1
1
1
2
2
1
2
0
0
1
2
1
0
0
2
1
0
1
2
1
1
1
1
1
1
0
0
0
2
1
2
1
0
0
1
0
0
0
2
1
0
0
0
2
1
0
0
0
2
0
0
2
2
0
0
1
0
1
1
0
0
0
0
1
0
1
2
0
1
0
0
0
1
1
0
0
1
1
0
2
0
0
2
2
0
0
0
1
0
0
2
0
2
0
2
1
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
4
0
1
0
0
0
0
1
1
0
0
0
0
1
0
1
0
2
1
0
0
1
1
0
1
2
0
0
2
0
0
0
1
0
0
0
2
1
0
1
2
2
0
0
2
3
1
0
2
0
0
3
0
0
0
0
0
0
1
1
1
1
2
0
1
1
2
2
2
0
1
2
1
0
3
0
0
1
0
0
1
0
1
0
0
1
0
0
0
1
0
2
0
0
0
2
0
2
0
0
2
0
0
2
0
1
2
2
0
1
2
2
3
0
2
3
0
0
0
1
0
2
1
2
2
0
1
2
0
1
2
1
0
0
0
1
1
0
0
0
1
1
1
1
0
2
0
0
2
0
0
2
0
2
2
1
0
2
0
0
0
0
0
1
1
1
2
0
0
1
1
0
2
2
0
1
0
2
1
0
2
2
0
1
2
0
1
0
2
0
0
0
0
1
1
2
2
2
2
0
1
0
1
2
1
0
0
1
1
0
1
2
0
0
2
1
0
1
0
1
0
0
0
1
2
0
0
2
2
2
0
0
1
0
0
1
1
0
0
1
0
0
0
1
1
0
1
1
1
1
0
2
1
0
1
0
1
0
0
0
0
0
1
1
4
1
0
1
1
0
0
1
0
0
0
1
2
0
1
0
2
1
1
0
0
2
1
0
1
0
0
2
2
0
0
2
1
2
0
1
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
3
1
1
0
0
0
2
0
1
2
0
0
0
0
0
1
2
1
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
2
1
1
1
2
0
0
0
1
0
0
2
1
0
0
1
0
2
1
0
0
0
1
0
0
0
0
1
0
1
1
2
1
0
1
2
1
2
0
1
1
0
2
1
0
0
0
1
2
1
1
0
1
0
1
2
0
1
1
1
0
2
0
1
0
1
1
2
1
0
2
0
0
0
0
1
1
2
0
0
0
1
1
1
0
0
1
1
1
1
1
1
0
1
2
2
0
0
2
2
1
0
0
0
0
2
0
1
1
0
0
1
0
0
1
0
0
0
0
2
1
0
0
1
0
0
0
2
0
2
0
0
0
1
1
0
1
0
0
0
2
1
2
2
0
1
0
0
0
2
1
0
0
1
2
2
1
0
3
4
1
0
1
3
1
2
2
2
3
0
1
2
0
0
1
0
0
3
0
2
2
0
0
0
0
1
0
1
0
0
0
1
2
1
0
1
1
0
0
0
1
2
3
0
1
0
0
0
1
0
1
0
1
1
2
1
2
1
0
2
1
1
1
0
0
0
1
0
0
1
1
0
2
2
0
1
0
0
2
1
2
0
0
2
1
1
0
0
0
1
1
1
0
0
1
0
1
1
1
1
0
2
2
0
1
0
1
0
1
2
1
1
1
0
0
1
1
2
1
1
2
0
1
2
2
0
1
1
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
2
1
1
1
2
0
1
0
0
1
0
0
2
2
0
0
1
1
0
1
2
2
0
0
2
1
1
2
2
0
2
2
1
1
0
0
0
0
2
1
0
1
0
0
1
2
0
0
1
0
0
1
0
2
2
1
3
0
2
1
2
0
0
1
0
2
1
2
0
0
1
2
0
2
1
0
1
1
0
1
1
0
3
2
1
1
0
0
1
1
1
2
2
2
0
2
2
1
0
2
1
1
0
1
0
1
0
0
0
0
0
0
1
2
0
1
1
1
0
0
0
0
1
0
0
1
1
0
1
0
0
1
2
0
1
0
0
1
1
2
2
2
1
0
1
1
1
1
0
0
1
2
2
1
0
1
1
1
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
1
3
0
2
0
1
2
0
2
0
1
2
0
0
1
1
1
2
2
0
4
2
2
0
1
1
0
2
0
1
0
0
0
0
1
2
0
0
2
0
1
0
0
0
0
0
1
2
0
2
0
1
1
0
1
0
0
0
2
1
1
1
0
2
2
2
2
2
0
1
2
0
1
1
1
0
2
1
1
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
2
0
1
0
0
0
0
1
2
2
0
0
1
0
2
2
0
0
0
0
1
1
0
1
0
2
0
1
1
1
2
4
0
0
1
1
0
1
0
1
2
2
0
0
1
0
1
7
0
4
0
2
1
0
3
1
0
1
0
1
1
0
1
0
0
1
0
2
1
1
1
0
0
0
1
2
2
1
0
0
3
1
1
1
0
0
1
2
1
0
1
0
0
2
0
2
0
0
2
1
0
2
0
1
1
1
0
0
2
1
0
1
0
1
1
2
2
2
1
2
0
1
2
1
2
2
1
0
1
0
0
1
0
0
2
1
2
0
0
1
1
0
0
1
1
2
2
1
0
1
1
0
0
0
1
1
0
2
0
0
0
0
1
0
0
0
0
2
2
0
1
2
1
0
0
1
1
1
0
1
1
1
2
1
1
1
2
2
2
0
0
0
2
0
0
0
0
0
1
1
2
0
0
1
0
2
2
0
0
0
0
0
2
1
0
1
0
1
0
0
1
2
2
1
0
1
0
1
1
1
0
0
2
2
1
2
1
2
0
2
2
1
1
1
1
1
1
1
0
0
0
0
0
2
0
1
1
0
1
1
0
2
0
0
1
2
0
1
1
0
0
0
1
2
2
2
0
2
0
2
0
0
3
0
1
2
0
1
0
2
0
0
0
1
1
1
0
0
1
1
0
1
1
0
2
1
0
1
0
2
1
1
0
1
1
2
1
1
0
3
0
2
0
2
2
0
0
0
1
1
2
1
1
2
1
2
1
0
1
1
0
1
0
2
0
1
2
1
2
1
0
0
2
0
0
2
0
0
1
2
1
0
2
0
3
1
1
0
2
1
0
0
0
1
2
1
2
1
1
0
2
0
0
0
0
1
0
2
1
0
0
2
0
0
0
2
2
0
1
0
0
0
0
1
0
2
1
2
2
0
2
1
1
0
0
2
0
0
1
6
1
1
0
1
3
1
1
2
0
0
0
1
1
2
0
2
2
0
2
0
0
0
0
1
0
3
0
0
0
1
1
2
0
1
1
1
0
1
2
0
0
1
1
2
1
1
0
1
2
1
0
0
0
1
1
1
0
0
1
0
1
11
0
2
2
0
0
2
0
1
1
0
1
0
1
1
0
0
1
0
0
0
2
1
0
2
2
0
0
0
1
1
0
1
0
1
1
2
0
0
2
0
1
2
0
1
0
1
3
2
0
0
1
0
1
0
2
1
0
2
1
1
0
0
0
0
0
0
2
0
0
0
2
0
1
0
1
0
1
2
2
1
1
1
1
0
2
1
0
0
1
0
0
1
2
2
1
1
0
0
1
2
1
1
1
0
1
1
3
1
1
0
1
1
1
2
0
2
2
1
1
1
0
1
6
2
2
1
2
0
0
2
2
2
0
0
2
1
2
1
0
1
2
1
0
2
0
1
2
1
0
0
0
1
0
0
0
0
0
2
2
2
1
2
0
1
0
2
0
1
0
1
2
0
0
0
2
1
1
0
2
0
0
2
1
0
1
0
0
1
0
0
2
0
1
0
0
1
0
1
4
0
2
0
1
1
0
0
0
0
1
0
0
2
0
0
0
0
1
1
1
2
1
1
2
0
4
2
2
0
2
1
0
0
2
1
2
1
0
2
0
0
2
0
0
1
0
0
1
1
1
1
1
1
0
1
0
1
0
1
0
1
2
2
0
0
0
2
0
1
2
2
1
0
0
1
0
2
0
0
1
0
1
1
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
3
1
2
1
0
1
1
1
1
2
2
0
0
1
1
0
1
2
0
2
2
1
0
0
2
2
0
1
2
0
0
1
1
0
3
2
1
2
0
1
0
2
1
1
1
0
1
0
1
0
0
0
0
0
0
0
2
1
0
1
1
3
1
0
1
1
0
0
1
1
1
0
0
0
0
2
0
0
2
0
0
1
0
2
2
2
0
2
1
2
0
0
0
1
2
1
1
1
0
0
2
2
0
0
0
1
0
1
3
0
1
3
0
2
0
1
0
0
2
0
0
0
0
1
1
0
0
3
0
0
1
2
2
2
1
0
0
0
2
0
1
1
1
0
0
1
2
1
1
1
0
1
1
0
0
1
2
0
1
0
0
0
2
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
1
1
0
1
1
1
1
2
1
2
5
1
1
1
1
0
0
0
1
0
0
0
1
1
1
1
0
1
2
0
1
0
1
1
0
0
0
1
1
0
0
0
0
3
1
1
0
0
2
1
2
2
4
0
0
1
1
2
1
1
0
1
0
0
1
0
2
1
0
0
1
1
1
4
1
0
2
1
0
3
0
0
1
1
0
0
0
0
2
0
2
0
1
0
1
0
1
0
0
1
0
0
2
1
1
2
1
1
0
0
1
0
1
0
2
1
1
0
0
2
0
0
2
2
0
1
1
0
0
0
0
0
0
0
2
0
1
0
0
1
1
0
1
1
0
0
0
0
2
2
0
0
2
0
0
2
2
1
1
2
1
0
0
2
3
1
1
2
0
0
0
4
2
1
1
0
1
0
0
1
2
2
0
0
2
0
0
1
0
0
1
1
0
2
1
0
0
1
2
2
3
0
0
1
0
1
1
1
0
2
1
0
2
0
0
0
0
0
0
1
0
0
0
1
2
0
2
0
2
0
1
1
2
1
1
2
3
0
2
0
0
0
2
0
1
2
1
2
0
0
0
1
0
0
0
1
2
2
1
2
1
2
2
1
1
2
1
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
2
1
0
0
1
0
0
1
0
2
0
2
0
0
1
1
1
0
1
2
1
1
0
0
4
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
1
2
1
2
0
0
0
0
0
0
4
1
1
2
0
0
0
0
0
0
0
0
2
0
1
0
1
0
2
2
0
0
1
2
0
2
1
0
2
1
1
1
0
0
2
0
5
2
1
0
0
0
0
2
0
2
1
0
2
1
0
1
1
0
0
1
1
0
2
0
3
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
2
0
1
2
0
1
0
1
0
0
0
1
1
0
1
2
0
1
2
1
1
0
0
0
2
3
0
0
0
0
0
1
1
1
1
2
0
1
0
1
2
1
0
0
2
2
2
2
1
0
1
2
1
0
2
1
1
0
0
0
0
0
2
0
0
0
0
1
1
1
1
1
0
0
1
0
1
1
2
1
1
2
2
0
0
0
0
0
1
1
1
1
2
1
2
0
2
1
0
0
0
1
0
0
1
0
1
1
2
1
1
0
2
0
0
2
1
1
0
1
1
0
1
2
1
0
1
0
2
1
2
0
0
1
0
2
1
0
1
0
1
1
2
1
0
2
1
0
4
0
0
1
1
2
2
0
2
0
1
1
1
2
0
1
2
0
0
2
0
0
1
1
2
0
2
0
2
0
0
0
1
2
0
0
0
0
0
0
2
2
0
0
0
0
0
1
2
0
1
2
1
1
1
0
1
0
0
1
1
0
2
0
2
2
0
2
1
1
0
0
1
0
1
0
1
0
1
0
2
2
0
0
0
2
2
1
2
2
0
1
1
1
0
1
1
2
0
0
1
0
0
0
0
2
1
1
1
1
1
0
1
0
0
1
0
2
2
1
0
0
0
0
1
1
2
1
0
1
0
1
3
0
5
1
1
1
1
2
1
0
0
0
2
0
1
0
2
2
4
1
2
1
2
0
2
0
1
0
2
0
0
1
0
3
1
1
0
0
1
1
0
0
1
0
1
0
1
0
0
2
1
0
1
0
0
0
2
0
0
1
1
0
0
0
1
1
1
0
0
0
0
2
1
1
2
0
2
1
0
0
0
2
1
0
1
1
1
0
2
0
1
0
0
1
1
1
2
1
0
2
2
1
1
1
1
1
0
0
1
0
0
0
1
0
2
2
0
0
0
1
1
1
0
0
0
0
0
1
1
1
1
0
0
1
0
2
1
1
0
2
2
0
1
1
3
0
0
0
1
2
1
0
2
0
2
2
1
0
1
1
0
2
0
3
0
1
0
1
0
0
2
0
0
1
1
2
1
2
1
0
1
0
0
0
1
1
0
0
0
0
0
0
2
1
2
1
0
1
2
2
1
0
0
0
0
1
0
2
0
1
2
0
2
1
0
0
0
1
1
0
0
2
0
0
0
0
0
0
2
0
2
2
0
0
0
1
0
0
1
0
0
0
2
0
0
3
1
0
1
3
1
1
0
0
1
0
1
2
0
0
2
2
0
1
1
0
0
0
1
3
2
0
0
0
0
0
0
1
0
2
2
1
0
1
1
0
2
1
0
0
1
1
1
0
1
2
0
0
0
0
2
1
0
1
1
3
0
1
0
1
2
1
1
1
0
2
0
0
1
0
1
0
1
0
2
0
2
2
1
1
1
1
1
0
1
1
1
1
2
1
1
1
1
1
2
0
2
0
0
2
0
1
1
2
0
0
2
0
1
0
0
1
1
1
0
2
0
1
1
3
0
1
1
0
2
0
2
2
2
1
0
1
0
1
2
0
3
0
0
0
3
0
0
1
0
1
0
1
2
0
1
2
1
1
2
0
3
0
0
1
2
0
2
1
0
1
0
2
1
0
1
1
0
0
1
0
1
1
0
1
0
2
0
0
0
0
1
0
2
1
1
1
0
1
2
2
0
0
0
1
0
0
2
2
0
1
0
1
2
0
0
1
1
1
1
1
0
1
2
0
1
1
0
0
0
1
1
1
0
0
0
1
0
1
0
8
0
0
0
1
2
2
1
0
1
2
1
0
1
1
0
0
0
1
1
0
1
1
2
0
0
0
0
1
1
1
0
0
0
1
1
0
1
1
0
0
2
2
1
2
1
1
1
0
2
1
1
2
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
2
0
0
1
0
0
0
1
2
0
0
1
0
0
1
0
0
2
1
2
2
2
1
1
1
2
0
2
0
2
2
1
1
1
2
0
1
2
3
0
2
1
1
1
1
0
0
1
2
0
0
0
1
1
0
0
2
2
1
0
0
0
2
0
0
1
0
1
1
0
1
1
1
1
0
2
0
2
0
0
0
0
1
1
0
0
1
0
0
1
0
2
2
0
0
1
2
2
1
0
1
1
0
0
1
2
1
0
1
2
3
0
0
1
0
0
1
1
1
1
2
1
0
1
2
1
0
2
1
0
0
2
2
2
0
2
0
0
1
0
0
1
0
1
1
2
1
0
0
2
1
2
0
0
0
0
2
1
1
0
2
0
0
2
0
0
0
0
3
2
0
1
0
2
2
1
0
1
0
0
1
1
1
2
2
2
2
0
1
1
1
0
1
0
0
0
2
0
2
2
0
2
1
0
0
0
1
0
0
0
1
1
0
1
0
0
1
2
0
1
0
0
2
2
1
1
0
0
0
0
0
1
0
0
1
2
0
0
1
0
0
0
2
0
1
1
3
0
0
1
0
2
2
0
1
0
1
0
2
0
1
3
0
1
1
0
0
1
0
2
0
0
1
2
0
1
1
2
0
0
2
1
0
1
2
3
1
1
0
1
1
2
0
0
1
2
0
1
1
2
2
0
0
0
3
2
0
2
0
0
1
0
0
0
1
0
0
0
2
0
0
0
1
0
1
2
1
1
1
0
0
2
1
1
0
0
0
0
5
0
1
0
2
0
0
0
0
1
1
2
1
1
1
0
0
3
0
2
1
0
1
1
0
3
2
0
1
1
0
0
1
1
2
0
1
0
1
0
0
1
1
1
0
1
0
1
1
0
2
0
0
0
0
0
0
1
0
0
1
2
2
1
2
1
2
0
1
0
0
1
0
1
1
0
1
1
0
0
3
2
0
2
0
0
0
1
2
2
0
1
1
0
0
0
0
0
2
0
0
0
0
2
1
1
0
0
0
0
0
0
1
2
0
0
1
1
1
1
0
0
0
1
0
3
1
1
0
0
2
2
0
0
1
2
4
0
1
0
2
0
0
1
0
2
1
0
0
1
0
0
0
2
1
2
0
0
2
1
2
1
0
0
1
2
0
2
0
2
0
1
0
0
1
2
0
0
0
1
1
1
0
2
1
1
0
2
1
1
1
0
3
0
0
2
0
0
0
0
1
0
0
0
0
2
2
1
0
0
1
0
0
1
1
0
0
0
0
1
1
0
0
0
3
0
2
0
0
2
1
0
1
1
1
2
0
0
1
1
1
0
2
1
2
1
1
2
1
2
0
0
1
0
0
0
1
1
1
0
2
1
0
0
0
1
0
1
1
0
2
4
0
0
2
1
0
0
0
2
1
0
2
1
2
2
0
1
1
0
1
0
0
1
2
0
2
1
1
1
0
2
0
1
1
0
0
0
0
2
0
1
1
0
1
2
0
0
0
0
1
0
2
1
3
0
0
2
0
2
0
0
1
1
2
0
1
0
0
1
0
2
0
1
0
0
1
1
0
0
0
0
0
0
1
0
2
2
2
0
1
0
5
1
2
2
0
1
0
0
0
2
1
2
1
2
1
1
1
0
0
3
1
0
0
0
1
0
0
1
2
0
1
0
2
1
0
0
0
2
1
2
3
1
0
2
1
1
0
1
1
2
0
1
1
0
2
1
0
0
2
0
0
1
0
2
1
0
1
1
0
0
0
1
2
0
0
0
1
1
2
0
1
0
2
0
1
0
1
0
0
1
1
0
0
1
1
2
1
0
1
0
0
2
2
2
0
0
0
0
2
2
0
2
1
0
0
1
0
1
2
1
2
0
2
1
0
2
1
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
2
2
1
0
1
2
2
0
0
0
2
2
0
2
1
1
2
1
1
0
0
1
0
1
1
0
1
1
2
0
0
1
0
1
0
2
0
3
1
0
1
0
2
0
1
0
2
2
0
0
0
3
0
2
1
0
2
2
0
0
0
1
0
0
2
1
1
0
1
3
0
1
1
0
2
0
0
2
1
0
0
0
1
0
0
1
0
1
0
2
0
2
0
2
5
0
1
1
1
0
0
0
0
0
1
1
1
0
1
0
2
2
0
0
1
1
1
0
0
0
1
2
0
0
0
0
2
0
2
2
1
0
0
2
0
0
0
0
2
2
2
0
0
0
2
2
0
0
1
2
1
1
1
0
1
3
1
0
1
1
1
2
0
0
0
0
0
1
0
0
0
1
1
1
1
1
0
0
1
1
1
0
0
1
2
1
1
1
0
1
0
0
2
0
0
1
2
0
0
0
0
1
2
0
0
1
1
1
0
1
1
0
2
0
0
0
0
2
0
0
2
0
1
0
1
2
1
2
1
0
0
1
2
0
2
0
0
1
0
2
0
1
1
2
2
0
0
0
0
2
0
0
2
2
2
0
2
0
0
2
0
0
0
1
1
0
1
1
0
0
0
1
2
0
2
0
0
2
2
2
0
2
1
2
1
1
0
0
1
1
1
1
0
0
0
1
1
2
0
0
0
1
0
2
1
1
2
2
0
2
1
0
0
1
1
2
2
2
2
2
1
2
0
1
0
0
2
0
1
1
2
2
0
0
0
1
2
0
1
0
1
2
1
0
1
0
3
2
0
0
2
0
0
0
0
0
1
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
1
2
1
2
1
0
0
1
0
0
0
1
1
0
0
1
1
1
2
1
2
1
1
2
2
2
0
0
1
2
0
0
0
1
2
2
2
0
3
2
0
0
2
0
2
0
0
1
2
1
2
1
0
2
0
0
0
0
2
2
1
0
1
0
2
0
0
0
1
2
0
1
1
0
0
1
2
0
2
2
0
2
1
2
2
2
0
1
0
0
0
1
0
1
1
0
0
2
2
1
0
2
1
1
0
0
1
2
0
1
1
0
1
2
1
2
2
0
0
1
2
1
1
0
0
0
0
0
1
3
1
0
0
0
1
1
1
2
2
1
0
1
0
0
0
2
2
0
1
0
1
1
2
0
2
1
0
0
1
0
1
0
1
4
1
0
0
1
1
0
0
1
0
1
1
1
0
0
0
1
0
1
2
1
0
0
1
1
2
0
1
0
0
0
6
0
1
1
1
0
1
0
2
0
0
0
0
1
1
2
1
2
1
2
1
1
1
0
0
2
0
1
0
2
2
1
0
0
0
1
0
0
1
1
0
0
0
2
1
1
0
1
0
1
0
0
2
1
2
0
0
1
0
2
1
2
3
1
1
1
0
1
2
0
1
1
1
1
2
1
1
0
0
0
2
2
0
0
2
2
0
0
0
0
2
1
2
2
1
2
1
0
2
1
0
1
1
2
1
1
0
1
0
0
0
2
1
0
2
0
1
0
1
0
1
1
2
1
1
2
1
0
0
1
2
0
0
0
1
1
1
0
1
0
1
3
1
2
1
1
0
0
0
0
0
2
0
2
0
1
1
1
1
1
1
2
0
2
0
2
1
0
0
2
6
1
1
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
1
1
1
2
1
0
0
0
0
1
1
0
0
2
0
1
2
2
0
2
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
1
1
0
2
1
2
1
0
0
2
0
0
2
1
2
1
2
1
0
1
0
0
0
1
2
4
1
0
1
2
2
0
0
0
1
1
3
0
2
1
0
0
0
1
2
0
2
0
0
0
0
1
1
3
1
0
1
1
1
0
1
1
2
2
2
0
0
1
0
0
2
1
2
1
2
2
1
1
0
0
0
0
0
0
0
1
1
1
1
1
2
1
0
0
0
1
4
2
1
1
0
3
0
0
1
1
1
2
2
0
0
0
2
0
1
0
2
0
1
1
2
1
0
2
0
0
1
1
2
2
0
1
0
2
1
1
2
0
1
0
0
1
0
0
0
0
1
1
1
2
0
2
2
0
3
0
0
2
0
0
0
0
0
0
3
1
0
0
2
1
0
0
2
2
1
1
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
1
2
2
0
0
2
1
3
1
1
0
0
0
1
0
1
2
1
2
1
2
0
1
2
1
0
1
1
1
2
0
2
2
0
0
2
0
1
2
0
0
0
2
1
0
1
2
3
1
0
0
0
0
0
1
1
2
1
1
0
1
0
0
0
1
0
0
2
2
0
0
1
1
0
2
1
0
1
0
0
0
1
0
1
0
2
0
0
0
1
0
1
0
1
0
2
0
0
2
1
0
1
0
0
2
0
0
0
0
1
0
1
0
1
0
1
0
2
1
1
0
2
2
2
2
0
1
0
2
2
1
0
0
0
1
1
2
2
0
0
2
2
0
0
1
0
1
1
1
1
1
0
1
1
0
0
2
0
1
0
2
1
1
2
1
2
0
2
0
0
0
1
0
0
1
0
2
1
1
0
2
2
4
1
1
2
0
0
0
2
1
0
2
1
2
2
0
1
1
0
0
0
0
0
0
2
2
0
1
2
1
0
0
1
1
0
0
2
3
1
2
2
1
1
0
0
0
1
2
2
2
1
1
1
0
0
2
0
2
0
0
0
2
0
0
0
1
0
0
0
1
0
0
1
1
0
1
1
0
1
2
1
0
2
1
0
2
0
0
0
0
1
0
1
1
1
1
0
2
0
1
0
2
1
1
0
1
1
1
0
1
0
1
1
0
0
0
0
1
2
0
1
1
1
2
2
0
0
0
0
1
0
0
1
2
3
1
1
1
2
0
0
2
1
0
1
0
0
2
1
2
1
0
0
2
0
0
0
0
2
0
0
3
0
2
1
0
0
1
2
1
1
3
0
0
0
0
0
1
0
2
2
0
0
0
1
2
0
0
0
2
1
0
0
2
2
1
0
0
0
1
0
1
1
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
1
1
1
2
0
0
2
0
0
1
2
0
0
0
0
0
2
1
0
0
0
0
1
2
1
1
2
0
1
0
0
1
2
2
0
0
0
2
1
0
2
0
0
2
0
0
1
0
2
0
2
2
1
0
0
0
0
0
1
2
1
2
2
2
0
0
1
2
0
0
8
1
0
0
0
0
0
0
2
1
0
0
2
0
0
1
2
1
1
1
1
0
2
0
0
1
2
0
1
1
1
0
2
1
2
3
1
1
1
2
0
0
1
1
1
1
0
2
2
1
1
1
0
1
1
1
0
2
2
1
1
0
3
1
1
0
0
1
1
2
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
2
2
0
2
0
0
0
0
0
1
3
2
2
0
2
0
0
0
0
2
0
2
0
1
0
1
1
1
1
1
1
0
2
1
0
0
0
0
0
1
1
1
0
0
1
0
1
1
0
2
1
2
0
0
0
0
2
0
1
0
2
0
0
3
0
0
0
1
0
1
0
0
2
1
1
1
3
0
1
2
0
1
0
0
1
1
2
1
0
1
2
0
1
0
0
0
2
0
8
0
2
1
2
0
0
1
1
1
0
0
0
0
0
1
0
1
1
0
1
2
1
1
1
0
0
0
0
2
2
2
0
2
1
1
0
0
0
0
2
1
1
0
1
0
0
2
1
2
1
0
0
0
2
2
0
0
0
0
0
1
0
0
1
2
0
1
0
1
1
2
1
1
1
1
0
0
2
0
1
0
2
1
0
0
1
1
1
1
2
0
2
4
0
3
2
1
2
0
0
0
0
0
3
0
0
0
1
1
0
0
2
0
0
0
1
1
1
1
0
1
0
2
0
1
0
0
0
0
1
0
0
1
0
1
2
1
0
2
1
1
1
0
0
0
0
0
1
0
0
0
2
0
1
0
5
0
0
1
0
1
0
0
1
0
1
2
2
2
0
1
1
3
1
0
0
2
1
0
2
1
0
2
1
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
1
0
0
2
2
1
1
0
0
2
0
2
0
2
0
0
2
0
0
4
1
0
2
1
0
0
1
1
2
0
0
2
2
0
0
1
0
0
2
1
1
1
0
0
1
0
0
1
0
1
1
1
0
1
1
1
1
2
0
0
2
0
3
2
2
2
2
1
2
1
0
1
2
2
2
0
1
2
1
1
2
0
2
1
2
2
0
2
1
1
0
0
1
0
0
0
0
1
2
1
0
0
2
0
2
0
1
2
1
0
1
1
2
0
1
1
2
0
0
2
1
0
0
0
0
1
0
1
0
1
1
0
0
2
2
1
2
0
1
1
1
2
2
2
0
1
0
1
1
1
0
0
2
2
2
0
2
0
0
0
0
0
2
0
1
1
2
2
2
2
0
3
0
2
1
0
1
0
0
1
1
1
0
0
1
0
0
2
0
0
1
2
0
1
0
0
3
3
1
0
0
1
2
0
2
0
1
0
0
1
0
1
1
2
2
1
1
1
0
1
0
0
1
0
1
2
1
2
0
2
2
0
0
0
0
2
1
0
0
2
2
1
0
1
2
2
2
1
1
0
0
1
1
1
0
2
1
1
0
2
2
1
0
0
0
0
0
0
0
0
0
2
1
1
1
1
0
0
2
1
1
0
0
1
0
1
2
0
0
1
0
2
1
0
2
2
1
2
2
1
1
0
2
0
1
0
0
0
0
2
2
1
1
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
2
1
1
2
1
2
0
0
2
1
2
1
2
1
0
0
2
0
2
0
0
0
0
0
2
1
1
2
0
0
1
1
1
2
1
0
3
0
1
0
1
1
2
0
2
1
1
0
2
2
1
0
2
0
2
0
0
1
1
0
2
2
1
0
2
0
0
1
0
1
0
1
0
1
0
0
0
1
0
0
0
0
3
2
0
0
2
0
0
1
0
2
1
1
0
1
0
1
1
0
0
0
0
1
1
1
2
0
1
2
0
2
1
2
4
1
0
0
0
2
0
2
1
0
1
1
0
0
2
0
0
0
0
0
0
2
0
2
2
0
0
1
0
2
1
1
0
0
1
0
1
1
1
2
2
2
0
2
2
0
1
0
1
0
0
0
2
0
1
0
0
1
2
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
2
2
0
2
0
2
1
0
2
0
0
2
2
0
0
1
1
1
0
0
1
1
2
0
2
0
2
0
2
0
3
0
2
1
1
1
1
0
1
0
1
0
0
0
0
0
2
2
0
1
2
1
1
1
1
1
0
0
1
0
0
0
2
1
2
0
0
1
2
0
0
0
0
1
2
0
1
0
0
2
1
0
1
1
0
0
0
0
1
1
1
0
1
2
1
1
2
2
1
0
1
0
1
1
1
0
0
2
0
2
1
0
2
1
0
3
1
1
0
0
0
0
0
1
1
0
1
1
0
1
1
0
0
2
0
0
4
0
0
0
1
1
0
1
1
1
0
1
0
0
0
1
1
2
0
2
0
2
1
2
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
2
0
1
2
0
0
1
1
2
0
1
1
0
2
2
1
0
0
0
1
0
0
0
0
2
0
1
2
1
3
3
1
0
0
2
1
1
0
1
0
2
0
1
0
0
2
0
0
1
1
1
0
2
1
2
0
0
0
1
1
0
1
0
0
2
1
0
1
2
0
1
1
0
0
0
0
0
0
1
1
0
1
1
0
0
1
0
1
2
0
1
0
0
2
1
0
1
0
0
0
1
1
3
1
0
2
2
0
0
1
2
0
0
0
2
0
2
1
2
1
2
1
3
2
1
3
2
0
3
1
0
3
0
2
2
2
3
1
0
0
2
1
0
0
0
0
0
0
1
0
1
2
2
0
0
2
1
1
0
0
2
1
1
1
1
1
0
0
0
2
1
0
0
1
0
2
0
0
2
0
1
0
0
1
1
0
0
2
1
2
2
0
2
0
0
0
2
1
0
1
0
0
0
0
0
0
1
0
2
0
0
1
0
0
1
0
0
1
1
0
1
1
2
2
1
0
0
1
0
0
0
2
1
0
0
2
0
0
1
1
0
0
1
3
1
2
0
1
0
1
2
1
2
0
1
1
0
0
0
4
0
2
0
0
0
0
0
1
2
0
0
1
0
0
0
1
1
0
1
0
0
1
1
0
2
1
0
0
2
1
0
1
0
0
1
1
1
0
0
0
2
1
2
2
0
0
1
0
1
1
1
1
0
0
2
0
0
0
1
0
1
2
1
0
0
2
2
1
2
2
1
0
0
0
0
1
0
1
0
0
2
0
0
0
2
1
0
2
1
0
0
0
1
2
0
1
1
1
1
2
1
1
0
1
1
1
1
1
0
0
0
0
1
2
1
2
2
2
1
1
1
1
1
1
0
0
1
0
1
0
1
2
0
2
0
1
3
0
0
0
2
0
1
2
1
0
0
2
0
0
3
2
0
2
2
0
0
0
0
1
2
2
1
0
2
1
0
0
2
0
0
1
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
1
2
0
0
1
0
1
1
0
0
2
0
0
1
2
1
0
1
1
1
1
1
2
0
0
2
0
1
2
0
2
2
0
0
1
0
0
0
1
1
2
0
2
1
0
0
2
0
0
1
1
1
1
0
1
1
0
2
1
0
5
1
1
1
2
0
1
2
0
0
0
1
0
0
1
2
0
0
0
1
1
1
0
2
1
2
1
2
0
1
2
1
1
1
0
1
0
1
2
1
1
2
0
1
0
0
0
0
0
1
0
0
0
2
1
0
0
2
2
0
1
0
0
0
2
1
0
0
2
1
1
0
0
2
1
0
1
1
1
0
0
1
1
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
2
1
0
0
0
2
1
1
0
0
2
1
1
0
0
1
0
1
2
1
2
1
1
0
0
4
0
1
0
2
0
0
1
0
2
1
2
1
2
2
0
3
0
1
0
2
0
0
0
1
0
1
1
0
0
0
2
0
0
0
0
0
2
2
0
0
0
2
0
1
2
2
0
0
1
1
2
0
0
1
0
2
1
1
1
1
2
1
1
1
1
1
3
2
1
1
1
0
0
0
0
1
0
1
2
2
1
1
2
0
0
0
2
2
1
0
1
2
1
1
0
1
4
1
1
0
2
0
2
2
2
0
2
0
2
1
1
0
0
0
2
1
0
0
0
1
0
0
2
1
2
0
2
2
0
0
2
0
1
0
1
1
0
2
0
1
1
2
1
0
1
2
1
0
0
0
0
2
1
0
1
2
2
1
1
0
0
0
2
1
1
1
2
1
1
0
2
1
2
0
0
0
0
0
1
0
0
0
1
0
1
2
1
1
1
2
0
1
1
1
0
0
2
2
0
0
0
2
0
0
0
0
2
0
0
1
0
2
0
1
2
1
1
0
0
1
2
0
0
1
0
0
2
0
0
2
0
2
0
1
0
0
2
1
0
1
0
2
0
1
0
1
1
1
1
0
1
2
0
1
0
1
2
0
1
0
1
0
1
1
0
3
2
1
1
2
0
0
1
1
0
2
0
2
0
0
0
0
2
0
0
0
2
1
0
1
2
1
0
0
0
0
0
0
1
1
0
0
2
2
1
3
2
0
2
1
0
1
0
2
0
1
2
2
0
1
2
1
2
2
0
0
1
1
0
2
0
0
0
2
1
0
0
0
2
1
1
0
0
1
1
1
1
0
1
2
1
1
0
0
1
2
0
2
2
1
2
2
0
1
0
1
0
1
1
1
0
0
1
1
1
0
3
2
0
1
0
0
0
0
1
0
0
1
2
1
2
0
0
1
1
0
2
1
0
0
0
0
2
1
0
2
0
0
1
1
1
0
3
2
0
2
2
1
0
1
1
0
0
0
3
1
0
1
2
1
1
0
3
2
0
1
0
0
1
0
1
1
0
0
0
1
2
1
1
3
2
1
1
0
1
0
0
0
0
0
1
2
2
0
2
1
0
0
2
0
0
1
0
0
0
1
1
1
2
0
0
1
0
0
1
1
1
1
0
0
1
2
1
0
0
0
1
2
0
1
1
0
0
0
1
0
1
2
0
1
1
0
3
1
1
2
1
1
3
1
1
1
0
1
0
1
1
1
1
1
1
0
1
0
1
0
2
0
0
2
0
2
2
0
2
0
0
2
0
0
1
0
2
0
0
0
1
0
0
2
0
1
1
1
0
0
0
1
2
1
1
1
1
0
2
1
2
0
0
0
0
1
2
2
0
0
1
1
0
0
0
0
0
0
1
2
1
1
1
1
0
0
0
1
1
1
1
0
1
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
1
2
0
0
1
1
0
0
2
3
1
0
1
1
2
1
1
0
0
1
2
0
0
1
1
1
2
0
2
1
1
0
0
2
0
1
0
0
0
1
0
0
1
2
1
2
1
1
0
1
2
0
0
0
0
1
0
1
2
1
0
0
1
0
1
0
3
0
1
0
0
1
1
0
0
1
0
2
2
1
1
0
2
2
1
1
0
0
0
0
1
1
0
1
0
1
0
0
1
2
1
0
1
0
0
0
0
1
0
0
1
1
2
0
2
1
1
0
2
1
1
1
0
0
0
2
1
0
2
1
0
1
1
1
2
2
0
0
0
1
0
2
0
2
0
2
1
1
0
1
2
1
0
2
0
2
0
1
0
0
2
0
0
0
0
1
0
0
2
2
2
1
0
0
1
1
0
2
0
1
0
1
0
0
0
1
1
1
0
0
2
0
0
1
0
1
0
0
1
0
1
1
2
2
1
0
1
1
0
1
0
1
0
0
1
3
0
0
0
0
0
0
0
2
0
2
1
1
0
0
2
1
1
0
0
0
2
1
0
2
2
1
0
1
0
0
1
1
1
0
1
0
1
0
0
1
0
1
1
2
0
1
1
2
1
0
0
0
0
1
0
1
1
1
0
2
0
1
4
0
0
0
0
0
1
0
0
1
2
1
0
1
1
0
0
0
1
0
4
2
0
0
1
0
1
1
1
1
1
1
0
0
0
0
1
0
1
0
0
1
0
2
1
0
1
1
0
1
0
0
0
1
1
2
2
1
1
0
0
1
2
0
0
1
1
0
1
0
0
2
0
1
1
2
0
0
2
2
2
2
1
0
1
2
2
0
1
0
1
1
2
1
1
0
2
0
1
1
0
0
1
1
1
2
0
0
1
1
0
0
3
1
0
2
0
1
0
0
0
2
1
1
0
1
1
1
0
0
1
1
2
1
0
1
0
0
2
0
0
2
1
0
0
0
1
0
0
0
3
0
2
3
2
0
2
1
1
0
0
0
1
2
0
2
1
1
1
1
2
2
2
0
0
2
2
2
0
0
0
1
2
1
2
0
2
0
1
2
1
2
0
2
1
0
0
1
3
0
1
2
0
0
2
0
1
0
0
2
0
0
0
0
2
0
2
1
1
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
1
0
1
1
0
1
0
1
1
1
2
0
0
0
1
1
0
0
2
0
1
0
3
0
1
4
0
0
0
1
0
0
0
0
1
1
1
0
0
0
1
2
0
0
0
0
1
0
3
0
1
2
0
1
0
0
1
1
1
0
1
2
0
1
1
0
2
1
1
1
1
1
1
0
1
1
2
1
0
1
1
1
1
1
0
0
0
1
2
1
1
0
1
2
0
0
0
0
2
0
0
3
1
0
2
1
0
2
1
1
1
1
0
2
0
1
1
2
0
0
0
0
1
0
1
1
1
2
1
1
0
0
1
0
0
0
1
0
0
0
0
1
0
1
2
1
2
1
0
0
1
1
1
0
0
0
1
1
1
1
1
2
1
1
0
0
2
0
1
2
1
1
0
0
0
1
0
1
1
0
0
1
2
1
2
1
0
0
1
2
0
1
0
1
0
0
2
0
1
0
1
2
0
0
0
1
1
1
0
2
2
1
3
1
1
0
2
2
2
1
1
0
1
0
0
0
0
2
0
2
1
2
0
2
0
0
0
0
2
1
2
1
3
0
1
0
1
1
1
0
0
1
0
1
2
1
2
2
0
1
1
2
2
1
2
2
1
2
0
0
1
0
0
1
3
0
1
1
0
2
1
0
0
1
1
1
0
1
0
2
2
0
1
1
0
2
0
0
0
0
0
0
0
0
1
1
2
1
1
1
2
1
1
1
0
3
1
2
0
0
1
1
1
1
2
2
0
1
1
0
1
1
0
0
1
2
1
1
0
0
1
0
3
0
0
2
1
0
0
1
1
0
0
1
1
0
0
0
1
2
0
0
1
0
1
0
2
2
1
2
1
2
0
0
1
2
0
2
1
1
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
1
1
1
1
1
1
0
2
1
1
2
1
1
3
0
0
0
0
2
0
0
0
1
0
2
1
0
0
2
1
1
2
0
0
2
2
0
2
0
1
1
2
0
2
1
0
0
1
2
0
1
1
2
0
1
0
0
1
2
2
2
2
1
0
1
2
2
0
0
1
1
2
2
1
0
0
0
1
0
1
2
0
1
0
1
1
0
1
1
0
0
1
2
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
1
1
2
0
2
0
0
1
0
0
1
0
1
0
0
2
2
2
0
0
1
0
1
0
1
2
1
2
0
1
0
0
0
0
0
2
1
1
0
2
0
1
2
1
0
2
0
0
0
0
2
1
0
1
0
2
1
2
0
0
1
1
0
1
1
1
2
0
1
1
0
2
1
0
0
0
0
0
0
1
1
1
2
1
0
1
0
2
0
0
0
0
2
0
0
1
1
1
1
2
0
1
2
1
0
2
0
2
2
1
1
1
2
0
2
0
1
1
0
1
1
2
1
0
0
0
2
0
1
2
2
1
2
2
0
1
1
2
1
2
1
1
0
1
0
0
0
1
0
0
0
1
1
1
2
0
0
1
2
3
1
0
1
0
1
1
0
0
1
0
3
1
2
1
1
2
0
0
1
0
1
0
1
0
0
0
0
0
2
1
0
0
0
1
0
1
2
1
0
0
2
0
0
0
0
1
2
0
0
2
0
1
0
1
0
0
0
3
1
1
0
0
2
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
2
1
0
1
1
0
1
1
1
0
1
2
0
1
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
2
1
1
1
0
1
1
1
0
0
0
0
1
0
0
1
1
1
0
0
0
2
1
1
1
0
0
2
1
0
0
0
1
1
1
0
2
2
1
2
0
1
0
2
2
0
0
1
2
2
3
1
0
1
1
1
1
1
2
0
0
1
1
1
0
0
0
0
2
1
0
2
2
0
0
0
1
2
0
1
0
2
0
0
2
2
1
0
1
1
0
1
2
1
0
1
0
0
0
1
2
0
1
1
1
0
2
0
2
2
0
0
2
0
0
1
1
1
0
1
1
1
0
1
2
0
1
3
1
1
0
1
2
4
0
0
1
2
1
1
1
1
1
2
0
0
0
2
1
2
0
0
2
0
1
1
0
0
1
0
0
1
0
1
0
1
2
0
1
0
0
2
0
0
1
0
0
1
1
1
1
0
0
2
1
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
1
2
0
1
0
2
0
0
0
2
1
2
1
2
0
2
0
1
0
1
1
1
2
0
2
1
2
1
2
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
2
1
2
1
1
0
0
1
2
0
0
3
0
1
2
1
0
0
1
2
1
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
3
0
2
0
2
0
1
0
0
2
0
0
1
0
1
1
0
0
0
0
1
1
0
1
0
0
0
2
1
0
0
2
2
1
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
1
1
0
1
1
2
0
1
2
1
2
0
2
1
1
1
0
1
2
1
0
0
2
1
0
2
1
0
1
1
0
0
1
1
1
2
3
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
2
2
0
0
2
1
0
1
1
0
2
1
2
1
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
1
0
1
1
1
1
0
0
1
1
0
1
1
0
0
1
2
1
1
0
1
0
0
1
0
0
1
1
2
0
1
2
2
0
1
1
1
2
2
2
0
0
0
3
0
2
0
2
0
1
0
0
1
1
1
0
2
2
0
0
1
0
0
2
0
1
2
0
0
0
3
1
0
1
0
1
0
0
0
0
1
0
2
2
0
1
2
0
2
0
1
3
1
0
0
0
0
0
1
1
0
1
1
0
1
2
1
0
1
0
2
1
1
0
1
0
1
1
0
2
1
0
0
1
2
0
2
0
1
1
0
0
0
0
2
0
3
0
0
1
2
3
1
0
2
1
1
1
1
2
2
0
0
1
1
1
0
1
1
3
2
1
2
0
0
0
0
1
1
2
0
0
0
2
0
0
0
0
0
2
1
1
0
0
0
2
1
2
1
1
2
1
0
1
1
0
2
0
2
1
1
1
1
0
2
0
0
0
0
1
0
1
2
0
2
0
2
0
0
0
1
1
0
0
1
1
0
1
0
0
0
1
1
0
1
0
1
1
0
1
0
0
1
1
0
1
2
1
1
2
0
0
0
1
0
0
2
0
1
2
0
1
0
0
3
1
2
1
0
1
1
0
0
2
0
1
0
1
1
1
1
0
0
1
1
0
1
0
1
1
0
1
2
0
2
0
8
0
2
2
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
1
2
1
0
0
1
1
2
0
0
2
2
2
0
0
1
1
2
0
2
0
0
1
2
2
0
0
0
0
0
1
2
0
1
1
2
0
1
0
1
0
4
2
1
0
0
0
2
2
0
0
1
0
0
1
4
0
1
0
0
0
2
2
0
2
2
0
0
1
0
0
0
2
0
1
0
1
1
2
2
0
0
0
2
1
0
0
0
0
2
0
2
1
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
2
2
0
0
0
1
1
0
2
0
2
0
2
0
1
0
5
1
0
1
0
1
1
0
0
0
2
0
0
1
1
0
1
0
1
0
0
1
0
1
1
2
0
1
2
1
3
1
1
1
0
1
1
1
0
2
0
0
0
0
2
1
0
0
0
0
0
1
1
0
3
2
0
1
0
0
2
2
2
0
0
1
0
0
0
2
1
2
0
1
1
2
1
2
0
0
2
2
2
1
1
0
2
1
0
0
2
0
2
0
0
1
1
2
1
0
1
0
0
1
2
3
1
2
0
0
1
0
1
0
0
0
0
0
0
2
0
2
0
2
1
1
1
0
1
1
0
2
2
0
0
0
0
0
0
0
1
1
1
0
1
0
3
0
0
2
0
0
2
1
1
2
0
0
1
0
1
1
1
1
2
1
0
0
1
0
0
2
0
2
1
0
1
0
0
2
1
0
0
0
0
0
0
0
1
1
1
0
1
1
0
0
1
2
1
1
1
0
1
2
1
1
0
1
0
1
1
0
0
2
0
0
2
0
0
1
2
1
1
0
0
1
1
0
0
1
0
2
2
0
0
0
1
1
0
0
0
2
1
0
2
2
0
0
0
0
0
0
0
0
0
1
0
2
1
1
0
2
2
0
0
0
0
1
0
0
1
0
0
2
0
0
1
0
1
0
2
2
1
1
1
0
0
0
3
1
1
0
1
0
2
0
2
0
2
2
1
1
5
1
0
1
0
0
1
0
0
3
2
1
2
1
1
2
2
0
1
0
1
1
0
1
0
0
1
1
1
2
1
1
0
2
1
1
0
1
1
0
0
0
1
0
0
0
1
0
1
1
0
0
1
2
0
1
2
0
0
1
1
2
0
1
2
1
3
1
0
2
2
0
0
2
0
0
0
2
1
0
0
0
1
2
2
2
0
0
1
2
1
0
0
1
1
2
2
0
1
1
0
1
2
2
0
0
1
2
1
0
0
1
2
1
0
1
0
1
0
1
1
1
1
1
0
2
1
1
0
0
1
0
0
2
1
1
1
1
1
1
1
2
0
2
1
1
0
0
0
1
0
2
1
0
0
0
0
1
3
2
0
0
2
1
1
1
1
0
0
1
0
0
0
0
2
3
1
2
1
0
1
0
1
0
1
0
1
1
2
1
2
0
0
2
1
0
0
1
2
2
0
0
0
0
1
1
0
0
2
0
2
2
0
1
1
1
0
1
0
0
0
1
0
2
1
1
0
0
1
0
2
1
0
1
0
1
1
1
2
1
2
0
0
0
0
1
1
0
1
0
1
0
2
0
1
0
1
0
0
2
0
1
0
1
1
1
1
1
2
1
0
1
1
1
0
0
0
1
1
0
0
1
0
0
0
0
1
1
1
0
1
1
1
0
1
2
2
2
0
0
0
1
1
0
1
1
0
1
0
2
0
1
1
2
2
0
0
0
1
1
0
0
2
1
0
1
1
0
1
1
1
0
0
0
1
0
0
1
0
0
1
2
2
0
1
0
0
2
0
1
0
0
0
4
1
1
0
2
0
0
1
1
0
1
1
2
0
1
2
2
1
0
0
1
3
0
1
2
0
0
0
0
1
1
0
1
0
0
0
0
2
2
2
2
1
0
1
0
0
0
1
1
1
0
2
0
1
2
0
0
0
2
0
0
1
1
0
2
1
1
0
0
1
2
0
0
0
1
1
2
2
0
1
0
1
0
2
0
0
1
1
1
1
1
0
0
0
0
0
0
1
1
0
1
0
0
1
2
2
0
2
0
1
1
2
1
2
1
0
1
1
0
2
0
1
0
0
0
0
1
1
0
0
1
1
2
3
0
1
0
0
0
0
0
1
1
0
0
0
1
1
0
1
1
0
0
0
0
0
1
0
2
0
2
1
0
1
1
2
1
0
0
0
1
1
0
2
0
0
2
1
0
3
0
1
1
0
0
0
2
1
2
1
1
0
1
1
1
1
1
0
2
2
0
0
0
0
1
0
1
0
1
0
2
3
0
1
0
2
2
3
0
1
3
0
1
0
0
1
0
0
1
1
2
0
1
1
2
1
1
3
1
2
1
1
0
1
1
0
0
3
2
0
1
1
3
2
0
1
0
0
0
0
1
2
2
0
0
5
3
2
0
0
1
0
1
2
2
1
1
0
0
0
1
0
1
2
0
1
2
1
0
2
0
1
1
0
0
0
0
0
2
1
1
0
0
0
0
1
0
0
0
1
1
0
0
1
1
2
1
1
1
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
1
1
2
0
0
1
1
1
2
0
1
1
1
3
0
1
0
0
1
1
0
0
0
1
1
1
0
2
0
1
2
1
1
2
2
2
0
2
0
0
2
0
3
0
1
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
2
2
0
0
1
0
0
2
0
2
1
0
0
0
1
0
0
0
1
0
1
0
0
1
0
1
1
0
2
2
0
0
2
1
0
0
2
0
0
0
1
2
2
1
2
1
1
1
2
1
0
0
0
0
2
0
2
0
0
0
0
2
1
2
0
1
0
1
2
1
1
0
1
1
0
2
2
1
0
0
1
1
1
0
0
2
0
0
2
0
0
0
0
2
0
0
0
1
2
1
6
0
1
2
0
2
2
0
0
0
1
2
2
0
2
0
0
1
0
0
1
1
1
1
0
1
0
0
1
0
2
0
1
0
1
0
1
2
0
2
1
1
0
2
1
1
1
0
0
1
2
2
0
0
0
0
2
1
1
0
1
0
1
2
0
1
0
3
0
0
0
0
0
1
0
0
0
1
2
1
1
0
0
2
0
0
1
0
0
1
2
1
1
1
2
1
1
0
1
2
1
1
2
0
1
2
1
1
0
2
0
1
0
0
0
1
0
0
1
0
1
1
0
0
2
0
1
2
0
0
0
1
0
0
0
1
1
0
0
1
3
0
2
0
2
2
1
0
1
0
1
2
0
2
0
1
2
1
2
0
0
1
2
2
0
1
1
0
0
1
0
2
0
0
1
0
1
1
0
0
0
1
1
2
0
2
1
1
1
1
1
2
1
2
2
2
2
2
2
0
1
2
1
3
1
1
0
2
1
2
0
0
1
0
0
2
1
0
1
0
2
1
2
0
2
0
0
2
0
0
0
1
2
1
2
0
1
1
2
0
1
0
1
2
1
1
0
1
2
0
1
0
1
0
0
2
2
2
0
0
0
0
2
2
1
0
0
1
1
1
3
0
1
0
0
2
0
1
1
2
0
0
0
1
0
0
0
2
0
2
2
1
2
1
2
0
1
2
0
1
0
1
1
2
0
2
1
1
0
0
0
0
1
1
0
0
2
1
0
1
0
1
2
0
0
2
1
0
0
2
0
0
0
0
1
2
1
1
0
0
1
1
2
0
0
2
0
0
2
1
1
0
0
1
0
0
0
0
0
2
1
0
2
1
0
1
1
1
4
0
2
0
1
0
0
0
2
0
0
1
1
1
0
0
0
2
2
0
1
0
0
1
1
0
0
0
0
0
1
0
2
0
0
0
2
0
1
0
1
1
2
1
1
2
1
0
0
0
2
0
0
0
0
2
0
2
1
1
1
0
0
0
0
2
2
1
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
1
1
0
1
2
0
2
1
0
1
1
2
0
1
0
0
0
0
1
1
0
0
0
2
0
1
2
0
0
2
0
0
0
0
0
2
0
1
0
2
1
2
2
0
2
0
0
1
1
0
0
0
2
1
0
0
2
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
2
0
2
0
0
1
2
0
2
0
1
2
0
0
0
0
1
1
0
2
1
1
1
0
0
0
0
0
0
1
3
3
2
2
0
0
1
0
1
0
2
0
1
0
0
0
0
1
0
0
1
0
1
0
2
1
1
1
2
0
2
1
1
0
0
2
0
0
0
0
0
2
0
1
1
0
1
0
0
0
0
1
0
0
0
2
2
1
2
0
1
0
0
2
0
1
2
0
0
0
1
3
0
0
2
2
1
1
2
1
2
1
1
1
0
1
2
0
0
1
1
0
0
1
0
1
1
3
0
0
1
0
0
2
1
0
0
0
1
0
0
1
1
0
0
0
0
1
3
6
1
3
1
2
0
1
0
0
0
0
1
2
3
0
2
1
1
0
0
1
0
3
2
2
1
2
0
1
0
0
0
1
0
0
1
0
1
0
2
1
1
0
0
2
1
0
0
1
0
1
1
1
0
1
1
2
2
0
0
2
0
2
0
0
1
0
1
1
0
0
1
0
0
1
0
0
0
0
1
0
2
1
0
0
1
1
2
0
1
0
0
1
0
0
2
1
1
3
2
0
0
0
2
1
1
1
1
0
1
0
1
0
0
0
0
1
0
3
2
0
0
2
2
0
1
2
1
0
2
0
1
2
1
1
1
0
2
2
0
1
1
1
2
0
1
2
1
2
2
1
0
0
1
0
2
1
0
1
2
1
0
1
1
2
1
0
0
0
0
2
1
0
1
2
1
0
0
1
0
0
1
0
2
0
0
2
0
0
0
0
0
1
0
0
0
2
1
2
0
1
1
2
6
2
2
2
2
1
2
1
0
0
2
1
1
2
1
0
1
0
0
1
1
2
2
0
2
2
1
0
1
0
0
0
1
2
1
0
1
0
1
1
2
0
0
0
0
4
0
1
1
0
1
2
2
1
2
1
0
1
0
2
0
2
0
2
2
0
2
2
0
0
0
0
0
2
0
0
1
0
2
0
2
1
1
0
1
0
1
2
2
0
2
0
1
0
2
1
1
1
1
1
2
1
1
0
1
2
0
1
1
0
0
1
1
0
1
1
0
0
1
2
0
1
0
4
2
0
1
1
5
1
0
0
0
2
1
0
2
0
1
1
1
0
2
0
1
0
2
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
1
0
1
2
2
0
0
0
0
1
1
1
0
0
1
1
1
0
0
0
0
1
1
1
0
1
0
2
1
0
2
0
1
1
2
0
1
1
2
3
1
2
1
0
0
1
1
0
1
1
0
1
0
0
0
0
1
2
1
0
1
0
0
1
0
0
1
2
1
1
1
0
0
0
0
1
0
1
2
0
1
0
1
0
2
1
1
2
2
0
0
1
1
0
0
0
0
1
2
0
1
0
1
0
1
0
1
1
1
1
2
2
0
0
0
0
1
2
2
1
0
2
0
0
1
1
2
1
0
2
2
0
0
0
1
2
0
2
1
0
0
2
2
0
0
1
1
2
1
1
2
0
2
0
0
3
2
1
1
0
1
1
3
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
2
0
1
1
0
0
0
2
2
0
1
0
1
2
1
2
0
1
1
0
1
0
1
1
1
1
2
0
1
1
0
1
0
0
2
1
1
2
1
0
1
1
2
2
1
0
1
1
0
0
1
2
2
0
1
1
0
1
0
0
1
0
1
1
2
1
0
0
0
1
0
2
1
2
0
0
2
2
1
2
0
1
0
0
1
0
1
0
1
1
1
1
2
0
2
0
0
1
1
0
3
0
1
2
0
0
0
2
1
0
1
3
2
1
2
2
2
1
2
0
3
1
0
1
0
3
0
1
1
2
1
1
2
0
0
2
0
1
0
0
0
0
0
2
4
2
0
0
0
1
0
1
0
1
0
0
1
0
0
2
1
0
1
1
0
0
4
2
2
1
1
1
3
0
1
1
0
0
0
1
0
0
0
0
3
1
1
2
2
0
0
0
0
1
1
1
1
0
0
1
1
0
1
0
0
3
1
0
0
1
2
1
0
0
1
2
2
0
0
1
0
1
0
2
0
2
1
0
1
1
0
1
0
0
2
2
0
0
2
0
0
0
0
0
1
0
1
0
2
1
3
1
0
0
1
0
0
0
1
2
1
2
0
0
0
1
4
0
0
0
0
1
2
1
0
0
1
2
0
1
2
1
2
0
2
1
0
0
0
1
1
0
0
2
0
0
1
0
2
0
0
0
1
1
1
1
0
1
0
1
0
1
2
0
2
0
0
0
1
0
1
0
0
1
1
0
0
1
0
0
0
1
2
0
0
0
0
0
2
2
1
2
1
0
0
0
0
1
3
1
0
1
5
1
1
0
2
6
1
1
1
0
2
1
1
3
0
0
0
1
0
1
0
0
0
1
1
1
0
0
1
1
0
2
0
2
1
2
0
1
1
1
0
2
0
0
1
0
0
0
0
0
0
1
1
0
1
0
2
0
0
0
0
1
0
1
1
0
0
0
0
1
1
0
0
0
1
0
2
0
2
2
0
0
0
1
0
1
0
1
2
2
1
0
1
0
0
1
1
1
1
0
0
1
0
0
1
0
0
1
0
0
0
1
0
1
2
2
0
0
1
0
1
0
0
1
0
0
0
4
1
0
2
2
2
2
1
0
1
1
1
1
2
3
0
0
1
0
1
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
1
2
1
1
3
0
1
2
1
0
2
1
1
2
1
2
0
0
2
1
2
1
0
1
1
0
2
0
2
0
1
2
2
1
0
1
0
0
1
1
0
0
0
2
0
0
1
0
4
1
0
0
1
0
1
0
0
3
2
1
1
1
1
0
2
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
2
0
0
1
1
2
1
0
2
1
0
0
1
0
1
0
0
2
0
0
0
1
0
3
0
2
2
1
0
0
1
3
2
0
0
0
2
2
0
0
0
2
1
1
0
0
1
2
1
1
0
0
1
2
1
1
0
0
2
2
0
1
0
1
1
0
0
0
2
0
1
0
2
2
0
1
0
0
0
0
1
0
1
0
1
0
2
0
0
0
0
2
1
0
1
0
0
0
1
2
4
1
2
0
1
0
2
0
0
1
0
2
3
1
0
2
0
0
0
0
0
2
0
0
1
0
0
0
1
0
1
0
0
2
0
1
2
1
0
0
1
0
2
0
1
1
1
0
2
0
2
1
2
1
1
1
1
0
0
1
1
0
0
0
0
2
1
2
1
1
0
2
13
2
0
0
0
1
2
0
1
0
1
1
1
0
1
2
0
1
1
0
0
0
0
0
0
0
2
2
1
0
0
0
1
3
0
0
0
0
2
1
1
1
1
0
2
0
2
0
0
1
1
0
1
1
0
0
1
2
2
1
0
0
1
1
1
2
2
1
0
2
0
0
2
0
1
3
0
1
2
0
0
0
1
0
0
2
1
0
0
0
0
2
2
0
1
2
0
0
2
0
0
1
0
1
0
2
1
0
0
1
0
1
0
0
0
0
2
1
2
0
0
0
1
0
0
2
0
2
1
0
2
0
0
0
1
2
0
0
0
0
2
0
1
1
0
0
2
1
1
1
0
0
2
0
0
1
0
1
0
2
1
2
0
1
2
0
1
2
0
1
3
1
0
0
1
2
0
0
0
1
1
0
0
0
0
2
2
0
2
0
0
0
0
1
2
0
0
3
0
1
0
2
1
1
0
1
0
0
0
1
0
3
1
0
0
1
0
0
0
0
1
0
1
0
0
1
0
2
2
0
1
1
1
1
0
0
0
2
0
0
1
1
0
2
1
1
0
2
0
1
0
1
2
1
0
1
0
0
1
1
0
1
0
0
0
0
1
0
0
2
2
1
2
2
1
0
0
0
0
1
0
0
0
1
0
0
2
1
1
2
0
0
0
2
1
1
1
1
2
1
1
0
2
2
0
2
1
2
1
0
0
0
0
0
0
1
1
1
2
0
0
1
1
0
1
0
2
2
0
0
0
0
0
1
2
0
2
0
1
1
2
2
1
1
0
1
0
2
2
0
1
0
0
1
1
0
3
0
0
1
1
1
0
0
0
1
0
0
1
1
2
0
0
0
1
1
1
2
0
0
0
1
0
0
0
2
2
1
2
0
2
0
0
0
1
1
1
0
0
0
2
2
2
1
2
1
2
1
0
1
2
9
2
1
1
0
1
0
2
1
1
0
2
0
2
0
2
0
2
0
2
2
0
2
1
2
1
2
1
1
1
0
1
1
0
2
1
2
1
0
1
0
0
0
1
2
0
0
0
2
0
1
3
2
0
1
0
0
1
0
1
0
1
1
0
3
1
2
0
0
1
0
0
1
0
2
0
2
0
0
1
0
0
0
0
0
1
0
1
1
1
2
0
0
1
0
1
0
1
1
0
1
0
1
2
2
0
2
0
1
1
0
0
2
0
0
1
0
1
0
0
0
0
0
2
2
1
0
0
0
2
2
1
0
1
2
0
0
1
1
1
0
5
3
1
0
0
2
1
0
1
1
0
1
0
0
1
2
1
1
1
1
0
0
1
0
0
1
1
0
0
1
1
0
1
1
1
2
1
0
1
1
0
1
0
1
0
1
1
0
2
1
1
0
0
1
0
3
0
2
1
1
2
2
1
0
0
0
1
2
0
0
2
0
0
1
0
1
1
1
1
2
0
2
0
1
6
1
1
0
1
2
1
1
0
0
1
2
0
0
0
1
1
0
0
0
2
0
2
0
1
0
1
2
2
1
1
1
1
1
9
0
2
0
2
2
1
1
1
1
0
0
0
2
2
1
0
0
0
2
0
0
0
1
1
2
2
1
1
1
2
0
1
0
1
1
3
2
0
2
1
0
0
0
1
2
0
2
0
0
0
2
1
1
1
0
1
1
2
0
1
0
0
0
1
0
0
2
0
2
1
2
0
1
1
1
0
0
0
2
0
1
0
0
0
1
0
0
0
2
0
1
0
0
2
2
1
0
2
0
2
0
1
0
0
0
1
0
0
1
0
1
2
2
0
3
0
0
1
2
1
0
4
2
1
1
1
0
1
0
0
0
1
0
2
0
1
1
2
0
0
0
2
0
1
1
0
2
0
0
0
0
0
0
1
2
1
0
0
2
1
0
0
0
1
1
1
1
1
0
1
1
1
0
2
0
0
2
0
1
0
0
1
0
0
0
1
1
0
1
0
2
1
1
0
0
1
0
1
0
0
0
0
0
1
1
0
2
1
0
0
0
1
0
0
0
0
1
1
0
0
0
2
1
0
0
2
2
0
0
1
2
0
0
0
0
0
1
1
1
1
2
1
2
1
1
0
0
0
1
1
2
2
2
2
0
0
1
1
1
0
0
0
0
1
1
0
1
2
0
1
1
0
1
0
0
0
0
2
0
1
3
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
1
0
1
0
0
1
1
3
2
1
2
1
3
0
2
0
2
0
1
1
2
0
0
1
2
0
0
1
0
2
1
0
2
1
0
0
2
0
2
1
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
2
1
1
1
0
1
2
2
0
0
0
1
1
2
1
2
0
0
1
2
0
1
2
2
0
0
1
1
0
1
1
0
0
0
2
1
1
2
2
2
1
2
1
1
1
1
1
0
2
0
6
0
0
1
0
1
0
1
0
0
1
0
2
0
2
2
2
0
1
1
1
1
0
1
2
0
0
1
0
0
1
0
0
1
0
0
0
0
2
1
1
0
2
2
1
1
2
0
1
0
2
1
0
2
1
1
0
0
2
2
0
1
0
1
2
1
1
1
1
0
2
0
2
1
0
1
0
1
2
0
1
0
0
1
0
1
2
0
1
0
1
1
2
0
1
0
0
0
2
3
2
4
0
0
3
0
0
0
0
1
1
0
0
1
0
0
0
1
2
0
0
0
2
0
2
1
2
2
0
1
0
0
2
1
0
2
1
2
1
0
1
1
1
2
1
1
0
0
0
0
0
0
1
0
1
1
0
0
2
0
0
2
1
0
0
0
0
4
0
0
2
2
2
0
2
0
1
2
0
0
1
2
0
2
0
0
0
0
2
2
0
0
0
1
2
1
0
1
2
1
2
2
1
1
1
2
0
2
2
0
0
1
1
1
0
3
1
0
3
2
0
2
0
2
0
2
0
0
1
0
5
0
0
1
0
2
2
0
0
0
0
1
0
0
1
1
1
0
1
2
0
2
0
0
1
1
0
0
1
1
0
1
0
0
1
0
1
1
0
0
0
2
2
0
1
2
2
0
1
1
2
0
1
2
0
2
2
2
0
0
2
0
1
1
0
0
0
1
2
0
2
0
0
1
0
0
0
0
0
2
1
0
1
0
2
0
0
1
0
0
0
0
1
1
0
0
3
0
0
2
0
0
2
2
0
0
2
0
0
1
2
1
1
1
0
0
0
0
0
1
0
0
0
2
2
0
2
0
0
0
1
0
0
1
0
1
2
0
2
0
1
0
0
1
1
1
0
2
2
1
0
1
1
0
0
0
2
0
1
0
0
0
2
2
1
1
1
1
2
0
0
1
0
0
0
2
1
0
0
0
1
0
2
1
2
2
1
0
1
0
1
0
0
2
0
1
2
1
2
1
1
0
0
0
1
2
0
0
0
0
3
0
0
1
0
1
1
1
3
1
1
1
2
1
0
1
0
0
1
0
2
0
1
0
1
1
0
0
0
0
1
0
1
0
2
0
0
0
1
0
1
2
2
1
1
0
0
1
2
0
1
1
1
0
2
0
1
2
0
0
2
0
0
2
1
0
2
0
1
1
2
1
0
0
2
1
0
0
0
1
4
0
0
0
1
0
1
0
0
1
0
2
0
1
1
2
0
1
1
0
2
0
0
2
0
0
1
1
1
0
2
2
1
0
1
1
1
1
3
0
2
0
0
1
2
0
1
1
3
0
0
2
2
0
1
0
1
0
2
0
0
0
3
2
1
1
1
2
0
0
0
0
1
1
1
2
2
1
1
2
5
0
1
1
1
1
1
2
1
2
1
0
1
2
3
1
2
0
0
0
1
2
1
1
0
0
0
1
1
2
1
0
0
0
0
0
2
1
1
1
2
0
1
2
2
1
3
1
1
1
0
2
1
1
2
2
0
1
2
1
1
0
1
0
0
2
0
2
1
1
1
2
1
0
1
1
2
0
0
0
0
0
1
1
1
1
1
1
1
2
1
1
1
2
2
1
1
0
1
1
1
0
0
0
3
0
1
0
0
0
0
1
0
0
4
1
0
2
3
0
2
1
1
1
1
2
2
0
0
0
0
0
1
1
0
2
1
1
0
1
0
0
0
1
2
0
2
0
1
1
0
0
0
4
2
1
1
0
1
2
2
0
1
0
0
1
0
1
2
2
1
1
0
2
0
1
1
0
1
2
1
1
0
0
2
0
0
1
1
1
0
2
1
2
0
1
0
1
0
3
1
1
1
0
0
0
1
1
0
0
2
0
1
3
2
1
1
1
0
1
0
0
0
0
0
1
2
0
0
2
0
1
0
1
0
1
2
2
0
0
0
1
0
0
2
1
1
0
1
2
2
0
1
0
3
0
0
0
3
0
1
0
0
0
1
1
1
2
2
1
0
2
0
0
0
0
2
1
1
1
0
1
0
2
1
1
3
0
0
2
0
2
0
0
0
1
2
0
1
3
2
2
1
0
0
2
2
1
1
2
0
0
2
1
1
2
1
3
1
0
0
1
0
0
2
0
0
2
1
0
0
1
1
1
0
2
0
2
0
1
0
0
0
1
1
0
0
0
0
0
1
2
1
2
0
0
1
0
1
2
0
1
0
0
0
2
1
1
1
1
0
0
1
1
2
0
1
0
1
0
0
1
1
0
3
0
0
1
1
1
2
1
2
0
2
1
1
2
1
2
0
0
0
0
1
1
0
2
1
0
1
1
1
0
0
0
0
0
1
1
0
0
1
2
0
1
2
0
3
0
1
0
1
2
0
0
1
4
1
0
1
1
2
1
3
1
2
1
1
0
1
0
0
2
1
1
2
0
1
0
1
0
0
1
0
1
1
2
0
0
2
1
1
3
0
1
0
1
0
1
2
1
1
1
0
1
2
1
1
0
1
1
0
1
0
0
2
0
0
0
2
0
0
0
0
0
1
1
0
2
0
1
2
0
1
2
1
0
0
0
0
1
2
1
0
0
0
0
0
2
1
1
1
1
1
0
1
1
0
0
0
1
1
0
1
2
1
0
0
1
0
0
2
0
1
0
0
0
1
1
2
3
0
0
0
1
0
0
1
0
2
2
0
2
1
0
2
1
1
1
0
0
0
0
0
0
2
0
1
2
1
3
0
0
0
0
0
0
1
1
2
2
0
0
1
2
3
0
1
2
1
1
0
2
0
2
1
0
0
0
2
1
0
1
2
1
2
1
0
2
0
2
1
0
0
1
1
2
1
0
2
0
0
0
1
0
2
1
0
1
0
1
0
1
0
1
1
0
0
0
1
1
0
0
1
2
1
0
2
2
1
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
2
2
2
1
0
1
1
1
1
3
0
2
1
1
1
1
0
0
0
0
1
1
1
1
0
2
0
2
0
0
1
0
2
0
0
2
0
1
0
2
0
1
0
2
0
0
1
2
1
1
0
2
1
1
0
2
0
0
2
1
0
1
1
2
1
0
0
2
2
0
2
2
1
1
0
2
0
0
1
2
1
2
1
0
1
0
1
1
0
0
0
2
0
1
1
0
2
2
1
0
1
1
1
1
0
0
0
1
0
1
0
0
0
2
1
0
1
1
2
0
2
1
1
0
0
2
1
2
1
0
0
2
2
0
0
2
0
0
2
0
1
1
1
0
0
1
0
0
2
2
1
0
0
1
3
0
0
0
1
2
1
1
2
2
2
1
0
1
0
2
1
1
1
1
1
2
0
0
0
0
1
2
0
2
0
1
0
1
0
0
0
2
1
0
0
0
2
1
2
1
0
1
1
0
0
0
1
0
1
2
1
0
0
1
0
2
2
0
0
1
0
2
2
0
0
0
0
0
2
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
1
2
0
0
0
1
1
0
0
2
2
1
0
0
0
0
2
1
1
4
3
0
1
0
1
0
1
0
2
2
2
2
0
0
2
1
0
0
0
0
0
1
0
2
0
2
0
2
2
1
1
1
1
0
1
0
0
0
0
2
1
3
2
1
0
2
0
0
0
2
2
0
1
0
1
0
0
0
0
1
1
1
0
0
0
0
2
0
0
1
1
2
4
1
1
0
1
1
0
1
2
3
2
2
0
0
0
0
1
0
1
1
2
0
1
2
0
1
0
0
1
2
1
2
2
0
0
10
0
0
1
1
2
1
0
0
2
0
0
0
0
2
2
0
0
0
0
1
2
6
1
0
2
0
0
0
1
1
0
0
1
0
0
2
0
0
1
0
0
0
0
1
0
0
0
1
2
2
0
2
0
1
1
2
0
1
2
0
0
0
0
1
2
1
0
0
1
0
2
0
0
0
1
1
0
0
0
1
2
1
1
1
1
0
2
0
0
2
2
0
1
0
0
0
0
1
2
1
0
1
1
1
1
0
2
0
0
0
1
1
2
2
1
1
1
0
0
0
2
0
0
1
0
1
2
2
0
0
1
0
2
1
0
1
0
1
0
0
0
0
1
0
1
0
2
1
1
1
2
1
0
1
2
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
1
0
0
2
0
0
0
1
2
0
1
0
0
1
0
0
2
0
0
0
0
1
2
2
0
0
0
1
2
2
1
2
2
1
0
1
0
0
1
0
1
2
2
1
2
0
0
1
2
1
0
0
2
0
0
0
2
0
0
1
0
0
0
2
0
0
1
0
2
0
1
1
0
1
2
0
2
3
2
2
2
0
0
1
2
2
0
0
0
0
2
0
0
0
0
1
1
2
1
1
2
0
0
1
2
1
1
0
1
2
1
0
1
1
0
0
2
1
0
0
1
2
0
0
0
2
0
1
1
0
0
1
1
0
0
1
0
0
0
1
0
1
0
0
2
0
1
0
0
1
0
0
2
0
1
0
0
1
0
0
1
2
2
1
1
2
0
0
0
2
1
0
0
1
0
0
2
1
0
2
1
0
0
0
0
1
0
2
1
1
0
0
1
2
1
1
0
2
0
2
0
1
1
0
2
1
0
2
0
0
0
0
2
0
1
0
1
1
2
0
0
0
0
3
2
1
0
1
1
2
0
0
1
0
1
2
0
1
1
1
0
1
0
0
1
0
0
5
0
2
1
2
1
2
1
0
0
2
0
1
0
2
2
0
0
1
0
1
0
1
2
0
1
2
1
0
1
0
1
0
0
0
0
2
0
2
1
1
1
0
2
1
0
1
1
1
1
4
0
1
0
0
0
2
0
2
1
2
2
2
1
0
2
0
1
2
3
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
1
0
2
1
1
0
0
0
1
5
2
0
0
0
1
2
2
0
2
0
0
2
0
0
0
1
2
1
0
0
0
2
2
2
2
1
0
0
1
2
0
0
0
2
2
0
0
0
1
2
1
0
0
0
0
0
1
0
0
0
1
1
2
0
0
0
0
0
1
0
1
0
0
0
1
0
0
2
0
0
0
0
2
2
0
1
2
2
0
1
0
2
1
0
0
1
1
1
0
0
1
0
1
2
1
0
3
2
2
1
1
0
0
0
2
1
0
1
2
1
0
1
1
0
1
0
0
0
2
1
2
1
3
2
0
0
1
0
0
0
1
2
2
2
0
1
0
2
0
2
0
0
0
0
0
0
1
1
0
1
0
2
2
2
0
1
2
1
0
1
1
0
1
1
0
2
2
2
2
0
0
1
0
0
2
0
0
4
1
1
2
2
1
1
6
1
1
2
1
1
0
1
0
1
1
0
0
2
2
1
1
1
2
0
2
2
1
2
2
0
2
1
0
2
0
1
1
2
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
2
2
0
2
0
0
0
0
1
0
0
1
1
0
1
0
1
1
0
0
0
1
0
5
0
0
1
3
2
0
0
0
0
0
0
2
1
2
0
1
1
1
1
0
1
1
0
2
1
1
1
0
2
3
1
2
1
0
1
0
0
0
3
1
0
0
3
2
1
1
2
1
0
0
2
2
0
1
2
0
1
0
1
0
0
2
0
0
0
0
0
1
0
1
0
0
0
1
2
0
0
1
0
0
1
0
0
2
1
0
1
1
2
0
0
0
2
4
0
1
0
1
1
0
2
1
0
1
1
2
0
1
0
1
0
0
0
0
0
2
1
1
0
1
1
0
1
2
3
0
0
0
1
0
0
0
1
1
2
0
0
0
0
0
0
2
0
0
2
2
0
1
2
0
0
1
1
1
1
0
0
0
1
0
0
1
1
0
0
1
0
0
0
1
0
0
0
1
1
2
1
0
0
1
0
0
0
2
0
1
0
2
0
2
2
0
0
1
1
1
2
0
0
1
0
0
0
1
2
1
0
0
2
0
1
0
1
1
0
2
0
0
1
3
0
1
1
2
1
0
0
0
1
2
0
0
3
0
0
0
1
0
1
2
1
1
1
0
0
1
2
1
2
1
2
0
0
1
1
0
0
0
1
1
1
0
1
1
2
2
0
0
1
0
1
0
2
0
0
2
1
0
0
0
1
1
2
0
1
2
0
0
1
1
1
2
0
0
0
1
0
0
2
0
0
0
2
2
0
0
1
2
0
1
1
0
1
1
1
0
0
2
0
2
0
1
1
1
1
0
1
2
2
0
0
0
2
1
0
1
0
1
1
2
0
0
0
0
1
0
0
0
0
0
0
2
1
0
1
0
0
0
1
1
1
1
1
1
1
3
0
1
1
1
2
2
0
1
0
0
0
1
3
2
0
1
1
0
1
0
2
0
0
1
1
1
0
1
0
0
1
0
1
0
0
2
0
0
2
1
1
0
1
1
1
2
0
0
0
2
2
0
2
2
1
1
1
0
0
1
1
1
1
1
0
0
1
0
1
2
0
2
2
0
1
0
2
0
1
2
1
0
3
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
1
1
0
0
2
0
2
1
2
0
0
0
0
0
2
0
0
2
3
0
0
0
2
0
1
0
0
0
2
2
1
0
0
1
1
0
0
1
1
2
0
2
2
0
1
2
0
2
2
1
0
2
2
2
0
2
1
0
1
2
2
2
1
0
0
2
2
0
1
0
0
1
1
0
2
2
0
0
0
0
1
0
2
1
0
0
0
1
1
2
0
2
0
1
1
2
1
0
1
2
0
1
2
0
3
0
0
0
2
0
1
0
1
1
1
1
0
0
1
1
1
2
1
2
1
2
0
0
0
0
1
1
0
2
1
1
0
2
0
0
0
1
0
1
0
1
1
0
1
1
1
1
0
0
0
0
0
0
0
1
2
1
0
1
0
0
1
0
0
0
0
1
1
2
1
0
2
1
0
1
0
1
1
1
0
2
1
2
0
0
0
0
0
1
0
1
1
0
2
0
0
3
0
0
2
2
0
5
1
0
1
0
0
0
0
0
1
0
2
1
1
2
1
1
1
1
2
0
1
0
1
0
2
1
0
1
2
3
2
1
1
1
0
1
1
1
0
2
0
2
2
0
1
0
0
0
1
0
0
2
0
1
4
2
1
0
1
1
0
1
1
0
1
0
0
0
2
0
2
1
0
0
0
0
1
2
1
1
2
1
1
0
1
0
1
0
3
1
2
0
0
1
1
1
0
1
0
0
0
0
0
1
1
1
0
0
1
1
1
1
0
2
2
1
15
0
3
1
2
0
0
2
0
0
1
1
2
2
3
2
0
2
2
0
0
1
2
1
0
0
1
1
0
1
0
1
1
2
0
1
1
0
0
2
0
1
2
0
0
2
1
0
1
2
0
0
0
1
0
0
0
1
0
1
2
1
0
2
0
0
2
0
0
0
4
1
2
0
3
1
0
1
2
1
1
0
1
0
0
0
2
1
2
0
1
1
2
0
1
0
0
1
2
2
1
2
1
0
1
0
2
0
0
0
0
1
1
3
0
0
0
0
2
0
1
1
0
0
2
0
0
1
2
1
2
0
1
0
0
1
0
0
1
2
2
0
0
2
2
1
1
0
0
1
1
1
1
2
0
1
1
2
1
0
1
0
1
2
0
1
0
0
2
0
0
0
1
1
1
2
0
0
0
2
0
1
0
2
2
0
2
0
0
1
2
0
1
2
1
1
1
2
2
0
0
2
2
2
0
0
0
1
0
1
2
0
0
1
2
1
0
0
0
0
2
1
1
0
2
2
2
1
0
0
0
1
3
2
0
1
1
0
0
0
1
0
1
1
1
0
0
0
1
2
0
0
1
0
0
0
2
2
0
0
0
0
0
0
1
1
1
1
0
0
0
2
0
0
1
0
0
2
0
0
0
1
2
0
0
1
0
2
0
1
2
0
0
0
1
1
1
0
0
0
0
1
2
0
0
2
1
2
0
1
2
0
0
2
0
1
0
1
0
1
0
2
0
0
2
3
1
1
2
0
2
1
0
0
1
0
2
0
1
0
2
1
2
0
0
0
3
0
0
1
0
0
0
1
0
0
0
0
1
1
1
1
2
1
2
2
1
0
1
0
2
1
0
1
1
0
1
0
1
2
0
2
1
0
1
4
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
4
1
3
1
2
2
0
2
0
0
1
1
0
0
0
0
2
2
1
2
0
0
1
3
1
1
0
1
2
0
0
1
1
0
0
1
1
0
0
0
1
2
0
0
1
1
0
0
0
0
3
0
1
0
2
0
2
1
0
1
1
0
0
0
1
2
0
0
0
0
0
1
2
1
0
1
2
2
0
0
1
0
1
0
1
1
0
0
0
0
1
0
0
1
1
1
1
2
0
2
0
0
1
2
0
1
1
1
1
0
2
2
1
1
0
2
0
0
0
0
0
1
2
0
1
0
0
0
2
1
0
1
1
0
0
2
1
1
1
1
0
0
0
1
1
2
0
3
1
1
1
1
1
0
4
1
1
0
0
1
0
0
0
1
0
1
2
2
0
0
0
1
1
2
1
6
0
2
0
0
0
2
1
1
0
2
2
0
0
0
2
1
0
0
0
0
0
0
2
2
0
0
1
0
1
1
1
0
1
2
1
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
4
2
2
0
0
1
0
0
0
0
2
1
2
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
1
1
1
1
0
3
0
1
0
1
2
0
1
0
1
0
2
2
0
1
0
0
0
0
2
0
0
0
0
2
0
0
1
0
1
1
1
1
0
1
2
0
2
1
0
0
1
2
2
1
2
1
0
0
1
2
1
2
1
0
1
1
1
0
0
0
0
2
2
2
1
2
0
1
1
0
0
0
0
1
0
1
2
1
1
0
1
0
1
0
1
1
3
1
0
0
0
1
1
0
0
6
2
1
0
1
2
1
2
1
1
2
1
0
2
2
0
0
1
0
2
0
0
0
1
2
0
0
0
0
0
2
1
0
4
1
1
0
0
0
2
0
1
2
0
1
0
0
0
2
0
0
1
1
0
2
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
2
1
0
0
1
2
0
2
1
1
0
1
0
0
1
1
0
0
3
2
1
2
0
1
2
0
0
1
1
0
0
2
0
2
0
0
0
1
1
2
0
2
2
0
2
0
3
2
1
1
0
0
2
1
1
1
2
0
1
2
0
2
0
0
1
0
2
1
2
2
1
0
1
0
1
0
0
1
0
1
2
1
1
1
0
0
1
0
2
1
0
1
0
0
1
2
1
1
1
1
2
1
1
1
0
0
1
1
2
2
1
0
1
1
0
0
0
1
1
0
1
1
1
0
1
2
0
0
0
1
1
1
0
2
0
2
1
1
1
0
2
1
0
1
1
2
1
1
0
0
0
0
1
1
1
0
2
0
1
2
1
1
0
0
2
2
0
0
2
0
0
0
1
2
2
0
1
1
2
2
0
2
2
0
2
2
1
0
2
1
1
0
1
1
4
0
1
0
0
0
1
2
1
1
2
1
0
2
0
2
2
0
2
2
1
2
1
0
0
1
1
1
2
1
2
1
2
0
0
1
0
2
1
0
2
1
1
0
2
2
2
1
1
1
1
2
1
0
0
1
0
0
1
2
1
0
0
1
0
1
2
0
0
1
0
1
1
0
0
1
0
1
2
1
1
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
2
0
1
1
1
3
0
1
0
1
1
0
2
0
2
1
1
1
1
0
0
1
1
2
2
2
0
1
1
0
0
2
0
0
1
2
0
2
1
2
2
1
2
0
0
0
1
0
0
0
1
1
0
2
2
1
0
0
2
0
2
2
1
1
2
2
1
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
2
1
2
0
0
0
1
0
1
2
1
2
1
1
0
0
0
1
3
0
1
1
0
0
1
0
1
0
2
0
2
2
2
2
1
0
1
0
1
1
0
2
1
1
1
0
1
0
0
0
1
1
0
1
1
2
0
1
0
0
0
1
2
1
1
2
0
0
2
0
0
0
2
0
2
0
1
1
2
0
0
2
0
1
0
2
1
1
0
0
3
0
0
2
1
0
0
1
0
0
2
0
1
2
0
0
0
1
2
0
2
0
0
1
2
1
1
0
2
0
0
2
0
0
0
1
0
1
2
0
0
1
0
0
1
1
1
0
0
2
0
0
2
1
2
0
0
1
1
1
0
1
0
0
0
0
1
0
1
2
0
1
0
1
1
2
1
0
1
1
0
1
1
1
0
0
2
0
2
1
1
2
0
0
0
2
1
0
3
0
0
2
1
0
0
1
0
0
0
1
0
0
1
2
0
0
2
0
1
0
3
1
0
2
0
0
2
1
2
0
2
1
1
0
0
1
2
1
0
1
1
0
1
2
1
1
1
0
2
1
2
0
0
0
1
0
2
1
1
0
0
1
2
0
0
0
0
0
0
2
1
0
0
0
2
2
0
0
1
0
0
0
0
0
1
2
0
0
2
2
0
0
1
1
1
2
1
1
0
0
0
0
0
1
0
2
0
0
1
1
0
0
0
1
0
1
1
2
0
1
0
0
2
2
1
0
1
1
2
2
0
1
0
0
0
2
0
0
0
2
1
0
0
2
1
0
0
0
2
1
0
1
1
0
1
2
0
2
1
0
0
1
0
0
1
2
0
2
0
0
2
2
1
0
0
0
0
1
2
0
0
1
2
0
0
1
1
2
0
0
1
1
0
1
2
0
0
0
1
2
1
1
1
0
0
3
0
2
0
0
0
0
0
2
2
0
1
1
1
3
1
2
1
0
0
2
1
0
1
0
0
0
0
1
0
1
0
2
0
1
1
0
2
1
2
1
0
2
2
2
0
0
1
3
0
2
2
1
0
0
1
0
0
1
1
0
1
1
0
0
2
0
1
1
3
1
2
1
1
1
0
2
1
1
2
0
1
1
0
1
0
0
1
2
0
1
0
2
1
0
1
1
2
2
0
0
1
1
1
1
0
1
2
0
1
1
0
0
0
1
0
0
0
1
2
0
0
1
2
2
1
1
1
0
2
1
1
1
0
2
0
2
2
0
0
0
0
2
1
1
1
2
0
0
0
1
0
0
0
0
1
1
0
1
1
0
1
0
0
0
1
0
0
0
1
0
1
0
1
0
2
3
1
0
2
0
0
2
2
0
1
1
0
1
0
0
8
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
2
3
1
2
0
1
1
1
0
0
0
0
1
0
3
0
1
0
3
0
1
0
1
1
2
2
2
0
2
0
2
0
1
0
1
2
0
0
2
2
1
0
0
2
2
0
1
1
1
0
1
2
0
1
0
2
2
0
1
1
0
1
0
1
0
0
2
0
3
0
0
2
2
1
0
0
0
2
1
1
2
1
1
0
0
2
2
0
1
1
0
2
1
1
3
1
1
2
0
2
2
0
0
0
0
2
1
0
0
1
1
0
0
1
1
0
0
1
1
0
1
0
1
2
0
1
0
0
0
0
0
1
2
1
1
1
1
1
0
0
0
2
1
0
0
0
2
0
2
1
0
0
1
1
1
1
2
1
2
0
1
2
0
2
1
0
2
1
1
0
0
0
0
2
0
0
0
2
0
2
2
2
1
0
2
0
2
0
0
1
1
1
1
1
0
2
0
2
1
0
0
2
1
2
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
1
2
1
1
2
2
0
1
0
0
0
1
1
1
1
0
1
0
0
0
2
0
0
2
1
0
0
0
0
0
0
1
0
1
1
1
1
6
1
1
1
0
1
0
0
1
0
0
0
0
1
1
0
2
0
2
1
0
0
0
2
1
0
1
0
1
0
1
0
0
1
2
2
2
0
0
0
2
2
1
0
3
2
0
2
3
0
1
0
1
0
2
0
0
2
1
1
0
2
0
0
1
1
0
0
2
0
0
0
1
2
2
1
0
0
1
1
0
1
1
0
1
1
1
1
0
2
0
1
0
2
1
2
0
2
0
2
2
0
0
1
0
2
2
1
2
0
0
1
0
0
1
1
1
0
0
0
0
1
2
1
0
0
0
2
2
0
0
0
1
1
1
0
1
1
1
2
1
2
1
0
1
1
2
0
0
0
0
1
0
1
1
1
1
2
0
2
1
0
0
1
0
1
0
1
2
2
3
1
0
2
4
0
1
0
1
3
1
0
2
0
2
0
0
2
0
2
0
1
0
0
0
1
2
1
1
0
0
1
1
2
0
2
2
0
1
2
0
0
1
0
0
2
0
3
2
0
0
2
0
0
1
0
0
1
0
0
0
1
0
1
1
1
0
2
3
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
2
2
0
0
1
0
1
0
0
0
1
1
1
0
0
0
1
1
0
1
1
1
2
0
0
2
0
2
1
1
2
2
2
2
0
1
1
1
0
1
0
0
0
2
0
1
0
0
2
1
2
1
2
1
0
0
0
1
0
1
0
0
1
0
0
1
1
0
0
0
0
2
4
2
1
1
0
1
0
0
0
0
0
2
1
1
0
0
1
1
0
1
1
1
0
1
0
0
0
1
1
0
1
0
0
0
0
1
1
1
1
2
0
0
3
1
2
0
2
0
2
2
1
1
7
2
0
1
0
0
2
0
0
1
1
0
2
2
1
1
5
0
0
1
2
0
1
1
1
0
1
0
0
0
1
0
1
1
0
2
0
1
1
0
2
0
2
0
0
1
0
2
0
0
1
1
2
0
0
0
0
2
0
2
1
0
1
0
0
2
1
1
0
2
1
0
0
1
1
0
1
0
3
3
2
2
0
2
0
1
0
1
1
0
0
1
0
1
1
0
0
2
0
0
0
1
2
2
1
2
0
0
0
1
1
2
1
0
0
1
0
1
0
2
0
2
2
2
2
0
2
2
2
0
1
0
1
1
0
2
1
1
0
1
1
2
0
2
1
0
2
2
1
1
0
0
1
1
0
0
0
0
0
2
0
1
1
0
2
1
0
0
0
1
0
2
1
0
0
0
1
0
2
1
0
0
0
1
2
1
2
0
0
0
2
2
2
0
0
1
0
1
1
2
0
2
1
2
1
1
2
0
0
0
0
0
1
2
0
0
2
0
0
2
1
1
2
0
0
0
1
1
1
0
0
0
0
0
0
0
1
2
1
1
0
0
0
2
0
0
0
0
1
0
0
0
1
2
2
0
1
1
1
0
2
0
1
1
0
0
0
1
0
1
3
0
0
0
1
1
1
1
0
2
1
1
1
1
0
0
1
1
1
1
0
1
1
0
0
0
1
1
1
1
3
0
0
1
0
0
1
2
0
1
0
1
2
1
0
0
1
1
0
0
0
0
1
2
1
1
1
0
2
1
0
1
2
2
0
0
0
1
0
0
1
0
0
0
0
1
2
0
0
1
1
1
2
1
0
1
2
0
0
0
0
0
2
0
1
0
2
0
2
1
2
0
2
1
1
1
0
1
1
0
1
1
1
2
0
0
0
1
0
1
1
1
0
2
0
0
1
1
1
2
0
0
0
0
2
0
1
1
1
3
0
0
0
1
2
1
0
0
0
0
1
0
2
1
1
1
0
1
0
1
0
2
2
1
2
2
1
1
0
0
0
2
1
1
0
0
0
0
2
1
1
2
0
1
0
0
0
0
0
1
1
1
2
0
2
0
0
2
0
2
2
1
0
0
1
1
1
1
0
0
0
0
1
0
0
2
1
1
0
0
1
1
0
1
2
0
0
0
0
1
0
2
0
2
0
0
0
1
0
2
1
1
0
1
0
2
2
2
0
0
0
0
1
3
1
1
2
0
0
1
0
1
0
2
0
1
0
0
0
1
1
0
0
1
2
2
0
0
0
0
0
0
0
1
1
0
2
1
2
0
0
2
1
0
2
2
0
2
0
0
0
0
0
0
2
0
1
0
1
2
0
1
1
2
2
1
0
0
0
0
1
2
2
0
2
1
2
1
1
0
2
0
2
1
2
0
2
1
0
0
1
1
1
0
1
0
1
0
2
2
0
0
1
1
0
0
0
0
2
0
2
0
3
0
2
2
0
2
0
0
0
2
1
0
1
0
2
1
0
0
1
2
0
2
0
0
0
1
1
2
0
0
2
0
0
0
0
0
0
1
2
0
0
0
1
2
1
0
2
2
0
1
0
0
0
0
0
0
0
2
1
0
2
0
0
2
0
1
2
2
2
2
4
1
0
1
0
0
0
1
1
1
1
1
1
0
1
1
1
1
0
0
3
2
1
1
1
2
0
0
2
0
0
1
0
0
2
0
0
2
1
1
2
0
0
0
0
0
1
2
0
1
1
2
0
0
0
0
1
0
0
4
2
2
1
1
1
1
1
1
1
2
1
1
1
0
0
1
0
1
1
0
0
2
0
0
0
0
0
0
2
0
2
2
3
2
0
0
2
2
2
1
0
0
0
0
2
2
2
1
1
2
1
1
1
0
0
0
1
2
2
1
0
1
0
1
1
1
1
0
1
0
0
0
1
0
0
0
1
1
2
1
0
0
1
0
1
1
2
3
0
1
0
0
0
0
0
1
0
1
1
0
1
2
0
2
0
2
1
0
2
0
0
0
1
0
0
2
0
0
0
1
2
0
0
1
3
4
0
0
0
0
0
0
2
2
0
0
2
1
2
1
1
0
2
1
1
0
1
0
0
0
0
0
1
2
0
0
1
0
2
1
1
1
1
0
1
1
2
3
1
1
1
0
2
0
0
1
0
0
2
1
0
0
0
0
0
0
2
0
1
1
0
1
0
0
0
0
2
1
0
2
0
7
4
0
0
1
0
0
1
0
2
2
1
1
2
1
1
0
1
0
0
1
1
0
0
1
1
0
1
0
0
0
0
0
2
0
0
0
0
1
0
3
1
0
2
1
0
1
0
2
1
2
1
0
0
0
0
1
0
0
0
0
2
2
0
0
3
0
2
0
1
2
2
0
1
0
0
0
0
2
0
0
0
0
2
2
0
1
2
1
1
0
1
1
0
1
3
0
0
1
0
0
1
2
3
0
1
0
0
0
2
0
1
0
2
0
0
0
1
2
1
0
0
1
1
0
0
0
9
0
2
1
1
0
0
0
2
1
0
0
0
1
0
1
1
2
2
0
1
0
2
0
0
0
2
0
1
0
2
2
0
0
2
0
0
0
0
0
1
2
0
0
0
1
4
1
2
0
0
1
1
1
0
0
2
0
2
2
1
0
1
1
3
1
2
0
1
1
1
1
0
2
1
2
1
2
1
0
0
0
1
0
1
2
0
0
1
1
0
2
0
1
1
0
1
0
1
1
0
3
1
0
2
0
0
0
1
2
2
0
0
1
2
0
2
2
0
1
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
2
1
2
0
1
1
0
1
0
1
0
0
1
0
0
1
1
0
0
1
1
1
2
0
0
1
2
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
2
2
1
0
2
0
1
0
0
1
2
2
0
1
1
6
2
1
0
2
0
0
0
1
2
1
1
0
1
0
2
1
2
1
0
1
1
1
1
0
2
1
0
2
0
1
1
0
2
1
0
2
0
1
0
1
1
0
0
0
2
0
2
1
1
0
2
2
1
0
0
0
1
1
1
0
2
1
0
2
1
1
0
0
1
1
1
1
0
0
0
2
2
4
2
1
3
0
2
1
0
0
2
2
2
0
1
0
2
1
0
1
1
1
0
1
0
3
1
1
1
0
1
1
1
1
1
2
2
1
1
2
3
0
2
2
1
0
0
1
2
0
0
1
1
1
1
1
1
1
1
4
2
1
2
1
1
0
2
2
0
2
1
2
2
0
0
0
1
1
0
1
2
0
2
0
0
1
1
1
0
0
0
1
1
1
2
1
0
2
2
0
1
1
3
3
1
0
2
2
0
2
0
2
0
2
0
0
1
0
1
2
0
1
0
0
2
0
0
1
1
1
2
2
0
0
0
0
0
1
0
1
1
0
1
2
0
0
0
2
0
0
0
1
0
0
1
0
1
0
1
0
1
0
0
0
0
1
1
0
0
0
2
0
2
0
0
0
2
1
1
2
0
0
2
0
1
1
0
1
1
0
2
0
0
2
1
1
0
2
1
2
2
0
1
2
2
2
0
1
1
0
1
1
0
2
1
0
1
1
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
1
2
0
0
1
0
1
2
1
0
0
2
0
2
2
2
0
0
3
0
0
1
1
1
0
0
1
2
0
1
0
2
0
0
0
1
2
1
0
1
2
0
0
0
1
0
1
0
0
2
0
0
0
1
3
0
1
0
0
0
1
1
1
1
0
0
2
0
1
1
0
0
0
2
0
0
1
0
1
0
2
1
0
1
0
0
1
1
2
0
3
1
0
2
1
1
0
1
1
0
0
2
1
0
0
0
1
2
0
1
2
2
0
0
0
0
0
2
2
2
0
2
1
0
0
3
0
1
1
2
1
1
0
1
0
0
0
1
0
1
0
1
2
1
2
2
0
1
2
0
0
0
1
2
2
1
4
2
0
1
1
1
1
0
0
0
0
1
0
0
2
1
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
1
0
2
2
2
1
1
0
0
2
0
1
0
1
1
2
0
0
1
2
0
1
1
3
0
0
1
0
0
0
2
1
1
1
1
0
1
0
1
3
1
0
0
0
2
0
1
0
0
3
0
1
2
0
0
0
1
0
0
0
0
0
1
1
1
0
0
1
1
2
2
2
1
0
1
0
2
2
2
1
0
0
1
1
1
2
0
0
0
1
0
0
2
0
1
2
2
2
0
1
0
1
0
1
0
1
1
1
1
2
0
1
1
0
1
0
0
0
1
1
0
2
1
0
2
0
0
2
2
0
2
2
1
2
0
2
0
1
0
0
0
1
1
1
2
0
3
0
2
1
0
0
1
2
1
0
2
0
1
5
1
0
0
1
1
2
0
0
0
2
0
1
0
0
0
0
2
0
0
1
2
0
2
0
2
1
1
0
2
0
1
0
1
0
1
1
0
0
2
0
1
0
1
1
2
2
0
0
0
3
0
0
0
2
2
0
1
0
1
2
0
0
0
2
1
1
0
0
2
0
2
0
0
0
2
2
0
0
0
0
2
1
0
0
1
1
0
0
2
0
0
0
1
0
2
1
1
1
0
1
1
1
1
1
0
2
0
0
0
2
0
1
1
0
0
2
0
0
1
4
0
1
1
1
0
0
0
0
1
1
0
1
0
1
2
0
1
0
1
1
1
4
0
0
1
0
1
3
2
0
1
2
1
1
1
0
0
1
2
2
0
0
0
1
2
1
0
1
2
0
1
1
0
1
2
0
0
1
0
1
1
0
0
0
1
1
0
0
0
2
2
0
1
2
1
0
0
2
1
2
0
2
1
1
0
1
1
1
1
1
0
0
2
1
1
1
1
0
2
1
1
0
1
1
0
1
0
2
1
1
0
0
1
2
0
2
2
1
0
0
0
1
2
0
0
0
0
0
1
1
1
0
1
1
0
1
2
1
0
0
1
2
0
1
1
1
0
2
2
2
0
2
2
2
0
0
2
1
1
1
0
1
1
2
0
0
2
0
3
1
1
1
2
4
0
1
1
1
2
1
0
0
0
1
1
1
1
2
0
1
2
1
0
1
1
0
0
1
0
1
1
0
1
0
1
0
2
2
0
0
1
2
0
1
0
0
0
2
1
2
1
2
2
0
0
1
2
0
1
1
3
1
0
3
0
1
0
1
1
2
0
0
2
1
2
1
1
0
1
1
0
2
0
1
2
2
0
1
1
0
1
1
0
0
0
2
1
1
0
1
0
0
2
2
2
1
0
0
0
1
0
2
0
2
0
1
0
0
1
0
2
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
2
2
0
0
2
2
2
0
1
2
0
0
1
0
1
0
1
2
0
0
0
1
0
1
2
1
0
1
1
0
2
2
1
1
1
2
0
0
0
1
0
0
0
0
2
2
1
0
2
0
2
0
0
1
2
0
0
1
0
0
1
2
2
2
3
1
0
0
0
2
0
1
2
0
0
2
2
0
1
0
0
1
0
2
1
0
1
0
0
1
0
0
1
1
0
2
2
1
0
2
1
2
0
0
2
0
1
0
0
0
2
0
2
2
2
2
0
0
2
1
0
1
0
1
0
3
0
0
0
0
0
2
1
1
1
0
3
1
1
2
0
0
1
2
0
1
0
0
0
0
0
1
1
0
1
0
0
3
2
1
0
1
1
1
0
0
1
1
0
1
2
1
0
0
2
2
1
0
1
2
2
2
0
2
1
1
0
2
2
2
0
0
1
1
0
1
0
0
1
1
2
0
0
0
1
2
2
2
0
1
0
1
1
0
1
2
1
2
0
2
2
2
0
1
0
1
0
2
2
0
0
1
0
0
2
2
0
0
0
1
0
0
3
0
2
0
2
3
1
1
1
0
1
0
2
3
0
3
0
0
1
0
1
0
1
0
1
1
1
2
2
0
1
1
0
2
1
0
1
0
1
1
0
0
0
0
2
0
0
0
0
1
0
1
0
2
0
1
0
1
2
0
1
1
1
0
0
1
0
0
1
0
1
0
2
2
1
1
0
0
1
0
1
0
2
1
0
2
0
0
0
2
0
1
0
0
0
2
0
2
0
1
0
0
0
1
0
0
0
1
0
1
0
2
3
2
1
1
0
1
0
0
1
0
2
0
0
0
2
2
0
1
0
0
2
0
2
0
0
1
0
0
1
1
0
2
1
1
0
0
1
0
1
1
2
1
1
0
1
0
2
0
1
1
1
0
0
0
2
1
1
2
1
0
0
1
1
0
0
2
1
1
3
2
0
1
1
2
1
1
2
0
0
2
0
0
0
1
1
0
2
0
1
2
2
1
1
0
0
1
0
1
2
2
1
0
0
1
1
0
2
0
2
0
1
0
1
0
2
1
0
0
1
1
0
0
2
2
0
2
2
0
0
0
1
0
0
1
0
1
0
1
0
0
2
1
1
0
0
1
1
0
0
0
0
0
2
0
2
0
1
1
0
1
0
1
2
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
2
1
1
1
0
0
0
0
2
0
2
0
1
0
0
2
3
0
1
1
0
2
1
1
1
0
0
0
1
0
2
1
1
1
0
1
1
1
0
0
0
0
0
0
0
1
1
3
1
0
0
0
2
1
2
0
3
0
1
0
0
0
1
0
0
1
0
0
0
1
1
0
0
1
0
2
1
0
1
2
1
0
0
1
2
2
2
0
2
1
0
1
1
0
0
1
1
0
1
0
2
0
0
0
0
0
0
2
1
2
2
1
1
1
2
2
1
0
2
0
1
0
1
2
2
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
2
1
1
2
0
0
1
0
1
0
0
0
0
1
0
0
0
1
1
2
0
1
1
5
0
0
1
1
0
0
1
0
1
0
1
1
0
2
0
2
0
0
0
1
1
2
1
4
2
0
1
1
3
1
0
0
1
0
0
0
1
1
2
1
0
1
2
2
1
2
1
0
0
2
0
0
1
1
1
1
0
0
0
1
1
1
1
2
1
1
0
1
0
2
0
1
0
1
2
2
1
2
2
0
0
0
0
0
1
1
2
1
0
1
0
3
0
0
2
1
0
0
2
0
2
0
2
1
2
0
2
2
1
1
0
0
0
2
2
0
2
1
1
2
0
1
0
2
0
2
1
1
2
2
0
0
2
0
2
3
3
2
1
2
1
1
2
0
0
0
2
0
1
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
1
1
1
1
1
0
0
0
0
1
2
1
1
2
0
1
1
2
2
0
2
0
1
0
1
3
0
0
0
0
0
0
1
1
0
2
2
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
2
2
0
2
1
0
1
0
2
0
0
1
0
1
1
0
0
1
1
0
0
0
2
0
0
0
2
0
2
1
1
0
1
1
0
1
1
0
0
0
1
1
2
1
0
1
1
0
1
1
2
2
2
1
0
0
0
2
1
0
1
1
1
1
0
2
1
0
1
1
0
0
0
0
0
0
1
1
0
0
1
2
0
1
1
0
3
0
0
2
0
1
2
1
0
2
1
1
0
0
0
1
0
2
1
2
2
0
1
1
0
0
2
1
1
0
0
2
1
1
2
1
2
1
2
2
2
0
0
1
0
0
1
0
0
1
1
1
1
1
0
1
0
1
0
1
1
0
1
1
1
0
2
1
1
0
1
0
1
0
2
1
1
0
0
0
0
0
2
0
0
2
0
2
2
0
1
1
0
1
1
1
1
1
0
0
1
0
0
0
2
0
0
2
2
1
1
1
2
0
0
2
0
0
0
1
2
0
1
1
1
0
1
1
0
0
0
1
1
0
1
0
1
0
1
1
0
1
0
3
0
0
1
3
1
0
1
0
0
1
1
2
1
1
1
1
2
1
1
0
1
1
0
1
0
0
0
1
0
0
0
2
0
2
0
0
1
0
0
1
1
0
1
1
0
1
0
0
0
1
1
1
0
1
2
1
0
1
1
2
0
0
0
1
0
1
0
0
0
1
1
1
0
0
2
1
0
0
0
0
0
2
2
0
0
0
1
0
1
1
0
1
1
2
3
0
0
0
1
1
0
0
2
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
1
0
2
0
0
1
0
0
1
0
0
2
2
0
0
0
0
0
1
2
2
2
1
0
0
0
2
1
1
2
1
0
2
2
0
0
0
2
0
0
0
3
0
0
2
2
0
0
0
0
1
2
0
1
1
1
0
1
1
0
0
0
1
0
1
0
1
0
1
0
1
1
0
2
0
0
0
1
2
0
0
0
0
0
2
2
1
0
0
0
1
2
1
0
0
0
0
0
0
2
0
1
0
1
1
2
0
2
2
1
0
0
2
1
0
2
0
1
0
1
0
1
1
2
0
2
0
1
0
1
0
1
1
1
0
1
1
0
0
2
0
1
0
0
1
2
0
0
0
1
1
0
0
0
1
1
0
0
1
1
1
0
1
0
1
1
1
1
1
2
1
2
1
2
1
1
3
0
0
1
1
1
1
1
0
1
2
2
0
1
2
2
1
2
0
1
1
0
2
0
2
1
0
1
1
1
0
0
0
2
1
1
3
2
0
0
0
1
2
2
0
0
1
0
1
0
3
0
1
2
2
0
0
0
0
1
0
3
5
1
2
0
2
2
2
0
1
1
0
0
1
1
0
1
2
0
0
0
0
0
2
1
2
1
1
2
0
0
0
0
0
0
2
2
0
0
0
2
1
0
0
0
0
2
1
1
1
1
1
0
0
0
1
2
7
2
0
1
0
0
1
1
0
1
1
0
2
0
0
0
1
1
0
0
2
0
0
0
0
0
1
1
0
0
4
1
1
2
0
0
0
2
1
2
2
0
0
2
1
1
0
0
1
0
1
2
1
1
0
2
2
2
2
1
0
2
0
2
2
1
0
1
1
2
1
0
2
1
0
0
1
0
1
0
1
2
2
1
2
1
2
2
0
1
0
0
1
2
2
1
0
0
0
0
1
0
0
1
2
1
0
1
2
0
0
1
2
2
1
0
1
0
2
2
0
2
0
1
2
2
1
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
2
2
2
2
2
0
0
1
0
0
1
1
2
0
2
1
1
2
0
1
2
1
0
0
3
0
2
1
1
2
0
2
2
1
0
0
1
1
1
2
0
1
0
0
1
0
2
0
1
0
1
0
1
2
2
1
2
1
0
0
0
0
1
0
0
0
0
0
2
2
2
0
1
0
6
2
1
0
3
2
1
1
0
0
1
0
2
2
3
1
0
2
2
1
2
1
1
1
1
2
1
1
0
1
0
0
0
2
2
0
2
0
1
1
1
0
1
0
2
0
0
1
0
2
1
0
0
0
2
1
0
1
2
1
0
0
1
0
1
0
1
0
0
0
0
0
0
2
0
1
2
0
2
2
0
1
0
0
0
0
1
2
1
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
1
0
0
2
1
0
1
0
0
1
0
1
2
1
0
1
0
0
0
0
1
0
2
2
0
2
0
1
0
2
1
1
1
0
1
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
2
2
1
1
0
4
2
1
0
1
0
1
0
1
2
0
0
0
1
2
0
0
0
2
1
0
2
0
2
2
0
2
0
1
2
0
0
0
1
1
0
1
2
0
1
1
1
0
0
0
2
0
2
2
0
2
1
1
3
0
1
2
0
1
0
0
2
0
1
0
2
0
0
3
1
0
0
1
0
0
0
2
1
0
0
0
0
1
0
0
0
1
0
1
2
0
0
1
2
0
1
0
2
2
2
0
2
2
2
1
2
2
0
1
0
2
0
1
21
1
0
2
0
1
0
1
1
1
0
1
1
1
0
0
0
0
2
0
0
0
2
2
1
0
1
1
0
0
1
2
0
0
2
2
0
0
0
0
0
1
1
0
0
0
2
2
0
2
4
0
1
1
0
1
1
0
2
0
1
0
0
1
2
2
1
0
1
1
0
1
2
2
0
0
0
0
0
1
3
0
1
2
1
2
2
1
3
3
1
1
1
0
2
0
2
0
0
1
4
1
1
2
0
0
1
1
1
1
1
1
0
11
1
0
1
0
1
2
0
1
1
2
0
1
1
2
2
1
1
5
1
0
1
2
0
0
2
0
1
1
1
1
1
0
1
0
0
1
2
1
0
1
0
0
1
1
0
2
1
0
0
0
0
0
0
0
1
0
2
3
0
1
0
1
0
2
1
0
1
1
0
1
1
0
2
2
1
2
2
0
2
0
1
0
1
0
0
0
2
0
0
1
0
2
2
1
2
1
2
2
2
0
0
0
1
0
0
1
2
0
0
2
1
0
2
0
1
1
1
2
1
0
0
3
1
1
1
2
0
0
1
0
1
0
1
6
2
0
0
0
2
0
1
0
0
1
0
1
2
1
0
1
0
1
2
0
0
0
0
1
2
1
0
0
0
0
1
0
2
0
0
2
0
0
0
1
1
2
1
0
1
2
0
1
1
0
0
1
0
1
0
0
0
1
1
0
2
1
1
1
2
2
0
0
2
2
0
1
1
2
1
1
0
0
2
1
1
2
2
0
0
2
2
0
0
0
2
0
2
0
1
2
0
1
1
0
1
0
0
2
0
0
1
1
0
0
2
2
0
1
0
1
2
0
0
0
1
1
1
2
2
1
2
1
0
2
2
0
1
1
0
0
1
1
0
0
1
1
0
1
0
1
0
1
2
0
2
1
2
1
0
0
0
0
0
0
2
2
1
1
2
1
1
1
1
2
0
1
1
0
0
0
2
1
1
1
0
1
0
2
1
0
0
1
0
1
0
0
2
0
2
1
3
0
2
0
0
1
1
1
0
1
1
2
0
0
2
2
0
1
1
2
1
0
0
1
0
0
1
2
2
0
0
1
0
2
2
0
0
0
1
0
1
0
2
0
0
0
1
2
1
2
2
0
2
0
0
0
1
3
0
1
1
0
0
0
1
0
0
2
0
0
2
2
2
0
1
0
0
0
1
1
0
0
0
0
2
1
0
1
0
0
0
1
0
2
0
1
1
1
0
2
1
2
1
2
1
2
0
0
1
1
0
0
4
2
2
3
1
0
0
1
1
0
1
0
2
1
2
1
2
2
0
0
0
2
0
1
0
0
0
2
0
1
0
0
2
0
1
2
2
2
2
1
1
1
2
1
2
1
0
0
1
1
2
0
2
0
2
0
1
0
1
2
3
1
1
2
1
0
0
0
0
1
1
1
2
2
1
0
0
1
0
1
0
1
0
1
1
2
0
0
0
0
1
2
1
1
0
0
1
2
1
2
0
0
1
0
1
0
2
1
0
2
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
3
0
0
0
1
1
1
0
0
2
0
2
0
1
1
1
0
1
1
1
1
0
2
1
0
0
3
0
1
0
0
0
1
1
2
1
0
1
0
2
1
0
1
0
1
1
3
0
0
0
0
0
2
2
0
2
0
0
2
1
1
2
2
0
0
2
0
2
0
1
1
0
1
0
1
1
0
2
1
1
2
2
0
1
2
1
1
1
1
0
0
1
0
1
1
1
0
1
0
2
1
1
2
2
1
2
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
2
2
2
1
2
0
0
1
1
0
0
1
0
2
0
1
0
1
1
1
2
2
0
1
1
0
1
0
0
0
2
1
2
0
0
0
1
0
1
0
0
0
0
2
1
0
0
1
2
0
1
0
0
1
1
0
1
2
0
2
2
2
0
1
1
0
0
1
1
1
1
0
2
1
1
1
1
2
1
0
1
0
0
1
2
0
0
2
1
1
1
1
1
1
0
0
1
1
1
0
1
0
1
0
1
0
1
2
1
0
3
2
2
0
1
2
1
0
0
0
0
1
2
1
1
1
1
0
0
0
0
1
2
0
1
0
0
0
0
0
1
2
0
0
2
0
0
1
0
0
1
1
3
2
1
2
0
0
0
0
1
1
1
2
0
1
1
2
2
2
2
1
0
0
0
0
0
0
0
2
1
0
1
0
1
2
2
1
0
0
2
0
0
0
2
0
0
0
2
5
0
1
2
2
1
0
0
0
1
0
1
1
1
2
1
1
0
0
2
1
1
2
1
0
0
3
2
0
0
0
0
2
1
0
3
1
1
2
0
0
2
1
1
0
1
0
1
0
0
1
2
2
0
0
0
0
2
0
1
2
0
0
0
2
0
0
0
2
1
2
2
1
0
0
0
2
0
0
0
2
0
1
0
1
0
2
1
2
2
2
0
2
0
0
1
1
2
0
0
0
0
0
0
0
1
1
0
0
1
0
0
2
2
0
1
1
1
2
0
0
1
0
0
2
1
0
2
0
1
0
1
1
2
2
1
2
0
0
0
1
1
1
2
1
2
1
2
1
2
1
0
3
2
1
0
1
2
2
1
2
0
1
1
0
0
3
1
0
0
1
2
0
1
1
1
0
2
1
0
1
2
2
0
0
0
0
0
1
0
1
0
2
1
0
2
1
0
0
2
2
1
0
1
0
1
2
1
1
3
1
1
0
0
1
0
0
1
0
1
2
1
2
1
1
0
0
2
0
0
4
3
2
0
1
0
1
0
0
2
0
2
0
2
2
0
0
1
2
0
0
1
2
0
1
1
1
2
2
0
0
0
0
0
1
1
1
2
0
1
0
1
0
1
1
1
1
0
1
0
2
1
2
0
2
1
0
3
1
0
0
0
0
0
0
0
0
2
1
0
1
0
0
1
2
0
1
1
0
0
1
2
0
0
1
0
0
4
0
0
1
0
0
0
0
1
0
0
1
1
0
1
0
2
0
2
0
0
2
0
0
1
1
0
2
0
2
1
1
0
1
0
2
1
1
0
1
2
2
0
1
0
1
0
1
1
1
0
0
0
0
0
1
0
0
2
1
1
0
0
0
0
1
2
1
0
0
0
0
1
1
1
0
0
0
2
2
1
1
1
0
0
1
0
2
3
0
0
0
1
1
0
0
2
0
2
0
0
1
2
0
1
1
2
0
0
0
3
2
0
1
2
1
0
0
2
0
1
1
0
2
0
3
0
0
2
0
0
0
0
0
1
2
0
0
0
0
2
0
0
1
0
1
1
1
1
0
2
1
1
2
0
1
0
0
1
0
1
2
1
0
0
0
1
0
1
0
1
2
1
0
1
0
0
0
0
1
0
2
1
2
0
0
0
0
0
1
0
2
0
1
0
2
0
0
0
2
0
1
0
0
1
0
0
2
0
2
2
0
2
1
1
2
0
0
1
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
1
3
0
1
0
1
1
1
0
1
0
1
2
1
2
1
1
0
0
0
1
1
1
1
0
1
0
1
1
0
2
0
1
0
1
1
0
1
1
0
2
0
1
0
0
0
0
2
1
2
0
0
2
1
1
0
1
2
0
2
2
1
2
0
0
2
2
2
0
0
2
2
0
1
2
2
2
1
0
0
0
0
1
1
0
0
2
0
0
0
2
1
2
0
2
1
0
2
1
0
0
0
1
2
2
1
1
2
0
0
0
1
0
2
2
1
1
0
1
0
0
3
2
0
0
0
1
0
2
0
1
0
1
0
0
0
1
0
1
1
0
2
0
1
0
2
1
1
1
0
0
0
0
2
0
0
0
2
1
0
0
2
1
2
1
0
1
3
0
1
0
0
0
0
1
1
1
0
1
0
0
1
1
0
1
0
0
2
1
1
0
0
0
0
0
1
1
2
2
2
0
0
0
1
0
1
0
4
0
1
0
0
2
1
2
1
1
1
1
2
0
0
0
1
0
1
1
1
2
1
1
0
0
1
1
0
0
1
1
2
2
0
0
0
2
0
2
1
0
1
2
0
0
0
0
2
1
2
1
0
0
2
1
0
0
1
0
1
1
1
0
1
0
2
2
2
1
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
1
0
2
1
0
4
2
2
0
1
1
1
1
0
2
0
1
0
1
1
0
1
3
2
1
0
2
0
1
0
1
0
0
0
0
0
0
2
0
0
2
0
2
1
0
3
1
1
2
0
1
2
0
0
2
1
0
1
1
0
2
0
0
2
0
0
0
2
1
2
0
0
2
2
1
0
2
1
0
0
0
0
0
0
4
0
0
0
1
0
3
0
0
0
0
1
0
1
1
0
0
1
0
1
1
1
0
2
1
2
0
0
0
0
0
3
0
1
0
0
0
0
0
2
1
1
1
0
0
1
0
1
0
2
1
1
1
1
1
0
0
2
1
1
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
2
0
0
0
1
1
2
1
2
0
2
2
0
2
0
2
1
0
2
1
0
1
0
1
1
2
0
1
2
1
2
0
1
1
0
0
0
0
1
2
0
2
1
1
1
0
0
1
0
0
2
2
0
2
1
2
0
2
0
2
0
0
1
1
0
0
2
0
1
1
1
0
0
0
1
1
0
0
0
1
2
0
0
0
0
1
2
0
1
1
1
0
0
2
0
0
1
0
1
0
0
0
1
2
1
0
0
0
0
0
1
0
0
0
0
2
1
0
3
0
0
2
0
1
0
1
1
1
0
1
0
0
2
2
1
0
1
0
1
1
0
0
0
0
0
2
0
0
1
1
3
1
2
2
2
2
1
0
0
1
1
0
2
0
2
1
0
1
0
1
0
2
1
2
1
2
2
0
1
0
0
2
2
0
2
1
0
1
1
1
2
0
0
2
0
0
0
2
0
1
0
1
1
1
0
2
0
2
0
0
0
2
1
5
1
0
1
1
0
0
2
0
1
1
1
0
1
1
1
1
1
1
1
0
0
1
0
1
1
0
0
2
0
0
0
2
0
2
0
1
0
1
1
1
1
1
2
2
2
0
1
0
0
0
0
1
2
1
1
0
2
1
2
0
0
1
1
2
0
1
1
1
1
2
1
1
0
0
1
2
0
0
0
2
0
0
1
2
1
0
1
2
2
0
3
1
1
0
0
0
0
2
0
0
1
0
0
0
0
2
0
1
0
2
0
0
2
2
0
2
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
1
2
0
0
4
0
0
1
1
0
2
1
0
2
2
1
1
0
1
0
1
0
0
2
1
2
0
1
0
1
0
2
1
0
0
0
0
1
1
1
0
1
2
4
1
1
0
1
2
1
0
0
2
0
1
2
1
1
0
0
0
1
1
0
0
0
0
0
1
0
2
1
0
0
0
1
1
0
0
1
2
1
1
2
0
0
0
2
0
2
2
1
0
0
2
0
0
0
0
2
1
0
0
0
3
2
1
0
2
0
0
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
2
0
0
1
1
0
2
0
1
2
0
1
0
0
1
0
0
0
2
1
0
1
0
0
1
1
0
3
0
0
2
0
0
0
0
1
1
2
2
4
2
0
1
1
0
0
0
2
0
1
2
0
1
0
0
1
2
1
2
0
0
2
0
0
1
2
1
2
0
2
0
0
0
2
1
1
2
2
0
0
1
1
0
1
0
2
2
1
1
2
1
0
2
1
1
2
1
0
0
1
2
2
0
1
2
1
2
0
0
1
0
1
0
1
0
0
1
0
1
0
0
0
1
0
0
0
1
0
2
2
0
0
0
1
2
0
0
1
2
1
0
1
1
1
0
0
0
0
0
2
2
1
1
0
3
1
0
1
1
1
1
0
0
2
1
0
1
0
0
2
1
1
5
2
3
1
0
0
0
1
3
0
0
2
2
1
0
1
1
2
1
0
0
1
1
0
0
1
1
0
1
0
0
0
0
1
0
2
0
1
0
0
0
0
0
2
1
2
1
0
1
0
1
0
0
0
1
0
1
2
0
2
1
0
0
0
1
1
3
0
1
0
0
0
0
0
2
2
1
1
1
1
2
2
0
0
2
1
0
0
2
2
1
1
1
1
2
0
1
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
1
2
1
1
0
2
1
0
3
0
0
1
0
0
2
1
0
0
0
1
0
0
1
1
0
1
1
0
1
1
1
1
2
0
0
0
1
0
0
0
1
0
2
1
0
2
1
1
0
0
1
0
0
1
1
0
1
1
1
0
2
0
0
1
0
0
3
0
0
0
1
0
1
1
0
2
2
2
1
2
1
2
0
1
2
1
0
2
0
2
0
1
1
0
2
1
0
1
2
1
0
1
1
3
0
1
2
1
1
1
0
4
0
0
0
1
0
0
0
0
1
0
2
0
2
0
0
2
1
0
1
0
2
0
2
1
1
1
0
2
2
1
1
4
0
1
1
1
2
0
2
2
0
1
0
2
0
0
0
0
1
2
1
0
0
0
1
2
1
2
1
1
0
1
2
3
2
0
0
2
1
0
0
1
1
2
3
2
2
1
1
1
0
1
1
1
2
0
0
0
1
1
0
2
2
1
0
1
0
1
1
0
0
1
1
0
0
1
1
1
2
0
2
0
1
2
1
0
0
0
0
0
1
1
0
0
2
2
0
2
2
2
0
1
1
2
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
2
1
1
1
1
0
0
1
1
1
2
1
1
0
0
1
0
1
1
2
1
0
0
1
1
1
0
1
0
2
1
0
0
0
1
0
0
0
1
0
0
0
1
2
2
1
0
1
0
0
0
2
1
0
1
1
1
2
1
0
1
0
1
0
1
1
0
1
0
0
2
2
0
0
1
1
1
3
1
0
0
1
0
2
0
0
1
0
0
0
3
0
0
2
0
0
1
0
1
1
1
1
1
1
0
0
2
1
0
0
1
1
0
0
0
1
0
0
0
0
0
1
2
1
0
0
0
0
1
2
0
1
1
2
0
1
0
2
1
0
1
0
0
1
0
1
0
1
1
0
0
2
1
1
0
1
0
2
0
1
0
0
2
1
2
0
0
1
1
1
1
1
2
0
0
1
0
2
0
0
1
1
2
1
2
2
2
1
0
2
0
1
1
0
0
1
0
2
0
2
1
1
1
2
1
2
1
0
0
1
1
1
1
0
0
2
1
0
0
0
2
0
0
0
2
1
1
1
0
2
1
1
0
1
0
1
2
0
0
2
0
0
0
0
2
0
0
2
2
1
0
0
0
0
0
2
1
1
2
1
0
0
2
1
0
1
1
1
2
2
0
0
0
1
1
0
1
1
1
1
2
0
1
0
0
1
1
0
0
0
2
0
4
3
0
0
1
0
1
1
0
1
0
1
0
0
0
2
0
1
0
2
1
0
0
0
2
1
2
2
0
1
1
1
0
0
1
0
0
3
2
1
1
2
2
0
1
1
2
1
0
2
1
1
0
2
2
1
0
0
1
1
0
0
2
1
0
1
0
1
2
0
1
0
1
0
1
0
0
1
0
0
2
1
2
1
1
3
0
1
0
1
1
5
0
1
2
2
1
1
1
0
1
0
2
1
1
0
0
1
0
0
1
1
0
2
0
0
1
1
0
1
0
1
1
0
1
0
0
0
1
0
1
1
0
1
1
0
1
2
0
1
0
0
1
0
1
2
0
2
2
0
0
0
0
2
0
1
0
0
0
0
0
0
2
1
0
1
0
0
1
1
0
1
0
0
1
0
1
1
0
0
0
2
0
0
0
0
1
1
2
2
0
2
2
0
1
1
1
2
0
1
1
1
1
1
0
0
2
0
1
2
1
1
1
0
0
2
0
1
1
2
1
1
1
0
2
1
3
0
2
2
1
0
0
0
1
2
1
0
2
0
0
1
0
2
2
2
0
1
0
0
2
0
0
1
1
1
1
0
0
1
1
0
2
0
0
1
0
0
0
0
0
0
1
1
0
2
2
2
0
0
1
0
0
2
1
2
1
1
2
0
2
1
1
0
1
2
2
1
2
0
0
0
2
0
0
0
0
1
0
0
0
1
0
2
2
2
0
0
2
1
0
1
2
0
2
0
1
0
0
1
0
4
2
1
0
1
1
1
2
1
1
1
2
0
1
1
1
2
1
1
1
2
1
0
2
1
1
4
0
2
2
0
0
1
0
0
1
0
0
2
1
0
2
0
0
0
2
0
0
0
1
1
0
4
1
1
2
1
0
1
1
0
1
2
2
1
0
0
0
2
0
0
0
1
2
2
0
1
1
1
1
0
0
0
0
1
0
1
0
1
1
0
0
2
0
0
1
0
0
1
1
0
0
1
0
1
0
1
0
0
2
1
1
2
1
0
2
0
1
0
1
1
0
0
2
1
1
0
0
1
1
1
0
0
1
2
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
1
0
3
1
1
0
1
1
0
2
0
0
0
0
0
0
2
2
1
1
2
3
0
2
0
1
2
1
1
1
1
1
1
2
1
1
2
1
2
1
2
0
2
0
2
1
1
1
2
2
2
0
2
1
2
1
0
1
1
1
0
2
1
0
1
1
0
1
0
0
1
1
0
0
1
0
1
2
0
1
1
2
1
0
0
1
0
1
0
0
1
0
2
1
0
2
0
2
1
0
1
0
1
0
2
1
0
1
2
2
2
1
1
1
1
2
0
0
0
0
0
2
2
1
2
1
1
2
0
2
2
0
0
1
0
1
0
0
2
0
3
0
2
2
0
2
1
2
0
0
0
1
1
2
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
1
0
2
0
1
1
1
1
1
0
1
1
1
1
2
1
2
2
0
1
2
0
0
0
1
0
0
0
0
2
0
2
1
0
1
1
0
1
0
0
0
2
2
0
0
0
0
0
0
2
1
1
2
1
0
2
0
0
0
1
0
2
1
0
2
0
2
0
2
1
1
0
2
0
1
2
1
0
1
0
1
0
0
1
2
0
0
1
2
0
0
2
2
0
1
1
0
1
2
0
1
2
0
1
0
0
1
1
0
2
3
0
3
3
1
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
2
0
1
1
1
1
1
2
0
0
0
0
1
1
0
1
1
1
0
0
0
0
1
1
0
1
0
1
0
1
0
1
0
1
0
0
0
0
2
0
2
2
0
2
0
1
0
2
1
0
0
1
1
0
1
1
0
0
1
1
1
1
0
0
1
0
0
1
0
1
1
2
2
1
1
0
1
1
0
1
2
0
1
2
0
1
0
0
2
0
1
1
2
1
2
1
0
0
2
0
1
0
2
2
1
0
0
2
0
0
2
1
0
1
1
1
0
0
0
1
0
1
2
1
1
0
0
1
1
1
0
1
1
0
0
1
2
0
0
1
0
2
0
0
1
1
2
1
1
0
0
2
0
0
0
1
1
1
0
0
1
1
2
0
0
1
4
1
2
0
2
0
1
2
1
1
2
1
0
1
1
1
2
1
2
0
0
1
0
0
0
1
1
1
2
0
1
1
0
1
1
2
0
1
1
2
0
0
2
0
1
1
0
1
0
1
0
0
1
1
1
0
1
2
0
2
0
0
1
1
1
1
2
0
2
0
2
0
0
0
1
0
2
1
0
2
0
1
0
1
2
1
0
0
0
0
1
0
1
0
2
0
1
2
1
0
0
1
0
2
1
2
0
0
2
1
1
2
0
1
0
1
0
1
0
0
1
0
0
1
1
0
1
1
0
0
2
0
0
1
0
2
0
1
1
0
0
0
0
0
1
0
1
1
1
0
0
0
0
1
0
1
1
0
0
1
0
1
1
2
1
1
0
1
0
2
1
1
0
0
0
0
2
2
0
2
0
0
0
1
2
2
2
2
2
0
0
0
0
2
0
0
0
2
2
0
0
2
0
1
1
0
1
1
1
1
1
1
2
1
2
2
2
0
1
1
1
0
1
1
2
1
0
2
1
0
0
0
2
2
3
0
0
0
0
1
2
0
0
0
0
0
0
2
2
0
0
2
1
0
1
0
3
0
1
2
0
1
0
3
1
0
1
2
3
2
1
0
0
0
0
1
1
1
0
0
0
2
0
1
0
0
1
2
1
0
1
2
1
1
0
0
1
1
1
1
0
2
1
3
2
1
0
2
1
1
2
1
1
0
0
1
0
1
0
2
1
0
1
2
1
0
0
0
1
1
1
0
0
2
0
0
2
1
0
0
1
0
1
0
2
1
2
1
0
1
0
2
2
1
1
1
0
0
1
1
0
0
0
2
7
0
3
0
0
2
0
0
0
2
1
2
1
1
1
1
0
0
0
1
0
1
0
1
2
1
1
0
1
1
2
2
0
0
0
1
0
0
2
2
1
0
0
0
1
0
2
0
2
0
0
1
0
2
0
0
1
0
2
1
0
0
1
2
1
0
2
2
0
0
0
1
0
2
0
2
0
0
1
0
4
1
0
0
2
0
1
0
0
1
0
1
0
3
2
2
1
2
0
1
1
0
0
2
2
3
0
1
0
0
2
2
1
1
0
0
0
1
0
0
0
2
1
0
0
0
1
0
3
0
2
1
0
0
0
0
2
0
1
1
0
0
0
1
0
0
0
2
1
1
1
2
0
1
2
1
2
0
0
1
1
1
1
0
0
2
1
1
1
1
1
0
2
0
0
1
0
0
0
0
0
1
0
1
0
0
1
1
0
0
1
0
1
2
5
2
0
0
1
0
1
0
2
5
0
2
2
0
0
1
2
0
1
1
0
0
0
2
1
0
1
1
0
0
2
0
1
2
1
0
1
0
1
1
2
0
0
2
1
0
0
0
1
1
1
0
0
1
0
0
3
2
0
2
0
1
2
0
2
2
2
2
0
0
1
0
0
0
0
0
1
1
0
2
1
1
1
1
0
0
0
1
0
1
0
1
0
0
0
0
2
2
0
2
0
0
1
0
1
1
0
2
0
1
0
1
2
1
0
0
0
0
3
1
2
0
0
1
0
1
2
0
3
2
0
0
0
1
1
0
2
1
0
2
0
0
1
2
0
0
1
1
0
1
0
0
0
0
1
2
0
2
1
0
1
2
2
1
0
4
1
1
0
0
1
0
2
2
2
1
0
2
0
1
2
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
4
1
1
1
0
0
1
1
0
1
0
1
2
1
0
0
1
1
2
1
0
2
2
0
0
0
0
0
1
1
2
0
0
1
0
1
1
0
0
0
2
1
2
1
1
1
1
0
1
1
0
2
2
0
2
1
1
1
0
2
2
0
1
2
0
0
1
0
0
1
2
0
0
2
0
2
1
0
1
1
1
2
1
2
0
0
1
0
2
0
0
1
1
0
1
0
2
2
0
0
1
1
1
0
0
1
1
2
2
2
0
2
1
0
0
0
0
1
1
1
2
0
1
0
1
2
1
1
1
0
0
0
2
0
0
1
0
2
0
1
0
0
0
0
0
0
0
1
1
1
1
2
0
0
0
1
2
1
2
0
1
1
2
0
2
1
0
2
2
0
1
2
1
1
1
1
0
1
0
0
1
0
2
2
1
1
2
0
2
2
0
0
2
0
2
1
0
0
2
1
0
1
1
1
0
0
1
0
0
0
2
0
1
1
2
2
0
1
0
2
0
0
1
0
0
0
0
0
1
2
0
0
2
0
1
2
1
1
1
2
1
0
2
1
0
0
1
0
2
0
0
3
0
3
2
1
1
2
1
1
0
1
1
0
1
0
0
3
0
0
1
1
1
0
0
0
0
1
0
0
0
0
2
0
0
1
1
0
0
1
0
0
2
0
2
0
0
1
0
1
1
1
2
1
0
1
0
0
2
1
1
0
1
0
1
2
1
0
2
1
1
1
0
2
0
1
0
0
1
0
1
0
0
2
1
0
0
0
3
0
0
1
3
0
0
1
1
1
2
1
2
1
0
1
1
0
0
0
2
1
0
0
2
0
2
1
0
2
1
0
0
0
2
1
2
0
2
2
1
1
1
2
0
2
0
4
1
0
0
1
0
1
2
1
0
0
0
1
0
2
0
0
0
4
1
2
2
0
0
0
0
0
2
1
1
2
0
1
1
1
2
0
2
2
0
0
2
0
2
1
2
0
6
0
0
0
0
1
0
1
1
0
2
1
1
2
0
0
1
2
0
1
0
2
0
1
0
0
0
2
1
1
0
1
2
1
0
1
0
1
1
2
1
2
0
2
0
0
0
0
0
0
1
0
1
2
0
2
0
1
1
1
0
1
1
1
0
0
0
2
1
1
0
1
1
1
2
1
0
0
1
0
1
1
0
0
0
2
2
0
1
0
3
4
2
0
0
1
1
0
0
0
1
0
1
1
0
0
1
0
3
2
2
2
2
2
2
1
0
0
0
1
1
0
0
1
0
2
2
2
2
0
2
1
2
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
1
2
1
0
0
0
1
2
3
3
1
0
2
1
1
2
1
0
2
1
1
0
0
0
0
2
2
1
2
1
2
0
0
0
0
0
0
0
2
1
2
0
1
1
0
0
2
1
1
1
1
0
1
0
0
2
0
1
0
0
2
0
1
2
2
0
0
1
1
0
2
2
0
2
0
0
1
0
2
1
2
0
2
1
1
0
2
1
1
1
1
1
1
0
2
1
1
1
0
0
2
1
2
2
0
1
0
0
1
2
3
0
0
2
0
1
0
2
0
2
1
0
1
1
2
1
2
1
2
2
0
1
0
2
2
0
2
0
1
0
2
2
0
0
0
1
0
0
2
0
0
1
1
0
1
1
2
1
0
0
0
3
0
1
0
1
1
3
1
1
0
0
0
2
2
1
0
1
0
2
0
4
0
0
0
0
0
1
1
2
0
0
0
0
2
1
0
2
1
2
2
4
2
0
1
1
0
0
0
1
2
0
1
1
1
2
1
1
1
2
2
0
2
0
1
2
1
0
0
1
1
2
0
0
3
1
1
0
1
0
0
2
2
1
1
0
1
0
3
0
1
1
2
0
0
2
1
1
2
1
0
0
0
1
0
2
0
1
2
0
1
1
1
0
0
0
0
2
2
1
1
0
0
1
2
0
0
0
1
0
0
0
1
0
1
1
1
0
0
0
0
0
1
0
2
1
2
0
0
0
0
2
0
2
2
1
1
0
0
0
0
2
0
0
1
2
1
1
2
0
1
0
1
5
0
2
1
0
1
2
1
2
0
2
1
2
0
0
0
0
0
1
1
0
2
2
2
1
0
1
2
1
2
2
1
2
0
0
1
1
2
1
1
2
0
2
1
1
0
0
1
2
2
1
4
0
2
1
0
0
0
0
0
2
1
0
0
1
0
0
1
2
2
0
1
0
0
0
1
2
1
0
2
1
1
0
1
2
0
1
1
0
1
0
0
0
1
0
0
1
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
3
1
1
1
1
2
2
0
1
1
0
0
0
0
2
0
1
1
1
2
0
0
2
1
2
1
1
2
1
0
1
0
1
2
0
0
1
1
2
2
0
0
1
0
2
1
0
1
1
2
0
1
1
0
1
0
2
1
0
2
1
1
1
0
0
0
0
0
2
0
2
0
1
1
0
0
1
0
1
0
0
1
0
0
2
0
0
1
0
0
0
0
1
2
0
1
1
0
1
0
0
0
1
1
0
0
0
2
2
2
2
0
0
0
0
0
1
1
0
0
0
0
1
1
0
2
1
0
0
0
0
1
2
1
0
2
0
1
3
3
0
1
1
0
0
0
0
1
3
0
1
1
0
0
1
2
2
1
2
2
0
1
1
0
0
2
1
0
2
1
2
1
2
1
0
0
1
1
1
2
0
2
1
0
1
0
0
2
1
0
0
0
0
1
2
1
1
2
0
1
1
2
0
0
0
2
0
0
3
0
2
0
1
0
5
0
0
0
0
2
0
2
1
1
3
0
1
0
2
0
1
1
1
1
0
1
0
1
0
2
1
1
1
0
1
0
0
0
0
1
0
1
0
2
0
2
1
2
0
2
1
1
0
0
0
3
3
0
2
0
1
1
0
0
2
1
1
1
1
1
0
0
0
1
1
1
2
2
2
1
2
0
0
0
0
2
2
0
0
2
1
0
0
1
0
1
0
0
1
0
0
2
3
0
0
0
1
0
0
1
2
2
0
0
0
1
2
2
1
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
1
1
0
1
0
1
2
2
0
0
1
1
0
1
1
1
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
1
1
1
1
0
2
0
1
1
1
0
0
0
0
0
0
1
0
1
1
2
1
2
0
0
2
0
0
0
3
0
1
0
1
1
1
1
0
2
1
0
1
0
2
1
1
4
2
1
0
2
0
1
0
0
0
0
0
3
1
0
1
2
2
1
0
1
2
1
0
2
1
0
1
1
0
0
0
2
0
0
0
1
2
1
0
0
2
1
1
0
0
0
1
0
2
2
1
2
0
0
1
1
0
1
0
1
0
1
0
0
0
0
0
1
0
0
2
0
1
1
0
0
0
2
0
1
1
1
0
1
1
1
0
2
1
1
0
0
2
0
1
0
1
0
1
1
2
0
1
0
0
1
3
1
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
1
1
0
1
0
2
0
1
0
0
1
1
1
2
1
1
1
0
1
0
0
0
1
1
0
1
0
1
0
0
2
1
2
0
0
0
0
0
0
0
1
1
2
2
1
1
0
1
0
2
0
1
1
2
0
1
1
0
0
0
0
0
0
0
1
1
1
1
0
1
1
1
2
1
1
1
2
1
0
0
0
0
0
0
2
2
0
0
2
3
0
1
2
1
1
1
0
0
0
0
2
2
0
1
1
1
1
1
0
3
1
2
0
1
0
0
2
0
2
1
0
0
0
0
0
1
0
0
0
1
0
1
1
2
2
0
0
0
0
0
0
1
0
2
2
0
1
1
0
0
0
0
0
1
0
2
2
0
2
1
2
1
0
1
0
3
2
1
0
0
1
0
1
0
0
2
1
1
2
1
0
0
1
0
1
0
1
0
1
0
0
1
2
1
0
0
2
0
1
0
0
2
0
1
1
0
0
2
0
0
0
0
0
2
2
0
0
0
0
1
0
1
2
1
0
0
0
0
2
2
0
1
0
0
0
0
1
2
2
2
1
1
0
3
1
1
0
0
2
1
0
1
0
0
0
1
2
0
0
2
0
0
1
1
1
1
0
0
3
1
0
2
1
0
0
4
1
1
0
1
1
1
0
2
1
1
1
0
1
0
0
3
0
0
2
1
1
1
1
1
2
0
1
0
0
2
0
1
1
0
1
0
1
2
0
0
0
0
2
0
0
0
1
1
0
1
1
0
0
0
0
0
0
2
0
1
2
0
0
0
1
0
1
1
2
1
0
2
0
0
0
2
0
0
0
4
2
1
2
0
0
1
0
1
1
0
2
2
0
1
0
0
0
2
0
0
1
0
4
1
0
0
0
0
0
0
0
0
0
0
3
1
1
1
0
2
1
1
0
1
2
1
0
0
0
0
2
0
2
1
1
1
0
1
0
0
2
1
1
1
2
2
0
0
0
2
1
0
1
1
1
0
0
2
0
0
1
0
2
1
0
1
2
0
0
1
1
0
0
1
1
1
2
0
2
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
2
2
1
1
2
2
0
0
0
1
2
2
4
1
0
0
0
0
1
0
1
0
1
0
0
2
3
0
1
1
2
2
0
1
2
2
1
0
0
1
1
0
2
0
0
1
2
2
1
0
0
0
1
0
1
0
1
0
2
0
1
2
0
0
0
0
1
1
0
1
0
0
1
1
2
1
2
1
2
0
1
1
2
1
0
0
0
2
2
1
1
0
2
0
0
0
2
0
0
0
1
2
1
0
2
2
0
0
0
0
1
1
0
2
1
0
1
0
0
1
1
0
2
0
0
1
0
2
0
1
0
0
0
0
1
0
2
1
0
2
2
0
1
0
1
1
0
2
0
1
2
2
0
0
0
0
2
0
0
0
1
2
2
0
0
2
1
2
0
1
1
0
1
1
1
0
0
1
0
2
0
1
0
0
0
0
0
1
0
0
3
0
2
2
0
1
1
0
0
2
2
0
2
1
0
0
2
2
0
1
1
0
2
0
2
0
0
1
2
0
0
0
0
1
0
0
0
2
0
1
0
1
0
0
0
1
2
1
2
1
0
0
2
2
1
2
0
0
1
2
0
2
0
2
0
0
2
0
0
2
1
1
2
0
0
0
0
0
0
2
1
1
1
1
0
1
2
2
2
2
0
0
1
0
2
0
2
2
1
0
2
2
0
1
1
1
1
1
1
0
1
3
2
2
1
0
1
1
0
1
0
0
0
0
0
0
2
2
0
0
2
4
0
0
2
2
0
0
1
2
1
2
0
1
0
1
0
0
0
2
1
0
0
1
1
0
2
2
0
2
3
1
1
0
1
0
0
0
2
0
0
1
0
1
0
2
0
2
1
1
1
0
2
1
0
1
0
1
1
2
2
1
2
0
1
0
0
2
1
1
0
1
0
0
1
1
1
0
0
0
0
1
0
0
0
0
2
1
1
0
1
0
0
1
2
1
0
2
0
0
1
0
1
0
0
2
1
2
0
1
0
1
1
1
0
1
2
3
0
2
0
0
0
0
0
1
0
0
1
0
1
1
1
0
1
0
0
1
1
0
0
1
0
0
0
1
2
0
2
0
0
0
0
0
1
2
0
2
1
0
1
2
2
0
0
1
2
0
3
0
1
1
2
3
1
2
4
0
1
0
0
1
0
0
0
1
0
3
1
0
0
1
1
0
2
1
2
2
1
1
2
1
0
1
1
0
1
2
1
1
2
0
2
2
0
0
2
1
0
0
0
1
0
0
1
0
0
0
0
2
0
0
1
0
1
0
0
0
0
1
2
0
1
0
0
0
1
0
0
1
0
0
2
0
2
1
0
2
2
2
2
0
0
1
2
0
0
1
1
1
1
0
0
0
0
0
0
0
5
2
0
2
2
0
0
2
1
1
1
2
1
0
0
1
0
2
0
0
1
0
1
0
1
0
0
1
0
1
2
0
1
1
0
1
3
0
1
0
1
1
1
3
2
0
1
1
0
0
0
0
2
0
1
0
2
0
0
0
2
2
2
0
2
2
1
0
5
0
0
1
0
0
1
1
0
1
1
0
1
2
0
0
2
1
1
0
2
1
0
0
0
0
2
1
0
2
0
0
0
0
0
1
0
0
1
1
1
2
0
1
0
2
1
0
2
1
1
1
0
1
2
2
2
1
0
1
2
0
2
0
1
0
0
1
0
2
0
1
1
2
0
2
0
1
0
0
2
1
0
1
1
0
1
2
1
1
1
0
0
0
0
0
0
2
0
1
0
0
4
0
1
1
1
2
1
0
0
0
1
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
2
1
2
0
0
2
1
2
0
1
1
1
0
0
0
1
1
0
2
2
0
2
0
1
1
2
2
2
2
1
0
1
1
0
1
1
1
1
2
0
0
0
1
1
1
1
2
0
1
0
1
0
2
2
0
0
0
2
0
1
1
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
1
0
2
0
1
3
0
1
1
1
2
0
1
2
0
0
2
2
1
0
0
2
0
2
0
0
0
0
0
2
0
2
1
2
0
0
0
1
0
2
2
0
0
0
0
1
1
1
0
2
0
2
2
0
0
0
0
2
1
3
2
2
1
0
0
0
1
0
0
2
0
2
0
1
0
0
2
1
1
1
1
0
0
2
1
2
2
0
1
2
1
1
2
2
2
2
1
0
2
1
0
0
0
0
1
2
0
0
1
0
0
0
0
1
0
0
1
1
2
2
0
0
0
2
0
0
2
1
0
0
2
1
2
0
1
1
2
1
2
0
0
0
2
0
2
1
0
1
1
1
0
0
0
0
1
1
2
0
0
1
1
1
0
0
1
0
1
1
0
1
1
0
1
1
0
1
0
0
1
0
3
2
1
0
0
1
1
2
1
0
1
0
0
0
0
1
0
0
0
1
2
1
0
1
1
0
1
1
1
0
0
1
0
1
0
1
0
1
3
0
2
0
0
0
1
2
1
1
1
1
1
1
1
2
2
0
2
1
0
2
1
1
0
1
3
1
0
1
0
0
0
0
2
0
0
1
0
0
2
1
2
0
0
0
0
1
0
0
0
0
0
2
1
1
0
0
0
1
1
1
0
1
2
1
0
0
1
1
0
0
0
3
0
1
1
1
0
0
0
1
1
2
0
1
0
0
2
0
0
0
1
1
1
3
2
1
0
1
0
0
2
0
2
0
1
0
1
0
0
2
1
0
1
1
0
0
2
2
0
2
0
1
1
0
1
1
0
1
1
1
0
0
1
2
1
2
1
1
0
0
0
0
1
0
1
0
2
2
0
0
0
1
1
0
2
0
0
0
0
1
2
1
0
0
1
2
1
1
0
1
0
0
1
2
0
1
1
1
0
1
0
1
1
1
0
1
0
0
1
1
0
0
2
0
2
1
0
0
1
0
0
1
0
1
0
1
0
0
1
1
2
0
0
0
2
0
1
1
1
0
2
0
0
1
2
0
1
0
1
2
2
0
0
1
0
1
4
1
1
0
1
1
0
0
0
0
0
1
1
0
0
2
0
1
0
1
0
2
0
0
1
1
0
2
1
0
0
1
1
0
0
1
0
2
2
0
0
0
0
2
0
0
0
0
0
0
3
1
1
0
0
0
2
0
0
0
0
2
0
1
1
0
2
0
1
0
1
0
1
1
0
0
0
1
0
2
3
0
0
0
0
1
1
1
0
1
1
0
0
2
2
2
2
0
0
1
0
1
0
1
0
0
1
2
1
0
2
2
0
1
1
2
2
0
1
0
1
0
0
1
0
1
0
0
0
0
1
1
0
0
1
0
1
0
1
0
2
0
0
2
0
0
0
2
0
0
1
1
0
1
2
1
3
3
0
2
2
1
0
1
0
2
0
0
1
0
1
1
1
0
0
2
2
0
0
2
0
2
0
1
0
0
2
2
1
1
0
0
1
1
3
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
1
2
1
2
1
1
1
2
0
2
0
0
0
2
2
2
0
0
2
2
0
1
0
1
1
1
1
1
1
0
0
0
0
1
0
1
0
2
0
2
0
1
0
1
0
1
1
1
1
0
1
1
0
0
1
0
2
1
0
2
0
1
0
1
1
1
2
2
0
2
0
0
0
1
0
2
1
0
0
0
1
0
2
0
1
1
2
0
0
1
1
0
1
0
0
2
1
2
2
0
0
1
0
0
2
3
0
1
0
1
1
2
1
2
0
1
2
2
1
0
2
0
0
0
0
0
0
1
1
2
2
0
1
1
0
2
1
2
2
0
1
0
2
1
0
0
0
1
2
2
2
1
0
2
1
0
0
2
4
2
1
0
0
2
2
1
0
0
2
2
1
1
0
0
1
2
0
2
2
0
1
0
1
0
2
2
2
0
0
2
1
1
0
0
0
0
1
1
0
1
0
0
0
1
1
0
1
0
0
0
2
0
0
2
0
0
1
2
2
1
1
1
1
0
0
1
1
0
0
2
1
0
0
2
0
0
0
0
2
1
1
0
2
1
0
1
0
2
0
2
0
1
2
0
2
2
0
0
2
2
1
0
1
0
0
0
1
2
0
0
0
2
0
0
1
0
1
2
1
2
1
1
0
1
0
0
0
3
2
2
1
3
1
1
1
1
0
0
0
1
2
1
2
1
2
2
0
0
2
0
0
1
1
1
2
2
0
2
1
2
1
1
2
0
1
0
2
1
0
1
1
0
1
2
0
0
0
1
0
1
0
0
0
1
0
2
0
0
2
2
0
0
0
2
2
1
0
0
0
2
1
1
0
1
1
0
5
0
1
1
0
0
2
1
0
0
0
2
0
0
2
0
1
2
1
1
1
0
2
1
0
1
2
1
0
0
2
2
0
1
1
0
1
1
0
2
0
0
2
1
1
0
1
1
2
2
0
0
0
2
2
0
2
0
0
2
2
2
0
0
1
1
0
1
1
0
2
1
0
0
1
0
0
0
0
2
0
1
0
1
1
1
1
1
1
0
0
1
0
1
0
0
0
0
2
0
1
1
2
2
0
0
0
1
0
1
0
0
0
2
0
0
1
0
2
0
0
0
0
1
2
1
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
1
2
0
0
1
1
0
1
0
0
0
1
2
1
2
0
1
0
1
0
0
0
1
0
2
0
1
0
2
0
1
1
0
2
1
2
0
1
0
1
0
0
0
2
2
1
0
0
1
1
1
1
1
1
0
1
1
0
1
2
0
1
0
0
0
1
0
0
2
3
1
0
0
2
0
2
2
1
0
0
2
0
1
0
2
0
0
0
0
0
1
0
0
2
1
1
0
2
2
0
0
0
0
0
2
0
0
5
0
1
0
0
0
1
1
2
3
0
2
2
2
0
2
0
3
0
2
1
1
1
0
1
1
0
0
0
2
0
0
1
0
1
0
0
0
0
1
0
0
1
2
3
2
2
1
1
0
1
2
1
0
2
1
1
0
1
1
1
1
2
0
0
1
1
1
0
0
1
0
0
0
1
0
0
1
2
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
2
2
0
2
0
0
0
2
2
2
0
1
0
2
1
1
0
2
1
0
1
1
1
1
0
2
0
1
0
0
2
0
2
2
0
2
1
1
1
1
0
1
2
0
0
0
1
1
2
0
0
0
2
1
2
2
0
2
1
0
0
2
0
0
1
0
0
1
2
0
0
0
0
1
0
1
1
0
3
2
0
0
0
0
2
0
0
0
0
0
1
0
2
6
0
0
0
0
1
1
2
0
1
0
0
1
1
0
1
0
2
0
1
1
2
0
2
0
0
0
0
2
0
2
0
1
2
0
0
1
0
0
2
1
1
1
0
0
1
6
0
1
3
0
1
1
1
1
0
0
1
0
1
3
0
2
2
3
0
0
2
0
0
0
2
1
3
1
0
1
0
0
1
1
0
0
0
1
2
0
2
2
0
0
0
2
1
2
2
2
0
1
1
0
2
0
0
0
1
0
1
1
2
0
1
2
1
1
0
2
1
1
0
0
2
2
2
0
2
1
0
0
0
1
2
0
2
0
1
0
2
0
0
0
0
1
2
0
0
1
1
0
0
1
2
0
2
1
1
1
1
0
0
1
0
1
1
2
1
0
0
2
2
1
1
0
2
0
0
2
1
1
0
0
1
1
0
2
1
1
0
2
1
0
0
1
1
0
0
0
0
0
1
2
1
2
2
3
2
1
0
0
0
1
0
0
0
1
0
1
2
1
1
1
0
1
0
0
0
2
0
0
0
2
0
2
2
0
0
1
2
2
0
2
0
0
2
0
0
1
0
0
0
0
0
0
1
2
2
0
0
2
2
0
0
0
3
2
0
0
0
1
0
0
0
0
0
2
0
1
0
3
0
0
3
0
1
1
0
1
1
2
1
0
1
1
1
0
0
0
2
2
0
0
2
0
0
0
2
1
0
2
2
2
0
2
3
0
0
2
0
0
0
0
1
3
2
2
2
2
1
0
2
0
0
0
0
1
0
0
1
1
0
0
2
1
1
0
0
0
1
1
1
0
1
0
0
0
2
1
2
1
1
0
0
0
2
2
2
1
2
0
2
1
1
1
1
0
0
2
1
1
1
0
0
1
0
1
2
0
0
0
1
4
0
1
1
1
0
0
1
0
1
0
2
0
0
1
0
3
2
0
0
0
1
1
1
2
2
0
1
0
0
0
0
0
0
0
0
0
2
1
1
2
1
0
2
0
0
2
1
0
3
2
2
1
0
0
2
0
0
1
2
2
2
0
0
1
1
1
1
0
0
0
1
1
0
1
1
1
1
1
0
0
2
1
1
0
0
1
1
0
1
0
2
1
1
0
0
0
2
2
0
2
1
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
1
2
0
2
1
0
1
1
0
2
0
0
0
0
0
1
0
0
0
1
0
3
0
0
1
2
2
1
2
1
1
1
0
0
4
0
1
0
2
0
1
0
0
1
2
2
0
1
0
0
1
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
1
2
0
0
2
1
1
1
2
0
1
0
0
2
0
0
1
0
1
1
0
0
0
2
1
0
2
0
1
1
0
0
2
2
0
2
0
2
1
0
1
0
0
1
0
2
0
2
0
1
2
0
0
2
2
1
1
1
1
2
2
0
1
2
0
0
1
1
0
0
1
0
0
0
2
0
2
1
1
0
1
1
0
0
0
0
0
0
1
0
0
2
1
0
0
0
1
0
0
2
1
1
1
2
0
0
1
0
0
1
1
1
0
2
1
0
1
1
1
1
1
3
1
0
2
0
0
0
4
0
3
0
1
0
2
0
0
0
2
2
2
0
1
2
1
0
0
2
2
2
1
0
0
0
0
0
1
2
0
1
0
1
1
2
2
0
0
1
0
1
1
1
1
0
1
0
0
1
1
1
1
0
2
0
0
1
2
1
0
0
0
2
1
0
0
0
2
1
0
1
1
0
2
0
0
1
0
0
0
0
1
5
2
0
1
2
0
0
2
1
1
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
2
1
0
0
0
1
0
2
0
1
1
1
2
1
0
0
0
1
0
2
1
1
0
1
0
0
0
1
0
2
1
2
1
1
0
1
2
1
0
0
1
1
1
2
1
2
1
2
0
0
1
0
0
0
1
1
2
2
1
2
1
2
0
2
0
1
0
2
2
1
0
2
0
1
2
0
2
2
0
1
2
1
2
0
0
0
1
0
0
0
1
0
2
4
2
0
0
0
1
0
0
2
1
1
0
1
0
0
0
0
0
2
0
0
1
0
0
2
1
0
1
1
1
0
2
0
2
0
1
2
0
2
1
1
0
1
1
2
2
1
0
0
0
1
2
3
0
0
1
2
1
2
0
0
1
2
0
0
2
1
1
2
1
0
0
0
0
0
0
1
0
2
1
0
0
0
1
3
0
1
1
2
0
2
1
0
0
1
0
2
1
0
0
0
0
0
0
1
1
0
1
0
0
1
2
0
0
2
0
0
1
1
0
0
1
1
0
0
2
0
2
0
0
0
2
0
0
0
2
1
0
0
1
2
0
2
0
2
0
0
0
0
2
1
1
0
0
2
1
2
1
2
2
1
0
1
0
2
1
2
1
2
1
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
2
0
1
0
0
2
1
1
0
2
0
0
1
1
2
1
0
0
2
0
0
0
1
1
1
0
1
0
2
0
2
2
1
1
1
0
0
1
1
0
2
0
0
0
0
0
0
0
1
0
1
1
0
2
0
0
2
0
1
0
0
2
1
1
0
1
2
1
1
0
1
0
1
1
1
1
0
1
1
0
1
1
1
1
0
0
0
0
0
0
0
2
0
0
2
2
0
1
1
1
1
1
0
1
2
2
2
0
1
2
0
1
2
0
0
1
1
2
2
2
1
1
1
1
1
1
1
2
0
2
2
2
0
0
2
1
3
1
0
0
0
4
0
1
1
1
2
0
2
2
2
2
1
0
1
0
0
0
1
0
1
2
2
2
1
0
0
0
0
0
0
1
0
0
2
2
0
1
2
2
1
1
0
1
1
0
3
2
1
0
0
0
0
0
1
2
1
0
0
1
0
1
0
1
1
0
1
2
2
2
1
0
1
1
0
0
0
1
1
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
2
1
0
2
1
0
0
0
1
2
1
1
1
0
0
2
1
0
0
0
3
2
0
1
1
0
0
0
2
1
1
0
1
2
0
1
1
0
0
1
1
0
2
2
0
2
2
1
0
1
1
1
0
5
2
0
0
0
2
1
0
0
1
2
2
1
0
0
1
0
2
1
0
1
2
0
2
2
0
0
0
0
1
0
1
0
2
1
1
0
0
1
2
0
1
1
0
3
0
2
1
1
1
0
2
2
2
2
1
0
0
2
2
0
2
0
0
0
1
1
0
0
1
0
0
0
1
2
1
0
0
0
1
0
1
0
2
0
0
1
1
0
2
1
2
1
0
0
1
2
1
0
0
1
1
1
1
0
1
1
2
1
1
1
1
1
1
0
0
0
2
0
2
0
2
2
1
0
0
2
0
0
0
0
0
2
1
1
0
1
0
0
1
2
0
0
1
0
0
2
3
0
0
0
1
0
2
1
0
2
1
0
0
0
0
2
2
1
1
1
2
1
0
1
2
2
1
0
2
1
1
0
1
1
0
1
0
0
1
1
2
2
0
1
2
1
1
0
1
1
1
0
0
1
3
0
0
0
1
1
0
0
0
0
2
1
1
0
0
1
0
0
1
1
0
2
1
1
2
1
2
0
0
0
0
2
0
0
0
1
3
1
0
2
0
0
1
2
3
0
0
1
0
2
1
2
1
0
1
0
1
0
0
1
0
2
1
0
0
0
0
2
1
0
1
1
0
1
0
2
1
0
0
0
0
0
0
1
0
2
0
0
2
1
0
0
0
1
1
0
0
1
2
0
1
0
0
0
1
0
0
2
1
0
1
2
2
1
1
1
1
3
1
2
0
0
1
1
1
0
0
1
0
1
0
0
2
0
2
0
0
1
0
1
0
2
1
1
0
0
2
2
1
1
1
0
1
0
1
0
0
1
0
0
0
2
1
2
0
0
2
1
0
0
2
1
1
0
1
0
2
0
0
2
0
1
1
0
2
1
0
2
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
1
1
2
1
2
2
1
0
1
2
0
0
1
0
0
0
2
1
0
0
1
0
0
2
0
0
1
2
1
0
0
0
0
2
0
1
1
2
1
1
0
0
2
0
0
2
1
0
2
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
1
0
1
1
1
2
0
2
1
0
1
1
1
1
1
0
2
1
1
0
0
0
2
0
2
0
0
2
2
1
1
0
1
1
2
1
1
0
0
0
0
0
0
2
2
0
1
0
2
1
0
0
0
0
1
0
0
0
0
0
1
1
1
2
0
0
1
1
2
0
2
0
2
0
2
0
0
1
1
2
2
1
1
0
1
2
0
1
1
0
0
0
2
0
1
0
1
0
2
0
1
2
1
1
0
0
0
0
0
0
0
0
0
1
2
0
1
1
0
1
0
0
1
0
0
0
2
0
0
0
1
2
1
0
1
0
0
0
1
2
0
2
1
0
2
2
0
0
0
2
1
2
2
0
0
0
0
2
0
2
2
1
0
2
1
0
0
1
0
0
0
2
1
1
0
0
0
0
2
1
0
0
1
1
2
0
0
0
1
0
0
0
2
2
0
1
2
1
1
2
2
1
1
2
0
0
0
2
2
0
2
0
0
1
1
1
0
1
2
1
0
0
0
0
2
1
0
0
1
1
1
2
1
0
0
1
1
0
0
0
9
1
1
0
3
1
1
1
1
1
2
1
0
0
2
0
0
0
0
1
1
1
0
0
2
0
0
0
1
2
0
2
0
0
2
2
0
0
4
2
0
1
1
0
0
2
0
1
1
0
3
2
2
0
0
2
0
2
0
0
2
1
0
0
0
0
1
2
1
1
0
1
1
0
0
2
2
0
2
2
1
1
0
0
0
0
1
1
1
0
1
1
0
0
2
0
0
2
0
1
1
1
0
3
3
1
0
1
1
0
2
1
0
1
0
1
0
0
0
0
2
0
2
1
0
0
1
0
2
0
0
1
1
0
3
2
3
1
1
0
1
1
3
1
0
1
2
0
0
2
0
2
0
2
2
2
2
0
0
0
0
0
2
0
3
0
1
0
0
0
0
2
1
2
0
2
2
0
0
2
0
0
0
2
6
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
2
0
0
0
0
0
2
0
0
4
2
0
0
0
1
1
2
1
0
2
3
1
2
2
0
2
0
0
2
1
0
1
2
1
2
0
1
0
0
0
0
0
2
3
2
0
1
2
1
1
0
0
1
0
0
0
0
0
2
1
0
0
1
1
0
1
0
0
2
2
1
0
0
1
1
2
0
1
0
1
0
1
2
0
0
0
2
1
2
0
0
1
2
1
1
0
0
1
0
1
2
0
0
1
1
1
0
1
1
0
1
1
1
3
2
0
1
1
1
1
1
0
0
0
0
2
0
0
2
1
1
1
0
1
1
0
0
0
1
2
0
1
1
2
1
0
0
0
1
1
0
0
1
2
1
2
1
2
0
2
0
1
2
2
1
0
0
1
0
2
1
0
0
3
0
0
0
2
2
0
1
0
1
0
2
1
1
0
0
1
0
1
2
0
0
1
0
1
1
1
0
0
0
2
2
0
2
1
0
1
1
3
0
0
1
0
1
1
0
0
0
1
0
2
1
1
0
0
1
1
0
2
0
1
1
0
0
0
2
0
1
0
0
1
0
3
1
1
0
0
3
0
0
0
0
3
0
2
1
0
1
2
1
0
1
0
0
0
0
3
0
2
0
0
0
2
0
1
0
0
1
2
0
1
0
0
2
2
1
0
1
2
0
2
1
1
2
1
0
0
1
0
1
1
0
0
1
0
1
1
0
0
2
0
2
2
0
2
2
1
0
0
1
0
1
1
0
2
0
0
0
2
0
0
1
2
1
0
0
2
2
0
3
0
0
0
0
1
5
2
1
1
2
1
0
0
0
2
1
2
0
1
0
0
1
0
1
1
0
2
1
2
0
0
1
0
1
0
2
1
1
2
3
0
1
2
1
1
0
1
1
0
0
0
0
2
0
0
0
1
0
2
2
2
1
1
0
1
1
0
0
0
1
1
0
0
0
0
0
2
0
1
0
0
1
1
1
0
1
0
1
2
0
0
0
0
1
2
0
0
2
2
0
1
1
0
1
1
0
3
0
0
0
2
0
1
0
2
0
1
0
1
0
1
0
1
0
0
2
1
1
2
1
1
0
3
1
0
1
0
1
1
2
1
0
0
0
2
2
0
1
2
2
1
1
1
1
0
0
1
2
0
1
0
1
1
0
2
1
1
0
1
1
1
0
0
1
1
1
0
0
1
0
0
0
1
0
2
2
1
1
0
2
2
1
1
1
2
1
0
0
0
4
0
1
2
2
2
2
0
0
2
0
1
0
2
1
1
1
3
0
2
1
0
0
0
1
0
0
0
1
1
1
0
1
0
0
2
0
1
0
0
0
2
1
0
1
0
0
1
1
0
2
1
0
1
2
0
1
0
0
2
1
0
1
2
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
2
0
1
1
0
1
2
0
0
2
0
0
0
2
0
1
1
0
0
0
1
1
2
0
0
0
2
2
1
1
0
0
0
0
1
1
1
2
1
2
0
2
1
0
0
0
0
0
0
2
1
1
1
0
0
1
0
1
0
0
1
0
0
1
0
0
1
2
0
1
1
0
1
0
2
2
1
1
0
0
2
0
0
0
0
0
1
1
2
1
0
1
1
0
0
0
2
2
0
2
1
0
0
0
2
0
2
0
0
2
1
0
2
1
0
0
2
1
2
1
0
1
1
0
1
0
0
1
1
0
0
1
0
1
2
2
2
0
1
2
2
0
0
1
1
1
1
0
0
1
0
0
0
2
1
2
2
1
2
1
0
1
0
2
1
0
0
1
1
1
0
0
2
1
0
0
1
0
0
0
2
0
0
0
2
0
1
1
0
2
0
1
1
1
2
0
2
0
0
0
0
1
2
0
1
2
2
0
2
2
1
1
0
1
2
0
0
2
2
2
0
1
1
0
1
0
1
0
1
0
0
0
1
0
0
1
0
1
1
0
0
0
1
0
0
1
0
0
0
2
0
2
0
0
0
0
2
2
0
1
0
1
0
0
1
9
0
1
2
2
1
1
0
2
0
0
2
2
0
1
0
1
0
0
1
0
1
2
2
0
0
0
2
0
1
2
1
1
2
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
1
2
0
0
0
0
1
1
1
1
1
1
1
0
0
1
2
0
2
0
1
0
1
0
2
0
0
2
0
3
1
0
1
1
0
2
1
8
1
0
2
2
1
2
2
0
0
1
1
0
1
1
2
0
2
0
1
0
0
0
2
0
1
1
2
0
0
0
0
1
2
0
2
0
0
0
1
1
0
2
2
1
2
1
1
0
0
0
2
0
1
0
1
1
2
2
0
0
1
2
1
0
1
1
0
0
1
1
1
0
0
0
2
3
0
2
0
2
2
2
0
1
0
0
1
0
0
2
0
2
0
0
0
0
2
0
2
2
2
0
1
0
0
1
1
1
0
1
1
0
2
0
2
5
2
1
0
0
0
0
1
0
0
0
1
2
0
2
1
0
2
0
0
2
0
1
0
1
2
1
0
2
0
0
2
2
2
2
1
2
1
0
1
1
1
0
1
1
0
1
0
0
0
1
1
0
0
2
0
0
1
2
0
0
0
1
1
1
0
0
2
0
0
1
0
0
0
2
0
2
0
1
1
2
2
1
1
0
1
1
0
1
2
1
1
1
0
0
0
1
2
0
1
0
0
0
0
1
1
0
3
2
1
1
1
1
2
0
1
2
1
0
2
0
2
2
1
1
0
1
0
0
1
1
1
1
2
1
0
0
0
2
0
2
1
2
1
0
0
1
0
0
0
2
0
0
1
0
0
4
1
0
1
2
2
0
0
0
0
1
0
0
1
1
0
0
0
1
0
1
2
0
2
1
1
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
1
1
0
1
2
0
3
0
0
1
1
1
0
1
2
1
1
1
2
0
0
2
1
1
1
2
0
0
1
7
0
0
1
0
0
2
0
0
0
1
0
0
1
2
1
0
2
0
1
0
0
0
2
0
0
1
0
1
0
0
1
1
1
1
2
0
0
1
0
1
0
0
0
1
0
2
2
2
0
1
1
0
1
1
0
0
0
0
2
0
1
1
1
1
2
1
2
0
1
2
1
1
1
0
0
0
1
0
1
1
1
1
4
2
2
1
0
0
1
0
2
1
1
2
0
0
2
1
1
0
1
1
0
0
2
0
0
2
0
2
1
1
0
1
0
1
1
0
0
1
1
0
0
2
1
2
0
0
1
0
0
0
0
1
1
2
0
0
1
0
0
1
0
1
3
2
1
2
0
2
2
0
1
3
1
1
0
1
0
0
0
1
2
1
1
2
2
2
2
0
1
0
0
2
0
0
0
1
1
0
1
2
1
0
1
1
2
2
0
0
1
0
0
1
1
0
1
2
0
0
3
1
0
0
1
0
1
0
0
0
2
0
2
0
1
2
1
1
0
0
3
0
2
0
1
1
0
1
0
0
2
2
0
0
4
0
0
1
0
0
0
0
6
0
2
2
0
0
2
3
0
1
1
1
2
1
0
4
1
0
2
0
1
0
2
0
0
0
0
1
1
1
1
1
1
1
2
0
0
2
0
1
0
3
0
1
0
0
0
1
0
0
0
1
0
1
0
1
2
0
0
0
2
1
1
1
0
0
1
0
1
1
1
1
1
1
0
0
0
2
1
1
2
1
1
0
0
0
0
2
2
2
0
2
4
1
0
0
0
2
1
1
2
2
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
2
1
2
1
0
0
2
1
1
0
1
0
0
1
2
2
1
2
0
0
1
0
0
0
0
0
1
1
0
2
1
2
1
2
0
0
1
2
0
0
0
1
0
1
1
2
1
2
1
0
2
1
0
0
1
0
1
2
0
0
2
0
1
1
2
1
1
1
0
0
2
0
2
0
2
0
1
0
0
2
0
1
1
1
2
1
1
1
0
1
0
0
1
0
2
1
0
1
0
1
0
0
1
1
0
1
2
1
0
1
1
0
1
1
1
0
0
0
0
0
2
0
1
0
2
0
0
1
1
2
0
2
0
1
1
2
2
0
0
2
1
1
0
0
0
1
2
0
1
0
0
1
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
1
1
1
1
1
1
1
2
0
1
2
0
2
0
1
1
1
1
1
0
1
1
2
2
2
0
0
2
2
1
1
0
1
0
0
2
0
0
0
1
1
1
0
0
2
1
0
1
0
0
2
0
2
1
0
1
1
0
1
0
3
1
0
1
1
0
2
1
0
2
1
1
1
0
1
2
1
1
0
1
1
0
1
2
1
1
1
2
0
0
1
0
1
0
1
2
0
0
1
0
2
2
1
1
1
0
2
1
2
2
2
0
0
2
0
1
0
2
0
2
0
0
0
0
0
1
1
2
2
2
0
1
0
0
0
1
1
1
1
0
0
1
0
2
2
0
0
1
0
1
1
2
0
0
1
0
2
0
0
1
2
1
0
0
1
0
2
2
2
1
0
2
0
1
2
0
0
2
2
0
0
2
0
0
0
0
0
1
1
1
2
1
1
0
0
0
0
1
2
2
1
2
0
2
1
0
2
0
1
0
1
0
0
2
0
0
2
2
2
2
0
1
2
0
2
0
1
0
2
0
0
1
0
0
0
2
1
1
1
0
1
2
0
1
2
1
2
2
0
0
2
2
0
2
1
1
0
2
1
1
0
0
1
2
2
0
3
1
2
0
2
0
1
0
0
2
0
2
0
1
0
2
1
2
1
2
1
0
0
0
1
2
0
0
1
1
2
0
0
0
1
0
0
2
1
0
2
2
1
0
2
0
1
1
0
1
0
1
2
0
1
0
0
0
0
0
1
3
1
1
1
2
0
2
0
0
0
0
0
2
0
2
1
1
0
1
1
2
0
0
2
1
0
1
0
1
0
2
0
0
0
1
1
0
2
1
1
2
1
1
2
2
1
0
1
0
2
1
1
0
0
0
2
1
1
1
1
0
1
0
0
1
0
2
0
0
0
1
1
0
0
1
0
4
2
2
1
1
1
0
1
0
0
0
1
0
0
1
2
0
1
0
0
0
0
0
0
1
0
2
1
1
0
0
0
2
2
0
0
2
2
0
0
0
0
0
0
1
1
1
0
0
2
0
1
0
1
0
0
1
0
0
3
2
0
1
1
0
1
0
0
0
3
1
1
1
1
0
0
0
1
0
0
1
1
0
2
0
2
1
2
2
1
0
0
0
1
1
0
0
0
1
2
0
1
2
0
0
1
0
2
0
4
0
0
0
0
0
1
1
2
2
1
2
2
2
2
1
2
0
0
2
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
2
1
2
0
0
1
0
0
1
0
1
3
1
0
0
3
0
1
2
0
0
0
1
2
2
2
1
0
2
0
0
2
1
0
1
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
1
1
2
0
0
0
1
1
0
0
0
0
0
1
2
2
0
2
1
1
1
4
0
1
2
1
0
0
1
0
1
4
2
0
0
0
1
0
0
0
1
1
0
1
1
0
0
0
0
2
1
0
0
0
1
1
1
3
1
1
0
1
1
0
0
1
1
1
1
0
1
1
1
3
2
1
2
0
0
1
1
2
0
2
0
2
0
0
2
1
0
0
1
0
1
1
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
1
2
1
0
1
2
2
2
1
0
0
0
2
2
0
0
1
1
0
0
2
0
1
1
0
1
0
1
1
1
1
2
1
1
0
0
1
0
1
2
0
1
1
1
0
1
2
1
1
0
0
1
0
2
0
3
1
2
0
1
0
0
1
2
1
0
1
1
1
1
0
2
1
2
1
0
0
1
2
0
1
1
0
0
0
1
1
0
2
0
0
0
0
1
0
2
1
0
0
1
0
0
2
1
1
0
1
0
1
0
1
0
1
0
0
0
0
0
1
2
0
0
0
2
2
0
1
0
1
1
0
0
2
0
2
0
0
0
0
0
0
2
1
1
2
2
2
0
0
0
2
1
0
1
1
0
0
0
1
1
0
2
1
2
0
2
0
2
1
0
1
2
1
0
0
1
0
0
2
0
0
2
0
0
1
2
1
0
1
2
2
0
2
0
1
0
2
0
1
0
0
0
1
1
1
1
0
1
2
0
0
2
0
0
2
0
1
0
0
2
1
0
0
2
1
0
1
0
1
1
0
0
1
2
0
2
1
1
2
1
1
1
1
0
1
0
1
1
2
1
1
2
1
0
2
0
2
0
1
1
1
0
0
1
1
0
0
1
0
2
1
1
0
0
0
0
0
0
2
0
1
1
1
2
3
0
0
0
0
0
1
2
1
1
1
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
1
1
0
1
0
2
0
2
0
1
0
2
1
0
0
1
1
1
1
1
2
0
0
2
1
3
1
0
2
0
2
0
0
1
1
2
0
1
0
0
2
1
0
1
4
0
1
1
0
0
1
1
1
0
0
0
1
1
1
0
1
2
1
0
0
1
0
0
0
0
0
1
0
2
2
2
0
1
2
1
1
1
5
0
2
0
0
0
0
0
2
2
2
2
2
1
0
2
1
0
0
0
1
2
1
1
0
1
1
1
0
2
1
1
2
1
1
2
0
0
2
1
1
1
1
0
1
1
0
1
0
0
0
2
1
1
1
0
0
1
0
0
2
1
0
0
1
1
0
0
0
0
2
0
1
1
1
1
2
2
1
1
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
2
1
0
0
2
0
2
0
1
1
1
1
1
0
1
0
2
0
0
2
0
0
2
0
0
0
2
0
0
1
2
1
2
1
1
1
1
1
1
0
1
2
2
1
0
1
1
0
0
0
0
0
0
2
1
0
2
1
0
1
0
0
2
0
1
3
0
0
0
0
2
1
0
0
0
1
0
0
2
0
0
1
2
1
0
0
1
0
2
0
1
2
2
0
0
2
0
1
1
0
1
2
0
0
1
0
0
2
2
1
0
0
1
1
1
2
0
0
1
2
1
2
2
1
0
0
0
1
1
0
1
1
0
1
1
0
1
2
1
0
0
1
1
0
0
1
0
0
3
2
1
0
0
0
1
1
1
1
2
1
0
2
0
1
1
2
2
0
1
2
1
2
2
1
0
0
0
0
1
1
2
0
0
0
0
1
1
2
0
0
0
1
0
2
0
0
1
1
0
1
0
0
0
1
1
0
0
0
1
3
0
0
0
0
1
1
1
2
1
1
1
0
0
0
2
2
0
1
1
2
0
1
1
1
0
0
2
1
1
0
0
2
1
1
1
2
0
1
0
1
1
0
0
2
0
1
0
0
0
0
1
1
1
2
0
0
2
2
0
2
0
2
1
1
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
1
1
2
0
0
1
0
1
1
1
1
0
0
0
1
1
1
0
0
0
2
0
2
0
1
0
2
0
0
0
1
1
1
2
2
0
0
0
2
1
2
2
2
1
0
2
0
2
2
5
0
2
0
0
1
1
2
0
0
1
0
0
0
1
0
1
0
0
1
1
0
1
0
1
0
2
1
1
1
2
1
1
0
0
1
0
0
1
2
1
0
0
0
5
0
2
1
2
0
1
2
1
1
1
2
1
2
2
1
1
1
0
0
0
1
1
2
1
2
0
1
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
1
2
0
1
0
1
1
0
0
3
1
1
1
0
1
0
3
0
1
2
1
0
2
0
3
0
0
2
2
0
1
2
0
0
1
2
1
0
0
1
2
1
0
1
1
1
0
1
0
2
2
1
0
2
2
1
0
1
0
0
1
1
0
1
0
1
1
1
1
1
0
1
2
1
0
0
0
0
1
2
2
1
0
0
2
0
0
0
2
0
2
2
2
0
1
1
0
0
1
0
1
0
0
1
2
1
0
2
1
0
0
2
0
1
0
2
1
1
0
1
2
2
2
0
2
1
3
2
0
0
0
0
1
1
1
0
0
1
1
0
0
2
0
0
1
0
0
1
1
1
1
1
2
2
2
0
0
2
2
0
1
1
1
0
0
1
2
0
0
0
2
0
0
0
1
0
0
1
1
1
0
1
2
0
0
0
1
0
1
0
0
0
2
2
0
0
0
2
1
0
2
0
1
0
1
1
0
0
0
0
1
1
2
1
0
1
1
0
1
1
2
0
0
0
1
1
0
0
2
0
0
0
1
2
2
1
0
0
0
0
2
0
1
0
0
1
1
1
1
0
2
0
1
1
2
0
0
2
1
1
1
1
1
0
0
0
2
3
0
2
2
1
0
2
2
0
0
2
0
0
0
0
0
1
1
2
1
1
0
1
1
0
0
0
0
0
0
0
1
0
3
0
1
2
1
0
2
1
0
1
0
2
0
0
2
1
1
0
0
0
1
0
1
2
2
0
1
2
0
0
2
2
0
0
0
2
0
0
3
4
1
0
1
0
1
1
1
2
2
1
0
1
0
0
0
1
1
2
2
1
2
2
2
1
1
2
2
2
2
2
0
1
0
1
2
0
1
1
0
2
0
0
0
0
0
0
1
0
2
0
0
0
2
2
0
0
1
1
1
2
0
0
0
0
1
1
1
1
2
0
1
1
1
2
0
0
1
0
1
0
2
1
0
0
1
1
2
0
0
2
1
0
1
1
1
0
2
2
0
2
1
0
1
0
0
0
1
0
2
1
0
1
1
1
1
0
0
1
1
0
2
0
2
1
0
1
1
2
0
1
3
0
1
0
0
1
0
0
0
0
1
0
2
1
0
1
1
0
1
0
1
0
1
0
0
0
0
0
0
1
2
1
0
1
1
1
1
0
0
0
1
1
1
2
0
0
1
1
1
0
2
0
2
2
1
0
2
1
0
0
1
1
1
0
2
2
0
0
0
1
0
2
0
2
0
1
2
1
0
2
1
1
1
3
0
0
1
1
1
0
0
1
1
1
1
2
2
0
1
0
2
1
0
0
1
1
0
0
2
0
2
0
0
0
0
0
1
0
1
2
1
2
0
0
2
1
0
1
2
0
1
0
1
0
0
0
1
1
2
1
0
0
0
0
1
0
1
0
2
2
0
0
2
2
3
2
0
0
0
0
0
0
2
0
0
0
1
2
0
1
1
0
0
1
0
0
0
0
0
0
2
0
2
2
0
1
1
1
1
0
1
1
0
1
0
1
2
2
1
0
1
0
2
2
2
1
2
0
1
0
0
0
1
0
0
0
0
2
0
0
0
2
1
1
0
0
2
0
1
1
1
0
1
1
1
0
0
0
1
1
1
0
0
1
1
0
1
1
0
0
0
1
1
1
0
0
0
0
0
1
0
1
0
2
0
1
1
1
0
2
0
1
0
0
1
1
2
1
0
2
0
0
0
0
1
1
2
0
2
0
1
0
0
1
2
1
0
0
1
1
2
0
0
3
0
0
0
0
2
1
2
0
0
0
0
0
0
0
1
2
0
2
0
1
0
0
1
1
0
0
1
1
0
2
2
1
1
0
1
2
1
1
1
2
0
1
0
0
2
0
2
1
2
0
1
2
0
0
0
1
0
1
0
0
2
1
0
0
1
0
1
0
0
0
1
0
0
0
2
1
0
0
1
1
0
2
0
1
0
0
0
2
1
0
0
1
0
2
0
0
0
1
2
1
0
0
2
1
0
0
2
0
1
0
0
0
0
0
1
2
0
1
0
1
1
2
0
0
1
2
0
2
1
2
1
2
0
2
1
1
0
0
1
0
0
1
0
1
1
0
0
0
1
1
0
0
0
0
1
0
0
0
1
2
0
2
1
0
0
1
0
1
1
1
0
0
1
0
2
1
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
1
0
0
0
1
0
0
1
0
0
1
1
0
2
0
2
1
0
1
0
1
1
0
0
2
0
2
1
1
2
0
2
1
1
0
0
1
2
2
0
0
2
2
2
0
0
0
1
2
0
0
0
4
1
1
2
0
0
2
2
2
0
2
0
0
2
0
0
1
1
2
0
2
1
1
2
1
0
0
1
0
0
1
3
2
0
0
0
0
0
1
2
0
0
0
0
1
1
2
2
0
1
2
1
1
1
1
0
1
1
0
1
0
1
26
0
0
0
1
0
0
0
0
0
0
0
1
1
1
1
2
0
1
0
0
0
0
2
0
1
2
0
0
0
2
2
2
2
0
0
2
0
1
0
1
1
3
4
1
0
2
1
0
3
0
0
0
1
0
1
1
0
1
2
2
1
0
2
1
1
2
2
1
0
1
1
0
2
0
2
1
0
2
0
2
0
0
1
0
1
0
0
2
0
0
1
2
0
0
0
0
0
1
2
0
2
2
1
1
0
0
1
0
1
0
2
1
0
0
1
2
4
4
0
3
2
1
0
0
0
1
2
1
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
2
1
0
2
2
2
1
1
2
1
0
1
0
2
1
0
2
0
1
1
1
3
1
1
2
0
1
2
2
0
0
2
2
2
0
2
1
0
0
0
1
1
0
0
0
1
1
1
0
1
1
2
1
2
2
0
2
1
0
2
1
3
3
1
1
1
0
2
2
2
0
1
2
0
1
0
0
1
0
1
1
1
1
1
0
1
1
0
0
3
1
0
3
0
0
1
1
1
2
1
7
1
1
1
1
2
1
2
2
1
0
0
1
0
0
0
4
1
2
0
1
2
1
0
2
0
0
0
0
1
2
0
2
1
0
0
0
2
0
2
1
0
2
0
0
0
1
0
0
1
2
2
2
1
1
1
1
1
0
1
0
2
0
0
2
0
0
0
0
1
0
1
0
1
2
0
2
2
1
0
0
1
1
1
1
1
2
0
0
2
1
0
2
1
2
0
3
2
1
3
2
1
1
2
1
0
1
0
0
2
0
0
1
0
0
2
0
0
2
1
1
2
2
0
1
0
1
1
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
2
0
1
2
0
1
0
1
1
0
1
1
1
2
2
2
1
1
2
1
0
2
0
0
1
0
0
2
1
1
2
2
2
0
2
3
1
1
0
0
2
1
0
1
0
3
0
2
0
2
2
0
3
2
1
0
1
1
0
1
0
0
0
1
1
0
1
2
1
1
0
2
1
0
2
2
0
2
1
0
0
0
0
1
1
1
2
0
0
2
0
1
0
0
1
2
1
2
0
0
1
1
0
0
0
0
0
0
1
1
2
0
1
2
2
0
1
0
0
0
1
2
2
1
2
0
2
0
0
1
1
1
1
0
1
3
0
0
0
1
1
1
0
0
0
0
0
1
0
2
1
3
0
2
1
0
1
0
0
2
1
1
2
2
1
0
2
0
1
1
0
1
0
1
0
1
0
1
1
0
0
1
0
0
1
1
0
0
1
0
1
1
1
0
2
0
0
1
2
1
0
2
0
1
0
2
0
1
1
1
2
0
2
1
1
0
1
0
0
1
1
2
0
2
1
0
1
0
2
2
0
0
0
0
2
0
0
0
1
1
1
0
1
1
1
1
0
1
1
0
0
0
2
0
0
2
0
0
1
0
2
0
0
0
1
0
1
2
0
2
0
1
0
2
1
0
0
2
1
0
0
0
0
0
0
0
1
0
1
0
1
0
2
0
0
0
1
2
1
2
0
0
0
1
0
2
0
2
2
1
0
1
2
0
3
1
0
2
1
1
0
0
1
0
0
2
1
0
0
1
1
1
0
0
0
0
2
1
1
0
2
2
0
0
0
0
0
0
0
3
1
0
1
0
1
1
3
1
1
0
0
0
1
2
0
1
0
0
3
0
0
0
1
2
0
1
0
1
2
1
1
2
0
2
0
1
2
1
0
0
2
0
0
2
1
0
0
0
1
0
0
2
1
0
1
1
0
1
1
0
0
2
2
2
1
0
0
1
1
0
0
0
2
1
2
0
0
0
0
0
0
1
0
1
0
2
1
2
1
0
2
0
1
1
1
0
1
0
1
1
2
0
0
0
0
0
0
0
2
1
1
1
0
0
1
0
0
1
1
2
3
1
1
1
0
1
0
1
1
2
0
0
0
0
1
0
2
0
2
1
0
1
2
2
1
1
2
1
0
0
0
1
2
0
0
2
1
0
2
2
1
0
0
1
0
2
2
0
1
2
0
0
0
0
1
2
1
2
0
2
0
2
2
0
2
1
1
2
1
0
0
1
2
1
2
0
0
0
0
1
2
0
2
0
2
1
1
2
1
0
0
2
0
0
3
0
1
0
0
2
0
3
0
1
2
1
1
0
0
2
2
0
0
2
0
2
0
0
0
0
2
0
0
1
1
0
1
1
1
1
2
0
2
1
1
2
0
2
1
1
1
0
0
1
0
2
1
0
1
1
1
0
0
0
0
2
0
1
1
0
1
1
2
0
0
0
2
2
1
1
1
1
0
2
1
1
1
2
0
2
2
0
0
2
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
3
2
0
2
0
0
2
0
0
1
2
0
2
1
0
1
2
2
0
1
2
1
0
1
1
1
2
0
0
2
0
1
0
1
1
0
0
1
0
1
0
0
2
1
0
1
1
0
0
0
2
2
3
2
2
0
1
3
0
1
2
2
0
0
0
4
0
1
0
1
1
0
1
2
1
0
0
0
2
1
0
1
2
0
1
2
2
0
2
1
2
1
0
2
2
0
2
0
1
0
0
1
0
2
0
1
1
1
1
0
0
0
1
0
0
1
1
0
0
1
0
2
1
1
1
1
1
0
2
1
0
0
0
0
1
0
1
4
0
0
1
0
0
1
1
0
0
0
0
2
1
0
0
2
0
1
0
0
3
1
0
0
1
1
1
2
0
1
2
0
0
0
1
0
0
0
3
0
0
2
3
0
1
2
1
0
0
0
0
0
1
0
0
2
0
2
1
0
1
0
0
1
0
1
2
1
2
0
2
0
0
1
0
0
1
1
1
1
2
0
1
2
2
0
0
0
1
0
1
0
1
0
2
0
0
0
1
1
1
2
0
0
1
2
1
0
0
0
0
0
0
1
1
0
0
3
0
1
0
2
1
1
1
1
1
2
1
1
0
1
0
2
1
2
0
3
2
0
0
0
0
0
1
1
1
1
0
0
2
1
0
0
0
0
0
2
0
0
0
1
1
1
2
0
1
1
1
0
2
0
0
0
1
0
2
2
1
0
0
2
2
2
2
0
0
0
2
2
1
0
1
0
1
1
0
0
0
0
2
0
1
2
0
2
3
2
0
0
1
0
0
1
0
1
0
1
0
2
1
1
0
0
0
2
0
2
2
1
2
2
0
1
0
2
1
0
1
0
0
2
1
2
2
0
0
0
1
1
0
2
1
1
0
0
0
0
0
0
1
0
1
1
2
1
0
2
1
1
2
0
0
0
2
1
0
1
0
1
0
2
0
0
1
1
1
0
1
0
2
0
1
0
1
0
1
0
1
1
0
0
2
1
2
0
0
2
0
0
1
2
1
1
0
1
1
0
2
3
0
1
2
1
0
0
0
0
1
0
0
0
1
0
0
3
0
2
2
1
2
1
0
0
1
0
0
0
0
2
0
0
1
0
2
2
3
2
0
0
1
0
1
1
1
2
1
0
0
0
0
1
1
0
2
0
1
0
0
2
1
0
0
1
1
1
3
0
2
1
1
0
2
0
0
0
0
0
2
0
0
2
1
1
0
2
1
0
0
0
0
0
2
2
1
3
2
1
0
0
0
1
0
0
0
1
0
1
1
2
0
1
0
0
0
0
2
1
0
1
0
0
0
0
1
0
2
1
2
1
0
0
0
0
0
0
1
1
1
2
0
0
1
0
0
2
1
0
0
0
1
2
0
1
1
0
0
2
2
0
0
2
0
2
0
0
1
0
1
0
1
2
0
0
0
1
0
0
2
1
1
1
1
1
2
0
1
2
0
1
1
2
1
1
2
1
2
0
0
0
1
0
1
1
1
1
0
0
1
0
2
2
1
0
0
1
2
0
1
0
3
1
2
2
1
1
1
2
1
1
1
0
0
2
2
3
2
0
0
0
0
0
2
0
1
0
1
1
1
0
2
2
2
2
0
1
0
2
0
1
0
0
1
0
0
0
2
2
0
1
0
1
1
0
0
0
2
1
0
1
0
0
0
0
0
0
0
1
1
1
1
0
2
1
0
0
0
0
0
2
2
1
1
0
0
0
1
1
2
1
2
1
1
1
0
0
0
2
0
0
1
1
0
1
0
2
0
0
1
0
0
0
0
1
1
0
0
0
2
0
2
0
0
2
2
0
1
0
0
0
2
1
1
2
0
1
1
0
0
2
0
0
1
1
0
0
0
2
0
0
0
0
1
2
1
1
0
0
0
1
1
0
1
2
2
1
1
0
2
0
0
0
2
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
1
0
2
0
1
0
1
1
1
1
1
1
0
0
0
2
1
2
1
2
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
1
1
2
0
1
3
1
1
0
2
0
0
2
0
2
0
0
1
0
0
2
4
2
2
0
2
2
0
1
0
0
0
1
2
1
2
0
1
1
1
0
0
0
1
0
0
1
0
2
1
0
1
0
0
1
0
0
0
1
0
2
0
1
0
1
3
0
1
0
1
0
0
2
2
0
0
0
1
1
0
1
0
1
1
0
0
1
3
1
0
1
0
0
3
0
0
0
2
1
1
1
1
1
1
0
1
0
2
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
1
2
0
1
2
0
0
0
2
0
1
2
2
1
0
0
0
1
1
0
0
0
1
0
0
2
1
0
1
0
2
0
1
2
0
0
0
0
4
0
0
0
1
2
1
0
1
1
0
0
1
0
2
0
1
1
1
2
2
1
0
1
1
1
2
1
0
0
2
2
0
1
2
1
0
0
0
0
0
1
2
1
0
1
2
2
0
0
1
2
1
0
0
0
1
2
2
0
1
0
0
0
2
2
2
0
2
0
0
2
0
0
2
0
0
1
0
2
1
1
1
1
1
2
1
0
1
0
0
0
0
2
1
0
0
0
1
2
0
0
0
1
2
1
0
0
1
0
0
1
0
2
0
2
0
0
0
2
2
1
2
0
0
2
1
0
0
0
0
1
0
1
2
0
2
0
0
1
1
0
1
0
0
0
3
0
1
0
1
2
0
0
2
0
1
1
1
1
1
2
0
1
0
1
2
0
5
0
2
1
0
2
0
0
1
1
1
2
2
0
0
0
2
3
2
0
2
0
0
0
0
0
1
1
1
1
1
0
0
1
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
2
0
2
2
1
0
0
1
0
0
1
0
2
0
1
1
1
1
2
1
0
0
0
0
0
0
1
1
0
1
2
0
2
0
1
0
0
0
0
0
1
0
2
0
1
0
0
0
3
0
1
1
0
0
0
2
0
0
0
0
1
1
1
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
2
1
0
1
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
2
0
1
1
2
0
4
0
1
0
0
1
1
0
0
2
0
0
0
0
0
2
1
0
2
1
0
0
1
0
0
0
0
1
0
0
0
0
3
1
0
1
2
0
0
1
0
1
0
1
0
0
2
0
2
0
1
2
0
0
0
2
1
0
1
0
0
0
2
1
1
0
0
0
2
0
3
1
2
0
0
0
1
1
1
0
1
0
1
3
1
2
0
0
1
1
1
1
1
0
0
0
0
0
2
2
1
2
2
2
1
2
0
0
2
1
0
0
0
0
1
1
0
2
1
0
0
0
2
1
2
2
1
0
0
1
2
0
2
2
2
0
0
0
0
1
1
0
0
1
1
2
1
2
1
1
2
0
1
1
0
1
1
0
0
1
0
0
2
0
2
1
0
1
1
2
0
2
2
1
0
3
2
0
0
0
0
1
0
2
1
2
1
0
2
0
1
0
2
1
1
0
1
1
0
2
1
0
2
1
0
0
3
1
2
2
1
3
1
0
1
0
1
2
0
1
1
1
1
0
2
2
0
1
1
0
1
0
0
1
2
2
0
0
0
2
1
0
0
1
0
0
0
2
1
0
1
2
1
2
2
1
0
0
1
1
1
0
0
0
0
0
1
1
0
1
1
1
0
1
1
1
0
1
3
1
2
0
0
2
0
2
0
0
0
1
0
0
2
1
1
1
1
0
0
2
0
0
1
0
1
0
1
0
0
0
4
1
1
1
4
0
0
1
1
0
1
2
0
1
2
0
2
2
0
2
2
1
0
0
1
0
0
1
1
0
0
2
0
2
2
1
0
1
1
1
2
2
0
2
2
1
0
1
2
0
2
0
1
1
2
0
0
0
1
2
1
1
2
1
0
2
1
0
0
0
1
0
1
1
2
0
2
1
0
0
1
0
1
0
0
0
0
5
0
3
0
0
2
3
0
3
1
0
1
0
2
1
1
1
0
2
0
2
1
0
0
0
0
1
2
1
2
0
1
0
0
2
1
2
2
0
2
1
0
2
1
1
2
1
2
1
1
0
0
0
1
0
0
1
0
1
2
0
2
2
0
2
1
0
0
0
0
0
1
0
1
0
0
0
2
0
1
1
0
0
2
1
0
2
0
1
0
1
0
1
1
0
0
0
1
1
0
1
2
0
1
2
0
2
1
0
1
0
0
0
1
0
2
2
1
1
1
0
2
1
0
0
0
0
1
0
1
0
1
0
2
0
1
0
0
1
2
2
2
0
1
1
1
1
0
0
1
2
0
0
2
1
2
1
0
0
0
1
1
0
1
1
0
0
1
1
0
2
3
2
1
2
1
1
1
0
2
1
2
10
2
0
0
0
0
0
1
0
0
1
2
2
1
0
2
0
1
0
0
2
0
0
0
1
1
1
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
2
0
3
0
0
1
1
0
0
1
0
2
0
0
2
0
1
1
1
2
3
0
1
1
0
1
0
0
6
0
0
1
1
2
1
0
1
0
1
0
1
2
0
1
0
0
0
2
1
2
0
2
2
1
0
0
1
1
0
2
0
1
0
0
0
1
0
1
2
2
0
1
1
0
2
2
1
1
1
2
1
2
1
0
2
1
1
1
0
0
1
0
0
1
0
1
2
0
0
1
1
1
0
1
1
2
1
1
0
1
1
2
1
0
0
1
0
2
2
2
1
0
2
2
1
1
2
1
1
1
1
0
2
0
2
0
0
1
1
0
2
2
0
2
0
0
2
0
0
0
0
1
0
0
0
1
0
0
2
0
2
1
1
1
1
0
0
2
0
1
2
0
2
2
2
0
1
1
1
1
0
1
0
1
1
1
0
0
2
2
1
1
0
0
1
0
2
1
2
0
1
1
0
0
0
0
1
1
0
0
2
1
0
0
2
0
2
0
1
0
0
1
2
1
3
2
3
0
2
0
0
0
1
0
1
2
1
1
0
2
0
1
0
2
2
0
1
2
1
1
0
1
0
1
2
1
0
2
1
0
0
0
1
2
0
0
1
0
0
2
0
0
0
2
2
0
0
1
0
0
0
1
1
0
0
2
2
0
0
0
1
2
1
0
1
0
0
0
2
0
0
0
2
2
0
1
2
1
1
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
2
0
2
0
1
1
1
1
2
0
1
0
1
1
0
0
0
1
1
2
2
0
2
1
1
2
5
1
0
1
1
0
0
0
2
1
1
0
2
0
1
0
1
1
0
1
0
1
2
1
1
1
2
1
1
0
1
0
0
0
0
0
0
0
1
0
1
2
1
1
1
1
1
1
1
0
0
2
0
1
3
1
1
2
1
1
1
0
1
0
0
0
0
0
1
1
0
2
2
2
0
0
0
0
0
0
2
1
0
0
1
2
0
0
0
1
2
0
1
0
0
2
0
0
0
0
0
2
2
0
0
0
2
0
2
1
1
0
0
1
0
0
1
1
0
2
0
1
1
0
0
1
0
0
1
1
2
0
0
1
1
0
3
1
2
0
0
0
0
2
0
1
0
0
0
0
1
0
1
1
0
1
0
1
1
0
0
1
0
1
1
1
0
0
0
1
0
2
1
1
2
2
0
0
2
2
2
0
2
0
1
0
0
1
2
1
2
1
1
2
0
2
3
1
2
0
0
0
0
2
3
1
0
0
2
1
1
1
2
1
0
3
1
1
0
0
0
0
1
2
1
2
1
0
0
0
1
1
1
0
1
1
0
2
1
1
0
0
1
2
2
2
0
1
0
2
1
2
0
1
2
1
0
0
1
0
0
1
1
2
1
0
1
1
1
2
2
0
2
1
1
0
1
0
1
0
0
2
1
1
0
0
1
0
1
0
1
1
1
0
1
0
1
0
0
0
0
0
2
0
2
2
0
0
0
1
1
0
1
1
2
0
0
0
2
1
0
0
0
1
0
1
2
0
1
2
1
0
2
1
0
2
0
0
2
0
2
0
0
1
0
0
0
0
1
1
0
0
1
2
0
0
1
1
2
2
0
4
2
1
4
0
0
2
1
0
0
1
0
0
2
2
1
1
0
3
1
0
1
0
0
1
2
1
0
0
0
1
1
1
2
1
2
0
0
2
2
1
4
2
1
1
2
2
0
0
0
2
2
0
1
0
0
1
1
1
3
1
0
1
0
2
1
0
0
0
2
2
0
1
1
1
0
0
1
0
1
1
0
6
1
0
0
2
0
0
1
1
1
2
0
1
2
0
2
0
0
1
0
1
0
0
1
0
0
2
2
2
2
2
1
0
0
2
1
0
0
0
1
0
1
1
0
2
0
2
0
0
1
0
2
0
0
1
1
2
0
2
1
1
1
1
0
0
2
2
0
1
0
0
2
2
0
0
3
1
2
1
0
0
0
1
1
1
2
0
0
0
1
0
2
0
1
0
1
0
0
4
1
0
0
1
1
1
1
0
0
1
0
2
3
0
0
0
1
0
0
1
1
1
1
1
1
2
2
1
0
0
3
1
0
0
1
1
0
2
1
1
0
1
2
1
0
2
2
0
1
0
1
0
0
1
3
2
1
3
2
1
1
0
2
1
2
0
0
0
0
1
2
0
1
0
0
3
0
2
2
2
0
0
0
0
1
0
1
1
0
0
2
2
0
0
2
0
0
0
2
2
1
1
1
2
0
0
0
0
0
0
1
1
0
2
1
1
0
1
2
1
2
0
0
2
1
1
0
0
0
0
0
1
0
1
1
2
0
0
1
0
1
0
1
1
0
0
1
1
1
0
0
1
1
2
1
2
0
2
0
1
0
2
0
2
2
4
0
0
0
1
2
1
2
1
2
0
2
0
1
0
0
0
2
2
2
2
0
0
1
2
0
1
1
0
0
0
2
0
1
0
2
2
0
1
0
2
0
2
0
1
1
0
0
1
0
1
2
0
1
0
5
1
1
1
1
2
1
1
2
1
0
0
0
0
1
1
2
0
0
0
0
1
0
2
2
0
1
0
1
0
1
2
0
0
0
2
0
0
2
2
2
1
2
0
0
0
2
2
1
1
1
0
2
1
2
0
0
1
1
0
1
0
1
0
2
0
1
1
0
1
1
0
0
0
1
1
0
1
0
1
1
0
0
2
1
1
2
0
1
1
0
1
1
2
2
0
1
0
2
1
1
1
0
1
0
1
0
2
2
1
0
2
0
0
0
1
0
2
0
2
1
2
1
2
0
1
1
1
1
1
2
0
1
0
0
2
2
2
1
1
2
2
0
0
0
2
2
0
0
0
0
1
2
0
0
0
0
0
2
2
1
1
1
0
0
0
0
0
2
1
1
0
1
2
2
1
2
0
0
2
0
1
2
0
0
1
0
0
0
0
1
2
1
2
0
2
0
1
2
0
2
0
0
1
1
0
1
1
2
1
0
0
0
2
1
0
0
0
1
0
0
0
1
0
0
2
1
0
0
2
0
0
1
0
1
1
0
0
0
1
2
1
0
3
0
1
1
2
1
1
2
1
2
0
2
1
0
1
1
2
0
0
0
1
1
1
1
2
0
2
1
0
0
1
2
1
0
0
1
0
1
0
0
2
0
1
2
1
0
0
2
0
0
1
0
0
0
2
0
1
0
2
0
0
0
0
2
0
0
1
0
4
0
1
0
2
1
0
2
2
0
1
2
1
1
0
2
2
0
2
2
0
2
1
2
0
0
0
2
1
2
2
0
1
1
0
0
0
0
3
2
2
0
0
0
0
2
0
0
3
0
0
1
1
2
0
0
1
1
1
2
0
0
2
2
1
1
0
2
0
0
0
0
0
2
0
0
2
1
0
2
1
1
0
1
0
0
1
1
0
0
1
1
1
1
2
0
1
1
1
2
0
0
0
0
1
1
3
0
1
0
0
0
2
2
2
2
2
0
1
1
1
1
1
0
0
0
0
2
1
2
1
1
0
0
0
1
0
0
1
2
0
1
1
0
2
0
1
1
0
0
0
1
0
0
1
1
1
0
0
2
1
1
0
1
0
1
0
0
0
1
1
0
0
0
2
1
1
0
0
2
1
2
0
0
1
1
0
0
0
2
1
0
0
0
1
1
1
0
0
0
2
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
1
1
0
1
0
1
2
0
1
0
0
0
0
0
0
2
0
1
1
1
0
0
2
0
2
0
0
1
0
1
1
0
2
0
0
1
0
3
1
2
2
0
1
1
0
2
2
2
0
2
1
1
1
0
2
0
0
2
0
0
0
2
1
1
0
1
1
1
1
0
1
0
1
1
0
0
0
1
1
1
1
0
0
1
0
1
0
2
0
0
1
1
0
1
2
0
1
0
3
1
0
0
0
1
0
1
2
0
1
1
1
1
1
0
1
0
2
2
0
0
0
1
0
1
0
0
0
2
1
2
1
2
2
0
0
2
1
1
1
1
0
0
2
0
0
1
0
2
0
0
0
1
0
2
0
0
0
2
1
0
1
0
0
0
1
1
0
0
1
0
2
0
3
0
0
0
2
2
0
2
2
2
1
1
1
0
1
0
0
2
0
1
0
1
0
0
1
1
0
2
1
1
0
0
1
0
1
2
1
0
2
2
1
1
2
2
0
0
2
1
1
1
0
2
2
0
0
0
1
2
0
2
3
0
1
0
0
1
0
1
2
2
1
2
1
1
0
0
0
1
1
0
0
1
1
0
0
1
1
0
2
0
4
2
0
1
0
1
1
0
1
0
0
2
0
0
1
1
0
1
0
2
0
0
0
2
2
1
0
2
1
1
0
0
1
0
1
1
1
1
1
0
0
0
0
0
0
1
1
1
1
1
1
0
0
0
2
0
2
0
1
2
0
0
0
0
0
1
1
0
1
0
0
0
0
2
2
0
2
0
2
0
3
0
1
0
0
1
0
2
0
0
2
0
1
1
1
2
0
0
1
2
3
1
1
1
0
1
0
0
1
2
1
1
0
2
2
0
2
0
0
1
2
1
2
1
1
2
0
0
2
2
1
0
0
0
0
1
0
2
0
0
2
0
2
0
1
0
1
1
2
0
2
1
0
2
0
0
2
1
0
0
1
0
2
1
0
0
2
1
2
0
1
0
0
0
0
1
0
1
1
2
0
1
2
2
2
0
2
2
2
1
1
2
2
1
0
1
1
2
1
0
0
2
3
1
0
2
2
1
1
1
1
0
0
1
0
1
1
2
1
0
2
1
0
2
0
2
2
1
0
2
0
1
0
0
0
1
2
0
1
0
1
0
0
1
1
1
1
2
0
0
2
0
0
0
0
1
2
1
1
0
0
0
0
0
1
0
1
1
1
1
1
0
0
1
0
1
0
2
1
0
0
1
0
0
1
1
2
0
0
2
1
0
0
1
0
0
0
0
1
0
0
2
2
2
1
0
2
2
0
1
0
0
2
4
0
0
0
0
2
1
2
0
0
1
0
0
4
1
1
1
2
1
0
2
0
1
0
0
1
0
1
2
2
0
2
2
0
1
0
1
1
0
2
2
0
0
1
0
0
1
0
1
1
0
1
0
0
1
1
0
0
2
1
0
0
0
0
1
2
0
0
1
0
2
0
0
1
0
0
0
1
2
2
3
2
1
0
3
0
2
1
2
0
1
0
1
0
0
0
2
2
1
0
0
2
0
0
2
0
0
1
0
1
0
1
1
1
0
1
0
1
0
1
0
0
0
0
1
0
2
0
0
2
1
0
1
0
0
3
0
0
0
0
0
1
0
0
1
0
1
1
1
0
2
1
0
0
0
0
1
2
1
0
0
0
2
2
1
1
0
1
2
1
1
0
0
1
1
1
0
0
1
2
1
2
1
1
0
2
2
0
0
0
2
0
0
0
0
1
1
0
0
2
0
1
0
0
0
1
0
2
1
0
0
2
2
0
0
1
1
1
0
2
0
1
1
2
0
2
1
0
0
0
1
3
0
0
0
0
1
0
1
0
2
0
1
1
1
1
1
1
0
0
1
0
1
0
0
1
2
1
1
2
1
0
0
0
1
0
1
2
2
0
0
0
2
1
0
1
0
2
0
0
0
3
2
0
0
1
2
0
0
0
0
1
1
1
0
0
0
0
2
2
0
0
2
2
0
0
1
1
0
1
1
1
0
1
0
1
1
0
1
2
1
1
1
1
0
1
1
0
0
1
1
1
0
3
0
0
1
1
1
0
1
1
0
0
2
1
2
1
0
0
0
2
0
1
0
0
0
1
1
1
0
2
1
1
1
2
1
0
0
0
0
4
0
1
0
1
1
2
2
2
0
1
1
2
1
1
0
1
1
0
1
1
0
0
1
3
0
1
2
0
1
1
2
0
1
1
1
0
0
2
2
0
1
0
0
1
4
1
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
2
1
1
1
0
0
2
0
0
1
0
1
1
3
0
0
0
1
0
2
1
2
0
1
1
1
0
4
0
0
0
1
2
2
1
1
2
1
1
1
0
0
1
0
0
3
1
0
3
1
1
3
2
0
2
0
0
0
1
1
0
0
2
0
0
3
0
2
1
1
1
0
1
0
2
1
0
0
1
1
0
1
1
1
0
1
0
0
2
1
0
0
1
1
1
1
1
1
2
0
2
2
1
0
2
0
1
1
2
0
0
0
4
2
0
0
1
1
0
0
2
0
1
2
1
2
0
1
0
1
0
2
0
1
0
1
2
0
0
1
2
0
1
0
0
2
2
1
1
0
0
0
0
1
1
2
0
0
1
1
1
0
0
1
0
0
0
1
2
2
2
0
0
0
2
1
1
1
2
0
1
0
0
0
0
1
2
2
1
1
1
0
0
1
2
2
1
2
1
0
0
0
1
3
2
2
0
0
1
2
1
0
0
1
2
2
0
0
2
1
1
0
0
1
1
2
0
0
0
1
0
0
2
1
0
0
2
1
1
1
0
1
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
2
2
2
0
2
1
1
2
1
3
0
2
0
1
0
1
0
2
1
0
0
1
1
0
1
0
1
2
1
0
2
2
1
2
0
2
0
2
0
2
2
1
1
1
0
0
1
0
0
2
0
0
1
0
0
0
2
2
0
2
0
0
0
0
1
1
2
0
1
2
0
0
0
1
0
1
2
1
0
0
0
2
0
0
0
1
1
0
1
2
2
0
1
0
0
1
1
0
2
0
1
0
3
0
1
1
1
0
1
0
1
1
1
2
0
0
0
2
0
2
0
1
0
0
1
3
1
2
1
0
1
2
1
1
1
2
0
0
1
1
2
0
0
2
0
1
1
3
1
0
0
1
0
0
0
2
2
1
3
0
0
0
2
1
0
0
1
1
0
0
0
0
0
0
1
2
2
1
1
2
0
1
0
0
0
1
1
0
0
1
0
0
2
0
0
0
1
4
0
1
1
1
0
0
1
0
0
2
0
0
0
0
0
1
0
1
0
0
2
0
2
2
0
1
0
0
1
0
1
0
0
2
1
0
1
1
1
0
1
2
0
1
0
2
0
1
1
1
2
1
0
0
0
3
0
0
0
2
1
1
1
1
1
1
0
1
2
1
2
1
0
0
0
0
1
0
1
2
2
1
0
2
1
1
0
1
2
2
0
1
1
0
1
1
5
0
2
0
0
2
0
1
1
1
0
2
0
1
0
1
2
1
2
2
3
1
0
0
0
0
1
1
2
0
0
0
0
0
1
0
1
2
1
0
0
2
1
0
0
2
0
2
1
0
0
0
2
1
0
0
1
2
0
1
2
2
0
1
2
1
2
0
0
1
1
1
0
0
0
1
0
0
0
2
0
1
1
1
1
2
0
0
0
1
0
1
0
0
0
2
1
0
1
1
0
2
0
0
1
1
1
0
2
2
1
1
1
1
1
1
1
2
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
2
0
1
2
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
2
1
1
0
2
0
0
1
0
0
0
2
1
2
0
2
2
0
1
2
0
1
0
0
2
1
0
1
0
0
1
0
2
1
0
0
2
0
1
1
0
2
0
0
0
1
1
2
0
0
0
2
2
0
1
0
0
1
1
0
1
2
1
1
1
1
0
1
2
2
1
1
1
1
2
1
2
2
2
0
0
0
0
2
0
2
0
1
0
2
0
0
0
2
0
2
2
0
2
0
0
0
1
0
1
0
0
0
2
0
1
2
1
1
1
0
1
1
0
0
1
2
0
0
0
0
0
1
0
0
0
2
0
0
1
1
1
0
2
0
1
1
0
0
2
0
0
1
2
1
0
0
1
0
1
1
2
2
1
0
0
0
0
0
1
1
0
2
0
2
2
0
1
0
0
0
1
0
1
2
0
0
0
1
1
2
1
0
0
1
0
0
1
0
0
2
0
1
0
0
0
0
0
1
0
1
1
2
0
0
1
1
0
0
0
0
0
1
2
1
1
1
1
0
2
1
1
2
0
0
1
0
1
0
2
0
0
0
0
2
2
0
3
0
1
0
0
0
0
1
1
0
1
2
1
3
0
0
0
1
1
1
0
0
1
0
2
0
0
1
0
1
2
0
0
0
0
0
2
1
0
2
1
0
0
0
1
0
0
2
0
0
2
0
1
0
2
1
1
0
0
0
0
0
0
2
0
1
1
1
0
0
1
0
0
1
1
1
1
0
0
3
2
0
1
1
0
7
0
2
0
1
2
0
2
0
0
2
2
0
2
0
2
0
0
0
0
2
0
1
1
0
2
1
0
0
0
1
0
1
0
1
2
0
0
0
2
2
0
3
2
2
0
1
1
0
1
0
0
0
0
0
2
0
0
1
2
1
0
2
0
1
0
1
0
1
1
1
1
1
0
0
1
0
0
0
0
0
0
2
0
1
0
2
1
2
2
0
0
1
0
0
3
0
0
1
1
0
1
1
2
1
2
0
0
0
0
2
1
1
0
2
1
0
0
2
0
4
0
1
1
2
0
1
2
0
1
0
2
0
0
1
1
3
0
1
1
1
0
0
0
0
1
0
0
2
0
0
0
2
1
0
0
2
2
0
0
1
0
1
2
2
2
2
1
1
0
0
2
2
1
0
0
2
1
2
0
2
2
2
1
0
0
0
0
1
2
1
1
1
0
1
0
2
0
0
2
0
1
2
0
0
1
1
1
2
0
0
0
0
2
1
1
0
0
0
2
0
0
0
1
0
0
1
2
2
0
0
1
2
2
0
2
1
1
0
2
1
0
0
2
2
1
1
0
1
0
0
1
0
0
1
0
1
0
0
1
2
0
0
0
1
0
0
2
1
3
0
1
0
0
0
0
0
1
2
0
2
0
1
0
2
0
1
2
0
0
1
2
0
0
1
0
0
0
0
2
0
1
0
0
1
0
0
1
2
2
2
2
0
1
0
0
0
1
0
1
0
1
2
0
2
1
0
0
1
0
1
0
2
1
0
1
0
0
2
1
0
1
0
0
2
0
1
0
1
1
3
0
2
0
1
0
2
1
3
0
0
2
1
1
2
0
1
0
2
0
2
0
1
1
0
0
0
2
2
0
0
1
0
2
0
1
4
0
2
0
0
2
1
0
1
0
1
2
0
0
0
0
1
0
3
1
1
0
0
0
3
1
0
1
3
1
0
0
0
0
1
0
0
0
0
1
1
2
1
0
1
0
1
0
0
0
0
2
1
0
0
1
0
1
1
2
0
0
1
2
0
0
3
1
2
0
2
2
1
2
5
1
0
0
1
3
1
1
0
0
0
0
1
0
2
0
1
0
0
0
2
0
0
2
2
2
0
2
1
2
0
0
1
0
1
2
1
2
1
1
1
0
0
0
0
2
1
0
0
1
1
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
1
0
1
1
1
0
0
2
0
2
0
0
1
0
0
0
0
0
2
1
1
2
0
1
2
1
1
0
0
2
1
1
2
1
0
2
1
1
1
0
1
2
2
0
1
1
0
3
0
2
0
0
0
2
1
1
1
1
1
2
1
0
1
2
0
1
1
1
1
2
0
3
1
0
0
0
0
0
1
0
0
0
2
2
1
1
2
0
2
1
1
1
2
1
1
0
0
1
1
0
0
0
0
2
1
0
0
1
0
1
1
4
2
1
1
2
0
1
0
0
0
1
2
2
2
0
2
1
2
0
1
1
2
1
0
2
1
0
0
0
1
1
2
0
0
1
0
2
0
0
1
1
3
0
2
2
2
0
2
0
1
2
2
0
2
0
0
2
0
0
0
1
0
1
0
1
0
0
2
1
2
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
1
1
0
1
0
1
1
0
0
2
2
2
0
0
1
0
2
1
1
0
0
0
1
3
0
2
1
1
0
0
0
0
1
1
1
0
0
2
1
0
1
2
1
0
1
0
1
0
2
1
0
2
0
0
1
1
0
0
0
0
0
2
1
2
2
0
2
0
2
0
0
0
0
2
1
2
0
1
0
0
1
2
2
0
2
0
0
0
1
1
1
1
0
2
0
1
0
1
0
0
0
2
0
1
0
0
2
1
2
0
1
1
0
1
1
1
0
0
0
0
0
0
2
5
1
1
0
1
1
0
1
1
1
0
1
1
1
1
0
1
2
0
1
2
2
1
1
1
1
1
0
1
1
1
2
0
2
2
2
2
0
1
1
1
0
2
0
0
2
2
0
2
3
0
0
0
1
1
1
2
0
0
1
1
0
0
2
3
0
0
1
1
1
1
0
1
1
0
1
1
0
0
0
0
1
1
0
1
1
1
0
2
1
3
0
2
2
0
2
0
0
2
2
0
1
0
1
0
1
2
0
0
0
2
0
0
1
2
1
0
0
1
1
1
1
1
0
0
3
2
0
0
1
0
0
0
2
1
0
0
0
2
2
0
0
0
2
2
0
2
1
1
2
1
0
0
0
1
1
1
0
3
1
0
0
0
2
1
2
2
0
0
1
2
0
2
1
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
2
0
3
1
2
2
0
0
0
2
0
1
2
0
0
1
0
1
0
1
0
2
1
0
2
1
2
0
1
9
2
0
2
0
2
2
0
0
1
1
0
0
2
0
1
1
0
2
2
1
0
1
0
1
2
1
0
0
0
2
2
1
1
0
0
2
0
2
1
0
2
0
1
2
1
1
2
0
0
2
0
0
0
0
0
1
0
0
1
1
1
1
2
0
0
2
0
0
2
0
1
1
0
2
0
0
0
0
2
0
0
0
0
2
0
1
0
1
3
2
2
0
0
1
2
0
1
2
1
2
1
2
0
1
0
1
2
2
2
0
0
0
2
1
1
1
2
0
0
0
1
1
0
1
0
2
0
1
1
1
0
1
1
0
2
1
0
0
0
1
1
1
2
0
1
1
0
0
1
1
1
0
2
0
0
1
1
0
1
0
2
1
2
2
2
1
0
1
1
0
1
0
0
1
0
0
1
1
1
0
2
1
0
0
0
0
1
1
1
2
0
2
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
1
1
2
1
2
2
2
0
2
0
0
2
0
0
1
0
1
1
0
2
1
1
0
2
1
1
1
2
1
1
2
3
0
0
2
0
2
0
0
2
0
0
1
0
0
1
1
1
0
0
1
0
0
0
0
0
1
1
2
1
0
0
0
1
1
0
1
1
1
0
0
1
0
1
1
0
1
0
2
0
1
2
0
1
3
0
0
2
1
0
1
1
0
1
2
0
0
0
1
1
2
2
1
2
0
0
0
1
0
1
1
0
6
0
2
2
1
0
0
0
0
0
1
2
0
1
0
1
0
1
0
0
1
3
0
0
0
2
1
1
2
1
0
1
2
0
0
1
1
0
0
0
0
0
0
2
0
0
1
0
0
1
1
1
0
0
1
1
0
2
1
1
3
2
1
1
0
1
0
1
0
2
0
1
2
1
0
1
2
0
0
1
0
2
0
0
0
2
2
1
0
0
2
2
1
0
1
1
2
1
1
2
0
0
0
0
1
2
2
2
0
1
1
0
2
0
0
2
0
0
1
0
2
0
1
0
0
1
3
0
0
1
0
4
1
0
2
1
0
1
2
0
2
0
0
2
1
2
0
0
0
2
0
0
1
0
1
0
1
1
0
1
0
1
1
1
2
2
2
2
2
1
0
0
0
0
1
2
1
0
0
1
0
1
2
1
1
2
0
2
2
1
0
2
0
0
0
0
1
0
0
0
1
2
1
0
2
1
0
2
0
0
2
1
0
2
0
2
0
0
2
1
1
0
1
1
0
3
0
0
0
1
0
0
0
0
1
1
0
0
0
2
0
1
0
1
0
0
1
0
0
0
0
0
0
1
1
1
2
1
1
0
0
1
0
4
0
0
2
1
0
0
2
1
1
1
1
0
2
1
1
0
2
0
1
0
1
1
0
1
0
0
0
0
0
0
1
1
0
0
1
1
0
2
0
1
0
1
2
0
2
0
2
3
0
0
1
2
0
0
0
1
1
1
1
1
1
0
0
0
0
0
1
2
1
1
1
2
0
1
0
1
0
0
1
0
1
1
0
1
1
2
2
0
1
0
2
0
0
0
1
0
2
0
1
1
1
0
0
2
0
2
0
0
1
0
2
1
1
0
2
0
2
0
0
0
0
0
0
1
0
1
2
0
2
2
0
1
0
0
0
1
2
1
0
1
0
2
0
1
0
2
2
1
0
0
0
0
1
0
1
0
0
0
0
0
0
2
2
0
0
0
1
0
0
2
0
2
0
1
2
1
2
0
2
0
0
0
2
2
2
1
1
0
0
3
0
0
1
0
0
1
0
1
0
0
0
2
0
2
0
3
0
1
0
0
2
1
0
1
1
0
2
0
0
1
0
0
2
0
1
0
0
5
0
1
0
0
0
2
0
0
2
0
1
1
1
0
1
1
0
1
2
2
0
0
0
2
2
0
0
4
1
0
2
0
2
1
0
0
1
1
0
0
0
2
1
1
1
0
0
1
0
0
0
3
0
2
1
1
1
0
1
1
1
1
2
2
0
2
1
1
0
1
1
2
1
2
3
0
0
0
0
1
1
4
0
1
1
1
1
2
0
0
0
1
0
0
2
1
0
2
0
1
1
1
0
0
0
0
1
0
0
0
2
2
2
0
2
1
2
0
1
1
0
1
2
2
1
1
2
0
4
0
0
0
2
0
0
2
1
0
0
2
0
2
0
3
2
0
2
1
0
0
0
0
2
2
0
1
0
2
0
0
1
1
1
0
2
0
2
0
1
2
2
1
1
0
1
0
2
1
0
0
0
0
1
0
0
2
0
0
2
0
2
1
0
1
0
0
0
0
1
0
1
1
0
0
0
2
0
0
2
1
2
0
1
1
1
0
2
0
0
2
1
1
0
1
0
2
1
1
1
0
0
1
1
0
0
0
0
2
1
0
1
0
1
2
1
0
0
1
0
0
0
2
1
2
0
1
2
0
0
2
0
0
1
2
0
0
0
0
0
1
0
1
2
0
1
0
0
2
1
2
2
2
1
0
2
0
0
1
0
2
1
0
2
0
1
2
0
1
0
1
0
0
2
0
2
0
0
2
0
1
0
0
0
1
0
2
0
1
1
1
0
1
2
0
1
1
1
0
1
0
2
1
0
1
1
1
2
0
1
2
0
3
0
1
1
2
0
2
0
0
0
0
2
2
2
0
1
1
1
0
1
1
0
1
0
1
1
0
2
0
2
0
2
0
1
0
1
2
0
1
1
0
0
0
3
1
1
2
1
1
0
0
2
1
0
1
0
0
0
1
2
1
1
0
1
2
0
0
0
1
0
0
0
0
1
1
1
1
0
2
0
1
0
1
0
1
1
0
2
2
1
2
1
0
0
2
1
0
0
2
0
0
1
0
0
1
2
0
0
0
0
0
0
2
0
0
1
1
1
1
0
3
0
0
1
1
0
1
0
1
2
1
0
0
0
1
0
0
1
1
0
0
2
1
0
0
1
1
0
0
1
0
0
0
1
2
0
1
1
2
0
2
0
1
1
0
2
0
0
1
1
0
1
2
1
1
3
0
0
0
0
0
0
2
1
0
1
0
1
0
0
0
1
1
0
0
1
0
0
0
1
0
0
1
0
0
1
0
2
1
1
2
0
0
0
2
2
0
0
1
2
1
1
0
1
0
0
0
0
2
2
2
2
1
2
2
1
0
2
2
1
2
3
0
0
2
1
0
0
2
1
0
0
0
0
1
2
0
1
0
0
0
0
0
1
0
0
2
0
1
2
0
1
1
2
1
1
1
1
1
0
2
1
0
2
1
1
1
0
0
1
2
0
0
1
0
1
2
0
0
2
1
2
2
1
1
2
1
0
2
1
0
0
2
0
0
0
0
1
1
0
0
0
1
0
0
1
1
1
1
0
4
0
2
0
0
0
0
0
0
0
2
3
0
1
1
2
1
1
1
2
1
2
0
0
2
0
0
2
0
0
0
0
0
0
1
0
1
0
1
1
2
2
1
4
0
0
0
1
1
1
0
1
1
2
0
1
1
1
0
0
1
2
0
0
2
2
0
2
1
0
0
1
1
2
0
0
1
0
0
0
0
0
1
0
0
2
0
0
1
0
2
0
0
0
0
1
2
0
2
2
0
5
2
2
2
1
1
0
0
0
1
1
0
2
1
1
3
0
0
0
2
0
0
0
1
1
2
1
2
0
0
0
1
0
0
2
0
1
0
2
0
1
2
0
1
1
0
2
0
1
0
1
0
1
1
1
1
0
1
0
0
0
1
1
1
0
2
2
0
1
0
1
2
1
0
1
1
0
2
0
1
1
0
0
2
0
2
0
0
2
0
0
1
0
2
1
1
0
0
2
0
0
0
1
0
0
0
0
2
0
1
0
1
0
1
2
2
0
1
0
0
0
3
1
0
2
1
1
1
0
0
0
2
0
2
1
0
1
2
1
0
1
0
2
2
0
2
2
2
0
0
0
0
2
0
0
1
0
2
1
0
1
1
0
0
0
0
2
0
1
0
1
0
1
0
0
0
1
0
2
0
2
2
0
1
0
0
0
0
1
0
0
2
0
2
0
2
0
1
1
1
0
2
2
2
3
0
0
1
1
2
0
2
0
6
2
2
3
0
2
0
1
1
1
0
2
1
1
1
0
0
1
1
2
1
1
1
2
0
2
1
1
0
2
0
2
0
1
0
1
1
0
1
0
2
1
2
2
1
1
1
3
1
0
0
1
0
2
0
0
0
2
0
1
0
0
1
1
3
0
0
1
0
1
2
0
0
0
1
1
0
1
1
1
0
3
1
1
1
0
0
0
0
0
1
0
3
0
0
0
0
0
0
2
1
1
0
1
0
0
2
1
0
0
1
0
0
0
0
1
1
0
0
0
1
0
1
2
0
0
0
2
1
0
1
0
0
1
0
1
1
0
1
0
0
0
1
2
1
0
1
2
0
1
0
2
1
1
0
2
0
2
1
2
1
0
2
2
0
0
1
0
1
1
2
0
0
0
0
1
0
2
0
1
1
1
1
0
0
0
0
2
1
0
1
0
1
2
2
0
2
0
1
0
2
1
0
0
1
0
2
0
0
1
1
2
1
2
2
1
1
0
0
2
2
2
2
0
1
0
2
1
2
1
2
1
0
2
2
1
0
0
1
0
2
2
1
1
0
2
0
0
1
0
2
0
0
1
1
3
1
2
0
1
2
3
1
0
0
2
0
1
1
1
0
0
1
1
0
0
1
1
1
2
3
0
0
0
0
2
1
0
0
2
3
0
0
0
0
0
2
0
0
2
0
2
0
1
2
1
0
1
2
1
0
1
1
1
0
0
1
0
0
2
0
1
0
0
1
1
1
0
0
0
0
0
0
2
0
1
1
0
2
2
1
0
0
2
1
1
0
1
0
1
2
1
1
0
1
0
2
0
2
0
0
1
0
1
1
0
1
1
0
2
0
1
0
1
0
0
2
2
2
1
1
0
0
1
2
0
1
1
0
4
1
0
1
1
0
0
1
2
1
1
0
1
0
1
0
0
0
1
1
0
1
0
1
0
0
2
0
1
0
1
0
1
0
2
0
1
1
1
2
2
1
0
0
1
0
1
1
0
1
1
2
0
1
0
1
1
0
2
2
0
0
1
0
0
0
1
0
1
0
0
2
2
0
0
2
0
0
3
1
0
2
1
1
0
2
2
0
2
1
1
0
0
0
0
1
0
1
1
0
0
0
0
2
1
1
1
2
0
3
1
0
0
0
1
1
0
0
1
0
1
0
1
0
1
2
2
1
0
0
1
2
0
2
0
1
0
0
0
1
1
1
1
2
1
0
0
1
2
0
2
0
2
1
2
2
0
0
0
0
0
2
1
0
1
0
2
2
2
2
1
0
1
0
0
2
0
1
0
1
0
2
0
0
2
1
3
2
3
1
2
0
0
2
3
0
1
0
0
4
0
2
0
1
1
0
2
1
0
2
0
0
1
2
0
0
3
1
1
0
2
1
0
1
0
0
1
0
1
0
0
0
1
0
0
0
1
0
2
0
2
2
1
0
0
1
0
1
0
0
0
1
0
0
2
1
1
0
0
0
1
1
1
1
0
1
0
1
1
2
1
2
4
2
1
2
1
1
1
1
1
0
1
1
2
0
1
1
0
1
1
1
1
0
1
0
2
0
0
2
1
1
0
2
0
0
0
2
2
1
0
0
1
1
0
0
2
1
2
2
0
1
0
2
1
1
0
2
1
0
0
2
0
0
2
1
1
0
0
0
0
1
2
0
0
3
0
0
2
0
0
0
3
1
2
2
0
2
1
2
1
2
1
2
2
0
0
1
0
1
0
1
0
1
0
1
2
1
0
0
2
2
0
0
1
0
1
0
0
0
0
0
0
0
1
1
1
2
0
1
1
1
2
0
0
2
1
0
1
1
1
0
0
0
0
2
2
0
0
1
2
0
1
1
0
0
1
1
1
0
0
1
0
1
0
1
0
1
0
1
1
0
2
0
1
1
0
0
1
0
0
4
2
2
0
1
1
1
0
2
1
0
1
0
0
0
1
0
1
2
0
2
1
0
2
0
2
0
1
0
2
2
1
2
0
1
1
1
0
1
2
1
2
1
0
1
0
2
1
0
1
0
1
1
1
2
1
0
0
1
0
0
1
0
1
0
0
1
0
1
0
1
2
2
0
0
0
0
2
2
1
1
1
0
1
2
1
0
0
2
1
1
0
2
0
4
0
2
0
2
1
1
2
0
3
1
0
0
0
1
1
1
2
0
2
1
2
1
3
2
2
0
1
0
2
2
1
0
0
0
0
0
1
0
0
0
2
0
2
0
1
0
2
1
1
0
0
0
0
0
1
0
0
1
1
2
0
0
2
0
0
1
0
1
0
0
0
0
1
2
0
0
0
1
0
2
0
1
1
0
1
2
0
0
0
1
2
0
0
0
1
0
1
2
0
0
0
0
2
2
0
1
1
0
0
0
0
0
2
0
0
0
0
0
1
1
3
1
1
1
0
1
0
0
2
0
2
1
0
1
1
2
2
1
1
0
2
1
2
0
1
0
1
1
0
1
2
2
0
1
0
1
0
0
0
2
0
1
0
0
0
1
1
1
2
1
2
0
2
1
0
0
2
1
2
1
1
0
2
0
2
1
0
1
0
0
0
1
1
0
1
0
1
1
2
2
1
1
0
0
0
1
1
1
2
2
3
0
0
2
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
2
1
0
1
1
2
2
2
0
0
0
2
0
0
0
1
1
2
1
2
0
2
1
0
0
2
1
1
1
0
1
0
2
1
10
0
2
0
0
1
1
1
0
0
0
2
0
0
1
2
0
1
0
1
2
0
3
0
0
0
1
2
0
1
4
2
1
1
2
1
0
2
0
2
0
0
0
1
1
2
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
1
1
0
0
2
0
0
0
1
1
1
1
0
2
0
2
0
0
0
0
2
0
2
0
0
3
0
1
0
0
2
1
0
0
2
1
0
1
2
1
1
2
2
0
0
1
0
0
0
0
1
1
1
0
0
1
1
0
0
0
0
0
0
2
2
0
2
0
0
1
1
1
1
1
1
3
1
1
2
2
0
0
1
0
0
2
2
1
0
1
2
0
2
0
1
0
2
1
0
0
1
1
1
0
2
1
0
2
0
1
0
2
0
1
0
0
0
0
1
1
0
1
4
2
0
2
1
1
2
1
2
0
1
1
1
0
1
2
0
2
1
0
0
0
1
0
1
2
2
2
0
2
0
1
0
0
1
1
3
1
0
0
1
3
1
0
0
2
0
2
1
1
0
0
0
0
0
0
0
1
1
2
0
1
2
2
0
2
1
0
1
1
2
1
0
0
2
0
1
0
2
0
0
0
2
0
2
0
2
0
1
2
1
0
0
1
0
0
0
1
2
0
2
0
0
0
0
1
2
0
1
1
1
0
1
1
0
0
2
1
0
0
0
0
0
1
1
0
2
0
0
2
0
0
2
2
1
1
2
0
0
1
1
0
0
0
2
0
0
1
0
1
0
1
0
0
1
0
2
1
0
2
0
1
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
1
3
0
2
0
1
0
0
2
2
1
1
1
0
2
1
0
0
0
0
9
0
0
0
0
2
3
2
2
0
1
1
0
0
1
2
0
2
1
0
2
1
1
1
0
2
0
0
0
0
1
1
4
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
2
0
0
2
0
0
1
1
1
1
0
0
0
2
0
1
0
1
0
3
0
3
0
1
0
0
0
0
1
2
2
1
1
2
1
1
0
0
1
1
1
0
0
2
0
2
1
1
1
0
0
0
2
0
0
1
2
1
4
1
1
1
0
0
0
1
0
2
0
1
1
1
1
1
2
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
1
0
2
1
1
0
1
0
1
0
1
0
2
1
0
1
1
1
0
2
0
2
1
2
0
2
0
0
0
1
1
0
1
1
0
0
1
2
1
0
0
1
2
0
0
0
0
1
2
0
0
1
0
1
1
2
2
0
1
0
0
2
2
2
0
1
2
1
2
0
0
0
1
0
0
1
0
0
0
0
1
1
1
0
1
1
0
0
1
0
1
0
0
0
1
0
2
1
1
0
1
2
1
1
0
2
0
0
1
0
2
1
3
0
2
0
0
1
0
2
1
2
2
0
0
0
2
0
0
6
0
0
1
2
0
0
0
0
1
2
0
0
1
1
2
2
2
1
0
0
3
0
0
1
0
2
2
0
1
1
1
1
2
0
1
0
0
2
0
1
1
1
0
1
1
0
1
1
1
0
2
2
2
1
1
1
1
2
1
0
0
1
0
2
0
2
2
2
0
0
2
0
0
2
0
1
0
1
1
1
2
0
3
1
0
0
1
1
0
1
2
2
1
0
1
2
2
1
0
0
2
0
0
0
0
1
2
1
2
2
0
0
2
0
1
0
0
2
2
0
1
0
0
0
1
0
2
0
1
1
0
1
1
0
1
0
1
0
0
1
1
0
2
0
1
2
0
1
3
2
0
0
2
1
0
1
3
0
2
0
1
1
1
2
1
2
0
0
0
1
1
0
2
0
3
0
1
2
0
0
0
1
1
2
0
0
0
1
1
3
1
1
0
0
1
0
1
0
0
2
1
1
1
2
0
2
0
0
1
0
2
0
6
1
0
0
2
0
0
2
0
1
0
2
1
1
0
2
0
0
0
0
1
2
1
0
1
1
0
0
2
0
0
0
0
1
1
0
0
0
1
1
0
2
0
3
1
0
0
0
1
0
1
0
3
1
0
0
1
1
2
0
1
0
0
0
1
2
3
1
0
1
0
2
0
1
1
2
1
0
0
1
4
1
1
1
0
0
1
1
0
0
0
1
1
2
0
1
0
2
3
0
3
0
0
0
1
1
0
2
1
0
0
1
0
1
9
1
2
2
1
2
0
1
0
0
0
0
0
0
1
1
1
1
0
1
1
0
0
0
1
1
0
0
0
2
0
1
0
1
0
1
0
0
0
1
2
0
2
0
0
1
1
1
0
0
1
0
0
2
1
0
2
2
1
1
0
1
0
0
2
1
0
0
0
1
2
0
1
0
0
0
1
1
2
0
2
0
2
0
0
1
1
2
1
2
0
1
1
0
0
1
1
0
0
2
1
0
0
1
7
0
1
1
0
0
0
1
0
1
0
1
1
0
0
1
1
2
0
1
2
0
1
0
0
0
1
0
0
0
0
2
0
1
1
2
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
1
1
1
0
0
1
1
1
1
0
1
1
1
1
0
2
2
3
2
0
0
0
0
1
0
2
2
1
0
0
2
0
0
0
0
0
0
1
0
0
1
2
0
1
2
2
0
1
0
0
0
0
0
2
0
0
2
1
2
0
1
0
0
1
1
0
0
2
0
1
1
2
0
2
0
3
0
0
0
1
2
1
2
0
0
0
1
0
2
2
0
1
2
1
0
1
2
2
0
0
0
0
2
1
1
0
0
1
2
1
1
0
3
2
1
1
2
0
0
1
0
1
1
0
0
0
1
0
0
2
0
0
0
0
0
1
2
0
2
0
0
0
0
2
1
1
1
0
1
1
2
1
2
2
2
1
0
0
1
0
0
0
0
0
0
0
1
1
0
1
2
0
1
0
1
1
1
1
2
1
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
2
0
0
0
0
1
0
2
1
1
1
2
2
2
1
0
0
2
1
0
2
1
0
1
1
1
0
0
2
0
2
2
1
2
1
0
0
1
1
0
1
2
0
0
1
1
1
0
0
0
1
2
1
1
0
0
0
0
1
0
0
0
1
0
2
4
3
2
1
1
1
0
2
0
3
1
1
0
0
0
1
2
0
2
1
1
0
1
0
1
2
0
2
1
0
2
1
0
1
0
1
0
0
1
0
0
1
1
2
1
0
0
1
0
2
1
2
1
2
0
0
0
0
1
0
1
2
0
0
1
0
1
2
2
2
2
2
2
1
0
0
0
0
1
1
1
1
0
0
0
1
2
0
1
1
1
2
2
4
2
1
0
0
0
1
5
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
2
0
0
1
0
0
0
1
1
0
0
1
1
2
0
1
2
2
0
0
1
1
1
0
0
0
1
2
2
0
0
2
2
2
2
1
0
1
1
0
0
0
1
1
0
0
4
1
1
0
2
1
1
1
0
0
1
1
0
0
2
0
1
1
1
0
2
2
2
1
0
0
0
0
1
1
0
1
0
2
0
0
0
0
0
1
1
0
1
1
1
0
2
1
2
2
0
1
0
0
1
3
1
1
0
0
2
1
4
1
1
0
0
0
0
1
1
1
2
1
1
1
1
0
0
0
0
0
1
1
1
0
0
1
1
0
0
1
0
0
0
0
1
0
2
0
2
0
0
0
1
0
1
1
2
0
1
0
1
1
0
0
1
0
1
2
2
1
1
0
1
0
1
0
1
0
0
1
0
0
2
1
2
1
1
1
2
2
2
2
1
0
2
0
1
0
1
1
1
0
1
1
0
1
1
1
1
3
0
2
0
1
0
0
0
0
0
2
0
2
2
1
1
1
0
1
1
2
1
0
0
1
0
0
0
0
1
2
0
1
0
1
0
1
1
0
0
0
2
2
0
2
1
1
1
1
1
0
1
0
1
0
1
0
1
0
0
1
2
0
1
1
0
1
3
1
2
0
1
0
0
1
0
0
0
2
1
0
1
2
0
2
0
0
2
0
0
0
1
0
1
1
1
1
0
1
0
0
0
1
2
1
0
0
1
1
0
0
3
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
3
0
0
0
3
0
0
0
2
2
0
2
4
0
1
0
0
0
2
1
0
0
2
1
2
1
1
1
0
0
0
3
0
1
0
0
1
1
0
0
0
0
0
0
0
2
1
0
0
0
2
1
1
1
0
0
1
0
0
1
2
2
0
0
0
1
1
0
0
2
1
0
0
2
3
0
1
1
1
0
1
0
2
0
0
2
0
0
1
2
0
1
2
2
0
1
1
0
0
2
0
0
1
0
1
0
0
1
0
0
2
2
0
0
0
2
1
1
1
0
1
1
0
2
0
0
1
0
0
0
2
1
1
2
2
2
0
1
2
1
1
0
2
0
1
1
0
0
0
0
1
2
0
1
0
0
0
1
0
1
0
1
1
2
1
1
0
2
0
0
1
2
1
1
0
2
0
0
1
2
1
0
1
1
0
0
0
1
4
1
1
2
1
0
2
0
2
1
4
2
0
0
1
0
0
0
1
0
0
2
0
1
1
3
1
2
0
1
0
1
2
0
0
1
1
0
0
2
1
0
2
1
2
1
0
2
2
1
2
1
0
0
1
0
2
2
4
1
1
0
2
1
1
0
2
0
0
2
1
1
1
0
0
0
0
1
0
0
1
0
1
0
2
2
1
2
0
0
1
0
2
0
0
0
0
0
1
0
0
1
1
1
1
0
1
2
0
0
0
0
1
0
0
0
2
2
0
0
0
1
0
2
0
1
0
0
1
1
0
1
1
3
2
1
1
2
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
2
1
0
0
1
0
0
3
1
0
1
0
2
1
0
0
0
1
1
1
0
2
2
0
1
1
0
0
0
0
0
1
0
2
1
1
1
1
2
0
0
0
1
0
0
0
0
0
0
1
2
0
1
0
1
1
2
1
1
1
1
1
2
1
5
0
0
2
1
3
2
0
0
1
1
0
1
2
0
0
0
0
2
0
0
1
2
0
1
0
1
0
0
0
1
1
0
0
0
1
0
0
1
2
0
0
2
2
1
0
0
2
0
0
0
1
2
0
1
0
1
0
1
0
0
1
1
1
1
1
1
0
1
0
1
0
0
0
2
3
2
1
0
1
1
0
1
1
1
0
0
1
1
2
2
0
0
1
0
0
0
0
1
1
0
1
1
2
2
2
0
2
1
1
0
0
0
1
1
2
1
1
0
0
1
0
0
0
2
0
0
0
0
0
1
1
2
0
0
0
3
0
1
1
1
1
0
0
1
2
1
1
0
0
1
2
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
1
1
0
2
0
3
0
1
0
2
0
1
0
0
0
1
1
1
1
1
2
0
0
0
2
0
0
0
1
2
1
1
0
0
1
3
1
1
0
1
0
2
2
2
2
0
1
2
2
0
2
1
2
0
0
0
2
1
2
0
0
1
1
0
0
0
1
1
1
1
0
1
2
0
0
2
2
0
1
0
1
0
0
3
2
0
1
0
0
2
0
2
0
1
0
0
2
1
0
1
0
1
0
1
0
2
1
1
0
0
0
0
1
1
1
0
3
0
0
3
0
0
0
1
0
2
0
0
1
0
0
2
0
2
0
0
0
0
0
2
1
1
2
0
2
0
0
0
2
2
1
0
0
0
1
3
1
0
0
0
1
0
0
1
0
1
1
1
0
0
2
2
1
0
0
1
2
0
0
1
1
0
1
0
0
3
2
0
0
0
0
0
1
0
0
2
1
0
1
2
0
1
0
0
0
0
0
2
2
0
1
2
1
2
0
1
0
2
1
0
1
0
1
0
0
1
2
3
1
1
1
0
2
0
2
0
0
1
2
1
1
0
0
0
0
0
0
1
1
1
0
1
0
0
0
1
1
0
1
0
1
1
1
0
0
1
1
1
0
0
3
0
2
2
1
0
1
1
1
0
1
0
2
0
0
2
0
1
1
0
2
3
2
0
1
2
1
0
2
0
0
1
1
2
2
4
0
2
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
2
1
2
0
1
3
1
2
1
1
1
1
1
0
0
0
0
1
1
0
1
2
0
0
1
0
3
0
0
0
0
0
0
3
2
1
0
2
0
1
3
2
2
2
2
0
1
2
1
2
2
1
1
0
1
0
1
0
0
1
0
1
1
0
0
1
0
0
0
1
1
0
0
1
2
0
0
2
0
0
2
1
1
2
1
2
0
0
0
0
2
1
1
0
0
0
1
1
0
0
0
1
0
2
0
0
1
0
1
2
0
0
2
0
0
1
0
1
0
0
0
2
1
2
1
0
0
1
0
0
0
1
0
0
1
1
1
1
1
0
2
0
0
1
0
0
1
0
0
1
1
1
0
1
2
0
0
0
1
0
1
2
1
0
0
1
0
0
0
1
0
1
1
0
2
2
2
4
0
1
1
1
0
1
0
1
1
1
0
0
2
2
0
0
1
1
2
2
0
2
1
2
0
0
0
2
1
1
1
2
2
2
1
0
1
0
0
0
0
0
1
2
1
0
0
2
0
0
0
1
1
0
0
1
2
1
2
1
0
2
1
2
0
0
0
1
2
1
1
0
1
0
0
2
2
0
1
0
0
2
2
0
0
2
0
2
1
0
0
0
0
0
0
2
1
1
2
0
0
0
1
2
0
0
2
1
0
2
2
1
1
1
1
0
0
0
0
1
0
0
0
1
2
1
0
0
2
0
0
2
0
1
2
1
3
1
0
2
2
0
2
0
1
0
1
1
0
1
2
0
0
0
1
1
1
0
0
1
0
1
2
1
0
0
0
0
2
0
2
0
1
0
1
2
0
2
0
1
0
1
2
0
0
0
2
2
0
2
0
0
0
2
0
1
2
2
3
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
1
2
0
1
1
0
1
1
2
1
0
0
2
1
0
1
0
1
0
0
0
0
2
0
1
2
1
0
1
1
0
2
0
2
0
2
0
1
1
1
0
0
0
0
2
2
1
1
0
1
1
0
2
0
0
0
1
1
0
1
0
1
0
1
0
0
0
0
1
1
1
0
1
0
2
2
2
2
1
2
2
1
0
1
0
0
0
0
0
1
2
0
0
2
0
0
1
2
1
0
0
1
0
0
1
1
1
0
0
1
0
0
0
2
0
1
2
1
2
0
0
3
0
0
0
1
2
3
0
0
1
1
0
1
2
1
0
1
2
0
2
1
0
0
0
2
1
0
0
1
2
0
1
0
2
0
1
1
0
1
0
1
2
0
1
1
1
1
1
2
0
1
2
2
1
3
0
1
0
0
0
1
0
0
2
0
1
1
1
1
1
0
0
0
0
0
1
2
0
0
2
1
0
0
0
0
2
0
1
0
2
1
1
1
1
0
0
0
0
2
1
1
1
0
2
1
1
1
1
0
2
2
0
0
0
0
0
0
1
2
1
2
0
1
1
2
2
0
0
0
0
0
0
0
0
1
2
0
1
0
1
2
1
0
0
0
0
2
0
2
1
0
1
2
0
0
0
0
0
2
2
0
1
1
1
0
2
1
0
0
0
2
2
2
1
0
2
1
1
0
0
0
2
0
0
2
0
0
1
0
1
0
1
0
0
0
1
1
0
2
0
0
1
2
1
1
2
0
0
0
1
0
1
2
0
2
2
2
0
1
1
1
0
0
0
2
1
2
1
0
1
0
0
2
0
0
0
0
0
1
1
2
2
0
2
2
1
0
0
1
0
1
1
1
1
0
0
1
1
1
2
1
0
0
0
0
0
3
0
1
0
0
2
1
0
2
0
1
1
1
0
1
2
1
0
1
0
0
0
1
0
0
2
2
0
0
2
0
2
0
1
2
1
0
1
0
1
0
0
0
0
2
1
0
1
0
2
1
0
0
1
0
1
1
1
2
0
2
0
0
3
0
2
0
0
0
1
0
2
0
2
2
1
0
1
1
2
2
0
0
3
2
1
2
1
1
0
0
2
1
0
2
1
0
1
1
0
0
1
2
2
0
2
2
1
0
2
0
0
0
0
0
1
0
1
1
0
1
0
0
1
0
0
3
0
0
1
0
0
1
1
0
0
0
2
0
0
1
0
0
0
0
1
1
2
0
1
0
1
1
0
2
1
0
1
0
0
0
2
0
1
0
1
0
1
1
0
1
0
0
0
2
0
1
1
1
1
0
1
2
2
0
0
1
2
2
1
1
1
0
0
1
1
1
2
0
1
2
2
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
3
1
0
2
1
2
0
1
1
2
0
1
0
0
0
0
0
0
1
0
0
2
0
1
2
0
2
1
0
0
0
1
1
2
0
0
0
1
2
0
0
0
1
0
0
0
1
1
2
1
1
2
0
1
1
1
1
0
0
1
0
1
1
1
1
1
0
1
2
0
2
1
0
0
2
1
0
0
0
0
2
0
0
0
1
2
0
1
1
0
1
2
1
2
0
1
0
1
1
1
0
0
1
1
0
0
2
1
0
0
0
1
3
0
0
2
0
0
1
2
0
0
2
1
2
0
1
2
0
2
0
0
2
0
0
0
0
0
2
1
0
0
0
2
0
2
1
0
0
0
1
1
1
0
0
0
2
2
1
2
0
0
0
1
0
0
1
0
0
2
2
2
0
1
0
0
0
0
3
3
2
0
1
1
1
2
0
0
1
0
1
0
1
1
0
0
1
2
0
1
0
0
0
1
1
0
0
1
0
1
0
0
1
0
1
2
0
0
2
0
1
0
0
2
0
1
0
1
0
0
0
0
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
1
5
1
0
1
0
0
0
1
0
0
0
0
1
0
0
2
1
0
0
2
0
0
1
0
1
1
3
1
2
0
0
0
0
0
0
0
1
0
1
0
1
5
1
1
0
0
2
1
2
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
1
1
0
2
2
2
0
0
2
1
0
0
0
2
0
0
2
0
0
1
1
0
0
0
0
1
0
0
2
0
2
2
0
0
2
2
0
2
0
1
2
0
0
2
0
1
1
0
0
2
2
0
0
0
0
0
2
1
1
1
0
0
1
1
1
1
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
2
1
1
1
0
2
0
1
2
0
1
0
0
1
0
0
2
0
0
2
1
1
0
0
2
0
2
0
1
0
0
0
2
0
2
0
0
0
2
2
0
0
0
1
2
0
1
0
2
1
0
1
2
2
0
1
0
0
0
2
1
0
0
1
2
2
2
1
2
0
2
2
0
1
2
1
0
0
0
0
0
0
1
0
0
0
0
1
0
2
1
1
0
2
0
2
1
0
0
2
0
1
0
1
1
1
0
2
0
2
0
2
0
1
1
0
1
2
0
1
1
0
1
0
3
0
0
0
2
0
0
1
0
0
3
2
1
1
2
1
0
0
1
0
0
0
1
0
1
2
1
1
1
0
1
0
2
2
0
0
0
1
2
0
0
2
1
2
2
0
0
2
2
0
1
0
2
1
1
1
2
2
1
1
0
1
0
1
2
0
0
1
1
1
0
0
1
1
0
1
1
2
0
1
2
2
0
0
1
2
1
0
2
0
1
0
1
2
0
1
0
1
1
0
1
0
3
0
0
0
1
1
1
0
2
0
3
1
1
1
0
0
1
0
1
0
1
1
1
2
1
1
0
0
0
1
2
0
1
1
1
1
2
0
0
2
0
2
0
1
2
1
1
2
1
0
2
1
1
2
2
1
2
1
0
2
2
0
1
0
1
0
1
1
0
0
0
0
0
2
0
0
2
2
1
1
0
1
1
0
1
0
1
0
2
3
0
0
0
0
0
2
1
0
0
0
0
0
1
1
1
2
0
2
2
0
1
0
1
1
1
0
1
0
1
0
0
2
2
1
1
0
1
1
4
0
0
0
0
0
0
2
0
0
0
1
1
8
0
0
0
1
1
2
0
2
2
0
1
0
1
1
0
0
0
0
1
1
0
0
1
0
0
0
1
2
0
2
0
1
6
1
1
1
2
0
0
1
1
0
4
2
2
2
0
2
0
1
0
1
3
2
1
2
1
0
0
2
2
2
1
0
0
0
0
1
0
0
0
0
0
2
1
1
1
0
0
1
1
2
0
0
0
0
1
1
2
2
2
2
1
2
1
1
2
0
2
0
1
4
0
0
0
1
0
2
2
2
0
2
0
0
1
1
0
0
0
0
2
1
3
0
0
0
0
1
0
0
1
2
1
0
1
0
4
0
2
0
1
0
0
0
1
0
2
1
0
0
2
1
0
0
0
1
0
1
0
1
2
0
0
0
1
3
1
1
0
0
2
0
0
2
1
2
1
2
2
1
1
2
1
0
0
0
0
2
0
2
1
0
2
1
0
1
1
2
2
1
0
2
1
2
2
0
1
1
0
0
0
0
2
1
0
1
0
2
2
2
1
3
2
1
1
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
2
0
0
1
1
1
0
2
0
0
0
0
0
0
1
1
0
1
1
1
1
3
0
1
2
1
1
2
1
2
1
1
0
1
0
2
1
3
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
1
0
2
2
2
0
0
0
0
0
2
0
0
1
2
2
1
1
1
0
0
0
0
1
1
3
2
0
2
0
2
2
1
2
1
0
2
0
1
0
0
0
2
2
0
0
1
0
2
0
0
0
2
0
2
0
1
0
2
1
1
2
2
0
1
2
0
0
0
1
2
0
1
1
1
0
2
1
3
1
1
2
1
3
0
0
1
0
2
1
2
2
1
1
1
1
1
0
0
1
0
2
0
1
1
0
0
0
0
0
0
2
0
2
2
2
2
2
0
1
0
0
1
2
3
1
2
1
1
0
0
1
4
0
2
0
11
1
1
2
0
0
0
0
1
1
0
0
1
2
0
1
2
0
1
1
2
2
1
0
2
1
2
2
1
2
1
1
0
0
1
0
0
0
0
0
0
0
2
0
1
0
1
0
0
2
0
0
1
0
2
0
0
2
1
1
1
2
2
2
0
0
1
0
0
0
0
3
1
1
0
2
1
0
1
1
0
0
2
0
1
1
0
1
1
0
0
1
0
0
0
2
1
0
1
0
2
3
2
2
2
0
1
0
1
0
0
1
2
0
0
2
0
1
1
0
1
1
0
2
2
1
1
0
0
0
0
1
0
2
1
0
1
0
0
0
2
2
2
2
2
1
1
0
1
3
0
1
0
1
2
1
0
0
1
2
1
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
1
0
0
0
1
1
0
1
1
1
0
0
0
0
0
1
1
1
2
2
1
0
0
0
2
2
0
0
0
1
0
1
2
1
0
0
0
2
2
0
2
0
2
0
0
0
1
0
1
0
0
0
0
2
2
0
2
0
2
0
0
2
0
2
0
0
2
1
0
0
2
0
1
1
0
1
2
1
3
1
0
0
2
1
0
1
0
0
2
0
0
0
0
2
2
2
1
0
2
1
1
0
0
0
1
1
0
1
1
0
0
2
0
0
2
0
2
1
1
1
0
1
1
2
1
2
1
1
3
0
2
0
2
1
2
2
0
0
0
0
0
1
1
0
0
1
2
0
0
0
1
0
0
0
0
1
1
0
2
0
0
1
1
1
1
0
0
0
3
1
0
0
2
0
0
2
1
0
0
0
0
1
0
1
2
1
0
2
1
1
0
0
0
1
1
1
1
0
0
1
2
1
1
0
1
0
1
1
0
1
1
2
2
1
1
1
0
1
0
0
0
0
2
1
0
0
2
0
1
1
1
2
0
0
2
0
1
1
1
2
1
1
0
2
3
2
1
0
2
0
2
2
0
0
0
0
0
1
0
0
0
0
2
0
1
0
2
2
0
1
1
1
0
2
0
1
0
1
2
3
2
1
0
1
1
0
4
1
1
0
1
0
1
0
0
0
1
0
2
0
1
1
1
0
2
0
0
0
0
2
2
2
0
2
0
2
1
0
2
2
1
0
0
1
1
2
1
3
1
2
0
1
0
0
2
1
2
2
1
0
0
1
0
1
1
0
0
0
0
1
0
1
0
1
0
1
1
0
0
1
0
2
1
0
0
0
0
0
0
1
0
2
1
2
0
2
1
0
2
1
0
2
0
1
1
2
2
0
0
1
0
3
2
1
1
0
0
3
0
1
2
1
1
0
2
0
0
0
1
1
1
0
0
0
2
2
1
1
1
1
2
0
2
0
1
0
0
8
1
1
1
2
1
1
2
2
1
1
0
1
2
0
0
1
2
0
0
0
0
0
1
0
1
0
0
1
1
0
0
2
1
1
3
1
3
2
0
0
0
0
1
2
2
2
0
2
0
1
0
0
2
1
0
2
2
1
4
0
1
1
1
2
1
2
0
2
0
1
1
1
1
1
0
1
1
1
2
0
1
0
1
1
0
2
0
1
2
1
1
0
0
0
1
0
3
1
0
2
0
3
2
1
0
0
1
1
0
1
0
1
1
1
1
1
0
2
1
0
0
1
0
0
0
1
0
0
2
1
2
1
2
1
0
0
1
1
0
1
0
1
0
0
0
1
0
0
0
1
2
0
0
0
1
0
0
0
1
1
0
1
0
1
0
0
2
0
1
0
0
0
1
1
2
1
0
1
0
1
1
0
0
0
0
1
0
2
0
0
2
0
0
2
0
0
0
0
1
1
1
0
0
1
0
0
1
0
2
0
1
0
0
0
2
0
0
2
1
1
0
1
0
0
0
1
2
0
1
1
0
4
0
0
1
2
0
0
1
1
1
1
0
1
1
2
0
0
1
0
0
1
0
2
0
0
0
1
0
0
2
0
1
2
2
0
1
1
1
1
1
0
1
0
1
0
1
1
1
2
2
0
0
1
0
0
1
1
1
0
1
0
1
0
0
2
0
2
0
1
0
0
0
1
2
2
1
1
1
0
0
4
2
2
1
0
2
0
2
0
1
0
1
1
1
0
1
1
1
2
0
0
0
2
1
1
1
2
0
0
1
0
1
2
2
2
0
1
2
0
2
2
0
1
0
2
1
0
0
0
1
0
1
0
0
1
2
0
0
0
2
1
0
0
0
4
0
1
0
2
0
2
1
1
1
2
1
0
0
0
1
1
1
0
0
1
0
0
2
0
0
0
1
0
2
0
1
1
0
2
1
0
0
2
0
0
0
1
0
1
1
2
1
2
0
1
0
0
1
0
1
2
2
1
0
0
1
1
0
1
0
1
2
0
2
0
1
1
1
0
0
0
0
0
2
0
1
1
1
2
0
1
0
2
2
1
1
0
2
0
2
0
0
0
1
2
2
2
1
2
1
0
1
0
1
1
0
1
0
2
1
2
2
0
2
1
0
1
0
2
0
2
0
0
1
2
2
3
1
1
2
1
1
0
2
0
1
1
1
2
2
0
0
0
1
0
0
2
2
2
0
3
1
1
0
1
1
0
0
1
0
1
0
1
1
2
2
1
0
0
0
2
2
1
0
0
2
2
2
0
0
2
0
1
1
2
1
0
1
1
2
1
0
2
2
1
0
1
1
2
0
1
2
0
0
2
1
0
2
0
0
1
2
0
1
1
2
2
1
0
1
0
0
1
2
0
0
0
2
1
1
0
0
2
0
1
1
1
1
0
0
0
0
2
1
0
1
0
0
2
0
2
2
0
2
0
0
0
0
2
0
1
0
1
1
0
1
0
1
0
1
3
0
0
1
0
1
0
0
2
0
0
0
0
2
0
0
0
1
2
1
1
1
2
2
0
2
2
2
2
1
2
0
1
1
0
1
0
2
1
1
0
1
0
0
0
0
1
1
0
2
0
0
1
1
1
0
0
0
0
0
1
1
0
0
3
2
0
0
1
0
1
1
1
1
2
1
0
1
0
2
2
0
0
1
2
0
0
1
2
0
0
1
1
0
0
1
2
0
0
0
2
1
0
2
2
1
1
1
3
1
0
3
0
1
1
2
1
0
1
0
1
0
1
0
0
3
2
2
1
0
1
0
1
1
0
1
0
0
1
1
0
1
0
0
2
0
0
0
0
0
1
0
1
1
2
2
2
0
2
0
0
1
0
1
0
0
0
1
3
0
2
0
0
1
0
0
0
1
0
1
2
1
2
0
0
0
2
1
2
2
1
1
1
1
0
1
0
0
0
0
0
0
0
2
1
1
0
0
2
1
0
1
0
2
0
0
1
0
2
0
0
0
1
0
3
3
2
0
1
0
2
0
1
0
0
2
0
2
0
2
1
0
0
0
1
0
0
0
1
1
0
1
0
2
0
1
0
2
0
0
0
0
2
0
0
0
1
1
1
0
1
1
1
1
1
0
1
0
0
2
0
1
2
2
0
0
0
2
1
0
2
1
0
3
0
2
2
1
2
0
0
1
0
2
1
1
0
1
1
2
0
2
1
4
2
1
1
0
0
1
0
0
1
0
0
2
2
0
2
2
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
2
0
0
0
1
0
2
1
1
4
0
2
0
1
1
1
0
1
1
0
2
0
0
0
0
0
1
1
3
0
0
0
1
0
2
1
0
1
2
0
1
2
0
1
0
2
0
2
1
2
0
0
0
1
0
1
0
0
2
1
0
0
3
0
0
1
2
0
0
0
1
0
0
1
1
0
1
0
2
2
1
0
1
0
1
1
1
0
0
0
1
1
1
2
0
1
2
3
0
1
1
2
2
1
0
0
1
2
1
2
0
0
1
1
1
0
0
2
0
2
0
1
0
2
2
0
0
1
0
0
0
2
1
0
1
1
1
2
2
0
0
1
2
0
2
1
2
1
1
0
2
2
0
2
1
2
0
0
1
0
0
0
1
0
2
0
0
2
1
0
2
1
0
3
2
2
0
0
0
0
2
2
1
0
2
2
1
0
2
1
2
0
1
1
0
2
0
0
0
2
1
1
0
1
1
0
1
1
1
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
1
1
0
1
0
1
1
2
2
2
0
1
0
2
0
0
0
1
1
2
0
0
0
2
2
0
1
1
2
0
0
2
3
1
1
2
1
0
0
3
0
2
2
1
1
0
0
1
0
0
1
1
1
0
2
1
0
0
2
2
0
0
0
1
2
0
1
0
0
2
0
2
0
1
1
1
0
1
0
0
0
2
2
0
2
0
0
2
1
2
1
2
2
0
0
1
1
0
1
1
0
0
1
0
1
0
2
1
1
1
1
1
0
0
0
1
0
2
1
1
1
0
1
0
1
1
1
0
1
2
0
0
0
0
2
0
1
0
1
0
0
0
0
2
0
0
1
2
0
0
2
0
1
0
1
2
1
0
0
1
2
1
0
1
1
0
2
0
1
1
0
2
2
1
1
0
2
1
1
1
0
2
2
1
3
1
0
0
1
1
1
1
1
1
0
0
2
1
0
1
0
0
0
0
3
0
1
0
1
0
0
1
0
0
1
0
1
1
0
0
0
1
0
0
1
0
0
1
1
0
2
0
3
0
0
2
0
1
1
1
0
2
1
1
1
0
1
0
3
1
0
0
2
1
0
0
0
0
0
1
0
2
2
0
0
0
1
0
2
1
1
0
2
2
1
0
1
2
0
1
0
2
2
0
0
0
1
2
1
0
1
1
0
1
0
0
2
0
0
1
1
1
1
0
0
0
2
1
2
0
1
0
1
1
0
0
1
0
0
1
0
1
0
2
0
0
1
2
2
1
0
1
0
1
1
0
0
0
1
1
2
2
0
1
0
0
3
1
1
0
2
0
0
0
0
0
1
1
2
0
0
0
2
0
3
0
1
0
1
1
1
0
2
1
0
0
0
2
1
1
1
1
1
2
0
1
2
2
2
0
2
0
2
0
2
1
1
1
1
0
0
1
0
1
2
1
0
0
2
1
0
2
2
0
1
0
2
0
0
1
1
1
2
0
0
1
1
0
1
1
0
1
0
1
0
0
0
0
1
2
1
0
0
0
1
0
0
1
1
0
1
2
0
0
0
0
1
0
2
1
2
1
2
1
1
2
1
1
0
1
1
2
2
1
0
0
2
0
0
2
1
2
2
2
0
0
0
1
1
0
0
2
2
1
0
2
1
1
2
2
0
0
1
0
2
1
2
2
0
2
2
0
1
0
2
1
2
0
3
2
1
2
0
0
0
1
0
0
1
2
1
1
0
2
1
0
0
2
1
1
1
2
0
1
1
1
1
0
0
0
1
1
2
2
0
0
0
0
1
1
2
1
1
1
2
0
0
2
1
1
0
0
1
2
0
3
2
2
1
1
0
0
0
0
1
2
2
0
2
2
1
2
1
0
1
1
2
1
0
1
1
2
0
1
1
1
1
1
1
0
0
0
1
0
0
0
1
1
0
0
1
0
1
1
1
0
2
1
2
0
1
1
0
1
1
2
2
2
2
1
0
0
2
1
2
0
2
2
2
1
1
2
0
0
0
2
2
0
0
0
2
1
2
3
1
2
0
2
2
1
0
1
0
1
0
2
0
2
1
1
0
0
0
0
1
0
0
1
2
1
0
1
0
2
1
1
0
0
2
2
1
1
0
0
0
0
0
1
0
0
2
0
0
1
2
0
0
0
0
1
0
1
2
2
3
2
1
0
1
2
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
1
1
3
0
2
1
1
0
0
0
0
0
1
0
1
0
2
1
1
0
1
1
4
0
2
0
1
2
1
0
0
1
1
0
2
2
0
0
2
0
2
0
0
0
1
0
0
0
1
2
0
2
2
1
0
0
0
2
0
1
0
0
0
0
2
0
1
2
0
2
0
2
1
0
0
0
0
2
0
0
1
1
1
0
0
1
2
0
1
0
0
1
0
1
0
1
0
1
0
1
0
1
1
1
2
1
0
1
0
1
0
0
0
0
2
0
2
0
1
2
2
2
0
0
2
0
0
0
1
0
0
0
1
0
1
1
1
0
1
0
2
1
1
0
2
4
2
1
1
0
2
2
1
0
0
0
1
2
1
0
1
1
0
1
2
1
3
0
0
1
0
2
0
0
0
1
2
0
0
1
1
0
0
1
0
0
2
0
0
0
2
0
0
1
1
4
1
0
0
1
0
2
1
0
0
0
1
2
0
0
0
1
0
1
0
1
2
1
0
1
0
0
1
1
0
1
2
1
1
0
1
0
1
1
1
1
2
0
0
2
0
1
0
2
0
2
0
0
0
6
2
0
1
1
0
0
2
0
1
0
0
0
4
0
2
0
0
0
2
1
1
0
0
1
2
0
0
0
0
2
2
0
0
0
0
2
1
1
1
0
0
1
2
0
0
1
0
1
0
0
1
0
0
1
0
0
2
1
2
2
0
0
0
0
0
0
2
1
1
2
0
1
0
0
1
1
0
0
1
1
1
0
1
0
3
0
0
1
0
2
0
0
0
0
3
1
0
1
1
0
2
0
1
0
0
1
0
0
2
2
1
0
2
1
1
1
0
1
1
0
1
0
2
0
0
1
2
2
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
1
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
2
1
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
2
1
0
2
2
0
1
1
1
1
1
0
0
2
3
0
1
1
1
1
0
1
0
2
0
2
0
1
0
2
0
0
0
1
0
2
0
1
1
0
0
1
1
1
1
2
1
1
0
1
1
0
0
0
0
0
2
0
0
0
2
0
1
1
0
0
1
1
0
2
0
0
0
1
0
1
1
2
1
0
1
2
0
0
2
0
1
1
2
1
1
0
0
0
0
1
0
0
0
2
0
0
1
0
2
0
0
0
1
2
0
1
2
2
0
2
1
0
0
2
0
1
1
1
0
0
0
0
1
1
0
0
2
0
2
0
0
0
2
1
2
1
0
1
0
2
2
1
2
0
2
0
0
1
1
0
1
0
0
0
0
0
1
0
1
2
2
0
0
2
0
0
0
2
2
1
0
1
1
0
0
1
1
1
0
0
2
0
1
1
1
1
0
1
2
1
1
1
2
1
0
0
0
2
2
0
2
2
1
1
1
2
2
1
0
1
0
1
1
2
0
2
1
1
2
2
0
1
2
1
0
0
2
1
0
0
0
1
0
1
1
2
2
0
2
1
0
2
1
5
1
2
2
1
1
1
0
3
1
1
1
1
0
1
1
0
1
2
1
2
2
0
0
1
1
0
0
0
0
0
1
0
1
0
2
0
0
0
0
1
1
1
4
1
2
0
0
0
1
1
2
1
0
1
1
0
1
0
1
0
2
1
0
0
2
1
0
0
1
0
2
0
0
0
1
0
2
1
1
2
0
1
0
2
1
0
1
0
0
0
2
0
1
1
0
0
2
2
1
0
0
1
0
0
1
0
2
1
2
0
0
2
0
5
0
0
0
1
0
2
0
1
5
0
1
3
2
2
2
0
2
0
1
0
0
0
1
1
1
2
0
1
0
0
0
2
0
2
1
1
1
0
0
0
0
0
0
1
1
2
0
0
4
0
1
0
1
0
0
0
2
1
1
0
2
0
2
1
0
0
1
3
2
2
2
0
0
0
0
1
2
2
2
2
1
0
0
1
1
0
0
1
0
1
0
0
0
2
2
1
2
0
2
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
2
0
0
1
2
0
0
1
1
2
0
2
0
2
1
2
0
1
2
0
4
0
4
0
0
0
1
1
1
1
2
2
1
0
2
0
0
1
1
0
0
1
0
0
1
1
2
0
0
1
1
0
1
2
0
1
1
2
2
2
0
1
2
0
0
2
1
2
0
0
2
0
2
2
1
1
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
1
1
2
0
0
0
2
2
2
0
0
1
0
1
0
1
0
0
2
1
1
0
0
1
1
0
1
0
2
0
1
1
2
1
1
1
1
0
1
0
0
0
0
2
1
2
0
0
1
0
0
0
1
0
0
2
2
2
2
0
1
0
0
1
0
0
2
0
1
1
0
0
0
0
1
1
0
2
1
1
0
1
1
0
2
1
0
0
0
0
0
2
1
1
2
1
0
0
0
2
1
2
1
0
0
1
3
1
1
1
1
1
0
1
0
1
1
1
0
0
1
0
2
0
2
1
1
0
0
2
1
0
1
2
0
2
0
0
0
2
0
0
0
0
1
2
1
2
2
0
1
1
0
0
0
0
1
1
0
0
2
0
2
1
1
1
0
1
2
0
0
0
2
2
0
0
0
1
2
2
0
0
0
0
1
0
0
0
0
0
0
2
1
2
1
0
1
1
1
0
0
0
2
0
0
1
1
0
0
1
0
2
2
0
0
0
1
1
1
2
0
0
1
0
0
2
0
0
0
1
0
3
2
2
0
0
0
2
0
1
3
1
0
1
0
0
2
1
1
1
0
0
1
0
0
2
1
0
2
1
1
2
2
0
0
0
1
1
0
2
1
1
2
2
0
2
1
0
0
0
1
0
0
1
0
2
0
0
0
1
0
0
0
3
0
1
1
1
0
0
0
1
0
1
1
0
2
2
0
1
0
1
2
0
1
0
2
0
2
1
1
1
0
1
0
0
2
0
1
0
1
0
0
0
0
2
1
1
0
0
0
0
2
0
1
2
1
2
2
0
0
2
0
2
1
1
2
0
1
1
2
1
1
0
1
1
2
2
1
0
0
2
1
2
1
0
1
0
0
1
1
2
0
0
0
1
0
0
2
2
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
2
2
0
2
2
0
0
0
1
1
1
2
0
2
1
2
1
1
0
0
2
2
1
1
1
1
2
0
0
1
1
1
2
1
0
1
0
0
0
1
0
0
0
0
2
1
0
0
2
1
1
1
0
0
1
1
0
1
1
0
0
1
2
0
0
0
1
2
1
0
0
2
0
2
1
0
2
2
0
2
0
0
1
0
2
1
2
1
0
0
1
1
2
2
2
2
1
1
0
0
2
7
0
1
0
2
0
0
1
2
0
0
0
0
0
1
0
0
0
2
2
1
1
1
0
1
0
0
2
1
1
0
0
1
0
0
0
0
2
1
2
1
0
0
0
1
1
2
2
1
2
1
0
2
0
0
1
1
3
1
1
1
1
0
0
0
0
1
1
0
0
3
0
2
0
0
2
1
2
0
2
2
0
1
0
2
0
0
0
1
1
1
1
0
2
0
0
2
2
0
1
1
1
3
1
1
0
2
0
0
1
2
1
2
0
2
0
2
2
0
0
1
0
1
2
1
0
2
0
0
2
1
1
0
1
1
1
2
1
1
0
5
0
1
0
0
2
0
1
1
0
0
1
0
0
2
0
0
1
0
0
1
1
0
2
2
1
0
1
0
0
0
0
1
2
0
2
0
1
1
2
0
2
0
2
0
1
1
2
0
0
0
0
0
0
0
5
2
1
1
1
0
0
0
1
0
1
2
0
1
1
0
1
0
0
0
0
0
2
1
0
0
2
1
1
2
1
2
2
1
0
4
1
1
1
1
0
1
3
0
0
0
1
1
0
0
0
0
1
0
0
2
2
2
2
0
1
1
2
1
2
0
1
0
1
0
1
1
2
0
2
2
0
0
2
2
1
0
2
0
2
0
1
2
1
2
2
0
1
0
0
0
0
1
0
0
2
1
0
0
1
0
1
0
1
1
1
1
2
1
2
0
0
1
0
0
1
0
0
2
0
1
2
0
1
0
1
1
2
1
1
0
0
3
0
1
1
2
1
1
1
1
0
0
2
1
0
1
0
0
0
0
0
0
0
0
2
0
1
2
1
1
0
2
2
1
0
2
0
2
0
1
1
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
2
4
2
0
0
1
2
2
1
0
1
2
0
1
0
0
0
1
0
0
2
2
0
0
1
0
0
1
0
2
0
0
1
2
0
0
2
0
1
1
0
1
1
0
2
1
0
0
2
1
0
2
0
0
1
2
0
2
0
0
1
0
1
1
1
1
2
1
1
0
2
0
1
0
1
0
0
1
0
0
0
0
0
0
2
2
1
0
2
0
0
1
0
3
2
0
0
1
1
2
0
0
1
0
0
0
2
0
1
1
0
1
3
0
0
1
2
2
2
1
0
0
0
0
0
0
1
0
0
3
1
2
1
1
0
0
2
1
2
0
0
2
1
0
0
2
1
2
0
1
2
2
0
1
0
0
0
0
0
1
0
2
1
0
1
2
0
1
0
0
1
1
2
1
0
2
1
2
0
1
1
1
1
0
1
0
2
1
0
0
1
0
0
0
1
0
1
1
1
0
1
2
0
2
1
0
0
2
1
1
0
0
1
4
2
0
0
1
0
1
2
2
2
1
0
0
0
0
0
2
0
1
0
0
1
2
0
1
0
2
0
1
0
2
3
1
0
0
0
0
1
0
1
1
0
2
0
1
1
1
1
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
2
1
0
0
0
2
0
1
0
0
0
0
0
2
1
2
1
1
1
0
1
2
2
0
2
1
0
0
1
1
2
0
0
2
0
2
1
1
0
2
0
1
2
1
0
2
3
0
1
0
1
0
1
1
1
2
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
2
2
1
0
1
0
0
1
1
2
1
2
0
0
0
1
0
1
1
1
1
0
1
1
2
0
1
2
1
0
0
0
1
2
0
1
0
1
1
0
0
2
0
0
1
2
1
1
0
2
0
2
0
1
1
2
0
2
0
0
0
2
1
1
2
0
2
0
2
0
1
2
0
0
0
0
2
0
2
0
3
2
1
1
1
2
1
0
0
1
1
1
0
0
1
2
1
0
0
0
0
0
1
2
0
2
1
0
2
2
1
2
1
0
0
2
2
0
1
0
0
0
2
0
1
1
2
0
0
0
0
1
1
1
1
1
0
2
1
1
1
0
0
0
1
1
1
2
2
0
1
1
0
0
2
0
1
0
1
0
0
1
1
0
0
1
0
0
0
0
0
1
1
0
1
0
1
1
2
0
0
1
1
0
1
2
0
1
1
2
2
0
0
0
0
1
0
1
1
1
3
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
1
2
1
1
0
2
2
0
0
1
0
1
0
2
0
1
2
0
0
2
2
1
2
1
1
2
2
0
1
1
1
0
0
1
0
2
0
0
1
0
2
1
0
2
3
3
2
1
0
0
1
0
2
0
2
0
1
1
0
0
1
2
1
1
1
0
0
0
0
0
1
0
2
0
0
0
0
2
0
2
1
2
2
0
1
2
3
0
1
0
0
0
1
0
0
0
0
1
2
0
2
0
0
1
1
1
1
0
2
0
2
0
2
0
1
3
0
0
1
1
1
1
0
1
0
0
2
0
0
1
0
0
2
0
0
0
1
0
1
1
0
0
2
2
0
0
1
0
0
0
1
1
0
0
1
0
2
0
1
0
1
1
0
1
0
2
0
0
0
1
1
0
0
1
0
1
1
2
0
1
0
0
1
0
0
1
1
1
1
1
2
1
0
0
0
0
0
1
0
0
1
1
0
1
0
0
1
1
1
2
3
1
1
1
1
0
1
2
0
0
1
0
2
0
0
0
1
0
2
1
1
2
0
0
2
2
1
2
0
0
1
1
2
1
0
0
2
1
1
1
0
0
1
2
0
0
0
0
0
0
1
0
0
2
0
2
0
0
2
0
2
1
1
0
0
1
1
0
0
0
0
0
1
1
0
1
2
1
2
0
1
4
2
0
2
1
0
2
1
0
0
0
2
0
1
2
1
2
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
11
2
0
0
1
2
1
0
1
0
0
0
0
2
0
2
0
0
1
2
2
0
2
0
0
0
1
0
1
1
0
1
1
2
0
1
1
1
0
0
0
1
2
1
2
0
1
0
0
1
2
1
0
1
0
2
2
0
1
0
0
1
2
0
4
2
1
1
0
0
1
0
1
1
1
1
0
0
0
0
1
1
2
3
0
0
0
1
0
2
2
0
0
0
1
0
1
1
1
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
1
0
0
2
0
0
3
1
0
1
0
0
1
1
0
0
2
0
1
5
2
1
0
1
0
0
1
2
0
1
2
1
0
1
0
0
2
1
0
1
2
0
0
0
0
0
1
1
0
0
2
0
0
2
1
0
0
0
0
0
2
0
0
0
2
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
2
2
0
1
0
1
0
2
0
0
0
2
2
0
0
0
0
2
2
0
1
0
2
0
2
2
2
0
0
0
0
0
0
1
2
2
0
0
1
0
0
2
1
2
0
1
1
0
0
1
1
0
2
0
2
1
0
0
0
1
0
2
2
2
2
2
2
4
2
0
2
0
0
2
1
0
0
2
2
1
0
1
0
0
1
2
0
1
0
1
0
1
1
0
0
0
1
2
0
1
0
1
1
0
2
0
1
2
0
1
1
1
1
3
0
0
0
1
2
4
1
0
2
0
1
0
0
2
1
1
0
1
1
2
1
0
1
0
0
0
1
0
0
1
1
1
0
0
1
0
0
0
2
2
0
2
0
2
0
0
1
0
1
1
2
0
0
1
1
2
4
0
3
1
0
2
2
2
0
0
0
1
0
0
0
2
1
2
2
0
0
0
1
2
1
1
0
0
2
2
2
1
1
2
0
0
0
2
0
0
0
2
2
2
0
0
1
0
1
2
1
0
1
2
1
0
0
1
1
0
0
0
1
0
1
0
1
1
1
2
0
2
0
2
0
1
0
2
1
2
0
1
0
1
0
2
0
1
0
0
2
1
2
0
0
0
2
0
0
0
1
0
2
1
0
0
1
3
2
2
1
1
0
0
1
0
0
1
1
0
1
2
0
2
0
1
0
1
0
0
1
1
0
1
0
0
0
0
1
1
2
0
0
2
2
2
0
1
1
0
2
0
1
1
0
0
1
0
1
1
2
0
2
0
0
1
0
0
0
0
2
0
4
2
1
0
0
0
1
2
2
1
1
2
2
0
0
0
2
2
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
1
1
0
1
0
0
0
1
1
1
0
1
1
1
0
2
1
0
0
2
2
0
0
0
2
0
1
2
1
1
1
2
0
1
1
1
0
0
0
0
1
1
0
0
2
1
2
0
2
1
1
1
2
1
0
1
1
0
1
0
1
8
0
2
1
0
0
2
0
2
2
0
0
1
1
0
0
1
0
1
0
1
2
0
1
0
0
0
2
1
3
2
1
0
1
1
1
1
1
0
1
2
0
1
2
0
1
0
0
1
1
0
1
1
0
0
1
1
0
2
0
1
1
2
0
1
2
1
0
0
0
1
1
1
0
0
0
2
0
0
2
1
1
0
1
2
1
2
0
0
2
1
3
2
1
0
0
0
2
0
0
0
1
2
0
0
0
0
1
1
1
1
1
0
0
0
1
0
2
0
0
1
3
0
2
1
0
2
0
1
1
1
2
0
0
2
1
1
0
1
1
0
1
0
0
2
0
1
0
0
0
0
1
1
1
0
1
2
1
1
0
0
1
1
2
0
0
0
1
0
1
0
1
1
1
0
0
0
1
1
2
0
0
2
0
0
2
0
0
2
0
0
0
0
2
2
0
1
0
0
0
0
1
1
0
1
1
1
1
1
1
0
0
0
2
1
1
1
0
0
0
1
0
0
0
1
0
0
2
1
2
1
1
0
1
0
0
1
0
2
0
2
0
0
0
0
2
0
1
0
0
1
0
1
2
0
0
0
0
1
1
0
1
0
0
1
1
2
0
1
1
0
0
0
0
0
1
0
1
0
2
0
1
0
1
0
2
2
0
0
2
1
0
2
0
0
3
0
1
1
1
2
2
1
2
0
1
0
2
0
2
2
2
1
0
1
2
1
0
0
2
2
0
1
2
0
2
2
0
0
1
0
2
0
1
0
1
1
2
0
0
0
0
2
2
1
0
2
1
1
0
2
1
2
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
1
0
2
2
2
0
1
2
1
1
0
0
0
1
0
0
0
0
3
0
2
2
1
3
0
2
0
2
5
0
0
0
0
0
0
1
0
1
1
0
0
0
0
2
1
0
3
0
0
1
0
0
0
0
0
1
2
0
2
0
2
0
0
0
2
0
0
1
0
0
1
2
0
0
2
1
1
0
0
0
0
2
0
0
2
0
0
1
2
2
0
0
1
0
0
2
1
1
0
0
1
1
0
2
2
1
1
1
0
0
0
2
2
1
3
1
0
1
1
2
0
0
1
1
0
0
2
2
0
0
1
1
2
0
0
0
0
2
2
0
0
0
1
0
2
1
0
1
1
0
3
1
0
0
1
0
0
0
2
0
1
2
0
1
1
0
2
1
1
1
0
1
0
1
1
0
2
0
3
0
1
0
0
1
0
1
0
0
0
2
1
2
0
1
0
2
1
0
2
0
2
2
2
0
1
0
1
2
0
2
7
1
2
1
0
0
1
1
2
0
2
2
1
1
0
2
0
2
0
2
3
0
2
0
0
0
0
0
0
2
0
1
0
2
2
1
0
2
1
2
1
2
2
1
2
1
0
1
0
0
0
0
0
0
0
0
3
1
0
2
0
1
1
0
1
1
3
2
1
4
2
0
0
0
0
2
2
1
1
0
0
0
2
1
2
0
2
1
0
1
2
0
1
0
0
0
2
0
0
3
0
0
0
0
1
2
1
0
0
2
2
2
1
0
0
0
1
1
2
0
1
1
2
2
2
0
0
2
0
2
2
0
0
0
0
1
1
0
0
0
0
2
0
1
0
1
1
0
0
2
0
1
0
3
0
1
0
0
0
0
0
1
1
0
0
1
2
0
2
0
1
0
0
2
0
1
0
0
0
2
1
1
1
2
1
1
1
1
0
2
0
1
1
2
1
0
2
1
1
1
0
1
2
0
1
2
0
0
0
1
0
1
2
0
0
0
0
1
1
0
1
2
2
1
0
2
0
1
0
0
2
1
2
0
1
0
0
1
0
2
1
1
1
1
1
0
0
0
0
0
1
1
1
0
0
1
1
0
1
0
1
0
1
0
1
0
0
0
0
0
0
2
2
1
0
1
1
0
2
0
0
3
1
0
1
1
0
1
0
2
0
0
0
0
0
2
1
1
1
0
2
2
0
1
1
0
0
0
0
0
0
2
1
1
1
2
0
1
2
1
1
0
0
1
0
0
0
2
0
1
0
0
0
1
1
2
2
0
0
0
0
0
1
2
2
1
2
0
0
1
1
1
2
0
1
1
2
0
3
0
0
0
2
0
0
1
0
3
0
2
0
0
0
2
0
0
1
0
0
1
0
1
0
0
1
2
1
2
0
0
1
1
0
1
0
0
0
0
0
1
0
2
2
0
0
1
1
1
0
1
1
1
0
1
0
0
1
0
0
0
1
1
1
0
3
0
1
1
2
0
0
1
1
1
1
1
0
1
1
0
2
1
1
1
0
0
1
2
2
0
1
0
1
0
2
2
0
0
0
2
1
1
1
3
0
2
0
0
0
0
0
4
0
0
0
0
1
0
1
0
2
1
2
2
1
1
0
0
0
0
0
0
2
1
1
2
1
2
1
1
1
0
1
0
2
0
1
1
0
3
1
0
0
1
0
0
2
0
0
2
0
1
2
0
0
1
0
2
0
2
0
2
2
1
2
0
3
1
0
0
0
2
1
0
0
1
0
1
0
1
1
2
0
0
1
2
1
0
0
1
2
2
0
2
0
0
1
2
0
2
1
1
2
1
2
0
0
1
1
2
1
2
1
0
0
1
1
2
0
1
1
1
0
0
1
2
3
0
0
1
0
1
1
0
0
1
0
0
1
2
0
0
0
2
2
0
0
0
2
1
2
0
2
1
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
2
0
0
0
2
1
0
0
0
0
0
3
1
2
2
1
0
0
2
1
0
0
0
2
0
1
0
0
1
1
0
0
1
0
0
1
1
0
2
2
0
0
0
0
2
0
2
0
0
0
0
2
0
1
0
0
0
1
1
0
0
1
0
1
2
0
1
0
2
1
0
0
1
0
1
0
1
0
0
0
0
2
0
2
0
0
1
2
0
1
2
0
0
2
2
0
1
0
1
0
1
2
0
1
0
1
0
1
1
0
2
4
0
1
3
2
0
0
0
1
1
0
1
3
1
0
0
0
0
0
3
1
0
2
0
0
0
0
0
1
2
1
2
1
2
1
1
2
2
0
1
1
0
1
2
0
0
0
0
0
2
0
2
2
2
2
2
1
1
1
1
0
1
1
1
1
0
0
0
0
0
0
2
0
0
2
0
1
0
2
0
1
1
1
0
0
0
2
2
0
0
0
2
2
0
2
0
0
1
0
0
1
2
0
1
0
1
1
1
1
0
1
0
1
0
0
0
1
1
2
0
2
0
0
1
1
1
0
1
1
0
2
0
1
1
1
1
0
1
1
2
0
2
1
0
0
1
1
1
0
0
2
1
0
1
1
1
1
0
3
2
0
2
1
0
2
0
0
3
0
0
2
0
2
2
0
2
0
0
1
1
0
2
2
2
1
0
0
2
0
0
0
1
1
1
1
0
1
1
0
0
2
1
1
0
0
0
0
1
0
3
1
0
1
0
1
2
2
0
2
1
0
2
1
1
1
2
1
0
0
0
1
0
1
0
1
2
2
2
1
1
2
0
0
0
0
0
0
1
0
1
2
1
0
0
2
1
1
0
1
2
0
0
0
2
2
0
2
0
0
0
0
0
3
2
0
0
1
1
1
3
2
0
1
0
2
0
0
0
0
1
0
1
1
0
0
1
1
0
0
1
0
2
1
1
2
2
2
0
1
1
0
2
1
0
0
1
0
2
2
0
0
0
2
1
2
1
0
2
0
1
0
1
0
2
2
1
0
1
0
0
1
2
0
1
1
0
1
1
2
0
0
2
1
0
3
1
0
0
0
1
0
1
2
1
0
2
0
0
1
2
2
0
0
2
0
1
2
1
1
2
0
2
2
0
0
0
1
2
0
2
0
1
0
0
2
0
3
0
1
0
0
1
0
0
1
1
0
1
0
0
1
0
1
0
1
1
0
0
0
1
0
0
0
2
0
0
1
2
2
2
1
2
2
0
2
0
1
1
0
0
0
1
1
0
0
2
1
0
1
2
1
1
0
0
0
0
1
2
1
2
2
0
2
0
0
1
2
0
2
0
1
1
0
0
3
0
0
1
1
0
0
2
1
1
1
0
2
1
1
1
1
0
0
0
1
1
3
0
1
1
2
0
1
0
0
1
2
0
1
2
0
1
2
0
2
2
1
1
2
0
1
1
1
1
1
0
2
2
0
1
2
0
0
1
2
0
1
0
1
1
1
0
2
0
0
1
2
1
0
0
1
0
0
1
2
0
0
0
0
1
1
0
0
1
3
0
2
1
0
1
1
1
1
1
2
0
0
1
0
0
0
1
6
0
1
0
1
1
2
1
0
0
0
2
1
0
0
1
1
1
0
0
2
0
0
0
1
2
1
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
2
0
0
0
0
2
2
1
1
1
2
1
2
0
0
1
1
0
0
2
0
0
1
1
3
2
2
1
0
2
1
0
0
0
0
2
0
2
0
0
2
0
2
0
0
2
0
1
0
0
0
1
0
0
0
1
2
0
1
1
0
2
1
1
0
0
1
1
2
1
1
1
1
2
1
0
1
1
1
2
0
0
0
0
2
0
1
0
0
1
1
2
1
0
0
2
0
1
0
2
1
0
1
2
1
3
0
2
0
0
0
0
1
0
0
1
2
0
2
0
0
0
0
0
2
1
0
1
0
1
0
2
1
0
2
1
2
0
0
0
1
0
1
0
2
0
2
0
2
0
0
2
1
1
0
1
0
0
2
0
1
3
0
0
0
2
0
1
2
2
2
2
1
1
0
1
0
2
2
1
1
1
1
0
0
2
2
0
0
1
2
0
2
1
1
0
1
1
1
0
0
0
1
1
2
1
1
1
0
2
0
1
1
1
0
1
0
0
1
0
2
2
2
0
0
2
1
0
1
0
2
1
2
0
0
1
0
0
0
2
2
1
0
0
0
2
3
1
2
1
0
0
0
0
3
0
0
2
2
1
0
2
2
0
0
0
1
2
1
0
1
2
0
1
1
0
1
1
2
0
1
0
0
0
2
0
1
0
2
0
1
2
0
0
2
0
1
0
0
2
1
0
0
1
1
1
3
1
2
2
0
1
1
1
2
1
0
1
1
1
2
2
0
1
0
1
1
3
0
0
2
0
2
0
2
0
0
0
0
1
2
0
0
0
0
1
1
2
0
0
2
1
1
0
0
3
2
0
2
2
1
0
0
0
1
0
1
2
1
0
5
0
0
0
2
1
0
1
1
0
0
3
0
1
1
1
1
0
0
2
1
1
1
0
1
1
0
0
2
0
2
2
0
1
1
1
0
0
3
1
2
0
0
2
0
0
0
0
0
0
1
1
1
1
1
1
0
0
0
1
1
2
1
2
2
1
0
2
0
1
0
1
1
1
1
1
0
1
1
0
2
1
1
2
0
0
0
0
0
1
0
1
0
0
1
0
2
3
2
1
2
2
2
2
2
2
0
0
0
1
0
1
2
0
0
0
0
0
1
0
0
1
1
0
3
0
2
0
2
1
1
2
1
1
2
0
0
0
2
0
1
0
1
2
2
1
2
1
2
2
0
2
0
2
1
1
1
2
2
1
1
3
0
1
1
0
0
1
1
2
0
1
0
0
1
0
1
1
1
0
0
0
0
0
1
1
0
1
0
2
1
1
0
0
0
1
1
1
2
1
0
0
0
1
1
0
0
1
0
0
1
1
0
2
0
0
0
1
0
2
1
1
2
0
1
1
0
2
1
1
0
0
0
1
1
2
2
2
0
0
0
2
0
1
0
1
1
1
0
0
1
1
2
1
0
2
2
1
1
2
0
2
0
1
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
2
2
2
0
0
0
0
2
1
0
2
2
0
0
0
2
0
2
0
1
2
0
0
1
1
0
0
2
0
1
0
1
0
0
2
1
0
0
0
1
1
2
0
1
1
0
2
0
0
0
0
0
3
1
13
2
0
2
4
0
2
0
0
1
0
0
1
0
0
0
1
0
1
1
1
1
1
2
1
1
0
2
1
1
1
1
2
2
1
0
0
2
0
1
0
0
0
1
1
2
2
1
0
2
0
2
0
0
1
0
1
0
2
1
2
0
1
1
0
1
1
0
2
1
1
0
2
1
1
0
0
6
1
1
1
1
0
2
1
1
1
1
1
0
2
2
0
1
1
0
0
1
2
0
0
0
0
1
1
1
2
1
2
1
0
0
0
1
0
0
0
1
1
0
2
0
0
0
1
0
1
0
0
2
0
1
2
0
1
0
1
0
0
0
2
0
1
0
1
0
0
1
1
1
2
1
0
2
0
1
1
0
0
0
1
1
1
1
1
1
0
0
0
0
1
1
1
0
1
2
0
0
1
2
0
0
1
1
1
1
0
0
0
2
0
1
1
1
0
0
1
0
0
1
0
0
1
0
0
0
1
1
1
2
1
0
1
1
0
3
1
2
1
0
1
0
1
1
0
1
0
1
2
0
2
0
0
0
0
2
1
1
0
1
1
1
2
0
2
1
1
2
0
2
2
1
2
2
1
1
1
0
0
0
1
1
0
2
0
0
0
2
1
1
0
1
0
0
2
0
4
1
0
1
1
0
2
2
1
0
1
0
2
0
1
0
1
1
0
0
0
1
1
1
2
0
1
0
2
0
0
2
0
1
0
0
1
3
0
1
0
1
1
1
1
0
1
1
1
0
0
1
1
0
0
0
0
2
0
0
2
1
0
0
2
1
1
0
0
0
0
1
0
3
2
0
2
1
2
2
2
0
0
2
1
2
0
1
1
0
2
0
1
0
0
0
4
0
0
1
1
0
0
1
1
1
2
1
1
0
1
1
2
2
0
0
0
0
0
0
1
0
0
2
1
1
0
1
2
1
0
1
0
0
2
0
0
2
1
1
1
0
0
0
2
1
1
1
2
0
0
2
0
1
0
0
1
1
1
0
3
0
1
2
2
1
1
2
0
1
0
0
0
1
1
0
0
2
1
1
0
2
2
0
0
0
0
1
2
1
1
0
0
0
0
2
0
1
1
0
2
0
2
0
2
1
1
0
0
0
0
0
0
0
2
1
2
0
0
0
0
2
0
1
1
0
0
2
0
2
2
2
1
0
1
2
1
0
0
2
1
0
0
1
1
1
1
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
2
0
1
0
1
0
2
1
0
1
1
0
1
0
2
0
1
0
0
2
3
0
1
1
1
0
0
0
0
2
3
0
0
0
0
1
1
1
1
0
0
0
0
0
0
1
1
1
0
0
2
1
0
0
0
2
2
1
0
2
2
0
1
0
0
1
1
0
1
1
1
0
2
1
2
0
0
2
3
0
1
0
2
0
0
1
0
0
2
0
3
0
1
0
0
1
0
0
2
0
3
1
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
4
0
1
2
1
0
1
0
0
6
0
1
0
1
1
1
0
0
1
1
0
0
2
0
1
0
0
0
0
0
1
1
0
1
1
1
0
2
1
0
1
0
1
0
1
0
0
0
0
0
1
0
2
1
1
0
2
2
1
1
2
0
2
0
0
0
1
0
1
0
0
0
2
1
0
0
0
2
1
1
2
0
2
0
1
1
1
1
0
0
0
1
0
1
0
0
0
2
0
1
0
2
1
1
1
0
1
0
0
1
0
1
0
0
0
0
0
2
1
2
2
0
1
1
1
1
0
1
2
0
0
0
1
0
1
0
2
0
0
0
0
1
2
1
0
2
3
0
1
1
1
2
2
0
0
0
0
1
0
1
1
0
0
2
1
0
2
1
0
2
1
1
1
0
1
1
1
1
2
0
1
3
2
2
1
1
1
2
2
0
0
1
0
2
0
0
2
1
0
0
0
0
2
2
2
0
0
0
1
0
0
0
0
1
2
1
0
2
1
0
0
1
0
1
0
1
1
0
0
0
0
1
0
1
0
0
2
0
1
1
0
2
2
2
1
1
0
1
1
2
1
1
1
0
0
0
1
0
0
1
1
2
0
0
0
1
1
3
1
0
2
1
1
1
1
0
0
0
0
1
0
2
1
1
0
1
1
0
2
1
3
0
1
1
4
1
2
2
1
1
2
0
0
2
0
0
1
1
0
0
0
3
2
0
1
1
0
0
1
2
0
1
1
1
2
1
1
1
1
0
0
0
0
0
1
1
1
0
0
0
1
0
0
1
1
0
0
0
1
0
2
1
1
0
0
1
1
1
1
1
3
0
0
0
1
0
2
1
0
2
1
2
0
1
0
1
2
1
0
1
0
0
1
0
0
2
0
0
1
0
0
0
2
2
0
0
0
1
0
0
1
1
0
1
0
1
0
0
1
0
1
1
1
2
0
1
2
0
0
4
1
0
0
0
0
0
2
0
1
1
0
1
1
0
0
0
2
0
1
0
0
0
0
1
3
0
0
0
2
2
0
0
2
1
0
2
1
0
1
1
2
0
2
1
1
2
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
1
2
1
2
1
1
1
0
1
0
1
1
1
2
0
0
0
1
1
2
1
0
0
1
1
0
0
1
1
0
1
0
0
1
0
0
1
0
0
0
2
2
0
1
0
1
0
1
0
0
1
2
2
1
1
1
1
0
0
2
0
2
2
0
1
1
0
0
1
2
0
3
0
2
0
2
0
1
2
0
0
0
0
0
0
0
0
1
0
2
0
0
1
2
0
0
0
2
1
2
2
0
1
1
2
1
2
1
0
0
0
2
1
1
0
0
2
2
0
0
0
0
0
2
1
2
0
1
0
1
2
2
0
1
0
0
0
0
1
1
0
0
2
2
2
0
1
0
0
0
0
2
0
1
0
0
0
0
1
0
0
1
2
0
0
2
2
1
1
0
1
1
1
0
0
0
1
2
1
2
1
0
2
0
0
0
0
1
0
0
0
0
1
1
2
0
0
0
2
0
2
2
0
2
0
0
0
0
0
2
1
1
0
1
0
0
0
0
1
0
1
0
0
1
0
1
2
1
1
2
1
1
0
2
0
0
1
0
1
0
0
0
3
0
0
0
0
1
2
1
2
0
2
0
0
1
0
1
1
1
1
0
0
0
1
0
1
1
0
1
1
0
2
1
1
0
0
2
2
1
0
1
2
1
0
2
1
0
0
1
0
1
0
0
1
0
2
2
2
1
1
1
0
0
1
0
0
1
2
1
1
2
0
0
0
0
0
1
0
2
1
0
1
2
2
1
0
1
0
1
0
0
1
0
1
0
0
2
1
1
0
0
1
1
0
1
0
0
0
2
1
0
0
0
0
2
0
0
3
0
1
1
0
1
0
1
0
1
1
1
0
0
1
0
0
0
0
1
1
1
0
2
1
0
2
0
1
0
1
1
0
1
0
2
2
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
1
2
0
1
1
1
1
0
1
0
1
1
0
2
2
0
1
0
1
1
2
1
1
1
1
0
0
1
1
0
2
0
0
2
2
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
2
0
1
1
2
2
0
1
2
0
0
0
2
1
3
0
2
1
0
3
1
1
0
0
1
0
0
1
0
1
0
2
0
0
0
2
1
1
1
1
1
0
0
1
1
0
0
3
2
0
1
0
2
0
1
0
0
0
2
2
3
0
1
6
2
0
1
0
2
0
1
0
1
0
3
1
0
0
0
2
1
0
0
2
1
0
1
0
2
0
1
2
1
1
2
0
0
2
3
0
2
1
3
2
0
2
0
2
4
2
0
0
2
2
2
0
1
1
1
0
0
2
0
0
1
0
0
1
0
0
1
2
0
0
0
1
0
0
1
2
0
1
1
0
1
2
0
1
0
1
4
1
0
1
0
0
0
2
0
1
2
0
0
2
1
2
1
0
0
2
1
2
0
0
0
1
0
1
0
1
0
2
2
0
1
3
0
0
2
0
0
0
1
0
2
0
1
0
0
2
0
1
0
0
1
0
2
0
1
1
0
0
0
2
1
0
0
1
2
1
0
0
0
2
2
0
1
0
0
1
0
0
1
1
1
2
1
1
0
0
1
0
0
2
1
0
0
1
0
0
0
4
0
1
1
1
2
0
3
0
2
1
1
0
1
1
2
0
1
2
2
1
0
2
0
2
1
1
2
2
0
0
0
0
2
0
2
0
1
0
0
1
0
0
1
0
0
2
1
1
1
1
0
1
1
0
1
0
0
0
2
0
1
0
2
1
0
0
0
0
0
1
0
2
0
2
1
4
0
2
0
0
1
0
0
3
1
1
1
1
0
1
1
0
1
0
1
2
0
0
0
0
0
2
0
0
1
1
0
0
1
0
3
0
3
0
1
2
1
1
1
1
1
0
1
0
2
1
1
0
0
2
0
0
2
0
0
0
0
0
2
1
1
1
2
1
2
0
0
0
2
2
0
2
1
2
0
0
1
1
0
0
2
0
0
0
0
2
0
1
1
1
0
1
0
1
0
0
2
3
2
1
2
0
0
1
0
1
0
1
0
0
0
1
1
0
1
1
0
1
0
1
1
0
2
0
1
3
0
0
0
0
1
2
1
2
0
0
0
1
0
7
0
0
2
0
0
2
1
3
0
0
1
0
2
2
0
0
1
1
1
0
0
0
0
2
1
2
1
0
0
1
2
0
3
2
0
8
0
1
0
2
0
2
2
0
1
0
1
1
1
1
0
0
1
1
2
0
1
2
2
1
2
0
1
2
2
0
2
0
0
0
0
0
1
2
1
0
2
0
1
1
0
1
0
1
0
2
0
0
0
1
0
1
0
0
0
2
1
0
1
1
2
1
0
0
2
1
1
0
0
1
0
3
1
0
0
1
1
0
1
1
0
0
1
1
1
0
1
0
0
2
3
2
0
0
2
1
0
0
2
0
1
1
0
0
2
0
0
1
0
0
0
1
2
2
0
0
0
2
2
0
0
2
1
1
0
0
2
1
0
2
1
1
1
0
0
1
0
0
0
0
0
1
2
0
0
2
1
0
2
1
0
2
1
0
1
2
1
2
0
1
1
4
1
2
0
1
1
0
1
0
0
1
1
2
1
0
1
0
1
0
1
2
0
1
0
2
1
1
1
1
1
1
0
2
1
2
1
2
1
0
3
2
0
0
0
1
0
1
1
0
0
0
2
1
2
1
1
0
3
0
1
0
0
1
1
0
0
0
2
2
2
0
1
0
1
0
1
1
1
1
0
1
0
0
1
2
1
0
2
2
2
1
1
0
0
1
0
0
0
0
0
1
0
1
1
1
0
1
0
2
0
2
0
1
2
0
2
1
0
2
0
0
1
1
1
1
0
0
0
0
0
2
0
1
0
0
0
0
0
1
1
0
2
0
2
0
0
0
1
0
2
0
0
1
1
1
2
1
1
0
1
1
0
0
2
0
2
1
0
0
0
1
1
0
2
0
1
2
1
0
0
1
0
1
0
0
1
0
2
0
0
0
0
0
0
0
1
1
1
0
1
1
2
1
0
2
1
2
0
0
0
1
2
2
1
0
2
1
2
2
2
2
0
1
0
0
2
1
0
0
0
1
0
1
0
1
0
0
2
1
0
1
0
1
2
1
0
1
2
1
1
0
2
0
0
0
1
1
1
0
1
1
0
1
1
2
0
1
0
2
1
0
0
2
1
2
0
0
2
0
1
0
0
0
2
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
3
1
0
0
1
3
2
1
1
1
1
1
1
1
2
1
0
2
1
2
0
1
0
1
0
0
0
0
0
1
0
1
1
0
1
2
0
2
1
2
0
0
1
0
0
2
0
0
1
0
0
0
1
0
2
2
2
2
0
1
0
1
0
0
2
1
2
2
0
2
0
0
1
1
1
2
1
2
0
2
0
1
1
2
0
1
2
0
1
1
2
1
0
2
0
0
1
0
0
0
2
1
1
0
1
1
1
0
0
0
0
1
2
0
0
1
0
0
2
0
1
1
0
0
1
0
2
0
0
0
0
1
0
2
2
1
2
0
2
2
0
0
0
0
2
0
1
0
0
0
2
0
1
0
1
2
1
1
1
1
2
0
0
1
1
2
2
0
1
0
1
2
1
1
0
0
1
1
0
0
0
0
0
0
2
0
0
1
1
0
0
1
0
2
0
1
1
1
0
2
0
1
2
1
0
0
1
1
0
0
0
2
1
1
0
1
1
2
0
0
0
1
0
0
2
1
1
0
0
1
2
0
2
0
0
0
1
2
0
0
1
0
0
0
1
0
0
0
0
2
1
0
1
2
0
2
2
0
0
1
2
1
2
0
0
1
2
0
1
0
0
0
1
1
2
1
0
1
0
0
0
0
0
0
1
2
0
1
2
0
0
0
0
1
0
1
1
2
0
1
2
1
2
1
1
0
0
1
0
0
2
1
0
1
0
1
1
1
2
2
0
2
0
1
0
0
1
1
0
1
1
0
2
0
1
1
1
0
1
0
1
0
0
1
1
0
0
0
1
0
1
0
1
0
1
1
1
2
2
1
1
2
0
1
1
0
0
1
0
2
0
0
0
0
0
1
3
2
2
1
2
0
1
2
0
0
2
1
0
0
3
1
1
0
2
0
0
0
1
0
1
0
0
1
1
1
2
2
1
2
1
2
1
2
3
0
0
1
2
0
1
1
1
0
0
3
1
0
2
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
2
2
0
0
0
2
1
1
0
1
3
0
0
1
3
1
0
1
0
1
0
0
0
0
2
2
2
0
2
0
0
0
1
0
1
0
0
0
2
0
1
0
0
0
2
0
1
0
2
0
0
2
3
0
0
1
1
0
2
0
1
1
3
4
0
1
1
0
2
0
1
0
0
0
1
2
2
1
0
1
1
1
0
2
0
0
2
1
2
2
1
1
0
0
1
0
0
1
2
1
0
0
0
0
1
2
0
1
0
0
0
0
2
2
0
0
0
0
0
1
2
0
1
1
0
0
0
1
1
1
1
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
2
0
2
1
0
0
0
0
1
1
1
0
1
1
0
0
1
0
2
0
1
0
0
1
0
2
0
0
0
0
0
3
0
1
1
1
0
0
1
1
1
0
0
1
1
2
1
1
0
1
0
1
0
2
0
0
0
0
0
2
0
0
0
1
1
2
1
0
0
0
0
1
0
0
0
1
1
1
2
1
1
0
0
0
0
1
2
1
2
1
1
0
2
2
0
2
0
2
2
2
0
0
1
2
0
1
0
0
0
2
0
0
2
0
2
1
0
1
1
2
1
0
0
0
0
1
0
0
1
0
1
0
1
0
1
1
1
0
1
1
1
1
0
0
0
1
3
1
0
0
2
0
1
0
0
0
0
1
1
1
1
2
2
1
0
0
1
0
1
1
0
1
0
1
0
0
0
1
1
1
0
1
0
2
0
1
1
2
0
1
1
0
0
1
0
0
0
1
0
2
0
0
1
1
0
0
0
0
2
0
1
0
2
1
0
1
0
0
0
1
2
2
2
1
0
0
2
2
1
0
0
1
1
1
2
0
1
2
1
1
1
0
0
0
2
2
1
2
0
0
1
0
0
0
0
3
1
0
2
1
0
1
1
0
2
1
0
0
1
0
0
1
2
0
0
1
1
2
0
0
0
0
0
0
0
1
0
0
1
0
1
1
1
2
0
1
0
0
5
0
0
1
1
0
1
2
0
0
0
1
1
1
0
0
1
0
1
4
0
1
2
0
1
0
0
1
0
0
0
1
1
1
1
0
0
1
0
1
1
0
2
1
1
0
0
2
0
0
1
0
0
0
0
1
0
0
1
0
2
0
0
4
1
0
1
1
1
0
1
1
0
2
2
2
1
0
0
1
1
1
0
0
2
2
0
0
0
1
0
0
0
2
0
2
4
0
0
1
0
0
0
0
1
0
0
2
1
1
0
1
0
0
1
1
0
0
2
0
0
1
0
1
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
1
2
0
0
3
1
0
0
1
0
1
0
0
1
1
1
2
1
0
0
1
1
0
0
0
0
1
0
2
1
0
2
1
1
2
0
0
2
1
0
0
0
0
1
2
0
1
1
0
1
2
1
2
0
2
1
2
0
2
1
1
3
0
0
0
0
1
2
1
2
0
1
1
0
2
0
1
2
2
1
0
0
0
1
1
0
0
0
2
1
1
0
0
0
1
0
0
0
1
1
0
1
2
0
2
1
0
0
1
0
1
0
0
1
1
0
0
0
1
3
0
0
2
0
1
0
0
0
0
2
0
0
0
0
2
0
1
0
1
1
2
0
0
0
1
1
1
1
0
1
0
1
1
0
0
0
1
2
0
2
0
0
1
0
0
0
0
2
0
0
0
1
1
2
1
1
0
2
1
1
1
0
0
3
1
0
1
0
1
3
0
1
1
0
0
0
1
1
1
0
0
0
2
2
0
2
1
1
0
0
0
2
2
2
1
1
2
1
1
1
0
0
2
1
1
1
0
0
0
1
1
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
2
0
1
0
2
0
1
0
0
1
0
2
0
2
2
0
2
1
2
0
3
1
1
0
0
1
0
2
1
1
0
2
0
0
1
0
2
0
2
1
0
2
2
2
1
0
1
2
0
2
1
1
0
0
1
1
0
0
0
1
2
1
2
1
0
0
1
1
0
1
2
3
1
0
2
1
1
0
0
1
1
0
0
0
0
0
0
2
2
0
1
0
0
0
1
1
1
1
0
0
3
0
2
0
0
0
1
0
1
1
0
0
0
0
2
0
0
1
0
1
2
0
1
0
0
0
0
1
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
2
2
4
0
2
0
1
1
1
1
0
2
0
0
2
0
2
0
0
0
0
0
0
3
0
1
0
0
0
2
1
2
0
0
0
0
1
0
0
2
0
2
1
0
2
0
1
2
2
0
2
0
0
1
2
2
0
0
2
1
0
2
0
0
0
1
2
0
0
0
1
1
1
0
1
2
2
2
1
2
1
1
1
0
4
1
0
2
0
0
0
0
2
0
1
3
0
1
0
2
1
2
0
2
1
2
1
0
1
1
2
1
1
1
1
1
1
1
1
0
1
2
2
2
0
1
2
1
0
1
2
0
0
2
0
0
1
1
0
1
2
2
0
1
2
0
2
0
0
1
2
1
1
0
0
0
0
1
1
1
1
0
1
2
1
1
0
0
1
1
2
0
2
0
0
1
0
2
0
0
1
0
1
1
0
0
1
1
0
0
0
2
4
1
1
1
1
2
0
2
2
0
1
0
2
2
0
1
1
0
0
0
5
0
0
0
0
0
1
0
2
2
1
3
0
0
0
1
2
0
0
1
1
0
1
0
0
0
0
1
2
0
2
1
0
0
0
0
2
0
1
0
0
1
2
0
0
0
0
0
2
2
1
1
0
0
1
0
1
2
0
0
0
0
2
0
1
0
0
1
0
0
2
0
0
1
1
0
1
0
0
1
1
2
0
0
1
0
1
0
0
0
3
0
1
0
2
1
1
0
2
2
0
0
0
0
2
1
2
0
2
0
1
2
0
1
0
2
1
0
1
0
1
1
0
1
0
1
0
1
1
1
0
0
1
0
1
2
2
0
0
1
0
1
0
0
0
0
1
0
1
0
1
0
2
1
1
0
2
0
1
0
1
0
0
1
0
1
2
1
1
2
0
0
0
0
0
1
0
2
0
1
2
0
0
2
3
0
0
0
1
1
1
0
1
1
2
0
0
0
0
3
1
2
0
0
2
1
2
0
0
0
2
0
0
0
0
1
1
1
1
0
1
2
2
0
1
0
1
2
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
2
1
0
1
0
1
1
2
0
1
1
2
1
2
2
1
1
1
0
0
0
1
2
0
2
0
0
1
1
0
0
1
1
0
0
0
2
0
3
2
2
1
0
1
2
0
1
1
0
2
0
0
0
3
0
1
0
0
2
1
0
0
1
1
1
1
0
2
0
0
2
2
1
2
1
1
1
1
0
1
1
0
1
2
0
0
1
0
0
2
0
0
0
2
1
1
0
1
2
0
1
1
0
1
2
0
1
1
1
1
3
0
0
0
1
1
0
3
0
2
2
0
0
1
0
2
2
1
0
0
1
1
1
0
0
2
0
1
0
0
0
1
3
2
1
0
0
1
2
2
0
0
0
0
2
0
2
2
1
1
1
0
2
2
0
1
0
0
1
2
2
2
1
0
1
0
1
1
1
0
0
2
0
1
0
2
1
1
0
2
0
0
1
0
0
0
0
0
0
2
1
0
0
1
1
0
1
0
1
1
2
0
1
0
0
1
1
1
1
0
0
2
0
0
1
1
0
1
1
1
1
0
2
0
2
1
1
1
5
1
2
1
3
2
0
0
0
1
1
0
0
0
1
0
0
0
2
2
1
1
0
3
0
0
0
0
2
0
1
0
1
0
0
2
0
0
3
0
1
0
2
0
1
0
0
0
0
1
0
0
1
2
0
0
1
1
1
2
1
0
0
2
0
2
0
2
2
0
1
2
0
1
0
0
0
2
1
1
2
1
0
1
0
1
2
2
0
1
1
2
2
0
0
0
0
1
0
1
0
1
2
0
0
2
1
1
1
2
1
0
1
1
0
1
2
0
1
3
1
2
0
0
0
0
2
0
1
3
1
1
0
2
0
0
0
1
1
0
2
0
2
0
0
1
0
2
2
2
0
2
0
0
0
0
0
0
0
1
0
1
1
1
0
0
2
0
1
1
1
1
1
0
0
1
1
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
1
0
2
0
6
2
0
1
1
1
1
1
0
1
0
2
3
0
0
2
2
0
0
0
1
0
0
2
1
0
0
0
2
0
2
2
0
1
1
1
1
1
0
0
0
0
2
0
0
1
0
0
1
0
1
0
0
2
0
2
0
3
1
2
1
0
1
0
1
0
0
0
0
1
2
0
2
1
0
2
0
2
0
2
1
0
1
0
1
2
1
1
0
0
2
2
1
0
0
1
0
0
0
1
2
0
2
2
1
0
0
0
0
0
0
2
0
0
0
1
0
0
2
1
2
2
2
1
1
1
1
1
1
0
1
0
1
2
1
0
0
0
2
2
0
2
2
2
0
1
1
0
1
0
1
0
1
0
2
0
1
0
2
0
0
0
0
2
2
2
1
0
2
0
2
0
0
1
1
0
0
0
1
0
0
1
0
2
2
1
0
0
2
2
0
0
1
1
0
2
2
1
1
2
0
0
0
0
1
0
2
1
2
0
2
2
0
2
0
2
1
2
2
0
0
0
1
0
1
0
0
0
0
1
1
0
0
1
0
1
2
2
0
0
1
2
0
0
2
1
0
0
0
1
4
2
1
0
2
0
0
0
1
1
1
0
1
0
2
0
1
0
2
0
0
2
1
0
1
1
0
1
0
0
2
0
0
1
0
0
1
1
0
0
0
1
2
0
0
1
0
0
0
0
1
3
0
2
0
0
2
0
2
2
0
1
0
0
0
0
1
1
1
1
0
0
0
2
1
1
0
1
0
1
0
2
2
0
1
1
0
0
0
2
1
2
1
1
2
0
3
0
0
2
0
3
1
0
1
0
1
0
0
2
1
2
1
2
2
0
0
2
2
0
1
0
1
0
0
2
0
1
1
0
0
2
1
0
0
2
0
0
2
2
0
2
0
1
0
0
2
0
1
0
1
1
0
1
0
0
0
0
1
2
2
1
0
2
1
2
2
2
0
0
0
1
1
1
1
1
0
0
0
2
1
0
0
2
1
0
0
0
1
1
0
1
0
1
0
3
0
2
0
0
0
0
2
0
1
2
0
0
0
2
0
2
1
0
1
1
1
3
0
1
1
2
1
1
0
0
2
2
0
0
1
8
2
2
1
0
0
0
2
0
0
1
1
3
0
0
1
1
1
1
1
0
2
0
2
2
0
1
1
2
2
1
2
1
2
1
0
1
0
1
1
1
0
1
0
2
1
0
0
0
0
3
2
0
1
0
1
3
1
1
1
1
1
0
1
0
2
0
1
1
1
0
2
2
1
0
0
0
0
2
0
1
2
1
0
1
0
0
0
2
0
0
1
1
1
2
2
0
1
1
1
1
0
1
1
2
2
2
0
0
0
0
2
1
3
1
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
2
0
1
0
2
1
2
0
3
0
1
0
2
2
1
0
0
0
0
3
0
0
0
0
0
0
0
2
1
0
1
1
0
2
1
1
4
1
0
1
1
0
0
2
2
0
2
0
2
0
1
1
1
1
2
0
2
0
1
1
0
1
0
1
0
0
0
1
0
0
1
0
2
1
1
0
1
0
2
0
1
2
1
0
0
2
1
1
1
1
1
2
0
2
0
0
0
2
0
2
0
0
0
3
2
2
0
2
1
0
1
1
2
2
0
0
2
2
0
0
1
1
2
1
3
0
2
0
1
1
1
2
0
0
1
0
0
0
2
1
2
0
0
0
1
1
9
1
2
0
1
0
0
1
1
1
2
0
0
1
2
2
2
1
2
1
2
0
0
2
2
0
0
2
0
0
1
0
0
0
1
2
2
2
0
1
2
1
0
1
1
1
0
1
2
1
0
1
2
1
0
2
0
1
1
0
2
1
1
0
1
0
0
1
1
2
0
0
1
0
0
1
0
2
0
2
0
1
2
0
2
2
1
0
1
1
0
0
0
1
2
0
1
0
0
1
2
0
1
1
0
0
1
0
1
0
2
0
2
1
0
0
2
0
0
2
0
1
2
1
0
0
2
1
2
0
0
0
2
0
1
1
0
2
1
1
1
0
1
0
0
2
1
1
0
1
1
0
1
1
1
1
3
1
1
1
1
2
0
0
2
0
1
1
1
2
0
0
0
0
2
1
1
0
3
1
1
1
1
1
0
1
0
0
1
0
2
0
1
0
0
0
1
1
1
1
0
2
1
0
1
0
0
1
0
1
2
0
0
1
2
0
1
0
1
1
1
1
0
1
1
0
1
1
1
0
0
1
0
0
2
0
2
0
1
1
2
1
0
0
0
2
1
0
0
0
0
2
0
0
0
1
2
1
1
0
1
1
0
2
0
3
0
1
0
2
0
0
1
2
1
0
0
0
0
0
2
0
0
1
2
1
1
2
2
0
0
1
2
1
0
2
2
2
0
0
1
0
0
2
0
0
0
1
2
0
1
0
1
0
2
0
2
1
2
0
1
1
2
1
0
1
2
0
1
1
2
2
2
1
1
0
2
2
0
3
0
1
0
5
0
0
0
1
0
1
1
0
4
1
1
2
0
2
7
0
0
0
2
0
1
1
2
0
0
1
0
2
1
0
2
1
0
0
0
2
0
0
2
1
0
0
0
3
0
0
0
0
2
0
2
0
1
1
0
1
2
0
1
0
0
1
0
2
0
0
2
0
1
2
1
2
2
0
0
2
0
1
0
1
1
1
1
0
1
0
1
0
0
1
0
2
1
2
2
0
0
0
1
1
0
0
0
0
0
2
2
1
0
1
2
2
0
1
0
0
2
2
1
0
0
0
3
0
0
0
0
0
1
0
1
0
1
1
1
1
0
0
1
0
0
0
0
1
0
1
0
1
0
1
1
1
0
0
0
2
2
0
1
2
0
0
1
1
0
1
0
0
0
0
1
0
0
2
0
1
2
1
3
0
0
0
2
1
2
0
1
1
0
0
0
2
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
1
2
1
0
1
1
2
1
1
0
0
0
0
0
0
2
2
1
1
2
0
2
0
2
0
0
1
1
0
2
0
1
2
0
0
1
1
0
1
0
0
1
0
0
0
0
1
2
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
1
2
1
2
0
0
1
2
2
0
0
0
2
0
0
0
0
2
0
0
2
2
0
1
0
1
0
2
0
2
1
0
1
2
0
1
1
2
1
0
0
1
2
0
1
0
1
0
1
0
0
0
0
0
2
2
1
0
1
0
1
1
0
2
0
2
1
0
2
2
0
0
4
0
1
0
0
0
0
0
1
2
2
0
1
0
2
1
1
4
2
2
2
2
2
1
0
1
0
2
1
0
0
0
0
0
1
0
0
2
0
2
1
2
1
2
1
1
1
2
0
2
1
1
0
0
3
1
2
1
1
2
2
0
1
2
1
0
1
2
0
0
0
1
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
2
1
0
0
0
0
2
1
1
1
2
2
0
0
1
0
2
1
0
0
1
0
1
7
0
0
0
0
0
1
1
0
1
3
2
1
1
1
0
0
0
1
1
0
0
2
0
0
1
0
1
1
0
2
0
0
0
0
0
0
0
0
1
2
0
0
1
1
0
1
2
0
1
0
0
0
0
1
1
1
2
0
1
0
2
0
2
0
1
0
1
1
1
1
1
1
0
0
0
2
1
1
1
1
1
0
0
0
1
0
1
1
1
2
1
1
1
1
1
1
0
0
1
1
1
1
0
0
0
0
0
1
0
0
1
2
1
1
0
1
0
0
1
0
1
1
0
1
0
0
0
2
2
1
0
1
0
1
0
1
0
2
0
0
5
0
0
1
0
2
0
1
3
1
1
0
1
0
0
2
1
1
0
1
2
0
0
1
0
1
0
1
2
0
3
2
1
0
2
0
0
0
2
0
0
1
2
1
0
1
2
1
1
2
1
0
0
0
2
2
0
1
0
2
2
2
0
1
0
1
1
3
0
1
2
0
2
0
1
0
2
0
2
0
0
1
0
1
1
0
1
2
2
1
2
0
1
2
1
0
0
0
0
0
1
0
1
1
1
0
1
0
0
0
0
1
2
1
1
2
0
1
1
0
0
0
1
1
1
0
0
1
1
2
0
0
1
1
1
1
0
2
1
0
1
1
1
0
0
2
1
0
0
1
2
1
0
2
1
1
0
1
2
0
1
0
2
4
0
0
0
2
0
0
1
0
0
1
0
0
0
1
0
0
1
0
2
0
0
2
1
1
1
0
1
0
1
0
1
1
0
0
2
1
2
0
0
2
1
1
0
1
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
3
0
2
0
2
0
2
2
1
2
1
1
1
2
1
2
0
0
1
0
0
2
0
2
0
1
1
0
0
1
0
1
0
2
0
0
0
1
1
2
2
0
0
1
0
2
1
2
1
1
2
0
1
1
2
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
1
0
0
0
1
0
1
3
1
0
1
0
1
0
2
0
1
1
0
1
0
0
0
0
1
0
0
0
2
1
1
2
0
2
2
0
0
0
2
2
0
0
0
0
0
1
0
0
2
2
0
2
0
0
0
0
0
1
0
0
1
2
0
2
1
0
0
0
0
0
1
0
1
2
2
0
1
0
0
0
0
0
2
0
0
2
2
2
1
0
0
0
0
0
2
4
0
0
2
2
0
2
0
1
2
0
1
1
0
1
1
1
0
1
0
1
3
0
1
1
0
0
0
2
0
0
0
0
1
0
1
2
0
2
0
0
0
1
0
1
1
0
1
1
2
1
1
0
0
1
0
0
2
0
0
1
2
0
0
1
1
0
1
0
1
0
1
1
2
0
2
0
1
1
0
0
1
3
1
1
2
0
2
0
2
0
1
0
0
0
1
1
0
0
2
0
2
1
1
1
1
1
2
4
2
0
0
1
1
0
1
0
0
0
1
0
0
0
1
1
1
0
0
0
2
2
1
0
0
2
2
0
0
1
1
0
0
2
1
0
0
1
1
0
0
0
1
3
2
2
1
1
0
2
1
1
1
2
1
1
1
1
1
1
0
1
2
0
0
2
2
1
0
3
1
0
1
1
1
1
2
1
2
1
0
2
0
0
1
2
1
0
1
0
2
2
2
1
0
0
1
0
3
2
0
2
1
1
0
2
0
1
1
1
0
1
0
1
1
1
0
2
0
0
0
0
1
1
0
2
1
0
1
2
0
1
0
1
0
0
0
1
1
0
1
0
1
1
1
0
0
0
1
0
0
1
0
0
1
1
1
2
0
2
3
1
0
1
0
1
0
1
0
4
0
1
1
1
2
0
1
1
2
1
0
2
2
1
1
0
0
0
0
2
0
0
0
0
0
0
1
2
1
2
1
0
0
0
0
2
0
1
0
1
1
1
0
0
1
1
0
0
2
0
0
2
2
0
1
2
0
0
1
1
1
0
2
4
0
2
1
1
0
0
5
1
2
2
2
2
0
2
1
1
1
0
2
2
2
0
0
2
0
2
2
0
0
0
1
0
1
2
1
1
0
3
2
0
0
2
1
2
0
0
2
3
0
0
1
1
5
0
0
1
0
1
0
0
1
1
1
1
1
0
0
0
1
0
0
0
2
0
1
1
1
0
1
0
0
1
0
1
1
1
0
2
1
1
2
2
0
0
0
1
0
2
0
1
1
0
1
0
0
0
2
1
2
1
2
2
2
1
1
1
0
0
1
2
1
1
0
0
0
2
0
0
0
0
0
1
0
2
2
0
1
0
0
0
0
2
0
0
2
0
0
1
3
1
2
1
0
0
1
1
1
0
2
2
0
0
2
1
1
0
0
2
1
1
0
2
0
0
1
0
1
3
1
2
2
2
1
0
0
0
1
0
1
2
2
1
0
2
1
2
0
2
2
2
2
2
0
1
0
0
1
0
2
1
0
0
0
0
1
1
0
2
0
0
0
0
1
0
2
0
1
1
0
0
0
3
0
0
2
1
2
2
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
1
1
0
0
0
2
1
0
0
0
0
1
1
1
2
0
1
2
1
1
2
0
0
1
0
0
1
2
2
2
0
0
1
0
1
0
2
0
1
1
0
1
2
0
0
2
1
0
2
2
1
0
2
1
1
0
0
0
0
0
0
1
1
2
0
0
2
3
1
0
0
2
0
0
0
1
0
0
0
1
0
2
1
0
0
0
2
0
0
1
0
1
0
1
1
0
0
1
2
2
0
1
1
0
0
2
0
0
2
2
1
1
0
1
0
0
2
1
0
0
0
1
0
1
1
2
0
1
0
0
0
2
0
1
0
0
1
1
2
1
1
3
2
0
0
1
2
0
1
1
0
1
0
0
2
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
2
1
1
3
0
1
0
0
0
1
0
1
2
2
0
0
2
2
1
2
2
0
0
1
2
1
1
1
1
1
1
0
0
0
0
1
0
0
0
1
1
0
0
4
0
0
1
1
1
1
1
2
0
0
1
2
0
0
0
0
2
2
0
1
1
0
2
0
0
1
1
0
0
1
0
1
0
2
1
1
1
0
0
8
1
1
2
0
2
1
0
2
2
0
0
2
2
2
0
1
0
2
0
1
0
1
0
1
3
0
0
2
2
1
0
1
0
0
0
1
0
0
1
1
2
2
1
2
1
0
0
1
0
0
0
1
1
1
1
2
1
1
0
1
0
2
1
0
1
0
0
1
0
2
1
1
0
0
1
0
2
1
1
2
2
0
0
1
2
1
0
0
2
0
1
2
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
3
0
2
0
1
0
1
0
2
2
0
3
0
0
2
1
0
2
0
2
2
1
1
1
1
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
2
1
1
0
2
1
2
1
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
1
2
0
1
2
1
0
4
0
1
1
0
1
0
2
0
0
0
2
0
1
2
0
1
0
2
1
1
1
3
2
2
0
0
2
0
2
1
1
0
1
0
0
2
0
0
2
0
1
1
0
1
0
2
0
1
1
0
0
0
0
1
0
2
2
1
1
1
1
0
0
1
0
2
0
0
0
1
2
0
1
0
0
1
2
0
1
0
0
0
1
2
2
0
1
1
1
2
1
1
1
0
1
0
1
2
2
1
0
1
1
0
2
1
1
1
2
1
0
1
0
1
0
2
1
0
1
3
1
0
1
1
1
0
1
1
1
0
1
0
0
1
0
0
0
1
2
0
0
0
0
0
0
2
1
2
1
1
0
4
1
0
1
0
0
0
1
2
2
1
0
1
0
1
2
1
1
1
2
0
2
0
1
2
0
1
0
2
1
1
2
0
2
0
1
1
1
1
0
2
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
2
1
0
0
0
2
1
1
0
1
0
0
0
0
2
1
1
0
0
0
2
1
0
0
1
0
1
1
1
1
1
0
2
0
0
0
1
1
0
1
0
0
1
2
2
2
2
2
1
0
1
0
0
0
1
2
0
1
1
0
0
2
0
1
0
2
1
0
0
2
1
0
2
1
1
1
1
0
1
0
0
1
0
1
2
0
0
2
0
0
2
1
0
2
1
0
0
1
2
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
1
3
0
1
1
2
1
4
0
1
2
2
0
0
0
2
0
1
1
0
3
3
1
0
0
2
0
1
2
0
2
2
0
1
0
1
1
0
0
2
0
0
1
0
0
2
1
1
0
0
1
0
1
0
1
2
1
0
1
1
1
0
2
2
0
0
1
1
0
2
2
0
2
1
2
1
1
1
0
1
0
1
0
3
0
1
1
0
1
0
1
0
0
2
2
0
1
1
2
4
2
2
1
1
0
1
2
2
0
1
2
1
2
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
2
2
0
2
0
0
1
1
0
1
0
0
0
1
1
0
2
0
2
0
0
1
0
0
0
2
1
1
2
0
2
0
0
1
1
0
1
1
0
1
0
2
0
1
1
1
2
0
2
1
2
1
2
1
0
0
0
2
0
1
1
1
1
1
0
1
0
1
0
0
0
0
0
0
1
0
1
0
2
2
0
0
1
1
6
2
1
2
0
0
2
1
0
1
0
1
1
0
2
0
0
2
1
3
1
0
0
0
0
2
1
1
1
1
0
2
2
2
2
1
1
1
0
1
1
1
0
2
1
0
1
1
1
0
1
0
0
0
1
0
2
0
0
2
0
1
0
0
0
1
1
0
0
3
1
2
1
1
0
1
2
0
1
0
1
1
0
0
0
0
2
1
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
2
2
2
1
1
0
0
2
2
1
0
1
4
1
0
2
2
0
1
2
1
0
0
1
1
0
2
0
2
1
0
1
0
0
1
1
1
0
2
1
0
0
0
2
1
1
1
1
1
1
1
0
2
2
2
0
2
0
2
1
0
0
2
0
2
0
2
0
1
0
1
0
1
2
1
1
2
0
0
0
1
0
0
1
2
0
0
2
1
1
0
0
2
0
0
0
2
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
2
2
2
0
0
2
0
1
2
1
3
1
1
0
2
0
0
0
2
2
2
2
2
2
0
1
1
2
2
0
1
5
2
2
1
1
2
1
1
0
1
0
1
1
1
1
0
0
1
0
0
1
1
1
0
1
1
0
0
0
1
0
2
1
1
1
1
1
1
0
0
0
1
1
1
2
0
1
1
0
0
1
1
0
2
1
2
0
1
0
0
2
2
1
0
1
0
0
1
0
0
1
0
0
0
1
2
0
0
2
2
0
0
0
1
1
0
2
2
1
0
2
0
1
0
0
1
1
0
1
0
2
0
0
1
0
0
2
0
0
2
0
0
1
0
0
2
2
0
0
2
1
0
0
0
2
0
0
0
2
0
0
2
1
1
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
2
1
0
2
1
1
2
2
1
0
0
1
1
0
0
1
2
1
0
0
1
0
0
1
0
0
0
0
0
0
0
2
1
0
0
1
1
0
0
1
0
2
0
2
0
0
0
3
0
1
2
1
0
1
1
2
1
0
0
0
2
0
1
2
1
0
1
0
1
0
0
0
0
1
0
0
2
0
0
1
2
0
0
1
1
1
1
0
0
1
1
1
0
2
2
1
0
1
0
1
0
0
2
1
1
1
1
0
1
2
0
2
0
0
0
1
1
0
2
2
0
0
2
2
0
0
1
0
1
0
2
2
0
1
0
0
1
0
0
0
1
0
2
0
1
0
1
0
0
1
2
0
0
1
2
0
0
1
0
0
2
0
0
2
2
0
0
2
1
0
1
0
0
0
0
1
1
1
1
1
0
1
0
0
1
2
2
1
1
0
1
2
1
1
0
1
1
0
1
2
0
3
0
2
1
0
2
0
2
1
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
1
0
0
1
1
0
0
2
0
1
1
1
0
0
0
2
0
2
0
2
0
0
1
0
0
1
1
0
2
0
0
1
3
1
2
0
1
1
2
0
0
2
1
0
1
3
1
0
2
0
0
0
0
1
0
1
1
1
0
1
2
0
1
0
0
5
0
2
1
0
1
1
0
0
2
0
0
1
0
1
0
1
2
0
1
0
1
2
0
0
1
2
1
0
0
0
3
1
0
1
1
0
1
1
0
0
1
1
0
0
1
0
2
0
0
0
0
0
2
3
0
0
0
1
0
2
2
2
1
0
0
1
1
1
0
0
0
0
1
0
1
1
0
1
0
1
2
0
1
1
0
0
2
1
1
2
2
1
1
1
0
1
0
0
1
2
0
1
0
0
2
1
1
2
2
0
1
2
2
0
0
1
2
0
1
2
0
0
1
1
0
1
2
1
0
0
2
1
0
1
0
0
0
0
0
2
0
0
2
0
1
1
2
0
0
0
0
0
1
1
1
0
0
1
0
1
1
2
0
0
1
0
1
1
1
0
0
0
0
1
0
0
0
1
2
2
0
2
1
0
0
1
0
2
0
0
0
2
0
0
2
1
1
0
0
0
1
0
0
3
0
0
3
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
2
0
0
1
1
1
1
1
2
0
1
0
1
1
0
0
1
0
1
0
1
2
1
2
2
3
2
0
0
0
0
0
1
3
1
1
0
0
0
0
0
0
1
0
0
1
0
2
0
0
1
0
0
1
1
1
0
0
0
1
1
1
0
2
0
1
1
1
1
2
1
3
0
0
0
2
0
0
1
0
0
1
1
1
2
2
1
1
0
1
0
0
1
0
0
1
0
0
2
1
0
1
1
1
0
0
4
1
1
2
1
0
2
0
1
1
2
1
0
2
0
2
2
0
1
1
0
2
1
1
2
0
1
1
0
0
1
0
0
1
0
1
0
4
2
0
2
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
1
1
1
2
0
0
1
1
1
2
0
0
1
1
0
2
0
0
1
1
2
0
0
1
0
1
0
0
0
0
2
0
2
0
1
0
2
0
2
2
0
1
0
0
0
0
4
0
0
1
2
0
1
1
1
0
2
0
0
1
1
0
0
0
1
0
1
2
2
0
0
0
0
2
0
1
1
1
1
0
1
1
2
0
0
1
0
1
0
0
1
1
1
0
0
0
2
2
1
0
2
1
0
0
0
0
0
1
2
2
2
0
0
0
0
0
1
0
0
0
1
0
1
1
2
2
0
2
0
0
0
0
0
0
0
2
0
1
1
0
0
2
0
0
0
2
1
2
0
0
2
0
1
0
0
2
2
2
0
2
0
0
1
2
1
2
0
1
1
0
1
1
0
0
2
1
2
0
0
0
1
2
1
0
1
1
0
1
2
0
0
2
3
1
1
1
0
2
1
2
0
0
1
0
0
0
2
2
1
1
1
1
0
0
0
1
0
0
0
0
0
0
2
0
2
1
1
2
2
1
0
0
2
1
0
2
2
0
2
0
0
1
0
0
0
1
2
1
0
0
0
0
1
1
2
0
0
0
0
0
1
1
2
2
1
2
0
1
1
0
0
1
0
0
0
0
0
0
2
0
0
1
0
2
0
1
0
2
1
2
0
1
2
0
0
1
0
1
2
0
0
0
0
0
0
1
0
2
1
0
1
2
1
0
1
2
1
1
2
0
1
2
1
1
0
0
0
2
0
1
0
0
1
0
2
0
1
0
2
0
0
1
0
1
1
0
0
1
1
1
0
0
0
2
0
0
1
2
0
0
0
1
1
1
1
1
2
2
0
0
2
0
1
1
0
0
0
1
2
0
2
1
1
1
2
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
2
1
1
0
0
1
0
0
0
0
0
1
1
0
2
1
2
0
0
2
2
1
1
0
0
0
0
2
0
0
2
0
0
1
1
0
0
1
1
0
1
0
1
0
1
0
1
0
0
1
0
0
2
1
0
1
2
2
2
2
1
0
2
0
1
1
1
3
0
0
0
0
1
0
1
1
0
0
2
0
1
2
1
0
0
1
0
2
2
2
0
0
0
2
0
0
0
2
2
0
1
0
0
0
0
2
0
2
0
4
0
2
0
0
1
1
0
0
0
1
2
0
2
0
1
1
1
2
1
0
0
0
1
2
0
0
0
2
1
0
2
0
2
0
0
1
1
2
0
1
0
1
0
1
0
0
1
0
0
1
1
0
0
1
0
0
1
0
2
0
2
0
2
0
0
2
0
0
1
0
0
1
1
0
0
1
2
2
0
2
0
2
0
0
0
0
1
0
1
1
0
2
0
2
1
2
0
0
0
2
1
1
1
0
1
1
0
0
0
1
1
0
0
0
0
1
0
1
2
1
1
0
0
0
0
0
1
1
0
1
1
0
1
0
1
1
0
0
1
1
0
1
0
0
0
2
0
0
2
0
2
0
2
2
0
0
1
0
1
2
0
0
1
0
0
1
0
0
1
0
0
0
0
1
2
0
2
2
0
0
0
1
0
1
2
2
0
0
0
0
2
0
0
1
1
0
0
0
0
1
0
0
0
0
0
2
0
0
1
1
0
1
2
2
0
1
1
0
4
2
2
0
1
0
0
1
0
2
1
2
1
0
2
0
0
1
0
0
0
0
2
1
2
1
0
0
1
2
0
2
0
0
2
0
2
1
1
0
1
0
0
0
2
1
0
2
0
2
2
1
2
2
1
0
0
3
0
4
1
1
0
1
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
1
1
2
1
1
0
2
0
1
0
0
2
0
2
1
1
1
0
0
1
0
1
0
1
0
0
0
0
0
0
1
1
2
2
1
0
1
0
2
2
0
0
0
3
0
2
0
1
1
0
1
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
1
2
1
1
0
0
0
0
2
1
2
0
1
1
0
1
0
0
2
0
0
0
0
2
0
2
0
2
1
1
0
1
0
1
1
2
2
0
2
0
1
4
0
2
1
2
1
0
2
0
0
1
0
1
1
1
1
1
1
0
0
1
1
2
0
0
2
0
2
1
1
1
1
1
0
2
0
0
2
2
0
1
1
1
0
0
2
0
1
0
0
0
1
2
0
0
0
1
2
1
2
1
1
0
1
2
1
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
1
1
2
0
1
0
2
1
2
0
2
2
0
0
0
0
1
0
2
1
0
0
4
0
0
0
0
0
0
1
1
1
0
2
1
0
0
0
1
1
2
2
2
0
0
0
1
1
0
2
1
1
1
0
0
1
1
1
0
1
2
1
0
1
0
1
1
0
1
2
1
1
1
2
1
0
2
0
1
1
2
0
0
0
1
0
0
2
0
1
0
0
0
1
0
0
1
0
0
2
0
1
2
2
0
1
1
1
0
0
0
10
1
0
2
0
0
0
2
0
1
0
0
2
2
2
0
1
3
2
0
0
1
1
1
1
2
3
1
1
1
0
0
2
0
1
0
2
0
1
0
2
1
0
1
1
0
0
2
1
1
1
1
2
0
0
2
1
0
1
1
2
0
1
1
0
0
2
0
0
2
2
0
1
0
1
2
1
1
0
1
0
0
0
1
1
0
2
2
2
1
1
2
1
0
1
0
1
1
0
0
2
0
0
1
2
0
2
0
1
1
2
0
0
1
0
1
2
2
0
0
0
0
0
0
0
0
1
2
1
0
1
0
0
0
1
1
0
0
0
0
2
2
1
0
0
0
2
0
0
0
2
0
0
1
1
1
1
2
2
1
1
0
2
1
3
1
1
0
0
1
0
0
1
1
0
0
2
0
2
1
0
1
1
1
0
2
2
1
1
0
1
0
2
1
1
0
1
1
0
0
0
1
0
2
1
1
0
1
1
0
2
0
0
0
0
2
0
0
0
0
1
2
2
0
0
0
0
2
0
0
2
1
2
0
0
0
0
2
2
1
0
0
1
0
1
1
0
0
1
1
0
0
1
2
1
0
0
0
1
2
2
1
2
1
0
2
0
0
0
0
0
2
2
2
1
0
0
2
3
1
0
0
1
0
0
1
0
0
0
2
2
1
0
0
2
0
0
0
1
0
0
1
1
1
0
2
0
1
1
0
0
1
2
2
0
0
0
1
1
1
0
0
0
0
1
2
0
2
1
2
0
0
1
2
0
1
0
0
0
1
0
1
0
1
1
1
2
1
1
2
1
1
0
0
1
0
1
0
1
0
2
2
0
1
1
0
1
2
1
1
2
0
0
1
1
0
0
1
2
0
2
0
0
1
1
2
0
0
2
1
1
0
0
0
1
1
0
0
0
2
2
0
2
1
1
2
0
0
1
2
0
1
1
2
1
1
2
2
1
0
2
1
1
1
0
0
1
1
1
0
2
2
3
2
1
1
0
1
2
1
0
0
1
0
2
2
1
0
0
0
0
0
0
2
1
0
1
3
2
0
0
1
1
2
0
2
4
0
0
0
1
1
2
1
1
0
1
0
0
1
2
1
0
1
0
0
0
2
0
1
0
1
1
0
0
0
1
2
3
0
0
0
2
1
1
2
1
1
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
1
0
0
2
1
0
0
0
1
0
0
0
1
2
1
0
1
1
1
2
1
0
1
0
1
2
0
0
0
0
1
1
2
0
0
0
1
2
2
1
0
1
2
0
0
3
0
0
4
0
1
2
0
0
0
0
1
0
1
1
0
2
0
0
2
1
2
0
0
0
1
2
0
0
0
0
0
0
1
0
0
2
0
1
1
0
1
0
0
0
1
2
0
2
1
0
1
0
0
1
1
1
1
1
0
2
1
2
1
1
0
0
1
0
1
0
1
1
0
0
1
1
0
1
0
0
2
2
0
1
0
0
0
2
0
0
1
1
0
0
1
1
2
4
1
1
1
0
1
0
2
0
0
0
0
1
2
0
0
0
0
0
1
1
3
1
1
1
1
2
0
0
2
0
2
2
0
0
0
2
1
2
2
1
1
0
2
1
0
1
2
0
1
0
0
1
1
0
1
0
2
0
0
1
1
1
1
0
0
0
0
0
2
2
1
2
1
1
1
0
2
2
0
0
0
1
0
2
2
1
0
1
1
2
1
0
1
1
2
2
0
0
0
0
0
1
0
2
2
1
2
0
1
1
0
2
0
0
1
0
1
2
2
2
1
1
0
1
2
0
2
0
1
3
1
1
0
1
0
0
3
2
0
2
1
0
0
2
0
0
2
0
0
0
2
1
0
0
0
0
2
1
0
0
0
1
2
0
1
1
0
0
1
2
0
1
2
1
0
1
3
0
2
2
2
1
1
2
2
2
0
0
2
0
0
0
2
0
1
3
1
1
2
2
2
0
2
2
0
1
0
0
0
0
3
1
0
1
1
0
2
1
0
1
1
0
0
0
0
1
2
1
1
0
0
0
0
0
0
0
0
0
1
0
2
1
2
0
2
1
0
0
0
1
2
1
3
0
2
2
1
0
1
1
0
0
1
2
2
1
1
1
0
1
1
0
2
0
0
2
0
0
1
1
2
0
1
1
0
0
0
0
0
2
1
2
3
0
0
1
1
0
0
0
0
1
1
0
1
1
1
0
1
0
2
0
0
0
2
0
2
0
1
0
1
1
0
2
1
1
1
0
0
1
1
0
0
2
0
3
2
3
0
1
1
0
0
2
1
2
0
0
0
1
2
1
1
1
0
2
0
0
0
0
0
0
2
2
0
0
0
1
1
0
1
1
0
0
0
0
0
1
2
1
2
0
2
1
1
1
1
0
2
0
0
0
2
0
0
1
1
0
0
0
2
2
1
0
0
0
2
2
0
0
0
1
2
0
1
0
0
0
0
0
2
0
2
0
2
0
1
0
2
1
1
1
1
1
0
0
0
1
0
0
0
2
1
1
1
2
1
2
3
1
1
1
2
0
1
0
0
2
2
1
0
0
3
2
0
0
0
0
0
2
2
0
0
0
0
0
1
0
1
0
1
0
2
1
2
2
2
2
0
0
0
0
0
2
0
2
1
0
0
1
2
0
0
0
2
1
2
1
1
0
0
0
0
0
0
0
0
1
1
2
2
1
1
0
0
0
1
1
1
0
0
0
1
0
1
1
1
2
0
0
0
2
0
0
1
1
0
1
0
2
1
0
1
1
1
0
2
0
0
1
0
2
1
1
0
0
1
2
0
0
1
0
0
2
0
2
0
1
0
0
1
1
1
1
1
0
0
1
0
0
0
1
1
2
0
4
0
0
0
0
1
0
2
0
1
0
0
3
0
1
0
1
0
0
1
0
1
1
0
0
0
1
2
1
0
0
0
0
1
0
1
0
2
1
1
1
0
4
0
1
0
0
0
0
1
0
2
1
0
0
1
0
1
1
1
1
1
0
1
0
2
2
2
1
1
0
0
1
0
1
0
0
2
1
0
2
2
0
2
0
1
0
1
1
0
0
1
2
1
0
1
2
0
0
0
1
2
2
0
1
0
1
1
1
1
0
2
0
0
0
0
1
1
3
0
2
0
1
0
1
1
2
1
3
0
2
1
2
0
0
1
0
0
1
0
0
1
1
1
2
0
2
2
1
2
1
0
1
0
0
0
1
0
2
0
3
1
2
0
1
0
0
1
2
1
1
0
3
1
0
0
0
0
0
0
0
2
1
2
2
0
1
1
0
0
0
0
2
0
1
0
0
0
2
0
1
2
0
1
1
0
1
0
0
0
2
1
3
0
0
1
1
0
0
0
0
1
0
0
3
1
2
2
1
1
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
2
1
0
1
1
1
0
0
0
0
0
1
1
1
2
1
2
0
2
2
0
2
0
0
1
0
0
0
1
1
1
0
0
1
0
1
1
0
0
1
2
1
1
0
0
1
0
1
2
1
2
0
0
0
0
2
1
1
2
1
0
1
1
2
1
1
1
2
1
1
0
2
0
2
0
1
1
0
0
1
1
2
2
0
1
2
0
2
0
2
1
1
2
0
1
1
1
0
0
2
0
1
1
1
1
0
1
0
1
0
0
1
1
1
1
0
3
2
1
0
0
0
0
0
0
0
0
1
1
0
1
1
1
2
1
1
0
0
0
1
1
4
2
0
2
0
1
0
0
2
1
0
0
2
2
1
0
2
1
0
2
0
1
1
2
0
1
0
0
0
2
0
0
0
0
2
1
1
1
2
2
1
0
0
1
1
0
0
0
1
0
0
0
2
1
3
1
1
2
0
1
1
0
0
0
0
0
0
1
0
0
2
0
0
2
0
1
1
1
1
0
2
2
0
0
0
2
2
1
0
0
2
0
0
0
0
0
0
3
1
0
0
0
1
0
1
1
0
0
1
0
0
0
0
1
1
0
0
1
0
0
2
0
1
0
2
0
2
2
1
0
1
1
0
1
1
0
0
0
3
0
1
1
0
0
1
0
0
1
1
1
0
1
0
1
1
1
0
0
3
0
0
2
0
1
0
0
0
1
0
2
0
0
2
2
0
1
1
0
2
1
0
0
1
0
0
0
2
1
1
0
2
1
0
1
0
0
0
2
0
0
0
1
0
0
2
1
0
0
2
1
0
1
2
0
0
0
1
1
1
2
2
0
2
1
2
1
2
2
1
0
1
1
0
1
0
0
0
1
1
0
1
1
2
1
1
0
1
0
1
1
2
1
1
0
2
1
1
0
0
0
0
2
0
3
0
0
0
1
1
0
1
0
1
1
1
1
1
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
2
1
1
1
2
0
0
0
2
1
2
0
2
0
2
2
0
0
1
1
0
1
2
0
2
1
2
1
2
1
1
2
0
0
0
0
1
0
0
0
2
1
2
0
0
0
0
3
2
2
0
1
1
1
0
2
0
2
0
1
2
2
0
1
1
0
1
0
2
0
2
6
1
2
1
0
0
2
0
1
1
1
0
1
2
0
0
0
0
1
0
4
1
1
1
1
0
1
2
1
0
1
1
0
1
0
0
2
0
0
0
1
0
0
1
1
0
0
1
1
1
0
2
0
2
2
1
1
0
1
1
1
0
0
0
0
1
0
1
0
0
0
0
0
2
1
0
1
2
0
1
0
2
2
0
0
2
0
1
2
2
0
0
0
1
2
1
1
0
2
1
0
0
2
1
1
0
0
0
0
1
2
0
1
0
0
1
1
1
1
1
0
0
1
0
0
1
2
0
1
0
1
2
1
0
2
0
0
2
0
0
0
2
0
0
1
0
0
0
0
2
1
0
1
0
0
0
1
2
17
0
0
1
0
0
0
1
1
2
2
0
2
2
0
0
2
0
0
0
1
0
5
0
1
0
1
1
2
1
0
2
0
1
0
1
0
0
0
0
0
1
1
0
0
2
1
1
1
0
1
0
0
1
0
0
1
0
1
0
1
0
2
1
0
2
0
0
0
2
0
3
1
1
1
1
1
2
0
0
0
1
2
0
1
0
0
0
2
0
1
1
0
1
0
1
0
0
0
1
0
0
1
1
0
2
1
0
1
2
0
0
2
2
1
1
0
1
1
0
1
1
0
2
2
3
0
1
2
1
0
0
0
1
0
1
0
1
1
2
1
0
1
1
0
0
1
2
0
1
0
0
1
2
0
1
0
1
1
2
2
0
2
0
0
1
2
0
1
0
1
0
2
0
2
0
1
0
2
0
1
1
1
0
0
0
0
2
1
1
0
1
0
1
1
2
0
2
2
0
0
1
0
3
1
2
0
2
1
1
0
1
0
0
1
1
1
1
1
0
0
2
1
0
0
1
1
1
1
0
1
0
0
1
1
0
0
0
0
0
2
2
1
0
1
1
2
0
0
0
0
1
0
0
0
0
0
1
1
1
1
0
0
0
0
0
1
1
1
0
2
0
1
0
0
1
3
0
1
1
0
1
1
0
1
0
1
2
1
0
2
2
1
1
0
0
0
1
1
2
1
0
2
0
1
0
2
0
0
0
2
1
1
1
2
1
0
2
0
0
1
2
1
0
2
1
0
0
2
0
3
0
2
1
0
1
1
2
0
0
2
1
1
4
2
2
1
3
0
0
0
0
0
0
1
2
2
0
1
1
1
1
0
1
1
0
2
1
2
2
4
2
0
1
2
4
2
0
0
0
0
1
1
1
0
0
1
0
1
2
0
2
1
0
0
1
0
1
2
2
2
2
2
3
2
0
1
2
0
1
1
1
0
0
0
0
1
0
0
0
2
1
1
2
2
0
2
1
0
2
1
1
0
2
1
0
3
0
1
2
0
0
0
1
1
0
0
0
0
3
0
1
1
2
2
0
1
1
2
2
0
1
0
0
0
1
0
0
1
1
2
1
2
1
1
2
0
0
0
0
1
0
3
1
1
1
0
0
0
0
2
1
0
0
0
2
0
0
0
2
4
2
1
0
2
0
0
1
0
0
1
1
1
0
1
2
0
1
0
0
1
2
1
1
0
0
0
0
0
0
1
1
1
0
2
0
0
3
0
1
0
0
1
2
2
2
1
0
1
1
0
0
3
1
2
0
3
2
0
2
0
2
1
0
0
2
0
0
1
0
2
2
2
0
1
1
0
0
2
1
0
1
0
0
0
0
2
1
0
1
0
0
1
0
1
0
2
1
0
0
0
2
0
0
2
0
1
1
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
2
1
0
1
1
0
1
0
0
2
0
0
0
1
0
0
1
1
0
1
0
1
1
1
2
2
1
1
1
1
1
0
2
1
2
1
0
0
2
2
0
0
0
3
0
1
1
1
0
0
1
0
0
0
1
0
2
1
0
0
0
1
0
0
0
0
0
1
1
1
1
2
0
2
2
2
1
0
2
1
0
1
0
1
0
1
0
0
0
2
0
1
1
0
0
0
1
1
1
0
0
1
0
2
0
0
1
2
1
0
1
0
1
0
0
1
0
0
2
0
0
2
1
2
1
0
2
1
0
2
1
1
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
2
0
0
0
2
1
1
1
1
1
2
0
1
2
0
0
1
1
1
0
2
0
0
1
0
0
0
0
2
1
0
0
3
0
0
0
0
1
1
1
0
1
1
0
1
1
0
0
0
2
0
1
0
1
2
1
0
2
1
2
1
1
1
1
0
1
1
0
0
2
1
0
0
2
0
2
1
0
1
0
0
0
1
1
0
2
1
0
0
0
3
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
2
1
1
2
0
1
0
0
0
2
1
0
0
0
0
0
1
1
0
2
0
0
1
1
0
0
0
1
2
0
0
0
2
0
2
1
2
1
0
0
0
2
0
1
1
0
1
0
0
0
1
1
0
2
1
1
0
0
0
1
1
0
1
0
0
1
2
0
0
0
2
1
1
1
1
2
0
1
1
0
0
2
0
1
1
0
2
0
0
1
1
1
0
2
0
1
0
1
0
1
0
1
0
2
0
0
2
0
2
0
0
1
1
1
1
0
1
1
1
1
0
2
0
0
0
1
1
1
1
1
1
1
0
2
1
0
3
2
1
0
1
3
2
1
1
2
0
0
0
2
1
0
0
2
0
1
1
0
0
2
2
0
1
2
0
0
0
0
0
1
4
0
0
5
0
0
0
2
2
1
0
1
0
2
0
1
1
1
0
0
1
2
1
0
1
1
1
2
0
0
1
0
0
1
0
1
0
1
2
1
2
0
0
2
0
0
1
1
1
2
1
1
1
1
1
0
0
1
0
0
2
1
2
1
0
1
2
0
1
2
0
1
2
1
2
0
0
0
0
0
1
2
0
0
1
0
2
0
1
0
1
3
1
0
0
0
2
1
0
1
1
2
0
1
0
2
0
0
1
0
0
0
1
0
2
1
0
0
0
0
1
1
1
2
1
0
2
2
1
2
1
2
1
1
0
0
0
0
2
0
1
1
0
1
1
0
0
0
0
2
2
0
2
0
2
2
1
2
0
0
1
0
2
0
3
0
0
1
1
0
0
0
1
1
0
1
1
0
0
2
0
2
1
0
1
0
0
1
2
3
0
1
1
0
1
1
1
1
0
1
1
0
2
0
0
1
0
2
0
1
0
0
0
0
1
1
0
2
1
0
1
0
1
1
1
2
2
2
0
0
0
1
2
2
2
0
1
0
1
2
1
1
1
1
0
1
2
0
1
0
1
0
1
0
0
0
1
0
0
1
1
0
1
0
2
0
1
0
0
0
0
0
1
0
0
0
1
1
1
0
3
0
0
1
1
2
0
1
1
0
0
2
0
0
0
0
0
0
1
2
1
0
1
1
0
2
1
1
2
1
2
0
0
1
0
0
1
0
0
0
0
1
1
1
2
0
0
1
0
2
2
0
0
1
0
0
2
0
1
1
1
0
3
0
1
0
1
0
0
1
0
0
1
1
2
0
0
0
2
2
2
2
1
0
2
1
0
2
1
2
0
1
0
2
0
0
1
0
1
3
0
0
0
0
1
1
1
2
0
1
0
2
1
1
1
0
3
0
0
0
0
0
0
1
1
0
1
6
1
1
0
0
1
1
1
2
2
0
2
1
0
2
0
1
1
2
0
2
0
0
0
0
1
0
2
2
2
2
0
0
0
2
0
0
0
1
0
2
1
1
1
1
2
0
0
2
2
1
1
1
0
1
1
2
0
0
2
1
0
1
1
0
1
0
0
2
0
1
1
0
0
2
1
0
0
0
0
0
0
1
1
0
0
1
1
2
0
1
1
1
1
1
0
0
1
0
2
0
1
0
0
1
0
1
0
2
1
1
0
0
0
0
2
1
1
0
2
0
2
0
2
1
0
0
1
0
0
2
2
1
1
1
0
0
2
1
0
1
0
2
2
0
1
2
0
0
2
1
1
1
0
2
2
0
0
0
2
0
0
0
0
2
0
1
1
1
1
1
0
2
3
0
2
1
0
2
1
1
2
0
1
1
0
1
0
2
1
1
4
2
0
1
0
0
1
0
1
1
0
1
1
0
0
1
2
2
0
0
1
1
2
1
1
2
1
2
0
1
1
1
0
1
2
0
1
2
2
2
0
0
2
0
0
0
1
2
2
0
0
2
0
0
2
0
2
1
0
0
1
0
0
2
0
0
1
1
0
1
1
1
2
1
1
0
0
0
2
0
1
0
0
2
1
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
2
1
1
2
2
2
1
0
0
2
0
1
0
0
0
2
0
1
1
0
0
0
0
1
0
0
2
1
1
0
1
0
1
3
1
0
1
2
1
1
0
2
0
0
2
0
0
1
0
1
2
1
0
0
1
0
0
0
0
2
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
1
2
0
1
1
1
0
1
1
0
0
1
0
1
0
2
0
0
0
1
0
1
1
2
2
0
2
0
1
1
0
2
0
0
2
0
1
1
2
0
1
1
0
0
0
0
1
1
4
2
0
0
0
2
1
2
1
1
0
2
1
0
0
1
9
0
1
0
1
1
0
1
1
0
2
0
1
2
1
0
0
2
1
0
2
0
1
1
1
1
0
0
0
0
1
0
1
2
0
0
0
0
0
2
0
2
0
1
1
0
0
1
0
0
0
1
2
0
1
0
0
1
0
0
0
0
0
0
0
1
3
2
0
0
2
2
0
0
2
0
0
0
1
1
1
1
0
0
0
2
1
1
2
0
0
0
1
0
0
0
0
0
1
2
1
0
2
0
1
0
1
0
2
2
0
2
0
0
3
1
2
1
1
1
2
0
1
2
0
0
0
1
1
1
1
1
1
0
1
0
1
0
1
2
0
1
2
0
0
8
0
0
1
0
0
1
0
0
0
0
0
2
1
1
1
0
1
0
0
0
0
3
1
2
1
2
1
0
0
0
0
0
0
0
2
1
2
3
1
1
1
0
1
3
1
0
0
1
3
2
1
2
2
3
0
2
0
2
1
2
1
0
2
0
0
2
0
1
2
0
1
0
0
2
2
1
0
2
1
1
0
0
2
0
2
2
1
0
1
0
3
1
2
0
0
1
2
1
2
1
2
0
0
2
1
0
2
2
2
1
1
1
2
0
0
0
0
0
0
0
1
1
1
2
0
1
0
0
2
2
1
1
0
0
0
0
1
0
1
1
0
0
2
1
2
1
0
1
0
2
0
0
0
0
1
2
1
2
0
0
1
2
2
0
2
1
0
2
0
0
2
0
1
2
2
2
1
0
1
0
0
2
0
1
0
0
2
0
2
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
2
0
2
1
2
0
0
1
1
2
2
0
1
0
1
0
0
0
0
0
1
0
1
0
0
1
2
1
0
1
0
0
1
2
0
0
0
2
2
1
2
2
0
0
0
1
0
0
0
1
1
0
0
0
3
0
2
2
0
2
2
2
2
0
2
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
1
2
1
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
2
1
0
2
0
1
0
2
0
0
0
0
0
0
0
1
0
2
0
1
2
1
0
2
1
1
0
2
1
1
1
0
2
0
2
1
1
0
2
1
2
1
0
2
1
1
0
1
0
0
3
2
1
0
1
0
1
0
0
1
1
1
1
0
0
0
0
2
2
2
0
0
2
0
0
0
0
2
1
2
0
0
0
0
1
0
2
2
0
1
0
2
0
0
0
1
1
0
1
0
0
0
1
0
2
2
0
1
0
2
2
1
0
0
0
2
1
1
2
1
1
2
0
2
0
1
0
0
0
1
1
1
1
0
4
0
0
1
2
0
0
0
0
2
2
2
1
2
2
2
1
0
0
2
1
0
1
1
0
0
0
0
2
0
2
0
1
2
2
2
0
0
0
0
0
0
2
1
0
0
2
1
1
1
0
1
1
0
0
1
0
0
0
0
0
0
2
0
0
0
2
1
1
1
0
2
1
1
0
2
0
0
1
0
1
0
2
2
1
1
0
1
0
1
2
0
1
1
0
0
2
0
0
1
0
1
2
0
4
0
2
1
2
0
1
2
0
0
1
3
0
2
1
0
2
0
0
2
1
0
1
1
0
2
4
0
1
0
0
0
2
0
1
0
0
0
1
2
1
1
1
0
0
2
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
1
2
1
0
2
1
3
0
1
0
2
0
0
0
2
0
1
0
0
0
0
2
1
0
0
0
1
2
0
0
1
1
0
0
0
1
0
0
0
1
0
1
1
1
0
4
0
3
1
0
2
2
0
2
0
2
0
1
1
0
0
2
0
0
1
1
1
1
0
2
1
0
0
1
1
2
0
0
1
0
2
1
2
0
1
1
1
0
1
2
0
1
0
1
1
0
1
1
2
1
0
1
1
0
2
1
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
2
2
0
2
0
1
0
1
0
0
0
2
0
0
0
2
0
2
0
1
1
1
2
1
0
2
1
0
0
1
1
1
0
2
1
2
0
2
2
1
0
1
0
0
0
0
1
1
2
2
0
2
0
1
1
0
2
0
1
0
2
2
2
0
0
0
0
2
0
0
2
1
1
1
0
0
1
1
1
0
3
0
1
0
0
0
0
0
0
0
0
2
2
0
1
2
2
0
0
0
1
0
1
0
1
1
1
0
0
0
0
1
1
2
0
3
0
0
0
0
0
1
2
0
1
2
2
0
2
1
2
2
0
0
2
1
1
2
2
0
0
1
1
0
2
0
0
0
0
1
1
1
1
1
0
0
2
2
2
0
2
0
0
1
1
1
0
1
1
0
2
0
2
2
0
1
1
0
0
2
1
0
0
2
0
0
1
1
0
0
0
1
1
0
1
1
0
2
1
1
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
2
1
0
1
2
0
0
0
1
0
2
2
0
0
0
0
0
0
1
0
1
0
2
0
2
0
0
1
2
1
1
0
0
0
2
2
2
0
1
1
2
2
2
1
1
0
2
1
4
2
1
0
1
2
1
0
0
2
0
0
0
1
0
0
1
0
0
0
2
1
2
1
0
1
0
0
1
0
2
0
0
0
0
0
0
2
0
0
1
0
1
1
2
6
0
0
1
2
0
1
0
1
1
3
0
1
0
2
0
0
2
0
0
2
1
1
1
0
0
1
0
0
3
0
0
2
1
1
2
1
0
1
0
2
0
0
1
0
0
1
0
1
1
0
0
1
0
0
0
1
0
0
0
1
2
0
0
0
1
0
0
2
0
2
4
0
0
1
1
0
0
1
2
1
0
2
1
2
1
0
0
1
1
0
3
0
2
1
0
0
0
1
2
0
0
1
2
0
1
0
0
0
0
2
1
0
0
1
3
0
1
0
2
0
1
1
0
0
1
1
0
2
1
0
0
0
1
0
0
2
0
2
0
0
1
0
1
2
0
1
0
1
2
0
2
3
0
0
0
2
0
0
2
2
2
0
0
1
1
0
1
0
0
1
0
2
1
0
2
0
0
1
0
0
1
0
1
2
2
3
0
0
0
1
1
1
2
0
2
0
1
0
1
0
0
2
2
2
0
1
0
1
0
2
0
0
1
0
2
3
0
0
0
1
1
1
0
1
0
0
0
0
2
0
1
0
2
1
1
1
0
0
1
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
2
2
2
0
2
1
2
2
1
1
1
2
2
0
1
0
0
1
2
1
2
1
1
1
0
1
0
1
0
2
1
0
1
0
0
1
0
2
0
0
0
2
0
0
0
2
2
2
2
1
0
1
2
2
1
2
2
1
1
0
1
0
1
0
0
0
1
0
0
0
1
2
1
2
0
1
1
1
1
1
0
0
0
1
0
0
1
0
2
1
0
1
0
1
0
0
1
1
1
2
1
0
0
1
0
1
0
2
2
1
2
0
0
1
0
0
1
0
0
1
0
0
0
0
0
2
1
2
0
2
0
0
2
1
1
2
1
0
0
1
2
3
0
2
1
0
0
1
1
0
2
1
1
1
0
0
1
1
0
1
1
1
1
0
0
1
0
2
1
0
0
1
1
2
0
0
0
2
0
0
0
1
0
2
1
0
2
0
1
1
0
0
0
2
0
1
1
2
1
0
1
0
1
1
0
0
3
2
2
1
1
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
1
1
0
1
0
1
2
1
0
0
0
2
2
0
1
1
4
1
0
0
0
0
0
0
1
0
4
0
0
2
1
1
1
2
3
0
2
0
0
0
0
2
2
1
3
1
1
2
0
1
0
1
0
0
0
0
1
0
2
1
1
1
0
0
2
0
0
0
1
0
1
1
0
0
0
2
2
2
3
1
1
1
1
2
1
0
0
0
0
2
2
2
2
0
1
2
0
0
1
1
0
0
1
0
0
1
1
1
1
0
1
0
0
1
1
1
1
1
1
2
1
0
2
0
1
0
1
0
0
0
0
0
2
1
0
1
0
0
0
1
1
2
0
1
2
0
0
1
0
0
1
2
2
0
0
0
0
0
0
1
0
1
1
1
2
0
0
2
2
1
0
1
0
1
0
0
1
0
2
2
0
1
0
1
0
2
2
0
0
0
1
0
0
0
0
2
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
2
2
0
0
0
1
2
0
2
2
1
2
1
1
0
0
0
1
0
1
1
1
0
1
1
2
0
0
2
0
3
0
0
1
0
1
1
1
0
0
0
0
0
0
0
1
0
2
0
0
2
0
1
1
1
0
0
1
1
0
0
1
0
1
0
0
0
1
1
0
0
2
1
2
2
1
1
1
1
5
1
1
1
0
0
2
1
1
1
1
3
2
2
0
0
0
0
0
2
0
1
0
2
2
0
0
0
2
0
0
2
0
0
1
1
0
0
0
0
2
0
0
1
1
2
1
0
0
0
0
0
2
2
1
0
0
2
0
0
1
2
0
0
1
2
0
0
0
2
2
3
1
0
3
0
0
0
2
1
0
2
2
0
1
0
1
0
0
1
1
0
1
1
0
0
0
0
1
1
0
1
0
1
1
2
2
2
2
0
1
2
0
0
0
0
0
0
1
0
2
2
0
0
0
0
2
0
0
1
0
3
1
1
0
0
0
2
0
2
0
1
0
2
0
2
0
0
0
0
1
0
0
0
1
1
1
2
0
2
1
1
0
1
0
2
0
2
1
1
2
0
2
1
3
0
0
1
1
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
2
1
0
2
1
2
0
1
0
1
1
0
0
0
2
0
2
0
0
2
0
0
1
1
1
1
1
0
2
9
0
0
0
0
0
0
0
0
0
0
2
2
1
0
1
2
1
0
1
0
0
1
1
0
0
2
2
1
1
2
1
0
1
0
2
1
2
0
1
1
2
0
2
0
0
0
0
0
0
1
0
0
1
2
1
1
0
0
1
1
1
2
2
2
0
1
0
2
1
0
1
0
0
0
1
3
0
1
2
0
1
0
1
0
2
2
0
0
2
1
2
0
2
1
0
0
2
2
2
0
0
2
1
0
1
2
2
1
2
1
1
1
0
1
0
1
0
3
1
0
1
2
2
2
1
0
0
1
0
1
0
2
0
0
1
2
0
0
1
1
0
4
1
2
0
2
0
0
1
2
2
0
2
0
0
0
0
1
1
0
0
2
0
2
1
1
0
0
0
0
0
1
0
1
0
0
0
1
2
0
1
2
1
0
1
0
0
0
0
1
1
0
0
1
0
0
2
0
0
0
2
0
2
0
0
2
1
2
2
1
1
1
0
1
2
2
2
0
1
0
0
2
0
1
2
0
0
0
0
2
1
0
0
1
2
0
0
1
1
2
2
0
1
0
1
0
2
0
0
2
2
1
0
1
2
1
0
1
0
1
0
0
1
2
2
0
2
0
2
1
2
1
0
0
0
2
0
1
0
2
1
1
0
2
1
2
0
2
1
0
0
2
1
1
0
2
2
1
0
0
3
0
1
1
1
0
0
1
8
0
2
2
0
1
1
0
0
0
1
0
0
0
2
1
1
2
0
1
0
1
0
1
2
0
1
0
2
0
1
1
0
0
0
1
2
0
0
0
1
1
0
0
2
0
1
0
1
2
1
2
0
0
0
1
0
1
1
1
1
1
1
0
1
2
0
0
0
2
1
1
0
1
2
1
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
2
1
1
0
0
0
1
2
0
1
0
0
2
0
1
2
1
1
0
0
1
2
2
1
0
1
1
0
0
0
0
1
0
1
0
1
1
0
2
0
0
2
0
0
0
0
0
2
2
1
1
2
0
1
2
1
2
2
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
2
2
0
1
0
1
1
1
0
2
1
0
0
0
0
0
0
1
1
1
1
0
1
1
0
2
1
0
0
2
1
0
2
2
2
0
0
1
1
0
2
0
1
1
0
2
0
1
0
0
1
2
0
1
2
1
1
0
1
1
1
0
0
0
1
1
0
0
1
2
2
2
2
2
0
0
0
0
1
1
2
1
1
1
0
0
2
0
2
0
0
1
1
2
0
0
2
3
0
0
0
0
2
0
2
0
0
0
0
0
0
4
0
1
1
0
1
0
1
2
0
0
2
1
0
1
2
0
0
1
1
0
0
1
1
0
0
0
0
0
1
2
0
1
1
0
1
0
0
1
0
0
1
1
0
1
0
1
0
0
2
2
0
0
0
0
1
3
1
0
1
1
2
1
1
2
2
2
0
0
1
1
1
2
0
0
1
0
0
2
0
2
2
0
2
2
1
0
0
0
1
0
1
1
2
0
1
1
2
0
0
0
2
2
0
1
2
1
0
0
1
1
1
1
2
1
0
1
0
0
2
0
0
2
1
0
2
0
1
1
0
6
2
2
1
0
0
1
1
0
0
0
0
0
0
1
1
0
1
1
2
0
2
1
0
0
1
0
1
2
2
0
2
2
2
0
2
1
1
0
0
1
1
1
0
0
0
0
2
0
0
0
1
2
0
2
1
1
0
0
0
1
0
0
0
1
1
1
1
1
1
0
0
1
1
0
2
0
2
0
0
0
0
2
2
1
2
1
2
0
1
1
2
0
0
2
0
0
0
0
2
0
0
2
0
3
0
1
0
1
0
0
0
1
1
1
0
2
0
1
1
1
1
0
1
2
0
1
0
0
0
0
1
2
0
0
2
1
0
0
0
2
2
1
0
0
1
1
0
1
1
0
1
1
0
0
0
1
1
0
2
1
0
0
2
1
0
1
0
0
0
0
1
0
0
0
2
0
0
1
2
0
0
2
1
0
0
1
0
0
2
1
1
1
2
2
0
0
0
0
0
1
0
0
1
2
2
2
3
0
0
1
1
1
0
1
1
0
0
0
1
1
2
0
1
0
0
0
1
2
0
2
1
0
1
0
2
1
0
0
0
0
0
0
1
2
0
1
1
0
0
1
2
0
0
0
0
0
0
2
0
0
0
1
1
0
1
0
0
2
0
1
0
2
0
1
1
2
2
2
2
1
1
0
0
1
0
2
1
0
1
0
0
1
1
0
0
0
1
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
2
0
1
1
4
0
0
0
0
1
1
2
0
0
2
2
2
0
0
2
0
1
1
0
0
2
0
2
1
0
3
0
1
1
0
1
0
0
0
1
0
0
0
0
1
1
0
2
0
1
0
0
0
2
0
0
0
1
1
0
0
1
0
1
2
2
1
2
1
2
2
0
2
0
0
1
0
0
0
1
1
1
2
0
0
1
2
0
0
2
0
1
0
0
0
2
0
1
2
0
0
0
0
1
2
0
0
1
0
2
0
0
0
0
0
1
0
0
0
1
2
0
2
0
2
0
0
1
2
1
1
1
1
2
0
1
2
0
2
0
0
3
0
0
0
0
1
0
1
6
0
2
0
0
0
1
1
0
0
0
0
1
0
2
1
1
1
0
1
0
0
0
1
0
1
0
1
2
0
0
0
1
2
0
1
1
0
0
1
0
1
2
1
0
1
1
0
0
2
0
2
1
1
1
1
1
2
1
0
0
2
1
1
1
2
0
2
1
0
1
0
0
1
1
2
2
2
2
0
1
0
0
0
2
1
0
1
1
1
1
0
0
0
2
1
2
0
0
0
1
1
2
1
0
0
1
2
0
0
0
0
1
2
1
1
2
2
2
1
0
0
1
0
1
2
0
0
1
1
0
0
1
2
2
2
1
1
0
0
2
0
0
0
1
0
0
2
0
1
0
1
1
1
0
0
2
2
0
1
2
2
1
0
0
0
2
0
0
2
1
0
2
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
1
1
1
0
2
2
0
0
1
1
1
0
1
0
0
0
0
2
1
0
1
0
1
1
0
1
2
1
0
0
1
2
1
2
0
1
0
1
2
1
1
1
1
1
0
0
2
2
1
0
0
2
1
2
0
0
0
0
2
0
1
0
3
1
1
0
2
0
1
0
1
1
2
2
1
1
0
0
1
2
0
1
0
0
0
1
1
1
1
4
1
1
1
0
1
0
1
0
2
1
2
0
1
2
0
3
0
2
1
0
0
1
2
0
0
2
2
0
1
1
2
1
2
1
2
2
0
1
2
0
0
1
0
0
2
0
0
3
3
0
0
0
0
2
2
0
2
1
1
0
0
1
0
0
1
2
0
1
2
2
0
1
0
0
2
0
0
2
1
2
0
0
0
0
1
1
0
0
3
1
0
1
0
2
2
0
1
2
0
2
0
0
0
0
1
0
0
1
1
1
2
1
0
0
2
2
2
1
1
1
0
2
1
0
2
1
4
2
2
0
1
0
0
2
0
1
1
2
0
2
1
0
1
2
2
3
0
0
0
0
0
0
1
0
1
0
0
1
1
0
1
2
1
0
0
0
1
0
1
2
0
0
2
1
0
1
0
0
0
0
0
0
2
0
0
0
1
0
1
1
0
2
0
0
2
1
0
0
1
2
2
2
1
2
0
2
1
1
1
1
0
0
2
0
2
1
0
0
1
0
3
0
0
0
0
1
0
3
3
0
0
0
1
1
0
2
0
0
1
0
2
1
1
1
1
0
0
1
1
0
2
0
1
0
2
0
2
0
2
2
0
0
1
0
0
2
2
2
0
1
1
1
1
0
2
1
0
0
1
1
0
1
0
1
1
2
0
0
1
2
0
1
1
0
0
1
0
1
0
2
0
0
4
1
4
1
2
2
1
2
2
0
0
1
2
2
2
2
0
1
0
2
0
1
0
1
2
1
0
2
2
3
1
0
0
0
2
0
1
0
1
1
2
0
1
2
0
1
1
0
1
0
2
0
2
2
0
1
2
1
2
1
0
0
1
2
0
1
0
1
1
2
1
1
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
1
1
0
0
3
0
1
0
0
1
2
0
0
1
1
1
0
0
0
1
1
0
1
0
2
0
1
0
0
0
0
2
1
2
0
1
0
0
0
0
1
0
4
0
0
2
1
2
1
2
2
0
1
0
0
0
2
2
0
0
0
1
0
1
2
0
0
0
0
2
1
3
0
2
0
1
1
1
1
0
0
0
1
0
3
2
0
1
1
0
0
0
2
0
0
2
2
2
0
2
0
0
1
1
1
0
0
2
0
2
0
0
0
0
2
0
1
0
2
0
2
1
0
0
2
0
0
1
2
1
0
0
0
0
1
1
0
0
1
1
1
0
0
1
1
0
0
0
0
0
0
1
2
1
2
1
0
2
0
2
1
2
0
2
2
0
0
2
0
2
0
0
2
0
1
0
0
0
1
0
0
1
1
1
2
2
1
0
2
0
0
2
1
2
2
2
0
1
1
0
0
0
0
0
0
1
0
0
0
1
1
1
0
2
0
0
1
2
0
2
1
2
1
2
1
0
0
0
1
0
2
1
0
1
0
1
0
2
1
2
0
0
0
2
0
0
1
1
2
1
0
1
0
1
2
0
0
0
1
0
2
1
1
0
1
0
2
1
1
2
0
0
0
1
1
0
1
2
0
0
0
0
1
0
1
1
0
1
0
0
1
0
2
0
1
3
0
2
0
0
0
1
0
1
1
1
1
1
2
1
2
3
2
0
1
0
0
2
0
0
2
0
2
0
0
0
1
0
1
2
1
0
0
1
0
0
0
1
2
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
1
0
1
2
1
2
1
0
0
1
1
0
0
0
0
2
0
0
0
2
0
1
0
2
1
2
0
0
0
1
0
2
3
1
1
0
0
0
1
0
1
0
0
0
2
0
0
0
0
2
2
0
1
1
1
0
1
1
2
0
0
1
5
1
2
0
0
2
1
0
0
0
2
2
2
0
0
0
2
0
2
1
0
1
0
1
0
0
2
0
0
0
0
1
1
0
2
1
0
1
0
0
0
1
1
2
0
1
2
0
0
0
0
2
0
0
2
1
0
0
0
0
1
2
1
1
0
1
1
2
0
0
1
0
2
0
0
1
0
1
1
2
2
0
1
1
2
1
0
0
2
2
1
0
0
0
2
1
2
0
1
0
1
1
1
1
0
0
0
1
1
0
0
2
0
0
0
3
0
0
0
1
1
1
0
1
2
0
1
0
0
1
0
1
0
1
0
2
0
1
2
2
2
2
0
2
2
0
2
1
2
1
2
0
0
1
2
0
1
0
0
0
2
2
1
1
1
0
2
1
0
3
2
0
0
1
0
0
0
0
0
0
0
2
1
0
1
1
0
1
2
0
0
2
1
1
1
0
2
2
1
3
0
3
2
0
0
0
0
1
1
0
0
3
1
2
0
1
1
0
0
1
0
1
0
0
2
2
0
0
0
2
2
1
1
0
2
2
0
0
2
2
2
1
1
1
2
1
2
1
0
0
1
1
1
2
1
1
1
1
1
0
1
0
0
2
0
1
0
2
4
1
0
0
0
0
2
1
0
1
2
1
1
0
1
0
1
1
1
1
1
0
2
0
1
0
2
2
0
0
2
0
0
0
1
0
2
1
0
0
2
1
2
0
2
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
1
1
0
2
2
0
0
1
0
2
0
2
1
1
2
0
1
1
1
1
1
2
1
2
0
0
2
0
1
0
0
0
1
2
0
0
1
1
1
2
1
1
1
3
0
2
0
0
0
0
1
0
0
2
0
0
1
1
2
1
2
0
2
0
0
1
1
0
1
0
1
1
0
1
0
0
1
2
1
0
0
1
0
1
2
2
0
1
1
0
1
0
2
2
0
2
2
0
2
0
1
1
0
0
1
2
0
0
2
1
0
0
1
1
1
1
0
0
0
2
2
2
0
0
0
0
0
1
0
0
2
1
1
0
0
2
0
1
1
2
2
1
0
0
0
1
1
1
0
0
1
1
0
1
0
0
2
0
0
0
1
0
0
2
2
1
0
0
0
2
3
0
1
2
0
0
0
0
2
0
0
0
1
0
4
1
1
1
0
2
1
0
0
0
0
2
0
0
1
1
2
0
1
2
1
2
0
0
0
0
0
0
1
0
1
1
1
0
0
1
1
0
1
2
0
1
2
1
2
2
0
2
3
1
1
0
0
1
0
0
1
1
2
2
0
0
2
1
2
1
0
0
0
2
1
2
0
0
0
2
0
2
2
0
2
0
4
2
2
0
2
2
2
2
1
0
1
1
0
1
1
2
2
2
1
0
0
1
0
0
1
0
0
0
0
0
1
1
0
1
1
1
1
1
0
2
0
2
0
0
2
0
0
0
0
0
1
0
2
2
1
0
1
1
1
0
0
0
2
0
0
0
0
2
0
1
1
1
1
1
2
2
0
0
1
0
0
1
1
0
0
2
2
0
0
0
2
0
2
0
0
1
1
2
0
1
2
1
2
0
2
0
0
1
1
0
0
2
0
0
0
0
2
0
1
2
1
0
2
1
0
0
1
1
0
1
0
2
0
1
1
1
0
0
1
2
1
0
2
0
1
0
0
0
0
0
2
0
0
1
1
1
0
2
1
2
0
0
0
0
1
0
0
2
1
0
1
1
0
0
2
0
0
1
1
2
0
0
1
1
2
2
2
0
1
0
1
1
0
0
0
0
1
2
0
2
1
1
0
1
1
0
1
2
1
3
1
2
0
1
1
2
0
2
2
1
0
1
0
1
0
3
0
1
0
0
1
2
0
0
0
0
2
1
2
1
0
0
0
0
0
0
1
1
2
1
0
2
0
1
1
0
2
4
0
2
0
3
0
0
1
0
1
1
1
2
1
1
1
0
0
1
0
0
2
0
0
0
2
0
1
0
1
1
0
2
1
1
0
3
1
0
0
1
1
0
1
1
2
0
1
1
0
0
1
0
0
0
0
0
0
1
1
0
0
2
0
2
0
2
2
0
1
0
1
1
1
1
0
1
0
1
0
1
0
0
0
0
2
0
2
1
0
1
1
0
0
1
0
0
1
1
2
0
0
1
1
2
1
0
1
1
0
0
1
2
1
1
0
0
0
0
1
0
4
0
0
2
0
0
0
2
2
1
0
2
1
0
0
1
1
1
0
2
2
1
0
0
2
1
2
2
0
1
2
0
1
0
0
2
1
1
0
0
0
1
0
0
1
0
0
0
2
0
0
1
2
1
0
2
0
0
0
0
0
0
0
1
2
2
3
1
1
1
0
0
2
1
1
0
2
1
2
0
1
0
0
1
0
1
0
0
1
1
0
1
0
0
2
3
0
0
1
1
2
1
0
1
1
2
0
0
0
0
1
1
0
0
0
0
2
0
0
0
1
1
1
1
1
0
0
2
1
0
2
0
0
1
2
0
0
2
2
1
0
1
0
1
0
0
1
0
0
1
1
1
0
1
2
2
0
0
2
0
0
0
0
1
1
2
0
0
2
2
0
1
1
0
0
0
0
1
1
1
0
2
1
0
2
1
0
2
0
1
0
0
2
1
1
2
0
2
0
0
2
0
2
0
0
2
0
1
0
0
1
1
1
0
0
0
0
2
1
1
2
0
0
0
1
0
2
0
0
2
0
1
1
0
1
1
1
0
0
1
2
2
1
0
1
1
0
0
2
0
1
1
0
0
0
1
0
2
1
2
2
0
2
0
1
0
2
0
2
0
0
0
0
0
2
1
0
1
1
2
1
0
0
0
1
0
2
1
1
0
1
1
0
1
2
1
0
0
0
1
2
0
0
1
0
2
3
0
1
2
1
0
3
1
1
0
0
0
0
1
0
0
2
2
2
1
1
2
2
0
0
0
0
2
1
0
2
0
2
2
2
1
0
2
0
1
1
1
0
0
3
2
2
1
0
0
3
0
0
1
0
2
0
0
2
1
1
2
1
1
0
0
0
0
0
3
2
0
2
2
2
1
0
1
0
0
2
1
0
0
0
2
0
1
2
1
2
1
2
2
0
0
0
1
0
1
1
0
1
0
0
0
0
0
2
1
1
0
1
0
0
1
2
1
1
0
1
2
2
1
2
0
2
1
0
2
0
0
1
0
1
0
0
0
0
2
2
0
0
1
0
1
0
2
0
1
1
1
0
0
0
2
2
1
1
0
0
2
1
2
0
1
2
0
1
0
1
2
1
0
0
1
0
1
0
1
2
3
0
0
0
0
1
1
0
2
1
1
2
2
2
1
0
1
0
1
0
2
1
3
0
1
2
0
0
1
0
0
2
0
0
1
0
1
1
1
0
0
1
1
1
1
1
0
2
1
2
1
1
0
1
0
0
1
0
0
2
1
0
1
0
0
1
3
0
0
0
2
0
0
1
1
2
2
1
3
1
1
1
0
2
0
2
0
1
0
1
2
0
0
0
1
0
3
2
0
1
0
0
0
1
0
1
0
1
1
0
1
1
2
1
1
2
0
1
1
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
1
2
0
0
0
2
0
1
0
0
2
0
0
2
1
1
1
0
0
0
1
1
0
2
1
0
1
2
1
2
0
1
0
1
1
0
0
0
0
1
0
1
0
2
1
0
0
1
0
0
1
1
0
1
2
1
1
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
2
0
1
2
2
0
2
0
2
1
1
1
1
1
3
0
0
0
0
0
1
0
0
2
0
1
0
1
1
2
7
2
2
0
0
0
2
0
2
1
1
1
0
1
0
1
0
1
2
0
0
1
1
1
1
1
0
1
0
0
2
1
0
2
1
0
2
0
0
0
0
2
0
0
2
0
1
0
0
2
2
0
0
0
0
2
2
0
1
2
2
2
1
2
0
0
3
0
0
1
1
1
2
2
0
0
1
2
0
0
2
2
0
0
1
0
0
1
0
0
0
2
1
0
0
1
1
1
0
0
0
1
1
2
0
1
1
0
0
2
0
0
1
0
0
1
1
1
0
0
1
0
2
1
1
1
1
0
0
1
2
0
0
0
0
0
0
0
0
3
1
1
0
1
2
0
0
1
0
0
2
2
2
1
2
0
0
0
0
2
0
0
0
1
0
1
1
0
1
1
1
2
0
1
2
1
1
0
1
0
1
1
1
1
1
0
0
0
0
0
0
2
0
0
0
1
1
1
2
2
0
1
0
1
0
0
1
0
2
1
0
2
1
0
0
0
1
1
0
2
2
0
1
0
1
0
2
0
2
0
2
2
0
2
2
0
2
0
1
0
0
1
0
1
1
0
2
0
2
0
0
0
0
1
1
2
0
0
0
1
0
1
2
0
0
1
1
0
1
0
0
2
1
1
0
0
1
0
3
2
1
0
0
0
0
0
1
2
0
2
0
1
1
1
2
1
1
0
1
2
1
1
0
2
1
2
1
1
1
0
1
2
2
2
2
0
0
1
2
0
0
1
5
1
1
2
0
0
0
1
1
0
1
0
0
0
0
0
1
2
3
0
2
0
1
0
0
2
2
0
0
1
0
0
1
0
1
2
0
2
1
0
2
1
0
1
1
2
1
2
2
0
1
1
1
1
0
1
0
2
2
2
1
0
0
0
3
0
1
0
2
0
1
0
0
2
0
1
2
1
1
0
0
2
0
2
0
0
0
0
0
1
1
1
0
3
0
0
1
0
0
0
2
1
1
1
0
2
0
0
0
0
1
0
1
0
2
0
1
1
1
1
1
0
1
0
2
2
0
1
1
1
0
0
0
0
1
2
2
2
0
2
1
0
1
0
0
0
0
2
0
3
0
0
0
0
1
0
0
0
1
0
1
0
0
0
2
0
1
0
2
1
0
1
0
1
1
0
2
0
0
0
1
0
1
1
1
0
0
0
2
0
1
0
0
0
1
0
1
1
3
2
1
0
0
0
1
0
0
0
0
2
0
1
1
0
0
2
1
3
0
1
0
0
2
2
1
1
1
0
0
2
2
3
0
1
1
1
1
0
1
0
1
2
0
2
0
1
2
0
0
0
2
0
0
1
2
3
1
1
1
0
0
1
2
1
1
3
0
0
0
0
1
0
0
2
1
0
0
0
0
1
1
2
1
1
1
0
1
0
0
1
0
1
0
1
0
2
2
0
2
0
0
0
2
0
0
1
0
1
1
2
0
3
1
1
1
2
1
3
0
1
1
0
3
1
2
1
0
0
0
2
2
0
1
1
0
1
1
1
0
0
1
1
0
0
1
1
2
2
0
0
0
5
0
0
1
0
0
0
2
3
2
0
0
0
1
1
0
1
2
2
1
0
0
2
1
0
0
0
2
0
0
2
1
2
0
2
1
1
1
0
0
1
0
1
2
2
0
0
1
0
2
1
0
0
1
1
0
1
0
0
0
2
0
2
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
1
0
0
2
1
2
1
1
2
1
3
0
1
3
1
2
0
1
1
1
0
0
0
1
0
1
1
1
1
0
0
1
1
1
1
0
2
0
2
1
1
3
0
0
1
1
0
0
0
1
0
1
1
2
0
1
1
1
1
0
2
0
0
0
1
1
0
0
0
0
0
0
0
1
2
0
2
0
2
0
1
0
2
1
1
0
3
0
0
2
2
0
0
1
0
2
1
1
0
0
0
1
0
1
1
2
1
0
0
2
0
0
1
0
1
0
0
1
1
0
0
0
0
0
2
0
1
0
2
1
0
3
0
2
1
2
0
0
2
0
2
1
1
1
0
1
1
0
1
1
0
2
0
1
2
2
0
0
1
0
2
2
0
0
0
2
0
1
2
0
0
0
2
1
0
1
1
1
0
0
1
2
2
1
2
1
1
0
2
0
1
0
2
0
0
0
0
2
2
0
0
2
0
1
0
0
0
2
1
2
0
0
1
0
0
1
0
0
1
2
1
0
2
1
0
0
1
0
1
2
0
0
0
0
1
0
2
0
0
1
2
1
1
2
0
0
0
0
1
0
0
1
0
1
2
2
1
0
0
1
1
2
0
1
0
0
0
2
4
2
0
2
0
1
0
0
2
2
0
0
0
1
1
2
1
0
1
1
2
0
0
0
2
0
0
0
1
0
1
0
2
0
0
0
2
0
0
2
0
1
1
0
1
0
2
0
1
0
2
0
0
0
1
1
0
2
0
0
0
0
1
1
0
1
2
1
1
0
0
2
0
0
1
0
1
0
0
1
0
3
0
2
1
3
1
1
0
1
0
0
1
2
1
0
4
0
1
0
0
1
0
0
2
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
2
1
1
0
0
0
0
2
0
2
1
0
1
0
1
2
2
0
1
0
0
1
1
2
1
1
0
1
1
0
2
0
1
2
2
0
0
0
1
1
1
0
0
0
0
1
2
1
2
0
1
0
0
1
0
0
1
0
2
1
0
2
0
0
0
2
1
1
1
0
1
0
0
1
1
1
1
0
0
2
0
1
2
1
1
2
0
1
0
0
0
0
1
1
1
0
0
2
0
0
0
2
1
1
2
2
1
1
2
1
1
1
0
1
0
0
0
2
1
0
2
1
1
0
0
1
0
1
0
1
1
0
0
1
6
2
1
1
0
2
0
0
1
1
0
0
0
2
0
2
1
1
2
0
2
0
0
1
0
2
0
0
2
2
0
2
1
0
0
1
0
0
0
2
2
0
2
0
0
0
0
2
1
0
2
2
0
1
0
1
2
0
0
0
1
0
2
2
0
1
1
0
0
1
0
1
0
2
0
0
2
1
0
1
1
0
2
0
1
1
2
0
1
1
1
0
1
2
2
2
1
2
1
0
1
0
0
1
1
2
1
2
0
0
2
0
0
0
0
1
0
0
1
1
2
0
0
0
0
0
1
0
0
1
2
0
2
2
1
0
1
0
0
1
0
1
1
2
0
0
1
0
0
0
0
1
1
1
0
4
0
1
1
0
1
1
1
0
2
1
1
2
1
0
1
0
2
2
2
1
0
2
1
2
0
0
0
0
0
0
1
1
0
2
1
1
1
1
2
1
2
0
0
1
0
2
0
2
1
1
1
2
0
0
0
0
1
0
1
2
1
1
1
2
0
0
1
1
0
4
0
0
0
0
1
1
0
1
0
2
1
2
0
0
0
0
1
1
1
2
2
0
0
0
1
0
0
3
0
2
0
0
0
0
2
2
1
1
1
0
1
0
0
2
0
0
0
1
0
0
3
1
1
0
0
1
0
0
1
0
0
1
0
1
0
0
1
1
0
2
0
0
1
0
2
1
0
0
0
2
0
0
0
2
1
0
2
1
1
0
0
1
1
1
0
0
1
0
1
1
0
0
0
1
2
0
1
1
2
2
2
1
0
0
0
0
1
2
0
0
0
2
1
1
0
1
0
1
0
0
0
1
2
1
1
0
1
1
1
0
1
0
1
1
2
1
0
1
0
2
1
0
4
1
2
1
3
0
1
0
0
1
1
0
1
0
0
2
0
2
0
1
0
1
1
0
0
1
0
1
0
1
2
0
0
0
2
1
2
1
1
1
0
2
1
2
2
1
0
2
0
0
1
2
0
1
0
1
2
2
0
0
0
1
2
1
1
0
0
0
1
0
2
0
2
2
1
1
0
0
1
1
0
0
2
0
0
0
0
1
1
2
1
1
0
2
1
0
1
1
0
1
1
2
0
2
1
0
1
0
0
0
2
0
2
1
0
1
1
0
0
1
1
0
0
1
0
2
2
0
0
2
1
0
2
0
0
0
1
0
0
2
1
1
1
2
0
0
2
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
2
1
1
0
0
1
0
4
1
1
2
0
0
0
0
1
2
1
1
0
1
0
0
0
0
2
1
2
2
0
0
1
1
0
2
0
0
2
1
1
1
1
0
2
0
0
1
0
0
2
1
0
0
2
1
1
1
0
2
2
0
1
0
2
2
2
2
0
1
0
1
0
1
0
2
0
1
0
0
1
0
0
1
2
0
0
0
2
0
0
2
1
0
1
2
0
0
0
1
1
1
0
0
1
2
2
2
1
1
1
0
0
2
0
1
2
1
0
1
0
2
0
0
0
1
0
3
2
0
0
2
0
0
1
0
0
0
0
1
1
2
0
1
0
0
0
1
0
1
1
0
1
2
0
1
1
0
1
1
1
2
1
0
1
0
0
0
0
0
1
0
2
2
0
3
1
2
0
0
0
2
2
0
0
1
0
0
1
0
0
0
1
0
0
0
2
2
0
1
1
0
0
1
2
1
0
0
1
0
0
2
0
0
0
0
2
1
2
2
3
2
2
2
2
0
2
0
0
0
2
0
1
1
0
2
2
2
0
0
1
0
1
2
2
1
0
1
0
0
5
1
0
1
2
2
2
3
0
0
0
1
4
0
0
0
7
0
0
0
1
2
0
1
0
3
0
1
1
1
0
1
2
1
0
1
0
0
1
1
1
0
1
0
0
1
0
0
1
0
1
0
0
1
2
2
0
0
0
1
0
0
0
0
2
0
0
1
1
1
0
3
1
1
1
2
1
0
1
1
0
2
1
1
0
1
1
0
0
0
0
0
1
1
0
0
2
2
0
0
0
0
0
1
2
2
1
0
1
2
0
1
1
0
1
0
0
1
0
0
1
1
0
1
2
2
0
0
0
0
1
0
0
0
1
0
0
0
0
2
2
0
1
2
0
0
2
2
0
0
0
1
2
0
0
0
2
0
1
0
1
2
2
0
1
2
0
2
1
1
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
2
0
2
1
0
0
1
1
0
2
0
2
0
1
1
0
0
0
0
1
0
0
1
0
0
1
1
0
1
2
1
0
0
2
0
1
1
2
0
1
0
2
1
0
0
0
0
0
1
1
0
0
2
0
0
1
1
3
0
2
1
1
2
2
1
0
0
0
0
2
1
0
2
0
0
2
1
0
0
1
1
1
0
1
0
1
1
2
0
0
0
0
0
0
2
1
0
1
0
0
1
1
0
0
1
0
1
0
2
0
0
0
1
1
0
0
3
0
2
1
1
1
2
3
0
0
1
0
0
0
2
0
2
0
2
2
1
0
0
1
2
2
0
2
1
2
2
0
0
1
2
0
1
0
0
1
2
1
0
2
0
0
0
1
1
0
2
2
1
0
0
1
1
1
0
1
2
0
0
1
2
2
2
1
1
1
1
2
1
0
2
0
0
1
2
0
0
2
0
1
1
0
0
0
1
1
1
0
1
0
2
0
1
0
0
1
2
1
2
1
0
0
0
0
0
0
2
0
0
0
1
2
1
0
0
0
1
2
1
2
2
0
2
0
0
1
0
0
0
5
2
0
1
2
1
1
1
3
0
2
0
0
1
0
1
0
0
0
1
0
2
0
1
0
1
0
0
0
1
0
1
1
0
0
0
2
1
0
1
1
0
2
1
0
0
1
0
0
2
2
0
0
0
0
0
2
1
0
1
1
1
2
1
2
1
0
0
2
0
1
1
1
0
1
1
0
1
1
2
0
1
0
0
0
0
1
0
2
1
0
1
1
0
2
0
2
0
2
3
0
0
2
1
1
2
1
2
2
2
0
1
1
0
0
0
0
0
0
1
0
0
1
2
1
1
2
1
2
0
0
1
3
1
0
0
0
1
1
2
0
1
0
0
0
1
1
2
0
0
2
2
2
1
1
1
2
2
1
2
0
1
1
1
3
2
2
0
2
0
0
0
0
2
2
1
0
1
2
0
0
2
2
1
2
0
1
1
0
1
2
0
2
0
1
1
0
1
0
1
1
0
0
0
3
2
0
1
1
1
0
4
0
1
0
0
1
0
1
0
0
0
0
2
0
0
0
1
0
1
0
1
0
1
0
0
1
2
0
1
2
0
1
1
1
1
0
0
2
0
1
0
0
1
0
0
0
1
1
0
2
0
1
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
2
1
2
0
0
0
0
0
1
1
0
2
1
2
2
0
1
0
0
1
0
1
0
1
0
2
1
0
1
1
1
0
2
0
0
0
1
0
3
0
0
0
0
1
1
1
1
0
0
1
0
0
0
1
0
0
1
1
0
0
1
2
0
1
2
2
2
0
2
3
1
0
0
0
0
1
1
1
0
2
0
2
0
0
0
4
2
2
0
2
0
0
1
0
1
1
0
0
0
2
1
1
0
1
0
0
0
1
0
0
0
1
0
0
2
2
1
1
1
1
0
0
1
0
0
1
0
1
2
1
1
0
2
2
0
2
2
1
2
1
1
2
0
1
0
0
2
0
2
0
0
1
0
1
0
2
0
1
1
1
0
1
1
0
0
0
3
0
1
1
2
1
1
1
2
0
0
0
1
0
0
0
1
2
0
1
0
0
1
0
1
0
2
3
2
2
1
1
0
0
0
1
0
1
3
0
0
0
1
2
0
0
0
1
0
0
2
1
0
2
1
2
2
1
1
2
0
0
1
0
0
0
0
0
2
1
0
1
0
0
0
2
0
0
0
0
0
2
0
2
0
0
2
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
3
0
0
0
1
1
2
2
0
1
2
1
2
1
2
2
0
1
0
0
0
0
2
1
1
0
0
1
0
1
2
0
4
0
2
1
2
2
1
2
0
1
0
0
1
1
2
0
0
0
2
1
1
0
0
0
1
0
0
0
1
0
2
0
0
0
0
1
0
1
3
3
1
1
0
2
0
0
1
2
1
1
2
1
0
2
0
2
0
0
0
1
0
1
2
1
0
0
2
1
1
0
1
1
1
1
0
2
1
1
0
2
1
2
0
0
0
2
0
0
2
1
0
1
1
2
0
0
0
1
1
0
0
2
1
1
0
1
2
0
0
0
1
0
1
0
0
0
0
2
0
0
1
1
1
2
2
1
0
0
2
0
0
1
2
2
2
1
0
0
1
2
1
0
2
1
0
0
0
0
2
1
0
0
1
0
2
1
0
2
1
2
1
1
0
0
0
0
2
0
0
2
2
0
2
2
2
0
2
1
0
0
0
2
1
2
1
0
1
1
1
1
0
2
2
2
1
0
1
1
0
1
1
2
1
1
1
1
2
2
0
0
0
1
1
1
2
1
0
1
0
0
1
0
0
1
1
1
0
0
1
0
1
0
0
0
1
0
0
2
0
0
1
0
1
1
2
1
0
0
0
2
2
1
1
0
0
0
1
0
0
1
1
0
1
0
1
1
1
2
0
2
2
0
0
1
1
1
2
2
0
1
0
1
1
2
2
0
2
1
1
0
1
0
0
0
0
1
0
1
0
1
1
2
2
1
0
1
0
2
1
0
0
1
2
0
1
0
0
0
2
2
1
2
0
0
0
0
1
0
1
0
0
2
0
2
1
1
0
0
0
0
0
1
0
0
2
1
2
3
1
2
2
1
2
3
1
0
1
0
1
0
1
0
1
0
2
0
0
1
0
2
1
1
1
3
0
2
2
1
0
1
0
2
1
0
2
1
0
1
0
0
2
0
1
2
0
1
1
2
0
2
2
0
1
0
0
0
2
0
0
1
1
2
3
1
1
0
3
0
1
0
0
2
0
1
0
0
2
1
0
0
5
0
1
0
0
1
0
1
2
1
0
0
1
0
0
2
0
0
1
1
1
1
2
3
2
1
0
0
1
1
0
0
0
0
0
0
1
0
1
0
2
2
2
0
0
0
2
2
1
1
2
2
0
0
0
0
0
0
0
0
1
2
1
0
1
1
1
2
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
1
2
0
2
1
0
1
0
1
0
0
0
0
0
0
2
2
0
0
1
2
0
0
0
2
0
1
1
0
1
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
1
2
0
1
0
0
1
2
0
0
1
0
0
1
2
2
0
0
0
1
0
1
0
1
0
2
0
1
0
0
2
0
2
2
0
0
0
2
2
0
2
1
0
1
2
1
2
1
2
0
1
0
0
1
0
0
1
2
1
1
0
2
1
2
1
1
0
0
2
1
2
0
2
2
0
0
0
3
0
1
1
0
2
0
0
0
0
0
0
1
1
0
2
1
1
1
2
0
0
2
2
2
1
1
0
1
2
1
0
1
0
0
1
0
1
1
1
0
1
0
2
0
0
0
1
0
0
2
0
1
1
0
0
0
0
0
1
2
0
0
2
2
1
0
2
0
2
2
0
0
0
2
1
0
1
2
1
0
0
1
1
1
1
0
1
1
1
0
2
2
0
1
1
1
0
2
0
1
0
1
1
1
0
1
0
1
1
0
0
1
1
2
0
0
1
2
2
0
0
2
0
0
2
2
1
2
0
0
0
2
2
1
0
1
1
1
0
0
1
0
1
1
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
1
1
2
0
1
0
0
7
1
0
0
0
1
0
1
1
0
2
0
0
1
0
0
0
2
0
1
0
0
0
1
0
1
0
0
2
1
0
2
0
1
2
0
2
0
1
1
0
1
0
0
1
0
2
1
0
0
1
1
0
0
1
0
0
0
0
1
2
1
2
1
1
0
0
0
0
2
2
1
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
3
0
1
1
8
0
0
1
2
0
0
0
0
0
2
0
0
2
0
0
1
1
1
0
0
1
0
0
1
0
0
2
1
1
2
0
1
1
0
1
1
0
0
0
1
0
0
1
1
0
1
2
0
1
0
1
2
2
1
1
0
2
1
0
2
0
0
0
1
0
2
1
1
1
2
0
3
1
0
0
0
0
0
0
0
1
0
0
2
1
1
1
1
0
0
0
2
0
2
1
2
0
0
3
0
1
0
1
0
0
2
2
1
0
1
1
1
0
1
2
1
1
0
0
0
2
0
2
1
1
2
0
1
1
2
0
0
0
2
0
1
0
1
2
0
0
1
0
1
1
2
0
1
0
0
2
1
0
0
1
0
0
1
0
2
1
1
1
0
1
0
2
1
1
0
1
1
2
0
1
0
1
0
2
0
2
1
0
0
1
1
0
1
0
3
0
0
2
0
0
0
0
0
1
1
0
1
2
1
0
1
1
2
0
1
2
1
1
0
1
2
0
1
1
1
2
0
2
0
1
0
3
1
1
0
2
0
0
2
1
1
0
1
1
0
1
0
0
0
0
0
1
0
0
2
2
1
0
0
2
2
1
1
1
1
0
0
0
1
0
2
2
0
0
0
1
2
1
0
0
0
1
0
1
2
1
0
1
1
0
0
2
0
1
0
1
2
1
2
2
1
0
2
0
0
2
0
1
0
0
0
0
1
2
1
0
0
0
2
1
0
1
1
0
0
0
0
0
0
2
2
2
1
0
1
2
0
0
1
1
2
0
1
0
0
0
0
0
2
0
2
0
2
1
0
0
1
0
0
1
1
1
1
2
0
0
2
0
1
0
0
2
2
1
1
2
1
0
2
0
0
1
3
1
0
1
1
1
0
1
1
0
0
0
1
0
0
2
0
0
1
2
1
1
1
1
0
0
0
2
0
0
1
1
1
0
0
0
1
1
0
0
1
0
1
2
1
0
1
1
0
0
2
0
1
1
1
0
0
3
0
1
0
1
2
0
0
1
0
0
1
1
2
0
2
0
2
1
0
2
0
1
0
0
0
1
0
1
0
0
0
3
1
2
1
1
2
1
3
0
0
0
1
0
0
2
0
0
0
1
1
0
1
1
0
0
0
0
1
2
1
2
1
0
1
0
2
0
1
1
0
2
0
1
0
2
0
0
1
1
0
0
0
2
2
0
0
2
3
0
0
1
0
0
2
1
1
1
2
2
1
2
2
2
1
1
0
0
1
0
1
0
1
2
1
1
1
0
2
1
1
3
1
0
3
0
2
1
0
3
1
0
1
0
0
0
2
0
2
0
2
2
0
0
0
2
0
0
1
2
0
0
2
0
0
2
0
1
0
1
1
0
2
1
0
1
1
0
0
1
1
0
3
0
0
0
1
0
0
2
1
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
1
2
1
1
1
0
2
0
0
2
0
0
0
1
0
0
0
1
2
1
1
0
1
0
0
1
2
0
1
0
2
0
1
1
0
0
2
0
0
2
0
0
0
2
0
0
2
2
0
0
2
1
0
0
1
1
1
0
1
2
0
0
1
2
2
1
2
1
1
1
1
0
2
0
0
0
1
2
1
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
2
0
0
1
0
1
2
0
0
0
2
0
1
0
0
1
0
2
1
0
1
1
0
2
0
1
0
2
2
0
2
0
0
0
0
0
2
0
2
1
2
0
2
2
2
2
1
1
2
1
0
0
1
0
0
2
0
0
0
4
1
2
0
2
0
0
0
1
0
1
1
0
2
1
1
2
1
1
0
0
1
1
0
0
1
0
0
1
2
1
1
0
0
1
1
2
1
0
0
1
1
1
1
0
2
0
1
2
0
1
1
0
1
0
0
2
0
0
2
1
0
0
0
0
0
0
0
1
0
1
0
1
2
1
0
1
2
0
1
0
1
1
0
1
1
1
1
2
0
2
0
1
2
0
2
1
3
1
0
1
0
2
1
0
1
3
1
2
1
0
0
1
0
0
0
0
1
1
0
1
1
0
0
0
2
1
0
0
1
1
0
1
1
0
1
1
0
0
1
0
1
2
0
0
2
0
1
1
2
3
1
0
2
1
2
2
0
2
1
0
2
0
2
1
0
0
1
0
0
2
1
2
1
2
1
0
1
0
1
0
0
1
3
0
0
0
1
0
0
0
2
0
0
1
2
0
1
1
0
0
1
1
0
0
0
0
2
0
0
0
2
0
0
1
1
2
2
2
0
1
1
0
2
2
0
0
0
0
2
0
2
1
1
0
0
0
0
2
0
1
0
0
0
0
2
1
2
0
0
2
0
2
0
0
0
0
0
1
2
1
1
0
2
0
1
2
0
0
2
0
0
1
1
1
2
1
0
3
0
0
2
1
2
2
0
2
0
2
2
0
1
0
1
1
2
1
1
0
0
1
1
0
1
2
0
2
0
2
1
2
2
0
2
2
1
0
0
0
0
1
0
1
2
1
0
2
0
0
2
0
1
1
1
1
2
1
0
0
1
1
0
1
1
2
0
0
0
0
2
2
0
0
1
0
2
1
1
0
0
0
2
0
0
0
0
0
2
0
0
1
0
1
0
1
0
2
1
0
1
1
1
0
0
6
1
0
0
1
0
1
3
0
0
0
2
2
0
1
0
0
0
1
0
0
1
0
1
2
2
1
0
1
0
1
0
2
0
1
0
1
0
0
0
0
1
1
1
1
0
1
0
4
2
0
1
1
0
0
1
0
0
0
2
0
1
0
1
1
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
3
0
2
2
0
0
2
0
0
0
3
1
2
2
4
1
1
0
2
1
0
2
2
0
0
2
0
1
0
0
2
1
1
0
0
1
1
0
2
1
1
1
1
2
2
1
1
0
2
0
0
0
2
0
0
2
2
2
2
0
1
0
2
1
1
0
0
2
2
2
0
1
3
1
0
1
1
0
1
1
0
0
1
0
0
0
1
1
1
1
1
0
0
1
0
1
1
2
0
0
2
1
2
0
1
0
1
3
2
2
1
0
0
2
1
1
1
2
0
1
1
1
0
2
0
0
2
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
2
1
1
0
0
0
1
2
0
2
0
0
0
0
2
2
0
0
1
0
0
0
0
2
0
1
2
1
0
0
2
0
2
1
0
1
0
1
0
1
1
0
2
1
1
1
0
2
1
1
0
0
1
0
0
1
2
0
1
1
0
0
0
1
2
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
2
2
0
0
1
0
1
0
2
2
0
0
1
0
1
1
1
0
1
0
1
2
0
2
1
0
0
0
0
0
0
1
0
2
0
2
0
0
0
1
2
0
0
0
1
0
0
1
2
1
0
0
1
0
0
2
3
1
6
2
0
1
1
2
0
2
0
2
0
0
2
0
0
0
1
1
1
2
0
0
2
1
3
0
0
0
0
0
1
0
2
0
1
1
1
1
2
0
0
1
1
0
2
0
0
1
2
0
1
0
0
1
0
0
0
0
1
2
2
1
0
1
0
0
2
2
0
1
0
1
0
1
2
0
1
2
1
1
0
0
1
2
1
0
1
2
2
2
1
0
0
3
1
0
1
0
2
0
1
1
0
1
0
0
1
1
2
0
1
0
0
0
0
0
2
0
1
0
0
0
1
0
1
1
1
1
1
0
0
1
1
0
1
0
1
1
1
2
2
2
0
1
8
3
2
2
2
0
1
0
0
0
1
0
2
1
0
0
0
1
0
0
1
1
1
0
1
0
1
1
6
1
2
0
0
2
0
0
1
0
1
0
1
2
0
0
1
0
0
2
0
0
0
2
0
1
0
1
0
1
0
1
1
0
1
1
0
1
1
0
2
0
1
0
0
0
0
1
0
3
0
1
0
3
1
1
0
1
1
0
0
1
0
0
1
0
2
0
1
2
1
0
0
1
1
1
2
2
0
0
0
0
1
1
0
0
2
1
1
1
0
3
2
0
0
0
1
0
2
0
0
2
0
2
1
0
0
0
0
1
1
2
0
0
1
1
1
0
0
0
1
0
0
2
1
0
0
0
1
0
0
1
0
0
0
1
2
0
0
1
2
0
0
0
0
0
1
0
0
2
0
1
2
2
0
2
2
1
2
0
2
2
0
1
0
1
0
2
0
0
1
1
2
0
0
0
2
2
1
1
2
0
0
2
0
0
0
0
2
1
1
1
0
1
0
1
1
0
2
0
2
2
1
1
1
0
2
1
0
2
0
2
0
1
2
0
1
1
0
0
0
2
1
1
0
0
0
0
2
0
1
0
0
0
2
0
2
0
0
0
1
1
1
1
0
1
2
0
0
0
0
0
1
0
1
1
0
0
0
2
0
0
0
2
1
2
0
0
2
1
2
2
1
0
2
1
2
2
2
1
1
0
2
1
0
0
2
2
2
0
0
0
1
0
0
0
0
1
1
1
2
1
1
2
1
2
1
0
0
0
1
0
1
0
3
0
1
0
1
0
0
0
0
1
0
1
0
1
0
0
0
1
0
1
1
2
1
1
0
1
1
0
1
0
1
1
0
0
0
1
1
0
0
1
0
0
1
0
1
0
1
2
1
0
0
1
0
1
1
0
0
1
1
1
2
0
0
2
2
0
2
1
0
0
0
1
0
3
0
0
1
1
2
0
1
0
0
1
0
0
0
1
0
1
1
1
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
1
1
1
0
0
2
0
0
1
1
0
0
0
1
0
1
0
1
0
2
0
1
0
1
2
1
0
1
1
2
1
1
0
0
1
0
1
3
2
0
0
1
0
1
1
0
1
0
2
2
0
0
0
0
1
1
0
1
1
0
2
1
0
0
1
1
1
1
0
1
2
0
1
0
1
1
0
1
0
0
0
0
2
1
1
1
1
2
1
1
0
0
0
0
1
0
1
1
1
2
1
0
1
1
0
0
0
0
0
1
1
2
0
0
0
1
0
0
0
1
0
1
2
1
0
0
0
0
2
1
1
2
1
0
0
1
2
2
0
0
1
0
0
1
1
2
1
0
2
0
2
0
2
0
1
0
0
1
1
1
0
1
1
1
3
0
0
1
1
1
0
4
0
0
0
0
1
1
0
1
0
1
2
0
0
2
1
0
0
0
2
0
2
0
1
0
0
0
1
2
1
1
1
3
1
0
2
1
2
1
0
0
0
0
0
1
1
1
2
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
1
1
0
1
1
0
2
1
1
0
1
1
1
1
2
2
0
0
0
0
2
0
1
2
0
0
0
0
0
1
0
1
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
1
0
0
1
1
0
1
0
0
6
1
2
0
1
1
2
2
1
0
1
1
0
1
1
0
2
9
1
0
2
0
1
2
0
0
1
2
0
3
2
1
2
2
1
2
0
0
0
2
2
0
0
0
0
0
1
2
1
1
0
1
0
1
0
0
1
2
0
1
2
0
0
0
0
1
2
1
0
2
0
1
0
2
0
1
0
1
1
2
2
0
0
1
1
0
0
1
0
0
0
1
0
1
2
0
0
0
2
0
0
1
1
0
0
1
1
0
0
0
2
0
2
2
1
0
1
0
0
1
1
1
0
1
2
0
0
2
0
3
2
3
1
0
1
1
1
0
2
0
2
1
0
0
1
0
1
1
2
0
0
0
0
0
0
0
0
2
1
0
2
0
1
0
1
0
1
1
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
1
1
1
0
1
2
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
2
2
0
2
2
0
2
1
3
2
0
2
0
0
1
1
0
2
0
0
1
1
0
0
2
2
0
0
1
1
1
0
2
1
1
2
0
0
0
0
0
2
0
1
2
0
1
0
2
1
1
1
1
1
0
0
1
1
2
0
0
0
2
1
0
2
1
0
1
2
0
1
1
1
1
0
0
0
0
3
0
0
1
1
0
0
1
1
0
1
0
0
0
2
1
0
1
0
0
0
0
0
0
2
2
1
1
0
0
1
2
0
1
0
1
0
0
1
0
1
0
4
1
0
1
1
2
1
0
0
2
0
1
1
1
1
0
0
1
1
1
2
1
1
0
0
0
1
0
1
2
0
0
1
0
0
0
1
0
1
0
1
1
1
0
1
0
2
0
1
1
1
2
2
2
0
1
1
1
1
1
0
1
2
2
1
0
2
0
0
0
0
1
0
1
1
0
1
0
0
0
1
0
0
0
1
1
0
0
1
0
0
1
2
0
2
2
0
2
3
1
0
1
0
1
0
2
0
1
1
0
1
3
1
1
2
1
0
0
0
2
2
0
2
0
0
2
0
0
1
0
1
2
2
1
2
0
0
0
1
1
0
0
2
0
0
1
2
0
0
1
1
2
1
1
1
2
1
0
0
0
0
0
0
0
1
1
1
1
0
0
3
3
2
5
0
0
0
0
0
1
1
1
1
1
2
2
0
1
0
2
0
2
0
1
0
1
1
1
1
0
2
0
0
2
1
1
1
1
1
1
0
1
0
2
0
2
1
2
0
0
0
1
1
0
1
10
2
3
0
1
0
1
0
2
0
1
0
0
0
0
1
1
1
1
2
4
1
1
2
0
1
1
0
0
1
0
2
2
1
0
0
0
1
0
0
0
1
0
1
0
1
1
1
0
1
0
1
0
2
2
1
1
1
1
0
0
1
1
1
0
0
2
2
1
0
1
0
0
1
1
0
0
2
0
0
1
0
0
1
0
1
1
1
1
2
2
0
1
1
3
2
2
1
0
1
0
1
1
1
0
2
2
0
0
0
1
2
0
1
1
0
2
0
0
1
1
0
0
0
0
2
2
0
0
0
2
0
0
1
0
0
1
0
2
1
0
1
1
0
2
1
1
1
2
1
0
0
0
2
0
3
0
1
0
0
1
0
0
0
1
0
1
3
0
0
2
2
0
0
1
0
2
1
0
1
1
0
0
2
0
0
2
0
2
1
1
2
0
0
1
0
0
1
0
0
0
2
0
1
1
2
1
0
1
0
2
2
2
0
0
0
1
1
1
1
2
1
2
1
1
0
2
0
1
1
0
1
2
0
1
1
1
0
0
1
0
0
0
0
0
0
1
1
2
2
0
0
0
1
2
2
0
1
1
0
0
2
1
0
0
0
0
1
1
0
0
1
1
0
1
2
1
0
1
1
0
0
1
2
1
2
0
0
1
2
2
0
1
1
1
2
0
0
2
0
1
0
1
1
1
0
0
0
0
1
0
1
2
2
1
0
2
1
0
0
0
0
0
2
0
1
1
0
1
1
0
0
0
0
3
1
0
0
0
1
0
0
0
1
2
0
1
0
2
1
1
1
1
2
3
0
2
1
0
2
1
0
2
1
2
0
1
0
1
2
1
1
1
0
2
0
0
1
0
2
0
1
2
0
0
2
0
1
0
1
0
1
0
2
2
2
0
0
0
1
1
0
1
0
0
0
0
1
1
0
1
1
0
2
3
0
0
3
1
1
2
1
0
1
0
0
2
1
2
0
2
0
0
2
0
0
0
0
1
1
2
1
0
0
1
1
1
2
1
2
2
2
1
1
2
1
0
0
1
1
1
0
1
0
1
0
2
1
0
0
0
3
0
2
1
0
1
0
1
0
0
1
5
0
0
2
1
3
0
2
1
0
1
0
0
0
0
2
1
2
0
0
1
0
0
1
3
1
3
2
0
0
0
2
2
0
0
0
2
0
0
1
0
2
0
1
2
1
0
0
1
1
0
1
1
1
2
1
0
1
1
0
1
2
0
1
2
1
1
0
0
0
1
0
1
0
2
0
0
0
2
0
2
1
0
0
0
3
0
1
0
0
2
0
0
1
0
1
0
0
0
1
0
2
2
0
0
0
0
1
0
0
2
0
1
1
1
0
0
0
1
0
2
1
1
1
2
1
0
0
1
1
0
0
2
2
2
1
2
0
2
2
0
1
1
1
1
2
0
1
0
2
0
1
1
0
2
1
0
1
2
0
1
1
2
0
0
0
2
0
1
0
1
1
2
2
2
0
0
0
1
2
1
0
0
1
0
2
1
0
1
0
0
1
0
2
0
0
1
1
1
1
0
0
1
1
2
1
2
1
2
1
0
1
2
1
0
1
1
2
0
1
1
0
1
0
2
3
1
2
2
2
0
0
2
1
1
2
0
0
2
0
2
0
0
0
1
0
0
0
2
1
0
0
1
1
1
1
2
0
2
1
1
0
1
1
1
2
2
2
2
0
0
0
0
1
0
1
0
0
0
1
1
1
0
0
2
0
0
0
0
0
1
2
0
1
2
3
0
0
1
2
2
0
1
2
0
0
1
1
2
2
2
0
0
1
1
0
0
2
2
0
1
0
1
1
0
0
0
2
2
1
2
0
0
2
1
0
1
1
1
1
1
1
0
0
0
0
1
1
0
1
1
2
1
1
0
0
0
0
2
1
0
1
2
2
2
0
1
0
0
1
3
1
0
0
1
0
0
1
1
0
1
0
2
0
0
1
0
3
0
1
0
2
0
2
1
0
1
0
1
0
1
0
0
1
2
1
1
0
0
0
1
0
2
0
0
2
0
2
1
0
0
0
0
0
2
2
0
0
1
2
0
1
0
0
1
1
1
0
1
0
1
3
1
2
0
2
0
0
0
1
0
0
2
1
0
0
0
1
2
2
2
1
1
1
2
2
2
0
0
1
0
0
1
0
2
2
0
0
2
0
1
2
1
1
0
0
1
0
0
1
1
0
1
2
1
0
1
1
0
1
0
1
0
0
1
1
0
0
0
1
1
1
0
0
3
0
0
0
0
0
0
1
0
0
0
2
1
4
0
0
0
0
2
0
1
2
0
1
2
0
2
0
2
0
2
0
2
0
1
0
1
1
0
0
0
1
2
0
0
1
2
2
1
0
1
1
0
0
0
0
0
2
0
0
1
1
1
0
3
1
2
0
2
0
0
0
2
0
0
2
1
0
0
1
2
1
0
0
0
1
0
0
1
1
0
4
1
0
2
1
0
2
1
0
2
1
2
0
0
0
2
0
1
0
0
0
1
2
0
0
2
2
1
0
2
2
0
2
0
1
2
0
0
1
1
1
2
0
0
2
1
3
0
2
0
0
0
1
0
3
0
0
1
1
1
2
2
0
0
0
0
0
1
1
2
0
2
1
0
0
0
1
0
2
2
0
1
0
1
0
1
2
1
0
2
0
0
1
2
0
0
1
0
1
1
0
1
2
3
0
3
1
0
2
1
0
0
2
1
2
0
1
0
1
0
0
1
2
0
0
0
2
2
1
1
1
2
0
1
0
2
0
2
2
3
1
0
2
0
0
2
0
0
1
2
0
0
2
4
1
3
2
0
2
0
0
0
2
1
0
1
1
1
0
0
0
1
0
1
0
1
2
0
1
0
2
2
0
2
1
0
0
1
1
0
2
2
1
0
1
1
1
1
2
5
2
4
2
0
0
2
0
1
1
1
0
0
1
2
0
0
0
0
0
1
1
3
0
1
0
3
2
3
2
0
2
1
2
0
0
0
1
0
0
0
0
1
0
0
1
1
1
0
0
2
0
2
1
1
2
1
1
0
3
1
2
0
1
3
1
0
2
2
0
2
2
0
1
1
2
0
0
0
1
2
0
0
0
1
2
0
1
0
0
0
1
0
0
0
6
1
0
1
1
1
0
0
2
2
0
0
2
0
0
1
0
0
0
0
0
1
2
2
0
0
1
1
1
1
0
1
2
0
1
2
3
2
1
0
0
1
2
2
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
2
1
0
2
1
1
1
1
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
2
0
2
2
2
1
1
0
1
1
1
0
0
0
2
1
1
0
1
1
0
2
1
0
0
0
1
1
0
1
0
0
0
0
1
0
2
1
0
0
0
1
1
2
0
0
2
0
2
1
0
0
0
0
2
2
1
0
2
4
0
3
0
0
2
2
1
0
2
0
0
0
1
1
0
1
0
0
1
1
0
2
1
1
0
1
2
1
2
0
2
0
0
2
1
1
0
0
2
2
2
2
1
1
0
0
0
0
2
0
0
0
1
1
1
2
0
1
2
0
2
1
0
0
1
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
1
0
1
1
0
1
3
1
0
2
2
2
1
0
0
1
1
1
1
1
1
2
0
1
2
1
1
0
1
1
0
1
0
2
1
1
1
0
0
0
0
2
1
1
0
0
1
3
1
1
1
2
1
2
1
0
0
0
1
0
0
0
0
2
4
0
0
0
1
1
0
2
0
3
0
1
2
0
2
1
1
2
1
0
0
3
2
1
2
0
1
1
2
0
0
2
1
0
2
0
0
2
0
0
0
0
0
1
2
0
1
0
1
0
0
1
2
1
0
0
0
2
0
2
1
2
0
1
0
0
2
1
0
1
0
0
1
0
1
2
0
0
1
2
1
2
0
0
1
1
1
1
0
2
2
0
0
1
1
3
0
0
0
0
0
1
1
1
1
1
1
0
1
0
0
0
0
0
0
2
2
1
0
0
2
0
1
1
2
0
1
2
0
4
1
2
2
2
2
0
1
2
2
2
0
0
0
2
0
0
0
1
0
0
1
3
1
0
1
0
0
0
2
0
1
2
0
0
2
0
0
0
0
2
1
0
0
0
1
0
1
1
0
2
2
1
1
2
0
1
1
0
2
0
1
2
0
1
0
0
1
2
2
1
2
2
3
2
0
6
2
2
0
0
2
0
1
1
0
1
0
1
1
0
0
0
2
1
1
0
0
0
0
0
0
0
2
2
0
1
2
2
0
1
2
2
1
0
0
1
0
0
1
0
0
1
0
1
2
0
1
1
0
0
0
1
0
0
0
0
2
0
1
0
0
2
0
1
1
0
0
0
0
0
0
1
0
0
1
0
2
0
2
2
2
2
0
2
0
0
2
0
0
0
2
2
1
0
1
2
0
1
0
1
0
0
1
0
1
0
1
1
0
0
0
0
2
2
0
0
0
0
0
1
1
2
1
0
1
1
0
0
2
2
0
1
2
0
1
2
0
2
2
1
2
1
1
0
0
0
0
0
0
0
0
0
1
2
0
2
2
0
0
0
0
2
1
2
1
0
0
1
1
0
0
0
1
2
1
2
1
2
2
0
0
1
1
0
2
1
1
4
0
1
1
2
2
0
0
0
0
2
1
0
1
2
2
1
0
1
0
1
2
2
0
1
0
1
2
1
2
0
2
2
1
0
0
2
0
0
0
0
1
1
2
2
1
0
1
0
0
0
1
2
1
1
1
1
0
2
0
0
2
1
0
1
0
2
1
2
0
2
1
0
1
0
2
2
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
3
1
1
0
1
0
1
1
1
0
0
0
0
1
1
1
2
2
0
1
2
1
2
1
2
1
1
0
0
1
1
0
0
0
2
0
0
0
0
2
0
0
0
1
5
3
0
1
0
0
2
0
1
1
1
1
0
2
0
1
2
1
2
0
1
2
0
1
0
1
0
1
2
1
0
1
0
1
0
1
0
2
1
2
2
0
1
0
0
0
2
1
1
0
3
0
2
0
1
1
0
1
0
1
0
0
1
1
0
2
1
0
2
0
0
1
0
1
2
1
1
0
2
2
0
2
2
1
1
1
1
0
0
0
1
1
0
0
0
1
1
2
0
1
0
0
2
0
1
1
3
2
1
1
2
0
1
3
0
0
0
0
0
2
0
3
1
0
0
2
0
1
0
0
0
1
2
0
1
2
2
0
0
0
0
3
2
0
2
0
1
2
1
1
1
0
0
1
0
2
0
0
2
1
1
1
1
2
1
2
0
2
0
0
0
0
0
1
1
2
0
1
2
1
0
1
1
1
1
0
0
1
0
0
0
2
0
3
0
0
2
0
0
0
2
0
1
1
1
0
0
2
2
1
1
2
1
1
1
0
2
0
0
0
0
1
1
1
0
0
2
0
2
2
0
0
1
2
1
0
2
1
0
0
1
0
1
1
0
2
0
1
2
1
0
0
2
0
2
0
0
1
1
0
0
2
1
1
2
2
1
0
0
1
2
0
2
2
0
0
0
1
1
1
1
0
1
1
0
1
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
1
1
2
1
0
0
1
1
0
0
1
0
3
2
2
2
1
1
1
2
2
1
1
0
0
1
1
0
0
1
0
1
0
2
1
2
1
1
1
0
0
0
1
1
2
0
1
1
0
1
2
1
1
0
1
0
0
1
1
2
0
1
2
0
0
0
2
2
1
2
2
1
0
1
0
1
0
0
0
0
2
2
0
1
1
1
1
1
1
0
1
0
0
1
1
0
0
0
0
0
2
0
0
1
1
1
1
0
9
1
2
2
1
1
2
1
1
2
0
0
3
0
2
0
1
1
0
0
1
2
2
0
0
0
0
1
1
1
0
2
0
2
2
0
0
0
1
0
0
0
2
2
1
2
1
3
0
0
0
1
1
2
2
2
1
0
2
0
1
0
1
2
0
0
0
2
1
1
2
0
0
2
0
0
2
1
0
0
0
1
1
1
0
1
1
2
1
2
0
0
0
1
1
1
1
1
0
1
0
1
2
2
1
2
0
2
2
1
1
0
0
2
0
1
0
0
1
0
0
2
0
1
1
2
0
1
0
2
0
1
2
0
1
0
1
3
2
0
0
1
1
1
1
1
1
2
1
0
1
0
0
2
1
1
0
0
1
0
0
1
0
0
0
1
0
0
1
2
1
1
1
0
1
0
1
2
0
0
0
0
1
0
2
1
0
0
1
1
1
0
0
1
0
1
0
1
2
1
1
1
2
0
0
0
0
1
1
1
0
0
1
0
1
0
1
0
0
0
0
2
2
2
1
0
0
1
1
1
0
1
0
0
1
0
0
0
2
0
1
0
0
1
1
0
0
0
1
0
0
1
1
1
1
0
3
2
1
0
0
0
1
0
1
2
0
0
0
2
1
0
1
1
0
2
0
0
0
2
0
1
0
0
2
0
1
1
0
2
0
1
0
0
1
0
0
1
2
2
0
0
0
0
2
2
0
0
1
2
1
0
2
2
2
0
0
1
0
0
0
0
2
0
0
1
3
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
1
0
2
0
0
0
2
0
0
1
0
0
1
0
0
1
0
1
1
2
0
1
0
1
1
0
1
0
0
1
0
1
1
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
2
2
0
1
0
2
1
2
0
2
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
2
1
0
1
0
1
3
0
0
1
0
0
0
1
2
0
0
0
2
0
1
1
1
0
1
1
1
1
2
0
2
1
2
1
1
0
7
0
0
0
0
2
1
1
2
0
1
0
1
0
2
0
0
1
0
0
1
1
1
0
0
1
1
2
1
0
0
0
2
2
0
0
2
0
0
1
2
2
0
0
2
0
1
3
1
1
1
0
0
1
2
1
2
0
0
2
1
1
1
0
1
0
2
0
1
0
0
0
0
1
1
1
1
0
0
0
0
1
1
0
0
0
2
2
0
0
0
2
0
2
0
1
3
1
0
0
1
3
1
2
0
0
0
1
2
2
2
0
0
2
2
0
0
1
0
1
1
2
1
1
1
0
0
0
0
2
1
2
1
2
0
0
0
2
0
0
1
1
2
0
0
0
1
1
1
1
0
2
1
2
0
0
1
1
2
2
0
0
1
0
0
1
0
1
4
0
0
1
1
1
0
0
0
0
0
1
2
0
1
0
1
0
2
2
2
1
3
0
1
1
1
1
0
1
0
1
1
0
1
0
1
1
2
2
2
1
1
1
0
1
2
0
2
0
1
0
0
4
2
1
0
0
0
0
1
2
0
1
0
2
1
1
2
2
1
4
0
0
0
0
0
0
3
0
1
1
0
1
1
2
0
0
1
0
0
2
0
2
0
2
0
1
1
0
0
0
2
2
1
2
1
4
1
0
0
0
2
0
0
1
2
2
0
0
1
1
1
0
0
2
2
0
1
1
1
0
2
1
7
1
2
0
2
1
1
0
0
1
0
0
3
0
0
0
0
1
0
0
0
2
0
0
1
1
1
2
2
0
1
1
0
2
2
1
2
0
1
2
2
0
1
1
2
1
2
3
0
2
1
0
2
0
0
2
2
2
0
0
1
1
2
2
0
0
2
1
0
0
1
0
1
1
3
0
0
0
1
1
2
0
1
1
0
0
1
1
2
1
0
0
2
0
3
2
1
1
2
0
2
0
0
1
1
1
0
0
2
1
0
0
0
0
2
1
0
0
0
1
2
3
2
0
0
1
2
0
0
0
0
0
0
0
0
1
1
2
2
0
0
2
1
1
0
0
0
2
1
1
1
2
0
2
0
0
1
0
0
0
1
0
2
0
2
0
0
0
0
1
1
0
1
0
2
1
2
2
1
1
0
1
2
0
1
0
0
1
1
0
0
0
0
1
1
0
0
0
0
1
0
0
2
0
3
0
0
2
2
1
0
5
0
1
2
1
1
1
0
0
1
1
1
2
0
1
0
0
2
2
0
2
0
0
0
0
0
0
1
0
3
0
0
0
0
0
1
2
0
1
1
1
1
0
2
2
0
0
1
0
2
1
1
0
1
2
0
0
2
3
0
0
0
0
2
0
2
3
0
0
0
2
2
0
0
0
2
0
2
0
1
0
0
1
2
1
0
2
0
1
0
1
1
0
2
0
1
0
0
0
0
1
2
0
0
2
1
0
3
0
0
0
2
0
1
0
0
1
2
0
2
0
1
2
0
1
0
2
1
0
1
1
1
1
1
0
1
2
0
2
0
1
1
0
0
2
0
0
1
1
2
0
1
1
0
2
2
0
0
0
2
2
1
0
0
2
2
0
1
0
2
0
1
0
1
0
0
0
0
0
1
1
0
0
2
0
1
1
0
0
0
2
0
1
1
2
0
0
0
0
0
0
1
1
2
1
0
1
1
1
0
2
2
0
1
2
2
0
2
0
1
2
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
3
1
0
1
1
2
1
0
0
0
2
2
1
0
0
2
1
0
0
2
1
0
1
1
0
0
0
1
0
1
0
0
1
0
0
0
0
2
1
0
0
0
2
1
1
0
0
0
0
0
1
1
0
2
0
0
0
0
0
1
0
0
0
0
1
0
1
0
2
0
0
0
0
1
0
1
0
0
0
1
0
1
1
2
1
0
1
2
0
2
0
0
2
2
1
0
1
0
1
1
0
0
2
1
0
0
1
2
2
0
1
1
1
1
1
0
1
0
0
0
0
1
0
5
2
0
0
0
3
1
0
1
0
2
0
0
1
2
0
0
1
1
2
1
0
0
2
0
2
1
0
0
1
0
0
0
1
1
8
2
0
0
0
0
0
1
0
2
0
1
0
2
1
1
1
0
0
2
2
0
0
0
1
1
0
2
1
1
1
0
0
1
2
1
1
1
1
0
0
1
1
1
2
0
1
0
0
1
0
2
0
0
0
0
0
0
1
1
1
2
1
0
1
0
0
0
1
2
0
2
0
0
0
0
2
0
0
0
1
1
4
2
1
0
2
0
2
2
2
0
0
0
2
0
0
1
1
1
2
0
1
1
0
0
0
2
1
0
1
0
0
0
0
0
1
2
0
1
1
0
1
0
0
0
0
0
0
0
2
1
0
0
2
1
3
2
2
1
1
0
1
0
1
2
1
1
2
0
0
1
1
1
1
0
2
3
1
0
0
0
2
0
1
0
2
1
1
0
0
0
0
1
2
2
2
1
0
0
2
0
0
0
1
0
1
0
0
0
1
1
2
0
2
0
1
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
2
0
2
1
1
0
2
2
0
1
1
0
1
1
0
0
1
1
2
0
2
0
0
0
0
2
1
2
0
1
1
0
0
0
1
2
1
1
1
0
0
2
0
0
0
0
1
1
0
1
0
0
0
2
2
2
2
2
0
1
2
1
0
0
1
0
2
0
0
0
0
1
0
0
2
2
0
2
0
2
1
1
2
0
3
3
0
1
0
3
0
2
2
0
1
2
0
0
1
3
0
2
0
1
2
0
2
0
0
0
2
0
1
0
1
2
0
1
0
0
0
0
2
0
0
2
0
0
0
1
2
2
1
1
1
0
1
0
0
0
0
2
1
1
0
2
0
0
0
2
0
0
6
2
0
2
0
0
2
5
3
1
1
0
0
0
0
2
2
2
1
0
0
0
0
2
2
1
0
1
1
0
1
0
0
2
1
0
0
0
0
0
2
0
0
2
0
1
0
1
0
1
0
0
1
1
1
0
1
2
2
0
0
0
4
0
2
2
0
0
1
0
1
2
0
2
2
0
2
0
1
0
1
0
1
2
1
0
2
2
0
2
0
2
2
1
0
1
0
0
0
0
0
1
2
0
0
1
1
0
2
0
2
1
1
0
2
0
1
0
2
0
0
0
0
2
4
1
1
0
0
2
1
1
1
1
1
0
0
2
0
0
2
4
4
2
1
2
0
2
0
0
0
0
0
1
1
0
0
1
2
1
2
1
1
1
0
0
1
1
0
1
2
0
0
2
1
0
0
1
2
2
2
0
0
1
2
1
0
2
0
1
2
0
1
0
0
3
0
0
1
0
0
0
0
1
0
0
0
2
0
1
0
1
0
0
0
0
1
0
0
1
0
2
0
0
2
1
0
1
1
0
1
0
2
0
1
0
2
0
0
0
1
2
2
0
1
0
1
1
1
0
2
1
1
2
1
0
1
0
1
2
1
0
0
2
4
0
0
0
0
1
1
0
0
0
0
2
2
0
0
1
2
0
0
1
2
0
1
0
0
0
0
0
0
2
1
1
0
1
0
2
2
0
0
0
0
0
1
0
2
1
0
1
1
0
3
1
0
0
2
0
1
0
0
1
1
1
1
0
0
0
0
0
2
0
1
0
0
1
0
0
2
0
0
1
0
1
0
2
0
0
1
1
0
0
1
0
2
2
1
2
1
1
1
1
0
0
0
0
2
2
1
2
0
0
0
0
0
0
1
0
2
2
2
0
1
0
1
1
0
0
0
0
1
2
1
1
1
2
0
2
0
1
0
0
1
2
1
0
1
1
2
2
2
0
0
0
0
1
2
0
0
0
0
1
0
0
2
2
2
0
0
0
1
0
1
0
1
2
1
2
0
2
0
0
2
2
1
0
1
0
0
0
0
1
0
2
1
1
4
3
0
0
0
2
0
1
1
2
2
1
0
0
2
1
2
0
1
0
0
1
2
1
2
0
1
2
1
0
0
0
0
0
1
2
1
0
2
0
0
2
1
1
1
2
0
0
1
2
2
1
0
1
0
0
1
2
0
0
0
1
0
0
1
2
1
1
0
1
2
1
0
1
2
1
1
1
0
1
2
5
0
2
0
0
1
1
1
1
1
2
2
1
1
0
3
2
1
1
0
1
2
1
1
2
1
0
1
2
1
1
1
1
0
1
0
2
0
1
2
2
1
1
2
1
0
1
0
3
1
2
0
1
0
2
0
0
1
2
0
0
2
1
2
1
0
1
2
2
0
1
1
2
1
6
0
1
1
1
1
0
1
0
1
0
1
2
2
0
0
0
0
0
0
0
1
1
2
0
1
1
2
1
0
0
2
1
0
0
1
0
0
1
0
0
1
2
0
2
0
1
0
7
2
1
0
2
0
2
0
1
1
1
0
1
2
0
0
1
0
0
1
2
2
0
0
0
0
1
1
1
0
1
0
2
0
0
3
0
0
0
0
2
2
1
0
0
2
1
1
0
1
0
0
0
1
0
0
0
1
2
0
0
0
0
2
0
0
1
0
0
0
0
1
0
1
1
2
0
0
0
0
1
2
2
0
1
0
0
0
0
0
1
1
0
2
0
1
1
2
0
0
0
1
0
1
0
0
2
0
1
1
1
0
0
2
0
0
2
2
1
0
2
1
1
2
1
1
1
0
1
1
0
2
0
1
0
2
1
0
0
0
1
2
0
2
0
1
1
0
1
0
1
0
0
0
1
0
0
1
1
0
0
2
2
0
1
1
2
0
1
0
1
3
1
0
2
0
0
0
0
0
1
1
1
1
0
2
0
2
1
2
0
1
0
1
1
0
2
1
1
0
1
1
1
0
1
1
2
2
0
2
0
0
3
0
1
2
0
0
0
1
0
2
0
0
3
0
0
0
1
0
1
1
0
1
2
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
1
1
0
2
2
0
3
4
0
0
1
0
1
0
2
0
1
0
1
1
0
1
2
1
0
1
2
0
0
2
1
0
1
0
2
1
0
0
2
1
0
1
0
0
2
1
2
1
2
1
1
0
1
1
1
0
0
2
2
0
2
1
1
1
0
1
1
0
0
0
1
0
0
4
0
0
1
0
0
0
2
2
1
1
4
0
1
1
0
0
0
1
0
0
0
2
0
2
1
1
1
1
2
1
1
1
0
1
1
2
1
1
2
0
1
0
0
3
2
0
1
2
2
0
1
2
0
1
0
1
0
1
1
0
1
1
0
2
0
2
0
0
1
0
1
0
1
0
1
2
0
1
1
2
0
1
0
0
0
0
2
1
1
1
1
1
0
0
1
1
1
0
0
0
0
1
0
2
2
1
0
1
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
2
0
2
1
0
1
1
1
2
0
1
0
0
2
0
0
3
0
1
2
0
1
0
0
0
1
1
0
1
0
1
2
0
0
0
0
0
0
5
0
0
2
0
1
0
0
0
1
1
0
0
1
0
1
1
0
2
1
1
1
0
2
2
1
0
0
1
0
0
1
2
0
1
0
3
0
0
0
0
0
1
2
2
2
1
2
1
0
2
0
0
0
1
1
3
0
1
1
0
0
0
1
2
1
0
1
1
2
2
0
2
1
0
0
0
0
0
1
0
0
0
1
1
1
0
1
2
1
2
2
0
2
2
0
0
4
2
0
1
0
1
0
0
1
1
0
1
1
3
0
1
2
2
2
0
1
1
2
0
1
1
1
0
2
0
4
1
2
1
1
1
0
2
0
1
0
1
0
0
0
1
2
2
1
1
0
1
2
2
4
0
1
0
2
1
1
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
1
2
1
2
1
3
1
1
2
1
0
0
0
1
0
2
0
2
1
0
1
1
0
0
1
1
0
1
0
1
1
0
2
1
1
1
1
1
2
2
2
1
0
0
1
1
1
0
0
1
2
2
0
0
0
1
1
2
0
0
2
0
1
0
0
1
2
0
2
1
2
1
2
0
0
3
1
0
2
1
1
0
2
0
1
2
0
0
0
2
1
2
3
0
1
0
1
0
3
0
0
0
0
1
0
2
0
2
3
2
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
1
1
8
0
1
0
0
0
0
0
2
0
2
0
1
1
0
1
2
2
0
1
0
0
0
2
0
2
1
1
0
1
2
1
0
0
2
2
0
2
0
0
1
0
0
0
2
0
1
0
2
2
0
1
0
1
1
0
0
1
1
0
1
0
1
0
0
2
1
0
2
2
0
0
1
2
1
0
0
0
1
0
0
0
1
2
0
0
0
0
2
0
1
1
0
1
0
0
2
1
0
2
0
1
0
2
1
1
0
2
2
1
1
0
1
0
1
1
1
1
1
2
2
4
1
1
0
2
1
0
1
1
0
2
1
0
1
0
1
0
3
1
2
0
0
1
0
2
0
0
0
1
0
0
1
0
0
1
2
2
2
0
0
0
2
1
1
0
1
1
0
1
2
1
2
0
1
1
1
2
1
1
0
1
2
0
2
0
1
0
0
2
0
1
2
1
0
2
0
0
1
0
0
0
1
1
0
0
0
0
1
1
2
0
1
0
0
1
1
1
0
2
0
0
1
2
0
0
2
1
2
0
0
2
1
0
1
0
1
0
2
1
2
1
1
2
0
0
1
1
0
0
0
2
2
1
0
0
1
0
1
1
0
0
1
2
0
1
0
0
0
0
2
1
2
0
2
1
0
0
0
1
2
0
0
0
0
0
0
2
0
2
1
2
2
0
1
3
0
1
0
0
0
1
1
0
0
2
0
1
1
1
0
0
2
0
2
1
2
0
2
1
3
1
1
0
0
1
0
0
1
1
0
0
0
2
2
0
0
1
0
0
0
2
0
1
1
0
0
1
2
1
1
0
2
0
0
0
2
0
0
0
0
0
2
2
0
1
0
3
0
1
1
0
0
1
2
1
0
0
1
0
0
0
0
2
0
0
0
1
2
1
1
0
0
0
2
0
1
2
1
1
0
0
2
0
2
2
1
1
0
2
2
0
1
1
0
2
0
1
0
0
1
2
2
1
0
1
0
0
0
1
0
0
2
2
0
0
0
0
1
1
0
1
2
1
2
0
0
1
0
2
0
3
1
1
2
0
0
0
0
0
2
0
2
1
0
2
0
0
0
1
1
1
2
0
0
2
2
1
3
0
1
0
0
0
1
2
0
1
0
0
0
1
0
1
0
1
1
1
1
1
2
0
2
0
0
0
0
1
0
1
2
0
1
0
2
1
0
0
2
1
2
2
0
0
3
1
0
0
0
0
1
0
1
1
1
0
0
0
1
0
0
0
0
0
1
0
2
2
0
0
1
1
2
0
1
0
2
0
0
0
1
0
0
3
2
1
0
1
1
1
1
1
2
2
1
1
0
1
0
1
0
0
0
1
0
1
0
0
1
0
1
1
1
0
0
1
0
2
0
0
1
1
1
1
2
1
1
2
1
2
0
1
0
0
1
1
0
0
2
0
1
1
0
0
0
0
2
1
2
1
0
2
1
0
1
1
1
0
0
0
1
8
0
1
0
1
1
2
2
0
0
0
0
0
1
0
0
0
3
1
1
0
1
0
2
0
2
0
3
2
0
0
1
0
0
2
1
0
0
1
0
2
0
0
1
0
0
2
3
0
2
1
1
1
0
0
1
0
0
0
0
2
0
0
0
1
1
2
2
2
1
2
2
1
1
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
2
2
1
0
0
1
0
0
1
1
0
1
0
0
0
0
0
1
2
0
1
2
1
2
3
0
0
0
0
0
0
1
1
1
0
1
1
0
1
0
0
1
0
1
0
1
1
0
2
3
0
0
0
1
2
0
0
1
0
1
0
0
0
2
2
0
1
4
0
0
0
0
0
2
0
0
0
0
0
0
1
2
2
0
0
0
2
0
0
2
2
1
1
0
1
1
0
1
2
0
1
2
1
1
1
1
1
0
1
1
1
0
3
1
2
1
4
2
2
1
0
2
1
1
1
0
0
0
2
1
0
3
0
2
1
0
1
0
0
0
2
0
1
1
1
0
2
2
2
0
0
2
0
0
0
1
0
2
0
0
1
2
2
7
5
0
0
0
1
1
0
1
1
0
2
2
1
1
2
0
1
0
0
0
0
0
0
0
2
1
2
2
1
1
2
0
1
0
2
0
1
0
0
1
0
0
0
0
0
1
0
1
0
2
0
0
1
0
0
0
0
1
0
1
0
0
1
0
1
2
0
0
2
0
1
1
0
0
0
1
1
0
0
1
2
1
0
0
0
2
0
0
2
0
2
1
2
2
0
0
2
0
0
2
0
0
0
0
2
0
1
0
0
0
0
1
0
2
0
0
1
0
0
0
2
1
1
1
1
2
2
1
1
1
0
0
1
0
0
0
0
1
0
1
1
0
1
2
0
0
1
0
0
2
0
0
0
1
1
1
0
2
1
5
1
1
0
1
1
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
1
2
0
2
1
1
2
0
1
1
1
2
2
1
0
1
0
1
1
0
1
1
2
0
0
1
0
1
0
0
1
0
0
1
2
2
0
2
0
2
1
0
0
0
1
2
0
1
0
0
0
0
0
0
2
2
1
0
0
0
1
0
2
1
2
0
2
1
1
0
0
1
0
0
0
0
0
0
1
1
0
0
2
0
1
1
1
0
0
1
2
1
0
0
1
0
0
0
1
1
1
0
2
1
2
0
0
3
1
0
1
0
0
0
0
1
2
2
1
2
1
2
1
1
1
0
0
1
1
1
0
1
1
1
0
1
1
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
1
2
1
1
0
1
1
2
2
0
0
2
1
1
0
0
1
3
1
1
2
1
0
0
1
2
0
1
0
0
1
2
0
1
2
0
1
0
2
0
0
2
1
0
1
2
0
7
0
0
0
0
1
2
1
1
2
1
1
2
2
0
1
1
1
0
2
3
2
1
1
0
0
0
2
0
3
0
1
0
2
2
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
1
1
2
0
0
1
0
2
1
1
1
0
2
0
0
2
3
1
2
1
0
0
0
1
0
2
0
0
2
1
0
1
1
1
0
2
0
2
1
1
2
1
0
0
0
2
1
0
0
1
1
1
0
1
0
1
0
0
1
2
1
0
3
2
1
0
0
2
1
0
0
0
2
0
1
1
0
2
0
0
2
1
1
3
0
0
2
3
0
1
0
0
1
0
1
1
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
1
0
0
0
1
0
0
0
1
0
1
2
0
0
0
1
0
1
1
0
0
1
1
1
1
1
1
0
2
0
1
1
0
0
2
0
0
0
2
0
1
0
1
0
1
1
0
1
1
0
2
1
1
1
2
0
2
2
1
2
1
2
1
1
2
1
0
2
0
2
0
0
2
0
1
2
1
0
2
2
2
0
1
2
0
0
0
0
1
1
1
2
2
0
2
0
0
0
0
0
1
2
1
0
1
1
0
1
0
0
0
0
3
0
1
0
2
0
0
1
0
0
1
2
8
1
2
0
1
0
3
0
0
1
1
1
1
2
2
0
1
1
0
0
1
0
0
1
0
1
1
2
2
0
1
2
1
0
1
0
0
1
2
1
2
1
0
1
0
0
0
2
0
0
1
2
0
1
0
0
2
1
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
1
1
2
1
2
0
0
1
2
0
0
1
0
0
0
0
0
1
0
2
1
0
2
1
3
0
2
0
1
1
1
0
1
1
1
2
0
0
0
0
1
0
0
3
1
1
0
0
2
1
0
2
0
1
0
0
1
0
1
2
0
2
0
2
1
2
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
1
1
0
1
1
1
0
1
1
2
0
1
1
2
0
0
0
0
0
0
0
1
1
3
1
0
0
0
1
0
0
0
0
0
0
2
1
1
0
1
0
1
1
0
0
2
0
1
1
0
2
0
0
1
2
2
3
0
1
2
0
0
0
2
0
0
1
2
1
0
0
0
0
1
2
1
1
1
1
0
1
0
0
3
2
0
1
2
1
0
0
0
0
0
1
1
0
0
1
1
2
1
0
2
0
0
2
0
1
1
2
0
0
0
1
0
0
1
1
0
0
0
0
2
1
0
0
2
2
0
1
1
0
0
1
0
0
0
2
0
0
0
2
0
0
1
1
1
0
1
1
0
2
1
0
2
0
1
1
1
0
2
0
0
2
0
1
0
0
1
2
1
2
0
2
1
1
2
0
1
1
0
0
2
0
0
0
2
0
0
0
1
0
1
1
2
1
1
1
0
1
1
1
0
1
1
1
0
2
0
0
2
1
0
1
0
0
2
2
0
1
2
2
1
0
1
1
2
0
0
0
0
2
1
2
1
1
1
1
0
0
0
1
1
2
0
2
0
1
0
0
1
2
0
1
0
1
1
2
2
1
0
0
0
0
2
1
1
1
0
1
0
1
0
1
2
2
0
1
2
0
2
1
0
2
0
2
0
0
0
0
0
0
1
0
1
2
1
1
1
1
0
2
1
2
2
0
2
0
0
1
2
0
1
0
0
1
0
0
3
1
2
1
0
2
0
0
2
1
1
0
1
2
2
1
2
0
2
0
0
2
1
1
2
1
1
0
1
0
0
1
2
1
0
1
0
2
1
0
2
2
0
1
0
0
0
1
0
2
0
2
0
0
1
0
1
2
2
1
1
1
2
0
1
0
2
1
2
0
1
1
0
0
2
2
2
0
0
0
1
1
1
0
1
0
1
1
0
0
0
1
0
0
1
1
0
0
2
2
0
2
1
0
0
0
1
0
1
1
0
1
0
2
0
0
0
0
0
0
0
0
0
1
1
3
0
0
1
0
1
2
0
1
0
1
2
1
0
0
2
2
2
0
0
0
0
0
0
1
2
0
0
0
0
1
0
2
0
0
1
0
0
1
1
2
1
1
0
0
1
0
2
0
1
0
1
1
0
0
3
0
1
0
2
0
2
1
0
1
0
1
0
0
0
2
0
2
0
1
2
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
1
0
2
1
1
0
1
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
2
0
0
0
0
0
2
2
0
0
0
1
0
0
2
0
1
0
0
0
2
0
2
1
0
0
0
0
0
0
1
0
0
1
0
2
0
0
1
1
2
2
3
1
0
1
1
1
2
0
2
0
0
0
2
1
1
2
1
0
1
0
1
0
1
2
1
2
1
0
1
0
1
0
0
4
0
2
2
3
2
0
2
2
1
2
0
1
1
2
2
0
1
0
2
0
1
1
1
0
2
0
0
1
1
1
3
0
1
0
1
0
0
0
0
0
0
0
1
2
2
1
0
2
0
0
0
0
2
1
0
0
2
1
0
0
1
0
1
0
0
0
0
2
0
0
2
1
0
2
1
0
0
0
1
2
2
2
1
2
0
0
1
1
1
0
1
2
0
2
0
1
1
0
0
0
1
1
1
2
2
1
0
1
1
1
1
0
2
0
1
1
0
0
0
0
1
0
1
0
1
1
0
0
2
1
2
2
2
1
0
0
0
0
2
0
2
0
0
1
2
1
1
0
2
0
0
0
2
1
0
2
1
1
2
1
0
1
0
0
2
0
1
0
0
2
0
0
1
2
0
1
0
3
1
0
2
0
2
1
2
1
1
1
0
0
1
1
0
0
0
0
1
0
1
0
2
0
1
1
2
1
0
1
3
1
1
0
2
0
2
1
0
1
0
1
2
0
0
0
0
1
1
0
0
1
0
2
1
0
0
7
1
1
0
0
1
0
2
0
1
1
0
2
1
0
2
0
0
1
0
0
0
0
0
2
2
1
0
0
1
3
1
0
0
1
1
0
1
1
0
1
0
0
1
1
0
1
2
1
1
0
1
1
1
0
0
1
0
2
1
0
2
0
2
1
1
2
0
1
1
0
1
2
0
0
1
0
1
0
1
0
2
0
0
0
0
1
0
1
1
0
1
0
0
2
1
1
0
1
0
1
2
2
1
1
0
2
0
0
0
2
0
0
1
1
0
0
0
0
1
0
2
1
0
1
0
0
1
0
2
0
0
2
2
1
1
1
2
0
0
0
1
0
0
2
2
1
2
0
0
2
0
0
2
0
0
1
1
1
2
0
6
0
0
1
1
2
0
0
0
1
0
0
2
0
2
0
2
2
1
2
1
2
1
1
0
1
0
0
0
0
0
0
2
2
1
0
1
0
2
0
0
1
0
1
1
2
1
2
0
1
1
2
1
1
0
0
0
0
0
0
3
1
1
0
0
0
1
0
1
0
1
2
1
2
0
1
0
0
0
0
1
1
0
0
0
0
2
0
0
1
1
2
2
1
0
0
0
0
2
0
2
0
1
2
1
1
1
2
1
1
0
0
2
0
1
2
0
0
2
0
0
1
0
0
2
1
0
1
0
0
1
2
0
0
1
1
2
1
1
2
0
0
1
1
0
0
0
0
1
2
0
2
0
0
0
1
0
1
0
1
0
0
1
0
1
0
1
3
0
1
0
0
2
1
1
0
0
1
0
1
1
2
0
2
0
0
0
0
0
0
2
1
1
2
1
1
1
0
1
0
2
1
1
1
1
1
0
2
1
0
1
1
0
0
1
1
2
0
0
0
0
2
1
0
0
1
5
0
1
0
2
0
0
2
0
0
2
1
1
2
0
1
0
1
0
2
0
0
1
0
2
0
0
0
1
0
1
2
1
2
2
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
1
1
1
1
0
1
0
0
1
2
0
2
1
1
2
2
1
1
0
1
0
0
0
0
2
2
0
1
1
2
1
0
0
0
2
1
1
1
1
1
0
0
1
1
0
0
1
0
1
1
2
0
1
0
1
1
0
0
0
0
2
2
0
0
1
1
0
2
0
0
0
1
1
2
0
0
0
0
0
1
1
1
0
0
0
1
0
1
2
2
1
1
0
0
2
2
0
1
2
2
1
2
2
2
0
0
0
0
0
0
0
1
0
1
0
2
2
1
0
0
2
1
0
1
0
1
1
1
1
2
0
1
2
0
1
1
0
0
1
0
0
3
1
0
0
0
0
0
0
1
1
0
2
0
1
1
2
1
0
0
0
1
0
0
1
1
1
0
0
0
0
1
2
3
0
0
0
1
1
1
0
2
0
0
1
0
1
2
1
0
0
0
0
0
0
0
0
1
1
0
0
2
0
1
2
0
0
3
0
0
1
0
1
2
0
0
0
0
0
1
0
0
1
1
1
1
0
0
2
1
0
1
1
0
0
2
1
0
0
0
2
0
2
2
0
1
1
1
0
0
2
1
1
1
0
0
0
1
1
0
0
0
2
0
1
0
1
0
0
1
2
0
1
0
2
2
0
2
2
0
0
1
2
1
0
0
2
0
0
1
1
1
1
0
1
0
1
0
0
0
0
1
0
2
0
0
2
0
1
0
1
0
2
2
1
0
0
0
0
0
0
0
2
0
0
2
1
0
2
2
1
2
0
0
0
1
0
0
0
1
1
0
0
1
1
1
2
1
1
0
0
1
0
2
2
2
0
1
1
2
0
2
0
2
0
1
2
1
2
0
2
0
2
1
1
0
0
1
1
0
0
0
1
1
0
0
0
2
2
0
0
0
0
1
2
0
0
0
1
0
2
0
0
0
1
0
1
1
2
0
2
1
0
0
2
1
0
0
0
2
0
0
1
1
0
0
1
2
0
0
2
0
2
0
0
0
0
0
0
3
0
2
0
1
0
0
1
2
0
0
1
0
1
1
0
0
1
0
2
0
1
1
1
0
1
1
0
1
0
0
0
0
1
2
0
1
2
1
1
2
1
1
1
0
0
1
1
2
1
0
1
0
1
0
1
2
1
0
1
0
1
0
0
1
2
1
0
0
0
0
2
2
0
0
0
2
1
0
1
2
1
1
1
0
2
0
0
0
1
2
5
0
3
2
1
2
1
1
1
0
1
1
0
1
0
1
0
0
1
0
0
3
0
0
2
0
0
2
1
0
2
2
0
0
0
2
1
0
0
1
1
1
2
0
1
0
0
2
0
2
2
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
1
2
0
0
1
1
1
2
0
2
1
6
1
0
1
0
0
1
0
0
0
2
2
0
0
0
0
0
0
2
0
0
1
1
1
1
0
2
1
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
2
0
1
0
1
1
0
2
0
1
1
0
3
0
0
2
1
0
0
0
2
0
0
2
1
0
0
0
1
0
1
1
2
0
2
1
0
1
0
2
0
0
3
0
1
1
1
1
1
1
0
0
1
0
1
0
1
1
0
1
1
0
0
0
1
2
2
1
1
2
1
0
0
2
1
2
1
1
1
1
2
1
1
0
0
2
0
1
2
0
0
1
2
2
1
1
1
0
1
1
0
0
1
0
1
1
0
1
0
0
0
1
0
0
1
1
1
1
0
2
0
2
0
1
2
2
0
0
0
2
1
1
1
1
1
1
0
2
1
2
0
1
0
0
2
0
1
2
0
1
0
1
0
2
0
0
1
1
0
2
0
0
1
0
1
1
1
0
0
0
1
1
0
1
0
0
2
2
1
1
0
1
0
1
2
0
0
0
2
0
0
1
1
1
0
0
2
0
1
2
1
2
1
2
1
0
1
0
0
0
0
0
0
0
1
1
0
3
0
0
2
0
0
0
0
0
0
0
0
0
2
1
2
0
1
1
0
1
0
0
0
1
0
0
1
1
1
0
1
1
0
0
0
2
2
3
1
2
0
1
2
1
1
0
1
1
0
1
1
1
1
1
1
0
1
2
1
1
0
0
0
2
0
1
3
0
1
1
1
0
0
1
0
1
0
2
0
2
1
0
0
0
2
0
0
0
0
1
0
1
2
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
2
2
0
2
1
2
2
0
0
1
0
2
0
0
2
2
1
1
0
1
1
1
1
2
0
0
0
1
1
0
2
1
1
2
0
0
4
2
1
1
1
0
2
2
1
1
2
0
1
1
0
2
0
2
1
0
2
3
2
0
0
1
1
1
0
0
0
0
1
0
1
1
0
1
1
0
2
1
1
1
2
0
2
1
1
0
0
1
1
0
0
2
2
0
1
0
0
1
1
0
0
0
0
1
0
0
0
2
1
0
1
1
1
1
0
2
2
0
0
0
1
0
0
0
2
1
8
0
1
1
1
0
1
1
0
0
1
0
1
2
0
3
1
0
1
1
1
0
0
0
0
1
0
1
1
1
2
0
0
1
0
1
0
0
1
0
1
0
1
0
2
0
0
2
0
0
2
2
0
2
0
2
0
0
1
2
1
3
1
0
0
0
1
1
2
1
1
2
2
0
1
0
0
2
2
0
0
0
2
1
0
0
0
0
2
0
0
3
1
0
0
2
1
0
0
1
2
0
0
0
1
0
0
1
0
0
1
1
0
2
1
0
0
0
0
0
0
1
0
1
1
2
1
1
1
0
0
1
1
0
2
0
0
0
1
0
1
1
1
1
0
0
0
2
0
1
0
1
2
1
0
0
0
0
1
1
0
0
2
1
0
0
0
1
0
0
1
2
0
0
0
0
0
0
1
3
0
1
1
2
2
1
0
0
0
1
0
0
1
1
2
1
0
0
2
3
1
0
1
0
1
1
0
0
0
1
0
1
0
0
1
2
2
0
1
1
1
2
1
0
3
0
1
2
2
1
2
1
0
2
2
0
2
1
0
3
3
0
1
0
1
0
1
0
1
1
0
0
0
2
0
1
0
2
0
0
1
0
1
0
0
0
0
1
2
1
0
2
0
2
1
0
1
2
2
3
1
2
0
0
1
0
0
1
0
1
1
1
0
1
1
2
0
1
0
1
0
0
2
1
2
0
1
2
0
1
0
2
0
0
1
1
0
0
0
0
2
2
0
2
0
1
0
1
0
1
1
2
0
0
0
0
0
1
1
1
1
1
2
0
2
0
1
0
1
1
0
2
0
0
1
0
0
1
0
0
1
1
0
1
1
1
2
0
0
2
2
0
0
2
2
1
0
0
0
1
0
1
0
1
0
0
0
1
1
1
1
1
0
0
0
0
1
1
0
2
0
1
1
0
1
0
0
0
1
0
0
0
1
0
0
1
0
2
0
1
0
2
2
0
0
1
4
1
0
0
0
1
0
1
2
1
0
0
0
0
0
0
2
0
0
2
2
0
2
0
0
0
1
0
1
1
0
0
3
0
0
0
2
1
0
1
2
0
0
1
2
0
1
3
1
0
0
2
0
2
0
0
0
0
2
0
2
1
1
0
0
0
0
1
0
1
0
2
1
2
0
1
1
1
0
0
0
1
0
0
0
0
1
0
1
0
2
1
0
0
0
0
0
1
1
0
1
0
0
3
0
0
1
2
0
2
2
0
0
0
0
0
0
0
1
1
2
1
0
1
1
0
1
1
0
1
0
1
2
0
2
1
2
1
0
1
0
0
0
0
0
0
1
0
0
2
0
1
1
3
1
1
1
1
0
2
0
0
0
1
1
0
1
1
2
1
2
2
1
1
1
0
2
1
2
0
2
1
0
2
2
2
2
0
1
1
0
0
0
0
0
2
0
1
0
1
1
0
1
0
3
2
1
1
0
0
0
0
1
1
0
2
0
2
0
0
0
1
0
1
2
0
0
1
1
2
1
1
0
0
0
0
0
2
0
0
1
0
0
0
0
2
1
0
0
0
0
0
1
2
0
0
2
0
1
1
1
2
0
1
0
1
2
0
1
1
1
0
1
0
0
2
0
3
0
1
2
1
2
0
0
1
0
0
2
0
1
3
0
1
2
1
0
1
1
0
0
1
2
0
2
0
0
0
0
2
2
1
1
1
0
1
0
1
0
0
2
2
1
0
0
2
2
2
1
1
2
0
0
0
2
2
2
0
0
2
0
0
2
1
1
0
2
1
1
2
0
0
0
0
1
1
0
0
1
2
0
4
1
2
2
0
2
0
2
0
2
2
0
1
0
0
1
0
0
1
1
0
1
1
0
0
1
2
0
2
2
1
1
1
1
2
2
1
0
0
0
1
0
0
1
1
1
3
1
1
1
0
0
1
1
0
0
0
1
2
0
0
0
2
1
2
1
0
1
0
1
1
2
2
1
1
1
1
0
1
1
0
1
1
1
1
0
0
1
0
0
0
0
0
1
0
0
2
0
2
1
0
0
1
1
4
1
1
0
2
0
0
2
1
0
0
1
0
1
0
1
1
1
0
1
1
0
1
0
1
1
1
1
0
0
2
0
1
0
0
1
0
1
2
0
0
0
0
1
1
2
0
1
0
2
0
2
0
6
1
2
2
1
0
1
0
1
0
3
3
0
1
1
1
0
2
0
0
1
0
2
0
1
0
2
1
1
0
2
0
0
0
1
0
2
1
1
0
1
0
1
1
0
0
3
4
0
1
2
1
0
0
1
1
1
1
2
0
2
0
0
0
3
0
1
2
1
0
0
1
1
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
1
1
1
0
0
2
2
0
0
0
0
0
1
0
0
1
0
1
1
1
2
2
0
0
1
0
1
2
2
1
0
0
0
1
2
0
1
1
2
0
2
0
0
0
0
2
0
0
2
1
1
1
1
0
3
0
1
1
0
0
1
0
1
0
0
0
2
2
0
0
2
0
1
2
0
0
0
1
0
1
2
1
1
1
0
1
1
0
0
1
0
0
1
2
1
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
1
1
1
0
1
0
1
1
0
0
0
1
0
2
0
2
1
1
1
3
1
0
0
0
1
0
0
1
2
0
0
2
1
0
1
0
0
0
0
2
0
0
0
1
0
2
0
0
1
1
2
1
2
1
2
0
2
2
0
2
0
0
3
2
1
2
1
2
1
0
1
1
1
0
2
0
2
1
0
0
0
0
2
1
0
2
2
2
1
2
0
1
1
2
1
0
0
1
2
0
3
1
1
2
0
0
0
0
0
0
0
0
0
1
2
2
0
1
1
0
0
2
0
2
1
1
1
2
1
0
2
0
1
1
1
2
2
0
0
1
0
2
0
1
0
0
2
0
1
1
1
0
0
0
0
2
1
0
0
1
2
0
2
0
2
2
1
0
0
2
0
2
1
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
2
0
2
0
2
0
0
1
0
2
1
2
0
2
2
0
0
2
1
2
0
1
1
0
1
2
0
0
2
1
0
0
0
0
0
2
1
3
0
1
0
0
1
0
0
0
1
1
0
1
0
3
1
0
2
0
1
0
1
1
1
2
0
1
2
0
4
0
0
2
1
0
0
2
1
0
0
1
2
0
0
1
0
0
0
2
1
1
1
1
1
0
0
1
1
2
2
1
1
4
1
1
2
1
1
0
3
0
1
1
0
1
0
2
1
0
0
3
0
0
0
0
0
0
1
1
0
0
1
2
0
0
0
1
0
2
0
2
0
1
0
2
2
0
1
0
0
0
2
0
2
2
1
1
0
0
0
1
0
1
0
0
1
2
1
0
0
0
1
0
1
0
3
0
0
0
1
0
1
1
0
0
1
1
0
1
0
0
0
0
0
2
0
2
1
0
4
1
0
0
1
0
2
5
1
1
2
2
1
0
0
0
2
0
1
2
1
1
0
2
1
1
1
1
2
1
1
1
1
0
2
3
0
1
1
0
2
1
1
0
0
0
2
4
1
0
2
1
0
0
1
0
0
0
1
0
2
0
2
1
1
2
0
0
0
1
1
1
1
1
1
0
2
0
1
2
1
0
1
0
0
0
1
0
0
0
0
0
0
1
1
1
0
1
0
2
1
1
0
1
0
1
1
1
0
0
2
1
1
2
0
1
2
0
0
1
1
1
2
1
0
1
0
1
0
0
1
0
2
1
0
0
0
1
0
1
2
0
3
2
0
0
2
1
1
1
1
1
0
1
0
0
1
0
2
0
2
0
1
0
1
0
1
1
1
2
1
1
0
0
1
0
4
2
0
0
2
0
0
0
2
1
2
0
0
1
2
1
0
1
1
1
0
0
0
3
1
1
1
0
1
0
2
0
1
0
0
1
6
1
0
0
0
1
0
2
1
1
0
1
1
1
1
0
1
0
2
0
1
2
0
0
0
1
0
3
0
3
0
1
0
1
0
0
1
2
0
2
2
1
0
1
0
1
0
0
0
1
2
2
0
2
0
1
0
1
1
0
2
1
0
1
0
0
0
0
1
3
1
0
2
2
0
1
1
0
1
2
1
0
1
1
0
2
0
2
1
0
1
1
0
0
1
0
0
2
1
0
2
0
2
3
0
3
0
3
1
0
1
1
1
1
0
0
0
1
2
0
0
2
1
1
0
3
2
3
1
2
0
0
1
0
0
1
1
0
0
1
1
0
0
1
0
2
1
1
1
0
0
1
0
1
1
1
0
1
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
1
1
0
1
1
1
1
0
0
0
1
1
0
2
1
0
0
1
0
1
2
0
0
1
1
1
1
1
1
1
2
1
1
1
0
0
2
0
0
0
0
0
1
0
1
1
0
1
0
0
0
1
1
0
0
0
0
1
3
2
2
2
1
1
2
1
0
2
0
1
0
1
1
1
1
2
0
2
1
1
2
0
1
0
1
0
2
0
0
1
1
0
1
2
1
1
0
2
2
2
0
1
1
1
0
1
1
2
1
1
2
0
0
0
2
1
2
1
0
0
0
2
0
1
1
0
0
0
2
1
0
1
0
1
1
2
1
0
2
0
1
1
0
0
1
1
1
0
1
0
1
2
2
0
0
1
0
0
0
0
0
1
1
2
1
2
1
0
2
0
1
0
1
1
0
1
0
0
2
0
0
1
0
1
1
0
1
0
2
1
0
0
0
0
0
2
2
0
2
2
2
0
1
0
0
0
0
0
1
2
0
0
0
1
2
0
2
0
1
1
0
0
0
0
0
2
2
0
2
1
0
1
0
0
0
1
2
1
1
0
1
1
0
1
0
2
0
0
2
1
2
0
1
0
1
0
2
0
1
1
1
1
2
1
1
2
2
0
1
1
1
1
1
1
0
0
0
2
1
0
0
0
2
2
1
0
2
0
1
2
2
1
1
2
2
1
0
1
0
2
2
0
0
0
0
1
2
2
2
1
0
0
1
1
0
0
0
2
0
1
0
0
0
0
1
0
0
1
1
2
1
1
1
2
1
0
0
0
2
2
1
0
2
0
0
0
2
1
0
1
1
2
1
0
1
2
0
0
0
1
0
1
1
0
0
1
1
0
0
2
1
1
0
0
1
1
2
0
1
2
0
0
2
2
0
0
2
0
1
1
0
1
2
0
0
1
0
2
2
0
2
0
2
1
2
5
0
0
0
2
2
0
1
2
2
2
0
2
0
2
1
2
0
2
2
0
2
2
2
0
1
0
0
0
0
1
1
0
0
1
0
1
1
2
0
0
0
2
0
2
0
0
0
0
1
0
2
2
2
0
2
4
0
0
2
1
0
1
0
1
1
0
1
1
0
1
2
0
1
0
0
0
0
0
1
1
0
1
1
0
0
0
2
2
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
2
0
0
3
0
0
1
1
0
1
0
0
0
3
1
1
0
2
5
1
2
1
0
0
0
0
2
0
1
1
1
0
0
1
2
2
2
2
0
1
0
0
0
2
3
0
2
0
2
1
0
1
1
1
1
0
1
1
1
1
0
2
2
0
0
1
2
0
0
1
0
0
1
1
0
2
0
0
1
2
1
0
0
0
0
0
0
1
1
0
1
1
1
0
1
0
1
1
3
0
1
2
1
0
2
2
1
2
4
0
2
1
1
0
1
0
0
0
1
1
1
0
0
2
1
1
0
1
2
1
1
0
2
2
3
0
1
1
2
2
0
0
2
0
1
1
2
0
0
0
1
1
0
0
0
1
1
0
2
1
2
2
2
0
1
2
0
1
0
2
1
0
2
1
1
0
2
0
1
1
0
2
0
0
1
2
0
1
2
0
0
1
1
2
1
1
1
2
0
1
1
0
1
2
0
0
0
1
3
1
0
1
0
0
1
2
2
0
0
0
5
0
0
1
1
1
0
0
0
0
1
1
0
1
0
0
1
0
0
2
9
1
0
0
1
0
1
0
1
2
1
0
0
0
0
2
2
2
0
2
1
0
0
0
0
0
0
1
0
0
2
1
0
0
1
1
0
0
0
2
1
2
0
0
2
0
0
0
0
1
2
1
1
0
2
0
0
1
0
4
0
0
1
2
1
0
1
0
1
2
2
1
1
1
0
0
1
0
1
2
3
1
0
1
1
2
0
0
1
1
1
0
0
0
0
1
0
2
0
0
2
1
1
2
0
1
1
1
0
0
1
0
1
1
0
2
0
0
1
0
1
0
2
0
0
0
1
1
1
2
0
0
2
1
0
1
2
0
0
0
1
2
0
2
0
1
3
0
0
1
1
0
0
0
2
1
1
0
0
0
2
0
0
7
0
1
0
0
2
1
2
0
1
2
1
2
1
0
0
0
0
2
2
2
2
1
0
0
0
1
2
1
0
1
1
0
1
0
1
0
0
2
2
1
2
2
0
3
0
0
2
1
1
2
2
1
2
1
0
0
2
0
1
0
0
1
0
0
0
1
0
0
1
1
2
1
0
1
2
0
1
0
1
2
0
2
0
0
1
0
2
1
0
0
1
0
0
1
1
2
2
1
0
1
0
1
0
1
2
0
0
1
1
1
1
0
1
0
0
1
0
2
0
2
1
2
2
0
2
0
2
2
1
2
0
0
0
0
1
0
0
1
0
0
1
0
2
0
1
1
1
0
0
0
1
0
1
1
0
1
1
0
2
1
1
0
0
3
2
0
1
1
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
2
0
1
0
1
0
3
2
1
0
1
0
0
1
0
0
2
2
2
2
0
1
0
2
0
2
3
1
0
2
1
0
1
1
0
0
0
3
0
0
0
0
0
0
2
0
2
0
1
2
1
3
1
2
1
0
2
2
1
0
0
0
1
5
0
0
0
0
1
0
0
0
1
1
7
0
3
2
0
1
1
0
1
2
1
0
2
0
2
0
0
2
2
1
1
0
0
0
0
2
1
0
0
0
2
0
0
2
0
2
1
0
1
0
0
2
0
1
0
0
1
1
0
1
1
3
0
3
1
1
0
2
1
0
2
2
2
0
0
0
0
0
0
0
2
0
1
3
0
0
1
0
1
0
0
1
1
0
1
0
3
2
0
0
0
2
1
1
1
2
1
1
0
1
0
1
2
1
0
0
1
0
0
2
0
0
1
1
1
1
0
0
2
0
0
0
1
2
1
0
0
1
0
1
0
0
2
0
1
1
2
0
0
0
2
2
0
0
2
0
0
0
2
2
1
0
0
2
0
2
1
0
1
1
1
0
1
0
1
0
2
0
0
0
1
0
1
0
0
2
0
0
2
2
1
0
2
1
0
2
2
1
1
0
1
0
0
2
1
0
1
2
0
1
0
0
1
0
1
1
0
1
2
1
1
1
0
1
1
1
0
0
0
0
1
0
2
1
0
0
0
0
0
2
1
0
0
1
2
1
0
0
1
2
2
0
0
2
3
0
0
0
2
0
0
1
2
0
0
0
1
0
2
1
2
2
0
2
1
0
0
1
0
0
0
2
0
0
0
1
1
1
1
0
1
0
2
0
1
1
0
2
1
0
1
1
0
1
2
0
1
2
1
0
0
1
1
1
1
0
0
0
0
0
2
2
0
2
0
1
0
2
1
0
0
2
0
2
3
0
0
2
0
0
2
1
0
1
0
1
2
1
0
1
2
0
2
0
0
0
0
0
2
1
2
0
1
0
1
0
2
1
0
2
0
0
3
1
0
2
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
2
1
0
0
0
1
1
1
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
4
0
0
1
0
1
0
1
0
0
0
0
2
1
2
2
2
1
2
2
0
0
0
1
0
1
1
0
0
1
2
0
2
1
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
1
1
1
0
2
0
2
1
2
0
6
0
0
1
1
0
0
1
1
1
2
1
1
2
2
1
2
1
1
1
2
1
2
2
0
1
0
0
0
0
0
0
0
0
0
0
1
1
2
1
0
2
1
0
1
0
1
1
1
2
2
2
0
0
1
0
0
1
0
1
1
1
1
1
1
1
1
2
3
0
1
0
2
1
0
1
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
1
3
1
1
0
0
2
0
0
0
1
1
0
1
0
1
0
1
0
1
1
0
0
0
1
0
0
1
0
1
0
2
1
0
1
1
1
1
1
0
1
1
2
1
0
0
0
2
0
0
0
1
1
0
1
1
0
0
3
1
0
1
0
0
0
2
1
0
0
1
0
0
0
2
3
2
2
1
0
0
0
0
0
1
2
1
0
2
1
0
1
1
0
0
0
1
2
0
1
2
1
0
0
0
1
2
2
0
2
2
1
1
0
1
1
0
0
2
0
2
1
0
4
0
0
1
2
1
0
0
0
1
2
2
0
0
0
2
0
2
1
1
2
0
1
0
2
1
0
2
0
1
0
1
1
1
0
0
0
1
2
0
1
2
1
0
0
0
2
0
2
2
1
3
0
1
1
1
2
0
2
0
2
1
1
1
2
0
0
0
1
1
2
1
0
1
0
0
1
2
0
2
2
0
1
0
2
1
1
1
0
0
3
1
1
0
2
2
2
0
0
0
0
1
1
0
1
1
0
2
2
1
0
1
3
0
1
0
1
0
0
2
1
0
1
1
1
0
2
0
1
2
0
1
2
1
0
0
0
0
0
1
0
0
2
1
1
0
1
0
0
3
1
1
0
0
1
0
2
1
0
2
1
1
0
1
0
0
0
0
2
1
0
1
2
0
0
2
2
0
2
1
2
0
1
2
0
2
0
2
1
1
2
1
0
3
0
1
0
2
0
1
0
2
0
0
1
0
1
2
0
2
0
0
0
0
1
2
1
1
2
1
2
1
2
1
0
1
0
2
0
0
0
1
2
0
1
0
0
1
0
2
0
1
0
1
1
2
0
0
1
1
1
1
2
0
2
0
1
2
0
0
0
2
0
0
2
2
1
0
0
0
0
0
1
1
1
1
0
2
1
0
1
2
1
0
0
0
0
0
0
0
0
1
1
1
5
2
1
2
0
2
1
0
1
0
1
2
0
1
1
0
1
1
2
1
1
0
2
1
0
2
0
0
1
0
0
0
0
0
0
1
0
2
1
1
2
2
0
0
0
2
0
2
1
0
0
2
1
1
2
2
0
1
3
2
1
2
0
0
1
0
0
1
1
1
0
0
0
2
0
0
2
1
0
0
0
1
0
2
1
2
2
0
0
1
1
0
0
0
0
1
2
2
1
1
1
0
1
1
2
1
2
1
0
0
0
1
3
1
1
1
1
0
1
0
0
2
2
0
0
1
0
0
1
1
1
2
0
2
0
0
1
0
0
0
1
2
2
1
1
1
1
0
0
1
0
0
2
1
0
1
0
2
0
1
1
2
0
0
2
2
0
1
0
1
2
1
2
0
0
1
0
1
2
1
2
0
1
1
1
1
3
2
2
1
2
1
0
2
0
2
2
2
2
2
1
1
1
0
0
0
0
2
2
1
1
1
1
1
0
1
1
2
1
1
0
0
1
2
1
1
1
1
1
1
1
2
1
1
0
2
1
2
0
1
2
0
1
1
1
0
1
1
0
1
1
0
0
2
0
2
1
1
2
2
1
0
0
2
1
0
1
0
2
0
1
0
1
1
1
1
0
1
0
1
2
1
1
1
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
2
1
0
0
0
0
0
0
0
3
1
1
0
2
0
2
1
1
1
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
3
1
1
1
3
3
1
0
0
1
0
3
0
1
1
0
1
1
1
1
0
0
0
0
1
1
1
0
0
2
0
3
2
1
3
2
0
3
2
0
0
0
0
0
2
0
0
2
0
1
0
2
0
1
0
0
0
0
0
1
2
1
1
0
1
0
0
1
1
0
1
0
0
2
0
1
0
1
1
0
2
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
2
2
2
2
0
1
1
0
1
0
0
1
1
1
0
1
1
1
1
0
1
0
0
0
1
1
2
0
1
0
0
0
0
0
1
1
2
2
2
1
0
1
0
0
0
0
0
1
2
0
0
1
1
1
1
0
1
1
2
0
0
2
0
1
0
1
2
2
1
2
1
0
0
0
2
1
1
2
1
2
1
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
2
1
1
1
1
2
1
1
0
2
1
1
0
0
0
0
1
0
0
0
1
2
1
0
0
0
1
3
0
0
0
0
2
0
0
2
2
1
1
0
0
0
3
0
0
2
1
0
1
0
2
1
0
1
0
0
2
0
0
1
1
2
1
1
1
0
2
2
0
2
2
0
0
1
0
1
1
2
0
2
0
2
0
0
2
2
0
1
0
0
1
1
1
0
0
0
0
1
0
1
1
0
0
0
1
1
1
2
2
0
0
2
2
2
0
0
1
1
1
0
1
0
0
2
0
0
2
0
2
1
0
0
1
0
2
0
1
1
0
1
0
1
2
2
1
0
0
0
1
2
0
2
1
1
0
0
2
1
0
1
1
0
0
1
2
0
0
1
2
0
0
1
2
1
0
1
1
0
0
0
1
2
0
1
2
1
2
0
0
0
2
0
1
1
0
0
0
1
2
1
0
1
2
0
0
0
0
0
2
2
1
1
2
0
2
1
1
0
0
2
1
0
0
2
0
1
1
0
2
1
2
0
0
0
0
0
1
1
1
0
1
1
1
0
0
0
1
1
1
0
1
2
0
2
1
0
2
1
3
0
0
1
1
0
1
0
1
0
2
0
0
1
0
0
0
1
0
0
2
0
1
0
0
2
1
0
0
2
0
0
0
1
2
1
2
1
1
0
1
1
0
0
0
1
2
1
0
0
1
2
0
0
0
2
1
2
2
0
0
3
1
0
2
2
0
2
0
0
0
2
0
1
2
0
1
0
0
0
2
2
1
2
1
1
1
2
0
1
1
0
1
0
0
0
1
0
1
0
2
0
2
1
0
1
0
0
1
2
0
0
1
0
1
1
1
1
0
2
0
0
0
0
0
0
1
1
2
2
1
1
0
0
1
1
1
0
0
1
1
0
1
1
1
1
0
1
1
1
1
0
1
1
2
2
1
1
0
2
0
0
0
0
0
0
1
0
0
2
1
1
0
2
1
2
3
1
2
1
1
0
0
1
1
1
1
1
0
3
1
1
1
0
2
0
0
1
0
0
0
0
2
1
0
0
1
1
1
0
0
2
1
0
0
0
2
0
1
0
2
0
1
0
1
1
0
0
1
1
1
0
0
2
1
1
2
1
1
1
2
2
1
0
0
0
1
0
0
2
0
2
1
1
1
2
2
1
0
2
1
1
3
2
1
0
2
0
0
1
0
0
0
0
0
2
0
1
0
1
2
0
2
1
2
0
0
2
1
1
2
2
0
2
0
0
0
0
0
2
1
0
0
2
1
1
1
1
1
0
0
2
1
2
2
0
0
2
0
2
0
1
0
1
2
0
0
0
2
0
5
1
1
1
1
1
0
0
2
1
0
2
1
1
2
1
2
1
2
0
2
0
0
2
3
0
2
1
3
1
1
0
2
1
1
0
0
0
0
1
0
0
1
0
1
0
0
0
2
0
1
0
1
0
1
0
0
0
1
1
0
2
1
1
0
3
1
1
2
2
0
0
0
0
2
2
1
4
2
1
1
0
0
2
1
1
2
1
0
0
0
1
2
2
0
1
1
0
1
0
2
1
2
1
0
0
2
3
0
0
0
1
1
0
0
1
1
1
2
2
1
2
1
2
0
1
0
1
1
2
0
2
0
2
2
0
0
0
2
0
0
1
2
1
0
0
0
0
2
0
0
2
2
0
2
0
2
2
0
0
0
1
1
1
1
0
0
0
1
0
1
0
0
1
1
0
0
1
1
0
2
2
0
1
2
1
1
0
0
1
2
0
2
0
0
0
0
0
2
0
1
0
2
0
1
0
0
0
1
9
1
0
2
0
0
2
0
0
1
1
1
0
0
0
0
2
0
3
1
2
1
1
1
0
1
0
1
0
1
1
0
0
2
0
0
2
2
0
0
0
0
1
0
0
0
0
0
2
0
2
2
0
0
0
1
1
0
0
2
1
0
0
0
1
2
0
2
0
0
0
2
0
2
2
1
0
0
1
0
2
2
0
1
1
0
1
0
0
0
2
0
0
0
1
0
2
0
0
2
1
0
0
1
0
1
1
0
1
1
1
1
1
0
0
1
1
0
1
0
0
0
2
1
2
0
1
1
2
2
0
0
0
0
2
0
2
0
1
4
0
0
1
1
0
0
0
0
0
0
0
2
0
2
0
2
0
2
0
2
1
0
0
1
1
0
1
0
1
0
2
0
1
0
0
0
2
0
0
0
0
1
2
0
0
2
2
0
2
0
0
1
0
2
2
0
0
0
0
0
1
0
0
1
2
0
0
1
0
1
1
2
2
1
1
0
2
0
1
1
1
2
1
2
1
1
1
0
1
0
0
1
0
1
0
0
2
1
1
0
0
0
0
3
0
0
1
0
1
0
1
1
2
1
2
0
0
0
1
1
0
2
0
2
0
0
0
1
0
0
0
0
1
3
2
0
0
0
2
0
2
1
0
1
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
3
2
0
0
0
0
1
0
0
0
1
1
0
1
1
0
2
1
0
0
1
1
0
0
2
1
2
2
0
1
1
0
0
1
0
1
1
0
1
2
0
1
2
0
0
2
0
0
0
1
0
0
1
0
0
0
1
1
2
0
0
1
0
2
0
1
2
0
0
1
2
0
2
1
0
0
1
1
1
1
0
2
1
0
0
0
1
1
1
1
2
1
0
0
0
1
1
2
0
1
0
0
1
0
0
1
0
1
2
0
2
2
0
0
1
0
0
1
1
1
1
0
1
0
3
1
1
1
2
0
0
1
0
0
0
0
3
0
1
1
1
0
1
0
2
1
0
2
1
0
2
1
1
3
0
2
0
0
0
2
2
1
0
0
0
1
1
1
0
0
0
1
0
2
1
0
1
1
0
1
1
0
0
0
0
0
0
0
1
2
1
0
1
0
0
0
0
0
0
0
1
1
0
0
2
2
0
2
1
1
0
2
0
0
1
0
0
1
1
0
2
0
1
2
1
4
0
2
0
1
0
1
2
2
0
2
0
0
1
0
1
0
0
0
0
3
2
0
0
3
0
1
1
1
0
1
0
0
2
0
1
1
1
1
1
3
0
2
1
0
0
1
2
0
0
0
2
1
0
1
1
2
0
0
0
0
1
0
0
0
0
0
2
0
0
4
0
1
0
0
0
2
0
0
1
1
0
1
0
1
0
2
0
0
2
2
1
0
1
1
2
1
1
0
0
1
1
1
0
1
0
1
0
0
2
2
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
2
1
1
1
0
0
1
0
2
1
2
1
1
1
0
2
0
1
0
0
1
2
0
1
0
0
2
0
1
1
2
1
1
0
1
2
1
2
0
0
0
1
0
1
1
0
0
0
1
0
1
0
0
1
3
0
0
0
1
2
0
0
0
1
2
0
2
1
1
1
0
2
2
0
2
0
0
1
0
1
1
1
1
2
0
2
0
0
1
2
2
0
1
0
1
0
1
1
0
1
1
1
1
1
2
1
0
0
0
2
0
0
2
2
1
1
2
0
1
1
1
1
0
0
0
0
0
0
1
1
1
3
0
0
0
2
0
0
0
0
1
1
0
0
0
2
1
0
1
1
0
0
2
1
0
3
0
1
0
0
0
0
2
1
1
1
1
0
0
2
1
1
0
1
1
1
0
0
0
1
1
2
2
0
2
2
1
1
1
1
2
0
0
0
0
0
1
2
0
0
0
1
0
0
0
2
2
1
0
0
2
0
1
0
0
0
2
0
1
2
0
0
1
0
2
1
2
1
1
0
2
1
1
1
0
0
0
0
1
0
1
1
0
1
1
0
1
0
2
0
0
2
0
1
0
1
1
1
1
0
2
0
1
1
0
1
1
1
0
1
0
1
0
0
0
1
0
1
0
2
0
0
1
1
0
1
2
2
0
2
1
0
1
0
1
0
0
0
1
0
0
0
2
2
0
0
0
0
1
0
0
1
2
2
0
0
0
3
0
1
0
0
1
1
3
2
1
0
2
0
0
0
2
2
0
1
1
0
1
0
0
3
1
0
2
0
1
1
1
0
0
0
1
1
0
1
1
0
1
2
1
1
0
1
0
2
1
1
0
1
0
2
0
0
0
0
0
2
0
1
0
1
1
0
2
0
0
0
1
1
1
1
1
1
1
0
0
0
0
0
2
2
2
2
0
1
0
0
0
0
2
2
0
1
1
1
0
0
2
2
0
0
2
2
0
2
1
2
2
0
3
0
1
2
2
0
2
0
1
1
0
0
1
1
0
1
0
0
0
1
0
0
0
0
1
2
0
0
1
2
1
0
2
1
0
0
2
0
1
0
0
1
2
0
0
2
0
0
0
2
1
2
0
1
1
1
0
1
1
2
0
2
0
0
1
0
0
2
1
2
0
0
1
0
0
0
1
2
0
2
0
0
1
1
0
0
0
2
0
1
1
2
2
1
0
1
0
0
1
0
1
2
1
1
0
0
2
1
2
2
1
1
0
1
2
0
0
0
0
2
1
2
1
0
0
0
0
6
1
2
1
2
2
0
0
1
0
0
2
0
0
0
0
2
0
0
1
1
1
1
0
0
3
0
1
2
0
0
3
2
2
2
1
0
1
0
2
2
2
0
1
2
4
1
2
0
0
1
0
0
0
2
0
0
0
0
1
0
3
1
1
1
2
0
1
0
0
1
1
0
2
0
1
0
2
1
2
0
1
2
2
1
0
2
0
0
0
1
1
2
1
0
1
1
1
0
0
0
0
2
1
1
0
0
3
1
0
2
1
0
0
1
1
0
2
1
0
0
1
1
2
0
0
3
0
1
0
1
1
0
2
1
1
1
0
2
1
0
0
1
1
0
1
1
1
1
2
1
0
0
3
1
0
0
1
2
0
1
0
2
0
0
1
0
0
0
0
0
0
1
1
2
0
0
2
2
1
1
0
0
0
2
0
1
2
1
1
1
1
0
4
0
2
0
1
0
0
1
0
0
2
0
1
0
0
0
1
0
0
1
1
0
1
1
1
0
2
2
0
2
1
1
1
2
0
2
1
0
1
0
1
1
2
1
2
0
2
0
0
0
0
2
0
0
2
1
1
0
0
2
0
2
0
1
0
1
0
2
1
0
1
2
1
0
0
1
1
2
1
1
2
1
0
2
0
0
0
0
2
2
1
2
1
1
0
0
1
1
1
0
2
0
0
0
0
0
0
0
0
1
1
0
1
2
0
1
0
2
0
0
1
1
0
2
0
1
0
1
2
1
1
1
2
2
1
1
0
1
1
0
0
2
1
1
1
1
0
0
0
0
0
1
0
0
1
1
1
0
2
1
0
2
1
2
2
1
0
1
3
0
2
3
1
0
1
1
0
0
2
1
2
0
1
2
1
1
1
1
0
0
0
0
2
1
2
0
1
1
0
1
0
0
0
2
2
0
0
2
0
0
2
0
2
1
2
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
2
1
0
2
1
1
0
0
1
0
0
2
3
1
0
0
0
2
0
0
0
0
1
0
1
1
0
0
2
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
2
0
0
1
1
1
0
0
2
2
2
2
1
1
0
0
0
0
6
0
0
1
1
1
0
2
1
1
1
3
0
1
0
1
1
1
0
0
2
0
1
0
1
0
2
1
0
1
0
2
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
1
0
0
1
0
0
1
3
1
0
1
0
0
1
2
1
1
0
1
1
0
0
2
0
0
0
0
1
2
0
1
0
1
1
0
2
1
1
1
2
2
0
0
1
0
1
0
0
2
0
2
2
1
1
1
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
1
1
1
1
2
2
1
1
2
0
2
1
1
3
0
1
0
1
1
0
1
0
2
0
0
2
0
0
0
1
0
0
1
2
3
1
1
0
2
2
1
1
0
0
2
1
0
0
1
0
1
1
0
0
2
0
1
0
0
2
0
0
1
1
1
0
0
0
0
0
2
0
0
2
2
2
0
0
2
1
0
0
1
2
0
1
0
0
0
0
0
0
0
1
2
0
0
2
1
0
0
1
2
0
0
0
2
0
1
1
2
0
1
3
0
2
0
0
0
2
0
1
0
1
0
0
1
2
1
2
1
0
0
0
0
0
3
2
0
1
1
1
0
0
2
0
1
0
0
2
0
1
0
1
1
1
0
0
0
2
1
1
0
1
1
0
0
1
2
1
0
0
0
0
0
2
1
0
2
0
1
0
2
0
1
1
0
0
0
2
0
1
0
9
1
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
2
1
0
0
0
1
0
1
0
2
0
2
2
0
0
1
0
0
0
2
0
1
1
1
0
1
2
0
2
1
0
1
2
0
1
0
1
1
1
0
0
1
0
2
1
0
1
1
0
2
0
1
0
0
1
2
1
0
0
2
3
1
0
0
0
0
1
1
1
0
0
2
1
1
1
0
1
1
2
1
0
1
0
0
0
0
1
0
0
0
2
1
2
2
0
1
0
0
2
0
1
1
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
2
1
0
2
1
2
2
1
0
2
0
0
0
1
1
0
0
0
0
1
0
2
0
1
1
0
0
1
1
1
2
1
0
1
2
0
2
2
0
2
0
0
2
1
2
2
0
2
1
2
1
1
0
0
0
1
0
2
1
1
1
0
2
2
0
1
1
0
2
1
0
0
1
0
0
0
0
0
1
1
1
0
2
1
1
1
0
1
4
2
0
0
2
2
2
0
0
0
2
1
0
0
0
1
2
2
2
1
0
0
1
0
1
0
1
1
0
0
0
1
1
0
1
0
0
2
1
1
0
0
1
1
0
0
0
0
0
0
1
1
2
2
0
0
1
2
1
2
1
0
0
0
1
1
2
0
1
1
3
0
0
2
1
1
1
0
0
0
0
1
2
1
2
0
0
1
2
1
1
1
0
1
2
2
0
2
0
1
1
2
0
2
2
0
2
2
3
1
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
2
0
2
1
1
3
0
0
1
0
1
0
0
2
1
0
1
1
2
2
0
1
1
0
2
1
0
0
0
0
1
1
2
0
1
0
0
0
1
0
0
0
0
1
2
0
0
1
2
1
0
0
0
1
0
0
0
0
2
0
2
2
2
1
2
1
4
0
1
0
0
0
2
2
0
0
1
0
3
1
2
0
1
1
0
2
1
2
0
0
1
0
0
0
2
1
1
0
0
2
2
1
1
0
0
1
0
0
2
0
0
1
0
0
1
1
0
0
1
1
1
1
0
1
0
0
0
0
0
1
1
1
2
0
1
0
1
2
0
0
1
0
1
1
1
0
2
0
1
0
0
0
2
0
0
0
1
2
1
1
0
2
0
0
2
2
1
1
1
1
1
0
2
0
1
2
0
3
0
1
0
1
2
0
1
1
2
1
1
2
0
2
1
1
2
1
1
0
0
1
1
1
0
0
0
0
0
1
0
1
2
0
0
0
1
2
0
0
0
1
1
2
1
2
2
0
0
2
0
2
1
0
0
1
1
0
0
1
0
0
2
2
0
1
2
1
0
2
2
2
0
1
2
1
0
0
1
1
2
2
2
1
4
2
1
1
1
4
1
1
0
0
0
2
1
1
1
4
0
0
0
0
1
2
2
1
3
2
2
1
3
1
0
1
2
0
3
1
1
2
1
0
0
2
1
1
1
0
1
1
2
0
1
1
0
1
1
2
0
0
2
0
0
1
0
1
1
1
1
0
1
2
2
0
0
0
2
0
1
0
1
0
0
0
2
2
2
3
0
0
1
1
0
0
0
1
2
3
0
2
0
1
0
1
0
0
2
1
1
1
1
2
0
0
0
0
1
2
2
0
1
1
2
0
0
1
1
0
2
0
1
1
2
3
1
0
2
1
1
0
1
1
0
1
0
1
1
1
1
0
2
0
2
2
0
0
1
1
0
2
2
1
1
1
0
2
0
1
1
2
0
0
2
0
2
0
1
1
2
0
0
0
1
2
0
2
2
0
2
0
0
1
1
1
1
0
0
0
2
9
2
2
1
2
1
1
0
0
0
1
0
0
1
2
1
2
2
0
0
2
0
3
2
0
2
0
0
2
0
2
2
1
1
2
0
0
1
2
1
0
0
0
2
0
0
0
0
0
0
0
1
1
2
1
1
0
1
1
1
1
0
0
1
1
1
2
1
0
0
1
1
0
0
2
2
0
2
2
1
1
2
0
2
0
0
3
0
1
0
0
2
0
0
0
0
2
0
1
0
1
1
0
1
0
0
1
0
0
1
1
2
1
0
0
0
2
1
2
0
1
0
2
2
0
2
1
1
2
2
1
1
1
1
2
0
0
1
0
0
1
4
0
3
1
0
0
1
0
0
4
1
0
2
0
0
0
2
0
0
0
2
0
1
0
1
1
1
1
2
2
2
0
2
2
0
0
1
2
0
0
1
0
0
0
1
2
0
0
3
1
0
2
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
1
1
2
1
1
0
0
0
0
0
2
0
2
0
0
4
2
0
2
2
1
1
1
1
0
0
0
0
0
1
1
2
0
0
2
2
0
0
2
1
1
5
2
0
0
1
1
0
0
2
2
0
0
0
0
0
2
1
2
0
1
0
2
0
0
0
0
0
1
1
1
1
1
1
0
0
0
2
0
0
2
0
1
1
0
0
1
1
1
0
2
0
1
1
0
2
0
2
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
1
2
0
0
0
1
0
0
0
1
0
1
0
0
1
1
1
0
0
1
0
0
2
0
0
0
1
2
0
0
2
1
0
0
0
1
0
1
0
1
1
1
1
0
1
1
1
0
2
0
0
2
1
1
0
0
1
1
0
2
0
1
1
0
0
0
2
2
0
1
1
1
1
0
1
1
0
0
2
2
2
2
1
2
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
2
2
1
0
0
0
0
0
1
2
2
0
0
2
0
1
0
0
0
0
0
0
0
2
2
1
1
1
2
0
1
0
0
0
0
0
1
0
0
1
2
1
1
2
0
1
1
0
0
0
2
0
0
2
2
0
1
2
2
0
1
0
1
2
2
2
0
0
1
0
1
0
1
1
0
0
2
2
2
2
1
1
0
1
1
2
1
2
0
0
2
0
1
0
2
0
0
1
1
0
2
2
1
2
0
2
0
0
1
1
0
0
1
0
2
1
0
0
2
0
1
0
1
2
3
0
0
0
0
1
1
0
0
2
1
2
0
2
1
0
1
1
1
0
0
0
1
2
2
1
0
0
0
0
0
3
0
0
1
0
0
0
0
2
0
1
0
0
3
1
0
0
0
1
0
0
1
1
1
1
0
1
2
2
0
1
2
0
0
0
1
0
1
1
0
2
0
0
1
0
0
0
0
0
0
0
1
2
2
2
0
1
0
0
0
1
0
0
2
0
1
2
0
0
0
1
1
0
2
1
0
0
0
1
0
0
1
1
2
1
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
1
2
2
0
0
0
1
1
0
0
1
1
0
0
2
1
0
0
0
1
1
1
1
0
1
1
0
0
1
0
1
0
2
2
1
1
0
1
0
2
1
1
1
1
1
1
3
0
0
0
0
1
1
0
0
0
2
0
0
1
1
1
1
1
0
0
3
2
3
0
0
1
1
1
1
1
0
0
2
1
0
2
2
2
0
1
0
0
1
0
0
2
2
0
0
1
0
0
0
0
1
1
1
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
1
2
0
0
1
2
0
1
0
1
0
0
1
2
1
2
0
2
2
1
1
2
0
1
1
1
1
0
0
0
1
2
1
0
1
1
2
1
1
1
0
0
1
1
1
0
2
2
1
1
3
2
0
1
0
1
1
0
0
0
1
0
0
0
1
0
1
2
0
0
0
0
0
2
0
0
2
0
1
1
0
0
0
0
0
1
2
0
1
0
0
0
1
2
1
0
1
1
1
3
0
0
0
1
1
0
2
2
2
0
1
0
1
0
2
0
2
0
2
1
0
0
1
1
1
2
0
2
5
0
0
2
0
1
0
0
0
0
2
0
0
0
0
2
0
0
1
2
2
2
2
1
2
0
1
1
2
2
0
1
1
2
2
0
1
1
0
0
2
0
2
1
2
0
0
0
1
2
1
0
2
2
1
1
0
0
2
0
1
0
2
0
0
0
2
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
1
1
0
1
2
2
0
0
2
0
0
1
0
0
2
0
1
2
2
1
0
1
2
1
0
2
0
3
2
1
1
1
0
2
1
0
0
0
2
2
1
1
3
0
0
1
1
0
0
2
2
0
2
1
1
0
0
0
0
2
0
1
0
0
1
1
0
1
2
2
1
2
2
0
0
2
2
0
0
1
1
0
1
0
1
0
0
1
0
2
0
0
0
0
0
2
1
1
0
0
0
2
1
0
1
0
1
1
1
0
0
0
0
0
0
2
2
1
0
0
0
1
2
0
1
0
0
1
2
0
2
2
0
1
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
3
1
0
1
1
0
2
0
2
0
1
1
0
1
1
1
0
0
0
0
1
2
0
0
2
2
1
0
0
0
2
1
0
0
0
0
1
0
2
2
1
0
0
0
0
1
0
0
2
2
0
0
1
0
1
0
2
0
2
0
2
1
1
0
0
0
1
0
2
0
2
1
0
1
1
0
1
0
0
2
0
1
0
0
1
0
0
1
0
0
0
0
2
0
0
1
1
0
0
2
2
1
1
1
0
1
2
0
1
2
3
1
0
1
2
0
0
0
0
0
2
2
2
1
0
1
0
2
1
1
0
0
1
2
1
2
2
2
2
0
0
0
0
2
1
2
1
1
1
2
2
1
2
2
0
1
0
0
0
0
2
0
2
1
0
0
1
1
0
1
1
1
2
0
3
1
2
0
0
1
2
0
3
1
0
2
0
0
0
2
1
0
0
1
0
0
1
2
0
0
0
1
0
0
2
0
1
0
2
1
2
1
2
0
0
0
2
1
1
0
1
0
1
1
0
0
1
2
1
2
0
2
0
0
0
0
0
1
1
2
1
0
0
0
0
1
1
0
0
3
0
1
0
0
1
1
1
4
1
0
1
0
2
0
1
2
1
2
0
1
2
1
0
1
0
0
1
2
2
1
2
1
0
1
2
1
0
2
1
0
2
0
2
0
2
2
0
1
0
1
2
1
1
0
2
1
1
0
1
0
2
2
2
2
0
0
1
2
3
0
0
2
0
2
0
1
0
2
2
2
2
0
0
1
0
0
2
0
0
0
0
1
1
0
0
0
0
2
0
2
0
0
0
1
0
0
1
1
1
2
2
1
1
2
2
0
1
2
1
0
0
1
1
0
0
2
0
1
4
1
2
1
1
1
0
2
0
1
1
0
2
0
2
2
0
0
1
2
0
1
0
1
1
0
2
1
2
0
0
0
0
2
0
1
0
0
1
1
1
1
0
0
1
0
2
1
0
1
2
0
2
0
0
0
0
1
2
2
1
0
2
2
1
0
0
0
2
0
1
2
2
3
2
0
0
1
1
1
0
1
2
1
1
0
0
1
0
1
0
0
1
2
0
1
1
4
2
0
0
0
0
0
0
0
1
0
1
0
1
1
2
1
1
0
1
1
1
1
4
0
0
1
0
1
2
1
2
0
1
1
0
0
1
0
1
0
0
1
0
0
0
0
0
1
1
2
1
2
0
1
0
0
0
2
1
1
0
2
0
1
0
0
1
1
0
1
0
0
0
1
2
0
0
0
0
2
2
1
1
0
2
2
2
0
0
0
2
0
0
0
0
1
1
0
0
1
0
1
1
0
1
1
2
2
1
2
0
0
2
2
0
0
1
1
1
2
0
0
2
0
0
2
2
0
0
0
1
0
2
2
0
2
1
0
0
0
1
2
0
2
0
0
1
0
1
0
1
0
0
0
1
1
2
1
4
1
1
2
0
1
0
0
1
1
0
2
0
0
0
1
0
1
3
2
2
2
1
0
1
0
2
1
0
0
1
2
2
1
0
0
0
2
1
3
0
1
0
1
1
1
1
1
0
1
0
0
0
1
1
0
0
0
1
1
0
0
2
0
1
0
2
1
1
0
1
0
2
0
0
1
0
2
2
1
1
2
0
1
0
0
5
0
1
2
1
0
0
1
0
2
1
0
2
1
2
0
1
2
0
0
0
1
1
0
1
0
0
2
0
0
0
0
3
0
0
0
3
0
3
0
2
2
0
0
0
1
0
1
2
2
1
0
2
0
2
0
0
0
0
0
2
2
1
0
0
1
1
0
0
2
0
0
1
0
1
0
0
0
0
2
0
0
2
2
0
1
0
0
0
0
0
1
1
1
1
2
1
0
0
2
2
2
1
0
0
0
3
1
1
2
1
1
2
0
1
1
0
1
0
1
1
1
1
1
0
1
0
1
1
2
1
3
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
2
0
0
0
4
0
1
1
1
1
0
1
0
0
1
0
0
2
0
0
0
0
1
0
0
2
2
1
2
5
1
2
2
0
0
0
0
0
1
1
0
1
0
0
0
0
0
2
1
0
0
1
0
1
0
3
0
2
0
1
0
2
2
2
0
1
2
0
0
0
2
2
1
0
2
0
1
2
1
0
1
1
1
0
2
1
1
0
1
1
2
1
0
0
1
1
0
2
1
2
1
0
2
1
1
0
1
1
0
1
5
0
0
0
0
0
0
0
1
0
2
0
1
0
2
2
1
1
2
1
1
2
1
2
1
0
0
0
1
1
0
2
1
1
1
0
0
3
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
2
2
1
1
0
1
1
0
1
1
0
1
2
0
0
2
0
0
2
0
0
0
1
0
1
1
0
1
2
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
1
2
0
0
0
3
3
0
2
2
0
2
1
0
0
0
0
0
0
0
2
0
0
1
0
1
0
1
0
0
1
1
2
1
0
2
0
0
0
0
0
4
1
1
0
1
0
1
0
2
2
0
0
2
0
2
2
0
0
0
0
1
3
0
0
0
1
1
0
2
0
2
0
1
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
2
0
1
2
1
0
0
2
1
2
0
0
0
2
0
0
1
0
2
0
2
0
0
2
0
2
0
0
0
0
0
2
0
1
0
0
0
2
1
0
2
0
1
2
1
0
1
1
0
0
1
4
1
0
1
0
2
1
2
1
1
0
1
0
0
0
0
3
0
0
1
0
3
0
0
3
1
1
0
2
1
0
3
0
0
1
1
0
2
0
2
2
2
1
1
0
2
1
0
2
0
1
0
0
2
2
2
0
0
0
0
1
0
1
0
1
1
0
2
1
0
0
0
5
0
1
1
0
0
0
1
0
1
0
2
0
2
0
0
2
1
0
0
0
1
1
2
0
1
2
1
2
2
0
0
0
1
2
0
0
2
0
2
0
1
2
2
0
2
2
1
1
1
1
1
0
1
1
1
0
1
1
0
1
2
0
0
0
3
1
0
0
0
0
2
0
0
0
0
0
1
0
0
2
1
2
0
1
1
0
1
2
1
4
0
0
0
0
1
0
2
0
1
0
0
1
0
1
0
0
2
1
1
1
1
0
1
1
1
1
0
1
0
0
0
1
0
1
0
2
1
2
1
1
0
1
2
2
0
1
1
0
0
0
0
2
1
0
2
0
1
0
1
0
2
2
0
0
0
0
0
0
0
2
0
2
1
1
0
1
3
1
0
1
1
0
0
2
1
2
0
1
0
0
0
2
1
2
0
1
1
1
2
1
1
1
1
1
0
1
0
1
0
0
2
0
0
0
2
0
2
0
2
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
1
1
0
0
0
2
0
2
0
1
0
0
2
2
1
2
2
0
2
3
0
4
0
0
1
2
0
1
1
0
0
0
0
0
1
0
0
2
1
1
2
1
1
2
0
2
0
2
0
0
1
0
1
0
0
1
2
1
0
0
0
0
2
2
0
1
0
1
0
0
2
0
0
0
0
1
2
0
1
1
1
0
1
1
0
0
1
0
0
0
1
2
1
1
2
2
0
1
0
0
1
0
0
1
0
1
2
2
0
1
0
3
0
2
1
1
0
0
0
1
0
0
0
0
0
1
0
3
0
1
0
1
0
0
1
0
0
2
0
2
0
1
0
0
5
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
2
1
0
2
1
1
1
1
2
2
1
0
0
2
1
1
0
0
0
1
1
0
1
0
0
0
0
0
1
2
2
2
0
2
3
1
0
1
0
0
0
0
2
0
0
0
0
0
1
0
1
3
1
2
0
2
0
1
1
2
0
0
1
0
0
0
2
0
2
0
0
0
2
0
2
0
1
0
0
0
0
2
1
0
2
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
1
2
2
2
1
0
2
0
0
2
1
1
0
2
1
0
2
1
0
0
0
1
0
1
0
2
0
1
1
0
0
1
0
0
0
0
1
1
2
0
2
1
1
0
1
2
1
2
2
0
0
1
1
0
2
2
1
2
1
1
2
1
0
0
2
2
2
0
0
1
1
2
1
0
0
0
0
0
2
1
0
2
2
0
1
1
0
4
0
1
3
0
1
1
1
0
0
2
0
2
0
1
0
0
2
1
1
2
2
0
1
0
1
2
2
3
0
2
2
2
0
0
2
2
1
0
0
1
1
1
2
0
1
2
0
1
1
1
0
0
1
0
1
1
3
1
0
3
2
0
3
0
1
1
0
1
1
0
0
2
1
0
2
1
1
0
1
0
0
1
1
1
1
0
0
0
4
2
0
1
0
0
0
1
2
1
0
0
2
2
1
1
0
0
1
1
3
0
2
0
1
0
2
1
2
0
0
2
2
0
0
2
1
1
0
0
0
0
3
1
0
1
1
1
1
1
0
0
0
1
0
0
0
0
0
0
1
2
1
0
0
1
0
2
0
0
2
1
0
0
0
2
0
0
1
0
1
2
1
0
1
1
1
0
1
0
1
1
1
0
2
2
0
1
0
1
0
1
1
0
1
0
0
0
2
1
0
0
1
2
0
1
3
0
0
1
1
1
0
0
2
0
2
0
1
0
0
0
1
0
1
0
2
1
0
0
0
1
1
0
2
0
2
1
0
1
1
0
1
0
0
0
0
1
1
0
0
0
0
0
3
1
0
0
1
1
0
0
1
1
0
0
2
1
0
0
2
0
2
1
1
2
2
1
0
1
2
2
0
1
0
0
2
0
2
0
0
0
0
0
0
2
0
2
2
2
0
1
1
1
0
1
2
0
1
1
0
1
1
0
0
2
2
0
1
1
1
2
0
0
2
2
0
2
2
0
0
1
1
2
1
0
1
1
1
0
1
0
0
1
0
0
2
0
0
1
2
3
1
0
1
1
1
1
1
2
0
0
0
0
2
0
1
1
2
0
0
0
0
1
0
0
1
0
0
1
0
3
0
1
0
0
0
0
2
0
3
2
2
2
0
0
2
1
1
0
1
0
0
1
2
0
1
0
2
0
1
1
0
2
2
0
1
2
0
2
1
2
0
0
0
1
2
2
0
2
0
0
1
0
1
0
1
2
2
2
0
0
0
0
2
1
0
0
2
1
1
1
0
0
2
1
1
0
1
0
0
0
0
1
0
2
1
1
0
1
0
2
2
0
0
2
0
2
0
0
0
2
2
1
0
1
0
1
1
1
0
0
1
0
1
0
1
0
0
1
0
0
1
0
3
1
0
2
0
0
0
0
1
2
0
2
2
0
0
2
1
2
1
1
0
0
1
1
0
0
2
0
0
1
0
0
0
0
1
0
0
1
1
1
0
2
1
0
2
2
0
0
1
0
2
1
1
1
1
0
0
0
0
0
1
1
1
1
2
1
2
1
0
0
2
2
2
0
0
2
1
1
0
1
1
0
1
2
1
0
0
0
1
2
0
0
0
0
0
1
1
1
0
1
1
0
0
1
2
0
1
2
0
2
1
2
0
3
2
0
0
1
0
0
0
1
2
2
1
0
2
1
0
1
0
1
2
1
0
0
0
2
2
0
0
2
0
2
0
0
2
1
0
2
2
0
0
0
1
1
2
1
2
1
0
0
2
1
1
1
0
0
1
1
2
2
1
1
2
0
1
3
1
3
1
0
0
2
2
0
0
0
2
2
0
2
2
1
0
0
1
1
2
0
1
2
2
0
1
1
2
1
1
2
2
1
1
1
0
0
0
2
1
0
1
2
1
0
1
1
0
2
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
1
2
0
1
0
0
4
1
0
1
2
0
0
0
1
0
2
2
0
0
0
2
0
0
2
1
1
1
1
1
0
0
2
1
0
1
2
1
2
0
0
2
1
0
2
1
0
2
0
0
2
0
0
2
1
1
2
1
1
1
0
1
2
1
0
1
0
0
1
1
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
2
0
2
2
2
0
1
0
0
1
0
1
2
1
0
0
1
0
1
0
0
0
0
0
3
0
1
2
0
0
0
0
2
2
1
0
1
2
0
1
0
2
0
2
0
0
0
0
2
1
0
0
1
1
2
1
0
1
0
2
0
0
1
1
1
0
1
0
2
0
2
2
0
2
1
1
2
2
1
0
1
1
1
2
1
2
2
2
2
1
1
0
2
0
1
3
0
2
0
1
2
2
2
0
0
0
1
0
0
2
2
1
0
1
1
2
1
0
1
2
0
0
0
2
1
2
0
0
1
2
0
1
0
0
0
0
0
2
1
2
1
2
4
2
1
2
0
1
1
1
0
1
0
2
0
1
2
0
1
0
1
0
2
0
0
0
1
0
1
2
2
0
0
2
1
1
0
0
1
0
0
2
0
0
2
0
1
2
6
1
1
0
1
1
0
0
0
2
0
1
1
0
0
1
0
1
2
0
1
1
0
1
0
1
0
1
0
0
2
2
1
1
1
0
2
2
2
0
2
1
2
0
0
0
1
2
1
0
0
0
2
0
0
2
0
1
1
0
0
0
0
2
0
0
1
0
1
0
1
0
2
2
0
1
0
2
1
0
0
2
0
0
0
0
0
1
1
1
0
1
1
3
2
0
2
0
1
2
2
1
2
1
1
0
2
3
1
0
1
2
0
0
1
1
2
2
1
1
1
0
1
1
1
0
1
0
1
1
1
1
0
2
0
0
1
1
0
4
1
1
3
2
1
2
1
0
1
2
0
1
0
0
1
2
0
0
0
1
1
1
0
1
1
1
2
0
1
0
1
0
0
2
0
1
2
2
3
0
0
0
1
2
1
2
0
0
1
0
1
1
1
1
2
0
1
2
0
1
0
2
0
1
0
0
0
1
2
2
0
2
0
0
1
0
2
2
0
2
1
1
1
2
1
1
1
0
1
0
1
0
1
0
0
0
2
0
0
0
0
2
1
1
4
5
1
1
1
0
2
1
0
0
0
0
1
1
0
0
2
2
1
0
1
3
1
1
0
0
0
0
1
1
1
1
1
1
1
2
0
1
2
0
2
2
0
1
1
1
0
0
0
1
0
0
0
2
2
1
1
0
0
0
0
1
0
2
1
1
1
1
2
1
0
0
1
0
0
2
1
0
2
1
0
2
2
0
1
1
1
0
2
1
1
0
0
2
2
0
2
0
0
0
1
1
1
1
0
1
1
0
0
0
1
1
2
1
0
2
0
2
3
0
1
2
2
1
0
0
1
0
1
5
0
2
0
0
2
0
0
1
1
0
0
1
0
2
2
1
0
1
0
2
1
1
1
1
0
0
0
0
0
2
0
2
2
1
0
2
0
0
2
0
1
0
0
2
0
0
0
0
0
1
0
1
0
2
0
0
1
2
2
2
1
2
2
1
0
1
0
2
2
1
2
0
1
0
1
0
1
0
0
2
0
0
0
0
2
0
2
2
0
0
0
2
1
2
1
2
0
0
2
0
2
1
2
2
2
2
0
0
1
1
0
0
1
1
2
0
2
0
0
0
0
1
2
0
2
0
1
1
0
0
0
2
0
0
0
2
1
0
1
1
2
0
1
0
0
0
1
2
2
0
0
0
1
0
2
1
0
1
4
2
2
1
0
2
0
1
2
0
0
2
1
3
0
1
2
1
0
1
0
0
0
0
0
0
0
2
0
2
0
1
2
1
1
1
0
0
1
0
0
1
0
0
0
0
4
1
1
1
1
1
0
2
0
2
0
1
1
0
1
0
1
0
0
1
0
2
2
0
2
0
1
0
0
3
1
1
1
1
1
1
1
0
0
1
1
1
0
2
1
1
0
1
0
1
0
1
2
2
1
1
1
1
0
0
0
0
0
1
0
0
0
1
1
0
1
0
1
2
0
1
1
0
0
2
0
1
1
0
0
0
1
2
1
0
0
0
1
1
1
2
1
1
1
0
0
1
0
0
0
0
1
0
2
1
2
2
1
1
0
0
0
2
2
1
0
0
1
1
3
0
0
1
2
0
1
0
0
0
2
2
0
0
2
1
0
0
1
0
0
1
1
0
0
0
0
0
2
0
1
0
2
0
1
2
1
1
0
0
2
2
1
0
1
0
1
0
1
1
1
1
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
1
2
1
1
1
1
2
0
1
0
1
0
0
2
1
1
0
2
0
1
1
0
1
1
2
2
1
1
0
0
0
1
1
1
0
0
1
0
2
0
2
0
1
0
1
2
1
0
2
2
1
1
0
1
2
0
0
1
0
1
1
2
0
2
1
0
1
1
1
1
0
0
0
0
1
0
1
0
3
0
1
1
1
2
0
2
1
0
2
2
0
2
0
2
1
1
0
0
1
0
2
3
1
2
1
1
0
0
2
0
0
1
0
1
2
1
1
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
3
2
0
0
4
0
0
2
0
0
0
0
0
4
2
1
1
1
0
2
0
0
0
1
0
4
0
1
1
1
1
2
1
2
0
1
0
1
0
1
0
2
1
1
1
0
2
2
0
2
0
1
0
0
1
1
1
1
0
2
0
0
2
0
0
0
1
1
1
1
1
1
0
1
2
0
0
1
0
2
0
0
1
2
0
0
0
0
1
0
0
1
1
2
1
1
1
1
0
2
1
0
0
1
0
1
1
0
1
0
0
0
1
1
0
0
0
1
0
1
0
0
1
1
2
0
2
2
2
2
1
0
0
0
0
0
0
2
2
1
2
1
1
2
1
1
0
0
1
0
0
1
0
1
2
0
0
1
2
2
0
2
2
0
1
0
0
1
1
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
2
0
1
3
0
0
1
1
0
0
2
0
3
0
0
1
0
2
1
2
0
0
1
2
0
2
2
1
0
1
0
3
1
0
1
0
1
0
0
0
4
0
0
1
0
2
0
0
0
2
2
1
1
0
1
1
1
1
0
0
0
2
2
2
1
0
0
2
1
2
0
0
0
2
0
0
1
0
0
0
0
0
1
0
1
0
1
1
2
2
1
0
1
1
2
1
1
0
1
1
0
1
3
1
1
1
2
0
0
0
0
1
0
2
1
0
2
0
1
2
1
1
2
0
1
2
0
1
1
2
2
0
1
2
0
0
0
2
0
1
0
1
2
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
3
0
1
1
2
0
2
1
1
0
1
0
0
0
1
1
0
1
1
1
0
1
0
0
0
1
0
0
1
1
1
0
0
0
0
1
1
2
1
1
0
1
1
0
1
2
2
0
1
0
1
1
1
0
1
0
0
0
1
1
0
2
1
0
0
1
1
2
0
1
1
0
0
2
0
1
1
2
2
0
1
2
0
0
1
0
0
1
1
1
0
1
2
1
0
0
1
0
0
0
0
0
0
1
0
0
1
1
1
2
2
1
0
1
1
2
0
2
1
0
0
2
0
0
0
3
2
0
0
3
0
0
2
2
1
2
2
0
1
1
1
0
1
0
0
1
2
0
3
0
0
1
0
1
2
0
0
0
0
1
0
1
0
1
0
0
0
1
0
2
0
0
0
0
2
0
1
0
2
0
0
2
0
1
1
1
0
0
1
1
1
1
2
0
0
2
0
0
0
1
1
1
0
2
0
1
1
1
0
1
0
0
0
2
0
0
0
1
0
2
1
1
1
1
2
0
2
0
0
2
1
1
2
0
0
1
0
1
1
0
0
0
2
0
1
0
1
2
1
1
1
1
0
0
1
1
0
0
5
2
2
1
1
1
2
1
1
1
5
2
2
1
1
2
0
1
2
0
0
2
1
0
0
0
1
2
0
0
1
1
1
1
0
1
1
1
0
0
1
0
0
2
1
0
2
1
2
2
0
1
0
0
1
0
2
0
0
1
1
0
1
1
1
0
1
0
0
2
0
1
0
1
0
1
2
1
1
0
0
0
2
2
0
1
0
1
1
2
1
1
0
1
2
0
1
2
1
0
0
2
3
0
1
1
1
1
2
3
0
3
1
2
2
1
0
1
2
0
0
0
0
1
1
0
1
0
0
1
0
2
0
1
0
1
0
1
1
1
2
1
0
0
1
0
3
0
0
0
1
2
1
0
0
2
0
0
1
1
1
0
0
1
2
0
0
1
1
0
0
0
0
1
1
1
1
1
1
0
2
0
2
0
3
1
2
0
1
1
1
0
1
0
1
0
1
0
0
1
0
0
2
0
1
0
0
0
0
0
7
1
1
2
0
0
0
1
0
0
2
1
0
0
2
1
1
0
1
1
0
1
0
1
1
1
0
2
0
0
2
1
0
0
1
2
1
1
0
1
0
5
0
0
1
0
0
2
0
2
1
1
1
1
0
0
2
0
1
0
1
1
2
0
0
0
0
1
2
2
0
0
0
1
0
1
1
0
0
0
2
0
2
1
1
0
1
0
2
1
0
2
2
0
2
1
2
0
2
0
0
1
1
0
1
1
0
2
2
2
0
1
2
3
0
0
1
0
1
0
1
0
2
2
0
4
0
0
1
2
1
0
0
0
0
0
2
0
1
2
1
1
2
2
2
0
2
1
1
0
1
0
0
0
1
1
2
1
1
1
1
1
2
1
2
0
0
1
0
1
1
1
2
0
2
0
0
0
0
2
1
1
0
1
0
1
2
0
1
0
0
2
2
2
2
2
1
2
0
0
1
0
0
0
1
2
2
1
1
0
1
2
0
1
2
0
0
1
0
2
0
0
1
3
0
2
0
0
2
1
1
2
0
0
0
1
1
2
0
0
0
2
2
0
1
0
2
1
1
2
1
0
1
0
2
1
0
2
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
2
1
0
0
1
2
0
1
1
0
3
2
0
0
0
0
3
0
0
1
0
0
1
0
0
0
0
2
2
1
1
1
0
1
0
0
0
2
1
1
0
1
0
0
1
2
0
1
1
1
1
0
0
1
2
1
0
0
2
1
2
0
1
1
0
1
0
2
0
1
2
1
1
1
0
0
11
0
2
1
0
0
0
1
0
0
2
0
0
0
1
1
0
0
1
1
1
1
0
2
1
0
1
3
2
2
0
0
1
0
2
2
2
0
2
1
0
2
1
1
0
2
2
2
0
0
1
0
1
1
0
2
0
0
0
0
2
2
0
1
1
0
1
0
1
2
1
2
1
0
0
2
1
1
0
0
1
0
0
1
1
0
1
2
2
0
1
0
2
1
0
1
1
1
1
1
1
2
0
2
2
2
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
1
2
2
0
1
1
1
0
2
2
2
0
0
2
2
2
0
0
2
2
1
2
1
2
1
0
0
2
0
0
0
1
1
0
0
1
0
0
0
0
1
2
0
2
0
0
1
0
0
2
1
0
2
0
1
1
1
2
1
0
1
2
1
0
0
1
2
2
1
0
3
0
0
2
0
1
1
1
1
2
1
2
2
0
0
2
0
1
0
0
1
2
0
1
1
2
0
1
0
0
0
0
2
2
0
1
1
0
1
1
1
2
2
0
1
0
2
0
1
0
0
1
1
1
0
3
1
0
2
0
3
0
0
0
3
1
0
0
2
1
1
0
0
0
1
1
1
0
1
2
0
0
1
0
0
2
1
1
1
2
0
0
1
1
1
2
1
0
1
2
1
0
0
0
2
3
0
1
1
1
0
2
0
2
0
1
2
2
2
0
0
2
1
0
3
1
0
1
0
1
0
0
1
0
0
1
1
0
2
1
0
1
1
1
0
1
2
0
0
1
0
0
1
1
1
0
2
1
3
1
0
0
1
1
0
0
0
2
2
0
2
1
1
2
0
1
1
0
1
0
1
0
1
1
1
1
1
1
0
1
1
4
4
0
0
1
2
1
2
2
0
3
2
0
0
2
2
0
2
2
2
0
2
2
2
1
0
3
0
2
0
3
3
1
2
0
0
0
1
0
0
1
2
0
0
2
1
0
0
2
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
4
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
2
1
1
1
0
2
0
0
0
1
1
1
0
0
1
0
0
0
0
2
1
2
0
0
1
2
1
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
2
0
2
0
3
3
1
1
1
2
1
0
0
1
1
2
1
0
1
1
1
0
1
1
2
2
2
0
2
2
0
0
0
0
0
1
1
1
0
1
2
0
1
0
1
2
0
1
2
0
0
2
1
0
1
0
2
2
0
0
0
0
0
0
1
0
1
1
0
1
1
2
1
0
2
1
0
1
0
0
0
2
0
2
1
0
0
0
2
2
2
1
0
2
1
1
1
1
2
0
0
0
2
0
2
0
1
2
0
1
1
0
1
1
0
0
0
0
0
0
2
2
0
1
1
1
0
0
0
1
1
1
2
2
0
1
3
0
0
0
0
0
2
1
0
0
1
2
4
1
1
1
1
1
0
0
2
0
2
2
0
0
0
0
1
0
0
2
0
0
0
1
1
0
2
0
1
0
1
0
0
0
0
2
1
0
1
2
1
2
0
1
0
1
2
0
1
1
0
2
0
0
0
1
0
2
1
1
1
2
0
0
0
0
0
1
0
2
2
2
0
0
0
1
0
1
1
2
0
0
0
0
0
0
1
0
4
2
2
0
0
1
2
0
1
0
2
0
2
0
0
0
0
0
0
2
0
0
1
2
2
0
0
2
1
0
1
0
0
0
1
1
0
0
1
1
1
2
0
0
0
3
1
2
1
1
0
0
0
2
0
1
1
2
1
1
1
1
2
0
0
0
0
0
2
0
1
0
2
0
1
0
1
0
0
0
0
1
1
0
0
1
0
0
1
0
1
1
0
1
1
0
0
0
0
0
2
1
1
0
0
0
0
1
0
0
1
2
1
2
3
0
1
2
1
2
2
2
1
4
0
1
2
2
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
1
0
2
0
1
1
2
1
1
0
1
2
1
0
0
1
2
0
2
0
0
0
0
1
1
2
2
0
1
1
0
0
1
2
0
1
1
0
1
2
1
1
1
0
0
1
0
2
0
0
5
1
1
0
0
0
1
0
1
0
1
0
1
0
2
0
2
0
1
1
1
1
1
1
2
1
2
2
1
1
0
0
2
0
0
1
2
1
1
0
1
0
0
0
0
1
2
0
0
2
0
0
1
0
2
0
2
0
0
0
0
0
2
2
0
1
2
0
0
2
0
2
0
1
0
2
0
1
0
0
1
1
0
0
0
1
0
0
1
1
0
2
2
0
1
0
0
1
0
1
2
0
0
0
0
2
2
1
1
0
0
1
2
0
1
0
1
0
1
2
2
2
2
0
0
1
0
0
2
0
2
0
0
0
1
0
2
0
1
0
2
0
1
0
3
2
0
1
0
0
0
1
1
2
1
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
2
0
1
0
0
0
1
2
2
1
0
1
2
0
2
0
1
1
3
2
2
2
2
0
0
0
0
0
1
1
2
0
1
0
1
1
0
1
0
0
2
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
2
1
0
0
1
2
0
0
0
1
2
1
0
2
1
2
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
1
2
0
3
0
1
2
1
2
0
2
1
2
0
1
1
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
1
1
2
2
1
0
1
0
1
1
0
2
1
0
0
0
0
0
1
0
1
1
0
2
0
2
1
0
0
0
0
0
0
2
0
0
2
0
0
0
2
2
0
1
0
1
1
2
0
0
1
2
0
1
2
0
0
0
2
1
1
0
1
1
1
1
1
2
0
0
1
2
0
1
1
1
2
0
0
2
0
1
2
0
1
0
0
2
0
0
0
0
0
0
1
1
2
2
0
2
1
1
1
0
1
1
1
2
2
2
0
1
0
0
1
1
2
0
1
3
0
0
0
0
1
0
2
0
0
1
2
1
1
0
0
0
0
0
0
2
2
0
1
1
1
0
2
0
1
1
2
1
2
1
1
2
1
0
0
1
2
1
0
1
1
1
0
1
1
1
1
2
1
2
2
2
0
0
0
2
1
1
2
1
1
0
1
3
2
0
2
0
1
0
1
0
1
2
0
0
2
0
2
2
0
1
1
0
0
1
1
0
1
0
2
1
1
1
2
1
0
2
0
0
0
0
2
2
1
0
2
1
0
1
2
0
0
1
0
2
0
1
0
1
1
1
1
0
0
1
1
0
0
2
2
0
2
1
0
0
0
2
2
1
1
1
0
2
2
1
0
2
2
0
0
2
1
0
0
2
0
0
1
1
0
0
2
1
0
0
0
2
2
0
0
0
2
8
1
0
2
0
2
0
0
2
0
1
1
0
0
0
1
0
2
1
2
3
0
1
1
0
0
2
2
1
2
2
1
0
2
2
0
0
2
0
2
2
0
1
0
0
1
1
1
0
0
0
0
1
1
0
2
1
0
2
0
0
2
1
0
0
1
1
0
2
2
1
1
1
0
0
0
0
1
1
0
2
0
0
0
2
0
0
1
2
1
1
4
0
2
0
1
0
0
1
0
2
1
2
0
1
1
0
2
2
0
3
0
1
0
0
0
0
1
1
1
1
2
2
1
0
0
0
2
0
2
0
1
0
1
0
1
0
0
0
0
1
0
2
2
1
0
2
1
1
2
1
0
0
1
2
1
0
2
0
0
0
0
0
1
0
2
1
0
1
2
1
0
0
0
0
0
0
2
0
2
1
0
2
0
0
0
2
2
2
0
1
2
0
1
0
0
1
0
1
1
1
2
1
0
0
0
1
2
1
1
0
0
0
0
1
1
1
2
2
0
0
1
0
0
0
0
3
0
1
1
0
0
2
0
0
0
2
0
2
1
2
1
0
2
0
1
0
2
0
3
0
0
1
0
0
0
1
1
2
2
2
2
1
2
0
0
0
1
0
1
1
1
0
0
1
0
0
0
1
0
0
0
2
0
2
0
0
1
0
2
0
1
0
1
0
1
2
2
1
0
0
0
2
2
0
0
2
0
2
1
0
2
1
1
0
0
0
0
2
0
2
1
0
1
0
0
0
1
0
1
1
2
2
2
0
1
3
0
1
0
1
2
2
2
1
2
0
2
1
0
1
1
0
0
0
1
1
2
1
1
0
0
0
1
0
0
0
0
2
0
0
0
2
1
1
1
2
0
0
0
0
1
1
0
0
0
1
1
0
0
2
1
0
1
0
0
0
1
0
0
1
0
1
0
1
2
2
2
1
1
2
0
1
0
0
0
2
1
1
1
0
0
1
2
0
0
1
0
1
0
0
0
0
2
1
0
1
2
2
1
1
1
0
0
0
2
0
0
2
1
0
2
0
0
1
1
0
1
2
1
1
1
1
0
2
0
1
0
1
0
0
1
0
1
1
2
1
0
0
1
0
1
1
0
0
0
1
0
1
1
0
1
1
1
2
0
2
2
0
0
0
2
1
0
2
2
1
1
2
1
1
1
0
1
1
2
0
0
1
0
0
0
0
4
0
1
1
2
1
1
1
1
0
0
2
1
0
1
2
1
1
0
2
0
1
3
1
1
1
0
0
1
0
0
2
1
0
0
0
1
0
2
0
0
1
1
1
0
1
0
2
0
1
2
3
0
2
5
1
1
0
0
0
0
2
1
0
0
0
0
1
1
0
1
1
0
0
0
2
1
0
2
0
0
0
2
2
0
1
1
2
0
1
0
1
2
0
1
1
0
0
2
0
2
1
4
2
0
1
0
2
0
0
2
1
1
2
0
0
0
0
0
0
0
1
1
1
1
0
0
1
1
2
0
1
0
0
0
0
1
2
0
0
1
0
0
0
3
2
1
0
0
0
1
1
2
0
2
0
0
1
2
0
0
1
2
2
0
0
1
1
2
1
0
0
0
1
0
2
1
1
0
0
0
2
1
1
1
0
0
1
0
0
0
1
0
1
0
0
0
2
1
1
1
1
1
1
1
0
0
2
0
2
1
1
0
0
2
1
0
2
1
2
0
1
3
1
1
0
1
0
1
1
1
0
1
2
1
0
1
2
0
0
0
1
0
0
0
1
0
1
0
2
1
0
0
0
3
1
1
0
1
0
1
0
0
1
2
1
0
0
0
0
2
1
0
0
4
0
1
2
1
0
0
1
0
1
1
1
2
0
2
1
2
3
0
1
2
0
1
1
0
1
1
1
1
1
0
1
0
1
0
0
1
0
2
1
1
0
0
1
0
1
1
1
0
0
0
2
2
0
0
0
1
2
0
0
0
0
0
0
2
1
2
2
2
0
1
0
1
1
0
0
0
1
0
0
0
2
2
0
0
2
1
2
0
0
1
1
2
3
2
1
2
0
0
2
1
0
0
0
0
1
0
1
0
1
1
2
1
0
0
0
1
0
2
2
3
1
0
2
0
2
0
0
3
0
1
1
0
0
0
0
1
1
0
0
2
0
1
1
2
1
2
0
0
0
0
0
2
1
1
2
1
0
0
0
0
1
2
1
1
0
2
0
1
0
0
0
0
0
0
1
2
1
3
1
2
0
1
1
1
0
1
0
1
2
0
1
1
0
2
2
0
2
1
0
1
3
0
1
1
2
1
1
0
2
1
1
0
0
1
0
0
1
0
2
0
2
1
0
0
1
0
0
2
1
0
0
2
1
0
0
2
2
1
2
0
1
2
0
1
0
0
1
1
0
2
1
0
0
1
1
4
1
1
1
1
1
0
0
0
1
1
0
0
0
1
0
0
1
1
1
2
2
1
0
1
2
2
0
2
1
2
0
1
2
0
1
0
1
2
0
0
1
1
0
1
0
2
0
1
0
0
1
2
0
2
0
0
0
1
0
0
1
2
0
0
1
1
1
2
0
0
2
1
3
1
2
2
1
2
0
2
1
1
0
1
1
0
2
0
0
2
0
1
1
0
1
1
2
2
0
0
3
1
2
0
1
1
0
2
0
0
0
1
0
0
0
2
2
0
0
2
0
1
1
2
2
0
1
0
0
1
1
2
1
0
2
1
2
1
0
0
2
1
2
0
1
1
2
2
1
0
1
0
2
0
3
0
1
0
0
1
0
1
0
1
1
2
2
0
0
1
1
2
1
1
1
0
0
1
1
1
2
0
1
0
1
1
2
2
0
1
2
0
1
2
1
0
2
0
1
1
2
2
2
0
2
0
2
1
1
0
1
0
0
1
0
0
0
0
2
0
0
0
1
1
0
0
2
1
0
1
0
0
2
0
2
1
1
1
1
0
0
1
2
0
0
1
0
1
0
0
0
2
2
2
0
1
1
1
2
0
1
0
2
1
2
0
1
1
2
1
1
0
0
0
1
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
2
1
1
2
2
0
1
2
0
1
1
1
2
0
2
0
2
0
0
0
0
3
1
1
1
1
1
0
0
1
0
2
2
0
2
2
0
0
0
1
1
0
0
0
0
2
1
0
1
2
2
1
0
1
2
1
2
3
1
7
2
2
0
2
0
1
0
2
0
0
1
0
0
2
1
2
1
1
2
0
1
0
2
2
0
2
0
1
1
0
0
0
1
0
1
0
0
0
0
0
2
0
2
2
0
0
0
0
3
1
0
0
2
2
0
0
1
1
0
4
1
0
0
0
0
1
0
1
0
1
1
1
2
0
0
2
0
0
1
0
0
0
0
2
1
0
0
1
2
1
1
0
2
3
1
0
0
0
0
0
1
1
0
1
0
0
1
0
0
2
0
0
0
2
3
1
0
2
0
2
0
0
1
0
1
2
0
2
0
0
0
0
0
0
0
0
3
2
1
0
2
1
0
0
2
0
0
0
2
0
0
2
1
2
1
0
1
1
1
2
3
2
0
0
0
2
1
2
0
1
0
0
1
0
1
2
1
1
0
2
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
2
0
0
2
1
0
1
1
1
0
2
1
0
1
0
0
1
1
2
0
2
0
1
1
2
2
0
0
1
0
2
1
2
2
2
0
0
2
1
2
0
0
1
0
0
0
0
1
2
1
0
1
0
2
0
1
1
0
0
2
0
1
0
0
1
1
1
0
0
0
2
0
0
2
2
0
1
0
1
1
0
0
1
3
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
1
1
2
2
0
0
1
0
0
1
0
0
0
2
0
1
1
0
2
0
2
1
1
1
2
0
0
1
0
1
1
3
0
0
1
0
2
0
3
0
0
1
1
1
1
2
2
0
2
2
1
0
0
0
1
2
2
1
0
2
0
1
0
2
0
0
1
0
0
1
0
2
0
1
1
0
0
0
1
1
0
0
0
0
0
1
3
1
6
0
1
0
2
2
0
1
2
1
1
2
2
2
0
0
0
1
0
0
1
0
1
1
1
1
1
0
0
1
0
0
0
1
1
2
1
2
1
0
0
1
0
0
2
2
1
0
0
1
0
0
1
0
1
0
1
1
0
0
0
0
2
1
1
1
0
1
0
1
2
1
0
0
0
0
0
1
0
0
2
1
0
0
0
1
0
1
0
0
2
1
0
0
0
1
0
0
2
2
1
0
1
1
0
0
1
1
0
0
2
4
1
2
2
1
1
0
0
0
0
0
0
2
1
1
1
0
1
0
0
0
1
0
2
1
1
1
2
0
1
1
0
0
0
0
1
1
0
2
0
0
0
1
0
2
0
1
0
1
0
0
0
2
1
0
2
1
2
4
0
0
0
1
2
0
2
0
1
0
1
2
2
2
0
0
2
0
0
1
0
0
0
1
2
0
0
2
2
2
1
0
0
0
1
2
0
1
1
0
0
0
1
2
0
1
0
2
1
0
1
0
0
0
2
0
1
0
2
0
0
0
1
0
0
0
2
2
2
0
1
1
0
0
0
1
0
0
1
1
0
0
1
0
0
1
0
0
1
2
0
1
0
1
1
2
0
1
0
0
0
0
2
0
0
1
1
0
1
1
1
1
1
0
0
0
0
0
0
0
2
0
0
0
1
1
2
1
2
0
1
1
0
1
1
2
1
1
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
1
2
1
1
0
2
2
0
2
1
0
0
0
1
0
2
2
0
1
2
1
1
2
0
2
0
0
1
1
0
0
1
0
1
0
1
0
1
3
1
4
2
0
1
0
0
2
1
1
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
2
0
0
2
2
0
0
0
0
0
1
1
0
1
2
0
0
2
0
1
1
1
0
1
0
0
1
2
1
1
0
0
0
0
0
1
0
2
1
1
0
0
2
2
1
0
1
0
0
0
1
1
0
0
0
0
1
0
2
1
0
1
0
0
1
0
0
1
1
1
0
2
0
2
1
0
0
1
0
0
0
2
0
0
1
0
0
0
2
0
0
2
1
2
1
1
1
0
0
0
0
1
2
0
0
1
0
1
1
2
0
1
0
1
0
0
1
0
0
1
0
1
0
0
1
2
1
0
2
0
1
2
2
0
0
0
0
1
1
1
1
1
0
0
2
2
0
1
0
1
0
1
0
0
0
0
2
1
2
1
0
0
2
0
0
2
0
3
1
0
2
2
2
1
1
0
1
1
1
2
0
0
0
0
0
0
1
1
1
0
0
0
0
3
0
1
2
0
0
1
0
2
2
1
0
2
1
1
2
2
1
0
0
0
0
0
2
1
1
0
0
0
1
0
2
0
0
2
0
2
2
1
1
0
1
1
0
1
0
0
0
0
0
1
2
0
0
0
0
0
2
2
2
1
1
1
1
0
1
0
0
2
0
2
2
1
1
0
1
1
1
2
0
2
0
0
2
0
0
0
1
1
2
0
0
0
0
0
1
1
1
1
0
0
0
0
0
1
3
0
1
3
0
1
2
2
1
0
0
3
0
0
0
0
0
0
1
1
0
0
2
2
0
2
2
0
2
2
3
2
0
0
0
0
1
0
0
1
2
0
1
0
0
1
1
0
3
0
1
1
1
2
2
0
1
0
2
1
1
1
0
2
2
0
2
0
2
1
0
1
1
1
0
0
3
0
0
1
0
0
1
0
1
0
2
0
0
2
2
1
0
1
0
0
0
0
0
0
2
0
2
1
1
1
2
0
0
1
2
1
2
0
1
1
1
1
1
0
0
3
0
0
0
0
0
1
0
2
1
1
1
2
2
0
2
1
1
1
1
1
0
0
1
0
1
1
2
0
0
0
1
0
0
0
0
0
3
1
0
2
1
0
0
2
0
0
1
2
0
1
0
1
0
1
0
2
1
1
0
1
2
1
1
1
0
1
2
0
0
0
2
0
0
0
0
1
1
6
2
2
0
0
0
1
1
1
0
2
1
0
2
1
1
2
2
0
2
4
0
2
1
2
0
1
1
0
1
2
0
0
1
0
0
0
0
0
1
0
1
0
1
1
1
0
0
1
0
1
0
0
0
1
0
2
0
1
0
0
0
0
1
1
0
1
0
1
0
2
2
0
2
1
0
2
2
0
2
1
2
2
0
0
1
0
1
0
0
0
0
3
1
0
0
2
1
0
2
1
1
0
1
1
0
1
0
0
0
1
1
1
0
2
2
2
2
0
0
0
1
0
1
0
0
0
1
2
1
2
2
1
1
2
1
0
2
2
0
0
0
0
0
2
2
1
1
1
0
0
1
0
0
0
1
1
1
2
0
0
1
0
0
1
1
1
1
3
0
0
2
1
0
2
0
0
1
0
3
3
0
0
0
1
1
1
1
1
0
0
0
0
0
1
0
2
0
5
0
3
2
1
1
0
0
0
2
1
1
1
0
0
1
0
2
0
0
2
2
0
1
1
0
1
2
1
0
1
2
1
1
1
0
0
2
0
1
0
0
0
0
0
0
2
0
0
1
0
0
1
0
1
1
0
1
1
1
0
0
1
0
2
2
0
1
0
1
0
0
2
2
1
0
0
3
1
0
0
1
0
1
0
0
1
1
2
1
1
1
1
2
0
1
1
0
0
2
0
1
0
1
2
1
0
1
1
0
1
1
2
1
2
1
1
1
2
1
1
1
1
1
0
0
2
1
0
1
1
2
0
1
0
0
3
0
1
2
0
0
1
2
1
0
0
2
1
0
0
0
0
0
1
1
1
1
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
2
2
2
0
1
1
0
1
0
2
0
0
1
0
1
0
1
0
0
1
0
0
0
1
0
0
1
2
1
0
2
0
2
0
2
1
0
1
2
2
1
0
1
0
1
1
0
0
0
1
2
0
2
1
0
2
0
2
0
1
0
1
1
2
0
2
0
1
0
2
0
0
1
2
2
0
2
0
2
1
2
0
1
1
0
0
0
0
1
1
1
2
2
0
7
0
3
0
2
1
0
2
0
0
0
2
1
0
1
0
1
0
0
0
0
0
2
2
1
1
0
0
0
2
5
0
1
1
1
1
0
0
0
1
0
0
1
2
2
1
0
1
0
0
0
0
2
2
2
2
1
0
0
0
2
0
1
2
0
2
0
2
0
1
0
0
0
1
0
0
2
2
0
1
0
1
0
2
1
0
2
1
1
1
2
1
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
2
0
2
0
0
1
1
2
2
2
0
0
0
0
1
2
0
1
0
0
0
0
1
1
0
0
1
0
1
0
2
0
2
2
2
0
0
0
1
1
1
1
1
1
0
0
1
0
0
0
0
1
1
1
0
1
1
1
0
0
1
0
0
0
0
1
1
1
1
0
0
2
1
1
1
0
1
0
1
0
1
0
0
2
1
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
1
1
1
0
0
0
1
2
0
0
2
1
3
0
1
1
2
1
1
0
2
1
0
1
0
0
2
1
1
2
0
0
0
0
1
0
1
1
1
0
0
2
1
1
1
0
0
1
1
2
0
2
2
0
0
0
1
1
2
0
2
0
0
0
0
0
0
2
2
0
1
0
2
0
2
2
0
0
1
0
2
0
2
0
0
1
0
0
0
2
0
0
1
1
1
0
1
1
1
1
2
0
0
2
1
0
2
1
0
0
1
1
0
1
0
1
2
2
0
2
0
2
0
1
1
2
1
2
2
1
2
1
0
2
0
1
0
2
0
1
0
0
2
2
1
0
1
0
1
1
0
0
1
0
0
0
1
1
2
1
1
0
0
0
0
0
2
2
0
1
1
0
2
0
1
1
0
0
1
0
0
0
1
0
2
1
0
1
2
1
0
0
0
0
1
1
0
2
0
0
0
0
1
1
0
5
1
1
1
0
0
0
0
0
0
0
2
2
2
0
0
1
0
0
2
1
2
2
1
0
1
0
1
0
0
0
1
0
0
1
1
1
3
0
0
2
0
1
0
0
3
1
2
2
0
1
1
2
1
1
0
1
1
2
1
0
1
0
0
0
2
0
0
2
0
2
0
0
1
0
0
1
1
0
1
0
1
1
0
0
0
2
0
0
1
1
1
0
0
0
0
0
2
1
0
2
2
1
0
0
1
0
1
2
0
1
0
0
2
1
0
1
1
0
1
0
2
0
1
0
1
1
2
2
1
0
0
1
1
2
0
1
2
0
0
0
0
1
1
2
3
0
0
1
2
1
1
1
2
1
2
2
0
0
0
0
0
1
2
2
1
0
1
2
0
0
1
0
2
0
0
1
1
1
0
0
0
0
1
2
0
0
0
0
0
0
1
1
0
1
0
1
0
2
0
0
2
0
1
2
0
0
0
0
0
1
1
0
2
0
1
2
1
2
1
0
0
2
0
3
1
0
2
2
0
1
0
1
0
1
2
0
0
2
1
0
2
0
1
0
0
0
1
0
1
0
1
1
2
0
1
2
1
2
2
0
0
1
1
0
3
1
2
0
1
1
2
2
0
0
0
2
2
0
0
0
1
0
1
1
1
1
0
1
1
0
0
1
0
0
0
1
0
1
1
0
1
0
1
1
1
0
1
0
2
6
0
2
0
2
0
0
1
0
1
1
5
0
1
0
1
0
0
2
1
1
0
0
0
2
0
0
1
0
0
0
1
0
2
0
2
0
0
0
0
2
2
1
0
0
0
2
2
2
0
0
0
0
0
0
2
2
0
0
0
0
1
1
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
2
2
1
0
0
0
0
0
1
2
0
2
0
0
0
0
1
2
0
2
0
1
2
4
0
1
0
0
0
1
0
1
0
0
2
0
2
2
0
0
1
0
0
2
1
0
1
2
0
1
0
1
1
2
0
1
0
1
0
1
0
1
1
0
0
2
1
0
2
1
2
1
0
1
0
1
2
0
1
0
0
0
2
2
0
0
0
1
1
0
0
1
0
0
3
1
0
2
0
0
1
0
0
1
0
1
1
2
1
0
0
1
3
0
0
1
1
1
2
2
0
1
0
0
0
0
2
2
1
2
0
3
1
1
0
1
0
0
1
0
0
2
1
1
1
0
1
0
1
2
1
2
2
2
0
0
2
0
0
1
1
1
1
0
1
0
0
1
0
2
0
0
2
0
0
2
0
0
2
1
0
0
1
0
2
2
0
1
0
1
0
1
1
1
0
1
0
1
1
1
1
2
1
0
1
1
0
1
1
1
0
1
0
1
2
0
0
0
1
2
2
1
2
1
2
0
0
1
0
0
0
1
2
2
1
1
0
0
0
0
1
0
2
2
0
0
0
2
1
1
1
1
0
1
0
0
3
1
0
2
0
0
2
2
0
0
1
1
0
0
1
0
1
0
0
0
0
0
1
1
1
2
1
2
1
2
1
0
1
0
1
1
1
0
0
1
0
1
2
1
1
1
0
2
1
1
0
0
0
1
2
1
1
2
0
2
1
2
1
1
0
1
0
0
0
2
1
0
1
1
2
2
0
0
2
0
0
0
1
1
1
1
2
0
1
1
1
1
0
2
0
2
2
2
1
0
2
1
0
1
0
2
2
1
1
2
1
0
1
1
2
0
1
2
1
0
2
1
0
0
1
0
0
0
1
2
1
1
1
2
0
0
1
0
0
1
2
0
0
0
2
0
1
2
1
3
0
0
1
2
0
0
0
0
1
1
0
2
1
0
1
1
3
0
1
1
1
1
0
0
0
0
0
0
0
0
1
1
0
1
2
1
1
0
0
1
1
2
0
1
1
2
2
0
2
0
1
0
1
1
0
1
3
0
2
1
0
0
1
1
2
0
1
0
1
1
0
0
0
1
0
0
0
0
0
1
1
2
0
0
0
0
2
0
1
0
1
2
1
0
0
0
0
1
1
0
0
1
0
1
0
0
1
0
0
0
2
1
3
2
1
1
1
2
2
2
0
2
0
1
0
0
0
1
2
1
0
2
0
0
1
2
1
2
0
0
0
1
0
1
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
2
2
0
2
0
2
0
0
0
0
2
0
0
0
1
1
2
0
0
1
1
2
0
2
1
2
2
0
1
0
2
1
1
0
0
0
1
0
0
1
0
2
0
0
0
1
0
0
0
1
1
1
2
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
1
2
0
2
2
1
0
0
1
1
1
2
0
1
1
0
1
1
1
1
1
1
0
2
0
0
0
0
0
1
1
1
1
1
0
2
0
1
1
1
1
0
0
2
0
2
0
0
0
0
1
1
0
1
2
0
2
0
0
2
1
1
0
1
1
0
1
2
0
0
2
0
0
2
0
0
1
1
2
1
1
0
1
0
1
1
1
0
1
1
2
1
1
2
0
2
0
1
0
0
2
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
1
1
1
1
0
0
0
2
0
2
1
0
2
0
0
0
0
2
0
1
1
0
3
0
0
1
0
0
1
0
1
0
0
0
2
1
0
1
2
0
1
1
1
1
1
0
0
2
0
0
0
1
0
0
2
1
2
0
1
1
2
0
1
0
1
0
0
1
2
0
0
0
2
2
0
0
1
2
1
0
2
2
0
0
1
2
0
3
0
9
2
0
1
0
2
0
0
3
0
1
1
0
0
0
1
1
2
0
2
1
1
0
2
1
1
0
1
0
1
1
0
1
0
0
1
0
1
0
2
1
2
1
0
1
2
2
0
0
0
4
0
1
1
2
1
0
1
1
2
1
2
0
1
2
0
0
3
0
2
0
1
1
1
1
1
0
1
1
2
0
0
0
0
0
1
1
1
2
2
0
1
0
1
1
1
0
0
2
0
4
2
0
0
1
0
0
0
2
0
0
2
0
2
1
1
2
0
1
0
2
1
0
0
1
1
0
0
1
2
2
2
2
0
1
0
1
1
0
1
0
1
1
0
2
2
0
2
1
0
0
0
0
1
1
2
1
1
2
2
1
1
2
0
0
0
1
0
0
0
1
2
0
1
2
0
0
1
0
2
1
3
3
0
0
0
1
0
1
1
1
0
2
0
2
2
0
2
0
1
1
0
0
0
0
1
1
1
0
0
1
1
2
2
1
1
0
0
0
1
1
1
0
3
0
0
2
1
0
1
1
0
2
1
1
0
0
1
0
0
1
0
1
2
3
0
0
2
0
2
2
0
0
0
2
0
1
0
1
1
0
0
1
2
0
0
1
2
0
0
0
0
1
2
2
2
1
0
2
0
0
1
0
2
1
1
2
0
1
0
1
2
1
0
1
2
1
0
1
2
1
1
2
0
2
0
2
0
0
0
4
0
1
0
2
0
2
2
0
1
1
1
0
0
0
0
0
2
2
0
1
0
1
0
0
1
0
0
1
1
0
2
0
0
0
0
0
0
0
2
0
0
1
0
5
0
1
0
1
0
2
0
0
0
0
3
0
1
2
0
1
1
1
1
0
0
0
0
1
1
2
1
0
2
1
1
1
1
1
0
1
1
0
2
2
0
1
0
0
1
1
2
1
1
1
2
0
1
1
0
0
2
0
1
0
1
0
1
0
1
0
1
0
0
2
1
2
0
1
1
2
2
0
0
2
1
0
1
0
0
1
2
0
0
0
0
0
0
1
1
1
1
0
0
1
0
2
1
1
0
1
2
0
1
1
4
0
0
0
1
1
0
1
1
0
0
2
2
0
2
2
0
0
2
0
1
1
0
1
0
0
0
2
2
2
3
2
0
1
0
0
2
1
0
2
1
2
0
1
0
1
1
2
0
1
1
0
1
1
2
0
2
2
0
0
0
2
0
1
2
1
0
1
2
0
2
1
1
0
0
2
0
1
1
0
1
0
0
1
0
0
1
2
2
2
0
1
1
2
1
2
0
2
1
2
0
0
3
2
1
1
2
2
0
1
1
0
0
1
0
4
0
2
1
1
1
1
0
0
1
1
1
0
0
0
1
2
1
2
0
1
1
1
1
0
0
1
0
1
0
0
2
1
0
0
0
2
0
2
0
0
2
0
0
3
1
0
1
2
0
1
0
2
1
0
1
0
1
1
2
0
0
2
0
1
0
0
1
1
0
0
0
2
0
1
1
1
2
0
1
1
1
1
1
1
2
2
1
1
0
1
1
0
1
0
1
0
0
1
0
1
0
2
0
0
1
0
1
0
1
2
1
2
1
1
0
1
0
0
1
1
2
2
1
2
0
2
2
2
0
2
1
1
0
0
2
1
0
4
0
2
1
2
0
2
3
0
1
1
1
1
2
2
1
0
1
0
1
2
0
1
1
1
0
0
0
3
2
0
2
0
0
2
0
0
1
0
1
0
0
1
0
0
1
2
0
0
2
2
1
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
1
2
3
2
1
0
1
2
0
0
2
0
0
0
0
1
2
1
0
0
1
1
1
0
2
0
0
0
2
1
1
1
0
0
0
0
1
0
0
0
2
1
2
0
0
0
2
1
0
0
1
2
1
0
1
1
0
0
2
1
1
1
1
0
0
0
0
0
2
1
1
0
1
1
1
1
0
2
0
2
0
0
0
1
1
2
0
3
1
2
2
1
1
1
1
0
0
0
2
0
2
1
1
0
0
0
0
0
0
0
2
1
1
0
1
1
1
1
1
0
1
1
1
0
0
2
1
0
0
1
2
3
2
1
0
0
1
1
1
1
1
1
2
1
0
1
2
0
0
1
0
2
1
1
0
1
8
0
1
0
2
0
0
1
0
0
0
0
0
3
1
1
1
1
0
0
1
1
2
0
1
1
0
0
0
0
3
1
2
0
1
2
0
0
0
1
2
2
1
1
1
1
0
2
2
1
1
2
1
2
2
1
0
0
0
2
2
0
0
1
0
1
0
0
0
2
2
2
2
0
3
2
2
0
1
2
0
0
2
1
0
1
0
0
0
0
1
0
1
2
0
1
1
1
0
0
2
0
0
1
1
1
0
1
1
0
2
0
0
1
0
1
1
0
2
0
1
0
2
1
0
2
0
0
0
1
0
0
1
2
2
2
2
0
0
2
2
1
0
0
0
0
2
1
0
1
2
0
0
0
1
1
0
2
0
2
0
3
2
2
0
0
0
0
2
1
2
0
0
0
1
0
0
1
2
1
0
1
1
1
2
3
0
0
2
2
1
0
1
2
1
0
0
0
0
2
1
2
0
0
1
2
0
0
1
0
1
1
1
1
1
1
2
0
2
1
1
0
2
1
2
0
0
0
0
2
2
2
1
3
0
1
1
0
2
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
2
0
1
0
1
0
1
1
1
0
0
0
0
1
1
0
0
1
1
0
1
0
1
1
1
0
1
2
2
0
1
2
1
0
1
0
1
0
7
1
0
1
0
1
1
0
0
3
1
1
0
1
1
0
0
0
0
1
1
0
1
2
0
0
0
0
2
2
1
2
0
5
2
0
1
1
1
0
1
1
0
0
2
0
1
0
3
0
1
0
0
1
0
1
2
0
1
2
6
0
0
1
0
1
2
0
0
1
0
2
1
2
1
1
0
0
2
1
2
0
0
2
0
0
0
0
0
1
0
1
0
2
2
0
0
1
1
0
0
0
0
1
1
1
2
1
2
1
1
0
0
0
1
2
2
0
0
1
0
1
0
1
1
0
0
2
1
1
0
0
0
1
2
1
0
0
0
1
0
0
1
2
2
1
3
0
0
1
0
1
0
1
0
0
0
1
0
0
2
1
1
1
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
2
4
1
2
1
2
0
0
2
1
0
1
1
0
0
1
1
1
1
1
0
1
0
0
0
0
0
1
2
1
1
2
1
1
1
2
2
0
1
1
2
0
0
0
0
1
0
2
0
0
1
0
0
1
0
2
0
0
0
0
0
1
1
0
1
0
2
1
2
1
3
0
2
1
2
0
1
0
1
0
0
1
2
0
2
0
0
0
1
0
1
2
0
1
2
1
1
0
2
1
0
1
0
1
1
0
0
2
0
2
1
0
0
0
0
1
0
2
0
1
1
0
0
1
0
1
2
2
2
0
0
0
1
1
0
1
0
1
2
0
0
2
2
0
1
0
1
0
1
0
0
1
1
0
2
0
1
3
1
0
2
0
1
0
3
1
0
1
1
0
0
0
0
2
2
2
0
0
2
1
0
0
1
0
1
0
0
0
0
0
2
0
1
0
1
1
1
2
1
0
1
0
2
0
1
1
2
2
0
1
2
0
0
2
0
0
2
0
0
2
1
1
1
0
0
0
2
0
2
1
2
0
2
1
1
2
0
0
0
0
2
0
9
1
0
0
1
3
0
0
0
1
1
2
3
0
1
0
0
1
0
1
2
1
2
1
0
0
1
1
1
0
1
0
0
1
0
2
1
0
0
3
1
1
1
2
0
0
1
2
0
0
2
0
1
0
0
1
1
0
0
1
0
2
0
0
0
0
1
2
0
0
0
1
2
0
0
1
0
0
1
0
1
0
1
0
1
1
1
1
1
0
2
1
1
1
2
2
1
2
0
2
0
2
0
0
1
0
2
0
2
0
0
0
2
1
0
0
1
1
0
1
1
1
0
1
1
0
1
0
0
0
0
2
0
1
2
1
0
1
2
1
0
0
0
0
1
0
2
2
1
0
0
3
0
0
2
0
0
0
0
3
0
2
1
2
0
2
2
0
0
0
0
0
0
0
1
3
0
1
0
2
0
0
0
2
0
2
0
1
1
1
2
0
0
0
1
1
2
2
2
2
2
2
1
2
2
0
0
0
0
0
0
1
1
0
2
2
1
2
0
1
0
0
0
2
2
0
0
1
2
0
0
0
0
2
1
0
1
0
0
2
0
0
0
2
1
1
1
0
0
1
0
2
0
0
1
0
0
2
0
0
0
2
0
1
0
0
1
0
2
0
1
0
1
0
0
0
0
2
0
3
1
2
0
2
1
2
1
0
0
1
0
1
1
1
0
2
2
0
0
1
0
1
0
1
1
1
0
2
0
1
1
0
3
0
1
0
0
0
2
1
0
1
0
4
0
1
0
1
0
1
2
1
3
0
0
2
3
0
2
0
0
0
0
0
0
2
0
2
0
0
2
2
0
2
0
0
0
1
0
0
0
2
0
0
0
2
0
0
1
3
3
2
1
0
2
1
2
2
1
0
0
0
0
1
2
2
0
1
0
1
1
1
1
0
2
1
0
1
0
1
2
0
3
2
0
2
1
2
2
2
1
0
0
0
0
0
2
0
2
2
1
0
0
0
2
0
0
0
0
1
0
3
2
1
2
2
0
0
0
1
1
2
1
0
2
1
0
0
1
1
0
0
2
1
2
1
1
0
0
2
0
1
1
2
1
0
2
0
2
1
1
2
2
1
0
1
1
0
1
1
2
3
1
1
1
0
1
0
0
2
0
2
0
1
1
0
2
1
0
1
2
0
1
1
1
1
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
2
2
0
2
1
1
0
2
1
0
2
0
0
1
1
1
2
0
0
2
1
0
1
0
0
2
2
0
2
2
1
2
0
3
0
0
2
2
2
0
1
0
0
1
1
0
0
1
0
0
1
0
1
0
0
0
0
3
1
0
3
1
1
0
0
0
1
0
0
0
2
2
1
0
2
0
0
2
1
0
1
1
0
1
2
0
1
0
0
0
0
0
2
2
0
2
0
0
0
1
1
0
0
0
0
2
1
2
1
0
0
0
1
1
1
3
0
0
0
1
1
0
1
2
0
0
0
2
1
0
2
1
0
1
1
0
2
0
0
0
0
1
0
2
0
1
1
2
2
0
2
0
2
0
0
0
1
0
1
1
2
0
0
0
0
1
1
2
0
2
2
2
0
0
0
0
2
2
1
0
3
2
0
1
1
1
2
0
0
1
1
0
2
0
0
1
1
1
0
0
0
0
0
2
2
2
1
0
1
0
2
1
1
1
0
1
0
0
1
0
1
0
1
1
2
0
1
2
0
2
0
2
0
1
0
3
0
1
1
1
1
1
1
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
1
1
2
0
0
1
0
1
0
0
0
0
0
2
2
2
1
2
2
2
0
0
2
1
3
0
0
0
4
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
1
0
2
1
0
0
0
1
1
1
2
2
1
0
1
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
3
0
1
0
1
0
0
0
2
1
1
1
0
0
1
3
1
0
2
2
1
1
0
1
2
1
3
1
2
1
2
0
0
1
0
1
0
1
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
2
0
0
0
1
1
1
2
0
1
2
1
1
1
2
0
0
2
1
1
0
2
0
0
0
1
0
4
0
1
2
1
0
0
1
0
1
0
0
1
1
1
1
0
0
1
2
1
0
0
0
0
1
0
1
1
3
0
1
0
0
2
0
2
1
2
1
0
0
2
1
0
0
0
2
1
0
1
2
2
1
1
0
1
1
1
0
1
2
2
0
2
2
1
1
0
1
0
2
2
0
2
1
2
1
2
0
0
1
0
1
1
0
0
2
1
0
0
2
1
0
2
0
0
1
0
1
1
0
1
0
1
0
1
0
2
2
2
0
1
1
0
1
1
1
1
2
1
0
1
0
2
0
0
0
0
0
1
2
1
0
2
0
1
0
0
0
1
1
2
0
1
1
0
0
0
2
2
1
1
0
2
0
1
1
0
2
2
0
0
2
0
0
0
0
1
2
1
1
2
0
1
0
2
1
0
0
0
0
0
0
1
1
0
0
1
1
1
0
3
0
0
1
0
0
1
0
2
1
1
0
0
1
1
1
2
1
2
0
0
1
2
2
1
2
1
1
1
1
0
0
0
0
0
0
0
1
2
0
0
1
0
1
1
2
1
0
0
1
0
1
2
2
1
1
1
1
0
1
0
2
2
0
2
1
2
1
0
1
0
1
2
1
0
2
0
0
2
1
2
2
1
0
1
0
0
1
1
0
1
2
1
0
1
1
1
1
2
1
0
0
1
2
0
0
1
0
1
0
2
0
3
2
1
0
1
0
2
0
2
1
2
1
0
1
1
2
0
1
0
1
1
2
2
1
1
0
1
2
2
0
1
2
3
0
0
2
1
0
0
0
2
2
1
0
0
0
1
0
1
0
0
0
0
0
0
0
2
1
2
0
0
0
1
1
0
1
0
1
1
1
0
2
0
1
2
1
2
0
1
1
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
3
0
0
0
1
2
1
0
0
0
0
0
2
0
0
1
0
0
0
0
2
1
1
0
1
1
0
0
0
1
1
0
1
0
1
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
2
1
0
1
0
0
1
0
2
0
0
1
2
2
2
1
1
0
0
0
0
2
0
1
1
0
1
2
2
0
0
0
0
1
1
0
1
2
1
1
1
0
2
0
0
1
1
0
2
0
0
1
1
1
0
0
1
1
0
2
0
1
0
2
1
2
2
2
2
1
1
0
1
1
1
1
0
1
0
1
1
0
0
1
2
1
0
0
0
1
1
1
1
2
1
1
2
2
0
0
0
2
1
1
0
2
0
2
2
0
0
1
1
1
0
0
2
2
1
0
0
0
0
1
2
0
0
1
0
1
0
2
0
3
1
0
1
0
1
1
0
1
0
0
1
0
1
1
2
1
2
1
1
0
0
1
0
3
1
2
0
2
0
0
0
2
1
1
2
0
0
0
0
1
0
1
2
1
1
1
2
0
0
2
0
0
1
2
1
1
0
1
2
2
2
0
2
0
0
2
0
1
1
0
0
2
2
1
0
2
2
1
2
1
1
2
1
1
0
2
0
1
1
0
2
2
2
0
2
0
1
0
1
0
0
2
0
1
1
0
1
0
2
0
1
2
0
0
1
2
0
1
0
0
0
0
1
0
0
1
1
0
1
1
0
1
0
1
2
1
0
2
4
1
0
1
0
0
0
1
0
0
1
1
0
0
0
0
2
1
0
1
1
0
0
2
1
2
0
1
2
0
0
1
1
1
0
1
0
1
0
1
0
2
0
0
1
3
2
2
0
0
1
0
0
0
1
0
0
2
0
0
0
1
2
2
1
1
0
1
0
1
1
1
0
0
0
0
3
0
2
0
0
0
0
1
0
0
1
2
1
0
0
0
2
1
1
0
0
0
1
0
1
0
1
4
2
0
0
0
2
1
2
1
1
0
0
0
1
2
0
0
1
0
2
1
1
0
1
1
1
1
0
1
0
1
0
1
0
0
1
1
0
2
1
0
0
1
2
1
1
0
0
1
0
2
1
0
0
2
0
0
0
0
1
0
2
0
2
2
0
0
0
1
2
2
0
2
2
0
0
0
1
0
1
0
2
2
1
2
0
0
3
0
0
1
0
1
1
0
1
1
0
0
0
0
2
0
0
1
1
2
0
2
0
0
0
1
0
0
2
2
1
1
1
1
0
2
2
0
1
0
0
0
0
0
2
1
2
2
1
1
0
1
1
0
1
2
2
0
1
0
1
3
1
1
0
1
0
0
0
0
2
0
0
0
0
0
2
2
0
1
1
0
0
1
2
0
0
0
0
1
1
0
2
0
0
2
1
0
0
0
3
1
0
0
0
0
6
0
0
0
4
1
2
0
1
2
1
1
0
1
0
0
2
0
1
2
0
0
0
0
1
2
2
1
0
1
0
2
0
0
1
2
0
1
1
0
0
0
0
0
2
1
1
0
0
1
0
0
0
0
0
0
2
2
1
1
0
0
0
2
0
2
0
0
0
0
3
1
1
0
0
0
0
2
1
2
0
0
0
0
0
2
0
0
1
2
0
1
0
0
2
0
0
0
0
0
1
1
1
1
0
1
1
1
0
3
1
0
0
1
1
1
0
2
0
2
0
1
0
2
1
2
0
2
1
0
2
0
0
2
2
0
1
0
1
0
0
2
0
1
0
0
2
1
1
0
2
1
1
1
2
1
2
1
0
0
1
0
0
0
2
0
0
1
0
0
1
1
2
2
0
0
1
2
2
0
2
2
0
0
1
2
2
0
0
0
0
0
0
1
0
0
1
0
0
0
7
0
0
0
2
0
1
0
2
2
0
0
0
3
0
0
1
1
0
0
0
1
0
3
2
1
0
1
0
4
0
1
2
1
0
0
1
0
2
0
3
1
2
1
0
2
1
1
0
2
0
0
0
0
1
1
2
2
2
0
0
0
0
0
1
0
0
0
2
0
1
2
0
0
1
2
2
2
0
2
0
0
0
1
0
0
0
1
0
2
0
1
1
2
1
1
0
1
1
0
1
0
0
0
1
0
0
0
2
0
1
1
1
1
2
0
2
0
2
0
7
0
0
2
2
1
2
1
0
1
2
2
0
2
0
0
0
0
0
0
1
0
2
0
2
1
1
2
0
1
1
0
0
0
0
2
0
2
0
1
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
1
1
0
1
1
1
0
0
0
0
2
0
1
0
1
1
1
0
1
2
1
1
2
0
1
0
0
1
0
1
1
1
0
1
0
0
1
0
1
0
0
0
1
1
0
0
1
0
1
0
0
1
0
1
0
2
2
1
0
0
1
0
1
0
1
1
1
1
1
0
0
1
0
2
1
1
0
0
0
3
0
0
0
0
3
1
1
0
2
0
1
2
0
0
0
2
2
2
1
1
2
1
0
1
0
1
1
0
2
1
1
2
0
2
2
1
0
1
0
2
0
2
0
0
1
0
0
1
1
2
0
1
2
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
1
0
1
0
1
1
3
1
0
0
2
2
0
2
0
2
2
3
0
1
0
0
2
0
1
0
1
0
1
2
2
0
0
1
1
2
0
0
0
2
0
0
2
1
0
2
1
1
0
0
0
1
3
1
1
0
0
0
2
1
1
0
1
0
0
1
0
2
2
2
0
2
1
2
0
1
2
1
0
2
2
0
1
0
0
1
0
0
0
1
0
0
1
1
0
0
1
1
0
1
0
0
0
0
2
1
1
1
2
1
0
1
0
0
0
0
0
0
1
0
0
0
2
0
2
0
1
1
1
3
0
1
0
2
1
1
1
1
1
0
0
0
1
1
1
1
0
3
1
0
1
2
1
2
0
0
1
1
1
2
0
1
0
1
1
2
1
1
3
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
2
1
0
1
1
0
1
0
0
1
0
0
0
0
1
1
0
1
0
0
0
3
1
1
2
0
2
1
0
2
2
0
1
1
2
2
2
2
1
0
3
2
2
1
0
0
0
0
0
1
0
0
0
0
1
1
1
0
2
1
1
2
0
1
2
1
1
0
1
2
0
1
1
0
1
0
1
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
2
0
1
0
1
1
2
1
0
2
0
0
1
0
0
1
0
1
1
0
2
2
1
1
1
1
0
2
1
0
0
0
1
0
2
0
0
0
1
2
2
0
0
0
0
0
0
0
2
0
2
1
0
1
0
3
0
1
1
2
0
0
2
1
2
0
0
0
1
2
1
0
2
2
3
0
2
0
0
0
1
0
1
1
0
1
0
1
0
2
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
1
1
0
1
2
0
0
0
2
0
2
0
1
1
0
0
1
1
0
1
1
0
0
1
1
1
1
0
0
0
2
0
1
1
0
1
2
1
1
1
0
1
0
2
2
3
1
2
0
2
0
0
0
0
0
2
0
1
1
2
0
0
0
1
0
1
1
0
2
1
1
0
1
0
2
2
2
1
2
2
2
3
1
4
1
0
0
1
5
0
0
2
0
0
1
0
0
1
0
0
0
1
1
1
2
1
0
3
1
0
1
2
1
1
0
1
0
0
2
1
0
1
1
2
0
0
2
1
0
0
1
1
1
1
0
0
0
0
1
1
0
0
0
1
0
1
0
2
0
1
1
1
0
0
0
1
0
0
0
0
0
0
1
0
2
1
1
2
1
0
0
2
1
1
0
2
0
0
0
1
1
1
0
2
2
1
0
1
1
0
0
0
0
0
0
1
1
0
1
1
2
2
0
0
1
2
1
1
1
2
0
2
0
1
0
1
2
1
2
1
1
0
0
1
2
2
1
0
1
1
0
0
0
1
2
0
0
0
2
1
2
0
2
0
0
1
1
5
0
1
0
2
2
2
1
1
2
2
2
0
0
0
0
2
8
1
0
1
2
1
0
0
1
0
0
0
0
1
2
2
1
0
0
2
0
2
2
0
0
1
1
0
1
0
0
1
2
3
2
0
0
1
2
1
1
0
0
2
2
2
1
2
2
2
2
2
1
2
2
3
0
0
0
0
1
2
0
0
2
0
0
2
2
3
0
0
1
1
2
1
0
0
0
0
0
2
2
0
0
1
2
1
1
1
1
0
1
2
0
0
0
0
1
0
2
0
2
0
1
1
2
1
1
0
0
0
0
2
1
0
0
1
0
0
0
1
1
0
2
0
0
0
1
1
1
1
0
1
0
0
1
2
1
1
0
2
0
0
2
2
0
1
0
2
1
0
2
1
1
1
1
1
1
2
1
0
1
0
0
0
0
1
1
1
0
0
2
1
2
2
2
3
0
0
0
0
1
0
2
2
0
0
0
2
1
1
0
0
1
1
0
0
0
1
0
1
2
2
3
0
0
2
1
0
2
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
2
1
0
1
0
0
1
0
0
0
2
1
1
1
2
0
0
1
2
0
1
0
2
2
1
0
0
0
0
1
1
6
0
0
1
0
0
0
2
0
1
0
1
1
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
1
0
1
1
1
0
0
1
1
1
0
1
0
1
2
0
3
0
2
0
0
2
0
0
2
0
0
0
1
1
1
0
0
0
1
0
1
0
0
0
2
0
0
0
1
1
2
2
0
1
0
1
0
1
1
2
1
1
1
0
0
0
1
0
2
1
0
2
0
1
0
0
1
0
2
1
0
1
0
1
2
0
0
2
0
2
0
1
0
0
3
3
2
2
1
1
1
1
1
2
0
0
0
1
0
1
0
2
0
0
1
1
1
0
1
2
1
0
1
2
1
1
1
1
0
1
0
1
0
1
2
1
0
2
0
0
1
1
2
2
1
2
1
0
0
1
2
1
0
0
1
0
0
0
0
1
1
2
0
1
1
0
0
0
0
2
1
0
1
0
2
1
1
0
1
2
0
1
0
0
2
1
2
2
0
0
0
1
3
1
0
1
1
0
1
0
2
0
0
0
1
1
0
1
1
0
2
2
0
0
0
0
1
1
1
0
0
0
2
0
0
1
1
1
2
1
2
1
0
2
1
0
0
0
0
1
0
0
2
1
1
0
0
0
0
0
1
0
1
1
0
1
1
0
0
0
0
0
0
2
1
1
2
0
1
0
0
0
1
1
4
0
0
0
0
0
0
0
1
2
2
1
0
3
1
0
0
1
0
1
0
1
1
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
1
2
1
1
2
2
0
2
0
0
0
1
0
2
1
0
0
0
0
2
0
0
2
0
0
2
1
0
1
1
2
0
1
2
1
1
1
1
2
1
1
0
1
1
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
2
2
0
0
1
1
0
0
1
0
1
0
2
0
0
0
0
1
1
0
0
0
2
2
0
0
0
2
0
1
0
2
1
0
2
2
1
0
1
0
0
0
0
1
1
2
2
2
0
1
2
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
1
0
2
0
2
0
0
0
2
2
2
0
0
0
0
0
0
3
2
1
0
0
1
1
1
0
0
1
1
1
0
1
0
0
0
0
2
0
1
2
0
1
1
1
3
0
0
1
2
0
2
0
0
1
2
0
0
0
0
1
1
1
1
2
0
0
0
0
1
0
0
0
0
1
1
2
1
0
0
0
2
1
0
2
1
0
0
1
0
0
1
1
1
1
0
0
1
0
0
0
0
2
0
1
0
2
0
1
0
0
3
0
1
0
1
0
1
1
4
2
2
3
1
1
0
2
0
2
2
1
2
0
0
0
0
1
0
0
0
2
0
0
0
2
2
1
2
0
2
1
1
1
2
0
0
0
0
0
0
2
0
0
0
0
2
2
1
1
0
0
0
0
2
0
0
0
1
0
0
1
2
0
2
1
1
1
0
1
0
0
0
2
1
2
2
2
1
1
1
1
1
2
0
0
5
1
1
0
0
0
1
0
0
1
0
2
1
0
0
0
1
1
1
0
1
2
1
0
1
0
0
2
2
1
2
1
0
1
1
1
2
1
0
2
1
0
0
0
1
0
1
1
1
2
0
1
0
0
2
5
0
2
1
0
2
0
0
1
2
0
0
2
2
0
0
1
0
0
1
0
0
0
0
2
2
1
0
0
2
1
0
2
2
2
0
1
1
0
0
0
2
1
0
2
0
0
1
1
1
0
0
0
1
0
1
0
2
1
0
1
0
1
2
0
0
0
2
0
2
1
1
1
1
0
1
2
1
0
2
1
1
0
0
0
1
0
1
0
1
2
2
0
1
2
0
0
1
2
2
3
1
1
0
2
1
2
0
1
0
0
0
2
0
0
0
1
1
0
2
1
0
2
0
0
2
0
0
1
1
0
1
0
2
0
2
1
1
2
0
0
0
1
0
0
0
1
0
0
1
2
2
0
3
0
2
1
1
1
0
0
1
2
1
0
0
2
0
0
1
1
2
1
1
0
2
2
1
1
1
0
0
2
2
1
1
0
2
0
0
0
0
0
0
2
1
2
0
0
0
1
2
2
0
0
0
1
1
0
0
2
2
2
0
1
1
2
0
0
2
3
0
2
1
1
1
2
2
1
0
0
1
0
0
1
2
1
1
1
1
0
1
2
0
0
2
0
1
2
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
1
1
0
1
2
0
1
1
1
0
2
2
0
0
0
1
0
0
0
2
2
3
1
0
1
0
0
0
0
1
0
2
2
2
1
0
0
2
0
2
2
2
3
0
1
0
1
4
0
0
2
1
0
1
1
1
2
0
0
0
2
1
0
0
1
0
1
0
1
1
1
1
2
1
1
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
2
0
0
0
1
1
1
0
0
0
0
1
1
1
0
1
0
1
2
0
2
1
0
0
0
3
1
2
0
0
0
0
0
1
0
1
2
0
0
0
1
1
0
0
1
0
1
2
1
1
0
0
0
0
1
0
3
2
0
2
0
2
0
3
0
0
0
0
0
1
1
1
1
0
0
2
0
1
1
0
2
1
0
1
1
1
0
0
1
0
1
1
0
0
0
1
0
1
0
2
0
0
2
0
0
2
0
2
1
0
0
0
2
1
1
1
0
0
0
1
1
2
1
1
1
2
0
1
1
1
0
0
0
1
1
1
1
2
1
0
1
1
1
0
1
1
0
0
1
0
0
0
2
1
0
0
0
1
0
0
0
2
0
0
2
1
0
1
2
1
0
1
0
1
1
0
2
0
1
0
0
0
2
1
0
0
1
1
0
1
1
0
0
1
2
1
2
0
1
0
1
2
1
1
0
1
0
4
1
1
0
0
2
2
1
2
2
1
3
0
0
1
0
1
0
1
0
0
1
1
0
1
0
0
1
2
0
1
1
0
1
0
1
1
0
1
1
1
1
1
2
1
1
1
0
1
0
1
0
2
2
1
1
0
0
0
1
1
1
0
1
0
1
3
0
0
0
1
1
1
0
0
1
0
0
3
0
1
2
1
1
2
0
1
2
0
1
0
1
1
2
2
0
0
1
0
0
2
1
1
0
2
2
3
1
0
0
0
2
1
1
1
0
1
2
1
0
1
1
1
5
0
0
1
0
0
1
0
1
1
1
1
0
0
1
1
0
0
0
0
0
1
0
0
1
1
1
0
1
0
1
2
2
1
0
2
0
1
0
0
0
0
1
0
2
1
1
0
2
1
1
0
1
0
2
1
1
1
1
1
0
3
1
1
1
0
0
0
1
0
0
0
0
0
2
0
1
2
0
7
0
2
1
0
1
2
0
1
0
2
2
1
0
1
1
0
1
1
0
0
0
2
2
0
0
0
2
0
1
0
2
0
0
1
3
0
0
0
2
2
2
0
0
0
0
0
1
1
2
1
0
1
2
1
3
0
0
0
1
0
2
2
0
2
0
0
2
2
4
1
2
1
0
0
0
1
0
0
0
0
1
3
2
0
0
2
1
1
1
1
1
0
2
2
1
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
1
2
2
0
2
2
0
1
1
3
1
1
0
1
0
1
1
1
0
0
1
1
1
0
2
2
2
1
0
2
0
0
0
0
0
2
0
1
2
0
0
2
1
2
0
0
0
2
2
1
1
0
0
0
0
0
1
1
1
1
0
1
1
1
0
0
2
0
0
1
0
0
1
0
2
1
0
1
2
0
1
0
2
0
0
1
1
0
0
0
0
0
0
0
3
0
0
0
2
0
0
2
2
0
0
1
1
0
2
1
0
1
0
0
2
1
1
0
0
0
0
0
0
0
0
2
0
3
0
0
2
1
1
1
2
2
0
1
0
0
2
2
1
0
1
3
0
1
7
0
1
0
1
0
1
0
0
0
1
0
0
1
0
0
1
1
0
2
1
3
1
2
0
0
0
2
0
2
2
1
0
1
2
1
0
2
2
0
0
1
0
2
0
2
0
1
0
0
1
2
1
0
0
2
0
0
0
2
0
1
0
1
2
0
1
1
0
0
0
2
0
2
1
3
1
0
2
0
0
1
0
0
2
0
1
0
0
0
0
1
0
2
1
2
1
0
2
1
1
0
1
0
1
1
0
0
1
2
4
0
0
0
2
2
0
0
1
6
0
1
1
0
0
1
0
1
1
2
1
0
2
1
2
2
0
0
2
0
0
1
0
1
2
0
1
0
2
0
2
0
2
2
0
1
1
1
0
5
0
0
1
0
1
2
1
0
2
1
1
0
1
0
1
1
0
0
1
0
0
0
2
0
2
2
2
2
0
1
2
1
1
0
1
1
2
2
1
0
0
0
2
0
2
0
1
2
0
0
0
1
1
1
1
0
1
1
1
0
0
0
2
0
0
0
1
3
0
2
2
0
1
0
1
2
0
1
1
1
1
0
0
2
2
0
1
2
2
0
0
0
1
1
0
0
1
1
1
1
2
1
0
0
2
0
1
0
1
1
2
0
0
1
0
0
1
0
0
1
2
0
3
0
1
3
0
0
0
2
1
2
2
0
2
1
0
0
1
0
1
0
1
0
0
0
1
2
2
0
1
2
2
2
3
2
0
5
0
1
0
0
1
1
1
0
1
0
1
2
0
2
0
0
0
0
1
1
1
0
0
1
2
1
0
2
0
0
0
1
0
1
0
0
1
1
0
2
1
1
0
2
0
0
0
0
2
0
0
1
1
1
0
1
1
0
0
2
2
1
1
1
1
2
0
1
0
0
0
2
1
2
0
2
0
0
2
1
0
0
0
0
1
2
0
1
0
0
0
0
1
1
0
0
0
0
0
1
1
2
0
1
0
1
2
1
1
2
1
2
2
1
0
1
0
2
0
0
0
1
1
0
0
0
0
1
1
1
2
1
2
1
0
0
0
0
0
1
2
1
0
0
0
2
0
2
2
0
0
0
0
0
1
1
2
0
0
2
1
1
0
0
7
2
2
0
0
2
0
0
0
2
0
1
0
1
1
0
2
0
2
2
2
0
1
2
0
1
2
0
1
2
0
3
0
1
4
1
3
1
0
1
1
2
0
1
2
1
0
1
1
1
0
2
0
1
1
2
2
0
2
0
0
1
0
2
1
3
0
0
0
0
2
0
2
1
0
2
0
0
1
0
1
2
0
0
0
1
0
0
1
1
0
0
3
1
2
1
0
2
0
2
0
1
0
2
0
1
0
0
2
1
0
0
1
3
0
0
1
1
2
0
3
3
0
1
2
2
0
0
0
0
1
2
0
0
0
2
0
0
0
2
1
2
0
0
1
2
0
1
1
0
1
0
2
2
0
0
2
1
1
0
1
0
2
2
0
0
0
0
0
0
1
0
0
1
1
1
0
0
1
1
0
0
0
0
0
1
2
2
0
1
0
0
2
0
1
0
0
1
1
1
1
0
0
1
0
0
0
4
2
0
0
1
0
0
0
0
1
1
0
0
1
0
1
0
0
0
1
2
0
1
1
0
1
0
1
0
1
2
2
0
0
1
1
1
1
0
2
2
0
0
3
1
1
1
0
0
0
0
0
2
0
0
0
0
1
2
1
0
2
0
2
3
1
2
2
0
0
2
2
0
1
1
1
2
0
2
0
1
2
0
1
1
2
0
0
1
1
0
0
2
0
2
2
1
0
0
0
2
2
1
1
0
0
0
0
0
0
1
0
1
1
0
1
1
1
1
2
1
0
1
1
0
1
1
2
1
0
2
2
3
2
1
0
0
0
0
1
0
0
0
1
0
1
0
2
0
0
0
0
0
1
1
2
0
1
1
2
2
1
2
1
2
1
3
1
2
0
0
1
1
0
0
1
2
1
1
0
0
1
0
1
0
1
0
0
1
2
1
1
0
1
1
2
2
2
2
0
1
0
1
2
1
0
2
2
0
0
3
1
2
1
2
1
1
2
1
0
0
2
2
1
0
2
0
1
2
0
0
0
0
1
1
1
1
1
1
2
1
2
1
0
0
1
1
0
0
0
2
1
0
1
1
1
2
1
2
0
0
1
0
0
1
2
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
1
1
0
0
0
0
1
1
0
2
2
0
0
2
0
0
1
2
0
1
0
0
0
2
0
1
2
0
2
2
2
1
1
0
2
0
1
2
1
1
0
1
0
1
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
1
1
1
1
0
2
0
0
0
1
0
1
1
0
2
2
0
0
0
0
1
0
0
1
2
1
1
2
0
1
0
0
1
1
0
2
0
1
1
7
0
2
2
0
2
1
1
0
0
0
1
0
0
2
2
0
0
1
1
2
0
1
0
0
0
0
1
0
2
2
0
1
2
1
0
2
2
1
0
2
0
2
1
1
0
0
0
2
0
1
1
0
0
2
1
0
0
1
1
0
1
0
1
2
2
0
2
2
1
0
0
0
0
0
1
0
0
2
2
0
1
3
0
0
1
1
0
0
0
0
2
0
0
2
0
0
1
1
2
0
1
0
2
1
0
0
2
0
2
0
0
1
0
0
1
2
1
2
0
1
1
0
0
0
1
0
1
1
0
1
0
2
1
2
1
1
0
1
1
1
0
2
0
1
0
0
2
2
0
0
1
1
0
1
0
2
2
1
1
0
2
1
0
2
1
1
1
1
0
0
1
1
2
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
1
0
1
1
1
1
0
2
1
1
0
2
0
1
0
0
1
0
1
2
1
1
0
0
1
0
0
2
1
2
0
0
1
0
0
0
1
1
0
1
0
1
0
1
1
1
1
1
1
2
1
1
0
1
0
0
0
2
0
2
0
0
2
1
0
0
1
0
2
1
0
0
0
0
0
0
2
0
1
0
0
0
2
2
1
1
0
1
2
0
0
1
1
1
0
1
0
1
2
1
0
1
2
2
0
3
1
1
2
0
2
0
1
0
0
0
1
2
1
2
0
1
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
2
0
2
0
2
1
2
2
0
3
1
2
1
2
1
2
0
0
0
0
2
1
1
0
1
2
1
1
1
0
2
1
0
0
2
1
1
0
0
2
0
0
0
0
1
1
2
1
1
1
0
1
0
2
2
1
1
0
0
0
2
0
0
0
6
2
1
1
0
2
0
1
0
0
0
2
1
1
1
0
0
2
2
1
1
1
1
1
0
0
1
1
1
0
1
0
2
2
0
0
2
1
0
2
0
0
0
2
2
0
1
0
2
0
0
0
1
0
1
2
1
0
2
2
0
1
0
3
1
1
0
1
0
1
0
1
0
1
0
0
2
2
1
0
0
0
1
1
2
1
1
0
0
0
1
1
1
1
2
0
1
1
1
1
0
0
1
0
1
0
2
0
2
1
1
1
0
2
1
1
0
2
2
1
0
0
1
1
0
0
0
1
0
0
0
2
1
1
2
0
1
0
1
0
0
0
0
0
0
1
0
0
1
2
0
1
1
0
0
1
2
1
1
0
2
0
2
6
1
0
1
1
1
0
1
0
0
0
2
1
2
0
1
1
1
0
1
1
0
1
0
1
1
0
1
2
2
0
0
1
1
2
2
2
2
1
3
0
1
0
0
2
1
1
0
0
1
1
1
1
0
1
0
1
0
2
0
1
1
1
2
0
1
0
0
2
1
1
0
0
2
0
2
1
1
1
1
0
0
1
2
0
0
0
2
1
0
0
0
1
0
0
1
2
1
2
1
1
0
1
2
1
1
0
0
1
2
0
2
0
2
0
0
2
0
1
1
0
0
0
0
0
2
0
0
1
1
2
1
1
1
0
0
2
3
0
1
0
0
0
2
0
2
1
0
1
1
1
1
2
1
1
2
0
0
2
2
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
2
1
0
0
1
0
1
2
0
2
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
1
0
2
0
0
0
0
1
1
3
2
1
0
1
0
0
0
0
1
0
0
2
2
0
1
0
0
0
1
1
1
0
0
0
0
0
1
0
1
0
2
1
0
1
2
0
0
0
2
0
0
2
1
1
1
2
2
2
0
0
0
2
2
2
2
0
1
0
1
0
1
0
1
1
2
0
0
0
1
0
1
1
2
1
0
2
0
1
2
0
1
0
1
0
1
0
2
0
1
0
0
1
1
1
1
1
0
0
2
2
1
2
0
1
0
0
2
1
0
0
1
0
0
1
0
1
1
1
1
0
1
1
2
1
0
1
2
0
1
1
1
0
0
1
0
2
0
0
1
1
0
0
1
0
1
0
1
0
0
2
1
1
1
0
1
1
0
0
2
1
1
0
1
1
1
0
2
0
1
1
0
1
0
2
2
1
0
1
0
2
0
1
1
1
3
0
2
0
0
0
2
0
0
2
0
2
1
0
1
1
1
0
0
1
1
0
1
0
2
0
0
0
1
2
1
2
0
2
2
1
1
0
0
0
0
1
0
1
0
0
1
2
0
1
2
0
2
0
1
3
2
1
0
0
0
1
1
1
1
0
2
0
0
3
0
4
3
2
2
0
0
1
0
1
0
0
1
2
1
2
2
0
0
1
0
2
2
0
0
1
1
2
0
0
1
0
2
2
0
1
1
0
0
2
2
1
0
1
1
0
1
0
1
0
1
0
0
0
0
0
1
2
2
1
0
0
0
1
1
2
1
2
1
0
1
0
2
2
2
1
0
0
0
0
2
1
0
0
0
0
1
1
0
2
1
1
0
0
1
0
2
3
0
2
2
2
1
0
2
0
1
1
2
1
0
0
0
0
2
2
1
0
0
1
0
1
0
0
0
0
2
2
0
0
2
0
0
2
0
1
1
0
1
2
1
0
1
0
0
1
0
1
0
2
0
1
1
2
0
2
2
2
0
1
1
1
1
0
0
0
0
1
2
2
0
2
1
1
2
0
2
0
1
0
1
2
0
2
0
0
1
0
1
2
1
0
2
1
0
1
0
1
2
1
0
2
1
2
3
0
1
1
1
1
2
1
0
0
1
0
1
0
1
1
2
1
0
1
2
0
0
0
2
2
1
1
2
0
0
0
1
3
1
0
0
0
0
1
1
1
1
1
0
2
1
0
0
0
0
2
1
1
1
0
0
2
1
2
1
0
0
1
1
0
0
2
2
1
2
0
1
0
0
1
0
1
0
0
0
1
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
1
2
1
2
0
2
0
0
1
1
1
1
0
3
1
0
1
1
1
2
1
0
1
2
0
0
0
0
1
0
0
2
2
2
0
0
1
0
1
1
0
1
1
0
0
2
0
2
0
2
4
1
2
0
3
2
0
1
0
2
2
0
2
1
0
0
0
0
1
0
0
0
1
0
0
1
2
2
1
2
2
2
1
0
1
1
0
2
0
0
1
2
0
0
3
1
0
0
0
1
1
3
0
1
0
0
2
0
1
1
2
0
0
0
2
1
0
0
0
1
0
0
0
0
1
1
0
2
2
0
1
3
1
2
2
2
2
0
0
0
1
0
2
1
0
0
0
0
0
0
1
2
0
1
2
0
2
0
0
1
2
0
0
2
2
2
1
0
1
0
1
1
0
0
1
0
0
0
2
0
0
0
0
1
0
0
1
1
2
0
0
0
1
0
1
1
1
0
1
0
1
0
2
0
0
1
0
3
0
0
1
0
0
2
0
0
0
0
0
0
0
1
1
0
1
1
0
2
0
1
0
0
0
1
1
0
1
0
0
0
1
0
2
0
0
2
0
2
2
0
2
0
0
2
2
2
0
0
1
0
0
0
1
0
0
2
2
0
0
1
0
0
0
0
2
1
1
0
1
1
1
0
2
1
0
1
0
1
4
0
2
1
2
0
1
1
1
0
0
0
1
0
0
0
2
1
0
0
1
2
0
1
0
0
1
0
0
1
1
1
0
2
0
1
2
0
1
1
1
0
0
2
0
1
0
1
0
2
0
2
0
1
0
0
0
1
0
0
0
1
2
0
2
2
0
1
1
0
1
2
0
0
0
0
0
1
0
0
1
1
0
1
2
2
0
1
1
2
2
1
2
1
0
0
1
0
1
1
0
2
1
0
0
1
1
1
2
2
1
0
0
1
1
0
2
1
5
2
1
0
1
0
4
0
0
0
0
1
0
1
0
0
0
2
1
1
0
1
0
0
2
1
1
0
1
0
0
0
0
0
2
1
1
0
1
0
0
0
2
1
0
1
0
0
1
2
0
0
1
2
0
0
1
0
1
1
0
2
0
0
0
2
0
0
1
2
2
0
0
0
2
0
1
2
0
0
1
2
0
0
0
1
1
2
0
0
3
0
0
1
0
1
0
0
0
0
0
2
3
1
0
0
3
1
0
1
0
0
0
1
2
0
0
0
1
1
0
0
1
0
0
1
1
0
0
0
1
0
3
2
2
2
2
0
1
0
0
0
0
1
0
1
1
1
0
0
2
1
2
0
0
2
0
1
2
0
0
0
1
0
2
0
0
0
2
2
0
0
1
2
1
2
0
0
2
1
0
1
0
0
2
1
0
0
1
1
0
0
2
0
1
0
2
0
2
0
0
0
0
1
0
0
1
1
0
0
2
0
0
0
2
1
1
0
2
0
0
1
2
0
1
0
0
1
0
1
1
0
0
0
1
1
3
0
1
1
0
0
0
0
1
1
2
2
2
1
0
0
0
0
1
1
0
0
2
1
2
0
0
1
1
1
0
1
2
1
0
0
2
0
0
1
1
0
0
0
1
2
1
0
0
0
2
0
0
0
1
1
0
0
0
0
0
1
0
2
1
2
1
0
0
1
0
0
0
0
1
0
1
2
1
0
0
1
1
2
0
2
1
0
1
2
2
0
0
1
0
0
0
2
1
0
1
0
0
1
1
0
0
1
0
0
1
3
0
0
2
0
1
0
1
2
1
1
0
0
1
0
1
1
0
0
1
0
2
0
1
1
2
0
1
0
1
1
0
1
1
1
0
2
1
0
0
0
2
0
0
2
1
1
2
1
2
1
1
1
1
0
1
3
0
1
0
0
0
1
2
0
0
2
7
0
0
0
2
0
0
0
0
1
0
0
1
2
0
1
1
0
0
0
0
0
0
0
2
0
0
0
1
0
2
1
2
0
1
0
2
0
1
1
0
2
0
1
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
1
1
0
0
2
0
1
1
1
0
2
1
0
0
1
2
1
1
1
0
0
0
2
0
2
2
0
1
2
1
2
0
0
0
0
1
1
0
1
0
1
1
0
1
1
0
1
0
2
1
0
1
0
0
0
0
2
0
0
2
0
0
1
1
0
1
1
1
2
1
1
1
2
1
0
0
0
1
1
0
0
1
0
1
0
1
0
3
0
1
1
2
2
2
1
2
2
1
0
0
1
2
0
1
2
1
0
2
1
2
0
1
2
1
1
2
1
1
2
0
0
1
0
0
1
1
1
2
1
0
0
1
1
1
0
1
3
1
0
1
0
0
1
1
2
1
1
3
0
1
2
2
0
1
1
0
2
0
2
1
1
2
1
1
0
0
1
0
1
0
0
2
3
2
0
0
1
1
0
0
1
1
0
0
1
1
1
1
2
1
0
2
0
2
2
1
2
1
1
0
0
1
1
0
1
0
0
0
2
1
1
1
0
0
2
1
1
0
0
0
0
0
0
0
1
1
2
2
2
0
0
0
1
0
0
2
1
0
0
2
0
0
0
1
0
2
3
0
2
1
0
0
0
1
2
0
0
1
0
1
0
2
0
0
2
0
2
2
2
0
0
1
1
0
0
0
0
2
1
1
2
0
1
1
1
0
0
2
2
1
1
1
2
0
2
1
1
1
2
0
6
1
0
3
2
0
1
0
2
0
2
0
0
0
1
2
1
2
0
0
2
1
2
1
1
4
1
0
2
0
1
0
0
0
2
0
2
0
1
0
1
0
1
0
1
2
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
2
0
1
0
1
1
1
1
0
2
1
1
2
0
1
3
1
0
1
2
2
0
0
0
1
1
0
0
2
1
0
1
1
2
0
0
0
0
2
1
2
0
2
1
0
2
2
2
1
0
0
1
0
2
0
1
0
2
0
0
2
0
1
0
2
0
0
1
1
0
1
1
0
1
0
0
1
0
2
0
0
1
0
1
2
0
1
0
1
1
0
1
0
1
1
0
1
0
1
1
0
0
0
1
0
2
3
1
1
1
2
2
1
1
1
0
2
0
1
0
0
1
0
1
2
1
0
1
1
1
1
2
2
1
0
1
0
0
0
0
0
1
1
1
2
0
1
1
1
4
0
0
0
2
5
0
1
0
1
0
2
2
0
1
0
0
0
0
2
0
1
0
1
0
0
1
2
0
2
2
0
0
1
1
2
0
0
1
1
1
0
1
1
1
2
0
1
0
1
2
0
2
0
2
1
0
2
0
0
0
1
1
2
2
0
0
1
1
2
1
2
1
0
1
1
2
1
3
0
0
2
0
1
0
1
0
2
2
0
1
0
1
4
1
2
2
0
1
2
4
1
0
2
2
1
0
0
0
1
2
2
0
1
0
0
0
1
0
1
0
2
0
2
0
0
1
0
2
0
0
0
0
2
2
1
0
0
1
2
0
1
1
0
2
1
1
1
0
0
0
0
0
0
1
1
0
0
0
1
0
1
2
0
1
1
1
1
2
1
0
0
1
0
0
2
1
2
1
0
1
0
2
0
2
0
2
0
0
2
0
1
0
1
1
0
2
0
0
2
2
0
0
0
1
0
2
0
0
0
0
1
1
1
2
0
0
1
0
0
1
0
3
0
2
0
2
0
0
1
2
0
0
1
2
0
0
0
2
1
0
1
1
2
0
0
1
0
2
0
1
1
2
0
1
1
1
1
0
0
0
1
1
0
0
1
0
1
2
0
0
0
1
0
0
0
1
0
1
1
2
1
0
0
0
0
2
0
0
0
2
0
0
1
2
0
0
0
1
0
1
2
0
2
2
2
2
2
0
1
0
1
0
1
0
0
1
0
2
0
1
1
0
2
2
1
0
1
1
0
2
1
1
2
3
1
1
1
0
2
0
2
1
2
1
1
1
1
2
0
2
0
1
0
0
1
0
1
1
0
2
0
2
1
3
0
2
0
0
1
0
0
1
0
0
1
2
1
0
2
0
2
0
1
2
0
1
1
0
0
0
1
2
2
2
0
1
2
2
1
1
2
1
1
2
2
1
1
0
2
0
0
2
2
0
3
0
1
1
0
0
1
1
2
1
1
1
0
0
3
3
1
0
2
0
0
0
1
1
2
1
2
2
1
0
0
2
1
2
0
1
2
1
0
0
0
1
3
2
0
2
0
1
0
0
0
0
0
0
7
2
1
1
2
1
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
1
0
2
1
0
0
1
1
0
1
0
2
2
0
1
2
0
2
0
0
0
0
1
2
1
1
1
0
0
0
0
1
0
1
0
1
1
0
1
0
0
0
0
1
0
1
1
1
0
3
1
2
0
0
0
2
0
0
0
0
2
1
1
1
1
0
0
1
0
0
2
1
0
2
1
0
0
0
2
1
0
2
0
0
1
0
2
1
2
0
0
0
1
0
2
0
1
0
1
0
1
2
0
0
1
0
0
0
2
0
2
0
2
2
1
0
0
0
0
1
1
0
0
1
2
2
0
0
0
0
1
0
1
0
0
0
1
1
3
0
0
1
0
1
1
0
1
0
1
2
1
0
1
2
1
0
2
2
2
0
0
0
2
2
0
2
0
2
1
0
0
2
1
0
1
0
2
1
0
0
0
1
1
2
2
1
2
2
1
0
0
1
0
0
2
1
1
1
0
0
0
0
1
2
1
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
2
0
2
0
1
0
2
1
3
0
0
3
4
0
2
1
0
2
1
2
0
2
2
2
0
0
2
2
0
2
0
0
0
1
0
1
1
0
3
2
1
0
1
4
0
1
2
0
1
0
0
1
2
0
0
1
0
0
1
1
1
0
0
2
2
0
1
1
0
1
0
2
1
0
2
0
3
0
0
2
0
1
1
0
2
1
1
1
1
2
0
1
0
0
2
0
0
1
1
1
0
2
3
1
0
0
1
0
0
0
2
1
1
1
0
0
1
0
0
1
1
0
0
0
0
1
2
2
2
1
0
1
0
0
0
1
2
3
1
0
0
0
2
0
2
0
1
1
0
1
2
2
0
1
1
1
0
0
1
0
1
0
3
1
0
0
2
2
2
0
2
1
0
1
0
0
2
0
0
1
2
1
0
1
2
2
1
0
0
0
2
1
0
1
0
1
1
0
1
2
1
1
0
0
1
0
2
1
2
0
0
1
0
2
0
0
1
1
1
0
0
0
0
0
2
0
0
0
1
2
2
0
1
2
2
1
0
0
1
2
2
0
2
0
0
0
2
0
2
2
1
0
2
2
0
0
1
1
0
1
0
1
2
0
1
2
2
1
0
3
0
0
0
0
3
0
0
0
0
1
0
2
0
2
1
1
0
0
0
1
2
2
0
1
1
2
1
2
2
1
0
1
1
0
1
1
2
0
1
1
0
4
0
2
1
2
1
0
2
1
2
0
1
0
0
0
0
1
1
1
1
0
1
1
0
2
0
2
0
0
1
0
2
1
1
0
0
1
1
1
2
1
2
0
2
0
0
0
2
1
1
2
0
2
2
1
0
1
2
0
0
0
0
1
1
1
1
0
1
9
1
0
0
0
1
0
2
1
2
0
0
1
0
1
0
3
0
2
0
0
1
0
1
2
2
1
1
1
0
0
2
0
1
2
2
0
2
1
0
3
1
1
0
0
1
1
2
0
2
0
0
2
0
1
0
0
3
0
1
2
4
2
0
0
0
1
2
0
0
0
1
1
2
0
1
0
2
1
1
0
0
1
0
2
0
0
0
0
0
0
1
1
0
0
1
1
2
0
0
2
1
5
0
0
0
0
0
2
0
1
1
2
1
1
2
2
1
0
2
1
0
1
1
0
0
0
1
0
1
0
2
1
1
0
0
0
1
0
2
0
0
2
2
1
0
0
1
2
1
0
1
0
0
1
0
0
2
2
0
0
2
2
2
0
1
1
0
1
1
4
0
0
0
1
0
0
1
1
1
0
0
1
0
0
0
1
0
1
2
1
0
1
0
0
0
0
0
0
1
1
1
0
1
2
0
2
1
1
1
0
1
2
2
0
2
1
0
0
2
0
1
1
1
0
0
1
1
2
0
0
2
0
0
1
2
2
0
2
0
0
0
0
2
0
0
2
1
1
0
1
1
2
0
0
0
0
2
2
1
1
1
2
0
2
2
1
0
2
2
0
0
1
1
0
2
0
2
0
0
0
0
0
0
0
1
0
1
1
1
0
3
0
0
2
0
2
1
2
0
1
0
1
0
0
0
1
0
0
0
0
2
0
2
0
2
2
0
1
1
0
1
2
0
0
0
1
2
0
0
2
2
0
0
2
0
1
2
0
2
1
2
2
2
4
0
1
2
1
0
2
0
0
0
0
2
0
1
0
0
0
0
2
0
0
2
1
2
1
2
0
0
0
0
0
2
1
2
0
1
1
0
0
0
1
2
0
0
0
2
1
2
1
1
2
2
1
0
1
0
0
2
1
0
0
2
0
0
2
1
0
1
2
1
2
1
0
2
2
0
3
1
1
0
1
0
0
1
1
0
1
0
0
2
1
1
1
0
2
2
0
2
1
1
0
1
1
1
3
0
0
0
1
0
1
2
0
1
0
2
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
2
0
1
1
1
0
0
1
3
2
0
0
1
0
0
0
0
1
1
0
2
1
2
0
0
1
2
2
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
1
0
0
1
0
0
0
0
0
1
2
0
1
0
2
0
1
1
0
2
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
2
2
0
1
0
0
2
0
0
0
1
0
2
2
1
0
1
0
0
0
0
0
2
0
1
2
1
0
0
2
0
0
0
0
2
3
0
2
0
0
0
0
1
3
1
0
0
1
1
1
0
0
1
2
1
1
1
0
0
0
0
1
0
1
1
0
1
0
2
1
3
0
0
1
1
0
1
0
0
1
0
1
0
0
0
1
2
0
1
2
0
0
0
0
1
3
0
2
2
0
2
0
0
0
0
2
2
0
1
0
1
0
1
0
2
2
0
0
1
0
0
0
1
0
1
0
0
1
1
0
1
3
0
0
0
1
1
1
1
2
0
0
0
0
1
1
1
1
0
2
0
0
0
1
0
0
1
0
1
1
0
0
1
0
0
2
0
1
1
0
2
2
1
0
0
1
1
0
0
0
0
1
1
0
0
2
2
1
2
1
0
1
0
0
2
0
1
2
0
0
1
0
0
2
0
0
0
2
1
2
2
0
0
2
0
0
0
0
0
0
2
1
2
0
0
0
0
1
0
0
0
1
2
0
0
1
1
2
0
1
2
1
0
0
2
1
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
2
1
2
0
0
0
0
0
1
0
0
2
0
1
2
2
1
2
2
1
2
2
1
0
1
0
1
7
2
0
0
1
1
2
0
1
0
1
1
2
1
2
0
0
0
1
0
0
1
1
0
0
2
0
0
1
1
0
0
0
0
0
1
1
0
0
2
0
0
0
1
0
2
1
0
2
0
1
0
0
2
0
0
0
0
1
0
0
0
1
2
1
2
1
1
0
1
0
0
2
0
1
0
1
1
0
0
1
1
1
2
2
1
2
1
1
2
0
1
0
0
0
0
1
0
1
2
0
0
2
0
0
1
1
0
0
1
1
0
2
1
1
0
1
2
0
0
1
1
0
0
0
1
2
2
0
0
0
1
1
0
0
1
0
1
0
1
0
1
2
2
0
1
0
1
0
2
0
0
0
2
0
0
0
0
2
1
0
0
1
0
0
0
1
3
0
2
1
1
2
0
1
1
0
2
0
1
2
2
2
1
1
2
2
0
0
1
2
0
0
1
2
1
1
2
0
0
1
0
0
1
0
0
0
0
1
2
1
0
1
1
1
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
1
1
1
1
1
0
1
2
2
0
1
2
2
6
1
1
0
0
0
2
2
2
1
0
2
0
1
2
0
1
0
0
1
0
2
2
2
0
0
1
0
0
0
0
2
2
1
0
0
0
1
0
0
1
0
2
1
1
2
1
1
0
0
1
1
2
1
1
2
0
2
4
3
0
1
1
1
1
1
1
0
0
0
2
1
2
5
0
0
0
1
2
0
1
0
1
1
0
1
0
1
1
0
1
0
1
1
1
1
0
1
0
1
0
1
4
0
0
0
2
1
1
2
1
1
1
0
1
2
1
2
0
2
1
1
2
0
2
1
0
2
0
1
1
2
0
2
0
0
0
0
0
1
2
1
0
1
0
0
0
2
1
0
0
2
1
1
0
0
2
1
0
0
1
1
1
2
2
0
2
2
0
2
1
2
0
1
0
1
0
0
0
0
1
0
2
0
0
0
0
0
2
1
2
0
0
1
2
0
2
0
0
2
1
0
0
1
0
1
1
0
0
0
0
2
0
0
0
0
3
2
1
0
2
1
2
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
2
1
0
0
2
0
1
0
0
1
1
0
2
0
1
0
0
1
0
1
1
2
0
1
0
0
1
0
1
0
2
1
0
2
2
1
0
1
1
1
0
2
2
1
0
2
0
0
0
1
0
2
1
1
1
2
0
3
0
2
0
0
1
0
1
2
0
0
0
2
1
1
1
0
0
0
1
2
0
2
1
0
1
0
1
1
0
1
1
1
1
1
1
0
1
1
0
2
1
0
0
0
0
0
1
1
0
0
0
2
0
1
0
0
2
2
0
1
4
0
0
0
1
0
0
2
0
1
0
1
2
0
0
2
1
0
0
0
1
2
0
0
0
0
1
2
2
0
1
1
0
0
0
2
0
1
2
1
0
1
0
0
2
0
0
0
0
2
0
0
1
0
0
1
2
0
0
0
1
1
2
2
3
1
1
0
0
0
0
1
2
0
0
2
1
0
0
0
0
1
1
0
2
0
0
1
1
0
0
1
1
1
1
1
0
0
2
0
1
0
1
1
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
1
2
0
1
0
2
0
0
2
0
0
0
3
0
1
2
2
0
1
0
1
1
2
1
1
1
1
1
1
0
0
1
0
1
0
0
1
1
0
1
0
1
1
1
1
1
0
0
2
1
2
0
1
1
2
0
0
1
1
2
0
2
2
1
0
2
0
0
2
1
2
1
0
0
0
2
0
0
2
2
3
2
2
1
1
1
0
0
0
0
0
1
1
0
0
1
5
0
0
0
2
2
0
0
2
1
0
1
0
1
1
2
1
0
0
0
1
0
0
0
0
0
0
2
2
2
0
0
2
1
1
2
1
1
0
2
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
2
0
1
1
1
0
1
2
0
0
0
0
0
0
0
1
1
1
1
4
1
2
0
1
0
0
0
1
2
0
2
0
2
1
1
1
2
1
0
2
1
0
4
0
2
1
1
0
2
1
3
1
0
0
0
0
3
0
2
0
2
1
2
0
1
1
1
0
2
1
0
0
1
1
2
1
1
1
0
0
0
0
0
1
1
1
0
0
0
0
0
1
2
0
0
0
1
0
1
2
2
0
0
1
2
1
0
0
2
1
0
1
0
1
0
0
2
1
0
1
0
0
0
0
1
0
0
2
1
0
3
0
1
0
1
0
0
2
1
0
2
1
0
0
1
1
0
0
1
1
2
1
0
0
0
2
0
0
1
2
2
1
0
1
2
1
1
0
2
0
0
1
3
0
1
1
1
1
1
0
1
0
0
1
2
1
0
1
1
0
1
2
0
1
1
0
0
0
0
1
0
0
2
2
1
0
1
2
1
1
2
0
0
2
2
1
1
1
2
1
0
0
1
1
2
0
0
0
1
0
1
1
1
2
0
1
1
0
0
0
1
0
1
1
0
0
0
1
0
0
0
1
0
1
2
1
0
2
0
0
1
1
0
0
0
0
2
1
0
0
2
1
0
1
0
0
2
1
0
2
2
1
2
1
0
0
2
1
3
0
0
1
0
2
1
0
0
0
0
1
0
1
0
1
0
0
2
0
1
0
0
1
1
1
1
0
1
0
2
1
2
0
1
0
2
0
0
2
1
1
1
0
1
1
1
0
1
0
2
0
1
0
2
0
1
3
0
0
0
1
1
2
0
1
1
2
0
0
0
2
2
2
0
0
0
0
0
1
0
0
1
1
0
2
0
2
1
1
3
2
0
1
0
0
0
0
1
1
1
0
0
0
1
2
1
2
2
1
2
3
0
3
1
0
1
0
2
2
2
0
1
2
1
2
1
2
1
0
0
0
0
0
0
1
2
1
1
0
0
1
2
1
1
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
1
0
3
1
0
0
0
1
0
0
0
0
1
0
0
0
2
0
1
2
0
2
1
0
0
0
2
1
1
0
1
1
0
0
0
0
0
1
1
3
0
1
2
0
2
1
1
2
0
0
2
1
0
1
1
0
1
0
0
2
0
0
3
0
0
0
0
0
0
2
1
0
1
1
0
1
0
0
0
0
1
0
1
1
0
2
2
0
2
0
1
2
1
0
1
0
0
0
1
1
2
0
2
2
0
1
1
1
0
0
0
0
0
0
1
1
1
0
1
1
2
1
2
0
0
0
2
0
0
0
0
0
0
1
2
0
2
0
2
0
0
1
0
0
1
0
1
2
2
0
2
1
0
1
2
2
1
0
0
1
0
2
0
1
2
1
1
0
1
2
0
0
0
2
2
0
0
2
1
0
0
0
0
1
0
1
1
0
1
0
1
1
0
0
1
0
0
2
2
0
2
0
0
0
0
1
2
0
1
0
0
0
0
1
0
0
1
2
0
0
1
0
1
2
0
0
0
1
1
1
1
0
0
1
0
2
2
1
2
0
0
0
0
0
1
2
0
2
0
1
2
0
1
0
0
2
2
2
1
0
0
1
0
1
0
0
1
0
0
1
1
1
0
0
0
0
2
0
0
0
0
0
1
1
0
0
1
1
0
0
2
0
1
1
0
2
1
0
1
0
2
0
0
1
1
1
1
0
1
0
1
0
1
0
1
1
0
1
1
0
0
0
0
0
2
0
0
0
0
0
1
2
0
2
0
2
1
0
0
0
1
0
1
0
2
0
0
1
1
1
1
2
2
0
1
0
1
2
1
1
0
0
0
0
2
0
0
1
0
0
1
1
0
0
1
0
0
1
0
0
2
1
2
1
2
0
1
1
2
0
0
0
2
2
1
0
0
2
0
0
2
0
0
0
0
0
1
0
0
3
0
2
0
0
0
0
1
0
0
0
0
2
0
0
2
1
0
0
0
2
0
0
0
0
2
1
1
2
0
3
0
0
0
0
1
2
1
0
1
1
0
0
2
2
0
2
0
2
0
1
1
0
1
1
1
0
0
0
0
0
0
0
0
0
2
0
1
1
2
2
0
1
0
2
1
0
0
1
2
2
0
0
2
0
2
0
0
1
0
2
0
2
0
1
1
0
0
0
0
0
1
4
1
1
0
1
0
0
0
2
1
0
0
2
1
0
1
0
1
1
1
0
1
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
2
2
2
0
0
0
1
0
0
0
0
1
0
0
2
2
1
0
2
0
10
0
0
1
0
1
0
1
0
2
0
0
1
2
1
1
0
0
0
0
2
1
1
1
1
0
2
1
0
0
1
0
0
1
2
2
2
1
1
0
2
0
1
1
0
2
0
0
1
0
3
0
0
0
0
0
1
2
1
0
0
0
1
2
0
2
0
0
0
2
1
0
0
2
0
1
1
2
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
1
1
0
1
2
2
1
2
1
1
2
1
0
0
1
1
2
0
0
0
0
1
0
0
2
2
0
0
0
2
2
2
0
0
0
0
0
2
1
0
2
1
0
1
2
0
3
0
0
0
0
2
1
0
1
0
2
1
2
0
2
1
0
0
2
0
0
3
1
0
0
0
0
1
1
0
0
0
1
1
2
1
0
2
0
2
1
0
1
2
1
0
2
0
2
1
1
1
0
0
0
2
2
1
1
2
0
0
3
1
2
0
2
1
0
2
2
2
0
0
0
2
1
2
1
2
1
2
0
0
0
2
0
1
0
0
2
0
0
0
0
1
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
1
0
0
1
2
1
1
1
0
1
1
0
0
0
1
1
0
2
2
0
1
0
0
0
1
0
1
0
0
1
0
2
0
1
0
2
0
0
0
2
1
0
1
1
1
2
0
0
1
1
0
0
1
0
1
0
0
0
0
1
0
0
2
2
2
1
1
2
0
0
2
1
0
0
0
1
0
1
2
2
0
0
0
0
1
2
0
2
0
0
1
0
1
1
2
0
1
0
0
1
0
0
1
0
1
0
1
0
1
2
1
2
1
0
0
0
1
0
0
1
2
1
0
2
0
1
1
1
0
2
1
0
1
0
0
0
0
0
0
1
0
0
0
1
2
1
2
0
0
1
0
0
2
1
2
1
0
0
0
0
2
2
0
0
1
1
0
1
1
1
1
0
0
1
1
1
1
1
3
0
1
1
1
1
0
0
1
0
1
1
2
1
1
0
2
0
0
2
2
2
1
1
0
0
2
1
0
0
0
0
0
1
0
1
1
1
0
1
1
1
0
1
1
0
2
1
1
1
0
0
5
0
1
0
2
1
0
2
0
2
1
1
1
0
1
0
1
2
1
1
0
1
0
0
2
0
0
1
0
0
0
0
1
2
0
2
1
1
1
1
0
2
0
0
1
0
3
0
0
2
4
0
1
0
0
0
1
1
0
1
1
0
2
2
0
0
1
0
0
0
0
0
1
2
0
0
1
0
2
1
0
0
0
1
1
2
1
0
0
2
1
0
0
1
1
1
0
0
0
1
1
2
1
0
1
2
1
1
0
0
2
0
0
1
1
0
1
2
0
2
0
0
1
0
1
0
1
1
0
1
2
2
1
0
1
0
1
2
1
0
0
2
2
1
1
1
2
0
2
1
2
1
2
0
0
1
0
1
0
1
0
0
0
3
0
0
0
1
1
2
0
0
1
1
1
0
0
1
2
0
0
1
1
1
0
0
2
2
0
0
0
1
1
0
0
2
2
0
2
2
1
0
1
4
1
2
1
2
0
0
1
2
2
2
2
2
0
0
1
2
1
0
0
2
2
0
0
2
1
1
0
0
1
1
0
1
0
0
0
0
1
2
1
0
0
1
0
1
0
0
0
1
2
0
0
1
1
1
1
0
1
1
2
2
1
15
0
0
0
0
1
0
0
2
1
0
0
0
0
2
2
0
0
0
1
2
0
0
1
0
1
0
1
1
2
2
1
0
0
2
2
0
2
0
1
0
1
0
1
1
1
1
0
0
0
0
1
1
0
0
2
1
0
0
0
0
1
0
2
0
1
0
0
2
0
0
1
2
0
1
0
3
0
0
1
0
2
0
0
1
1
0
1
2
0
0
0
0
3
1
2
0
0
0
0
1
2
2
1
2
1
1
2
3
1
0
4
1
0
0
1
1
1
0
0
2
1
2
0
0
0
1
0
1
0
0
1
0
0
0
2
0
1
1
0
0
0
1
0
2
0
0
0
0
0
0
0
2
2
2
0
2
2
1
1
2
1
1
2
1
1
1
2
0
2
2
2
0
2
2
0
1
1
0
0
2
1
2
1
1
1
1
0
0
0
2
1
0
0
2
0
1
2
1
1
1
2
0
0
2
2
0
2
2
0
0
0
1
1
1
1
2
1
0
2
1
0
0
0
0
0
1
2
1
1
0
1
2
2
0
1
0
0
3
0
0
0
0
0
0
0
1
1
1
1
2
0
0
0
1
0
2
0
0
2
0
0
0
1
0
1
0
2
0
0
0
0
0
2
1
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
1
1
0
2
1
0
2
0
1
0
2
0
1
1
2
3
0
1
1
2
0
0
0
1
0
0
1
2
0
0
2
0
0
1
2
0
1
0
0
0
1
2
1
0
0
2
1
1
0
2
0
0
0
1
2
0
1
2
0
0
0
2
1
1
1
0
0
3
0
3
4
0
1
2
1
0
1
0
1
0
0
0
0
0
2
2
2
0
2
0
0
2
0
1
2
2
0
0
0
2
1
1
0
0
0
0
1
1
0
0
0
0
1
0
0
6
2
0
0
1
1
1
0
0
1
1
0
1
0
2
0
2
1
1
2
1
2
1
1
1
0
0
0
0
0
2
0
0
0
1
0
1
1
1
2
0
1
0
0
2
1
0
1
0
2
0
0
1
0
1
1
1
0
2
0
0
1
2
1
0
2
2
0
0
0
1
2
0
0
2
2
0
3
0
0
1
0
1
0
2
0
0
0
0
1
0
0
0
1
1
2
1
1
0
1
0
1
1
0
0
1
2
1
0
0
1
0
1
0
1
1
1
3
0
1
1
0
1
2
0
2
0
0
0
0
2
1
1
0
0
1
0
0
0
0
1
0
0
0
1
2
0
1
2
0
1
0
0
2
1
0
1
2
0
0
0
1
1
1
2
0
1
0
0
0
1
0
0
1
1
2
0
2
0
2
2
1
2
1
2
0
2
2
1
0
1
3
0
1
0
2
2
1
0
2
3
0
1
1
0
1
0
2
0
0
3
2
0
1
0
2
0
0
1
1
0
1
2
0
2
0
0
0
0
0
2
2
1
0
1
0
1
0
0
1
1
0
1
0
0
1
1
1
0
0
0
2
0
0
0
1
0
0
0
1
0
2
1
0
2
0
3
2
0
0
1
1
0
0
1
1
0
0
1
1
0
0
1
1
0
1
0
2
1
1
1
0
2
1
1
0
0
1
1
1
1
0
0
0
0
0
0
0
3
0
1
2
0
2
0
2
0
1
0
1
0
2
0
1
1
0
0
2
1
0
0
0
2
0
2
0
1
1
0
2
0
0
2
1
1
1
0
2
2
0
0
2
1
1
0
2
1
2
0
1
1
1
3
0
0
1
0
2
0
0
2
0
2
1
0
2
1
0
0
1
0
1
0
1
2
2
0
1
1
0
1
0
2
2
2
1
1
0
1
0
0
0
1
0
2
0
2
1
0
2
2
0
0
1
0
2
1
0
7
1
0
1
0
0
1
1
0
1
1
1
3
0
0
0
0
1
0
0
2
2
2
1
2
1
2
2
0
0
2
1
2
0
1
0
0
0
2
0
1
1
0
0
0
2
2
0
0
2
0
0
0
1
2
0
1
1
0
0
0
0
1
0
0
2
0
0
0
1
1
0
0
0
0
1
1
1
2
1
2
2
1
1
0
0
0
2
0
2
1
0
1
0
1
1
1
1
0
1
0
0
1
1
1
0
1
0
0
0
2
0
1
1
2
0
1
0
1
2
1
2
0
0
0
0
0
0
0
1
4
0
0
0
1
2
1
0
0
0
0
1
0
2
0
1
2
2
1
2
0
1
0
1
0
2
1
0
2
1
2
1
0
0
1
1
1
2
0
1
2
2
2
0
1
1
0
0
0
2
2
0
1
0
2
0
1
0
2
0
0
2
1
0
0
4
0
0
0
0
1
1
2
0
1
0
2
2
2
2
0
1
1
2
1
0
2
1
2
0
0
2
1
1
0
0
1
2
2
2
1
1
1
0
2
0
1
0
1
1
0
2
1
0
0
2
0
1
1
0
1
2
1
1
0
2
0
2
2
0
0
0
1
1
2
0
0
0
1
0
0
1
0
0
0
0
2
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
2
1
1
2
1
3
1
2
2
2
0
0
0
1
0
0
0
2
0
0
1
3
0
2
1
0
2
1
2
0
0
1
0
0
2
1
1
0
0
2
1
0
1
2
1
0
0
1
0
0
2
0
1
1
0
0
0
0
2
1
0
1
1
1
2
3
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
2
1
0
2
0
0
0
1
2
1
1
1
0
0
1
0
0
0
1
0
0
2
0
1
0
0
1
0
0
1
1
0
0
0
1
0
1
0
0
1
0
1
2
2
5
0
2
0
1
1
2
0
0
1
0
1
1
0
0
1
0
1
0
0
0
0
1
1
1
1
0
2
0
2
0
2
2
0
2
2
1
1
2
0
2
0
1
2
0
0
0
2
0
2
0
2
0
0
2
1
0
0
0
1
0
2
1
0
1
0
1
2
2
0
6
0
0
0
2
1
1
0
2
0
1
1
3
0
0
0
1
0
0
1
2
1
1
0
1
0
1
2
1
0
2
2
2
0
0
0
1
0
0
2
2
1
2
1
0
1
0
0
2
2
0
2
2
0
1
1
0
0
0
0
2
1
0
0
1
0
1
1
1
0
1
1
0
0
1
0
0
1
1
0
0
1
2
1
2
0
0
2
1
1
1
2
0
0
0
0
2
0
1
1
2
0
0
1
0
0
0
1
1
2
1
1
1
2
1
0
0
2
2
1
1
0
1
1
1
1
1
1
2
1
2
2
1
2
0
2
0
0
0
0
1
0
0
1
1
1
0
0
1
1
0
0
1
0
1
1
0
1
0
0
0
1
2
0
0
0
0
1
0
0
1
0
2
1
2
0
2
0
1
1
1
0
1
2
0
1
0
1
0
0
1
0
0
2
1
1
1
0
2
1
1
0
0
1
0
1
2
1
1
0
0
0
0
0
1
0
0
0
0
4
2
0
0
0
0
1
0
1
0
0
0
2
0
2
2
2
3
0
1
1
0
0
0
1
2
1
1
0
1
1
2
2
0
1
0
3
2
0
2
0
1
0
0
0
1
1
1
0
1
4
1
0
0
2
0
1
1
1
0
2
0
0
2
1
2
0
2
0
0
0
0
0
0
0
1
1
0
1
1
0
1
0
0
0
0
0
2
1
0
1
2
1
1
0
2
2
1
0
0
1
1
0
0
0
0
0
0
1
0
0
2
0
1
1
1
1
0
2
1
1
1
0
1
0
1
0
1
1
0
0
1
1
2
1
2
1
2
0
0
0
1
0
0
0
2
0
2
1
0
1
1
0
0
1
0
0
1
2
1
0
1
1
1
1
1
0
1
0
2
2
1
0
1
1
1
3
0
0
0
1
1
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
3
1
1
1
2
2
1
0
1
0
0
0
1
0
2
0
1
0
0
0
2
1
0
0
0
0
0
0
1
1
0
3
1
1
2
0
1
0
0
0
0
0
0
2
0
1
0
0
1
0
0
1
0
0
1
2
0
2
2
1
2
0
2
2
2
0
0
0
2
2
1
0
1
1
1
0
0
3
0
1
0
1
0
1
0
2
2
2
1
1
1
1
0
2
1
2
1
0
0
1
1
2
2
1
2
1
3
2
0
0
0
2
1
1
0
2
0
0
2
0
2
2
2
2
0
0
1
0
0
0
1
1
0
1
0
1
0
0
1
2
1
0
0
0
1
1
1
2
0
1
0
1
0
2
0
1
1
0
1
0
0
1
0
0
1
0
0
0
0
3
2
1
1
1
0
0
2
1
0
0
0
0
2
2
0
1
2
0
1
0
2
0
2
0
1
2
0
2
2
1
1
1
0
0
0
2
0
1
0
0
2
1
1
1
1
1
0
0
0
1
2
2
2
1
0
0
1
1
1
1
2
1
3
2
1
0
0
0
0
0
0
0
1
1
1
2
2
2
0
0
0
1
1
0
2
0
2
2
0
2
0
1
1
1
1
0
0
1
2
0
1
0
2
0
3
0
0
1
0
0
2
2
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
2
1
0
0
0
1
1
2
2
0
1
0
2
2
0
2
1
1
0
0
2
1
1
0
0
1
0
0
1
1
1
0
1
0
1
0
1
0
0
2
0
0
0
0
0
0
2
2
0
0
0
2
0
0
1
2
1
0
1
1
1
0
2
1
0
0
1
1
1
0
1
1
2
0
2
2
1
0
2
0
0
2
2
2
2
0
0
1
0
0
0
1
0
2
1
2
0
1
2
1
0
0
2
0
1
1
0
0
0
0
1
2
0
2
2
0
0
0
0
0
0
2
1
2
1
1
1
0
0
2
1
0
0
2
1
2
0
1
1
0
2
0
1
1
3
0
0
0
0
2
1
0
1
1
1
0
2
2
0
0
1
1
2
2
0
0
0
0
1
2
0
0
1
0
1
0
0
0
2
1
0
1
1
0
3
0
2
1
0
5
0
1
1
1
1
1
2
0
0
2
0
2
1
0
0
1
2
0
1
1
0
0
3
0
2
0
0
1
1
0
2
3
2
0
0
0
0
0
1
1
1
1
1
2
0
1
2
0
0
2
1
1
2
0
0
0
3
1
0
2
0
1
2
0
2
1
0
2
1
0
1
1
1
0
2
2
1
1
0
0
1
2
0
0
0
7
1
1
0
1
0
0
2
1
0
0
0
0
1
2
0
2
0
0
0
0
1
1
2
1
1
0
2
1
1
0
1
0
0
2
1
2
0
0
0
1
0
0
0
0
1
2
1
0
1
1
2
2
0
1
1
0
1
2
2
1
0
1
2
0
0
0
1
1
1
2
2
1
2
1
0
1
2
1
1
0
1
0
0
0
0
1
0
1
1
1
0
1
1
0
2
2
1
1
0
1
0
1
2
1
0
1
0
1
2
0
2
2
1
3
0
0
0
2
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
1
2
1
0
2
0
1
0
1
2
0
1
0
1
0
1
1
0
0
0
1
2
0
0
1
1
0
1
0
0
1
1
1
1
2
0
0
3
1
0
0
0
0
1
0
2
0
0
1
0
1
0
1
1
1
0
1
0
0
0
0
1
1
2
0
1
1
1
0
1
1
1
0
1
1
5
1
0
0
2
0
2
0
0
2
1
1
1
0
0
2
0
0
2
1
1
0
1
2
0
0
0
0
1
0
1
0
0
0
2
0
1
0
3
1
0
0
0
0
0
1
1
1
2
0
0
0
0
1
0
1
0
1
1
0
0
2
1
0
3
0
0
1
0
2
1
0
0
1
0
1
1
1
0
0
2
0
0
0
2
0
0
2
1
1
0
0
0
0
1
3
0
0
1
0
1
0
0
1
1
0
1
1
0
1
2
0
1
1
0
0
2
0
2
0
1
0
0
1
1
2
0
0
0
0
0
1
1
1
1
1
0
0
0
0
1
1
0
0
1
0
0
1
2
1
0
1
0
2
0
2
0
1
1
1
1
2
2
2
2
0
1
1
1
2
0
2
0
1
2
3
2
1
1
1
1
1
2
2
2
0
0
2
1
1
0
1
1
0
0
3
2
0
0
2
0
1
0
2
1
0
0
1
0
0
0
0
2
1
0
0
0
2
0
2
0
2
0
0
2
1
0
1
2
2
2
1
0
2
1
0
1
1
1
1
0
1
1
1
2
4
1
2
0
1
1
1
3
0
2
1
1
0
0
0
1
0
0
2
2
2
0
1
1
1
1
2
0
2
1
1
0
0
1
2
0
1
2
2
1
1
0
1
0
3
1
1
1
2
0
1
0
1
0
1
0
2
0
1
0
0
1
2
1
0
1
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
2
0
0
0
1
0
2
1
2
0
1
0
1
0
0
1
0
2
1
0
2
1
0
1
0
0
1
2
2
0
0
0
2
1
1
1
1
0
0
0
2
0
0
0
2
1
1
1
0
0
0
0
1
0
0
3
1
0
1
0
1
0
0
0
2
0
2
1
0
1
2
1
0
1
0
0
0
2
0
0
1
1
0
0
0
2
2
2
0
0
2
0
2
0
1
0
3
2
0
0
1
1
1
1
1
0
2
0
0
1
0
0
1
2
0
0
1
1
0
0
1
0
1
0
0
0
0
1
1
2
2
1
2
4
2
2
0
1
2
0
1
1
0
1
1
0
1
2
0
3
1
0
1
1
0
2
2
0
2
2
1
2
2
1
0
0
3
2
2
2
0
0
1
0
0
0
0
2
2
0
0
1
0
2
1
0
0
1
1
0
1
2
1
0
1
1
2
1
0
1
0
0
1
2
2
2
0
2
0
0
2
1
0
0
2
0
1
0
0
2
0
0
1
1
0
0
0
0
1
1
0
2
0
1
0
2
0
0
0
0
1
0
2
1
1
0
1
2
0
1
0
3
2
1
0
0
0
2
1
0
1
0
2
1
0
0
0
1
1
1
1
1
0
1
2
0
0
0
0
0
0
0
2
0
2
0
3
0
1
0
0
2
0
1
0
2
0
0
0
2
2
1
0
0
4
2
1
2
1
0
0
1
1
1
1
2
0
0
1
1
1
2
1
2
1
0
0
1
2
0
0
2
0
1
0
1
0
1
1
0
0
2
0
1
1
2
0
1
0
1
1
2
1
0
2
0
2
1
1
2
2
1
0
1
0
0
1
0
4
0
2
0
0
1
1
0
0
0
1
2
2
0
1
0
1
0
0
2
2
2
0
2
1
2
1
1
1
1
0
1
1
1
0
1
0
0
0
0
1
2
1
2
2
2
1
2
1
0
0
0
1
2
0
1
0
0
1
0
2
0
1
0
0
1
2
1
1
2
0
1
2
0
0
1
0
3
1
1
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
1
1
1
0
1
2
1
0
1
2
2
2
0
1
3
0
1
0
0
3
1
3
2
0
1
0
1
0
0
0
0
1
0
0
2
0
2
1
3
1
2
1
2
2
2
1
0
0
1
1
2
1
2
1
1
2
2
2
0
0
1
0
2
1
1
0
1
1
0
0
0
1
0
2
0
1
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
1
1
1
1
1
0
0
1
0
2
1
1
0
2
1
1
0
1
0
2
0
0
0
0
0
2
0
1
2
0
1
2
1
1
1
1
2
2
0
2
0
0
0
2
2
2
0
1
1
0
0
0
1
0
0
3
0
0
0
2
1
2
0
1
0
0
2
1
0
0
1
1
0
0
0
0
2
0
1
0
0
2
1
1
1
1
0
1
2
0
2
1
1
0
2
2
0
0
0
1
0
2
0
1
0
0
2
1
2
0
0
1
0
1
0
0
0
1
0
0
0
0
1
2
1
0
1
0
1
0
2
2
0
0
1
0
1
1
0
2
1
0
0
0
1
1
1
2
0
4
1
0
2
0
0
1
2
0
0
1
2
0
0
0
1
1
0
1
0
2
4
1
1
1
1
0
2
0
1
0
0
0
0
1
1
2
0
1
0
0
0
2
0
0
1
0
2
2
2
2
1
0
0
0
1
0
3
0
1
1
0
0
1
2
1
1
0
3
2
0
1
1
0
2
1
0
0
2
0
0
1
2
0
0
1
2
1
0
1
1
0
0
0
0
0
1
0
1
1
2
0
1
0
2
0
0
0
0
3
0
1
0
0
2
1
1
1
0
1
0
2
1
3
1
2
0
2
0
0
2
1
2
0
1
0
0
0
0
0
2
3
0
2
0
1
0
0
0
0
0
2
0
1
2
1
2
1
2
0
2
1
1
2
1
0
0
1
0
0
0
1
1
0
0
2
1
2
1
0
0
2
0
0
1
0
2
1
0
0
1
0
1
1
0
0
0
2
0
0
1
1
2
2
1
1
1
0
2
1
0
1
0
1
1
4
1
2
3
1
2
0
0
0
0
3
0
0
0
0
0
2
2
1
2
0
0
0
0
2
1
0
0
0
0
1
1
0
1
2
1
1
1
0
2
2
0
1
1
1
1
0
1
0
2
1
0
2
2
0
0
0
0
2
1
2
0
0
2
0
1
0
1
0
2
2
0
0
1
2
2
1
2
3
0
0
0
0
0
2
2
1
2
1
0
2
0
0
1
1
2
0
0
0
0
0
0
0
1
0
1
1
1
1
1
0
1
1
0
0
1
0
0
0
1
1
0
1
0
0
2
0
0
1
0
1
1
2
1
2
0
1
0
1
0
0
1
2
0
0
0
0
2
0
0
2
2
1
1
1
1
1
1
2
0
1
0
2
1
1
6
0
1
0
1
1
1
1
0
1
1
0
0
1
1
1
0
0
1
2
0
0
1
1
1
0
0
0
2
0
3
1
0
1
2
1
0
0
2
0
0
1
0
0
2
1
0
1
0
0
2
0
0
0
2
2
1
1
1
2
1
0
1
0
0
0
0
2
2
2
0
0
1
2
1
2
1
0
0
0
0
1
1
0
1
1
0
0
0
0
0
1
2
1
2
1
1
0
0
1
0
0
2
1
1
1
1
0
0
1
1
0
0
0
2
1
1
2
2
2
0
1
0
1
0
2
2
1
2
0
0
1
0
1
0
1
2
1
1
0
1
2
1
1
1
2
1
0
1
2
1
2
0
0
1
0
0
1
0
0
1
2
2
0
1
0
0
0
1
1
0
2
0
0
1
0
0
1
2
0
1
1
0
1
0
1
2
0
0
1
1
0
1
0
2
0
1
0
0
0
2
0
0
0
0
1
1
0
1
1
0
0
0
2
2
2
0
0
0
1
0
0
0
0
2
1
0
0
2
0
1
0
0
2
1
1
0
2
1
0
0
0
0
2
0
0
0
0
1
0
1
1
2
2
2
2
0
1
0
4
1
2
1
2
1
2
0
1
0
2
1
0
0
0
1
1
0
1
1
2
1
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
1
2
2
1
0
2
1
1
1
1
0
1
2
0
0
0
0
1
1
2
1
0
1
0
1
1
0
0
0
1
0
1
1
1
1
1
2
2
1
0
1
1
1
1
2
1
1
2
2
1
1
0
1
0
0
2
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
1
0
1
2
2
2
3
2
0
2
1
1
1
1
2
2
0
0
0
1
1
0
1
0
0
1
0
0
2
0
0
0
0
2
0
1
1
0
0
0
2
1
0
2
1
0
2
1
1
0
0
0
0
0
1
0
4
0
1
1
0
0
0
0
0
0
0
1
0
2
0
1
1
1
3
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
5
2
0
0
1
0
0
2
2
1
0
1
1
2
0
0
1
0
1
0
1
1
0
1
1
1
3
1
0
0
1
1
1
1
1
2
1
2
0
1
1
0
0
2
0
0
1
1
2
2
2
1
1
0
0
1
0
0
0
0
2
0
0
0
0
2
1
0
0
1
2
1
1
0
1
0
2
0
0
0
2
0
0
0
1
1
0
0
1
0
1
1
1
0
0
0
0
1
0
1
0
1
0
2
0
0
1
1
0
2
0
0
2
0
0
0
1
1
2
0
0
0
1
0
0
0
1
1
0
0
1
2
0
2
0
1
0
2
1
1
0
0
1
0
1
0
1
0
4
0
1
2
2
0
1
2
0
0
0
2
0
1
0
2
0
2
0
0
1
0
2
0
0
1
2
1
1
2
0
0
0
0
0
2
0
0
0
2
2
2
1
2
1
2
1
1
2
1
1
2
2
2
0
1
2
2
1
0
2
2
4
0
0
0
0
1
2
1
2
1
0
2
0
1
0
2
2
1
1
0
2
0
1
0
0
1
2
2
2
0
0
1
1
2
1
2
2
0
0
2
0
1
0
1
1
0
1
2
0
2
1
1
2
1
0
0
2
1
0
2
2
3
0
1
0
1
1
0
0
2
1
1
0
1
2
1
3
1
1
0
0
1
1
0
0
1
1
1
0
1
1
0
0
0
2
1
2
2
2
1
1
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
2
1
0
0
2
2
0
2
1
1
0
1
0
2
0
0
2
2
0
0
0
0
2
0
1
0
1
1
1
0
1
2
0
2
0
0
2
1
2
0
0
0
0
0
2
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
1
1
0
1
1
2
1
0
0
0
0
0
0
0
1
1
0
0
2
1
1
0
2
0
1
1
0
1
0
0
0
1
1
1
0
1
1
0
0
0
2
2
0
0
1
0
0
1
0
2
1
0
1
1
1
1
1
0
0
0
0
2
0
2
1
1
1
2
1
2
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
2
1
0
1
0
0
0
1
2
0
0
1
2
0
2
0
0
2
1
0
1
0
1
2
0
0
2
1
0
2
1
2
1
2
0
1
1
1
0
1
0
1
0
0
0
2
1
0
0
2
2
0
0
2
2
0
2
2
0
1
2
0
1
2
1
1
1
1
1
0
2
0
1
0
0
0
1
0
1
1
0
0
0
0
1
1
1
4
0
0
1
2
2
1
1
2
1
2
0
0
0
0
1
2
1
0
0
0
0
2
2
2
0
0
2
2
2
1
1
0
1
1
0
1
0
1
3
2
0
1
2
0
0
0
0
2
1
1
1
1
1
0
0
1
2
1
0
0
1
0
0
0
0
0
0
1
2
0
0
2
0
2
2
0
1
2
0
1
2
1
2
1
0
0
0
2
0
0
0
1
1
2
0
2
0
2
0
0
0
0
1
0
0
2
2
3
2
3
0
0
1
0
1
1
0
2
1
2
0
1
2
1
2
0
2
0
2
0
1
0
1
0
1
0
0
2
1
1
0
0
0
2
2
2
2
2
2
1
0
1
2
1
0
0
2
0
2
2
1
0
0
1
0
0
2
3
1
0
2
1
2
2
0
1
0
0
2
0
1
2
0
0
1
2
1
2
1
0
1
0
0
0
2
0
1
0
1
0
1
1
0
0
2
0
1
0
2
2
0
2
2
1
1
0
0
1
1
2
1
0
1
3
1
0
0
0
1
1
0
1
1
0
0
2
1
0
0
1
2
0
0
1
2
0
0
0
1
0
0
0
0
2
0
2
0
0
2
1
0
1
0
1
3
1
0
0
1
0
0
1
1
1
1
0
0
1
1
1
0
2
0
0
1
1
0
0
2
0
0
1
0
1
0
2
1
0
0
0
1
1
1
2
1
1
0
0
0
0
2
0
1
0
0
1
0
0
0
1
2
1
0
1
0
2
1
1
0
0
0
1
2
1
1
2
1
2
0
0
0
1
0
1
1
0
0
1
0
0
2
0
1
0
0
2
0
1
1
2
1
0
1
0
0
2
2
0
2
0
1
1
1
2
0
3
1
1
0
1
2
0
1
0
0
0
1
0
0
2
1
0
0
2
1
0
1
1
0
1
0
2
1
1
2
0
0
0
1
2
0
1
0
2
1
2
2
1
1
0
1
0
0
1
0
1
0
1
1
1
0
0
0
2
2
5
2
0
0
2
0
1
0
1
0
0
0
2
1
0
0
0
2
0
0
2
0
1
0
1
0
2
1
2
0
2
0
2
2
0
0
2
0
0
1
0
0
1
0
2
0
0
0
1
0
3
2
2
2
0
1
2
1
1
2
0
0
1
0
2
1
0
2
0
1
2
0
0
1
0
2
1
0
0
0
0
1
0
0
2
0
0
0
2
1
2
2
0
1
0
0
0
1
2
0
1
2
2
0
0
0
0
0
2
1
0
0
2
0
0
2
0
0
3
0
0
6
0
1
0
5
0
0
0
1
0
1
0
0
2
1
1
1
0
0
2
2
0
0
0
0
0
0
1
0
1
2
0
1
0
0
4
1
1
0
1
1
1
0
1
0
0
1
1
0
0
1
0
1
0
0
0
0
0
2
0
1
0
0
0
2
0
0
2
2
1
2
4
0
1
0
0
1
1
0
0
0
2
1
1
0
1
0
0
0
0
0
2
1
0
1
1
2
2
0
1
0
0
1
0
2
1
0
1
0
0
0
1
0
1
1
1
0
1
1
0
0
2
0
0
1
0
0
0
1
1
1
0
0
0
2
2
2
0
0
0
0
1
1
0
2
1
1
2
1
2
0
1
2
0
0
1
0
0
2
0
2
0
0
0
2
2
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
1
0
0
1
0
1
1
0
0
0
0
1
2
1
1
2
0
0
0
0
0
1
1
2
2
1
0
0
1
1
0
0
0
0
2
2
1
0
1
0
2
1
0
0
1
2
0
2
2
0
0
0
1
1
2
1
0
0
3
1
1
1
0
1
1
1
1
0
2
0
0
2
1
0
0
1
1
1
1
2
2
2
1
0
0
0
1
0
0
2
1
0
1
0
0
0
1
1
1
2
0
2
1
0
0
1
1
1
1
1
0
0
1
1
0
0
2
0
2
1
2
1
0
0
1
0
0
0
1
1
2
1
2
0
1
1
2
1
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
1
0
1
0
1
2
0
0
0
2
2
1
0
2
0
0
1
0
0
1
0
2
0
1
2
1
2
0
1
1
0
0
0
0
1
1
2
2
1
0
0
4
0
2
1
1
0
1
1
1
0
1
1
0
0
2
0
0
1
1
0
2
0
1
0
0
0
1
1
0
0
0
1
2
1
1
1
1
1
1
1
0
1
1
2
1
1
1
3
1
2
1
2
1
0
0
2
0
1
0
0
1
0
1
1
0
0
3
1
0
1
0
1
1
2
1
0
0
0
0
2
0
2
0
0
1
0
2
2
1
0
2
0
3
1
0
2
1
1
0
0
1
2
2
3
0
2
2
0
0
1
1
0
0
0
1
0
1
0
2
0
1
2
1
0
2
0
0
0
0
1
2
1
0
0
1
0
1
1
2
0
0
0
1
0
0
2
0
0
1
0
2
1
0
0
3
0
1
2
1
1
2
1
2
2
0
2
0
0
2
1
0
0
0
1
0
1
1
2
2
0
0
0
0
1
0
2
0
0
0
2
0
0
0
2
0
0
0
0
3
0
2
1
0
0
1
0
1
0
0
2
2
1
1
1
1
0
0
1
0
1
0
1
1
2
1
0
0
0
1
0
1
1
1
0
1
2
1
0
0
1
1
1
1
1
0
0
0
0
0
2
1
1
1
2
1
0
2
0
2
0
0
0
1
1
1
1
2
1
1
0
1
0
0
2
5
0
0
1
1
1
2
0
0
0
1
0
2
2
0
2
0
1
0
0
2
0
1
1
0
2
1
0
1
0
1
0
0
1
0
1
1
0
2
2
0
1
0
0
0
1
0
0
0
1
1
2
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
2
2
8
1
0
6
0
2
1
1
0
1
2
1
0
0
1
2
1
0
2
2
0
0
3
0
0
0
0
0
2
1
1
1
0
0
0
0
0
0
1
0
2
0
0
1
2
0
2
2
0
2
1
2
0
0
1
1
0
1
0
0
0
2
2
1
1
0
1
0
0
0
0
0
2
2
1
1
0
1
3
0
1
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
2
0
1
1
1
2
0
1
2
0
1
0
1
0
2
2
1
1
1
1
0
0
0
1
1
0
0
2
2
2
2
1
1
2
1
1
0
3
1
1
1
2
0
1
1
1
0
0
1
1
0
1
2
1
0
0
1
2
1
2
1
2
2
1
1
2
0
2
0
0
0
0
0
1
1
0
0
0
0
2
1
1
1
0
1
0
0
0
0
2
0
0
0
1
0
1
0
0
2
4
0
0
1
2
2
0
1
0
0
1
1
2
0
0
1
1
1
0
2
1
0
2
0
0
1
2
3
3
2
1
0
0
2
1
2
1
1
2
0
1
2
1
1
2
2
1
0
2
0
0
1
0
1
0
0
1
1
1
2
0
1
0
3
0
1
2
1
0
2
0
2
0
0
0
1
0
0
0
2
0
1
2
0
2
1
1
0
1
1
1
2
0
0
0
0
1
0
0
0
0
2
1
2
2
2
1
0
1
2
0
0
0
4
2
2
1
1
1
1
1
2
0
0
0
1
1
0
0
1
1
0
1
1
0
2
0
0
0
2
1
1
0
1
0
0
0
0
0
0
0
1
2
0
0
0
1
0
1
1
0
0
1
2
0
0
0
0
1
1
1
0
1
0
1
0
2
1
0
2
2
0
0
1
0
0
2
2
2
1
0
1
1
0
0
1
0
0
1
1
2
0
1
2
0
0
1
0
1
0
1
0
1
1
0
0
0
0
1
0
1
2
1
1
0
0
0
0
0
0
1
1
0
1
2
0
0
1
0
0
0
0
0
1
0
2
1
1
1
0
3
1
0
0
0
1
0
0
2
0
0
0
0
2
2
1
2
0
0
2
0
2
1
0
1
1
2
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
2
2
1
1
1
2
1
0
0
0
2
2
1
1
0
1
1
0
0
1
0
1
1
0
1
1
1
3
2
1
0
2
2
0
0
0
3
0
0
0
1
1
0
1
1
2
0
0
1
0
0
1
0
2
3
1
1
1
1
0
0
0
0
2
0
1
1
0
0
0
2
2
0
1
0
0
0
1
1
0
0
1
0
3
1
0
1
2
1
1
2
0
1
2
0
1
0
0
0
1
2
2
1
1
1
1
0
0
0
1
2
0
1
2
0
0
0
0
1
2
0
0
0
2
2
1
1
1
1
1
1
0
0
0
2
0
1
2
6
1
0
1
1
0
0
0
0
0
2
0
2
0
1
2
0
1
1
2
1
0
1
2
2
1
1
1
0
0
1
0
2
0
0
2
0
0
2
0
1
1
2
1
3
0
0
1
0
1
1
0
2
1
2
0
0
1
2
1
1
0
1
1
0
2
2
0
0
0
1
0
1
0
0
0
2
1
1
1
1
2
0
0
0
0
0
2
1
1
1
1
0
0
2
1
0
1
0
0
2
0
0
1
0
2
0
1
0
0
0
0
1
2
0
0
2
1
1
0
0
1
1
1
2
0
0
2
0
1
1
2
1
1
3
0
0
2
0
0
0
0
1
1
2
3
0
0
0
0
1
2
0
2
0
1
1
1
0
0
1
1
1
0
0
1
0
2
1
0
1
0
1
0
0
1
1
2
0
0
0
1
0
0
1
1
0
2
4
1
0
1
2
1
1
0
1
0
0
0
1
1
0
0
0
0
1
2
0
2
0
2
1
1
2
2
1
1
1
3
1
0
0
1
0
2
0
2
2
1
0
0
1
0
0
2
0
1
2
0
1
1
0
2
1
3
1
2
0
0
1
1
2
2
0
0
2
1
2
1
2
2
1
1
0
0
0
0
0
0
2
1
0
0
1
0
1
2
2
0
0
2
1
2
1
2
1
0
0
0
0
0
0
2
1
1
1
1
2
0
1
1
0
0
1
2
0
0
1
2
1
0
0
0
1
1
0
1
1
0
0
1
0
1
1
1
2
2
2
0
2
1
0
2
2
0
0
2
2
0
0
0
1
2
1
2
0
1
0
0
0
1
0
0
0
2
1
0
0
0
1
0
0
2
0
1
0
2
2
0
1
2
0
2
0
0
0
0
2
0
0
1
1
0
0
0
1
1
2
0
1
1
2
0
1
0
0
1
1
0
2
0
1
1
1
0
2
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
2
1
2
0
2
1
1
1
2
1
0
2
0
0
0
0
1
0
2
1
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
1
0
2
0
0
0
1
2
1
1
0
0
0
1
0
0
1
1
1
2
1
2
2
0
0
1
0
1
0
1
2
0
0
1
0
2
2
1
3
0
0
0
0
0
1
1
2
1
2
0
0
1
2
0
0
2
0
1
0
0
1
1
2
1
0
1
0
0
1
1
0
1
1
2
2
1
0
2
2
1
0
0
0
0
0
0
1
1
0
2
0
2
0
0
0
0
1
1
0
1
2
1
0
0
0
2
0
2
1
0
2
0
2
2
0
0
2
0
1
0
4
0
2
1
1
1
1
2
1
0
0
0
0
2
0
1
1
1
1
0
1
0
1
2
0
0
0
0
2
1
0
2
0
2
2
0
3
2
0
1
0
0
1
0
1
2
1
1
1
0
2
0
0
0
0
1
0
2
1
1
0
0
0
0
2
0
2
1
1
0
2
1
0
0
1
0
0
1
1
1
2
2
1
0
2
1
2
4
0
1
0
2
2
2
2
2
0
0
1
0
3
2
1
1
0
2
0
0
1
0
0
0
0
0
1
0
1
2
1
0
1
0
0
2
1
0
0
0
1
0
2
1
0
2
0
1
1
0
2
1
0
1
0
2
1
1
0
1
2
2
0
0
2
1
2
0
0
1
0
2
2
0
1
0
1
0
0
1
0
1
2
2
1
1
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
2
1
0
3
1
0
0
0
2
0
2
0
1
0
1
1
0
1
1
1
0
2
0
2
2
1
0
0
1
2
2
0
2
1
0
3
0
0
2
0
1
2
1
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
1
2
0
1
0
2
3
0
2
0
0
2
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
2
0
0
1
1
2
1
0
1
2
0
0
2
1
2
1
2
0
0
0
0
0
0
1
1
2
0
2
0
2
1
0
0
0
0
0
2
0
0
2
1
1
1
1
1
0
0
0
2
1
0
2
0
2
0
0
1
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
1
1
3
2
0
0
1
0
2
1
1
0
1
1
1
0
1
0
0
0
0
1
1
2
0
1
2
0
1
0
0
0
2
1
0
1
0
2
0
1
0
0
0
1
2
0
0
0
1
0
0
1
0
0
0
2
2
1
1
0
0
2
2
1
0
0
1
1
1
1
0
1
1
0
1
0
1
0
1
1
0
0
0
0
1
1
0
0
1
0
0
1
0
1
2
0
1
1
2
0
1
0
1
0
1
0
1
0
0
1
2
1
0
0
5
1
0
0
1
0
6
1
1
1
0
1
1
2
0
0
0
1
0
2
0
0
0
1
0
1
0
1
0
2
4
0
0
2
2
2
1
1
0
1
1
1
2
0
1
3
1
0
0
1
0
1
0
1
2
1
2
0
0
1
0
1
1
0
1
0
1
0
0
0
0
1
0
0
0
1
0
2
0
1
1
0
0
2
1
0
1
1
1
1
0
0
0
0
2
1
0
0
0
1
0
1
0
0
2
2
0
2
1
0
1
2
1
0
0
1
1
1
0
1
1
2
1
0
1
0
0
2
2
1
1
0
1
0
0
2
0
0
2
1
1
2
1
1
1
1
2
2
0
2
2
2
1
1
0
0
0
0
1
0
2
0
2
2
2
1
0
0
2
1
0
0
1
2
0
0
0
1
0
1
2
0
1
0
1
1
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
2
0
1
0
1
0
2
0
0
1
0
2
1
1
0
2
0
0
0
1
1
1
0
1
0
2
1
0
0
1
2
1
0
2
1
0
0
2
1
1
2
0
0
2
2
1
0
2
0
1
0
1
1
0
0
1
0
0
0
1
0
2
2
0
0
2
0
1
0
0
0
1
0
0
0
1
0
0
3
1
0
0
1
0
1
0
1
2
0
1
0
0
0
0
0
1
0
2
0
1
0
1
0
0
2
0
1
0
0
1
1
0
0
2
0
1
0
0
0
2
1
2
0
1
1
0
0
1
0
1
2
1
0
0
0
0
1
0
0
1
0
0
1
2
1
0
0
0
0
2
1
1
1
1
0
0
1
1
0
0
0
1
2
1
0
2
0
2
1
1
0
0
0
1
0
0
2
0
0
0
1
0
1
2
2
0
1
2
2
0
0
1
0
1
2
0
3
0
1
0
0
3
0
0
1
1
4
0
1
0
1
1
0
2
0
0
1
1
0
1
1
0
0
1
1
0
1
1
1
1
0
3
1
0
0
1
0
0
1
0
1
1
1
0
0
1
0
1
0
2
0
2
1
2
1
2
0
0
1
0
2
0
0
1
0
2
1
1
0
0
1
2
0
1
0
2
0
0
1
1
2
0
0
1
0
2
1
0
1
0
2
1
1
1
0
0
0
2
0
0
1
2
1
0
1
0
1
0
1
0
0
1
2
1
0
1
1
1
0
1
0
0
0
2
2
0
0
2
1
0
1
1
1
0
0
1
2
1
1
0
0
0
0
0
0
1
0
0
1
1
1
1
0
0
1
0
0
0
1
3
0
1
0
1
0
1
2
2
0
1
0
0
0
0
0
0
0
1
1
1
2
0
2
0
3
0
0
2
1
0
1
0
0
0
2
1
1
2
0
2
0
1
2
0
0
1
0
2
0
3
1
1
0
0
0
0
1
2
0
0
0
0
1
2
2
0
1
0
0
0
0
0
1
2
1
1
1
0
0
0
1
2
0
0
0
0
0
1
1
0
1
0
0
1
2
1
1
0
0
0
1
2
4
0
0
2
1
2
1
1
0
1
0
1
3
1
1
2
0
0
0
2
2
2
0
1
0
1
1
0
1
0
0
1
0
2
1
1
2
0
0
0
2
1
2
0
0
0
1
5
2
1
0
0
1
2
1
3
0
1
1
0
2
1
2
0
1
3
1
0
2
1
2
1
1
0
0
1
0
0
1
0
1
0
0
0
0
2
1
0
1
2
1
1
2
1
0
2
0
0
0
2
0
0
1
2
1
0
0
1
1
1
1
1
1
0
1
1
0
2
0
1
0
1
1
1
0
2
0
2
0
0
1
1
1
1
0
0
1
3
0
2
1
0
0
0
0
1
0
2
1
0
0
0
0
2
0
2
0
1
3
1
1
2
0
3
0
0
1
1
3
2
0
2
2
1
0
1
1
1
0
0
0
0
0
2
1
0
0
1
1
1
1
1
0
1
0
0
1
1
1
2
0
0
0
0
0
1
1
1
0
0
1
0
0
0
1
1
2
1
0
1
0
1
2
2
2
2
1
0
1
0
0
2
2
1
1
1
1
1
1
2
1
0
1
0
0
2
1
0
0
3
1
1
2
0
0
1
1
2
2
2
0
0
0
2
2
2
2
0
2
2
0
1
0
0
2
2
2
1
1
1
1
1
1
0
0
0
3
0
0
2
0
1
2
0
0
0
1
2
2
1
1
2
2
2
0
1
2
1
1
1
0
2
1
0
2
0
2
0
1
0
0
0
0
0
2
0
1
0
2
0
1
1
1
1
0
1
0
0
1
0
2
1
1
1
1
2
1
0
0
1
1
1
0
2
0
1
2
1
1
1
1
2
0
1
1
0
0
1
0
0
0
0
0
0
0
1
2
2
0
0
0
0
4
1
0
0
2
3
1
0
0
2
2
0
1
0
0
1
3
1
1
0
2
2
0
1
1
1
0
1
1
1
0
1
1
0
1
0
0
2
1
1
0
1
1
2
6
2
2
0
0
1
1
2
0
0
2
0
0
0
2
0
2
0
2
1
1
2
0
0
2
1
0
1
0
1
0
0
2
1
0
0
0
2
1
0
1
0
1
0
2
1
2
3
0
1
2
1
2
2
4
1
2
0
0
1
1
0
0
1
1
2
0
2
1
0
1
0
0
0
1
0
1
0
2
0
1
0
2
0
1
1
1
1
2
0
0
0
2
0
0
0
1
2
1
0
0
0
1
2
2
0
1
1
1
2
1
1
2
1
1
1
0
1
0
1
1
2
1
2
1
0
0
2
0
1
1
2
1
1
1
2
0
0
0
0
1
0
1
0
0
1
1
0
0
1
0
1
0
1
1
2
1
0
1
0
0
1
0
2
1
1
0
2
1
1
0
2
1
0
1
1
0
0
0
0
1
2
0
0
1
0
1
1
0
2
0
2
0
1
0
1
0
1
1
1
0
2
1
1
1
1
0
1
1
0
1
0
3
0
1
2
2
2
0
1
3
2
0
1
2
0
2
0
0
0
1
0
2
0
0
1
0
1
0
0
0
1
0
0
0
0
2
0
0
1
1
0
1
0
1
2
2
2
1
1
0
0
2
2
0
0
0
1
0
2
2
1
1
0
1
0
2
1
0
1
0
2
0
0
2
2
0
0
0
2
2
1
0
2
1
0
1
1
2
1
0
0
1
1
2
1
0
0
0
0
0
1
1
2
0
1
1
2
0
2
0
0
0
0
2
0
0
0
2
1
1
1
0
2
0
0
0
1
2
1
0
0
0
0
0
1
0
0
0
1
1
1
1
1
1
1
0
1
1
1
2
0
1
0
0
0
0
0
1
1
2
0
1
2
1
0
0
0
0
1
0
1
0
1
0
1
1
2
0
2
3
1
1
1
1
0
0
1
1
0
1
2
2
2
2
0
0
0
1
2
0
0
0
0
1
2
1
0
0
0
2
1
2
1
0
1
0
0
1
2
1
2
4
1
0
2
2
0
2
0
0
1
1
0
0
0
1
0
2
1
2
0
0
1
0
0
0
0
0
0
1
0
0
1
2
1
0
2
1
0
1
0
1
1
1
2
1
0
0
3
0
1
0
0
1
0
0
0
0
0
1
0
1
0
1
0
2
2
1
1
2
1
2
1
2
2
1
0
0
0
1
1
0
2
0
3
0
1
0
0
0
1
0
2
0
0
0
1
2
1
0
1
1
1
1
4
0
1
0
1
0
1
2
0
0
1
1
0
1
1
0
0
1
0
0
0
1
1
2
1
0
0
1
2
0
0
0
1
1
0
0
0
1
0
2
1
1
0
0
0
0
0
1
2
1
0
1
0
0
0
0
1
0
1
1
1
0
1
0
2
0
0
0
0
1
1
0
1
2
2
0
0
2
1
2
1
0
2
2
1
1
2
1
1
2
0
1
1
0
0
0
0
2
1
1
0
3
0
1
2
1
0
0
0
0
1
2
5
1
0
0
2
0
1
0
0
1
0
0
0
0
0
1
0
0
2
0
1
0
2
1
2
1
2
1
0
2
1
0
2
0
1
0
2
0
1
2
0
2
1
1
0
1
0
1
1
0
2
2
2
1
1
0
0
1
0
3
2
0
1
0
1
1
1
2
2
1
2
1
0
2
1
2
1
1
0
1
2
0
0
1
0
2
0
1
1
1
0
0
0
0
2
0
1
1
2
1
2
1
0
2
2
2
0
1
2
0
1
1
2
0
1
1
1
1
0
0
0
0
1
1
0
0
1
2
0
0
0
0
2
0
1
0
0
0
1
1
2
0
0
0
0
2
2
1
0
2
1
2
1
0
0
0
0
0
2
1
0
0
1
0
0
0
2
1
1
1
1
0
1
2
1
1
0
2
1
1
0
0
0
1
2
3
2
1
0
0
1
2
1
0
0
1
1
2
3
1
0
1
2
0
1
2
1
0
0
1
1
0
0
1
1
1
0
0
2
0
1
0
1
0
2
1
0
2
0
2
1
0
2
1
0
1
0
0
1
1
2
0
0
0
0
0
2
0
1
1
1
2
0
5
0
0
0
4
1
2
0
0
2
0
2
0
2
0
1
1
1
0
1
1
1
1
1
0
0
0
0
1
2
0
2
1
0
2
0
1
2
1
1
1
1
2
0
2
0
0
0
1
1
0
0
2
1
0
0
1
0
1
1
1
1
1
2
0
1
1
1
2
0
2
0
2
1
1
1
1
2
0
2
1
0
2
0
2
1
0
1
0
1
1
0
1
0
0
0
0
2
0
1
1
0
0
0
0
0
2
0
0
0
0
2
1
1
0
2
0
0
2
0
1
1
0
0
0
0
1
0
1
0
2
0
1
0
2
0
0
0
2
0
1
1
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
1
2
0
0
1
2
1
1
1
2
0
1
1
1
1
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
2
1
1
0
0
0
1
0
0
1
0
1
1
0
2
2
1
0
1
0
1
1
1
2
2
1
0
3
0
0
1
1
1
2
0
0
0
0
1
1
0
1
1
2
2
0
1
1
0
2
0
0
0
0
1
0
2
0
2
0
1
0
1
0
0
1
0
0
1
0
0
0
2
1
1
1
0
0
1
0
1
2
1
0
0
0
1
1
1
0
2
0
0
0
1
0
1
2
0
2
1
1
4
1
1
0
1
0
1
2
2
0
1
1
0
2
0
0
1
0
1
1
1
0
0
2
1
1
2
1
0
1
1
2
0
0
0
0
0
0
2
1
1
0
0
1
0
1
0
1
1
1
1
1
0
1
0
0
1
0
0
2
2
0
0
0
0
2
0
0
0
1
1
2
1
2
1
0
1
0
0
1
1
2
0
2
2
1
0
0
0
0
1
1
0
0
1
3
1
0
0
0
1
0
1
2
1
0
2
0
0
0
0
0
1
0
0
2
2
0
0
0
0
2
0
0
0
0
0
1
2
2
0
1
1
0
1
2
0
0
2
1
0
2
0
1
0
0
0
0
0
0
1
3
1
1
0
1
1
1
1
1
1
0
1
1
1
1
0
1
0
1
2
0
1
0
0
1
0
1
1
2
1
0
0
0
2
1
1
0
0
0
2
0
0
0
1
0
0
1
1
0
1
0
1
0
2
0
0
0
0
1
1
0
2
2
0
1
0
2
1
0
0
0
1
0
2
0
1
0
0
0
0
0
1
1
0
1
1
0
1
0
1
2
0
1
1
0
0
1
1
1
0
0
0
1
1
1
1
0
1
0
0
0
1
2
0
1
0
1
2
0
1
0
1
0
0
0
2
1
0
0
0
0
0
0
0
3
2
2
3
0
1
0
2
0
0
3
0
2
2
2
2
0
1
2
1
1
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
2
0
3
0
2
4
2
0
1
1
2
0
2
0
1
0
2
0
0
0
0
0
0
1
0
0
1
1
0
0
3
2
1
2
0
1
2
1
0
0
1
0
0
2
2
1
0
1
1
1
0
0
2
1
1
1
1
2
0
0
1
1
2
1
2
0
0
1
0
2
1
0
0
0
0
1
0
1
0
0
1
1
1
2
1
1
2
2
2
0
2
1
0
2
0
2
1
1
1
2
2
1
0
0
0
0
2
0
1
1
0
0
1
0
0
0
1
2
0
0
0
2
0
1
2
2
1
2
0
1
2
1
0
3
1
1
1
2
0
2
1
0
0
2
1
1
0
1
0
2
1
0
0
0
0
1
1
0
0
1
0
0
2
0
2
1
1
0
0
1
0
0
1
1
0
2
0
1
1
0
0
0
2
1
0
0
0
2
0
1
1
0
2
1
0
1
1
1
1
1
0
0
1
2
0
0
1
0
0
0
1
0
0
0
0
2
0
1
1
1
0
0
1
0
1
0
0
2
0
1
1
2
0
2
1
0
2
1
1
0
2
1
0
0
1
0
0
1
0
0
1
0
0
0
0
1
1
0
0
2
0
0
1
0
0
3
0
0
0
0
0
1
0
1
0
1
2
0
0
1
2
0
1
2
0
2
1
2
0
0
1
2
2
0
0
2
0
1
1
1
1
2
0
0
1
1
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
1
1
0
0
2
0
2
2
0
0
2
0
0
0
1
2
2
0
2
2
0
1
0
2
0
1
2
1
1
2
0
0
0
0
1
2
0
2
0
1
0
2
0
0
3
0
0
2
1
0
1
0
2
0
1
0
1
0
0
0
1
0
0
1
0
0
0
1
2
0
1
0
1
1
1
1
0
0
1
0
1
1
0
0
0
0
1
1
0
0
1
0
0
0
0
1
1
3
2
1
2
0
2
0
1
0
3
1
1
0
1
0
0
0
0
0
0
2
1
0
1
2
1
0
0
2
1
1
0
1
1
1
5
1
2
2
2
2
0
0
2
2
2
1
2
0
0
2
2
0
1
1
0
0
1
1
0
2
0
0
1
1
1
1
1
2
1
1
1
0
2
2
1
0
0
0
1
2
1
1
0
0
1
1
1
2
1
0
0
1
1
1
1
0
1
0
1
0
1
0
1
1
1
2
1
0
0
0
0
1
0
1
0
2
1
1
2
0
0
0
0
0
0
1
3
0
0
1
1
0
1
1
2
0
1
0
0
1
1
0
0
1
1
1
1
2
1
2
1
0
3
0
1
2
0
1
0
0
0
1
1
2
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
2
2
0
2
2
1
1
0
0
0
2
0
1
2
1
1
0
0
1
0
1
0
1
0
2
0
0
1
1
0
2
1
2
1
1
1
2
1
2
0
2
0
0
1
2
1
0
0
3
0
0
2
0
0
0
1
0
1
1
1
1
1
2
0
1
2
1
0
1
1
0
0
0
0
0
1
2
0
0
0
0
1
1
1
1
2
2
0
0
2
2
1
0
0
1
0
0
1
1
0
1
0
0
1
2
1
0
2
0
1
0
0
0
0
1
1
0
1
0
0
1
0
1
1
1
2
1
0
1
0
1
1
0
0
0
0
0
0
0
2
1
0
1
0
0
0
1
2
0
0
1
0
1
1
0
2
1
1
1
2
0
2
1
1
1
1
0
3
1
1
1
1
0
0
1
2
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
2
3
1
1
0
0
0
0
1
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
1
2
1
0
1
0
0
0
0
0
0
2
0
0
1
2
1
0
1
1
1
0
0
2
0
0
1
1
0
0
2
1
2
0
0
0
1
0
0
2
0
1
2
1
0
1
0
1
0
1
0
2
0
2
0
2
0
2
1
2
0
2
1
2
1
0
1
0
1
0
1
0
1
0
0
2
0
1
2
0
1
0
0
1
0
2
1
1
1
1
0
4
1
2
2
1
1
2
0
1
0
2
1
0
2
0
2
1
1
1
0
1
0
0
1
3
0
1
0
0
0
0
1
0
0
0
2
1
1
1
0
3
0
2
1
0
2
2
2
1
1
1
1
1
1
1
0
0
0
0
1
1
2
4
2
1
0
1
1
0
1
1
0
2
0
0
1
2
0
0
1
0
1
1
0
0
0
3
1
0
0
0
0
0
0
0
2
0
2
0
2
0
1
1
0
0
2
1
0
0
1
2
1
0
2
2
2
1
3
2
0
0
1
0
0
0
2
1
1
2
0
0
0
1
0
1
0
0
3
3
0
0
1
0
3
0
0
1
0
0
0
1
2
1
0
2
2
0
2
1
2
0
2
1
2
1
1
1
0
1
0
2
1
0
0
0
1
0
2
0
0
0
2
1
0
1
1
1
1
1
1
1
0
1
0
0
2
1
1
2
0
0
1
0
1
0
1
2
0
2
1
0
1
0
1
3
0
1
2
3
0
0
2
0
0
1
0
2
0
0
2
2
1
2
0
0
1
1
3
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
2
2
1
2
1
0
2
0
0
1
2
1
1
0
1
1
2
0
2
0
0
3
1
0
0
1
0
1
0
1
0
0
1
1
2
1
2
0
0
0
1
3
0
2
1
1
0
0
0
2
0
1
1
0
3
0
2
0
1
2
9
1
0
0
1
0
1
0
1
2
2
0
1
0
0
0
1
1
0
1
0
0
1
0
2
0
0
1
2
2
0
0
0
0
1
1
1
0
1
1
0
0
2
0
1
0
1
0
0
1
1
2
0
2
2
0
0
1
1
0
3
0
2
1
1
1
2
1
0
0
2
0
1
2
2
0
1
0
0
1
0
0
0
1
1
1
1
1
3
2
0
0
1
2
2
0
1
1
0
0
1
1
2
0
0
0
1
0
0
0
1
0
2
2
0
0
0
0
0
1
0
2
1
0
0
3
1
1
1
0
0
1
2
1
0
1
0
2
1
0
2
1
0
2
0
1
1
2
1
1
0
0
1
0
1
2
0
2
1
0
0
1
2
0
1
2
2
0
2
0
1
1
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
1
0
0
0
0
2
0
2
1
0
0
2
0
1
0
0
0
0
0
1
0
1
0
1
2
1
0
0
2
0
2
1
1
1
0
1
1
0
1
0
2
0
1
0
5
1
2
5
1
0
2
0
1
2
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
2
0
0
1
1
2
2
1
0
0
1
0
1
2
0
0
0
0
1
1
0
1
0
1
0
1
1
0
0
0
0
0
1
0
1
0
1
0
0
1
0
2
2
0
0
0
2
1
1
0
1
1
0
0
0
1
2
1
0
0
1
0
2
0
1
0
0
2
0
0
0
1
0
1
1
0
0
2
0
2
0
1
2
1
0
3
2
1
2
0
0
1
2
1
2
0
2
2
1
0
1
2
1
0
1
2
0
2
1
0
0
1
0
0
1
3
0
1
1
3
2
1
1
2
1
0
1
1
0
1
0
1
2
2
1
0
1
0
1
1
1
1
2
0
2
0
2
1
2
0
0
2
0
2
0
3
0
0
1
0
0
0
1
0
1
2
1
0
1
1
0
1
0
2
1
1
0
1
1
1
0
0
0
1
0
0
0
0
1
0
0
0
2
1
0
0
2
1
1
2
0
0
1
0
0
0
0
0
1
0
0
1
1
2
1
0
1
0
1
1
1
1
0
1
0
1
2
0
1
0
0
1
1
3
1
0
0
0
0
3
0
4
1
0
1
2
0
0
1
0
2
0
0
0
0
2
0
0
2
1
0
0
0
0
0
2
2
0
1
0
0
0
0
2
0
1
0
0
1
0
1
2
1
0
0
0
0
1
2
0
2
0
2
0
0
0
0
2
2
2
1
0
1
1
0
1
3
1
0
0
1
2
1
2
0
1
1
1
0
0
0
1
1
1
0
1
0
1
0
0
2
0
0
2
0
1
0
2
2
2
0
0
1
2
1
0
1
1
2
1
0
2
0
0
1
2
0
2
0
2
0
0
2
0
2
1
1
2
0
0
1
0
0
0
1
2
0
2
2
2
0
4
0
2
0
2
0
1
0
0
1
1
2
0
2
1
0
0
1
0
2
0
2
1
0
1
0
0
1
1
0
0
1
0
1
1
0
1
0
1
1
1
2
0
0
0
0
1
2
0
0
1
2
0
1
2
1
1
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
2
1
1
0
0
0
0
0
0
1
2
2
2
2
2
2
0
0
1
1
0
1
3
2
0
0
0
0
2
1
0
1
1
2
2
2
1
2
2
0
2
0
1
0
1
0
1
1
1
0
0
1
1
0
0
1
1
0
1
1
0
2
0
0
2
1
2
1
0
0
0
2
1
0
1
1
0
1
0
1
0
1
0
2
2
0
1
0
1
1
1
0
2
0
0
0
1
0
0
0
2
1
0
0
0
3
0
1
0
3
0
0
0
0
1
1
0
1
0
1
1
0
2
0
1
0
1
0
1
4
1
1
1
1
1
1
0
2
2
1
0
2
0
0
1
1
1
0
2
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
2
1
0
0
1
2
2
0
2
1
3
0
2
0
0
2
1
1
0
2
1
0
2
2
0
1
0
0
0
0
0
0
1
1
0
2
1
1
2
0
0
1
2
1
3
1
0
1
0
1
1
1
0
0
0
1
1
0
0
0
0
2
0
1
0
0
0
2
2
2
0
2
1
2
0
0
0
2
0
4
2
1
1
0
1
2
2
0
1
0
0
2
0
0
0
0
0
1
1
1
2
1
0
0
2
1
2
2
2
1
0
0
0
0
1
0
2
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
1
2
2
0
0
0
1
1
1
2
2
0
2
1
2
1
0
1
0
1
0
1
0
0
0
1
1
0
1
1
1
1
1
1
1
2
2
1
0
2
1
0
2
2
0
2
0
1
1
0
1
1
2
1
0
3
0
0
0
0
0
0
2
1
2
1
1
0
2
2
1
0
2
0
0
0
1
0
2
2
0
0
1
2
2
0
2
0
0
2
1
2
0
0
1
1
1
0
0
0
1
0
0
0
1
2
1
2
1
0
0
0
1
1
1
0
0
2
1
0
1
0
0
1
0
0
2
0
1
0
0
2
0
0
1
1
1
2
1
0
1
0
1
0
0
0
0
0
0
0
0
2
3
1
1
0
1
1
0
1
1
1
1
0
0
1
1
2
0
1
0
0
1
2
0
1
0
0
1
1
3
0
0
0
2
0
1
1
0
2
0
0
2
1
0
1
1
0
2
1
1
0
1
0
1
1
0
0
2
0
1
1
0
1
0
0
0
1
0
0
1
1
0
0
1
0
1
0
6
2
0
0
0
1
0
2
4
0
0
0
2
2
0
0
0
0
0
0
0
2
0
1
0
1
0
2
0
1
2
3
2
0
1
0
2
2
0
1
1
2
1
1
0
0
0
0
2
2
1
1
2
0
1
0
1
0
0
0
0
0
1
0
0
0
1
2
1
0
1
1
0
0
2
1
0
1
0
2
0
1
0
0
0
1
1
0
0
2
2
1
0
1
0
1
0
1
1
1
0
0
0
0
1
1
0
2
0
0
0
1
0
1
1
2
0
2
0
0
1
2
2
0
0
0
0
0
1
1
2
0
0
0
1
2
0
4
0
1
0
0
0
1
2
1
2
1
1
0
0
1
0
0
0
0
0
1
2
1
2
0
2
2
1
2
0
2
0
2
0
0
2
0
1
0
0
0
1
1
1
1
1
2
1
1
0
2
0
1
2
1
0
0
1
0
1
2
2
2
0
0
0
4
2
1
2
1
0
1
0
1
2
2
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
1
0
1
1
1
1
1
1
0
1
1
2
0
0
1
0
1
1
1
3
0
0
3
1
0
2
0
2
0
1
0
0
2
1
2
2
1
0
1
0
0
1
0
3
0
0
1
1
2
1
0
1
0
1
1
0
1
0
2
1
0
0
1
0
1
1
1
0
2
0
0
8
0
1
2
1
0
1
2
1
1
0
2
2
0
0
0
1
0
2
0
7
0
0
0
1
2
2
2
2
0
0
0
0
1
0
1
2
0
0
1
0
1
0
2
0
0
0
2
0
0
1
2
1
0
0
2
2
0
2
2
0
0
1
1
2
0
2
0
1
1
0
1
0
0
0
1
1
0
1
0
0
0
0
1
2
1
0
2
0
0
1
0
0
0
2
1
1
1
0
0
0
0
2
2
1
0
1
1
2
0
0
1
1
1
1
1
1
0
2
0
4
1
1
0
0
0
0
3
1
1
1
0
0
1
0
2
1
0
0
3
2
1
0
1
1
1
0
1
1
2
0
2
0
1
2
0
0
0
2
0
0
1
0
0
2
0
1
2
0
0
1
1
1
0
1
0
0
0
2
0
1
0
0
0
2
2
0
1
2
0
0
2
1
1
1
2
0
0
0
1
0
0
0
0
1
1
2
0
0
0
1
2
1
0
2
2
0
2
1
0
1
1
1
1
2
0
2
1
0
1
1
0
2
2
0
0
1
0
1
2
2
2
2
2
0
0
2
1
1
0
1
2
1
1
1
0
0
2
0
2
1
1
2
2
1
1
1
2
0
2
0
0
2
0
1
0
1
2
0
1
2
0
0
0
0
0
1
1
2
0
1
0
1
1
2
0
2
1
0
0
0
0
1
1
0
0
1
1
0
2
0
0
0
0
0
0
0
1
1
2
1
1
0
0
0
1
1
0
3
0
2
0
2
2
2
2
0
1
0
1
2
2
0
2
1
1
0
0
0
2
1
1
0
1
0
0
2
2
0
2
1
2
1
0
0
0
0
0
1
1
1
1
1
0
0
1
1
0
0
1
0
0
2
0
2
1
1
1
1
1
1
1
0
1
2
2
0
0
2
1
1
1
1
0
0
1
0
0
1
0
0
2
1
1
1
1
0
1
0
0
2
2
1
2
1
0
1
4
1
2
2
1
0
2
0
1
0
1
0
1
0
0
0
0
0
1
0
1
0
1
0
2
1
0
1
0
0
2
1
2
0
0
1
0
0
1
2
1
1
1
2
0
0
1
1
1
2
1
0
1
1
0
2
1
0
0
0
1
2
1
0
2
1
1
0
0
2
1
1
1
2
0
0
2
1
2
2
0
0
1
0
1
1
1
1
2
1
0
0
2
1
0
1
0
1
0
0
3
0
0
1
0
0
1
0
2
0
0
0
0
1
0
4
0
0
0
2
0
2
1
1
1
0
0
1
0
2
0
1
0
2
2
0
1
1
0
1
2
1
1
1
1
0
1
1
0
0
0
2
0
1
0
0
1
1
0
3
2
1
0
0
1
1
1
0
1
1
1
0
2
2
0
0
0
1
0
2
1
2
1
0
0
0
1
0
0
1
2
0
0
1
2
2
2
0
1
1
2
0
0
0
1
1
2
1
0
1
0
2
1
0
0
0
1
0
0
0
0
0
2
0
0
0
4
2
0
2
0
0
0
0
0
1
0
1
2
0
12
0
1
2
1
0
1
0
1
2
1
0
1
2
0
1
1
0
0
2
0
0
1
0
0
0
0
0
0
1
1
1
0
0
2
0
2
0
1
0
3
0
1
0
1
1
1
1
0
0
1
2
0
2
2
0
0
0
0
2
0
1
2
0
0
0
2
0
2
0
0
0
2
0
2
0
2
1
0
0
0
0
0
2
1
2
2
1
1
0
1
2
1
0
2
1
0
1
0
1
0
0
1
0
0
2
0
0
0
0
1
0
0
1
2
2
2
1
1
0
1
0
0
1
1
2
0
0
2
0
1
2
1
1
0
0
3
1
0
1
0
1
0
0
0
0
0
0
0
2
0
1
1
1
0
2
2
2
0
1
0
0
1
2
1
2
0
0
2
1
1
2
0
1
0
3
2
2
0
1
0
2
2
2
0
0
1
0
2
2
0
1
1
0
0
2
0
0
0
1
1
0
2
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
2
0
1
0
0
0
0
2
1
1
1
0
1
0
1
0
0
0
1
0
0
0
2
2
1
0
0
0
0
2
0
2
1
2
0
1
2
2
1
2
0
1
0
1
2
0
0
1
2
2
1
0
1
0
0
0
1
0
1
1
0
1
2
0
1
2
2
0
0
1
2
1
3
2
2
0
0
1
0
0
0
0
0
0
3
2
0
1
1
0
1
0
1
1
1
0
0
0
1
0
2
1
0
1
0
1
1
0
2
1
0
2
0
1
1
0
0
1
1
0
1
3
1
2
0
2
0
1
1
2
0
4
3
1
1
0
0
1
2
0
0
0
0
2
1
0
2
0
0
2
3
1
3
0
1
1
2
1
1
1
0
1
2
2
0
2
0
1
1
1
0
0
1
0
0
1
0
2
0
2
2
0
1
1
1
1
0
1
2
0
0
1
0
1
2
0
1
1
1
0
2
1
0
1
0
0
0
1
1
1
1
0
1
1
0
0
0
2
0
0
3
1
0
0
0
0
1
1
0
1
0
0
0
1
7
2
0
0
1
2
2
1
0
0
0
0
0
1
1
1
1
1
0
5
2
1
0
0
1
2
2
0
1
0
0
1
1
2
1
1
0
2
0
0
3
0
0
1
0
0
2
0
1
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
1
1
0
1
2
0
0
0
0
0
0
0
2
1
1
0
0
0
0
1
0
0
0
2
2
0
1
1
0
2
3
0
1
2
1
2
2
0
1
2
2
0
0
0
0
0
2
1
0
0
1
0
2
0
0
1
1
0
0
0
0
1
2
2
0
1
0
1
1
1
0
1
1
2
1
2
2
1
0
0
0
1
1
0
1
1
1
1
0
1
1
0
0
1
0
0
0
0
1
2
0
1
2
0
1
0
3
2
1
1
0
2
1
2
1
1
0
1
0
2
0
0
0
2
2
0
0
0
2
3
0
1
1
1
0
1
0
1
0
1
10
0
1
0
1
0
1
0
0
0
2
3
0
0
1
2
1
2
2
1
1
0
0
0
2
1
0
0
1
1
0
2
0
0
1
0
2
0
1
1
0
1
1
2
2
2
0
0
1
1
1
0
0
1
0
2
2
1
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
1
1
0
0
2
1
2
0
1
0
1
2
1
0
0
1
1
1
1
1
2
0
3
0
1
1
0
2
1
0
2
0
0
0
0
1
1
0
2
0
2
1
0
1
1
1
1
0
2
1
0
1
0
0
2
1
1
2
1
0
2
1
2
2
0
0
0
2
0
0
1
1
1
0
0
2
0
2
0
2
0
0
0
0
0
1
0
1
1
0
0
2
0
1
2
1
0
1
1
2
1
1
0
0
1
0
1
0
0
1
0
0
2
0
0
1
1
1
2
0
2
2
1
1
1
0
2
1
1
1
2
2
0
0
2
1
0
0
1
0
0
2
0
2
1
1
2
0
2
0
0
1
1
2
0
0
0
1
2
0
1
0
0
0
1
0
0
0
1
2
1
1
2
0
0
0
1
2
0
1
0
0
0
2
2
0
0
1
4
2
0
0
2
1
1
1
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
2
2
2
1
1
0
1
2
1
1
0
2
0
2
0
2
1
1
1
0
2
1
2
2
1
1
1
1
1
2
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
1
1
2
1
0
2
1
2
1
1
0
2
0
0
0
2
1
0
1
0
0
1
0
1
1
0
2
2
2
1
0
0
0
0
0
0
2
1
1
0
1
0
0
0
2
2
1
0
1
0
1
1
1
1
0
0
2
0
2
1
0
1
0
4
0
0
1
0
1
1
0
0
0
0
0
1
1
1
2
1
2
0
0
1
1
1
0
1
1
0
1
0
0
2
1
1
1
1
1
0
2
0
0
0
2
0
0
1
0
0
1
1
2
2
1
1
0
1
2
0
0
2
1
0
1
1
2
0
1
0
2
0
1
2
2
2
0
1
2
0
1
1
2
0
0
1
0
1
2
1
0
1
0
0
0
2
0
2
0
1
2
1
2
0
1
3
1
0
1
1
0
1
2
1
0
0
2
1
1
1
0
0
0
1
1
1
1
0
1
2
0
2
0
1
2
0
2
1
0
1
0
2
1
0
0
1
0
2
0
0
1
1
0
0
0
0
0
4
2
1
0
2
0
3
0
0
0
0
0
1
1
0
0
2
0
0
2
0
2
2
2
1
0
1
0
0
1
0
0
0
1
1
0
2
0
2
0
0
0
3
1
0
0
1
0
0
0
0
1
1
0
1
1
2
2
1
0
0
1
0
0
0
2
2
2
1
2
0
1
2
2
0
0
2
1
1
1
1
0
0
1
2
0
1
0
1
0
1
2
2
0
0
0
1
2
1
1
2
0
1
1
1
1
0
2
2
2
1
0
0
2
1
0
2
1
0
2
0
0
1
2
2
0
0
1
0
2
2
0
0
1
0
0
1
0
1
2
1
1
2
1
2
0
0
2
0
0
2
2
0
0
1
1
2
1
0
1
1
2
1
0
1
0
1
0
1
1
1
2
0
0
0
2
0
1
3
0
2
1
2
1
0
0
1
1
2
2
0
1
0
2
1
0
2
1
1
1
0
0
0
0
2
2
1
1
1
0
0
2
1
2
1
1
0
2
1
1
0
2
0
1
0
1
1
0
1
0
0
0
0
1
0
0
2
1
0
0
3
1
0
1
0
0
0
0
1
1
0
0
2
1
0
0
0
0
2
0
0
0
2
1
0
1
1
1
0
0
1
0
0
0
0
0
0
2
1
0
1
1
0
0
3
0
1
0
0
0
1
1
0
2
2
1
0
0
0
2
1
1
2
1
0
2
1
1
0
1
2
0
2
0
0
0
0
1
2
2
1
2
0
1
0
1
1
0
0
1
0
0
0
3
1
1
1
6
0
2
0
0
0
0
0
2
1
2
0
2
0
0
2
0
1
1
0
1
1
0
0
0
0
4
0
1
0
0
1
1
1
2
2
0
1
1
0
2
1
1
1
1
1
0
1
0
0
1
1
2
0
0
0
0
0
2
1
0
0
0
0
1
0
1
0
0
0
0
1
0
2
0
0
2
2
1
1
0
0
1
1
0
0
0
1
2
1
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
1
1
1
1
1
1
1
0
1
2
0
0
2
0
1
1
1
2
0
2
0
1
2
1
0
1
2
1
2
0
0
0
0
1
1
0
0
0
1
0
2
0
0
2
1
0
1
1
0
2
0
2
0
0
0
2
0
0
1
2
0
0
1
2
0
1
0
0
0
2
2
1
5
0
1
0
3
2
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
1
0
1
1
2
1
2
1
1
2
2
2
0
1
0
1
1
0
2
1
0
2
1
1
1
1
1
0
0
1
0
0
2
1
0
0
1
1
1
2
1
0
2
1
0
2
0
1
1
0
1
0
1
0
1
0
2
1
2
2
0
0
0
0
1
0
1
2
0
0
1
0
1
1
1
1
1
1
1
0
1
1
0
2
0
1
1
0
2
1
2
0
0
1
1
1
1
7
1
1
1
1
2
1
0
1
0
1
2
1
0
0
2
0
0
0
2
1
1
2
0
0
0
1
2
3
0
2
1
1
1
2
2
1
0
0
0
2
0
0
0
1
1
2
1
1
2
0
2
1
0
0
0
0
1
3
0
1
0
3
0
2
0
1
0
0
0
0
2
2
0
1
0
0
1
0
2
0
0
1
0
2
0
1
0
2
0
0
3
1
2
0
1
2
4
0
0
2
0
2
0
0
1
0
0
0
0
2
1
2
0
0
0
0
1
2
1
2
1
0
0
0
2
0
0
0
1
0
1
2
3
0
2
0
3
1
1
0
2
1
0
1
1
1
1
0
0
0
0
0
1
2
1
0
0
2
0
2
0
0
0
0
0
1
0
1
1
1
1
2
0
0
0
2
0
2
0
2
1
1
0
2
0
0
0
0
2
0
0
0
2
2
1
0
0
1
0
0
0
0
0
1
2
0
0
0
0
2
0
0
2
0
0
0
1
0
1
2
0
0
0
0
1
2
1
0
1
0
0
1
6
1
1
1
0
2
1
1
2
1
2
1
2
0
1
1
2
0
0
1
1
0
2
3
1
1
2
2
0
0
2
1
1
1
1
2
1
4
0
0
2
1
0
0
1
1
0
2
2
2
0
1
0
0
2
0
0
0
0
1
0
1
2
0
0
0
2
2
0
1
0
1
0
1
0
0
0
0
2
2
0
1
0
0
0
0
1
1
0
0
1
2
0
2
0
0
2
1
0
1
1
1
0
0
2
0
1
0
0
0
0
2
1
1
0
0
1
1
0
0
1
0
1
1
0
0
1
2
0
0
0
0
0
1
0
2
2
2
2
2
0
2
0
1
1
0
0
1
1
1
1
2
1
2
1
1
1
3
0
1
0
0
2
0
1
0
2
0
3
1
0
0
0
0
1
0
0
0
0
0
0
1
1
1
1
1
0
1
2
0
1
1
0
2
1
1
2
0
2
0
0
0
1
2
1
3
1
0
0
1
2
2
0
1
1
1
1
0
1
2
0
0
0
0
0
1
0
2
0
0
2
0
0
0
1
0
2
0
1
4
2
2
1
2
0
0
0
1
0
0
0
2
2
1
0
1
2
1
0
1
1
0
0
0
3
2
0
0
2
2
1
0
0
1
1
0
0
3
0
1
1
2
0
2
1
1
0
1
1
1
0
2
0
0
2
1
0
2
0
0
1
0
1
2
2
2
2
1
1
2
0
1
0
1
1
0
0
0
2
2
1
1
1
0
1
1
0
1
0
2
2
1
1
1
0
0
1
1
0
0
1
0
1
2
1
0
0
2
2
2
0
0
0
1
0
1
0
2
2
0
2
1
2
0
0
1
0
0
2
0
2
1
0
0
1
2
2
2
0
2
1
1
0
0
0
0
0
0
1
2
1
0
1
2
2
0
1
0
0
1
2
0
1
2
1
0
0
1
2
0
0
1
0
2
2
2
0
0
1
0
1
0
2
1
1
0
1
1
0
1
0
2
2
0
2
0
1
1
1
0
2
2
0
1
0
2
0
2
0
0
0
2
0
0
1
0
2
0
2
1
0
2
1
0
1
0
1
2
2
0
1
1
1
4
1
0
2
0
0
0
0
1
1
1
0
2
2
0
0
1
0
0
2
2
0
0
1
1
0
1
1
1
0
1
0
0
0
0
2
2
0
1
1
2
2
0
2
1
0
2
0
1
0
0
0
1
1
0
1
0
2
1
2
0
0
0
1
2
2
1
1
0
1
0
1
1
0
2
1
0
1
0
1
2
0
1
1
0
0
0
1
3
1
2
0
2
0
1
1
1
2
3
0
0
1
3
1
0
2
0
1
0
2
0
0
0
0
0
1
0
1
0
0
1
0
1
0
1
0
1
0
2
0
1
1
0
1
0
1
0
2
2
1
1
0
3
2
1
0
0
1
0
0
0
2
1
1
0
3
1
1
0
1
1
2
1
0
0
1
3
1
1
0
0
2
0
2
2
0
0
2
1
0
0
2
0
0
1
0
2
1
1
1
2
1
0
0
0
1
0
1
2
1
0
0
0
1
0
1
1
0
1
0
0
0
1
2
2
0
0
0
2
0
2
2
0
0
0
0
0
0
1
0
1
1
0
1
1
1
1
2
0
0
0
0
1
0
2
1
0
0
3
0
0
1
1
0
2
0
0
0
0
2
2
1
0
0
0
1
0
0
0
2
1
2
0
2
2
0
0
0
1
2
0
1
0
0
1
0
0
2
1
1
1
0
0
0
0
1
1
1
0
0
2
1
0
1
0
1
1
0
1
0
2
0
0
1
1
1
0
0
1
0
1
1
0
0
0
0
0
2
1
0
2
1
0
1
1
2
0
2
0
0
0
0
0
2
0
1
4
0
1
1
0
1
0
0
0
1
1
3
0
1
0
0
2
2
0
1
0
0
1
1
0
1
1
0
0
0
0
1
1
2
0
0
0
0
1
1
0
0
1
1
1
0
2
1
0
2
1
0
2
2
0
1
2
2
0
0
1
0
1
0
1
0
1
1
0
0
0
2
0
1
1
2
0
2
2
2
0
2
1
1
0
0
1
2
2
0
0
2
1
0
2
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
1
0
2
1
0
1
0
0
1
1
0
0
1
2
1
1
0
1
0
0
0
2
0
1
2
2
0
0
0
1
0
2
1
1
0
1
0
1
0
0
1
0
2
0
0
1
0
0
2
0
0
0
1
0
2
2
1
1
0
1
0
1
0
0
3
2
0
1
0
0
1
1
0
1
0
0
0
0
0
3
1
2
0
0
2
0
0
1
0
0
0
0
2
0
1
0
0
3
2
1
1
1
1
0
0
2
0
1
2
2
0
2
0
1
1
2
2
1
1
2
0
1
1
2
0
1
0
2
2
0
0
0
2
0
2
1
0
5
1
0
0
0
1
2
3
0
1
3
0
1
0
1
2
1
2
1
1
0
0
1
2
2
2
2
0
0
1
0
1
2
2
1
0
2
0
0
0
0
2
0
0
0
2
0
2
2
2
2
0
1
1
1
1
0
2
2
0
1
0
0
2
0
0
1
0
2
1
0
1
0
1
1
0
0
0
1
0
1
1
0
1
1
0
1
2
0
1
0
1
1
0
0
1
1
0
0
2
1
0
2
2
2
1
3
0
1
1
1
1
1
1
1
0
0
0
2
0
2
1
1
1
1
0
1
1
2
2
2
1
1
2
2
1
1
2
1
1
0
0
0
1
1
2
0
1
0
1
1
0
0
0
0
0
1
1
0
1
0
2
1
0
2
0
0
1
0
2
0
2
0
1
0
0
2
2
0
2
2
0
1
1
0
0
1
1
1
1
1
0
2
0
0
0
0
0
0
0
1
0
2
2
1
1
1
2
0
2
0
2
2
1
0
0
2
0
0
2
0
0
1
0
2
2
1
0
0
0
2
1
2
2
0
1
0
0
1
0
1
1
1
0
0
0
2
2
1
0
2
2
2
3
2
0
0
0
1
2
1
1
1
1
1
0
1
0
0
2
2
2
0
1
0
0
0
0
2
1
2
2
0
0
1
0
0
1
0
2
1
0
0
2
1
1
0
2
1
0
0
0
1
1
1
0
0
0
2
1
0
1
0
1
0
0
1
2
1
1
0
1
0
1
0
0
1
0
0
1
2
2
0
1
2
1
2
1
2
2
0
0
1
1
1
1
0
0
0
0
0
1
2
1
1
0
0
2
1
0
1
3
1
2
2
2
0
0
1
0
0
0
0
0
1
0
0
0
0
2
2
1
1
2
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
2
1
0
0
2
0
0
1
0
0
0
2
1
0
1
3
2
0
1
1
2
2
1
2
2
1
0
1
3
0
2
0
1
1
0
0
1
1
1
0
0
0
0
1
2
0
1
1
0
1
0
2
0
1
1
1
1
1
0
0
1
1
0
0
1
1
0
1
1
0
1
1
0
0
1
0
0
2
0
2
1
0
1
0
1
0
0
1
2
0
0
0
3
1
1
1
0
2
0
0
0
0
2
1
1
0
2
2
0
1
2
1
1
1
1
0
1
0
1
0
1
0
0
1
0
2
0
0
1
1
1
0
1
0
0
2
0
0
1
1
1
1
2
0
2
2
1
0
0
0
2
0
0
0
1
0
5
0
2
1
5
2
0
1
1
2
0
0
0
1
0
2
0
1
1
1
2
1
2
0
2
0
2
0
2
1
1
0
2
0
0
1
2
2
0
0
2
1
0
0
1
1
1
2
0
1
0
1
0
0
0
2
0
0
2
2
0
1
1
0
0
1
1
0
1
2
0
2
0
0
1
0
0
1
1
1
1
0
2
0
2
1
2
2
1
1
1
0
0
0
1
2
0
8
2
1
1
0
1
2
2
2
2
0
1
1
1
0
1
1
0
0
0
0
1
0
2
1
1
1
1
2
0
1
0
2
1
0
0
0
1
1
0
0
0
1
0
0
1
1
2
2
0
0
2
2
2
0
0
0
2
0
1
0
1
1
0
0
2
1
0
2
0
2
1
1
1
1
1
2
1
0
2
1
0
0
1
0
1
1
0
1
0
1
1
1
1
0
0
2
1
0
0
1
1
1
1
1
0
1
0
0
0
1
1
0
0
0
0
1
1
0
2
1
2
2
0
0
2
1
1
0
0
0
0
0
0
0
0
0
3
2
3
0
2
1
1
1
0
0
0
2
1
1
1
2
0
0
2
1
2
2
0
2
0
0
0
1
0
1
2
0
1
1
1
2
0
1
1
0
0
2
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
1
2
0
0
1
2
1
0
0
0
0
1
0
1
1
1
0
2
0
0
0
1
0
2
0
1
2
1
1
0
0
1
2
1
0
1
0
3
1
0
1
1
0
0
0
0
1
1
0
1
0
1
1
0
0
2
0
0
0
2
0
0
0
1
0
3
0
0
1
1
2
2
1
0
1
0
2
0
1
0
0
0
1
0
0
2
0
0
0
2
1
1
0
1
0
1
0
1
1
0
1
0
1
1
2
4
0
2
1
2
0
2
0
1
1
2
2
1
0
1
0
1
2
2
0
0
0
0
6
2
0
0
1
0
2
0
0
0
0
2
1
1
0
0
5
1
1
0
0
2
2
0
1
1
1
1
0
1
0
0
2
1
0
2
1
1
5
1
0
2
1
2
0
2
0
1
0
0
1
1
1
2
1
1
1
2
2
0
1
1
1
0
2
0
2
2
0
1
1
0
1
1
0
0
1
2
1
0
1
2
1
0
1
1
0
0
1
2
1
0
1
1
0
1
1
0
0
1
3
1
0
1
1
0
3
1
1
2
0
1
0
2
2
3
1
2
2
0
1
5
0
0
3
0
1
0
0
1
1
0
1
0
1
2
0
0
1
1
1
2
4
1
0
0
1
0
0
1
0
0
1
0
1
3
2
1
2
1
0
0
1
0
3
0
0
0
0
1
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
1
1
0
2
0
0
2
1
0
2
2
1
0
0
0
0
0
0
1
2
0
0
1
1
0
0
1
1
0
1
0
1
0
1
0
0
0
2
0
0
1
0
1
0
0
2
1
0
0
1
0
1
1
2
1
2
0
0
2
2
0
1
2
1
0
0
0
2
0
0
0
2
0
1
0
0
1
1
0
0
0
1
0
0
2
0
0
0
0
1
1
1
1
0
0
0
0
0
1
0
0
2
1
1
0
1
2
1
0
0
2
2
2
0
1
0
0
0
0
0
0
2
0
1
2
0
2
2
0
1
1
0
1
1
0
1
0
0
0
2
1
0
0
1
2
0
2
1
0
0
0
1
1
2
1
0
0
2
0
0
0
0
2
2
0
1
1
0
0
1
2
2
2
0
1
0
0
2
1
2
1
1
2
1
1
0
0
1
1
0
0
0
0
1
0
1
0
1
0
0
1
1
0
1
1
0
0
0
1
0
1
0
0
1
2
0
0
2
0
1
2
1
0
0
1
0
1
0
0
1
0
0
1
3
0
0
0
2
1
0
0
1
0
1
1
0
0
1
2
0
1
0
0
0
1
0
1
0
0
2
1
2
1
0
2
0
0
0
1
0
0
1
0
1
0
1
0
1
0
1
0
3
1
0
1
2
1
1
0
1
0
1
0
0
0
0
0
0
1
2
1
0
2
1
2
2
1
3
1
1
1
0
1
0
0
0
0
2
1
1
2
2
1
0
1
1
0
1
1
0
3
1
0
0
1
2
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
2
0
0
2
0
0
0
1
0
1
0
1
1
0
1
1
1
2
2
0
0
0
1
1
2
1
0
0
2
2
1
2
0
0
2
0
1
0
2
1
1
2
0
0
1
0
2
0
1
0
2
1
0
0
1
1
1
1
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
2
0
0
1
1
0
2
1
0
1
1
0
4
1
1
0
0
0
1
1
0
1
1
0
0
0
0
1
0
0
0
1
0
1
0
1
2
0
1
2
1
1
2
0
2
0
0
2
1
1
1
1
0
2
0
2
1
2
0
1
0
1
1
2
3
1
1
0
1
0
0
0
2
0
0
1
2
0
1
1
0
2
0
2
1
0
0
0
1
2
1
1
1
0
1
1
2
2
0
0
0
1
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
1
2
0
2
0
0
2
0
2
2
0
1
0
1
1
2
0
0
0
0
0
2
0
0
0
2
0
1
1
1
1
0
0
0
0
2
0
2
1
0
1
1
0
1
0
0
0
0
0
2
0
2
1
1
3
2
2
1
1
1
1
1
0
0
3
0
0
2
2
0
0
2
1
2
2
1
0
1
1
0
1
0
1
1
0
1
1
1
0
0
1
1
0
1
0
1
2
0
0
0
1
0
1
2
2
0
1
1
1
0
1
0
2
0
0
2
0
1
0
0
1
0
1
1
1
0
1
0
2
0
0
0
4
0
2
0
0
2
0
2
2
0
2
1
2
1
1
2
1
2
0
2
2
0
1
1
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
2
2
1
0
2
1
0
0
1
0
0
0
2
1
1
1
0
0
1
0
2
0
0
2
1
1
1
0
0
1
1
2
0
0
1
0
0
1
1
0
1
0
2
1
0
1
1
2
0
0
2
0
1
0
0
1
0
2
0
0
0
2
0
0
1
2
0
0
1
0
2
2
1
0
1
0
0
2
0
1
0
1
0
0
0
2
0
1
1
2
0
0
0
0
0
0
1
0
1
0
4
0
0
1
1
0
0
3
0
1
0
2
1
0
1
0
0
1
0
0
1
0
0
2
2
1
0
2
0
1
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
3
0
1
2
0
2
1
3
0
0
1
1
0
1
1
1
0
0
1
2
0
0
1
0
1
1
1
3
1
1
0
0
2
2
2
1
0
1
2
1
1
2
0
1
1
0
1
0
2
0
0
1
0
1
1
0
2
0
2
1
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
1
0
1
0
1
0
1
0
1
1
0
0
1
0
1
2
0
1
3
2
2
0
0
0
0
0
0
1
1
2
2
1
0
0
1
0
0
1
0
0
0
1
1
0
2
2
3
2
0
2
1
0
1
0
2
1
1
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
4
1
0
4
0
1
1
1
2
0
2
1
0
1
2
0
2
2
0
1
0
1
0
2
0
0
1
2
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
1
1
2
1
1
1
1
0
0
1
0
0
0
0
0
1
1
1
2
0
2
1
2
1
1
0
0
0
0
2
0
0
2
1
1
0
2
0
1
0
1
2
0
2
0
0
0
0
0
1
0
2
0
0
1
1
2
2
1
0
3
1
2
0
0
2
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
2
1
0
0
1
1
0
0
0
2
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
2
1
1
0
2
2
1
2
0
0
2
0
1
2
2
1
1
0
1
1
0
2
0
1
0
0
1
1
1
1
0
1
0
1
1
1
1
0
1
2
1
0
1
1
0
1
2
0
1
3
0
2
2
1
0
2
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
1
2
0
0
0
0
2
1
0
0
0
2
1
2
1
0
0
0
0
2
1
2
0
0
1
0
1
2
0
0
0
0
0
0
2
0
0
1
1
0
0
2
0
1
0
2
3
0
1
1
0
0
1
1
2
0
1
2
1
0
0
0
0
2
2
1
2
2
0
1
2
0
1
0
0
1
0
2
1
1
2
0
0
2
2
1
1
1
1
1
1
3
2
0
0
0
0
1
0
2
0
0
2
0
0
0
0
2
0
0
0
1
0
1
0
1
1
0
0
0
3
0
3
2
0
1
0
0
2
1
0
1
0
2
2
0
1
0
0
0
0
2
1
2
0
1
0
2
1
1
0
1
0
2
0
2
0
1
1
0
0
1
0
2
2
2
2
0
1
2
1
0
0
0
1
1
1
0
2
4
0
1
2
0
1
2
0
0
2
0
0
0
2
2
0
1
1
1
0
1
1
2
1
0
0
0
1
0
0
1
1
0
1
0
0
0
1
2
0
1
0
1
1
0
0
1
0
0
0
0
1
1
0
1
0
0
2
1
1
1
2
1
1
0
0
1
0
0
1
1
1
0
0
1
1
2
2
2
0
0
1
0
1
0
2
0
1
0
2
0
1
0
1
2
2
0
0
2
1
1
1
0
0
1
2
0
1
2
1
1
0
2
1
0
1
1
1
1
0
1
2
1
2
1
1
1
0
1
2
1
0
0
0
0
1
0
1
1
0
1
0
1
2
1
1
2
0
2
0
3
0
2
0
0
1
1
0
3
1
0
0
0
1
1
0
1
0
0
1
1
1
0
1
0
1
1
0
1
2
0
1
1
0
1
1
1
2
0
2
2
2
1
2
2
0
0
1
1
0
1
1
0
3
1
1
3
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
2
1
0
1
0
0
0
1
2
0
1
0
1
0
2
0
1
0
0
0
1
2
1
0
2
0
1
2
1
1
0
0
2
0
1
2
2
2
1
1
0
1
0
1
1
0
0
1
1
0
1
0
0
0
0
3
1
1
1
2
1
0
2
1
1
0
2
0
0
1
0
2
1
0
0
0
1
0
1
0
2
0
1
2
1
2
0
0
0
0
0
1
0
2
0
0
0
1
2
1
1
1
0
1
0
1
0
1
0
1
0
2
0
1
2
2
0
1
1
0
0
0
1
0
2
0
1
0
1
0
3
2
2
2
0
2
2
2
0
0
1
1
2
0
1
0
1
0
2
0
2
1
2
0
1
2
1
2
1
1
0
1
1
0
1
0
1
1
2
2
0
0
0
0
0
2
0
0
1
2
0
1
0
1
1
2
2
2
0
2
0
0
0
2
1
0
2
0
0
0
1
1
0
0
1
2
0
3
2
0
0
0
2
0
0
1
0
0
0
0
2
1
2
0
2
2
0
1
3
0
0
0
3
1
1
0
0
0
0
2
1
0
2
1
1
1
2
0
1
0
1
0
0
0
0
0
3
0
0
0
3
0
0
0
2
2
1
1
0
2
1
0
2
0
2
1
1
0
0
0
0
2
3
0
1
0
0
0
0
0
0
0
2
2
0
1
1
1
0
1
1
0
0
1
3
0
2
1
1
2
0
0
0
0
0
0
0
1
0
0
1
0
1
2
0
0
0
0
0
0
0
1
2
0
0
0
1
1
1
0
0
1
0
2
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
1
2
0
2
0
0
0
2
0
1
1
1
1
1
1
0
1
2
0
0
2
1
2
1
0
1
2
1
0
2
0
2
1
2
1
1
1
1
1
2
0
1
0
0
2
1
0
2
2
2
2
0
1
1
0
1
0
1
0
2
1
0
0
1
0
0
1
0
0
0
1
0
0
1
1
0
1
0
1
0
1
1
0
1
0
0
1
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
1
1
0
2
2
2
1
0
0
0
1
0
0
0
0
0
0
1
0
2
0
3
0
1
0
2
0
2
0
0
1
2
1
0
2
2
1
0
0
2
1
1
2
1
2
0
0
0
1
0
1
1
0
0
0
0
0
1
0
1
1
0
0
0
1
1
2
0
2
0
0
0
2
0
1
1
0
0
0
0
0
2
0
1
0
2
0
1
2
0
1
1
0
1
0
0
0
0
1
0
0
2
1
1
0
0
1
0
1
1
0
0
0
2
0
1
0
0
1
0
1
0
0
0
1
1
0
1
1
0
0
0
0
1
2
0
1
0
1
0
0
1
0
0
0
1
2
1
1
1
2
1
2
1
1
1
1
0
2
0
1
1
0
0
1
0
1
0
2
1
1
0
1
1
0
1
1
0
0
1
2
0
3
1
0
1
0
0
0
2
0
0
2
1
3
1
1
2
0
0
2
0
2
2
2
0
2
1
0
0
1
1
0
2
0
0
1
1
2
0
0
0
0
0
0
0
1
2
2
1
1
0
0
0
0
0
0
2
0
1
0
1
0
0
0
1
1
0
2
0
0
2
1
1
1
1
1
0
0
1
4
0
0
0
1
1
0
1
1
0
2
2
2
0
0
2
1
2
0
1
0
0
1
1
0
1
2
0
2
1
1
1
2
0
1
0
0
0
0
2
1
0
0
0
0
2
2
1
0
0
0
0
0
2
1
1
0
2
1
5
0
1
1
1
2
0
1
2
2
2
0
1
0
1
0
2
0
2
0
1
1
1
1
0
0
0
1
1
0
1
2
1
0
0
1
0
2
1
0
1
1
1
1
0
0
0
0
1
0
0
2
2
0
1
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
2
4
0
1
0
0
2
0
0
2
0
0
0
1
0
1
1
0
2
2
0
3
1
0
0
0
0
0
0
2
1
1
0
2
2
1
1
1
0
4
0
1
0
0
1
0
0
0
1
1
0
1
1
2
0
0
0
1
1
1
0
2
0
0
2
0
0
0
0
2
1
0
0
2
1
1
0
0
2
0
0
2
0
2
1
1
1
0
1
2
2
0
1
0
1
1
2
2
0
1
2
1
1
1
3
2
2
0
2
0
1
1
0
2
1
0
2
1
1
1
0
2
0
1
1
0
1
2
0
0
0
0
2
0
1
2
1
1
0
0
0
1
1
1
0
0
0
0
1
1
0
1
0
1
3
0
0
2
2
1
2
0
2
0
2
0
0
4
1
1
1
0
1
1
1
0
0
0
2
0
0
0
1
1
0
0
2
0
2
6
2
0
1
1
2
1
0
1
2
0
0
0
0
1
1
1
0
0
2
0
0
1
1
1
0
2
2
0
2
1
0
1
1
1
0
2
1
1
1
0
0
2
0
0
1
0
2
0
0
0
2
1
1
1
0
0
0
0
0
0
1
0
1
2
2
2
0
2
0
0
1
2
0
2
1
1
0
1
1
0
2
0
1
2
1
1
2
0
0
2
1
3
2
0
2
0
1
0
0
0
1
2
1
0
0
2
1
2
0
1
0
1
0
0
1
1
1
3
2
0
0
2
0
2
0
1
1
0
0
0
0
3
0
2
1
0
1
0
2
1
1
2
1
2
1
0
0
1
1
2
0
1
0
0
1
0
0
1
0
0
0
0
0
2
0
1
1
0
2
0
1
1
2
0
0
0
0
1
0
2
2
0
1
0
1
0
0
0
2
1
0
0
3
2
0
1
0
0
0
0
1
0
0
2
3
0
0
1
1
2
2
1
0
0
0
0
1
0
0
0
1
0
1
0
0
1
2
1
0
2
1
1
2
3
0
2
0
0
1
1
1
2
1
0
2
2
0
1
2
1
0
2
0
1
1
1
2
2
0
1
0
0
0
1
0
1
0
0
0
1
0
2
0
0
1
1
2
0
0
0
0
1
0
2
1
0
1
1
0
0
1
0
1
0
0
3
1
0
0
2
1
4
1
2
2
0
2
0
0
2
1
0
0
0
2
2
0
0
0
0
0
1
0
1
1
0
1
0
2
0
0
2
2
1
0
0
0
0
0
2
1
0
2
0
1
1
2
0
0
0
0
0
1
1
1
1
1
0
0
0
1
0
0
0
0
1
0
0
1
1
1
0
0
1
0
1
2
0
1
2
0
4
0
2
2
0
0
3
0
1
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
2
2
0
1
1
1
0
0
2
0
2
0
0
0
0
1
1
1
1
1
1
1
0
0
1
1
0
0
0
0
1
0
2
2
0
1
0
0
0
2
2
0
0
0
0
2
1
1
0
0
0
0
1
0
0
0
1
1
0
1
2
1
0
1
0
0
0
2
1
0
0
2
0
1
0
0
1
0
1
0
1
1
0
1
1
0
1
2
1
0
1
0
0
0
0
2
2
1
0
1
1
0
0
1
1
0
0
1
0
0
0
3
1
1
0
1
1
2
1
1
2
0
1
1
0
0
1
2
0
0
2
0
2
0
0
1
0
1
2
1
2
1
0
0
0
0
0
0
1
0
0
0
1
0
2
0
2
0
0
0
0
2
2
0
2
1
1
0
0
0
0
1
0
1
1
2
2
0
0
2
1
2
1
2
0
2
1
1
0
1
0
1
0
1
1
0
1
1
0
0
0
1
1
0
1
1
0
0
2
2
0
0
1
1
0
4
0
1
2
0
0
0
0
0
1
0
0
2
2
2
2
0
2
0
1
0
1
1
0
1
0
0
0
0
2
0
0
1
0
2
0
2
2
0
1
0
0
2
1
2
0
1
1
0
1
0
1
1
2
2
1
1
1
0
2
0
0
0
0
2
1
0
0
0
1
1
1
1
2
2
0
0
2
0
1
2
0
0
2
1
0
0
0
2
0
1
1
1
1
0
0
1
2
2
0
1
2
2
1
0
1
1
0
0
0
0
1
0
0
0
0
2
1
0
1
0
2
0
1
0
2
0
0
0
0
2
0
2
0
0
1
1
0
2
0
0
4
0
1
0
1
3
0
0
0
0
0
0
2
0
2
1
1
0
0
0
0
0
1
1
1
1
0
0
1
0
1
1
1
2
0
1
3
2
0
1
3
1
2
0
1
2
1
0
1
0
0
0
0
2
2
1
0
1
2
0
0
0
0
1
1
0
1
1
0
2
1
1
2
0
0
2
0
2
1
2
1
1
0
2
0
0
1
2
1
0
1
2
2
1
0
0
1
1
0
2
1
2
0
2
1
2
2
2
0
0
0
1
0
0
0
1
1
2
1
0
0
0
0
1
0
0
0
0
1
0
2
1
0
3
1
0
1
1
1
2
1
0
1
0
0
1
0
0
1
0
2
1
0
0
1
0
0
1
1
0
1
2
0
0
1
1
1
0
1
0
1
1
1
2
1
0
1
1
2
2
1
0
0
0
0
1
0
1
0
1
2
0
0
0
0
0
2
2
0
1
0
0
2
0
0
1
1
0
2
0
0
0
0
0
1
2
0
0
0
0
1
2
1
1
0
1
0
0
1
2
1
0
2
0
2
2
0
0
2
0
2
0
1
0
2
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
2
0
0
0
1
2
0
0
0
1
1
0
1
1
0
0
0
1
0
1
0
1
0
0
0
1
1
0
0
1
1
1
1
0
0
0
2
1
0
0
0
1
1
2
2
0
0
1
0
1
0
2
2
2
1
2
2
0
1
1
1
0
1
0
0
1
2
0
1
0
2
2
2
0
0
2
1
1
1
1
1
2
0
0
0
1
2
2
1
0
2
0
1
1
0
0
0
2
1
0
1
2
0
2
1
0
1
0
2
1
2
0
1
0
1
2
2
0
0
1
1
1
1
1
2
1
0
0
1
1
1
1
0
1
0
0
2
0
2
0
0
2
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
2
0
0
1
0
0
2
0
0
1
0
0
1
1
1
1
2
1
1
0
1
0
1
0
0
1
2
2
2
1
0
0
0
0
3
1
0
0
2
3
1
2
1
0
2
1
0
1
2
2
2
0
2
1
0
1
2
1
1
0
1
1
0
2
2
1
1
2
0
1
0
0
1
0
0
1
2
1
0
0
1
1
1
0
1
1
0
2
0
2
0
0
2
1
0
0
2
0
0
0
0
1
1
1
0
2
1
0
0
1
1
0
0
1
1
0
1
0
1
2
1
1
2
0
1
2
0
2
1
1
0
3
1
2
0
0
2
0
0
1
0
2
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
1
1
2
2
1
0
0
1
0
1
1
0
1
1
0
0
2
2
0
1
0
2
0
0
1
1
1
1
0
0
0
0
1
0
1
0
1
0
0
1
2
0
3
2
2
0
1
0
0
0
1
0
2
1
1
0
1
2
0
0
1
1
0
0
2
0
1
2
1
1
0
0
1
0
2
0
0
1
0
0
0
0
1
0
0
1
2
0
0
1
0
3
0
0
2
0
1
2
0
1
1
2
2
0
0
1
2
1
0
0
2
2
1
2
0
1
0
0
0
0
2
0
0
0
2
0
0
0
2
1
2
0
0
1
1
2
0
2
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
1
1
1
2
0
0
2
0
0
0
3
2
0
1
1
6
1
0
0
3
0
2
0
0
1
0
2
1
1
0
0
2
0
1
2
1
2
3
1
0
0
0
0
1
1
1
1
1
4
0
2
2
1
1
0
1
1
1
0
0
0
0
3
0
1
0
0
2
0
0
0
2
2
0
0
2
0
1
3
0
0
0
0
2
0
1
0
1
2
2
0
0
2
1
1
1
1
6
1
2
0
0
1
2
0
2
2
0
0
0
0
1
0
0
0
1
2
2
1
0
0
2
0
0
2
1
0
0
1
2
2
0
0
0
1
1
0
3
0
1
2
1
0
0
0
0
0
0
2
3
1
2
2
0
0
1
1
0
1
2
2
0
2
0
2
2
0
0
1
0
2
0
1
1
1
1
0
0
1
2
0
1
1
0
1
0
0
0
0
0
1
1
0
1
1
0
0
2
2
0
1
1
0
0
3
2
0
0
0
0
2
1
0
3
0
0
1
0
0
1
0
1
1
0
0
2
0
0
0
0
1
2
0
1
0
0
2
0
1
0
0
0
1
0
1
0
1
1
0
0
0
3
2
0
0
0
2
0
0
2
2
1
2
0
0
2
0
0
1
0
1
1
0
0
2
0
2
2
0
1
0
0
1
1
0
2
1
1
1
2
0
1
1
1
1
1
1
1
2
0
0
2
0
0
0
0
1
0
2
1
0
2
0
1
1
2
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
1
1
0
0
2
0
2
0
2
2
0
1
2
2
1
2
0
3
1
1
0
0
1
1
0
0
0
1
2
1
1
1
2
0
0
1
1
0
0
1
0
0
2
0
0
2
2
0
0
0
0
1
2
5
0
1
0
0
0
0
2
1
0
7
0
0
1
0
2
1
0
2
0
1
1
2
0
0
1
0
0
2
0
0
2
1
0
1
2
0
2
0
0
1
1
1
1
2
0
2
0
1
1
2
0
1
0
0
0
0
0
0
0
0
1
2
2
2
2
1
1
0
2
0
0
0
0
2
1
1
0
0
2
1
1
2
1
1
2
2
0
1
1
0
2
0
0
1
0
0
1
0
0
1
0
1
0
0
0
1
2
0
2
2
0
0
1
1
0
1
1
1
1
2
0
1
1
1
0
0
0
1
1
2
2
2
1
2
0
3
1
0
2
0
2
1
1
1
0
0
0
1
1
0
0
1
2
3
0
1
0
1
0
0
1
1
0
2
1
2
0
2
1
1
3
2
0
2
2
0
0
2
0
2
1
2
0
2
0
1
2
1
0
0
2
1
0
1
0
1
0
0
2
0
0
0
0
1
1
0
0
0
1
2
0
2
0
1
2
2
0
0
0
1
0
2
0
1
0
1
0
1
1
1
2
0
1
2
2
2
0
0
0
2
0
1
0
0
0
1
1
0
2
2
0
2
0
0
1
0
0
0
0
1
2
0
1
0
1
2
1
1
2
0
1
1
1
0
1
2
1
0
0
2
1
1
0
1
0
1
0
1
2
1
0
1
1
1
2
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
3
1
1
0
2
1
0
1
2
2
1
0
1
0
0
0
0
0
0
1
0
3
2
0
1
0
1
2
0
1
0
1
0
1
2
0
0
0
0
0
0
0
0
2
0
0
1
2
0
1
0
1
2
0
0
1
0
0
0
0
2
2
0
0
0
1
0
1
0
0
2
0
0
2
0
1
2
1
2
1
0
0
0
1
0
0
1
0
1
1
1
0
1
1
0
1
0
1
0
0
2
1
0
1
2
1
2
2
0
0
1
2
2
1
1
1
0
0
1
0
1
2
0
1
0
2
0
0
2
0
2
0
2
1
1
1
1
0
0
0
0
0
1
0
2
0
1
2
0
1
0
2
1
2
0
1
0
0
1
1
0
0
0
1
0
0
1
0
1
0
2
1
0
2
2
3
0
0
2
2
0
0
1
0
0
0
1
1
2
0
2
1
0
1
1
0
0
0
0
0
2
0
2
1
2
0
1
0
0
2
1
1
0
1
1
0
1
0
1
1
1
1
0
2
0
2
1
2
2
0
1
1
0
0
0
1
2
0
2
1
0
1
1
2
0
0
0
0
1
0
0
1
0
2
1
0
0
2
2
2
0
0
1
1
0
1
6
2
1
0
2
1
0
2
2
1
1
0
0
1
0
0
1
0
2
2
1
1
0
2
1
1
1
1
2
1
0
1
0
0
1
0
1
1
0
0
1
1
0
2
0
0
1
1
1
1
2
0
0
0
0
1
1
1
2
0
2
1
2
0
0
2
0
0
0
2
1
2
1
0
0
0
1
0
1
2
1
0
1
1
1
0
1
2
0
0
0
1
1
1
0
1
0
1
1
1
1
0
0
2
1
2
1
2
0
1
1
0
0
0
0
1
0
0
1
2
0
2
2
2
0
1
0
2
1
2
2
0
0
0
1
0
2
0
1
0
0
1
0
1
0
2
2
2
3
0
1
0
0
1
1
2
0
0
0
1
0
1
0
1
0
2
1
2
0
0
1
0
0
1
1
2
2
2
1
0
0
2
0
1
1
0
2
1
2
2
0
1
1
0
0
1
0
2
0
0
0
1
0
0
0
0
1
1
2
0
2
0
0
0
0
1
1
0
0
1
2
0
2
1
2
1
0
0
0
1
0
0
2
0
3
1
0
2
1
0
1
0
1
0
0
0
2
2
3
2
0
0
0
0
1
1
1
1
0
1
1
0
0
1
1
2
2
0
2
0
0
0
0
0
1
1
1
1
0
2
0
1
4
2
0
1
1
0
2
2
0
0
3
0
2
1
2
0
1
3
2
0
1
0
0
0
0
0
0
0
1
1
3
2
1
0
2
0
1
0
0
0
0
2
2
1
0
0
0
1
2
2
1
0
0
0
0
0
1
0
0
1
1
2
1
1
0
4
2
1
0
1
0
1
2
0
0
2
0
0
0
0
0
2
1
0
0
1
1
2
0
2
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
1
1
1
0
1
1
0
0
1
0
0
0
0
1
2
2
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
2
1
1
0
2
0
0
6
1
1
1
0
2
2
2
0
2
0
1
0
1
0
0
2
1
3
1
0
2
1
1
0
1
1
1
0
2
2
0
1
0
2
0
2
0
1
1
1
0
0
0
1
0
3
0
1
0
1
0
0
1
0
0
2
0
1
2
0
1
1
2
4
0
0
0
0
1
0
0
2
0
1
1
0
2
0
1
1
2
0
2
2
0
0
1
0
2
1
0
1
0
0
0
1
1
1
0
1
0
1
1
0
0
1
1
1
1
1
0
0
1
0
1
0
0
0
0
0
0
2
2
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
2
1
1
0
0
2
0
1
1
1
1
2
0
4
0
1
2
1
0
1
2
0
0
0
1
2
2
2
0
2
0
0
0
2
2
0
2
1
2
0
2
0
0
1
3
1
2
1
0
1
0
2
0
0
2
0
1
2
1
0
2
2
1
1
2
0
1
2
2
1
1
2
1
0
1
0
0
0
2
0
0
2
2
1
2
2
0
0
0
0
0
0
0
1
0
2
0
0
0
1
1
1
0
4
0
0
2
0
0
0
2
1
0
2
0
2
1
2
1
1
2
1
1
1
2
0
0
2
0
0
0
2
2
0
2
0
0
1
1
1
0
1
1
0
1
1
0
2
0
0
1
0
0
0
0
1
1
2
4
0
0
1
0
1
0
1
1
2
5
0
2
0
0
1
1
1
0
2
1
1
0
2
0
2
1
2
4
0
0
1
1
2
0
0
0
1
1
2
1
0
0
1
0
1
1
2
0
2
2
2
1
0
1
0
2
0
0
0
1
1
2
1
0
2
1
0
1
2
1
2
0
0
1
1
0
2
0
1
1
1
1
1
0
2
2
2
1
2
2
1
2
0
0
0
2
2
0
0
0
1
0
0
1
0
2
0
0
2
0
0
0
1
0
2
1
0
1
2
3
1
1
1
1
0
1
0
3
1
0
0
4
0
0
0
0
2
1
0
2
1
1
0
0
0
2
0
2
4
1
1
0
1
1
0
1
1
0
1
2
0
1
1
1
1
0
0
1
1
0
2
0
1
2
1
1
2
1
0
1
1
1
2
1
0
2
2
0
1
0
0
2
1
1
1
0
2
2
2
0
0
0
0
1
1
0
1
2
2
1
0
0
1
0
1
0
1
1
0
0
1
1
0
1
0
2
0
0
1
1
2
1
0
1
1
3
0
2
1
2
0
2
0
2
0
2
0
0
0
1
0
0
2
0
0
0
0
0
2
0
2
1
0
1
3
1
0
2
0
0
0
0
0
0
0
1
1
1
0
1
0
0
2
2
1
0
1
1
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
2
2
0
1
1
1
0
2
1
1
0
0
0
0
1
1
2
0
1
0
0
0
1
2
1
2
0
0
0
2
1
1
1
0
2
2
0
0
0
0
1
0
1
0
0
0
1
1
1
1
0
1
0
0
1
1
2
1
1
1
1
0
1
0
0
1
0
1
0
0
0
1
1
0
1
0
2
1
1
2
1
1
0
1
1
0
0
0
0
0
2
0
0
3
0
0
1
1
0
0
0
1
1
0
0
0
3
1
2
0
0
1
2
1
1
1
1
0
1
0
0
1
0
0
2
1
0
1
0
0
0
1
0
1
0
0
0
2
2
2
2
0
0
1
0
0
2
2
0
1
0
1
2
0
1
0
0
0
2
0
1
1
1
0
0
0
1
0
2
2
2
0
1
1
0
1
2
0
1
0
0
2
1
0
0
2
0
0
0
2
0
1
1
2
3
1
0
0
2
0
1
1
0
2
0
1
2
2
0
1
0
1
0
2
0
1
2
1
1
1
1
0
0
2
1
1
0
2
1
2
1
0
2
2
0
2
0
0
2
1
2
2
2
0
1
1
0
0
0
2
1
1
2
0
0
0
1
0
1
0
0
0
1
1
0
1
0
1
0
2
1
0
0
1
0
0
2
2
0
1
1
0
0
0
0
1
1
0
0
0
2
0
2
0
1
0
0
1
0
1
1
1
2
0
2
0
1
0
0
1
0
1
1
1
1
2
1
1
1
0
2
0
1
0
0
2
0
0
0
2
0
0
3
0
1
1
0
2
1
2
2
1
1
1
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
1
2
1
1
0
2
0
0
2
0
0
2
0
0
0
0
1
1
2
1
0
0
0
0
0
0
2
1
0
0
1
2
1
0
0
0
1
1
1
0
1
0
1
2
2
1
0
1
0
2
0
2
0
2
0
1
0
2
0
0
2
1
0
3
2
1
1
0
2
0
0
1
0
2
0
1
0
0
0
0
0
0
1
1
1
1
0
0
0
2
0
4
0
0
2
1
0
1
2
2
0
0
0
1
1
1
0
0
0
1
2
0
1
1
1
1
0
1
0
0
1
0
1
0
0
1
0
0
1
0
1
1
0
0
1
1
2
0
0
2
1
1
1
1
2
1
0
0
0
1
1
2
2
2
2
1
2
1
0
0
3
1
0
1
0
2
2
1
2
3
2
0
1
0
1
0
1
0
1
0
1
1
0
1
2
1
2
2
2
0
0
1
0
0
2
0
1
1
1
2
1
1
1
2
1
0
0
2
0
0
0
0
1
0
0
1
0
0
0
1
0
0
2
0
0
1
0
0
0
1
2
0
1
0
0
2
2
1
2
0
1
2
1
0
0
0
0
1
0
0
0
0
2
0
2
1
1
0
1
0
2
1
1
0
1
0
2
0
1
1
0
0
1
2
0
3
1
0
0
2
0
1
0
1
1
2
0
1
0
0
0
1
1
0
2
0
1
1
1
1
1
2
0
1
0
1
2
0
2
1
0
1
2
1
0
2
2
1
0
2
2
2
1
2
1
1
0
1
1
0
1
1
0
2
1
1
0
0
2
2
1
2
1
2
2
1
0
0
1
1
1
0
0
0
2
1
1
2
0
1
0
0
0
0
1
1
0
0
0
2
0
1
0
0
2
1
0
1
0
0
1
1
1
0
1
0
0
2
0
2
0
1
2
2
1
2
0
1
1
1
0
2
0
1
0
0
0
0
0
1
1
2
2
2
2
0
1
1
1
1
1
0
2
0
0
2
2
2
0
1
0
2
1
0
0
0
2
1
0
1
2
1
1
0
0
0
1
1
2
0
2
1
1
2
2
0
0
1
1
1
3
2
0
2
1
1
0
1
1
0
1
3
1
0
2
0
2
0
1
1
0
1
0
2
0
0
1
0
0
0
0
2
1
0
2
1
2
1
0
1
0
0
1
1
0
1
1
1
2
1
2
2
1
0
1
1
0
0
1
1
0
2
1
1
0
2
0
0
0
0
0
2
1
0
1
0
0
1
0
2
1
1
1
2
1
2
0
1
0
0
1
1
2
0
0
1
2
0
2
1
0
2
0
0
1
0
0
0
4
0
1
1
0
1
0
1
1
0
0
1
2
1
0
0
0
1
0
0
0
1
1
1
0
0
1
2
0
1
0
1
1
2
1
0
0
0
0
0
0
1
0
2
2
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
1
3
1
2
1
2
0
0
0
1
1
0
0
2
1
0
0
1
3
2
3
0
1
0
0
0
1
2
1
0
1
1
0
0
2
0
2
2
1
1
2
0
1
0
0
1
0
4
0
1
0
0
1
0
0
2
1
2
0
0
1
2
0
0
0
1
0
0
2
0
0
0
1
0
2
1
1
2
1
1
0
1
2
1
0
1
1
1
0
0
3
1
0
2
2
0
1
1
2
0
0
0
0
1
0
2
2
1
2
0
0
2
0
0
2
0
0
0
0
1
0
0
2
1
2
0
0
1
2
2
0
0
0
1
2
2
0
1
0
0
0
0
1
3
0
0
1
0
0
2
0
1
2
1
0
0
0
0
0
1
2
0
1
0
0
2
2
1
2
1
0
0
1
0
0
0
1
2
0
0
1
0
2
2
0
0
2
1
0
2
2
0
0
1
0
1
1
2
1
0
0
2
0
0
0
2
0
0
0
0
3
2
2
1
1
0
2
0
0
0
0
2
0
0
0
1
0
0
2
0
2
1
0
0
0
0
2
1
0
3
1
3
0
1
0
0
1
0
2
4
2
0
2
0
0
0
1
0
1
2
0
0
1
1
1
0
1
0
0
1
2
1
1
0
0
2
1
1
0
2
0
1
2
0
0
2
0
1
2
0
0
1
1
0
2
1
1
2
1
0
1
0
1
0
0
0
4
0
2
1
1
0
2
2
1
1
1
0
0
1
2
3
1
1
0
1
0
1
0
0
0
1
1
1
0
2
0
0
1
1
0
1
2
2
1
0
0
0
1
0
1
2
1
1
1
0
0
1
1
1
1
0
0
0
0
0
1
2
1
1
1
0
0
0
0
1
1
0
0
1
1
1
1
2
0
1
2
0
2
0
0
1
0
0
0
0
0
2
1
0
0
1
0
0
0
1
3
2
0
2
0
2
1
1
0
1
0
1
0
2
2
0
1
2
2
1
1
1
2
1
1
0
0
0
1
1
0
0
0
4
0
0
1
0
2
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
1
1
2
0
2
2
0
0
0
1
0
2
2
0
0
1
1
0
2
1
0
1
2
0
0
1
0
0
1
1
1
0
0
0
1
0
2
0
0
1
0
0
0
2
1
2
2
1
0
1
1
1
0
0
0
0
2
2
0
0
1
0
1
0
1
0
0
1
1
0
0
2
2
1
2
1
1
0
0
1
2
2
0
2
0
0
0
0
2
1
1
2
3
1
0
2
1
0
0
0
2
0
0
1
1
0
0
1
0
1
0
1
0
0
0
1
1
2
2
1
2
0
3
1
2
0
0
0
1
0
2
0
0
0
0
0
1
1
1
2
1
0
1
0
1
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
1
1
1
1
0
2
0
0
0
0
2
1
1
2
0
1
1
0
0
0
2
0
1
0
1
2
1
0
1
2
2
2
2
0
1
0
2
0
1
0
0
2
1
0
2
0
1
0
0
0
1
1
0
0
1
2
0
0
0
2
0
0
0
0
1
1
2
1
1
1
0
1
0
1
0
4
0
0
0
1
2
2
1
1
1
0
2
2
1
2
1
0
0
0
1
1
2
0
0
0
0
2
2
0
0
0
0
1
1
0
2
2
0
0
1
0
1
2
2
2
0
1
0
0
1
1
0
2
1
1
0
2
2
3
0
1
1
0
0
2
1
0
1
1
1
0
2
0
0
0
0
1
0
0
1
0
1
1
1
1
1
0
0
1
0
2
0
3
2
0
1
0
1
0
0
2
2
1
0
1
0
0
1
0
2
0
1
1
1
1
1
2
1
1
0
0
1
0
1
2
0
2
0
2
0
0
3
0
0
1
1
0
1
0
1
2
1
2
0
0
2
1
1
0
1
2
0
1
2
3
0
1
1
0
0
1
1
0
0
1
2
0
0
1
0
1
0
2
0
0
1
0
0
11
0
1
2
2
0
0
1
0
0
1
1
0
0
1
1
0
2
0
1
1
0
2
2
0
0
1
0
1
2
0
2
0
1
0
2
2
2
1
1
2
2
2
2
0
1
0
2
0
2
1
0
1
0
2
1
0
1
1
2
1
1
0
0
2
2
0
0
0
2
1
0
0
1
0
1
0
0
1
2
0
1
2
1
0
1
0
1
0
0
2
0
0
1
2
0
2
2
1
0
0
0
0
0
1
0
0
1
2
0
1
0
2
0
2
0
2
1
0
0
1
1
1
2
1
0
0
0
0
2
1
0
0
0
2
1
0
0
1
0
2
1
0
0
0
1
0
1
4
0
0
2
1
0
2
2
2
4
2
2
0
1
0
1
1
1
0
0
0
1
1
1
2
2
1
0
0
0
0
0
0
0
1
1
0
0
2
1
0
0
2
1
0
0
1
2
0
2
0
0
1
0
0
1
0
0
1
2
0
1
1
1
1
0
2
0
0
3
1
0
0
0
1
0
1
2
0
2
0
1
0
2
1
0
2
0
0
0
1
2
4
0
1
0
1
4
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
2
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
2
1
0
2
0
0
2
0
0
2
1
2
1
0
0
1
0
1
0
1
1
2
2
2
2
0
0
0
1
0
2
0
0
0
2
0
1
1
2
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
1
1
0
1
1
2
1
0
1
0
2
1
0
2
1
0
0
1
0
0
1
0
0
2
1
0
1
1
0
2
1
0
0
4
3
1
0
0
1
2
1
1
1
0
0
2
1
0
1
0
0
2
0
0
1
1
2
2
2
0
1
1
0
2
0
0
1
1
1
2
0
0
1
2
1
2
0
0
1
1
2
2
0
1
0
1
1
2
0
2
2
1
2
0
1
1
0
0
2
2
2
0
0
1
1
1
2
2
1
1
1
2
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
1
0
2
0
0
1
0
1
0
1
1
1
2
2
0
1
0
0
0
3
1
0
1
0
0
0
1
1
2
1
1
0
1
0
0
2
0
0
0
1
1
1
0
1
1
0
1
0
1
0
2
0
0
1
0
0
2
0
0
2
0
2
0
2
1
1
1
2
1
0
2
0
1
1
2
0
0
0
2
0
0
0
0
1
0
0
1
1
0
1
2
0
0
2
1
0
0
1
1
0
0
2
0
1
0
1
1
0
2
1
2
0
2
1
2
1
1
1
2
0
0
0
1
0
0
0
1
0
0
0
0
2
2
0
0
0
2
1
1
0
1
1
1
2
1
0
0
2
1
1
2
1
0
2
2
1
0
2
1
1
1
1
0
0
1
1
1
0
1
0
0
2
0
0
2
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
2
2
0
2
4
0
2
1
2
0
0
0
0
1
2
0
0
0
3
0
1
0
1
0
2
1
2
0
2
2
2
0
0
1
2
10
1
1
0
2
1
0
2
0
0
1
2
2
2
1
1
1
0
0
0
0
1
2
1
1
2
0
1
3
0
0
0
0
0
0
1
1
1
1
2
1
0
1
0
2
0
0
0
0
1
0
1
0
1
0
1
1
1
1
0
0
2
1
0
2
1
2
0
1
2
1
2
0
0
0
0
0
1
2
0
0
0
1
1
0
0
0
0
1
1
3
1
2
0
1
2
2
2
0
0
0
1
0
0
0
0
1
1
1
0
0
1
1
1
0
0
2
0
0
0
0
1
0
1
1
1
1
1
1
2
1
1
2
0
0
0
1
0
0
0
2
0
0
2
1
0
1
2
0
2
0
0
2
1
1
1
0
0
1
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
1
2
1
2
1
2
1
1
1
0
3
0
1
0
0
0
0
0
0
0
1
0
1
2
1
2
1
2
2
1
0
0
1
0
0
0
1
1
2
2
0
1
1
1
0
0
1
1
0
2
0
1
2
0
0
2
3
0
0
0
1
2
0
1
2
2
0
2
0
2
2
0
0
0
0
1
1
1
0
0
1
0
1
1
1
0
2
0
2
0
0
1
0
1
2
0
0
1
0
2
1
0
1
1
7
0
0
0
0
1
0
0
1
0
1
1
1
1
0
1
0
2
2
0
0
2
0
2
0
0
1
0
2
1
0
2
0
2
0
0
1
0
2
0
2
1
0
1
2
1
2
0
1
2
2
0
1
1
1
2
1
1
0
1
0
0
0
1
2
0
0
1
1
1
1
0
0
1
1
1
2
3
0
0
2
0
1
1
3
2
1
0
1
0
2
0
0
1
0
1
0
1
1
2
1
0
0
0
0
0
0
0
2
2
0
1
3
0
1
0
0
0
0
2
0
0
1
2
0
2
1
2
0
0
1
2
0
0
0
0
1
0
0
1
2
1
2
1
0
1
0
0
2
2
0
0
0
1
1
0
0
2
0
1
1
0
1
2
0
0
0
1
2
0
0
1
0
0
2
2
0
0
1
2
1
0
1
2
0
0
0
0
2
0
0
1
2
1
1
0
0
1
2
0
1
2
2
2
0
2
0
2
0
1
1
1
2
1
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
1
1
1
2
0
0
2
0
2
1
1
0
1
0
2
1
1
1
1
2
0
1
2
1
1
1
2
1
1
0
1
1
0
1
0
0
0
0
0
1
1
1
2
0
0
2
4
0
1
0
0
1
0
1
0
1
0
0
1
1
0
0
0
2
3
0
3
2
1
1
0
0
1
1
0
2
1
0
1
0
2
3
0
0
2
0
0
0
2
2
1
0
0
1
1
0
2
0
2
2
0
0
2
1
0
1
0
1
0
3
3
2
1
0
0
1
3
1
1
0
1
0
0
0
1
0
0
1
0
3
0
1
0
0
0
2
1
1
2
1
2
0
1
1
0
0
1
1
2
1
0
1
2
1
1
2
2
0
0
1
0
1
0
1
1
3
1
0
1
0
1
1
1
2
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
2
1
0
0
2
2
0
1
1
1
0
0
1
2
0
1
2
1
0
0
2
2
0
0
0
0
1
1
1
2
0
2
0
1
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
1
1
0
0
1
0
1
1
1
2
0
1
2
1
0
1
0
3
0
1
1
2
0
1
1
1
1
1
2
1
2
0
1
0
1
2
2
0
2
0
2
0
2
0
1
2
1
1
0
1
0
0
0
0
0
0
0
1
0
1
2
1
1
0
0
1
2
1
0
0
0
0
1
0
1
2
2
2
1
2
0
0
2
0
0
0
0
0
1
2
0
0
2
1
1
0
0
0
1
2
0
2
0
1
1
0
0
0
1
1
0
0
1
2
1
0
0
0
0
0
0
1
2
2
0
0
1
1
1
1
1
0
0
0
0
0
0
1
1
0
0
2
0
1
0
0
0
2
2
0
0
0
1
0
3
1
2
0
1
0
0
0
0
0
0
1
2
1
0
2
2
0
1
2
1
0
0
0
0
0
0
1
0
1
1
0
0
1
1
3
1
0
0
2
1
0
0
1
2
2
2
0
0
1
1
1
2
0
1
1
1
2
0
2
1
2
1
0
0
1
2
0
0
0
1
1
1
1
1
0
1
0
0
1
1
1
0
0
0
1
0
0
2
2
2
2
0
0
0
0
1
0
1
0
2
0
2
0
1
1
1
0
1
0
1
0
0
1
2
1
1
0
1
1
0
1
2
0
1
2
0
2
2
1
1
2
0
0
2
0
0
0
1
2
1
2
2
0
1
0
1
0
0
0
1
1
1
1
2
1
0
5
0
1
0
0
0
0
0
0
1
0
1
0
1
0
2
2
2
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
1
2
0
0
1
0
0
1
1
1
1
1
2
1
1
1
0
2
0
0
0
2
2
1
0
1
0
1
2
0
2
1
1
2
0
2
0
2
0
0
0
1
0
1
0
1
1
0
1
1
0
0
1
1
0
2
0
0
0
2
2
0
0
2
1
0
0
1
2
2
2
2
0
1
2
0
1
2
2
1
3
1
1
1
1
1
1
0
0
0
0
0
0
2
0
0
0
0
1
0
2
2
1
2
0
1
0
1
2
3
0
1
0
0
0
0
1
1
0
1
0
1
0
1
1
0
1
2
0
1
0
0
1
0
3
0
0
1
0
1
2
2
1
0
3
0
2
1
2
0
1
1
1
1
0
1
0
2
0
1
1
1
0
2
2
2
0
1
2
1
1
1
0
1
1
2
1
2
1
2
2
0
2
2
0
0
1
2
2
0
0
0
2
0
1
0
2
0
0
1
0
0
0
2
0
1
1
1
1
1
1
0
0
0
0
1
2
0
0
2
0
0
0
2
1
0
1
1
0
1
2
0
2
0
2
0
0
0
0
1
0
2
2
0
2
2
0
2
0
0
2
0
1
1
1
1
2
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
1
1
1
1
2
1
2
1
1
3
1
0
0
0
1
1
0
1
2
1
1
0
0
2
1
1
1
0
0
0
0
1
1
1
0
2
0
0
1
0
2
1
1
1
0
1
0
1
1
2
0
0
1
0
1
0
1
0
0
0
1
1
1
2
1
2
1
0
0
1
2
0
2
2
0
0
1
2
2
3
2
0
0
0
1
1
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
2
1
2
0
0
1
1
0
0
0
1
2
0
2
2
0
1
1
2
1
2
0
1
0
0
1
1
0
2
0
2
0
0
1
1
2
1
1
2
0
0
1
1
0
0
1
3
1
2
2
0
0
0
1
1
1
1
1
0
0
0
2
0
2
2
0
0
0
1
0
1
0
1
1
0
1
0
0
0
0
0
0
0
1
1
1
2
1
0
0
1
1
1
1
1
0
1
1
2
1
1
1
1
0
1
2
0
1
1
0
0
1
2
1
1
0
1
1
1
0
0
0
2
2
0
1
0
2
1
0
1
0
0
2
0
0
4
2
1
1
0
0
2
2
0
1
1
2
0
0
1
1
1
2
0
0
1
2
1
0
1
2
0
1
1
1
2
0
2
2
2
1
0
0
2
0
0
1
0
1
0
0
0
1
2
2
2
0
0
2
0
0
1
2
0
0
2
0
0
2
0
0
0
1
0
1
0
0
1
2
1
1
0
0
0
2
1
2
2
1
0
1
1
1
1
0
0
0
0
1
1
3
0
1
0
0
1
2
1
1
0
2
1
0
1
1
1
0
0
1
0
2
0
1
1
1
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
2
1
0
2
0
3
1
1
0
1
0
1
1
0
2
2
0
0
1
0
1
1
0
1
0
2
2
0
0
1
1
2
0
0
2
1
0
1
1
1
5
0
0
2
0
0
1
1
2
1
0
0
1
1
0
1
0
0
2
1
0
0
0
0
0
1
1
0
1
0
1
1
1
2
0
1
1
1
3
0
0
0
0
1
0
0
2
2
1
1
0
1
0
2
1
0
2
1
0
0
0
1
1
2
3
1
0
0
0
0
1
0
0
1
2
0
0
0
2
0
1
2
0
2
1
1
1
2
2
1
2
1
0
0
1
0
2
1
1
0
1
0
1
0
2
1
0
1
1
1
1
2
1
0
0
0
1
2
0
0
0
1
1
2
2
0
0
0
1
1
1
2
1
0
0
1
2
0
1
0
1
0
1
1
0
0
0
0
2
0
2
1
0
1
1
1
0
2
9
0
0
0
0
0
2
1
1
0
1
0
0
1
0
3
2
1
0
1
0
0
2
0
0
0
2
2
1
1
0
1
0
1
1
1
0
0
1
2
0
2
2
1
2
2
1
0
2
2
0
0
1
1
0
0
0
0
0
0
2
0
1
0
1
0
0
0
1
1
2
0
2
0
1
0
1
0
2
2
0
0
1
2
0
3
0
1
2
1
0
0
1
0
1
1
3
0
0
2
0
1
0
1
1
1
0
0
1
1
0
0
0
2
0
0
1
0
0
1
2
0
1
0
0
2
0
1
0
1
2
0
1
2
0
1
0
1
0
2
1
1
0
0
0
0
0
2
0
1
2
1
0
0
2
0
0
1
3
0
2
0
1
1
2
1
1
1
0
0
0
0
2
2
0
2
0
0
0
1
2
1
0
0
1
0
1
2
0
2
2
1
1
1
2
0
2
2
0
1
0
1
0
1
2
1
2
1
1
1
0
0
0
2
0
1
0
0
0
1
2
0
0
2
1
0
0
4
1
1
1
4
1
1
1
0
0
0
0
2
0
0
0
1
2
2
1
1
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
1
1
0
0
1
0
2
2
0
0
2
0
2
1
1
0
1
2
1
0
0
1
1
1
0
1
0
0
0
2
2
1
0
0
2
1
0
0
0
1
2
1
1
0
1
0
2
0
1
0
1
0
1
1
0
1
1
2
0
0
1
0
0
0
0
1
2
0
1
1
0
0
0
0
1
2
1
1
1
1
0
0
2
1
1
1
3
2
1
2
0
2
1
1
0
0
1
0
1
1
1
3
1
0
1
2
1
1
2
3
0
0
1
2
2
1
0
1
2
2
1
0
0
2
0
0
0
1
2
0
2
0
0
1
0
0
1
0
0
1
1
0
0
2
0
1
0
0
4
1
2
0
1
0
0
0
0
0
0
1
0
1
0
0
2
1
1
0
0
3
0
0
2
0
0
1
2
1
1
0
0
0
0
2
0
0
2
2
0
1
1
1
1
0
0
1
0
2
0
1
0
0
0
2
0
2
0
0
2
1
0
0
2
2
0
0
1
0
0
1
0
1
1
0
2
1
0
0
0
5
0
2
2
0
0
2
1
1
1
0
0
0
0
1
2
0
0
0
0
0
0
1
1
2
0
1
0
0
0
1
0
1
0
2
2
1
1
1
2
0
1
0
1
2
0
0
0
0
0
1
1
2
0
0
1
2
2
1
2
0
2
1
2
0
0
1
2
1
1
0
1
1
1
0
0
0
1
0
1
2
0
1
0
3
2
0
1
0
0
0
2
2
0
1
2
0
0
2
0
0
0
0
1
2
1
2
1
0
1
1
1
0
0
0
1
0
0
0
0
1
1
0
1
1
1
0
2
1
20
0
0
1
1
1
1
1
2
0
1
0
0
1
1
0
2
1
0
0
0
0
1
0
2
2
0
1
0
1
1
0
2
0
2
2
1
0
1
2
2
1
0
2
1
1
0
0
1
0
0
1
1
0
1
1
0
0
1
0
0
0
1
1
0
1
7
2
0
2
3
1
1
1
0
0
1
2
1
0
0
1
0
0
0
0
1
1
2
0
1
2
2
2
2
0
1
0
2
0
1
0
0
0
3
0
0
2
0
1
2
0
1
0
0
2
1
2
0
1
1
1
2
1
1
2
2
1
0
0
1
2
0
2
1
2
1
2
1
0
1
1
0
0
0
0
2
0
0
1
3
2
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
2
0
0
0
1
1
1
2
1
1
1
2
0
0
2
0
0
0
0
0
0
0
0
1
2
0
1
0
0
1
1
1
0
2
1
1
1
0
0
2
1
1
0
0
1
1
2
0
2
0
0
0
0
1
2
1
1
1
0
0
0
6
0
1
2
0
0
0
1
0
0
2
0
2
2
0
2
0
0
0
1
0
2
2
0
1
0
0
2
0
0
0
0
0
0
0
1
0
2
0
2
0
0
2
1
2
0
0
1
1
1
2
1
0
1
0
1
2
0
1
0
1
2
1
1
0
1
1
2
0
0
1
1
2
0
1
1
1
0
2
1
2
1
1
1
0
1
2
2
2
1
0
0
2
0
1
0
2
0
0
0
2
1
1
1
1
1
0
0
0
0
0
0
1
2
1
0
1
1
1
1
2
2
1
1
1
0
1
1
1
1
1
3
1
0
1
0
1
0
0
0
2
2
2
3
2
1
1
2
1
0
1
2
0
0
1
2
1
2
2
0
2
1
2
0
2
0
1
2
1
0
0
0
0
2
1
0
2
0
1
1
1
2
0
0
0
0
1
2
0
0
0
1
1
1
0
2
0
1
1
2
1
0
0
1
0
2
0
0
1
0
1
0
1
0
0
0
1
2
1
0
1
2
1
2
1
1
2
1
1
0
0
0
0
1
1
1
2
1
0
2
0
0
0
1
1
1
2
0
1
0
0
2
0
2
0
0
0
0
1
1
1
2
1
2
0
2
0
0
1
3
1
1
1
0
1
0
0
1
0
0
1
0
0
1
1
2
1
0
0
0
2
1
2
1
2
0
2
0
1
0
0
0
2
0
0
2
1
1
0
1
1
0
1
0
0
0
1
1
0
0
1
0
2
0
1
0
1
1
0
1
2
1
1
0
2
1
0
2
2
2
2
2
1
1
0
0
0
1
0
1
0
0
4
1
2
1
0
0
1
0
1
2
0
0
2
0
0
1
3
0
2
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
1
1
1
0
2
0
0
1
0
1
0
0
1
0
2
0
0
2
1
0
0
0
1
0
2
1
1
2
2
1
0
0
1
0
1
1
1
2
0
1
1
0
0
4
0
0
2
1
0
0
2
1
0
1
1
0
1
2
2
0
2
0
3
0
0
0
1
2
0
0
1
2
0
0
1
1
0
0
1
1
1
1
1
0
0
0
0
1
2
0
0
0
1
1
1
1
1
1
1
2
5
0
1
2
2
2
0
0
4
0
2
0
1
2
0
0
0
1
0
1
2
0
2
0
3
1
1
2
0
2
0
0
1
0
0
1
0
0
1
1
2
2
0
1
1
1
2
2
0
0
1
2
0
0
1
1
2
2
2
2
2
2
0
0
2
1
2
1
1
2
1
0
0
0
0
1
1
2
2
1
2
1
0
0
0
2
3
2
0
1
1
2
1
0
0
2
0
1
1
1
0
2
3
2
6
0
0
0
3
1
2
2
0
1
0
2
1
0
0
0
0
1
0
0
2
1
2
1
1
3
0
2
0
0
1
1
1
1
0
1
0
0
0
2
2
0
2
2
0
2
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
2
0
1
0
0
0
0
0
3
1
0
1
1
0
0
0
2
1
0
0
0
2
2
0
2
1
1
0
1
1
0
2
0
0
0
1
0
1
1
0
0
4
1
0
1
0
0
0
1
0
2
0
0
1
0
1
2
0
0
1
1
1
1
0
2
0
0
2
2
0
1
0
0
1
0
1
1
1
0
0
2
1
1
0
3
0
0
0
0
0
0
1
0
1
0
1
2
2
1
1
2
0
1
1
0
1
0
1
0
1
2
0
1
0
1
1
1
0
0
1
2
1
2
0
0
0
0
0
1
0
0
1
2
1
1
0
0
0
1
0
0
0
0
0
1
1
2
1
1
1
0
1
1
0
1
0
1
0
0
1
0
0
0
1
0
0
3
0
1
1
2
0
1
2
1
0
0
1
1
1
1
1
0
0
5
1
0
0
0
0
0
0
0
0
0
1
1
0
0
2
1
1
1
0
0
0
1
1
2
0
1
1
2
2
0
0
2
2
1
0
0
0
0
1
0
0
1
2
0
2
1
2
0
2
0
0
1
0
0
1
2
1
0
1
0
1
1
2
0
0
1
0
0
1
0
0
0
2
0
1
0
0
0
1
1
0
0
0
2
1
0
0
2
1
2
0
0
0
1
1
1
1
0
0
2
0
0
0
0
1
1
1
2
0
2
2
2
0
0
1
0
0
2
0
0
0
1
0
2
1
0
1
1
1
0
2
1
0
1
0
1
1
1
0
0
0
1
2
0
0
2
2
0
1
1
1
3
1
0
2
1
0
0
0
0
0
1
0
0
1
1
0
1
0
0
1
1
0
1
0
1
0
1
0
1
0
2
1
2
1
2
1
2
1
1
1
1
0
0
1
2
2
2
2
0
0
1
1
0
1
1
3
0
1
0
0
0
0
1
1
2
0
2
0
0
0
0
0
0
0
0
1
1
1
0
2
1
0
2
2
0
0
0
1
2
0
1
1
2
1
0
0
0
1
2
1
1
0
0
1
2
0
2
2
2
1
0
1
0
0
0
2
1
0
0
0
1
0
0
0
2
2
1
0
0
1
2
3
1
1
2
1
1
0
0
1
1
0
0
1
0
0
0
2
3
1
4
3
1
2
0
1
1
1
2
0
0
0
1
1
0
1
2
0
0
1
0
4
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
2
1
0
0
0
0
1
2
0
0
3
1
0
0
1
2
2
0
1
0
1
0
1
0
2
1
1
2
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
2
1
2
2
1
0
0
0
0
0
1
1
2
0
2
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
1
2
1
0
2
2
0
1
0
0
0
1
0
0
1
0
1
1
0
1
2
1
1
1
0
0
0
1
0
0
0
1
0
0
0
1
1
1
3
0
1
2
0
0
0
1
1
0
1
0
3
1
1
0
3
1
1
1
0
0
1
0
2
2
0
1
0
0
0
0
2
0
1
1
1
1
1
1
2
1
2
0
1
1
1
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
4
2
0
0
2
2
0
0
0
1
0
2
0
0
1
1
0
1
1
0
2
1
0
2
1
2
0
2
1
0
2
0
1
0
0
0
0
0
0
2
1
0
1
2
0
0
0
0
2
0
0
1
1
0
1
1
2
0
1
2
1
1
0
0
0
1
2
1
1
0
1
1
0
0
0
2
1
2
2
1
0
1
2
0
0
2
3
2
1
1
0
1
0
1
1
3
0
1
0
0
1
1
1
0
1
0
0
0
1
2
1
2
0
2
2
0
1
0
0
0
0
0
0
0
2
0
1
1
0
0
1
0
9
1
0
1
0
0
2
1
0
2
2
2
1
2
1
2
0
2
2
2
0
0
0
2
0
0
0
1
2
0
2
1
2
0
0
2
0
2
1
0
0
1
2
1
1
0
1
0
0
2
0
0
1
0
2
0
0
0
0
1
2
0
0
1
0
0
1
2
0
0
0
1
0
0
1
0
1
1
2
0
2
2
3
1
0
1
2
0
1
0
0
1
2
1
1
0
1
0
2
1
0
2
1
2
0
1
0
2
0
0
1
1
0
0
0
1
0
2
0
1
1
0
1
0
1
0
0
0
0
1
2
0
0
0
0
0
2
0
2
2
1
0
1
1
2
2
0
0
1
2
0
0
2
0
0
2
0
0
0
2
0
1
0
0
1
1
0
0
2
0
1
1
1
0
0
0
2
0
0
2
0
1
0
0
2
1
2
1
0
0
2
1
1
1
0
2
0
2
0
1
0
0
0
1
0
1
1
2
2
2
2
1
1
1
1
1
0
1
0
2
0
0
0
0
1
0
2
0
2
2
1
0
1
2
2
1
1
0
2
0
0
1
0
0
0
2
0
1
0
1
1
0
2
1
2
0
0
1
0
0
0
2
1
2
2
1
0
0
0
0
0
0
3
1
1
0
1
0
2
2
0
1
0
0
0
0
1
2
0
1
0
2
1
1
0
0
2
0
0
0
0
2
2
1
1
1
1
2
0
0
0
0
2
1
2
0
1
1
2
1
2
0
0
0
2
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
1
1
2
2
0
1
2
2
2
0
1
2
0
2
0
2
0
0
0
0
0
0
2
2
0
0
0
0
1
1
0
2
1
1
1
0
2
0
2
2
0
1
1
0
0
0
0
1
2
1
0
0
0
2
2
1
0
1
2
1
0
0
1
1
1
1
0
1
0
2
0
2
0
0
0
2
4
0
0
1
1
0
1
0
0
2
0
0
1
2
0
0
1
0
0
2
1
0
1
2
1
0
0
2
0
2
2
0
1
2
2
2
0
0
1
1
1
2
0
1
0
0
1
1
1
1
0
0
0
1
0
0
0
1
0
1
1
0
0
2
1
1
2
0
2
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
5
0
1
0
1
1
1
0
2
0
1
0
0
0
0
1
0
1
1
0
1
0
5
0
0
0
1
1
0
0
2
0
1
1
0
0
0
2
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
2
1
0
2
1
1
1
1
1
0
1
1
1
1
0
1
1
0
0
0
0
0
1
1
0
1
0
3
2
1
1
0
0
0
0
1
0
2
0
0
0
0
2
0
0
2
1
2
0
0
0
2
2
0
1
0
0
2
0
0
1
1
1
2
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
1
0
1
0
0
1
1
0
0
3
0
0
0
0
2
1
1
0
0
1
1
1
0
2
1
1
0
2
0
0
1
0
2
0
0
0
1
1
0
0
0
0
1
1
0
2
0
0
2
0
0
1
1
1
1
1
1
0
0
0
0
2
0
2
2
0
0
1
0
0
0
0
0
1
1
1
0
2
0
0
1
0
0
1
1
2
1
0
4
0
1
1
1
0
1
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
8
1
0
0
2
1
0
2
1
2
2
0
1
2
1
0
0
0
0
0
0
1
1
0
1
0
1
0
1
0
1
2
1
1
0
1
0
1
1
0
0
0
1
2
0
2
2
0
0
3
0
0
0
0
1
0
2
1
1
0
1
2
1
1
2
0
1
1
0
0
0
0
0
0
2
1
0
0
1
2
1
1
1
0
2
2
0
0
2
2
0
0
2
0
2
0
0
2
0
1
1
0
0
0
0
1
0
1
0
0
0
0
1
3
0
0
0
2
1
2
1
2
0
0
0
0
2
2
0
4
0
2
0
1
0
1
0
0
1
0
1
1
0
1
0
2
2
2
2
0
0
0
0
0
0
0
2
1
2
1
0
1
2
2
2
0
2
0
2
1
1
2
0
1
2
0
2
0
0
2
2
1
1
1
0
0
0
0
1
0
0
2
1
0
0
0
2
0
0
0
2
0
0
2
0
1
0
0
1
1
0
0
0
1
3
1
0
1
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
2
0
2
0
2
0
1
1
0
2
4
0
2
2
1
0
0
0
0
1
2
1
1
0
0
2
2
0
1
2
1
0
0
0
0
1
1
1
0
1
0
1
0
1
1
0
1
3
0
1
1
0
1
2
0
1
1
1
2
1
2
1
0
0
0
2
0
2
2
0
2
1
0
2
1
1
3
0
0
0
0
1
0
0
0
1
2
1
1
0
0
1
0
2
0
2
1
0
0
0
0
1
1
2
0
2
1
1
2
0
1
0
0
2
0
1
0
0
1
2
2
0
0
0
0
0
1
0
1
1
0
2
1
0
1
1
2
0
1
1
1
1
1
1
0
0
0
0
1
0
0
1
1
1
0
1
1
1
0
1
1
1
0
0
1
0
1
1
0
0
2
0
0
1
0
1
2
0
2
2
1
0
0
1
1
2
3
1
1
1
3
0
1
0
0
2
0
0
1
0
2
0
0
1
2
0
0
0
0
0
1
0
0
2
0
0
0
1
1
0
2
1
0
0
0
0
1
1
1
2
2
2
0
0
0
1
0
0
2
0
1
0
0
2
0
0
0
0
1
0
2
0
2
1
0
1
1
2
1
2
0
0
2
1
1
0
1
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
2
2
0
2
1
0
1
2
0
0
0
2
0
1
0
0
1
0
1
0
5
0
0
1
2
3
1
0
0
0
0
2
2
0
1
1
0
0
1
2
2
2
0
1
0
1
1
2
0
1
0
1
1
1
0
0
0
2
1
2
1
0
0
0
1
2
0
0
2
1
1
2
1
0
0
1
1
0
2
0
1
2
2
1
0
1
2
0
0
0
0
0
0
2
2
0
0
1
0
2
1
2
1
0
1
2
0
2
1
2
2
0
0
0
1
1
0
0
0
2
2
1
0
0
0
0
0
1
0
2
0
0
3
1
0
0
0
2
0
0
1
0
0
0
1
0
2
0
0
0
0
0
2
2
1
0
0
2
1
0
2
2
0
1
2
1
1
2
2
0
0
0
0
1
0
2
1
1
1
0
0
0
0
0
1
0
0
0
0
1
2
1
2
0
0
0
0
0
2
0
0
2
0
4
0
0
2
1
0
2
1
1
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
1
0
1
1
2
1
0
0
0
2
0
1
0
1
0
0
3
2
1
0
0
3
0
1
2
0
0
0
1
0
0
1
0
0
1
0
0
1
0
2
1
2
1
0
1
1
1
0
0
1
0
1
2
1
1
1
0
1
1
2
0
1
1
0
1
0
0
2
1
0
1
1
1
1
0
1
0
0
0
0
1
0
2
2
2
0
0
1
0
0
1
1
0
0
2
1
3
2
0
0
0
0
0
0
3
0
3
0
1
1
0
1
2
2
0
0
2
0
1
0
0
2
0
3
1
0
0
0
0
1
0
1
0
0
1
1
1
2
0
1
1
1
0
0
2
0
1
0
1
1
1
0
0
0
1
2
1
0
1
0
0
1
0
0
0
1
2
3
1
1
0
2
1
0
2
0
0
2
2
0
0
2
0
1
1
0
0
1
2
2
1
0
2
0
3
0
2
1
1
1
1
0
1
2
1
0
2
0
1
2
2
2
0
1
2
0
0
2
7
2
1
0
0
1
0
1
0
0
0
1
1
0
2
2
1
1
0
0
0
1
1
2
0
0
0
0
0
0
2
0
2
2
0
0
2
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
1
1
0
0
0
0
0
1
2
1
1
1
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
1
1
2
1
0
2
0
1
0
0
0
1
0
1
0
0
0
1
1
0
1
1
0
0
1
0
0
2
0
0
1
2
1
0
0
1
1
0
1
0
0
0
1
2
1
2
0
0
0
1
2
2
1
2
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
2
2
0
2
1
0
0
0
1
2
1
2
1
1
0
0
0
1
3
2
0
2
2
2
1
0
0
2
2
1
1
0
0
2
0
1
2
2
0
1
2
2
1
2
1
0
1
0
2
2
2
2
1
0
2
2
2
2
0
2
1
1
0
1
0
0
0
0
0
1
1
1
0
1
0
1
0
0
0
0
0
1
0
0
2
1
1
1
0
1
2
2
0
0
0
2
0
1
1
2
2
1
2
0
1
2
0
1
0
0
0
0
1
1
0
1
2
2
0
1
1
2
1
0
2
1
0
0
0
0
0
1
0
1
1
0
1
2
1
1
0
0
1
1
1
0
2
1
0
1
0
2
1
0
0
0
0
1
0
0
0
0
2
2
0
2
1
2
3
1
1
0
0
0
0
1
0
0
0
0
0
2
1
0
0
1
1
1
0
0
1
3
0
1
2
1
0
0
2
2
1
0
1
0
1
0
2
2
1
0
0
1
2
0
2
0
2
2
2
0
0
0
0
1
1
2
2
3
1
0
0
0
1
0
0
0
0
1
1
0
2
2
5
0
0
1
1
0
0
0
2
0
2
2
1
0
1
1
2
0
3
1
0
2
0
1
1
1
0
0
1
1
2
0
0
0
1
0
1
0
1
2
2
2
2
0
0
0
1
0
1
1
0
0
1
0
1
0
0
0
0
0
1
1
0
2
0
0
1
2
0
0
1
0
1
2
1
1
1
0
1
0
1
0
1
0
0
0
1
1
1
1
0
1
3
0
0
2
1
1
4
1
0
1
0
0
0
1
0
1
1
0
1
0
0
1
1
0
1
1
2
1
2
2
0
2
2
2
2
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
2
1
1
1
1
0
3
0
0
1
1
1
2
1
1
1
2
2
1
1
1
0
1
0
1
1
1
1
1
2
1
1
0
0
0
0
2
0
1
1
0
0
0
0
0
1
1
1
0
1
2
1
2
1
1
0
1
0
0
0
0
0
0
2
1
1
0
0
0
0
0
1
0
1
0
1
1
2
0
1
2
2
1
1
0
0
0
0
1
2
0
0
1
0
2
0
0
1
2
0
2
1
0
0
1
0
0
1
1
0
1
1
0
5
1
1
0
0
1
0
0
2
2
1
2
1
0
1
0
2
0
2
1
1
2
2
2
2
0
0
0
0
0
1
1
0
3
0
1
0
2
0
2
2
1
0
2
0
1
1
0
0
0
0
2
0
0
2
2
2
1
1
0
1
1
1
1
1
1
2
0
1
0
1
0
1
0
0
2
0
0
0
2
0
0
0
0
1
2
0
2
2
0
0
5
0
0
1
0
0
1
2
0
1
2
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
2
0
2
0
2
0
0
0
0
1
0
0
2
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
2
2
2
0
2
1
0
1
1
1
0
0
0
0
0
1
0
2
0
1
1
0
1
1
2
0
0
1
1
1
0
0
1
0
1
2
2
1
2
1
0
1
1
1
1
1
2
1
0
1
2
0
1
2
1
0
0
1
0
0
2
0
1
1
0
0
2
0
2
2
0
1
2
0
1
0
0
0
1
0
1
2
0
1
0
0
0
2
0
1
2
0
2
1
1
0
2
0
2
0
0
0
1
0
0
0
1
4
0
1
0
4
1
1
2
1
2
3
1
0
2
0
2
0
0
0
1
0
0
1
1
2
1
0
1
0
0
0
1
0
0
2
1
1
0
0
0
0
2
2
2
1
1
0
0
0
0
2
0
1
1
0
3
2
0
0
0
1
0
1
0
0
0
0
0
2
0
2
3
0
0
0
1
0
1
0
1
0
1
1
2
3
3
0
0
1
0
1
1
0
0
0
2
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
1
1
0
2
0
0
1
0
2
0
2
3
2
0
2
1
2
0
1
1
0
0
0
0
1
0
1
0
0
1
1
1
0
0
1
1
2
0
0
0
1
0
0
0
0
0
1
1
0
0
0
3
1
0
2
0
0
2
1
1
1
0
2
0
1
0
0
1
0
0
2
0
2
1
1
0
1
1
1
0
0
0
2
0
0
0
0
0
1
2
2
0
0
1
1
1
1
2
1
0
0
0
1
2
0
0
0
1
2
2
2
0
0
2
0
1
2
0
1
1
1
0
1
1
1
0
1
1
0
0
1
0
0
0
0
1
2
0
2
1
1
0
1
1
2
2
1
1
0
0
0
1
1
0
1
1
1
0
1
0
1
1
2
2
2
0
0
0
2
2
0
1
0
1
0
0
4
1
2
0
5
1
1
2
0
0
1
0
1
1
1
0
0
1
0
0
0
0
2
2
0
1
1
1
1
2
1
0
0
0
0
0
0
2
0
1
0
1
1
0
1
3
0
0
2
0
0
0
0
0
0
1
0
0
2
0
1
1
1
2
0
2
0
0
0
0
2
0
2
0
2
0
0
1
1
2
0
0
0
1
2
1
0
0
0
1
1
1
0
2
1
0
1
0
0
0
2
1
1
2
2
0
1
1
0
0
1
0
2
0
0
0
1
0
0
0
0
1
1
1
0
1
2
1
1
0
1
0
2
1
0
0
0
0
1
0
2
0
1
0
2
0
0
0
2
1
0
0
1
1
1
2
0
0
2
0
0
0
0
2
0
2
1
1
0
1
1
0
0
0
1
1
2
0
1
0
2
1
0
0
2
1
1
0
1
0
2
2
2
0
0
0
0
1
1
1
2
1
0
1
5
2
0
0
2
0
2
0
3
2
0
2
0
2
1
2
2
0
0
0
2
1
1
2
0
2
0
1
1
1
2
1
0
0
0
1
0
0
2
0
2
0
3
0
0
1
2
0
1
1
0
0
2
0
0
1
1
0
1
1
0
2
2
0
2
1
2
0
1
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
2
2
1
0
2
1
0
0
0
0
0
1
0
0
1
1
0
1
1
1
0
2
1
2
1
1
0
1
1
1
0
2
2
1
2
0
1
3
0
1
0
2
2
0
0
0
0
0
2
0
0
0
0
2
1
1
0
1
0
0
2
1
2
1
2
0
0
0
2
2
0
0
2
0
0
2
0
0
0
0
2
0
1
0
0
2
1
0
0
0
1
0
0
2
2
1
2
1
0
4
0
1
0
2
0
0
1
0
1
1
0
1
1
1
0
1
1
1
0
0
1
0
1
2
0
1
0
0
1
0
0
2
2
2
1
1
2
1
0
1
0
1
1
0
0
1
1
1
0
2
0
0
0
1
2
2
2
2
0
0
1
1
1
0
2
1
0
2
1
0
1
0
0
2
0
1
2
0
2
0
1
2
1
2
1
0
0
2
0
1
0
2
2
1
0
1
0
0
0
1
0
1
1
0
0
1
1
0
1
2
1
0
2
0
1
1
0
2
1
0
0
1
1
1
0
1
0
1
0
0
2
0
2
0
0
0
0
1
0
0
1
0
2
1
0
2
0
1
0
1
0
0
0
3
0
0
1
0
0
2
0
1
1
0
0
2
0
0
0
2
1
1
0
1
2
1
2
0
0
0
0
0
0
1
1
2
2
1
0
0
0
0
0
0
1
0
0
2
1
0
0
1
1
1
0
1
0
0
0
1
0
1
1
1
0
1
0
2
1
1
1
0
6
0
0
0
2
0
0
1
1
0
2
1
3
3
2
2
2
2
2
0
1
1
0
0
1
1
3
0
0
0
2
0
0
1
0
0
1
1
0
0
0
1
0
0
1
3
0
1
2
0
1
2
2
0
0
2
0
2
2
2
0
1
0
0
1
0
1
0
0
0
0
0
1
1
0
2
0
2
1
0
2
0
2
0
0
0
2
2
0
1
0
0
1
0
0
0
0
2
0
1
1
1
1
0
0
0
1
0
0
0
1
2
2
0
0
0
1
1
0
1
1
0
0
0
1
0
1
2
0
0
1
1
1
1
0
2
1
1
1
0
1
2
0
2
0
2
1
0
0
0
0
0
0
2
0
0
2
2
1
1
1
0
1
1
0
0
1
0
3
0
1
0
0
2
2
1
2
1
1
1
0
0
1
0
1
2
0
0
1
0
2
1
1
0
0
2
0
0
1
0
0
0
0
1
2
0
1
0
0
0
0
0
0
2
1
1
1
2
3
1
0
2
0
1
1
0
0
1
0
0
0
2
0
2
1
2
0
1
0
2
1
0
1
1
2
0
1
1
0
1
0
0
0
2
1
0
0
2
0
0
0
0
1
1
2
0
1
2
2
0
2
1
0
1
0
0
0
1
1
0
0
2
0
0
1
1
0
1
1
2
0
1
0
0
2
1
0
2
0
0
1
2
1
0
1
2
2
0
1
0
0
0
0
1
1
1
0
0
0
1
1
1
2
2
0
0
0
0
2
2
0
0
0
0
0
0
1
0
1
0
1
0
1
0
2
0
0
1
0
1
0
0
2
1
0
2
2
2
0
1
1
0
1
1
2
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
1
1
1
0
0
0
1
3
2
1
1
0
0
0
1
1
0
0
1
2
1
1
0
1
0
0
2
1
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
1
1
0
1
0
0
1
1
0
0
0
0
0
1
0
1
1
0
0
2
0
1
2
0
1
1
1
0
1
0
1
0
1
0
0
0
0
3
1
1
0
0
3
0
0
0
0
2
2
0
1
0
0
1
1
0
0
1
1
1
1
0
0
0
1
0
0
1
0
1
0
1
0
0
2
0
0
1
1
0
1
1
1
1
0
0
0
2
0
2
0
2
1
1
2
0
1
1
0
2
1
2
0
1
0
0
0
0
0
0
0
1
1
1
2
1
2
0
2
0
1
1
0
2
0
0
1
0
2
0
1
2
0
0
0
1
1
1
1
0
0
2
0
0
1
1
0
0
0
0
0
0
1
2
2
1
0
1
1
0
0
2
1
0
0
2
0
3
2
2
0
0
0
0
1
1
2
0
0
0
1
0
1
0
1
2
1
1
1
2
1
0
2
2
1
1
2
2
2
0
1
1
1
0
1
0
1
2
0
1
0
2
0
0
0
1
1
1
0
0
1
0
0
0
2
0
2
2
0
0
0
0
0
0
0
1
2
2
2
2
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
2
4
2
0
0
0
0
0
0
2
1
1
1
0
0
0
0
1
1
2
0
0
0
0
0
0
3
1
0
2
0
2
0
1
1
0
2
1
0
2
1
0
0
0
2
0
2
1
0
1
1
0
1
0
2
0
1
0
2
0
1
0
1
2
3
0
2
1
0
2
0
0
2
1
2
0
1
2
1
2
2
0
0
0
0
0
2
0
0
0
2
0
1
0
1
2
1
0
1
2
0
1
1
1
1
1
2
1
2
1
0
1
1
1
0
0
0
1
2
0
1
0
0
0
2
2
0
0
3
1
0
1
1
0
0
1
1
1
1
1
3
0
0
0
2
1
0
0
1
0
2
2
1
1
1
0
2
0
1
0
1
1
0
0
1
1
1
0
0
0
2
1
0
0
3
0
1
0
1
0
1
0
1
0
1
0
0
2
0
1
0
0
0
2
0
2
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
1
1
1
0
0
0
1
1
0
0
1
0
0
1
2
2
1
1
1
0
1
2
1
0
1
1
2
1
1
1
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
2
0
0
0
1
0
0
2
1
0
1
2
0
0
1
0
0
0
1
2
1
1
0
0
0
0
2
0
1
1
0
2
0
2
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
1
0
2
0
0
0
0
1
1
1
1
1
2
0
0
2
2
0
1
0
2
0
0
0
0
2
0
0
2
0
0
1
1
2
1
0
2
1
0
1
0
1
0
0
1
2
0
3
0
1
2
1
0
2
2
0
0
1
0
2
1
2
1
0
0
1
1
0
1
0
1
0
2
2
2
2
0
1
0
0
2
0
2
1
1
2
0
1
0
0
0
1
1
1
1
1
0
2
1
0
1
0
0
1
2
2
1
0
1
0
3
1
0
1
1
2
0
3
1
2
2
2
1
0
0
2
1
2
1
0
0
0
2
0
2
0
1
1
1
1
1
1
0
0
1
0
0
2
2
2
0
1
0
0
0
1
0
0
1
1
1
0
2
0
1
2
1
1
2
0
1
2
3
1
2
0
2
2
0
2
1
1
0
2
2
1
2
2
1
0
0
1
1
0
2
0
0
2
2
2
2
0
2
0
0
2
0
1
0
0
0
0
3
0
0
2
0
0
0
0
0
1
1
1
1
1
0
0
1
1
1
1
0
0
0
2
1
1
2
0
0
2
1
0
0
0
1
1
1
0
1
0
0
0
0
1
1
2
2
2
2
1
2
1
2
2
1
0
0
0
1
0
0
2
0
0
2
1
0
2
0
0
2
0
0
0
1
0
0
2
1
0
2
2
1
1
0
1
0
1
0
1
0
0
0
1
1
0
0
4
3
2
2
0
1
0
1
0
1
1
1
2
0
0
1
1
0
0
2
2
2
0
1
0
0
0
0
0
1
1
0
0
0
1
2
1
2
0
3
1
1
1
2
0
0
2
1
1
0
2
1
0
1
2
2
3
0
1
1
0
0
1
1
0
0
1
0
2
1
2
0
2
0
2
1
0
1
0
1
1
0
1
3
1
0
0
0
1
0
1
1
3
1
2
1
1
0
1
0
0
0
0
1
0
1
0
2
2
2
2
0
1
1
0
1
0
0
0
0
0
2
1
2
0
2
0
1
0
0
0
2
0
0
1
1
1
0
1
2
0
1
0
1
2
0
0
2
2
3
1
1
2
1
1
0
0
1
0
0
0
2
2
6
0
0
1
1
0
0
1
0
0
2
1
1
0
1
0
0
2
0
2
1
0
2
1
1
1
1
2
2
2
1
2
0
1
0
1
2
2
0
0
2
1
2
1
2
2
2
1
0
0
0
1
0
0
0
1
1
0
2
0
1
0
0
0
0
0
0
0
1
0
2
0
2
1
1
1
0
2
2
2
2
0
2
2
1
0
0
1
0
0
0
1
1
2
0
1
2
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
2
0
1
0
1
0
1
1
0
2
0
0
0
1
2
0
1
1
2
1
1
0
4
0
0
1
0
1
1
1
1
1
2
1
0
0
0
0
2
0
2
0
0
2
2
0
1
0
1
0
0
1
2
2
2
0
0
0
2
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
2
2
0
0
1
0
1
1
0
0
0
1
0
1
0
1
2
2
2
1
0
0
0
0
2
1
0
0
0
3
0
0
0
2
1
1
1
0
1
0
0
0
1
1
1
2
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
2
2
0
0
2
1
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
1
4
2
1
0
0
0
1
1
0
1
1
0
0
0
1
1
2
2
0
0
0
0
2
1
3
1
2
0
0
0
0
0
1
1
0
0
1
0
3
1
2
0
0
0
2
2
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
1
1
0
3
1
0
0
0
1
0
1
0
1
2
1
0
2
2
0
0
2
0
2
1
1
0
2
0
2
0
1
0
1
1
4
2
0
0
0
1
0
1
1
2
3
0
1
1
0
2
1
0
0
0
0
1
1
1
1
1
0
0
1
1
1
2
4
2
1
0
0
2
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
1
0
1
1
2
2
0
0
0
1
0
0
2
1
0
2
0
0
1
1
0
1
0
3
0
2
1
0
0
2
0
1
2
0
0
1
0
2
0
0
1
0
2
0
0
3
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
2
0
0
0
1
1
1
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
1
1
2
1
0
0
0
2
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
1
2
0
2
0
2
0
0
0
2
2
0
0
0
1
0
2
0
1
0
1
3
1
0
2
1
1
0
1
0
0
0
1
2
0
1
2
2
2
1
0
0
2
1
0
0
1
2
1
2
2
1
1
0
3
1
0
0
2
0
2
0
2
0
1
1
2
0
1
0
2
2
0
0
0
0
0
1
0
0
0
1
1
0
1
0
1
0
1
1
2
2
2
0
0
0
0
0
0
2
0
1
0
1
1
1
1
2
0
1
0
0
1
0
0
1
1
2
1
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
1
1
0
1
1
0
0
0
1
0
0
1
0
3
1
1
0
1
1
2
2
2
1
0
1
0
2
0
0
1
0
0
2
1
1
0
0
0
1
0
1
2
1
0
0
1
2
0
2
0
2
1
0
2
0
0
0
1
2
0
3
0
1
1
0
1
0
1
0
0
0
0
0
1
0
1
0
2
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
2
1
0
2
0
0
1
2
0
2
0
5
0
1
1
0
1
0
0
2
0
2
0
1
1
2
1
0
0
1
2
1
1
2
2
0
1
0
0
1
0
0
1
1
0
2
0
0
1
0
2
1
2
0
2
2
2
2
0
0
0
0
2
2
0
0
1
1
0
1
1
2
2
0
2
2
0
1
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
1
3
0
1
0
1
1
1
2
1
0
1
2
2
0
1
0
0
0
0
0
2
1
0
2
1
1
0
0
0
0
0
0
0
0
1
1
1
1
2
0
1
1
1
2
2
1
1
1
1
0
1
3
0
0
0
2
1
1
2
5
0
0
1
1
0
0
1
0
0
2
2
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
2
0
0
2
0
2
0
0
2
0
2
0
0
1
0
0
1
0
0
0
0
2
2
0
1
1
0
1
0
2
0
1
3
0
0
1
0
0
1
2
1
0
2
1
1
1
0
0
0
2
0
1
1
0
1
0
1
0
0
2
1
2
1
1
1
2
2
2
1
1
0
2
1
0
0
0
0
2
1
0
0
2
2
2
2
0
0
0
0
2
0
0
0
1
0
3
2
1
2
0
0
1
0
2
0
0
0
2
1
0
2
0
0
2
3
1
1
0
1
0
0
1
2
0
1
0
1
2
2
2
1
1
1
1
0
1
0
0
2
0
0
0
1
2
1
2
2
0
1
0
0
2
0
2
0
0
1
1
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
2
0
0
0
0
0
1
0
1
0
0
0
3
1
0
0
1
0
0
0
1
0
0
0
2
0
0
1
0
0
0
1
0
2
1
0
2
1
1
1
0
1
1
0
1
0
0
2
1
1
0
1
1
0
1
2
2
2
0
0
2
0
2
1
0
1
1
1
0
0
0
0
0
2
0
0
2
0
0
1
1
1
0
1
2
2
0
2
0
0
0
1
1
0
1
0
1
2
0
1
1
0
0
1
1
0
2
0
0
1
0
0
1
1
0
0
2
0
0
0
0
1
2
2
1
0
1
0
1
1
1
1
3
2
0
2
0
0
2
0
1
0
2
0
1
1
0
0
1
1
0
1
0
1
1
0
1
0
1
0
2
0
2
1
0
1
0
0
0
0
2
0
2
0
1
0
0
0
1
0
1
2
0
1
1
0
0
1
0
1
1
0
2
0
0
3
0
0
0
1
0
1
1
1
1
1
2
2
0
0
0
2
0
0
1
0
0
1
0
2
2
0
0
0
1
1
2
2
2
0
3
1
2
0
2
0
0
2
1
2
0
2
0
2
1
1
0
2
1
1
1
1
1
1
1
2
2
1
0
0
0
0
0
1
1
0
0
1
1
0
2
0
1
0
2
1
0
2
1
1
1
0
0
0
3
0
2
0
2
0
0
1
2
1
0
1
1
1
1
2
0
2
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
1
2
0
2
1
2
2
1
0
0
1
0
3
1
1
0
1
1
0
2
1
2
2
0
2
0
2
1
0
0
1
3
2
1
3
2
0
1
1
0
3
2
1
1
1
0
0
0
0
0
2
1
0
1
0
0
0
1
0
0
2
1
2
1
0
0
2
1
1
1
2
2
2
0
0
0
0
2
2
0
0
1
2
0
1
1
2
2
2
1
1
0
1
1
2
2
0
1
1
1
0
0
1
1
1
0
1
1
2
2
2
0
0
0
2
0
1
0
0
0
0
4
2
0
0
2
0
0
0
1
2
0
0
0
0
1
1
2
1
0
2
2
2
0
1
0
1
2
2
0
0
1
0
0
2
2
1
2
0
0
2
2
0
3
1
0
3
0
0
2
2
2
3
2
1
0
0
0
0
1
2
1
0
2
1
1
0
2
0
2
1
1
2
0
0
0
1
1
2
1
0
1
2
0
0
2
0
3
1
2
1
0
0
1
1
0
2
2
0
0
1
0
2
0
1
2
0
0
1
1
0
1
0
1
1
0
0
0
0
0
1
0
0
1
2
0
0
2
0
2
0
1
1
1
1
1
0
1
0
0
1
1
0
0
0
2
1
2
0
1
0
2
0
0
0
0
2
2
0
2
0
2
1
2
2
0
2
0
0
2
1
0
0
1
1
1
0
0
0
0
0
2
0
1
3
1
0
0
0
1
1
0
1
0
2
0
2
0
1
0
0
1
2
2
2
2
0
1
0
1
3
1
0
0
2
0
1
1
0
0
0
2
1
0
1
0
0
0
2
0
2
0
0
0
1
0
1
0
1
0
0
0
1
0
1
1
0
1
1
0
2
0
2
2
2
1
1
0
0
0
0
2
0
2
0
1
1
2
1
2
0
0
1
0
2
1
1
0
2
0
0
0
2
1
1
0
0
0
0
1
0
1
1
1
0
2
1
0
0
2
0
0
0
1
0
1
0
1
2
0
1
0
0
0
0
2
2
1
3
0
1
4
2
0
1
1
0
6
1
1
0
0
2
0
1
1
1
1
1
0
1
2
0
1
1
0
2
0
2
0
2
1
0
2
1
0
1
1
1
0
3
0
0
0
0
0
1
1
0
1
0
2
1
2
2
1
2
0
2
3
1
1
2
1
1
0
0
1
0
0
2
1
1
3
0
2
0
1
1
0
2
1
1
0
0
1
2
0
1
0
0
0
2
1
1
1
0
0
2
1
0
2
0
0
0
1
1
1
0
0
0
1
0
0
0
0
1
2
2
0
0
2
3
2
0
0
0
0
0
2
2
2
0
1
1
2
0
1
1
1
0
0
0
0
1
0
2
1
0
0
2
2
1
0
0
2
0
0
1
1
0
1
0
1
1
2
1
0
3
2
2
0
0
0
2
0
1
0
1
0
0
2
2
1
1
0
0
0
0
1
1
1
0
1
2
1
0
0
2
2
1
0
2
1
2
1
0
13
0
1
1
1
2
0
1
0
1
2
0
0
2
1
1
1
0
2
1
2
0
0
1
0
0
1
0
0
2
0
1
0
2
2
0
0
2
0
1
1
0
0
0
1
2
2
2
0
0
1
0
1
0
0
0
2
0
1
0
1
0
1
1
0
0
0
1
1
0
1
0
2
2
2
0
1
0
1
2
2
1
1
2
0
1
0
0
0
2
1
2
2
1
0
0
0
0
1
1
0
0
1
2
1
2
0
1
0
0
0
0
0
1
0
2
1
2
0
0
1
0
2
0
1
1
1
0
0
2
0
0
0
1
2
0
3
0
0
2
1
0
0
0
2
1
0
1
0
1
0
2
0
1
0
1
2
0
1
2
1
0
0
0
1
1
0
1
0
1
0
2
2
0
0
2
0
1
2
1
1
0
0
1
2
0
0
1
2
0
3
1
1
1
1
1
0
1
0
2
0
0
1
1
1
1
2
1
0
0
0
0
0
0
1
1
0
0
2
4
0
1
1
0
2
1
1
0
0
2
1
1
2
1
0
1
0
0
1
0
1
0
2
1
0
2
2
0
0
2
0
0
1
0
0
2
2
1
2
1
1
0
1
2
2
2
2
0
1
1
3
0
2
2
1
2
0
2
1
1
0
0
0
1
2
1
1
0
1
1
2
1
2
1
2
1
2
0
1
0
0
1
0
1
0
1
1
0
0
1
1
2
2
1
0
1
0
0
0
3
2
0
1
2
2
1
0
2
6
0
0
1
0
0
0
0
2
0
0
0
1
2
1
0
0
1
0
1
0
2
2
1
1
1
1
2
2
0
2
0
0
0
0
1
0
0
0
0
0
2
1
0
2
1
0
0
2
1
0
1
0
2
0
0
0
0
0
1
2
2
0
0
0
0
0
2
1
0
1
0
2
2
0
1
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
2
1
0
2
1
0
6
0
1
0
1
2
0
0
0
0
0
0
0
2
0
2
0
0
2
2
0
0
1
2
2
0
1
2
1
2
2
1
0
0
0
0
1
0
0
1
1
2
1
0
0
1
0
1
2
0
1
1
1
0
1
1
0
1
0
2
3
0
0
0
2
1
1
1
1
2
0
1
0
2
2
0
0
0
0
1
0
1
1
2
1
0
2
1
2
1
1
2
1
0
1
1
0
0
1
0
3
0
0
0
2
0
0
0
1
2
2
2
0
2
2
1
1
2
0
0
0
0
0
2
0
2
0
0
1
0
0
0
1
0
0
0
1
0
1
1
0
2
1
0
1
0
0
0
1
2
2
0
1
2
1
0
0
0
1
0
0
1
0
2
3
1
0
0
0
0
1
0
0
0
1
0
1
2
2
1
1
0
0
0
1
1
0
0
1
1
1
0
2
0
2
0
1
0
2
0
0
1
1
1
2
2
0
2
2
1
0
2
0
0
1
1
2
0
0
0
0
2
0
1
1
1
0
0
0
0
0
1
1
2
0
2
0
2
2
2
2
2
1
1
1
1
8
1
0
0
0
0
0
2
0
0
2
1
1
1
0
2
1
1
0
0
0
2
2
1
0
0
2
1
0
0
0
1
0
0
0
1
2
0
1
1
0
0
0
1
1
2
2
0
0
2
0
2
0
3
5
0
2
0
1
1
0
0
2
0
1
1
2
2
3
1
2
0
2
0
0
0
0
2
0
2
0
0
0
1
1
0
0
1
1
0
0
1
0
0
1
1
1
0
0
1
1
0
2
1
1
0
0
0
1
0
0
1
0
2
0
0
0
1
2
2
2
2
0
1
0
1
0
1
0
1
2
0
1
0
0
2
2
0
1
1
0
1
0
1
0
0
1
0
1
1
1
2
1
1
0
1
1
2
0
1
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
2
0
1
0
0
0
0
2
1
1
1
0
0
0
1
0
1
0
1
0
1
1
0
0
1
1
1
0
1
1
2
2
1
0
0
2
1
1
2
2
2
2
2
0
0
0
2
1
0
2
0
0
2
1
2
1
2
0
1
1
0
0
0
1
1
0
1
1
2
2
0
1
0
0
1
0
0
0
0
4
0
0
1
0
0
0
2
2
2
0
0
1
0
2
0
1
2
1
0
1
0
0
1
0
1
0
2
0
2
1
1
0
1
1
1
1
0
0
2
0
0
1
3
0
0
0
0
1
0
0
1
1
0
0
2
2
0
0
1
2
0
2
2
1
0
1
0
2
1
0
0
2
0
0
0
0
0
0
1
0
0
2
0
2
2
1
0
0
0
2
1
0
0
1
1
0
0
1
2
0
0
1
0
2
0
0
0
0
0
1
2
1
0
0
0
1
2
2
1
0
0
0
1
2
1
2
2
0
0
0
0
1
2
1
0
0
1
1
0
2
0
0
2
0
2
2
0
1
1
2
0
0
0
1
0
0
0
0
1
2
1
1
1
0
0
2
1
0
0
0
2
0
2
1
2
0
0
0
0
1
1
0
0
0
0
0
2
0
0
2
0
1
0
0
0
2
3
0
1
1
0
3
0
2
0
0
0
0
1
0
0
0
1
3
1
1
1
1
0
0
1
0
0
0
1
0
2
1
1
1
0
1
0
0
2
2
1
1
0
3
0
0
1
0
0
0
1
0
2
0
1
1
0
2
1
0
0
1
0
1
2
0
1
0
0
1
0
1
1
0
0
1
1
0
2
0
0
1
2
1
2
2
0
0
3
2
0
0
1
2
2
1
1
2
1
0
0
1
1
2
0
0
2
3
0
1
0
1
2
2
1
3
0
0
0
0
0
1
1
0
2
0
1
1
2
1
2
0
1
2
0
1
0
0
2
2
0
0
2
4
0
0
1
0
1
1
0
0
0
1
1
2
3
0
0
2
0
0
1
1
0
0
2
0
0
1
0
0
1
2
1
2
0
0
1
2
0
1
0
1
1
1
0
0
1
2
1
2
0
0
2
3
2
1
2
0
2
0
1
0
0
0
1
0
2
2
2
0
2
1
2
1
0
2
0
1
0
2
1
0
1
0
2
2
1
1
0
0
2
1
1
0
0
0
2
0
0
4
0
1
1
3
2
0
1
0
2
0
1
0
2
0
0
1
0
0
0
0
2
0
1
0
0
2
1
2
2
1
2
1
1
1
0
0
0
0
2
0
1
1
1
0
0
2
1
2
0
0
1
1
1
2
0
0
0
2
1
1
1
0
1
0
0
1
0
0
0
1
0
0
0
1
0
1
1
1
1
1
2
2
0
2
0
0
2
0
1
0
1
0
0
0
1
2
0
0
2
0
1
1
2
0
1
1
1
1
0
2
2
0
1
0
0
0
2
0
2
2
0
1
0
0
0
1
2
1
2
1
2
0
1
1
0
0
0
0
1
6
1
2
1
2
0
0
1
1
1
1
0
1
2
1
0
2
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
2
0
0
0
2
1
0
2
0
0
2
2
0
0
1
2
0
2
0
1
0
1
1
1
1
2
1
2
1
0
1
0
2
1
1
1
1
1
1
2
0
0
2
0
0
0
0
1
2
0
0
1
1
1
1
2
1
0
1
1
3
0
0
2
0
0
0
1
0
0
2
0
1
0
0
0
2
1
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
1
2
0
0
0
0
1
1
1
2
0
0
1
0
0
2
0
0
2
1
0
0
0
2
0
1
2
2
1
2
0
1
2
2
1
0
0
0
1
0
2
0
0
2
1
0
1
0
1
1
0
0
0
0
1
0
0
1
0
1
1
1
1
1
3
1
0
0
2
2
0
0
0
0
0
1
1
0
2
2
0
0
0
2
0
1
2
0
1
0
0
1
1
0
0
0
2
1
0
0
0
1
0
2
0
0
0
1
1
7
0
2
1
2
0
1
0
1
0
1
1
0
0
1
0
1
1
1
1
1
0
0
0
0
2
0
0
0
0
2
1
0
3
0
0
0
0
1
1
1
1
1
0
2
1
0
0
1
0
1
2
2
0
0
1
0
1
0
0
1
1
0
2
0
1
1
0
0
1
2
0
2
0
1
0
2
1
0
0
1
1
1
0
1
0
1
1
2
1
1
2
1
1
0
1
0
1
0
2
1
2
0
0
1
2
2
0
0
0
2
0
2
1
0
2
0
0
2
1
1
2
1
1
2
0
0
2
2
0
0
0
0
0
2
0
1
2
0
2
0
1
0
0
1
0
0
2
1
1
0
1
0
0
2
1
1
1
1
2
2
1
0
0
1
0
1
2
2
1
0
0
0
0
0
0
0
0
1
0
1
0
2
2
1
0
2
0
2
1
0
2
2
1
2
4
0
0
1
1
1
1
2
2
1
0
1
2
0
1
1
0
2
0
2
1
0
0
1
1
0
0
0
1
1
1
0
0
1
0
1
2
1
0
0
0
2
0
1
1
1
2
0
0
0
2
0
1
1
1
0
2
2
0
2
0
1
0
2
0
0
3
2
4
1
0
0
0
1
0
2
0
1
1
2
1
1
0
0
0
2
0
2
1
0
0
1
0
1
0
0
0
2
0
2
0
2
1
2
2
0
1
0
2
0
0
1
1
0
1
1
2
1
1
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
2
1
0
1
0
2
1
0
0
1
1
1
1
1
0
0
1
0
0
2
1
0
1
1
0
2
1
2
2
0
0
0
0
1
1
0
2
0
0
0
1
1
0
2
1
1
0
1
0
0
0
1
1
0
1
1
1
0
0
0
1
1
1
0
0
0
2
0
2
1
1
0
0
0
0
0
0
1
1
0
0
0
2
2
0
0
0
1
0
1
2
2
1
0
1
2
0
0
2
1
0
1
0
1
2
0
0
0
0
2
0
0
0
1
0
0
2
1
2
1
0
7
3
2
0
0
1
0
2
2
0
0
1
0
2
1
0
1
0
0
0
2
1
0
1
0
3
2
0
2
0
0
0
0
0
2
1
2
0
1
0
0
0
2
1
0
0
1
2
0
2
0
0
0
1
2
0
0
2
0
1
2
0
1
0
0
0
0
0
0
1
1
2
1
0
2
2
0
0
0
1
0
0
2
0
1
0
1
1
2
1
1
2
0
1
0
1
2
1
1
0
1
0
1
1
1
1
1
0
0
2
0
0
2
0
2
1
2
0
1
2
1
0
2
0
3
0
0
0
0
1
1
0
1
2
1
0
0
1
2
1
1
0
2
2
1
0
0
2
2
0
1
0
1
1
3
2
2
0
2
0
0
0
0
2
0
1
1
0
1
1
1
2
0
1
0
0
2
0
1
1
1
0
0
1
0
0
0
1
2
1
0
2
0
2
1
0
2
1
0
1
0
0
0
0
0
1
1
2
1
0
2
1
0
0
0
1
0
1
0
0
0
0
2
0
2
0
0
0
2
0
0
1
1
3
0
0
0
0
0
0
1
1
0
2
1
0
0
1
0
0
2
0
0
0
0
2
2
1
0
0
1
0
0
0
1
2
0
0
2
0
1
1
0
1
0
0
0
0
1
0
1
0
0
1
2
1
2
2
0
1
1
1
0
1
1
0
0
0
0
0
2
1
1
2
0
0
2
0
2
0
0
2
0
1
0
1
0
3
0
0
2
1
1
0
1
1
0
0
2
1
0
2
1
0
0
1
0
0
2
2
2
1
0
2
0
2
0
1
1
1
0
1
2
1
2
0
1
4
0
1
0
0
2
1
1
2
0
1
0
0
1
2
0
1
1
0
0
1
1
1
2
1
1
0
1
2
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
1
2
1
0
0
0
0
1
0
2
0
2
1
3
0
0
1
0
0
1
0
1
2
2
1
1
0
0
0
1
0
0
1
0
0
1
1
1
1
0
1
1
0
0
1
0
1
2
1
1
0
3
0
0
0
1
1
0
0
0
2
1
0
0
2
0
2
0
0
1
1
0
0
0
2
1
0
0
0
0
2
0
1
2
1
2
0
0
1
1
0
1
0
0
2
1
1
0
1
1
0
1
1
1
1
1
0
2
2
0
0
1
1
2
1
1
0
0
0
0
0
0
1
2
0
1
2
0
1
0
1
0
1
0
0
1
0
2
0
0
1
0
1
1
0
1
0
0
2
1
2
0
0
0
0
2
2
0
0
0
0
2
2
0
2
0
0
0
2
2
1
2
1
0
0
1
0
0
3
0
1
1
1
2
0
1
0
2
1
0
0
0
0
0
1
1
1
1
2
0
3
1
0
0
2
0
2
1
0
0
0
1
0
0
0
2
1
1
2
0
2
2
0
1
0
0
1
2
0
0
2
3
1
1
0
0
0
1
2
0
0
0
0
2
2
0
1
0
2
0
2
1
1
0
1
1
1
1
2
0
0
0
1
0
0
0
0
0
2
1
1
0
2
0
0
2
2
0
0
1
1
1
2
1
0
2
0
0
1
0
2
0
0
0
0
0
2
3
0
1
0
0
0
0
0
0
3
1
2
0
0
1
1
0
0
2
1
0
1
0
2
1
0
2
1
1
0
0
0
1
1
1
2
0
0
2
1
1
0
0
1
0
0
0
0
1
1
0
1
1
0
1
1
2
0
0
1
0
2
0
1
2
0
2
0
0
0
1
1
1
0
0
0
0
0
0
0
1
2
0
0
0
1
1
1
0
1
2
1
1
0
1
0
2
2
0
0
1
0
0
1
1
2
1
0
0
2
1
1
2
0
2
2
1
2
1
1
1
0
2
0
2
2
0
0
2
2
1
0
1
0
1
0
0
1
2
1
0
1
2
0
1
1
2
0
1
2
2
0
3
1
0
0
1
1
1
2
0
0
0
1
1
2
0
1
1
2
2
1
2
2
0
0
0
2
0
0
2
2
1
1
1
1
2
2
1
0
1
0
0
2
1
1
1
1
0
0
0
1
1
0
1
0
0
0
1
1
2
1
1
1
2
1
0
0
1
0
0
2
0
0
2
1
2
0
0
2
1
0
1
1
0
0
1
1
1
1
0
1
0
0
0
2
2
0
0
0
1
0
0
2
0
0
0
1
2
1
0
0
2
1
0
1
0
0
0
0
2
1
2
0
0
1
1
1
1
0
1
0
0
0
1
2
1
3
1
0
1
0
0
0
0
0
0
0
0
3
1
1
0
0
0
1
2
2
1
2
1
0
1
1
1
0
1
0
0
0
1
0
0
0
1
0
0
2
0
2
0
1
0
0
0
0
0
0
0
1
1
1
2
0
0
0
0
1
0
0
0
0
1
1
1
0
0
2
1
1
1
0
2
2
1
1
1
0
1
1
1
2
1
0
1
0
0
0
1
1
1
1
3
1
0
0
1
0
0
0
0
2
0
1
0
1
1
0
1
2
1
0
1
0
0
2
1
0
1
1
1
1
1
1
1
1
1
0
1
0
1
0
0
1
2
1
0
0
0
0
0
0
0
2
5
0
1
2
1
1
0
0
2
0
0
1
2
1
1
0
1
0
0
0
0
0
1
2
1
0
0
0
0
1
2
1
0
0
1
1
1
0
0
0
2
1
3
1
1
1
2
2
1
0
0
0
0
0
0
1
1
1
0
1
0
2
0
1
0
0
0
1
1
1
1
0
0
0
1
0
2
0
0
0
2
0
0
1
1
0
2
0
0
2
2
2
1
2
0
0
1
1
1
2
0
0
0
1
1
0
1
2
0
0
0
0
2
0
0
0
2
0
0
1
2
0
1
1
1
1
0
0
1
0
1
0
1
0
1
2
1
2
1
1
0
1
0
0
1
1
2
0
1
0
3
0
1
2
2
0
1
3
1
1
1
0
0
0
2
1
1
1
0
0
2
2
2
0
1
0
1
1
1
1
0
0
0
2
2
0
0
0
2
0
1
2
1
1
1
1
2
0
2
1
1
0
0
0
1
0
0
0
1
0
1
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
2
0
0
1
1
0
3
0
1
0
0
0
0
2
2
2
1
0
2
2
0
2
1
3
2
0
1
3
0
2
0
0
0
1
0
0
0
0
2
1
2
1
0
0
1
1
1
0
0
2
0
0
0
0
0
0
3
1
1
2
1
0
0
0
2
1
0
2
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
1
0
0
0
2
2
0
0
2
1
1
2
0
0
0
2
0
0
2
0
0
0
0
2
0
1
1
0
0
2
1
2
0
0
1
2
2
0
1
1
1
0
1
2
1
0
0
1
1
0
0
0
2
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
1
2
0
0
1
2
1
1
0
1
1
1
0
1
1
1
0
2
1
0
2
2
0
1
1
1
3
0
1
0
2
0
0
1
1
0
0
2
0
0
0
0
1
0
2
2
1
0
1
0
2
0
0
0
0
1
2
0
1
1
0
0
2
0
1
1
0
0
2
2
2
2
2
0
2
0
0
1
1
0
1
2
2
0
2
2
0
1
2
1
0
2
0
1
1
1
0
0
1
2
1
0
2
1
1
0
2
0
0
2
0
1
0
1
2
0
1
2
0
1
0
2
0
2
1
2
2
0
1
2
3
1
0
2
1
0
1
2
0
1
1
0
1
3
0
0
1
1
2
2
0
0
1
2
0
2
2
0
3
1
0
0
0
2
0
1
0
0
1
0
0
0
0
2
1
1
0
0
0
2
0
0
0
1
0
3
0
0
1
1
1
1
1
1
0
3
0
0
2
0
1
2
1
0
1
0
0
0
1
1
0
2
0
1
0
0
1
0
1
1
1
0
0
1
0
1
2
0
0
1
0
2
0
0
0
0
1
0
0
0
1
3
1
2
0
0
2
0
1
0
0
1
1
0
1
1
0
2
1
1
2
0
2
0
1
1
1
0
2
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
2
0
0
1
2
1
0
1
0
0
0
0
0
1
2
2
0
1
1
2
2
0
2
2
1
2
0
2
0
0
1
1
0
0
2
2
1
1
2
0
0
2
1
1
0
1
3
1
1
0
1
1
0
4
2
1
1
0
1
2
0
0
0
1
0
0
0
1
1
1
1
0
0
0
0
1
1
0
0
2
0
0
0
2
1
2
0
0
0
0
2
1
0
2
1
2
1
0
0
1
0
2
0
2
0
1
1
2
2
1
0
1
0
0
0
1
0
1
0
0
0
1
0
2
0
0
1
0
0
0
1
0
2
2
2
1
3
1
0
1
1
0
2
0
1
1
1
1
0
1
1
1
0
0
1
0
0
1
0
1
0
0
2
1
0
1
2
2
1
1
0
4
1
1
1
3
0
0
0
0
0
0
1
2
1
1
1
1
0
0
0
1
2
2
2
0
1
1
0
1
0
1
0
0
1
3
2
1
0
0
0
1
0
2
0
1
0
1
0
2
2
2
1
0
0
0
0
1
2
2
0
0
0
1
1
0
0
0
1
0
0
1
1
1
1
0
0
3
1
0
1
2
0
1
2
0
0
0
1
1
0
1
1
1
0
0
2
1
0
2
1
2
1
1
2
2
0
0
1
0
2
0
0
1
0
1
2
0
0
2
0
0
0
0
0
0
0
1
1
0
0
1
0
0
2
1
2
0
0
0
1
1
0
1
1
3
2
0
1
2
0
1
1
1
2
2
1
0
1
0
0
2
1
1
2
0
1
1
0
0
0
1
2
1
2
1
1
0
3
2
1
1
0
0
0
0
0
0
0
0
0
3
1
2
0
0
0
1
1
1
0
0
0
0
0
2
0
1
0
0
2
2
0
0
0
1
1
2
0
1
0
8
1
1
0
0
0
2
1
0
0
0
2
0
2
1
0
0
0
2
0
0
1
1
0
0
0
2
1
1
0
2
2
1
0
0
0
2
0
1
1
0
1
0
1
0
0
0
0
1
0
3
2
0
0
0
0
0
1
1
1
1
0
0
1
0
0
0
1
2
0
0
0
1
1
2
0
0
1
0
2
2
2
0
1
0
2
2
1
0
1
0
0
1
0
0
0
0
2
0
0
2
1
0
1
0
1
0
1
1
1
2
1
1
1
1
0
2
0
0
2
2
1
1
1
2
0
0
1
0
0
1
1
1
2
0
0
2
1
0
0
0
0
0
0
1
0
2
0
0
2
2
0
0
0
0
1
1
0
1
1
2
0
0
0
0
3
1
1
1
0
2
1
0
0
0
0
0
3
1
0
2
0
0
1
2
1
1
1
0
2
0
0
1
1
0
0
0
0
0
2
0
0
0
1
1
0
0
2
1
0
0
1
0
0
0
0
0
0
0
3
1
1
0
0
1
1
1
0
2
1
1
0
2
2
0
0
1
0
0
2
0
2
2
0
1
1
2
1
0
1
1
1
2
0
1
0
2
1
0
1
3
0
0
2
1
0
0
0
2
0
1
2
1
2
0
1
2
0
2
2
1
0
1
2
1
0
1
1
0
1
0
1
2
3
0
0
0
2
0
2
1
0
0
1
2
1
0
0
1
0
0
0
0
0
2
0
0
1
1
1
0
1
0
1
1
2
0
0
2
1
0
1
2
4
0
0
2
0
1
0
0
0
2
2
1
0
2
1
0
1
1
0
2
2
0
0
0
0
0
2
0
1
0
0
0
2
1
2
2
1
1
1
2
0
0
0
1
0
0
1
0
1
2
2
1
0
0
0
0
0
0
1
0
1
0
2
2
0
2
0
1
0
0
0
3
0
2
1
0
0
2
1
0
0
1
1
2
2
1
0
0
2
0
2
1
0
0
1
0
2
1
0
0
1
1
1
1
0
0
0
2
0
0
0
1
0
0
1
1
0
2
1
2
0
2
2
2
1
2
1
2
1
2
0
2
1
0
1
0
1
1
1
1
1
0
0
1
1
1
1
1
2
0
1
0
0
2
0
2
1
1
0
1
2
0
1
0
2
1
4
0
0
0
1
2
0
0
0
0
2
2
0
0
0
2
2
1
2
2
0
1
0
2
0
2
0
0
0
1
2
0
0
1
2
0
0
0
1
1
0
1
2
0
0
0
0
0
2
2
1
0
2
0
1
1
1
0
2
1
0
1
2
0
2
2
1
0
2
1
0
0
0
2
0
2
0
0
0
1
2
0
0
0
2
0
0
1
1
1
0
0
2
0
0
2
2
2
1
1
1
1
1
1
2
0
1
0
0
0
1
0
1
0
2
1
0
0
0
0
1
1
0
0
0
1
1
0
0
1
0
0
0
0
1
1
1
0
0
0
0
4
1
0
0
1
0
1
0
1
6
1
0
0
1
0
2
1
0
2
1
1
0
2
1
0
0
1
0
0
1
1
1
0
0
1
2
1
1
2
0
0
1
1
0
1
2
2
1
1
0
0
1
0
1
1
1
2
0
0
0
1
1
1
0
0
0
1
1
2
1
2
1
0
0
0
0
0
2
2
1
1
1
0
1
2
2
0
2
0
0
1
2
1
0
1
0
0
0
2
0
1
0
0
2
0
1
1
0
1
0
2
1
1
2
1
0
1
1
0
2
1
0
1
3
0
0
2
0
0
0
1
1
0
0
0
2
1
2
0
0
1
2
1
1
2
0
0
0
0
2
1
0
0
0
3
2
0
2
1
1
0
2
1
1
0
2
0
0
2
0
1
0
1
2
0
0
0
0
2
0
2
0
1
0
2
1
2
1
0
1
1
0
1
2
2
0
1
2
1
0
2
1
2
1
2
0
1
0
1
1
1
0
1
0
0
0
0
1
1
0
0
0
1
1
1
0
0
0
2
2
2
0
1
2
0
1
1
2
0
1
0
0
1
2
2
2
0
0
0
0
1
2
0
0
0
0
2
0
0
2
0
2
1
0
0
2
0
0
0
0
0
2
1
2
1
0
0
1
0
1
3
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
1
0
1
0
1
0
2
1
1
0
1
1
2
2
2
2
1
0
1
2
0
1
0
1
3
1
1
0
0
0
0
0
0
0
2
2
2
0
0
1
0
0
1
0
1
1
2
0
1
2
0
1
1
2
2
0
2
4
1
1
1
2
1
1
0
2
2
1
1
0
0
1
0
2
0
0
0
1
2
0
0
1
1
1
0
0
1
1
0
0
0
2
2
1
2
0
1
0
2
1
0
1
1
0
1
0
0
0
1
1
0
1
0
0
1
1
1
0
1
1
2
1
0
1
1
2
0
0
1
0
2
2
0
2
1
2
1
0
2
0
1
0
1
2
1
2
0
1
2
1
0
0
1
2
1
0
2
1
2
1
1
0
0
0
1
1
1
0
2
0
1
0
2
1
0
2
1
0
0
0
2
1
0
0
2
0
1
3
0
0
0
1
1
1
0
2
0
0
1
0
1
1
2
0
2
2
0
0
1
0
0
2
0
0
2
0
1
1
2
1
2
1
0
1
1
2
2
2
0
2
1
2
0
2
1
1
1
1
0
0
0
1
2
1
1
2
2
2
1
0
1
0
0
1
1
1
0
0
2
0
2
0
2
1
2
1
1
1
0
1
0
0
2
1
2
0
0
1
1
0
1
0
1
0
0
1
2
0
0
1
0
0
0
1
1
2
0
0
2
0
1
0
0
0
0
2
1
0
1
1
3
1
2
1
0
0
1
1
0
0
1
1
0
2
2
0
0
0
0
1
1
0
0
0
1
0
0
0
1
1
0
0
1
1
0
4
0
1
0
0
0
1
1
0
0
0
1
1
0
2
1
0
1
4
0
2
2
0
2
1
0
2
0
0
1
0
1
2
1
1
0
0
0
1
1
1
0
1
1
1
0
1
0
0
1
1
2
1
0
0
2
0
0
0
0
0
2
2
1
0
0
3
1
0
0
0
2
1
1
1
0
2
2
1
2
0
1
1
0
2
0
1
0
1
0
0
0
2
0
2
2
0
1
1
0
1
0
1
0
0
0
0
1
0
1
2
1
2
0
0
2
1
0
2
1
0
2
0
1
0
1
0
1
0
0
2
0
1
1
0
1
1
2
0
1
0
0
0
2
0
0
1
1
2
1
1
2
0
1
0
2
0
1
0
0
0
0
0
1
2
0
0
2
1
0
2
2
2
0
0
0
1
0
0
1
2
0
1
2
2
0
3
2
2
2
0
0
0
0
2
0
0
0
1
0
2
0
1
0
0
2
0
1
0
0
0
2
2
0
2
0
0
2
0
1
1
2
0
2
0
1
1
1
0
2
1
2
2
1
2
1
0
1
1
2
0
0
2
2
1
0
1
1
2
2
1
0
2
0
2
0
2
0
1
0
1
1
0
0
2
2
2
1
1
0
0
0
0
0
0
1
1
2
1
1
2
0
0
0
1
2
1
0
4
2
0
1
1
0
0
2
2
0
0
0
0
1
0
2
0
2
1
2
0
0
1
1
0
1
0
0
1
1
0
1
0
0
1
0
0
0
2
2
0
1
1
1
2
0
0
0
1
0
1
0
1
1
2
0
2
1
2
0
2
0
0
2
0
3
0
0
0
2
1
1
0
1
1
1
1
1
0
0
1
0
0
0
1
1
2
0
3
1
2
0
0
0
1
1
6
2
0
3
2
1
1
1
1
0
0
3
0
2
0
2
1
1
1
0
0
2
0
1
2
2
1
0
0
2
1
0
1
0
2
1
0
0
0
2
0
0
0
0
2
0
0
2
2
1
0
2
0
1
0
0
1
0
0
0
1
0
0
0
2
1
0
1
0
1
0
1
2
1
1
2
0
1
0
2
0
1
1
0
2
0
1
0
1
1
2
2
2
1
2
1
1
1
0
2
0
0
1
0
0
2
1
0
0
2
0
2
1
2
0
0
0
2
1
0
2
0
0
0
0
0
1
1
0
2
1
1
1
2
1
0
1
1
1
2
0
0
0
0
1
0
0
0
0
1
0
0
2
1
0
2
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
1
1
0
1
2
2
2
0
1
1
2
2
2
0
2
0
0
1
0
1
0
2
6
2
0
0
0
0
2
2
0
2
0
2
2
1
1
0
0
0
1
0
2
0
2
2
0
0
2
0
2
0
2
0
2
1
1
1
0
0
1
1
0
0
1
1
2
1
0
0
0
0
0
1
1
1
1
1
2
0
1
0
0
0
2
0
0
2
2
0
0
0
1
0
2
0
1
2
0
0
0
2
1
3
0
6
2
0
0
0
1
0
0
1
2
2
2
1
2
0
1
0
0
2
0
0
1
0
0
0
2
2
2
1
1
2
1
0
2
1
1
0
0
1
0
0
2
2
0
1
1
0
0
1
1
0
1
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
2
0
1
1
1
0
0
1
0
2
0
1
0
1
1
0
2
2
1
1
1
0
1
0
0
0
2
1
1
1
0
2
0
0
1
2
0
0
0
0
0
1
0
2
1
0
1
1
3
0
1
0
0
0
1
0
1
1
1
2
1
2
0
2
0
0
0
0
1
2
1
0
0
1
2
0
0
1
1
0
0
0
0
0
0
2
0
1
0
2
0
1
0
0
2
0
0
0
0
1
2
0
2
0
1
0
1
0
1
0
0
1
1
0
1
2
2
0
1
1
0
1
3
1
2
0
1
0
2
2
2
0
0
1
1
1
0
0
0
0
0
2
1
0
2
2
0
0
1
0
0
1
0
0
0
1
0
2
0
0
1
0
0
0
2
1
1
2
1
1
0
1
0
2
0
0
1
1
0
0
0
2
1
0
0
0
1
1
2
0
0
1
0
1
2
0
0
2
1
0
1
1
2
2
1
0
2
0
2
2
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
2
0
0
2
1
0
2
0
1
2
0
2
2
1
0
2
0
0
2
2
0
0
1
0
2
0
1
1
0
2
3
2
1
0
2
0
1
1
0
1
2
0
2
1
0
0
0
0
0
0
1
3
0
0
0
1
0
1
2
2
1
0
2
0
0
1
0
1
1
0
3
1
2
0
0
1
2
1
1
1
0
0
1
2
0
1
0
0
1
1
0
2
0
2
2
0
1
2
0
1
1
1
0
2
1
2
0
1
1
0
2
1
1
0
2
0
1
4
0
2
0
0
1
0
0
0
0
1
1
0
2
1
1
0
2
0
0
1
2
0
0
0
1
0
2
0
0
1
0
0
0
2
0
2
3
1
1
0
1
2
2
0
0
1
2
0
0
0
1
0
0
0
1
0
1
0
1
1
1
0
0
0
1
0
1
0
1
0
2
0
1
1
0
2
1
1
2
2
1
1
0
1
1
1
0
1
0
2
0
1
0
0
1
1
3
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
1
1
2
1
0
1
0
0
1
0
1
1
1
0
1
2
0
1
0
2
1
0
2
1
3
0
3
0
5
2
0
0
2
0
0
0
1
1
0
0
1
2
0
0
0
0
0
1
0
1
1
2
2
0
1
2
2
1
2
1
0
1
3
0
2
0
0
1
0
1
0
0
0
0
0
0
1
0
2
1
0
0
2
0
0
2
1
0
1
0
0
1
0
0
0
0
1
2
2
2
1
2
0
1
0
0
2
0
0
0
2
1
1
0
1
1
0
2
3
0
0
1
1
0
1
1
0
0
1
0
1
1
1
0
0
0
0
1
0
1
0
1
3
1
1
0
1
0
0
0
2
0
1
1
0
2
0
0
0
0
2
2
0
1
1
0
1
0
2
0
0
1
0
0
2
0
0
0
0
1
1
1
2
0
2
1
1
0
0
0
1
1
0
0
2
0
1
2
1
1
0
2
1
0
1
0
0
0
0
1
1
0
1
1
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
2
1
0
3
1
1
0
0
0
1
2
1
0
0
1
0
1
0
1
1
1
0
0
0
0
0
0
0
0
1
1
1
2
0
1
0
2
0
2
2
0
2
2
0
1
2
2
1
1
0
0
2
2
2
2
1
0
0
0
0
1
0
0
1
1
0
0
1
0
0
1
0
1
1
0
0
3
0
0
2
1
0
2
1
1
0
0
1
0
0
0
1
0
1
2
1
0
1
1
1
2
0
0
0
1
0
2
0
2
1
0
1
1
2
1
0
1
2
0
1
0
0
0
0
0
1
1
2
0
0
0
2
1
0
0
3
2
0
1
0
2
2
0
1
1
0
0
1
0
0
0
2
0
0
2
1
0
0
0
2
0
0
0
2
0
1
0
1
0
0
1
2
2
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
2
0
2
1
2
2
0
2
1
0
0
2
1
1
0
0
0
1
1
1
1
1
1
0
1
0
1
2
1
2
0
1
0
1
0
0
1
0
0
2
0
0
2
1
1
0
1
0
2
0
2
0
0
0
0
2
3
0
0
0
0
0
2
1
0
1
0
0
1
0
0
2
0
0
1
1
0
0
1
1
2
0
0
0
1
0
2
0
1
1
0
0
0
0
0
0
1
1
1
0
1
1
0
2
2
1
0
1
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
2
1
1
2
0
0
2
0
0
0
1
2
2
0
0
1
1
2
0
1
1
0
1
1
0
1
2
2
0
0
0
2
0
1
1
0
2
2
0
1
1
0
1
0
0
2
1
1
2
2
1
0
1
0
0
2
1
0
2
2
1
1
2
2
2
0
0
0
1
0
1
0
2
0
0
1
0
0
1
0
3
1
0
0
0
0
1
1
0
0
0
1
1
1
3
0
0
1
1
0
0
1
0
1
0
0
1
0
1
0
2
1
0
0
0
2
2
0
0
0
0
1
1
0
0
0
1
0
0
1
0
2
0
0
1
0
1
1
1
0
1
1
0
0
1
0
1
1
0
1
0
1
0
1
2
1
1
1
1
2
1
0
0
0
2
1
0
5
0
0
2
1
1
1
0
2
1
0
0
0
2
0
0
0
0
1
1
2
0
2
0
0
0
1
0
0
1
0
2
0
0
0
0
0
1
1
0
0
2
0
1
1
2
0
3
2
2
1
0
1
1
0
2
2
1
1
0
1
1
2
2
1
0
1
2
2
1
3
0
0
2
1
0
2
1
2
2
0
1
2
2
0
1
0
0
0
0
0
0
1
1
0
0
4
2
2
2
2
1
1
0
1
1
1
0
1
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
1
2
2
1
0
1
1
0
0
2
0
0
1
2
2
0
2
0
1
2
1
0
2
1
0
1
0
0
0
0
1
0
1
0
0
1
2
1
0
0
1
5
0
1
1
1
0
0
0
0
2
0
1
1
0
2
0
2
1
0
0
0
1
0
2
2
1
2
1
1
2
1
1
0
3
0
0
2
0
2
0
1
0
0
1
2
0
1
0
0
1
0
1
2
0
0
1
1
0
2
0
2
2
2
0
1
1
2
1
2
1
1
0
0
2
0
0
1
0
0
0
1
0
0
0
2
2
1
1
1
1
0
0
1
0
1
0
2
1
0
0
0
2
2
0
1
0
2
0
2
2
0
0
0
0
2
0
0
0
0
2
1
1
2
0
1
1
1
1
0
0
1
1
3
0
1
1
0
2
1
1
0
0
2
0
0
2
1
0
1
1
2
0
2
1
1
1
3
2
1
0
0
2
0
0
0
0
0
2
2
2
0
2
0
2
2
2
0
0
2
0
1
0
0
0
2
1
0
1
2
0
0
0
0
0
1
1
0
2
1
4
0
2
0
2
2
2
0
0
2
1
1
0
0
0
1
1
1
0
0
1
2
3
0
1
1
0
0
0
0
2
1
0
1
0
1
0
0
0
1
0
0
2
1
0
0
1
2
0
0
2
0
0
1
0
0
1
2
1
1
0
2
2
0
4
2
0
1
0
1
1
0
1
2
1
2
1
1
1
0
1
0
0
2
0
1
1
1
0
2
1
2
0
0
0
0
1
3
0
1
0
1
0
0
0
0
1
1
0
2
0
0
0
0
0
2
0
2
1
1
0
2
2
2
3
0
1
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
3
1
1
0
1
1
2
1
1
1
1
0
0
2
1
0
0
1
0
1
0
2
1
0
1
1
1
1
0
1
0
1
0
1
0
2
0
0
0
1
1
0
0
0
1
0
0
3
1
0
0
1
0
0
0
2
0
0
0
0
0
0
2
1
0
1
1
0
1
1
1
0
0
2
2
1
1
1
0
1
0
2
1
1
0
0
0
0
1
0
1
1
2
9
0
0
1
0
0
0
0
1
2
0
0
0
1
0
0
1
0
0
1
2
1
0
1
2
2
0
0
0
0
0
2
1
0
0
1
0
0
1
0
1
2
0
0
1
2
0
1
2
0
0
2
1
2
1
0
1
1
1
0
1
0
2
0
1
1
0
0
0
0
0
0
0
1
2
0
0
0
1
0
1
1
0
0
2
1
0
0
3
0
1
2
2
1
2
1
0
0
0
2
2
1
0
0
1
1
1
3
1
1
0
0
1
0
0
0
1
2
0
0
1
1
0
0
0
0
0
0
1
3
2
1
2
1
1
1
1
0
0
2
1
2
0
1
1
2
0
0
0
0
0
1
0
2
2
1
0
1
0
0
1
0
1
1
1
4
0
0
1
0
2
1
2
1
4
1
0
0
1
0
1
2
1
2
0
1
1
0
2
0
1
0
2
0
2
0
2
0
0
0
0
1
1
0
1
0
2
2
1
1
0
2
0
0
2
1
0
1
2
2
0
0
1
1
1
0
1
0
2
2
0
0
0
0
2
1
0
2
0
0
0
2
0
0
3
1
0
0
1
0
1
0
2
0
2
0
0
0
1
1
0
1
1
2
2
0
1
0
2
0
1
0
0
0
2
0
0
0
1
0
0
2
0
1
0
0
0
0
1
2
1
0
2
0
0
0
1
1
1
2
1
2
0
2
0
0
0
0
0
0
1
0
1
0
2
1
0
1
1
0
1
2
1
1
0
0
0
1
2
0
0
2
0
1
0
2
0
1
1
0
1
0
1
1
3
0
0
0
0
2
0
0
2
0
1
2
1
1
2
2
0
0
2
0
0
1
0
2
1
1
1
1
0
0
2
0
0
2
0
1
0
1
0
0
0
1
1
1
0
1
2
0
0
1
1
0
2
1
1
0
0
2
0
2
2
0
0
2
2
0
0
0
2
0
0
1
1
1
1
1
0
2
0
1
1
0
2
0
0
1
2
0
0
0
1
1
1
2
0
0
0
0
1
0
2
1
2
0
1
0
1
0
1
1
0
1
0
0
2
2
0
1
2
1
0
1
1
0
2
0
1
0
0
1
2
1
0
1
1
0
0
0
0
0
2
2
1
1
0
1
2
2
0
0
2
0
0
0
0
1
1
0
1
0
2
2
1
0
0
1
0
0
0
2
1
1
2
0
1
0
0
0
2
1
2
1
1
0
2
0
2
2
0
1
1
1
2
1
1
1
3
1
1
1
0
2
1
0
1
0
0
0
1
2
0
3
1
0
0
0
1
0
0
1
0
0
1
0
2
0
1
1
0
0
2
2
2
1
0
1
0
1
1
0
1
1
0
0
0
0
2
0
0
0
0
2
1
1
0
0
1
2
0
0
1
0
0
1
1
0
0
0
2
0
1
1
1
0
2
1
1
2
1
0
3
2
0
2
0
1
0
0
1
2
2
1
0
0
0
1
2
0
2
0
0
0
2
0
0
0
0
0
0
1
0
2
0
1
2
1
0
2
0
0
2
1
1
1
1
0
0
0
1
1
1
1
0
0
1
1
0
1
0
0
1
1
2
2
0
1
1
0
0
0
2
0
0
0
0
1
0
0
2
1
0
0
0
0
1
1
0
1
0
6
0
0
0
0
4
1
2
0
1
2
1
0
2
3
1
1
1
0
2
0
1
0
1
0
0
0
1
0
0
1
1
2
1
0
1
0
1
0
2
2
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
1
3
1
2
1
1
2
1
2
0
0
1
1
0
0
2
0
0
2
0
1
1
0
1
1
0
0
0
0
2
0
2
1
1
0
1
1
2
0
2
1
2
0
1
1
1
2
2
1
0
0
0
2
0
3
0
1
0
1
0
1
0
0
2
0
2
0
1
1
2
0
0
1
1
0
1
2
0
1
1
0
2
0
0
1
0
0
0
1
1
0
0
1
1
0
1
1
0
1
0
1
1
1
1
0
1
1
0
0
1
0
0
0
2
0
0
0
0
1
1
2
1
0
0
2
1
0
0
0
2
0
1
0
2
0
0
2
0
0
0
0
1
1
1
1
1
1
0
1
2
0
0
2
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
2
2
0
0
1
0
0
0
1
1
0
2
0
1
1
0
2
1
0
1
1
1
2
1
1
0
2
2
0
0
0
1
1
0
1
2
1
5
2
0
0
0
0
0
0
2
2
1
0
1
0
1
1
0
0
0
2
0
1
0
2
1
0
2
0
0
0
1
0
1
0
0
2
0
1
0
1
1
1
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
2
1
0
1
1
1
0
2
2
0
1
1
1
2
0
0
2
2
0
0
0
3
1
0
0
1
0
1
0
0
2
1
0
0
3
0
1
1
2
2
1
1
0
1
0
1
0
0
0
0
2
3
1
0
0
0
2
1
2
0
0
0
2
0
0
0
0
0
1
0
2
2
2
0
0
2
2
0
0
0
1
1
0
2
0
0
1
1
2
1
1
1
0
1
1
0
2
0
0
2
1
0
1
0
0
1
0
0
2
0
1
1
2
1
0
0
0
0
0
0
1
0
0
0
1
1
2
0
1
0
2
1
0
1
2
0
1
2
1
1
0
0
2
1
0
1
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
1
1
0
0
1
2
1
0
1
0
1
1
1
0
0
1
0
1
1
0
2
2
1
0
0
2
2
0
0
0
0
1
2
2
0
0
1
0
1
1
1
1
0
0
0
1
0
1
2
0
1
1
2
0
2
0
0
1
0
2
0
3
0
0
2
0
1
2
1
0
1
1
1
1
0
1
0
1
0
0
0
2
2
0
0
0
3
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
1
0
0
0
1
1
2
1
0
2
0
2
1
0
2
1
3
2
1
1
0
0
1
1
1
0
0
0
0
1
0
1
1
0
0
2
2
1
0
0
2
1
0
1
2
1
0
0
1
1
2
0
1
2
1
1
1
0
1
2
1
1
0
2
0
3
0
1
1
0
0
2
3
0
1
1
1
2
0
0
0
2
0
1
2
0
1
0
1
0
1
2
4
0
0
2
0
0
1
0
3
1
2
1
1
1
0
0
0
1
0
1
0
3
1
1
2
1
0
0
1
1
0
0
0
1
0
1
0
0
0
1
1
1
0
0
1
2
0
0
0
1
2
0
1
0
0
2
0
2
1
2
0
0
1
0
1
0
2
3
0
0
2
0
0
0
1
0
1
2
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
1
1
0
0
0
3
2
0
1
1
0
1
0
1
0
1
2
0
0
1
1
1
0
1
0
1
0
2
0
0
0
0
1
0
2
2
0
3
2
0
1
0
1
1
0
1
0
1
0
0
1
1
1
2
0
0
2
2
0
2
1
1
2
7
2
0
1
1
1
1
1
2
0
0
1
0
0
1
1
0
0
2
1
0
0
0
2
2
1
0
1
0
1
2
0
0
2
1
1
0
0
1
2
1
1
1
2
0
1
2
0
0
0
1
0
0
1
1
0
0
0
0
0
1
2
0
0
0
1
1
0
1
1
2
0
0
2
2
2
0
1
0
4
0
2
0
1
1
0
2
1
0
0
2
0
0
1
0
0
7
1
0
2
2
1
1
1
1
1
2
0
2
1
0
2
1
0
1
2
0
0
0
1
1
1
1
0
0
0
0
2
2
2
1
0
2
0
1
2
0
1
1
2
1
0
0
0
1
2
2
1
0
1
1
0
0
0
1
0
0
2
0
0
0
1
1
2
0
0
0
2
2
0
1
0
2
1
3
1
0
1
2
2
1
0
0
2
1
1
0
0
2
0
0
0
0
0
1
1
0
1
0
2
1
1
0
1
1
0
1
1
2
1
1
0
0
1
1
0
0
0
1
2
0
1
1
2
1
2
0
2
0
2
1
0
0
2
2
1
0
1
0
2
1
0
1
1
0
0
0
1
2
1
0
2
0
1
1
0
0
2
1
0
2
0
0
0
0
0
0
1
2
1
2
0
1
1
0
0
1
1
1
1
2
1
0
1
1
3
0
0
0
0
1
0
0
0
1
0
2
0
0
2
1
0
2
1
2
2
0
0
0
2
0
1
1
2
2
1
1
0
0
3
0
0
2
0
2
0
0
0
0
1
1
1
0
0
2
1
2
0
1
1
1
0
2
1
2
1
1
0
2
0
0
2
0
0
1
1
0
2
2
1
1
1
0
2
1
0
1
0
0
1
0
0
1
2
2
1
1
0
1
0
0
0
0
0
0
0
2
1
1
0
2
2
1
0
2
1
0
1
1
3
0
0
0
1
0
1
1
1
0
1
2
1
2
0
1
1
2
2
0
0
0
2
0
0
2
0
0
1
1
0
2
2
1
2
0
1
0
1
0
0
0
0
2
1
1
2
0
1
0
2
1
1
0
0
1
1
1
1
2
1
0
0
1
0
0
1
0
0
0
0
1
2
1
1
0
1
2
1
1
1
1
2
1
0
1
2
2
0
1
2
1
0
4
0
2
1
0
1
0
1
1
0
0
0
1
1
0
0
1
0
0
0
0
0
1
1
0
1
1
0
1
0
0
2
1
2
0
2
2
1
1
0
2
0
0
1
0
0
1
2
0
1
2
1
0
0
0
2
1
0
2
1
2
0
0
0
1
1
0
0
1
0
2
0
0
2
0
0
0
0
0
0
2
0
1
1
0
2
2
0
2
1
1
1
1
2
0
1
1
0
1
2
0
1
1
0
1
0
1
0
1
0
2
1
1
1
2
1
1
1
0
2
1
1
0
1
0
0
1
1
0
1
0
2
0
0
3
0
0
0
0
1
1
0
2
3
1
0
1
1
1
2
0
1
0
1
0
2
0
0
1
2
0
2
0
0
2
0
2
0
2
1
1
0
1
0
0
2
2
2
1
1
0
1
1
0
2
0
0
0
1
1
0
2
1
0
0
0
1
1
0
2
0
0
3
0
1
0
0
0
1
0
0
0
0
2
1
0
2
1
0
0
1
1
0
2
0
0
0
0
1
1
0
1
2
1
0
0
0
1
2
0
3
0
0
1
0
2
0
2
3
0
2
0
2
0
2
1
0
2
0
0
0
2
2
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
1
0
0
0
1
2
0
3
1
0
1
0
1
0
0
0
0
0
1
2
0
0
0
2
2
2
0
1
1
1
1
0
3
2
2
1
1
1
1
1
0
1
0
0
0
0
0
1
1
0
2
0
0
0
2
1
2
0
2
2
2
1
0
1
0
1
0
0
0
1
1
0
2
1
1
2
1
1
0
1
2
0
0
0
0
1
0
1
0
0
0
2
2
0
2
1
0
0
3
0
2
0
1
1
0
1
0
1
0
2
2
1
1
0
1
1
2
1
2
1
4
0
0
1
1
0
0
1
1
1
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
4
0
1
0
1
2
1
0
0
0
2
0
1
0
0
1
2
0
1
0
0
2
1
0
2
1
0
1
0
1
1
2
0
0
1
0
1
1
1
3
2
1
1
0
2
0
0
0
0
0
0
0
1
2
1
2
1
0
0
2
0
0
1
0
2
1
0
2
0
1
0
0
1
0
2
2
1
1
0
0
0
1
2
0
2
2
1
2
1
2
0
0
0
2
1
2
1
0
1
0
3
2
1
0
1
2
1
1
0
2
1
2
0
0
1
0
1
3
0
2
0
1
0
0
0
0
0
0
2
1
2
1
0
2
0
0
1
2
0
0
2
1
0
0
1
2
1
4
1
0
2
1
0
0
0
0
0
0
1
1
0
0
2
1
0
1
1
2
1
0
2
1
1
0
2
1
0
0
0
0
0
0
1
1
0
1
0
1
1
0
0
1
1
0
0
2
0
2
2
1
0
0
2
1
0
0
0
2
0
1
0
2
1
2
0
0
1
0
1
0
2
1
2
0
0
2
0
2
1
1
0
2
0
1
0
1
0
1
0
1
2
0
1
1
1
1
0
0
0
0
0
1
0
1
0
2
3
2
1
0
1
1
0
1
1
0
1
0
0
0
1
0
2
0
1
2
0
0
1
2
0
0
0
2
2
0
0
1
0
2
1
2
0
0
1
1
2
0
1
1
0
0
0
1
1
0
0
0
0
1
1
1
0
1
1
1
0
2
0
0
1
2
1
2
0
0
1
1
0
0
1
0
1
0
0
0
0
1
0
1
1
0
1
0
1
0
0
2
0
1
1
3
0
2
2
2
1
1
1
0
2
1
0
0
4
0
0
1
1
1
0
2
1
0
1
2
2
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
2
0
2
1
0
1
0
1
1
0
0
0
1
0
2
0
0
2
0
0
2
2
2
0
1
2
0
1
0
2
1
2
2
2
0
2
1
0
1
0
1
2
1
2
0
0
2
0
0
3
2
0
0
1
1
0
0
1
1
0
0
0
2
0
0
0
1
0
0
1
2
0
1
1
2
0
1
1
0
0
0
0
2
1
0
0
1
0
2
1
0
0
0
0
0
2
0
1
0
2
1
1
0
0
2
0
2
0
2
1
2
1
0
1
1
0
1
0
2
2
1
0
0
3
0
0
1
0
2
1
2
0
2
1
0
2
1
0
2
1
1
0
0
0
1
1
0
0
0
1
0
1
0
2
0
0
2
1
0
2
0
0
1
2
0
0
1
0
0
0
2
1
1
0
2
0
0
0
1
0
0
1
2
1
1
0
0
0
0
1
0
0
2
0
0
0
1
2
1
0
1
0
1
1
0
1
0
1
0
0
0
0
1
0
1
1
0
2
0
0
0
0
2
1
0
0
0
0
0
2
1
2
0
0
1
0
2
0
2
0
0
1
2
1
1
0
0
1
2
0
1
0
1
0
0
0
1
1
1
1
0
1
1
2
1
1
2
1
0
1
2
0
1
1
0
1
0
0
0
0
0
1
2
0
1
1
2
1
0
1
1
0
0
0
1
0
2
1
0
2
2
0
0
0
0
1
0
2
0
0
1
0
1
1
2
0
0
0
2
2
1
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
2
0
1
2
0
1
2
0
1
2
2
0
0
2
2
2
0
1
0
0
0
0
0
2
1
0
0
0
0
2
1
1
0
1
1
0
1
0
0
0
1
1
1
1
0
2
0
2
2
0
0
0
0
0
0
1
1
1
0
0
2
2
1
1
0
0
1
1
2
1
2
0
0
1
0
1
2
1
0
2
2
2
2
1
1
3
0
0
2
0
0
1
1
1
0
0
0
0
1
0
1
0
1
1
1
0
0
0
2
2
0
0
1
1
2
3
1
0
0
2
0
0
0
2
0
1
0
0
2
1
0
2
1
1
0
1
0
2
0
2
1
0
0
0
0
0
3
0
0
1
2
0
0
0
0
2
1
1
1
2
0
0
0
0
1
0
1
2
1
0
0
0
0
0
2
0
1
1
0
1
2
1
0
0
1
1
2
0
0
0
2
1
1
1
0
0
0
2
2
2
2
1
0
1
1
2
2
0
1
0
0
2
1
1
1
0
2
2
2
0
0
1
2
2
0
2
0
0
0
2
1
1
2
1
0
0
0
1
0
0
2
0
2
0
3
2
1
1
2
0
2
0
0
1
3
1
0
0
0
0
0
0
1
2
0
0
1
0
2
0
1
0
0
1
0
0
0
1
2
0
1
1
1
0
0
0
0
0
2
1
0
5
1
1
1
0
1
0
1
0
2
1
0
2
0
0
1
2
0
0
5
3
0
0
1
1
1
0
2
2
0
2
1
0
1
0
1
0
2
1
0
1
0
2
1
0
1
0
1
2
2
0
1
1
2
0
1
0
2
0
1
2
2
1
1
2
0
1
0
2
0
0
1
0
0
0
0
0
2
0
0
2
0
1
1
1
1
2
1
0
2
0
1
3
0
0
0
2
0
1
1
1
2
1
1
1
0
1
2
0
2
1
1
0
0
1
1
0
2
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
2
0
1
0
2
2
1
1
0
2
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
2
2
1
1
0
0
1
2
1
0
0
0
2
2
0
0
0
0
1
1
0
1
2
0
0
0
0
0
2
2
0
1
0
0
0
1
0
2
0
0
0
0
0
2
1
1
1
1
0
2
0
1
2
0
0
0
0
0
0
2
0
1
0
1
0
1
2
0
0
0
0
0
3
2
1
0
0
1
2
1
0
0
2
1
0
2
0
0
3
1
0
2
0
0
1
2
1
1
0
0
2
2
1
1
1
2
1
0
2
0
1
0
0
0
0
2
0
2
1
1
0
0
0
0
2
1
0
0
2
1
0
1
1
0
0
0
1
1
0
1
1
2
0
1
0
2
1
1
0
1
0
0
2
1
0
0
0
2
0
0
0
0
2
2
1
0
1
0
0
0
0
1
1
1
0
1
1
0
2
2
1
1
0
0
3
0
1
1
0
1
1
0
2
1
0
0
2
0
2
1
0
2
1
0
1
2
0
1
0
3
1
0
1
0
2
1
1
1
1
1
0
0
1
1
0
1
0
0
1
0
1
1
2
2
2
0
1
0
0
0
1
1
1
1
1
1
1
2
1
1
2
0
0
0
1
0
2
1
0
2
0
2
0
2
2
0
0
1
1
0
0
0
2
2
0
2
0
2
0
4
0
1
1
1
0
1
1
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
1
0
0
2
0
0
1
1
0
0
2
1
2
0
0
1
2
0
1
2
3
0
1
0
0
0
2
2
1
2
1
0
0
2
1
0
2
0
0
1
0
4
2
1
1
0
1
2
2
0
0
2
1
2
1
1
0
1
1
1
0
0
1
1
0
0
2
1
1
0
1
0
0
0
2
1
0
0
0
0
1
2
2
1
3
0
0
0
2
2
1
0
0
0
1
2
0
1
2
1
0
0
0
1
0
0
0
1
0
0
1
0
0
1
2
1
0
2
0
0
0
0
1
1
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
1
1
0
1
1
1
0
0
2
0
1
2
3
0
2
4
0
0
1
0
0
1
0
0
0
1
0
2
0
0
2
1
0
1
0
0
2
0
1
0
0
1
0
0
1
1
0
0
0
0
0
1
0
1
1
1
1
0
2
1
0
2
0
2
1
0
0
0
2
0
0
2
1
1
0
0
0
0
1
0
1
0
0
1
2
0
0
2
2
1
0
2
2
0
1
1
0
0
0
0
2
2
0
0
0
0
1
0
0
1
1
1
1
1
1
2
0
1
3
3
0
1
1
0
0
0
1
0
1
1
2
0
1
1
1
0
1
2
1
1
0
0
0
0
0
1
1
0
0
0
0
1
1
1
0
1
0
2
0
2
3
0
0
0
1
0
1
0
1
2
1
1
0
0
0
0
0
0
2
0
0
1
2
0
1
6
1
1
2
0
1
0
0
0
0
2
0
1
2
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
1
1
0
1
2
1
1
1
1
1
0
1
7
1
1
1
2
1
0
1
0
0
0
1
2
1
1
0
2
1
0
1
1
1
0
0
1
0
2
1
0
0
1
0
1
1
1
0
0
2
1
2
0
0
0
1
0
1
1
2
0
1
0
1
1
0
2
0
1
1
0
0
0
2
0
2
3
2
0
0
0
1
2
0
1
1
0
1
1
2
0
0
0
0
0
0
0
0
0
0
1
3
0
2
0
2
1
2
2
1
2
0
1
0
0
0
1
1
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
2
2
0
0
1
2
0
0
0
1
0
1
0
0
0
0
1
1
1
0
1
2
0
0
1
1
0
0
0
2
2
0
1
0
1
1
1
2
0
2
0
0
2
0
1
0
2
0
1
0
1
0
0
1
0
1
2
2
0
0
0
1
3
0
2
0
1
0
0
0
1
2
0
1
0
0
2
1
2
1
1
0
0
0
0
0
0
0
0
2
1
0
1
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
2
0
1
0
2
0
1
1
2
0
0
1
0
1
2
0
0
0
2
0
2
0
0
1
1
4
2
0
1
2
1
0
0
0
0
0
0
2
0
2
0
0
1
2
0
0
2
1
0
1
0
0
1
0
1
0
1
0
0
2
2
0
1
1
1
0
0
2
0
2
0
0
0
2
2
2
0
1
0
1
0
1
0
2
1
1
0
0
0
1
0
0
0
0
0
2
0
1
1
0
0
0
1
1
0
2
0
0
0
2
0
0
2
2
0
0
2
0
2
0
2
0
1
0
1
0
0
0
1
0
0
1
0
0
0
2
2
0
2
0
0
1
0
0
3
0
3
1
0
0
1
0
0
1
0
1
2
2
0
1
2
1
1
0
0
1
1
0
2
0
0
2
0
0
0
2
1
0
1
0
0
3
0
0
0
0
0
0
1
1
2
2
2
0
2
0
2
1
2
1
0
1
1
1
1
1
0
1
0
1
1
0
0
2
0
2
1
0
0
0
0
1
1
0
0
1
2
2
0
0
1
3
2
2
1
1
2
1
0
2
0
0
0
2
0
0
1
1
2
0
0
0
1
1
2
0
2
2
0
1
1
1
0
0
0
0
2
0
0
0
0
3
1
1
0
0
0
1
1
1
1
3
0
1
0
0
1
1
0
1
1
0
2
1
2
1
0
1
1
1
2
1
0
0
1
0
1
1
0
0
0
0
0
0
1
1
1
1
0
1
0
2
0
0
1
1
2
0
0
1
1
0
1
0
0
1
1
2
0
1
2
2
3
0
0
0
1
1
2
0
1
1
4
0
1
0
0
0
1
0
1
1
1
2
1
0
1
2
2
2
1
1
0
1
1
2
1
0
0
2
0
1
0
2
0
2
0
0
0
1
0
1
0
1
1
2
1
0
3
1
2
0
0
1
2
0
1
2
2
1
2
2
2
0
0
3
1
0
1
2
0
1
1
2
1
1
1
0
0
0
1
1
1
0
1
0
2
0
0
0
1
0
2
1
1
1
1
1
0
1
0
1
0
2
2
0
1
0
0
3
0
0
2
0
0
2
0
0
0
4
2
1
0
0
0
0
0
0
0
0
0
2
3
0
1
1
0
1
0
0
0
1
1
0
2
0
0
1
0
0
0
0
0
1
1
2
0
2
2
0
1
2
1
0
0
0
0
0
0
1
1
0
1
2
1
0
0
2
0
0
0
2
1
1
1
0
0
1
0
4
0
2
2
1
0
0
0
0
0
1
0
1
0
1
2
0
2
0
1
0
0
1
3
0
2
0
0
1
1
1
0
0
1
2
1
0
2
1
1
0
0
0
0
2
0
2
2
1
1
1
1
2
0
1
2
0
0
1
0
1
0
2
0
0
2
0
0
0
1
1
2
1
0
1
2
0
1
2
1
2
0
1
1
0
0
1
2
2
1
1
1
1
0
0
0
0
1
2
0
0
0
1
0
1
0
1
2
1
0
0
3
0
2
2
0
2
1
1
0
2
1
1
1
0
0
2
0
1
1
0
2
1
2
0
0
1
0
0
0
1
0
0
1
1
2
0
1
0
2
1
1
1
1
0
1
0
2
2
0
0
2
0
0
2
1
1
2
0
2
0
2
0
0
0
0
2
1
0
0
0
1
1
0
1
0
2
0
2
1
2
0
0
0
0
0
0
0
0
0
2
0
0
2
1
1
1
2
1
0
0
1
1
0
0
0
0
0
0
1
1
1
0
0
0
1
0
2
0
1
2
0
0
0
1
1
0
2
5
0
0
0
1
2
0
1
2
1
2
0
0
0
1
3
0
0
3
0
0
1
0
2
1
0
2
1
2
0
2
0
1
1
1
1
0
1
0
0
1
2
0
1
0
0
1
1
2
2
0
1
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
1
0
2
1
1
0
1
0
2
2
2
3
0
1
0
1
1
1
2
1
0
1
0
1
2
0
0
0
1
0
0
0
1
0
2
0
0
1
1
0
1
1
2
2
1
0
2
1
0
2
1
2
0
1
1
0
0
0
0
2
2
1
0
1
1
1
1
0
1
2
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
2
2
0
1
0
1
0
1
2
0
2
1
1
1
1
0
2
0
2
1
0
2
1
0
2
0
1
1
1
0
2
1
2
2
0
2
2
0
1
0
1
0
2
0
0
1
0
1
2
0
1
0
2
2
0
1
2
2
0
0
0
1
1
0
0
0
1
1
3
1
1
1
2
0
0
2
0
1
2
2
2
0
0
0
1
2
1
0
2
0
0
0
1
0
0
0
1
2
0
0
1
1
1
0
0
0
1
2
1
0
1
0
1
0
0
0
0
0
2
0
0
0
1
0
0
2
0
1
1
0
1
1
2
2
1
0
0
1
0
2
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
2
2
1
1
1
1
1
1
0
1
1
2
0
0
1
0
2
0
1
1
0
0
0
0
1
0
0
0
0
1
0
1
1
1
1
0
1
0
0
0
1
1
1
1
1
0
1
0
1
0
0
1
1
1
0
0
2
0
0
1
2
0
0
0
1
1
0
2
1
0
1
0
1
2
1
1
2
1
1
1
0
2
2
1
0
0
1
2
1
1
0
2
0
1
1
1
1
0
2
1
1
1
0
0
1
0
0
0
1
1
1
1
0
0
0
0
0
2
0
1
0
0
0
0
0
1
1
2
3
0
0
1
0
2
0
0
1
0
0
0
0
0
1
0
2
1
0
0
1
0
0
0
1
0
1
2
0
1
0
0
1
1
0
1
2
0
2
2
1
0
0
1
0
1
2
0
0
1
0
0
0
0
0
0
1
1
2
0
2
2
2
2
2
1
2
1
2
0
0
2
1
2
0
0
2
0
0
0
0
0
0
2
0
1
0
1
2
0
1
0
0
0
2
0
1
2
2
0
2
0
0
0
2
0
2
1
2
0
1
3
0
2
0
2
1
0
0
0
1
0
1
0
2
1
0
1
0
0
0
0
0
1
1
2
1
0
0
0
1
0
0
1
2
1
2
1
0
1
0
2
0
1
0
0
0
0
0
0
2
1
1
0
2
1
0
0
0
2
2
2
0
0
0
0
2
0
2
2
0
0
2
0
1
2
2
0
0
2
4
1
1
0
0
1
2
0
0
0
1
0
1
3
0
0
1
2
1
0
0
1
1
1
1
1
2
2
0
0
1
0
0
2
1
0
0
1
0
1
1
1
2
1
0
1
1
1
2
0
0
0
2
0
0
1
0
0
3
3
1
2
1
0
3
1
1
1
1
2
0
1
0
0
1
0
1
2
1
1
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
2
0
2
1
0
1
3
2
2
0
0
1
3
1
0
1
2
0
0
0
1
0
0
1
2
1
0
0
0
1
1
0
0
2
0
2
1
0
0
0
0
0
0
0
0
2
2
1
1
0
2
1
1
0
1
1
1
0
1
0
1
2
1
1
2
0
0
1
1
0
2
1
0
0
2
1
1
1
0
2
1
0
0
0
7
0
1
0
0
2
1
1
1
1
0
2
0
1
1
0
0
2
0
2
2
1
1
0
1
2
0
1
2
0
1
0
2
2
1
1
1
1
1
1
1
0
2
1
0
0
2
2
1
1
1
0
1
1
0
0
0
2
1
2
2
0
2
0
2
0
0
0
0
1
1
0
0
1
0
1
1
2
0
0
0
0
0
0
1
0
0
1
1
2
0
0
0
0
0
2
0
1
0
0
2
1
2
2
1
1
1
2
0
2
0
0
0
0
0
2
1
0
0
0
1
2
4
0
0
1
0
2
0
0
1
1
2
2
0
0
0
1
0
1
1
1
1
2
0
1
1
1
1
0
0
0
0
2
0
1
0
4
2
0
1
0
1
0
0
0
0
0
2
0
1
1
0
1
1
0
0
2
2
0
2
0
0
0
2
0
2
2
0
1
2
0
1
1
0
1
1
1
1
0
2
0
0
2
0
1
0
0
1
0
1
0
0
2
0
1
1
1
0
0
1
0
1
2
2
1
2
2
1
0
1
1
0
1
2
0
0
0
1
1
0
0
2
1
2
1
1
0
1
2
1
1
0
0
0
0
1
1
2
1
0
6
0
0
0
1
0
0
1
0
1
1
2
1
0
2
1
3
0
0
1
0
0
0
0
0
0
2
0
1
0
1
1
1
1
0
1
2
1
2
1
1
0
1
0
1
0
2
2
2
2
0
3
0
1
0
0
0
1
0
2
0
0
0
0
0
2
1
0
2
0
2
0
0
0
2
0
0
0
0
0
1
0
0
2
2
1
0
0
2
0
0
1
2
0
0
1
1
0
0
3
1
0
0
1
1
2
1
0
2
2
0
0
1
2
0
0
0
2
2
1
0
2
2
0
0
1
0
0
1
1
1
0
1
3
1
0
1
1
1
3
0
0
0
0
0
1
1
0
0
1
1
1
1
2
0
0
1
0
2
0
1
2
2
0
2
0
0
0
1
1
0
0
4
1
2
1
0
0
1
0
0
0
2
0
0
1
1
0
2
0
1
0
0
0
1
0
1
1
1
2
1
1
0
0
0
0
1
2
0
0
1
0
1
0
0
0
0
1
2
2
1
2
0
0
0
0
0
0
1
0
2
0
1
1
0
0
1
0
0
0
1
1
1
0
1
0
1
2
1
2
2
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
1
1
2
2
1
1
0
1
0
0
1
2
0
2
0
0
2
0
0
1
0
0
0
0
0
1
0
1
0
0
1
1
4
1
0
0
2
0
0
0
0
1
0
0
0
1
1
0
1
0
2
0
0
2
0
0
0
0
0
2
0
1
1
2
1
2
0
1
1
0
0
0
1
0
0
2
1
1
0
0
0
1
1
2
1
1
0
1
0
0
2
0
0
2
0
0
0
1
0
1
1
2
0
1
0
0
0
0
0
1
0
1
0
1
1
1
1
0
0
2
1
1
3
0
2
1
0
1
0
0
0
0
0
2
2
1
0
1
1
1
1
1
2
2
0
0
0
2
1
2
0
2
1
0
0
1
1
0
0
1
1
0
1
0
0
1
0
4
2
1
0
2
0
2
2
0
1
2
2
0
0
0
0
0
0
2
0
1
0
0
0
2
1
0
1
2
1
1
0
0
0
1
0
1
2
1
3
0
2
0
1
0
1
0
0
1
0
0
11
1
0
1
1
0
1
0
2
1
0
0
1
1
0
0
2
0
1
0
0
2
0
2
0
0
1
0
0
0
1
2
0
0
0
0
0
1
2
0
0
2
1
2
1
2
1
1
0
0
0
0
2
1
0
3
0
0
1
0
0
1
0
1
2
0
2
1
0
1
1
0
1
1
0
1
0
0
1
1
14
1
0
0
0
2
0
0
1
0
1
1
2
0
1
1
2
0
1
1
0
2
0
2
0
0
0
0
2
1
1
1
2
0
0
2
2
0
1
2
2
0
2
1
1
0
0
0
0
0
0
2
0
2
2
0
2
2
2
0
0
2
0
2
0
0
1
0
1
2
0
1
0
1
1
1
1
1
1
0
0
1
2
1
1
1
1
0
1
0
2
0
0
2
0
1
2
1
4
1
1
1
0
2
1
0
0
1
1
0
3
2
0
1
0
0
0
0
0
1
1
2
0
1
0
0
2
0
0
0
0
1
0
0
1
0
2
1
0
1
1
2
3
0
1
3
1
0
0
0
0
1
0
1
2
1
2
0
1
0
1
0
0
0
0
0
0
1
1
0
1
0
2
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
1
1
2
2
1
1
0
1
1
1
1
0
0
0
0
1
2
1
0
1
0
1
0
0
0
1
1
0
1
2
2
0
0
0
1
2
1
1
0
0
0
4
0
2
1
1
0
0
1
0
2
2
2
0
1
0
0
1
0
1
1
1
1
0
3
2
0
1
1
2
0
0
1
0
2
2
1
1
1
2
2
0
1
0
0
0
0
2
0
1
0
0
0
2
0
1
1
0
1
0
0
1
0
0
2
2
1
0
0
2
0
2
0
1
0
2
0
0
1
1
0
0
1
0
9
0
1
2
0
1
2
0
0
0
0
2
0
1
0
0
0
0
1
0
1
2
1
0
2
0
3
2
1
1
0
2
1
1
0
2
2
1
2
0
0
0
1
0
1
0
1
1
0
0
1
1
1
2
0
0
0
0
0
0
0
0
2
2
2
1
0
1
1
3
1
1
1
0
1
2
1
1
1
1
1
0
1
0
0
0
2
0
2
0
1
2
2
1
2
0
0
1
0
0
0
0
0
1
1
0
0
2
0
3
2
1
2
0
0
2
0
1
2
1
0
0
1
0
2
2
1
0
1
0
1
2
1
0
0
1
1
1
2
1
1
2
0
1
0
4
0
0
1
0
0
1
0
0
0
0
0
1
0
1
1
0
0
1
2
3
0
0
0
1
0
0
2
0
1
0
0
2
1
0
2
0
0
0
0
1
2
0
0
1
1
1
0
0
0
0
0
0
2
0
2
2
1
2
0
0
0
0
0
0
1
0
0
0
0
1
3
0
0
1
1
0
1
3
0
0
0
0
0
1
0
0
0
2
1
0
1
2
1
2
0
1
0
2
1
0
0
0
1
0
1
1
1
1
1
0
0
0
1
1
0
1
0
2
0
0
0
0
1
2
0
1
2
1
1
1
1
2
0
2
0
2
0
0
0
0
0
1
0
0
1
2
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
2
1
1
2
0
2
0
2
2
0
0
2
3
1
0
1
0
1
1
0
0
0
1
2
2
0
0
2
1
1
1
2
0
1
0
2
1
1
2
1
2
0
3
1
0
1
1
0
0
0
1
0
2
0
0
0
0
0
2
0
0
2
1
4
1
0
0
1
0
0
2
0
0
1
0
1
0
2
1
1
2
0
0
0
0
0
2
1
0
1
1
0
0
1
0
1
2
0
1
1
2
1
1
2
1
3
1
2
1
3
1
0
1
2
0
0
0
0
1
1
2
0
0
0
0
0
2
2
2
0
1
0
0
2
2
1
0
0
0
0
1
0
0
1
0
0
2
0
0
1
1
0
0
0
0
0
0
0
1
0
0
2
2
1
0
2
3
1
3
1
1
0
1
0
1
1
0
2
0
2
2
2
1
0
5
1
0
1
0
0
1
1
2
0
0
1
1
0
0
0
2
0
2
1
2
0
2
1
1
1
2
1
1
1
0
1
0
2
1
1
2
0
0
0
1
2
2
1
1
1
0
0
0
1
1
0
0
1
1
0
0
0
2
2
0
1
1
0
1
2
1
1
0
0
2
0
0
0
0
0
0
2
0
2
1
0
1
0
1
0
1
0
0
1
1
2
2
0
1
0
1
0
2
1
0
2
2
1
1
1
0
0
1
0
2
0
0
1
0
3
2
0
0
1
0
0
2
1
0
1
0
1
0
1
0
0
1
0
0
0
2
0
0
0
0
0
1
1
0
1
1
0
2
1
0
1
1
1
0
0
2
0
0
1
2
0
1
2
2
1
1
1
0
0
0
0
1
2
1
0
1
0
1
1
0
1
1
0
1
0
1
1
0
0
2
0
0
2
0
1
0
0
0
1
1
2
0
1
2
0
0
2
2
2
0
1
2
2
2
0
1
1
2
2
0
2
0
1
1
0
1
0
1
2
0
1
0
0
1
1
1
0
1
2
1
2
0
0
1
0
0
1
1
0
1
0
0
1
3
0
1
0
1
0
0
2
1
0
2
1
0
2
0
3
0
1
0
2
1
0
1
0
1
0
1
1
0
0
0
2
1
1
0
0
1
0
0
0
0
1
2
1
1
1
1
0
0
0
1
1
0
0
0
2
4
3
2
1
0
0
1
1
0
1
0
0
1
3
0
0
2
0
2
0
1
0
0
3
2
4
2
2
1
0
1
0
0
2
0
1
0
1
0
3
2
1
0
2
0
1
2
1
1
2
1
1
0
0
0
0
1
1
1
0
0
0
2
1
2
0
0
0
0
0
0
0
1
2
1
1
0
1
0
2
0
0
0
1
0
1
2
1
0
1
0
0
0
0
1
1
1
2
0
1
1
0
0
1
0
1
1
0
2
2
0
0
0
1
0
2
0
1
0
2
0
0
0
0
1
1
0
2
1
1
0
2
2
2
0
0
2
2
0
2
1
2
0
1
1
0
0
0
1
0
1
1
0
0
0
2
2
1
0
0
2
1
2
0
2
0
0
0
0
2
0
2
0
1
0
2
2
0
1
0
2
3
3
1
1
1
1
1
2
1
1
0
2
1
0
2
1
0
0
2
1
0
0
0
1
0
1
0
1
0
0
2
1
0
2
0
1
3
1
1
0
1
1
2
1
0
0
0
1
0
1
0
1
0
1
2
0
1
0
1
0
3
2
0
1
1
3
1
0
0
2
1
0
0
2
2
1
0
2
0
0
1
1
0
1
2
0
1
1
2
0
1
0
0
1
1
1
1
0
0
1
0
0
2
0
0
1
0
2
0
2
0
1
1
2
2
2
1
1
1
0
1
0
1
2
0
1
0
0
0
0
0
1
2
0
2
2
0
2
1
1
0
0
2
0
2
0
0
0
0
0
0
1
2
2
0
1
1
1
2
0
0
2
2
0
0
2
0
0
1
2
0
0
0
0
2
1
1
0
0
1
0
0
1
0
1
3
0
2
0
0
0
1
1
1
0
1
1
0
1
1
1
0
1
2
0
0
0
2
0
0
1
0
1
1
0
1
0
1
0
0
1
0
1
1
2
1
0
1
1
2
0
0
2
0
1
0
2
1
0
1
0
2
0
1
1
1
0
2
2
0
0
0
1
1
2
0
1
0
2
1
2
0
2
1
0
0
1
0
1
1
0
0
1
2
1
1
0
0
1
0
0
2
2
0
1
1
0
0
1
0
0
1
0
0
1
0
1
1
1
1
2
2
1
0
2
5
1
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
2
1
1
1
0
0
2
0
1
0
3
1
2
2
3
1
1
0
1
0
0
0
1
0
1
0
1
2
1
2
1
0
0
2
2
1
2
1
0
0
2
0
1
0
0
2
1
0
2
3
1
0
0
0
1
0
1
0
1
2
0
0
2
0
2
1
1
1
2
0
0
0
0
0
1
2
0
1
1
0
1
0
1
0
1
0
0
0
2
0
0
0
0
1
0
1
0
0
1
0
0
1
4
1
1
1
1
0
2
0
0
1
0
2
2
1
2
0
0
1
0
1
0
1
0
1
0
1
0
0
1
0
0
1
1
0
0
2
1
0
0
0
2
1
1
0
0
2
1
1
1
2
2
0
0
1
0
0
2
4
1
0
0
0
1
2
0
0
2
0
2
0
0
2
0
0
0
2
0
0
3
1
0
0
2
0
2
2
0
1
0
2
0
0
0
0
0
1
1
1
0
0
2
2
2
0
0
0
1
0
1
0
0
0
1
2
1
1
3
0
0
2
1
0
1
0
2
0
1
0
0
0
0
0
2
2
0
0
2
2
0
0
3
0
0
1
0
0
2
0
2
0
1
0
1
0
0
1
0
2
2
0
2
1
2
0
2
1
2
0
1
2
2
0
0
0
0
0
0
1
4
1
0
1
1
2
0
0
0
2
1
1
1
0
2
1
0
1
0
0
1
2
0
1
1
0
0
0
0
2
0
0
0
1
1
1
1
0
1
1
1
0
0
0
3
1
2
2
2
1
1
1
0
2
0
1
0
2
0
0
0
1
2
1
1
3
1
1
1
0
2
0
0
2
0
0
2
0
0
1
0
0
2
0
2
2
2
0
0
2
1
0
0
0
1
2
0
1
1
1
1
0
0
2
1
3
2
1
2
2
1
1
1
0
0
0
0
1
1
2
2
1
2
0
3
0
2
2
1
0
1
1
0
0
2
2
2
1
0
0
0
0
1
2
0
2
1
2
0
0
1
1
2
1
2
1
4
1
1
2
0
0
0
1
0
2
0
1
0
0
0
0
1
1
0
1
1
0
0
0
0
0
2
0
0
0
0
0
1
0
1
1
1
1
2
0
1
1
2
4
0
0
0
0
1
1
1
1
1
1
1
0
1
0
2
0
0
1
2
0
2
0
1
2
0
0
1
0
0
0
0
1
0
2
1
0
0
1
1
0
0
1
0
0
0
1
0
1
0
1
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
1
1
0
0
2
1
0
1
0
0
1
2
1
0
1
0
0
0
0
1
0
0
0
1
1
2
0
1
0
0
1
0
2
2
2
0
1
2
0
0
1
2
2
1
0
1
1
0
1
2
2
0
2
1
0
0
2
1
0
1
1
1
0
0
1
0
0
2
1
0
0
1
2
1
1
0
0
1
1
1
2
1
0
2
0
2
2
2
1
0
2
1
2
1
1
0
1
1
0
0
1
2
0
2
1
1
2
2
0
0
2
0
0
3
2
1
1
0
0
1
3
2
2
0
2
0
1
1
2
1
1
1
0
2
0
2
0
0
1
0
2
0
2
0
2
1
0
1
0
2
2
1
0
1
0
1
0
0
0
0
0
0
0
1
0
1
2
0
1
0
3
2
1
1
1
2
2
0
0
1
2
1
1
0
2
0
2
0
1
2
2
1
2
0
0
2
1
3
0
0
2
0
2
0
0
0
0
2
0
0
1
0
0
2
0
0
0
1
0
3
1
0
2
1
0
0
0
0
2
2
0
0
0
1
0
0
1
2
0
2
1
1
1
1
0
0
0
1
0
2
0
0
0
2
1
3
0
1
0
0
1
2
2
1
1
0
1
2
0
1
0
0
2
5
1
0
2
0
2
1
2
0
1
0
2
0
0
1
3
0
1
1
2
1
2
0
2
0
2
2
1
2
0
0
1
0
0
0
2
0
2
1
0
1
0
1
1
2
1
0
1
0
1
1
0
0
0
0
0
3
0
0
0
1
0
1
0
2
3
2
0
1
1
1
0
0
2
0
0
0
0
0
0
0
0
0
2
2
1
4
1
1
1
0
0
1
0
0
1
0
1
1
1
0
5
1
0
2
1
0
0
1
0
0
0
1
0
1
0
1
0
0
2
0
1
2
0
1
1
2
0
0
3
1
0
0
2
0
1
2
2
0
2
4
0
1
2
3
0
2
0
2
1
1
2
0
0
1
0
3
1
0
0
1
2
1
1
0
2
0
2
2
0
1
1
1
0
2
1
0
0
0
0
0
1
0
0
1
0
1
0
1
2
0
0
1
3
2
2
2
2
3
2
0
2
2
0
0
0
0
1
1
2
0
2
0
0
1
2
2
1
2
1
0
0
0
0
0
2
2
0
1
2
0
1
0
0
1
0
0
1
0
2
0
0
1
2
0
0
1
1
1
2
1
1
0
0
1
2
0
1
2
0
1
1
0
0
0
1
2
0
0
2
2
0
2
2
1
1
0
0
0
0
0
0
2
0
0
0
0
1
0
2
2
0
1
4
0
0
2
0
1
1
0
1
0
1
0
0
0
8
1
0
0
2
1
1
0
0
2
0
2
0
2
1
0
0
0
2
1
1
2
0
0
0
1
1
1
1
1
0
0
2
0
0
5
2
2
0
1
0
1
1
2
1
0
0
0
1
0
2
0
2
0
2
0
2
1
1
2
1
0
0
0
0
0
1
1
0
0
0
1
1
1
1
1
0
0
0
2
0
0
0
3
2
1
0
2
0
0
0
0
1
2
2
1
0
2
3
1
0
1
0
0
1
1
1
0
2
0
3
0
1
0
1
2
0
0
0
1
0
1
0
1
0
0
1
0
0
1
1
0
0
0
0
1
0
1
1
2
0
1
1
1
1
1
0
1
1
0
2
0
1
0
1
1
0
0
1
1
1
1
0
2
1
1
1
1
2
0
0
3
0
1
1
0
0
0
0
0
0
2
2
2
1
0
0
0
2
1
2
1
2
5
1
1
0
1
0
0
1
0
2
0
2
2
1
0
1
1
0
2
1
0
3
0
0
0
0
0
0
0
2
2
2
0
0
2
0
1
2
1
1
1
0
1
0
0
2
1
0
0
0
0
1
3
1
1
1
1
2
0
1
2
1
0
2
2
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
2
0
1
1
2
1
0
0
0
2
0
1
1
0
0
2
0
2
0
1
1
0
2
2
0
1
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
1
0
2
2
1
0
0
1
1
0
1
0
0
0
2
0
1
2
0
2
1
1
1
2
0
0
4
0
0
1
0
0
0
0
1
1
0
0
1
0
0
2
0
0
0
0
1
3
0
1
0
0
2
2
0
0
0
2
0
0
0
2
1
0
2
2
3
0
0
0
0
2
0
2
0
1
0
1
2
0
0
3
0
1
2
1
0
2
2
1
0
0
1
0
2
1
0
0
1
0
0
2
1
0
0
2
1
2
2
0
0
1
0
1
0
1
0
2
1
0
2
1
0
2
1
0
1
2
0
2
1
2
1
0
0
0
0
0
1
1
0
3
0
1
2
1
0
1
0
0
2
2
1
0
0
1
0
1
1
1
1
0
2
0
2
0
0
0
0
2
1
1
0
0
2
1
1
1
1
2
1
2
2
0
1
1
0
2
0
3
0
2
0
0
0
0
0
1
0
1
2
1
0
0
1
1
1
0
5
0
1
2
1
0
0
2
0
0
2
1
0
0
0
1
3
1
2
2
0
0
2
0
0
0
0
2
0
0
0
0
1
1
0
1
2
0
2
0
1
0
0
1
2
1
0
1
0
1
0
2
1
0
0
1
0
0
1
1
0
1
0
1
2
2
1
0
1
0
2
1
0
1
0
1
1
0
1
0
0
0
0
1
0
1
0
1
0
2
0
0
1
0
0
0
0
0
1
2
0
0
0
2
0
0
1
0
0
2
0
1
2
1
1
1
0
1
1
2
2
2
1
2
0
1
2
2
1
1
0
2
2
2
1
0
2
1
0
2
0
1
2
1
2
2
0
1
0
1
1
2
0
0
1
2
2
0
0
0
0
0
2
0
0
0
0
0
1
1
1
0
0
0
0
2
0
0
0
4
1
0
1
1
0
0
0
1
0
0
0
1
0
0
0
2
3
0
2
0
0
1
2
1
2
2
0
0
2
0
1
0
1
0
0
1
0
2
1
0
1
1
1
0
1
1
1
2
1
1
1
1
1
0
0
0
1
0
2
0
0
2
0
0
1
2
1
1
0
1
0
0
0
0
0
0
2
0
2
0
0
2
1
0
0
2
0
0
2
0
0
0
1
1
0
2
1
1
0
2
1
1
0
1
0
2
2
0
1
0
2
2
2
1
0
0
0
0
2
0
1
1
1
0
2
0
1
0
0
1
1
0
0
1
1
0
2
0
2
0
1
0
2
0
0
1
1
0
2
0
1
1
2
1
2
1
1
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
2
0
0
1
0
1
0
2
1
2
1
2
1
2
1
1
1
0
0
0
1
1
0
0
2
0
0
0
1
1
0
0
1
2
2
1
2
0
1
0
0
0
1
0
1
1
1
2
0
2
2
2
0
1
2
0
0
1
1
2
0
1
1
0
1
0
1
0
1
1
1
1
1
0
1
1
0
1
2
0
0
2
1
1
2
1
2
2
2
0
2
1
1
2
1
0
0
1
2
1
1
1
0
0
0
1
2
1
0
1
0
1
1
0
0
1
2
2
0
1
0
1
0
0
2
1
0
2
1
2
1
1
1
1
0
1
2
2
2
0
1
1
1
1
1
2
0
0
1
0
0
1
1
0
0
2
0
0
0
2
0
0
3
1
0
1
1
0
1
0
0
5
0
0
1
2
0
0
0
1
2
1
0
0
1
0
2
1
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
1
0
1
0
2
1
0
0
0
0
2
1
1
2
1
0
0
0
0
0
1
0
0
1
1
1
1
0
0
0
1
1
1
0
0
1
1
0
1
0
1
0
0
1
0
0
0
1
0
1
1
0
0
0
0
4
0
1
1
2
0
0
1
1
0
0
0
2
0
1
2
2
1
0
1
1
2
1
2
1
0
0
0
0
0
2
1
0
1
4
1
0
1
1
1
0
1
0
2
0
1
0
1
0
1
1
2
0
0
3
2
0
0
1
0
2
0
0
0
0
1
0
0
2
1
2
1
1
0
1
2
1
2
1
1
2
2
1
0
1
0
1
1
2
0
2
2
0
0
0
0
0
0
0
2
0
0
0
2
2
1
0
0
2
2
0
0
1
2
1
2
2
0
1
0
0
0
1
1
1
1
1
2
0
1
0
1
0
0
1
2
0
1
1
2
2
2
0
1
1
0
0
2
3
0
2
1
1
1
1
1
1
0
2
1
0
0
2
0
0
0
1
0
1
0
0
0
2
2
2
2
1
0
2
2
1
1
1
0
0
4
2
2
0
0
1
0
1
0
0
0
0
1
1
1
0
2
10
1
2
2
0
1
0
2
1
1
1
2
0
1
2
3
0
2
1
0
0
2
2
0
1
0
0
3
0
2
0
1
0
0
1
0
2
0
1
1
1
1
0
1
0
1
4
0
1
2
0
1
1
2
0
0
0
1
0
1
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
2
0
0
1
1
1
0
3
2
0
1
2
1
0
0
0
0
3
1
2
1
1
2
0
0
0
0
1
2
0
1
0
0
1
1
0
1
1
0
0
2
0
0
2
2
0
0
2
0
0
2
0
2
2
0
0
0
0
2
1
0
0
0
0
2
2
0
0
0
1
0
2
0
2
1
0
1
0
0
0
0
0
2
1
0
0
2
1
1
0
2
0
2
0
1
1
2
0
2
2
3
1
1
0
0
0
0
0
0
1
2
3
0
0
0
1
1
1
1
0
0
2
0
0
0
1
1
1
1
1
0
1
0
2
0
1
2
2
0
0
2
1
1
0
0
2
0
2
0
1
0
0
0
1
0
1
0
0
2
1
0
0
0
1
1
1
0
0
0
0
1
1
0
0
2
0
0
1
0
1
2
2
1
2
2
0
0
1
2
0
0
2
2
1
2
1
0
0
0
2
2
0
1
2
1
1
1
2
0
2
2
0
1
0
1
1
0
0
1
0
0
0
2
0
1
0
1
2
0
0
0
2
1
2
1
1
0
2
0
2
0
1
1
1
0
1
2
0
1
2
2
0
1
0
2
0
0
0
0
0
3
1
1
1
2
0
1
2
2
0
1
2
1
2
3
2
1
0
0
0
0
1
0
1
1
2
0
0
2
1
0
0
1
0
0
0
2
2
0
0
1
6
1
0
1
0
0
1
0
2
1
0
2
2
0
0
1
1
0
0
1
1
0
0
1
0
2
0
0
1
2
2
0
1
0
0
0
1
1
2
0
2
0
0
0
1
1
1
2
0
0
0
0
0
2
0
0
0
0
0
1
0
1
1
1
0
0
3
2
1
2
2
0
2
0
0
0
0
0
3
0
0
0
0
0
0
2
2
0
0
1
0
0
2
0
1
0
0
2
0
1
2
1
1
0
0
1
1
0
0
0
1
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
1
2
1
1
0
1
0
2
0
1
2
0
2
0
2
0
2
0
1
0
2
0
0
2
1
2
1
1
2
1
1
0
0
2
1
2
0
1
1
1
0
1
1
1
0
2
0
0
0
1
1
1
1
2
1
2
1
1
1
2
1
0
0
0
0
0
0
2
1
0
0
0
0
1
0
1
2
0
1
0
0
0
1
0
0
1
1
0
2
1
0
0
1
1
0
0
1
2
0
1
2
1
0
2
0
1
0
2
2
0
1
3
2
2
0
0
0
0
1
1
0
1
1
3
1
0
0
0
1
2
2
0
2
1
1
0
2
0
0
1
0
1
0
1
2
2
1
0
1
1
1
0
0
1
1
1
3
0
0
0
0
0
1
1
1
3
2
5
6
0
0
2
2
0
0
1
2
1
1
1
0
1
1
4
0
2
0
1
0
0
3
0
2
0
1
2
0
0
0
0
1
1
0
1
0
1
0
1
3
0
2
1
2
0
0
1
0
1
0
0
1
2
2
2
2
0
0
1
2
0
1
0
0
2
2
1
1
0
1
1
0
1
0
1
1
0
0
4
2
1
1
1
1
0
1
3
2
1
1
2
0
2
1
2
1
0
0
0
1
0
0
0
0
2
0
1
0
1
0
0
0
1
0
0
1
0
0
0
2
1
2
0
1
0
2
2
0
2
0
1
0
2
1
1
1
0
2
1
1
1
2
0
0
0
1
1
1
0
1
0
0
1
0
0
0
1
1
0
2
0
0
0
0
0
3
2
3
1
0
1
0
1
0
0
2
0
0
0
0
2
0
1
1
1
1
1
1
0
0
1
0
0
1
0
0
1
1
0
1
1
1
1
1
0
0
0
1
0
1
0
2
2
1
0
2
1
0
0
2
1
2
1
2
1
0
1
0
0
1
1
2
0
1
2
0
1
1
0
1
2
0
1
4
0
1
1
1
2
0
2
0
0
0
2
0
0
2
0
1
2
0
1
1
1
2
0
2
0
2
3
1
0
0
0
2
1
0
0
0
1
1
1
0
1
1
0
0
2
1
0
1
2
0
0
0
0
1
1
2
0
0
1
0
1
3
2
0
0
0
1
1
1
0
2
0
2
0
0
2
0
3
1
0
2
0
2
0
0
0
0
0
3
2
0
0
0
1
0
0
1
0
0
0
2
2
1
2
0
1
1
1
1
0
1
1
1
2
2
2
2
1
0
1
2
1
0
0
0
0
0
2
0
2
0
0
2
0
0
0
2
1
0
0
0
0
0
1
1
1
0
0
1
2
2
0
1
1
0
1
1
1
0
0
1
0
2
0
1
0
0
0
1
1
3
1
0
1
2
0
1
1
0
0
2
0
0
1
0
2
2
0
3
1
1
0
1
0
0
0
1
2
0
2
0
1
0
0
0
1
0
0
0
2
3
1
1
1
2
2
1
2
0
1
0
0
0
1
0
1
1
0
1
2
2
0
1
0
1
1
1
2
1
2
1
0
0
2
3
1
0
1
0
0
0
0
1
2
1
1
2
0
0
2
2
0
2
2
0
0
0
1
0
1
2
0
0
1
2
0
0
3
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
2
2
2
0
0
1
0
2
2
0
1
1
0
0
0
1
1
0
1
1
0
1
0
0
0
2
0
1
0
1
2
2
1
2
1
1
1
3
0
0
2
1
1
2
1
0
0
2
0
1
2
2
0
3
1
1
0
5
2
0
0
2
0
3
0
1
1
0
2
2
0
2
2
2
0
1
2
0
0
0
1
1
2
0
0
1
1
0
1
1
1
2
0
1
0
1
1
0
0
1
4
0
0
2
0
1
0
0
2
1
0
1
0
2
0
3
1
0
3
1
1
1
0
1
0
0
1
1
0
1
0
2
0
0
1
0
1
2
1
1
0
2
0
1
0
2
1
2
0
1
1
1
0
1
2
0
0
2
1
0
2
0
2
1
0
0
1
0
0
0
0
2
0
0
1
1
1
2
2
0
0
0
0
1
1
2
0
0
1
1
0
1
0
2
1
0
1
0
2
0
2
0
2
0
2
0
0
1
1
1
1
2
0
0
0
0
2
0
0
2
3
2
0
1
2
1
1
2
1
1
1
1
0
0
0
1
1
1
1
0
0
0
0
1
1
2
0
1
0
0
0
2
0
0
1
2
2
1
0
1
0
1
1
0
2
1
1
1
1
0
1
0
0
1
0
0
0
5
1
2
0
0
2
1
0
0
0
0
0
0
0
0
0
2
2
4
0
0
0
2
0
1
0
0
0
0
0
2
1
1
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
2
0
0
0
1
0
0
2
0
2
1
2
2
0
1
2
0
0
1
1
1
0
0
1
0
1
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
4
0
0
1
0
2
1
0
1
0
1
2
0
0
0
1
0
2
1
0
2
0
1
0
0
1
0
1
0
0
2
3
1
0
1
1
0
1
1
2
1
0
0
1
2
2
0
0
0
0
1
0
2
0
1
0
3
0
1
2
0
0
1
1
0
1
0
1
0
1
2
0
1
0
0
2
0
0
0
1
0
1
0
0
3
0
4
1
1
3
1
1
0
2
1
0
2
1
0
0
1
1
0
0
0
1
0
1
3
0
0
0
0
0
1
4
2
0
0
1
2
2
0
0
1
0
2
0
1
2
1
1
2
2
2
1
0
0
1
2
0
1
0
0
1
1
1
0
2
0
1
0
0
2
2
2
5
2
0
1
0
1
1
0
0
0
0
0
4
0
2
1
0
0
1
0
0
0
1
0
1
1
0
0
1
2
0
1
1
1
0
2
0
1
2
2
1
1
1
0
1
1
1
2
0
1
1
2
1
0
2
1
0
1
3
0
2
1
0
1
2
0
0
0
2
0
1
0
3
0
1
0
0
0
1
0
1
1
0
1
2
1
1
1
2
2
0
2
0
2
0
0
0
2
0
1
1
0
0
0
0
0
0
0
1
1
2
0
0
0
2
0
2
1
0
1
2
0
0
0
0
2
4
2
2
0
0
1
0
0
2
0
0
2
1
1
0
0
0
0
2
0
0
1
0
0
1
1
0
0
2
0
2
1
0
0
0
0
2
1
2
0
2
2
1
0
2
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
1
2
0
0
2
1
0
0
0
0
1
2
0
1
2
2
0
0
0
2
2
0
1
0
2
0
0
0
1
0
1
0
0
0
1
1
0
4
1
0
1
0
1
1
2
0
2
0
0
2
0
0
0
1
1
0
0
0
2
0
0
0
1
1
2
0
0
0
0
1
0
2
0
0
2
0
1
0
1
1
0
0
0
1
0
1
1
1
0
2
0
0
0
2
1
0
0
1
0
2
2
0
1
2
2
0
0
1
3
4
2
1
2
1
2
0
0
0
0
0
1
0
2
0
2
2
0
1
0
0
1
0
0
0
1
1
2
0
0
1
0
1
0
2
1
1
1
1
0
0
2
0
1
1
2
0
0
0
0
1
1
0
2
1
2
1
2
2
2
1
0
1
1
1
0
2
2
2
1
1
0
1
0
1
1
0
1
0
2
1
0
1
1
2
2
0
0
1
1
0
1
1
1
1
1
0
0
0
0
0
2
0
1
2
1
1
0
0
0
1
2
1
0
1
0
0
1
1
0
0
0
2
0
0
3
0
1
0
0
2
2
1
0
1
0
0
2
2
0
0
0
0
1
3
0
0
0
0
0
0
1
0
2
1
0
2
0
3
0
2
1
0
2
0
0
1
1
1
0
0
1
0
1
2
2
0
2
0
0
0
6
1
0
0
2
0
0
0
1
1
1
0
2
0
0
0
0
1
1
2
0
1
1
0
0
0
0
1
2
1
0
1
0
1
0
1
0
0
1
3
1
1
0
0
2
2
0
0
1
0
0
1
0
0
1
1
1
0
1
1
1
1
1
2
1
1
2
1
2
0
1
0
1
0
0
0
1
0
1
0
0
1
0
0
1
0
1
1
0
0
2
2
0
2
1
3
2
0
2
2
0
1
2
1
0
0
0
0
0
0
1
1
2
2
1
1
2
0
2
0
1
0
0
2
0
1
0
1
0
0
1
2
2
0
0
1
0
0
1
0
0
1
2
2
0
1
1
0
2
0
0
1
0
2
0
1
2
1
1
1
1
0
1
1
1
1
1
0
0
2
0
0
0
1
1
0
0
2
3
1
2
2
2
0
0
2
0
0
0
2
2
1
0
1
1
1
1
0
1
1
0
2
0
0
1
5
1
0
2
0
0
2
0
0
0
0
2
0
1
2
2
1
1
0
1
0
1
1
0
0
2
1
0
0
2
0
2
2
2
0
0
1
1
0
2
2
2
2
2
1
2
1
2
0
1
1
1
2
2
1
1
0
1
1
0
0
2
2
0
0
2
2
0
0
2
0
0
0
0
0
2
1
0
0
1
0
0
0
1
2
0
0
2
0
2
0
0
6
0
0
1
0
0
2
2
1
1
0
0
2
0
1
1
1
0
0
1
1
2
1
1
0
0
0
0
1
2
3
1
1
1
1
0
0
0
0
0
2
0
0
2
0
0
2
0
1
0
0
0
1
0
0
2
1
0
2
0
0
0
3
1
2
0
1
2
2
1
1
0
0
2
1
0
1
1
1
0
1
1
1
0
1
1
1
2
0
0
2
0
0
1
1
2
1
0
0
1
1
0
0
0
1
0
2
0
0
0
0
0
2
1
1
0
0
0
1
0
0
2
0
2
0
1
1
1
1
0
3
0
0
1
0
0
0
1
10
0
1
1
1
0
2
0
2
0
0
0
0
2
2
2
0
1
1
2
0
2
1
1
2
1
1
0
0
2
0
1
0
1
0
0
2
1
2
1
1
1
1
0
3
0
1
1
1
1
2
0
2
1
1
1
0
2
2
0
2
2
0
0
1
0
1
0
1
2
1
0
0
0
0
2
1
1
1
0
3
0
0
0
0
0
2
0
2
1
1
1
0
0
0
1
2
0
1
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
1
0
1
1
2
0
1
1
0
0
0
0
1
2
1
2
0
2
2
0
2
0
1
0
2
0
1
0
1
2
1
0
0
2
1
0
1
2
1
0
2
1
0
3
0
1
0
0
0
0
0
0
0
2
2
1
2
1
0
3
1
0
0
1
1
0
2
2
1
0
1
3
0
1
1
0
0
0
0
1
1
0
0
1
2
1
4
0
0
0
0
2
0
2
2
4
0
0
1
0
1
1
0
1
0
0
0
0
1
0
3
0
1
1
0
0
0
1
1
0
0
1
2
1
0
0
2
0
1
0
1
1
1
0
0
1
2
0
0
0
0
0
0
1
1
1
0
0
1
0
1
1
3
0
0
2
0
1
4
1
0
1
3
0
1
0
2
1
0
1
0
0
2
4
0
2
0
0
2
2
2
0
1
0
1
0
2
0
0
0
1
0
1
1
2
2
0
1
0
2
1
1
1
0
1
0
0
1
1
1
0
2
0
0
1
1
0
2
0
2
0
2
0
0
1
2
0
0
2
0
1
2
2
1
1
1
0
0
2
0
0
0
1
1
1
2
2
2
1
1
3
2
1
2
0
0
2
2
2
1
0
0
1
2
0
0
0
2
1
2
1
2
0
1
2
1
1
0
3
1
2
1
0
1
1
0
2
1
2
0
1
1
1
2
2
0
0
0
0
2
3
0
2
2
1
1
0
2
3
1
1
1
2
0
1
1
0
1
0
1
0
1
0
0
0
1
0
0
1
2
0
1
2
0
1
0
0
0
0
0
0
1
2
1
0
0
4
1
1
1
0
0
0
1
3
1
2
2
1
1
1
1
2
0
0
2
1
0
3
0
1
0
1
1
0
2
0
0
1
1
0
2
0
0
0
0
1
2
2
0
0
0
2
0
0
0
1
1
2
2
0
2
1
2
0
1
2
1
1
2
1
0
1
0
2
2
0
0
2
0
1
0
0
2
0
2
0
0
0
0
0
0
1
1
1
1
1
4
0
0
1
1
0
1
0
0
0
0
1
0
2
0
0
2
2
1
0
0
0
2
2
0
0
0
0
0
1
0
1
0
0
2
0
2
0
0
1
0
2
0
0
1
0
0
2
0
1
1
0
1
0
1
1
0
1
1
0
0
0
0
2
1
0
1
1
1
2
1
0
1
2
1
0
0
1
0
0
2
0
0
0
0
0
1
1
0
1
1
1
0
3
0
1
0
1
1
0
0
1
0
0
1
2
1
1
0
0
0
0
1
1
2
1
2
0
2
0
0
0
2
1
0
1
2
2
0
1
1
2
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
1
2
0
1
0
0
1
1
0
0
0
0
1
1
0
2
0
0
1
1
1
0
0
0
0
2
1
2
0
2
0
2
0
1
0
0
1
2
0
1
1
0
0
0
0
0
1
0
0
1
2
1
0
2
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
1
1
2
2
1
0
0
0
2
3
0
2
0
0
0
2
2
0
0
1
0
1
0
0
0
0
0
0
0
1
2
0
2
1
1
2
0
1
2
0
0
0
0
1
1
0
0
1
0
0
0
1
2
2
3
0
0
2
0
0
0
2
1
1
0
0
2
1
0
1
0
1
2
0
2
2
2
1
2
0
0
2
0
1
0
1
0
1
0
0
0
0
2
0
0
2
0
0
0
2
2
2
2
0
1
0
1
0
0
0
2
0
0
2
0
0
0
0
2
0
0
1
2
0
1
0
1
0
2
0
0
0
1
1
1
0
0
0
0
2
0
0
1
0
1
2
2
0
1
0
1
2
0
0
0
1
1
0
1
1
0
1
0
1
1
0
0
1
0
0
0
0
1
0
1
2
0
1
2
1
0
0
0
3
2
1
1
0
1
1
2
1
2
0
0
2
0
1
1
1
2
0
3
0
0
0
1
2
2
1
0
0
0
1
1
0
0
1
0
0
2
2
0
0
2
1
0
1
1
1
1
2
1
0
0
1
1
1
1
0
1
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
2
2
0
0
0
2
0
0
1
1
0
0
1
0
0
2
1
0
7
0
0
1
0
1
0
1
0
1
0
2
1
1
0
0
1
2
0
0
0
0
0
0
4
0
0
0
1
0
1
2
0
0
0
0
1
0
0
2
0
1
1
2
1
0
2
0
2
2
1
1
2
2
0
2
2
2
1
0
1
2
1
0
1
1
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
2
0
2
0
1
1
0
1
0
0
0
0
0
0
2
0
0
0
1
1
1
1
1
1
0
0
2
1
0
1
0
3
0
1
2
2
1
0
0
2
1
2
0
1
0
2
0
1
0
0
1
1
0
1
0
0
0
2
0
1
2
0
0
0
0
0
0
2
2
0
0
1
2
0
1
0
1
2
0
1
1
1
0
0
1
1
0
0
0
0
1
2
1
0
0
1
0
2
1
1
0
1
2
1
2
1
0
1
0
3
0
0
0
0
2
3
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
1
0
2
1
2
0
1
0
0
0
2
0
2
1
0
0
1
1
0
1
1
0
1
1
2
2
0
1
0
2
1
0
1
0
2
1
0
0
0
1
1
2
1
2
1
2
0
2
2
1
0
1
1
0
0
1
2
1
0
2
3
0
0
0
1
0
0
2
0
0
0
2
0
1
2
0
1
1
0
0
1
0
0
0
0
2
0
1
0
0
2
1
0
0
2
0
0
1
2
1
0
1
0
2
2
0
0
0
2
0
0
3
1
0
2
0
1
0
2
1
1
0
0
0
2
0
1
0
1
1
2
0
0
0
1
2
1
1
0
0
2
1
1
1
1
1
2
0
1
1
0
1
0
0
2
2
1
0
2
0
1
0
0
4
1
0
1
1
0
2
1
1
0
1
1
1
0
1
0
2
2
1
1
0
0
2
0
1
0
0
1
1
0
1
1
0
2
1
0
3
2
2
0
3
1
1
0
0
2
2
4
1
0
0
0
1
1
1
3
1
2
1
3
0
1
1
1
0
0
1
2
0
1
0
0
0
1
0
1
0
1
0
0
4
1
0
1
0
0
4
0
0
0
1
1
2
0
2
1
0
0
0
2
2
1
1
0
0
0
0
1
1
2
0
0
0
2
1
1
2
0
2
0
1
1
0
0
0
0
0
1
2
1
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
1
3
2
2
1
0
2
0
0
0
0
1
0
0
0
1
2
1
0
1
2
3
2
0
0
2
1
3
2
1
1
1
0
2
0
3
2
0
1
0
1
2
0
2
1
0
2
1
1
0
0
2
2
1
1
1
0
0
0
0
3
1
1
2
1
1
1
2
0
2
1
1
0
0
1
2
0
2
0
1
0
3
1
0
0
1
2
1
0
1
0
2
1
1
2
1
0
1
2
0
2
1
2
0
0
0
1
0
0
2
0
0
2
0
2
2
0
0
1
1
2
2
0
0
1
0
2
2
1
0
0
0
0
3
1
0
2
1
1
0
0
1
1
0
2
1
1
0
1
2
0
1
1
0
2
0
2
1
0
0
1
0
0
0
0
1
0
0
2
1
2
2
1
0
0
1
1
0
2
0
2
2
1
1
0
2
2
1
0
0
1
0
1
0
1
1
0
1
1
1
1
0
0
2
1
0
0
1
0
0
1
0
1
2
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
4
0
0
0
0
0
2
1
0
0
0
1
1
0
1
0
0
1
2
1
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
1
2
2
2
0
1
0
0
0
2
1
0
0
2
1
1
0
0
1
2
2
0
0
2
2
0
0
1
0
2
2
0
2
0
0
2
1
0
1
1
0
1
0
0
0
1
0
2
0
0
2
0
0
1
0
0
0
2
0
0
2
0
0
2
0
8
1
3
0
0
0
1
0
3
1
1
2
3
0
1
4
0
0
1
1
1
0
1
0
2
0
1
1
1
1
0
0
2
0
2
0
0
1
2
0
0
1
0
0
0
0
0
3
2
2
1
0
0
1
2
0
1
2
2
4
1
1
0
0
0
0
1
0
0
2
0
1
0
1
0
1
0
0
0
0
0
0
0
0
2
0
2
0
1
1
0
1
2
0
2
0
0
1
2
0
0
0
0
0
1
0
1
0
0
1
2
0
0
2
0
0
1
1
0
0
0
1
0
1
0
1
0
1
1
1
0
0
0
0
0
1
0
2
2
1
0
2
1
0
1
0
1
1
1
1
0
0
2
2
1
0
1
0
0
2
0
1
0
0
0
2
0
1
1
2
2
1
2
2
0
0
2
2
1
0
0
1
0
0
0
0
1
0
2
0
1
1
1
0
1
0
2
0
0
1
0
0
2
0
1
1
2
2
1
0
0
0
1
0
2
2
0
1
1
0
1
0
1
1
0
0
0
1
0
2
0
2
3
0
1
0
1
2
2
1
0
0
0
1
2
2
2
2
0
1
2
2
2
2
0
1
1
1
1
1
0
1
0
0
0
0
2
2
2
1
1
0
2
0
0
3
0
2
1
1
2
0
2
1
0
2
0
2
0
1
0
2
0
1
2
0
0
0
0
2
0
0
0
2
0
0
0
1
1
0
1
0
1
0
0
1
0
2
0
1
2
0
1
1
0
0
0
0
0
0
2
0
1
0
0
0
1
1
0
0
1
2
2
0
1
0
0
0
0
2
1
0
1
2
0
3
0
0
1
0
1
1
0
0
5
0
0
1
2
0
2
2
2
0
2
0
0
0
1
2
1
1
3
2
0
0
0
1
1
1
0
1
2
0
1
0
1
0
1
1
0
0
1
1
1
1
2
1
1
1
1
0
0
0
1
2
0
1
0
0
1
2
2
0
0
2
0
1
2
0
0
0
1
2
1
1
1
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
1
1
1
1
1
0
1
2
1
0
2
0
0
3
0
0
1
0
2
1
0
0
1
1
0
2
1
0
2
1
1
2
1
2
1
0
0
1
1
2
0
0
0
0
0
1
1
1
0
0
0
0
2
1
0
1
0
1
0
0
0
1
2
0
0
1
1
2
0
2
3
1
1
1
2
0
0
1
0
0
1
1
2
0
1
1
2
0
2
0
0
2
2
1
0
1
0
0
1
0
0
1
1
0
0
0
1
2
0
2
1
1
0
2
1
6
0
1
0
2
1
1
0
2
1
0
1
1
1
2
1
0
0
0
0
0
1
2
2
0
2
0
0
0
0
0
0
0
0
1
1
2
0
0
0
2
1
1
2
1
1
2
0
0
2
0
0
2
2
0
0
0
1
0
1
2
2
2
4
2
1
1
2
0
0
0
2
1
0
1
0
0
1
1
2
1
2
0
1
0
2
0
1
0
1
0
0
1
0
2
1
0
2
1
2
1
1
0
1
0
1
1
0
2
0
1
2
2
2
0
0
2
0
2
2
0
2
0
0
1
0
0
0
1
1
0
1
1
0
1
0
2
1
1
1
2
0
1
0
2
1
0
1
1
2
0
0
0
0
1
0
0
1
2
1
0
2
2
0
0
0
1
2
2
0
2
0
1
0
1
0
0
0
0
2
2
0
0
0
0
0
0
1
2
0
0
1
1
0
0
0
0
1
0
0
2
0
2
1
1
0
1
0
1
0
2
0
2
1
0
0
0
0
0
0
2
1
2
2
2
0
1
1
1
1
0
2
0
2
0
1
2
1
0
0
0
0
0
1
0
1
0
0
1
2
1
1
0
0
1
1
1
0
1
0
0
0
0
2
0
2
0
0
2
1
1
0
0
0
1
1
0
2
0
0
0
4
2
2
1
0
0
0
0
2
0
1
1
0
0
1
0
1
2
1
0
0
0
0
1
3
1
0
2
1
2
0
0
1
1
1
0
1
0
1
2
1
0
2
1
1
0
0
0
1
1
1
0
0
0
2
1
1
0
0
0
0
0
1
0
2
0
3
2
0
0
0
1
0
1
0
1
2
0
1
0
0
1
0
1
0
0
0
0
0
2
0
2
1
0
1
1
1
0
0
1
1
0
1
0
1
1
1
0
0
0
0
2
0
1
0
0
0
0
2
2
0
0
1
2
0
1
2
2
2
0
2
2
1
0
0
3
0
1
0
1
1
1
0
2
0
0
1
0
1
1
0
1
0
1
0
2
0
0
2
0
1
2
1
0
0
2
0
2
2
2
0
0
1
0
0
0
0
0
1
0
0
1
1
1
0
1
0
2
0
1
0
1
0
0
0
0
3
0
2
0
0
0
0
1
0
1
1
1
1
0
1
1
0
0
2
2
1
1
1
2
0
0
0
0
2
1
0
0
1
2
1
1
2
2
0
1
2
0
1
0
1
0
1
0
2
2
0
0
0
0
1
0
0
1
0
2
0
0
1
0
0
2
2
0
1
1
1
0
0
1
2
0
3
1
0
2
1
2
1
2
0
1
0
1
2
0
0
1
2
0
0
0
1
4
1
1
0
0
0
2
0
0
0
2
0
1
0
1
2
1
0
1
1
0
0
0
1
0
1
0
2
1
0
6
0
0
2
0
1
0
0
0
2
0
1
0
0
0
1
0
1
2
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
2
1
2
2
1
0
0
3
0
2
1
2
0
2
0
0
0
1
0
3
0
1
0
0
0
1
1
1
0
0
0
2
1
2
0
0
0
1
1
0
1
1
0
2
5
2
0
0
0
1
0
0
2
1
1
0
1
1
2
1
0
1
1
1
2
2
1
0
0
0
0
1
1
1
0
2
0
1
1
1
1
0
1
0
2
0
0
0
0
0
1
0
1
0
1
0
2
0
0
0
2
0
0
3
0
2
2
2
1
0
0
0
0
0
1
1
1
1
1
2
0
1
0
2
0
2
1
1
0
3
0
1
0
1
0
0
1
0
0
1
2
2
0
0
1
0
0
2
0
0
1
1
0
1
1
0
2
1
1
1
1
2
0
0
1
1
1
1
0
2
1
1
0
2
0
1
0
2
0
1
0
2
0
2
2
1
1
0
0
0
2
1
0
1
2
0
1
3
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
1
1
1
0
2
0
1
1
0
0
0
0
0
1
1
1
1
0
0
0
0
1
2
0
0
2
0
0
2
0
0
1
0
2
1
0
2
0
0
0
0
1
0
2
0
1
2
1
2
0
2
1
1
0
0
1
1
0
1
1
1
0
1
2
0
0
0
1
0
0
2
1
0
0
1
3
0
0
0
1
1
0
0
0
0
0
1
2
2
2
1
0
1
1
1
1
1
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
2
2
3
1
0
1
0
0
1
1
0
3
2
2
1
0
1
0
2
2
0
0
0
2
1
0
2
0
1
1
1
0
0
1
1
3
0
1
2
3
0
1
0
1
1
0
0
1
0
0
0
0
0
2
1
1
0
0
0
0
1
1
0
0
0
3
2
0
1
1
1
0
0
1
2
0
1
1
0
1
2
1
0
0
7
1
0
0
1
1
1
0
0
1
1
2
4
1
1
1
0
2
0
2
2
1
1
0
1
1
1
1
2
1
0
2
1
0
1
0
2
1
0
0
0
1
0
3
1
0
0
0
1
1
0
0
2
0
0
0
1
1
1
1
0
1
2
2
2
1
0
0
1
1
1
1
0
0
0
1
0
0
3
0
1
1
1
2
1
0
2
2
0
0
0
1
2
0
0
0
0
1
1
1
1
0
0
3
0
2
0
2
0
2
1
2
0
1
0
0
0
1
1
1
1
0
0
0
2
0
2
0
0
1
1
1
0
2
0
0
0
3
4
1
0
1
1
0
0
2
0
2
0
0
1
1
1
0
2
0
0
0
0
1
0
2
0
0
2
1
0
1
0
2
0
1
1
0
1
0
2
0
1
0
1
2
0
0
2
0
1
0
1
2
1
0
2
2
0
0
2
0
0
0
1
0
0
0
3
3
1
0
2
1
1
1
1
0
1
2
0
0
1
1
2
4
0
0
2
1
0
0
1
0
0
0
0
0
0
1
1
0
2
1
1
0
2
0
0
2
0
0
2
1
2
1
1
1
0
1
0
1
1
0
0
0
2
1
0
0
1
1
2
0
0
1
1
1
2
0
1
1
0
2
1
1
2
1
0
0
1
2
2
0
1
1
2
0
1
1
1
0
0
2
1
2
0
0
1
2
0
1
2
1
0
0
0
1
1
1
2
1
1
0
0
2
1
0
2
1
1
0
0
0
1
0
2
0
0
0
1
1
2
0
1
0
1
2
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
2
2
0
0
2
0
0
1
1
0
1
0
0
2
1
0
1
1
0
2
1
2
1
2
0
0
1
1
0
2
0
1
1
0
2
0
0
0
0
2
2
1
0
0
0
0
2
2
0
0
1
1
0
1
0
0
0
1
2
0
1
1
1
0
2
1
0
0
0
0
0
0
2
0
1
2
1
1
0
0
1
0
0
1
2
0
2
2
1
0
0
1
0
0
0
1
0
0
2
2
2
0
1
0
0
0
0
0
2
0
1
0
4
1
1
0
2
0
1
1
1
1
0
1
0
2
2
1
0
0
1
2
2
2
1
1
0
1
0
2
1
1
0
1
0
1
0
0
0
1
0
2
1
0
0
0
1
0
0
1
1
1
2
2
1
0
0
2
1
1
1
2
0
1
0
0
1
1
0
1
1
0
1
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
1
0
1
1
0
0
2
0
2
0
2
0
0
1
0
1
2
0
0
0
2
0
2
2
1
0
0
2
0
2
1
1
0
1
0
0
1
1
0
0
0
1
0
0
1
0
0
2
2
2
0
0
0
1
2
1
0
2
1
1
0
2
0
1
0
2
2
1
1
1
2
0
1
1
2
2
1
0
2
0
1
2
0
1
1
0
0
0
3
2
1
1
1
0
1
1
1
2
1
2
2
1
1
2
1
1
0
1
1
2
4
0
0
1
1
1
2
0
2
0
2
1
2
0
1
2
0
0
1
1
0
0
0
1
0
0
0
0
1
1
0
2
0
2
1
0
0
0
0
1
1
0
1
1
2
1
0
1
0
1
0
0
0
2
0
0
1
0
2
1
0
0
0
0
2
1
0
0
0
2
0
2
1
0
2
0
0
1
3
2
0
1
0
0
2
0
2
0
1
2
0
1
0
0
0
0
0
1
2
2
0
1
1
0
0
2
2
2
0
0
0
0
0
1
3
1
2
2
0
0
0
0
1
0
2
1
2
0
2
0
2
2
1
1
0
1
0
2
2
0
0
0
1
0
2
2
2
1
1
1
0
0
1
4
1
1
1
0
1
0
2
0
0
0
1
0
0
2
0
1
2
0
0
1
0
2
0
1
1
0
2
0
1
0
1
1
0
0
0
2
0
1
2
0
2
0
1
2
0
0
2
0
0
1
2
0
1
0
0
0
2
0
0
2
0
0
0
2
0
1
0
0
0
1
0
0
1
0
1
0
0
3
1
1
0
2
1
1
0
0
1
0
0
0
0
1
2
2
1
2
0
3
2
0
1
0
2
1
2
0
0
1
0
0
0
2
1
0
0
2
1
0
0
1
2
0
1
0
1
2
2
0
2
0
0
0
1
2
1
0
0
0
0
1
2
1
0
2
0
0
0
1
1
1
1
1
0
0
1
0
0
0
2
1
0
0
0
0
0
1
1
0
1
1
0
1
0
0
0
0
1
2
2
0
2
1
1
0
0
2
2
0
1
1
1
0
0
1
1
0
1
1
0
2
0
0
0
2
1
2
1
1
0
1
2
1
2
2
1
0
1
2
0
2
0
1
0
1
1
1
1
0
0
2
1
0
1
1
0
0
1
1
0
1
1
1
1
1
1
0
2
2
0
2
0
1
0
0
0
1
2
1
2
0
0
0
1
0
1
2
3
0
1
2
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
2
2
0
0
1
1
0
0
0
0
0
1
1
0
2
2
0
2
1
0
0
0
1
2
2
1
1
0
1
1
0
0
2
0
1
1
2
0
2
0
0
0
1
1
1
0
0
0
2
1
1
1
0
0
0
1
0
0
1
1
0
1
2
1
1
0
0
0
1
0
2
0
0
0
1
0
1
0
0
3
0
0
2
1
0
0
1
0
0
1
2
0
0
0
1
0
0
0
0
0
1
1
0
3
1
0
1
1
0
1
1
0
1
0
0
0
0
0
0
2
1
2
1
0
0
0
2
0
0
2
0
0
0
0
1
0
3
1
1
0
0
0
0
0
1
0
0
2
1
2
2
1
2
1
0
2
1
2
2
1
0
1
3
1
1
0
1
0
2
2
1
2
0
1
0
1
0
1
2
2
0
1
0
2
0
1
1
1
1
1
2
0
0
0
0
0
1
0
0
1
1
0
1
0
2
1
2
2
1
0
1
0
1
1
2
2
1
0
0
2
2
0
1
2
0
0
1
0
0
1
0
0
0
1
1
3
3
0
1
0
2
2
0
2
2
0
2
0
2
1
0
0
0
0
1
2
0
0
0
2
2
0
1
2
0
0
0
0
2
0
2
1
0
0
1
1
0
1
0
1
0
3
1
1
1
2
1
1
0
1
1
1
0
0
2
0
0
2
2
1
2
1
0
0
1
1
0
0
1
0
1
2
0
1
2
0
2
1
2
0
4
1
0
1
0
1
0
0
0
0
2
2
2
0
0
1
1
2
0
1
0
1
2
0
2
1
2
0
0
1
0
2
0
0
1
1
2
2
2
0
0
0
0
1
1
1
0
0
1
1
0
1
0
0
2
1
1
0
2
0
0
0
0
2
0
0
1
0
0
0
2
1
0
0
1
1
1
0
1
1
1
0
0
0
0
0
2
3
4
1
1
1
1
0
1
0
2
2
1
0
1
0
0
1
0
1
1
1
1
1
1
2
1
0
0
1
0
3
1
2
2
2
1
0
1
2
1
0
1
0
2
1
0
0
3
0
2
1
0
0
0
1
0
0
0
1
1
0
1
3
2
0
0
0
0
0
0
0
2
2
2
1
1
1
0
1
1
0
0
0
1
0
0
0
1
0
1
0
0
2
2
0
0
1
1
0
0
1
1
0
1
0
2
0
0
0
0
0
1
2
1
2
1
1
0
2
1
0
0
0
1
0
1
0
2
0
0
0
2
3
1
0
0
0
0
2
0
0
0
0
1
1
1
2
0
3
0
2
0
1
0
0
0
0
0
1
0
2
2
0
1
1
2
2
3
2
2
0
1
0
0
1
0
1
0
0
0
0
0
1
3
2
0
1
1
1
1
1
1
1
0
0
0
1
0
1
0
0
2
1
2
0
2
0
1
1
0
2
1
0
2
0
1
0
1
2
1
0
0
0
0
2
0
1
0
0
1
1
0
0
1
0
1
0
0
0
2
1
1
0
0
2
0
2
0
0
2
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
1
1
2
0
1
2
2
1
0
0
0
0
2
1
0
1
4
0
0
0
0
1
0
2
0
0
1
0
2
1
1
0
1
2
1
1
0
1
0
0
0
1
1
0
0
1
0
2
2
2
0
0
2
1
0
0
1
0
1
0
0
2
0
1
2
1
0
0
0
1
1
2
2
1
0
2
0
0
1
2
0
1
0
0
0
0
2
1
1
1
0
1
1
0
2
1
0
1
0
1
0
1
1
0
1
1
1
1
1
1
0
1
0
0
1
2
0
0
2
0
2
1
1
2
0
0
0
0
2
0
0
0
3
2
0
2
0
2
2
2
2
1
0
2
0
0
0
0
1
2
1
1
0
0
0
2
2
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
2
1
1
0
0
1
0
0
0
2
0
1
2
1
0
0
0
0
2
2
0
0
2
0
1
2
1
0
1
0
0
2
0
1
2
0
0
1
0
1
0
1
1
1
0
0
1
0
0
2
0
1
0
1
0
2
1
1
0
1
1
0
0
1
2
1
0
0
2
0
0
2
1
1
2
1
1
0
2
1
0
1
1
2
1
0
0
1
0
1
0
0
1
2
1
0
1
1
1
0
0
1
0
1
0
1
3
1
0
2
0
0
0
0
0
0
1
2
1
0
2
0
2
0
1
1
0
0
6
1
0
1
0
2
0
1
1
0
2
3
0
0
1
2
0
2
2
1
1
0
2
1
1
1
0
1
1
1
0
0
0
0
1
2
0
1
1
1
1
0
0
0
1
1
1
1
2
0
1
1
0
0
2
0
0
0
1
1
0
0
2
2
0
2
1
0
2
1
0
2
1
1
1
0
0
2
2
2
1
0
1
2
0
2
1
2
0
0
1
0
0
2
2
1
2
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
2
0
0
2
1
1
1
1
0
0
2
2
0
1
3
1
2
2
0
2
0
1
1
2
2
0
0
0
2
0
0
1
2
0
0
1
0
0
1
0
0
3
1
2
1
2
0
2
0
0
0
2
0
0
0
0
0
2
2
1
0
0
2
2
1
0
1
1
0
0
0
0
2
1
1
0
1
0
2
2
0
1
0
1
2
0
0
0
0
0
0
2
0
1
0
1
2
0
0
2
0
2
0
1
1
0
1
1
0
1
1
1
0
1
1
0
0
0
2
0
2
0
1
0
1
1
2
0
2
0
0
2
1
1
2
1
0
1
2
1
1
0
2
1
2
1
1
1
4
2
0
1
1
0
1
2
1
1
1
0
0
2
1
1
1
0
2
0
1
0
0
0
0
1
1
1
0
1
0
1
0
0
0
2
0
0
1
0
0
0
2
0
0
2
1
0
1
1
0
0
1
2
0
0
2
1
0
1
2
1
1
0
1
0
2
0
0
1
0
2
1
1
1
2
1
0
2
0
1
0
1
2
1
2
0
0
0
2
0
0
1
0
1
0
1
0
2
1
0
1
1
0
1
0
1
1
0
0
1
1
0
0
1
1
0
0
1
1
0
0
1
0
0
1
0
0
2
0
1
1
0
1
0
1
0
0
0
1
1
1
1
0
1
0
0
2
1
0
0
1
2
1
2
1
0
1
1
0
2
1
1
0
1
1
1
2
0
0
3
1
0
0
0
0
2
0
0
0
2
1
0
2
0
1
1
0
2
0
0
2
0
1
2
2
0
1
1
0
0
1
0
0
1
1
2
2
1
1
0
1
0
0
1
0
0
2
2
0
1
2
2
0
0
0
1
0
0
2
2
1
1
0
2
1
2
1
2
3
2
1
2
1
0
0
1
1
1
2
0
0
1
2
0
1
1
0
1
1
1
0
0
0
1
0
0
3
0
1
0
0
0
0
0
0
1
2
0
1
1
1
1
1
1
1
1
2
0
1
2
2
2
1
2
1
2
0
0
1
3
2
2
0
1
1
0
0
1
1
1
1
0
1
0
0
2
1
3
2
2
0
0
1
0
0
0
1
0
1
0
2
2
0
2
1
2
1
0
0
0
0
1
1
1
1
2
1
1
0
0
1
0
0
0
1
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
1
1
0
0
0
2
1
0
2
0
2
0
0
2
0
0
0
1
0
1
0
1
3
2
1
0
1
0
0
0
0
1
1
0
1
0
1
1
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
2
0
1
1
2
2
0
0
1
1
2
2
0
2
2
0
2
1
1
0
1
1
1
1
0
2
1
2
1
0
1
0
1
1
2
1
0
1
3
0
0
0
0
0
1
2
0
1
1
0
1
0
1
1
1
1
0
1
1
1
0
1
0
0
0
0
0
0
1
1
2
1
2
1
1
0
0
0
0
1
1
0
2
2
0
0
2
1
0
0
1
2
0
0
0
0
1
0
1
1
2
0
0
1
1
2
0
0
4
0
1
0
2
0
1
1
0
2
0
2
1
1
2
1
1
0
0
1
7
2
0
0
1
0
1
0
0
0
1
2
1
0
1
1
0
1
0
1
0
0
0
1
1
0
2
1
2
1
2
0
2
1
2
1
2
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
2
0
0
2
1
0
0
1
2
0
0
0
0
1
1
1
0
0
0
2
2
0
1
1
1
0
1
1
1
0
2
1
3
0
1
2
0
0
1
0
0
0
1
2
1
1
0
2
0
0
1
0
0
0
0
2
3
0
1
0
1
2
1
1
1
0
0
1
0
0
0
1
1
2
0
0
0
2
2
1
1
1
2
1
0
0
1
1
0
1
0
2
0
1
0
2
0
0
0
0
1
0
0
2
3
1
0
2
0
0
1
1
0
0
2
0
2
2
2
1
1
1
0
0
1
0
1
0
0
2
0
1
2
0
0
1
1
2
1
0
0
0
1
0
0
0
0
2
1
2
2
0
1
1
0
1
0
0
0
3
2
0
1
1
2
1
0
0
0
0
1
1
0
1
1
0
0
1
0
0
0
0
1
0
1
1
0
0
0
2
1
1
1
0
2
0
0
0
0
1
1
0
0
0
2
1
0
1
1
0
1
0
1
1
1
2
2
1
3
1
2
0
1
1
1
0
0
1
1
1
0
2
2
0
2
2
0
2
0
0
2
1
1
0
0
1
1
0
1
1
0
0
2
0
2
0
0
2
1
4
1
0
0
2
2
3
2
1
2
0
0
0
2
0
0
1
0
2
0
0
0
2
0
1
0
0
1
1
1
1
2
2
0
0
0
2
0
0
2
0
3
2
0
2
0
1
0
1
2
1
1
0
0
0
0
0
0
1
0
1
1
1
1
0
1
0
0
0
0
3
1
0
0
1
1
2
1
0
0
1
0
0
2
0
0
2
1
2
0
0
1
0
1
2
0
0
1
0
1
1
0
1
0
0
2
2
1
1
2
1
1
0
1
0
0
1
0
2
0
0
1
0
0
0
2
0
0
1
1
0
1
1
1
0
0
1
0
1
1
1
0
0
0
0
3
0
0
0
1
0
1
1
0
0
1
1
0
0
0
0
1
1
2
0
1
1
2
1
0
1
0
1
1
1
1
0
0
1
2
0
0
2
0
0
2
0
1
0
0
2
0
1
1
0
2
0
1
2
3
0
2
0
0
0
2
0
0
0
2
2
0
1
0
2
1
0
0
0
1
2
3
0
0
2
0
0
0
0
0
2
0
0
1
1
1
2
0
1
0
0
2
0
1
1
1
0
1
1
1
0
2
2
1
1
2
1
0
0
1
1
2
0
0
0
2
2
0
0
2
2
2
1
1
1
0
1
2
0
0
1
0
1
0
0
3
0
2
1
1
0
1
0
0
2
1
0
0
0
1
1
1
0
1
1
1
0
0
1
0
0
1
0
1
0
2
1
0
1
0
1
2
1
0
0
2
1
0
0
1
1
2
2
0
1
0
1
2
0
0
0
0
2
0
2
0
0
1
1
0
0
2
2
2
1
2
0
0
2
2
2
0
2
0
0
0
0
1
0
2
0
2
0
0
1
1
1
1
2
0
0
0
2
2
0
2
0
0
1
0
2
0
2
2
1
0
2
0
2
1
1
0
1
0
0
0
0
1
1
0
0
0
1
1
0
1
1
2
2
0
1
0
1
2
1
1
2
1
0
0
2
3
0
1
0
1
1
3
1
1
0
0
0
2
0
0
1
1
0
1
0
1
0
0
0
2
1
0
2
0
1
0
0
0
1
0
0
0
2
0
1
0
0
1
0
3
2
1
2
0
0
1
0
0
0
0
1
0
0
1
0
1
4
0
2
0
0
0
2
0
5
2
0
0
0
1
1
2
0
0
1
2
1
0
0
0
0
0
1
0
0
2
0
2
0
2
0
1
1
0
0
1
2
1
0
0
1
2
1
0
1
0
0
0
0
0
2
2
0
0
1
2
0
1
0
1
0
0
0
2
0
2
2
1
0
0
0
1
0
0
2
1
0
0
1
0
1
0
2
0
0
0
0
1
0
0
2
0
1
0
0
1
0
0
1
1
2
1
1
0
1
2
1
1
1
2
2
1
2
2
0
2
0
0
2
1
0
1
0
0
0
2
1
2
0
2
1
0
1
0
0
0
0
0
1
1
2
4
0
0
0
0
0
1
0
1
3
0
0
2
0
0
1
0
2
2
2
1
0
3
2
0
0
0
0
1
0
2
0
2
0
1
1
0
1
0
1
0
0
0
0
1
2
1
2
2
0
0
0
2
0
0
0
0
2
4
0
1
2
1
1
1
2
0
0
1
2
1
1
1
0
0
2
1
2
1
1
0
0
0
0
1
2
0
0
1
1
1
2
0
2
0
1
1
1
2
1
1
0
1
3
2
0
0
2
0
1
0
2
0
2
0
2
1
0
1
1
0
1
1
0
1
0
0
0
1
1
2
0
2
1
0
1
1
2
2
2
1
2
1
1
0
2
0
0
0
2
0
2
2
0
0
1
2
2
0
2
0
0
1
1
1
0
2
2
0
0
0
1
1
2
0
1
0
1
0
0
2
1
3
1
0
2
0
1
2
4
2
1
0
1
0
0
2
1
0
1
0
0
2
1
1
0
2
2
1
2
2
0
1
1
0
0
2
0
1
1
0
2
0
0
0
2
0
0
6
2
1
0
0
0
0
1
0
1
0
1
0
1
0
2
1
1
1
2
4
0
1
2
2
0
0
1
1
1
2
1
2
1
0
1
0
0
0
0
0
0
0
1
1
1
1
2
0
0
0
1
0
2
0
0
1
0
0
0
1
1
0
2
2
1
0
2
1
1
1
1
1
2
0
0
0
0
0
1
2
0
0
1
1
0
0
1
2
2
1
1
1
2
0
1
0
2
1
2
0
1
2
0
1
2
1
2
0
0
2
0
1
0
1
1
0
0
1
0
1
1
0
2
2
1
0
3
1
0
1
1
0
2
0
2
2
1
1
2
1
0
0
3
1
1
0
0
0
1
0
0
1
0
0
2
1
1
0
0
0
0
1
2
2
1
0
0
0
0
1
0
0
0
0
0
2
1
0
0
1
2
2
1
1
1
1
1
1
2
0
0
0
0
1
1
1
3
2
2
1
0
2
1
2
0
0
0
0
0
0
1
0
0
2
2
0
1
0
1
0
2
0
1
0
1
0
0
2
0
2
0
0
2
0
0
2
1
0
0
0
2
1
0
0
0
1
0
1
0
0
0
1
1
0
4
1
0
1
1
2
2
2
0
1
1
0
2
2
0
0
0
2
0
1
0
1
0
0
2
0
3
2
0
2
2
0
0
1
1
2
2
0
0
1
0
0
1
0
0
0
2
2
0
1
0
2
2
1
0
1
2
1
0
1
0
2
2
0
0
0
2
0
0
0
0
1
0
0
1
0
1
0
1
2
1
0
0
1
1
0
0
2
0
0
1
0
0
0
2
1
1
1
0
1
2
1
2
0
0
0
0
1
2
0
2
1
0
0
0
1
0
0
0
2
1
0
0
2
1
0
0
1
1
5
0
1
0
1
0
0
0
1
2
0
0
1
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
1
0
0
1
0
0
0
2
1
0
0
1
0
1
0
0
2
2
2
0
1
2
1
0
1
0
0
0
1
1
0
2
1
2
1
2
0
2
1
0
0
1
1
2
1
0
1
1
0
0
1
0
2
2
2
0
2
0
0
1
2
1
0
0
0
1
0
1
1
0
0
2
0
1
1
1
2
1
1
1
1
0
1
1
1
0
1
1
0
2
0
0
0
0
1
1
0
0
0
3
0
0
2
0
0
0
0
2
0
0
1
3
0
1
0
1
0
2
0
0
1
0
0
1
0
1
0
0
1
0
1
1
1
2
0
0
0
2
2
1
0
1
0
0
2
0
0
1
2
0
0
0
0
1
0
0
1
0
0
2
1
0
0
2
0
1
0
0
0
0
1
0
0
1
1
0
0
2
2
1
0
2
0
1
3
0
1
0
0
1
1
0
2
1
1
1
2
1
0
0
1
0
0
1
0
1
2
0
0
0
2
2
0
0
2
0
1
2
2
0
1
1
0
1
0
2
1
1
0
1
0
2
1
1
0
0
1
2
0
0
0
2
0
0
1
2
2
0
2
2
0
0
2
0
2
1
1
2
0
1
0
1
0
2
1
2
0
2
2
0
0
0
0
0
0
2
0
0
2
0
0
1
1
0
0
1
0
2
0
0
1
0
2
1
0
2
0
0
1
0
0
0
1
1
0
0
0
2
1
0
1
2
0
1
1
2
1
2
0
0
0
2
2
0
1
0
2
2
2
2
2
1
0
1
0
2
0
2
0
0
0
1
1
1
1
0
1
0
0
1
0
2
1
2
0
1
2
1
1
0
1
0
0
0
0
4
0
0
1
0
1
1
0
0
0
1
1
1
1
1
2
2
0
0
1
1
0
1
2
2
0
0
0
0
1
1
1
1
0
0
1
0
3
0
0
2
2
0
1
0
0
0
0
2
1
0
1
1
0
0
2
0
2
1
1
0
0
0
1
1
0
2
1
1
1
1
0
0
0
1
2
1
2
0
2
2
0
0
0
0
1
1
1
0
2
0
0
0
2
0
1
2
0
0
0
1
1
2
0
0
2
0
0
1
0
1
0
0
2
0
0
2
0
2
1
0
0
1
0
0
2
0
0
2
0
0
1
1
0
2
0
2
1
1
1
2
0
0
1
0
2
0
2
2
0
1
1
2
1
0
1
0
0
2
0
0
1
0
1
0
2
0
2
1
0
0
0
0
1
0
1
1
2
0
1
0
1
1
0
0
0
0
2
2
1
0
2
0
1
2
0
1
0
1
0
2
0
0
2
0
0
0
1
2
0
1
1
1
2
2
0
2
0
1
1
2
1
0
1
0
1
2
0
0
0
1
0
1
2
0
2
0
0
1
0
0
1
0
1
1
1
0
1
2
1
1
0
2
0
2
1
0
0
0
1
0
1
1
0
0
0
1
0
1
0
0
1
0
1
2
1
1
0
2
0
0
2
1
1
2
1
1
2
1
0
2
2
1
1
0
0
0
2
0
2
0
1
2
0
2
0
2
1
0
0
2
0
1
1
1
2
1
0
0
2
2
1
1
1
1
1
0
2
0
0
4
1
1
1
2
0
1
0
0
2
2
1
0
0
0
0
1
0
2
0
2
0
0
3
2
1
0
0
1
1
0
0
2
0
1
1
0
1
2
2
1
1
0
0
2
0
0
0
0
0
1
0
1
0
1
2
1
1
0
0
0
0
0
0
2
0
1
1
2
0
2
0
1
2
2
1
0
0
2
3
2
0
1
0
2
1
2
2
0
2
0
0
0
0
0
0
2
2
1
0
0
0
2
1
0
0
1
0
1
2
0
1
1
1
0
0
0
1
0
2
0
0
2
1
0
1
1
1
0
1
1
1
1
0
2
2
1
0
1
2
2
1
0
0
2
0
1
2
1
0
1
2
0
1
1
1
0
1
0
1
0
0
1
1
0
1
0
1
1
0
0
0
2
1
1
0
0
1
1
2
1
0
2
1
2
0
2
0
0
0
1
1
1
0
0
0
0
1
0
1
0
0
1
0
0
2
2
1
2
0
0
1
0
0
2
1
1
0
1
0
0
1
2
1
1
1
2
0
0
0
0
0
0
0
1
0
0
2
1
0
2
2
0
2
2
0
0
2
1
0
2
2
0
1
0
0
0
0
2
1
0
0
2
1
1
2
1
1
0
0
1
2
0
0
1
1
2
0
1
0
0
1
0
0
1
0
0
2
0
2
0
2
1
0
1
2
0
0
1
2
0
0
0
0
0
1
0
0
2
1
0
1
0
1
1
2
0
0
1
2
2
0
1
2
0
0
0
0
2
0
0
1
1
1
2
2
0
0
2
0
0
0
1
1
1
0
1
1
2
1
1
0
0
1
1
0
0
0
0
1
2
0
0
1
2
2
2
0
0
0
0
0
0
2
1
0
0
0
0
2
1
0
0
0
0
0
1
0
2
1
1
1
0
0
2
0
1
1
0
1
1
0
1
1
0
0
2
0
0
0
0
0
1
2
1
1
1
1
2
1
1
0
1
1
0
0
0
1
0
0
0
1
0
0
2
0
2
0
2
0
1
0
0
0
0
2
0
0
1
0
0
0
2
0
2
1
1
2
0
0
0
2
0
0
0
0
0
1
1
0
2
2
1
1
1
0
4
2
0
0
4
1
0
0
1
1
2
0
1
0
1
2
0
0
2
1
1
2
0
0
0
0
2
0
2
2
0
1
0
0
1
0
2
1
0
2
0
1
1
0
0
1
1
1
0
0
2
2
2
0
0
0
1
1
1
1
2
0
2
0
1
0
0
2
1
2
1
1
1
0
1
0
0
0
1
0
0
1
0
0
0
1
0
2
0
0
0
2
1
0
1
1
1
2
0
0
0
0
2
0
0
1
0
2
1
0
0
0
0
1
1
1
1
0
0
2
2
1
0
0
0
0
0
0
1
0
1
1
0
2
0
1
2
0
0
0
0
2
2
0
1
2
0
1
0
0
1
1
1
0
1
2
1
0
0
1
0
1
1
0
0
2
2
2
2
0
1
0
2
0
1
0
1
1
1
1
1
0
0
0
1
0
0
0
1
3
0
1
1
1
2
0
1
0
1
1
0
0
0
0
2
0
0
0
2
1
0
1
0
0
0
1
1
0
0
1
0
2
1
0
2
1
1
2
2
2
0
2
0
0
1
0
1
0
2
0
0
0
8
1
0
1
1
2
0
0
0
1
0
1
0
1
2
0
2
1
1
0
2
2
0
2
0
1
1
2
1
2
1
1
0
0
0
1
1
1
1
2
1
2
1
0
0
1
0
0
0
0
1
0
1
2
2
0
1
1
0
1
0
1
0
1
0
0
2
0
2
0
2
0
2
1
0
0
0
1
1
0
0
2
0
0
0
0
0
1
0
0
1
1
0
1
2
1
0
0
0
1
3
0
1
0
0
2
0
2
1
0
2
0
1
0
0
2
2
0
0
1
1
0
1
1
1
1
0
0
2
0
0
1
2
0
0
1
1
2
1
2
2
2
0
2
0
1
1
2
0
0
0
0
0
1
0
2
0
0
0
1
1
2
1
2
0
0
1
1
3
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
1
2
0
2
0
2
1
0
0
0
0
2
2
1
0
0
1
0
1
0
1
0
1
0
0
1
1
0
3
1
2
0
1
0
0
0
2
2
0
0
2
0
0
0
1
1
1
0
1
0
0
0
0
2
2
2
0
0
0
1
1
0
1
0
2
0
0
1
0
1
2
1
1
1
2
1
0
0
0
1
2
0
1
2
0
2
1
0
0
0
0
2
0
0
0
2
3
2
0
0
2
0
1
0
0
0
2
0
2
3
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
1
1
0
1
0
0
1
1
0
1
0
0
1
1
1
0
1
0
2
2
0
2
0
1
0
2
1
1
0
1
0
2
1
0
1
1
2
1
0
0
1
1
2
0
0
1
2
0
2
1
0
2
2
1
0
0
1
2
1
0
2
0
0
0
2
2
1
0
0
1
0
1
1
1
1
2
0
0
2
0
1
0
1
1
0
0
1
2
2
1
1
1
0
0
2
0
0
2
0
1
1
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
2
1
0
0
0
1
2
0
0
2
0
1
0
1
2
0
1
3
0
0
0
1
0
0
2
0
0
1
1
0
1
1
0
0
1
1
0
0
1
2
0
0
1
2
0
1
1
0
0
2
0
0
1
1
0
0
1
1
1
1
1
1
0
0
2
1
0
2
0
0
1
2
0
0
0
1
0
1
0
1
1
2
1
0
1
2
2
0
0
2
0
0
0
1
1
1
2
0
2
1
0
2
0
0
1
2
0
1
2
0
1
1
2
1
0
1
3
2
0
0
1
0
1
2
0
0
0
1
0
4
1
0
0
0
0
1
1
1
0
0
0
1
2
1
1
1
0
0
2
0
0
0
0
0
0
0
3
1
2
2
0
2
0
0
2
0
1
1
2
0
3
1
0
1
1
2
2
1
2
0
2
0
1
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
1
0
0
0
3
0
1
1
1
2
0
2
0
2
2
1
0
1
0
1
0
1
1
1
0
0
0
0
0
0
0
1
1
1
1
1
2
1
1
1
0
0
1
2
2
0
1
0
0
0
2
0
1
0
0
2
1
2
0
0
0
1
2
0
0
1
1
1
2
0
0
2
1
1
1
0
0
2
0
1
1
1
2
2
1
2
3
0
0
0
1
3
2
1
0
0
1
1
0
0
0
0
1
0
1
0
1
0
0
0
0
2
0
2
1
0
1
0
0
2
0
2
5
0
0
0
1
0
0
2
1
0
0
0
0
0
2
1
0
1
1
1
0
2
2
1
2
0
0
1
1
1
1
1
1
2
0
5
1
0
0
0
0
4
1
2
1
2
1
2
0
0
0
0
0
1
0
1
2
1
1
2
0
0
0
0
1
2
0
2
2
0
0
0
1
0
2
1
0
0
2
1
0
0
1
1
0
1
1
0
2
2
1
0
1
1
0
0
0
1
1
1
2
0
2
0
0
0
0
0
1
0
0
0
1
0
1
0
2
1
0
0
0
1
2
1
0
0
2
0
0
1
0
2
1
0
4
0
1
0
2
0
0
1
4
1
2
0
0
0
0
1
1
2
0
1
1
0
2
1
1
0
1
0
2
1
0
0
2
0
1
0
0
0
2
0
0
1
1
0
2
0
0
0
2
0
1
0
1
1
3
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
2
0
0
0
2
1
2
2
0
0
1
0
1
0
2
0
0
0
2
1
0
1
1
1
2
1
0
0
0
1
2
0
0
1
0
0
1
0
2
0
0
1
0
1
1
1
0
0
0
0
1
0
0
2
1
1
1
0
0
0
0
1
1
2
2
0
0
1
1
0
0
0
2
0
1
0
2
2
2
1
0
0
0
2
0
1
0
0
1
0
0
0
0
0
2
2
0
2
1
2
1
1
1
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
2
0
0
2
2
0
0
2
0
1
1
1
1
0
0
0
1
1
2
1
1
0
0
0
1
2
0
0
1
1
0
2
2
0
1
1
0
2
1
0
0
0
2
2
1
0
0
0
1
1
1
0
1
1
2
1
1
0
1
0
0
2
0
0
1
2
0
1
1
2
2
1
1
0
1
2
0
0
1
0
0
0
0
0
1
0
1
0
2
2
0
1
1
1
0
0
0
0
0
1
2
1
0
0
2
1
0
1
0
0
1
0
0
0
1
0
1
0
1
1
0
1
2
0
2
0
1
1
1
0
2
2
0
2
0
1
1
1
1
2
1
1
2
0
0
0
1
2
1
0
1
0
1
0
0
0
0
2
2
0
0
0
0
0
1
1
0
0
1
0
2
0
1
1
1
1
0
2
1
1
0
0
0
0
1
0
2
2
0
0
1
0
0
2
1
1
0
0
1
1
0
1
0
0
0
1
0
0
1
0
0
1
0
1
3
0
0
0
4
0
2
0
1
1
2
0
0
0
0
0
2
1
0
2
2
1
2
0
0
0
0
1
2
1
2
0
1
0
1
1
0
0
2
0
2
1
0
0
0
2
1
2
2
2
2
1
0
0
2
2
2
0
0
2
0
0
0
0
0
1
1
0
2
2
0
0
0
2
0
1
0
0
1
0
1
1
2
0
1
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
2
0
1
0
1
1
0
2
1
0
2
0
0
0
0
1
2
1
0
2
0
0
1
0
2
0
1
2
1
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
1
0
2
0
0
1
1
2
0
0
2
0
1
2
0
0
1
0
2
0
1
1
2
1
0
1
1
0
2
1
0
1
0
2
0
1
0
1
1
0
0
1
2
2
2
1
0
2
1
2
0
1
2
0
1
1
1
0
1
1
2
0
1
0
0
1
2
0
3
2
0
2
0
0
0
1
0
0
0
0
1
1
2
0
0
0
0
0
2
0
1
0
2
1
0
1
0
2
1
2
2
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
2
1
1
0
0
2
3
0
1
1
1
0
0
0
0
1
2
2
2
0
2
0
1
1
0
1
2
2
0
2
1
0
1
0
1
1
2
1
1
0
2
0
2
0
1
1
0
0
1
0
2
1
0
0
2
2
2
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
2
0
0
1
1
0
0
1
0
0
0
1
0
0
1
0
0
2
2
0
2
2
1
0
0
2
0
0
0
2
2
0
0
2
0
0
0
0
2
1
1
1
0
0
1
1
2
0
2
0
1
0
1
1
1
0
0
1
1
0
0
0
0
1
0
0
0
1
1
0
1
2
0
2
1
1
0
2
0
2
0
0
2
0
2
0
0
0
1
2
1
2
0
1
1
2
0
1
1
2
0
1
0
0
1
1
1
0
1
2
0
0
0
0
2
0
0
1
2
0
0
1
0
1
2
0
1
2
0
0
0
1
0
1
0
0
1
2
1
3
2
1
1
0
1
1
0
0
0
0
2
0
1
1
0
1
0
0
2
1
0
2
0
0
1
0
0
1
2
1
1
0
1
0
2
0
2
1
1
0
1
1
1
0
2
2
0
2
1
1
0
4
0
0
1
2
0
1
1
1
1
0
2
0
2
0
0
2
0
0
0
2
2
1
1
0
2
0
0
2
0
1
2
0
2
2
0
1
1
1
0
2
1
0
0
0
0
0
2
0
1
1
2
0
0
1
1
0
0
1
2
2
2
2
0
1
0
2
1
1
0
1
1
1
2
1
0
1
0
1
0
1
1
2
0
0
0
1
0
1
0
1
2
0
1
0
1
0
2
1
1
2
1
0
3
0
1
1
0
2
0
2
2
1
0
1
0
0
0
1
0
0
1
1
0
0
0
1
1
2
0
0
0
1
1
0
0
2
3
0
1
0
0
4
5
1
0
0
0
2
1
0
0
0
1
0
2
0
2
0
1
2
3
2
1
0
2
0
0
1
0
1
0
2
2
0
1
2
2
2
2
1
2
0
1
0
2
2
1
0
0
1
0
0
1
2
2
0
1
2
1
1
0
1
0
0
0
0
1
2
2
0
0
2
1
2
2
2
1
2
0
1
1
0
0
0
1
0
0
2
1
2
0
0
2
0
1
2
1
1
2
1
1
1
3
0
2
0
0
0
2
1
1
0
1
1
0
2
1
0
0
1
1
0
2
0
2
0
3
1
1
2
0
0
0
0
0
0
0
0
1
1
0
2
1
0
0
1
2
1
2
1
2
1
0
3
1
0
2
1
1
0
1
0
1
2
1
0
0
1
0
0
2
1
0
0
2
0
2
2
0
2
0
1
0
1
0
2
1
1
0
1
0
1
1
1
0
0
1
2
6
0
1
0
0
0
1
0
1
1
0
0
1
0
1
2
0
2
0
0
0
1
1
1
2
1
0
2
1
0
1
1
1
0
0
0
0
2
1
0
0
1
0
2
1
3
0
0
2
1
0
1
0
0
0
1
1
0
0
1
2
0
1
1
1
1
0
1
1
1
1
1
0
1
0
0
2
0
0
1
1
0
1
3
1
0
2
0
1
0
0
2
1
1
0
2
1
2
2
1
0
1
2
0
1
2
1
1
1
1
0
0
0
2
0
0
1
2
1
1
1
0
0
0
0
1
1
0
0
0
2
0
1
0
0
2
0
1
1
1
1
0
1
0
1
2
0
1
0
1
2
2
0
0
0
0
2
1
2
1
2
2
1
1
0
2
0
1
2
0
2
0
0
1
0
0
2
2
2
1
2
1
1
2
2
0
1
4
0
1
0
2
1
0
2
0
2
1
0
0
0
0
0
0
2
1
0
1
0
0
0
3
0
2
0
0
1
1
0
1
1
1
2
1
2
0
2
0
2
0
1
0
1
0
1
0
1
0
2
0
0
0
0
1
1
2
0
1
2
2
1
0
0
0
0
1
1
0
0
0
1
0
1
0
1
0
2
0
2
1
0
1
0
1
0
0
0
1
0
0
0
1
1
0
0
1
0
1
1
0
0
1
0
0
0
1
0
2
1
0
2
1
0
0
0
1
1
0
0
1
0
2
3
0
0
1
2
0
2
0
0
0
0
0
0
0
1
1
0
0
0
2
2
0
2
0
2
1
2
1
0
0
1
1
1
0
1
0
0
1
1
0
0
1
2
0
2
2
2
1
0
0
1
0
1
2
1
1
1
1
2
1
2
0
3
1
0
1
0
0
0
0
0
0
0
2
0
1
0
1
1
1
1
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
1
4
0
1
1
0
0
0
2
1
2
1
2
1
0
0
2
0
0
0
1
1
0
3
0
1
1
0
1
2
1
0
0
0
0
1
1
2
6
0
2
1
2
0
2
2
1
2
2
0
0
0
0
1
1
0
3
0
1
2
1
0
2
0
1
1
0
0
2
0
0
1
0
1
2
1
1
1
2
1
0
0
1
1
0
1
1
1
1
0
0
2
1
0
0
0
0
0
0
0
2
1
2
1
1
1
1
0
1
1
0
0
1
3
0
1
2
0
0
2
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
1
2
0
0
0
1
1
0
1
1
1
1
1
2
0
0
0
0
4
0
0
1
2
0
2
0
1
1
0
1
0
0
1
2
0
0
2
0
0
4
0
0
1
1
1
3
0
2
1
2
0
1
1
0
2
0
0
1
0
0
3
0
3
0
2
1
1
1
1
0
2
1
0
1
0
2
1
1
2
0
0
2
1
2
0
0
1
0
1
1
0
1
0
0
2
2
1
0
0
1
2
0
1
1
1
2
1
1
0
0
1
2
1
1
0
1
2
1
1
2
0
0
1
2
1
2
4
0
0
0
0
1
0
2
0
0
2
2
1
1
1
0
2
0
0
0
0
0
1
2
1
0
2
0
0
0
0
0
0
1
0
0
1
0
1
0
2
2
1
0
1
3
0
1
0
2
2
1
2
1
0
1
2
0
1
1
1
0
1
1
0
0
2
2
2
2
0
0
2
0
2
1
0
2
0
2
1
1
1
1
1
0
0
0
0
0
1
0
0
0
1
0
0
2
1
2
0
0
0
1
2
1
2
2
1
0
1
0
1
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
1
1
2
1
0
0
1
1
0
1
1
0
1
0
1
0
2
2
2
1
0
2
1
2
2
0
1
1
0
1
0
2
2
2
0
0
0
2
1
0
0
0
3
0
1
0
2
0
1
0
1
1
0
0
1
1
0
2
2
2
2
0
1
2
0
0
0
2
0
2
2
1
0
0
1
0
1
1
0
0
1
0
2
4
1
1
0
0
3
0
0
1
0
1
0
0
0
0
2
1
1
0
1
0
2
0
2
2
1
1
0
0
0
2
0
2
0
2
0
2
0
2
1
0
3
0
2
0
1
0
0
0
1
1
2
0
2
0
0
1
2
1
0
0
2
2
1
0
0
0
2
0
2
0
0
1
0
0
0
2
1
0
0
1
1
0
0
0
2
0
0
2
0
1
2
0
0
2
2
1
0
1
0
0
1
0
0
2
0
2
2
1
1
0
0
1
1
0
1
0
0
0
2
1
1
0
2
1
2
1
1
2
0
2
0
1
3
2
0
1
0
2
0
0
0
1
2
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
2
0
1
1
0
2
1
1
0
2
2
1
1
1
0
0
0
1
0
1
2
1
0
0
2
0
1
0
2
0
1
0
0
1
0
1
1
1
2
0
0
0
2
0
1
0
0
0
0
1
0
0
2
0
1
0
2
1
1
0
1
0
1
0
0
2
1
1
1
1
0
0
0
2
1
0
1
2
0
2
2
1
2
1
0
2
0
0
1
0
2
0
2
0
0
0
1
2
2
1
0
0
1
0
2
0
2
1
1
1
2
1
3
0
2
0
0
1
1
0
0
0
1
1
2
2
1
1
1
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
1
0
2
2
2
2
0
0
0
1
0
0
0
0
0
2
2
0
2
1
2
0
0
2
2
2
1
0
0
0
2
0
0
0
0
0
2
1
0
0
2
1
0
0
1
0
1
0
0
1
1
0
0
0
1
2
2
1
0
0
1
1
2
1
2
0
1
1
0
0
0
2
1
1
1
0
0
1
0
1
1
1
3
1
2
1
1
1
0
1
1
0
1
0
2
2
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
1
0
2
0
2
1
1
1
2
1
0
2
1
0
1
0
0
1
0
0
0
0
2
0
2
1
0
1
0
1
2
2
0
0
0
0
2
0
0
1
0
1
0
0
2
0
1
0
1
2
0
0
0
2
0
0
0
1
3
0
0
1
0
0
0
0
1
1
0
1
0
2
1
0
2
2
1
0
1
0
0
0
0
1
0
0
0
1
2
1
1
0
0
2
0
0
1
1
1
1
0
2
0
0
1
0
0
0
0
1
1
0
1
0
2
1
1
1
2
2
1
1
1
0
0
2
2
1
1
0
0
0
2
0
0
2
0
0
2
1
0
2
2
7
0
1
2
0
2
1
0
0
1
2
2
1
0
0
1
0
0
1
1
1
1
1
2
2
1
2
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
3
2
0
1
0
1
2
0
2
0
1
1
0
0
2
0
2
0
0
2
1
2
0
1
2
2
0
0
0
0
2
1
1
1
0
0
1
0
2
0
1
0
0
1
0
1
0
1
0
0
0
0
1
0
1
2
0
0
0
1
1
2
0
1
0
0
0
0
1
0
1
0
0
4
1
1
0
1
2
1
0
1
0
0
0
0
3
1
0
0
1
0
2
1
1
1
0
2
0
1
0
1
0
2
1
2
2
1
1
0
1
1
3
0
0
2
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
2
1
1
0
1
2
0
2
1
0
1
0
0
0
1
0
0
1
3
0
1
1
0
1
2
0
1
1
1
1
1
1
0
2
0
1
0
1
2
2
0
1
2
2
0
0
2
2
0
0
0
0
0
4
2
1
0
5
0
2
0
0
1
1
1
0
1
0
0
0
0
1
2
0
2
1
2
0
0
0
0
0
1
0
1
0
0
0
0
2
1
1
0
0
0
0
1
2
0
0
0
2
1
1
1
1
0
2
2
2
1
0
1
2
0
1
2
0
0
0
2
1
1
2
2
2
2
1
0
0
2
1
0
1
0
0
0
1
0
1
0
0
2
0
0
1
1
2
0
2
1
0
0
2
2
0
2
1
2
1
2
2
0
2
1
0
0
0
2
0
0
0
0
1
0
1
2
0
0
2
0
1
0
0
0
0
0
0
0
1
2
0
1
1
2
1
2
2
0
1
0
0
0
0
0
0
1
2
1
1
0
1
1
1
0
0
0
0
0
1
1
0
1
1
0
2
0
0
1
0
1
1
2
4
0
0
0
0
1
0
2
1
2
2
0
1
1
1
2
1
1
0
0
1
1
2
0
2
0
1
2
0
0
0
0
1
0
0
1
1
1
1
0
1
0
0
1
1
0
0
0
1
2
0
1
2
2
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
2
1
0
2
4
1
1
0
0
0
2
1
1
0
0
1
2
0
0
1
0
1
0
2
2
0
2
0
1
1
1
0
1
0
0
2
0
1
1
1
1
1
1
1
0
0
2
2
1
1
0
1
0
2
0
2
0
1
3
2
3
0
1
0
0
2
2
0
0
1
0
1
0
1
2
1
1
1
0
1
0
1
1
1
0
0
0
0
0
2
0
1
1
0
0
0
2
1
2
0
0
0
0
0
1
1
0
0
1
2
1
1
2
1
1
2
2
0
1
0
0
0
0
0
1
0
1
2
1
0
0
0
0
0
0
1
0
1
0
0
1
1
1
2
1
2
2
1
0
0
0
0
0
0
2
0
1
0
0
1
0
0
1
1
2
2
0
0
0
0
2
1
1
0
0
1
0
0
2
0
1
1
0
2
0
1
0
1
3
0
2
2
1
0
1
1
0
0
0
0
0
1
1
1
0
0
2
2
0
1
2
2
0
0
2
2
1
2
0
0
0
1
2
0
2
2
0
0
0
1
2
0
1
2
0
3
0
2
0
2
0
2
1
0
1
0
2
1
2
1
0
0
0
1
0
0
0
2
2
0
0
0
2
1
1
0
0
2
1
1
1
2
2
0
0
2
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
1
1
0
2
1
1
0
0
0
1
0
0
0
2
0
1
1
1
0
0
2
0
1
1
2
1
0
2
1
1
2
1
1
1
1
0
1
2
2
3
3
0
0
1
4
1
0
0
1
0
0
0
1
2
0
1
0
2
0
2
0
0
0
2
1
1
1
3
1
1
3
1
1
1
0
1
1
2
1
1
0
0
2
0
2
0
0
0
1
1
1
0
1
2
2
0
0
2
1
1
1
2
0
0
1
2
2
0
0
2
0
0
0
0
1
0
2
1
0
0
0
0
1
1
0
1
1
1
0
0
1
1
1
1
1
0
2
1
1
2
0
0
0
0
0
0
0
2
0
2
0
1
0
1
0
1
1
0
0
0
0
0
1
1
0
0
1
0
1
0
3
1
2
0
0
1
1
0
0
0
0
1
1
0
1
2
1
0
2
0
0
0
0
0
2
0
0
1
1
1
0
1
1
0
1
1
0
14
0
1
1
0
0
1
0
0
0
1
1
1
1
1
0
1
2
0
0
0
1
2
1
2
0
0
0
2
1
0
1
1
2
0
1
0
0
0
0
1
2
1
2
0
2
3
1
0
1
0
1
2
0
2
0
1
4
1
0
1
0
2
0
0
0
1
0
0
1
2
0
1
0
0
0
1
1
0
1
0
2
1
2
1
1
0
0
2
0
0
0
1
0
2
0
2
2
0
0
0
0
2
1
3
2
2
0
0
1
1
0
1
0
1
1
0
1
0
0
0
2
0
0
2
1
0
0
2
2
1
0
0
1
0
1
0
1
0
1
0
2
0
1
1
0
1
0
3
1
0
2
0
1
1
0
1
1
0
0
1
3
0
0
0
0
0
0
0
0
0
0
2
6
2
2
0
0
2
1
0
2
0
3
1
0
1
1
1
1
2
1
1
1
1
2
1
1
2
0
1
0
0
0
0
2
1
0
0
0
0
0
1
0
0
2
1
0
1
1
1
1
2
2
2
0
2
1
0
0
0
2
1
0
2
0
0
0
1
0
1
2
2
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
1
0
1
2
0
0
1
2
0
2
1
0
2
0
2
2
1
0
1
1
0
0
0
2
0
1
2
0
0
0
1
0
2
0
0
2
1
1
0
2
0
1
0
2
1
1
0
1
1
0
1
0
0
1
2
1
1
2
0
1
0
2
0
1
1
2
0
1
2
1
0
1
0
0
0
2
0
0
1
0
1
1
2
0
0
0
0
0
1
2
1
1
1
0
1
1
1
0
0
1
0
2
0
1
0
0
0
2
0
0
0
0
0
1
0
1
1
0
0
2
0
1
2
0
2
1
0
0
2
1
1
0
0
0
1
0
0
0
0
1
1
2
0
0
0
1
2
1
0
0
1
2
0
0
0
0
5
1
2
0
0
0
1
2
1
0
0
0
3
0
2
2
0
1
1
0
0
1
0
0
2
0
2
1
0
0
0
1
0
1
0
0
1
1
1
2
0
0
1
0
2
0
0
1
1
2
0
2
1
0
1
0
0
1
0
0
0
0
1
0
0
1
1
1
2
1
2
1
0
1
0
2
0
1
2
2
1
0
0
2
0
0
0
3
1
1
1
1
2
1
1
0
0
0
0
2
1
1
1
0
1
0
0
0
1
0
0
1
0
0
0
1
1
0
1
2
0
2
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
1
2
0
0
0
2
0
1
2
2
0
0
0
0
3
1
2
1
0
0
0
1
0
0
2
1
0
1
1
0
2
0
1
0
1
0
0
1
2
0
0
0
2
2
0
2
0
0
0
0
1
1
0
0
0
1
1
1
0
1
0
1
2
0
2
0
1
0
0
1
0
2
1
2
0
0
0
0
2
0
0
1
0
1
1
0
2
2
1
1
0
1
0
0
1
0
1
0
1
0
0
2
1
2
0
0
1
1
1
0
2
1
1
1
1
2
1
1
1
1
1
2
0
2
1
0
2
1
1
0
1
1
0
0
2
1
3
1
2
0
0
0
1
1
1
0
1
0
0
1
0
2
1
2
0
0
0
1
0
0
0
2
2
0
1
0
1
1
0
0
0
1
2
0
1
1
1
1
0
1
1
0
2
1
1
0
1
0
0
0
1
1
1
0
0
1
0
2
1
0
0
2
0
0
0
0
0
2
0
0
1
0
0
2
2
2
0
0
1
1
0
2
0
0
0
0
0
1
1
1
1
1
1
1
2
0
2
1
1
3
2
0
1
2
0
0
2
2
2
0
1
1
1
0
0
3
0
0
1
2
0
0
3
0
0
2
2
1
2
0
0
1
0
2
0
0
2
1
0
0
0
1
1
0
1
0
2
1
1
0
0
1
0
1
1
0
0
1
3
0
0
0
1
0
0
1
2
1
1
1
0
0
0
0
0
1
0
0
1
2
1
2
0
0
0
0
2
1
1
0
0
1
0
1
0
2
0
0
0
2
0
2
2
1
2
1
2
2
1
3
0
0
1
2
0
0
1
1
1
0
1
0
0
2
1
1
2
1
1
1
1
0
0
1
0
0
0
1
2
2
1
1
1
1
0
2
1
2
0
2
0
0
2
2
1
0
1
0
0
0
1
1
1
1
1
2
1
1
0
2
2
0
0
1
0
0
0
1
3
0
0
0
0
0
1
1
0
2
1
1
0
1
1
2
2
1
1
2
0
0
0
2
2
0
1
0
0
1
2
1
2
0
1
2
2
0
0
2
0
1
0
2
0
0
1
0
2
0
2
0
0
1
1
2
2
0
0
0
2
0
0
1
2
1
0
2
1
2
0
0
1
2
2
0
1
2
0
0
2
3
0
0
0
3
1
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
2
0
1
2
1
2
0
0
0
0
0
2
1
0
2
3
1
2
0
0
0
1
0
2
0
1
0
0
3
0
1
1
0
0
1
1
1
0
2
1
0
0
0
2
1
0
1
2
2
0
0
1
2
2
2
0
1
2
0
1
0
0
2
0
2
0
0
0
1
2
0
2
0
0
1
0
0
1
2
1
0
0
0
1
1
0
0
0
3
0
0
2
2
2
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
1
0
2
1
0
1
0
0
2
1
3
0
2
0
1
2
1
2
1
1
2
1
2
1
2
0
2
1
2
1
1
1
0
0
0
2
1
2
1
0
2
0
1
0
1
1
2
2
1
0
0
0
1
0
0
0
1
2
2
0
0
2
2
1
0
1
0
0
0
0
0
1
1
2
0
2
0
0
2
2
0
0
2
1
1
1
0
0
1
1
1
0
1
0
0
2
0
1
1
0
2
1
0
2
1
0
0
0
1
0
1
2
1
0
1
2
0
0
4
0
0
1
0
2
1
0
1
1
1
2
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
1
2
0
0
0
0
1
1
1
2
1
2
0
2
0
0
0
2
0
1
2
0
1
1
0
0
0
1
1
0
2
0
0
0
1
0
0
1
1
0
0
0
2
1
1
1
2
0
0
2
0
1
0
1
0
2
1
1
1
1
0
2
0
2
1
1
0
1
1
0
2
2
0
0
2
1
1
2
0
1
2
2
0
1
8
2
1
2
2
1
0
0
1
1
1
0
0
0
1
0
2
2
2
1
1
0
0
0
2
1
0
2
0
1
0
2
0
2
1
1
1
1
0
0
1
0
2
0
0
0
0
0
0
1
1
2
1
0
2
1
0
1
2
0
1
1
2
2
2
2
0
0
2
1
1
0
0
1
1
0
0
0
0
2
0
1
0
0
1
2
0
1
0
0
0
2
0
2
2
1
0
0
2
1
0
0
1
1
1
0
0
2
1
1
0
1
0
2
1
2
1
2
1
1
1
1
0
1
1
0
1
1
0
3
0
3
0
0
0
1
2
2
0
1
1
1
1
0
2
0
2
0
2
2
1
0
2
0
2
0
0
0
2
1
0
0
3
1
2
1
0
0
1
0
0
1
1
0
3
2
0
1
0
1
0
1
0
2
0
1
1
1
0
0
0
1
1
2
1
0
1
1
1
1
1
2
2
2
0
1
0
0
0
1
0
0
1
0
0
0
1
2
0
2
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
1
0
1
0
1
0
0
2
0
2
0
1
2
1
2
0
0
0
0
1
0
1
1
0
0
0
1
7
2
2
1
0
2
0
1
3
2
0
1
1
1
2
0
2
1
2
1
0
1
0
0
0
1
0
2
2
0
2
1
0
2
1
0
1
1
0
0
1
1
1
0
0
1
0
2
0
0
0
1
1
0
0
0
1
1
1
1
0
1
0
0
2
1
2
2
0
0
1
0
0
0
0
0
0
1
0
0
1
1
1
1
1
1
1
0
1
4
0
0
1
0
0
1
1
1
0
0
1
1
1
1
1
0
0
0
2
2
1
1
0
0
0
1
0
1
1
0
0
3
2
2
1
0
0
0
2
0
1
1
2
2
1
1
1
2
1
0
1
1
0
1
2
0
1
0
0
0
1
0
0
0
0
2
1
1
1
0
0
3
1
0
2
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
2
2
2
1
0
1
2
2
1
1
0
2
1
0
0
0
1
2
0
2
1
0
1
2
2
1
0
0
0
0
1
0
1
1
0
2
2
1
1
1
0
1
2
0
1
1
1
0
0
1
0
0
2
1
0
0
1
2
0
0
2
0
1
0
3
0
0
0
0
1
1
1
2
1
1
0
2
2
1
2
0
1
0
1
0
0
1
1
0
0
0
2
2
2
1
0
2
0
0
2
1
0
0
0
0
0
1
0
0
3
1
1
0
0
1
2
1
1
0
0
1
3
2
1
1
0
0
2
0
0
0
1
0
2
2
0
2
0
0
2
2
0
1
1
0
0
1
2
0
0
1
2
0
1
2
0
1
1
0
1
2
1
0
1
1
0
1
0
0
0
2
1
2
1
0
2
0
2
0
1
0
1
2
0
0
0
0
0
0
0
2
1
0
1
2
1
0
2
2
0
0
0
0
2
3
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
2
2
1
0
0
1
0
0
0
2
0
1
0
0
0
2
3
1
0
2
1
1
0
1
1
0
1
0
0
0
0
0
0
0
0
1
1
1
2
0
2
0
1
2
2
0
1
0
1
2
1
1
0
1
1
0
0
0
0
2
1
2
0
2
0
1
2
0
1
0
2
2
2
1
0
1
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
1
0
0
1
1
0
0
2
0
0
0
0
1
0
2
2
2
0
0
0
0
0
0
0
1
0
0
1
1
1
1
2
0
0
0
0
0
2
1
0
1
1
2
1
0
0
0
2
2
0
1
0
0
0
0
2
1
1
1
2
2
0
2
0
1
0
0
1
1
1
0
2
0
1
0
2
2
1
0
1
0
1
0
2
0
0
0
1
2
0
2
0
2
0
1
1
0
1
1
0
2
0
1
0
0
0
2
0
0
2
2
2
0
2
0
1
2
1
2
0
0
1
0
0
0
1
0
2
2
0
1
1
1
1
2
0
3
1
0
0
0
0
0
0
0
2
0
0
1
0
1
1
2
1
0
0
0
1
0
2
2
0
2
0
0
0
2
0
0
0
1
1
0
0
2
0
3
0
0
1
2
1
2
0
2
0
0
2
1
1
0
1
0
1
0
2
0
0
0
1
0
2
0
1
1
0
0
2
0
2
1
0
2
0
0
1
2
0
0
0
0
0
1
0
0
1
1
2
0
0
2
0
0
1
0
1
1
2
2
2
2
0
1
0
1
0
1
0
0
0
2
1
0
1
1
1
2
0
0
0
1
0
1
1
2
2
0
1
0
0
2
0
0
1
1
0
0
0
0
0
0
0
2
0
2
1
0
0
1
2
0
1
0
0
0
1
2
2
3
0
1
2
0
0
2
0
1
1
0
1
1
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
1
0
1
2
0
0
1
0
1
2
1
1
2
0
2
1
0
0
2
2
0
1
1
0
0
0
1
1
0
2
0
0
0
1
0
0
2
2
0
0
0
2
2
1
1
0
0
0
0
0
0
2
0
1
0
0
0
1
1
0
1
0
1
1
1
0
2
2
0
0
0
1
0
0
2
0
0
1
1
2
0
0
2
7
0
1
1
2
1
2
1
2
1
1
2
1
2
0
0
0
2
1
0
0
1
0
0
1
3
2
1
2
0
0
2
1
1
0
0
0
2
1
0
2
2
0
2
1
1
1
2
0
1
1
0
0
0
0
1
0
2
2
0
1
1
1
2
0
2
1
0
2
0
1
0
2
0
1
0
2
0
1
0
0
2
0
1
2
0
0
1
4
0
0
1
1
0
0
2
2
1
0
3
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
2
0
0
1
0
4
0
2
1
1
1
2
0
2
0
1
1
0
2
1
0
0
3
0
2
1
0
0
0
2
0
1
1
0
0
0
1
1
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
2
1
0
0
0
1
0
2
1
1
1
1
0
1
2
1
0
1
1
0
0
0
0
1
1
1
0
0
0
1
1
0
2
0
2
0
1
0
2
0
2
1
2
0
0
1
0
2
1
1
0
1
1
2
2
1
0
2
2
0
1
0
0
1
1
3
1
0
0
1
1
0
0
0
0
1
2
1
0
1
1
1
4
0
0
0
0
0
1
1
2
0
0
1
1
2
2
1
0
0
0
1
0
0
0
1
1
2
1
2
2
2
2
0
1
2
0
7
0
2
0
1
0
1
0
0
1
1
2
1
2
0
0
1
2
1
0
1
0
4
1
0
0
1
1
0
1
1
0
0
0
0
2
2
2
1
0
1
0
0
1
0
0
0
2
0
1
0
0
1
0
1
1
2
0
0
1
1
1
2
0
1
0
0
0
1
1
1
2
0
0
0
0
2
2
1
1
0
1
0
2
1
1
0
1
0
1
2
1
2
1
0
2
0
1
1
1
1
1
1
0
1
2
1
1
1
2
1
2
1
0
0
0
0
2
0
0
0
0
1
0
1
2
0
0
2
0
1
2
0
1
1
1
1
0
0
1
1
2
1
1
2
0
3
1
2
0
2
0
1
1
0
1
1
0
1
0
1
2
1
1
2
1
1
2
0
0
0
1
3
0
1
2
2
2
1
1
1
2
0
0
1
0
0
0
3
0
2
2
1
1
1
0
2
0
1
1
1
0
1
0
0
0
1
0
0
0
1
2
0
1
0
2
0
2
1
0
1
0
1
1
0
0
0
0
0
2
0
2
0
1
2
1
0
1
2
5
2
2
0
1
0
0
0
1
1
0
1
1
1
1
1
1
1
1
0
1
2
0
0
0
1
0
2
2
1
0
0
1
1
1
1
1
1
2
2
0
1
1
0
1
0
0
0
1
1
3
0
0
0
2
1
1
0
1
0
2
2
0
0
1
2
0
1
1
0
0
1
0
0
3
1
0
0
0
0
0
0
0
1
1
1
0
1
1
1
2
0
0
0
0
2
1
1
1
1
2
0
0
0
0
2
0
0
0
1
1
1
2
2
2
0
2
1
0
1
2
1
0
0
0
2
1
1
0
0
0
0
0
2
0
1
1
0
0
2
2
2
0
2
1
0
1
0
1
3
1
0
1
1
1
1
2
0
0
2
2
0
2
0
0
0
2
2
2
2
0
0
0
2
0
0
0
0
2
2
1
0
0
1
1
1
2
2
1
0
2
1
0
1
1
1
0
0
2
0
0
1
0
2
0
0
0
2
0
2
1
0
0
2
2
0
1
0
0
0
2
0
1
1
2
0
1
2
1
2
2
0
2
1
1
2
0
2
1
1
2
1
0
1
0
0
2
1
2
1
1
1
0
0
2
1
0
0
1
3
2
0
3
0
2
0
1
0
0
0
2
0
1
1
2
0
1
0
0
0
0
1
2
4
1
1
1
0
0
0
2
0
0
0
2
0
0
0
0
0
2
1
0
1
1
1
0
1
2
0
0
1
0
0
1
0
0
1
1
0
2
1
0
0
1
2
2
0
0
0
0
0
0
1
0
1
2
0
1
0
0
0
1
0
0
0
1
0
0
2
0
0
0
1
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
2
2
2
0
0
0
0
0
0
1
1
2
1
1
0
1
0
1
1
0
0
1
2
0
1
0
0
0
1
1
1
0
1
0
2
1
0
1
1
1
1
0
1
0
2
0
0
2
2
0
0
0
1
2
1
2
1
2
0
0
1
0
0
1
1
2
2
1
0
0
0
0
2
2
2
0
0
1
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
2
0
1
2
1
0
1
1
1
0
0
0
0
1
0
1
1
0
2
2
1
0
1
0
0
2
0
0
0
0
1
2
0
0
1
0
2
1
1
0
1
0
2
2
2
1
2
0
0
2
1
0
1
0
1
1
0
0
2
0
2
0
0
0
0
1
0
0
0
0
1
2
0
0
1
1
2
1
1
0
1
1
1
2
1
0
1
2
2
0
0
0
0
0
1
2
0
1
0
0
0
0
0
3
0
2
2
1
1
0
2
0
0
0
2
1
1
0
2
1
1
1
1
0
1
0
1
2
1
3
1
1
0
1
2
1
0
2
0
2
0
0
0
1
0
2
4
1
1
1
0
1
1
0
0
0
0
0
0
0
0
0
2
0
2
2
1
1
0
0
1
0
1
2
1
0
0
1
1
2
2
1
2
0
0
1
0
2
1
1
3
0
0
0
0
1
1
1
0
0
0
0
0
0
1
2
0
0
2
0
1
2
1
0
2
2
2
1
0
2
1
0
0
3
0
1
2
0
1
0
0
0
1
0
1
1
1
2
0
0
2
1
0
0
1
0
1
2
1
0
0
1
1
1
0
0
0
1
1
2
0
0
0
0
1
1
2
1
1
0
1
0
0
2
0
2
1
0
0
0
1
1
0
2
0
0
0
2
0
5
1
0
0
0
0
3
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
3
1
0
1
1
0
0
2
1
2
1
0
1
2
2
0
1
0
1
1
1
1
0
1
1
3
0
1
0
0
2
2
1
1
1
0
2
0
2
1
1
2
0
1
2
0
1
0
2
0
0
0
0
1
0
2
2
2
1
0
1
0
0
1
0
1
0
1
1
0
0
1
2
1
2
2
0
2
0
2
2
0
0
2
1
2
1
0
2
0
0
0
1
1
0
1
2
0
0
1
0
0
0
1
0
2
0
1
2
0
2
2
2
1
1
1
0
0
1
0
1
1
0
0
2
1
0
0
1
1
0
2
0
2
1
1
0
0
1
1
0
0
0
2
0
0
2
0
3
2
0
0
1
0
3
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
2
2
1
0
0
1
1
1
0
0
0
0
0
0
0
2
0
0
2
2
1
2
1
1
0
1
1
0
0
2
0
0
0
0
0
0
1
2
0
0
0
2
2
0
1
2
0
1
0
1
1
0
0
0
2
1
0
0
0
0
0
1
0
0
1
2
2
0
2
0
1
0
1
0
0
0
0
1
1
1
2
0
0
0
0
0
0
2
0
2
0
1
2
0
1
2
1
3
1
0
2
1
0
2
0
0
1
1
1
1
0
2
0
1
0
0
0
1
0
1
1
1
1
1
2
1
1
1
1
0
0
2
0
1
1
0
2
2
1
0
2
2
2
2
1
2
0
0
1
0
0
1
0
0
0
1
0
1
0
2
0
0
0
1
0
0
2
2
0
0
0
0
1
1
0
1
0
0
0
2
0
2
1
2
0
0
1
2
1
2
0
1
2
2
2
0
0
2
1
0
0
0
0
0
1
0
0
1
0
2
1
0
0
1
1
0
0
0
0
0
0
0
1
0
1
1
1
2
2
2
2
0
1
2
0
0
1
2
2
1
1
1
2
0
0
0
0
0
0
0
2
0
0
1
2
1
1
0
0
0
2
1
0
2
0
2
0
0
0
0
1
0
0
1
0
0
3
0
1
0
0
0
0
0
0
0
2
2
0
2
0
1
2
0
2
1
1
0
2
5
0
0
1
1
1
0
2
2
1
1
2
1
0
0
0
2
1
2
1
2
0
0
0
1
0
1
0
1
0
0
6
0
2
1
2
1
0
0
0
0
0
0
1
2
1
0
2
1
0
2
0
2
0
0
1
0
0
0
0
4
1
0
0
1
0
0
2
0
2
0
1
2
0
0
2
1
2
1
0
0
2
1
2
1
2
0
1
2
0
1
1
1
2
0
1
2
2
2
0
2
0
1
0
0
0
1
1
1
1
1
1
0
1
1
0
4
0
2
2
0
1
0
1
0
0
1
1
0
0
2
2
0
0
2
1
1
1
0
0
1
0
0
0
0
0
0
1
2
2
0
0
1
2
0
0
2
2
1
0
0
2
0
2
1
1
0
3
2
4
2
0
0
1
1
0
1
1
1
2
0
0
0
0
0
0
1
2
2
0
0
1
0
0
1
0
0
2
1
2
6
2
1
0
0
1
2
0
1
0
2
1
1
1
1
0
0
1
1
1
0
1
1
0
0
2
2
1
0
2
1
1
1
1
0
0
0
1
2
1
0
1
0
2
0
0
0
1
1
0
1
0
1
0
2
0
2
1
0
1
2
2
0
0
0
1
0
0
0
1
2
0
1
1
1
0
1
2
0
0
0
2
0
1
0
0
2
0
0
1
1
1
0
0
2
0
0
2
0
1
2
0
1
2
0
0
2
0
2
0
0
2
0
0
0
2
0
0
0
2
0
1
0
1
0
1
2
1
0
1
0
0
0
1
0
0
0
0
0
1
2
1
0
0
1
0
2
0
2
0
2
1
1
0
1
2
0
0
0
0
1
2
2
0
0
0
2
0
0
1
1
1
2
2
1
1
2
1
1
0
0
0
1
0
0
1
0
0
2
1
0
1
1
0
2
2
0
0
0
0
0
0
0
0
1
0
1
2
2
0
1
1
1
0
2
1
0
0
1
0
0
0
0
0
2
2
0
0
0
2
1
0
0
1
2
0
2
1
0
1
0
1
0
1
1
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
1
4
1
0
0
0
1
0
1
2
1
0
1
0
0
0
2
0
1
0
2
2
0
1
0
1
2
0
2
1
2
1
0
0
0
1
1
0
0
0
2
1
2
0
0
1
2
0
0
0
0
0
1
1
0
1
2
2
1
2
1
0
1
1
0
1
0
1
0
0
1
2
0
2
1
2
0
0
0
2
0
1
0
1
2
1
1
0
1
2
0
3
2
2
1
2
0
1
0
0
0
1
0
1
1
0
1
0
1
2
1
0
1
1
1
1
1
1
2
0
0
1
0
2
0
1
0
1
1
2
1
0
0
1
2
0
1
1
1
1
1
0
0
0
1
1
2
0
0
2
1
0
0
0
0
1
0
2
2
2
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
1
1
0
2
0
0
1
1
2
1
1
3
2
3
0
0
0
1
0
1
2
2
0
0
0
0
0
0
1
0
2
3
1
1
0
1
1
0
2
1
1
0
0
1
1
0
0
0
1
1
2
2
0
0
1
0
1
0
0
0
0
2
2
2
0
0
0
0
0
1
2
0
1
0
0
1
0
1
1
2
0
1
0
1
1
1
2
0
0
0
1
1
0
1
0
0
1
2
0
0
1
0
1
2
1
2
0
0
2
0
0
0
0
2
1
0
1
0
0
1
2
0
1
0
0
2
1
0
1
0
0
2
2
2
1
1
1
2
0
1
1
1
0
0
1
0
2
1
0
1
1
0
3
2
1
1
2
1
0
0
0
1
0
0
0
0
0
0
2
1
0
1
1
1
1
0
0
0
2
4
0
2
0
0
0
0
1
1
0
0
1
2
0
1
1
2
0
2
0
0
0
0
0
2
2
0
1
0
0
1
2
0
0
0
0
0
1
2
1
2
0
1
0
1
0
0
0
1
2
2
1
0
0
0
2
0
2
0
2
1
1
0
0
2
0
2
2
0
2
0
0
1
2
0
0
0
0
1
0
1
0
2
0
2
2
0
2
1
1
0
1
0
0
0
1
2
1
0
2
2
1
0
1
0
1
0
1
0
0
1
0
0
1
2
0
0
0
0
0
2
1
0
2
1
1
0
3
5
0
2
0
2
0
1
1
0
0
2
0
1
1
2
1
0
2
1
1
2
1
2
0
0
0
2
0
1
0
2
1
1
0
0
0
2
1
2
1
0
1
1
0
2
0
0
2
0
1
2
0
0
0
2
0
1
0
1
2
0
1
1
0
0
1
0
0
0
0
0
2
2
1
0
2
2
2
0
0
1
1
0
1
1
1
0
2
0
2
1
0
1
0
1
1
1
1
1
2
1
0
0
0
1
1
1
0
2
1
0
1
0
0
1
0
0
2
0
1
1
0
0
0
0
1
2
0
1
0
2
1
2
2
1
1
0
0
0
1
1
0
2
0
1
0
0
2
0
2
0
2
1
1
1
2
0
0
1
0
0
0
0
1
1
0
1
1
1
1
0
1
1
0
1
1
0
1
1
0
1
1
0
0
0
0
1
2
0
2
2
1
0
2
2
1
0
1
0
1
0
1
2
0
2
1
0
2
2
1
0
0
2
2
0
0
0
1
1
0
1
1
0
0
0
4
0
2
1
0
2
1
1
3
2
1
1
1
1
0
1
2
0
0
1
4
0
1
0
2
2
2
0
1
0
0
1
0
1
2
2
0
0
0
1
2
1
1
1
0
0
0
1
1
1
1
1
0
0
0
2
1
2
1
1
2
0
0
1
0
1
0
0
3
0
2
2
0
0
0
0
0
1
2
0
0
1
0
0
0
0
2
0
0
1
0
2
0
2
0
0
0
0
1
2
2
0
2
1
2
0
0
1
2
2
0
0
0
0
1
0
0
2
1
0
1
1
1
0
0
1
3
0
0
0
0
1
0
0
0
2
2
0
0
2
2
2
1
0
3
1
1
0
0
0
2
0
2
1
0
0
0
3
2
0
2
1
1
0
2
2
0
2
1
0
2
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
2
1
1
2
1
2
2
1
0
1
0
0
0
0
0
2
1
2
2
2
0
1
0
1
2
1
1
1
0
2
1
0
2
0
0
2
1
1
1
0
0
1
1
0
2
0
0
1
2
0
2
2
1
2
2
1
0
2
2
0
0
1
1
1
0
2
0
0
1
0
2
2
0
2
0
1
0
1
0
1
0
1
2
2
1
1
0
0
1
0
1
0
1
1
2
0
0
1
0
2
0
0
1
0
1
0
2
0
1
0
0
1
0
2
0
1
0
1
1
0
0
0
1
0
0
2
2
1
0
0
0
0
0
0
0
0
1
0
0
2
0
1
2
2
0
2
1
0
1
1
3
0
1
0
0
1
0
0
1
1
1
0
0
1
1
2
1
0
1
1
1
0
0
0
1
3
3
1
0
0
2
2
1
1
2
0
2
1
1
0
1
1
2
2
0
1
2
2
0
0
2
1
2
1
1
1
1
0
1
0
0
1
0
1
2
1
0
3
0
2
1
0
0
0
1
0
0
2
1
0
0
1
2
2
0
0
1
0
1
0
0
1
0
2
2
0
0
0
0
1
2
0
1
0
1
1
1
1
1
0
2
1
0
0
0
0
1
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
1
3
1
0
0
1
0
2
2
2
0
0
0
1
2
1
2
0
1
2
0
0
1
1
1
0
0
0
1
0
0
1
0
2
1
0
1
0
2
0
3
2
2
2
2
1
0
2
2
1
1
0
0
1
1
0
0
1
0
2
0
0
1
1
0
2
0
0
1
1
0
0
1
2
1
3
0
1
1
0
0
1
0
0
0
1
2
0
1
1
0
0
0
2
0
0
0
0
1
1
2
0
2
0
2
0
1
2
0
2
1
1
0
1
1
2
2
0
1
0
1
0
0
1
0
2
1
0
0
0
0
1
0
0
1
2
1
0
0
1
0
0
2
0
0
0
0
1
0
1
1
1
1
0
1
0
2
2
1
1
2
2
2
0
1
0
0
0
1
4
1
1
2
0
1
1
0
0
1
2
1
1
0
1
1
0
0
2
1
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
2
0
1
0
1
0
0
0
0
0
2
0
3
0
0
0
1
1
2
1
1
1
0
1
1
0
0
0
2
0
0
0
0
1
2
2
0
0
1
2
0
0
0
2
0
0
0
0
2
2
0
2
1
2
2
2
2
0
1
1
0
1
0
2
0
0
0
0
2
1
0
1
0
1
2
0
1
2
0
2
0
2
2
0
0
0
0
2
1
0
1
1
1
1
0
1
1
2
0
0
0
2
0
2
2
0
0
0
1
1
2
1
1
1
1
1
1
1
2
1
1
0
1
2
0
0
0
0
2
0
0
0
2
0
2
1
2
1
0
0
0
1
1
0
0
2
1
2
2
0
2
0
0
1
0
2
0
1
2
1
0
0
1
0
0
0
0
1
0
1
1
1
2
1
0
1
0
0
0
1
2
3
1
1
1
1
0
0
1
0
1
0
0
0
0
1
1
1
2
2
1
0
1
2
0
0
2
0
0
0
2
1
1
0
0
1
1
1
0
1
0
1
0
0
2
1
1
2
0
0
1
2
1
0
1
0
0
3
0
0
1
0
1
0
1
0
1
0
0
0
1
1
0
1
1
1
2
2
2
0
2
0
2
0
0
0
0
1
0
1
1
0
1
2
0
0
2
0
2
1
1
0
2
1
0
0
0
1
0
0
0
0
2
0
3
0
1
0
2
2
1
1
1
1
1
1
0
0
0
1
0
0
1
0
1
0
2
0
2
0
0
0
2
1
1
1
2
0
2
2
2
2
1
0
0
2
2
0
1
0
2
0
2
2
0
2
0
0
1
1
2
1
0
3
0
1
1
0
0
2
1
2
1
2
1
0
1
3
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
1
2
0
0
0
0
1
2
0
0
1
0
0
0
1
1
0
0
1
0
1
0
2
1
2
0
1
0
0
0
1
0
3
0
0
0
1
2
1
0
1
1
2
2
0
1
0
1
1
0
1
2
0
0
0
0
0
2
1
0
1
1
3
0
1
0
1
2
1
2
0
0
2
0
0
0
0
1
0
1
0
0
1
0
0
0
2
0
0
0
0
1
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
2
0
2
1
1
1
1
1
0
1
2
0
2
1
0
0
1
1
1
0
0
0
1
0
0
1
1
1
0
1
1
0
0
0
0
1
1
0
0
1
0
0
0
0
1
1
2
1
1
1
0
1
1
0
0
1
1
0
0
0
0
1
0
1
1
1
1
0
0
0
2
0
0
2
2
1
0
1
2
1
0
0
1
0
2
0
0
1
0
1
0
1
0
1
0
2
2
2
0
0
0
1
0
2
0
2
1
1
1
1
2
0
1
0
1
1
1
0
1
1
0
0
1
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
1
1
0
1
0
2
0
0
1
0
0
1
0
0
1
0
0
1
2
0
0
0
0
2
0
2
1
2
0
0
1
2
0
0
0
1
2
0
0
0
1
2
0
2
0
0
0
0
0
2
0
1
2
0
0
0
0
0
2
0
1
0
1
1
0
1
0
0
1
1
0
0
1
1
0
1
1
2
0
3
2
2
0
2
0
1
1
0
1
0
2
0
2
0
1
1
1
2
0
1
1
1
0
0
0
0
2
2
0
2
0
1
1
1
1
0
2
1
1
0
1
2
0
2
0
2
1
2
1
2
2
3
0
1
0
0
1
0
1
0
0
1
2
0
2
0
1
1
0
2
2
0
0
0
0
0
0
3
0
1
0
0
0
0
1
2
2
2
1
0
1
1
0
0
0
2
0
0
2
0
0
0
3
0
0
1
1
0
0
0
0
2
0
1
0
2
0
1
0
0
1
0
1
2
1
1
1
0
0
0
1
1
0
0
1
0
0
1
0
1
0
0
0
3
0
1
2
0
1
1
1
1
2
1
2
1
2
0
0
0
0
1
1
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
1
1
1
0
1
1
0
0
2
2
2
1
0
0
0
1
2
0
2
2
1
2
0
0
1
0
1
0
0
0
2
0
0
0
1
2
0
0
0
0
1
1
1
1
0
1
1
0
1
0
0
0
0
0
2
1
1
0
2
3
0
0
1
1
0
0
2
0
0
0
1
1
1
0
1
0
1
2
1
0
1
2
2
0
1
1
1
0
1
0
0
0
0
0
1
0
1
1
0
0
1
1
2
2
0
2
0
1
1
0
0
0
2
1
2
2
0
1
0
0
1
1
0
1
1
2
2
0
0
0
2
0
2
3
1
1
0
0
0
0
2
0
1
1
1
0
0
1
0
0
1
1
0
1
0
1
2
0
1
1
1
3
1
1
0
2
0
1
1
0
2
0
0
2
0
0
0
1
1
0
1
1
1
2
1
0
1
1
0
1
1
0
0
0
0
1
1
0
0
1
0
0
0
0
3
0
1
1
0
1
1
0
1
1
0
0
1
0
0
0
0
0
3
0
0
1
2
0
1
0
0
0
2
2
0
2
2
1
0
1
0
0
4
0
1
1
2
0
0
0
0
0
2
0
1
0
2
2
1
2
2
0
1
0
2
2
1
2
1
2
0
0
2
2
0
0
2
2
1
2
2
1
0
0
1
1
1
1
1
2
1
0
1
0
2
1
1
2
1
2
0
1
0
1
3
0
1
0
0
0
1
1
2
0
0
2
0
0
0
1
0
1
0
2
0
0
0
1
0
0
2
0
2
0
2
2
2
1
1
0
1
0
1
1
3
2
1
0
2
0
0
0
0
0
0
1
2
1
0
1
1
0
0
0
0
1
2
1
4
1
2
0
0
1
2
0
0
1
2
0
0
1
1
0
1
2
2
0
3
0
0
1
2
2
0
1
1
1
2
0
2
1
0
2
1
1
2
0
4
0
0
2
0
0
0
1
1
1
0
0
0
1
1
0
0
0
1
0
0
0
2
0
0
0
2
1
0
1
2
0
0
1
2
2
0
0
0
2
2
0
1
0
0
0
1
1
1
0
0
2
1
0
2
0
1
0
1
0
0
0
0
2
2
2
0
0
0
1
1
0
0
2
1
0
0
1
2
0
2
1
0
1
1
1
3
0
2
1
1
0
2
0
2
1
3
2
0
2
2
0
0
0
0
0
0
2
0
0
1
0
2
1
0
0
2
1
0
0
0
0
0
0
2
0
1
0
0
2
0
2
1
2
2
2
0
1
0
0
0
0
2
0
1
2
1
0
1
1
0
1
1
0
0
1
1
0
1
1
1
0
0
0
1
0
0
1
1
2
0
2
1
1
0
0
1
0
2
0
1
0
2
1
0
0
1
1
0
0
0
0
1
2
0
0
0
0
0
0
1
2
1
0
1
1
0
0
1
1
1
1
2
0
1
0
1
2
0
0
1
2
1
1
2
0
2
0
0
0
2
1
2
0
0
1
0
0
0
2
1
1
0
0
2
1
1
2
0
3
0
1
1
2
1
0
1
2
1
2
0
1
1
0
0
0
2
0
1
0
2
1
0
1
1
1
0
0
1
0
1
1
0
0
0
2
1
0
0
0
2
0
2
0
1
1
2
2
0
1
0
0
1
2
0
0
1
0
0
0
1
0
0
0
0
1
1
0
2
1
0
2
1
1
0
0
2
1
0
1
1
1
1
0
2
1
1
1
0
0
0
1
1
0
1
0
1
0
0
0
2
2
1
0
1
1
2
0
0
0
1
2
2
1
1
0
1
0
1
0
1
0
0
0
0
1
1
1
2
1
0
3
0
2
0
1
1
3
0
1
0
2
1
0
0
0
2
0
1
0
2
2
0
1
1
0
1
0
0
0
1
2
1
0
0
1
0
0
0
1
2
0
0
1
1
2
0
1
0
1
1
1
1
2
0
0
1
0
2
0
1
0
1
0
1
0
0
1
2
1
1
1
0
2
0
1
0
2
1
0
2
2
2
0
0
1
2
0
1
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
1
1
0
1
0
0
2
0
1
1
0
0
1
0
0
2
1
1
1
1
1
0
1
0
1
2
0
0
2
1
1
0
1
0
2
2
0
0
0
0
2
0
2
1
0
0
2
2
5
0
0
0
0
3
1
1
0
0
2
0
0
1
0
0
2
1
0
0
0
1
0
2
2
0
2
0
0
1
1
0
0
1
3
3
1
0
1
1
0
0
2
2
2
2
0
1
0
2
1
0
1
2
2
1
0
0
1
1
0
0
0
1
1
0
1
0
2
0
0
2
1
0
0
0
0
0
1
1
0
0
1
1
0
2
0
0
0
2
1
2
2
0
0
1
0
0
1
1
1
2
0
0
0
0
2
2
0
1
0
0
2
2
0
0
4
0
0
0
1
1
0
1
1
1
1
0
2
3
0
0
0
1
0
1
0
1
0
3
2
0
0
2
2
1
0
0
1
3
0
0
0
1
1
0
1
2
1
1
0
2
0
1
2
0
0
0
2
0
0
1
0
1
1
1
0
0
1
0
0
1
1
0
1
0
1
0
2
0
1
2
0
1
0
2
1
2
1
2
1
2
0
2
0
1
1
1
1
0
1
1
1
2
0
2
0
2
0
0
0
1
2
1
0
1
1
0
0
2
0
2
2
2
0
0
1
1
2
0
2
1
0
0
1
2
0
1
0
1
2
2
2
1
0
1
0
0
2
2
2
2
0
0
1
0
0
2
0
1
0
0
0
0
0
2
0
1
2
0
0
1
2
0
0
0
2
1
0
2
0
1
0
3
2
0
2
1
1
2
0
1
0
2
1
3
0
0
1
2
2
0
0
0
1
0
0
1
1
0
1
0
2
2
1
1
2
1
0
1
2
0
1
3
1
2
1
2
0
0
0
1
0
0
1
2
2
0
0
2
1
0
0
1
0
1
2
0
0
0
2
1
2
0
0
0
0
2
1
1
2
1
0
1
0
1
2
0
1
0
1
0
0
1
0
2
0
2
2
1
1
1
2
0
0
1
0
0
0
0
2
2
2
2
2
0
1
1
0
0
1
1
0
0
0
0
1
1
0
0
1
0
1
1
0
0
0
0
1
2
0
1
1
1
1
1
0
0
0
0
1
1
0
1
0
2
2
1
0
0
0
0
0
2
0
0
1
0
1
0
1
1
0
1
1
0
0
0
1
1
2
0
0
1
0
2
1
0
0
0
1
0
1
1
0
1
1
2
0
1
0
0
1
1
1
2
0
0
1
2
0
1
0
0
0
0
2
0
0
0
0
3
0
0
0
1
1
1
1
1
1
2
1
1
2
1
1
0
0
1
0
2
0
0
0
0
0
2
0
2
0
2
0
0
1
0
0
2
1
1
2
2
1
0
0
0
3
0
0
0
1
0
2
2
0
2
1
0
0
0
1
1
0
0
0
2
0
1
1
0
0
2
2
2
0
0
0
0
1
0
3
2
0
1
0
1
2
0
2
0
0
1
2
0
1
1
0
2
0
0
0
0
0
1
2
1
1
0
4
1
1
3
2
0
0
0
1
0
0
0
2
0
1
2
1
2
0
1
0
0
3
0
0
2
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
1
2
0
1
0
0
0
0
0
2
1
1
1
1
1
1
0
0
0
0
1
0
1
0
2
1
2
2
2
2
0
0
2
0
0
1
0
0
1
2
1
0
1
1
0
0
0
0
2
0
0
0
1
0
2
2
0
0
1
1
0
0
1
1
1
0
0
1
1
2
0
1
0
1
0
1
0
0
1
2
4
0
0
0
1
0
0
1
1
0
0
2
0
0
3
2
1
1
1
2
2
2
1
1
0
0
0
1
2
1
0
2
0
2
2
0
1
2
0
0
2
0
1
0
2
2
0
1
0
0
1
2
0
1
1
2
0
2
2
0
0
3
4
1
1
0
0
2
0
0
1
1
1
0
0
0
2
1
0
2
1
0
0
0
2
1
0
3
1
0
2
0
0
1
3
1
0
1
1
0
3
2
0
0
0
0
2
2
2
0
0
0
1
0
0
1
0
0
1
0
0
2
2
1
0
2
0
1
0
1
0
0
1
0
2
0
1
1
0
0
1
1
0
0
0
1
2
1
0
0
0
1
1
2
2
0
1
3
0
0
1
0
0
3
0
0
0
0
2
1
0
2
2
0
0
0
1
2
1
0
0
0
1
0
2
0
1
0
0
1
0
1
0
1
1
2
1
0
1
0
2
0
1
1
0
0
0
2
2
2
1
2
1
1
1
2
0
0
0
0
1
2
1
1
0
2
1
0
1
0
2
2
0
1
0
2
1
2
1
1
1
0
2
0
2
1
2
0
1
1
3
1
1
2
1
0
2
1
2
2
1
0
0
0
1
0
0
1
0
0
1
0
1
2
0
0
2
1
1
1
0
2
0
2
0
0
1
0
1
2
2
2
1
0
0
0
1
0
0
1
1
0
0
0
1
0
2
0
2
1
2
1
1
1
0
0
2
0
0
0
0
2
1
2
2
1
1
1
0
0
0
0
0
1
2
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
2
0
1
1
0
0
0
1
1
0
0
1
0
1
1
1
0
1
0
0
2
2
1
0
0
0
1
1
0
0
1
3
0
0
2
0
1
2
2
0
0
1
0
0
1
0
2
0
1
1
1
0
1
1
2
2
2
2
0
0
0
1
1
1
1
0
0
2
1
2
0
0
0
0
2
2
2
0
1
0
0
2
2
0
1
0
2
1
1
2
1
0
1
0
2
0
0
2
2
1
0
0
1
1
1
0
0
0
1
0
2
1
1
1
0
2
0
2
0
0
0
0
0
0
0
2
0
2
1
0
1
2
2
0
0
1
0
0
1
0
1
2
1
1
0
2
2
2
1
2
0
1
1
1
3
1
1
0
1
0
2
0
0
2
0
1
0
1
0
1
1
0
1
2
1
2
1
1
1
2
0
1
1
0
0
0
0
1
0
0
0
2
1
1
2
0
1
3
1
3
0
0
0
2
1
1
2
2
0
4
2
0
0
0
1
1
1
0
2
1
0
0
2
1
1
2
2
1
1
0
1
0
0
1
2
0
0
2
1
1
0
1
0
0
2
1
0
0
0
2
0
1
0
1
0
0
0
0
0
0
2
2
0
0
0
2
1
1
1
1
2
0
1
1
0
2
0
0
0
0
0
1
0
0
2
0
2
0
1
2
2
1
0
0
0
2
0
0
0
0
3
2
0
2
0
1
0
1
0
3
0
0
0
2
2
0
0
0
0
0
2
2
1
1
1
1
2
0
0
2
0
1
1
4
1
0
0
0
2
0
1
2
0
0
0
0
0
0
2
0
1
1
0
1
0
1
0
0
0
0
2
1
1
0
0
0
2
1
0
0
2
0
1
0
0
0
1
2
0
2
0
0
2
0
0
0
3
0
0
0
1
0
0
1
1
1
2
0
1
0
2
1
1
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
2
1
0
0
0
0
0
1
2
0
0
0
0
0
1
0
1
2
0
1
2
1
1
1
2
0
1
0
1
1
0
2
0
2
0
0
0
0
0
2
0
2
2
0
2
0
2
1
0
2
0
0
2
1
1
2
0
1
2
0
0
2
2
1
1
2
0
1
1
2
0
0
0
1
0
2
1
1
1
1
0
1
1
0
0
2
0
1
2
1
0
2
1
1
0
1
1
0
0
0
1
0
1
0
0
1
2
1
0
1
1
0
0
1
2
2
1
2
0
0
0
1
2
0
0
2
0
0
0
1
0
0
2
1
0
0
0
0
0
1
0
1
1
0
0
2
2
0
2
1
0
1
2
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
1
2
1
0
0
3
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
1
0
1
0
2
0
1
1
2
1
1
2
1
0
1
0
0
2
0
0
0
2
0
1
0
0
0
3
1
0
1
1
1
1
1
0
0
1
0
0
1
1
0
1
2
3
0
0
0
1
2
1
1
2
1
0
0
1
2
1
1
2
0
0
3
1
1
1
1
1
0
1
1
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
2
0
1
1
1
0
0
0
1
0
1
0
0
2
0
1
0
0
1
1
1
2
0
1
1
0
0
0
1
0
0
1
2
2
2
8
0
1
0
2
2
0
0
2
1
0
0
2
0
1
0
1
1
0
0
0
1
0
0
1
1
1
0
0
1
0
1
1
0
1
3
1
0
0
0
1
1
2
2
1
1
0
11
2
0
0
2
2
1
1
0
0
0
3
2
1
1
1
1
0
2
2
0
2
1
2
0
2
0
1
0
2
0
0
0
0
2
1
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
1
0
1
2
0
0
1
0
1
1
2
0
2
1
0
0
1
1
1
0
1
1
2
2
1
0
1
0
2
1
1
2
2
2
0
2
3
0
0
0
1
1
0
0
0
0
0
0
1
0
2
0
1
0
1
2
0
0
1
0
0
1
2
1
2
0
0
2
1
1
0
0
1
2
2
0
0
2
0
0
2
1
0
0
0
2
0
1
0
0
0
1
0
4
1
0
2
0
1
1
1
0
0
1
1
0
0
2
0
1
0
0
0
0
1
1
0
1
1
0
0
1
0
2
0
1
0
1
1
1
0
0
2
1
0
1
2
0
2
0
0
0
0
1
3
1
0
2
0
0
2
2
1
1
0
1
2
1
1
2
0
0
0
1
1
0
0
2
0
1
2
0
1
1
2
3
1
0
0
1
1
0
2
0
2
2
3
0
1
1
1
0
0
1
0
0
2
0
0
1
0
1
0
1
1
0
1
1
0
2
1
0
2
0
1
1
0
0
1
0
2
2
0
0
2
2
1
0
0
2
0
0
0
1
0
2
2
0
2
2
2
6
0
0
0
0
0
1
0
2
1
0
1
0
0
0
2
0
1
0
1
0
1
2
0
1
0
2
0
0
0
2
1
0
2
1
1
1
3
0
0
1
1
1
2
1
1
2
1
1
2
0
1
1
1
0
0
0
0
1
0
1
0
0
0
2
0
0
0
1
1
1
1
0
0
0
1
1
0
1
0
2
2
0
2
1
1
0
0
1
1
1
1
0
0
2
1
1
1
2
1
1
1
2
2
1
0
1
0
0
1
2
0
2
2
0
0
0
1
0
3
2
2
2
0
0
1
1
1
0
0
0
1
0
0
3
2
0
0
1
0
0
1
1
1
0
0
0
1
1
0
1
1
2
0
0
0
1
0
0
1
0
0
0
1
0
1
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
2
1
1
2
1
0
1
0
2
0
0
0
0
1
1
1
0
0
1
0
0
2
2
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
1
1
3
0
2
2
0
0
1
0
0
2
0
0
2
1
1
0
2
0
1
2
2
0
1
2
1
1
0
1
0
0
0
2
2
1
0
2
0
0
1
0
0
1
0
1
1
3
0
2
0
2
0
0
0
0
3
0
1
1
2
0
2
2
0
1
0
1
1
0
0
0
0
1
0
0
0
2
2
0
2
2
1
1
0
2
0
0
2
0
0
2
0
2
1
3
1
1
0
0
1
1
1
1
1
1
0
0
1
2
1
0
1
2
1
0
0
1
1
0
2
1
0
0
0
0
2
1
0
0
1
2
0
1
1
1
0
1
1
0
1
1
2
1
0
1
1
1
0
0
1
0
2
0
1
2
1
0
2
1
1
0
0
1
0
2
0
1
0
0
0
0
0
0
1
2
1
0
0
2
2
0
2
0
2
1
2
2
2
1
0
0
0
0
1
0
0
0
4
1
1
1
2
0
1
0
1
1
1
0
0
0
0
2
0
0
1
1
0
0
0
0
1
0
0
0
1
0
1
0
2
1
0
0
2
1
0
2
1
0
0
1
1
2
1
0
2
0
2
0
1
1
0
0
1
0
0
1
1
1
1
1
0
1
1
1
0
0
1
0
2
1
1
1
0
1
0
0
0
2
1
1
1
0
0
1
1
2
0
0
1
0
0
1
0
0
0
0
0
3
2
0
0
2
1
1
0
1
1
2
2
2
3
1
1
0
0
1
0
2
1
1
3
0
2
2
2
2
1
1
0
0
1
2
1
0
0
1
2
0
1
0
2
1
3
0
0
0
2
0
0
2
0
0
0
0
1
0
2
1
1
1
1
1
2
0
0
1
0
1
0
0
0
2
2
1
0
0
2
0
1
1
0
0
0
1
0
0
1
1
2
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
1
2
2
0
0
1
2
1
2
1
0
0
1
0
0
1
3
1
0
0
2
0
2
1
1
0
1
2
0
2
1
2
0
0
0
2
0
1
1
1
0
2
2
1
1
0
0
2
0
0
0
1
1
1
0
1
0
1
0
0
0
1
0
0
0
1
0
0
2
2
1
0
1
1
2
0
2
0
0
1
1
1
2
0
0
0
0
0
1
1
1
1
1
1
2
0
2
1
1
0
0
4
0
2
0
0
0
0
0
0
0
1
1
1
0
0
2
1
0
0
1
2
2
1
0
0
0
1
1
2
0
0
1
0
0
3
0
1
0
2
3
2
0
1
3
0
0
0
1
0
0
0
2
1
2
1
0
1
0
1
0
0
0
0
1
0
1
0
1
2
0
1
2
0
3
0
0
2
1
0
0
0
0
1
1
1
0
0
0
1
0
0
0
1
0
0
1
1
0
0
2
0
2
0
2
0
1
0
2
1
0
1
1
0
0
0
0
0
2
1
1
0
0
2
0
2
0
3
1
1
2
0
0
1
0
0
1
2
0
0
0
1
0
1
0
1
0
0
2
2
0
0
1
0
1
0
0
1
0
0
0
1
1
1
1
3
1
2
1
1
0
2
1
0
1
0
0
0
1
0
0
0
2
0
0
2
2
1
2
2
0
2
2
1
0
6
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
2
0
2
0
0
0
0
1
2
0
0
2
0
1
0
0
0
2
2
1
0
0
0
0
2
1
0
0
0
0
0
2
2
0
1
2
0
1
2
0
0
0
1
1
1
0
2
0
1
1
0
2
0
0
1
0
0
0
1
1
2
1
1
1
0
0
1
0
1
0
1
2
0
0
1
0
0
1
1
0
0
2
1
0
0
1
2
1
0
2
2
2
1
3
1
2
1
3
0
2
0
3
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
1
2
0
0
0
2
0
1
0
0
0
0
1
1
0
1
2
1
1
1
1
0
1
0
0
1
1
0
0
0
1
0
2
2
1
0
1
2
0
1
2
1
2
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
1
1
1
2
0
1
0
0
1
3
0
0
2
1
1
0
1
1
0
1
0
1
2
1
0
0
2
0
0
0
1
0
1
0
1
2
0
2
1
0
1
0
0
0
0
0
2
0
1
1
2
1
1
0
1
0
1
1
1
2
0
0
2
0
0
1
1
0
2
2
0
2
0
1
1
0
0
0
0
0
2
0
3
0
2
2
1
1
2
0
1
2
0
2
2
0
2
0
1
1
0
0
0
0
0
0
1
1
3
1
1
0
0
0
1
1
1
2
1
1
2
0
1
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
1
2
0
1
2
1
2
0
1
1
1
0
1
1
1
1
2
0
0
0
0
1
1
0
0
0
1
1
0
0
1
0
0
1
0
0
0
2
0
0
0
0
1
0
3
0
0
0
0
0
2
1
0
0
2
1
1
1
0
0
1
0
1
1
0
0
1
0
1
1
0
2
0
1
0
1
0
1
1
1
2
1
0
1
0
1
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
1
2
0
1
0
1
1
1
0
1
0
0
0
0
1
0
0
1
0
0
0
1
1
1
1
0
0
0
1
0
2
0
3
1
0
0
0
1
3
0
2
2
0
0
2
0
0
2
1
0
0
2
2
2
0
1
1
0
2
0
0
0
1
0
2
1
1
1
2
2
0
0
0
1
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
2
0
1
0
0
1
1
2
1
1
0
2
1
0
1
2
0
2
0
0
0
1
1
0
1
2
0
0
0
1
0
0
0
0
0
0
2
1
0
1
0
2
1
2
1
0
0
1
0
0
3
0
0
1
1
1
2
0
2
1
1
1
0
0
1
0
1
1
1
0
0
2
0
1
2
2
1
3
1
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
1
1
1
0
0
1
2
1
1
2
0
0
0
2
0
2
1
0
0
2
0
2
0
0
0
2
2
0
1
2
0
0
0
1
0
1
0
1
0
2
0
0
0
1
1
1
0
0
1
0
0
1
0
0
0
1
1
1
1
0
1
0
0
0
0
2
2
2
0
1
0
1
1
2
1
1
1
0
4
1
0
2
1
1
1
0
0
0
0
2
0
0
2
0
2
0
0
2
0
0
2
1
0
0
0
0
1
0
1
0
2
0
1
0
0
1
0
1
0
0
1
0
1
0
2
0
1
1
2
0
1
2
2
0
0
1
2
0
0
1
1
0
2
0
1
1
1
1
2
1
0
0
1
1
0
1
0
1
1
2
1
2
0
2
0
0
0
1
1
1
3
1
2
1
0
0
0
1
2
0
2
0
1
0
0
1
1
1
0
0
2
1
1
0
0
1
2
1
0
0
1
1
2
1
1
0
1
1
0
1
0
2
1
0
0
1
0
1
0
0
2
0
1
0
0
1
1
1
1
0
0
1
0
1
0
2
1
0
0
1
0
0
2
1
2
0
0
1
2
2
0
0
1
2
2
2
0
1
1
0
0
1
2
0
2
2
1
0
2
2
0
1
1
2
0
0
0
1
0
1
0
1
1
1
1
1
0
1
0
1
0
1
0
0
1
0
0
2
1
2
0
0
1
1
1
3
0
2
0
0
1
0
2
0
2
2
1
1
0
1
0
0
1
2
0
1
2
0
0
1
1
0
1
2
1
1
1
0
1
2
1
2
0
0
0
2
2
0
1
0
0
1
1
1
1
0
0
3
0
0
1
1
1
2
1
0
0
2
2
0
0
0
1
2
1
2
1
0
2
0
2
1
1
0
0
0
1
0
1
0
0
2
1
0
0
0
0
2
0
0
1
1
0
0
0
2
2
0
1
5
0
1
1
0
2
0
1
0
1
0
2
0
0
0
1
0
1
2
1
1
4
1
1
1
2
1
0
1
3
2
0
0
0
1
0
1
2
0
0
0
0
0
2
0
2
0
0
0
1
0
1
1
0
2
1
1
1
0
2
0
0
0
1
1
1
1
0
0
0
0
2
0
0
1
2
0
1
2
0
1
0
1
0
0
0
1
2
0
0
1
2
0
0
4
1
1
0
1
1
0
1
1
1
0
0
0
0
1
0
2
0
1
2
1
0
1
1
1
1
0
2
1
1
1
0
1
0
0
2
1
1
0
0
0
0
0
0
0
0
0
1
2
1
2
1
1
0
0
1
2
0
2
0
0
0
0
2
0
0
0
0
0
0
1
2
2
1
1
2
2
0
2
0
1
2
1
1
0
1
1
1
0
0
0
0
1
1
1
1
0
2
1
0
0
0
0
0
2
0
1
0
2
2
1
0
0
0
1
1
0
0
1
1
0
0
0
0
0
1
0
1
2
0
2
1
1
2
1
1
0
0
2
0
1
2
1
1
1
2
0
2
2
0
0
1
1
0
0
0
2
2
1
0
0
1
2
0
1
1
1
2
1
1
1
0
1
1
0
1
1
1
1
1
0
0
0
2
0
3
1
3
4
0
0
0
1
0
0
0
1
0
0
2
0
1
2
2
0
2
0
0
0
0
0
2
0
1
0
1
1
0
0
0
0
2
1
2
1
0
1
0
0
2
0
0
1
0
0
13
0
1
0
2
1
1
2
1
1
2
2
1
1
1
2
2
1
2
0
2
0
0
1
1
0
1
2
0
2
2
0
1
1
0
2
0
0
0
1
2
1
1
0
1
0
0
2
0
1
0
1
1
0
0
0
1
1
0
0
1
2
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
2
1
2
0
0
0
3
1
0
0
0
2
1
0
0
2
1
0
0
0
1
1
1
1
1
0
1
2
1
1
1
0
0
2
1
1
2
2
0
2
1
0
2
0
2
1
2
0
1
0
0
1
0
1
0
1
0
1
1
0
1
0
0
1
1
1
1
1
3
1
1
2
1
0
0
1
0
2
0
1
0
2
1
2
1
1
2
2
1
2
2
0
2
0
3
0
2
0
0
1
0
2
0
2
0
0
1
0
1
0
0
0
0
0
1
2
0
1
0
0
0
1
0
1
1
1
0
1
0
1
0
0
1
2
0
1
2
1
0
2
2
1
0
1
0
2
0
0
1
0
0
0
0
1
0
2
1
2
0
1
1
1
0
0
1
2
0
0
1
1
1
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
2
1
1
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
1
1
0
0
2
0
2
0
1
0
0
3
0
1
0
0
0
1
0
2
1
2
1
2
0
0
0
0
0
0
0
0
0
2
0
2
0
2
2
0
2
1
0
0
1
1
1
2
0
3
0
1
0
0
0
0
0
0
0
2
0
0
1
1
2
1
1
0
2
0
2
0
1
0
0
2
2
1
0
0
0
2
0
1
1
1
2
1
2
1
2
2
1
0
0
2
0
0
0
1
0
1
1
2
1
0
1
2
0
0
1
2
1
0
1
0
2
1
1
1
1
0
0
0
1
1
0
0
0
0
0
0
0
1
2
1
1
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
1
0
2
0
0
0
1
1
1
2
2
2
2
0
2
1
1
0
0
1
1
2
2
1
1
1
1
0
1
0
1
1
2
0
2
0
2
0
1
2
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
2
1
1
2
2
2
3
2
0
0
1
2
1
0
1
2
2
0
0
1
0
0
0
1
0
0
1
1
0
1
0
0
0
2
0
0
1
0
0
1
1
5
2
0
3
2
1
0
0
0
2
1
1
2
0
4
0
2
2
1
1
1
0
0
1
1
0
0
1
0
0
0
3
0
1
2
0
1
1
0
2
0
3
2
0
1
0
0
1
1
1
1
2
0
1
1
0
1
1
1
0
2
1
0
0
0
0
0
1
2
2
0
1
0
1
2
0
0
0
2
0
0
2
1
1
0
0
0
0
2
1
2
0
1
0
1
4
2
0
0
0
3
1
2
2
0
2
0
0
0
0
0
0
1
1
1
1
0
2
1
0
0
2
1
0
2
0
0
0
1
0
0
0
0
1
1
2
0
0
0
1
1
0
1
1
2
2
0
0
2
0
0
1
0
2
0
0
2
0
0
1
0
2
0
1
0
1
0
1
1
4
2
1
0
0
0
0
1
1
1
1
0
0
1
0
1
2
1
2
0
0
1
1
0
0
1
2
0
0
1
1
1
0
1
2
0
2
0
1
1
2
0
1
0
0
0
0
1
1
2
0
0
1
1
1
0
2
2
0
2
1
0
1
6
1
2
1
0
0
0
2
0
1
2
0
2
0
2
1
2
0
0
0
0
1
1
2
0
0
0
0
2
0
0
2
0
0
2
2
0
1
2
2
0
1
0
1
2
2
2
0
1
0
0
1
2
0
2
0
1
2
1
2
2
0
0
0
1
0
0
0
0
2
2
0
2
0
0
2
0
2
0
0
3
0
1
2
1
2
1
2
0
1
2
0
0
0
0
1
2
2
0
1
1
0
2
1
1
1
0
2
1
0
2
1
0
2
1
0
2
0
0
1
0
1
1
0
1
0
0
2
1
0
0
0
0
1
0
1
0
3
1
1
1
1
0
1
1
2
2
0
1
1
1
0
1
1
0
0
2
0
2
0
0
0
2
1
1
2
0
2
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
2
2
0
0
2
0
1
0
0
2
0
2
1
0
2
1
0
1
0
0
0
2
0
0
0
0
4
0
1
1
0
2
1
2
2
1
0
1
1
0
2
0
0
1
2
0
0
3
0
0
0
1
1
2
0
0
0
0
2
0
0
0
1
1
0
2
1
1
1
2
2
1
1
3
2
2
0
2
0
1
1
1
1
0
0
0
2
0
1
1
0
2
0
1
0
1
2
2
0
0
2
1
0
1
0
1
0
1
0
0
1
0
1
1
1
0
1
2
0
0
0
0
1
0
0
0
0
2
0
1
1
1
0
3
2
1
0
0
0
0
0
0
1
2
0
0
2
2
1
0
1
1
2
3
2
0
2
3
0
0
0
2
2
1
0
1
1
0
1
1
1
0
0
1
1
1
2
1
3
2
1
0
2
0
1
0
0
0
1
0
1
1
2
2
1
0
0
0
1
1
2
2
1
0
0
0
1
0
0
0
0
0
1
1
0
2
0
0
0
1
2
0
0
1
0
0
1
0
1
0
0
0
2
0
1
0
0
0
1
0
1
5
0
1
0
0
1
2
2
1
2
2
1
1
2
0
0
2
2
0
0
0
2
2
1
0
2
2
0
2
1
0
0
1
0
0
2
2
0
1
0
0
0
2
2
0
1
1
0
1
1
0
1
0
0
0
1
0
2
0
0
1
2
0
0
2
0
0
0
0
1
0
0
0
1
2
2
1
1
0
0
1
0
1
0
1
1
1
0
2
2
0
2
0
2
1
0
0
0
0
0
2
1
0
2
1
1
0
2
0
1
0
0
1
1
0
0
1
0
1
0
1
0
1
0
1
0
0
0
1
1
0
2
0
0
0
2
2
1
0
1
0
2
1
1
0
1
1
1
0
0
2
0
0
0
1
1
1
1
2
1
0
0
1
1
0
0
2
2
1
1
0
0
2
0
1
1
0
0
2
1
0
2
2
0
0
1
0
0
0
2
1
0
2
0
0
1
1
0
0
1
0
2
0
0
1
1
1
1
0
0
0
0
2
0
0
1
0
0
0
1
2
0
2
0
0
2
0
1
0
1
0
1
0
1
2
0
0
1
0
1
0
0
2
0
2
2
1
1
1
0
0
0
2
1
2
0
0
1
1
2
0
0
1
1
2
1
0
1
1
0
1
0
0
1
0
0
0
1
1
2
1
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
1
1
1
0
1
0
0
2
1
2
2
1
2
0
2
2
0
0
0
0
1
0
0
2
1
3
1
0
0
2
0
0
0
3
1
0
2
2
2
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
2
2
2
1
2
1
0
1
0
1
1
0
0
2
2
1
1
2
0
3
0
1
2
0
0
2
1
0
0
1
1
1
2
1
0
0
0
0
0
1
0
1
0
2
2
1
0
0
0
1
2
0
1
1
0
2
0
0
0
0
0
0
1
2
1
2
0
0
2
0
0
0
0
2
1
0
0
0
1
1
1
0
0
1
0
1
0
1
2
1
1
2
2
0
0
0
0
2
1
1
0
0
1
0
1
0
1
1
0
0
0
1
2
0
2
1
1
2
0
1
0
1
0
0
1
1
0
1
2
0
0
1
0
2
0
0
1
0
1
0
2
2
0
0
0
1
0
2
0
1
1
1
2
0
1
0
0
0
1
0
1
2
0
2
1
2
0
0
0
0
0
0
0
0
0
2
1
0
1
1
0
1
2
0
0
2
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
1
1
1
1
0
0
2
0
0
0
0
2
0
1
2
0
0
0
0
0
2
0
1
1
0
1
0
0
1
1
1
2
0
0
1
1
1
2
2
1
1
1
1
1
0
0
1
0
1
0
3
1
1
1
2
0
0
0
2
0
0
3
2
1
0
2
2
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
3
0
1
1
0
2
0
2
1
1
0
0
2
2
1
0
0
0
1
2
1
0
2
0
1
0
1
1
1
1
0
0
1
0
1
0
0
1
1
1
0
0
1
0
1
1
1
1
1
0
0
0
0
1
1
0
1
1
1
1
1
2
0
0
0
1
2
1
1
1
0
0
0
1
2
0
0
0
2
2
0
3
1
1
1
2
0
1
0
0
1
0
2
2
2
0
1
3
1
2
2
2
0
0
0
0
2
2
0
0
3
0
0
0
0
2
1
0
0
2
2
0
2
0
0
0
1
1
0
0
1
1
2
0
2
2
0
2
1
0
0
0
1
0
1
1
2
2
1
1
0
1
0
2
0
0
1
0
2
0
0
0
1
0
0
0
0
0
2
1
2
0
2
0
1
1
1
1
2
1
2
0
1
2
0
0
1
0
0
0
1
1
0
1
1
0
0
2
2
1
0
0
0
1
2
2
2
0
1
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
1
2
0
2
0
1
0
1
1
1
0
0
1
1
2
0
2
0
5
5
2
0
0
3
0
2
2
0
0
1
0
0
1
0
2
2
2
1
1
0
1
0
2
1
2
1
1
1
0
0
1
1
0
0
1
1
1
1
0
2
1
1
0
1
1
1
0
0
1
0
1
1
2
3
1
1
1
0
0
1
1
1
0
1
2
0
0
2
0
0
2
2
1
0
0
0
1
0
1
0
0
1
1
0
0
1
0
0
2
1
0
0
0
2
1
0
2
0
2
0
0
0
1
0
1
0
2
0
0
0
1
1
0
1
0
0
1
0
1
1
1
1
0
2
1
2
0
0
0
0
0
0
1
1
2
0
2
0
0
0
1
1
0
0
0
0
1
3
1
1
2
2
0
1
1
1
1
2
1
0
0
2
0
0
2
1
1
1
1
0
1
1
1
1
0
2
0
1
2
1
1
0
0
2
1
0
1
2
1
1
1
0
0
0
1
0
0
0
1
2
0
0
1
0
1
0
1
0
0
1
0
1
1
0
1
0
2
2
1
3
1
2
2
4
1
1
1
1
0
0
1
0
0
2
1
1
2
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
2
1
2
2
0
2
2
1
2
4
0
1
1
1
0
0
0
1
2
2
0
1
0
0
1
1
1
1
0
1
2
0
1
1
2
0
2
2
0
2
2
0
2
2
0
2
2
0
1
0
0
0
2
0
0
1
2
0
0
0
1
1
0
1
0
0
0
1
0
1
1
2
1
0
2
1
2
0
1
2
1
0
0
0
1
0
1
0
1
0
2
1
2
0
2
0
0
0
0
0
2
1
3
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
1
2
2
1
2
0
2
1
0
0
1
2
1
2
0
0
1
1
0
1
2
1
0
0
1
1
0
1
2
0
0
2
0
0
1
1
0
1
2
0
0
0
0
1
0
1
1
0
0
0
1
0
2
0
0
1
2
2
0
1
1
0
1
1
1
2
0
1
1
1
1
2
1
1
2
0
0
2
1
2
3
1
3
1
0
0
0
0
0
1
2
1
0
0
0
0
1
0
1
1
1
2
0
0
1
0
0
1
0
0
0
1
3
0
0
0
2
0
1
0
0
3
1
0
1
1
0
0
2
0
0
1
0
1
0
0
2
1
0
1
0
1
0
0
0
0
1
2
1
0
2
0
0
2
0
0
0
0
2
3
1
2
1
0
2
0
1
2
0
2
2
0
1
0
1
2
1
0
0
2
1
2
0
1
1
1
0
0
1
1
0
0
0
0
2
0
1
0
1
0
1
2
2
0
0
0
1
0
2
1
0
1
0
2
1
1
3
1
1
2
0
0
1
0
1
2
2
1
2
1
1
1
2
2
1
0
2
1
0
1
2
1
0
0
0
0
1
2
2
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
2
0
2
2
1
1
1
0
2
0
1
0
1
0
3
1
1
0
2
0
0
2
0
1
0
1
0
0
2
0
0
0
2
1
1
0
2
0
1
1
0
0
0
0
1
1
1
0
0
2
0
1
0
0
0
0
1
0
0
2
1
1
1
0
0
2
0
1
1
0
1
0
1
2
0
1
3
2
0
0
1
1
0
1
1
1
1
0
2
0
2
1
0
2
2
2
2
1
2
0
1
2
0
1
2
1
0
1
2
2
0
0
0
1
2
1
2
0
0
0
2
0
1
0
0
1
0
2
0
2
0
1
2
0
0
1
1
0
0
1
1
0
1
2
2
0
1
1
1
0
1
0
1
1
1
1
1
1
1
0
1
1
0
0
0
1
2
2
1
2
1
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
2
1
2
0
0
0
0
0
0
1
1
0
1
0
0
2
0
1
1
1
1
0
0
3
2
0
3
1
2
0
1
0
0
1
1
1
1
2
0
1
2
0
2
1
0
1
1
1
1
1
2
0
0
2
0
0
0
0
1
1
0
0
4
0
0
0
2
0
0
0
0
2
0
0
2
1
0
1
2
0
1
0
2
0
0
0
0
2
1
1
0
1
1
0
0
0
2
0
2
0
0
0
1
0
1
0
0
2
0
2
0
0
3
1
1
1
0
0
2
1
0
0
2
0
0
1
0
0
3
0
0
0
1
0
2
1
0
1
1
0
2
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
1
2
0
2
0
1
0
2
1
0
2
1
1
1
0
0
0
2
2
1
2
2
1
0
2
1
0
0
1
0
0
2
0
1
2
0
1
1
0
0
0
0
0
1
1
2
0
1
1
1
0
4
2
1
1
0
0
0
1
1
1
1
2
0
1
0
3
1
1
1
0
0
0
0
0
1
1
0
1
0
1
1
0
0
1
2
0
2
0
1
0
1
2
2
1
0
2
1
2
0
1
1
2
0
0
2
0
0
2
2
0
2
0
1
2
0
2
0
0
1
0
0
0
0
1
0
0
2
0
2
6
0
0
2
0
0
0
2
1
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
1
1
0
0
2
1
1
0
2
0
2
2
1
0
0
1
0
1
2
2
1
2
0
0
2
0
1
1
1
1
1
1
0
1
0
0
1
0
0
0
0
3
1
1
2
1
0
0
2
0
0
0
1
1
0
0
3
1
0
2
1
1
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
2
1
2
3
1
1
2
0
0
1
1
0
1
0
2
0
1
2
2
0
1
0
0
0
1
1
2
1
0
2
0
0
0
2
0
2
2
1
0
0
1
0
2
1
0
0
2
0
0
0
2
1
1
0
0
0
1
1
2
1
2
0
2
2
1
1
0
0
1
0
2
2
1
0
2
0
1
1
0
1
0
2
1
2
0
0
1
1
0
0
0
4
0
2
1
1
0
1
0
1
0
1
0
0
2
1
2
2
2
0
2
2
0
2
3
0
0
2
1
1
2
0
2
1
0
1
0
2
1
1
0
0
0
0
1
1
0
0
1
0
2
0
1
2
2
0
0
0
0
2
1
1
0
1
1
0
1
1
0
0
1
1
0
2
2
0
1
0
0
0
0
0
1
0
2
2
0
2
0
1
1
2
1
1
0
2
0
0
1
1
0
2
0
0
2
0
0
1
1
2
0
0
2
1
0
2
1
0
0
1
0
1
1
0
0
0
2
1
0
2
0
0
2
1
2
0
1
0
0
2
2
0
0
2
0
0
0
1
0
0
1
2
2
1
1
0
0
0
0
0
1
3
1
1
0
0
0
0
1
2
2
0
0
0
0
1
1
1
0
0
2
2
1
2
0
1
0
0
1
2
1
1
1
2
0
2
0
1
0
2
1
0
3
1
1
1
0
0
1
0
1
0
1
1
2
1
1
0
1
0
2
0
0
1
0
1
1
1
1
0
0
0
1
0
0
0
0
0
3
0
0
2
2
1
0
0
0
0
0
1
1
0
1
0
0
2
1
2
2
1
1
0
1
1
2
1
0
1
0
1
0
2
0
0
0
0
2
3
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
1
2
1
0
1
2
2
2
0
2
1
0
1
0
1
1
0
2
0
0
1
1
1
1
1
1
2
0
2
2
1
2
1
1
1
1
0
2
0
1
0
2
0
1
1
1
0
0
2
0
0
1
2
0
0
0
1
1
1
2
2
2
1
0
2
1
1
0
2
0
0
2
0
2
1
2
0
1
0
1
2
1
2
0
1
1
1
0
0
1
0
0
0
0
1
3
0
1
0
0
1
0
1
2
0
2
1
1
0
0
0
0
1
0
0
1
0
0
0
0
1
1
2
0
2
0
0
0
1
1
1
0
0
1
0
0
2
1
2
2
1
2
1
0
2
2
1
2
0
0
0
1
0
0
0
1
2
0
0
0
2
0
0
0
0
1
1
2
0
0
0
2
0
0
0
2
1
0
0
0
2
1
0
0
0
1
1
0
1
0
0
1
0
1
0
1
2
1
1
1
7
0
0
0
1
1
2
0
0
2
0
1
0
2
1
0
2
2
1
1
0
0
2
0
0
2
1
2
1
0
2
1
1
0
1
1
0
0
2
0
0
1
2
0
1
0
0
0
1
2
0
2
0
2
0
1
0
1
1
0
2
0
1
2
0
2
1
1
0
0
1
1
0
0
0
2
1
0
0
0
0
1
0
0
1
1
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
1
1
2
0
0
0
0
2
0
0
2
0
0
0
1
2
2
1
0
1
2
0
2
0
0
2
1
1
0
0
1
0
0
0
1
0
0
0
2
1
1
0
0
1
0
1
2
0
0
0
1
1
0
1
1
0
0
1
0
1
1
1
0
2
2
0
1
0
1
0
2
1
0
1
2
2
1
1
0
2
1
0
0
1
2
0
1
1
1
1
1
3
2
0
0
0
0
2
0
1
1
0
1
0
1
0
0
0
2
2
1
1
1
0
2
0
2
1
2
2
0
0
0
0
1
1
0
0
1
0
2
0
1
0
1
1
0
1
0
2
2
1
2
0
0
1
0
0
1
0
1
1
0
2
1
2
1
0
1
0
1
0
2
0
0
2
0
0
0
0
0
1
1
2
1
0
0
2
0
0
2
2
1
1
1
1
2
1
0
1
2
1
0
2
2
1
0
1
2
0
2
1
0
0
1
0
2
2
0
1
0
2
0
0
0
2
2
0
0
2
1
1
0
1
1
1
2
1
1
2
3
0
0
1
0
0
1
0
2
1
2
0
2
1
1
1
0
0
0
1
2
0
1
1
1
0
0
1
0
0
0
0
0
3
1
0
1
0
2
0
0
0
2
0
0
0
1
2
1
1
0
0
1
2
1
1
0
1
0
1
0
2
0
1
0
0
0
1
0
0
0
1
0
1
0
0
2
1
0
2
2
2
0
1
1
0
1
1
0
0
0
2
0
1
1
0
2
0
0
0
2
0
0
1
0
2
0
1
2
2
2
2
0
0
1
0
0
1
1
0
0
1
2
1
0
1
1
1
1
0
1
2
0
0
1
2
0
1
0
0
1
0
1
1
2
2
1
1
2
1
1
2
1
0
0
1
2
0
0
0
3
1
0
0
1
2
1
1
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
1
0
2
0
2
1
0
2
0
0
1
0
1
2
0
2
1
0
0
1
0
2
1
0
0
2
0
3
3
0
1
0
0
2
2
0
0
3
2
1
0
0
1
0
0
2
0
0
0
1
0
1
1
0
1
1
0
0
0
1
2
0
2
0
5
0
1
2
0
2
2
1
0
0
0
1
0
0
1
1
0
1
0
2
2
0
1
2
1
2
2
2
2
1
2
0
1
0
1
1
0
0
1
2
1
1
0
0
0
1
1
1
2
0
2
1
0
0
1
1
1
1
0
1
0
2
1
2
1
1
0
1
2
0
0
1
1
1
2
2
2
2
1
0
0
0
2
0
0
0
0
0
0
0
1
1
0
1
0
1
1
0
1
0
1
1
3
0
1
0
2
0
0
2
1
0
2
2
0
1
0
0
1
0
0
0
1
2
1
2
1
1
1
0
0
0
0
1
2
1
0
0
0
1
2
3
0
0
0
0
0
1
3
1
0
1
0
0
0
0
1
1
1
1
1
2
0
0
1
1
0
2
0
0
1
1
2
1
0
0
0
2
2
1
2
0
2
1
2
1
2
0
1
2
1
1
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
2
2
0
1
0
1
0
0
2
1
1
0
2
2
2
0
1
2
2
1
0
2
0
0
0
0
0
0
1
0
2
1
1
2
1
1
0
0
1
0
1
1
0
0
1
1
0
0
2
0
1
0
2
1
0
0
1
0
1
0
1
2
1
0
0
1
0
2
2
0
2
0
1
1
2
0
0
0
0
1
0
0
1
1
0
1
1
2
1
0
2
2
0
2
0
2
1
3
0
0
0
1
0
0
3
0
0
1
1
0
1
1
1
0
0
0
0
3
1
0
1
1
1
0
0
1
0
1
0
1
2
1
3
0
2
0
1
1
1
5
0
0
2
1
0
1
0
0
2
2
1
1
1
1
1
1
2
0
1
0
2
2
2
0
0
1
2
0
0
2
1
0
0
0
0
0
1
2
0
0
0
1
0
1
3
0
0
1
0
2
1
0
0
1
0
2
0
2
0
0
1
0
0
1
0
0
1
1
0
1
1
1
2
2
0
3
2
0
3
2
1
2
0
0
0
0
2
0
2
0
1
0
1
1
1
1
4
0
1
2
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
2
1
0
1
1
0
0
2
1
1
1
0
0
1
0
1
1
0
0
0
0
2
2
2
0
0
0
0
2
0
0
2
0
1
3
0
0
0
1
0
0
1
0
1
2
2
1
2
0
1
0
2
2
2
2
1
0
0
0
0
1
0
2
0
0
0
0
0
1
0
1
0
1
1
0
2
2
1
0
0
0
0
1
1
1
1
1
0
2
0
5
0
1
0
0
0
1
2
1
2
1
1
2
0
1
0
0
1
1
2
0
1
1
0
1
0
0
0
2
2
0
0
0
0
0
2
0
2
1
0
0
2
1
0
1
1
0
2
1
2
0
1
2
2
1
0
0
0
0
0
0
1
1
0
1
1
1
0
1
1
1
0
2
0
0
0
0
0
2
0
0
0
1
2
0
1
1
1
2
1
1
1
1
0
2
0
0
0
2
0
2
0
1
0
1
0
0
1
2
2
2
1
0
1
0
1
1
2
2
2
0
1
0
1
0
0
0
0
1
0
0
0
2
2
0
2
0
0
1
0
0
0
0
1
1
1
0
2
0
0
1
2
0
2
0
1
2
1
0
3
1
2
0
1
0
0
1
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
2
1
0
1
1
0
0
0
1
2
0
0
1
2
0
0
1
0
1
2
2
0
0
0
1
1
0
0
0
0
0
0
1
3
1
2
0
1
0
1
0
0
0
0
0
0
1
2
1
2
0
0
1
0
3
2
0
0
0
1
2
1
2
1
2
2
2
0
2
0
0
1
1
1
1
0
1
1
1
1
1
0
2
0
1
1
0
2
1
1
1
0
0
0
1
0
1
1
0
2
1
2
0
2
0
0
0
0
2
2
0
0
1
1
1
2
1
1
1
1
2
0
2
0
2
1
2
3
0
1
2
0
0
0
0
0
2
0
1
0
0
1
0
1
2
0
0
1
2
0
1
0
0
1
1
2
1
0
0
2
1
2
2
1
0
2
2
0
0
0
2
0
0
2
1
0
2
1
2
1
0
1
0
1
0
0
0
0
2
0
0
2
1
0
0
0
0
0
1
0
1
1
0
0
1
1
1
1
0
2
0
1
2
1
0
0
2
2
1
0
0
0
0
2
2
1
2
1
1
0
1
2
1
2
0
2
3
1
0
0
0
1
0
1
1
1
1
1
0
0
0
1
1
0
0
1
1
0
0
0
0
0
2
1
2
0
0
2
1
0
2
0
2
0
1
1
0
0
0
0
0
1
0
0
0
1
0
2
2
1
1
0
2
0
0
0
2
0
1
1
1
0
1
1
0
0
1
0
1
3
1
1
1
1
0
1
2
1
1
1
1
1
1
0
7
0
0
0
0
1
0
1
0
2
0
1
3
0
1
1
1
1
1
1
0
0
0
2
0
0
1
2
1
0
0
2
0
2
3
0
0
1
0
2
1
0
2
0
0
2
0
0
0
0
1
2
0
1
0
1
0
2
0
1
1
0
0
0
1
0
0
1
2
0
1
0
0
0
1
1
1
1
2
2
0
1
1
0
2
1
0
0
1
2
1
0
0
2
2
0
1
2
0
2
0
0
0
2
1
1
0
0
0
0
1
2
2
0
0
2
0
0
0
2
3
0
0
1
0
2
0
1
2
3
1
1
1
1
0
0
1
0
0
2
1
0
2
2
0
1
0
0
0
0
0
1
0
1
2
0
1
0
1
0
2
0
0
1
0
0
1
1
0
1
0
1
1
1
1
1
0
2
0
1
1
0
0
0
2
0
0
0
1
3
0
1
0
1
1
1
0
2
0
0
2
2
1
0
1
2
1
0
0
1
2
1
2
1
0
0
1
2
0
0
2
2
1
2
0
1
1
0
3
0
0
1
0
0
0
0
0
2
0
2
2
0
1
1
2
0
0
1
2
1
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
1
2
0
0
0
2
0
0
0
0
0
3
1
0
0
1
0
3
0
0
3
0
1
0
0
1
2
0
0
0
2
0
1
1
1
0
1
2
0
1
1
1
0
0
2
1
0
2
1
0
1
2
2
1
1
1
0
0
1
1
0
0
1
0
2
2
1
2
2
0
1
2
1
1
1
0
0
0
2
0
0
0
2
2
1
0
0
0
3
0
1
2
0
1
0
1
6
1
2
0
1
1
1
0
1
0
0
0
0
0
3
0
2
0
1
1
2
1
0
0
1
1
0
0
1
0
1
1
2
1
1
0
0
0
1
1
3
1
0
0
2
0
2
0
1
0
0
0
2
0
1
0
2
0
2
0
0
0
2
1
0
0
0
0
2
0
1
2
2
0
3
0
0
0
0
0
0
0
0
1
1
0
2
1
1
0
0
0
6
1
0
0
0
1
1
1
0
1
2
2
3
1
2
2
2
1
1
0
0
0
1
0
0
1
4
2
1
0
0
0
1
1
0
0
0
2
0
0
1
2
2
0
0
1
1
0
0
1
2
0
0
0
0
1
1
0
2
0
0
0
2
0
0
0
1
0
1
0
8
1
1
0
2
0
2
1
0
0
1
1
0
2
0
1
0
0
0
2
2
0
3
0
0
0
1
1
2
1
1
1
0
2
0
1
2
0
1
0
1
1
0
1
0
0
2
0
0
1
1
1
0
2
1
1
0
0
0
2
0
0
1
0
1
2
3
0
1
1
0
1
0
2
1
0
2
1
1
1
2
1
0
0
1
0
0
0
0
0
2
1
2
0
2
0
2
0
0
0
1
1
0
1
0
0
2
2
0
2
0
1
1
1
0
0
1
0
1
2
2
2
0
1
1
2
0
1
1
0
0
2
1
1
2
1
1
2
0
1
2
0
2
0
2
2
2
0
1
1
2
2
1
1
0
1
0
1
1
0
2
1
1
2
1
0
1
0
1
1
2
0
2
0
1
2
1
1
0
2
0
1
1
0
1
1
1
0
2
2
1
1
0
0
1
2
0
1
0
2
0
1
0
1
2
2
0
2
0
1
1
3
1
0
2
1
1
2
0
1
0
1
1
0
1
1
2
0
0
2
0
1
0
0
2
0
0
0
2
1
0
0
0
2
1
2
0
2
1
1
0
1
2
0
1
1
0
1
1
0
1
1
0
2
0
1
0
1
1
1
2
2
1
1
0
0
0
0
0
0
0
0
1
1
0
1
0
1
1
0
0
1
2
1
0
1
0
0
3
2
2
0
1
0
1
0
1
2
1
1
1
0
0
0
0
2
0
1
0
0
0
0
0
0
1
1
1
1
2
0
0
1
1
0
1
0
2
1
2
0
1
0
1
2
0
0
1
0
2
1
2
1
1
1
2
0
2
1
0
2
0
0
0
0
1
0
2
2
2
1
2
0
1
3
2
0
0
0
1
0
0
1
3
2
0
0
0
0
1
0
1
1
2
2
0
1
0
0
1
2
2
0
0
1
0
1
1
0
1
0
0
0
0
2
0
2
1
1
0
1
0
2
2
0
0
0
0
1
0
1
2
1
0
2
0
0
1
1
1
2
2
1
2
2
2
0
0
0
0
2
1
2
1
1
0
0
2
0
0
1
2
2
1
0
0
2
0
1
0
0
0
2
2
2
0
0
1
0
1
0
2
1
2
1
2
0
0
2
0
0
0
3
2
1
3
1
0
4
0
2
1
0
0
0
3
1
0
0
1
0
1
0
2
0
0
0
0
0
0
0
2
1
0
2
3
0
0
0
0
0
1
1
1
2
0
0
1
2
0
2
0
1
0
1
1
1
0
1
0
1
0
0
1
1
0
1
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
2
0
2
0
2
2
0
0
0
2
3
2
0
0
0
0
0
1
1
0
1
2
2
1
0
2
1
0
1
0
1
0
1
1
0
3
1
2
2
1
0
2
0
1
0
0
1
0
0
1
1
2
0
0
0
0
0
0
0
0
0
2
1
0
1
0
1
0
1
0
1
0
2
1
1
0
0
1
1
0
0
1
0
0
0
0
2
0
1
1
2
1
1
0
4
0
0
0
0
1
0
2
0
2
1
0
1
1
0
0
0
2
0
0
1
2
0
1
1
0
1
2
0
0
2
0
1
2
0
1
2
0
0
0
0
0
0
1
1
0
0
0
2
0
1
2
0
0
0
1
2
1
0
0
0
1
1
2
1
1
0
0
0
1
0
1
0
1
0
2
0
0
0
1
2
2
2
0
1
1
1
0
1
1
1
0
0
0
1
1
0
0
0
0
2
1
2
0
2
0
0
0
4
2
0
0
2
2
0
2
0
0
2
3
0
0
1
1
1
0
0
1
0
0
1
1
0
1
0
1
1
1
1
0
1
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
2
1
2
0
0
1
2
2
0
0
0
0
0
1
1
0
1
1
2
2
0
2
0
1
2
1
0
0
1
0
6
2
0
1
0
1
0
0
1
1
0
0
0
0
0
1
2
1
0
0
0
0
0
2
0
0
2
0
1
2
1
0
1
1
1
2
0
1
0
0
0
0
0
0
0
1
1
2
1
1
2
1
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
2
1
1
2
1
0
0
2
1
0
1
0
0
1
0
2
0
2
0
0
0
0
1
2
0
1
1
0
1
0
0
0
0
1
0
0
0
2
0
1
1
2
1
2
0
2
1
0
0
1
1
0
1
0
1
1
2
0
2
1
1
1
1
1
0
2
1
1
2
1
1
0
0
2
1
0
0
1
0
2
0
1
2
0
0
1
1
0
0
0
1
1
0
1
0
1
0
1
2
2
1
1
2
0
0
2
1
0
1
0
1
0
0
0
1
0
0
1
1
0
2
0
0
1
0
0
0
3
3
1
1
0
2
0
1
0
2
1
2
2
0
0
2
0
0
0
1
0
0
1
0
0
2
0
2
2
0
2
0
0
1
0
1
1
0
0
0
1
0
1
0
1
1
2
0
0
2
1
0
1
0
1
2
0
2
0
2
1
0
1
0
1
0
2
1
1
2
2
2
1
0
0
0
2
2
1
0
1
0
0
1
0
2
0
2
1
0
1
1
1
0
0
0
1
1
0
0
2
0
1
0
1
2
0
1
2
0
2
0
1
2
2
0
1
1
0
2
0
0
0
2
1
1
0
1
0
0
2
0
0
0
0
1
1
1
0
1
0
0
3
1
1
2
2
0
1
2
0
1
1
0
1
2
1
0
1
0
1
0
3
2
1
0
1
0
2
0
1
1
1
1
0
1
2
1
1
2
0
1
0
0
1
1
2
2
1
0
0
0
0
0
2
0
1
0
0
1
1
0
0
2
0
0
0
0
0
2
0
0
1
1
0
1
1
0
0
1
0
0
0
0
1
0
1
1
0
0
0
2
0
0
1
1
3
2
2
0
0
1
2
0
2
0
0
0
2
2
2
0
0
1
0
0
0
0
0
1
2
1
0
1
0
0
0
0
0
0
3
0
2
0
0
1
0
0
0
0
0
0
1
1
1
1
0
0
2
0
0
0
1
2
2
3
1
0
0
2
2
1
0
0
2
1
1
1
1
0
1
0
0
0
1
0
0
0
1
1
1
0
1
1
0
2
0
0
1
1
0
1
1
0
1
1
1
2
1
2
1
3
0
1
1
0
0
0
2
0
2
0
1
0
0
1
0
2
0
1
0
1
0
0
0
1
0
1
0
0
0
1
0
1
0
0
6
1
1
2
1
2
0
1
0
0
1
1
2
0
0
1
2
0
2
0
1
0
2
2
3
1
3
0
2
0
2
0
0
0
0
0
0
1
0
1
1
0
2
1
1
1
1
1
1
0
1
0
0
0
2
3
0
2
1
2
2
2
1
0
1
3
1
0
0
2
1
0
1
1
2
2
0
2
0
2
0
0
1
2
1
1
1
0
1
1
4
0
2
0
2
1
0
2
0
1
2
2
1
1
1
0
0
0
2
0
0
2
2
0
1
0
0
0
1
0
0
1
0
0
1
0
2
2
0
0
1
0
1
2
2
2
0
2
1
1
0
0
1
2
1
1
0
0
2
3
1
0
2
1
0
0
1
1
0
0
3
2
1
1
2
1
1
2
1
0
0
1
0
2
0
3
0
0
0
2
0
1
0
0
1
0
0
1
0
2
0
1
0
1
0
1
1
0
2
1
0
1
0
0
0
0
1
0
1
0
2
2
2
1
1
0
0
1
0
0
0
2
2
0
0
0
2
0
0
1
0
0
2
1
2
2
3
1
1
1
1
2
0
0
0
0
0
0
1
2
0
0
2
0
2
0
1
1
0
1
2
0
1
1
1
1
0
1
0
2
1
0
0
0
0
2
1
0
0
0
1
1
0
2
2
2
0
1
1
3
0
1
2
1
1
1
0
1
0
0
1
0
1
1
1
2
1
0
1
1
2
0
0
2
1
0
2
1
1
2
1
0
2
1
0
1
0
1
1
0
0
1
2
2
1
3
2
2
2
1
0
0
2
0
2
1
1
2
0
1
0
1
2
0
0
4
0
0
0
0
1
1
2
0
0
2
1
1
1
1
0
1
0
2
9
0
0
1
2
0
1
0
1
2
0
0
0
0
2
0
1
4
1
0
1
0
1
0
1
0
1
1
0
0
0
2
0
0
0
2
1
0
1
0
0
1
1
0
0
0
0
1
0
2
0
0
1
0
0
2
2
0
1
1
0
2
1
0
0
0
0
0
2
0
1
1
1
1
0
1
0
1
0
0
0
1
0
0
0
0
0
2
2
0
1
0
1
0
2
2
2
1
1
2
2
1
2
1
0
0
0
0
2
0
1
0
1
2
0
2
0
2
2
1
2
1
0
0
1
2
1
0
2
2
0
2
2
0
0
1
1
1
1
1
2
0
0
0
0
0
0
0
1
1
2
2
1
0
0
1
0
0
0
0
0
1
0
1
0
1
1
1
0
0
1
0
1
0
1
0
0
1
1
0
1
0
2
1
5
2
0
2
0
2
1
0
0
1
0
1
0
2
0
0
1
1
1
1
0
1
2
3
2
2
4
1
1
1
2
1
1
0
4
1
0
0
0
2
2
0
2
0
1
0
0
1
4
2
2
1
1
0
1
0
0
0
0
1
1
0
1
0
0
0
0
2
3
0
0
0
2
2
0
1
2
0
1
0
0
1
1
2
0
1
0
2
0
1
0
1
2
1
0
0
0
0
1
3
0
1
1
0
0
0
0
2
0
2
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
1
1
1
0
2
1
0
0
2
1
3
0
2
1
0
0
1
1
0
0
2
1
0
0
2
1
1
0
2
1
2
0
2
0
0
1
0
1
0
1
2
2
0
2
1
0
0
1
0
0
2
2
1
0
0
2
1
0
3
0
1
1
0
0
4
4
1
0
0
1
2
1
1
0
1
2
1
1
2
2
1
0
0
0
1
0
0
1
2
1
2
0
2
1
0
0
1
1
0
0
1
3
0
2
0
2
0
1
0
1
0
1
0
0
2
1
0
2
0
0
1
0
0
2
2
2
1
1
1
4
1
0
0
2
2
1
1
0
0
0
1
1
0
0
2
1
2
0
0
3
1
2
0
2
1
1
0
0
0
1
0
1
2
0
1
1
1
0
0
1
1
1
1
0
0
1
0
1
1
0
0
0
0
2
2
0
1
0
1
1
2
2
0
0
2
1
0
1
1
2
0
0
0
0
0
0
1
0
1
1
0
2
0
3
0
2
0
1
0
1
0
0
2
1
0
2
0
1
2
1
1
0
0
0
0
0
0
0
0
0
4
1
1
1
3
0
2
2
1
1
2
1
2
0
0
0
0
0
0
1
1
2
2
1
0
1
0
1
5
0
2
0
0
0
0
0
2
1
0
1
2
3
5
0
0
2
1
1
1
2
1
2
1
2
0
0
2
0
0
0
0
0
0
0
1
1
2
2
0
0
2
0
1
0
1
0
2
1
0
1
0
0
2
1
2
1
2
0
0
2
0
0
3
0
1
1
1
0
2
0
0
1
1
1
0
0
2
1
0
1
1
0
0
0
1
2
1
1
1
1
2
1
0
0
1
1
0
0
1
0
1
1
0
2
0
0
1
1
1
1
0
2
1
0
0
1
1
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
2
2
0
0
0
0
1
1
0
2
0
0
0
1
0
1
1
2
1
1
2
2
1
0
1
1
0
1
0
0
0
1
0
1
0
0
2
0
0
0
0
2
0
0
1
1
0
0
0
0
0
2
2
1
1
2
0
0
1
0
0
0
1
1
0
1
1
1
0
2
2
2
0
0
1
0
2
1
0
1
0
1
2
2
1
1
1
2
2
0
0
1
1
1
0
0
2
1
2
2
1
2
2
1
0
1
0
0
1
1
2
0
2
0
2
1
2
1
0
3
1
2
0
2
2
0
2
1
1
0
1
1
2
0
0
0
1
0
0
2
0
0
1
0
1
0
1
1
1
2
1
3
2
0
0
0
1
2
1
3
2
0
0
0
2
2
0
0
0
0
2
0
0
0
0
1
2
3
0
1
1
2
1
0
0
0
3
1
1
2
1
2
0
1
1
0
1
1
0
0
0
2
0
1
1
0
1
2
3
0
1
1
0
1
1
1
1
0
0
0
0
0
0
2
0
0
1
0
3
0
0
0
2
0
1
2
0
1
0
0
1
0
0
2
0
0
0
2
1
2
2
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
2
1
2
0
2
0
0
1
1
0
0
1
2
0
2
2
0
1
0
1
0
0
0
2
0
0
0
0
0
1
0
0
1
1
2
0
0
2
0
1
1
0
1
3
1
0
0
2
0
1
0
1
1
0
1
1
0
1
2
2
1
0
1
0
0
0
1
0
0
0
0
0
1
2
0
1
1
2
1
2
0
0
2
2
0
1
0
0
2
1
0
0
0
1
0
1
2
0
2
0
2
2
1
1
2
0
0
0
1
0
1
0
1
0
1
0
0
1
1
0
1
1
0
1
0
0
1
0
2
1
2
0
0
1
0
1
0
1
1
2
2
1
0
2
0
1
0
2
0
2
1
1
0
0
2
2
1
0
0
1
1
0
1
0
0
2
0
0
0
0
0
2
0
0
0
2
1
1
1
0
1
0
1
0
1
1
0
0
2
0
0
0
0
1
2
2
2
0
0
0
0
3
0
0
1
0
0
1
1
1
0
2
0
0
0
1
0
1
2
2
0
1
1
0
2
2
1
0
1
1
2
2
0
1
1
0
0
0
0
0
1
0
0
0
0
0
3
2
0
2
1
0
1
0
2
0
0
2
0
2
2
2
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
1
1
1
1
1
2
2
2
0
0
1
1
1
1
1
1
1
1
0
0
0
0
2
0
2
2
1
2
0
0
1
0
1
1
0
2
2
0
1
1
0
1
0
1
0
0
0
4
0
0
2
0
0
2
1
0
0
2
1
0
6
2
1
1
2
0
0
1
0
1
2
0
1
2
1
0
0
1
0
1
1
0
2
2
1
0
0
0
1
0
0
2
1
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
1
1
2
2
1
0
2
2
2
1
0
0
0
0
2
0
1
1
0
2
0
3
1
0
1
0
2
0
0
2
0
2
0
0
0
2
0
2
0
0
2
0
2
1
1
2
2
1
0
0
0
3
0
1
1
0
0
2
0
0
2
0
0
0
0
0
2
1
1
2
1
0
1
3
2
0
0
0
2
1
1
0
3
0
1
1
0
0
1
1
1
0
0
0
0
1
2
1
1
2
2
0
1
0
0
1
2
1
0
1
0
1
0
1
0
0
1
0
0
0
1
2
0
2
0
0
1
0
2
0
0
2
0
1
0
0
1
0
0
0
2
2
0
0
0
0
1
2
0
1
0
2
0
0
0
1
2
1
3
0
0
1
0
0
0
1
0
0
1
1
2
2
0
0
0
0
1
0
2
0
0
1
0
2
0
0
1
1
1
1
1
1
1
0
2
0
0
2
0
2
1
0
0
1
1
2
0
0
0
1
0
2
4
0
1
2
0
2
0
0
2
1
1
0
0
0
2
5
0
0
0
1
1
0
0
0
2
0
1
0
1
0
0
1
5
1
2
0
2
0
2
0
0
0
0
1
0
0
1
0
0
1
2
1
1
0
0
0
1
0
2
0
0
1
0
0
0
1
1
1
0
0
0
0
0
2
0
7
1
1
0
0
1
2
0
0
0
1
1
0
2
2
0
0
0
0
0
1
0
1
1
2
0
0
2
3
1
2
2
2
2
1
1
1
1
1
0
2
2
2
1
1
1
1
0
0
0
2
0
2
1
1
2
0
1
1
1
0
0
0
0
0
2
0
1
0
1
0
0
0
0
1
0
1
0
2
1
0
0
0
0
0
1
1
0
2
2
1
0
0
2
0
1
1
0
1
2
0
1
2
0
1
3
2
0
1
1
1
0
1
0
1
1
0
0
0
0
1
0
1
2
0
1
0
1
0
1
3
1
0
0
2
0
2
3
0
0
2
0
2
0
1
0
0
0
0
2
0
2
0
1
0
1
1
0
0
0
0
0
1
0
1
0
0
2
0
1
2
0
2
0
0
2
0
1
1
4
0
2
0
0
2
3
1
2
0
1
2
0
1
1
0
2
1
2
0
0
1
1
1
0
0
2
1
3
1
0
0
2
0
0
0
0
1
0
0
0
0
0
2
1
0
1
2
0
1
1
0
1
1
1
1
1
1
0
1
1
2
2
2
1
2
1
1
0
0
1
1
2
0
3
2
0
1
0
2
0
1
0
1
1
0
1
0
0
1
0
3
1
1
2
0
0
0
0
0
1
0
2
1
1
2
0
1
2
0
1
1
1
1
0
0
0
0
0
0
1
1
0
0
0
3
1
0
2
1
0
0
2
1
0
0
0
1
0
0
0
0
0
0
1
1
1
2
0
2
2
1
0
0
1
1
1
1
2
2
1
2
2
0
2
0
0
1
0
0
2
0
1
0
0
2
1
1
0
0
1
0
1
2
0
1
1
0
1
1
1
0
0
0
2
1
1
0
2
0
0
1
2
0
2
1
2
1
0
1
2
1
2
0
0
0
1
1
0
0
0
0
2
0
1
2
2
2
2
0
2
0
0
2
1
1
0
2
1
0
1
0
0
0
1
1
1
0
1
1
1
1
2
0
0
0
0
0
0
1
1
2
0
0
0
1
2
2
2
0
0
2
0
2
1
1
0
1
1
0
2
1
0
1
0
1
0
0
1
0
1
0
1
1
1
1
1
1
1
1
1
0
0
0
1
1
1
1
0
1
0
1
0
0
2
2
0
1
0
0
3
0
1
2
0
2
2
0
1
1
0
0
2
0
2
0
0
1
0
2
0
0
0
0
1
0
2
0
1
1
1
1
0
0
0
2
1
0
0
0
0
0
0
0
1
1
0
1
3
0
0
0
1
0
0
1
1
0
0
0
0
2
1
0
1
3
0
1
0
1
1
1
1
1
1
2
0
0
2
2
1
1
0
0
1
2
0
1
0
0
1
2
0
1
1
1
0
0
0
2
0
1
2
1
1
0
0
0
2
0
1
1
0
0
2
0
2
0
0
0
0
0
1
0
2
2
0
1
0
1
1
2
1
0
0
1
1
0
1
1
0
0
0
0
1
1
1
1
1
1
0
1
1
1
0
0
1
2
0
0
1
0
1
2
0
1
0
0
1
0
0
1
0
0
1
0
0
1
0
1
1
1
1
0
0
0
1
0
0
1
2
0
0
2
0
1
0
1
1
0
0
0
1
2
0
1
2
2
1
0
0
0
0
2
1
0
2
2
2
0
1
1
0
2
1
0
2
2
0
0
0
2
2
1
0
2
1
0
0
2
0
0
1
2
1
0
2
1
0
2
0
0
0
0
2
2
1
2
0
0
0
2
3
0
0
0
0
2
0
1
0
1
0
0
0
1
2
2
0
1
1
1
1
1
0
0
0
2
0
1
0
2
0
0
1
0
1
1
0
0
0
0
1
1
3
2
2
2
1
0
0
0
1
0
2
1
0
0
1
0
1
1
0
1
0
0
1
1
0
1
1
0
2
0
1
0
0
0
1
0
1
0
2
2
1
2
1
0
1
1
0
1
1
0
2
0
0
0
2
2
2
1
1
1
1
1
0
1
1
1
1
0
2
0
2
0
0
0
1
1
1
0
0
0
0
2
2
0
0
1
2
1
2
0
2
0
0
0
1
1
1
1
0
2
2
1
0
2
0
0
2
0
0
0
0
1
3
0
1
0
0
0
2
2
10
0
0
0
2
2
0
1
0
0
0
0
3
1
1
1
1
0
2
1
0
2
0
0
2
1
2
1
0
0
0
2
1
1
1
1
0
0
0
0
0
1
0
0
0
2
1
0
1
2
0
0
2
2
1
4
0
2
1
0
2
2
0
0
1
0
0
2
0
0
1
0
3
2
1
1
0
1
0
0
0
1
1
2
1
0
2
0
0
0
0
0
1
2
2
1
0
0
1
1
0
3
0
1
2
2
1
0
0
0
2
2
0
1
0
0
2
0
0
0
1
1
1
2
1
0
0
1
2
1
4
2
0
0
1
2
1
2
2
0
1
2
2
2
2
2
0
0
1
0
0
0
1
2
1
0
0
0
2
0
0
1
0
0
2
0
2
1
2
3
1
5
1
1
0
0
1
1
0
0
0
3
1
0
1
2
0
1
1
0
1
0
0
0
1
2
0
1
0
0
1
1
1
0
0
1
1
1
1
0
0
1
0
0
1
2
2
0
1
0
2
0
1
1
0
1
0
0
3
1
0
1
1
0
0
1
0
1
0
0
1
2
0
0
1
1
6
2
0
0
0
0
1
0
0
0
0
1
0
2
0
1
0
1
0
0
0
2
1
2
1
0
0
0
2
0
0
1
0
2
2
2
2
0
1
1
1
2
1
0
0
0
0
1
3
0
0
1
0
0
1
0
0
2
0
0
1
1
0
1
0
0
0
0
2
0
0
1
0
0
0
1
0
0
2
2
1
0
2
0
1
0
0
0
1
2
1
0
2
2
0
1
2
2
1
1
0
0
0
0
0
1
0
1
1
1
0
1
2
0
0
1
0
2
0
0
1
2
0
0
0
0
1
0
1
0
0
0
0
2
1
1
1
0
0
1
3
1
0
1
1
0
2
0
0
0
0
0
0
0
0
2
2
1
1
1
2
0
0
0
1
0
0
1
1
1
1
0
1
0
2
2
0
2
1
0
1
1
0
0
2
1
0
1
3
0
0
0
0
0
1
0
0
0
2
0
2
1
1
2
1
1
0
2
1
2
0
1
1
1
2
0
0
1
0
0
1
3
1
0
2
0
2
1
1
1
2
0
0
1
1
1
2
0
0
0
2
1
0
2
0
0
0
1
1
1
1
1
2
0
1
2
2
0
0
1
0
1
0
0
0
0
0
2
0
2
0
1
0
0
1
1
2
0
0
1
2
2
1
0
0
0
0
0
0
0
0
1
1
2
1
2
0
1
1
2
2
1
0
0
1
1
0
1
0
2
0
1
0
0
0
2
0
0
1
1
2
1
1
0
1
2
2
2
1
0
1
1
2
0
1
2
0
0
0
0
2
0
1
2
1
1
0
0
2
0
1
0
2
1
0
0
1
1
0
1
0
0
0
0
0
0
1
3
0
0
1
0
1
0
0
0
1
0
0
1
2
1
0
0
0
1
1
1
0
0
2
0
0
1
0
0
0
0
0
1
1
0
1
1
1
1
1
0
1
0
0
2
2
2
2
0
0
0
0
0
1
0
1
1
1
2
1
0
0
0
1
1
0
2
0
2
1
0
0
0
2
1
1
2
0
0
1
1
2
0
0
0
2
2
0
0
0
0
0
2
0
1
0
1
0
0
1
0
0
1
2
0
2
1
0
1
0
0
2
0
1
2
3
1
0
1
1
0
2
0
0
4
1
1
0
0
0
1
2
1
0
1
0
0
1
0
0
2
3
0
0
1
0
1
0
1
0
2
0
0
2
2
0
0
2
3
0
1
0
1
1
0
1
2
0
0
2
1
2
0
0
1
1
2
1
0
0
1
0
1
0
0
0
1
1
0
4
1
0
0
1
0
1
1
2
1
0
1
0
1
1
0
0
1
1
0
1
0
1
0
0
1
2
1
2
0
0
1
2
0
1
0
0
0
1
0
0
4
0
1
3
0
0
1
0
0
2
2
2
2
0
1
0
1
0
1
0
0
2
0
0
3
0
0
0
2
0
2
2
0
0
1
1
0
0
0
1
1
0
2
0
1
2
2
1
0
1
1
1
0
0
0
1
2
0
0
0
1
0
0
0
1
2
0
2
1
0
0
1
1
2
0
1
2
1
1
0
2
0
2
0
0
0
1
0
2
1
1
1
2
0
1
0
0
1
0
1
0
1
1
1
0
1
1
0
0
1
3
2
0
1
2
0
2
1
0
1
1
0
1
0
0
2
1
0
1
1
3
1
2
0
1
1
2
0
1
1
1
0
1
0
2
0
0
1
0
0
0
1
1
1
2
1
2
0
0
2
2
0
0
2
1
2
1
2
2
0
0
0
1
1
0
0
0
2
1
0
0
2
0
2
0
2
2
0
0
0
0
0
0
0
2
2
1
0
0
1
0
0
0
0
1
3
0
2
1
2
2
0
0
1
0
0
0
1
0
1
1
0
0
1
1
2
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
1
0
0
1
0
1
0
2
2
1
0
4
1
2
1
1
2
0
0
0
0
1
0
0
1
2
1
0
1
2
0
2
2
1
1
1
0
0
2
1
0
1
0
0
0
0
0
0
1
2
1
2
2
0
0
1
0
0
2
1
0
0
0
0
0
1
0
2
0
0
0
1
0
1
2
0
1
0
0
2
1
0
0
3
0
0
0
0
1
0
0
0
1
2
0
2
2
0
2
0
0
1
0
2
1
0
1
0
3
0
0
2
0
2
2
0
1
1
0
0
1
1
1
0
0
0
0
1
1
1
0
1
1
1
1
1
2
1
0
1
0
0
2
1
1
2
0
0
0
2
1
1
2
0
0
2
0
2
0
0
2
1
0
0
1
0
0
1
0
0
0
2
3
0
2
0
0
2
2
0
0
0
2
2
1
1
1
0
1
2
2
0
1
1
0
1
2
0
0
0
0
0
0
0
2
0
1
2
3
3
0
1
0
0
0
2
0
0
1
1
0
0
2
0
2
5
2
0
0
1
1
1
0
2
1
0
1
0
1
1
0
1
1
0
0
0
0
1
1
0
0
1
0
1
0
2
1
0
1
0
0
2
1
2
0
2
0
0
0
0
0
1
1
0
0
1
0
6
0
4
1
1
0
1
1
1
2
1
1
1
2
1
2
1
2
1
0
0
1
2
0
2
0
0
0
1
1
0
0
0
1
3
2
0
1
2
1
2
0
0
0
1
2
2
0
0
0
4
0
2
0
0
0
0
1
1
2
1
0
0
1
0
1
1
0
2
0
1
2
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
1
0
1
2
1
0
0
1
1
0
3
0
0
0
2
0
1
0
2
2
0
2
2
0
0
2
0
0
1
0
1
2
1
2
0
2
0
2
1
0
1
0
2
0
1
1
0
0
1
1
2
0
1
1
2
1
1
0
0
2
3
2
1
1
1
0
1
2
1
1
0
1
1
2
0
2
1
0
1
1
0
1
0
0
0
0
0
1
0
2
0
0
3
1
0
0
1
0
2
0
0
1
0
0
2
1
1
1
0
0
1
0
1
2
0
2
1
0
2
1
0
0
1
2
2
1
2
2
0
0
0
0
1
1
0
1
1
2
2
2
1
0
1
0
0
0
0
1
2
0
1
0
1
1
2
1
0
0
2
0
0
0
1
0
0
1
0
0
2
1
1
0
0
1
2
1
0
1
0
2
1
0
2
0
1
2
0
1
1
0
0
0
0
1
0
1
0
0
1
0
0
1
0
1
2
2
0
0
2
0
2
0
0
1
0
1
2
1
0
2
1
0
0
1
0
2
2
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
8
0
1
1
1
1
0
0
0
1
2
1
0
0
2
0
2
1
1
1
0
0
1
0
1
1
1
2
0
2
1
1
0
1
1
0
1
0
0
1
0
2
2
2
1
1
2
2
1
3
1
0
1
0
0
2
0
1
0
1
2
1
0
0
2
0
0
0
0
1
2
0
2
1
1
1
0
0
1
2
0
1
1
0
2
0
0
2
0
0
2
0
0
0
2
0
0
0
1
3
1
1
0
0
0
0
1
0
1
3
0
0
0
3
2
0
0
0
1
0
1
1
0
0
0
1
1
0
1
1
2
2
0
2
2
0
1
0
0
2
0
2
0
1
1
1
1
1
0
2
1
0
1
2
2
1
0
1
2
0
1
2
0
1
1
0
1
1
1
1
3
0
0
0
0
0
1
0
1
0
1
1
0
0
0
1
0
0
5
0
1
1
2
0
1
0
1
0
0
1
0
0
2
2
2
2
1
0
0
0
1
0
0
1
1
0
1
1
0
1
2
2
1
2
0
0
1
0
2
1
0
1
0
0
2
0
0
1
1
0
0
1
2
2
0
2
0
0
0
1
1
1
2
1
2
0
0
2
0
1
0
0
0
1
0
2
2
0
2
1
2
2
1
1
1
1
0
1
0
1
2
0
0
2
0
1
2
1
1
1
2
0
0
1
0
1
0
2
2
0
2
1
1
0
1
2
2
0
2
0
0
0
1
1
2
0
0
0
0
0
0
0
2
0
2
1
2
2
1
0
3
0
0
0
0
0
1
0
1
0
1
1
0
0
2
0
1
0
2
1
0
0
1
2
1
0
1
0
0
0
0
0
1
0
1
2
1
0
2
2
0
0
0
1
0
0
2
0
2
1
0
1
0
0
0
1
0
2
0
1
1
0
1
0
0
2
1
0
1
3
2
0
0
0
0
0
1
1
1
2
2
0
0
1
0
0
2
1
0
2
1
0
0
0
1
1
0
2
2
0
0
1
2
1
2
0
1
2
2
0
0
0
1
0
1
0
2
1
1
1
1
1
0
2
1
2
0
2
0
0
0
0
3
1
1
2
0
0
2
0
3
2
0
1
0
0
0
1
1
2
0
0
0
1
2
2
1
0
0
0
1
0
0
0
1
1
0
0
0
1
1
1
0
1
0
0
2
2
0
0
0
1
1
0
0
2
0
1
2
0
0
1
0
1
1
0
1
2
1
0
2
1
0
1
0
1
4
2
0
3
0
2
0
0
0
0
0
2
0
1
0
0
2
0
0
0
1
2
0
1
1
2
0
2
0
2
0
0
0
7
2
1
0
0
1
0
0
1
1
2
2
0
1
1
1
2
2
1
1
2
1
1
1
1
2
2
2
1
0
1
0
1
1
0
1
0
0
0
2
0
1
0
2
0
1
1
2
0
1
0
0
2
1
0
2
1
0
1
0
0
0
2
2
2
0
1
0
0
0
0
2
2
1
1
0
2
0
0
0
2
0
1
2
0
0
1
0
2
0
0
1
0
0
2
0
1
0
0
2
1
1
1
1
0
0
1
0
0
1
2
0
1
2
1
1
1
2
1
1
0
2
0
0
1
1
1
1
1
0
1
0
1
5
0
2
1
1
1
0
0
2
2
0
1
0
1
0
1
0
1
0
0
0
0
0
2
0
1
0
3
0
1
2
2
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
2
1
1
1
2
0
0
0
2
0
0
0
0
0
0
2
2
0
0
3
1
1
0
0
0
0
2
1
2
1
1
3
2
1
1
1
0
0
2
1
2
1
1
3
0
0
0
0
1
0
0
0
2
1
2
0
0
0
0
0
0
2
1
1
1
0
2
0
1
0
0
1
0
0
2
1
0
2
0
0
1
2
0
0
2
0
1
3
1
0
1
0
1
0
2
0
1
0
2
0
1
2
1
2
2
1
0
1
2
0
0
0
2
1
1
1
1
0
1
2
0
1
2
1
2
0
2
1
2
0
2
0
1
0
0
2
0
0
1
0
1
1
2
0
1
0
0
2
1
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
1
0
0
1
2
2
0
0
1
1
1
0
0
1
1
0
1
2
2
2
0
2
0
0
0
2
1
1
0
2
2
0
2
0
0
1
0
0
1
0
1
0
2
2
1
0
0
2
2
0
1
1
1
0
0
3
2
0
0
1
0
2
2
0
1
2
0
1
0
1
2
0
0
0
0
1
2
0
2
0
0
0
1
0
0
1
0
1
2
0
1
0
2
3
1
2
1
0
1
2
0
1
0
0
2
0
2
2
2
0
0
2
1
0
0
1
2
1
2
0
3
0
2
1
1
0
1
0
0
2
0
0
1
0
0
0
0
0
2
1
1
1
2
2
1
0
0
0
1
1
0
0
2
1
0
1
1
1
0
0
0
0
1
0
1
2
0
1
2
1
2
0
0
0
0
1
2
2
0
0
1
0
0
2
3
2
0
0
0
0
1
2
1
2
2
0
1
1
0
1
2
0
1
1
0
0
2
2
0
0
0
2
0
1
2
0
2
2
2
1
2
0
0
1
3
0
2
0
1
0
0
0
1
0
0
2
0
1
0
1
0
2
0
0
2
1
2
1
1
0
2
0
0
1
0
0
1
1
0
2
1
0
1
0
0
0
0
0
2
0
0
3
0
2
1
0
1
1
0
0
1
1
1
1
0
2
1
2
0
1
0
0
0
2
0
1
0
1
0
0
2
0
2
1
0
0
1
0
0
0
1
1
1
2
1
1
0
0
1
0
2
0
0
1
1
0
1
2
1
2
0
1
0
1
0
0
3
1
0
1
0
1
0
2
0
0
0
1
0
2
0
1
0
1
0
1
1
2
2
1
1
0
2
1
1
0
0
0
3
0
0
1
1
0
1
0
1
2
0
1
0
0
1
0
0
1
1
0
1
1
0
1
0
2
6
0
1
0
0
2
1
0
2
2
0
2
0
0
2
1
0
1
0
1
1
2
0
0
2
1
1
1
0
1
1
2
1
0
0
0
0
1
0
0
0
2
1
2
1
2
0
1
0
3
2
1
0
0
1
0
1
1
2
0
1
0
2
0
0
1
0
1
0
0
0
7
1
2
0
0
0
2
2
1
0
0
1
2
2
0
1
2
1
1
1
2
0
1
0
3
1
1
0
1
1
1
2
0
1
2
0
1
4
1
2
0
0
0
2
1
1
0
2
0
1
1
1
0
0
2
1
3
1
0
0
2
1
2
0
2
0
1
0
1
0
1
2
1
0
0
0
1
1
2
1
2
1
1
1
0
0
0
0
0
0
1
0
2
3
0
0
0
2
0
1
0
1
0
0
0
0
0
0
1
2
3
0
0
0
0
0
1
0
0
1
2
0
1
0
1
0
1
2
2
1
2
0
0
0
1
1
1
2
1
0
1
1
1
0
3
0
2
0
0
0
0
1
0
1
1
0
0
0
2
4
0
1
0
0
0
0
0
1
1
1
2
1
0
0
0
0
1
0
1
1
2
1
2
0
0
1
0
1
2
0
2
1
0
1
2
2
2
2
0
1
0
1
0
0
0
1
1
0
1
0
0
0
2
2
0
1
0
1
2
1
0
2
2
0
0
2
1
0
0
1
0
2
1
2
1
0
1
0
2
1
1
2
2
0
2
1
1
0
0
0
2
0
1
0
0
0
1
2
0
1
0
1
0
1
1
0
0
0
0
1
1
1
0
2
1
2
0
2
1
0
0
1
2
1
0
1
2
1
2
0
0
2
0
0
2
0
0
0
1
1
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
6
0
2
0
1
1
0
1
1
2
1
1
1
1
0
0
1
1
0
0
0
1
1
1
0
1
0
2
1
2
0
0
1
1
0
2
0
2
0
0
1
1
0
0
0
0
1
0
0
0
1
0
2
0
2
0
1
1
0
1
0
0
2
1
0
2
0
2
1
0
2
1
0
0
1
0
1
0
1
0
1
2
1
1
0
2
0
2
2
0
2
0
0
0
1
1
1
1
3
1
0
0
2
0
1
0
0
2
0
0
0
1
1
1
3
0
2
0
0
0
1
1
2
2
0
1
2
2
1
1
1
2
0
0
0
0
1
0
0
0
0
1
0
1
1
0
2
0
1
1
1
0
2
1
1
0
0
0
0
0
0
1
0
2
0
0
0
2
0
4
0
1
0
0
1
2
2
0
0
1
1
1
1
0
0
2
2
1
0
0
0
1
2
0
0
0
2
0
2
2
0
2
1
2
0
0
0
0
1
0
2
0
0
2
0
2
1
2
1
0
0
0
0
2
0
0
1
0
1
0
0
0
0
2
2
0
2
1
0
0
0
0
0
1
0
1
0
2
0
1
2
0
1
0
2
2
2
0
1
2
1
1
0
0
0
0
0
1
2
2
0
1
0
0
1
1
0
0
1
0
0
1
1
1
0
1
0
1
2
2
2
1
0
0
2
0
0
1
2
1
0
2
0
1
1
1
2
2
1
0
0
0
1
1
1
1
1
1
0
0
1
0
0
0
0
1
0
1
1
0
1
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
1
1
0
1
1
1
1
2
1
2
1
1
1
1
1
0
0
1
0
3
2
1
0
1
0
0
0
1
2
1
0
1
1
0
0
0
1
2
2
1
0
2
0
0
1
0
0
0
2
1
0
2
0
1
0
1
0
0
0
1
2
2
1
2
0
0
0
0
3
0
0
2
0
3
0
1
0
1
0
0
0
0
2
1
1
2
0
1
2
0
1
0
0
1
2
2
1
1
1
0
0
2
0
0
1
1
0
0
2
1
2
1
0
1
1
1
0
0
0
0
1
1
0
1
2
0
0
0
0
7
0
0
2
1
2
2
0
2
1
0
1
2
0
2
1
0
1
1
1
0
0
2
1
0
1
1
1
0
1
0
2
1
0
2
1
0
1
0
0
2
1
0
0
1
1
1
0
1
0
2
0
1
1
0
2
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
2
1
3
1
1
0
1
1
0
2
0
1
3
1
0
0
0
0
0
0
0
2
2
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
1
0
2
2
1
1
0
0
0
0
1
0
1
0
1
2
0
0
0
0
0
1
1
1
6
1
2
2
1
0
0
1
0
0
3
2
0
1
2
1
2
0
2
1
1
2
1
0
2
0
0
0
0
0
0
2
0
1
2
1
1
1
2
1
2
1
0
2
2
0
0
1
0
0
1
0
1
2
0
2
2
1
1
0
0
0
1
1
2
0
0
0
2
1
1
2
2
0
0
0
0
1
1
0
0
2
0
0
1
1
0
2
0
0
1
0
0
0
1
1
2
2
1
0
1
1
0
2
1
2
2
1
2
1
0
0
0
0
1
0
3
1
2
0
2
0
0
1
2
1
0
0
0
0
1
0
0
1
0
2
0
1
2
0
0
1
1
0
0
1
2
0
0
2
0
2
0
2
0
0
2
0
4
2
0
0
0
1
1
1
2
1
0
1
5
2
0
0
0
0
1
0
0
0
2
0
1
2
1
0
0
1
2
0
0
1
1
1
0
1
2
0
0
0
0
0
1
1
1
0
1
0
2
0
0
2
2
0
0
1
1
0
0
1
0
1
0
1
1
2
0
0
0
2
0
1
0
2
2
1
0
0
1
1
2
1
0
2
2
1
1
1
0
1
2
0
1
1
0
1
2
1
2
2
0
1
0
1
0
0
0
2
0
0
1
2
1
0
1
4
1
1
1
0
1
1
0
1
2
2
0
0
1
1
0
0
0
0
2
2
0
1
1
1
1
2
1
1
1
0
2
1
0
2
0
1
1
0
4
0
2
2
0
2
2
1
0
1
2
0
1
0
1
1
1
1
1
0
1
0
1
1
0
1
0
1
0
0
1
0
1
1
0
2
0
0
1
1
1
2
0
2
0
1
2
2
2
0
1
0
1
0
0
1
1
2
0
2
1
0
0
0
0
2
0
2
0
0
1
1
2
0
2
2
0
0
0
0
1
0
0
2
1
1
2
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
2
0
2
1
0
1
1
1
1
1
1
0
2
1
0
0
0
0
0
0
1
0
3
1
0
2
0
1
2
1
1
2
0
0
0
2
1
1
2
1
0
2
1
0
1
0
0
0
1
1
1
1
0
1
0
0
0
0
2
2
0
2
2
1
0
0
1
0
2
1
0
1
1
0
0
2
0
0
5
2
0
0
0
0
0
0
2
0
2
0
1
2
0
2
2
0
2
0
0
1
0
0
0
2
1
0
2
2
0
2
0
1
1
0
0
0
0
1
2
1
0
2
2
2
0
1
0
0
0
1
0
0
2
2
2
1
1
2
0
1
1
1
2
0
0
0
1
0
1
0
2
0
2
2
2
1
0
0
0
2
1
0
2
2
2
0
0
2
0
0
2
1
1
1
1
0
0
0
0
0
1
0
0
2
1
1
0
3
1
0
0
2
0
1
3
1
0
0
1
0
0
1
1
0
2
0
0
0
0
1
1
2
0
0
2
0
0
0
1
0
0
0
1
1
0
0
2
2
0
2
0
1
0
1
0
0
0
2
2
2
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
1
0
0
0
1
0
0
2
2
2
2
1
1
0
1
0
0
0
0
2
0
1
0
0
0
0
5
0
1
1
1
1
0
0
1
1
2
0
0
3
0
1
0
1
2
1
0
3
1
2
0
2
0
2
0
0
2
1
0
0
1
2
0
0
0
1
0
1
1
2
0
1
0
1
0
0
0
0
1
2
2
0
0
1
0
2
1
0
0
0
1
1
5
1
2
1
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
2
0
0
0
0
1
0
2
1
0
1
1
0
0
0
0
0
0
2
0
0
0
1
1
2
0
0
0
2
1
1
0
0
0
1
1
1
0
0
1
2
1
0
0
0
1
0
1
0
1
0
0
0
0
2
2
1
0
2
1
0
0
1
1
1
2
0
0
0
0
1
2
0
0
2
1
2
1
0
1
2
0
1
0
1
0
2
0
0
0
0
1
3
0
1
0
1
0
0
1
0
0
2
1
0
0
1
1
2
1
2
2
1
2
2
0
1
3
0
2
2
1
1
1
0
0
0
1
0
2
0
2
0
0
0
1
1
1
0
0
0
0
0
2
0
2
0
0
2
1
3
0
1
0
3
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
2
0
0
1
0
1
2
0
0
2
0
1
0
2
0
0
0
0
2
2
0
2
0
0
0
1
1
0
2
0
1
0
2
2
0
0
0
0
0
0
0
1
0
1
0
2
0
0
2
2
0
0
0
2
2
2
0
0
0
0
1
0
2
0
0
1
0
0
1
1
1
0
0
1
1
1
0
1
0
3
2
0
1
0
2
0
1
0
2
1
0
1
0
1
2
0
1
2
1
0
1
0
1
0
0
1
2
1
2
1
0
3
0
0
1
0
0
2
2
0
0
2
0
1
2
0
2
2
0
0
0
0
0
1
2
1
0
2
1
1
0
0
0
0
0
0
1
1
1
1
3
0
0
0
1
2
2
1
0
0
0
0
1
0
1
1
1
0
0
1
0
0
1
0
0
1
0
1
1
0
1
2
2
1
2
2
2
1
0
1
0
0
1
0
0
1
1
0
2
1
0
0
0
0
1
0
0
2
0
0
2
2
1
0
0
0
1
1
0
1
0
0
0
2
0
2
0
0
0
0
2
0
0
0
2
1
0
1
1
0
0
0
0
1
1
0
0
1
2
0
0
0
2
1
0
1
1
0
2
1
0
1
1
2
1
1
1
1
0
1
1
1
2
0
2
1
1
1
2
1
1
0
0
1
1
2
2
0
2
2
1
0
1
0
2
1
0
1
1
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
1
0
2
0
2
0
1
0
2
2
0
2
1
1
1
1
2
1
2
0
1
0
0
0
1
2
0
1
1
0
0
2
1
0
1
1
0
0
2
0
2
1
0
2
1
2
2
1
0
0
2
1
2
0
4
1
3
0
1
1
0
0
1
0
1
0
0
0
2
1
0
1
1
0
0
1
0
0
1
1
0
0
0
1
1
1
0
0
0
0
1
0
1
1
1
0
0
2
0
1
0
1
1
0
0
1
1
0
2
0
0
0
0
0
1
2
1
1
0
1
0
1
1
0
0
3
0
2
0
2
0
2
0
2
2
0
2
0
0
0
0
1
2
1
1
1
0
0
1
0
1
2
2
1
1
2
0
0
1
1
0
2
1
0
1
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
2
0
2
2
0
2
1
0
0
2
0
0
2
0
1
0
0
2
0
2
2
1
0
1
0
0
0
1
3
1
0
0
0
1
0
0
2
1
0
1
0
1
2
0
1
2
0
1
0
2
0
1
1
0
0
1
0
0
0
1
1
0
2
0
1
2
1
1
2
0
0
0
1
0
2
2
1
2
0
2
0
1
2
0
1
0
0
2
0
2
0
1
1
2
0
0
0
0
0
0
2
1
2
0
2
0
1
3
0
0
0
1
0
1
1
1
1
0
1
2
2
2
1
0
0
0
2
2
0
1
2
1
0
1
0
2
0
2
2
2
1
1
2
0
2
2
1
1
0
1
1
2
1
1
2
1
0
2
0
1
0
2
1
2
2
0
1
1
0
1
0
1
0
0
0
2
1
0
1
1
0
2
0
0
0
0
1
2
0
2
1
1
0
0
0
0
2
0
0
0
1
0
2
1
2
1
1
1
2
1
2
0
2
2
1
1
1
1
0
1
1
0
1
0
1
2
1
0
0
0
3
0
0
4
0
0
2
1
0
1
1
0
2
1
0
0
0
1
1
1
1
0
2
2
2
4
1
2
0
0
0
0
0
0
0
1
1
1
0
0
1
1
0
0
0
1
0
0
0
2
1
1
1
2
0
2
0
0
1
1
0
1
0
0
2
0
0
0
1
0
1
1
2
1
1
1
1
0
2
0
1
1
1
0
0
1
0
0
1
2
1
2
0
2
2
1
2
0
0
0
0
0
0
0
1
2
0
0
1
0
1
1
1
1
0
1
2
1
0
1
1
0
1
0
1
0
0
0
2
0
1
1
2
0
1
2
0
0
0
1
2
0
2
1
2
1
0
1
0
2
0
0
1
2
5
1
2
1
2
0
2
0
1
1
2
0
0
2
1
0
0
0
2
0
1
0
2
0
1
1
0
1
1
2
0
0
0
0
1
0
0
0
1
1
1
0
0
1
0
0
2
2
0
1
0
0
0
0
2
0
3
0
0
0
0
0
0
0
2
0
0
1
1
0
1
1
1
0
1
0
1
2
0
1
1
2
0
2
1
1
0
2
2
0
0
0
0
0
0
1
2
1
0
1
0
0
3
2
2
1
0
0
1
2
2
1
0
1
1
1
1
2
0
0
2
1
0
1
0
2
1
2
0
4
0
1
0
2
1
2
0
1
0
0
1
1
1
0
1
1
2
3
0
1
1
0
1
1
0
0
0
0
2
0
0
1
0
1
1
0
0
0
1
2
0
2
2
0
1
0
0
1
2
0
2
0
0
1
2
0
1
2
0
1
2
0
1
1
0
0
1
0
1
1
0
0
1
0
1
1
1
1
2
0
0
1
0
2
1
1
1
1
1
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
2
1
0
0
2
0
0
1
0
0
0
1
0
0
1
1
1
0
0
1
0
2
0
0
0
1
1
0
1
0
2
2
0
0
1
0
2
1
1
1
1
0
0
2
2
0
0
2
0
0
0
0
2
2
0
1
2
2
0
1
1
1
0
0
1
0
0
1
0
0
2
0
2
0
2
0
1
0
0
2
1
1
0
1
0
0
0
2
0
1
1
1
0
2
0
2
1
2
1
0
1
0
2
2
0
1
1
0
0
1
0
3
2
2
0
0
2
0
0
2
1
2
0
0
1
0
0
1
2
0
0
0
0
0
1
1
1
0
1
1
0
1
0
1
0
0
0
0
0
2
2
1
1
2
0
0
0
2
5
1
0
0
1
1
0
1
1
1
2
2
0
1
0
0
0
2
0
0
0
1
1
1
1
1
0
1
0
2
0
0
1
0
1
1
1
0
2
3
1
1
0
0
1
0
1
0
1
1
0
0
0
0
0
2
1
0
1
0
2
0
0
0
1
1
1
1
0
1
1
1
1
0
2
1
0
1
1
0
0
0
1
2
0
0
1
0
1
2
0
0
2
0
0
2
0
1
2
1
1
2
2
2
1
0
0
0
0
0
1
0
2
0
2
1
1
1
1
0
0
2
1
0
1
2
1
1
1
0
2
0
1
1
2
1
0
0
0
1
1
0
1
0
0
1
1
2
0
1
1
0
2
0
0
1
0
2
0
1
1
0
0
0
1
1
1
2
2
0
0
0
0
2
1
1
2
2
2
1
0
0
2
0
1
0
1
1
0
2
1
2
0
0
2
0
2
1
1
1
1
0
1
0
0
1
0
2
0
0
0
0
0
2
0
0
1
0
1
0
0
0
1
1
6
1
0
2
0
1
0
0
1
1
1
0
0
1
0
1
2
1
2
0
0
1
1
1
1
0
1
0
0
2
0
1
0
1
2
2
1
0
0
2
0
1
0
1
0
0
2
1
1
0
1
1
1
0
0
1
0
0
1
0
0
0
2
1
0
2
0
2
1
2
2
1
1
0
0
0
1
2
2
3
1
0
0
1
1
1
0
0
0
0
0
1
0
2
1
0
1
0
0
0
0
0
2
0
2
1
0
0
0
0
0
2
0
0
2
2
0
0
1
1
1
0
0
1
1
0
1
1
0
1
1
0
0
0
1
0
1
1
0
0
1
0
0
1
0
1
1
1
0
1
1
1
0
0
0
0
0
0
1
2
2
0
2
1
1
2
0
0
1
0
0
3
2
0
0
2
2
1
2
1
1
2
0
2
0
0
1
1
0
0
1
0
0
1
1
2
2
1
0
1
0
0
1
0
1
0
0
1
1
1
0
0
0
2
0
1
0
1
0
0
1
0
1
1
0
2
0
2
0
3
0
0
2
2
0
0
1
0
2
0
2
0
2
0
0
0
2
0
1
0
0
0
2
0
2
0
2
1
2
1
0
2
1
0
1
0
0
0
2
0
3
2
0
0
0
0
1
0
0
0
1
2
0
1
0
1
1
0
0
1
1
0
1
0
0
1
2
0
0
1
1
1
2
2
0
0
2
1
2
1
0
0
2
1
0
1
0
1
0
1
0
0
0
1
0
0
1
0
1
0
1
1
0
1
1
1
2
0
2
2
0
2
0
0
1
0
0
2
1
2
3
1
1
0
0
0
0
1
3
2
0
0
0
0
1
1
0
1
3
1
0
1
0
0
0
1
2
0
0
1
0
0
0
1
3
1
0
1
2
0
0
2
0
2
0
0
0
2
1
0
2
0
0
0
1
0
0
1
0
2
1
0
1
0
0
2
0
0
0
0
0
2
1
0
1
2
0
0
0
0
1
1
1
0
0
1
0
2
0
0
1
1
5
1
0
0
1
2
0
0
2
2
1
0
0
0
1
0
0
0
0
1
0
1
1
1
2
0
2
0
1
0
0
2
0
0
0
2
1
2
1
1
3
2
0
1
1
0
1
2
0
1
0
1
0
0
2
0
2
0
0
1
0
0
1
1
1
2
0
0
0
1
0
1
2
2
1
2
0
2
0
0
1
0
0
0
2
2
2
2
0
0
3
1
1
1
2
1
0
2
0
0
1
2
0
2
1
1
1
2
0
0
1
0
1
1
0
2
0
1
0
0
0
0
0
0
1
2
1
3
0
0
1
0
1
1
1
2
1
1
1
0
2
2
0
1
0
0
2
0
1
1
0
1
0
0
0
0
0
1
0
2
1
0
0
0
0
2
0
1
0
0
3
1
2
2
0
0
1
0
1
2
2
0
1
0
1
2
0
1
1
0
0
0
1
0
2
1
1
2
0
1
1
0
1
1
1
0
2
0
2
2
1
0
1
1
2
2
0
0
0
0
1
1
1
0
2
2
2
0
0
1
1
0
0
0
1
2
1
1
1
0
0
1
0
2
0
0
1
1
2
0
0
1
1
0
0
0
2
0
0
0
1
1
2
0
1
0
0
0
2
0
2
2
1
0
1
2
2
1
1
0
2
0
2
0
0
1
0
2
2
0
1
1
1
1
1
1
0
0
1
2
1
0
0
0
0
0
0
0
2
0
0
0
2
1
0
2
0
1
0
2
0
2
2
1
0
2
0
0
1
2
0
1
0
1
2
0
1
1
0
0
0
1
0
1
0
1
2
0
1
1
1
2
0
1
0
0
0
2
0
0
0
0
2
2
1
0
0
2
0
1
0
0
1
2
0
0
1
2
1
0
0
0
1
0
1
1
1
1
0
1
0
1
1
0
0
1
1
1
2
2
1
1
2
1
0
0
0
4
1
0
1
1
2
0
0
2
0
2
0
0
1
1
1
0
2
1
0
1
0
0
1
1
0
3
1
0
0
2
1
0
2
0
1
0
1
0
1
0
1
0
2
0
0
2
0
1
0
2
1
0
0
0
1
0
0
1
1
2
1
1
2
0
0
2
0
2
1
0
0
0
1
0
2
2
0
1
1
0
2
0
4
0
0
1
1
0
1
1
1
0
1
0
0
0
1
0
1
0
0
1
0
0
1
1
0
1
0
0
1
0
0
1
0
2
1
2
2
1
0
1
0
0
1
0
0
2
0
1
0
2
0
1
1
2
2
0
0
2
0
1
1
2
0
0
1
1
0
0
0
2
0
2
0
1
0
0
0
0
0
1
0
1
1
0
0
0
1
2
2
0
0
1
0
0
0
1
2
1
0
0
0
0
2
0
0
2
0
0
3
1
0
0
1
0
0
1
2
0
1
0
0
2
0
0
2
0
1
1
0
1
1
0
0
0
1
3
2
2
0
2
1
2
2
0
0
0
1
1
3
3
1
0
0
0
0
0
1
1
0
0
1
1
0
0
1
2
1
2
1
0
3
0
2
0
2
2
0
0
0
0
0
0
2
1
0
0
0
0
2
0
1
1
2
0
2
0
0
1
2
1
1
1
0
0
1
0
2
1
1
0
0
0
2
0
0
2
0
2
0
1
1
1
1
0
0
2
1
1
0
0
1
1
0
1
0
1
0
2
1
2
0
2
1
2
0
2
0
1
0
0
0
1
0
0
2
1
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
2
0
2
1
2
0
0
1
1
0
0
1
0
1
2
1
0
0
0
1
1
0
0
0
0
1
0
1
0
0
2
1
0
0
1
2
1
0
1
0
0
1
1
0
2
2
1
1
2
2
2
1
0
1
2
0
3
0
0
0
0
1
0
2
0
2
1
5
0
0
1
2
1
0
1
0
1
1
1
1
0
4
1
0
0
3
1
1
1
0
1
1
0
2
0
2
2
0
0
1
0
0
0
1
0
0
0
2
1
1
2
0
0
1
2
0
2
2
1
0
0
0
2
0
0
1
2
0
1
0
1
1
1
1
0
1
0
1
2
1
0
1
0
0
0
1
1
1
2
0
2
4
1
1
0
0
0
1
1
0
2
0
1
2
0
1
0
3
0
2
1
1
2
0
0
2
0
1
2
0
1
1
0
0
2
0
0
0
1
0
1
2
1
1
1
0
0
1
1
0
0
1
3
1
0
2
0
0
0
0
2
1
3
0
1
2
0
1
2
1
0
0
1
0
1
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
2
1
1
0
1
1
2
2
2
1
2
1
0
0
0
1
2
0
2
1
0
0
1
1
1
0
0
1
0
0
0
0
1
0
2
0
0
2
1
1
3
0
1
0
0
0
0
0
1
0
2
0
1
0
0
2
1
1
1
0
1
1
3
1
1
1
2
2
0
1
0
1
0
0
0
2
0
0
2
0
1
0
2
1
2
3
2
0
0
1
2
1
0
0
2
0
1
1
0
0
1
0
1
0
0
0
1
1
0
0
2
2
1
1
0
2
1
2
0
0
1
0
0
1
0
1
2
0
1
2
2
3
2
2
0
0
0
1
0
1
2
1
2
2
2
2
1
3
1
0
2
0
2
1
1
0
2
0
0
0
1
2
0
0
1
2
1
1
1
1
1
2
2
0
2
0
0
2
0
0
0
2
0
1
0
0
1
0
1
0
0
1
1
0
0
1
0
0
2
0
1
0
1
1
0
1
0
2
0
1
1
0
0
2
2
0
0
0
0
0
0
0
1
0
1
1
2
0
2
0
2
0
1
3
0
1
0
2
0
0
0
3
0
0
2
3
1
0
2
0
0
2
1
1
2
0
0
1
0
3
2
0
0
2
0
1
0
2
2
0
2
0
0
0
2
1
2
0
2
2
1
0
0
1
1
0
1
0
2
2
1
1
0
2
0
1
1
0
0
1
1
1
2
2
1
0
2
1
0
1
0
3
1
1
3
2
1
0
0
0
0
1
1
3
2
0
2
1
0
1
2
2
1
2
2
0
0
2
0
1
2
2
1
0
0
0
0
0
0
1
1
1
1
1
1
1
0
2
2
0
0
0
2
1
0
1
0
0
0
0
1
0
0
0
1
3
1
1
0
1
0
0
0
1
1
1
1
2
0
0
1
2
1
2
2
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
2
1
0
2
0
1
0
0
0
0
0
0
2
0
0
1
2
1
0
2
0
1
1
0
0
0
0
0
0
0
1
0
1
2
0
1
0
0
0
0
0
1
0
2
1
1
2
0
0
0
0
1
3
1
1
0
0
0
0
1
0
2
2
1
1
6
2
0
2
3
1
0
0
1
0
2
1
0
0
1
1
2
0
0
2
1
1
2
0
0
0
1
0
0
0
0
0
0
1
0
2
3
1
0
0
0
1
1
0
4
0
1
1
2
0
0
1
1
0
0
3
1
0
0
0
1
1
1
2
0
0
1
0
1
1
2
0
1
1
1
1
0
0
0
1
1
1
0
2
2
0
0
1
0
1
1
5
1
0
0
2
0
0
0
2
3
1
0
0
0
0
2
0
2
1
2
1
1
2
2
3
0
1
0
0
2
0
0
0
0
1
1
1
0
0
0
2
2
0
2
1
2
2
0
0
0
1
1
1
0
2
1
0
2
0
0
1
2
1
2
0
1
0
1
2
2
3
0
0
0
2
0
2
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
1
0
2
2
1
1
1
0
3
1
1
2
0
1
1
0
2
2
0
2
1
1
0
1
1
0
2
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
1
2
2
0
2
0
0
1
0
0
0
1
2
0
2
2
1
0
1
0
1
1
1
1
0
2
1
0
0
0
1
2
1
1
0
0
1
2
2
2
0
0
1
2
1
2
1
0
2
0
0
1
2
0
0
1
0
0
0
0
1
1
0
1
1
2
1
1
0
1
0
2
1
5
2
1
0
1
1
1
2
0
0
0
1
1
2
1
0
0
1
1
1
0
1
1
0
0
0
0
2
0
0
1
1
2
1
0
2
0
0
3
1
0
0
1
1
0
1
2
2
0
1
0
0
0
2
1
0
0
2
0
0
0
0
1
2
0
1
0
0
0
1
0
1
2
2
1
1
2
2
1
0
1
0
2
0
0
2
1
1
0
0
0
0
1
1
0
2
1
2
0
1
0
0
2
0
1
0
0
0
0
2
0
0
0
0
1
1
2
2
2
2
0
0
0
1
0
0
1
0
1
0
1
0
1
0
1
0
1
0
0
2
2
1
1
2
2
0
1
1
1
0
1
0
1
2
0
0
1
1
0
1
2
3
0
2
2
0
2
1
1
0
0
0
0
1
0
1
3
0
1
1
0
0
1
0
1
0
2
0
0
0
0
2
0
2
2
1
1
0
2
0
2
1
0
2
2
2
1
0
0
2
0
1
0
0
0
2
1
0
1
0
1
1
1
0
0
0
2
2
0
1
0
2
0
0
1
0
1
1
1
2
0
1
0
0
2
2
0
0
2
1
2
0
0
1
1
0
1
1
0
1
0
0
1
0
2
0
1
1
1
0
0
1
0
1
0
1
1
0
0
0
1
0
0
0
2
0
0
1
0
1
1
1
1
1
0
0
1
0
2
1
0
0
0
1
2
1
1
4
3
0
0
2
0
2
0
2
0
1
1
0
0
1
1
0
0
0
0
1
1
0
2
2
0
2
1
1
0
0
0
0
0
3
0
1
1
2
0
1
1
1
3
0
2
0
1
2
0
0
0
0
0
1
1
0
4
1
1
0
0
0
1
0
0
0
2
1
0
0
1
0
2
2
1
1
2
1
2
2
0
0
0
1
1
2
0
0
1
0
1
1
1
1
2
2
1
2
1
2
1
0
0
1
0
1
1
0
2
1
0
0
0
0
0
0
2
2
0
3
0
1
1
0
0
1
0
1
2
1
0
2
1
2
0
0
2
2
0
1
1
2
0
0
1
1
1
1
0
0
0
1
2
0
1
0
0
0
2
1
2
0
0
0
1
1
3
0
0
0
0
0
1
0
0
0
2
1
1
0
1
2
0
0
0
0
1
1
0
2
2
2
2
0
0
1
0
0
0
0
0
2
1
2
0
0
0
2
1
1
0
1
0
1
1
0
1
2
0
0
2
0
1
1
1
2
1
0
0
0
1
0
1
2
1
1
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
1
1
1
0
1
0
0
1
0
1
1
0
1
0
2
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
2
0
2
1
1
2
2
0
0
1
0
0
1
2
2
0
0
0
1
2
0
0
2
0
0
0
0
1
0
0
0
2
1
2
2
0
0
2
0
0
1
0
0
1
0
0
1
2
0
0
1
1
0
0
1
0
1
0
0
0
2
0
0
2
1
0
2
0
0
1
1
2
0
2
0
2
0
0
0
1
1
0
0
1
1
0
1
1
1
0
1
1
1
0
1
1
0
1
0
0
2
1
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
2
1
0
0
2
1
0
1
1
2
0
4
0
0
3
0
0
0
1
0
2
0
0
1
0
0
0
1
2
0
0
0
1
0
0
0
3
0
2
0
2
0
1
0
1
0
1
2
0
2
0
1
0
2
0
2
0
0
2
0
1
0
1
2
1
0
0
0
2
0
1
2
0
0
2
2
1
0
0
2
0
0
1
1
1
0
2
0
1
2
0
0
2
1
2
0
0
2
2
0
1
0
0
1
0
2
0
1
1
1
0
1
2
2
0
0
0
2
0
0
0
0
0
1
2
1
2
0
0
0
0
0
0
1
1
0
1
3
1
1
0
1
0
2
0
0
1
0
1
1
2
0
1
0
2
1
1
2
1
0
0
1
0
0
0
2
1
0
0
0
1
0
0
0
2
2
1
0
0
0
0
0
2
2
2
1
0
0
0
0
1
1
0
2
1
2
1
0
0
2
2
1
2
1
0
0
0
0
0
0
1
7
0
0
1
3
1
2
1
0
0
2
2
0
2
1
1
0
0
0
0
1
1
1
0
0
2
0
1
3
1
1
0
2
0
0
0
0
1
2
0
2
1
0
0
0
0
0
2
1
0
1
1
0
0
2
0
1
1
3
2
0
0
1
0
2
0
0
0
2
1
1
2
2
1
1
1
1
2
1
2
0
2
2
2
0
0
0
0
1
1
0
1
1
1
1
1
0
0
2
0
2
2
1
3
1
1
0
3
0
2
1
1
2
1
5
0
0
2
1
1
1
1
0
0
7
1
0
0
1
1
0
1
1
1
0
1
2
2
0
1
0
0
2
2
0
1
0
2
1
1
0
0
1
0
1
0
0
1
0
1
0
1
0
0
0
2
0
1
0
2
2
2
0
2
2
0
0
3
0
0
1
0
2
2
0
2
2
2
1
1
0
1
1
0
0
0
1
2
0
2
1
0
0
1
1
0
1
1
2
0
0
0
0
0
0
0
0
1
2
0
0
1
1
2
0
1
0
0
2
0
0
1
1
0
1
0
0
0
0
1
2
1
1
0
1
0
0
1
0
2
2
1
0
1
1
0
0
3
0
0
2
0
0
1
2
1
1
0
1
1
0
0
2
0
0
1
0
0
0
2
0
1
0
2
0
1
0
1
2
1
1
2
2
2
0
0
0
0
2
3
2
0
0
0
1
1
1
1
0
0
1
1
0
1
2
0
1
1
2
1
0
2
1
1
1
0
0
0
2
2
2
0
2
0
1
1
1
0
0
0
0
0
0
0
1
0
2
2
0
1
1
1
2
0
0
0
0
0
1
1
2
1
0
0
0
1
0
1
0
0
2
3
1
1
0
0
2
0
0
0
1
0
1
0
5
0
1
3
1
1
0
2
0
0
1
1
2
1
2
0
1
0
1
0
0
0
0
0
6
2
2
0
2
0
0
1
2
0
0
0
0
0
1
0
0
0
0
4
0
0
1
1
0
2
1
0
1
2
0
0
1
0
0
1
0
1
2
0
0
0
1
1
1
0
2
0
2
0
1
2
1
2
0
2
0
2
1
1
2
0
2
2
2
0
0
0
1
1
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
2
1
1
1
0
2
0
0
1
2
1
0
0
0
3
2
0
0
2
0
0
0
3
0
1
1
0
2
0
0
1
0
1
1
2
0
0
2
1
2
1
1
1
1
0
0
1
1
1
0
1
1
0
2
0
0
0
2
1
2
0
1
0
0
0
2
1
1
1
1
2
0
1
0
1
0
0
1
1
0
0
1
0
2
1
0
1
2
1
2
0
0
0
0
4
0
1
2
0
1
0
2
0
2
3
0
0
0
2
2
0
1
1
0
0
0
0
2
1
1
1
1
0
2
0
0
2
1
0
1
1
0
1
1
0
1
0
1
1
1
0
0
0
0
0
1
2
0
0
1
0
1
0
0
2
1
1
0
2
0
2
1
0
1
1
2
1
1
1
0
0
0
2
2
0
3
0
0
0
1
2
1
2
2
0
0
0
2
0
0
1
0
3
1
2
2
0
2
0
2
1
2
0
0
3
2
1
0
0
1
0
1
0
0
3
1
1
0
1
1
1
1
1
2
0
0
0
1
2
1
0
0
0
0
0
0
0
2
0
1
1
0
2
0
1
0
1
1
0
0
1
0
3
0
1
0
2
1
0
2
1
0
1
0
0
0
1
1
0
0
1
1
1
1
0
0
0
1
0
0
3
0
3
0
1
0
0
1
2
1
2
2
2
0
1
0
2
0
2
0
0
1
0
0
2
2
0
1
0
2
0
2
1
2
1
0
0
2
0
1
1
2
2
2
1
0
0
1
3
0
1
1
1
1
0
0
0
0
0
4
0
1
2
0
1
2
0
0
2
1
3
0
0
1
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
1
0
1
2
1
1
0
2
2
0
0
2
1
1
2
0
1
2
0
0
1
0
1
0
0
0
1
1
0
1
0
1
0
2
0
0
0
2
2
1
1
2
2
0
1
0
0
1
2
2
1
0
2
1
1
2
1
1
0
2
0
0
0
0
2
0
0
1
0
0
0
1
3
1
1
1
0
0
0
0
2
1
0
1
1
0
0
0
1
1
1
1
0
0
0
2
2
1
1
0
1
0
0
1
0
1
1
0
1
0
0
2
0
0
2
0
0
0
1
0
0
2
1
0
2
0
2
0
0
0
0
1
0
0
0
0
0
1
2
2
0
0
1
1
1
1
2
0
0
0
1
0
0
1
1
1
0
1
0
0
4
2
1
0
0
1
2
0
0
2
1
0
2
0
1
0
0
2
1
2
2
1
2
0
1
0
2
1
1
2
1
2
2
3
0
0
2
1
0
0
2
1
1
1
0
1
2
1
0
1
1
0
0
2
0
0
2
2
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
1
1
2
2
0
0
2
2
1
2
2
0
1
1
1
0
2
0
0
0
1
0
1
0
2
1
1
0
2
2
0
1
0
1
0
1
0
2
0
1
1
0
1
1
0
0
0
0
1
3
1
0
1
1
1
2
0
0
1
2
2
1
0
0
0
0
1
1
1
1
1
1
0
1
0
0
0
1
0
1
0
2
1
0
1
2
0
0
0
2
0
2
1
1
1
1
0
0
1
0
0
0
1
0
0
1
0
0
1
2
0
0
2
2
1
1
2
0
0
2
2
1
0
0
1
1
1
1
2
0
0
1
0
2
1
1
0
0
2
2
3
0
0
1
0
1
2
1
0
3
0
0
1
2
2
2
0
0
1
1
0
0
0
0
0
0
0
1
2
1
0
1
2
1
1
2
2
2
0
1
0
2
2
1
0
1
1
1
2
2
1
1
2
1
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
1
1
0
1
2
0
1
2
1
0
0
1
1
0
2
2
0
1
2
0
1
3
0
1
2
2
1
1
0
0
0
0
1
0
2
2
0
2
3
0
1
1
1
0
1
1
5
1
0
1
1
1
0
0
2
3
0
0
1
1
0
2
2
1
2
2
0
0
1
2
1
1
2
2
2
1
1
0
1
1
0
2
2
1
0
2
1
2
0
0
2
0
1
0
0
0
1
0
2
1
1
2
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
2
0
1
0
2
2
2
0
2
2
0
2
0
0
1
1
0
0
0
0
1
0
0
0
1
2
2
0
2
1
1
1
1
2
1
1
1
0
2
0
0
0
1
0
0
0
1
0
1
1
0
1
0
0
0
2
0
2
1
0
0
0
0
1
0
0
1
0
1
0
0
1
3
0
1
1
0
0
0
1
1
0
1
0
1
2
1
2
2
1
0
0
0
1
0
1
2
1
1
0
2
0
0
0
0
1
0
1
1
0
1
3
2
1
0
2
0
0
1
0
0
2
0
0
2
1
1
1
1
1
1
1
0
1
0
0
1
0
0
0
1
0
2
0
0
2
2
1
1
0
1
0
2
0
1
0
2
1
0
1
0
1
1
1
1
1
1
2
1
1
1
0
3
0
1
0
1
0
0
0
1
2
0
0
0
0
1
1
1
0
0
0
0
1
0
0
2
1
2
0
0
2
3
1
0
0
1
1
2
0
1
1
0
0
0
0
0
1
1
2
2
0
0
1
2
2
2
1
1
1
0
2
2
2
0
1
1
1
1
1
1
0
2
1
1
2
0
1
0
0
0
0
0
1
0
1
1
2
0
0
0
0
0
1
0
0
2
1
0
2
0
0
0
1
2
1
0
2
0
0
1
0
0
0
1
0
0
0
2
0
1
1
0
2
2
0
1
1
2
0
0
0
0
1
1
1
2
0
1
0
0
1
1
2
0
0
0
2
1
2
1
2
0
0
0
2
1
0
1
0
1
1
0
0
2
1
0
0
1
0
2
2
1
1
0
0
0
1
0
1
0
1
2
0
0
0
0
1
0
0
0
1
2
1
0
1
0
1
1
2
0
2
0
1
0
0
0
3
2
2
1
1
1
0
1
1
0
0
0
0
0
0
0
0
1
3
2
0
2
1
1
0
1
0
1
1
1
2
2
1
0
2
0
0
0
0
2
0
0
1
2
0
2
1
0
1
2
0
2
2
2
0
0
0
1
0
0
0
1
0
0
0
1
1
2
0
1
0
1
0
0
1
0
1
0
1
0
1
2
1
0
0
0
1
2
2
0
0
0
0
1
0
2
0
0
2
0
0
0
1
0
0
0
1
1
2
2
1
1
0
0
1
1
1
0
1
0
2
2
0
4
1
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
2
1
0
2
0
0
0
0
1
1
0
0
2
0
1
2
2
2
1
0
1
2
1
1
0
1
0
1
1
0
0
0
1
1
2
0
2
0
1
1
2
0
2
0
0
0
0
1
1
0
2
1
0
0
0
1
0
2
0
1
2
0
0
1
2
0
0
0
1
0
1
1
2
1
3
1
0
1
0
1
0
0
2
1
1
1
1
2
1
1
0
1
0
0
0
0
0
1
2
1
0
0
1
0
0
2
0
0
1
0
2
2
2
0
1
0
1
1
0
1
1
1
2
0
2
1
0
0
2
0
1
0
1
0
0
1
0
0
1
2
0
0
1
2
0
1
0
1
2
2
1
0
1
5
0
0
0
1
1
1
0
0
0
1
0
1
0
3
0
2
2
0
0
1
0
0
1
1
1
0
0
0
1
0
3
1
1
0
0
0
2
1
0
1
0
0
0
1
1
2
2
3
0
2
0
0
1
0
1
1
2
1
0
1
1
0
0
0
1
1
0
0
0
0
2
0
2
1
0
0
0
0
1
2
1
0
1
0
1
1
0
2
3
2
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
2
2
0
2
2
0
1
2
0
0
0
1
0
1
0
0
1
0
1
2
2
0
2
0
3
1
1
0
1
0
0
1
0
0
2
0
1
2
0
1
0
0
2
0
1
1
1
0
0
1
0
0
0
2
0
2
1
0
0
1
0
0
1
1
3
1
1
1
1
1
1
2
1
1
0
2
0
0
1
2
1
1
0
2
1
1
2
0
0
0
1
1
1
0
0
1
0
0
1
2
0
1
2
0
1
0
0
0
0
2
0
2
0
1
1
0
1
1
0
1
2
0
0
0
0
1
1
0
0
0
1
1
0
2
0
2
0
3
0
1
0
2
0
1
2
2
2
0
0
1
0
1
0
0
0
2
1
2
1
2
0
0
0
1
2
1
2
0
0
1
0
0
1
2
2
0
0
0
1
1
0
4
1
0
0
2
1
0
0
1
0
1
0
2
2
0
0
1
1
0
0
0
3
1
1
0
1
2
0
0
3
0
0
1
0
1
2
2
1
0
2
1
0
1
1
0
0
0
0
0
0
2
2
0
0
1
0
0
2
0
0
2
1
1
2
2
0
1
1
0
0
0
3
1
1
0
0
1
2
0
2
0
0
2
2
1
1
0
1
0
1
0
0
1
1
0
0
0
0
0
1
2
1
0
0
2
1
2
0
1
1
2
1
2
0
2
1
0
0
1
2
0
1
1
1
2
1
2
0
1
2
0
2
1
0
1
0
1
1
1
1
0
0
1
2
0
2
2
0
0
1
0
1
2
0
3
1
0
0
0
0
1
0
2
1
0
2
1
0
1
0
1
0
1
0
0
0
1
2
1
1
1
0
1
0
1
2
0
0
0
0
2
2
2
0
1
0
0
0
0
1
2
0
1
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
1
3
2
2
2
1
0
1
0
0
0
1
0
2
0
0
0
1
1
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
1
2
2
2
2
0
0
0
0
1
1
1
1
1
0
0
0
0
2
1
0
0
1
2
4
0
1
1
0
0
1
0
0
1
2
1
2
2
1
2
1
0
2
0
0
2
2
2
1
2
1
1
0
2
3
1
0
1
1
1
2
2
2
0
0
2
1
1
2
2
1
1
0
2
0
2
0
1
2
2
0
1
0
0
1
1
1
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
2
1
0
2
0
2
1
1
0
0
0
1
0
1
4
0
1
0
2
0
2
0
1
0
1
0
0
0
2
2
0
0
0
2
2
1
1
0
2
0
0
0
0
1
1
1
2
0
1
0
2
1
0
2
2
1
1
0
1
2
1
0
1
0
2
1
1
1
0
1
0
0
1
1
0
2
0
0
1
1
2
0
1
2
0
2
1
2
1
0
0
1
4
2
0
2
2
0
1
0
0
0
0
0
1
1
2
2
1
0
0
1
2
0
0
1
1
0
0
0
2
0
1
1
1
1
0
1
0
2
0
1
0
0
0
0
0
1
2
2
0
2
2
2
0
1
1
0
1
2
0
2
2
1
0
0
1
1
0
0
1
0
1
1
0
2
0
0
0
0
2
1
2
0
2
3
1
0
0
1
0
2
1
1
0
1
0
0
0
2
1
1
0
1
1
0
1
0
0
0
0
0
0
2
0
1
0
2
2
2
0
1
4
1
0
0
1
3
1
1
0
1
2
0
2
0
0
1
0
1
0
0
0
1
1
1
2
0
3
0
0
1
1
2
0
0
0
2
2
0
1
2
0
3
0
1
1
1
0
1
0
4
0
1
0
0
1
0
0
1
2
0
0
0
0
2
0
1
2
1
0
1
0
2
2
2
1
0
0
1
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
1
2
0
2
2
2
2
0
2
2
0
0
1
2
1
1
0
1
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
2
0
2
1
0
1
0
0
1
1
1
0
0
1
0
0
1
1
0
1
0
2
1
1
3
0
0
1
0
2
0
0
2
1
1
1
1
0
0
0
1
1
0
1
0
0
0
0
1
0
0
2
0
0
1
2
0
0
0
0
2
2
0
1
1
2
1
2
1
0
1
1
1
0
0
1
1
0
0
0
0
0
1
2
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
1
1
1
1
2
1
0
2
1
1
1
2
1
1
0
2
2
1
0
0
1
2
2
0
1
0
0
2
2
2
2
0
2
0
0
1
1
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
2
1
2
2
2
0
1
1
0
0
0
0
2
2
0
0
2
2
2
0
1
0
1
2
0
1
0
3
1
1
0
0
0
1
2
1
0
1
0
1
0
0
0
2
1
0
0
1
0
0
0
1
0
1
0
0
1
0
2
0
0
0
0
2
0
1
0
1
2
2
1
2
0
1
1
1
1
1
2
2
0
1
1
2
1
11
0
1
1
1
1
1
2
0
1
2
0
0
2
0
0
2
1
0
0
1
2
2
1
0
1
0
0
1
1
0
1
2
1
1
1
0
0
0
0
3
0
0
1
1
1
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
2
0
0
0
1
2
0
0
0
3
0
0
0
0
2
2
2
1
1
2
0
0
2
0
2
1
0
0
0
0
1
2
1
2
1
0
1
3
0
1
1
0
0
1
0
0
1
0
1
0
0
0
0
0
1
1
0
1
0
0
1
0
0
2
1
2
0
1
1
0
2
1
1
1
0
0
2
1
1
2
1
1
2
0
0
0
1
0
0
1
0
1
1
1
0
0
1
1
2
2
1
1
2
2
1
0
3
2
1
0
0
1
0
0
2
3
0
2
0
0
0
0
0
2
0
2
0
1
2
2
1
0
0
2
0
0
1
2
4
0
0
1
0
1
0
2
1
1
1
0
1
2
0
1
0
1
0
0
1
2
0
0
1
0
0
1
0
0
2
1
1
2
2
0
0
1
2
0
1
2
1
1
0
0
2
0
2
0
0
0
1
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
1
3
0
0
0
2
1
3
0
1
2
1
1
0
2
1
0
2
1
0
0
0
0
1
0
2
1
1
0
2
1
0
1
1
0
0
0
0
1
1
0
0
0
2
0
0
2
0
0
2
0
2
0
1
1
1
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
2
1
2
0
0
1
0
0
0
1
1
1
0
2
3
2
1
1
2
0
2
1
0
2
0
1
0
0
0
0
1
0
1
0
0
1
2
1
2
1
0
1
0
0
1
0
1
0
0
1
1
0
2
0
1
0
0
1
0
1
0
0
0
2
0
0
0
0
1
2
2
0
0
1
1
2
0
0
2
4
2
0
2
1
2
2
1
1
2
1
0
0
0
1
0
1
0
1
0
0
2
0
1
0
0
0
0
1
1
0
1
0
1
0
2
0
2
0
0
1
0
1
1
1
1
2
0
2
2
2
1
0
0
1
1
0
0
1
2
1
1
0
0
0
1
3
0
1
1
0
0
0
1
2
0
1
0
0
0
1
0
1
1
1
1
0
0
0
0
1
1
1
1
0
0
0
2
0
1
1
0
0
0
1
1
0
2
0
0
1
1
1
2
1
2
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
1
2
1
1
0
0
0
1
2
2
1
2
0
2
2
1
0
2
1
1
2
0
0
1
1
0
0
2
0
0
0
0
1
0
1
1
0
0
0
0
0
3
0
0
0
1
0
1
0
2
0
2
1
0
0
1
0
1
0
2
1
2
0
2
0
0
0
0
1
0
0
0
2
1
2
0
0
0
0
1
0
1
1
2
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
2
2
2
0
0
2
0
0
0
0
0
0
0
1
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
3
1
1
1
0
2
0
1
1
0
1
0
1
0
1
0
1
0
2
0
2
2
1
0
0
0
0
0
2
0
1
0
1
2
0
1
0
0
0
1
0
0
1
1
0
1
0
0
1
1
1
1
1
2
1
2
1
0
0
1
2
0
1
1
1
0
0
1
1
2
2
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
1
2
0
1
0
1
2
0
0
0
1
2
0
1
2
1
2
0
0
3
1
1
0
0
2
2
0
2
1
2
0
2
0
1
2
1
0
1
1
0
1
1
0
0
1
2
0
1
5
1
2
0
1
2
1
0
2
2
1
0
0
0
2
2
0
1
1
0
0
2
0
1
1
0
2
2
2
0
0
0
1
1
1
2
1
0
2
1
0
0
0
2
1
0
0
1
0
0
2
0
0
0
2
1
1
0
1
0
0
0
1
0
1
1
0
1
0
1
2
2
0
1
0
1
0
1
0
0
1
1
1
1
0
0
1
2
1
2
1
1
2
1
1
3
0
0
0
0
0
1
2
1
1
1
1
2
2
1
1
0
0
0
0
3
1
0
0
1
0
0
1
0
0
2
0
0
1
2
0
0
1
0
0
0
1
0
0
0
1
1
1
2
0
2
2
1
2
0
3
0
2
1
0
2
1
0
2
0
1
0
0
0
0
0
3
0
2
2
2
2
0
4
1
0
1
2
0
1
0
2
0
3
1
0
0
1
2
1
0
0
0
1
0
1
2
0
1
1
1
2
2
0
0
2
1
1
2
1
1
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
1
1
0
0
1
1
3
0
0
1
2
1
0
0
2
1
0
0
1
0
2
0
1
1
0
1
0
0
0
0
2
2
1
1
2
0
1
2
0
1
2
2
1
1
2
0
0
0
0
0
0
2
0
1
0
1
1
0
0
1
0
0
1
1
0
1
0
2
0
3
0
0
0
2
2
1
0
1
2
3
1
0
1
2
2
2
1
1
0
1
0
0
0
0
1
0
0
0
1
1
0
3
1
1
1
1
2
0
0
1
1
0
0
1
2
1
0
0
0
1
1
1
0
1
1
0
0
0
0
2
1
2
3
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
1
2
0
0
0
1
0
0
1
1
1
0
1
0
0
0
1
1
1
2
0
0
0
2
4
5
0
2
4
1
0
2
3
2
0
0
1
2
0
2
0
1
0
1
1
0
0
2
0
1
1
0
2
0
2
0
0
0
1
1
1
0
0
1
0
0
0
2
0
0
0
2
1
0
0
1
2
0
0
2
2
0
0
1
1
0
1
0
1
0
1
2
1
1
0
0
0
2
0
0
1
0
1
0
3
1
1
0
3
0
2
0
1
1
1
0
2
0
1
2
0
0
0
2
0
1
0
0
0
1
0
2
0
0
0
1
1
2
0
0
0
2
3
0
0
1
2
0
2
0
2
1
0
1
1
0
2
0
0
1
2
0
1
2
0
0
1
0
1
2
1
0
1
0
2
1
1
2
0
2
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
1
3
0
2
0
1
2
0
0
1
0
1
1
1
1
1
0
1
1
1
1
1
2
0
0
1
0
1
0
1
2
1
2
0
0
2
1
0
0
1
2
0
1
1
0
0
0
0
2
1
0
0
0
0
0
0
1
2
2
0
1
1
0
0
2
1
0
0
0
1
0
2
0
0
3
1
0
1
2
2
1
1
0
2
1
0
2
0
0
0
0
0
2
2
0
1
1
0
2
1
0
2
2
0
0
0
1
2
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
2
2
2
0
0
0
0
1
2
1
2
1
0
1
0
2
2
0
2
1
1
2
2
1
2
2
0
0
1
0
0
0
1
0
0
1
2
0
1
1
1
0
2
0
2
1
0
0
0
1
0
0
0
2
1
1
3
2
2
0
0
0
1
0
0
1
0
2
1
2
1
0
3
0
1
1
2
0
1
1
2
1
1
2
2
1
0
0
1
0
0
0
0
1
1
2
2
0
1
0
0
0
0
1
0
0
0
0
0
2
0
1
0
5
1
0
1
0
1
0
1
0
1
1
0
0
1
0
0
1
0
3
2
2
1
2
2
1
0
0
1
0
1
1
0
1
0
1
0
0
0
2
0
0
0
2
2
1
0
0
1
2
3
0
0
0
0
1
0
2
1
2
1
0
0
0
1
0
1
2
0
0
3
1
2
0
1
2
1
0
0
0
0
1
1
1
2
1
0
2
2
0
1
0
2
0
0
0
0
1
0
1
1
2
1
0
1
2
0
2
3
2
2
0
0
1
2
0
0
0
1
0
2
1
1
2
2
0
1
0
2
0
2
0
1
2
1
0
1
0
1
0
0
0
1
1
1
2
1
0
2
2
2
0
3
1
2
0
0
2
1
2
1
2
0
2
1
0
2
2
0
0
1
2
1
0
2
0
0
1
0
0
3
0
0
0
1
2
0
2
2
0
0
1
1
0
1
1
3
1
3
1
1
0
0
1
1
0
1
0
0
0
1
2
0
0
0
2
0
1
0
1
1
2
0
1
0
1
0
2
1
0
0
0
1
2
0
2
2
1
1
0
1
1
2
0
1
0
2
1
1
1
1
0
0
0
0
0
1
4
0
0
0
1
1
1
0
2
1
0
0
1
1
2
0
0
0
0
0
2
2
0
1
0
1
2
0
1
0
1
0
2
1
1
0
3
1
1
0
1
1
1
1
0
0
1
1
2
0
0
0
2
1
0
1
0
2
1
0
1
0
0
1
0
1
4
1
2
1
1
0
0
0
0
0
1
0
0
1
1
2
1
3
0
0
0
0
1
2
2
1
0
2
1
2
1
1
2
0
0
0
0
0
2
1
0
2
2
0
2
1
0
0
1
0
2
0
2
1
2
0
1
1
0
3
0
2
0
0
0
0
0
0
2
0
0
1
0
1
0
0
1
0
1
0
0
1
1
0
2
0
1
1
0
1
0
1
1
1
1
0
1
2
1
1
0
0
0
0
1
1
2
0
1
2
0
0
0
0
2
0
2
2
0
0
2
2
0
0
0
1
1
1
2
0
0
2
2
0
0
0
1
0
1
2
0
2
0
2
1
1
0
1
1
0
0
0
2
1
2
1
4
2
2
0
0
0
0
0
1
1
1
1
1
1
1
1
2
1
0
0
0
1
0
0
1
1
0
0
2
0
2
0
1
1
0
2
2
1
1
2
0
1
2
1
0
0
2
1
0
1
2
0
1
0
1
1
1
0
2
0
2
1
1
0
0
2
0
0
0
2
0
0
0
0
1
1
1
0
0
0
1
1
1
1
1
0
2
0
0
0
1
0
2
3
1
1
1
2
1
1
0
2
2
0
2
2
0
0
1
1
2
0
0
0
0
0
2
0
0
1
1
1
2
0
0
1
0
0
1
1
1
2
2
0
0
0
0
1
0
1
2
2
0
2
0
1
0
1
1
2
2
2
2
0
0
0
1
2
0
2
0
1
0
0
2
2
0
1
1
3
1
0
1
1
1
0
2
0
0
2
2
0
2
0
0
1
1
1
1
0
0
1
1
2
1
1
2
0
0
0
1
2
1
1
2
1
2
2
0
0
1
0
0
0
1
0
0
2
2
0
0
1
2
3
1
2
0
2
1
0
0
1
2
0
1
3
1
3
1
1
0
1
3
0
1
1
0
0
2
2
0
1
0
0
2
0
0
2
0
0
1
0
0
0
2
0
0
1
1
1
1
1
0
2
1
0
0
2
0
2
1
1
1
0
0
2
0
1
1
0
0
1
2
0
0
2
0
0
0
0
2
1
1
1
1
1
2
0
0
2
2
0
1
2
0
1
2
3
0
3
1
1
0
1
1
1
0
0
2
0
0
0
2
2
1
0
2
1
0
0
0
0
1
0
0
1
1
1
1
2
0
1
0
0
1
0
1
1
0
1
1
1
0
1
2
0
0
0
0
2
0
0
1
0
0
2
2
0
0
0
0
0
0
0
1
0
1
1
0
0
1
1
0
2
1
0
0
0
1
0
0
1
0
1
0
1
0
2
1
2
0
1
0
0
0
0
0
0
0
0
2
2
0
2
1
0
0
2
2
1
0
1
2
2
0
4
2
0
2
0
1
0
0
0
2
1
1
2
1
0
2
0
4
0
0
1
0
3
0
1
0
1
0
0
0
1
2
0
2
2
0
0
0
0
0
0
1
1
0
1
0
1
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
1
0
2
1
1
1
0
0
0
0
0
0
1
0
0
0
2
0
1
1
1
0
0
0
1
1
0
1
2
0
0
0
1
1
1
1
1
2
0
0
1
2
0
1
0
1
1
0
2
2
0
0
0
2
0
1
0
0
1
1
0
0
2
1
0
1
1
0
0
1
0
0
4
1
2
1
0
0
2
1
0
0
0
0
0
1
0
1
0
1
1
1
0
1
0
1
0
0
0
0
0
0
1
1
1
0
1
2
0
0
0
1
2
1
1
1
1
1
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
1
3
0
0
0
1
2
0
0
0
0
0
0
2
0
0
3
0
0
1
0
1
2
0
0
1
0
0
1
2
1
1
1
1
1
2
2
0
2
1
1
0
1
2
1
0
0
2
0
0
2
0
0
0
0
2
0
1
2
0
1
0
0
0
0
0
0
1
2
1
1
1
0
1
4
1
1
0
0
1
1
0
0
2
3
0
2
1
2
2
2
1
2
0
0
0
0
2
0
1
1
1
1
1
0
2
1
2
0
0
0
1
2
2
0
0
1
0
2
2
0
0
0
2
0
0
2
0
0
2
1
0
0
1
0
0
0
1
0
0
2
1
0
1
0
1
0
0
1
0
0
2
0
2
0
1
0
1
0
0
1
1
2
0
2
0
2
1
0
0
2
0
1
2
0
1
0
1
1
2
0
1
0
1
0
1
0
0
0
0
1
0
3
0
0
1
1
0
1
1
3
0
2
0
0
0
1
0
1
0
0
1
0
0
1
1
0
0
1
1
0
0
0
0
1
0
1
0
1
0
0
2
1
1
3
0
0
0
0
2
0
1
0
1
0
3
0
1
0
1
2
2
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
2
1
0
1
3
1
0
2
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
4
0
0
0
0
0
2
1
1
0
2
0
1
0
0
0
0
1
0
1
2
5
1
0
0
0
0
0
1
0
0
2
0
0
0
2
0
1
2
0
2
2
0
2
1
1
3
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
2
1
2
0
1
0
0
0
1
0
1
1
0
0
1
1
1
0
2
1
0
1
1
2
1
0
1
1
0
0
0
2
0
2
2
0
0
1
0
0
2
2
0
1
0
1
2
1
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
1
2
0
1
0
0
0
0
1
0
0
0
2
0
0
0
1
2
2
0
1
1
2
0
0
1
1
2
0
0
0
0
2
2
1
0
0
0
1
1
1
0
1
1
2
1
2
1
2
2
0
1
0
0
0
0
0
1
0
1
1
1
3
0
1
2
2
0
1
1
2
1
2
0
0
2
0
1
1
0
1
0
0
1
0
0
2
0
2
1
1
1
2
2
0
3
0
1
0
1
1
0
0
0
2
0
0
0
1
1
0
0
4
0
3
1
0
0
1
0
1
2
1
0
1
0
0
0
0
0
1
2
2
1
0
2
0
1
1
2
2
0
0
2
1
0
0
1
0
1
1
1
1
1
1
0
0
0
2
1
1
1
2
2
1
1
0
0
0
0
1
0
1
1
0
0
2
1
2
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
1
2
2
2
1
2
3
0
0
1
0
0
2
0
0
0
1
1
2
0
1
1
1
1
1
0
1
0
1
0
2
0
0
1
2
0
2
2
0
0
1
0
0
1
0
2
1
1
0
0
2
2
0
0
0
3
2
1
0
2
0
0
0
1
1
2
2
1
0
2
0
0
0
2
1
3
2
1
1
1
1
2
2
1
3
1
1
1
0
0
2
1
2
0
0
2
1
0
1
1
0
2
1
0
2
1
0
0
1
0
0
0
0
1
0
1
1
2
0
1
2
0
1
0
0
1
0
0
1
1
1
0
2
1
0
2
1
0
0
2
0
1
0
1
2
2
0
0
2
1
0
1
1
0
1
3
1
0
0
0
1
0
1
0
1
1
2
2
1
0
1
2
1
0
1
0
0
2
0
1
1
0
0
0
0
3
0
0
1
0
2
0
1
0
1
2
0
1
0
1
2
1
1
0
1
0
0
0
1
1
0
0
2
0
2
1
0
0
4
0
2
2
0
1
0
1
1
1
3
0
1
0
0
0
0
0
0
2
2
0
1
0
0
2
0
2
0
0
2
2
0
1
0
0
0
0
1
0
1
0
1
1
1
1
1
1
1
2
0
2
2
1
2
0
0
1
2
0
0
0
1
1
0
1
0
2
1
1
0
0
0
1
2
0
1
0
2
0
0
1
1
2
0
0
2
1
1
0
0
1
2
1
2
0
0
0
2
1
1
8
0
1
2
0
0
1
3
1
0
3
0
1
0
0
0
0
0
0
1
1
0
1
2
2
1
0
0
0
0
1
0
1
0
2
0
2
1
0
0
0
2
2
0
0
1
1
1
0
0
1
0
2
0
0
0
3
1
0
1
0
0
1
2
0
0
0
1
1
0
1
1
0
1
2
0
0
0
0
2
1
3
2
1
2
0
0
2
0
0
0
4
1
2
1
1
0
0
3
1
0
1
1
2
2
0
0
0
2
0
0
0
0
0
4
2
2
1
0
2
3
2
0
0
0
1
0
1
1
2
0
2
2
1
1
0
0
1
1
0
0
1
0
2
0
1
0
1
0
0
1
1
2
1
2
1
1
1
0
2
0
0
0
2
1
0
1
2
0
1
0
1
2
1
0
2
0
0
2
1
1
2
1
1
1
2
1
2
1
1
1
0
0
1
1
0
1
0
2
1
1
0
0
1
0
0
1
0
1
1
0
0
0
0
1
0
0
1
0
1
2
1
1
0
4
0
2
0
1
0
1
1
0
0
2
2
0
0
0
0
2
0
0
1
0
2
1
1
0
4
3
0
1
0
1
0
0
1
0
1
0
2
0
0
1
0
1
1
1
0
1
0
0
0
1
0
0
2
0
1
0
0
0
2
2
0
1
4
0
0
0
1
0
0
0
1
0
2
2
0
1
2
1
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
2
2
0
1
2
2
1
0
0
1
1
0
1
1
1
0
0
1
1
0
0
1
1
0
0
0
0
3
0
1
1
2
0
0
0
2
1
1
0
1
1
0
0
0
5
1
0
1
0
0
0
0
1
0
2
0
0
0
0
3
1
0
0
0
0
0
1
0
0
0
2
0
1
0
2
2
0
2
1
2
1
1
0
0
0
2
2
2
2
0
1
1
2
1
1
0
1
1
0
0
1
4
2
1
2
0
1
1
3
1
2
0
0
0
0
0
0
1
0
1
2
0
2
2
1
1
1
0
2
1
1
0
1
1
1
0
0
1
2
0
1
0
0
2
2
1
1
1
2
1
0
0
0
2
2
0
2
1
2
1
0
1
0
0
1
0
0
1
2
1
0
1
0
0
0
1
0
0
1
1
0
0
1
0
1
0
1
0
2
0
2
1
2
0
1
0
2
0
0
1
2
0
0
6
0
1
0
0
0
0
0
1
2
2
3
0
2
2
1
2
1
2
0
0
1
1
1
1
2
1
0
0
3
0
2
1
2
2
0
0
1
2
0
0
1
0
0
1
0
4
1
0
1
1
1
0
0
2
1
1
0
2
1
0
1
0
1
1
2
0
0
1
2
1
0
2
1
1
0
0
0
1
1
0
1
2
0
0
0
2
1
0
0
1
1
1
1
1
0
4
0
1
0
0
0
1
0
0
1
1
1
0
0
2
0
0
0
0
2
1
0
1
0
0
2
1
1
1
0
2
2
0
0
0
2
1
2
0
0
2
2
1
0
2
0
0
0
0
0
2
1
1
0
2
0
0
3
0
0
1
0
2
1
0
0
1
0
1
0
0
1
0
0
0
1
2
2
1
2
0
1
1
2
5
1
2
0
1
0
1
2
1
2
1
3
1
1
0
1
0
0
1
2
1
1
1
0
0
0
0
2
0
0
2
1
0
1
3
0
1
2
1
1
0
3
1
2
0
1
1
0
2
1
0
2
1
0
2
0
1
2
0
1
0
0
1
2
0
0
0
1
0
1
0
2
2
0
0
2
0
0
2
0
1
1
1
0
0
1
0
1
0
1
0
2
0
0
1
2
0
1
0
1
0
2
2
1
0
1
1
2
1
0
0
0
0
0
1
0
1
0
1
0
2
2
1
0
0
1
1
1
0
1
2
0
0
0
1
0
0
1
0
0
0
2
0
0
3
2
2
1
1
2
0
0
2
3
1
0
0
0
2
0
2
0
0
2
0
1
0
0
2
1
2
1
0
0
1
0
0
0
2
1
2
2
2
0
0
1
1
1
1
0
1
0
2
0
1
1
2
0
2
0
1
2
1
0
1
2
2
1
0
1
1
1
1
2
1
0
0
0
0
2
0
2
2
1
0
0
1
0
1
0
1
2
1
2
0
2
1
0
0
0
1
1
1
2
0
1
2
0
0
0
0
0
1
2
1
1
0
2
0
0
1
0
1
0
0
0
0
0
0
2
2
0
1
0
0
0
2
1
0
2
0
0
0
2
0
0
2
0
2
0
2
1
0
1
1
0
2
0
1
0
1
0
0
1
2
4
0
0
1
2
0
0
0
1
0
3
3
0
2
0
1
1
0
2
0
2
0
0
1
2
0
3
1
2
2
1
1
1
0
0
1
0
1
0
0
1
0
0
2
0
1
0
2
5
2
1
0
1
0
0
0
0
2
1
1
0
1
1
1
2
0
0
1
1
0
1
2
1
0
0
1
0
2
0
2
0
0
2
0
0
2
2
0
1
0
0
2
2
1
0
1
1
0
2
1
2
0
1
2
0
2
1
0
2
1
0
0
1
0
0
0
2
0
1
1
0
0
0
1
0
2
2
1
1
2
1
1
0
2
1
2
0
0
2
0
0
2
1
2
1
1
2
0
1
1
0
1
1
1
0
0
2
1
0
0
1
0
1
0
1
1
1
0
0
0
0
0
0
0
2
0
1
2
1
0
1
0
0
0
0
0
2
0
3
0
0
3
1
1
0
3
1
2
1
1
0
0
1
0
2
2
0
0
1
1
0
0
2
0
0
1
1
1
3
1
0
1
2
2
2
0
1
2
2
1
1
0
2
0
0
0
2
1
1
0
2
0
0
1
0
1
2
0
1
2
0
2
0
0
0
1
1
0
1
1
1
0
1
0
1
1
0
1
3
1
0
2
2
1
2
3
2
0
1
1
0
1
2
1
0
2
0
1
1
1
0
2
0
1
0
0
2
0
1
1
2
1
0
0
1
0
2
0
0
1
0
1
2
0
1
0
0
1
1
1
2
1
1
0
1
3
0
0
0
2
0
2
0
2
0
3
0
0
0
0
0
0
2
0
0
0
3
2
2
0
0
0
2
3
1
1
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
1
0
2
0
0
0
0
0
1
1
1
1
0
0
0
0
1
2
1
0
0
0
1
0
1
1
0
2
0
0
2
1
0
0
0
0
1
1
2
2
1
0
1
0
0
2
1
0
1
2
2
1
2
0
0
1
2
0
1
1
1
0
1
1
0
0
1
1
1
1
2
0
2
0
0
0
2
1
2
1
0
2
0
0
1
2
0
0
1
2
0
1
0
1
2
0
0
1
1
0
2
0
1
2
1
1
0
0
2
1
1
0
0
2
0
0
0
1
2
1
0
1
1
2
2
0
1
1
0
1
1
2
0
2
0
3
1
3
0
0
0
0
2
0
0
1
0
0
1
1
2
0
1
1
0
0
2
1
1
0
0
0
1
0
0
2
1
0
1
2
2
1
1
0
1
0
0
1
1
2
0
0
0
0
0
2
1
2
1
0
0
0
0
0
2
1
1
0
0
2
2
1
0
1
0
0
2
0
0
0
1
0
0
1
1
0
1
0
2
0
2
2
0
0
1
0
2
1
2
0
2
1
2
0
1
0
2
0
2
1
0
0
0
1
1
0
2
2
0
2
1
1
0
2
0
1
2
0
0
1
1
0
1
1
0
0
0
0
0
2
1
0
2
0
1
0
1
0
0
1
0
0
0
0
2
0
1
2
0
2
1
0
1
2
0
2
2
0
2
1
0
0
1
1
1
1
1
2
0
2
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
1
2
1
1
2
0
0
1
0
0
2
1
1
0
0
1
2
1
2
0
0
2
1
0
0
0
0
3
1
0
0
0
0
0
0
2
1
1
2
0
2
0
2
1
2
1
1
0
1
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
1
1
2
0
2
0
0
0
0
1
2
0
1
2
0
0
2
1
0
0
0
1
1
0
1
0
1
0
1
0
1
0
0
0
4
2
1
0
0
0
0
2
0
3
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
1
2
1
2
0
1
0
2
2
2
1
0
1
0
0
2
0
0
2
0
3
1
3
2
0
0
0
1
0
2
1
0
0
1
1
2
1
0
1
0
1
0
0
2
0
2
0
0
1
2
1
0
2
0
0
0
1
1
0
0
2
2
0
2
1
0
3
0
2
1
2
0
0
0
1
1
0
1
0
2
1
12
0
0
2
1
0
2
1
1
1
0
0
0
0
2
2
0
0
0
0
2
0
0
1
1
1
2
0
0
0
0
2
2
1
0
0
2
1
2
3
0
3
2
0
0
1
0
0
3
1
0
1
0
1
1
0
2
0
0
1
0
1
2
0
2
1
1
0
1
0
2
0
0
0
0
0
1
2
0
0
0
2
0
1
2
2
0
1
0
2
0
0
0
0
0
0
0
0
2
2
1
1
0
0
1
0
0
1
2
2
0
0
2
2
1
2
0
1
1
2
1
2
1
0
1
0
3
1
0
1
1
0
2
2
1
0
1
2
0
1
0
1
1
2
0
0
0
1
2
0
1
1
0
0
2
1
0
1
0
0
0
0
0
1
2
0
0
1
0
2
2
2
0
0
0
1
0
0
1
1
2
1
0
1
0
0
1
0
2
0
2
0
1
2
0
1
0
2
1
0
0
1
1
1
2
1
2
0
1
2
0
0
1
3
1
1
1
1
2
1
1
2
1
0
1
1
0
0
1
1
0
1
2
1
0
0
0
1
2
0
0
2
0
2
0
0
0
1
2
0
2
1
0
0
1
0
0
0
1
1
2
1
0
2
1
1
1
1
2
1
0
0
0
1
1
0
1
1
1
2
2
2
2
0
1
0
1
0
1
0
2
2
1
0
0
0
0
0
1
0
2
0
1
2
0
0
1
1
0
1
0
1
0
1
1
2
1
1
1
0
2
1
1
1
1
0
2
1
2
1
0
0
1
0
0
0
3
2
1
0
2
0
0
0
0
2
1
2
0
1
2
0
2
2
1
5
0
1
0
2
1
2
0
0
0
2
1
1
0
0
1
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
3
1
0
0
2
1
1
0
0
0
0
1
0
0
2
1
1
0
0
0
0
0
2
0
2
0
2
0
0
1
0
0
1
2
0
0
1
1
0
1
2
2
0
0
2
0
0
1
0
3
1
2
1
1
0
0
1
2
1
2
0
0
1
2
0
1
1
2
1
1
2
0
1
0
0
1
0
0
2
0
1
0
0
0
0
2
0
0
0
2
0
2
1
0
1
1
0
2
2
1
2
0
6
1
0
0
0
1
2
2
1
0
2
1
1
0
0
0
1
2
1
2
0
1
1
1
0
1
0
2
0
0
0
0
0
0
0
0
2
0
1
0
2
1
0
1
0
1
0
2
2
0
0
1
2
1
0
0
3
2
0
2
2
2
2
1
0
2
1
1
0
1
0
1
2
0
0
0
0
0
0
0
0
2
2
0
2
4
0
0
0
0
0
1
2
0
1
1
0
1
0
0
2
0
0
0
2
0
0
1
0
1
0
1
2
1
1
0
0
1
1
0
0
0
0
0
0
2
1
2
1
0
0
0
1
4
1
2
0
0
0
2
0
2
2
0
2
1
0
0
2
0
2
0
2
1
1
2
1
0
0
2
1
0
0
2
0
0
0
0
2
0
0
0
2
0
0
1
0
0
2
0
1
1
0
1
0
2
1
0
0
3
0
0
0
0
0
1
2
0
1
2
1
1
2
0
2
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
1
0
2
0
2
1
1
1
0
2
0
0
0
2
1
1
0
1
1
2
2
0
1
1
1
0
0
0
1
0
0
0
1
0
0
2
3
0
0
1
1
1
0
1
0
0
0
0
1
1
2
1
2
2
0
1
1
0
0
0
1
0
0
1
2
1
1
0
1
0
1
1
0
2
0
2
0
0
2
0
0
2
2
0
0
0
3
0
1
0
1
0
0
0
0
2
1
0
0
0
1
0
1
1
1
2
1
1
0
0
0
2
2
1
1
1
1
0
2
2
1
0
0
1
0
0
1
2
0
0
1
0
1
0
0
1
2
0
2
1
2
2
2
0
1
0
0
1
1
2
0
1
1
2
1
1
2
0
0
0
2
0
0
0
0
0
1
1
0
2
2
0
0
1
0
0
2
2
1
0
0
0
0
1
1
2
2
2
0
0
0
1
0
0
2
1
2
0
1
0
0
1
2
0
1
0
0
1
2
1
1
0
3
2
0
0
0
1
2
1
1
2
1
0
2
0
1
1
1
1
2
2
0
2
1
0
1
3
2
0
2
2
1
2
1
1
1
0
0
1
2
0
3
1
1
0
1
0
1
0
0
1
0
2
2
2
1
1
1
0
1
2
0
0
1
0
1
0
1
0
1
0
1
0
0
0
0
0
0
2
1
1
0
0
1
2
2
1
0
0
1
2
1
0
1
1
0
1
0
0
0
0
0
0
0
2
1
0
2
0
0
0
2
0
0
1
0
2
2
1
0
2
0
2
0
0
1
0
2
0
2
0
1
2
2
0
2
0
0
0
0
0
1
2
0
0
1
0
1
1
1
3
0
0
0
0
0
2
1
1
0
7
0
0
0
1
0
1
1
2
1
1
0
0
0
0
0
1
1
0
1
3
1
1
1
3
1
2
0
0
2
2
0
1
2
0
0
0
0
0
1
0
3
0
1
0
1
0
0
1
2
0
0
1
1
2
1
0
2
1
0
1
0
3
1
1
1
0
1
0
0
0
0
1
2
0
0
1
0
0
0
2
0
2
1
1
2
2
3
0
0
0
1
0
0
0
1
2
1
0
0
1
2
0
1
1
0
1
3
1
0
0
1
2
1
1
2
2
0
1
0
1
0
1
3
1
2
2
0
1
0
0
0
0
2
0
0
0
1
2
0
1
1
0
1
0
1
0
0
0
1
0
0
0
0
2
0
1
1
0
2
0
0
0
1
2
2
0
0
0
0
1
1
0
2
0
2
1
0
2
1
0
0
1
1
0
0
0
0
0
0
1
1
1
1
1
0
0
0
1
2
0
0
0
2
1
0
2
0
1
0
0
1
0
1
1
0
2
1
2
0
0
2
0
1
2
0
0
1
0
0
0
0
2
0
1
0
1
4
0
2
1
2
1
1
0
1
1
1
1
0
2
0
1
0
0
0
0
0
0
7
2
1
0
1
1
0
0
2
0
0
0
0
0
1
0
2
3
1
1
2
2
2
0
1
0
1
0
1
1
0
1
0
0
0
1
2
2
2
0
1
0
2
0
1
0
0
2
1
0
0
0
1
1
0
0
1
0
2
0
3
1
2
1
0
2
0
3
0
1
0
0
2
0
1
0
1
2
2
0
1
1
0
1
0
0
1
0
0
0
0
0
1
2
0
0
0
0
2
0
2
0
2
1
0
0
0
0
1
2
0
0
0
2
0
0
0
5
0
1
0
0
0
0
1
1
0
2
0
1
0
0
2
3
1
1
1
0
1
1
0
0
0
0
1
1
2
1
1
0
0
2
0
1
1
0
0
1
1
2
2
2
2
1
2
0
0
1
0
0
1
0
0
1
2
1
1
1
0
0
0
1
0
0
2
1
0
0
0
1
1
2
0
0
2
1
0
0
0
0
0
2
1
0
0
1
1
0
0
2
0
1
1
0
0
4
1
1
1
1
0
0
1
1
1
0
0
2
1
0
0
0
2
0
1
0
1
0
3
1
1
1
0
1
0
0
3
0
0
0
2
0
1
2
1
0
2
0
2
2
2
0
1
0
2
2
2
0
3
0
1
1
2
0
1
2
0
0
2
0
0
2
0
0
0
0
2
0
0
1
2
1
0
0
6
1
1
2
2
1
1
3
2
0
1
1
2
0
0
0
0
1
0
0
0
0
2
3
1
0
2
0
0
4
1
0
0
1
1
2
0
0
0
2
1
0
1
1
1
2
1
0
1
0
0
0
0
2
2
0
2
0
0
0
0
2
0
2
2
0
2
0
2
0
0
0
1
2
0
1
0
1
0
1
2
2
2
2
1
1
0
2
1
0
0
2
0
0
0
2
0
0
1
0
0
0
3
1
1
0
1
0
0
0
2
0
2
0
1
0
2
0
1
0
0
0
2
1
2
0
0
1
1
1
0
1
2
0
0
0
1
0
0
0
0
1
1
0
0
1
1
0
0
2
0
0
1
0
5
0
1
1
2
1
0
0
1
0
2
1
1
0
0
0
0
1
0
1
1
0
2
0
2
0
2
1
1
0
0
1
0
1
0
1
2
0
1
0
1
2
0
0
0
2
2
2
0
0
0
0
1
0
0
2
1
3
1
2
1
2
2
0
0
1
0
1
0
0
3
0
0
0
1
0
0
0
0
1
0
2
2
1
0
0
0
0
2
0
1
2
0
0
0
2
1
0
0
0
0
0
2
0
0
1
0
2
0
1
1
2
0
1
0
1
0
1
0
0
0
0
0
1
0
1
1
1
0
1
3
0
1
2
3
0
1
0
1
0
2
1
1
0
1
0
0
0
1
0
0
2
1
0
2
2
0
1
1
0
0
1
0
0
1
2
1
0
0
0
0
1
0
3
2
1
1
0
0
1
2
0
1
2
2
2
0
0
1
1
0
0
1
0
2
1
0
0
1
0
0
1
1
0
1
1
1
0
0
0
2
0
0
1
1
3
0
0
1
1
1
0
1
0
1
1
2
1
0
1
0
0
0
1
0
1
1
1
1
1
0
2
1
1
1
2
0
0
0
0
2
0
2
1
1
1
1
0
0
2
0
0
1
1
2
0
1
1
0
1
1
1
2
3
0
1
1
0
0
0
0
1
3
0
0
2
1
1
1
2
1
1
0
2
0
1
2
1
0
1
0
1
1
1
0
1
2
0
1
2
1
2
1
2
1
0
1
0
1
0
2
0
0
4
1
1
0
0
1
2
1
2
0
0
0
0
2
2
0
1
1
0
2
1
2
0
0
2
0
0
1
1
1
0
1
0
2
2
0
1
0
0
1
0
2
1
1
0
0
0
0
0
1
0
0
0
0
1
1
1
0
3
0
0
0
2
0
2
0
0
0
2
2
1
0
0
1
1
1
2
0
0
2
1
1
1
1
1
2
0
0
0
0
0
0
2
0
2
0
2
0
0
1
0
0
2
1
9
2
0
0
0
0
0
0
2
0
0
0
0
2
1
0
2
0
2
2
1
2
1
1
2
0
2
2
1
1
0
2
2
2
0
1
2
1
0
0
1
2
0
0
1
1
2
1
1
0
1
0
1
1
2
0
0
0
0
0
0
2
0
1
1
0
1
0
1
0
1
0
2
0
0
1
0
2
0
1
0
2
0
0
0
1
3
0
1
1
0
0
2
1
0
0
0
0
0
1
1
1
0
1
1
0
2
1
1
0
1
2
1
2
0
0
0
2
0
0
1
1
0
0
0
0
1
0
0
1
1
0
1
2
0
1
0
1
0
1
0
2
2
0
2
0
2
0
1
2
2
1
2
0
1
0
2
0
0
0
0
2
0
1
0
2
2
0
0
0
0
1
1
1
0
1
1
2
0
1
0
0
1
1
1
0
0
0
1
0
0
2
1
2
1
1
1
1
2
0
2
0
1
0
1
1
0
0
0
1
1
2
2
0
0
2
0
1
0
0
0
0
2
0
0
2
0
2
0
0
0
0
1
1
1
0
0
2
0
0
2
2
1
0
0
2
1
0
4
0
0
2
1
1
1
1
1
1
0
1
0
1
2
1
0
2
1
0
0
2
0
1
0
2
3
2
0
1
0
2
1
0
1
0
2
2
2
0
1
0
1
0
2
1
2
0
1
1
0
1
1
0
1
0
0
0
2
0
2
1
0
1
2
0
1
2
0
0
1
1
1
1
2
1
1
0
1
1
0
2
2
0
1
1
1
0
0
0
0
0
2
0
0
1
0
2
1
2
0
0
0
0
1
2
1
0
2
0
0
2
2
1
0
3
1
0
0
0
2
1
0
0
0
2
2
1
1
2
0
0
1
1
1
1
1
2
1
2
0
0
0
1
0
0
0
1
2
0
1
1
1
0
1
0
0
0
2
2
0
0
1
2
1
0
2
1
0
0
2
0
1
0
0
2
1
2
2
2
0
2
0
0
0
2
0
1
1
0
2
0
2
1
1
0
0
2
1
1
2
0
1
2
2
1
2
0
2
0
1
3
0
0
1
0
1
2
0
1
0
0
2
0
0
1
0
0
1
0
3
0
3
1
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
1
1
2
1
1
0
0
0
1
1
1
0
0
0
1
0
2
0
1
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
1
2
1
0
0
0
1
1
2
1
0
1
0
0
2
0
1
0
0
1
1
0
1
1
1
0
2
2
1
0
2
1
2
2
2
2
2
2
0
2
1
0
0
2
1
1
2
0
0
0
2
2
0
1
0
0
0
1
1
1
1
1
0
0
0
2
2
1
0
1
2
1
0
1
1
2
1
0
2
0
0
1
0
1
1
0
1
0
1
0
0
0
2
0
2
2
2
0
1
2
1
1
0
0
0
0
0
1
1
2
2
2
1
1
2
0
2
1
0
1
2
1
0
0
0
1
2
1
1
0
1
0
0
0
0
1
1
1
0
2
0
0
0
0
1
0
2
0
1
1
1
0
2
1
0
0
1
1
0
2
2
1
0
1
2
1
0
1
1
1
3
0
1
0
1
3
2
0
1
1
0
0
1
1
0
1
2
1
2
1
0
2
2
1
0
0
0
0
2
0
1
0
0
0
1
0
0
2
0
0
2
0
1
0
1
1
0
2
2
0
1
1
0
0
2
0
1
0
0
0
0
1
1
1
2
1
0
2
2
1
2
0
1
3
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
2
0
2
0
1
0
0
0
0
0
0
0
0
2
0
1
1
2
0
1
2
2
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
1
1
0
2
1
2
0
1
1
0
1
2
0
1
0
0
2
1
0
3
2
0
1
1
3
1
0
0
2
2
0
2
0
2
0
0
0
0
1
0
2
1
0
1
0
2
0
1
1
0
1
1
0
0
1
0
1
0
2
1
2
1
0
1
1
2
0
0
0
1
0
0
2
1
0
0
0
0
0
0
2
2
0
0
0
1
1
1
0
1
1
1
0
0
0
1
0
1
0
0
0
2
0
0
0
0
1
0
0
0
3
2
1
0
0
1
0
2
1
0
2
1
1
1
0
0
1
0
1
3
0
1
2
0
0
0
1
0
0
0
1
2
1
0
0
1
0
2
0
1
1
1
2
0
0
1
1
1
2
1
0
2
1
2
3
0
0
1
0
2
1
0
0
0
0
0
1
2
1
8
1
2
0
0
0
0
2
0
1
1
1
1
0
0
1
1
2
1
2
2
2
4
0
2
0
0
0
0
1
1
0
0
0
0
0
0
1
1
2
0
0
2
0
1
0
1
1
1
0
1
0
0
0
2
2
0
0
0
1
0
0
1
0
0
0
0
2
2
0
2
0
1
1
0
1
1
0
1
2
0
3
0
1
1
2
2
1
1
1
2
2
1
1
2
0
1
2
0
0
2
1
0
0
0
0
2
2
1
0
0
1
2
0
1
0
0
1
0
0
2
0
2
1
1
2
0
0
0
1
0
0
0
0
2
0
0
1
1
1
0
0
0
2
0
0
1
0
0
2
0
0
0
1
1
0
0
2
0
1
1
0
1
0
0
2
0
1
1
2
2
0
2
0
0
0
2
1
0
0
1
1
0
3
0
1
1
3
0
1
0
1
0
1
0
0
1
1
0
0
0
2
3
0
1
0
0
2
0
2
2
2
0
0
1
0
1
0
2
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
1
1
0
1
0
0
1
0
1
0
0
1
0
2
0
2
1
1
0
2
2
2
0
1
2
2
1
0
2
1
2
2
2
1
0
0
1
2
1
2
0
1
3
0
2
0
2
2
1
0
1
0
1
1
1
0
1
0
1
1
0
1
1
2
0
1
0
2
1
0
1
0
2
0
0
0
2
0
0
0
2
0
0
0
1
4
0
1
0
1
0
2
2
1
2
2
1
1
0
0
0
1
1
0
2
0
0
2
2
2
0
0
1
2
2
0
1
0
0
2
0
0
1
0
0
0
1
0
1
1
0
0
0
2
0
0
0
0
2
0
1
1
1
0
1
2
0
2
1
1
1
0
2
0
1
0
2
1
1
1
2
1
0
2
0
0
0
1
1
0
1
0
1
0
0
2
1
0
1
1
1
0
0
0
1
1
0
0
0
3
2
0
0
1
1
0
1
1
0
1
0
1
2
1
1
0
0
1
0
0
2
1
0
0
1
0
0
1
1
0
0
1
1
1
0
0
2
1
2
2
2
0
2
1
2
0
0
0
0
0
0
1
1
1
2
1
0
1
0
0
1
1
2
2
2
0
0
0
1
1
0
1
1
2
0
0
2
2
2
0
2
0
1
0
1
0
2
0
2
0
0
0
0
0
3
0
1
1
0
2
1
1
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
2
2
0
0
1
1
0
0
1
1
0
1
0
1
0
1
1
1
2
0
2
1
0
2
1
0
1
2
2
2
0
0
1
2
1
1
0
0
0
1
1
0
2
0
1
0
1
2
1
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
1
2
0
0
0
2
1
1
0
0
2
0
1
0
0
0
0
1
1
0
2
1
1
2
0
0
0
0
0
1
0
2
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
1
2
2
0
0
0
0
0
2
1
0
1
2
1
0
0
1
2
2
1
1
2
0
0
1
0
2
0
1
0
2
0
1
1
2
0
0
0
4
0
1
2
1
2
1
1
2
2
1
2
2
2
1
0
2
0
0
0
1
0
2
0
0
1
1
0
1
0
2
1
0
1
0
0
1
1
0
1
1
1
2
2
0
0
2
2
1
0
2
0
5
1
1
2
2
2
0
0
0
0
2
0
0
0
0
0
1
2
1
5
0
1
1
2
2
0
2
0
0
1
0
0
1
0
2
0
2
2
2
1
0
2
0
2
0
0
0
1
1
2
1
0
2
0
0
2
2
2
1
0
2
0
0
0
2
0
1
0
1
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
2
2
2
1
0
1
1
0
1
1
1
1
2
0
0
1
0
1
0
2
2
0
2
1
0
0
0
1
1
2
0
2
0
1
0
0
2
2
2
2
0
0
2
2
2
1
0
1
1
0
1
0
0
0
0
0
2
0
1
1
0
2
3
0
0
1
0
0
1
2
1
1
3
0
1
2
2
1
1
0
0
0
1
1
3
0
2
1
1
0
1
0
0
0
0
1
1
1
1
2
1
2
0
1
2
0
0
0
0
3
0
1
0
0
0
0
0
2
0
2
1
1
2
1
0
2
0
1
1
0
0
0
0
0
0
0
2
1
1
0
1
2
1
0
2
0
1
1
1
1
0
0
1
0
1
1
0
2
1
2
1
2
0
0
0
1
0
1
2
0
2
0
2
2
1
0
1
2
2
1
1
1
0
0
1
0
1
0
1
2
1
0
0
1
0
0
1
0
0
0
3
0
2
0
2
0
1
0
0
0
0
2
0
0
0
1
2
0
1
0
1
2
0
0
0
1
2
0
1
2
2
0
2
0
0
1
1
1
1
2
1
2
1
1
0
2
1
2
0
1
0
2
0
2
2
2
0
0
0
1
2
2
0
4
0
0
0
0
1
1
1
0
3
2
1
1
0
2
0
0
1
1
2
1
0
1
1
2
0
0
0
2
1
0
0
4
2
1
2
2
0
1
0
3
0
0
1
0
1
0
1
0
0
0
0
0
3
2
0
1
2
1
0
2
0
0
0
1
0
1
1
0
2
1
1
1
2
2
0
1
1
0
1
0
0
2
1
1
0
1
0
1
2
2
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
2
1
1
3
0
0
1
1
1
1
0
0
1
2
0
1
1
2
2
1
1
2
0
0
2
1
0
0
0
4
0
0
1
0
1
1
1
0
1
0
0
0
2
2
0
1
0
1
2
1
1
0
0
2
1
1
2
3
0
0
0
2
0
0
0
1
0
2
0
0
2
1
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
1
2
0
1
0
1
2
1
0
0
2
2
2
1
1
1
1
2
1
1
0
4
2
2
0
0
2
2
0
2
0
2
1
2
0
2
2
1
0
1
0
0
2
1
0
0
0
0
1
0
2
0
1
1
1
0
2
0
0
1
0
0
1
0
0
2
0
1
2
0
0
0
2
1
0
0
0
0
1
1
0
0
2
2
0
0
2
0
0
2
0
1
0
1
1
2
2
0
1
0
2
0
0
1
0
1
1
1
1
1
0
3
0
0
1
0
1
0
2
2
0
0
2
0
0
2
1
2
1
2
1
0
2
2
1
0
1
0
1
1
0
1
2
0
1
2
1
2
1
0
1
2
2
1
0
0
0
2
0
1
1
2
1
0
0
1
1
0
0
2
3
1
2
0
1
0
1
1
1
1
1
1
1
0
1
2
1
0
0
0
1
0
2
2
0
1
1
0
0
2
0
2
2
0
2
2
0
1
1
2
0
1
0
1
1
0
1
0
3
0
2
2
1
0
0
0
2
0
0
2
2
0
0
0
0
1
0
1
2
2
1
1
1
2
1
2
0
0
2
0
2
1
1
2
0
1
0
3
2
2
1
2
2
2
0
0
0
0
2
2
1
2
0
1
1
1
1
0
0
1
0
0
0
0
2
0
1
0
1
1
1
0
2
1
1
0
1
1
1
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
1
0
2
2
0
1
1
2
0
0
0
1
2
1
0
2
0
1
0
0
1
1
0
0
0
1
0
1
0
2
0
0
2
2
0
1
1
1
2
0
2
0
0
0
1
0
0
1
0
0
0
2
1
2
0
0
0
2
1
0
1
0
0
0
2
1
3
0
0
0
1
0
1
2
0
1
2
0
1
2
0
2
2
2
0
1
0
0
3
0
0
0
1
0
3
0
1
1
0
0
1
1
1
0
1
0
0
2
0
1
1
1
0
1
1
1
2
1
2
2
1
2
1
1
0
0
1
1
2
0
1
1
1
0
3
0
2
1
0
0
1
2
1
2
1
0
0
2
0
0
0
2
0
1
3
1
0
1
0
2
2
1
0
2
1
0
3
1
0
0
2
1
2
2
1
0
1
2
0
0
0
2
0
1
1
0
2
0
0
1
1
0
2
2
0
2
0
0
0
1
2
0
2
0
0
0
1
1
1
0
0
1
0
1
0
0
0
0
1
2
2
1
1
0
2
0
1
0
1
0
0
2
0
1
1
1
0
0
0
0
0
0
2
2
1
1
0
1
1
1
0
0
0
0
1
1
2
2
0
0
2
0
0
0
1
1
1
2
4
0
0
1
1
0
0
0
1
1
2
2
1
3
1
1
0
2
1
1
1
1
0
0
0
2
2
2
0
0
0
2
2
0
0
0
0
2
2
0
0
1
0
1
0
0
0
1
0
0
1
2
0
0
0
0
1
0
3
0
2
0
1
0
1
0
0
1
0
1
1
2
0
1
2
1
1
1
1
1
0
3
1
0
0
0
0
0
0
2
1
1
2
1
0
0
0
0
1
1
0
0
2
0
2
1
0
1
1
1
1
0
0
1
2
0
1
0
0
0
0
0
2
0
0
2
2
0
2
2
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
2
1
0
0
0
1
2
0
0
1
1
0
1
0
1
1
2
1
0
1
0
1
1
0
0
2
2
0
2
2
2
2
0
2
0
0
0
1
1
0
2
0
2
2
0
0
0
0
1
0
0
1
1
2
0
1
0
1
0
2
0
1
0
1
1
2
2
1
0
0
1
1
2
0
0
0
1
0
0
2
0
2
2
2
0
0
0
0
0
2
0
0
0
2
0
1
0
0
1
0
2
0
1
2
0
0
0
0
1
0
2
1
0
1
2
3
1
0
0
1
0
0
2
1
0
0
0
1
2
0
0
0
0
2
0
1
1
0
1
1
0
0
0
0
0
1
0
0
0
1
1
1
0
0
2
0
1
1
0
1
0
0
1
1
1
0
2
0
0
1
1
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
1
1
2
1
1
2
0
0
0
0
0
0
0
1
0
1
2
0
0
0
2
0
2
1
0
1
0
0
1
2
1
1
0
0
0
0
2
1
2
0
1
1
1
0
3
2
0
2
0
2
1
0
0
2
0
0
2
1
0
1
0
2
0
0
1
2
0
2
0
0
1
2
0
1
0
0
1
2
0
0
1
0
2
0
1
1
0
0
0
0
2
2
0
2
0
2
0
1
2
0
1
2
2
0
0
0
0
1
2
1
0
1
3
0
0
3
2
2
2
1
1
1
2
1
0
2
1
0
2
1
1
1
0
0
0
0
0
0
0
0
1
2
1
0
2
1
1
1
1
0
1
0
0
1
1
1
0
1
0
2
0
1
0
0
0
3
0
2
0
0
2
1
0
0
0
2
0
2
1
1
1
0
0
1
0
1
1
1
1
0
0
0
2
0
1
1
0
0
0
2
2
0
0
1
0
2
1
2
1
0
0
2
1
0
1
1
2
2
0
1
0
0
1
2
0
2
1
0
1
1
1
4
0
3
2
1
0
2
1
1
1
0
1
0
2
2
1
0
0
1
1
1
1
0
0
0
0
0
0
2
0
1
2
1
0
1
0
0
0
0
0
2
0
0
0
1
2
0
2
2
0
0
0
0
2
0
0
1
0
1
0
0
1
0
1
1
0
2
0
1
0
0
1
1
1
1
2
0
0
1
0
0
2
0
1
2
1
0
1
1
1
0
1
1
0
0
0
2
1
1
0
3
0
0
0
0
1
0
0
1
1
1
0
0
0
0
2
2
1
2
0
0
0
1
0
2
0
0
2
1
0
2
1
2
0
2
0
1
0
1
1
0
2
2
1
1
0
0
0
0
1
1
0
2
0
0
2
2
0
1
1
0
0
0
0
0
1
0
0
1
1
1
0
2
0
1
0
1
2
1
0
1
2
1
1
1
0
0
0
2
1
1
1
1
0
0
1
2
0
0
0
2
2
0
0
0
1
1
0
0
0
0
2
0
0
1
0
0
0
0
1
1
0
1
0
0
0
2
0
1
2
2
1
1
1
2
1
1
2
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
1
1
0
0
0
1
0
2
2
0
0
1
0
1
2
0
0
1
0
1
0
1
0
0
1
1
0
0
1
2
0
2
0
2
0
1
1
2
2
0
0
1
0
0
0
1
5
0
2
0
1
0
1
1
0
0
3
1
1
2
2
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
2
1
0
0
0
2
2
1
1
1
1
1
1
2
0
0
1
0
1
0
0
0
0
1
0
3
1
2
0
0
0
0
0
0
0
1
1
0
0
1
1
1
0
0
0
1
1
1
1
0
0
0
0
0
1
6
0
1
1
1
5
2
0
0
0
0
0
1
0
1
0
1
0
1
0
2
0
0
2
0
0
1
2
0
1
1
1
1
1
0
2
0
0
1
0
1
0
0
0
0
1
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
3
0
3
2
2
2
1
0
8
0
0
1
0
1
0
0
0
2
0
0
0
0
0
1
2
2
2
0
2
0
1
0
2
2
0
0
2
1
0
1
1
2
2
0
0
0
0
0
1
0
1
1
0
0
2
3
0
2
1
0
2
0
1
0
0
0
1
1
1
0
0
1
0
1
0
0
0
3
0
0
0
1
1
0
0
1
0
2
0
0
1
1
0
2
0
2
1
1
0
0
0
1
0
0
1
2
0
0
4
0
0
2
1
0
2
1
0
3
0
0
0
2
1
1
0
0
7
1
0
0
2
2
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
2
1
0
1
0
1
0
0
1
0
1
0
1
0
1
0
0
2
1
3
1
1
0
0
1
0
0
1
1
0
2
2
0
1
1
0
1
0
0
1
0
2
1
0
0
1
2
1
2
1
0
1
0
1
3
0
0
0
0
2
0
0
2
3
2
0
1
0
0
2
1
0
1
1
0
0
0
0
0
2
0
1
0
0
1
1
2
0
0
0
2
0
0
1
1
1
1
0
1
2
0
0
1
1
0
0
2
0
0
1
1
1
1
0
2
0
0
1
1
0
0
0
2
2
0
2
1
0
0
0
1
0
2
1
2
0
0
1
2
0
0
0
1
2
1
0
0
0
0
2
2
0
1
1
4
0
1
1
0
0
1
1
2
0
0
1
1
2
0
0
0
0
0
0
1
0
1
0
1
2
1
2
0
0
0
0
1
0
0
1
0
3
0
0
0
0
0
2
0
0
0
1
1
1
0
0
0
1
1
2
1
1
1
1
0
0
0
0
1
0
3
1
1
0
0
0
0
0
2
1
0
0
0
0
0
2
1
0
1
0
0
1
1
2
0
1
0
0
5
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
2
1
0
0
0
1
1
2
0
1
2
0
1
0
1
0
0
2
0
1
2
1
0
1
1
0
2
1
1
0
1
1
0
2
0
0
1
3
1
2
1
0
0
1
0
1
2
0
0
0
1
0
2
0
0
1
1
2
0
0
1
0
0
2
0
1
0
0
0
1
1
1
1
0
1
0
0
0
2
2
0
0
1
0
1
2
0
2
0
0
1
0
0
1
2
0
0
0
2
0
0
0
1
0
1
2
0
0
0
1
1
0
1
0
1
2
0
0
4
1
0
1
0
3
0
0
1
0
2
0
0
0
0
2
2
2
1
2
0
0
2
0
2
1
0
0
0
0
2
2
1
0
0
2
0
0
0
3
2
0
1
1
2
1
0
0
0
0
1
1
0
2
2
0
4
0
1
1
0
0
2
2
0
1
2
2
0
0
2
0
2
0
0
0
1
2
1
1
0
0
0
1
2
0
2
0
1
2
0
1
1
2
2
1
0
0
4
2
0
0
0
1
0
2
0
2
2
0
1
0
1
0
0
2
1
1
0
1
0
0
1
2
0
0
0
1
0
1
0
2
2
1
2
1
0
0
0
1
1
2
1
1
0
2
0
0
2
2
0
1
2
0
2
2
2
0
0
2
1
2
1
1
0
0
1
0
2
1
2
0
1
1
0
0
0
1
1
0
2
0
4
0
1
0
0
2
1
0
0
2
0
2
0
2
2
1
1
1
0
0
2
2
0
2
1
2
1
0
1
0
0
1
0
1
0
2
0
1
1
0
0
1
2
0
1
0
0
0
0
2
0
2
0
0
4
0
2
1
2
0
0
0
0
0
0
1
0
2
0
1
1
1
2
1
2
0
2
0
1
2
1
1
0
1
1
1
0
3
0
0
0
0
1
0
1
0
1
0
2
1
0
0
2
1
0
0
0
0
0
0
2
2
0
0
0
0
2
1
2
0
0
0
0
2
0
1
0
2
1
0
1
0
0
0
0
0
1
2
1
1
0
0
1
0
0
0
1
0
0
1
0
0
0
2
1
0
1
2
0
1
0
2
1
2
1
1
2
0
2
0
2
1
2
3
2
1
2
1
2
0
4
2
0
0
0
0
1
1
1
1
0
2
0
2
0
0
1
2
2
2
0
0
1
1
0
0
2
2
1
0
2
1
0
1
0
1
0
0
0
1
0
0
2
2
1
2
2
0
2
1
2
1
1
0
2
0
0
0
1
0
0
0
2
0
1
0
1
0
0
0
2
0
1
0
2
2
0
1
1
1
2
2
1
0
0
0
0
0
0
1
0
0
2
2
2
1
0
0
0
1
1
0
0
1
0
0
2
2
0
1
0
2
1
0
0
3
2
0
0
0
2
2
1
1
0
1
1
1
0
2
0
1
0
1
1
2
1
0
0
0
1
1
0
0
1
0
0
0
2
2
0
0
2
0
1
0
1
1
2
0
2
0
0
0
1
1
0
0
0
2
0
2
1
2
1
0
0
0
0
2
0
0
2
0
1
0
1
2
0
0
0
0
2
0
0
1
1
0
1
0
0
1
2
0
1
2
3
1
1
1
0
1
0
2
1
0
2
2
1
1
0
0
0
1
0
1
0
2
2
0
1
0
0
1
2
3
2
2
1
0
0
0
0
0
2
0
4
2
0
2
0
1
2
0
1
2
2
1
0
2
0
1
2
0
2
0
1
0
0
1
0
0
0
2
1
3
0
0
0
1
0
0
0
1
1
2
0
1
0
2
2
2
0
2
1
0
2
2
2
1
2
1
0
1
0
0
0
0
1
0
0
0
3
0
2
1
0
2
0
0
1
1
1
1
0
1
2
0
0
1
0
2
1
1
1
1
0
0
0
0
1
0
2
1
1
0
2
0
0
1
1
0
0
1
0
1
2
0
0
0
1
0
0
1
2
0
0
0
0
2
1
1
3
2
0
1
0
2
0
1
1
2
1
2
1
0
0
1
0
1
0
1
2
2
1
0
0
0
2
0
0
0
0
1
2
1
2
1
2
0
2
2
0
2
1
0
1
2
1
3
2
0
1
1
0
0
1
0
3
0
0
3
2
0
0
1
1
0
0
0
2
3
0
1
0
0
0
1
0
1
0
0
0
1
0
1
0
0
1
0
0
2
2
1
2
2
2
1
1
0
1
0
1
0
1
0
0
1
1
0
2
0
1
1
0
2
4
1
0
1
0
0
0
3
0
1
0
1
0
0
1
0
1
0
0
1
0
1
0
0
0
1
3
0
0
2
1
0
0
1
1
0
0
0
1
2
1
0
1
1
0
0
2
4
1
2
0
0
0
1
1
0
1
1
0
3
3
0
1
2
1
0
2
0
2
0
1
1
1
0
1
2
2
0
0
0
0
0
2
2
0
1
1
0
2
0
1
0
0
0
0
2
1
0
0
1
2
1
0
0
2
0
1
1
1
2
1
2
1
0
2
2
0
2
0
1
1
0
2
0
0
0
0
0
0
3
1
1
1
0
0
1
0
0
0
0
1
1
2
0
2
2
1
1
1
0
5
1
1
1
2
0
2
1
0
0
1
0
0
2
0
0
0
1
0
2
0
1
0
1
0
3
0
0
0
0
2
1
0
0
0
1
1
0
1
1
0
0
1
2
2
0
0
0
0
1
0
2
0
0
4
1
0
1
2
0
1
0
1
0
2
1
0
1
1
1
0
2
0
1
2
1
2
0
0
0
3
2
0
0
0
1
1
2
1
1
1
2
3
0
1
2
1
0
1
0
1
1
2
0
0
1
1
0
0
2
2
1
0
2
0
1
0
0
0
0
1
0
0
0
0
0
3
0
0
0
2
1
1
0
2
1
1
3
1
0
0
0
0
2
3
1
0
2
0
2
0
0
1
0
0
0
1
2
1
0
0
1
1
2
1
0
2
0
1
0
0
2
0
1
1
0
2
0
0
1
1
0
0
1
1
0
0
0
0
0
1
0
2
2
0
0
0
1
1
1
0
1
1
0
0
0
0
1
2
1
1
0
1
1
1
0
2
0
1
0
1
2
0
0
1
0
1
0
0
0
0
1
2
1
1
0
0
0
2
0
2
2
2
2
0
0
1
0
0
0
1
1
2
0
2
1
1
0
1
0
0
1
0
0
1
0
1
2
1
2
1
2
1
1
0
1
2
1
2
1
0
0
1
0
2
0
0
2
1
0
3
1
0
0
1
2
1
0
1
1
1
0
0
0
1
2
0
2
0
0
0
1
0
1
2
2
1
2
0
0
0
1
0
0
1
1
2
0
0
0
0
2
1
0
1
1
0
1
1
0
1
0
1
0
1
1
0
1
0
3
2
2
1
1
0
0
0
2
0
2
0
1
0
2
0
0
0
1
0
2
1
3
2
2
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
2
1
2
1
1
1
1
1
2
0
1
0
1
1
0
0
2
2
0
0
1
1
0
0
0
0
0
1
0
1
0
1
0
1
0
2
2
0
2
0
1
0
2
1
0
0
1
2
1
0
1
2
0
0
0
1
0
2
2
0
1
0
0
0
2
0
1
1
0
0
0
0
1
1
2
1
1
2
0
1
1
0
0
1
1
0
1
2
2
2
0
0
2
2
9
3
1
0
0
1
0
1
1
0
0
2
1
1
1
0
2
0
2
1
0
0
0
2
1
0
1
0
1
0
2
2
1
2
2
0
0
2
0
1
0
0
1
0
2
0
0
0
0
1
1
0
2
1
1
2
0
0
1
1
1
1
1
0
0
2
2
0
1
0
2
0
1
1
0
0
1
0
0
1
0
2
1
1
1
1
2
0
0
1
0
1
0
1
0
1
0
1
1
1
0
1
1
0
0
0
0
1
1
0
0
0
0
1
0
1
0
2
1
0
0
1
3
2
2
2
2
0
0
1
2
0
0
2
2
1
1
2
2
1
2
2
2
1
2
2
0
2
2
2
2
0
2
0
2
0
0
0
2
0
1
2
0
0
0
0
2
1
0
1
3
1
0
0
1
0
0
1
0
3
1
0
2
0
0
0
0
0
0
0
3
1
0
0
1
0
2
2
0
1
1
1
1
2
0
0
1
1
0
1
0
2
0
2
1
2
1
0
0
0
0
2
0
0
0
1
1
1
1
2
2
0
1
2
2
0
1
0
1
2
1
0
1
1
1
2
1
0
2
0
2
1
0
0
2
0
2
0
1
1
0
0
0
1
1
1
0
0
2
0
0
0
0
0
0
0
4
0
2
0
0
0
1
1
0
1
0
2
0
0
2
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
1
2
0
0
0
0
0
1
1
0
0
1
0
0
2
0
0
0
1
2
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
1
1
1
1
0
0
0
0
0
2
2
2
1
0
1
0
0
0
0
2
1
0
0
1
1
0
1
1
1
1
2
0
1
0
1
2
0
1
0
1
1
1
4
1
2
0
0
0
0
0
2
0
1
0
0
0
0
1
1
2
2
0
0
1
0
0
1
0
1
0
1
0
0
1
1
2
0
1
1
1
0
1
2
0
1
0
0
0
1
2
0
1
1
0
0
2
0
0
0
0
0
1
1
1
1
0
0
0
1
0
1
0
2
0
5
0
0
0
0
2
2
1
1
0
0
1
0
1
2
0
1
0
0
0
1
2
1
0
0
1
2
2
0
2
1
1
2
0
1
0
0
0
2
0
1
0
2
1
1
0
0
0
0
0
1
2
1
0
1
0
2
1
1
0
2
2
2
0
0
0
0
0
0
2
0
2
0
0
1
0
1
4
0
2
0
1
1
0
0
2
0
0
1
2
1
1
2
0
1
0
2
0
0
2
0
0
0
0
1
0
0
1
0
2
1
0
0
2
0
0
2
1
1
1
0
0
0
2
0
0
0
0
2
0
1
1
2
1
2
1
1
1
1
0
0
2
1
0
1
0
0
0
2
1
0
1
1
0
0
0
0
2
0
0
0
0
0
2
1
1
1
0
1
0
0
0
0
0
2
1
3
1
1
0
0
0
0
0
0
0
1
1
0
0
2
0
0
1
1
1
1
0
1
1
9
2
2
0
2
1
0
2
1
0
1
0
1
0
2
2
0
0
1
1
0
0
1
1
0
0
2
1
1
0
1
0
0
0
0
0
2
1
0
2
0
1
1
0
0
2
2
2
0
0
0
0
1
0
0
0
0
2
0
1
1
0
1
0
0
0
0
0
2
2
0
1
2
1
1
0
0
1
0
2
1
1
0
2
1
1
2
0
1
0
0
2
0
0
2
1
2
0
0
0
1
2
1
0
1
0
0
1
0
0
1
2
0
0
1
1
0
0
0
0
0
0
1
2
0
2
1
2
2
2
0
0
2
0
0
0
1
1
2
1
0
2
0
1
1
2
1
0
1
2
1
0
2
2
1
2
1
0
0
1
0
0
2
1
1
4
1
0
2
2
0
1
0
1
0
0
3
1
2
0
0
1
1
1
2
0
0
1
0
0
1
2
2
1
1
0
0
0
0
1
0
1
1
0
1
1
1
2
0
0
2
0
0
0
0
0
0
1
2
0
0
0
1
0
0
1
0
1
2
0
2
1
0
1
0
1
0
3
1
1
0
0
1
0
3
1
0
0
0
0
1
0
2
0
1
2
1
2
0
0
1
1
2
1
1
0
0
1
0
0
1
1
0
0
0
2
1
0
2
2
1
0
0
1
0
1
0
0
0
1
0
2
4
0
2
0
1
2
0
2
1
2
1
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
1
0
1
2
1
2
0
0
1
1
1
2
4
0
0
1
2
0
2
0
0
2
0
1
1
0
2
0
1
1
0
1
2
0
2
3
0
0
0
0
0
1
1
0
1
2
0
2
0
0
0
2
0
0
0
0
0
0
0
3
0
0
1
0
1
0
1
1
1
1
0
2
0
1
1
0
0
1
2
0
0
1
0
2
2
1
1
0
0
2
0
0
0
2
1
0
1
1
0
2
0
0
0
0
0
1
1
0
0
0
1
0
2
2
1
1
1
0
1
0
1
0
0
1
0
0
0
0
0
1
2
0
1
3
0
0
1
0
2
2
0
1
0
1
1
4
2
0
0
0
0
0
0
0
2
2
1
0
2
0
2
0
4
1
0
1
0
0
0
0
0
0
2
0
0
0
1
0
1
1
2
2
0
1
0
1
0
2
1
0
1
2
1
0
0
0
0
2
1
1
1
1
0
0
1
0
1
0
0
1
1
0
1
0
0
0
2
2
0
2
1
2
0
0
1
1
2
0
1
4
0
1
0
2
2
0
0
0
1
2
2
0
1
1
1
0
0
0
1
0
0
2
0
1
1
1
0
0
1
0
0
2
1
1
2
0
0
1
2
2
2
1
0
1
0
0
2
2
2
1
0
1
0
0
0
0
0
0
0
1
0
1
7
1
2
0
0
2
1
0
0
0
0
0
1
0
0
1
2
3
0
0
0
1
1
1
2
0
0
3
2
1
3
0
1
0
0
2
2
0
1
0
0
0
1
1
0
3
2
0
0
1
2
2
0
1
2
2
1
2
0
2
0
1
0
2
0
1
0
1
4
1
0
1
0
0
2
0
0
0
1
0
1
2
1
2
1
1
1
1
1
0
1
2
0
1
1
1
1
1
1
1
1
1
2
0
0
0
0
1
0
0
1
0
1
1
0
0
2
3
1
0
1
1
2
0
0
1
0
0
1
0
1
1
1
0
2
0
0
2
1
2
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
2
2
0
0
1
1
0
2
2
1
1
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
1
1
2
2
1
5
1
1
0
0
1
0
0
0
1
2
0
0
1
2
1
0
2
1
1
2
0
0
0
5
0
0
0
2
1
1
0
0
1
0
2
0
2
2
1
0
2
1
0
1
3
2
0
0
1
1
2
2
1
1
1
1
0
3
0
1
0
1
0
1
0
2
0
0
2
0
1
3
2
2
2
0
1
0
2
0
1
1
0
0
1
0
0
0
0
1
2
2
1
0
0
2
2
0
0
0
0
1
0
1
0
0
2
1
0
0
1
2
2
0
0
0
1
0
0
1
1
0
0
2
0
1
0
0
0
1
1
0
0
0
0
2
0
2
1
1
2
0
1
0
0
0
0
0
1
0
0
2
0
2
1
2
0
0
0
1
1
2
2
2
0
2
2
1
0
1
1
0
2
0
1
0
0
1
2
0
0
0
0
1
0
0
1
2
3
0
0
2
0
1
1
5
0
1
0
1
0
1
2
0
0
1
0
0
0
0
0
2
0
2
2
1
1
0
0
1
0
0
0
1
1
0
2
0
0
0
0
1
1
1
1
2
0
1
2
1
2
1
1
0
0
0
0
0
0
1
0
0
0
1
3
1
1
1
0
0
1
2
2
2
0
0
2
0
0
0
0
0
0
2
0
0
2
2
1
1
0
1
1
2
0
0
0
1
2
1
2
0
1
0
1
0
1
2
1
1
1
1
2
1
2
0
0
0
1
1
2
0
0
2
0
0
0
1
2
2
0
3
1
0
1
0
1
0
1
0
1
1
1
1
1
1
0
0
1
1
0
0
1
3
0
1
0
4
0
2
0
0
0
0
2
1
0
1
0
0
1
0
2
1
3
0
1
1
0
0
0
0
1
1
2
0
0
1
0
0
0
0
0
1
0
0
2
1
0
2
0
1
0
2
1
1
0
0
0
1
2
0
1
0
1
0
0
2
2
0
1
0
1
0
0
0
1
1
2
0
1
0
0
1
1
0
1
2
0
2
0
1
1
2
2
1
0
2
1
1
0
0
0
1
1
0
0
3
2
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
2
1
0
2
1
0
1
1
2
0
1
1
1
1
0
1
1
1
0
2
2
2
2
2
0
0
2
0
1
0
1
1
0
2
2
2
1
0
2
1
0
1
0
0
1
2
1
2
1
1
2
0
0
0
1
0
0
2
1
1
0
1
0
0
1
1
0
1
0
0
0
0
0
1
1
1
1
0
0
1
1
3
2
2
0
0
0
2
1
1
1
0
0
2
2
0
1
0
0
0
2
0
2
1
0
1
2
0
2
0
0
1
0
0
1
0
1
2
1
2
1
1
2
0
1
1
1
1
0
2
2
1
1
1
1
0
0
0
0
0
1
0
0
1
2
0
0
1
0
1
0
0
2
0
1
0
1
1
0
0
0
0
0
0
1
1
1
0
0
0
2
1
0
0
1
1
2
0
1
0
1
0
1
1
0
1
2
0
1
1
2
2
1
0
0
1
1
1
1
0
2
0
0
0
0
1
1
0
1
1
2
1
0
0
0
0
0
0
2
0
1
0
0
1
1
1
1
0
0
0
3
1
0
1
0
0
0
4
0
0
0
0
0
1
1
1
0
1
1
1
0
0
2
0
1
0
2
0
0
1
0
1
0
1
0
2
0
0
1
0
2
1
0
0
0
2
0
0
0
4
0
0
2
1
0
1
0
0
2
0
0
2
0
2
1
2
0
0
1
1
0
1
0
0
2
0
0
1
1
1
1
0
2
1
0
1
1
0
1
2
0
1
1
1
2
0
0
1
0
0
2
1
0
2
0
2
1
1
2
0
0
1
0
0
0
1
0
1
0
1
2
0
0
0
2
1
2
2
2
0
0
0
2
2
0
1
1
0
1
0
0
0
0
0
1
0
0
1
0
1
1
0
1
2
0
1
0
1
1
2
2
0
1
1
2
1
2
0
0
1
3
1
0
1
1
1
1
0
0
1
0
2
1
0
1
2
0
0
2
0
0
0
1
1
0
1
0
1
0
2
0
0
1
1
2
0
0
2
0
0
0
1
1
0
1
1
0
0
1
0
0
1
0
2
0
1
1
0
1
0
0
1
0
1
0
2
0
1
0
2
0
2
1
2
2
0
1
1
2
1
0
0
1
1
0
0
1
1
1
1
0
1
0
0
1
2
0
0
0
0
2
2
2
1
0
0
0
1
1
0
0
0
0
1
1
0
1
1
0
0
1
0
2
1
0
1
2
0
0
1
0
1
0
0
0
0
2
0
0
0
2
1
0
1
1
1
0
2
0
2
2
2
2
1
0
2
0
0
0
1
0
1
1
1
2
2
1
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
1
2
1
0
2
2
0
1
0
2
1
0
2
0
1
2
1
2
0
1
1
2
2
0
0
0
2
0
0
1
2
1
2
1
0
1
1
2
0
1
0
0
1
1
1
0
1
1
2
1
3
1
1
1
2
0
1
0
2
1
2
0
1
5
1
2
0
1
1
0
0
1
2
0
3
1
1
1
1
1
0
1
2
1
1
1
0
1
1
0
1
0
0
0
0
0
0
1
0
1
1
3
2
1
0
0
1
1
2
1
1
0
0
0
0
0
0
1
0
1
0
1
2
0
2
0
1
1
0
0
1
0
2
1
0
0
2
0
1
2
0
0
1
1
1
2
0
1
0
2
2
0
2
0
0
2
1
0
1
0
0
2
1
2
2
0
3
0
2
0
0
0
2
0
1
0
1
0
2
1
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
1
0
2
1
1
1
0
0
1
2
0
2
0
0
0
1
0
2
0
0
0
1
0
0
0
1
1
0
0
0
3
0
3
1
1
1
1
0
2
1
2
1
1
0
1
1
1
2
0
0
0
0
0
0
2
1
2
0
0
1
0
1
2
1
1
2
0
2
0
0
0
1
0
3
2
2
1
0
0
2
1
1
2
0
0
1
0
3
0
0
0
1
0
2
0
0
2
1
2
0
0
2
0
0
0
1
3
1
1
0
0
2
0
0
1
2
2
0
0
1
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
1
1
1
1
2
0
4
1
0
1
0
2
0
0
1
0
0
0
2
0
0
1
0
0
1
0
0
0
0
1
1
1
0
0
0
1
2
1
0
0
1
3
0
0
0
1
0
2
0
1
1
0
0
2
0
1
0
1
1
0
2
1
0
0
0
1
1
0
1
1
2
0
1
1
2
2
1
0
0
0
1
1
1
1
0
1
2
1
0
0
2
1
0
0
2
1
2
2
1
1
0
3
1
1
1
0
0
1
0
2
0
0
2
0
1
1
0
0
0
0
1
2
0
1
0
1
0
1
2
2
0
1
0
2
1
2
1
2
0
0
0
1
0
2
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
3
2
0
0
0
0
0
1
1
1
0
1
0
0
1
2
1
1
0
1
0
1
1
0
0
0
1
1
1
0
2
2
0
0
0
2
0
1
0
0
1
1
2
2
2
0
1
0
0
0
0
2
1
1
0
1
0
0
1
0
2
1
0
1
1
2
0
2
1
1
2
1
0
1
1
1
1
0
0
2
2
3
0
2
1
0
0
0
1
1
2
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
1
4
0
0
1
0
2
0
0
0
1
1
1
1
2
2
2
1
0
0
0
2
0
0
0
1
1
0
1
2
2
0
1
0
0
2
0
2
1
0
0
1
2
0
0
1
1
1
0
0
2
0
0
2
0
0
1
2
0
2
1
1
0
1
0
1
1
1
0
0
0
1
1
4
0
0
0
1
0
0
1
1
0
2
0
2
1
0
0
0
1
0
2
2
0
0
1
0
0
2
0
4
1
0
2
1
0
1
2
2
2
0
2
0
1
1
0
1
1
0
0
0
1
0
2
0
1
0
2
0
0
2
1
1
1
0
2
0
0
0
0
1
1
0
2
0
2
0
1
1
1
0
0
2
0
1
1
1
2
0
0
0
0
1
2
1
1
1
2
2
2
1
2
1
1
1
2
0
2
1
0
1
0
1
1
0
2
1
2
1
2
1
0
1
1
2
3
1
2
1
2
1
1
0
1
0
0
2
0
1
0
2
1
0
2
2
2
0
0
0
1
1
2
0
1
0
0
1
1
0
2
2
0
2
0
1
2
0
2
2
2
2
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
1
1
2
0
0
1
0
0
1
0
2
2
0
0
1
0
1
1
2
0
0
2
0
1
0
1
1
0
0
0
0
1
1
0
3
0
0
1
0
0
1
0
2
0
2
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
2
0
1
0
2
1
1
0
2
0
0
2
2
1
0
1
0
2
0
1
0
1
1
2
2
1
1
1
1
0
0
0
0
2
0
1
1
0
2
0
0
0
0
1
0
1
1
0
2
1
0
0
0
0
0
0
1
1
0
1
1
1
2
0
0
0
0
0
0
1
1
2
0
2
2
0
0
1
0
0
1
0
0
0
2
0
0
0
0
1
0
1
2
1
0
1
0
0
0
0
2
2
0
1
1
1
1
0
0
0
0
2
1
2
2
1
1
0
0
1
0
0
0
1
1
1
2
1
1
0
2
0
0
3
0
0
0
0
2
0
2
1
2
1
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
1
0
1
2
1
0
1
0
1
0
0
0
2
0
2
2
1
0
0
0
0
1
1
1
0
0
1
1
2
0
2
1
1
1
0
2
0
2
1
0
2
0
0
0
0
1
2
1
1
0
2
0
0
1
2
1
0
2
1
1
1
1
1
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
2
1
0
0
2
1
2
0
0
0
1
0
0
1
3
0
0
0
1
1
1
0
1
1
0
3
1
1
0
0
0
0
1
1
0
3
1
2
1
1
0
1
1
2
2
1
3
1
0
0
0
1
1
0
1
0
0
0
0
1
2
0
1
2
1
1
0
2
0
1
0
0
1
0
1
0
0
6
0
2
0
0
1
0
1
0
0
0
0
0
1
0
0
2
2
0
0
0
1
0
1
2
2
0
1
1
0
0
2
0
1
1
1
0
2
2
0
0
1
0
0
3
1
1
1
2
0
0
2
0
2
2
0
0
2
2
0
0
1
0
0
0
0
1
2
0
1
0
1
0
1
2
0
0
1
2
0
2
0
0
0
1
2
1
0
1
0
0
1
0
2
2
0
1
2
2
2
1
0
2
0
0
2
0
0
1
2
0
1
1
2
1
0
0
2
0
1
1
2
0
0
0
0
0
1
2
2
0
2
0
1
1
0
0
0
2
0
0
0
0
3
0
1
0
2
0
0
2
0
0
1
2
1
0
2
0
2
2
0
1
0
2
1
0
0
1
0
0
1
0
1
0
1
0
0
1
2
1
0
1
1
0
0
2
2
1
0
0
1
1
1
0
0
1
0
2
0
1
2
2
1
1
1
0
0
0
0
0
2
1
2
2
0
0
0
1
2
2
1
0
1
2
1
1
0
2
2
1
0
1
0
0
2
0
1
2
1
1
0
0
1
0
0
0
1
2
3
0
0
1
0
1
1
0
0
0
0
1
0
2
0
2
0
0
2
1
1
2
2
0
1
2
0
2
1
0
0
0
1
0
2
0
0
0
0
2
1
1
0
0
1
1
2
2
1
0
0
0
0
0
1
1
0
0
0
1
0
0
2
0
1
0
0
0
0
1
0
0
0
0
1
2
1
0
0
0
2
1
2
1
1
0
0
1
1
0
1
0
2
1
0
0
0
0
1
0
0
1
0
0
1
0
2
0
0
2
0
1
0
0
0
1
0
0
2
0
2
1
0
0
1
0
0
1
2
1
0
1
0
0
1
2
1
0
0
0
0
1
2
1
0
2
0
3
1
2
6
0
1
2
1
0
0
0
0
0
1
0
0
0
0
2
1
1
0
0
1
1
0
0
0
2
0
1
2
1
0
1
1
2
0
2
1
1
1
1
0
1
1
3
0
0
0
3
0
1
2
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
1
2
0
0
0
4
0
1
0
0
0
0
1
0
0
1
2
1
1
2
0
0
2
1
1
1
2
0
0
0
1
0
2
1
1
2
0
1
0
1
0
3
1
2
0
2
1
0
2
0
1
3
0
1
1
0
1
0
0
1
1
1
1
0
0
0
1
5
1
2
0
1
0
0
0
0
1
0
0
1
2
0
1
0
2
2
2
0
2
0
0
0
1
1
2
2
0
1
0
1
1
1
0
0
1
0
0
2
2
1
0
0
0
0
0
1
1
0
0
2
1
1
1
1
0
0
2
2
2
0
2
1
0
4
0
0
1
2
0
1
2
1
2
0
0
0
0
0
2
0
0
0
4
0
0
0
1
1
1
2
1
0
0
2
1
0
1
0
2
1
1
0
0
0
1
2
1
2
0
2
1
3
3
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
1
0
2
0
0
1
0
0
2
0
1
0
0
0
0
1
2
0
0
2
0
1
1
2
1
1
1
0
0
1
3
0
1
0
0
0
0
0
3
1
2
0
0
0
0
2
2
2
0
1
2
0
0
0
1
0
0
1
2
0
1
0
1
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
1
1
1
1
2
2
1
0
0
0
0
1
2
0
0
1
0
0
0
0
1
1
1
2
1
2
0
1
0
1
0
0
0
0
4
0
1
1
1
1
1
1
2
0
1
0
0
1
0
2
2
0
0
2
0
2
0
1
1
0
0
0
1
0
1
0
1
0
0
0
2
0
0
0
3
0
1
1
0
2
2
0
0
1
0
2
0
1
1
0
1
1
1
1
0
3
1
0
0
0
1
1
1
1
2
0
0
2
0
0
0
1
1
2
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
1
0
2
2
0
0
0
2
2
0
0
2
0
1
2
0
0
0
0
1
0
1
1
0
1
0
0
0
2
1
0
0
2
0
0
0
0
0
1
2
2
0
0
0
2
1
1
1
0
1
1
0
2
1
0
1
0
0
1
2
0
0
1
0
0
0
0
0
1
2
2
0
2
2
1
2
2
3
1
0
2
0
1
2
0
2
1
0
0
0
4
0
0
0
2
0
1
1
1
0
0
2
0
1
1
2
0
2
0
0
1
2
0
0
1
0
0
2
0
2
0
0
1
1
1
1
2
1
1
1
2
1
1
0
0
1
0
2
0
1
0
1
1
2
1
1
0
3
0
0
2
0
0
0
2
0
0
0
2
0
2
0
2
0
2
1
1
0
0
0
3
0
1
2
0
1
0
1
0
0
1
1
0
2
0
0
2
0
0
0
1
1
1
0
0
0
1
0
1
0
2
0
1
0
1
0
0
0
1
2
1
2
0
1
0
2
0
0
1
0
1
1
1
2
1
0
1
3
0
0
2
0
1
2
0
0
1
1
0
1
2
2
0
2
1
0
1
0
1
2
2
0
2
2
2
1
1
2
0
0
0
0
0
1
0
0
0
2
1
1
0
1
0
0
1
0
0
0
4
0
2
2
2
3
0
0
0
0
0
1
0
1
4
1
0
1
0
1
1
2
2
1
0
2
0
0
1
1
1
0
0
2
1
1
1
0
2
2
0
1
0
1
1
2
1
0
2
0
2
1
1
0
0
1
0
0
0
1
0
0
0
1
1
2
1
0
2
1
1
0
0
0
2
2
1
2
1
2
2
1
0
0
0
0
0
2
0
0
2
0
1
0
1
0
1
2
1
0
1
2
2
1
2
1
0
0
0
0
2
0
1
2
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
2
2
1
1
2
1
1
1
1
2
1
2
0
0
3
0
2
1
1
0
1
2
1
1
0
0
1
2
0
0
0
0
0
0
1
0
0
2
1
2
0
0
0
0
0
1
2
1
1
1
0
0
0
1
2
0
0
0
0
0
2
1
0
2
0
0
2
2
0
0
4
0
2
1
0
0
0
1
1
0
1
1
2
0
2
3
2
1
0
2
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
2
1
0
0
1
1
1
2
1
1
0
0
2
1
0
1
0
1
1
0
0
0
1
2
0
1
0
2
0
0
0
1
0
0
0
3
2
1
0
5
2
0
0
1
2
1
1
1
1
1
0
2
1
0
0
1
0
0
0
2
0
1
1
0
1
0
2
0
0
2
1
1
2
0
0
0
0
0
2
0
0
1
0
1
0
1
0
0
1
0
3
1
1
0
0
0
1
0
1
0
1
0
2
1
0
1
2
1
0
1
0
1
1
0
1
1
0
1
0
0
0
1
3
0
0
1
1
1
1
0
2
1
1
2
1
0
1
2
0
1
1
0
2
1
1
2
1
1
1
0
0
1
1
0
0
2
2
0
2
1
2
0
0
2
2
0
1
0
0
2
2
0
0
1
1
0
1
3
1
2
2
0
2
1
0
0
2
1
2
1
0
1
0
0
0
3
2
0
0
0
1
2
0
0
0
0
1
1
0
0
0
0
2
0
0
1
2
1
1
1
0
0
0
2
0
0
0
0
0
1
0
1
1
1
0
2
1
0
0
3
1
1
1
0
0
0
0
1
2
0
1
0
1
0
0
0
1
2
2
1
1
1
1
2
2
0
1
1
1
0
2
1
0
0
0
1
2
0
1
1
1
0
0
1
2
0
0
1
0
1
2
1
2
0
2
0
0
0
0
1
0
0
0
2
0
1
1
0
0
0
1
0
1
1
0
1
0
1
0
0
1
2
0
2
2
0
1
0
2
0
0
1
2
0
2
0
2
1
0
0
1
1
0
0
0
1
0
0
0
0
0
1
2
1
0
0
1
1
0
2
0
0
0
2
0
0
1
1
1
0
1
1
0
2
1
2
1
2
1
1
0
1
0
1
0
1
1
1
0
0
0
2
0
0
1
0
0
3
1
2
2
0
1
1
0
0
2
0
0
0
1
1
0
0
4
0
1
2
0
0
0
1
0
1
0
1
0
0
0
0
1
1
0
0
2
0
1
0
1
1
0
0
2
0
0
1
2
0
1
0
0
0
1
0
0
1
3
2
0
0
1
1
2
2
0
2
2
0
1
0
2
1
0
0
0
2
1
0
2
1
1
0
0
1
0
1
2
1
3
2
2
2
0
1
0
0
0
0
1
2
1
1
2
1
0
0
1
0
2
1
1
0
2
0
0
2
1
0
2
2
3
0
1
0
1
0
1
0
1
0
1
1
2
0
0
1
0
0
0
1
1
0
0
1
1
2
1
1
0
0
1
2
1
0
1
2
3
0
2
1
0
1
0
0
2
0
2
2
1
2
0
1
0
1
1
1
2
0
0
1
1
0
2
0
0
2
0
0
0
2
2
1
1
0
0
1
1
1
0
0
2
0
2
1
2
1
1
0
1
2
0
2
0
1
1
0
0
1
0
0
1
0
1
1
1
0
0
1
2
0
2
1
1
2
2
0
1
0
2
2
2
2
2
0
2
0
0
1
2
1
1
0
1
0
1
2
0
2
2
2
2
0
2
0
0
1
0
0
0
3
0
1
0
1
1
0
1
2
2
1
0
1
1
1
0
2
0
0
0
1
0
0
1
0
3
3
1
1
0
1
1
2
0
2
0
1
1
0
0
4
0
0
2
1
2
2
2
1
2
2
2
0
0
0
0
2
0
0
0
0
1
2
1
2
0
0
2
2
1
0
0
2
1
2
0
2
0
0
1
1
2
0
0
1
0
0
0
1
1
0
1
0
0
0
1
1
2
1
0
0
0
0
1
2
1
0
1
1
1
2
0
0
2
0
1
0
0
1
1
1
2
1
1
2
0
1
0
0
0
0
1
1
1
0
0
0
0
0
2
1
2
0
1
0
2
0
1
0
0
0
0
0
2
1
0
1
1
0
2
0
1
0
1
2
2
2
0
0
1
0
1
2
1
0
1
0
1
0
1
0
1
0
0
0
1
4
0
0
2
1
2
0
1
1
0
2
1
1
2
0
1
0
0
0
2
0
2
1
1
0
0
3
1
0
0
0
0
2
0
2
2
0
0
0
0
0
1
0
0
0
0
2
0
1
1
2
0
0
0
0
0
0
1
0
0
1
0
1
1
0
1
0
0
0
2
0
0
1
0
0
0
1
0
0
0
2
2
2
0
0
0
0
2
2
1
1
1
0
0
1
1
0
2
1
2
0
1
2
0
1
0
0
1
1
2
1
0
1
2
0
1
1
0
3
0
1
0
1
0
0
1
0
0
0
2
1
1
0
1
0
1
0
0
0
1
1
0
0
0
0
1
2
1
1
2
1
1
1
0
0
2
0
0
0
0
1
2
2
2
1
0
0
1
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
1
1
1
2
0
0
0
0
0
3
0
2
1
1
1
1
1
1
0
2
2
1
2
2
0
2
0
0
2
0
1
2
0
0
0
1
0
1
1
1
0
2
1
0
0
0
0
0
1
1
2
1
1
2
0
1
1
0
1
3
1
2
2
0
1
1
2
2
1
2
1
0
0
0
1
2
1
0
3
0
1
1
0
1
0
0
1
0
1
0
0
0
2
0
0
3
1
1
0
0
1
0
1
0
1
0
0
0
0
1
1
0
2
0
1
1
0
0
0
0
0
2
0
1
0
0
1
1
0
0
0
0
0
0
0
2
1
1
1
0
1
1
4
1
2
1
0
2
1
1
0
0
0
1
0
0
2
0
0
1
0
1
0
1
0
1
0
2
2
2
1
2
0
2
0
0
1
0
0
4
0
2
1
0
2
0
0
2
0
1
0
0
1
0
1
0
2
1
1
1
0
0
1
3
0
2
2
1
2
0
0
1
1
1
0
0
0
2
1
0
0
3
0
0
1
1
2
0
2
1
1
1
0
0
1
1
0
1
0
0
0
0
0
0
1
0
1
2
0
0
0
2
1
1
0
1
1
1
1
0
0
0
0
2
1
1
2
1
1
2
1
0
1
1
1
1
0
1
1
0
0
0
1
0
1
5
0
2
0
1
0
0
0
2
0
0
1
1
0
0
1
2
1
0
0
1
1
2
2
1
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
1
0
0
1
1
2
0
1
1
4
1
1
0
0
0
0
1
0
1
0
1
1
1
2
3
1
0
1
2
3
1
0
1
0
0
1
1
0
3
0
1
0
0
1
0
3
0
1
0
1
0
0
0
1
1
0
0
1
2
3
1
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
2
1
1
1
1
1
1
0
0
0
1
1
0
3
2
0
1
0
0
0
2
0
1
1
1
0
1
2
5
1
0
2
1
1
2
1
0
0
1
1
0
2
2
0
0
0
0
0
0
1
0
1
1
0
1
2
2
1
2
1
0
2
0
2
1
0
1
0
1
0
2
1
0
0
0
1
0
0
0
0
1
3
1
2
0
0
2
0
0
1
0
0
1
0
0
0
0
2
2
0
0
0
2
1
2
3
2
1
1
2
1
1
0
0
1
1
2
0
1
0
2
2
3
2
0
0
2
1
0
0
1
0
2
1
2
0
0
1
2
0
0
0
0
0
2
0
1
0
1
0
1
0
1
0
0
0
0
2
2
1
0
0
1
2
2
2
1
1
2
2
0
2
1
0
1
2
0
1
1
1
0
1
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
2
1
1
0
0
2
0
0
1
1
0
0
1
1
1
1
0
0
2
2
0
2
0
0
0
0
0
1
0
2
1
0
1
1
2
0
1
1
0
1
2
0
3
0
0
1
0
1
0
2
2
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
1
1
1
0
0
1
1
0
1
0
2
1
2
0
0
0
2
0
0
0
1
0
1
0
1
0
0
1
1
0
1
0
1
2
0
0
0
2
1
2
0
1
0
0
0
0
2
2
1
0
1
2
0
1
3
0
1
1
2
0
2
0
2
2
1
0
2
1
1
1
2
2
2
2
0
2
1
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
2
1
0
1
2
0
0
0
0
1
0
0
0
1
0
1
1
0
1
0
0
1
2
0
2
1
1
0
0
0
0
1
1
0
0
0
1
1
0
0
1
0
2
0
0
0
0
0
0
0
1
4
3
1
0
2
0
0
0
0
2
1
0
1
0
2
0
0
0
1
1
1
0
0
1
0
0
2
1
1
0
2
1
0
0
0
0
0
1
0
1
1
0
1
0
0
2
2
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
2
0
2
3
0
0
0
0
0
0
2
3
1
0
0
0
0
0
1
2
1
0
0
2
0
1
0
0
0
1
2
1
0
2
0
1
0
1
1
2
0
0
0
0
0
1
8
2
2
0
1
1
1
2
1
0
0
0
1
0
0
1
1
1
0
2
0
0
3
0
1
0
0
1
1
2
1
1
0
2
1
2
1
1
2
0
2
0
1
2
0
1
0
0
0
0
2
2
0
2
1
2
1
0
0
1
2
0
0
1
0
1
2
1
0
2
1
1
1
1
0
0
0
2
1
0
0
0
0
1
0
1
0
2
0
1
0
1
0
0
0
0
0
0
0
6
2
1
0
2
1
2
0
1
0
0
1
0
2
1
0
0
0
1
0
1
0
0
1
0
0
2
0
2
0
0
1
1
2
0
2
2
0
2
1
3
1
1
0
0
2
1
0
0
0
1
0
0
1
1
1
0
1
0
0
0
1
1
0
3
0
1
0
1
1
2
2
0
1
0
0
0
2
2
0
0
2
0
0
0
0
0
0
4
0
0
0
0
0
1
0
1
1
1
2
0
0
1
2
1
0
0
0
1
0
2
3
1
0
2
1
2
0
0
0
2
1
0
0
2
2
0
2
0
1
1
1
0
0
2
0
2
1
0
1
0
1
2
0
2
0
1
0
0
1
0
0
1
2
1
0
0
0
1
0
0
2
1
1
1
0
0
0
1
1
2
1
0
0
1
0
0
0
2
1
1
1
0
0
0
0
0
2
0
1
0
1
1
1
0
0
1
1
1
0
2
0
0
2
0
2
2
0
0
0
1
2
1
0
2
1
0
2
0
2
0
1
3
2
1
1
0
0
0
2
0
2
0
3
2
0
1
1
0
1
2
0
1
1
1
0
2
1
0
0
0
0
1
0
0
0
2
0
0
1
1
0
0
0
2
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
1
1
1
1
2
1
0
0
1
2
0
0
0
0
0
0
1
4
1
2
1
0
0
0
0
0
1
1
0
1
2
2
0
1
1
0
0
0
0
1
2
2
0
0
1
2
0
0
0
0
1
1
0
1
2
0
2
2
0
1
1
1
2
0
0
2
2
1
0
0
2
0
0
0
1
1
0
1
1
2
2
0
0
0
2
1
3
0
0
1
1
1
0
1
1
0
2
0
1
1
1
2
0
2
1
1
2
3
1
1
0
1
1
0
2
0
0
1
0
1
3
1
1
1
2
2
1
0
0
1
0
3
0
0
0
0
0
0
2
0
0
1
2
2
1
1
0
1
0
2
2
1
1
0
0
2
1
0
0
0
1
0
0
1
0
0
1
0
1
0
2
1
0
0
1
1
0
1
0
2
1
2
1
0
0
0
1
0
0
0
1
1
2
1
1
0
1
0
3
1
1
1
1
1
0
2
1
0
0
2
0
0
2
2
1
3
1
1
2
0
1
0
0
1
0
0
1
0
0
0
0
2
1
0
0
1
0
1
1
1
1
2
0
0
0
0
1
0
0
1
1
1
0
0
0
1
0
0
2
2
1
0
0
3
0
2
1
2
0
0
1
0
0
1
2
0
0
1
0
1
2
0
2
1
1
0
0
1
2
3
1
2
2
0
0
0
0
1
0
3
0
0
0
2
1
2
2
1
3
0
0
0
0
1
0
0
1
2
1
0
0
0
0
0
1
1
3
2
0
1
4
1
0
2
0
2
2
0
2
2
1
0
0
0
2
2
1
0
0
0
0
0
3
0
1
0
1
0
1
1
0
0
0
2
0
0
2
0
1
2
1
0
0
1
1
0
0
0
1
2
0
0
1
1
0
1
2
0
1
0
0
0
0
1
0
1
1
0
0
0
0
1
0
3
0
0
0
2
1
0
0
2
1
1
1
0
0
0
1
0
1
1
1
0
1
1
1
0
0
1
2
1
1
0
0
1
0
0
2
0
1
1
0
2
1
1
0
1
1
0
0
1
2
2
2
1
2
0
0
0
0
2
0
0
0
1
1
0
0
0
1
0
0
2
1
1
0
2
1
0
0
0
0
1
2
0
0
1
1
1
0
2
1
0
1
1
0
1
1
0
2
1
0
1
2
2
0
1
0
2
2
1
2
1
2
1
2
0
0
0
0
2
2
2
1
0
1
0
0
1
1
0
1
0
1
1
2
1
2
1
0
1
0
0
0
0
2
2
0
1
2
1
0
1
0
1
0
0
2
0
0
2
0
1
2
0
1
1
2
1
0
1
1
1
0
0
0
0
1
1
1
0
0
1
0
1
0
2
1
1
2
2
2
0
2
1
3
2
0
1
1
1
2
0
1
0
0
1
1
1
0
0
0
0
0
0
1
0
2
2
1
1
1
1
2
0
0
0
1
0
2
1
0
0
2
1
0
0
0
1
1
0
0
0
2
2
2
0
1
2
1
2
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
1
0
1
0
2
0
2
1
1
0
1
3
2
1
1
3
0
0
0
1
1
0
0
1
1
2
2
1
0
1
2
2
0
1
2
0
2
0
0
0
0
1
2
0
1
0
1
1
0
1
2
1
0
1
0
0
1
0
0
0
0
2
0
2
2
0
2
0
1
0
0
1
1
1
0
0
0
1
0
2
2
2
1
0
2
0
0
1
2
2
0
0
0
1
0
0
1
0
1
1
1
0
0
1
0
0
2
0
1
1
0
0
0
0
0
1
2
1
0
0
0
0
0
0
3
1
0
1
0
0
0
0
0
0
0
2
0
0
1
1
0
2
1
2
0
0
4
0
1
1
1
1
0
0
1
0
2
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
2
0
2
1
0
0
1
0
0
0
2
0
1
1
1
0
1
1
0
1
0
0
0
1
1
1
0
4
2
1
0
1
1
0
0
1
1
2
0
0
1
1
2
2
3
1
0
1
0
0
3
1
1
2
1
0
0
2
1
2
1
1
1
1
1
0
0
0
1
1
0
0
0
2
0
2
0
0
2
1
0
1
0
1
0
2
1
0
0
0
0
2
0
1
1
2
0
1
0
1
0
0
0
0
0
2
0
2
0
0
1
0
0
1
0
0
0
5
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
1
0
0
1
1
2
1
0
1
0
1
1
2
0
1
1
0
2
1
0
0
0
1
0
3
2
1
1
2
0
1
1
1
0
1
1
0
0
0
0
2
1
1
2
2
0
0
1
0
1
0
0
0
1
0
2
2
1
1
1
1
1
1
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
3
2
0
0
0
1
1
2
0
0
0
0
2
1
1
0
1
0
0
0
3
1
0
0
0
1
0
1
1
0
2
0
0
1
2
0
0
0
0
0
1
0
0
1
1
4
0
0
1
0
1
0
2
0
1
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
2
0
2
0
2
0
0
0
2
2
0
0
1
0
1
0
1
0
1
0
0
0
1
2
1
0
3
2
0
0
1
2
0
2
0
1
0
0
0
2
0
2
2
0
1
0
0
0
2
1
0
1
0
0
1
1
1
1
1
2
3
1
2
1
1
0
1
0
0
0
1
1
2
1
0
1
2
0
1
0
0
0
2
0
0
2
1
0
1
0
2
1
0
1
0
2
1
1
4
2
0
2
0
2
2
0
0
2
1
1
1
1
0
0
1
0
2
0
2
0
1
1
0
0
2
2
0
0
1
0
1
0
1
2
0
2
1
2
1
2
2
2
0
2
1
0
0
0
1
2
1
0
0
0
0
0
1
0
2
0
0
0
2
0
1
1
2
0
0
2
0
0
2
2
1
1
1
0
1
2
2
1
2
0
0
0
2
0
2
1
1
3
2
0
1
0
2
0
1
0
2
5
2
0
0
1
0
0
2
0
0
0
0
1
2
1
0
0
1
1
0
2
0
0
2
2
0
0
0
1
1
2
1
1
0
1
1
0
0
0
0
0
1
1
0
2
2
0
1
1
0
1
0
0
0
0
2
2
2
0
2
1
2
1
1
0
2
0
0
0
2
1
0
1
1
2
0
0
2
0
0
2
1
1
1
4
2
1
3
1
0
0
2
1
1
0
2
1
2
1
1
0
1
0
1
0
0
1
0
1
0
1
1
1
2
0
2
0
0
2
0
0
1
2
0
0
0
0
1
2
1
1
0
1
1
1
2
0
0
0
3
2
0
0
1
1
0
1
0
0
0
0
0
0
1
1
0
3
0
2
1
2
0
0
2
1
2
2
0
1
1
1
1
1
1
0
1
0
2
1
1
3
0
1
2
0
2
0
0
1
2
1
0
0
0
2
0
1
0
0
2
0
0
1
0
0
3
2
1
0
0
2
0
0
2
0
1
1
1
0
0
2
0
1
0
1
0
0
0
3
0
0
1
0
2
1
3
1
1
1
0
1
0
1
0
0
2
0
0
2
0
0
0
1
0
1
0
1
0
0
1
0
0
1
2
1
1
0
2
1
0
0
0
0
1
1
0
0
2
0
1
0
1
2
1
0
1
0
1
0
0
0
1
3
0
0
1
0
0
0
0
0
2
2
1
0
1
1
0
2
0
0
1
0
1
1
2
2
0
1
0
0
0
0
0
1
0
1
1
1
2
0
0
1
2
2
1
0
0
2
0
2
2
1
1
1
0
0
0
1
1
0
0
1
0
0
3
1
1
1
1
0
0
2
0
0
1
1
1
0
0
4
1
2
1
0
2
0
1
0
0
1
0
0
1
1
0
0
1
0
0
0
0
1
1
0
0
0
1
0
1
0
1
0
2
0
0
0
0
1
0
2
1
0
0
0
0
1
2
1
0
1
2
2
1
1
1
1
0
3
2
0
2
1
0
0
0
0
0
2
4
0
0
0
2
0
0
2
1
1
0
0
2
1
0
1
2
2
1
0
3
0
0
2
0
0
0
0
0
1
1
2
0
1
2
0
0
0
1
0
0
1
0
0
0
1
2
0
0
1
0
2
2
1
0
0
0
2
0
0
0
4
2
1
1
2
0
0
0
0
1
0
2
0
1
1
0
1
0
5
2
2
2
0
0
0
1
1
0
0
1
1
1
0
2
0
2
0
2
0
1
1
2
2
4
0
1
1
1
1
3
0
1
1
2
1
0
0
2
0
1
0
0
0
0
2
2
0
0
1
0
1
0
0
0
0
0
1
2
0
0
4
0
0
0
0
0
0
0
0
2
1
1
2
0
0
0
1
2
0
0
0
0
0
1
2
0
1
0
2
0
1
1
2
2
0
2
2
0
0
2
0
2
1
2
0
2
2
1
0
2
0
1
1
1
0
0
1
1
0
1
0
0
0
0
1
0
2
0
0
2
0
1
0
1
1
1
0
0
0
0
1
1
1
2
1
2
0
0
1
0
0
0
1
0
0
0
0
1
0
2
1
2
0
1
1
0
0
0
1
0
1
0
0
1
0
0
1
2
1
0
0
1
1
0
0
2
1
1
0
1
0
0
0
0
2
1
0
2
0
0
1
1
1
0
0
1
0
0
2
0
0
1
2
1
0
2
0
0
1
0
0
0
1
2
0
0
0
1
1
0
0
0
0
1
0
0
1
2
0
2
2
1
0
0
1
2
0
0
1
2
1
1
1
0
0
0
1
1
1
0
0
1
2
0
2
1
2
0
2
2
1
2
2
0
0
1
1
1
2
0
2
2
0
0
0
2
1
1
0
0
0
0
0
2
1
2
0
2
1
0
0
1
0
0
1
1
1
1
0
1
2
2
0
0
1
3
0
1
0
1
0
0
1
1
1
0
0
2
0
0
2
0
2
2
0
2
1
2
0
0
2
0
2
1
0
2
0
0
3
2
2
0
2
2
3
0
0
0
2
0
0
1
0
2
0
2
0
0
0
3
0
0
0
0
0
2
0
2
0
0
2
1
0
2
2
1
2
0
2
0
1
3
2
1
1
1
0
1
1
1
1
2
2
0
1
1
5
1
0
1
2
3
1
0
0
0
1
1
0
1
1
0
1
2
0
1
1
1
0
2
1
0
1
0
1
1
0
1
0
1
0
0
3
2
0
1
0
0
1
0
0
0
1
0
0
0
0
1
2
0
2
1
0
1
1
0
3
2
2
0
0
0
2
2
0
1
0
0
1
0
0
1
0
0
0
2
0
0
1
2
0
2
1
1
0
2
0
1
0
1
1
1
0
0
1
2
0
1
2
1
0
0
2
1
0
1
0
1
0
2
0
0
1
4
1
0
1
0
2
0
1
0
1
0
1
1
2
0
1
1
0
0
2
1
1
0
0
1
0
1
2
2
0
1
1
1
1
1
0
0
1
2
0
2
2
0
0
1
3
0
0
0
0
0
1
1
0
2
0
0
1
0
1
0
0
0
2
0
0
1
0
0
1
1
0
0
0
1
1
0
2
0
0
3
1
0
0
1
0
0
1
1
1
3
1
0
1
1
0
1
1
1
0
0
1
3
0
2
2
1
0
2
1
0
0
0
1
1
1
2
1
2
0
3
1
2
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
2
0
0
1
1
1
1
0
1
1
2
2
0
2
0
2
0
2
1
1
1
0
0
2
0
1
0
0
2
0
0
0
0
0
2
0
0
0
1
1
1
0
2
2
0
1
1
3
3
1
0
0
2
1
2
1
0
1
0
1
2
0
1
3
0
0
1
1
1
1
2
1
2
0
0
0
0
0
1
1
0
1
2
0
0
1
1
0
2
0
0
1
0
2
0
1
2
1
1
1
0
0
0
0
0
0
1
2
1
0
1
2
2
1
0
2
2
0
1
0
1
1
0
1
2
1
1
0
1
0
1
2
0
2
0
0
0
1
0
1
1
2
0
2
0
1
1
0
1
0
2
2
0
2
1
0
1
3
1
0
2
0
0
0
0
0
1
2
1
0
1
1
2
0
1
2
1
1
2
0
0
1
0
1
0
0
0
0
1
1
0
0
2
1
0
0
2
2
1
1
0
0
0
0
2
0
0
0
0
0
1
2
0
0
1
1
0
0
0
1
2
1
0
1
1
0
1
2
1
1
0
1
1
1
0
0
2
1
1
0
0
1
1
2
1
1
0
0
0
1
0
0
0
1
1
2
0
0
2
1
1
1
1
0
1
1
1
1
2
2
0
0
0
1
1
0
0
0
0
1
2
2
2
0
0
1
0
2
0
2
0
0
0
1
0
2
2
0
2
0
1
1
1
0
1
0
0
1
0
2
0
0
2
2
1
0
1
0
0
0
0
2
0
1
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
2
0
2
0
2
1
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
2
0
0
1
0
0
0
2
1
0
2
1
0
2
1
1
2
1
1
0
2
0
1
1
1
0
1
1
1
1
3
1
2
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
2
1
1
0
1
0
1
1
1
0
0
2
0
1
1
1
0
0
0
0
0
2
2
0
2
0
0
0
2
0
1
1
0
0
0
2
2
0
0
0
1
0
0
0
1
0
0
0
3
2
1
0
1
2
0
0
0
0
2
0
1
0
0
2
1
1
1
0
0
0
0
0
0
2
1
0
1
2
0
2
0
0
0
0
2
0
1
1
0
2
1
0
0
0
0
1
2
0
2
0
2
0
0
0
0
0
0
2
1
0
0
1
1
0
1
1
0
1
1
0
1
0
1
1
0
1
1
2
2
2
0
2
0
1
0
0
0
2
2
2
0
0
2
1
1
0
0
1
0
1
0
1
1
1
0
0
1
0
2
2
1
0
0
1
0
1
1
0
0
1
1
1
0
1
0
0
0
0
1
2
0
1
0
1
2
0
0
0
0
2
1
1
1
0
1
0
0
0
0
0
1
0
0
2
0
2
0
0
2
0
0
2
1
3
2
1
2
0
0
1
0
0
1
0
0
0
1
1
0
0
2
0
0
0
0
0
1
0
1
0
0
0
1
1
0
1
1
0
0
1
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
1
1
1
1
2
2
0
1
1
1
1
1
0
0
1
2
2
2
2
1
0
0
1
1
0
0
3
0
0
1
0
0
0
1
1
2
1
1
0
1
0
1
0
1
0
1
0
0
0
3
0
1
1
1
1
0
0
2
0
0
1
0
0
1
1
1
2
2
1
1
0
0
1
1
0
2
0
0
0
0
2
0
1
0
1
1
0
1
1
1
1
1
0
0
2
0
1
0
2
0
0
1
0
0
0
2
0
2
2
0
0
0
2
0
0
1
0
0
2
1
1
0
1
2
1
0
1
1
1
2
0
2
0
1
0
2
1
1
0
0
0
2
2
0
3
0
1
2
3
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
1
1
0
2
1
1
0
5
0
2
2
0
0
0
1
0
1
1
0
2
0
0
2
0
1
1
0
2
1
2
2
0
1
0
1
1
1
0
1
0
0
1
1
1
0
1
2
1
0
1
0
0
2
1
1
1
2
1
0
1
1
0
0
2
2
0
1
0
2
0
0
2
0
2
7
0
2
0
2
1
0
0
0
0
1
0
1
0
0
0
2
2
0
1
4
1
0
0
0
0
2
0
1
1
2
0
1
1
1
1
2
1
0
1
0
1
2
2
0
2
2
1
1
1
2
0
0
0
1
3
0
0
1
0
0
0
1
1
1
0
1
0
1
3
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
2
0
0
0
0
2
0
0
0
1
1
1
0
0
1
1
0
0
1
1
0
1
0
1
0
1
1
0
0
0
2
1
0
1
1
1
2
1
2
2
0
1
0
1
2
0
0
1
0
4
2
2
1
0
2
1
1
2
4
1
1
0
1
0
2
0
0
1
1
2
0
0
0
0
0
2
2
1
1
0
2
2
1
0
0
2
2
1
2
0
1
0
0
1
0
4
1
2
0
0
1
1
2
1
0
0
1
2
0
1
2
1
2
1
2
1
1
1
0
0
1
0
1
0
1
0
1
3
1
0
1
1
3
1
1
1
0
2
0
0
0
0
0
1
0
0
1
2
0
1
1
0
1
1
1
0
1
1
2
0
0
0
0
0
1
0
0
0
2
1
0
2
1
2
0
0
2
1
0
1
0
0
1
0
0
0
1
0
1
4
1
0
0
0
0
0
0
0
2
0
0
2
0
1
0
1
0
0
1
1
0
2
0
0
0
0
0
2
1
0
0
1
0
2
1
1
0
2
0
4
2
1
2
1
0
1
1
0
0
0
0
0
0
0
2
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
6
0
0
0
0
0
0
0
2
0
0
0
0
1
1
2
0
2
0
1
1
0
0
0
1
0
4
2
0
0
2
1
2
0
2
1
1
0
1
1
1
0
2
1
0
0
0
0
0
3
0
2
0
0
1
2
0
1
0
0
2
2
0
0
1
0
1
1
1
1
1
1
2
1
0
2
0
1
3
0
0
0
2
0
0
1
1
1
2
1
2
0
1
1
1
0
0
1
1
0
2
0
0
0
0
2
0
1
2
2
0
0
2
0
1
0
2
0
1
1
0
1
2
0
2
1
0
0
0
2
0
0
1
0
0
0
1
1
0
0
0
0
0
2
2
0
0
0
1
0
0
1
1
0
0
2
0
1
2
2
1
0
0
1
1
0
0
1
1
2
0
0
1
2
1
0
2
1
0
1
2
1
1
2
1
1
1
0
0
1
1
0
1
2
1
0
0
1
1
2
2
0
0
1
0
0
0
0
0
2
1
0
0
1
1
2
0
1
1
0
0
1
0
2
0
2
0
0
2
2
1
2
0
0
2
1
2
0
2
1
0
2
0
1
4
0
1
2
0
0
0
1
0
0
0
2
2
1
1
1
0
2
1
0
0
1
0
0
0
0
1
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
2
0
0
2
1
0
2
4
1
1
1
3
1
2
2
0
0
1
2
1
1
1
1
1
1
0
0
1
0
1
1
2
1
0
0
2
1
2
1
0
2
0
1
1
1
1
1
2
3
1
2
0
1
1
0
1
1
0
1
1
0
2
0
2
1
0
2
0
1
1
1
0
0
0
1
0
0
0
0
2
1
0
1
0
0
1
0
0
0
1
2
0
1
1
0
0
2
1
0
0
2
0
0
0
1
0
1
0
0
1
2
0
0
1
1
0
0
0
0
1
0
1
1
0
1
2
1
2
0
0
0
1
0
1
0
1
2
0
1
0
0
1
0
1
1
1
0
2
1
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
2
0
2
0
0
1
0
1
0
0
0
1
1
1
0
4
2
1
1
0
1
0
0
0
2
2
2
2
1
0
1
0
2
0
0
2
0
4
2
2
0
1
2
2
0
0
0
1
1
0
0
1
2
1
1
2
0
0
0
0
0
0
1
3
0
0
0
1
3
0
1
1
0
2
1
0
2
0
1
0
2
1
2
0
2
0
1
1
0
0
0
0
0
0
1
1
0
0
1
0
1
2
0
0
0
1
0
0
2
0
0
0
2
0
2
2
1
2
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
1
1
0
2
1
1
1
0
2
0
0
0
2
1
0
0
1
0
0
2
1
1
2
1
2
0
2
1
1
0
0
2
0
0
1
0
2
2
0
3
0
2
0
2
2
0
0
1
0
1
0
1
1
1
0
3
1
1
1
2
0
0
0
0
0
0
0
0
2
0
1
1
0
0
1
0
0
2
2
2
1
2
0
0
2
2
0
2
1
0
0
0
1
0
1
0
0
1
0
0
1
1
0
1
0
1
0
0
0
1
1
1
1
0
1
2
0
2
7
0
0
4
0
1
1
1
0
0
1
1
2
0
1
0
2
2
0
2
0
0
0
2
0
0
1
1
0
2
2
1
2
0
0
2
1
0
2
2
0
1
2
1
1
2
0
0
0
1
0
0
0
0
0
0
1
0
1
0
2
0
2
0
1
1
0
1
1
2
0
0
1
0
1
1
0
0
0
1
1
0
0
1
1
0
0
1
1
3
1
0
0
1
1
1
0
0
0
1
1
2
0
0
3
0
0
0
0
0
2
0
0
1
0
1
1
0
2
1
0
0
1
0
0
0
2
3
0
1
0
0
0
0
0
2
1
1
0
2
0
0
1
0
1
0
0
0
1
2
0
0
5
1
0
2
1
0
1
1
2
1
2
1
1
0
0
0
2
0
0
1
0
0
1
2
0
0
0
0
1
1
1
0
2
0
0
1
1
1
0
0
1
0
2
0
1
0
2
2
0
1
0
1
1
0
1
2
2
2
2
0
0
2
0
0
0
1
1
0
0
1
0
0
0
1
2
1
2
0
1
2
2
0
1
2
1
1
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
1
2
2
0
1
0
1
0
2
1
1
1
0
0
1
0
1
1
1
0
1
1
2
1
0
0
1
0
0
0
0
1
2
0
1
1
2
1
1
2
1
1
1
1
0
0
0
0
2
1
1
1
2
0
2
1
1
0
0
0
2
2
0
0
1
0
2
0
1
2
1
1
0
0
0
0
1
1
0
2
1
0
1
1
1
1
0
0
0
0
0
1
2
2
2
2
1
1
0
0
1
0
0
1
1
1
2
1
2
1
0
1
0
0
1
1
2
0
0
1
2
0
0
0
0
2
0
0
0
1
1
2
1
1
1
0
0
0
0
0
1
0
2
0
1
0
1
1
0
1
2
0
0
0
2
0
0
2
1
0
2
0
0
0
2
1
0
0
3
0
0
0
1
0
2
2
1
0
0
1
0
2
0
0
2
1
2
0
1
0
0
1
2
1
2
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
1
1
1
0
0
1
1
0
1
2
0
0
1
2
2
1
0
1
0
2
0
0
1
1
0
1
0
1
0
1
1
0
0
1
0
0
1
2
1
0
1
0
1
0
1
1
2
0
1
1
0
1
1
2
2
1
2
1
1
0
1
0
2
0
2
2
0
0
1
1
2
0
2
2
1
0
0
1
0
0
1
2
1
2
0
1
2
1
0
1
0
0
2
0
0
2
0
0
0
1
2
0
1
0
0
2
0
1
0
1
4
1
1
0
1
1
0
2
2
0
1
1
3
2
1
1
0
1
1
0
0
2
1
2
0
0
0
1
0
1
0
0
1
0
0
0
0
2
1
1
2
2
0
0
1
0
2
0
1
0
0
0
1
0
1
1
0
1
0
2
0
0
1
1
0
2
0
0
1
2
0
0
0
0
1
1
1
1
0
0
0
0
1
0
2
1
0
0
0
1
2
0
0
1
1
2
1
0
1
0
1
0
1
1
1
0
0
2
1
2
1
1
1
1
0
3
1
0
1
0
0
2
0
1
0
1
1
1
0
1
0
1
2
0
1
1
2
1
1
0
0
2
0
0
0
1
1
2
0
0
1
2
2
2
1
0
0
1
0
2
1
0
0
1
0
0
1
0
0
0
0
2
1
0
0
1
0
0
0
1
0
1
0
1
1
2
0
0
1
0
0
0
0
2
3
2
1
0
0
2
0
1
2
0
0
0
0
2
0
2
1
0
2
2
0
1
0
0
0
1
1
1
0
1
1
1
1
0
2
1
0
0
0
1
2
0
0
2
0
3
0
0
1
1
0
1
1
0
2
3
0
0
0
1
1
0
1
0
2
0
0
1
0
1
0
0
1
1
0
0
1
1
2
0
1
1
0
0
0
2
1
0
0
0
1
0
0
1
1
3
0
1
3
0
0
1
0
1
2
2
1
1
1
0
1
1
0
1
1
1
1
1
1
1
0
0
1
1
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
1
0
0
1
0
0
2
0
2
0
0
0
1
0
0
0
0
0
1
2
0
1
0
0
1
1
0
0
1
1
2
0
1
0
0
2
1
0
2
2
1
0
0
1
0
0
3
0
0
1
0
2
0
0
2
0
1
0
2
2
0
3
0
1
1
1
1
0
0
0
1
0
0
1
0
0
2
0
2
0
1
0
2
0
0
0
0
4
0
0
1
0
0
1
3
0
0
1
2
0
0
0
1
0
0
1
2
1
1
1
0
0
0
2
2
0
1
2
1
0
1
0
2
1
0
0
1
0
2
1
0
1
0
2
0
0
0
1
0
0
0
4
1
0
0
0
0
1
1
1
0
0
1
0
2
1
2
0
1
2
0
0
1
2
2
1
0
0
0
0
0
0
0
1
1
0
1
0
2
0
0
1
0
0
1
2
2
0
1
0
0
0
1
0
0
0
0
2
0
0
2
3
2
0
0
1
0
2
1
0
0
1
0
0
0
0
0
1
0
1
1
2
1
1
0
2
0
2
2
1
1
1
0
2
0
1
2
1
0
1
2
0
0
2
1
0
1
1
0
2
2
0
2
2
1
2
1
1
0
0
1
1
0
2
1
1
3
0
3
0
2
1
0
2
0
0
0
7
1
0
0
1
1
1
0
2
0
1
1
1
0
1
1
0
0
1
0
0
2
2
0
2
0
1
1
2
0
0
0
0
1
1
2
0
2
1
1
2
1
0
1
0
1
0
0
0
0
0
2
1
0
0
0
2
0
0
2
1
0
1
0
3
1
3
0
2
1
0
0
2
0
1
0
0
1
0
0
0
0
1
1
0
0
1
1
1
0
0
0
0
1
0
2
0
0
0
2
1
2
1
1
0
1
0
0
1
0
1
0
0
0
0
0
1
2
0
0
1
0
1
0
1
0
0
0
1
3
1
0
0
1
2
1
4
0
1
0
2
1
0
0
1
0
0
0
0
1
2
0
0
2
1
1
2
2
0
0
2
1
0
1
0
2
2
0
1
1
2
1
2
1
0
1
1
0
0
0
1
1
0
0
1
0
1
3
2
0
0
2
2
1
2
0
0
1
1
0
0
0
0
1
0
1
3
2
1
0
0
0
0
0
0
0
0
0
1
0
2
2
0
1
1
0
1
0
0
0
0
2
0
0
1
2
1
1
2
1
1
1
1
1
2
2
0
1
1
1
0
4
0
0
0
0
2
2
1
1
0
0
2
2
0
2
0
0
1
1
0
2
0
0
1
0
2
1
1
0
2
1
0
2
1
0
1
0
0
1
1
0
0
0
0
1
0
1
0
1
2
2
0
0
1
0
3
0
1
0
2
2
1
1
1
2
2
1
2
0
6
0
2
0
1
0
1
0
0
0
0
0
2
1
0
0
0
0
0
1
1
0
1
0
0
2
0
1
1
2
2
1
2
2
0
1
0
1
0
1
2
1
1
0
1
0
2
0
0
0
2
2
0
1
1
0
0
1
0
0
1
0
0
0
1
0
2
0
1
2
0
2
0
0
0
0
2
1
0
2
0
1
0
0
1
0
2
2
1
0
0
1
0
2
1
2
0
2
1
1
0
2
1
0
0
2
1
0
0
1
0
1
2
2
0
2
2
1
1
0
0
0
2
1
3
0
2
0
0
1
0
3
1
1
2
5
2
1
2
0
0
0
1
1
2
2
1
1
1
0
0
0
1
3
0
1
0
1
1
2
1
2
1
0
0
1
1
0
1
1
2
1
1
1
0
1
2
0
2
0
2
0
1
1
1
0
1
0
0
0
0
0
2
1
0
1
1
0
1
0
1
0
1
0
2
2
0
2
0
0
0
0
0
2
1
0
0
2
0
2
2
1
0
2
1
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
1
0
0
1
1
2
1
1
2
2
1
1
1
0
0
1
1
1
0
0
2
0
0
0
1
0
0
0
0
0
2
1
3
2
0
0
1
0
2
0
3
0
1
1
0
2
0
0
2
0
2
2
0
2
1
0
0
0
0
2
2
0
0
1
2
1
1
0
2
0
0
1
0
0
2
0
1
0
0
2
1
1
0
0
0
0
0
1
1
0
2
2
0
1
1
1
1
0
1
1
1
1
1
0
2
0
0
0
0
0
0
1
0
0
0
2
1
0
0
2
0
0
0
0
1
0
0
0
1
0
1
0
1
0
1
2
1
1
1
0
0
2
0
2
0
1
1
1
0
2
1
0
0
0
1
1
1
0
0
0
1
1
0
0
0
0
1
1
1
1
0
1
1
2
1
0
2
2
0
0
2
2
1
0
0
0
0
1
1
0
2
0
0
1
0
2
1
0
1
2
0
0
1
1
0
0
1
0
0
1
1
1
2
1
0
0
0
2
0
0
0
2
1
0
1
0
2
1
0
0
0
1
1
0
1
2
0
0
0
1
1
2
1
2
1
1
2
0
2
1
0
1
0
0
3
0
5
2
0
3
1
1
0
1
0
0
0
2
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
2
1
1
1
0
1
1
2
1
0
0
4
0
1
2
0
0
1
0
1
1
0
1
2
0
3
1
0
2
2
2
0
0
1
0
1
1
0
1
2
0
0
1
1
2
1
1
1
0
1
1
0
0
1
0
2
2
1
1
1
0
0
1
0
1
0
2
0
0
0
10
0
2
1
0
2
1
2
0
0
0
0
0
0
0
2
0
0
2
2
2
0
1
0
0
0
0
1
1
0
0
0
2
0
1
2
2
2
1
0
1
1
0
0
1
1
0
2
2
0
2
0
0
0
2
2
0
2
0
1
2
0
1
0
0
0
0
1
1
1
2
0
3
2
1
1
1
1
0
2
1
0
0
1
1
0
0
1
2
1
0
0
0
0
0
1
1
0
1
0
1
1
1
0
1
1
0
1
0
0
1
0
1
2
1
0
1
0
1
0
0
1
0
0
0
0
1
0
3
0
0
0
1
0
1
0
2
1
1
0
0
3
2
0
1
1
1
0
0
1
1
1
1
2
0
1
0
2
1
2
0
3
2
0
1
1
0
3
0
0
1
0
0
0
3
0
1
0
2
2
0
1
1
0
1
1
3
0
0
1
0
0
1
0
0
1
2
0
1
1
0
1
0
0
0
0
1
0
1
0
1
2
1
2
0
2
0
0
0
1
0
0
1
2
4
1
2
1
0
0
2
0
0
0
2
1
0
1
1
1
1
2
1
1
0
2
1
0
2
2
1
2
1
1
1
0
0
1
1
2
0
2
0
0
0
1
0
3
1
1
1
0
0
0
0
0
0
0
1
2
1
3
0
1
2
0
1
0
0
1
0
1
0
0
0
1
1
2
1
1
0
0
0
0
2
2
0
0
2
0
1
0
0
0
1
1
0
2
0
2
0
0
0
0
1
0
0
0
0
1
0
1
1
0
1
0
0
1
0
1
0
0
2
1
0
0
0
2
2
1
0
2
0
0
2
0
0
0
0
0
3
1
1
0
0
0
0
0
0
1
3
0
0
1
2
4
2
1
1
0
0
1
0
2
0
0
1
1
1
1
1
2
0
0
0
2
0
1
2
1
2
4
0
1
2
2
0
1
1
2
0
0
2
0
0
1
1
1
1
0
1
1
0
0
2
1
1
0
2
0
1
1
2
0
0
1
1
1
0
2
1
1
2
2
1
1
3
1
0
3
1
0
1
0
0
0
1
1
2
1
0
2
0
2
0
0
2
1
2
0
1
1
0
1
1
0
0
0
1
0
0
0
2
0
1
1
2
2
0
3
1
1
0
2
0
2
1
2
1
0
0
0
1
0
1
1
0
0
0
2
1
1
1
1
1
1
2
0
1
0
0
2
1
3
1
1
0
1
0
1
2
0
0
1
1
3
0
0
1
0
0
0
0
2
2
0
0
0
2
2
1
0
1
0
1
2
0
1
0
2
1
0
2
0
0
1
1
1
0
2
0
0
0
2
0
2
0
0
6
1
0
0
0
0
0
0
0
2
1
1
1
0
0
0
0
0
1
0
1
2
1
0
0
0
0
0
0
1
2
2
1
0
0
0
2
1
0
0
1
0
0
0
0
0
1
1
0
0
0
1
2
0
0
2
2
0
2
1
0
2
2
0
1
2
1
0
1
2
1
0
1
2
0
1
1
0
2
1
1
1
1
0
2
0
1
0
0
1
0
0
0
0
0
0
1
0
1
2
2
0
1
0
0
1
0
2
1
0
1
0
0
0
0
1
1
2
0
1
0
1
1
2
1
1
2
0
2
0
0
2
0
2
2
1
1
1
1
0
0
0
1
1
0
2
1
1
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
1
2
2
2
0
2
0
1
0
1
1
2
1
0
1
0
2
0
1
0
0
0
1
0
1
0
2
0
1
1
1
0
1
1
1
0
0
0
1
0
1
2
2
1
1
2
0
1
0
1
0
0
0
2
1
0
0
2
1
1
2
0
0
2
1
0
0
2
0
2
0
0
1
1
0
1
1
0
1
0
0
0
1
1
0
1
0
1
2
0
1
3
1
0
0
0
1
1
0
1
1
1
1
1
1
0
1
1
0
0
0
2
0
0
1
1
1
2
1
0
0
1
1
2
0
0
0
1
2
2
3
1
1
2
2
0
2
1
1
1
0
0
0
1
2
3
0
0
0
1
0
2
2
1
0
0
1
0
0
0
1
2
0
1
1
1
0
0
1
0
1
1
0
0
1
1
0
1
1
0
2
0
0
1
0
0
2
1
0
1
3
1
0
0
3
1
0
1
0
1
0
0
0
1
1
0
2
1
2
1
1
0
0
0
2
0
0
2
0
0
0
0
1
1
0
3
1
2
1
0
1
0
2
0
0
1
1
2
0
2
0
0
0
0
0
2
0
0
0
2
1
0
1
1
2
0
0
0
0
1
3
2
0
0
1
1
0
2
0
1
0
0
2
1
0
1
1
0
1
1
1
1
0
0
1
0
1
2
2
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
2
1
0
1
1
2
0
1
0
0
0
2
1
1
1
2
0
0
1
2
1
1
2
0
0
0
0
0
1
2
2
0
1
2
0
0
2
1
0
0
2
0
0
0
0
0
2
1
1
2
0
2
1
0
2
0
0
2
0
2
0
1
1
2
2
0
2
0
1
2
0
1
1
0
0
0
1
0
0
0
1
1
1
0
0
2
0
0
1
0
0
1
0
0
0
2
1
1
0
1
0
1
0
2
1
1
1
0
4
0
0
1
1
1
2
0
0
1
2
1
0
0
1
1
0
2
0
1
1
1
0
0
0
0
1
4
0
1
0
0
0
0
0
1
0
0
1
1
1
0
2
1
1
0
2
1
0
0
0
0
0
1
1
2
0
1
0
0
0
0
1
1
0
1
3
0
2
2
0
1
0
0
2
1
1
2
2
0
1
3
1
1
1
2
2
0
1
1
2
1
1
2
1
1
0
0
2
1
0
2
1
1
1
2
2
1
0
0
2
3
0
0
0
2
1
0
1
1
1
1
1
0
1
2
0
0
0
1
0
0
0
0
0
0
3
0
1
1
0
0
0
1
1
0
0
0
0
0
0
1
2
1
1
2
0
2
1
1
1
0
0
2
1
0
0
1
0
0
1
1
0
1
1
0
0
2
2
0
1
1
1
0
1
0
0
1
0
2
0
1
1
0
0
0
1
1
0
0
2
2
1
1
0
0
0
0
0
1
1
0
2
2
2
2
2
0
0
1
0
0
2
2
2
3
0
1
0
1
0
0
0
2
1
0
1
1
3
0
0
2
0
0
2
0
1
0
0
2
0
0
0
2
0
1
1
0
0
1
0
0
2
2
2
1
0
1
2
1
2
0
1
2
0
0
0
0
2
2
0
2
2
0
2
1
1
2
1
0
1
0
0
1
0
0
0
1
0
1
2
0
0
2
0
0
0
1
1
1
0
2
1
2
2
1
2
1
2
1
1
2
1
0
0
1
1
1
1
0
0
0
1
2
0
0
0
0
0
1
0
1
0
2
0
0
0
2
1
0
0
0
2
2
0
1
2
0
0
1
1
0
0
2
3
0
0
1
0
0
2
3
0
0
0
0
0
0
1
1
2
0
1
1
0
0
1
0
0
2
1
1
1
0
1
0
0
0
1
0
2
1
0
1
0
0
1
1
2
0
2
0
1
1
0
0
0
1
0
0
0
0
2
2
0
2
2
0
0
2
2
1
1
0
1
0
0
0
0
0
1
1
0
2
1
1
2
0
0
1
2
0
0
0
2
0
1
1
1
1
1
0
1
0
2
0
4
1
0
0
0
1
0
2
1
1
0
0
0
1
0
2
2
0
1
2
0
1
1
2
0
1
1
0
1
1
1
0
1
2
0
1
0
0
0
0
0
1
1
1
0
1
1
0
0
2
1
0
0
1
0
1
0
2
0
0
1
0
0
1
1
0
0
0
2
0
2
1
0
1
0
1
2
1
0
2
0
1
0
1
1
3
0
1
0
0
0
0
0
0
1
0
0
1
1
1
0
1
1
0
0
0
2
0
2
1
0
2
0
0
0
0
1
1
0
1
1
1
0
1
2
0
0
2
1
1
0
0
2
2
1
1
0
2
2
0
1
1
2
2
0
2
1
1
0
1
1
1
0
0
2
1
0
1
0
1
0
0
1
0
0
0
0
0
0
2
0
2
1
3
1
1
2
2
0
2
0
1
1
0
4
0
0
1
0
2
0
2
0
2
0
2
1
0
2
0
0
0
0
1
0
0
1
2
0
0
0
1
0
1
1
0
2
2
0
0
1
1
1
1
0
0
2
0
1
1
0
2
0
0
1
0
0
0
1
1
1
1
2
0
1
0
0
1
0
2
0
1
1
0
1
0
1
0
0
0
1
1
0
1
0
1
1
0
1
1
0
2
2
0
2
0
1
1
0
0
0
0
2
0
0
1
1
0
0
3
1
0
0
1
1
1
0
0
0
2
0
3
0
1
0
0
1
2
0
0
0
0
0
1
2
1
4
1
0
1
0
0
0
0
1
0
1
1
2
2
2
0
2
2
2
0
1
0
0
0
0
1
2
0
0
0
2
1
1
1
2
0
0
0
0
1
1
0
1
1
1
0
3
0
1
1
0
2
0
1
2
0
1
0
1
0
0
0
0
1
1
2
0
0
0
1
0
1
2
1
0
1
0
0
2
2
0
0
1
1
4
1
0
0
2
2
0
1
1
1
2
1
2
1
1
0
1
1
0
1
0
1
0
1
1
0
0
0
2
1
1
0
2
0
0
0
0
2
0
0
1
1
0
0
2
1
2
0
1
0
1
0
0
0
1
2
0
0
1
0
0
0
1
1
2
1
1
0
0
2
1
0
0
1
1
0
2
0
0
1
0
0
0
0
1
0
2
0
1
1
1
3
0
1
0
1
1
0
2
2
2
0
2
2
1
2
0
1
0
3
0
1
1
0
2
2
1
2
0
1
0
1
0
0
0
1
0
0
2
1
0
1
2
2
0
0
1
0
0
2
3
1
1
0
2
0
3
0
1
1
0
1
2
2
0
0
0
1
0
3
2
1
0
0
2
1
0
1
0
2
4
2
0
1
1
2
1
0
1
0
0
2
2
1
1
1
1
0
0
1
3
0
1
0
1
0
0
0
0
1
0
1
1
1
1
2
1
1
0
0
0
1
2
1
1
0
0
1
1
1
0
1
1
1
1
0
1
0
0
1
1
0
0
0
0
0
2
2
1
0
0
0
2
0
2
0
1
1
0
0
1
0
3
1
0
2
0
2
2
2
0
1
1
1
0
0
0
1
0
0
2
1
0
1
0
4
1
0
1
2
2
0
2
0
0
0
1
0
10
0
1
1
1
0
0
2
0
1
0
2
2
1
0
2
0
0
0
0
1
0
0
2
0
2
1
0
1
1
0
1
0
0
2
0
1
1
2
0
1
1
2
0
0
1
1
0
1
2
0
1
0
1
1
2
1
1
0
0
0
0
1
0
2
0
2
0
1
1
1
2
0
3
1
0
1
0
3
2
1
1
1
1
0
1
0
1
0
0
0
0
2
0
2
1
0
0
1
1
1
1
1
1
1
1
2
2
1
1
0
1
0
2
1
0
1
1
0
1
0
0
1
2
0
1
1
2
0
0
0
0
1
0
1
0
2
2
0
0
2
0
1
0
1
0
2
2
2
0
0
2
0
0
0
0
0
1
0
1
0
2
1
1
0
0
0
0
2
0
1
1
0
0
0
1
2
0
0
2
0
1
1
1
1
0
1
0
1
1
0
1
0
1
2
0
0
9
2
1
2
1
1
0
1
0
0
0
1
2
1
1
3
0
2
1
1
0
2
0
0
0
0
0
1
1
0
0
0
1
0
1
2
1
2
0
0
6
1
0
0
3
3
1
2
1
0
0
0
1
0
0
1
0
0
0
1
1
2
0
3
1
1
0
1
0
1
0
2
2
3
2
1
0
0
2
1
1
0
0
0
1
0
1
0
1
0
1
0
0
0
0
1
1
1
0
0
0
1
1
1
0
2
2
0
0
0
0
0
0
0
1
2
0
0
0
1
2
2
2
2
0
3
2
1
1
1
1
0
1
1
1
1
2
0
1
1
0
2
1
0
0
2
0
0
0
0
1
0
0
2
2
0
2
0
0
0
2
1
1
1
2
0
0
0
0
1
1
2
1
1
0
1
1
0
0
0
0
0
1
1
2
2
0
1
0
0
2
0
0
0
0
4
2
0
1
0
2
1
1
0
1
1
0
1
2
1
0
0
1
2
1
0
1
0
0
1
2
2
0
1
2
0
1
1
0
0
2
2
1
0
2
1
1
2
1
1
0
1
0
1
1
0
1
4
0
0
1
0
2
0
2
0
0
0
0
0
4
0
2
2
1
1
1
1
0
0
3
1
1
0
0
2
1
0
0
0
1
2
0
0
1
1
0
1
1
0
2
0
0
0
1
2
1
2
0
0
1
1
2
2
0
0
0
2
1
0
0
0
1
0
2
1
2
1
0
0
1
1
0
2
0
1
1
2
0
1
0
0
2
1
1
1
2
1
1
0
0
0
0
0
0
0
1
1
2
1
0
2
0
2
1
0
0
0
0
0
0
1
2
0
2
2
2
0
1
0
0
2
1
0
2
0
0
0
1
0
2
1
2
0
2
1
2
1
1
0
1
1
0
2
0
2
0
0
2
0
2
0
1
0
0
1
2
1
0
2
1
1
1
2
0
1
0
0
0
0
3
1
1
1
1
0
0
1
1
1
0
0
0
1
2
0
1
0
0
0
0
1
0
1
1
1
0
0
1
0
0
2
2
2
2
0
0
0
0
1
0
2
0
1
1
0
1
1
1
2
2
0
1
1
2
2
0
1
2
2
1
0
0
1
0
0
0
2
2
0
2
1
0
1
1
0
1
2
2
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
2
0
1
2
2
0
2
0
0
1
0
2
1
0
0
0
1
0
1
0
2
1
0
0
2
0
2
1
2
0
0
0
0
1
1
2
1
2
0
1
0
0
2
0
2
1
0
2
0
0
0
0
1
0
4
2
0
1
0
1
1
0
0
0
2
1
2
0
2
1
0
0
1
2
1
1
5
0
2
0
1
1
2
0
1
1
0
0
1
2
0
0
1
0
1
3
2
1
1
0
0
0
0
0
0
1
1
1
1
0
0
2
2
0
0
1
0
0
0
1
0
0
1
1
1
0
0
0
1
0
1
1
1
2
0
0
2
1
2
0
0
1
1
1
1
1
0
0
0
1
1
0
1
0
3
0
0
0
1
2
0
0
2
1
1
0
0
0
1
0
0
1
1
0
3
0
2
0
1
1
2
0
0
1
1
1
2
1
0
2
2
0
0
0
0
2
1
2
0
1
0
0
0
0
1
0
1
0
1
0
2
2
1
0
2
2
2
1
2
0
2
0
1
2
2
0
1
0
0
0
1
2
0
1
0
2
0
0
0
0
0
0
2
0
1
2
0
2
0
1
0
1
2
2
0
0
1
3
2
1
1
1
0
0
0
0
2
1
0
0
2
2
0
1
0
2
0
2
1
0
0
0
0
0
0
0
1
0
0
2
0
1
2
1
0
0
2
0
2
0
0
0
0
0
1
1
0
0
1
0
1
1
1
0
0
0
3
1
2
2
1
1
0
0
0
1
0
2
1
2
0
1
0
1
0
0
1
1
2
1
0
0
0
1
1
0
0
0
0
0
0
2
0
0
1
1
0
1
1
1
2
2
0
0
2
0
0
2
0
0
1
1
0
2
1
1
1
0
3
0
1
0
0
0
0
0
1
0
0
0
2
0
1
0
0
1
1
0
2
0
0
0
1
1
1
1
0
2
2
1
1
1
2
0
1
0
0
1
0
1
0
2
0
2
0
1
0
0
2
0
0
0
0
2
1
0
3
0
4
0
0
2
0
1
0
1
1
4
0
0
0
0
0
0
0
1
1
0
1
2
1
2
1
0
2
2
1
0
2
2
0
1
0
2
1
0
0
3
2
1
1
0
0
1
0
3
0
2
0
0
1
2
0
1
0
0
3
0
0
2
0
1
0
0
0
2
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
2
1
0
1
0
2
1
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
1
1
0
0
0
0
0
2
2
2
0
1
1
0
0
0
0
1
1
1
0
1
1
1
0
1
2
1
1
2
1
1
0
0
0
0
0
2
1
2
1
0
0
1
2
1
0
2
1
2
0
0
0
1
0
0
0
0
2
1
2
0
1
1
0
0
1
0
0
0
1
0
1
0
2
1
0
0
2
0
0
4
0
1
1
1
2
0
0
1
1
0
3
0
0
0
2
1
1
0
0
1
1
2
1
0
0
1
0
0
2
2
4
2
0
0
1
2
2
2
0
2
2
0
0
0
0
1
0
1
0
1
1
1
0
1
1
0
2
1
0
1
1
2
2
0
2
0
2
0
0
0
1
2
0
0
1
2
1
0
0
0
0
0
0
1
2
1
0
0
0
0
1
1
1
0
1
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
1
1
3
0
0
2
1
2
0
1
0
1
0
1
0
0
2
0
0
1
1
0
0
1
1
2
2
1
1
1
0
0
0
0
0
1
1
0
1
2
0
2
0
2
0
0
0
1
0
0
2
1
0
0
1
2
1
0
2
0
0
0
1
1
1
0
1
0
0
2
0
2
2
1
2
1
2
0
1
0
0
0
1
0
2
2
0
1
1
0
0
1
2
2
1
1
0
0
2
1
1
1
0
1
0
1
0
0
1
1
0
1
2
0
0
1
0
2
1
2
0
1
0
2
4
1
2
0
3
2
0
1
2
1
1
0
0
1
0
0
0
1
1
1
2
0
2
1
0
2
0
1
0
0
0
0
2
2
0
1
1
0
2
0
1
1
1
1
0
2
0
0
0
0
1
0
0
0
2
0
1
0
2
2
0
1
1
0
1
0
0
1
1
1
1
1
0
2
0
0
2
0
0
0
2
0
0
0
2
1
0
0
0
1
0
0
0
2
1
2
2
1
0
0
0
0
1
1
2
0
1
0
1
1
0
1
0
0
1
1
0
1
1
0
0
1
0
2
2
0
1
2
0
0
1
0
1
1
0
1
2
0
2
0
2
1
1
1
2
0
1
1
1
0
1
0
2
0
2
2
1
0
1
0
1
0
1
0
0
0
1
1
1
2
0
0
0
0
0
0
0
0
1
0
3
2
2
2
1
0
0
1
1
1
0
0
1
1
0
1
1
1
1
0
0
0
2
0
2
1
0
0
2
1
1
0
2
0
0
1
0
0
0
1
1
2
0
0
2
1
2
0
1
0
1
2
0
2
1
1
1
0
0
0
2
0
0
1
0
0
0
0
2
2
0
1
1
4
0
0
1
1
2
1
0
4
2
2
0
2
1
1
2
0
1
2
0
1
0
0
1
0
1
0
1
1
2
2
0
0
1
0
1
0
0
1
0
1
3
0
0
0
0
0
1
0
1
2
0
1
0
2
1
0
0
0
2
1
1
2
2
3
1
1
1
0
0
1
2
2
0
1
2
2
2
2
0
1
2
0
0
0
1
0
1
0
2
1
2
1
1
1
1
0
0
1
1
1
1
0
1
1
0
0
0
1
0
1
1
2
0
0
0
0
1
0
0
2
0
0
2
0
2
0
1
4
0
0
1
0
0
2
0
0
2
1
2
0
2
2
0
0
0
0
2
0
2
2
1
5
1
0
1
0
1
0
1
1
0
1
0
0
0
1
1
0
2
1
0
1
2
0
0
0
0
0
2
0
0
0
0
2
1
1
2
1
1
0
0
2
1
2
1
2
2
2
0
2
1
0
1
3
1
1
0
0
0
2
1
1
0
0
1
1
0
1
0
1
2
0
2
0
1
2
2
1
2
0
0
0
0
0
1
1
1
1
2
2
0
2
2
0
0
2
1
1
0
0
1
0
0
0
0
0
1
1
2
1
2
0
0
0
0
1
1
0
1
1
0
1
2
1
1
0
1
1
0
2
2
2
5
1
3
1
2
0
0
2
2
2
2
1
1
1
0
0
0
0
2
1
1
0
1
1
2
0
3
0
0
0
0
0
0
0
0
1
2
0
0
1
1
0
1
2
0
1
0
0
0
0
1
0
0
0
1
1
2
1
1
0
2
0
0
0
0
0
1
2
2
0
0
2
1
0
1
1
2
1
0
0
2
1
0
3
1
2
1
0
1
1
0
1
0
0
0
2
0
0
1
2
0
1
3
1
0
1
0
2
2
2
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
2
2
0
2
1
1
0
2
2
2
1
0
0
0
0
2
1
1
0
1
1
0
0
1
0
2
0
0
3
0
0
1
0
2
0
0
2
0
3
2
0
0
1
1
0
1
0
0
1
1
1
0
1
0
1
2
0
0
1
1
0
1
0
1
0
1
0
2
2
1
0
2
0
1
1
2
0
2
0
0
0
0
1
1
0
2
1
0
2
1
1
0
1
1
1
0
2
1
0
0
1
0
0
1
1
1
0
1
2
0
2
1
0
2
0
0
1
0
0
1
1
0
1
0
0
0
1
2
0
0
0
1
0
1
0
0
2
0
1
2
0
0
0
2
0
0
2
0
0
0
0
1
0
1
1
1
1
1
2
1
1
1
0
1
0
0
0
2
0
0
0
2
1
1
0
4
0
0
0
0
0
2
4
0
0
0
2
0
0
1
0
1
2
1
0
2
0
0
0
0
0
0
2
0
1
1
1
0
3
2
0
0
1
0
1
2
0
0
1
0
1
1
2
0
1
1
3
1
0
2
2
1
2
2
0
1
0
1
2
0
0
0
2
1
0
0
0
1
0
1
3
0
0
0
1
0
0
0
1
0
0
2
2
2
2
0
2
0
0
2
0
2
0
2
0
0
2
2
0
2
2
1
2
0
1
0
2
1
2
2
2
0
0
0
1
0
0
0
0
3
2
0
0
1
1
2
0
0
1
0
0
1
1
1
2
0
0
0
0
1
2
1
0
2
1
3
1
2
2
1
0
2
1
2
0
2
1
0
1
0
0
0
0
1
1
0
2
0
3
0
2
3
0
2
1
0
0
1
1
2
2
0
0
0
0
1
1
2
1
0
1
1
1
0
1
2
1
0
1
1
1
1
0
1
2
1
1
0
2
0
2
1
0
1
2
0
1
2
2
2
1
0
0
0
0
0
1
0
1
1
1
2
1
1
0
1
0
0
3
0
3
2
2
2
1
1
2
0
2
2
0
0
0
0
1
1
0
1
1
2
2
0
0
1
0
1
0
1
2
0
0
0
1
0
2
0
2
1
3
2
2
1
0
2
1
1
0
0
0
0
0
1
0
0
0
2
0
1
1
1
0
1
1
0
0
2
0
0
2
2
0
2
8
0
2
0
0
0
1
3
0
0
0
1
0
0
1
1
0
3
0
2
1
0
0
0
1
2
0
1
0
0
0
1
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
1
1
0
1
0
0
2
0
0
0
1
0
0
0
1
2
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
2
1
1
1
0
2
3
0
0
2
0
0
0
2
0
1
1
0
1
0
0
1
1
0
1
0
0
1
0
1
0
1
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
2
2
1
1
1
1
2
2
2
2
2
2
0
0
0
2
0
0
2
1
1
1
2
2
1
0
0
0
1
2
0
2
1
2
2
3
0
0
2
2
2
1
1
0
2
0
0
0
2
2
2
1
0
1
2
1
0
1
0
1
0
0
0
3
1
0
2
0
2
0
0
0
0
2
0
1
0
0
1
0
1
2
1
0
2
2
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
2
2
0
0
2
0
0
1
2
1
0
0
0
0
1
2
1
0
0
0
0
2
2
1
1
2
0
0
0
0
0
1
0
2
0
0
1
1
0
1
0
1
0
0
0
0
0
1
1
2
0
0
1
1
1
5
2
0
1
2
1
2
2
2
0
2
2
1
2
0
0
1
2
0
0
2
1
2
1
2
0
0
0
1
1
0
2
1
0
1
2
0
0
0
0
1
2
0
2
2
1
0
2
0
2
0
1
1
1
1
0
2
0
0
0
1
1
2
0
0
1
2
0
1
0
2
0
1
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
1
2
0
1
1
3
0
0
0
0
0
0
0
0
1
0
0
0
1
2
1
0
1
0
1
1
1
0
0
1
2
1
1
2
0
1
0
1
2
0
0
0
2
1
0
0
1
0
1
2
1
1
0
1
2
0
1
1
1
0
0
0
1
0
1
0
1
6
2
1
1
0
0
2
1
1
0
0
0
0
1
0
1
1
1
1
0
0
1
0
2
0
1
1
0
0
1
1
0
0
1
2
0
1
1
0
1
1
0
0
1
0
3
0
0
0
0
0
4
0
0
0
1
1
1
2
0
1
1
0
0
2
0
1
1
0
0
0
0
2
2
1
0
0
2
1
1
0
0
0
1
2
0
0
0
0
1
2
2
0
1
1
0
0
2
2
2
0
0
0
3
1
1
1
1
0
1
0
1
2
2
1
0
2
0
1
0
0
2
2
1
2
1
1
1
1
0
0
0
1
1
1
2
0
0
0
1
2
0
1
0
0
2
0
0
2
2
0
0
1
1
2
1
0
0
1
1
0
0
2
0
1
0
0
0
1
2
0
1
2
0
1
0
1
1
0
2
1
0
0
1
3
1
3
0
1
2
0
0
0
1
1
1
0
1
2
0
1
1
0
0
2
0
1
0
1
0
0
2
0
2
2
1
1
3
1
1
3
1
0
2
2
2
0
1
2
2
2
2
1
1
2
0
1
0
0
1
1
0
0
0
0
0
1
4
0
0
0
0
0
0
0
1
0
2
2
2
2
0
1
2
1
0
1
0
0
2
0
0
1
0
0
1
1
1
1
1
0
0
3
1
2
2
1
3
0
2
0
1
0
2
0
0
1
1
1
1
1
0
0
0
2
1
1
0
0
2
0
1
1
0
3
2
0
0
0
2
2
2
2
1
1
0
0
0
1
1
1
1
3
2
0
1
1
3
2
0
2
1
1
1
0
0
1
0
2
1
0
0
1
1
1
0
0
0
0
0
0
1
2
2
0
0
0
2
0
2
0
2
2
2
0
2
0
1
2
2
1
1
0
1
2
0
0
0
0
1
2
0
2
1
0
0
0
0
1
0
0
0
0
3
0
1
1
0
2
0
2
0
0
0
0
0
2
0
2
0
0
1
0
0
2
2
1
1
1
1
10
1
0
0
1
0
2
0
0
0
0
0
2
2
0
0
0
2
1
1
1
1
2
0
0
0
1
1
2
1
1
1
1
2
1
0
1
1
1
0
0
1
1
0
1
0
1
1
0
1
1
2
0
1
0
0
2
0
2
0
1
0
2
3
1
2
0
1
4
0
2
1
1
1
1
1
0
0
0
0
0
0
1
0
0
1
0
2
1
0
0
2
2
0
1
1
2
2
1
2
0
1
0
1
0
2
0
2
0
2
0
1
0
0
0
2
2
1
0
1
0
0
2
0
0
1
2
2
1
1
0
0
0
1
0
4
0
0
0
0
2
1
0
0
1
1
1
0
3
1
2
0
1
1
0
2
1
0
1
0
1
1
2
1
0
0
1
1
1
1
0
0
3
0
0
0
1
2
2
0
1
0
0
1
2
1
0
1
2
0
1
1
0
2
2
2
1
1
2
3
0
1
3
1
2
0
1
0
1
0
1
0
0
2
0
1
0
1
2
2
0
0
0
2
1
0
1
2
2
0
0
0
2
0
0
0
2
1
1
0
0
0
0
2
1
0
2
2
0
1
2
1
1
1
0
0
0
0
2
1
1
0
0
0
0
0
0
0
2
1
2
0
0
0
1
0
2
1
0
2
0
3
1
0
1
0
1
1
2
2
1
1
0
1
2
5
0
1
0
1
0
1
0
1
0
0
1
0
2
2
0
0
1
0
0
1
2
4
1
1
0
0
1
1
0
0
1
0
0
1
0
1
0
1
0
1
0
1
0
0
2
0
1
0
0
1
0
2
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
2
2
1
2
3
1
1
0
0
1
2
1
2
0
2
0
0
0
0
1
0
2
2
1
0
0
1
1
0
0
0
1
0
2
0
0
1
2
1
2
1
0
0
0
1
0
0
0
1
0
0
1
0
1
2
2
0
1
1
0
1
0
0
1
1
0
0
0
2
1
2
0
1
1
1
1
2
2
1
0
0
0
2
2
1
1
0
1
1
1
2
2
0
0
1
0
2
3
0
3
1
1
1
2
2
2
0
2
2
0
1
1
0
1
1
0
0
2
0
1
2
0
0
2
0
0
0
2
0
0
2
0
1
0
0
3
0
1
1
0
0
0
0
1
2
0
2
0
1
0
2
1
1
2
0
0
0
2
0
1
1
1
0
0
0
0
1
1
3
1
1
0
3
1
1
0
0
0
1
0
0
1
1
0
0
1
0
0
1
0
1
0
1
0
1
0
0
2
0
1
0
1
0
0
2
2
1
1
0
2
0
2
1
0
0
0
2
0
0
1
0
0
1
0
0
1
0
2
0
0
1
2
0
1
1
1
1
0
1
0
1
2
1
2
2
1
2
2
0
0
0
1
0
0
2
0
0
1
0
1
1
1
0
0
0
5
1
4
0
0
1
2
1
0
0
1
0
0
2
2
0
0
0
0
2
1
1
0
0
0
1
2
1
0
1
0
1
0
1
1
0
0
1
0
0
0
0
1
2
1
1
2
1
1
2
1
0
2
1
0
3
0
1
0
0
1
1
1
3
2
1
0
0
0
0
0
2
0
1
1
1
0
0
1
3
0
2
0
1
1
1
0
0
0
2
2
0
0
2
1
0
2
0
1
1
1
0
2
1
0
2
0
2
2
0
1
0
0
2
0
2
2
0
1
0
2
2
2
0
0
1
1
0
0
0
0
2
1
0
0
0
1
0
2
1
0
2
2
2
0
1
2
1
0
1
0
2
2
0
1
2
1
1
1
2
0
2
0
1
1
2
0
2
0
1
0
1
0
1
2
1
0
0
0
1
1
0
0
1
1
0
0
0
0
2
0
0
1
2
1
1
0
0
1
0
1
0
1
0
1
1
2
0
0
1
0
1
1
1
0
1
2
0
1
0
2
0
1
0
0
0
1
0
1
0
2
0
1
1
0
2
1
0
0
0
2
0
1
0
2
0
0
1
1
1
0
1
1
1
0
0
1
0
0
0
0
0
1
2
2
0
1
0
0
0
2
2
1
2
0
0
0
0
2
2
2
0
0
0
1
1
1
0
0
0
2
1
0
0
1
0
0
0
2
1
2
2
2
0
0
2
0
2
0
1
0
2
1
0
0
2
0
0
0
0
0
0
0
0
13
0
1
2
0
0
1
1
0
2
1
1
0
2
2
1
1
0
2
0
0
0
1
0
0
2
2
1
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
2
0
0
0
2
0
2
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
1
0
0
1
2
1
0
1
0
0
1
0
0
2
0
2
0
2
0
1
2
0
2
4
1
0
0
0
0
1
2
0
0
1
1
0
0
2
0
1
2
0
0
3
0
0
2
1
1
1
0
2
1
0
3
1
0
2
0
1
0
0
2
0
2
0
0
1
0
2
0
2
2
0
2
2
0
2
2
0
1
0
0
2
0
0
2
1
1
0
1
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
2
1
0
1
1
1
0
0
0
0
0
1
0
1
0
2
1
2
0
0
3
0
3
2
0
1
1
0
0
0
1
0
0
2
1
2
0
1
2
1
2
0
1
2
1
0
0
0
1
2
1
0
1
2
1
1
1
0
0
0
0
1
1
1
0
8
0
2
0
0
0
1
2
1
0
0
0
2
5
1
0
2
1
0
0
1
0
1
2
1
3
3
1
0
1
0
0
0
1
1
0
2
1
1
0
1
3
2
0
1
1
0
2
0
1
0
2
1
2
1
0
0
0
0
1
2
0
0
0
0
2
1
3
0
1
1
1
0
0
0
2
0
0
0
0
2
0
2
0
2
2
1
1
1
2
1
2
0
2
0
0
0
0
0
0
1
2
0
0
0
1
0
2
0
1
0
0
0
0
2
0
1
1
0
2
2
0
1
0
2
0
0
0
2
0
0
1
0
2
0
1
1
2
1
2
2
0
3
1
2
1
0
0
1
3
0
0
0
1
0
1
1
0
0
1
1
0
1
1
1
1
1
2
0
0
1
1
1
0
0
0
1
1
1
1
1
1
0
0
1
1
2
1
0
1
0
0
0
2
1
0
0
1
0
0
0
1
1
2
0
0
0
0
0
0
0
2
2
0
0
1
0
3
1
0
1
0
2
0
1
1
3
2
0
1
2
0
1
1
0
1
0
2
0
1
1
0
1
0
2
1
0
1
0
1
0
1
0
1
1
1
0
1
2
1
0
2
0
0
0
1
1
0
0
1
0
0
1
0
2
0
0
1
2
0
1
0
2
0
1
2
1
3
1
1
0
3
1
1
1
1
0
1
0
0
2
1
1
1
0
1
0
0
0
0
0
1
0
0
2
0
2
0
1
0
1
2
1
0
0
0
0
2
1
1
2
2
2
1
2
2
1
1
0
0
1
1
1
0
2
0
1
2
0
0
0
1
0
0
0
1
1
0
0
1
1
1
1
0
2
2
0
2
0
1
1
0
1
0
2
1
1
0
1
1
2
1
1
2
0
2
0
1
0
2
1
0
0
1
2
0
1
1
1
2
0
1
0
0
2
0
0
2
1
0
0
0
3
0
0
2
2
0
2
2
2
0
2
1
0
1
2
0
0
0
2
1
0
1
1
0
2
0
0
1
1
1
1
2
0
2
1
0
1
0
0
1
0
0
2
0
2
2
0
0
0
1
0
0
0
2
3
0
1
1
1
0
0
1
2
0
0
0
0
0
2
1
1
0
0
1
1
1
0
1
1
0
1
2
0
2
0
0
1
0
0
1
0
2
1
2
4
1
2
2
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
2
2
0
0
1
0
0
2
2
2
0
0
1
0
0
1
0
1
3
0
0
2
0
1
0
0
0
0
2
1
2
0
1
0
1
0
0
0
1
1
2
0
0
2
0
0
0
0
1
1
1
0
1
1
1
0
0
2
0
2
0
1
0
0
0
1
1
2
0
1
0
0
2
1
0
2
0
0
1
1
0
0
0
1
2
1
0
0
0
1
0
0
1
1
1
1
2
1
1
2
1
0
0
0
1
0
2
0
0
0
0
0
1
2
0
0
1
0
1
1
0
0
0
2
0
2
0
1
0
1
0
0
1
0
0
1
0
2
3
0
0
1
2
0
1
2
0
2
0
1
1
0
2
1
0
1
0
1
0
0
1
0
2
0
1
0
0
1
1
0
2
0
0
0
1
1
0
0
0
0
0
0
1
1
0
2
1
1
0
0
2
0
1
2
0
1
1
0
0
2
2
1
1
0
2
2
2
0
0
0
2
3
2
2
1
0
0
2
1
1
0
0
0
0
1
2
2
0
3
0
2
1
0
2
1
0
3
0
0
0
0
1
1
1
2
1
0
2
0
1
0
2
0
1
0
1
0
2
1
0
1
1
0
0
2
0
2
2
0
0
0
2
1
0
1
0
1
0
1
2
1
0
0
1
0
1
0
2
0
0
0
0
0
1
0
0
3
0
1
1
0
2
1
2
0
2
1
0
2
2
0
1
0
2
0
1
1
0
1
0
2
2
0
0
1
0
0
0
2
6
0
0
1
2
2
2
2
3
1
0
0
2
1
1
1
0
3
1
3
0
0
0
2
0
3
3
0
0
1
0
2
0
0
0
0
0
1
1
1
2
2
1
0
1
0
1
0
0
0
2
0
1
2
1
0
0
0
2
1
1
1
0
1
1
0
1
0
0
5
0
0
1
1
1
0
1
0
1
0
2
1
2
0
2
0
1
0
0
1
0
0
1
0
0
1
0
1
0
1
0
1
0
0
1
2
0
0
0
2
1
0
0
0
0
1
1
2
0
0
0
0
0
1
1
1
0
1
1
0
2
2
0
1
2
1
1
2
1
1
2
1
0
0
0
1
0
1
1
2
0
2
1
0
1
0
0
2
0
0
1
0
0
0
1
0
2
1
1
1
2
0
1
0
0
0
0
1
0
0
0
1
1
0
2
1
0
2
0
0
0
1
0
1
1
0
2
0
1
1
0
0
1
0
0
1
0
1
1
1
1
2
2
1
0
0
1
1
0
2
1
1
1
0
1
0
0
2
0
2
2
0
1
2
0
0
0
2
1
0
0
0
0
3
2
1
0
1
0
0
0
0
1
0
2
2
0
1
0
2
0
0
1
0
0
0
1
2
0
0
0
0
0
1
0
0
2
1
1
0
0
1
0
0
0
1
0
0
1
0
1
1
0
0
1
2
0
0
0
0
2
0
0
0
0
0
1
0
0
1
2
1
1
2
0
1
0
0
2
1
1
1
1
0
0
0
0
2
0
2
2
1
0
0
2
0
0
0
0
0
2
2
0
0
1
0
1
1
0
0
0
1
1
0
0
0
1
1
0
0
1
1
0
1
0
1
2
2
1
0
1
1
0
0
0
0
0
1
0
2
1
2
1
0
0
0
2
2
1
0
1
0
0
1
2
0
0
1
1
1
2
1
1
2
0
1
1
0
1
0
1
0
0
0
0
1
1
1
2
0
1
0
0
0
2
2
0
1
1
2
0
1
0
0
0
0
0
0
2
1
1
1
1
0
1
0
2
0
1
0
1
1
2
2
0
1
0
1
2
0
1
1
1
0
0
0
0
1
0
1
2
1
0
0
1
0
1
2
1
1
0
0
2
0
0
0
1
0
1
0
0
1
1
0
2
0
2
0
1
0
0
1
1
0
0
0
0
1
0
0
1
2
1
0
2
0
0
0
0
1
2
0
0
1
1
0
1
0
2
0
1
0
0
1
0
0
1
1
1
0
2
0
1
3
0
2
1
1
1
0
1
3
0
0
1
0
0
0
2
0
0
2
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
1
0
0
1
1
1
2
0
0
0
0
2
0
0
0
1
1
1
2
1
0
2
0
2
2
0
1
2
0
2
0
1
1
1
0
1
0
0
0
0
2
1
0
0
0
2
0
1
0
1
1
0
0
1
3
2
1
0
1
0
0
2
1
0
2
2
4
0
0
1
1
0
1
1
1
0
1
1
0
0
1
1
5
0
2
0
0
0
1
2
1
2
0
0
1
0
0
0
0
0
1
2
2
0
0
1
2
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
1
1
1
0
1
0
2
0
0
2
0
2
0
1
1
0
1
0
1
0
0
3
0
0
1
0
1
2
1
0
0
0
1
0
1
1
0
2
0
3
2
0
0
0
2
1
2
1
0
2
0
0
1
0
0
0
0
1
0
0
0
0
1
2
0
0
1
0
1
1
2
1
0
2
0
2
0
1
0
2
1
0
2
1
1
0
0
0
1
1
0
1
0
0
0
0
1
1
1
1
2
2
1
0
0
0
0
1
0
0
1
0
0
0
0
2
2
0
0
0
2
0
1
0
1
0
0
0
1
0
2
2
0
1
1
2
0
0
1
2
2
0
1
0
2
1
2
0
0
0
0
1
1
0
2
2
1
1
0
1
1
4
1
1
0
0
1
2
2
0
1
0
1
1
0
1
1
1
0
1
0
0
2
0
1
1
0
1
0
0
1
0
0
2
1
0
1
0
0
2
0
0
2
1
0
1
0
4
2
2
2
2
2
0
0
0
0
0
0
2
0
1
1
0
2
3
0
0
2
1
2
2
0
2
2
0
1
1
0
0
2
0
2
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
1
0
0
2
1
2
0
0
0
1
0
0
1
1
1
0
1
0
1
0
0
1
1
1
0
2
1
0
0
1
2
0
0
3
0
0
1
0
1
1
3
1
1
0
0
0
0
2
1
0
0
0
0
0
1
0
1
2
1
1
2
1
1
0
0
0
0
1
0
0
0
0
0
0
2
2
1
0
1
1
1
0
0
0
0
1
1
2
0
2
0
2
1
1
2
1
1
2
2
0
0
1
0
1
0
1
2
0
1
2
3
0
0
0
0
1
2
0
0
2
0
0
1
0
0
0
0
1
1
0
1
0
0
0
1
0
1
0
1
1
1
2
1
0
1
1
1
0
0
1
1
1
0
2
2
0
2
2
0
0
0
1
0
0
0
1
1
2
0
0
1
1
0
0
0
2
2
2
0
0
0
0
1
0
2
0
3
1
2
1
1
0
0
0
1
1
2
0
0
1
0
1
0
0
2
1
0
1
0
1
1
0
0
1
2
1
2
0
1
0
0
1
0
0
0
1
1
0
2
0
0
2
1
1
0
2
0
0
0
1
0
1
2
0
0
0
0
0
1
2
2
1
1
0
0
0
0
1
2
0
2
1
0
1
1
0
1
1
0
0
2
0
0
1
0
0
1
0
1
0
0
2
2
0
2
1
0
0
0
1
0
0
1
0
0
2
0
1
0
0
1
0
0
1
0
2
0
1
1
0
1
1
0
1
0
2
0
1
0
0
1
0
1
0
0
2
1
0
1
0
0
0
1
0
0
0
0
0
0
0
2
2
1
1
0
1
2
0
0
2
2
0
1
0
0
0
1
1
2
0
2
0
0
1
0
0
1
0
1
0
0
2
0
0
2
1
1
1
0
1
0
0
0
0
2
1
1
0
0
0
1
2
3
1
2
0
1
2
0
0
1
1
0
2
0
1
0
1
1
2
0
1
2
0
0
1
0
0
2
0
1
0
1
0
2
1
0
0
2
0
0
0
1
2
2
0
0
2
0
0
0
0
1
0
1
0
1
0
0
0
2
1
2
0
2
0
1
1
0
0
0
0
1
1
1
1
1
0
0
3
0
1
2
0
1
0
1
0
1
0
0
0
2
0
0
1
2
1
1
1
0
2
1
2
0
0
2
2
0
0
0
0
1
1
1
0
1
0
0
0
1
1
0
0
0
0
0
1
0
1
2
0
0
2
2
1
0
0
1
2
0
1
1
2
0
0
2
0
1
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
1
3
1
0
0
1
1
1
2
0
0
0
0
0
0
2
1
1
2
1
0
0
0
0
0
2
2
1
1
0
1
0
2
1
2
0
2
1
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
1
0
2
1
0
0
0
2
1
2
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
2
0
2
1
2
2
1
2
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
1
1
1
2
1
0
0
0
0
0
1
2
0
1
0
0
1
2
1
1
1
0
0
0
1
1
0
1
0
1
1
0
0
2
1
1
0
0
1
0
0
1
0
1
0
0
1
0
0
1
0
2
1
2
0
0
0
1
1
1
2
0
0
0
0
0
0
0
1
0
2
0
1
0
2
0
1
0
0
1
2
1
0
1
0
1
1
1
1
0
1
1
2
1
0
0
0
0
0
1
0
0
0
0
2
1
1
0
2
2
0
1
2
2
0
2
3
2
2
0
0
0
0
0
0
1
0
1
1
0
0
0
2
0
1
0
1
0
0
1
2
1
0
0
0
1
0
1
1
1
5
0
0
1
0
0
2
0
1
0
1
0
2
1
0
1
0
1
1
1
2
2
1
0
2
0
0
0
0
1
1
0
1
0
1
1
1
2
1
1
0
0
0
1
0
1
0
1
0
0
3
2
0
1
3
2
0
0
1
1
0
0
2
1
0
2
1
1
2
1
2
0
1
0
0
0
1
0
1
1
3
1
0
1
1
2
0
0
0
0
2
2
1
0
1
2
0
0
0
0
0
1
0
1
0
0
1
0
0
1
1
0
0
1
0
1
0
1
1
0
1
0
1
0
2
0
0
1
2
2
0
2
0
0
2
2
2
0
1
1
1
1
1
1
0
1
1
0
1
0
1
2
2
1
0
1
1
0
1
0
1
1
0
0
1
2
0
0
1
1
1
1
0
2
0
2
1
1
1
1
0
0
1
0
0
1
2
2
2
2
2
0
0
0
2
1
0
2
2
1
0
0
2
0
0
1
2
1
0
1
0
1
0
1
0
1
1
0
1
0
0
0
2
3
2
2
0
0
1
1
0
1
1
0
0
2
0
2
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
1
0
2
1
0
0
1
2
1
0
0
0
1
0
0
2
0
0
0
1
0
2
0
1
1
2
0
0
1
1
1
1
0
0
0
1
0
2
0
5
0
0
0
0
1
1
0
0
2
0
0
6
1
2
2
1
0
0
0
0
0
1
0
1
0
0
1
1
2
2
2
2
0
0
0
3
2
0
1
1
0
1
0
0
0
0
1
1
0
1
1
2
1
2
0
1
0
0
1
0
1
0
0
1
4
0
1
0
1
1
1
1
1
1
0
2
1
2
1
0
0
0
0
1
0
1
1
1
0
0
0
1
0
1
0
2
0
1
2
2
1
0
0
1
0
0
1
2
0
1
2
1
0
2
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
2
2
0
0
2
1
1
1
0
2
1
2
2
2
0
2
2
0
2
2
2
1
0
1
0
4
2
1
1
1
1
1
2
0
1
2
1
2
0
0
1
1
0
1
0
1
1
0
0
2
0
0
0
0
1
0
1
1
0
0
1
0
0
1
1
0
2
0
0
2
2
0
1
0
0
0
2
0
1
0
1
1
0
0
0
0
0
2
1
0
0
1
0
0
0
1
1
1
2
0
0
0
0
1
0
1
0
0
2
1
0
2
0
0
1
0
1
0
2
0
1
1
0
1
2
1
0
2
2
0
2
1
1
0
0
0
1
2
0
1
0
2
3
1
0
0
0
0
1
0
0
0
0
0
2
0
1
1
0
2
0
1
0
1
0
0
0
2
0
1
2
0
0
0
0
0
0
1
0
0
0
0
1
2
0
2
1
0
1
2
1
2
1
0
1
1
3
1
0
0
1
2
2
2
0
0
1
1
1
2
0
0
0
0
1
1
2
0
2
1
1
0
1
0
0
0
1
2
2
0
0
2
1
1
3
0
0
0
1
1
0
0
1
0
2
2
1
1
2
1
0
1
0
0
0
0
2
0
1
0
0
1
1
2
1
2
0
1
0
0
0
1
2
2
2
0
1
0
0
3
1
1
0
2
2
0
1
1
0
2
0
0
2
0
0
2
0
2
1
1
2
2
0
0
0
1
2
0
0
1
0
0
2
2
1
0
0
2
0
2
1
0
0
2
0
2
1
0
1
2
1
1
1
0
1
1
0
2
0
1
1
2
0
0
0
1
2
1
1
1
0
0
0
0
0
0
0
0
0
0
1
2
1
0
1
0
1
1
0
1
2
0
2
1
0
0
2
1
0
3
0
1
0
0
1
1
2
0
0
3
0
1
1
0
0
2
2
1
2
2
0
0
0
0
0
0
1
1
0
0
0
0
1
0
2
0
0
1
2
0
2
1
2
2
2
0
0
2
2
1
1
1
1
0
1
1
2
0
1
1
0
0
1
0
0
0
0
1
0
2
2
0
2
2
0
2
0
0
2
1
0
1
2
0
0
0
0
0
0
1
0
1
2
0
0
0
1
2
0
1
1
2
1
1
1
0
0
0
0
0
0
0
1
2
0
0
2
2
0
1
1
0
0
0
3
0
0
0
0
2
2
0
0
1
1
0
0
1
2
2
2
2
1
1
0
0
1
2
0
0
0
3
1
0
2
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
1
1
0
0
0
3
1
1
0
1
0
0
3
0
1
2
3
4
1
1
0
0
0
0
0
0
2
0
1
1
0
1
1
0
0
1
1
0
2
1
1
1
1
0
0
1
1
0
0
0
0
0
1
2
1
0
0
1
0
2
1
0
0
0
2
1
0
1
2
0
0
0
0
1
1
0
2
0
1
2
2
0
1
2
0
0
0
2
2
0
1
1
0
0
2
2
0
2
0
0
0
1
3
0
0
2
0
2
0
2
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
1
0
1
0
1
1
1
0
2
4
1
2
2
0
1
0
2
1
1
2
0
0
2
0
0
2
1
2
0
0
0
2
1
2
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
2
0
2
2
2
2
0
1
0
1
0
0
0
1
0
0
0
0
1
1
0
1
0
1
2
0
0
1
1
2
1
1
0
3
5
2
0
1
1
1
1
1
0
0
0
0
2
1
0
0
2
0
1
1
1
0
0
0
0
2
0
0
2
1
0
2
1
0
0
0
0
0
0
0
1
2
1
1
1
1
0
1
1
0
2
1
2
0
2
0
0
0
0
1
1
2
0
1
2
2
2
1
0
0
0
1
0
0
1
0
1
0
0
0
0
1
1
0
1
1
0
0
0
1
2
1
2
0
1
0
0
0
1
1
1
0
0
0
0
0
0
2
0
0
1
0
1
1
2
0
0
2
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
1
0
3
1
2
1
1
1
0
0
0
1
2
2
1
1
0
2
0
1
1
1
0
1
0
0
0
0
2
1
0
2
2
0
0
1
0
0
1
0
1
0
0
2
2
0
0
2
2
1
0
0
1
0
1
0
0
0
0
1
0
1
1
0
1
0
0
2
0
0
0
0
0
2
2
0
1
0
1
2
2
1
0
0
0
2
0
1
2
0
2
2
2
1
0
0
2
0
2
0
2
1
1
1
0
2
0
1
2
0
2
2
0
0
0
0
2
1
1
0
1
0
0
0
0
2
0
1
1
2
1
2
1
1
2
2
1
1
0
2
3
2
1
1
0
0
0
0
0
0
2
2
0
0
0
1
1
0
0
1
0
0
0
0
0
0
2
0
2
2
0
2
0
1
0
2
1
1
0
0
1
0
0
1
1
0
1
0
0
2
2
0
0
1
0
1
0
1
0
4
2
0
2
0
3
2
1
0
0
1
0
2
0
1
0
0
2
2
1
1
0
0
2
0
1
0
0
1
0
1
0
1
0
0
0
0
2
0
3
1
0
1
0
0
0
0
0
1
1
0
2
1
0
1
1
0
2
1
0
0
0
2
2
0
0
0
0
2
1
2
0
0
2
0
0
2
1
0
0
0
0
0
0
1
2
4
1
0
2
1
0
1
0
1
0
1
0
0
0
0
1
2
1
1
0
0
1
0
0
0
1
1
0
0
0
0
1
2
0
0
2
2
2
0
1
1
1
1
2
0
2
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
2
0
0
0
1
1
2
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
1
1
1
0
0
1
1
0
0
0
0
2
2
0
1
2
1
1
0
1
2
1
1
1
1
0
0
0
0
1
2
2
0
0
2
0
0
0
0
0
0
1
0
2
2
1
1
0
1
2
0
1
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
1
1
0
2
2
1
1
0
2
0
0
1
0
3
1
1
1
1
0
1
0
2
0
1
1
2
0
0
2
1
0
1
1
0
0
1
1
1
0
0
2
0
1
0
0
1
0
0
2
0
0
1
2
1
2
0
0
0
1
1
1
2
0
0
2
1
0
0
0
1
1
5
1
1
0
2
2
0
0
1
1
0
1
1
0
0
2
0
3
1
2
0
2
0
2
0
1
1
0
0
2
2
2
0
1
1
0
2
1
1
3
0
0
1
1
2
0
1
2
1
0
1
0
0
2
2
1
1
0
0
2
0
2
0
0
0
2
2
2
1
1
0
2
1
1
2
1
0
0
0
2
1
0
0
0
2
2
0
1
0
0
0
0
1
1
0
0
0
2
2
0
1
0
1
0
0
0
1
1
2
0
1
3
0
0
0
1
1
0
2
2
0
2
0
0
0
0
1
1
0
1
1
0
0
0
1
0
1
0
0
0
0
1
0
1
1
0
1
1
0
0
2
0
0
2
0
0
1
0
1
0
1
0
1
3
0
1
2
2
2
1
1
0
0
0
1
1
0
1
0
1
0
2
0
1
1
1
0
1
0
0
1
2
1
1
2
0
1
0
0
2
0
1
1
1
0
2
1
1
2
0
0
0
2
0
0
2
2
1
0
2
2
4
1
0
0
0
0
1
1
0
3
1
0
1
0
1
1
0
0
0
0
1
1
0
2
0
1
1
0
1
0
0
1
0
1
0
0
2
1
1
0
2
1
2
0
0
0
1
1
2
1
0
0
1
0
0
1
0
1
0
1
1
2
1
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
2
1
0
1
0
0
1
1
0
1
2
2
0
0
3
0
2
2
1
0
0
0
0
0
1
0
1
1
1
0
0
0
2
2
1
0
1
2
1
0
0
1
1
0
0
1
1
0
0
0
1
0
0
0
0
1
2
1
1
0
0
1
1
2
1
0
2
0
0
3
1
0
2
1
1
0
0
2
0
1
0
2
1
0
1
0
0
2
0
1
1
0
0
0
0
1
0
2
0
0
1
0
2
0
0
2
0
1
0
0
1
1
1
0
1
0
2
0
2
2
1
2
1
1
1
1
1
1
0
0
0
2
1
1
0
0
1
0
0
0
0
0
0
1
0
1
1
2
0
1
1
0
1
0
0
1
1
0
3
2
0
0
2
0
0
1
1
1
0
0
1
1
2
1
1
1
1
0
1
1
0
1
0
0
0
1
1
0
0
1
2
0
0
0
1
0
2
1
2
0
4
0
2
0
0
1
1
2
0
1
1
0
0
2
2
1
1
2
1
0
0
0
1
2
0
0
0
1
2
0
2
0
0
1
1
2
0
0
0
0
0
0
0
0
1
0
0
1
0
2
2
0
1
2
1
1
1
2
1
3
1
1
0
2
2
1
2
0
5
0
0
0
2
2
1
0
0
0
0
0
1
2
2
1
1
2
2
0
0
1
0
2
2
0
1
0
0
0
0
2
1
0
0
2
1
1
0
2
1
0
2
2
0
0
0
0
2
0
2
0
1
1
2
0
0
0
0
1
2
1
3
0
2
2
1
1
0
0
2
0
0
0
1
1
0
2
2
0
1
0
0
2
2
0
1
2
0
2
1
2
1
1
2
1
0
4
0
2
0
0
1
0
0
1
0
0
1
1
0
1
2
1
0
0
1
1
1
0
0
1
7
1
2
0
1
2
0
0
0
1
1
2
0
1
0
2
0
2
2
0
0
1
2
0
0
2
0
0
1
1
0
1
0
2
0
0
0
1
0
0
1
0
0
1
0
2
1
0
1
0
0
0
1
1
2
1
1
0
2
0
1
1
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
2
2
0
0
0
2
1
1
1
1
2
0
1
0
0
1
1
0
0
0
1
0
0
1
1
2
2
1
2
1
0
1
2
0
1
1
0
0
0
0
1
0
1
0
1
0
1
0
1
0
0
2
2
0
0
2
0
0
0
2
1
0
0
0
1
2
0
0
2
1
1
1
2
0
1
2
1
1
1
0
1
1
0
0
2
0
0
0
1
0
0
2
0
0
1
1
0
0
2
0
0
0
1
2
2
0
1
1
0
1
1
1
0
2
1
2
1
2
1
1
2
1
1
0
2
1
0
1
1
2
0
0
0
0
2
1
1
0
7
0
0
0
1
0
0
0
2
2
0
2
2
0
2
1
0
2
1
0
0
1
0
2
0
0
0
3
0
0
1
1
1
0
0
1
2
1
1
0
1
2
1
1
2
1
0
0
0
2
2
1
1
0
0
1
0
1
1
1
2
0
2
0
0
2
0
1
2
1
0
0
2
1
1
0
2
0
0
1
0
2
1
2
1
0
1
0
2
1
3
1
0
0
2
1
1
2
1
1
0
1
1
0
0
2
0
0
1
1
1
1
0
2
1
1
0
1
2
0
0
0
0
0
1
0
2
1
0
1
0
0
0
2
0
1
2
2
1
1
0
1
0
1
0
1
1
0
2
0
2
2
0
1
2
1
0
0
0
0
0
0
2
0
2
0
1
0
2
0
2
1
0
2
0
0
0
1
2
2
0
0
1
0
0
0
1
2
1
0
1
0
1
0
2
4
0
1
1
1
0
2
1
0
0
0
1
0
1
0
1
2
0
1
0
0
1
0
0
0
0
0
0
0
2
1
0
2
0
0
0
1
0
1
2
2
1
0
0
3
1
0
1
0
3
0
1
1
0
0
2
2
0
0
0
1
0
0
1
0
1
0
1
2
0
0
0
2
0
0
0
2
1
0
2
0
0
1
1
1
0
1
0
0
0
2
0
1
3
1
0
1
0
1
2
2
0
2
1
0
1
0
1
0
1
1
0
1
1
2
1
2
1
0
1
0
1
0
2
1
0
2
1
0
0
0
1
0
1
0
0
1
1
0
0
2
1
2
0
0
1
2
2
0
0
1
0
1
1
2
1
0
1
0
0
0
2
0
0
1
0
0
0
1
0
3
2
0
1
0
0
2
2
3
1
2
1
1
2
0
0
1
0
2
2
1
2
1
1
1
1
0
1
0
1
0
1
0
1
1
0
2
0
1
2
2
0
0
0
1
0
0
0
0
0
1
2
0
2
0
3
1
0
0
1
1
2
1
2
0
0
0
0
1
1
0
2
3
1
1
0
0
0
1
1
0
2
0
1
2
0
0
2
3
2
0
1
0
0
0
0
2
0
0
0
0
2
2
0
1
0
0
0
0
1
0
2
2
0
0
3
0
0
1
2
0
3
0
1
1
0
2
0
2
1
1
0
2
2
2
0
2
1
2
0
3
0
0
0
1
1
0
0
2
0
2
0
1
0
0
1
0
0
2
2
0
1
1
0
0
1
2
0
0
1
2
0
1
0
1
1
1
0
2
1
1
2
0
2
2
2
1
0
1
0
1
0
0
0
1
2
0
2
1
1
0
2
1
1
1
0
1
1
0
0
1
2
1
0
3
0
1
0
0
2
0
1
0
3
0
2
0
2
1
1
1
0
0
1
4
0
1
0
3
0
1
1
2
1
1
0
0
1
0
1
3
0
0
0
1
3
1
2
1
0
2
1
0
1
1
1
0
2
0
2
1
0
2
2
0
0
0
1
2
1
0
2
0
1
2
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
2
2
0
0
2
0
1
0
1
0
2
0
0
2
3
0
0
0
1
1
1
1
0
0
0
0
2
1
1
1
1
4
2
1
2
0
0
0
0
0
0
1
0
0
1
1
1
1
1
2
0
1
2
2
2
3
1
0
1
0
2
0
1
2
0
2
1
1
2
0
2
2
0
1
2
0
1
0
1
1
0
0
1
1
0
0
0
0
2
0
1
1
2
1
1
2
1
1
1
0
0
0
0
2
2
0
3
0
0
2
0
1
0
1
5
0
2
1
1
0
0
0
0
0
1
3
1
1
0
0
0
0
0
0
0
0
1
1
2
2
0
1
0
1
0
2
0
0
1
0
0
1
0
0
1
0
1
2
4
1
0
1
0
0
1
0
1
2
2
0
2
0
2
0
1
1
1
0
0
0
0
2
2
3
1
0
1
1
0
1
2
1
1
0
0
0
1
1
1
1
2
0
1
1
2
1
2
0
2
1
0
2
1
0
0
2
0
0
2
1
0
2
2
0
1
0
0
2
2
0
1
0
0
1
0
1
2
1
1
0
0
0
0
2
0
0
1
0
2
1
1
2
0
0
0
0
0
2
0
0
1
0
0
1
0
0
2
1
1
1
0
1
0
0
1
0
1
1
0
0
2
0
0
0
0
0
1
2
0
1
1
0
0
1
2
2
1
1
0
0
1
2
0
0
0
4
0
0
0
1
2
1
1
1
2
2
1
0
0
0
0
0
2
0
2
1
0
2
1
1
1
0
0
0
2
0
1
1
0
0
1
2
2
1
3
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
2
0
4
0
0
1
2
0
2
1
0
0
0
0
3
0
0
1
0
0
0
0
0
1
0
3
0
0
2
1
2
1
1
1
1
0
1
1
0
1
2
1
0
0
2
0
1
1
0
0
2
2
2
0
0
0
0
1
1
0
0
2
0
1
2
1
2
2
0
1
0
2
1
2
1
0
2
0
0
2
1
2
0
2
1
2
1
1
1
2
0
1
0
0
1
0
1
0
4
0
1
1
0
0
2
1
1
1
0
1
1
0
1
1
0
0
0
2
0
2
0
0
2
3
0
1
2
1
1
2
2
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
2
1
2
2
0
0
2
1
0
2
1
0
2
0
3
1
1
3
1
1
1
2
1
0
2
1
1
0
0
1
2
0
1
1
1
1
1
0
0
2
0
0
0
2
2
0
0
1
1
0
2
0
0
0
1
0
0
0
0
0
1
0
3
1
0
0
0
1
1
2
0
2
0
2
0
1
2
0
1
0
6
1
2
1
1
1
0
0
1
1
2
10
2
0
1
1
1
1
0
0
2
0
0
1
1
0
1
0
2
0
0
1
2
1
2
1
1
0
2
1
1
1
0
0
0
0
2
1
1
2
1
0
0
2
1
2
1
0
1
0
0
1
1
0
0
2
1
2
1
2
0
1
0
2
0
0
1
1
2
1
2
1
1
2
0
0
0
2
2
2
1
1
1
1
2
2
2
0
0
0
0
1
0
1
0
0
0
2
1
0
0
0
0
1
1
0
0
0
1
0
0
1
0
2
2
0
0
1
0
1
0
0
2
1
0
5
0
0
0
0
1
1
1
0
0
0
0
1
0
0
1
1
1
1
1
0
0
1
2
0
1
2
2
0
1
0
1
0
3
0
0
0
0
0
0
1
1
2
1
0
1
0
1
1
1
0
0
0
2
2
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
1
1
0
2
2
1
1
0
0
4
2
0
2
2
2
0
0
0
2
2
2
0
1
0
0
0
1
1
0
1
2
2
1
2
0
0
1
0
0
1
3
0
1
2
0
1
0
0
0
1
0
0
1
0
2
1
0
0
0
2
2
2
1
2
1
1
0
0
0
0
4
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
1
1
0
2
0
1
0
2
1
0
2
0
3
0
1
1
1
0
0
0
2
0
3
2
0
1
0
1
0
0
0
0
0
0
0
1
2
1
0
1
1
1
3
2
1
0
0
0
0
2
0
1
0
1
0
0
0
1
0
0
0
1
2
1
1
0
0
0
0
0
0
1
1
0
0
1
1
0
2
1
1
0
0
0
1
1
1
1
2
0
0
0
1
0
1
2
0
0
1
0
2
2
2
0
1
0
0
0
1
1
2
1
1
1
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
2
1
0
1
0
1
0
1
1
0
1
1
0
0
1
1
0
0
0
0
1
1
2
0
0
0
1
1
3
1
0
0
1
0
0
2
2
1
1
0
3
1
2
2
0
2
2
1
1
1
0
2
0
0
0
0
0
0
1
0
0
1
0
1
1
2
2
1
2
0
0
1
0
0
1
1
0
1
0
0
1
1
2
0
1
0
1
0
2
1
1
0
3
0
2
1
1
0
1
1
0
1
1
0
0
0
0
1
0
2
2
1
1
2
0
0
2
2
0
0
1
2
1
2
0
0
0
1
2
1
2
2
0
0
0
2
1
0
1
1
0
0
0
1
0
1
1
1
0
2
3
1
0
3
2
0
0
0
0
0
3
1
3
2
2
1
2
1
1
1
1
0
0
0
0
0
1
0
1
2
0
0
3
0
1
0
2
0
2
0
0
0
0
1
0
0
0
1
0
1
0
0
0
2
0
2
0
0
2
1
1
0
0
0
3
2
1
1
1
0
1
1
0
1
0
2
0
1
1
1
0
1
1
0
0
2
1
1
0
0
0
0
0
1
0
0
2
1
1
1
0
1
2
1
0
0
0
0
1
0
2
1
2
1
1
1
0
3
0
0
3
0
0
1
0
2
0
2
0
1
2
0
0
0
1
1
0
0
2
1
0
2
1
0
2
2
1
2
0
0
2
0
2
2
0
0
0
1
0
0
1
1
0
2
1
2
0
1
0
0
0
0
0
1
1
0
0
1
1
1
1
1
0
0
3
0
3
1
0
0
2
1
2
0
1
1
0
0
0
2
0
1
1
2
1
2
0
1
2
2
1
1
1
1
0
0
0
0
1
0
1
1
0
1
0
1
2
0
1
0
1
0
0
2
2
1
1
1
1
1
0
2
2
2
0
0
1
2
3
0
0
1
2
0
0
2
1
1
1
0
2
2
0
1
3
0
2
1
2
0
0
1
0
2
1
1
2
1
0
1
1
1
0
1
0
1
1
0
1
2
0
2
1
0
1
1
2
0
0
2
1
0
1
0
1
0
1
2
0
1
3
1
0
0
2
0
2
0
1
1
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
2
0
1
0
0
1
0
0
2
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
2
1
0
2
0
0
0
0
1
2
0
0
1
1
2
1
0
1
0
0
3
0
2
1
0
0
0
1
0
1
0
2
1
1
0
0
2
1
1
0
0
0
1
1
0
0
0
2
0
0
2
1
0
1
1
1
1
0
0
1
1
0
1
0
1
0
0
2
1
0
0
2
1
2
2
2
1
0
0
0
1
0
0
1
0
1
0
0
0
1
2
0
1
0
2
1
0
0
0
0
0
1
2
1
2
0
1
1
2
0
1
2
1
1
2
2
2
1
2
0
0
0
0
0
0
0
0
1
2
0
2
1
2
0
2
0
0
0
1
0
1
1
3
0
2
0
2
1
0
3
0
0
0
0
2
0
1
0
2
1
0
1
1
0
0
2
0
1
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
2
0
2
2
0
1
0
0
2
0
0
0
1
0
0
2
1
0
0
0
0
2
0
0
1
1
1
1
0
0
0
2
2
1
0
2
1
1
0
0
1
1
1
1
0
1
2
0
1
0
0
1
0
0
1
2
1
1
1
1
0
1
0
0
1
2
0
0
2
1
1
1
0
1
0
2
2
2
2
0
0
1
2
0
0
1
1
0
0
0
1
0
2
1
0
0
3
0
0
1
2
1
1
1
2
2
2
1
2
0
1
1
0
1
0
2
0
2
1
2
1
1
0
0
0
1
2
2
1
1
0
1
2
2
1
0
0
1
2
2
1
0
2
1
1
0
1
2
0
0
0
0
1
2
2
0
0
2
1
1
1
2
1
0
1
0
0
0
0
2
2
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
1
0
0
2
2
0
1
3
1
2
0
0
1
2
1
1
0
0
2
0
0
2
2
2
0
1
2
0
0
1
2
0
0
2
0
1
1
1
2
0
1
0
2
1
2
3
0
0
0
1
1
0
2
1
1
2
0
0
1
0
0
0
0
2
0
0
2
0
3
0
1
1
1
0
1
1
0
2
2
1
2
2
2
0
2
0
1
2
1
0
2
2
1
0
0
1
1
0
1
0
1
0
2
1
0
2
2
0
2
2
2
0
1
2
1
1
1
0
2
4
3
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
2
1
1
2
1
0
0
0
0
2
0
0
0
0
1
0
0
1
2
0
2
1
1
2
0
1
0
1
2
2
0
2
0
1
1
2
0
1
0
0
0
0
2
0
0
0
0
3
0
0
2
0
2
0
0
0
1
1
2
0
2
1
1
1
3
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
1
2
0
0
0
1
0
1
2
0
1
0
2
2
2
4
1
1
0
2
2
0
0
1
1
0
2
0
1
0
1
2
2
0
2
0
0
1
1
2
1
1
1
0
0
1
0
0
1
0
0
0
2
0
2
2
0
4
1
0
0
0
1
2
2
1
0
0
0
0
0
1
0
4
0
0
0
1
1
1
0
1
4
0
0
2
1
0
1
0
0
1
2
2
11
1
0
2
3
0
0
0
0
0
0
2
1
2
2
1
0
0
1
0
0
2
1
0
0
1
2
1
0
0
0
1
1
0
1
1
0
2
0
0
0
2
0
1
0
1
2
1
0
2
0
0
2
0
0
0
0
2
0
0
0
2
1
0
2
0
0
1
0
1
0
3
0
0
1
0
0
0
2
2
0
2
2
0
0
2
0
1
0
0
1
1
0
2
2
0
1
2
2
0
1
1
0
0
0
1
0
1
2
0
1
2
0
0
1
0
1
2
0
0
0
0
0
0
0
0
1
1
2
2
0
0
1
0
0
1
0
0
1
2
0
0
2
0
1
0
1
0
2
2
2
1
1
3
1
1
0
1
0
4
1
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
1
2
0
0
1
0
0
0
1
0
0
0
2
0
0
1
1
0
0
0
0
1
0
0
0
0
1
3
0
1
2
0
2
0
0
1
1
2
3
1
2
0
0
1
1
0
0
0
0
0
0
3
0
2
0
2
0
2
0
0
1
2
0
1
1
1
0
2
0
0
1
1
2
0
0
0
1
2
1
0
0
2
2
0
2
0
0
0
1
0
1
1
1
1
0
0
0
1
2
2
0
0
0
0
1
0
2
1
0
1
0
0
1
0
1
2
1
2
1
0
0
2
0
1
0
0
4
1
1
0
0
2
1
0
1
1
0
1
1
0
0
1
0
0
1
2
1
0
0
2
2
1
0
0
1
0
2
2
1
0
0
3
0
1
2
0
1
0
1
0
0
0
0
0
0
2
1
0
0
0
1
0
2
0
1
0
2
1
0
1
2
0
0
1
0
0
1
0
1
1
1
2
0
0
1
0
0
0
1
1
2
0
0
1
2
0
0
1
0
0
2
0
0
0
0
0
0
0
1
1
0
2
1
0
0
2
0
0
0
0
0
3
0
0
0
2
0
1
1
1
0
0
1
1
0
2
0
1
0
1
0
0
0
0
0
1
0
1
0
0
1
2
1
2
1
2
1
0
0
0
0
0
1
0
1
0
1
1
1
0
1
0
0
2
0
0
0
0
2
2
1
0
0
1
1
0
0
0
1
0
1
0
0
1
0
2
0
0
1
0
0
0
0
2
1
0
0
1
2
0
0
2
0
0
1
0
0
1
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
2
2
0
0
0
0
1
0
1
1
1
1
1
3
0
1
0
0
2
0
1
0
0
1
2
2
0
0
1
1
1
0
2
0
0
1
0
2
1
1
1
0
0
0
0
0
1
1
1
0
1
0
0
0
1
1
1
1
1
2
0
2
0
0
2
1
0
2
0
1
0
2
0
0
0
1
1
1
1
3
1
3
2
0
0
0
0
0
0
2
1
0
1
1
0
1
1
1
1
1
1
1
1
1
0
0
1
2
0
2
2
2
1
0
0
0
1
1
1
2
2
1
1
2
0
0
1
0
2
1
1
1
2
1
2
1
1
2
0
0
1
1
0
0
1
1
2
1
0
0
2
0
0
0
1
1
0
3
0
0
1
2
2
1
2
2
2
1
0
1
0
2
3
0
4
0
0
1
1
1
3
0
0
1
0
0
0
3
1
0
1
0
0
1
0
1
0
0
2
0
0
1
1
1
1
1
1
1
0
0
2
1
0
2
1
1
0
1
2
0
0
2
3
1
1
0
1
0
1
1
0
1
1
0
2
0
0
1
1
1
2
2
1
1
0
0
1
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
2
1
2
1
2
1
0
2
0
2
1
0
1
0
2
0
2
0
0
0
1
2
0
2
0
1
0
1
0
0
0
0
0
1
1
1
1
4
1
1
0
0
0
0
0
1
0
1
0
1
0
0
1
1
1
0
0
1
2
0
1
0
0
1
1
0
2
2
0
1
0
0
0
1
0
0
1
0
0
1
0
1
0
0
1
1
1
1
0
0
1
0
0
2
0
0
2
0
0
1
1
1
0
0
1
0
2
0
0
1
1
2
0
2
0
1
0
0
2
2
0
0
2
2
1
0
0
1
1
0
2
0
0
0
2
1
2
0
0
0
1
0
0
0
1
0
0
2
0
1
2
3
1
0
0
0
0
0
0
1
0
1
0
0
0
1
3
2
1
2
0
0
1
0
1
0
1
0
0
2
1
1
1
1
0
2
0
0
3
0
2
0
1
0
0
1
2
2
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
2
0
2
0
0
0
0
1
0
0
1
0
0
0
2
1
0
0
0
1
0
1
0
1
2
0
1
2
1
0
0
1
0
1
1
2
1
0
1
0
0
2
1
1
2
2
0
1
1
3
0
1
0
0
1
2
2
0
0
1
1
0
0
0
0
0
2
0
1
0
0
2
0
0
0
2
1
0
1
2
0
0
0
1
0
2
0
1
0
1
2
2
0
1
0
0
1
0
2
0
1
1
0
1
0
0
1
1
2
0
2
2
0
2
0
0
1
1
3
0
0
2
0
1
2
0
0
2
0
0
1
0
1
1
0
0
2
0
2
0
1
1
0
1
1
0
1
1
0
0
0
0
3
1
0
1
0
0
0
2
0
1
2
0
0
0
2
0
0
0
1
1
0
0
0
1
0
0
0
4
5
2
3
1
0
3
1
0
0
1
2
3
1
1
2
0
1
1
1
2
1
0
1
1
2
1
1
1
2
0
1
0
2
1
0
0
1
0
2
3
1
3
0
0
3
0
1
1
0
2
0
0
1
0
2
1
2
0
1
2
2
1
2
0
1
2
0
3
0
2
0
0
1
0
0
2
1
1
2
0
2
1
2
0
0
0
2
0
1
2
0
3
0
0
1
0
1
1
1
2
1
0
0
2
1
0
0
1
2
0
2
0
1
1
0
1
0
0
0
0
0
0
2
0
2
0
0
3
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
1
1
0
1
2
1
2
0
0
2
0
1
0
2
1
0
1
2
2
0
1
0
0
1
0
0
0
0
2
1
2
0
1
1
0
2
1
1
0
0
0
1
1
0
0
2
1
0
2
0
1
2
2
0
2
1
2
2
2
2
0
1
0
0
0
1
2
0
1
3
0
1
1
1
1
1
0
0
0
1
0
1
1
0
1
1
2
1
2
0
0
0
1
1
1
2
0
1
1
0
1
0
2
1
2
0
0
0
0
1
3
0
0
0
0
1
0
0
0
1
0
1
3
0
2
0
2
2
0
2
0
0
0
1
1
2
2
0
0
2
1
0
0
0
2
1
2
0
2
2
0
0
1
1
0
1
0
0
0
1
0
1
1
2
0
1
1
2
0
0
0
1
0
0
0
1
1
0
0
0
1
1
1
0
1
1
1
1
0
0
0
0
0
2
2
1
2
2
1
2
0
0
0
0
0
0
1
0
2
2
1
0
1
3
0
1
1
1
0
0
1
2
1
2
1
1
1
0
1
1
1
0
1
2
0
0
1
0
1
0
0
0
0
0
0
1
0
2
1
0
0
0
2
2
0
0
1
0
2
3
1
2
2
0
1
1
0
0
1
1
1
3
0
2
1
1
0
2
1
0
0
0
0
0
2
2
2
0
0
1
0
2
1
5
0
1
0
0
0
1
0
2
1
2
0
0
2
2
2
0
0
2
3
0
1
1
0
0
1
0
2
1
1
0
0
0
1
2
0
1
2
2
0
0
0
1
0
2
0
0
0
0
0
0
1
2
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
2
0
1
2
2
0
2
0
0
0
1
2
1
2
0
2
1
0
0
2
1
3
1
0
0
1
4
0
2
0
0
2
2
2
1
2
1
1
1
0
1
1
2
2
1
1
0
1
0
0
0
0
1
1
2
2
1
1
0
1
0
1
1
0
1
1
1
0
1
0
1
0
1
0
0
0
0
2
0
0
2
0
1
1
1
2
1
2
0
0
1
0
0
0
0
1
1
0
2
1
0
1
1
0
0
1
0
2
1
1
1
0
1
1
0
0
2
1
2
1
0
2
3
1
0
2
0
2
1
1
1
0
1
2
2
1
1
0
0
0
0
2
0
0
1
2
0
2
2
0
3
0
2
1
3
1
1
0
1
0
0
1
0
0
0
2
0
0
2
0
1
2
2
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
2
0
0
1
1
0
0
0
0
1
0
0
2
1
0
1
3
0
1
1
0
1
1
1
1
0
2
1
0
0
0
2
0
2
2
0
0
1
0
2
1
0
0
0
1
2
1
1
1
0
0
1
0
0
2
2
2
0
1
2
1
0
1
0
1
1
0
1
1
0
0
0
1
0
1
2
0
0
0
0
2
0
0
1
1
0
2
0
0
1
2
1
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
2
0
2
0
0
2
1
2
1
0
2
1
1
0
2
0
1
2
1
0
1
0
0
0
1
1
1
2
0
1
2
1
1
1
0
0
1
2
1
0
0
0
0
0
0
0
2
0
2
1
0
3
1
0
1
0
1
0
0
0
1
2
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
1
2
0
0
0
0
2
1
0
1
1
0
1
1
0
2
0
1
2
0
2
0
0
1
0
0
2
0
0
0
1
0
0
1
0
0
2
0
1
0
1
0
0
0
2
1
0
2
2
0
0
2
2
1
1
0
1
0
1
2
0
0
2
2
2
1
0
0
1
2
0
0
0
0
1
1
0
0
0
1
2
0
0
0
1
2
2
0
1
1
0
0
0
0
2
2
0
0
2
2
1
1
0
0
1
0
2
5
0
0
0
1
2
2
2
2
2
1
1
0
0
1
1
1
0
1
1
1
0
1
1
0
1
1
0
1
2
0
0
1
0
0
0
0
0
2
0
0
0
2
1
1
1
2
0
0
0
0
1
1
3
2
2
0
0
1
2
1
1
2
1
1
0
0
1
0
0
1
1
0
0
0
0
1
1
0
2
1
2
0
0
0
1
0
2
1
0
1
1
2
0
0
2
0
2
2
0
0
0
0
0
0
0
0
2
1
1
0
2
0
1
1
0
2
0
2
1
1
1
0
1
2
3
0
0
2
0
1
0
0
2
0
2
4
0
0
2
2
2
1
4
0
0
0
0
4
0
1
0
1
1
0
2
1
0
0
1
0
2
3
0
2
1
2
2
1
2
1
0
1
0
0
1
3
1
0
0
0
1
2
0
0
0
1
0
2
0
1
1
0
0
2
0
2
1
2
0
0
0
0
1
1
2
1
1
0
1
0
2
2
1
2
0
0
2
0
2
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
1
0
2
2
1
0
0
1
1
0
1
1
0
2
0
0
0
2
2
1
0
1
1
1
0
2
0
2
1
0
1
2
0
2
0
1
1
1
2
0
1
4
1
0
1
2
0
0
1
0
0
1
2
0
0
0
1
0
0
0
0
1
0
0
2
0
0
1
0
0
1
2
1
1
0
2
0
0
0
0
0
1
0
1
3
1
0
0
0
1
1
2
0
0
0
0
0
1
2
0
2
2
2
0
1
0
0
1
2
0
3
0
3
0
1
1
1
2
1
0
0
0
1
2
0
0
0
1
0
0
0
2
2
1
2
0
2
0
2
1
0
1
0
0
3
1
1
0
1
1
2
0
1
1
0
0
0
2
0
0
1
0
0
0
0
1
0
0
2
0
0
1
0
1
0
2
0
0
0
2
1
2
2
1
1
0
1
0
0
0
0
0
2
1
1
0
1
2
2
0
1
0
1
2
2
0
1
0
0
2
1
0
0
1
2
2
1
0
1
0
0
1
4
2
0
1
1
1
1
0
0
0
1
1
1
0
0
0
2
0
0
1
0
0
0
0
1
1
2
0
2
1
0
0
2
2
2
1
0
0
1
2
0
1
0
1
2
0
2
0
1
0
2
0
2
1
0
1
1
0
2
0
1
0
2
0
1
1
0
0
0
1
0
1
2
1
0
1
2
0
1
0
0
0
2
0
0
0
0
1
1
1
1
0
1
1
0
3
1
2
1
0
0
1
0
1
1
0
0
1
2
0
0
2
1
0
0
0
0
0
1
0
1
5
0
2
0
2
2
2
2
2
1
1
1
0
3
2
0
1
1
1
1
2
2
0
1
1
1
2
1
2
1
0
1
1
2
0
1
1
1
1
0
3
1
0
1
2
2
1
0
0
1
2
0
0
2
2
1
1
0
2
0
3
1
3
1
0
1
0
1
0
0
1
0
2
2
0
0
2
0
1
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
2
1
1
0
1
2
0
0
1
0
0
2
0
1
0
0
2
2
1
2
1
0
0
2
1
0
0
3
0
0
0
1
0
0
2
0
2
0
0
1
0
1
2
0
1
1
0
0
1
0
0
0
0
2
0
2
1
2
1
1
0
0
1
1
0
0
2
1
1
1
0
0
2
2
1
0
0
0
1
0
1
0
1
2
0
0
0
2
0
1
1
2
2
0
0
0
0
0
2
0
1
1
0
0
1
0
3
0
0
1
0
0
2
0
2
1
1
1
0
0
1
0
1
0
0
1
0
0
2
1
0
1
0
1
2
1
1
0
0
2
2
0
0
2
1
0
0
0
2
0
2
0
0
2
2
1
0
1
0
2
0
1
0
1
0
1
2
0
0
0
0
0
2
1
2
1
0
0
2
1
0
1
0
1
2
0
1
0
1
1
1
1
0
2
0
1
2
0
2
2
1
0
2
0
2
1
0
0
2
1
0
1
2
1
2
0
0
0
0
1
1
0
0
1
1
1
2
0
1
1
1
2
2
1
0
0
1
1
1
0
1
0
1
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
3
2
1
0
0
1
0
2
0
2
0
0
0
0
1
1
0
0
1
0
2
0
1
1
2
0
0
1
0
0
0
0
2
0
1
2
0
2
0
0
1
0
0
0
1
1
1
0
0
2
2
0
0
1
0
2
1
0
2
0
0
1
1
0
1
1
0
1
1
1
0
2
1
0
1
0
3
0
0
1
3
1
0
1
2
1
1
1
0
0
1
0
0
2
1
0
2
1
1
1
2
1
1
2
1
1
0
2
2
0
3
0
0
2
1
1
2
1
0
0
0
2
1
0
1
0
1
1
1
0
0
3
1
1
0
1
0
1
0
0
0
0
0
1
0
2
0
1
0
2
1
2
1
1
2
0
1
0
2
2
0
0
1
0
0
1
1
0
0
2
2
0
0
0
0
1
1
1
1
1
1
0
0
1
2
0
1
1
1
1
0
0
2
2
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
1
2
0
2
6
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
2
1
2
1
0
1
0
0
0
0
1
1
0
1
0
0
1
0
1
2
1
1
0
1
1
1
0
1
0
1
2
0
2
0
0
0
0
1
3
1
0
1
0
2
1
1
1
0
1
0
0
0
0
0
1
0
1
2
0
2
0
2
0
0
0
1
0
0
2
0
2
2
1
6
0
0
1
2
2
1
0
0
1
1
0
0
0
1
1
0
0
0
1
2
2
0
2
1
0
2
0
1
2
0
0
2
0
1
0
1
0
0
0
0
1
0
0
1
2
0
1
0
2
1
0
1
0
2
0
1
1
1
1
0
0
1
0
1
2
0
2
1
0
1
1
1
1
1
1
1
0
1
1
0
2
1
2
0
2
1
1
0
1
1
0
1
1
1
0
1
1
0
0
1
0
0
0
2
0
1
0
1
0
1
0
1
0
0
0
1
1
0
0
2
1
2
1
1
0
0
1
1
2
2
1
1
1
0
0
0
0
0
0
1
1
0
1
2
0
2
0
2
0
0
1
2
0
0
1
1
2
2
0
0
1
1
0
0
0
0
1
0
2
0
2
1
0
2
1
2
1
0
0
0
0
1
1
0
2
0
0
1
1
0
1
2
0
1
1
1
0
0
1
0
0
1
0
0
1
1
0
1
0
0
1
1
1
2
1
0
2
0
0
0
2
0
1
0
0
1
0
2
0
0
2
0
0
1
1
1
0
2
2
1
1
1
0
0
0
3
1
2
1
1
2
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
2
0
0
1
1
1
0
0
0
1
0
0
1
0
2
1
0
2
0
0
2
1
2
2
1
0
0
0
0
0
0
0
1
2
3
0
1
1
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
1
1
1
2
0
0
2
0
0
0
0
0
1
0
0
2
0
1
0
1
0
0
2
1
1
0
2
0
2
0
0
1
0
0
0
0
0
2
0
0
2
2
0
2
1
1
1
2
0
1
0
0
0
0
1
2
1
0
0
1
2
0
0
1
2
0
2
2
0
2
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
1
1
1
0
0
1
1
0
0
2
3
0
0
0
0
0
1
0
0
0
0
2
2
0
4
0
0
1
0
1
0
0
2
3
0
0
0
2
0
0
0
1
0
0
2
0
0
2
0
3
0
0
0
1
1
1
1
1
0
1
1
1
1
3
0
2
0
1
0
2
2
1
0
1
0
0
2
0
2
0
2
1
1
2
1
0
2
2
0
0
1
0
2
0
0
0
0
2
2
2
0
0
1
1
1
1
0
2
2
0
0
1
0
2
0
0
1
2
1
0
3
2
1
4
0
0
1
1
0
0
0
0
1
0
0
0
2
0
1
1
1
2
0
0
0
2
2
0
2
2
2
2
1
2
0
1
1
0
0
0
0
0
0
2
2
0
1
0
1
1
0
0
1
1
2
0
0
1
1
0
0
2
0
0
0
1
1
1
2
1
2
0
1
1
0
0
1
1
2
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
2
2
1
2
0
1
2
2
3
0
0
1
0
2
1
1
0
2
0
1
1
2
2
0
0
2
1
0
0
0
1
2
0
0
1
0
0
0
0
2
1
1
0
1
0
1
0
2
0
1
1
0
2
2
1
0
0
2
2
0
0
1
0
0
0
2
1
0
0
1
1
0
2
4
0
2
0
1
1
1
3
0
1
2
0
0
1
0
1
0
2
0
2
1
2
0
2
2
2
1
2
0
0
1
0
2
1
2
0
2
1
1
2
0
0
0
2
0
0
1
1
2
2
1
0
1
0
2
2
0
1
1
0
0
0
1
1
1
0
3
3
0
1
1
0
0
0
1
0
0
0
2
0
2
1
3
2
0
2
4
0
1
0
0
1
0
0
2
1
0
0
0
1
0
0
1
0
1
2
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
1
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
2
2
2
1
0
0
0
2
2
0
2
1
0
2
0
0
2
1
0
0
2
1
2
0
0
2
1
0
2
0
0
1
1
2
0
3
1
2
1
0
1
0
1
0
2
1
0
1
1
1
1
0
2
1
0
2
2
0
1
1
1
0
2
2
0
2
2
0
2
1
2
2
1
1
1
2
1
2
1
1
0
1
0
2
0
2
0
2
0
0
1
1
0
0
2
0
0
0
0
0
1
2
0
2
1
1
0
3
1
0
0
1
2
0
0
1
0
2
2
2
0
2
2
2
1
1
1
1
5
0
1
1
2
1
0
1
1
2
0
0
0
0
0
0
2
0
0
0
0
0
1
1
1
1
1
0
2
2
1
1
0
0
1
2
2
0
2
1
2
0
0
1
2
1
0
0
0
0
1
0
1
2
0
0
0
2
1
0
1
1
2
2
1
1
0
0
0
0
2
0
2
1
1
1
0
0
0
1
2
1
0
0
1
0
1
0
1
0
2
2
1
4
0
0
1
1
1
3
1
0
1
1
0
1
1
0
0
0
1
0
0
1
0
1
0
1
3
2
0
0
1
3
0
2
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
1
1
0
0
2
0
0
1
0
2
0
1
0
0
0
2
0
0
0
2
0
2
1
0
0
2
2
0
0
2
0
2
2
2
1
0
0
1
1
0
1
2
2
0
1
0
0
0
3
0
1
0
0
0
0
0
0
2
0
0
2
1
0
0
0
1
0
2
1
1
0
2
2
2
0
1
0
1
1
0
0
0
0
0
2
0
0
2
0
2
0
0
1
1
1
2
0
2
0
1
0
0
1
0
1
1
0
2
0
0
0
1
0
0
1
0
1
0
3
1
1
0
0
2
0
2
0
0
1
1
1
0
2
2
0
0
1
2
1
0
1
0
0
0
0
2
1
1
2
2
1
2
0
3
1
0
2
1
0
0
2
0
0
1
2
1
0
2
1
0
2
1
0
0
0
0
0
3
2
1
1
1
2
0
1
0
1
1
0
0
0
0
2
1
5
1
0
0
1
1
1
2
0
0
0
1
3
0
7
0
0
1
2
1
0
0
2
1
0
2
0
1
1
1
0
0
0
2
0
1
0
1
1
3
0
2
0
2
1
0
1
0
2
0
2
2
1
1
2
1
0
0
0
0
0
0
1
1
1
2
2
1
2
2
0
1
0
0
2
0
0
0
0
0
1
1
1
1
0
0
0
1
1
0
0
0
0
2
1
0
0
0
0
1
1
2
1
0
0
0
2
1
1
2
2
1
0
2
0
2
1
2
1
0
0
0
2
2
2
1
0
0
1
1
0
1
0
1
0
0
1
0
0
2
0
0
0
0
1
0
2
2
1
0
2
3
1
0
0
0
1
1
1
1
0
0
0
0
1
0
2
0
0
1
1
0
0
2
1
1
0
2
1
1
0
0
2
1
0
0
0
0
2
0
2
0
1
1
0
1
2
0
0
0
1
0
1
1
0
1
0
0
0
3
0
1
1
2
0
0
0
1
0
0
2
2
1
0
0
1
1
0
0
1
2
0
1
1
0
0
1
0
0
0
1
0
0
0
1
2
2
0
2
0
0
0
0
0
0
1
3
0
1
2
0
1
2
2
0
0
0
1
0
1
0
0
2
2
0
2
3
0
1
0
0
0
0
0
1
2
1
0
2
0
2
1
1
0
1
1
2
0
1
2
0
1
1
0
1
0
0
1
0
0
0
0
1
1
2
0
2
2
1
1
1
1
2
2
0
1
0
0
0
1
2
1
1
0
1
2
2
2
1
0
1
0
0
1
2
1
1
0
0
0
0
2
0
1
0
0
2
2
1
0
0
1
2
2
1
2
1
0
0
0
0
2
1
0
1
0
2
2
2
0
0
0
1
1
1
2
0
0
2
0
0
0
0
1
1
2
1
1
1
0
0
1
2
1
0
1
2
0
0
0
2
0
0
1
1
2
1
2
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
1
2
2
1
1
0
0
0
0
0
1
0
3
1
1
1
0
1
1
1
1
0
1
2
1
0
3
0
0
1
2
1
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
1
0
2
0
2
1
1
0
1
0
0
0
1
1
0
0
2
2
0
1
2
1
0
0
1
2
1
1
0
0
1
1
2
0
0
0
0
2
1
2
0
1
0
0
0
1
0
1
0
1
1
2
2
0
1
1
1
2
2
0
0
0
1
1
3
0
2
0
2
2
2
1
1
0
2
1
1
0
0
0
1
1
0
0
2
0
0
0
1
0
0
0
0
1
1
0
1
2
1
0
1
0
1
0
3
2
0
2
0
0
0
0
0
2
1
1
1
0
0
1
1
1
2
0
1
2
0
0
1
0
0
0
2
2
1
2
1
0
0
2
0
0
3
0
0
0
0
1
0
0
0
0
1
2
0
3
1
0
0
1
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
2
1
0
2
0
0
0
0
2
0
0
0
0
3
0
1
0
1
1
0
0
0
0
0
2
0
1
0
1
0
2
0
2
0
2
1
1
0
0
0
1
0
1
0
0
0
0
0
1
2
1
0
1
0
2
2
0
0
0
1
0
0
1
0
2
0
0
0
0
2
2
2
0
0
0
1
0
1
0
1
2
0
1
1
1
0
2
1
0
0
0
1
2
0
1
0
0
0
1
0
0
2
0
0
2
1
0
0
0
1
0
0
0
0
1
0
4
0
1
0
0
0
2
1
1
0
1
0
1
2
1
1
1
0
0
1
0
0
0
0
1
0
1
1
2
0
0
0
0
1
0
2
1
0
0
0
1
1
0
0
1
1
0
2
1
0
0
1
1
1
2
0
0
0
2
0
1
2
0
0
2
1
2
0
0
0
2
2
0
0
0
0
0
0
0
1
1
1
1
1
0
0
0
0
2
0
0
0
0
0
7
1
0
2
0
1
0
1
0
2
0
0
1
0
1
1
1
1
0
1
0
0
0
1
1
1
0
0
0
0
1
0
0
2
2
0
0
0
1
2
2
1
0
1
0
0
2
2
0
0
0
0
1
1
2
3
0
1
0
1
1
0
0
0
0
0
1
0
0
0
2
1
0
2
0
1
2
0
0
1
1
0
1
1
0
0
0
0
0
0
1
1
2
1
1
1
2
0
3
0
0
2
0
2
2
0
0
0
1
0
2
0
2
2
1
2
0
0
1
0
0
3
2
1
0
0
1
1
0
1
1
1
1
0
0
0
0
0
1
1
0
2
1
0
0
0
1
1
0
1
0
2
1
1
1
1
1
0
1
1
1
2
1
1
2
0
2
0
0
1
0
0
0
0
1
2
1
1
0
0
1
1
0
0
0
1
0
2
2
1
2
0
1
1
0
2
0
0
1
0
0
1
1
2
1
0
1
1
1
0
0
2
3
2
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
1
0
1
2
0
0
0
0
1
1
2
0
1
1
1
0
2
0
0
0
0
0
2
1
1
2
1
2
2
1
3
0
0
1
0
1
0
1
0
2
0
1
2
0
0
0
1
1
1
0
1
0
0
1
0
0
2
0
0
0
1
2
2
2
1
1
0
1
0
3
2
1
0
1
1
0
0
0
0
0
2
0
2
0
2
0
2
1
0
2
0
0
1
1
2
1
2
0
0
0
2
0
2
1
0
0
0
0
0
1
1
0
0
0
2
0
0
0
1
1
1
0
0
0
2
1
1
1
0
0
0
1
0
1
2
1
2
2
2
1
1
0
0
1
1
0
0
2
2
0
0
1
0
1
0
1
1
0
1
1
0
1
0
0
1
1
1
0
1
0
0
2
0
2
2
0
0
0
2
3
0
1
0
2
1
2
0
2
0
0
0
0
0
2
1
2
1
0
0
3
1
1
0
1
0
2
2
1
0
0
1
2
0
1
1
0
1
0
2
1
0
0
0
1
0
0
2
1
1
1
0
0
1
1
2
1
2
0
2
1
1
1
2
0
2
0
1
0
1
1
1
1
0
1
0
0
0
2
0
0
2
0
2
2
2
0
1
2
4
1
0
2
0
1
2
1
0
0
0
0
2
0
1
2
2
2
2
1
0
1
0
0
1
2
1
1
0
1
0
0
0
1
2
1
2
2
2
1
0
1
0
0
1
4
1
0
0
2
1
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
2
2
1
0
0
0
0
0
1
2
0
0
1
0
1
0
1
0
1
1
0
1
0
0
1
2
2
0
2
1
0
1
0
0
1
1
0
0
1
0
1
1
0
1
1
1
0
0
2
2
0
0
1
1
0
2
0
0
0
2
0
1
0
0
0
2
0
0
0
2
0
0
0
1
0
2
1
2
2
0
2
0
2
1
1
0
2
0
0
0
0
2
0
2
0
0
0
0
1
1
0
0
1
1
1
0
0
0
1
1
1
0
0
1
0
2
1
0
0
0
1
1
0
0
0
0
0
2
0
2
0
1
0
1
2
1
0
0
0
0
2
0
2
1
2
1
0
1
0
2
0
0
2
2
0
2
1
0
0
3
2
1
1
1
1
1
2
1
1
0
0
0
2
0
1
2
0
0
2
2
2
0
2
1
1
0
0
0
1
0
0
0
0
1
0
0
0
1
2
2
0
0
1
0
0
2
0
1
1
0
1
0
0
1
0
0
0
0
2
0
1
0
2
1
0
1
2
0
1
1
3
0
0
1
1
3
0
0
1
0
1
1
0
2
1
0
0
0
1
1
0
0
0
2
1
1
1
0
0
2
0
1
0
1
1
0
0
0
1
0
0
2
0
2
2
1
0
1
2
2
0
0
0
0
0
0
1
2
1
1
1
2
0
0
1
1
0
1
2
1
0
1
1
2
0
0
2
0
1
0
0
1
0
0
0
1
2
0
0
0
0
0
1
1
0
4
0
0
0
1
2
2
2
2
1
1
0
1
1
2
0
1
0
1
0
1
2
1
2
1
2
1
1
0
0
0
0
2
0
0
0
0
2
0
0
0
1
1
0
1
0
0
1
1
0
2
0
0
1
2
2
2
1
1
2
1
2
2
2
2
0
0
1
2
1
0
0
1
2
1
2
0
0
0
0
0
0
2
0
2
0
1
1
0
0
0
0
1
2
1
0
2
0
1
1
1
0
0
1
0
1
1
1
0
0
0
0
0
0
1
0
3
2
0
1
0
1
0
0
0
2
2
1
1
0
0
0
1
1
1
1
0
2
0
0
2
0
1
0
2
0
0
0
0
0
1
2
1
0
0
2
2
1
0
1
1
2
0
0
1
1
1
1
0
0
0
0
1
1
0
0
0
0
1
0
1
1
0
3
0
2
2
0
1
1
2
1
1
0
0
0
0
1
0
1
4
1
0
0
1
1
1
2
1
0
0
0
0
2
0
0
0
0
1
0
0
1
1
0
1
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
3
0
0
0
2
1
1
0
1
0
1
0
1
1
1
0
0
2
0
0
1
0
0
1
2
1
1
1
2
1
0
1
0
0
1
1
1
1
0
0
1
0
1
3
1
0
2
2
2
2
1
0
0
0
1
2
0
0
0
2
0
1
0
0
0
0
1
0
0
0
2
1
2
0
1
0
2
0
0
1
0
2
0
0
1
3
0
1
2
3
2
0
0
1
0
0
1
0
0
1
1
0
1
2
0
0
1
1
2
0
2
0
2
2
0
0
1
1
0
1
0
1
2
0
0
1
0
2
0
2
1
0
0
1
1
0
0
1
0
1
0
1
1
1
1
2
0
0
0
2
0
1
0
2
0
0
1
1
0
3
0
2
0
2
0
1
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
1
2
0
0
2
2
2
1
0
0
2
2
2
0
0
0
1
0
0
2
0
0
1
0
0
2
2
2
1
0
0
0
0
0
0
2
3
0
1
0
1
0
0
0
3
1
0
0
0
0
1
2
1
2
0
2
1
0
3
1
0
1
0
1
1
0
0
0
1
1
0
0
0
0
1
0
2
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
3
2
1
1
0
1
1
2
2
2
1
0
0
1
1
1
0
0
0
0
1
0
0
1
1
0
0
1
2
1
2
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
1
1
0
0
1
1
3
0
0
0
0
1
0
0
1
2
0
1
2
0
0
0
0
0
0
2
2
0
2
0
0
0
0
1
1
0
1
0
0
1
0
1
0
0
1
0
0
1
0
1
2
2
2
2
0
0
0
0
2
1
0
2
2
1
1
2
0
0
0
0
0
1
0
0
1
0
1
0
2
2
0
2
1
1
2
0
1
2
0
0
0
2
2
1
0
2
2
1
0
0
0
0
2
0
2
1
0
2
2
1
2
1
1
0
0
0
0
0
0
1
2
1
0
0
2
1
1
1
2
0
1
1
0
2
1
0
0
1
0
0
2
2
3
2
0
1
3
0
1
2
0
1
1
0
0
0
2
1
1
0
1
0
1
2
0
1
0
2
1
0
0
0
1
3
0
1
0
1
0
0
1
1
2
1
0
1
0
1
0
1
2
0
1
1
2
2
0
0
0
1
0
0
1
1
1
0
0
0
1
2
0
1
1
1
2
2
1
0
0
1
0
1
2
0
2
1
0
1
1
0
1
2
0
2
1
2
0
1
1
1
0
2
1
0
1
0
0
1
1
2
2
2
0
1
1
2
1
0
1
3
0
1
0
0
1
1
2
0
0
0
0
2
1
0
1
1
2
0
2
0
2
3
2
2
0
1
1
0
1
2
1
1
0
0
0
0
2
0
0
2
1
0
0
0
0
1
0
1
0
1
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
1
0
2
0
2
0
0
2
1
0
0
0
0
1
2
2
1
0
2
1
2
1
0
1
5
1
1
0
0
0
0
1
0
2
0
0
2
1
1
0
1
2
1
1
0
1
0
0
0
1
1
0
0
0
0
3
1
1
2
1
2
1
2
1
0
0
1
0
1
1
0
2
0
2
1
1
1
0
0
2
1
0
1
2
0
1
0
1
0
1
1
1
0
1
1
3
1
0
0
2
0
0
0
1
0
1
2
0
1
1
1
1
0
3
0
0
1
1
2
0
2
2
1
0
0
0
2
0
0
1
1
1
2
1
0
2
1
1
2
1
1
2
0
0
4
0
1
0
5
1
1
0
0
1
2
1
0
3
2
0
0
2
0
0
1
1
0
0
1
0
0
0
0
1
0
1
2
0
1
0
2
0
0
1
0
1
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
1
1
0
0
0
3
2
0
1
0
0
1
0
1
0
1
0
0
0
1
2
1
1
0
1
1
1
0
0
2
1
1
1
2
3
1
1
0
0
0
0
0
2
1
2
0
0
2
0
0
1
1
1
2
0
1
1
0
0
1
2
0
0
2
2
2
0
0
1
0
0
0
0
0
1
2
0
0
2
2
1
0
0
1
0
0
1
0
0
2
0
0
1
0
0
2
2
0
0
0
1
1
0
0
0
0
0
1
0
0
2
1
0
0
0
1
0
0
0
0
0
1
1
0
0
2
1
2
0
2
0
1
0
1
2
2
1
2
2
1
1
0
0
0
1
0
0
0
2
0
0
2
2
1
1
0
0
1
1
1
0
0
2
0
1
1
1
2
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
3
2
1
0
1
2
0
0
1
1
1
1
1
0
0
0
2
1
0
1
1
0
0
2
2
0
1
0
2
0
1
1
2
0
1
1
0
1
1
1
0
0
0
1
1
1
0
0
1
1
0
1
1
0
1
0
0
0
1
2
2
0
1
2
2
0
1
2
2
0
1
1
1
1
0
1
2
0
1
0
0
1
0
2
0
1
1
0
2
1
1
0
0
1
0
0
1
1
0
0
0
1
1
0
1
1
1
1
2
1
1
2
1
0
0
1
0
0
0
1
0
0
0
1
1
1
0
2
0
2
0
0
0
0
0
0
2
2
1
1
0
0
0
2
1
2
4
2
1
2
0
0
1
0
0
0
1
1
0
0
0
0
2
0
0
2
0
1
2
3
1
1
1
1
0
1
2
2
1
0
0
0
2
1
2
2
2
0
0
1
0
0
0
0
2
2
2
2
0
1
1
0
1
1
1
0
1
0
1
0
0
0
0
1
0
2
2
1
0
2
0
0
1
0
1
2
1
2
0
0
1
2
1
0
0
0
1
0
0
1
0
0
1
2
1
1
3
0
1
2
0
0
0
0
1
2
0
2
1
2
0
0
0
2
1
2
0
0
0
2
2
1
0
2
0
2
1
0
1
1
0
0
2
1
1
1
2
0
0
0
2
1
0
0
0
2
1
1
1
0
0
1
0
1
2
2
1
0
1
0
0
0
0
0
2
0
0
1
1
0
0
1
1
0
2
2
1
2
0
2
0
0
2
2
0
0
0
2
2
1
1
2
0
1
1
2
2
1
1
0
2
0
0
1
2
0
0
0
0
0
2
0
2
1
2
0
0
2
1
0
2
0
2
1
2
2
0
1
1
0
0
0
2
0
1
0
2
0
2
0
0
1
2
2
2
0
2
0
0
0
1
2
2
1
0
0
0
1
1
2
1
1
1
2
0
0
0
0
0
0
2
0
0
0
2
1
0
1
0
1
0
2
0
2
0
0
1
1
0
1
0
1
0
1
0
0
1
1
3
1
0
1
0
1
1
0
0
0
0
1
1
0
0
0
2
1
0
0
0
2
0
1
1
2
2
1
0
0
0
1
1
0
1
1
2
0
0
0
3
0
0
0
1
2
2
2
0
0
0
2
2
0
0
0
1
1
0
2
1
0
1
1
0
1
0
0
2
1
2
1
0
0
0
2
1
1
0
1
1
1
3
1
1
1
0
1
1
0
1
1
0
0
1
1
0
0
0
0
2
0
4
2
1
1
0
0
0
1
0
1
0
1
1
1
2
1
0
1
0
0
1
2
1
1
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
1
1
1
0
2
0
0
0
1
0
0
1
2
0
1
0
2
1
0
2
2
0
0
2
0
4
2
0
0
2
0
1
0
1
1
0
0
0
0
1
0
2
1
1
0
1
0
0
0
1
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
2
1
2
0
0
1
2
1
0
0
0
0
0
1
1
1
1
1
2
0
0
1
1
0
1
0
2
0
1
1
0
1
2
1
0
0
1
1
1
1
1
1
0
2
0
1
0
0
0
0
0
2
0
2
0
1
2
0
1
0
1
0
0
0
1
0
2
1
2
2
0
0
0
2
0
2
1
0
1
0
0
2
0
0
0
2
0
0
2
2
1
0
1
2
0
1
2
0
0
0
0
0
1
1
1
1
1
0
0
2
0
0
2
0
0
2
1
1
2
2
1
0
1
2
1
1
0
0
1
1
1
0
0
0
0
1
2
1
2
1
0
1
0
2
0
1
2
0
2
1
0
1
1
0
1
1
0
0
0
0
0
0
2
2
1
2
1
0
1
0
1
2
1
0
2
1
0
0
4
1
0
2
0
1
1
2
0
0
1
0
0
0
1
1
0
2
0
1
0
0
2
0
0
0
0
1
0
2
1
0
1
1
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
1
0
1
2
1
0
0
2
1
2
2
1
0
0
2
2
0
1
0
2
0
0
3
1
0
0
0
1
0
0
0
0
0
0
1
1
1
1
1
1
0
0
0
0
1
0
0
1
2
1
0
0
0
1
0
1
1
0
2
1
2
0
1
0
0
2
0
2
1
1
1
0
0
0
0
1
1
1
0
1
1
2
1
1
0
0
0
0
1
0
1
1
1
0
0
1
1
2
2
0
1
0
0
0
1
1
0
0
1
1
0
0
1
2
2
0
1
0
1
0
1
1
0
1
1
1
0
0
0
0
0
0
2
0
2
0
0
0
3
1
2
2
0
2
0
0
1
3
0
0
0
1
2
0
0
0
2
1
1
0
0
1
0
3
1
0
0
0
0
1
2
1
0
1
1
1
2
0
1
0
2
0
0
1
0
2
0
0
1
0
0
1
0
1
0
0
0
0
1
4
2
1
0
2
2
0
0
1
0
2
1
2
0
0
0
2
2
1
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
2
1
0
0
1
0
1
1
0
0
1
2
0
1
1
2
0
1
1
0
1
2
0
0
2
0
1
2
1
2
0
0
0
0
2
2
3
1
0
0
0
1
2
0
2
1
1
1
0
0
0
2
2
0
0
3
2
1
0
1
2
0
0
0
0
0
1
1
0
1
2
0
1
0
0
0
1
2
0
2
0
1
0
0
0
2
0
0
1
1
0
0
0
0
1
0
0
1
0
0
1
0
0
2
1
0
1
1
0
2
0
2
2
1
1
2
1
0
0
2
1
0
1
2
0
2
0
0
1
1
0
1
2
0
0
0
0
2
0
1
0
0
1
0
2
1
0
0
0
1
1
2
1
2
0
2
0
2
0
2
0
0
0
2
2
0
1
1
2
1
2
0
0
0
0
0
2
0
2
1
0
0
0
1
0
1
0
0
0
0
0
2
1
0
1
2
2
0
0
0
1
1
0
2
0
1
0
1
0
2
0
0
0
1
0
0
0
2
0
2
2
0
0
0
0
2
1
1
2
0
2
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
1
1
0
0
1
1
1
0
0
0
0
0
1
0
2
2
2
0
1
1
0
2
0
1
0
2
2
0
0
0
1
0
0
1
0
1
0
0
1
1
0
0
1
0
1
3
1
0
0
0
1
0
1
0
1
0
0
1
0
1
0
1
1
1
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
1
1
0
2
0
2
1
0
0
1
0
0
0
2
1
1
0
2
0
0
0
0
2
2
2
2
3
0
1
1
0
0
2
3
1
0
0
1
0
0
2
1
1
0
1
1
2
1
0
0
2
0
0
1
0
0
0
0
2
2
0
1
0
2
0
2
1
0
1
2
2
2
0
0
0
0
1
0
0
0
1
2
2
0
0
2
1
2
2
0
0
1
1
1
0
2
2
2
1
2
2
1
0
1
0
2
3
1
2
0
0
0
1
0
0
1
1
0
1
2
2
2
0
1
0
0
1
2
0
0
0
0
1
2
2
1
1
0
2
0
0
2
0
0
1
2
0
2
0
0
2
0
0
0
1
0
0
0
0
1
2
0
0
1
1
2
0
2
0
0
0
2
0
1
1
1
2
2
0
1
0
1
1
0
0
0
1
1
1
1
2
1
1
2
0
2
1
0
2
0
1
2
2
0
0
0
0
0
0
1
0
0
1
0
1
1
1
0
1
0
0
1
0
0
0
0
3
1
0
0
1
0
0
0
0
0
2
0
1
0
1
2
2
2
0
0
0
2
2
0
0
0
2
0
1
0
0
0
0
0
1
1
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
2
0
0
2
1
0
2
1
1
1
0
0
2
0
1
0
1
2
0
0
1
0
0
1
0
2
0
2
1
1
1
0
1
2
0
2
2
0
1
1
0
0
2
0
0
0
0
2
0
0
2
3
0
0
0
1
2
0
0
1
1
2
1
1
0
1
0
1
1
1
1
0
0
1
0
1
0
1
0
1
1
1
0
1
0
0
2
0
1
0
1
2
0
0
6
0
0
2
1
0
0
1
0
1
2
0
0
3
0
0
2
0
1
1
0
0
0
2
1
0
1
0
1
1
1
1
1
0
0
0
0
0
0
2
0
1
1
2
0
0
1
0
1
0
0
0
1
0
1
1
1
0
0
1
0
1
1
2
1
0
2
1
0
0
0
0
1
1
1
1
2
1
0
0
1
0
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
2
1
0
0
0
4
0
0
2
1
1
1
0
1
0
0
0
2
1
2
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
2
2
0
0
0
0
0
2
2
0
0
1
1
0
0
1
0
1
0
0
2
2
1
1
0
1
0
0
2
0
1
0
0
0
0
1
2
1
1
0
0
1
2
2
0
2
2
0
2
2
0
0
0
0
0
1
0
0
0
2
1
2
0
0
2
1
0
1
1
1
0
0
0
0
0
1
0
1
1
0
0
1
2
0
0
2
2
1
0
0
1
0
0
2
2
1
11
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
2
1
0
0
0
1
2
2
0
2
2
0
1
0
1
0
2
0
1
0
0
2
1
0
1
1
1
1
2
0
0
0
0
0
0
1
0
2
1
0
1
1
1
0
0
0
1
1
0
0
2
1
1
1
2
0
5
0
1
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
2
2
0
1
7
0
1
0
1
0
0
3
1
0
2
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
1
2
1
2
0
1
0
2
1
1
0
0
0
1
0
2
0
0
0
0
0
0
0
1
1
2
2
0
3
1
0
0
0
2
1
0
0
2
1
2
2
0
0
0
0
0
0
0
2
0
1
0
0
0
2
2
0
2
0
0
0
0
0
2
0
0
2
0
0
0
1
2
0
2
2
0
1
1
2
0
0
1
0
0
5
0
0
2
3
0
0
0
0
1
2
0
1
1
0
0
0
2
0
1
0
1
1
2
0
1
0
2
0
1
0
3
2
1
0
2
1
0
0
0
0
2
0
0
1
1
0
2
0
1
2
1
2
0
1
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
1
0
1
1
0
2
1
1
1
0
1
0
1
2
2
1
0
0
0
1
0
1
2
0
0
0
0
0
0
2
0
2
1
0
2
2
2
0
0
1
0
0
0
0
1
0
2
1
0
2
1
2
0
1
0
0
2
1
0
0
0
1
0
2
1
0
2
0
0
0
2
2
2
1
1
0
0
1
0
1
1
0
1
1
0
0
0
1
0
1
1
1
0
2
0
0
1
1
0
0
2
1
2
0
1
0
0
0
0
0
0
0
2
1
0
1
2
1
0
2
0
1
0
0
0
0
2
1
0
0
2
0
2
2
1
1
1
1
1
1
0
0
1
0
2
0
0
2
1
1
1
2
0
1
0
2
1
1
2
0
0
0
0
0
0
2
1
0
1
2
0
0
1
0
2
0
0
3
0
0
2
2
1
1
0
1
2
1
1
0
1
0
2
0
0
0
0
0
0
0
2
0
0
1
1
1
0
0
2
0
1
2
1
1
1
0
0
0
0
0
0
0
1
0
1
1
2
2
2
1
2
1
1
0
0
1
0
0
1
2
1
2
0
0
1
0
2
0
0
2
0
0
2
1
2
1
1
1
0
1
0
1
0
0
0
0
0
2
0
0
0
1
1
1
2
0
3
0
1
0
0
0
2
0
2
0
0
0
2
0
2
0
0
1
1
2
1
0
0
2
0
1
1
0
1
0
0
1
0
2
0
0
1
0
0
0
0
1
0
1
1
0
2
0
1
0
0
1
0
0
1
1
2
2
0
1
1
0
2
1
1
1
2
2
1
0
0
1
1
0
1
2
0
1
2
2
0
1
0
1
1
0
2
0
2
0
1
0
0
2
1
0
2
0
0
0
1
0
0
1
0
1
2
1
1
2
2
2
1
1
0
0
2
0
0
2
1
1
2
2
0
1
0
2
0
0
1
2
1
0
1
0
2
0
0
0
0
0
1
1
2
2
3
0
2
0
2
0
0
1
1
0
0
1
2
1
0
2
0
0
3
0
0
1
0
0
1
1
2
1
1
0
1
1
0
1
1
2
2
2
0
1
1
1
0
1
0
0
0
1
0
0
2
0
0
0
0
1
2
0
0
2
0
0
1
2
1
0
2
2
1
0
1
3
1
1
0
0
0
0
0
0
0
1
1
1
0
0
1
1
0
1
0
1
1
1
1
1
1
1
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
1
2
1
0
1
1
0
2
0
0
0
3
1
2
0
2
0
0
1
1
1
1
1
0
2
2
0
2
2
0
0
2
2
1
0
0
1
1
2
0
2
0
1
2
0
1
2
0
2
1
0
1
0
0
0
0
1
0
0
1
0
1
1
2
0
0
1
2
0
0
2
0
2
3
1
2
2
1
0
0
2
1
0
1
2
0
0
0
1
0
0
2
2
1
2
2
1
0
0
0
0
0
1
1
0
0
2
2
2
0
2
1
0
1
0
0
1
0
0
1
0
0
0
2
0
1
0
0
0
1
3
1
0
0
2
2
1
1
1
1
0
3
2
2
0
0
1
0
2
1
1
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
1
2
2
1
0
0
0
0
0
2
2
0
0
1
0
0
1
2
0
2
2
2
1
2
1
0
0
1
0
1
0
1
1
0
0
0
0
1
0
0
0
2
2
1
2
0
1
0
0
2
1
1
2
2
0
0
0
2
1
4
1
0
1
1
2
0
0
0
0
0
1
1
2
2
0
0
0
1
2
0
0
0
1
2
2
0
0
1
1
2
1
1
0
0
0
1
1
2
0
1
0
1
1
2
1
1
0
1
1
0
2
0
2
0
1
2
1
0
0
0
2
1
2
0
1
3
0
1
0
1
1
0
1
0
0
2
2
0
0
2
0
1
0
0
1
1
1
1
0
0
0
0
1
0
0
0
0
2
2
1
2
1
0
1
0
0
2
1
1
0
1
1
0
0
2
0
0
0
0
1
1
1
0
0
2
1
0
0
1
2
2
0
1
1
2
0
0
1
2
1
1
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
2
2
0
0
0
0
0
0
0
1
1
0
0
1
0
2
2
2
1
0
0
1
0
0
2
2
2
1
1
2
0
0
0
0
1
0
0
0
1
2
2
1
0
1
1
2
0
2
1
2
0
0
0
0
0
2
1
0
2
0
0
1
0
0
1
0
0
1
0
1
2
0
1
0
0
0
0
0
2
2
0
2
0
0
1
0
0
1
2
0
0
0
1
0
0
2
0
0
0
0
0
2
0
2
1
1
0
0
2
1
0
1
1
0
1
2
1
1
0
0
4
1
0
1
2
1
0
1
0
0
0
0
1
1
2
0
1
0
1
1
1
1
1
0
2
2
0
1
2
2
0
0
0
1
0
2
2
2
0
1
1
1
0
2
0
0
0
1
0
1
1
0
0
0
0
0
0
2
1
0
0
2
1
3
1
0
1
3
2
0
1
1
0
0
1
1
1
2
1
1
1
0
0
0
0
0
1
0
1
0
1
1
2
2
0
1
0
2
0
2
0
0
0
1
0
0
0
0
0
2
0
1
0
0
1
1
0
0
2
2
1
1
0
2
0
2
1
2
1
2
0
0
1
0
0
0
0
0
0
2
0
1
2
0
1
1
1
0
1
0
0
0
0
2
0
1
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
6
0
0
0
2
0
2
2
0
1
1
0
2
1
2
1
0
0
1
1
0
1
0
1
0
1
0
0
2
0
1
1
0
0
0
0
0
1
0
1
0
0
0
2
0
2
0
1
1
0
0
0
1
1
0
1
0
0
0
1
2
0
1
1
1
2
0
2
1
0
0
1
0
1
0
0
1
2
2
1
0
0
2
1
0
0
0
1
1
2
1
1
0
0
1
2
0
1
1
0
0
3
0
1
1
2
0
1
0
2
1
0
0
0
0
0
2
1
2
0
0
0
0
0
2
0
0
0
1
0
2
1
1
1
2
0
2
1
0
0
1
1
0
0
1
2
0
1
1
0
1
0
0
2
1
0
0
0
0
2
1
0
0
0
2
0
2
0
1
0
3
1
1
1
1
1
1
2
1
0
0
0
1
1
1
1
0
0
1
0
0
1
0
0
3
0
0
1
2
1
2
1
0
1
1
1
0
0
4
2
0
1
0
2
0
0
0
1
0
2
1
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
1
2
2
1
2
0
0
0
1
2
1
2
2
1
1
0
0
2
1
1
0
0
0
0
0
0
1
0
2
0
0
1
2
0
1
2
0
1
0
2
1
2
3
0
0
0
0
2
0
2
0
0
1
2
1
0
0
0
0
0
1
2
1
0
0
1
0
1
0
0
2
0
0
3
0
1
0
1
0
1
0
2
0
1
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
1
2
1
0
0
1
1
0
1
1
1
0
0
0
2
1
1
1
1
1
0
0
0
0
1
0
0
0
0
1
1
2
0
1
1
0
1
1
2
2
1
1
1
1
0
1
0
0
0
2
0
0
2
0
1
2
0
0
2
0
0
0
1
0
0
1
0
0
2
0
0
0
2
1
0
2
0
1
0
0
0
0
0
0
1
0
0
1
0
1
2
0
1
2
1
0
0
0
0
2
1
3
0
2
0
2
0
0
0
1
1
0
3
0
0
0
2
0
0
0
1
0
1
1
0
1
0
1
1
1
0
0
2
1
0
1
0
0
2
1
3
0
0
1
0
0
0
0
2
2
0
2
0
1
1
0
2
1
2
0
1
1
0
0
0
0
0
1
0
0
1
0
0
1
2
0
1
1
2
0
0
2
1
0
1
0
0
2
1
0
0
0
0
0
2
0
0
2
0
0
1
0
0
1
0
2
1
2
0
0
0
1
2
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
1
0
0
1
2
1
1
2
1
0
0
1
1
0
0
1
0
1
2
1
1
0
0
0
2
1
1
0
2
0
2
0
1
2
0
1
2
0
0
2
2
1
1
1
1
0
0
0
0
0
0
0
1
2
2
1
1
2
0
0
2
0
0
2
0
1
1
0
2
1
2
0
0
1
0
1
1
1
2
1
0
0
3
0
0
1
0
0
1
1
0
1
4
5
0
2
0
1
2
0
1
2
2
0
0
0
2
0
0
2
2
1
1
2
2
1
1
0
1
0
1
2
0
1
1
0
0
1
1
1
0
3
2
2
1
2
0
2
2
0
0
2
1
0
1
1
0
0
3
0
2
0
1
0
0
0
1
0
2
0
2
0
2
0
0
1
2
2
0
4
0
1
0
0
0
1
1
1
2
1
2
1
0
0
1
1
0
0
0
2
0
0
0
2
1
0
0
2
2
0
0
1
0
0
1
2
1
0
2
0
0
2
1
0
1
0
1
0
1
1
1
0
0
1
0
1
1
0
1
0
2
0
0
1
0
1
2
1
0
0
2
0
1
0
0
1
0
0
0
0
1
0
4
0
0
1
1
0
2
2
0
2
1
0
1
0
0
1
1
0
1
0
1
1
0
0
1
1
1
1
2
0
1
0
1
0
0
0
0
2
0
1
0
1
3
1
1
1
0
1
1
2
0
1
1
1
0
1
1
1
1
0
1
1
1
1
0
4
0
0
0
1
1
1
1
0
1
1
1
0
0
1
0
2
1
0
1
2
0
0
0
2
0
0
0
1
1
2
0
0
2
2
1
1
0
2
0
0
0
1
0
0
1
1
2
0
1
1
0
2
2
1
0
2
1
0
1
0
0
0
0
1
1
0
1
1
2
7
1
2
2
1
2
1
0
1
2
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
1
0
1
2
1
0
1
1
1
1
1
0
0
0
1
0
0
0
1
2
0
0
1
1
0
2
2
1
0
2
2
1
1
1
0
1
0
0
0
1
0
2
0
0
2
1
0
1
2
2
1
0
0
0
0
2
2
2
0
1
0
2
2
2
0
2
1
2
1
0
0
1
0
2
1
0
1
1
0
1
1
0
0
0
1
1
1
1
1
2
1
0
0
5
2
1
0
0
0
0
0
2
0
0
2
0
2
0
2
2
1
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
2
0
0
2
0
2
0
0
0
0
0
1
0
0
1
0
1
0
1
1
0
0
2
0
0
0
1
1
0
0
1
2
1
0
1
2
1
0
0
1
1
0
0
1
1
2
1
1
0
2
2
0
1
0
0
1
2
1
1
1
4
1
1
0
1
0
0
1
0
0
0
2
2
1
2
2
0
0
2
0
2
1
0
0
1
2
1
0
1
2
1
0
1
1
0
1
0
1
1
1
1
1
0
0
1
0
0
0
0
0
0
0
0
2
2
0
1
1
0
1
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
2
1
0
2
1
2
1
1
1
2
2
2
0
1
1
1
2
1
0
0
1
2
2
0
1
1
0
0
0
2
0
0
1
0
0
0
2
0
0
0
1
2
1
1
0
2
3
1
1
3
2
1
0
0
1
0
0
1
2
2
0
0
0
1
0
0
2
1
1
1
1
2
2
0
0
1
1
1
1
1
0
1
0
2
0
1
1
0
0
0
2
0
0
0
0
1
1
0
1
1
1
1
1
0
1
1
1
2
1
1
1
1
2
3
2
2
1
0
0
1
0
0
0
2
1
1
2
1
0
1
0
1
2
1
0
1
0
2
0
1
0
1
1
0
0
1
1
2
0
1
2
0
2
0
0
0
0
2
0
1
2
0
0
1
0
1
2
1
1
2
2
2
0
0
0
1
0
1
0
0
0
1
0
1
0
2
1
0
0
1
0
1
0
0
0
2
0
0
0
1
0
2
0
0
1
0
1
1
2
0
0
0
0
1
0
1
0
2
2
0
0
0
1
1
5
1
1
0
1
0
3
2
0
1
0
1
1
0
0
1
1
0
0
1
0
2
1
2
0
0
0
2
0
2
3
0
0
1
1
1
1
0
2
0
1
0
2
0
1
3
2
1
0
0
0
1
0
2
2
1
0
0
0
0
1
1
0
0
3
0
0
0
1
2
1
0
3
1
0
0
1
1
0
0
0
1
1
2
0
2
1
1
1
0
2
0
0
2
1
0
1
3
1
2
2
1
2
0
2
2
0
1
2
1
0
2
0
0
0
1
1
2
0
0
2
1
0
0
0
0
1
0
1
0
1
1
2
2
1
1
0
0
1
2
2
2
1
1
0
2
0
1
1
0
1
0
3
1
1
1
1
2
0
1
1
0
0
0
2
0
0
0
0
0
2
0
1
1
1
1
0
1
0
2
1
2
2
2
1
1
1
1
0
0
0
1
0
2
1
0
3
1
0
0
2
0
0
1
0
1
0
1
0
0
2
2
0
0
0
0
1
0
0
0
0
2
0
1
2
2
2
1
0
0
0
0
1
1
2
0
1
2
1
2
1
1
2
1
1
2
0
1
1
1
0
1
2
1
1
0
1
1
0
1
1
0
2
0
0
0
1
0
0
2
0
0
0
0
2
1
1
0
1
2
0
0
0
0
1
1
2
1
0
1
3
2
0
0
1
3
1
1
3
0
1
1
0
0
0
0
2
0
0
1
1
1
0
2
0
1
2
0
1
1
1
0
1
1
1
2
0
2
0
2
1
0
0
1
2
1
1
0
0
0
1
1
0
0
1
1
1
0
0
2
0
2
1
2
0
0
0
1
1
0
0
0
0
0
0
2
0
2
0
2
0
0
0
2
2
0
1
0
0
1
2
2
1
2
1
0
2
1
0
1
1
0
1
1
1
0
0
0
1
1
1
1
1
0
0
1
1
0
2
0
0
2
0
1
0
0
1
2
0
0
0
1
1
0
0
0
0
2
2
2
0
1
0
0
2
2
0
0
3
2
0
1
1
0
0
2
0
2
2
0
0
0
2
2
1
1
1
0
1
0
1
0
1
1
0
2
1
0
0
1
0
1
1
0
4
1
0
0
0
2
2
0
2
2
1
3
0
0
0
0
0
1
0
0
1
0
1
0
0
2
0
2
0
0
1
0
2
0
0
0
2
0
2
2
0
0
0
0
1
0
1
2
0
2
2
1
0
1
0
0
2
0
1
0
0
0
0
2
1
2
0
1
2
2
2
1
2
2
0
0
0
1
2
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
2
1
1
2
0
0
2
0
2
1
2
0
0
1
2
0
0
2
0
0
0
0
1
0
1
2
1
0
1
0
0
1
0
2
0
2
1
1
0
0
0
0
2
1
2
0
0
2
0
1
1
2
0
2
2
1
1
0
2
0
2
0
1
0
0
0
0
0
2
2
0
1
2
0
0
0
0
2
0
0
2
1
0
2
0
0
0
1
1
0
1
0
1
1
0
0
1
1
0
2
0
2
2
1
1
0
1
0
2
1
0
1
2
0
2
2
1
1
0
0
0
0
1
1
2
0
2
1
3
1
2
2
0
0
2
0
2
0
1
0
0
1
0
2
2
5
0
0
1
2
0
2
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
2
2
0
1
2
0
1
0
0
2
2
0
2
1
0
1
1
2
0
0
1
2
0
1
0
0
1
1
2
0
0
0
1
2
0
1
0
2
0
2
0
2
0
0
1
2
0
0
3
2
0
0
2
2
1
0
0
0
0
0
0
0
1
1
0
2
0
0
2
0
1
0
1
2
0
0
0
0
2
0
0
2
1
0
1
0
1
2
0
0
1
0
0
3
2
2
0
0
1
0
0
2
0
0
0
1
0
0
0
1
0
1
2
1
1
0
0
0
1
1
1
0
1
2
1
0
1
0
1
0
0
0
0
2
1
0
0
2
1
0
1
2
3
2
0
0
1
1
1
0
1
0
0
1
2
0
0
2
2
3
2
0
0
0
1
1
0
2
1
1
1
0
0
2
0
0
4
3
1
2
0
2
0
0
2
2
2
1
1
0
0
2
2
1
0
2
0
0
1
0
0
0
1
0
1
0
1
2
0
1
1
0
1
0
0
1
0
0
0
0
1
2
1
2
1
0
0
1
1
0
1
1
0
1
0
0
0
0
0
0
1
0
1
1
2
0
0
0
1
0
0
0
1
2
0
2
0
1
2
1
0
0
1
2
0
1
2
1
0
0
2
1
0
0
1
0
0
1
0
0
0
0
2
1
0
0
0
0
1
0
0
1
0
0
0
0
3
1
2
0
0
0
1
2
2
0
0
0
1
0
2
0
0
1
0
2
1
1
1
0
2
1
1
0
1
1
1
0
2
0
0
2
0
0
1
0
1
2
0
0
2
0
0
0
2
0
1
1
2
0
2
0
1
0
1
2
1
1
0
1
0
0
1
0
0
7
2
2
1
1
2
1
0
0
1
2
0
0
0
0
0
3
0
0
1
0
0
2
0
0
0
2
0
1
0
0
2
0
3
0
1
1
0
2
0
0
1
0
0
1
1
0
1
1
0
2
1
2
1
1
0
1
1
0
0
0
1
2
1
1
0
1
1
1
0
1
2
0
2
2
1
1
2
1
3
0
1
1
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
2
0
0
1
1
0
2
0
0
0
1
0
1
1
1
2
0
0
0
0
2
1
0
2
2
2
0
0
0
2
1
2
0
0
0
1
1
1
1
0
2
0
1
0
1
0
1
1
0
0
1
1
2
0
1
2
1
0
1
0
1
1
2
0
0
1
2
0
1
0
1
2
0
1
1
0
0
1
1
0
0
0
2
0
0
0
0
1
1
0
1
1
0
1
1
1
0
1
1
0
0
0
0
0
2
0
1
2
1
0
0
0
0
0
0
1
0
0
0
1
1
0
2
0
0
0
0
2
2
1
1
0
0
2
2
0
0
1
0
0
0
0
2
0
0
0
2
0
1
2
2
0
2
0
0
1
1
1
1
1
1
0
1
1
1
1
1
1
0
1
1
1
2
1
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
2
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
2
0
0
2
1
1
1
2
1
1
0
0
1
2
2
1
2
1
0
0
0
1
0
1
1
0
1
1
0
0
3
1
0
2
0
0
1
0
0
3
1
0
0
0
2
0
1
0
2
2
1
0
2
0
2
2
0
2
1
0
0
0
2
0
1
1
2
1
1
1
0
1
1
0
1
1
1
1
1
1
0
0
0
2
2
0
1
0
0
1
0
1
1
1
0
2
1
1
0
1
0
0
2
0
1
0
1
2
0
1
0
0
2
2
0
0
0
1
0
0
0
0
2
0
1
1
0
0
1
1
0
0
1
1
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
1
2
1
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
1
0
1
4
0
2
0
2
2
2
0
0
1
1
1
2
2
2
0
2
0
2
0
0
0
0
1
0
1
2
1
0
0
1
0
0
0
1
2
0
0
0
1
0
0
0
0
2
2
1
2
0
3
1
1
0
0
1
0
2
1
0
0
1
0
3
3
2
1
2
1
1
1
0
0
1
0
2
0
1
2
0
0
2
0
0
0
0
1
1
1
1
0
0
1
1
1
0
0
0
0
1
0
1
1
0
0
1
0
1
1
1
1
0
0
0
1
0
2
0
0
1
0
0
2
0
0
0
2
0
0
0
0
1
1
1
2
0
0
1
0
1
1
0
1
0
0
3
1
0
2
0
1
0
0
0
3
0
1
1
0
2
0
1
0
1
1
0
2
2
1
2
1
1
1
0
0
0
1
1
2
1
0
0
2
0
3
0
0
2
2
1
1
2
0
0
0
0
1
2
0
0
0
0
1
0
1
0
0
0
0
1
5
1
0
1
0
1
0
2
1
1
1
0
0
0
1
2
1
0
0
0
1
0
0
1
2
2
0
2
1
0
0
1
2
0
1
1
0
0
1
0
0
0
2
1
0
1
1
1
0
0
2
2
1
0
1
0
1
0
2
2
1
0
0
2
2
2
1
2
1
0
0
0
1
0
3
1
2
0
0
0
0
0
0
2
0
0
0
1
3
0
2
1
0
0
1
2
0
1
0
0
1
0
1
0
2
1
2
0
0
0
1
2
1
3
2
0
2
1
0
1
1
0
2
1
0
0
2
0
2
2
1
0
0
2
0
2
0
1
1
0
0
1
1
0
1
1
0
0
0
1
2
1
1
0
0
2
1
3
0
2
1
0
0
1
2
0
2
0
0
1
0
0
0
1
2
0
0
0
2
2
0
1
2
0
0
2
1
0
0
1
1
2
3
0
1
0
2
1
0
0
3
0
0
2
1
2
2
1
1
0
0
0
2
1
2
2
2
1
1
0
0
1
3
2
0
0
1
0
0
0
3
0
0
1
3
0
2
0
2
1
2
0
0
0
0
2
0
0
1
0
2
1
2
0
1
2
0
1
0
2
0
1
2
0
0
1
2
1
0
2
1
2
0
0
0
0
1
0
1
1
2
2
2
0
0
1
0
1
1
2
0
1
0
0
2
0
0
1
0
2
0
0
2
1
2
0
1
2
1
1
0
1
0
2
0
2
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
2
2
1
0
1
1
0
1
0
0
2
0
1
0
0
0
2
0
1
0
2
1
1
0
1
1
0
1
0
2
0
1
1
0
1
1
2
2
1
2
2
1
1
0
2
2
0
2
0
0
4
1
0
1
0
0
0
2
0
0
0
2
1
1
1
0
2
0
1
0
1
0
1
1
2
0
0
0
0
5
0
0
1
2
0
0
0
0
0
1
0
0
2
0
0
1
0
2
1
1
2
0
0
0
2
0
0
2
1
0
1
0
0
1
1
2
2
0
0
0
1
0
0
1
2
2
2
0
0
1
3
2
1
1
0
2
0
1
2
2
2
2
1
1
0
0
0
1
1
0
2
1
0
0
2
0
1
0
1
0
2
1
1
0
1
1
1
0
0
1
0
1
2
0
1
0
3
0
1
1
0
2
0
1
0
0
0
2
0
0
1
0
0
1
2
1
0
1
1
0
0
2
1
0
2
1
2
0
0
0
2
0
0
1
2
0
0
1
1
0
2
1
0
0
0
0
0
0
1
0
1
1
1
0
3
2
1
1
0
2
0
0
2
1
0
1
0
4
1
1
2
0
1
1
1
2
1
0
1
0
1
0
0
1
0
1
2
1
0
0
0
0
0
2
0
0
4
1
0
1
1
1
0
0
2
1
0
0
0
1
0
0
0
1
0
1
0
0
0
1
2
1
0
1
0
2
2
0
2
0
0
0
0
0
0
2
0
1
1
1
1
0
0
0
0
1
1
3
2
0
0
2
0
2
0
2
0
0
2
0
1
0
1
2
1
0
3
1
2
2
0
1
0
1
1
0
0
2
1
0
1
0
0
0
1
1
1
2
0
1
1
1
0
2
1
1
0
0
2
0
2
0
1
0
2
2
3
0
1
2
0
1
1
0
0
2
1
1
0
0
2
1
1
2
2
2
0
0
3
0
2
0
1
0
1
1
0
2
2
0
0
1
0
2
1
2
1
0
1
1
0
0
1
1
1
0
1
0
0
2
0
0
1
1
0
2
1
0
2
0
1
0
0
1
3
1
2
0
3
2
1
2
0
0
0
0
0
1
0
1
1
1
0
1
1
1
0
2
2
0
1
1
1
0
1
0
0
1
2
3
0
0
1
1
0
2
1
1
2
0
0
1
0
0
0
2
1
0
0
1
0
1
0
0
0
0
0
1
2
0
0
2
1
0
0
0
0
0
0
2
0
0
2
1
1
0
0
2
3
0
1
0
0
2
2
0
0
2
0
0
1
1
1
1
1
0
1
2
1
0
0
1
2
0
0
1
1
0
0
2
0
0
0
2
0
1
1
2
1
2
0
0
0
1
1
0
2
0
1
1
2
0
0
1
0
2
0
1
2
0
2
2
2
1
0
2
0
0
1
0
2
2
0
2
1
0
1
0
1
1
1
0
1
1
4
0
0
2
1
1
0
0
1
1
1
2
0
0
0
1
0
0
1
1
2
2
2
0
1
3
2
1
0
3
1
1
0
1
0
0
1
1
0
0
2
0
1
1
0
0
0
0
2
1
2
1
1
1
0
0
2
0
2
1
1
1
0
0
0
1
2
1
0
2
1
1
0
0
2
1
0
0
0
1
1
1
0
0
0
0
2
0
2
0
0
0
0
1
2
4
0
1
2
1
1
0
1
0
0
2
1
0
1
0
0
0
1
0
1
0
0
1
1
0
1
0
0
1
0
2
1
1
2
0
0
3
2
0
0
0
0
0
2
1
2
2
0
2
1
1
0
0
1
0
0
1
1
0
1
0
1
0
1
0
0
0
0
2
0
2
0
0
1
0
2
0
0
2
2
2
2
2
1
0
0
0
0
1
1
2
0
0
0
1
1
3
0
0
0
2
0
1
0
2
2
1
0
0
0
2
0
4
1
0
0
0
1
0
1
0
2
0
1
1
3
1
1
1
1
0
0
0
2
5
0
0
1
0
1
2
0
0
2
0
0
1
0
2
0
2
1
1
0
0
2
0
2
0
0
2
2
0
0
1
1
0
0
0
0
2
1
0
0
0
0
1
0
3
2
2
2
3
0
1
1
1
2
1
1
4
0
0
2
2
0
0
0
1
2
2
1
2
1
1
0
1
0
1
1
2
0
0
2
2
0
0
2
2
1
2
0
0
2
2
1
0
0
2
1
0
0
0
0
2
3
0
1
1
0
1
2
0
0
0
0
0
1
2
0
1
3
1
1
1
0
0
1
0
1
2
1
2
0
0
3
2
1
1
0
1
0
2
1
1
1
1
1
1
0
2
0
1
2
2
1
0
0
2
0
0
0
0
0
1
0
1
2
0
3
2
0
0
1
0
0
0
1
1
2
1
1
2
1
0
0
1
0
0
0
2
0
0
0
1
0
1
0
1
1
0
0
2
1
0
1
0
0
2
0
1
0
0
0
2
1
0
0
0
0
1
0
2
2
2
0
1
1
0
0
0
0
0
0
1
0
1
0
1
1
0
0
1
1
1
2
2
0
1
0
2
1
1
0
0
0
0
0
2
1
2
0
1
1
2
0
1
1
0
0
0
0
0
1
0
0
0
2
0
1
0
0
2
1
0
0
1
0
0
1
2
2
1
2
0
0
0
1
1
0
0
1
0
1
1
2
0
0
2
0
1
0
2
1
2
0
1
1
2
0
0
1
0
0
0
1
0
2
1
0
2
1
1
2
0
0
0
0
2
1
2
1
0
2
1
2
2
1
2
1
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
2
1
2
1
1
0
1
0
0
0
0
1
0
1
0
2
2
2
1
0
0
1
1
0
0
0
2
0
1
1
0
0
0
0
1
0
1
2
1
2
0
0
0
0
0
1
1
2
0
1
0
1
1
1
1
2
1
0
0
2
1
0
1
0
2
1
0
1
0
2
1
0
1
0
0
1
0
0
1
0
1
2
1
0
1
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
2
2
1
1
0
1
0
0
1
0
2
0
2
0
2
1
0
0
1
4
2
2
1
1
0
1
0
2
0
2
0
0
1
0
1
6
2
0
1
1
0
0
0
0
1
1
1
2
2
0
0
2
0
0
0
0
1
0
1
1
1
0
0
1
1
1
1
1
1
2
2
0
2
1
2
1
0
1
0
0
1
0
0
2
1
1
0
1
1
1
0
0
0
0
1
0
2
0
1
1
0
2
1
0
0
1
0
1
1
3
1
0
3
0
0
0
1
0
0
0
5
0
0
0
1
0
1
1
0
2
0
2
2
1
0
0
1
2
2
1
0
1
0
1
1
0
0
0
1
2
0
0
2
0
0
0
0
1
1
1
1
0
0
0
0
0
3
0
2
1
1
1
1
1
1
0
0
1
0
1
0
1
2
0
3
2
0
1
0
1
2
0
0
0
0
1
0
0
1
1
1
0
1
0
0
0
2
2
0
2
0
2
0
2
2
0
2
1
1
0
2
1
1
2
2
1
1
0
1
1
1
1
0
0
0
1
2
1
2
1
0
0
0
0
0
1
1
0
2
0
0
1
0
2
2
2
2
0
1
1
0
2
1
0
1
1
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
1
1
2
0
0
1
1
2
0
0
2
1
1
1
2
0
0
1
2
0
1
1
1
0
0
2
1
1
2
0
2
0
0
1
0
0
2
1
0
2
0
0
0
0
0
1
0
1
2
1
1
0
0
0
3
1
1
1
0
0
1
2
0
0
0
0
1
0
1
0
2
0
1
1
1
0
0
0
3
1
0
1
0
1
1
0
0
0
0
1
1
0
0
1
1
1
0
1
1
2
2
0
0
0
2
0
1
0
0
1
0
1
1
2
0
0
0
1
1
0
0
0
0
2
2
1
0
0
0
1
0
0
2
2
0
2
0
0
1
0
0
2
0
1
1
0
1
0
0
1
0
2
1
2
0
1
1
2
2
2
0
0
0
1
1
2
0
1
0
0
2
0
1
1
1
1
1
1
1
0
1
0
0
0
1
1
1
3
0
0
0
0
0
1
1
2
0
1
2
0
0
0
0
1
1
0
3
0
0
1
1
0
2
0
0
0
0
2
0
1
1
0
0
2
0
2
0
2
1
0
0
1
0
1
2
1
0
0
2
0
1
1
0
1
1
1
0
2
1
2
0
2
2
1
2
2
0
1
0
0
1
2
0
2
0
1
2
1
1
1
0
1
0
1
2
0
0
2
1
1
2
1
2
1
2
0
1
1
0
2
0
0
1
0
0
1
0
0
1
2
0
0
2
1
0
0
0
0
0
0
0
0
2
1
1
4
1
1
1
1
2
2
0
1
0
0
0
0
0
1
0
1
0
1
0
4
0
1
1
0
1
0
0
2
1
2
2
0
2
1
0
2
1
2
0
1
2
2
2
0
0
1
0
0
0
1
0
1
1
1
0
0
0
2
0
2
1
1
2
2
0
1
2
0
0
1
1
0
1
1
2
3
0
0
0
2
1
1
0
0
2
2
0
0
2
1
2
0
0
0
0
0
1
0
1
0
0
2
2
0
1
1
0
1
1
2
1
1
0
0
1
0
0
2
2
0
0
1
0
2
2
2
2
1
1
2
1
1
0
0
0
1
1
0
2
0
0
2
0
0
0
1
2
1
0
0
2
2
2
2
2
0
2
0
0
0
0
0
0
0
2
1
2
1
0
1
1
1
0
1
0
1
0
1
0
0
0
0
0
1
0
3
1
1
0
0
0
2
0
0
0
2
1
0
0
1
0
0
2
0
0
0
0
1
0
2
1
0
7
0
1
1
0
1
1
3
0
0
1
0
1
2
2
1
1
1
0
0
2
0
3
1
0
2
1
1
0
0
1
2
1
0
1
0
0
0
2
0
1
0
0
1
0
1
1
0
0
1
1
0
2
2
0
1
1
2
0
1
1
0
2
2
1
2
0
0
0
1
0
1
0
1
1
1
0
2
1
1
0
1
1
0
0
0
0
2
0
0
2
2
2
0
0
0
0
1
0
1
0
2
0
1
0
3
1
1
1
2
0
1
0
0
0
1
0
2
2
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
1
2
2
2
0
1
1
0
1
1
2
1
0
0
0
2
0
1
1
0
0
1
2
0
2
1
1
1
0
0
0
0
1
0
2
1
2
0
0
1
0
1
0
2
0
1
2
1
2
1
2
1
0
1
0
0
0
2
2
1
1
1
0
0
1
0
1
0
0
1
1
0
0
1
0
2
1
2
0
0
1
1
1
0
1
1
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
2
4
0
0
2
2
0
0
0
0
1
1
0
1
1
0
1
1
0
0
1
0
0
1
0
0
1
2
0
1
0
2
0
1
1
0
1
0
0
0
1
2
0
2
0
0
2
3
0
1
0
0
0
0
0
0
2
0
0
0
1
1
0
1
0
0
1
2
1
1
1
0
0
0
0
1
0
2
0
0
1
1
2
0
0
0
0
0
0
0
0
4
1
2
2
0
2
1
1
0
1
2
0
0
0
0
1
0
1
1
2
1
0
0
1
0
0
1
0
2
0
1
0
0
3
0
0
1
5
0
2
1
2
0
1
0
1
1
0
1
0
0
0
1
3
0
0
0
1
0
0
2
1
1
0
1
0
1
0
1
0
0
1
0
0
0
0
1
0
2
1
2
0
0
1
0
2
0
1
0
0
0
0
1
1
2
0
1
0
0
2
0
1
0
1
2
0
3
2
2
0
1
2
0
0
1
0
2
2
1
0
2
0
1
2
2
2
0
1
0
2
2
2
1
0
0
1
1
1
1
0
1
0
0
1
0
2
2
2
0
0
0
1
0
2
0
0
1
1
0
2
0
1
0
2
1
0
0
0
0
2
2
0
3
1
0
0
1
1
0
0
0
0
0
1
3
1
0
0
0
1
1
0
0
2
1
1
1
2
0
1
2
2
0
0
7
1
2
1
1
2
0
2
2
0
1
2
0
0
1
2
0
1
2
0
0
2
1
0
0
3
1
1
0
1
0
0
0
1
0
0
0
2
0
1
1
0
1
0
0
2
0
1
0
0
0
1
0
1
1
1
0
0
1
0
0
1
0
0
1
2
0
1
3
1
0
2
1
1
0
2
0
1
1
0
1
1
0
1
0
0
0
2
0
1
0
0
0
2
0
1
2
2
0
2
1
0
1
0
0
0
0
2
1
1
1
1
0
2
0
2
0
1
0
1
0
0
0
0
0
1
2
0
0
1
0
1
1
0
1
0
0
0
0
0
1
2
1
0
1
1
2
0
0
2
0
1
2
1
1
0
0
0
0
0
2
0
2
2
0
1
0
1
2
1
1
0
0
4
0
1
1
1
0
0
0
1
0
0
0
1
0
1
0
0
1
1
1
0
0
1
0
2
2
0
0
4
0
1
0
2
0
0
3
0
2
1
0
1
2
0
2
1
2
0
1
1
2
5
0
0
3
0
1
1
2
1
0
2
1
1
0
0
0
1
0
1
0
0
0
1
3
2
0
0
0
1
1
0
3
0
0
0
2
0
0
0
1
1
2
2
1
0
1
0
2
1
1
2
0
0
1
0
1
1
3
2
0
0
0
1
0
0
0
1
2
0
1
0
1
1
0
1
1
0
1
2
0
0
0
1
1
0
0
2
8
0
1
0
1
0
0
1
0
2
0
0
1
1
0
1
0
0
2
2
0
2
1
1
0
1
1
1
1
0
1
2
1
2
0
0
2
0
0
0
0
1
2
1
1
0
1
1
1
0
1
0
2
2
1
0
2
0
0
2
1
0
0
0
0
2
1
1
0
1
2
1
2
1
1
2
1
1
2
0
0
0
0
1
2
0
1
0
0
1
0
0
1
1
0
1
0
1
1
0
1
1
0
0
1
0
1
2
1
0
1
0
0
3
0
3
0
0
0
0
1
1
1
1
1
1
1
3
0
0
1
0
1
1
1
1
0
1
2
0
0
0
1
1
0
1
0
1
0
0
0
0
2
0
0
1
0
0
1
1
2
0
1
0
2
2
0
0
1
1
0
1
1
0
2
2
0
0
1
0
2
0
1
0
2
0
2
0
1
2
2
0
1
0
1
0
1
1
0
0
2
1
0
0
0
1
0
0
0
0
1
0
0
0
2
1
0
0
1
1
0
0
0
1
1
0
0
0
0
1
2
0
0
1
1
1
2
1
0
1
2
0
0
0
1
0
1
1
0
2
2
1
0
1
0
0
0
2
1
0
2
1
0
2
1
0
1
0
2
2
2
2
1
1
0
1
0
2
1
1
1
1
2
0
0
0
2
0
1
0
0
0
1
0
1
0
0
3
1
0
1
0
0
0
0
2
2
0
0
1
0
1
1
2
2
2
2
2
1
2
0
1
0
2
1
2
1
0
1
0
0
0
4
4
1
2
1
2
0
0
1
0
1
0
1
1
1
1
2
1
1
0
2
0
1
1
2
1
1
0
0
0
1
1
0
0
0
1
1
1
1
1
1
0
1
1
0
2
0
0
1
0
0
2
0
1
1
0
2
1
1
1
2
0
1
2
0
2
1
1
0
0
2
0
1
0
2
1
0
0
0
0
1
0
1
0
1
0
2
0
2
0
0
2
1
1
1
1
0
0
0
1
0
0
0
1
0
1
0
0
1
1
1
1
2
0
2
0
1
3
3
1
1
0
0
1
1
1
0
2
0
0
2
0
1
0
2
0
1
0
1
2
1
0
1
3
2
1
0
2
0
2
0
1
1
0
1
3
1
0
0
1
1
1
1
0
0
0
0
0
0
0
1
0
0
1
0
1
2
2
2
0
2
0
2
1
0
0
0
1
0
2
2
0
1
0
0
0
0
0
1
2
1
0
1
0
1
1
1
0
0
0
2
0
0
0
2
2
1
2
0
1
0
0
1
0
1
0
0
2
2
0
3
1
1
2
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
2
3
2
0
1
1
1
3
1
2
1
2
0
2
1
2
0
1
1
0
0
1
1
2
0
2
0
0
0
2
1
1
2
0
0
1
1
0
1
1
1
0
0
1
0
0
2
1
1
1
2
2
0
0
0
1
2
1
1
0
1
1
1
0
1
0
0
0
0
0
0
1
1
1
0
2
0
0
1
0
2
0
1
2
2
0
1
0
1
0
2
0
1
2
0
0
1
2
1
0
0
0
1
1
1
0
0
0
2
2
1
1
1
0
1
2
1
0
0
0
0
2
2
0
1
0
0
0
2
0
1
0
0
1
0
2
1
1
1
0
0
0
3
0
0
0
1
0
1
1
0
0
0
1
2
1
0
0
1
1
1
2
1
1
0
0
1
0
0
2
1
1
2
0
1
0
1
0
2
1
0
2
0
1
2
0
0
3
0
2
1
0
0
0
0
1
0
1
0
0
0
0
1
1
1
1
0
1
1
0
0
2
1
0
0
0
0
2
0
1
0
0
1
2
1
1
2
2
2
0
0
0
1
1
1
2
1
0
0
1
1
0
2
0
1
1
0
1
1
1
0
2
0
2
0
0
0
2
0
1
0
2
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
1
1
1
0
1
1
0
2
2
0
0
1
2
1
0
3
0
0
0
1
1
0
1
0
2
0
1
2
0
0
1
2
2
2
0
0
1
0
0
3
2
1
0
1
1
0
2
1
0
1
1
0
2
1
0
1
2
1
1
2
0
1
0
1
1
1
0
1
0
2
1
0
2
0
0
1
1
1
2
0
2
1
0
1
2
1
2
0
0
0
0
1
1
1
0
0
3
1
1
1
0
1
1
0
0
2
1
2
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
2
0
0
0
2
0
2
1
0
0
0
0
2
0
0
2
1
0
1
1
2
1
0
1
0
1
1
1
1
1
0
0
1
1
1
0
0
0
2
0
0
0
0
8
0
1
1
0
1
0
2
2
0
0
2
0
1
1
0
1
0
0
1
1
1
2
0
1
3
0
0
2
0
0
1
0
2
0
0
0
2
2
2
0
1
1
2
0
1
2
0
1
2
0
0
0
0
3
0
0
2
0
0
2
1
1
0
0
1
0
0
2
1
3
1
0
0
1
0
1
1
0
2
2
0
2
0
1
0
0
0
1
0
0
0
1
1
2
0
0
1
0
0
1
2
1
0
1
0
1
1
0
2
0
0
0
2
2
0
0
2
0
0
2
0
1
0
2
1
2
0
2
2
0
1
0
1
0
2
2
3
1
1
0
1
1
1
2
0
0
1
1
2
5
0
0
0
0
0
0
0
1
0
0
0
2
1
2
0
3
1
0
0
0
2
0
1
0
0
0
2
2
0
0
0
1
0
0
0
2
0
0
1
0
0
1
2
0
1
0
0
0
0
1
0
0
2
1
2
1
0
0
0
1
2
1
1
5
0
0
0
0
1
0
0
4
1
1
0
1
0
1
1
3
0
0
1
1
0
0
0
1
2
2
0
0
0
2
0
1
0
1
0
0
2
1
1
2
1
0
2
0
0
3
1
0
0
0
0
0
0
1
0
2
0
2
1
1
2
1
0
0
2
0
2
1
1
2
0
0
0
1
0
0
1
1
0
0
1
1
0
1
0
1
1
2
1
2
1
1
0
0
3
0
0
2
0
0
1
1
0
1
1
2
0
0
2
2
1
1
0
2
1
0
1
2
1
1
0
1
1
0
0
2
0
2
1
0
1
1
1
0
0
0
2
1
1
0
2
1
0
2
0
1
0
2
1
0
0
0
2
0
2
2
1
0
0
1
0
1
2
0
2
0
1
1
0
0
2
0
0
2
2
0
2
0
4
1
0
0
1
0
0
0
2
0
0
0
0
0
1
2
2
1
1
2
0
0
1
1
1
0
0
1
1
2
0
2
0
1
1
1
2
1
0
1
2
2
1
0
0
0
0
0
0
0
0
0
0
3
1
0
2
1
1
1
0
1
0
0
0
4
0
0
1
2
0
1
2
1
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
1
0
2
0
0
1
0
2
0
0
0
2
2
0
2
2
0
0
1
0
0
1
0
2
2
0
0
2
1
0
0
1
1
2
0
0
2
1
1
0
1
0
2
2
0
0
0
2
1
1
1
2
1
4
0
0
0
0
0
0
0
6
1
1
0
0
2
1
2
0
1
0
2
0
2
1
0
1
2
0
0
0
0
0
0
2
2
0
1
1
0
1
0
2
0
1
0
2
2
1
0
2
0
1
0
1
0
0
1
0
0
0
2
2
1
0
2
0
2
0
0
2
0
0
2
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
2
1
1
1
1
1
2
1
0
1
2
1
2
0
0
1
1
0
2
0
0
1
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
1
1
0
2
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
3
1
1
0
1
2
2
0
0
0
0
0
1
0
1
0
0
2
0
0
2
1
0
1
0
1
1
0
2
0
0
1
2
0
0
0
0
2
2
1
1
1
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
1
0
1
1
1
1
2
1
2
2
1
0
2
0
1
0
1
0
1
0
0
2
1
2
2
1
2
1
3
1
2
1
0
2
1
0
2
1
0
0
0
0
0
1
1
1
3
1
0
2
0
2
1
0
0
0
0
1
0
1
0
0
1
0
0
2
1
1
0
0
1
3
1
2
1
0
1
0
0
0
1
2
0
0
1
0
0
0
0
0
0
2
0
2
0
0
2
0
1
0
1
0
2
2
1
1
2
0
0
0
0
0
0
2
2
0
0
1
2
0
0
0
2
1
0
2
1
0
1
2
0
0
0
0
0
2
1
1
0
1
0
2
2
0
1
1
2
0
1
1
1
1
2
2
2
0
2
0
1
1
1
0
0
1
1
0
0
0
2
2
0
3
0
0
0
2
1
1
2
0
1
0
2
0
1
0
1
1
0
2
1
0
0
1
0
0
2
0
0
0
1
0
0
1
0
1
0
2
0
1
0
1
0
0
0
2
2
2
2
1
0
2
0
0
0
1
0
0
1
1
2
1
0
2
2
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
2
2
1
0
0
0
0
0
2
1
2
0
0
0
2
1
0
0
1
1
0
1
0
0
1
0
1
0
1
0
2
0
1
0
1
2
1
0
0
0
0
0
1
1
0
1
0
1
2
0
1
0
0
0
1
0
1
0
1
2
3
0
0
2
1
1
1
1
0
1
1
1
0
0
1
1
1
0
2
1
2
0
1
1
0
1
1
0
0
0
0
0
2
0
0
0
0
1
0
0
1
1
1
0
2
0
1
0
1
0
1
0
2
2
2
0
0
1
1
0
2
0
0
1
0
0
1
0
0
1
1
2
0
2
0
1
1
0
0
0
0
2
1
0
0
0
0
2
2
1
0
1
2
0
1
2
0
2
0
1
0
0
1
1
0
1
0
1
0
0
2
0
2
1
1
1
1
0
2
0
1
0
1
2
0
2
1
0
2
0
0
0
2
2
0
1
2
1
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
2
1
2
0
1
1
0
0
1
0
0
1
0
1
1
0
0
1
0
1
1
2
1
0
0
0
1
0
1
0
0
0
0
1
1
1
1
0
0
2
1
0
0
1
1
2
1
1
0
2
2
1
0
0
3
2
0
2
0
0
0
0
2
0
1
1
1
0
1
1
0
0
1
0
1
0
0
0
2
1
1
0
1
1
0
0
1
1
1
0
0
0
2
0
0
2
0
0
1
1
0
2
0
1
1
2
1
2
1
1
1
2
2
1
0
0
1
0
1
0
1
1
1
0
0
2
1
1
2
2
1
0
1
0
1
0
1
1
0
0
2
0
1
0
0
0
1
1
1
0
1
0
1
0
0
2
0
0
1
0
0
1
0
1
1
0
2
0
0
0
2
0
0
1
0
2
0
0
0
0
0
1
0
1
0
1
0
0
2
1
0
0
0
0
0
0
1
3
0
0
1
0
2
1
2
2
0
0
0
0
2
0
1
2
0
0
1
2
1
0
0
1
0
1
0
0
1
2
1
2
2
1
0
0
2
2
0
0
1
0
0
0
1
0
2
0
0
2
0
0
2
1
1
0
1
1
2
1
1
0
1
0
1
2
0
0
0
2
1
1
1
0
2
2
2
1
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
2
1
2
0
1
0
1
0
0
0
0
0
1
2
0
0
0
0
1
1
2
1
1
0
0
2
0
1
1
0
0
0
0
1
1
0
0
0
1
1
0
0
0
4
1
2
0
0
0
2
1
0
1
0
1
2
1
2
2
0
0
0
0
2
0
1
1
0
1
1
0
1
0
1
0
0
2
2
1
0
2
0
2
0
1
0
2
2
2
1
0
1
1
1
0
0
1
1
2
2
1
0
0
1
1
0
2
3
2
1
0
2
0
0
0
0
1
0
1
1
3
0
2
2
2
2
0
0
1
1
3
0
2
0
0
0
1
1
2
1
1
0
2
2
1
1
0
0
0
1
3
2
0
1
2
2
1
0
2
0
0
0
0
1
0
0
0
2
1
0
1
0
1
0
1
0
1
0
0
0
2
0
0
1
2
1
0
2
0
1
1
1
0
2
2
0
1
0
0
0
2
2
0
1
0
2
1
1
0
0
2
1
0
1
2
2
1
0
2
0
0
0
0
2
0
0
1
1
1
2
0
2
2
0
0
0
2
1
0
0
1
0
1
2
0
2
0
1
0
0
2
2
0
2
1
0
0
0
1
0
1
1
1
2
2
0
2
2
0
0
1
1
0
0
0
0
3
1
2
2
0
1
1
1
2
0
0
2
0
0
0
1
2
0
1
0
0
1
0
1
0
0
2
1
1
0
0
0
0
1
0
2
2
0
1
0
2
5
1
0
2
0
0
0
1
1
2
0
0
1
1
0
0
1
1
2
1
1
1
2
2
0
1
1
0
2
1
1
0
1
1
2
1
0
0
3
0
0
2
2
1
2
1
0
0
0
0
1
0
0
0
1
1
0
1
2
2
1
2
0
0
0
1
0
0
1
0
0
1
1
1
1
0
0
0
2
2
0
0
3
1
1
0
2
2
2
1
2
1
0
0
1
0
2
0
0
0
1
0
0
2
0
1
0
1
1
0
1
0
0
1
1
1
1
2
0
0
0
2
2
1
1
0
2
1
1
0
1
0
0
0
0
1
2
0
0
1
1
0
1
0
0
0
0
1
1
2
0
0
1
0
0
0
2
0
0
0
2
0
0
1
2
2
0
0
0
1
1
2
2
0
0
1
0
6
0
2
1
1
1
1
0
0
1
1
0
2
1
2
0
1
2
2
2
2
0
0
0
5
1
3
1
2
0
0
0
2
0
1
0
0
2
0
0
0
0
1
2
2
1
4
0
0
0
0
0
1
0
2
0
1
0
0
0
2
0
0
0
1
2
2
2
2
0
1
1
0
1
3
1
1
2
0
2
1
1
0
1
1
2
1
2
0
0
1
0
0
1
1
2
1
2
1
0
0
3
0
0
0
0
0
0
2
1
0
0
1
0
2
0
0
0
1
1
2
1
0
1
0
1
0
0
1
1
1
0
2
1
0
3
0
0
0
2
1
0
0
0
2
0
0
1
1
2
0
1
0
1
2
0
1
1
0
2
0
2
0
1
1
0
1
1
0
0
1
1
0
1
2
0
0
0
0
0
0
1
0
0
1
1
2
2
0
1
1
1
3
0
0
1
0
2
0
0
1
0
0
0
2
1
0
0
1
2
0
1
0
0
1
2
0
2
1
2
1
0
0
1
0
1
1
8
1
2
0
0
0
1
2
2
2
1
0
1
2
0
1
1
0
0
1
2
1
2
1
0
0
0
0
0
2
1
0
1
1
1
2
2
1
0
1
0
0
0
2
2
2
0
0
2
3
1
0
1
0
2
1
1
1
0
0
1
1
0
0
0
2
1
1
1
0
1
0
2
1
0
1
2
2
0
0
1
0
0
2
0
0
2
1
0
1
0
0
0
0
1
1
0
0
1
1
0
1
0
1
0
1
1
2
1
0
0
0
0
0
1
1
1
0
1
0
0
0
1
1
1
1
0
1
1
0
2
2
1
0
1
2
0
0
2
0
2
2
0
3
2
1
1
0
0
0
2
1
2
0
0
4
1
1
1
0
0
1
0
0
2
2
2
1
0
1
1
1
0
1
0
0
1
2
1
0
0
1
0
0
1
1
0
1
2
0
2
0
0
0
0
0
0
1
2
2
0
0
0
1
0
0
2
1
2
2
0
1
0
2
1
1
2
2
0
0
2
0
1
0
1
0
2
0
2
1
0
0
1
0
1
1
0
0
1
2
1
0
1
0
0
0
1
0
2
1
1
0
2
0
2
0
2
1
0
1
0
0
1
0
0
0
1
0
0
0
1
0
1
1
0
1
0
0
0
1
2
0
0
1
3
0
1
0
1
1
1
0
2
1
1
1
0
2
1
0
1
0
0
0
2
2
1
2
1
2
0
2
0
3
1
0
0
2
2
0
0
1
0
1
2
2
2
1
0
1
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
1
1
1
1
1
1
0
0
2
2
2
1
4
1
2
0
1
0
0
0
0
0
3
1
0
0
2
1
0
0
2
0
1
0
1
0
0
1
0
0
0
0
0
1
0
1
1
1
1
0
0
0
1
0
0
0
0
3
1
0
0
2
0
0
4
0
2
1
1
1
2
1
0
0
0
1
0
2
1
1
0
2
2
0
0
0
1
0
1
0
1
0
2
0
1
0
1
2
1
0
1
1
0
2
0
1
1
0
0
1
0
1
0
0
0
1
2
1
1
2
1
1
1
0
1
0
2
1
1
1
1
0
0
0
2
1
1
0
0
0
1
2
0
0
1
1
1
0
0
2
1
0
0
0
0
1
1
0
1
0
2
1
0
2
1
1
2
1
2
1
1
0
1
1
1
1
1
2
2
0
0
1
0
0
2
0
1
1
0
1
0
0
1
1
0
0
2
1
0
0
1
2
1
1
0
1
0
2
1
1
1
2
1
1
1
0
1
0
0
2
2
0
1
2
0
0
1
0
1
2
2
1
1
2
2
2
0
2
1
5
0
1
0
0
3
0
1
1
0
1
2
1
0
1
0
1
2
0
1
1
0
0
0
2
1
0
0
0
0
0
0
1
1
0
1
1
0
2
0
0
0
0
2
0
2
1
0
0
0
0
1
1
0
0
2
1
1
1
1
0
0
1
1
0
0
1
0
1
1
1
0
0
1
0
0
0
2
0
0
0
1
1
0
0
0
0
0
2
1
0
0
0
0
0
2
2
0
2
2
0
0
0
0
2
0
1
2
0
0
0
0
2
2
1
1
0
0
0
2
2
1
0
0
1
1
2
0
0
0
1
2
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
2
0
1
3
1
0
0
2
1
1
0
1
1
1
2
1
0
2
0
1
0
0
3
0
0
1
2
2
0
1
2
0
0
1
0
1
2
1
0
0
1
2
0
0
0
1
2
2
0
1
1
0
1
1
0
3
1
0
1
0
0
2
0
0
0
2
0
1
2
0
1
0
0
4
2
0
0
1
0
0
2
0
1
0
1
0
2
1
1
1
1
2
0
2
2
2
1
0
0
2
0
0
2
1
0
0
1
0
0
2
1
1
0
1
2
0
0
1
0
0
2
0
2
0
1
0
0
1
1
1
2
1
0
0
0
2
0
0
0
0
2
0
0
0
0
2
1
1
2
0
1
0
1
1
0
0
2
0
1
0
1
0
1
1
0
1
0
2
2
0
0
0
0
0
2
0
0
1
2
0
1
2
1
1
1
1
0
1
1
1
0
1
0
2
1
0
3
0
1
2
1
2
2
2
0
2
0
0
0
1
1
0
0
0
2
1
0
0
2
0
2
2
1
1
1
1
2
2
1
0
0
0
1
0
2
1
1
0
0
0
0
0
0
1
1
2
1
1
0
0
0
0
2
1
0
1
1
0
2
1
1
1
0
0
0
0
1
0
2
0
1
1
0
0
1
2
0
0
3
0
0
1
0
0
0
0
0
2
2
1
0
0
2
0
2
1
0
0
1
1
1
2
1
0
0
2
1
1
2
2
2
2
1
0
0
3
0
0
1
0
0
1
2
0
2
0
2
1
0
0
1
2
2
4
0
0
1
0
1
0
3
0
1
0
1
0
0
1
0
1
1
2
1
0
1
0
0
2
0
0
0
1
1
1
1
1
2
0
0
2
0
0
0
2
1
1
2
0
0
2
0
0
1
2
2
1
0
2
0
1
2
0
0
0
2
1
1
2
2
2
3
0
2
1
1
0
2
1
1
1
0
1
0
2
1
1
0
0
0
0
1
0
0
0
1
2
0
1
0
0
0
1
0
1
2
0
2
2
1
0
1
1
0
1
1
2
1
0
2
0
0
1
1
1
0
0
1
0
2
1
1
0
1
0
0
8
1
0
0
0
0
2
0
2
2
1
0
0
1
0
3
1
0
0
1
1
0
1
1
0
2
1
1
0
2
1
2
2
2
0
0
1
0
0
1
0
2
0
2
1
2
0
0
1
1
2
1
2
0
0
1
2
0
0
1
1
2
1
1
0
4
2
2
0
2
0
2
1
0
2
0
0
0
1
0
0
0
2
0
0
1
0
0
0
2
0
1
0
0
1
0
0
2
0
1
1
1
2
2
0
1
0
0
0
0
0
0
0
0
2
1
2
1
0
0
0
2
0
1
0
1
1
0
2
2
0
0
1
0
2
1
0
0
0
0
1
1
0
1
2
1
1
1
2
1
1
3
2
0
2
1
0
0
0
1
2
0
0
2
0
2
1
0
0
1
0
1
0
0
0
1
1
2
0
4
1
0
0
2
0
0
1
0
1
2
0
1
0
2
1
0
0
1
0
0
0
2
1
0
2
0
2
0
0
1
0
0
0
1
0
1
3
0
0
1
1
1
0
0
1
2
0
2
0
1
1
2
1
0
1
0
0
2
0
0
1
0
2
1
0
0
2
0
1
0
1
1
0
1
2
0
0
0
1
1
0
0
2
0
2
0
1
2
1
0
1
2
0
0
2
1
2
2
0
0
1
2
0
0
1
3
2
0
0
0
1
0
2
0
1
0
0
1
1
2
0
0
0
1
0
2
3
0
1
2
0
0
0
0
2
0
0
0
2
2
2
0
1
0
0
0
1
1
1
1
0
1
0
1
0
1
2
0
0
2
2
0
2
1
0
2
0
1
2
1
1
1
0
1
1
0
2
1
0
2
1
2
1
0
1
0
0
0
2
0
1
1
0
1
0
1
1
0
0
2
2
1
1
0
0
1
0
0
1
0
1
1
0
2
2
1
0
2
0
1
0
1
2
1
2
1
1
1
1
0
1
0
0
0
0
2
1
0
0
0
0
2
1
2
1
0
1
2
0
1
0
0
1
0
0
2
0
0
0
0
0
0
1
0
2
1
1
1
0
2
1
0
1
0
0
1
0
1
0
1
0
0
1
2
2
0
0
2
0
1
0
0
1
2
2
0
2
0
1
1
1
1
0
0
1
1
1
0
0
0
2
0
1
1
2
1
3
1
0
0
0
1
2
1
1
1
0
0
0
0
2
0
1
1
2
9
0
2
0
0
2
0
0
2
0
1
2
2
2
1
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
1
1
2
1
0
0
1
0
2
2
0
0
0
4
1
2
2
0
1
1
1
2
0
0
0
0
0
2
2
1
0
0
0
0
1
0
1
1
0
0
1
1
1
0
1
1
1
1
0
3
2
1
1
1
0
2
2
1
1
2
1
0
0
1
0
0
0
2
2
0
0
2
1
1
2
0
0
0
1
1
1
2
0
2
2
0
0
0
2
0
2
1
0
0
1
2
1
2
0
0
1
0
0
1
0
2
2
2
0
1
0
1
2
2
3
1
0
0
0
1
0
2
0
0
0
2
1
0
1
0
2
0
0
0
1
1
0
0
0
1
0
0
1
2
1
0
2
0
2
1
2
1
0
1
1
0
2
1
1
2
1
2
1
0
1
0
1
0
0
1
1
0
1
1
1
0
2
0
1
1
1
1
3
2
1
0
0
0
1
0
0
1
0
0
0
0
1
1
0
2
2
1
2
0
1
1
1
1
0
0
1
0
2
2
1
0
0
1
0
0
1
0
2
1
0
0
0
0
1
0
1
0
1
2
0
2
2
1
1
2
0
1
1
0
2
1
1
0
2
2
1
1
1
0
0
2
0
2
2
2
0
0
0
0
1
2
1
0
0
0
0
0
1
1
0
2
0
1
2
0
1
1
1
0
0
0
1
0
1
0
0
1
1
2
0
0
0
0
0
1
1
0
0
3
1
0
0
0
2
1
0
2
0
2
0
0
0
4
2
0
0
2
1
0
2
1
2
1
0
1
0
0
1
0
2
0
0
0
1
0
1
1
0
0
0
1
0
1
0
1
0
0
0
0
0
2
0
0
2
0
2
0
1
1
1
0
0
0
0
0
0
0
1
2
1
1
0
0
0
2
2
1
0
0
1
0
2
0
0
1
0
1
2
1
1
0
0
0
1
2
1
0
0
1
1
2
1
2
1
2
1
0
1
0
2
0
0
2
0
1
2
1
1
0
0
1
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
1
0
1
0
1
2
2
1
4
0
0
2
0
0
0
0
1
0
2
1
0
0
2
2
1
2
1
0
1
0
1
0
2
3
0
0
1
1
0
3
1
1
0
0
0
1
0
1
0
2
2
5
2
0
2
0
1
2
2
2
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
1
1
0
1
0
3
1
0
0
0
1
2
0
1
0
0
1
2
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
2
0
1
0
1
1
2
0
1
0
0
2
0
0
0
1
2
2
0
1
0
0
0
0
0
2
0
0
0
0
3
0
1
0
1
0
0
1
0
0
0
1
0
1
0
0
1
0
1
1
1
1
1
2
1
0
2
0
1
1
2
0
1
1
0
0
1
0
2
2
0
1
1
1
0
0
2
0
0
0
0
1
0
1
1
0
0
0
0
1
0
1
2
0
0
2
0
0
1
0
1
2
1
0
0
3
0
0
1
1
3
0
0
0
0
1
0
2
0
1
1
0
1
1
2
3
0
1
2
0
0
0
0
0
1
2
1
0
2
0
0
0
1
0
0
1
1
1
0
0
2
2
0
2
1
1
0
2
2
0
0
1
1
1
0
1
2
1
2
1
0
0
0
2
2
2
0
1
0
1
0
1
0
0
1
1
0
0
2
2
0
0
0
0
0
2
1
1
0
0
0
0
0
2
0
0
1
1
2
2
0
0
1
0
2
1
1
0
1
0
2
0
1
2
2
2
2
0
0
0
1
0
0
2
0
0
0
0
1
2
2
1
0
2
0
2
0
1
0
1
0
2
0
2
2
2
0
0
1
0
2
0
0
1
0
0
3
0
0
2
0
0
0
1
2
0
1
2
2
0
0
0
1
0
2
2
0
0
1
0
2
1
1
1
1
1
0
0
0
0
0
1
1
0
0
0
1
2
2
0
1
2
0
1
0
1
0
0
1
0
0
0
0
2
1
0
0
1
0
2
0
1
0
1
1
0
0
2
1
2
0
2
1
1
0
0
2
2
1
2
0
1
0
0
1
0
2
0
1
2
0
2
3
1
0
1
0
1
1
1
0
1
2
0
1
2
0
0
0
0
1
0
2
1
0
2
1
1
0
0
2
0
1
2
2
0
2
5
1
0
0
1
1
6
0
1
1
1
0
2
0
1
0
2
0
0
1
0
2
0
1
1
0
1
0
0
0
0
2
0
0
1
1
0
1
1
2
0
1
1
0
0
0
0
0
1
0
1
1
0
0
0
1
0
2
1
0
0
1
0
0
0
0
1
2
1
0
2
0
0
1
1
0
0
1
3
0
1
1
1
0
0
1
2
2
2
2
0
0
2
0
2
0
1
0
0
0
0
1
1
2
2
2
0
0
0
0
1
0
0
0
0
1
1
1
2
0
0
0
0
2
0
1
0
0
0
1
0
0
1
1
1
0
2
0
1
2
0
0
0
1
0
1
0
0
0
1
1
1
1
1
2
1
0
0
2
0
2
0
0
0
0
0
1
1
1
2
2
3
2
2
1
0
1
0
0
1
0
0
0
0
2
0
4
2
2
0
3
0
1
0
0
0
1
0
1
1
0
0
0
0
0
1
1
2
0
0
2
0
2
0
2
1
2
3
0
0
0
2
1
2
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
1
3
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
2
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
2
1
2
1
1
1
0
0
1
0
0
0
0
0
0
1
0
0
2
1
0
0
2
0
0
1
2
0
0
1
1
1
3
1
0
2
0
0
1
2
0
2
0
2
0
1
1
0
1
0
2
2
0
0
0
1
1
2
0
1
1
0
0
0
0
1
1
0
3
2
0
1
0
2
1
0
0
0
0
0
3
1
1
5
1
1
0
0
1
0
0
1
2
1
2
2
2
0
0
0
0
2
2
1
2
2
1
0
0
0
0
0
0
1
0
0
1
1
1
1
0
0
1
4
1
1
2
2
1
2
0
0
2
0
1
0
1
0
0
0
0
1
2
0
2
2
1
2
0
0
0
0
0
1
0
0
1
2
0
0
2
1
0
0
0
1
1
1
2
1
0
1
0
1
1
1
0
2
1
0
0
0
0
2
0
0
2
0
3
0
0
1
0
2
0
0
0
1
1
0
0
1
1
1
1
0
0
0
2
0
0
0
2
1
0
0
2
1
2
2
2
2
0
0
0
0
1
0
1
2
0
0
0
1
0
0
0
0
0
1
1
2
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
2
2
1
0
1
1
0
2
1
1
0
2
0
1
0
1
1
0
0
0
1
0
0
0
2
0
1
2
0
0
1
0
0
0
0
0
1
0
1
0
1
0
2
0
2
1
2
1
0
1
1
0
2
0
0
0
0
1
0
1
1
0
0
1
0
1
0
1
0
1
1
2
1
5
0
1
2
0
1
0
0
0
1
2
0
0
0
1
2
1
0
1
2
1
2
0
2
2
0
0
0
0
1
1
2
1
1
2
1
1
0
0
1
1
1
1
2
0
1
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
1
2
2
2
1
0
1
0
0
1
1
1
2
1
0
2
1
5
1
0
0
0
0
1
0
0
1
0
2
1
0
0
0
1
1
1
0
0
0
0
1
2
1
1
0
1
0
0
1
1
0
2
0
1
1
1
2
2
0
0
2
0
2
0
0
0
1
0
1
1
1
0
1
0
0
1
1
0
1
1
1
1
0
1
0
1
0
1
0
0
1
0
0
1
0
2
2
2
0
1
0
1
0
0
1
2
2
1
0
2
0
1
1
2
2
1
0
2
1
1
0
0
2
1
0
0
0
0
0
3
0
1
0
1
2
0
2
0
1
0
2
0
1
1
1
1
0
1
1
2
0
1
0
0
1
2
2
1
1
0
1
1
2
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
1
2
0
2
0
0
1
0
1
2
1
0
2
0
0
1
0
2
1
0
0
0
0
1
0
1
0
1
1
0
0
2
9
2
0
0
2
0
4
3
2
0
1
2
0
1
1
0
1
1
0
0
0
1
0
2
0
0
0
2
0
2
0
0
0
0
2
0
2
1
0
0
1
0
1
1
2
1
1
0
1
2
2
0
1
2
2
1
0
0
0
1
0
0
1
1
2
0
0
0
1
0
0
0
1
0
1
0
2
2
1
1
0
1
2
0
2
2
1
2
1
2
1
0
0
1
1
0
1
0
2
2
1
2
0
1
1
0
0
0
2
2
1
0
2
2
0
2
0
0
0
2
0
1
2
0
0
0
0
1
2
2
1
0
0
2
0
3
2
1
0
1
0
0
0
0
2
1
2
0
0
1
1
0
0
1
1
2
0
2
0
1
2
1
2
0
3
1
2
0
1
1
1
2
2
0
0
1
1
1
2
1
3
0
1
1
0
1
0
1
0
1
0
2
0
2
0
0
0
1
2
0
2
2
1
1
2
0
0
0
0
2
2
2
0
0
0
1
1
0
3
1
0
3
2
2
0
0
0
0
1
1
0
2
0
0
0
3
2
0
1
0
0
2
0
0
0
1
2
0
3
0
0
1
2
0
0
0
1
2
0
0
0
1
0
0
0
1
1
1
0
2
2
1
2
0
2
0
2
1
0
0
1
1
0
0
0
1
2
2
1
0
0
2
2
0
1
0
0
0
0
0
2
0
0
2
2
2
2
0
0
0
1
0
0
1
1
2
1
0
1
1
0
1
1
2
1
1
0
0
0
2
2
1
1
0
0
0
0
0
0
1
0
0
0
1
2
1
0
0
0
1
0
0
1
2
0
1
0
0
2
0
1
1
0
0
1
2
2
0
0
2
0
1
2
0
2
1
1
0
0
1
0
2
0
2
0
1
0
0
0
2
0
0
1
2
0
2
2
1
1
0
0
2
0
1
3
0
0
1
0
0
0
1
0
0
2
2
0
2
2
1
2
0
2
0
1
2
1
2
0
1
1
1
0
0
0
0
1
2
0
1
2
0
0
1
1
2
0
2
0
1
2
0
0
0
0
1
0
2
1
0
1
1
1
2
0
2
1
0
2
1
2
1
2
0
1
0
0
0
0
0
1
0
0
0
0
2
0
2
5
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
1
0
0
1
1
1
2
1
0
0
1
1
1
3
1
0
2
0
2
0
0
2
1
0
0
1
1
2
0
0
1
1
1
0
2
1
0
0
0
1
0
1
1
2
0
0
1
0
0
0
1
1
0
1
2
0
2
1
0
0
1
1
0
0
1
0
1
1
0
1
1
0
1
1
0
2
0
2
0
0
2
2
1
2
1
1
1
0
2
1
0
2
0
0
2
0
0
1
0
0
1
0
2
0
0
2
0
1
0
0
1
0
1
2
1
2
0
0
2
2
2
2
2
1
1
0
0
3
1
2
0
0
0
0
4
2
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
1
1
0
0
0
0
0
2
2
1
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
3
1
1
0
0
0
0
1
1
1
0
0
0
1
1
1
1
2
2
2
0
2
2
0
0
0
0
1
2
3
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
1
1
0
2
0
0
0
2
1
1
1
2
1
0
4
0
1
0
0
2
1
2
0
0
1
2
0
1
2
2
0
0
0
0
1
2
1
2
1
1
1
1
1
0
1
0
0
0
2
1
0
1
2
0
2
1
0
0
0
0
0
0
1
0
1
1
1
2
0
0
0
1
2
0
2
2
0
1
1
0
1
0
0
0
0
0
1
1
0
1
3
0
1
0
1
0
1
1
1
0
0
3
0
1
2
1
0
1
0
0
2
1
0
1
0
1
1
2
0
2
1
1
1
0
1
0
1
0
1
0
0
2
1
0
0
2
0
0
0
0
1
2
2
0
1
1
1
1
0
0
0
0
2
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
1
0
0
1
0
0
1
1
3
1
2
0
1
0
1
2
0
1
0
0
2
1
2
2
2
0
2
1
0
0
1
0
2
0
0
0
1
0
0
0
2
0
0
1
0
2
0
2
0
0
1
2
0
0
0
0
2
0
0
2
0
2
1
1
1
0
1
2
0
2
0
2
0
1
0
0
1
0
2
1
1
0
0
2
1
0
0
1
1
0
0
1
0
0
2
0
0
1
0
1
1
2
0
0
0
2
0
1
0
2
2
1
0
2
2
2
0
0
2
2
1
1
0
1
2
0
1
0
1
1
1
0
1
1
0
2
0
0
1
0
0
0
1
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
2
0
0
2
2
0
0
2
2
1
0
0
0
0
1
2
0
1
1
2
1
2
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
2
1
2
0
2
2
0
1
0
0
0
0
1
0
0
1
1
0
2
0
1
0
0
0
1
0
0
1
0
1
2
1
0
1
1
2
1
1
1
1
0
2
0
0
0
2
1
0
1
0
0
0
2
1
1
1
1
0
0
0
0
2
2
1
0
0
1
0
1
2
0
0
1
0
1
1
0
0
0
0
2
1
1
1
0
1
2
1
1
1
0
0
2
1
1
1
0
1
2
2
1
0
0
0
0
0
1
0
0
1
2
0
0
0
0
2
0
2
1
2
1
2
0
1
1
0
0
0
2
0
1
0
0
0
2
2
0
1
3
0
1
1
2
0
0
1
0
0
0
2
1
2
2
1
1
1
0
0
0
2
2
2
1
2
0
2
1
0
0
0
0
1
2
0
1
0
0
0
1
0
1
1
2
0
2
2
1
1
2
2
0
1
0
0
0
2
1
1
2
0
1
2
1
0
0
2
0
0
2
1
1
1
0
1
1
0
0
0
2
0
1
0
0
1
2
2
0
1
0
2
0
1
0
2
0
0
0
2
2
0
0
2
1
0
0
2
1
2
0
0
2
1
1
1
0
1
0
2
0
0
1
0
0
0
2
0
2
0
2
1
1
1
0
0
0
0
2
0
1
1
2
1
0
0
3
0
1
0
0
1
0
0
1
0
0
0
0
1
2
2
0
1
2
0
0
0
0
0
1
0
2
0
2
0
0
1
0
1
0
2
1
1
2
0
2
1
2
1
2
0
0
0
1
0
2
1
0
0
0
1
0
2
1
0
0
0
0
0
0
0
2
1
1
0
2
0
0
2
2
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
1
1
0
0
0
3
0
1
0
0
0
2
1
0
0
2
1
0
0
1
1
1
1
0
1
0
0
1
0
1
2
0
1
1
1
2
0
0
2
1
0
1
2
2
1
0
0
1
0
2
0
0
0
1
0
1
1
0
0
1
2
0
1
1
2
0
2
0
0
2
2
1
0
1
0
2
0
1
1
2
1
0
0
1
1
1
0
6
0
2
1
2
2
0
0
0
0
0
0
1
2
1
1
2
0
0
1
0
0
0
0
1
1
0
0
2
0
0
0
1
1
1
2
0
0
2
1
1
1
0
0
1
1
2
0
1
1
0
0
0
1
1
2
0
1
1
0
1
0
2
2
0
3
1
1
1
1
0
0
0
0
0
0
1
0
1
3
1
2
0
0
1
1
0
0
0
0
4
0
2
1
1
0
0
0
3
1
1
1
1
0
1
2
0
0
0
1
0
1
0
2
1
0
0
1
0
0
0
1
1
1
1
0
0
1
0
1
0
0
0
1
0
1
2
1
0
0
1
1
1
0
0
0
0
1
0
1
0
0
2
0
1
0
0
1
0
0
1
0
3
0
0
1
2
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
1
0
0
2
0
2
0
2
1
0
0
1
1
1
0
0
0
2
1
2
0
1
0
1
0
2
0
0
1
1
2
1
1
0
1
4
1
1
0
2
0
2
0
1
2
3
0
4
0
0
0
2
1
1
0
0
0
1
0
0
0
0
1
2
2
1
1
1
2
1
1
1
0
1
1
1
0
2
1
2
0
1
3
0
0
2
1
0
1
2
0
0
2
2
2
1
1
0
0
2
2
0
1
0
0
0
0
1
2
1
1
1
1
2
1
0
1
1
0
0
2
2
1
2
0
2
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
1
1
3
0
0
1
1
1
0
0
0
0
1
1
2
0
0
2
1
1
0
2
2
2
1
2
2
0
1
1
2
1
1
0
2
0
1
0
1
0
1
0
1
1
3
1
0
0
6
1
1
1
0
2
1
2
1
0
0
3
0
0
1
0
2
0
0
1
1
0
2
0
1
1
0
0
0
0
0
2
1
1
0
1
0
0
0
1
2
1
1
2
2
0
2
0
0
1
2
2
0
2
1
2
2
0
1
2
0
1
0
0
0
2
1
2
2
1
1
2
2
2
0
1
1
1
0
1
2
1
0
1
2
0
1
2
1
0
1
0
2
2
1
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
1
2
0
0
2
1
0
1
1
1
0
0
0
0
5
1
0
1
0
2
0
0
1
1
1
1
2
1
2
2
1
0
1
0
1
0
0
0
4
0
0
2
1
0
0
1
0
1
2
3
1
0
2
2
0
0
1
1
2
0
2
1
0
0
0
1
0
0
1
1
3
0
1
2
1
1
2
2
1
1
0
0
0
1
2
0
0
1
2
0
0
0
0
1
0
0
0
0
2
1
0
1
0
0
1
1
0
2
1
0
1
0
1
1
1
0
2
0
0
0
0
2
0
0
0
2
0
2
0
2
0
0
1
0
0
0
2
2
1
2
0
0
1
1
0
1
0
0
1
2
1
0
0
2
2
1
0
0
0
1
0
0
3
0
0
0
1
0
2
0
7
0
2
1
1
0
0
1
0
0
2
1
0
1
1
2
0
1
1
0
1
2
0
0
0
3
1
0
0
0
0
0
0
2
0
0
1
0
1
2
4
1
2
1
1
1
0
3
2
0
1
2
1
0
2
0
1
1
1
1
0
1
0
2
0
0
3
2
1
2
2
2
3
2
0
2
1
0
0
2
1
0
1
1
0
2
2
2
2
0
0
2
1
1
1
0
0
1
0
0
2
0
0
1
0
0
2
1
0
0
2
2
0
0
1
1
0
1
1
0
0
0
2
1
2
0
3
1
1
1
0
2
1
0
0
2
1
0
1
1
1
1
1
1
1
1
0
1
1
1
0
0
1
0
1
2
1
2
0
2
2
0
1
1
1
1
0
1
0
1
0
0
0
1
0
0
0
0
0
2
2
0
1
1
1
0
0
1
0
0
0
1
0
2
0
2
0
1
0
2
1
0
2
0
3
1
1
0
1
2
0
1
1
1
0
1
0
0
1
1
0
0
0
0
1
1
0
1
2
1
2
1
2
0
2
2
0
0
1
1
0
1
1
0
0
1
0
1
0
0
0
1
1
0
1
1
1
0
1
1
1
0
0
1
0
1
2
0
0
1
0
2
2
0
1
0
0
1
0
0
0
1
1
0
0
1
0
1
1
0
2
0
2
1
2
0
2
2
2
0
0
2
0
0
1
1
2
0
0
1
1
0
2
2
0
0
0
0
0
2
0
0
0
0
1
1
2
1
1
1
0
1
1
0
1
0
2
0
0
1
1
0
2
2
0
1
2
2
2
2
0
0
2
0
1
1
0
0
1
0
2
1
1
1
2
1
1
0
5
0
2
0
0
0
0
1
0
0
1
1
1
1
2
0
1
0
1
1
0
2
2
0
0
1
2
0
0
0
1
0
3
1
0
1
1
1
0
1
1
0
0
4
2
1
0
0
0
0
0
2
0
0
1
0
1
1
2
0
1
0
0
2
2
1
0
0
0
2
0
0
2
1
1
0
1
1
0
2
0
0
1
0
2
1
0
1
0
0
1
2
0
0
0
0
2
2
0
1
2
7
0
0
0
2
1
2
2
0
0
0
1
0
0
0
1
1
2
0
1
1
0
2
1
0
1
0
1
1
2
0
2
2
0
1
0
0
0
2
2
0
1
0
2
0
1
2
1
0
0
0
1
0
0
2
0
2
2
0
2
2
0
0
1
0
2
1
1
2
0
0
1
2
0
1
0
1
2
0
0
0
1
1
1
1
1
0
1
0
2
1
1
2
0
0
1
1
0
0
0
2
1
0
0
0
0
1
0
2
1
2
0
1
0
1
0
0
0
1
0
1
0
1
2
0
1
0
2
1
0
0
0
2
1
0
0
0
0
0
1
0
0
0
1
0
2
0
0
1
1
2
2
0
1
0
1
4
1
0
0
0
1
3
0
1
0
2
2
0
1
0
1
0
1
2
2
1
0
0
0
0
0
1
2
0
0
2
0
1
0
1
1
1
1
0
1
0
0
1
0
0
1
0
0
0
1
2
2
2
1
1
1
0
2
1
0
0
2
1
2
0
0
1
1
0
0
0
0
0
0
0
0
0
1
2
1
1
1
0
1
0
0
1
1
0
2
2
0
2
1
0
0
0
1
1
0
0
0
0
0
0
1
1
2
2
2
0
1
0
2
0
2
1
1
1
1
0
0
1
1
2
1
1
0
0
1
1
0
0
0
0
0
1
0
0
1
1
1
1
0
2
0
1
0
1
0
1
1
2
2
1
1
1
0
1
1
2
1
2
1
2
2
0
0
0
2
1
2
0
0
0
0
1
0
0
0
2
0
0
0
2
1
2
0
0
2
1
0
0
1
0
2
0
1
0
0
1
2
2
1
1
1
2
0
1
0
0
1
0
0
1
2
2
1
0
1
0
1
0
2
1
2
2
0
0
0
0
0
0
2
0
0
1
2
0
2
3
0
4
2
2
1
0
0
2
0
2
5
1
1
2
2
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
1
1
0
0
1
2
2
1
0
1
0
1
0
0
2
1
1
1
3
1
0
4
1
1
0
1
0
1
2
0
1
2
1
1
1
0
2
1
2
2
1
1
0
2
0
0
0
0
1
1
0
0
1
0
1
1
2
0
0
1
1
1
2
0
1
0
0
2
1
1
2
1
0
1
1
2
1
1
0
0
0
0
0
0
1
1
2
0
0
0
0
1
0
0
0
1
0
1
1
1
0
0
2
0
0
2
2
0
1
0
1
0
0
0
0
1
1
1
0
0
0
0
2
0
1
2
0
0
0
0
2
1
0
0
0
0
2
0
0
1
0
2
0
0
0
1
1
0
2
2
0
0
1
1
1
0
0
1
1
4
2
0
1
0
1
1
2
0
2
0
2
1
0
0
0
1
0
1
0
2
0
2
0
0
1
1
0
0
0
0
1
1
0
1
1
0
0
1
2
0
2
0
0
1
1
1
0
0
0
2
2
1
0
0
1
1
2
0
0
1
0
2
0
1
0
1
2
1
0
1
1
0
0
1
1
0
0
4
0
0
0
0
1
1
0
0
1
2
2
1
0
2
0
0
0
0
0
0
1
0
0
0
0
2
1
1
1
0
1
2
1
1
0
2
0
2
0
2
0
0
0
0
1
1
1
1
2
2
2
0
2
0
1
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
1
1
1
0
2
1
0
1
1
1
0
1
1
0
0
2
1
0
0
0
2
1
0
1
0
1
1
1
1
0
1
1
1
0
2
2
0
0
0
0
0
0
1
1
2
2
1
2
0
1
1
0
4
1
0
2
1
1
0
2
0
1
0
0
0
2
0
0
0
2
0
2
0
3
0
0
0
2
2
0
0
0
1
2
1
1
1
0
1
1
2
0
0
2
1
2
0
0
0
0
1
0
0
2
1
1
1
2
1
0
0
0
0
0
0
1
1
1
1
0
0
1
0
0
1
1
1
1
1
0
0
0
0
3
0
1
0
1
0
0
1
0
1
0
0
4
1
2
0
0
1
1
0
2
0
4
2
2
0
2
1
2
2
3
0
1
0
0
0
1
3
2
1
1
0
0
0
0
1
0
0
0
0
0
1
1
2
0
2
0
2
3
0
1
0
0
0
1
1
1
2
0
1
0
0
2
2
0
0
2
2
0
0
1
0
0
0
1
2
0
0
2
2
2
0
0
0
2
1
2
0
1
1
1
0
0
0
2
0
2
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
1
2
1
0
2
1
0
2
0
0
2
2
0
2
1
0
0
0
0
3
1
0
1
1
0
1
0
0
2
0
1
1
1
0
1
0
0
1
0
2
1
1
0
0
0
0
2
0
1
0
3
1
0
0
3
1
0
2
1
0
2
0
0
0
1
0
1
0
1
0
2
1
0
1
1
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
4
1
1
0
1
0
1
0
2
1
2
0
0
2
2
0
0
0
1
0
2
1
2
0
0
0
2
2
2
0
1
1
3
2
1
1
1
0
2
1
2
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
2
1
2
2
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
1
0
1
0
0
2
1
0
0
2
1
1
2
1
1
2
2
0
0
1
0
0
0
0
0
0
1
1
1
0
1
1
1
0
0
0
0
0
1
2
1
1
1
0
1
2
1
0
2
0
0
1
0
2
2
0
0
0
0
0
1
2
2
1
2
1
0
1
0
0
2
2
0
1
0
1
0
0
0
1
1
0
3
2
3
0
1
0
1
1
1
0
0
1
0
1
0
0
0
0
0
1
0
0
2
0
1
0
0
1
0
0
0
1
0
1
1
0
0
2
2
1
0
1
0
2
0
2
1
1
0
0
0
3
0
2
0
3
1
1
2
2
0
1
1
0
1
0
2
0
1
0
1
0
2
1
2
0
0
1
1
2
1
0
0
2
2
1
0
0
0
1
1
0
2
0
2
1
2
0
2
1
0
1
1
1
0
2
1
1
1
0
1
0
1
1
0
0
1
1
0
2
2
2
0
2
1
0
2
2
0
0
1
0
1
0
0
0
0
1
0
1
0
0
1
2
0
2
0
1
2
1
1
1
0
0
1
0
0
0
1
0
1
1
0
1
0
0
1
0
2
0
0
0
0
2
0
1
0
1
0
0
0
0
1
1
0
1
0
2
0
0
0
2
2
0
0
1
1
2
1
2
2
0
0
1
2
0
0
1
0
2
0
2
0
0
1
0
1
2
2
0
0
1
0
0
2
0
2
0
1
1
2
0
2
2
0
0
2
2
0
0
1
0
1
1
2
0
0
0
0
0
1
2
1
2
0
2
0
0
0
2
0
1
0
2
0
2
0
0
1
0
1
1
1
0
1
0
0
1
2
0
2
0
0
0
1
1
0
2
0
1
2
1
1
1
1
1
0
1
2
0
1
1
2
2
2
0
2
2
2
2
0
0
0
0
0
0
1
0
2
0
1
0
0
1
0
1
0
0
1
1
1
0
0
1
0
0
1
1
1
0
1
0
2
0
0
2
3
0
0
1
0
0
1
0
2
1
1
1
2
1
0
1
1
1
4
0
0
0
0
0
0
0
0
0
1
2
1
0
1
2
1
0
0
0
2
1
1
1
1
0
2
1
1
0
1
0
1
1
0
0
0
0
1
0
2
0
2
0
2
1
2
2
0
0
1
2
0
0
1
1
1
0
1
0
0
0
0
2
1
1
1
0
0
2
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
1
0
1
2
0
2
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
2
2
0
0
2
1
2
7
1
1
1
1
1
2
0
1
1
1
1
0
0
1
0
1
0
2
1
1
0
3
1
2
0
0
0
0
0
2
0
0
0
0
1
0
1
3
0
1
0
1
1
0
1
0
0
1
2
2
2
2
2
0
0
7
2
1
2
0
1
2
0
0
2
0
0
0
2
0
1
2
0
0
0
0
1
2
0
0
1
1
0
0
1
4
0
0
0
3
0
1
2
0
0
0
2
0
1
0
0
2
1
0
0
0
2
0
0
0
1
1
0
1
0
0
2
2
1
0
0
2
0
0
1
2
1
0
1
0
1
1
1
1
1
2
1
2
0
0
0
0
1
1
0
1
2
1
0
1
1
0
1
1
0
2
1
2
1
0
2
4
0
0
2
1
1
0
0
1
0
1
1
0
1
2
0
0
2
2
1
1
2
0
0
2
2
2
1
2
0
1
0
1
2
0
1
1
1
1
1
2
1
1
1
2
0
1
2
1
0
0
2
0
0
1
1
1
1
1
0
1
0
1
2
0
1
1
2
0
1
1
0
2
1
1
1
0
2
0
0
1
0
1
1
1
0
2
0
1
0
0
2
2
1
2
0
1
0
1
0
1
0
0
2
0
2
1
0
1
2
0
0
1
0
1
2
0
1
0
0
0
2
1
1
1
2
0
2
1
0
1
2
1
2
0
0
1
0
2
1
1
2
0
0
2
2
2
0
0
0
2
0
1
0
0
2
2
2
1
0
1
0
2
2
0
2
1
0
1
1
0
0
1
2
0
2
0
0
0
2
0
0
0
1
0
0
0
2
1
0
2
1
0
0
1
0
0
2
4
2
2
0
0
2
2
0
2
1
0
2
1
1
0
0
0
1
0
1
2
0
0
0
2
0
1
2
0
0
0
0
2
0
2
1
0
1
1
1
0
1
0
1
0
0
2
2
0
0
2
0
1
1
2
0
2
1
1
0
1
0
0
1
0
0
0
0
1
1
0
0
2
1
2
1
0
0
1
2
3
1
0
0
2
0
0
1
1
1
0
1
0
1
0
1
0
0
1
0
0
0
1
2
2
0
1
2
0
0
0
0
1
1
1
2
0
1
0
1
2
1
3
0
1
0
1
2
0
2
0
0
3
2
0
0
0
0
2
1
0
0
1
1
0
0
2
0
4
1
0
0
2
0
0
1
0
1
2
1
2
2
1
0
0
1
1
1
1
3
0
2
0
0
2
6
2
0
1
0
1
0
0
2
1
0
0
0
1
3
0
1
0
0
1
6
2
2
1
2
1
0
0
0
1
0
1
0
1
2
1
0
2
0
2
0
0
1
1
0
1
0
1
0
0
1
0
0
1
1
2
2
0
0
2
0
2
0
0
1
0
0
1
1
1
0
0
0
2
1
0
0
0
0
1
1
0
1
2
0
2
0
0
0
1
0
1
2
1
2
3
0
2
1
0
0
0
1
0
2
2
2
0
1
1
1
1
1
0
0
0
1
0
1
0
2
0
3
0
2
2
0
0
0
1
1
1
2
1
2
0
2
0
2
2
1
0
1
1
0
2
0
2
0
0
0
1
0
0
1
2
3
0
1
0
2
1
2
0
1
0
2
2
0
1
0
2
2
0
2
0
2
0
2
0
2
1
2
0
1
0
2
0
2
0
1
1
1
1
0
0
3
0
2
0
2
0
0
1
0
0
0
2
0
0
0
0
1
0
2
0
0
0
2
1
2
0
0
1
0
0
0
2
0
0
2
0
1
1
2
2
2
2
0
0
1
1
0
0
3
3
0
1
0
0
1
1
1
1
1
2
1
1
0
0
1
0
0
0
2
0
0
0
0
1
2
2
1
1
1
2
0
1
1
1
1
2
0
2
1
0
2
2
2
1
0
2
4
2
0
0
1
0
0
1
1
1
1
2
2
0
1
1
3
0
0
0
1
0
2
2
0
2
0
2
1
2
1
0
0
0
0
0
0
2
0
0
1
0
1
0
0
2
0
1
1
1
1
0
0
0
1
0
0
0
0
1
1
1
0
1
0
1
0
1
0
0
0
0
2
2
0
0
2
1
0
2
2
2
0
2
0
0
1
0
2
0
0
1
1
1
0
0
1
0
1
0
2
0
0
0
0
1
1
2
1
0
2
1
0
1
2
2
2
0
0
0
3
1
1
1
0
0
0
0
0
0
0
1
1
0
0
2
0
2
1
2
0
0
0
0
2
0
2
2
0
0
1
1
0
0
1
0
0
0
2
1
1
1
0
0
0
0
2
0
1
0
1
2
2
1
0
1
1
0
0
2
1
1
0
2
2
0
0
1
0
1
0
0
1
2
2
1
0
1
0
2
1
0
1
0
0
2
0
2
0
2
0
1
1
0
2
1
1
1
0
0
0
1
0
2
1
0
2
0
0
1
2
0
2
0
3
0
0
0
0
1
0
1
0
2
2
0
1
0
0
0
2
1
1
0
0
0
1
0
0
2
1
2
1
1
0
2
0
1
1
1
2
0
0
0
1
1
3
0
0
0
0
1
1
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
1
2
0
1
0
2
2
0
0
0
1
0
1
0
1
1
0
0
0
0
1
0
1
1
1
0
2
1
0
0
0
0
0
2
2
1
1
1
1
0
1
0
1
1
0
1
0
1
2
0
2
2
1
0
1
0
1
3
1
2
1
1
0
0
2
0
0
2
0
2
1
0
2
2
2
0
1
0
0
0
2
2
0
1
1
0
1
0
2
0
0
1
0
2
2
0
1
0
0
0
0
0
1
0
2
0
0
1
0
1
0
7
1
1
1
0
1
1
0
0
0
0
2
1
2
2
1
0
2
0
0
0
0
1
1
0
1
2
1
2
2
2
2
0
0
1
0
0
0
1
0
0
0
2
2
0
1
2
1
0
1
1
0
1
1
0
0
0
0
1
0
0
0
0
3
1
1
1
2
0
1
1
0
2
0
0
0
0
1
2
2
1
0
0
0
1
1
2
1
1
1
1
1
2
2
0
1
1
1
2
0
0
0
0
4
2
0
0
1
0
0
0
0
1
1
0
0
1
1
1
1
1
2
1
0
0
0
2
0
2
0
0
1
1
2
0
1
1
1
2
2
0
1
2
1
1
0
2
2
0
2
0
2
0
0
0
0
0
0
1
0
1
0
2
2
1
0
0
1
1
0
0
0
2
0
4
0
0
1
0
0
0
0
1
2
1
2
0
0
0
0
1
2
2
0
0
2
1
0
2
2
0
0
1
1
0
1
1
0
0
1
1
0
1
0
0
1
1
0
1
0
1
0
1
1
1
0
1
1
1
1
2
2
0
0
2
1
1
2
3
1
2
1
1
2
1
0
1
2
0
0
0
0
1
2
1
2
0
1
2
0
2
0
0
3
1
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
2
2
2
0
2
0
0
0
0
1
0
1
0
0
2
0
1
1
0
1
0
2
2
2
0
1
2
1
1
1
0
1
0
1
2
2
1
1
0
1
2
1
2
3
2
0
1
2
0
0
1
0
0
0
2
2
1
1
0
1
0
1
2
0
0
0
0
1
2
1
1
0
0
0
1
0
0
0
1
0
0
1
0
2
0
1
1
0
2
2
2
3
0
1
1
1
1
1
0
3
0
0
0
0
1
1
0
2
0
2
1
1
1
1
0
0
0
1
0
0
0
0
0
2
3
2
1
0
0
2
0
2
1
0
0
1
0
1
0
1
0
0
1
1
0
0
1
1
0
1
0
0
0
2
0
3
1
0
0
2
2
2
0
1
2
2
2
2
1
1
0
0
0
0
2
1
0
1
0
0
1
0
2
2
2
0
0
1
1
0
0
1
2
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
1
0
0
2
0
0
0
1
3
1
1
0
1
2
0
2
0
2
2
1
0
1
0
2
1
0
1
0
0
2
1
2
0
2
1
0
2
0
0
1
0
1
0
2
0
0
1
0
2
1
2
3
0
1
1
0
0
0
1
2
0
1
0
0
0
2
0
0
0
0
0
0
2
1
1
1
0
2
0
2
1
2
0
0
0
2
3
1
1
1
0
0
0
0
0
2
1
0
0
0
2
1
0
0
0
0
0
0
0
2
1
1
1
1
2
0
1
0
0
1
0
3
0
0
2
1
1
1
0
1
0
0
2
1
0
2
0
3
2
0
0
0
0
1
1
1
0
1
1
1
0
0
1
1
1
2
0
0
0
1
2
2
1
1
0
2
0
0
0
2
1
1
0
0
0
0
0
0
0
1
0
1
2
3
0
0
0
1
1
2
1
1
1
2
1
0
0
0
0
1
1
3
0
0
0
0
0
1
0
1
2
0
1
1
0
1
0
0
6
0
2
0
1
0
1
2
0
2
2
1
1
2
1
1
1
1
0
0
0
1
1
1
0
0
2
0
1
0
0
1
0
0
1
1
1
2
1
0
0
2
1
1
1
2
0
1
1
1
0
0
2
0
0
0
0
1
0
0
2
1
1
0
0
0
1
0
0
1
1
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
1
2
1
2
0
0
1
1
0
0
2
1
1
1
0
1
0
0
0
1
2
0
1
2
2
2
1
0
1
0
1
0
1
2
2
2
1
0
0
0
0
0
0
0
1
2
0
0
1
1
0
0
1
1
0
1
1
0
0
0
1
0
0
1
0
1
0
2
0
1
0
1
0
1
0
1
0
0
2
0
2
0
1
0
0
0
0
1
0
1
1
0
1
1
0
1
0
0
3
2
0
1
0
1
1
0
1
0
0
0
1
1
1
0
2
2
1
3
0
2
0
1
0
1
1
0
1
0
0
0
1
1
2
0
1
2
1
0
1
0
1
0
0
2
1
0
0
2
0
0
1
1
1
0
1
0
2
0
0
0
2
1
1
4
0
1
1
0
2
0
2
0
1
1
0
1
0
1
1
0
1
0
0
2
0
0
2
0
2
1
0
2
0
1
1
0
1
0
0
0
2
0
0
1
0
0
0
0
0
2
2
1
0
0
1
3
0
1
2
1
0
4
0
2
2
3
1
0
0
0
1
2
0
0
2
1
2
0
0
0
0
1
0
2
1
1
3
1
0
1
0
2
2
1
2
1
2
2
0
2
2
1
1
1
1
0
1
0
0
1
2
0
0
1
0
3
1
2
1
1
1
1
1
0
1
0
1
0
1
1
0
0
0
1
2
0
0
2
1
2
0
1
0
2
1
0
1
2
0
2
0
0
0
2
2
0
0
0
1
1
1
3
1
2
0
2
0
2
2
0
0
1
0
2
1
0
2
0
1
1
2
1
0
0
3
0
2
2
2
1
1
1
2
0
0
0
1
0
2
0
0
0
0
0
1
2
0
2
0
2
1
2
2
0
0
0
2
0
0
1
1
1
0
0
0
1
0
0
2
0
0
2
1
2
1
0
4
0
1
0
2
2
0
1
1
1
1
2
0
0
0
0
0
0
2
1
2
2
0
0
0
0
1
0
0
0
2
1
2
0
0
0
2
0
0
2
0
0
2
1
0
0
1
0
0
2
2
0
1
0
2
1
0
0
1
1
0
2
1
0
1
1
0
0
2
1
0
1
1
0
0
1
0
1
0
0
0
5
2
2
2
0
0
2
3
1
1
0
1
0
1
1
0
0
0
0
1
0
2
0
0
2
0
1
0
1
0
1
0
2
0
1
0
1
2
0
2
1
0
0
0
1
0
1
0
1
1
0
1
0
3
0
0
1
0
1
2
1
0
1
2
1
0
0
2
0
0
1
0
0
2
0
0
0
1
1
2
1
2
2
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
3
2
1
1
2
2
0
0
0
2
0
0
2
0
0
0
0
1
0
1
1
0
2
1
0
1
0
0
1
0
0
1
0
2
0
2
1
2
1
2
0
0
0
0
0
1
1
1
2
0
0
0
0
0
1
1
0
0
1
0
0
2
2
1
2
2
0
0
2
1
0
0
0
2
1
0
0
2
0
0
1
1
0
0
1
1
1
2
2
0
1
0
0
1
1
0
0
1
1
0
1
0
1
1
0
1
0
0
2
2
1
1
1
1
0
2
0
3
0
1
0
1
1
1
2
1
0
0
1
0
0
1
2
2
2
1
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
2
0
0
2
0
0
2
2
2
1
0
1
1
1
0
0
1
2
0
0
2
0
0
0
0
1
2
0
0
0
1
0
0
0
2
0
0
2
1
2
0
1
1
2
0
2
0
1
2
2
1
0
1
0
0
2
2
0
2
0
0
0
2
0
0
1
2
0
1
0
1
0
1
0
2
0
0
1
0
2
1
0
0
1
0
1
0
1
1
2
1
3
0
0
1
0
2
2
2
0
0
0
1
0
1
0
1
1
1
1
1
1
0
0
0
0
2
2
1
2
1
1
0
0
1
0
0
1
2
1
1
1
1
1
0
1
1
0
0
1
0
1
1
0
1
0
2
2
0
2
0
1
0
2
0
2
0
2
1
0
2
0
0
0
2
0
1
0
0
0
2
1
0
2
0
2
1
3
0
0
2
0
2
0
1
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
2
0
0
1
0
2
1
1
0
2
0
0
0
1
1
1
2
1
1
2
1
0
1
0
1
0
0
1
0
1
5
1
0
0
0
1
0
1
1
0
0
0
1
0
0
16
1
3
1
1
0
0
0
0
2
2
0
1
1
2
2
1
2
1
1
1
2
1
0
1
2
1
1
1
1
0
0
1
2
2
1
0
0
1
0
1
0
0
0
1
2
2
1
0
0
0
1
0
0
0
1
0
1
1
0
2
1
0
2
1
1
0
1
0
1
0
0
0
1
1
2
0
0
0
1
0
0
0
0
0
1
1
0
0
0
2
0
0
0
1
0
0
3
2
2
1
1
0
1
1
0
2
2
0
1
2
2
2
0
0
1
1
0
1
0
0
1
0
3
0
2
0
0
1
1
1
1
1
0
2
1
0
0
2
0
0
0
1
1
0
1
0
1
1
1
2
1
2
1
1
0
0
1
0
0
0
1
1
3
2
0
1
2
2
1
0
0
0
0
1
2
2
0
2
0
2
1
0
1
2
1
2
2
0
1
0
1
0
1
0
0
0
0
1
1
2
2
2
0
1
0
1
1
0
2
1
0
0
0
2
0
1
0
2
1
1
0
0
1
1
0
0
2
2
0
0
0
0
1
2
0
1
2
1
2
0
0
0
0
1
0
0
1
2
0
0
0
0
1
1
0
1
2
1
0
0
0
0
0
1
2
2
0
1
0
0
0
0
1
0
2
1
1
2
0
0
1
1
1
0
0
2
1
2
0
0
1
2
0
0
1
0
2
0
1
0
1
1
0
1
1
2
0
0
0
0
0
0
2
2
0
2
1
1
1
1
0
0
1
2
0
0
0
0
1
0
2
0
1
1
0
0
0
0
1
0
2
0
0
0
0
1
0
2
0
1
0
0
3
0
1
1
1
0
0
0
1
0
1
3
0
0
1
1
0
1
0
1
0
0
0
0
0
1
0
0
1
1
0
0
1
2
1
1
0
0
0
0
0
2
0
2
0
0
0
0
2
2
0
2
0
1
1
2
1
0
1
0
0
2
1
0
0
0
1
0
0
0
2
2
1
2
1
0
1
1
1
1
0
3
0
0
1
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
2
2
1
0
1
1
2
0
1
2
0
0
1
1
2
0
1
2
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
2
0
3
1
0
0
2
1
0
0
2
1
1
2
1
1
1
0
0
0
2
0
6
2
1
2
1
0
0
1
1
0
0
0
0
3
1
0
2
2
0
0
1
2
0
1
0
0
1
0
0
0
0
2
1
0
2
0
0
1
0
0
0
2
0
1
0
0
0
0
1
0
1
1
0
1
1
0
5
0
2
3
2
0
1
0
0
0
0
1
1
1
0
2
0
1
2
1
1
0
0
0
0
2
0
0
0
0
0
0
0
2
2
1
2
0
1
1
1
0
1
0
2
0
2
0
0
1
0
2
0
2
1
1
0
2
0
1
1
1
0
0
1
1
0
0
1
1
2
2
2
3
1
1
1
1
1
1
0
5
1
1
1
2
0
0
2
2
1
0
2
0
1
0
0
0
1
1
0
2
0
0
0
0
2
2
0
1
0
0
1
3
1
2
0
0
2
1
0
2
0
0
0
2
0
1
0
0
0
1
0
0
1
0
1
0
0
1
0
0
2
0
1
0
0
2
1
0
1
1
1
2
1
0
1
0
2
0
0
1
0
0
0
0
0
1
2
0
0
1
0
1
0
0
0
0
1
0
1
1
0
2
0
2
1
0
1
0
0
2
2
1
0
0
1
0
1
0
0
0
2
2
0
0
1
0
2
1
0
1
3
0
2
3
2
2
1
0
1
1
0
1
1
1
0
1
1
1
1
0
0
0
0
0
0
1
0
2
0
0
1
2
0
2
1
0
0
0
0
0
1
1
0
1
0
1
0
1
0
0
0
0
0
2
0
1
2
2
1
0
0
0
0
0
0
1
0
2
2
0
2
1
1
2
2
1
0
1
0
1
1
0
3
0
0
2
0
0
0
1
0
0
0
1
0
2
2
0
0
0
2
0
1
1
0
1
0
0
1
4
0
1
0
0
0
1
2
2
0
1
2
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
2
0
0
0
1
2
0
1
1
1
1
0
0
0
0
0
2
0
6
1
1
0
2
0
2
1
0
2
0
1
0
0
1
0
1
2
1
1
0
2
1
0
1
1
0
1
1
2
0
0
0
1
1
1
0
2
1
1
0
0
1
1
0
0
2
0
2
0
2
1
1
0
0
1
0
1
1
2
2
0
0
0
2
0
0
0
3
2
0
0
0
1
2
0
1
0
1
1
2
2
0
0
0
0
1
0
2
1
1
0
0
3
0
0
1
2
1
0
0
1
1
0
0
0
0
1
2
2
1
0
0
0
2
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
1
2
0
2
1
2
2
0
3
0
2
0
0
1
2
3
1
1
1
1
1
2
1
2
0
0
0
1
1
1
1
2
2
0
0
1
1
2
0
3
0
1
0
0
0
0
1
0
0
1
1
1
0
2
1
1
1
0
0
1
0
2
0
0
0
2
1
1
0
0
0
0
1
0
2
1
0
1
0
0
0
1
1
2
0
0
0
0
0
1
0
1
3
1
2
0
0
0
0
0
1
0
3
0
0
0
0
2
0
1
2
1
2
2
3
0
1
0
1
0
0
0
1
2
0
0
1
2
1
0
0
0
2
2
2
0
1
1
0
1
0
1
0
0
0
0
2
1
0
1
1
1
0
2
1
1
2
0
0
2
1
2
1
2
2
0
1
2
0
1
0
0
0
0
1
2
1
0
1
0
2
0
1
0
0
2
1
0
0
1
0
2
1
0
0
0
0
2
2
0
0
2
0
1
0
0
1
1
0
0
1
0
1
0
2
0
1
0
0
1
1
1
0
2
0
1
2
1
2
0
0
0
1
2
0
2
0
0
1
1
1
1
0
2
1
2
2
0
2
2
0
1
2
0
0
0
1
2
0
1
0
1
1
1
1
2
0
0
0
1
1
1
0
0
1
1
0
2
1
0
2
0
0
0
0
1
0
2
1
0
2
1
0
0
2
0
0
1
1
0
0
3
1
0
0
0
0
2
1
2
1
0
0
1
2
0
1
1
0
0
1
0
0
2
0
1
0
0
0
0
1
2
2
1
0
0
0
2
2
2
2
1
1
2
1
2
1
2
1
2
0
0
0
0
1
0
1
1
0
0
0
1
1
1
0
0
1
0
0
1
0
1
1
0
1
2
0
1
2
1
2
2
2
1
2
1
0
0
0
0
0
0
0
4
2
1
0
0
0
0
2
1
4
0
0
2
1
2
0
0
3
1
0
1
2
0
1
0
0
2
4
1
1
1
0
0
0
0
2
1
0
1
0
1
0
0
1
0
2
0
1
2
1
4
2
1
0
1
1
2
0
0
1
0
0
1
0
2
0
2
0
2
1
0
0
2
0
1
1
0
0
1
1
0
2
2
0
1
0
0
0
0
1
1
0
2
0
0
0
0
1
0
0
0
2
2
1
1
1
1
1
1
1
0
1
0
1
2
1
1
1
2
2
0
0
0
0
1
0
0
0
0
0
1
0
1
1
1
2
0
1
0
2
1
1
0
0
2
0
0
0
0
2
0
0
1
0
1
1
1
0
0
1
0
1
1
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
2
2
0
0
4
1
2
1
2
0
1
1
0
2
1
0
0
0
0
0
2
0
1
1
0
3
0
2
2
0
1
1
0
0
2
0
0
0
2
1
0
0
1
0
0
0
1
0
3
0
0
1
0
2
0
1
2
0
0
0
0
0
0
0
1
0
0
1
0
1
2
0
1
0
0
0
0
0
0
2
1
1
0
0
2
0
1
2
2
1
1
2
0
0
2
0
0
0
0
1
0
0
0
1
2
0
1
1
0
1
1
0
0
0
0
2
1
0
0
0
0
0
0
1
1
2
2
0
0
1
2
1
2
0
0
0
0
0
0
1
0
1
0
0
0
0
1
2
0
0
0
1
2
2
1
0
1
2
0
0
0
2
1
1
1
0
2
0
2
0
1
2
0
1
0
1
2
0
1
0
1
0
1
0
1
0
0
1
0
0
2
2
0
1
1
0
0
0
0
1
2
0
0
1
0
1
2
0
1
0
1
0
0
1
0
2
0
0
1
0
0
1
1
1
0
0
6
1
0
0
0
0
0
0
1
1
3
0
0
2
1
1
0
1
0
2
0
2
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
2
1
1
1
2
0
1
0
2
1
2
0
0
3
1
0
2
0
1
2
1
0
0
2
1
1
1
1
0
1
0
1
0
0
1
0
0
1
2
0
0
0
1
0
0
2
1
0
0
0
0
0
2
2
0
0
0
2
0
0
2
2
1
0
2
0
0
0
0
1
1
0
1
0
2
1
0
1
1
0
0
0
2
1
0
2
4
0
0
3
0
2
1
2
1
2
0
1
0
0
0
0
1
2
0
1
2
0
0
0
0
1
0
1
1
1
1
0
0
0
0
2
1
0
0
0
2
2
2
2
1
0
0
2
1
2
0
0
0
0
1
1
1
0
1
1
1
1
0
2
1
2
0
0
0
1
1
1
0
2
0
3
0
0
2
1
2
0
1
0
1
1
1
1
2
3
0
0
1
1
2
0
2
0
0
2
0
2
0
1
1
0
0
0
2
0
0
2
1
1
1
3
0
0
2
0
0
0
0
2
0
1
1
1
0
0
2
1
2
0
2
0
1
0
1
5
0
0
2
0
0
0
2
1
0
2
0
0
2
1
4
0
0
2
1
1
0
1
2
0
1
0
1
0
1
0
0
1
1
0
1
3
0
1
2
1
0
0
1
1
0
2
2
0
0
2
0
2
0
2
2
2
1
1
1
0
1
0
0
1
0
2
1
2
1
0
2
2
0
0
1
1
0
1
1
1
0
1
2
0
0
2
0
0
0
2
1
0
0
0
0
1
0
0
0
0
1
0
2
0
2
0
1
2
1
0
0
1
0
0
1
1
1
0
2
1
1
0
1
1
1
2
0
2
0
1
0
3
2
1
0
0
1
2
1
0
2
1
0
1
1
0
2
1
1
0
0
0
1
0
1
2
1
0
1
0
0
2
0
0
0
0
1
2
1
0
1
1
0
2
1
0
0
1
1
1
2
0
2
0
0
0
1
0
0
0
0
1
2
0
1
0
0
0
2
0
2
1
0
3
2
1
0
1
0
0
6
0
2
0
0
2
1
0
0
2
1
1
2
0
1
2
0
0
0
2
1
1
0
0
0
0
2
0
0
0
2
0
1
1
0
2
1
0
0
0
0
2
2
2
0
0
0
2
2
0
0
3
2
0
0
1
1
2
0
0
0
0
3
0
1
0
0
2
1
0
1
1
0
1
1
0
0
1
2
0
3
0
0
2
0
0
6
2
2
1
1
0
1
0
0
0
1
0
0
0
0
0
0
2
1
0
0
1
2
1
0
3
0
0
2
1
1
0
0
0
1
2
1
0
1
0
1
0
0
1
0
2
0
0
1
1
0
0
0
1
2
1
1
3
2
1
0
0
1
0
0
0
1
1
0
2
0
3
1
1
1
0
1
0
0
0
0
2
1
1
0
0
0
0
0
1
0
2
1
0
0
0
0
0
1
2
1
2
1
0
1
0
1
2
1
0
2
1
1
2
1
2
0
3
1
1
1
0
1
0
0
0
2
1
0
0
1
2
0
2
1
2
0
2
2
2
0
2
1
0
0
1
0
1
1
0
0
0
1
1
1
2
2
0
1
0
2
2
0
0
0
1
0
2
1
1
0
0
1
1
3
0
0
2
0
1
1
1
0
0
0
1
0
1
1
2
0
0
0
0
0
0
0
1
3
2
1
2
1
0
2
0
1
1
0
1
2
2
1
0
2
2
0
2
2
0
0
0
3
1
1
2
1
1
1
1
0
1
0
1
1
2
0
2
1
1
0
0
2
1
1
3
2
0
0
1
2
1
2
0
0
2
1
0
0
0
1
1
1
0
1
0
1
0
0
1
1
0
1
1
2
0
2
1
2
1
0
0
0
0
2
2
1
2
1
1
0
0
1
1
2
0
1
1
3
1
1
1
0
1
0
1
1
2
1
0
0
3
0
1
0
1
1
1
1
1
1
0
2
1
1
2
1
0
0
0
2
0
1
0
0
2
1
1
0
0
0
2
0
1
0
0
0
0
1
0
1
1
0
2
2
2
1
0
1
1
0
1
2
2
1
0
0
1
2
0
1
1
1
0
1
2
1
0
2
0
1
1
2
0
2
4
1
0
2
1
2
0
2
2
1
2
0
1
0
1
0
0
1
2
3
0
0
0
0
0
1
0
0
1
1
0
2
0
0
1
1
1
2
2
1
2
2
2
2
1
0
2
1
1
1
0
1
2
1
0
1
1
0
1
1
0
0
2
0
0
0
2
1
1
0
1
0
2
2
0
1
2
2
2
2
1
0
0
0
0
1
0
2
1
0
1
0
2
0
1
0
1
0
0
1
2
2
1
0
0
0
0
0
1
2
2
1
2
1
0
0
1
0
1
0
0
0
0
0
1
0
1
2
0
2
2
1
0
0
0
2
1
0
1
1
0
0
2
0
2
1
1
0
1
0
0
0
0
2
2
1
0
0
0
0
2
2
0
0
1
0
2
1
2
2
2
1
1
0
2
1
0
1
2
0
0
0
1
2
2
2
0
1
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
1
1
1
0
0
1
2
0
1
2
0
0
0
0
1
0
0
0
0
2
2
3
7
0
1
0
0
0
0
0
1
2
1
0
0
0
1
0
0
1
3
0
0
0
0
2
4
0
2
0
1
1
0
0
0
0
1
1
0
3
1
2
1
2
0
1
2
1
0
0
0
0
1
0
0
0
2
1
0
0
0
0
1
1
1
1
1
0
2
2
1
2
1
1
1
0
0
0
1
1
0
2
0
2
0
2
0
1
1
1
1
1
1
1
1
0
0
1
0
2
1
0
5
0
1
0
0
2
0
1
2
2
1
1
2
0
0
0
0
0
1
0
2
0
0
1
5
0
2
0
0
0
1
1
0
0
2
0
0
0
1
0
2
0
0
0
0
0
1
3
1
0
0
1
0
0
0
1
2
2
0
0
1
1
0
2
0
1
1
2
1
1
2
1
2
1
2
0
0
1
0
2
0
0
0
0
0
0
0
1
2
1
0
0
2
0
1
1
1
1
0
1
0
0
0
1
0
2
1
0
0
0
1
1
2
0
1
0
0
0
2
2
0
2
1
0
0
0
2
1
0
1
0
0
2
1
0
2
0
1
2
1
2
0
1
2
2
2
0
0
2
0
0
2
1
1
1
0
4
1
0
0
2
0
0
0
1
0
2
2
1
1
0
0
1
1
2
0
0
0
3
0
0
2
0
1
1
2
0
1
1
2
0
2
8
3
2
0
2
1
4
1
2
2
0
0
2
0
0
1
0
0
0
1
2
1
2
1
2
0
0
2
2
1
0
0
0
2
0
0
1
1
1
0
0
1
1
2
1
1
2
0
0
0
0
2
1
2
1
1
2
0
0
1
1
1
0
1
3
1
1
1
1
0
0
0
0
1
0
1
0
2
0
1
1
1
1
0
1
0
1
2
1
0
1
0
2
0
1
0
0
1
2
1
0
0
2
2
0
0
0
2
1
1
2
0
1
0
0
1
1
0
0
2
1
1
1
0
0
2
0
1
2
1
1
0
2
0
2
2
2
0
1
0
2
2
1
1
2
1
0
2
2
1
1
0
2
2
0
1
0
0
2
0
0
0
1
0
1
2
2
1
0
0
1
0
1
0
0
2
2
0
0
0
0
2
2
3
0
0
1
1
1
1
0
2
0
0
2
1
0
1
2
0
0
0
1
0
1
1
2
0
1
1
0
0
1
0
2
1
0
2
0
1
0
0
1
0
1
1
0
0
2
0
0
2
0
1
0
2
1
3
3
2
1
2
2
1
1
1
0
2
0
1
0
0
0
0
1
1
1
0
2
1
0
1
1
0
0
0
1
2
0
0
2
1
1
0
1
0
1
0
0
0
0
1
2
1
0
0
0
0
0
2
0
0
0
0
1
0
0
1
1
1
2
1
1
0
1
0
0
1
0
1
0
0
1
1
0
0
1
0
0
2
1
0
0
0
2
0
1
0
0
0
0
2
0
1
2
0
0
1
0
0
0
1
0
2
0
0
0
0
0
2
0
0
1
0
2
1
1
1
1
0
0
0
3
1
1
1
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
1
1
1
0
1
2
1
2
1
0
1
2
1
1
0
0
2
2
1
5
0
2
1
0
0
0
1
0
0
0
0
2
1
0
0
0
0
2
2
1
2
2
0
1
1
2
0
0
2
1
1
0
2
1
2
0
2
1
0
1
1
0
0
1
2
0
0
2
2
1
2
0
1
2
1
2
1
2
1
0
0
0
0
0
2
1
0
0
0
0
2
0
1
1
2
0
0
2
0
1
0
1
2
1
1
2
1
0
1
0
0
1
0
2
1
2
1
2
1
2
2
1
2
0
0
2
2
0
2
0
1
0
0
2
1
0
0
0
0
1
1
0
1
2
2
0
0
4
2
1
1
1
2
0
1
0
0
1
3
2
0
2
2
2
1
0
2
0
0
1
0
0
1
0
0
1
0
2
2
0
1
0
1
0
3
1
0
1
2
1
2
2
0
2
1
1
1
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
1
3
11
1
0
0
0
2
0
0
2
1
0
0
1
0
2
1
2
0
0
0
1
1
1
0
0
1
1
2
2
0
0
0
1
2
0
1
1
1
2
0
0
0
0
2
0
0
1
2
0
1
1
0
1
0
0
1
0
0
0
0
2
2
0
1
0
0
1
0
2
1
1
0
0
0
1
2
2
1
2
0
0
0
0
1
5
2
2
1
0
0
1
0
0
0
0
2
1
0
1
0
0
2
0
0
2
2
1
1
0
0
1
0
0
1
0
1
0
0
0
2
1
3
1
1
0
0
0
1
0
1
2
0
0
0
0
0
2
1
0
1
0
1
0
2
0
1
0
1
3
1
0
2
0
2
1
2
0
0
0
1
0
2
1
0
1
1
1
0
0
2
0
2
1
0
0
0
2
0
1
2
0
0
0
0
2
1
1
0
1
0
1
3
3
0
1
0
0
1
0
1
0
0
0
0
2
2
2
2
3
1
2
2
1
1
2
0
2
0
2
1
1
1
1
1
2
1
0
1
1
0
2
1
1
2
0
0
0
0
0
0
3
3
1
1
0
1
0
0
0
0
0
0
0
3
1
0
1
1
2
0
1
1
0
0
1
2
0
0
2
1
0
2
1
1
0
1
0
1
1
1
1
1
0
1
2
1
1
0
1
1
0
1
0
0
0
0
0
2
0
3
1
2
0
2
1
2
2
1
1
0
0
1
1
0
0
1
2
1
2
2
3
1
1
1
1
0
0
2
1
2
0
0
1
1
1
1
7
1
0
0
0
1
0
0
1
0
1
0
0
0
2
1
1
0
0
0
0
2
0
2
1
0
0
1
0
2
0
1
0
1
0
2
2
1
0
0
1
0
1
2
0
1
2
1
0
0
0
3
0
2
0
1
0
0
0
2
1
0
1
1
0
0
0
0
0
2
0
2
0
2
1
0
1
0
2
1
1
0
0
0
0
0
2
0
1
1
0
1
0
0
0
0
1
1
2
1
0
1
0
0
0
1
0
0
0
0
0
2
1
2
0
0
0
2
0
2
1
0
2
1
0
0
2
2
0
0
0
0
0
1
0
2
0
0
1
0
2
0
0
2
0
0
1
0
0
1
1
0
1
0
2
1
0
0
0
2
1
0
0
1
1
0
2
0
1
1
0
1
1
0
0
1
1
0
0
0
0
0
0
1
0
2
0
1
0
0
2
0
2
2
1
2
2
1
0
0
1
0
0
0
0
2
0
0
2
2
1
0
0
0
1
1
1
2
1
1
0
0
0
0
1
0
1
0
1
1
0
2
0
0
0
1
0
0
0
0
0
1
1
3
0
1
0
1
0
0
2
1
0
0
0
0
0
2
2
0
2
1
1
2
0
2
1
0
2
1
0
0
0
1
0
0
0
2
1
0
0
0
4
0
0
0
1
0
1
1
3
0
0
0
1
1
0
1
0
1
0
0
0
2
0
0
0
1
2
2
0
2
0
1
0
0
2
2
1
2
0
1
1
2
0
0
2
0
0
2
0
2
1
0
0
0
0
0
0
1
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
1
0
1
1
0
1
2
0
0
1
1
0
1
2
0
1
0
0
2
0
2
2
2
0
0
2
1
2
2
1
1
1
1
0
0
1
0
0
2
0
0
1
1
1
0
1
0
2
2
1
1
1
2
0
1
0
0
1
0
1
1
2
2
0
1
1
1
0
0
1
1
1
1
0
0
1
1
0
1
0
1
0
0
0
2
0
1
2
0
1
0
1
0
0
1
2
0
1
2
1
0
0
0
2
0
1
0
2
1
1
0
1
0
0
1
0
0
0
0
0
1
2
1
0
0
0
0
2
0
2
0
3
0
0
0
0
0
0
0
0
1
1
0
1
3
0
2
1
1
0
1
0
0
0
0
0
0
0
2
4
0
0
0
0
1
0
4
0
1
1
1
0
2
0
2
0
2
0
1
0
1
2
2
2
0
2
0
2
1
0
2
0
2
0
0
1
0
0
1
0
1
0
0
0
1
1
2
0
2
0
0
2
2
0
0
0
2
2
1
1
2
1
0
0
2
1
1
1
2
3
2
0
0
2
1
2
1
0
4
1
1
1
0
0
0
2
0
1
0
1
2
0
1
2
0
1
1
0
2
0
0
2
0
1
0
2
0
0
1
0
0
3
1
0
2
0
0
2
2
1
1
0
0
2
2
0
0
2
1
0
2
2
0
0
0
0
2
1
1
0
2
0
0
2
0
2
1
0
0
0
2
2
2
0
1
1
0
0
0
2
0
1
0
2
2
0
0
8
0
1
0
0
2
1
0
0
0
0
0
0
0
0
1
1
0
2
0
1
1
1
0
1
2
0
1
0
2
0
1
1
1
1
2
1
0
1
0
0
0
2
1
2
2
0
3
0
0
1
1
1
1
1
0
2
0
0
0
1
2
0
0
1
3
0
2
2
0
2
1
1
0
2
0
1
0
0
2
0
0
1
2
0
0
1
0
2
0
2
0
1
1
1
0
0
2
0
2
0
2
0
1
0
1
1
0
1
0
1
0
1
0
0
1
0
0
2
1
2
0
2
0
0
1
1
0
0
1
0
0
1
0
2
2
0
1
0
0
0
0
2
0
0
2
0
0
1
1
1
2
1
2
1
1
2
0
0
2
2
0
0
1
2
1
3
1
1
0
2
0
1
1
2
0
0
0
2
1
1
0
1
0
1
0
1
0
2
2
1
0
2
1
0
0
0
2
2
1
1
1
1
1
1
1
1
1
0
0
2
0
0
2
0
0
2
0
1
1
1
0
0
0
0
1
2
0
1
0
2
0
1
0
2
0
1
1
2
0
2
2
0
0
2
0
1
1
0
0
1
1
0
2
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
1
0
0
0
1
0
0
1
0
1
1
0
0
0
1
2
0
1
1
1
0
0
0
2
0
1
1
1
0
0
0
2
2
1
1
3
0
0
2
1
0
2
1
1
0
2
0
0
2
0
0
2
1
2
0
1
0
2
0
0
0
0
0
1
1
0
0
0
0
1
1
1
0
1
1
1
0
2
1
0
0
0
0
2
2
0
1
0
0
1
0
1
1
0
1
2
0
1
2
2
1
1
0
0
1
1
0
0
0
2
0
1
0
0
0
0
1
1
2
2
0
3
0
2
0
1
1
1
0
0
0
3
1
0
1
0
2
0
0
2
0
1
0
1
4
1
0
0
0
1
0
0
0
0
0
0
1
1
2
1
1
2
0
0
0
0
0
1
0
2
0
2
0
0
0
2
0
1
0
0
0
0
2
0
2
0
1
2
0
2
2
2
0
0
1
0
1
1
1
0
0
1
2
0
0
0
2
0
1
3
0
0
1
0
1
2
0
0
0
3
0
1
1
1
2
0
1
2
0
1
0
2
1
1
2
1
0
0
1
2
0
2
1
1
2
2
0
0
0
1
1
0
2
2
1
1
0
0
0
3
0
0
1
4
2
0
0
2
2
1
1
2
0
0
0
1
2
0
0
1
0
2
2
0
0
0
0
2
0
1
0
1
1
1
0
0
1
0
2
0
1
0
1
0
0
1
1
0
1
0
1
0
0
0
0
0
1
0
2
0
1
1
2
0
0
0
1
0
0
1
0
1
0
2
0
0
1
2
0
0
0
3
1
1
0
1
2
0
2
0
1
0
1
2
0
2
1
0
2
1
1
0
1
0
1
0
1
1
1
1
1
1
0
1
0
2
1
0
1
0
0
1
1
0
0
2
0
0
0
0
1
1
1
2
3
0
2
0
2
2
1
1
2
0
2
0
1
0
0
0
10
0
0
2
0
2
0
1
2
1
1
1
0
2
3
0
1
0
0
1
0
2
2
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
3
0
1
1
0
2
0
1
1
1
2
1
3
0
0
1
2
0
0
0
1
0
1
1
2
2
0
12
1
2
0
1
0
3
0
2
2
2
0
0
0
0
1
0
1
0
1
0
0
1
2
0
0
0
1
0
0
1
2
1
1
1
1
1
1
0
1
1
0
0
1
1
2
1
0
2
1
1
3
1
1
2
2
0
1
0
1
0
0
2
1
0
1
0
1
1
0
2
0
1
2
3
2
0
0
0
2
2
2
1
0
0
1
0
0
1
1
2
2
2
1
1
2
0
1
0
1
1
0
2
0
0
0
2
0
2
2
0
0
2
0
2
0
2
1
1
0
0
2
0
0
1
0
0
1
0
0
0
2
2
0
0
1
2
1
0
2
0
2
0
0
0
0
2
0
1
2
0
1
0
0
1
0
0
1
0
1
2
1
0
0
0
3
0
0
1
0
0
1
3
1
1
1
0
1
0
0
2
0
1
1
0
1
0
0
2
2
2
0
0
1
0
0
0
0
1
2
2
0
2
0
1
0
0
0
0
2
1
2
0
0
1
0
0
0
0
0
0
0
2
1
2
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
1
1
0
2
1
2
0
2
2
0
0
1
2
2
1
0
1
0
0
1
2
2
2
1
2
2
2
1
0
1
0
1
0
0
1
2
0
0
1
1
0
0
0
2
0
1
0
0
0
0
0
1
0
1
0
1
1
0
2
0
1
0
0
1
0
1
1
2
1
0
2
1
1
0
1
0
0
0
0
0
0
0
0
1
1
1
0
1
1
1
0
1
1
1
1
1
0
2
0
0
0
2
1
1
1
0
0
1
0
2
2
2
0
1
1
1
0
0
0
1
1
1
1
0
1
1
0
0
1
1
0
2
0
1
1
0
0
0
1
2
1
3
1
0
0
0
0
6
0
2
1
1
0
1
2
1
1
2
1
1
0
2
0
2
1
1
0
1
0
0
0
0
1
0
0
1
2
2
2
0
0
1
0
1
0
2
2
0
0
1
0
0
1
1
0
0
0
0
3
1
2
0
1
2
0
2
2
0
0
0
0
0
2
0
0
0
0
0
3
1
2
1
0
1
0
0
0
2
0
0
2
1
0
1
0
2
1
2
0
0
0
0
1
0
0
2
2
2
0
0
0
1
1
0
1
0
1
1
0
0
0
1
2
2
0
1
2
1
0
2
0
0
1
0
2
0
2
1
0
2
1
2
0
0
1
0
2
0
2
1
2
2
2
1
1
1
0
2
0
0
1
1
0
0
0
1
0
3
1
1
1
0
1
0
0
1
1
0
2
1
0
1
1
0
0
0
2
0
0
2
0
2
2
0
3
2
0
0
1
0
0
1
0
0
0
0
0
1
1
1
1
1
1
1
1
1
0
0
0
1
0
0
1
1
1
1
0
2
0
3
0
2
0
1
0
0
1
2
1
0
0
1
0
0
1
0
1
0
0
0
1
2
0
0
0
1
0
1
1
1
1
1
0
0
1
2
0
1
2
0
1
0
1
0
1
0
0
2
0
0
0
0
2
2
1
1
1
0
1
0
3
0
2
0
0
1
2
2
1
3
0
2
1
1
1
1
0
1
0
0
0
1
1
2
0
0
0
1
0
2
0
0
0
1
1
0
2
0
0
2
0
0
1
2
0
0
0
0
2
0
2
1
0
0
2
0
0
2
2
1
0
0
2
2
1
0
1
0
1
0
0
1
0
0
1
2
2
0
1
3
2
5
1
0
0
0
0
0
0
4
0
0
1
0
2
0
1
1
0
1
0
0
1
1
1
0
0
0
0
0
1
1
0
1
0
2
1
1
1
1
1
2
1
1
0
0
2
0
0
2
0
0
1
0
0
1
1
0
2
2
0
0
1
0
1
2
2
2
0
1
0
0
1
2
0
2
0
2
1
0
2
0
0
1
2
1
1
1
2
1
1
1
1
1
0
0
1
2
1
2
0
0
1
0
1
1
0
0
0
3
1
1
1
1
0
2
1
0
0
0
1
1
2
0
1
0
0
0
1
2
0
2
0
0
0
0
0
0
1
0
0
0
0
2
1
0
1
2
2
1
0
1
2
0
0
0
2
0
2
1
0
2
1
1
0
0
0
1
0
2
0
0
0
0
1
2
2
0
2
0
0
2
2
0
0
0
1
2
2
0
1
0
2
1
2
0
0
1
0
0
1
0
0
1
0
2
1
0
0
2
2
0
1
0
1
1
0
1
0
2
0
0
2
0
0
1
0
1
1
1
0
2
3
2
1
2
1
0
1
2
1
0
2
2
1
2
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
1
1
2
0
0
1
1
0
0
2
2
0
2
0
0
0
0
0
2
2
1
3
2
1
1
0
2
1
1
2
0
1
1
1
1
1
0
0
1
1
2
0
0
1
0
0
0
1
1
2
1
0
0
2
1
0
0
0
0
0
0
2
1
2
0
0
0
2
0
2
2
0
1
2
0
2
0
1
0
2
0
0
0
0
1
1
0
0
2
0
1
1
2
0
0
1
1
1
0
1
1
0
0
0
0
0
0
1
0
0
2
0
5
0
2
0
2
0
0
0
1
0
0
1
1
0
0
0
1
2
0
0
1
1
1
0
1
2
0
0
2
0
0
0
0
0
1
2
0
0
2
1
0
0
2
0
1
1
0
0
2
1
0
0
1
0
0
1
3
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
1
0
2
1
0
1
0
0
1
0
2
0
0
1
1
0
0
1
0
0
1
2
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
1
1
0
1
1
2
2
1
0
1
1
0
2
1
1
1
0
1
0
0
0
1
1
2
0
1
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
2
1
0
1
1
1
0
1
0
1
0
0
1
2
1
0
1
2
0
1
1
0
2
0
0
2
0
2
2
0
0
0
0
1
1
2
2
1
2
2
1
1
1
1
1
2
2
0
1
0
0
2
0
2
2
2
0
0
1
2
0
0
1
1
2
0
2
2
1
0
0
0
2
1
0
2
0
2
1
1
0
0
1
1
1
1
2
2
6
1
1
1
1
0
1
0
0
1
0
0
0
0
0
1
1
1
0
1
2
1
1
0
0
1
0
1
4
0
0
1
1
0
3
1
2
0
1
1
1
1
1
0
1
3
1
0
1
0
0
1
0
0
1
0
1
1
3
0
2
1
1
1
0
0
2
2
0
1
0
2
0
1
0
0
2
1
0
1
0
0
1
1
1
0
1
0
2
2
2
0
0
1
1
0
0
1
1
1
1
2
0
0
0
0
0
0
2
2
1
1
0
0
2
0
0
0
1
0
2
2
2
0
0
1
1
2
1
2
0
0
4
2
2
1
1
2
0
1
1
1
0
1
0
0
0
1
2
0
1
0
2
0
1
0
1
0
0
1
0
1
2
1
2
0
0
0
0
1
1
1
2
0
2
1
1
3
0
0
1
0
2
0
2
0
0
2
1
0
1
0
1
1
0
3
1
0
0
0
1
1
0
0
2
0
0
0
1
2
0
1
0
1
0
0
0
1
1
0
0
2
2
1
0
2
2
2
2
1
0
1
1
2
1
2
0
2
0
0
2
0
0
0
2
2
1
2
3
1
0
2
2
0
1
0
0
2
0
0
2
0
2
1
1
0
0
0
0
2
1
2
2
0
0
0
0
1
2
1
1
1
0
0
0
0
0
1
0
2
0
1
0
1
1
1
0
2
0
2
0
1
0
2
1
0
0
0
1
1
0
2
1
1
0
0
0
1
0
0
1
2
0
0
3
0
0
0
1
0
1
1
1
2
1
2
2
2
0
0
0
1
0
0
1
1
1
1
2
2
2
1
2
1
2
0
0
0
1
0
0
1
0
2
2
3
0
0
0
0
0
2
1
1
2
1
0
0
2
0
1
2
1
0
0
2
1
0
1
0
0
2
1
2
1
2
0
1
0
1
1
1
1
1
1
0
2
1
2
4
0
0
1
1
2
0
2
1
2
0
2
0
0
0
0
0
2
0
1
0
1
2
2
3
1
0
1
2
0
1
2
1
2
2
2
0
1
1
0
0
0
1
1
0
2
0
0
1
2
1
1
0
0
1
1
1
2
0
0
1
0
0
2
2
0
2
1
0
0
0
1
2
2
5
1
2
3
0
0
0
1
0
2
0
2
0
1
1
2
0
1
1
1
1
1
2
0
1
2
1
0
1
0
4
1
0
2
0
1
0
2
1
0
2
0
0
2
0
2
1
0
1
1
1
0
0
1
0
1
1
1
0
0
0
1
2
0
1
1
0
2
1
2
0
0
0
0
0
1
0
0
1
0
1
0
0
1
1
1
1
1
1
0
0
1
1
0
0
1
1
2
0
1
0
1
0
1
0
0
0
1
2
0
0
0
0
0
0
1
1
0
0
2
1
2
1
1
1
0
1
0
0
1
3
0
2
1
0
0
1
2
1
0
2
1
2
2
2
0
0
0
1
1
3
0
0
0
0
0
1
2
0
0
1
0
0
2
0
1
2
0
0
0
0
1
2
0
0
0
2
0
0
1
1
1
0
1
3
0
2
0
1
0
0
0
0
0
1
2
0
1
0
2
1
0
0
1
1
2
0
0
1
1
0
2
1
0
1
1
0
2
1
0
0
1
0
2
0
0
2
0
2
1
0
1
3
0
2
2
0
1
0
0
0
2
0
1
0
1
0
0
0
1
1
1
2
0
2
0
1
1
0
0
0
1
0
3
1
0
2
2
0
2
0
0
1
0
1
0
2
1
1
2
0
0
1
0
0
2
2
1
1
1
1
1
0
0
0
0
0
2
0
1
0
0
0
0
2
1
1
0
0
2
1
0
1
1
1
0
2
2
0
0
1
1
0
0
1
0
0
0
0
1
0
0
1
1
0
0
1
0
1
1
1
0
0
1
0
2
2
3
0
1
0
5
0
1
0
2
0
0
1
1
0
1
0
2
0
0
0
1
0
1
6
0
1
0
1
0
2
0
0
1
1
1
0
0
0
0
0
1
0
1
1
0
0
2
0
1
1
0
0
0
3
2
0
0
2
1
2
0
0
2
0
1
0
2
2
0
1
1
1
2
2
2
1
0
1
0
2
1
1
0
1
1
1
2
1
0
0
1
4
0
2
0
0
1
2
2
1
0
2
0
0
1
0
2
0
1
0
0
2
1
0
0
1
0
0
2
1
2
0
0
1
2
2
1
0
0
0
0
1
3
1
0
1
2
1
2
0
1
1
0
0
0
2
1
2
0
2
0
0
1
0
1
1
1
1
1
1
2
1
0
1
2
0
2
0
1
1
0
1
1
0
1
0
1
1
1
1
0
3
0
1
0
0
2
0
1
0
1
0
0
1
1
0
1
1
0
1
1
0
2
0
0
1
1
1
1
2
1
0
2
2
0
0
0
0
1
2
1
0
2
2
0
0
0
0
0
1
0
1
2
2
0
1
0
1
1
0
0
0
2
0
0
1
1
0
1
2
1
1
2
1
1
1
1
0
0
1
2
2
2
0
1
0
1
1
1
0
0
0
2
1
2
0
0
2
0
2
2
1
2
1
0
1
1
0
1
0
0
2
1
2
0
2
0
2
1
2
0
0
1
0
1
1
2
0
0
0
2
1
0
2
0
0
2
2
0
0
0
0
1
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
2
2
0
1
1
0
2
1
0
0
0
1
2
1
3
0
1
1
1
0
1
2
0
1
2
0
0
0
1
0
0
1
0
1
1
2
0
0
1
1
2
1
1
2
0
2
0
1
3
0
0
0
0
1
0
0
0
2
0
2
1
0
0
0
1
0
2
1
1
0
1
0
0
2
2
0
0
2
2
2
0
2
2
7
0
2
0
0
0
0
0
0
0
0
3
2
2
1
0
1
0
0
0
0
2
0
2
0
2
1
2
4
0
1
2
2
2
0
1
2
1
2
1
1
1
1
0
1
4
2
0
1
1
1
0
1
0
2
0
0
2
0
0
0
0
2
1
2
0
1
1
0
0
0
2
0
2
2
2
1
0
0
0
2
0
0
1
0
2
1
1
1
1
2
1
0
1
1
2
2
2
2
0
0
0
2
0
1
0
0
4
1
1
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
2
0
0
0
2
2
0
1
0
0
0
0
2
1
0
0
0
1
1
0
0
1
0
0
0
2
2
0
1
0
0
2
0
0
1
0
1
1
2
0
1
0
2
0
2
1
2
2
1
0
0
2
0
0
0
0
0
0
1
2
1
0
1
2
1
1
0
0
0
2
0
1
1
2
0
0
0
0
2
0
2
0
0
1
0
1
0
0
0
1
1
0
0
0
1
1
1
0
0
0
0
2
0
0
1
1
0
0
0
0
1
1
0
0
0
1
0
2
2
1
1
1
2
0
2
2
1
0
0
0
0
0
0
1
2
0
2
1
1
2
1
2
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
2
1
0
1
0
1
0
1
0
0
0
1
0
0
0
1
0
1
0
0
2
0
0
2
0
2
0
2
2
0
0
1
0
1
1
1
0
0
1
0
0
2
0
1
1
0
2
1
2
2
2
0
1
0
2
1
2
0
0
0
2
0
0
1
1
0
3
0
0
1
0
1
0
1
2
0
0
1
0
0
0
1
0
0
0
2
1
0
0
0
1
1
0
1
0
0
0
3
1
1
0
2
2
1
0
0
0
2
2
2
0
0
0
0
0
0
1
1
0
0
1
1
0
1
0
1
0
0
2
2
0
1
0
1
0
0
0
0
1
0
1
1
0
1
0
0
0
2
2
1
2
0
0
1
0
1
1
0
2
2
2
2
1
0
2
0
1
0
0
1
2
1
1
0
0
0
2
2
0
0
1
0
1
0
0
1
2
2
1
0
1
2
2
2
2
1
0
1
0
0
0
0
0
1
2
1
0
1
1
1
0
2
2
0
1
1
1
0
0
2
0
0
0
0
0
2
0
2
1
0
1
2
0
0
0
2
0
2
2
1
1
0
0
0
1
1
0
2
0
0
0
2
1
2
2
1
0
0
1
1
0
0
2
0
0
1
0
2
0
0
1
0
1
0
2
1
0
1
1
1
0
1
2
1
0
0
0
0
0
4
0
1
1
0
2
2
1
1
0
0
1
0
0
1
0
2
2
0
1
0
0
2
1
4
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
2
1
1
1
0
0
2
0
2
1
0
1
0
0
1
4
1
0
1
2
0
3
1
0
1
1
0
0
0
2
1
0
1
1
0
1
0
2
1
1
1
0
1
1
2
2
1
0
0
2
0
1
0
2
2
1
2
0
0
0
0
0
2
1
2
0
1
0
1
2
0
4
1
0
0
0
2
2
0
1
2
1
1
0
0
2
0
1
4
2
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
2
0
0
1
1
0
0
1
0
0
2
2
0
0
1
0
0
1
1
2
0
0
0
0
0
1
2
0
0
2
0
1
0
1
1
0
0
1
2
1
2
1
1
0
0
1
1
0
0
1
2
2
1
0
1
2
0
1
0
1
2
1
1
1
2
1
0
1
0
2
2
0
2
2
2
0
1
0
1
0
1
2
0
1
2
0
1
3
0
2
0
0
0
1
1
0
0
1
0
0
0
0
2
2
1
2
1
0
0
0
0
1
0
0
1
0
0
1
0
0
3
2
0
0
1
1
0
0
1
2
1
0
1
1
0
0
0
2
2
0
2
0
1
1
0
2
1
1
0
0
0
1
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
2
1
1
0
1
0
1
0
0
4
0
0
1
0
1
0
1
1
0
0
0
1
2
0
0
2
1
0
1
0
0
0
2
0
0
0
2
1
1
2
0
1
1
2
1
2
0
2
1
1
0
2
1
0
0
1
2
1
2
1
0
0
1
2
0
2
0
2
2
1
0
0
1
1
0
2
0
3
1
0
0
2
0
0
1
0
1
1
0
1
0
0
1
2
0
1
0
0
1
1
0
0
1
2
0
0
1
0
2
0
2
0
1
1
1
0
1
0
0
1
1
0
3
0
1
2
0
0
0
1
0
1
0
1
0
2
1
0
1
2
2
0
3
1
0
1
1
0
2
1
0
0
0
0
0
1
2
0
0
0
2
0
1
1
1
1
0
1
0
1
0
1
0
0
2
5
0
0
0
0
2
1
0
0
0
0
1
0
1
0
1
0
2
0
0
2
1
7
0
1
0
2
1
0
1
0
1
0
1
0
0
0
0
1
0
0
4
0
2
1
0
2
0
0
2
0
0
1
0
2
0
1
2
1
0
0
1
0
0
0
1
0
0
0
1
1
1
0
1
0
0
1
1
0
1
0
1
1
0
1
0
1
1
1
11
0
1
1
2
0
1
2
0
2
0
0
0
1
1
1
0
1
0
1
2
2
0
3
0
1
1
0
1
1
0
2
0
1
0
1
1
0
2
0
2
0
0
2
1
0
0
2
3
0
0
1
1
2
0
1
0
0
2
0
0
0
0
2
0
0
1
0
0
3
1
0
1
3
1
2
1
0
0
1
0
0
0
0
2
2
2
2
2
1
0
1
2
0
1
2
1
2
0
0
0
0
0
1
1
1
1
0
1
2
1
0
0
1
1
0
1
0
0
2
0
2
0
0
1
0
2
0
1
0
1
1
2
2
0
0
1
0
0
2
1
1
1
0
0
1
1
2
0
0
1
3
2
1
1
0
0
0
0
0
1
2
0
1
1
1
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
1
1
2
0
2
1
1
1
0
1
3
1
0
0
1
1
2
0
1
3
2
0
1
0
1
3
1
0
0
2
0
1
1
0
0
0
1
1
0
1
0
1
2
2
2
1
0
0
1
0
3
0
0
0
1
0
1
0
0
0
1
0
1
1
2
2
2
0
1
0
0
1
0
0
0
2
2
1
1
1
2
1
1
1
0
1
1
0
0
1
0
0
0
1
1
0
1
0
2
0
1
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
3
0
1
1
2
2
1
0
0
0
0
0
1
2
1
2
2
0
1
0
1
0
0
2
1
2
0
1
1
0
0
2
1
1
0
0
1
1
1
1
0
0
0
2
0
0
0
1
0
2
1
2
0
1
1
1
1
0
1
0
2
1
1
0
0
2
1
0
1
0
0
1
1
1
0
0
0
0
0
1
0
0
0
1
0
2
1
0
0
0
0
1
1
0
0
1
1
1
0
0
2
0
0
1
0
1
0
0
0
1
2
1
0
0
0
0
0
2
0
1
2
3
0
1
1
0
0
0
0
1
0
1
0
2
0
2
2
2
0
0
0
2
0
1
1
1
0
1
0
1
0
1
2
0
0
0
0
0
0
0
1
2
0
0
0
0
3
1
1
2
2
2
0
1
2
0
1
0
0
2
1
1
0
0
0
0
1
2
0
0
0
1
2
1
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
1
1
0
1
0
2
0
1
1
0
0
0
0
0
0
0
0
1
1
0
2
0
0
1
0
0
0
0
2
0
1
0
1
1
2
0
0
0
1
2
0
1
1
1
1
0
0
0
1
2
2
1
0
0
2
0
2
1
0
0
0
1
0
0
2
0
0
0
1
1
2
1
2
0
1
1
0
0
1
1
2
1
2
1
0
1
1
2
1
2
1
0
0
1
1
0
1
1
0
0
3
0
0
1
1
2
0
0
1
0
1
1
1
0
2
2
0
0
0
2
2
0
1
1
6
1
0
2
0
1
1
0
1
1
4
1
0
0
4
1
0
0
2
0
1
0
0
2
0
2
2
1
0
0
0
1
2
1
0
0
0
0
1
0
2
0
1
0
1
0
0
2
0
18
0
0
0
0
0
0
1
0
1
2
1
0
0
0
0
2
1
2
0
8
0
0
0
0
1
0
2
0
1
1
1
0
1
0
1
0
1
1
1
0
0
0
1
0
0
0
0
1
1
1
1
1
1
1
1
2
2
0
2
0
0
0
2
4
1
0
2
0
1
0
0
1
0
2
2
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
1
1
0
2
0
0
2
0
0
1
1
0
0
0
0
0
0
2
2
0
0
0
1
0
1
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
2
0
0
1
0
2
1
0
0
0
0
0
3
1
0
0
0
2
2
1
1
1
1
0
0
2
0
1
0
0
0
0
0
2
2
1
2
0
2
1
1
0
0
0
1
2
0
1
2
1
2
0
0
0
2
1
0
0
0
1
1
3
0
0
1
1
0
1
1
0
0
0
2
0
0
2
2
0
1
0
1
0
2
1
0
1
0
1
0
1
0
0
2
1
0
2
1
2
0
0
0
2
0
1
2
0
0
0
0
0
0
1
1
3
0
1
1
0
0
1
1
1
0
2
1
0
1
0
0
1
0
1
0
2
0
0
1
0
0
0
1
1
0
0
1
0
1
1
3
1
2
2
1
1
0
0
0
1
2
0
1
0
0
1
0
2
2
0
4
0
0
0
0
0
1
2
2
1
0
0
0
0
1
2
1
2
0
2
0
2
0
1
1
1
1
1
1
1
0
1
1
1
2
0
0
0
0
2
1
0
1
1
1
1
2
1
1
1
0
1
1
0
0
0
0
1
2
2
2
0
0
2
1
1
0
0
0
2
1
0
0
2
2
0
2
2
2
0
0
1
0
4
1
1
2
0
0
2
0
0
2
0
0
2
2
2
0
1
0
1
1
2
1
0
1
0
0
0
1
0
1
1
1
1
0
0
1
0
0
1
2
0
1
0
0
0
0
2
0
0
1
1
0
0
0
2
1
2
1
1
1
0
0
1
2
1
1
0
0
0
0
1
0
1
1
1
0
0
1
0
0
0
2
0
1
0
2
0
0
0
1
0
0
1
2
1
1
1
2
1
2
0
0
0
2
1
0
0
1
0
2
1
1
0
0
0
1
1
1
0
0
1
1
2
0
2
1
1
0
0
2
0
1
0
1
0
0
2
2
2
0
2
0
0
0
0
0
0
2
0
1
0
0
1
0
2
0
1
0
1
1
6
1
1
0
2
2
0
1
0
1
1
1
0
2
0
0
0
2
0
1
0
1
1
2
1
2
0
0
0
0
2
1
3
0
1
0
2
1
0
0
2
2
0
0
0
1
2
2
2
0
0
1
1
1
0
1
0
0
0
2
1
1
2
1
1
0
0
2
1
1
4
0
0
1
1
0
1
2
1
1
4
1
0
2
1
0
1
0
1
1
0
2
0
1
3
2
0
0
2
1
0
0
0
2
0
0
2
0
1
0
0
2
0
0
0
1
1
1
0
1
0
2
0
1
0
1
0
0
1
0
0
0
0
0
1
0
1
1
1
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
1
2
1
0
0
1
1
1
2
2
2
1
0
1
1
2
1
0
2
1
2
1
1
2
1
0
0
2
1
1
1
0
2
0
0
0
2
1
0
0
2
0
1
1
0
1
0
0
0
1
1
2
0
0
1
0
1
0
2
0
2
0
2
0
2
0
1
0
0
0
1
2
2
1
1
1
2
2
2
2
1
0
1
1
1
2
1
0
1
0
0
0
1
2
0
0
1
0
0
0
0
0
0
1
2
1
0
1
0
1
0
1
1
1
0
1
0
1
0
1
2
1
2
0
0
1
0
2
0
2
0
1
2
0
1
0
1
1
2
2
1
0
1
1
1
2
1
0
2
0
2
0
1
1
0
1
1
0
3
1
0
2
1
2
0
1
2
1
0
0
0
0
2
0
2
1
1
1
0
2
0
3
0
0
2
1
0
0
1
2
1
1
0
0
0
3
0
0
0
2
2
1
0
2
0
0
1
3
0
3
2
1
2
1
2
0
0
9
1
1
0
0
0
1
1
2
0
0
0
2
0
1
1
3
1
1
0
0
1
1
0
1
0
2
1
1
2
1
2
0
2
2
1
1
0
1
1
2
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
1
0
0
0
1
0
1
0
0
0
0
1
1
0
3
1
2
0
0
0
0
0
1
0
1
1
1
1
1
1
1
0
0
1
0
2
1
0
1
2
0
2
1
0
1
1
0
1
2
0
2
2
0
0
0
2
0
0
0
0
0
2
0
0
1
1
1
2
0
2
0
2
0
0
0
1
1
2
2
0
2
0
0
1
1
0
0
0
1
1
1
2
0
0
0
2
0
0
1
0
0
2
0
1
1
0
1
1
0
1
0
2
1
1
0
2
1
0
0
2
0
2
1
0
2
1
0
0
0
2
0
1
1
2
1
2
2
2
0
0
1
0
2
0
0
1
0
2
0
1
0
2
2
0
0
1
0
2
1
0
0
0
2
0
1
1
1
1
0
0
0
0
2
0
1
1
0
0
2
0
0
2
0
1
2
1
0
0
0
2
0
7
0
1
1
0
0
1
0
2
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
3
0
1
1
0
1
0
1
0
1
1
2
1
2
0
2
0
1
1
0
0
1
2
0
0
2
0
1
1
2
0
0
1
0
0
2
0
1
2
0
0
0
4
0
1
0
2
1
0
0
2
1
0
0
0
1
0
0
2
0
1
2
2
0
0
0
3
1
1
0
0
1
0
0
0
0
1
0
0
1
1
1
1
0
0
2
1
1
2
0
1
0
1
2
0
0
2
1
0
4
0
0
2
0
1
2
1
0
1
2
0
1
0
1
1
0
0
0
0
1
0
1
1
1
0
2
1
2
0
0
1
0
1
1
0
0
1
0
2
1
2
2
0
1
2
0
0
1
1
0
0
2
0
2
1
1
0
2
1
0
1
1
0
1
1
1
1
0
1
0
2
1
2
1
0
0
1
2
0
1
2
0
0
1
0
0
1
2
2
0
2
1
2
0
1
0
1
1
0
1
2
0
1
1
2
0
1
0
1
0
2
1
0
0
1
0
1
0
3
1
2
2
0
0
2
1
0
2
1
0
3
2
0
2
0
0
0
0
1
0
1
2
0
2
0
2
0
0
1
1
1
2
1
2
1
1
2
0
1
2
2
0
0
2
0
0
0
1
0
1
0
0
0
1
1
2
0
1
0
1
0
0
0
0
0
2
1
0
1
1
1
0
0
1
0
0
1
1
1
0
1
0
9
0
1
0
0
0
0
4
1
1
2
1
3
1
0
0
0
2
0
2
2
1
1
1
2
1
2
2
0
1
1
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
1
0
1
1
3
0
0
1
1
0
2
1
0
0
0
2
2
2
2
0
1
0
1
0
0
2
1
0
2
0
0
2
0
1
2
1
0
0
0
0
2
0
0
2
1
0
0
0
1
0
0
0
0
0
2
1
0
0
1
1
1
1
0
1
1
0
1
0
2
1
2
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
2
1
1
0
1
1
1
1
2
0
1
2
0
1
1
3
1
0
0
2
1
2
1
1
2
1
0
0
0
1
0
2
0
2
3
0
0
0
1
1
0
0
2
0
1
2
2
0
0
1
1
1
2
2
0
2
1
1
0
0
2
0
0
0
1
0
2
0
2
0
0
0
0
1
1
0
0
0
0
1
2
1
0
1
1
1
1
1
0
0
1
1
0
2
0
1
1
2
0
0
2
1
0
2
1
2
1
1
0
0
2
0
0
0
1
1
2
0
0
1
1
2
1
0
0
0
1
1
0
2
0
0
0
2
2
2
0
1
0
0
0
1
1
0
2
2
0
1
2
6
0
0
0
2
2
1
1
1
0
0
1
1
1
0
2
0
0
0
0
1
0
1
1
1
0
1
0
2
0
0
2
1
1
2
2
2
0
0
0
0
1
1
0
0
2
2
1
0
1
2
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
2
1
0
2
2
2
2
2
0
1
0
0
0
0
0
1
2
1
0
0
0
0
2
0
2
1
1
0
0
1
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
1
0
1
2
0
1
1
0
1
2
2
0
1
2
0
0
0
0
0
0
0
1
2
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
2
0
0
1
1
7
1
2
0
2
1
1
1
0
1
0
1
0
1
1
0
1
1
0
0
0
0
2
0
4
1
3
0
1
2
0
0
0
2
0
2
2
3
0
0
2
2
2
2
0
1
1
1
0
1
2
1
1
1
1
1
1
1
0
2
0
0
2
2
0
0
1
0
0
1
3
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
2
2
0
0
0
0
1
2
2
0
2
0
0
0
1
1
2
1
1
0
1
2
0
0
0
2
1
2
0
1
2
2
0
2
2
2
1
0
1
1
2
0
1
2
0
1
0
0
0
0
2
1
0
1
0
0
0
0
1
1
2
5
0
1
1
0
2
0
0
1
0
1
1
1
2
0
1
1
2
1
2
1
0
0
0
0
0
1
0
1
2
1
1
1
2
1
0
0
0
1
2
2
0
0
0
0
0
1
0
1
0
0
2
1
0
0
0
0
1
2
0
1
1
0
0
0
0
2
2
2
0
2
1
2
1
2
0
1
0
0
0
1
2
0
0
1
0
2
2
0
0
0
1
0
1
0
1
0
0
0
1
3
1
0
2
0
4
0
1
1
0
0
2
0
0
2
0
1
0
1
2
1
0
1
2
0
1
0
2
1
0
0
2
0
1
0
0
1
0
1
0
0
1
1
4
1
0
2
2
1
1
0
1
1
1
1
1
1
0
1
2
2
0
0
0
1
1
2
2
1
0
0
0
1
1
1
1
0
2
1
0
1
3
1
0
0
0
2
0
2
1
1
0
1
0
2
1
0
0
2
0
1
1
0
2
1
1
0
0
0
1
1
0
0
0
1
1
1
1
0
0
2
0
2
1
1
0
0
2
0
1
1
2
1
0
0
0
0
1
2
2
0
0
2
1
0
2
0
0
1
1
0
1
1
1
1
0
1
0
2
2
2
0
0
0
1
1
1
0
1
1
1
1
0
2
1
2
0
0
0
0
1
1
0
0
1
2
0
0
2
0
1
0
1
1
0
2
0
0
1
0
0
1
0
0
2
0
0
0
2
0
0
0
0
2
2
2
0
0
2
1
0
2
1
0
0
1
0
0
1
1
1
1
0
1
0
1
0
1
0
0
2
2
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
1
0
2
2
0
2
1
1
1
0
2
2
0
0
2
1
0
1
1
0
0
0
1
1
0
3
2
1
1
1
2
0
1
0
1
1
0
2
1
0
2
2
0
0
1
0
1
0
2
1
0
1
1
0
1
1
0
1
2
0
0
1
0
0
3
0
0
1
0
0
2
0
2
0
0
1
0
0
1
0
0
0
0
1
0
2
0
2
1
1
0
2
1
3
1
2
2
1
1
0
2
1
1
0
0
2
1
0
0
0
0
2
1
2
1
1
0
0
1
3
1
0
1
1
1
1
0
2
0
1
0
2
2
1
1
0
1
0
2
0
0
0
1
1
0
2
1
0
1
1
1
0
0
1
1
0
0
1
1
0
0
0
2
2
0
2
1
0
0
0
0
1
1
2
0
1
0
0
0
0
2
0
0
0
0
2
2
2
0
1
1
2
0
2
1
2
2
2
0
0
2
1
0
1
1
1
0
0
1
2
2
0
0
1
1
0
2
1
2
1
1
2
2
2
2
1
1
1
1
2
1
2
2
1
0
1
2
0
0
1
2
1
2
0
2
0
0
1
1
1
1
0
2
1
1
1
0
1
0
0
0
0
2
0
0
1
0
2
0
0
0
1
1
1
1
0
1
1
0
2
2
0
1
0
1
1
1
0
1
1
1
2
0
0
1
4
0
1
0
0
0
2
0
2
0
0
2
1
0
1
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
1
1
4
0
2
0
0
1
2
1
0
0
0
0
0
0
1
2
1
1
0
0
0
2
0
1
0
2
1
1
0
0
1
1
0
0
1
1
0
2
0
1
0
1
0
1
0
1
0
1
0
2
0
1
0
0
0
2
3
1
1
0
2
0
2
1
0
1
1
0
0
2
0
1
1
2
1
0
1
2
0
1
0
2
2
0
2
0
1
3
1
0
2
2
0
2
0
0
0
0
2
1
0
1
3
0
0
0
0
0
2
1
3
2
0
1
2
0
3
0
1
0
1
2
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
2
0
2
0
1
0
2
1
1
1
1
1
0
0
1
1
0
1
0
0
1
1
1
1
0
0
1
0
2
0
2
0
0
3
0
1
2
0
0
1
1
1
0
1
0
2
0
2
1
0
1
1
1
1
0
1
1
0
0
1
0
0
2
1
2
1
0
1
2
2
0
0
1
1
0
0
1
0
0
0
0
2
0
0
1
1
0
2
0
1
0
1
1
1
1
0
0
1
1
2
1
0
0
1
2
0
0
1
0
1
1
1
0
2
0
0
1
0
1
1
0
2
0
2
0
0
2
1
0
0
1
0
1
2
0
2
1
0
2
2
1
0
2
0
0
1
1
1
1
2
1
1
1
0
3
0
0
0
0
1
2
0
0
0
0
2
0
0
2
1
0
1
1
0
0
2
2
2
0
1
1
1
2
0
2
2
0
0
2
2
2
0
2
1
0
2
1
1
3
0
1
0
1
1
0
1
0
1
2
0
2
0
1
0
1
2
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
2
0
2
0
3
0
0
0
0
1
0
0
0
2
0
2
1
0
2
1
1
1
0
1
1
0
0
0
2
1
0
0
0
1
1
2
1
0
2
0
0
0
0
0
0
0
1
1
0
1
1
0
1
2
0
2
0
2
0
0
0
1
0
1
1
0
4
2
0
2
1
0
0
1
1
0
1
1
0
0
0
13
0
0
0
1
2
0
0
0
0
0
0
3
0
0
0
1
2
0
4
1
0
2
2
1
1
0
2
0
1
1
0
0
0
1
0
1
2
1
0
0
1
0
0
2
0
0
1
1
0
0
1
0
0
1
0
0
2
1
1
0
2
0
2
0
0
0
1
1
0
0
0
0
1
0
3
0
0
0
0
0
2
2
0
1
0
0
0
1
2
0
0
2
0
0
0
1
0
0
0
1
0
1
1
1
0
0
2
2
1
0
0
1
2
2
1
1
0
0
0
1
0
0
2
0
0
1
0
0
1
1
1
0
1
2
1
1
1
0
0
0
0
2
1
0
0
0
1
1
0
0
1
0
2
0
3
2
0
0
0
2
1
1
0
0
0
0
0
0
1
0
2
1
2
1
0
2
2
1
2
0
1
2
1
0
2
0
1
0
1
1
1
1
2
0
0
0
0
1
1
2
0
1
2
1
0
0
0
1
0
1
1
1
2
0
2
2
0
3
0
0
0
1
1
1
0
1
0
0
0
0
1
1
0
0
0
5
2
0
0
0
0
0
2
0
0
0
1
0
1
1
0
0
2
2
0
2
2
0
2
2
2
0
0
1
1
2
3
0
0
0
0
1
0
1
0
2
0
0
0
1
1
0
0
2
0
0
0
0
2
0
1
0
1
0
2
1
0
0
1
2
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
2
0
0
2
2
0
0
0
2
1
0
0
0
1
1
0
0
2
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
2
2
0
0
0
2
1
0
2
0
0
0
1
0
1
1
2
1
0
0
0
0
0
1
2
0
2
1
0
0
0
0
2
0
0
2
0
1
1
0
1
0
2
0
2
0
1
1
2
0
0
1
1
1
1
1
0
0
2
1
0
2
1
0
0
1
2
2
0
0
1
0
0
1
1
1
1
2
0
0
1
1
2
1
0
0
2
0
1
1
0
1
1
2
0
2
0
1
0
0
1
2
1
1
3
0
0
0
0
0
2
0
0
2
0
1
0
0
2
0
1
0
1
2
1
0
1
1
1
1
2
0
0
2
1
0
0
2
2
2
1
1
0
0
0
0
0
0
0
0
1
1
0
0
1
3
2
1
1
1
2
1
2
0
1
0
1
0
0
0
0
0
0
0
1
2
1
0
1
0
1
0
1
1
0
0
1
1
1
3
1
1
0
1
1
0
2
0
1
1
0
0
2
0
0
2
0
0
1
2
0
0
0
0
0
0
1
0
1
0
2
0
2
0
0
2
0
1
1
0
0
2
1
1
1
0
0
1
1
1
0
0
0
1
3
2
1
2
0
1
0
0
0
1
2
1
0
1
0
1
2
0
0
1
0
1
2
0
2
1
1
2
0
0
0
0
1
1
0
1
0
0
0
2
1
0
0
0
1
2
0
1
0
2
2
2
0
2
0
0
1
0
1
0
2
0
2
0
1
1
1
0
0
1
2
2
0
1
1
0
0
4
0
2
1
1
0
1
0
2
0
0
0
0
0
1
0
1
0
1
0
2
0
0
2
2
0
1
2
1
0
0
1
0
2
0
0
0
2
2
0
2
0
1
0
1
0
0
2
1
0
2
0
0
0
0
1
1
0
0
1
1
1
0
0
1
1
0
0
0
1
1
2
0
0
0
0
1
1
1
0
0
0
0
2
1
0
1
4
2
0
2
1
2
0
0
0
1
0
0
0
2
1
0
1
0
1
2
1
0
2
0
1
0
0
0
1
0
2
2
0
0
0
1
1
0
1
2
0
1
2
0
2
0
1
1
2
0
1
0
2
0
1
1
1
1
0
0
2
2
0
1
1
0
0
1
3
0
0
0
1
0
1
2
2
2
0
0
3
0
1
4
1
1
0
0
1
1
1
2
0
0
1
0
2
0
0
0
1
0
0
3
0
1
0
1
2
0
2
1
0
0
0
0
0
2
0
0
0
0
1
1
1
2
0
2
0
0
1
0
2
0
1
0
1
1
0
0
2
0
1
1
0
4
2
2
1
1
0
2
1
1
1
1
2
2
1
1
0
1
0
0
0
0
1
0
0
0
0
1
2
1
0
0
2
2
0
0
2
2
1
0
0
2
1
1
1
2
1
0
1
1
1
1
0
1
0
0
1
2
2
2
0
1
2
0
0
0
1
0
0
0
3
1
1
2
0
0
0
1
0
3
0
0
1
0
1
2
1
0
1
1
0
0
0
0
2
2
0
0
0
0
0
2
0
2
0
2
0
0
1
2
0
2
2
0
0
1
0
0
2
1
0
0
0
1
1
0
1
1
1
0
0
0
0
1
0
1
1
2
0
0
3
0
0
2
0
1
1
0
0
0
1
0
0
1
0
0
1
2
2
0
0
0
0
2
1
1
0
0
0
0
0
0
2
0
1
0
1
2
0
2
2
1
1
0
0
0
1
0
1
0
0
1
1
0
1
1
2
0
1
2
1
1
1
0
0
2
2
1
0
2
2
0
0
1
2
2
0
2
2
0
2
4
1
1
0
1
1
1
0
0
1
1
2
1
1
0
1
1
1
0
1
1
2
0
3
2
1
0
0
0
1
2
2
0
1
1
2
1
1
1
0
1
1
1
1
1
0
2
3
1
0
0
2
2
0
2
1
1
1
0
1
1
1
0
0
0
2
0
1
0
1
1
0
2
0
0
2
0
0
3
0
1
0
2
2
0
0
1
0
1
0
0
0
2
0
2
3
1
0
1
2
0
2
0
1
0
2
1
2
1
2
2
2
1
0
2
1
0
2
0
0
2
1
0
0
0
0
3
1
0
0
2
0
1
1
2
2
2
2
0
2
12
3
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
1
0
0
1
2
1
0
1
1
1
1
0
0
0
0
0
1
2
1
0
1
0
2
2
2
0
0
2
0
0
0
0
0
2
0
1
1
0
1
2
1
1
0
2
0
1
0
2
0
0
2
0
2
1
0
2
0
0
1
1
0
2
0
1
2
0
1
1
2
2
0
0
1
0
1
0
2
1
1
1
1
2
1
0
1
0
0
0
2
0
0
1
0
2
0
0
1
1
2
1
2
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
2
1
0
0
0
1
0
1
0
1
1
1
1
0
2
2
0
0
0
0
0
1
0
0
0
0
0
2
2
1
1
0
1
0
1
1
0
0
0
1
0
1
1
3
1
1
0
0
1
0
0
0
1
1
0
1
0
0
2
0
1
0
2
0
1
1
1
1
0
0
1
1
2
0
0
2
0
0
1
0
1
0
2
0
1
0
2
0
0
0
0
3
0
2
1
0
2
1
1
1
2
0
0
1
1
1
0
1
0
2
2
0
1
0
2
0
0
3
1
2
1
0
0
0
2
1
1
0
0
0
1
0
0
1
0
1
0
1
2
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
2
1
1
2
0
0
0
2
1
0
1
0
3
2
1
1
0
1
1
0
1
0
0
2
2
0
1
2
2
0
2
1
0
0
0
0
3
2
0
1
0
0
2
0
2
1
0
2
0
1
2
1
1
0
1
0
1
1
0
0
1
0
2
2
0
2
2
2
0
0
1
0
0
0
0
0
0
2
2
2
1
0
0
1
1
0
1
2
0
1
1
1
1
1
0
0
0
0
0
0
1
2
1
0
1
0
0
0
0
0
1
0
2
1
2
0
1
1
0
1
0
0
1
0
0
0
2
1
2
0
0
2
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
1
2
2
0
2
0
2
1
0
0
0
1
2
0
0
1
1
0
2
2
2
0
2
0
1
0
2
2
1
0
0
1
0
0
1
1
1
0
1
0
2
2
1
0
0
0
1
2
2
0
2
0
1
0
2
2
0
0
1
0
0
0
2
0
2
4
1
1
0
0
0
1
0
0
2
1
0
0
0
2
1
1
0
0
0
1
2
2
1
1
0
1
1
0
1
1
0
2
0
0
1
2
1
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
2
1
2
0
0
0
1
2
1
1
2
0
1
0
0
2
2
0
1
1
2
0
1
0
2
4
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
7
1
0
1
2
0
0
0
1
2
2
2
0
0
1
0
1
1
1
0
1
0
1
2
0
3
1
1
0
1
0
1
2
2
0
0
0
2
3
0
0
0
0
1
0
2
2
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
1
2
0
0
1
2
1
1
2
0
0
0
0
0
1
2
1
1
1
0
0
2
0
0
0
1
0
0
1
1
0
0
1
0
1
2
0
1
1
0
2
1
0
0
0
0
1
0
1
1
1
0
2
3
1
0
3
0
1
0
1
0
3
0
1
1
0
1
1
1
2
0
0
2
0
0
1
1
2
2
1
0
0
0
1
0
0
1
1
0
0
1
1
2
2
1
1
0
0
2
1
3
1
1
0
1
1
0
2
2
1
0
1
2
1
0
0
1
0
1
1
1
1
1
2
2
0
0
1
0
1
1
0
1
0
1
1
1
1
1
0
0
0
0
1
0
2
2
1
1
0
0
0
0
1
0
1
2
1
2
1
2
0
1
1
2
0
2
1
2
1
0
0
1
0
1
2
0
1
0
1
1
0
0
1
0
1
0
0
2
0
2
0
0
0
1
0
0
0
0
1
1
2
0
1
0
0
2
1
0
1
2
2
0
0
1
0
1
2
1
0
1
0
0
0
3
1
1
2
0
1
0
0
1
2
1
1
0
2
0
2
1
0
2
0
3
0
2
1
0
2
1
0
0
0
2
0
1
1
2
0
2
2
2
0
0
1
1
2
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
2
1
0
4
0
0
1
1
0
1
1
0
1
0
0
1
2
2
0
1
1
1
0
0
2
0
0
1
2
0
1
1
2
0
0
0
0
0
1
1
0
0
2
0
1
1
0
0
0
1
0
2
2
1
0
0
1
1
0
2
0
0
1
0
2
0
0
2
1
1
1
0
1
0
0
1
0
1
1
1
1
0
0
0
1
0
2
0
0
1
0
1
0
1
3
2
0
0
1
1
2
0
2
0
0
1
0
1
0
0
1
1
0
0
0
0
1
1
0
1
1
0
2
2
0
0
1
0
2
0
0
0
0
0
0
1
2
1
0
1
2
1
0
1
2
0
1
1
0
2
2
1
2
0
1
1
0
2
2
1
0
0
0
0
0
1
0
0
2
0
1
0
0
1
2
1
0
0
1
1
2
1
1
0
2
0
0
2
0
1
0
7
2
0
0
1
0
2
2
1
0
1
0
0
0
0
1
0
2
2
0
0
1
1
0
2
0
2
0
0
0
2
1
1
1
0
0
0
0
0
0
2
1
0
0
1
0
0
0
1
2
1
0
3
0
0
1
2
1
1
0
0
0
1
1
1
1
2
0
2
2
0
1
0
0
0
1
1
2
0
1
0
1
0
0
0
2
1
2
1
0
0
0
0
1
0
2
1
0
0
0
2
1
4
0
0
0
0
0
1
2
1
0
0
1
1
0
1
0
1
0
0
0
0
0
0
1
1
0
1
2
0
1
2
1
1
1
1
2
0
1
2
0
0
0
0
1
0
0
0
0
2
0
0
1
2
2
0
1
1
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
1
1
2
0
1
0
0
0
1
1
2
1
0
0
0
0
0
2
2
0
1
0
0
1
0
0
2
1
0
0
1
1
0
1
2
0
0
0
0
2
0
0
0
2
1
0
1
0
0
2
1
0
1
1
2
0
1
0
2
0
0
0
0
0
2
1
1
0
0
1
2
2
0
1
0
1
0
2
0
3
1
0
0
1
0
1
1
1
1
1
0
0
2
0
0
0
0
0
1
2
1
1
1
0
0
1
0
0
2
1
1
0
0
0
1
2
0
2
1
1
0
1
0
1
2
1
2
2
1
0
2
0
1
0
1
1
0
0
1
0
1
1
2
0
0
0
0
0
0
2
1
0
1
3
1
3
0
2
2
0
0
0
1
2
1
1
0
0
1
0
0
0
0
1
0
2
1
1
0
1
0
1
1
1
2
3
0
3
1
0
0
0
2
1
2
0
0
0
2
0
1
0
3
1
2
0
0
1
2
2
0
2
0
1
0
0
0
0
2
0
0
0
0
1
1
1
0
2
2
0
0
0
2
1
0
1
1
0
0
0
0
0
0
1
1
0
2
0
0
1
0
0
0
0
1
0
0
1
0
0
1
1
1
0
1
1
0
3
0
1
0
1
1
1
1
0
1
0
0
3
1
2
1
0
1
0
1
2
0
1
0
0
0
0
1
0
0
1
0
0
0
1
1
1
2
1
0
0
2
1
0
1
0
2
0
0
2
1
0
0
0
0
1
1
1
3
1
1
0
1
0
0
0
1
0
0
0
1
0
0
0
1
1
2
2
3
1
2
0
0
2
2
2
0
2
1
2
0
1
3
1
0
0
1
1
0
1
2
2
0
2
1
0
3
1
0
2
0
0
0
2
0
0
0
0
1
1
0
2
0
0
1
1
0
1
2
2
0
1
0
2
1
0
0
2
2
0
0
2
0
1
1
1
0
1
0
2
1
0
2
1
1
1
1
0
1
2
1
1
1
0
0
2
1
2
1
0
0
2
2
2
2
2
1
0
1
0
1
3
1
0
0
1
0
0
1
0
0
1
1
1
1
0
1
1
1
0
1
0
0
4
1
0
0
0
1
0
1
1
0
2
1
2
0
1
1
2
1
1
1
2
0
2
2
0
0
0
0
0
1
1
1
2
1
0
0
1
2
1
2
0
0
0
2
1
1
1
1
4
0
0
1
0
2
1
0
0
0
0
0
2
0
0
1
0
1
1
2
0
0
0
0
1
0
2
0
0
2
0
1
0
2
2
2
0
1
0
0
2
2
0
0
0
1
1
2
1
1
1
1
0
0
0
0
1
1
1
1
0
2
1
0
0
0
0
2
1
1
0
0
0
0
0
3
2
0
2
2
2
1
1
2
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
1
1
1
0
0
2
1
2
1
0
0
0
1
0
1
0
2
1
2
1
2
2
1
2
2
1
4
0
0
1
1
0
1
1
1
0
1
0
0
1
0
0
0
1
1
0
0
0
0
1
2
1
0
1
1
1
1
1
0
0
2
0
0
0
0
0
1
0
0
1
2
0
0
0
2
2
0
3
0
1
0
1
0
0
0
0
0
2
0
0
0
0
2
2
2
2
1
0
1
0
0
0
1
1
0
0
1
0
0
1
0
0
2
0
0
0
0
1
0
0
1
1
1
1
0
1
0
2
0
1
0
0
1
1
1
0
0
0
1
0
1
2
1
2
0
2
0
1
1
0
0
0
2
0
1
1
2
1
1
0
0
2
2
1
2
0
1
0
0
0
1
0
0
1
2
2
1
2
2
0
0
1
2
0
2
2
0
0
1
2
1
0
1
1
0
0
0
1
0
2
0
2
1
0
2
1
0
0
0
0
0
1
1
1
0
2
0
0
0
1
1
0
1
0
0
1
0
1
1
0
0
0
0
1
0
1
0
1
0
0
1
0
5
0
0
0
2
1
1
1
2
0
2
0
0
3
1
1
0
0
1
0
0
1
0
2
1
2
0
2
2
1
2
2
0
2
1
0
2
0
1
1
0
0
0
0
2
0
1
1
0
0
1
2
1
0
2
0
1
1
0
1
0
0
1
0
1
0
0
0
1
0
2
0
2
0
1
0
2
2
1
1
1
0
0
1
1
0
0
1
1
1
0
0
2
0
1
1
1
1
1
0
0
2
1
0
1
0
2
0
1
0
0
3
0
0
2
0
0
0
0
0
3
3
2
1
0
1
0
0
0
2
1
1
1
2
1
0
1
0
1
0
0
0
0
1
2
0
0
1
1
0
2
1
0
0
0
0
0
0
2
0
0
0
0
1
1
0
2
1
2
0
1
0
0
0
0
0
2
0
1
0
0
0
1
2
0
0
0
0
1
2
2
0
1
0
0
0
3
0
0
1
2
1
0
0
2
1
1
1
0
1
0
2
0
2
0
0
2
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
1
1
2
1
0
1
2
0
2
1
2
0
1
0
1
1
2
2
0
0
0
0
2
0
0
0
1
0
0
0
1
1
0
0
0
1
0
1
0
1
0
0
3
0
2
1
0
0
1
0
0
0
1
0
1
2
1
0
1
2
0
0
0
1
2
0
0
1
0
1
2
1
1
1
2
1
2
0
0
1
0
0
2
0
1
0
2
1
1
1
0
1
0
0
1
0
2
1
1
0
2
0
2
2
2
0
1
0
1
0
1
0
1
0
4
0
1
0
1
1
3
2
0
1
2
0
0
1
0
1
2
0
1
0
1
0
1
2
2
2
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
1
1
0
0
1
1
0
0
2
0
0
0
0
0
0
0
2
1
2
2
0
0
0
0
1
0
2
0
1
2
2
2
2
1
2
0
0
2
0
1
2
1
0
1
0
2
1
2
1
2
1
1
0
0
0
2
0
0
0
1
1
2
0
0
2
2
0
1
1
0
2
0
2
1
3
0
1
1
0
2
0
1
0
1
0
2
1
1
1
0
2
1
1
1
0
1
0
2
1
0
2
0
1
0
0
0
0
0
2
2
0
1
0
4
0
0
2
3
1
4
0
0
1
1
0
2
1
4
1
0
1
1
2
2
2
1
1
0
1
0
1
0
2
1
0
0
2
1
0
2
0
0
0
1
0
1
1
0
0
1
1
1
0
0
0
0
5
1
1
0
1
1
0
2
0
0
0
0
0
0
0
1
1
8
1
1
0
0
0
0
0
0
1
0
4
0
0
2
0
1
2
2
1
2
1
2
2
1
1
0
0
4
1
2
0
0
2
1
0
1
0
1
1
2
1
0
1
0
0
1
3
2
2
1
1
0
1
0
0
0
1
2
1
0
2
0
1
0
0
1
2
0
1
2
2
0
0
0
1
0
2
0
0
0
0
1
1
0
3
2
0
0
2
0
0
0
0
1
1
2
1
0
4
0
0
1
1
1
1
1
1
0
1
1
2
0
0
0
1
2
0
1
0
0
0
0
0
0
0
1
0
0
3
0
0
0
2
0
0
0
1
1
2
2
1
1
0
1
0
0
0
1
3
1
0
1
0
1
2
2
0
0
0
0
1
0
2
0
1
0
0
1
0
0
3
0
1
0
0
2
1
1
1
0
0
1
0
0
1
2
1
0
0
0
0
1
2
0
0
2
1
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
1
0
2
1
1
4
0
2
1
0
3
2
2
1
0
1
1
1
0
0
2
0
2
1
1
0
1
0
0
0
0
0
1
0
1
0
0
0
2
2
1
1
0
0
1
0
1
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
2
2
1
2
1
0
0
2
1
2
0
0
0
0
1
1
0
2
0
2
0
0
1
0
0
1
0
1
0
0
0
2
0
1
1
1
2
2
1
1
2
1
0
0
1
1
0
2
2
2
1
2
0
1
2
0
0
1
0
1
1
0
0
0
0
2
0
2
0
0
2
1
2
0
0
1
1
2
1
0
1
0
2
1
0
0
0
1
0
1
0
1
2
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
2
0
2
1
0
0
1
1
1
1
1
2
1
0
0
0
0
0
1
1
0
2
1
1
1
0
0
2
1
0
0
1
0
0
0
1
1
1
1
1
0
1
0
1
0
0
2
1
1
0
3
0
1
3
1
2
0
0
1
0
0
2
1
0
1
0
2
1
0
1
1
2
0
2
0
1
0
2
1
0
1
2
0
0
0
0
0
0
0
1
0
2
2
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
2
1
0
0
2
0
1
0
0
0
2
0
2
0
1
1
0
4
2
1
1
1
1
1
0
0
0
1
1
0
0
0
0
2
2
0
1
0
1
1
0
1
0
0
2
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
1
1
1
2
0
0
0
2
0
0
1
2
1
0
0
1
0
1
0
1
0
2
1
1
1
0
2
1
0
1
1
2
0
2
1
1
0
0
0
1
0
1
0
0
0
0
2
1
0
2
0
1
0
1
0
2
1
2
2
1
1
1
1
0
0
1
1
0
1
1
2
2
3
0
1
0
1
1
1
2
1
2
1
2
0
2
1
0
0
2
0
2
0
0
0
1
0
2
2
1
0
1
2
1
0
1
1
0
1
0
0
2
0
0
1
2
0
0
2
1
2
0
2
1
0
1
1
0
1
2
0
2
1
1
1
0
0
1
2
0
0
3
2
2
0
0
3
0
2
2
1
1
1
1
0
0
0
0
0
1
0
0
1
1
1
0
2
1
0
0
0
0
1
1
0
3
0
0
0
0
0
1
0
0
0
1
0
1
2
0
1
2
1
2
2
6
0
1
0
2
0
2
1
1
0
0
2
0
0
2
0
2
0
1
1
0
0
2
1
1
0
1
0
1
1
2
1
0
0
1
0
1
0
1
0
0
1
2
0
1
2
0
2
0
2
2
0
1
1
1
1
2
1
1
1
0
0
0
2
2
2
1
1
0
0
0
1
0
0
0
1
1
3
0
2
1
0
0
2
2
1
0
2
1
0
0
2
2
0
0
2
1
0
0
1
0
1
0
0
0
0
1
0
2
0
0
1
2
1
0
2
0
0
0
1
1
3
0
0
0
0
0
0
2
0
0
1
1
2
2
0
1
1
1
1
1
0
0
2
0
2
1
1
0
1
1
0
2
1
0
0
2
2
0
0
5
1
0
0
2
1
1
1
0
2
1
2
0
2
0
0
0
2
1
0
0
0
1
0
1
0
0
0
2
1
0
0
1
0
0
2
0
1
0
0
0
0
2
2
0
1
1
0
0
2
2
1
1
0
3
1
0
0
0
2
0
1
1
1
0
1
1
1
0
0
0
1
2
0
0
0
1
0
2
0
1
1
1
0
0
2
0
0
0
0
1
0
0
1
1
1
0
0
2
2
2
0
0
2
0
2
2
1
0
2
1
1
0
1
1
1
1
2
1
1
0
0
1
0
0
0
0
1
0
1
2
1
2
0
0
0
1
2
0
0
1
0
2
2
0
1
2
0
0
2
1
1
1
0
1
0
0
1
1
0
0
0
2
1
0
1
0
0
0
0
0
2
0
0
0
1
1
2
0
0
0
2
0
1
0
1
2
1
0
0
2
2
0
1
0
0
1
0
0
0
2
1
0
2
1
0
1
2
2
0
0
1
0
2
0
2
1
0
0
1
3
0
1
1
1
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
1
0
1
1
0
2
2
0
2
1
0
0
2
0
0
2
1
2
0
1
0
2
0
2
0
2
1
0
1
2
0
2
0
2
1
1
1
1
2
1
1
0
1
1
5
2
0
3
0
0
0
1
2
0
1
1
1
0
1
1
0
0
0
0
0
1
1
2
0
0
2
1
0
0
1
2
0
0
2
0
1
1
2
1
0
1
0
2
1
0
1
2
2
0
1
0
0
1
2
0
0
0
1
1
2
0
3
1
0
1
0
2
2
1
2
0
0
4
0
0
0
0
1
1
1
2
0
0
1
1
2
0
1
0
0
1
0
1
1
0
0
1
1
1
0
0
0
0
0
0
1
1
0
2
0
0
1
1
0
0
0
0
1
1
0
0
1
2
3
0
0
1
0
0
1
0
2
0
2
0
0
0
1
0
1
2
1
0
0
2
1
0
1
1
0
0
0
0
1
0
2
1
1
1
1
0
1
0
0
0
0
0
1
0
1
0
1
1
0
2
0
1
0
1
1
2
1
2
0
2
0
0
0
0
2
1
2
0
1
0
0
2
2
1
2
0
1
1
1
2
2
0
0
2
0
1
0
0
2
1
2
1
1
0
1
2
0
1
1
1
1
2
0
0
0
0
1
0
0
3
0
0
0
2
0
0
2
0
1
0
2
0
0
0
1
2
0
2
2
0
2
1
0
2
2
0
0
0
2
1
2
1
1
0
0
1
0
1
0
0
1
0
1
1
1
1
1
2
2
2
1
1
0
2
0
0
0
1
2
1
0
0
0
2
0
0
0
2
1
1
1
1
1
0
1
0
0
1
0
1
1
0
0
1
1
2
2
0
0
0
1
2
0
0
1
1
0
1
0
0
2
0
2
0
1
1
2
1
2
0
1
0
1
2
0
1
2
0
2
1
1
0
2
2
2
0
3
8
1
1
2
0
2
1
1
1
0
2
1
2
0
1
2
0
1
2
2
2
3
0
0
1
1
0
1
1
0
0
0
2
1
1
0
1
0
2
0
0
0
0
2
2
2
0
0
0
2
1
0
2
0
0
1
1
0
2
1
0
2
0
2
0
0
2
0
1
2
1
0
2
0
0
0
0
0
2
1
1
0
0
2
2
1
2
1
0
0
0
0
2
2
2
0
0
2
0
1
0
0
1
0
0
2
1
0
0
2
1
1
0
0
2
1
1
1
0
0
8
0
2
0
2
1
1
0
0
0
2
0
1
2
1
0
1
2
0
2
0
2
2
4
2
2
1
0
1
1
1
0
0
0
0
1
0
1
0
2
1
1
0
3
1
2
0
1
0
2
0
1
1
0
1
1
1
0
0
1
0
2
0
1
2
1
2
2
1
0
1
1
2
1
1
1
0
2
2
0
1
1
1
2
0
0
2
1
0
0
1
2
0
1
1
2
0
2
0
0
0
0
0
1
2
0
0
0
1
2
2
1
0
0
2
0
1
0
2
2
0
0
1
3
0
1
0
2
1
0
1
0
1
0
2
0
0
1
0
1
0
1
1
0
1
1
0
0
1
0
1
0
0
0
0
0
0
2
0
1
0
0
0
2
1
0
1
0
2
0
0
2
1
1
1
1
1
1
0
2
1
2
0
0
0
0
0
0
2
0
2
2
1
1
1
1
0
0
3
0
0
0
1
2
1
1
1
0
0
0
0
1
0
1
2
0
1
2
1
1
0
2
2
0
1
0
1
0
2
1
0
0
0
2
0
0
0
0
0
2
1
0
1
1
2
1
1
0
0
0
2
0
0
0
1
2
3
0
0
0
2
1
0
1
0
0
1
2
0
0
0
0
0
0
0
1
0
1
0
0
2
2
2
1
2
0
2
2
1
1
1
0
0
2
0
0
0
0
2
0
1
2
0
3
1
0
0
2
0
1
1
0
1
1
0
0
1
2
5
0
1
2
0
1
0
1
2
0
0
0
1
0
2
2
0
1
1
0
0
0
1
1
2
2
0
2
1
2
0
2
0
2
1
2
2
1
1
0
0
1
2
0
0
2
1
0
1
2
0
1
3
1
1
1
0
0
0
2
0
2
0
1
0
0
1
0
0
0
1
2
2
1
1
1
1
0
0
0
1
0
1
1
2
2
2
1
2
0
1
1
0
2
1
0
0
2
0
1
0
4
1
0
1
3
0
0
1
2
0
0
1
0
1
0
0
0
0
2
0
2
2
0
0
0
1
0
0
1
0
2
2
0
2
2
0
0
1
1
1
0
0
0
0
3
1
1
0
0
0
1
0
0
1
1
0
0
2
2
1
0
0
1
0
0
1
1
1
1
0
1
0
0
0
1
0
1
0
0
1
2
1
0
1
0
0
2
1
1
1
1
0
0
0
1
1
0
1
0
1
1
0
2
0
0
1
0
2
2
0
0
1
0
0
1
1
0
1
2
1
0
1
2
0
1
0
0
2
1
0
0
1
2
0
0
1
1
2
1
2
1
0
0
0
1
0
0
0
0
0
1
1
2
2
0
0
0
0
1
0
0
0
0
0
1
1
1
1
0
0
2
0
0
0
1
0
0
1
1
2
0
0
0
2
0
0
2
0
0
1
0
1
1
1
0
0
1
1
2
0
0
1
1
0
0
0
1
1
1
1
0
1
0
0
1
1
2
2
0
2
0
0
2
1
0
1
1
0
1
0
1
2
1
2
1
2
1
0
0
2
0
1
1
1
0
0
2
0
2
0
0
0
0
0
1
0
0
2
0
2
2
2
0
1
0
2
0
2
0
1
0
2
0
1
0
1
0
0
0
1
0
0
1
2
2
1
0
1
0
2
1
2
1
0
0
2
0
1
1
0
0
1
1
0
0
1
0
1
0
2
1
3
0
0
1
0
2
0
2
2
2
0
2
0
0
0
0
1
1
0
4
2
0
0
1
1
2
0
0
0
2
0
0
1
0
0
1
1
1
1
1
2
1
0
0
0
1
2
0
1
0
1
0
0
0
2
2
0
0
0
2
2
0
2
1
0
1
0
2
0
0
0
2
1
1
1
1
2
0
1
0
1
0
2
0
1
2
1
0
1
0
0
1
1
2
2
2
0
2
0
0
1
0
0
2
0
1
0
0
1
1
0
1
0
0
1
0
2
0
1
0
2
1
2
0
0
0
0
1
2
0
1
0
0
1
0
2
2
0
0
2
0
1
1
1
1
0
1
1
2
1
0
2
1
2
1
0
0
0
1
1
0
0
0
0
0
1
2
2
2
0
1
0
0
0
0
1
1
2
0
0
0
1
1
8
1
0
0
0
1
0
0
1
1
1
0
1
1
1
0
0
2
2
0
0
1
1
0
0
0
0
1
0
3
0
3
0
2
2
2
1
1
1
1
0
0
3
0
0
0
0
1
1
1
1
0
1
1
1
2
1
0
0
0
2
0
0
0
0
2
0
2
1
2
0
1
1
1
0
0
0
0
1
0
0
1
1
1
1
2
1
0
0
2
1
0
2
2
0
0
0
2
2
1
0
0
2
1
1
1
0
2
1
0
0
2
0
0
2
1
1
1
0
0
0
2
1
0
2
0
0
2
1
1
2
0
0
2
0
1
0
1
0
0
2
1
2
2
1
0
1
0
0
0
1
2
1
0
0
1
1
2
0
0
0
2
1
1
0
1
2
2
1
0
1
2
0
0
1
1
0
2
0
0
0
0
0
0
1
2
0
1
2
0
1
2
2
0
0
0
1
0
2
1
0
0
0
1
0
0
0
1
0
1
0
1
2
0
0
1
0
0
1
2
1
1
1
2
2
1
2
1
0
2
1
1
2
0
1
1
1
2
2
1
0
1
0
1
2
1
1
1
2
1
2
1
0
0
0
0
0
0
0
0
1
1
1
2
0
0
1
3
0
2
0
0
2
0
1
2
0
1
1
0
0
2
0
0
1
2
2
0
1
1
0
1
0
1
2
0
0
0
2
1
1
1
1
0
0
2
0
0
2
2
1
2
1
2
0
2
0
0
2
1
1
1
0
1
0
0
0
1
0
1
1
1
2
0
0
0
1
1
1
0
0
0
1
0
2
1
2
2
1
2
1
0
2
0
0
1
2
1
0
1
0
0
0
1
0
2
0
0
2
1
1
1
0
0
1
2
1
0
2
1
1
2
1
1
0
2
0
1
2
0
2
0
0
0
0
2
2
0
0
3
1
5
0
0
0
0
1
1
0
1
1
1
0
1
1
1
1
0
0
0
2
0
2
0
0
1
0
0
2
1
1
1
1
1
0
0
1
1
0
1
1
0
0
0
1
1
1
1
0
2
0
0
1
1
1
3
0
3
0
1
1
0
2
0
0
0
0
0
0
2
1
2
2
0
0
0
1
0
0
0
2
1
1
1
3
0
0
1
1
0
0
1
1
2
1
0
2
1
0
1
0
1
0
2
0
0
2
2
1
1
0
0
1
0
1
1
2
0
0
2
0
3
1
2
0
2
0
2
1
0
1
2
0
0
2
2
1
1
1
0
0
0
0
0
4
0
0
2
1
1
0
0
0
0
0
1
1
0
0
0
2
1
1
0
1
0
2
0
0
0
2
0
0
0
0
0
1
0
0
2
2
1
1
0
0
2
0
0
1
2
1
1
0
1
0
1
2
0
2
0
1
0
0
1
2
1
1
1
0
2
1
2
2
0
0
1
0
1
1
0
0
0
1
1
2
0
1
0
1
1
1
2
1
1
0
0
1
1
0
0
0
1
0
0
2
2
1
0
0
0
0
1
1
2
0
2
1
0
0
1
0
1
2
0
2
2
0
1
2
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
1
0
1
0
1
0
0
3
1
0
2
0
0
1
0
2
1
0
0
0
1
1
0
0
2
0
1
2
0
0
0
1
2
1
1
1
1
2
0
0
2
1
0
2
2
2
0
2
2
1
1
0
1
2
2
0
1
0
0
0
1
0
0
2
1
1
0
0
3
0
0
0
1
0
0
1
1
1
1
1
0
0
1
2
2
1
0
0
0
1
2
2
2
1
1
0
2
1
1
2
0
2
0
2
2
0
0
1
0
0
0
3
2
0
1
0
1
0
2
2
1
0
1
2
2
1
0
0
2
2
0
2
1
2
1
0
0
2
0
2
0
0
2
0
1
2
1
1
0
0
0
1
1
1
1
0
0
0
0
0
1
0
1
1
0
0
1
0
0
1
0
0
0
2
0
1
0
0
0
1
2
1
1
2
1
1
1
0
2
0
0
0
2
0
0
2
0
0
2
1
0
1
0
2
0
0
1
0
1
2
1
0
1
2
1
1
2
0
1
0
2
0
0
0
1
2
1
1
0
0
2
2
2
1
0
1
1
1
2
1
0
2
1
1
1
0
1
1
0
0
1
0
0
1
0
1
1
1
1
0
0
6
1
2
1
1
1
0
2
0
0
1
0
2
2
0
1
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
1
1
1
4
0
0
1
0
0
2
1
1
3
2
1
0
0
1
1
0
1
0
0
0
1
0
3
1
2
0
0
0
1
1
0
0
2
0
1
0
0
0
0
0
0
2
1
2
0
2
0
0
0
0
0
1
0
2
1
1
1
0
0
0
0
0
0
2
0
1
0
1
3
1
0
2
1
0
0
0
0
1
2
2
0
1
1
0
2
1
0
0
0
1
2
0
2
1
0
1
0
1
0
1
1
1
0
2
0
1
2
0
0
2
1
2
0
0
1
1
2
0
1
0
0
1
0
2
8
0
1
1
0
0
0
0
0
0
2
1
1
0
1
0
2
2
0
1
1
1
0
0
1
0
2
3
1
1
1
2
2
1
2
1
0
2
0
0
2
1
1
0
0
1
1
0
0
1
0
0
1
1
0
0
1
0
2
1
1
0
1
0
0
2
0
0
0
0
1
4
0
3
0
2
1
0
0
1
1
2
2
2
2
2
1
0
0
0
0
0
2
1
3
0
0
1
2
2
2
0
1
1
0
1
0
0
0
2
1
1
0
1
2
0
0
1
2
1
3
2
0
0
0
1
1
0
0
1
1
0
0
0
1
0
2
1
0
2
1
2
0
0
0
1
1
0
0
2
0
0
2
0
0
1
2
0
0
1
1
0
0
0
2
2
0
2
2
0
0
1
1
1
3
1
1
0
1
0
1
2
2
2
1
2
1
1
0
1
2
2
1
1
0
4
1
1
0
1
1
0
0
1
0
1
2
1
0
1
0
0
0
1
0
2
2
1
0
0
1
1
1
1
1
0
1
0
0
1
2
0
1
1
1
1
1
0
1
0
0
1
0
1
2
2
0
0
2
2
0
2
0
1
2
1
0
1
2
1
1
1
0
2
1
0
1
1
0
1
0
1
0
2
2
0
0
1
1
2
2
1
0
1
1
0
0
0
0
0
3
2
1
0
1
0
0
0
1
2
0
0
1
0
1
0
0
2
2
0
0
0
0
0
1
2
0
0
0
0
2
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
4
1
2
1
1
1
0
0
1
0
1
0
1
0
2
1
1
2
1
0
0
0
0
0
0
0
0
0
2
2
1
2
1
0
1
1
0
0
1
2
0
0
1
2
1
0
3
0
0
1
0
0
2
2
3
0
1
0
1
1
1
0
1
1
1
0
1
3
1
2
1
0
0
0
1
0
0
1
1
0
1
0
2
1
0
0
1
1
0
0
1
2
0
0
0
1
1
0
2
1
0
1
0
2
1
1
1
2
0
1
1
0
1
0
0
2
0
0
1
1
2
1
0
2
0
0
2
0
2
0
1
1
0
1
0
2
1
0
0
0
2
0
0
1
1
0
2
2
1
0
0
1
0
2
1
1
1
1
0
0
1
1
1
0
0
1
1
0
0
0
1
0
0
1
0
3
0
1
2
1
0
0
2
1
0
0
1
0
0
0
1
0
0
0
1
1
0
2
1
0
1
1
1
0
0
0
0
1
2
1
2
1
1
0
3
1
2
0
2
2
1
1
0
1
0
0
0
1
0
2
0
0
0
1
0
0
2
0
0
1
1
3
2
0
2
0
2
0
0
2
1
0
1
1
2
1
0
1
1
1
2
0
0
0
2
2
2
0
0
1
1
2
0
1
0
0
2
0
1
1
0
0
0
0
0
0
1
0
2
0
2
0
0
1
0
1
1
2
1
0
1
1
1
0
1
2
1
0
4
1
0
0
1
1
1
0
2
0
1
0
0
0
1
0
0
2
1
1
2
1
2
0
1
1
2
1
0
2
0
1
1
0
0
0
2
1
1
1
0
1
0
0
0
2
1
0
1
1
1
2
1
0
1
2
0
2
1
1
1
0
0
1
1
0
0
0
0
0
0
2
1
0
0
1
0
0
1
0
2
1
1
1
1
0
0
1
0
2
1
2
0
1
0
0
2
0
1
2
2
1
0
1
2
3
1
2
1
1
1
0
0
1
0
3
2
0
0
3
0
1
0
0
0
2
0
1
0
0
0
0
0
1
1
0
0
1
1
0
1
1
2
0
0
1
1
1
0
0
0
1
1
2
1
0
2
1
0
0
2
1
1
1
1
2
1
3
1
1
0
2
0
1
1
1
2
2
0
1
3
0
0
0
0
0
0
0
0
1
1
0
1
1
1
2
0
1
0
0
1
2
2
1
1
0
2
0
0
0
2
2
1
2
0
1
2
0
0
2
0
1
2
2
1
1
1
2
1
1
1
0
0
0
0
1
0
1
1
1
0
0
1
2
0
1
2
1
1
0
0
1
0
0
0
0
2
1
2
1
0
1
1
0
0
0
2
0
2
2
0
0
1
0
2
0
0
0
0
0
2
0
3
0
0
0
2
2
2
2
0
0
2
1
2
1
2
0
0
0
4
1
1
1
0
1
0
0
0
0
2
1
1
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
1
2
0
1
0
0
1
0
1
5
2
0
0
1
0
0
1
0
0
2
2
2
0
2
0
2
0
0
2
1
1
0
0
1
3
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
1
1
1
0
0
1
2
0
1
0
0
0
0
1
0
1
2
1
0
2
1
1
1
0
2
2
0
0
0
1
1
0
0
1
0
1
1
1
2
2
0
0
1
1
0
0
0
1
0
0
2
0
0
0
0
1
1
0
0
0
1
1
1
1
1
1
0
1
0
0
0
0
1
1
1
0
1
0
0
0
0
0
1
1
0
0
1
1
1
0
2
0
0
0
0
0
2
0
2
3
0
0
2
0
0
0
1
0
0
4
0
1
0
0
0
0
0
2
1
0
0
1
2
1
0
0
0
2
2
2
0
1
2
1
0
1
0
0
0
1
1
1
0
0
0
1
0
1
0
1
2
1
2
2
0
0
1
0
0
1
0
1
0
2
0
2
1
2
2
0
2
0
2
1
1
1
2
1
2
1
2
2
1
3
1
2
2
1
1
0
0
1
2
2
0
1
1
2
0
0
1
1
0
0
1
0
0
1
0
1
0
1
0
0
0
2
0
0
1
0
1
0
2
2
3
2
2
0
0
1
1
0
2
0
0
2
1
1
0
1
1
0
1
1
1
2
1
1
0
1
1
2
1
2
0
2
2
2
0
0
2
0
0
0
2
2
1
0
2
0
0
2
1
2
0
0
1
0
0
1
0
0
0
2
1
2
2
0
1
1
2
0
1
2
0
1
1
1
0
0
2
0
1
2
1
0
1
1
2
0
2
2
2
0
0
1
0
1
2
2
3
1
0
1
2
0
0
1
1
0
1
2
2
2
0
1
2
1
0
2
0
1
0
2
1
0
0
0
0
0
0
0
1
1
0
0
1
2
0
1
1
1
0
2
0
0
0
0
2
0
0
0
1
1
0
0
2
2
2
1
0
0
2
1
2
0
1
0
1
0
0
1
0
1
2
2
0
0
0
0
2
0
0
0
1
1
0
1
1
1
0
1
0
0
0
1
2
2
3
1
1
2
0
1
0
1
2
2
1
1
2
2
0
1
2
0
0
1
0
1
0
0
2
1
0
0
0
2
1
2
1
0
0
2
1
0
2
0
0
0
0
3
0
0
0
0
0
1
2
0
0
2
0
1
0
1
1
2
2
0
0
0
0
2
1
1
0
1
2
0
0
1
1
1
1
0
1
2
1
1
1
2
1
0
1
0
1
0
0
0
0
0
2
1
2
0
2
0
1
1
0
2
0
0
2
1
0
0
2
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
2
1
0
2
0
0
0
1
2
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
1
0
2
0
0
3
0
0
1
1
0
1
0
1
1
0
1
0
1
2
0
0
2
1
1
0
1
0
1
0
1
2
2
1
0
0
0
1
2
2
0
0
0
1
1
2
2
0
3
0
2
2
1
1
2
0
2
2
0
2
1
2
2
3
1
1
0
1
0
1
0
1
0
0
1
1
1
2
0
3
1
1
0
1
2
2
2
1
0
1
0
0
1
1
0
1
1
3
0
2
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
1
1
0
2
1
0
0
0
0
1
2
2
0
1
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
2
1
0
0
0
1
1
2
1
0
0
2
2
0
1
0
0
0
0
0
2
2
1
0
0
0
0
1
2
2
2
2
1
0
2
0
1
0
0
1
2
1
1
0
1
1
1
0
0
1
0
0
0
0
1
2
0
2
2
2
0
0
1
0
0
0
2
0
1
2
1
0
1
2
1
0
1
0
0
0
0
0
0
0
2
1
0
1
0
2
0
3
1
1
1
0
0
1
0
2
1
0
1
0
0
0
0
0
0
0
0
3
0
1
0
1
2
0
2
2
1
2
1
2
2
0
0
1
0
0
0
1
0
0
1
2
0
0
1
0
1
0
2
0
0
0
1
0
0
1
0
1
0
0
1
1
0
1
1
0
0
0
0
2
0
0
2
0
1
2
0
2
0
0
0
1
1
1
0
0
0
1
1
0
3
1
1
0
0
0
2
1
1
0
0
2
1
1
1
1
1
1
2
1
0
1
2
0
2
0
1
2
0
0
1
0
0
0
1
0
0
1
2
0
0
0
1
1
1
0
1
0
0
0
2
0
1
1
3
0
0
0
0
1
0
0
2
1
2
0
1
0
1
0
0
2
0
0
1
1
0
0
0
1
0
1
2
1
4
0
1
2
2
0
0
1
0
1
1
0
2
0
0
0
0
0
0
0
1
2
0
2
0
0
2
0
0
0
0
0
2
0
1
0
1
1
0
1
0
1
2
1
0
0
0
0
1
0
1
0
0
0
2
1
3
0
0
0
0
0
0
2
0
2
0
0
0
2
1
0
5
1
0
0
0
0
1
0
1
0
0
2
0
0
2
1
2
1
0
1
2
0
2
0
1
2
2
2
1
1
0
0
0
1
0
0
0
0
2
1
1
1
1
1
1
2
3
2
0
1
2
1
1
0
1
1
0
1
2
1
0
0
0
1
0
1
1
0
1
1
0
0
0
3
0
0
0
1
0
2
2
2
1
0
0
1
1
1
0
2
1
0
0
0
0
0
2
0
1
0
0
2
1
1
2
1
0
1
2
0
0
2
1
1
0
1
1
1
1
0
2
0
0
2
1
0
2
2
1
0
1
1
1
1
0
2
0
0
0
1
1
1
0
1
1
0
0
1
0
1
0
2
1
0
2
1
1
2
2
1
2
2
1
0
0
1
2
0
0
1
0
0
0
0
2
1
0
1
0
0
0
0
2
0
1
2
1
0
2
2
0
1
0
1
2
1
0
1
0
0
0
0
2
1
2
1
2
2
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
1
0
1
1
1
0
1
0
0
1
0
2
0
2
1
1
2
0
1
1
0
0
2
2
3
0
1
0
2
2
0
2
1
0
0
1
0
2
0
1
1
1
1
1
1
3
1
0
1
1
1
0
0
1
1
1
2
2
2
2
2
0
2
1
0
2
0
0
1
1
0
2
0
0
0
1
0
1
0
2
1
0
0
2
2
1
0
0
2
2
1
0
0
3
0
2
0
3
0
2
1
1
1
0
0
1
0
1
0
0
0
3
0
0
1
1
0
0
1
2
2
2
0
0
2
1
0
2
0
1
1
0
1
0
0
0
0
1
0
3
0
0
1
1
0
3
1
2
0
1
0
0
0
1
3
1
2
2
0
1
1
0
0
2
1
2
0
0
1
1
2
2
1
0
1
2
2
2
1
0
0
0
2
0
0
1
1
1
0
0
1
2
2
2
0
0
0
1
1
2
1
0
0
2
0
1
1
1
1
1
0
0
1
0
0
0
1
0
2
0
0
1
0
1
0
1
0
1
0
0
1
0
0
1
1
2
1
1
1
0
1
0
2
0
0
0
2
1
2
0
0
1
0
0
1
0
1
1
0
1
2
1
0
1
2
0
3
0
2
2
1
1
0
1
4
2
2
1
0
0
0
0
1
1
0
0
0
0
1
1
0
1
2
0
1
0
2
1
1
1
1
2
2
0
1
0
0
0
2
1
0
2
3
0
0
1
0
1
0
0
1
0
0
0
2
0
2
2
0
0
0
1
1
0
0
0
0
1
2
0
2
0
2
0
0
0
2
0
0
1
0
2
0
2
0
0
0
2
0
1
0
0
0
1
0
1
0
0
2
1
1
1
0
1
0
0
0
1
1
1
0
0
1
0
3
0
1
0
1
1
2
0
1
0
2
0
0
0
0
2
1
0
0
2
2
4
1
1
0
1
3
0
1
0
2
0
0
1
0
1
0
1
1
0
2
0
0
2
0
1
2
1
1
0
0
1
0
2
1
0
0
1
0
0
1
2
1
0
1
0
1
0
0
0
2
0
2
0
0
1
1
0
1
0
0
1
1
0
2
0
1
1
1
1
0
0
2
1
2
1
0
0
2
1
2
1
0
1
2
0
1
0
0
1
2
0
2
2
0
1
1
0
2
0
2
1
0
0
0
1
0
1
1
0
0
0
1
1
0
0
1
0
1
1
1
1
0
1
0
0
1
0
0
0
0
2
1
1
0
1
2
0
2
0
0
0
0
0
0
1
0
1
1
0
1
0
2
2
0
2
1
0
0
1
1
2
1
0
1
0
1
0
0
1
0
0
0
0
0
0
1
2
1
0
0
0
2
0
1
2
1
0
1
2
4
1
0
0
2
2
2
0
0
1
0
1
1
1
0
0
1
1
0
1
0
1
0
1
0
1
0
0
1
2
1
1
1
0
4
4
2
0
0
2
2
1
1
1
0
0
1
0
0
0
0
2
0
1
0
0
0
2
0
0
0
2
1
0
0
2
3
0
0
0
1
0
0
0
0
0
0
1
1
0
2
2
0
0
0
1
1
0
1
0
0
1
2
0
0
1
0
1
1
1
1
3
0
2
0
1
1
1
1
0
0
1
1
1
3
0
0
1
2
0
1
2
0
1
0
0
0
0
3
0
0
1
0
1
0
0
1
3
0
1
0
0
0
2
1
0
3
0
0
0
0
0
0
1
1
0
1
0
0
2
2
0
2
1
2
2
0
0
0
2
0
2
0
0
1
2
1
2
0
0
1
0
2
0
2
2
1
2
0
1
1
0
1
2
0
0
1
2
0
0
2
0
1
0
1
1
1
1
0
0
2
2
2
1
0
0
1
0
2
0
1
0
2
0
1
2
0
1
1
1
2
1
0
2
1
1
2
0
3
1
0
0
0
0
0
2
3
0
2
0
1
1
0
0
0
1
0
0
2
0
0
0
0
0
2
0
2
0
1
0
2
0
2
2
0
0
0
0
0
2
1
0
1
1
0
1
0
0
0
0
0
1
0
2
0
0
0
3
1
2
1
0
0
0
0
0
1
0
2
0
1
1
0
3
2
2
2
0
0
0
1
1
0
1
2
1
1
1
2
0
0
0
0
1
0
0
0
1
1
2
0
0
0
2
0
0
0
2
0
0
1
0
1
1
1
0
2
0
1
1
0
0
2
2
1
0
1
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
2
2
0
1
2
1
0
1
0
1
1
0
0
1
2
2
0
0
0
0
2
1
2
0
1
0
0
0
0
1
0
0
1
0
1
0
1
1
1
0
1
1
0
1
1
0
1
0
1
0
0
0
1
1
1
0
1
0
0
0
0
1
2
1
0
0
1
0
2
0
0
2
1
2
2
1
0
1
0
0
0
0
0
1
1
1
0
0
2
0
0
0
1
0
0
3
1
2
1
0
1
1
2
0
0
0
1
1
2
1
0
0
2
2
1
1
0
0
1
2
1
0
0
0
0
0
1
0
0
0
1
2
1
1
0
0
1
0
2
1
0
2
1
1
0
1
1
0
1
1
2
1
1
0
1
1
1
1
1
0
1
0
0
1
0
0
2
2
0
1
0
1
1
0
1
0
1
0
0
0
2
0
2
1
1
1
1
2
1
0
0
1
2
0
0
2
0
2
2
0
0
0
1
0
1
0
0
0
0
1
2
1
0
1
1
0
1
1
0
1
2
1
0
0
1
0
2
0
2
2
1
0
2
0
1
0
0
1
1
2
1
0
1
3
2
2
2
0
0
0
2
0
1
0
2
1
0
2
0
2
1
1
1
1
0
2
0
4
2
0
1
1
2
0
0
2
2
2
1
0
0
0
0
2
1
0
1
0
2
2
0
2
0
1
0
0
0
4
1
0
0
2
1
1
2
2
0
1
1
0
2
1
0
0
1
8
0
1
1
2
2
2
1
0
0
0
1
0
1
1
0
2
0
1
0
0
0
1
1
0
2
2
2
2
0
0
0
2
1
0
0
1
1
0
2
4
0
0
0
0
0
0
2
2
1
1
0
2
0
0
2
0
1
0
1
2
1
0
1
0
0
0
0
2
0
0
2
0
0
0
0
1
7
0
0
1
1
0
2
1
2
0
0
1
1
1
0
1
0
0
0
0
0
2
2
1
0
1
0
0
0
0
0
1
1
0
2
0
1
1
1
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
2
0
2
2
0
1
1
0
0
0
2
2
0
1
0
2
0
1
1
0
0
0
0
1
0
1
1
1
1
0
0
0
2
1
0
0
1
2
1
0
0
0
2
1
1
1
0
0
0
2
2
0
0
2
0
1
1
0
0
0
1
1
0
2
2
0
0
1
1
0
2
0
1
2
2
2
1
1
1
1
2
1
1
1
0
1
0
0
0
0
0
1
0
0
1
0
2
0
2
2
0
0
3
0
2
3
0
1
1
0
2
2
1
0
1
1
1
1
1
0
0
0
2
0
0
1
1
0
1
0
1
2
1
0
0
0
1
2
2
1
0
0
2
0
1
1
1
0
2
1
0
1
1
0
2
2
1
0
2
0
1
0
0
1
0
0
2
0
0
0
2
3
1
1
1
2
1
1
0
0
2
0
1
1
2
0
2
1
0
1
0
1
0
2
3
0
0
2
0
0
1
0
0
1
1
0
0
0
1
2
0
0
0
0
0
1
1
0
2
1
0
0
1
0
1
2
0
1
1
2
3
0
2
0
0
2
2
1
0
0
2
0
0
0
1
0
0
0
1
1
2
0
0
0
1
2
1
0
2
1
0
0
0
0
1
0
2
0
1
1
0
0
2
0
0
0
1
1
1
0
0
0
1
1
0
2
1
1
0
1
7
1
0
2
1
2
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
1
2
1
2
0
0
0
0
0
0
1
1
0
0
1
0
0
1
2
0
1
1
0
0
0
0
1
2
0
1
1
2
0
0
0
1
0
0
2
1
1
0
1
0
2
1
2
1
2
0
2
1
0
0
1
1
2
0
1
2
0
0
2
1
1
0
0
1
0
1
0
0
1
0
1
1
2
1
0
0
0
3
0
2
0
1
1
0
1
2
0
1
0
1
0
2
1
3
1
0
1
1
0
2
0
1
0
0
1
0
2
0
0
1
1
0
1
0
2
0
0
0
0
0
0
2
1
2
1
2
1
2
1
0
1
1
0
1
1
0
2
0
2
1
0
0
1
1
0
1
2
1
0
1
0
0
1
0
0
0
0
1
1
0
2
0
1
0
0
0
0
0
0
1
0
0
1
1
1
1
0
0
1
0
1
0
0
1
0
0
0
1
0
2
0
2
1
0
1
1
0
1
0
0
0
1
0
1
2
2
1
0
1
0
1
0
0
2
0
0
0
1
2
0
0
1
0
0
2
0
1
1
0
1
0
0
1
0
0
0
1
2
2
0
3
0
0
1
0
2
0
1
0
0
2
0
1
1
1
0
0
2
0
1
3
1
0
1
2
1
2
0
1
2
0
0
1
2
1
2
0
2
2
0
0
1
0
1
2
0
0
1
2
2
0
2
1
0
1
0
0
2
0
2
0
0
1
0
0
0
1
1
0
0
2
2
1
3
0
1
0
1
2
0
0
1
0
0
1
1
0
0
1
1
0
0
0
0
2
1
1
0
1
0
2
0
2
0
1
1
1
0
1
0
1
0
2
1
0
0
2
0
0
2
0
0
0
0
2
2
0
1
2
2
0
0
1
0
1
0
0
0
1
2
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
1
0
1
1
0
2
0
0
0
1
0
0
0
0
1
2
1
1
1
0
1
0
0
0
2
0
5
2
2
2
0
0
2
1
3
0
1
0
0
2
0
1
1
1
0
0
0
2
1
1
2
0
0
0
0
2
0
2
0
1
1
0
1
1
1
2
1
0
0
0
1
2
2
0
0
0
1
3
0
0
1
1
0
0
1
1
3
1
0
0
0
0
0
2
2
2
0
0
0
0
0
0
1
1
1
0
1
1
1
1
1
0
0
2
1
1
1
0
0
0
1
2
0
0
0
1
0
2
0
0
0
2
1
0
1
0
2
2
1
0
0
0
0
0
0
2
0
0
0
0
2
0
2
2
1
1
0
3
0
1
0
0
1
1
2
0
1
2
2
1
1
0
0
1
0
2
1
1
0
1
1
0
1
1
1
1
0
1
2
0
1
0
0
2
2
2
1
1
0
2
1
1
0
0
0
1
0
1
0
0
2
2
0
1
2
2
0
1
1
1
0
2
1
0
1
0
0
1
1
0
0
0
0
2
2
0
3
0
2
1
0
1
2
1
1
1
0
0
0
2
1
0
1
1
1
0
2
1
1
0
2
0
0
1
1
0
0
0
1
0
1
2
0
0
0
0
2
2
8
2
0
1
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
1
0
2
0
1
0
2
2
1
1
0
2
1
0
1
2
1
0
0
1
0
2
0
0
0
1
0
1
0
1
0
0
0
1
0
2
1
2
1
0
0
0
1
2
0
1
3
0
1
2
0
1
1
1
1
0
1
0
1
1
2
2
1
0
0
0
0
2
1
2
1
0
2
0
1
2
0
1
2
2
1
1
2
1
1
3
2
0
2
0
1
2
1
2
0
1
1
1
2
1
0
2
1
2
1
1
0
1
2
1
2
1
1
1
2
0
2
0
0
1
0
0
2
1
1
0
0
0
0
1
2
0
0
1
2
0
2
1
0
2
0
0
0
0
2
0
0
2
0
1
2
0
0
1
0
0
0
0
0
2
0
2
2
0
1
1
0
2
0
0
2
0
3
0
0
1
3
0
0
0
0
0
0
0
0
0
2
0
2
1
1
1
2
0
0
0
2
2
0
2
0
1
0
0
2
0
0
0
0
0
2
2
0
0
2
0
0
2
5
2
0
0
1
1
7
1
0
2
0
0
1
1
0
0
0
0
3
1
1
2
1
1
3
0
2
0
0
2
1
0
1
0
0
1
0
1
0
4
1
1
2
0
2
3
1
0
12
1
0
0
1
1
2
1
0
2
0
0
1
1
1
1
2
0
1
0
0
0
1
2
0
2
0
1
1
1
0
0
1
1
0
0
1
2
1
0
1
0
1
1
0
0
1
1
2
2
2
0
0
1
0
1
2
0
0
0
1
0
1
0
0
0
2
2
0
3
2
2
0
2
1
0
0
0
1
0
0
2
0
0
1
0
1
0
0
2
0
0
0
0
1
0
1
0
2
3
2
0
1
0
0
1
1
0
1
0
1
2
0
1
1
2
0
1
2
0
1
0
0
1
1
0
2
0
0
2
0
2
0
0
0
1
0
1
0
0
0
0
1
1
2
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
2
2
1
1
0
1
2
1
2
2
0
1
0
2
0
0
1
0
2
0
1
1
0
0
1
1
0
2
1
0
1
0
0
1
1
1
2
1
1
1
2
1
0
1
1
0
0
2
2
6
1
0
1
0
0
1
0
1
1
2
0
1
1
0
1
0
2
0
1
0
0
0
0
1
0
1
2
2
1
1
1
1
1
2
0
0
2
1
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
2
1
0
1
1
0
1
0
0
2
1
1
1
0
0
1
0
2
0
0
0
0
0
0
1
2
1
1
2
0
0
0
1
0
0
1
2
2
1
0
1
1
1
0
0
0
1
1
2
2
0
0
2
0
0
0
1
2
1
0
1
1
2
0
0
2
1
0
2
1
2
0
1
0
0
1
0
0
1
0
2
1
1
0
0
0
1
0
0
0
0
0
0
0
1
2
0
1
0
0
0
1
2
0
2
0
0
0
1
0
0
1
0
2
2
2
2
2
0
1
1
0
1
1
0
1
0
0
0
2
1
2
3
2
0
0
1
1
0
1
0
0
1
1
0
0
1
0
1
1
0
0
2
1
2
0
2
1
1
1
1
1
1
1
0
1
0
2
0
1
2
0
1
0
0
1
1
1
2
0
0
0
2
0
0
2
2
0
0
0
1
1
1
0
0
0
0
0
1
1
1
0
0
0
2
0
2
2
2
0
0
0
2
0
1
0
0
0
0
2
1
0
1
0
0
2
0
2
0
3
2
1
1
0
0
0
0
1
2
0
2
1
1
1
0
1
0
0
1
1
0
1
0
0
0
0
1
0
3
1
2
0
1
1
1
0
1
0
1
0
3
0
0
0
0
0
0
1
0
1
0
2
1
2
1
1
0
6
1
2
1
1
2
1
1
0
0
0
2
0
1
0
1
1
1
1
1
0
2
2
2
1
0
0
1
0
0
1
2
0
0
1
0
2
1
0
2
2
0
1
0
4
2
0
1
1
0
2
0
0
0
1
1
2
2
1
0
1
1
0
0
0
2
1
2
2
0
1
2
2
1
2
0
1
0
2
0
0
0
0
1
0
0
1
1
0
0
2
0
0
0
1
0
0
1
0
2
2
1
1
0
0
1
0
0
0
1
1
1
2
1
1
0
0
0
0
0
2
0
1
1
0
1
0
1
2
2
0
4
2
0
0
0
0
2
1
1
1
0
0
0
1
0
2
1
1
0
1
0
3
1
2
2
0
1
0
0
1
0
0
1
0
0
2
2
2
2
0
0
0
0
1
0
1
2
2
0
0
1
2
0
2
3
1
0
1
0
2
1
1
2
2
1
1
0
0
0
0
0
0
0
0
1
1
2
0
0
1
1
0
0
0
1
2
0
0
0
2
2
1
0
0
1
0
1
0
0
0
2
2
1
2
0
3
0
1
2
1
2
1
2
1
0
0
2
2
2
1
0
0
0
1
1
0
1
2
1
0
0
1
0
1
2
3
1
1
2
2
0
1
0
1
0
0
0
1
0
2
1
0
1
2
1
0
1
2
1
2
1
0
0
0
1
1
2
0
2
1
0
1
1
0
0
2
0
0
1
1
1
0
0
2
0
0
2
2
2
0
1
0
2
0
0
0
0
0
1
1
0
2
1
1
2
0
0
2
2
1
1
0
0
1
0
1
2
1
0
1
1
0
0
0
0
1
0
1
0
2
0
1
0
0
1
0
0
0
0
1
0
2
1
1
1
1
0
1
0
0
1
3
1
2
0
0
1
0
0
2
1
0
1
1
1
2
2
0
2
0
0
0
2
0
2
0
1
1
0
0
0
0
0
0
1
1
1
2
0
1
2
1
1
1
1
1
0
0
0
2
0
0
2
2
2
0
0
3
0
0
0
0
2
1
1
1
0
2
0
2
1
0
0
2
0
3
0
1
1
1
0
0
0
0
0
0
0
0
1
1
1
0
1
0
1
1
0
1
0
2
1
1
0
2
1
0
1
0
1
0
1
0
0
2
2
0
2
0
2
0
0
0
1
0
0
2
2
1
1
0
1
0
0
0
0
1
0
0
0
0
1
0
1
2
1
2
1
0
3
3
0
0
0
3
0
0
2
1
0
1
0
1
0
4
0
2
2
1
0
0
1
0
2
2
0
0
0
0
2
2
1
0
1
0
0
2
0
1
0
1
1
0
0
0
1
0
1
0
1
2
1
1
0
0
1
1
0
1
2
2
1
0
1
0
0
2
0
1
2
0
0
0
1
1
0
0
1
1
0
0
2
0
1
0
1
2
0
1
2
2
0
0
1
1
0
1
1
1
1
0
2
1
1
2
2
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
1
1
2
2
1
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
1
1
1
1
0
2
0
2
2
0
0
2
2
0
1
0
1
2
0
0
0
0
1
0
0
0
2
0
0
0
2
1
1
0
1
0
0
2
3
0
2
0
0
1
1
0
0
1
1
0
2
0
0
0
0
2
0
0
1
1
2
1
1
3
1
1
2
3
0
0
0
0
2
1
0
0
0
0
2
0
0
1
0
1
0
1
0
0
0
0
0
2
0
0
1
0
1
0
2
1
2
2
1
0
0
0
1
1
2
1
1
0
1
0
2
2
1
2
0
2
0
0
1
1
1
1
0
0
1
1
1
0
2
2
1
2
0
0
0
0
1
2
0
0
0
0
0
2
0
0
1
1
1
1
2
0
2
0
1
1
0
0
0
1
1
0
0
0
1
1
1
0
1
0
0
0
1
1
2
0
2
1
2
1
1
1
2
0
1
0
0
2
0
2
1
1
0
0
1
0
0
2
0
2
2
0
0
2
1
0
0
0
1
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
1
0
1
1
1
0
6
0
0
0
0
0
0
2
1
0
0
0
2
1
1
0
1
2
0
0
1
2
2
1
2
3
0
1
0
1
0
0
0
2
0
2
0
0
1
0
1
1
2
1
0
1
1
0
2
1
0
0
1
0
0
0
2
0
5
0
0
0
1
1
0
0
0
1
1
0
2
0
2
0
1
2
0
0
1
1
1
0
1
0
1
1
0
2
0
1
3
2
1
1
1
2
0
0
0
1
1
2
1
0
2
1
1
1
1
0
2
1
1
0
1
0
1
0
1
1
0
1
0
1
2
0
1
0
1
0
0
1
1
0
0
1
1
0
0
1
0
0
1
0
0
1
1
1
0
1
1
0
2
2
0
1
0
0
1
2
0
2
1
0
1
0
0
2
0
0
0
0
0
1
0
0
2
1
0
2
0
0
2
0
2
1
1
1
2
0
2
1
1
0
0
1
2
0
0
0
0
1
0
1
1
0
0
0
1
0
0
1
0
1
0
1
2
0
0
0
0
0
2
0
0
0
2
2
2
1
0
0
1
0
1
1
2
1
1
0
1
3
0
0
2
0
0
0
1
1
1
0
0
1
0
0
0
1
0
1
0
1
0
1
1
1
1
0
0
1
2
1
0
1
0
0
0
0
0
0
1
1
0
0
2
0
0
2
0
1
1
0
2
1
2
0
0
2
2
2
0
0
0
0
0
0
0
1
2
0
0
2
0
1
1
0
1
0
0
0
1
0
0
0
2
0
0
1
2
0
1
0
1
0
2
0
1
0
1
0
1
2
1
0
0
0
0
0
0
0
0
0
2
1
1
0
0
2
0
0
1
0
2
0
0
0
2
0
2
0
4
2
0
1
0
2
0
0
0
1
1
0
0
0
0
0
2
0
2
0
0
1
1
0
0
0
2
0
1
1
1
0
2
0
0
2
3
0
0
0
0
1
2
0
0
0
2
1
0
1
0
2
0
1
1
1
1
0
1
0
0
0
2
2
0
2
1
2
1
2
2
0
1
2
0
0
1
0
1
0
2
1
2
2
1
1
0
0
2
0
0
0
0
0
0
0
0
1
1
1
2
0
0
0
2
1
1
1
3
0
0
1
0
1
0
0
1
0
0
1
2
0
0
0
1
1
2
0
0
1
2
1
2
0
1
2
2
2
0
1
1
0
1
1
2
0
1
1
1
0
0
1
1
0
0
1
1
0
1
0
2
2
0
0
2
0
0
2
2
0
2
2
0
0
1
0
2
5
1
1
2
2
0
0
1
0
0
0
0
1
2
0
0
2
0
1
1
1
1
0
0
0
2
2
0
1
1
0
0
2
1
0
1
0
1
1
0
1
0
0
0
0
0
0
1
2
1
2
1
2
0
2
0
1
0
2
1
0
0
2
0
1
1
2
0
1
0
0
0
1
1
1
0
3
0
0
0
0
0
0
1
2
2
1
0
1
0
1
0
2
0
0
1
1
1
1
1
0
0
2
1
0
1
0
0
0
0
2
2
0
1
0
2
1
1
0
0
1
0
1
0
1
2
0
1
1
0
0
0
0
2
2
1
1
1
0
0
0
0
2
0
0
0
1
2
0
0
1
0
1
1
0
1
0
0
0
0
1
1
0
2
1
1
0
0
1
1
0
0
0
0
1
1
0
1
2
1
0
2
1
1
1
1
0
1
0
1
1
0
0
1
2
1
0
2
1
0
1
0
0
0
0
0
0
1
0
2
1
0
2
2
2
0
0
1
2
0
0
1
0
2
1
0
1
0
1
0
1
2
0
0
0
0
1
0
0
0
2
1
1
0
0
0
0
0
2
1
1
0
1
1
0
1
0
1
0
0
0
1
1
2
0
1
0
2
2
1
0
0
1
0
0
2
1
0
0
0
0
2
0
2
2
2
1
1
0
1
0
0
1
0
1
0
0
1
0
0
0
1
2
0
3
0
0
1
0
0
0
1
1
2
1
0
1
0
0
2
0
2
2
2
0
0
2
1
0
0
1
1
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
1
0
1
2
2
1
2
0
0
1
1
0
0
1
0
0
1
2
0
1
2
1
0
2
0
0
0
1
0
1
0
0
0
1
1
0
0
3
0
3
0
1
0
1
0
1
1
0
2
0
0
1
0
2
0
1
2
1
1
0
0
1
2
0
0
2
1
0
0
0
2
1
0
0
1
2
1
0
1
0
0
2
0
2
0
0
0
0
1
3
0
0
0
0
1
1
1
1
2
0
1
0
1
2
2
1
1
1
0
0
1
1
0
2
0
1
1
0
1
2
0
0
0
1
2
4
0
0
0
1
1
0
0
1
1
7
0
1
0
0
0
0
0
0
0
1
0
1
2
1
0
1
0
0
1
1
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
1
1
0
1
1
0
1
2
0
2
2
0
1
0
2
0
2
0
0
0
0
2
2
1
1
2
1
1
1
2
1
0
2
0
2
5
2
1
0
1
1
2
0
0
1
1
1
0
0
0
0
2
2
1
2
2
3
1
1
1
2
1
0
0
0
0
4
0
0
1
1
1
0
0
2
0
1
2
1
0
2
0
0
2
1
2
0
0
2
0
2
2
1
0
0
1
0
0
0
1
0
0
1
0
1
0
1
0
1
1
0
1
2
0
0
1
1
0
2
0
0
0
1
2
0
0
0
2
0
0
1
1
2
1
1
0
2
1
1
0
2
3
1
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
2
1
0
3
1
1
0
1
0
2
0
1
1
0
0
0
0
1
0
1
1
1
1
0
0
2
0
1
0
0
0
1
1
0
0
0
1
0
0
2
1
0
2
0
0
2
1
2
2
1
0
0
0
1
0
3
2
1
1
1
1
1
0
2
0
0
1
0
0
1
0
2
2
0
0
3
0
1
2
0
0
2
0
1
0
0
2
0
0
0
5
2
1
0
1
0
1
1
1
1
0
0
0
2
1
0
0
0
0
0
0
1
0
0
1
1
0
1
2
1
0
0
0
2
2
0
0
2
0
0
0
0
0
1
0
0
0
0
1
2
0
2
0
2
0
1
2
2
1
0
2
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
2
0
2
1
0
0
1
0
1
2
1
2
0
0
0
0
2
0
1
2
0
1
0
0
0
1
1
0
1
0
0
2
0
0
2
0
6
1
0
0
1
1
0
1
0
0
0
0
2
0
1
1
2
0
0
1
0
1
0
0
0
0
1
0
1
0
4
0
0
1
0
1
2
1
1
1
1
1
0
1
1
0
0
1
0
0
0
1
0
1
1
0
2
0
1
0
1
2
2
2
1
2
2
1
1
1
2
1
0
2
0
0
0
2
0
1
0
0
0
0
0
0
1
2
0
0
1
1
0
1
0
0
1
1
1
2
1
0
2
0
1
2
1
0
2
0
0
0
0
2
0
0
0
2
0
2
2
0
1
2
1
0
1
2
2
0
2
1
0
0
0
2
2
0
0
0
0
1
0
1
1
1
2
1
1
1
2
2
1
2
0
2
2
0
1
1
0
0
2
1
2
0
2
2
2
2
0
2
2
0
1
0
2
1
0
1
0
0
2
1
0
1
0
2
0
1
0
2
2
1
2
2
1
0
0
2
0
0
0
0
0
2
0
2
0
1
1
0
0
2
2
0
1
0
1
2
2
0
0
0
1
0
0
1
0
1
0
0
0
2
3
0
0
2
0
1
1
1
1
1
0
2
1
2
1
0
0
0
0
0
0
1
1
1
2
2
1
0
0
2
0
1
0
0
1
1
0
1
0
0
2
2
0
3
5
1
0
0
0
1
2
3
1
2
0
2
2
0
0
2
0
2
0
0
1
0
0
0
1
1
2
0
0
2
1
0
1
1
0
2
1
0
0
2
1
2
0
0
1
0
0
1
1
0
2
1
2
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
1
2
0
2
1
1
1
0
0
3
2
1
1
0
0
0
2
2
1
0
1
0
1
1
0
2
0
0
0
0
0
0
0
1
2
1
0
2
0
2
1
1
0
0
1
0
1
1
1
1
0
2
0
0
1
1
0
0
0
2
1
2
0
0
1
1
0
0
1
0
1
0
0
0
2
0
0
1
0
0
1
0
1
0
1
1
0
2
0
0
0
1
2
0
2
0
1
2
1
0
1
2
1
1
0
0
0
1
0
0
0
0
1
1
2
1
1
1
2
1
0
2
2
2
2
1
0
1
2
1
2
0
1
1
0
2
3
1
2
0
0
0
1
1
2
0
1
0
2
3
0
0
0
1
1
2
0
0
1
0
1
1
2
1
0
2
1
1
0
1
0
1
0
2
0
1
1
0
1
2
2
0
1
0
2
3
0
0
0
2
2
1
2
1
1
0
1
0
2
0
0
2
1
2
0
0
0
2
1
0
0
2
0
0
2
0
2
1
2
1
4
0
1
2
1
0
0
0
1
0
2
1
1
1
2
0
0
0
0
1
0
0
1
0
1
0
2
0
1
0
0
0
0
1
1
0
0
0
1
0
1
0
1
1
2
2
2
2
2
1
0
1
2
1
1
1
2
1
0
1
0
0
1
0
2
2
0
2
3
3
0
2
2
2
1
1
0
2
0
1
1
1
1
0
1
1
0
1
1
1
1
2
2
1
0
0
2
2
1
0
1
1
1
1
1
0
0
0
1
1
2
0
1
0
0
0
2
0
1
0
1
1
0
1
0
1
1
0
0
2
1
1
0
2
0
1
1
1
1
1
0
0
0
0
2
1
0
1
0
2
0
0
1
0
0
0
2
2
1
1
0
2
0
0
1
2
2
2
2
0
2
2
1
1
1
1
0
1
2
2
0
0
0
2
2
1
2
1
2
0
0
0
1
2
2
1
2
2
1
0
1
1
0
0
1
1
1
1
1
0
0
0
4
1
1
1
2
1
0
1
0
2
1
0
1
1
1
0
1
0
2
1
2
0
2
1
0
2
0
5
2
1
1
0
1
0
1
0
0
0
1
1
0
1
0
0
0
0
1
1
1
0
1
0
0
1
0
0
2
0
1
0
1
3
0
0
0
1
1
1
1
0
2
0
0
0
0
0
1
1
0
1
0
1
2
0
0
0
0
1
0
1
2
0
1
2
1
0
0
1
1
0
0
2
2
4
2
0
2
2
0
0
2
1
0
2
0
0
0
1
0
1
0
0
1
1
1
0
1
0
1
0
1
2
2
1
0
1
0
0
1
1
1
1
0
0
2
0
1
0
2
2
2
1
2
2
0
1
1
1
1
0
0
1
1
2
0
1
2
2
0
0
0
0
0
1
0
0
1
0
0
0
2
1
0
2
0
1
2
1
0
1
1
0
3
1
2
1
0
1
1
0
1
0
2
0
1
2
2
0
2
0
1
0
0
0
0
0
0
3
0
1
0
2
2
1
2
0
0
0
1
1
0
0
2
2
0
1
0
0
1
0
1
0
2
2
1
0
0
0
2
2
1
1
2
1
0
0
0
0
0
0
0
2
0
0
2
2
0
0
1
0
0
2
0
0
2
1
0
0
1
0
2
2
1
0
1
2
1
0
2
0
2
0
1
2
2
1
1
2
1
0
2
0
0
0
0
0
1
1
0
0
2
4
0
0
2
0
2
0
0
1
0
0
0
0
0
0
2
0
1
0
2
1
0
1
0
0
0
0
2
1
0
0
0
2
0
1
1
2
2
0
0
2
0
0
2
2
1
0
2
1
2
0
1
1
0
1
2
1
1
1
1
1
1
2
0
0
2
4
0
2
0
1
0
0
0
0
1
1
0
0
1
0
0
1
1
0
1
4
2
2
1
0
2
2
0
0
2
3
0
1
2
0
0
0
0
2
1
0
0
0
0
2
1
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
1
1
0
1
1
2
0
2
1
2
0
0
2
2
1
0
0
1
1
2
2
0
1
1
1
0
0
0
1
2
1
0
1
0
1
0
0
0
1
2
0
1
1
2
1
1
0
0
1
2
0
0
2
0
1
0
0
2
1
2
1
2
1
3
0
2
1
0
2
0
0
1
2
1
0
2
0
0
1
2
0
0
0
0
2
2
0
0
0
1
0
1
2
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
1
0
2
1
2
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
2
0
2
0
2
0
0
2
0
0
1
1
3
0
1
0
0
1
0
0
0
0
0
1
2
1
1
0
0
0
0
2
0
1
1
0
0
1
1
0
0
2
1
1
0
0
0
0
2
2
1
0
1
0
2
0
0
0
2
2
1
0
2
0
2
1
0
0
1
0
0
2
0
0
0
0
1
0
1
2
0
1
0
0
0
0
2
1
1
2
1
1
0
1
2
2
3
0
1
1
0
1
0
0
1
1
1
1
4
0
0
0
0
1
1
0
2
1
1
0
1
3
0
1
0
1
0
2
1
0
1
1
1
1
2
0
0
2
1
0
2
2
0
0
0
1
1
2
2
1
1
0
2
1
1
0
0
0
2
1
1
1
0
1
0
0
0
2
0
1
1
0
2
0
2
0
1
0
1
0
0
1
0
2
0
1
0
0
0
0
1
2
1
0
2
2
1
1
2
1
2
0
1
1
2
0
0
0
0
1
0
2
2
1
2
0
1
1
1
1
0
0
0
0
1
0
0
1
2
0
0
1
0
0
0
1
0
1
0
0
0
0
1
1
1
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
2
2
0
0
0
0
3
0
1
0
0
0
0
1
1
0
1
1
1
0
0
1
2
2
0
1
2
0
2
1
2
1
2
0
1
0
0
1
2
1
1
1
1
1
1
0
2
0
2
0
0
0
2
0
1
2
0
0
2
2
0
1
1
0
0
0
0
1
1
0
2
1
1
2
2
0
2
1
1
1
0
1
1
0
1
0
0
2
0
0
0
2
1
0
2
1
0
2
1
0
0
1
0
0
0
0
1
0
0
1
0
2
1
2
2
0
1
0
1
1
2
0
1
0
0
1
1
0
0
1
1
0
2
2
0
1
0
1
0
2
0
0
2
0
2
1
1
0
0
1
1
1
0
1
1
1
1
0
0
1
1
1
0
0
0
2
0
1
0
0
0
0
2
0
0
0
1
1
0
0
0
0
1
2
1
1
2
0
0
0
0
1
0
0
0
1
2
0
1
2
0
0
0
2
2
0
2
0
0
0
1
1
0
1
0
0
1
0
0
1
1
0
2
0
2
0
2
2
0
1
0
2
1
1
0
0
1
0
0
0
2
0
0
0
2
1
1
0
0
1
0
2
1
0
0
0
0
2
0
1
1
0
2
0
0
1
0
1
0
0
0
0
1
0
2
0
1
1
1
0
1
1
0
1
2
1
0
2
1
0
0
1
0
0
0
0
2
2
0
0
2
0
1
1
0
0
2
1
2
2
0
1
0
2
0
0
1
2
0
2
1
1
0
0
1
2
1
1
0
0
1
0
0
1
1
0
0
1
0
2
0
1
1
0
1
1
0
1
0
0
1
1
1
2
1
0
0
2
0
0
0
2
1
1
0
0
0
2
1
3
2
0
2
0
0
1
1
1
0
2
0
1
2
2
1
2
2
2
1
0
2
0
1
0
1
1
3
0
0
0
0
1
0
2
2
1
1
0
2
0
0
0
0
4
0
0
0
4
0
2
0
2
1
1
1
1
1
0
0
2
0
0
1
0
2
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
2
1
2
1
0
1
0
3
0
1
0
0
2
2
2
0
0
0
0
1
1
1
2
2
2
0
2
1
0
0
2
0
3
0
0
0
1
1
0
1
0
1
1
0
1
1
2
2
0
1
2
0
1
2
0
1
1
1
0
1
0
0
0
0
1
1
0
2
0
0
0
0
0
2
1
0
1
0
2
1
0
0
2
2
0
0
1
2
0
0
0
4
0
0
0
1
1
1
0
0
2
1
1
0
0
0
0
0
1
0
1
1
0
1
0
1
0
0
1
2
2
0
1
0
1
0
2
1
0
1
0
0
1
2
0
1
1
0
1
2
0
1
1
0
0
2
0
1
1
1
0
2
0
0
0
0
0
1
0
1
1
1
2
0
2
1
2
0
0
1
1
2
0
0
0
0
1
1
1
1
1
0
2
0
1
0
1
2
2
0
1
1
1
0
1
0
1
1
0
1
0
2
1
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
2
1
0
0
1
2
1
4
1
2
0
1
1
2
1
0
1
0
2
0
0
0
4
1
0
0
1
2
0
2
0
0
0
1
1
0
2
0
0
1
1
2
0
1
0
1
0
0
2
2
2
0
0
1
2
4
1
1
1
2
0
0
1
1
1
0
2
3
1
0
0
2
0
0
0
0
1
0
1
2
0
2
1
0
0
0
0
2
1
0
0
0
1
0
1
0
1
0
1
0
2
0
0
1
0
1
1
2
2
0
1
0
2
0
2
0
0
0
0
2
1
0
2
0
1
1
0
0
0
1
1
0
2
0
0
1
3
0
3
0
0
2
1
1
0
1
0
1
3
0
2
0
1
0
0
1
1
0
0
0
0
1
0
0
1
1
1
0
0
1
2
2
0
0
0
1
1
0
1
1
0
0
0
2
1
0
0
2
1
1
0
1
2
0
1
0
1
1
2
0
2
1
0
0
1
0
0
2
1
0
0
2
0
2
1
1
1
1
2
2
0
0
2
0
0
0
0
0
0
1
1
2
2
1
2
1
0
0
1
0
2
4
2
1
2
0
1
0
0
1
1
0
0
2
2
1
1
1
0
0
1
1
1
0
0
0
0
0
0
1
0
0
1
2
0
0
0
2
1
2
0
1
1
1
1
0
1
0
0
1
1
1
2
0
1
1
1
2
0
0
0
1
0
0
1
2
0
0
2
0
0
1
2
1
0
1
0
1
3
1
1
0
1
2
1
1
0
0
1
0
0
2
2
0
0
1
0
0
2
1
1
0
0
1
0
1
1
1
2
0
0
0
0
1
0
0
1
1
2
2
2
2
2
0
0
2
2
0
0
2
0
1
0
1
0
2
0
1
0
2
0
0
0
0
3
0
2
0
0
1
2
0
0
0
1
0
0
1
0
0
0
0
0
1
2
0
1
0
0
0
1
0
0
0
1
2
0
2
1
0
0
2
1
5
2
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
2
0
0
1
0
2
2
1
1
1
0
1
0
2
0
0
2
2
1
0
1
1
0
0
0
0
1
0
2
0
0
0
1
0
0
2
1
1
0
0
1
0
2
1
1
0
0
1
0
2
0
0
2
2
0
0
0
2
3
0
0
2
1
1
1
2
0
3
0
0
0
2
1
2
4
0
2
0
0
1
0
1
2
4
1
0
1
1
0
0
0
0
2
0
0
0
0
1
0
2
0
1
2
2
0
2
1
0
0
2
1
0
0
1
0
1
0
4
2
1
0
0
0
0
1
0
0
0
1
1
0
1
0
1
1
0
1
1
0
1
0
1
1
2
1
0
0
0
0
1
0
1
0
0
0
2
1
0
1
2
1
0
0
0
1
1
2
3
2
1
0
1
0
1
0
0
2
1
1
0
0
0
1
2
0
0
2
0
1
2
0
0
0
0
0
2
0
2
0
3
1
1
1
0
2
2
0
0
0
1
1
0
0
1
1
0
0
1
1
0
0
2
1
0
0
0
1
0
0
2
0
1
0
2
0
2
1
0
2
0
0
2
0
2
1
0
1
1
0
1
0
0
2
2
0
1
1
2
1
1
0
1
3
2
1
0
1
2
1
0
1
0
1
0
2
0
0
1
1
1
2
0
0
2
0
0
2
1
2
0
1
0
0
2
1
0
0
0
1
0
2
0
0
2
1
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
2
1
2
0
2
0
0
1
2
3
1
0
1
1
0
0
0
1
0
0
2
0
1
4
0
3
2
1
0
2
1
1
1
2
2
2
1
0
1
0
0
2
0
0
0
1
1
1
0
1
0
2
1
0
0
0
1
1
2
1
2
1
1
0
0
2
2
0
1
2
2
1
1
4
1
1
1
0
0
2
2
1
1
1
0
0
1
0
1
1
1
0
2
1
2
0
1
0
0
0
2
1
1
2
0
0
2
2
1
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
1
2
0
1
0
0
0
2
0
1
0
0
0
2
1
5
0
1
1
1
0
1
0
2
1
1
2
1
0
2
0
2
2
1
1
1
1
1
1
1
0
1
0
0
0
1
1
2
0
0
0
1
1
0
0
1
0
1
1
1
0
1
0
2
0
1
1
1
2
1
1
2
0
0
1
1
1
0
0
1
0
2
1
1
1
1
2
1
1
1
0
0
3
1
1
0
2
0
0
0
0
0
1
0
1
0
1
0
1
2
0
0
1
0
0
0
2
1
2
0
2
0
0
2
2
0
0
1
0
2
2
0
1
0
0
1
0
0
1
0
0
1
0
1
0
0
1
2
0
2
0
1
1
1
1
0
2
0
0
1
1
2
1
1
0
0
1
0
0
1
1
1
2
1
2
2
0
0
2
2
0
0
0
0
0
1
3
0
2
0
1
0
0
0
2
0
2
3
1
1
0
1
1
0
1
0
2
0
0
0
0
2
0
1
2
2
0
0
0
2
0
0
1
0
1
0
0
2
0
2
0
1
1
0
3
1
0
0
0
0
1
0
0
1
1
1
0
2
1
0
1
2
0
2
1
0
1
0
0
2
1
0
0
0
1
0
0
2
1
2
0
1
1
1
1
0
1
1
1
0
0
1
3
2
0
1
2
1
0
1
2
1
1
1
2
4
2
0
1
0
0
2
2
0
1
0
2
2
1
1
1
0
0
2
1
1
0
2
2
0
0
0
1
1
1
0
0
1
0
0
0
2
0
1
2
1
0
0
1
2
1
0
2
0
1
0
0
2
1
0
0
3
2
1
0
0
1
0
2
0
0
0
2
0
3
1
0
0
0
0
1
2
0
0
0
2
0
3
0
1
1
0
0
1
0
1
1
0
1
0
0
1
0
1
0
2
0
0
1
0
0
0
1
0
0
1
1
1
0
1
0
0
0
2
0
0
0
2
2
0
0
2
2
1
0
0
2
2
1
1
0
0
1
1
2
0
2
0
0
1
1
2
2
0
0
1
1
0
1
1
0
0
2
1
1
2
1
1
1
1
0
0
0
0
0
0
1
1
2
2
0
2
0
3
0
2
0
0
2
0
0
0
0
2
2
1
1
2
0
0
2
0
1
0
1
0
0
0
1
0
1
0
0
1
0
0
3
0
1
0
2
1
0
1
0
0
0
1
0
1
1
0
0
2
2
2
2
0
0
1
2
2
1
1
1
1
0
0
1
1
1
0
0
0
1
1
1
4
1
1
2
1
1
0
1
0
0
1
0
1
1
1
2
2
0
1
0
0
2
0
2
0
0
2
1
2
0
1
0
1
1
0
1
0
2
1
0
2
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
1
2
0
1
0
0
0
1
3
2
1
1
0
0
2
0
1
2
0
0
1
1
0
0
0
0
0
1
0
2
2
0
0
2
0
2
0
0
1
0
0
1
0
1
0
0
0
1
0
2
0
2
2
2
1
0
0
3
1
1
0
1
0
2
2
0
0
0
1
0
0
0
1
3
2
1
1
0
1
1
1
0
0
0
2
1
1
1
0
1
0
0
1
1
1
0
1
1
0
2
1
1
1
0
0
0
1
0
1
0
0
2
2
1
0
0
1
0
1
1
4
0
1
1
0
1
1
1
0
0
1
0
1
0
2
1
2
2
0
1
0
1
0
3
0
0
0
0
0
1
3
1
0
1
0
1
0
0
2
1
0
2
2
0
0
1
2
2
0
1
2
0
2
2
2
0
2
1
0
1
0
2
2
2
3
0
0
1
2
0
1
0
2
0
1
0
2
0
2
1
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
2
2
1
0
1
0
0
1
1
0
1
1
0
2
0
0
1
1
3
1
1
0
0
2
0
2
2
1
1
1
1
0
2
0
0
0
0
1
1
2
2
2
2
0
1
0
0
0
0
1
0
2
2
0
0
0
0
2
1
1
1
1
0
0
2
0
1
0
0
1
0
3
0
0
2
2
1
0
2
1
0
4
1
1
0
2
1
1
0
1
0
0
1
1
0
0
2
3
0
2
2
1
0
1
2
0
0
2
0
1
0
2
2
1
0
2
0
1
0
1
0
2
1
0
0
0
0
0
0
0
3
0
1
1
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
2
1
1
0
0
0
1
2
2
1
0
0
1
0
1
2
2
4
1
0
0
0
0
1
1
1
0
0
0
0
1
3
1
0
0
3
2
1
2
2
1
2
0
0
2
0
0
2
0
2
1
0
0
1
1
1
0
0
1
0
0
2
3
1
0
1
0
0
0
0
1
0
0
2
2
1
1
1
0
0
1
1
1
0
2
2
0
0
0
1
0
0
1
0
1
0
0
0
2
2
2
2
0
2
1
2
0
1
2
1
0
2
0
1
2
1
3
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
2
0
2
1
0
2
2
0
1
1
1
2
0
0
0
0
0
0
2
2
2
0
0
2
1
0
0
1
1
2
0
0
0
0
2
0
1
0
0
0
1
2
8
1
0
2
1
2
0
0
1
2
1
0
0
1
0
0
0
1
0
0
0
3
1
2
0
2
1
0
1
2
1
2
1
0
0
0
1
0
0
2
0
1
0
2
1
1
0
1
1
1
0
1
0
1
2
1
0
0
0
0
1
0
0
1
0
2
1
2
1
2
3
0
1
1
0
0
1
0
0
0
1
1
0
2
0
2
1
1
1
0
2
0
1
1
0
1
1
1
2
0
1
0
0
2
2
1
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
1
2
0
4
1
1
0
0
2
2
0
1
0
1
2
2
1
2
2
1
0
1
2
3
1
2
0
1
1
4
0
0
2
0
2
2
0
1
1
2
2
1
0
2
1
0
0
1
0
2
2
0
1
0
0
0
0
2
1
1
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
2
0
0
1
0
1
2
0
1
1
0
0
1
0
0
0
0
2
2
0
0
2
1
0
2
0
2
2
0
0
0
1
0
1
0
1
0
0
0
1
0
1
0
0
2
1
1
0
0
1
0
1
1
2
3
0
1
1
2
2
2
0
2
0
2
0
0
0
0
1
2
0
0
0
1
1
0
1
0
2
2
0
0
0
0
1
0
1
2
1
0
1
2
1
0
0
0
0
0
1
1
0
1
1
0
0
1
1
0
2
1
0
0
0
2
1
1
0
1
1
1
0
0
2
0
1
2
0
2
2
0
1
0
0
2
0
1
0
2
0
1
2
0
1
0
0
1
2
0
1
1
0
0
0
0
1
2
0
0
1
2
1
0
2
0
0
0
2
1
0
2
2
1
0
1
2
0
0
0
0
0
1
0
0
0
0
1
2
1
2
1
3
0
1
0
0
0
2
0
1
0
0
0
1
0
3
0
2
0
1
2
0
0
0
2
1
1
0
1
0
1
0
2
1
1
2
0
1
2
0
0
1
1
0
1
0
1
0
0
0
1
1
0
1
0
0
0
2
0
3
1
0
3
1
0
1
0
0
0
0
0
2
1
1
0
0
1
0
2
1
0
1
0
0
0
1
2
0
1
1
0
0
2
2
0
0
0
0
2
2
2
1
2
0
2
0
0
2
0
2
1
1
2
0
1
2
2
0
0
0
0
2
1
2
1
1
0
0
0
1
1
0
2
0
1
0
0
0
2
1
0
1
0
0
1
0
0
0
1
2
1
2
2
0
0
1
0
0
0
1
0
0
0
0
2
0
1
2
1
0
1
0
0
0
2
0
0
0
0
1
0
0
0
2
1
1
0
0
0
0
2
0
0
2
1
1
1
0
1
0
0
1
0
0
0
1
1
1
0
1
1
1
1
1
0
0
2
0
0
1
2
2
0
1
0
0
0
1
2
0
1
1
0
0
1
0
1
0
0
2
2
1
0
2
4
0
1
0
3
4
1
0
0
0
1
0
0
0
0
0
0
1
0
1
1
2
0
2
0
1
0
0
2
1
1
0
1
0
0
2
0
1
0
1
0
2
0
0
0
0
0
0
1
4
2
0
0
0
0
0
3
1
0
0
0
2
0
2
2
0
0
0
1
0
1
1
0
0
2
1
2
1
1
1
0
0
0
0
0
0
1
1
1
2
0
0
0
1
3
1
2
0
0
0
0
0
1
2
1
0
0
2
0
2
0
0
1
2
0
0
0
0
0
2
0
1
1
0
2
0
1
1
1
0
1
2
2
0
1
1
2
2
1
0
0
0
0
0
1
2
1
1
0
1
1
0
0
0
0
2
0
1
0
2
0
0
2
0
0
1
0
1
0
1
0
0
6
1
2
1
0
1
0
0
1
0
0
2
1
1
2
0
0
1
1
0
0
1
2
1
0
1
1
0
2
1
0
1
0
0
1
2
0
0
1
0
0
0
2
1
0
0
2
2
1
2
2
2
0
1
1
2
1
1
0
1
3
2
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
1
1
2
0
3
2
0
1
0
0
2
1
0
1
0
0
0
1
1
5
1
0
0
2
2
1
1
1
2
1
1
0
2
2
0
0
0
0
1
2
1
0
0
1
1
1
1
1
0
0
0
1
2
0
0
2
0
0
1
0
1
1
1
0
0
1
0
0
1
0
0
1
0
2
1
1
0
0
0
2
1
0
0
3
2
1
0
3
0
0
0
0
0
0
1
1
0
2
0
0
1
1
0
0
1
0
1
1
2
2
1
1
0
0
2
1
1
0
0
2
0
2
2
2
0
1
0
0
0
1
0
0
0
1
0
1
0
0
1
0
1
0
0
1
2
0
2
0
1
1
1
1
2
2
2
2
0
0
1
2
1
2
0
2
0
0
0
1
2
1
0
0
3
0
0
0
1
0
0
0
1
2
0
1
0
0
0
2
1
0
2
0
0
2
1
2
0
0
0
0
2
0
3
0
0
0
1
2
0
1
1
0
0
0
0
0
0
0
0
0
2
0
1
1
0
1
0
1
0
1
1
0
2
0
0
0
1
1
1
0
1
1
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
1
4
0
0
1
0
0
0
0
0
2
0
1
1
0
0
0
2
2
1
0
0
0
2
2
0
1
2
2
0
0
2
2
0
0
0
1
2
0
2
0
2
0
1
1
0
2
0
0
0
0
0
0
0
0
2
1
2
0
0
0
1
0
0
0
2
0
1
0
1
1
0
0
1
2
3
0
0
2
0
0
1
1
0
0
1
2
0
0
0
0
1
0
0
1
0
0
0
1
1
0
1
0
2
0
1
0
1
0
0
0
0
2
0
0
0
3
1
1
0
1
0
2
1
0
0
1
1
0
2
0
0
0
1
2
2
1
0
2
0
0
0
2
0
1
1
1
4
0
0
1
2
2
2
0
0
0
2
2
0
1
1
0
2
1
1
1
2
1
1
1
2
0
0
1
0
1
4
0
1
0
0
1
1
0
1
1
1
0
0
1
1
0
2
0
1
2
0
0
1
0
0
2
1
2
0
1
0
1
2
2
0
0
2
2
1
1
0
1
0
2
0
1
0
0
1
0
0
2
1
0
2
0
2
0
1
2
0
0
1
1
0
0
2
1
1
0
0
1
2
0
1
0
0
2
1
2
0
0
0
0
0
0
0
0
2
2
0
1
2
0
2
0
1
0
0
0
0
2
1
0
0
1
2
0
2
0
2
0
1
1
1
0
2
2
0
0
2
2
1
2
1
2
1
0
0
2
0
1
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
1
0
1
2
2
0
1
2
4
1
0
0
0
0
2
0
1
0
0
0
0
1
1
1
0
0
1
0
0
1
0
2
1
2
1
0
2
1
0
0
0
0
0
1
0
2
0
0
1
2
0
2
1
1
1
1
2
0
0
1
2
0
2
2
0
1
0
0
0
0
0
1
0
2
0
2
0
0
0
2
1
1
2
1
2
0
1
1
1
2
1
1
0
1
0
1
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
1
2
2
0
1
1
1
1
0
1
0
2
2
2
1
1
0
1
0
2
0
1
1
0
1
1
0
0
2
0
2
2
1
0
2
0
0
1
2
2
1
3
1
0
1
1
1
3
2
1
0
0
0
2
1
0
0
1
0
0
0
1
2
0
2
0
1
1
3
0
0
1
2
1
2
1
0
0
0
0
0
1
1
0
2
1
2
1
2
2
0
0
1
0
0
0
0
1
2
0
0
0
0
1
1
1
1
0
2
2
1
0
0
1
2
1
2
1
2
1
1
1
1
0
3
1
2
0
2
0
0
0
0
0
1
0
2
1
0
0
0
1
0
0
1
0
1
1
2
0
1
0
0
0
1
0
0
1
2
2
0
1
0
0
0
1
1
1
0
2
0
2
1
1
1
3
2
0
1
0
0
1
2
2
2
2
1
1
0
3
2
1
0
0
1
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
2
1
1
0
0
0
0
1
0
0
1
0
2
0
0
0
0
2
2
0
0
2
1
0
0
0
0
2
2
2
1
2
1
0
1
1
1
1
1
0
1
0
0
1
1
2
1
1
2
0
1
0
1
1
0
1
2
0
1
0
1
1
0
1
2
2
1
2
0
1
0
0
0
1
2
0
1
2
0
1
0
0
1
0
0
2
0
0
3
1
0
0
1
2
2
2
0
1
2
0
0
0
0
1
0
2
0
2
0
2
2
0
1
0
2
2
0
0
1
0
2
1
1
1
1
0
2
0
0
1
0
2
1
0
0
0
1
0
1
2
0
2
1
0
1
1
0
0
0
0
0
1
0
1
0
1
1
0
1
2
0
1
0
0
2
0
1
0
0
0
0
1
0
0
0
0
1
2
1
0
0
0
0
1
1
0
0
1
1
0
1
0
0
0
2
2
2
0
2
0
0
2
1
1
0
1
1
1
1
0
1
1
2
0
0
2
0
2
0
1
0
1
0
2
2
0
2
0
0
1
0
1
0
2
1
1
0
0
0
0
1
2
0
0
1
0
2
0
2
0
2
0
0
0
0
2
2
0
1
2
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
2
1
0
0
0
1
0
0
2
0
1
1
2
0
1
1
0
1
0
0
0
1
1
1
1
2
0
1
2
1
0
0
0
0
0
0
0
1
2
2
2
2
0
0
1
0
0
0
1
0
0
1
1
2
0
1
1
2
1
1
1
0
0
2
0
0
0
2
2
1
1
0
0
2
0
2
0
2
0
1
0
1
0
1
0
1
1
0
0
1
1
1
2
2
2
1
0
0
0
1
0
0
1
0
1
0
0
1
0
0
1
0
1
1
1
1
0
1
2
1
0
1
0
0
1
0
0
1
1
0
0
0
1
3
0
0
1
1
0
1
1
2
1
0
2
1
1
0
0
2
0
0
0
0
0
1
0
1
0
1
2
0
1
2
1
1
1
1
1
0
0
0
0
2
0
1
1
2
1
0
1
1
1
2
0
1
1
1
0
1
1
0
0
2
0
0
2
0
1
2
0
1
0
0
1
2
0
0
0
2
1
0
0
1
1
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
3
1
3
2
1
1
1
0
1
2
2
2
1
1
2
2
1
2
0
2
1
0
2
1
1
0
0
4
0
1
1
0
0
1
1
1
2
0
1
0
1
2
2
0
0
2
0
1
2
1
1
1
0
0
0
0
2
0
0
1
0
2
0
1
0
2
2
0
0
1
0
2
2
1
2
1
0
2
2
0
0
2
0
0
1
2
2
0
0
0
1
4
0
0
0
0
2
2
0
1
0
2
1
2
0
0
2
2
0
1
0
0
1
0
1
0
0
2
0
0
1
1
0
1
3
2
1
2
2
0
0
2
2
4
0
1
0
1
0
0
1
1
2
0
1
0
0
1
1
1
1
2
0
0
1
0
2
2
0
0
2
0
0
0
0
2
2
0
2
2
1
0
0
2
1
3
0
2
0
0
0
1
0
2
1
2
0
1
0
0
1
2
0
2
0
2
1
1
2
1
0
1
0
2
0
0
1
0
0
0
0
1
0
0
2
2
0
1
0
0
1
0
1
0
0
0
0
0
2
1
1
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
2
1
2
0
1
2
0
2
0
1
1
1
0
0
0
1
0
0
0
1
2
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
2
2
0
1
2
0
0
0
1
2
0
1
0
2
0
1
2
1
0
2
2
0
1
0
1
0
1
1
0
1
0
0
0
0
0
0
1
0
2
0
1
1
0
1
0
0
0
2
1
1
1
0
0
0
1
2
1
1
0
2
0
2
1
0
0
2
1
1
0
0
0
1
0
2
0
0
2
0
0
0
0
0
2
0
2
0
0
1
0
0
0
1
0
2
0
4
0
2
0
2
1
1
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
2
0
0
1
1
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
1
2
2
1
1
0
2
1
0
1
1
0
3
2
2
2
0
0
0
1
0
1
0
0
0
1
1
0
0
2
0
2
1
1
1
3
2
1
0
2
0
0
1
0
1
0
2
0
0
2
1
0
1
0
0
2
0
1
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
3
0
0
1
3
0
0
2
0
0
0
0
1
0
0
0
0
1
1
2
2
0
2
0
1
0
1
0
0
2
1
2
1
1
0
0
2
1
1
2
0
0
2
1
3
0
2
0
1
1
1
0
1
0
1
1
1
3
0
0
1
1
0
0
2
1
0
1
0
0
2
1
1
1
0
1
1
1
0
0
1
1
2
0
3
0
2
0
1
0
2
0
0
2
0
2
0
1
2
1
1
0
1
0
3
0
1
0
1
0
0
0
0
1
1
0
1
1
1
1
0
0
1
1
0
0
2
0
1
1
1
2
0
0
2
0
2
1
2
1
0
0
0
0
0
1
1
1
0
1
0
0
0
1
1
2
2
0
0
0
1
2
0
2
1
0
2
1
1
1
1
0
0
0
2
1
1
0
0
1
0
2
0
1
0
2
0
2
1
1
0
1
0
0
1
0
1
1
0
0
0
0
0
0
2
2
0
0
1
0
1
0
1
0
0
1
0
0
1
2
0
1
0
0
1
2
0
2
0
2
1
1
0
0
2
2
0
0
0
0
0
0
1
1
0
0
1
1
2
2
0
0
2
1
0
0
0
0
0
2
2
1
0
0
0
2
1
3
0
1
1
2
0
1
2
2
0
0
1
1
3
0
1
2
1
0
1
1
0
0
1
1
2
0
0
0
0
2
1
2
0
0
1
0
0
0
3
0
2
1
2
2
0
0
1
4
2
2
1
1
0
1
1
2
1
1
1
2
2
0
2
0
0
0
2
1
0
1
2
2
0
0
0
0
1
1
2
0
2
1
1
0
2
1
1
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
2
1
0
0
2
5
0
1
0
1
0
0
2
2
1
0
0
0
1
2
0
1
1
0
1
2
0
3
1
1
0
2
0
0
0
2
2
3
1
0
0
0
0
6
1
0
2
2
0
2
1
2
0
1
1
1
1
1
1
0
0
0
1
1
2
0
2
0
0
1
1
1
1
1
2
2
0
0
1
2
1
0
0
1
2
0
1
0
0
0
1
0
1
0
1
1
2
1
2
0
0
0
1
1
1
1
1
0
0
2
1
0
0
1
1
1
0
2
2
2
1
0
0
2
1
2
1
2
1
1
1
1
1
1
1
0
0
0
1
2
1
1
1
0
0
1
1
0
0
0
0
2
1
2
2
0
1
3
3
0
1
2
1
0
1
1
1
0
1
2
0
0
1
1
0
0
0
1
2
0
0
1
0
1
1
3
0
1
1
0
2
1
2
0
0
2
3
0
0
1
2
0
0
0
0
1
1
1
0
0
0
0
1
1
1
2
1
1
0
0
2
0
0
2
2
2
2
1
1
0
1
1
0
2
1
2
2
0
1
2
0
0
1
2
2
2
0
0
1
1
0
0
1
0
1
0
1
2
0
0
1
0
1
1
0
0
2
0
0
0
1
2
0
0
2
0
0
1
0
1
2
2
0
0
2
2
0
1
0
0
0
0
0
1
1
0
0
2
0
1
0
0
4
0
0
1
0
1
1
0
1
0
2
1
2
1
1
0
0
1
1
0
0
0
2
1
1
1
2
0
1
1
0
1
1
1
2
2
1
0
0
0
1
1
2
0
1
0
0
1
1
0
1
0
2
2
2
3
2
2
1
0
1
2
1
2
0
0
1
2
1
2
0
2
0
1
0
0
1
0
0
0
2
1
1
1
1
2
0
2
0
1
0
2
1
1
0
1
0
1
1
0
2
1
2
2
0
1
1
1
1
2
0
3
1
0
2
2
0
0
1
0
0
1
0
0
1
0
0
1
0
0
2
2
1
1
0
1
0
1
2
0
0
0
0
2
1
0
0
1
0
0
0
0
2
1
1
3
1
0
1
0
2
0
0
0
0
0
1
2
0
1
1
1
2
0
1
0
2
1
0
0
0
2
0
0
0
1
0
0
2
2
3
1
1
0
1
2
2
3
1
0
0
3
0
0
2
2
2
0
1
0
0
0
1
0
2
0
0
1
0
1
0
0
0
1
1
2
0
1
1
1
0
0
1
0
2
2
0
1
2
2
0
1
1
0
0
0
0
1
2
2
0
0
0
0
0
1
0
1
1
3
1
1
0
1
0
0
1
0
0
2
0
2
1
1
1
1
0
0
0
0
1
2
1
2
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
1
1
1
0
2
0
2
0
2
1
0
1
0
0
0
0
0
2
0
1
0
1
1
0
0
1
1
1
0
2
3
0
2
2
0
0
0
2
0
1
1
0
0
1
2
0
0
0
2
0
2
0
2
0
1
1
0
2
0
0
1
1
1
1
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
2
1
1
0
0
1
0
0
2
1
0
0
0
0
1
0
0
1
2
1
2
0
0
0
3
2
0
0
0
0
1
0
0
1
2
2
0
1
0
1
0
0
2
0
1
0
0
0
1
0
1
0
0
0
1
1
0
2
1
1
0
0
2
0
0
0
1
1
2
0
2
0
0
1
1
0
2
3
1
2
0
1
0
0
0
1
0
2
2
2
0
0
0
2
0
0
0
0
0
2
1
1
0
0
1
0
0
1
1
1
1
1
1
0
0
2
0
0
0
1
2
0
0
0
2
2
1
0
0
0
2
1
1
1
0
0
0
0
0
1
0
1
1
1
0
0
0
1
0
0
1
2
2
2
1
2
0
1
0
0
0
1
0
0
1
2
0
0
1
1
0
2
1
2
0
0
1
0
2
1
0
0
2
0
0
1
1
0
1
1
1
2
1
1
3
2
0
0
2
2
2
0
0
1
0
0
0
0
0
2
1
1
1
1
1
0
0
2
0
0
1
0
1
2
2
1
0
1
1
0
0
2
0
0
2
1
0
0
2
1
0
0
0
0
1
2
2
0
0
0
2
1
0
0
0
0
1
1
1
0
0
0
1
1
1
0
0
0
0
2
4
1
0
0
4
0
1
0
1
2
0
0
0
0
0
0
0
1
0
0
2
1
2
0
1
0
1
1
0
2
0
0
2
0
1
0
0
0
1
0
2
0
0
2
0
0
2
1
2
1
1
0
1
0
2
1
1
2
2
0
0
1
0
2
1
2
2
0
2
1
0
5
0
2
1
1
0
1
0
0
0
0
0
1
2
1
0
0
0
1
2
2
2
0
2
2
0
3
0
1
0
0
1
0
2
2
0
4
2
1
1
0
1
0
2
1
0
0
0
0
1
0
0
2
1
1
1
0
3
0
0
2
1
0
0
1
0
1
0
1
2
0
0
1
1
0
0
1
1
1
3
1
2
2
2
1
0
0
0
1
3
1
0
0
0
1
0
1
0
0
0
0
2
1
0
0
0
2
0
0
0
2
1
0
2
0
0
1
0
1
1
0
2
0
1
1
2
0
0
0
1
0
0
0
2
0
0
1
1
1
2
0
0
0
0
2
0
0
0
0
0
2
1
1
0
1
0
2
2
1
1
0
0
0
1
0
1
0
1
0
2
0
0
2
2
1
1
1
0
2
0
1
0
1
0
2
2
1
0
0
0
1
0
0
1
2
0
0
0
3
0
0
1
0
0
0
1
0
1
2
1
3
0
2
0
0
0
0
0
2
0
0
0
1
0
0
2
2
0
0
2
0
0
0
1
1
0
0
0
0
2
0
0
0
1
0
1
0
1
0
1
0
0
1
1
0
1
1
0
2
2
0
0
0
1
0
2
0
0
0
1
0
0
0
1
0
1
1
2
2
1
2
0
1
0
1
1
0
1
1
0
3
0
0
1
1
0
2
0
0
1
0
0
0
1
0
1
0
0
1
1
2
1
1
1
0
0
1
0
1
1
0
0
0
2
1
1
2
0
2
1
0
0
0
2
5
3
1
0
1
1
0
0
2
0
2
1
0
2
0
0
2
1
1
2
1
2
2
0
0
1
0
0
1
1
0
0
1
1
1
2
0
0
1
0
0
1
1
1
1
1
1
0
0
2
1
0
0
2
1
1
1
2
0
1
2
1
0
0
1
1
0
0
2
2
3
2
0
2
0
0
1
1
1
2
2
4
2
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
1
1
1
2
0
1
1
1
0
1
1
0
0
2
0
1
1
1
1
0
0
1
1
1
2
0
1
2
1
1
1
0
2
0
2
2
3
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
2
1
1
1
1
2
0
1
0
2
0
0
2
3
0
0
0
1
1
2
3
0
2
1
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
1
1
0
0
0
0
0
4
6
1
0
1
0
0
2
1
1
0
0
0
2
0
0
0
2
2
1
1
0
1
2
0
1
0
0
2
0
0
0
1
2
2
2
2
0
2
2
0
1
1
0
0
0
1
1
1
0
0
1
1
0
0
1
2
2
0
0
1
0
0
0
0
0
2
2
2
1
0
1
1
2
1
0
0
0
2
1
2
0
0
2
2
0
1
2
1
2
0
4
0
0
1
0
0
2
0
1
2
0
1
0
1
1
2
0
1
0
2
2
1
2
0
0
3
1
2
0
0
0
1
2
0
1
1
2
1
0
0
1
0
2
2
1
0
1
2
0
2
2
1
1
0
1
0
2
0
2
1
1
0
2
1
1
1
1
1
1
0
0
1
1
0
2
0
3
0
2
2
0
0
1
0
1
0
0
0
2
3
0
0
0
0
2
0
1
0
0
0
0
0
1
1
0
1
1
1
0
0
1
1
1
1
1
0
0
1
1
2
2
0
0
0
0
1
1
2
2
2
0
1
2
1
1
1
4
2
0
3
1
0
2
0
0
0
0
1
1
0
2
0
2
1
1
2
0
0
1
2
0
2
0
0
1
0
0
0
1
0
0
1
2
1
1
1
1
1
1
0
0
1
0
0
1
1
0
1
2
2
0
0
2
1
1
0
0
0
1
1
0
3
0
1
0
0
0
0
1
0
0
0
1
2
0
1
0
1
0
1
2
0
1
1
0
0
1
0
0
0
0
0
0
0
1
1
2
0
0
0
0
2
0
0
0
0
2
0
0
0
1
1
0
1
2
3
3
1
1
0
1
0
0
1
1
0
0
1
1
2
1
1
0
1
0
2
0
0
0
0
2
0
1
1
2
2
1
0
2
0
0
0
0
0
0
0
1
0
1
1
1
1
0
1
1
0
0
1
1
0
0
1
1
1
1
0
0
1
0
1
2
2
2
1
0
1
0
0
0
0
2
1
0
0
1
0
0
1
0
2
0
0
0
2
0
0
0
1
0
0
1
2
1
1
2
1
2
1
0
1
1
0
2
0
1
0
2
0
2
1
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
1
2
2
2
1
0
2
1
2
1
0
0
1
1
0
0
0
1
1
0
1
1
2
0
0
2
1
0
0
0
1
1
0
0
0
1
0
2
0
0
1
0
0
1
0
2
0
2
1
0
1
1
0
3
2
1
0
2
0
0
2
0
2
2
0
2
2
0
1
0
1
0
0
0
1
0
1
0
2
0
0
1
0
0
1
1
1
1
0
1
0
1
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
3
0
0
0
1
0
1
2
1
0
0
1
2
2
0
0
0
1
0
0
0
0
2
1
1
0
1
1
2
1
0
2
2
0
1
1
1
2
1
0
0
2
1
0
1
0
1
0
0
0
0
0
2
1
2
2
1
2
0
0
0
1
0
1
0
2
1
0
1
1
1
2
0
1
1
2
1
0
1
0
0
0
2
1
0
1
1
0
0
1
0
2
0
0
2
1
1
2
2
1
2
0
0
2
1
0
3
1
0
1
1
0
0
0
1
0
1
1
0
1
0
1
0
1
0
0
1
1
0
2
0
1
0
2
1
0
2
0
0
2
0
1
1
2
1
1
0
0
1
1
2
1
0
1
0
0
2
1
2
0
0
1
0
0
2
0
1
0
1
0
0
2
0
0
0
1
2
2
1
1
0
0
1
2
0
2
1
1
1
0
2
2
0
1
0
1
2
1
0
2
1
0
0
0
0
1
0
1
0
2
0
2
0
0
2
0
0
2
1
0
1
1
1
0
1
0
0
0
2
1
0
0
1
1
1
0
0
1
0
3
2
1
2
0
0
1
1
2
0
0
0
0
1
1
0
1
1
0
0
3
2
1
2
2
2
2
1
1
1
1
0
0
0
2
2
1
0
1
0
0
0
0
0
0
0
1
1
2
4
1
2
1
0
2
0
0
1
0
2
1
0
0
0
1
0
0
0
1
1
2
0
0
0
0
3
0
2
0
0
2
0
0
0
2
2
0
0
0
0
2
0
0
0
2
4
0
0
0
0
1
1
0
1
1
2
0
0
1
1
3
0
2
2
4
2
0
0
2
3
2
1
0
0
1
0
2
2
2
1
2
0
1
1
0
0
0
1
0
1
0
0
0
2
0
0
0
1
0
1
1
1
1
0
1
0
0
2
0
2
0
0
0
1
2
0
0
0
0
0
0
0
1
3
0
2
0
2
1
0
0
2
2
0
0
2
0
0
0
1
2
1
0
0
1
0
2
0
0
0
2
0
0
2
2
0
2
1
2
0
1
1
0
0
0
2
1
0
1
0
0
1
2
1
7
4
0
0
1
1
1
1
1
0
1
0
2
2
0
1
0
1
2
1
2
0
2
1
1
1
0
0
1
0
0
1
0
2
0
0
0
1
0
1
0
0
2
1
2
1
1
1
0
0
2
2
0
2
0
0
1
1
0
1
1
1
2
2
0
1
0
2
1
1
1
0
0
1
0
0
1
1
1
1
1
1
1
0
0
0
1
2
0
2
2
0
1
2
0
0
2
1
1
0
0
0
0
1
2
1
0
3
2
2
2
1
2
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
2
2
0
0
1
0
0
2
2
1
0
2
1
1
1
1
1
0
0
2
1
2
0
1
0
3
1
2
1
1
1
3
0
0
0
0
1
1
1
0
0
2
0
0
0
0
1
0
0
1
0
1
1
1
0
1
1
0
0
1
0
3
1
4
2
2
1
1
1
1
1
2
3
1
1
2
0
1
0
0
1
0
1
0
1
2
0
0
0
2
0
0
1
0
0
0
0
1
0
2
0
1
1
0
0
1
2
0
0
0
0
1
1
0
1
0
0
0
0
1
0
2
1
1
0
0
1
0
1
0
0
1
2
0
0
1
0
0
0
0
2
1
2
1
2
1
3
0
1
1
0
0
2
0
0
1
0
0
1
0
1
1
0
0
0
1
1
0
1
0
0
1
2
0
2
2
1
0
0
0
1
0
3
3
0
1
1
2
2
0
0
0
1
0
0
2
2
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
2
1
0
0
1
1
2
0
0
0
2
0
2
0
0
1
0
0
0
1
1
2
2
0
0
0
0
2
0
0
1
1
1
0
0
0
0
0
0
0
0
2
2
1
0
0
1
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
1
1
0
1
1
1
2
0
1
2
2
0
2
2
0
1
0
0
0
1
1
0
0
2
1
0
1
0
2
0
0
1
2
0
1
0
0
2
1
0
1
1
0
1
1
0
0
0
0
1
0
0
1
0
2
0
0
1
1
1
1
0
0
2
1
0
0
0
1
1
2
0
0
0
1
2
1
0
1
1
0
1
1
2
2
0
0
0
1
1
1
0
1
0
2
0
2
0
1
0
0
3
0
1
0
1
0
0
2
1
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
2
1
0
1
1
2
0
2
0
0
0
0
0
1
0
3
1
0
1
1
1
3
2
0
2
0
0
0
0
0
2
1
1
0
0
0
0
2
2
0
0
1
0
1
0
2
0
1
1
0
1
2
2
1
4
2
2
0
1
2
0
1
0
1
1
0
1
0
1
0
0
2
2
0
0
2
1
1
1
1
0
2
0
1
2
1
2
1
0
2
0
1
2
0
1
0
1
0
0
1
1
1
1
4
0
0
1
0
2
0
2
1
2
0
0
2
2
1
0
1
0
0
1
0
1
1
2
1
2
2
0
0
1
2
1
1
2
1
1
0
0
0
2
0
0
2
0
0
1
1
0
1
0
1
1
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
1
1
1
2
0
2
1
1
1
0
0
0
0
1
2
1
0
0
1
0
2
0
1
1
0
1
0
0
2
0
1
1
2
0
1
1
2
0
0
0
2
1
0
0
1
1
0
2
3
2
2
1
1
2
1
0
0
1
1
2
0
1
1
1
4
1
0
1
1
0
1
0
2
1
2
0
0
0
0
1
0
0
2
2
1
1
1
3
1
1
0
0
2
0
2
1
0
0
2
1
2
1
1
1
0
0
1
0
1
0
0
1
1
0
0
0
1
1
2
3
2
3
1
2
0
1
0
0
1
0
0
0
2
1
0
1
2
2
2
1
0
1
0
0
0
0
0
0
3
0
0
0
0
2
2
0
2
0
0
2
0
0
2
0
2
2
0
1
0
2
2
0
0
2
0
0
0
0
1
0
0
0
2
1
0
0
4
1
1
0
0
0
2
0
2
2
2
1
3
0
2
0
1
2
2
2
2
0
0
1
2
1
1
0
0
0
0
0
0
1
2
0
2
1
2
0
0
2
1
1
2
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
2
5
1
0
0
1
0
1
1
0
1
0
0
2
1
1
0
1
1
0
3
2
0
1
1
0
0
2
2
0
0
1
1
0
1
1
2
1
0
1
2
0
0
1
0
2
0
0
1
2
1
2
1
0
3
0
0
0
0
1
1
1
0
0
1
1
1
1
0
2
0
0
1
0
0
2
2
2
1
2
0
0
1
2
0
2
1
0
1
0
1
1
0
2
3
1
0
0
0
0
0
0
0
0
1
0
2
0
2
0
1
0
0
1
0
0
2
0
1
1
0
0
1
2
0
0
0
1
0
1
0
0
1
2
0
2
0
1
2
2
2
1
0
2
2
2
0
1
0
0
1
1
2
1
0
1
1
1
1
0
2
0
2
1
1
0
1
0
0
0
1
0
2
0
0
0
0
0
2
0
0
1
1
3
1
0
0
0
0
0
2
2
2
0
0
0
2
0
0
2
2
0
0
1
0
2
0
0
1
2
1
2
1
2
0
1
1
0
2
0
0
3
0
2
2
2
0
1
0
0
2
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
2
1
2
1
0
2
2
0
2
0
0
0
0
0
1
1
0
2
1
2
0
2
0
1
0
0
2
2
2
0
2
2
1
0
0
2
2
1
1
0
0
0
1
0
1
3
0
0
2
4
1
1
0
1
0
2
1
0
1
0
0
1
0
0
0
1
1
0
1
2
2
2
1
2
1
2
0
0
0
1
2
0
0
1
0
0
2
0
0
0
0
1
2
0
0
0
1
1
3
1
0
1
1
0
0
0
2
1
1
0
0
0
0
2
1
2
1
1
2
1
0
0
0
0
1
0
2
1
1
0
0
0
0
1
2
2
0
0
0
2
1
1
0
2
1
0
0
1
1
1
1
1
0
0
1
2
0
1
1
0
0
0
1
0
1
0
0
0
1
1
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
2
1
0
0
0
1
0
1
1
1
0
0
0
0
2
1
2
1
2
1
2
0
0
0
2
0
1
1
0
0
0
0
2
1
2
2
1
0
0
0
2
1
1
1
1
0
2
1
1
0
1
1
1
0
2
0
0
0
0
0
1
2
1
0
2
2
0
1
0
4
2
0
2
0
0
1
2
2
1
1
1
0
1
2
0
0
1
2
0
0
1
1
0
2
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
1
2
0
0
2
1
0
0
0
0
0
2
0
0
1
0
2
0
0
1
0
0
3
1
0
0
0
0
0
1
3
0
2
0
1
0
2
1
1
0
0
0
2
1
0
0
0
2
1
2
0
1
1
0
1
1
2
1
0
1
0
1
0
2
0
2
1
1
1
0
1
0
1
2
1
0
0
1
0
2
1
2
1
0
2
2
0
2
0
1
1
0
0
2
0
0
1
2
0
0
0
0
2
0
0
0
1
0
1
0
0
0
1
1
2
0
2
0
0
1
2
1
1
2
0
1
0
0
2
0
2
0
1
0
1
1
1
1
2
1
0
0
0
2
0
2
2
0
0
0
0
0
0
0
1
0
2
1
1
2
3
2
0
0
2
0
1
0
0
2
1
4
0
1
2
1
0
0
0
2
2
0
0
0
1
0
1
0
2
0
1
0
2
0
0
0
1
1
1
1
1
1
0
0
2
1
2
2
0
0
1
1
2
0
0
2
0
2
0
0
1
1
0
0
1
0
1
1
2
2
3
1
0
0
0
2
0
0
0
0
1
2
2
0
0
2
0
1
0
1
1
0
1
1
0
0
1
1
0
0
2
0
0
1
0
0
0
1
0
0
2
0
2
1
1
0
1
0
0
0
0
0
1
0
2
1
1
0
0
0
0
2
1
1
1
2
1
1
1
0
1
2
0
0
0
1
0
1
2
0
1
2
0
2
0
0
0
1
0
2
2
0
0
0
1
1
1
1
0
1
0
0
0
0
2
0
0
2
1
2
2
0
2
0
2
0
0
2
1
0
1
1
0
0
0
2
2
0
0
0
0
0
0
1
0
1
1
1
1
1
0
0
0
2
0
2
2
0
1
1
0
0
2
0
1
1
1
1
0
0
4
1
1
2
0
0
2
0
1
4
0
0
1
0
3
0
0
1
0
0
0
0
1
1
0
0
0
2
1
1
1
1
1
2
0
0
2
1
0
3
0
0
1
2
0
2
1
0
1
2
0
2
1
2
1
0
1
0
0
0
0
0
1
0
1
0
1
0
2
0
1
4
0
4
1
2
0
2
0
0
0
1
0
1
1
1
0
0
1
2
2
2
1
2
0
1
1
2
0
0
0
2
2
1
0
2
0
2
2
0
0
2
1
1
0
0
1
0
0
1
1
2
0
1
0
0
1
0
0
0
0
1
0
4
0
0
2
0
0
0
2
0
0
1
0
0
0
1
1
2
2
2
0
1
1
1
0
0
1
2
0
0
2
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
1
1
0
0
0
0
2
0
0
0
0
1
2
2
0
0
1
2
0
2
0
0
0
0
2
0
1
2
1
0
1
1
1
0
1
0
2
1
0
1
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
3
0
0
1
0
0
2
0
2
2
0
1
1
2
1
2
2
0
1
0
2
0
1
1
1
2
0
1
1
1
0
0
2
2
0
1
2
1
0
2
1
1
0
0
1
0
1
1
1
1
0
2
0
2
0
0
0
0
2
0
0
0
1
2
0
0
1
0
0
0
0
1
1
1
0
0
0
0
1
4
1
3
1
0
1
2
1
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
2
1
0
1
1
2
1
1
0
2
0
0
2
0
1
1
2
1
0
0
2
0
1
0
2
1
0
1
0
0
0
0
1
2
1
1
1
2
1
0
0
2
2
1
0
1
1
1
1
0
2
1
1
1
0
0
0
0
0
2
0
0
1
2
1
0
0
1
2
0
0
1
0
0
1
0
0
1
2
0
0
0
1
1
0
0
0
1
1
1
2
2
2
0
1
2
0
1
1
1
2
2
0
1
0
1
0
1
2
1
0
0
1
1
1
1
0
1
0
2
1
0
0
1
1
0
0
2
0
0
1
0
4
0
2
2
0
1
2
1
1
1
0
1
1
1
2
1
1
1
0
0
2
2
0
1
0
1
0
1
0
1
0
1
1
1
0
0
1
1
0
1
0
2
1
0
0
0
0
0
1
0
0
1
0
1
1
0
0
1
0
0
0
2
3
1
2
0
1
1
0
1
0
0
1
0
1
2
0
0
2
2
0
1
0
0
0
0
4
0
0
0
0
1
1
1
1
0
0
0
2
0
1
0
0
0
0
1
0
1
1
3
0
0
0
1
1
1
1
0
1
1
3
0
0
1
2
0
0
0
2
0
2
1
1
1
0
1
2
1
0
1
1
0
2
0
0
0
0
2
1
1
1
1
1
1
1
0
0
0
2
0
1
0
1
0
2
0
1
0
0
0
1
2
1
0
0
0
1
0
1
1
0
3
2
0
2
1
0
1
1
2
1
0
1
0
1
1
1
1
0
1
1
1
0
1
0
1
0
1
1
1
0
0
0
2
0
2
0
0
2
1
0
0
0
1
0
0
1
2
0
0
0
1
0
1
0
0
0
0
1
0
0
2
2
1
0
1
1
0
0
0
0
1
1
1
1
0
0
0
0
2
1
1
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
2
0
2
2
0
0
2
0
4
0
0
0
2
2
2
0
2
0
1
0
0
0
1
0
2
1
0
0
1
0
0
0
2
2
1
1
0
0
3
1
1
2
0
0
1
0
1
0
0
0
1
2
1
0
2
1
0
0
0
0
0
0
1
2
1
1
0
1
1
0
3
1
1
2
1
1
0
2
2
1
4
1
2
0
1
0
0
1
1
0
2
0
0
0
0
1
2
2
4
2
1
1
1
1
2
1
1
1
0
0
2
2
1
2
0
1
2
2
1
0
0
0
2
2
0
2
1
0
0
0
1
0
1
1
2
1
0
0
2
2
1
0
0
0
1
0
1
0
0
2
0
0
1
0
0
1
1
0
0
1
2
0
1
0
2
0
2
1
2
3
0
0
1
1
2
0
0
2
1
0
1
1
0
1
1
1
1
0
1
2
0
2
0
0
0
1
1
0
0
1
0
2
0
0
0
0
1
2
0
1
2
2
3
0
2
1
0
2
2
3
1
0
2
0
1
2
1
0
0
2
2
2
0
0
1
1
1
2
0
1
0
1
0
2
1
1
0
1
0
0
2
0
1
0
1
0
0
1
0
0
0
1
0
0
0
2
0
1
0
0
0
0
2
1
0
1
0
0
1
1
2
0
1
0
2
0
1
0
0
0
1
2
0
1
0
0
1
0
0
0
0
1
2
0
0
3
2
1
0
0
0
3
2
0
1
1
1
0
2
0
2
2
1
0
0
0
0
0
1
0
0
2
2
0
1
0
1
1
0
0
1
2
0
2
1
1
1
1
0
1
0
0
0
2
0
0
1
2
1
1
1
1
0
0
0
0
3
0
1
0
1
2
0
1
1
3
0
0
2
3
2
2
0
0
1
1
0
0
0
1
1
1
2
2
1
1
0
1
1
1
2
1
0
1
0
1
0
0
4
2
0
0
0
0
0
0
0
1
1
1
0
1
1
0
0
1
0
2
0
2
1
1
2
0
0
1
0
0
0
2
0
3
0
1
1
2
2
1
0
0
0
0
1
0
1
2
1
0
0
1
0
2
1
1
2
1
2
1
0
0
1
2
1
1
1
0
2
2
1
0
0
1
2
0
0
1
0
2
0
1
0
1
0
1
1
3
1
1
0
1
0
3
0
0
1
1
0
2
2
0
0
1
0
0
0
0
2
2
1
1
2
0
1
0
2
0
0
2
0
2
0
2
1
1
0
0
1
0
0
0
2
0
0
0
1
0
0
1
3
2
0
2
1
1
1
2
0
2
4
0
2
1
1
2
1
2
1
1
2
0
0
0
1
0
1
1
2
1
2
1
1
1
2
1
1
0
0
1
2
0
2
0
1
0
0
1
2
0
0
1
1
0
1
1
0
2
1
2
1
0
0
0
1
0
0
0
0
2
0
1
0
0
2
0
0
1
0
1
2
2
3
2
1
0
2
1
0
0
1
2
0
0
2
2
0
1
0
1
0
1
1
0
0
1
0
1
0
1
0
0
2
2
2
1
2
1
2
2
3
2
2
0
0
1
1
0
1
1
2
1
2
0
0
3
2
0
2
0
2
1
2
0
0
0
0
2
2
0
1
2
2
0
2
2
1
1
1
1
2
0
2
2
1
2
2
3
0
0
2
1
0
0
0
2
0
1
0
0
1
1
2
2
0
0
0
2
0
2
0
0
2
2
0
1
0
1
2
0
1
1
1
1
0
0
0
2
0
2
0
0
0
2
2
2
1
0
2
1
3
0
2
0
1
3
1
1
0
1
1
0
0
2
1
1
2
2
0
1
0
0
1
2
2
2
2
0
0
0
1
0
2
0
0
1
1
0
0
1
1
2
1
0
0
0
3
1
3
1
0
2
0
0
1
0
0
2
0
1
0
2
0
1
1
1
0
0
0
2
0
1
2
0
1
0
0
2
1
0
3
2
0
2
0
0
0
0
2
3
2
3
1
0
0
0
1
2
0
1
2
0
1
1
2
1
0
0
1
0
0
2
1
2
0
2
0
2
1
1
1
3
0
0
2
2
1
0
0
0
0
2
0
0
0
2
1
0
1
0
2
0
0
2
0
0
0
1
0
2
4
0
2
2
2
0
0
1
0
0
2
3
0
0
2
1
2
0
0
0
1
1
2
2
1
0
0
0
2
1
0
0
2
0
0
1
0
2
0
0
0
0
2
1
2
1
0
0
0
0
0
0
1
1
1
2
1
0
0
1
2
0
0
2
0
1
1
3
1
1
1
1
0
1
0
0
0
1
1
2
1
1
2
1
0
1
0
1
1
0
0
0
1
0
2
1
0
1
2
1
0
0
1
0
0
0
1
0
2
1
1
0
1
2
0
0
1
0
2
1
2
1
0
0
0
2
0
1
1
2
1
1
2
2
2
2
0
1
1
2
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
2
1
1
2
0
0
0
1
4
0
0
1
1
0
0
2
0
0
1
2
0
0
2
1
0
1
1
0
2
1
1
2
0
0
3
0
2
0
0
3
0
0
0
0
0
1
1
0
0
0
1
1
1
0
0
1
1
0
0
2
0
0
2
1
1
0
2
1
2
0
1
2
1
0
0
0
0
0
0
1
1
1
0
1
0
1
0
2
1
0
2
1
2
1
1
1
2
1
2
0
0
2
0
0
1
1
0
0
0
2
2
0
0
2
1
2
0
0
0
0
0
1
1
2
0
0
5
0
0
0
2
1
2
1
1
2
0
1
0
0
0
0
0
1
0
0
2
0
2
0
0
0
2
1
0
2
1
0
1
0
1
2
2
1
0
0
0
1
2
0
2
1
0
0
0
1
0
2
0
1
1
1
0
2
0
1
2
0
0
0
1
2
1
0
0
2
1
0
0
2
0
0
0
1
1
0
2
0
2
0
1
1
0
0
0
1
2
1
1
2
1
0
1
0
1
0
0
0
1
1
0
0
0
1
2
0
0
1
1
0
0
0
1
1
1
0
0
2
1
2
1
3
0
0
2
2
0
0
1
2
2
0
2
0
2
1
1
1
0
0
1
0
0
0
0
2
0
1
1
0
2
0
1
1
6
1
2
0
1
0
0
1
0
2
2
0
1
1
0
0
0
0
1
1
1
0
3
2
0
1
0
1
1
1
1
2
1
0
0
0
0
2
1
0
1
1
2
1
0
0
0
0
2
0
2
0
1
0
2
0
0
1
1
0
1
2
1
2
0
0
2
1
2
2
1
1
0
0
1
0
0
0
0
0
1
1
0
0
0
2
0
1
2
2
1
3
0
0
0
0
1
2
0
0
2
1
2
1
0
2
2
0
2
1
2
1
1
0
1
1
2
2
0
2
0
1
1
0
0
0
1
1
1
1
2
2
0
3
0
0
0
0
2
1
0
0
1
1
0
0
0
2
2
1
1
0
1
0
0
2
2
0
0
0
1
2
0
2
0
2
1
0
0
0
0
2
2
1
0
2
0
0
0
0
1
2
1
0
1
0
1
1
0
0
0
0
2
1
0
0
0
1
2
1
1
2
2
0
2
1
0
0
2
0
0
1
0
2
2
1
0
0
0
2
2
0
0
1
2
0
0
0
0
2
0
1
2
1
1
0
1
0
2
0
1
1
2
0
2
2
1
2
0
0
1
0
2
2
1
2
1
0
2
1
2
1
2
0
0
0
0
1
1
0
0
2
2
1
1
0
2
2
1
0
1
1
0
0
0
1
2
0
1
0
2
0
1
2
2
0
1
0
0
2
2
0
0
0
0
1
0
0
1
0
0
0
0
2
0
1
0
0
0
1
0
0
0
3
1
0
1
0
0
1
0
2
0
1
2
0
1
1
1
0
2
0
2
0
1
1
2
2
1
0
0
0
1
2
0
0
0
2
3
1
2
0
1
2
0
2
2
2
0
1
1
2
0
1
1
1
1
2
2
0
2
2
1
0
0
1
2
0
1
1
0
2
0
0
0
2
1
0
0
0
0
1
1
1
2
1
0
2
1
1
1
1
0
0
1
2
2
0
0
0
0
1
2
0
0
1
0
2
0
2
3
0
1
1
1
2
0
2
0
1
2
11
2
0
0
1
1
1
0
0
0
0
1
0
2
11
0
0
0
2
0
0
0
1
0
2
0
1
1
0
0
0
1
2
0
0
0
0
0
0
0
1
2
2
3
0
4
3
0
3
1
0
0
0
1
0
0
0
1
0
1
1
1
0
2
2
2
0
1
1
0
0
1
0
1
0
1
0
0
1
3
0
0
1
1
1
2
1
0
0
1
2
1
0
0
1
1
0
1
0
1
0
2
0
0
2
2
1
1
0
0
0
0
5
2
0
0
0
1
0
0
0
1
1
2
0
1
0
0
2
0
1
0
0
2
0
1
0
0
0
0
1
2
0
0
1
0
1
0
2
0
1
1
1
0
1
0
1
1
1
1
2
1
1
0
1
0
2
2
0
0
2
0
0
2
1
0
2
0
0
1
1
0
1
0
0
0
0
1
1
2
2
1
1
1
0
1
2
0
1
2
0
2
1
0
2
1
0
0
0
0
2
0
2
0
1
2
2
3
0
1
0
0
1
0
1
0
0
0
0
0
0
1
1
1
1
1
2
5
0
2
1
0
1
2
3
0
0
0
0
2
0
0
2
0
1
0
0
1
0
1
0
1
1
1
1
0
0
1
0
0
0
0
0
2
1
0
0
1
2
0
1
1
1
1
0
1
1
2
2
0
0
0
2
1
0
0
1
0
0
1
0
1
1
1
1
1
0
1
1
0
0
0
0
0
0
1
2
2
1
1
0
1
1
0
0
1
2
2
0
2
0
0
0
3
1
0
0
2
1
1
0
2
1
0
1
0
0
2
2
1
1
1
0
1
1
1
2
2
0
1
1
1
2
2
1
1
0
0
0
0
1
1
1
0
0
0
2
0
1
2
0
1
1
2
2
0
0
2
0
2
0
0
0
2
2
0
2
1
0
0
1
0
1
0
1
0
1
0
0
1
0
1
0
0
0
0
0
3
1
0
0
1
2
2
0
0
0
0
3
0
0
0
1
0
1
0
1
0
0
1
0
2
0
1
0
1
1
0
0
2
2
2
2
0
2
1
1
0
1
0
1
0
0
0
0
1
1
2
1
0
1
1
0
1
1
0
0
1
0
0
0
0
1
0
0
1
1
1
0
2
1
1
0
1
0
1
0
1
2
2
0
2
1
0
0
0
1
0
1
0
4
2
0
0
0
2
2
0
0
0
1
2
0
1
0
0
1
2
0
0
2
0
1
1
0
0
2
2
2
0
1
1
3
1
0
1
1
0
1
0
0
2
1
0
2
1
2
0
0
0
2
0
2
0
2
0
0
0
0
0
0
4
0
0
1
0
0
1
2
1
0
1
0
1
1
0
0
0
2
0
2
1
0
1
2
0
0
1
0
0
1
0
0
0
0
1
1
1
1
2
0
0
1
1
0
2
1
0
0
1
0
2
0
1
1
2
0
1
1
1
1
0
1
2
0
0
0
0
0
0
0
0
1
1
1
1
1
1
2
0
0
0
0
1
0
1
0
1
1
1
2
0
1
0
0
2
1
1
0
0
1
1
0
0
1
0
1
0
1
1
0
0
1
1
0
0
1
0
2
0
0
2
1
0
0
0
1
2
0
1
1
1
0
1
2
0
1
0
0
1
0
0
1
1
0
1
0
0
2
2
2
2
0
2
1
0
0
0
0
0
0
0
1
2
3
0
0
0
0
0
0
2
0
2
2
0
0
2
0
1
1
0
2
3
2
1
1
0
2
0
2
1
2
2
0
0
2
0
3
2
0
0
1
0
0
2
0
2
0
1
1
1
0
2
0
1
1
0
0
1
1
1
0
0
3
0
0
1
0
1
0
0
0
1
2
0
0
2
1
0
0
1
0
2
0
0
2
1
0
0
0
0
0
2
6
1
1
0
2
0
2
0
0
2
0
2
0
2
0
3
2
1
0
1
0
0
1
1
0
0
0
0
2
0
1
1
0
0
0
1
2
1
0
1
2
0
2
0
0
2
1
1
0
0
0
1
0
0
0
2
0
1
1
2
1
0
0
0
0
1
2
1
0
1
0
0
2
0
0
0
2
0
0
0
2
1
2
3
2
0
1
2
0
0
1
0
1
2
0
2
1
0
0
1
2
2
2
2
2
2
0
0
2
0
1
2
0
1
1
0
1
0
0
2
0
1
2
2
1
0
0
0
0
0
0
1
1
0
0
1
0
2
2
0
0
0
1
2
1
0
2
0
2
0
2
2
0
1
1
2
3
0
1
0
1
0
0
1
1
0
0
1
0
0
0
0
0
1
1
1
1
0
2
0
1
1
5
1
2
1
1
0
0
0
0
0
0
0
1
0
1
1
2
0
1
1
2
2
0
1
1
0
0
0
0
0
1
0
2
2
0
1
0
2
1
2
1
0
0
0
2
2
1
0
0
0
0
2
0
1
2
2
0
0
1
1
2
2
2
0
0
0
0
1
0
1
1
1
0
0
2
0
0
1
0
1
0
1
0
1
1
1
0
1
0
0
0
0
2
0
0
0
0
3
0
2
2
0
0
2
0
0
0
0
0
3
1
2
0
2
1
0
2
1
0
0
1
2
1
1
0
0
0
1
2
0
1
0
1
2
0
1
1
0
1
1
0
1
2
1
1
1
1
2
0
1
0
0
2
3
0
0
0
0
2
0
2
3
0
1
0
0
2
0
1
1
2
0
1
0
2
0
0
1
2
1
1
0
2
1
0
0
1
0
0
0
0
2
0
2
0
1
0
0
0
1
2
1
0
0
0
1
0
0
1
1
0
1
0
2
0
5
0
0
2
0
0
0
1
0
0
2
2
0
0
0
0
0
1
1
2
0
0
0
0
2
0
2
1
1
0
0
1
2
1
2
0
0
1
0
1
0
0
0
2
1
2
2
0
1
0
1
0
1
2
2
0
1
0
1
0
0
2
0
1
1
0
0
1
2
1
0
0
0
2
1
0
0
0
2
0
2
2
0
1
3
1
0
1
1
0
1
2
0
0
0
0
1
2
2
0
0
2
0
2
1
0
1
1
1
1
0
0
0
1
0
0
2
0
2
1
0
0
1
0
1
0
1
0
2
2
0
3
1
2
2
0
2
2
0
0
0
0
0
1
1
0
1
0
1
2
0
1
2
3
1
0
1
1
0
0
0
2
1
1
2
1
0
2
0
1
2
1
1
1
3
0
1
2
1
2
1
0
1
1
1
1
1
1
1
0
0
2
1
1
2
0
1
2
1
3
1
0
2
1
0
0
3
2
0
0
5
0
2
0
0
0
0
1
0
0
0
0
1
2
0
0
0
3
1
0
0
0
1
1
0
0
2
1
0
1
0
0
1
0
0
1
0
0
0
0
1
0
1
1
0
0
1
2
0
0
0
1
0
2
0
0
2
0
0
0
2
0
0
1
2
0
1
1
0
0
0
1
0
0
1
0
1
2
0
1
0
2
0
1
1
1
0
1
0
1
1
1
0
0
1
0
2
2
1
1
2
0
1
2
0
0
0
0
1
0
2
0
2
1
0
0
0
0
1
0
0
2
0
1
0
0
1
2
0
1
0
0
1
1
2
0
2
2
0
0
2
0
2
0
1
0
1
0
0
1
0
0
0
1
2
2
1
0
0
0
1
1
0
1
0
2
1
0
2
2
0
0
2
2
0
1
0
2
0
2
2
0
2
0
1
1
0
0
0
2
0
1
1
0
1
0
0
1
1
1
2
1
0
1
0
0
1
0
1
0
1
0
1
1
1
0
0
1
0
2
1
0
0
0
0
1
0
0
0
0
0
1
0
2
1
0
1
0
1
1
0
0
1
0
1
0
1
2
0
1
0
1
1
1
1
1
0
0
0
0
0
0
1
0
1
0
0
0
1
1
2
1
0
0
0
0
1
1
2
0
1
0
2
0
1
1
0
1
2
0
0
1
0
1
0
1
0
0
1
1
2
0
1
2
1
0
0
0
0
1
0
0
0
1
0
1
1
0
0
2
2
1
2
2
0
0
0
1
0
1
2
0
0
2
2
0
2
0
1
0
1
0
2
1
0
0
0
1
0
4
0
2
0
2
0
1
0
1
1
2
2
1
1
1
0
1
1
0
0
2
2
1
0
1
0
1
0
2
1
2
2
2
0
2
0
0
0
0
2
3
2
1
2
2
0
1
1
1
1
0
2
1
0
1
0
1
1
0
0
0
0
1
1
0
1
1
0
0
1
2
0
0
1
1
0
1
0
0
0
2
1
2
0
2
0
1
1
0
2
1
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
1
0
0
2
2
0
1
1
1
0
1
0
0
2
2
1
2
2
0
2
2
0
2
1
1
0
1
1
0
0
1
1
1
2
0
0
2
0
0
0
1
1
0
2
3
0
0
2
0
2
0
0
2
0
0
1
2
1
1
1
0
0
0
1
0
0
1
0
2
0
1
0
1
0
1
2
0
2
2
0
0
0
0
2
1
1
1
2
2
0
1
1
0
0
2
2
2
2
0
0
0
0
1
0
1
1
1
0
0
0
2
0
0
1
1
0
1
1
0
0
0
1
0
0
3
2
0
0
1
2
0
0
1
2
1
1
1
0
1
1
1
0
0
0
2
1
0
1
2
0
2
1
0
0
1
0
1
2
1
0
0
0
1
0
0
2
0
0
2
2
0
1
2
1
2
0
0
1
1
0
0
1
2
0
2
0
0
2
3
0
1
0
1
1
2
2
2
1
0
2
1
0
0
2
0
0
1
0
1
2
2
2
1
1
1
0
0
2
2
0
0
0
0
2
2
0
1
0
0
2
0
0
2
1
1
2
0
2
2
0
0
0
0
0
0
1
1
0
0
1
0
0
0
2
1
2
1
0
1
1
0
1
0
1
0
0
2
1
0
0
0
1
0
1
0
0
2
2
2
1
1
1
2
0
1
0
1
2
2
0
0
0
0
1
1
1
2
2
0
2
1
1
0
1
0
1
0
2
0
0
1
0
0
0
2
0
0
1
0
2
1
0
3
1
0
0
0
0
1
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
2
3
2
0
1
0
1
0
1
1
0
0
1
1
0
0
0
1
0
1
1
0
1
0
0
2
0
0
2
1
0
0
0
2
2
1
0
0
2
1
1
0
1
1
1
0
0
2
2
0
0
0
1
0
2
1
2
0
0
1
2
1
1
1
0
1
1
1
2
2
0
1
0
1
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
1
2
0
0
0
1
0
1
0
1
1
2
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
1
1
1
1
1
1
0
1
0
1
1
0
0
0
0
1
1
1
2
0
0
1
1
2
1
0
1
0
1
0
2
1
1
0
0
0
1
3
1
1
0
2
1
0
1
2
0
0
2
2
0
1
0
1
0
1
0
0
1
2
0
2
0
1
0
3
0
0
0
1
1
0
2
2
0
0
2
1
1
1
0
1
0
1
0
1
0
1
1
1
2
0
1
0
0
2
2
1
2
1
1
1
0
1
0
1
0
0
0
1
0
1
0
0
2
0
0
1
1
0
1
2
0
2
1
2
0
1
0
0
2
2
1
2
1
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
1
2
1
2
1
0
1
1
0
0
0
1
2
0
2
1
0
1
1
0
0
0
0
0
0
1
0
3
0
0
2
2
1
0
0
1
1
0
0
1
4
0
0
0
0
1
1
1
0
0
0
0
1
4
2
1
0
2
1
1
0
0
0
0
2
0
0
0
2
0
0
0
1
1
1
1
0
1
1
4
2
0
1
1
0
0
0
1
0
1
0
0
1
0
2
1
1
0
1
0
1
1
0
0
1
1
0
0
1
1
3
1
1
1
4
2
2
2
0
0
0
2
2
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
2
2
0
2
0
0
1
1
1
1
1
0
1
2
0
0
1
2
0
0
1
0
1
1
0
0
1
0
0
0
0
0
1
1
2
0
0
0
0
2
1
1
0
1
0
0
1
1
1
0
1
1
1
0
0
1
0
3
0
2
0
1
0
0
1
0
0
0
1
0
1
1
0
2
0
0
0
0
2
0
1
0
0
1
3
1
2
1
1
1
0
2
1
1
0
0
1
0
1
0
0
0
0
0
2
2
1
1
2
2
1
0
0
1
2
1
1
1
0
1
2
1
0
1
0
0
0
1
1
3
0
0
0
0
2
0
0
0
1
0
1
1
1
1
1
0
1
0
0
2
1
0
1
0
0
0
0
0
1
2
0
0
0
2
0
0
2
0
0
0
2
2
1
0
0
2
1
2
1
0
3
0
0
0
0
2
3
0
0
0
2
0
6
1
2
2
2
0
1
2
0
1
0
2
0
0
0
2
0
0
1
0
1
1
1
2
0
0
0
1
1
0
0
2
2
0
0
0
1
1
0
0
0
0
0
2
1
2
0
1
0
1
0
1
2
1
3
1
1
1
1
0
1
1
0
1
6
2
1
1
2
1
1
0
0
0
0
1
2
2
0
0
0
2
1
1
1
2
2
2
1
0
0
0
0
0
1
1
0
1
0
2
1
0
2
0
0
1
0
0
2
0
1
1
0
1
1
1
0
1
2
1
0
1
2
0
2
0
4
2
1
0
1
2
0
0
0
1
1
0
2
1
2
2
1
1
1
0
1
0
1
1
2
0
1
0
2
0
0
1
1
0
2
2
0
1
0
0
1
0
0
1
0
1
1
0
0
2
0
0
0
0
2
2
1
0
0
1
1
1
2
1
2
1
2
0
1
0
0
0
0
0
0
1
2
2
0
1
1
1
1
0
0
0
2
0
0
1
0
0
2
1
1
0
2
1
1
0
1
1
1
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
4
1
0
2
0
1
0
1
1
0
0
0
0
0
0
0
0
2
1
0
1
0
2
1
2
0
2
0
0
0
2
0
1
1
2
2
2
0
0
0
0
1
1
0
1
2
1
1
0
0
0
0
2
1
0
1
1
0
2
0
1
1
1
0
0
0
2
0
0
2
2
1
0
2
2
2
0
0
0
0
0
1
1
0
1
2
0
2
0
1
0
1
0
2
1
2
1
1
0
0
2
2
0
2
0
0
2
1
0
0
2
1
0
0
2
0
0
0
5
1
0
1
0
1
2
0
1
2
1
1
0
0
1
0
0
2
0
1
0
0
2
0
1
3
1
1
0
1
0
1
1
1
1
1
2
2
2
1
2
1
0
1
1
2
0
1
2
0
0
1
0
1
0
0
0
2
1
0
1
0
1
0
1
2
0
0
2
2
0
1
0
2
0
0
2
0
0
1
0
0
0
1
0
1
1
1
1
0
0
0
1
1
2
0
0
0
1
0
0
0
0
0
2
0
1
2
1
1
1
0
2
0
1
1
1
0
1
1
0
1
1
0
0
0
0
1
0
2
0
3
0
1
0
0
0
0
0
1
1
1
1
5
1
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
1
1
0
0
2
0
1
2
0
2
0
0
1
0
1
0
0
2
0
0
2
0
0
2
1
0
0
1
2
0
1
1
0
0
0
1
0
1
1
1
0
2
0
0
2
2
1
0
1
2
0
0
2
2
0
0
0
0
0
1
1
1
2
1
0
0
1
0
0
1
2
0
0
2
0
0
1
0
1
0
1
0
1
2
0
0
0
0
1
0
1
0
0
2
1
2
2
0
0
0
1
0
0
0
2
1
0
0
1
0
1
1
1
0
0
2
1
0
2
1
0
0
0
0
0
2
2
1
1
0
2
1
1
2
1
0
2
1
1
2
0
1
0
2
2
0
2
1
2
1
1
0
1
1
1
1
1
2
0
1
1
1
0
0
1
2
2
0
2
2
1
0
2
0
1
1
0
0
1
0
2
0
0
0
1
0
1
1
0
2
0
0
1
2
1
0
1
2
0
1
1
2
0
0
1
1
0
2
0
2
0
1
0
0
1
0
1
1
1
2
2
0
2
0
0
0
0
0
2
1
0
0
1
1
1
0
0
1
2
0
1
0
0
0
1
0
1
1
1
0
1
0
2
0
1
1
1
0
1
0
1
0
0
1
2
0
1
2
0
0
0
1
2
1
1
1
0
2
1
2
2
1
1
0
1
2
0
2
0
2
0
1
1
0
0
1
2
1
2
1
2
0
0
1
0
0
0
0
1
1
2
1
0
2
1
1
1
1
0
0
1
0
0
2
1
0
0
1
0
1
2
1
2
2
0
1
1
1
0
0
0
0
1
0
0
0
0
1
0
0
2
1
0
1
0
1
0
1
1
0
1
0
0
0
1
1
1
2
1
0
2
1
0
0
1
0
0
0
0
0
0
1
1
2
2
1
0
0
1
0
0
1
1
0
1
2
1
0
0
1
0
0
0
0
2
0
1
0
1
2
1
0
0
1
1
1
0
1
1
2
2
2
0
1
0
0
0
2
0
1
0
0
0
0
4
0
0
2
0
1
0
1
1
0
1
1
0
1
0
0
1
2
0
1
1
0
2
1
1
1
0
0
1
1
0
0
0
0
0
2
0
0
0
1
2
1
0
1
0
1
0
1
0
0
0
1
1
2
0
2
0
0
1
0
0
2
0
1
1
1
1
2
2
0
1
0
1
2
2
0
0
0
0
2
2
1
2
0
1
2
0
1
0
0
0
1
0
0
2
1
0
0
0
1
0
1
1
0
2
0
0
0
0
0
1
2
0
1
0
1
0
0
0
1
0
0
0
1
1
0
1
1
0
0
2
0
0
2
1
0
0
0
0
3
0
1
2
0
0
1
2
0
0
0
2
0
1
0
2
0
1
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
2
1
1
1
2
0
1
0
0
0
0
1
0
0
0
0
2
2
1
0
2
0
0
1
0
0
2
0
1
0
2
0
0
0
0
0
0
1
2
0
0
2
0
1
0
2
0
1
1
0
0
0
0
0
1
1
0
1
0
0
1
2
2
1
0
0
2
0
0
0
0
0
0
2
1
0
0
1
2
0
0
0
2
1
1
1
6
0
2
1
0
3
0
0
0
0
1
1
2
0
2
1
2
2
2
0
2
1
2
0
0
0
0
1
1
2
1
1
0
0
0
0
0
1
0
0
0
0
0
2
0
2
1
1
1
0
0
2
0
1
1
0
0
2
0
0
1
0
0
1
0
1
1
3
1
1
2
1
0
3
0
1
1
0
1
0
0
1
0
2
1
2
0
0
0
1
1
0
0
0
0
1
0
0
2
0
0
2
2
0
1
1
1
0
1
0
0
1
1
0
1
2
2
1
0
1
2
0
1
0
0
2
4
0
0
1
3
1
1
1
0
0
0
2
1
0
0
0
2
0
0
2
2
1
1
0
2
2
0
2
2
0
1
0
1
0
1
1
2
0
0
1
1
0
1
0
1
1
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
1
1
0
2
1
1
0
0
0
1
0
0
0
0
1
0
1
2
0
0
0
1
0
0
2
2
1
2
2
2
0
0
0
2
1
0
2
1
0
0
2
1
2
0
0
1
1
1
2
2
0
2
0
1
1
0
0
0
0
1
2
4
1
0
1
2
1
0
0
2
1
0
2
0
0
0
1
1
2
0
0
1
0
1
0
1
2
0
0
0
0
1
0
1
1
1
2
0
1
0
1
1
0
0
1
0
0
0
0
1
0
0
1
2
0
0
0
0
0
1
1
2
2
2
0
1
1
0
1
0
2
0
1
1
1
1
0
1
0
1
1
1
0
0
0
0
0
0
2
1
1
0
0
2
1
1
0
1
1
0
0
1
0
0
0
1
0
0
1
1
1
0
0
1
0
0
1
0
0
2
0
1
0
1
2
0
0
2
2
1
0
2
1
0
1
2
0
0
0
1
2
0
2
0
2
0
1
1
0
0
1
2
2
1
0
2
2
1
1
2
2
1
0
1
1
2
0
2
0
0
2
0
2
1
0
2
1
0
1
2
2
0
0
0
0
0
2
1
1
0
1
2
2
0
1
0
1
1
2
4
0
0
1
1
0
0
0
0
1
3
0
2
0
0
0
0
0
1
1
1
2
1
1
2
0
1
0
0
2
1
0
2
0
0
0
1
0
0
2
1
0
2
1
1
0
1
1
2
1
2
2
0
0
1
0
0
2
0
0
0
2
0
0
0
0
2
1
0
1
1
0
0
0
1
1
2
1
2
0
2
1
0
2
0
0
0
0
4
1
0
1
0
0
0
1
1
1
0
0
0
1
0
1
2
0
0
1
1
1
2
1
0
1
2
0
1
0
2
0
1
1
0
0
0
3
0
2
1
0
4
2
0
1
0
0
0
1
2
2
0
0
2
3
0
0
0
2
0
1
0
1
3
3
2
2
0
2
0
1
1
1
0
2
0
2
0
1
0
0
1
2
0
0
0
2
0
2
0
1
0
0
0
1
0
0
2
1
0
0
2
1
1
2
0
0
0
0
0
1
1
2
1
0
0
1
0
1
0
0
0
0
2
1
1
0
1
0
1
2
2
1
0
0
2
0
0
0
2
0
2
1
1
2
2
0
1
2
1
0
0
0
2
0
0
1
1
0
1
0
1
0
0
0
1
0
1
0
1
2
0
1
0
1
0
0
0
4
0
1
2
2
1
2
0
0
3
1
0
1
1
2
1
3
2
0
0
0
2
1
0
2
0
0
0
0
1
2
0
0
0
1
2
1
0
2
2
0
0
0
0
0
1
0
3
0
0
1
1
0
3
0
0
2
1
0
2
1
0
0
1
1
1
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
4
0
0
2
0
2
1
1
0
1
1
1
1
2
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
1
0
1
1
0
0
0
2
1
2
0
2
2
0
1
0
1
1
2
1
2
1
2
2
1
1
0
2
1
1
0
0
1
1
1
0
0
2
2
0
2
0
0
1
0
0
0
1
0
0
0
2
1
1
1
1
0
2
1
0
2
0
0
0
2
1
2
2
0
1
5
0
3
1
2
1
0
0
2
2
0
0
0
0
1
0
1
1
1
0
1
1
3
1
0
2
0
1
1
1
1
1
0
0
0
0
0
1
2
1
2
2
1
2
0
0
0
0
1
0
2
1
0
2
0
0
1
1
0
1
0
1
3
2
0
0
0
0
0
0
1
0
1
1
0
0
0
2
0
0
1
0
0
2
2
2
1
3
2
1
0
1
0
2
0
0
2
0
1
4
1
0
1
0
2
2
1
1
0
0
1
0
2
0
0
0
0
0
2
0
2
0
2
0
0
0
0
2
0
0
0
0
1
2
0
0
1
1
0
1
1
0
1
0
1
2
0
1
1
0
0
2
0
0
0
1
2
0
1
0
2
1
0
0
4
0
0
1
0
1
2
1
1
0
0
1
2
0
0
0
0
1
0
2
1
2
2
2
0
0
1
0
2
2
1
0
2
1
0
0
0
2
0
0
2
3
0
0
0
2
0
0
2
2
1
0
1
1
2
0
1
4
0
0
1
0
1
0
1
1
1
1
0
1
0
0
0
0
2
0
0
2
0
0
0
1
2
1
1
1
0
0
2
2
1
2
0
0
0
0
1
0
2
2
2
0
0
1
0
1
1
2
0
1
0
1
0
0
1
0
0
1
0
2
0
1
2
2
1
0
1
0
1
0
0
3
2
0
0
1
0
1
0
0
0
1
0
1
0
2
1
0
0
0
2
1
0
0
0
2
0
1
2
2
3
1
0
1
1
0
0
2
0
0
2
0
0
2
1
0
2
0
0
1
1
1
0
1
1
0
1
2
1
0
0
0
1
2
0
0
1
2
1
0
0
0
0
0
0
2
0
1
0
2
1
1
0
0
0
0
0
1
2
2
0
0
0
1
0
2
1
2
2
1
0
1
0
0
0
2
0
0
0
1
0
0
0
2
0
2
0
0
1
0
0
0
1
2
0
0
2
0
0
0
1
1
0
0
1
1
2
1
0
0
0
0
0
2
1
1
1
2
1
0
3
0
1
1
2
2
0
2
1
1
2
1
2
2
1
1
0
2
0
2
0
2
1
2
0
1
1
3
2
0
0
0
1
0
1
1
2
0
1
0
0
0
1
0
0
1
2
0
1
0
2
2
0
2
7
1
1
2
0
1
1
0
0
0
1
0
0
2
1
0
2
1
2
0
0
2
2
0
2
0
2
1
0
1
2
0
2
0
1
0
2
1
0
0
0
0
1
2
2
0
1
3
0
1
2
0
0
1
0
2
0
0
1
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
1
2
1
1
0
0
2
0
2
0
2
0
2
0
1
1
0
1
2
2
0
1
1
1
1
0
0
1
1
0
1
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
2
0
0
1
1
1
0
0
0
1
0
1
1
1
1
0
0
0
1
2
0
0
1
1
0
0
0
0
0
0
2
1
0
0
1
1
1
0
1
0
3
1
0
1
2
0
2
1
1
0
0
0
0
0
0
0
2
1
1
0
1
2
1
1
3
0
0
0
1
0
1
1
0
1
1
2
1
1
0
1
0
0
0
1
0
2
1
0
0
0
1
0
1
2
1
0
1
1
2
0
0
2
0
1
0
1
0
1
0
0
1
1
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
2
2
2
2
0
0
0
1
0
0
0
2
1
1
1
0
1
0
0
1
0
1
2
1
1
0
1
2
1
0
1
0
1
1
0
1
2
2
0
0
2
1
1
0
2
0
0
1
1
2
1
0
0
1
1
0
1
2
2
1
0
0
0
1
2
0
1
0
0
1
1
0
0
0
1
0
0
2
1
0
0
0
1
2
0
0
2
0
0
0
1
3
0
1
0
0
2
2
0
1
2
0
0
1
0
0
0
0
0
0
0
1
0
2
2
1
0
0
0
1
1
1
0
0
0
1
0
0
0
0
3
2
1
1
0
0
0
0
0
0
2
1
1
2
0
2
2
1
1
0
1
1
3
0
0
2
1
2
1
1
1
0
0
0
0
1
0
0
0
0
2
0
2
2
0
1
2
0
0
2
1
0
2
0
0
0
0
0
0
2
2
2
0
2
0
0
1
1
0
0
0
1
1
0
0
1
0
2
0
0
2
0
0
2
0
1
2
1
1
3
0
0
1
2
0
2
0
0
0
1
0
1
0
0
2
2
1
0
0
0
0
0
0
0
0
1
0
2
4
0
0
0
1
2
0
1
0
1
0
0
2
1
0
1
0
0
0
0
2
0
2
1
0
2
1
0
4
0
0
1
2
0
2
0
1
1
1
1
0
0
0
1
3
0
2
0
1
0
2
0
2
0
0
1
1
4
0
1
0
1
0
0
0
0
0
2
1
0
0
0
2
0
0
1
0
2
1
2
0
0
2
0
0
2
2
1
1
1
0
0
1
1
0
2
2
1
1
0
0
1
1
0
0
1
1
0
1
0
1
1
1
0
0
1
1
1
0
0
2
0
0
0
0
0
2
2
0
1
1
0
0
0
0
0
2
0
0
1
0
2
1
1
0
2
0
1
2
0
0
1
0
2
1
0
1
0
1
1
2
0
1
0
0
0
0
1
1
0
0
4
0
1
0
1
2
2
0
1
2
1
0
0
0
1
1
0
1
1
1
1
0
0
1
1
0
1
0
0
1
2
1
1
2
1
0
1
1
2
0
2
1
0
0
4
1
1
0
2
0
1
1
2
0
0
0
0
1
0
0
2
2
1
0
1
1
0
1
0
0
0
2
1
2
2
0
2
0
1
1
0
2
1
0
0
1
0
0
0
2
0
0
2
0
2
0
2
0
0
1
1
0
0
2
0
0
1
1
0
0
1
1
0
2
1
1
0
0
1
0
1
0
0
2
0
2
1
0
0
0
0
0
1
1
0
1
1
0
0
2
0
7
0
0
0
0
0
0
0
1
0
1
0
1
2
0
0
1
1
3
2
2
1
1
2
0
2
1
1
3
1
1
2
1
2
1
0
2
1
0
0
2
1
0
0
2
1
0
0
3
1
1
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
1
0
0
1
1
0
0
0
2
0
0
0
0
1
0
0
1
0
1
0
2
1
1
0
0
1
1
2
0
1
0
1
1
2
0
0
1
0
0
0
1
1
2
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
1
1
2
2
1
0
0
2
2
0
2
0
0
1
1
0
0
2
1
2
1
0
2
0
1
1
2
1
0
0
0
0
0
1
2
1
0
1
2
0
1
1
0
0
1
2
0
0
0
1
1
2
2
0
1
0
1
1
0
1
2
1
1
0
0
2
0
1
0
2
1
0
0
0
1
1
0
0
0
0
0
2
0
2
2
0
0
2
0
1
2
0
2
0
1
0
1
0
0
0
1
2
0
3
2
0
1
0
1
2
1
1
0
0
0
1
1
0
1
2
1
0
2
1
0
1
1
2
0
1
0
1
0
0
0
1
0
1
1
0
0
0
1
0
0
0
2
0
0
1
2
0
0
1
0
0
0
2
0
0
1
2
1
0
1
0
1
1
2
1
1
0
0
0
1
0
0
0
3
0
0
0
1
0
2
0
0
2
0
1
2
0
1
2
2
1
0
1
0
2
1
1
0
2
1
0
0
2
1
0
0
0
1
0
1
0
2
2
0
2
0
3
0
0
0
0
0
0
1
0
0
2
0
0
2
0
1
1
1
1
0
2
4
1
1
0
0
0
1
2
1
0
1
2
0
0
1
1
0
2
1
0
1
0
0
0
0
1
2
2
1
0
0
0
2
0
1
0
2
1
3
0
1
0
0
1
2
1
2
0
0
2
1
0
0
1
2
0
2
2
0
2
1
0
0
3
2
1
0
1
0
1
1
0
0
0
2
1
0
1
0
0
0
1
2
1
2
0
2
2
0
0
1
0
1
1
1
0
0
0
1
1
0
0
2
1
2
0
0
1
0
1
1
0
0
2
0
2
1
1
0
0
0
0
0
1
2
0
2
2
2
0
1
2
1
0
0
0
0
0
2
2
1
1
1
0
0
2
1
0
0
0
0
2
0
2
1
3
2
2
3
0
2
9
0
3
1
0
1
1
0
2
0
0
0
0
0
0
0
2
0
0
1
1
0
1
2
2
1
1
3
1
0
0
0
2
0
1
2
0
2
1
0
0
0
1
0
0
1
0
0
2
1
2
2
0
1
0
1
0
1
0
1
0
0
1
2
1
2
1
2
1
1
1
0
0
0
0
2
0
0
1
0
1
1
2
2
1
1
0
0
0
0
0
2
0
0
1
2
0
2
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
1
0
3
0
0
1
0
0
2
0
1
2
2
2
2
0
0
0
0
2
1
1
0
0
1
1
1
0
0
0
2
1
1
0
1
1
0
1
0
1
1
1
1
2
0
1
2
2
2
2
0
0
1
2
0
0
2
0
1
2
2
0
1
1
0
0
0
2
0
2
2
0
0
1
1
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
2
1
1
0
0
0
3
0
0
0
0
0
0
1
0
2
2
0
0
1
1
1
0
1
1
0
2
2
0
3
1
1
0
1
0
0
1
2
2
0
0
0
1
0
0
1
1
0
1
0
2
2
0
0
0
3
1
5
0
0
1
0
0
1
0
1
1
2
0
2
1
1
0
1
0
2
0
0
2
2
0
0
0
2
0
1
2
0
0
1
0
0
0
1
3
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
1
2
0
2
2
1
0
1
1
0
2
1
0
0
1
0
0
1
0
1
0
0
0
2
0
2
0
1
3
0
1
1
2
1
0
2
1
2
2
0
2
0
0
1
0
0
2
0
2
0
2
0
1
0
0
2
2
0
1
2
0
0
0
4
0
2
0
0
1
2
0
2
0
1
1
2
1
0
1
2
0
0
1
0
2
1
1
2
1
2
0
1
0
1
0
0
1
1
1
0
1
1
1
1
0
2
2
0
2
0
2
1
0
0
0
0
2
2
0
2
0
1
2
2
1
1
0
2
1
0
0
0
2
3
1
0
0
0
1
0
2
0
0
2
2
0
0
1
0
1
1
1
0
2
2
0
0
0
2
1
1
0
2
0
0
1
0
0
0
0
2
1
0
0
1
2
1
2
0
1
1
0
2
1
1
0
1
2
0
3
1
1
0
2
0
1
0
0
0
0
0
0
2
1
1
2
0
1
0
0
1
0
1
1
2
1
0
2
0
1
0
2
0
0
0
1
0
1
2
2
0
1
0
2
2
1
0
0
2
0
0
0
0
1
1
2
2
0
1
1
0
0
0
0
2
0
0
0
0
1
1
1
0
2
1
2
1
1
2
0
2
0
0
1
2
0
0
1
0
1
0
0
0
0
3
1
0
0
2
1
0
1
1
1
2
0
2
1
0
0
0
0
0
2
0
1
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
1
3
0
0
0
0
2
0
5
1
2
0
0
6
0
0
1
0
2
1
1
1
1
2
0
2
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
2
2
3
1
2
0
0
0
1
1
2
1
2
0
0
0
0
2
0
0
2
1
2
2
0
2
0
1
0
1
0
2
0
0
0
1
1
0
1
1
0
1
0
1
1
0
1
0
1
0
1
1
0
2
1
0
0
2
1
0
0
0
1
0
1
2
2
2
0
1
0
1
1
0
2
2
0
2
0
0
1
0
0
0
0
1
1
1
0
0
1
1
1
0
1
0
1
1
2
1
1
0
2
0
0
0
1
0
2
1
2
2
0
0
0
0
0
0
1
2
2
1
1
1
0
0
0
2
0
0
0
0
3
1
1
0
0
2
0
0
0
0
0
1
0
2
0
1
0
0
1
0
0
1
0
0
1
1
0
1
1
1
1
0
0
0
2
0
1
0
0
1
0
2
1
1
1
0
0
1
1
0
0
0
2
0
0
1
2
0
1
1
0
0
1
1
0
0
1
2
0
1
0
0
0
0
0
0
0
0
2
1
0
2
2
1
1
0
1
0
1
1
2
1
1
1
1
2
0
0
1
2
1
1
2
0
2
1
0
0
1
0
0
1
2
1
0
0
1
0
1
0
0
0
1
0
0
0
1
1
0
1
2
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
1
2
0
1
1
0
1
2
1
0
0
1
1
1
0
2
0
1
0
4
1
1
2
1
2
1
0
1
0
1
2
0
0
0
2
1
0
2
0
2
1
0
1
2
1
0
2
2
0
0
0
0
0
0
1
0
1
0
0
0
1
2
2
1
2
2
0
1
0
1
1
1
2
0
2
0
0
1
0
1
0
1
0
0
1
0
1
0
1
1
2
1
1
2
2
0
2
0
0
2
2
0
1
2
0
2
1
1
0
1
1
1
1
1
2
1
0
0
3
0
0
0
2
1
1
0
0
1
0
0
2
1
1
2
0
0
1
1
0
1
0
2
2
1
0
1
1
0
0
1
0
2
0
1
1
0
0
0
0
2
2
0
1
0
1
1
0
0
0
0
2
1
1
3
0
0
0
1
1
1
0
0
2
2
2
0
1
0
1
2
0
0
0
0
0
0
0
0
1
0
1
2
1
2
0
1
0
1
1
1
0
2
1
0
1
2
2
0
0
2
0
2
2
0
2
1
0
0
1
0
1
0
1
0
0
1
0
1
0
1
0
1
0
1
0
3
1
1
0
0
2
0
0
1
0
1
0
0
1
0
0
2
0
2
0
1
0
2
1
2
2
1
0
2
0
2
1
0
0
1
2
1
0
1
1
1
0
0
3
0
1
2
1
1
2
1
2
1
2
0
1
1
2
0
2
2
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
1
1
0
0
2
2
1
3
1
0
2
0
0
2
0
0
2
1
0
1
1
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
2
0
1
0
0
2
0
3
1
0
1
0
0
1
0
1
0
0
2
1
2
1
0
0
1
2
1
1
2
0
1
2
2
0
1
1
1
0
2
0
2
0
0
1
2
0
2
0
0
0
0
0
1
0
0
1
1
2
0
0
2
1
1
1
0
2
0
2
0
1
0
1
0
0
1
1
2
0
0
0
1
0
0
1
2
0
0
1
2
0
0
0
1
2
0
2
0
0
0
1
1
0
1
0
0
2
1
1
0
0
1
2
0
2
0
1
0
0
1
2
2
0
0
0
0
1
1
2
3
0
1
0
0
0
2
0
1
0
2
1
0
2
1
0
2
0
1
1
0
0
0
1
0
2
0
0
0
1
1
2
0
0
0
0
2
2
2
2
1
1
0
0
1
0
1
1
0
0
2
2
0
1
2
0
1
1
1
0
0
1
0
2
1
0
0
0
1
2
0
0
2
1
5
1
1
1
0
0
0
0
0
0
2
0
0
0
0
1
1
1
0
0
0
0
0
1
0
2
0
0
1
2
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
1
2
1
2
2
1
0
2
1
2
1
0
0
2
1
1
0
0
2
0
1
1
0
1
0
1
1
2
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
1
2
0
2
2
1
1
0
2
1
0
1
1
0
0
1
1
1
1
1
2
1
0
2
0
0
0
2
1
0
3
0
0
0
1
0
0
2
2
1
0
1
1
0
1
1
0
1
1
2
0
2
0
0
2
1
1
0
1
0
0
0
1
1
0
1
0
1
0
0
1
1
1
1
0
0
1
1
0
1
0
0
1
1
1
1
0
0
1
0
2
0
0
1
0
2
1
0
0
0
2
2
2
0
0
0
1
0
0
1
0
1
0
2
0
0
0
1
0
0
1
0
1
0
1
1
2
0
4
0
0
1
1
2
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
3
0
1
0
2
1
0
2
0
0
2
2
1
1
1
1
0
0
2
0
0
2
2
1
0
1
2
0
0
0
1
1
0
1
2
0
0
2
0
2
2
1
0
2
1
0
2
0
2
2
0
0
0
0
2
1
2
1
1
1
0
0
0
0
3
1
0
2
2
1
0
0
2
0
1
0
1
2
1
2
1
0
0
0
0
1
1
0
1
0
0
0
0
1
2
0
0
0
2
1
2
1
2
0
0
0
0
3
2
0
2
2
0
0
0
0
0
1
1
1
1
1
0
0
2
0
2
0
1
2
0
2
1
2
1
2
0
1
1
2
0
0
2
1
1
1
1
0
0
1
0
1
1
0
1
0
0
1
1
1
1
1
1
0
0
0
0
0
2
1
1
0
0
1
1
0
0
0
0
0
0
2
0
1
2
1
0
0
0
2
1
1
0
0
1
4
0
2
1
1
0
0
1
2
0
2
0
2
2
0
0
1
0
0
0
0
1
0
2
1
2
1
0
1
1
0
1
0
0
2
1
2
2
0
0
0
0
0
0
0
1
1
1
2
0
1
0
0
1
0
0
0
0
2
1
1
0
1
1
1
0
1
1
1
0
0
1
0
1
0
2
0
2
1
0
0
0
0
1
0
1
1
2
0
0
0
1
2
3
2
0
0
1
1
2
0
1
1
2
1
0
1
0
0
2
0
0
0
0
1
2
0
1
0
2
0
2
0
2
0
1
1
1
0
0
2
0
2
0
1
1
1
0
1
2
1
0
0
0
0
2
2
2
2
0
0
0
0
2
1
0
2
1
1
2
1
1
0
0
2
0
0
2
1
1
0
2
0
1
0
0
2
0
0
0
1
0
0
0
1
0
2
1
0
0
2
1
1
1
0
1
0
0
0
0
0
0
1
1
0
1
0
0
2
2
2
0
0
0
0
1
1
1
2
0
0
1
0
2
0
2
0
0
0
1
0
0
0
2
0
2
1
0
2
0
1
1
1
2
2
1
2
2
2
1
0
2
1
0
0
0
7
1
2
0
0
0
1
1
2
1
0
2
1
1
0
0
0
0
2
0
0
0
0
2
2
0
1
3
1
0
0
1
2
2
1
1
3
0
1
2
0
1
0
2
2
1
0
0
1
1
2
5
0
0
1
1
0
2
2
3
0
2
1
0
1
1
0
1
0
2
0
1
2
0
1
5
1
1
0
0
0
0
0
0
0
1
1
0
2
2
0
0
0
0
2
0
0
2
1
0
1
0
0
1
0
0
0
0
3
1
0
1
2
2
1
1
1
2
1
3
0
0
0
2
0
0
1
0
1
0
1
2
1
2
0
0
1
0
1
0
1
1
0
2
1
1
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
2
0
1
1
0
1
1
1
0
1
2
1
0
0
1
1
0
0
2
1
1
2
0
0
2
1
0
0
1
0
0
1
1
2
0
0
0
1
1
1
3
1
0
1
1
0
1
1
2
1
2
1
1
0
0
1
0
1
1
0
1
0
0
0
0
3
1
2
0
2
0
2
0
2
2
0
1
0
0
1
1
0
0
2
1
0
0
0
2
1
1
1
0
0
0
0
2
0
0
0
1
1
1
1
0
2
0
0
0
2
0
0
2
0
1
1
2
2
1
2
0
0
2
0
2
0
2
0
0
1
0
0
0
1
0
0
1
2
0
0
2
2
0
0
0
0
0
2
1
2
0
1
0
1
1
0
0
1
1
0
0
2
0
1
0
0
0
0
1
0
2
0
2
2
2
0
0
0
0
2
2
3
1
0
0
1
1
0
0
0
2
2
0
0
0
2
0
1
1
1
1
1
1
1
2
0
2
2
2
1
1
0
1
1
1
4
0
1
1
2
2
1
1
0
2
2
1
2
2
1
1
0
1
1
0
2
0
1
1
0
2
0
1
0
2
1
1
0
3
1
0
0
1
1
1
0
1
0
0
1
0
0
3
1
0
0
1
0
3
1
2
0
0
2
1
0
1
0
0
2
2
0
0
1
0
2
2
0
0
0
2
2
2
0
2
1
1
1
1
1
0
0
2
1
1
1
0
0
0
1
1
1
0
0
3
0
0
2
1
4
0
2
1
1
1
0
1
1
1
2
0
0
0
1
1
2
0
2
0
2
0
1
2
1
0
0
0
0
1
0
0
0
0
1
2
1
3
0
2
1
1
0
2
0
0
0
2
0
1
2
2
2
0
0
1
1
1
1
0
1
1
0
0
1
1
0
2
0
1
0
0
1
1
1
0
0
1
1
1
0
1
1
1
2
0
0
1
0
0
0
1
0
2
0
0
0
3
4
4
0
0
1
2
1
1
0
1
0
0
0
2
2
0
0
2
0
9
3
1
1
1
1
1
0
2
2
0
0
1
1
1
0
1
0
0
0
2
0
0
0
1
0
1
0
0
2
0
2
1
0
2
1
1
2
1
2
1
1
2
0
0
1
0
2
0
1
0
4
0
0
0
0
2
2
0
0
0
2
2
2
0
1
1
0
1
0
0
1
1
2
0
0
0
0
0
2
1
1
2
0
0
0
1
0
0
2
0
2
0
0
0
1
1
0
0
0
0
0
1
0
0
1
2
0
1
0
1
0
0
1
0
0
0
1
1
0
2
1
1
0
2
1
2
0
0
0
0
0
0
1
0
2
1
2
1
0
1
0
1
1
0
2
1
0
1
0
0
2
0
0
1
0
0
0
2
2
1
1
1
0
0
1
1
0
2
1
0
0
0
2
0
0
0
0
0
0
1
0
2
2
1
2
0
2
5
0
0
1
0
1
1
0
0
2
1
0
0
0
2
2
3
0
1
0
2
1
3
1
3
1
2
0
1
1
0
2
4
2
1
1
0
0
1
2
1
0
0
2
0
0
1
0
0
1
0
0
2
0
1
2
1
2
0
1
1
1
1
0
0
2
0
0
1
0
2
2
1
0
0
1
1
1
0
2
0
2
0
1
0
0
0
2
0
0
1
0
0
1
0
0
2
2
1
0
0
1
0
1
2
0
1
0
0
2
0
1
0
0
0
0
0
0
1
2
1
2
1
2
1
2
1
3
0
0
0
0
0
0
2
0
1
0
0
2
2
2
0
0
0
1
0
1
0
0
0
0
0
2
1
0
2
1
2
1
0
0
1
1
0
1
1
1
2
2
0
1
1
1
2
1
1
2
2
0
1
0
0
1
1
0
1
0
1
0
1
2
1
0
0
0
0
0
1
1
1
1
0
0
1
0
0
0
2
1
0
1
0
3
0
0
0
1
2
2
0
2
2
0
0
0
2
0
0
2
0
1
1
5
1
0
2
2
1
2
2
1
4
0
0
0
2
1
1
0
2
0
2
1
0
1
2
0
0
0
0
1
0
0
1
0
1
2
2
0
1
1
1
2
2
0
1
0
0
1
1
1
1
2
0
1
1
0
2
0
4
2
2
1
1
1
1
0
0
2
1
0
1
0
2
0
0
1
0
0
6
1
3
0
2
1
0
0
0
1
0
0
1
0
1
1
0
2
1
2
2
0
0
0
0
0
2
1
0
2
0
1
1
0
0
0
2
1
2
2
1
2
1
0
2
1
0
0
4
0
0
1
0
0
0
2
0
2
1
2
1
0
0
1
0
0
1
0
1
1
0
2
1
0
1
0
0
2
1
1
0
2
1
2
2
1
2
1
0
2
1
0
0
2
0
2
0
0
1
0
0
0
1
1
0
2
1
1
0
2
2
1
0
0
2
0
1
0
1
0
0
0
1
2
1
0
0
3
0
0
0
2
0
2
2
0
2
2
2
2
0
1
0
1
0
1
0
0
2
1
1
0
0
0
0
1
2
1
0
0
1
1
2
2
2
0
1
0
2
1
0
1
0
1
2
2
1
2
0
1
2
2
1
0
0
0
0
1
1
0
0
7
1
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
1
0
1
1
1
0
2
0
1
0
1
1
0
0
1
2
1
0
0
1
0
2
2
1
2
1
0
1
1
2
0
0
2
0
2
2
2
0
0
2
0
2
1
0
1
1
0
1
0
1
1
1
0
0
1
2
2
1
1
1
1
2
0
2
1
0
1
0
0
0
0
2
2
2
1
1
1
1
1
2
1
0
2
0
1
0
1
1
0
1
1
0
0
0
0
1
1
0
0
0
2
1
2
2
0
0
0
0
2
1
1
1
1
1
1
1
2
2
1
1
0
0
1
0
0
2
2
0
0
2
0
3
1
1
1
1
1
1
1
1
0
0
3
0
0
0
2
0
2
0
1
0
0
0
1
0
2
0
1
0
0
0
0
4
0
0
0
0
2
0
1
0
1
0
2
1
0
2
0
0
2
2
0
1
0
1
1
2
0
0
1
0
2
1
2
0
0
0
1
0
0
0
0
2
0
0
1
0
1
1
1
1
5
3
0
0
0
0
0
2
1
1
1
0
0
1
0
0
0
0
4
0
0
0
1
0
0
2
1
0
1
0
0
1
0
0
0
1
0
1
2
1
0
2
2
0
0
1
1
0
0
0
2
0
4
0
2
0
2
0
1
1
2
2
0
1
0
2
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
1
2
1
2
0
2
2
1
2
1
1
1
1
0
0
0
1
0
1
0
1
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
2
0
2
0
2
1
2
0
1
0
1
1
0
1
1
1
0
1
2
0
0
2
0
0
0
2
0
0
1
0
0
2
1
0
1
1
1
0
0
0
0
2
0
2
1
2
0
0
1
1
0
0
0
0
1
2
1
1
1
0
1
0
1
0
2
2
1
2
2
0
2
1
1
2
2
0
1
3
2
0
0
0
0
0
0
0
0
1
1
1
2
0
0
0
1
0
1
1
0
0
1
1
0
0
0
0
3
1
2
0
0
0
1
3
0
2
0
2
0
0
0
0
1
0
0
1
0
1
0
2
1
1
1
0
1
0
3
1
1
0
2
1
0
0
0
0
0
1
2
0
0
0
2
1
2
0
1
2
2
2
0
1
1
0
0
0
2
2
1
1
1
2
0
0
0
0
2
1
0
0
0
1
0
1
1
1
1
1
1
0
0
0
1
2
2
1
1
0
0
0
0
0
2
1
1
2
0
1
2
0
2
0
0
2
0
2
0
1
2
2
1
0
2
2
1
0
0
1
2
1
1
2
1
2
1
0
2
0
0
0
1
3
1
2
1
0
0
1
1
0
1
1
0
1
0
0
0
1
0
1
0
1
1
0
1
2
2
0
2
1
0
1
0
1
1
2
1
0
0
0
0
1
0
0
1
0
0
0
2
0
0
2
2
1
1
0
0
2
0
0
0
2
2
2
0
0
1
0
0
1
0
2
2
0
1
2
0
1
0
0
4
0
0
0
1
2
0
1
0
2
1
2
0
0
1
1
1
1
0
0
2
1
0
0
0
1
1
0
1
1
0
1
0
1
0
2
0
2
0
1
1
0
1
0
0
0
0
0
0
0
2
1
1
3
0
1
0
0
0
0
0
0
1
2
0
1
2
1
1
0
0
1
2
1
0
1
2
1
0
2
0
0
0
0
2
0
0
2
1
2
0
2
0
2
1
1
0
2
3
1
0
0
0
2
0
1
1
0
0
1
1
1
2
0
1
0
1
0
1
2
1
2
1
2
3
0
0
1
1
1
2
0
1
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
2
0
1
0
2
1
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
1
1
0
3
2
2
1
0
1
1
2
1
1
0
0
0
2
1
6
2
1
1
0
1
1
0
1
1
0
1
0
1
2
0
2
0
1
0
0
1
1
0
2
0
2
0
1
1
0
0
2
0
1
0
4
0
0
2
2
1
1
0
2
2
2
1
0
0
1
0
1
2
0
0
1
2
1
1
2
0
0
2
0
0
0
1
0
1
1
0
0
1
1
1
1
0
0
0
0
0
1
2
0
1
1
2
0
1
0
2
1
0
1
0
1
2
1
1
0
0
0
1
0
2
3
2
0
1
1
1
1
0
0
0
0
1
0
0
0
0
2
0
0
3
0
1
1
0
2
0
0
0
1
0
2
0
0
0
0
1
0
2
1
0
1
3
2
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
1
2
0
1
0
0
1
1
1
1
0
0
1
1
0
0
1
0
1
2
0
2
0
1
2
1
1
1
0
0
2
2
0
0
1
0
0
0
0
0
1
2
1
1
2
2
0
0
0
0
0
0
2
1
0
1
1
2
0
1
0
2
0
1
2
0
0
1
0
0
0
0
1
1
1
1
1
1
0
0
1
0
0
0
0
1
0
2
0
0
1
0
0
0
1
0
3
0
0
0
1
0
1
1
1
0
2
0
1
1
3
0
1
0
0
1
0
0
0
1
1
1
0
0
1
0
2
0
0
1
1
1
0
0
2
0
2
0
1
1
1
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
1
1
0
2
0
0
1
0
2
0
0
1
1
1
0
1
3
0
0
0
0
0
0
1
1
1
2
0
0
0
1
1
1
1
0
1
1
1
2
0
1
1
0
2
2
0
1
0
1
0
3
1
1
0
0
0
0
0
1
0
2
2
0
2
1
0
0
0
0
0
0
0
1
1
3
2
1
0
2
1
0
1
0
0
1
2
0
1
0
1
3
1
0
2
0
0
0
2
0
0
0
2
0
1
1
0
0
0
0
0
0
1
0
2
1
0
2
1
0
0
1
1
0
0
1
0
0
0
1
2
0
2
0
0
0
0
0
0
2
1
1
2
2
0
1
0
2
0
1
0
0
1
1
0
1
2
1
0
2
1
1
1
2
0
2
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
1
1
0
2
1
4
1
0
0
0
1
0
3
0
1
2
1
2
0
1
1
0
2
1
1
0
0
0
0
2
1
0
2
0
0
2
0
0
2
2
0
1
1
2
1
1
0
1
1
0
0
0
2
1
0
0
0
2
1
0
2
0
0
0
0
2
0
2
0
1
2
0
0
0
2
1
1
1
0
2
2
0
0
0
0
2
1
2
1
3
0
3
0
1
1
1
0
0
1
1
0
1
0
0
2
0
0
0
1
0
1
1
2
0
2
0
0
2
1
1
3
1
2
2
0
0
0
1
0
1
0
0
2
0
0
0
1
0
1
2
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
2
1
1
2
1
0
2
0
0
0
0
1
2
2
0
1
2
1
2
1
2
1
0
1
1
1
1
1
2
1
3
2
0
3
2
4
2
2
0
1
0
1
1
0
0
0
0
2
0
2
0
0
1
1
2
0
2
0
1
0
0
0
0
0
2
1
3
1
1
0
1
0
2
2
0
0
0
0
0
0
0
0
3
2
2
1
2
1
1
1
2
2
2
0
0
1
0
0
1
0
0
1
2
0
0
0
2
0
0
1
0
0
0
0
2
1
2
1
2
4
2
1
3
1
0
2
0
0
0
2
0
0
1
0
1
0
0
0
2
0
2
0
2
1
0
2
0
2
1
0
0
1
1
0
2
0
0
0
0
0
0
0
2
1
2
1
1
0
2
1
2
0
2
0
1
0
0
0
0
1
0
1
2
1
0
1
0
0
1
1
2
0
0
0
1
1
1
1
0
1
0
1
2
1
2
1
0
1
0
1
2
0
1
0
0
1
2
0
2
0
1
2
0
0
0
0
2
2
0
0
2
1
0
1
2
0
1
1
0
1
1
0
1
1
0
0
2
0
2
0
0
2
2
0
2
2
1
1
0
0
2
0
2
3
0
1
1
0
1
0
0
2
1
0
2
0
1
2
0
0
0
1
0
0
0
1
0
0
1
1
2
0
1
2
0
0
2
1
2
1
0
2
1
0
1
1
2
1
0
1
3
1
1
1
2
1
0
2
0
0
0
1
2
10
0
0
0
0
0
3
0
0
2
1
0
2
0
2
0
5
0
0
0
0
0
0
1
0
0
0
2
2
0
2
0
0
0
0
0
1
2
2
1
1
1
2
2
0
2
1
2
2
1
0
1
0
1
0
2
0
2
0
2
0
0
0
0
1
1
2
0
1
1
1
0
1
0
3
1
1
0
0
0
1
1
1
2
0
2
2
0
1
1
0
1
0
2
0
0
1
0
0
1
1
1
0
1
2
0
2
1
0
0
0
1
2
0
1
1
1
0
0
1
2
0
0
1
0
0
0
0
0
1
0
0
1
2
0
0
1
2
2
1
0
1
0
2
1
0
0
1
1
1
1
0
0
0
0
1
1
0
2
2
2
2
2
1
2
0
0
1
1
0
1
1
2
0
1
1
1
0
3
1
1
0
1
1
2
0
0
0
0
2
1
1
2
0
1
1
0
1
0
0
0
0
0
0
1
1
0
0
2
1
1
0
2
1
0
0
0
3
1
2
0
1
1
0
2
2
2
1
2
2
1
1
1
0
0
2
0
2
0
2
1
0
2
1
1
0
0
0
0
1
1
1
4
0
0
2
0
0
1
1
2
1
0
0
1
4
1
0
0
0
0
1
1
1
0
0
1
0
0
1
2
1
2
2
0
2
1
0
1
2
0
1
0
1
0
0
2
1
1
0
2
2
1
1
0
2
0
1
1
0
0
1
0
0
3
2
1
0
0
0
0
0
2
1
1
0
1
1
0
1
3
0
1
0
1
0
0
2
1
0
2
2
2
1
1
1
1
0
0
0
1
2
0
1
2
0
1
0
0
2
0
1
0
1
2
2
0
0
0
2
1
0
1
2
0
2
1
0
1
0
0
1
0
0
1
1
0
4
1
1
2
1
0
1
0
1
0
1
2
0
2
2
0
0
2
1
0
0
0
1
0
0
1
3
0
0
2
0
0
1
1
0
1
2
1
0
1
0
1
1
1
0
0
1
0
2
1
2
1
0
2
0
0
2
0
0
2
2
2
0
0
2
0
2
1
0
0
0
2
2
2
1
2
0
0
0
0
0
1
2
1
0
1
1
1
0
0
0
0
2
1
0
1
2
1
0
0
0
0
2
2
0
2
0
0
2
0
2
0
1
1
0
0
0
1
1
0
0
1
0
2
2
2
1
1
2
0
2
2
3
1
0
1
1
1
1
0
2
2
2
0
0
0
1
0
1
2
0
0
0
1
2
1
1
1
1
2
2
2
0
0
2
0
1
0
1
0
1
4
3
0
1
2
0
0
0
0
2
2
1
1
0
1
1
1
2
1
2
0
0
0
0
1
1
1
0
2
1
1
0
1
0
0
0
2
0
0
0
0
1
2
0
0
0
1
1
1
2
1
0
0
0
1
0
0
0
0
1
2
1
1
2
0
2
0
1
0
0
0
0
0
0
1
2
2
0
0
1
1
1
0
0
0
3
0
0
0
0
2
0
0
1
0
0
1
0
1
1
1
0
0
2
0
0
0
1
1
1
0
0
0
0
1
0
0
1
1
2
0
0
0
2
1
2
0
0
1
0
2
0
0
2
0
1
2
1
0
1
1
2
0
2
0
1
0
1
0
1
1
0
0
0
0
2
0
0
0
1
1
0
1
0
2
1
1
2
0
0
1
1
0
1
2
0
1
1
0
1
1
1
0
0
1
0
1
0
0
1
0
0
1
0
2
2
0
1
0
1
0
1
0
2
2
2
0
0
0
1
2
1
0
0
1
0
1
1
0
0
0
0
2
1
2
0
0
2
1
1
0
1
0
2
2
1
1
0
0
1
0
2
0
1
0
2
0
0
1
1
0
2
1
0
1
2
0
1
1
0
1
0
3
2
1
1
2
1
0
0
0
2
0
1
1
0
0
0
2
0
1
0
0
1
0
0
0
2
0
1
0
0
2
0
0
1
2
2
0
0
1
0
0
1
1
1
0
2
1
0
1
2
0
1
0
2
0
2
0
0
2
1
0
0
1
1
0
0
0
0
1
0
1
1
1
1
1
0
0
0
1
0
0
0
2
0
0
2
0
0
2
1
2
0
0
1
1
2
0
1
0
0
0
1
2
1
2
0
2
1
0
1
1
1
2
1
0
0
1
2
2
0
0
0
1
1
2
1
1
0
0
0
1
2
0
1
1
0
0
0
2
1
2
1
1
2
0
0
2
0
1
1
0
0
2
1
0
2
0
1
0
2
0
1
1
1
1
0
1
1
1
2
3
0
0
1
1
1
2
1
1
2
0
0
0
0
1
0
0
2
2
1
0
0
0
0
2
1
0
1
2
0
0
0
0
1
0
1
0
0
1
1
1
2
2
0
2
0
0
0
1
2
1
2
0
1
0
1
2
0
1
0
1
2
0
1
0
0
0
0
1
1
0
1
2
0
1
0
0
0
0
2
0
1
0
2
2
1
0
0
2
2
1
0
0
1
1
1
1
2
0
1
2
2
0
1
0
0
0
1
2
0
1
2
1
1
0
1
1
2
0
0
0
0
0
0
1
1
1
0
1
0
1
1
0
2
0
2
2
1
1
1
0
0
0
2
3
1
1
2
1
0
0
1
1
1
0
0
0
1
1
1
0
0
1
1
1
0
0
1
0
0
0
1
1
0
0
1
0
1
0
0
1
2
1
0
0
2
2
1
0
2
0
1
0
0
2
0
1
1
2
0
0
0
2
0
0
0
0
2
0
1
0
2
2
1
2
0
1
0
0
0
2
1
0
0
1
1
0
0
0
1
0
1
0
1
0
0
1
1
0
2
0
1
2
1
1
2
2
1
1
2
0
1
3
0
0
0
1
0
2
1
0
0
1
1
0
1
1
0
0
0
1
0
0
1
0
2
0
2
0
2
2
0
1
1
0
0
3
0
3
0
0
0
1
2
1
0
1
0
1
0
1
2
1
0
0
1
0
0
1
1
1
2
0
1
3
0
0
0
0
0
2
0
2
0
2
0
0
1
0
1
0
0
2
2
2
1
2
1
2
0
2
1
1
0
2
1
0
1
0
1
0
1
0
2
1
1
2
0
0
1
1
0
1
1
0
1
1
1
1
0
2
0
0
0
2
1
2
2
0
1
0
0
0
0
1
0
0
0
3
0
1
0
1
0
0
1
0
2
0
0
2
0
1
1
1
1
1
0
2
1
1
0
0
0
0
1
1
0
1
0
1
2
0
1
0
2
1
1
0
1
2
2
2
0
0
1
0
2
2
1
1
0
0
2
1
1
1
2
2
2
0
0
0
2
2
0
1
0
0
0
1
2
2
0
2
0
1
2
1
1
1
1
1
1
1
0
0
1
0
0
0
1
1
0
0
1
2
0
1
0
1
0
0
0
1
0
5
0
1
2
0
0
1
0
0
0
1
1
0
2
0
1
1
2
1
1
0
0
0
2
0
0
1
0
0
1
2
1
0
1
0
2
1
0
2
0
0
1
1
0
1
0
1
1
0
1
0
1
1
0
0
0
0
2
0
1
0
1
0
0
0
1
1
3
1
0
2
0
0
1
1
1
0
1
1
0
1
0
0
1
1
1
1
2
0
0
2
0
1
0
0
1
1
0
0
0
1
2
1
2
2
3
0
0
2
1
0
1
0
0
1
1
2
1
1
1
0
1
0
7
1
2
1
1
1
2
1
2
0
0
2
1
2
0
0
0
1
0
1
1
1
1
0
1
0
0
0
1
1
0
2
2
2
0
2
2
0
0
2
3
0
1
1
0
1
0
1
0
1
0
1
0
2
0
0
0
1
0
0
0
0
1
1
0
0
1
1
0
0
2
0
2
1
0
0
0
2
2
0
1
1
1
0
0
0
1
0
1
0
0
0
1
1
1
0
1
1
0
1
2
0
0
1
0
2
2
0
1
1
0
1
2
1
2
0
1
0
1
1
1
0
2
1
0
1
0
1
0
2
1
1
1
1
2
2
1
1
0
2
1
0
0
0
1
0
2
1
0
2
1
0
2
1
0
2
2
1
0
2
1
1
0
1
0
2
1
0
0
2
1
1
2
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
1
1
0
1
0
0
0
1
0
1
1
1
0
1
1
2
1
0
1
2
0
1
0
0
0
0
1
2
2
0
0
0
1
1
0
0
2
2
2
1
0
1
0
0
0
1
0
1
2
0
0
0
0
0
0
0
2
1
1
0
1
0
1
0
1
1
0
2
0
0
0
1
0
2
2
0
1
1
1
1
0
1
5
0
0
1
2
0
0
2
1
2
0
1
0
1
1
1
0
2
0
0
0
0
0
0
1
0
0
1
2
2
2
1
0
0
1
0
2
2
0
1
1
1
2
0
1
0
0
1
0
2
2
0
0
2
0
1
0
0
2
1
0
3
0
0
1
1
0
1
0
0
0
0
0
2
1
0
1
2
0
3
1
1
2
1
1
2
2
0
1
1
0
1
0
0
0
1
1
0
0
0
2
1
1
1
0
0
0
0
1
2
0
1
0
0
0
1
1
0
2
0
0
0
2
2
2
0
2
3
0
1
2
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
1
1
2
0
2
3
2
0
2
0
0
0
3
1
0
0
0
0
0
0
2
1
1
0
0
0
1
1
1
1
2
0
2
0
0
2
1
0
1
1
1
0
3
1
0
1
0
2
2
0
1
1
1
1
0
0
0
1
2
2
2
2
0
2
0
1
2
0
1
0
0
2
0
1
2
0
1
1
1
1
0
2
1
1
2
1
2
1
1
2
0
0
1
2
2
0
1
2
1
0
1
0
1
0
2
0
1
2
0
1
1
0
0
0
0
2
0
0
1
2
0
1
2
5
0
0
1
1
0
0
0
0
3
0
1
0
1
1
0
0
1
2
2
1
1
0
1
0
0
2
2
1
0
0
0
1
0
1
1
2
2
1
1
0
0
0
1
3
0
0
1
2
0
0
1
2
0
1
0
0
0
1
0
0
3
0
1
1
1
2
1
2
1
2
0
0
1
0
1
0
2
2
0
1
0
2
0
1
1
2
0
0
4
1
0
0
1
0
2
2
0
2
0
1
0
0
2
2
1
0
0
0
2
1
3
0
2
1
1
2
3
0
0
1
2
0
1
1
0
2
1
0
2
1
2
0
2
2
0
1
0
0
1
2
2
2
1
1
0
2
0
0
4
1
2
0
0
1
1
2
1
0
1
2
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
1
1
1
1
2
2
0
0
0
0
1
2
0
1
1
0
0
2
1
1
0
1
2
0
1
0
0
0
1
1
0
1
2
1
0
0
0
1
2
2
2
2
0
0
2
1
1
1
0
1
1
2
1
1
0
2
1
2
1
0
0
1
0
1
0
1
2
1
0
2
0
1
0
0
0
0
1
1
1
0
0
0
0
0
2
0
0
1
1
0
2
0
0
1
0
0
0
0
2
1
0
0
0
1
2
1
1
0
0
1
1
0
1
2
1
0
0
1
0
2
2
1
0
0
1
2
0
1
1
0
1
0
0
0
2
0
2
0
2
9
1
2
2
1
0
1
0
1
0
0
0
2
1
2
0
2
1
0
0
0
2
0
0
0
2
0
1
0
0
1
0
0
0
2
2
1
0
0
0
0
3
0
1
1
0
0
2
2
0
2
0
1
1
2
1
1
2
2
2
1
2
1
2
1
1
3
2
0
2
0
2
1
1
0
0
2
1
0
0
1
2
2
2
0
0
0
1
0
0
2
0
0
1
1
2
1
0
2
1
2
2
1
1
1
2
0
1
2
0
1
0
0
0
0
1
1
0
2
2
2
1
0
1
2
0
1
0
2
1
0
0
0
1
0
1
0
1
0
0
0
1
0
1
0
0
0
2
0
0
0
1
1
0
0
2
0
0
2
0
2
0
0
0
0
1
2
2
1
1
1
0
2
0
0
1
0
0
2
1
1
1
2
1
1
0
1
0
1
0
1
0
2
2
1
0
1
0
0
0
0
0
1
1
0
2
1
0
2
1
2
1
0
1
0
2
1
2
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
2
1
0
0
0
0
0
0
1
2
0
0
1
1
2
0
1
2
3
0
0
1
0
0
1
1
0
1
0
0
1
2
0
0
0
2
0
1
0
0
3
0
0
0
0
0
1
0
1
1
1
1
0
0
2
1
2
1
0
2
0
0
0
1
1
0
0
0
0
1
2
0
1
2
1
0
0
1
1
0
1
0
1
0
1
0
1
1
1
0
0
0
0
1
1
1
0
0
1
1
0
3
0
0
1
0
0
0
0
0
2
2
2
0
1
0
2
1
0
0
1
1
0
1
0
2
0
0
0
1
0
0
0
0
3
2
1
0
2
1
0
0
2
0
2
0
2
0
1
1
0
1
0
0
1
1
0
0
2
2
0
0
1
0
0
2
0
0
0
0
0
1
0
1
2
2
0
2
0
1
0
3
2
0
0
1
0
0
1
0
0
3
0
1
0
1
0
0
2
2
2
1
0
1
0
1
2
0
1
0
1
1
1
0
0
2
1
1
3
1
2
1
0
1
0
0
2
3
3
1
0
1
2
0
0
0
1
0
2
0
1
1
1
0
0
1
0
0
0
2
0
0
1
0
0
0
0
3
0
0
0
0
2
0
2
2
2
0
1
1
2
1
0
0
2
1
0
0
0
1
2
0
0
2
0
0
1
2
2
0
1
0
0
1
1
1
1
1
1
0
1
0
0
1
0
0
0
2
2
0
0
1
2
1
1
1
1
2
0
0
0
1
0
0
0
2
0
1
1
0
2
2
1
0
2
1
2
0
2
1
0
1
0
2
2
1
0
1
1
1
1
1
2
0
0
1
0
1
0
0
0
0
1
2
3
1
1
0
2
1
2
2
2
0
0
0
0
2
2
0
0
1
0
1
0
0
1
1
2
2
2
2
1
0
1
2
2
0
0
0
1
1
0
1
0
2
0
0
0
3
1
2
1
1
2
1
0
2
0
1
2
0
1
2
1
0
0
2
2
0
0
2
0
2
1
1
0
0
1
1
2
1
0
2
1
0
0
0
0
0
2
0
0
2
1
0
1
1
1
2
2
1
1
0
0
1
1
0
0
0
1
2
2
1
0
1
2
0
2
3
1
0
0
0
1
2
0
0
0
2
1
0
0
2
2
0
0
2
1
0
2
0
1
1
0
1
2
0
1
2
0
1
2
2
1
0
1
2
0
0
0
1
1
0
0
0
0
2
0
1
1
1
0
1
0
1
0
1
0
3
1
1
2
5
1
1
0
0
2
1
1
0
0
1
1
2
0
0
1
1
0
0
0
0
0
0
1
1
1
2
1
1
2
0
1
0
0
1
1
1
1
1
0
1
0
0
0
2
0
1
1
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
1
3
1
2
0
0
1
0
1
6
0
2
3
3
1
0
1
2
2
0
0
1
0
1
0
2
1
0
2
0
0
0
2
1
0
2
2
0
1
0
0
2
0
0
0
0
0
1
1
1
2
1
1
0
0
0
1
0
0
2
0
0
1
2
0
2
2
1
1
1
0
0
1
0
2
0
1
0
1
0
2
2
0
1
1
2
1
1
1
0
2
0
2
1
1
0
0
2
2
2
0
0
1
2
0
0
1
1
2
2
1
1
0
0
2
1
1
2
2
0
0
0
0
0
0
1
0
0
2
2
2
0
1
0
0
2
2
0
1
0
0
0
0
0
0
1
1
0
1
2
0
2
0
1
1
0
2
1
0
0
0
1
1
0
1
0
0
0
0
2
1
1
1
0
0
2
2
0
2
0
1
1
0
0
1
0
1
1
0
0
1
0
2
1
2
2
0
2
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
1
2
1
1
1
0
1
0
1
1
0
1
0
0
0
2
0
2
0
0
1
1
1
0
0
0
1
1
2
2
0
1
0
1
1
2
2
0
1
0
2
2
1
1
0
0
0
0
0
1
1
2
1
1
0
2
0
1
0
2
0
0
1
1
1
2
1
1
1
0
0
0
2
0
0
1
0
1
0
3
0
1
0
0
1
2
1
2
0
1
0
1
0
1
2
0
1
0
2
1
1
0
0
0
2
0
0
0
1
0
0
1
0
1
0
0
0
0
0
4
0
0
2
0
2
0
2
2
1
2
2
1
1
0
1
0
1
0
0
0
1
1
2
1
0
0
1
0
0
0
0
0
0
3
0
1
1
1
1
1
0
1
2
0
2
1
1
0
0
0
1
0
1
1
0
1
0
2
1
2
0
0
1
0
0
2
1
0
1
0
1
1
2
1
2
1
0
0
1
1
2
1
2
0
2
0
1
2
2
0
2
2
2
0
1
1
2
0
0
1
2
0
2
0
2
0
1
0
0
1
1
0
3
1
2
0
0
1
0
0
0
0
0
0
0
2
1
2
1
0
2
1
0
0
1
0
0
2
0
1
0
3
1
0
1
2
0
0
0
0
0
0
0
0
0
1
0
1
1
1
2
0
0
1
0
0
1
1
0
1
2
0
0
1
2
0
1
1
1
0
0
0
0
0
0
0
0
0
3
1
1
1
1
0
0
1
1
1
0
0
1
0
1
2
1
0
0
2
1
2
1
0
0
0
2
1
2
2
0
0
0
0
1
1
2
0
1
0
2
1
0
0
0
1
1
0
1
0
1
1
0
1
2
0
1
1
0
0
2
2
0
1
2
1
1
1
1
0
0
0
0
0
1
0
2
0
1
0
1
0
1
1
2
0
0
0
0
0
1
0
1
1
0
1
1
2
1
0
2
0
2
0
0
0
2
2
1
0
2
1
2
1
1
0
0
0
0
0
2
2
0
0
2
0
2
1
3
2
0
1
0
1
0
1
2
1
1
1
1
1
2
0
2
0
0
0
0
0
0
2
1
2
1
1
0
2
2
2
3
0
0
2
0
1
0
0
1
1
0
0
2
1
1
0
2
0
1
0
1
0
0
0
0
2
1
0
1
0
1
1
0
1
1
0
0
0
1
1
1
0
2
2
0
2
1
0
1
1
0
2
0
1
0
1
2
0
2
0
1
1
3
0
2
3
0
1
1
1
0
0
1
0
1
0
0
0
3
1
2
2
0
0
1
0
2
1
0
2
0
1
0
1
1
1
0
0
2
2
0
2
2
1
1
0
1
0
1
0
0
1
0
2
0
1
1
1
0
0
0
0
0
0
0
0
2
2
0
2
2
0
2
2
2
0
0
0
0
2
1
0
1
0
1
1
0
1
0
0
1
0
0
2
1
2
0
0
0
2
0
0
0
1
2
0
0
1
0
2
0
1
0
2
0
0
1
0
1
2
2
0
4
1
1
0
1
1
2
2
1
0
1
2
1
2
2
1
0
2
1
1
1
2
1
0
0
1
0
0
1
1
1
1
0
0
0
1
2
0
0
0
2
2
0
2
0
0
2
1
1
0
0
0
0
0
2
1
1
0
0
2
1
0
0
0
1
1
1
2
2
2
0
0
0
0
0
2
0
1
0
2
2
0
2
2
2
0
0
0
1
2
2
0
1
0
0
0
2
1
2
1
1
0
0
1
2
0
1
2
1
0
0
3
0
0
1
1
0
1
0
0
1
1
0
2
0
2
0
1
0
0
0
0
0
0
2
0
0
1
1
0
1
2
1
0
0
2
0
0
1
1
0
1
2
0
1
2
0
0
0
0
2
1
0
0
0
0
2
0
1
2
2
0
0
0
1
0
0
0
1
0
1
0
2
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
2
0
0
2
0
2
2
0
2
4
1
0
2
2
0
0
0
1
1
2
0
0
2
0
0
1
0
0
1
0
1
0
0
0
0
0
1
2
1
1
2
2
2
0
1
0
2
1
0
2
0
1
1
2
1
2
0
1
0
1
2
0
0
2
0
1
2
1
1
0
0
0
1
2
2
0
1
0
0
0
5
0
1
0
0
2
1
1
0
2
1
1
1
2
1
1
0
0
1
0
0
0
0
0
1
0
1
2
1
0
2
1
2
1
0
1
1
0
0
2
1
0
0
0
0
0
1
0
3
1
0
2
0
1
0
0
0
2
1
2
0
0
1
0
1
1
2
1
1
1
1
2
1
1
0
0
0
2
0
0
1
0
1
1
1
2
2
0
0
0
2
1
2
2
1
0
0
0
0
0
1
0
0
1
0
2
2
0
0
0
2
1
1
1
0
1
0
0
0
0
0
0
0
2
0
1
1
0
2
1
0
1
0
2
2
0
1
1
0
0
0
1
1
1
1
1
0
1
1
1
1
0
1
1
0
0
0
1
0
2
0
0
2
0
1
1
1
2
2
1
0
0
2
1
2
1
0
0
0
0
1
2
0
0
0
0
1
1
0
0
1
1
0
2
1
0
1
0
0
2
2
0
1
1
0
0
1
2
0
0
0
0
1
0
2
0
2
2
1
1
2
1
2
0
2
2
0
1
1
2
2
1
0
1
0
0
0
0
1
1
0
1
0
0
0
1
1
0
1
1
1
2
0
2
2
0
0
0
0
1
0
0
1
2
2
0
1
1
0
0
2
0
0
1
2
0
2
0
2
3
2
2
1
0
1
0
2
0
0
1
2
1
2
2
2
2
1
2
1
0
1
0
2
0
1
1
1
1
1
0
0
3
1
0
0
0
0
4
1
1
0
0
1
1
0
1
2
0
0
0
1
1
0
1
1
0
0
2
1
1
0
2
0
0
2
2
2
0
0
1
1
2
2
2
1
2
1
0
2
0
2
1
1
0
0
1
1
0
3
0
0
1
0
0
0
0
1
1
1
2
0
0
0
1
0
6
0
0
1
0
1
0
0
2
1
0
0
1
0
1
2
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
2
1
0
0
2
2
0
0
0
0
0
0
0
0
1
1
1
2
0
1
0
0
0
1
2
1
0
0
0
1
0
2
2
0
0
0
1
2
2
0
0
1
1
0
1
0
0
0
1
2
1
2
0
1
1
0
0
2
1
0
0
1
0
1
0
2
1
0
2
2
0
1
1
1
1
0
1
2
0
2
2
0
0
2
1
2
0
1
1
2
0
1
1
0
0
0
0
1
0
1
2
3
0
1
1
2
0
1
3
1
1
1
1
0
0
0
2
0
0
2
0
0
0
0
2
0
1
0
0
2
1
0
2
0
1
1
2
0
0
0
0
0
2
3
1
0
2
0
0
1
0
0
1
0
1
1
0
0
0
2
1
1
1
0
0
1
0
1
0
2
0
1
0
1
0
2
1
2
1
1
0
1
0
1
0
2
0
0
1
1
0
1
0
1
0
1
2
0
0
0
1
2
0
1
0
0
1
0
1
2
0
0
2
0
0
1
2
0
2
1
0
1
0
0
0
1
2
2
2
2
1
0
2
0
0
2
2
0
1
1
2
2
1
1
1
0
1
1
0
1
1
1
2
0
0
2
2
1
0
0
1
1
0
0
1
0
0
0
2
1
1
2
0
1
1
0
1
1
2
0
0
2
0
0
1
1
2
2
0
1
0
1
0
1
0
2
2
1
1
0
0
0
0
0
2
1
0
0
1
1
1
0
0
0
1
1
1
1
0
0
0
1
1
1
0
0
0
1
2
2
0
0
1
0
0
0
0
1
2
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
1
0
1
1
3
1
0
0
0
1
0
2
0
2
1
0
0
1
0
0
0
2
1
0
0
0
1
2
1
1
0
2
0
1
0
0
0
0
0
2
0
1
1
0
1
0
0
2
2
0
0
0
0
0
0
2
1
1
0
0
1
1
1
1
0
0
1
2
1
0
1
0
0
1
0
2
0
1
2
2
0
0
0
2
0
0
0
2
1
0
2
0
1
2
0
0
2
0
1
0
2
2
1
0
0
0
1
0
0
1
0
0
2
3
2
0
3
2
0
1
1
2
0
2
2
0
1
0
1
1
0
0
1
0
0
1
0
1
0
1
2
0
1
1
0
2
0
0
0
0
0
0
0
1
0
1
1
0
1
1
0
0
1
2
0
2
2
0
0
0
0
0
0
0
2
1
2
1
2
8
2
2
0
1
2
1
0
2
2
1
2
0
2
1
1
2
2
3
0
0
2
0
0
0
1
1
2
0
0
0
1
1
0
1
2
0
0
0
1
2
2
1
1
3
2
2
0
0
1
0
2
0
1
3
1
2
0
1
2
1
2
0
0
2
0
2
2
2
0
0
1
0
0
2
1
2
1
0
2
0
0
1
1
1
1
0
1
1
0
2
0
2
0
1
1
2
0
1
0
0
0
0
0
0
1
0
0
1
1
1
0
2
1
2
0
1
2
1
1
1
0
2
2
2
1
0
0
1
2
0
1
2
1
1
2
0
1
0
2
1
2
0
0
2
2
1
0
1
1
1
1
1
5
0
1
0
0
2
1
0
0
0
1
1
0
0
1
2
0
0
2
2
1
1
1
0
0
2
2
2
2
1
1
1
0
2
2
0
0
1
0
0
1
0
0
0
1
2
0
4
3
1
0
0
0
1
1
0
2
0
0
0
0
0
1
1
1
0
0
1
0
0
0
2
1
2
0
1
2
0
2
1
1
1
0
0
0
0
1
1
0
0
1
0
1
0
2
1
0
1
2
0
1
1
2
0
2
2
0
2
1
0
1
0
1
1
0
0
1
1
0
2
0
0
2
0
1
2
0
0
2
2
0
1
2
1
0
0
1
0
1
2
0
1
0
0
0
2
0
2
0
2
0
1
2
1
4
0
2
1
0
2
0
0
0
0
2
2
0
2
1
1
0
0
1
1
0
0
1
0
2
2
1
1
0
0
2
1
0
2
1
2
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
1
2
0
2
0
2
1
2
1
0
1
1
0
2
1
3
0
1
0
2
1
0
1
0
2
1
2
0
0
2
0
1
4
1
1
0
0
0
0
1
1
0
1
0
1
0
2
1
0
0
1
1
2
0
1
0
3
2
1
0
0
1
1
2
0
0
0
0
1
0
2
0
1
0
1
1
1
0
1
2
0
0
2
0
0
0
0
1
1
0
0
0
3
0
1
3
0
1
0
1
0
2
0
2
0
2
2
0
1
0
0
1
0
0
0
4
2
0
0
0
2
1
1
0
2
1
0
0
1
0
0
0
2
3
1
0
2
0
1
0
1
2
0
0
0
0
0
0
1
1
0
0
0
0
2
1
0
1
0
2
1
5
1
0
2
0
0
0
0
2
0
0
1
1
0
0
0
1
1
2
0
1
1
0
3
1
1
0
1
0
0
0
0
2
1
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
2
0
2
0
1
1
0
4
1
1
0
0
1
2
1
0
1
1
1
0
1
0
2
0
0
6
1
2
0
2
1
1
2
1
0
0
0
1
1
1
2
2
1
0
1
0
1
0
0
3
2
2
1
2
1
2
2
1
0
0
1
0
1
2
1
0
0
0
0
0
0
1
0
1
0
2
2
2
1
0
0
0
0
1
1
1
0
1
1
1
0
1
0
1
0
2
1
0
0
1
2
0
2
1
0
0
2
1
1
1
0
1
0
1
1
0
2
1
0
0
0
1
0
2
1
0
0
0
1
0
2
0
1
0
0
0
0
0
1
1
1
1
2
0
0
0
0
2
0
2
1
1
1
0
2
1
3
0
1
1
3
0
0
1
2
0
1
0
0
0
2
2
0
2
0
0
0
1
2
0
1
0
3
2
0
0
2
2
1
0
0
0
0
0
0
0
0
2
0
1
1
0
2
0
1
2
2
0
1
2
1
1
1
1
0
1
0
2
0
1
1
0
0
1
0
2
1
0
0
1
0
0
0
2
2
0
1
0
1
1
0
1
0
0
0
1
1
0
2
1
0
2
1
0
1
2
0
0
2
1
1
2
0
1
2
1
0
2
2
0
0
0
0
0
1
0
0
2
1
0
0
1
1
1
0
2
2
2
1
1
1
1
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
1
2
0
0
1
0
0
1
0
0
2
0
0
1
0
0
1
0
1
1
3
1
2
0
0
0
0
0
0
0
2
1
0
0
2
0
1
0
0
0
2
1
1
1
1
0
0
2
0
1
0
0
0
1
0
2
0
0
1
2
2
1
0
1
0
1
0
0
1
0
0
2
2
1
0
0
1
1
1
2
0
2
0
0
0
0
1
2
2
0
0
0
2
0
0
2
0
2
0
2
0
1
1
2
1
1
0
0
1
0
0
0
1
2
0
0
0
0
1
3
1
0
1
0
2
2
1
0
5
0
0
2
0
0
0
1
0
0
1
0
1
2
0
1
2
2
2
1
1
0
1
0
0
2
0
3
1
0
2
2
0
1
0
0
2
2
0
0
1
0
0
0
0
0
2
0
0
1
0
0
1
1
0
1
0
2
2
2
1
0
2
2
0
2
2
1
0
2
3
1
0
0
1
0
0
0
3
0
2
0
1
0
0
0
1
2
2
0
1
0
2
0
2
1
1
1
0
0
0
0
0
1
1
1
2
1
0
3
2
0
1
0
0
2
2
0
2
0
1
0
0
1
2
1
1
1
0
0
0
0
1
0
1
0
0
1
1
0
2
0
0
1
2
2
2
1
1
1
0
0
0
0
1
1
1
1
2
1
0
1
0
0
2
0
1
2
0
2
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
1
2
0
1
1
0
0
1
1
0
1
0
0
0
2
0
1
0
0
1
1
1
0
0
0
0
2
0
0
0
1
0
0
0
2
1
0
1
2
0
1
1
2
1
0
1
2
0
1
2
1
2
0
2
2
2
1
0
0
1
1
0
0
0
2
2
0
1
2
2
0
2
0
0
0
0
1
3
1
0
1
2
1
0
0
0
1
2
0
0
1
0
0
1
2
2
1
1
0
1
1
1
1
2
1
0
1
0
0
2
1
1
0
1
1
1
1
0
1
0
2
1
1
0
0
1
0
1
0
1
2
2
0
0
1
1
1
0
0
1
2
0
2
1
1
1
2
0
4
1
2
0
0
2
0
3
2
1
0
1
2
0
0
1
1
2
1
1
4
1
0
1
0
2
1
1
0
0
2
0
0
2
1
1
0
2
1
1
0
2
1
0
0
2
1
2
1
0
1
1
2
1
1
1
0
0
0
1
0
0
0
1
0
0
1
0
0
2
0
2
2
2
0
0
2
3
1
0
0
0
1
1
0
0
0
0
2
1
1
1
0
0
1
0
1
0
0
1
0
0
2
1
0
2
0
0
0
0
0
3
0
0
0
0
2
1
1
1
0
0
1
0
2
0
1
2
2
3
0
0
1
0
2
0
0
3
0
2
2
0
1
0
0
0
1
2
1
1
0
1
1
0
1
0
0
1
2
1
1
0
0
2
1
0
1
2
1
0
0
0
1
0
1
0
1
0
1
0
0
0
2
1
0
1
2
2
2
0
1
2
1
0
2
1
1
1
0
2
1
1
0
0
0
0
0
3
0
2
0
1
0
1
5
1
2
0
0
2
2
2
2
1
1
0
0
2
1
1
2
1
0
0
1
2
3
1
1
0
1
2
1
0
0
2
0
3
0
2
0
1
0
1
1
1
2
0
1
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
2
0
1
0
1
1
0
0
1
2
1
0
0
0
1
1
0
0
2
0
2
0
1
0
0
1
0
1
0
2
2
2
0
0
1
0
0
0
1
0
1
0
0
1
2
0
1
1
2
0
2
0
1
1
0
2
0
0
0
0
1
0
0
0
2
1
1
0
2
2
2
0
1
1
1
0
0
1
2
0
0
0
1
1
0
3
0
1
0
2
0
0
2
2
1
0
0
1
0
0
0
0
0
0
1
2
2
2
2
2
0
1
0
2
0
1
0
0
2
2
0
0
1
1
2
2
1
2
2
1
1
2
2
0
1
1
0
2
0
1
1
0
0
1
2
0
1
0
3
5
1
0
1
0
0
1
1
0
0
0
2
0
0
2
1
1
1
0
0
0
0
1
1
2
0
0
1
0
0
0
1
1
0
2
0
2
1
1
1
2
1
1
1
0
1
1
2
0
0
0
1
2
1
1
0
2
2
0
0
0
0
0
0
2
0
0
0
1
1
0
1
1
1
2
0
0
0
0
0
0
0
0
2
3
0
0
2
2
1
0
0
1
1
1
2
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
1
2
0
2
0
2
1
0
2
1
0
1
0
3
2
0
0
4
1
1
0
1
2
1
1
0
0
0
0
2
0
1
0
1
0
0
0
1
3
2
0
1
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
1
2
0
1
1
2
1
0
0
0
0
0
2
1
2
1
0
0
0
0
2
0
1
2
0
0
0
1
0
1
1
0
0
0
1
0
3
0
1
0
0
1
2
0
3
2
0
1
0
0
0
1
1
1
0
0
1
0
1
0
0
2
2
1
0
1
0
1
0
0
2
1
2
2
1
1
1
0
0
0
0
0
0
0
0
0
0
0
3
2
3
1
1
1
2
1
1
2
0
1
2
1
0
0
0
1
2
1
3
1
1
0
2
2
1
2
1
1
0
0
1
2
2
0
2
0
1
0
1
0
3
0
3
0
0
2
1
0
1
0
0
2
1
0
0
0
0
0
0
2
1
0
0
1
2
1
1
2
1
0
0
2
1
2
2
0
0
2
1
0
0
0
0
1
0
0
0
0
0
2
1
2
0
1
1
1
0
0
2
1
1
2
1
2
0
1
0
0
2
1
2
0
0
0
1
2
0
1
2
0
2
2
1
0
2
0
1
1
2
0
2
1
2
0
2
2
0
2
1
1
0
2
1
1
0
0
0
1
1
1
2
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
1
1
0
0
1
1
0
0
0
0
1
1
1
0
0
0
1
0
2
0
0
2
2
0
0
1
0
1
1
0
0
0
2
0
2
0
0
0
1
0
1
0
0
2
0
3
1
2
0
1
1
0
0
0
0
2
0
2
0
2
1
1
0
0
1
1
0
0
3
2
0
2
0
1
2
2
0
0
1
2
1
2
1
0
0
0
0
0
0
2
1
1
0
2
0
2
0
0
0
2
0
2
0
0
2
0
0
2
0
2
0
0
0
1
1
1
1
1
0
1
0
2
2
0
0
1
0
2
0
2
2
0
2
1
0
1
1
1
1
0
0
2
0
0
0
0
0
2
0
1
0
2
1
1
0
1
1
0
2
0
0
2
0
1
3
1
0
2
0
0
0
0
0
1
1
0
2
1
0
0
1
1
0
0
0
0
3
0
2
2
2
3
0
0
2
0
0
0
0
1
1
2
1
2
0
1
1
0
0
0
2
2
2
1
1
1
0
1
1
0
3
1
0
0
0
0
1
0
0
0
1
1
2
0
2
0
1
0
1
0
1
0
2
4
2
0
1
0
0
1
0
0
0
1
1
1
1
2
0
0
1
0
1
1
2
0
1
0
1
1
1
0
0
1
0
2
0
1
0
1
2
1
2
1
1
2
0
2
0
2
0
2
0
0
2
1
2
0
1
2
0
1
2
0
2
2
1
2
0
0
0
0
1
3
1
2
2
0
1
1
0
0
1
0
1
1
1
2
1
1
1
2
1
2
0
0
1
0
0
2
0
2
0
1
2
1
0
1
2
1
1
0
1
0
1
0
0
1
0
0
0
1
2
0
0
0
1
1
0
1
0
0
0
2
0
1
0
1
0
0
0
1
1
1
0
0
0
0
0
2
0
0
1
0
0
0
0
1
1
0
1
1
0
0
2
0
2
0
3
1
2
1
1
1
2
0
0
0
3
1
1
0
0
1
0
1
2
0
0
3
2
0
0
0
2
2
0
1
1
2
0
0
0
1
2
0
1
0
1
0
0
2
0
1
1
0
1
0
0
2
0
0
0
1
3
2
2
0
0
0
0
0
2
0
2
1
1
2
0
0
2
2
0
0
0
0
1
0
2
2
2
0
1
0
1
1
2
0
1
0
2
1
1
0
0
1
0
0
0
0
0
2
2
0
1
0
0
2
2
2
1
0
1
0
0
2
0
0
1
0
2
0
0
0
2
1
0
2
1
2
0
1
2
0
0
0
0
0
0
1
0
0
1
0
1
1
0
1
0
0
2
1
1
0
0
0
0
0
0
0
0
1
1
2
1
2
1
1
2
0
1
3
1
0
1
0
0
2
2
0
1
2
0
2
0
1
0
2
2
0
1
1
0
2
1
1
0
0
1
3
2
2
0
0
1
1
0
0
2
0
1
2
0
1
1
3
0
2
0
1
0
0
3
0
2
0
1
1
1
1
0
0
0
2
1
2
1
1
1
0
1
1
0
1
0
1
0
1
1
0
0
2
1
0
2
1
2
1
0
0
1
0
2
3
2
1
4
0
2
0
1
0
0
3
1
0
1
0
0
0
1
0
0
1
2
1
0
3
0
0
0
0
0
1
0
0
1
2
0
0
2
1
2
0
1
1
2
2
0
1
0
0
1
2
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
2
0
0
0
1
2
1
1
0
0
0
0
0
0
1
1
0
0
2
1
0
2
1
3
0
1
1
0
2
2
2
0
2
0
0
0
2
1
0
0
0
2
0
0
1
1
2
1
0
0
0
1
0
0
3
0
0
1
0
0
1
0
2
1
0
2
2
0
2
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
1
1
0
0
1
0
1
1
2
0
2
2
1
1
1
0
0
2
0
2
0
0
1
0
1
0
0
1
2
0
1
1
0
1
0
0
2
0
0
2
1
0
1
0
4
1
1
2
1
0
0
0
2
2
0
2
2
1
1
1
3
2
2
1
0
0
2
2
0
0
1
0
2
2
1
0
0
2
0
0
0
0
1
0
1
0
0
0
1
1
0
1
0
0
0
2
2
1
0
0
2
2
1
0
1
1
0
0
1
1
1
0
1
0
2
0
0
3
0
1
0
2
0
2
0
2
1
1
2
0
1
2
0
1
1
0
0
2
1
2
0
1
0
0
0
1
1
0
0
2
0
1
2
2
0
0
2
0
2
1
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
2
2
2
0
0
1
2
0
1
0
3
1
1
1
1
1
1
1
0
0
1
3
0
2
4
1
0
1
2
2
2
1
1
0
3
0
2
0
0
1
2
0
2
0
1
1
2
0
1
1
0
1
1
0
1
2
0
0
0
2
1
2
1
1
1
2
1
0
0
1
0
2
0
1
0
2
0
1
0
2
0
0
0
1
2
0
1
0
3
1
0
2
0
0
0
2
2
2
1
0
1
0
0
2
0
2
1
1
2
0
1
1
1
0
1
2
2
0
1
0
1
0
0
0
0
0
1
0
1
0
1
1
1
0
2
0
1
0
1
1
2
0
0
1
1
1
2
0
1
0
1
1
0
0
1
0
1
0
1
1
1
1
1
0
1
0
1
2
0
0
1
2
0
1
0
0
0
2
0
1
1
0
0
1
2
2
0
1
0
1
0
0
1
0
1
0
1
1
2
1
1
0
0
1
0
0
0
0
0
0
1
0
2
1
1
1
2
1
1
1
7
1
0
0
2
1
1
1
0
0
0
0
2
0
1
0
0
1
0
0
0
1
1
1
2
2
1
2
7
2
0
1
0
1
1
1
0
1
2
2
1
1
3
1
0
0
0
1
1
2
0
2
0
1
1
0
0
0
0
0
0
2
1
1
1
1
1
2
1
0
0
1
3
0
2
0
1
2
1
3
1
2
0
0
1
0
0
0
0
2
2
1
1
1
2
0
2
2
0
0
0
2
0
1
0
0
0
2
1
0
0
0
1
0
0
0
1
3
1
1
2
0
2
0
0
2
1
2
0
2
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
2
1
1
2
1
0
1
0
0
1
0
0
1
0
0
1
2
2
2
0
2
0
0
1
0
1
1
0
1
2
0
0
0
3
0
0
2
1
2
2
0
0
2
1
0
2
0
0
0
0
0
2
2
1
0
0
1
1
2
0
1
0
0
1
2
0
1
2
0
0
1
0
0
0
2
2
1
1
2
1
3
2
2
0
1
0
0
2
2
0
3
1
0
0
1
1
0
0
1
2
1
1
0
0
0
2
0
3
2
0
1
1
0
1
0
0
2
2
0
0
1
2
0
1
0
2
1
2
1
1
0
0
2
0
3
1
0
0
1
0
0
0
0
2
0
0
1
0
2
0
1
0
1
1
1
1
0
0
0
0
0
1
2
1
0
1
1
0
1
1
0
0
2
2
2
0
0
0
0
2
0
0
2
1
0
0
2
0
1
0
0
2
0
0
1
1
1
0
1
2
0
1
0
0
1
2
2
1
1
1
1
1
1
2
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
2
0
1
1
2
0
0
2
2
1
2
1
2
2
2
0
2
2
1
1
0
0
0
0
0
2
0
1
2
0
0
1
0
0
0
1
0
1
2
0
6
0
2
0
0
2
2
2
1
0
1
1
1
0
1
0
2
0
0
0
0
0
2
0
2
0
1
2
2
1
1
0
2
2
2
2
0
1
0
2
2
2
2
0
0
0
1
2
0
0
1
1
2
1
1
0
1
1
1
2
0
0
0
0
0
1
1
0
1
0
4
1
1
2
0
1
2
0
1
1
0
0
0
0
1
0
1
0
0
2
1
2
1
0
0
0
1
1
0
0
2
0
0
1
1
0
1
1
1
2
1
0
1
1
1
0
0
0
2
0
0
1
0
1
2
0
0
0
0
1
0
2
1
0
0
0
0
8
2
0
1
0
1
3
1
1
1
1
1
0
0
0
2
0
0
0
1
0
1
1
1
1
1
1
0
1
2
0
0
1
0
0
1
0
0
2
0
1
1
0
1
1
0
0
0
2
1
0
1
0
0
0
0
0
0
2
1
1
2
2
2
0
0
1
2
1
0
1
0
1
1
0
1
1
1
1
0
1
2
1
1
1
0
0
2
2
2
0
0
0
2
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
1
2
0
0
6
0
2
2
0
0
0
3
0
2
0
2
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
2
2
2
0
3
0
2
2
1
0
1
0
2
0
3
1
4
0
0
0
0
0
1
0
1
1
0
1
0
0
2
1
0
0
2
1
0
1
3
0
0
0
0
0
1
0
1
2
2
0
0
0
0
1
0
1
1
1
0
0
0
1
1
2
2
0
0
0
0
2
1
0
0
1
0
0
1
2
0
0
0
2
0
1
0
0
2
1
0
1
1
2
1
0
1
0
1
0
0
0
0
0
0
0
2
1
2
0
0
1
0
2
1
0
2
1
1
1
0
2
0
0
0
1
1
0
0
0
2
0
2
0
2
1
0
0
0
0
0
0
0
1
0
0
1
0
2
0
1
2
1
0
0
1
0
0
0
2
0
0
0
2
1
1
1
1
1
0
0
2
1
0
0
1
0
0
2
2
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
1
0
0
1
0
0
0
2
0
1
1
0
1
0
0
1
1
4
0
2
2
1
2
0
2
0
0
0
2
0
1
2
1
0
0
1
1
3
0
0
2
0
1
1
0
0
1
0
0
2
0
0
0
0
2
0
0
1
1
0
2
0
0
1
1
0
2
0
1
2
1
1
0
0
0
1
1
0
1
2
1
0
1
0
2
0
2
2
0
1
0
2
0
1
0
1
1
2
2
0
1
1
0
2
0
0
0
2
0
1
1
2
0
1
0
1
0
0
1
0
1
0
0
0
1
0
2
1
0
2
1
2
2
0
0
0
0
0
0
1
0
1
1
1
1
1
0
0
3
0
0
1
0
0
0
2
2
0
1
2
1
0
0
2
1
0
0
2
0
0
0
0
2
2
0
0
0
0
1
1
1
0
1
1
2
1
0
0
1
0
0
0
2
0
0
0
2
0
1
0
0
2
2
0
2
0
0
3
0
0
1
1
2
0
2
0
0
1
2
0
1
0
1
2
1
2
0
1
1
2
2
0
0
1
0
1
0
0
0
2
1
0
1
2
0
2
0
0
0
0
1
0
2
0
0
1
0
0
1
0
1
0
0
0
1
2
2
0
1
0
0
0
0
1
1
1
1
2
2
1
1
1
1
0
2
0
0
1
0
0
0
1
0
0
0
1
2
0
3
1
0
1
0
0
1
0
0
1
1
0
1
0
2
0
0
0
1
0
2
0
2
0
0
2
2
1
0
0
2
0
0
1
0
0
0
1
0
0
2
0
1
1
0
0
2
1
0
0
1
2
2
1
0
1
2
0
0
0
1
0
1
1
1
1
1
0
0
3
0
0
0
0
0
2
1
1
0
0
2
2
0
2
2
0
0
1
2
0
3
0
2
2
0
1
0
0
2
2
0
0
0
0
2
1
0
0
2
2
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
2
2
0
0
2
1
2
1
0
0
0
0
1
1
0
0
0
0
1
3
0
0
2
1
0
0
0
1
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
2
2
2
2
0
1
3
1
0
1
0
0
2
0
1
1
2
1
2
0
2
1
0
1
0
1
0
0
0
2
0
2
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
2
0
2
2
0
0
0
0
1
0
1
0
1
2
1
2
0
2
0
0
0
1
0
2
1
2
1
0
0
0
0
0
0
2
1
0
1
1
1
0
1
1
1
2
1
0
0
2
0
1
1
0
0
0
0
0
2
4
2
1
0
1
0
2
2
2
0
2
0
0
1
0
0
2
1
2
0
1
1
0
1
1
0
0
1
3
3
2
0
0
1
0
0
1
2
1
1
0
1
2
0
2
2
1
1
1
0
0
2
0
2
0
0
1
1
2
1
1
0
0
0
1
2
0
2
0
1
1
2
0
2
1
2
1
2
0
0
2
0
2
0
1
1
0
0
2
1
2
0
0
0
1
0
0
0
1
0
1
2
1
0
0
2
0
2
1
1
0
0
2
1
0
1
1
0
0
0
1
0
1
2
1
0
0
2
2
2
0
1
0
0
1
0
0
2
0
0
2
1
1
3
1
1
1
0
1
2
1
3
0
1
0
0
0
1
1
2
1
2
0
0
2
2
2
0
1
2
0
0
0
0
1
0
1
1
0
0
2
2
0
2
1
0
2
1
0
0
2
0
0
0
2
1
1
2
0
2
1
1
0
0
1
1
0
2
2
1
1
2
0
2
0
1
0
2
0
2
0
0
0
0
1
0
1
1
0
1
0
2
0
2
0
0
1
2
1
0
0
0
1
1
2
5
1
2
0
0
0
2
0
0
0
1
0
2
2
2
0
0
1
1
0
0
0
0
1
2
0
1
1
1
2
1
2
2
0
3
0
1
1
0
1
1
1
0
0
3
0
1
0
1
0
1
1
0
1
1
0
0
1
2
0
1
1
0
0
0
3
2
0
0
1
0
1
0
1
0
1
0
2
1
0
0
0
0
1
0
0
0
0
2
1
1
0
0
0
0
1
0
0
1
0
1
0
0
1
0
3
0
2
1
0
0
2
0
2
0
2
1
0
2
0
0
1
1
0
3
1
0
1
1
0
0
1
2
0
0
3
1
1
0
1
1
2
2
0
1
0
2
0
2
0
1
0
0
0
0
2
0
0
2
0
2
0
4
2
0
1
0
0
1
1
1
0
2
0
0
0
2
0
2
1
1
1
1
2
0
0
0
0
1
0
1
2
0
1
1
0
0
0
0
0
1
2
0
2
0
0
2
1
1
0
0
0
1
2
0
1
0
1
0
2
2
1
0
0
3
0
0
0
5
0
2
0
2
0
1
2
1
0
0
0
1
0
0
2
0
0
0
0
0
0
1
1
1
0
0
1
1
1
0
0
1
0
1
1
2
0
0
2
1
0
0
0
2
1
1
0
0
0
1
1
1
1
0
0
1
1
0
1
0
0
0
1
2
0
0
0
0
2
1
1
0
1
1
0
1
2
1
1
1
1
0
0
1
2
4
2
0
0
4
1
0
2
3
1
2
2
1
0
0
0
0
0
0
2
1
2
0
0
0
1
2
1
0
0
0
0
1
0
1
2
0
0
0
0
1
0
0
0
0
0
1
2
0
2
1
0
2
3
1
1
1
1
0
1
2
0
1
1
1
0
0
0
1
1
1
0
2
2
0
0
2
0
0
0
0
2
2
2
1
1
1
1
1
2
1
0
0
0
2
0
1
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
2
1
1
2
0
1
1
2
0
1
2
1
1
2
1
1
1
1
1
0
1
3
0
1
0
2
2
1
1
1
0
0
1
1
1
0
0
2
1
0
0
1
3
2
0
2
0
1
0
0
6
0
0
1
1
0
1
0
2
4
2
2
1
1
2
1
1
2
1
2
1
0
2
1
0
2
0
0
0
1
1
0
1
5
0
1
0
2
1
0
0
0
2
2
2
1
1
0
0
0
0
0
2
1
0
2
0
2
0
1
2
1
2
0
0
0
1
0
1
0
0
0
1
0
2
0
0
1
1
1
0
1
0
1
1
0
0
0
0
2
0
1
0
1
0
0
1
0
1
1
0
0
2
0
0
3
2
1
0
2
0
1
0
0
1
0
1
0
0
0
2
0
0
0
0
2
1
2
0
1
1
0
1
2
2
0
1
0
1
1
0
2
2
1
0
2
0
0
1
0
2
2
2
0
2
1
3
0
0
1
1
1
0
1
0
1
2
2
1
0
1
1
2
1
0
1
0
1
1
0
1
1
1
2
0
0
0
1
1
0
1
1
1
0
0
1
0
0
0
0
0
1
1
2
1
2
0
2
1
0
0
0
1
0
1
2
0
1
1
0
0
2
1
0
1
0
0
0
0
2
0
0
0
1
0
2
0
1
0
0
0
1
2
0
0
0
0
0
2
1
0
2
1
0
2
0
0
0
0
0
0
2
2
1
2
0
2
0
1
0
0
2
2
0
0
0
2
2
1
0
0
0
0
1
0
0
1
1
0
1
1
0
0
2
0
2
0
1
0
0
1
0
2
0
1
2
2
0
2
0
1
0
0
1
0
1
0
2
0
1
1
1
0
0
0
2
0
0
2
2
3
0
0
2
0
2
3
1
0
2
0
0
0
2
0
0
1
1
0
2
1
0
2
2
1
0
0
2
1
2
0
1
2
0
2
0
2
2
0
0
0
0
1
0
1
1
2
2
0
1
2
1
1
0
0
1
0
0
0
0
0
0
0
1
2
0
0
1
0
0
1
2
0
2
2
2
1
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
1
2
0
0
0
0
2
1
1
0
1
1
0
1
0
1
0
2
0
0
1
2
0
5
0
2
2
0
1
0
0
0
0
2
1
0
2
0
2
1
0
0
0
1
1
0
1
0
2
1
0
2
1
2
1
0
2
0
1
0
0
1
1
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
1
0
1
1
0
0
0
1
1
1
1
1
0
0
0
0
1
1
2
1
2
0
0
0
1
2
1
1
1
1
0
0
0
0
1
0
0
3
0
0
1
0
1
0
0
0
0
1
2
2
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
2
1
1
0
0
0
1
4
0
0
2
0
0
2
1
0
1
0
1
2
0
0
2
0
1
0
2
1
0
0
1
2
1
0
0
0
0
2
3
1
0
1
0
1
0
0
2
2
2
0
1
2
1
2
1
1
0
0
1
4
0
0
0
2
1
0
2
1
0
1
1
0
0
1
1
0
0
0
1
1
0
0
1
0
0
0
1
0
1
0
0
1
0
1
1
0
0
2
3
1
0
1
2
1
0
1
0
0
1
0
0
0
1
1
0
0
0
2
1
3
2
1
0
1
0
0
0
1
1
0
0
2
0
0
0
2
0
2
1
1
1
0
1
0
1
0
0
1
1
0
0
1
1
0
0
0
4
0
2
0
1
2
0
2
1
0
3
0
2
1
2
0
0
1
0
1
0
1
1
0
0
1
0
4
0
1
2
1
2
2
0
1
0
1
2
2
0
0
0
0
1
0
0
0
3
2
0
1
0
0
1
0
0
0
2
0
0
2
0
1
2
2
1
1
2
1
0
1
1
1
2
0
0
0
1
1
0
0
0
0
2
0
0
2
1
1
0
0
0
1
1
1
0
0
0
1
1
0
0
0
1
1
1
0
1
1
0
0
4
2
0
0
0
0
1
1
0
2
1
0
0
1
2
0
0
0
0
0
1
0
2
0
0
3
0
0
0
1
1
1
1
0
1
2
1
0
0
2
1
1
0
1
1
2
2
0
0
1
0
0
0
0
0
0
1
2
2
2
0
0
1
0
1
0
2
1
0
0
0
0
1
0
1
1
0
2
0
0
1
0
0
2
1
0
2
0
0
0
2
0
0
1
2
1
2
2
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
3
1
0
2
1
1
3
1
2
1
2
1
0
2
1
0
1
0
1
0
1
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
1
2
0
0
1
3
2
0
0
1
0
0
1
1
0
1
2
1
0
0
1
0
2
0
2
0
0
0
1
0
0
2
0
0
0
0
1
1
0
1
2
0
1
1
0
1
0
0
0
1
2
0
0
0
0
2
1
0
0
0
1
1
1
0
0
0
3
0
1
0
0
0
0
1
1
1
1
0
0
0
0
2
0
1
2
0
2
0
1
1
2
0
0
1
0
0
1
2
1
0
0
2
0
1
0
2
1
2
1
1
1
3
0
1
2
1
2
0
2
1
1
2
0
0
0
1
3
2
1
0
0
0
2
1
0
0
0
1
0
2
2
2
0
2
0
0
0
2
2
0
0
0
0
2
2
0
1
2
2
2
0
2
1
0
2
2
2
1
2
2
3
2
0
0
1
1
2
0
0
2
0
1
1
0
0
0
1
1
0
2
1
1
0
0
1
1
0
2
0
1
0
2
0
2
0
0
0
0
3
0
2
1
0
2
1
1
0
0
0
0
2
0
1
0
0
2
1
2
0
0
1
2
0
1
1
1
2
2
1
1
1
1
0
2
2
0
0
0
1
1
0
0
0
0
2
2
0
0
1
0
2
0
1
0
2
1
0
0
0
0
0
1
0
1
1
0
1
1
0
2
0
1
1
0
0
0
1
1
0
1
1
2
1
1
0
2
0
0
2
0
1
1
2
0
0
0
1
2
0
1
1
1
1
0
1
1
0
2
0
2
0
1
1
0
0
1
1
0
0
2
1
0
1
0
1
2
0
2
1
0
2
0
0
2
1
0
2
0
1
2
0
2
0
1
1
1
1
0
0
0
2
2
0
0
1
0
1
1
1
0
1
0
2
1
0
0
1
2
1
0
2
1
0
0
1
1
2
2
0
0
1
2
1
0
0
0
1
0
0
1
1
1
2
1
0
0
0
0
2
0
0
1
0
2
0
0
1
0
0
1
1
0
2
0
0
0
0
1
1
2
1
1
2
0
0
0
0
1
2
0
0
1
2
1
0
0
0
2
1
1
0
0
1
0
1
0
0
3
1
2
2
0
2
0
0
0
1
0
0
2
2
0
0
1
0
1
1
0
1
1
0
0
1
0
2
0
0
2
1
0
2
0
0
0
1
2
0
1
0
0
0
0
2
2
2
1
0
1
0
1
1
0
0
0
1
1
0
2
1
0
1
0
0
0
0
2
0
2
0
0
0
2
0
0
1
1
1
0
0
2
0
2
1
2
2
0
0
1
0
1
0
0
3
1
1
0
0
0
0
1
1
0
2
0
1
1
1
1
2
2
0
0
2
4
0
0
1
2
0
2
3
0
0
1
1
1
2
1
0
2
1
0
1
1
1
1
0
1
0
0
0
0
2
0
0
0
1
0
1
1
2
0
1
0
1
0
0
1
0
0
1
0
0
0
1
0
0
1
1
1
0
0
1
0
1
0
1
0
0
1
2
2
0
0
0
1
0
0
1
0
0
0
0
1
1
2
0
0
2
0
0
1
1
0
3
1
0
2
3
2
0
0
0
2
2
2
1
2
2
1
0
0
0
1
1
3
1
0
2
0
2
1
0
0
1
1
0
1
0
0
0
0
0
1
0
0
2
1
1
1
1
1
1
2
2
1
0
1
1
0
2
0
0
1
0
0
1
0
2
2
0
0
0
2
0
1
1
0
0
0
1
1
0
0
3
1
1
1
0
0
1
2
2
0
1
0
0
2
0
0
2
1
1
1
0
0
0
1
0
1
2
2
2
0
2
0
0
0
2
0
1
0
0
1
1
1
0
1
1
2
0
1
1
1
0
0
0
0
1
0
0
1
1
0
1
2
0
0
1
1
1
0
1
1
2
1
0
2
2
0
1
1
0
2
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
2
2
2
1
1
2
0
1
1
1
0
1
0
1
1
0
2
1
1
0
1
3
0
0
1
0
2
1
1
2
0
0
2
0
0
0
1
1
0
2
1
1
1
0
2
0
0
0
1
0
0
1
1
2
1
1
0
1
0
0
1
2
0
2
0
1
0
2
2
0
1
0
1
0
1
1
0
2
1
1
0
0
1
2
0
0
0
1
0
0
0
3
2
2
1
0
0
1
2
1
0
1
2
0
2
0
2
0
0
1
0
0
2
0
2
0
0
1
1
0
0
1
1
0
0
1
2
1
0
2
2
1
0
0
0
0
0
2
2
1
2
0
2
0
0
0
0
0
1
1
2
0
1
2
1
0
0
1
2
1
0
0
1
1
0
1
0
2
0
1
0
0
0
1
0
1
1
0
2
1
0
0
0
0
1
0
0
1
0
0
1
0
0
2
2
0
2
0
1
1
0
0
0
1
1
0
2
2
1
1
0
0
0
1
1
5
0
0
0
2
0
1
1
1
0
3
0
1
2
0
0
0
0
0
0
1
2
2
2
0
0
1
2
1
0
0
2
1
1
2
0
0
3
0
0
0
0
0
2
2
1
0
0
1
1
2
2
2
1
1
1
1
2
1
1
0
1
2
0
2
2
0
2
0
0
0
1
1
0
0
2
0
2
1
2
1
0
4
1
0
0
1
0
2
0
0
0
1
1
0
0
1
0
0
1
0
0
2
1
1
2
1
1
0
1
1
0
1
0
2
0
0
1
1
1
0
0
0
2
3
0
0
2
1
2
2
0
0
0
0
0
2
0
0
1
2
0
0
0
0
1
1
2
1
0
0
1
2
1
0
1
1
1
2
2
0
2
0
2
0
0
1
0
1
2
0
0
1
1
2
0
0
0
2
0
1
0
1
0
1
0
2
1
1
0
1
0
0
2
0
0
0
0
0
0
5
1
1
2
1
1
1
1
1
1
0
1
0
0
0
2
0
0
2
1
0
1
1
0
1
0
1
0
2
0
0
0
2
2
0
2
0
2
2
2
2
1
0
0
1
0
0
1
0
1
1
2
0
3
0
1
0
1
0
1
1
2
1
0
1
0
0
0
1
2
1
0
0
2
0
2
1
2
0
1
0
1
1
1
1
2
2
0
0
1
2
0
0
0
1
1
2
0
1
0
0
0
2
1
0
1
2
2
2
0
1
0
1
1
0
0
1
0
1
1
2
0
1
0
0
1
2
0
0
1
0
1
0
2
2
0
2
1
0
0
2
1
0
0
0
2
0
0
2
0
3
0
1
0
0
2
1
2
0
1
1
0
0
0
0
0
1
1
1
0
1
1
0
1
2
1
0
0
0
0
1
1
0
0
0
1
2
1
1
2
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
1
1
0
1
0
0
2
2
0
2
0
2
0
0
2
0
1
3
0
1
1
0
2
0
0
1
0
1
0
2
0
1
1
0
2
2
0
0
2
1
2
0
1
0
0
0
1
0
1
0
0
0
2
2
0
0
1
0
0
1
1
1
0
1
0
1
1
2
0
1
2
2
1
1
0
1
0
0
0
2
2
2
2
0
3
1
0
0
1
1
0
1
0
0
0
1
2
0
0
0
2
0
2
1
2
1
0
0
0
0
0
1
0
1
2
0
0
0
0
1
0
2
1
2
0
0
1
1
0
1
2
0
2
2
2
0
0
0
2
0
1
0
0
0
2
2
0
0
0
0
0
1
0
1
0
1
2
0
1
2
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
4
1
0
0
1
0
1
2
0
4
2
3
1
1
1
0
0
0
0
0
3
2
1
1
2
3
2
0
0
1
2
1
0
0
0
2
1
0
0
0
0
2
0
0
0
0
1
1
0
1
2
0
1
2
1
2
0
0
0
0
0
2
0
0
1
0
0
2
5
2
0
1
0
0
0
1
0
0
4
2
2
1
0
2
1
0
1
2
0
1
2
1
2
1
1
1
0
0
0
0
0
0
2
2
1
1
0
2
0
0
1
0
1
2
0
0
1
1
0
0
0
0
1
1
2
1
1
1
2
2
1
0
1
2
2
0
0
2
0
2
1
1
2
2
1
2
0
1
1
0
1
0
1
0
1
0
2
0
1
2
2
0
0
1
0
2
0
2
1
1
0
1
0
2
2
0
2
1
2
0
2
0
0
0
2
0
0
0
1
0
2
2
0
0
0
0
0
0
1
1
2
0
1
1
1
0
1
0
1
1
1
2
0
0
0
2
2
1
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
1
0
0
1
3
0
1
0
1
1
1
0
2
1
2
1
0
0
1
0
0
0
0
1
1
2
1
0
2
0
2
0
1
0
1
0
2
1
0
1
1
0
2
2
2
1
0
1
2
0
0
2
0
2
0
0
0
0
2
1
4
0
0
0
0
2
1
1
2
0
2
1
0
0
1
0
1
1
1
0
2
0
0
1
0
2
0
0
2
0
3
0
1
0
1
1
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
2
0
2
0
0
2
1
2
1
0
0
0
0
2
0
1
2
0
0
0
0
0
2
0
0
1
0
0
3
1
0
1
1
5
2
1
0
2
0
1
0
2
2
0
0
2
1
0
0
0
2
0
0
0
2
0
1
0
2
2
1
0
0
0
1
0
0
2
1
0
0
0
2
1
2
2
1
1
0
0
2
1
2
0
0
2
0
0
0
2
2
0
0
1
0
0
0
1
2
1
2
0
1
0
0
1
1
0
2
2
1
1
0
1
1
0
1
0
1
1
1
0
2
0
0
0
0
0
0
1
1
2
0
1
1
1
0
0
0
0
1
2
2
1
0
0
2
1
1
0
0
1
0
0
1
2
0
1
1
0
0
1
1
1
0
0
0
2
1
0
0
3
0
1
2
2
0
2
2
0
2
0
0
1
2
0
1
0
1
1
2
1
0
2
2
2
0
2
0
3
0
0
0
0
0
2
0
0
0
0
2
1
1
3
3
1
0
2
0
2
0
0
0
2
2
1
1
2
1
1
2
1
2
1
2
2
0
0
0
1
1
1
0
5
0
0
0
1
2
1
0
0
2
0
1
1
0
0
0
1
1
0
1
1
0
2
2
0
0
2
0
0
0
0
2
1
0
1
1
0
0
1
1
0
1
0
2
1
3
1
1
0
0
0
0
2
0
1
0
1
0
1
2
0
0
0
0
1
1
0
0
0
0
3
0
2
1
0
0
0
1
1
1
2
0
1
0
0
2
1
0
0
2
1
1
1
1
2
1
0
2
2
1
0
2
0
1
2
1
2
2
1
0
2
0
0
1
1
1
0
0
1
1
0
2
2
0
3
0
2
2
0
0
2
0
1
3
0
1
2
1
2
0
0
0
0
2
0
0
1
4
2
0
0
1
1
0
1
2
1
0
0
1
2
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
2
1
1
0
1
1
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
2
1
0
2
2
1
0
1
0
2
1
0
1
0
2
2
0
1
0
0
0
0
0
2
0
0
1
0
0
2
1
2
1
2
1
1
0
0
0
0
1
2
0
0
0
2
1
1
0
2
0
0
1
0
0
0
0
1
0
2
1
0
1
2
0
0
1
0
0
2
2
0
0
1
2
0
1
1
0
2
1
1
0
2
0
0
0
0
2
2
0
2
0
1
1
2
2
2
0
1
1
1
0
0
1
2
1
0
0
1
1
0
1
0
3
0
1
0
0
0
1
4
2
1
0
4
0
1
0
2
0
0
0
1
1
1
0
2
2
0
0
0
0
0
0
0
2
1
0
2
1
1
0
0
0
1
2
0
1
2
0
0
0
0
0
0
0
2
0
0
0
1
1
0
1
1
0
0
0
1
0
1
1
1
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
2
1
0
2
2
1
1
2
2
2
0
1
1
0
1
0
0
0
2
1
2
0
0
0
0
0
2
0
0
1
1
0
1
1
0
0
0
0
0
2
1
1
0
1
0
1
1
1
2
0
0
0
2
0
0
2
1
0
1
0
0
0
0
1
0
0
1
2
0
0
0
1
2
0
1
1
0
1
0
1
2
1
0
1
1
0
1
1
0
1
0
0
1
0
3
0
0
2
1
1
0
2
1
1
0
1
1
0
2
1
1
0
0
2
2
0
1
0
0
2
3
2
1
0
2
0
0
3
0
0
0
1
0
0
2
4
2
0
0
1
1
1
0
0
2
0
3
1
1
2
0
0
0
0
1
1
0
0
2
2
0
0
1
2
0
1
0
1
0
1
1
1
0
1
1
2
2
1
0
0
0
1
0
0
0
0
0
0
0
2
1
1
0
1
1
0
1
0
1
1
1
0
3
0
1
1
3
1
1
1
1
0
2
1
1
0
1
0
0
1
2
1
2
0
0
2
1
1
2
0
0
1
2
1
0
2
1
1
0
0
2
1
1
0
0
0
0
1
0
0
0
0
0
2
1
2
0
0
1
0
0
2
1
0
2
1
1
0
2
0
1
2
1
1
2
1
1
1
0
1
2
1
0
2
0
1
2
0
0
0
0
0
1
2
1
1
1
1
0
0
1
1
0
1
1
0
0
1
1
1
0
0
1
2
2
1
0
2
0
1
0
1
0
2
0
1
2
1
0
0
1
3
2
0
0
2
0
2
0
1
0
1
2
1
0
0
0
2
0
0
2
0
1
0
0
0
1
1
2
0
0
1
1
1
1
2
0
0
0
0
0
2
0
1
0
0
0
1
0
1
0
1
1
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
1
2
1
1
0
1
1
1
1
0
0
0
0
2
2
0
0
0
1
0
2
0
0
2
0
0
0
2
0
2
1
3
1
0
0
0
2
0
0
1
1
1
2
1
0
0
3
0
1
1
1
2
0
1
0
0
0
1
0
2
1
0
1
0
1
0
0
0
0
1
0
0
1
1
1
0
3
0
0
1
1
0
1
0
0
3
1
0
1
1
1
1
1
0
1
1
1
0
0
2
0
2
1
1
1
0
0
0
0
0
0
1
2
2
0
0
0
2
2
0
0
1
0
2
2
1
0
2
3
0
1
0
1
1
0
2
0
1
1
0
0
0
0
1
1
0
3
0
1
0
1
0
0
2
0
1
1
1
1
0
2
0
0
0
0
1
0
0
2
0
0
4
2
2
0
0
2
0
2
0
0
1
1
1
1
1
1
2
2
0
0
0
0
0
2
0
0
1
2
0
2
0
1
2
0
1
1
1
0
0
1
1
1
1
0
0
0
2
1
1
2
1
0
0
1
3
0
0
0
0
0
1
0
2
1
1
0
0
1
0
0
1
0
2
2
2
0
0
1
0
0
2
0
1
1
1
2
0
1
2
1
0
1
2
2
2
0
1
1
0
1
0
3
2
0
0
1
2
1
0
1
2
0
1
0
1
0
0
0
1
1
0
0
1
0
2
0
0
0
4
0
1
0
2
0
0
2
0
0
3
0
1
0
0
0
2
2
2
0
0
0
1
1
0
3
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
2
2
1
0
0
1
0
0
2
1
2
1
2
0
2
1
0
1
0
1
1
1
0
1
0
0
0
1
0
2
1
2
2
1
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
1
2
2
0
1
2
0
0
1
1
1
1
2
2
1
1
1
2
0
0
0
0
0
2
0
2
0
2
1
1
1
1
1
1
1
2
2
0
1
0
1
2
2
0
1
0
1
0
2
0
1
2
0
0
0
0
0
1
0
0
1
0
1
0
2
0
0
0
1
1
0
0
0
1
2
1
0
1
0
2
1
0
0
0
0
0
1
2
0
0
1
2
2
1
0
2
0
2
0
0
0
2
0
2
0
1
2
1
1
2
2
2
1
2
0
1
0
0
0
0
2
0
0
1
0
0
1
1
0
1
0
2
2
0
1
1
2
0
0
1
1
0
0
0
0
0
0
1
0
3
0
1
0
1
0
1
0
0
2
0
1
0
0
1
1
2
1
0
2
0
0
0
0
1
1
0
0
0
1
2
2
2
2
2
2
1
2
0
2
1
1
1
1
0
0
1
1
0
0
0
0
3
5
0
1
0
1
1
2
0
1
2
0
0
1
1
0
2
0
0
0
0
0
1
0
2
0
2
0
2
0
0
1
2
0
2
2
1
1
0
0
1
1
1
0
2
0
0
0
1
1
0
1
1
2
0
2
0
1
0
2
0
1
0
1
0
2
0
2
0
0
2
0
1
0
1
0
0
1
1
0
0
1
0
0
1
0
0
2
1
1
0
0
0
0
0
1
0
0
2
1
0
2
2
2
0
1
1
2
1
2
0
1
0
1
1
2
2
0
0
1
2
0
0
0
0
0
2
1
0
0
2
0
0
1
0
1
1
1
0
0
0
0
0
0
2
2
1
0
2
1
2
0
2
2
3
1
3
2
2
2
1
0
0
0
0
1
0
2
2
0
0
0
0
0
1
1
0
0
1
2
0
0
2
0
0
1
1
1
1
0
0
0
1
0
1
0
0
2
2
0
0
0
0
0
0
2
0
0
0
2
2
1
0
0
0
0
1
2
1
2
1
0
1
0
0
0
0
0
1
0
0
0
1
2
0
1
1
2
0
1
0
1
0
1
0
1
1
0
0
3
0
0
0
0
2
1
2
0
2
1
0
0
0
1
0
2
2
1
0
2
1
2
0
1
0
0
0
0
2
0
1
1
1
1
2
1
0
1
1
1
0
0
0
0
1
2
0
1
1
0
0
1
1
0
0
2
1
0
1
2
0
0
2
0
1
0
1
3
0
0
0
1
2
0
0
0
2
1
1
0
0
0
0
1
0
1
0
1
0
1
0
1
1
0
0
1
0
0
0
2
1
1
0
0
1
2
2
0
0
1
0
0
0
3
1
1
1
0
1
2
2
0
1
0
6
0
0
0
1
1
0
1
1
0
2
0
0
0
0
2
0
0
0
0
1
0
2
0
2
1
2
1
2
0
0
2
0
0
0
1
1
1
0
1
0
3
0
0
2
0
2
2
1
0
1
2
0
1
0
0
0
0
1
1
0
2
0
0
1
0
0
0
0
1
0
0
0
1
1
1
0
0
0
1
1
2
1
2
2
2
1
2
2
1
0
1
0
1
0
1
1
1
3
0
1
1
0
1
0
2
0
2
1
2
0
0
0
2
0
0
1
1
0
2
1
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
2
2
0
0
2
1
0
0
0
0
2
0
1
0
0
0
0
1
1
1
2
0
0
2
0
1
1
0
0
1
2
0
2
2
1
2
0
0
0
2
1
0
0
0
0
6
0
1
0
0
0
2
1
0
0
1
0
2
0
0
0
1
0
0
0
0
0
1
2
2
0
1
0
0
1
1
2
1
2
1
1
2
0
2
0
0
3
0
0
0
0
0
2
0
3
0
0
0
0
1
0
0
1
1
2
2
0
0
0
1
0
0
0
1
0
2
1
2
1
0
0
1
1
1
0
0
2
0
0
0
2
3
1
2
1
2
0
2
0
2
0
0
0
2
0
1
1
0
0
0
2
0
0
3
0
2
0
1
0
0
2
0
0
2
0
0
2
1
2
0
0
0
1
0
0
0
0
1
1
1
1
0
2
0
0
1
1
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
2
1
0
1
0
0
0
1
1
0
0
0
0
1
2
2
0
0
2
3
2
2
0
0
1
0
3
1
1
2
1
1
1
2
1
1
0
0
0
2
2
1
1
2
2
0
0
1
0
0
1
2
2
0
0
0
1
0
1
2
2
1
2
2
1
1
2
1
0
1
0
0
1
0
0
0
0
0
1
1
0
0
1
1
0
0
1
2
0
0
0
3
0
2
0
2
0
0
1
1
0
0
0
0
1
1
0
0
0
2
0
0
1
0
1
0
0
0
0
1
0
1
1
0
0
1
0
0
2
2
0
2
0
1
1
2
0
0
1
1
0
0
0
1
0
1
1
1
0
0
1
0
3
0
1
1
2
0
1
0
1
0
0
1
1
1
2
1
0
0
1
1
0
1
1
1
0
1
0
1
1
2
0
0
2
0
0
0
0
0
1
2
0
0
1
0
1
2
0
0
2
1
2
0
1
0
0
0
1
1
2
0
0
0
1
1
0
0
0
1
2
0
1
1
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
3
0
1
1
0
0
0
0
1
1
1
2
2
1
2
1
1
0
0
0
0
2
2
0
0
0
1
2
1
1
1
0
1
2
2
0
3
1
6
1
1
2
0
2
0
1
1
0
0
0
0
1
1
0
1
2
2
1
0
3
1
0
1
1
1
0
0
0
0
0
2
2
3
1
0
1
1
1
1
0
4
0
0
0
1
0
1
0
1
2
1
1
1
1
1
1
2
0
0
1
1
0
0
0
0
1
1
0
1
2
1
2
2
0
2
0
0
1
2
0
0
0
0
1
0
2
1
1
0
0
0
2
0
4
0
1
0
2
2
0
0
0
1
0
2
0
1
1
0
0
0
0
0
1
0
0
0
1
1
0
0
2
1
2
2
0
0
0
0
0
2
1
1
2
1
0
0
1
1
1
2
1
0
2
1
0
1
0
0
2
2
0
2
2
2
1
0
1
0
2
0
1
0
0
0
1
0
0
0
0
3
0
1
0
1
1
1
2
0
0
2
2
0
2
0
2
0
1
2
2
0
1
1
0
2
0
0
1
0
2
0
2
1
0
1
0
0
0
0
2
1
0
0
1
1
2
0
2
1
0
1
1
1
1
2
0
2
0
1
0
0
2
5
1
1
1
1
1
1
1
2
1
0
0
0
1
1
2
1
2
1
0
0
1
0
0
1
1
0
3
2
0
2
0
1
2
0
2
2
1
1
1
2
0
2
0
0
0
1
2
2
0
0
2
0
2
0
0
1
3
1
0
2
0
2
0
0
1
0
0
0
1
0
0
0
2
2
2
0
2
0
2
2
0
1
0
0
0
1
1
0
0
0
1
2
1
0
0
0
1
0
0
1
2
2
1
1
0
2
0
2
0
0
0
0
1
0
1
0
1
0
0
1
0
2
0
1
1
2
1
0
1
2
0
2
0
2
1
2
0
0
0
2
0
2
1
2
0
0
0
1
0
0
2
1
0
0
0
1
1
1
2
0
1
1
2
0
0
2
2
0
1
2
0
0
1
1
2
0
2
0
0
0
1
1
0
0
0
1
1
0
4
0
0
1
2
1
0
0
1
0
1
2
2
0
1
1
2
1
1
0
0
1
0
2
0
0
2
1
1
0
2
1
2
0
2
0
0
1
0
1
0
2
1
0
0
1
0
1
1
1
1
0
1
1
2
2
0
1
2
1
1
0
0
0
0
0
0
0
1
0
2
1
1
1
1
2
1
0
1
0
0
0
0
1
1
0
2
2
2
0
0
0
0
1
1
2
2
1
0
0
0
1
1
0
0
2
1
0
0
0
0
0
2
0
3
1
0
0
0
2
1
2
0
0
1
2
0
2
0
4
0
1
1
0
2
0
1
1
2
0
1
0
1
1
1
0
0
2
2
2
1
1
0
1
1
0
1
1
1
3
0
1
0
2
2
2
2
1
2
0
1
2
0
0
0
0
0
3
0
0
3
0
1
2
0
1
1
0
1
0
1
0
0
2
1
1
0
0
0
0
0
1
0
0
2
0
2
0
0
0
1
0
0
0
2
0
0
2
0
2
0
1
1
0
0
0
0
2
1
0
1
2
2
1
1
1
1
0
0
0
2
0
0
2
1
0
0
2
2
0
3
1
0
0
0
1
0
2
0
0
0
0
1
0
0
0
2
2
2
0
3
0
1
0
1
0
2
2
3
0
0
1
1
1
1
1
0
0
0
1
1
0
1
0
0
0
1
0
3
2
1
0
0
2
0
0
0
1
0
0
1
2
1
1
2
1
1
0
0
0
0
2
0
0
2
1
1
0
1
2
1
0
0
2
0
0
1
0
1
2
0
1
0
1
2
2
1
1
1
2
2
1
1
1
2
0
0
0
0
1
1
0
1
1
0
0
2
1
1
0
0
1
1
0
1
2
0
2
0
1
1
2
0
1
1
1
1
0
2
1
1
1
2
1
1
1
0
1
0
2
0
1
0
1
0
0
2
0
0
2
2
1
2
2
1
0
1
0
1
0
0
1
0
0
1
0
2
1
1
1
3
1
0
0
1
2
2
1
2
2
2
1
1
1
0
0
2
1
1
2
1
0
0
2
0
2
1
0
0
0
1
1
0
0
1
0
0
2
2
0
1
0
0
0
1
2
0
0
1
2
0
1
0
0
0
1
0
0
0
0
1
0
2
0
2
1
1
0
0
0
1
0
1
1
0
2
0
2
0
1
0
0
0
1
0
1
1
0
1
1
2
1
0
0
0
1
2
1
0
2
1
0
1
0
1
0
0
0
0
0
1
2
0
0
1
1
2
0
0
1
1
1
0
1
2
0
0
1
0
1
3
0
0
0
0
0
2
1
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
1
1
0
1
1
3
1
0
1
1
3
2
1
0
0
0
2
1
0
2
0
2
1
1
0
1
0
0
2
1
1
0
0
1
1
0
1
1
1
0
1
1
1
1
1
0
0
1
2
2
0
0
0
0
0
1
2
1
0
1
4
2
0
2
1
0
1
2
3
2
1
2
0
2
1
0
1
0
0
1
2
0
1
6
2
2
1
1
0
2
2
0
2
1
1
0
1
0
0
0
0
1
0
0
2
0
0
1
1
0
1
2
2
1
0
2
0
1
0
1
2
0
0
0
0
1
2
2
0
0
0
0
0
2
0
2
0
1
0
2
0
0
0
2
0
1
0
3
2
0
0
0
0
0
2
1
3
2
0
1
1
2
1
2
0
1
0
1
1
1
2
0
0
0
2
2
1
1
2
0
1
1
0
0
0
3
1
0
0
0
0
2
0
1
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
1
2
0
1
0
0
0
1
2
0
0
0
1
2
1
1
2
0
2
0
0
2
1
1
0
0
2
1
1
2
1
1
0
0
0
1
0
2
1
1
0
0
1
0
0
2
2
2
0
2
0
1
0
1
1
2
2
0
1
1
1
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
1
1
2
3
0
0
2
2
2
2
1
2
1
0
0
1
2
1
0
3
1
1
1
1
0
1
1
0
2
0
1
0
0
1
0
1
2
0
0
1
1
2
1
2
2
2
2
0
3
1
1
0
1
1
1
3
1
2
0
0
1
0
3
0
0
1
1
1
0
1
0
0
2
2
1
0
0
1
2
0
1
2
0
1
0
0
2
1
1
0
1
0
0
0
1
0
0
2
1
0
0
1
1
1
0
1
1
1
0
0
1
2
0
1
0
0
0
2
0
0
1
0
1
1
0
1
3
1
0
0
0
2
3
0
5
0
2
1
1
1
0
1
0
0
0
3
2
2
1
2
2
2
1
2
0
1
0
2
2
1
0
2
0
2
0
0
0
0
0
2
2
2
1
3
1
1
0
0
0
1
2
2
0
2
2
1
0
0
1
0
0
0
2
0
1
1
2
1
1
0
1
1
0
0
0
0
1
2
2
0
2
0
0
2
3
0
2
1
1
0
0
0
0
1
2
1
0
0
2
2
0
1
0
0
0
0
0
0
1
1
2
2
0
0
2
1
0
1
0
0
1
0
1
0
0
0
1
0
1
0
1
2
1
0
2
0
1
0
0
1
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
2
1
1
1
0
0
0
2
1
0
1
0
1
2
1
1
2
0
2
2
0
0
1
0
2
0
0
3
1
1
0
1
0
1
1
0
0
1
2
2
1
0
0
1
2
1
0
1
0
1
0
1
1
2
2
2
0
2
2
1
0
1
1
1
2
2
0
2
0
1
2
0
2
0
1
1
1
0
0
1
2
1
2
1
1
0
0
2
0
1
0
0
2
1
0
1
2
0
0
2
2
0
0
0
0
0
0
2
0
0
1
2
2
2
0
0
1
0
0
1
0
0
1
0
0
0
1
1
0
1
0
1
0
0
1
0
1
0
1
0
3
0
0
2
0
1
0
1
0
0
1
0
1
0
0
1
2
1
2
0
1
3
1
2
0
0
0
1
0
0
0
0
2
1
0
0
1
0
1
2
1
2
0
0
0
2
0
0
1
1
0
2
1
0
1
1
0
0
0
10
0
0
0
0
1
0
1
0
0
2
2
0
0
1
1
0
1
1
0
1
2
1
0
2
0
0
0
1
0
1
2
0
0
1
2
2
0
0
0
0
1
1
2
2
1
1
0
1
0
0
0
0
2
2
1
1
0
1
1
2
2
0
0
0
0
0
0
1
1
0
0
2
2
0
0
1
0
3
0
0
0
0
0
0
1
0
0
0
2
1
0
1
1
2
0
2
2
2
0
1
1
1
0
0
0
1
2
0
0
1
1
0
1
0
0
0
0
1
2
0
1
0
2
0
1
0
1
2
0
0
1
0
1
0
0
0
0
2
2
1
1
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
2
0
1
0
1
0
0
0
1
0
2
0
0
0
0
2
0
0
1
0
0
2
1
0
1
0
1
0
0
0
2
1
1
0
2
1
1
1
1
0
1
2
0
0
2
0
0
0
2
1
0
0
1
0
2
0
0
1
1
1
1
2
0
2
0
2
0
0
0
0
0
1
1
0
1
1
0
0
1
0
0
0
1
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
1
0
3
2
0
2
1
0
0
0
1
0
0
2
0
0
0
0
2
2
0
0
1
0
1
0
2
0
1
0
0
0
0
0
1
0
2
2
0
0
0
0
2
0
0
2
1
0
0
0
2
0
0
2
2
0
1
1
1
1
2
0
0
2
0
0
1
0
1
1
0
0
0
2
0
0
0
0
0
0
1
0
1
1
1
2
1
1
1
0
1
0
1
0
2
0
0
0
2
0
1
0
0
0
0
2
0
1
0
0
0
1
0
0
1
1
1
0
2
2
1
0
0
0
0
1
0
0
1
1
0
0
1
1
0
2
2
1
0
2
0
1
1
2
0
2
0
2
0
2
1
0
1
2
2
2
0
2
0
1
2
0
0
0
1
1
1
1
2
1
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
2
0
1
1
0
2
0
1
3
1
0
0
0
2
2
0
0
0
1
0
1
0
0
0
0
1
0
2
0
2
1
0
0
0
0
0
0
1
2
0
0
1
0
1
0
2
1
0
3
1
0
1
0
2
1
1
2
0
0
2
1
2
0
0
1
1
0
0
1
0
1
1
0
1
1
0
0
0
0
0
1
2
0
1
1
1
1
2
1
1
0
1
0
0
0
0
0
2
1
0
3
0
2
0
1
0
2
0
0
2
1
0
0
1
0
1
2
1
1
0
2
0
0
0
0
0
3
2
0
0
0
0
2
1
0
0
0
1
0
1
2
1
0
1
2
0
0
0
2
2
0
0
0
1
1
0
0
5
0
2
2
2
1
1
0
0
0
0
2
0
1
1
0
1
2
1
2
2
1
1
0
2
0
1
1
0
2
1
0
2
0
2
1
1
0
1
0
0
0
2
2
0
0
2
4
0
1
0
0
1
0
0
0
0
1
1
0
1
2
0
0
1
0
0
3
1
1
0
2
0
1
0
2
0
1
2
0
0
0
2
0
0
1
0
0
0
2
1
1
0
0
0
1
1
0
0
0
0
0
1
1
2
0
1
0
1
0
0
2
0
0
1
5
0
0
0
2
1
1
3
0
1
0
0
1
1
2
0
0
2
1
1
1
2
1
1
1
0
2
1
2
0
1
0
0
0
0
1
1
0
1
0
0
2
0
1
0
1
0
1
1
0
0
0
1
0
2
0
2
1
0
0
3
0
0
1
1
1
2
0
1
0
0
0
1
0
2
2
0
1
1
1
0
0
1
0
0
2
1
1
0
2
0
1
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
1
2
0
0
0
1
2
2
2
0
0
1
1
2
0
1
0
1
0
0
0
0
0
1
0
1
1
2
0
1
1
0
1
1
2
2
1
0
1
0
1
1
2
0
1
2
1
2
1
0
1
2
0
0
2
0
0
2
2
0
2
1
0
2
2
0
0
0
2
0
0
1
0
2
0
1
4
0
1
3
1
0
0
1
0
0
1
2
5
0
2
1
0
0
1
1
2
0
0
1
2
1
0
0
1
2
0
0
0
1
0
2
0
2
1
1
0
1
2
0
0
0
0
0
0
0
2
0
2
0
2
0
0
1
0
0
1
1
2
2
1
0
1
0
0
1
1
1
1
1
1
1
2
0
1
0
0
0
0
0
0
0
0
2
1
0
1
1
2
1
2
3
1
2
1
1
1
0
0
2
0
0
0
2
0
0
0
1
0
0
1
0
0
0
1
1
0
3
2
0
0
0
0
2
2
2
0
1
2
0
1
1
1
1
2
2
0
0
1
0
0
2
0
2
0
1
2
0
1
0
1
0
0
1
1
0
0
2
0
0
0
0
0
2
0
0
1
1
0
0
1
0
0
2
0
1
0
1
1
1
1
0
2
2
2
0
1
2
0
0
0
1
0
0
0
0
1
1
2
1
1
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
2
1
1
0
0
2
0
0
0
0
0
0
2
1
0
2
1
1
1
1
0
0
0
2
0
1
0
2
1
0
0
0
0
0
0
0
0
2
0
1
2
1
2
0
0
0
0
2
2
3
0
2
1
1
0
0
1
0
1
1
0
1
0
1
1
0
0
2
2
1
0
1
2
2
0
1
2
0
2
1
0
0
0
0
0
0
0
1
0
2
0
2
1
0
0
0
2
1
2
1
0
0
1
0
2
0
2
0
0
0
2
0
0
0
2
2
2
0
2
0
2
2
0
1
1
0
2
0
5
2
1
1
1
2
2
0
0
1
1
1
1
1
1
0
2
3
0
2
0
0
0
2
2
0
1
2
0
0
2
0
2
1
0
2
1
2
0
1
0
0
0
0
0
1
1
1
0
1
2
2
2
1
0
1
0
1
0
2
2
1
0
0
2
0
0
1
0
1
0
1
0
2
0
0
1
0
2
2
1
1
1
1
0
0
0
0
1
2
1
1
0
2
1
0
1
0
0
0
0
0
0
2
1
1
1
0
1
2
1
1
0
1
3
2
0
1
0
1
0
1
1
0
0
0
1
0
0
0
1
0
1
0
0
1
1
1
1
0
2
0
0
0
1
0
3
0
0
0
0
1
2
0
1
0
0
2
1
2
0
1
1
1
1
2
0
0
0
1
7
2
0
1
0
0
2
2
1
1
0
0
1
0
2
1
1
1
1
0
1
1
0
1
1
1
0
1
0
2
0
0
2
1
1
2
1
0
0
1
2
0
0
0
2
0
0
0
0
0
2
0
0
1
0
2
1
0
3
0
1
4
0
0
1
0
1
0
0
0
0
0
0
1
0
1
1
0
0
2
0
2
0
0
0
0
1
1
1
1
0
0
0
0
1
0
2
0
1
1
1
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
2
0
2
0
2
1
0
0
2
1
1
2
0
0
0
0
4
1
0
0
0
0
1
1
0
2
1
1
0
1
2
1
1
1
0
2
1
1
1
1
0
1
0
2
0
0
0
1
0
1
0
0
2
2
0
1
2
1
0
1
1
2
0
0
2
0
2
2
2
0
1
2
0
1
2
0
0
0
0
2
0
2
1
1
0
0
0
0
0
1
2
1
2
0
1
4
0
0
1
1
1
0
2
0
0
1
0
2
0
2
2
1
0
1
1
2
0
2
1
0
0
0
2
0
0
0
2
2
1
1
0
2
0
0
0
1
0
2
0
1
1
2
3
1
2
2
0
2
0
0
1
0
0
0
1
1
0
0
2
1
2
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
1
1
1
0
0
0
0
1
2
1
2
1
0
0
1
0
1
0
2
0
2
0
3
0
0
2
0
1
2
0
1
0
1
0
0
0
0
0
0
1
0
0
0
5
0
1
2
1
0
2
2
0
0
1
1
2
1
0
0
0
0
0
2
0
1
0
1
0
0
0
0
1
0
2
2
0
1
2
2
0
2
0
2
0
2
0
0
1
0
6
1
1
0
0
1
0
1
2
2
1
2
0
0
0
2
0
0
1
2
3
1
1
1
2
1
0
0
0
1
1
2
0
1
0
1
0
2
2
0
1
0
0
1
2
2
0
1
0
0
0
2
0
0
0
0
0
2
0
3
1
2
0
1
0
0
2
0
0
2
0
0
1
2
2
2
0
0
1
1
0
0
1
0
1
0
2
1
1
0
0
0
1
1
0
0
1
0
0
0
1
0
1
1
1
1
0
2
1
0
1
1
0
0
1
2
2
0
0
1
0
1
2
2
1
2
1
0
1
2
0
0
0
2
0
2
2
2
1
1
1
2
0
0
1
1
2
1
0
0
0
2
0
0
0
2
2
1
0
1
0
2
1
1
2
2
1
2
1
0
0
2
2
1
0
0
0
1
1
0
0
0
0
2
2
0
1
1
0
0
2
1
0
1
2
0
1
0
0
0
0
0
1
1
3
0
0
2
0
1
0
0
1
0
0
0
0
0
1
0
1
2
0
2
2
1
0
0
0
0
0
3
0
0
1
0
2
0
0
0
0
1
1
1
0
2
0
0
0
2
3
0
0
1
2
0
1
0
2
0
1
2
2
0
1
0
1
0
0
0
0
0
2
2
0
0
1
1
0
2
1
1
1
1
1
2
0
0
0
0
1
2
1
2
0
0
1
1
0
2
1
1
1
0
0
2
0
0
0
2
1
1
0
0
1
1
0
0
1
1
0
0
1
0
1
1
2
2
0
2
1
1
1
2
1
2
0
1
1
1
2
0
2
0
1
0
2
2
0
0
1
0
0
0
0
0
1
0
0
0
1
1
2
1
0
1
0
0
1
2
1
2
2
0
0
2
0
2
1
0
0
1
1
0
0
0
0
0
0
0
0
1
1
1
1
1
1
2
0
0
2
1
0
1
0
0
2
0
1
2
0
1
0
0
0
0
2
0
0
1
2
0
2
0
2
0
0
2
2
0
1
2
0
0
0
0
2
1
0
1
0
2
0
1
0
2
2
1
2
2
1
0
0
0
2
2
0
1
0
0
0
1
1
1
0
1
0
1
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
2
1
0
0
1
1
0
1
0
1
1
1
0
0
3
0
0
1
0
1
0
1
2
2
0
0
1
0
0
0
4
0
2
2
0
2
1
1
2
1
0
3
2
3
2
2
0
2
1
4
1
0
0
0
1
2
0
0
1
1
2
1
0
1
1
0
1
2
0
0
2
2
0
0
0
2
2
1
0
0
1
2
2
0
0
2
1
1
0
1
0
1
2
1
0
1
1
0
1
0
1
0
0
1
1
1
1
0
2
0
1
0
0
0
0
2
2
0
0
1
1
0
2
0
0
1
1
0
0
0
0
1
0
0
0
1
2
1
1
1
2
2
0
0
0
1
2
2
0
0
0
1
3
0
1
1
1
1
1
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
2
0
0
1
0
1
1
2
2
1
2
1
2
1
1
1
3
0
1
0
1
0
2
3
1
1
0
1
1
0
1
0
1
1
1
2
0
0
1
0
1
1
0
0
0
0
2
0
2
2
0
2
2
0
1
0
0
0
0
1
2
0
0
1
0
2
0
1
0
0
1
0
0
2
2
0
0
0
1
1
0
0
1
0
0
4
1
2
2
0
1
0
0
1
0
0
0
2
1
1
1
2
0
0
0
0
0
1
0
0
3
0
0
0
2
0
1
1
2
0
1
1
0
1
2
0
1
1
0
3
0
0
0
3
0
0
0
0
3
0
2
0
0
0
0
0
1
0
2
0
1
1
1
0
1
0
0
0
0
0
0
2
2
2
4
0
2
0
2
2
0
0
0
0
0
2
0
1
1
0
1
0
1
2
0
2
2
0
0
1
0
1
0
0
1
0
1
0
2
0
1
1
1
0
0
2
0
1
0
1
1
0
1
1
2
1
1
2
0
2
2
0
0
1
0
2
1
0
1
2
2
0
0
2
3
1
1
2
2
2
0
2
1
0
2
1
0
0
0
0
1
1
2
1
1
0
0
0
2
1
0
0
0
0
2
2
2
2
2
0
2
2
1
0
0
0
1
2
1
1
0
1
1
1
0
1
1
2
2
2
2
0
0
0
2
0
0
1
2
0
0
0
2
0
0
1
0
1
2
0
1
2
1
0
2
1
1
1
1
1
1
0
0
2
1
0
0
0
1
1
0
2
0
1
2
1
0
0
1
0
0
0
0
0
2
2
1
0
0
1
1
0
0
0
0
0
1
2
0
1
1
1
2
0
1
0
2
0
1
0
1
0
2
2
0
2
2
2
1
2
2
2
0
0
0
1
0
0
1
1
2
0
0
0
2
0
2
0
1
1
1
2
1
0
1
0
2
1
1
1
0
0
0
0
7
2
1
2
2
0
0
0
0
0
2
1
0
2
0
0
0
2
0
1
2
0
0
0
2
2
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
2
0
2
0
0
0
1
0
0
0
1
0
0
1
0
1
0
2
0
1
0
2
2
0
0
1
0
2
1
0
0
1
2
2
0
2
2
0
0
0
1
0
0
0
2
1
0
1
1
0
1
0
0
0
2
1
1
2
1
1
0
0
0
1
1
0
0
1
2
1
0
2
1
0
0
1
0
0
0
1
1
1
2
0
1
2
1
2
1
1
2
2
0
0
2
1
0
0
2
1
0
0
0
1
2
2
2
2
0
1
2
1
1
1
2
0
0
1
1
0
0
0
1
0
1
0
0
1
0
2
0
2
2
0
0
0
2
3
1
0
1
0
2
1
0
0
0
0
0
1
0
1
0
2
0
0
1
0
1
0
0
1
2
2
2
1
2
2
0
0
0
1
1
1
0
0
0
1
2
0
0
2
0
0
0
2
2
2
0
0
0
2
1
1
1
2
0
0
0
0
1
0
0
1
1
2
1
1
2
3
3
0
3
1
1
1
1
1
1
1
1
1
0
1
2
0
1
1
0
2
1
1
2
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
2
0
2
1
0
1
0
1
0
0
1
0
1
2
1
0
0
1
0
0
0
1
2
0
1
0
2
0
0
0
2
0
0
0
1
1
2
1
0
1
1
1
0
2
2
0
0
0
1
0
0
0
1
0
2
2
1
0
1
0
0
0
1
3
1
0
2
0
0
0
1
1
1
2
0
1
0
2
0
1
0
1
2
1
1
0
0
0
0
0
1
0
0
0
1
1
1
0
1
0
0
0
1
0
0
2
0
2
2
0
0
1
1
1
0
1
2
1
2
0
0
0
0
1
2
2
0
0
0
1
0
0
1
1
0
2
2
1
0
1
0
0
0
0
0
0
0
1
1
0
0
2
1
1
0
0
1
0
0
0
1
0
0
0
2
1
2
0
0
0
0
2
0
4
0
0
3
0
2
1
1
2
0
0
0
0
1
1
1
0
0
0
0
0
1
2
0
3
1
0
1
3
2
0
1
1
0
0
2
0
0
1
0
1
2
0
0
1
0
0
1
2
2
0
0
1
2
0
2
0
2
0
0
0
2
1
0
1
1
1
1
1
0
2
2
0
0
1
0
0
1
2
2
1
0
1
1
0
1
2
2
1
0
0
0
0
2
0
1
0
0
0
1
0
0
1
0
0
1
0
2
1
0
1
1
0
2
1
1
0
0
0
2
0
0
2
1
0
2
1
0
0
0
0
1
2
0
0
1
0
0
0
2
0
1
1
3
1
0
0
2
0
0
2
2
2
0
0
0
0
0
1
1
0
1
0
2
0
0
1
0
0
2
2
0
2
1
0
0
0
0
0
2
0
0
4
1
0
1
1
1
2
0
0
2
2
0
0
2
0
1
1
1
0
0
1
1
3
1
4
2
1
0
0
0
1
3
1
0
0
0
1
0
0
0
2
0
2
0
0
0
1
1
0
0
0
2
0
2
3
1
0
2
1
0
2
1
2
0
0
1
0
1
1
1
2
0
1
0
0
2
0
1
0
2
0
2
1
2
0
0
0
0
0
0
2
1
2
1
1
0
1
1
1
1
1
1
1
2
0
0
2
0
2
1
2
0
2
0
2
1
2
2
0
2
2
1
0
0
1
0
0
0
0
2
0
2
1
0
1
1
1
1
0
0
2
1
1
1
0
0
1
2
1
0
2
1
0
2
1
1
0
1
2
2
1
1
0
1
1
0
0
1
1
1
0
3
0
0
1
1
0
0
0
2
2
0
0
2
0
2
1
2
2
1
0
0
1
0
0
1
0
0
1
1
1
1
0
0
2
2
0
1
0
1
0
2
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
1
1
2
1
1
0
2
0
0
2
0
0
1
3
1
1
1
0
1
0
1
0
0
0
0
1
2
1
1
0
2
0
1
1
0
0
1
0
1
0
2
2
2
0
2
2
2
0
0
0
2
0
2
3
0
1
0
3
0
2
0
0
0
1
1
0
3
0
0
1
1
0
0
0
1
0
0
0
1
1
0
0
0
0
2
0
2
1
0
2
0
2
1
1
1
0
0
1
0
0
0
2
0
1
1
1
0
0
1
0
0
0
0
0
1
1
0
2
1
0
0
1
0
1
0
1
0
1
2
0
2
1
1
0
0
1
0
0
1
1
2
0
0
2
2
0
1
0
0
1
1
1
0
0
1
1
1
0
1
0
2
1
0
0
2
0
1
1
2
1
0
0
1
2
1
1
1
0
0
0
1
0
0
2
2
0
1
0
0
0
1
2
0
1
1
1
1
2
3
1
1
2
0
1
1
1
0
2
0
2
0
0
0
2
1
0
1
1
2
3
0
1
0
1
0
0
0
2
1
0
0
1
1
2
2
1
0
1
0
1
0
2
0
0
1
0
0
2
1
0
2
0
2
1
0
0
0
5
1
1
2
1
2
0
1
0
0
1
1
1
0
1
0
1
0
1
2
1
2
0
1
0
0
1
0
1
0
1
0
0
0
4
0
0
1
1
2
0
0
1
0
1
2
2
1
0
0
2
1
0
2
0
1
2
1
3
1
3
0
1
1
1
0
1
0
0
0
3
0
1
0
0
1
0
2
0
0
0
0
0
0
2
0
2
0
3
2
1
1
0
1
0
0
1
2
0
0
0
0
1
1
1
1
1
1
2
0
0
2
0
2
2
2
0
2
0
0
0
2
1
1
2
2
0
1
2
0
0
0
0
1
0
2
0
0
1
0
1
1
0
1
2
3
1
0
0
0
0
0
2
2
1
0
2
2
0
0
1
1
0
0
1
2
1
1
1
0
1
0
1
0
1
2
4
3
0
2
1
0
0
2
1
2
1
0
1
1
3
3
2
0
1
3
1
1
0
1
1
0
0
1
1
0
2
5
1
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
1
1
1
2
0
1
0
1
0
2
1
0
1
1
0
3
1
1
1
0
1
0
0
1
1
2
0
0
0
0
0
0
0
0
2
2
1
0
1
1
0
1
1
0
1
0
0
0
1
0
2
0
1
2
1
1
1
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
1
1
1
0
1
0
2
0
1
0
2
2
0
0
1
0
1
0
0
1
0
0
2
0
0
2
0
1
0
0
0
1
0
0
2
1
0
0
3
1
0
0
1
1
0
1
0
2
1
0
0
1
0
2
1
0
1
2
0
3
0
1
2
2
2
1
0
1
1
2
0
1
0
1
0
0
2
0
2
1
0
0
0
2
1
1
1
0
0
1
2
2
0
0
1
1
2
1
1
0
2
2
2
2
1
1
1
1
0
2
2
0
0
0
1
1
0
1
2
0
2
0
2
1
0
0
0
1
0
1
2
1
2
1
0
2
2
0
2
0
2
0
1
1
0
0
0
2
0
0
1
1
0
1
1
0
0
0
1
2
1
2
0
0
1
1
0
1
0
1
2
1
0
0
0
2
0
1
0
0
2
1
2
1
0
0
2
3
0
0
2
0
0
2
0
1
2
0
0
1
0
1
1
1
1
0
2
2
0
0
0
0
2
1
1
0
2
1
2
1
0
0
1
0
0
0
0
2
0
1
0
0
2
0
1
0
0
0
1
2
1
4
0
0
1
0
1
0
0
0
0
2
0
1
0
1
0
2
3
0
0
0
1
0
0
1
0
2
1
2
1
0
1
1
0
2
2
0
0
1
0
0
1
2
0
1
0
2
0
2
1
1
2
2
0
0
0
0
2
1
2
1
1
0
0
2
1
2
2
0
1
2
1
0
1
3
0
0
0
2
0
1
0
0
3
0
0
1
0
0
2
1
3
1
0
0
1
2
0
2
1
0
0
2
0
2
0
1
1
0
0
0
1
0
1
1
0
0
1
2
0
1
2
1
0
0
0
1
0
0
2
0
1
0
0
1
1
2
1
1
1
1
2
2
1
0
1
2
1
0
0
1
2
2
1
0
0
0
0
1
1
2
1
1
1
0
0
2
1
1
1
0
2
1
0
2
1
1
0
2
0
0
1
1
1
2
0
1
2
1
0
0
1
0
2
1
2
0
1
0
0
2
0
0
0
2
2
1
0
2
1
1
0
0
2
0
1
0
1
1
0
1
1
0
1
1
0
0
3
0
0
0
0
0
0
3
0
0
1
0
1
0
0
0
1
0
1
2
1
2
1
0
2
2
0
0
0
2
0
1
0
0
0
1
0
0
0
1
0
0
0
0
3
1
0
2
2
1
1
1
0
0
2
0
2
1
0
2
0
1
1
1
0
0
0
1
0
0
2
0
1
1
1
0
0
2
1
5
1
0
0
1
0
0
1
0
1
2
2
1
0
0
1
2
3
1
0
2
0
1
2
0
3
0
0
0
1
2
0
1
0
1
1
0
0
3
0
0
1
1
0
1
0
1
0
1
1
0
2
1
0
2
0
1
0
1
0
0
0
1
0
2
0
1
2
0
0
1
1
0
2
1
2
2
0
0
3
1
1
1
3
1
0
0
2
1
1
1
2
0
1
0
0
3
2
2
0
1
0
1
0
0
1
2
0
0
2
0
0
0
2
0
1
1
0
2
0
0
0
0
1
1
0
1
0
2
2
0
0
0
1
0
0
0
1
1
0
2
0
0
1
0
0
0
0
0
1
2
0
1
1
0
0
0
1
2
0
1
0
0
0
1
1
2
2
0
2
0
1
1
0
0
1
2
2
0
3
0
1
2
0
1
0
0
0
1
0
0
0
1
2
0
0
2
1
0
0
0
0
0
1
0
0
2
1
2
1
2
0
1
0
2
0
1
0
0
2
1
1
0
2
0
1
2
2
0
0
0
0
1
1
1
2
0
2
0
0
0
1
0
0
1
1
0
0
1
0
1
2
0
0
2
0
0
2
0
0
0
1
2
0
1
0
1
0
0
1
1
0
0
0
0
0
0
1
2
1
2
0
1
1
0
0
1
2
1
2
0
0
1
1
0
0
1
0
0
1
0
2
2
1
1
1
0
2
0
0
0
2
0
0
1
0
0
0
0
2
2
2
0
0
1
0
1
0
1
0
0
1
1
0
1
0
2
2
2
1
1
2
1
0
2
0
2
2
0
0
2
0
3
0
1
0
2
0
0
2
0
0
0
0
0
0
2
2
0
1
1
0
0
1
0
2
2
1
0
2
1
2
0
0
0
2
2
0
1
0
0
1
1
0
1
1
0
0
1
1
0
0
0
1
1
0
2
0
1
0
2
0
2
2
2
0
1
0
2
2
0
2
0
0
1
0
0
0
2
0
2
0
1
0
1
1
0
2
0
2
2
2
0
1
2
2
0
0
2
0
1
0
1
0
1
0
0
1
0
2
0
0
0
1
2
0
0
1
2
2
1
4
0
0
0
0
1
0
1
0
0
1
0
1
0
2
1
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
3
2
2
0
1
1
0
1
0
0
0
0
1
0
2
0
0
0
2
2
3
0
2
2
1
0
1
0
0
0
2
2
0
1
0
0
2
0
0
1
0
1
1
0
1
0
0
1
2
0
2
0
1
1
1
2
1
0
1
0
0
0
0
0
0
2
1
1
1
1
0
0
1
1
0
0
0
0
2
1
0
0
1
1
1
0
0
2
1
0
0
0
1
2
1
2
2
1
0
0
0
0
1
1
1
0
0
2
0
0
1
0
1
0
1
2
0
0
1
2
0
0
0
2
0
1
2
1
0
1
0
0
0
1
0
2
0
0
2
0
0
1
0
0
0
0
2
1
0
1
0
0
0
1
0
0
2
5
1
1
0
0
0
2
2
1
2
2
0
1
0
1
1
0
0
0
0
2
1
0
0
0
1
0
2
1
2
1
0
0
1
1
0
1
1
1
1
1
2
2
2
0
1
1
2
1
1
1
0
0
1
1
0
2
3
0
2
1
1
1
1
1
0
2
0
3
2
0
0
2
2
2
0
2
0
1
0
1
0
2
0
0
0
0
0
1
1
1
0
0
1
0
0
2
1
2
2
0
1
0
0
1
1
1
1
2
1
0
1
1
2
0
1
1
0
0
0
1
0
0
4
0
0
2
0
0
2
1
2
1
1
0
0
0
0
2
2
2
2
0
1
1
1
0
0
0
0
0
2
0
2
2
1
0
1
0
1
0
0
0
0
0
1
0
0
2
1
1
0
0
0
0
1
1
1
1
2
2
3
2
1
1
0
0
0
0
1
1
0
0
2
0
2
0
0
2
2
0
0
2
0
0
2
0
2
2
0
0
2
3
1
1
2
1
2
1
0
1
0
1
0
1
2
0
1
0
1
1
0
0
0
0
0
2
0
0
0
1
1
0
0
2
2
1
0
0
2
0
2
1
1
0
2
0
2
0
1
1
1
1
0
3
0
1
2
0
0
1
2
0
0
1
0
1
2
0
1
0
2
1
2
2
2
0
0
0
0
2
0
2
0
2
0
1
2
0
0
0
1
0
0
1
1
0
1
0
1
1
0
2
0
1
2
0
0
0
2
1
0
1
2
0
0
2
2
0
2
2
2
0
1
0
0
2
1
2
0
0
0
0
1
1
1
1
0
1
2
1
0
0
1
0
0
0
0
2
0
0
1
1
0
0
1
0
0
3
2
1
0
0
0
0
0
1
0
0
2
0
2
0
1
0
2
0
1
1
2
0
1
2
0
1
1
1
2
0
0
2
2
1
0
0
0
0
0
0
1
0
2
1
2
1
1
2
0
0
1
1
0
0
1
1
0
0
0
0
0
1
2
1
2
0
1
1
2
1
1
0
0
0
0
2
2
0
2
0
3
0
0
2
0
1
1
1
0
1
1
1
1
1
0
0
1
1
2
0
2
1
1
1
1
0
0
0
1
0
2
0
1
1
1
0
0
1
2
1
0
1
0
1
0
0
1
0
0
0
0
0
1
1
1
1
1
0
0
2
2
0
0
0
1
0
0
4
0
2
0
0
0
0
0
1
1
1
0
1
0
0
0
1
1
2
3
0
0
1
0
0
1
0
0
2
0
0
1
0
1
1
0
2
1
0
0
0
0
2
1
1
1
2
1
1
0
2
0
0
0
0
0
1
0
0
1
4
1
0
1
0
2
2
1
0
1
1
1
0
2
1
0
1
0
2
0
0
3
0
1
0
2
0
1
2
2
1
0
1
1
2
1
3
2
2
0
0
1
0
2
1
1
2
1
2
0
1
0
2
2
1
1
1
1
0
2
0
1
2
1
2
2
0
0
1
1
0
0
0
1
0
1
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
2
1
1
0
2
1
0
1
2
0
1
0
2
0
0
0
1
2
1
0
0
0
0
0
2
2
1
1
1
2
0
0
1
0
0
1
2
1
1
0
0
0
1
2
1
1
0
0
0
2
0
0
2
1
0
0
0
0
0
1
0
4
1
1
0
1
0
0
1
1
2
0
0
0
1
2
1
1
2
2
0
2
0
1
2
2
0
0
0
2
2
0
2
1
0
0
2
1
0
2
0
1
0
0
0
0
1
0
1
2
0
1
0
2
2
1
1
0
1
1
0
0
0
0
0
0
0
2
2
1
0
0
1
0
0
0
0
0
0
2
0
2
1
2
2
0
1
0
0
0
1
0
1
0
1
2
2
0
0
0
2
0
1
0
1
0
0
0
0
1
4
0
0
0
1
1
0
0
2
2
2
0
1
1
0
0
2
0
1
1
1
0
0
2
0
0
1
2
1
0
1
0
1
0
0
2
1
0
3
2
2
2
0
1
1
2
3
1
0
1
0
1
1
2
0
0
1
2
1
0
2
1
1
0
2
1
0
0
0
1
2
1
0
1
0
0
3
1
0
1
0
2
0
0
0
2
1
2
0
0
0
1
0
1
1
0
0
2
1
1
1
0
1
0
1
0
0
0
0
0
2
1
5
1
2
0
0
0
0
1
0
0
5
2
1
2
0
0
1
2
0
1
1
0
0
0
0
0
1
1
1
0
2
0
1
0
1
0
0
1
0
0
0
2
1
0
1
2
1
1
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
2
1
0
0
0
2
2
2
0
1
0
0
2
1
0
2
1
1
0
0
1
0
1
0
2
0
0
1
0
0
0
0
0
2
1
1
2
1
0
0
0
0
0
2
0
2
0
0
1
0
4
2
1
0
0
0
1
0
1
2
0
0
1
0
0
0
2
0
1
2
4
1
1
1
1
2
1
0
0
0
0
0
1
2
0
0
0
2
1
1
1
0
1
1
0
2
0
2
1
0
1
1
1
1
4
2
2
0
2
1
1
2
2
0
2
0
0
1
1
1
0
0
1
1
1
0
0
0
2
2
1
0
0
1
1
1
1
0
2
0
2
1
0
2
1
3
0
0
1
0
0
1
1
0
0
1
2
0
0
0
0
0
0
0
2
0
1
2
0
1
0
2
2
0
0
1
2
0
0
0
0
0
1
1
2
0
1
2
2
2
1
0
1
1
0
2
1
1
1
2
0
0
1
2
2
1
1
0
0
0
0
0
0
1
0
1
1
1
1
0
0
1
0
0
0
1
2
0
2
0
1
2
2
0
0
1
0
0
1
1
1
2
2
2
1
0
1
0
0
1
0
1
0
2
1
2
1
2
0
0
1
0
1
0
2
0
1
0
2
0
0
0
1
0
1
2
0
0
0
1
0
1
1
1
0
1
0
2
0
2
0
0
1
0
2
2
0
0
1
1
0
2
2
2
0
1
0
0
0
1
1
0
1
0
0
2
1
1
1
1
2
1
0
0
2
2
0
1
0
0
0
2
0
3
1
0
2
1
0
0
1
1
2
0
2
1
0
2
0
1
1
0
0
0
1
1
0
2
1
0
1
1
2
3
2
0
0
1
0
1
2
2
2
0
0
0
2
0
1
2
3
0
3
1
0
0
0
1
1
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
2
0
2
0
1
0
2
1
3
0
0
2
0
0
1
0
1
1
2
1
2
1
2
0
1
0
1
0
0
2
0
4
0
1
2
0
0
0
1
2
0
2
1
3
2
0
0
1
0
1
2
1
1
0
2
0
0
0
0
1
1
0
1
1
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
1
1
0
0
0
1
2
0
0
0
0
0
1
0
0
0
1
0
1
0
2
0
2
0
0
0
2
0
0
1
0
2
1
2
1
1
0
0
0
0
0
1
1
1
1
1
0
1
1
2
1
0
0
2
2
0
2
1
1
1
1
2
1
2
0
1
0
1
1
1
1
2
0
1
0
2
2
0
1
2
0
2
0
0
1
0
2
0
0
0
2
1
1
0
2
0
0
0
0
2
1
0
0
0
2
2
1
1
0
0
1
2
1
1
0
0
2
1
1
2
1
0
0
1
0
1
1
1
0
2
1
0
0
0
0
0
2
0
1
0
1
2
1
1
1
1
1
2
2
2
0
0
0
1
0
4
0
1
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
1
1
0
1
0
0
0
1
2
1
0
0
0
0
0
0
0
1
1
1
1
1
2
3
1
0
0
1
2
2
1
0
0
0
0
0
2
1
1
1
1
2
1
0
2
1
1
0
0
0
0
1
0
0
0
2
0
0
1
1
3
3
0
1
1
1
0
0
0
1
1
1
2
0
0
0
0
2
0
2
0
0
0
0
1
2
2
0
1
0
1
0
0
1
0
1
0
1
2
0
1
1
2
1
2
0
2
0
0
1
1
0
1
2
0
0
0
2
0
0
0
2
1
0
2
1
1
2
1
0
0
0
0
2
0
2
0
0
0
0
1
1
0
0
2
0
1
0
1
0
1
1
1
0
0
0
0
0
0
2
0
0
2
1
1
0
0
0
0
0
0
1
0
1
2
1
1
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
1
0
0
0
1
2
2
0
0
0
1
0
1
0
1
0
1
0
1
1
2
1
0
2
0
1
0
0
0
1
0
0
3
0
1
1
1
3
1
0
1
0
0
0
1
0
1
0
2
1
0
2
1
1
0
0
1
1
2
1
0
2
1
0
1
0
0
0
2
0
0
1
0
2
0
0
0
2
0
1
0
0
0
1
2
1
1
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
1
0
1
1
0
1
0
2
1
2
0
2
1
2
1
1
0
0
0
2
0
0
0
0
0
1
0
2
1
2
0
2
1
0
0
2
0
1
1
0
0
1
2
0
1
1
0
1
0
1
0
2
0
0
1
0
0
1
2
1
2
1
2
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
2
2
2
1
0
3
2
2
2
0
1
0
0
0
2
0
1
1
1
0
0
1
0
1
0
0
0
1
1
1
2
1
0
0
1
0
0
2
0
0
0
0
0
0
1
2
1
1
0
3
0
1
1
0
0
1
0
2
2
0
0
2
1
1
1
0
0
0
0
2
1
0
2
0
0
1
0
2
0
1
0
0
3
1
0
0
1
2
0
0
0
0
0
1
0
2
0
2
2
1
1
2
1
0
1
1
1
1
0
0
2
1
0
0
0
1
1
1
0
0
1
1
0
0
0
1
0
2
0
1
0
0
2
2
0
0
1
1
3
0
2
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
2
0
2
1
1
0
0
0
2
2
0
0
2
2
2
0
0
2
2
2
2
2
0
0
0
0
0
0
0
2
1
1
0
1
1
2
0
2
0
0
0
1
0
2
0
0
0
2
0
0
0
0
1
0
0
0
2
0
1
2
0
2
0
1
1
2
0
0
0
3
0
0
0
2
0
0
2
1
1
1
1
0
0
2
0
0
2
2
0
1
0
0
0
2
1
0
1
0
0
0
0
2
2
2
0
0
2
2
2
1
1
0
0
1
0
2
2
0
1
1
2
1
2
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
1
1
2
1
0
0
2
0
2
0
0
2
0
0
2
0
2
1
1
1
2
0
1
1
0
2
0
0
0
0
0
2
0
0
1
2
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
1
1
0
1
1
1
0
0
1
4
0
1
0
0
2
0
0
0
1
1
0
1
0
0
4
1
1
0
1
2
0
0
0
0
0
2
1
0
1
2
0
1
2
0
1
0
1
1
1
2
1
0
2
2
0
0
1
2
0
0
1
0
2
2
0
1
1
1
0
0
1
0
0
0
0
0
1
1
2
2
1
1
0
1
0
0
1
1
1
1
3
0
1
0
0
0
0
0
1
2
1
3
0
1
0
2
2
0
0
1
1
0
0
0
2
1
0
2
0
2
0
0
2
0
1
0
0
1
1
1
0
1
0
1
1
4
0
0
1
0
0
0
1
0
2
0
1
0
1
1
0
1
0
0
1
2
2
1
1
0
0
1
0
0
1
1
0
0
1
1
0
0
1
1
0
1
2
0
0
1
1
2
1
2
1
0
0
0
1
0
0
2
0
2
0
0
2
2
2
1
2
0
0
0
0
2
1
2
0
0
0
2
0
0
1
2
0
0
0
0
0
1
1
0
1
4
0
1
2
2
0
3
0
1
1
1
2
0
0
0
0
1
0
1
0
0
1
0
1
0
1
0
0
1
1
1
0
1
0
2
0
1
0
0
2
1
2
2
0
1
1
1
1
0
0
0
1
1
2
2
0
0
0
0
1
0
1
0
2
2
1
0
1
1
0
1
0
0
2
1
2
1
0
1
1
0
0
0
0
1
0
4
0
0
0
0
0
1
0
1
0
0
0
1
1
2
2
1
0
0
0
0
0
0
1
0
0
2
0
2
0
0
2
0
0
2
0
3
0
0
0
0
2
0
1
1
0
1
0
1
0
1
0
1
0
0
1
1
2
0
0
0
0
0
1
0
0
5
2
0
1
0
2
2
1
0
2
0
0
0
1
0
0
0
0
1
0
0
1
2
1
0
0
1
0
1
0
3
0
0
0
0
1
0
2
0
1
1
0
0
1
2
1
2
0
2
0
1
2
0
0
2
0
2
1
2
0
1
0
1
2
0
0
1
2
1
0
0
1
1
0
0
2
0
0
0
1
0
1
0
0
0
2
1
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
2
1
0
2
0
0
0
1
2
3
2
1
1
1
1
1
0
0
2
0
1
0
0
0
0
1
1
0
0
1
1
1
0
1
0
0
2
1
0
1
2
2
1
0
1
0
0
1
1
2
2
2
1
0
2
2
2
0
1
0
1
1
1
0
0
1
0
0
2
2
2
2
0
1
0
2
1
1
0
2
0
2
0
2
0
1
1
0
1
1
1
0
1
1
0
2
0
1
1
0
0
1
0
2
0
0
2
1
2
0
0
1
1
0
0
0
2
1
2
0
0
0
1
2
1
0
1
0
0
2
2
0
1
0
0
0
2
1
0
1
1
0
2
2
0
1
1
1
0
1
2
1
2
3
1
0
0
0
0
0
0
1
0
2
1
1
0
0
1
1
2
1
1
0
0
0
5
0
0
2
1
0
0
0
2
1
0
0
2
0
0
1
1
2
1
1
0
0
0
0
0
0
2
1
1
2
2
1
1
2
1
1
2
0
2
0
1
0
2
0
1
0
1
0
1
2
0
1
1
0
2
0
0
1
1
0
0
0
0
1
0
1
0
2
1
0
0
1
1
0
2
0
1
1
1
1
0
0
2
0
2
0
1
0
2
1
1
0
0
0
0
1
1
2
1
0
2
0
2
1
0
2
1
2
1
0
1
2
2
1
0
1
1
0
0
0
0
1
0
0
1
1
2
1
0
0
1
0
1
0
2
2
0
0
0
0
1
0
1
0
0
1
1
2
1
2
0
2
2
2
1
1
0
1
0
2
0
1
0
0
1
0
0
1
2
2
1
2
0
1
0
0
0
0
2
0
2
1
0
1
2
1
0
0
2
1
1
0
0
0
0
1
1
0
1
2
1
1
0
0
1
1
1
0
1
1
0
0
0
0
1
0
1
2
0
0
0
0
0
1
0
2
1
1
1
0
1
1
1
1
1
2
0
0
2
0
1
0
1
2
1
0
3
1
1
1
1
2
2
0
0
1
0
1
1
1
1
0
0
1
1
0
0
0
1
0
0
0
1
1
0
0
0
0
2
1
0
2
1
2
1
2
0
0
0
2
0
1
0
2
1
1
1
0
1
0
2
0
0
0
0
1
0
0
1
1
1
0
0
2
1
0
0
1
2
2
2
2
1
0
1
0
0
2
0
2
1
1
0
2
2
0
0
0
0
0
1
0
1
2
1
0
0
1
0
2
2
2
0
0
1
0
1
3
1
1
0
2
2
2
2
0
0
1
0
0
2
0
3
0
2
2
0
2
2
0
0
0
0
1
0
3
2
0
0
0
0
3
1
1
1
1
2
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
1
1
2
1
0
1
1
0
0
2
2
0
1
0
1
0
2
2
1
2
0
0
0
1
2
2
1
0
0
1
0
0
2
0
1
0
1
0
0
1
1
2
1
2
0
1
0
1
0
1
0
0
2
2
1
0
0
2
2
1
0
1
1
1
2
2
1
1
0
1
0
0
1
0
0
0
0
1
2
2
0
0
0
2
0
1
2
3
1
2
0
0
0
0
0
1
0
2
2
1
2
1
0
0
0
0
0
1
1
1
3
0
0
0
1
1
0
1
1
0
1
2
0
1
1
2
2
0
0
2
0
0
1
0
0
0
0
0
2
2
1
0
0
2
1
0
0
0
1
1
0
1
1
0
2
1
0
0
0
0
1
1
1
1
0
0
2
0
1
1
1
1
2
0
1
2
1
1
1
3
2
4
3
2
0
0
0
0
3
0
2
0
1
0
0
0
0
0
0
3
0
2
0
2
2
1
1
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
2
1
0
0
0
1
0
0
2
1
0
1
0
2
0
2
1
1
0
1
1
0
0
2
1
0
0
2
1
1
1
2
2
0
0
1
1
1
1
2
0
0
0
2
1
1
1
1
0
2
1
2
0
2
1
1
0
2
2
1
1
0
3
0
2
1
1
0
0
1
0
0
0
2
2
0
1
4
2
1
1
0
3
0
2
1
1
0
2
1
2
2
1
0
1
0
0
2
0
2
0
1
0
0
0
2
1
0
1
2
1
0
0
2
0
1
0
1
1
1
0
1
0
0
1
1
1
1
1
0
0
0
1
1
2
1
1
0
1
1
2
1
0
1
0
3
0
1
0
0
1
0
0
0
1
1
2
1
0
1
0
1
1
1
1
1
0
0
1
0
0
1
2
0
0
1
1
2
1
0
1
0
0
1
0
2
1
0
1
0
0
2
0
0
1
2
0
0
0
3
2
0
2
0
1
2
0
2
1
0
2
0
1
0
1
2
1
1
0
1
2
0
0
0
0
2
1
1
0
0
0
1
3
0
1
0
1
1
1
1
1
0
0
1
0
0
2
1
0
0
1
0
1
0
1
3
0
1
1
2
0
2
0
1
1
1
0
1
1
0
1
0
0
1
1
2
0
0
3
1
1
0
0
1
1
0
2
0
1
1
2
0
1
0
1
1
1
0
2
1
0
1
2
1
2
1
0
1
0
0
0
0
0
1
1
1
1
1
1
2
1
0
0
2
0
1
1
0
0
1
0
2
1
0
2
0
0
2
0
0
1
0
2
1
2
0
0
1
1
1
2
0
1
0
0
1
1
1
1
2
1
0
0
1
0
0
0
2
0
0
0
0
0
0
1
2
0
0
1
0
1
0
0
0
0
1
0
0
2
2
0
1
0
0
1
1
2
1
0
2
1
0
4
1
0
1
2
1
1
0
1
1
1
2
2
0
1
2
2
0
2
2
0
2
0
0
1
0
0
2
0
0
0
3
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
1
2
0
0
1
1
0
1
2
1
0
2
0
2
0
3
1
2
2
2
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
1
2
2
0
1
1
1
0
0
1
0
2
1
1
2
1
2
0
1
2
0
2
1
0
1
0
1
1
1
2
0
0
2
1
0
1
1
0
0
1
0
1
0
0
2
0
2
1
0
0
1
0
0
2
0
1
2
1
0
2
2
0
1
0
1
0
2
1
0
1
3
0
0
2
1
3
0
1
1
1
0
2
0
1
1
0
1
0
3
1
2
1
0
1
0
1
2
2
0
2
0
0
2
1
2
2
0
1
1
0
1
0
1
1
0
1
2
2
0
2
1
1
1
0
0
1
2
2
0
0
1
0
2
0
0
1
4
2
2
0
0
0
0
0
1
0
1
0
2
0
0
0
0
2
1
2
2
1
1
2
0
1
3
0
0
1
2
1
1
0
1
2
0
1
0
1
2
1
0
2
1
0
0
1
0
0
1
2
2
0
0
0
0
0
0
1
1
2
0
1
1
0
0
0
0
0
2
1
2
1
0
0
2
1
0
0
0
1
0
3
0
4
2
2
2
2
2
2
1
2
0
0
1
1
2
0
2
1
2
1
0
0
1
1
1
1
1
0
0
2
0
2
0
1
0
0
2
1
2
1
1
0
1
0
0
1
1
2
0
1
2
0
2
2
2
0
1
0
0
0
0
0
0
1
0
1
2
1
0
0
1
1
1
0
0
0
1
0
1
1
2
1
0
2
2
1
1
0
0
2
1
1
1
1
0
0
1
0
2
1
2
1
0
0
2
1
2
2
0
0
0
1
1
2
1
0
1
1
2
2
1
1
0
0
0
0
0
0
0
1
0
0
0
2
0
7
1
2
3
1
0
1
2
0
1
2
0
1
0
0
0
2
4
1
2
0
2
0
1
0
1
1
0
1
1
2
0
1
1
1
0
1
1
0
0
2
0
0
2
1
1
0
0
2
1
1
0
0
1
1
2
0
0
2
2
0
3
1
0
0
1
0
1
2
0
2
1
1
0
0
1
0
3
3
0
0
0
1
1
1
0
2
0
1
2
0
1
0
2
1
1
0
0
0
1
0
1
0
1
1
1
0
1
2
2
1
2
1
2
3
0
0
0
1
2
2
2
2
2
2
1
0
0
0
0
0
1
0
2
1
2
1
0
0
1
0
2
0
2
0
0
1
1
0
0
1
2
1
1
0
2
0
0
0
2
2
0
1
2
0
2
3
2
0
2
0
1
1
0
1
2
3
1
0
0
0
0
1
0
1
0
0
1
1
1
1
0
2
2
0
2
0
0
2
0
0
0
2
2
0
0
1
0
0
1
0
0
0
2
1
1
0
1
0
1
0
0
1
0
0
1
1
2
0
2
1
2
3
0
1
1
0
0
2
1
0
1
0
1
0
0
2
1
2
2
2
0
1
0
2
0
1
0
0
0
2
0
2
1
0
1
0
0
0
0
0
1
3
0
0
2
2
1
0
2
1
0
1
0
0
0
0
1
0
0
0
0
1
1
1
0
0
2
0
1
2
1
2
1
0
2
2
1
0
0
0
0
2
2
2
0
0
0
1
1
1
0
1
1
2
2
1
0
0
1
1
0
0
0
0
0
0
0
1
1
1
2
0
2
2
1
1
0
1
1
0
2
0
2
1
0
0
2
0
0
1
2
2
0
2
2
2
0
0
1
2
2
1
0
1
0
1
0
1
0
2
0
0
0
0
1
1
0
1
1
0
1
1
1
2
1
0
0
2
1
0
0
1
0
0
0
1
2
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
2
2
0
2
0
1
0
0
1
0
2
0
0
2
0
0
0
0
0
0
2
2
1
1
1
0
2
3
0
0
0
2
0
0
0
0
0
1
2
0
0
2
0
0
2
1
0
0
2
1
1
1
1
1
0
1
1
2
0
0
1
0
0
1
2
0
1
2
1
1
0
1
0
1
0
0
0
1
0
2
1
1
0
1
0
1
2
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
1
1
1
2
0
1
0
0
4
0
0
2
0
0
1
0
0
0
1
1
0
0
1
3
2
0
2
2
0
1
0
0
0
0
1
1
0
0
2
0
1
0
2
0
0
0
0
1
2
0
0
1
1
1
1
0
2
0
1
0
1
0
1
0
1
0
1
1
2
0
1
0
1
1
0
2
2
1
1
0
2
0
1
0
2
2
0
0
1
0
0
1
0
0
1
0
0
2
0
0
0
0
1
1
0
1
1
0
2
0
1
2
1
1
2
1
1
2
0
0
1
1
0
1
0
1
1
1
0
0
1
2
0
1
0
0
2
1
0
0
0
1
2
1
0
1
0
0
0
0
1
2
3
0
2
0
0
1
0
1
0
0
0
2
2
1
2
1
0
0
1
0
2
0
1
1
0
1
1
0
1
2
0
0
1
0
1
0
1
4
2
2
0
1
1
0
0
2
1
0
1
0
1
0
1
2
0
0
0
2
0
0
0
0
0
2
1
0
2
1
2
1
0
2
0
0
0
0
0
0
1
0
2
0
1
2
2
0
2
1
0
1
1
1
0
2
0
1
2
1
1
3
0
0
2
1
2
0
1
1
2
0
0
2
0
1
0
1
0
1
0
1
0
0
1
3
1
0
0
0
0
2
0
0
0
2
0
0
1
0
1
1
1
1
2
4
0
0
0
2
2
1
0
0
2
0
2
0
1
2
2
0
2
1
1
0
0
1
0
1
0
0
1
2
1
0
0
0
0
1
0
0
0
1
1
2
2
2
2
1
2
2
1
1
0
2
1
2
0
2
0
2
0
0
0
1
1
0
0
0
1
0
2
0
1
3
1
0
0
0
1
1
1
0
1
0
2
0
1
0
2
0
2
0
2
1
1
2
1
4
1
0
4
0
0
1
0
0
0
0
0
0
0
4
1
0
2
0
0
0
1
2
1
0
0
0
1
1
0
1
1
1
0
1
0
1
1
0
2
0
1
1
2
0
1
1
0
1
1
1
1
0
0
1
0
1
1
2
0
0
1
0
1
2
0
0
0
1
1
0
0
0
0
2
1
1
1
2
1
3
0
0
1
0
2
1
0
2
1
0
1
0
1
0
0
0
0
0
1
2
0
2
0
0
1
2
1
2
0
0
1
2
0
1
1
2
0
2
0
0
0
1
0
2
0
1
2
0
0
0
2
0
2
1
2
0
2
2
1
0
0
1
0
0
1
0
2
0
2
1
0
0
4
0
1
0
0
2
0
2
1
2
1
2
0
1
0
0
1
2
0
1
1
0
0
1
0
1
0
1
2
1
2
2
1
1
0
1
0
0
0
2
0
0
1
0
0
0
0
1
1
0
1
1
2
1
0
0
0
0
0
0
0
0
2
0
0
1
2
1
1
0
0
1
0
0
1
0
0
2
0
1
0
1
0
2
0
0
1
0
0
2
1
0
0
0
2
1
2
1
1
1
2
0
1
0
0
0
1
0
2
0
2
2
1
0
1
1
0
3
1
0
0
1
1
1
0
1
0
0
0
1
0
2
1
1
1
1
0
2
1
0
0
1
0
1
0
2
1
0
0
1
0
0
0
2
0
0
0
1
2
1
0
1
2
0
0
0
0
0
0
0
1
2
2
2
1
1
0
0
0
0
2
2
1
0
0
1
0
0
1
1
0
0
0
0
0
0
2
0
0
1
0
0
0
2
1
0
0
0
1
2
2
2
1
0
2
0
2
0
0
0
1
2
0
1
0
0
0
0
4
1
0
0
0
1
0
2
2
1
0
2
1
0
0
2
0
0
1
1
1
1
1
1
1
0
0
2
1
0
1
0
0
2
1
0
2
0
0
1
1
0
2
2
1
0
1
1
1
0
2
1
0
2
1
0
0
0
2
2
1
2
0
1
0
4
0
0
0
2
0
2
0
1
1
0
0
0
0
1
1
0
0
0
2
1
0
0
1
0
0
0
0
2
0
2
2
0
2
2
0
1
0
0
1
1
0
2
1
0
2
1
1
2
0
1
0
0
1
0
1
1
0
1
1
0
0
0
0
0
0
1
1
0
2
0
2
0
2
0
0
0
2
0
1
0
0
0
0
1
1
0
2
2
0
1
0
0
0
1
0
0
1
1
1
0
2
1
1
0
1
1
0
0
0
0
0
2
1
0
1
2
0
1
0
0
2
0
2
1
0
1
0
0
0
2
2
1
0
2
0
1
1
0
1
1
0
2
2
1
1
2
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
3
1
1
1
0
0
0
1
1
3
0
1
0
0
0
0
1
0
1
2
0
0
2
2
2
1
1
0
2
0
1
2
1
1
1
1
1
0
0
2
1
0
0
0
1
1
0
1
0
0
0
1
2
1
1
0
1
0
1
2
0
2
0
0
2
2
0
0
1
0
5
0
1
0
0
0
0
0
0
0
0
0
1
0
2
2
0
1
1
0
0
0
2
0
0
0
0
0
0
0
2
0
1
1
1
2
0
1
0
1
0
0
1
0
0
0
2
0
2
1
2
0
0
0
1
0
2
1
1
2
1
1
1
2
0
1
0
1
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
3
0
0
1
2
0
1
0
0
0
2
2
0
1
2
0
1
1
1
1
0
1
0
1
1
3
0
0
0
1
0
2
1
0
0
1
0
0
0
1
0
0
2
1
2
1
0
1
0
0
0
0
1
1
2
0
2
0
1
0
1
1
0
1
0
4
1
1
1
2
0
1
2
1
2
1
1
1
0
2
0
1
1
1
3
1
2
2
2
0
1
0
0
1
0
0
2
0
1
0
1
0
0
2
0
2
0
0
2
1
0
1
2
1
0
1
0
0
0
2
0
2
0
1
1
0
0
0
1
1
2
0
0
0
2
1
2
1
0
2
0
1
1
0
1
2
2
2
1
0
1
0
0
0
0
0
2
1
1
0
0
0
0
0
1
2
0
1
2
0
1
0
2
2
1
0
2
1
2
1
0
2
0
0
2
0
2
0
1
1
1
2
0
0
2
1
2
1
0
0
1
0
0
1
0
2
0
0
0
0
0
0
3
0
1
0
0
2
1
0
0
2
0
0
2
1
0
0
0
2
1
2
2
2
0
0
2
0
1
0
0
0
0
1
0
3
1
0
2
0
0
0
0
1
1
2
0
0
1
0
0
0
2
0
0
0
1
2
1
0
1
2
0
2
0
1
1
1
0
1
0
1
1
1
0
0
0
0
0
1
0
0
1
2
2
0
0
2
0
0
1
0
1
1
1
0
1
0
2
0
0
0
0
1
0
1
0
0
0
0
2
4
2
0
2
0
0
2
1
2
2
2
0
1
0
1
1
5
0
2
0
0
1
1
1
0
1
1
0
0
0
1
0
0
0
1
0
1
0
1
2
1
3
1
1
0
0
0
2
0
1
1
0
0
0
0
0
1
1
0
2
2
1
1
1
1
1
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
2
1
0
0
0
2
2
1
1
0
1
0
1
1
0
0
1
0
0
3
2
1
2
1
2
1
0
2
1
2
0
2
2
0
0
0
0
0
1
2
0
2
0
1
2
1
0
1
2
1
1
2
0
0
0
0
2
1
3
2
1
0
0
0
1
2
2
1
0
2
2
0
0
0
0
1
0
1
0
0
0
0
1
2
0
2
0
0
0
2
0
2
0
0
0
1
1
0
0
0
1
0
0
1
1
0
0
0
2
0
0
0
1
0
2
0
1
2
1
0
0
1
2
0
0
0
0
0
2
0
0
0
0
2
1
2
0
0
1
2
1
0
2
0
1
4
0
2
1
1
1
3
2
1
0
0
0
1
0
0
0
0
2
0
0
0
0
2
1
1
2
1
0
0
0
2
2
1
0
0
1
2
0
0
1
1
0
1
0
1
2
0
0
0
2
2
0
2
0
1
1
2
1
2
2
0
1
0
1
1
0
0
1
0
2
0
2
2
0
2
0
2
2
0
1
1
0
0
0
1
1
0
0
0
2
1
1
1
1
1
0
2
1
0
0
1
0
0
0
1
2
1
1
0
1
2
2
1
1
1
1
0
0
2
0
0
1
2
0
2
2
1
0
1
0
1
2
1
0
1
1
0
0
0
1
2
1
1
1
0
1
0
2
0
2
0
1
1
0
0
0
2
1
1
0
0
1
1
1
3
0
2
2
4
1
1
2
1
0
1
1
0
1
0
0
0
2
1
1
1
1
2
2
0
2
0
1
0
0
0
0
1
0
1
1
2
2
0
0
0
1
2
1
2
0
0
1
0
0
1
2
1
0
0
1
1
0
1
1
1
0
1
0
0
3
2
2
2
1
2
1
0
0
0
2
0
1
0
1
0
0
0
0
1
0
1
0
2
1
0
2
1
1
0
0
0
0
0
0
2
0
1
1
1
1
0
0
1
0
0
2
0
0
1
1
0
0
0
1
0
0
1
2
0
1
2
0
0
1
0
0
0
0
1
0
2
2
0
1
0
0
0
1
0
1
1
0
0
1
2
1
2
2
0
1
1
2
0
0
1
2
0
0
0
2
1
1
0
0
0
1
1
1
1
1
0
0
0
1
0
1
1
0
1
0
0
2
0
1
2
0
1
0
0
0
0
0
1
0
0
2
2
0
2
1
2
0
0
1
1
1
0
2
0
0
4
0
0
2
1
0
0
0
0
0
1
0
0
1
1
1
0
2
1
1
0
1
0
0
2
1
1
0
0
2
2
2
0
2
0
1
0
0
0
1
2
0
0
0
0
1
1
1
0
0
1
0
0
0
0
1
0
2
2
1
0
0
0
0
1
2
1
1
2
0
2
2
1
0
0
1
2
2
0
1
1
1
1
2
0
0
1
0
0
1
0
0
0
0
0
0
2
1
1
0
2
1
0
0
0
1
2
3
2
1
0
0
2
1
2
0
0
1
2
3
1
2
0
0
0
0
1
1
2
0
0
1
1
0
1
0
0
2
1
1
1
1
0
0
0
0
2
2
2
2
0
1
1
3
3
0
0
0
2
1
0
0
0
1
1
0
2
0
0
1
2
0
0
0
1
0
1
2
1
1
1
0
2
0
1
2
0
2
0
0
0
0
0
0
1
0
1
1
2
0
0
0
1
0
1
1
0
2
2
1
0
0
2
1
1
2
0
0
0
1
0
1
2
0
1
1
0
1
0
1
1
1
0
1
0
0
2
1
0
0
1
0
0
2
2
1
0
2
2
2
0
0
1
0
0
2
0
0
0
0
0
1
1
0
1
2
1
1
0
0
2
0
2
2
0
0
1
0
0
1
0
1
3
2
0
0
0
1
1
2
0
1
3
2
1
0
2
2
1
1
1
0
2
0
1
1
0
0
1
0
0
6
0
5
1
0
0
1
0
3
0
0
2
1
2
3
0
2
0
1
0
2
0
1
2
0
2
1
0
1
0
0
0
0
0
0
1
1
0
0
1
1
2
3
2
0
1
0
2
0
1
0
0
0
0
1
2
0
1
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
2
2
0
0
1
0
0
1
2
0
0
0
0
2
0
2
8
1
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
1
2
0
1
0
1
0
1
1
2
0
0
1
0
0
2
0
1
0
1
2
0
0
1
2
1
2
2
0
0
2
1
1
1
1
2
0
1
3
2
2
0
2
0
0
0
0
1
0
1
0
0
1
2
0
0
1
1
2
2
1
0
1
0
2
0
0
3
0
0
2
1
0
0
1
0
0
0
0
0
0
0
2
0
2
0
1
0
2
0
1
1
1
0
1
0
0
2
0
0
2
0
2
2
2
2
1
0
0
0
0
3
0
1
1
0
2
0
0
0
0
2
1
1
0
2
1
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
3
0
2
1
1
2
1
0
1
0
0
0
1
0
0
1
0
2
2
2
0
0
0
0
1
0
0
1
2
0
2
1
1
2
0
1
3
1
1
0
0
2
0
1
0
0
1
0
1
2
0
2
0
0
2
1
3
4
2
1
1
2
2
1
3
0
0
1
1
0
1
1
0
1
1
0
0
0
0
0
0
2
1
0
1
2
0
0
0
0
0
1
0
0
0
2
1
2
2
1
1
0
0
1
3
2
3
2
2
1
1
0
2
0
0
2
0
1
1
2
0
1
0
1
0
0
0
0
0
1
0
0
1
2
0
0
1
0
1
0
1
0
1
2
2
2
0
1
1
0
1
2
2
0
2
1
1
1
1
0
0
0
1
2
0
1
2
1
2
2
2
1
0
1
1
0
1
1
1
0
1
0
0
0
0
2
1
2
2
1
2
1
0
2
0
0
2
0
0
1
0
1
1
1
1
2
0
0
2
0
1
1
1
0
2
2
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
1
2
0
0
1
2
2
0
0
1
1
0
0
0
0
2
1
1
0
1
0
0
2
0
0
0
0
0
1
0
1
0
2
2
2
1
1
2
3
1
1
1
0
0
0
0
2
1
2
2
0
0
1
0
2
0
0
1
0
1
0
1
1
1
1
0
1
1
1
1
0
0
0
1
1
1
1
0
0
1
0
0
3
1
1
2
0
0
1
2
1
0
1
0
2
2
0
1
1
0
2
0
0
0
1
1
1
2
1
1
1
2
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
2
0
2
0
2
0
2
0
1
0
0
2
1
1
0
1
1
1
1
0
1
0
0
0
1
1
2
0
1
0
0
0
0
1
0
1
0
0
1
0
2
2
1
0
0
0
2
0
1
0
0
1
0
0
0
0
2
0
0
2
1
0
2
0
0
0
1
1
3
4
2
0
0
2
2
0
0
1
0
1
0
2
0
1
0
0
0
3
2
2
0
2
1
2
0
0
0
0
0
1
0
0
1
0
0
5
2
0
2
2
0
0
0
1
2
0
0
0
0
0
0
0
2
1
0
1
0
0
1
1
2
2
0
0
2
2
1
0
2
1
0
1
1
1
1
0
1
0
0
1
2
0
2
1
0
1
1
2
2
5
0
2
2
1
1
0
1
0
0
0
1
2
0
1
1
0
1
0
0
0
0
4
1
1
0
0
1
0
3
0
1
0
0
2
1
2
0
2
0
1
1
0
0
0
0
0
2
1
1
0
0
1
1
0
0
0
1
2
3
2
1
1
0
2
1
0
0
1
0
1
0
1
0
0
2
1
0
0
1
2
0
0
0
0
1
1
1
2
2
2
0
1
1
2
0
0
0
0
2
0
1
1
2
0
0
1
0
0
1
1
2
0
1
0
2
2
2
0
2
1
0
0
1
0
2
0
0
1
0
2
1
0
1
0
0
1
0
1
1
0
0
0
2
0
1
0
1
0
1
2
2
0
0
1
1
2
1
0
0
1
1
0
0
0
1
1
1
0
0
1
0
2
0
1
1
0
0
0
1
0
2
0
1
1
0
0
0
1
2
0
0
1
1
1
2
0
1
1
0
0
0
0
0
0
2
1
2
0
0
0
0
1
1
1
1
2
1
2
0
2
0
1
0
0
1
1
1
0
1
0
0
0
2
0
0
1
2
1
2
0
2
0
2
0
2
0
0
0
1
2
1
1
1
0
0
0
1
1
1
0
0
0
0
0
1
1
2
1
0
0
0
0
2
0
1
1
0
3
1
1
1
0
1
2
0
0
1
0
2
1
2
0
1
0
2
1
1
2
0
1
2
2
1
1
1
0
0
1
1
1
2
2
1
1
2
0
0
0
1
1
2
1
0
3
2
0
2
0
0
2
0
1
0
2
0
2
2
1
0
1
0
0
1
0
0
1
1
0
0
0
0
2
2
1
2
0
0
1
0
0
1
0
1
0
1
0
1
0
3
2
0
0
1
1
1
0
0
1
1
1
1
1
0
0
0
0
1
2
2
0
0
2
0
0
0
0
0
0
0
0
2
1
1
1
0
0
0
0
0
2
0
1
1
0
0
0
0
2
0
0
1
0
1
1
1
1
2
0
2
0
0
2
0
0
1
1
2
1
2
1
2
0
0
1
1
2
0
0
2
0
2
1
1
0
1
1
0
0
2
0
0
2
1
0
2
1
1
0
0
0
2
0
0
0
1
0
1
0
1
0
2
1
0
1
1
1
0
1
2
1
1
1
2
0
0
0
0
0
0
1
0
1
0
1
0
0
4
0
2
2
1
3
0
2
0
0
1
2
1
1
1
1
1
0
0
1
0
1
1
0
2
0
1
0
0
0
5
0
2
0
0
2
1
1
0
2
0
0
2
1
0
1
3
1
0
1
1
0
1
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
2
0
2
0
2
0
0
1
1
1
0
1
0
2
0
2
2
1
0
0
0
0
1
0
0
2
2
0
0
2
1
2
0
1
0
0
1
0
0
0
0
0
1
0
2
0
0
2
0
0
0
1
3
0
0
0
0
0
1
0
2
0
0
3
0
0
0
2
1
1
1
0
0
0
2
1
1
0
1
0
1
0
1
1
0
1
2
2
2
1
0
0
1
0
0
0
3
2
0
2
2
3
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
1
2
1
1
0
1
1
0
0
0
0
0
2
0
0
2
0
0
0
0
1
1
1
2
0
1
1
1
2
2
0
2
0
0
0
2
0
1
1
2
0
1
1
1
1
1
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
1
1
0
0
2
2
0
0
0
3
0
0
2
0
1
0
0
0
2
1
0
2
0
0
0
1
1
0
1
0
2
0
2
2
0
1
1
2
2
0
2
2
0
1
0
1
0
1
0
2
1
1
1
2
0
3
1
0
1
0
1
0
1
0
0
2
0
0
1
0
0
1
0
1
0
0
1
0
0
1
1
1
2
0
0
1
0
1
1
1
0
0
3
1
0
0
2
1
1
1
2
2
0
1
0
2
0
1
0
2
0
1
4
0
4
2
0
0
0
0
0
0
1
0
2
0
1
0
0
2
0
0
1
2
2
0
0
1
0
2
0
2
1
1
0
1
3
1
1
0
0
0
1
0
5
0
1
0
1
0
1
2
1
0
1
1
2
2
2
1
0
2
1
0
2
0
1
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
2
1
1
2
1
0
1
1
0
0
0
0
1
0
0
0
2
2
2
0
1
2
0
0
0
0
0
0
1
1
0
2
2
0
0
2
1
1
1
0
0
0
0
0
0
1
3
1
0
0
1
1
0
0
2
0
2
2
2
3
1
1
1
2
1
1
1
0
0
1
0
1
0
1
2
0
0
1
0
0
0
0
1
1
0
0
1
1
1
1
1
0
1
0
0
1
1
0
0
1
0
1
0
4
0
0
0
1
1
0
1
0
0
1
0
1
1
0
1
0
1
1
2
1
2
0
0
1
0
1
1
0
0
1
0
0
0
2
1
0
2
2
1
2
0
0
0
2
2
1
2
2
0
0
0
2
0
2
1
2
2
1
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
1
0
0
0
0
1
1
0
2
1
1
0
2
0
2
0
2
0
2
0
1
1
1
2
0
3
0
0
1
1
0
1
0
1
1
0
1
2
2
2
0
0
2
0
1
0
2
0
1
1
0
0
1
0
1
2
1
2
0
0
0
1
2
0
2
2
0
3
0
0
2
1
0
2
0
0
0
0
1
1
0
2
0
1
2
0
0
0
0
0
1
2
1
0
0
0
1
0
0
0
0
1
10
0
1
0
1
1
1
0
0
1
1
1
1
1
0
2
6
0
2
2
3
1
0
0
2
2
2
0
2
0
0
1
2
1
0
0
1
0
2
0
1
0
1
1
0
1
1
1
0
0
2
0
1
0
0
0
1
1
1
1
0
0
0
2
2
1
1
2
0
0
1
0
0
0
0
2
2
0
2
2
0
0
1
0
1
0
2
1
2
1
1
0
0
1
2
2
0
0
0
2
1
1
1
0
2
1
2
2
0
2
0
0
0
0
1
0
0
1
1
0
0
1
0
0
1
1
0
1
1
2
0
1
0
0
1
0
0
0
2
0
0
0
1
0
0
1
1
1
0
2
0
1
0
0
1
1
1
2
1
2
0
0
0
1
0
2
1
0
0
2
0
0
0
1
0
0
2
2
2
0
1
0
0
0
1
0
1
1
0
1
0
0
1
1
0
1
1
2
0
0
2
0
3
1
0
0
0
0
2
0
1
0
0
0
0
0
1
1
0
1
2
0
0
0
0
0
0
1
2
0
0
0
0
1
0
1
0
2
0
0
1
0
0
2
0
0
1
0
0
0
1
1
1
2
0
1
0
2
0
0
0
0
0
0
0
1
1
2
2
0
0
0
1
0
2
1
1
2
0
1
0
2
2
0
0
0
2
0
2
1
1
1
2
0
0
0
0
0
0
1
0
2
0
0
1
2
0
0
2
0
1
0
1
2
2
1
1
1
0
2
2
0
2
1
0
2
2
0
2
0
1
2
2
0
0
1
0
1
2
0
2
0
1
2
1
1
2
1
0
1
4
1
1
0
2
0
2
1
1
2
2
2
0
0
1
0
1
0
2
1
1
0
0
0
0
0
1
2
0
1
0
1
1
0
1
0
2
1
0
2
1
1
1
0
1
1
0
0
0
0
1
0
2
0
0
0
0
0
2
0
1
1
0
0
2
1
1
2
0
0
0
0
0
0
0
2
1
0
0
1
1
0
1
1
0
1
0
0
0
1
0
0
0
3
1
4
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
2
0
1
0
0
0
0
1
1
1
0
0
0
2
0
1
0
2
0
0
1
2
2
2
2
1
1
0
2
0
1
3
0
0
1
1
0
1
0
0
0
0
1
2
0
1
0
0
0
0
0
4
0
0
1
1
0
0
1
0
0
0
1
2
2
2
0
2
0
1
2
0
3
1
1
0
0
0
2
1
1
0
0
0
1
1
1
0
0
1
2
2
1
1
2
1
1
2
2
0
2
0
0
0
0
2
2
2
0
0
1
1
1
0
2
2
0
0
2
1
3
1
0
2
1
1
0
1
0
2
0
2
0
2
2
0
2
0
0
2
3
0
2
0
0
0
2
0
1
2
0
2
2
1
0
2
1
1
2
0
1
0
2
2
1
0
0
0
0
0
0
1
1
1
2
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
3
0
0
1
1
2
0
0
1
0
0
2
3
1
0
2
0
0
0
0
1
1
2
1
0
0
1
1
1
0
0
2
0
1
1
4
1
1
0
2
2
1
2
1
0
0
0
1
0
0
2
1
0
0
0
3
0
2
0
1
1
0
0
1
1
1
2
0
2
0
1
0
2
1
0
0
0
0
0
0
0
1
0
0
2
1
0
0
2
0
0
2
2
2
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
3
2
1
1
1
4
1
0
2
3
0
0
0
0
2
1
2
0
0
0
0
0
2
0
2
0
0
0
1
2
0
0
2
0
1
2
1
0
0
1
2
1
0
0
0
2
2
1
1
0
3
1
0
1
0
1
1
2
0
1
2
0
4
0
2
0
4
1
0
0
2
2
1
0
0
0
0
0
1
1
0
1
0
2
1
1
1
1
2
0
1
0
0
0
0
0
1
1
2
0
0
2
0
0
0
2
0
0
1
1
2
0
0
1
2
1
0
1
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
2
0
1
1
0
1
0
0
0
1
0
1
0
1
0
0
1
0
0
0
1
0
1
2
0
0
2
1
2
2
0
1
0
0
2
2
0
0
0
1
1
3
0
1
0
2
0
1
0
0
2
2
1
2
1
1
0
1
1
0
0
2
1
0
0
0
0
1
1
0
0
0
1
2
2
0
0
0
0
1
2
2
0
1
1
2
2
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
1
2
1
0
1
1
0
0
1
0
0
2
0
1
2
1
1
2
3
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
2
0
0
0
1
1
2
0
2
0
0
0
1
0
2
1
1
0
1
1
0
1
1
1
1
2
1
0
0
2
1
1
0
2
0
0
1
1
0
0
1
0
1
0
1
0
1
2
0
1
2
4
1
0
0
0
0
1
1
2
0
0
2
0
1
2
2
2
0
0
1
1
2
0
2
2
1
1
2
0
0
2
1
1
0
1
0
1
1
0
0
2
1
1
2
1
0
0
1
0
0
0
0
2
0
0
1
1
0
2
1
0
1
1
1
0
0
2
2
2
0
1
0
1
0
2
0
2
0
0
0
1
2
0
0
0
1
0
2
1
0
1
2
0
2
1
0
0
1
1
0
1
2
0
1
1
1
2
2
1
0
0
2
0
0
0
1
0
2
1
0
2
1
0
1
0
0
1
0
1
2
0
1
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
1
1
1
1
0
0
1
0
1
2
0
0
3
0
0
0
1
0
0
1
0
0
1
1
0
0
2
1
4
1
0
0
0
0
0
0
2
1
1
1
1
1
1
3
1
1
0
2
1
0
1
1
1
0
1
0
2
1
0
0
2
0
0
0
1
3
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
2
2
0
0
1
0
2
0
0
1
0
0
0
0
1
0
2
3
1
1
0
1
0
1
0
1
0
1
1
0
2
1
0
1
2
0
0
0
1
2
0
0
1
2
1
0
1
1
1
0
0
1
0
0
0
2
0
1
1
1
0
0
0
2
1
0
1
2
1
1
0
0
0
0
0
1
0
0
1
2
1
1
0
1
0
2
1
2
0
0
2
1
0
0
1
0
2
0
1
2
0
2
2
2
0
0
1
0
2
0
2
2
0
1
1
0
1
0
1
2
2
1
3
0
1
0
2
0
3
0
1
0
1
0
1
0
1
0
2
0
0
0
2
1
0
0
0
0
2
2
1
1
1
0
0
0
0
2
2
1
1
0
2
0
2
1
2
1
1
0
1
1
0
0
2
0
1
1
1
0
0
0
3
2
2
2
0
0
0
2
2
0
0
2
1
1
0
0
0
0
0
1
0
0
1
2
1
0
1
2
3
1
0
0
2
1
1
2
1
0
0
2
0
0
1
1
1
1
0
2
2
1
1
1
0
0
2
1
0
0
0
1
0
0
2
2
0
1
0
0
0
1
1
1
2
2
0
1
1
2
1
0
1
0
1
1
0
1
1
0
0
0
1
1
2
0
1
1
1
1
1
0
0
2
2
2
0
0
1
1
0
0
0
2
1
1
1
0
3
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
1
1
2
2
1
0
0
0
2
1
2
0
0
1
1
1
1
0
1
0
1
2
1
0
1
0
1
0
0
0
0
0
1
0
2
0
1
0
0
0
0
1
2
0
0
2
1
1
1
0
1
0
2
1
2
0
0
0
1
1
1
0
0
0
0
1
1
2
0
0
1
2
0
0
2
0
0
0
0
1
0
0
3
0
1
0
1
0
1
0
0
0
1
0
1
0
0
2
0
1
1
0
1
1
1
0
0
0
2
2
0
1
0
1
0
1
0
2
0
0
0
0
1
0
1
0
0
0
2
1
0
0
0
0
2
2
0
1
0
2
0
1
0
0
0
2
1
1
0
1
0
1
0
0
1
1
1
0
0
1
2
1
0
2
0
0
1
0
0
1
1
1
0
0
2
2
1
2
1
2
1
0
0
1
1
1
2
0
1
0
1
1
1
2
0
0
1
2
0
0
1
0
1
0
2
0
1
1
0
0
1
0
1
1
1
2
1
2
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
1
0
0
0
0
0
1
0
0
0
1
1
1
0
1
2
1
0
0
0
1
1
1
0
0
0
2
1
1
0
2
0
1
1
2
0
2
0
2
0
1
0
1
0
1
0
1
0
0
0
1
1
2
0
1
0
0
0
0
1
2
2
2
2
1
1
0
1
0
0
1
0
2
1
1
1
0
1
1
1
2
0
0
0
0
1
0
1
0
2
0
1
0
2
1
2
0
2
0
0
0
0
1
0
1
1
2
0
0
1
1
1
0
1
0
1
1
0
0
0
1
2
0
0
1
2
1
2
0
0
1
0
0
1
0
2
0
1
0
0
3
1
1
0
0
1
2
2
1
0
0
0
0
2
0
0
0
2
2
1
0
0
0
1
0
1
2
0
0
1
1
0
1
1
0
0
0
2
1
2
0
1
1
1
1
1
1
2
2
2
0
0
0
1
0
5
0
1
2
1
2
0
0
1
2
0
2
0
0
0
1
0
0
0
1
0
2
0
0
0
2
1
2
2
1
1
0
2
1
1
1
0
0
1
1
2
0
0
1
1
1
1
0
1
0
0
1
0
1
0
0
0
0
2
0
0
0
0
1
1
0
0
3
2
2
1
2
0
1
1
0
1
2
1
2
0
0
0
2
2
0
2
0
0
1
1
0
2
0
1
0
0
2
4
0
1
1
0
1
1
0
0
0
0
1
2
0
3
0
0
0
1
0
1
0
1
0
1
2
2
0
0
1
1
1
1
2
1
1
0
0
1
2
2
1
2
0
2
1
1
2
0
8
2
4
1
2
1
1
4
0
0
1
0
2
0
0
1
2
0
0
2
1
2
1
0
1
1
0
2
2
1
1
0
0
0
2
2
0
2
1
0
0
1
3
0
1
0
0
2
1
0
4
2
1
2
1
1
0
0
0
0
2
0
2
1
1
1
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
1
1
1
1
0
2
1
0
0
0
0
2
2
0
0
3
1
2
0
1
1
0
1
2
0
0
0
2
0
1
0
0
1
1
2
3
0
1
1
3
1
2
0
1
2
1
0
0
2
0
2
2
0
1
0
2
2
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
2
2
0
2
0
2
2
0
0
2
1
1
1
1
0
2
0
0
0
3
1
1
2
1
1
1
0
2
0
2
0
0
3
0
1
1
0
0
0
1
2
2
0
0
1
0
2
0
2
0
1
0
1
2
0
0
0
2
0
0
0
2
1
1
1
1
3
0
0
1
1
0
1
1
0
2
1
1
1
0
0
0
1
0
1
2
0
1
1
2
0
1
0
1
2
1
2
1
2
0
1
1
1
2
1
1
0
0
0
0
0
2
0
2
0
0
0
2
1
2
1
1
0
2
2
0
2
0
1
0
0
1
0
5
1
2
1
0
0
0
0
0
2
1
1
0
0
0
1
1
0
2
0
0
1
0
2
0
1
0
0
0
0
1
1
1
1
1
1
0
0
0
0
0
2
1
0
0
2
0
1
0
1
0
2
0
0
2
1
0
2
0
2
0
1
1
0
0
0
2
0
0
0
0
0
0
2
0
0
1
2
0
0
1
1
2
0
0
0
0
0
1
0
2
0
1
0
0
1
0
0
0
3
0
0
1
0
0
0
0
1
1
1
2
1
0
2
2
2
0
0
1
3
0
2
1
0
2
0
0
0
0
0
2
2
1
3
1
1
1
2
0
1
0
0
0
2
1
0
2
2
0
1
1
1
0
0
2
1
0
2
2
0
0
0
2
0
2
2
2
1
2
1
1
0
0
1
0
0
2
0
1
1
1
1
0
2
1
1
0
0
2
0
0
1
1
1
0
0
0
3
0
1
0
0
0
0
2
0
0
0
1
1
0
2
2
2
1
0
2
0
0
0
2
1
1
2
2
0
1
0
0
3
0
1
2
0
1
2
2
1
0
1
2
0
1
0
0
2
0
0
0
1
1
1
2
1
1
2
0
2
2
0
1
2
2
2
2
1
0
2
1
4
0
0
0
0
0
1
0
0
1
0
0
2
1
1
2
0
0
0
1
1
1
0
1
1
0
1
0
1
2
0
2
0
0
0
0
0
2
1
1
1
1
1
1
1
1
1
2
0
1
0
1
1
1
2
2
1
0
0
0
1
1
1
0
0
1
2
0
1
0
1
1
0
1
2
0
0
1
1
2
0
1
0
0
0
2
1
1
2
1
0
0
0
1
0
2
0
1
0
1
2
0
1
1
0
1
2
0
1
0
0
0
0
1
0
2
0
1
1
2
2
0
0
0
1
0
2
3
0
0
0
2
0
0
1
2
0
2
0
0
0
2
1
2
0
0
1
1
1
0
0
2
0
1
1
0
1
1
0
2
0
2
1
1
2
1
2
1
1
1
0
2
1
0
0
0
0
1
0
1
0
0
1
2
1
0
0
1
0
2
1
1
0
2
1
0
0
2
0
0
0
0
4
1
0
1
1
2
0
2
1
1
1
0
2
3
2
1
1
0
0
0
1
0
1
2
2
0
0
0
1
3
2
0
0
0
1
1
0
0
0
1
0
0
0
1
2
0
1
1
0
1
0
1
1
0
0
1
2
0
2
1
1
2
0
2
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
1
2
2
1
1
0
1
0
1
2
1
2
0
0
1
0
1
2
1
0
0
0
2
1
0
0
1
0
0
1
2
1
0
0
0
0
1
0
0
2
0
0
1
0
5
0
2
0
0
0
0
0
2
0
2
0
0
1
0
1
1
1
1
0
1
0
0
2
2
1
0
1
1
0
2
0
1
2
0
1
0
2
2
2
2
0
0
2
1
2
0
0
2
0
2
1
1
0
0
5
1
1
2
0
0
2
1
2
2
2
0
1
1
1
0
2
0
2
0
1
1
0
1
0
0
0
0
1
0
1
1
0
0
1
0
0
2
1
1
0
3
0
2
1
2
0
2
0
0
1
1
1
1
0
1
1
0
0
0
0
0
0
1
2
0
0
0
0
1
1
2
2
0
0
0
1
2
2
0
0
2
0
0
2
0
3
1
0
3
1
1
0
0
1
1
0
1
0
1
0
0
0
0
2
0
1
2
0
1
0
1
0
2
1
0
2
0
2
0
0
0
1
2
2
1
0
1
0
0
1
0
0
0
1
0
1
0
0
1
2
0
2
0
0
1
0
1
1
0
2
0
0
2
0
0
0
0
1
1
1
0
2
1
2
0
0
0
1
0
0
2
2
0
0
2
2
1
2
0
1
0
2
1
1
1
2
0
1
1
0
4
1
1
2
0
0
0
2
0
0
1
1
2
0
0
1
0
0
2
0
1
2
1
0
0
0
0
0
1
0
0
1
1
2
0
0
1
3
1
1
0
0
0
0
2
2
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
2
0
2
1
0
1
1
2
0
0
0
2
1
0
2
0
0
0
2
0
0
1
0
1
0
0
0
1
0
0
1
3
1
0
2
0
0
2
0
0
0
1
1
1
0
2
0
2
2
0
1
1
0
0
2
2
0
0
0
0
2
0
2
1
0
1
1
1
2
1
0
2
0
1
1
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
1
1
0
1
0
1
1
1
1
0
0
0
1
0
0
0
1
2
0
0
1
1
0
2
0
2
2
1
1
1
1
0
2
0
2
1
1
0
1
2
0
2
2
1
0
0
2
1
1
1
0
1
1
0
0
1
1
1
1
0
0
2
0
0
2
1
0
0
0
2
3
1
1
0
1
0
0
1
1
2
0
0
0
0
0
0
0
0
2
1
3
0
1
0
0
0
0
0
2
0
2
2
1
0
0
1
1
0
1
1
1
0
1
1
0
0
0
0
0
0
2
0
1
1
1
0
0
1
1
0
2
1
0
1
2
3
1
0
1
1
2
0
0
3
0
1
2
2
0
1
1
0
1
1
1
0
0
2
1
0
1
0
0
0
2
1
1
0
0
1
0
1
1
1
2
0
0
2
2
0
0
1
0
2
0
1
0
0
1
2
0
2
0
0
0
0
1
1
0
2
2
0
2
1
4
2
1
1
0
0
1
0
1
0
2
1
0
1
1
0
2
2
0
1
1
0
0
0
0
1
0
2
2
2
0
1
0
1
1
6
0
0
0
1
0
0
0
1
0
1
0
1
0
2
0
1
0
2
0
2
0
0
0
2
1
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
1
0
1
0
1
2
2
0
2
1
0
1
1
1
0
0
1
1
1
0
1
2
0
1
1
0
0
0
0
2
0
1
0
0
0
1
1
2
1
0
0
2
2
1
0
0
1
0
1
2
0
2
0
0
1
1
0
1
0
1
0
1
0
0
1
1
0
1
0
2
0
1
2
0
2
2
1
1
0
0
2
2
2
1
1
0
0
1
0
0
2
0
1
1
0
2
0
2
0
0
0
0
0
1
1
1
1
1
1
1
0
0
3
0
1
0
1
1
1
2
0
1
3
1
1
2
2
1
0
0
0
0
2
1
1
1
1
1
0
0
2
1
2
0
0
1
1
1
0
1
1
0
1
1
1
1
1
1
2
1
1
0
0
0
0
2
1
0
0
2
0
0
0
0
0
2
1
0
1
0
1
2
1
1
1
0
1
0
1
1
1
0
2
0
0
0
0
1
0
0
2
1
1
1
3
2
0
1
1
0
0
1
1
2
0
0
2
1
0
1
0
2
2
0
0
1
0
2
0
1
1
0
1
2
0
2
0
1
1
2
1
2
2
1
0
1
2
0
0
0
0
2
0
0
1
1
0
1
1
2
2
1
0
1
0
2
0
2
1
0
0
1
1
1
1
0
0
1
0
1
0
1
0
0
9
0
0
2
0
2
1
1
0
2
2
0
1
0
3
0
1
0
0
0
1
0
2
2
0
2
2
0
0
0
3
0
2
2
2
0
1
1
1
0
0
0
1
0
1
1
0
0
0
0
1
2
1
1
1
2
1
0
1
0
0
1
0
0
0
0
0
2
0
1
0
0
1
0
0
1
0
3
0
0
1
2
0
0
0
0
1
1
1
0
1
0
2
0
0
0
2
3
0
0
1
1
1
1
1
1
1
0
0
1
0
0
1
2
2
1
0
0
0
0
2
0
0
2
1
0
0
0
1
2
0
0
1
0
0
0
0
0
2
0
2
1
0
0
1
2
2
0
0
0
5
1
1
1
2
0
0
2
1
0
1
0
0
0
1
1
0
2
1
1
0
0
2
1
0
0
2
0
0
2
2
0
1
3
0
0
0
1
0
2
0
1
1
0
0
1
1
2
1
0
1
2
0
1
0
1
1
0
1
0
0
1
0
2
1
2
0
0
2
0
0
1
0
0
2
0
0
0
0
2
1
1
1
2
1
2
0
0
2
1
2
1
0
0
2
0
0
1
2
1
0
0
0
0
0
2
0
1
0
5
2
1
0
1
0
1
1
0
2
1
0
0
0
1
2
1
2
0
1
1
0
1
0
2
0
2
0
3
0
1
1
1
1
0
2
0
0
0
2
0
0
2
0
0
0
0
1
0
1
0
1
1
0
2
2
2
2
1
1
2
2
2
0
0
2
1
2
0
1
0
0
0
2
2
1
1
1
2
1
0
0
1
0
0
0
2
1
0
1
0
1
0
0
2
2
0
0
1
1
1
0
0
2
0
0
1
0
1
0
1
1
2
0
0
0
0
0
2
1
2
0
1
1
1
1
1
0
0
1
1
1
0
2
0
1
0
0
0
0
0
0
2
1
0
0
2
0
0
2
0
2
1
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
2
1
0
1
1
1
0
0
1
1
2
0
0
1
0
0
0
1
0
0
1
1
0
1
0
2
2
0
2
0
1
0
1
0
0
2
1
0
1
1
1
0
1
2
1
2
0
0
2
0
0
1
1
1
1
0
0
0
1
0
1
2
0
0
2
1
1
1
0
0
0
0
1
0
2
0
1
0
0
4
2
0
0
1
0
0
1
0
0
0
0
2
1
1
0
2
0
0
1
2
1
1
1
0
0
1
0
0
1
1
2
1
0
0
1
0
0
0
1
1
2
0
2
2
0
2
3
2
2
1
1
0
0
0
2
0
0
2
0
1
0
0
0
1
1
0
2
2
0
2
2
1
0
0
1
0
2
0
2
0
0
2
2
0
2
0
1
0
0
1
1
0
0
1
0
0
2
3
2
0
0
0
0
2
2
0
0
0
0
0
0
2
0
3
0
0
1
2
2
0
2
2
2
0
2
0
0
1
1
2
2
0
2
2
0
0
0
0
2
0
0
1
2
0
1
0
1
1
0
0
1
2
0
3
1
0
1
2
0
3
1
2
1
1
1
2
0
1
0
0
0
1
2
1
1
0
0
0
0
1
0
0
0
1
1
1
1
0
0
0
0
0
0
0
2
0
0
0
0
1
1
2
1
0
0
2
4
1
2
1
0
2
0
0
0
0
0
1
0
2
0
0
1
1
0
0
1
1
1
0
0
0
0
0
1
0
0
0
2
0
4
0
0
1
1
0
0
1
0
1
2
0
0
0
1
0
0
0
0
1
0
2
1
0
0
2
2
1
1
2
0
0
0
1
0
1
0
1
2
1
0
0
2
1
0
1
3
2
2
1
3
0
0
1
1
2
1
2
1
1
0
2
1
4
0
1
0
1
0
1
0
0
2
1
0
1
3
2
0
4
2
0
2
1
1
0
1
1
1
1
1
0
2
1
2
1
2
2
2
0
2
2
0
0
2
1
0
0
0
1
1
1
0
1
2
0
0
2
1
0
1
1
1
1
1
2
1
2
0
0
1
3
0
2
2
0
1
0
4
0
1
0
0
0
0
0
0
0
2
1
0
2
0
0
1
0
2
0
0
0
3
0
1
2
2
0
1
1
0
1
2
2
1
0
2
0
1
0
0
0
0
0
1
2
0
1
1
0
1
0
2
0
0
2
2
0
0
3
0
0
0
1
0
1
1
1
0
2
2
0
1
0
1
0
1
2
2
0
2
2
0
2
2
0
0
0
2
0
1
0
0
2
0
0
1
1
1
1
0
0
0
1
1
1
0
2
0
0
1
1
1
1
0
0
1
3
0
1
2
0
3
0
0
2
1
1
0
2
2
0
0
0
1
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
4
0
0
0
0
0
0
1
0
0
1
1
0
2
0
0
0
0
1
1
0
0
0
1
0
1
0
0
7
0
0
2
0
0
1
2
0
2
0
3
2
0
2
1
2
0
0
0
1
0
1
2
1
0
0
1
0
1
1
0
2
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
1
1
2
0
0
0
2
0
2
1
0
0
0
1
1
3
0
1
2
0
0
0
0
1
1
0
1
0
2
0
1
1
0
2
2
2
1
0
0
2
0
0
1
1
2
0
1
1
0
2
2
0
1
0
1
1
1
2
0
1
2
1
2
0
5
1
0
0
3
1
3
1
0
2
2
2
0
0
0
0
1
1
1
0
0
1
1
1
1
0
1
1
1
1
0
2
1
1
1
2
1
0
1
2
1
0
0
0
2
1
2
0
1
0
0
0
0
0
0
1
0
2
1
0
0
0
2
1
0
1
1
2
3
2
0
2
1
2
2
0
1
0
1
0
2
2
0
0
0
0
1
2
1
0
1
2
0
0
0
0
0
0
1
1
1
0
2
0
1
0
2
1
0
0
0
2
0
1
1
1
0
0
0
2
1
0
1
0
1
1
1
0
1
0
1
1
0
2
1
0
1
0
0
2
0
1
2
0
0
0
0
0
0
0
1
1
3
1
2
2
0
0
0
1
0
0
1
2
0
0
0
0
2
0
0
0
1
0
0
3
0
0
0
2
0
0
0
2
0
0
1
0
0
2
1
1
0
1
0
0
1
0
0
0
0
1
2
0
1
1
0
1
0
0
1
0
1
0
1
1
1
1
0
2
1
0
0
1
0
1
2
1
0
1
0
1
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
2
1
2
0
1
0
1
0
2
0
0
0
1
0
2
1
0
2
0
0
0
1
2
0
0
1
2
0
1
0
3
1
0
0
0
1
2
0
0
0
2
2
0
0
0
2
2
0
1
0
0
2
0
0
0
2
0
1
0
1
0
0
0
1
1
1
1
1
1
1
0
1
0
2
0
0
0
0
0
1
2
0
2
0
0
0
2
0
1
2
0
1
1
1
1
1
0
2
0
1
1
0
0
0
0
1
0
0
1
0
1
0
0
1
1
1
1
2
0
0
1
1
1
1
1
2
1
2
2
0
1
2
1
3
1
1
1
0
1
2
1
0
1
0
2
0
1
0
2
1
0
0
1
0
2
0
1
1
0
2
1
0
2
0
1
2
1
1
1
1
0
1
2
0
0
2
0
0
0
0
0
0
2
2
0
1
1
2
1
0
1
0
1
1
1
0
2
1
1
0
1
0
0
3
2
0
0
0
1
0
1
1
0
1
1
2
0
2
0
0
6
0
0
0
2
0
0
0
0
2
1
0
0
2
1
1
1
1
2
2
1
2
0
0
1
1
0
2
2
2
0
1
0
0
0
0
1
0
2
1
1
0
1
0
0
0
1
2
1
1
0
0
0
0
1
1
0
1
0
0
2
2
2
1
0
0
0
2
2
1
2
2
0
0
1
0
1
0
0
3
1
1
3
1
0
1
1
0
1
1
0
0
0
0
2
2
0
0
2
1
1
1
0
0
2
0
0
0
0
0
0
2
1
1
0
0
0
1
0
0
2
0
0
0
1
1
2
0
0
0
0
0
1
1
0
0
0
1
1
0
1
2
1
1
0
0
2
2
1
2
3
2
0
0
2
2
0
2
0
0
1
1
0
0
2
1
0
0
0
0
0
1
1
0
1
0
2
0
1
1
1
0
1
0
2
1
1
2
1
0
0
1
0
0
0
1
1
0
2
1
1
0
1
0
0
2
1
1
0
2
0
0
2
1
1
1
2
0
2
0
2
1
1
0
1
2
0
2
2
1
0
0
0
0
0
1
0
2
0
0
0
1
0
2
0
0
1
0
1
0
1
2
0
2
2
2
2
0
1
1
0
2
0
1
1
2
1
2
1
2
0
0
2
1
0
2
0
0
0
2
1
0
0
0
0
2
1
0
3
0
2
0
0
2
0
1
0
1
1
1
0
0
1
0
1
1
1
2
2
1
1
0
1
0
2
1
0
1
0
0
0
1
1
1
2
0
1
0
1
2
0
0
0
1
0
2
0
1
0
0
1
1
0
0
0
2
0
2
1
1
3
0
0
0
2
0
0
1
0
0
0
1
1
1
0
2
2
1
1
0
2
2
2
1
0
1
1
0
0
1
0
2
1
0
1
0
1
1
0
0
1
0
1
0
1
1
1
3
2
0
2
1
0
0
0
1
1
1
1
0
1
1
2
0
2
0
2
1
2
2
2
2
0
0
0
1
2
1
2
0
0
2
1
0
2
0
0
2
0
0
2
0
1
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
1
0
2
0
3
1
1
2
0
0
0
2
0
1
0
1
2
1
0
0
2
2
1
0
2
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
2
1
1
1
0
0
1
0
0
0
1
0
0
0
0
2
1
1
1
2
1
0
1
0
2
1
1
1
0
0
0
1
0
1
0
0
0
2
2
0
2
1
1
1
0
0
2
0
0
0
2
1
2
1
2
0
0
2
0
1
0
0
2
1
2
0
0
2
1
1
0
0
1
0
2
0
0
2
0
1
1
0
2
0
1
1
1
1
0
0
2
1
1
0
1
1
0
0
2
2
1
0
2
0
0
1
0
0
2
1
1
0
0
0
0
0
2
1
0
2
0
1
1
2
1
1
0
3
1
2
2
0
3
0
1
1
1
1
0
0
0
1
2
0
1
1
0
0
2
0
0
1
1
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
1
0
0
0
2
1
2
2
1
2
0
0
0
0
1
1
2
2
0
0
0
0
1
1
1
0
1
1
2
0
0
0
1
2
0
0
2
1
0
0
0
2
1
0
1
1
2
2
0
0
1
1
0
0
0
0
2
0
0
0
1
0
0
2
0
0
1
2
0
0
1
2
2
0
0
0
0
2
1
0
1
1
2
2
0
2
2
1
1
0
0
0
1
2
0
2
0
0
0
0
1
2
1
1
2
0
0
2
0
0
0
3
0
1
0
0
0
0
1
0
2
1
2
2
2
1
1
0
0
1
1
2
0
0
0
1
0
0
0
0
2
0
0
1
1
1
0
0
2
0
0
0
0
1
0
0
0
1
0
0
1
2
1
0
0
0
1
1
0
0
1
0
1
0
0
1
1
1
1
1
1
1
2
1
0
0
1
1
0
0
2
2
1
1
0
0
0
1
1
0
0
2
1
1
0
0
2
0
2
1
1
0
0
0
1
1
0
0
1
1
1
1
1
0
2
0
1
0
0
0
1
0
0
0
0
0
1
2
0
0
0
1
0
1
0
0
0
0
1
0
2
2
1
1
1
0
0
0
2
2
1
0
1
1
0
1
1
1
1
2
0
1
0
1
0
0
0
0
0
1
0
1
2
2
0
0
0
2
2
0
0
2
0
0
1
1
1
1
1
1
1
0
1
1
1
0
1
0
2
1
0
0
2
0
1
2
2
0
0
0
1
1
0
0
1
2
0
0
1
1
1
2
0
1
0
2
0
0
0
0
0
1
0
0
1
2
0
2
0
0
1
0
2
2
2
1
1
0
0
0
0
0
0
2
0
2
0
1
0
0
2
0
0
1
0
2
2
0
1
1
1
0
0
2
2
0
0
1
2
0
3
0
1
1
1
0
0
0
2
1
0
0
0
2
0
0
2
2
2
2
2
1
2
2
0
1
2
0
0
0
1
0
0
1
0
1
0
1
2
1
1
1
0
0
0
2
0
2
1
0
1
1
2
1
0
5
1
1
2
1
0
1
1
1
2
2
2
0
0
1
1
2
2
3
0
0
0
0
0
0
0
2
0
0
2
2
1
1
1
0
1
0
0
0
2
0
0
0
1
0
1
0
1
0
0
0
0
0
1
2
1
1
1
0
1
0
1
1
1
0
1
2
1
0
0
0
0
0
1
2
2
2
0
1
1
3
0
0
0
0
2
2
2
0
1
0
0
1
3
1
0
0
0
0
1
0
2
0
0
1
2
0
0
0
0
0
0
1
0
2
2
1
1
1
2
0
2
0
0
1
1
2
0
1
1
0
0
0
0
0
0
0
2
1
1
1
1
0
1
0
0
2
2
0
2
0
1
0
0
0
2
0
1
1
0
0
0
2
1
1
0
2
2
0
0
0
0
1
2
1
1
1
0
0
2
0
0
2
0
2
1
3
0
2
1
0
2
1
1
2
2
2
1
0
1
1
2
2
1
2
2
1
0
1
2
2
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
1
0
1
0
1
1
0
0
0
1
1
0
1
1
1
0
1
2
0
0
1
1
2
0
0
0
2
0
1
0
2
2
1
0
2
0
2
0
0
1
0
0
1
1
1
2
1
2
0
1
0
1
1
2
2
0
1
0
1
0
2
0
0
0
0
2
1
0
0
0
0
1
0
0
1
2
0
0
2
1
2
1
2
3
0
1
0
1
2
1
3
0
0
0
1
0
2
0
0
0
0
0
2
1
0
0
2
1
0
1
2
2
0
1
2
0
2
2
1
1
1
0
1
0
0
2
1
1
1
0
0
2
0
0
0
0
0
0
2
1
0
2
0
0
1
2
2
0
1
0
1
2
0
2
0
0
0
2
0
0
2
0
1
1
0
0
0
2
0
0
1
1
0
0
1
2
0
1
1
0
1
0
0
2
2
0
2
2
0
1
0
0
1
1
2
2
0
2
2
2
0
2
0
0
0
0
0
0
2
0
1
1
2
1
2
2
0
0
0
0
0
2
1
0
0
0
2
1
0
0
0
1
1
1
2
1
1
0
1
2
3
0
0
2
0
0
0
0
2
1
0
2
1
2
0
0
1
0
0
1
1
0
1
2
1
0
1
0
0
0
0
2
0
2
3
1
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
2
2
0
1
0
1
1
1
0
0
1
0
1
0
1
0
1
0
1
2
2
1
0
0
0
0
0
0
1
0
1
0
1
1
1
0
0
1
1
1
2
0
2
2
0
0
0
2
0
1
0
0
1
0
0
0
0
0
2
1
0
1
1
0
0
3
1
2
1
0
1
0
1
1
1
0
0
0
0
1
0
0
0
0
1
0
1
1
0
1
0
0
0
0
1
0
0
0
0
2
1
1
0
0
2
1
0
1
1
2
1
1
1
0
0
1
1
1
1
1
2
2
0
0
2
0
0
0
0
0
2
1
2
2
0
1
0
0
0
0
2
1
0
0
1
1
0
1
0
0
0
1
0
1
1
0
0
0
1
1
0
0
0
2
2
0
2
0
0
1
2
2
2
1
0
1
1
1
1
0
1
1
0
0
2
0
0
0
0
1
0
0
0
0
2
2
0
0
1
0
0
1
0
2
1
0
1
0
1
0
0
2
0
1
0
6
2
1
1
1
2
0
1
1
0
0
0
2
0
2
1
2
2
0
2
0
1
1
2
2
0
0
1
1
2
0
1
1
2
0
0
0
2
0
0
0
1
1
0
2
0
0
1
0
1
2
1
0
1
0
1
1
0
0
0
2
2
0
2
0
0
2
1
0
0
0
2
2
1
1
2
0
1
1
1
1
1
1
1
1
1
0
0
0
3
2
0
1
0
0
1
0
5
1
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
4
1
1
0
2
1
2
1
1
1
1
1
1
2
2
1
1
0
1
0
2
0
0
2
0
2
1
0
2
2
0
2
1
1
0
2
0
2
2
0
1
0
0
1
2
0
1
0
0
1
1
2
1
1
1
1
1
0
0
0
1
2
1
0
0
0
1
0
2
0
0
0
0
1
1
0
1
1
3
1
0
1
0
1
0
2
0
1
0
1
1
2
0
2
0
1
2
0
0
1
2
0
1
2
0
0
0
1
1
1
0
2
1
2
0
0
1
2
1
2
2
0
1
0
0
0
1
1
2
0
2
0
0
0
0
0
0
0
0
2
0
1
1
1
1
0
1
1
1
0
0
0
0
0
0
0
1
2
2
2
0
0
0
0
2
0
0
1
2
0
0
0
2
2
0
2
2
0
2
2
0
0
2
2
1
1
0
0
1
0
0
0
1
1
1
2
0
2
1
0
0
0
0
1
0
0
0
0
3
0
1
2
2
1
2
0
4
0
2
1
2
1
2
0
0
3
0
0
0
0
1
2
0
1
1
1
2
1
2
0
1
2
0
3
0
1
0
1
0
2
2
2
0
0
0
1
0
0
3
0
2
0
0
0
0
1
1
2
1
0
1
3
0
1
1
1
0
0
2
1
0
1
0
1
1
0
2
1
2
0
1
0
0
1
1
0
0
0
1
2
0
0
0
0
0
0
1
1
0
2
1
0
1
1
1
1
0
0
1
0
1
0
0
1
1
1
1
0
1
0
0
1
0
0
0
2
1
0
0
0
2
0
1
0
1
0
2
1
2
0
0
1
0
0
2
1
0
2
0
0
0
0
0
1
2
0
0
2
1
0
1
0
0
0
0
0
2
0
2
3
0
2
0
0
1
1
0
0
2
5
1
0
2
2
1
0
1
1
0
0
2
0
1
2
8
1
2
1
0
0
1
0
1
1
1
0
2
2
1
1
0
2
0
1
2
1
0
0
0
1
0
0
1
1
1
2
0
2
1
1
1
0
0
0
0
0
0
0
2
0
1
0
0
2
0
2
0
3
2
0
0
0
0
1
2
2
0
0
0
1
0
0
1
0
0
0
2
0
2
2
1
0
0
1
0
2
0
1
1
2
2
0
0
1
2
2
2
1
2
2
2
1
1
0
0
0
0
0
1
2
0
0
0
2
1
0
1
2
0
0
0
1
1
1
2
1
0
0
0
0
2
0
2
0
1
0
0
2
1
2
0
2
1
1
1
0
1
1
1
1
2
0
0
0
2
1
2
0
1
0
1
2
2
0
0
0
0
0
1
2
1
0
1
1
1
0
0
1
0
1
0
2
0
0
0
0
2
0
1
0
1
1
0
0
1
1
1
1
1
0
1
2
1
1
0
0
1
2
2
1
1
1
1
1
1
1
1
1
0
2
1
0
2
2
1
0
1
1
0
0
2
0
0
0
0
1
1
0
1
2
1
1
1
2
0
0
0
0
2
0
1
0
1
1
2
0
3
0
2
0
0
2
2
0
0
1
1
1
0
1
0
0
0
4
0
1
1
0
0
1
2
0
1
0
1
1
2
0
0
1
1
2
1
2
2
1
1
0
0
2
0
1
0
2
0
0
0
0
4
0
0
0
0
0
0
1
0
1
0
0
1
2
2
1
1
1
3
1
0
2
0
1
0
2
1
0
0
1
0
1
1
0
2
1
1
0
0
0
1
1
0
1
0
1
0
1
2
2
0
1
1
0
2
2
2
2
1
0
1
2
1
0
0
0
1
1
1
1
0
0
1
0
1
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
1
2
1
2
1
0
1
1
1
0
1
0
1
2
0
1
0
1
2
1
0
1
0
0
1
1
1
0
1
0
0
0
0
1
0
0
1
0
0
0
1
1
0
1
0
2
2
1
0
3
2
0
2
0
2
1
2
1
1
0
2
0
1
0
0
0
1
3
0
1
2
0
0
0
1
1
0
0
0
1
0
2
0
0
2
1
0
2
0
1
0
1
0
0
2
2
0
0
0
0
1
0
2
0
0
0
1
1
0
0
1
0
0
1
0
1
0
1
0
1
0
0
2
1
2
0
1
0
0
1
0
0
2
2
2
1
1
1
0
2
0
2
0
1
1
2
1
0
0
0
1
0
1
1
2
0
2
2
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
1
1
2
2
0
1
0
0
0
0
0
2
1
1
0
0
1
0
1
2
2
1
0
0
2
0
0
0
1
3
1
1
2
0
1
2
3
2
1
0
0
0
1
1
0
0
1
0
1
0
0
1
0
0
1
1
0
1
0
0
0
0
1
1
1
0
0
1
1
0
0
1
1
2
1
1
1
0
1
0
1
0
0
1
0
2
0
0
1
0
1
0
0
0
0
2
0
4
1
2
0
1
0
0
1
0
2
0
0
0
0
2
0
1
0
1
1
1
0
0
1
1
1
0
1
0
1
0
0
0
2
2
1
0
0
2
0
2
0
1
0
0
2
2
2
0
0
0
0
0
0
2
0
0
2
2
0
0
2
2
0
0
0
0
4
2
1
2
0
1
1
2
2
0
2
2
1
1
1
0
2
0
0
2
0
2
2
0
2
0
0
2
0
2
0
1
2
0
2
0
0
1
0
1
0
0
2
2
0
1
1
0
2
2
0
0
0
1
0
0
0
0
1
1
0
0
0
1
1
2
0
1
2
0
2
1
0
0
0
2
1
0
0
0
1
2
2
0
1
2
1
0
0
1
1
0
2
0
0
0
1
1
1
0
1
0
3
2
1
1
1
0
0
1
0
1
0
0
1
1
1
2
0
0
0
1
0
2
0
1
0
0
0
2
1
0
2
0
0
1
0
1
1
0
0
0
2
1
2
2
0
0
0
0
2
0
1
0
0
2
2
0
1
0
1
1
0
2
1
0
0
0
0
0
0
1
0
0
1
2
1
0
0
1
0
0
0
2
0
0
0
2
2
1
0
0
1
1
1
0
2
2
0
0
0
0
0
2
1
0
1
2
0
1
0
2
0
1
2
0
0
2
1
0
0
0
2
2
0
0
1
2
0
0
0
1
0
0
2
1
0
1
0
0
2
2
0
1
0
0
2
0
1
0
1
2
0
0
0
0
0
2
1
0
0
0
1
2
1
1
0
0
1
0
1
0
1
1
1
2
2
0
2
0
1
1
1
0
0
0
0
0
1
1
0
0
2
0
0
0
2
0
0
0
2
1
0
0
1
0
2
0
0
1
1
0
1
0
1
0
2
0
0
1
0
1
1
2
1
0
0
0
0
0
1
0
2
1
0
1
0
2
1
1
2
0
1
1
1
1
2
1
1
2
0
0
0
0
0
0
1
2
0
2
0
0
1
1
0
0
1
2
1
2
3
0
0
0
0
0
0
0
0
1
2
0
1
1
0
1
1
2
1
0
1
1
0
1
1
2
0
0
0
1
2
0
0
0
3
0
0
0
0
2
2
2
0
0
2
1
2
1
2
2
0
1
0
0
2
1
2
1
0
0
0
1
2
2
0
0
0
0
0
0
1
1
3
0
1
1
1
1
0
0
0
0
1
1
1
0
1
2
0
0
2
1
1
0
0
0
2
0
1
0
1
1
1
0
2
1
2
0
0
2
0
0
2
0
1
2
1
1
2
0
0
0
0
0
0
4
1
1
0
2
0
0
1
2
0
2
1
0
1
0
1
0
1
1
0
0
2
0
2
0
2
2
1
1
1
1
0
2
0
0
1
1
0
0
1
2
1
2
0
0
0
0
2
3
1
0
1
1
1
1
0
2
0
0
2
1
0
2
2
0
0
2
0
0
0
2
0
0
2
0
2
0
0
2
1
1
0
0
0
0
0
0
2
1
0
1
1
1
0
0
0
0
0
1
0
1
1
0
3
0
0
2
0
0
0
0
1
0
0
2
1
0
0
0
1
1
1
0
1
2
2
1
0
1
0
0
1
2
2
0
1
1
0
1
3
2
0
0
0
1
0
0
2
0
0
0
1
1
2
0
1
0
0
1
0
2
0
1
0
0
0
0
0
1
1
0
2
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
2
1
2
1
0
0
0
1
2
2
2
2
1
0
0
0
0
0
0
0
0
0
1
0
2
1
2
0
1
0
1
0
1
0
1
2
0
1
0
1
0
0
2
0
1
0
1
0
2
1
0
0
0
0
1
0
0
1
0
2
0
1
2
0
1
1
2
0
2
1
0
2
2
0
1
2
0
0
0
0
0
1
0
0
2
0
1
0
2
0
0
0
0
0
2
0
2
1
2
2
0
0
1
1
0
2
0
0
1
1
0
0
2
2
1
2
1
0
1
1
2
2
1
0
0
0
1
2
1
1
0
0
0
1
1
2
2
1
1
0
2
2
2
2
2
2
1
0
1
1
2
0
0
1
0
0
1
4
0
1
2
3
0
2
0
1
1
2
0
0
1
1
1
0
0
0
1
1
0
1
2
2
2
2
1
0
1
0
0
0
0
0
3
1
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
1
0
1
1
0
2
1
2
1
0
0
1
1
1
1
2
0
0
2
0
0
1
0
1
2
0
0
0
0
2
1
1
0
0
1
1
1
0
0
2
0
0
2
0
0
0
0
0
0
0
1
1
2
0
1
0
0
0
1
0
0
2
1
0
0
0
0
1
0
1
1
1
2
0
0
0
1
2
2
0
0
1
1
2
0
0
0
0
2
0
0
1
0
1
0
0
0
0
2
0
0
1
1
2
0
0
0
0
0
2
0
2
2
0
1
2
0
0
0
1
2
0
2
1
2
1
0
0
1
0
1
1
2
0
2
1
1
2
1
0
2
0
0
0
0
0
0
1
2
1
0
1
1
0
1
0
0
0
0
2
3
1
0
0
0
0
0
1
0
0
2
1
1
0
0
0
0
1
0
1
4
0
1
2
0
2
0
0
1
2
1
0
2
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
1
2
0
1
1
2
0
1
1
1
0
1
0
0
0
3
1
0
0
3
0
1
0
2
2
0
0
0
0
0
0
0
2
1
0
0
0
1
1
1
2
1
0
2
2
0
1
2
1
0
0
2
2
0
0
2
0
0
1
1
1
0
0
2
0
2
0
0
1
1
0
0
2
2
0
1
0
0
0
1
2
0
2
2
2
1
1
1
0
0
0
1
1
4
0
0
2
0
2
1
0
1
3
2
2
3
0
3
1
0
2
0
1
1
0
0
1
0
0
1
1
1
0
1
0
1
1
0
1
0
0
2
2
1
1
2
1
0
0
2
0
1
1
0
1
2
2
3
1
1
1
1
0
2
0
0
0
1
2
1
0
0
1
1
1
0
1
2
1
2
1
0
1
1
1
2
0
0
0
0
0
1
1
2
3
2
0
1
0
2
1
0
2
1
2
0
0
1
1
0
0
2
2
0
0
2
0
2
2
0
1
1
0
0
0
0
0
0
2
0
1
2
1
2
0
1
0
1
0
1
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
1
0
0
2
0
5
1
0
2
4
1
1
0
0
2
1
0
1
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
1
1
0
2
1
1
0
0
1
0
0
1
0
1
1
0
0
0
0
1
0
2
0
0
1
0
0
2
1
0
0
1
0
0
0
1
2
0
0
1
0
3
1
1
1
0
1
1
1
1
2
2
2
2
1
2
1
0
0
1
2
2
1
1
0
0
1
2
2
2
0
0
0
3
2
1
1
2
1
0
0
0
0
1
0
0
1
0
0
1
1
2
1
2
0
1
1
0
0
1
1
0
0
1
0
2
1
2
0
1
2
1
1
2
1
0
0
1
0
2
1
1
1
2
1
1
1
2
1
1
1
0
1
1
0
0
0
1
2
2
0
0
0
1
0
0
0
1
2
0
0
2
0
0
1
2
1
0
1
1
1
2
1
2
0
0
0
1
0
1
3
0
2
2
1
0
1
2
2
3
0
1
0
0
0
0
2
0
0
0
2
1
1
0
2
0
1
2
0
1
1
0
2
0
1
1
0
0
1
2
0
0
0
0
2
1
1
1
0
1
0
1
0
1
0
0
1
1
1
1
1
0
1
0
2
1
0
1
2
0
1
0
2
2
0
0
0
3
2
0
1
0
1
0
1
0
0
1
0
1
3
2
1
1
0
2
1
0
0
0
0
1
0
2
2
0
2
0
0
2
1
1
0
2
2
0
1
1
0
2
2
1
0
2
0
0
0
0
1
0
1
0
0
0
1
1
0
1
0
1
0
1
1
0
0
0
2
0
2
0
3
2
1
0
0
1
0
0
1
0
0
1
0
2
2
0
1
1
1
3
0
0
0
1
2
2
2
2
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
1
1
0
2
1
0
0
0
2
2
0
0
2
0
0
0
0
1
0
0
1
1
0
1
1
0
1
0
0
0
0
0
1
1
2
0
0
0
1
0
0
1
0
1
0
1
0
2
0
0
3
0
1
0
1
0
1
0
0
1
0
0
0
1
1
1
2
0
0
2
1
1
0
0
0
0
2
2
0
1
2
0
0
0
0
0
0
0
0
1
0
0
1
1
2
0
1
0
0
0
1
1
0
2
0
2
2
1
1
0
3
1
0
1
1
0
0
1
0
1
1
1
1
1
0
1
3
0
1
2
1
1
1
1
2
0
0
0
1
0
0
2
1
0
0
0
1
2
4
1
1
0
0
1
0
1
0
0
0
1
2
1
2
0
0
0
1
0
1
1
1
0
0
2
1
0
1
1
0
1
0
0
0
2
0
2
1
0
2
0
1
1
0
1
0
0
0
1
1
2
0
0
0
2
1
0
1
3
1
1
0
2
2
0
0
2
2
0
0
1
0
0
1
2
0
0
0
2
0
0
0
1
0
1
0
0
0
2
2
0
2
0
0
1
3
1
0
1
1
1
0
0
1
2
1
0
0
1
0
5
2
2
0
2
0
1
0
2
0
1
2
0
1
1
1
2
0
0
1
0
0
1
1
3
0
2
0
0
1
0
1
2
1
0
0
2
0
1
0
1
2
0
0
0
0
0
1
1
0
0
1
4
1
0
0
2
0
0
0
0
1
0
1
2
1
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
2
1
0
2
1
1
1
0
0
1
0
1
1
2
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
1
1
1
1
0
1
1
2
1
1
0
1
1
1
1
1
0
1
0
1
2
2
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
2
0
2
1
2
1
2
0
1
0
2
0
0
2
1
1
1
2
2
0
1
0
1
0
1
0
2
1
2
1
0
0
1
0
2
0
0
0
1
1
0
2
2
0
2
2
1
0
2
0
2
2
0
2
3
1
2
0
6
0
2
1
0
2
1
2
0
1
1
0
0
0
1
0
0
2
2
0
1
1
0
0
1
0
1
2
0
2
1
0
0
2
1
1
0
2
1
0
2
0
0
0
1
1
1
0
0
2
2
0
0
0
2
0
0
1
0
1
2
2
0
1
0
4
0
2
0
1
0
1
1
0
0
1
0
0
1
1
0
0
0
1
2
2
0
0
3
2
0
0
1
2
2
5
0
0
0
0
0
1
2
0
0
1
0
0
1
0
0
0
0
1
0
0
1
1
2
1
0
0
0
0
1
1
0
0
1
0
1
0
1
0
1
2
0
0
2
0
0
1
1
1
1
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
2
0
0
0
2
2
0
0
0
1
2
2
1
2
2
0
1
0
2
2
0
0
0
0
0
1
2
0
2
2
1
2
2
0
1
0
2
0
0
0
2
0
2
1
1
3
0
0
0
1
1
0
0
1
2
1
0
0
1
0
0
1
1
2
2
2
2
1
0
1
0
0
0
1
1
0
0
0
1
2
2
2
1
1
0
0
2
1
1
2
1
1
1
1
2
1
2
0
1
0
0
0
0
2
2
0
1
1
0
1
0
1
1
1
1
2
0
0
1
0
0
0
2
2
2
1
1
1
2
0
0
1
0
0
1
0
0
0
1
1
1
0
1
0
0
0
1
0
0
1
1
0
0
2
0
1
1
2
0
1
2
0
2
0
0
0
0
1
0
1
0
1
2
2
1
1
0
1
0
1
1
2
0
1
0
2
1
1
0
1
0
0
0
2
1
1
0
0
1
1
0
0
1
2
0
0
0
0
1
2
2
1
1
1
0
0
0
0
0
1
0
0
1
1
2
2
2
1
2
2
0
0
0
1
0
0
0
1
1
1
2
1
0
0
0
1
0
0
0
0
2
1
1
0
2
2
0
0
0
0
0
1
2
0
2
1
0
0
1
0
0
0
0
1
0
1
0
0
1
5
2
0
1
1
0
0
0
2
0
2
1
0
0
0
0
1
0
0
1
0
3
0
0
2
1
1
2
0
1
1
1
1
1
0
0
0
2
1
0
1
0
1
0
1
0
0
1
0
2
0
1
0
2
2
0
0
1
2
0
0
2
0
2
2
2
2
0
2
1
2
1
1
1
1
0
1
0
1
0
0
2
0
0
0
0
1
2
2
0
1
0
2
2
0
1
0
0
0
0
0
1
0
1
1
1
0
0
3
0
1
0
0
0
0
0
0
0
1
3
1
1
0
0
2
2
0
0
0
0
2
1
2
1
0
1
1
0
1
0
0
0
0
3
2
0
2
1
1
1
1
1
0
4
1
0
0
0
1
0
0
1
0
1
2
0
0
1
2
0
0
0
1
0
2
1
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
4
0
1
1
1
0
2
1
2
0
0
1
0
0
2
0
1
2
3
0
1
0
1
0
0
2
2
1
0
2
1
0
0
1
2
0
1
1
0
1
0
2
1
0
0
1
2
0
1
0
0
0
0
1
2
1
1
2
1
2
2
0
0
2
3
0
2
0
1
0
0
1
0
1
2
0
0
0
3
1
1
0
0
1
0
1
1
2
1
1
0
0
0
1
0
0
2
1
1
1
2
0
2
0
1
2
0
1
0
3
0
0
2
0
0
1
2
2
1
0
0
0
0
0
2
0
1
0
0
0
1
2
1
1
0
1
0
1
2
0
0
0
0
2
0
2
1
1
0
0
2
0
3
0
0
1
0
0
1
1
0
2
0
1
0
4
1
0
0
1
0
0
1
2
1
2
0
1
0
1
1
2
0
1
2
2
0
1
1
1
2
1
2
0
1
1
1
0
0
1
2
0
1
1
0
0
1
1
1
1
0
1
2
1
0
1
1
1
0
0
0
0
2
1
2
1
0
1
2
2
0
0
0
0
2
0
2
0
0
2
1
0
0
0
1
0
0
0
1
0
0
2
1
0
0
1
1
1
1
1
1
2
1
2
0
0
2
1
1
0
1
2
2
1
0
0
0
1
1
0
1
0
0
2
1
1
1
1
1
1
0
0
2
0
1
0
1
1
0
1
1
1
0
2
1
1
0
1
0
0
1
1
0
0
1
1
2
0
1
0
0
0
2
1
0
0
0
0
2
0
0
4
3
0
2
1
2
0
1
0
2
0
2
0
0
2
2
1
0
2
0
0
2
2
0
1
0
0
0
2
0
2
0
1
0
2
1
1
1
0
2
0
0
0
1
1
0
0
0
0
2
1
1
2
0
1
0
0
1
0
2
2
0
2
1
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
1
0
1
2
2
0
3
0
0
0
0
0
2
1
2
2
1
0
0
0
1
1
1
2
0
1
0
0
0
2
1
1
1
0
3
2
1
1
2
1
1
2
1
0
1
1
0
0
1
0
1
1
2
0
0
1
1
0
0
1
1
0
0
0
0
2
2
1
0
1
1
2
0
0
1
0
0
3
0
2
0
1
0
0
2
1
0
2
2
0
2
0
1
1
0
0
2
2
0
1
0
2
2
2
1
2
0
2
2
2
1
1
0
2
1
0
2
0
1
1
0
2
1
1
0
0
1
0
0
1
1
3
2
1
0
1
0
1
0
0
2
0
1
2
1
1
2
0
3
2
1
1
1
0
2
0
1
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
2
0
0
0
0
1
2
0
1
2
0
1
3
2
2
0
0
0
1
2
1
0
2
1
1
0
0
0
0
0
1
0
0
2
1
1
2
0
0
2
1
1
1
2
0
0
2
1
2
1
0
2
1
1
0
0
2
2
1
1
1
0
2
1
1
1
0
0
2
2
2
1
0
0
1
1
0
0
2
0
0
0
0
0
0
2
1
0
1
1
2
1
1
0
1
0
0
0
1
2
1
0
2
0
0
2
0
1
0
1
1
2
1
0
1
1
0
0
0
1
0
0
1
0
2
1
0
1
0
2
4
0
0
0
2
2
0
2
1
0
0
1
0
0
1
0
0
24
0
0
0
2
0
0
0
2
0
2
2
0
2
1
1
0
1
0
1
0
1
1
2
1
1
1
2
0
0
1
2
2
2
1
0
1
0
2
1
2
2
0
0
0
0
0
1
2
2
0
0
0
0
0
0
1
1
0
2
0
0
2
0
2
1
0
2
0
0
0
1
0
2
1
1
0
1
2
2
1
1
0
1
0
1
0
1
1
1
2
2
0
0
0
1
2
2
0
1
0
1
0
0
1
2
1
1
2
0
0
2
2
0
1
1
1
2
1
0
0
1
0
0
1
1
2
0
0
0
2
0
2
0
1
1
1
0
0
2
1
0
1
1
1
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
3
1
2
2
1
1
3
4
0
0
1
0
1
1
1
1
1
0
2
0
0
1
0
1
0
0
2
0
0
1
2
0
1
1
2
0
0
1
0
0
0
0
1
2
1
2
1
0
2
0
0
0
0
0
2
2
0
1
1
0
1
0
0
1
1
2
0
2
0
1
1
0
0
2
0
0
0
0
0
1
0
1
0
1
0
0
1
1
0
0
3
0
2
1
2
0
0
1
1
0
0
0
0
1
1
0
0
1
0
1
1
1
2
0
1
0
1
1
0
2
0
0
1
0
0
0
2
1
0
0
0
0
1
2
1
2
0
0
1
2
1
1
1
4
0
0
0
0
1
0
1
0
0
0
2
0
0
1
2
1
1
0
1
0
0
1
0
1
3
2
0
0
0
0
1
1
0
0
1
1
2
2
0
1
0
1
0
0
0
1
0
1
0
1
2
2
1
2
0
0
1
0
0
1
0
0
0
1
1
1
1
0
1
2
0
0
0
0
1
1
0
0
0
0
1
2
1
1
1
2
1
2
0
2
1
1
3
0
0
0
0
1
1
0
1
2
0
0
0
0
1
0
0
0
2
3
2
2
1
1
0
0
1
0
2
1
1
0
0
0
0
1
0
1
1
0
2
0
2
1
1
0
0
0
0
0
1
0
1
0
2
1
0
1
0
5
1
2
2
1
1
0
2
0
0
0
1
0
2
2
0
0
1
1
1
0
2
0
0
1
0
0
1
2
2
1
2
1
1
0
1
1
2
1
0
1
2
2
2
1
1
0
1
1
2
2
0
0
2
1
1
1
0
1
0
0
0
0
1
2
0
0
2
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
3
0
1
2
0
0
1
0
0
0
0
1
0
2
1
0
2
1
0
0
2
2
0
1
2
0
1
0
0
2
1
0
1
1
0
0
1
2
0
1
2
0
1
1
0
2
2
0
0
0
0
1
0
4
0
0
0
0
0
1
0
0
0
2
1
1
0
0
1
2
1
1
2
0
0
1
0
0
2
1
1
0
2
0
2
2
2
0
2
1
0
1
1
2
2
5
0
0
4
2
2
0
0
1
0
2
2
1
2
1
1
0
1
1
2
1
0
3
0
0
1
1
1
2
0
2
0
0
0
0
2
1
0
2
1
1
2
2
2
0
0
0
1
0
2
1
2
0
2
0
1
0
0
1
1
2
0
1
0
0
0
0
1
1
2
1
1
1
2
1
0
1
0
1
2
1
1
0
1
1
1
0
1
0
0
2
0
0
0
0
0
0
1
1
0
2
0
0
0
1
0
2
0
1
0
0
1
0
1
0
0
0
2
1
2
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
2
2
1
0
0
1
2
0
0
0
1
0
0
2
0
1
1
0
1
1
0
2
1
2
1
1
0
1
1
1
1
1
2
1
0
0
1
1
0
1
0
0
2
0
1
0
1
1
1
2
1
1
0
0
0
0
2
0
2
2
1
0
1
0
0
0
2
1
2
1
1
0
0
0
0
2
0
0
2
1
0
0
1
1
0
0
3
0
0
1
0
1
1
0
0
2
2
0
1
1
0
0
0
0
4
2
1
0
2
1
2
0
0
2
0
0
0
0
1
0
1
0
0
1
2
2
0
2
2
0
2
1
1
0
1
1
0
0
0
0
1
0
1
0
0
0
1
0
1
1
1
0
0
0
1
1
0
0
0
2
1
1
0
2
1
2
1
0
2
0
2
0
1
1
2
0
1
0
1
2
1
1
2
2
1
1
1
2
1
0
1
1
1
2
1
0
1
0
2
0
1
0
1
2
0
0
0
0
1
1
2
1
1
0
1
0
1
1
0
0
2
2
0
0
2
0
2
0
1
1
2
0
0
0
0
1
1
1
2
1
1
2
0
0
1
0
0
1
0
1
0
1
1
0
1
2
0
1
2
0
2
0
2
1
0
1
0
2
0
0
2
0
2
1
0
1
3
0
0
2
0
2
1
0
0
3
0
2
0
0
0
0
0
0
1
1
0
2
2
0
0
0
2
1
0
0
1
2
0
2
0
0
0
2
2
0
1
0
1
0
1
0
1
1
1
0
0
0
1
0
0
1
0
2
0
1
1
0
3
1
2
2
0
1
0
1
1
2
0
0
2
0
1
2
0
0
2
1
1
2
0
0
2
1
1
1
0
0
0
2
2
2
1
0
0
0
1
0
1
1
0
2
1
5
0
0
1
0
0
0
2
0
2
1
1
1
1
2
3
0
0
2
0
0
0
1
2
0
1
0
0
1
1
2
2
0
1
0
0
1
2
1
0
0
2
0
1
1
1
0
0
2
1
0
2
0
0
0
0
0
2
0
0
0
1
2
2
1
0
2
0
2
1
0
1
0
2
0
0
2
1
0
1
0
0
0
2
0
0
0
2
0
2
1
0
2
0
0
0
2
1
0
0
1
2
0
2
1
1
1
2
2
1
1
0
0
2
1
0
2
1
0
2
1
0
1
1
0
0
1
0
0
1
0
1
2
2
0
1
1
1
2
1
1
1
1
0
0
0
1
2
1
0
2
1
1
0
0
1
0
1
0
2
0
0
3
0
0
0
0
0
2
1
2
1
0
1
1
2
0
0
1
2
1
0
1
1
0
0
0
4
0
1
0
1
1
0
2
2
0
0
2
0
0
0
1
1
0
0
0
0
3
0
0
1
0
1
0
1
2
0
0
2
0
2
0
0
2
0
1
0
1
0
0
2
1
0
1
0
0
2
0
2
1
2
0
1
1
2
0
1
0
1
4
0
2
0
1
0
0
1
0
2
1
2
0
2
1
2
2
0
0
1
0
2
2
0
1
1
2
0
2
1
2
0
0
0
1
1
0
1
0
2
1
0
0
0
2
0
2
0
0
0
0
0
2
2
0
2
1
0
0
2
0
1
2
0
0
2
0
0
0
0
1
1
0
1
0
0
2
2
0
2
0
0
0
0
0
2
0
1
2
1
0
2
2
1
2
0
0
1
0
0
3
0
2
0
0
2
1
0
0
0
0
2
1
0
1
2
1
0
0
1
0
0
0
0
1
1
1
1
2
2
0
1
1
1
2
1
2
0
0
2
0
0
1
0
0
0
0
1
0
0
0
1
0
2
0
1
2
2
2
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
1
0
1
0
1
0
0
2
0
0
0
1
2
0
0
1
2
0
2
2
1
0
2
1
0
1
1
1
0
1
1
0
1
0
1
1
0
0
1
1
0
0
0
1
0
0
2
1
2
2
4
0
1
2
0
0
2
0
1
1
0
0
2
2
0
0
0
0
2
1
0
2
0
2
0
0
1
2
2
2
0
0
2
0
1
0
0
1
1
3
2
1
0
0
0
2
1
2
0
2
2
0
0
0
1
0
1
0
1
2
1
1
0
2
1
0
2
0
0
1
1
0
0
1
0
1
0
0
0
0
0
1
0
0
1
1
0
0
1
2
2
0
2
0
1
1
0
0
0
0
0
2
2
0
1
0
0
2
0
1
1
1
1
1
2
1
1
0
2
0
1
1
2
2
2
0
0
0
0
0
2
1
0
0
2
1
0
1
2
1
0
1
1
0
0
2
0
0
1
1
1
0
1
1
0
0
0
0
0
0
2
0
0
0
1
0
0
1
2
2
2
1
3
0
0
0
2
2
0
0
0
2
0
0
0
0
2
0
3
0
1
1
1
0
0
0
1
1
1
0
2
1
0
1
0
0
1
1
1
2
0
0
0
0
1
1
1
0
1
0
1
0
0
0
0
0
1
0
2
0
1
2
2
0
1
0
1
0
1
1
0
0
0
2
0
2
0
0
0
1
1
1
0
0
2
1
0
2
0
0
0
2
4
0
1
1
1
1
1
2
1
0
0
2
0
2
0
1
2
0
0
0
0
1
0
0
2
1
0
0
2
2
2
0
0
2
0
2
2
3
0
0
2
0
0
0
1
2
0
1
1
0
1
1
3
0
2
0
2
0
1
0
1
0
0
0
2
1
7
0
0
1
1
1
1
0
1
2
0
0
2
1
0
0
0
0
1
0
3
2
2
0
0
0
1
1
0
0
1
0
0
0
1
1
1
1
1
0
0
0
2
1
2
0
1
1
1
0
0
0
1
0
2
0
1
0
0
0
2
1
0
1
1
0
1
0
0
2
0
2
0
1
2
0
0
0
2
0
1
0
1
2
0
2
1
0
0
1
1
0
0
0
0
1
2
3
0
2
0
2
2
1
0
1
0
1
2
0
0
0
0
0
0
2
0
0
2
0
2
0
1
2
0
2
0
2
1
1
1
0
1
0
0
1
1
0
0
0
1
1
0
2
1
0
0
0
2
1
0
2
1
2
0
1
0
0
1
1
1
0
0
1
0
1
0
1
2
0
0
0
1
2
1
1
0
3
0
0
0
0
2
1
0
2
0
1
1
0
0
1
2
0
2
0
1
2
1
0
0
1
0
2
2
1
1
1
0
1
0
1
1
1
0
1
0
1
0
0
0
1
1
0
0
1
0
0
1
1
2
0
1
2
0
0
1
2
0
0
1
0
1
2
0
1
0
0
1
1
0
2
0
0
0
0
0
0
2
0
0
0
1
1
0
1
2
0
1
0
0
0
2
1
2
0
0
0
2
0
1
2
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
1
1
0
1
2
0
0
2
0
0
1
1
0
1
1
0
0
0
2
2
1
0
0
0
1
0
1
0
0
0
2
0
1
0
0
1
1
1
0
0
0
0
0
4
0
0
2
1
0
0
2
0
0
0
1
0
0
1
0
0
2
0
1
1
1
2
1
1
0
1
2
1
0
2
1
2
0
0
0
2
3
1
0
1
1
2
1
1
1
2
2
0
0
2
1
0
0
2
1
0
1
1
0
0
0
1
2
0
1
1
0
1
1
0
0
1
1
0
0
0
2
1
0
1
1
2
1
2
2
1
0
1
2
1
1
0
1
2
0
0
0
1
2
0
2
0
2
0
1
0
0
0
0
2
0
0
0
0
1
0
0
2
4
1
0
0
0
1
2
0
1
2
1
2
1
2
2
1
1
2
0
1
0
0
0
0
2
0
1
0
0
1
0
0
0
2
0
0
0
2
1
2
0
1
1
0
0
2
1
3
2
1
0
2
1
0
0
0
2
0
2
0
1
1
2
2
0
0
0
0
0
0
1
2
1
1
1
1
1
2
0
1
0
4
1
1
2
1
0
0
0
2
2
0
1
3
0
0
2
1
1
1
1
2
1
2
2
0
1
2
2
2
1
1
0
1
1
2
0
0
0
0
1
0
0
2
1
2
1
1
1
1
2
0
0
2
0
2
0
0
0
0
0
1
1
0
0
0
0
1
1
1
0
2
0
2
6
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
2
1
0
2
1
0
0
0
1
2
1
1
0
0
1
1
0
0
0
2
1
1
0
0
0
1
2
0
2
1
1
1
0
1
2
1
0
0
1
3
0
1
1
2
1
1
0
0
2
0
1
1
0
0
2
0
0
0
0
2
2
3
0
0
0
0
1
2
0
5
2
0
0
0
0
1
0
0
0
1
0
2
1
3
0
0
0
2
0
0
2
0
1
0
3
1
0
2
0
0
0
0
0
2
0
0
0
2
0
1
1
0
0
1
1
0
1
0
0
1
2
0
1
1
0
0
0
0
1
1
0
2
0
0
1
2
2
0
0
1
0
0
1
2
1
1
0
0
0
0
3
0
0
0
0
2
0
2
0
0
0
3
0
0
0
2
1
0
3
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
2
2
1
1
2
1
1
1
0
2
2
0
3
2
0
0
1
0
2
1
1
0
2
0
2
0
0
1
1
0
0
0
1
0
0
2
0
1
0
0
1
1
0
1
2
2
0
2
2
0
1
0
2
1
1
2
0
0
2
2
1
0
2
0
2
2
0
0
0
0
2
0
0
2
0
0
2
0
0
2
0
0
1
1
2
0
1
0
2
0
3
2
1
0
1
1
1
0
1
1
0
0
0
0
0
1
1
2
0
0
1
0
2
0
1
2
0
2
1
1
2
0
0
0
0
2
0
0
1
0
0
0
0
2
0
2
0
1
0
1
0
2
0
1
0
0
2
1
1
0
0
0
3
0
1
1
0
0
0
0
2
0
0
2
0
1
0
0
1
0
0
2
0
0
0
0
0
2
2
0
1
0
0
1
1
2
3
0
0
0
2
2
0
1
0
0
0
2
2
0
1
2
1
0
1
0
0
1
0
0
2
1
1
1
1
0
1
1
1
1
0
1
0
1
0
1
2
1
0
0
1
2
2
1
0
2
0
0
0
2
0
2
2
2
1
2
0
0
1
0
1
2
1
1
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
1
3
1
0
0
0
1
1
2
0
1
0
0
1
0
0
1
0
2
1
2
1
0
0
1
0
0
2
1
2
0
0
0
0
0
2
0
0
1
2
0
2
1
0
1
2
0
0
1
2
2
0
1
0
2
2
0
1
0
0
0
1
1
1
2
2
1
0
2
0
0
0
1
0
2
0
1
0
1
1
0
0
2
0
1
0
0
1
0
2
1
0
3
0
0
0
2
2
0
2
1
2
0
0
0
1
0
1
0
0
2
0
0
0
2
0
1
0
0
0
1
0
3
0
2
1
1
0
1
1
0
1
1
1
2
0
0
0
1
1
1
0
1
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
1
0
2
0
1
1
0
0
0
1
0
0
0
0
2
1
2
1
2
0
0
0
0
1
3
0
2
1
2
1
2
0
1
0
1
2
1
0
2
2
0
2
0
1
0
3
1
1
0
0
2
2
0
1
1
2
0
1
1
0
2
1
1
1
0
0
0
1
0
0
1
1
0
0
2
2
0
0
2
2
1
1
2
0
0
1
0
0
1
0
2
2
1
3
0
2
0
3
1
2
0
0
1
1
1
1
0
2
2
1
2
0
0
1
0
1
1
2
2
0
1
0
1
0
2
0
1
0
0
1
1
0
1
0
0
1
0
1
0
1
3
0
0
0
0
2
0
1
1
0
0
3
2
0
1
1
2
3
1
2
0
2
0
0
0
1
0
0
1
2
0
0
2
0
0
1
0
1
1
0
1
2
0
1
2
0
0
3
2
1
0
0
0
1
1
0
0
1
0
0
2
0
2
0
0
0
2
0
0
1
1
0
0
0
1
1
0
0
0
0
2
1
1
2
1
0
0
0
2
0
0
1
0
1
2
0
0
1
1
1
0
1
1
1
0
1
1
0
1
1
0
1
1
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
1
1
0
0
1
2
1
2
0
2
0
1
0
2
0
1
1
0
1
2
0
2
1
0
0
2
0
2
1
2
2
2
1
2
1
1
1
1
1
2
1
1
2
1
2
1
0
0
2
0
2
1
0
1
1
0
0
0
0
0
0
1
0
2
1
1
0
0
0
0
1
0
1
1
1
0
0
0
1
0
0
0
0
0
0
1
1
1
2
0
0
0
0
1
1
0
1
2
0
0
0
0
1
0
0
0
0
2
2
2
0
0
1
0
0
1
1
1
0
0
0
4
0
1
2
2
0
0
2
1
2
1
1
0
0
0
0
1
3
1
0
0
0
2
0
2
2
3
0
1
0
2
0
0
2
0
1
2
1
0
2
0
1
0
1
0
2
1
4
0
0
0
0
1
0
2
0
0
0
1
0
1
1
1
0
2
0
1
2
1
0
2
0
2
0
1
1
0
0
1
0
0
0
2
0
2
0
0
1
1
0
1
1
2
1
1
0
2
1
2
2
1
3
1
0
0
0
1
2
1
2
2
0
0
1
1
0
1
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
1
1
0
0
2
2
1
2
1
1
2
2
2
0
0
0
0
1
2
0
0
0
2
4
2
2
0
0
1
0
1
1
0
1
1
0
0
0
0
2
2
0
1
3
2
0
2
1
0
0
1
0
1
1
1
2
0
0
1
1
0
1
0
1
1
0
2
1
0
0
0
0
0
1
1
2
0
0
2
0
0
0
0
0
2
0
1
0
0
5
0
1
0
0
1
0
2
1
0
0
0
3
0
2
0
1
0
3
0
1
2
2
0
0
2
2
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
3
1
1
0
1
1
2
2
1
1
0
0
0
1
0
2
0
1
0
0
1
1
0
2
0
2
0
1
1
1
0
2
0
1
2
1
0
1
0
1
0
1
2
0
2
0
1
1
1
2
1
1
1
2
0
0
0
4
0
0
1
0
1
0
0
1
0
0
1
0
1
1
2
0
1
0
0
0
1
1
0
1
0
1
2
0
0
1
1
0
0
2
1
1
1
0
1
1
0
0
0
1
1
1
1
1
1
1
0
0
2
0
1
0
0
0
2
2
1
3
0
0
0
2
0
0
0
0
0
1
1
1
0
0
0
2
0
0
0
0
0
0
2
1
0
1
2
2
2
0
0
0
1
1
0
1
0
0
0
2
2
2
2
0
1
0
1
0
2
0
0
0
1
0
1
0
2
1
1
0
1
0
0
1
2
1
1
0
1
0
0
0
1
1
1
1
0
2
0
1
1
0
1
1
0
3
0
2
0
2
0
0
0
1
0
0
1
1
0
0
1
0
2
1
1
0
1
2
1
1
1
1
0
1
1
0
0
1
1
1
1
1
0
0
0
1
1
2
1
1
1
0
0
2
0
0
2
1
2
0
0
2
0
1
0
1
0
1
1
0
0
0
2
0
1
2
0
0
2
0
0
1
0
0
1
1
0
0
0
2
0
0
0
1
2
2
2
0
2
0
0
2
0
2
0
0
2
1
0
1
0
1
1
0
0
1
1
1
1
1
0
0
0
1
1
0
0
0
1
0
1
2
0
3
0
0
2
1
2
2
0
0
1
1
2
2
1
0
1
0
0
0
2
0
2
0
0
0
0
1
1
0
2
1
2
0
1
0
2
1
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
2
1
0
0
0
0
0
1
2
0
0
0
1
0
1
0
0
0
1
0
2
1
1
0
2
0
0
0
1
2
0
1
1
0
0
0
2
0
0
1
0
3
0
0
2
5
0
1
0
0
1
1
1
1
0
1
0
1
0
1
2
2
0
0
2
0
2
2
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
2
2
1
1
1
1
2
0
2
2
1
0
1
1
2
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
2
0
0
1
2
1
1
1
0
1
2
1
0
0
0
1
0
0
0
1
1
1
1
0
3
0
2
0
1
0
2
0
0
1
0
1
1
0
1
1
0
1
1
1
0
1
0
1
1
1
1
0
0
0
2
2
0
0
0
0
1
1
1
1
0
2
1
0
2
0
0
0
2
1
1
0
0
0
2
0
1
1
1
2
0
2
0
0
2
1
0
0
1
1
0
0
0
1
2
0
0
2
1
0
1
3
1
0
1
1
1
1
0
0
0
2
0
2
1
2
0
0
1
2
0
1
2
0
0
0
0
0
0
0
2
0
1
0
1
1
2
0
0
0
1
2
3
0
0
1
0
2
0
1
2
2
1
0
4
2
1
0
1
3
0
1
0
0
2
1
0
0
1
0
6
2
0
0
2
0
0
0
0
2
0
1
0
1
1
0
2
2
0
0
1
0
1
1
0
0
0
2
0
2
2
0
2
1
0
0
0
0
1
1
1
1
0
1
1
1
0
1
1
0
0
2
1
1
1
1
0
1
0
1
1
0
3
0
1
1
1
0
1
2
0
1
2
1
1
2
0
0
0
2
2
1
0
2
1
0
0
0
0
0
0
0
1
1
0
0
2
0
1
1
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
2
1
0
0
1
2
0
2
2
1
0
2
1
0
2
1
1
2
0
0
0
0
2
1
0
1
1
0
0
2
0
2
0
0
4
2
1
0
2
0
0
0
0
1
2
2
1
0
0
0
2
2
0
0
1
0
1
0
0
0
0
1
1
1
0
2
0
0
2
0
0
2
2
1
0
3
1
1
0
0
0
1
0
2
0
0
1
2
0
0
0
1
1
1
1
0
0
1
0
3
1
0
2
1
1
0
0
0
2
0
2
0
1
1
1
0
1
0
0
1
0
3
0
0
2
0
1
2
2
1
1
0
0
0
0
1
0
0
1
0
2
1
1
0
1
1
1
0
0
2
0
1
2
0
1
3
0
0
2
0
2
1
1
2
0
2
0
1
2
1
0
0
2
1
0
1
1
1
1
1
1
1
2
1
1
0
0
0
1
1
1
0
2
1
0
1
0
2
0
1
2
2
0
1
2
1
0
0
1
1
0
0
0
1
1
1
1
1
1
0
0
0
1
0
1
0
1
0
1
0
4
0
0
1
1
0
1
0
0
2
1
2
2
0
2
0
0
0
2
1
2
0
0
0
2
2
1
1
0
2
0
0
1
0
2
1
0
1
1
0
0
2
2
2
1
0
1
2
2
0
0
0
1
0
2
1
0
0
0
0
1
0
1
1
0
2
1
1
0
0
0
1
2
1
0
0
1
1
1
0
1
0
1
0
2
1
2
0
2
0
0
2
0
2
1
1
1
0
1
1
0
1
2
0
0
0
2
0
1
2
0
0
1
2
1
1
0
1
0
1
1
0
0
0
0
1
0
1
0
1
1
1
1
2
2
0
1
0
1
1
2
1
2
1
0
1
2
1
1
2
0
0
2
0
0
1
2
0
0
0
1
2
1
1
1
2
0
0
1
2
1
0
1
0
0
2
2
2
1
0
3
0
1
2
2
2
1
1
0
1
1
2
1
0
0
2
0
1
1
0
1
1
2
0
2
0
2
0
0
0
0
3
2
0
0
0
0
1
1
0
1
0
0
0
0
3
0
1
2
0
0
1
1
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
1
0
1
2
1
1
2
1
2
0
2
1
0
0
2
2
0
1
2
2
0
2
0
1
1
0
1
0
1
0
1
1
0
2
1
2
1
2
2
0
0
1
0
0
2
1
1
0
2
0
1
0
0
0
2
0
2
1
0
0
0
0
0
1
2
0
1
1
1
3
1
2
0
1
1
0
1
0
0
0
0
0
1
2
1
0
1
1
1
0
2
0
3
3
0
1
2
1
0
0
1
1
1
2
1
0
1
1
2
0
0
1
1
0
2
0
0
1
0
2
0
1
1
0
0
0
2
2
0
1
1
1
0
4
1
0
0
0
0
1
0
1
0
0
0
0
1
0
2
1
2
0
1
0
0
2
1
1
1
0
2
0
0
0
2
1
1
0
0
2
1
0
1
1
0
0
0
1
0
0
0
1
0
0
1
0
0
3
0
0
0
0
0
2
2
0
1
2
0
2
1
2
0
0
1
0
2
1
0
1
2
0
0
0
0
0
1
0
0
1
0
1
2
2
1
0
0
0
0
1
0
2
1
1
2
1
1
1
1
2
1
0
0
0
0
1
0
0
0
2
1
0
0
4
1
0
0
0
0
0
0
1
0
1
2
1
1
2
5
0
0
0
0
2
1
0
1
2
1
1
0
1
2
0
0
2
0
1
1
0
1
1
2
1
0
1
0
3
0
2
1
1
0
1
1
0
1
1
0
0
0
2
0
0
2
1
1
0
1
2
0
0
0
0
2
1
0
1
1
0
2
0
0
0
0
1
0
2
0
0
0
1
1
0
0
1
1
2
1
2
1
1
0
1
0
0
1
0
0
2
0
0
1
0
0
0
0
1
1
0
1
0
0
0
3
1
2
0
0
0
1
0
2
0
1
0
0
0
1
0
0
1
0
0
0
0
2
0
1
1
1
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
1
0
0
1
2
1
0
0
0
0
0
0
1
0
2
1
0
4
2
1
0
0
3
0
0
0
0
0
1
0
1
0
0
1
0
2
1
1
1
0
1
0
0
1
1
0
0
0
0
1
1
1
0
2
0
1
2
0
0
2
0
1
0
0
0
2
0
1
0
0
0
0
2
1
0
0
0
1
1
0
2
0
0
0
0
2
2
1
1
0
0
2
0
0
1
1
0
0
0
1
2
0
0
1
0
0
1
2
1
1
1
0
1
2
1
1
1
0
0
1
3
1
1
0
1
1
0
2
0
0
0
1
1
0
2
0
1
0
1
1
0
0
0
0
0
1
0
0
1
1
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
2
1
0
0
1
0
0
0
2
1
0
1
3
1
0
2
2
1
0
0
0
0
1
0
2
1
0
1
2
2
0
1
0
1
2
1
1
1
0
2
2
1
0
0
0
1
0
2
0
2
1
2
0
0
2
0
2
0
1
0
1
1
0
0
1
0
2
0
1
2
0
1
1
3
0
1
0
0
0
2
0
1
1
1
2
2
1
2
0
0
0
0
0
2
0
1
2
2
1
2
0
2
0
0
0
1
1
2
0
0
0
0
1
0
2
0
0
1
2
1
1
2
2
2
1
1
2
0
1
0
2
1
0
0
2
2
1
1
1
0
1
0
1
0
0
1
0
2
0
0
0
0
0
0
0
1
1
0
1
1
2
0
0
1
2
0
0
2
1
1
2
1
0
1
2
2
5
1
2
0
0
0
1
2
0
2
0
1
2
1
0
0
1
0
2
2
2
1
2
1
2
0
0
0
0
1
1
0
1
0
1
0
1
0
1
0
0
0
1
0
0
1
0
1
1
2
0
0
2
0
1
0
1
1
0
0
3
1
1
0
2
0
0
0
2
0
1
1
0
1
1
0
0
1
0
0
0
0
3
0
2
1
2
0
0
0
1
0
2
0
0
1
0
0
1
1
0
1
0
2
0
1
0
1
0
1
2
1
1
1
0
1
0
1
0
1
0
1
0
1
0
1
1
0
0
0
1
0
0
2
1
4
0
2
2
1
1
1
0
0
2
0
2
1
1
1
0
0
3
0
3
1
1
0
2
0
0
0
2
1
2
0
0
0
1
0
0
2
0
0
0
1
1
1
0
0
0
1
0
3
0
2
0
0
1
0
1
0
0
1
0
2
1
2
1
1
0
0
2
1
2
0
0
1
1
0
1
0
0
0
0
0
1
0
1
1
0
0
0
2
0
2
0
0
2
0
0
1
1
2
0
0
1
0
1
2
2
0
1
0
0
1
0
0
0
0
0
1
0
0
2
2
0
0
1
0
1
0
2
0
2
2
0
1
1
2
0
0
1
0
0
0
0
0
2
0
1
0
1
0
2
0
1
0
2
0
0
2
1
2
1
0
0
0
0
2
2
0
1
1
0
0
0
1
1
2
2
0
2
0
0
0
0
1
1
1
1
0
0
0
1
0
1
0
1
1
0
0
0
1
1
1
0
0
0
1
1
0
1
1
2
0
0
0
0
0
4
1
0
0
0
0
0
0
2
0
0
2
0
1
0
2
0
1
1
1
0
1
0
1
0
2
0
0
2
0
0
0
0
0
0
1
1
2
0
0
1
0
0
1
0
0
1
0
2
1
1
1
2
0
1
1
0
0
2
2
0
1
2
1
0
0
0
1
2
0
0
1
0
1
2
3
0
0
0
1
1
0
1
0
1
0
1
0
2
0
0
0
1
0
0
1
0
1
2
0
1
0
0
1
1
1
0
0
2
0
1
0
1
1
1
1
1
2
1
0
1
3
0
0
2
0
2
0
1
1
0
0
0
1
0
2
0
0
0
0
0
0
2
1
0
0
2
1
0
0
2
0
0
0
1
6
1
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
1
1
1
1
0
0
0
2
1
0
1
1
1
2
0
0
0
1
1
0
1
0
0
2
0
0
0
0
0
2
2
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
1
1
0
1
2
1
2
1
0
0
1
1
0
1
0
0
0
1
2
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
2
2
0
0
0
0
2
0
1
3
1
2
1
1
1
1
0
0
0
2
0
1
0
2
0
3
1
0
1
1
0
1
2
0
2
2
2
0
0
0
1
0
2
0
1
2
0
0
0
0
1
2
0
2
1
1
1
0
0
1
0
1
2
3
2
0
1
1
0
1
1
0
2
1
1
0
0
1
1
1
0
0
0
1
2
0
0
1
2
2
1
0
2
2
0
0
0
2
0
1
0
2
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
2
0
0
0
0
2
2
2
2
0
1
2
2
2
0
0
2
0
0
0
0
0
0
0
2
2
0
2
1
0
1
1
0
1
5
1
3
0
0
1
0
0
2
2
0
1
0
1
0
0
1
1
0
0
1
0
2
0
0
0
1
1
1
1
0
1
2
2
0
0
0
2
2
0
2
0
2
0
0
1
1
0
2
0
3
1
0
0
1
1
0
2
0
1
2
0
0
1
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
1
1
1
2
1
1
0
1
2
1
1
2
0
1
0
1
0
0
0
1
0
1
2
0
0
1
0
0
2
2
1
1
1
2
1
0
1
0
0
2
1
1
0
0
0
1
0
0
0
1
3
0
1
1
0
0
0
1
1
1
2
1
2
0
1
1
2
1
0
0
2
1
1
2
1
2
1
0
1
1
0
0
0
1
0
0
0
2
0
1
1
2
1
1
0
1
3
1
2
1
1
0
1
0
2
0
0
0
1
0
0
1
2
1
2
0
0
1
1
1
1
1
1
2
3
0
1
1
3
2
2
1
1
3
2
0
0
1
1
1
0
1
1
0
2
0
1
0
0
3
2
1
2
0
2
1
0
2
0
2
1
1
1
0
0
1
0
0
0
0
2
0
0
2
3
0
2
1
2
3
1
1
1
1
0
1
0
1
0
2
0
0
1
1
1
2
0
2
0
2
2
1
1
0
3
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
2
0
0
2
0
1
0
2
2
0
2
2
2
2
1
1
1
1
0
1
0
2
0
0
2
0
0
2
0
1
1
0
2
0
1
2
1
0
1
2
2
2
0
1
2
0
2
0
0
2
1
0
0
0
1
0
1
0
1
0
3
0
1
1
2
0
0
0
0
0
0
0
0
1
1
1
1
0
1
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
1
2
0
0
1
0
1
1
0
0
1
0
0
2
2
1
0
0
1
1
0
2
3
0
0
2
0
0
2
1
0
1
1
0
0
0
1
1
2
0
2
0
3
0
2
0
2
0
1
1
0
1
0
1
1
1
1
0
1
1
0
0
1
0
1
0
1
2
0
1
1
0
0
0
2
1
2
1
0
4
2
0
0
0
0
2
0
0
0
0
0
0
1
2
0
1
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
1
2
2
0
1
2
0
0
0
1
1
0
2
0
0
2
3
0
2
0
2
2
2
0
1
1
2
0
2
0
0
2
1
2
1
1
1
0
0
0
3
1
0
1
3
1
1
0
1
1
0
4
1
2
1
3
2
1
1
0
1
2
0
0
0
1
0
1
1
1
1
0
2
2
2
0
1
2
0
0
0
1
1
1
4
1
2
1
1
1
2
0
1
1
2
0
0
0
0
0
0
1
2
0
2
0
1
0
1
1
2
2
1
2
0
0
0
1
0
2
2
0
1
1
3
1
1
1
2
0
1
0
0
0
6
0
0
0
1
1
1
0
0
1
1
0
0
2
1
1
0
0
1
1
2
0
2
1
2
1
0
1
0
1
2
0
1
0
1
1
1
1
0
1
0
1
2
1
0
3
1
0
2
0
1
1
2
0
2
0
0
1
1
2
1
1
1
0
1
2
2
0
0
1
2
2
0
2
0
0
0
1
0
1
0
0
1
1
2
3
0
0
1
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
2
2
1
1
2
1
0
1
1
1
2
0
1
0
0
0
2
2
1
2
2
1
3
0
1
0
2
0
0
1
0
0
1
0
1
1
0
1
1
1
2
1
2
1
0
1
2
1
0
0
0
2
0
2
1
0
1
0
1
1
0
0
2
2
0
1
2
1
0
3
2
2
1
1
2
2
0
1
0
1
0
0
2
2
0
1
1
0
0
1
0
0
2
1
1
0
2
0
0
0
1
0
1
2
1
1
0
0
0
1
0
0
1
0
0
3
0
0
1
2
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
1
0
0
0
1
1
1
0
1
0
2
0
0
0
1
0
0
0
1
1
1
0
1
2
0
1
1
0
0
1
0
3
0
0
2
2
0
1
2
0
2
0
2
0
1
1
0
0
0
2
0
1
1
0
2
0
2
1
0
1
0
0
0
2
0
1
0
2
1
0
2
1
0
0
2
0
3
0
0
2
0
2
0
2
0
1
1
1
1
0
1
0
1
0
2
1
2
2
2
1
2
0
0
1
1
0
1
0
1
1
3
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
2
3
0
1
0
0
0
0
2
0
1
0
1
1
1
2
0
0
0
0
1
2
0
0
0
0
1
0
0
2
0
2
0
2
0
2
2
0
2
2
2
0
2
0
0
2
1
0
3
2
0
1
0
0
0
0
2
0
2
1
2
0
0
1
2
0
0
0
0
2
0
0
0
1
2
2
1
0
0
1
0
0
0
0
1
0
2
1
0
0
0
1
2
0
0
2
1
1
2
0
0
1
0
0
1
0
2
2
2
0
0
2
0
1
1
1
2
1
0
0
0
2
0
1
1
0
0
2
0
2
1
1
0
0
1
0
1
0
1
0
0
0
0
0
1
0
2
0
0
0
1
1
0
0
0
1
1
0
0
0
1
0
1
1
0
2
2
0
0
1
2
0
0
1
1
0
0
1
0
1
1
0
2
0
0
3
1
1
0
1
0
0
1
2
1
0
1
1
0
0
1
1
0
0
2
0
0
0
1
1
1
3
1
1
1
0
0
0
0
0
1
3
2
0
0
0
2
2
1
1
1
0
1
0
0
2
1
1
1
1
0
0
1
1
2
0
2
2
0
1
0
0
0
2
0
2
1
0
0
2
0
2
0
0
2
1
1
2
2
1
0
1
2
0
0
2
2
0
0
1
0
1
0
2
0
0
0
1
0
0
0
0
1
3
0
0
1
1
0
0
3
1
0
0
1
0
2
2
0
0
1
1
1
0
2
0
0
0
2
2
1
0
1
0
1
1
0
2
2
1
0
2
1
2
0
0
0
0
2
1
1
2
0
2
0
0
1
0
1
0
1
0
1
4
1
0
2
0
2
0
0
0
2
1
0
0
1
0
0
0
0
2
1
0
1
0
0
0
2
2
2
1
2
2
2
1
2
0
0
0
0
0
0
0
1
0
1
1
0
0
2
0
1
0
1
1
0
2
1
2
1
0
1
0
1
1
2
1
0
0
0
0
2
0
0
1
0
0
1
0
2
2
1
0
0
0
2
0
1
0
0
1
0
1
2
0
0
0
0
2
1
2
0
2
1
1
1
0
1
0
0
0
3
0
0
2
2
0
0
1
3
0
0
1
0
1
1
3
1
0
0
1
2
1
1
0
1
2
0
1
1
2
2
0
0
1
4
2
1
1
2
1
0
0
0
1
0
0
1
0
0
0
1
3
0
2
1
0
0
0
1
2
0
0
1
0
2
0
1
1
0
0
0
1
0
0
3
0
1
1
0
0
2
2
0
0
0
0
0
0
2
2
0
0
1
0
1
1
0
1
1
2
0
1
2
1
1
1
0
0
0
2
0
0
0
2
1
2
0
0
2
0
0
0
1
0
1
1
2
0
2
0
1
2
0
0
1
0
0
0
2
3
1
0
0
2
1
0
2
0
1
2
2
2
1
2
0
2
1
2
2
0
1
1
0
1
1
1
0
1
0
2
1
1
0
2
0
2
1
0
0
1
0
0
0
2
0
2
0
1
1
1
0
0
2
0
1
0
1
0
1
0
0
1
1
0
1
0
1
0
1
1
2
0
1
1
1
1
2
2
2
2
1
1
1
0
2
1
2
0
0
0
1
1
0
1
0
2
1
1
1
0
0
0
0
0
0
0
0
0
2
1
1
0
2
0
1
0
1
0
0
0
0
1
2
1
1
1
0
1
0
0
0
0
0
1
0
2
1
1
0
0
2
0
0
1
3
0
1
4
0
0
1
0
0
1
1
1
0
0
0
2
1
0
1
0
1
5
0
1
0
1
2
1
1
1
1
1
1
1
2
0
2
0
1
1
1
1
1
0
0
1
1
0
1
0
0
0
1
2
0
0
1
2
1
2
1
2
1
0
0
2
0
1
0
1
0
2
1
1
0
3
1
1
1
1
0
0
2
0
1
0
0
1
2
0
0
1
0
0
2
1
0
1
0
0
1
1
1
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
1
1
0
0
0
2
0
0
1
1
0
2
0
2
0
0
0
1
1
1
1
1
0
1
1
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
1
0
0
1
2
1
0
3
0
0
1
0
1
0
0
1
0
2
1
2
1
2
0
1
0
1
0
1
0
1
0
2
1
0
2
1
0
1
0
2
2
1
1
0
1
2
0
1
3
1
1
1
0
0
2
1
0
1
0
2
1
0
0
0
1
0
0
1
1
1
1
2
2
1
0
0
1
0
1
2
0
0
0
2
3
0
1
2
0
1
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
1
2
1
1
1
0
1
0
0
0
2
0
0
2
0
1
1
0
1
2
1
0
0
0
1
0
0
2
1
0
2
0
0
0
1
0
0
2
1
0
0
0
0
1
0
2
1
1
0
0
0
2
1
0
1
0
2
0
2
0
0
0
1
0
1
0
2
0
1
0
2
0
2
2
0
0
0
1
0
1
0
0
0
1
1
0
2
0
1
0
1
1
0
1
1
0
0
2
0
0
0
0
0
1
0
1
0
3
1
0
1
1
0
0
1
0
2
1
1
0
0
1
0
1
1
0
2
0
1
0
2
1
0
2
0
0
1
2
0
0
0
0
0
0
0
4
0
1
2
0
2
2
0
2
1
1
0
2
2
1
0
2
0
0
1
1
0
1
1
0
0
2
0
0
0
1
1
1
2
2
0
0
0
0
0
0
0
2
0
2
1
2
0
1
1
0
0
0
3
1
0
0
1
1
0
0
0
0
1
1
1
1
1
1
0
1
1
1
0
0
0
0
0
1
0
2
0
0
1
1
0
0
2
0
1
2
1
2
1
2
0
1
0
2
2
1
0
1
1
1
2
2
1
1
1
0
1
0
0
1
2
0
1
1
2
0
2
0
1
1
0
0
0
1
1
2
2
0
0
0
0
1
1
0
2
1
1
0
1
2
1
0
0
0
0
0
1
1
0
2
4
1
1
3
0
1
0
0
0
1
0
0
0
1
0
2
0
0
1
3
0
1
1
0
1
0
2
1
0
0
2
1
0
2
0
0
1
0
2
1
1
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
2
5
0
1
0
0
1
1
2
0
0
0
0
2
2
1
2
1
0
6
0
0
2
2
0
0
1
0
2
0
1
0
0
1
2
2
1
1
0
0
2
2
0
0
0
1
0
0
16
2
0
0
1
0
1
1
0
0
1
3
0
1
0
1
0
0
1
0
1
0
1
2
0
1
2
2
2
1
0
1
0
1
2
1
0
0
0
1
2
0
1
0
2
0
0
2
0
0
0
0
2
0
2
2
2
1
1
2
1
2
0
0
0
0
2
0
0
1
0
0
1
0
1
0
1
0
0
1
2
2
2
1
0
0
0
2
2
0
1
2
1
0
0
2
1
0
0
0
2
1
2
2
0
1
1
1
0
0
1
1
0
0
1
0
0
0
0
2
0
2
1
0
0
1
2
1
0
2
1
1
1
1
0
0
1
2
1
1
2
0
0
0
0
2
2
1
0
2
0
2
2
0
0
1
0
1
1
0
2
1
0
1
0
0
0
0
0
0
0
1
3
0
0
2
0
0
1
0
2
1
1
0
1
1
1
1
2
1
0
0
1
0
0
0
0
0
0
1
0
2
1
2
2
1
2
1
0
0
1
3
0
1
1
1
0
0
1
1
1
0
1
0
0
0
0
1
0
1
2
2
1
1
1
3
2
0
0
2
0
2
1
0
2
0
1
0
2
0
0
1
1
0
0
0
1
2
0
2
0
2
0
1
0
0
2
2
0
0
0
2
1
0
1
1
2
1
0
0
1
0
0
2
1
0
2
2
1
1
0
0
2
1
0
0
0
0
0
1
1
0
2
1
0
0
2
0
1
0
1
0
2
2
2
1
0
1
1
1
2
1
0
1
0
0
1
0
2
1
1
1
1
0
1
2
1
2
2
2
0
1
1
1
0
0
0
0
0
0
0
0
3
2
0
2
1
2
0
0
0
0
0
1
2
1
2
0
0
0
2
0
0
2
0
0
0
0
1
0
0
1
2
1
0
0
2
1
2
0
1
0
0
0
1
0
1
2
0
2
1
2
0
0
1
0
0
0
0
2
2
2
0
1
0
0
0
0
0
0
2
2
2
0
1
0
2
0
1
0
3
2
0
0
1
0
0
2
1
1
1
2
1
0
1
2
2
1
0
0
0
0
0
1
0
0
2
3
0
0
0
2
1
0
1
1
0
1
0
1
1
0
1
0
1
0
1
2
1
1
0
3
2
2
0
2
0
0
0
0
1
1
0
1
2
0
1
0
2
0
1
0
1
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
2
1
0
1
0
0
2
0
0
1
0
0
0
2
1
0
2
0
0
0
1
0
1
0
1
0
0
0
2
0
2
0
0
1
0
0
0
0
0
2
0
2
0
0
1
0
0
0
1
1
1
2
3
1
0
2
0
1
1
1
0
2
0
0
2
1
1
0
1
2
0
0
1
2
0
0
0
1
1
2
1
0
1
1
1
1
2
1
0
1
2
3
1
1
1
0
0
1
0
2
0
1
0
0
1
1
0
0
0
0
1
1
2
0
1
1
0
0
0
1
2
1
0
0
0
0
0
2
0
0
2
0
1
0
0
0
1
0
0
1
1
0
1
0
1
0
0
0
0
1
2
0
1
2
0
1
0
1
0
4
2
1
1
2
2
0
1
1
1
0
0
0
0
0
0
0
1
0
1
2
1
1
0
0
1
0
0
2
0
1
1
2
1
0
2
0
1
2
2
0
0
0
0
1
1
0
0
1
2
2
0
1
0
1
1
1
1
0
0
2
0
1
1
2
0
0
5
0
0
1
0
2
1
0
2
2
0
0
0
1
0
0
0
2
1
2
0
1
0
1
0
2
0
0
0
1
0
0
1
2
0
2
1
1
0
1
2
3
1
0
1
0
1
0
0
0
1
0
1
0
0
0
2
0
1
2
2
0
0
2
0
2
0
0
0
1
1
1
0
2
0
1
1
2
0
0
0
1
2
1
2
1
1
1
0
0
0
1
1
2
0
0
0
0
7
2
0
1
0
2
0
1
0
2
0
1
1
1
0
0
1
2
0
0
0
1
0
0
0
2
1
0
2
1
0
2
0
0
0
1
0
0
1
1
2
1
2
0
0
1
2
6
2
2
1
1
3
1
2
0
1
2
0
0
0
1
2
1
0
2
1
0
0
1
2
0
0
0
2
2
2
2
0
1
1
2
1
0
2
2
0
2
1
0
0
2
0
1
1
1
1
1
1
1
2
0
0
2
0
1
0
2
0
0
0
1
1
0
1
3
0
0
1
0
0
2
2
0
1
1
1
2
0
2
1
2
0
0
0
2
0
0
0
1
1
0
2
1
0
1
0
3
0
2
2
1
1
0
1
2
2
0
0
0
1
0
2
1
1
0
1
0
1
0
0
1
0
1
0
0
1
0
0
2
1
1
0
0
0
1
1
0
1
0
0
1
2
1
0
0
1
0
1
0
0
2
0
0
2
0
0
3
1
0
1
0
2
1
0
1
0
2
0
1
0
1
3
1
2
1
1
0
1
0
0
2
1
0
3
0
0
1
1
0
0
0
2
2
1
2
1
1
2
0
2
2
2
1
2
1
0
0
1
2
3
0
0
1
0
0
0
0
1
2
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
1
0
0
1
1
1
0
1
1
2
1
1
0
0
1
0
0
0
0
2
0
2
0
0
2
1
1
0
0
0
3
2
0
3
0
1
1
0
4
0
0
0
0
0
0
1
0
2
0
0
0
1
0
2
2
1
2
2
0
1
0
0
0
0
1
0
1
1
2
1
0
0
2
1
1
2
0
0
0
1
0
1
1
1
2
0
0
2
0
0
0
1
0
0
1
1
0
3
0
1
2
2
0
2
0
1
0
0
0
0
0
1
0
2
0
0
2
0
1
0
1
2
0
2
1
2
0
3
0
1
1
1
1
0
1
2
2
2
0
0
0
1
0
2
2
0
0
2
1
0
0
1
0
0
0
0
0
0
2
0
2
0
1
0
0
0
1
2
0
0
0
0
1
0
0
1
0
0
1
1
1
2
0
1
2
1
1
0
0
0
1
1
0
1
2
0
1
2
0
0
2
1
0
2
1
0
2
0
0
0
1
0
0
0
1
0
2
0
0
0
2
0
3
0
1
1
2
0
1
0
0
2
0
1
1
0
0
0
1
0
0
0
0
2
2
0
1
2
0
1
0
0
1
1
0
2
0
2
2
0
1
2
0
0
0
0
2
0
1
0
0
0
0
2
2
2
0
1
1
0
2
0
1
1
0
1
0
2
6
0
0
2
2
1
2
3
0
0
1
0
1
0
2
1
1
1
0
0
0
2
2
2
1
0
1
1
0
0
1
1
0
0
2
0
0
3
0
1
2
2
2
0
2
0
0
0
0
1
1
1
1
0
1
1
1
0
0
0
1
1
1
0
0
0
1
0
0
3
0
1
1
2
0
1
2
1
1
2
3
0
0
0
2
0
0
2
1
1
0
0
1
1
2
0
0
1
1
0
1
4
1
2
0
7
1
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
2
0
0
0
0
4
1
0
2
2
0
0
1
1
0
0
1
0
0
2
1
1
1
2
1
2
0
0
1
2
0
2
0
0
0
1
0
1
2
1
0
1
1
1
2
1
1
0
0
1
1
1
1
1
0
1
2
1
0
2
0
0
0
1
1
0
1
0
0
0
0
1
2
1
2
0
1
0
1
0
0
0
0
0
0
1
1
2
1
0
0
2
1
1
1
0
1
2
2
2
0
2
3
1
0
2
1
1
1
2
1
2
2
0
0
2
0
0
0
0
1
0
0
1
0
0
0
1
1
0
2
0
1
0
0
1
0
0
0
0
0
2
2
0
1
1
2
0
0
0
0
2
0
1
0
0
1
0
1
1
2
0
1
1
0
1
1
2
0
1
0
2
0
0
2
0
0
0
2
0
0
0
1
0
1
0
2
0
1
1
4
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
2
2
0
0
2
0
2
0
0
1
0
3
3
0
1
1
0
2
0
2
2
0
1
1
0
0
0
2
2
1
2
0
0
1
1
0
1
0
1
1
0
0
1
0
0
2
0
1
0
1
1
0
1
0
0
0
2
0
0
1
1
1
2
2
0
2
0
0
2
2
1
0
0
0
1
0
0
0
0
1
1
0
0
1
2
1
0
1
0
2
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
2
1
0
1
1
0
0
2
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
2
1
0
1
1
1
0
2
1
1
2
2
1
0
0
3
0
0
1
2
0
0
0
0
0
0
1
1
0
2
0
1
0
0
2
0
0
1
2
2
1
0
2
0
2
1
0
2
3
2
1
0
1
1
2
0
1
0
3
0
0
1
0
1
1
0
1
1
1
2
1
0
2
2
1
2
2
0
1
2
2
0
2
0
0
1
2
1
0
1
0
0
2
2
0
1
1
0
2
0
0
0
1
1
0
2
1
0
0
0
0
2
0
0
2
0
2
0
0
1
0
2
1
0
2
1
0
1
1
0
0
1
0
1
1
0
1
1
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
1
0
0
1
0
0
2
2
0
1
3
0
0
0
0
1
1
1
0
0
1
0
0
0
2
0
2
0
0
3
1
1
1
0
0
2
0
2
1
0
1
1
0
1
2
3
2
2
0
0
0
2
0
2
0
0
0
0
2
0
1
2
0
1
1
1
2
0
0
2
1
0
2
0
0
0
1
0
0
1
2
1
0
0
1
1
1
1
2
1
2
0
1
0
0
0
0
0
0
1
2
2
2
0
1
1
1
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
2
3
1
2
1
2
0
1
2
0
0
0
1
0
0
1
2
0
2
0
0
0
1
0
3
1
0
0
2
1
0
2
1
2
0
1
1
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
1
1
0
0
1
0
0
1
1
2
1
0
2
2
1
0
0
2
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
1
1
0
1
0
0
0
0
2
2
0
0
1
0
0
1
2
1
0
0
2
1
2
0
2
0
0
0
2
0
2
0
1
1
0
1
0
2
0
0
0
0
0
1
0
2
0
0
0
0
2
1
0
0
0
1
2
0
1
0
0
0
1
0
1
2
0
1
1
3
1
0
0
1
1
2
6
1
0
2
0
1
0
1
1
1
1
0
0
1
1
2
1
1
1
1
0
1
0
1
0
0
0
0
0
2
2
0
1
0
0
0
0
1
1
1
2
0
1
3
0
2
2
1
0
1
1
2
1
0
1
1
0
1
2
3
0
2
0
2
0
2
0
0
0
0
0
0
1
0
0
2
2
2
0
1
1
1
0
2
1
1
2
2
0
1
0
0
0
1
1
1
0
1
1
1
0
0
2
1
2
0
0
0
1
0
0
1
1
0
1
2
0
3
1
0
1
0
2
2
0
2
0
1
2
0
0
2
2
1
0
1
0
1
0
0
2
2
1
0
2
1
2
1
1
0
0
1
1
0
0
1
1
1
1
1
0
0
1
0
0
1
2
1
1
0
0
2
2
2
2
2
0
1
0
0
2
1
2
0
2
0
0
1
0
1
2
0
1
1
0
0
0
0
0
0
2
0
0
1
1
0
0
1
2
1
1
1
1
0
0
1
0
0
2
2
0
1
0
0
0
2
1
0
2
0
2
0
0
1
1
0
0
0
2
0
2
0
0
1
0
2
2
0
0
2
0
1
0
1
1
2
0
1
2
0
0
1
0
0
1
2
1
0
0
0
0
2
0
1
9
1
2
0
2
2
0
1
0
0
0
2
0
1
1
1
1
0
0
2
0
2
2
0
1
1
2
0
3
0
1
1
1
1
1
1
2
2
0
2
0
0
0
1
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
2
1
5
0
2
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
1
0
0
1
0
0
1
0
0
0
1
1
0
0
0
1
0
2
1
2
1
0
2
3
2
0
1
1
0
1
0
0
2
0
1
1
4
2
0
0
0
0
0
0
0
0
1
1
2
0
2
0
2
1
2
0
1
1
0
1
0
0
1
2
1
1
2
1
0
1
1
2
1
2
3
2
2
0
2
0
0
0
2
1
3
1
0
1
2
0
0
2
3
0
0
1
0
0
0
1
0
0
2
2
0
2
1
1
0
2
2
0
0
2
0
1
1
2
0
1
0
2
2
1
1
2
0
2
0
0
0
0
2
0
1
0
1
0
0
0
1
1
0
2
0
0
0
2
0
1
1
0
0
4
3
1
1
0
1
0
1
0
1
2
2
0
0
2
0
2
2
0
0
1
0
1
0
2
0
2
0
4
1
1
0
0
1
1
0
1
0
0
0
2
2
0
0
1
1
2
0
0
0
0
0
2
0
2
0
2
2
1
0
1
2
2
0
1
0
0
1
0
1
2
1
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
2
1
0
0
0
0
0
2
1
0
2
0
0
0
1
0
1
0
2
1
0
1
1
0
1
0
1
1
1
1
2
1
0
2
1
0
2
0
0
2
1
0
2
2
0
1
2
0
1
1
0
0
2
1
0
1
0
0
1
0
0
0
1
0
0
1
2
2
2
1
1
2
1
2
1
2
0
0
2
2
1
0
1
0
1
0
0
3
1
0
1
0
1
0
2
0
1
1
1
0
3
1
0
1
1
0
1
0
0
2
1
0
2
1
2
1
2
0
0
2
1
1
2
0
0
1
0
1
1
2
0
0
0
0
0
0
0
2
2
0
2
0
0
1
1
0
0
0
1
0
0
1
0
0
1
0
2
0
1
1
1
2
2
0
0
1
0
2
1
0
0
2
2
0
0
2
2
0
1
1
1
2
1
3
0
0
0
1
0
0
2
0
1
4
0
0
0
2
0
2
1
1
0
0
2
0
0
0
1
1
0
0
0
2
2
1
1
1
1
1
0
0
1
1
0
0
0
1
0
2
1
0
2
1
2
0
0
1
0
0
1
2
1
0
0
1
1
0
2
2
0
1
1
2
2
0
2
0
1
0
2
1
1
1
2
2
1
0
0
2
0
0
1
2
1
0
1
1
1
0
1
0
1
1
0
0
2
0
2
0
2
0
1
2
2
2
0
1
0
1
2
0
1
0
0
0
0
2
0
0
1
1
0
2
0
0
2
0
2
0
0
1
0
0
1
0
1
0
1
0
1
0
0
0
1
0
0
2
0
0
0
1
1
0
0
2
1
2
0
2
0
0
1
1
1
0
0
0
0
0
1
1
0
0
0
0
3
0
1
2
1
0
1
0
0
1
1
0
4
1
0
1
1
1
1
1
0
1
0
1
0
1
0
0
1
2
1
0
0
0
2
2
0
0
1
0
0
0
0
2
0
1
1
0
2
0
2
2
2
1
1
1
2
0
0
2
0
1
0
0
1
2
0
1
2
0
2
0
1
0
1
0
0
0
0
1
2
0
1
1
2
1
0
1
2
0
0
0
0
1
0
2
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
1
2
2
1
0
0
1
0
0
1
0
0
1
1
2
1
0
0
1
0
0
0
0
0
0
0
2
2
3
2
1
1
0
0
0
0
1
1
0
0
1
1
2
1
0
2
0
0
1
0
0
3
1
1
1
0
0
1
1
2
1
1
0
0
0
0
1
0
0
3
1
0
2
0
0
1
1
2
0
2
1
2
2
1
0
1
2
3
0
0
0
1
1
0
1
0
0
0
0
3
0
1
0
0
0
0
2
1
2
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
2
0
0
2
0
1
2
1
0
1
1
2
1
2
1
0
0
2
2
0
1
0
2
0
0
1
2
2
1
0
1
0
1
1
0
0
1
0
0
0
2
0
2
0
0
2
0
2
2
1
0
1
2
1
2
0
2
0
0
1
0
1
0
1
0
2
0
0
0
1
2
2
2
2
0
0
1
2
1
0
0
1
2
1
1
0
0
1
0
0
0
2
0
0
0
0
0
0
1
1
1
2
0
0
2
0
2
0
0
0
0
2
0
0
1
2
0
0
0
1
0
1
0
0
0
1
2
2
0
2
0
1
0
0
2
2
1
0
0
0
0
1
1
1
0
2
2
0
0
1
1
0
0
0
1
1
0
1
2
2
1
2
0
1
1
0
0
0
0
2
1
1
1
0
1
1
1
0
0
0
2
1
0
0
1
0
0
2
2
0
1
1
0
0
1
1
0
1
0
1
0
0
0
0
1
0
0
3
2
1
0
0
1
0
0
2
2
1
0
0
2
1
1
0
1
1
0
1
0
0
0
0
2
1
0
1
1
1
0
1
1
0
0
0
0
0
2
1
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
1
2
1
2
1
1
0
1
1
1
0
0
0
0
1
1
0
0
0
1
1
0
0
2
2
1
2
0
1
2
2
0
1
0
0
2
2
1
1
0
1
1
1
1
0
0
0
2
2
0
0
2
1
0
1
0
1
1
0
1
0
0
0
0
0
0
1
1
0
1
1
0
0
0
2
0
0
2
1
0
2
0
0
1
1
0
1
2
0
2
2
0
0
0
1
0
2
2
0
0
0
2
0
0
0
0
1
0
1
0
0
0
1
2
0
0
1
0
1
0
1
0
1
2
2
3
1
1
2
0
0
1
0
0
1
2
2
0
1
3
0
1
2
0
1
2
1
0
0
2
0
0
1
1
2
1
0
0
2
1
0
0
0
0
1
0
0
1
0
2
1
1
2
1
1
1
1
1
0
0
1
1
0
0
0
2
0
2
0
0
0
1
1
0
1
0
1
1
1
2
0
0
2
1
2
0
0
0
2
0
1
2
0
2
2
2
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
2
0
0
2
1
2
2
0
0
2
0
0
0
2
1
1
1
0
2
0
0
0
0
2
0
0
2
1
1
0
0
1
0
0
0
2
2
0
1
2
1
4
0
1
1
1
1
1
1
0
0
0
2
1
0
0
0
1
0
1
2
0
1
1
3
2
0
1
1
1
1
0
0
0
0
0
2
2
1
0
0
1
2
1
0
1
1
0
1
0
1
0
1
0
0
0
2
1
0
0
0
0
0
2
1
0
0
1
0
1
2
1
0
1
1
0
2
2
0
2
0
1
1
1
0
0
0
0
0
0
1
1
1
0
0
2
0
1
0
0
0
0
1
1
0
0
0
1
1
1
0
1
1
0
1
0
0
0
0
0
1
1
1
0
2
1
1
0
0
0
2
1
1
0
3
1
0
1
2
1
0
0
1
0
1
2
0
1
1
0
1
0
1
0
2
0
2
0
1
0
1
0
0
0
0
2
1
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
2
1
0
0
1
2
0
2
1
0
0
0
1
0
0
0
0
2
1
0
0
0
1
0
2
0
1
3
2
0
1
2
0
2
1
0
0
1
2
1
2
0
2
0
0
1
0
0
0
1
0
2
2
0
0
0
2
1
1
1
0
0
0
1
1
0
2
1
0
0
0
0
1
2
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
2
2
0
0
1
0
2
3
0
0
0
1
0
1
1
0
2
0
2
0
2
2
0
1
1
2
3
0
2
0
1
1
0
1
0
2
0
2
0
1
0
1
1
2
1
1
1
1
2
0
1
0
0
2
1
1
1
2
2
2
1
0
1
0
1
0
1
1
1
1
0
0
0
1
0
1
1
0
2
0
3
0
2
1
0
2
0
1
1
0
0
0
0
0
0
0
0
1
1
0
1
0
1
2
2
1
2
0
1
1
1
1
0
3
1
0
0
1
1
0
0
1
1
1
2
0
0
1
0
0
1
0
0
1
0
1
1
1
1
0
0
1
0
0
0
0
1
0
0
1
1
0
0
1
1
0
2
2
0
2
0
0
1
1
0
1
0
1
1
3
0
0
1
1
0
0
1
3
1
0
0
0
1
1
2
0
2
1
1
2
0
2
0
2
0
2
0
0
0
0
2
0
0
2
0
0
0
1
1
2
0
1
0
0
2
2
1
0
2
1
1
1
0
2
1
0
1
1
2
1
0
1
2
1
1
2
1
0
1
2
0
0
1
2
0
0
0
1
0
1
0
0
0
1
0
1
1
0
1
2
2
0
2
1
1
0
0
2
0
2
0
2
0
0
1
1
0
0
2
2
1
2
2
2
1
0
2
2
0
0
0
0
0
1
0
0
0
0
2
1
2
0
0
1
2
0
0
0
0
1
1
2
1
2
0
0
0
2
0
0
4
2
1
2
1
0
1
0
0
0
0
0
1
2
0
0
2
0
1
0
0
1
0
2
2
1
1
0
1
0
0
0
1
1
1
1
1
2
0
2
2
1
0
2
0
1
0
0
1
0
0
2
1
1
0
0
2
0
2
2
2
1
1
2
0
0
0
0
1
0
0
2
1
1
0
2
1
2
2
1
1
0
0
0
1
0
0
0
2
0
0
1
0
1
0
1
2
1
2
0
1
1
1
2
0
1
0
1
3
0
1
2
0
1
2
0
0
1
1
2
0
0
0
1
0
0
0
1
2
1
0
0
1
0
0
1
0
0
1
1
0
0
1
0
1
0
0
0
2
0
0
0
0
2
1
2
0
0
1
5
1
0
0
0
0
1
1
1
0
1
0
1
2
1
1
0
7
1
2
2
0
2
0
0
1
0
0
2
1
0
0
1
2
1
1
0
1
0
0
0
1
0
0
0
2
0
1
0
2
0
0
0
1
2
1
0
2
0
2
0
2
0
1
0
0
0
2
2
0
0
1
1
1
0
1
0
1
0
1
1
0
0
2
1
1
0
1
1
0
1
1
1
0
0
9
0
0
1
1
0
1
0
2
0
1
0
1
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
1
2
1
2
0
1
0
1
0
0
1
1
1
0
0
0
1
0
1
0
2
0
0
3
0
0
1
0
1
1
0
0
0
1
2
1
3
1
0
1
1
0
0
0
0
0
1
1
1
1
0
1
0
0
2
0
0
1
0
0
1
0
2
0
2
0
3
1
0
1
0
0
1
0
2
0
2
1
2
1
1
1
0
1
0
0
0
0
0
0
2
2
2
3
1
2
0
2
2
1
0
0
0
0
0
0
0
2
2
1
2
1
0
1
2
1
2
2
1
1
2
1
0
1
1
0
2
0
0
0
0
1
1
1
0
0
2
1
0
0
2
3
0
0
2
2
2
0
1
1
1
0
0
0
1
0
2
0
0
0
2
2
1
0
0
1
0
0
0
1
0
0
1
0
0
2
3
0
2
1
1
0
0
0
0
0
1
0
2
1
0
1
0
1
0
1
0
0
4
1
2
0
2
1
0
2
0
0
1
2
0
1
1
2
0
0
0
0
1
2
1
0
1
0
0
2
0
0
1
1
0
2
0
1
3
1
0
1
0
0
0
0
1
1
1
1
0
2
0
2
0
0
1
0
2
2
2
0
0
1
1
0
0
0
0
1
0
1
1
1
1
1
1
1
1
0
0
0
0
2
1
0
1
2
2
1
0
1
0
0
0
1
2
0
2
2
1
2
0
0
2
1
0
2
0
0
0
2
1
2
0
0
0
0
1
1
0
0
0
2
1
2
2
0
0
0
0
2
1
1
1
1
1
1
1
1
0
2
0
0
0
0
1
0
2
1
0
2
0
0
1
2
2
1
0
1
0
1
2
0
0
0
0
1
0
3
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
1
2
2
0
1
2
0
0
0
1
0
1
0
1
0
0
1
1
3
0
0
1
0
0
0
0
2
0
2
1
1
1
1
1
1
0
1
0
2
1
0
0
1
0
1
1
0
1
1
2
1
1
0
2
0
3
2
2
1
1
1
0
1
0
0
0
1
2
2
0
0
0
2
0
0
0
0
2
0
2
1
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
2
1
1
1
0
2
1
0
0
0
1
2
0
0
2
2
0
0
0
0
0
2
0
1
2
1
3
0
1
0
1
0
3
0
2
1
2
0
2
0
0
1
1
1
0
2
0
2
1
0
0
0
1
1
0
1
2
0
2
2
0
0
0
1
0
0
1
0
2
2
2
1
0
0
0
0
2
2
0
0
1
0
0
0
2
0
0
2
2
1
1
0
1
2
1
2
3
2
2
0
2
0
2
2
2
0
3
0
2
0
2
0
2
1
0
0
1
1
0
1
1
0
2
0
0
0
2
0
1
0
2
0
1
2
1
0
2
1
1
0
0
1
1
0
1
0
1
0
2
2
1
0
0
1
1
2
2
2
0
0
1
2
2
0
1
0
2
1
0
1
0
1
1
0
2
1
0
1
0
2
2
1
1
0
2
0
0
1
0
1
5
2
1
0
0
0
0
0
0
1
1
1
0
1
1
2
0
1
1
2
1
0
2
1
1
2
1
0
0
2
2
2
2
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
1
1
1
0
2
0
0
0
1
2
2
0
2
0
0
0
0
0
1
0
0
0
1
2
2
2
2
1
1
1
2
1
0
0
0
2
1
3
0
1
0
0
1
0
0
0
2
1
0
2
0
0
0
1
1
1
0
0
0
1
0
0
0
1
2
2
0
0
0
1
0
0
1
1
0
2
1
0
2
0
0
1
0
0
0
1
1
2
1
0
0
0
2
0
1
1
1
0
2
1
1
1
0
2
0
1
1
1
1
1
0
1
0
1
0
0
0
0
0
1
0
0
1
2
2
3
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
2
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
2
0
0
1
0
2
0
0
1
2
1
1
1
0
2
0
1
1
0
0
1
1
0
1
1
2
1
1
0
0
1
1
2
0
1
1
0
0
0
0
1
2
1
1
0
3
1
2
1
0
0
1
0
0
0
1
2
1
0
2
0
0
2
0
1
0
2
0
0
2
0
2
0
2
2
1
1
1
0
0
1
0
0
2
0
1
1
1
2
0
0
0
0
0
0
1
0
2
0
0
0
0
1
1
0
0
1
0
0
1
0
1
1
0
1
1
0
1
0
2
2
0
0
0
0
2
0
1
1
1
3
1
1
0
1
1
1
0
0
0
0
3
0
2
0
0
1
2
3
2
0
0
0
1
0
2
2
1
1
0
0
1
2
1
1
1
0
0
0
1
1
2
1
0
0
1
0
0
2
1
0
2
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
1
0
0
2
0
0
0
0
0
2
1
0
0
1
0
0
0
1
1
1
1
2
0
0
0
1
1
1
1
1
2
1
2
1
0
0
0
1
1
2
2
0
1
1
1
1
0
0
1
0
0
1
0
2
1
2
0
2
1
2
0
0
0
1
1
1
1
2
4
1
1
2
1
1
0
1
0
0
2
0
1
3
1
2
0
1
1
1
2
2
0
1
0
0
1
0
2
1
0
1
0
0
1
1
2
0
1
1
2
2
2
2
0
0
1
1
0
1
0
0
0
1
0
1
0
0
0
0
2
0
2
0
0
0
1
0
0
0
1
0
1
2
2
0
1
1
0
1
0
1
1
2
1
1
0
1
1
0
0
1
0
0
0
2
2
1
0
0
5
2
0
1
1
0
2
0
1
0
0
1
1
1
0
0
2
0
0
0
2
1
2
1
1
0
0
0
1
1
0
1
0
1
2
0
2
2
0
1
0
0
0
2
0
1
1
2
0
4
0
2
0
0
2
0
0
0
1
0
1
0
0
1
2
1
2
1
0
0
2
0
0
0
0
1
0
0
1
0
4
1
1
0
1
0
0
2
1
0
0
0
0
2
1
0
0
1
0
0
0
0
0
1
0
1
1
0
1
3
1
1
2
1
2
1
2
1
0
0
0
1
0
1
0
1
0
1
2
2
2
2
0
1
0
0
2
0
0
1
0
0
2
0
0
2
0
1
1
1
0
0
1
0
0
1
1
2
2
2
0
3
0
1
0
1
0
2
0
2
0
0
0
1
1
1
1
1
0
1
0
2
1
0
1
2
0
2
0
2
0
0
1
1
0
2
1
0
2
1
0
2
0
1
0
0
0
0
2
0
2
1
1
0
1
2
1
0
0
0
1
0
0
2
2
0
3
0
1
2
0
2
2
0
0
1
0
1
0
2
0
1
0
1
0
2
1
0
2
2
1
0
1
0
2
3
0
0
0
0
1
1
1
2
2
1
1
0
1
0
2
0
1
1
1
0
0
2
0
0
0
1
0
0
0
0
0
1
1
0
0
0
2
0
0
0
2
1
3
1
2
1
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
2
0
3
2
1
0
2
0
0
0
0
1
0
0
2
1
2
0
3
1
2
2
2
0
2
1
1
2
1
0
0
0
1
2
1
0
0
2
1
1
2
1
2
0
0
2
0
0
0
0
0
2
0
1
1
1
0
1
1
0
2
1
0
1
0
2
2
0
0
1
0
0
0
0
0
2
1
2
2
0
1
0
0
0
0
0
0
1
0
2
1
0
1
1
0
0
0
7
2
0
1
0
0
0
1
2
0
0
0
0
0
1
0
2
3
0
2
1
0
0
2
3
2
1
0
1
0
0
2
1
0
0
0
0
0
1
0
2
1
0
0
0
0
4
4
2
2
2
0
1
0
0
1
2
2
0
1
0
1
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
3
4
0
0
2
0
0
1
1
0
0
2
2
2
1
1
2
0
7
2
0
1
0
1
2
2
2
1
1
0
2
0
2
0
2
0
1
0
1
1
2
0
0
2
0
0
0
0
0
0
2
1
1
1
0
2
0
2
0
0
0
1
1
2
0
0
0
0
0
0
0
2
1
2
1
1
0
0
2
0
2
0
2
2
2
3
1
2
1
1
0
1
2
2
1
0
1
0
2
1
0
1
3
1
0
1
1
1
1
0
0
1
1
1
0
0
0
3
2
0
5
1
1
1
0
2
3
2
2
0
0
0
3
1
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
1
0
0
1
0
1
1
1
2
1
2
0
1
0
0
0
3
2
1
2
1
2
0
0
0
0
1
0
1
0
0
0
2
0
1
2
0
0
0
1
2
0
1
2
1
0
1
1
1
2
2
0
1
0
0
0
2
2
0
1
1
1
2
2
2
2
0
0
0
0
1
2
1
1
0
1
0
1
0
0
2
1
0
0
2
2
1
2
0
0
1
1
0
0
0
1
2
1
3
1
1
0
2
0
0
1
1
1
0
0
0
2
2
1
0
2
1
0
1
1
0
0
0
0
0
0
1
3
2
0
0
1
0
1
0
0
0
1
1
2
2
0
2
1
2
1
2
0
0
0
1
1
3
0
0
0
1
0
3
0
1
0
1
0
0
1
0
2
0
2
1
1
1
1
0
0
0
0
1
0
1
0
1
1
1
0
0
1
2
0
1
0
0
1
0
2
2
0
1
0
0
0
1
0
0
1
1
0
0
1
1
1
0
0
0
1
0
2
1
1
0
0
1
0
0
0
0
1
0
0
2
1
2
0
0
1
1
1
0
0
0
0
1
2
0
0
0
2
1
0
0
3
2
0
0
1
0
0
0
0
1
1
2
3
1
1
0
0
1
0
0
1
0
0
1
1
1
1
0
0
1
1
0
1
3
0
2
0
1
1
2
2
0
1
1
1
0
1
0
2
0
0
2
2
0
2
2
0
0
2
1
1
0
0
0
2
0
1
1
2
0
0
0
0
1
0
1
0
0
1
2
2
1
0
2
0
2
0
0
1
1
0
0
0
0
1
0
2
2
1
2
0
0
1
0
1
1
1
1
0
1
0
0
0
1
0
0
2
0
2
1
2
0
2
2
1
0
0
0
2
0
2
1
1
1
1
0
0
2
0
0
0
1
0
0
2
1
1
1
2
1
2
2
2
0
0
1
2
0
0
1
0
0
1
2
1
0
0
2
1
1
1
1
0
1
1
0
1
3
0
0
0
0
0
0
3
1
0
0
2
0
0
0
0
1
1
0
2
0
1
0
1
0
0
4
1
2
0
0
0
0
2
2
0
1
0
0
1
0
0
2
1
2
1
0
2
1
0
0
1
2
1
0
0
0
0
1
1
0
0
0
2
1
0
1
0
1
0
2
2
0
3
0
0
1
1
4
1
0
0
0
1
0
0
0
2
1
0
1
2
1
0
1
1
1
1
1
2
1
0
0
2
0
0
1
1
1
2
2
0
0
1
0
0
0
1
1
0
0
0
2
0
0
0
2
0
1
1
1
2
2
0
0
0
2
1
2
2
0
0
1
1
1
2
1
0
0
0
4
1
2
1
1
1
2
2
2
1
1
0
0
1
0
0
0
1
2
0
0
1
0
0
1
2
3
1
0
1
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
2
1
2
0
0
0
1
2
2
0
0
0
0
1
0
1
0
1
1
1
0
0
0
0
2
0
0
2
5
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
1
0
0
3
1
1
0
1
2
1
2
0
0
1
0
2
2
1
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
1
2
1
2
1
1
1
2
1
3
0
0
1
2
1
0
0
0
0
0
2
0
2
0
0
0
0
0
2
1
0
0
1
0
1
2
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
2
1
1
1
0
3
2
0
0
2
2
1
0
0
0
1
0
0
0
0
0
1
2
0
1
0
2
1
0
0
1
0
1
0
1
1
0
2
0
0
0
0
0
2
1
1
2
0
2
2
1
0
1
2
2
1
1
2
1
2
1
1
0
0
5
1
0
2
1
1
2
1
1
0
2
0
0
1
0
2
1
3
2
1
0
2
1
1
2
2
0
2
0
1
0
3
0
1
1
0
0
0
0
0
2
0
1
1
0
0
0
0
0
1
0
0
2
1
0
0
2
0
0
1
0
2
0
1
0
1
2
1
1
0
1
1
2
1
2
1
0
1
0
0
0
2
0
0
1
1
2
1
2
1
0
1
2
1
1
0
2
0
1
0
2
0
0
0
1
1
0
1
0
1
0
2
2
1
0
0
2
0
0
0
3
3
2
0
0
1
0
0
0
1
2
1
2
0
1
0
0
0
1
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
2
0
0
1
0
1
0
2
1
1
2
0
1
2
0
0
1
2
1
1
2
1
2
0
2
0
0
2
0
0
0
0
0
0
0
1
0
1
0
2
0
1
0
0
0
0
0
0
0
1
2
1
2
1
1
1
0
0
0
0
1
0
1
1
0
1
1
1
1
1
0
1
1
0
0
2
0
0
1
1
0
1
0
0
1
0
0
0
0
0
2
2
0
0
1
1
1
0
2
2
2
0
0
0
1
2
2
1
0
0
1
0
2
1
0
1
2
2
0
1
0
2
0
0
0
2
0
0
0
1
0
2
3
1
1
1
0
0
1
2
0
2
0
0
1
1
18
0
1
0
1
2
2
1
1
0
0
2
2
1
1
0
0
0
0
1
1
0
2
2
0
1
1
1
1
0
1
0
1
0
0
2
0
0
1
0
1
1
0
2
1
0
0
1
2
0
2
1
0
2
0
1
0
0
0
1
2
2
1
0
0
1
0
0
1
0
1
1
1
0
1
0
1
0
0
0
0
1
0
2
0
1
0
0
2
2
0
1
0
1
1
2
1
2
2
1
0
0
0
1
1
1
1
2
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
1
1
0
0
0
1
1
1
0
1
0
1
1
1
0
0
0
0
0
0
1
0
1
0
1
1
0
2
1
0
0
0
0
1
3
2
0
0
0
0
2
1
1
1
1
1
0
2
0
0
0
0
2
0
1
0
0
1
0
0
0
2
1
0
0
2
2
0
2
0
0
0
0
0
1
0
0
0
0
0
2
2
0
2
0
1
2
1
1
0
1
0
0
0
0
0
1
0
1
0
0
0
1
1
2
0
3
2
0
0
0
1
0
1
3
0
1
0
0
0
0
2
0
0
0
0
0
0
1
2
2
0
0
2
0
0
0
0
0
0
2
0
0
1
2
2
0
0
1
1
0
0
0
1
1
2
0
2
1
0
1
0
0
0
2
1
1
2
2
0
2
0
0
0
1
0
2
1
0
0
0
2
4
1
0
1
0
2
0
1
2
0
1
2
0
0
1
1
1
1
0
0
2
2
0
0
1
0
0
0
1
2
0
2
2
1
0
0
1
1
0
1
0
0
2
0
0
2
2
0
3
2
0
1
0
0
0
0
2
1
3
1
0
0
0
0
1
1
0
2
2
1
2
2
2
1
1
1
0
2
0
1
2
0
1
2
2
2
1
2
0
2
1
2
0
1
2
0
2
0
0
1
1
1
0
0
2
1
0
1
2
2
1
2
0
0
1
0
0
0
1
0
0
0
0
0
1
2
2
0
3
2
1
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
1
0
1
1
2
1
2
1
0
1
1
1
0
0
0
0
4
1
0
3
2
1
0
2
1
0
1
1
0
1
1
0
1
0
2
2
1
1
0
0
0
0
0
0
2
0
0
0
3
2
2
0
0
1
1
1
1
1
0
1
2
1
0
1
0
1
0
0
1
0
1
0
1
1
1
2
2
0
1
0
1
2
0
0
0
0
0
2
0
2
2
1
1
0
1
0
0
1
2
0
1
1
0
2
1
2
0
0
0
0
1
0
1
0
0
1
0
0
0
2
0
1
0
0
0
0
0
2
0
0
1
3
0
0
1
0
1
2
1
0
2
0
0
1
0
1
1
4
2
1
0
0
0
2
0
1
0
0
0
2
0
1
0
2
0
0
3
0
1
0
0
2
0
0
7
1
2
2
0
1
0
0
0
0
0
0
0
1
0
1
2
0
1
1
1
0
0
0
1
2
0
0
1
2
2
0
0
0
0
0
1
1
0
0
0
1
0
2
0
2
1
1
0
0
1
0
2
0
1
1
1
0
1
0
1
0
0
2
0
0
0
0
1
1
2
2
1
0
1
1
1
1
0
0
0
3
1
1
0
1
0
2
1
0
0
0
0
0
1
0
0
1
0
0
0
2
2
1
0
0
2
0
0
1
0
0
1
0
1
2
0
1
2
0
0
2
1
2
1
1
0
0
0
0
1
0
0
1
0
0
1
1
1
2
0
0
0
0
0
0
2
0
2
0
1
0
1
1
2
2
1
0
2
0
2
1
0
1
1
2
0
1
0
0
0
2
1
1
2
0
1
0
2
2
0
2
1
0
0
1
0
2
1
1
1
0
2
1
0
2
1
0
2
0
2
0
1
2
0
0
2
0
0
0
0
0
1
1
1
1
2
3
2
1
0
0
0
1
0
0
2
2
0
0
1
1
0
1
1
1
0
2
0
1
1
2
0
0
4
0
1
1
2
2
0
1
0
0
1
1
0
2
0
0
0
2
1
0
1
2
1
2
1
3
1
1
0
0
1
2
0
2
2
0
1
2
2
1
1
2
0
1
2
1
2
2
0
2
0
0
0
0
0
2
1
0
1
0
0
0
1
2
2
0
0
1
0
3
0
1
1
1
2
0
2
0
1
1
1
1
2
1
2
0
0
1
0
2
2
0
1
1
0
1
2
2
0
0
1
1
1
1
1
3
1
1
0
2
2
1
0
0
3
2
0
0
1
5
0
0
0
1
1
1
2
1
1
1
2
2
0
0
2
1
0
2
0
0
0
1
0
1
2
2
1
0
0
1
2
1
2
1
1
1
1
0
0
1
1
0
0
0
1
2
0
1
1
0
1
2
0
2
0
1
0
1
0
0
1
0
0
0
2
1
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
1
0
1
1
2
0
0
1
0
1
0
2
0
1
1
0
0
1
0
0
3
0
1
0
0
2
1
1
1
2
4
2
0
1
2
0
1
2
0
1
0
3
0
0
0
0
1
0
1
2
1
1
2
1
2
0
0
1
2
0
1
0
2
1
0
0
0
2
1
0
2
1
2
0
0
1
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
1
1
0
1
0
0
1
0
0
0
1
0
0
2
0
2
1
0
2
1
0
0
0
2
0
1
1
1
1
3
0
1
0
2
0
0
1
0
2
0
0
2
2
0
0
1
1
1
2
0
0
1
1
0
2
1
0
1
0
2
1
2
2
0
1
1
2
2
0
0
0
1
1
1
1
2
0
0
1
1
3
1
0
0
0
0
1
1
0
3
1
1
2
0
1
0
0
1
2
0
1
0
2
0
0
0
1
0
2
2
2
2
0
2
0
0
2
2
0
0
0
0
2
2
0
1
0
1
0
2
0
1
0
1
1
3
1
1
2
0
2
1
1
2
0
1
2
0
0
1
1
1
2
1
2
0
1
5
1
1
1
1
0
2
0
1
1
1
0
1
1
0
1
1
1
1
0
2
0
1
0
0
0
0
3
0
2
0
0
0
1
0
0
1
1
2
0
2
1
0
0
0
1
2
1
0
0
0
2
1
0
2
1
0
2
1
2
0
1
0
2
0
1
0
0
1
2
2
2
0
0
0
2
0
1
0
0
1
2
1
1
0
0
2
0
2
0
1
0
1
0
1
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
1
0
0
1
0
1
1
2
1
1
0
1
0
1
1
2
2
2
1
0
1
0
2
1
2
0
3
0
1
0
1
2
0
0
1
2
2
1
1
2
2
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
2
0
1
1
0
1
0
0
1
0
1
0
0
1
0
2
1
1
0
0
1
1
0
0
0
2
1
2
2
1
0
0
1
0
0
1
0
1
1
0
0
2
1
0
1
0
0
0
0
0
2
0
2
1
0
1
0
2
2
1
0
0
2
0
0
0
1
0
1
1
0
0
1
2
0
0
2
0
0
0
1
1
0
1
0
0
3
2
0
2
0
1
2
0
0
0
0
0
2
1
2
0
0
0
1
2
1
2
0
1
0
2
0
1
0
0
0
0
1
1
1
0
1
0
0
0
0
0
2
2
2
0
0
0
2
0
0
0
1
0
0
1
2
1
1
1
1
1
2
0
2
0
0
1
1
1
2
0
1
1
0
1
1
1
0
0
0
1
1
2
0
1
2
0
1
0
0
0
0
0
0
2
0
2
2
0
0
1
0
2
1
0
1
0
0
0
1
1
2
0
2
1
2
1
0
2
0
0
2
1
0
1
0
2
0
0
2
3
1
0
0
1
0
0
1
0
0
2
1
3
1
2
2
1
1
3
0
3
1
0
0
2
0
0
2
0
0
1
0
2
0
0
2
0
1
2
0
1
2
1
0
0
0
1
0
0
0
0
2
0
0
1
1
0
0
0
0
1
0
1
1
2
0
1
0
2
1
1
0
1
1
0
2
0
2
1
1
0
2
2
4
0
2
0
0
1
0
0
0
0
1
1
1
1
1
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
2
2
0
0
0
1
3
2
0
2
0
1
0
0
1
1
2
2
1
1
0
0
0
2
1
1
0
2
0
1
0
1
0
0
2
0
2
0
1
0
0
1
1
1
1
0
0
1
2
2
0
0
0
2
1
0
1
3
1
2
2
0
1
0
0
1
5
2
0
0
0
2
1
0
0
0
1
2
2
2
1
0
0
0
2
1
2
0
0
3
0
0
0
0
2
0
0
0
2
1
1
1
0
2
2
0
0
0
1
2
1
2
2
0
1
2
2
0
1
0
2
0
2
0
2
0
3
0
2
1
2
2
0
0
0
1
0
2
0
1
1
1
0
0
0
0
0
0
3
2
0
0
1
0
0
0
0
1
2
0
0
0
0
0
2
2
2
0
1
2
0
4
2
2
0
1
0
1
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
1
1
1
1
0
0
0
2
1
0
0
0
2
0
1
1
0
2
0
0
2
0
0
0
0
1
2
0
1
2
0
0
0
2
2
0
2
0
1
0
0
1
0
0
3
0
3
0
0
1
0
0
0
2
0
2
0
0
2
0
0
0
1
0
2
0
1
0
1
1
2
0
0
0
0
1
1
1
1
0
0
0
2
0
1
1
0
1
3
0
0
0
1
2
0
3
0
0
1
1
1
0
1
0
2
2
0
0
0
2
2
2
0
0
0
1
0
1
3
0
1
2
0
1
1
0
0
0
2
0
0
0
1
0
1
2
1
2
2
2
0
2
1
2
1
0
0
1
1
1
0
2
0
1
0
1
2
0
0
2
0
1
0
1
2
1
0
2
1
0
2
2
0
0
0
1
1
0
1
0
1
0
3
0
1
0
1
1
2
0
0
1
2
0
1
0
1
3
0
0
0
0
1
0
2
0
0
0
2
0
1
1
2
0
1
0
1
1
0
2
0
0
1
0
0
1
1
1
1
0
0
2
2
1
0
1
0
0
0
0
2
0
1
1
1
0
1
0
2
1
0
0
2
0
0
1
0
0
1
0
0
1
1
2
2
1
2
1
2
2
0
0
2
0
1
0
0
2
2
1
1
0
0
0
1
1
0
2
1
0
1
2
0
0
1
0
2
0
0
0
2
1
0
0
0
0
1
1
0
0
2
0
2
1
0
0
2
0
1
0
2
0
2
0
0
1
0
0
0
1
2
0
0
0
1
0
2
0
0
1
2
1
0
1
0
1
1
0
0
0
1
2
1
1
1
0
0
0
0
1
4
0
2
0
2
0
0
1
0
0
0
1
2
0
1
1
0
0
1
0
2
0
1
0
1
0
0
0
2
2
2
1
1
0
1
1
0
0
1
0
1
0
3
0
0
0
1
1
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
1
2
1
0
1
0
1
1
0
1
0
2
0
0
1
1
0
1
2
1
1
2
0
0
2
0
2
0
0
1
1
1
0
2
0
0
2
2
0
2
0
0
0
0
2
0
2
1
0
0
1
2
1
0
2
2
0
0
1
2
1
1
0
0
1
0
0
0
1
0
1
0
1
0
0
2
1
0
0
2
2
0
0
1
0
1
0
2
2
0
0
2
1
0
2
0
1
0
2
1
0
2
1
1
0
2
1
1
0
0
1
2
2
1
1
0
0
0
2
1
0
4
1
2
2
2
0
0
0
0
2
2
0
2
0
0
2
1
0
1
1
1
0
0
0
0
0
0
2
1
1
1
1
1
0
0
2
0
1
0
0
1
0
1
0
0
0
0
0
1
2
0
1
1
1
0
0
0
0
1
1
1
1
0
0
1
2
1
0
0
2
1
2
0
1
0
1
1
2
0
0
1
0
1
2
0
1
2
1
1
0
0
1
2
0
2
1
2
2
2
0
0
0
0
2
1
2
2
0
1
1
0
0
0
1
1
2
0
0
1
1
0
1
0
0
1
1
0
1
2
0
3
0
0
1
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
2
1
1
1
0
1
5
2
2
2
0
0
0
0
0
0
0
1
0
0
0
3
1
0
0
1
2
2
0
0
0
1
0
2
0
0
0
0
1
1
1
0
1
1
0
0
2
0
0
0
2
1
2
0
1
1
0
0
1
1
1
2
2
0
1
1
1
0
0
0
2
1
0
1
0
1
2
1
1
1
0
0
1
0
1
0
0
0
1
0
0
3
1
1
0
0
1
1
1
2
2
2
0
1
0
1
0
1
1
0
0
3
0
2
1
1
0
0
2
0
0
1
1
0
1
3
2
1
2
2
2
0
0
0
0
1
0
2
0
0
1
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
1
0
2
0
1
1
2
0
0
0
2
0
1
1
0
0
0
1
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
1
0
0
0
1
0
2
0
1
1
0
0
0
0
1
0
1
0
2
1
1
0
0
2
2
0
1
1
0
0
1
2
1
0
2
0
0
1
6
0
1
1
1
4
2
1
2
0
0
0
0
0
1
2
0
0
2
1
2
0
0
1
1
0
2
2
0
0
1
1
0
2
1
0
1
0
0
0
1
0
0
0
0
0
2
2
1
0
0
2
0
2
0
0
0
0
0
3
0
2
0
1
1
0
2
1
0
0
2
2
2
0
1
0
0
2
2
0
0
0
2
1
0
2
1
1
0
2
1
0
1
0
1
0
2
1
2
1
2
1
1
2
0
0
1
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
2
1
2
0
0
1
2
2
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
1
2
0
0
1
2
0
2
1
0
1
0
0
0
1
0
1
1
2
1
1
1
3
0
2
3
1
0
2
0
2
1
0
2
2
0
0
1
6
2
0
1
2
2
0
0
0
2
1
2
1
1
0
0
0
0
0
0
0
0
2
2
0
1
1
0
0
2
0
2
1
0
0
1
2
0
1
0
1
0
2
0
2
1
1
1
0
1
1
1
1
2
1
2
0
0
1
1
1
0
0
2
0
2
2
0
0
1
1
3
0
2
0
1
1
1
2
1
1
1
0
0
1
1
1
1
2
0
0
1
1
1
1
0
0
1
1
0
0
0
0
0
2
1
1
0
1
0
1
0
0
1
2
0
2
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
2
0
2
0
0
0
1
2
0
2
0
1
2
1
2
1
0
2
0
0
0
0
0
1
0
0
1
1
0
1
0
2
1
2
1
0
1
0
0
0
5
0
1
0
1
1
0
0
0
2
1
0
0
0
1
1
0
2
1
1
0
0
2
1
2
1
1
1
1
1
0
1
0
1
0
0
0
3
2
2
1
0
1
1
0
0
0
0
2
1
1
0
3
1
0
2
2
0
0
1
1
0
2
2
1
0
0
1
1
0
4
2
0
2
1
2
0
0
0
0
1
2
1
0
0
2
1
0
0
1
0
1
1
0
1
0
0
1
1
3
1
0
1
1
1
0
1
0
0
0
1
1
0
5
2
1
2
1
1
2
0
0
2
1
0
0
1
0
1
2
1
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
1
2
0
2
0
1
0
1
0
1
0
1
0
1
2
1
1
0
1
0
3
1
0
1
1
1
1
1
2
1
0
0
1
0
0
0
4
0
1
1
3
2
1
1
2
0
0
2
0
2
2
1
1
1
0
0
2
2
0
0
0
0
2
0
0
2
0
1
2
1
2
1
1
2
2
2
1
1
2
3
1
2
1
1
2
1
1
0
0
0
1
0
2
2
0
0
1
1
2
0
0
2
0
0
2
0
1
0
1
2
0
0
0
0
2
0
2
0
0
2
0
0
1
2
1
1
1
2
0
1
1
2
0
2
1
1
1
1
2
0
0
0
0
1
0
0
0
0
2
1
0
0
2
2
0
0
1
2
2
1
2
1
0
2
0
0
0
0
0
1
1
1
0
1
1
0
0
0
0
2
0
0
3
0
0
0
0
1
0
1
0
0
1
0
0
0
0
2
2
0
2
2
0
0
0
1
0
1
0
2
2
0
0
1
0
0
2
0
0
1
1
0
0
0
1
0
2
1
2
0
2
0
1
0
1
0
2
0
1
2
1
1
1
0
1
1
1
0
2
0
1
0
0
2
0
1
0
0
0
0
2
1
2
0
1
0
1
1
1
2
0
1
0
0
1
0
0
0
4
1
2
0
3
0
1
1
2
0
1
1
0
1
0
2
0
1
1
1
2
1
0
0
0
0
1
0
2
1
0
0
1
3
0
1
0
1
2
0
2
2
0
0
0
2
0
0
2
1
2
1
1
0
1
1
1
0
1
0
1
1
0
1
2
1
1
0
0
1
1
1
0
2
0
0
1
0
0
0
1
1
1
1
2
1
1
1
2
1
1
0
0
1
0
1
2
0
1
1
0
0
1
2
0
1
1
1
0
1
0
2
0
1
0
0
2
0
1
0
0
0
3
3
1
1
0
0
0
2
0
0
0
3
1
0
0
0
0
1
1
1
0
1
0
0
0
1
0
0
1
1
2
0
0
2
1
2
1
0
2
0
2
1
0
0
2
1
1
0
1
0
1
1
2
0
2
0
2
0
1
0
1
2
2
1
0
1
1
0
1
0
0
0
0
0
0
0
2
4
2
0
0
0
0
1
0
0
1
1
1
1
0
0
1
0
2
0
0
2
0
0
0
1
0
1
1
1
0
2
2
0
0
0
2
2
1
1
2
1
1
1
0
2
1
0
0
1
1
1
0
0
2
0
1
2
0
0
1
2
1
3
1
0
0
0
1
1
0
0
0
0
2
1
0
0
1
1
0
0
1
0
0
0
0
2
0
1
0
0
0
1
0
0
2
1
0
1
0
0
2
0
0
2
1
0
0
0
0
0
2
1
1
2
1
1
1
2
0
0
2
1
1
1
0
0
0
1
0
1
1
3
0
0
0
2
0
0
1
0
2
0
0
0
1
0
0
0
0
0
1
2
2
1
0
1
0
1
1
0
1
0
0
0
4
0
0
0
1
0
2
1
1
1
0
1
2
1
0
0
1
1
2
2
0
1
1
1
1
1
1
1
0
1
2
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
1
1
0
0
0
0
1
1
0
1
1
0
1
1
0
1
0
2
0
0
1
2
1
1
2
0
0
0
1
2
0
1
1
0
1
1
2
0
1
1
2
3
2
1
2
1
1
1
2
0
1
0
1
0
0
0
0
1
0
1
0
0
1
0
1
0
1
0
0
2
0
1
2
0
0
2
1
1
0
2
1
0
0
1
0
0
0
0
0
2
0
1
2
1
1
0
0
1
0
0
1
0
1
1
0
0
0
2
1
1
1
0
1
1
0
1
0
0
0
0
0
2
1
0
0
1
0
1
0
0
2
0
0
1
1
0
0
1
0
3
1
0
2
1
0
0
1
0
0
0
0
0
2
0
2
2
1
1
2
0
0
0
2
0
0
2
0
0
0
0
0
1
1
1
1
0
2
1
0
1
0
2
2
0
2
2
1
0
1
0
0
1
1
0
2
1
0
0
2
2
1
1
0
0
1
2
1
1
1
0
0
1
1
1
1
0
0
2
1
0
1
0
1
0
0
1
0
0
1
3
2
0
2
0
1
0
0
2
0
1
0
0
0
0
1
0
0
1
0
2
1
2
0
0
0
1
1
2
0
2
0
2
0
1
1
0
1
1
0
0
0
2
0
2
0
2
0
1
0
0
2
0
0
0
2
0
0
2
1
2
1
0
5
2
2
0
0
1
0
0
0
1
0
0
0
2
0
1
1
1
3
1
1
1
0
5
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
2
0
1
0
0
1
2
0
0
1
0
2
1
1
2
0
0
5
2
2
0
0
0
1
2
0
0
2
0
1
0
0
0
2
1
0
0
1
1
1
0
3
0
1
0
0
0
1
1
0
0
1
0
2
2
0
0
0
1
0
0
1
1
1
2
0
2
0
0
0
0
0
0
2
2
0
1
1
0
0
1
1
3
0
0
2
0
0
0
1
4
2
0
2
2
0
1
0
0
2
0
0
2
1
0
0
1
1
0
2
0
0
1
2
0
2
0
1
2
1
0
1
2
0
0
0
0
0
1
1
1
2
0
1
0
0
1
2
0
0
0
4
2
0
0
0
0
1
1
0
0
1
0
0
1
0
1
0
1
1
3
0
1
2
2
1
0
0
2
0
0
0
0
1
1
0
1
2
0
1
1
0
0
0
1
2
0
0
0
2
0
0
0
3
1
2
2
0
1
2
1
0
1
0
0
2
0
3
1
1
0
0
2
0
0
1
0
0
1
0
2
1
2
1
0
0
1
0
0
1
1
1
1
0
1
1
2
1
1
0
0
0
1
0
1
0
2
0
2
1
2
1
0
0
0
0
0
0
1
0
1
0
2
0
0
1
0
0
2
1
3
0
0
0
0
0
1
0
0
0
2
0
0
1
0
1
0
0
0
1
1
1
1
2
2
0
2
0
0
0
0
2
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
1
1
2
1
0
0
0
1
1
1
0
0
1
0
0
0
1
0
1
1
1
1
1
0
2
0
2
0
1
0
2
2
0
0
1
0
0
0
0
0
2
2
0
1
0
0
0
0
2
0
1
0
1
1
1
0
0
1
1
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
2
2
1
0
1
2
0
3
0
0
1
3
1
0
1
0
0
0
0
1
1
1
1
0
2
1
0
2
0
2
1
0
0
0
0
1
0
1
0
0
2
0
1
0
0
0
1
0
1
2
2
0
0
0
1
0
0
1
3
2
0
0
0
0
2
2
2
1
0
0
1
2
0
0
1
1
2
3
0
0
1
1
0
2
1
2
0
0
1
0
0
0
0
2
0
0
1
0
2
0
1
0
1
2
0
1
0
0
1
1
2
2
1
0
0
2
0
1
0
2
0
0
2
0
1
0
1
0
0
2
2
0
1
1
0
0
2
1
2
0
1
2
0
2
0
0
0
1
2
2
2
1
1
0
3
0
0
2
0
3
0
0
0
1
0
0
0
1
1
1
2
0
3
0
0
0
2
0
1
2
0
2
0
1
0
0
0
2
2
1
1
1
1
0
0
2
1
1
0
1
0
1
1
1
2
7
2
2
1
2
0
2
0
1
0
1
1
0
2
0
1
0
0
0
0
1
0
2
1
0
0
2
0
0
2
1
2
2
0
2
5
1
0
0
0
1
0
3
0
0
1
0
2
2
2
0
3
3
1
0
0
0
0
2
0
1
0
1
0
1
0
0
0
0
0
0
1
2
2
0
0
0
0
1
0
2
2
0
2
0
1
0
2
0
0
2
2
0
1
0
1
0
2
0
1
0
1
2
0
0
1
0
2
1
0
1
2
0
1
2
3
1
1
0
0
2
2
1
2
0
2
0
0
0
0
2
0
0
1
1
3
0
0
1
0
0
0
0
0
0
0
2
1
2
2
0
1
0
1
1
0
0
0
5
0
2
0
2
0
2
1
1
0
2
0
2
0
0
2
2
2
0
1
2
0
1
0
0
3
1
0
0
2
1
2
1
1
0
2
0
0
2
0
0
2
2
0
2
1
1
0
1
1
2
0
1
0
1
2
0
1
0
1
0
0
0
0
1
0
1
0
0
0
4
0
1
2
1
0
1
1
0
2
0
0
2
0
0
0
0
0
2
0
1
2
1
2
0
1
2
1
0
2
0
1
2
0
0
1
1
0
1
0
1
1
0
1
2
1
0
0
0
2
2
0
2
2
0
0
0
0
1
2
4
1
0
2
3
0
1
2
0
0
4
1
2
2
1
0
1
1
0
0
1
2
1
1
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
1
1
0
1
0
1
0
1
0
0
0
1
0
1
0
0
0
1
1
1
0
0
0
2
1
0
1
1
0
1
2
3
1
0
0
2
1
2
0
0
0
0
0
1
1
1
0
0
1
1
1
0
1
1
0
0
0
0
1
0
2
0
2
2
2
1
2
2
1
0
0
0
0
1
2
1
2
1
0
0
0
0
0
1
0
1
1
2
0
0
1
1
1
1
3
0
0
0
2
0
0
0
0
0
2
0
0
0
1
2
1
0
0
1
1
2
0
1
0
1
0
2
2
2
0
0
0
2
0
0
2
2
2
2
1
0
1
0
1
2
0
0
1
2
0
0
2
1
1
1
0
2
1
1
1
1
0
2
2
1
0
1
0
1
0
0
2
1
1
2
0
0
0
0
0
1
2
1
0
0
2
2
2
1
0
1
2
2
2
2
0
1
1
2
1
2
1
0
1
0
0
0
2
2
0
2
1
1
0
2
1
1
0
1
0
0
2
1
1
2
1
0
0
0
0
1
0
2
2
1
2
0
0
1
0
0
1
2
1
1
0
0
1
0
0
2
2
2
0
0
1
2
0
2
0
0
6
1
0
1
1
1
1
0
1
1
1
2
2
1
0
1
0
0
1
2
1
0
1
1
0
2
0
0
0
0
0
0
2
0
1
1
1
0
1
2
1
0
1
0
2
0
2
0
1
0
3
0
2
2
0
0
0
0
1
1
0
1
0
1
2
2
0
2
1
2
0
1
0
0
2
0
1
0
0
0
1
0
1
1
1
0
0
0
1
0
1
2
0
0
0
0
0
1
1
0
0
2
1
0
1
1
0
0
0
0
1
0
2
0
1
0
2
0
2
0
0
1
2
0
0
0
0
0
1
0
0
2
2
0
0
0
1
1
2
1
0
0
0
1
1
1
3
2
3
1
0
1
0
0
2
1
0
0
2
0
1
1
1
1
1
1
1
0
2
0
0
1
1
0
2
1
0
0
1
2
1
2
0
1
1
0
0
1
0
2
1
2
1
0
0
1
1
1
0
1
1
0
0
0
0
0
1
2
1
2
1
1
2
2
1
1
1
0
0
1
0
0
1
2
1
0
3
2
0
0
2
0
2
2
0
2
1
0
0
0
1
0
1
0
0
0
1
0
0
1
1
2
0
0
0
0
0
2
0
0
0
1
2
1
0
1
0
1
0
0
0
2
0
1
0
1
0
2
2
0
0
1
0
1
0
0
1
1
1
0
1
0
2
1
2
0
2
1
1
0
0
0
0
1
1
2
0
1
2
0
0
1
2
0
2
1
2
0
1
1
0
2
2
1
0
0
2
0
0
0
0
1
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
2
0
2
2
2
1
0
0
2
2
1
0
0
2
0
1
0
0
0
0
0
2
1
2
0
1
0
0
0
0
1
0
0
1
0
1
1
0
2
1
1
2
1
0
0
1
2
0
1
2
1
0
2
1
0
1
0
0
2
0
0
0
0
0
2
0
2
0
1
1
3
0
1
0
0
0
1
0
1
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
2
3
1
0
1
0
0
2
2
3
1
0
0
1
0
0
0
1
0
0
0
1
2
1
0
2
0
0
2
1
0
1
0
0
0
0
1
1
1
0
0
0
0
0
1
2
2
0
2
0
1
0
1
1
0
2
0
1
0
0
1
0
0
0
2
0
2
1
0
2
2
0
1
1
0
0
1
1
0
1
1
0
1
0
1
1
0
1
1
0
0
1
1
1
2
0
1
0
0
0
0
4
0
2
1
1
0
2
2
1
0
1
2
0
0
1
1
1
4
1
0
1
0
1
0
1
1
0
1
0
1
1
1
1
0
1
0
0
2
2
1
2
0
0
2
0
1
1
0
1
0
0
0
0
0
2
0
0
1
1
0
2
1
2
0
0
0
2
1
0
0
0
1
0
0
1
0
1
0
1
0
0
0
1
0
1
0
0
1
2
0
1
0
1
2
0
3
2
0
1
0
0
1
1
0
2
0
2
1
1
0
0
0
1
0
2
1
2
0
1
0
0
0
0
0
2
0
1
0
0
0
0
2
2
2
1
2
1
0
0
0
0
1
0
2
0
0
1
1
1
1
1
2
0
0
0
0
1
2
1
2
1
0
0
2
0
1
0
0
0
0
1
0
0
0
2
2
0
1
2
0
1
0
1
0
0
1
2
0
0
1
0
0
0
1
0
2
0
1
0
2
0
1
0
1
2
4
0
0
2
1
0
0
2
2
0
0
1
1
0
1
1
1
0
1
1
1
0
1
0
2
0
0
0
0
2
2
2
0
2
1
0
0
0
0
0
1
0
1
0
0
2
1
2
0
2
1
2
2
1
1
1
2
2
1
2
1
0
2
0
0
0
0
2
2
0
2
1
0
2
0
0
2
2
0
0
0
2
1
3
0
1
1
1
2
0
2
0
2
1
2
2
1
0
1
2
2
1
0
0
1
2
0
1
2
0
2
0
1
0
1
0
0
0
0
1
0
0
2
0
0
1
0
2
2
0
0
1
0
0
1
1
2
2
2
1
3
2
0
1
0
0
2
1
0
0
1
0
0
1
0
0
0
2
0
0
0
0
2
0
2
0
1
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
1
1
0
1
0
0
0
1
1
0
0
0
0
0
1
0
2
0
1
2
0
1
1
0
0
1
0
2
0
2
1
0
2
1
1
0
0
2
0
2
0
1
0
0
1
2
0
2
3
0
1
1
0
2
0
2
2
2
0
2
1
0
0
0
2
2
0
1
2
1
2
1
0
1
0
1
0
0
0
1
2
1
1
1
0
0
0
0
0
2
1
0
0
1
0
1
1
0
1
1
4
0
0
0
0
0
1
0
0
2
1
1
0
2
1
1
2
2
0
0
0
1
2
0
0
1
2
0
1
0
0
1
1
1
1
1
1
1
1
2
0
2
0
1
0
0
2
0
0
1
1
3
2
0
2
0
1
1
1
3
1
0
2
0
0
2
1
0
1
2
0
0
1
1
1
1
0
2
2
0
0
2
2
2
0
0
0
0
1
1
0
0
1
0
0
0
1
0
1
0
1
0
1
0
0
0
0
1
3
1
1
0
1
0
0
2
0
2
0
0
0
1
7
0
1
2
0
1
2
0
0
0
0
1
3
2
1
1
0
1
2
2
2
0
0
2
1
0
2
1
2
2
0
1
1
0
0
0
1
1
0
1
0
1
0
0
0
0
1
2
0
0
0
0
2
1
0
0
1
0
0
1
0
0
2
0
0
0
2
0
1
0
0
1
1
0
0
0
2
0
0
2
2
0
1
0
1
0
0
0
1
0
1
2
0
0
0
0
2
0
1
0
0
2
0
1
0
0
0
1
1
1
0
2
0
0
0
0
2
0
1
0
1
0
0
1
2
1
0
1
0
0
1
2
0
2
0
1
0
2
0
0
0
0
0
1
1
1
0
2
1
0
1
1
0
2
0
0
2
0
0
0
3
0
0
2
1
2
1
1
0
1
1
0
0
1
1
1
1
0
0
3
2
2
0
0
1
0
1
3
0
0
1
1
1
0
1
0
2
0
0
2
1
0
1
1
0
0
2
2
0
0
0
0
1
2
0
0
0
0
0
0
1
1
1
2
2
0
0
2
1
0
2
0
0
0
1
2
2
2
1
1
0
2
0
2
1
2
0
2
1
1
0
0
0
0
0
2
2
0
0
2
0
1
0
1
2
3
1
1
1
1
0
1
0
2
0
2
2
1
0
2
0
0
1
0
2
0
1
0
2
1
1
2
2
3
0
1
0
1
0
1
1
1
1
0
0
2
0
0
1
1
0
0
0
0
0
1
0
2
2
1
1
0
1
0
1
1
1
0
0
0
1
1
1
0
0
2
0
1
1
0
0
0
0
2
1
1
0
1
0
1
0
0
0
1
1
3
0
0
0
2
1
1
0
0
1
2
0
2
1
1
2
3
0
1
0
0
1
1
0
2
1
2
2
0
0
1
1
1
0
2
3
2
0
0
0
1
0
0
1
1
1
2
0
1
1
1
2
1
0
2
1
0
0
1
0
0
1
2
0
0
1
0
0
0
1
0
1
1
2
2
1
1
0
0
1
0
1
2
0
0
1
1
0
1
1
2
0
1
0
2
3
0
0
1
2
0
1
1
0
0
1
2
1
0
1
1
0
1
1
1
0
0
1
0
1
0
2
1
0
0
0
0
4
1
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
2
1
0
0
2
0
1
0
1
2
1
0
0
0
0
0
2
1
0
0
1
0
0
2
2
0
0
0
0
1
0
0
0
0
1
2
0
2
0
1
1
0
0
1
1
0
2
0
0
1
6
1
2
0
1
2
1
4
0
2
0
0
1
1
0
1
1
0
0
1
1
1
1
1
0
0
2
0
0
1
0
0
2
0
2
0
0
2
1
1
2
1
3
1
1
1
2
0
0
0
1
0
1
0
2
0
1
2
1
1
0
2
2
0
1
0
2
0
0
3
0
0
1
0
1
0
0
1
2
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
2
1
0
2
0
0
1
2
0
2
0
0
2
0
1
1
0
0
0
0
0
2
0
1
0
1
2
0
1
0
1
0
2
0
0
2
0
2
1
2
0
0
1
1
0
0
0
0
0
0
1
1
0
1
1
0
2
0
0
2
0
2
1
0
0
0
0
1
0
1
0
1
0
2
2
0
1
0
1
1
2
2
0
2
1
0
2
1
2
1
2
2
0
0
0
1
0
2
1
0
0
1
0
1
1
0
0
1
0
1
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
1
0
1
0
0
1
2
0
1
0
0
0
0
0
2
0
0
1
0
0
1
1
6
0
1
2
0
1
0
0
2
0
2
1
1
1
1
0
2
0
1
2
1
2
2
0
2
1
1
0
0
3
0
0
0
1
0
1
1
1
0
2
1
1
0
0
2
1
3
1
1
0
1
2
1
2
5
1
0
2
2
1
0
1
0
2
0
2
1
2
0
0
1
0
0
0
1
2
2
1
0
0
0
0
2
0
0
3
0
0
1
0
0
0
0
0
7
4
0
0
2
1
2
3
0
0
1
0
0
0
1
2
2
1
1
0
0
0
0
0
0
0
2
0
0
2
2
1
2
1
2
1
0
2
0
2
0
0
2
0
0
1
0
1
2
0
1
1
0
0
0
0
0
0
0
0
1
3
1
2
1
0
2
0
1
2
1
1
0
1
0
0
1
1
0
2
0
0
1
0
0
0
0
1
0
2
1
0
0
0
1
1
1
2
0
1
0
0
2
1
2
0
0
1
1
0
0
1
0
1
1
0
3
2
5
1
2
1
1
0
0
0
1
1
0
0
1
2
3
0
0
1
2
1
1
1
0
1
0
0
0
0
1
2
0
0
0
2
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
1
1
1
1
0
1
0
0
1
1
1
1
0
2
1
1
0
1
1
2
0
2
0
1
1
2
2
2
2
0
2
2
2
1
0
2
1
0
1
1
0
0
0
2
0
1
0
0
2
1
3
0
0
0
0
1
0
0
2
2
0
2
1
0
2
0
0
0
0
1
1
0
0
0
2
0
2
2
0
1
0
2
0
1
0
0
1
2
0
0
2
2
0
1
0
0
0
0
0
1
2
1
0
2
1
0
1
2
1
0
0
1
1
0
0
1
2
1
2
2
1
1
0
2
1
1
1
0
1
2
0
2
2
0
0
2
0
2
1
1
1
0
1
0
0
1
0
2
0
1
0
2
0
1
0
0
0
2
0
2
1
1
1
1
1
2
0
0
1
1
0
1
0
1
2
1
0
1
2
2
1
0
1
1
0
0
0
0
0
1
0
1
0
0
1
0
1
2
1
0
2
1
0
2
0
0
1
2
0
1
2
0
1
0
0
1
0
1
0
2
0
2
0
1
0
1
0
2
0
1
1
0
0
0
1
0
0
1
0
1
0
1
1
0
0
0
0
0
3
2
0
0
2
0
1
0
2
0
1
2
1
1
0
1
0
0
0
2
1
2
0
1
4
0
0
2
0
0
0
0
1
1
0
2
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
2
0
2
1
2
1
1
1
0
1
1
0
0
2
0
1
2
0
1
2
0
0
2
1
0
1
0
2
2
0
0
1
0
2
1
2
0
1
0
0
0
0
0
2
2
2
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
2
2
1
0
1
0
0
0
1
0
2
1
1
0
1
1
0
1
1
2
2
0
0
0
1
0
2
0
0
0
0
2
1
1
1
1
2
1
2
1
0
0
5
0
1
2
0
0
1
2
1
2
0
2
0
1
2
0
2
0
1
1
2
0
0
0
2
1
1
0
2
1
0
2
0
0
1
2
1
0
0
1
1
1
2
0
1
1
0
0
0
1
1
1
0
0
1
1
0
1
0
1
0
1
0
1
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
1
1
1
1
0
1
13
1
4
2
0
1
2
2
1
0
0
3
2
1
2
0
1
0
2
0
1
4
0
0
1
1
2
2
0
1
1
1
1
2
0
1
1
1
2
0
0
0
2
0
2
0
1
0
1
0
1
1
1
1
1
0
1
1
2
0
0
2
0
0
0
0
2
1
0
0
2
1
0
0
1
0
0
1
0
0
2
1
0
1
0
1
0
2
0
1
2
0
0
1
1
0
1
0
0
0
0
1
2
1
0
0
0
1
1
0
3
1
0
0
2
0
0
1
2
2
1
1
0
0
0
0
1
0
2
0
2
1
2
0
2
0
0
1
0
0
0
1
1
0
2
0
0
2
0
0
2
0
0
0
0
1
0
0
1
2
0
1
1
2
0
0
2
1
1
1
1
0
1
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
2
2
1
1
2
2
1
1
1
0
1
0
0
0
0
1
2
1
1
2
1
1
1
1
2
0
0
2
0
0
0
0
0
1
1
0
0
1
1
2
1
0
4
0
0
0
2
0
2
0
0
1
1
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
2
0
2
1
0
1
0
1
0
1
1
2
0
2
2
0
0
0
1
2
2
2
0
0
2
0
0
0
1
2
2
0
0
0
0
1
0
5
2
0
1
2
1
1
2
0
1
1
2
1
2
2
0
0
0
1
5
0
1
0
2
1
2
1
1
2
3
2
1
1
2
0
0
0
4
0
0
0
1
0
0
0
1
1
0
2
1
0
0
0
0
2
2
0
1
2
0
2
1
0
0
0
0
0
1
1
0
0
1
0
0
2
0
0
1
0
0
2
1
1
2
2
1
1
1
0
1
2
1
2
2
2
1
0
2
0
0
1
0
1
1
0
0
2
0
2
0
0
0
1
1
1
1
1
2
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
1
1
1
0
1
0
0
0
1
1
0
1
2
2
0
2
1
0
1
1
0
0
0
0
0
0
1
2
1
1
1
2
0
1
1
0
0
0
1
0
2
0
2
1
0
0
1
0
0
1
1
0
1
1
0
1
1
0
0
2
0
1
2
2
0
0
0
2
0
0
1
0
0
0
0
2
0
0
1
0
1
1
0
0
1
0
1
0
0
2
0
2
2
0
1
0
2
1
1
2
1
3
1
0
1
0
0
0
2
1
0
0
0
0
2
0
1
2
1
0
0
0
1
2
0
0
0
1
0
0
0
1
0
0
1
0
2
1
4
1
2
0
0
1
0
2
0
0
1
2
1
0
0
2
2
0
0
0
2
2
0
0
2
1
0
1
2
2
0
1
0
0
1
0
2
0
1
1
0
2
2
1
0
0
1
0
1
1
0
1
0
0
1
1
2
1
0
0
0
1
1
0
2
1
0
0
0
4
0
0
1
0
0
2
1
2
1
1
1
1
0
2
0
0
1
1
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
1
1
1
0
0
2
0
1
2
1
2
0
0
0
0
0
1
1
0
0
1
0
0
1
0
2
0
2
2
0
1
0
0
1
0
1
1
2
2
0
0
0
0
0
1
0
0
2
0
1
0
0
0
2
0
1
0
0
1
1
1
0
1
2
1
1
0
0
0
0
2
1
1
0
0
1
0
0
1
0
1
2
1
1
2
1
0
0
0
0
0
2
0
2
2
0
0
2
1
2
1
0
1
1
0
1
0
1
2
0
0
0
0
1
0
0
2
0
0
0
1
0
1
1
0
1
2
1
1
0
1
0
1
2
0
0
2
2
0
0
1
1
1
0
0
3
0
0
0
0
0
0
2
0
2
1
0
2
2
0
0
0
1
1
0
0
1
1
1
0
1
1
1
0
0
0
2
0
1
1
0
0
0
0
0
0
1
1
3
0
1
1
1
0
0
0
1
0
0
0
0
0
1
2
1
0
1
2
1
2
2
1
2
0
3
2
0
2
1
1
0
0
0
0
2
1
0
0
1
0
0
2
0
2
0
0
1
0
0
0
2
0
1
1
1
2
1
0
2
0
0
0
0
0
2
1
0
0
1
0
0
2
0
0
1
1
1
1
0
1
0
1
3
1
0
0
0
1
0
1
2
2
0
0
0
4
1
0
1
0
2
0
2
2
0
0
1
3
1
1
1
2
0
1
0
0
2
1
2
1
0
0
2
2
0
1
0
0
0
0
1
1
0
0
1
1
0
0
1
2
0
0
0
2
0
1
1
1
1
0
1
0
0
0
0
2
0
0
0
3
1
1
1
0
0
0
0
0
1
1
1
0
2
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
2
2
0
1
0
0
0
1
0
0
0
1
1
0
0
1
1
0
0
0
0
0
1
2
1
1
2
2
0
1
0
2
1
0
1
0
1
1
1
0
0
1
1
1
1
1
2
2
1
0
0
1
2
0
1
2
0
1
0
2
0
0
2
0
2
0
3
0
2
0
0
1
0
2
1
1
0
2
0
1
0
1
1
1
2
0
2
1
0
3
0
1
0
1
1
0
0
0
0
2
2
0
2
0
1
0
0
1
1
1
2
1
1
0
0
1
1
0
0
1
1
0
1
2
0
0
0
1
1
0
1
2
0
0
0
0
0
1
0
0
2
0
0
0
1
1
0
1
0
0
2
0
0
0
1
0
0
1
0
1
0
1
1
1
2
1
0
0
2
0
0
0
0
1
1
1
0
0
0
0
2
0
1
0
1
0
1
0
1
0
0
0
1
0
2
0
1
2
2
0
0
1
2
2
2
2
1
0
1
2
1
2
0
0
0
0
0
2
0
0
2
0
0
1
1
4
0
0
1
1
0
0
0
2
0
0
1
2
2
0
2
0
1
0
2
0
0
1
0
1
2
0
2
0
0
2
0
1
2
0
0
1
2
0
0
0
2
2
0
2
0
1
0
1
4
0
0
2
0
0
0
0
1
0
0
2
2
2
1
0
0
2
0
1
0
0
1
1
0
3
0
0
0
1
0
1
2
2
1
2
0
2
0
0
1
1
0
1
1
2
1
0
2
1
0
2
2
0
0
0
0
0
1
0
2
0
2
1
0
2
0
0
0
1
1
0
1
0
2
0
0
0
0
2
2
0
1
1
0
0
2
2
1
0
1
2
0
0
0
0
0
0
1
0
2
0
0
2
0
1
0
0
2
0
0
0
2
1
2
0
1
0
2
2
0
2
0
2
2
2
0
0
0
1
2
3
0
1
1
0
0
1
0
2
1
2
1
1
1
0
1
1
1
1
0
0
0
1
1
1
1
0
0
0
0
0
1
0
1
0
2
1
0
1
1
2
0
1
1
1
0
1
2
2
0
0
2
1
1
0
0
0
1
2
2
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
1
0
2
2
1
2
1
1
1
0
2
2
0
1
0
0
1
0
2
1
1
2
0
1
0
0
0
3
0
1
0
0
2
0
0
0
0
1
1
0
1
2
1
1
0
2
0
2
1
0
2
0
1
1
2
1
0
0
0
1
0
2
1
1
0
1
0
0
1
0
2
3
1
1
1
1
1
0
0
0
1
1
1
0
1
0
0
1
0
7
2
1
2
0
0
1
2
0
0
2
1
2
1
0
0
0
0
0
0
0
1
1
1
0
0
2
0
0
2
2
2
0
0
0
1
2
1
0
0
2
2
2
0
2
0
0
1
0
3
1
1
1
1
1
2
3
1
0
0
0
2
1
0
0
0
1
2
1
1
1
0
2
0
2
0
1
0
1
0
2
1
0
1
1
2
0
0
2
0
2
0
1
1
3
0
2
1
0
1
1
0
1
0
0
2
2
2
0
1
2
0
0
2
2
1
1
0
0
2
1
0
1
2
1
0
1
2
2
0
0
0
0
2
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
1
2
0
1
1
1
2
1
0
0
2
2
0
0
0
2
0
2
0
0
0
0
0
0
0
3
0
2
0
0
2
0
0
2
0
2
1
0
0
1
0
1
0
0
0
1
0
0
2
0
2
2
0
1
0
1
0
3
1
0
0
2
1
0
1
0
0
1
1
2
0
3
0
0
0
0
1
1
0
0
2
0
1
0
0
1
4
0
0
0
0
0
1
2
1
3
0
0
1
0
2
0
2
1
2
0
1
0
0
0
1
1
0
0
1
1
1
0
0
1
0
0
0
1
0
0
1
0
2
0
0
2
1
2
2
0
2
0
0
1
2
1
0
0
0
0
1
0
1
0
2
0
0
2
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
1
1
0
1
0
2
0
0
0
0
1
2
1
0
0
0
0
1
2
1
1
0
0
1
0
0
0
0
1
0
2
0
0
0
1
2
1
2
2
0
2
0
0
2
3
0
2
1
0
1
1
0
0
2
2
1
0
2
0
0
1
2
0
0
1
0
2
0
1
0
0
1
0
0
0
1
0
2
2
2
0
0
0
2
1
1
0
1
0
2
1
0
1
0
2
2
0
1
0
4
2
0
2
2
1
1
0
2
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
1
0
0
2
1
0
1
1
0
2
1
2
1
1
3
5
1
0
0
0
0
0
0
1
1
0
2
2
1
1
1
0
0
2
2
0
0
2
0
1
0
0
0
0
1
1
1
0
1
0
0
0
2
1
0
0
1
0
0
2
1
1
0
0
1
0
1
0
1
1
0
1
0
0
2
1
0
1
2
2
0
0
0
0
0
1
1
2
1
1
0
1
0
1
2
0
9
1
0
2
2
2
2
0
1
0
0
0
0
0
0
0
1
1
1
1
2
0
0
0
2
0
0
0
2
5
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
2
1
2
0
2
1
1
0
0
0
1
1
2
1
1
2
2
0
1
0
0
0
1
0
0
0
1
2
2
2
2
0
0
1
0
0
1
0
1
1
1
0
0
1
0
1
2
0
3
0
0
2
0
1
0
2
0
0
0
0
0
2
0
1
0
2
1
2
2
0
1
1
1
0
0
1
0
2
2
2
1
0
1
1
0
0
0
0
0
2
2
2
0
1
2
0
2
0
0
2
0
0
2
0
1
0
1
0
0
0
1
0
2
1
2
2
0
0
1
0
2
2
0
2
0
0
0
1
0
0
1
0
0
1
1
0
1
2
1
0
0
0
0
1
0
2
0
1
0
2
0
0
1
0
2
1
1
0
0
1
0
0
0
1
0
2
0
1
2
0
0
0
1
0
1
0
2
2
2
0
0
1
0
0
1
0
1
0
0
2
2
2
1
0
1
2
0
1
0
0
0
1
0
0
2
2
0
1
0
0
2
0
2
0
0
0
1
2
0
0
0
0
1
0
2
1
2
2
0
0
0
2
1
1
2
0
1
2
1
2
0
1
0
0
2
0
1
0
1
1
1
1
0
0
1
2
2
1
1
0
2
2
2
0
0
0
1
1
1
0
0
1
0
2
1
0
0
0
0
0
1
0
0
3
1
0
2
2
0
1
2
1
0
0
0
0
0
0
6
0
2
0
0
2
2
0
1
0
0
0
2
0
1
0
0
2
0
1
1
1
2
0
0
2
0
2
0
0
1
0
0
1
0
1
2
0
0
0
2
1
0
1
0
2
0
0
1
1
1
0
0
1
0
1
0
2
0
1
0
2
2
1
0
0
0
1
0
1
1
1
1
2
2
2
0
0
1
0
0
1
0
1
0
0
0
1
0
1
0
1
0
0
1
2
0
0
1
1
2
3
2
0
2
2
1
2
0
0
0
0
2
0
1
1
1
0
0
0
0
0
1
1
0
1
1
0
0
1
0
0
1
3
1
0
1
0
1
1
1
1
0
0
1
2
0
1
1
2
0
0
2
0
0
0
1
0
0
0
1
2
1
1
2
0
2
0
2
1
1
1
0
3
1
1
0
1
0
2
2
2
0
0
0
2
1
0
2
0
0
0
0
1
2
2
2
0
2
0
0
0
0
0
0
2
3
0
1
1
0
2
2
1
1
0
0
0
2
0
1
1
0
0
0
2
1
2
0
1
2
0
1
0
2
3
2
1
0
1
0
0
2
0
1
0
0
2
2
0
0
0
0
2
2
1
0
2
0
2
0
0
2
0
0
2
0
0
0
0
1
0
0
0
1
0
2
2
0
3
0
1
1
0
1
1
1
0
1
0
1
0
2
3
1
2
2
2
1
1
1
0
0
1
1
0
0
1
2
1
0
0
1
1
0
0
1
0
1
0
0
0
2
0
0
2
2
0
1
1
0
2
1
0
1
2
0
1
0
0
0
1
0
2
0
1
1
2
0
0
1
0
1
1
2
2
2
2
1
1
5
2
0
1
1
0
0
0
0
1
1
0
2
2
2
1
2
1
0
0
0
2
1
0
1
0
1
0
1
1
1
0
1
2
0
2
0
0
1
0
0
0
2
0
0
1
2
1
0
2
0
0
2
0
1
1
0
0
0
0
3
1
0
1
2
1
0
0
1
1
0
0
1
0
2
1
0
1
0
6
0
1
0
1
2
0
0
0
0
0
1
0
0
0
1
2
1
2
0
1
1
0
0
0
0
0
0
2
1
0
2
2
2
1
2
0
1
3
0
2
0
0
0
0
0
0
1
0
1
0
1
2
0
0
1
0
1
1
1
1
0
1
0
1
0
0
1
0
2
2
1
0
2
0
0
2
1
0
0
1
1
1
0
0
0
2
1
2
0
1
1
1
0
1
2
2
1
0
1
0
4
2
0
0
1
1
1
2
1
0
2
2
2
1
0
0
1
0
0
0
0
0
1
1
1
2
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
2
0
1
0
0
1
2
1
0
0
0
0
1
1
0
1
0
1
0
0
2
0
0
0
1
2
0
0
0
0
0
0
2
0
1
1
0
0
2
2
0
1
1
0
2
0
1
2
2
2
2
0
2
1
1
0
1
1
0
1
0
1
1
4
0
1
0
1
0
1
4
0
2
1
1
0
0
0
3
1
0
1
0
2
2
1
1
0
0
0
0
1
2
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
1
3
2
0
1
1
0
0
0
0
1
0
1
0
0
0
1
2
2
0
0
2
2
2
0
1
1
0
0
0
1
0
2
0
0
0
1
1
1
1
1
2
1
0
2
0
1
0
0
2
0
1
0
1
1
0
0
0
1
1
0
0
0
0
2
0
1
1
1
1
1
0
1
0
0
0
0
0
2
1
0
0
1
1
0
0
0
0
0
1
1
0
1
1
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
2
0
1
1
0
1
2
2
0
1
1
0
0
0
0
1
0
0
1
0
2
0
0
0
2
1
0
0
1
2
0
3
0
0
1
0
0
2
1
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
1
1
1
2
1
0
1
2
1
1
0
2
1
1
0
1
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
4
0
0
0
0
1
2
2
0
1
1
1
0
0
0
2
2
0
1
2
1
0
2
0
1
2
0
0
1
1
2
0
1
0
2
0
0
0
1
0
0
0
0
1
1
0
1
0
0
1
2
1
2
2
0
1
2
1
1
0
1
2
2
0
1
3
0
0
1
1
0
0
1
0
2
0
0
1
1
0
1
2
0
2
1
1
0
0
1
1
1
0
0
2
0
0
1
1
2
1
0
0
0
0
1
0
0
1
0
0
0
0
1
2
1
0
0
2
0
2
2
0
2
1
0
0
0
0
1
0
1
0
2
1
1
0
2
1
1
1
2
1
1
5
2
0
1
1
1
0
2
0
1
0
1
2
0
2
1
0
0
0
10
0
0
1
0
2
1
1
0
0
1
2
2
1
0
2
1
1
0
1
1
2
0
1
0
0
0
2
2
1
0
1
1
3
0
1
2
0
1
0
1
1
2
0
1
1
1
0
1
2
0
0
0
0
0
0
0
0
0
1
2
1
2
0
1
2
0
0
0
1
1
0
1
1
0
0
0
2
0
0
0
1
1
2
0
1
0
1
0
0
1
1
1
1
0
2
0
0
1
1
1
0
0
0
0
0
1
0
0
2
0
0
1
0
1
1
2
1
2
1
2
2
1
2
1
0
2
0
2
0
0
1
1
1
0
1
0
0
0
2
1
0
2
2
1
1
1
0
1
0
2
0
0
2
0
1
2
2
0
1
0
1
2
0
1
1
0
1
0
0
0
0
1
1
0
1
0
0
5
0
2
0
0
0
0
1
0
2
0
0
0
1
0
1
0
1
0
1
1
1
0
0
1
1
0
0
2
0
2
0
1
2
1
0
0
1
0
0
0
0
2
2
0
2
1
0
2
2
1
1
3
0
2
1
0
2
2
0
2
1
0
1
0
0
0
2
0
2
1
0
0
0
0
0
1
1
3
2
1
0
0
2
0
0
1
1
1
1
1
1
2
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
1
2
2
0
0
1
0
0
0
1
1
0
0
2
0
0
2
0
0
2
0
0
1
0
2
3
1
1
0
0
0
0
0
0
2
2
0
1
2
0
1
1
2
0
1
2
2
0
2
0
1
1
0
1
0
2
2
0
0
1
2
2
2
1
0
0
0
1
0
2
2
1
0
1
1
0
0
1
2
0
1
0
0
0
0
0
0
1
1
0
2
0
1
0
0
1
1
1
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
2
1
1
0
0
1
1
0
1
1
2
1
0
0
2
1
1
0
0
0
0
0
0
1
2
1
0
2
1
0
0
1
0
0
0
1
0
1
2
1
0
1
0
0
0
0
0
0
2
0
0
0
1
2
1
1
0
0
0
0
0
1
2
1
1
1
0
0
0
1
0
1
0
1
1
1
0
1
0
2
2
1
2
0
1
0
0
0
0
2
1
0
1
0
1
1
0
0
0
0
2
0
1
3
1
0
2
0
1
3
0
1
0
0
1
0
1
0
2
0
0
1
0
1
0
0
2
1
2
0
2
0
2
0
0
3
2
0
0
0
1
0
0
0
2
0
2
0
0
0
1
2
1
2
2
0
0
1
0
2
0
0
2
2
0
0
1
3
0
0
0
0
0
0
2
0
0
0
1
1
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
2
1
1
0
0
0
0
0
0
2
0
0
2
0
0
0
1
1
2
0
0
1
0
2
1
0
0
0
1
0
1
2
2
2
1
2
1
0
2
1
1
1
0
0
0
2
0
1
0
1
1
0
1
1
1
1
1
0
0
3
0
2
0
1
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
1
0
1
2
0
0
2
0
1
2
2
2
1
0
0
1
0
2
0
0
0
0
0
3
2
0
0
2
0
0
0
0
0
0
2
1
0
0
2
1
2
2
0
0
3
1
0
2
0
0
1
3
0
0
1
2
0
2
0
0
2
1
2
1
0
1
2
0
0
0
0
2
2
0
2
2
0
0
2
0
2
1
1
1
4
0
0
0
0
2
0
2
1
0
0
2
1
2
1
0
2
3
1
0
1
2
0
2
3
2
0
1
6
0
1
1
1
0
2
1
0
1
1
1
0
1
0
1
2
2
1
2
1
0
0
2
2
0
0
1
2
0
0
1
0
0
1
2
0
1
0
3
1
1
2
0
3
3
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
1
2
0
2
2
0
0
9
0
0
1
1
0
0
0
0
1
1
1
0
2
1
0
2
0
0
0
0
1
2
0
0
0
2
1
0
1
2
1
0
0
1
2
2
1
0
1
0
1
0
0
1
0
0
0
2
0
1
2
1
1
0
0
1
0
1
0
1
0
1
2
0
1
0
11
2
0
2
1
0
0
2
0
0
0
0
2
0
3
0
2
1
0
0
1
0
2
2
1
0
0
1
0
2
0
2
2
0
1
1
2
2
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
1
2
1
1
0
1
1
0
1
5
1
0
2
1
0
0
0
1
1
0
0
3
2
1
2
0
0
1
1
1
0
0
0
0
1
0
3
0
2
2
2
0
2
0
2
1
0
0
0
2
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
1
2
3
0
0
1
2
1
1
0
2
0
1
0
1
1
2
3
0
1
1
0
2
0
1
1
0
1
1
0
0
0
0
1
1
0
1
2
2
0
0
0
1
3
0
2
0
0
2
0
0
2
2
1
0
0
1
1
0
4
0
1
0
0
2
2
0
1
1
0
0
1
1
0
0
1
1
0
2
1
0
0
2
0
1
1
1
0
1
1
0
2
2
1
0
0
1
1
2
1
1
1
0
1
1
2
0
0
1
0
1
0
0
1
2
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
1
0
0
1
2
2
2
2
0
0
3
0
1
1
0
0
2
0
1
2
0
0
0
1
0
0
2
0
0
0
1
1
0
1
2
1
1
0
0
1
0
1
0
2
0
1
1
0
0
0
1
0
0
2
2
2
2
2
0
1
1
1
1
2
0
2
0
0
1
1
0
1
0
1
2
2
1
1
2
2
2
0
1
1
1
2
0
3
1
2
0
2
2
1
1
1
2
1
1
2
0
2
0
0
0
0
1
2
0
1
0
0
0
0
1
0
2
3
1
2
2
0
1
1
2
0
1
1
0
0
1
1
0
3
0
0
1
1
2
1
1
1
0
2
0
2
0
1
1
0
0
1
1
0
1
2
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
1
0
1
2
0
2
2
2
0
0
0
1
1
1
0
1
1
0
0
1
0
0
1
1
1
0
0
2
0
1
2
2
1
0
1
1
2
1
3
2
1
2
2
2
2
5
1
0
1
2
2
2
1
2
2
2
2
1
2
2
2
0
0
0
0
0
0
0
2
1
0
0
0
1
1
1
0
1
1
1
0
0
0
0
0
1
0
0
0
0
1
1
1
2
2
0
0
1
1
0
1
1
1
0
0
0
3
0
1
2
0
1
0
0
0
2
1
2
0
0
1
0
1
0
0
0
0
1
1
0
2
0
0
0
1
0
0
0
2
0
0
2
2
3
1
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
1
0
0
2
2
1
2
1
3
2
3
2
2
0
1
0
0
0
0
0
1
1
0
0
0
1
0
1
1
0
1
2
0
2
2
0
0
0
0
1
1
1
1
0
0
0
1
0
0
0
0
0
0
0
1
2
0
1
1
0
1
0
0
0
2
1
1
0
0
0
1
2
1
0
0
2
1
0
0
0
0
2
2
2
0
0
2
0
1
3
1
0
0
0
2
1
0
2
0
0
1
2
0
0
0
1
3
0
0
1
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
2
0
1
0
0
1
0
2
2
1
0
0
1
1
1
2
1
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
2
4
0
2
2
2
1
0
1
1
1
1
0
2
0
1
1
0
0
0
0
0
0
0
2
0
2
2
1
0
3
1
0
0
0
2
0
0
2
0
0
1
0
2
1
0
1
0
0
1
0
0
0
1
1
1
0
2
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
2
2
1
1
0
1
0
0
0
3
1
0
1
2
0
0
0
1
2
1
1
0
0
0
1
1
0
0
0
0
1
0
0
2
3
0
2
2
0
1
0
0
0
0
0
2
0
0
0
0
2
2
0
2
2
0
0
0
2
2
2
0
0
2
0
0
1
1
1
2
0
0
1
2
2
1
1
2
0
0
2
1
1
2
0
0
1
0
1
0
0
1
0
0
2
0
1
0
1
0
0
0
1
0
1
1
2
0
1
1
1
1
0
0
2
0
1
0
0
1
2
0
0
1
2
0
0
1
1
1
0
2
1
0
1
1
0
0
0
0
2
1
0
0
0
1
1
0
1
0
1
0
2
1
0
3
2
0
1
2
1
2
2
0
0
1
1
1
0
0
0
0
0
0
1
0
1
3
2
1
0
0
2
1
0
0
0
1
1
2
0
1
0
0
2
0
1
1
1
0
0
2
0
0
0
1
0
0
1
0
2
1
0
0
0
0
0
0
1
0
1
0
2
1
2
1
0
1
0
1
0
2
0
0
2
0
0
2
1
1
0
1
0
1
2
0
0
1
1
1
0
1
0
1
1
0
2
0
1
2
1
0
1
1
0
1
1
0
0
0
1
0
0
1
0
2
3
0
2
0
0
1
0
1
0
1
0
2
2
1
1
0
1
1
0
0
0
0
1
2
0
0
2
0
0
2
0
1
1
1
0
0
0
0
1
2
0
1
0
0
1
1
2
0
0
0
2
2
1
2
0
6
1
0
2
1
2
0
1
0
0
0
1
1
1
0
1
1
1
2
0
0
0
2
1
0
1
1
1
0
3
2
0
0
0
2
1
0
0
1
0
1
1
1
1
1
1
0
0
2
0
1
1
2
0
0
0
2
1
2
2
2
2
2
1
2
0
0
0
0
2
0
1
2
1
2
2
1
0
2
0
1
2
1
1
1
1
1
0
2
1
0
0
2
2
2
0
1
0
0
0
1
0
1
1
2
0
0
2
0
1
2
0
0
0
0
1
1
1
1
0
2
0
0
0
1
2
1
0
0
0
1
2
1
3
3
1
1
1
0
0
2
1
1
0
0
0
0
0
0
2
1
0
0
2
0
0
3
1
0
1
1
0
0
1
0
0
2
0
1
0
1
0
0
1
1
1
2
3
1
0
1
0
1
2
0
0
1
1
0
1
2
1
1
0
1
1
0
1
1
1
2
2
0
1
1
1
0
0
2
0
2
3
1
1
3
3
0
1
0
0
0
2
1
2
0
2
0
0
0
1
0
0
3
1
0
0
0
1
1
2
2
0
0
2
2
1
7
1
0
0
1
0
1
0
0
1
0
0
2
2
0
0
0
0
1
2
0
0
0
0
1
0
2
2
1
2
0
0
0
1
1
2
0
2
3
0
1
1
1
2
2
1
1
0
1
0
2
1
2
1
1
0
0
0
2
1
1
0
0
2
2
1
0
2
1
0
0
0
0
0
0
1
0
0
1
0
1
1
1
2
0
1
0
0
2
2
1
1
0
0
0
0
0
0
1
1
2
0
1
2
2
0
0
0
2
2
0
3
2
0
2
2
0
2
0
2
1
0
0
2
0
2
1
3
0
1
10
1
0
0
0
0
0
0
2
0
1
1
1
0
0
0
0
0
0
0
2
0
2
2
2
0
0
1
2
0
0
1
1
0
1
0
1
0
1
1
1
1
2
0
0
2
0
0
2
2
1
0
0
1
0
0
1
0
0
0
0
0
2
1
1
2
0
0
0
0
0
2
1
1
1
2
0
0
2
1
0
0
2
0
2
1
0
0
0
2
1
2
1
0
1
2
0
0
0
0
0
1
1
1
2
0
1
1
0
1
0
0
1
1
1
0
1
0
1
1
2
0
0
0
2
1
0
0
0
1
0
1
0
0
0
0
1
0
2
0
0
0
1
0
0
2
0
0
0
1
2
1
0
0
0
1
1
0
0
0
0
2
0
0
1
2
0
0
0
1
2
1
0
2
0
0
1
1
0
1
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
3
1
1
0
1
1
1
0
2
1
1
0
2
1
0
1
2
0
2
1
2
0
0
1
0
1
2
0
0
2
1
0
1
1
0
0
1
2
1
1
0
1
1
2
0
1
0
1
0
1
1
0
1
1
0
1
0
1
1
1
2
0
1
0
0
1
0
2
0
0
1
1
0
0
0
0
0
1
0
2
1
0
2
1
0
0
2
1
2
0
0
2
0
0
1
1
0
2
0
2
2
0
0
0
0
0
0
0
1
1
2
0
1
0
2
2
2
1
0
1
0
1
1
2
1
0
0
0
0
2
1
0
1
0
1
1
2
0
1
1
1
1
1
2
0
1
1
2
1
1
0
1
2
0
2
0
1
0
1
3
1
1
0
2
2
2
0
0
0
0
1
1
2
0
1
1
1
2
0
0
1
0
2
1
0
0
2
2
2
2
0
1
0
1
0
1
0
0
0
0
2
2
2
3
1
0
0
1
2
2
0
2
1
0
0
1
1
1
0
1
0
0
0
0
0
1
1
0
0
0
0
1
1
0
1
1
0
0
1
1
2
2
2
2
1
1
2
1
2
0
2
0
2
1
1
1
1
0
0
2
0
1
2
1
2
1
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
2
1
2
0
0
1
0
0
0
0
1
2
0
2
0
0
0
2
0
1
0
2
0
2
1
0
0
3
0
0
0
0
0
1
1
0
1
0
1
1
0
1
2
1
0
1
0
1
0
0
0
0
0
2
2
1
0
1
0
2
0
0
0
2
1
0
0
0
1
2
0
0
1
0
1
2
1
2
2
1
1
0
1
0
2
1
0
2
0
2
1
2
0
0
0
0
1
2
1
0
0
1
0
0
2
0
2
2
0
1
2
1
0
0
0
0
0
2
0
0
2
1
2
0
1
1
1
0
0
0
2
0
1
0
1
1
0
1
2
0
0
0
2
0
1
0
1
2
0
2
0
0
0
0
3
1
0
0
0
2
0
1
1
0
1
0
0
0
1
3
0
1
1
0
0
2
0
1
2
0
2
1
0
1
1
1
0
0
0
0
0
2
0
1
2
0
0
0
1
0
1
0
0
0
0
2
0
1
0
0
1
0
1
2
1
2
1
1
1
0
1
1
1
1
1
0
2
2
0
1
0
1
2
1
1
2
0
1
0
1
0
1
2
1
0
0
2
1
1
1
1
0
0
0
1
0
0
2
0
0
2
2
2
1
1
0
2
0
2
0
0
1
0
2
0
1
1
2
2
3
1
0
2
2
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
1
0
1
1
0
2
2
1
0
0
1
2
0
1
4
1
0
2
1
1
2
0
1
1
1
0
2
2
2
2
0
1
0
1
1
2
0
0
0
1
2
2
2
1
1
0
0
1
2
1
2
1
1
0
1
0
1
1
1
0
3
4
0
1
1
2
2
0
2
1
1
1
2
0
0
0
0
2
0
1
0
2
0
0
1
2
1
1
0
1
2
1
1
0
0
2
0
0
0
1
0
1
0
1
1
1
0
0
0
1
0
1
1
0
0
0
0
2
2
1
0
2
0
0
1
0
2
0
0
0
1
2
1
2
0
0
1
1
2
1
0
1
0
1
1
0
2
1
2
1
1
0
1
0
2
1
0
1
0
1
2
0
2
2
0
0
0
1
0
0
0
2
0
0
1
0
1
0
3
0
0
2
2
2
0
2
1
0
1
1
0
0
1
0
1
3
0
1
1
0
1
0
2
0
2
0
1
2
2
2
3
0
1
2
0
1
1
0
1
1
0
0
1
3
1
1
1
0
0
0
1
1
0
0
2
1
2
0
1
0
1
1
2
0
1
1
0
0
1
1
1
1
0
0
0
0
1
1
3
2
0
2
0
0
0
1
2
2
1
1
1
0
1
0
1
0
1
0
2
0
0
1
1
0
0
0
1
0
2
0
1
0
1
0
0
0
0
2
0
1
0
2
2
1
2
0
0
1
2
0
0
1
0
1
2
1
1
0
0
2
0
1
0
1
2
2
0
2
0
1
0
3
0
0
2
1
1
2
0
2
1
1
0
0
1
0
1
1
1
0
0
0
2
0
0
2
1
2
2
0
1
1
1
0
2
2
0
1
0
2
2
0
0
0
1
2
1
0
3
2
0
0
1
0
0
0
0
0
1
2
0
0
2
0
0
0
1
1
2
1
1
2
1
0
0
2
2
1
0
1
1
1
0
1
1
2
0
1
1
0
0
0
2
1
2
0
0
0
0
0
0
1
1
1
0
1
1
0
0
1
0
0
0
0
0
0
2
0
0
1
0
2
0
0
2
0
0
0
0
0
2
2
2
2
1
0
2
0
0
1
0
0
0
0
0
2
0
0
1
4
1
1
1
0
1
0
2
1
1
1
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
4
1
0
0
2
0
0
0
2
1
0
2
2
2
1
1
0
0
0
1
0
0
2
1
0
1
0
1
0
1
2
2
0
1
1
0
0
2
1
4
1
0
0
1
2
2
0
0
0
1
0
0
0
1
0
2
0
0
0
0
1
0
0
0
1
1
1
2
0
0
1
1
1
2
0
1
2
2
1
1
0
0
1
0
0
1
0
2
0
1
2
1
1
2
0
2
3
0
0
0
0
1
1
2
0
1
1
1
0
1
2
1
1
0
0
2
0
0
0
1
0
0
2
2
0
0
1
0
0
2
0
0
1
0
1
1
1
1
2
2
0
2
1
1
1
0
0
0
0
1
0
1
1
0
0
0
2
1
1
0
2
0
1
1
1
0
0
2
0
0
1
1
0
1
0
2
1
1
0
2
0
0
2
0
0
1
2
1
0
1
0
1
1
2
1
0
1
2
0
1
0
0
0
0
1
1
1
5
0
1
0
2
0
0
1
1
1
0
1
0
2
2
2
0
2
2
1
2
1
0
2
1
0
0
2
2
0
0
0
1
2
1
1
0
0
0
0
1
2
0
1
1
2
1
2
1
0
0
2
1
1
0
2
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
2
0
0
2
2
1
0
1
0
0
0
0
2
1
2
0
1
1
0
0
0
1
1
0
2
1
0
0
3
0
2
1
1
1
0
0
0
1
0
2
0
2
1
0
1
0
0
1
1
1
2
1
0
0
0
1
1
0
0
1
0
2
0
0
1
0
0
0
1
0
0
0
0
1
3
2
0
0
0
1
0
0
0
1
1
1
0
0
2
2
0
2
0
0
0
2
0
1
0
0
0
2
0
0
1
1
0
1
0
0
0
1
1
0
0
0
0
2
2
0
0
0
0
2
0
1
1
3
2
0
0
1
2
1
1
0
1
0
1
0
0
1
0
0
2
1
0
0
0
2
0
0
2
0
1
0
1
0
2
2
3
1
0
0
1
2
2
1
0
1
1
0
0
2
0
0
0
1
2
0
0
0
0
0
1
0
2
2
1
2
1
1
0
1
0
0
1
0
0
0
1
1
2
0
0
0
2
0
0
0
0
0
0
1
0
2
2
0
0
1
0
0
2
1
2
1
2
0
0
1
0
0
0
2
1
0
0
0
2
1
0
1
0
0
2
1
0
2
1
0
0
0
1
0
0
1
1
1
2
1
2
0
1
0
2
1
0
1
1
0
0
0
0
1
2
1
2
0
1
1
0
0
0
0
2
0
0
1
1
2
2
1
0
2
0
1
1
2
2
0
0
1
1
0
4
0
1
2
1
0
2
0
0
1
1
0
2
1
1
1
0
1
1
2
1
2
0
0
1
0
1
0
1
1
2
1
1
1
0
0
1
2
1
0
0
2
2
0
0
0
1
1
0
0
3
1
1
0
2
0
3
2
0
1
0
2
1
0
0
0
2
1
0
1
2
0
2
0
0
0
0
1
0
0
2
0
1
0
1
1
0
0
0
0
0
1
1
0
1
2
0
1
0
1
0
2
0
0
1
0
2
2
0
0
2
0
1
2
2
1
3
0
1
0
2
1
2
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
2
2
0
0
2
2
1
0
1
0
1
2
1
0
1
0
1
0
0
0
2
2
1
1
1
1
0
0
0
2
2
0
1
0
0
2
1
2
1
1
1
1
1
0
1
1
0
0
0
1
1
2
2
2
1
2
0
0
1
1
1
0
2
1
0
1
0
0
0
1
1
0
1
2
0
1
1
0
0
0
0
3
0
1
1
1
0
0
0
1
2
1
1
0
0
1
2
0
0
1
0
1
0
3
0
1
0
1
3
0
0
2
1
2
3
0
3
0
0
1
0
2
2
1
0
0
1
2
1
1
1
0
1
0
2
0
1
0
0
2
2
1
0
2
0
2
1
0
0
1
0
1
2
0
0
1
1
0
2
1
1
1
1
0
0
0
1
0
3
0
0
1
2
2
1
1
1
2
0
0
0
0
2
0
2
0
1
0
2
1
2
0
1
1
2
1
1
1
0
1
1
0
2
1
0
1
0
1
0
1
1
1
2
0
1
0
3
0
0
0
2
2
0
0
2
2
0
0
0
0
0
2
0
2
0
0
2
0
1
0
0
0
0
1
1
0
2
0
0
0
0
0
1
0
2
0
0
2
0
1
0
0
1
1
0
1
1
2
1
0
0
2
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
2
0
0
1
0
0
0
1
2
0
1
0
1
0
0
2
1
0
1
0
2
0
2
0
0
2
2
0
1
0
2
0
0
0
1
0
1
1
0
1
0
0
1
0
1
2
0
0
0
0
0
0
0
0
4
1
1
0
1
2
0
0
2
1
2
0
1
0
1
0
0
0
0
0
0
0
1
1
1
0
2
0
0
1
2
1
0
2
0
0
2
0
2
2
0
0
0
0
0
0
0
0
2
2
2
0
0
0
1
0
0
1
2
0
0
0
1
1
0
1
0
3
0
0
0
0
1
0
0
4
0
2
0
1
0
0
2
0
1
2
0
2
2
0
2
1
2
1
2
1
0
1
0
1
0
1
0
0
2
2
0
0
1
2
0
1
0
0
2
1
0
0
0
0
1
0
1
1
2
2
2
0
1
0
1
0
1
1
0
2
0
0
1
1
1
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
3
1
1
2
1
0
1
0
2
0
2
1
2
0
0
1
0
0
0
2
0
2
1
1
1
0
1
1
0
2
0
1
1
1
1
1
0
3
0
0
3
2
0
0
0
1
0
1
0
0
0
1
3
0
1
0
1
1
1
1
1
0
1
0
2
0
0
0
2
2
0
1
0
0
1
0
1
0
2
1
0
2
1
2
0
2
0
2
0
2
0
2
0
2
2
0
0
1
0
10
3
1
0
1
1
1
0
1
4
0
2
1
0
3
1
0
0
0
1
0
1
2
0
0
0
1
2
1
0
1
0
2
2
1
1
0
1
1
0
1
1
0
1
1
1
1
2
0
0
1
1
0
1
0
1
0
1
0
2
2
0
1
1
2
0
0
0
0
0
0
0
1
2
1
1
0
0
0
2
1
0
0
0
1
0
1
1
0
2
0
0
0
1
1
0
0
0
2
2
0
0
1
1
1
1
0
2
1
0
1
1
2
0
0
1
1
0
2
2
0
2
1
1
1
0
0
1
1
0
0
0
2
2
0
1
0
0
1
0
1
1
0
2
1
0
0
1
1
0
1
0
1
0
1
0
0
1
1
2
1
0
0
0
0
2
0
0
2
0
0
0
2
2
1
0
0
1
0
1
0
0
2
0
0
0
0
1
1
4
0
0
0
1
2
3
2
0
1
0
0
1
0
0
1
1
0
1
1
1
1
1
0
1
0
4
0
0
1
0
0
1
0
1
0
0
1
2
0
2
1
2
1
2
2
0
2
0
1
2
0
0
0
1
1
1
2
0
0
0
0
1
1
1
0
2
0
1
1
2
0
0
1
0
1
1
2
0
0
0
1
0
1
1
2
2
0
1
2
1
0
1
2
0
0
0
0
1
2
0
0
0
1
0
0
1
0
1
2
0
1
2
1
0
1
2
0
2
0
0
0
2
1
0
2
1
0
0
2
0
0
2
1
0
0
0
1
0
0
0
0
1
3
0
1
0
1
2
2
0
1
2
2
2
0
1
1
2
0
2
0
0
2
1
1
1
1
2
0
2
2
1
2
1
3
1
0
0
0
2
0
1
1
0
0
1
1
0
1
0
0
2
1
0
1
0
1
0
0
1
2
1
1
1
2
0
0
2
0
1
1
1
0
0
1
0
0
0
2
0
1
1
0
2
2
0
0
1
0
2
1
0
0
2
2
0
0
1
1
0
0
1
1
1
1
0
0
0
2
0
0
1
0
1
0
1
2
2
0
0
0
1
0
1
0
0
0
2
2
0
0
0
3
0
2
2
0
1
0
2
1
1
1
0
1
4
1
1
0
0
0
2
0
0
1
2
0
5
2
2
2
0
1
1
0
1
0
1
1
1
1
1
0
2
1
2
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
2
0
3
1
2
2
1
2
0
0
0
1
1
3
0
1
2
0
0
0
1
2
1
1
0
1
2
1
0
2
2
0
0
1
0
2
0
0
2
1
1
0
0
1
0
1
2
0
0
1
1
0
2
0
0
1
2
1
0
0
1
0
1
2
0
2
2
2
0
0
0
0
1
2
1
0
1
0
1
1
0
1
0
1
1
2
2
0
1
0
1
1
0
1
1
1
0
2
0
2
0
0
0
1
1
0
2
0
0
2
0
0
0
2
0
2
2
0
2
1
1
0
0
0
1
0
2
2
1
0
0
2
2
3
0
1
2
1
1
0
2
0
0
0
0
0
0
2
2
1
1
0
1
1
0
1
0
2
2
2
1
0
0
0
0
1
0
0
2
0
0
1
2
1
0
0
1
2
2
0
0
2
1
0
2
0
0
0
0
0
2
2
1
1
0
0
0
0
0
1
0
0
1
2
0
0
1
0
0
0
2
2
0
0
2
3
2
3
0
0
0
0
0
0
1
0
0
0
1
0
2
2
1
0
0
0
0
1
1
1
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
2
1
2
1
0
2
0
1
0
1
0
1
1
2
2
1
1
0
1
0
1
0
3
2
0
0
0
2
0
1
0
0
2
1
1
0
0
1
0
0
0
0
1
0
0
1
0
2
0
2
0
0
0
2
2
0
0
0
1
1
1
0
0
1
2
0
0
0
0
0
1
0
1
0
1
0
1
2
2
0
0
1
1
1
0
0
1
0
0
1
2
0
0
1
0
1
0
0
2
2
0
0
1
0
1
0
0
1
6
1
1
1
2
1
0
1
0
0
2
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
1
0
2
1
1
0
1
0
3
0
1
0
1
0
1
0
2
0
0
0
0
1
0
2
0
0
0
1
0
0
1
4
0
1
2
1
2
0
0
1
2
0
0
1
1
1
0
3
0
1
0
0
1
1
1
0
2
0
0
0
0
2
0
1
1
0
2
0
0
0
0
1
0
1
0
1
0
2
0
1
0
0
0
1
2
1
1
0
3
1
3
2
2
0
0
1
1
4
3
1
0
0
0
0
1
2
0
2
3
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
1
1
0
0
1
0
0
0
2
0
2
0
2
0
1
1
1
1
1
0
2
1
2
1
1
1
0
0
0
1
1
3
2
0
0
0
0
1
0
1
0
1
1
0
1
2
0
1
0
0
1
0
0
0
0
0
2
3
1
1
0
0
0
1
2
1
0
2
1
0
1
0
0
1
1
0
1
2
1
0
1
1
1
0
0
0
0
0
0
0
0
1
2
2
1
1
1
0
1
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
1
2
0
2
2
0
1
2
0
2
1
0
5
1
1
0
1
1
0
2
1
0
0
2
1
0
1
1
0
0
0
2
4
1
0
0
1
1
0
0
2
0
2
0
0
1
0
2
0
1
2
0
1
0
1
0
1
0
0
0
0
1
1
2
0
1
0
0
0
0
0
1
0
1
0
2
3
2
2
0
0
0
1
0
0
0
0
1
1
1
0
2
0
1
0
2
1
1
0
0
1
0
0
1
0
1
0
1
1
0
1
0
1
1
0
1
0
2
2
0
0
2
0
1
0
0
0
2
0
2
0
0
0
2
0
0
1
0
2
1
2
0
0
1
0
0
0
2
0
0
0
1
0
1
2
1
0
1
0
2
2
2
1
0
0
0
0
1
1
1
2
2
1
0
0
1
2
2
0
1
0
1
0
0
2
1
1
0
1
1
0
1
0
1
0
0
0
0
0
2
1
0
0
2
2
2
0
2
0
1
0
0
2
1
0
2
0
0
0
0
0
2
1
1
2
2
0
1
0
0
0
1
0
1
1
0
0
3
1
1
1
2
2
1
1
0
2
0
0
0
0
1
0
0
1
2
1
2
1
1
1
1
0
0
0
1
1
0
1
1
0
0
1
0
0
1
0
0
2
0
0
1
2
2
1
0
0
1
1
0
2
0
2
2
1
2
4
0
2
0
0
0
2
0
0
0
0
0
2
0
1
1
1
0
0
1
0
0
1
1
1
0
0
0
2
1
0
1
0
2
0
0
1
1
0
0
0
1
1
1
0
1
0
2
0
2
0
2
2
1
1
0
0
0
1
2
0
1
0
1
0
1
2
0
0
1
1
1
1
0
1
2
1
2
0
0
0
0
1
2
1
1
2
1
0
2
0
2
2
0
0
0
2
1
1
1
1
2
0
1
1
1
0
0
0
0
0
1
0
2
0
1
1
2
0
2
1
0
1
0
1
0
1
0
0
1
2
0
0
1
2
1
1
2
2
0
0
1
5
0
0
0
1
0
0
2
0
1
0
1
0
2
0
1
2
1
0
1
0
2
0
2
2
0
0
0
1
2
1
0
1
2
0
0
0
0
0
2
1
0
2
2
1
0
2
0
0
0
1
0
1
2
0
1
0
0
0
0
2
1
0
2
2
0
0
1
1
0
0
2
1
1
0
2
0
0
1
0
0
0
0
0
2
2
0
2
0
0
1
2
0
1
0
0
0
1
0
1
0
1
0
0
2
1
1
0
0
3
0
0
2
0
3
0
0
2
0
1
0
2
0
0
0
2
2
0
2
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
2
2
0
0
1
0
1
5
2
4
3
1
0
2
2
0
0
0
1
1
1
0
2
0
0
1
2
1
1
2
0
2
1
0
1
0
3
0
1
0
0
1
1
0
0
1
2
0
0
0
0
2
1
2
2
1
1
2
3
2
0
0
2
2
1
0
2
0
0
1
0
2
2
0
1
0
0
0
1
0
1
2
0
0
0
0
0
1
2
1
0
1
0
1
0
1
1
0
2
1
0
3
0
0
0
3
0
1
0
1
1
2
0
0
0
0
2
0
1
0
2
0
0
0
2
0
1
1
2
0
2
0
1
1
0
1
1
2
0
0
0
1
0
2
2
0
3
2
0
3
2
1
1
1
0
0
0
2
2
0
1
2
0
1
1
2
2
1
1
1
1
1
1
2
1
1
1
0
0
1
0
0
0
0
1
1
2
0
1
0
0
1
2
2
0
0
1
1
1
0
0
4
0
0
1
1
0
0
0
1
0
1
2
0
1
0
1
2
1
2
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
1
1
0
1
1
2
0
0
2
0
1
1
2
2
0
0
1
1
0
1
1
2
2
0
0
0
0
0
2
0
0
1
0
0
3
2
1
2
1
0
0
0
2
0
2
0
0
0
0
1
1
0
1
0
2
0
1
0
2
0
0
0
0
0
0
1
0
1
1
0
0
1
0
2
1
0
3
1
2
0
2
1
1
0
0
0
2
2
0
3
0
0
2
0
1
0
1
2
0
0
1
2
1
2
0
1
1
0
0
1
0
3
1
1
0
0
0
0
0
2
0
0
2
2
0
2
0
1
1
0
0
2
0
2
1
2
0
1
0
0
0
1
0
1
1
0
0
0
2
1
0
0
2
1
1
1
1
0
1
0
1
0
0
1
3
0
0
1
2
1
0
0
1
1
0
0
3
1
1
0
0
2
2
0
0
1
0
0
0
2
0
0
0
0
0
1
2
2
1
0
0
1
0
0
1
2
0
0
0
1
1
2
0
2
1
1
0
1
1
2
0
0
0
1
0
1
1
0
0
2
0
0
1
0
1
2
2
1
1
2
0
0
0
0
0
1
3
2
0
1
2
1
0
0
0
1
1
1
0
0
1
0
1
1
0
2
2
0
0
1
0
0
0
2
1
1
1
1
1
5
0
0
1
0
0
0
0
0
2
1
0
0
1
2
0
1
2
0
2
0
2
0
0
0
0
0
0
4
0
0
2
0
1
3
2
2
1
1
0
0
0
0
1
1
0
2
0
1
1
2
2
0
0
0
3
0
2
0
1
2
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
1
2
0
0
0
0
0
1
0
0
1
0
0
1
1
1
1
0
0
0
1
0
0
0
1
1
0
1
1
1
1
1
0
1
1
1
0
2
1
0
2
1
1
0
0
0
0
0
1
0
2
0
1
2
0
0
2
0
0
2
0
2
0
0
1
1
0
0
0
0
0
0
0
0
2
1
0
2
1
0
2
0
0
2
1
0
2
1
0
1
1
0
0
0
1
0
1
0
0
0
0
2
2
2
0
2
0
2
0
1
1
0
0
3
0
1
1
0
2
1
1
0
2
0
1
0
0
1
1
1
2
1
1
1
2
1
0
0
2
2
0
2
0
6
2
0
1
2
0
2
0
0
2
0
1
1
1
2
0
0
2
1
1
0
1
0
0
0
1
1
0
2
1
1
2
0
1
2
2
0
1
1
0
3
0
1
1
2
0
2
1
0
2
0
0
1
0
1
0
1
0
1
2
0
0
2
0
2
0
1
0
0
2
1
2
0
0
1
2
0
1
1
0
0
3
2
0
2
2
0
0
0
0
1
1
2
0
0
0
0
1
1
1
0
1
0
2
0
1
0
1
2
1
2
2
0
0
1
0
0
0
1
1
2
0
0
0
1
0
0
2
1
1
0
0
0
0
2
0
1
1
0
0
0
1
0
0
0
0
2
0
2
1
1
1
1
1
0
0
1
1
0
1
2
1
0
1
0
1
0
1
0
1
0
0
0
2
2
1
0
1
0
0
1
1
0
1
0
0
0
1
2
2
1
0
0
1
0
2
0
2
2
0
0
2
1
3
0
1
2
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
1
0
1
0
1
3
2
2
1
0
1
0
0
1
0
2
0
1
0
2
2
0
0
0
1
2
2
1
0
0
0
1
0
1
0
2
1
0
1
0
1
0
0
1
0
1
0
0
0
1
0
1
1
1
1
0
0
0
0
2
0
2
0
2
0
2
0
1
2
0
2
0
1
0
0
1
1
0
0
1
0
1
1
2
1
2
2
1
2
0
2
0
2
1
0
0
0
1
0
2
0
2
0
1
0
1
0
0
0
0
3
1
0
2
0
0
0
2
0
0
0
1
2
0
1
3
2
0
0
1
0
1
0
0
0
0
2
2
1
0
1
0
0
1
1
2
0
3
1
2
0
1
0
1
1
1
2
1
0
0
1
1
1
0
0
2
0
0
1
0
0
0
0
2
2
1
0
1
2
0
2
1
0
0
1
2
1
0
2
2
0
0
1
1
2
1
0
1
0
2
0
0
0
0
1
0
0
0
0
0
1
2
0
0
1
1
2
3
1
0
0
1
0
2
0
1
2
2
1
1
0
2
1
1
1
0
2
0
0
3
1
1
0
0
0
0
3
0
0
0
2
2
0
1
1
0
0
0
0
0
1
2
0
0
0
0
1
0
1
2
0
1
1
1
1
1
0
1
0
0
1
0
0
2
0
2
0
0
2
1
0
0
0
1
1
0
0
0
0
2
1
1
2
0
0
0
0
1
0
2
1
0
2
1
0
0
0
0
2
0
1
0
2
0
1
1
2
3
0
0
1
1
0
2
0
0
1
1
0
0
1
1
0
2
1
2
1
2
0
0
2
1
0
0
1
0
1
1
2
2
2
1
0
0
0
1
6
0
3
2
0
0
2
1
1
0
0
0
0
1
0
2
0
1
2
0
2
2
0
0
0
1
0
2
1
1
1
2
1
2
0
3
4
3
0
0
1
0
0
1
0
0
0
1
0
0
1
1
1
0
0
1
1
3
2
0
2
1
0
1
3
0
0
1
4
2
0
0
0
1
0
0
2
0
0
0
2
0
1
0
2
0
0
2
0
2
0
3
1
2
1
1
0
0
1
1
0
0
0
1
0
0
2
0
2
0
0
1
0
1
2
0
2
1
0
0
0
0
0
1
1
1
3
2
0
0
1
1
2
0
1
0
1
2
1
2
2
0
0
1
2
0
0
2
1
2
1
0
0
0
0
0
1
2
2
2
0
0
1
1
2
1
1
0
1
0
1
1
2
2
0
0
0
0
1
0
0
0
0
2
0
0
1
1
1
2
0
0
1
1
1
2
0
1
0
0
0
0
2
1
2
0
1
1
1
0
1
0
1
0
0
0
1
1
0
0
2
1
0
1
2
2
0
0
0
1
2
0
0
0
0
1
0
1
1
1
0
1
0
0
0
2
1
1
1
1
2
2
1
2
1
1
1
0
0
0
0
0
0
1
1
2
1
1
0
1
0
0
0
1
0
0
1
1
0
2
0
0
0
1
1
1
1
1
0
0
1
2
0
0
1
0
0
1
0
0
1
0
0
2
0
2
1
0
0
2
0
1
0
0
1
1
0
0
1
2
1
1
1
1
0
1
2
1
0
0
0
1
0
1
2
0
0
1
0
1
1
0
1
0
1
0
1
0
0
0
0
1
2
0
0
0
0
0
0
1
0
1
2
1
2
0
0
1
1
0
2
0
0
2
0
1
2
0
1
1
0
0
0
0
1
1
2
0
1
2
0
2
0
1
1
1
0
2
1
2
0
0
2
7
1
2
1
0
1
0
0
2
1
0
0
0
1
0
0
2
1
1
2
0
2
3
0
0
2
2
0
0
1
0
2
1
0
1
0
1
1
2
1
1
0
0
0
1
1
2
2
0
0
0
0
2
0
1
1
2
1
2
2
0
0
0
0
0
0
2
1
1
0
2
0
1
0
0
0
2
1
0
0
0
1
4
0
2
1
1
2
0
1
0
1
1
1
2
0
0
1
2
1
0
0
0
0
2
0
1
0
2
0
1
0
2
2
0
2
0
0
0
1
0
2
1
2
1
1
0
0
0
1
2
2
0
3
0
0
2
2
1
0
0
0
2
1
2
0
0
0
2
2
0
1
1
2
0
0
1
0
2
0
1
0
0
0
1
0
2
0
1
0
1
0
0
0
1
1
0
1
1
0
0
0
1
0
0
1
0
0
0
2
2
1
0
2
0
0
1
1
1
0
0
2
0
0
0
0
0
1
2
1
0
0
1
1
0
2
0
1
1
1
0
1
0
1
3
0
2
2
0
1
2
1
0
0
0
0
1
1
1
0
2
0
0
1
0
1
1
2
0
0
1
0
1
1
0
2
1
0
0
0
1
0
0
2
2
0
2
0
0
0
1
0
0
2
0
2
1
2
2
0
0
1
1
1
0
0
1
1
1
0
1
1
1
0
2
0
1
0
1
2
0
0
1
1
0
1
1
0
2
2
1
2
0
1
0
2
2
2
0
0
0
2
3
1
0
1
0
1
1
0
3
1
1
1
1
0
0
1
2
1
1
2
1
2
1
0
2
0
2
0
0
0
0
0
0
1
0
2
2
0
1
1
0
0
1
2
0
2
0
1
0
0
0
1
1
1
2
0
3
2
1
1
0
0
2
0
0
0
1
0
1
2
2
0
2
0
0
0
1
1
0
0
2
0
1
0
1
0
0
0
2
1
2
1
1
2
0
0
1
1
1
0
0
2
0
2
0
0
0
1
0
1
0
1
2
0
2
0
0
2
0
0
1
0
2
1
2
1
0
0
2
0
1
0
1
0
1
0
1
3
0
0
2
0
0
0
0
0
0
1
1
0
1
1
0
2
1
2
1
1
0
0
0
0
0
2
1
0
2
0
0
1
1
2
0
1
1
0
1
1
0
1
0
0
1
1
1
2
0
1
0
1
1
1
0
0
1
2
1
0
2
2
0
0
2
0
1
2
2
2
2
2
1
1
0
3
2
0
0
2
1
0
1
0
0
1
0
2
0
2
0
1
0
1
1
1
0
1
0
2
1
2
1
0
0
1
2
0
2
0
1
0
0
2
0
0
0
0
0
1
0
1
1
1
0
0
0
0
2
1
0
1
0
1
2
0
2
1
2
0
2
1
1
2
1
0
1
1
2
2
0
2
1
1
1
0
0
2
2
0
0
1
2
0
0
0
2
1
0
1
2
0
1
0
2
0
0
0
0
1
1
1
2
1
2
2
0
2
0
1
0
0
3
0
1
1
1
0
0
0
2
0
1
0
0
1
1
0
0
3
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
2
1
0
2
0
1
2
0
2
0
0
0
2
1
0
1
0
2
0
2
0
0
1
0
1
1
3
0
0
0
0
0
0
1
1
1
0
2
1
2
0
1
0
0
1
0
1
0
2
1
0
1
1
1
0
0
1
1
1
0
1
1
0
1
1
2
0
0
0
2
0
0
2
2
2
1
2
2
4
2
0
2
0
2
0
2
1
2
0
0
0
0
0
1
0
0
1
1
0
0
2
1
0
2
2
1
0
1
1
1
0
1
0
2
0
1
1
1
0
0
0
3
0
0
1
1
0
0
0
1
0
1
1
1
0
2
0
0
0
1
2
0
0
0
1
0
1
1
1
0
0
0
1
1
1
1
1
0
2
1
0
0
1
0
0
1
0
1
0
1
0
2
0
1
1
0
0
0
2
0
0
0
0
0
2
0
1
2
0
0
0
1
1
0
1
0
1
0
0
0
1
2
0
0
2
1
0
2
0
0
0
1
2
1
4
1
0
1
2
1
1
2
0
1
2
0
1
0
0
1
0
1
1
0
0
0
2
1
1
0
2
1
0
1
1
1
1
0
0
3
0
0
0
0
2
2
1
1
0
0
0
2
0
1
3
0
1
1
0
1
4
1
1
0
0
0
1
0
0
0
0
0
1
1
1
1
1
0
1
2
0
1
0
0
0
0
0
0
0
1
1
0
2
2
0
0
0
2
1
1
1
0
0
2
0
0
0
2
2
2
0
0
2
0
2
1
1
1
1
2
1
0
1
1
2
0
1
0
0
2
0
1
0
0
0
0
3
0
0
0
0
0
2
2
0
1
1
1
1
0
0
2
2
0
0
0
0
0
1
0
2
0
1
1
1
1
0
0
0
0
2
0
2
2
0
1
0
1
0
1
0
1
0
0
1
0
2
0
0
0
1
1
2
0
0
2
1
2
1
1
0
2
1
0
2
0
0
0
0
1
0
0
0
2
0
1
0
2
0
0
0
2
1
1
0
1
0
1
2
1
0
0
1
1
1
2
1
0
2
0
0
0
0
0
1
1
1
1
0
0
0
2
1
2
0
0
2
1
0
0
1
1
1
0
2
2
2
2
1
1
0
2
1
0
0
0
4
0
0
3
0
2
2
1
0
0
0
1
0
0
1
0
1
1
0
2
1
1
0
0
0
1
0
0
0
1
1
2
0
0
0
1
2
1
0
1
2
0
0
0
2
0
1
0
1
1
1
1
0
2
1
2
0
1
1
0
2
1
1
0
0
0
1
1
1
1
2
0
0
1
0
1
1
2
1
0
1
0
2
1
1
1
1
0
1
1
3
1
0
2
0
1
2
1
0
1
0
3
2
0
0
2
0
0
0
0
0
0
2
1
1
0
0
2
2
2
0
0
0
0
0
0
0
1
0
0
1
2
0
1
3
0
2
0
0
1
1
2
2
0
2
0
1
1
0
0
0
0
2
0
0
1
0
2
0
1
0
1
2
1
0
1
2
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
2
1
0
2
1
0
1
1
0
2
0
0
1
3
1
0
1
1
0
0
0
0
0
1
0
2
0
0
1
1
0
1
2
0
1
0
0
0
2
1
0
2
0
1
0
2
0
4
1
1
0
1
1
1
1
0
0
1
0
0
1
2
2
0
0
1
0
0
2
0
1
0
2
2
1
1
0
0
2
1
0
2
0
1
2
0
2
1
0
0
1
0
0
1
0
0
1
2
0
2
1
1
1
0
1
2
0
2
1
0
2
2
2
0
0
1
0
0
1
1
1
0
1
0
1
0
0
2
0
1
0
0
0
2
0
1
0
2
2
2
1
0
2
0
0
2
0
1
0
0
1
2
1
2
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
2
2
4
1
1
1
1
1
0
1
0
0
2
1
2
0
0
1
1
0
1
0
0
0
2
0
0
1
2
4
1
2
1
1
0
2
0
0
0
0
2
0
2
3
2
1
2
0
1
2
0
1
2
0
2
2
0
0
0
0
2
1
0
2
1
0
2
2
0
1
3
2
1
1
1
1
0
1
0
1
2
0
0
2
0
1
0
0
1
0
2
1
1
1
0
2
1
1
2
1
0
1
3
1
1
0
0
1
1
1
2
2
0
0
1
2
0
1
0
1
1
0
0
1
2
0
0
1
1
1
0
1
0
0
0
1
0
1
0
1
1
2
0
1
1
2
1
0
0
2
2
2
0
1
0
1
1
0
1
0
1
0
2
0
0
0
2
3
2
1
1
1
2
1
1
1
1
1
0
2
1
0
3
2
0
3
1
0
1
2
2
0
0
1
0
2
2
0
1
1
1
2
0
1
2
0
1
1
0
1
1
1
2
0
0
0
0
0
2
3
2
0
0
2
2
2
0
0
1
2
2
0
1
0
1
0
1
1
0
0
0
2
1
0
0
1
2
0
2
1
1
2
1
3
0
1
1
0
0
0
0
5
1
0
0
0
0
0
1
0
0
0
1
0
2
0
2
0
0
0
0
1
1
0
1
1
0
1
1
0
1
1
0
0
1
1
1
0
1
1
1
2
1
1
0
2
1
2
1
0
1
1
2
0
1
0
1
1
2
0
1
0
1
0
1
2
1
1
0
1
1
0
2
0
2
0
2
0
1
0
2
0
1
0
0
3
0
1
2
0
6
4
2
2
0
0
0
1
1
0
1
0
1
0
0
2
0
1
1
0
3
1
2
0
1
1
0
2
1
0
0
0
1
1
0
1
1
2
0
2
0
1
1
1
1
1
1
0
1
2
0
1
0
0
0
1
1
2
1
2
2
1
0
0
2
1
0
1
1
0
0
0
1
3
0
1
3
0
1
0
1
1
2
2
0
1
0
2
2
1
2
2
1
2
0
2
0
2
2
0
0
0
1
0
1
2
0
0
1
0
0
2
2
1
0
0
0
1
2
1
1
0
2
0
0
0
0
2
0
1
0
3
0
2
0
0
1
0
0
0
0
2
1
1
0
2
0
0
0
1
1
0
2
1
0
2
0
1
1
2
1
0
2
0
0
1
0
1
0
0
0
1
4
1
1
1
0
0
2
0
0
0
0
1
3
0
1
0
0
1
0
1
0
1
2
0
1
2
2
1
1
1
1
1
2
2
0
0
0
0
2
1
0
0
2
1
0
1
1
0
1
0
1
0
0
3
1
0
2
1
1
0
0
0
2
0
1
1
0
0
1
1
0
1
1
1
0
2
0
1
2
1
0
1
1
2
0
1
0
0
2
0
0
2
1
0
1
1
0
1
2
1
1
0
1
1
1
0
1
0
0
1
1
0
1
1
0
2
0
1
2
0
2
1
1
0
1
0
1
2
0
1
2
0
2
2
2
1
1
0
1
1
0
1
1
2
0
1
0
1
1
0
1
0
0
2
0
0
1
0
0
0
0
2
0
0
1
0
1
0
0
1
0
0
1
1
0
2
0
0
0
0
0
1
2
2
1
1
0
1
0
1
1
0
2
1
1
0
2
0
1
0
1
0
2
0
2
0
0
0
0
1
0
0
0
1
1
0
3
0
0
1
0
2
0
1
0
1
1
1
1
1
2
0
0
0
0
0
0
0
1
1
1
0
2
0
0
0
1
2
0
1
0
0
0
0
2
2
1
0
0
2
1
0
0
0
0
1
1
3
0
1
0
1
1
0
0
1
0
0
2
1
1
1
1
1
0
0
1
1
0
1
0
0
2
0
2
1
0
0
2
2
1
2
0
0
1
2
1
2
0
0
0
0
0
1
1
0
0
0
1
2
2
3
1
2
1
0
1
1
1
2
0
0
0
2
0
0
0
0
2
1
1
2
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
1
1
1
2
1
0
1
0
0
1
0
0
0
1
0
0
0
1
0
1
1
0
0
1
0
1
0
0
0
0
1
0
0
1
0
1
1
0
2
0
0
2
0
0
2
1
1
0
0
0
1
0
1
2
1
0
2
0
0
0
0
0
1
1
1
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
1
2
1
3
1
0
0
1
1
0
2
0
0
0
1
0
0
1
0
1
1
1
0
0
0
1
1
2
0
2
1
1
2
0
2
1
1
2
0
0
2
2
1
0
0
0
0
1
0
1
1
2
0
0
0
2
0
2
1
1
4
2
2
0
1
2
0
2
3
1
0
0
0
0
1
3
2
0
0
2
0
1
1
1
0
0
1
2
1
1
2
3
0
0
0
3
2
0
2
0
0
0
1
0
1
0
0
2
0
3
0
0
0
2
2
2
0
1
1
2
2
2
2
0
0
2
1
0
0
2
1
0
0
2
1
1
0
0
2
2
0
1
0
2
1
0
2
0
0
0
2
0
0
1
2
0
0
2
0
2
0
0
0
1
1
2
0
0
1
1
0
1
1
0
0
0
0
5
1
0
2
2
0
0
2
2
1
1
1
2
1
0
0
1
2
3
0
1
1
1
1
1
2
2
3
2
1
0
0
0
1
0
0
0
2
0
2
2
1
2
0
0
1
1
2
0
0
2
0
0
1
2
0
0
0
0
0
2
1
1
2
0
3
0
1
2
0
2
1
1
0
0
0
2
1
1
0
0
1
2
2
1
2
2
0
1
0
2
2
1
0
1
0
2
1
0
0
2
1
1
1
0
2
1
0
1
2
0
2
0
1
0
0
0
0
1
1
2
1
1
0
0
0
1
0
0
0
2
1
1
0
0
0
2
2
1
0
0
0
1
0
0
1
1
0
0
1
2
1
1
0
0
1
1
2
0
0
2
0
2
0
3
0
0
2
1
2
1
2
1
0
0
0
2
0
0
2
0
2
2
0
1
1
1
0
0
0
2
0
0
0
1
1
0
1
1
0
2
0
2
0
1
1
2
3
0
0
2
0
0
2
1
0
1
1
2
0
0
2
2
1
0
3
0
2
1
0
1
0
0
0
2
0
2
2
0
2
1
1
0
0
0
2
0
1
1
1
1
0
0
0
2
0
1
1
2
2
0
3
2
0
1
0
1
1
0
2
0
0
1
0
1
2
1
0
1
0
0
1
0
2
0
1
1
0
0
0
0
2
2
0
1
2
1
2
2
1
0
0
1
3
0
0
2
2
0
3
0
1
0
2
2
1
1
2
0
0
1
0
0
0
1
0
2
0
0
1
0
1
1
0
0
0
1
1
0
2
0
0
0
2
1
1
0
2
0
0
2
0
2
1
2
0
2
1
2
0
0
2
2
0
0
0
1
1
2
1
0
2
2
0
2
3
0
1
1
2
1
2
1
1
2
0
1
0
2
0
0
4
0
1
2
1
0
0
1
1
3
2
1
0
0
2
1
0
0
0
0
1
1
2
1
0
1
2
0
0
0
1
1
1
1
1
2
0
1
0
1
0
2
0
0
1
1
0
0
1
0
2
2
3
0
0
0
0
0
1
1
1
0
0
2
1
0
1
0
1
1
0
0
1
2
2
0
2
1
1
1
1
0
0
0
2
0
0
0
1
0
0
0
0
2
0
2
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
2
1
0
1
1
1
0
3
0
0
0
0
1
0
0
0
1
2
0
1
2
0
0
0
1
0
2
0
1
1
0
1
1
0
0
2
1
1
0
0
2
1
0
1
1
0
0
0
1
0
1
1
0
0
0
0
2
2
0
2
1
1
0
1
2
1
2
0
1
0
0
0
0
2
0
1
0
0
2
0
1
1
0
0
0
1
1
1
0
0
0
0
1
2
3
0
1
2
0
0
0
0
1
0
1
0
0
0
2
1
1
0
0
0
2
0
1
0
0
1
1
0
0
0
1
0
1
0
0
0
1
2
1
1
2
1
0
0
1
0
0
0
0
0
1
2
2
0
0
2
1
0
0
2
0
0
0
0
0
1
1
0
0
1
0
1
2
1
0
0
1
0
0
0
2
0
0
1
1
1
1
1
0
2
1
0
4
1
0
1
2
1
1
1
1
0
0
1
2
2
1
1
1
0
0
0
1
2
1
0
0
0
2
0
1
0
1
0
0
1
1
0
0
0
0
1
2
2
1
0
2
1
1
0
0
1
1
0
0
3
1
0
0
2
0
3
0
2
0
0
0
0
1
2
1
0
0
0
0
1
0
0
1
1
0
0
0
0
1
1
1
1
1
1
2
0
2
0
0
3
0
0
0
2
1
0
2
2
2
0
2
1
1
1
1
2
1
1
2
0
1
0
0
0
0
0
1
1
0
5
1
1
0
0
0
0
1
0
2
2
0
2
0
2
2
1
2
0
0
0
1
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
2
0
1
1
0
1
1
1
1
0
0
1
1
1
1
0
2
1
0
1
0
0
1
2
1
2
0
0
1
2
0
0
1
0
2
0
2
0
0
0
0
2
0
0
1
1
0
0
2
1
1
0
1
2
1
5
1
0
0
0
1
0
2
1
0
0
2
2
2
0
1
2
0
1
0
0
1
0
0
1
3
2
1
0
1
0
2
0
0
0
0
0
1
0
2
1
0
2
0
2
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
2
1
0
2
1
0
0
1
1
0
0
0
4
2
2
1
0
0
1
2
0
1
0
0
2
0
0
2
1
1
1
1
0
0
0
1
1
1
0
2
0
0
0
2
2
2
0
1
1
1
0
0
1
2
0
1
1
0
1
1
0
0
1
1
1
0
1
0
1
0
1
0
2
2
0
2
0
2
0
0
2
0
0
0
1
1
0
2
1
1
1
0
1
1
0
0
1
0
0
0
0
1
2
0
1
1
0
0
0
2
0
0
0
0
2
0
1
2
2
0
1
0
0
0
0
1
1
2
2
0
0
0
1
0
0
2
2
1
0
2
2
1
2
2
0
0
1
1
2
0
2
1
1
2
0
2
0
1
0
3
0
0
1
1
2
0
0
2
4
1
1
1
0
0
0
1
2
2
0
0
0
2
0
0
0
0
2
1
0
0
2
0
0
1
0
0
0
0
1
2
1
1
0
1
0
1
0
2
1
1
2
0
2
2
1
1
1
0
1
1
1
1
1
1
1
0
1
2
1
2
0
1
0
0
0
0
1
0
1
0
0
2
1
2
0
0
1
0
0
0
0
2
2
3
0
0
0
0
2
0
0
2
2
1
0
0
0
1
0
0
0
1
2
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
1
1
0
1
0
0
1
1
2
0
2
0
1
0
0
0
0
0
2
0
0
2
1
0
0
1
2
0
0
0
1
1
1
0
1
2
2
2
1
1
0
1
2
1
2
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
1
0
1
1
2
0
0
0
1
0
0
1
0
0
1
1
0
2
1
0
0
1
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
1
1
1
1
2
1
0
1
0
2
0
0
0
1
0
1
0
0
1
0
1
0
0
1
0
1
0
1
0
1
0
0
0
2
1
0
1
2
4
0
2
1
2
1
1
0
2
0
1
0
0
1
0
1
2
0
1
2
1
1
2
1
0
0
0
0
0
1
2
0
0
1
3
0
1
1
0
1
0
0
0
2
1
0
2
0
1
1
0
0
0
1
0
1
1
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
2
1
0
2
0
0
1
1
1
1
0
1
0
0
0
0
0
0
1
3
0
2
0
2
0
0
0
2
0
0
1
2
1
1
2
1
2
0
2
0
1
0
1
2
1
0
0
0
2
0
0
1
1
1
0
2
1
0
1
1
2
0
1
1
2
1
2
0
3
2
0
1
1
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
1
0
1
0
1
2
1
2
1
0
0
1
0
1
0
1
1
0
0
1
1
2
1
1
0
1
2
1
0
1
0
2
11
2
1
1
2
2
1
1
1
2
1
1
0
0
2
2
0
1
0
1
0
0
1
1
0
1
0
0
0
0
0
0
1
0
1
0
2
0
0
0
1
1
1
1
1
1
1
0
0
0
2
0
1
0
2
1
2
0
0
0
1
2
3
0
1
0
0
0
0
2
0
2
2
2
2
1
0
1
1
1
2
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
1
2
2
0
2
1
0
0
1
2
1
2
0
1
0
0
2
0
1
2
0
2
0
0
0
0
1
1
1
0
2
1
2
0
0
0
3
1
1
0
0
0
0
0
2
0
1
2
1
0
2
0
0
1
2
2
0
1
2
1
0
1
0
0
0
2
1
1
2
0
0
0
0
0
0
0
2
0
2
0
0
1
0
1
1
1
1
1
0
3
0
0
1
2
0
4
0
0
0
0
0
0
0
2
1
0
1
1
1
2
0
2
0
0
2
1
1
3
0
1
0
1
0
1
1
1
1
0
1
0
1
3
0
1
0
0
2
0
2
0
1
2
0
1
1
0
0
1
0
0
2
2
1
1
1
1
0
1
2
1
1
3
0
0
1
1
1
0
0
1
0
0
1
0
1
1
0
0
2
0
0
1
2
2
0
0
1
0
1
1
0
0
0
1
0
1
0
1
0
0
1
1
0
1
0
2
0
2
2
1
1
1
0
2
2
0
1
1
0
0
1
2
0
1
0
1
2
0
0
0
2
0
1
2
2
2
0
1
0
2
0
0
1
1
1
1
3
0
1
1
0
0
3
0
2
0
1
2
0
1
1
1
0
0
2
0
1
0
2
1
0
2
1
0
2
2
1
1
1
1
0
1
1
1
1
1
0
2
0
1
0
0
0
0
2
1
1
0
0
1
0
1
2
0
2
0
4
2
0
0
0
0
2
0
1
0
0
0
1
1
0
2
2
1
0
0
1
0
0
0
2
1
0
0
2
3
0
1
2
0
1
1
0
1
1
1
0
0
0
0
2
1
0
0
1
1
1
0
1
2
0
0
1
1
0
0
0
0
0
1
1
1
1
2
2
2
2
0
0
0
0
0
0
1
1
0
0
3
2
0
3
1
2
1
1
0
1
1
2
0
1
0
1
1
0
0
0
1
3
1
1
1
1
1
2
0
0
0
1
1
1
1
1
0
0
0
0
2
0
1
0
1
2
0
0
2
1
0
0
0
1
2
1
1
0
0
0
2
2
1
0
0
1
2
1
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
2
1
0
2
1
0
2
1
2
0
1
1
1
2
2
0
2
1
2
0
0
1
1
0
3
0
0
0
0
1
2
0
2
2
0
0
0
3
0
2
0
0
1
0
0
0
0
2
2
1
0
1
0
0
0
0
0
1
1
1
1
2
1
0
1
0
1
0
0
2
1
1
1
2
0
0
1
0
1
2
0
0
1
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
3
3
0
0
0
0
1
0
0
1
0
0
0
0
2
2
2
2
2
0
0
1
0
0
1
0
0
0
0
1
2
2
1
1
0
0
0
1
2
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
1
2
0
2
0
1
1
1
2
1
1
2
2
1
2
0
2
0
2
0
2
1
0
2
2
1
2
2
0
0
2
0
2
1
0
0
1
1
0
0
0
1
2
0
1
0
0
0
0
2
1
0
0
0
0
1
2
0
1
2
0
0
0
1
0
2
1
2
2
2
2
0
2
0
0
0
2
1
1
2
0
2
1
1
0
2
1
0
1
0
5
4
2
0
2
2
0
2
0
1
2
0
0
1
0
2
0
1
0
1
2
0
1
1
1
3
1
0
2
1
0
0
2
0
0
0
1
0
1
2
0
1
1
0
0
2
0
2
2
0
1
2
1
0
0
2
2
1
0
0
1
1
0
0
1
0
2
0
1
2
0
0
0
1
1
0
0
1
0
0
2
1
0
0
0
0
1
1
0
0
1
0
2
2
2
1
0
1
0
1
0
0
0
2
0
0
0
0
0
1
2
1
0
0
1
0
0
2
1
0
1
2
2
0
0
1
0
0
0
0
0
0
0
1
2
1
1
2
1
2
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
1
0
2
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
2
2
0
1
0
0
2
1
0
1
1
0
1
2
0
0
0
1
2
2
3
0
1
0
1
0
2
2
1
1
1
0
2
0
7
0
1
2
0
1
0
1
1
2
0
1
2
0
0
1
2
0
2
0
0
1
2
0
1
1
0
0
0
0
0
2
1
0
3
1
1
1
0
0
0
1
2
0
1
2
2
0
3
1
0
0
1
0
0
1
1
3
0
0
0
0
0
0
0
2
2
1
0
1
1
1
1
0
0
1
0
0
1
0
0
0
1
0
2
0
0
2
0
1
0
1
2
0
1
2
0
1
0
2
0
1
2
2
1
1
1
2
2
0
1
1
0
1
0
2
3
0
0
0
1
1
0
2
1
0
1
1
0
0
2
1
1
0
0
0
0
2
1
1
2
1
0
1
2
1
2
1
0
2
0
2
0
1
0
2
2
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
3
1
2
2
0
0
0
1
2
0
0
0
0
2
2
1
0
1
0
1
2
0
1
1
0
0
0
1
0
0
2
0
1
2
1
1
0
2
0
2
2
2
1
0
0
1
0
1
1
0
0
0
3
0
0
0
2
2
1
0
2
0
0
0
0
2
1
1
0
0
1
0
0
0
2
2
2
1
2
1
0
2
1
1
0
1
1
3
1
0
1
0
0
1
1
2
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
2
0
1
0
1
0
0
0
1
1
0
1
0
0
0
0
0
1
1
1
2
2
1
1
0
1
0
1
1
1
0
0
4
2
1
0
2
2
0
1
0
1
2
1
0
0
3
2
0
0
0
0
0
1
0
1
1
2
0
1
1
1
0
2
2
1
3
0
0
0
1
2
0
1
1
0
0
0
0
1
0
0
1
2
1
2
1
0
0
0
1
2
1
0
0
0
0
0
0
0
2
0
1
1
1
1
0
2
1
1
0
0
1
2
0
1
0
1
2
1
1
1
0
0
1
1
0
0
1
1
0
2
2
0
0
1
0
0
0
2
2
0
2
1
0
1
1
2
0
0
0
1
2
1
1
1
2
0
1
1
2
0
1
1
0
1
0
1
0
0
0
0
1
1
1
1
0
1
1
0
1
1
1
2
0
1
2
4
1
0
1
0
0
0
0
2
1
0
1
0
1
0
0
0
2
2
0
0
1
1
2
2
1
2
0
1
2
2
2
0
0
1
0
0
1
1
0
0
1
0
0
3
1
1
0
0
1
2
0
0
1
1
1
2
2
0
1
0
0
0
1
2
0
0
0
0
2
0
0
0
2
1
0
1
0
0
0
0
2
2
0
0
0
2
0
2
2
2
1
0
1
2
1
2
0
0
1
4
1
0
0
0
1
1
0
0
0
1
2
2
2
1
0
0
2
1
1
1
1
1
1
0
0
1
1
3
1
0
2
0
1
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
1
0
1
4
0
0
1
0
1
0
2
2
2
1
1
0
0
1
0
0
2
0
1
0
1
0
1
2
0
0
0
1
0
2
0
1
0
2
1
2
1
1
1
0
0
1
0
2
1
0
2
1
1
0
0
0
1
0
0
0
2
0
0
1
2
1
0
1
0
0
0
1
0
1
0
1
1
1
0
2
0
0
2
0
1
0
2
0
2
1
2
2
1
0
1
1
1
1
0
1
1
0
0
1
0
2
0
1
1
0
0
3
1
1
2
0
0
1
1
0
0
0
1
0
0
1
0
1
0
0
1
1
1
0
0
1
2
0
0
1
2
0
1
1
1
1
2
0
2
0
3
0
2
0
0
0
1
0
1
2
1
0
0
0
1
1
0
2
0
2
1
0
1
1
0
0
1
2
2
0
2
2
0
0
0
3
0
1
0
1
1
0
1
0
2
1
1
0
0
0
1
2
1
0
2
0
1
1
1
0
2
2
0
0
0
0
0
0
0
0
0
1
2
1
0
0
2
0
0
1
0
2
1
2
2
1
2
0
0
0
4
0
1
1
1
2
2
0
1
0
1
2
0
1
2
1
1
0
2
1
1
0
0
0
1
0
0
2
0
1
1
0
1
2
1
0
1
0
0
2
0
1
2
1
2
1
2
2
0
2
1
1
0
1
0
0
0
1
0
3
2
1
0
0
2
1
1
1
1
1
0
2
1
2
1
0
2
1
0
2
0
1
0
0
1
2
1
1
0
0
2
0
1
0
0
1
0
2
0
0
0
1
1
1
1
2
2
1
0
0
0
2
0
0
0
0
1
1
0
2
2
3
0
1
2
0
0
0
2
0
0
1
0
0
2
0
1
0
0
1
0
0
1
1
0
0
0
2
2
0
0
0
1
1
2
0
1
0
1
0
0
0
1
2
2
1
2
2
1
1
0
2
2
0
0
0
2
1
0
0
0
0
3
0
0
1
0
2
0
2
0
1
2
2
1
1
2
0
0
2
0
0
0
2
2
0
2
1
0
2
1
0
1
1
1
0
1
1
2
1
1
0
1
0
0
0
0
3
2
1
0
2
1
1
1
0
1
2
0
1
2
1
2
2
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
1
1
2
0
0
1
2
2
0
0
1
2
0
0
0
0
1
1
1
0
0
2
0
0
2
0
1
2
1
0
0
0
1
1
0
2
0
1
1
0
0
0
1
0
0
1
0
1
1
2
0
0
0
0
1
1
0
2
0
1
1
2
1
0
1
0
1
0
1
0
1
1
0
1
0
1
0
0
0
1
0
1
2
0
0
0
0
1
2
0
0
1
1
1
1
1
1
1
0
1
1
0
0
1
0
1
1
0
2
2
2
1
0
1
1
2
2
0
0
0
0
0
1
1
2
2
0
3
1
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
1
0
1
2
2
1
0
1
0
2
1
0
0
1
0
0
1
1
1
0
4
0
1
0
0
0
0
0
0
0
6
1
1
2
0
2
1
2
0
0
0
0
2
0
0
2
0
2
1
2
0
1
0
3
0
0
2
1
0
0
1
0
0
1
1
0
1
0
1
2
2
1
1
0
1
0
0
1
0
1
1
2
1
0
0
1
4
2
0
0
0
1
0
1
0
0
0
2
0
0
1
1
1
1
1
0
0
0
1
0
1
1
2
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
1
0
0
2
0
0
1
0
1
0
0
2
0
0
1
0
1
0
2
0
0
0
1
0
2
1
3
2
0
0
0
2
1
2
1
1
0
1
2
2
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
1
2
3
0
0
0
1
2
0
2
1
0
0
0
0
2
1
0
0
0
1
1
2
0
2
0
2
1
2
1
2
1
0
0
2
1
0
3
0
1
0
0
0
0
1
1
2
0
2
1
0
2
1
1
0
1
0
1
2
1
1
0
1
0
1
1
2
0
0
0
1
2
2
0
1
3
1
0
0
0
2
0
1
0
0
0
1
1
2
0
0
2
0
2
0
1
0
2
2
0
1
1
2
1
2
1
0
2
1
0
2
1
0
2
0
0
0
2
2
0
2
0
1
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
1
0
2
1
0
0
2
0
1
0
0
2
1
1
0
0
2
0
0
2
1
0
0
1
2
0
0
0
0
0
0
0
2
1
0
2
0
1
1
0
2
0
1
1
2
2
0
0
1
0
1
2
2
0
1
0
0
1
0
2
1
2
2
1
1
1
0
2
1
2
0
0
1
0
0
0
0
0
0
1
0
0
2
1
0
1
0
2
1
0
0
0
1
0
1
1
0
1
2
0
1
0
1
1
2
1
1
3
0
1
1
1
0
0
2
1
1
0
0
0
2
0
1
2
2
2
2
0
0
3
0
0
1
0
0
0
1
2
0
1
2
1
1
2
2
1
0
1
0
0
0
2
0
1
0
1
2
0
1
1
1
0
2
2
0
0
0
0
0
1
1
1
2
0
0
2
1
0
2
1
1
0
0
0
1
0
1
1
2
2
2
0
1
2
0
2
2
0
1
0
2
0
0
1
0
0
1
0
2
0
0
0
1
2
0
2
2
1
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
2
1
0
1
1
2
0
0
0
0
3
1
0
0
1
1
1
2
0
1
1
0
2
1
0
1
0
1
0
0
3
0
0
0
0
2
1
1
1
0
0
1
0
1
0
0
0
0
1
0
2
0
1
2
2
1
0
2
1
3
1
1
1
0
0
1
0
1
2
0
0
0
0
0
1
3
1
0
1
1
0
0
2
2
0
1
0
0
0
2
0
3
0
1
1
1
0
0
2
1
1
1
2
0
0
1
0
1
0
0
1
1
0
2
3
2
0
0
1
0
1
1
0
1
3
0
0
0
2
0
0
1
2
0
0
0
2
2
1
2
2
0
2
1
2
1
2
0
1
0
2
2
1
0
0
1
0
1
1
1
0
2
0
2
0
0
0
2
1
2
0
1
0
0
1
1
0
1
1
0
0
1
1
0
1
0
1
1
2
0
0
1
1
0
0
2
0
0
2
2
0
2
0
0
0
0
1
1
2
0
0
1
0
0
2
1
0
2
3
0
2
1
0
0
1
2
2
1
0
0
0
0
2
0
0
0
2
2
0
0
0
0
1
0
1
2
0
0
1
1
2
0
1
1
0
0
0
2
1
0
0
0
0
2
2
1
0
3
0
1
0
0
0
0
1
1
0
0
2
1
1
0
0
0
0
1
1
2
0
1
2
0
0
0
2
2
0
0
0
1
2
2
1
1
1
1
0
0
2
0
0
0
0
1
1
0
1
0
0
0
1
2
2
0
1
1
0
0
0
1
1
0
1
1
1
0
0
1
1
0
0
2
1
0
2
1
0
2
0
1
1
1
0
0
2
2
0
2
0
2
0
0
1
2
2
0
1
0
0
1
2
0
1
0
1
0
1
0
2
0
2
1
0
1
0
2
2
0
1
2
3
1
0
0
0
1
1
0
1
0
0
2
0
0
1
1
2
1
0
2
1
1
1
0
0
0
2
0
0
0
0
1
2
1
1
1
0
1
0
0
0
2
0
3
0
1
0
0
2
0
2
0
1
0
0
1
1
0
0
0
2
0
0
1
1
1
0
1
1
0
1
1
0
1
1
1
0
1
0
1
0
2
2
5
0
1
1
1
2
2
1
1
0
0
1
1
0
0
0
1
0
0
0
1
2
0
2
0
1
0
0
1
1
1
1
0
3
2
0
1
0
1
0
0
0
0
1
1
1
1
0
1
1
0
1
2
0
1
0
0
1
0
1
0
1
2
1
0
1
0
0
0
1
0
0
0
1
2
1
1
2
0
1
1
0
0
0
0
3
0
0
0
0
0
0
0
0
1
2
1
1
1
2
1
0
0
0
1
1
1
0
2
1
0
1
1
0
2
1
1
0
1
2
0
0
0
1
1
1
1
1
0
0
0
0
0
2
0
0
0
2
2
0
0
1
2
1
1
2
0
0
1
2
0
2
1
0
0
2
1
1
0
1
2
0
0
0
0
0
0
0
0
1
1
0
1
1
2
0
1
2
1
1
1
1
0
1
2
1
0
2
1
0
0
1
1
0
0
0
0
2
1
1
0
1
2
1
1
1
0
2
1
1
0
4
1
0
0
1
0
0
1
2
2
2
0
0
0
2
1
1
2
0
0
2
0
0
1
1
0
1
0
2
0
0
1
0
2
1
0
0
1
0
0
0
2
1
1
1
2
0
0
0
2
2
1
1
2
1
0
2
1
1
0
1
2
1
2
1
0
1
2
0
0
0
2
0
0
1
1
1
2
1
1
0
0
1
2
0
0
0
2
0
2
1
1
1
1
0
0
1
1
1
0
1
1
0
0
2
0
1
0
0
2
1
0
1
0
0
2
2
0
2
0
2
1
1
0
0
2
0
0
1
0
0
1
0
2
0
1
1
1
0
0
0
2
2
1
1
0
1
1
1
1
0
0
5
1
2
0
1
0
0
1
4
1
0
1
0
0
2
0
0
0
1
1
2
2
0
2
1
0
0
0
2
1
0
0
0
2
0
1
1
0
2
1
1
1
2
0
2
0
0
1
2
3
0
1
0
2
0
2
2
0
2
0
2
0
0
1
1
0
1
3
1
0
0
0
2
2
0
1
1
2
0
0
0
0
0
1
0
1
2
1
1
1
1
1
0
0
1
0
2
0
1
0
2
2
1
1
0
0
0
0
2
1
0
0
2
0
0
1
1
0
2
2
0
1
2
0
0
0
2
1
1
0
0
0
2
2
0
1
2
4
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
1
1
0
1
0
2
0
0
1
0
1
0
0
1
0
1
1
2
1
1
0
2
1
1
0
2
2
0
0
1
0
2
0
0
1
0
2
0
0
1
0
1
0
1
0
2
1
0
2
2
1
0
0
2
0
0
1
0
2
1
0
0
0
1
1
0
2
0
2
0
0
0
0
2
0
1
0
0
2
0
2
0
0
0
1
1
2
2
0
1
2
1
0
1
2
0
1
2
2
2
0
2
0
1
0
3
1
1
1
0
0
0
1
0
2
1
0
2
3
3
0
0
1
0
0
0
0
0
1
2
1
2
1
3
0
1
1
0
1
0
0
0
0
3
0
2
2
0
0
0
0
0
2
0
1
1
1
0
2
0
0
0
0
0
1
2
1
0
2
1
0
2
1
2
0
1
0
0
1
1
0
1
0
1
0
0
0
2
1
3
0
0
0
0
0
0
1
0
2
0
0
0
1
2
2
0
2
0
0
1
1
1
0
1
1
1
0
1
2
0
0
1
0
0
1
2
0
0
1
2
2
1
1
1
4
1
1
0
0
0
1
0
0
0
1
2
0
0
0
1
1
0
2
0
2
0
0
0
1
0
0
2
0
0
1
2
0
0
0
0
1
0
1
0
2
0
0
0
0
2
1
0
1
2
1
1
0
1
2
0
1
1
0
2
0
1
0
0
0
0
0
1
0
0
1
1
0
0
1
1
1
0
1
1
1
0
1
0
1
1
0
1
0
0
0
2
0
0
2
0
2
0
2
2
2
1
0
1
0
1
0
0
0
2
0
1
0
1
0
0
1
0
1
0
0
2
2
2
0
1
0
0
0
0
0
2
1
0
0
0
0
2
1
1
1
1
3
2
0
0
2
1
0
0
0
0
1
0
0
1
0
1
2
1
0
0
0
1
1
0
2
0
0
2
1
0
0
2
1
0
0
1
0
0
2
1
1
1
2
0
0
1
0
0
0
2
0
1
0
0
1
2
1
0
0
1
0
1
0
1
0
0
0
0
0
0
2
0
0
0
1
1
4
1
1
0
1
0
2
0
2
1
0
1
2
0
3
0
0
3
1
0
2
1
1
2
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
1
1
1
0
0
0
0
1
3
2
2
0
1
0
1
0
1
1
1
0
2
2
0
0
1
2
1
1
1
1
1
0
1
0
1
1
0
1
2
2
1
0
1
0
8
2
1
0
0
2
2
1
0
0
2
1
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
1
1
0
0
2
1
0
0
1
1
0
0
0
3
1
0
1
0
0
2
1
0
2
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
1
2
1
2
0
1
1
0
0
2
0
2
0
0
0
0
0
0
2
1
2
1
1
0
2
2
1
0
2
0
0
0
2
0
1
1
2
2
0
2
1
1
1
1
0
0
0
0
0
2
0
0
2
3
2
1
0
0
2
1
0
0
0
2
0
0
0
1
0
1
0
0
1
0
1
0
1
0
0
1
0
2
2
0
1
2
2
0
0
2
1
1
0
0
1
0
1
1
1
0
5
0
1
0
0
1
2
0
1
0
2
1
1
1
2
1
0
1
0
0
0
0
0
1
1
2
0
1
2
1
2
1
1
0
0
1
0
0
0
0
2
1
1
0
1
0
0
0
0
0
2
1
0
1
2
0
0
1
0
0
0
1
1
0
0
0
1
0
2
0
0
0
0
0
2
1
2
1
0
1
2
2
0
1
0
0
0
0
0
0
0
2
1
2
1
2
2
0
1
2
2
0
0
2
0
0
0
0
0
0
0
0
1
1
0
1
1
0
1
0
0
1
2
0
0
0
0
0
1
1
2
0
0
0
1
0
2
0
2
0
2
0
0
2
0
2
0
0
0
0
3
2
0
0
0
1
1
0
1
2
2
0
0
1
0
1
0
0
2
2
0
0
1
0
1
1
0
0
0
2
0
0
2
1
1
0
0
0
0
0
2
0
0
6
0
0
0
2
2
2
2
2
0
1
0
0
1
2
2
0
0
0
0
0
1
0
2
0
2
0
0
0
0
1
0
2
0
1
3
0
2
0
1
0
2
1
1
0
1
1
2
0
0
0
2
2
2
2
0
2
0
1
0
2
1
0
0
2
1
1
0
0
0
0
1
1
1
1
0
0
0
1
0
1
2
1
2
2
1
0
0
2
2
0
2
1
1
0
2
0
2
0
0
1
1
2
0
2
1
0
0
0
0
1
0
1
2
0
2
2
1
0
2
2
0
2
0
0
1
2
1
0
0
0
2
1
1
0
2
0
0
2
0
1
0
0
0
1
1
1
1
2
2
2
0
0
0
0
0
2
0
0
0
0
0
2
1
0
1
0
2
2
0
0
1
0
0
0
2
1
1
0
2
0
1
0
2
0
1
2
0
1
2
1
1
0
0
0
0
2
2
1
0
2
1
1
0
1
0
1
0
0
1
0
1
2
0
1
0
1
0
2
0
0
0
1
0
0
1
1
0
0
0
0
0
1
1
0
0
0
1
1
1
0
0
0
2
0
2
0
1
2
0
2
0
2
0
1
0
1
1
3
0
1
0
2
0
4
1
0
0
3
0
1
0
0
0
0
2
2
0
2
1
0
0
1
0
1
0
2
0
2
1
1
1
0
0
0
1
1
1
1
0
2
1
0
2
0
1
2
0
0
2
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
1
1
1
3
1
0
1
0
2
1
1
1
1
0
0
1
0
0
0
2
2
2
0
2
0
0
0
0
2
0
2
2
1
1
1
0
1
1
2
0
0
0
2
2
1
1
0
2
2
1
0
1
0
0
2
1
0
1
0
1
0
1
0
1
1
2
1
2
0
0
0
0
1
0
0
0
0
0
1
2
0
1
0
0
1
0
0
0
1
1
0
2
0
0
0
1
0
3
1
0
0
0
0
1
1
0
2
1
0
0
1
0
1
2
2
1
0
2
0
0
2
0
0
0
1
0
1
0
1
2
1
0
0
2
0
1
2
0
1
0
1
0
0
2
0
0
1
0
2
0
0
1
1
1
2
1
0
0
1
1
2
2
2
0
1
1
1
2
0
0
0
0
2
1
1
2
1
2
1
0
1
2
1
0
1
0
1
1
1
1
2
0
0
2
1
0
1
0
0
0
0
0
3
1
0
0
1
1
0
0
0
0
1
0
0
0
1
0
1
1
0
2
1
1
2
2
2
1
2
1
2
1
0
1
1
1
0
1
0
1
0
1
0
1
0
1
0
1
0
0
0
1
2
0
0
2
0
0
2
1
1
0
2
2
1
1
3
1
0
0
0
1
2
2
0
2
2
0
1
0
3
0
0
1
2
0
0
0
0
0
0
2
1
0
0
1
0
1
0
1
1
0
0
2
0
0
0
2
0
2
1
0
2
0
1
1
0
1
0
1
1
0
0
1
2
0
0
1
0
0
3
0
0
0
0
2
0
2
0
0
2
0
0
1
0
2
0
0
3
0
1
0
2
0
0
0
0
0
2
1
1
0
0
0
3
0
2
2
0
1
0
1
0
0
0
2
2
1
1
0
2
1
0
0
0
2
0
0
1
1
1
0
2
0
1
1
0
0
1
2
1
0
1
1
0
1
0
0
2
1
0
1
0
1
0
2
2
0
2
2
0
2
2
0
0
2
2
2
1
0
2
2
2
0
2
2
2
0
1
0
0
0
3
1
2
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
2
2
0
1
2
2
0
0
2
0
0
0
1
2
0
1
0
0
1
0
1
1
2
0
0
1
0
0
2
0
2
0
0
1
0
0
2
1
1
0
0
1
0
0
0
0
0
2
1
0
1
0
1
0
1
0
0
1
2
0
1
0
2
0
0
0
1
2
2
0
1
0
1
0
2
2
0
0
0
0
0
0
0
2
1
0
0
0
2
1
1
0
0
0
1
1
0
1
1
0
1
1
2
0
0
2
2
0
0
1
1
0
0
0
1
0
0
1
0
0
2
0
2
0
0
1
2
2
0
0
0
2
3
0
0
0
1
0
0
0
0
2
1
0
0
0
2
0
1
2
0
1
1
2
2
2
2
2
1
0
2
1
0
1
0
0
0
0
0
2
0
0
0
2
2
0
4
0
2
0
0
2
2
2
0
0
1
1
1
0
0
0
1
1
1
0
2
0
1
0
0
1
1
0
0
1
2
0
0
0
1
0
1
0
2
0
0
1
2
1
0
0
2
0
1
0
2
1
1
0
0
0
2
3
0
2
2
0
0
1
0
0
0
2
0
2
0
0
0
0
1
2
1
1
0
0
0
0
0
0
1
0
0
1
0
1
0
1
2
3
0
0
1
1
0
2
2
1
1
0
0
0
0
1
1
2
1
2
1
0
2
2
0
2
0
1
2
0
0
1
3
0
0
0
0
1
1
0
0
0
2
0
0
1
1
0
1
2
1
1
0
1
0
1
2
1
1
0
2
2
0
0
0
2
1
0
1
0
0
1
0
0
4
0
0
2
0
2
1
1
0
1
1
1
2
2
0
0
2
2
1
1
1
2
1
2
1
2
2
1
2
0
0
1
0
1
1
0
0
0
1
1
0
0
1
3
0
1
1
1
2
0
2
0
0
0
1
1
1
2
0
2
0
0
0
1
0
1
0
0
2
0
2
1
0
0
0
0
1
0
1
0
1
2
0
0
1
0
2
0
1
2
0
1
0
0
0
0
0
2
0
1
0
1
0
0
2
1
0
0
0
2
2
1
1
0
0
0
1
1
1
0
0
0
0
1
1
1
2
1
1
0
1
0
0
0
2
0
1
1
0
1
0
0
0
3
2
1
1
2
1
0
0
2
0
1
0
1
2
2
0
2
0
2
0
2
0
0
1
2
1
1
0
0
1
0
0
1
0
0
0
3
0
0
1
0
0
0
1
0
1
1
1
1
2
0
0
0
0
1
0
0
2
0
1
2
2
0
1
0
1
0
0
0
0
2
1
0
1
1
0
1
1
1
2
0
0
1
1
0
0
0
2
1
1
0
0
1
0
3
2
0
0
0
0
0
2
0
1
1
0
1
0
2
0
1
1
2
0
0
1
1
1
1
1
0
2
1
1
0
1
0
0
0
2
1
2
2
0
1
1
1
1
2
0
1
0
3
2
0
0
2
1
2
1
0
0
0
2
0
2
1
2
2
0
2
2
1
0
0
0
1
1
1
0
0
0
2
1
0
1
0
0
0
0
0
1
2
0
0
0
0
2
0
0
1
1
1
1
1
1
1
1
1
1
2
0
1
0
2
1
1
1
0
1
2
1
0
2
1
2
0
4
2
0
2
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
2
2
0
1
2
1
2
1
1
0
1
0
0
0
1
0
1
2
0
2
0
1
2
0
2
2
0
1
0
1
0
0
1
2
0
0
0
1
2
0
0
0
0
3
0
0
1
0
0
0
0
0
0
2
0
0
0
2
2
0
0
6
2
2
0
0
0
2
1
2
1
1
2
2
0
1
0
0
2
1
0
0
2
0
1
0
1
1
0
0
2
0
1
0
1
0
0
2
0
0
0
2
0
0
1
0
0
1
0
1
0
1
0
0
0
1
0
0
0
1
0
2
2
0
0
0
1
1
1
0
1
1
1
1
1
0
1
0
1
2
2
0
1
1
0
0
0
2
0
0
0
0
1
2
1
0
1
1
0
0
0
0
1
1
1
1
0
0
2
0
0
2
0
2
0
0
1
0
1
1
1
0
0
0
1
0
0
1
0
0
2
2
1
1
0
0
2
2
0
0
0
0
0
1
0
2
0
1
2
0
1
0
0
0
1
1
3
0
1
0
1
0
0
2
1
1
0
1
1
0
0
0
2
0
0
1
1
2
2
0
2
0
2
0
2
1
1
2
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
2
1
2
0
1
1
0
2
2
0
1
2
2
1
0
0
0
1
2
0
1
0
1
3
1
0
1
2
1
1
0
0
0
2
1
0
2
0
1
1
0
2
2
0
1
0
2
2
0
1
2
2
0
1
0
0
2
0
0
0
1
1
0
2
1
1
1
0
2
1
0
0
0
0
1
1
0
0
0
0
1
2
0
0
1
3
1
2
2
1
0
1
2
1
0
0
0
0
0
0
0
2
0
1
1
0
1
0
0
1
2
0
0
0
2
0
2
2
1
0
2
0
0
2
2
0
1
2
2
1
0
1
2
2
2
2
2
2
2
1
2
0
2
0
1
0
1
1
1
0
1
0
0
1
0
1
2
0
2
0
0
1
1
0
2
0
0
2
1
0
1
2
1
2
0
0
1
0
0
2
1
1
1
1
0
0
0
1
1
1
0
0
1
1
3
1
2
0
0
1
2
2
0
0
0
1
2
1
2
0
1
0
1
0
0
1
0
3
0
0
2
0
0
0
0
1
0
1
0
0
1
1
1
0
0
0
1
0
0
1
2
0
0
0
0
1
0
3
1
0
2
2
2
0
2
1
0
1
0
2
1
0
0
1
1
0
0
2
0
0
0
2
0
2
0
0
0
2
1
0
2
2
1
0
2
1
0
1
0
0
0
0
0
4
0
2
1
0
3
1
2
2
1
0
2
1
6
1
0
0
2
1
0
1
1
2
0
0
0
0
0
1
2
1
0
0
0
2
0
0
3
2
0
1
1
0
0
0
0
0
1
1
1
0
0
1
0
2
0
2
1
0
0
0
0
2
1
1
1
0
0
0
1
1
0
2
0
1
0
0
1
3
0
0
2
0
1
2
1
0
0
2
0
0
0
0
0
2
2
0
2
1
2
1
0
2
0
0
2
5
0
2
0
0
1
1
1
0
0
1
1
2
2
1
0
2
0
2
1
0
1
1
1
1
1
1
0
0
0
1
0
0
0
1
0
1
1
0
0
1
1
2
0
0
1
0
1
2
0
1
1
0
0
1
0
0
0
1
0
2
2
2
2
1
1
1
2
0
1
0
0
0
1
0
2
0
0
1
2
0
1
2
0
0
1
1
2
2
0
0
2
0
0
0
2
1
0
2
1
0
1
2
0
1
0
2
0
0
3
0
2
0
1
2
0
0
1
0
0
2
1
0
2
0
0
0
2
1
0
0
1
2
0
0
0
0
0
0
1
2
0
0
2
2
1
1
0
1
0
1
2
1
0
1
1
0
0
1
2
0
0
2
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
2
0
0
1
2
0
0
0
0
0
2
0
2
2
0
4
0
0
1
1
2
0
0
0
0
0
0
2
2
2
2
2
1
1
2
2
1
2
1
1
1
0
1
0
2
1
0
1
0
0
2
0
1
0
2
2
0
1
2
0
0
2
0
0
0
2
0
0
1
1
0
0
1
0
1
0
2
0
1
2
2
0
0
0
2
2
2
2
0
1
1
0
2
0
0
1
0
1
1
1
0
0
1
1
1
0
1
2
3
1
1
1
0
1
0
1
0
0
0
0
0
1
1
1
0
0
2
0
0
2
1
2
0
1
2
0
1
0
2
0
2
0
0
0
0
1
5
2
0
0
1
1
1
0
1
0
2
1
1
1
1
0
1
0
5
0
0
1
2
0
2
0
1
1
0
0
3
1
0
0
2
0
1
1
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
1
2
1
1
1
2
1
0
0
0
0
0
0
0
0
1
1
1
1
0
0
2
0
0
2
2
0
2
0
3
1
0
2
1
2
2
0
1
0
0
3
0
1
2
0
0
1
1
0
0
1
1
1
2
2
2
0
2
1
2
2
1
2
2
0
1
0
1
0
0
1
0
0
2
2
1
3
1
0
2
2
1
1
1
2
1
0
2
1
2
0
2
1
0
2
0
0
0
2
1
0
0
2
0
0
0
0
1
1
0
1
1
0
1
0
0
0
0
2
1
0
1
0
2
0
0
1
3
2
0
1
0
0
4
2
1
1
0
0
0
1
0
0
1
0
0
0
1
0
2
1
0
0
0
2
1
0
0
2
1
0
0
0
0
1
0
2
2
1
0
0
0
2
1
0
0
0
0
0
0
1
1
1
1
0
1
0
0
2
0
1
2
1
2
2
0
2
1
1
0
1
1
1
2
2
0
2
1
0
2
1
0
0
0
0
2
1
2
0
1
1
1
0
0
0
0
1
2
0
0
1
2
0
0
2
0
2
1
0
1
0
1
2
0
1
2
1
2
1
1
2
2
1
3
0
0
2
1
1
0
0
1
0
2
2
2
1
1
0
2
0
1
0
2
1
2
1
2
1
2
0
2
2
1
0
1
0
1
1
1
1
2
0
0
0
2
0
0
0
0
0
1
2
1
2
0
2
0
0
2
1
1
1
0
0
0
2
1
3
0
0
1
0
1
0
0
2
0
0
2
0
0
2
0
0
0
2
0
1
0
1
3
1
2
1
0
2
2
0
1
2
1
0
0
1
2
1
0
0
0
0
0
1
1
0
2
0
1
0
0
1
0
0
1
0
1
1
1
2
0
0
2
1
2
1
0
0
0
0
1
0
1
0
0
2
0
0
2
1
0
0
0
0
1
2
0
2
0
0
0
1
0
1
1
1
1
0
0
0
1
0
1
1
0
2
1
0
0
0
0
1
0
2
0
1
0
0
1
2
0
1
0
2
1
0
1
0
1
0
3
0
0
0
2
0
2
0
1
0
1
2
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
2
0
0
2
1
2
2
0
0
1
0
0
1
1
0
0
1
0
1
2
1
0
0
2
0
1
2
1
2
2
1
0
1
0
2
0
1
0
0
0
1
0
0
0
1
2
0
2
1
2
0
1
1
1
0
1
2
1
0
3
1
0
2
1
0
0
0
1
0
2
0
1
0
3
1
0
0
0
0
0
1
3
0
2
0
0
0
1
2
1
0
0
0
1
1
1
2
0
0
0
0
1
1
0
0
2
2
0
2
0
0
2
1
0
2
2
2
0
1
1
0
0
2
1
1
0
0
1
1
2
2
0
0
1
1
0
1
1
2
0
0
0
1
0
1
1
0
1
2
0
0
0
2
0
1
2
0
0
1
0
0
0
1
1
1
1
1
1
1
2
0
1
1
2
1
1
1
0
0
1
0
1
1
2
0
0
1
1
2
0
0
0
0
0
1
2
2
0
4
0
1
1
0
0
0
0
1
0
0
1
2
1
1
1
1
1
1
0
2
1
3
1
2
1
0
1
1
1
0
0
0
0
1
1
0
1
0
1
0
2
0
0
1
1
1
1
1
1
1
0
1
1
1
1
2
1
0
0
0
1
1
0
2
0
0
1
1
2
1
1
0
2
0
1
0
0
2
0
0
2
1
0
3
0
0
0
1
0
2
0
0
0
2
0
0
1
1
0
2
0
0
0
2
0
1
1
1
2
0
0
0
0
1
0
0
2
0
2
0
1
0
0
0
0
2
0
2
0
0
0
2
0
0
0
5
0
0
0
2
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
2
0
2
0
0
0
0
2
2
1
1
0
0
2
0
2
1
1
0
0
0
0
1
0
1
0
2
0
0
0
2
0
0
3
0
1
1
0
1
1
2
0
0
2
0
2
0
2
2
0
2
1
1
1
2
0
0
0
0
2
1
2
0
0
1
2
0
0
2
0
1
0
0
2
1
0
0
0
2
0
0
1
0
2
0
0
1
0
0
0
2
0
0
0
2
2
2
2
0
0
6
0
0
0
2
0
1
0
0
2
0
1
0
1
0
1
0
0
0
2
0
2
1
0
0
0
1
2
0
1
0
2
1
0
0
2
0
1
1
0
0
1
0
0
0
0
1
1
3
0
2
2
0
0
1
0
0
1
0
0
0
1
2
0
0
1
0
0
0
2
0
2
0
0
0
0
1
3
0
0
2
1
1
1
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
2
1
0
0
1
0
1
1
1
1
1
0
2
2
1
1
0
1
0
0
0
0
0
2
1
1
1
0
0
0
0
1
1
0
2
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
1
0
2
2
0
1
0
2
0
0
1
1
2
1
2
0
0
1
1
1
0
1
2
0
1
1
2
0
2
2
0
0
0
0
2
0
0
2
0
0
0
2
0
2
0
0
1
0
2
2
1
0
0
1
0
2
0
0
0
2
1
1
2
0
0
0
0
0
1
1
1
0
1
1
0
1
0
0
2
0
0
1
1
1
1
2
0
0
2
0
0
0
0
1
2
1
2
0
1
2
2
2
1
1
1
1
0
0
0
1
0
1
1
0
2
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
2
0
1
1
0
1
0
0
2
1
1
0
1
0
1
0
0
0
2
0
0
1
1
0
0
0
0
2
2
0
1
0
1
0
2
0
0
1
1
1
0
0
0
0
1
1
2
0
1
0
0
1
1
0
1
1
0
0
0
0
2
1
0
1
0
2
0
0
3
0
0
0
0
2
0
0
1
1
1
0
0
1
0
1
2
0
1
0
2
2
0
0
0
0
1
1
0
0
0
2
1
2
0
1
2
2
1
0
2
0
1
0
0
2
2
1
1
2
1
0
1
1
0
0
0
1
0
2
1
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
1
0
1
2
1
1
0
0
1
0
2
2
0
0
0
2
2
0
1
2
0
0
1
4
0
0
1
0
0
0
3
1
0
1
0
0
0
2
1
2
0
1
2
1
0
0
1
2
0
0
1
0
0
1
0
0
1
0
1
1
0
0
1
0
0
2
3
2
0
0
0
1
3
1
0
1
2
0
3
1
0
1
0
2
2
0
0
0
1
0
1
0
2
0
1
0
0
1
1
0
0
2
1
0
1
2
1
0
2
0
1
0
1
2
2
0
1
0
0
0
1
1
0
0
0
2
0
3
1
1
2
1
0
3
0
0
2
1
1
2
1
0
0
0
0
0
0
1
0
0
0
0
2
2
0
1
0
0
0
0
0
0
1
2
3
0
1
2
1
2
1
0
1
0
1
0
2
2
1
0
0
0
2
2
0
0
0
2
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
2
0
2
0
0
0
0
2
2
2
1
0
2
1
0
1
2
0
0
1
0
0
0
2
0
2
3
1
0
0
2
0
2
0
0
0
0
2
0
0
0
0
2
2
1
1
0
0
2
0
0
0
0
1
2
0
1
0
1
0
2
0
1
0
0
0
2
0
0
1
0
0
0
0
2
0
2
1
0
0
0
3
1
0
0
0
1
0
1
1
2
1
3
0
1
1
1
1
2
0
0
0
1
0
0
0
0
0
2
1
0
2
1
0
2
0
2
2
0
0
0
1
0
2
0
1
1
1
0
1
1
0
1
1
0
0
0
2
0
1
0
0
1
0
0
0
1
0
1
2
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
2
0
2
2
0
0
2
0
1
2
0
1
0
2
3
1
3
0
0
0
1
2
1
1
0
0
0
1
1
0
2
1
1
2
0
0
1
1
0
0
0
2
2
1
0
0
1
1
0
2
1
2
0
2
0
0
1
1
1
1
0
0
0
1
1
0
0
0
2
0
2
1
0
0
2
2
2
2
0
2
1
1
1
0
0
0
0
1
2
2
0
0
1
0
0
1
0
1
1
0
1
1
0
1
0
1
0
2
2
0
1
0
0
2
2
0
0
1
2
0
0
0
0
3
2
1
0
0
0
2
1
0
0
0
2
2
1
2
2
0
1
0
2
1
0
2
2
1
0
0
0
0
1
2
0
0
0
1
1
2
0
0
1
0
0
0
0
0
1
0
2
2
0
0
0
0
1
2
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
1
0
0
0
1
0
1
1
0
2
0
0
1
4
0
0
2
1
1
0
0
2
0
1
1
1
0
0
0
0
2
2
1
1
2
2
1
0
2
2
0
0
1
0
1
0
1
1
2
0
0
2
1
2
2
0
2
0
0
0
2
1
2
0
0
1
0
0
0
1
1
1
0
1
0
2
1
1
2
0
0
0
2
0
0
1
0
2
1
0
1
1
1
0
0
1
0
0
1
1
0
0
0
1
2
3
2
2
1
0
2
1
0
1
0
1
1
1
0
2
1
0
1
0
0
1
0
0
1
2
1
1
0
2
0
0
0
2
2
0
1
2
2
0
1
0
2
0
0
1
0
1
1
0
1
0
0
2
0
1
0
0
0
0
3
2
2
4
2
0
1
1
1
2
0
2
1
2
0
1
1
0
0
0
0
0
0
2
0
1
1
1
2
0
0
1
1
0
0
1
0
2
1
0
0
1
0
2
0
0
0
1
1
1
1
0
1
2
0
0
1
1
0
0
0
0
4
0
1
1
0
1
1
0
1
0
1
2
1
0
2
2
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
2
0
1
0
1
1
0
0
1
1
1
0
0
1
1
1
1
0
0
3
2
0
0
2
0
1
1
2
0
1
2
0
1
1
0
2
0
2
1
1
1
0
0
0
0
1
0
1
0
0
2
2
1
1
0
0
1
0
1
0
0
0
0
1
0
2
2
2
2
0
2
0
1
0
0
2
1
0
2
0
0
1
0
0
1
0
4
1
2
0
2
0
0
0
2
1
0
0
1
0
1
1
1
1
0
0
1
2
0
2
1
0
0
2
2
1
2
0
0
1
1
1
0
0
0
2
0
1
1
1
1
1
1
1
1
1
1
1
2
0
1
1
1
2
0
0
0
0
1
0
1
1
0
1
2
0
1
0
0
0
0
2
0
1
0
1
0
1
0
1
3
0
0
1
0
1
0
1
0
1
2
0
0
0
1
0
2
1
1
2
1
1
0
1
2
0
1
1
0
0
0
1
1
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
1
2
0
1
0
1
0
2
1
1
2
0
1
1
2
0
0
1
0
2
2
0
3
0
1
1
0
0
1
2
1
2
0
1
1
2
0
0
0
1
0
1
0
0
2
2
0
2
1
0
1
0
0
0
0
1
0
0
0
0
1
0
2
0
1
0
2
0
0
0
1
0
0
1
1
0
0
2
0
1
0
1
3
1
2
0
0
0
2
1
0
1
2
0
1
1
0
2
1
0
1
1
1
0
2
2
1
0
0
0
0
2
1
1
1
1
0
1
0
0
2
1
0
2
1
0
0
0
0
2
0
2
1
1
0
2
2
0
0
2
0
2
1
0
0
1
2
1
0
2
0
0
0
1
1
0
0
1
2
1
1
1
0
0
0
2
0
0
1
2
1
0
0
1
1
1
2
2
0
0
0
2
2
0
1
1
0
0
1
2
0
1
0
0
2
0
0
0
1
2
0
1
0
1
2
1
1
0
1
2
0
0
0
1
1
0
0
2
0
0
0
1
2
0
0
0
0
1
0
3
1
2
0
1
2
0
0
2
1
0
0
1
0
0
0
1
1
0
2
3
1
0
2
1
1
2
1
3
2
2
1
1
3
0
0
2
0
0
2
0
2
1
1
2
1
2
0
1
1
2
2
0
0
1
1
0
0
0
2
0
2
0
2
2
0
1
1
2
1
0
1
1
1
1
0
0
0
2
0
0
1
2
0
0
0
2
1
0
1
1
1
3
0
1
0
2
2
0
1
1
0
4
0
0
0
0
3
1
1
0
1
0
1
0
0
1
2
0
0
0
1
0
2
0
1
2
2
0
0
0
0
0
2
1
0
2
1
2
0
1
2
5
0
0
2
0
0
0
0
0
0
4
2
2
0
1
2
2
0
0
0
0
1
0
1
1
0
0
1
4
1
0
1
0
2
0
0
2
0
1
1
2
1
1
1
1
1
1
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
3
0
2
0
1
2
1
1
0
0
1
0
0
3
0
2
0
0
2
0
1
1
0
1
0
2
1
1
2
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
3
1
1
1
2
2
0
0
0
0
0
1
1
0
0
1
1
1
1
1
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
1
0
1
0
0
3
0
0
1
0
0
0
0
2
1
1
0
0
0
0
1
0
0
0
2
1
2
0
1
0
0
0
1
1
2
0
0
2
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
1
1
1
0
0
1
3
1
0
0
2
1
0
0
2
0
0
1
0
0
0
1
1
0
0
2
1
0
0
2
1
2
0
0
0
0
0
2
0
2
1
0
1
2
0
0
2
1
0
1
2
2
2
0
1
0
1
0
2
2
1
0
0
1
0
0
1
0
0
0
1
1
1
0
0
2
2
0
0
0
2
0
2
0
1
0
1
0
1
1
0
0
1
0
0
2
1
0
0
0
2
0
0
2
2
0
1
0
0
0
0
2
1
2
1
0
1
1
1
0
1
0
0
2
2
2
0
0
0
2
1
1
2
0
0
1
0
1
0
2
1
1
1
1
0
1
1
0
0
2
0
2
0
1
1
2
0
4
0
1
1
0
1
1
1
1
2
0
1
1
2
0
0
0
2
0
0
0
1
1
1
2
1
2
2
1
1
0
0
0
0
0
1
0
2
2
1
1
1
2
0
1
1
2
0
1
2
1
2
1
0
1
0
1
1
0
1
2
1
0
1
0
1
1
2
2
0
0
1
2
0
0
0
1
0
0
2
1
0
0
2
2
1
0
0
0
2
1
0
1
0
1
0
0
1
0
2
2
1
0
2
1
0
2
0
0
2
0
0
0
1
2
0
0
0
1
0
0
1
0
2
1
2
1
0
0
0
2
2
2
1
1
2
0
1
1
0
1
0
1
1
2
2
1
1
1
1
1
1
0
1
0
0
1
0
2
2
0
1
1
0
1
0
0
1
0
1
1
0
3
2
2
1
0
2
1
0
2
1
0
0
0
1
2
0
1
2
1
1
0
0
0
2
2
2
0
0
0
2
2
0
2
0
1
1
0
0
0
0
0
0
1
0
1
0
1
0
2
0
0
0
2
0
2
1
0
0
0
2
2
0
0
0
0
2
0
0
0
1
1
1
1
0
1
1
1
0
1
2
1
1
1
2
1
1
1
1
1
1
2
2
0
0
0
0
1
2
0
0
1
1
2
0
0
1
2
0
2
1
2
1
0
1
1
1
0
1
0
0
2
0
0
2
0
3
1
0
0
1
1
1
1
0
2
0
0
2
2
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
1
1
0
0
0
2
0
0
0
1
2
0
0
2
2
1
1
0
2
0
0
1
0
1
0
1
1
1
0
0
0
0
0
1
1
1
1
0
0
0
1
1
1
2
1
0
2
1
2
1
1
0
2
1
2
0
0
0
2
1
2
0
2
1
2
2
2
0
1
2
0
0
0
1
2
0
1
1
1
2
0
2
2
1
0
0
1
1
1
0
2
1
2
2
0
1
0
1
3
0
0
0
0
1
1
2
0
0
2
0
0
0
1
1
0
0
0
1
0
2
1
1
0
2
1
0
1
1
0
1
0
1
2
1
0
0
0
0
1
2
0
0
0
0
0
1
0
1
1
0
1
0
2
1
0
0
2
0
1
1
2
4
0
0
0
0
0
0
1
0
0
0
1
1
0
1
2
1
0
0
1
0
0
1
1
0
0
2
0
1
1
1
1
2
0
1
1
0
1
2
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
1
2
0
2
1
1
0
0
0
1
0
0
2
1
0
0
0
12
0
0
1
0
2
1
0
0
0
1
0
3
1
0
0
0
2
0
0
1
0
0
2
2
1
0
0
2
2
0
0
1
0
2
0
2
1
1
0
0
0
1
0
2
1
1
1
0
0
0
1
1
0
1
0
1
0
1
0
2
0
0
0
0
0
0
1
1
0
0
3
1
1
2
1
2
0
0
2
0
2
1
0
2
1
1
0
0
1
1
1
0
0
1
1
1
0
1
0
0
1
0
1
0
0
0
2
0
1
0
2
2
0
0
0
2
0
0
0
1
2
0
1
0
0
1
0
2
1
0
1
1
0
0
1
0
1
1
0
2
0
2
0
0
0
0
3
0
0
2
0
1
1
2
2
0
0
0
2
1
0
0
0
1
0
1
0
0
1
0
1
0
0
0
1
0
1
1
1
1
0
1
0
3
2
0
0
0
1
0
0
2
1
0
1
1
2
2
2
0
0
0
2
0
1
2
0
0
0
1
0
1
0
0
1
0
1
2
1
1
2
1
0
1
1
1
0
2
0
0
1
1
2
0
0
1
0
1
1
1
1
0
2
1
1
0
1
2
2
2
1
1
0
0
0
0
2
1
2
0
2
0
0
0
4
1
1
0
2
0
1
1
1
1
2
1
0
0
1
1
2
0
1
0
0
1
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
1
2
0
0
0
2
2
2
0
1
1
1
0
2
5
2
0
0
2
0
2
0
0
1
2
1
1
1
0
0
2
2
2
1
3
2
0
0
0
2
0
0
0
0
0
1
0
0
1
3
0
1
0
2
2
1
0
0
1
0
1
1
2
0
3
0
2
0
2
0
1
3
2
1
1
1
2
0
0
0
0
1
2
0
1
0
0
0
1
0
1
0
1
0
0
2
2
1
1
0
0
0
0
0
0
1
0
1
0
0
2
2
0
0
1
0
1
0
1
1
1
2
1
0
0
0
1
1
0
0
1
0
1
1
0
2
1
0
1
1
2
2
0
2
0
0
1
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
2
1
0
3
2
1
0
1
1
1
1
0
4
1
2
0
2
0
1
0
1
1
0
0
2
0
2
0
0
2
1
2
1
1
1
1
2
1
0
0
3
3
0
1
0
0
2
0
1
1
0
1
2
0
0
2
2
0
0
1
0
1
1
1
1
0
0
1
0
0
0
2
0
1
0
2
2
1
2
1
0
1
0
0
2
0
0
1
2
1
0
0
0
1
1
0
0
0
0
1
0
1
2
0
2
0
0
0
0
1
0
1
1
2
0
2
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
1
2
0
1
2
2
2
2
2
1
0
0
1
1
0
2
2
2
1
0
1
1
1
1
0
0
0
1
1
1
0
1
0
0
0
2
2
1
0
1
1
1
0
0
0
0
0
1
0
0
1
2
1
1
0
1
0
2
1
1
0
1
1
2
0
1
2
1
1
2
2
2
0
1
0
1
0
2
2
0
1
1
1
0
0
0
0
0
2
0
2
1
1
1
0
1
0
2
2
1
0
1
3
0
0
0
1
2
2
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
1
0
2
1
2
1
2
1
2
0
1
0
0
0
2
1
0
1
0
0
1
0
1
0
3
1
0
0
0
0
1
0
1
0
0
1
3
2
1
1
1
0
1
1
1
1
2
2
0
0
0
0
1
2
0
1
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
2
1
0
0
1
2
0
0
1
1
2
0
0
1
0
2
0
0
2
0
1
0
2
0
1
2
0
1
1
1
1
0
0
1
0
1
1
0
2
2
0
1
1
2
1
2
1
2
1
0
1
0
1
0
0
2
2
2
0
1
0
1
0
1
0
0
0
2
1
0
0
0
1
0
3
1
0
1
2
1
3
0
1
0
1
0
2
0
2
1
1
2
0
0
0
1
1
1
1
0
0
1
0
2
0
0
1
2
0
0
0
0
2
2
0
0
2
0
2
2
1
0
0
0
2
1
0
1
1
0
1
0
0
0
1
0
2
0
0
2
1
1
0
2
0
0
0
0
1
1
1
1
0
0
0
0
0
0
1
2
1
0
0
1
2
0
0
0
0
0
1
0
1
0
0
1
0
0
2
2
0
0
3
0
0
2
0
2
0
1
2
0
0
2
1
2
0
1
1
0
1
0
4
2
0
0
1
1
1
0
1
1
0
0
0
0
2
1
0
2
1
1
0
3
1
1
1
0
0
2
2
1
0
0
2
2
2
0
1
0
0
0
1
0
0
0
1
2
0
0
1
0
0
0
0
2
1
0
2
2
1
2
1
0
0
0
2
0
0
1
0
0
1
1
2
1
3
2
0
0
0
1
0
1
0
1
1
2
0
1
0
1
0
0
3
0
1
0
1
0
2
0
0
0
2
0
1
0
0
2
0
1
2
1
0
1
1
0
2
1
1
1
1
2
1
2
2
1
2
0
1
1
2
0
2
1
2
0
0
1
2
1
0
0
1
0
4
1
0
1
0
1
2
1
1
0
0
0
0
1
1
2
0
0
0
1
2
1
1
0
1
1
0
0
0
0
0
2
1
0
0
2
0
3
2
0
0
0
0
2
0
1
1
1
2
0
2
0
2
0
0
0
0
0
2
0
1
2
1
0
0
0
1
0
2
0
0
0
1
1
2
0
0
0
0
0
1
2
0
1
1
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
2
1
0
0
0
0
0
1
1
1
2
2
0
0
1
0
0
0
1
1
0
0
1
0
1
2
3
2
0
0
0
0
1
0
0
0
1
2
1
2
3
2
1
1
1
2
0
0
1
1
1
2
1
0
1
0
0
1
0
0
0
1
0
1
0
1
0
1
2
1
2
0
0
1
1
0
1
1
1
2
1
0
0
1
0
0
1
1
0
2
1
1
2
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
2
0
0
1
2
2
2
1
2
1
1
1
0
0
3
1
1
0
1
1
0
0
1
0
0
0
0
3
0
0
1
0
1
0
0
2
1
0
0
0
1
2
0
0
0
0
2
0
1
1
2
1
1
2
2
0
0
0
1
0
1
0
0
2
1
0
2
1
0
0
0
0
1
2
2
2
1
0
0
1
0
1
0
1
0
0
0
1
1
0
2
2
4
0
1
1
1
1
0
0
2
0
2
3
1
0
1
0
1
0
2
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
2
1
0
0
2
0
1
1
0
0
2
0
0
0
0
1
2
0
1
0
2
0
0
2
0
2
1
0
1
2
1
0
0
1
0
0
2
1
1
1
1
2
0
0
0
0
1
1
2
0
1
1
0
0
0
1
1
2
1
0
2
1
2
0
2
0
2
1
1
0
1
1
1
0
1
0
0
0
0
2
0
1
0
0
1
1
1
1
1
3
1
0
0
2
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
1
1
1
0
0
2
0
0
1
0
2
0
1
0
2
0
1
0
0
2
1
1
1
0
2
1
0
1
0
0
0
5
2
0
0
2
0
1
0
0
0
2
0
0
0
1
2
0
6
1
1
0
0
1
0
0
1
0
1
2
1
1
2
0
1
0
0
0
3
1
1
0
2
0
0
0
0
2
0
1
2
1
1
0
1
1
0
2
1
2
0
2
2
0
3
0
2
2
1
0
3
0
0
0
0
0
1
3
1
2
0
2
0
0
0
0
0
0
0
0
0
5
1
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
1
1
1
0
0
3
1
1
0
0
1
0
0
2
1
1
1
1
1
1
1
0
2
1
1
0
0
0
1
2
3
1
2
0
1
0
1
0
3
1
1
0
3
0
1
1
2
2
0
2
1
1
0
0
0
0
1
0
0
1
0
0
1
1
1
0
2
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
1
1
0
3
0
0
0
0
1
0
0
1
0
1
1
3
1
1
0
1
0
1
2
0
1
0
0
2
0
1
2
0
0
2
1
1
0
0
1
1
0
1
0
2
2
2
1
2
0
0
1
1
2
0
2
0
2
1
2
0
2
1
0
1
1
0
0
2
0
1
0
2
0
0
1
0
1
2
2
0
2
0
0
1
0
1
0
1
0
2
0
1
0
2
2
0
2
0
0
1
1
1
1
1
0
2
1
1
3
0
0
0
1
1
1
3
1
1
1
0
1
0
2
1
0
1
0
1
0
0
0
1
0
2
1
1
0
0
0
0
2
0
0
2
0
1
3
0
0
0
1
1
2
2
0
0
2
2
0
1
0
0
0
2
2
0
2
0
0
0
0
0
2
1
0
1
2
2
0
0
0
0
0
1
1
2
2
0
1
0
0
1
1
0
1
0
0
1
0
0
0
2
0
0
0
1
1
0
0
0
1
0
0
1
1
1
1
2
1
1
1
1
0
0
0
0
0
0
1
0
2
0
1
0
1
1
1
1
1
0
0
2
0
2
3
1
0
2
2
0
0
0
2
0
0
1
2
0
0
2
0
0
0
0
1
1
1
1
1
0
0
1
2
0
0
0
0
0
1
0
0
2
0
0
1
2
0
2
2
1
0
2
0
0
2
1
0
0
0
1
1
0
0
2
0
1
0
3
0
2
1
2
3
0
1
1
1
2
3
2
0
1
2
1
1
0
0
1
0
2
3
1
1
0
0
2
0
2
1
1
0
0
0
2
1
0
1
2
2
1
0
0
0
0
1
2
1
1
2
0
1
3
0
0
0
0
2
0
1
0
1
1
1
2
2
2
0
2
1
2
0
0
1
0
0
1
0
1
1
3
2
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
1
0
1
1
1
1
0
2
2
0
1
2
1
0
0
0
0
0
0
0
2
4
0
0
0
2
0
0
1
1
1
0
2
2
1
2
1
1
4
2
1
0
1
0
0
0
0
0
0
2
0
0
0
1
2
0
2
2
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
2
3
1
0
2
1
1
0
0
0
0
1
2
0
1
2
0
0
0
2
0
1
0
0
2
0
1
1
1
0
3
1
0
1
0
0
0
1
0
0
0
1
0
0
2
0
0
0
2
2
0
0
2
1
0
0
1
0
0
0
1
1
1
0
0
2
1
0
1
2
1
0
0
0
2
0
0
1
2
1
2
1
0
1
1
0
0
0
2
1
2
1
2
1
2
2
0
0
2
0
1
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
1
3
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
1
2
1
0
1
2
1
1
1
0
2
0
0
0
1
0
3
0
2
2
2
2
0
1
1
1
1
0
0
1
2
1
2
1
0
0
0
0
0
0
0
1
1
0
2
2
0
0
0
0
2
0
2
1
0
0
2
0
0
0
2
0
0
0
1
1
0
0
1
2
0
2
1
2
0
1
0
3
0
2
1
2
2
0
1
1
1
0
0
1
0
2
1
0
0
1
2
0
2
0
2
0
0
1
1
1
0
1
2
0
1
2
0
1
2
0
0
1
2
0
1
0
0
0
0
2
0
0
1
1
0
0
0
2
0
0
1
0
0
1
1
1
0
0
1
0
2
0
0
0
2
1
2
1
1
0
1
1
1
0
1
2
0
0
1
2
0
0
1
0
2
0
1
0
0
0
2
0
0
1
0
0
0
2
0
1
0
0
0
0
2
0
2
0
1
0
0
0
0
2
0
1
0
0
0
0
1
1
1
0
2
0
1
2
0
1
0
1
0
0
2
0
1
0
2
0
0
0
1
0
0
0
2
0
0
1
0
0
0
1
0
1
1
0
2
1
0
0
2
2
2
1
1
1
2
1
1
2
1
0
2
0
0
0
1
0
1
1
2
2
1
0
2
2
2
0
1
1
1
1
1
0
2
1
1
2
0
0
0
0
0
1
2
1
0
0
1
0
1
0
1
0
2
1
1
2
2
0
1
2
1
0
1
1
2
2
0
2
0
0
0
1
2
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
2
1
0
1
2
2
2
0
1
1
1
0
0
2
0
1
0
0
0
2
1
0
2
1
0
0
1
1
0
0
0
2
1
0
0
0
2
0
0
2
1
1
2
0
0
1
0
1
0
2
0
0
0
0
2
2
2
2
2
0
1
1
1
0
2
2
0
2
0
0
2
0
2
2
0
0
1
1
2
0
1
1
0
1
0
2
2
1
0
1
0
1
0
0
1
1
4
0
1
1
0
0
2
1
1
0
0
2
0
1
1
0
0
2
1
1
0
1
1
2
1
2
0
0
1
1
0
1
0
0
1
1
1
2
0
0
0
1
1
0
0
1
2
0
1
1
2
1
0
5
0
0
2
1
0
0
1
0
0
0
0
0
0
2
2
0
0
1
0
1
1
2
0
0
0
0
0
0
0
1
1
0
1
1
0
1
0
2
0
0
2
0
0
1
1
1
1
2
0
1
1
0
0
0
0
0
0
2
2
2
0
0
0
1
0
1
0
0
1
2
0
1
3
0
0
1
2
0
1
2
0
2
0
1
2
0
1
2
0
0
0
1
2
0
1
0
1
1
1
1
0
0
2
1
1
1
0
0
0
0
1
0
0
1
3
2
0
0
0
1
0
3
1
0
1
0
0
1
0
0
1
0
1
0
1
1
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
2
1
2
1
0
2
0
1
0
0
2
1
0
2
2
4
1
2
2
0
0
1
2
0
0
0
0
1
1
2
1
0
0
0
1
0
2
1
0
0
1
1
2
0
1
0
1
3
0
0
0
1
1
1
1
1
2
1
0
0
2
0
0
1
1
2
2
1
2
2
2
2
1
2
1
1
1
1
2
0
4
1
0
0
0
0
1
0
0
1
0
1
0
0
2
1
0
0
0
0
1
2
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
11
1
1
0
0
0
0
1
0
1
0
1
0
0
0
1
1
2
0
1
0
2
0
1
2
1
0
3
0
1
0
0
1
1
0
1
0
2
0
0
0
1
0
0
0
1
2
0
1
0
1
0
0
0
0
2
0
1
1
0
0
0
1
2
0
2
1
0
2
0
1
0
2
0
0
2
2
2
0
0
1
0
0
1
0
1
0
0
0
1
0
2
1
0
0
1
0
2
0
2
0
2
0
1
1
0
1
0
0
1
0
0
1
1
2
0
2
3
1
2
0
0
2
1
0
1
2
1
1
1
3
0
1
2
1
0
0
0
0
0
2
1
0
1
0
1
0
1
1
2
1
0
1
2
1
0
0
1
0
1
1
1
2
1
0
0
1
1
0
0
1
1
0
0
2
0
0
0
2
0
1
0
0
1
0
1
1
4
1
1
0
0
2
1
1
0
2
2
0
1
0
2
2
1
1
0
0
1
1
1
1
2
7
0
1
0
0
0
0
1
2
1
2
0
0
0
3
2
1
0
1
0
1
1
2
1
0
1
0
2
0
0
2
1
0
1
1
2
3
3
1
0
0
2
2
2
0
0
1
0
1
2
0
0
2
0
1
2
1
0
1
0
0
0
2
1
1
0
0
0
0
3
0
0
1
0
2
1
1
0
0
0
0
1
1
0
2
1
2
0
0
1
1
0
1
1
0
2
2
2
0
1
0
0
3
1
1
1
0
0
1
1
1
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
1
1
2
1
1
1
2
1
1
1
1
2
0
0
0
2
0
0
0
0
1
0
0
0
1
5
2
1
1
1
0
1
1
1
0
0
1
0
0
2
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
2
1
0
0
1
1
2
3
0
0
0
1
0
0
1
0
2
0
1
0
0
1
0
2
0
0
2
0
0
1
0
1
0
0
1
0
1
0
2
1
1
1
2
0
0
1
0
0
2
0
0
0
1
0
0
1
0
2
1
2
1
1
2
0
2
1
0
1
0
2
1
0
0
1
0
1
0
1
1
0
0
2
0
1
3
0
0
0
2
0
0
2
2
1
0
0
2
1
0
0
0
1
0
0
0
0
0
2
2
0
1
0
1
0
0
0
0
0
2
1
0
0
1
2
1
1
0
0
2
1
0
0
0
2
0
0
0
0
1
1
1
0
1
0
2
0
0
0
1
1
0
0
0
2
0
0
0
1
1
0
1
0
2
1
1
1
1
0
2
1
0
0
0
1
0
1
2
1
0
1
0
0
2
0
1
0
0
1
0
0
0
1
0
1
1
0
0
1
0
0
1
1
2
0
0
1
4
2
0
1
1
0
1
1
0
0
0
2
0
2
1
1
1
0
2
1
1
0
0
0
1
1
0
0
2
1
2
2
1
1
1
1
0
0
0
2
0
2
0
0
0
0
0
1
2
1
1
0
2
0
0
0
0
0
1
1
1
3
2
0
0
1
1
1
1
0
2
0
1
1
0
1
2
0
2
2
0
2
0
0
0
2
1
0
0
0
1
0
2
0
0
1
0
2
2
1
1
0
1
1
0
1
0
2
1
2
1
1
1
0
2
0
0
0
2
2
1
0
1
0
2
2
0
0
2
2
1
2
1
0
1
0
1
0
2
0
1
2
0
0
1
1
0
0
0
0
1
0
0
0
2
0
2
0
0
0
2
0
1
0
0
0
0
1
0
1
1
0
0
1
2
1
0
1
0
1
1
2
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
1
2
1
1
2
1
3
1
1
1
1
0
0
0
2
2
0
2
1
0
2
2
1
0
0
2
0
1
1
0
0
1
1
0
0
1
1
0
2
1
0
0
2
0
1
0
1
0
0
2
0
0
2
0
1
0
0
1
0
0
0
1
0
0
2
0
1
0
1
1
2
2
1
0
1
0
2
1
2
1
0
0
0
0
1
0
1
2
2
1
1
0
2
2
0
0
1
1
0
0
0
2
1
0
1
2
0
1
0
0
2
1
2
1
1
0
0
0
0
1
1
2
0
1
2
0
2
0
0
1
0
2
2
0
1
0
0
0
2
1
1
1
1
2
2
1
0
1
1
1
1
0
0
0
0
2
0
2
0
0
0
0
1
0
0
1
2
1
0
0
0
1
0
2
0
1
1
1
0
1
1
2
2
0
1
2
1
1
1
0
1
2
1
1
0
0
0
0
2
0
1
0
0
1
1
0
0
2
1
2
2
0
0
2
1
0
1
0
1
1
0
1
2
0
0
2
0
0
0
0
0
2
0
1
0
1
2
2
0
2
0
1
1
2
0
1
1
0
1
1
0
0
0
0
1
0
1
2
1
1
1
2
1
1
0
2
4
2
4
1
0
1
2
0
2
0
1
1
2
1
2
2
0
1
1
1
1
0
0
2
0
0
0
0
0
0
1
1
0
0
1
0
1
0
1
0
1
0
0
0
1
1
1
2
1
1
1
0
0
0
2
1
2
1
1
1
5
0
1
2
0
0
2
0
2
1
1
2
0
1
0
1
1
1
0
1
0
0
0
0
1
1
1
1
1
1
0
0
2
2
0
0
0
1
2
0
0
1
1
0
2
2
1
2
1
0
0
2
0
0
0
2
1
0
2
0
1
0
2
1
0
0
0
1
0
0
2
0
1
0
0
2
0
0
1
1
3
1
1
2
1
0
1
2
0
1
1
0
0
1
1
0
0
0
1
0
0
1
0
0
2
1
0
1
0
2
0
0
0
1
2
1
1
0
2
1
1
1
0
2
1
1
0
2
0
3
0
1
0
0
1
0
2
1
0
1
0
2
0
0
1
0
1
0
2
1
1
0
1
2
0
2
1
1
0
0
0
2
1
0
2
2
0
1
1
0
1
1
0
1
0
2
0
0
2
0
1
1
0
2
0
2
1
0
1
0
0
2
0
2
0
0
2
0
2
0
2
0
0
0
0
1
0
0
2
1
0
2
0
1
0
3
0
2
1
1
0
0
0
2
0
0
0
1
0
2
1
1
2
0
0
1
1
1
1
1
0
0
0
1
0
2
0
1
1
2
0
0
0
1
0
2
0
1
2
3
0
0
2
0
3
0
0
0
1
1
0
0
0
0
2
2
0
1
1
1
4
1
1
2
1
1
0
0
0
0
1
1
2
0
0
2
1
2
1
0
2
1
1
0
0
0
0
0
1
0
2
2
2
0
0
1
1
1
0
0
2
1
1
2
1
0
1
2
2
0
0
0
0
0
1
2
2
1
0
0
0
1
2
0
0
1
0
2
1
0
1
2
1
2
1
1
0
0
1
0
0
1
1
1
0
2
0
1
2
1
0
0
1
1
1
0
0
0
0
1
2
0
0
0
0
1
1
0
0
1
0
2
2
0
0
0
2
0
1
1
0
0
1
1
1
0
0
0
2
2
0
0
3
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
1
2
2
2
1
0
0
1
1
1
0
0
2
0
1
0
1
0
0
1
0
2
1
0
1
2
0
1
2
0
1
0
0
1
2
1
0
0
1
0
2
2
1
1
0
2
0
0
1
0
2
1
0
1
1
1
0
1
0
0
0
0
0
0
1
0
2
2
0
0
2
0
1
2
1
3
1
2
1
2
1
1
0
1
1
0
0
0
1
1
2
1
0
0
0
0
1
0
0
1
1
0
1
2
0
0
0
0
0
0
0
2
1
1
2
1
1
0
3
2
0
1
1
1
1
2
3
1
2
1
1
0
2
0
0
2
0
0
0
2
0
1
2
1
0
1
0
0
1
0
0
1
0
0
1
1
0
0
1
1
1
1
4
0
0
1
0
2
0
2
0
0
2
1
0
1
2
0
0
0
3
1
0
2
1
0
1
1
1
0
4
0
1
2
0
0
1
0
0
1
1
2
0
2
0
0
0
0
2
0
2
2
0
1
1
0
1
3
0
1
1
2
1
1
2
0
0
1
2
2
0
2
2
0
1
0
1
0
0
2
0
1
1
0
1
2
1
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
2
0
0
0
1
2
1
0
1
2
2
0
0
3
0
1
1
1
1
0
0
2
0
0
0
0
2
0
1
0
0
0
0
2
2
0
0
2
0
1
0
0
0
1
2
0
1
0
0
1
1
0
0
0
0
1
1
0
1
1
0
0
0
0
0
1
2
1
3
0
2
1
1
0
0
2
0
2
1
1
0
2
1
0
1
1
1
0
0
1
0
2
2
0
1
2
2
0
1
1
0
1
1
0
2
0
0
0
0
1
1
0
0
0
2
0
0
1
1
1
2
0
1
0
4
0
0
2
0
0
2
2
0
0
0
0
0
6
1
0
2
1
1
0
0
1
0
1
0
2
2
1
0
2
0
0
0
1
0
0
2
1
0
0
2
2
0
2
2
1
0
1
2
1
1
1
1
1
1
2
0
3
0
2
0
0
2
0
1
0
0
0
2
0
0
0
2
1
1
1
0
1
1
2
0
1
1
2
0
0
0
3
0
2
1
0
1
1
0
1
0
1
2
1
1
0
2
1
0
0
0
0
2
0
0
0
1
0
1
1
1
0
2
0
3
1
0
1
0
0
0
2
0
1
1
0
0
1
2
0
0
2
0
2
2
2
0
1
0
0
0
2
0
0
0
0
0
0
0
1
1
2
1
0
0
2
1
2
0
1
0
0
0
1
2
1
2
0
0
0
0
0
0
0
0
2
0
3
0
0
0
1
2
0
1
2
0
1
0
1
0
2
1
1
1
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
1
0
0
0
3
0
1
0
2
1
0
0
2
0
0
0
2
1
1
0
1
1
0
1
1
0
1
0
0
2
0
0
1
1
0
1
2
0
0
0
0
2
1
3
2
3
0
0
0
2
0
0
2
2
0
0
1
2
0
3
0
0
0
1
2
1
0
1
0
1
2
0
2
0
2
2
0
0
0
0
1
0
0
1
3
1
2
1
0
0
1
2
2
1
0
0
0
0
1
1
0
0
2
0
0
1
1
0
2
0
1
0
0
0
0
0
1
0
2
0
0
1
2
1
1
2
0
2
1
0
2
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
1
1
0
0
2
0
0
0
0
0
2
0
1
1
1
0
1
2
1
1
1
0
1
0
0
1
2
0
0
2
2
1
1
0
0
0
0
1
1
0
2
1
0
0
0
1
0
1
2
3
1
1
0
0
1
2
1
2
2
2
0
0
1
2
0
1
2
2
1
1
0
0
1
2
1
2
0
1
0
3
1
1
2
1
1
1
1
2
1
0
1
0
0
1
1
0
0
1
2
0
2
0
0
0
0
0
2
1
0
1
1
0
0
0
1
0
1
1
4
2
1
1
1
0
1
1
1
0
0
0
0
2
0
0
0
1
0
1
0
1
0
0
0
0
0
0
2
1
1
0
1
1
1
0
0
1
0
0
1
2
1
1
0
0
1
1
1
2
0
0
0
2
0
0
1
0
2
0
0
2
1
0
1
0
1
2
1
2
0
1
0
1
0
2
0
0
2
0
0
1
1
2
1
0
2
1
0
1
2
1
1
0
2
1
0
1
0
2
2
0
0
1
1
0
0
0
1
1
1
0
0
2
1
0
2
1
0
1
0
2
1
1
2
0
2
0
1
1
2
0
0
0
0
2
0
1
0
2
0
0
0
2
0
0
0
0
1
1
0
1
4
1
1
0
0
2
1
1
2
3
0
2
2
1
1
1
1
3
1
1
0
1
1
2
0
1
2
1
0
1
2
0
0
0
0
0
1
1
0
2
0
0
2
1
1
0
0
0
1
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
1
2
2
1
1
1
2
0
1
0
1
1
2
0
3
0
1
1
1
1
2
1
1
0
1
2
0
1
2
1
1
2
1
0
0
0
2
1
1
1
0
0
0
0
1
0
0
1
1
0
2
0
1
0
1
1
0
1
0
0
1
1
1
1
0
1
2
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
1
0
1
0
1
2
0
0
1
1
0
1
0
2
0
1
0
1
0
1
1
1
1
1
2
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
1
0
0
1
1
2
1
0
0
0
1
1
1
2
1
0
0
1
0
0
0
2
1
2
0
0
0
0
2
0
0
0
1
0
1
1
0
1
2
0
2
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
2
2
2
0
0
0
1
0
1
1
0
0
0
1
2
3
0
1
0
1
1
0
0
0
0
2
2
1
0
1
2
1
3
0
0
0
0
1
2
0
0
0
1
3
2
2
1
1
0
1
0
0
0
0
0
0
1
2
1
0
2
0
0
0
0
1
2
1
1
0
1
0
1
0
2
0
1
0
1
1
0
1
1
1
0
2
1
0
0
1
1
0
0
0
2
1
0
2
0
1
0
0
0
0
1
0
0
1
1
1
1
1
1
2
2
0
2
0
0
0
1
0
0
1
1
1
2
1
2
0
0
0
1
0
2
0
1
1
0
2
0
0
0
1
0
0
0
1
0
3
3
1
0
2
0
0
2
1
1
1
1
0
1
0
0
1
9
1
0
0
2
1
1
1
0
2
2
1
0
0
0
2
0
0
0
1
2
0
0
1
0
0
0
0
0
0
2
0
0
1
1
0
1
0
1
2
0
1
0
1
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
2
0
1
0
0
1
1
0
1
1
0
1
0
0
0
2
1
0
0
1
3
0
1
2
1
1
1
0
0
1
0
2
0
1
0
1
0
1
0
2
0
2
2
0
1
0
0
0
0
0
0
0
2
1
2
0
0
0
1
0
1
0
0
0
1
4
1
2
2
0
0
0
0
2
0
0
2
1
1
1
0
1
1
1
0
0
0
1
1
2
2
1
1
0
1
1
0
1
0
2
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
2
1
0
0
0
0
2
0
1
0
2
1
1
0
0
0
0
1
1
0
0
1
0
0
0
1
0
1
1
2
1
1
0
0
1
1
2
0
1
1
0
0
0
1
1
1
1
1
2
2
1
0
0
2
1
2
0
0
0
1
2
1
0
1
1
0
2
0
0
2
1
1
0
0
0
2
0
2
0
0
0
0
2
0
1
0
0
1
1
1
1
0
0
1
1
1
0
0
1
0
2
1
2
1
0
1
2
1
1
1
0
0
2
1
2
1
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
2
1
0
1
0
1
1
1
1
1
0
2
0
0
0
1
0
0
1
1
0
1
1
1
0
0
0
0
1
1
0
0
2
1
0
0
0
0
0
2
1
0
1
0
0
2
0
0
2
0
2
0
0
2
2
0
1
1
1
1
2
2
1
0
1
2
0
0
3
0
2
1
3
1
0
1
0
2
1
2
1
1
2
1
1
0
0
0
0
0
1
0
0
0
2
0
1
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
2
1
1
0
1
1
0
0
1
0
0
0
1
2
1
1
0
1
0
0
1
0
0
0
1
0
2
2
0
1
2
1
1
0
0
1
1
0
0
2
2
2
2
1
0
0
0
1
1
1
2
0
2
0
2
0
0
2
1
0
0
2
1
0
0
0
0
0
1
2
0
0
2
0
0
0
1
2
2
0
2
2
3
2
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
1
0
2
2
1
1
2
0
0
0
1
0
1
1
0
0
0
0
1
1
0
0
1
2
0
0
2
0
0
0
2
0
0
0
1
1
0
0
0
2
1
0
2
0
1
2
1
0
0
1
2
1
1
1
1
1
0
1
0
1
2
1
0
1
0
0
1
2
0
1
0
0
0
2
0
0
3
0
0
0
0
0
1
1
2
1
3
0
0
2
2
2
3
0
2
2
1
2
0
3
2
0
0
2
0
2
1
0
3
3
0
0
0
0
2
1
0
0
2
2
0
2
1
1
1
2
0
1
2
0
1
0
0
2
1
0
0
0
1
0
0
1
0
1
2
0
1
0
2
1
0
0
0
2
1
1
0
0
0
0
3
1
0
2
0
0
1
0
0
0
0
2
1
0
0
2
0
0
1
0
0
0
0
0
2
2
1
2
1
0
0
0
0
1
0
1
0
0
0
0
0
2
1
2
1
0
0
0
1
2
0
0
2
1
0
1
2
0
0
1
2
0
0
1
0
1
2
1
0
1
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
3
2
2
0
0
0
1
0
0
2
1
1
1
2
1
1
2
1
0
0
0
0
1
0
0
0
1
0
1
1
0
0
2
0
1
1
0
0
0
0
0
0
0
2
1
2
1
1
0
1
0
0
1
0
0
0
0
1
0
1
1
0
2
1
0
1
2
2
2
1
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
1
0
0
2
0
0
1
2
2
0
2
0
2
0
0
0
0
2
1
3
0
2
0
1
0
0
0
0
1
0
1
2
0
1
2
1
1
2
0
1
0
2
1
0
0
1
1
0
2
0
0
1
1
1
0
0
1
2
2
0
0
2
1
2
1
0
0
0
0
2
0
1
1
0
0
0
1
3
1
0
0
0
1
1
1
1
0
0
1
3
0
0
1
2
3
2
1
0
0
0
1
0
1
0
0
2
1
0
1
0
1
1
1
0
0
1
2
2
0
0
0
1
2
0
0
0
0
2
0
0
1
1
2
1
0
0
2
0
0
0
1
2
1
0
0
1
2
1
1
0
2
0
1
0
1
2
0
2
0
0
0
2
1
0
2
1
0
3
1
1
0
1
2
0
0
1
1
2
0
0
2
0
0
2
2
3
0
0
2
1
1
0
1
1
1
2
1
2
2
5
0
0
0
0
1
0
0
2
0
0
2
1
0
0
3
0
1
1
0
2
4
2
2
1
1
0
0
1
0
0
2
0
0
0
1
0
0
2
1
0
0
1
0
0
0
0
0
2
2
1
1
3
0
1
0
2
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
3
0
1
1
3
0
2
1
0
0
0
0
1
3
0
0
0
2
0
1
0
2
1
2
2
1
2
1
0
0
1
0
0
0
1
1
1
0
4
1
0
1
0
0
1
0
0
1
0
2
1
0
0
0
3
2
1
1
1
1
1
2
0
1
0
0
1
1
1
1
1
1
2
4
0
0
0
0
0
1
1
0
2
1
1
0
2
0
1
1
0
0
1
0
0
2
0
0
0
0
0
0
1
1
0
1
0
3
2
0
1
0
0
2
0
0
0
0
2
1
0
1
1
0
0
1
0
0
1
1
1
0
1
1
0
0
0
1
2
0
2
2
0
0
0
2
2
1
0
0
0
0
0
1
0
0
0
1
0
1
0
2
0
2
0
2
0
0
2
1
2
0
1
0
0
1
0
1
1
0
2
1
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
1
0
1
0
2
1
1
1
1
0
0
0
1
0
0
1
0
0
1
0
0
1
0
1
1
0
1
2
2
0
2
1
1
0
2
0
0
0
0
2
1
0
0
0
1
0
1
0
2
1
1
0
1
1
2
0
0
0
0
1
1
0
1
0
1
0
2
0
1
1
1
2
0
0
2
0
1
1
0
0
0
0
2
0
1
1
0
3
0
0
2
1
1
0
0
1
5
1
0
1
0
0
1
1
1
0
1
0
2
0
0
1
0
0
0
3
0
2
0
2
0
2
3
0
2
0
0
0
1
0
2
0
1
1
0
0
2
0
1
1
2
0
0
0
0
0
1
0
1
0
1
2
2
0
0
1
2
0
0
2
1
0
0
2
0
0
0
1
0
0
2
2
0
2
2
2
1
1
0
1
0
0
0
0
1
2
2
1
1
0
1
0
1
1
1
2
2
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
1
1
1
2
0
0
2
0
3
1
2
2
1
1
1
0
0
1
2
2
3
0
1
0
1
0
1
1
0
0
1
0
1
0
0
0
0
0
1
0
2
0
1
1
2
0
1
0
0
0
3
2
0
1
1
0
1
1
0
2
0
0
1
1
0
1
1
0
1
0
0
0
1
0
1
2
0
1
1
0
1
2
0
0
1
0
0
2
0
2
0
1
0
0
1
1
0
1
2
0
1
0
1
1
0
1
0
2
1
0
1
1
1
0
0
1
1
1
0
0
1
1
1
2
1
0
0
1
0
0
2
1
0
0
1
1
1
2
1
2
0
0
1
0
0
0
2
1
0
0
1
0
0
0
1
1
0
0
1
2
2
0
1
2
0
1
1
0
1
0
1
0
1
0
1
0
0
1
0
0
1
2
1
1
2
1
1
0
2
1
0
1
1
1
2
1
1
0
1
0
0
0
0
2
1
1
2
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
2
1
1
2
2
1
2
2
2
1
1
0
1
1
0
0
0
1
0
2
2
0
0
0
0
0
1
3
0
0
2
2
1
0
3
0
0
2
1
0
0
0
0
0
0
0
2
0
0
2
2
1
2
2
1
1
0
0
0
2
0
1
0
1
2
0
0
2
0
1
2
1
1
2
1
1
1
0
0
0
2
0
1
1
2
2
2
0
2
1
1
1
0
0
0
1
2
0
2
2
0
0
0
0
0
0
2
0
0
2
2
2
1
1
0
1
1
0
0
0
0
0
3
2
1
1
1
0
1
0
2
1
1
2
0
0
1
1
0
2
0
1
0
0
0
1
2
1
0
0
1
0
1
0
1
0
0
0
3
0
3
0
2
1
0
0
1
0
0
0
2
0
0
0
0
0
1
0
1
2
0
0
0
0
2
1
2
0
0
0
0
1
0
2
0
2
2
0
2
0
0
2
2
0
3
1
0
2
0
2
1
1
0
1
0
0
0
1
0
1
1
3
1
2
1
1
0
0
0
0
1
2
2
0
2
2
0
1
0
0
2
1
1
0
1
3
0
1
1
0
2
1
0
2
2
2
2
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
1
1
2
1
0
0
1
2
0
0
0
0
0
1
1
2
0
0
1
2
0
0
0
1
1
1
0
1
0
2
1
1
3
2
0
1
0
1
1
2
2
1
0
0
2
2
2
0
0
1
0
0
0
2
2
0
1
1
0
1
0
0
1
0
0
0
0
1
0
0
3
2
0
0
0
1
2
1
1
1
0
0
0
0
1
0
0
0
1
1
0
2
0
1
0
0
0
0
0
1
0
3
0
0
0
2
0
1
1
0
1
0
1
1
0
1
0
1
1
1
1
0
1
0
0
0
1
2
1
0
2
1
0
1
0
1
0
0
1
1
0
2
0
1
2
1
2
2
0
1
0
0
0
0
0
0
1
1
0
1
1
1
0
0
0
0
2
0
1
0
0
0
0
1
0
1
1
0
0
1
0
0
2
1
1
0
0
1
3
0
0
1
2
3
2
1
1
0
2
1
2
1
2
0
1
0
0
0
1
0
1
0
3
1
2
0
1
0
0
0
1
0
0
2
0
2
2
1
1
0
2
0
0
1
1
2
0
0
2
0
1
1
0
0
0
1
2
1
2
0
0
1
1
0
1
0
0
1
1
1
0
1
0
0
1
1
0
0
0
0
0
0
0
2
0
0
1
1
1
0
0
0
1
1
0
0
0
2
0
0
0
2
0
1
2
0
0
2
0
0
0
1
0
2
0
0
2
1
0
1
2
1
1
0
1
1
1
2
1
0
0
1
0
2
0
1
0
0
1
2
1
0
1
1
1
0
3
0
2
0
0
1
0
0
2
1
0
0
0
0
0
2
1
1
0
1
0
0
0
1
0
2
1
0
0
1
2
1
0
3
2
1
1
0
0
1
0
2
1
1
1
0
0
1
1
0
0
0
0
0
1
2
5
1
1
0
0
0
1
0
1
0
2
2
2
0
0
0
1
2
0
1
0
2
1
0
1
1
0
1
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
1
2
2
1
1
1
0
1
2
0
0
0
0
1
2
0
0
2
2
1
0
1
0
2
1
1
0
2
0
0
2
1
0
0
0
0
0
1
1
0
0
1
0
5
1
0
1
1
1
0
0
1
0
0
0
0
1
2
2
0
2
0
1
0
2
0
0
0
0
1
2
0
1
1
1
0
0
1
0
1
0
2
1
1
2
1
0
4
1
5
0
0
1
0
2
1
2
0
2
1
0
0
1
1
2
0
1
0
1
1
1
2
0
0
1
0
1
0
0
0
1
0
0
1
0
0
2
0
0
0
1
1
0
2
0
0
3
0
0
0
4
0
1
0
0
0
2
2
0
1
0
2
1
0
0
1
0
2
1
0
0
1
2
0
0
0
0
1
1
2
1
0
0
0
1
0
1
0
0
1
1
1
1
0
0
1
2
1
1
1
0
2
2
0
0
0
1
0
2
1
0
0
2
1
0
0
0
1
0
0
1
1
0
1
0
0
0
1
2
2
2
1
0
0
3
3
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
1
1
1
0
1
0
1
1
0
0
0
0
0
0
2
1
1
2
0
2
1
2
0
1
0
0
2
0
0
2
2
1
1
0
1
0
2
2
0
1
0
1
0
0
0
0
3
0
2
1
0
0
2
0
0
1
0
0
1
0
0
2
2
2
1
1
1
1
0
0
0
0
1
0
0
2
1
1
2
0
1
1
2
2
1
1
1
0
1
1
1
0
0
2
0
1
0
0
1
0
0
0
0
0
1
0
2
0
2
1
0
1
0
0
0
0
0
1
0
0
1
0
0
1
3
1
1
0
1
0
2
0
1
1
2
1
1
0
0
0
0
0
1
0
0
2
2
2
2
1
0
0
0
0
1
1
0
0
0
0
2
2
1
1
0
0
1
1
2
2
2
0
0
1
2
0
0
1
0
2
1
1
1
1
1
2
1
1
1
1
0
2
0
0
1
0
0
0
0
2
0
0
2
1
0
0
1
0
0
1
1
2
1
1
0
0
0
0
2
0
2
1
0
0
2
1
0
1
0
1
3
0
1
2
0
1
1
1
0
0
0
0
0
2
1
1
1
2
1
0
1
1
0
1
0
2
2
0
1
2
0
0
1
0
1
0
0
0
1
1
0
0
0
2
1
0
1
2
1
0
1
0
0
2
2
2
0
0
0
0
0
0
0
1
1
2
0
0
0
1
0
2
0
0
0
2
2
1
2
1
0
1
2
2
1
4
0
2
0
1
0
1
0
0
0
1
1
0
0
0
0
2
0
0
2
1
3
0
0
1
0
1
2
0
2
0
0
0
1
1
4
0
0
2
1
0
1
0
2
0
1
0
0
0
2
1
1
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
2
0
1
2
1
0
0
2
0
1
1
2
1
1
1
2
0
2
1
1
2
1
1
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
2
2
0
2
0
0
0
0
1
0
2
1
1
1
0
0
0
1
0
3
0
2
1
2
0
2
1
0
2
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
1
0
2
0
0
0
0
0
1
0
2
2
0
0
2
0
0
1
0
1
1
2
0
0
2
0
2
1
0
0
1
1
3
0
2
0
0
0
0
0
0
1
2
3
2
1
0
0
1
0
2
0
2
0
1
0
0
0
0
0
2
0
0
0
2
1
2
2
1
2
0
0
0
0
1
2
0
1
0
0
0
0
1
2
1
0
0
0
1
0
1
0
1
1
1
0
0
0
0
2
2
0
1
1
0
2
3
2
0
1
0
1
0
2
0
1
1
0
0
0
0
1
0
1
0
2
2
1
0
1
0
2
1
1
2
1
1
0
0
1
2
1
1
1
2
2
0
0
0
0
0
2
4
0
0
2
1
0
0
2
0
0
0
2
0
0
2
1
2
0
1
1
0
0
0
0
2
2
0
0
0
1
0
0
0
0
2
1
0
2
0
1
1
0
1
1
0
2
1
0
0
1
1
2
1
0
1
0
0
0
0
1
0
0
2
1
3
2
2
0
2
0
1
0
0
1
1
1
1
1
0
0
0
0
2
2
1
2
2
1
1
0
2
1
2
0
2
1
0
0
2
1
2
0
0
2
0
1
2
1
1
1
2
0
0
0
2
0
1
1
0
1
0
0
2
0
1
2
0
0
0
0
0
0
1
1
0
0
0
0
1
0
2
0
1
2
0
1
0
0
0
0
1
2
0
0
1
1
0
1
0
0
0
0
2
0
1
2
0
1
0
1
2
2
1
0
0
0
1
1
2
1
0
0
2
0
2
1
1
0
0
1
1
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
3
0
1
0
2
2
0
1
0
0
2
1
0
0
1
1
1
2
0
3
0
1
0
1
0
2
0
0
1
0
0
2
0
1
1
1
0
2
0
1
1
0
2
1
1
2
0
1
0
0
0
0
0
0
0
1
0
1
1
0
1
2
0
0
0
0
1
0
0
2
0
1
0
2
2
2
0
1
1
0
0
0
2
0
2
2
2
0
1
0
0
0
1
1
1
1
1
0
3
3
0
1
0
1
1
2
2
1
0
1
0
0
1
0
1
0
2
0
1
1
0
0
3
0
0
0
0
0
1
0
2
0
1
0
1
0
0
0
0
1
1
0
2
1
1
0
0
1
1
1
1
0
0
0
0
0
0
1
0
2
0
0
2
0
1
2
0
0
0
2
2
0
2
2
0
0
1
2
1
1
0
1
0
0
1
0
1
2
0
2
0
0
2
0
0
0
1
0
1
2
0
2
1
0
0
1
0
0
0
2
2
2
2
0
1
3
2
0
2
1
1
1
1
0
1
0
2
0
0
0
0
0
2
0
1
1
0
0
0
2
4
2
0
0
1
0
0
0
1
0
1
1
0
1
1
1
1
2
2
0
0
1
2
1
0
2
0
0
1
2
0
2
1
2
0
0
0
0
2
2
2
2
2
0
1
2
0
1
1
1
0
3
2
0
3
0
0
0
1
0
1
1
0
2
1
0
1
0
2
0
0
1
1
2
1
1
1
2
2
0
0
0
0
0
1
2
1
2
0
3
0
1
2
0
0
1
1
1
0
1
0
3
0
1
0
1
1
0
2
1
1
1
0
2
0
2
0
0
0
0
0
1
1
2
0
0
0
2
0
1
1
4
2
0
0
1
0
0
0
0
1
0
1
2
0
0
0
2
0
2
2
2
0
2
0
1
0
1
1
0
0
0
1
2
1
0
0
1
0
1
2
1
1
0
1
1
0
0
0
0
0
0
2
1
2
0
0
1
0
2
0
2
0
0
0
1
0
2
2
2
0
0
2
1
2
1
1
0
0
1
0
1
2
0
0
2
0
0
3
0
2
1
2
0
1
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
1
0
0
2
0
0
0
1
0
1
3
2
0
2
2
0
0
1
0
1
1
1
0
0
2
0
0
1
1
2
2
2
0
0
1
2
1
0
0
1
1
1
0
0
2
1
0
2
0
1
0
1
1
0
2
0
0
1
2
0
0
0
1
0
0
1
0
0
1
2
0
2
1
1
1
2
0
2
2
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
1
2
1
0
0
0
1
1
1
0
0
1
1
2
1
0
0
0
0
2
1
0
2
1
1
2
0
0
0
0
2
0
0
1
0
2
0
1
0
1
0
0
0
0
2
0
1
1
0
0
1
1
2
0
0
3
0
2
0
0
1
0
0
0
0
1
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
2
0
1
0
1
2
0
2
1
2
2
2
1
1
1
0
0
0
0
0
0
1
0
1
0
1
2
2
1
0
1
0
1
0
2
2
0
0
1
1
2
0
1
1
1
0
2
1
1
2
1
1
0
0
1
2
2
0
0
0
1
0
1
0
1
0
1
2
3
1
0
1
1
2
2
1
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
2
0
2
1
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
2
0
2
0
1
0
3
0
1
0
1
0
0
1
0
1
0
0
1
2
0
1
0
0
0
0
0
2
0
0
1
0
1
0
0
1
0
1
0
1
1
0
1
1
0
2
1
4
0
0
5
1
0
0
0
0
0
2
0
1
0
2
2
2
0
0
1
1
1
1
0
0
1
0
0
1
0
1
2
2
2
0
0
0
2
2
1
0
0
3
0
1
3
1
1
0
0
1
0
1
1
0
2
0
0
0
0
1
0
2
1
1
1
0
2
2
0
2
1
1
1
0
1
0
0
1
1
2
0
1
1
2
1
0
2
0
3
0
2
1
0
2
0
3
0
0
0
0
0
1
1
1
0
2
2
0
1
0
1
0
0
1
1
1
1
1
1
0
0
0
2
1
0
0
1
0
2
2
0
1
0
2
0
1
2
0
1
1
1
2
2
2
0
0
1
1
0
1
0
0
0
1
0
1
2
1
1
1
1
1
0
1
2
1
0
0
0
0
2
0
1
1
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
2
1
2
0
0
1
0
0
0
1
1
2
0
2
0
1
2
0
2
0
0
1
0
0
1
2
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
2
0
0
0
1
2
0
1
0
0
0
2
0
2
1
2
1
0
0
1
0
0
0
2
0
1
2
2
2
0
0
1
0
2
0
0
0
0
0
0
1
0
1
0
0
0
2
1
0
0
0
2
2
2
0
0
1
0
0
0
0
0
2
0
0
0
1
0
2
0
0
1
2
1
1
0
3
2
0
0
1
0
1
0
0
2
2
1
1
0
0
2
2
0
1
1
0
0
0
1
1
0
1
1
2
0
1
1
1
0
3
2
1
1
0
2
1
1
0
0
0
2
1
1
2
2
0
0
1
0
0
0
0
1
0
0
1
0
0
1
1
1
1
1
1
1
1
0
1
0
1
0
0
0
0
1
1
0
1
0
0
0
0
1
0
1
0
2
0
0
1
1
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
2
1
1
2
0
2
0
0
2
1
0
0
2
0
0
1
2
1
2
0
0
0
1
0
1
2
0
0
1
0
1
0
0
0
0
0
2
2
1
0
2
2
2
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
2
1
2
2
0
0
2
0
1
1
1
0
2
0
1
0
0
1
0
1
2
2
1
0
1
1
2
0
2
0
3
2
0
0
0
2
2
2
2
1
0
1
2
3
0
0
0
0
1
0
2
0
1
1
0
4
1
0
1
0
0
1
2
2
0
0
0
0
1
1
4
0
0
0
0
2
0
1
2
2
1
1
0
1
0
0
0
0
2
0
1
0
0
2
2
0
2
2
0
0
0
0
6
1
0
1
0
0
2
2
1
1
0
2
1
5
0
1
1
0
1
0
0
0
0
1
1
1
0
0
1
0
0
2
0
1
0
0
0
1
0
1
0
1
1
2
1
0
0
1
1
1
3
1
3
0
1
1
2
2
0
0
2
1
0
1
0
0
2
1
0
0
0
1
2
0
1
1
1
2
0
2
0
1
1
2
0
0
0
1
2
2
0
0
0
0
1
0
0
2
1
2
1
0
0
0
0
2
1
2
0
0
1
0
0
0
2
0
2
2
0
1
0
1
2
2
0
0
0
1
0
2
0
0
0
0
1
1
2
1
1
0
2
1
1
1
1
0
0
0
0
1
0
1
1
0
1
2
2
0
1
1
0
1
0
1
0
2
1
1
0
0
1
1
1
1
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
1
0
2
0
0
2
0
0
1
0
2
0
0
0
2
1
2
0
1
0
0
1
1
1
0
0
1
0
0
0
2
1
1
0
0
1
1
0
1
1
0
0
0
1
2
2
0
0
1
1
1
0
0
1
1
0
0
1
0
1
0
2
2
0
2
2
2
1
0
1
2
0
1
2
0
0
2
0
0
2
0
2
1
2
2
1
2
0
1
0
0
2
0
3
2
2
0
2
3
0
0
0
0
1
0
0
0
0
1
4
0
1
0
0
1
1
0
0
2
1
0
1
1
1
3
2
1
1
0
0
2
0
2
0
0
1
1
1
1
0
1
0
1
0
1
1
1
0
0
0
0
0
0
1
0
1
1
1
0
1
2
1
2
0
0
2
2
0
2
1
0
1
1
0
2
1
0
1
0
1
1
0
0
2
0
0
1
0
0
1
0
0
0
1
1
1
0
1
2
2
0
1
0
1
1
0
2
2
0
0
1
0
0
0
2
0
0
1
1
0
4
0
2
1
2
2
1
1
1
2
0
0
0
1
0
2
0
2
1
1
0
0
0
0
2
2
1
0
0
2
2
1
0
1
4
1
0
0
2
0
0
2
2
1
0
1
2
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
1
2
1
1
1
1
0
1
0
0
0
0
1
0
2
0
2
0
1
2
1
0
0
1
1
0
0
1
0
0
2
2
2
0
2
0
1
1
1
1
1
2
1
3
1
0
0
0
0
0
2
2
0
1
0
0
0
2
2
0
2
2
2
0
0
0
1
2
1
2
0
0
0
0
2
2
2
0
1
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
1
2
1
1
3
2
0
0
0
1
0
0
1
2
1
1
0
0
2
2
2
1
2
1
1
0
1
1
0
1
1
2
2
0
1
1
1
0
2
0
1
0
0
1
1
1
1
1
0
0
0
0
2
0
1
2
1
1
0
0
1
2
0
1
0
1
0
1
0
2
1
0
1
0
1
0
0
1
1
1
0
1
0
0
2
2
0
1
2
0
0
0
1
1
1
1
2
2
2
1
1
0
0
0
0
1
0
2
1
1
0
2
0
1
2
2
0
0
1
2
0
0
0
0
0
0
2
2
0
1
0
0
0
0
2
1
1
0
0
0
2
1
0
0
0
1
2
2
0
0
3
1
2
0
0
1
2
1
0
0
0
0
0
1
2
0
0
1
1
1
0
0
0
0
1
0
0
0
1
0
2
0
1
0
2
0
0
1
1
1
0
0
1
1
2
0
1
0
1
0
0
1
0
0
0
0
0
1
1
1
0
2
0
0
1
2
4
0
2
0
1
2
0
2
1
0
1
1
0
0
2
0
0
0
0
1
0
0
1
0
1
1
1
1
0
1
1
2
1
1
2
0
0
0
1
0
0
1
0
0
2
0
2
2
0
1
1
0
0
0
2
0
1
0
0
0
0
1
0
1
0
0
1
0
3
0
1
0
0
0
1
1
0
2
2
0
2
2
3
0
1
1
0
2
2
1
2
1
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
1
1
0
0
1
2
1
0
0
2
2
0
0
0
0
0
0
0
2
1
0
0
0
2
1
3
2
0
2
1
3
0
0
1
1
2
2
0
0
2
3
0
0
0
0
0
1
1
1
0
0
1
1
1
0
0
0
0
1
2
0
2
1
0
1
0
1
0
1
0
3
2
0
0
1
0
1
1
0
0
1
0
0
0
0
1
1
0
2
1
2
0
0
1
0
2
0
0
0
2
0
2
1
1
0
0
0
2
0
0
0
2
2
0
1
2
0
1
1
1
0
1
1
1
2
1
0
1
2
2
0
0
0
0
0
0
2
1
2
2
0
0
0
1
3
0
0
1
1
1
1
3
0
1
0
1
0
1
0
0
0
1
1
0
0
0
0
2
1
2
0
0
1
0
1
1
1
1
2
0
0
0
1
0
1
1
1
1
2
1
0
0
1
1
1
0
1
1
0
1
2
1
1
0
1
1
1
0
0
0
0
1
0
0
1
0
1
0
0
0
1
3
2
0
0
0
0
2
0
1
0
1
1
0
1
2
0
0
1
0
2
1
1
1
1
1
1
0
0
2
2
0
2
2
1
0
0
0
1
0
0
1
0
1
0
0
1
1
0
0
0
0
1
0
1
1
0
0
0
2
0
0
1
0
0
2
0
0
1
0
1
2
0
2
0
0
1
1
4
1
1
2
0
0
0
1
2
0
0
3
2
0
1
2
1
1
2
0
0
1
1
1
0
1
3
0
0
2
0
2
0
1
0
2
1
1
0
0
0
0
0
1
1
0
1
1
0
0
1
0
0
2
1
0
1
0
1
1
2
1
0
0
0
1
2
1
1
1
0
1
0
2
1
1
1
1
1
0
0
0
1
0
1
0
1
2
1
0
0
1
1
2
0
1
0
2
1
0
0
2
0
0
2
1
1
1
1
0
0
0
0
0
0
1
4
0
0
1
1
2
0
2
1
0
0
1
0
0
0
1
1
1
2
1
0
0
0
0
0
1
1
1
0
1
0
2
0
0
1
1
2
2
0
0
2
0
2
1
1
0
2
1
1
1
1
1
3
1
2
0
4
1
2
0
0
0
1
3
1
0
0
0
1
1
2
0
0
1
0
0
0
0
0
1
0
1
0
0
1
2
2
0
1
2
1
2
0
2
1
1
0
1
2
0
0
0
0
1
2
0
2
2
1
1
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
2
0
3
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
2
1
1
0
1
0
0
2
2
1
0
1
2
1
1
2
0
0
0
1
1
0
0
0
0
2
1
1
1
0
1
1
1
2
0
0
0
0
0
1
0
1
1
0
2
1
0
0
1
0
3
2
0
0
1
1
2
0
0
2
0
1
0
0
1
1
1
0
1
1
0
1
2
0
0
0
1
0
0
0
1
1
0
1
0
2
0
2
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
1
1
1
2
0
2
2
1
0
1
2
1
2
0
0
1
1
2
1
2
2
0
1
0
1
0
1
0
1
2
0
1
2
0
2
2
1
0
1
2
1
0
0
2
2
0
2
0
2
0
1
1
1
0
0
2
3
0
0
2
1
1
0
1
2
1
1
1
0
0
2
0
0
1
1
1
1
0
0
1
2
1
2
1
1
0
1
0
2
0
0
0
0
2
1
2
2
0
0
0
1
0
2
1
0
0
0
1
2
0
0
1
0
0
1
1
0
0
2
2
1
0
0
2
0
1
0
0
1
2
3
0
1
2
0
0
1
0
1
2
0
1
0
1
1
0
1
0
0
1
0
1
1
0
1
1
2
1
3
1
0
0
0
0
0
0
0
1
0
0
0
1
2
0
2
0
0
0
0
2
1
2
1
0
1
1
1
0
1
1
2
1
2
1
2
2
1
0
0
2
1
2
0
3
0
2
1
0
0
1
2
0
1
0
0
2
0
1
1
0
1
0
0
0
0
0
0
2
2
0
2
0
1
0
0
2
0
0
3
1
0
0
0
2
1
0
1
0
1
2
0
0
2
2
0
0
2
0
0
0
0
1
1
1
0
3
2
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
3
1
0
1
0
0
1
0
0
0
2
0
0
0
0
2
0
2
0
0
2
1
0
1
2
1
0
0
0
2
1
2
0
0
1
1
0
2
0
0
2
2
2
0
2
0
1
1
0
1
0
2
0
2
0
1
1
0
1
0
1
1
3
1
0
1
1
0
0
1
0
1
1
0
0
1
1
1
2
2
0
0
0
0
2
2
0
0
0
0
2
2
1
0
1
1
1
1
2
1
0
1
2
1
0
0
1
0
0
0
1
1
0
0
0
1
0
2
0
0
0
1
0
1
0
0
1
0
2
1
2
1
2
1
1
0
0
2
0
0
1
0
2
0
0
2
0
0
2
2
2
0
0
2
5
2
1
0
2
0
0
1
0
0
0
1
0
0
2
0
0
0
1
0
1
0
1
1
2
1
0
1
0
0
1
0
2
2
0
0
1
2
1
2
0
1
2
0
1
1
0
1
0
0
1
0
0
0
0
2
0
0
0
1
2
2
0
1
0
0
3
0
1
0
1
6
0
3
1
5
0
1
2
0
0
1
0
0
1
0
2
2
0
1
0
1
0
0
1
1
2
0
2
3
2
1
1
0
0
2
0
1
0
1
0
2
2
1
2
0
2
0
1
2
0
1
1
1
1
2
1
0
3
1
0
1
0
0
0
0
0
2
0
2
1
2
0
1
2
1
0
2
1
0
1
1
1
0
0
4
2
1
2
1
2
1
0
0
2
2
0
0
1
0
2
3
0
0
0
0
1
0
1
0
0
0
0
0
1
0
3
0
0
1
1
0
3
0
0
1
0
1
1
0
0
2
2
0
0
0
1
0
0
1
0
0
0
0
0
1
2
1
1
1
0
2
0
2
0
0
0
2
1
0
0
1
0
1
1
1
0
0
1
0
0
0
1
1
0
0
1
1
0
1
1
0
1
0
1
1
0
0
2
0
0
0
1
0
0
0
0
0
0
2
2
1
2
7
1
1
2
0
0
3
0
0
2
1
2
0
0
1
0
0
0
0
0
1
1
1
0
0
0
1
0
0
2
2
0
0
1
0
2
1
0
1
0
0
0
1
0
0
1
1
1
1
1
0
0
2
0
0
0
1
11
0
2
1
0
1
1
0
2
2
0
0
1
1
1
0
2
0
0
1
1
0
1
1
1
0
2
1
2
1
0
2
1
2
2
2
0
0
0
0
1
1
2
1
0
1
1
0
0
0
2
0
0
0
0
1
0
1
0
0
1
0
2
0
0
1
1
0
0
0
2
1
2
2
0
1
3
0
2
0
2
0
2
1
0
0
0
2
2
2
2
2
1
0
0
0
1
0
1
0
1
1
0
2
0
0
0
0
2
2
2
0
0
1
1
1
0
0
1
0
0
0
2
0
0
2
0
1
2
2
0
2
0
1
1
0
0
2
1
1
0
0
0
0
0
0
2
2
0
0
0
0
2
0
2
0
0
0
0
1
1
0
0
0
1
2
0
0
0
2
2
0
1
0
1
1
2
0
1
0
0
2
2
2
1
1
0
0
1
1
1
0
0
0
2
0
0
0
0
1
0
1
1
0
2
2
1
1
1
2
1
1
1
2
1
0
2
0
1
2
0
0
2
2
0
2
1
1
1
1
2
0
1
1
1
0
1
0
0
0
1
1
0
0
1
2
0
1
0
2
0
1
0
0
1
1
0
0
1
1
1
1
0
1
1
0
1
0
2
1
3
1
1
0
2
0
1
2
2
1
0
2
0
0
0
0
0
2
1
1
0
2
0
2
1
0
0
2
0
0
0
0
1
1
0
4
0
0
0
0
2
0
0
0
0
1
1
2
2
2
1
2
0
1
2
2
1
0
1
0
0
0
0
0
1
1
0
2
2
0
2
2
2
1
2
1
2
2
1
1
1
0
1
0
1
0
2
0
0
0
0
1
0
0
0
3
2
0
2
0
1
0
3
0
0
1
1
0
3
1
0
2
1
2
0
0
0
0
0
0
1
0
1
1
1
0
1
1
2
0
1
2
0
2
1
0
0
0
1
0
1
0
0
1
0
0
0
0
2
2
0
2
1
0
0
1
0
0
1
2
0
0
1
1
2
1
1
0
0
1
0
0
1
1
0
1
0
2
0
0
2
0
1
0
0
2
2
1
2
1
0
0
0
1
0
1
1
2
0
1
1
2
1
0
0
0
1
1
0
0
3
1
0
1
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
2
1
0
2
1
2
0
1
1
2
1
2
0
0
0
2
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
2
1
0
1
2
3
2
1
0
0
1
1
1
1
1
2
0
0
0
0
1
0
0
2
1
0
0
1
0
0
0
0
1
0
0
2
1
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
2
0
2
1
0
0
1
1
2
1
1
1
0
0
1
0
1
1
0
0
1
1
2
0
0
2
0
1
0
1
1
1
0
2
0
2
0
0
1
0
1
0
1
1
0
2
0
2
0
0
0
2
1
0
1
1
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
5
1
2
0
2
0
0
0
1
2
2
1
2
0
1
0
1
2
0
0
2
0
2
1
0
1
0
0
1
0
0
0
2
1
2
0
1
0
0
0
1
1
0
0
0
0
1
2
2
0
1
1
2
0
0
1
2
0
0
2
0
0
2
0
2
2
0
1
1
0
1
0
1
0
2
2
1
0
1
0
0
0
0
1
0
1
0
1
1
2
1
1
0
5
2
0
2
2
1
0
2
1
0
0
3
0
1
0
1
2
2
0
1
0
0
0
0
1
0
1
1
2
2
0
1
0
1
1
0
2
1
1
1
4
1
0
1
1
1
0
1
2
0
1
0
0
0
0
0
1
2
1
1
0
0
2
0
0
2
0
1
0
0
0
1
1
1
0
0
0
1
2
0
1
2
1
0
1
0
0
0
2
0
2
0
1
1
1
0
1
0
1
0
1
1
0
2
2
1
0
1
1
2
0
2
2
0
1
1
1
0
1
2
0
1
0
0
2
1
0
2
2
1
0
0
0
2
1
1
0
1
0
1
1
3
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
2
1
2
2
0
0
6
0
0
1
2
1
0
0
1
0
2
1
0
2
2
1
2
1
2
0
1
2
2
0
1
2
2
1
0
1
0
0
2
0
0
1
0
0
1
2
0
0
3
2
1
1
1
1
0
1
0
1
1
2
0
0
3
1
1
0
0
1
1
2
0
2
0
0
3
1
0
0
1
0
1
2
0
0
2
0
2
1
0
0
0
0
1
0
0
0
1
0
1
2
0
0
0
1
0
0
2
2
2
2
0
0
2
0
0
3
0
0
1
0
0
0
0
1
1
0
1
1
0
1
2
0
0
0
0
2
0
0
2
0
1
2
2
5
2
2
1
0
2
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
2
0
0
1
0
1
1
0
2
0
2
0
2
1
1
2
1
2
0
2
2
1
0
0
1
1
1
6
0
0
1
0
0
1
2
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
2
0
1
0
0
1
0
2
0
2
2
2
0
0
0
0
0
1
1
1
0
2
0
0
0
0
1
2
1
2
2
1
0
2
0
2
0
1
2
0
0
0
2
2
2
1
2
0
0
0
2
2
0
0
1
2
0
2
0
0
2
1
0
0
0
0
0
1
1
0
1
0
0
1
0
2
1
1
2
0
2
1
0
1
2
0
2
0
1
1
1
0
2
0
2
1
1
1
0
0
1
2
0
2
2
0
1
0
0
0
0
3
2
2
1
0
2
0
0
2
2
1
0
1
2
2
0
1
0
2
1
2
1
0
0
0
2
0
1
1
0
0
0
1
1
0
0
2
1
1
1
0
2
0
1
0
2
1
0
1
2
1
0
1
0
1
0
0
0
2
2
2
0
0
0
0
2
0
0
0
0
0
0
0
1
1
1
0
1
2
0
0
0
0
1
2
0
2
0
2
0
1
0
0
0
0
0
0
0
4
1
2
2
1
1
1
2
1
1
0
2
0
0
2
2
1
0
2
0
3
0
0
2
1
0
0
2
0
1
1
0
2
0
1
0
2
1
2
0
1
0
2
0
0
1
0
1
0
0
0
1
2
1
1
0
0
0
7
0
0
0
0
2
2
0
1
0
0
0
0
0
1
1
1
0
0
0
0
1
2
2
3
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
2
0
1
0
2
1
0
0
0
0
1
0
1
1
1
1
0
1
0
0
2
1
2
0
1
2
2
2
0
0
1
2
0
1
0
0
0
1
0
1
1
2
1
0
2
0
0
0
0
1
0
1
1
2
2
0
0
0
2
0
2
1
0
1
1
0
1
0
0
1
0
2
0
1
0
0
0
3
1
0
1
2
2
0
0
2
0
2
0
0
2
2
2
0
0
2
2
0
1
1
0
2
1
0
1
1
1
1
0
0
0
0
1
2
0
2
2
0
2
2
0
0
0
0
0
0
0
0
1
0
1
0
2
1
0
0
1
2
0
0
0
1
2
1
1
2
0
1
1
1
0
2
0
0
1
0
0
0
1
0
1
0
2
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
1
0
2
0
0
0
1
1
0
0
2
2
4
2
0
1
0
1
1
3
1
1
1
0
0
0
0
2
1
2
1
2
0
1
0
0
1
1
0
0
0
0
1
0
1
1
0
2
0
0
0
2
0
0
1
0
0
1
0
2
1
0
1
1
0
1
1
1
0
2
0
0
0
1
0
1
0
0
2
1
0
0
1
1
2
0
0
1
1
0
0
2
0
0
0
1
0
2
0
0
1
1
1
0
0
0
0
1
1
1
1
1
2
1
1
2
1
1
1
0
0
1
0
0
1
1
2
0
0
0
1
0
0
0
0
1
0
0
2
0
2
2
1
2
1
0
0
1
1
3
0
0
1
1
1
1
1
3
2
2
2
1
1
0
0
0
1
1
1
2
0
0
1
1
0
3
0
1
1
0
0
1
0
0
1
0
1
0
0
2
0
0
2
1
1
0
0
0
0
2
0
0
2
2
0
0
0
2
0
1
0
1
0
1
1
1
1
1
2
1
2
2
1
0
0
2
0
0
0
0
1
0
1
2
1
1
0
1
2
0
3
0
1
2
0
2
0
0
2
2
1
0
2
1
0
0
1
0
1
0
0
1
0
2
2
2
2
2
0
2
2
0
1
0
2
0
1
0
2
0
2
3
0
2
1
0
0
1
1
0
2
2
1
1
1
0
1
0
1
0
0
0
2
3
0
1
2
0
0
1
2
0
2
0
0
2
1
1
0
1
2
2
0
0
2
2
1
0
1
1
2
1
0
1
2
2
0
1
1
0
0
0
0
1
1
1
0
2
1
2
1
0
0
2
2
1
1
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
6
1
1
0
2
0
0
1
2
1
1
1
0
0
1
0
0
0
0
0
0
0
1
2
0
1
2
0
2
0
0
1
2
0
1
0
0
1
1
2
1
1
1
0
1
0
0
0
0
1
2
0
0
2
1
0
0
0
0
1
0
0
1
2
1
2
1
0
0
0
0
0
1
2
0
0
0
1
1
2
1
2
1
1
0
0
1
0
0
2
0
2
0
0
2
0
2
1
3
1
1
0
0
0
1
2
0
1
0
3
0
0
0
0
0
2
0
2
0
0
0
0
1
0
1
0
0
1
0
0
2
0
2
0
0
0
0
0
0
2
1
1
0
1
1
1
0
0
2
0
1
0
2
2
0
1
1
1
0
0
0
0
2
1
0
0
1
0
0
2
1
0
2
0
1
1
0
0
0
0
0
1
1
1
0
1
2
2
0
0
2
0
2
0
0
1
1
2
0
2
2
0
0
0
1
1
0
2
0
0
0
1
1
1
0
1
2
0
1
0
0
0
1
0
0
1
1
0
1
1
1
1
1
2
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
1
0
2
0
0
0
2
1
1
2
0
1
1
1
0
2
2
2
0
0
0
1
2
1
1
0
0
0
1
0
0
1
2
1
0
0
2
2
2
2
0
0
1
1
2
0
1
0
0
0
0
1
2
2
0
1
0
0
1
0
1
2
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
2
0
0
0
1
0
0
1
0
0
1
2
0
1
1
0
0
1
2
2
0
1
1
0
0
0
2
1
1
1
0
1
1
0
0
0
1
0
1
2
0
0
4
1
0
0
0
0
2
1
1
0
1
0
1
0
2
1
0
1
0
2
1
1
2
0
1
0
2
0
1
0
1
2
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
10
0
1
0
0
0
1
2
2
1
0
0
1
1
0
2
1
2
0
1
1
2
0
1
1
0
1
1
1
2
0
1
1
1
2
1
1
0
0
0
0
0
1
2
0
0
2
2
1
0
1
0
1
0
1
0
0
1
2
2
0
0
0
0
1
2
2
1
0
2
2
0
0
0
1
0
0
0
1
2
1
1
0
0
0
0
0
1
1
1
0
1
0
1
0
3
1
2
0
0
1
1
0
0
0
1
0
1
2
1
0
0
0
1
0
2
0
0
0
0
2
0
0
2
0
1
2
0
0
0
1
1
0
1
4
0
1
0
2
2
0
2
2
1
0
0
0
1
0
0
0
0
1
1
1
0
2
0
1
0
0
1
0
0
1
1
1
0
0
0
0
1
2
1
1
0
2
1
0
2
2
3
0
0
2
1
0
0
2
0
2
1
2
1
0
0
0
1
0
3
1
2
4
0
0
1
1
0
1
2
1
0
1
1
0
1
0
0
0
2
0
1
2
0
0
0
0
0
2
1
0
1
0
0
1
2
1
2
1
1
2
2
2
1
0
0
0
0
2
1
1
2
2
1
1
1
0
2
0
0
0
1
0
1
0
0
0
1
1
1
1
0
2
2
0
0
0
1
0
0
0
1
3
0
0
0
1
1
0
0
0
0
1
1
1
1
0
0
1
1
1
1
1
0
0
0
1
0
0
0
1
2
0
0
2
2
1
1
1
0
0
1
1
0
2
0
0
0
0
1
0
2
0
0
0
2
2
1
1
1
1
1
3
0
2
0
0
0
1
1
0
1
1
0
1
0
1
2
1
0
2
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
1
1
3
2
0
1
1
1
0
2
0
0
2
1
1
2
0
1
0
0
0
1
0
0
0
0
2
0
2
2
0
0
0
1
0
0
0
1
0
0
0
1
1
0
1
3
1
0
0
0
0
0
0
1
0
2
1
1
1
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
1
0
0
1
0
0
1
1
1
0
0
1
0
0
0
1
2
1
0
2
0
2
0
1
0
0
0
2
2
2
1
2
1
0
1
1
1
2
0
0
2
0
2
1
0
2
0
0
2
0
1
3
0
2
3
0
2
0
0
0
2
2
0
2
1
1
2
1
0
2
0
0
2
1
0
1
2
0
0
0
0
1
0
0
1
0
1
2
2
0
0
1
0
2
0
0
1
0
3
0
0
0
2
0
2
1
1
0
0
0
3
1
1
2
1
2
2
0
2
2
1
1
2
0
0
0
2
0
1
1
0
0
1
1
1
0
1
0
2
1
1
0
2
0
1
0
0
0
0
0
1
0
1
0
0
1
1
1
1
0
0
0
0
1
0
1
1
0
0
1
2
3
0
2
1
0
0
2
1
1
2
1
2
1
2
1
0
1
1
2
8
0
1
1
2
2
0
2
0
2
2
0
1
2
0
0
0
1
2
0
2
1
2
4
0
2
3
0
0
1
0
0
1
1
1
0
0
0
0
0
1
0
2
2
2
1
1
2
0
0
0
1
0
0
0
1
2
1
0
2
0
0
1
0
2
0
1
0
0
1
0
1
0
0
0
1
0
1
0
0
1
1
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
2
1
0
2
0
1
1
1
1
2
1
1
0
0
2
1
1
0
0
2
1
0
0
2
0
1
2
0
0
2
1
2
2
1
1
1
1
0
0
2
1
0
1
1
1
0
0
0
0
1
0
0
0
1
1
1
0
0
2
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
3
2
1
0
0
0
2
2
2
0
0
0
2
0
0
0
0
1
1
0
0
0
2
2
0
0
2
1
2
0
0
2
0
1
0
0
1
1
0
2
2
1
0
0
0
2
0
1
2
0
1
0
2
0
0
0
0
0
3
1
1
1
0
2
0
0
1
0
1
0
2
0
2
0
1
2
0
1
0
0
1
1
0
1
2
1
2
1
1
2
0
2
0
1
2
0
1
0
1
0
0
0
0
2
0
1
0
1
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
1
8
2
2
2
0
0
0
2
2
0
0
2
0
1
0
0
0
1
1
0
2
0
2
1
1
0
0
0
2
2
1
0
0
3
0
1
1
1
1
0
2
0
1
0
1
2
2
0
0
0
1
0
1
0
0
0
0
0
0
2
2
2
1
1
2
0
0
2
0
2
1
0
1
1
1
0
0
0
2
1
0
0
1
1
0
0
0
2
2
1
3
0
0
2
0
1
2
0
0
1
2
1
0
2
1
2
0
1
2
2
1
0
0
0
0
0
0
0
2
0
2
2
0
0
1
1
0
0
1
2
0
1
0
1
1
1
2
0
2
1
2
2
0
0
1
0
1
1
1
3
0
2
2
2
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
2
0
1
0
0
1
1
0
2
2
1
1
1
0
1
0
0
0
0
1
0
0
1
0
1
2
1
0
1
1
2
0
0
1
1
1
0
1
1
3
0
4
0
2
1
0
1
1
0
0
0
2
0
0
0
1
0
2
0
0
1
0
0
2
1
1
1
0
0
0
1
1
0
1
3
2
2
0
1
1
0
0
0
1
2
0
2
1
0
2
0
0
0
0
0
3
0
0
0
0
2
0
1
2
2
0
1
1
0
0
2
0
1
0
1
0
1
2
0
2
0
0
1
1
0
2
1
2
0
0
0
2
0
0
0
1
0
0
0
0
1
0
1
0
1
0
1
1
2
1
2
1
0
0
0
1
0
1
1
0
2
1
2
1
1
1
1
1
0
1
0
2
0
1
1
2
1
0
0
3
0
0
1
1
0
0
1
1
2
2
2
1
0
0
0
0
0
0
1
0
1
2
0
1
0
1
1
0
2
0
0
2
0
0
0
0
1
2
0
2
1
2
0
1
2
2
0
3
0
2
2
1
2
0
0
1
2
0
2
1
0
0
0
1
2
2
0
0
1
0
0
0
1
2
2
0
1
1
2
0
1
0
1
0
0
0
0
1
0
1
0
1
0
0
1
2
0
0
1
0
0
0
1
0
0
1
1
0
0
0
1
0
0
2
0
0
0
2
1
0
1
1
1
1
0
0
0
0
1
0
2
0
1
0
1
0
0
1
1
0
0
0
2
1
0
1
0
0
1
1
1
2
3
1
0
2
0
2
0
2
1
0
1
1
1
1
2
0
0
0
1
1
0
1
0
1
0
1
0
0
0
1
0
0
0
0
1
1
0
1
0
1
0
0
2
2
1
0
0
0
2
1
2
1
2
2
0
1
2
0
2
2
1
1
0
2
0
1
2
1
0
1
1
0
0
0
2
0
2
2
1
2
0
0
1
0
0
2
2
2
1
1
2
2
0
2
2
2
0
0
0
1
1
1
0
1
0
0
0
2
0
0
0
1
1
2
0
2
1
0
0
2
1
0
1
2
2
1
1
0
1
0
1
0
1
1
1
1
1
0
0
1
0
1
1
0
0
1
0
0
2
0
0
0
2
1
0
0
0
2
0
3
0
1
0
0
0
2
0
1
1
1
1
1
0
0
0
1
1
0
2
0
0
2
1
2
2
1
1
0
1
0
2
2
0
0
2
2
0
0
0
3
0
2
0
0
2
1
0
1
0
0
0
0
0
0
1
1
0
1
1
0
0
1
0
1
0
1
2
0
0
0
0
0
1
0
2
0
0
1
1
0
1
0
1
3
0
0
1
0
0
0
1
2
1
0
0
0
2
1
2
2
0
1
0
0
1
0
1
0
0
0
1
0
0
2
2
0
1
1
0
0
0
2
1
1
0
5
1
0
1
0
0
0
0
0
0
0
1
3
1
1
1
0
2
0
0
0
1
0
0
0
0
2
1
2
2
1
2
1
2
0
4
2
0
0
1
2
0
0
0
0
2
2
0
1
1
2
0
2
0
0
1
1
0
0
1
1
1
1
2
1
1
1
2
0
0
0
2
0
0
1
2
1
1
0
0
1
1
0
1
0
0
1
1
1
0
0
1
0
2
1
0
2
0
0
0
0
0
3
1
1
1
0
1
0
0
0
0
1
2
1
1
0
1
1
0
0
0
2
0
2
0
0
1
0
1
2
2
0
1
0
0
0
0
2
2
1
1
0
2
1
1
0
1
1
0
1
0
0
1
0
1
0
0
1
1
0
0
2
1
0
2
0
0
2
3
0
1
0
1
1
2
0
1
0
2
1
1
1
0
0
0
0
0
0
2
1
2
1
2
1
2
0
0
2
2
1
0
0
0
1
3
1
0
0
0
0
2
2
0
0
1
1
1
1
0
2
0
2
1
0
1
0
0
1
2
0
2
1
2
1
0
2
0
2
0
2
0
1
0
1
0
2
0
0
0
0
0
1
0
0
1
2
1
0
1
2
1
0
0
2
2
0
0
0
0
4
0
1
0
1
0
2
0
0
1
1
0
2
0
0
0
2
1
2
2
1
2
0
0
0
0
3
2
1
0
0
1
0
0
0
1
2
0
1
0
1
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
2
0
1
1
1
0
1
2
0
1
0
2
0
1
1
3
1
1
0
0
1
2
1
0
0
0
1
0
1
0
0
0
1
1
0
0
2
1
0
0
1
2
1
1
0
0
1
0
0
0
0
1
0
1
0
0
1
1
0
0
0
1
2
2
2
0
2
1
0
0
1
1
0
0
1
0
1
2
0
0
2
1
1
1
1
0
2
2
0
0
0
0
2
0
0
1
0
1
2
0
0
1
0
2
2
1
0
0
1
0
1
1
2
0
2
0
0
1
1
0
1
0
2
0
0
2
2
2
0
1
0
1
0
1
2
1
4
0
1
1
2
1
1
1
2
1
1
0
1
0
2
0
0
1
0
0
0
0
0
2
2
0
0
0
0
1
2
2
1
1
0
0
0
2
1
2
2
0
0
0
1
0
1
0
0
0
1
1
2
0
0
0
2
0
0
0
1
0
1
0
2
1
2
0
0
0
0
0
0
0
1
2
1
0
1
1
1
0
2
1
1
0
1
1
0
1
1
2
0
2
2
0
1
0
2
0
2
0
0
1
1
1
0
0
2
1
2
2
0
0
0
0
0
0
0
3
1
1
0
0
0
1
0
1
0
2
0
1
2
0
1
0
0
1
2
0
1
1
1
0
0
3
0
3
0
1
0
1
0
1
0
0
1
0
0
1
0
0
0
1
2
0
4
0
2
0
0
1
0
0
0
0
1
1
1
1
1
1
1
0
1
1
2
2
0
2
5
0
1
0
2
2
0
3
0
1
2
0
1
0
0
0
2
1
2
1
1
0
2
0
0
0
0
1
1
1
0
2
1
0
1
2
1
0
1
1
0
0
1
0
2
0
0
1
0
0
1
0
0
1
0
0
0
2
0
1
1
1
1
2
2
2
0
1
2
2
2
2
0
1
0
0
2
0
0
1
0
0
1
0
1
1
0
0
1
1
1
2
0
0
0
0
0
0
0
1
1
0
0
1
0
2
0
0
0
0
0
0
0
2
1
1
1
1
0
1
1
1
1
1
2
1
2
2
2
0
0
0
1
0
0
1
2
1
0
2
1
0
0
1
0
1
1
2
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
2
0
2
2
1
0
0
0
1
5
2
0
0
2
1
0
2
0
1
0
0
1
0
0
2
0
1
0
0
0
0
0
0
1
0
0
1
2
2
1
0
0
1
0
0
0
0
1
2
0
1
0
0
2
2
2
1
0
1
1
0
0
1
0
1
0
2
0
1
2
0
1
0
0
0
0
1
0
0
2
0
1
1
1
0
0
2
0
1
0
1
1
0
1
0
1
1
0
1
1
0
0
0
1
0
1
0
0
1
0
0
0
1
2
1
1
0
4
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
2
1
0
0
0
0
0
1
2
2
1
0
0
2
0
0
1
2
2
0
0
0
0
2
1
0
1
1
4
1
0
1
1
1
0
1
2
1
0
0
1
0
1
1
1
0
0
4
0
1
1
0
3
0
2
2
0
0
0
0
0
2
0
2
2
1
1
2
0
0
1
1
0
0
1
2
1
0
0
1
0
0
0
1
1
0
0
1
0
3
1
0
0
1
2
2
0
0
2
1
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
1
1
2
0
0
4
1
2
0
0
0
1
2
0
0
0
1
1
2
1
2
0
1
0
0
0
0
0
0
1
1
2
1
1
2
0
0
0
1
0
2
2
0
1
0
1
0
0
1
0
0
2
0
1
1
0
1
0
7
2
2
2
1
1
0
0
1
1
1
2
1
0
0
1
1
0
1
0
0
0
0
0
0
2
0
2
1
0
2
0
0
0
2
1
1
0
2
0
0
2
2
0
2
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
1
2
0
0
2
2
0
0
0
0
2
2
2
1
1
1
0
2
0
0
0
0
0
0
0
0
2
2
1
2
1
1
0
0
0
1
0
2
0
0
1
4
1
1
2
2
1
2
1
0
1
1
0
1
0
0
0
2
0
0
0
0
1
1
0
1
2
2
1
2
0
0
0
1
1
0
2
0
0
1
2
0
0
1
2
0
0
2
2
1
2
1
2
1
2
0
2
3
1
1
2
0
1
0
0
1
0
1
0
0
0
0
2
0
2
0
0
0
0
0
1
2
0
2
1
0
1
1
0
3
1
0
1
1
0
1
0
1
0
0
0
0
1
0
1
2
0
2
1
0
0
0
3
1
2
2
1
1
1
2
4
1
1
1
0
0
0
0
2
1
1
0
1
1
3
1
1
2
0
0
1
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
1
0
2
1
0
2
0
1
0
1
0
0
0
1
0
1
0
1
2
2
1
1
2
1
1
2
0
1
2
0
2
1
0
0
1
0
2
0
0
2
0
1
1
1
2
0
0
0
0
1
2
0
0
2
0
1
0
0
1
2
0
2
0
1
1
0
2
2
1
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
1
0
2
1
0
0
0
1
1
0
4
0
0
0
0
0
2
0
3
1
0
2
0
1
0
1
0
1
1
1
0
0
2
0
0
2
0
1
0
0
0
2
0
0
2
0
2
0
0
1
1
0
1
1
1
0
0
0
2
0
0
1
1
2
2
1
1
0
1
0
1
2
0
0
1
0
0
1
0
0
0
0
1
3
0
1
0
0
1
2
0
2
1
1
0
0
2
0
1
0
0
2
2
1
1
0
2
0
2
0
0
3
2
3
1
0
0
3
0
0
1
0
0
1
1
0
1
1
2
1
0
0
1
2
0
0
3
3
0
0
1
2
3
0
2
0
0
1
1
0
2
1
0
0
1
1
2
0
2
1
0
0
2
2
2
2
1
2
0
2
1
0
0
1
0
0
0
0
0
2
1
1
0
1
1
0
0
1
2
2
0
1
1
0
0
0
1
2
2
0
0
1
0
0
0
1
1
1
5
0
1
2
1
0
0
0
0
1
0
0
0
2
0
2
1
1
1
0
0
0
3
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
3
1
0
0
2
0
1
0
1
0
0
3
2
0
2
2
3
0
1
0
0
2
0
1
0
2
0
0
1
0
0
0
0
2
0
2
1
0
0
0
2
1
0
1
0
2
0
0
2
3
0
0
1
0
0
0
1
1
0
1
0
1
0
0
1
1
0
0
1
0
1
0
1
0
2
2
1
0
2
1
0
1
2
2
1
2
0
0
2
0
0
0
1
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
2
0
1
0
3
2
4
0
0
2
0
0
0
0
0
0
1
2
0
2
0
1
0
1
0
0
2
0
0
1
3
2
0
0
0
2
0
2
1
0
1
2
0
1
0
0
1
1
0
2
1
0
0
1
0
0
1
0
2
1
0
1
0
0
2
0
1
1
0
1
1
1
3
1
1
2
0
2
1
0
1
1
0
0
1
0
0
0
2
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
1
1
1
0
0
2
3
0
1
0
2
2
1
0
0
2
0
2
0
0
1
0
2
0
0
1
2
0
1
2
1
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
1
2
0
0
0
0
2
1
0
0
1
1
0
0
0
0
0
0
0
0
3
0
0
1
0
1
0
1
1
0
1
0
1
2
0
1
0
1
1
1
0
0
2
0
2
1
2
0
0
1
1
0
1
1
1
0
0
1
0
0
2
0
0
0
2
1
1
0
0
0
0
2
1
1
1
1
0
1
1
0
0
0
0
0
0
1
0
0
1
0
2
2
2
1
0
0
1
2
0
0
0
2
1
0
1
1
2
0
7
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
2
0
1
1
0
2
1
0
0
0
0
0
0
0
0
2
0
2
0
2
0
1
2
0
0
0
0
0
0
1
0
0
2
1
0
1
0
0
0
1
0
1
1
0
0
2
2
0
3
1
0
0
1
1
0
1
0
0
1
0
0
1
1
0
1
0
2
0
0
1
1
1
0
3
0
0
1
0
2
2
1
0
2
0
1
1
0
1
2
1
0
2
0
0
1
0
0
0
0
0
1
2
1
0
2
1
0
1
2
2
1
0
1
0
1
0
1
0
1
0
0
0
0
0
0
1
1
0
0
1
2
0
1
1
0
3
0
0
1
0
2
0
2
1
0
1
0
2
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
2
1
1
1
0
1
1
0
0
1
2
0
2
2
3
2
0
0
2
1
0
1
0
0
2
1
1
0
2
1
0
0
0
0
0
0
1
2
0
1
1
0
0
0
0
2
1
1
2
1
0
0
1
0
0
0
3
0
0
0
1
2
0
2
0
1
2
0
1
0
0
0
0
0
2
0
0
0
0
0
1
2
1
0
0
0
1
1
0
0
1
0
1
0
1
0
0
2
1
0
0
0
1
0
2
1
1
0
0
1
2
2
3
2
1
0
0
4
2
0
0
0
0
1
0
1
0
0
2
2
0
2
0
3
1
0
0
1
1
0
2
0
0
0
0
2
1
0
4
1
0
1
0
0
0
2
0
1
0
0
2
1
0
0
0
0
2
1
0
1
0
0
2
0
1
0
0
1
0
1
2
2
0
0
0
0
0
0
1
1
0
0
1
2
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
1
0
0
0
1
0
1
0
0
0
0
0
2
3
1
2
2
1
1
0
0
2
0
0
2
2
1
1
0
0
0
2
2
2
1
0
0
0
0
2
1
0
2
1
0
2
1
2
1
1
1
0
2
2
1
1
0
2
2
1
0
0
0
0
1
0
1
2
0
1
1
0
0
1
1
0
1
1
2
4
0
0
0
0
1
0
1
0
2
0
1
0
1
2
0
1
1
0
0
1
0
0
1
0
0
0
1
0
1
2
0
0
1
0
1
0
1
2
0
0
1
1
1
2
2
1
1
0
0
0
0
0
0
1
3
0
0
0
2
0
1
2
1
0
0
0
1
0
1
1
0
2
0
0
0
2
1
1
0
0
2
2
2
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
1
0
1
1
1
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
2
1
0
2
0
1
0
0
0
1
2
2
1
2
1
0
0
0
3
0
1
0
1
2
0
1
1
2
0
0
2
2
0
0
0
1
1
0
2
0
2
0
1
2
0
0
0
0
1
1
0
2
0
0
0
5
0
2
1
0
0
2
1
1
0
0
1
0
1
0
1
0
2
1
2
0
0
2
0
0
2
0
1
2
2
0
1
2
1
0
0
2
0
0
1
0
1
0
2
0
0
1
2
0
0
1
1
2
1
2
0
0
1
0
0
0
2
0
0
0
4
1
1
2
0
0
1
0
0
0
1
0
0
0
0
0
1
2
3
3
0
0
1
2
0
0
0
0
1
1
1
2
2
1
2
1
0
0
1
2
0
2
1
2
0
0
1
2
0
0
0
0
0
0
0
1
1
1
1
1
2
1
0
0
0
1
2
2
0
2
1
1
0
0
0
0
2
0
0
0
1
1
0
0
1
0
1
1
1
1
0
1
0
1
2
1
0
0
0
0
0
2
0
1
0
0
2
0
0
1
2
0
1
1
2
0
2
0
0
0
1
1
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
2
1
0
2
1
1
2
2
0
0
2
1
0
0
2
0
1
0
0
2
1
2
0
0
0
0
0
0
1
0
2
0
1
1
0
1
0
1
0
2
1
0
2
1
0
1
1
0
1
0
0
1
1
1
0
2
2
0
2
2
0
0
0
1
0
2
0
0
1
0
2
1
0
1
0
0
1
1
2
0
1
0
2
1
0
0
0
2
2
0
1
1
0
1
1
0
1
1
1
0
0
0
0
0
0
1
0
1
1
1
1
1
1
0
0
0
0
0
1
0
2
2
1
2
0
1
0
0
0
1
3
0
1
0
0
1
0
0
1
3
0
0
0
2
2
2
0
0
1
1
0
1
0
0
1
0
1
1
0
2
0
1
0
1
1
2
1
2
0
2
1
1
1
0
0
0
0
1
0
0
1
1
0
0
1
0
0
1
2
0
1
1
0
0
0
2
1
0
1
2
2
2
1
0
0
0
1
1
0
1
0
2
0
2
0
2
0
1
1
2
0
1
2
1
2
0
0
0
1
1
0
0
0
2
2
0
0
0
0
1
0
0
0
1
2
2
0
0
0
2
1
1
0
1
1
1
1
0
0
1
2
2
0
0
0
2
1
0
0
1
1
0
0
0
0
0
0
1
2
1
0
1
0
1
0
2
1
1
1
0
6
1
0
0
1
0
2
1
0
1
0
2
0
1
2
1
0
0
1
2
1
0
0
2
0
0
1
0
2
1
0
0
1
0
1
1
0
4
2
0
2
1
2
0
2
0
0
0
1
0
0
2
0
0
2
2
0
1
1
1
0
1
0
2
1
2
0
1
2
0
1
2
1
0
1
2
0
2
0
0
3
0
1
5
0
0
0
2
1
2
1
0
1
0
1
1
2
0
0
0
1
1
0
0
0
1
1
1
0
0
1
1
0
0
0
0
1
1
0
1
1
1
0
2
1
0
0
0
0
1
2
0
0
5
0
0
2
0
0
1
1
0
2
2
0
0
0
0
0
3
0
1
0
0
0
3
1
0
2
0
1
0
2
2
0
2
1
0
1
0
0
1
2
0
1
1
0
1
2
1
0
0
1
2
1
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
1
0
0
1
0
0
2
1
1
0
1
1
2
0
1
0
1
1
2
1
0
2
0
0
2
0
0
3
2
0
0
1
0
0
0
0
0
2
1
2
3
0
1
0
0
0
0
0
0
2
1
0
0
0
1
0
1
0
0
0
1
2
2
1
1
0
1
0
1
2
1
0
0
1
0
0
2
0
1
2
1
0
0
0
2
0
0
2
1
1
2
1
1
0
0
0
2
1
2
1
0
1
2
1
0
1
0
1
2
0
0
1
0
1
0
4
2
1
1
0
1
0
0
0
0
1
0
0
2
0
1
1
0
1
0
1
1
0
0
1
2
0
1
2
0
1
0
0
0
2
2
0
0
1
0
2
1
1
0
1
0
0
2
0
0
0
2
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
1
1
2
0
0
0
1
0
0
0
2
0
1
2
0
2
2
0
0
0
1
1
0
0
2
0
0
0
3
2
0
0
2
2
1
0
3
1
2
0
0
2
2
1
1
2
2
1
1
0
0
2
0
0
1
2
0
2
2
1
0
1
1
1
2
0
0
0
0
0
1
0
0
0
2
1
1
2
0
1
2
0
0
0
0
0
0
1
1
0
0
2
2
1
2
0
0
0
1
0
2
0
0
2
0
0
2
0
1
0
2
0
0
1
0
0
1
1
2
2
2
0
1
0
2
1
2
2
2
2
1
1
0
0
1
2
0
2
0
0
1
0
0
1
1
2
2
2
1
0
0
2
1
1
1
0
0
1
2
0
0
1
1
0
0
1
1
2
2
0
1
1
2
0
1
0
0
2
0
2
0
2
1
1
1
1
0
2
0
0
0
0
1
0
2
2
2
2
0
0
0
0
1
0
0
1
1
2
0
1
0
1
1
2
3
0
2
2
1
0
1
0
0
2
2
2
1
1
2
1
1
0
2
1
0
0
1
2
0
0
0
0
0
0
1
0
2
0
0
2
0
1
0
0
2
2
1
0
2
2
2
2
0
1
1
0
0
3
0
2
1
0
3
1
1
1
1
0
1
1
2
2
1
1
0
0
0
1
0
0
0
1
0
0
0
2
0
0
2
0
0
2
0
2
0
1
1
0
0
0
0
1
0
3
2
0
1
0
0
0
0
0
2
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
1
1
0
2
1
0
0
1
0
1
1
2
2
1
1
0
1
1
0
1
0
0
2
0
0
0
1
0
0
2
0
1
1
0
1
1
0
0
2
0
1
0
0
0
2
0
1
0
1
0
0
0
0
1
2
1
0
0
2
2
0
1
0
1
2
0
0
1
0
0
0
1
0
1
0
2
1
2
1
1
3
1
0
1
0
0
1
1
0
2
2
0
0
0
1
1
0
0
0
2
1
2
2
0
1
2
1
1
1
2
2
0
0
0
0
1
1
0
2
0
0
0
1
0
0
1
2
2
1
2
0
0
2
0
0
1
0
0
1
1
0
0
0
0
0
0
2
2
0
0
0
1
0
0
1
1
0
0
1
1
0
1
0
0
0
0
2
2
0
0
1
1
2
2
0
1
2
0
2
2
0
0
2
1
1
0
1
0
1
0
0
0
0
0
2
0
1
1
2
1
0
1
1
2
1
1
2
1
2
1
0
0
2
1
0
2
0
1
0
1
2
2
2
0
0
2
2
0
1
2
0
0
0
0
2
1
0
0
1
0
0
0
0
1
2
3
0
0
1
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
1
1
1
2
1
0
1
4
1
2
0
0
0
1
0
1
0
2
0
2
0
0
2
1
0
2
0
2
1
0
2
0
0
0
0
1
0
1
0
0
2
0
0
2
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
1
2
0
0
1
1
2
2
2
0
1
0
1
0
1
0
0
1
0
0
2
2
0
2
0
0
0
2
0
1
0
1
2
0
0
0
2
2
2
1
1
2
1
1
0
0
1
0
2
0
1
1
0
0
2
0
0
1
2
1
2
1
2
0
0
0
1
0
0
1
0
2
0
2
1
0
0
0
2
0
0
1
2
0
0
0
2
1
1
1
1
1
0
0
1
2
0
1
2
0
1
2
0
1
2
1
0
1
2
2
0
1
0
0
1
0
0
0
0
0
0
1
1
0
1
1
1
2
0
0
1
1
0
1
0
1
0
3
2
2
1
1
1
2
2
1
0
2
0
2
0
1
0
0
2
0
0
0
1
2
2
0
2
3
0
0
1
1
1
0
1
0
1
2
2
2
3
1
0
1
2
0
0
0
1
0
0
1
0
0
1
1
2
0
0
0
1
1
0
0
0
3
1
0
0
1
0
1
2
1
0
1
2
0
0
1
0
0
0
1
0
1
2
1
0
0
1
0
2
1
0
0
0
0
2
0
1
0
2
1
0
0
0
2
0
2
0
0
0
0
0
0
1
1
2
0
1
1
2
0
1
2
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
2
0
1
1
2
0
0
1
1
1
0
0
2
0
2
1
0
0
1
2
1
1
1
2
2
0
0
1
0
2
0
3
0
0
0
0
1
0
0
2
0
0
0
1
0
2
2
0
1
1
0
1
2
1
1
0
0
2
1
1
1
1
1
0
1
0
0
1
0
2
0
0
1
1
0
0
1
0
0
2
1
0
1
1
0
1
0
2
1
2
2
0
0
0
0
2
2
1
0
0
0
2
1
0
0
0
1
0
1
2
0
1
0
2
0
1
5
0
0
0
0
0
0
1
1
0
0
0
3
2
0
1
0
1
0
1
1
2
1
0
2
0
2
0
1
1
1
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
2
1
0
1
0
0
2
0
1
1
0
0
0
1
0
0
0
2
0
1
0
1
2
0
0
0
0
2
2
2
0
1
0
0
1
0
0
0
2
0
0
0
0
0
1
1
0
2
2
0
0
1
2
0
0
0
0
0
2
2
0
1
0
0
1
1
2
0
0
0
1
0
1
2
1
2
2
1
1
0
0
2
1
1
2
0
0
2
1
1
0
0
1
0
0
2
0
0
1
3
1
0
1
0
0
0
0
1
2
4
1
0
1
0
0
0
0
0
0
2
2
0
2
1
0
0
2
0
0
1
2
0
0
1
1
0
0
4
2
0
1
0
1
1
1
2
0
1
1
0
0
1
2
0
1
1
0
1
0
1
1
1
0
0
2
1
1
1
0
2
0
0
0
0
1
0
0
0
0
2
0
1
2
0
0
0
1
1
0
0
0
2
0
1
1
1
0
2
2
1
1
0
3
1
2
1
0
1
2
2
1
2
1
1
1
2
1
0
0
1
1
1
0
2
0
0
1
0
0
1
0
1
1
2
2
1
0
1
0
2
0
0
1
3
2
1
2
0
0
0
1
1
2
1
0
2
0
1
2
2
2
2
1
0
1
2
1
1
1
0
0
2
0
1
1
2
0
1
1
2
1
0
1
0
0
0
0
0
2
1
0
1
0
0
1
1
2
0
0
0
0
1
0
0
0
0
1
0
0
1
2
1
0
0
0
0
1
1
2
0
1
0
2
0
0
2
2
2
0
1
2
0
0
1
1
0
0
0
2
2
2
0
1
1
1
0
0
0
2
0
0
2
2
0
0
2
0
3
2
2
0
1
0
0
0
0
0
1
0
0
0
0
2
1
0
0
1
1
0
1
0
0
0
2
1
2
2
0
1
1
2
1
0
2
2
0
2
1
0
2
2
0
2
0
0
0
0
1
1
0
2
2
0
0
0
0
0
2
4
1
1
0
1
1
2
0
0
1
0
0
1
1
0
0
0
0
1
1
0
2
0
2
2
1
1
0
0
1
0
0
2
1
1
0
1
2
0
0
0
0
1
1
0
0
2
0
0
1
4
1
0
2
1
2
2
2
2
1
0
1
2
2
2
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
2
1
0
0
0
2
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
2
0
1
2
1
2
3
0
0
2
1
1
1
0
0
0
0
1
1
1
1
0
1
0
0
1
2
2
0
1
2
0
0
1
0
0
2
1
0
1
1
3
0
1
0
0
0
1
0
0
1
1
1
3
0
1
2
1
2
1
0
0
0
2
0
0
1
1
3
2
1
0
2
1
2
2
0
2
0
0
0
0
1
0
0
2
2
0
0
0
0
0
1
1
1
0
0
0
1
1
2
1
0
1
2
2
0
0
0
0
0
2
0
1
0
1
1
0
0
0
1
0
0
0
0
0
2
0
0
2
0
1
2
0
10
0
1
0
0
1
1
0
1
0
2
0
0
2
0
3
0
1
1
0
2
0
0
2
1
1
1
0
1
1
0
0
0
0
2
0
0
0
3
2
0
2
2
0
1
1
2
0
0
1
2
2
1
0
0
1
0
1
0
0
1
1
1
0
0
2
0
2
1
0
1
2
1
4
1
0
0
3
0
2
0
1
0
0
0
2
0
0
2
0
1
0
1
2
1
3
0
0
1
1
2
2
1
0
0
0
1
1
0
0
1
1
1
0
1
2
2
1
1
0
1
0
1
0
2
1
0
1
0
0
1
1
0
0
1
1
0
0
0
0
2
0
3
1
0
0
0
0
0
0
0
0
0
1
1
2
2
2
0
0
1
1
1
0
3
0
1
0
0
1
2
1
2
2
3
1
0
0
1
0
0
0
0
0
6
0
2
2
1
0
2
0
2
2
2
1
2
0
0
2
0
0
1
1
0
2
1
1
0
2
0
0
1
0
1
2
0
1
1
2
1
1
0
0
1
0
1
2
0
1
0
2
3
0
0
0
1
0
0
1
0
2
0
1
1
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
1
2
1
2
4
0
1
1
1
0
1
3
0
0
2
2
1
2
0
2
0
2
1
2
0
1
1
1
0
0
0
0
1
1
0
1
0
2
0
2
2
0
2
2
0
1
0
1
0
0
2
0
1
1
1
2
1
0
1
1
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
1
2
2
1
4
0
0
0
3
1
2
2
0
0
1
0
2
1
2
0
2
0
0
0
1
0
1
0
2
0
2
2
3
0
0
0
1
2
0
1
0
2
2
0
2
1
0
1
1
2
0
1
1
1
1
1
1
0
3
0
2
0
0
2
1
0
1
0
2
1
1
0
0
1
1
1
1
2
0
0
0
1
0
0
1
0
2
2
1
1
2
1
0
3
0
2
0
0
0
2
1
0
0
0
2
0
0
0
1
1
2
0
1
0
0
2
0
0
2
0
0
0
0
2
2
0
0
0
0
2
0
0
2
2
0
1
0
0
1
1
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
1
0
0
1
3
0
2
1
1
0
2
2
0
0
0
1
0
0
1
2
0
0
2
2
0
3
1
0
2
4
0
0
0
1
0
1
0
1
0
1
4
2
0
2
0
0
0
1
0
1
1
2
0
1
0
2
0
0
0
0
0
0
0
0
1
1
1
0
0
0
2
0
0
0
0
2
1
0
0
0
1
1
0
1
1
0
0
1
2
1
1
1
4
1
1
1
0
0
1
1
0
0
0
0
3
1
1
1
0
0
1
0
0
1
1
0
2
0
1
1
0
2
0
0
1
0
0
1
1
0
1
2
0
0
0
0
0
0
1
0
0
2
1
1
0
2
0
1
0
0
1
2
0
0
0
1
1
2
2
0
0
1
1
0
0
0
1
0
0
1
2
1
0
1
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
3
2
2
0
0
1
0
0
0
1
0
0
2
2
0
0
0
0
1
1
1
1
0
2
2
0
0
2
1
1
1
2
1
1
0
2
1
1
0
0
0
0
0
2
0
2
1
0
0
0
0
0
2
1
0
0
0
2
1
0
0
0
2
1
1
0
1
2
1
0
0
2
1
0
1
2
1
1
1
1
1
0
0
0
1
1
1
1
0
0
0
0
1
2
2
1
1
1
0
1
0
1
0
0
0
1
0
1
0
0
2
0
0
1
1
0
1
0
2
1
1
0
0
0
1
1
2
1
0
1
0
0
1
2
0
0
0
2
0
1
1
2
2
1
0
0
2
2
0
0
0
0
1
1
2
0
1
0
2
0
1
0
2
0
1
2
0
0
1
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
1
2
0
1
2
2
1
1
0
2
0
2
1
1
1
0
1
0
0
1
0
0
1
1
0
0
0
2
0
2
0
1
0
0
0
0
1
2
0
0
2
0
0
2
1
0
2
2
1
0
1
1
0
1
0
0
1
1
1
3
1
1
0
2
2
1
0
0
0
2
1
0
0
1
1
1
1
0
1
1
1
2
0
0
1
0
0
1
1
0
0
0
0
1
1
0
1
0
0
2
2
1
0
1
0
3
1
0
0
1
1
1
2
0
1
2
1
1
7
0
1
0
1
2
1
2
2
1
0
0
1
1
1
0
1
0
0
1
0
1
1
0
2
0
1
0
4
1
2
0
0
2
0
0
0
0
1
2
0
1
1
1
2
1
1
2
0
2
0
2
1
1
1
1
0
0
0
1
2
1
1
0
1
0
0
0
1
0
0
0
0
0
2
1
0
1
1
0
1
1
1
1
2
0
2
0
1
1
0
0
2
1
0
0
2
1
1
2
1
1
0
0
0
0
1
0
0
1
0
0
0
0
3
0
1
0
1
2
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
2
1
1
1
2
2
0
0
1
0
1
0
0
0
0
0
1
0
0
2
1
0
1
2
2
1
1
0
0
2
2
1
0
1
2
2
1
1
0
0
1
0
2
3
0
1
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
2
3
2
2
0
1
0
0
1
2
2
1
0
2
1
0
1
2
0
0
1
0
2
0
0
0
0
2
2
0
1
0
0
2
2
1
1
0
0
1
1
2
0
1
0
0
2
0
0
0
1
1
0
1
2
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
3
2
1
1
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
1
2
0
0
2
1
1
1
0
0
0
1
2
2
1
0
2
0
0
0
0
1
0
1
0
2
0
1
1
1
0
0
1
0
1
0
0
0
0
1
1
1
0
0
1
2
0
1
2
3
2
0
0
1
1
1
2
0
0
1
1
1
0
1
0
1
2
2
0
1
0
1
0
0
0
0
0
1
2
2
0
1
0
1
1
0
2
1
0
1
0
0
0
1
0
2
1
1
0
0
1
0
0
0
2
1
2
0
1
0
1
1
0
0
2
2
1
2
0
2
0
0
0
0
0
0
1
3
0
2
0
1
2
1
0
0
0
0
2
0
0
0
0
2
2
2
0
0
0
0
1
0
1
2
0
1
0
0
0
2
2
1
1
1
0
2
0
0
0
1
1
2
0
2
0
0
2
1
1
0
1
1
0
1
0
1
1
1
1
0
0
1
1
0
0
0
1
1
0
1
1
0
2
0
2
1
0
0
1
1
2
0
0
2
1
1
1
0
0
0
1
2
0
1
0
1
3
0
1
3
0
0
1
1
2
0
0
1
3
0
2
1
0
0
1
0
0
2
0
1
0
2
0
0
2
2
0
1
1
1
0
1
0
0
0
1
1
0
2
0
0
1
0
2
0
4
0
0
1
1
1
1
1
1
1
0
3
0
1
1
0
0
2
2
2
0
1
0
1
1
1
2
0
0
1
1
2
2
1
1
0
2
1
0
0
2
0
2
2
0
1
1
2
0
3
0
0
0
0
2
2
0
0
0
2
1
2
1
0
0
2
0
1
1
2
0
0
0
0
2
1
2
1
0
2
0
1
0
0
1
2
1
0
0
1
0
2
2
0
2
1
0
1
2
1
1
2
2
0
1
0
1
1
0
0
1
0
1
1
0
2
1
3
1
0
0
1
0
0
0
1
0
1
0
1
6
0
1
1
2
1
1
0
0
2
0
2
1
2
2
0
0
2
0
0
0
1
0
0
0
1
2
2
0
2
1
1
0
0
0
0
1
1
1
1
1
1
0
2
4
0
0
2
1
0
2
0
0
0
1
0
0
0
2
2
1
1
0
0
2
0
2
0
0
3
0
2
0
2
0
1
0
0
1
2
0
0
0
1
0
0
1
1
0
0
1
1
1
0
2
2
0
0
0
2
0
1
0
0
0
1
1
1
0
4
0
0
0
0
2
1
1
0
0
1
0
1
0
2
2
0
2
0
0
0
1
1
2
1
0
1
1
0
1
0
0
1
0
0
0
0
1
0
2
2
0
0
0
0
2
1
0
1
0
0
2
2
0
2
2
0
0
1
1
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
3
2
0
2
1
0
2
0
0
1
0
1
1
0
0
2
0
0
2
2
1
1
1
1
0
1
1
0
1
0
2
1
1
0
0
1
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
1
1
1
1
2
1
1
2
1
0
0
1
1
1
2
2
1
2
2
1
0
2
2
1
1
1
1
0
0
1
0
1
0
0
0
1
1
1
0
1
1
0
1
0
1
1
0
0
1
0
0
1
3
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
3
0
0
2
0
1
0
1
3
0
1
0
1
2
0
2
0
0
0
0
1
0
1
2
1
0
2
0
0
0
2
1
2
1
2
2
0
1
0
0
1
0
1
1
1
1
0
0
2
0
1
1
0
0
1
3
0
1
1
1
0
0
1
0
1
0
0
0
1
2
0
0
2
1
1
1
1
0
1
0
1
0
1
0
0
1
0
1
2
2
0
0
0
1
1
4
0
0
0
0
2
1
2
0
1
0
2
0
1
2
0
1
1
2
1
1
1
1
1
0
0
0
1
0
2
1
0
0
0
0
1
0
0
1
0
1
1
2
0
0
1
0
1
1
0
2
1
2
0
2
0
0
2
1
1
0
0
1
1
1
0
0
0
0
0
1
0
2
2
0
0
1
0
0
0
1
3
0
1
0
1
0
0
1
0
0
0
0
2
2
0
2
1
1
1
1
1
0
1
0
1
2
1
0
1
0
0
1
1
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
1
2
1
0
0
1
2
0
0
0
1
1
2
1
2
2
0
1
2
0
2
2
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
1
0
2
0
0
0
0
0
1
2
0
1
0
0
2
0
0
0
0
4
0
1
0
0
1
0
0
0
2
2
0
1
0
1
1
1
0
2
2
1
2
2
0
0
1
1
0
1
0
0
0
1
2
2
2
2
0
0
1
0
1
0
1
0
1
0
2
0
2
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
2
0
2
0
0
1
0
0
2
1
1
0
2
0
1
0
0
2
1
0
2
3
0
0
0
0
0
0
0
0
0
1
1
1
2
0
0
1
0
0
1
0
1
0
0
0
1
2
0
1
1
0
2
0
2
2
0
0
1
1
0
0
0
0
0
1
0
1
1
2
0
0
1
1
0
2
2
0
0
0
0
0
1
0
0
0
2
0
0
2
1
0
2
0
0
0
1
1
1
2
0
1
0
1
1
2
0
1
2
1
3
1
0
0
1
2
0
0
1
0
0
0
0
0
2
2
0
3
1
0
2
1
1
0
0
0
2
1
0
1
2
1
0
0
1
1
0
1
0
1
2
1
0
1
0
2
0
1
1
1
0
2
0
2
1
0
0
2
1
0
0
1
1
1
1
0
0
0
1
1
1
1
2
0
2
1
2
2
0
1
0
0
0
1
1
0
2
0
0
1
1
1
0
0
1
1
1
0
2
0
1
1
0
1
0
1
0
0
0
1
4
1
2
1
0
0
0
1
2
1
0
1
0
0
1
0
0
2
2
0
0
2
1
2
4
0
0
0
6
2
0
0
0
0
0
1
2
0
2
1
0
0
0
2
0
2
0
1
0
2
0
2
0
1
1
0
2
1
0
0
1
2
1
0
0
0
2
1
2
0
0
1
0
0
2
0
0
1
0
0
0
0
2
1
1
1
2
0
2
2
0
0
2
2
2
2
0
0
0
0
1
2
1
1
1
1
1
1
0
0
0
0
1
2
1
0
0
4
0
1
0
0
0
0
1
2
0
2
0
0
0
2
1
0
0
1
1
0
1
1
0
0
2
1
0
2
0
0
0
1
1
0
1
2
0
1
0
0
2
1
0
0
0
0
0
2
2
0
0
0
0
1
0
1
0
1
1
1
1
2
0
1
2
0
1
2
0
2
0
1
1
2
1
0
1
0
0
0
0
0
2
2
1
0
1
0
2
2
2
1
2
2
0
1
0
1
0
0
0
1
0
0
0
2
1
1
0
1
0
0
0
0
1
0
0
1
2
2
0
1
1
1
0
2
1
1
6
0
2
2
0
0
2
2
1
0
0
1
0
1
0
0
2
0
1
0
1
0
0
0
2
1
2
0
2
0
1
0
0
0
2
0
1
2
0
1
1
2
1
0
1
2
1
0
0
0
1
0
0
2
1
2
1
1
0
1
2
1
0
0
2
0
2
0
0
2
0
0
0
1
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
1
2
3
1
2
1
0
0
1
0
1
0
1
2
1
0
0
0
0
0
0
2
2
0
1
1
0
0
0
0
2
2
0
2
0
0
1
2
0
2
2
2
2
2
2
1
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
1
0
2
0
1
1
1
2
2
0
1
0
3
2
2
0
1
1
2
1
0
2
0
2
1
0
0
0
0
2
0
1
1
0
1
1
2
1
0
0
0
0
1
1
1
1
1
0
2
0
0
1
0
2
0
0
0
1
2
0
0
1
0
1
1
0
0
2
1
2
0
2
2
1
0
1
1
0
0
1
2
0
0
0
2
1
1
1
0
1
2
3
1
0
0
0
1
0
0
1
2
0
0
1
0
0
0
1
0
0
2
1
0
0
2
0
0
1
2
0
5
1
2
0
0
0
0
2
1
0
1
0
0
1
1
1
1
0
1
1
0
1
1
1
2
2
0
1
1
1
0
1
2
0
0
2
1
2
1
0
2
0
2
3
2
3
2
0
1
0
0
0
1
1
2
0
1
0
0
0
2
1
1
0
1
0
2
0
1
2
1
1
2
0
0
1
0
0
2
1
0
0
1
0
0
0
2
1
2
2
0
2
0
1
0
0
1
1
0
1
2
0
1
1
2
0
0
1
0
0
0
2
0
1
0
1
2
1
1
0
0
0
0
2
1
0
2
2
0
0
0
1
1
0
0
0
2
2
2
1
0
0
0
1
0
0
0
1
1
0
2
1
1
0
2
2
0
1
0
1
1
0
2
0
2
1
0
1
1
0
0
0
0
0
0
1
1
2
0
2
2
1
2
1
1
0
2
0
0
2
0
0
1
0
2
1
1
0
2
1
0
2
1
1
0
0
2
0
0
1
0
0
0
1
1
0
1
0
5
2
1
0
2
2
1
0
4
1
0
0
0
2
0
1
0
1
2
1
3
0
1
2
0
0
0
2
1
2
0
1
0
0
2
0
1
0
0
5
2
2
1
1
2
1
0
0
0
1
1
0
2
2
0
1
0
2
1
1
0
1
1
1
1
2
1
0
5
0
0
0
2
0
2
0
1
2
0
2
0
1
0
0
1
1
1
0
0
1
2
1
0
1
1
1
0
0
0
0
1
1
1
1
0
0
0
2
0
2
1
0
2
1
0
1
0
1
0
2
2
2
0
2
2
1
0
1
0
2
1
0
2
1
0
3
1
2
0
0
1
0
0
0
0
1
1
1
0
2
2
0
1
0
2
1
1
2
1
0
1
0
3
0
0
1
1
2
0
2
1
0
1
2
1
2
1
1
0
0
1
2
0
0
1
0
0
2
0
0
0
0
0
0
1
0
1
0
2
0
3
1
1
1
0
1
0
0
0
0
0
1
2
1
1
1
1
0
0
0
0
0
0
1
1
1
0
0
2
1
1
3
0
0
0
0
1
0
2
0
0
0
1
0
1
1
1
0
0
1
0
1
1
2
0
0
0
0
1
1
0
2
2
0
0
2
0
0
2
1
0
0
0
0
0
0
1
2
2
2
0
2
1
0
1
0
1
1
2
0
0
1
0
2
2
1
0
0
1
0
0
2
0
0
1
0
2
0
0
1
2
0
2
2
1
2
0
1
0
1
0
0
0
0
0
1
0
0
0
4
0
0
2
2
0
1
1
0
2
0
0
0
0
0
0
0
0
1
0
1
0
1
2
0
0
1
1
0
1
2
2
2
0
0
0
1
1
0
1
1
0
0
1
1
1
0
1
2
2
2
0
4
1
1
0
1
0
0
2
2
0
3
0
1
3
0
2
0
2
0
0
0
0
0
1
0
0
0
2
1
2
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
2
0
0
0
1
0
1
2
1
0
2
1
0
0
2
1
0
1
1
0
1
2
1
0
0
2
0
0
2
0
1
2
0
0
2
0
1
0
1
0
0
0
0
0
1
1
2
1
1
1
3
1
0
0
2
0
0
1
0
0
2
0
0
0
0
1
0
3
0
0
0
2
0
0
0
2
1
1
0
2
1
1
0
0
0
2
1
0
0
0
0
0
1
0
2
1
0
0
1
0
0
1
0
0
0
0
0
3
0
2
0
1
0
0
1
0
0
0
0
0
0
1
2
0
1
0
0
0
1
0
0
2
2
0
1
0
2
2
1
1
0
0
1
1
0
0
1
1
1
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
3
2
2
2
2
2
1
0
1
1
2
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
2
1
0
0
1
2
0
0
0
2
0
0
1
1
1
0
0
1
1
2
0
0
1
2
0
0
1
0
1
1
0
1
0
0
0
1
1
1
1
0
2
0
2
0
2
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
1
1
0
1
2
3
1
1
0
0
1
0
0
5
0
2
0
1
1
1
0
0
2
1
1
2
1
0
0
2
0
2
0
4
0
0
0
1
2
1
0
1
1
0
3
1
0
1
2
0
0
1
2
0
0
1
2
1
1
2
0
2
0
0
0
0
1
0
2
0
0
0
0
2
0
2
2
0
0
1
2
0
0
0
1
0
0
1
2
2
0
0
2
0
0
1
1
0
0
0
1
1
0
0
0
1
2
2
3
0
1
0
0
0
3
1
2
1
0
1
0
1
1
0
0
1
3
2
1
2
4
0
2
0
0
1
1
1
0
2
0
0
0
1
0
1
0
2
1
0
0
2
1
1
0
1
1
2
2
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
1
0
2
0
1
0
0
1
0
0
0
1
1
0
1
0
1
1
0
0
0
2
2
0
0
2
0
0
1
0
0
1
1
0
0
1
0
1
2
1
0
0
0
0
1
0
2
2
0
1
0
1
3
0
0
0
1
0
0
1
2
0
1
1
0
0
2
0
0
0
1
1
0
2
0
0
0
0
1
0
1
0
2
0
1
2
0
1
0
0
0
0
1
0
0
1
1
0
0
1
1
1
0
1
0
0
1
1
0
1
1
0
2
1
2
1
0
1
1
2
0
0
2
0
0
1
0
0
0
0
1
0
1
1
0
1
1
0
0
0
1
1
0
0
1
0
0
1
1
0
0
2
0
2
0
2
1
1
0
2
0
1
2
2
1
2
1
1
0
2
1
1
1
1
2
2
0
0
1
0
1
1
0
0
2
0
1
2
2
1
0
0
2
0
0
0
0
1
1
0
0
2
1
0
0
0
0
1
0
0
2
0
0
0
2
0
1
2
0
1
0
0
0
2
1
1
0
0
1
0
2
1
0
0
1
1
1
0
2
2
0
0
2
0
0
0
1
0
1
1
1
0
0
2
1
2
1
0
0
2
0
0
0
0
0
0
2
2
0
2
1
0
0
2
1
0
2
1
2
1
0
1
0
0
1
3
0
1
0
1
0
0
0
1
3
0
0
0
0
1
2
0
0
0
0
1
0
1
2
2
0
1
2
1
1
0
1
0
0
0
1
0
1
2
1
1
0
0
2
1
0
1
1
2
2
0
2
1
0
0
1
0
2
2
1
1
0
0
1
2
2
0
2
1
1
1
0
2
1
2
1
1
0
2
1
0
1
0
1
0
0
0
0
0
1
2
0
2
1
0
1
0
1
0
0
1
0
0
0
2
0
0
0
2
1
2
2
2
0
1
0
1
0
1
1
0
1
0
0
1
1
0
1
2
0
0
1
2
1
1
0
0
3
1
0
3
2
1
0
1
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
1
1
2
0
2
0
2
1
1
0
0
1
1
2
0
0
1
2
0
0
0
0
0
1
1
1
1
1
1
1
0
0
1
0
1
1
1
2
0
1
2
3
0
1
0
1
1
0
2
1
0
2
0
0
1
1
2
1
2
0
1
0
0
0
2
2
0
0
1
0
6
5
0
0
0
0
1
1
0
1
0
2
0
1
2
1
0
1
1
1
0
0
2
1
1
1
2
0
2
1
0
0
0
2
1
1
0
1
3
0
1
2
0
1
0
1
4
1
1
2
1
0
2
0
0
0
0
1
1
1
0
0
1
0
1
1
0
2
0
0
0
1
1
2
0
1
0
1
1
1
0
2
2
0
0
2
1
0
0
0
0
0
0
0
0
1
0
1
1
1
3
0
1
2
1
2
0
1
0
0
0
0
0
0
1
5
0
0
1
0
0
1
0
0
1
1
2
2
1
2
2
0
0
1
0
0
2
0
0
1
1
0
0
0
2
0
0
0
0
0
1
0
1
0
2
0
0
0
1
1
0
0
1
0
2
1
0
0
0
0
0
1
0
1
0
0
2
0
0
2
0
0
0
0
2
0
0
0
2
2
0
0
0
2
1
2
2
2
0
3
0
1
2
3
1
2
0
0
0
1
3
0
0
1
0
1
0
0
2
1
1
1
0
0
2
1
1
0
3
2
0
0
0
0
0
2
1
1
0
1
2
1
1
0
1
0
0
0
0
0
1
2
0
0
0
2
0
1
0
0
1
0
0
1
0
0
2
1
2
0
1
0
0
0
3
2
1
1
1
0
1
2
1
0
1
0
0
1
1
0
1
0
0
0
2
0
0
1
0
0
0
0
0
1
2
1
0
0
0
0
0
1
0
2
1
0
0
2
1
0
0
2
2
0
0
0
1
1
1
1
2
1
0
0
0
1
0
0
1
2
1
0
2
0
0
0
0
2
1
2
0
2
1
2
0
0
0
1
1
1
0
0
2
1
1
2
2
0
2
2
2
0
1
1
0
2
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
1
0
0
2
1
0
0
2
0
1
0
0
0
1
0
0
0
1
0
0
1
1
0
2
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
3
0
1
0
2
1
0
3
1
2
1
1
0
0
2
0
0
0
0
1
1
0
0
1
1
1
0
1
0
0
0
0
2
0
1
0
0
0
2
1
1
2
0
1
0
1
0
2
0
1
0
2
1
0
2
0
1
2
0
1
2
2
1
1
2
2
0
1
0
0
0
1
0
1
2
1
1
1
1
0
0
0
1
4
0
0
2
1
2
0
0
0
2
2
0
2
2
0
2
0
0
2
1
1
2
2
0
0
0
0
0
1
2
0
2
1
0
1
0
0
0
1
2
2
1
0
0
2
3
2
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
1
0
1
0
0
2
2
0
2
0
1
1
1
0
1
2
0
1
0
0
0
1
0
1
1
0
0
0
1
2
0
1
2
2
2
1
0
1
2
0
1
0
0
2
1
2
0
0
0
1
0
0
0
0
1
0
2
1
0
0
1
0
2
0
2
0
2
2
1
0
0
0
0
0
0
1
0
2
1
0
0
2
0
0
1
2
0
2
2
0
1
2
1
2
1
1
0
0
0
0
0
0
1
1
0
0
2
1
2
2
0
0
2
1
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
1
1
2
1
1
2
2
2
1
0
0
2
1
0
0
2
1
1
1
0
0
0
1
1
0
0
3
0
0
1
1
3
2
2
0
1
3
0
0
1
0
0
0
0
1
1
0
0
1
1
2
1
0
0
1
2
2
1
2
2
0
2
1
0
1
1
2
1
2
1
2
2
1
0
1
1
1
0
0
1
0
0
2
1
0
2
0
1
0
2
2
0
1
0
0
2
1
2
0
0
2
0
2
0
2
0
2
2
0
1
2
1
2
0
0
1
3
0
0
1
2
1
2
1
1
1
0
2
1
0
1
2
1
2
2
1
0
1
1
2
0
1
2
0
2
0
2
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
2
1
0
1
0
1
2
0
0
1
0
0
1
0
2
0
0
2
0
1
1
1
2
2
0
0
1
0
0
2
0
1
0
0
0
2
0
2
2
0
1
1
0
1
1
2
2
0
2
2
2
0
1
1
2
2
0
2
3
1
1
0
1
0
1
2
1
0
0
0
1
0
1
0
0
1
2
0
0
0
2
1
5
1
1
2
1
2
0
0
0
2
1
0
1
1
2
1
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
1
1
0
1
1
0
1
3
1
2
3
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
1
0
0
2
0
1
1
1
0
2
1
1
1
0
1
0
1
2
0
0
1
0
2
1
1
2
0
0
3
1
1
1
1
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
1
2
1
0
2
2
2
0
0
2
1
1
2
1
0
1
0
0
0
1
2
0
1
0
1
0
0
0
0
0
0
1
0
0
0
2
0
2
2
0
1
2
1
0
1
2
0
1
0
0
2
1
2
1
0
2
1
2
0
0
0
2
2
1
1
1
2
2
1
1
0
2
1
0
0
1
0
0
0
1
1
0
1
1
0
2
1
2
0
0
1
1
0
2
1
0
0
0
0
2
0
1
1
0
2
0
0
0
1
2
0
3
1
2
1
1
3
0
0
1
0
3
0
1
4
0
0
0
1
0
1
2
0
0
0
2
1
0
1
0
0
1
1
1
2
0
2
1
1
0
0
1
2
0
1
1
1
2
0
0
2
1
1
0
0
2
0
0
1
1
1
0
0
1
0
0
1
0
2
0
2
0
0
1
2
1
0
0
0
2
1
1
0
1
0
0
0
1
1
1
0
2
0
0
2
0
0
0
1
1
0
1
0
2
0
1
1
2
1
0
0
1
0
1
0
0
0
1
1
0
1
1
2
1
0
2
1
2
1
2
0
1
1
1
1
0
0
0
1
0
0
1
2
1
0
1
0
0
0
1
0
1
2
2
0
0
1
1
0
2
2
0
1
0
0
0
2
0
1
2
1
2
2
0
0
3
0
0
1
1
1
0
1
2
0
2
1
2
0
1
0
0
1
0
0
0
0
1
0
1
1
0
1
1
2
1
1
1
0
0
0
2
2
1
0
0
0
0
0
2
1
1
0
0
0
1
0
1
1
1
2
0
0
0
1
1
1
1
2
1
1
0
0
0
2
0
1
1
1
2
2
0
0
0
3
2
0
1
1
0
0
1
0
0
0
1
0
0
2
2
1
2
2
0
0
1
2
0
1
0
1
0
2
0
1
0
0
0
1
0
0
0
0
2
0
1
0
0
1
2
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
2
0
0
1
2
1
0
2
1
0
2
0
1
1
2
1
2
2
0
0
0
2
2
1
0
1
0
1
0
1
0
0
0
0
0
0
0
2
0
2
1
3
0
1
1
2
2
2
0
0
2
3
2
0
0
0
0
1
2
0
1
0
1
1
0
2
0
0
0
1
0
1
0
1
2
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
1
2
0
1
0
1
0
1
2
2
1
0
2
0
2
1
0
0
0
0
0
2
0
2
1
0
0
1
2
1
0
2
1
1
0
1
2
1
1
0
0
0
2
1
1
1
0
1
2
1
2
2
1
1
2
1
0
1
0
0
1
0
1
0
0
1
2
1
0
0
4
1
0
0
2
0
1
0
0
2
1
0
0
2
1
0
2
1
2
0
2
0
1
1
0
1
0
2
3
1
1
0
0
0
1
3
1
0
2
2
0
2
1
1
0
1
1
0
2
2
0
0
2
2
1
2
2
0
1
0
2
2
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
2
1
0
1
0
3
0
2
0
0
1
1
2
0
0
2
1
1
1
1
2
2
2
1
0
2
2
0
0
0
2
0
0
2
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
2
0
0
1
0
0
1
1
0
2
1
0
1
0
0
0
2
1
2
0
1
0
2
0
3
0
1
0
0
1
1
1
1
0
2
0
2
0
1
1
0
1
0
0
0
0
1
0
3
0
1
0
0
1
2
0
0
2
0
1
2
1
0
2
0
1
0
0
0
2
0
1
0
1
4
1
0
1
0
1
1
0
2
0
0
0
1
0
0
1
1
0
0
0
1
1
2
2
1
0
2
2
2
1
0
0
1
0
0
2
0
0
1
1
0
0
2
1
0
0
1
1
2
0
0
0
0
0
1
0
2
0
0
0
1
0
2
1
2
1
0
0
1
2
0
0
2
0
1
2
0
1
0
1
1
0
2
0
1
0
0
0
1
0
2
0
1
1
0
0
1
0
2
1
0
0
1
0
0
1
0
1
0
0
0
0
2
1
3
0
2
0
0
0
0
1
2
0
0
0
1
0
0
0
2
0
1
0
1
2
0
1
1
1
0
2
3
1
2
2
1
0
0
1
1
0
0
0
0
1
0
1
2
0
1
1
0
0
0
0
1
2
1
2
1
2
3
2
1
1
1
0
2
2
3
1
1
0
2
0
0
1
0
1
2
0
2
6
0
0
2
1
0
0
1
0
2
1
1
0
0
2
2
0
2
2
0
0
1
2
2
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
1
1
0
1
0
1
2
1
1
0
0
1
0
0
0
0
0
2
1
2
1
0
1
2
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
2
0
1
1
2
0
1
0
2
0
0
0
0
1
0
2
1
3
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
3
1
0
0
1
2
2
2
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
1
1
0
2
0
1
0
0
2
0
1
0
0
1
0
1
1
1
3
1
1
1
2
0
1
1
0
1
2
0
1
0
0
2
1
0
2
1
0
2
0
2
0
0
2
1
1
0
1
0
2
2
2
1
0
0
0
2
1
2
0
0
0
1
0
0
0
1
0
2
2
1
1
0
1
1
0
1
2
2
2
2
0
0
0
0
0
0
1
2
3
1
0
2
1
0
2
0
2
1
1
1
0
0
1
0
3
5
0
2
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
1
1
2
1
0
1
0
1
0
1
2
2
2
0
1
1
0
0
1
3
2
1
1
0
2
2
0
2
0
2
0
1
1
1
2
0
0
0
1
2
1
1
0
0
0
0
2
1
1
2
0
1
0
1
1
0
0
2
2
3
0
0
0
1
1
1
0
0
0
1
1
1
2
0
1
1
3
0
0
1
0
0
1
2
0
1
0
1
0
0
0
0
2
0
0
1
0
1
1
1
1
0
1
0
2
0
0
1
0
1
0
0
2
0
0
1
1
0
1
0
1
1
2
1
1
1
1
1
1
0
0
0
1
0
3
0
0
2
1
0
1
0
0
5
1
0
2
0
0
0
2
1
2
0
0
1
2
0
1
0
0
0
2
1
2
1
0
2
1
2
1
0
0
1
2
1
0
0
2
1
0
3
1
0
0
0
0
1
0
2
0
2
0
0
0
0
2
1
2
0
2
0
1
2
2
2
0
1
1
2
1
0
2
1
1
0
0
1
1
2
0
0
0
2
2
1
1
0
2
2
0
0
0
0
0
3
0
2
2
2
0
0
0
1
0
0
2
1
0
2
2
0
1
1
3
2
1
2
0
0
1
1
1
2
0
3
0
0
0
0
1
1
0
1
0
1
0
0
0
0
1
0
0
2
2
0
0
2
0
1
0
1
2
2
2
0
0
0
1
0
0
2
1
0
1
0
1
0
0
1
2
0
0
0
0
2
1
1
1
0
0
1
0
1
1
0
0
1
1
4
2
0
0
0
0
1
2
3
1
0
4
2
0
0
1
1
1
2
2
1
0
0
2
0
2
1
1
1
0
0
0
0
0
1
1
0
1
0
2
0
1
0
1
2
2
0
0
1
1
0
2
1
0
0
0
2
2
2
0
0
1
0
2
2
0
1
0
0
0
1
0
0
3
2
1
1
2
0
1
2
1
1
0
0
1
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
1
2
0
2
1
0
1
2
1
2
0
0
1
2
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
2
1
1
1
0
0
3
0
0
2
2
0
1
0
0
2
0
0
0
0
1
2
1
1
1
0
2
1
0
0
2
1
1
0
1
0
1
1
0
2
1
0
1
1
0
1
0
0
2
1
0
0
1
2
0
0
0
0
0
0
0
0
1
0
1
0
2
0
1
1
0
1
1
1
0
0
1
0
0
0
2
0
0
1
0
0
0
0
1
2
1
0
0
2
0
0
1
1
0
1
1
0
1
2
1
1
2
2
0
1
1
1
2
0
0
2
0
0
1
1
0
1
1
1
0
3
2
0
0
2
2
2
0
1
0
0
0
1
1
1
1
1
0
0
1
2
1
1
0
0
0
2
0
2
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
2
2
2
0
2
1
2
0
2
2
2
1
0
0
1
2
1
0
0
0
0
0
1
2
2
0
0
1
1
1
0
2
0
0
0
2
0
1
2
2
0
1
0
2
1
0
0
0
1
0
1
0
0
0
1
1
1
0
2
0
0
3
1
0
0
0
1
0
1
1
0
0
0
1
0
1
0
0
1
0
2
2
1
0
0
0
2
2
1
0
0
2
1
1
0
0
1
0
1
1
0
1
0
2
1
1
2
1
0
2
2
0
1
0
1
0
2
1
2
2
0
0
1
0
2
1
1
0
0
1
2
0
0
2
1
0
1
0
0
1
1
0
0
1
1
0
2
0
1
1
2
0
0
1
0
1
1
7
0
2
1
2
1
2
0
0
2
2
0
0
0
3
0
1
1
0
2
1
2
0
2
0
2
1
0
2
0
1
0
1
0
0
0
0
2
1
0
0
0
1
1
0
1
1
1
0
1
1
0
2
1
2
0
0
2
0
0
1
1
2
1
0
1
0
0
3
2
1
0
1
0
2
1
2
0
2
0
0
1
1
1
1
0
0
0
0
0
1
1
1
2
3
0
0
0
0
2
0
0
2
2
2
1
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
2
1
0
0
0
1
2
0
0
2
0
2
2
0
0
0
0
1
1
0
1
0
1
1
1
0
1
0
1
0
0
0
0
2
0
1
1
0
0
1
2
2
0
1
0
0
2
1
1
0
1
1
0
0
0
0
1
3
2
0
2
1
2
1
1
2
0
0
2
0
0
2
1
2
0
1
0
1
1
1
0
0
2
1
2
1
3
0
0
0
0
2
2
0
0
1
2
2
2
2
1
0
0
0
0
1
0
1
0
0
0
2
0
1
1
0
4
0
0
0
0
3
0
1
1
0
0
1
2
0
1
2
1
2
1
0
0
0
2
1
0
2
1
1
0
0
2
0
0
1
2
0
0
0
1
0
0
0
2
0
2
2
0
3
0
0
0
0
0
0
1
1
1
0
1
0
0
2
1
0
1
0
0
0
2
0
0
0
0
1
0
2
0
2
0
0
0
2
0
0
0
0
1
0
1
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
2
0
1
0
0
0
0
0
1
1
0
0
0
2
1
2
2
2
0
1
0
1
0
1
1
0
0
1
0
0
1
0
1
1
0
0
2
1
0
0
2
2
2
0
2
1
2
1
2
0
0
0
0
0
0
0
0
2
2
2
1
0
1
2
0
1
0
1
1
1
0
0
0
0
3
1
0
0
0
1
0
0
0
1
1
3
1
2
1
1
0
1
1
0
0
1
1
0
4
1
0
2
0
1
1
0
1
1
1
0
0
0
2
0
1
1
0
1
2
1
1
1
0
0
2
1
2
0
0
2
1
0
0
1
0
0
1
2
0
1
2
1
1
2
0
1
1
2
2
0
0
0
2
0
1
0
1
0
1
0
1
1
2
2
1
0
0
0
0
2
1
2
1
0
0
1
1
1
0
2
2
0
0
1
0
0
0
0
0
2
0
2
2
1
1
0
0
0
2
0
0
1
0
2
0
1
2
1
2
2
0
2
1
1
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
1
2
2
0
2
1
0
3
1
0
2
1
0
0
2
2
1
1
1
1
0
1
2
1
0
1
2
1
2
0
0
1
1
2
0
1
2
0
0
1
1
0
0
0
0
2
4
2
2
0
2
0
2
0
1
0
0
1
1
0
1
0
1
0
1
0
0
2
1
1
0
0
1
1
0
0
0
2
0
2
1
1
1
0
0
0
2
0
1
0
0
1
1
2
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
1
2
1
0
1
2
0
0
1
2
1
0
0
0
1
0
1
0
1
3
2
2
0
1
1
1
0
0
1
0
2
0
0
0
0
0
2
1
1
2
0
1
1
0
1
2
0
0
0
0
2
1
1
2
1
1
2
1
0
2
1
1
2
2
0
0
0
1
0
0
0
0
2
1
0
2
0
0
1
1
0
2
0
0
0
2
3
1
1
1
1
1
0
0
0
2
0
0
0
1
0
3
1
1
1
2
0
0
1
0
0
0
2
2
0
1
0
0
1
1
1
1
0
0
0
0
0
0
0
0
1
0
1
2
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
2
1
0
0
0
0
0
2
1
1
1
1
0
2
2
1
2
0
0
0
0
0
0
1
2
0
2
0
3
2
2
0
2
6
2
1
1
2
3
1
0
0
2
0
0
0
1
0
0
2
0
0
0
1
0
0
0
1
1
1
0
3
1
1
2
0
0
0
1
3
1
1
1
0
0
1
2
1
0
0
0
0
0
0
1
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
2
1
2
1
0
1
0
1
1
0
0
1
0
1
0
2
2
1
0
0
0
0
1
1
0
0
2
1
1
0
0
2
2
0
1
1
1
0
1
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
2
0
0
0
1
0
1
0
0
2
1
2
1
0
1
0
1
0
0
2
0
1
0
0
3
0
1
0
0
1
2
0
1
1
0
0
1
0
0
2
0
0
0
0
0
1
1
0
2
0
2
6
0
1
0
1
1
0
1
0
0
1
0
0
1
2
2
0
2
1
1
0
0
2
0
2
0
0
1
1
1
0
1
0
0
0
0
2
2
0
1
1
0
2
1
0
0
2
2
1
0
2
1
0
1
0
1
2
0
0
0
0
0
2
0
0
4
0
0
1
0
0
0
1
0
1
1
2
2
1
0
1
2
2
0
0
0
2
1
0
1
2
1
0
0
0
2
2
2
0
2
0
0
1
0
1
9
0
1
0
2
2
1
2
0
0
1
0
2
1
0
0
0
0
1
0
2
0
1
1
1
0
0
1
1
1
0
0
0
0
1
1
0
1
0
7
0
1
1
1
1
2
0
1
1
0
2
2
2
0
0
0
1
0
2
0
0
0
0
1
0
0
0
2
1
0
0
2
0
1
1
1
1
0
0
2
0
1
1
1
0
1
1
1
2
2
1
0
1
1
0
1
0
0
1
2
0
1
1
0
1
2
0
0
2
1
0
1
2
1
0
1
1
0
0
0
0
2
2
1
2
0
0
2
1
2
0
0
2
0
2
1
0
0
0
0
0
3
3
0
0
0
0
2
0
1
0
0
2
0
0
1
1
1
0
2
0
1
1
2
1
2
2
0
1
0
0
0
2
1
1
0
0
2
2
0
0
2
0
0
1
2
0
0
0
1
2
1
0
1
0
1
2
1
0
0
1
1
2
0
0
0
0
2
1
2
1
1
2
0
1
2
1
0
0
0
0
0
1
2
0
2
0
0
0
1
0
2
0
1
0
0
0
0
0
0
2
1
0
0
2
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
1
3
1
0
0
0
1
0
0
1
0
0
2
0
0
0
1
0
0
1
1
2
0
2
2
1
0
0
2
0
2
1
1
0
0
2
1
0
2
0
0
0
0
0
0
0
0
1
2
0
0
3
1
2
2
0
1
0
0
0
0
3
1
0
1
0
2
1
0
1
1
0
1
1
1
0
0
1
1
0
0
3
0
2
0
1
0
1
0
0
0
0
0
0
0
1
1
0
1
0
3
0
0
0
0
1
1
1
0
2
1
1
0
2
1
1
2
0
1
0
0
0
0
1
1
2
2
0
3
2
0
2
0
0
0
1
0
0
0
0
2
1
1
3
1
0
0
0
1
1
0
0
1
2
0
1
0
2
2
0
1
0
0
0
0
2
1
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
3
0
1
1
1
1
1
2
0
1
0
0
1
1
1
1
0
2
0
2
2
1
2
0
0
1
0
0
1
0
2
0
2
0
0
0
0
1
1
0
1
0
1
2
0
0
0
0
0
0
0
1
1
2
1
2
0
1
2
0
0
0
2
0
2
2
0
1
2
2
0
0
2
0
1
1
0
0
1
1
1
0
0
0
1
1
2
1
0
1
2
0
0
1
2
2
1
0
0
1
2
0
0
0
0
0
0
2
1
0
2
0
0
1
0
0
1
1
2
2
0
2
1
2
2
0
0
1
0
0
2
0
0
0
1
0
2
2
0
1
0
0
0
1
0
1
1
1
0
1
0
1
0
0
3
1
0
1
0
0
1
1
3
1
0
0
3
0
2
2
0
1
0
0
2
1
2
3
0
0
0
0
1
0
0
2
0
1
2
0
2
0
0
0
0
2
2
0
0
0
1
2
1
0
1
0
0
1
2
0
0
2
2
0
0
1
0
1
0
1
2
2
2
6
1
1
0
1
0
1
0
1
0
0
0
1
1
0
0
1
0
1
1
2
1
0
1
0
1
1
1
2
2
2
0
0
2
0
0
0
0
1
0
0
0
1
2
0
0
0
0
2
2
0
1
0
2
2
0
0
2
0
2
0
1
4
0
2
0
2
0
2
1
1
0
0
1
0
0
0
0
1
0
1
1
0
2
2
1
1
0
1
0
2
0
0
1
1
3
0
0
0
2
1
1
2
1
0
0
2
0
0
1
0
0
1
0
0
0
2
2
0
0
1
0
2
2
0
0
0
0
0
2
0
0
0
0
0
2
1
1
1
2
1
0
2
0
2
0
1
0
1
0
0
2
1
2
0
1
0
0
0
0
2
1
0
2
3
0
0
1
2
0
0
0
1
1
1
2
0
0
2
1
1
0
1
2
0
0
1
1
0
0
0
0
1
2
1
2
1
0
2
2
0
0
2
1
1
1
0
1
2
2
3
1
0
0
2
2
0
3
0
1
0
0
0
0
0
2
0
0
0
1
1
0
1
1
1
2
2
0
2
1
1
1
1
1
1
0
2
0
2
0
0
0
0
1
0
0
3
1
1
0
1
0
0
2
0
0
0
0
2
1
1
1
2
2
0
0
0
1
0
2
2
2
0
1
2
0
0
1
1
1
1
0
0
0
1
2
1
1
1
1
0
0
0
1
0
2
0
2
0
0
1
0
2
0
1
2
0
0
5
0
1
0
2
0
1
0
0
1
0
0
1
1
1
0
0
0
1
2
2
0
2
2
1
0
0
2
0
0
0
1
0
1
0
0
0
0
0
2
1
0
0
0
1
1
2
1
2
0
0
1
0
0
0
1
0
1
4
2
2
1
0
4
1
0
0
1
0
1
0
0
0
1
0
1
2
0
0
0
2
0
0
1
0
0
0
0
1
2
2
0
0
0
1
0
1
1
0
0
2
0
0
1
0
1
0
2
1
0
2
2
0
1
0
1
3
0
0
0
0
1
1
3
0
2
1
1
0
1
0
5
0
2
0
0
2
1
0
2
0
1
2
1
0
1
1
2
0
1
3
1
0
0
0
0
0
1
0
0
0
1
1
0
0
1
1
0
0
0
1
2
0
1
0
0
0
1
0
1
0
1
2
0
0
2
0
0
2
2
1
1
1
0
1
1
3
0
0
1
2
0
0
2
0
0
0
1
2
0
2
2
1
2
0
2
1
1
0
2
0
0
0
1
0
1
1
0
1
0
0
2
0
0
0
0
0
1
0
2
1
2
0
1
1
1
1
2
0
0
1
2
1
0
1
1
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
1
2
0
0
1
0
0
0
0
0
3
2
1
0
2
1
1
0
1
0
2
1
0
1
1
1
0
1
2
0
0
2
0
0
1
1
0
2
0
1
0
0
0
0
1
0
1
0
0
0
1
4
0
2
2
0
1
0
0
0
2
1
0
1
0
0
0
0
2
1
0
0
0
0
2
0
1
0
2
0
0
0
0
1
5
1
0
1
2
0
0
2
1
1
1
1
1
1
0
2
1
1
1
0
1
2
2
0
1
0
1
1
2
0
0
1
0
0
1
1
1
0
0
0
0
2
0
0
0
1
1
2
1
1
1
0
1
0
3
1
0
2
2
0
1
1
0
2
0
0
1
1
2
1
0
2
2
0
2
0
0
0
0
2
0
2
1
0
1
1
2
0
0
1
2
2
0
2
0
2
1
2
0
0
0
1
0
0
0
2
1
2
1
0
1
0
1
0
2
0
1
2
1
1
0
2
1
1
2
2
1
0
0
1
1
2
0
1
0
0
3
3
0
0
0
0
1
0
0
0
1
0
1
1
0
1
0
0
0
1
2
0
1
2
1
0
2
2
0
0
0
1
0
0
0
0
1
0
2
0
2
2
0
1
0
0
1
0
2
1
3
2
1
0
1
1
0
0
0
2
2
0
1
0
0
1
0
1
1
0
1
1
1
1
0
0
0
2
1
0
1
1
0
0
2
0
0
1
0
1
0
0
1
2
0
0
0
3
2
0
1
0
0
0
1
2
2
1
7
1
0
0
1
1
1
1
0
2
2
1
3
0
0
1
0
0
0
2
2
0
2
1
0
0
2
0
0
0
1
0
1
0
0
0
2
0
1
0
0
1
0
2
0
2
2
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
3
1
1
0
0
0
1
1
0
2
1
0
2
2
0
1
1
0
1
2
2
2
2
2
2
2
0
0
1
2
0
1
2
0
3
1
1
1
0
0
1
0
2
2
1
1
1
1
0
0
1
1
1
2
1
1
0
0
0
2
2
2
2
1
0
0
1
1
0
0
0
2
1
0
0
0
1
0
0
0
1
5
1
2
0
2
0
1
1
2
0
2
1
0
1
2
0
2
0
1
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
1
0
1
0
0
2
1
2
1
1
3
0
0
0
2
0
1
2
1
0
1
0
1
1
0
2
0
2
2
0
2
0
3
2
0
4
0
0
2
2
2
0
1
0
0
1
0
2
1
2
0
1
0
1
0
1
1
2
0
0
2
0
1
2
0
2
2
2
1
0
1
0
0
0
0
1
1
2
0
2
0
0
0
0
1
2
2
2
0
0
1
0
1
5
0
0
0
0
2
1
0
2
0
1
2
1
1
0
1
0
0
0
0
0
0
1
1
0
0
0
2
2
1
1
0
0
2
0
1
0
1
1
0
2
2
3
1
0
0
2
1
1
0
0
0
1
0
1
0
1
2
0
2
1
1
0
0
0
2
0
1
0
2
3
1
2
0
2
0
2
1
2
1
0
1
3
1
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
1
0
1
1
0
2
1
1
0
2
0
2
0
0
1
2
1
0
0
0
0
1
1
2
0
2
0
2
0
2
2
0
0
1
1
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
2
0
0
2
0
1
0
1
1
0
1
0
0
2
0
1
2
1
3
1
1
0
1
0
1
1
0
0
2
2
2
0
1
1
2
0
0
1
3
0
1
2
0
0
1
0
0
2
0
0
2
1
2
0
1
2
0
2
0
1
0
0
1
0
2
1
0
1
1
0
0
1
1
2
0
0
3
0
2
0
0
1
0
0
2
0
0
0
0
0
0
1
1
1
2
0
1
1
2
0
0
1
1
0
1
0
1
1
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
1
1
1
1
0
1
1
0
0
3
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
2
1
1
1
2
1
2
0
1
2
1
1
0
2
0
0
0
1
2
2
1
2
1
1
0
0
0
0
0
1
1
0
0
0
1
1
0
2
0
1
2
1
1
1
4
2
0
0
0
0
0
0
0
0
1
1
2
1
0
2
0
1
2
0
1
3
1
1
2
2
2
0
1
0
1
1
0
2
2
2
0
0
0
2
0
0
0
2
0
0
1
0
1
0
0
0
0
0
1
1
1
2
1
2
1
0
1
0
3
1
1
2
1
1
0
1
1
0
1
1
0
0
1
1
1
1
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
2
0
0
1
0
2
2
0
1
0
2
0
0
0
2
2
2
0
2
2
0
1
2
2
2
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
2
1
0
2
2
1
0
0
0
0
1
0
1
1
2
4
0
1
1
1
1
1
2
0
2
1
0
0
1
0
2
2
2
1
1
0
0
1
1
0
4
0
1
0
1
1
0
0
2
0
0
1
0
1
2
1
0
1
0
1
0
0
0
2
0
0
1
1
0
0
0
0
0
1
0
0
1
3
0
3
0
0
2
0
0
0
0
2
0
0
1
0
0
0
1
1
1
2
0
0
0
2
1
2
0
1
0
2
1
2
0
2
1
1
0
2
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
2
0
0
0
1
2
2
2
1
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
1
2
0
0
0
1
1
0
1
1
1
1
1
1
0
2
0
0
0
0
2
0
0
1
2
1
0
2
0
1
0
0
1
0
1
1
0
0
0
0
1
0
1
2
0
1
1
1
2
0
1
0
0
1
0
0
1
1
1
1
0
1
0
1
0
0
1
2
0
1
0
0
1
0
1
2
0
1
2
0
4
0
0
0
1
1
2
1
2
2
0
2
2
1
0
1
0
0
2
0
1
1
1
0
0
1
0
0
1
2
1
0
0
1
0
0
0
1
1
1
2
1
0
0
2
0
1
1
2
0
2
0
2
1
2
0
1
0
1
0
1
0
0
2
1
1
2
1
0
0
1
0
2
0
1
0
0
0
0
1
2
0
1
1
1
2
1
1
0
2
1
0
2
1
0
0
0
1
0
0
1
1
2
0
2
2
2
0
0
1
1
0
0
0
1
1
1
2
1
2
0
1
0
1
1
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
3
1
0
3
2
0
2
2
0
2
0
0
2
2
2
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
1
0
2
1
1
0
0
0
0
0
2
2
2
1
0
2
0
1
2
0
0
0
0
1
0
0
2
2
0
0
0
3
0
2
2
1
0
0
1
1
1
0
0
3
1
1
0
1
1
1
1
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
1
1
0
1
0
2
2
0
1
1
1
0
0
2
1
0
0
0
1
0
1
0
0
1
2
0
1
0
2
1
2
0
1
2
0
0
2
0
0
1
2
2
0
1
0
1
0
0
0
0
0
0
2
2
0
1
0
0
0
2
0
0
1
0
4
0
0
0
1
2
0
0
1
0
1
1
1
1
0
0
0
2
2
2
1
0
0
0
1
0
2
1
1
1
0
3
2
0
0
2
0
2
0
2
0
1
0
1
1
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
1
1
2
1
0
3
1
2
1
3
0
3
1
1
0
2
2
2
0
1
0
0
1
0
0
4
0
0
0
0
0
1
1
0
0
1
0
0
2
0
0
0
1
1
0
1
2
1
0
1
1
1
0
0
0
1
2
4
1
1
1
0
1
0
0
1
0
1
0
0
0
1
0
1
2
0
0
0
0
1
3
0
0
0
0
0
0
1
2
0
2
0
0
2
1
1
0
1
1
0
1
0
0
2
0
1
1
1
0
1
0
1
2
0
3
0
0
0
0
0
0
2
0
2
1
1
0
0
0
1
0
3
1
2
0
0
1
0
1
1
0
0
2
1
2
2
0
1
2
1
0
2
2
1
0
0
1
1
0
0
1
2
0
1
1
0
0
0
1
0
4
1
2
0
3
0
1
1
1
0
1
1
1
0
1
0
2
2
0
1
1
1
0
0
0
1
2
2
0
0
1
1
0
0
2
0
4
1
1
1
1
1
0
0
1
0
0
0
2
0
0
0
1
1
0
1
1
0
1
1
0
0
1
0
0
0
0
2
2
0
0
4
0
2
1
1
0
0
0
0
1
0
1
0
3
2
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
1
1
1
0
2
1
1
0
2
2
0
1
0
0
1
1
0
0
1
0
0
0
2
1
2
1
1
2
2
0
0
2
2
0
0
1
0
0
1
1
0
0
0
1
1
0
0
1
1
1
1
0
1
2
0
1
1
0
0
0
2
0
2
0
3
1
2
2
0
0
0
3
1
1
0
1
0
1
0
1
0
0
1
2
1
0
1
1
1
1
0
1
2
2
1
0
1
1
2
0
0
0
0
2
0
0
0
1
0
0
2
0
0
2
1
1
0
2
0
2
1
0
1
1
0
1
2
0
1
1
0
0
1
1
3
0
2
0
0
0
2
0
0
1
1
0
0
2
0
0
0
2
0
0
1
1
2
0
1
1
2
1
1
2
0
1
2
0
0
1
0
0
0
1
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
2
1
0
1
0
2
3
0
1
1
0
2
0
0
1
1
1
1
0
1
1
1
2
0
0
1
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
1
1
1
0
1
1
1
0
0
0
1
1
0
1
0
0
0
2
1
1
0
0
1
0
1
0
3
1
0
2
2
0
0
3
3
0
0
0
0
1
0
0
1
1
1
1
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
2
2
0
1
0
0
0
2
0
0
0
0
0
0
3
0
0
2
0
0
1
2
1
0
0
2
0
2
0
0
0
0
0
1
0
0
2
2
0
1
2
0
0
0
0
0
1
2
0
1
2
0
0
2
0
0
1
1
0
2
0
0
2
2
1
1
1
2
0
1
1
0
0
3
1
0
1
1
0
1
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
2
0
2
2
2
0
0
2
0
1
0
1
0
1
2
0
1
1
2
0
0
0
0
1
1
1
1
1
1
0
0
0
2
0
2
2
1
7
0
0
1
1
1
2
1
1
2
1
2
2
1
1
1
1
0
2
0
0
1
1
0
0
1
1
2
2
0
2
1
1
0
1
0
1
1
0
0
0
2
1
0
2
0
1
1
1
2
0
2
0
0
1
0
1
1
1
1
2
3
0
0
1
1
1
1
2
0
1
0
0
0
0
1
0
0
1
0
0
0
2
0
1
0
0
0
0
2
0
1
2
0
0
0
1
0
0
2
1
0
1
0
0
1
1
0
0
2
0
0
0
1
4
0
1
1
0
2
0
2
1
0
0
0
0
0
1
2
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
1
0
2
0
1
0
1
1
2
2
2
2
1
0
1
0
0
1
1
0
0
1
0
0
0
2
0
0
0
1
0
0
1
1
0
0
0
1
1
0
2
2
0
0
0
0
0
1
0
3
1
0
1
1
1
0
1
0
1
1
1
3
2
1
0
0
1
0
1
1
1
2
2
1
0
0
0
0
0
2
1
1
0
0
2
0
1
2
2
0
2
2
1
0
0
0
0
1
0
0
2
0
1
0
1
0
1
1
1
0
1
0
0
1
0
2
0
0
1
1
0
0
0
1
1
0
1
1
1
2
0
0
0
2
1
1
2
1
1
2
0
3
1
0
2
0
0
2
0
1
0
0
0
0
1
0
2
2
1
0
0
4
0
0
2
0
1
0
2
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
1
2
0
0
1
1
0
1
0
0
3
0
0
0
0
1
1
1
1
0
2
0
1
0
0
0
2
0
1
0
3
0
1
1
0
1
2
1
2
0
0
0
2
0
0
2
1
0
2
1
1
1
0
0
0
2
1
0
0
0
1
0
2
1
0
2
1
2
0
0
0
0
0
0
1
2
1
2
0
0
1
1
0
0
1
0
0
0
0
0
1
2
1
1
1
0
0
2
3
1
3
2
1
2
0
0
0
2
2
1
1
0
1
0
1
0
1
1
0
0
1
1
0
2
1
0
1
2
0
2
0
1
1
2
0
0
2
0
0
0
1
0
1
0
0
2
0
2
0
0
0
0
0
0
1
2
2
0
1
0
2
1
0
1
1
2
1
2
0
0
1
0
0
1
2
1
1
1
1
2
1
0
1
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
1
0
0
1
0
2
1
1
1
0
1
1
0
0
0
1
1
2
0
1
0
1
1
2
0
1
1
1
0
2
0
2
1
1
0
2
1
0
0
0
2
0
2
0
0
0
1
1
1
2
2
2
1
2
0
1
0
0
1
0
1
1
1
2
0
0
1
0
0
1
0
2
0
1
1
1
1
0
0
0
1
4
0
1
0
1
1
2
0
2
1
2
2
0
0
1
3
0
1
1
0
0
0
2
1
2
1
1
2
1
0
0
0
0
0
2
1
0
2
0
0
1
2
1
1
1
0
0
1
1
0
0
1
0
2
1
0
0
2
1
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
1
1
0
0
2
1
1
2
0
2
0
0
0
0
0
2
1
1
1
1
1
1
2
0
0
1
2
0
0
1
1
0
0
0
2
1
2
2
0
0
0
2
1
0
0
1
0
0
3
0
0
0
0
2
0
1
0
0
0
2
0
0
2
1
1
2
1
0
2
0
0
1
0
1
0
0
1
1
1
0
0
2
2
0
0
0
0
0
0
0
0
1
0
1
0
2
0
1
1
0
0
0
0
1
1
1
1
1
1
1
1
1
0
0
0
2
0
0
1
2
0
0
1
2
0
1
0
2
0
0
2
0
0
1
0
0
2
2
0
2
1
1
0
2
1
1
0
0
1
2
0
0
2
0
1
0
0
0
0
1
1
0
0
1
0
1
0
0
1
1
2
0
1
0
1
0
0
0
0
0
2
0
2
5
1
0
2
2
0
1
0
2
1
3
0
0
2
0
1
0
0
1
2
1
1
0
1
1
0
1
0
1
1
0
1
0
1
2
0
0
0
0
1
2
0
1
1
1
1
3
1
0
1
1
2
1
0
0
0
2
3
1
1
2
0
0
0
0
1
1
0
2
1
0
0
0
2
0
0
0
1
0
0
0
0
1
1
1
1
0
1
2
1
1
1
0
1
0
2
0
2
1
1
0
2
0
0
2
1
0
2
1
0
1
1
2
0
1
1
1
0
0
0
2
0
0
1
1
0
0
0
1
2
0
1
2
0
0
0
2
0
1
1
0
1
1
1
1
4
0
0
0
0
1
1
2
1
1
2
1
0
0
0
0
0
0
3
0
2
1
1
0
0
0
0
0
1
0
1
2
1
2
0
1
2
2
1
0
0
1
0
2
1
0
0
0
0
0
2
2
0
0
1
1
0
1
0
2
0
0
0
0
0
1
2
0
2
2
0
0
0
1
1
0
2
0
2
1
1
0
0
1
2
2
1
1
0
0
0
0
2
1
2
0
1
0
0
0
0
0
0
0
1
1
2
0
0
1
0
0
1
1
0
1
0
2
0
1
0
0
0
1
1
2
1
0
0
1
2
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
1
1
2
2
2
3
1
1
1
2
0
2
1
2
2
1
0
1
0
2
0
1
0
0
2
1
0
0
1
0
1
5
0
1
0
0
0
1
0
2
0
0
0
0
0
1
1
0
0
0
1
0
2
2
0
0
1
1
1
1
1
0
2
0
2
1
0
0
0
0
2
1
1
0
1
0
0
0
1
1
1
1
0
0
2
0
0
1
0
1
2
0
2
1
0
0
1
0
2
0
1
2
0
1
0
4
1
2
0
1
6
2
1
1
2
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
1
2
0
0
1
0
0
0
0
0
0
2
1
1
1
2
2
0
0
0
1
0
2
0
0
1
0
0
0
0
0
2
2
2
0
0
1
0
2
6
1
1
0
0
1
1
1
1
2
0
2
0
0
1
0
2
0
0
2
2
0
0
0
1
1
0
1
0
1
1
2
1
1
0
0
1
0
0
2
2
0
0
2
0
2
2
2
1
2
2
1
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
1
2
0
0
0
0
1
1
0
2
2
2
1
0
0
0
0
0
0
0
2
0
4
1
1
0
1
0
1
0
1
0
0
1
1
0
2
0
1
1
2
1
1
0
0
1
0
0
0
1
0
1
0
2
0
0
2
0
0
2
3
0
0
1
0
0
0
2
0
0
1
1
2
0
2
1
2
0
0
0
2
1
2
0
1
0
0
0
0
2
2
0
0
0
0
1
0
2
1
0
0
0
1
0
2
2
0
0
2
2
1
0
0
1
2
1
0
1
0
1
0
0
1
0
0
1
0
1
2
2
0
2
0
2
1
0
1
1
2
1
2
1
0
2
2
4
2
0
2
2
0
1
1
0
0
0
0
2
1
0
0
1
0
1
2
1
2
0
1
2
2
1
1
2
2
1
0
2
1
1
1
0
0
0
0
3
0
0
2
0
2
2
0
2
0
0
1
0
0
0
1
0
0
1
1
0
0
0
2
2
2
2
1
2
2
1
1
2
1
0
0
0
0
0
1
0
0
0
1
1
1
2
2
0
1
1
0
0
2
1
1
1
0
2
2
2
0
1
0
0
1
0
0
0
0
0
0
3
0
0
2
2
0
0
0
0
1
1
1
0
1
1
1
1
0
0
0
2
0
0
2
1
2
2
1
0
1
0
2
2
1
1
2
0
2
1
1
1
1
0
1
1
2
1
0
1
1
1
1
0
2
1
0
1
1
1
1
0
2
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
2
0
1
0
2
2
0
1
1
1
1
0
1
2
0
1
0
0
0
0
1
1
2
1
0
0
1
0
2
0
0
0
1
0
2
1
0
0
0
0
1
0
1
2
0
1
2
1
1
0
2
0
1
1
2
0
1
0
0
1
0
1
2
0
0
1
0
1
3
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
1
0
2
2
0
1
0
0
1
1
1
0
1
0
0
0
0
1
1
0
1
2
1
2
0
0
0
1
1
1
0
0
0
0
1
0
1
1
1
1
0
0
2
0
0
0
2
1
0
0
1
1
1
3
0
0
0
2
1
1
1
1
1
1
0
0
0
1
2
0
1
0
1
0
2
1
0
0
0
1
0
0
2
2
0
1
1
1
1
0
1
2
0
0
1
2
1
2
2
0
2
3
0
0
1
2
0
1
1
1
1
1
0
0
0
0
0
1
1
2
0
0
2
1
1
0
1
0
0
2
1
1
2
8
2
1
0
0
0
1
1
0
0
1
2
1
1
0
2
1
0
1
2
1
0
1
0
3
0
0
0
3
0
2
1
1
0
0
0
0
0
3
0
0
0
2
2
0
1
2
0
0
1
3
1
0
0
0
1
1
0
3
1
0
2
0
0
0
0
0
1
1
1
0
0
2
4
0
2
0
0
2
2
1
0
0
1
1
2
1
0
1
0
0
2
1
1
0
1
0
0
0
0
1
0
0
2
1
1
1
1
0
2
1
1
0
0
1
2
1
0
0
0
2
1
0
2
0
0
1
1
0
0
2
0
0
3
0
0
2
2
2
1
0
2
2
0
0
1
0
0
0
0
1
0
1
2
0
1
0
2
1
1
0
0
1
1
3
0
0
3
1
0
1
1
1
0
1
1
0
0
2
1
0
2
1
0
0
1
1
0
2
0
0
1
0
1
0
0
1
1
1
0
0
0
0
0
0
0
2
0
1
2
1
2
2
1
1
0
0
2
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
1
1
4
1
0
1
2
1
0
1
2
0
1
0
2
0
0
2
1
0
1
3
0
1
0
1
2
0
0
0
1
0
0
1
0
0
3
1
0
1
1
0
1
1
2
0
0
0
2
0
1
0
1
0
0
1
0
2
1
0
0
0
0
2
1
0
1
0
2
2
0
2
0
2
0
2
1
0
2
0
1
2
0
0
0
0
1
1
2
0
0
2
0
2
2
0
1
1
0
1
0
0
0
0
1
0
2
1
1
2
0
1
0
1
1
0
2
2
2
0
1
1
2
0
1
0
1
1
0
1
0
1
2
1
2
2
0
1
1
1
2
1
1
0
1
0
0
0
2
1
0
0
0
0
0
0
1
1
0
0
1
0
1
0
1
1
0
2
1
0
0
0
2
1
1
1
1
1
0
0
1
1
0
1
0
0
1
0
0
0
1
0
0
1
0
0
2
0
0
2
0
0
0
1
1
2
0
0
0
0
3
0
2
0
0
2
2
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
1
1
1
1
0
0
0
2
1
0
0
0
2
0
0
0
0
1
0
1
1
2
1
1
0
0
0
0
1
1
1
1
0
0
1
0
1
1
1
1
0
1
0
0
0
1
2
0
2
2
0
0
0
1
0
2
1
1
0
1
2
1
0
0
2
0
0
0
1
1
1
2
0
0
1
0
0
2
1
2
0
2
0
1
0
1
1
3
1
1
2
1
1
0
0
0
1
1
0
1
1
2
0
1
1
0
0
0
0
0
1
2
1
0
0
1
1
1
0
2
0
0
1
0
0
2
2
0
1
0
1
1
0
0
2
1
0
0
2
1
1
1
0
0
0
2
0
2
1
1
0
2
0
0
0
0
2
2
2
0
1
0
0
0
1
2
0
2
0
2
0
2
0
1
0
1
1
0
0
0
1
1
0
0
2
1
0
0
0
0
2
0
1
0
2
1
2
0
0
1
1
3
2
0
1
1
0
0
0
0
1
1
0
0
0
0
2
0
0
0
2
1
0
2
0
0
0
3
0
0
1
0
0
0
2
0
0
1
1
0
1
2
0
0
1
0
0
0
0
3
2
1
0
0
0
1
0
0
1
2
1
0
1
0
0
2
0
1
0
0
0
0
1
0
0
1
0
1
1
0
0
0
2
0
0
1
0
1
0
0
1
0
0
0
0
2
2
3
0
0
1
0
0
0
0
1
1
0
0
2
0
1
2
0
2
0
0
2
1
2
0
0
1
1
0
0
2
0
0
1
0
2
2
1
2
1
4
0
1
0
3
0
2
0
2
1
1
1
1
2
0
2
1
0
1
1
1
0
2
0
0
1
0
1
1
1
0
2
2
0
2
2
0
2
1
0
0
1
0
1
0
1
0
2
0
0
2
0
1
0
1
0
0
0
0
1
1
0
1
1
0
0
0
4
2
2
0
0
2
0
2
2
1
0
0
2
2
1
1
1
0
0
2
0
0
2
2
0
0
0
1
0
0
1
0
0
1
0
1
0
0
1
1
0
2
0
0
0
1
0
1
2
0
1
0
0
0
0
0
1
1
3
0
1
1
0
1
1
0
1
0
1
0
1
1
2
1
1
1
2
1
0
0
2
0
1
1
0
2
0
1
1
4
0
0
1
1
2
0
0
0
0
1
0
1
1
1
1
0
2
0
0
1
0
0
2
0
0
1
2
1
1
0
0
1
0
2
0
1
2
1
0
0
0
0
1
2
0
0
1
1
0
0
0
4
2
0
0
1
0
0
2
1
0
2
1
0
0
0
1
2
1
0
0
0
0
2
1
2
0
0
1
1
0
2
0
0
2
2
0
1
0
0
0
0
1
0
2
0
0
0
1
1
1
0
0
2
0
0
2
0
1
1
1
1
2
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
2
0
2
0
1
0
1
0
1
1
1
1
0
0
0
0
0
0
0
0
1
0
1
0
2
0
2
0
0
1
3
0
0
0
2
1
1
0
0
0
0
1
1
2
0
0
0
0
0
0
1
2
0
0
0
0
2
2
0
1
0
0
2
0
0
2
1
0
0
1
0
1
0
0
0
2
1
0
1
2
1
0
1
0
1
0
2
0
1
0
2
0
0
2
0
1
0
0
0
1
0
2
0
1
1
2
1
1
0
1
1
2
1
2
0
0
0
2
0
0
1
0
0
0
0
1
0
0
1
2
2
0
2
0
0
0
0
0
1
0
1
1
1
0
1
1
0
2
0
0
1
0
2
1
0
0
1
0
0
0
0
0
2
3
1
2
0
1
0
2
1
1
3
0
2
1
3
0
1
0
0
0
2
0
3
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
2
0
1
1
0
1
1
2
0
2
2
0
1
0
0
0
0
1
2
0
0
2
1
1
1
1
0
0
2
0
2
0
0
1
1
5
5
1
2
2
0
1
0
1
1
0
0
1
0
2
2
2
2
1
2
0
0
0
2
1
0
0
2
0
3
3
2
0
2
0
2
1
0
0
1
0
0
2
0
2
0
1
1
1
0
2
1
0
0
0
0
0
2
0
1
3
0
0
0
0
1
1
1
2
5
1
0
2
2
1
2
1
2
0
0
0
1
1
1
2
2
0
0
2
0
0
1
0
2
2
1
0
2
1
0
1
1
2
1
1
0
2
2
2
2
0
0
1
1
1
0
1
1
0
0
0
1
2
0
1
0
1
6
2
1
2
1
1
1
1
0
1
2
2
2
1
0
2
2
0
1
0
0
1
1
2
0
0
0
0
1
0
2
1
0
0
0
1
0
1
2
1
0
2
2
1
0
2
0
0
0
0
3
0
1
2
0
0
0
6
0
1
0
0
3
0
2
1
2
1
1
0
1
0
0
0
1
0
0
0
0
3
0
1
1
0
1
0
2
0
0
3
1
2
0
0
0
2
0
2
1
2
0
0
3
1
0
1
2
0
1
2
0
0
2
1
0
0
0
3
1
1
1
0
0
2
0
4
0
2
1
1
0
0
1
0
1
1
0
0
1
2
0
1
0
0
0
0
0
1
0
0
0
1
2
0
2
0
1
1
1
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
1
1
0
2
1
2
0
1
1
1
2
0
0
2
1
1
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
3
1
2
0
0
1
1
1
0
0
0
0
0
2
1
1
0
0
3
0
0
1
0
2
1
2
1
0
0
2
0
0
2
1
2
1
1
1
0
0
1
0
0
0
2
0
1
0
0
1
0
1
1
1
1
2
0
0
2
0
1
0
0
1
0
1
0
1
1
1
0
4
1
2
0
2
2
2
0
0
0
0
2
1
2
2
1
2
2
0
0
1
0
0
0
0
0
2
0
1
0
1
0
2
2
0
1
1
1
1
0
0
0
0
1
2
0
0
1
1
1
1
0
1
1
1
2
0
0
2
1
1
0
2
3
0
1
1
0
1
0
2
0
3
0
0
0
1
0
0
1
1
1
0
0
2
0
0
1
2
0
0
2
2
1
1
0
2
1
0
0
0
2
0
0
0
0
0
0
0
2
2
0
2
0
0
1
0
2
0
2
0
1
2
0
1
0
0
0
1
0
1
1
0
1
0
0
1
0
1
2
1
2
0
1
0
1
1
1
1
0
1
0
1
0
1
0
2
0
0
2
0
0
2
0
1
0
2
0
0
0
0
3
1
0
2
1
0
1
1
1
0
0
2
0
0
1
1
0
2
2
0
1
0
2
1
1
0
0
0
1
0
1
0
0
1
0
2
1
0
0
2
0
0
1
1
0
1
0
0
1
0
0
2
0
1
1
1
1
1
1
0
1
0
0
0
0
0
0
0
2
0
2
1
0
0
1
0
0
2
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
2
2
0
0
0
0
1
0
2
0
2
1
2
2
0
0
0
2
0
1
0
5
0
0
2
1
0
0
0
1
1
2
1
2
2
1
0
2
0
0
1
0
2
0
1
0
1
0
0
1
0
2
0
1
0
1
1
1
0
2
0
0
1
2
2
2
0
0
3
2
1
0
2
0
1
2
1
0
2
1
2
0
0
0
1
0
0
2
0
0
1
2
0
1
0
2
1
0
0
1
0
0
0
2
0
1
1
0
0
0
0
0
0
1
1
0
1
0
1
0
2
2
1
0
2
0
0
3
0
3
2
1
0
1
1
2
1
2
0
0
1
0
1
1
2
0
0
2
0
1
2
0
1
0
0
0
1
1
2
1
2
0
0
1
0
0
1
0
0
0
0
1
2
0
2
0
0
0
2
1
1
1
0
1
2
1
0
0
2
2
2
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
2
0
1
0
2
1
0
0
2
0
1
1
0
0
0
0
0
1
2
0
1
0
0
0
1
2
2
1
0
1
0
1
1
2
0
1
0
1
0
1
0
2
2
1
0
1
2
0
2
0
0
0
0
2
0
0
1
1
0
2
1
3
1
0
1
0
2
0
0
1
2
1
3
2
1
0
0
1
0
2
0
2
1
1
1
0
1
0
1
0
1
0
0
1
0
2
1
0
0
2
1
0
2
0
0
0
2
0
0
1
2
2
2
2
1
0
1
2
0
1
2
1
0
0
1
2
1
2
0
1
1
1
0
0
2
1
2
0
0
2
0
1
1
1
2
1
0
0
2
1
1
1
0
2
1
1
0
1
1
1
0
0
2
0
2
1
2
2
1
0
2
2
2
2
0
1
1
1
0
0
0
2
0
1
2
0
0
1
1
0
1
0
2
0
1
2
1
0
1
0
2
1
0
0
2
2
0
0
1
2
2
2
1
1
0
1
1
1
1
2
1
1
0
0
0
1
1
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
2
0
0
1
2
0
1
1
1
0
0
1
2
0
0
0
0
1
1
2
0
0
1
0
0
1
1
3
2
2
1
0
1
1
0
1
0
2
2
0
1
1
1
0
0
0
2
0
0
1
0
1
0
1
1
0
0
1
1
0
2
2
1
0
2
2
0
3
2
0
0
1
0
0
2
0
0
2
2
0
0
1
3
1
0
0
0
0
2
0
0
0
1
0
0
0
0
2
1
1
1
0
1
2
0
0
1
1
0
2
2
0
0
1
1
1
1
0
0
2
2
1
0
2
1
1
0
0
1
0
3
1
0
1
2
2
1
0
0
1
2
0
8
2
0
0
1
0
1
1
0
0
0
2
1
0
0
0
2
0
0
2
2
0
0
1
2
0
1
0
1
1
1
0
1
1
0
0
2
2
2
2
0
2
2
0
0
0
0
1
2
2
1
0
2
1
1
0
1
1
0
0
0
0
0
0
0
0
2
0
1
0
1
0
1
0
2
0
0
0
0
2
0
0
0
1
0
1
3
0
3
2
1
0
0
0
1
0
1
2
1
2
0
2
0
2
1
0
0
0
0
2
0
0
0
0
2
1
0
0
1
1
2
1
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
2
0
0
0
1
0
0
0
0
1
1
2
1
0
0
1
0
2
0
2
0
1
1
0
1
1
1
0
1
1
0
0
2
3
0
0
0
1
1
0
1
0
0
2
1
0
0
0
6
1
0
0
2
0
0
1
2
0
0
0
2
1
0
1
0
2
1
1
0
1
1
0
0
0
1
0
2
2
1
1
1
0
1
1
1
0
0
2
0
0
1
1
2
1
2
2
1
1
0
2
2
1
0
3
0
1
1
0
1
2
1
1
1
1
1
0
0
0
1
3
2
2
2
2
1
0
0
0
0
1
1
0
1
1
1
0
2
0
0
0
1
2
0
1
0
1
1
0
2
1
2
0
1
0
0
0
0
0
0
2
2
0
1
1
0
0
0
2
1
0
2
0
2
1
1
0
0
2
2
3
2
1
0
2
0
1
0
1
0
1
0
1
0
0
0
1
0
1
2
0
1
0
0
0
1
1
0
2
1
1
0
2
0
2
2
4
2
2
1
1
0
1
2
1
1
0
1
0
0
1
1
0
0
2
0
0
1
1
2
0
0
0
0
3
0
0
2
1
1
1
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
1
0
1
1
1
2
0
2
0
2
1
2
0
0
1
2
1
0
0
0
0
1
0
1
1
0
1
1
2
0
1
1
1
2
1
0
1
0
2
0
1
2
1
0
0
2
1
0
1
0
0
0
1
0
0
1
0
1
1
2
0
0
2
1
1
0
3
0
1
0
0
1
2
1
0
1
2
1
0
2
1
0
0
1
0
2
2
0
2
0
0
2
1
0
0
1
0
0
3
0
2
1
1
1
0
0
0
1
0
1
1
0
2
0
0
2
2
2
0
0
2
0
0
2
0
0
1
0
2
1
0
2
2
0
1
0
2
1
0
1
2
1
0
1
1
0
2
0
1
0
2
1
0
0
1
0
0
2
0
2
1
1
0
2
1
2
1
0
1
2
1
2
1
0
0
0
1
0
1
0
2
0
0
1
2
0
0
0
1
0
1
0
0
1
2
1
2
2
2
0
0
0
0
0
0
0
0
0
1
2
0
1
2
1
2
0
0
1
1
1
1
0
0
0
1
0
4
0
2
0
1
1
0
0
2
2
1
1
0
0
1
1
0
2
2
0
0
2
1
0
2
0
4
1
0
1
2
1
1
1
1
1
3
0
1
1
1
0
1
0
0
1
1
2
1
1
0
2
1
0
0
0
0
1
2
0
1
0
5
2
1
0
2
0
2
0
0
0
2
2
0
2
2
2
0
0
0
2
1
1
0
0
0
0
0
1
0
0
1
1
2
0
1
0
0
2
0
0
1
1
0
0
2
1
0
0
0
1
0
0
1
2
0
2
2
0
1
3
2
1
2
0
1
0
1
0
1
0
0
1
1
2
0
0
0
2
0
1
1
2
0
2
1
0
0
0
1
0
0
1
0
2
1
1
0
0
3
0
0
0
2
2
2
0
2
0
0
0
0
1
1
0
2
0
0
1
0
2
2
0
0
2
1
0
0
2
1
1
2
0
0
0
0
0
0
0
0
0
1
2
2
1
1
2
2
0
1
0
1
0
0
0
0
1
3
1
0
0
2
0
2
0
2
2
0
2
0
0
2
0
0
2
0
0
2
0
1
2
0
0
0
1
0
1
0
0
0
1
0
0
2
1
2
0
0
0
0
0
1
2
2
0
1
0
2
2
2
1
0
0
1
0
0
0
2
1
2
0
1
2
1
2
2
0
2
0
1
0
1
2
0
3
0
0
0
0
1
0
0
0
0
1
0
2
1
2
2
1
1
1
0
1
0
0
1
0
1
0
0
0
1
1
1
1
2
1
0
1
0
1
1
1
2
1
0
0
1
1
0
0
0
0
1
0
2
1
1
1
0
2
0
0
0
0
2
0
3
0
0
0
0
0
0
1
0
0
2
0
1
0
0
1
0
1
1
2
0
0
0
1
0
1
2
1
2
2
1
2
0
2
0
0
1
0
1
0
2
0
0
0
0
3
0
1
3
1
2
0
1
0
1
1
2
0
1
0
1
0
0
0
2
2
0
1
1
0
0
1
1
0
2
1
1
0
1
0
2
0
0
2
0
0
2
0
1
1
0
1
0
0
0
1
0
0
1
0
0
1
1
2
0
0
0
0
1
0
0
0
1
1
0
0
2
2
0
1
1
2
1
0
0
0
1
0
0
0
0
1
2
0
1
0
0
1
0
0
0
0
1
0
2
1
2
1
1
1
2
2
3
1
0
2
0
2
1
0
0
2
0
2
0
1
0
1
1
0
1
2
0
2
1
0
1
0
1
1
2
1
2
0
0
0
1
0
0
0
1
0
0
1
0
2
2
0
1
0
1
2
0
1
0
0
0
0
0
2
0
0
0
2
2
0
1
0
1
0
0
0
2
0
1
0
0
1
2
0
0
2
1
1
0
0
0
0
0
1
0
1
0
0
0
0
1
1
2
1
0
0
1
0
2
1
0
0
1
1
2
0
2
2
2
0
0
0
0
0
0
1
1
0
2
0
2
2
2
0
0
1
1
1
0
0
2
1
0
0
0
0
1
0
1
1
0
1
0
0
1
0
0
2
1
2
0
1
0
0
0
2
0
1
0
0
1
1
2
2
3
0
1
0
1
1
2
1
0
0
0
1
0
0
0
2
0
1
1
1
0
1
0
0
1
0
0
2
1
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
1
1
1
0
0
2
0
2
0
0
0
2
2
0
1
0
0
1
0
0
1
1
0
2
0
0
1
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
3
1
1
0
1
0
2
1
1
1
1
2
3
2
1
1
0
2
0
3
1
0
2
1
2
0
1
0
1
0
2
0
1
1
0
0
0
0
1
2
2
1
0
2
0
1
0
1
2
0
1
2
1
0
0
0
1
0
2
1
0
2
0
1
0
1
2
1
0
0
0
0
0
0
0
1
0
0
2
0
1
0
1
0
0
1
0
2
0
1
1
0
0
2
0
1
1
0
1
2
1
1
0
0
1
1
2
0
0
0
0
1
1
2
0
0
0
1
1
1
1
1
2
1
0
1
0
0
0
0
2
0
1
1
0
0
1
1
1
0
0
2
1
1
0
0
0
2
0
2
1
1
0
1
1
0
2
2
1
0
0
0
0
1
0
0
0
0
1
2
2
1
0
2
0
0
2
1
1
1
1
1
0
2
2
1
0
0
1
2
0
1
0
0
1
0
1
1
0
1
2
1
2
3
2
0
1
2
0
0
1
0
1
0
2
0
0
0
2
0
0
1
0
1
1
2
0
2
1
2
1
1
2
0
1
1
0
0
1
0
0
2
2
0
0
0
2
0
0
0
0
1
0
1
2
1
1
1
1
1
2
0
2
0
1
2
0
3
1
1
2
1
1
1
0
1
2
1
2
2
0
2
2
0
0
2
2
0
0
0
1
1
2
1
0
2
0
0
1
0
0
2
1
1
0
0
3
1
0
2
2
1
1
1
0
2
0
0
0
0
1
1
0
0
0
0
0
2
2
2
0
1
1
0
0
1
0
0
0
0
0
2
0
1
0
1
0
0
0
1
0
1
0
1
0
0
0
1
2
0
2
0
1
2
0
0
0
1
0
0
2
0
1
1
2
0
0
0
2
0
1
0
2
0
0
1
0
2
1
2
0
0
2
0
0
0
0
0
1
2
0
1
1
1
0
1
1
3
1
1
1
2
0
1
2
0
0
2
0
2
3
0
0
1
2
0
1
0
2
0
0
0
0
2
1
1
0
0
0
1
1
2
0
0
2
1
0
1
0
0
1
1
0
1
0
0
1
2
0
0
0
0
1
0
0
2
2
0
2
1
2
1
2
1
0
1
1
2
2
1
0
1
1
0
2
0
0
0
2
1
2
0
0
1
0
1
0
2
0
0
0
0
2
2
2
2
1
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
2
2
1
2
2
0
2
0
0
0
2
0
0
0
1
0
0
0
1
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
1
0
1
3
0
1
0
1
0
0
1
0
0
0
0
1
2
1
0
1
1
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
2
0
1
1
0
0
2
2
0
1
2
1
0
0
0
2
0
0
1
0
1
1
0
0
0
2
1
0
1
1
1
1
1
0
2
0
0
0
1
1
2
0
0
0
0
1
0
0
2
1
0
1
2
1
1
0
0
2
0
2
0
1
2
2
2
2
0
1
0
2
0
1
1
0
2
0
1
0
1
0
2
2
2
2
0
1
2
1
0
2
0
1
1
0
1
2
0
0
1
1
0
2
1
1
0
2
0
2
0
0
0
2
0
1
1
2
0
1
2
2
0
1
2
2
0
1
1
0
0
2
0
0
2
1
1
2
0
0
2
0
0
0
2
2
3
0
2
1
0
2
1
1
0
1
2
1
1
1
0
0
1
0
0
3
0
0
0
2
2
0
0
1
0
0
1
0
2
1
0
1
1
0
1
0
0
1
0
1
0
0
1
0
2
0
0
1
2
1
1
1
0
0
2
1
0
1
0
2
2
2
1
2
2
0
0
1
2
0
1
1
0
0
2
1
2
1
0
0
0
2
1
1
0
1
0
1
2
0
0
0
2
2
0
2
0
2
2
0
0
0
1
0
0
2
2
0
0
0
0
0
2
1
1
0
1
0
1
2
0
1
1
0
0
0
1
0
1
2
0
0
1
2
0
0
1
1
0
0
2
0
0
1
2
1
0
0
2
0
2
1
1
0
0
0
0
0
2
2
0
3
2
0
2
0
0
2
1
0
0
0
1
0
0
0
1
0
0
2
2
0
0
0
1
0
1
1
0
0
0
1
1
0
2
2
2
0
2
0
0
0
0
1
0
1
0
0
0
2
0
1
1
0
0
1
1
1
2
2
0
0
0
0
0
2
0
0
2
0
0
1
0
2
2
4
1
2
0
2
0
0
1
1
4
2
2
0
0
0
0
0
2
0
0
1
0
0
2
1
2
0
0
2
1
0
0
0
0
3
2
0
0
2
2
1
2
1
0
0
2
1
1
1
0
1
0
2
1
1
1
2
0
2
1
1
2
0
0
0
2
1
1
0
2
2
1
0
0
2
0
1
0
2
0
1
1
1
0
2
0
1
0
0
0
1
2
1
1
0
0
1
0
0
2
1
1
1
1
2
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
1
2
2
0
2
0
1
3
0
1
0
0
0
2
0
0
1
2
1
1
2
1
0
1
0
0
0
1
0
2
2
2
0
2
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
2
0
1
0
2
1
0
0
1
0
0
1
0
0
0
0
3
1
2
4
1
0
0
0
0
0
2
1
2
0
2
2
0
0
0
1
0
2
2
1
0
0
0
2
0
0
0
1
0
2
1
0
1
0
1
0
1
2
1
2
1
1
0
1
1
2
1
2
1
1
0
2
0
0
0
1
0
2
1
0
1
0
2
0
2
2
2
0
1
2
2
0
0
0
4
0
2
2
1
1
0
2
0
2
1
2
0
2
0
0
2
0
1
1
0
3
1
1
0
2
2
0
0
1
0
3
0
0
0
0
2
0
1
1
2
0
0
0
0
2
2
0
0
0
0
2
0
0
0
1
2
1
1
0
0
0
1
0
1
0
2
0
0
0
2
1
0
0
2
0
2
1
1
1
1
2
1
2
1
0
0
1
2
0
0
2
0
0
0
2
1
2
0
0
1
0
0
1
0
1
2
1
1
1
2
0
0
1
1
1
0
0
2
2
1
0
1
2
0
2
2
2
1
1
2
1
1
0
2
0
1
1
2
0
0
0
0
0
1
2
0
2
2
2
0
0
0
2
1
0
0
0
1
2
2
0
0
0
1
0
0
2
0
0
0
1
1
0
0
0
2
0
1
0
1
0
1
0
0
1
0
0
1
2
1
1
0
0
0
1
1
1
0
1
0
1
0
2
1
2
0
1
0
0
3
0
0
0
1
0
0
0
0
1
0
0
1
1
0
2
1
0
0
1
0
0
1
1
2
0
2
1
1
1
1
1
0
0
1
1
2
0
0
0
0
2
1
0
0
1
1
2
2
0
1
1
1
1
2
1
0
0
3
0
2
1
2
1
1
0
1
0
1
1
1
0
0
0
0
1
0
1
2
1
2
2
1
0
2
0
2
0
2
0
1
1
0
3
2
2
2
0
4
2
2
1
0
2
0
0
0
1
2
0
0
1
0
0
1
0
1
2
2
0
0
0
2
0
1
2
3
2
0
1
0
0
0
1
1
7
0
0
0
0
0
1
2
0
5
0
0
1
2
0
0
2
0
1
1
1
4
0
0
1
0
1
0
0
1
0
1
2
1
2
0
1
3
2
0
1
2
0
1
0
0
1
2
0
1
0
0
0
1
0
2
0
0
2
1
0
0
0
0
1
0
1
0
1
1
1
2
1
2
0
0
0
1
1
2
1
0
2
0
0
2
1
2
0
2
0
0
0
0
2
0
2
0
0
1
0
1
0
0
0
1
2
1
0
0
3
2
1
1
0
2
2
2
0
1
1
0
0
0
2
0
1
1
0
0
2
0
0
1
0
1
1
0
0
2
1
3
2
0
0
0
2
1
2
2
2
0
2
2
0
3
0
1
0
0
2
0
0
2
0
0
2
1
0
1
0
0
0
0
0
2
1
2
0
1
0
0
1
2
0
0
1
2
0
1
2
1
2
1
1
2
2
0
1
2
1
0
0
0
0
0
1
1
0
0
0
2
0
2
0
2
0
1
0
0
0
0
0
2
2
0
1
2
1
0
1
2
2
0
2
0
2
2
1
2
1
0
0
2
1
0
0
1
2
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
1
1
2
0
1
1
1
1
0
1
0
0
2
1
0
1
1
1
1
2
0
1
0
0
2
2
0
2
1
0
0
0
1
0
1
2
2
0
0
0
0
1
0
0
2
2
1
0
0
0
2
0
1
1
0
1
1
0
0
0
0
0
0
0
1
2
2
2
0
2
0
2
1
0
0
0
1
1
2
1
0
0
1
1
2
2
0
0
1
2
1
0
0
0
1
0
0
0
1
0
1
0
2
0
1
0
1
2
0
2
0
2
1
0
0
0
2
0
2
0
0
0
0
2
0
1
0
0
0
0
0
2
0
2
1
1
1
1
1
1
0
2
2
0
2
0
0
0
0
1
2
0
0
2
1
0
1
0
0
1
1
2
1
0
2
1
0
0
2
0
3
0
0
0
1
1
0
2
1
2
0
0
0
0
2
0
0
0
0
0
1
1
0
3
1
0
0
2
0
0
1
1
2
0
0
2
0
0
2
2
2
1
1
1
0
1
1
1
1
0
0
2
0
0
0
0
0
0
0
1
1
1
0
0
1
2
0
1
1
0
0
0
0
0
0
1
0
1
0
2
0
2
1
2
0
2
0
2
2
0
0
0
3
1
0
2
1
1
0
2
0
1
0
3
2
2
1
0
0
2
0
0
0
1
0
2
0
2
1
1
1
0
0
0
0
0
0
0
1
2
2
2
0
1
1
0
1
1
1
1
0
0
1
1
0
0
3
2
1
0
1
1
2
0
1
0
0
1
2
2
0
0
0
2
0
0
1
1
0
1
2
2
1
0
1
0
1
1
0
0
0
2
0
1
0
2
2
0
0
0
2
0
1
2
2
0
1
0
2
0
2
1
2
1
1
2
1
0
0
2
2
1
1
0
2
0
0
1
2
2
1
0
1
1
1
1
2
0
0
0
1
1
2
1
0
0
1
0
1
1
1
0
0
0
0
0
3
2
0
0
0
0
0
2
0
3
1
0
0
2
0
0
2
1
1
0
0
2
2
1
0
1
0
1
2
0
0
0
1
2
0
0
0
0
0
2
2
1
0
0
0
2
0
0
0
1
0
1
2
1
0
1
3
0
0
2
0
2
0
2
0
1
1
2
2
1
1
1
1
1
1
0
0
2
0
0
1
3
1
1
0
2
0
0
2
2
1
0
0
1
0
2
1
2
2
0
0
2
2
1
0
0
2
1
0
1
1
2
2
2
1
1
1
1
0
2
0
0
0
0
0
0
1
1
0
0
0
1
1
0
2
0
2
0
1
1
0
0
2
1
0
2
0
1
0
2
2
1
0
0
0
0
0
2
2
2
1
0
0
1
0
1
0
1
0
0
2
0
0
0
0
1
0
1
2
0
2
1
2
1
1
1
2
0
0
2
0
0
2
4
0
0
0
1
1
1
0
2
0
0
2
2
0
2
0
0
1
1
0
2
1
0
0
2
1
2
0
0
0
0
1
1
0
1
2
0
3
0
0
1
1
2
2
0
0
0
2
2
0
2
0
1
0
0
1
0
0
2
1
0
0
0
0
2
0
1
1
1
1
0
0
0
2
0
0
1
0
0
0
0
0
3
0
1
2
0
2
1
1
2
0
0
0
0
0
2
0
0
1
0
0
2
0
1
0
2
0
2
1
0
2
0
2
2
0
0
1
2
1
1
0
0
2
0
2
0
0
1
1
0
0
0
2
2
2
2
0
1
2
1
0
1
2
0
2
2
0
0
1
0
0
0
0
0
0
2
0
2
0
1
1
1
0
1
1
2
0
1
1
2
0
1
0
0
0
2
4
2
0
0
1
1
0
1
0
0
1
1
0
0
1
0
0
0
0
3
0
0
0
0
2
1
1
0
0
0
1
1
2
2
1
0
0
1
0
2
1
0
0
2
1
1
0
1
0
2
1
0
0
0
2
0
1
0
0
0
3
0
1
0
0
1
2
0
1
1
0
0
1
2
1
2
1
0
1
1
0
0
1
0
2
1
0
2
0
2
3
3
0
0
1
2
0
1
0
0
0
0
1
0
0
0
2
1
2
1
0
0
0
2
0
1
0
0
0
1
0
2
1
0
1
1
1
0
2
0
0
1
0
0
1
0
2
1
0
0
2
2
2
1
2
0
1
0
1
1
0
2
0
1
0
2
0
1
2
2
0
1
0
1
1
1
2
0
2
1
2
0
0
0
0
2
0
0
0
0
1
0
1
0
1
0
3
0
0
0
0
1
0
0
1
2
0
1
1
1
1
1
2
1
1
0
0
1
2
0
0
0
0
2
1
0
2
1
0
0
0
0
2
1
1
1
3
1
2
3
0
1
0
0
0
0
0
2
0
0
2
0
2
0
0
0
1
0
0
1
1
1
0
1
0
0
1
0
2
0
1
1
0
1
2
0
0
1
0
2
0
0
1
0
2
1
0
2
2
0
1
0
0
2
2
0
1
2
1
1
0
2
0
0
1
0
2
2
0
0
1
0
1
0
0
2
1
0
1
1
0
0
0
0
0
0
1
0
0
2
1
0
1
1
2
0
0
0
1
1
2
1
0
0
1
2
0
1
1
1
2
4
2
1
0
0
0
0
0
0
1
0
0
0
1
2
1
1
3
0
1
0
1
2
3
0
0
1
0
0
2
0
0
0
1
2
2
1
2
0
1
1
1
0
0
2
1
1
0
0
0
0
1
0
0
0
0
2
1
1
0
2
1
2
1
1
1
0
0
2
1
0
1
0
1
0
0
0
1
0
1
0
2
2
2
1
0
1
0
1
0
0
0
0
0
2
2
0
2
1
2
3
0
2
2
2
1
1
0
1
0
0
0
2
1
1
1
1
0
1
1
2
1
0
0
0
3
0
0
1
1
0
1
0
0
0
1
1
0
2
2
0
0
1
0
2
1
0
0
0
0
0
0
1
1
0
0
0
2
1
1
0
2
1
0
0
0
1
2
0
1
1
2
0
1
1
1
0
0
0
0
1
0
0
0
2
0
0
0
0
1
2
2
1
2
0
2
0
0
1
3
1
3
1
0
1
1
0
2
0
1
0
2
1
0
0
0
1
2
0
2
1
0
1
1
0
1
0
0
1
0
0
0
1
0
0
0
2
1
1
0
0
1
2
0
1
3
0
0
1
2
0
2
2
0
0
1
7
0
0
0
1
1
1
1
1
1
2
0
1
0
0
0
2
0
0
3
0
1
1
1
0
1
0
0
0
0
0
0
1
1
2
1
1
0
1
0
2
0
0
0
1
0
1
0
1
0
2
0
1
0
1
0
2
0
2
0
0
0
0
1
0
0
2
1
0
1
0
2
0
1
0
1
2
3
0
0
1
2
0
2
0
0
0
1
2
2
2
0
0
1
1
1
0
2
1
1
1
0
2
0
0
3
1
0
0
1
0
1
0
1
0
0
2
0
0
2
1
1
1
0
0
2
2
0
0
1
0
2
1
0
1
1
1
0
0
0
0
1
0
0
1
0
0
1
0
2
1
0
0
1
0
2
2
0
0
0
2
2
2
1
1
1
0
1
1
1
0
0
2
2
1
0
0
1
0
0
1
1
0
0
2
0
0
2
1
0
0
2
1
0
0
2
0
0
0
1
0
1
0
0
1
1
0
1
1
0
1
1
1
1
0
0
1
1
2
1
0
1
2
2
0
2
0
0
0
0
0
2
0
1
0
0
1
0
1
2
0
1
0
1
0
1
0
0
2
2
2
0
1
1
0
0
0
1
0
0
0
1
1
1
1
0
1
0
1
0
2
0
0
0
0
1
0
0
0
2
1
0
3
1
1
2
2
0
0
2
1
1
0
3
0
2
0
0
0
0
2
2
0
2
1
1
1
2
0
1
0
0
0
0
0
1
0
3
1
2
1
1
1
1
2
1
1
0
2
2
0
1
0
0
2
1
1
0
1
0
2
1
0
2
1
0
2
1
0
1
0
2
2
2
0
2
1
3
2
1
2
2
0
2
1
2
0
2
1
1
0
0
2
1
2
2
0
1
0
1
1
1
0
0
1
0
1
0
1
1
0
1
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
1
1
1
1
0
2
0
1
1
1
0
1
0
0
2
0
0
1
0
0
0
1
0
0
1
2
2
5
0
0
1
2
2
1
1
2
1
2
1
2
0
0
3
2
0
0
0
1
1
0
0
2
2
0
0
0
0
1
1
0
2
2
2
1
0
0
0
1
0
0
1
1
1
0
2
2
1
0
1
0
0
1
0
1
1
2
2
1
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
1
0
0
1
1
1
0
2
0
0
2
2
2
0
0
0
1
1
3
1
0
1
0
2
1
0
1
0
0
0
0
3
1
0
0
2
0
0
0
1
2
0
1
0
1
0
0
1
3
1
1
2
3
0
1
0
1
1
2
0
1
1
0
2
0
0
0
3
1
3
2
0
1
0
1
0
0
2
2
0
0
1
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
1
1
0
2
2
2
0
0
0
0
2
1
3
0
1
0
1
2
1
2
2
0
2
2
0
1
0
1
1
2
0
0
0
2
0
2
0
0
1
0
0
1
0
1
3
0
0
0
1
1
0
0
2
1
2
1
2
0
0
0
1
1
0
0
2
0
0
2
0
1
1
0
0
0
1
1
2
0
2
0
1
1
1
0
2
2
2
1
0
2
1
2
0
0
0
1
1
2
1
0
0
2
0
0
1
0
0
0
2
2
3
0
0
1
0
0
1
0
2
1
0
1
1
0
0
1
1
1
0
2
2
0
1
2
2
0
1
1
0
0
1
1
1
0
0
0
2
1
2
1
0
2
1
1
0
0
1
0
1
2
0
1
1
1
2
1
0
0
2
1
1
0
1
1
1
0
2
0
2
2
1
1
3
0
2
0
1
1
0
0
0
1
0
2
0
1
2
1
1
0
1
1
2
1
0
0
0
0
1
0
1
0
1
0
2
2
0
1
2
1
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
2
1
1
3
0
0
0
0
0
0
1
0
0
2
0
0
1
0
1
0
1
0
1
3
1
0
2
0
1
0
2
1
3
0
1
0
1
1
0
0
2
3
0
0
1
1
0
0
1
0
0
0
0
0
3
1
0
1
1
4
1
0
0
1
0
0
2
1
1
1
3
1
0
0
0
4
0
0
1
1
2
2
0
0
0
0
0
1
0
0
2
1
4
1
2
0
1
2
0
2
1
1
0
0
0
1
0
2
0
0
1
1
0
0
1
0
0
0
0
2
1
0
0
0
0
2
0
0
0
2
1
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
2
0
0
0
0
1
1
0
0
1
0
0
1
0
1
0
1
1
0
0
1
0
1
0
0
0
1
0
1
2
2
2
0
2
0
0
1
2
0
0
2
0
0
1
0
0
0
1
1
0
1
2
1
0
0
1
0
1
0
0
0
0
2
1
1
1
0
0
2
0
2
1
7
0
2
0
2
0
1
0
1
1
1
1
0
0
2
0
0
2
2
0
1
0
0
0
2
0
1
0
1
0
1
0
0
0
0
0
0
8
2
1
1
0
0
1
0
2
0
0
0
0
0
0
1
1
1
2
1
2
2
2
0
0
0
2
2
2
2
2
2
0
0
0
1
0
2
0
0
0
1
2
1
0
0
1
0
0
2
0
2
3
2
4
1
2
0
0
0
1
0
3
0
0
0
1
0
0
1
2
1
1
2
0
1
1
1
0
2
3
0
1
0
1
2
2
1
1
0
0
0
0
1
0
1
0
0
0
2
6
2
0
1
1
1
1
0
0
1
0
2
1
1
2
3
1
2
1
2
0
0
0
0
0
2
0
1
1
0
1
0
1
1
0
0
0
1
2
2
0
1
0
0
0
1
2
0
0
1
0
1
2
2
0
0
0
1
0
0
0
0
1
2
0
0
2
2
2
1
0
2
0
0
0
0
1
1
0
1
0
2
1
0
0
1
1
2
0
1
2
0
0
0
2
2
0
2
0
0
2
0
1
2
0
1
0
1
1
1
1
3
0
0
2
1
3
1
0
1
1
1
1
1
0
1
0
0
1
3
1
0
2
0
0
0
0
0
1
1
1
0
2
0
0
2
1
0
2
0
1
0
1
0
0
0
1
2
2
1
2
2
0
1
0
2
0
1
1
2
2
2
0
0
1
0
1
0
1
0
2
0
1
0
0
0
2
1
1
2
0
0
1
0
0
2
0
0
2
2
1
0
0
0
1
1
2
1
2
0
5
2
0
0
1
0
0
0
0
2
1
1
0
2
1
2
0
0
0
2
0
1
3
1
1
0
1
1
1
1
1
2
1
1
2
2
0
1
0
1
0
1
0
2
1
0
0
0
0
2
0
1
1
1
2
2
0
1
1
1
2
1
0
0
2
2
0
0
2
2
0
1
0
0
1
2
0
1
1
0
2
0
2
2
1
0
0
2
1
2
2
0
2
2
1
1
1
0
0
1
0
0
2
2
0
0
0
2
1
2
0
1
0
0
2
0
1
0
0
0
0
1
0
2
0
2
1
0
1
2
0
2
2
3
1
1
2
0
0
0
1
1
0
1
0
2
0
1
0
1
0
0
2
2
0
0
0
0
1
0
2
0
1
0
1
0
2
1
2
0
0
0
1
0
0
1
0
1
1
0
0
2
0
0
1
1
1
0
0
1
2
2
0
0
1
2
1
0
0
1
2
9
1
0
1
1
0
1
0
0
0
0
1
0
0
2
2
0
0
2
0
0
0
1
1
0
1
1
1
1
0
1
0
0
1
0
1
0
0
1
1
1
0
1
1
1
2
0
0
0
0
1
3
2
2
0
2
0
1
0
1
2
2
2
0
0
0
1
2
0
0
0
2
0
0
1
2
1
0
1
2
0
0
0
0
1
0
0
1
0
0
0
4
0
0
1
0
2
2
1
1
0
3
1
2
2
0
0
2
0
0
0
2
0
0
1
2
1
1
0
1
0
1
1
0
0
1
0
1
0
0
2
2
1
1
1
0
1
1
6
1
0
1
1
0
1
0
0
0
1
0
2
0
1
0
1
0
0
0
1
1
0
0
1
1
2
1
1
1
0
0
1
0
2
0
1
1
0
1
1
1
0
1
1
1
1
0
0
1
1
2
1
0
2
0
2
0
2
0
1
0
1
0
2
0
0
0
0
0
2
0
2
0
1
1
1
0
1
3
0
1
0
0
1
0
0
1
0
0
0
2
2
1
2
2
0
0
0
2
0
0
2
2
2
2
0
1
1
1
2
1
0
2
0
1
2
0
1
0
2
0
1
2
0
1
0
2
2
0
0
1
1
0
0
1
0
0
0
0
1
2
2
0
2
1
0
0
1
1
0
0
1
0
1
0
0
1
2
0
0
2
0
2
1
0
1
1
2
0
2
0
0
1
2
0
0
2
0
1
0
0
0
0
0
2
0
1
0
0
0
1
4
0
0
0
0
1
2
3
0
2
0
2
1
0
1
0
0
1
1
1
1
1
1
1
0
0
0
1
2
2
2
1
1
0
2
2
2
0
0
4
2
2
0
0
0
2
0
0
1
3
0
2
1
2
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
2
2
2
0
0
0
0
0
0
2
1
2
1
0
0
0
2
0
0
1
0
0
0
0
1
2
2
1
2
1
0
0
2
1
1
1
0
0
1
1
1
1
1
0
0
0
2
2
0
1
2
0
0
0
1
1
1
1
0
1
1
1
0
0
0
0
1
0
1
1
0
1
1
2
1
0
0
0
1
2
1
3
1
0
1
0
1
1
1
0
0
2
2
0
0
2
1
1
2
2
1
0
0
1
2
4
0
1
1
2
0
2
0
0
0
1
1
0
2
0
0
0
0
0
2
0
0
2
0
2
1
1
2
2
1
0
1
1
0
0
0
2
1
1
0
0
1
1
1
0
2
1
1
1
0
1
2
1
0
2
0
1
1
0
2
3
0
0
0
0
0
2
0
2
0
1
1
1
1
0
2
0
1
1
1
2
0
2
0
0
1
1
1
1
2
0
0
0
1
1
0
1
1
0
0
0
1
2
0
1
1
0
1
0
1
2
0
0
1
1
1
1
1
1
1
0
0
2
0
0
1
2
1
2
0
0
1
1
2
1
0
1
1
1
1
1
1
0
3
0
1
3
0
2
0
1
2
1
2
2
0
1
0
0
0
2
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
2
0
2
2
1
0
1
2
1
0
0
1
1
1
0
1
0
2
2
0
1
0
2
0
2
0
0
2
1
1
1
0
1
1
1
0
0
0
1
1
0
2
1
1
0
2
1
2
0
0
2
2
1
0
1
0
1
2
0
0
2
0
2
1
2
0
1
0
2
2
2
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
7
1
0
0
1
0
1
0
1
2
0
1
0
0
0
1
0
2
0
2
2
1
2
1
1
0
0
0
2
2
2
1
2
1
0
0
0
0
2
0
1
2
0
1
2
1
2
0
0
0
2
1
0
2
0
1
1
0
2
0
0
0
0
0
1
0
2
1
1
0
0
2
0
2
0
1
0
0
2
2
0
0
0
0
1
0
2
0
0
0
0
0
0
2
1
0
1
1
1
1
1
1
0
1
2
3
2
1
2
2
0
2
0
2
0
0
0
0
0
2
1
0
1
1
1
1
2
0
2
0
0
0
1
0
0
0
0
1
0
2
0
0
1
0
0
0
1
2
0
1
2
2
2
1
2
0
0
0
2
0
0
0
2
1
0
0
1
0
0
0
0
0
1
1
1
0
1
0
0
1
0
0
0
2
1
2
0
0
0
1
0
0
0
0
1
0
0
2
2
1
0
2
1
2
2
0
0
1
1
3
2
0
0
0
2
0
0
0
1
2
2
0
1
3
1
1
1
1
0
2
0
0
3
0
0
0
1
2
1
0
0
0
2
2
0
2
2
0
0
0
2
1
1
1
1
0
1
1
0
0
0
0
2
0
1
0
2
0
0
1
0
0
0
2
0
0
0
0
1
0
2
0
0
3
0
0
2
0
1
0
2
0
1
1
0
0
1
2
0
2
0
2
1
0
0
0
0
0
0
1
0
0
0
2
1
2
1
2
1
0
1
0
2
2
0
1
1
0
0
2
2
4
0
0
1
0
0
2
1
1
0
1
1
2
0
0
1
0
1
0
0
0
0
0
1
1
2
1
0
2
1
3
2
0
0
0
0
0
1
1
1
1
1
3
0
0
2
2
2
1
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
2
0
0
2
2
0
1
1
0
0
0
2
0
0
1
0
1
0
0
1
0
0
1
0
0
1
2
2
2
1
0
1
2
0
0
0
2
0
0
1
2
1
0
0
1
0
1
0
1
1
1
0
0
2
0
0
0
1
2
2
1
1
0
0
1
0
1
2
2
1
0
0
0
1
1
0
0
0
0
1
2
0
0
1
2
0
0
1
2
1
0
0
2
0
2
0
1
0
2
1
1
2
1
0
0
0
0
2
1
1
0
0
1
0
2
0
2
0
1
0
0
0
2
1
2
1
1
1
1
0
0
2
0
0
0
1
1
1
1
2
2
0
2
0
0
2
1
0
2
2
0
0
0
0
2
1
0
1
0
2
2
1
3
2
0
1
1
0
0
2
0
1
0
1
0
0
1
1
0
0
2
2
0
0
2
0
1
0
0
3
1
0
0
0
0
0
0
0
2
2
0
0
1
1
0
0
1
0
1
1
0
1
1
1
2
1
0
0
0
0
2
2
0
1
0
0
1
1
2
1
0
1
2
0
0
0
2
0
1
0
0
0
1
1
0
0
0
0
0
4
0
0
0
0
1
0
1
1
2
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
1
0
2
2
0
2
8
1
0
0
0
1
2
1
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
3
0
2
0
0
1
0
2
1
0
0
2
2
1
1
1
1
0
1
1
0
2
0
0
1
0
2
1
2
0
2
0
0
0
2
2
0
0
2
1
1
0
3
1
0
0
1
2
1
0
0
0
0
0
2
0
2
1
1
0
0
1
0
0
2
1
1
2
1
2
2
2
1
0
2
1
1
0
0
1
0
1
0
1
2
1
0
2
1
2
2
0
2
1
0
0
6
0
0
2
0
1
1
0
1
1
0
3
0
1
2
0
0
0
2
0
0
1
2
0
1
0
1
0
0
0
0
1
0
1
2
0
0
0
2
1
2
0
1
0
1
1
1
1
1
0
1
1
2
0
1
1
1
2
1
1
1
0
1
0
0
0
0
0
0
1
1
1
0
2
2
0
3
1
1
1
1
1
0
1
1
2
0
0
0
0
1
0
2
0
1
2
0
0
0
0
1
0
0
0
2
2
0
0
1
0
0
0
0
2
2
0
1
0
1
1
0
0
0
0
1
1
1
0
2
0
1
0
2
0
2
1
0
1
0
0
0
1
0
2
2
1
0
1
2
1
0
0
0
1
0
2
2
0
1
2
2
2
0
1
2
1
0
1
0
1
0
2
0
0
2
0
2
0
1
2
2
2
1
0
0
0
0
1
2
1
0
0
0
0
1
0
2
0
0
1
2
0
0
2
1
0
0
0
1
2
2
2
2
1
2
0
0
2
2
0
1
0
0
1
0
0
1
1
3
1
0
0
1
2
1
0
0
2
1
0
2
1
1
0
0
0
1
1
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
2
0
2
0
2
0
0
2
2
0
1
1
0
0
1
0
0
2
1
0
1
2
0
1
0
2
2
1
0
1
1
0
0
1
1
2
0
0
1
1
0
3
2
0
0
0
1
0
1
1
0
1
0
1
2
0
0
0
1
0
0
1
1
1
0
1
2
0
2
1
0
2
1
0
0
0
2
0
1
2
0
1
0
2
0
1
2
0
2
1
2
2
1
0
1
0
0
0
1
1
2
0
1
2
0
0
1
0
0
0
1
2
2
2
0
1
2
0
1
1
0
1
0
1
0
1
0
1
1
0
1
1
0
1
0
0
2
1
0
1
0
0
1
1
0
0
3
2
0
2
3
1
1
2
0
0
2
1
1
0
0
0
2
0
1
1
0
0
0
1
2
2
0
1
1
1
0
1
0
0
1
2
1
2
2
2
0
1
0
1
0
0
0
2
2
0
1
2
2
0
1
0
0
1
0
2
2
1
2
0
1
1
1
0
0
2
1
1
0
0
2
0
0
0
0
1
1
0
2
1
0
0
0
0
0
1
2
2
2
0
1
0
2
0
1
1
0
1
0
2
2
0
1
2
1
0
2
2
0
0
0
4
2
1
1
3
0
1
0
0
1
3
0
0
2
0
0
0
1
0
3
2
1
0
1
0
1
0
0
1
1
1
2
0
0
2
2
0
5
0
0
0
1
1
0
0
0
0
2
1
0
2
1
2
2
0
2
1
0
2
0
1
0
0
2
1
2
0
2
0
1
0
1
2
2
2
2
0
2
0
0
0
3
2
2
1
0
0
2
0
0
2
0
1
0
2
0
2
0
1
2
2
1
0
1
0
0
2
0
1
1
1
2
0
2
1
3
0
2
1
2
1
1
0
0
0
0
0
0
1
1
1
1
0
3
2
1
0
2
0
0
1
0
1
1
0
0
1
0
0
1
1
0
2
2
3
2
1
1
0
0
0
1
0
0
2
1
0
1
1
0
0
0
0
1
1
1
0
0
0
0
1
0
3
0
0
0
3
1
1
1
1
1
0
0
0
1
1
0
2
0
0
1
0
1
1
0
2
0
0
1
0
1
2
0
2
1
1
2
0
2
0
1
2
1
0
1
0
1
0
2
1
0
1
0
0
1
1
0
1
0
0
0
0
1
0
1
1
2
1
1
2
1
0
0
1
0
0
2
0
1
0
1
2
0
1
0
1
0
0
0
2
1
0
1
0
2
1
2
0
0
0
0
0
0
0
2
1
0
1
1
2
0
0
0
0
0
2
1
0
0
0
1
0
2
1
0
0
0
0
0
1
0
2
1
0
0
0
1
0
0
1
1
0
2
2
0
0
0
2
3
1
1
2
0
0
1
1
0
0
1
2
0
0
0
1
0
0
2
0
0
1
0
4
0
2
2
0
2
0
0
2
1
2
0
0
2
0
2
0
2
1
1
0
2
0
2
0
0
1
1
1
0
2
0
0
2
0
0
1
0
1
1
1
1
0
0
1
0
1
2
0
0
0
1
2
2
0
0
2
0
1
1
0
1
2
1
0
0
2
1
1
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
1
0
1
2
0
1
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
4
1
2
0
0
0
1
3
2
0
0
1
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
2
1
2
0
2
1
0
2
1
1
0
1
0
2
0
0
2
0
0
0
3
0
3
2
1
0
2
1
1
1
2
0
2
0
0
1
1
2
0
1
2
1
3
1
2
0
5
1
1
0
1
1
0
0
2
0
1
1
1
0
0
2
2
1
0
0
0
0
0
0
2
0
1
1
1
1
0
0
1
1
1
1
0
1
2
2
2
0
0
1
1
0
1
0
1
1
0
1
2
1
2
1
2
0
0
1
1
0
2
0
0
1
1
1
0
0
1
2
0
1
1
1
0
0
1
1
2
0
1
1
2
1
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
2
2
0
1
1
0
0
0
0
1
1
1
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
2
0
0
0
0
2
2
1
0
0
0
0
0
2
0
2
2
1
2
1
0
1
2
0
1
0
1
1
1
0
2
1
2
0
1
0
0
2
0
2
0
1
1
0
0
1
1
2
0
2
1
0
0
0
0
0
1
0
2
0
2
2
0
0
1
1
2
0
3
2
1
2
1
0
0
2
0
1
2
0
2
0
0
1
1
2
1
0
1
0
0
2
1
1
0
0
1
1
1
2
2
2
1
1
1
2
0
0
1
0
0
1
2
0
3
0
2
0
1
1
0
0
0
0
0
2
0
2
2
1
0
0
0
0
1
0
1
3
2
1
2
0
2
2
3
1
0
0
1
2
2
2
2
1
2
2
0
1
1
0
1
0
0
0
2
0
2
1
0
0
0
1
0
1
0
0
2
1
0
2
2
1
0
0
0
0
0
1
1
1
0
0
0
2
1
2
0
0
1
0
1
1
2
0
0
0
2
1
0
1
0
1
9
0
2
0
2
1
0
1
0
2
1
2
0
0
1
0
2
0
0
0
0
0
0
1
2
1
0
2
0
1
0
2
1
1
2
1
1
1
1
0
3
1
1
2
0
2
0
0
0
0
0
2
0
2
0
0
2
0
1
0
2
1
2
1
1
2
0
0
0
1
1
0
2
2
1
2
0
2
1
2
0
1
0
1
0
0
0
0
0
0
1
2
1
1
0
0
1
0
1
0
2
0
1
1
1
1
1
0
0
0
0
0
2
1
0
1
0
0
0
1
1
0
0
1
2
2
1
2
1
2
0
1
1
2
0
0
1
0
2
1
0
0
1
1
0
1
0
0
0
0
1
1
0
1
3
0
1
1
0
0
1
0
0
0
0
0
2
2
0
0
1
0
0
0
2
1
1
2
0
0
0
2
1
0
1
1
0
0
2
0
0
1
0
2
1
0
0
0
2
0
0
1
1
0
1
2
0
0
1
0
1
1
0
0
0
1
0
0
1
0
3
2
0
1
2
0
0
0
2
2
0
3
0
1
0
4
0
0
0
1
2
1
0
1
0
1
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
1
0
0
1
1
2
0
0
0
1
0
0
0
0
0
0
0
2
2
1
0
2
1
0
2
2
0
2
1
0
3
0
2
1
1
0
2
0
0
0
1
1
1
2
0
2
0
0
1
1
0
0
2
0
0
2
1
2
1
0
0
0
2
2
2
2
0
0
0
0
0
0
2
1
2
0
0
2
0
2
1
2
2
2
1
1
1
1
0
0
2
0
1
2
2
1
2
1
2
0
0
2
2
1
1
0
1
2
2
4
0
0
2
1
2
2
0
0
2
1
0
0
0
0
0
1
0
0
1
1
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
2
0
0
2
1
2
1
0
0
2
6
0
0
1
2
1
2
0
0
2
2
2
1
1
1
1
3
2
1
1
0
1
0
3
0
0
2
2
0
0
0
2
2
2
2
1
2
3
1
1
1
2
2
3
0
0
2
1
0
1
0
2
1
1
2
0
0
0
0
0
0
1
1
2
1
1
0
0
1
1
1
3
0
1
1
0
4
0
2
1
0
1
0
2
0
0
1
0
2
1
1
0
0
2
1
2
2
0
1
0
0
2
0
1
1
0
0
0
0
0
1
0
0
0
0
2
1
0
1
0
2
0
0
2
2
2
1
1
1
0
0
1
0
1
0
1
3
1
1
0
1
0
0
0
2
0
1
1
2
1
0
1
1
1
1
2
0
3
0
0
2
0
1
0
1
0
2
0
0
0
0
0
2
0
0
1
3
1
0
0
0
2
0
1
0
0
1
1
0
1
2
0
2
0
0
0
2
2
0
1
0
0
0
0
1
1
0
0
0
1
1
2
0
0
0
0
0
1
2
0
0
1
1
0
0
0
0
1
0
0
2
1
1
1
0
2
0
0
1
1
0
1
2
0
1
1
0
0
2
1
0
2
0
2
1
0
2
2
0
0
0
3
0
1
2
2
2
2
2
2
1
2
1
0
0
0
1
1
2
1
2
0
1
1
2
4
1
0
1
0
2
2
2
1
0
0
1
1
1
2
0
0
0
0
0
0
0
2
2
1
2
0
1
2
0
2
0
1
1
0
4
1
1
1
0
0
0
1
1
0
0
0
0
2
2
0
0
1
0
0
1
2
0
2
0
0
0
0
2
2
2
0
0
2
0
0
0
0
2
2
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
1
1
1
2
0
0
0
1
2
0
0
2
2
0
2
1
1
0
0
2
1
0
2
0
1
2
0
0
1
0
1
2
3
0
1
2
0
2
0
0
1
1
1
0
1
1
0
2
2
2
2
3
1
1
2
0
0
0
0
2
0
0
2
0
2
0
1
1
0
0
1
0
0
2
1
0
2
1
0
2
0
0
2
1
0
0
0
0
5
1
0
1
0
2
2
0
0
0
1
0
0
0
0
3
0
0
1
1
0
1
0
0
2
2
0
2
1
0
2
1
1
0
0
0
1
0
0
0
1
0
1
3
0
0
0
3
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
2
1
1
2
2
0
3
1
1
0
0
0
0
1
0
0
0
1
0
1
2
2
0
0
4
1
0
0
0
2
0
0
0
0
1
0
0
0
2
1
0
0
0
0
3
2
1
1
0
2
2
3
1
2
1
2
0
0
2
0
1
1
0
2
2
1
0
0
0
0
0
2
1
0
1
1
1
0
1
0
1
2
0
1
0
0
1
0
1
1
0
1
1
2
1
1
1
1
0
1
0
0
0
1
2
1
1
2
0
1
0
0
0
0
1
1
1
0
0
1
0
1
0
2
0
1
2
0
2
0
2
1
8
0
0
0
0
2
2
0
2
0
1
0
1
2
0
1
1
2
0
0
0
0
0
1
1
1
2
1
0
2
3
0
0
0
1
0
1
0
2
1
1
0
0
2
1
0
0
1
0
2
1
1
1
0
2
0
2
2
2
1
0
0
0
2
0
0
0
1
0
1
1
0
2
0
1
1
0
2
2
0
0
1
1
0
0
1
0
3
1
1
0
2
1
0
0
2
1
2
0
1
1
1
2
0
1
0
0
0
0
0
2
0
0
1
0
0
1
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
1
0
2
1
1
1
0
0
2
2
0
0
0
0
1
1
0
0
0
0
2
1
0
1
1
0
1
2
0
0
1
2
2
0
0
2
0
0
1
1
2
0
0
0
0
0
1
2
1
0
0
2
0
0
0
0
0
1
0
0
2
2
2
2
2
0
1
2
2
2
0
0
1
1
1
0
2
0
0
0
0
0
2
1
2
0
0
0
1
0
1
2
0
1
0
1
0
0
1
0
0
1
0
1
0
1
2
2
1
0
1
0
1
2
3
1
0
0
2
2
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
2
2
0
0
0
0
0
0
0
2
1
0
0
2
1
0
0
1
0
1
0
0
2
2
0
2
0
1
0
0
0
1
1
1
0
0
1
0
0
1
0
1
1
0
1
2
1
1
0
1
2
0
1
2
2
1
0
0
0
1
0
2
0
0
1
2
0
0
0
2
0
0
3
1
4
1
1
0
2
1
1
2
1
1
0
0
2
0
1
1
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
2
1
2
0
1
1
0
0
1
1
1
0
0
1
2
0
0
1
0
0
2
1
1
0
1
2
0
0
1
0
1
1
0
1
0
1
0
0
0
0
1
1
0
0
0
0
1
1
1
1
0
0
2
0
0
0
0
0
1
2
0
0
0
2
0
1
0
0
1
1
0
1
1
1
0
1
0
1
0
0
0
1
2
1
3
1
0
0
1
0
3
2
1
1
1
1
0
1
2
1
1
0
0
0
0
2
1
0
1
2
2
2
0
0
1
2
1
1
2
2
0
2
0
1
1
1
0
2
0
0
1
1
1
0
0
2
1
1
0
1
0
1
2
1
0
0
0
1
1
1
2
0
0
0
1
0
1
2
0
1
0
1
1
2
0
1
1
0
0
0
0
2
2
2
2
1
0
0
0
2
1
0
0
0
0
1
0
2
0
1
0
2
0
0
0
0
0
2
0
0
1
0
3
0
1
1
0
0
1
0
0
1
1
2
0
0
1
0
1
2
0
0
0
0
2
0
1
0
2
0
0
0
0
0
1
1
0
2
0
2
2
0
2
1
1
0
1
2
2
0
0
0
1
0
2
2
0
0
2
2
0
0
0
0
0
0
0
0
2
1
0
1
0
0
2
3
5
2
0
3
3
2
0
0
0
1
0
0
1
1
2
3
1
2
0
0
0
1
0
0
2
1
0
1
0
2
2
0
0
1
2
0
0
1
1
0
1
0
0
2
3
1
2
1
0
1
1
1
2
1
0
0
0
0
2
2
1
2
0
2
1
0
0
2
0
0
0
0
0
1
0
1
0
0
1
1
1
2
0
0
0
1
1
2
1
1
0
0
0
1
0
0
0
1
2
0
0
0
0
3
2
0
1
0
3
0
0
0
0
1
1
0
2
0
0
0
0
0
1
0
0
1
0
1
0
1
0
1
0
2
0
0
1
2
0
1
1
1
0
0
2
0
1
0
1
1
0
0
0
0
0
2
0
1
1
2
2
0
0
0
2
1
0
0
1
1
2
0
2
0
0
0
1
2
1
1
2
2
1
2
1
0
0
0
0
0
0
1
0
0
0
0
2
1
2
0
0
1
1
2
0
0
1
1
2
1
2
0
1
2
0
0
1
0
0
1
2
0
0
2
0
0
2
0
0
1
1
0
0
1
0
0
0
1
0
2
2
1
0
0
2
0
1
0
0
2
0
0
0
0
1
0
0
1
0
0
2
1
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
2
1
1
0
2
2
1
1
0
0
1
1
0
0
0
1
0
0
2
0
0
1
1
1
1
1
1
0
0
0
0
2
1
0
2
1
1
1
1
0
1
0
5
0
0
0
0
0
0
0
2
1
0
1
2
2
2
1
0
0
0
0
1
0
0
0
0
0
1
0
2
1
0
1
0
0
1
1
0
2
1
0
1
1
2
1
2
0
1
0
1
2
1
1
4
2
0
0
0
2
2
0
1
1
3
1
1
2
0
0
1
0
2
1
1
2
0
2
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
2
0
1
0
1
0
2
1
0
2
2
2
3
1
0
0
2
1
2
1
0
0
2
2
0
1
2
2
1
0
1
1
1
1
1
0
1
0
0
1
0
1
2
2
0
0
1
2
0
2
1
0
1
1
1
1
0
0
2
2
1
0
1
0
2
0
1
1
2
1
1
0
1
2
0
4
0
0
2
1
2
1
0
0
2
1
1
0
2
2
0
0
0
2
0
0
2
2
0
0
0
3
0
0
2
0
0
0
1
0
2
2
1
1
0
0
0
1
1
1
0
1
0
2
0
1
1
1
0
2
2
1
1
1
2
0
0
3
1
1
1
0
0
1
0
0
0
1
1
3
1
0
2
0
2
0
3
1
1
1
1
1
1
1
1
3
1
3
2
0
0
1
1
0
0
1
2
2
1
0
0
0
1
1
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
2
1
0
2
1
0
1
0
2
0
0
0
3
2
1
2
1
1
1
1
1
0
1
1
1
1
0
1
0
2
1
1
0
0
2
2
2
0
2
0
0
2
0
1
0
2
0
1
1
0
2
2
1
1
0
1
2
1
1
1
1
0
0
0
2
0
0
2
1
0
0
0
2
0
0
1
0
1
0
1
0
1
0
0
1
1
1
1
0
0
2
0
0
1
1
2
1
0
0
1
0
0
2
1
1
1
4
1
0
0
2
1
1
1
2
0
1
0
0
1
0
1
0
0
0
2
0
0
2
1
0
2
0
0
2
0
0
0
1
0
0
2
0
2
0
2
0
0
2
1
1
2
0
0
2
0
1
1
1
0
1
2
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
2
1
1
0
2
2
0
0
0
0
2
0
0
0
0
0
1
1
0
1
1
2
0
0
1
2
0
1
0
0
2
0
1
0
1
1
1
2
1
0
0
1
1
0
1
1
0
1
1
0
0
0
0
1
0
2
1
0
0
0
0
0
2
1
1
2
1
2
0
0
0
0
2
0
0
2
2
1
2
0
0
0
1
1
1
0
0
1
0
0
2
1
1
1
0
2
0
2
0
1
1
0
1
0
2
0
1
0
1
0
0
1
0
0
0
1
2
2
0
0
0
0
1
4
0
1
0
1
1
1
0
0
1
1
1
0
1
0
0
2
1
0
0
1
1
2
1
0
1
0
0
4
3
0
0
1
2
0
0
2
2
1
2
2
2
0
0
2
1
1
2
1
0
0
2
0
0
0
0
1
2
0
1
1
2
2
0
0
2
2
0
2
1
0
1
0
0
2
0
0
0
1
0
0
2
0
2
1
2
0
2
2
1
0
2
0
0
0
1
2
3
2
1
0
2
1
0
0
0
0
0
1
2
1
2
0
2
0
0
1
0
0
3
1
1
1
0
1
0
1
1
1
0
2
2
1
2
1
0
2
2
0
0
0
1
0
2
0
1
0
0
1
2
0
0
3
1
0
2
0
0
1
1
0
1
0
1
1
2
0
0
0
0
0
1
0
1
1
2
1
0
0
1
0
1
0
0
0
0
0
0
2
0
2
1
0
2
0
0
1
1
0
1
1
0
1
1
2
0
0
2
2
0
1
2
1
0
1
1
1
0
2
2
2
0
0
0
0
1
1
0
1
2
1
0
1
1
0
1
2
2
2
0
0
0
0
0
0
2
1
0
0
0
1
2
0
0
0
2
0
1
0
1
1
0
1
1
1
0
1
0
0
0
0
2
0
0
0
2
1
0
1
0
1
1
0
1
0
1
0
1
0
0
0
2
1
0
0
2
1
2
0
1
1
2
2
1
0
0
1
1
0
0
2
0
0
1
1
1
0
0
0
1
2
2
0
2
0
1
1
2
2
1
0
0
1
0
2
2
0
2
0
0
0
0
0
1
2
3
0
0
1
1
1
1
0
0
1
1
1
1
1
0
0
3
0
1
0
0
2
2
1
0
0
1
1
1
1
1
1
1
1
1
0
2
0
1
0
0
0
3
1
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
2
0
0
0
1
0
2
1
0
1
1
0
0
0
0
2
2
0
0
2
3
1
0
2
0
0
2
0
2
0
2
0
1
1
0
2
0
0
0
1
0
0
1
0
1
0
1
0
1
2
1
1
2
0
0
0
1
0
0
1
2
1
1
1
2
0
0
0
0
0
1
2
1
0
1
1
0
0
0
1
0
1
2
0
0
1
2
0
0
1
1
2
1
0
0
0
0
0
0
1
1
0
0
3
2
1
1
1
0
0
0
2
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
4
0
2
0
1
1
0
0
2
0
1
1
0
0
0
1
0
2
0
2
2
1
1
0
0
1
2
1
1
1
1
0
2
2
0
0
0
0
0
2
0
2
0
2
1
0
3
0
0
0
0
0
1
1
0
0
0
2
1
2
0
2
0
1
1
2
0
1
2
2
2
1
1
0
0
0
0
1
2
0
1
0
1
2
0
1
1
0
2
0
0
0
1
2
0
2
2
0
1
1
0
0
0
1
0
2
2
2
1
0
2
0
2
0
0
1
1
2
1
0
0
0
0
2
2
2
0
1
1
1
0
1
1
1
2
0
1
0
0
0
0
1
2
2
2
1
1
0
1
0
2
0
1
0
0
0
1
0
2
0
2
0
1
0
0
1
2
1
0
0
2
0
2
0
2
0
1
2
1
0
2
0
0
0
2
1
1
1
1
0
0
1
0
1
2
1
0
0
1
1
2
2
0
3
2
0
2
3
2
0
0
1
1
0
0
3
2
3
1
1
0
1
1
0
1
0
3
2
0
0
1
1
0
1
0
0
1
0
1
0
0
2
1
0
1
0
0
0
0
2
0
0
0
1
1
0
1
0
2
2
0
2
1
1
0
0
0
3
1
1
1
0
2
0
1
1
0
2
2
0
0
1
1
1
1
0
0
0
1
2
0
2
0
1
1
0
2
0
0
0
0
0
2
0
0
3
1
0
0
1
1
0
0
0
0
0
1
3
0
1
2
0
1
0
1
1
0
0
1
0
0
2
1
2
0
0
2
1
0
0
0
1
0
0
0
0
1
0
0
2
1
2
0
0
0
0
2
1
1
0
0
1
1
0
0
0
1
0
2
1
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
2
0
2
0
0
1
3
2
0
1
2
1
2
0
0
0
0
0
1
1
2
2
1
1
0
0
1
0
0
0
1
0
0
0
1
2
0
0
0
0
1
1
0
0
0
0
1
1
1
1
0
1
1
0
2
0
2
0
1
0
0
0
0
1
2
0
1
1
0
0
0
0
0
1
1
2
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
1
0
0
0
1
3
1
2
2
2
0
0
1
0
0
0
0
0
0
2
0
1
1
2
0
1
0
1
2
1
0
1
1
0
2
1
0
1
2
0
2
0
0
0
0
0
1
0
0
2
1
1
0
0
2
1
0
0
2
1
2
3
0
1
0
0
1
0
0
2
1
0
1
1
2
0
0
1
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
1
1
2
2
1
0
0
1
0
1
0
0
0
0
2
2
0
0
0
1
0
2
2
0
2
1
1
1
1
2
1
0
2
1
1
2
1
0
0
1
1
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
1
0
1
0
2
1
1
1
2
0
1
0
0
2
1
2
0
1
3
2
2
1
0
0
1
0
1
0
3
2
0
0
1
1
2
1
2
2
2
2
0
0
1
0
1
0
0
0
1
0
0
0
0
2
1
1
0
2
0
1
0
0
1
1
1
1
1
2
1
0
0
1
0
2
1
0
2
1
1
2
0
0
0
0
1
3
1
0
1
0
0
1
1
0
2
1
0
1
0
2
0
1
2
0
0
2
2
2
0
0
0
1
1
0
0
1
0
1
0
0
2
0
0
1
0
2
0
0
1
1
1
0
2
1
0
0
0
0
0
0
2
0
0
4
1
1
1
1
0
2
0
1
2
1
1
1
1
1
1
1
0
0
0
1
0
2
0
0
1
4
1
0
2
2
0
2
0
0
0
2
2
0
2
0
0
1
1
1
0
2
1
1
0
0
0
0
2
2
2
0
1
0
3
1
2
5
0
0
1
1
0
2
4
0
1
2
1
0
1
0
0
1
0
0
1
1
0
0
2
0
1
2
0
0
0
2
2
0
1
0
0
2
2
2
1
0
0
0
1
1
2
0
0
1
0
1
0
0
0
0
2
2
2
1
0
0
0
0
0
0
0
0
0
0
3
1
0
4
0
0
0
0
2
1
1
0
2
0
2
0
0
0
1
2
2
2
0
1
1
0
1
2
2
0
0
0
2
1
1
2
0
2
2
1
1
1
0
2
1
1
0
0
0
0
0
1
1
0
1
0
2
0
2
2
2
2
2
0
0
2
0
0
0
1
0
1
1
1
0
1
0
1
1
0
1
0
0
0
0
2
1
1
2
0
1
0
2
0
2
0
2
0
1
0
0
0
0
0
0
0
1
1
0
0
1
1
1
1
2
0
2
1
0
0
1
0
0
0
0
0
2
1
0
2
1
0
0
0
0
2
0
3
2
0
1
2
0
1
0
0
2
1
0
0
1
2
0
0
1
0
1
0
1
1
0
0
1
0
0
0
2
0
0
2
1
1
0
0
2
2
1
2
0
2
2
0
0
2
0
2
1
2
2
0
2
3
3
0
1
1
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
3
0
1
0
0
2
2
0
1
0
1
0
0
0
0
2
2
0
0
2
0
2
1
0
0
0
1
1
0
2
1
0
0
0
0
0
1
0
2
0
1
0
1
0
0
1
1
0
0
1
2
1
0
0
0
0
0
1
0
1
0
1
1
2
2
0
1
2
0
1
0
0
2
2
1
2
0
1
0
2
1
0
0
2
1
0
0
2
0
1
0
2
1
1
1
0
1
1
0
1
0
0
1
1
1
0
1
0
1
2
0
1
0
1
2
1
2
0
1
0
1
2
0
0
0
0
0
2
1
2
0
1
0
1
0
4
0
2
1
1
0
1
1
2
1
2
1
0
0
0
0
1
1
0
0
0
2
0
0
2
0
0
1
2
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
2
2
2
1
0
1
2
0
1
0
1
0
0
0
0
0
3
0
2
0
2
0
0
1
0
0
2
0
2
1
0
0
1
3
1
1
1
0
0
2
0
1
0
1
0
1
0
2
0
2
2
0
2
0
1
0
2
5
2
0
1
1
1
2
0
2
3
2
2
1
0
0
0
0
2
1
0
0
2
0
1
1
0
1
1
0
0
0
0
1
0
1
2
2
0
1
0
0
2
1
0
0
0
1
1
2
0
2
0
0
0
1
0
1
1
2
2
2
2
0
0
2
0
0
0
0
0
0
0
1
1
2
0
0
0
2
0
1
1
0
1
0
2
0
2
0
0
0
1
2
1
2
0
0
1
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
2
1
0
0
2
2
0
1
1
0
1
2
0
0
0
2
0
1
1
0
2
1
1
2
2
2
2
2
0
0
3
2
0
1
1
1
2
2
2
3
1
2
1
1
1
0
1
1
1
0
1
1
2
0
2
1
0
1
0
1
0
0
0
2
2
0
1
1
2
1
0
0
2
0
1
0
0
1
0
1
3
1
1
1
0
0
0
0
1
0
0
0
2
1
0
1
0
1
1
0
0
1
0
3
0
0
0
1
0
1
2
0
1
0
0
0
2
2
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
4
0
2
0
2
2
1
2
1
0
0
0
0
0
1
1
0
2
2
0
2
3
2
1
0
0
0
1
1
1
0
0
1
1
0
0
0
0
0
0
1
1
1
2
1
0
2
2
2
0
1
0
0
2
0
1
1
1
0
1
0
0
0
0
0
2
1
1
0
0
0
0
0
1
0
1
1
1
1
2
2
0
1
1
0
0
0
1
2
0
0
2
1
2
0
1
0
2
1
1
0
0
0
2
2
1
1
1
0
2
0
2
1
0
0
1
2
0
0
1
0
1
1
0
0
1
2
0
0
1
0
0
1
1
2
0
1
0
2
0
0
2
0
1
1
0
2
0
0
2
0
0
2
0
1
2
1
1
0
0
0
0
0
0
1
0
1
1
2
0
1
0
2
1
0
3
1
0
1
1
0
0
2
2
1
0
0
1
0
1
2
0
1
0
0
1
0
0
3
2
1
0
2
0
1
0
1
1
0
0
2
0
1
3
2
1
1
1
1
2
0
0
1
1
1
0
2
0
0
1
1
2
1
0
0
1
2
0
0
1
2
0
1
1
1
2
0
0
2
0
1
0
1
1
0
0
0
1
1
0
1
0
0
0
0
2
0
2
0
1
1
0
0
0
0
1
0
0
0
0
1
1
0
1
1
2
0
0
1
1
0
2
1
1
1
0
1
2
1
1
0
0
1
2
0
0
0
2
1
0
0
2
2
0
0
0
1
1
0
0
2
0
1
0
2
2
1
1
0
2
1
0
0
0
1
1
1
0
0
0
0
0
1
0
2
1
0
2
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
3
0
2
0
1
0
0
2
2
1
2
1
2
1
1
2
2
0
0
0
0
2
2
0
0
1
1
1
1
0
1
0
1
0
1
2
0
0
1
1
2
1
0
2
1
1
0
2
0
1
0
1
0
0
2
1
2
0
0
1
0
0
1
0
0
0
2
1
0
0
1
1
2
2
2
0
1
1
2
2
0
1
0
1
0
1
0
0
0
1
0
4
0
1
0
1
1
0
0
2
0
2
0
0
0
2
1
2
2
1
1
0
0
1
2
1
0
1
0
0
0
0
0
0
1
3
2
2
0
0
2
1
1
2
1
1
0
1
2
1
0
0
1
1
0
1
0
1
0
0
2
0
0
0
0
1
2
0
0
1
1
1
1
0
1
1
1
0
0
0
1
2
1
0
0
2
2
0
0
0
0
0
1
0
1
2
1
2
0
0
0
2
0
0
0
2
2
0
0
1
0
0
2
3
2
0
0
1
0
0
3
0
0
1
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
1
0
2
0
1
0
2
0
0
0
0
0
0
2
1
1
0
0
2
2
2
0
0
0
0
0
0
1
0
2
1
3
1
0
1
1
1
0
0
1
1
1
0
2
0
0
1
2
0
1
1
1
2
1
0
1
1
0
2
0
0
1
1
2
1
0
0
2
2
0
0
2
0
0
0
2
0
0
0
0
1
1
0
0
0
2
1
0
1
0
2
0
1
0
1
0
2
1
0
1
1
2
0
2
0
0
1
3
2
0
1
0
0
0
2
1
1
0
2
0
0
2
0
0
1
0
2
0
0
2
0
0
1
0
0
0
2
1
0
0
0
0
2
0
0
2
2
0
0
1
0
0
0
0
1
0
1
3
1
0
1
2
2
2
0
0
0
1
2
1
0
2
0
0
0
2
0
2
0
1
2
0
2
1
0
1
3
1
0
1
0
0
1
1
2
0
4
3
0
1
0
1
1
0
0
0
2
1
1
1
0
1
1
0
0
0
0
1
0
0
2
0
0
1
0
1
2
0
2
0
1
0
1
2
0
1
1
1
2
2
2
1
2
0
0
0
0
0
0
0
1
0
2
1
1
0
1
2
0
0
2
2
1
1
0
1
1
0
2
1
0
2
0
1
3
1
1
0
0
1
0
0
2
0
0
0
0
1
0
1
0
1
2
1
1
0
1
0
2
0
0
1
1
2
2
2
2
1
1
0
0
2
1
1
1
0
2
0
0
0
0
1
1
0
0
0
2
1
0
0
1
1
0
0
0
1
0
0
0
3
1
1
0
1
0
0
0
1
0
1
2
0
0
1
1
1
1
2
2
2
0
0
2
0
2
0
0
1
0
1
1
0
1
0
1
2
4
0
1
0
2
1
2
0
2
0
2
2
0
0
0
1
0
0
2
0
0
0
1
1
1
2
0
2
0
0
0
3
2
1
1
2
0
1
0
0
1
0
2
2
0
2
1
0
0
1
0
2
0
0
2
1
2
0
0
0
0
0
0
1
0
0
0
0
1
2
0
1
1
0
0
0
2
1
0
0
0
0
0
1
1
0
1
2
2
0
2
0
1
1
1
0
3
1
0
1
0
1
0
0
0
1
1
1
0
6
0
0
1
1
0
1
1
0
2
0
2
1
1
0
2
2
0
0
0
2
0
0
1
1
0
1
0
1
1
1
0
0
0
1
0
0
0
0
0
1
1
1
0
4
1
0
0
1
0
0
1
1
0
0
2
1
1
1
2
0
2
0
0
1
0
2
0
0
1
0
2
0
0
0
2
0
0
0
0
0
1
2
0
0
1
0
0
0
1
0
0
0
1
1
2
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
8
2
1
0
0
0
0
1
2
0
1
0
1
1
0
0
0
0
1
0
1
0
2
0
0
1
0
0
1
1
0
0
0
1
0
1
2
2
1
2
1
0
1
0
0
0
2
1
2
0
0
2
0
2
4
0
1
0
0
0
0
0
1
1
0
2
0
2
0
0
2
1
0
0
1
0
1
1
1
0
0
2
0
0
0
0
2
1
0
0
1
1
2
0
1
0
1
1
1
0
0
1
3
0
2
1
1
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
1
0
0
0
2
0
1
2
2
1
0
2
0
0
1
0
2
1
0
2
0
0
0
0
1
0
2
2
2
0
0
0
0
1
0
0
0
1
1
0
0
1
0
2
0
0
1
2
1
0
1
1
1
1
1
0
0
2
0
0
2
1
2
0
0
0
0
1
1
0
2
1
1
0
1
0
0
0
0
1
0
2
1
2
0
2
0
2
0
0
0
0
1
3
1
1
0
1
1
1
1
1
1
2
2
3
1
0
0
2
0
1
1
0
0
0
0
2
0
1
0
4
0
2
0
0
0
0
0
2
1
1
2
2
0
2
0
1
2
0
2
2
1
0
2
0
0
1
1
2
0
1
2
1
2
2
0
0
1
2
1
1
1
0
2
0
0
1
0
0
2
2
2
1
1
1
0
1
0
0
0
1
2
0
1
1
0
0
0
2
1
1
0
1
2
1
2
2
2
2
1
1
1
0
0
1
0
1
0
2
0
0
0
1
1
0
1
2
2
0
0
0
0
0
2
1
0
2
0
2
0
2
2
0
0
2
0
0
1
1
0
0
0
0
0
0
1
0
1
0
1
0
1
1
4
0
2
0
1
2
1
0
0
2
2
1
0
2
1
0
2
2
0
1
0
0
1
2
1
2
0
1
2
1
1
1
1
0
1
0
0
2
1
0
0
2
0
2
0
0
1
0
0
0
2
0
0
0
2
1
0
1
0
1
0
1
0
0
0
1
0
2
1
0
4
0
1
0
0
0
1
1
1
0
2
0
1
2
0
1
0
1
0
2
0
1
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
2
2
0
2
0
0
2
0
2
3
2
1
2
0
1
1
2
2
1
0
0
2
0
1
1
1
0
0
1
0
0
0
1
2
2
1
0
1
1
0
0
2
0
0
2
0
0
0
0
0
1
0
1
1
0
0
2
0
0
0
2
0
3
0
0
0
0
0
1
0
1
0
0
1
0
1
2
1
2
1
1
0
2
1
2
1
1
2
4
0
1
0
0
0
1
2
0
2
1
0
1
1
0
2
1
0
3
0
0
2
1
0
1
1
2
2
0
0
1
0
2
1
1
1
1
0
1
0
0
1
0
1
1
0
1
0
0
0
0
0
6
1
0
0
0
0
0
1
1
0
1
0
2
3
0
3
1
3
0
1
0
2
0
2
1
1
0
2
1
2
2
0
0
0
1
3
2
0
2
0
1
2
2
1
0
2
0
1
1
0
0
1
0
0
0
1
1
0
1
0
0
0
1
1
2
2
1
1
1
1
2
2
1
2
0
0
0
1
2
2
1
2
0
1
1
0
0
0
2
2
3
2
0
2
1
1
2
1
0
2
2
2
0
0
0
1
1
0
1
2
0
1
1
1
2
0
0
0
1
0
1
1
0
1
2
2
2
1
0
1
1
1
2
2
0
1
0
1
0
0
1
0
0
1
0
0
1
0
0
0
2
0
2
1
1
0
0
0
1
2
1
0
0
1
0
0
0
0
0
0
0
2
1
0
2
0
0
2
1
1
0
1
1
1
0
2
1
0
0
0
0
1
0
0
1
1
2
0
1
2
0
2
0
2
0
0
2
0
0
0
1
1
1
0
0
0
1
1
2
0
1
0
2
2
2
1
1
1
1
1
1
0
0
7
0
0
0
2
0
0
2
2
0
1
0
1
0
1
0
0
0
0
0
1
1
0
1
0
1
0
0
2
1
1
1
0
0
1
2
2
0
0
1
0
0
0
0
2
2
1
0
0
0
0
0
1
2
1
2
0
0
3
0
2
0
1
0
2
1
0
1
0
1
1
0
0
0
0
1
2
0
0
0
1
0
1
1
0
0
1
2
1
1
1
0
1
2
2
2
0
0
1
1
1
0
0
0
2
2
0
1
0
1
1
0
1
1
2
0
1
2
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
2
2
1
0
0
0
0
0
1
0
1
1
2
2
1
0
2
0
1
0
0
3
0
1
0
1
2
0
0
1
1
2
0
1
2
1
1
0
1
0
0
1
2
1
0
0
0
0
0
0
0
0
0
1
1
2
0
0
2
1
0
1
0
0
0
2
1
0
0
1
2
1
1
1
0
0
1
2
2
0
3
0
1
0
0
1
2
0
2
2
2
1
0
1
1
1
1
2
2
0
0
0
2
1
0
1
1
0
1
0
0
1
0
1
0
1
1
0
2
0
2
1
1
3
1
0
0
1
3
3
1
0
0
0
2
0
0
1
0
1
1
0
3
0
0
1
0
0
0
1
2
0
2
0
0
2
0
0
0
0
1
1
0
0
2
0
0
0
1
2
0
0
0
2
0
1
0
2
0
1
0
1
0
1
1
0
1
2
1
2
0
1
2
1
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
1
2
1
1
0
0
0
3
0
0
1
0
2
0
2
1
0
2
2
1
0
0
2
2
1
2
2
1
1
1
1
2
2
0
1
2
2
0
2
1
0
1
0
2
1
1
2
1
1
0
1
0
3
0
2
0
1
0
0
2
1
0
0
0
0
1
0
1
5
1
2
0
0
0
1
0
2
2
0
0
1
0
0
0
0
0
1
2
3
0
2
0
1
0
2
0
0
0
5
1
0
0
0
1
2
0
0
2
0
2
0
1
0
1
1
0
1
0
0
0
1
0
0
0
2
2
0
1
1
0
1
1
0
1
0
0
1
0
1
0
1
0
0
2
1
0
2
0
0
0
3
1
0
2
1
0
0
0
1
1
2
2
1
0
0
1
0
1
1
2
0
2
0
2
1
2
0
2
0
2
1
2
0
2
0
2
1
0
0
1
0
1
0
1
0
1
0
1
0
1
0
1
1
1
2
2
1
0
0
1
1
2
2
0
0
2
2
4
0
0
1
1
0
0
2
0
0
0
1
0
2
0
0
0
1
0
2
1
2
6
0
0
1
1
0
1
1
0
0
1
1
1
0
2
0
1
0
3
1
2
0
1
0
0
2
2
0
0
0
1
0
1
0
3
0
0
0
0
0
1
0
1
1
1
1
0
1
2
0
2
2
0
1
0
0
0
2
1
0
0
3
1
0
0
1
1
1
2
0
0
0
0
1
1
1
2
0
2
0
0
0
2
0
0
0
0
0
1
1
0
1
2
1
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
1
2
1
1
0
0
2
1
0
1
0
1
1
0
1
1
0
0
1
1
0
2
1
0
0
1
1
0
2
2
0
0
1
2
1
0
0
0
0
1
2
4
0
3
2
2
0
1
2
2
2
0
0
1
0
0
0
0
2
0
0
0
0
0
1
2
1
0
2
1
0
0
0
2
1
1
0
0
0
2
2
2
0
0
1
1
1
0
0
0
0
1
0
0
2
0
1
0
2
3
2
1
1
0
1
2
0
1
0
1
0
1
1
1
0
0
0
0
0
2
1
0
2
0
1
0
2
2
0
0
1
0
1
0
0
0
1
1
2
1
0
0
2
3
1
0
2
2
0
1
0
0
1
1
0
1
0
2
1
0
0
3
0
1
0
0
0
2
0
0
0
3
0
0
0
1
1
2
1
0
0
2
2
2
0
1
0
0
0
0
0
0
2
2
0
2
0
2
0
2
2
0
1
0
1
2
0
2
2
1
0
0
0
0
0
0
2
1
1
0
1
2
1
0
1
1
0
2
0
0
0
1
1
2
2
0
0
1
0
0
1
1
1
3
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
4
1
1
0
0
2
0
1
1
1
0
1
1
0
2
0
0
1
2
2
3
0
1
1
1
0
1
0
0
0
0
2
0
0
0
1
0
2
6
0
2
1
0
1
1
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
2
1
1
0
1
1
0
0
1
0
1
1
0
0
1
0
1
0
0
0
1
0
2
0
0
0
0
0
0
2
1
0
2
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
2
2
3
0
1
1
0
0
2
0
0
3
1
2
1
0
2
4
0
1
0
0
0
2
1
2
0
0
1
2
1
0
1
0
0
0
2
1
0
0
0
1
1
1
2
1
2
3
2
2
1
0
2
1
0
1
1
1
0
2
0
1
1
1
1
0
0
2
2
0
0
1
1
0
0
0
1
0
2
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
2
2
1
0
2
0
1
1
2
1
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
1
2
0
1
0
0
0
2
0
1
0
1
1
0
0
0
2
0
0
2
0
0
0
1
0
0
0
1
2
1
1
0
0
0
2
1
2
0
1
1
1
2
0
0
0
3
2
1
0
0
0
0
1
0
0
0
0
1
1
2
0
1
0
0
0
1
0
0
2
2
1
0
0
0
0
2
2
1
0
1
0
1
1
0
0
0
1
1
2
0
2
1
1
0
0
2
0
0
3
2
2
0
1
2
0
0
3
0
2
1
1
0
0
0
0
2
0
2
0
0
0
1
1
1
1
0
1
0
0
1
0
1
0
1
1
1
0
2
1
0
0
0
0
1
2
1
0
1
0
0
0
2
0
1
1
1
2
0
1
2
1
1
0
0
1
1
2
1
1
2
1
1
0
0
2
0
0
2
1
2
0
0
0
0
0
2
1
0
0
1
1
2
0
0
1
0
1
0
0
0
1
0
1
0
0
1
0
0
2
1
0
1
0
0
0
1
0
2
0
4
1
0
0
1
0
1
3
0
0
0
0
1
0
0
2
1
0
0
2
0
1
1
0
0
0
0
0
1
2
2
0
1
0
2
0
0
1
0
0
1
1
0
0
0
0
0
2
2
0
0
1
1
0
1
2
0
0
0
1
1
0
0
1
2
1
0
1
2
2
2
0
1
1
2
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
2
3
0
0
0
0
0
2
2
0
2
1
0
2
2
1
0
2
0
2
2
0
1
1
2
1
0
0
1
1
1
0
2
0
1
1
0
0
2
0
0
0
1
0
1
0
0
2
1
0
2
1
0
0
0
0
2
0
0
0
0
1
0
3
0
0
0
2
1
0
0
1
2
2
1
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
1
0
0
0
1
0
1
2
2
0
2
0
2
0
0
0
0
0
1
1
0
0
2
0
1
2
1
2
2
0
1
1
0
0
0
1
1
0
1
0
0
1
1
0
0
2
0
0
2
2
1
0
0
1
1
1
0
0
0
0
3
0
2
0
1
0
1
1
1
0
0
4
0
1
0
0
2
0
1
1
0
1
1
2
1
0
1
0
1
2
0
1
1
0
2
0
0
0
0
0
0
2
2
1
0
1
1
0
0
1
0
0
2
0
0
3
0
0
2
1
1
5
1
0
0
1
1
2
2
2
0
0
1
1
1
0
0
0
1
1
2
0
0
0
2
0
1
1
0
0
0
0
1
1
0
0
0
0
2
1
0
1
0
2
0
0
1
0
0
1
2
1
2
0
0
0
1
0
0
0
2
0
2
1
0
0
0
2
1
2
0
0
1
0
0
1
1
0
0
0
1
1
0
0
1
0
0
0
0
1
0
2
0
0
1
1
2
0
0
0
2
0
0
0
2
0
1
1
1
0
1
1
0
2
0
1
1
1
0
0
2
0
0
0
1
0
0
0
1
0
0
2
1
0
0
2
1
0
0
0
0
1
1
2
0
0
2
0
0
1
1
2
1
1
1
0
1
2
0
0
1
0
0
2
0
2
0
0
1
0
0
0
1
2
0
0
1
0
1
0
0
0
1
1
1
1
0
1
3
0
2
1
1
2
0
1
2
1
0
0
0
2
1
0
0
2
0
0
0
1
2
1
2
1
1
0
2
1
0
1
2
1
0
0
1
2
0
0
1
0
1
0
0
1
1
2
1
0
1
1
2
2
2
1
0
0
0
0
2
1
1
1
2
1
0
2
1
1
0
1
0
0
0
1
0
1
0
0
0
0
0
2
0
2
0
1
0
1
0
0
0
0
0
0
0
0
2
0
1
0
3
0
2
0
2
1
0
1
0
1
0
2
0
1
0
0
1
2
2
2
2
0
1
0
0
1
1
1
2
2
2
2
0
0
0
0
1
1
1
1
2
0
0
0
1
1
0
1
0
0
0
0
2
0
2
0
1
0
1
0
1
1
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
1
0
0
1
0
2
0
3
0
1
2
2
1
0
1
2
1
1
0
1
1
2
0
1
0
0
1
1
0
0
0
0
0
0
0
1
1
2
0
2
1
0
0
0
2
1
2
0
0
2
1
0
0
2
0
1
1
0
2
1
1
0
1
2
0
2
0
2
2
1
2
0
0
0
0
0
1
2
2
0
1
0
2
3
0
0
0
0
2
0
0
0
0
2
1
1
2
0
0
1
0
0
0
2
1
0
1
0
1
1
0
0
0
1
1
0
1
1
1
3
1
2
2
0
0
0
0
1
0
2
0
0
0
1
2
0
1
1
1
0
0
1
1
0
0
2
1
2
0
2
0
2
2
1
2
0
0
1
0
1
1
1
0
1
2
0
1
2
0
0
1
0
1
1
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
1
0
1
0
2
0
0
2
2
0
0
0
2
0
0
1
0
1
2
1
1
0
1
1
1
0
2
1
0
0
0
2
0
2
1
1
2
2
2
2
2
2
1
2
0
1
0
1
0
0
2
1
0
0
0
0
1
0
1
2
2
2
0
0
0
1
1
0
0
0
1
2
1
0
2
0
0
0
0
1
2
0
0
0
0
1
2
0
1
0
1
0
1
0
2
2
2
0
0
1
2
0
0
0
0
2
1
1
0
1
0
1
1
1
1
0
1
0
2
0
0
0
2
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
2
2
1
0
0
0
1
1
2
4
2
1
1
0
0
0
0
2
1
0
1
0
2
0
0
1
2
0
0
1
0
2
0
0
2
0
2
1
0
2
1
0
1
1
1
0
1
1
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
1
0
2
0
2
0
1
0
1
0
2
2
0
0
2
0
0
2
1
0
0
0
2
0
0
1
1
1
0
1
2
0
0
0
1
0
0
2
1
0
1
0
1
0
1
2
0
0
1
1
1
1
0
0
1
4
0
1
1
1
0
1
2
0
1
0
0
0
1
1
0
0
2
2
0
0
0
1
2
0
2
0
1
0
1
0
2
1
0
0
0
0
0
0
1
2
2
0
0
2
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
3
2
2
1
0
0
1
0
1
2
2
1
1
0
2
2
1
0
1
2
1
2
1
0
1
2
0
1
0
0
2
0
0
2
0
2
1
1
0
0
0
0
0
1
1
2
0
0
0
0
0
2
0
1
1
2
1
2
0
2
1
0
0
2
0
1
0
1
2
1
0
1
0
0
2
1
0
0
3
0
0
1
1
2
0
0
0
1
0
1
2
1
1
1
0
2
1
0
0
2
2
1
0
1
0
2
0
0
2
0
2
0
1
0
0
0
2
2
0
0
0
0
0
2
2
0
1
1
1
2
0
0
1
0
1
0
0
0
1
0
0
0
0
0
2
1
1
1
1
0
0
1
0
0
0
0
0
0
0
1
0
2
0
1
3
1
1
0
0
3
0
0
0
0
1
1
0
0
0
0
0
1
2
1
0
4
1
1
0
2
0
1
4
1
2
0
0
1
0
0
1
0
0
0
0
0
0
0
1
3
1
1
2
1
3
1
0
0
2
2
0
1
0
0
0
1
2
1
0
0
2
0
2
0
0
0
0
0
0
0
1
0
2
1
2
0
1
1
1
1
0
0
1
2
0
1
2
3
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
1
2
2
0
1
0
0
1
0
0
0
0
0
0
0
1
1
1
1
0
2
2
0
0
2
1
0
1
0
1
2
1
0
1
0
0
0
2
1
0
5
1
0
1
0
2
0
0
0
0
0
2
0
1
1
0
0
2
1
2
0
0
1
0
0
1
0
3
1
0
0
0
0
1
2
1
0
0
2
2
2
1
0
1
2
2
0
0
0
0
2
1
1
2
0
0
2
1
1
1
0
0
2
2
1
2
0
2
0
0
2
0
2
0
1
2
0
1
0
0
0
2
1
0
0
2
0
2
1
0
2
0
0
2
0
0
2
0
0
0
1
0
0
1
1
2
1
1
0
1
0
1
1
2
0
1
2
3
0
0
0
1
0
2
0
0
1
3
0
0
2
0
1
0
0
2
1
1
0
0
1
0
1
1
0
2
2
0
0
1
1
0
1
1
0
1
0
0
1
2
1
2
0
1
0
1
0
0
2
0
2
0
2
1
0
1
0
0
1
1
1
2
1
1
2
1
0
0
0
0
0
1
1
0
0
2
1
0
1
2
1
1
2
0
2
0
0
1
1
2
2
2
0
0
0
0
1
1
0
1
0
0
1
0
1
0
1
0
1
1
2
0
1
0
0
0
0
0
2
2
0
0
0
0
0
2
0
7
0
0
1
0
4
1
0
4
2
0
0
0
0
1
0
0
0
1
1
0
1
0
2
1
1
0
2
1
1
0
2
2
0
2
0
0
1
1
0
1
0
1
1
1
0
1
0
2
0
0
1
0
1
1
2
0
0
0
1
0
0
0
1
2
2
0
1
0
2
2
1
0
2
0
2
0
2
2
0
0
1
1
0
2
0
0
0
1
0
2
0
2
0
1
2
0
0
1
1
1
0
0
2
0
1
2
0
0
1
0
1
1
0
2
1
1
2
0
0
0
0
1
2
0
1
1
1
0
0
2
0
1
2
0
1
1
0
2
0
0
1
1
1
0
1
1
0
1
2
0
0
1
0
1
1
0
2
0
0
4
1
2
1
0
2
0
0
0
1
0
0
0
0
0
2
0
1
0
1
0
1
0
0
0
2
0
0
1
0
1
3
0
1
2
0
1
1
0
1
1
3
0
1
1
1
0
2
1
1
0
2
2
1
2
1
3
1
1
1
1
1
1
0
2
0
1
0
1
2
2
1
0
1
1
0
1
1
1
0
0
2
0
0
0
0
0
2
1
0
1
1
1
2
1
0
1
0
2
0
0
0
0
0
1
0
2
0
2
1
0
0
1
1
1
0
0
0
1
2
1
2
3
0
0
1
1
0
0
0
0
0
1
0
0
1
2
1
2
0
0
0
0
0
1
0
0
1
2
1
0
2
2
2
1
0
2
0
2
2
0
1
0
1
2
0
1
0
2
3
1
2
2
0
0
0
1
2
0
1
0
0
0
1
0
0
0
2
1
2
0
1
2
1
1
2
0
1
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
2
2
1
0
1
0
0
1
0
0
1
0
2
2
1
0
0
0
1
0
2
0
0
0
1
1
1
1
1
0
0
0
0
0
0
0
1
0
2
0
0
1
1
1
0
0
2
2
0
2
2
2
0
0
0
2
1
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
1
2
0
1
0
0
2
0
0
0
1
1
0
1
2
2
0
0
1
1
1
2
0
0
0
0
1
0
0
0
0
0
0
1
2
0
1
2
1
1
2
0
2
0
1
1
6
0
0
1
0
0
0
1
1
0
1
0
0
0
0
1
2
0
1
2
1
1
0
0
2
0
2
1
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
2
0
0
1
1
0
2
0
0
0
0
0
1
2
2
1
2
2
1
3
0
1
2
1
2
1
1
0
0
0
2
0
1
2
0
1
1
2
2
1
1
1
0
1
2
1
0
0
2
1
0
0
0
1
1
1
2
0
1
0
0
1
1
0
1
0
0
0
1
1
2
1
2
1
2
2
1
2
1
0
0
2
0
1
2
0
0
1
0
0
3
1
0
1
0
2
0
1
1
1
1
0
1
0
1
1
1
1
2
2
0
0
0
1
1
1
1
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
2
1
1
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
2
2
0
2
0
2
0
1
0
1
1
1
0
0
1
2
1
2
0
1
0
0
0
1
0
2
2
0
0
1
1
0
1
1
1
0
2
1
0
0
0
0
0
1
2
2
1
2
1
1
1
0
0
0
1
1
1
0
0
1
2
1
1
1
0
0
0
1
0
2
1
0
2
0
0
2
0
0
1
2
1
2
1
1
2
2
0
1
0
0
1
2
1
0
1
0
0
2
0
2
0
1
2
0
1
0
0
1
0
2
0
1
1
2
0
0
0
0
0
2
0
1
2
0
2
1
0
0
1
0
0
2
0
0
1
0
0
0
0
1
3
0
1
0
0
0
1
1
1
1
1
1
0
0
2
0
0
2
2
0
1
2
1
1
0
1
1
1
2
1
1
0
2
0
0
1
2
0
0
0
0
0
0
0
1
1
1
2
2
3
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
4
2
1
0
0
0
0
2
1
0
0
0
0
2
1
2
1
0
1
1
2
0
2
0
0
0
2
2
2
2
0
2
0
1
0
1
0
1
2
0
1
2
0
0
1
0
1
0
1
0
0
2
1
2
2
1
0
2
1
0
0
0
0
0
1
1
1
1
0
2
1
2
0
0
1
0
0
0
0
0
0
1
0
2
0
1
1
1
2
0
0
1
0
0
1
1
0
0
1
1
3
0
1
1
0
0
2
1
1
1
2
0
0
1
0
0
1
0
0
0
0
1
1
2
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
1
0
2
0
1
1
0
0
1
1
2
1
2
1
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
2
1
0
1
0
0
0
0
0
1
1
1
2
0
1
1
3
1
1
1
0
0
0
2
1
2
0
1
0
1
2
2
0
0
2
0
0
0
0
0
4
1
1
0
1
0
2
1
1
0
1
0
2
1
0
0
0
2
0
2
1
2
2
0
0
1
0
1
3
0
2
0
3
0
2
0
1
1
0
2
1
2
0
1
0
0
0
0
0
1
2
0
1
1
0
3
1
1
2
2
2
1
0
0
2
0
0
1
1
2
0
1
0
0
2
1
2
0
1
3
2
1
1
0
2
2
1
2
0
1
2
0
1
0
2
0
0
0
1
0
2
0
1
2
0
0
0
0
0
0
0
3
0
13
0
1
0
1
0
1
1
2
0
2
0
2
1
0
0
1
2
0
0
1
0
3
1
0
1
1
0
2
1
1
2
0
0
1
0
1
2
0
1
2
1
2
3
1
1
0
2
1
1
1
0
2
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
2
2
2
2
0
2
2
1
1
2
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
1
2
2
0
0
0
2
1
1
1
2
0
1
0
0
2
1
2
3
0
0
1
1
1
2
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
1
5
2
1
2
0
1
2
0
0
2
2
2
0
0
2
0
2
2
1
1
0
0
1
1
1
0
0
0
1
0
0
0
0
2
1
0
1
2
1
2
0
0
1
0
0
0
1
0
0
0
0
0
0
3
0
0
2
0
1
1
0
0
1
2
0
3
0
1
3
2
0
2
0
0
1
2
0
0
0
0
2
2
0
2
0
1
0
4
1
1
1
1
0
1
1
2
0
0
0
0
1
2
0
1
1
0
1
0
1
0
4
0
0
1
0
0
2
0
2
0
2
0
0
0
1
0
0
1
2
1
2
0
0
1
0
1
1
2
0
2
1
1
2
0
2
0
1
0
2
0
0
1
2
0
0
1
2
1
2
1
2
0
0
2
1
1
1
0
1
1
1
0
0
0
0
0
3
0
0
1
2
1
0
1
0
1
0
0
2
1
2
1
1
2
2
1
0
1
1
0
0
0
1
0
0
1
1
0
0
2
0
1
2
0
0
2
0
1
3
0
2
1
0
2
1
1
2
3
0
1
1
0
0
0
2
0
2
1
3
1
1
1
1
0
1
2
0
2
0
0
1
1
1
0
3
1
0
0
1
1
0
1
0
0
0
2
2
0
0
0
0
2
1
0
0
1
0
0
1
2
1
0
2
0
0
0
0
2
2
1
1
0
1
1
0
2
0
2
0
1
0
0
1
0
1
1
0
1
0
1
2
2
0
1
3
0
0
1
1
0
0
2
0
1
1
0
1
2
0
2
2
0
0
1
1
0
2
1
2
1
0
1
1
0
0
2
0
0
1
2
1
0
1
0
1
0
0
2
0
1
1
0
0
1
0
1
0
0
0
1
1
1
1
0
1
1
0
2
2
0
0
1
0
1
0
2
3
1
1
0
0
0
1
0
1
0
1
0
0
0
1
0
1
2
0
0
0
1
0
3
1
0
0
0
0
0
1
0
2
1
1
2
0
0
0
0
1
0
0
0
0
0
0
2
1
2
0
0
1
2
2
2
2
1
1
2
1
0
2
0
1
1
1
1
0
1
0
0
1
1
2
0
0
0
0
1
0
0
0
1
0
3
1
0
1
1
1
1
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
2
2
2
0
0
0
2
1
2
2
0
1
1
0
0
1
2
0
0
0
0
0
0
2
2
2
1
2
0
2
0
1
0
0
0
1
2
0
0
2
0
0
0
0
0
1
2
1
0
0
0
0
1
0
0
1
2
1
1
0
0
3
1
2
0
0
2
0
2
0
1
0
0
0
1
1
1
2
0
2
0
1
1
2
0
0
2
1
1
0
2
2
0
0
1
2
1
0
0
1
2
0
0
0
0
1
0
0
1
0
2
0
1
0
2
2
1
2
1
0
2
2
1
1
2
2
1
0
1
2
0
0
2
0
1
1
1
1
1
1
1
1
2
0
0
1
1
1
1
0
0
1
1
0
2
2
2
0
0
0
0
1
0
1
0
0
0
0
1
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
1
1
1
1
1
0
0
2
0
1
0
2
0
1
2
0
1
0
0
2
2
1
0
2
2
0
2
1
1
1
0
2
1
1
2
0
1
0
2
0
1
0
2
2
1
0
0
2
1
2
1
0
0
0
1
2
0
1
0
0
0
1
0
0
1
0
0
0
2
0
0
0
2
2
0
2
0
2
0
2
2
1
1
1
0
0
2
0
1
1
1
0
0
1
1
0
1
1
1
1
0
0
1
0
1
1
0
2
4
0
0
1
0
1
0
2
1
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
2
1
2
0
0
1
2
3
0
1
0
0
1
0
0
0
0
0
0
0
1
2
0
1
2
3
1
0
0
0
0
1
0
1
1
1
2
2
0
2
2
1
0
1
1
0
0
1
0
1
2
0
2
0
0
1
1
0
1
1
0
1
0
1
0
1
0
2
0
0
0
0
2
1
0
1
0
0
0
0
2
0
1
0
1
0
1
1
1
1
1
1
0
1
0
1
0
2
1
1
1
0
2
0
0
1
1
1
0
0
2
0
1
0
0
2
2
0
0
2
1
0
0
1
0
1
0
1
0
0
1
0
0
0
2
2
1
4
1
1
0
1
1
0
0
2
2
1
0
1
1
0
1
0
1
0
1
0
1
1
0
0
1
1
0
0
3
0
1
2
2
2
0
1
1
1
2
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
2
2
0
0
0
0
1
1
0
0
0
0
1
1
0
2
2
0
1
1
2
3
0
1
0
0
0
0
0
0
1
0
0
1
1
2
0
0
1
1
0
1
0
0
0
0
0
0
2
0
0
1
0
1
0
1
0
0
1
2
0
2
1
0
1
2
1
0
1
0
0
1
0
1
0
0
2
1
0
1
1
1
0
2
0
0
2
1
0
0
0
0
0
2
1
0
0
1
2
0
2
0
2
2
0
2
2
0
2
0
0
0
0
1
1
0
0
4
0
0
2
0
1
0
0
1
1
1
0
0
0
1
0
2
0
1
0
0
0
0
1
0
0
0
0
0
1
1
2
0
2
0
0
2
0
1
1
4
0
1
0
0
4
1
0
0
1
2
1
0
1
1
1
0
2
2
0
0
0
2
2
0
0
1
1
0
1
0
1
2
0
0
0
1
0
0
0
0
0
0
1
3
1
1
0
0
0
2
0
0
2
2
2
0
0
1
0
2
1
1
0
0
0
0
1
0
2
0
2
1
1
1
0
2
0
0
0
0
0
2
0
0
0
2
0
1
0
2
2
2
2
1
2
1
1
2
0
0
2
0
2
0
2
3
0
0
2
1
1
0
2
1
1
2
0
2
2
1
1
2
0
2
0
1
2
0
0
1
2
10
2
2
1
0
1
1
0
1
1
2
1
2
0
0
0
0
0
0
0
1
0
0
1
1
2
1
2
2
0
0
0
2
1
1
0
2
0
0
2
0
0
0
1
1
1
2
0
1
2
1
0
0
1
2
1
0
1
0
0
0
1
0
0
1
1
2
0
0
2
0
1
1
2
0
1
1
1
0
2
0
2
0
1
0
2
1
1
2
0
0
2
1
1
1
0
1
0
0
2
1
1
1
1
1
1
0
0
0
0
1
0
1
0
0
2
0
0
2
0
1
1
1
0
3
0
1
0
2
1
1
0
1
0
1
0
1
0
0
2
0
1
1
1
0
0
0
0
0
0
0
1
4
0
0
0
0
2
0
0
1
0
2
0
2
0
1
0
1
2
0
0
0
1
0
0
2
0
0
1
2
0
0
0
0
0
0
1
0
0
1
1
1
0
2
2
1
0
0
0
0
2
0
0
0
2
2
0
0
0
0
2
1
2
1
0
1
0
0
1
1
2
1
1
0
1
0
3
0
2
1
0
0
0
0
0
1
2
2
0
1
0
1
0
0
2
1
0
1
0
2
1
0
1
1
1
1
0
0
0
0
2
1
1
1
0
0
0
0
2
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
1
2
2
1
0
0
0
0
0
0
1
1
0
0
1
0
1
0
1
1
0
2
0
1
2
2
2
0
1
0
0
1
0
2
0
0
0
1
1
2
1
1
0
1
0
2
0
2
1
1
1
1
0
0
1
1
0
0
1
1
0
0
1
0
2
0
0
2
0
2
2
0
0
0
2
1
2
0
1
0
1
1
0
0
0
0
0
1
0
2
0
0
0
1
1
1
3
0
1
0
1
0
1
3
2
2
2
2
0
1
0
0
1
1
2
0
1
0
2
0
0
0
1
0
1
0
0
0
1
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
1
0
2
0
1
2
1
1
2
0
0
2
0
0
2
0
0
0
1
1
2
2
2
1
1
4
0
1
1
1
2
1
0
0
0
2
1
1
2
2
1
0
0
1
1
2
1
0
2
1
0
1
1
0
0
0
1
0
1
2
0
0
0
0
1
0
1
2
1
1
0
2
1
2
0
0
1
0
2
0
0
0
1
0
2
1
0
0
1
1
1
2
1
1
0
0
2
2
1
1
1
0
0
1
0
1
0
0
2
0
2
0
0
0
0
2
1
3
1
1
2
1
2
0
1
2
1
0
0
0
2
1
1
1
2
0
1
1
0
0
0
2
2
1
0
0
2
0
2
0
3
0
0
1
0
0
1
0
0
2
1
0
0
1
0
0
0
1
1
2
2
0
0
0
0
2
1
1
0
1
3
0
0
1
1
2
0
1
2
1
0
0
2
2
0
3
1
0
2
0
2
2
1
0
0
0
0
1
0
0
1
2
0
1
0
2
0
0
0
0
2
0
1
0
0
0
1
2
3
1
0
1
1
0
1
0
0
1
1
0
0
0
1
0
1
2
0
2
0
1
2
1
0
0
3
3
0
1
0
0
1
0
0
0
0
2
1
1
0
1
2
2
1
1
0
1
2
0
2
0
2
0
0
1
1
0
2
0
0
0
0
0
2
2
2
2
0
0
2
0
0
1
1
0
2
0
0
0
0
0
0
1
0
1
0
1
2
1
2
0
1
1
0
1
0
1
1
0
0
1
0
0
3
0
2
2
0
0
1
2
0
0
0
0
1
1
0
2
1
2
0
1
0
1
2
2
4
0
1
2
0
0
0
1
0
0
0
1
2
0
0
0
0
2
1
0
1
0
0
1
0
0
0
0
1
3
0
1
1
0
0
0
1
1
0
0
0
3
0
0
0
0
0
1
1
0
1
1
0
0
3
1
1
0
1
0
2
1
0
1
0
2
0
0
2
1
2
1
2
0
0
0
0
1
0
0
2
0
1
0
2
0
0
0
0
0
0
2
1
1
1
0
1
0
1
0
0
2
3
0
1
1
0
2
0
0
3
1
0
2
0
0
0
0
2
2
0
1
0
0
0
0
0
1
0
2
1
1
0
2
1
1
1
2
2
0
1
0
0
0
2
0
1
2
0
0
0
0
1
2
1
0
0
0
1
1
0
1
1
1
0
2
0
2
0
0
0
2
0
1
0
0
2
0
0
2
2
1
1
0
1
0
4
0
0
0
0
0
1
1
1
0
0
0
2
2
1
2
0
1
2
0
0
1
1
0
1
0
0
2
2
0
1
2
1
2
0
1
1
2
1
0
2
2
2
1
1
0
0
0
1
0
2
2
0
2
1
0
0
1
2
0
2
1
0
0
0
2
0
4
0
0
0
1
0
1
0
0
1
0
1
2
0
1
0
1
1
0
0
2
0
2
0
1
2
2
1
1
0
0
1
0
1
0
1
0
0
0
1
3
1
0
0
0
1
3
0
2
2
0
0
1
2
2
0
0
0
1
0
0
2
2
0
1
1
1
1
2
0
0
0
0
1
0
0
2
1
1
0
0
2
0
1
1
2
0
0
0
0
1
1
0
0
1
2
0
2
3
2
0
1
0
0
0
1
1
1
2
0
0
1
1
1
0
1
0
0
1
0
1
0
1
0
2
1
2
1
0
0
1
2
0
1
2
0
1
1
1
2
2
0
0
0
0
1
0
0
0
1
1
0
2
3
2
1
0
2
0
2
0
0
0
0
0
0
1
1
0
1
0
0
0
1
2
0
1
2
2
1
1
1
0
0
0
0
0
0
2
0
1
1
0
1
0
1
0
0
0
1
0
1
1
0
2
1
1
1
0
1
1
2
2
0
0
0
0
0
0
1
0
0
3
2
0
1
1
2
1
0
2
2
1
1
0
0
0
1
0
1
0
2
1
2
0
0
1
2
1
0
1
2
0
1
0
1
0
0
0
1
0
0
2
1
0
1
2
1
1
2
2
0
2
0
0
0
0
0
0
2
2
1
1
0
2
1
1
0
0
0
1
1
0
2
0
1
0
1
2
1
0
2
1
0
2
0
0
1
0
2
1
1
1
1
0
0
0
1
1
0
1
0
1
1
0
2
1
0
0
2
0
0
3
1
0
1
2
1
1
0
1
1
0
1
0
2
2
2
0
0
1
1
0
0
1
2
0
1
0
0
0
0
1
2
0
2
0
0
1
1
0
2
1
0
2
0
0
0
2
2
0
0
1
0
0
1
1
0
1
2
2
0
1
1
0
0
0
0
2
0
1
0
1
0
0
0
0
0
2
0
0
1
0
1
0
1
1
2
0
0
0
2
0
2
1
0
1
0
1
0
0
2
0
0
1
2
0
1
3
0
3
0
1
1
0
1
0
2
1
0
3
2
0
0
0
1
0
1
0
3
0
0
0
1
0
0
1
1
1
1
0
0
0
0
0
1
0
0
2
1
1
0
1
0
0
0
1
0
1
0
2
1
1
2
0
2
0
0
0
2
1
0
0
2
1
0
0
1
0
2
1
0
0
2
1
0
3
3
2
1
2
0
0
2
1
2
1
0
0
0
0
0
0
2
1
0
0
0
0
1
0
2
0
1
0
2
1
1
1
0
1
2
1
1
1
0
0
1
0
1
0
0
1
0
1
0
0
1
2
2
0
1
2
1
1
2
0
0
1
0
0
0
1
2
0
1
1
1
0
2
0
0
1
2
2
1
3
1
1
0
2
1
0
0
2
0
0
1
1
0
2
0
0
1
1
0
0
0
1
0
0
2
0
0
0
1
1
0
1
0
0
0
1
0
1
0
2
1
0
1
0
2
1
1
0
1
0
0
2
0
0
1
2
1
1
1
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
2
1
0
0
0
0
3
1
3
2
0
0
1
2
1
2
1
0
1
1
0
2
1
2
0
1
1
0
0
1
2
0
0
1
2
1
0
0
2
1
0
1
3
1
0
2
0
0
1
0
1
0
0
0
2
3
1
1
1
1
0
0
0
0
1
0
1
2
0
0
0
0
2
0
1
2
2
1
0
0
0
1
1
2
2
1
0
0
2
2
0
0
1
1
0
0
1
2
2
0
0
1
0
2
0
2
2
2
2
1
0
1
0
0
2
0
1
0
0
0
1
0
2
1
2
1
2
2
1
2
0
0
1
3
0
1
1
0
0
1
0
0
2
0
3
2
0
2
1
0
3
2
0
0
1
1
0
0
0
0
0
0
5
1
0
2
1
0
0
0
0
1
2
0
0
0
0
1
2
0
0
1
2
0
0
0
1
0
1
0
0
0
0
0
2
1
2
2
2
0
0
0
0
0
2
2
0
1
1
0
0
1
0
2
0
2
0
0
1
0
0
1
0
1
0
0
0
2
3
0
2
2
2
1
0
0
2
0
0
0
1
1
0
0
0
1
0
0
0
1
2
0
0
2
1
1
0
2
2
0
0
2
0
2
1
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
2
0
0
1
1
1
2
2
1
2
1
0
2
0
2
0
0
2
2
0
1
0
2
0
2
0
1
3
1
2
2
1
2
0
0
0
0
2
0
0
0
0
1
2
2
0
1
1
0
2
0
0
1
0
1
1
2
0
1
2
0
2
0
0
0
0
0
0
0
0
0
1
4
2
0
1
0
2
0
1
0
0
1
1
1
0
1
1
0
0
0
0
1
0
2
0
1
0
0
1
1
0
0
3
0
2
0
2
0
1
0
1
1
1
2
0
2
1
0
0
0
0
1
1
0
2
0
2
1
0
2
2
0
1
2
0
0
0
1
0
1
1
2
0
0
2
1
0
0
1
0
3
1
1
2
0
1
2
0
2
0
1
2
2
1
1
0
0
0
2
1
1
0
0
1
2
0
2
0
0
1
1
2
2
0
1
0
1
0
0
0
0
1
1
0
3
1
1
3
1
0
0
1
0
0
0
0
2
2
0
1
0
2
2
0
0
2
0
1
1
1
0
1
0
1
0
2
0
0
0
2
1
0
1
0
0
2
0
0
2
2
0
0
1
0
1
0
0
0
1
1
0
2
0
1
0
1
1
0
0
2
1
1
0
0
1
1
0
1
1
0
1
0
0
0
0
2
2
0
1
0
0
1
0
1
0
2
0
2
1
0
2
0
3
0
0
0
2
0
1
0
1
2
0
0
2
0
3
0
0
0
2
1
0
2
0
0
0
1
0
1
2
2
2
1
2
1
0
1
2
0
0
2
0
0
0
1
0
1
1
2
0
2
1
0
0
2
0
0
0
1
0
0
2
0
2
1
1
0
0
0
1
0
2
1
0
0
2
1
2
0
0
0
0
2
2
0
1
0
0
2
0
2
0
1
1
1
1
0
2
0
1
2
3
0
2
1
0
0
2
1
2
1
0
0
0
0
1
1
1
1
2
2
1
0
4
0
0
0
2
0
0
0
2
1
1
0
0
1
0
2
1
0
1
1
0
2
1
0
0
1
1
1
0
0
0
3
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
2
1
0
0
1
2
0
0
2
1
1
2
0
0
2
1
1
0
1
2
1
0
0
1
0
2
1
2
0
1
0
0
0
2
0
0
2
0
2
1
1
1
0
0
2
1
1
0
0
1
0
0
0
1
0
1
0
2
1
0
0
1
1
2
0
0
1
1
1
1
1
0
0
1
1
2
3
2
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
2
0
1
1
2
0
0
0
2
0
2
1
1
0
1
1
1
0
1
2
0
1
0
0
0
0
0
2
0
2
1
0
0
2
0
2
1
1
0
0
1
1
2
0
0
0
0
2
0
2
2
0
2
2
0
1
0
1
0
0
2
0
2
2
0
2
1
1
2
0
1
2
0
0
0
1
1
0
0
2
1
1
1
2
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
1
1
2
1
1
2
1
0
0
2
1
1
0
0
0
0
0
0
0
0
0
2
1
0
2
0
1
0
0
0
1
1
1
1
0
1
0
2
2
1
0
0
1
0
2
2
0
2
0
0
2
0
1
2
1
1
2
0
2
0
2
2
1
0
0
0
1
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
3
1
2
1
1
0
0
2
0
1
2
1
0
0
0
0
0
0
0
1
4
0
1
0
2
1
1
1
2
0
1
2
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
4
2
2
0
2
1
2
1
0
0
2
1
0
1
1
1
1
0
0
1
1
0
0
1
1
1
2
2
1
2
1
1
0
2
2
0
0
0
1
1
0
2
0
2
2
3
2
0
0
0
1
0
1
0
0
0
1
1
2
0
0
0
1
0
0
2
1
2
0
0
0
2
0
1
1
1
0
0
1
1
1
1
1
1
2
0
1
2
0
0
0
1
1
0
1
0
1
2
0
0
2
0
0
1
0
0
2
0
2
0
1
1
0
2
0
1
1
1
0
1
0
1
0
1
1
0
2
0
2
0
1
1
0
0
2
1
0
1
0
1
1
0
1
2
0
0
0
0
0
0
2
1
1
0
0
0
2
0
1
2
1
0
0
1
2
3
1
0
1
0
2
2
1
0
2
1
0
1
0
0
1
1
0
1
1
2
0
2
0
1
1
2
0
1
2
0
0
0
2
2
1
0
2
2
0
0
2
1
2
1
0
0
0
1
0
0
1
0
0
2
0
0
0
0
1
0
2
0
2
0
1
0
1
0
2
1
0
0
0
1
1
0
1
2
2
0
2
2
1
0
0
1
1
1
0
1
2
0
0
1
2
0
1
1
0
0
2
2
0
2
2
0
2
1
1
2
0
4
2
2
1
4
2
0
0
0
1
0
2
1
2
2
1
0
2
0
0
2
2
0
1
2
1
1
2
2
0
0
2
0
2
2
0
0
1
0
0
0
0
1
2
2
1
0
1
2
3
2
1
1
2
2
2
0
0
0
1
1
0
1
0
1
1
0
1
0
1
0
0
1
1
0
0
3
0
1
1
2
0
2
1
1
1
2
0
1
1
0
1
1
0
0
0
0
2
0
1
1
0
1
2
2
0
0
0
1
0
2
0
0
1
0
0
2
2
1
0
2
1
1
1
1
2
2
2
0
0
0
0
0
0
1
2
0
1
0
1
2
0
1
0
0
1
0
0
0
1
1
0
0
1
2
1
1
0
0
0
2
1
0
0
4
2
0
1
1
0
0
1
1
1
0
0
1
2
2
0
0
1
2
0
2
1
2
0
1
1
2
2
1
0
0
1
0
1
0
0
2
0
0
1
4
0
0
2
1
0
1
2
1
0
2
1
0
1
0
2
0
2
0
1
0
2
2
1
0
1
2
1
0
1
0
0
0
1
0
0
0
1
1
0
0
2
2
0
1
0
0
0
1
2
0
1
1
2
0
0
0
2
0
0
1
2
0
0
0
0
2
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
1
1
3
2
0
2
2
1
1
1
0
1
2
2
1
0
2
0
0
2
1
0
1
0
0
0
0
1
2
0
0
2
0
0
1
1
0
1
0
0
0
1
0
0
1
1
1
2
1
0
0
0
0
0
2
1
2
1
0
0
0
5
0
0
1
0
1
2
0
0
0
1
2
2
2
1
0
1
1
1
1
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
2
2
0
0
1
1
0
0
0
0
1
1
1
0
2
0
1
0
0
1
0
1
0
0
1
0
0
2
0
0
0
1
2
0
0
1
1
0
1
0
1
1
0
1
1
1
1
1
1
1
1
0
2
2
0
2
0
0
1
0
4
1
0
2
0
2
0
2
0
1
0
0
0
1
0
0
1
3
1
0
2
0
0
1
1
0
0
0
0
0
2
0
2
0
0
2
2
0
0
0
2
0
3
1
1
0
2
0
0
0
1
1
2
0
1
2
0
2
0
0
1
1
0
0
0
2
1
0
2
2
0
0
0
0
1
2
0
0
1
0
2
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
2
1
2
1
1
0
1
0
1
0
2
0
2
1
0
2
0
0
0
1
0
5
2
1
0
2
2
0
1
0
0
0
0
1
1
4
0
1
0
0
1
1
1
2
2
1
1
0
1
1
0
2
2
0
2
0
0
1
0
0
1
2
1
0
0
0
0
1
1
1
0
0
0
1
0
1
1
0
0
1
0
2
1
0
0
0
1
1
1
1
0
1
2
0
0
2
2
1
2
1
1
0
1
1
1
0
0
0
0
0
1
0
0
2
2
1
1
0
0
0
1
1
0
0
1
0
0
0
0
1
0
1
0
2
2
1
1
2
0
2
1
1
1
0
0
1
1
0
0
0
0
0
1
1
2
1
0
0
1
0
0
0
2
0
0
0
0
0
0
1
2
0
0
2
2
0
2
1
0
0
1
0
1
1
2
2
0
0
1
1
1
0
0
2
0
2
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
1
1
1
2
0
1
0
0
0
0
0
0
0
2
1
2
0
2
0
0
0
0
0
2
1
0
2
0
0
2
0
2
0
1
1
0
0
0
2
1
2
2
0
0
0
2
0
0
0
0
2
2
0
0
0
2
0
3
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
2
0
1
2
1
2
0
0
0
1
0
0
3
0
0
2
2
1
0
2
0
2
0
1
0
1
0
1
0
0
1
0
1
0
0
2
1
0
1
0
2
0
1
1
1
0
1
0
0
1
1
1
0
0
0
2
2
1
1
1
0
0
0
2
0
0
3
1
0
0
0
2
1
1
0
2
0
0
2
0
0
1
1
2
0
0
1
2
0
2
2
0
1
0
1
2
0
2
0
1
0
2
0
0
1
2
0
1
0
0
1
2
1
0
0
1
0
1
0
0
1
1
2
0
0
2
0
1
0
2
1
1
2
0
0
1
0
1
1
0
0
1
0
2
0
1
0
0
0
0
0
1
1
0
1
0
2
0
1
1
1
0
0
2
0
1
0
2
0
2
0
0
1
1
1
0
0
1
0
2
0
1
2
0
1
0
0
0
0
0
0
0
1
1
1
2
1
1
1
0
2
0
1
1
0
0
1
0
1
2
2
3
3
0
1
0
0
0
0
0
2
0
0
0
1
1
1
0
1
1
0
1
0
1
1
1
1
0
0
0
0
11
0
0
0
0
0
2
0
0
0
1
2
2
2
1
0
2
1
0
0
1
1
1
0
0
2
0
0
0
0
2
0
0
0
2
0
0
4
0
1
0
0
0
0
0
2
2
0
0
2
2
0
1
0
0
1
0
1
3
0
0
1
0
0
0
1
0
1
1
0
1
0
0
1
1
0
1
2
2
0
0
0
1
0
0
2
1
0
0
2
0
0
0
0
2
1
2
2
0
0
0
0
1
0
0
1
1
1
2
0
0
1
0
1
0
2
1
0
0
0
2
1
2
0
0
2
0
2
1
1
1
0
1
0
2
0
0
2
0
0
1
2
1
1
0
0
0
0
0
1
0
1
0
0
0
2
1
1
0
0
2
0
0
1
2
1
0
2
1
0
0
0
4
1
0
0
2
1
0
1
0
0
1
0
0
0
0
0
2
4
1
3
0
2
0
0
2
2
3
1
0
2
2
0
0
2
1
0
1
0
0
0
0
1
0
1
0
0
0
0
2
0
1
1
0
2
1
0
0
1
1
0
1
0
0
0
0
0
2
2
1
1
0
0
0
1
1
0
0
1
0
0
2
1
0
2
2
0
0
0
2
1
1
1
0
1
1
3
1
0
2
0
1
0
1
2
1
1
0
3
2
0
0
1
0
0
0
0
0
1
0
2
0
2
0
0
1
2
0
1
3
0
1
2
2
2
2
1
0
0
1
2
1
0
1
2
0
2
2
1
0
1
1
1
1
0
1
2
1
0
1
0
0
1
1
2
2
1
2
1
0
2
1
1
1
0
0
0
1
2
0
1
1
0
2
1
0
2
1
0
0
1
2
0
0
1
0
0
1
0
0
1
0
0
0
1
1
0
0
1
1
1
0
2
5
1
2
0
2
1
1
1
2
0
1
1
0
0
4
1
1
1
1
0
0
0
1
2
2
0
0
2
1
1
2
1
1
1
0
1
1
0
2
0
2
2
2
2
0
1
0
0
2
1
2
0
1
0
0
0
0
0
1
0
0
1
1
0
0
2
3
1
0
1
0
2
0
1
1
1
1
0
0
2
0
1
0
2
2
2
0
2
2
0
1
2
2
0
0
1
0
0
2
0
0
1
0
0
0
1
1
2
2
0
0
0
0
0
1
0
0
0
0
2
0
0
2
1
1
0
1
0
2
0
1
1
2
1
1
0
1
0
0
1
1
1
2
0
2
0
2
0
0
0
2
1
0
3
1
0
0
0
1
0
1
0
1
1
2
1
1
0
0
0
0
1
2
2
0
2
1
1
0
0
1
0
2
0
2
1
0
1
0
1
1
2
0
0
0
1
1
1
0
0
1
1
0
1
0
2
1
0
1
0
1
2
1
3
1
0
2
0
0
1
2
1
1
1
1
0
2
2
0
0
0
0
0
1
0
1
2
1
1
0
0
0
0
0
1
3
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
1
2
2
2
0
0
0
0
0
1
1
2
2
0
1
0
2
2
0
0
0
2
1
0
0
1
1
3
2
1
0
0
2
0
0
1
0
1
1
2
0
1
1
0
1
0
0
0
0
1
1
2
1
0
0
1
2
0
1
0
2
0
2
1
0
0
0
0
2
2
2
0
1
1
2
0
2
0
0
2
2
1
0
0
0
1
0
1
2
2
0
0
1
1
0
0
1
0
1
0
1
0
0
0
0
1
2
1
0
2
0
2
1
1
2
0
1
1
1
0
2
0
0
1
1
1
1
0
2
1
1
2
1
1
2
1
1
0
1
2
1
0
2
0
2
1
0
0
2
2
0
2
0
2
0
0
0
1
1
1
0
1
3
0
0
0
2
0
0
1
0
1
1
1
0
0
0
0
2
1
2
1
0
0
0
2
1
1
1
0
0
1
2
2
0
0
0
1
2
0
0
2
2
2
1
1
0
1
0
0
1
0
2
0
0
0
1
0
2
1
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
2
3
2
0
0
1
1
1
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
2
0
0
1
2
0
0
1
0
0
1
2
0
0
2
2
0
0
0
1
1
2
1
1
0
2
0
1
0
1
1
0
2
2
0
0
2
0
0
1
0
1
0
0
0
0
1
0
0
0
0
2
1
2
0
2
0
0
2
0
1
2
0
1
1
2
2
0
0
0
1
1
2
0
1
0
0
1
1
1
0
1
2
0
0
0
1
1
1
1
1
0
1
2
2
2
1
1
0
0
0
0
0
0
0
2
1
0
0
2
0
0
2
1
1
0
0
0
1
2
0
1
0
0
1
0
0
2
0
0
0
0
1
0
2
1
1
2
3
1
2
0
1
0
1
0
0
0
1
2
1
6
0
2
2
1
0
2
1
2
2
0
0
0
1
2
0
0
0
0
0
1
0
1
2
2
0
0
1
1
0
0
2
2
0
2
2
0
0
3
1
0
0
1
0
1
1
0
2
1
1
1
2
0
0
0
0
0
1
0
1
1
0
1
1
0
1
1
1
0
1
0
0
2
1
0
0
2
0
0
0
0
1
1
1
4
2
3
0
0
1
1
1
0
1
0
0
2
0
1
1
0
1
0
0
0
0
0
3
0
0
2
0
0
2
1
0
0
2
0
0
2
0
0
1
2
0
1
1
2
0
1
0
2
1
1
0
0
0
0
2
3
1
0
0
0
2
0
1
1
0
1
1
0
0
0
0
1
0
1
0
2
1
0
2
1
0
1
2
2
1
2
0
1
0
2
1
0
1
1
0
0
1
0
0
0
0
1
0
1
0
0
1
0
1
0
1
0
0
0
0
0
2
0
2
1
1
1
0
1
0
1
0
1
1
2
0
0
1
0
1
2
0
2
2
0
0
2
1
0
2
0
0
0
2
1
1
0
0
0
1
0
0
1
1
0
2
0
0
0
1
1
0
2
0
2
1
0
0
2
0
1
1
9
0
0
0
0
0
2
0
0
0
0
0
0
1
1
2
1
0
2
0
2
0
1
1
0
2
0
1
1
0
1
0
1
0
1
1
2
0
0
0
0
0
0
2
0
0
0
2
0
1
1
0
0
0
1
1
0
0
2
0
1
0
0
2
2
0
1
0
0
0
0
1
0
1
2
2
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
1
2
0
1
1
1
1
1
0
0
1
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
2
1
0
1
0
0
0
0
0
1
1
2
0
1
2
1
2
0
0
1
1
1
1
0
0
0
1
0
0
0
2
1
0
0
0
0
0
1
1
0
1
2
2
0
1
2
0
2
2
2
0
0
0
0
0
2
2
1
2
1
0
1
2
0
3
0
0
1
2
0
1
1
0
0
1
1
1
1
0
1
1
0
0
1
1
1
0
2
2
0
0
1
0
1
2
0
0
0
2
0
4
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
1
0
2
2
0
2
1
2
1
4
0
3
1
1
0
0
0
2
0
0
1
2
0
1
1
0
0
1
1
0
0
0
2
0
1
1
0
1
0
0
0
0
1
0
2
0
1
2
2
1
1
0
0
0
0
2
0
0
0
0
0
1
0
1
0
3
0
2
1
0
0
1
1
0
1
0
0
1
1
0
1
1
0
1
1
0
2
1
1
2
0
1
0
1
1
1
0
0
1
1
2
0
2
2
0
2
0
1
2
1
0
0
0
2
0
1
0
1
0
0
0
0
1
1
0
2
1
2
1
0
0
0
2
2
0
0
3
0
0
0
2
0
0
2
0
1
1
0
1
0
2
1
0
2
1
0
1
1
0
2
0
0
1
0
0
2
1
0
0
1
0
0
1
2
1
0
0
1
0
3
3
0
1
2
1
0
3
2
1
1
0
0
0
0
3
0
2
1
0
0
1
0
0
2
0
0
0
0
0
1
1
1
0
2
0
0
5
1
1
2
0
2
0
1
0
1
0
1
2
0
1
2
1
2
0
0
0
0
0
2
2
0
2
2
0
0
2
0
1
1
0
2
4
5
0
1
1
2
0
1
1
1
0
0
0
1
0
0
1
0
1
0
1
0
0
1
0
0
0
0
1
0
0
1
2
2
0
0
2
2
0
1
0
1
0
0
2
1
1
1
0
2
2
1
0
0
1
2
0
0
1
0
0
0
1
0
1
0
1
2
0
2
2
0
2
2
2
2
2
0
0
0
0
0
0
2
0
2
0
0
2
2
0
1
0
2
0
1
0
1
1
1
1
1
0
0
2
0
0
2
0
1
2
0
0
0
0
2
2
0
0
0
0
0
0
2
1
0
0
2
0
2
1
0
0
1
3
0
2
0
1
0
0
0
0
0
1
2
7
2
0
1
0
0
0
0
1
1
2
2
0
2
2
0
1
2
1
0
0
0
1
2
0
0
0
0
2
0
0
1
1
0
0
0
1
0
2
1
0
0
2
0
1
1
1
1
0
1
1
0
0
0
1
1
0
4
1
1
1
0
1
0
1
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
2
1
1
2
0
2
0
2
2
2
2
1
1
1
2
0
0
1
1
0
0
0
1
2
1
1
0
1
0
1
0
0
0
0
1
2
1
1
1
1
1
1
0
0
1
1
1
1
0
0
0
1
3
0
0
1
0
1
1
1
0
0
2
0
2
1
0
0
1
0
1
1
0
0
0
2
1
0
1
0
2
0
0
1
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
1
1
2
2
0
1
0
0
2
1
0
0
1
1
0
0
0
1
2
1
2
0
0
1
1
0
1
1
1
1
1
0
0
0
0
2
0
1
1
2
2
1
1
1
1
1
0
0
2
2
1
0
1
1
1
0
0
2
1
0
0
1
2
2
1
1
1
1
2
1
0
0
0
0
2
0
1
2
1
1
0
0
1
1
0
1
1
0
0
0
0
1
0
0
2
0
0
1
0
0
3
0
0
1
2
0
2
0
2
2
0
1
0
1
0
0
0
0
0
0
1
1
1
0
1
1
0
2
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
5
2
0
1
0
2
1
1
1
0
0
0
0
2
0
2
1
2
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
2
0
2
2
0
0
0
1
0
0
0
2
0
1
0
2
2
4
0
0
3
0
1
1
0
0
1
0
1
1
0
0
1
0
2
2
1
1
1
1
0
0
1
0
1
0
0
0
3
1
0
1
0
2
0
0
1
0
0
2
0
0
0
2
0
0
0
2
1
1
1
2
1
1
1
0
1
1
0
0
2
1
1
0
1
1
0
0
0
0
0
0
2
1
0
2
1
1
2
1
0
0
1
0
2
1
1
1
0
2
1
1
0
0
1
1
1
1
1
1
0
1
0
0
0
2
0
0
1
2
2
1
0
0
0
1
0
1
1
2
1
1
0
0
1
0
0
0
0
0
1
0
1
1
1
0
2
0
2
2
1
1
2
1
0
0
0
3
1
0
1
1
0
1
0
0
2
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
2
3
2
2
1
0
0
2
0
2
2
1
1
0
1
2
0
0
0
2
0
0
1
1
1
2
1
0
0
2
0
0
2
0
0
1
0
0
0
0
0
3
1
0
1
0
0
0
0
0
3
1
1
1
0
2
1
2
2
0
0
0
2
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
2
1
0
1
1
1
1
1
0
2
0
0
2
0
1
2
0
0
0
3
3
0
0
0
1
0
0
0
0
2
0
0
2
1
0
2
1
1
1
0
0
0
0
0
0
0
1
2
2
0
0
1
0
0
2
2
0
0
0
1
1
0
1
0
2
0
1
0
1
2
0
1
1
0
0
0
0
0
2
1
2
4
1
0
1
0
1
0
0
0
0
1
0
2
0
2
0
1
0
0
0
1
0
1
0
1
5
0
2
1
0
1
2
1
0
0
2
1
4
0
0
0
1
0
0
1
1
1
1
2
0
0
0
2
0
1
0
1
0
0
0
0
0
0
1
2
0
0
2
1
1
1
0
0
1
0
1
0
0
0
1
1
0
0
1
1
3
0
1
0
1
1
0
0
2
1
0
1
1
2
1
0
0
3
1
1
1
0
1
0
0
0
1
0
0
1
0
0
0
1
2
0
0
0
0
0
0
2
0
1
1
0
0
1
2
0
1
0
0
0
0
0
1
1
1
0
0
1
1
1
1
1
0
1
1
0
0
0
0
1
1
0
1
0
0
1
0
0
1
0
1
2
1
1
2
1
2
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
1
2
1
0
2
0
2
2
8
1
0
1
0
2
0
0
0
1
1
0
0
0
0
2
2
0
0
2
0
0
0
2
1
0
3
0
0
0
0
0
1
0
0
1
1
2
0
2
1
2
0
0
1
1
2
0
1
3
0
2
1
1
2
0
0
0
1
1
2
0
0
0
1
0
0
0
2
0
0
2
2
1
0
0
1
0
0
1
0
0
0
0
0
2
1
0
0
2
2
1
2
0
2
1
1
0
1
1
0
0
1
0
1
1
2
0
1
0
0
1
3
0
0
1
1
2
1
0
2
0
1
0
3
1
1
0
0
2
1
1
0
0
0
0
0
0
2
0
1
1
1
0
1
0
1
2
0
0
1
2
0
0
1
1
1
2
0
3
2
0
0
0
2
0
0
0
0
0
1
0
1
1
0
1
0
0
0
3
2
0
1
2
0
0
3
0
0
0
2
1
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
1
2
0
0
0
1
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
1
3
0
3
1
1
0
2
2
0
1
0
2
1
1
1
0
0
2
1
0
1
0
0
0
2
0
2
0
0
0
1
2
0
0
0
0
1
2
3
0
0
0
0
0
0
2
2
1
0
1
0
2
3
0
0
1
0
0
1
0
0
2
0
0
1
0
1
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
1
1
0
0
0
0
0
1
1
1
1
0
2
0
0
1
0
1
1
0
0
1
0
0
2
1
0
1
0
0
2
2
2
1
0
0
0
0
1
0
0
0
0
0
2
1
0
1
0
0
0
0
2
1
0
0
1
1
1
0
0
0
0
2
0
0
1
2
0
0
0
1
1
1
0
2
0
0
0
0
2
0
0
2
0
2
1
2
2
0
1
1
2
1
1
0
0
0
0
0
0
3
0
1
1
2
0
0
0
0
0
0
1
0
1
2
0
2
0
1
0
0
2
2
2
0
1
1
0
0
0
1
1
0
0
1
0
0
0
0
0
2
2
1
0
0
0
3
0
2
1
2
1
1
0
1
0
0
2
0
0
1
2
0
0
0
2
0
1
2
1
2
1
1
4
1
1
1
1
1
1
0
0
0
1
2
1
2
2
0
0
1
0
2
0
1
0
2
0
1
2
2
1
0
0
0
2
0
1
2
0
0
1
0
2
2
0
1
1
1
0
1
2
0
0
0
0
1
1
1
2
2
2
1
0
1
0
0
2
2
0
2
1
1
0
4
2
1
2
1
0
0
0
2
0
0
1
1
1
1
2
0
1
0
6
0
1
2
2
0
0
0
2
0
0
0
2
0
1
1
0
2
1
1
1
0
2
0
1
1
1
0
0
1
2
2
1
0
0
1
0
0
0
0
2
2
0
2
2
0
3
1
2
0
0
2
0
1
0
0
2
1
0
0
1
1
2
1
0
2
0
0
0
2
1
2
2
0
2
2
0
1
2
1
3
0
0
1
0
0
1
0
1
1
1
1
1
0
0
1
1
2
1
1
1
0
2
0
2
1
0
0
0
1
0
0
0
1
1
2
0
0
1
2
0
0
1
0
1
2
0
0
1
1
0
1
0
0
1
0
2
2
0
0
1
0
0
0
0
2
2
2
2
0
1
1
0
1
2
1
0
1
1
1
0
0
0
2
0
2
0
0
0
0
2
2
2
0
1
10
2
0
0
0
0
1
1
0
0
2
1
1
0
0
0
0
0
1
2
0
0
2
0
0
0
1
2
0
2
0
0
1
1
2
0
1
0
0
1
0
0
2
1
0
2
2
1
0
2
2
2
0
1
1
2
1
1
2
2
0
0
0
0
0
0
4
1
0
2
0
1
1
0
2
0
1
0
2
2
0
1
1
2
0
0
1
0
0
0
2
1
1
0
2
0
0
1
1
3
2
1
0
0
0
0
0
2
0
2
0
0
2
1
1
0
5
0
1
0
0
0
0
1
2
0
2
0
1
0
0
0
1
1
2
0
0
2
3
0
1
0
0
1
1
0
4
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
2
2
0
0
0
0
0
0
0
1
0
1
0
0
1
3
0
0
1
0
0
1
0
2
0
1
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
1
0
0
3
1
0
1
1
0
0
1
1
0
1
0
2
0
2
2
0
0
2
0
1
0
2
0
1
4
1
1
1
0
0
2
0
0
0
1
2
1
1
2
0
2
1
0
0
2
1
1
0
1
1
1
0
2
1
2
1
0
1
1
0
2
1
0
0
0
1
0
0
2
0
0
0
1
2
3
1
0
2
0
0
1
0
1
0
0
2
0
1
0
2
0
0
0
0
1
1
2
2
1
1
2
0
0
2
0
1
0
1
0
0
0
1
0
1
2
1
0
2
0
2
0
0
1
0
2
0
0
1
1
0
1
1
0
0
0
0
1
1
0
0
0
0
2
1
1
1
0
1
2
0
2
1
0
0
0
0
0
2
1
2
0
0
0
2
0
1
0
2
0
1
0
1
1
1
0
0
1
1
0
0
1
0
2
1
2
0
0
0
0
2
2
0
2
2
0
1
0
2
0
0
0
1
1
2
1
2
0
2
1
0
4
1
2
1
1
2
3
0
1
0
2
0
0
0
0
0
0
1
1
1
0
0
1
0
2
1
1
1
1
2
1
1
1
0
0
1
1
1
0
0
2
1
2
2
0
1
2
3
5
1
0
0
2
1
0
0
1
0
0
0
0
3
0
0
2
0
2
0
0
0
0
1
1
0
0
0
0
1
0
0
2
0
1
2
1
0
1
0
1
0
1
0
2
1
0
1
1
2
0
2
1
1
1
0
0
1
1
1
3
0
1
0
0
0
0
2
2
2
1
2
2
0
0
2
0
0
1
2
2
2
1
0
1
0
0
0
1
0
1
0
0
1
1
0
0
6
1
2
1
0
4
1
0
2
2
0
2
0
0
0
0
1
2
0
0
1
2
1
0
2
2
1
0
0
2
0
1
0
1
0
0
0
0
1
3
1
0
2
0
2
1
1
1
1
1
2
1
1
0
1
2
2
0
0
0
0
0
0
1
0
2
0
0
1
0
0
2
0
0
1
0
0
0
2
1
0
0
0
0
1
1
0
0
0
0
1
3
0
0
0
1
1
1
2
1
2
1
1
1
1
2
0
1
3
0
1
0
2
0
0
3
0
0
0
1
1
0
2
0
2
0
0
0
1
0
1
0
2
0
0
0
0
2
0
0
0
0
2
1
2
0
0
0
2
1
1
0
1
1
2
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
2
0
0
0
0
1
1
1
0
0
0
2
2
1
2
0
1
0
1
2
1
2
1
1
2
2
1
0
1
1
1
0
1
1
2
1
2
0
1
0
1
0
0
0
4
2
1
0
0
1
1
0
2
1
2
2
1
0
0
1
0
0
0
2
0
0
2
0
0
1
0
1
0
1
1
0
2
1
0
0
1
0
2
1
0
1
1
4
2
0
1
2
2
0
1
0
0
1
0
1
1
1
2
0
0
0
0
1
0
1
0
2
0
0
1
2
1
1
1
1
1
1
1
1
2
0
1
1
1
1
0
0
0
0
1
2
1
2
1
1
0
0
1
1
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
1
1
0
3
3
2
0
2
1
2
0
0
0
1
1
0
2
0
2
0
1
1
2
2
0
1
0
0
0
1
1
0
2
0
1
0
0
1
0
0
0
1
0
1
0
1
0
1
1
0
0
1
0
0
0
0
1
0
2
0
0
0
1
0
1
2
0
2
0
1
2
2
1
2
1
1
0
1
1
2
0
0
0
0
0
1
2
0
1
2
0
0
0
2
1
0
1
1
0
0
1
0
0
0
0
2
2
0
1
1
1
2
1
1
2
0
1
1
0
2
1
0
2
2
2
0
0
0
0
0
1
1
0
0
0
1
0
1
2
1
2
0
0
1
0
1
0
2
1
0
1
0
2
1
0
2
2
1
2
1
0
2
2
0
4
2
1
2
0
1
2
1
0
0
1
0
0
0
0
2
1
1
0
0
0
0
2
0
1
0
0
3
0
0
0
1
0
0
1
0
1
0
0
2
1
0
2
0
0
0
1
0
1
0
1
0
1
1
0
2
2
0
0
0
0
2
1
0
1
0
0
0
1
0
4
0
0
1
1
0
1
1
0
1
0
0
2
2
1
0
1
0
0
0
1
0
0
0
1
0
0
0
1
1
2
0
0
0
2
0
0
0
1
2
2
2
1
0
1
1
1
3
2
0
1
1
1
0
2
3
1
1
1
0
0
4
0
1
2
2
0
0
0
0
2
2
0
0
0
1
0
1
0
2
0
2
1
0
1
6
3
0
1
0
1
1
1
0
1
2
0
2
0
0
1
1
0
1
0
0
0
2
1
2
0
0
0
2
0
0
2
2
1
1
2
0
2
0
0
0
0
0
0
1
0
1
1
0
0
2
2
0
0
2
2
0
1
1
1
1
0
2
2
0
0
2
2
0
0
0
0
0
1
2
1
1
1
1
0
2
1
1
0
2
2
0
1
2
0
1
1
1
2
0
1
2
1
1
2
1
0
2
0
0
0
1
0
0
0
0
2
1
1
0
2
2
0
1
0
0
0
3
0
0
0
1
1
0
1
0
2
2
0
2
0
2
1
1
0
0
1
0
1
0
0
0
0
1
1
1
2
2
0
1
2
1
0
0
0
1
0
1
0
1
2
1
1
2
0
3
2
2
0
1
0
0
0
2
1
1
1
1
0
1
0
0
0
1
2
0
2
0
0
0
1
1
0
2
2
1
2
0
2
0
2
0
1
0
3
1
3
0
0
2
1
0
0
2
0
0
0
0
0
1
1
2
2
1
1
0
1
1
0
0
2
2
0
0
3
0
2
2
1
0
2
0
0
0
0
0
2
1
0
0
0
0
0
1
3
0
1
1
0
2
0
0
2
1
1
1
4
0
0
0
2
2
0
1
2
0
1
0
0
0
0
0
1
4
1
0
0
2
0
3
0
2
1
2
2
4
1
0
1
1
0
2
0
3
0
2
1
1
2
1
0
0
0
0
0
1
1
1
2
0
1
2
2
0
2
0
1
0
0
0
1
1
0
1
0
2
1
0
0
1
1
1
0
1
1
2
2
0
2
0
0
1
1
0
1
0
2
1
2
0
0
1
1
0
0
1
0
1
1
1
2
1
0
1
2
0
2
0
1
0
0
1
0
0
0
2
2
1
1
0
2
1
1
1
1
1
1
1
1
1
2
2
0
0
0
0
0
0
1
1
0
1
1
1
1
1
1
0
0
1
2
0
0
2
0
2
0
2
0
1
1
0
0
2
0
0
2
1
0
1
1
2
2
1
0
0
0
2
1
1
1
0
2
2
0
0
1
0
0
2
2
0
2
0
2
0
1
0
0
1
0
1
1
0
2
0
0
0
0
3
0
0
1
1
1
0
1
1
0
1
2
1
3
0
0
1
0
0
0
1
0
0
1
1
0
0
0
1
0
2
0
0
1
0
2
0
0
1
1
2
1
1
1
0
1
0
1
0
0
1
1
2
1
0
0
1
2
1
0
2
0
2
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
1
0
1
1
2
1
0
0
0
2
2
2
0
0
1
0
1
1
0
1
0
1
0
1
2
2
0
0
0
0
0
2
3
0
2
0
2
2
1
2
2
1
1
0
1
0
0
0
0
0
0
0
1
2
0
0
0
1
0
1
0
0
0
2
0
0
0
1
1
0
2
0
0
1
2
1
1
0
0
0
1
2
0
1
1
1
0
1
1
1
0
0
1
0
1
0
0
1
2
0
0
1
0
2
0
2
1
0
0
1
1
1
0
0
0
1
0
0
0
0
0
1
0
0
2
1
2
1
1
0
0
1
0
0
0
2
0
0
2
1
3
1
1
1
0
0
2
1
0
2
0
2
0
0
0
1
0
2
1
0
0
2
1
0
0
0
1
2
2
1
0
2
0
0
0
1
0
0
1
0
2
2
0
0
1
0
1
0
0
1
0
0
1
1
1
1
1
0
2
1
0
0
0
0
1
0
1
1
0
0
1
0
2
0
1
1
0
2
0
2
0
2
0
2
1
1
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
2
0
2
0
1
1
0
4
0
1
2
1
0
1
3
0
0
0
0
0
1
0
1
1
0
1
0
0
0
2
0
2
1
1
0
1
1
0
0
2
0
0
0
1
1
1
1
0
2
0
0
0
0
4
0
0
0
2
0
0
0
1
0
1
1
0
1
0
0
0
1
0
1
1
1
2
0
2
0
1
0
0
1
2
0
1
2
2
0
2
0
1
0
3
0
0
1
1
0
0
1
0
0
0
1
2
2
1
3
3
1
0
0
0
1
0
2
2
1
3
2
0
0
1
1
2
0
0
1
2
2
2
1
0
2
2
0
0
2
1
2
1
1
2
0
2
1
0
0
0
0
2
0
0
3
2
2
2
0
1
0
1
0
0
0
2
0
1
0
1
0
0
2
0
2
1
0
1
0
0
1
0
2
1
0
0
2
0
0
0
0
0
0
1
2
1
0
0
0
1
0
0
1
0
0
1
0
1
1
1
1
0
2
0
0
1
0
2
1
0
2
2
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
1
0
1
0
2
1
1
0
2
0
2
0
0
3
0
0
0
0
1
1
1
0
0
1
2
0
1
0
2
2
0
0
0
0
1
0
0
2
2
0
0
2
1
2
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
3
1
0
1
0
0
1
1
0
2
0
2
0
2
0
0
0
2
1
1
0
0
0
2
0
0
0
2
1
2
2
0
1
0
0
1
0
0
2
0
0
0
0
2
0
0
1
0
2
0
0
0
1
0
1
2
0
0
0
2
2
2
5
0
1
0
2
1
3
0
1
1
1
0
2
1
2
0
1
0
0
0
2
1
1
1
3
0
0
3
0
0
1
0
4
0
2
1
0
1
1
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
2
0
1
2
2
1
0
0
1
2
0
2
0
0
1
0
0
2
1
1
1
1
1
1
2
0
0
1
1
0
1
0
1
0
0
0
0
1
1
1
0
1
1
0
2
0
0
0
0
1
0
2
1
0
0
2
0
0
2
1
0
0
1
1
0
0
0
2
0
2
0
0
3
2
0
1
1
1
1
1
1
0
0
0
0
0
0
1
0
2
1
0
1
1
0
0
0
0
1
0
2
0
0
2
0
0
0
0
1
0
2
0
2
1
1
0
2
0
1
1
0
1
0
1
2
0
0
1
1
2
0
1
2
2
1
1
0
0
1
0
2
1
0
2
0
2
1
0
0
0
0
2
0
2
0
0
0
1
0
0
0
1
0
2
2
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
2
2
2
1
1
0
2
2
0
0
0
0
0
2
1
0
3
0
1
1
2
2
2
2
1
0
1
0
0
2
1
1
1
0
1
0
2
2
2
1
2
2
0
0
1
0
1
1
0
2
2
0
1
0
2
1
0
0
1
0
0
0
0
1
0
2
0
2
0
0
1
2
0
0
0
0
0
2
1
1
0
0
0
0
0
2
0
1
2
1
0
1
2
0
0
1
2
2
1
1
1
0
0
2
1
1
0
0
1
0
1
0
0
0
0
3
0
1
0
0
1
1
0
0
2
2
0
1
1
2
0
0
1
0
2
0
0
2
2
0
0
1
0
1
0
0
0
2
1
1
1
0
1
1
0
2
0
1
0
2
1
1
0
1
0
2
0
0
0
3
1
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
2
2
0
0
2
2
2
1
2
2
0
0
0
2
1
0
0
2
0
1
0
0
1
2
0
0
1
0
1
0
1
2
2
2
0
1
1
2
2
0
0
2
0
0
1
0
1
0
2
2
0
0
0
2
0
0
0
0
1
0
2
2
1
0
2
0
2
0
1
0
0
0
0
2
1
0
0
1
1
1
0
2
1
1
0
0
0
1
1
2
1
0
0
2
1
0
3
1
0
0
1
0
1
1
4
1
2
0
2
0
0
0
0
0
1
1
2
0
0
2
0
1
0
1
1
1
1
1
1
1
3
0
1
1
0
1
1
1
2
0
1
0
1
0
1
0
0
1
2
0
1
1
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
3
0
2
1
1
1
1
0
0
0
2
0
0
0
0
2
0
0
2
1
0
0
1
0
2
0
2
0
0
0
0
0
3
0
0
0
1
0
0
2
1
1
1
0
1
2
0
0
1
0
0
1
0
1
0
1
1
0
0
1
1
1
0
0
2
0
1
2
1
1
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
1
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
2
0
0
1
1
1
0
0
1
5
2
0
0
1
1
2
1
1
0
1
4
0
0
0
0
2
0
0
0
0
1
0
0
2
1
1
0
2
0
2
1
0
2
0
0
1
1
0
0
2
0
0
1
1
0
2
0
0
0
0
2
0
1
0
2
0
0
2
2
2
2
0
2
0
0
0
0
0
0
1
1
2
1
1
2
1
0
1
0
0
1
1
1
1
1
1
1
0
0
1
1
1
0
0
0
1
0
0
2
0
1
0
1
1
2
1
2
2
1
1
0
1
1
0
2
2
0
1
0
0
0
1
1
1
1
0
2
1
1
1
1
1
1
0
0
2
2
1
2
1
2
0
0
1
0
2
0
0
0
0
1
1
2
0
0
0
0
0
1
0
2
0
1
2
0
0
0
0
0
0
0
1
1
3
1
0
1
2
2
2
0
1
1
1
1
2
1
1
2
0
0
0
1
0
2
2
1
1
1
0
1
0
1
1
1
0
1
0
1
0
1
2
0
0
0
0
2
2
1
0
2
0
0
1
1
0
0
1
0
1
2
0
0
0
0
1
0
0
1
4
0
2
1
0
0
0
1
2
0
1
2
0
0
1
1
2
0
2
0
0
0
0
1
0
2
1
0
1
0
0
0
0
0
1
0
1
2
1
1
1
1
0
1
1
1
1
0
1
1
1
1
0
0
1
0
1
1
0
1
2
1
1
1
2
1
1
0
1
2
0
0
0
1
1
0
0
0
2
1
1
2
0
0
0
0
0
0
2
0
0
2
1
2
0
0
0
0
0
0
0
0
1
5
1
0
2
0
1
0
0
0
0
1
3
0
0
2
0
2
2
0
1
0
0
1
0
0
2
0
0
2
2
0
1
1
1
0
2
0
0
0
0
0
4
0
0
1
2
0
0
0
4
1
2
0
0
0
2
0
0
0
1
1
2
0
1
0
0
2
1
1
2
0
0
2
0
0
0
0
1
0
1
1
0
1
2
0
1
1
0
0
0
0
0
0
2
1
0
0
0
1
2
2
1
1
1
0
0
0
1
0
0
1
0
1
1
1
2
0
1
1
1
1
1
0
0
1
2
0
0
0
1
1
0
2
0
0
0
0
0
0
0
2
0
1
1
1
0
2
1
0
2
0
0
0
0
2
0
1
0
0
2
2
2
1
0
0
1
2
0
0
1
0
0
0
2
0
0
0
0
1
4
1
1
1
0
0
2
0
2
0
0
1
1
1
1
1
2
0
1
1
0
1
0
0
1
2
2
0
0
1
1
0
1
0
1
1
2
0
1
1
2
0
1
2
0
1
1
2
2
1
1
0
1
0
0
1
1
0
0
1
0
0
1
1
0
2
0
2
0
0
1
2
0
0
1
1
1
2
0
0
0
0
0
1
1
0
0
2
0
1
0
0
2
1
0
2
0
0
0
2
0
0
2
2
1
0
2
2
0
0
1
1
1
0
2
2
0
0
1
0
0
1
1
0
1
0
2
0
1
0
1
0
1
1
0
2
0
1
1
0
0
0
1
0
1
1
2
0
0
1
0
1
2
1
0
0
3
1
0
1
0
3
2
0
0
1
0
0
0
1
0
1
2
2
0
2
0
0
2
3
2
1
0
1
0
1
1
1
0
2
0
0
0
2
0
0
1
2
1
2
3
1
0
2
2
0
0
0
0
1
0
0
1
2
1
1
0
1
1
0
0
0
1
1
0
0
1
0
2
1
1
0
0
0
0
0
1
1
0
0
2
1
1
1
0
0
1
1
0
0
1
2
0
0
2
2
2
1
1
0
1
0
0
0
2
1
0
1
0
3
1
0
1
2
1
0
0
0
0
0
1
0
2
0
0
0
1
2
0
0
2
2
0
1
2
2
1
2
0
1
0
2
0
0
0
1
2
0
1
2
2
1
2
0
0
0
0
1
2
0
0
3
1
1
0
1
0
2
1
0
2
1
0
1
0
0
0
1
0
0
2
2
1
0
1
0
0
0
0
0
0
1
0
0
1
4
0
0
2
1
0
2
0
0
0
1
0
0
1
1
1
0
0
1
0
1
2
1
2
1
1
1
1
2
2
0
0
0
1
2
0
1
1
1
0
0
1
0
1
0
2
0
0
2
2
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
1
0
1
2
0
0
0
0
2
0
0
0
0
2
1
1
3
1
1
0
0
2
1
0
2
2
0
1
0
1
1
2
0
2
1
0
2
0
3
0
1
2
2
0
0
1
0
0
0
1
0
1
0
2
0
0
1
2
0
1
2
1
1
2
1
1
0
1
0
0
1
1
2
2
0
1
0
2
0
1
0
1
3
0
0
0
2
2
1
2
1
0
0
1
2
0
0
0
1
2
0
2
1
0
0
1
1
2
0
2
0
3
0
5
1
0
2
0
1
0
1
1
0
2
0
0
0
2
2
0
0
0
1
2
0
0
2
0
0
1
3
1
1
1
0
2
1
1
1
0
0
1
0
2
3
1
1
0
0
0
1
2
1
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
1
2
0
0
0
0
0
1
1
0
0
3
0
2
1
1
1
0
2
2
0
1
0
0
0
0
0
1
2
2
0
0
0
1
1
0
0
0
0
0
1
1
2
1
1
2
0
0
3
3
1
2
0
0
0
0
1
0
2
1
1
0
1
0
1
1
2
1
0
0
2
1
0
1
1
0
0
2
2
0
1
2
0
0
0
1
1
0
2
0
2
1
2
2
0
0
1
0
0
2
1
2
1
0
0
0
0
3
2
0
1
1
1
0
0
1
0
0
2
0
2
0
0
0
1
0
1
2
0
1
0
0
0
1
0
3
0
2
2
1
0
0
1
1
0
1
0
0
0
2
0
3
1
0
1
0
1
1
0
1
2
2
0
2
0
0
2
2
0
0
0
1
0
0
0
0
1
0
0
2
0
1
0
2
0
1
1
2
2
1
0
0
1
0
0
1
0
1
0
2
2
0
1
1
2
0
0
1
1
2
1
1
0
0
0
2
0
0
1
0
0
1
1
2
2
0
0
0
0
0
0
1
1
1
0
1
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
1
0
1
1
0
0
1
2
0
0
0
2
0
0
1
0
1
1
0
0
0
0
0
1
2
1
1
1
1
2
2
0
0
0
2
1
1
2
1
0
1
1
0
2
2
0
1
0
1
0
1
0
2
0
0
0
2
1
1
0
1
0
0
2
2
2
0
2
0
0
0
1
1
1
1
0
2
0
4
0
2
0
0
0
0
0
0
1
0
2
0
0
1
0
2
2
0
2
0
1
2
2
0
0
2
2
0
1
3
0
0
1
0
1
0
2
0
0
0
1
0
2
0
1
2
1
0
1
0
0
0
1
1
2
1
0
0
0
1
0
0
2
2
1
1
2
2
0
0
1
2
2
2
0
2
0
1
2
0
0
0
3
0
1
1
1
0
1
0
0
0
0
2
0
1
1
0
1
0
1
1
2
0
1
1
0
1
2
1
1
1
0
0
2
0
0
0
1
0
0
1
2
2
2
2
0
1
2
0
1
2
1
0
0
0
0
1
3
0
0
0
0
0
1
0
0
1
1
1
0
2
0
0
3
0
0
2
1
0
1
0
0
2
0
0
2
0
0
1
0
1
0
0
0
2
0
0
1
2
0
0
1
1
0
4
0
2
1
1
2
0
2
1
0
1
0
2
1
0
1
0
2
0
1
0
0
1
0
2
1
1
2
2
0
0
0
0
0
0
2
1
2
0
2
3
0
1
2
0
1
0
0
0
2
0
1
0
1
0
1
1
0
0
0
1
1
1
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
1
1
1
1
0
0
0
2
1
0
1
1
1
0
0
0
1
1
0
2
2
1
0
1
2
0
1
1
0
1
0
2
1
1
3
1
1
0
1
0
0
0
0
1
0
2
0
1
2
2
0
0
0
2
2
2
0
0
2
2
0
0
2
2
1
0
2
1
0
0
2
0
2
1
2
0
1
0
0
0
0
1
0
0
0
1
1
1
1
1
1
1
0
1
1
2
1
0
1
2
1
2
0
0
0
2
0
0
2
0
0
1
1
1
2
1
2
2
1
1
2
0
0
0
0
0
0
2
0
1
0
1
1
1
1
2
0
2
1
0
0
0
0
0
1
0
0
1
2
0
1
2
0
0
0
0
2
0
0
1
0
1
0
1
2
1
2
1
2
2
0
0
1
2
0
0
2
0
0
1
2
2
0
1
1
1
1
2
1
0
0
1
1
0
0
0
0
1
0
2
2
2
1
1
1
0
1
0
2
1
2
1
2
1
2
2
2
1
0
0
2
2
2
1
2
2
1
0
3
1
0
1
1
2
0
2
0
1
2
2
1
0
2
1
1
1
1
0
2
1
0
0
0
0
2
1
0
0
0
2
2
0
0
0
1
0
0
1
0
0
0
0
0
1
2
1
0
1
1
1
0
0
0
1
2
2
0
1
1
1
4
0
1
0
0
1
1
0
2
1
0
2
2
1
0
0
0
2
0
0
0
2
1
0
0
0
2
0
1
0
0
2
2
1
1
1
0
0
1
0
0
1
1
1
0
2
0
0
1
0
1
2
1
1
1
0
1
0
1
0
2
0
1
0
0
0
1
1
0
0
0
2
0
0
0
2
0
0
0
0
1
2
0
2
2
1
2
1
0
0
1
2
0
0
0
1
1
2
0
0
0
0
0
0
0
1
2
1
2
0
0
1
3
2
0
0
1
1
0
1
2
2
1
1
0
0
1
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
1
0
1
1
0
2
1
1
1
2
1
0
2
1
0
0
1
1
1
0
1
2
1
0
0
0
0
0
0
0
1
1
0
1
0
2
0
0
2
1
0
1
4
0
2
0
1
0
0
2
3
0
2
2
0
1
0
0
0
1
0
0
2
0
0
0
0
1
0
2
3
6
0
2
1
1
0
2
1
1
1
2
1
0
0
2
0
0
2
0
0
1
2
1
2
0
0
0
0
3
0
0
1
1
0
0
0
1
1
0
0
0
2
1
2
1
0
1
0
0
2
1
0
0
1
0
0
1
0
2
0
1
2
1
0
0
2
2
1
0
1
2
0
2
0
2
0
0
2
2
2
2
1
0
0
0
1
2
1
2
1
2
0
2
0
0
2
0
0
0
0
1
0
0
0
1
0
1
1
1
0
0
0
1
0
0
0
0
1
1
0
1
1
0
0
0
0
1
2
3
0
2
0
0
1
2
0
1
2
0
0
2
0
2
1
0
0
2
0
2
1
2
1
0
0
0
0
1
0
0
0
0
1
1
0
1
2
2
1
1
1
1
1
2
1
0
0
0
0
0
0
1
2
1
2
2
2
1
0
1
1
0
1
0
0
1
0
1
1
1
1
1
2
1
1
0
0
1
0
0
3
1
0
2
2
1
2
0
2
1
1
1
0
0
0
0
1
0
1
2
1
0
1
0
2
0
0
1
2
0
0
1
0
2
0
0
0
0
0
0
1
1
1
1
1
0
0
2
3
0
0
0
1
2
0
0
1
1
0
0
0
2
2
0
0
0
0
2
1
1
2
1
1
2
2
2
1
0
2
0
1
0
2
1
2
0
1
0
0
0
1
1
1
1
0
0
0
0
1
0
0
1
4
1
0
0
1
1
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
1
1
2
0
1
0
2
2
1
2
2
2
2
0
1
2
0
1
0
2
2
1
0
2
1
0
0
2
1
1
0
0
2
0
0
2
1
0
2
3
0
1
0
2
1
0
1
0
0
1
0
2
0
1
1
1
1
2
0
0
0
2
0
1
0
2
1
1
1
3
0
2
2
1
0
0
2
2
0
1
2
1
2
0
0
1
3
0
0
2
2
0
1
2
0
1
0
0
1
2
0
2
0
0
0
2
0
0
0
0
0
1
0
0
2
0
1
2
0
0
1
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
1
0
2
0
2
0
1
2
1
1
0
0
2
0
0
2
0
0
1
1
1
0
0
2
0
0
1
0
0
2
0
0
3
0
0
0
1
1
0
1
0
2
0
2
2
0
2
3
1
2
0
1
1
0
0
2
1
0
1
0
1
1
2
1
1
1
2
1
2
0
0
0
1
0
0
1
1
1
1
1
0
2
0
0
0
0
0
0
1
0
0
2
1
1
0
0
0
2
1
0
1
0
0
0
0
2
1
0
0
0
0
1
0
0
2
1
1
1
2
2
2
1
0
0
0
2
1
0
0
0
2
1
0
1
0
2
1
0
0
0
0
0
0
2
0
0
0
1
2
1
2
0
2
0
0
1
1
1
0
0
2
1
0
1
1
0
0
1
0
0
0
1
1
1
2
1
0
1
2
0
2
0
0
1
2
0
0
0
0
1
0
0
2
2
1
0
0
2
1
0
1
0
0
0
3
1
2
0
0
2
0
0
2
0
0
1
0
0
1
2
0
0
1
2
1
0
1
0
1
1
0
0
2
0
0
2
1
0
1
2
2
1
1
0
0
2
0
1
2
1
0
0
2
1
0
1
0
1
0
2
2
0
0
1
0
1
2
0
2
1
0
1
0
1
1
1
0
0
1
0
3
0
2
1
1
1
0
0
0
3
1
1
1
2
0
0
1
0
2
0
0
0
1
1
1
0
0
0
1
1
0
0
1
1
0
0
0
0
2
0
2
0
1
0
1
2
0
2
0
1
2
0
2
0
0
0
0
0
2
0
1
0
1
1
0
1
0
0
1
2
0
0
2
0
2
1
1
0
1
0
1
1
0
0
0
0
0
1
2
0
1
0
1
0
0
1
0
2
0
0
1
1
0
1
1
2
1
2
0
0
1
0
1
0
0
0
0
0
0
1
1
0
2
0
1
0
2
1
1
0
1
0
0
1
0
2
1
2
2
0
0
2
0
2
2
0
1
0
1
2
1
1
0
1
1
2
2
1
0
0
0
1
0
0
2
0
2
0
0
0
2
0
0
2
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
2
1
0
0
2
0
0
1
0
0
0
0
1
0
1
0
0
2
0
2
0
1
1
2
0
2
2
2
2
0
1
0
1
0
1
0
1
0
1
0
1
0
1
1
2
0
1
2
1
0
1
1
2
1
1
0
0
2
0
2
1
1
2
0
2
0
1
1
1
1
0
0
2
0
0
0
1
2
1
0
1
1
1
0
0
1
1
1
2
1
1
0
2
2
0
0
0
1
2
1
1
2
0
0
0
0
1
2
0
1
1
0
1
0
0
1
0
0
0
0
2
0
1
2
2
0
1
0
1
1
0
0
2
1
0
1
0
1
2
1
1
1
0
3
0
1
0
1
2
0
2
0
0
0
1
1
2
1
0
1
1
0
0
0
1
0
2
0
0
2
0
1
0
0
0
2
1
0
2
0
0
0
1
0
1
1
2
1
1
2
0
0
0
2
1
2
0
2
3
0
1
0
1
0
2
1
0
0
0
0
1
0
0
1
0
4
1
2
0
1
2
0
0
0
2
0
0
2
0
0
2
1
1
0
0
0
1
0
0
0
0
0
0
0
4
0
0
2
2
3
0
0
0
2
0
0
1
1
0
0
0
0
1
0
0
3
2
1
0
0
2
1
2
0
2
0
0
0
0
1
1
0
2
2
0
2
0
1
2
1
0
1
0
1
0
1
0
1
1
1
1
2
1
2
2
2
1
0
0
0
0
0
0
1
0
0
1
0
0
2
0
2
1
1
3
0
0
0
0
1
0
1
0
1
2
1
2
0
1
2
1
0
2
0
2
1
0
0
1
1
2
0
2
0
2
0
0
0
0
0
0
0
1
2
0
1
0
0
2
0
0
2
0
1
0
0
2
2
1
0
1
0
0
2
1
2
0
1
1
0
1
2
0
1
1
0
2
0
1
0
4
1
3
0
1
2
0
0
2
0
0
2
1
3
0
0
0
1
2
0
1
0
0
2
0
0
1
0
1
2
2
2
2
1
0
1
2
0
0
0
1
1
1
1
2
0
1
0
1
0
0
0
1
1
1
0
1
0
2
0
0
2
2
1
1
1
2
0
0
1
1
1
0
0
0
1
1
3
1
0
0
0
0
1
0
1
0
1
0
1
0
2
1
0
1
0
0
2
2
2
0
0
0
0
0
1
2
2
0
0
0
0
2
0
1
0
0
1
2
0
0
0
0
2
1
0
1
1
2
0
1
0
0
1
1
0
1
0
1
2
0
2
0
0
1
0
3
0
0
0
0
0
2
1
2
0
1
2
1
1
1
2
0
1
2
1
0
2
0
1
0
0
1
0
0
1
2
0
2
0
0
2
0
0
1
0
0
0
0
0
2
1
0
4
1
0
1
0
0
1
2
2
1
1
1
1
1
2
0
0
0
1
1
0
2
2
0
1
0
2
0
1
2
0
0
0
0
0
2
1
0
1
2
0
2
0
0
1
1
2
0
2
1
0
0
0
0
1
0
1
2
1
0
0
2
1
2
3
0
0
1
0
0
2
1
0
2
1
0
0
2
0
2
0
0
1
1
2
0
2
1
3
1
0
2
1
2
1
1
1
2
0
1
0
1
1
0
1
1
1
0
0
0
1
2
1
0
0
1
0
1
0
1
2
0
0
0
0
2
0
2
0
0
2
1
1
0
0
0
2
2
0
0
1
2
0
0
0
1
0
2
1
0
0
1
0
2
2
1
0
0
1
1
0
1
1
1
0
0
2
0
0
0
1
2
4
1
0
1
0
0
1
0
0
2
0
2
0
1
0
0
0
2
0
1
0
2
0
2
1
1
1
0
1
1
2
0
1
1
3
0
2
2
2
0
2
1
1
3
2
2
1
1
1
0
0
0
2
2
1
1
0
1
0
1
0
0
1
0
1
1
1
0
3
0
0
0
2
1
0
0
1
2
2
1
2
2
0
1
0
1
0
0
0
0
0
0
1
1
1
2
0
4
1
1
2
0
0
0
2
0
1
1
0
0
0
0
2
0
0
2
2
1
0
1
0
2
1
0
1
1
0
0
2
3
1
1
0
1
1
0
1
0
0
0
0
1
2
0
0
0
1
0
0
1
0
1
2
2
2
1
0
2
5
4
1
2
2
0
0
2
0
1
1
2
0
0
1
2
1
1
1
1
0
2
0
1
1
0
0
0
1
1
0
1
1
1
2
0
0
1
0
0
2
0
0
0
0
0
0
1
2
2
0
0
0
0
1
0
0
0
1
0
0
2
0
1
0
0
1
2
1
0
0
1
0
1
1
1
0
0
0
1
1
1
1
0
4
0
2
0
0
1
0
0
1
1
2
1
0
1
0
0
0
3
2
0
0
1
2
1
3
1
1
0
1
1
0
0
0
2
0
0
0
1
0
2
2
0
0
0
0
0
1
0
8
1
2
0
0
0
2
1
2
1
1
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
1
1
0
2
2
2
0
0
0
0
1
0
2
0
1
1
1
1
1
0
1
0
0
0
1
2
1
0
0
0
0
1
0
0
0
4
0
1
1
1
2
2
0
2
2
1
1
2
0
1
2
1
1
0
2
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
2
1
0
0
0
2
1
1
0
1
2
2
0
2
0
0
0
2
1
0
0
2
0
2
1
2
1
0
1
1
0
1
0
0
0
1
1
1
0
0
2
2
1
1
0
1
0
2
2
2
1
0
2
0
1
1
0
2
1
0
2
2
0
1
1
2
0
1
0
1
1
0
0
0
2
2
1
0
1
0
1
0
1
2
0
1
2
1
2
0
2
1
0
0
0
0
4
0
0
0
1
2
0
0
1
0
0
0
1
2
0
2
0
0
2
2
0
1
0
1
1
2
1
2
0
5
0
1
1
0
0
2
0
2
1
2
1
1
2
0
0
2
0
1
4
0
0
0
2
1
6
0
1
1
0
0
0
1
0
2
2
0
1
1
0
1
1
0
0
2
2
2
2
0
2
0
0
2
0
0
0
0
1
1
1
1
2
1
0
0
0
1
3
0
0
0
1
1
0
0
1
1
1
1
2
0
1
0
1
0
0
0
1
0
1
0
2
0
2
0
1
1
1
1
0
1
0
2
0
0
1
1
0
1
1
0
0
1
0
2
0
2
0
0
1
2
2
1
0
1
0
0
2
1
0
1
0
0
1
0
1
0
2
0
0
1
1
0
2
2
0
2
2
1
2
0
2
1
1
0
0
1
0
1
2
0
0
0
0
0
0
0
3
0
0
1
0
2
0
0
1
0
0
1
0
0
0
2
0
1
1
1
2
0
0
0
1
3
0
0
1
0
1
0
0
1
1
0
3
0
0
0
1
1
0
1
2
2
0
3
0
0
1
0
1
0
0
0
0
2
1
0
0
1
0
1
2
0
1
1
1
0
1
1
2
0
0
0
1
2
0
1
0
1
2
0
2
2
1
0
2
2
0
2
1
4
0
1
0
0
2
1
1
0
1
0
1
0
0
0
0
0
1
1
1
1
2
0
0
0
0
1
0
2
1
0
2
1
1
0
0
1
0
2
0
2
1
2
1
1
1
0
1
0
0
0
1
1
0
0
2
1
0
2
1
0
0
0
1
0
1
0
0
1
0
1
1
0
2
0
0
0
2
0
0
1
0
1
1
1
0
3
2
1
2
0
2
0
4
1
2
0
1
0
0
2
0
0
0
3
2
0
2
0
1
0
0
1
0
1
0
0
3
0
1
1
2
1
1
2
1
0
0
0
0
0
2
0
1
0
1
0
0
0
1
2
1
0
0
0
0
1
0
2
2
0
0
5
2
1
1
0
0
1
0
0
2
0
1
2
0
2
0
1
1
0
0
0
0
2
0
1
0
4
0
2
2
1
2
2
1
1
1
0
1
2
4
2
0
0
1
0
1
2
0
0
2
0
1
0
2
0
0
0
0
1
1
0
0
2
0
0
0
2
0
0
1
0
1
1
0
1
1
0
0
0
0
0
1
1
0
0
0
2
0
0
0
2
0
2
0
2
0
2
1
2
0
0
0
0
0
0
1
0
2
2
2
0
2
1
1
1
0
1
1
1
2
0
0
1
0
1
0
0
0
3
0
1
1
0
0
0
1
0
2
0
2
2
1
1
0
1
0
1
0
0
0
2
1
0
1
0
0
0
0
1
1
2
0
1
1
1
0
0
1
0
0
1
0
0
0
1
0
1
0
2
1
1
2
0
1
0
1
1
0
0
0
0
0
0
0
0
2
0
1
1
2
2
2
0
1
1
0
0
0
2
0
1
1
0
0
2
2
1
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
2
2
0
0
0
1
0
1
1
2
0
0
0
1
2
1
0
1
1
1
2
0
0
1
0
0
0
1
2
1
1
2
2
1
0
0
0
2
0
0
2
1
0
1
0
0
0
2
0
1
1
4
1
2
2
2
0
2
1
1
1
0
0
1
1
0
1
2
1
0
2
1
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
3
0
0
0
0
0
2
1
0
0
1
1
0
0
0
0
2
2
0
1
2
0
1
0
1
2
0
0
0
2
1
2
0
2
1
1
1
1
0
0
1
0
1
1
2
2
0
0
0
1
0
1
2
0
1
0
0
1
1
0
4
2
1
1
0
1
1
1
1
2
2
0
0
1
0
1
0
0
0
0
1
1
0
1
0
0
1
1
0
0
0
0
1
3
1
0
0
1
0
2
0
0
2
1
0
0
2
1
2
2
2
0
2
0
0
0
2
0
1
2
1
0
1
3
1
0
0
0
1
0
0
0
3
1
0
0
0
0
0
1
0
0
2
1
0
1
2
0
0
0
1
0
0
2
0
1
2
0
0
0
0
1
5
0
2
2
0
2
0
1
0
0
1
0
0
0
1
0
1
2
1
0
2
1
0
0
0
0
0
2
2
1
0
0
1
0
2
1
0
0
0
0
1
2
0
0
0
0
0
2
2
0
1
2
1
1
0
2
1
1
0
0
0
1
0
0
0
1
2
0
1
0
1
0
0
0
0
1
1
1
1
2
2
2
0
2
1
0
0
0
1
0
1
1
0
2
0
4
2
1
0
2
1
0
2
2
2
0
2
0
0
1
0
0
1
1
1
0
2
0
2
1
0
0
1
1
1
0
0
0
2
2
0
1
1
0
0
0
2
1
2
0
0
1
0
2
2
0
3
0
0
0
0
0
1
0
1
2
1
1
0
1
0
2
0
0
1
1
3
0
2
1
1
1
1
2
1
2
0
1
1
0
2
0
1
1
2
0
1
1
2
2
0
0
2
2
0
2
0
0
0
0
2
1
0
0
0
0
1
1
0
2
0
1
2
0
1
0
1
2
0
0
0
1
0
0
1
0
0
1
2
1
0
3
1
0
0
1
1
2
2
2
0
0
0
2
1
1
0
1
0
0
0
0
2
2
0
0
0
1
1
0
0
2
0
0
2
0
2
1
0
2
0
1
1
0
2
0
1
1
0
2
0
0
0
2
2
0
2
3
0
2
0
0
1
2
1
1
1
2
0
1
0
1
0
0
1
1
2
1
1
0
1
2
0
0
0
1
1
2
0
1
1
2
0
0
2
0
2
0
0
2
1
0
1
1
1
0
2
0
2
1
1
2
0
2
1
1
1
0
2
0
0
1
0
1
2
0
1
2
0
0
1
2
2
2
0
0
0
2
0
1
1
0
1
0
0
1
2
2
0
1
2
2
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
2
2
2
1
0
0
1
2
0
2
2
2
1
1
1
0
1
1
0
0
1
2
0
3
2
1
0
2
0
2
0
1
1
2
2
0
0
0
1
0
2
2
1
1
0
0
0
1
0
2
0
0
2
2
1
1
1
0
2
0
2
0
2
0
2
1
0
2
0
2
1
0
0
0
1
1
2
0
0
0
1
1
0
1
2
0
0
0
2
0
0
1
2
0
2
0
1
0
1
1
0
0
0
4
1
1
0
0
0
0
0
0
2
2
1
0
0
0
1
2
0
1
1
0
2
2
1
0
1
1
1
0
0
0
2
1
0
1
0
2
0
1
0
2
0
0
1
0
0
0
1
0
0
0
2
1
1
0
0
0
0
2
2
1
1
0
2
0
0
1
1
0
0
1
1
0
0
1
1
0
3
0
0
2
2
0
1
0
0
1
1
2
0
3
1
0
1
0
0
1
1
2
0
0
0
1
0
1
0
1
1
1
0
0
0
1
2
1
2
1
0
0
2
2
2
0
1
0
0
1
2
0
0
0
0
3
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
1
2
1
0
1
1
1
0
0
1
0
0
2
1
1
0
0
0
0
0
2
1
1
1
0
0
0
1
0
0
2
0
1
0
0
2
1
1
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
2
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
6
1
0
1
0
1
1
0
1
2
2
2
2
0
0
0
0
1
0
2
0
1
2
1
1
0
3
2
0
3
2
1
1
0
2
0
1
2
1
0
2
2
0
1
0
0
2
0
0
0
1
1
1
0
0
0
1
2
2
0
0
0
1
0
2
1
0
0
0
0
1
0
2
0
1
1
3
0
1
1
0
0
0
0
2
0
1
0
1
1
0
0
0
0
2
0
0
2
0
0
2
0
0
1
0
2
2
2
0
1
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
1
0
2
0
1
2
1
1
2
1
2
1
0
1
0
0
1
0
0
2
0
1
1
1
0
0
0
1
2
0
2
1
2
0
0
0
0
0
1
1
0
0
1
0
0
0
2
2
2
0
0
1
1
2
0
1
0
0
1
2
0
0
0
1
2
0
0
1
2
0
2
1
0
1
0
0
1
1
2
0
0
0
0
2
1
2
0
2
1
2
2
2
0
2
0
0
0
1
1
0
2
0
0
0
2
2
2
0
1
1
2
1
1
1
2
2
0
0
0
0
0
1
1
1
2
1
0
0
0
1
0
0
1
1
1
1
2
1
0
0
1
1
1
2
0
1
1
2
2
1
0
0
2
0
1
2
0
2
1
1
0
0
0
2
1
2
0
1
0
1
1
1
1
1
0
0
0
0
1
1
0
1
0
1
2
2
1
0
2
3
1
2
1
1
1
0
0
1
1
0
1
1
1
1
1
1
2
2
2
0
2
3
3
0
2
1
1
2
0
0
0
1
2
0
0
0
1
1
0
1
2
2
0
0
0
0
1
1
1
1
2
0
1
0
2
0
1
1
1
2
1
1
0
1
1
0
1
1
0
1
2
1
1
2
0
0
1
0
2
0
2
0
1
0
0
0
1
1
1
1
0
1
0
2
0
2
0
2
0
0
1
1
1
1
1
0
0
2
2
0
1
0
2
2
0
1
2
1
1
1
0
1
0
2
0
0
2
1
2
2
0
1
1
1
0
0
0
0
0
1
0
0
2
1
0
2
3
1
0
2
2
0
2
2
1
0
0
1
1
2
1
0
1
1
1
1
2
0
0
0
0
0
1
2
0
0
4
2
1
0
0
0
0
2
1
0
2
0
1
0
0
0
2
0
0
0
2
1
1
2
0
2
2
0
1
1
0
0
0
1
2
0
2
0
1
2
2
2
0
2
2
0
4
1
2
2
2
2
1
0
0
2
2
1
1
0
1
1
0
0
1
1
0
0
1
0
0
0
2
1
0
1
0
2
0
0
2
0
1
1
0
2
0
0
0
2
1
2
1
0
1
0
0
0
0
0
0
1
0
1
1
1
0
0
0
2
0
1
0
0
2
2
0
2
0
0
2
0
2
0
2
1
0
2
1
0
0
2
1
2
0
0
0
0
1
0
0
2
2
0
0
1
0
0
1
0
1
0
2
0
0
0
1
1
2
0
0
1
1
1
0
2
1
0
2
1
0
0
1
2
0
0
1
0
0
1
0
0
0
0
1
3
1
0
0
1
4
2
0
0
2
2
0
0
1
1
1
0
2
0
1
2
1
1
0
0
0
0
1
0
1
0
0
0
0
2
1
2
0
1
1
2
0
0
2
1
0
0
0
0
0
2
1
0
2
2
0
1
0
0
2
1
1
2
0
0
1
1
1
2
1
0
1
0
2
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
2
0
3
0
1
1
2
1
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
3
1
1
0
0
0
0
0
1
0
1
0
2
0
1
2
2
0
0
1
0
0
0
1
0
2
0
2
2
0
2
1
0
1
0
2
1
2
0
0
0
0
2
0
0
2
1
0
0
1
2
0
0
1
0
0
0
1
0
0
2
2
0
0
2
0
2
0
0
0
0
1
0
2
2
1
0
2
1
0
2
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
2
2
3
1
1
0
2
1
0
1
1
2
2
0
2
1
2
2
1
2
1
3
2
1
1
1
0
2
1
0
1
0
0
0
2
2
1
1
0
2
1
1
1
0
2
0
2
0
2
1
0
0
2
0
0
0
0
0
2
2
0
2
0
0
2
1
2
0
0
0
2
0
3
2
2
0
1
1
1
0
1
0
3
1
1
0
0
1
0
0
2
0
0
2
0
1
2
1
1
1
2
1
0
0
1
0
3
0
1
1
1
0
0
0
0
1
0
1
1
2
0
0
0
0
0
0
2
0
0
0
1
0
1
1
0
0
0
2
1
2
0
2
1
0
2
0
1
0
0
1
1
2
0
2
0
3
1
2
0
0
0
1
0
2
0
0
0
0
1
0
3
1
0
2
3
0
1
1
0
1
0
2
1
2
2
1
0
2
1
3
1
2
2
1
0
2
1
1
0
2
1
0
0
2
0
0
0
0
0
1
2
0
2
0
3
0
0
2
1
2
1
1
1
1
1
0
2
1
0
1
1
1
0
1
2
0
0
1
0
0
2
0
0
0
2
0
0
0
0
1
0
0
1
1
2
0
0
2
0
1
1
2
2
0
2
0
1
1
1
3
0
1
0
0
1
1
1
0
1
0
2
2
0
1
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
1
2
0
0
0
1
1
1
1
3
0
2
0
2
1
1
0
0
0
1
1
0
0
1
1
0
1
0
1
1
0
2
1
0
0
1
2
1
0
2
0
1
1
0
1
1
2
3
0
2
2
2
0
0
1
0
0
0
1
0
1
0
0
1
0
0
1
0
2
0
0
0
0
0
2
2
0
0
2
1
2
0
1
2
2
1
0
2
0
1
2
1
0
0
2
1
1
1
2
0
0
1
1
0
0
1
1
0
1
0
0
1
1
1
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
1
1
0
1
0
0
1
0
1
0
2
2
1
2
0
0
0
0
6
1
1
0
1
2
0
2
1
0
2
0
2
0
1
2
1
2
0
0
1
3
2
1
1
1
0
2
1
2
2
2
0
1
1
1
2
1
1
0
0
0
2
2
0
1
1
0
0
0
0
1
0
0
2
2
0
2
1
0
0
0
1
0
0
1
1
1
0
2
0
0
1
0
0
0
0
0
2
2
1
1
2
1
0
1
2
4
0
0
1
1
1
1
1
1
0
2
2
0
1
2
2
2
0
4
0
4
0
0
0
1
0
0
0
1
1
0
2
3
1
1
0
2
0
1
1
0
0
0
0
0
0
0
0
0
1
3
0
2
0
0
1
1
1
0
0
2
3
0
1
0
0
1
0
0
0
1
2
1
0
0
0
0
0
2
1
0
0
0
0
0
1
0
1
1
2
0
0
2
1
0
0
1
0
2
0
1
1
2
0
1
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
2
1
0
1
0
0
1
1
1
1
0
1
1
1
1
2
2
0
1
1
0
0
0
0
0
1
0
1
2
0
2
2
1
2
2
0
2
2
2
2
0
0
1
1
0
1
0
1
1
3
0
0
0
2
0
2
0
0
2
0
0
0
0
1
0
2
2
1
0
1
0
2
0
0
0
0
1
2
1
2
0
0
1
1
0
2
2
0
0
1
2
2
2
0
0
0
1
0
0
0
2
0
0
0
0
1
0
1
0
0
2
0
0
2
0
0
0
0
1
1
1
1
1
2
0
1
1
1
0
0
1
0
0
0
2
0
0
0
0
0
1
1
1
2
0
1
0
0
1
1
2
1
0
2
0
2
0
0
1
1
1
0
1
0
1
0
0
1
2
1
0
0
2
2
0
1
0
0
1
2
1
0
1
1
0
0
1
0
0
0
2
2
2
0
1
2
0
1
0
0
0
0
0
1
2
1
0
0
2
1
1
1
1
0
2
0
0
0
0
1
0
0
2
2
2
0
0
0
0
2
0
1
0
0
2
0
1
1
1
0
1
0
0
1
2
0
1
1
0
0
0
1
2
0
2
1
2
1
0
0
0
0
0
0
3
0
1
0
0
0
0
0
1
1
0
0
0
1
1
0
1
3
0
1
0
1
2
0
1
1
0
0
2
3
0
2
1
0
0
1
4
1
1
0
1
0
0
2
0
0
0
0
0
0
0
1
1
2
1
0
1
0
1
2
0
2
2
1
2
0
2
1
0
0
0
0
1
0
0
1
0
2
1
1
0
0
0
2
0
0
0
0
0
2
1
1
2
2
1
4
0
0
0
2
2
0
1
0
2
1
0
1
2
1
0
1
0
1
2
2
2
1
1
1
0
0
1
1
0
1
2
0
1
1
0
1
0
0
1
0
1
1
1
2
1
2
0
2
0
0
1
1
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
2
1
0
1
2
1
2
2
0
1
1
0
1
0
2
0
2
0
1
1
1
1
2
1
1
0
2
3
0
0
0
1
2
0
1
2
3
0
0
1
1
0
0
0
2
1
0
2
1
2
1
2
1
0
0
1
0
0
0
1
0
2
1
2
0
0
2
1
1
0
1
1
0
1
1
0
2
1
2
0
3
0
0
2
0
0
0
1
0
2
3
1
0
2
0
5
0
0
1
0
1
0
1
1
1
1
1
0
2
1
1
2
1
2
0
1
1
1
0
2
1
1
1
1
0
0
0
0
0
1
1
1
0
2
1
1
0
1
0
2
0
1
0
2
1
0
1
2
2
1
5
2
1
0
0
2
0
1
1
0
1
1
1
0
1
0
0
2
0
1
0
0
0
1
0
2
0
2
2
1
2
1
0
1
2
0
1
0
0
0
1
0
0
2
0
2
0
0
2
0
0
0
2
2
0
2
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
2
0
1
0
2
0
0
0
1
0
2
1
1
0
0
1
1
1
2
0
0
1
0
0
1
1
1
0
0
0
1
0
0
1
2
0
0
0
0
1
0
1
0
2
0
1
0
0
2
0
1
0
1
2
2
0
0
1
1
2
1
2
1
2
0
0
1
2
0
0
1
2
1
0
0
1
0
1
0
2
2
2
1
0
0
2
0
1
1
0
0
1
0
1
0
0
0
0
0
2
0
0
2
0
1
0
0
2
0
1
2
2
1
2
2
1
0
1
1
1
1
2
2
0
0
0
0
0
3
0
0
0
0
0
1
2
2
1
0
0
0
0
2
1
0
2
2
1
1
2
1
1
0
1
0
2
0
1
2
0
2
2
2
1
1
1
0
2
0
0
2
1
2
0
0
0
0
0
0
3
1
2
2
0
0
0
1
0
1
0
0
0
0
1
0
1
1
2
1
1
3
0
2
0
1
0
0
0
0
1
2
0
1
0
0
2
1
0
1
1
0
1
0
0
0
0
0
2
0
0
2
1
1
1
2
1
1
0
0
0
1
0
0
0
2
1
2
0
0
0
2
0
1
2
1
0
0
1
0
1
0
2
2
0
0
1
1
0
1
3
0
0
2
2
0
1
0
1
1
0
2
2
1
0
0
1
0
0
0
2
0
1
3
0
0
0
2
2
0
2
0
0
0
1
2
2
1
0
1
1
0
1
0
1
0
1
0
1
1
0
1
1
1
1
0
2
0
2
0
0
0
1
1
1
1
3
1
0
0
2
1
0
0
2
2
2
0
3
2
2
1
1
0
2
0
2
0
0
2
0
2
0
1
0
2
0
2
2
0
2
0
1
1
0
1
0
1
3
0
1
1
1
0
0
1
0
2
0
0
2
1
1
0
1
0
2
2
2
0
2
0
1
0
1
2
1
2
0
0
0
0
0
0
2
0
0
0
0
0
1
2
1
0
1
1
0
2
0
1
0
1
1
0
0
2
0
0
2
1
0
2
1
0
2
1
0
1
1
1
2
0
1
0
2
1
0
5
0
0
2
0
1
0
0
1
0
0
0
1
2
1
0
1
0
0
1
0
1
0
1
0
0
1
0
2
1
3
0
0
2
0
2
1
0
0
0
0
0
1
1
2
1
2
0
4
0
0
1
0
2
2
2
0
1
0
2
2
1
0
2
0
0
2
1
0
0
0
1
0
1
1
2
1
0
3
1
1
1
0
2
1
0
0
2
1
0
1
2
1
0
0
0
1
1
1
1
1
1
2
0
0
0
0
1
0
1
0
0
2
0
0
0
0
1
2
2
0
0
0
2
2
0
0
1
2
2
0
0
1
0
1
0
2
3
0
2
0
1
0
1
0
0
2
1
1
0
0
0
2
2
0
2
0
1
1
1
1
2
0
0
0
0
1
0
1
1
1
1
1
0
0
2
0
0
2
2
0
1
1
0
1
2
1
0
2
0
0
1
0
2
0
0
1
2
2
2
1
1
0
0
2
0
0
2
0
0
2
0
1
0
1
0
1
1
0
0
2
0
0
0
0
2
0
0
0
0
1
0
1
0
1
1
2
1
1
2
2
0
0
0
2
0
0
0
1
2
0
2
2
2
1
0
1
0
1
0
2
0
2
0
1
0
0
0
2
1
2
0
0
1
1
1
2
0
1
0
0
2
0
2
2
0
0
0
0
0
1
1
2
0
4
2
1
0
0
1
1
1
0
1
0
0
2
1
1
1
4
2
0
0
2
2
1
1
2
1
2
1
0
1
2
1
0
0
0
1
0
0
1
0
1
2
0
1
0
2
0
1
0
1
1
1
1
1
0
1
2
2
0
0
1
2
0
0
2
1
0
0
2
0
0
0
1
0
1
3
1
2
0
2
0
0
1
0
1
1
0
0
1
2
2
0
1
1
1
0
2
0
2
1
0
0
1
0
1
0
1
1
0
2
0
1
0
2
1
2
0
0
0
1
0
1
2
1
2
1
0
2
0
2
0
0
0
0
1
3
0
2
0
2
0
1
1
0
1
2
2
1
1
1
0
2
0
1
1
0
0
1
0
1
2
0
2
0
2
0
1
0
0
2
1
0
0
0
9
0
0
0
1
1
2
1
0
0
2
1
2
0
1
0
2
1
0
0
0
1
0
0
0
1
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
2
1
2
1
0
3
1
2
2
0
0
1
2
0
0
0
2
1
0
1
0
0
2
1
1
1
2
1
2
0
2
0
0
1
1
0
1
1
0
0
0
0
2
1
0
2
1
0
0
1
0
0
0
0
0
1
0
0
3
1
0
1
0
0
1
1
2
0
0
2
1
2
0
1
0
0
0
1
3
2
0
1
0
2
0
2
2
2
1
1
2
0
2
1
0
2
0
2
1
0
2
1
1
0
1
0
1
0
0
0
0
1
1
1
0
0
0
1
2
1
2
2
2
1
0
1
2
1
0
1
0
0
0
2
0
0
1
0
1
3
1
0
1
1
0
2
2
0
0
0
2
0
1
0
0
0
1
0
2
0
2
0
1
0
0
2
0
1
1
0
2
0
1
0
0
2
1
3
0
0
1
1
0
0
0
1
1
0
1
0
0
1
0
2
1
1
1
0
0
0
0
3
0
1
0
0
0
1
2
2
1
0
0
0
0
0
2
2
0
1
1
0
1
2
1
0
1
0
0
0
0
0
2
0
1
0
1
1
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
3
0
0
2
2
0
0
2
0
0
1
0
0
2
2
0
1
1
1
0
1
0
4
2
0
1
0
1
0
1
0
2
2
0
2
1
0
1
1
0
1
1
0
2
1
0
2
0
0
1
0
1
0
0
1
0
0
0
0
1
1
1
0
0
2
2
5
2
1
0
0
0
1
0
2
0
0
0
1
1
0
1
0
0
0
1
2
0
0
1
1
1
2
1
0
0
2
0
0
0
2
1
0
2
0
1
0
0
2
0
0
2
0
0
0
0
2
0
0
2
1
1
1
1
0
0
1
1
1
0
0
2
3
1
1
2
2
1
1
0
0
0
0
2
2
2
2
0
1
1
2
1
1
0
0
2
2
0
0
0
0
1
0
0
1
1
0
0
1
1
0
2
2
0
0
2
2
0
2
0
1
0
4
0
0
1
0
0
0
0
0
0
0
1
2
0
1
0
2
1
1
2
0
0
1
0
1
2
0
0
0
1
1
0
1
2
3
1
1
0
1
0
1
0
0
1
0
0
0
0
0
2
0
1
1
0
1
0
1
1
0
0
1
0
1
1
0
1
3
0
0
2
0
1
0
2
2
0
0
1
0
1
0
0
0
2
2
0
1
0
2
2
0
1
0
2
0
1
1
1
2
1
0
0
1
0
0
1
1
0
1
0
0
1
1
0
0
0
1
1
0
2
0
0
0
0
1
1
1
0
2
2
0
2
0
1
0
0
0
1
2
0
2
0
0
0
1
0
0
2
1
0
2
1
0
0
2
0
5
0
3
0
2
0
1
0
1
1
0
0
0
1
1
0
1
1
0
1
0
0
2
0
1
0
0
2
0
0
0
2
1
0
1
0
0
2
0
0
0
1
0
0
1
0
2
1
0
1
0
0
2
2
0
0
2
1
1
0
1
1
1
2
0
1
2
0
0
2
0
0
0
0
1
1
1
0
0
2
0
0
0
1
1
0
0
0
2
0
1
1
0
2
1
0
2
1
0
0
0
0
0
1
1
1
2
2
1
0
1
0
3
0
0
1
0
0
0
0
0
0
0
0
2
0
2
1
1
2
2
2
1
0
0
0
0
1
2
1
0
0
1
1
1
2
0
3
1
2
0
1
0
1
1
0
2
0
2
1
1
0
0
0
0
0
1
1
0
0
1
0
1
0
2
0
0
0
0
0
0
0
1
2
0
1
0
0
1
2
1
1
2
0
2
2
0
1
0
2
1
2
1
2
1
0
1
1
0
1
0
1
0
0
2
0
1
0
0
2
0
0
0
2
1
0
0
0
0
2
1
0
1
1
0
0
1
0
0
1
1
1
0
2
0
3
0
1
1
1
0
2
1
2
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
1
2
2
0
0
1
1
1
1
1
0
1
1
0
2
2
2
2
0
2
1
1
0
0
2
0
1
1
0
1
1
2
0
0
2
2
2
1
0
2
0
1
2
0
0
0
2
2
0
1
1
2
2
0
0
0
1
1
0
0
1
1
1
2
0
2
0
2
0
0
0
0
0
1
1
2
1
0
1
2
2
0
1
1
2
2
0
1
0
0
2
2
1
0
1
0
2
0
0
2
1
0
0
0
0
1
1
0
1
0
1
0
1
0
2
0
0
2
0
1
0
0
2
0
0
2
1
0
1
1
0
2
1
1
0
0
0
2
1
1
0
0
0
2
0
0
1
0
1
0
0
0
1
1
0
0
0
1
0
0
0
2
0
0
2
0
0
0
2
0
1
2
2
0
0
1
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
2
1
1
0
1
0
0
1
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
1
0
2
2
0
2
0
0
1
0
1
2
0
2
1
2
2
0
2
1
2
1
1
2
1
0
1
1
0
0
1
1
1
1
0
2
0
0
1
1
1
0
0
0
1
2
2
2
1
0
0
0
0
2
0
0
0
2
0
2
1
0
1
0
2
1
2
0
2
2
0
1
1
1
0
1
0
2
2
1
0
1
0
0
0
2
0
1
0
0
1
0
1
2
1
0
2
0
1
1
1
1
1
0
0
0
0
1
2
3
0
1
0
1
1
0
2
3
1
0
0
0
10
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
1
0
1
0
0
1
1
0
2
0
0
1
1
0
0
0
0
2
0
0
0
0
1
0
1
0
0
2
0
1
2
1
0
0
1
1
1
1
1
2
2
0
2
0
1
0
2
2
0
0
0
0
0
0
0
1
0
1
2
0
2
0
0
2
2
1
0
0
0
0
1
0
3
0
0
0
0
0
2
2
2
0
1
0
0
0
1
4
0
0
0
0
0
2
0
2
2
1
0
3
1
0
2
1
0
0
0
1
0
0
2
0
0
1
1
0
0
1
0
1
0
1
1
2
2
1
0
1
0
0
0
0
0
1
1
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
2
0
0
1
1
1
1
1
1
0
0
0
0
1
2
0
1
1
2
0
1
0
1
1
0
2
0
1
1
2
1
0
0
0
0
0
2
0
0
0
1
1
1
0
2
0
0
0
1
1
0
1
0
0
1
0
2
1
0
0
0
0
0
0
0
0
1
1
2
2
1
1
1
1
0
1
2
0
0
0
1
0
1
0
0
0
1
2
2
0
1
2
0
2
0
0
2
0
0
1
0
2
0
0
0
2
1
0
0
1
0
0
0
2
1
2
2
0
0
0
2
0
1
1
0
2
0
0
2
0
2
1
1
1
2
1
0
2
1
2
2
0
1
1
2
2
1
0
0
2
0
1
0
1
1
1
0
0
1
0
2
1
1
0
0
0
2
2
2
0
0
0
1
2
0
0
0
0
0
0
2
2
1
0
3
1
2
2
0
0
1
1
0
0
0
2
0
0
1
1
0
2
0
0
1
0
1
0
0
2
1
0
0
0
0
2
0
0
0
0
0
1
1
2
0
0
0
1
1
2
0
0
1
0
1
2
0
3
2
0
1
2
0
0
2
1
0
0
1
0
0
1
2
2
1
2
2
0
1
1
2
2
0
2
0
2
1
2
1
2
1
1
1
1
2
2
0
2
2
1
2
0
2
0
0
0
1
1
1
2
1
0
2
0
0
0
0
2
0
1
1
0
0
2
0
0
1
0
0
2
2
1
0
1
0
1
0
2
0
2
0
0
2
1
0
0
2
0
1
1
0
0
2
1
0
0
0
2
1
1
0
0
2
1
1
0
0
0
0
0
1
0
0
1
2
1
1
0
0
1
2
2
0
3
0
0
0
2
0
1
1
1
2
0
0
0
2
0
2
0
1
0
3
1
2
1
2
1
0
2
1
2
0
0
1
2
2
3
0
3
1
0
0
0
0
2
2
2
0
1
0
0
2
1
0
0
0
0
1
0
1
0
2
0
0
0
1
0
0
0
1
0
1
0
2
0
0
1
0
1
0
0
0
0
0
1
1
1
2
1
0
3
2
0
0
1
0
1
2
2
1
1
0
0
0
1
1
1
1
2
1
0
0
0
2
1
0
2
0
1
0
1
1
1
1
0
2
2
0
1
1
2
0
1
1
2
1
0
0
1
0
0
0
0
2
0
13
1
1
0
0
2
0
1
2
1
0
0
2
1
0
0
0
0
0
1
0
2
3
2
0
0
0
0
0
1
1
0
1
1
0
1
0
0
1
1
0
0
0
1
0
1
0
2
1
0
2
2
0
2
2
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
2
1
1
1
1
0
1
0
1
0
0
0
0
2
1
1
2
2
0
1
0
0
1
0
0
0
0
1
2
0
0
0
0
1
1
0
1
2
1
1
2
0
0
1
2
1
1
1
2
0
1
2
0
2
1
2
2
0
0
1
1
1
1
0
1
0
0
0
2
2
0
0
0
0
2
2
0
1
0
0
0
1
1
1
0
0
0
0
1
0
0
0
1
0
1
1
0
0
2
1
0
1
0
0
0
0
1
0
1
0
2
2
0
1
0
3
0
0
0
1
2
0
2
2
0
2
2
0
0
1
1
1
0
0
0
2
0
2
0
1
1
2
0
1
0
0
2
1
1
2
0
0
0
0
1
0
1
0
1
1
1
1
2
2
0
1
0
1
0
0
1
0
0
0
1
1
0
0
2
1
0
1
1
2
0
1
2
0
0
2
1
0
1
1
1
0
1
3
2
0
0
3
0
0
1
2
0
1
0
1
2
0
1
2
0
2
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
2
1
1
0
0
0
2
2
1
0
0
0
1
1
1
0
2
1
1
2
0
0
1
0
2
3
1
0
2
0
2
0
1
0
1
1
2
1
0
0
1
0
0
2
0
1
1
2
6
0
0
0
0
1
0
0
1
0
0
0
2
0
3
0
0
0
0
2
1
0
2
1
0
1
0
1
3
2
0
2
2
0
2
2
0
2
5
0
0
0
0
0
0
2
0
2
0
1
1
0
0
2
1
0
0
1
2
0
0
1
2
1
2
2
0
0
0
0
1
2
2
1
0
1
0
1
0
2
0
1
0
0
1
1
0
1
0
2
1
1
1
0
1
4
0
1
3
1
0
2
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
1
2
0
2
0
1
1
1
0
0
0
1
0
2
2
0
0
1
1
2
1
1
1
0
0
0
1
0
1
2
0
0
0
2
1
0
0
2
0
1
0
0
2
3
0
0
1
0
1
1
1
0
0
1
0
2
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
1
0
2
0
1
0
0
0
1
1
0
0
0
0
0
0
2
1
1
0
0
1
0
2
0
2
2
0
0
0
0
0
0
0
2
4
0
0
0
0
2
1
1
2
0
2
2
0
2
2
0
2
1
1
0
0
1
0
1
0
2
0
0
2
0
1
0
0
1
1
2
1
2
2
0
1
0
1
0
1
1
1
0
0
2
0
1
0
0
2
1
1
0
1
0
0
1
0
0
0
0
2
0
0
3
1
1
1
0
1
0
1
1
1
0
2
0
2
2
0
0
0
0
2
0
0
2
1
2
2
1
1
0
2
0
0
1
0
0
0
1
7
0
0
2
2
0
4
2
0
2
1
2
0
1
0
0
0
0
0
1
0
3
0
1
1
0
2
0
0
1
0
0
1
2
1
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
2
2
2
1
0
1
0
0
0
0
1
0
0
1
0
1
0
2
0
1
1
2
0
0
1
1
1
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
1
0
1
0
0
1
1
2
1
0
2
1
2
0
2
0
0
0
2
1
0
1
1
2
1
1
0
1
2
1
0
0
0
0
1
2
0
1
0
2
1
0
0
0
1
2
1
1
0
0
1
1
1
0
2
1
1
1
0
0
1
0
1
0
1
0
2
1
1
2
1
0
1
3
0
0
1
1
1
0
0
1
0
0
0
0
0
2
2
1
0
0
1
0
0
0
0
1
1
0
0
0
3
1
2
0
1
2
0
2
3
0
0
0
2
2
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
2
1
2
0
0
1
2
1
0
1
1
2
0
1
1
0
0
2
1
2
2
0
1
0
0
2
2
1
0
0
1
0
0
1
7
1
0
0
0
0
0
0
1
0
1
2
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
5
0
0
1
1
0
0
0
0
1
0
0
2
1
1
0
0
1
0
0
2
0
0
1
0
1
2
0
0
1
0
0
2
0
1
0
0
0
1
2
1
1
0
2
0
2
0
0
1
2
0
0
2
1
0
0
2
0
1
0
0
1
0
1
0
1
0
2
1
1
0
0
1
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
4
0
1
1
2
2
2
1
0
0
0
1
1
2
0
1
1
1
0
1
0
1
0
1
1
3
0
0
0
0
1
2
0
0
1
0
0
0
0
0
2
1
0
1
2
0
1
0
2
0
0
1
0
0
2
0
0
15
1
0
1
2
2
2
1
1
0
0
0
0
2
2
0
0
0
1
0
0
0
2
2
1
1
0
2
1
0
0
1
0
1
0
2
0
0
1
0
0
1
0
2
0
0
0
2
1
0
0
0
1
0
2
0
0
0
0
2
0
2
0
2
0
1
0
0
0
1
0
1
0
0
1
0
1
1
1
0
2
1
0
0
1
1
0
0
1
0
0
0
0
0
1
2
1
0
0
2
0
0
0
1
0
2
1
0
0
0
0
1
0
0
1
0
1
1
3
0
0
2
0
2
0
1
2
0
1
1
0
0
0
2
1
2
0
1
0
1
1
2
2
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
2
2
0
1
1
1
0
1
1
0
1
0
2
2
1
1
0
0
0
0
1
0
1
2
1
0
2
1
2
0
0
0
2
1
1
2
0
1
0
0
1
2
1
1
1
1
1
0
0
1
0
1
0
0
1
0
1
0
0
0
0
2
1
3
1
1
2
1
1
2
1
2
0
0
0
1
0
1
1
1
0
0
1
1
0
0
0
1
1
0
0
1
1
1
0
2
0
1
1
2
2
2
0
1
0
0
0
0
0
0
0
0
1
0
2
1
2
1
2
2
0
2
2
0
2
0
2
2
0
0
0
2
0
2
1
2
0
2
2
1
5
1
1
1
2
0
0
0
1
0
2
1
2
0
2
0
2
0
1
0
0
1
2
1
0
1
1
1
1
0
1
1
2
2
0
0
0
2
0
0
1
1
0
0
0
2
1
2
1
0
0
1
3
0
0
0
1
0
0
0
1
1
1
0
0
0
1
1
1
2
0
2
2
0
2
0
0
0
0
0
1
2
0
0
2
0
1
1
2
1
2
2
0
0
1
0
1
2
1
0
0
0
0
1
0
0
1
1
0
2
0
0
2
1
0
1
1
0
0
0
0
0
1
1
1
2
1
1
0
0
2
1
1
0
1
1
0
0
1
1
2
1
0
2
2
1
0
1
1
1
0
2
2
2
2
0
2
0
3
2
0
0
0
0
2
2
0
0
0
1
0
0
1
2
1
0
0
2
0
0
0
0
2
0
2
0
1
2
1
1
0
1
1
0
1
1
0
0
0
1
1
2
1
2
0
2
2
1
1
0
3
2
2
0
2
1
1
0
0
0
0
1
0
1
2
0
0
2
0
2
0
2
0
0
0
1
0
0
0
2
5
0
0
0
0
0
2
0
0
2
1
0
1
2
2
1
1
0
1
2
1
0
0
1
0
0
3
2
0
1
3
0
2
0
2
2
1
0
0
1
0
0
1
2
0
2
0
1
1
0
0
1
2
2
0
0
1
1
0
2
0
1
1
0
0
5
2
0
1
2
1
1
1
0
1
2
2
2
0
0
2
1
0
1
0
2
1
2
0
0
3
1
0
0
0
1
0
0
1
1
1
0
1
1
0
0
1
2
0
1
0
0
4
0
0
2
0
2
2
1
1
0
0
2
1
1
0
1
1
1
0
0
0
1
0
0
2
1
1
1
1
2
2
0
0
0
0
3
2
0
1
0
1
1
0
0
2
1
1
1
2
2
2
1
0
2
1
2
1
0
2
0
1
1
2
0
0
0
1
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
2
1
3
1
0
1
0
1
2
1
1
2
1
1
0
1
1
2
0
0
0
3
2
0
0
2
1
1
0
0
1
0
3
0
1
0
0
0
2
1
2
0
0
0
0
0
2
1
3
0
0
0
0
1
0
2
0
1
1
0
0
1
0
0
0
0
0
0
0
1
2
2
0
0
0
0
1
0
1
2
2
0
0
2
1
0
1
0
1
0
2
1
1
0
0
2
0
2
1
2
2
0
1
0
0
0
2
0
2
0
0
2
0
1
0
0
2
1
1
2
1
2
1
2
3
0
0
1
3
0
0
1
0
0
1
0
2
1
1
0
0
0
1
1
1
0
1
1
0
1
2
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
2
0
2
1
0
0
2
1
1
1
2
0
0
1
0
2
0
0
0
2
0
1
2
2
0
0
0
1
2
0
2
2
2
1
0
0
2
1
2
0
1
0
0
1
0
2
0
0
1
2
1
0
1
2
0
2
2
0
2
1
1
0
0
1
1
1
1
0
1
0
2
1
1
1
0
0
0
2
1
3
1
0
0
0
1
5
0
2
0
0
1
0
1
0
1
1
0
2
0
0
0
0
1
0
0
0
0
0
0
3
3
0
0
0
0
0
1
0
0
1
3
1
0
0
0
0
1
0
0
0
1
1
2
2
0
2
0
1
0
1
0
1
1
1
0
1
0
0
2
0
0
2
1
0
0
1
1
0
1
2
0
1
0
1
1
1
0
2
2
0
1
1
2
0
0
0
0
0
2
1
0
0
1
1
1
3
1
2
1
0
1
0
0
0
1
0
1
2
0
1
0
2
0
2
0
1
0
1
0
0
3
0
0
0
0
0
0
0
1
0
2
0
1
1
0
0
0
0
0
2
1
1
2
0
0
0
2
1
0
0
2
2
0
2
0
0
0
1
0
2
0
0
1
0
0
0
1
0
2
1
1
1
0
0
1
1
0
0
1
1
3
2
0
0
0
2
2
1
0
1
0
0
0
2
0
0
2
1
0
1
0
1
0
0
1
1
0
1
2
0
2
2
2
1
1
0
1
0
0
0
1
2
0
0
2
0
1
0
1
1
0
0
0
2
0
1
0
1
0
1
0
0
2
1
1
0
2
0
1
0
0
1
1
0
0
0
0
0
1
0
1
3
1
0
2
0
1
0
1
1
2
0
2
0
0
0
0
0
1
0
1
1
0
2
2
1
0
0
0
0
2
0
1
0
2
1
0
1
0
0
0
0
1
1
1
0
0
1
0
1
0
1
0
0
1
0
0
1
2
0
2
0
2
1
1
1
2
1
2
1
2
1
0
0
0
0
1
1
0
2
0
2
0
1
1
1
0
1
0
0
2
1
1
0
0
0
0
2
0
0
1
1
0
1
0
2
1
0
0
2
0
1
1
1
0
0
0
0
1
0
0
1
0
0
2
2
0
0
2
3
0
1
1
2
1
0
2
0
2
1
0
2
2
0
1
0
0
1
0
0
1
1
1
1
0
0
0
1
0
0
1
0
1
0
0
3
0
1
1
2
1
0
0
0
0
1
0
1
2
0
2
0
4
0
6
1
2
0
2
0
1
1
2
0
1
2
1
2
0
1
0
0
2
1
1
1
0
0
1
0
0
1
2
1
0
0
1
0
0
2
1
1
1
0
0
0
2
1
0
2
1
3
1
1
2
6
0
0
2
0
0
1
1
1
3
2
2
2
2
1
0
1
1
1
1
1
1
0
0
2
1
0
0
1
0
0
2
1
1
1
0
3
1
1
0
0
0
1
2
3
0
1
1
0
1
1
1
0
1
1
0
2
0
0
1
1
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
1
1
2
0
0
1
0
1
1
0
1
2
1
0
2
2
1
0
0
0
1
0
0
0
1
0
3
2
0
0
0
1
0
0
1
0
2
2
1
0
2
0
1
0
2
0
0
0
2
0
2
1
0
1
1
2
2
0
0
0
2
0
1
2
0
2
0
0
1
0
1
0
0
0
2
1
0
1
0
0
1
0
0
0
1
1
0
0
1
1
1
0
1
1
1
0
2
1
0
2
1
1
2
1
0
1
1
2
0
1
2
1
1
1
0
0
0
1
1
0
2
1
1
1
0
0
1
1
0
1
2
1
2
1
0
0
0
1
1
0
2
0
1
0
0
0
2
0
0
0
2
2
2
2
1
0
0
1
0
3
1
1
1
0
1
2
0
0
2
0
2
0
2
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
1
1
1
0
0
1
0
0
0
0
0
0
0
1
2
0
1
0
1
0
0
1
2
0
2
0
0
0
0
2
1
0
0
2
1
1
0
0
1
1
2
1
0
0
0
0
0
2
2
0
1
0
0
1
0
2
1
1
1
1
2
2
1
0
0
0
0
0
0
0
1
2
0
1
1
2
0
2
0
1
0
1
0
2
0
0
0
0
1
0
1
0
0
1
1
0
0
1
0
0
2
0
1
0
1
1
0
2
2
1
0
1
1
0
0
0
2
1
1
2
0
0
1
1
1
0
0
0
0
0
0
3
2
0
1
2
1
1
1
1
0
1
2
2
2
1
1
3
0
2
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
4
0
0
1
1
2
1
0
2
0
2
1
0
1
1
0
0
1
1
2
0
0
1
0
0
0
0
2
0
1
2
1
0
1
1
1
2
0
1
0
2
2
0
0
2
0
0
1
0
2
0
0
2
1
0
2
0
2
1
1
0
0
1
1
0
0
0
0
1
0
1
1
0
1
0
1
0
2
0
2
0
3
0
1
0
1
0
1
0
1
2
0
1
0
2
1
0
1
0
2
0
1
2
0
0
0
0
2
1
0
2
0
1
0
0
2
1
0
0
1
1
1
2
0
0
4
1
2
0
0
0
1
0
0
0
0
0
2
0
2
1
0
1
0
0
0
0
2
0
2
0
0
0
1
0
1
1
1
1
1
2
2
0
0
0
0
1
0
0
0
1
2
0
4
0
0
1
0
2
2
2
2
0
1
1
2
1
1
0
1
0
0
0
2
2
2
2
2
0
1
0
1
1
0
3
1
2
0
1
1
2
0
2
1
1
0
0
0
1
0
1
0
3
0
0
0
0
1
2
0
0
0
1
1
1
0
0
2
0
0
1
2
0
0
1
2
0
2
0
1
0
1
0
1
1
0
0
0
0
1
1
2
0
1
0
1
1
0
0
1
2
4
1
0
0
0
0
0
0
1
0
0
2
0
2
2
0
0
0
0
1
0
1
1
1
0
1
0
0
1
1
0
1
2
0
1
0
1
1
0
0
1
0
1
0
1
0
0
0
1
0
2
0
2
0
0
1
0
1
2
2
1
0
0
0
0
0
1
1
2
2
0
0
1
1
3
1
0
2
0
2
1
1
1
1
1
2
1
0
2
1
2
1
0
1
1
0
0
0
1
1
0
2
2
2
2
2
1
0
0
2
2
2
0
0
0
0
0
0
1
0
1
0
2
2
0
2
1
0
0
0
1
2
1
0
1
0
1
1
0
1
2
0
0
1
1
1
1
2
2
0
0
0
0
0
1
1
1
1
1
1
2
0
0
0
0
0
0
0
1
2
2
1
2
2
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
2
0
1
1
2
1
2
0
0
1
0
0
2
2
2
1
0
2
2
2
1
0
1
1
0
0
0
0
1
1
1
1
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
2
2
3
0
1
2
0
0
0
1
0
1
0
0
1
0
1
0
0
2
2
0
0
0
0
1
0
0
1
0
4
0
0
2
1
2
1
2
0
2
0
0
1
0
0
2
1
2
0
0
1
1
2
1
1
0
0
0
1
1
1
1
0
0
0
1
0
0
0
0
2
0
1
0
0
0
1
0
1
2
1
0
0
1
1
0
1
0
0
0
0
1
0
0
0
1
2
0
2
0
0
0
0
2
0
0
0
3
0
2
1
0
2
2
0
3
2
0
1
1
0
0
2
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
2
1
0
2
0
0
0
1
0
2
1
0
2
2
0
1
2
0
0
0
2
2
2
0
0
1
0
1
0
1
0
0
0
2
0
1
0
1
2
0
0
2
0
0
0
2
3
1
1
2
1
1
0
2
0
1
0
0
3
0
1
2
1
0
1
2
0
0
0
0
1
1
2
0
2
0
0
0
2
2
0
1
0
1
2
1
2
1
3
1
0
0
0
1
1
2
2
2
1
0
0
1
1
0
2
0
0
0
0
1
2
1
2
2
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
1
0
4
2
1
2
1
0
1
0
1
1
2
2
1
0
2
0
1
2
0
0
2
2
0
0
3
0
0
0
0
0
1
1
1
1
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
1
1
2
1
1
0
2
0
1
1
0
1
2
0
0
0
0
0
0
0
0
1
0
1
1
0
2
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
1
0
0
1
0
1
2
1
0
0
0
0
0
0
1
2
6
0
0
0
0
1
1
2
1
1
1
2
0
2
1
1
0
3
1
0
1
0
0
2
1
0
0
0
0
0
0
1
1
0
2
0
1
0
0
2
1
0
2
1
0
2
1
1
1
0
1
1
0
0
0
0
0
2
1
2
0
0
1
2
1
0
1
2
0
0
0
0
0
1
0
3
0
0
0
0
0
1
2
1
0
0
0
2
2
2
0
0
1
1
0
0
1
0
0
1
0
1
0
0
1
1
0
2
3
2
1
0
3
1
0
1
0
0
1
0
1
1
1
0
3
0
1
2
0
0
0
0
0
0
2
2
1
1
1
2
0
1
1
1
2
2
0
1
0
3
0
2
1
0
0
0
2
2
1
0
1
2
1
0
1
0
0
1
0
1
1
0
0
2
1
1
4
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
1
1
1
0
3
0
1
0
1
0
0
0
2
1
1
1
1
1
0
3
0
0
1
2
0
0
1
0
1
1
0
1
0
0
1
0
1
0
1
2
0
2
2
1
1
1
1
1
0
2
1
0
1
1
2
3
1
2
1
2
1
1
0
1
0
1
1
0
2
2
1
2
0
2
1
0
0
2
0
2
1
0
1
1
0
1
1
1
2
0
0
2
1
2
0
0
2
0
2
2
0
2
0
3
0
2
1
1
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
1
1
1
0
1
1
0
2
1
0
0
5
0
0
4
0
0
0
2
2
1
2
1
0
0
2
1
0
0
0
2
0
1
0
0
2
1
0
1
2
0
0
0
1
1
1
2
1
0
0
0
0
1
0
0
1
2
2
0
1
2
0
0
0
2
1
0
2
1
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
1
0
2
0
1
0
1
0
2
1
0
0
2
1
0
1
0
1
0
1
1
0
2
0
0
1
0
0
0
1
1
0
0
0
2
2
1
0
1
2
0
1
1
1
0
0
1
0
1
0
0
2
0
0
1
3
0
0
0
0
1
1
0
1
1
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
2
0
1
2
1
1
0
2
1
0
0
1
0
1
0
0
0
2
0
0
1
1
0
1
2
2
0
0
0
1
2
0
0
2
2
0
1
2
0
0
0
0
1
1
0
1
1
1
1
1
0
2
0
1
0
0
1
0
2
0
2
0
0
1
0
1
2
0
1
2
1
1
1
0
0
0
0
0
1
0
2
0
2
1
0
0
1
2
1
1
0
0
2
0
0
2
2
0
0
1
1
1
2
0
0
0
1
0
2
0
1
2
1
1
1
0
0
2
0
1
0
0
3
2
0
0
0
0
0
0
0
1
0
1
0
1
1
2
2
1
0
1
0
0
0
1
2
1
0
1
1
0
0
1
2
2
2
0
2
3
1
1
0
1
0
0
0
1
2
1
1
2
1
0
0
1
0
1
1
0
2
1
0
1
0
0
1
1
0
2
1
0
0
3
2
0
0
1
0
0
0
2
1
1
2
1
0
2
2
0
0
0
0
0
2
0
5
0
0
2
0
0
2
0
1
3
2
1
2
0
1
0
0
1
0
1
1
0
0
0
0
2
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
2
1
2
2
1
1
0
0
0
0
2
2
1
0
3
0
0
0
0
1
0
2
0
0
2
0
0
2
1
3
5
0
1
2
1
3
0
1
1
0
2
0
0
2
0
0
1
2
1
1
0
0
0
0
2
0
0
1
2
0
1
0
2
2
0
1
0
1
3
0
2
1
1
0
1
0
0
2
1
0
0
0
1
1
0
1
2
1
1
1
0
2
0
2
0
0
1
0
0
2
1
2
0
0
0
0
0
1
1
1
2
0
1
2
0
2
0
2
2
0
2
0
0
2
0
0
2
0
1
0
0
0
3
1
0
0
2
0
0
1
0
0
1
0
1
0
0
1
2
1
0
1
0
1
0
2
0
0
0
0
0
0
1
0
0
0
1
0
1
1
2
2
0
2
0
0
0
1
0
0
2
0
0
0
0
1
0
1
0
0
2
0
1
0
0
1
0
2
0
0
1
0
2
1
0
0
0
0
1
0
0
2
0
0
1
2
0
0
0
1
1
2
1
1
0
0
1
1
0
4
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
2
1
0
0
1
2
0
2
0
0
1
0
0
1
0
0
1
0
1
2
1
0
1
3
0
1
0
0
0
0
0
1
2
0
0
1
0
1
1
0
2
1
1
1
2
0
1
0
2
2
1
0
0
0
1
0
1
1
1
0
1
0
2
2
2
1
1
2
0
5
1
2
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
1
1
1
0
1
0
2
3
0
1
0
1
0
0
1
0
1
1
0
1
2
2
1
0
2
0
1
0
2
2
0
1
1
0
0
0
2
0
0
1
0
0
0
0
0
2
0
1
0
2
0
0
1
2
0
1
0
1
1
2
1
1
0
0
0
0
1
1
0
1
0
0
1
0
0
2
0
2
0
1
1
0
2
2
0
0
1
1
0
0
0
2
1
1
0
2
0
0
0
2
1
2
0
0
1
2
0
2
0
0
0
0
0
0
1
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
2
2
1
2
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
1
1
1
1
1
7
3
1
1
1
2
1
0
2
1
2
0
0
2
0
2
2
0
1
0
1
0
0
2
0
0
0
0
0
2
0
2
2
0
0
0
0
2
1
1
0
2
1
1
1
2
3
2
0
0
1
0
3
1
0
0
2
0
0
1
0
2
2
1
1
1
0
0
3
1
0
0
1
0
1
0
0
0
1
2
2
1
1
0
0
1
2
1
2
0
1
0
0
2
0
1
1
2
0
0
0
1
0
2
0
0
0
0
2
0
2
2
1
9
0
2
1
1
1
0
0
1
1
1
0
0
3
0
2
2
1
0
1
2
2
1
2
1
1
0
1
2
1
0
1
1
0
0
1
1
2
1
2
0
2
1
6
1
0
1
0
1
2
0
1
0
0
0
1
0
1
1
0
1
1
1
2
2
1
0
1
0
0
1
1
0
0
0
0
1
1
2
0
1
2
2
2
1
1
0
2
0
0
1
2
1
0
2
2
1
0
1
2
1
2
1
0
2
2
2
2
0
3
0
1
2
0
1
1
1
1
0
1
0
1
0
1
2
0
2
0
0
1
2
0
2
1
1
1
0
1
0
0
2
1
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
2
1
1
1
1
1
0
1
1
0
2
0
0
1
2
0
1
1
0
2
1
1
0
1
1
2
0
2
0
0
1
0
1
0
1
1
0
0
2
0
0
1
0
1
1
2
0
2
2
2
2
0
2
1
1
0
0
1
2
2
1
0
0
0
1
0
0
0
0
1
1
2
0
0
0
0
0
0
1
0
1
0
0
0
0
1
2
2
0
2
0
0
0
1
0
0
1
0
0
0
1
0
2
1
0
1
0
0
1
0
1
1
0
0
0
0
0
1
2
2
1
2
2
1
1
1
1
0
0
1
0
0
0
1
1
0
0
0
0
0
2
2
0
1
1
0
0
0
0
2
1
2
0
2
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
1
1
0
0
0
0
2
0
15
1
0
0
1
0
1
0
1
1
0
0
1
1
2
0
1
2
2
0
0
0
1
2
0
0
1
2
2
0
2
1
0
1
2
1
0
0
1
1
1
0
1
2
1
0
2
2
1
1
0
0
1
0
0
2
1
1
1
0
0
2
0
1
0
2
0
1
1
2
1
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
4
1
1
0
1
0
2
0
0
2
1
0
0
0
0
0
0
0
1
3
1
2
0
1
0
1
0
0
0
0
2
0
1
0
1
2
0
1
2
0
2
2
2
0
2
0
1
2
2
1
0
0
0
0
1
1
1
0
1
1
0
0
1
0
1
0
2
2
0
0
1
3
0
1
1
1
2
1
2
1
0
0
0
0
0
0
0
0
1
2
0
1
0
1
1
0
0
0
2
1
1
2
0
0
2
0
0
0
0
1
1
0
1
6
1
1
0
1
1
2
2
2
1
1
2
0
2
2
0
0
1
0
0
2
0
1
0
0
2
1
0
1
0
0
1
2
0
0
1
1
0
1
0
0
2
0
1
0
0
2
0
1
2
2
0
2
0
1
2
1
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
1
0
1
0
0
2
0
0
0
0
2
0
1
1
0
1
2
0
0
0
0
2
0
1
1
2
0
0
0
2
2
1
0
1
0
2
0
0
0
0
1
1
1
0
0
0
2
2
4
1
1
0
0
2
0
0
2
1
3
0
0
1
3
0
4
0
0
0
1
2
2
2
0
0
0
0
1
0
0
2
1
0
0
0
2
0
1
1
1
0
1
1
1
2
0
0
1
0
0
1
0
0
0
1
2
2
0
0
1
0
0
2
2
2
0
1
0
1
1
0
0
0
1
0
1
1
1
1
1
0
0
2
1
2
0
2
2
3
0
1
1
0
0
0
0
0
0
0
1
1
0
0
2
1
1
0
1
0
0
0
0
0
2
0
0
1
0
0
1
0
0
2
2
1
1
1
0
0
3
0
1
0
0
0
2
1
0
0
2
0
2
0
0
1
0
0
0
0
0
1
3
1
0
0
1
2
0
2
0
1
0
2
1
2
0
3
1
1
2
1
0
2
0
1
1
1
1
1
0
1
0
2
0
1
2
0
1
0
1
1
0
0
1
1
0
2
0
1
0
3
0
1
1
2
1
0
0
2
0
0
0
0
2
0
0
1
2
2
1
0
1
0
1
1
0
2
1
0
0
2
0
0
0
2
1
0
1
2
0
0
0
1
1
1
1
0
0
1
2
0
0
0
1
2
1
0
0
0
1
2
2
2
2
0
1
0
1
1
3
0
0
2
0
1
0
2
0
0
1
0
2
0
0
2
0
2
1
0
2
1
0
2
0
0
0
1
0
0
1
0
0
1
1
0
0
0
1
1
0
0
1
1
1
2
0
1
0
1
0
1
1
2
1
1
0
1
0
0
0
1
0
0
2
1
2
2
2
1
0
1
2
2
2
0
0
2
0
0
2
0
0
0
1
0
0
2
0
3
1
0
0
0
2
4
2
1
2
2
1
0
0
0
2
1
0
0
0
0
2
0
1
1
2
0
1
2
0
0
2
1
0
0
1
0
2
0
2
3
1
1
1
0
0
1
0
1
1
2
0
0
0
1
1
1
0
1
2
1
2
0
1
0
0
0
2
0
1
0
0
1
0
1
0
3
1
2
0
1
1
1
1
0
2
1
0
2
0
0
1
0
3
1
0
0
0
1
0
0
0
1
2
0
2
2
1
1
0
0
2
2
1
1
0
2
0
0
2
0
1
2
2
1
4
2
2
2
1
2
0
4
0
0
2
0
2
0
0
0
0
0
1
0
0
3
0
1
1
1
1
2
0
1
0
2
0
2
2
0
1
1
9
0
0
2
2
1
2
1
1
2
0
0
0
0
2
1
2
0
1
4
1
0
1
0
2
2
0
0
0
0
0
0
0
2
1
0
0
2
1
0
1
1
0
2
1
0
0
0
0
2
0
1
0
2
0
0
2
0
2
0
1
0
0
1
0
1
0
0
1
0
1
2
1
0
0
0
0
0
0
0
0
0
1
0
2
1
2
2
2
0
0
2
0
2
2
0
0
1
1
1
1
0
1
2
0
0
3
1
0
1
2
2
2
1
3
1
2
1
2
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
1
2
1
0
2
2
1
1
2
1
0
0
0
0
2
0
2
2
0
0
0
2
1
0
1
2
1
0
0
1
0
0
1
3
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
2
0
2
1
1
0
1
2
0
0
0
0
2
2
0
1
0
2
0
0
0
0
2
1
1
2
0
2
0
1
1
0
0
1
1
0
0
1
1
2
2
4
2
0
0
2
0
1
0
1
1
1
0
2
0
1
0
0
2
1
1
0
1
1
2
2
0
0
0
0
1
2
0
0
2
1
1
1
2
1
2
3
1
1
1
0
2
2
2
0
2
1
0
0
1
2
0
0
2
0
0
1
1
0
0
0
0
1
0
0
1
0
1
1
0
3
1
0
1
0
0
2
0
2
1
2
0
1
2
0
1
2
0
1
0
0
1
1
4
1
0
1
1
2
0
1
1
0
0
1
1
1
1
1
0
1
2
0
3
0
0
0
0
0
0
1
0
2
0
1
0
0
1
1
1
2
2
2
0
2
0
2
1
2
1
2
0
0
3
0
0
2
1
1
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
2
1
2
0
1
0
0
0
0
0
0
1
1
1
1
0
1
2
0
0
0
2
0
0
0
0
0
0
1
0
2
1
0
0
2
0
1
0
2
2
3
4
0
2
1
1
1
1
0
2
1
0
1
1
2
1
2
3
0
0
0
2
4
1
0
1
1
2
0
1
1
0
1
0
1
0
0
3
1
1
0
0
0
1
1
1
1
0
1
1
1
0
0
0
2
0
2
2
0
2
0
1
0
0
1
0
0
0
0
2
1
0
1
1
1
2
0
0
2
0
0
2
0
2
0
2
0
0
2
2
2
1
1
2
0
1
2
0
1
0
0
0
0
0
0
0
3
2
3
1
2
0
0
0
0
1
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
4
0
1
1
2
0
0
2
0
1
0
0
2
2
0
2
1
0
2
1
0
0
0
1
0
1
0
0
1
3
1
1
1
0
0
1
1
1
1
1
1
0
0
1
2
2
0
0
2
0
0
1
0
2
0
2
2
1
0
0
0
1
0
0
0
1
0
2
0
0
1
0
0
0
1
2
0
1
0
0
0
2
1
0
0
3
0
2
0
1
2
1
0
1
2
1
2
2
2
1
1
2
1
1
1
0
0
0
0
0
0
1
0
1
1
2
0
0
0
1
2
1
1
0
0
1
0
0
0
0
0
2
1
0
2
1
2
3
1
0
1
0
0
0
1
2
2
0
2
0
0
1
0
2
2
2
0
1
2
2
1
0
0
1
0
0
1
1
0
0
0
1
2
0
2
3
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
2
1
0
1
1
0
1
0
0
0
0
2
0
0
2
0
1
3
0
0
2
1
0
0
0
1
0
2
2
0
0
1
2
0
1
2
0
2
1
2
1
1
0
0
0
1
2
0
1
0
1
0
0
1
3
1
0
1
2
2
2
1
0
2
2
0
1
0
1
2
0
0
1
1
2
0
0
0
0
1
2
0
0
1
2
0
2
1
0
2
2
0
0
1
2
0
1
1
2
0
2
0
1
0
2
2
1
2
0
0
2
0
0
1
0
0
2
1
0
1
1
1
0
1
0
1
0
1
0
0
0
0
0
2
0
1
0
0
2
0
1
2
1
0
2
2
0
0
1
0
0
0
1
0
2
2
1
0
0
1
2
0
1
2
2
0
0
0
0
1
0
0
1
0
1
2
0
0
0
1
0
0
2
2
0
0
0
1
2
2
0
2
0
1
0
1
0
0
1
3
1
0
2
0
2
2
1
1
2
1
1
0
2
0
1
1
2
0
1
0
2
1
2
0
1
0
0
2
0
1
2
1
0
0
0
0
0
0
0
0
2
1
1
1
2
1
1
1
1
0
1
0
1
0
0
0
1
0
0
0
0
0
2
2
0
0
0
2
3
2
2
1
1
1
2
2
2
0
2
0
2
0
2
0
2
2
2
1
0
2
2
1
0
0
2
0
2
0
0
0
2
0
2
0
2
0
0
1
0
2
0
1
1
1
0
1
2
2
0
2
0
0
0
0
0
1
2
0
0
2
0
0
0
2
2
1
2
1
2
2
1
0
0
1
1
1
1
0
2
1
1
2
1
2
0
1
0
1
1
0
1
3
0
1
0
0
1
2
0
0
2
1
1
0
0
0
1
0
2
1
0
1
0
2
2
0
2
2
1
0
0
2
1
1
0
3
0
0
0
0
1
0
2
0
0
1
1
0
0
1
0
1
0
1
2
0
1
0
0
1
0
1
0
2
1
1
1
1
1
0
0
0
1
1
0
0
1
0
0
0
2
0
0
0
1
2
0
0
1
0
0
2
1
2
1
1
0
2
2
2
1
0
0
0
1
1
1
1
0
2
3
0
0
1
0
0
1
0
0
2
2
2
0
2
0
0
0
1
2
1
0
0
1
1
1
1
1
0
2
0
0
1
2
0
2
0
0
1
0
1
2
1
1
0
0
1
2
1
0
0
2
0
2
0
0
0
2
1
0
0
1
0
0
0
2
1
0
2
0
0
1
2
0
0
0
1
0
0
0
2
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
2
2
2
0
0
1
0
1
0
2
0
2
1
0
0
1
0
0
1
1
0
2
1
0
0
1
2
1
1
0
0
2
0
0
1
2
2
0
1
2
1
0
0
0
0
2
0
0
2
2
2
1
1
0
0
2
2
0
0
1
0
2
2
1
0
0
1
1
2
0
1
2
6
0
0
1
0
2
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
2
0
2
3
1
0
1
0
1
1
0
0
0
2
1
0
0
0
1
3
2
0
0
2
1
2
0
0
0
1
0
1
0
4
0
0
1
1
0
1
0
1
1
1
1
1
0
1
1
2
2
1
0
1
1
2
1
2
0
0
0
1
2
0
1
0
0
0
1
0
1
0
1
0
2
0
3
2
2
1
2
1
0
1
1
1
2
0
0
1
1
3
2
1
1
1
1
2
0
0
0
2
0
0
0
2
0
0
0
2
2
1
0
1
2
0
0
2
1
1
0
0
2
0
0
1
2
0
1
0
0
0
2
1
2
0
0
0
0
1
1
1
2
1
0
0
0
1
0
1
1
1
1
0
3
2
1
0
2
0
1
0
0
1
2
2
0
0
0
0
2
0
1
2
2
0
0
0
0
1
1
2
2
1
0
0
2
1
0
2
2
0
0
0
0
0
6
1
0
0
1
1
0
1
0
1
2
1
0
0
1
1
1
0
2
0
0
0
0
0
0
1
2
2
0
0
1
0
0
1
2
2
1
1
0
1
1
0
1
1
0
2
0
0
0
0
0
0
1
0
0
0
0
2
2
1
0
0
0
0
0
0
1
0
0
2
1
1
1
1
0
1
0
2
0
0
1
1
0
1
0
1
0
1
0
1
2
0
0
1
1
2
1
1
2
2
2
0
0
1
1
1
2
1
1
0
1
2
1
0
1
0
1
2
1
1
1
0
1
2
0
1
0
2
0
0
0
1
0
2
1
2
1
1
1
0
0
2
1
1
2
0
2
0
2
0
1
2
0
0
1
0
1
0
1
0
0
0
1
1
0
1
0
0
1
0
1
1
2
2
0
2
0
2
0
0
0
0
0
6
2
1
0
2
1
2
2
0
0
0
1
0
1
2
0
0
1
0
2
2
2
0
1
1
1
1
1
1
1
1
0
0
2
1
0
0
0
0
0
1
0
1
1
0
0
0
1
1
2
0
0
2
0
3
2
1
0
0
2
0
0
0
0
0
1
1
0
1
0
1
0
0
1
0
0
2
1
1
0
0
1
1
2
0
0
0
1
1
1
0
0
0
0
1
0
1
0
0
1
2
0
0
0
2
2
1
1
0
0
1
0
2
0
0
2
1
0
1
1
2
2
0
0
2
0
0
1
0
0
2
1
2
0
0
1
0
2
0
1
1
1
1
0
1
1
0
0
1
2
2
1
0
1
0
0
0
0
1
2
2
0
0
2
2
2
0
0
0
1
4
0
2
0
2
1
0
0
0
0
0
1
1
1
1
2
1
0
1
2
0
0
2
0
0
1
0
1
0
2
1
0
2
2
2
0
0
0
0
3
1
2
1
0
0
0
0
1
0
3
0
0
1
2
2
0
2
0
1
1
1
0
1
1
2
0
0
2
0
1
1
0
2
1
0
0
1
1
1
0
1
2
2
0
2
1
2
1
1
0
1
1
0
2
2
0
2
0
2
0
0
1
2
1
0
2
0
2
2
1
2
1
1
1
0
3
1
0
2
2
1
2
0
1
0
0
1
1
0
0
0
2
0
0
0
1
2
1
1
1
1
0
2
1
0
0
1
2
0
2
0
8
0
1
0
1
1
0
0
0
0
0
2
1
0
1
1
0
1
0
0
0
2
0
1
3
1
1
1
2
0
0
1
1
2
1
0
3
2
1
1
0
1
2
0
0
0
1
0
1
1
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
3
2
0
1
0
0
0
1
1
2
2
1
0
0
1
0
0
0
2
0
1
2
1
0
1
0
0
1
2
1
3
1
0
1
0
0
2
0
2
0
0
1
1
1
0
0
1
0
0
1
0
0
0
2
0
2
2
1
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
1
2
0
0
2
0
1
2
1
1
3
4
1
0
0
0
1
2
2
0
2
0
2
2
0
0
0
1
1
1
2
1
0
1
2
0
0
0
1
2
2
1
1
1
1
0
1
1
2
0
2
1
1
1
1
0
0
1
1
0
0
1
1
0
1
1
0
0
0
0
2
0
0
0
0
2
1
2
3
1
2
0
1
1
0
0
1
1
1
0
0
1
1
2
1
1
1
0
2
1
1
2
0
1
0
0
0
0
1
0
0
0
0
0
1
2
1
2
0
0
1
1
0
0
1
0
2
0
0
0
0
1
0
0
1
0
0
1
2
1
0
0
2
2
1
0
1
2
0
0
0
1
1
1
0
2
1
0
0
1
1
0
0
1
1
1
1
1
0
1
0
0
2
2
1
2
1
2
1
2
1
1
2
0
0
0
0
0
1
2
0
2
2
0
1
0
0
0
0
1
0
1
2
2
0
0
1
2
0
2
1
0
0
0
0
1
1
1
2
0
0
0
0
0
1
1
1
1
1
1
2
1
0
2
1
0
2
0
2
0
0
1
0
0
1
0
1
1
2
0
0
0
0
0
1
0
0
1
0
2
0
2
2
0
0
2
2
0
2
0
2
0
1
3
2
1
0
0
0
1
1
1
0
5
1
0
2
0
2
1
1
0
0
0
1
0
0
1
1
0
2
0
0
1
3
1
1
0
0
0
1
1
2
0
1
2
0
0
0
0
1
1
1
1
0
1
0
2
1
0
2
0
0
2
0
0
0
0
0
2
1
0
2
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
1
0
1
2
1
2
0
0
0
1
2
1
0
1
1
0
1
1
1
1
2
0
2
0
2
0
1
2
1
0
1
3
0
3
1
2
2
1
0
1
0
0
0
2
1
1
1
0
1
1
1
2
1
0
0
0
1
2
2
2
1
0
2
0
0
2
2
1
1
0
2
1
0
2
1
0
0
0
2
0
1
0
0
3
2
0
0
1
1
0
0
0
2
0
2
0
0
0
1
1
2
1
0
2
1
1
0
2
1
0
0
0
0
1
1
0
0
0
1
0
1
0
0
2
1
2
1
0
1
0
1
0
2
0
2
0
0
1
0
0
1
0
1
1
1
1
1
0
0
0
0
0
0
2
1
1
1
0
2
0
1
0
3
2
0
2
0
0
0
0
1
2
2
0
0
2
0
0
2
2
0
1
0
0
0
1
1
0
0
1
0
0
0
2
0
0
0
0
0
0
2
1
0
0
1
0
1
2
0
0
0
0
2
1
0
3
2
1
0
2
0
0
0
2
0
1
1
4
2
0
2
1
1
0
1
0
0
2
0
1
1
1
3
0
2
1
0
0
0
2
2
2
1
0
0
2
1
2
0
1
0
0
1
1
1
1
1
0
2
1
1
0
0
0
1
0
2
1
0
2
0
4
1
2
2
0
1
1
2
2
1
0
0
0
1
1
1
0
0
0
3
0
2
1
0
0
0
2
1
2
0
2
0
0
2
1
0
1
0
2
2
2
1
1
0
1
0
0
2
0
0
1
0
0
1
1
1
1
1
1
1
0
2
1
1
1
2
0
1
2
1
0
1
0
0
0
0
0
0
3
0
1
0
2
0
1
1
2
1
1
2
1
0
0
0
0
0
2
0
5
0
0
0
0
1
1
2
2
1
1
1
0
0
2
0
1
2
0
1
1
1
0
0
0
1
0
0
2
1
2
1
0
0
0
0
0
2
0
0
0
1
2
1
1
2
0
0
2
1
0
1
1
0
0
1
0
1
0
2
2
1
0
0
0
1
0
1
2
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
3
2
1
1
3
2
2
1
2
0
1
1
1
1
0
2
1
2
0
2
0
0
2
0
2
1
1
1
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
1
0
2
1
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
1
2
1
0
1
1
2
1
2
1
0
1
0
2
0
2
2
0
1
2
1
1
1
2
1
0
1
1
1
2
1
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
1
0
1
1
2
2
2
2
0
2
1
0
0
0
1
1
1
2
0
2
0
0
1
0
0
0
0
0
1
0
0
2
0
0
2
0
0
2
2
2
0
0
1
1
1
2
2
2
0
1
0
0
0
1
1
2
0
0
0
1
2
0
0
0
2
0
1
1
1
0
0
2
1
1
2
2
2
0
0
2
0
2
0
0
1
1
1
1
0
2
0
2
2
1
0
2
1
1
0
0
2
0
1
0
1
0
0
1
1
0
0
1
2
0
1
0
1
1
0
1
1
0
1
2
0
0
0
0
1
0
1
0
2
2
0
0
0
1
2
0
2
1
2
0
1
2
2
1
1
0
1
2
1
2
1
2
0
0
1
0
4
2
2
0
0
2
1
1
1
0
0
0
1
0
0
0
0
1
0
2
2
0
1
0
1
1
1
1
0
0
1
0
1
1
0
0
1
1
0
0
2
2
1
2
2
0
0
0
2
1
2
1
0
0
0
1
0
2
1
1
1
0
0
1
1
1
0
0
0
1
1
2
0
0
0
0
2
2
2
2
0
0
2
0
0
1
0
0
1
0
0
2
1
1
1
1
0
1
1
0
1
0
3
0
4
0
0
2
1
1
2
0
1
1
0
0
1
2
1
0
0
0
0
2
1
0
1
1
0
2
0
0
0
2
0
1
2
1
0
0
1
0
2
0
1
1
2
1
0
1
4
0
0
0
1
3
0
0
0
0
0
2
0
0
2
0
3
2
0
2
0
0
2
1
0
0
0
2
0
2
1
0
0
1
0
1
0
0
2
0
2
1
1
0
0
0
1
0
1
0
1
4
0
2
0
0
0
0
2
1
0
0
2
0
1
0
1
2
0
0
1
2
1
2
1
0
0
1
2
4
2
0
0
0
1
0
1
1
0
0
2
0
0
0
1
0
0
9
1
0
0
0
1
2
0
0
2
0
0
1
0
2
2
1
2
0
0
2
1
0
2
2
0
0
0
0
0
1
0
1
0
0
1
2
2
0
2
0
2
0
0
0
0
1
2
1
0
0
2
2
1
0
0
0
1
0
2
0
1
0
0
0
0
0
1
0
0
1
1
2
2
1
0
0
4
3
0
1
2
0
0
2
2
2
0
0
0
1
2
1
0
1
0
0
1
0
0
1
0
0
2
1
2
1
0
2
1
1
0
0
0
0
1
2
1
1
1
1
1
0
0
0
1
0
0
0
0
1
0
0
1
2
1
1
0
3
0
0
0
0
0
0
0
1
0
1
2
2
1
0
0
1
0
1
0
1
0
0
0
2
2
2
1
0
0
0
0
1
2
0
0
0
0
1
2
0
0
1
1
0
2
0
2
0
0
1
0
2
0
0
0
2
1
2
0
1
1
2
2
2
0
4
2
2
0
1
1
0
0
1
2
0
2
0
0
0
0
0
1
1
2
1
1
1
0
1
0
0
1
0
0
1
1
0
1
2
3
0
0
1
2
1
0
2
0
0
0
1
1
0
0
0
1
2
0
2
0
0
0
2
1
0
0
0
0
1
0
2
0
1
1
2
0
2
2
0
0
0
0
1
1
0
0
1
1
2
2
1
2
0
0
0
0
0
1
0
0
1
0
1
0
1
1
2
1
0
0
0
3
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
2
0
1
2
2
1
0
2
0
0
2
0
1
1
2
1
0
1
0
2
1
2
2
0
0
2
0
1
2
0
0
1
0
1
0
0
1
0
0
0
1
0
2
2
2
0
1
0
0
0
1
0
3
2
1
0
1
0
1
1
0
0
1
0
0
3
1
1
1
0
1
2
0
0
0
2
0
2
0
2
1
0
1
2
0
1
0
1
1
3
2
0
1
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
1
2
0
0
0
0
0
1
0
0
1
1
1
0
0
1
0
0
2
0
2
0
3
1
1
2
1
0
1
0
2
1
1
1
2
0
2
0
0
1
0
1
0
2
1
1
1
2
0
2
1
2
0
1
0
0
0
0
2
0
0
0
2
0
4
0
1
1
1
1
0
0
0
0
0
1
1
1
0
1
0
2
2
0
0
1
1
1
0
0
2
1
0
0
1
1
1
1
0
0
1
0
0
0
2
0
0
0
2
2
0
1
0
1
1
1
0
0
0
1
1
0
2
1
3
1
0
0
0
1
3
0
1
2
0
0
2
1
0
0
0
0
0
0
1
0
0
3
0
1
0
1
0
1
2
0
0
1
0
1
1
0
1
1
0
2
0
1
0
1
0
2
0
1
0
0
0
1
0
1
3
2
3
2
0
0
1
0
0
0
1
1
1
2
1
0
0
2
2
2
0
1
0
2
0
1
1
1
1
0
2
1
1
0
0
0
1
0
1
1
2
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
2
3
1
0
1
3
2
0
0
0
0
2
1
0
1
1
0
0
1
0
0
2
0
0
0
3
1
2
1
0
1
0
1
1
1
4
1
0
2
3
2
2
0
1
0
0
0
1
1
0
0
0
2
0
0
1
0
0
2
0
0
0
1
0
1
0
0
0
1
0
0
2
0
2
0
0
0
1
0
0
1
0
2
0
2
0
1
1
0
0
0
2
0
1
0
1
1
0
2
1
0
1
1
2
2
1
1
2
0
1
1
1
0
0
0
1
1
0
0
1
1
2
1
2
1
2
0
0
0
0
0
0
1
0
0
0
1
2
1
0
0
3
0
2
1
0
2
2
0
0
2
1
0
2
0
0
0
1
2
0
0
1
0
0
0
0
2
2
0
0
1
0
1
1
1
0
1
2
2
2
1
0
1
2
1
1
0
0
1
2
1
2
2
0
1
0
0
2
2
1
0
2
0
0
1
0
0
0
1
1
0
1
2
2
2
2
1
0
0
0
0
1
1
1
0
1
2
0
0
2
2
3
2
0
1
0
0
0
0
1
0
0
1
2
1
1
1
2
0
2
1
0
0
0
1
1
1
0
0
0
0
2
2
0
1
1
0
1
1
0
1
0
0
1
2
0
0
1
1
2
1
1
0
0
0
0
0
2
2
0
0
0
2
1
3
1
1
0
0
1
0
0
1
1
2
1
0
0
1
0
1
1
1
1
1
0
2
0
1
2
0
1
0
1
2
1
0
1
1
0
0
1
1
0
0
1
0
0
2
1
1
2
0
1
1
0
2
1
0
0
2
2
1
1
0
1
1
1
2
0
0
2
1
2
1
1
0
0
0
0
0
0
0
0
0
2
0
2
0
2
2
3
0
1
2
0
0
1
0
2
1
1
1
0
0
2
0
1
1
1
1
0
1
2
0
0
1
1
0
0
0
2
1
1
1
1
1
2
0
1
1
0
0
0
2
2
0
1
1
0
0
0
0
1
2
2
1
1
2
0
0
0
1
1
0
0
1
0
0
2
6
1
1
1
0
1
0
1
0
0
2
1
2
1
1
2
2
2
0
1
0
1
2
0
1
0
0
0
1
0
0
0
1
1
0
1
0
1
0
1
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
2
1
0
1
0
0
1
2
0
0
0
2
1
1
0
0
0
1
1
0
1
1
0
1
0
2
0
0
0
2
0
2
0
1
0
0
2
0
2
1
1
1
0
0
2
2
0
1
1
1
1
0
2
1
0
1
2
1
0
0
1
0
0
0
1
0
1
0
2
0
1
0
1
0
0
0
1
1
0
1
1
2
2
1
0
0
0
0
2
0
2
0
2
1
0
1
1
0
0
0
0
1
0
1
1
0
1
0
2
1
1
0
0
1
0
4
1
0
3
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
6
0
1
0
2
2
2
1
0
0
1
0
0
0
0
1
2
1
1
0
0
0
0
0
1
2
2
0
1
1
1
2
0
1
1
2
1
1
1
1
0
1
2
0
0
1
0
0
0
0
3
0
0
0
0
1
1
1
1
0
0
0
2
2
0
1
1
0
0
1
2
0
1
0
0
0
2
1
1
0
0
0
0
0
2
1
2
0
1
1
2
0
0
0
0
0
1
0
2
0
1
1
0
0
0
2
0
0
2
0
0
2
2
2
1
1
1
1
0
0
1
0
2
1
1
2
1
1
1
2
1
0
0
2
1
0
1
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
2
2
1
1
0
0
3
1
1
2
1
0
2
2
1
1
0
0
1
0
1
0
0
0
0
1
0
2
0
1
0
1
0
1
1
1
0
2
0
0
1
0
2
2
0
0
1
0
1
0
2
0
0
1
0
1
1
0
0
2
2
1
0
0
2
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
1
0
3
1
0
2
0
2
2
1
0
0
1
0
2
1
1
2
1
0
1
1
0
2
0
2
3
0
0
0
0
0
0
0
2
0
0
0
1
2
1
0
1
1
0
1
2
2
0
0
1
0
0
2
1
0
1
0
1
0
2
0
2
0
0
0
0
2
1
0
2
0
0
1
0
0
1
1
0
1
0
1
0
0
3
0
2
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
2
0
2
0
2
0
2
0
1
0
1
0
1
1
2
0
1
0
0
0
1
0
2
0
0
1
1
1
2
0
0
0
2
1
0
0
1
2
1
1
2
1
0
1
2
0
0
0
0
0
0
0
1
1
2
1
0
2
0
1
2
1
0
0
2
1
0
0
2
2
0
0
1
1
1
2
0
1
0
0
0
1
0
0
0
2
1
2
1
0
0
0
0
0
1
0
0
1
1
0
0
2
0
0
2
6
0
1
1
0
0
0
0
0
0
1
1
2
1
0
0
2
1
0
1
0
0
0
0
1
1
2
0
1
1
0
0
2
0
2
0
1
0
1
2
0
0
0
0
0
0
2
0
0
1
2
0
0
1
0
3
0
0
1
0
0
0
1
2
2
2
0
1
1
2
2
2
1
0
1
1
0
0
0
1
1
0
0
1
0
0
0
1
0
0
1
0
1
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
2
0
3
2
1
1
1
1
0
2
2
1
1
2
1
0
1
0
0
2
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
2
0
1
2
0
1
0
1
0
3
0
2
0
2
1
2
0
0
1
1
0
0
1
1
3
0
0
2
0
0
0
0
1
2
0
2
1
2
4
0
2
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
1
2
0
2
1
1
0
1
0
0
1
1
1
1
1
1
2
0
1
0
1
2
0
2
3
0
0
1
0
0
0
0
1
0
2
0
0
0
0
1
1
0
2
1
0
2
0
2
0
0
1
2
2
1
1
0
0
1
1
0
1
0
1
1
0
1
0
1
0
0
0
1
0
0
1
1
1
1
2
2
0
1
0
2
0
2
0
0
1
1
0
2
0
0
1
0
2
1
1
1
1
1
0
0
0
0
0
2
0
1
0
1
2
1
0
0
2
0
1
1
2
2
0
1
0
0
0
0
1
1
1
0
0
0
1
0
2
2
1
1
2
1
0
1
0
1
0
0
2
1
0
1
0
0
2
1
1
0
1
0
1
0
0
0
2
1
1
1
2
1
1
2
1
0
1
0
1
1
2
0
1
0
0
0
1
1
1
2
1
2
1
0
2
1
0
1
2
0
1
1
0
2
1
2
0
0
0
0
0
1
0
0
1
1
2
0
2
0
0
2
2
2
2
1
1
3
1
0
2
2
1
1
0
0
2
0
0
2
0
1
1
0
1
1
1
0
0
2
1
0
0
0
1
2
0
2
1
0
0
2
0
2
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
1
0
2
1
1
0
1
2
0
0
1
0
0
1
2
0
0
0
0
0
0
1
0
0
1
1
1
0
2
2
1
0
1
0
0
0
2
0
0
1
1
1
0
1
0
0
0
1
1
1
0
0
2
1
1
1
1
1
0
0
2
1
2
1
0
1
0
0
1
1
1
2
0
0
2
1
0
0
0
1
0
1
0
2
0
1
0
2
2
2
0
1
0
1
2
0
0
1
1
2
2
0
0
1
0
1
1
1
1
1
0
2
0
1
0
0
0
2
2
0
1
1
1
0
0
1
2
0
0
0
0
1
1
0
0
2
1
0
0
3
1
0
2
1
1
3
1
1
0
1
1
3
0
2
1
1
0
2
0
0
1
1
1
0
0
2
2
1
1
0
0
1
0
2
0
0
0
0
2
2
0
0
1
0
0
0
0
2
0
1
0
2
0
1
1
2
2
0
0
1
0
0
1
1
3
0
1
1
0
10
1
2
1
1
1
1
0
1
0
1
1
0
0
0
2
1
0
2
0
2
1
1
0
0
2
2
0
1
0
1
1
1
2
0
1
0
1
1
1
1
2
0
0
0
0
0
0
1
0
0
2
1
0
1
0
0
1
0
0
0
0
2
1
1
0
0
0
0
0
2
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
1
2
2
0
1
0
1
2
3
2
1
1
0
2
0
0
2
0
1
0
0
3
0
2
0
0
0
2
0
1
0
0
2
1
0
0
1
1
0
0
1
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
2
1
0
2
0
2
2
0
1
0
2
0
0
2
2
0
0
0
0
1
2
2
1
0
2
0
0
0
0
0
0
2
0
2
2
0
1
1
0
2
0
2
0
2
2
1
0
0
1
2
2
0
1
0
0
1
2
1
2
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
2
1
1
0
1
1
0
0
1
0
1
1
0
1
0
0
0
2
2
2
1
0
2
0
0
0
2
1
0
0
0
2
1
0
1
2
2
0
0
1
0
2
0
1
1
3
0
1
0
0
0
2
2
0
0
0
1
0
0
1
1
1
0
1
0
0
1
1
2
1
1
0
0
0
0
1
0
0
1
1
0
2
0
0
0
0
1
2
1
0
1
0
1
0
2
0
1
0
2
0
2
0
0
2
1
0
1
2
0
0
2
0
0
1
3
2
0
0
1
0
0
2
1
0
1
1
0
0
1
0
2
2
1
0
0
1
0
0
1
1
2
0
0
0
0
0
0
0
2
2
0
1
1
1
1
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
3
0
1
0
0
0
0
0
2
1
0
1
0
2
0
1
0
0
0
1
1
0
2
1
2
1
0
1
1
0
0
2
2
2
0
1
2
0
0
0
0
0
1
1
2
0
0
0
0
0
10
1
0
0
1
2
1
1
0
0
0
0
2
1
2
0
1
2
0
0
1
0
1
3
2
0
2
0
1
0
2
1
2
2
0
2
1
0
3
2
1
1
1
1
0
2
0
0
1
1
0
2
0
0
2
1
0
0
1
0
0
1
2
1
0
2
0
2
0
1
0
1
0
1
0
1
0
0
1
0
0
0
0
2
0
0
0
0
1
2
0
0
1
0
0
0
1
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
1
2
0
4
1
0
1
0
1
2
0
2
0
0
0
1
0
1
1
2
3
1
0
0
1
0
1
0
0
1
0
0
1
1
4
1
0
2
0
0
0
0
1
1
1
2
1
1
0
2
0
1
2
1
2
1
0
0
0
0
3
1
0
2
1
1
2
0
0
0
1
0
0
3
0
0
1
2
1
1
1
2
0
0
0
0
0
0
2
2
1
0
0
0
0
4
3
0
2
0
2
0
2
1
2
0
1
2
2
2
1
2
1
2
1
1
2
0
2
2
1
1
1
1
0
1
2
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
1
1
0
1
0
0
1
1
0
1
0
2
1
0
1
1
0
0
0
2
1
1
1
0
0
0
0
1
0
0
1
4
2
2
0
2
3
0
0
0
1
0
1
0
0
1
1
1
2
1
2
2
0
0
1
0
0
3
1
1
2
1
1
1
2
3
2
0
0
2
1
0
0
1
1
0
0
1
1
0
0
1
1
1
0
0
1
2
0
1
0
0
0
1
1
1
0
1
1
1
0
0
0
0
0
1
0
0
1
1
1
0
1
1
2
1
1
2
2
1
0
1
1
0
1
1
0
1
1
3
1
0
0
1
0
2
1
0
1
0
1
1
0
1
1
1
0
0
2
0
2
0
0
0
0
0
1
2
2
1
0
0
1
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
1
2
2
0
0
2
0
2
2
0
0
0
2
1
1
0
1
0
0
2
2
2
1
1
0
1
1
2
2
1
1
1
3
3
0
1
1
0
0
2
1
1
1
0
0
2
1
1
2
1
1
2
3
0
0
1
1
0
0
2
0
1
0
0
0
2
2
0
0
0
0
1
0
2
1
0
2
0
0
0
0
1
0
0
2
0
0
0
0
1
2
2
4
1
0
0
0
0
1
1
0
1
0
0
2
1
1
0
0
3
2
0
0
2
1
0
0
1
0
0
0
1
0
0
0
0
1
1
0
2
0
1
2
0
1
0
0
0
1
1
0
0
1
0
1
2
2
0
0
2
0
1
2
0
0
0
0
0
0
1
0
0
1
0
2
2
0
0
0
0
0
0
2
0
3
0
1
2
2
2
0
0
0
1
2
0
2
0
0
0
0
0
1
2
0
2
0
1
1
1
0
0
1
1
2
2
1
5
0
0
0
0
0
1
1
2
0
1
0
1
0
0
1
2
2
2
0
3
1
0
0
1
2
0
2
0
3
2
2
0
0
0
1
0
0
0
2
2
0
2
0
2
2
1
1
0
2
0
0
1
2
0
0
0
1
1
2
1
0
0
1
2
0
0
0
0
0
2
0
1
2
1
0
1
0
2
0
1
0
1
0
2
2
0
0
0
1
0
1
3
1
0
2
0
1
2
1
2
1
2
1
0
0
1
1
0
1
1
1
1
0
1
2
2
0
0
1
1
0
1
1
1
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
1
2
2
2
0
1
1
0
0
0
0
2
2
0
0
1
2
1
2
2
1
2
1
1
2
1
0
0
0
2
0
0
0
2
3
2
2
0
0
0
1
1
0
2
0
2
1
0
0
0
0
1
0
1
0
0
0
1
2
3
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
1
0
2
0
1
2
0
0
1
1
1
0
1
1
1
1
1
2
2
1
2
0
0
0
1
0
0
1
2
0
0
0
0
0
1
0
0
1
1
1
0
2
0
0
0
0
2
2
1
0
2
0
2
0
0
2
0
0
2
2
1
2
0
0
1
0
1
1
2
0
1
0
1
2
1
1
0
0
0
0
0
1
1
0
0
2
3
0
0
3
3
0
0
0
2
2
0
1
0
0
0
1
0
0
1
0
0
2
2
1
0
0
1
0
0
0
2
3
0
1
0
0
1
1
0
2
0
1
1
0
0
0
0
1
1
4
2
1
1
2
1
2
2
0
0
1
3
2
0
0
0
1
0
2
0
1
0
0
1
0
2
0
1
0
1
0
2
2
1
0
1
1
2
0
0
0
1
0
2
1
2
0
2
2
1
0
0
1
1
2
1
1
1
2
0
1
1
1
2
0
1
2
2
1
0
1
2
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
1
2
2
1
0
0
2
0
2
0
1
0
1
1
0
0
0
0
2
2
1
0
0
1
1
1
1
2
0
1
1
1
0
1
0
2
0
2
2
1
1
2
2
0
1
1
0
0
1
2
1
0
0
1
1
0
0
2
1
2
1
0
1
0
2
0
1
0
0
0
2
1
0
1
2
0
0
0
0
0
0
0
0
1
1
1
3
1
0
1
0
0
2
0
1
2
2
0
0
0
2
1
0
0
0
1
1
0
1
0
2
0
0
0
1
2
0
1
2
1
1
0
0
0
1
1
2
1
6
1
0
0
1
2
1
1
0
1
1
1
3
2
1
0
0
2
0
0
0
2
1
2
1
0
0
0
1
2
2
2
2
0
0
0
1
0
3
1
0
2
1
2
1
0
1
0
1
0
0
0
0
0
2
0
0
1
2
1
2
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
2
2
2
0
0
0
0
2
2
1
2
1
0
0
1
0
2
0
1
2
0
1
1
2
2
1
1
0
0
0
1
2
0
2
1
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
2
1
0
1
0
2
1
2
1
1
0
1
0
0
1
1
1
1
0
1
1
0
0
1
2
1
1
2
0
1
1
1
0
0
1
0
0
0
3
1
1
1
0
0
1
1
2
0
0
3
0
0
1
5
0
0
1
1
2
0
1
1
1
1
0
1
0
1
1
0
1
0
1
6
2
0
1
2
0
2
1
0
0
2
0
4
1
0
0
1
1
1
0
2
0
0
2
0
0
2
2
2
0
1
1
0
1
0
0
1
0
0
0
1
0
0
1
1
1
0
2
0
2
2
2
0
0
3
4
0
0
1
0
0
1
2
1
1
0
0
0
0
2
2
1
0
0
0
2
1
1
1
1
1
1
1
0
0
0
0
0
0
0
2
0
2
0
2
0
4
2
2
2
0
0
1
1
2
2
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
1
0
0
1
1
1
0
0
2
0
0
0
0
1
0
0
1
1
2
1
0
0
0
2
2
0
1
1
1
0
2
1
1
0
0
1
0
1
0
0
0
1
1
0
0
0
1
1
2
0
0
2
2
2
2
0
0
0
1
1
2
1
0
0
0
0
0
1
0
1
1
1
0
1
0
1
1
0
0
0
1
2
2
0
1
0
1
1
0
0
1
0
0
0
0
1
2
0
1
1
2
0
0
2
1
2
0
3
0
1
2
1
2
1
1
0
1
2
0
0
0
1
0
1
0
0
0
1
1
1
0
1
0
1
2
0
2
0
1
0
1
1
0
0
2
1
1
0
0
0
3
0
0
1
1
0
0
0
0
1
2
2
2
0
0
0
2
0
0
0
2
2
1
1
1
1
2
0
0
2
1
0
2
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
2
0
0
1
0
1
0
1
2
0
0
2
1
0
0
1
1
1
0
0
2
0
0
1
0
2
0
0
0
0
0
1
1
0
2
2
1
2
0
3
2
0
0
1
4
0
0
1
0
1
1
0
0
1
1
2
2
2
0
0
2
2
0
0
1
2
1
0
1
2
1
0
0
1
1
0
0
0
0
1
1
0
2
2
0
0
0
0
1
0
0
0
1
1
0
1
0
0
1
2
0
0
0
1
1
0
1
1
0
2
1
0
0
0
1
2
1
2
2
2
1
1
0
1
2
2
0
2
2
1
2
2
0
1
2
0
1
0
0
2
0
0
1
0
1
0
0
0
2
1
0
0
2
2
0
0
2
1
2
1
0
0
2
1
2
0
0
1
1
0
1
3
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
1
0
0
1
1
2
2
0
0
1
1
0
3
2
2
0
1
2
0
0
2
0
2
0
0
0
0
0
1
1
0
2
0
0
1
0
1
2
1
2
2
1
0
0
0
2
0
0
0
0
0
0
1
1
0
0
1
0
2
1
0
0
0
0
2
1
2
0
0
0
0
1
2
2
2
0
0
0
0
0
0
0
0
2
1
1
2
0
0
0
2
2
0
2
2
2
0
0
0
0
1
0
1
0
0
1
1
0
2
1
2
0
0
2
2
0
1
0
1
2
0
2
0
0
3
0
0
1
1
0
2
1
1
0
1
1
1
0
0
1
0
1
1
1
0
0
0
0
2
0
0
0
1
0
0
1
0
0
3
1
2
1
0
1
2
2
2
0
0
1
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
1
3
0
2
0
0
0
2
0
1
0
1
1
0
0
0
0
1
1
1
0
0
3
2
0
0
0
0
1
2
0
2
0
0
0
2
1
0
1
0
0
3
0
2
1
0
0
1
0
0
0
2
0
2
1
0
2
1
2
0
1
0
0
1
2
0
0
0
0
0
2
2
0
0
1
2
2
1
2
0
1
0
1
1
3
1
2
2
2
1
0
0
1
1
2
0
1
0
0
0
0
1
0
1
0
2
0
0
2
2
0
2
1
2
0
1
0
2
1
2
1
1
2
1
0
0
1
2
0
1
0
1
0
0
1
0
2
0
1
2
0
1
3
0
0
1
2
1
2
1
1
1
3
1
0
2
0
0
2
0
1
0
0
1
0
2
2
0
0
1
2
1
0
0
0
0
0
2
0
1
1
0
1
1
2
1
2
1
2
1
1
2
0
1
0
1
0
2
2
0
1
1
2
1
1
0
1
0
0
0
2
2
1
1
0
1
0
0
0
0
0
2
2
1
1
0
0
1
1
0
1
0
0
1
0
0
0
1
0
1
0
0
0
1
1
0
2
0
0
1
1
2
1
0
2
1
0
0
0
0
2
1
0
1
0
0
1
2
0
2
1
2
2
1
0
1
0
1
2
0
2
1
0
2
0
1
2
2
0
0
1
0
0
0
2
2
0
2
2
1
1
0
1
0
0
0
0
2
2
1
0
0
1
1
2
0
2
0
0
0
0
0
0
0
0
2
1
0
1
1
1
2
1
1
2
1
0
0
0
0
3
0
0
2
0
0
1
1
2
1
0
0
0
2
2
1
1
2
0
0
1
1
0
1
0
0
1
0
0
0
0
3
0
0
0
0
2
0
1
2
1
1
2
0
1
1
2
0
1
2
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
2
0
2
2
1
2
1
0
0
2
0
1
0
0
0
0
1
1
2
0
1
0
1
1
0
2
0
1
1
0
0
1
2
1
1
0
1
1
0
1
0
0
0
1
2
0
0
2
0
1
0
0
0
2
0
2
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
4
1
0
2
0
2
0
1
0
2
1
2
0
0
0
0
0
3
0
0
1
1
0
0
1
0
0
1
0
0
0
3
0
0
0
0
0
1
1
1
0
1
1
2
0
1
2
0
0
0
0
2
0
0
0
2
1
0
1
1
0
1
0
0
0
2
1
1
0
0
1
1
0
1
1
1
1
0
0
0
1
0
0
1
0
2
0
0
1
0
0
0
2
1
1
1
0
0
0
4
1
0
1
2
1
3
0
0
2
1
0
1
2
0
0
0
0
2
1
0
1
1
0
0
0
0
1
0
0
0
1
0
1
2
1
1
2
1
1
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
1
1
1
1
1
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
1
1
0
0
0
1
0
1
0
2
0
0
2
2
0
1
0
1
0
1
0
2
0
2
1
0
0
0
1
0
2
0
3
0
2
2
0
1
2
2
0
0
1
0
2
1
0
2
1
2
0
0
0
0
1
1
1
2
0
2
0
0
0
0
0
0
2
1
1
2
1
0
2
1
0
0
0
0
0
1
1
1
0
3
2
2
1
1
1
0
0
1
2
1
1
1
1
1
1
0
0
1
0
0
1
2
0
0
0
0
1
0
0
1
2
0
0
0
2
0
0
2
3
1
2
0
0
2
0
0
0
0
1
2
0
1
0
0
1
1
1
2
0
0
0
0
0
0
1
0
0
0
1
1
2
0
3
0
0
2
0
0
0
0
0
0
1
1
0
2
2
3
2
1
0
0
0
0
2
0
2
0
2
1
1
2
0
0
0
1
0
1
0
2
1
0
0
0
0
1
2
0
1
0
1
0
2
0
1
1
0
2
0
0
1
0
1
2
1
0
0
1
1
0
3
1
1
0
0
1
1
1
0
1
2
1
1
1
1
0
0
0
1
2
1
2
1
1
0
2
1
2
0
0
0
0
2
0
0
0
1
2
1
1
3
1
0
1
2
2
1
0
1
2
0
0
2
1
0
2
1
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
1
1
1
2
1
0
0
1
1
0
1
1
2
0
0
0
0
2
0
1
1
0
0
1
0
1
1
0
2
2
0
1
0
2
1
0
0
0
1
0
1
6
0
0
2
1
1
0
0
0
1
0
1
1
0
1
1
1
1
0
1
0
0
1
1
1
0
0
1
0
0
0
2
0
1
2
1
0
0
1
0
2
0
0
0
0
1
1
1
0
0
0
0
0
1
0
1
2
1
1
1
2
2
0
0
0
1
1
0
0
0
2
2
2
2
0
0
1
2
0
0
2
0
2
1
1
1
1
2
1
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
1
0
0
1
2
1
2
1
3
1
2
1
1
4
1
2
0
0
0
1
2
0
0
1
0
0
0
2
2
2
2
2
1
0
1
3
0
0
1
1
0
3
0
0
1
1
0
1
1
1
0
1
0
2
0
1
2
0
0
2
0
0
2
2
0
0
0
0
2
2
0
0
2
1
0
0
0
0
1
2
0
0
0
1
0
2
8
0
0
0
1
2
0
2
0
0
0
0
2
1
2
1
0
1
1
1
2
0
1
1
1
1
0
2
0
2
0
2
0
0
1
0
0
2
2
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
1
1
0
0
2
3
0
0
2
0
0
0
1
0
0
0
1
1
0
0
1
1
2
1
2
0
2
0
2
0
2
0
0
1
1
0
2
0
1
2
0
1
0
0
1
0
0
0
2
0
0
0
1
0
2
1
1
2
1
0
0
1
1
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
1
0
2
2
0
0
0
0
1
0
2
1
2
1
2
1
0
0
0
0
0
1
1
0
0
1
0
4
1
2
0
0
2
1
1
2
0
0
1
0
0
0
1
1
0
2
0
2
0
2
0
1
2
1
0
2
1
0
0
1
1
2
0
0
1
0
1
0
2
0
0
0
0
4
1
0
1
2
1
0
0
0
1
1
2
0
4
0
1
1
0
0
0
2
1
0
2
2
0
0
2
0
3
0
1
2
2
1
2
0
4
1
1
1
0
1
1
0
1
2
0
2
1
0
0
0
1
0
2
2
0
0
0
2
0
1
0
1
0
0
3
0
0
0
2
0
1
0
0
1
1
2
2
0
2
2
0
0
0
0
2
0
1
0
0
2
0
2
0
2
0
2
1
4
0
2
0
0
0
0
1
3
0
1
0
1
0
1
2
1
0
0
1
0
0
1
1
0
0
0
2
0
1
2
3
0
1
0
1
1
0
0
0
0
2
0
1
0
0
0
0
2
1
3
0
1
0
0
0
0
2
0
0
0
1
1
0
0
2
0
0
2
0
0
0
2
0
0
1
3
1
1
0
0
0
2
0
1
0
0
0
2
1
2
0
1
0
0
2
0
0
0
5
0
0
1
0
1
2
2
1
0
2
0
1
0
1
0
2
2
0
1
4
0
1
1
0
0
0
0
0
0
0
1
0
1
1
2
1
0
0
1
0
0
0
2
1
2
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
2
1
0
1
2
0
0
1
2
0
1
0
0
0
2
2
0
0
0
1
2
1
2
1
0
0
0
0
2
2
2
1
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
3
0
0
2
1
1
1
0
2
1
1
0
0
1
0
2
0
4
1
1
0
2
0
2
1
2
0
1
1
1
1
1
1
0
2
0
0
2
1
0
0
0
0
2
1
1
1
1
0
2
1
0
0
1
0
1
0
1
0
0
0
2
1
1
2
1
1
1
1
1
1
2
1
1
2
0
1
4
0
1
1
0
0
2
0
1
2
1
0
2
0
2
1
2
1
0
2
2
0
2
1
0
1
0
0
3
2
1
2
1
1
0
0
0
0
0
1
2
2
1
0
0
0
0
2
0
0
1
1
2
0
0
0
0
1
0
2
0
1
1
0
0
0
2
1
1
1
2
0
0
2
2
2
1
0
1
2
1
2
1
1
1
1
0
0
1
1
0
1
1
2
2
0
1
1
2
0
1
0
0
0
0
2
0
2
0
2
0
1
0
1
2
0
0
0
0
0
0
1
0
0
1
2
0
1
4
0
0
0
2
2
0
2
2
0
0
2
0
1
1
1
1
2
1
1
0
1
3
2
0
2
0
2
0
2
1
0
1
0
1
1
2
0
0
0
0
1
0
1
2
2
0
1
2
0
2
1
1
1
0
0
2
0
2
2
1
2
1
0
1
3
1
0
1
0
0
1
0
0
0
1
1
0
3
1
0
1
1
0
1
1
1
2
2
1
1
0
1
2
2
0
2
1
1
1
0
1
1
0
0
2
1
0
1
1
1
2
0
0
0
0
1
0
1
0
1
0
0
1
1
2
1
0
0
0
7
0
0
1
1
1
0
0
0
1
0
0
2
1
0
3
0
1
1
0
2
1
1
1
0
1
1
2
0
2
0
1
2
2
0
0
0
0
1
1
1
1
2
0
1
0
2
1
0
0
2
0
0
1
0
1
0
2
1
1
1
1
1
1
0
3
0
0
2
1
0
0
1
0
2
0
0
0
1
0
2
1
0
0
1
1
0
0
0
2
0
1
2
1
1
0
2
0
1
0
1
0
2
1
0
0
2
0
0
2
2
2
1
2
1
2
2
1
1
1
0
0
0
1
0
1
0
0
2
2
0
0
1
1
0
1
2
1
1
2
1
0
0
2
0
0
0
2
1
0
0
0
0
2
0
1
0
1
1
0
1
1
2
0
0
3
5
0
0
1
0
0
1
0
0
0
0
1
0
0
2
2
2
1
0
0
1
1
1
2
1
0
1
2
1
1
2
2
1
1
0
1
2
2
0
0
2
0
0
0
0
0
0
2
0
1
0
0
1
1
0
0
2
0
3
0
1
0
0
0
0
0
0
0
0
1
1
2
0
0
0
1
1
1
0
2
0
1
0
1
1
2
0
1
2
0
0
0
0
2
0
0
0
0
0
7
0
1
2
2
1
1
1
1
2
0
0
0
0
0
2
1
0
1
2
0
1
0
1
1
0
0
1
1
2
2
0
0
1
1
0
0
0
0
1
0
2
2
1
2
1
1
1
1
1
2
2
2
0
1
1
2
0
0
1
2
2
0
1
0
0
0
0
1
1
0
3
1
2
1
1
0
0
0
1
0
1
2
0
0
2
0
0
1
1
2
0
0
0
0
1
1
1
0
0
0
0
2
1
2
2
0
1
2
0
0
0
2
1
1
0
1
0
1
1
0
1
0
3
1
1
0
0
2
1
0
0
0
0
0
1
0
2
1
1
2
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
2
2
1
1
1
0
0
1
6
1
0
0
2
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
2
1
0
1
1
0
0
2
2
1
0
2
2
0
0
1
0
1
0
2
1
0
0
0
0
1
0
1
0
0
1
0
1
2
1
0
0
1
4
0
1
2
0
1
1
0
2
0
0
2
4
0
0
2
0
1
0
0
1
1
2
1
0
0
2
1
1
1
0
0
2
1
2
1
0
1
1
2
0
0
0
0
2
1
0
2
0
0
2
0
2
2
0
1
0
1
0
1
0
1
0
1
0
0
2
1
1
0
0
2
0
0
1
0
1
0
1
2
0
0
2
1
7
0
0
1
3
0
2
0
2
0
1
0
2
1
0
1
0
2
1
3
0
1
0
1
2
2
0
1
1
0
0
0
0
2
0
1
1
1
2
1
1
1
0
2
3
1
0
0
1
1
0
1
0
0
1
0
0
1
0
1
0
0
2
0
0
1
1
0
1
0
0
1
2
0
2
0
1
1
2
1
0
0
0
0
2
0
1
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
1
1
2
2
0
1
1
0
0
0
1
2
0
2
1
1
0
0
0
1
1
0
1
0
0
0
1
1
2
0
1
1
0
1
1
3
1
2
0
0
0
0
1
1
2
1
2
0
0
0
0
0
0
1
2
0
0
1
0
1
0
0
2
1
2
0
0
0
0
2
1
1
0
2
0
1
0
0
1
0
1
2
1
0
0
0
1
0
1
0
1
1
2
0
1
0
0
0
1
2
0
1
0
0
0
2
0
1
0
0
0
1
1
1
0
0
1
4
0
0
3
0
0
1
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
2
2
2
0
0
2
3
2
0
0
0
0
0
0
0
0
0
1
0
1
1
2
0
0
0
1
1
3
2
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
2
1
2
0
0
1
2
0
1
1
2
0
0
2
0
0
0
1
1
1
1
1
2
0
1
0
1
0
2
2
0
2
1
0
0
0
0
0
1
0
1
0
1
0
2
1
1
1
0
0
0
0
0
0
2
0
2
1
2
0
1
0
2
2
0
2
4
0
1
0
0
2
2
0
1
0
0
1
0
2
0
0
0
2
0
0
1
0
0
1
1
0
0
2
2
3
3
2
0
3
1
2
2
0
1
2
1
0
1
2
0
0
0
3
0
1
1
1
0
2
1
2
0
1
0
0
0
3
0
0
1
0
2
1
1
1
2
0
0
1
0
0
0
0
0
0
2
1
2
0
0
0
2
2
0
1
0
1
1
2
0
0
1
2
1
1
2
2
0
0
1
1
1
0
1
0
0
0
3
0
0
0
0
2
1
0
2
0
0
0
0
1
0
1
0
0
3
1
0
2
1
0
0
2
0
0
0
2
0
1
0
0
0
2
3
1
1
2
0
0
2
1
1
0
4
0
0
1
0
0
2
0
0
1
0
2
1
0
2
0
0
0
0
0
0
1
1
1
2
0
0
2
1
0
1
1
0
2
0
1
0
0
1
0
1
0
0
0
1
0
0
1
1
1
0
0
1
1
0
0
2
0
2
0
0
2
2
1
0
1
0
2
0
1
0
0
0
0
0
0
1
3
0
2
0
0
0
2
1
1
1
0
2
0
0
1
0
0
1
1
2
3
2
0
3
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
1
0
1
1
0
0
2
1
2
0
2
0
2
0
0
1
1
1
0
0
0
2
1
0
0
0
1
0
1
1
2
1
1
2
1
0
2
0
2
0
5
2
0
1
1
0
0
0
2
0
2
0
0
2
2
2
2
2
1
0
2
0
0
2
0
0
2
0
1
1
0
0
0
1
1
1
0
0
0
1
0
2
0
0
1
0
0
1
0
1
1
0
2
1
1
1
2
1
0
0
0
0
2
2
2
0
0
0
2
1
2
1
1
0
1
0
1
0
1
0
0
1
0
0
2
2
0
0
0
0
1
0
1
0
0
1
0
0
2
0
0
2
0
1
1
2
2
1
0
0
2
0
2
0
0
2
0
1
1
0
2
0
2
0
2
1
1
0
0
1
1
0
1
2
0
2
0
2
0
0
1
1
1
1
2
0
0
0
2
0
1
1
1
1
0
2
1
1
2
0
1
0
0
1
0
2
0
2
1
0
2
2
0
0
0
0
0
1
0
0
2
0
1
0
1
0
0
0
1
0
1
1
0
1
2
1
1
0
0
0
0
0
1
0
0
2
2
1
1
2
0
1
1
0
1
0
0
0
2
1
0
0
1
1
3
0
2
1
0
0
1
2
0
1
1
0
0
1
1
1
0
1
1
1
0
0
0
1
0
0
0
0
0
2
0
1
2
1
1
2
3
0
0
1
0
1
0
1
1
2
1
0
2
0
0
1
2
0
0
1
0
1
1
1
2
2
2
1
1
2
2
1
0
2
1
1
2
0
1
2
1
0
0
2
1
0
0
1
0
0
1
0
2
0
3
0
1
1
2
0
0
2
1
0
0
0
1
0
2
1
1
1
3
1
0
1
0
1
0
3
2
0
0
1
0
1
0
2
0
1
0
0
0
1
3
1
2
2
0
1
0
0
0
1
1
1
1
0
0
0
3
0
1
0
0
3
2
1
0
1
2
2
0
2
0
0
0
1
0
2
1
1
0
2
2
0
2
1
0
1
0
0
0
1
1
0
2
0
2
1
0
2
1
1
0
2
0
0
0
0
0
0
1
1
1
1
2
0
1
2
2
0
1
2
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
2
0
1
1
0
1
0
0
0
0
2
0
0
1
2
0
0
0
1
1
0
1
0
0
0
0
0
1
0
1
2
0
1
0
0
0
0
0
0
0
1
1
2
0
1
0
1
1
2
0
1
0
0
2
0
0
1
2
2
0
1
0
1
0
0
0
2
2
0
0
0
2
0
0
1
0
2
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
2
1
1
0
1
1
2
2
0
0
1
1
0
0
1
0
0
1
0
0
2
0
1
0
0
1
1
0
0
0
0
0
1
1
2
0
0
1
0
1
2
1
1
1
2
0
1
2
1
1
2
0
1
1
0
0
2
1
2
0
2
0
0
2
1
0
0
0
0
0
2
0
0
3
2
1
0
0
1
1
0
2
0
0
0
0
0
1
0
0
1
1
0
1
1
0
0
0
1
0
0
1
2
1
2
1
2
2
1
0
1
2
0
2
0
0
0
0
2
2
2
1
1
1
0
0
1
1
2
0
1
2
2
0
1
0
2
0
0
1
2
2
1
0
1
0
2
2
2
2
1
0
1
0
1
1
2
1
2
0
0
1
0
0
2
2
1
0
0
1
1
2
2
1
0
0
2
1
2
0
1
2
0
1
1
1
2
2
0
1
1
2
1
1
0
1
0
1
1
1
0
0
1
0
2
1
0
0
0
1
0
0
1
1
1
0
0
1
0
0
1
2
0
1
0
1
0
2
2
0
2
0
0
0
0
2
0
1
2
0
2
1
0
0
0
2
0
1
1
0
1
1
0
1
1
0
1
0
1
3
1
0
0
1
0
2
1
0
2
0
0
1
1
2
1
0
0
2
0
0
0
0
2
2
1
2
2
1
0
1
2
2
0
2
2
0
2
0
0
0
0
0
0
1
1
0
1
1
0
0
0
1
1
1
1
2
3
0
2
0
1
2
0
0
2
0
0
0
2
2
1
2
0
1
0
1
1
3
2
0
2
0
2
1
0
1
0
0
1
0
0
0
3
0
0
0
1
0
2
1
0
0
1
0
0
1
0
0
0
0
0
1
2
2
0
0
1
0
2
1
0
1
0
2
1
0
0
0
1
1
0
0
0
5
2
0
0
1
2
2
1
1
0
1
2
2
2
0
0
2
0
0
0
0
0
2
1
1
0
1
1
0
2
0
0
0
2
0
1
0
0
0
0
0
2
0
0
1
1
2
0
2
0
2
2
2
0
2
0
0
0
1
1
0
2
1
1
1
0
0
0
1
0
0
0
1
1
1
0
1
0
1
1
2
0
0
2
0
1
0
1
0
4
0
2
1
0
0
0
2
0
0
2
0
1
1
0
0
1
0
0
2
1
1
1
0
0
0
1
1
1
0
0
1
0
0
1
2
0
2
0
0
0
2
1
0
1
2
2
0
2
2
0
1
1
1
0
0
1
1
1
2
1
0
0
1
0
1
0
0
1
0
1
2
0
0
1
1
1
2
0
2
0
1
0
1
1
1
0
1
0
2
1
2
0
0
1
0
2
0
0
0
2
0
0
2
0
0
0
1
0
1
0
1
1
1
4
0
2
0
0
2
1
0
2
2
0
0
0
0
1
0
0
1
0
0
0
1
1
5
1
0
1
1
0
2
0
1
0
0
0
2
0
0
1
2
0
2
1
0
1
3
4
3
0
4
2
2
1
0
0
2
0
2
2
1
0
0
1
2
1
2
1
0
1
2
2
0
0
1
2
1
0
0
2
0
2
2
0
2
1
1
1
2
0
2
0
0
0
0
1
0
0
1
1
1
1
0
0
1
1
0
0
0
2
0
2
0
0
2
0
1
0
1
1
0
0
0
1
0
0
1
2
1
2
2
2
2
0
2
1
0
2
1
1
1
0
0
1
1
1
1
1
2
1
2
1
0
2
0
0
0
1
2
0
1
2
2
0
0
2
1
0
1
1
0
0
0
0
1
1
0
2
2
0
1
0
1
2
0
0
0
1
1
0
2
0
1
0
2
1
0
1
1
0
0
1
1
2
0
0
0
0
1
1
0
0
1
1
0
1
2
1
1
0
1
2
1
0
2
0
0
2
2
2
1
0
1
1
0
1
0
2
1
1
0
0
1
1
0
2
1
1
0
2
0
2
0
0
1
0
0
2
0
0
0
0
0
1
1
1
1
2
0
1
0
8
2
0
1
7
2
0
0
0
0
0
0
2
0
3
0
0
0
2
0
0
2
6
0
0
0
2
0
2
2
0
0
0
0
0
0
0
4
2
0
2
0
1
0
1
2
0
2
2
1
2
0
0
0
0
2
2
1
1
1
0
1
0
1
0
1
0
2
0
0
0
1
0
2
1
1
2
0
0
2
1
1
0
1
2
0
1
2
0
0
1
0
2
0
0
1
0
1
0
0
0
0
2
1
0
2
0
0
2
2
1
0
2
1
0
2
2
0
1
2
0
2
0
2
1
0
0
1
1
1
0
2
0
0
1
0
2
0
0
2
1
0
0
1
2
0
2
0
0
0
0
0
0
0
0
1
1
0
1
2
1
1
1
0
0
0
0
1
1
1
1
2
0
0
0
0
0
1
2
0
2
0
0
1
2
2
3
2
2
1
2
0
1
0
0
0
1
0
0
2
0
2
0
1
2
0
0
8
3
1
0
0
1
0
0
0
0
0
0
1
1
1
0
1
0
2
2
2
0
1
1
2
0
1
2
0
0
0
0
2
0
1
1
0
2
0
0
2
2
1
0
1
0
0
3
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
1
1
1
0
1
2
0
2
2
0
0
0
0
0
1
0
0
0
0
0
2
1
1
2
1
1
0
1
2
0
0
0
0
1
1
1
2
1
1
1
0
0
2
0
1
0
0
0
0
0
2
0
3
1
0
2
2
1
1
0
1
0
2
0
0
1
0
0
0
2
1
1
2
1
0
0
0
0
1
3
1
2
0
3
2
0
0
2
0
1
1
0
1
0
0
0
0
1
0
0
1
2
1
2
1
1
0
0
0
0
1
0
0
0
2
2
0
0
0
2
2
2
0
0
1
0
1
0
1
0
0
2
5
1
0
0
0
0
0
0
1
2
0
2
0
1
2
1
0
2
1
0
0
0
0
0
0
1
0
1
0
2
0
0
2
0
1
1
0
0
1
0
1
1
0
0
0
0
0
1
1
0
0
1
1
1
0
1
2
0
0
0
1
0
0
0
0
1
1
1
0
0
0
2
1
3
1
0
0
1
1
0
0
1
2
2
1
0
1
0
2
1
1
1
1
0
1
0
1
1
0
0
2
0
0
0
1
0
2
0
0
0
1
0
2
0
0
0
1
0
2
0
0
1
1
2
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
1
1
2
0
0
0
1
1
0
2
1
2
0
1
3
0
0
0
0
1
1
0
1
2
0
5
2
0
0
2
2
1
0
1
0
2
2
3
0
0
0
0
2
2
0
0
0
0
2
0
1
0
0
1
0
0
0
1
2
0
2
2
1
2
1
1
0
2
0
0
0
0
0
0
0
0
1
2
2
0
1
0
0
0
1
2
2
1
1
0
1
0
0
0
0
1
2
0
0
0
2
0
1
1
1
0
0
0
1
1
0
0
0
0
1
0
2
0
2
2
1
0
1
0
4
3
0
0
0
0
0
1
2
1
0
1
0
0
2
0
0
1
1
1
1
1
0
0
1
1
0
1
0
2
0
0
2
1
1
0
1
1
1
1
0
2
0
1
1
2
2
1
1
0
1
2
2
0
2
0
2
0
2
0
1
1
2
0
1
0
0
1
0
0
0
0
0
1
1
1
0
3
1
2
0
2
1
2
0
1
2
1
0
0
0
0
0
0
2
1
0
1
0
1
0
1
0
2
1
1
2
1
0
0
0
0
1
0
1
1
2
1
0
0
0
2
0
0
0
1
1
1
0
0
1
0
1
0
2
1
0
0
2
1
2
1
1
0
0
0
1
2
1
0
1
2
1
1
1
0
0
2
2
0
2
0
2
1
0
1
0
0
3
0
0
1
0
0
1
1
0
1
2
1
2
0
1
0
2
0
2
1
1
1
2
0
1
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
2
0
0
0
1
2
2
0
0
0
0
2
0
0
1
0
3
0
0
0
2
2
0
1
0
1
1
0
0
0
0
0
2
0
0
1
1
0
2
2
1
1
0
0
2
1
1
2
0
2
0
0
1
0
2
2
1
1
1
1
0
1
0
0
2
0
1
3
0
2
2
1
0
1
0
0
1
0
1
0
2
2
0
1
0
2
1
0
2
0
0
0
1
2
0
2
2
0
0
2
0
0
1
2
2
0
2
0
0
1
0
1
0
1
0
2
3
1
0
0
1
0
2
1
0
1
2
0
2
0
0
0
2
0
2
0
0
0
3
2
0
1
0
0
2
0
0
2
0
1
2
0
1
1
1
1
0
1
0
1
0
2
1
2
1
2
1
1
2
1
0
0
0
1
2
1
0
2
2
0
1
0
1
0
0
0
1
1
0
0
0
0
0
1
0
2
0
1
0
1
4
0
2
5
0
1
1
2
0
0
0
2
0
0
0
1
0
1
1
1
0
1
1
1
0
0
0
0
0
0
0
1
0
2
1
2
0
1
2
1
2
0
0
0
0
0
1
1
2
0
0
3
0
1
0
1
2
1
0
1
2
0
1
1
0
0
1
0
2
0
0
3
1
1
0
0
1
2
2
2
0
1
1
0
1
0
2
2
1
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
2
2
2
0
0
0
1
0
1
1
1
1
1
1
1
1
2
0
2
1
2
3
1
0
0
2
1
1
0
1
0
0
1
1
0
0
1
0
1
1
2
0
0
0
1
0
0
1
2
0
1
1
1
0
0
0
0
0
0
0
0
2
1
2
0
2
0
1
0
0
2
1
1
2
0
0
1
1
0
2
1
0
2
0
1
0
2
2
1
0
1
2
0
1
0
0
1
0
1
1
2
0
2
0
0
0
0
0
0
0
2
0
0
1
1
2
0
0
1
0
1
0
0
0
0
1
0
1
2
0
0
0
2
2
0
2
0
1
0
0
2
0
3
0
1
1
1
3
0
0
0
0
2
2
2
2
1
1
1
1
2
1
1
1
0
0
0
2
0
0
0
0
2
2
1
1
2
1
0
0
1
0
0
1
2
0
0
0
2
0
0
1
0
0
1
0
2
2
1
3
0
0
3
0
1
0
1
0
1
2
0
0
1
2
0
1
1
0
0
0
2
2
0
0
0
1
1
2
1
0
2
1
0
1
1
2
2
1
0
0
2
0
2
0
0
2
0
0
0
1
0
0
2
2
0
1
0
0
0
0
0
0
0
1
2
0
1
0
2
1
2
0
0
0
2
1
0
0
1
0
1
0
1
0
0
0
0
1
0
2
2
0
0
1
1
0
0
2
2
0
2
1
2
2
2
1
0
2
0
1
1
0
1
1
2
1
2
1
0
4
2
1
2
0
0
0
1
0
1
2
1
1
1
1
1
1
0
0
0
2
0
0
1
0
1
0
0
0
0
2
0
1
0
2
0
1
2
2
0
0
2
2
0
0
2
2
1
1
0
0
1
2
0
1
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
2
0
0
0
6
0
1
0
1
2
2
3
0
2
1
1
0
0
0
2
1
0
1
3
2
2
0
1
2
1
0
1
0
1
0
2
0
0
1
0
0
0
0
0
1
1
2
0
0
2
1
2
2
1
1
0
2
1
2
0
1
0
1
2
1
0
0
0
0
1
0
2
2
0
0
0
0
3
1
0
2
2
0
0
0
0
1
0
2
0
1
2
2
2
2
2
2
0
0
1
1
2
1
0
2
0
0
0
2
1
2
1
1
2
0
0
3
2
5
0
2
1
1
0
0
0
2
0
0
2
0
0
2
0
0
1
2
2
0
2
1
1
2
0
0
0
1
1
0
0
1
0
0
2
1
0
1
1
2
1
0
0
0
0
1
1
2
0
1
0
1
2
1
0
1
0
2
0
1
1
0
0
0
0
1
0
1
1
1
1
2
0
0
1
0
0
1
0
0
1
0
3
0
0
0
0
2
1
2
2
0
2
0
1
2
0
0
1
1
1
0
0
2
0
1
1
2
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
3
0
0
2
2
0
1
0
1
0
1
0
0
0
1
0
0
0
2
0
1
1
0
1
2
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
2
1
0
2
2
1
0
2
0
4
0
0
0
0
2
0
0
2
0
0
1
0
0
0
1
1
1
2
1
0
0
1
2
0
1
2
1
0
1
1
2
0
0
0
1
0
2
1
1
1
1
0
0
2
1
0
1
0
0
2
0
0
2
1
0
0
1
1
1
0
0
1
0
1
0
2
1
2
2
3
0
0
1
1
1
1
0
1
0
0
0
0
2
0
2
2
0
1
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
2
1
0
1
0
1
1
2
0
0
1
0
0
1
0
1
2
0
0
0
2
0
1
0
2
2
1
1
1
2
2
2
0
2
2
1
0
2
0
2
0
0
0
0
0
1
2
1
2
0
0
1
2
1
0
2
1
0
2
0
1
0
1
1
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
2
0
0
1
1
0
2
0
0
2
1
1
1
0
2
2
2
1
1
0
1
1
1
2
2
0
0
0
1
0
2
2
0
2
0
2
3
1
0
0
0
0
1
0
2
0
0
0
0
1
0
1
2
0
1
0
2
0
1
2
2
0
1
2
2
0
1
0
0
2
2
1
0
2
1
0
2
2
0
2
0
1
2
1
1
2
0
0
0
0
1
0
0
2
0
2
0
0
1
0
2
2
2
1
1
0
1
1
2
0
1
2
1
1
1
1
0
1
2
1
0
0
1
2
2
4
2
1
0
0
0
1
0
2
2
2
2
0
1
0
0
0
0
1
1
1
0
0
0
1
0
0
1
1
0
0
0
2
0
0
0
1
1
0
2
2
1
1
0
2
0
1
1
0
1
0
3
1
1
0
0
1
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
1
0
1
0
0
1
0
1
1
1
1
2
0
4
0
1
1
1
0
1
2
0
1
0
1
1
1
0
0
1
1
0
0
4
1
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
2
2
0
1
0
0
1
2
1
2
1
0
1
1
0
0
0
1
0
0
0
0
2
1
0
0
1
0
0
0
0
1
0
1
2
1
0
0
1
0
2
1
0
0
0
0
2
1
1
0
0
0
2
2
2
1
14
2
2
1
1
0
0
1
1
1
1
0
1
0
0
1
0
1
0
1
0
0
2
2
1
0
0
0
0
2
0
2
1
1
1
2
1
1
0
0
0
0
0
0
0
3
2
0
0
0
0
1
1
0
0
0
2
0
0
1
2
1
1
2
0
0
0
1
1
2
0
2
2
1
0
2
1
0
1
0
2
1
0
0
0
1
1
0
2
0
2
1
2
0
1
1
0
1
0
1
0
1
2
1
2
2
0
1
1
1
0
0
0
0
2
1
1
1
0
2
0
1
0
0
2
0
2
0
0
0
0
0
2
0
0
2
0
0
0
1
1
0
2
1
1
1
3
0
1
0
1
2
0
1
1
2
0
1
2
2
0
1
2
0
0
1
0
0
0
1
1
2
1
0
0
1
0
0
0
0
0
2
2
2
0
0
1
0
0
0
0
1
0
0
0
0
0
3
1
1
1
1
0
0
2
1
2
0
0
0
2
1
7
1
1
1
1
0
0
0
1
0
0
0
0
2
1
0
1
1
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
2
2
1
0
0
2
0
2
0
0
1
0
0
0
0
2
1
1
0
1
0
0
1
1
2
5
2
0
0
2
0
1
1
1
0
1
1
0
0
1
0
2
0
0
1
0
2
2
0
0
0
0
1
0
0
2
0
0
3
0
0
0
1
0
1
0
1
1
1
2
1
2
3
0
0
2
1
4
0
2
2
1
0
1
1
1
0
0
2
0
0
2
2
1
1
0
2
1
1
1
0
2
2
1
2
0
1
2
1
0
1
0
0
1
1
0
1
0
0
0
0
0
2
0
1
0
0
0
2
2
1
0
0
1
1
1
0
2
0
0
2
1
0
0
0
0
0
0
2
0
0
0
2
0
2
0
1
1
1
1
1
0
0
0
1
0
4
4
0
1
0
0
0
1
2
1
0
1
0
0
0
1
1
1
0
0
2
2
3
0
1
1
2
0
0
1
1
0
1
2
1
1
2
1
0
0
2
2
1
2
0
1
1
0
0
0
1
0
0
1
3
1
0
1
0
1
0
0
0
1
0
0
1
2
0
1
1
0
0
0
2
1
1
2
1
1
2
1
3
0
2
1
2
0
0
0
1
1
0
0
0
2
2
0
2
0
0
0
0
0
2
2
2
1
2
0
0
2
0
2
2
1
1
1
0
0
1
0
1
0
0
0
1
1
2
2
1
2
0
1
1
0
1
0
0
0
0
0
0
0
1
1
2
0
2
0
2
0
0
0
2
0
0
1
3
1
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
2
2
2
0
0
0
2
1
2
0
2
0
1
2
1
1
1
1
0
0
1
0
1
1
0
0
2
0
1
0
0
0
1
1
0
1
0
0
2
0
2
0
1
0
1
0
0
2
0
0
0
0
0
2
1
2
0
2
0
0
2
0
2
1
2
0
0
0
1
0
0
0
2
1
1
2
0
0
3
1
1
0
0
3
0
2
2
2
0
1
1
1
0
1
2
1
1
2
1
2
0
0
2
0
2
2
0
1
0
1
0
1
2
2
0
3
0
1
0
0
0
2
1
0
2
1
0
0
1
0
0
3
1
0
0
0
2
0
2
1
0
1
1
2
1
0
0
0
0
2
2
2
1
1
2
0
0
0
1
2
0
0
2
1
1
2
1
0
1
0
1
1
0
1
2
1
1
0
0
0
0
0
1
1
2
2
0
0
0
2
1
4
1
1
1
0
2
0
1
0
1
1
0
2
0
0
2
0
0
1
0
0
2
0
0
0
2
0
0
1
2
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
2
0
1
1
0
1
0
2
1
0
0
0
1
0
2
2
2
1
1
0
1
0
0
2
1
1
2
0
0
2
1
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
1
0
1
2
1
3
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
1
0
0
1
1
4
1
1
1
0
0
2
1
0
1
1
2
1
0
1
2
0
0
2
0
1
0
1
0
0
0
1
1
1
1
1
1
2
0
0
2
1
2
0
0
1
2
1
0
1
0
1
2
0
2
2
1
1
0
1
1
1
0
0
1
1
0
0
2
1
1
2
1
1
2
0
1
0
0
0
1
1
0
1
0
0
2
0
1
0
0
2
0
0
1
2
1
0
2
0
2
0
3
1
0
2
1
1
2
1
0
2
0
0
0
1
2
0
0
1
0
1
1
1
0
0
0
2
2
1
0
0
0
2
0
2
0
2
0
0
2
1
1
0
1
0
0
0
0
0
1
2
2
1
1
0
0
0
0
1
2
1
2
0
0
0
1
2
0
2
0
1
0
2
1
0
0
1
1
0
3
1
0
0
0
2
1
1
1
1
0
1
0
1
0
0
1
0
1
0
1
1
0
2
0
1
5
1
1
0
0
0
0
0
0
0
1
0
0
1
2
2
0
1
0
0
2
2
0
1
0
0
1
0
0
1
0
2
0
0
0
0
1
0
2
1
1
0
1
0
3
2
2
0
0
0
0
2
1
0
0
1
1
0
1
0
1
2
2
0
0
0
1
1
0
2
0
0
0
1
2
1
1
0
0
1
0
2
3
0
0
0
0
0
2
1
3
4
0
0
0
0
0
2
0
0
1
0
1
2
0
0
0
0
0
1
1
2
0
2
1
2
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
1
0
0
0
2
0
2
0
0
1
2
1
0
2
0
2
2
0
1
0
0
1
2
0
0
0
0
0
1
2
0
0
1
0
1
1
0
0
2
1
0
1
0
0
1
2
1
0
0
1
1
2
0
0
1
0
1
1
1
0
1
0
0
0
0
0
2
1
1
1
0
0
1
1
0
0
1
1
0
1
0
0
1
2
0
0
2
0
0
0
1
2
0
1
1
1
1
0
0
0
0
2
0
0
0
1
2
2
0
2
1
1
1
0
1
0
0
2
0
1
0
0
1
0
3
0
0
0
0
1
0
1
1
0
0
0
1
2
0
0
0
0
1
1
2
0
2
0
0
0
0
0
1
0
0
0
0
1
0
2
1
1
0
1
1
1
1
0
2
0
0
0
2
1
2
1
2
2
0
1
0
1
1
0
0
2
1
2
0
0
2
0
2
2
2
1
0
1
2
0
0
2
1
2
0
0
0
1
1
0
2
0
1
0
0
1
1
0
1
0
0
0
0
2
0
0
3
1
1
1
1
2
0
2
0
2
0
0
1
0
0
1
0
1
0
2
2
1
0
0
1
2
2
2
0
1
1
2
1
0
0
2
0
0
1
0
2
0
1
3
0
0
0
1
0
0
0
0
0
1
1
1
2
2
1
0
1
0
1
1
0
2
2
0
1
2
1
0
1
0
1
0
0
0
3
2
0
1
3
1
1
0
3
0
3
0
2
1
1
1
0
1
0
3
0
0
3
2
1
0
1
5
0
2
1
2
0
1
0
0
6
0
0
0
1
0
0
0
2
1
1
0
1
0
1
2
1
1
1
0
0
1
1
2
2
0
0
0
2
0
0
0
2
0
0
2
2
3
0
0
0
0
0
0
2
1
2
0
1
2
0
1
0
2
1
0
0
0
2
0
1
1
0
0
1
1
0
0
0
2
1
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
1
0
1
1
1
2
1
0
0
0
1
1
1
2
1
0
1
0
0
0
2
0
2
1
0
0
1
3
2
0
0
0
0
0
1
0
0
0
1
0
2
0
2
0
0
0
0
2
2
1
0
0
0
1
0
2
0
0
1
1
0
0
0
1
0
2
0
0
0
0
3
0
2
2
2
2
2
0
0
1
0
1
1
2
2
2
2
0
0
2
0
0
1
0
1
0
1
0
1
0
0
1
2
0
0
2
1
3
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
2
0
1
3
0
1
0
0
1
0
1
0
1
1
1
0
0
2
0
1
2
2
1
0
0
1
0
1
0
1
0
2
1
1
1
0
0
0
0
2
0
0
0
0
2
1
2
2
0
0
0
0
1
1
2
2
2
0
0
2
1
0
0
1
1
0
2
0
0
1
2
0
0
1
0
0
1
2
0
0
2
0
0
0
1
1
0
0
2
0
4
0
1
1
0
2
2
1
0
1
2
2
1
0
0
2
0
2
1
1
0
1
2
1
1
2
1
0
1
2
0
0
1
6
1
1
2
1
0
2
2
1
2
2
2
0
2
1
1
1
0
2
0
1
0
0
2
1
1
0
0
0
1
2
0
0
0
0
1
1
1
0
0
1
1
2
0
1
1
1
0
0
1
0
1
0
1
1
1
2
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
1
1
0
1
0
0
1
2
0
1
0
1
2
1
2
2
0
0
1
1
0
2
2
0
2
0
0
0
2
0
0
0
0
1
1
0
1
2
1
0
2
2
0
0
3
0
1
0
2
0
2
1
1
1
1
0
1
3
2
1
2
0
0
2
0
1
0
0
0
0
1
2
2
0
1
2
0
0
1
4
0
0
1
0
0
0
1
2
1
0
0
0
0
1
2
2
2
1
1
1
0
0
0
1
0
1
1
1
0
2
1
1
0
0
1
1
0
1
1
0
3
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
1
3
1
0
0
2
2
0
0
0
1
0
1
2
1
0
0
2
1
1
0
0
0
0
1
0
0
2
1
3
2
0
1
2
0
0
0
2
2
1
0
1
1
1
1
1
3
0
1
1
2
1
0
0
0
1
0
0
1
0
2
1
0
0
1
0
0
2
0
0
1
2
1
2
0
0
0
1
2
1
0
1
0
1
1
0
1
3
1
0
0
1
0
1
2
1
2
0
2
1
1
1
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
1
1
2
0
1
2
0
2
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
1
2
0
1
0
0
0
2
1
0
1
3
0
1
2
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
1
1
1
1
2
1
2
0
1
1
1
1
1
0
1
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
2
2
1
1
2
0
0
0
3
0
0
1
0
2
2
0
7
1
1
0
2
2
0
0
2
1
0
2
0
1
1
0
0
0
2
0
1
1
1
0
0
0
2
1
1
1
0
0
1
2
1
1
1
2
0
3
2
1
1
2
0
1
0
2
2
1
0
0
2
0
1
1
0
0
0
2
0
0
1
0
0
2
2
0
0
0
2
1
2
1
1
0
0
0
1
1
0
0
1
1
2
1
0
0
2
0
1
0
1
1
2
2
2
2
1
0
0
0
1
0
2
2
1
0
1
0
0
1
0
0
1
0
0
0
1
2
2
0
1
0
0
1
0
1
2
0
0
0
0
2
1
2
0
1
0
1
0
0
0
0
1
1
0
0
1
1
1
2
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
2
2
0
1
1
0
2
1
1
1
0
0
1
0
0
0
0
2
0
1
0
0
2
1
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
1
2
1
0
2
0
0
1
2
1
2
2
0
1
2
1
0
0
1
0
0
0
0
1
1
2
1
1
1
0
1
2
1
1
1
0
0
1
1
2
2
1
0
0
0
1
0
1
2
1
1
2
0
2
0
1
0
3
0
0
2
0
2
0
1
0
1
2
1
1
4
2
0
1
0
0
2
0
0
0
0
2
1
0
1
2
4
2
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
2
1
2
1
0
1
0
0
0
0
2
2
1
1
0
0
0
0
2
0
2
0
6
2
1
0
1
0
2
1
0
0
0
1
0
1
0
0
1
2
1
1
0
3
2
0
3
0
2
0
0
1
0
0
2
2
1
0
1
2
0
0
0
0
0
1
1
1
0
0
0
1
1
0
0
1
0
0
1
2
2
0
2
0
0
0
1
1
0
0
0
0
2
0
0
0
2
0
2
1
1
2
2
2
0
2
0
0
1
0
0
0
0
1
1
0
0
0
1
2
1
1
1
0
0
0
0
0
0
1
0
0
2
1
1
1
0
2
1
0
6
0
2
0
2
1
2
0
2
0
0
0
1
0
1
1
0
0
1
0
0
0
0
2
1
1
0
0
0
0
1
0
2
0
1
0
0
0
1
1
3
1
0
0
0
2
0
0
0
1
0
0
2
1
2
1
2
0
1
1
0
1
0
0
1
0
0
2
0
2
1
2
0
0
0
0
2
1
1
0
0
0
1
1
0
0
2
0
0
0
2
2
0
1
2
1
0
2
1
2
2
2
2
0
0
0
0
0
1
0
0
2
1
0
1
1
1
1
2
1
1
2
2
0
2
0
2
0
2
1
0
0
0
0
1
0
0
0
1
2
1
0
2
0
1
0
0
0
3
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
2
1
2
0
0
0
0
1
1
0
0
0
2
0
1
0
1
0
1
1
0
0
0
2
1
0
1
1
0
0
0
0
0
0
1
0
1
1
2
1
1
0
2
0
1
0
0
1
1
1
0
2
1
1
2
1
0
2
1
2
0
1
0
0
0
0
2
1
1
0
0
0
1
0
1
0
0
2
2
2
1
0
1
1
1
0
0
0
1
1
0
1
0
1
3
0
1
0
0
2
0
1
1
0
2
2
1
3
2
0
0
0
2
2
1
2
0
0
3
2
0
3
2
1
1
0
0
2
2
0
2
0
0
1
0
1
2
2
1
2
0
2
2
1
2
1
0
0
0
2
0
1
0
2
0
1
0
1
2
0
1
1
0
0
2
0
0
1
0
0
0
0
0
2
1
1
2
2
1
1
0
0
0
1
1
0
0
0
1
2
3
1
1
0
3
0
1
0
1
0
0
1
0
0
1
0
1
1
0
2
1
1
1
0
2
1
0
1
1
1
2
0
0
0
1
1
2
2
0
2
2
0
3
0
2
0
1
0
2
0
1
0
2
0
1
1
0
1
0
0
1
0
0
1
5
1
2
0
0
1
0
2
0
0
0
2
0
1
0
1
2
1
0
1
0
0
1
0
1
1
2
0
2
1
0
1
0
1
0
0
2
0
2
0
1
0
0
0
1
2
0
1
0
0
2
2
1
0
0
0
1
1
2
2
1
1
0
0
0
2
0
1
0
1
0
0
0
4
0
2
0
0
2
2
1
0
0
0
1
1
0
0
0
1
0
1
1
3
1
1
0
0
2
1
0
1
1
0
0
1
1
0
2
0
0
0
1
0
2
1
0
0
1
4
1
0
1
2
1
0
0
0
2
0
2
2
0
0
1
1
0
2
0
1
1
0
0
0
1
2
1
0
1
0
0
2
1
0
0
2
1
0
1
0
1
1
0
0
1
0
1
0
0
1
0
1
0
0
2
0
1
1
0
0
1
1
0
2
1
1
0
1
0
2
2
0
1
0
1
2
1
0
0
0
0
0
0
2
2
0
1
0
0
0
2
0
1
3
0
1
2
0
2
2
2
2
1
0
2
2
0
0
2
1
3
1
1
0
0
1
0
2
0
0
0
0
1
2
2
0
1
0
0
1
0
0
0
3
0
0
2
1
1
0
0
2
0
0
0
2
1
1
0
1
2
2
0
1
2
0
2
0
0
1
0
2
0
1
1
1
2
1
1
2
2
0
1
0
0
1
2
0
0
1
1
0
0
2
1
2
0
2
2
0
0
0
2
0
1
1
1
2
1
1
1
2
0
2
0
1
1
2
0
0
0
1
0
0
0
1
0
2
2
2
0
1
0
0
1
0
1
0
0
1
1
1
1
0
0
1
2
0
1
0
2
1
0
1
2
0
2
0
1
1
2
2
0
1
0
2
0
1
0
1
1
1
0
1
0
0
0
1
2
1
0
0
1
1
1
3
0
0
0
0
1
0
0
9
1
0
0
0
2
1
2
2
2
0
2
2
0
0
0
1
1
2
0
2
2
1
0
3
1
1
0
0
0
0
0
0
0
1
1
2
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
2
0
1
2
0
0
0
0
0
0
1
0
1
0
2
0
0
2
1
0
1
1
1
2
0
3
0
0
1
2
0
0
1
1
1
2
0
0
1
0
1
5
1
1
1
0
2
0
3
2
1
1
0
2
2
1
2
2
0
1
0
0
2
0
0
0
2
0
0
0
2
1
0
0
1
0
0
2
2
2
0
2
2
0
2
0
0
0
0
1
2
2
0
2
2
2
2
1
1
0
0
0
2
0
0
0
0
1
1
0
1
0
0
0
0
0
0
2
2
0
2
2
0
0
0
0
2
1
0
1
0
0
1
0
3
0
0
0
1
2
1
0
1
2
0
0
0
0
1
0
0
2
0
1
0
1
1
2
1
1
1
1
2
2
1
0
2
2
1
2
1
1
0
1
2
0
0
1
3
0
0
1
2
1
1
1
1
1
0
0
0
2
2
2
0
1
1
1
0
0
0
0
1
1
1
0
1
1
0
0
0
2
1
1
2
0
2
0
1
1
0
0
0
0
0
0
0
0
1
1
1
2
1
2
0
0
0
2
0
1
0
1
0
0
0
1
1
0
2
1
0
0
0
1
0
0
2
2
1
0
0
1
1
0
0
1
2
0
0
1
1
1
2
0
0
1
2
0
0
4
0
1
1
1
0
9
2
0
0
1
1
0
3
1
1
1
2
1
2
1
0
3
0
1
7
2
0
0
1
0
2
1
1
0
1
0
2
0
1
1
1
0
0
2
0
0
1
1
2
3
0
0
0
2
1
0
0
1
0
2
0
2
0
1
1
2
2
1
0
2
0
1
1
2
0
0
1
1
0
2
0
0
0
0
0
1
1
2
0
1
0
0
0
2
0
2
2
0
0
0
0
0
2
1
0
1
1
0
0
0
0
1
3
2
1
0
0
0
0
0
0
1
0
0
0
2
0
0
1
3
0
1
0
0
0
1
1
0
0
0
1
2
1
1
1
1
0
0
2
1
0
2
1
1
0
0
0
0
0
0
0
1
9
1
3
1
0
0
1
2
2
2
0
2
0
2
1
2
2
0
2
0
0
0
1
1
1
2
1
2
1
0
0
0
0
1
0
0
1
0
1
0
1
0
0
1
1
0
0
1
0
0
0
0
2
0
1
2
2
1
0
1
1
0
0
2
0
0
0
0
1
0
2
1
0
0
1
1
1
1
1
0
2
0
2
0
6
1
0
0
1
1
1
0
2
1
0
1
2
0
1
0
2
0
0
0
0
1
1
1
1
1
1
0
2
1
0
0
1
0
2
0
1
2
0
2
0
1
0
1
0
0
1
0
0
2
1
0
0
0
1
1
0
0
2
1
0
1
0
1
0
2
0
3
0
1
2
1
2
0
1
0
1
1
1
0
1
2
0
0
1
2
5
0
1
1
0
0
0
1
1
1
2
1
0
1
1
1
0
0
0
0
0
0
1
1
1
1
1
0
1
0
2
1
0
0
1
2
0
1
1
0
1
1
0
2
0
0
1
1
0
0
2
3
3
1
1
2
0
0
2
2
0
1
0
0
0
1
0
2
0
0
1
1
0
1
2
0
2
1
0
1
0
1
1
0
2
0
1
1
3
0
1
0
1
2
0
2
0
2
0
1
3
1
0
0
0
0
2
1
0
1
1
2
0
0
0
2
1
1
0
0
1
1
0
0
0
1
1
0
1
1
0
2
0
0
1
0
0
0
1
1
2
0
0
0
0
0
0
1
0
0
0
0
0
1
1
2
0
2
1
0
0
1
0
1
0
3
2
0
0
0
0
1
0
0
0
1
2
0
2
0
2
3
1
0
2
2
1
2
0
0
0
2
0
0
0
0
0
1
2
0
0
1
1
0
0
2
0
0
0
0
1
0
2
0
0
0
0
1
2
0
2
1
0
0
0
0
1
1
0
1
0
0
2
0
1
2
2
0
1
1
1
0
0
0
1
3
1
0
1
0
1
1
0
0
0
0
0
3
0
2
0
1
0
0
2
1
1
0
1
2
1
0
1
1
1
0
0
0
1
0
0
0
2
1
0
2
0
2
0
2
2
0
0
0
2
0
0
1
0
1
0
1
1
1
1
4
0
1
0
0
0
0
0
1
2
1
1
1
0
0
0
2
0
0
1
0
3
0
1
0
0
1
1
1
0
0
0
2
0
2
1
2
0
1
0
1
2
0
1
2
1
0
2
2
2
2
0
1
0
0
0
2
0
2
3
2
0
2
2
0
2
0
3
0
2
0
0
2
1
1
1
0
1
1
1
0
1
0
1
1
1
1
0
1
0
2
0
2
1
0
0
0
0
0
0
3
0
0
1
1
1
0
1
2
1
0
0
1
1
2
0
2
1
1
0
0
1
1
1
1
0
2
1
0
0
1
1
1
1
0
2
0
0
2
0
2
0
0
0
1
0
0
1
0
2
2
0
2
0
2
1
0
0
2
2
0
0
1
2
0
0
0
2
0
2
2
2
1
0
1
2
0
1
0
1
0
0
0
0
0
0
0
0
1
5
0
1
0
2
2
2
0
0
2
3
1
1
0
1
0
0
1
0
0
2
1
0
2
0
1
1
2
0
1
0
1
1
0
0
0
0
0
1
1
2
0
0
1
0
2
2
1
2
0
0
1
0
3
0
1
2
1
1
1
0
1
2
0
1
0
1
0
0
1
2
0
0
0
3
0
0
0
1
0
0
0
3
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
1
2
1
5
4
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
1
1
0
1
0
2
0
0
1
2
2
1
0
0
1
1
1
2
1
1
2
0
2
0
1
1
1
2
0
0
0
2
2
1
0
2
0
3
0
0
1
2
0
1
2
0
0
2
2
0
0
0
1
8
2
1
1
0
0
6
1
1
0
0
0
0
1
0
1
0
2
2
0
0
1
1
0
0
0
0
0
1
0
0
1
2
0
0
1
0
0
0
0
2
1
1
2
0
1
1
1
1
0
1
1
0
1
2
0
0
0
0
2
1
0
1
0
0
0
1
0
0
1
1
0
1
1
2
1
0
1
1
0
0
1
0
0
1
0
0
0
3
1
0
0
1
0
0
0
2
2
0
0
0
1
0
0
0
2
1
0
0
2
1
1
2
2
1
0
0
2
1
0
1
1
0
0
2
0
0
0
0
0
1
1
0
0
1
0
2
0
1
0
2
1
0
2
0
1
1
1
2
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
1
2
0
2
0
2
1
0
0
1
1
0
0
0
0
0
2
0
0
1
1
1
1
0
1
1
1
0
1
0
0
1
2
2
0
1
0
1
0
1
0
1
0
2
0
0
1
0
0
2
1
1
0
0
2
17
0
1
0
0
0
4
0
1
0
1
1
0
1
1
1
0
0
2
0
1
0
1
1
0
2
2
3
2
2
1
2
0
1
2
1
1
0
0
2
2
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
2
2
1
2
2
0
1
0
1
0
0
1
0
1
1
0
1
0
0
1
2
0
0
1
1
0
1
0
0
0
1
1
2
0
0
1
0
0
0
1
1
1
2
1
1
0
0
0
1
1
2
2
1
1
2
3
1
0
0
0
2
2
0
3
0
0
2
0
0
0
2
0
0
2
1
2
1
0
2
0
0
0
0
0
0
2
1
2
1
0
2
0
0
0
0
0
2
1
2
0
2
1
1
0
0
0
2
0
2
1
2
0
0
1
2
2
1
0
0
0
1
0
0
2
0
0
1
0
0
0
1
1
1
0
0
0
0
2
0
1
1
1
1
1
2
0
0
0
2
1
0
0
1
0
2
0
0
2
1
0
0
2
1
0
2
2
0
0
1
0
0
0
4
0
0
1
0
2
1
5
0
0
2
1
1
0
2
0
0
1
0
0
2
1
0
0
3
1
1
1
1
1
0
0
0
0
1
0
1
0
0
2
2
2
0
2
0
2
2
2
0
0
0
0
2
2
0
0
0
1
0
2
0
0
1
2
2
0
0
0
2
2
1
2
2
1
0
1
2
2
0
2
1
0
1
0
0
1
0
0
0
0
0
1
2
1
0
1
2
0
5
1
0
0
0
0
0
0
0
2
1
1
0
2
1
0
2
0
1
0
2
1
1
1
0
0
0
1
0
1
1
1
1
0
0
0
1
2
0
0
0
3
2
2
0
1
1
1
1
0
0
1
0
2
0
0
0
0
2
1
1
0
0
1
2
1
2
1
2
1
1
0
3
0
4
0
1
0
0
2
0
1
1
2
0
1
0
0
1
0
0
1
2
0
1
2
0
0
2
0
0
1
1
0
0
1
0
0
1
1
0
0
0
1
2
2
0
0
3
2
0
0
2
1
2
0
2
0
1
1
2
2
0
0
0
2
0
1
0
3
0
0
2
0
0
0
2
1
2
3
0
2
2
1
0
1
2
0
0
1
0
0
2
1
1
1
2
0
1
0
0
2
0
0
2
2
1
0
1
0
0
0
2
0
0
2
2
0
0
1
0
0
0
0
0
1
0
0
2
2
0
0
0
0
1
2
0
0
0
2
0
2
2
0
0
0
1
0
1
0
2
1
2
0
0
1
0
0
0
1
2
2
0
1
0
0
0
2
2
0
0
1
1
1
0
0
0
0
0
0
2
1
0
1
2
0
1
0
0
2
0
2
1
2
0
1
0
2
1
2
1
1
0
2
1
0
1
1
0
2
0
2
0
1
0
0
1
1
4
1
0
0
1
0
1
0
1
0
2
1
2
2
1
0
0
0
2
0
0
2
0
1
0
0
1
2
1
2
2
1
0
0
0
0
0
2
0
2
3
0
1
0
1
1
0
2
1
0
0
0
1
0
1
1
0
0
0
1
1
0
0
0
0
0
2
0
2
0
1
2
1
2
1
2
0
0
2
1
0
2
2
0
0
1
1
2
1
0
0
0
0
0
0
0
0
1
1
1
0
1
0
2
0
3
0
0
1
1
0
2
1
0
0
2
1
0
1
1
0
1
0
0
0
2
1
0
0
2
1
0
0
1
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
2
2
0
0
1
2
0
1
1
1
0
0
1
2
0
0
2
2
2
3
2
2
0
0
1
0
1
0
1
1
1
0
1
1
2
0
0
0
2
3
1
1
0
1
0
0
0
1
2
1
0
0
0
0
1
1
0
0
1
2
1
1
0
1
2
0
2
1
2
2
1
0
0
0
0
0
1
2
2
2
1
0
2
2
1
2
0
0
0
0
2
1
0
0
0
1
0
1
0
0
2
0
2
0
0
0
0
1
0
1
0
2
2
0
0
1
0
0
2
0
0
1
2
0
2
0
0
2
1
2
2
1
0
2
0
1
2
0
2
1
0
2
1
0
0
0
2
1
0
0
0
0
2
2
2
0
0
0
0
0
1
0
1
2
0
2
0
0
2
0
0
1
1
1
2
2
0
0
1
0
1
0
2
1
1
0
0
0
2
0
2
0
2
0
1
0
1
1
1
0
0
0
0
0
0
0
0
2
1
3
1
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
1
2
1
2
2
2
1
2
0
0
1
0
2
0
2
0
0
0
0
0
0
0
2
1
2
1
0
1
1
0
2
2
1
0
0
2
2
1
2
1
1
1
0
1
0
0
2
2
2
0
1
0
2
1
0
0
1
2
0
0
1
0
0
1
0
0
0
0
1
0
2
2
1
0
0
1
1
2
0
0
1
1
0
0
1
1
0
2
0
0
0
0
0
1
1
0
0
0
0
1
0
1
1
2
1
1
0
0
0
1
0
0
1
1
0
2
0
0
1
1
1
0
0
1
0
1
2
1
1
0
1
2
2
0
0
0
1
2
0
0
0
0
1
1
2
0
0
1
1
0
0
0
2
1
1
0
2
0
3
0
2
0
2
0
1
1
0
0
0
0
0
2
0
1
0
0
0
1
0
0
1
0
0
2
1
1
0
1
0
0
2
1
0
1
0
1
3
2
1
0
1
2
0
2
2
0
0
1
0
0
1
0
1
2
0
0
2
0
1
0
1
1
0
1
0
1
2
0
2
0
1
0
0
0
2
2
1
3
2
2
1
0
2
0
0
0
2
0
1
1
0
0
0
2
0
0
0
0
1
0
0
1
0
1
1
0
2
2
1
1
3
1
0
1
0
2
2
1
2
0
0
0
1
0
0
2
3
0
1
2
2
1
2
0
6
1
0
1
2
1
0
0
0
1
0
1
0
1
2
1
0
0
0
1
1
2
1
2
1
0
0
0
1
0
0
2
1
0
1
1
2
1
1
1
2
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
2
2
0
1
0
0
0
0
2
1
1
0
1
1
2
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
2
1
1
1
1
1
2
2
0
2
2
2
1
2
0
2
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
1
1
1
1
1
1
1
3
0
1
1
0
0
2
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
2
2
0
0
1
1
0
0
0
2
2
0
1
0
2
0
0
1
1
1
0
3
0
2
0
2
1
0
2
0
0
1
0
0
1
1
1
0
1
0
0
1
0
1
0
1
0
0
1
1
1
2
0
1
2
0
0
2
0
1
0
1
0
2
1
1
1
2
2
0
0
0
2
0
1
0
1
1
0
2
1
1
0
1
3
0
1
0
1
0
1
1
1
2
1
1
0
3
2
0
0
0
3
0
2
2
1
0
0
2
2
0
0
1
0
1
1
1
1
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
1
2
0
0
1
0
0
0
0
0
1
0
2
0
0
1
0
0
0
3
1
0
0
0
0
0
1
1
1
0
2
1
0
0
0
2
0
2
0
0
1
2
1
2
0
0
2
0
2
5
1
0
1
0
0
1
0
0
1
0
2
0
1
0
0
0
2
1
0
4
1
0
1
0
0
0
0
1
1
0
0
1
0
2
1
0
1
0
0
0
2
0
1
0
0
1
0
2
0
0
2
0
0
0
0
1
2
2
0
2
0
3
1
0
0
1
0
0
0
0
0
2
0
2
0
0
1
2
1
2
0
1
1
1
1
0
0
1
0
0
1
2
0
2
2
0
2
1
1
0
1
2
1
1
1
0
0
1
0
0
0
2
0
2
1
0
0
1
2
0
2
0
2
1
0
2
1
1
0
0
0
0
2
0
1
0
1
2
2
0
3
0
0
1
0
2
0
3
0
1
0
1
0
1
2
2
0
0
1
1
1
1
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
1
0
0
0
0
2
3
1
0
1
0
2
0
1
0
0
1
0
1
0
2
0
0
0
1
0
0
0
0
0
2
0
1
1
0
1
1
2
0
1
2
0
0
1
1
0
0
1
1
0
0
0
2
2
3
2
1
2
2
0
0
0
1
0
0
1
1
0
0
1
1
1
1
0
0
0
0
0
1
0
0
1
1
0
0
1
2
1
0
1
1
0
1
0
1
1
0
0
2
0
0
2
1
2
1
0
2
5
1
2
0
1
1
0
1
0
1
3
0
1
2
1
1
2
0
2
1
3
0
0
1
0
0
0
2
1
1
1
1
1
0
0
0
2
0
0
1
0
0
2
1
1
0
1
1
0
1
0
1
1
3
2
1
0
2
0
0
0
0
0
1
1
0
1
2
1
0
0
0
0
0
1
2
0
1
1
2
0
0
0
0
2
0
0
0
0
0
1
2
0
2
4
1
2
0
2
0
1
2
1
1
0
0
0
2
2
1
2
0
2
2
2
2
2
0
2
0
0
1
1
0
0
0
1
1
2
0
0
0
3
0
0
0
2
1
0
1
1
0
2
2
1
0
2
0
0
1
0
0
1
1
1
1
1
0
1
2
0
1
0
2
0
1
0
1
1
1
0
1
0
2
1
0
0
1
0
1
2
2
2
0
0
1
1
0
0
3
1
0
2
0
2
3
1
1
0
0
1
0
1
1
2
0
2
0
0
0
0
1
1
1
3
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
1
1
1
2
0
1
0
0
0
2
0
0
0
0
0
2
1
0
0
1
1
1
2
1
0
0
2
1
2
1
1
0
0
0
0
1
0
1
0
0
0
2
0
2
3
2
1
1
0
0
0
2
1
2
0
0
3
1
1
1
0
0
0
0
0
1
1
1
0
1
2
1
2
0
0
1
1
2
2
1
0
1
0
2
0
0
0
0
0
0
0
1
0
0
1
0
1
2
2
0
1
2
0
0
0
0
2
0
0
1
1
0
1
0
1
1
0
0
3
2
1
1
0
1
2
0
2
0
1
0
2
4
1
0
2
1
0
2
2
0
0
0
1
1
1
0
2
1
0
0
0
2
1
0
1
2
1
2
1
0
0
2
2
0
0
0
1
1
0
0
1
1
2
2
2
0
0
1
2
0
0
1
2
0
2
2
0
1
1
0
2
3
0
0
2
1
0
0
1
2
2
1
1
0
0
1
1
2
0
2
2
2
1
0
1
1
1
1
1
1
2
0
1
3
0
2
2
0
2
1
0
0
0
0
2
0
0
1
1
1
0
0
2
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
1
2
2
0
0
0
2
0
0
2
1
1
0
0
1
1
0
1
0
0
1
0
1
0
1
0
2
1
0
0
1
0
1
1
2
0
1
0
0
0
2
1
2
1
0
0
0
2
1
2
0
2
1
0
0
0
1
1
1
1
0
2
0
1
0
0
1
1
0
0
2
0
2
2
0
0
1
1
0
0
1
1
1
1
0
0
1
0
0
1
2
0
1
0
2
0
1
0
2
1
0
0
0
0
0
1
2
2
1
0
2
0
0
1
0
1
1
0
1
0
1
1
2
0
1
0
0
0
1
2
1
2
0
0
1
0
2
2
1
2
1
2
1
2
0
0
2
1
0
1
1
0
1
0
0
0
2
0
1
1
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
2
0
0
0
2
2
0
0
0
1
2
2
2
0
0
0
0
0
0
0
0
2
0
2
0
1
0
1
1
2
0
0
1
0
0
1
1
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
1
1
2
0
1
0
1
1
0
0
0
2
1
2
0
1
1
0
0
0
2
1
1
1
2
0
0
0
2
1
1
2
0
1
1
0
0
1
0
1
0
0
0
2
0
0
1
0
0
0
2
1
1
2
2
0
1
1
1
2
2
0
0
1
1
0
1
1
0
1
1
0
0
0
0
1
1
0
2
2
0
1
6
0
1
0
1
1
2
1
0
3
1
2
0
2
1
0
1
0
2
0
0
1
0
0
0
0
0
0
0
1
0
2
1
1
0
1
1
0
0
1
0
2
2
2
2
1
2
0
1
0
2
1
0
0
0
1
2
0
3
0
0
0
2
0
1
0
2
0
0
1
0
0
0
0
1
0
0
1
1
1
1
2
0
1
1
0
0
3
1
0
1
0
0
2
2
1
0
2
0
2
0
1
1
0
0
1
0
0
2
1
0
0
2
0
1
1
1
1
0
2
0
1
0
0
0
0
0
0
1
1
2
2
2
2
0
0
0
1
0
1
1
0
3
2
0
1
0
1
1
0
0
0
1
1
0
1
1
0
0
0
0
1
0
0
2
1
0
3
1
1
1
0
0
2
0
0
0
2
0
0
0
1
1
1
0
2
1
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
1
2
1
2
2
1
1
0
0
2
1
0
0
1
0
1
0
1
0
0
1
1
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
2
1
0
1
0
1
0
0
4
0
2
0
0
0
0
1
0
1
2
0
0
2
0
1
0
0
0
1
0
2
0
0
0
2
1
1
0
0
0
1
0
2
0
0
2
1
0
1
0
0
1
2
0
0
2
0
3
0
0
0
1
2
0
1
0
0
2
1
0
1
0
2
0
0
0
0
1
3
2
1
1
0
0
2
0
1
1
1
2
1
1
2
1
1
2
2
1
0
2
0
0
1
2
0
0
1
0
0
0
0
2
0
0
1
0
1
1
0
0
1
0
1
0
2
0
0
0
0
0
0
1
2
0
0
1
1
1
2
1
0
0
1
0
2
0
0
0
1
0
1
0
0
0
1
0
0
3
2
1
0
0
0
1
2
0
0
1
1
2
7
0
0
0
2
3
1
2
2
1
1
0
2
2
0
0
1
0
0
1
1
0
2
3
0
1
2
1
0
2
2
0
1
0
1
1
0
0
0
0
1
0
1
0
0
0
1
0
2
0
0
1
0
0
0
1
1
1
0
1
0
0
1
1
0
0
0
1
0
1
0
2
0
1
0
0
1
2
2
0
1
0
0
0
1
0
0
2
1
2
0
1
0
1
0
0
1
2
1
0
1
2
0
0
0
0
0
0
2
1
1
1
0
0
0
0
2
0
1
3
0
2
1
1
0
1
1
1
0
1
0
1
0
1
0
1
0
0
2
2
0
0
0
0
0
2
0
0
1
1
1
2
1
1
1
1
0
0
2
0
0
0
0
1
2
1
1
2
0
0
2
0
1
1
1
1
0
0
2
0
0
1
1
0
2
1
1
1
2
0
0
0
1
2
2
0
1
0
0
0
1
3
0
0
3
0
2
2
0
1
2
0
0
1
1
0
0
2
1
0
1
0
1
0
1
2
0
0
0
0
1
0
1
0
2
0
0
0
0
1
0
2
0
0
0
1
2
0
0
0
2
1
1
0
0
1
1
2
1
0
0
0
1
0
0
1
0
1
1
2
0
0
0
1
0
1
0
0
0
0
1
0
2
2
1
2
0
0
0
0
1
0
2
2
2
2
0
2
1
0
1
2
1
1
1
0
0
0
1
0
2
1
1
2
1
0
1
0
0
1
1
2
1
1
2
1
1
3
1
1
0
0
0
1
0
0
1
0
2
0
0
0
0
1
0
2
1
0
1
0
0
0
2
1
0
0
1
1
0
1
1
0
3
0
2
0
0
0
1
1
1
1
0
0
0
1
1
2
2
0
0
2
1
2
1
1
0
1
1
6
1
0
0
1
0
1
0
1
2
1
0
1
3
2
1
1
0
2
1
2
2
2
2
3
1
1
1
2
1
1
1
0
0
2
1
1
1
1
0
1
2
0
1
0
0
2
2
0
0
2
0
0
2
0
1
1
1
0
0
0
0
2
1
0
0
0
3
0
2
1
2
2
0
0
0
2
0
1
2
0
0
1
1
0
0
0
1
0
0
0
1
0
1
1
1
0
1
2
2
0
2
2
0
0
0
0
1
2
0
1
0
0
0
1
2
1
0
1
1
0
0
0
3
1
2
2
1
1
1
3
0
0
0
2
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
5
1
0
0
1
0
4
1
2
2
0
0
2
2
0
2
0
1
0
1
1
2
1
1
2
1
1
0
0
1
4
1
2
1
1
0
1
0
0
2
0
0
0
1
0
2
0
0
3
1
0
1
1
0
1
1
0
0
1
0
2
2
0
2
1
0
0
2
0
1
1
1
1
0
1
0
0
1
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
3
0
2
0
2
2
2
0
1
0
2
1
0
0
2
4
0
0
2
2
1
2
1
0
2
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
2
0
1
0
1
0
1
0
1
1
0
0
1
0
1
0
0
1
1
1
0
2
0
0
0
1
2
1
0
1
1
1
1
1
0
1
0
1
0
0
2
0
2
1
2
0
0
1
1
1
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
1
0
1
2
1
1
0
1
0
0
1
0
1
0
0
0
0
0
1
1
0
0
2
0
0
0
1
0
0
0
0
0
1
0
1
0
2
0
0
1
0
4
1
1
2
1
0
1
0
0
0
1
0
0
0
1
2
0
1
0
0
0
1
1
2
0
3
0
0
2
0
0
2
0
1
1
1
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
1
0
0
1
0
0
1
3
1
0
1
0
2
2
1
0
1
2
0
1
2
0
0
0
1
1
1
2
0
0
0
2
1
2
0
1
2
2
0
1
0
0
2
0
2
0
2
0
0
0
2
1
2
2
0
2
1
2
1
1
2
0
1
2
0
0
2
1
0
0
1
0
0
0
0
0
1
0
2
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
2
1
1
1
0
0
1
1
1
0
2
2
0
1
1
0
1
0
1
0
0
1
1
0
1
0
0
0
1
2
0
1
1
2
1
1
0
0
0
2
1
0
0
0
0
3
2
2
0
0
0
2
1
0
0
0
0
1
1
0
1
1
0
1
0
2
2
0
2
0
0
0
0
4
1
0
1
2
2
0
0
0
1
0
0
2
0
2
0
2
2
5
2
2
2
1
1
1
2
0
1
0
1
1
0
1
1
2
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
1
2
2
0
2
0
0
1
0
1
1
0
2
2
0
1
1
0
0
0
0
0
0
2
0
0
0
1
1
1
2
1
0
0
0
1
0
2
0
1
1
0
0
1
1
0
2
0
0
2
0
1
1
0
0
0
0
0
1
2
0
1
1
1
6
2
1
1
1
0
2
2
1
0
1
0
1
0
2
1
2
5
1
1
1
2
0
1
2
0
1
0
2
3
0
2
1
0
2
2
1
0
0
1
2
1
0
1
2
2
0
1
1
1
1
1
2
1
0
0
0
1
1
0
1
0
2
0
0
1
0
2
0
0
0
1
0
1
2
1
0
1
0
0
1
0
2
0
1
0
0
0
2
0
0
0
1
0
2
1
0
2
2
1
0
2
0
0
2
2
0
1
0
1
2
0
2
0
1
1
1
0
0
0
1
1
0
0
0
1
0
2
1
0
0
0
0
1
1
1
2
1
0
2
0
0
0
1
0
0
2
2
0
0
2
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
4
1
1
0
1
2
0
2
1
0
1
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
2
2
1
0
0
0
1
0
1
1
1
0
0
0
2
1
0
0
1
0
0
1
1
0
0
0
0
1
1
0
0
1
1
1
1
0
2
2
0
0
1
0
2
1
0
2
1
0
2
1
2
0
0
0
0
2
1
0
1
1
1
1
0
2
0
0
2
0
1
0
2
0
0
0
2
2
0
1
0
0
2
0
0
1
0
1
0
0
1
0
1
0
1
0
1
0
0
0
3
4
0
1
2
2
0
0
1
0
0
0
1
0
1
3
0
2
0
0
1
0
0
0
2
1
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
2
3
0
0
1
1
0
1
0
0
1
1
0
2
2
0
1
0
1
2
0
0
1
1
2
0
0
1
0
1
1
2
2
1
1
1
0
0
0
0
0
1
1
0
1
0
1
0
0
0
2
2
2
1
2
1
0
0
1
2
0
2
1
2
0
1
2
1
0
0
3
2
0
1
0
0
0
0
2
2
1
0
0
0
1
0
1
0
2
0
1
0
0
0
1
1
2
0
1
1
0
2
0
1
3
1
2
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
2
2
2
1
1
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
1
2
2
1
0
0
0
2
0
2
0
0
1
0
2
0
1
1
0
1
1
2
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
2
1
0
1
0
1
2
0
2
1
0
1
0
0
0
0
0
0
2
0
0
3
0
0
0
0
1
0
1
0
1
0
1
1
1
0
1
0
1
0
1
0
2
0
2
0
2
0
1
2
0
2
2
0
0
0
2
2
2
2
11
1
1
1
0
0
2
0
1
2
2
0
1
1
0
0
0
1
1
1
0
0
2
0
0
1
0
2
2
2
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
1
1
1
0
2
0
1
1
0
1
1
0
1
0
0
0
0
4
0
0
1
1
0
2
2
1
2
1
1
2
0
0
2
3
2
0
1
0
2
0
0
1
1
2
2
0
0
2
2
0
1
0
2
0
1
0
0
1
1
0
3
1
0
0
1
1
1
0
0
0
0
0
0
0
2
2
0
0
1
1
2
0
2
0
3
0
0
1
2
0
0
1
0
2
2
0
1
1
2
0
0
4
1
0
0
2
1
2
0
0
2
0
0
1
1
1
0
1
0
0
0
2
1
2
2
2
1
1
1
1
2
1
0
2
1
1
1
0
0
2
0
0
0
0
2
2
0
2
1
0
0
2
0
0
2
0
1
0
1
0
1
0
0
0
0
2
0
1
2
2
1
0
1
1
2
0
2
0
1
0
0
0
1
2
0
0
2
1
2
0
0
0
1
0
0
0
2
1
2
1
1
1
1
2
2
1
0
1
1
0
0
0
0
1
0
1
0
2
1
2
1
0
0
0
1
1
1
2
1
1
0
0
0
2
1
0
0
2
0
1
1
1
1
1
0
4
1
2
0
2
0
2
3
0
1
2
0
0
1
0
0
1
0
0
1
0
0
0
1
1
0
2
0
0
0
1
0
0
0
0
0
2
0
0
1
0
1
1
1
2
1
1
0
0
1
2
1
1
0
1
1
0
0
0
0
0
2
2
0
1
1
0
1
0
0
2
1
3
0
1
3
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
1
0
1
1
2
1
0
2
2
0
0
0
0
1
0
0
0
1
0
1
0
0
1
1
0
1
0
0
0
0
2
1
0
1
0
1
0
0
0
1
1
1
0
0
1
0
1
2
0
0
1
1
0
1
1
1
1
2
0
2
2
0
2
2
2
1
0
0
0
0
0
1
0
1
0
1
2
0
1
2
2
1
0
0
0
2
1
2
3
1
2
0
2
1
1
0
0
2
0
1
0
1
2
2
1
0
0
2
0
0
2
1
0
1
0
1
0
0
0
2
2
0
0
1
0
1
1
1
1
0
0
2
1
1
2
0
1
1
3
1
3
0
2
2
1
1
0
1
2
0
0
1
1
4
0
0
1
0
0
1
0
0
1
0
2
2
1
1
0
2
1
2
1
2
0
0
1
0
0
1
1
2
1
0
1
0
0
2
0
2
1
2
1
0
2
2
2
0
2
0
1
1
0
0
0
2
1
2
2
0
1
1
0
0
4
0
1
0
0
0
2
3
0
0
0
1
0
0
0
2
1
0
1
1
0
0
0
2
0
1
1
0
0
2
1
2
1
1
0
1
0
3
1
1
0
0
1
0
0
0
2
1
2
0
0
1
2
0
1
0
1
0
0
1
0
2
1
0
0
0
0
0
1
0
0
1
2
1
2
2
2
0
2
0
0
0
0
0
1
1
0
0
0
2
1
0
0
1
2
1
0
2
1
0
0
0
0
1
0
1
2
0
1
0
0
0
1
1
1
2
2
0
0
1
0
2
1
2
0
0
1
0
1
0
1
0
0
1
0
2
0
2
0
1
1
0
1
0
1
0
1
0
2
1
0
1
2
0
0
2
0
0
0
2
0
0
1
0
0
2
0
2
0
0
3
0
2
0
0
1
0
1
0
1
0
0
0
1
0
0
2
2
1
0
2
1
0
1
0
1
1
0
1
1
2
0
0
0
0
1
2
0
2
0
2
1
1
1
0
0
2
1
1
2
2
0
0
2
0
5
1
2
0
2
0
2
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
1
2
0
2
0
1
1
2
2
0
0
1
1
1
1
0
0
2
2
0
1
1
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
2
0
3
0
0
0
2
1
0
0
6
2
0
1
0
0
0
0
2
2
0
0
0
1
0
0
1
0
0
2
0
0
0
2
2
0
1
2
0
1
1
0
0
0
0
0
2
3
0
1
1
0
1
1
0
0
0
1
0
2
0
2
1
0
2
0
2
0
0
0
0
1
1
1
1
1
0
2
0
1
0
1
2
1
0
1
0
0
0
1
1
1
2
1
0
0
0
3
0
2
0
0
1
0
1
2
0
1
1
1
0
2
0
1
0
0
0
0
0
1
0
2
1
0
1
1
1
0
0
0
0
0
1
2
0
0
2
0
0
0
0
1
0
1
1
0
7
1
0
0
1
0
0
0
0
0
2
1
0
0
0
2
1
0
0
0
0
0
3
0
2
1
2
1
0
0
0
0
1
0
1
0
1
0
0
2
1
3
2
0
2
1
2
2
0
0
0
1
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
2
0
1
0
1
0
0
0
0
2
2
0
0
0
0
2
2
1
0
0
0
1
1
2
0
0
0
0
0
1
0
1
0
0
1
2
0
2
1
1
2
1
1
1
2
0
1
1
0
2
3
1
1
0
1
0
1
1
1
0
1
0
0
0
0
0
0
0
1
1
2
0
1
2
1
1
1
1
0
2
1
0
1
1
0
2
0
0
2
1
0
1
1
2
0
1
1
0
0
1
2
1
0
1
2
1
0
0
0
0
1
2
0
1
0
2
1
0
0
1
0
1
1
0
2
1
0
1
0
1
0
0
2
2
1
2
2
0
0
2
0
0
2
0
2
3
1
0
0
1
2
3
0
0
0
0
1
0
1
0
0
0
0
0
2
3
1
0
2
0
1
2
0
1
0
2
1
0
0
0
2
0
1
1
2
0
3
0
2
1
1
0
0
1
0
1
0
2
0
0
0
0
1
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
1
1
0
2
0
1
0
2
1
0
1
0
1
2
3
1
0
1
0
0
1
0
0
0
2
0
1
0
1
0
0
2
2
2
0
1
1
2
1
2
2
2
2
0
0
0
0
2
1
0
0
0
1
0
1
0
1
1
1
1
2
1
0
1
0
0
1
0
0
0
1
0
2
0
1
1
0
0
2
1
0
1
0
1
1
0
2
1
0
0
4
0
0
0
3
2
1
0
1
1
1
0
2
0
1
1
2
0
2
1
1
0
0
1
0
0
2
0
1
0
1
0
2
3
0
0
2
1
0
1
0
2
1
1
1
0
1
0
1
1
0
1
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
1
1
1
0
1
0
0
0
1
0
1
0
0
0
2
0
0
1
1
0
0
1
1
2
1
2
0
0
0
0
1
0
1
8
1
1
0
0
0
2
0
1
2
1
2
0
0
4
1
0
0
2
1
2
0
1
0
2
0
1
1
0
1
0
2
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
1
2
1
0
2
1
1
0
0
1
0
0
1
1
1
1
0
2
2
3
0
0
0
0
1
1
2
0
1
0
0
2
0
1
1
0
2
0
1
2
0
0
2
1
0
1
2
0
1
0
0
1
0
0
0
0
1
0
1
1
0
2
5
1
1
3
2
0
0
1
0
2
0
0
1
0
0
0
0
1
0
0
1
0
1
0
2
0
0
0
0
0
0
3
0
0
0
0
0
1
1
0
1
2
0
0
1
1
0
0
0
2
0
1
0
0
0
0
0
2
2
2
0
0
2
0
0
1
1
2
0
2
2
0
0
0
0
1
1
0
0
1
2
2
2
0
0
0
0
1
0
0
1
1
1
0
1
0
0
1
1
2
0
0
0
0
0
2
1
0
0
1
1
1
2
0
1
1
1
0
0
1
0
1
2
1
0
1
1
0
2
1
1
0
2
0
0
0
1
1
0
0
1
0
0
0
1
0
0
3
1
2
0
1
0
1
2
2
3
1
2
0
1
0
2
0
2
0
1
1
2
0
1
3
1
0
2
1
0
2
0
0
1
1
1
1
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
1
0
1
1
0
0
1
0
0
0
0
2
1
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
2
1
0
2
1
0
3
0
1
0
0
0
0
0
0
1
1
1
1
1
1
0
1
2
0
1
0
0
0
0
1
0
0
2
0
2
1
0
1
2
0
0
0
1
2
2
1
1
0
0
0
0
0
0
1
1
2
1
0
2
0
0
5
1
0
1
0
1
0
1
2
0
0
2
0
1
1
1
2
1
2
0
0
0
1
1
1
0
0
0
0
2
2
0
1
1
2
2
0
0
0
1
0
2
1
0
0
1
1
2
0
1
1
0
1
1
1
0
1
0
0
2
0
0
0
1
1
0
0
0
0
0
3
1
1
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
2
0
1
0
2
1
0
0
0
0
2
0
2
1
1
0
3
2
0
2
1
0
0
0
0
0
1
0
1
2
1
0
0
0
0
0
0
0
1
1
2
1
1
0
2
0
0
1
0
2
0
3
0
0
0
0
0
0
2
2
1
1
1
2
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
1
0
1
2
1
2
0
0
0
1
0
2
1
0
0
2
1
0
0
2
0
1
0
1
1
0
3
0
0
1
0
0
0
1
0
2
0
2
2
0
0
0
0
0
0
0
0
0
1
0
2
1
0
2
0
3
0
0
0
2
1
1
1
1
0
3
0
2
2
2
2
0
1
0
0
0
1
1
1
2
1
1
0
0
0
0
0
0
1
1
1
0
0
1
2
0
0
0
1
2
0
2
1
1
2
0
2
2
1
2
0
6
1
1
1
2
2
1
0
2
2
2
1
2
2
0
1
1
0
1
1
0
1
1
0
2
2
0
1
1
1
1
1
1
2
1
1
2
0
0
2
0
1
0
2
1
1
0
0
2
3
1
0
3
0
1
0
0
0
1
0
2
1
0
0
1
1
0
1
0
0
1
2
0
0
0
0
1
2
0
0
0
1
0
1
2
0
1
0
0
1
1
0
0
0
1
0
2
1
0
2
2
2
0
2
0
0
0
0
1
0
2
0
0
0
2
2
0
0
1
2
1
1
0
0
1
2
1
1
2
0
0
0
0
0
2
2
1
2
0
0
0
0
1
0
0
0
2
0
2
0
0
2
0
1
0
2
0
1
2
0
1
2
2
1
0
1
1
0
1
0
0
2
1
0
2
1
2
2
0
1
2
0
0
2
1
1
0
1
0
2
2
2
2
1
1
0
1
1
1
2
2
1
0
0
3
0
2
0
0
0
1
2
1
1
0
0
1
0
0
2
2
2
2
1
2
0
0
1
0
2
0
1
0
0
0
0
2
2
1
0
1
2
2
2
0
1
1
0
2
2
0
0
0
1
1
2
2
1
1
0
1
1
1
0
0
2
0
0
1
0
0
0
0
2
0
1
1
0
2
1
1
2
2
1
0
1
0
1
0
0
0
0
2
1
1
2
0
0
0
1
2
1
0
0
2
0
0
0
1
1
2
0
0
0
0
0
0
1
1
0
1
0
1
0
0
2
0
0
0
2
2
0
1
0
0
0
0
1
0
2
0
1
0
0
1
1
0
2
0
0
2
0
1
0
0
0
0
1
0
0
0
4
1
1
0
1
0
1
1
1
0
0
1
0
0
0
2
2
0
0
0
2
0
1
0
1
1
2
1
0
1
1
1
0
1
0
0
0
0
0
0
0
3
0
2
0
1
0
0
2
1
0
1
1
0
1
1
1
1
0
0
0
0
1
1
2
0
0
1
0
1
0
0
2
2
0
0
4
1
0
1
2
0
0
2
0
0
1
1
1
0
1
0
2
4
2
0
2
1
0
1
1
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
1
0
1
2
2
2
1
1
1
2
1
0
0
1
1
1
0
0
1
1
2
2
1
2
2
0
1
1
2
1
0
1
0
1
2
1
1
0
1
2
2
1
2
1
1
2
1
0
0
0
0
2
1
0
0
2
4
0
2
0
0
1
1
0
1
1
2
0
0
1
2
1
1
1
2
0
1
2
1
0
1
0
0
1
2
0
1
2
0
0
2
3
0
0
0
0
1
2
1
2
2
1
1
0
0
0
1
1
0
1
2
1
1
2
0
2
2
2
2
0
0
1
2
2
1
2
0
0
0
0
1
0
0
0
6
2
0
1
2
0
2
0
1
0
1
0
0
0
0
1
0
0
0
2
0
0
0
1
1
1
0
0
2
1
0
1
2
0
2
2
2
0
1
0
2
0
2
1
0
0
2
0
1
0
2
0
0
0
0
1
1
2
0
2
2
0
0
0
0
2
0
0
0
0
1
0
0
1
1
0
0
1
0
2
2
2
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
1
2
2
1
0
0
0
2
2
0
1
1
0
1
0
2
1
1
0
0
1
1
0
0
1
1
1
0
0
1
0
0
1
2
0
2
0
0
0
2
1
0
2
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
3
1
1
0
0
2
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
1
2
1
2
0
0
2
1
3
1
1
1
2
0
1
0
0
1
1
1
1
0
0
1
0
1
5
0
0
2
0
2
0
0
1
0
3
1
2
0
1
0
0
1
1
1
1
0
0
2
1
1
0
0
0
1
1
1
0
0
0
0
0
1
2
1
0
2
2
0
1
0
1
1
1
2
1
2
3
0
0
1
2
0
1
1
2
1
2
0
1
0
2
1
2
1
0
2
0
0
1
0
0
2
2
0
1
1
1
1
0
2
0
0
1
0
0
0
1
3
0
0
0
1
1
0
1
1
0
0
1
0
1
0
1
0
0
0
0
0
2
0
2
1
1
0
2
2
2
0
0
0
0
2
2
1
0
0
0
0
0
0
1
1
2
0
0
2
0
0
1
1
2
1
1
1
2
0
0
0
1
1
2
1
1
0
2
2
0
0
2
1
0
0
0
2
0
1
1
0
1
2
0
0
1
1
0
3
1
1
2
1
0
0
0
2
2
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
1
1
0
2
0
2
2
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
2
1
0
0
0
1
0
1
0
0
0
0
2
1
1
0
0
0
1
1
0
0
2
0
1
1
0
0
1
0
0
3
1
0
0
1
0
0
1
1
1
1
0
2
2
0
1
0
1
2
0
0
1
0
0
0
1
0
2
0
1
1
0
1
1
0
1
0
2
0
0
0
2
1
1
1
1
0
2
1
0
2
0
2
0
2
0
0
1
4
2
2
1
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
1
1
1
0
1
0
2
0
2
1
0
0
0
1
0
1
1
1
0
1
1
0
1
0
1
0
0
2
0
0
0
1
1
0
1
0
0
0
1
0
2
0
2
0
0
0
0
0
1
1
1
2
1
0
2
0
0
1
1
0
0
0
1
0
1
0
1
2
1
1
0
2
0
0
0
1
2
0
0
1
0
1
2
2
0
0
1
0
2
2
0
0
2
1
0
1
1
0
0
3
1
0
0
2
0
0
0
1
1
2
2
0
1
1
0
0
1
0
1
2
0
1
1
2
2
1
0
0
0
2
2
2
2
0
0
0
0
0
0
1
1
0
1
0
1
0
2
0
0
0
3
1
0
0
1
0
0
1
0
1
1
0
2
1
0
1
1
1
0
0
0
1
1
2
0
1
0
1
0
0
2
0
1
0
0
2
2
0
0
1
0
1
2
1
0
2
1
1
2
0
0
2
1
1
0
0
0
2
2
0
1
1
1
1
0
2
1
2
0
2
0
2
0
0
0
0
0
1
2
0
0
0
1
0
2
3
0
0
0
1
0
0
1
0
2
1
0
1
1
0
1
0
2
1
0
0
0
1
0
1
0
1
0
0
0
1
0
1
2
1
1
1
2
0
5
0
2
1
2
0
0
2
0
2
0
2
0
0
0
0
3
1
2
1
2
1
0
0
0
0
1
1
1
0
0
0
2
1
0
2
0
1
1
1
0
0
0
1
0
1
0
2
1
1
0
1
1
1
0
0
2
0
2
1
0
0
1
0
0
2
0
0
1
1
0
0
1
0
0
1
1
0
2
0
1
0
1
0
2
0
0
0
2
1
2
0
1
1
1
2
1
1
2
0
0
0
2
1
1
0
0
0
1
2
2
1
0
1
1
1
1
1
0
1
2
2
0
1
1
0
1
0
4
1
0
2
0
0
1
1
1
0
1
1
0
1
1
0
2
0
0
0
0
1
1
0
1
1
1
0
0
2
2
1
0
0
0
0
2
0
1
0
0
0
1
0
0
0
1
1
0
1
0
1
1
0
1
0
1
2
2
0
0
0
0
2
0
2
0
0
0
2
2
0
2
1
0
0
2
0
2
2
0
1
1
1
0
0
0
2
0
0
2
1
2
2
1
1
0
0
2
2
1
2
0
1
0
1
1
0
1
1
1
1
1
0
1
0
0
2
1
2
1
0
0
0
1
1
0
0
0
1
0
1
0
1
0
0
1
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
2
1
0
0
3
1
1
1
0
1
2
2
1
0
2
2
2
0
1
0
0
0
2
3
2
2
0
2
2
0
1
1
1
2
0
1
1
0
1
0
1
0
1
2
1
2
0
2
0
0
1
1
2
0
1
1
2
0
0
1
1
0
2
0
0
0
0
0
0
1
0
1
0
2
1
0
0
0
1
0
0
1
1
2
1
2
0
0
1
2
0
0
1
1
1
0
0
1
1
1
0
0
1
1
0
0
0
1
1
1
1
0
2
0
1
1
0
2
2
2
1
1
0
2
0
0
0
1
0
0
2
0
0
2
0
0
1
0
0
0
0
2
1
0
1
2
2
0
0
0
1
2
0
0
2
0
1
0
1
0
1
1
0
0
1
0
0
1
0
0
2
0
1
1
0
0
1
1
2
0
1
0
1
0
1
0
0
0
2
1
1
0
0
2
0
2
1
0
0
0
2
0
1
1
0
0
0
1
0
1
0
2
2
1
0
0
0
2
2
0
1
1
0
0
1
0
1
0
0
1
1
2
0
2
2
1
0
2
0
0
0
2
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
2
1
0
2
0
1
0
1
0
0
0
0
0
1
2
1
1
1
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
1
0
0
1
2
0
0
1
2
0
3
0
1
2
0
0
1
2
0
1
1
1
2
0
1
1
0
0
2
1
1
3
1
2
2
1
1
0
0
0
1
2
1
1
0
0
0
0
1
1
1
3
0
1
4
0
0
3
1
1
1
0
1
1
0
1
2
2
1
3
2
0
0
0
1
1
0
1
0
0
2
2
0
2
2
0
0
1
2
0
0
1
1
1
0
2
2
1
2
1
1
0
2
0
0
0
0
1
0
2
0
0
1
1
0
0
1
2
1
0
1
0
0
0
0
3
2
0
1
0
0
2
0
0
0
1
1
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
3
0
1
1
1
1
0
0
0
1
1
1
2
2
1
1
0
2
1
0
1
0
1
0
0
1
1
0
1
2
1
2
2
0
2
1
0
1
1
0
2
0
1
0
0
0
1
1
0
0
2
2
0
2
2
1
1
1
1
0
1
0
0
0
0
1
2
1
0
2
1
0
2
0
2
2
0
1
0
0
1
1
0
1
1
1
1
1
1
0
0
1
0
2
0
0
2
0
0
2
2
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
1
1
0
2
0
1
1
1
2
0
1
3
3
0
2
1
1
0
3
1
0
1
0
0
1
0
0
0
1
2
1
0
0
0
1
0
0
1
0
1
0
1
0
1
1
0
0
0
2
0
1
0
0
1
1
0
0
1
1
0
0
2
1
0
2
1
0
1
1
1
1
0
2
1
0
0
0
0
0
0
0
2
1
1
0
1
1
1
0
2
1
1
0
1
0
1
0
0
1
1
2
2
0
0
1
1
2
0
0
1
2
2
0
0
0
1
1
2
0
0
2
1
3
0
0
0
2
0
2
2
0
0
1
1
0
1
1
1
3
1
2
2
1
2
6
0
0
0
0
0
2
0
0
0
0
2
2
2
1
0
0
2
0
0
0
1
2
0
1
2
1
0
0
4
0
0
1
0
1
0
1
2
0
1
2
0
0
0
2
1
1
2
0
2
1
1
1
2
2
1
1
2
1
0
1
2
1
2
1
1
1
1
0
1
0
1
0
2
0
0
1
2
1
1
1
1
1
1
2
1
0
2
1
1
0
5
0
1
0
0
2
0
0
2
3
0
0
1
2
0
0
0
0
1
2
2
1
1
0
0
0
1
0
0
0
1
2
0
0
2
2
2
1
1
3
1
2
2
2
0
3
0
1
0
0
1
1
1
0
0
0
0
0
0
2
0
1
1
0
0
0
1
1
1
1
2
0
0
1
0
1
0
1
0
2
0
0
1
0
2
0
0
0
0
1
0
1
0
1
0
0
2
0
2
0
1
1
2
1
2
0
0
1
3
0
2
1
0
1
1
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
2
0
1
0
0
2
1
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
2
0
0
0
0
1
1
1
2
4
1
0
1
2
1
0
0
1
0
0
0
1
0
0
1
0
2
0
0
2
0
0
0
0
0
0
1
2
1
1
0
0
2
1
2
2
1
0
2
0
1
0
2
0
1
2
1
1
2
0
0
0
2
2
1
0
0
2
0
1
0
2
1
0
2
0
0
2
1
0
0
0
0
5
1
1
2
0
1
2
0
1
0
0
0
0
0
2
0
2
1
2
0
0
0
0
2
3
0
0
0
0
2
2
0
0
1
0
0
2
0
1
2
0
0
0
2
0
3
1
0
0
0
1
0
0
0
0
1
0
2
1
3
3
2
0
0
1
0
0
1
2
0
2
2
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
5
1
0
0
2
0
1
0
0
0
0
0
1
1
0
2
0
0
0
1
0
0
0
2
0
0
1
0
0
1
0
2
0
0
0
0
0
2
3
1
0
1
0
1
1
0
0
0
0
1
1
0
0
1
0
2
0
0
0
1
1
0
1
0
1
2
1
0
0
0
2
1
1
1
0
0
0
0
0
1
1
2
2
0
1
1
0
2
0
0
2
1
2
2
0
1
0
0
0
0
0
1
0
0
3
2
0
1
0
2
0
0
0
0
2
2
0
1
0
1
1
0
1
0
0
1
0
0
0
0
0
0
1
0
3
0
0
0
1
0
1
0
0
1
0
0
2
6
0
2
0
0
0
0
0
0
1
1
2
0
1
2
0
1
2
1
1
1
0
0
0
0
0
1
2
1
0
2
2
0
0
2
0
0
0
2
1
0
1
0
2
2
0
1
2
1
1
0
0
2
0
0
0
1
0
1
0
1
0
1
1
0
0
0
2
1
3
0
1
0
0
1
1
1
0
1
1
0
2
2
2
1
0
2
2
1
1
0
1
0
2
0
2
1
1
0
0
2
1
2
0
4
0
0
2
0
0
2
0
2
0
1
0
1
0
1
2
1
3
1
0
0
0
1
1
0
1
0
0
0
0
0
1
2
2
0
0
1
1
1
0
0
0
1
0
0
0
0
2
0
0
2
0
0
1
0
2
0
1
1
2
0
0
0
1
2
1
2
1
0
1
0
0
0
0
2
0
0
0
1
0
2
0
1
0
0
0
0
1
1
1
2
0
2
0
1
2
0
1
1
0
0
0
2
0
1
1
1
0
0
2
1
2
0
1
2
1
0
0
2
1
2
1
0
1
2
0
0
0
2
1
2
0
0
2
0
0
2
2
0
0
0
1
0
2
2
0
1
2
0
1
1
1
1
0
0
0
0
0
2
2
1
1
3
2
1
0
0
0
1
0
3
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
1
0
0
1
1
2
1
0
0
1
2
1
0
1
1
2
1
2
0
0
0
0
2
0
0
0
0
1
0
0
1
1
2
0
1
0
0
0
0
14
0
0
1
0
0
3
2
1
0
2
2
2
1
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
2
1
1
2
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
2
0
0
1
0
2
2
0
0
0
1
0
0
0
1
1
0
1
1
0
0
1
1
0
2
1
2
1
0
1
0
0
2
1
0
1
1
2
1
2
2
0
2
2
1
0
1
0
0
3
0
1
0
0
1
0
0
0
1
0
1
2
2
1
0
0
0
3
0
1
2
0
2
0
1
1
0
2
1
0
0
2
0
0
1
2
1
1
1
0
0
1
0
4
1
1
0
0
0
0
0
1
2
0
0
1
0
0
2
1
1
0
1
1
1
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
2
1
0
2
1
2
2
2
0
0
0
0
1
0
1
0
3
2
2
1
0
0
0
1
2
0
0
0
0
0
1
0
0
0
1
2
0
0
1
1
1
0
1
0
1
1
0
0
0
1
0
2
2
0
0
1
1
0
0
1
3
0
0
0
0
1
0
1
1
0
2
0
1
0
0
0
2
0
1
0
0
1
0
0
1
2
2
1
0
1
0
2
0
1
0
1
0
0
2
2
0
1
0
0
1
2
0
0
2
0
1
0
2
0
2
1
0
2
0
2
0
1
4
0
0
4
0
0
0
0
1
0
3
1
1
0
0
1
0
0
0
0
0
2
2
0
1
2
1
2
1
2
0
1
0
0
0
1
2
0
2
0
1
2
0
2
2
0
2
0
0
1
1
1
1
1
2
1
1
0
0
0
0
2
0
2
1
0
0
1
2
1
1
0
0
1
1
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
2
0
2
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
1
1
1
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
1
2
2
1
0
1
0
0
0
0
2
2
1
0
0
1
0
4
0
1
1
1
2
0
0
1
2
0
0
0
0
0
1
2
2
0
0
1
0
0
0
1
1
0
0
0
1
1
1
0
0
0
1
1
0
1
0
0
0
3
1
1
1
0
1
1
0
0
2
0
1
0
0
0
0
0
0
0
2
1
1
0
1
0
0
2
0
2
1
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
2
0
1
2
1
1
0
0
0
2
1
1
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
1
3
1
1
0
0
1
0
1
0
0
0
1
1
1
1
2
1
1
1
0
1
1
2
0
0
3
1
1
0
0
1
2
2
1
0
0
2
2
2
1
1
0
0
0
2
2
2
0
0
1
2
1
2
1
1
0
1
1
0
0
0
1
0
0
2
0
0
1
2
1
1
2
2
1
0
0
0
0
2
0
0
2
3
0
2
1
2
0
0
0
0
0
0
1
2
0
2
2
2
0
1
2
1
1
1
0
2
1
0
0
0
0
0
1
0
2
2
0
0
1
1
1
0
0
1
0
0
2
1
1
1
0
0
2
0
1
2
0
0
1
1
0
6
0
0
0
0
2
1
0
1
0
0
0
0
0
0
1
1
0
2
2
2
0
0
0
1
0
0
1
0
1
0
0
0
1
0
2
2
0
0
0
1
2
1
1
1
1
1
0
0
1
1
0
0
2
0
2
0
2
2
1
0
1
0
2
0
0
0
0
1
2
0
0
0
0
2
2
0
1
0
0
2
0
1
1
0
0
0
0
2
2
1
0
1
0
0
0
1
0
1
0
1
0
1
0
0
0
0
1
0
1
0
1
1
1
1
2
0
1
1
2
1
1
0
0
1
0
2
1
0
2
0
0
1
1
0
1
2
0
2
1
0
1
0
1
0
0
1
2
0
0
0
2
0
0
1
2
0
1
1
5
0
0
0
2
0
1
0
1
2
0
2
1
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
1
0
1
2
1
2
0
2
2
1
1
0
3
0
2
0
1
1
0
2
1
1
1
2
1
2
1
0
2
3
0
0
0
0
1
0
1
0
2
2
0
0
0
0
0
0
2
0
0
1
2
3
0
0
0
0
1
0
1
0
1
0
2
0
0
0
0
11
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
2
1
2
0
0
1
0
0
1
1
0
1
0
1
0
0
0
0
0
0
1
1
2
0
2
2
1
1
2
1
2
1
0
1
0
0
0
0
1
3
0
0
2
2
0
2
2
0
0
2
2
0
1
1
0
0
0
0
1
1
2
0
2
0
1
2
0
1
0
1
0
0
1
0
1
0
0
0
0
1
0
1
1
0
0
0
0
1
1
0
0
2
2
0
2
1
0
0
0
0
0
1
1
0
2
1
3
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
3
2
0
0
1
0
3
1
0
0
0
0
0
1
0
1
1
1
1
2
0
2
2
0
1
0
2
1
2
2
0
1
0
2
0
1
0
0
1
0
0
0
0
1
0
2
0
0
0
1
0
1
1
2
1
1
0
0
0
1
0
2
1
1
0
0
1
1
1
1
3
0
1
2
1
1
0
2
2
2
0
0
2
0
0
2
1
1
0
0
0
1
0
2
3
0
0
2
1
0
1
0
1
0
0
2
1
1
0
0
1
0
4
2
0
0
0
0
1
1
0
1
0
0
2
1
1
1
0
0
0
0
0
1
0
0
1
0
0
2
0
0
2
0
1
0
2
0
1
1
2
2
2
2
0
1
1
0
1
0
0
0
2
2
1
1
1
1
0
0
0
1
0
0
2
0
2
0
0
1
0
2
1
0
0
1
0
0
0
2
1
1
1
1
1
0
1
0
0
1
0
1
2
0
1
0
0
0
2
0
1
0
1
0
0
0
1
1
0
0
2
0
1
2
2
1
1
1
0
0
0
2
2
0
2
0
1
2
0
1
1
0
0
2
1
1
2
1
1
2
2
2
0
0
2
0
0
2
2
3
0
0
0
2
1
1
2
0
0
2
2
0
0
1
1
1
0
0
2
0
0
0
0
2
1
0
2
1
0
1
0
0
0
1
2
0
3
1
0
1
0
2
1
2
1
1
0
1
0
0
2
1
2
2
1
2
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
1
1
2
1
0
1
0
1
0
0
2
0
2
0
0
1
1
2
0
0
2
1
2
0
2
0
1
2
2
2
3
2
1
0
0
1
0
0
2
0
0
0
2
0
0
2
0
2
1
2
0
1
0
1
0
1
1
2
2
0
0
2
0
0
3
0
2
1
0
0
0
0
0
0
1
2
1
2
0
0
1
1
0
0
2
0
2
1
0
0
0
2
0
0
0
0
1
2
2
0
1
2
2
2
0
0
0
2
0
1
0
0
0
2
0
1
0
2
1
1
1
0
0
2
1
2
1
2
1
0
1
2
0
2
0
2
0
1
2
1
0
1
0
0
2
2
0
0
0
1
0
2
2
0
1
0
1
0
2
1
1
1
2
0
0
0
1
0
0
0
0
0
2
1
2
4
1
1
1
1
1
2
1
1
2
1
3
2
0
1
0
1
0
2
0
0
1
0
0
0
1
1
0
1
1
1
0
0
1
1
1
1
2
0
0
2
0
1
0
0
2
0
2
1
0
0
1
0
1
0
0
1
1
0
0
0
0
0
2
0
2
1
2
0
1
1
1
0
1
2
2
0
0
0
0
0
0
0
1
1
1
3
1
2
0
1
1
2
0
1
2
2
2
2
1
4
1
1
1
0
0
0
1
0
1
2
1
1
0
1
0
2
1
0
0
0
2
1
0
0
2
0
0
1
1
1
0
0
1
2
2
1
0
0
1
1
2
0
0
0
0
2
1
1
1
1
1
2
2
0
0
0
1
1
2
0
0
2
2
0
0
0
0
1
2
0
0
0
0
0
2
0
1
2
0
5
0
1
2
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
3
2
2
1
0
0
1
1
2
1
0
2
2
0
2
2
0
1
0
0
2
1
2
0
2
2
2
0
1
1
2
0
2
0
0
0
0
2
0
1
0
0
1
0
0
0
1
0
0
1
0
0
3
0
0
0
0
2
2
0
1
0
1
1
0
2
0
1
1
0
0
2
0
0
1
3
3
2
2
0
1
2
2
1
1
1
1
1
0
2
1
1
0
0
0
0
1
0
0
1
1
0
0
1
0
0
1
2
0
2
0
2
0
2
0
0
2
1
3
0
1
0
1
1
0
1
2
0
0
1
0
3
2
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
2
1
1
0
0
2
1
0
0
1
0
1
0
2
3
1
1
0
0
2
1
0
0
1
1
2
2
0
0
2
0
1
0
0
0
1
0
0
1
1
0
0
2
0
1
1
2
1
2
0
1
2
0
2
0
1
0
1
0
2
2
0
0
0
0
1
1
2
0
2
0
0
0
1
0
2
2
0
1
1
0
2
1
0
1
2
0
1
0
0
0
1
0
0
2
2
2
0
0
0
1
2
1
0
2
1
0
0
0
3
0
0
0
1
0
2
0
3
0
0
0
1
2
0
0
0
0
0
1
0
2
0
1
3
1
2
1
1
2
2
0
1
0
1
0
1
0
1
0
1
0
0
2
1
0
0
0
0
2
0
0
1
1
1
2
0
2
0
0
0
0
1
2
0
0
1
1
0
1
1
0
1
2
0
0
1
1
1
0
2
0
0
2
2
1
0
2
0
0
1
0
0
2
0
2
0
1
0
2
0
2
2
0
0
1
1
0
2
0
1
2
0
0
0
0
0
0
1
1
1
0
0
1
1
1
0
0
1
0
2
0
0
0
0
0
0
2
0
0
1
2
0
0
0
2
0
2
0
0
0
0
0
0
1
1
2
2
0
0
1
0
0
2
1
0
1
0
0
0
0
1
2
0
2
0
0
0
1
2
0
0
2
0
0
0
1
1
2
2
0
2
2
0
0
1
0
1
0
1
2
2
2
0
1
2
0
2
0
0
0
2
0
0
1
0
0
0
0
1
0
1
0
1
2
1
1
0
1
0
0
1
1
0
0
2
2
2
1
1
2
1
2
1
0
1
2
0
0
0
0
2
1
0
2
1
0
1
3
2
0
2
0
0
0
2
1
0
0
1
1
2
0
1
1
0
0
3
1
2
1
0
1
0
0
0
1
2
2
1
0
0
2
2
2
0
1
1
3
5
1
0
1
1
0
0
1
0
0
2
2
0
2
1
2
0
0
0
2
1
1
2
2
2
2
0
0
1
1
2
0
0
0
0
0
0
0
0
1
0
0
2
2
1
1
2
0
0
2
2
1
0
1
0
1
0
0
1
1
0
1
0
2
0
0
1
0
1
1
2
0
1
2
1
1
0
2
1
0
1
1
2
1
1
0
0
1
1
1
0
0
2
0
0
2
1
0
2
0
0
0
0
0
3
0
1
1
0
0
2
0
0
1
2
2
2
0
1
1
3
2
1
1
1
1
3
2
0
1
2
2
0
1
0
0
0
0
1
0
0
2
0
0
0
1
0
0
1
0
0
2
0
0
0
2
0
1
2
1
1
0
1
1
0
0
0
1
2
0
2
1
1
0
0
0
0
2
2
5
0
0
0
1
2
0
0
0
1
0
1
2
0
2
1
1
1
0
1
2
0
0
0
4
0
2
1
0
0
2
1
0
2
2
2
2
1
0
0
1
2
2
0
0
0
0
0
0
0
0
2
0
0
3
2
1
0
1
0
1
0
0
1
2
1
2
2
1
0
2
2
0
0
1
0
0
0
1
1
1
0
0
2
0
1
0
1
0
0
0
0
2
0
2
0
1
0
0
0
1
0
1
0
0
0
1
1
2
2
1
0
0
0
0
0
0
1
2
0
1
1
0
0
1
1
2
1
1
0
1
0
0
2
0
1
0
1
0
0
2
0
1
2
0
0
0
2
0
0
0
0
1
0
1
1
2
1
1
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
2
2
0
0
1
0
0
0
0
0
2
0
0
0
2
2
2
0
2
1
0
1
0
0
0
1
0
0
0
0
1
0
0
1
2
4
0
1
1
1
0
0
0
0
0
2
2
2
0
0
1
0
2
0
1
2
1
2
2
0
0
2
0
2
1
0
1
1
0
0
1
0
1
1
0
1
2
1
2
1
1
1
2
0
1
0
0
0
0
0
1
0
2
1
3
0
0
0
0
0
2
1
2
2
0
0
0
0
0
1
1
0
1
1
2
0
3
1
2
1
0
0
1
0
0
0
2
0
0
1
0
2
0
0
0
2
1
0
0
1
0
1
0
0
1
0
1
1
1
1
2
0
1
0
1
1
0
0
5
1
0
1
0
0
2
0
0
1
2
2
0
0
0
2
1
0
3
2
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
3
0
0
3
2
2
1
1
0
0
0
2
2
2
1
1
2
0
0
1
2
0
0
0
2
0
0
1
2
1
1
0
1
0
0
1
2
1
2
2
0
0
0
1
1
0
0
0
1
0
0
2
1
1
2
1
0
0
0
2
1
1
2
2
0
3
1
0
2
0
0
2
0
1
0
0
0
0
1
1
0
2
0
1
0
0
1
1
1
0
1
0
0
2
0
2
0
0
1
1
1
0
1
0
0
0
1
1
0
0
0
0
2
2
0
2
0
2
0
2
2
1
0
0
1
2
0
0
1
1
0
1
0
0
1
12
1
1
2
0
0
0
1
2
1
1
0
0
0
0
1
0
0
0
2
1
0
0
1
1
1
0
1
2
2
2
0
6
1
2
0
0
1
0
1
0
0
4
2
1
0
0
0
2
0
2
0
0
2
2
0
1
2
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
2
1
1
1
0
1
0
2
0
1
1
1
2
0
0
1
0
0
2
2
0
0
1
2
2
2
0
1
1
2
1
2
1
2
2
2
0
0
3
1
1
0
0
0
0
1
0
2
3
0
1
2
0
2
0
0
2
1
1
1
0
0
2
0
0
1
0
1
0
1
0
0
1
0
0
2
1
0
2
0
1
1
2
0
2
4
0
2
0
0
0
0
0
1
0
1
0
0
0
2
2
1
0
0
0
1
2
0
0
0
2
1
0
0
0
0
4
0
1
1
0
0
1
0
1
0
0
1
1
1
2
2
1
1
1
1
1
0
1
1
0
1
0
1
0
2
0
1
1
1
0
0
1
1
0
0
1
0
1
0
2
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
2
0
1
2
2
1
1
0
1
0
1
0
2
0
2
0
0
0
1
0
1
0
2
2
0
3
1
2
2
1
1
0
0
0
1
2
1
0
0
1
2
1
1
1
0
0
0
1
1
0
1
0
1
1
2
0
2
0
0
2
0
0
1
0
0
2
0
1
0
2
0
1
2
0
1
1
1
2
0
2
2
1
2
0
0
2
2
0
2
0
0
0
0
2
1
1
2
0
0
1
1
0
0
0
2
2
1
1
0
0
0
0
0
2
1
2
1
0
0
3
2
1
0
2
0
0
0
1
0
2
2
0
0
1
1
3
1
0
1
0
0
2
1
0
0
1
1
0
0
2
2
0
0
0
0
1
0
2
0
1
1
1
0
2
0
0
2
0
0
1
0
1
0
0
0
0
0
1
2
0
0
1
1
1
2
5
0
0
1
0
0
2
0
0
0
0
1
0
1
0
1
0
1
0
0
1
1
0
0
0
0
2
1
1
1
1
0
0
0
1
0
0
7
1
2
1
1
2
2
1
1
0
1
2
1
2
0
1
1
0
0
1
0
0
1
0
1
0
1
0
2
0
0
1
1
1
2
0
0
0
1
1
1
0
0
1
0
2
0
0
0
0
1
1
0
0
0
0
0
2
1
2
2
1
2
2
0
2
0
0
0
1
2
0
1
0
2
1
1
1
0
1
0
2
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
1
0
1
1
1
0
2
2
0
0
1
0
1
0
1
0
2
0
0
0
1
1
1
0
0
1
0
0
1
2
0
0
0
0
1
1
2
1
2
0
2
1
1
0
1
1
1
0
0
2
2
1
1
0
0
2
1
1
0
2
2
1
0
2
1
1
2
0
1
3
0
0
1
1
0
0
0
1
1
1
0
0
1
0
0
1
2
1
1
0
2
3
0
1
0
1
1
1
0
0
2
2
0
0
0
2
1
1
1
1
0
2
1
1
0
1
2
2
0
1
0
2
1
0
2
0
1
0
0
0
0
1
1
0
2
1
0
0
3
0
0
1
1
0
1
1
0
0
0
0
1
0
0
0
2
0
0
0
1
2
0
1
1
0
0
2
1
0
0
0
0
0
0
1
0
1
0
2
0
1
0
1
1
0
0
0
2
0
2
2
2
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
1
0
2
2
0
2
0
1
0
0
1
1
2
0
1
2
1
1
2
2
1
1
0
1
2
0
1
1
2
0
1
0
0
0
0
2
0
2
1
1
0
1
0
0
1
1
0
0
2
0
0
0
1
0
1
1
2
0
0
1
1
2
0
0
0
1
2
2
2
1
2
0
0
0
2
1
0
3
1
0
1
0
2
2
0
1
1
0
2
0
1
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
1
0
1
0
1
1
0
0
2
1
1
1
0
2
2
0
0
0
2
0
0
2
3
2
0
0
2
0
0
1
0
0
0
1
0
0
1
0
0
1
1
1
1
0
1
0
1
1
2
2
1
1
2
3
0
2
0
0
0
0
1
0
0
0
2
0
2
1
2
0
2
1
1
0
0
1
0
1
2
1
1
1
1
0
1
2
0
2
0
0
0
1
0
1
1
0
0
1
0
0
0
1
0
0
0
2
0
0
0
2
1
1
0
1
0
0
1
1
1
3
2
1
0
0
0
0
1
0
0
0
1
2
0
0
0
0
1
2
1
1
0
2
1
2
0
2
1
2
1
1
0
0
2
2
1
1
1
0
0
1
0
1
1
2
0
0
0
0
0
1
1
0
0
0
1
1
0
0
2
1
0
2
2
2
0
2
1
0
0
1
1
1
2
2
2
0
0
0
1
1
0
1
1
2
0
1
2
2
2
2
0
2
0
2
1
1
1
0
2
0
0
0
2
1
1
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
2
0
2
2
1
2
1
1
2
2
3
1
0
2
0
1
0
0
1
0
0
0
1
0
0
0
1
2
0
0
1
1
0
1
2
0
1
0
0
1
0
0
1
0
0
0
0
0
1
1
1
2
2
0
0
2
0
2
0
1
2
0
0
0
0
0
1
2
0
0
1
0
0
1
0
0
1
1
2
2
2
0
1
0
0
2
0
1
2
0
1
2
0
1
0
2
0
0
1
1
1
1
0
1
2
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
2
2
0
2
0
0
1
0
0
0
1
0
0
0
0
2
0
1
2
1
1
1
0
0
2
0
1
0
0
0
1
0
2
1
1
0
2
0
1
0
0
1
1
1
0
0
0
1
1
2
0
1
1
0
2
0
0
0
1
1
0
2
1
2
2
0
0
0
0
0
0
1
0
1
1
1
0
1
0
1
0
0
0
0
1
1
0
0
0
2
0
1
1
0
3
0
1
0
1
0
2
2
1
1
1
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
4
2
1
2
0
1
2
0
0
2
1
0
2
4
3
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
1
0
1
0
0
1
0
2
0
0
1
0
1
0
1
0
2
1
0
0
1
1
0
2
1
0
0
0
1
0
1
0
0
2
1
1
2
1
0
1
1
1
0
0
1
0
0
0
2
1
1
0
0
2
0
2
2
0
0
0
2
2
2
1
0
0
0
2
0
1
0
0
1
0
1
0
2
1
0
1
1
0
1
0
0
1
1
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
1
0
0
2
1
0
2
2
0
0
0
1
0
0
0
2
0
0
0
0
1
1
0
1
0
0
2
0
2
1
0
1
0
0
0
3
2
2
0
2
1
0
0
1
2
1
0
0
1
0
1
0
1
0
0
14
2
1
0
1
1
1
0
0
2
1
0
2
1
2
2
2
0
0
2
2
0
0
0
2
1
0
1
0
0
1
0
0
0
1
1
1
1
0
1
1
2
0
1
1
1
2
0
0
0
1
0
0
0
0
0
1
1
1
2
1
0
0
2
0
0
0
0
1
1
0
2
1
0
1
1
0
1
1
1
2
2
1
2
0
1
0
2
0
0
0
2
2
0
1
0
1
0
1
0
1
1
2
0
0
0
0
2
0
2
2
1
2
2
3
0
0
2
0
0
0
1
1
5
0
0
2
0
0
2
1
1
1
0
0
0
0
1
0
2
0
0
1
0
0
0
1
1
2
2
1
0
0
0
0
0
0
1
0
1
0
1
1
2
0
1
0
1
2
0
0
2
1
1
0
0
1
0
0
0
0
0
2
2
0
0
2
0
1
0
2
0
1
0
0
1
0
0
0
0
1
1
2
0
0
0
0
0
0
0
5
2
1
2
2
0
1
0
2
0
1
2
1
0
1
0
0
0
2
0
0
0
1
0
2
0
0
1
2
0
2
1
0
0
0
2
2
0
1
2
1
2
0
0
0
0
2
0
1
0
2
2
0
2
0
0
2
1
2
1
1
0
0
0
1
1
1
2
0
0
1
1
2
0
1
2
1
2
1
0
2
1
1
2
0
1
0
2
0
0
0
1
1
0
2
2
0
0
0
0
0
1
0
0
2
1
0
1
0
2
0
1
1
3
1
0
2
0
2
1
1
2
0
0
0
0
1
0
3
0
0
0
0
2
1
0
2
0
0
0
1
0
0
0
1
1
0
1
0
1
0
2
0
1
1
2
0
2
0
0
0
2
0
2
1
0
0
1
0
1
1
0
1
1
1
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
2
0
2
0
0
0
2
1
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
1
2
2
0
0
1
0
0
0
2
0
0
2
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
2
1
0
1
0
0
0
2
1
0
1
0
2
0
0
1
0
1
0
1
0
0
0
0
2
0
2
0
0
0
0
0
3
1
2
1
0
2
0
0
0
0
1
0
2
1
0
0
2
2
0
2
0
0
0
1
2
1
2
2
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
2
0
0
1
2
0
1
1
0
2
1
1
1
2
0
0
1
0
0
1
1
0
5
1
0
1
1
0
1
0
1
0
1
0
0
0
1
0
2
1
2
0
1
2
0
0
0
0
1
1
1
0
0
1
1
1
0
0
0
0
0
1
0
0
2
0
0
1
1
0
0
0
0
2
1
1
0
1
2
0
1
0
0
0
0
0
0
2
0
2
1
2
1
0
2
2
1
0
2
1
0
0
0
0
2
2
1
0
0
1
0
2
1
0
1
0
2
1
0
0
0
0
1
0
3
1
2
0
0
2
1
0
2
0
1
0
1
0
0
1
1
0
2
2
0
2
1
1
1
1
0
1
0
1
2
0
2
0
0
1
0
2
0
0
1
0
1
2
1
2
0
2
0
3
0
0
0
2
1
1
2
1
0
0
3
0
0
0
2
0
0
0
2
0
0
0
2
1
1
0
2
0
0
1
0
2
1
0
3
2
1
1
1
0
0
1
0
1
0
0
0
2
2
1
0
1
1
0
1
1
0
1
0
0
2
0
0
1
1
0
0
2
0
1
0
0
0
0
0
1
2
1
0
2
1
0
1
1
0
0
0
1
1
0
2
0
0
1
0
1
1
0
0
0
0
2
0
3
0
0
1
1
1
0
0
2
1
1
0
1
0
1
0
2
0
0
0
1
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
3
0
1
1
1
0
0
2
1
2
0
1
0
0
1
1
1
1
1
1
2
1
2
0
0
1
0
0
0
1
0
1
0
0
1
2
0
1
1
2
0
2
1
0
0
1
0
1
1
0
2
1
0
1
0
1
1
2
1
0
0
1
0
2
0
0
1
0
0
0
1
2
0
0
0
1
0
0
0
2
0
1
2
0
1
2
1
0
1
0
0
1
0
1
0
0
1
1
0
2
6
1
0
0
4
0
1
0
1
0
0
2
2
1
0
0
1
1
0
0
1
2
1
2
2
1
0
0
1
0
1
1
2
0
0
0
0
0
2
1
0
3
0
2
0
0
1
2
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
2
0
0
2
1
1
0
0
0
1
0
2
2
2
0
1
0
1
0
1
1
2
2
0
1
1
1
1
0
0
0
1
0
3
0
0
0
2
0
0
0
0
0
3
0
0
0
1
2
0
1
0
0
0
1
0
0
0
0
2
1
3
1
1
0
1
2
0
0
0
0
0
1
0
0
2
0
0
1
2
2
0
1
2
1
1
2
2
1
0
1
0
0
2
2
0
2
0
2
1
1
0
2
1
1
0
0
1
1
0
2
0
0
2
0
1
0
0
0
1
1
1
1
0
1
1
0
0
1
2
0
0
8
3
0
0
1
0
1
2
0
1
1
1
0
1
0
0
2
0
0
0
1
1
0
0
2
2
1
1
2
1
1
0
0
1
1
1
5
0
0
1
1
0
0
3
1
0
0
0
0
0
0
0
0
1
0
0
2
0
1
2
1
1
0
1
1
0
0
0
2
1
2
1
0
2
1
0
0
2
2
1
1
2
0
0
1
1
0
1
2
0
0
1
2
0
0
0
1
0
2
2
0
0
0
1
1
0
0
0
1
2
1
0
2
0
1
1
0
1
1
1
0
0
5
0
1
2
1
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
3
1
0
0
2
1
0
0
1
1
0
0
0
0
2
2
0
0
0
2
0
1
2
1
0
0
0
1
0
0
0
2
0
2
2
0
2
0
1
0
0
1
1
0
0
1
0
0
2
2
0
2
1
1
0
0
2
1
0
1
0
0
0
0
0
2
0
1
2
0
0
1
1
1
1
0
1
0
0
3
0
0
1
2
0
1
1
4
0
0
0
0
2
0
0
1
2
2
0
0
1
0
0
0
1
0
0
0
2
2
1
0
0
1
0
1
2
1
2
0
0
0
1
2
0
0
2
3
1
1
0
1
2
2
2
0
0
1
1
0
2
0
1
2
1
0
4
3
0
0
2
2
1
1
0
2
2
1
0
0
2
1
1
1
0
6
0
2
1
1
2
0
1
1
0
0
2
1
0
0
0
0
2
2
0
0
2
2
3
1
0
0
2
0
2
1
0
2
0
1
1
1
2
0
0
1
0
0
0
3
1
1
1
0
2
1
0
1
0
3
0
0
1
0
1
2
1
2
2
2
1
0
1
1
1
1
0
0
0
0
1
1
1
2
2
2
1
2
0
1
0
0
0
1
2
0
2
0
1
1
0
1
0
2
1
0
1
0
1
2
1
2
0
0
0
2
0
1
1
0
2
0
3
1
2
1
1
0
2
1
1
1
0
0
0
2
2
2
0
0
0
0
1
2
0
2
0
2
2
1
0
2
0
0
1
0
0
0
2
3
1
0
1
0
0
1
0
0
0
1
1
0
0
1
1
0
2
1
0
1
2
0
0
1
0
0
2
0
2
0
2
0
0
1
0
2
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
1
0
1
1
0
0
2
0
0
2
0
0
2
0
0
1
1
0
1
0
1
0
2
2
2
1
2
0
0
1
0
1
0
0
2
1
2
1
1
1
0
0
0
0
0
0
0
2
2
1
1
0
2
0
2
1
2
1
0
0
2
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
1
1
1
1
1
0
0
1
0
1
0
2
0
1
0
0
0
0
2
1
0
2
0
1
0
0
0
1
0
0
0
2
0
0
1
0
0
0
1
1
0
0
0
0
1
2
0
1
0
0
1
1
0
0
0
2
0
1
0
0
0
0
0
2
0
0
3
1
0
1
0
0
1
1
0
1
2
0
0
2
0
4
0
0
1
0
1
1
0
1
1
0
0
3
1
2
1
1
0
1
0
0
1
0
0
2
0
0
2
2
1
1
0
2
2
0
0
2
2
0
1
0
0
1
1
0
0
1
0
0
1
0
1
2
2
1
0
1
1
0
0
2
2
1
0
2
0
1
0
1
0
0
1
0
2
0
1
0
2
1
3
0
2
1
2
2
2
1
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
2
0
1
1
2
1
2
2
0
2
0
0
0
2
1
0
0
2
1
0
1
0
0
0
0
1
2
0
0
1
0
2
2
0
0
2
2
1
1
2
0
2
0
1
1
1
0
0
1
1
0
0
0
2
0
0
0
0
2
1
1
1
1
0
2
0
0
1
1
0
0
0
0
1
0
2
1
0
1
1
0
2
1
1
1
2
1
0
1
2
0
2
1
2
0
2
1
1
0
1
0
2
0
0
0
1
2
0
1
1
0
1
0
2
1
1
1
2
1
0
1
1
1
1
1
0
0
1
0
1
1
2
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
1
0
1
0
1
1
1
0
0
2
2
0
1
2
1
1
2
1
2
0
0
0
2
0
0
1
2
0
2
2
1
1
0
0
0
0
0
2
2
0
2
2
0
1
1
0
0
0
0
1
0
1
0
1
1
1
0
0
0
0
1
0
1
1
0
1
0
0
1
0
2
0
0
0
0
2
0
1
0
0
0
1
3
0
1
1
0
0
2
1
1
0
0
0
1
1
0
1
0
2
2
1
0
0
1
2
1
2
1
1
0
0
2
1
2
1
1
2
2
2
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
3
0
2
1
0
0
0
0
2
2
0
0
1
0
3
2
0
2
0
0
1
1
0
0
0
0
2
0
1
0
0
0
1
2
2
3
1
1
1
0
2
1
1
0
1
0
0
1
0
1
0
2
1
1
1
0
2
2
0
2
1
2
1
1
1
0
1
0
0
0
1
0
0
1
3
1
1
2
2
0
0
0
2
0
2
0
1
1
2
0
2
1
0
1
2
0
1
0
1
0
1
0
1
2
0
2
1
0
1
0
1
0
0
0
2
0
1
1
11
0
2
1
2
1
0
0
0
2
0
1
0
1
0
0
1
2
0
1
1
2
1
0
0
0
0
0
1
2
0
2
0
1
2
0
0
0
1
0
0
0
1
0
0
2
0
0
1
1
0
0
0
1
0
0
2
1
0
1
0
0
0
1
0
1
2
2
0
0
2
1
0
2
0
0
2
0
0
0
0
0
0
0
2
2
0
0
1
0
3
2
0
1
0
0
0
2
0
1
0
1
0
1
2
1
0
0
1
0
0
0
0
3
1
1
2
0
2
0
0
1
2
1
0
0
0
0
2
0
1
1
0
0
1
0
0
0
1
0
2
1
1
2
1
0
0
2
0
0
2
2
0
0
2
1
0
1
0
2
2
0
0
2
1
0
1
0
1
1
0
1
1
1
0
1
2
0
0
1
2
0
0
0
2
0
1
0
1
0
0
2
0
0
0
0
2
2
1
1
0
1
1
2
0
0
2
0
0
2
1
0
0
1
0
1
0
1
0
1
1
0
0
1
2
1
2
0
1
0
0
1
0
1
1
0
2
0
1
1
1
1
1
0
0
1
0
0
1
1
1
1
0
0
1
1
0
0
0
0
2
0
0
0
0
0
1
2
2
2
0
1
1
1
2
0
1
1
2
0
0
0
0
0
1
1
0
1
2
1
2
0
0
0
0
1
0
0
2
1
0
3
1
0
0
2
0
1
1
1
0
0
0
0
1
0
2
1
1
0
2
1
1
0
2
0
0
0
1
0
1
1
1
1
1
1
0
0
0
1
1
0
2
0
0
0
0
1
0
1
0
1
3
0
1
0
0
2
1
0
0
2
1
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
1
0
1
8
0
1
2
2
1
2
0
0
0
2
2
0
0
0
0
0
0
3
1
0
2
0
2
2
0
2
0
0
1
2
0
0
1
0
1
1
2
1
0
0
0
0
0
2
1
2
0
0
1
0
0
3
2
0
0
0
0
0
2
0
2
0
0
2
0
1
0
1
2
0
1
0
0
0
5
2
1
2
0
1
0
2
0
0
0
0
0
1
0
0
0
1
1
0
0
1
1
0
2
1
0
0
0
0
0
0
0
0
1
0
1
0
0
2
1
2
3
1
0
0
0
0
1
0
1
1
0
0
1
0
1
1
1
4
0
0
0
0
0
0
0
0
0
0
0
1
1
2
2
2
0
1
0
0
0
2
0
0
0
1
0
2
0
0
2
2
0
1
0
1
2
0
1
0
0
0
0
1
0
0
1
0
0
1
0
2
0
0
1
0
0
1
0
0
1
1
2
0
0
0
0
0
2
0
1
0
0
0
0
0
1
1
0
1
0
2
0
0
2
2
0
1
1
0
1
0
0
0
0
0
0
1
2
2
0
2
0
0
1
0
0
0
1
0
1
1
2
0
1
0
1
2
1
0
2
0
0
2
1
0
3
1
1
0
1
0
1
0
1
0
2
1
1
0
1
1
1
0
1
1
1
1
0
0
2
1
0
1
2
0
0
1
0
0
2
1
2
0
1
2
3
1
1
0
0
2
1
0
0
0
5
1
0
1
2
0
2
0
2
1
1
3
0
0
1
0
1
0
1
1
2
1
1
3
0
0
0
0
1
1
2
1
2
0
3
2
0
1
0
0
0
2
1
0
1
0
1
0
1
1
2
0
0
0
2
1
1
0
0
2
1
1
1
2
0
2
0
2
0
0
2
0
2
1
2
1
0
1
1
0
0
1
2
1
0
1
1
1
1
1
1
0
0
1
2
1
0
1
0
0
0
1
2
0
1
0
0
0
2
0
1
0
1
0
2
1
1
1
0
1
1
2
1
1
0
0
2
1
0
3
0
0
0
2
0
2
2
0
1
1
0
1
0
2
0
0
2
1
1
2
1
0
0
0
2
1
1
1
2
0
1
0
1
1
0
1
1
2
0
2
1
0
2
0
0
0
1
0
1
0
0
0
0
0
0
2
0
3
1
1
1
0
1
0
0
0
0
0
1
0
1
1
1
1
0
1
2
0
0
2
1
2
0
1
0
1
0
0
0
0
2
3
4
0
2
0
2
2
2
2
2
0
2
1
0
0
0
1
1
0
0
1
1
1
0
2
0
0
0
0
0
0
1
0
1
0
2
0
2
0
2
0
0
0
0
2
0
2
2
0
0
1
2
2
0
1
2
1
0
2
0
0
1
1
2
0
0
2
1
2
1
1
1
0
0
0
1
1
0
1
2
0
1
2
0
0
1
1
2
0
1
1
1
2
2
1
2
2
1
1
2
1
1
0
0
1
0
2
0
0
0
1
2
1
1
0
0
0
0
0
1
1
1
0
1
1
3
2
1
1
2
0
0
1
0
0
0
0
3
0
2
0
0
1
0
1
0
2
2
0
2
1
1
0
2
2
1
0
0
1
0
1
0
2
1
1
0
0
1
2
1
2
2
0
0
2
0
1
0
0
1
0
0
1
0
1
1
0
1
2
2
2
1
2
2
1
0
0
1
0
1
0
0
0
2
2
0
1
0
2
0
2
2
1
1
0
1
0
0
2
0
1
1
2
1
1
1
2
2
0
0
0
0
1
0
1
1
1
2
0
2
2
1
0
0
0
0
0
1
1
2
2
0
1
0
0
0
1
1
0
1
1
5
1
0
0
0
0
0
1
1
2
1
0
1
1
1
0
2
1
0
1
2
0
0
0
1
0
0
0
1
2
0
0
1
0
0
1
0
0
0
0
1
2
2
3
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
2
0
2
2
2
0
2
2
2
0
0
2
0
1
1
0
1
0
3
2
1
1
0
1
0
0
0
1
0
2
1
0
2
1
1
0
0
2
1
1
0
0
0
2
0
1
2
0
4
1
0
0
2
0
0
1
0
0
1
1
0
0
1
0
1
0
1
0
0
3
0
1
0
0
0
2
0
1
0
1
1
0
2
1
4
0
1
2
0
0
1
2
2
0
2
1
2
0
2
0
0
0
1
1
0
0
0
0
0
0
2
1
0
0
1
0
2
1
1
0
0
2
0
0
0
2
1
0
0
0
2
0
1
0
6
1
0
0
0
1
0
0
1
0
0
0
6
1
1
0
0
2
1
0
0
0
0
0
1
0
0
0
0
1
2
1
2
0
1
0
3
2
0
0
0
0
1
0
1
0
1
0
0
1
2
0
0
0
0
1
0
1
0
0
1
1
1
1
1
0
0
0
2
0
1
1
1
0
1
1
2
0
0
0
2
0
2
0
1
1
0
0
1
0
2
1
2
2
2
1
0
2
0
1
0
1
2
0
2
0
0
1
1
0
0
1
1
0
1
1
1
0
1
0
0
1
0
0
0
0
2
3
0
1
2
1
2
1
0
0
0
1
1
0
0
2
1
0
1
1
0
0
1
2
0
0
1
2
1
2
1
0
1
2
2
0
0
2
0
0
0
1
1
1
3
1
0
0
2
0
0
1
1
0
1
0
2
1
0
0
0
1
0
1
0
0
0
0
0
0
2
1
0
1
2
1
1
0
0
0
0
0
0
2
1
3
1
1
2
1
0
0
1
2
2
1
1
0
0
2
0
0
1
2
1
2
1
0
2
1
1
2
0
2
2
0
2
1
2
2
0
0
1
0
2
2
0
2
0
0
1
0
1
1
1
1
2
0
1
1
0
1
0
0
1
1
0
2
1
0
0
2
1
0
1
0
0
0
1
1
1
2
2
2
0
1
0
0
0
0
0
0
0
2
0
1
1
1
0
1
0
2
1
0
0
1
1
0
1
0
2
0
0
0
2
0
0
1
2
2
0
2
2
1
1
0
0
2
0
2
0
0
0
2
0
1
0
0
0
1
1
1
0
0
0
1
2
1
0
1
0
0
1
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
1
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
2
1
1
0
0
1
0
1
2
0
0
1
1
1
2
2
0
0
0
0
1
2
2
0
0
2
2
0
2
1
1
1
1
0
1
1
0
0
2
1
0
1
2
0
0
0
0
2
3
2
1
1
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
2
2
0
0
1
0
1
0
1
2
1
1
0
1
0
0
1
1
1
0
2
0
1
1
0
3
2
1
1
0
0
1
1
0
0
1
1
2
0
0
1
3
1
0
0
0
2
0
0
1
0
0
1
1
0
1
1
0
2
1
0
1
0
0
1
2
2
0
1
1
1
2
2
1
0
1
1
2
0
2
0
2
0
0
0
1
0
2
0
1
1
2
0
1
1
2
0
2
2
1
0
0
1
0
0
1
1
0
0
2
0
1
1
0
0
0
2
0
0
2
0
0
1
0
0
0
1
2
1
2
1
1
2
3
1
1
1
0
0
1
0
1
1
0
0
0
0
0
0
0
1
1
0
2
0
1
0
1
0
1
0
2
0
0
2
0
0
0
1
0
0
0
1
1
0
2
2
0
2
1
1
0
1
0
0
0
0
0
1
0
0
3
0
1
2
2
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
2
0
0
0
1
1
4
2
0
1
1
0
1
1
2
2
2
0
0
2
2
1
4
1
1
2
0
0
1
1
1
0
1
2
1
2
1
0
0
0
0
1
2
0
0
0
2
0
1
0
1
3
1
0
0
0
1
2
0
2
0
0
0
0
1
0
0
0
0
1
0
1
2
2
1
1
0
0
1
1
0
1
1
0
2
4
2
2
0
2
2
1
1
0
2
1
0
0
0
1
0
0
2
0
1
1
1
2
2
0
1
0
1
2
1
2
0
1
0
0
0
1
2
0
2
2
2
0
2
0
0
1
0
2
0
0
0
1
0
0
0
1
1
2
1
0
1
0
1
0
1
0
1
0
0
1
0
2
1
0
2
1
0
0
0
1
0
0
1
2
0
1
3
0
0
0
0
1
1
0
2
2
0
0
0
1
1
0
1
0
1
1
1
0
0
1
1
0
0
0
1
1
1
1
2
2
2
3
2
2
1
2
2
2
1
0
0
1
2
0
0
1
0
1
2
1
0
1
3
0
1
0
1
0
0
1
1
1
0
2
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
2
1
0
1
1
2
1
1
0
1
0
2
0
1
0
0
3
0
0
1
1
0
1
1
0
1
1
1
2
1
1
1
0
2
1
3
0
1
1
2
2
0
2
0
0
2
1
2
0
0
0
0
0
0
0
2
0
0
1
0
3
4
1
0
2
0
1
1
0
2
6
0
1
0
0
0
1
1
0
0
0
0
1
1
1
1
0
0
3
2
0
0
0
0
0
0
0
0
1
0
0
2
0
2
1
0
2
0
0
2
0
0
0
1
0
1
1
0
1
0
0
0
1
1
2
1
0
0
0
1
0
1
2
2
0
0
0
2
0
2
1
2
2
2
1
2
0
0
0
8
2
2
0
0
0
0
1
2
0
0
2
1
0
1
1
0
0
2
0
2
0
2
1
2
1
1
2
0
1
3
2
1
1
1
0
2
0
0
1
0
0
0
2
2
1
0
0
2
1
0
1
0
0
2
2
1
0
0
1
0
0
1
0
1
1
1
1
0
0
2
1
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
2
0
1
1
2
1
0
0
2
0
0
0
0
1
0
0
1
1
1
0
0
0
0
2
0
1
0
1
1
1
2
0
0
0
0
0
0
0
6
0
0
1
0
2
1
0
1
0
2
0
0
0
3
2
0
0
1
1
0
0
2
0
1
2
0
0
0
0
1
1
0
1
0
0
1
2
1
1
1
2
1
0
1
0
0
0
0
1
1
0
1
0
1
1
2
1
0
2
0
0
0
0
0
1
2
0
0
1
0
2
0
0
0
0
0
2
0
0
0
1
3
2
0
2
0
0
1
0
2
2
0
1
1
0
1
0
2
0
0
1
2
1
2
1
0
1
0
1
1
2
0
1
0
1
0
0
2
0
1
0
2
1
0
0
0
1
1
0
0
1
2
1
1
0
0
2
1
0
2
0
2
0
0
0
1
0
0
0
1
0
0
0
1
1
2
0
1
0
0
0
1
0
1
2
1
1
1
0
2
0
0
0
1
0
0
0
0
2
1
1
2
0
2
2
1
0
0
0
0
1
2
1
1
0
0
1
1
1
2
1
1
0
2
0
1
0
0
0
2
3
0
0
2
1
0
0
0
2
2
1
0
0
0
0
1
1
0
0
2
3
0
0
0
2
0
0
0
2
0
1
0
1
1
0
1
1
0
1
0
1
2
1
1
0
1
0
2
2
1
2
0
0
0
0
0
1
0
2
2
2
2
1
0
1
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
2
0
2
0
0
2
2
1
0
3
0
0
1
2
0
0
2
1
0
2
2
0
0
0
0
1
1
1
0
0
2
1
0
0
0
0
0
0
1
0
2
1
1
2
2
0
0
1
0
0
0
1
1
0
1
0
0
0
0
1
1
0
0
0
0
2
1
0
1
0
0
0
0
1
0
0
1
2
0
0
2
1
1
0
0
2
0
1
0
1
3
0
1
1
2
0
2
0
2
0
0
1
0
1
2
0
1
1
0
1
0
2
0
0
1
2
1
2
1
2
1
1
1
0
2
0
2
1
0
0
1
0
0
0
1
2
0
1
2
0
2
1
1
1
0
0
0
0
0
2
2
0
1
0
1
1
0
0
1
1
0
0
0
0
2
2
0
2
1
0
2
0
0
1
2
2
1
0
0
2
1
0
0
0
0
0
2
1
2
1
1
2
1
0
1
2
1
1
2
2
1
1
0
0
0
1
1
1
0
0
1
0
0
0
2
2
0
2
1
0
0
0
1
0
4
0
0
2
1
0
0
1
2
1
0
0
1
1
1
0
0
0
0
0
1
2
2
1
0
2
0
0
0
1
1
1
0
1
2
0
0
1
2
0
0
0
2
2
2
0
2
0
1
1
0
1
2
2
0
2
0
1
3
1
0
1
0
1
2
2
1
0
0
1
0
0
0
1
3
0
0
0
0
0
0
2
1
0
0
0
2
2
1
0
0
0
0
2
2
2
1
3
0
1
1
1
1
0
0
3
0
0
1
0
2
0
2
2
2
1
0
0
0
1
0
0
1
0
2
2
1
0
2
0
2
0
1
0
0
0
1
0
0
2
2
0
0
0
2
2
0
2
0
1
0
0
0
0
1
0
2
2
2
1
0
0
0
2
0
0
2
0
0
0
0
0
0
2
1
1
0
1
0
1
0
1
1
1
2
4
2
0
0
0
1
0
2
1
0
1
0
0
1
0
1
0
2
1
0
0
1
2
1
0
0
0
0
3
1
1
2
0
0
0
2
0
2
0
0
2
1
1
0
0
1
0
2
0
0
0
1
1
0
2
1
2
0
1
1
1
0
1
1
0
0
1
1
2
1
2
2
0
2
1
2
2
1
0
2
0
0
2
2
0
0
2
1
0
1
1
1
1
1
0
1
1
2
1
0
0
1
0
0
0
0
2
0
1
0
0
1
0
2
0
0
0
0
2
0
2
0
0
0
0
1
1
0
0
2
0
1
1
0
1
0
1
0
2
0
2
0
1
1
0
0
0
0
1
0
0
0
2
0
0
1
1
0
1
0
2
0
1
1
1
2
1
2
0
2
1
0
0
0
1
0
2
1
1
0
1
0
1
2
0
2
2
0
0
1
0
0
1
0
0
0
1
2
3
0
0
0
1
2
2
0
0
1
2
2
1
2
1
1
1
0
0
0
1
1
0
0
0
0
0
2
0
0
2
2
1
0
1
2
0
0
1
0
4
0
0
0
2
2
0
0
0
2
1
1
0
1
1
0
0
2
0
1
0
2
0
2
0
0
1
0
0
1
0
0
2
0
0
1
0
0
0
2
0
2
0
0
0
2
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
1
1
1
0
0
1
2
1
1
0
0
1
1
1
4
0
0
2
0
0
0
2
0
0
0
0
2
0
0
1
1
1
0
2
0
1
1
0
1
0
1
0
1
2
3
1
1
1
0
0
2
0
0
0
1
2
0
0
0
0
1
2
1
1
1
1
1
0
1
0
0
0
0
2
0
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
2
1
0
0
1
0
0
2
0
1
0
2
2
2
1
0
1
1
0
1
0
0
1
1
2
0
1
1
0
0
0
1
0
1
0
0
0
1
2
0
3
1
1
1
1
0
0
0
1
0
0
1
2
2
1
1
1
1
1
0
1
0
0
0
1
0
0
2
1
2
0
1
1
2
0
0
0
1
2
1
1
1
1
1
1
1
0
0
2
2
1
0
1
0
1
4
0
0
1
2
2
0
0
1
0
1
1
2
1
0
1
0
1
2
0
1
1
2
0
1
0
1
1
1
0
0
2
0
0
1
0
0
1
0
0
2
2
1
1
1
1
1
0
2
1
0
3
0
0
0
0
2
1
2
2
2
1
0
2
0
0
1
2
0
1
1
1
1
0
0
0
2
1
0
1
0
0
2
0
2
1
1
0
2
1
1
2
1
2
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
1
1
2
1
0
0
0
0
0
0
0
1
0
2
1
2
2
0
2
0
0
0
2
0
1
0
2
0
0
0
1
0
0
0
0
1
1
1
0
1
2
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
2
1
1
1
2
2
2
1
1
1
0
0
0
0
1
1
2
0
3
0
0
2
2
1
0
0
1
2
0
2
1
2
0
0
1
0
1
0
0
1
0
2
0
0
0
0
2
1
1
0
0
0
1
0
0
1
0
0
2
0
1
0
1
1
2
0
7
2
0
0
3
1
0
0
1
1
2
2
1
1
3
1
0
1
1
2
2
0
0
0
2
1
2
1
0
1
2
2
1
0
0
0
0
0
0
0
1
1
1
1
0
0
0
1
0
0
0
0
0
1
0
1
2
0
1
0
1
0
0
1
2
0
1
1
0
0
2
1
0
1
0
0
1
0
0
1
1
0
0
0
0
0
1
2
1
0
2
0
3
0
1
2
1
0
0
1
0
0
2
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
2
1
0
0
1
0
2
1
0
1
3
0
0
0
1
2
2
1
0
0
0
0
0
1
0
0
1
0
2
0
0
1
0
1
2
1
0
0
2
3
0
1
0
1
1
0
1
1
2
0
1
1
1
1
0
1
0
0
0
1
1
1
0
0
1
0
2
1
0
1
2
5
0
0
2
2
2
1
4
2
0
2
1
1
0
2
0
2
4
2
0
0
0
2
0
0
0
2
2
0
1
0
1
2
2
1
1
2
1
0
0
1
1
1
0
1
0
2
0
1
0
0
1
0
0
0
0
1
2
1
0
0
2
0
1
0
0
2
0
1
1
1
1
0
0
2
1
1
2
0
0
2
2
0
1
1
0
0
0
2
0
1
1
1
1
2
2
0
0
0
0
2
0
2
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
1
0
1
0
1
1
2
1
0
0
0
0
0
0
0
2
0
2
2
0
1
2
0
0
1
1
0
1
0
1
0
2
0
0
2
1
0
0
0
1
2
1
1
0
2
0
0
2
0
1
0
2
2
2
1
0
1
1
0
1
2
2
0
0
1
1
0
2
0
0
2
0
0
2
0
1
0
1
1
0
1
0
0
1
0
0
1
0
1
0
2
0
1
2
2
1
1
0
1
0
2
0
0
2
2
0
2
3
2
0
2
0
2
1
0
0
1
2
0
1
0
0
0
1
1
0
1
1
0
1
0
1
0
0
2
0
0
2
1
0
2
2
0
2
0
0
0
2
0
0
0
1
3
0
0
1
1
1
0
2
2
2
1
2
1
1
1
2
1
0
0
0
2
1
1
1
1
1
2
0
1
0
0
0
0
0
0
0
1
0
2
1
0
1
1
0
0
1
2
0
0
2
2
6
1
1
0
0
0
0
2
1
1
0
2
1
0
1
0
1
1
0
0
2
0
1
0
2
1
1
2
0
2
2
0
0
2
1
2
1
1
2
0
2
2
1
2
0
0
1
0
1
0
0
1
0
2
0
0
2
1
2
1
0
2
0
0
1
0
1
1
0
1
2
1
0
1
1
2
1
2
2
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
1
0
1
1
0
1
2
2
2
2
2
0
0
2
0
1
1
0
2
1
1
0
1
0
0
0
0
1
1
1
0
3
1
1
2
0
2
0
1
2
1
0
0
1
1
2
1
0
1
1
2
2
0
0
2
0
0
0
0
1
0
1
1
0
2
2
1
1
0
1
2
2
0
2
0
0
1
1
0
2
1
0
1
2
1
2
0
2
0
0
1
2
0
2
2
0
0
1
0
2
1
2
0
1
0
0
1
2
1
0
2
0
0
2
0
1
1
0
2
0
1
0
2
1
1
1
4
0
0
0
0
0
0
1
1
1
1
1
0
0
2
0
0
0
0
2
0
0
2
1
1
0
3
0
3
0
1
0
2
0
0
1
4
1
2
1
2
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
2
0
1
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
3
0
1
0
2
2
1
2
1
1
0
2
0
0
0
1
0
1
2
2
1
0
1
1
2
4
0
0
0
0
2
1
0
1
0
0
0
2
0
2
0
1
2
1
1
1
0
0
0
1
1
2
0
0
0
0
2
0
0
0
2
2
1
2
2
1
0
0
2
0
0
2
2
0
0
0
2
0
2
0
0
2
1
1
0
2
0
0
0
2
0
1
0
2
2
0
0
0
1
1
0
1
2
0
1
0
0
0
0
2
2
0
1
0
1
0
0
2
1
1
3
1
0
2
2
0
0
0
0
0
0
1
2
2
2
0
0
0
0
2
1
1
0
1
0
0
2
0
0
0
2
0
1
0
0
1
0
1
2
1
0
1
0
1
1
1
1
1
1
0
1
1
2
0
0
2
0
0
0
0
1
0
2
1
1
0
1
2
0
3
1
2
1
0
1
0
0
0
0
0
1
0
2
2
1
1
2
0
1
0
1
0
0
0
0
2
0
0
3
0
1
1
2
0
3
0
4
2
0
1
0
0
1
1
1
1
2
0
1
2
0
0
1
1
0
0
1
1
1
0
1
0
0
0
2
1
1
0
0
5
2
1
1
0
0
2
2
0
2
0
2
1
0
1
1
0
0
1
0
0
0
0
0
2
0
2
1
0
1
2
1
2
2
0
0
0
1
0
0
2
1
2
0
0
2
0
0
1
0
2
0
2
1
0
0
0
0
1
0
1
1
1
1
2
0
1
1
1
1
1
1
2
0
1
2
0
2
2
1
0
2
2
0
0
1
2
1
0
2
0
1
0
0
2
0
0
2
0
2
1
0
2
0
0
2
0
2
2
1
2
1
2
1
1
0
1
0
1
0
1
0
0
1
0
0
1
2
1
0
0
3
0
0
1
0
1
1
2
0
1
1
0
0
0
0
0
1
0
2
0
0
0
1
0
1
1
0
0
0
1
2
1
1
1
0
1
2
0
0
0
0
2
0
0
0
1
1
2
1
0
0
0
1
0
0
2
2
0
1
0
0
0
0
2
0
2
0
2
2
0
1
1
0
2
1
2
1
1
0
0
0
1
0
2
1
2
1
0
1
1
1
0
2
0
0
2
0
0
2
1
0
0
1
0
0
1
0
2
0
1
0
0
2
1
0
1
2
1
0
2
1
1
1
2
0
0
0
2
0
0
0
1
0
2
0
2
0
0
2
2
0
2
4
1
1
0
1
2
0
0
0
0
0
0
1
2
0
1
0
0
1
0
0
1
1
2
1
0
0
0
0
0
2
1
0
1
1
2
0
1
0
2
0
0
1
0
1
1
0
2
2
0
0
0
2
1
1
0
2
2
0
0
2
1
0
0
1
0
2
0
0
1
1
1
0
1
1
1
1
0
2
0
2
1
0
0
1
2
0
1
1
2
3
0
0
0
1
0
0
1
0
0
1
1
0
0
2
0
0
2
2
0
0
0
1
0
1
0
1
1
2
0
0
1
0
1
0
1
0
1
0
0
1
2
0
1
0
0
0
0
0
2
0
0
1
0
0
1
0
0
1
0
0
0
0
2
1
1
2
1
0
0
0
2
0
0
0
0
0
1
0
0
2
1
0
1
0
0
0
2
2
2
0
0
0
1
0
1
0
0
2
0
1
2
0
0
2
0
1
0
2
1
2
0
1
1
0
2
2
0
1
2
0
1
0
5
1
0
0
2
0
0
0
3
1
2
1
0
0
1
2
0
1
2
2
0
0
0
1
2
1
1
0
0
2
0
1
2
0
1
0
2
0
0
0
0
0
2
0
2
0
0
1
2
0
0
0
0
0
1
0
2
1
0
1
2
2
1
0
2
0
0
0
0
1
0
0
0
1
2
3
0
0
2
1
1
2
1
1
1
1
1
0
2
0
1
2
2
1
1
1
2
0
1
0
0
2
2
0
1
0
1
3
2
1
1
1
0
1
1
0
0
0
0
2
1
0
1
0
0
1
1
0
1
1
0
2
1
0
0
2
0
0
1
0
0
0
1
0
1
1
0
1
1
2
0
2
0
1
0
0
2
0
1
0
0
0
2
0
1
1
0
0
0
2
2
1
2
1
1
0
1
1
2
0
0
2
0
0
1
0
0
0
1
1
2
2
1
1
0
2
2
0
2
0
0
0
1
1
0
0
0
2
1
0
1
3
0
2
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
1
1
0
2
1
0
0
0
0
0
1
1
3
1
0
0
0
0
1
0
2
2
2
0
0
0
1
1
2
0
2
0
1
2
0
0
0
0
1
0
0
0
1
2
0
3
1
0
1
2
1
2
4
1
0
2
0
0
1
0
1
1
0
0
0
3
0
1
2
1
0
1
1
0
2
2
1
13
1
0
1
1
2
3
0
0
1
0
0
0
0
0
2
2
0
0
0
0
1
1
1
2
0
0
0
1
0
0
0
1
1
1
0
1
0
2
3
1
1
1
1
2
1
1
3
1
0
2
2
2
1
2
1
0
0
0
1
0
1
0
1
1
1
0
1
1
2
0
1
1
0
0
1
2
0
1
1
0
0
0
1
0
1
0
0
1
2
0
1
2
0
1
0
0
0
1
0
0
1
2
1
1
1
0
0
2
1
2
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
1
1
0
1
1
0
0
2
0
4
2
1
0
0
0
0
0
0
1
2
0
0
1
0
0
2
0
0
0
0
0
2
0
1
0
0
1
1
2
0
0
1
2
0
1
1
0
1
0
0
0
2
2
2
0
2
1
2
1
2
0
2
0
1
2
2
0
0
0
0
1
1
1
1
1
1
1
0
2
2
0
1
0
0
2
2
0
0
0
1
1
2
2
1
0
2
0
2
0
0
1
2
2
2
0
1
0
1
1
1
2
1
0
0
1
2
0
2
2
2
0
0
0
1
0
0
1
1
0
1
1
0
1
1
1
1
0
0
1
1
1
0
1
2
0
0
1
0
0
1
0
1
1
2
0
0
2
0
0
2
0
0
0
1
3
0
0
1
1
2
1
2
1
0
0
0
1
1
2
2
1
1
0
0
1
0
0
0
2
0
0
1
0
1
3
2
1
0
0
1
1
0
1
1
0
0
1
2
0
0
1
0
2
2
1
0
0
1
0
0
0
1
1
0
2
1
0
2
0
0
1
2
0
0
0
0
0
0
2
0
0
2
1
2
0
0
1
2
1
1
2
2
1
0
1
0
0
0
2
3
2
0
0
0
2
0
2
1
1
2
1
0
2
0
0
0
0
1
0
2
1
0
1
0
0
2
1
2
1
0
0
2
1
2
2
0
0
1
1
2
2
0
2
2
1
1
1
1
0
2
0
1
0
0
1
2
0
1
1
0
1
0
0
1
1
2
1
2
0
1
0
1
2
0
1
0
1
1
1
1
0
0
0
0
0
0
2
2
2
1
1
0
1
2
1
1
1
1
2
1
0
2
0
0
2
2
0
1
1
2
1
0
1
2
0
1
1
1
0
0
1
0
0
0
0
0
0
0
2
0
1
2
0
1
2
0
0
0
2
0
0
2
1
0
1
1
0
0
1
0
1
0
0
0
2
0
2
0
1
0
2
2
2
0
0
1
1
1
1
0
1
1
0
0
1
0
0
1
1
1
0
0
0
4
0
1
0
2
0
0
1
0
1
0
0
2
1
0
1
0
0
0
0
0
1
1
0
1
0
0
1
1
1
1
2
0
0
0
0
0
1
0
1
1
2
0
2
0
3
0
0
0
0
0
0
0
0
3
0
0
1
2
0
0
1
1
0
0
1
2
2
2
0
1
2
0
1
0
1
0
0
1
0
0
0
0
2
1
1
1
2
2
1
2
2
0
0
2
1
2
1
0
0
0
2
2
0
2
2
3
2
0
0
1
0
1
0
0
1
2
2
0
2
1
0
0
1
0
2
1
2
0
1
0
0
0
0
0
2
2
2
2
2
1
0
0
0
1
2
1
0
0
1
0
2
1
0
1
2
0
2
0
0
0
0
2
1
0
0
1
0
0
2
0
0
0
1
1
1
0
0
1
1
0
1
1
1
0
1
0
0
2
0
2
0
0
2
1
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
1
1
1
0
0
0
0
0
0
0
1
1
0
1
1
2
6
0
0
2
0
2
0
0
2
2
0
0
6
1
0
1
1
1
2
1
0
0
0
1
3
0
1
0
0
1
0
1
2
2
0
3
1
2
2
2
0
1
0
0
3
2
2
0
2
1
0
2
2
1
0
0
0
0
2
0
1
0
1
0
2
1
0
1
0
0
1
0
0
0
2
1
1
0
2
2
0
0
3
2
2
0
1
2
0
0
1
0
0
0
1
1
0
4
0
2
2
0
1
0
0
1
0
0
1
1
1
0
0
0
1
2
0
1
2
1
1
1
0
0
0
0
2
0
1
0
2
0
1
1
1
1
0
2
0
0
2
0
1
0
1
1
1
0
1
0
1
1
0
0
0
1
2
0
0
0
1
2
2
0
1
0
2
0
0
2
0
0
1
1
2
0
0
0
0
0
2
1
0
0
0
1
0
0
1
2
0
2
1
0
0
2
2
2
1
0
0
0
1
1
2
0
1
1
2
0
1
0
2
0
2
0
0
2
3
1
1
1
1
0
2
0
1
1
1
0
1
2
0
0
3
0
1
2
2
1
1
0
0
0
0
1
0
1
0
0
0
1
0
0
1
2
0
1
0
0
1
6
0
0
1
1
0
1
0
1
0
1
1
3
0
0
1
0
1
1
2
0
2
0
2
1
2
1
2
2
0
2
0
0
0
1
1
0
2
0
0
0
2
0
2
2
0
0
2
0
0
0
2
1
2
2
2
0
0
1
0
5
0
0
1
1
0
2
2
1
2
2
2
0
1
0
2
0
0
0
2
0
0
1
1
0
0
0
1
2
0
0
1
0
0
0
0
0
0
1
2
1
1
1
0
0
1
2
2
1
0
0
2
1
0
3
0
0
1
0
0
2
0
1
0
2
2
2
4
2
1
0
1
1
2
1
1
1
1
0
1
2
0
2
1
2
1
0
2
1
0
0
2
1
0
1
0
1
0
0
0
0
2
0
0
1
1
0
2
0
1
0
2
0
0
1
1
1
2
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
1
1
1
0
0
0
1
2
2
1
1
0
0
0
2
0
0
0
2
1
0
2
0
0
0
0
2
1
2
1
2
0
0
2
1
1
0
0
2
0
1
0
2
1
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
2
1
0
0
0
4
0
1
2
2
1
1
0
0
2
1
0
0
1
0
2
0
0
0
1
0
2
1
0
0
1
2
2
1
0
2
0
0
2
0
2
1
1
0
2
1
0
1
1
0
2
1
0
0
1
0
1
1
0
1
1
1
0
2
1
1
1
0
0
1
0
1
2
1
0
0
0
4
2
1
1
0
2
2
0
2
2
0
0
0
1
2
2
0
0
2
0
1
0
1
0
1
0
0
0
1
5
0
1
0
0
3
1
0
1
0
1
1
0
1
4
2
2
0
0
2
1
1
2
1
0
0
0
1
0
0
1
0
0
0
0
2
2
2
0
2
1
0
0
1
0
1
0
0
1
2
1
2
0
2
1
0
0
0
0
1
0
0
1
1
1
0
0
1
1
0
0
0
0
1
0
0
2
1
2
0
0
0
0
1
0
0
0
2
1
0
0
1
1
4
1
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
2
0
1
1
2
1
0
0
0
2
1
0
0
1
1
0
1
1
1
3
0
0
2
2
0
0
2
1
0
0
0
0
1
1
0
1
0
0
0
1
2
0
2
0
1
0
1
0
1
1
2
1
0
2
2
0
1
1
0
0
2
0
0
2
0
1
1
0
1
2
0
1
1
0
0
0
0
1
2
1
1
1
2
0
0
0
1
1
1
0
0
2
1
0
0
2
1
0
1
1
2
0
0
1
0
0
0
1
1
1
2
1
0
1
0
0
0
2
1
1
1
1
0
1
1
2
2
1
2
0
0
0
1
1
1
2
1
0
0
0
0
2
0
1
0
1
2
1
2
1
1
2
1
0
2
0
0
1
1
0
0
2
0
0
0
0
2
1
2
0
2
0
0
1
0
1
1
1
1
0
1
0
0
0
0
1
0
0
0
2
0
1
0
0
2
2
0
0
0
0
0
0
0
2
1
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
2
2
0
0
0
2
1
0
0
0
1
0
0
0
1
1
2
1
2
0
2
0
0
2
0
0
0
0
2
1
1
0
1
2
0
0
1
0
1
0
2
0
0
0
1
0
1
0
2
1
2
1
0
0
1
1
0
0
0
2
0
1
0
1
0
2
2
1
0
1
0
0
2
0
0
1
0
1
2
1
0
1
0
0
1
0
0
1
0
1
0
1
0
0
1
2
1
1
2
2
0
0
1
0
1
1
1
0
0
0
1
0
1
0
0
0
1
2
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
2
1
0
1
0
0
0
1
0
1
0
0
0
0
0
1
1
0
1
1
2
1
1
0
2
1
1
0
0
0
1
0
0
1
1
0
0
1
0
2
1
0
0
0
1
1
0
1
0
1
1
2
0
1
0
0
0
1
0
0
0
0
2
0
2
0
1
0
0
0
0
2
1
2
1
0
0
2
2
2
2
0
2
0
0
1
0
0
2
0
0
1
0
0
1
1
1
0
2
2
3
0
1
1
1
2
0
0
2
1
2
1
0
2
0
0
0
2
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
1
1
1
0
0
0
1
1
2
1
1
0
1
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
1
1
1
2
0
0
1
2
0
2
0
0
0
1
1
1
0
2
2
1
1
0
1
0
1
0
0
1
0
1
2
0
1
0
0
0
0
1
3
1
2
0
1
0
2
1
1
0
2
2
0
1
0
0
1
0
1
0
2
1
0
0
0
0
1
1
0
1
1
2
0
1
0
0
1
5
2
2
0
0
0
0
0
2
0
2
1
1
3
0
1
0
1
1
1
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
2
1
0
0
0
0
1
0
0
1
0
2
1
1
3
1
0
2
0
1
2
0
5
1
0
0
1
1
2
1
0
2
0
2
0
0
0
0
0
0
1
1
2
1
1
0
2
1
0
0
1
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
1
1
0
2
1
0
0
1
0
0
1
1
0
0
1
1
0
0
0
0
0
0
1
1
2
2
0
1
1
1
0
1
2
2
0
1
1
0
1
0
0
0
2
0
3
1
1
0
2
2
1
1
0
2
0
0
4
0
0
2
0
0
1
0
0
2
2
1
2
1
0
0
0
1
0
1
0
0
2
1
0
2
2
0
2
2
0
0
0
0
2
2
1
2
2
0
0
0
3
1
0
1
1
0
0
1
2
0
0
8
0
0
2
0
1
3
2
0
0
2
1
0
0
1
1
0
1
0
0
1
2
1
1
0
0
0
0
0
2
2
0
1
1
6
1
0
1
0
1
0
0
0
2
0
0
0
2
1
2
1
1
1
2
0
0
0
2
1
1
1
2
0
0
1
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
2
0
1
0
1
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
2
0
2
0
0
0
0
1
0
2
2
0
1
3
0
0
0
2
1
0
1
0
1
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
1
2
1
2
0
1
1
0
2
1
1
1
0
0
2
1
0
0
1
0
1
2
0
0
0
1
1
1
1
0
1
2
1
1
1
1
2
0
0
2
0
1
0
0
1
3
2
0
0
0
0
0
3
0
2
0
2
0
1
0
1
0
1
2
2
2
0
1
0
2
1
0
0
2
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
1
2
0
1
0
1
1
2
1
1
3
1
0
2
1
1
0
0
0
1
0
0
1
2
0
0
1
2
2
0
0
0
0
0
1
0
1
2
0
0
0
1
1
0
0
1
0
1
1
1
0
2
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
4
0
1
2
2
0
2
1
2
1
1
0
0
1
1
0
0
0
1
2
0
0
0
2
0
0
0
2
1
3
0
0
1
0
0
0
2
1
0
1
0
2
0
1
1
0
1
1
1
1
0
0
2
2
1
0
0
0
1
2
0
0
0
1
1
2
0
0
2
1
0
0
0
0
0
2
0
2
2
1
1
1
1
0
0
2
0
1
1
1
0
1
0
0
0
0
0
1
2
0
0
2
0
0
1
2
2
0
0
1
1
0
2
0
1
1
0
0
0
1
2
0
0
0
0
0
0
0
2
1
1
1
1
2
0
0
0
2
0
1
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
1
0
0
2
0
2
1
0
1
0
1
0
0
0
0
0
2
0
1
0
0
2
1
2
0
1
0
0
0
0
2
0
1
1
0
0
0
2
1
1
2
0
1
0
1
1
0
0
1
2
2
0
0
2
2
0
1
0
0
1
1
1
0
0
1
0
0
2
0
2
2
0
1
0
2
1
1
1
1
0
0
2
0
0
0
0
0
1
0
0
0
1
0
1
2
1
1
0
1
1
2
1
0
0
0
1
1
0
1
1
0
1
0
2
2
1
1
0
1
1
1
2
1
1
0
1
1
3
2
0
0
2
0
1
0
0
1
2
1
0
0
0
2
0
2
1
0
0
1
2
0
2
0
0
0
0
2
1
0
2
0
2
0
0
0
0
1
1
0
1
0
0
2
0
0
0
1
1
1
0
0
1
1
1
0
0
0
2
0
0
0
0
1
0
0
1
0
0
1
0
0
2
1
1
0
0
1
2
1
1
1
1
2
1
2
0
1
0
0
0
1
2
1
0
0
1
0
0
1
2
1
1
1
0
1
0
0
0
0
0
1
1
0
1
0
2
0
1
0
0
0
0
0
0
1
0
2
2
1
0
0
0
0
0
0
1
0
2
1
0
0
1
2
1
1
1
0
0
0
1
2
0
1
0
0
0
0
0
2
2
0
0
1
0
0
0
0
2
2
0
1
0
1
0
3
2
0
0
0
0
2
2
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
1
0
0
1
0
0
2
0
0
0
0
0
1
1
2
2
1
1
2
1
0
1
2
0
0
1
0
1
1
0
2
0
0
0
2
0
0
0
1
0
2
0
1
2
2
0
1
1
1
2
0
1
2
0
0
0
0
1
0
0
2
1
0
0
1
0
1
1
0
2
1
0
2
1
2
0
0
1
1
0
0
1
1
1
2
0
1
2
2
0
0
2
0
3
4
1
1
1
2
0
0
2
0
0
1
0
0
1
0
0
0
5
0
0
0
0
1
0
0
1
0
1
2
0
1
0
0
0
0
1
2
0
1
0
0
2
0
0
0
1
1
0
2
2
0
0
1
0
1
2
0
0
1
0
0
0
0
0
0
2
2
0
1
1
2
0
0
0
1
0
0
0
3
0
2
0
0
1
1
2
1
1
0
0
0
2
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
2
2
1
0
2
2
0
0
2
2
3
1
0
1
2
0
1
0
0
1
0
0
3
2
1
0
2
1
0
0
2
0
2
1
2
1
1
1
2
0
1
2
0
0
0
2
1
1
0
0
0
0
0
0
2
0
2
7
2
2
0
0
2
0
1
0
0
0
0
1
2
0
0
1
0
2
2
0
0
0
0
0
0
1
1
1
1
2
0
0
2
0
1
2
1
0
2
0
0
2
0
0
0
0
0
0
1
0
1
1
0
0
2
2
2
1
2
0
2
0
0
2
1
1
0
0
1
0
0
0
0
1
2
1
1
0
0
0
0
0
1
2
2
0
2
1
1
1
0
1
0
1
2
0
0
0
1
2
0
0
1
0
0
1
2
0
2
1
0
1
2
1
1
1
0
0
2
0
1
1
1
1
0
0
1
0
0
1
0
0
0
3
2
1
2
2
1
1
0
1
0
1
0
0
0
1
1
1
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
1
2
0
0
2
1
2
2
0
1
0
0
0
2
1
0
0
2
1
0
0
1
1
1
1
0
0
0
0
0
0
0
2
2
2
1
0
0
0
1
0
1
0
0
1
0
1
0
0
0
1
0
0
0
1
0
2
1
0
0
1
0
2
0
2
1
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
1
1
0
1
1
1
0
0
0
0
1
1
1
1
2
2
0
0
2
0
0
2
1
2
0
1
0
0
1
1
1
0
0
0
0
0
0
2
0
1
2
2
0
1
0
0
2
2
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
1
1
0
0
0
0
0
2
0
2
0
1
0
0
2
1
1
2
0
1
0
2
2
2
1
2
1
2
1
2
2
2
0
1
2
0
1
1
0
1
0
0
0
2
1
0
0
1
0
0
1
2
1
0
0
1
0
0
0
2
1
1
0
0
0
2
1
2
2
2
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
2
1
1
0
0
0
0
2
0
2
1
0
0
0
1
0
1
2
2
0
1
1
0
0
0
2
2
1
0
1
0
1
2
0
2
0
1
2
0
2
0
0
1
0
0
0
1
2
0
2
2
0
0
0
2
0
1
0
1
1
3
0
2
1
1
1
0
2
3
1
0
2
0
1
0
2
1
1
0
2
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
2
1
1
0
0
0
0
0
0
1
0
2
2
6
0
1
0
1
1
0
0
2
1
0
0
0
1
0
1
0
1
1
0
0
0
0
1
1
1
0
0
0
1
2
0
0
0
3
2
0
0
0
0
2
1
5
1
0
2
0
0
1
1
2
0
0
2
1
1
0
0
0
0
0
0
1
2
0
0
1
3
0
2
2
1
1
1
2
2
1
0
2
0
0
0
2
2
0
0
2
0
1
0
0
1
0
0
0
0
0
1
2
1
1
0
0
0
1
2
1
0
0
2
0
0
1
0
1
1
0
2
0
0
0
2
0
0
1
1
0
0
0
0
2
0
0
0
2
0
0
1
2
0
1
2
0
2
0
1
2
0
0
0
0
0
1
0
1
0
2
1
0
1
0
1
0
1
0
1
0
2
2
0
2
0
2
2
2
0
0
1
0
2
1
1
1
1
2
2
1
0
0
1
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
1
1
1
2
0
0
1
1
0
0
2
0
0
0
1
0
0
0
2
1
0
0
1
0
1
0
0
0
2
0
1
0
1
0
1
0
1
1
2
1
0
0
0
0
2
0
2
0
1
1
1
2
0
0
3
1
0
1
0
2
0
0
2
2
2
4
3
1
2
0
2
0
0
1
0
1
1
2
2
0
0
2
0
0
1
0
0
2
0
2
2
1
0
2
2
1
0
0
2
2
0
1
0
0
0
0
2
0
1
0
0
2
0
1
2
1
0
0
0
0
2
0
2
0
1
2
1
2
0
2
1
0
1
1
0
0
0
0
1
1
0
2
1
4
0
0
2
0
1
1
1
0
2
1
0
0
0
0
1
1
0
0
0
0
1
0
1
0
2
1
1
1
2
1
2
0
0
2
2
0
2
0
1
1
2
1
0
0
1
1
1
0
1
1
0
1
1
0
1
0
2
0
0
0
0
0
1
2
2
2
1
0
0
2
0
0
0
1
1
1
2
2
0
1
1
2
1
0
0
0
0
1
0
1
1
0
0
2
1
1
2
0
2
0
0
2
0
0
2
2
0
0
0
0
2
9
0
0
3
1
0
0
0
0
0
0
1
1
1
1
0
0
2
0
1
0
1
2
0
0
0
0
1
1
0
0
0
1
0
1
0
1
0
0
2
0
0
2
0
1
0
0
0
0
0
0
1
0
2
0
1
1
1
2
1
0
0
0
1
1
1
1
2
0
0
1
2
1
1
0
1
3
2
1
0
0
2
1
1
1
0
0
1
2
2
1
0
2
0
0
2
0
0
0
0
1
1
3
1
0
0
1
0
1
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
2
1
1
1
0
2
2
0
3
0
1
2
0
0
0
1
1
0
1
0
0
2
0
1
0
1
0
1
1
1
0
0
1
0
1
0
1
1
0
0
0
1
1
0
0
2
0
2
1
1
2
2
0
0
0
0
1
0
1
1
1
1
0
1
0
1
0
0
2
0
0
2
0
0
0
0
2
0
2
0
0
0
2
1
1
0
1
1
1
0
1
0
0
0
1
0
2
0
2
2
1
2
0
0
0
0
0
0
1
2
0
0
2
1
1
0
0
0
2
2
0
1
6
0
0
0
1
0
0
2
1
2
2
0
0
0
2
2
0
0
1
0
2
1
2
0
0
1
2
0
1
0
2
0
1
0
1
1
0
0
2
0
0
1
0
0
0
1
2
0
1
0
0
1
1
3
0
3
0
2
0
1
0
1
1
1
0
0
1
0
2
1
3
0
0
0
2
1
1
0
1
0
1
0
0
2
0
0
0
1
0
0
0
0
3
1
0
0
1
0
0
0
2
1
0
0
1
0
0
0
0
2
0
0
1
2
1
0
1
0
0
1
2
0
2
0
0
0
1
0
0
0
2
2
0
0
0
1
1
1
0
0
0
0
0
1
1
0
1
0
1
0
0
0
1
1
0
1
0
2
2
0
1
1
0
0
1
0
1
0
0
1
0
2
1
2
1
0
0
0
2
2
0
0
1
1
0
1
2
1
6
0
1
0
0
1
5
1
1
1
1
1
3
2
0
2
2
1
0
1
1
0
0
0
0
1
0
0
0
0
0
2
0
3
2
1
1
1
1
1
0
1
0
0
1
0
0
1
2
0
0
2
2
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
3
1
0
1
2
0
0
0
2
0
0
0
0
1
2
1
1
2
1
2
1
0
0
0
1
0
2
1
2
0
0
0
2
0
1
1
1
2
0
0
1
2
0
1
1
0
2
3
2
0
0
0
0
0
0
1
2
1
0
2
1
4
0
1
0
1
1
0
0
2
1
1
0
1
1
2
0
1
2
0
0
0
0
0
0
1
1
0
1
0
0
1
1
0
1
0
0
1
1
0
0
0
0
2
1
1
2
0
0
0
0
2
2
0
0
0
0
0
2
2
1
1
2
0
0
1
2
0
2
0
0
0
1
1
2
0
2
1
1
0
0
1
4
0
0
0
0
0
2
0
1
0
0
2
1
0
0
1
0
0
4
0
2
0
0
1
0
1
0
1
1
1
2
1
0
0
2
0
2
0
0
0
1
0
1
0
2
1
1
3
2
1
0
0
0
0
1
0
0
2
1
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
1
1
0
0
0
2
0
2
2
2
1
1
0
2
0
1
1
0
0
0
0
1
1
0
1
0
0
2
0
1
1
1
4
1
0
0
0
0
0
0
1
1
1
2
0
2
0
2
0
0
0
1
0
0
0
2
1
0
1
0
2
1
0
0
0
0
2
2
1
3
1
0
0
0
1
8
1
0
1
0
4
0
0
0
1
1
0
0
1
2
1
2
0
2
0
0
2
2
0
0
2
1
0
1
0
0
1
0
0
1
0
1
0
0
0
0
2
0
0
2
2
0
0
2
1
1
1
0
2
2
0
1
2
1
1
2
0
0
0
0
0
2
2
2
3
0
0
1
2
2
0
0
3
0
1
1
1
2
1
2
0
0
0
0
0
3
1
1
0
2
0
2
0
1
1
0
0
1
0
0
0
1
1
2
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
1
1
2
0
2
0
0
0
0
0
0
4
1
0
2
2
2
1
0
0
1
1
0
0
0
0
2
1
0
1
0
0
2
0
0
2
3
0
2
0
1
1
0
0
1
1
2
0
0
0
0
1
0
2
0
2
1
2
0
1
0
1
1
1
2
2
0
2
1
0
0
1
1
1
1
1
1
2
1
2
1
0
1
0
0
0
0
1
1
1
2
0
0
0
1
0
1
1
1
2
0
1
1
0
0
0
0
3
0
5
0
2
0
0
2
0
1
0
1
1
0
2
1
1
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
1
0
1
1
0
0
2
0
2
0
0
0
0
2
2
0
0
1
2
2
1
0
0
0
0
1
2
0
0
0
0
0
1
0
2
1
0
0
2
0
0
0
2
1
0
1
0
2
0
0
1
2
2
1
0
2
1
2
0
1
2
0
0
0
0
1
0
1
1
2
1
2
1
0
0
1
0
0
0
0
0
1
1
0
1
0
0
2
0
0
0
1
2
1
0
0
2
1
1
0
1
0
1
0
0
0
0
3
2
0
3
4
0
0
0
2
0
1
0
2
2
2
0
1
1
0
0
2
0
1
2
0
1
1
0
1
2
1
2
0
0
0
2
2
1
0
1
0
0
0
1
1
0
1
2
0
0
1
0
0
0
1
1
2
0
1
0
2
0
2
2
1
0
0
0
0
0
0
0
1
2
0
0
0
2
0
1
0
0
0
0
3
0
1
1
0
0
1
1
0
3
1
0
0
1
2
1
2
0
0
0
0
0
2
0
0
2
1
2
1
1
3
1
1
0
1
0
1
1
0
1
1
0
1
0
2
2
1
0
2
0
0
2
0
0
2
0
1
0
0
2
2
1
0
1
0
1
1
0
2
0
1
1
1
0
0
0
2
0
0
2
2
0
1
1
1
0
1
0
0
0
1
0
0
0
0
2
0
0
2
1
2
0
0
0
0
1
0
0
0
1
1
1
0
1
1
0
0
1
0
0
2
0
1
0
2
1
0
0
0
0
0
0
0
1
1
2
0
4
1
3
3
2
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
1
0
0
1
0
0
1
2
1
0
2
0
0
0
2
1
0
2
2
0
0
1
1
2
1
0
2
1
2
1
1
1
0
0
1
0
0
0
1
2
2
0
1
0
0
2
1
2
2
0
0
1
0
1
0
0
0
4
1
1
2
0
0
0
1
2
0
2
2
1
0
0
2
1
2
0
2
1
0
0
2
1
2
0
2
0
2
0
0
0
0
0
1
1
0
1
1
1
1
0
2
2
0
0
2
0
1
0
1
0
0
1
0
0
3
0
2
0
0
1
0
1
1
1
1
1
2
1
2
2
0
2
0
2
0
3
0
0
2
1
0
0
5
0
1
0
0
0
2
1
1
0
2
1
0
2
2
0
0
1
0
1
0
0
0
1
0
0
1
1
0
0
0
1
2
0
0
0
0
1
0
0
0
1
1
2
2
0
0
0
0
0
1
0
2
0
0
0
0
1
0
1
2
0
0
1
2
0
2
1
0
1
1
0
1
1
0
0
2
0
1
1
0
1
0
1
1
0
0
1
2
0
0
1
0
2
0
2
0
0
0
1
2
0
1
0
2
0
0
1
0
0
0
0
0
1
1
2
2
1
1
1
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
1
1
1
0
0
1
1
0
2
1
0
1
2
1
1
0
0
0
2
3
1
1
1
1
1
0
0
0
1
0
2
1
0
0
0
1
1
0
0
0
0
0
1
1
0
2
1
0
2
0
1
0
2
0
2
0
1
0
1
2
1
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
1
0
3
0
2
1
1
2
0
0
1
1
0
2
2
6
1
2
1
0
0
2
2
0
1
2
0
0
2
2
2
0
1
0
1
1
0
0
2
1
2
1
1
1
0
1
0
2
1
2
0
1
0
0
0
2
1
0
0
0
2
0
2
0
2
1
0
2
0
2
2
0
1
2
3
3
1
1
0
0
0
2
1
0
2
0
1
1
0
2
0
0
0
1
1
1
0
2
1
3
0
0
1
0
3
1
0
2
1
0
0
2
0
0
2
0
0
1
1
3
0
0
1
1
1
1
0
0
0
1
0
0
0
0
3
3
0
1
2
2
2
0
1
2
0
1
1
1
2
0
0
0
0
2
1
2
0
1
0
1
0
0
0
0
2
1
2
0
1
2
0
1
0
0
2
2
0
0
0
0
1
1
0
0
0
1
0
0
2
0
3
1
0
0
0
0
1
2
0
2
2
0
1
1
0
0
2
0
0
2
2
0
2
0
2
1
1
1
2
0
2
0
1
1
0
2
1
0
0
0
0
0
0
1
0
1
3
0
0
0
1
0
1
0
0
4
0
0
2
0
0
1
0
0
1
0
0
0
0
0
2
0
0
2
0
2
0
0
0
2
1
0
0
2
0
0
0
2
1
0
0
0
0
0
2
1
0
1
1
0
0
1
0
0
1
0
1
1
2
0
2
1
0
1
1
0
2
1
1
1
1
1
1
0
1
0
0
1
0
1
1
0
0
1
2
0
1
0
0
0
0
1
1
2
1
0
0
0
2
0
0
2
0
0
0
0
1
0
1
0
1
3
0
2
1
0
0
0
2
0
1
1
0
0
2
0
0
2
2
0
1
0
0
1
1
2
2
2
3
1
1
1
1
2
0
0
1
1
0
1
0
0
0
3
0
2
1
1
1
1
1
2
0
0
0
0
1
1
1
2
0
0
1
1
0
0
2
0
0
2
1
0
0
3
1
2
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
2
3
1
1
1
0
0
1
1
0
2
0
0
1
0
0
1
1
2
0
2
0
1
0
2
0
0
0
2
2
1
2
0
0
1
1
1
1
0
0
1
0
0
0
0
0
0
0
2
0
1
0
1
1
1
0
0
1
1
2
1
2
1
0
0
0
1
0
0
0
1
0
1
1
0
2
0
1
0
2
0
0
2
0
2
2
1
1
0
0
1
2
2
0
2
1
0
0
1
0
2
1
0
1
2
0
0
0
0
0
1
2
2
1
1
0
0
2
2
2
1
0
0
0
0
0
0
1
0
1
2
2
0
1
1
3
2
0
0
0
2
1
1
1
1
0
1
1
0
0
0
1
0
1
1
0
0
0
1
1
1
0
1
2
2
1
0
0
1
0
0
2
2
0
0
2
0
2
0
1
1
0
0
1
0
2
0
0
1
0
2
0
1
0
1
0
1
0
0
2
1
0
0
0
1
0
2
0
1
2
0
1
0
2
0
0
1
2
2
2
1
0
1
1
0
1
0
0
0
2
0
0
1
1
0
0
0
2
0
0
1
0
1
1
1
0
1
0
2
2
0
0
0
2
0
0
1
1
2
1
2
0
1
0
0
2
2
1
0
2
2
1
0
0
1
0
0
1
0
0
1
0
1
2
1
2
1
1
2
0
0
2
0
0
0
0
0
1
2
0
1
2
0
0
0
0
1
1
0
0
0
2
2
0
0
0
1
0
0
2
2
2
2
1
1
0
2
0
0
2
0
0
0
0
2
2
1
0
0
2
2
2
0
0
0
2
2
0
0
3
2
0
3
0
0
0
0
0
1
1
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
1
0
0
0
0
0
1
2
0
2
1
1
0
1
1
0
0
0
0
2
0
0
3
2
1
0
1
2
1
1
1
0
2
0
0
0
0
0
2
5
0
2
0
1
0
0
0
0
1
1
1
0
2
2
0
1
1
0
0
0
0
1
0
2
0
2
1
0
1
5
0
0
0
1
1
1
2
0
0
0
2
1
3
0
0
2
0
1
2
1
0
0
2
0
1
0
0
1
1
2
0
0
1
0
0
0
0
0
1
0
1
1
1
1
1
2
0
1
0
2
0
0
0
0
0
0
0
2
0
2
0
2
1
0
1
2
0
0
0
0
2
0
2
0
1
1
0
1
1
2
2
0
2
0
2
2
0
1
0
0
0
0
0
0
0
0
1
2
1
1
1
0
2
0
1
1
1
1
1
2
1
0
2
3
0
0
2
1
0
0
0
2
2
0
2
1
0
0
0
2
2
1
0
2
1
1
2
2
1
2
0
0
1
0
1
3
0
3
0
1
0
0
3
0
0
0
3
2
1
1
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
2
0
2
2
0
0
0
2
0
2
1
2
0
1
0
0
0
0
2
0
0
1
1
1
0
1
2
0
0
1
0
1
0
0
0
2
0
1
0
0
0
2
1
0
1
1
0
2
2
1
1
1
0
1
0
1
0
0
0
1
2
0
0
0
0
2
1
1
1
2
0
0
0
0
0
1
0
0
0
0
1
0
2
1
2
0
0
2
1
2
1
0
0
1
0
0
1
0
1
0
1
1
1
4
1
0
2
0
1
0
0
0
0
0
0
0
2
0
2
1
0
1
2
0
0
1
1
0
2
2
0
4
2
1
1
0
0
1
1
0
0
1
0
2
2
0
0
1
2
1
1
1
1
0
2
1
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
1
0
0
1
0
1
0
2
1
2
0
0
2
1
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
2
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
1
1
2
1
1
0
1
1
1
0
2
1
0
0
0
2
0
1
1
1
0
0
2
2
0
0
1
1
3
0
0
0
0
0
1
2
0
0
0
1
2
0
0
0
1
0
0
2
1
1
0
1
0
0
2
0
2
1
0
0
0
1
2
2
1
0
2
2
2
0
2
0
0
2
1
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
3
0
1
0
0
1
1
1
0
2
0
0
1
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
3
0
1
2
1
1
2
0
0
0
1
2
6
0
1
2
2
0
0
1
0
1
0
2
1
1
0
2
1
1
0
3
0
2
1
0
2
0
1
1
2
1
1
0
1
0
0
1
2
2
1
1
0
2
1
2
0
0
0
1
0
0
1
0
0
2
1
0
1
1
0
0
0
0
0
1
2
4
1
1
1
2
1
2
2
1
0
0
0
0
1
0
1
2
0
2
0
1
1
0
0
1
1
2
1
2
2
2
0
0
0
0
1
2
0
1
2
0
0
2
1
2
0
0
0
0
1
1
2
1
0
1
0
2
0
2
0
1
0
1
2
1
0
2
2
1
2
3
1
1
0
0
0
2
0
1
0
0
1
0
2
5
2
0
0
0
2
1
0
0
1
0
1
0
1
1
0
2
1
0
0
0
0
1
2
1
2
0
1
0
0
1
0
0
1
1
0
2
0
1
0
0
1
2
0
0
1
0
0
1
0
1
2
0
2
0
1
1
2
0
1
2
2
2
0
0
0
1
0
0
2
0
1
2
0
0
0
0
1
0
0
1
0
1
1
0
3
0
1
0
0
0
0
0
2
1
2
0
1
2
1
4
0
1
0
2
0
1
2
0
0
2
0
0
1
0
0
1
0
2
0
2
0
1
0
0
0
0
0
1
1
3
2
0
0
0
0
0
1
2
0
2
0
1
0
1
2
0
0
1
0
0
1
1
0
1
1
1
1
0
0
2
0
1
0
0
2
0
0
0
2
0
0
1
1
0
1
1
1
1
0
1
1
1
2
1
1
2
1
1
0
2
1
2
0
0
2
2
0
0
2
1
0
1
3
1
0
0
0
0
0
1
1
0
2
0
2
2
0
1
0
1
0
2
2
0
0
0
0
2
1
1
0
1
0
0
0
0
2
3
1
0
1
1
1
2
2
0
0
2
0
1
0
0
0
2
1
0
0
1
0
0
1
0
2
0
0
2
0
0
1
0
1
0
1
0
0
1
0
2
1
3
0
0
2
1
1
0
0
2
0
2
0
0
1
0
2
0
0
0
3
0
1
0
0
0
0
1
1
1
1
0
0
0
1
1
0
2
1
0
1
0
0
0
1
1
2
1
1
0
1
2
0
2
0
0
1
0
1
0
0
0
0
0
0
0
1
2
2
2
0
2
2
0
1
2
0
0
0
1
0
0
0
1
0
0
0
2
1
0
0
2
0
2
0
1
0
0
2
0
1
1
2
0
1
1
0
1
2
2
2
1
2
0
1
0
1
1
1
0
0
2
1
3
2
2
2
0
0
2
0
2
1
1
2
1
0
2
0
1
5
0
0
1
1
1
0
1
1
1
0
1
1
0
2
1
0
0
0
0
0
0
1
1
0
1
0
0
1
0
2
1
0
0
2
2
1
2
2
0
1
2
1
0
0
0
1
1
1
2
0
0
1
1
0
2
2
1
1
1
0
2
0
1
0
3
1
0
2
0
1
0
2
1
0
0
1
0
0
0
2
0
2
0
1
2
0
0
1
0
0
1
0
0
0
0
2
0
1
0
0
0
1
0
1
1
0
0
2
0
0
1
0
1
0
0
1
1
1
1
0
1
0
1
0
1
3
3
0
2
0
1
0
0
1
1
2
0
2
0
1
0
2
0
2
1
1
0
0
1
0
0
1
0
0
2
1
1
2
2
1
0
1
0
1
1
1
2
1
0
0
0
1
1
1
0
1
1
1
1
0
0
1
0
0
1
0
1
0
0
2
0
1
0
0
0
2
0
0
0
1
1
2
2
0
0
1
1
0
1
0
0
0
1
2
0
0
1
1
0
2
0
0
1
2
1
1
1
2
0
2
1
0
0
1
0
0
1
1
0
0
0
1
1
0
1
3
0
0
2
2
0
3
1
0
1
2
1
2
0
1
1
1
2
0
0
1
1
0
2
0
1
0
2
0
0
2
0
0
0
0
1
0
2
0
1
1
1
1
0
0
0
1
0
1
0
2
0
0
0
0
1
0
0
1
0
2
1
2
0
1
2
2
1
1
2
0
1
1
0
2
1
0
1
0
1
1
2
2
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
2
0
1
0
1
0
2
2
0
1
2
1
0
2
0
0
0
2
2
2
1
1
0
2
1
0
0
1
0
2
2
1
2
0
0
2
2
1
1
2
0
0
0
1
2
0
0
0
2
2
1
0
1
0
0
0
2
0
0
1
2
0
2
0
2
1
0
0
1
0
0
1
2
0
2
0
0
2
0
2
1
0
2
0
0
0
2
0
0
1
3
2
0
0
6
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
1
2
0
1
1
1
1
0
0
2
0
2
2
1
1
2
0
0
0
0
2
0
1
1
1
0
0
0
0
1
1
0
1
0
1
0
2
2
2
2
2
2
2
0
4
0
0
0
0
0
2
0
0
1
0
1
0
0
2
0
1
0
0
1
2
1
2
1
2
0
2
0
4
1
1
0
0
1
2
0
2
2
0
0
1
0
0
1
1
0
0
1
0
1
1
0
0
2
1
0
0
2
2
1
0
0
1
0
2
0
2
3
0
2
0
0
0
2
2
0
2
0
0
0
1
0
0
0
1
2
0
0
0
0
0
1
0
1
2
1
0
2
2
1
1
0
1
1
1
0
0
1
0
0
1
1
0
3
0
0
2
0
1
0
0
1
0
1
0
1
0
1
2
1
0
0
1
2
1
1
0
2
0
1
1
0
0
2
2
0
2
3
0
1
1
0
3
2
1
1
0
0
0
1
0
1
2
1
4
1
1
1
0
0
1
1
1
0
1
1
0
2
1
0
1
0
0
0
0
1
1
0
1
0
0
0
0
2
0
1
1
1
0
0
0
0
2
0
0
0
0
1
0
1
1
1
0
1
1
2
0
0
2
0
1
1
1
0
2
1
0
0
1
1
3
0
1
2
1
2
1
1
0
0
1
0
1
1
3
0
0
3
0
0
3
0
1
1
3
0
1
0
1
0
1
1
0
0
1
0
0
2
2
1
1
2
0
1
1
1
0
0
0
0
0
2
1
0
2
2
0
0
1
0
0
1
2
1
2
3
0
2
1
0
0
0
0
1
0
0
0
0
0
1
0
1
1
1
2
0
1
0
0
1
2
1
2
1
0
0
1
1
1
1
0
0
0
0
0
1
1
0
3
0
1
0
2
0
1
0
1
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
2
0
2
0
0
1
2
1
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
1
0
2
1
2
0
0
0
1
1
2
0
0
0
0
0
0
1
1
5
2
0
0
1
3
1
0
2
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
2
2
0
1
0
2
1
2
0
2
0
0
1
0
0
1
1
1
0
1
0
1
0
0
0
1
2
2
1
0
1
0
1
1
0
0
0
1
2
1
3
1
2
0
1
0
1
1
0
3
0
4
0
1
1
1
1
1
0
2
1
0
0
2
2
0
0
0
1
2
1
2
2
1
0
1
1
0
0
2
2
1
2
2
0
0
0
0
0
0
1
0
1
0
2
0
0
1
0
0
0
0
2
0
1
0
0
2
2
1
0
0
1
2
2
0
2
0
2
1
2
1
2
2
1
1
0
1
0
1
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
1
0
1
0
0
1
0
2
0
0
2
1
1
2
2
0
0
2
0
1
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
1
2
1
0
0
1
1
0
0
2
0
2
0
0
1
2
1
1
1
2
1
0
0
1
1
0
1
0
1
0
1
0
0
2
2
2
0
1
2
1
0
2
0
0
2
0
0
1
1
1
1
0
1
1
1
0
0
1
0
0
2
2
1
0
0
0
2
0
0
0
1
0
1
1
1
0
2
1
0
0
0
2
2
1
2
0
0
1
0
1
2
0
1
2
1
1
0
1
1
1
2
2
2
1
1
2
0
1
2
0
1
5
0
1
1
0
0
0
1
1
2
0
1
1
3
2
0
1
0
0
1
0
1
1
0
0
0
2
2
1
0
0
1
1
1
1
0
2
1
2
0
1
1
4
2
0
0
1
0
0
1
0
0
0
1
1
0
2
1
1
1
0
1
0
1
0
0
0
0
0
0
2
8
2
0
0
0
0
1
1
1
0
1
0
0
1
2
0
1
0
1
1
1
1
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
1
0
1
0
2
2
0
0
0
0
2
0
1
0
0
0
1
2
0
1
2
1
0
0
2
1
2
1
2
1
0
0
0
2
0
0
0
1
0
0
0
1
1
0
0
0
1
1
2
1
0
1
0
0
1
0
1
1
0
2
0
1
1
0
0
0
1
2
0
0
1
1
2
0
2
0
3
4
0
0
0
0
1
0
0
0
0
3
2
0
2
0
2
0
0
2
3
0
2
2
1
1
0
2
0
0
0
1
2
1
0
0
0
1
0
2
2
1
0
0
0
0
0
0
0
2
0
1
1
0
0
0
2
2
0
1
0
1
2
1
2
0
0
0
0
1
1
1
1
0
0
2
2
0
0
1
1
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
1
1
2
0
0
1
0
2
1
0
0
1
1
0
3
2
0
1
0
2
3
2
0
1
1
1
1
1
1
2
1
2
1
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
2
1
1
2
0
0
0
0
1
0
0
2
0
1
0
0
2
1
0
2
1
0
1
0
0
0
1
1
1
0
1
1
1
1
0
0
2
1
1
0
0
0
0
1
2
0
0
0
1
2
1
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
1
1
2
0
0
0
0
1
0
0
0
1
4
0
0
2
2
0
0
0
0
0
1
1
1
2
3
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
2
1
0
0
1
0
1
2
1
0
0
0
0
2
2
0
0
2
1
1
0
0
0
0
0
0
0
2
0
2
1
1
0
2
1
0
1
1
2
2
1
1
1
0
1
0
2
2
1
1
2
2
1
0
2
1
0
0
0
1
1
2
1
0
2
0
1
3
1
1
2
2
0
1
0
2
1
1
1
0
1
1
0
1
1
2
0
0
0
1
2
3
0
0
0
0
0
2
2
1
3
1
0
0
1
2
1
0
0
2
1
1
2
0
0
1
0
0
2
0
2
0
1
0
1
0
0
0
2
2
0
0
0
0
0
1
0
2
1
3
0
0
0
1
2
1
2
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
2
0
0
2
1
6
0
1
0
0
0
1
1
0
2
2
0
1
0
2
1
0
1
0
1
2
0
0
0
2
0
0
0
1
1
1
2
0
1
0
1
0
2
0
0
1
2
2
0
1
0
1
2
0
2
3
2
0
0
0
0
1
0
1
0
0
2
1
0
2
1
0
1
2
1
0
2
0
0
0
0
2
2
0
1
0
2
1
1
2
1
1
1
0
0
2
0
0
0
1
0
0
2
0
1
0
0
1
0
1
1
1
0
0
0
0
1
2
1
2
0
0
0
0
1
0
2
1
0
0
0
0
1
1
1
1
0
0
0
2
1
0
3
0
1
1
1
0
0
2
1
1
0
0
2
1
1
0
1
2
0
0
1
1
1
0
0
2
0
0
0
2
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
1
2
2
2
1
2
0
3
0
0
2
0
0
2
1
1
0
1
1
0
2
2
2
2
0
2
1
0
0
0
0
2
0
0
2
1
1
2
2
0
2
3
2
0
1
1
1
2
0
0
0
1
2
1
0
2
2
0
1
0
0
2
1
0
1
1
1
1
0
0
0
0
1
0
2
1
0
0
0
2
0
0
0
0
1
1
1
2
0
0
1
1
0
1
1
1
2
2
0
0
0
0
0
2
0
1
1
1
1
1
2
0
0
2
0
1
0
0
1
0
0
0
1
6
0
0
0
1
1
0
1
1
1
1
0
2
1
2
2
1
0
2
0
2
1
1
0
2
2
0
0
1
2
0
1
0
2
0
1
1
2
2
0
1
1
2
0
1
2
0
2
0
2
0
0
0
2
2
0
1
0
0
0
0
0
0
2
0
0
0
2
2
0
0
1
2
0
0
1
1
2
2
0
0
0
2
2
2
1
0
0
3
2
0
0
2
2
1
1
2
2
2
0
1
1
2
2
0
0
0
0
0
1
0
0
0
2
1
1
2
0
0
3
0
0
1
0
0
0
1
1
0
0
0
0
0
2
0
1
0
0
1
1
2
0
0
0
0
0
2
0
0
1
2
0
1
1
0
0
1
0
0
0
0
1
2
0
0
1
0
1
0
1
2
0
0
1
0
0
1
0
0
0
0
0
0
2
0
2
2
0
1
1
0
0
0
1
1
1
1
0
0
2
0
0
0
1
2
2
0
0
1
0
2
0
0
2
2
1
1
0
0
1
0
0
1
1
0
0
1
1
2
0
0
2
0
0
2
1
0
0
0
2
0
0
0
1
0
1
0
3
0
1
1
0
2
1
3
0
1
3
0
0
1
2
0
2
0
0
0
2
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
1
1
0
2
1
0
0
0
2
1
1
0
1
0
1
0
0
0
0
1
1
0
0
2
0
1
0
0
0
1
2
0
1
1
0
1
0
2
0
0
0
1
1
1
0
2
1
0
2
0
2
0
0
0
1
2
2
2
2
0
0
0
1
0
0
0
0
2
1
0
0
2
2
0
2
0
2
1
0
0
0
1
1
1
0
2
0
2
1
1
1
1
1
1
1
0
1
0
1
0
0
1
0
1
0
0
0
2
0
1
1
0
1
2
0
2
0
3
1
2
1
1
0
0
0
0
3
0
2
0
0
0
1
2
2
0
0
1
0
0
1
0
1
1
0
0
0
0
2
0
2
0
0
1
1
0
1
0
0
0
0
1
2
0
2
1
0
2
1
2
0
1
1
2
2
2
2
1
0
0
1
0
1
1
0
0
0
1
0
1
0
0
1
0
0
1
0
0
2
0
1
0
1
2
2
0
0
0
0
0
2
1
0
0
1
0
0
0
0
1
2
1
2
0
2
1
0
1
1
1
2
0
0
0
0
0
0
0
3
1
1
1
0
0
1
3
1
0
0
0
0
1
0
1
1
2
0
2
3
2
2
1
0
0
0
1
0
0
1
1
1
2
0
1
1
0
0
0
0
0
1
0
0
1
1
0
0
1
2
2
2
0
1
0
0
0
0
0
1
0
2
0
2
1
0
0
0
1
0
2
2
0
1
1
2
2
1
1
1
0
0
0
1
0
1
0
1
2
0
2
0
0
0
0
2
0
0
1
0
1
0
0
0
1
0
1
0
2
1
0
1
1
0
0
2
2
2
1
1
0
1
1
1
1
1
0
0
1
1
2
0
0
2
0
0
0
1
1
1
0
1
0
0
1
0
2
0
0
0
1
0
0
1
2
0
0
0
0
2
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
1
1
2
2
0
0
0
1
0
2
1
0
0
2
0
2
1
0
1
0
0
0
0
1
1
0
2
0
0
0
2
0
1
1
1
1
0
3
0
0
2
0
1
0
0
2
0
0
1
3
0
0
0
2
1
1
0
0
2
2
1
0
0
0
2
1
2
1
0
1
0
0
1
2
1
1
0
0
0
2
0
0
0
1
1
0
0
2
2
2
0
1
0
0
2
1
1
0
0
0
1
0
1
0
0
1
0
0
1
2
2
2
0
0
2
1
1
1
0
0
2
1
0
0
0
1
1
2
1
3
1
0
1
0
1
0
0
1
0
1
0
1
0
0
0
3
0
0
2
0
0
0
1
2
1
2
1
0
2
1
0
0
0
0
1
0
1
2
0
1
0
2
0
1
2
0
0
1
1
0
1
2
1
1
1
1
2
2
0
0
2
0
2
0
1
0
1
1
0
0
0
1
0
0
4
1
1
0
2
2
2
0
1
0
2
0
0
0
1
2
0
1
1
0
2
1
4
0
0
1
0
0
1
1
0
0
1
1
2
2
0
0
0
0
2
0
2
0
1
1
1
0
0
2
2
2
1
2
0
0
0
0
0
0
0
1
1
0
1
1
0
2
1
1
3
0
1
1
0
0
2
2
2
1
2
1
0
0
0
0
0
1
0
2
1
2
1
0
1
0
0
1
2
1
2
0
0
1
0
1
2
0
1
0
0
0
2
1
1
1
0
2
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
2
2
0
0
2
1
0
0
1
1
0
0
0
0
0
1
1
4
2
0
1
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
2
0
0
3
0
0
0
1
0
0
0
0
2
1
1
1
1
1
0
1
1
0
0
0
1
0
1
0
2
0
0
1
0
0
0
1
0
1
0
1
0
0
1
2
5
0
0
1
1
2
1
2
1
1
3
0
1
0
0
1
0
0
0
0
0
2
1
2
0
1
2
2
3
1
1
0
0
2
2
0
2
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
2
0
1
0
0
1
1
0
0
2
0
2
2
0
2
0
1
0
2
1
0
0
0
1
3
1
1
2
1
1
0
0
1
1
2
0
0
0
1
1
2
0
0
1
0
2
0
2
2
1
2
1
1
0
0
1
2
1
1
1
0
2
0
0
0
2
0
0
0
0
1
1
1
2
2
1
1
2
0
1
0
2
0
2
0
0
0
0
1
0
1
2
0
2
3
0
0
0
2
1
1
0
1
1
1
1
1
1
1
0
0
0
0
0
1
2
2
1
0
1
0
1
2
0
2
1
0
0
3
2
1
0
1
0
0
2
2
0
0
0
2
0
1
3
0
2
0
1
2
2
1
1
0
1
1
0
2
0
0
2
0
0
0
1
0
1
0
0
1
1
0
1
1
1
0
1
2
1
0
0
0
2
1
1
1
2
1
2
0
1
1
2
0
0
1
0
1
1
2
0
2
0
2
2
0
2
0
0
2
1
1
0
2
2
0
1
0
2
1
0
2
0
1
2
1
0
2
0
2
2
1
0
0
1
0
0
2
0
0
2
0
0
0
0
1
0
2
2
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
2
0
2
0
0
1
1
2
2
1
0
1
0
0
0
1
2
0
0
0
0
2
1
1
0
1
1
0
0
1
0
0
2
0
0
0
1
0
2
0
2
0
1
0
1
0
0
1
0
2
3
0
1
0
0
0
0
0
0
1
2
0
0
1
0
0
2
1
0
0
0
1
0
0
0
2
1
2
0
1
1
2
1
0
0
1
1
0
0
1
0
0
1
0
0
1
0
0
1
0
1
1
0
0
1
0
1
1
1
2
0
0
0
2
0
0
1
1
1
0
2
1
1
1
1
1
0
0
1
1
1
1
0
0
0
3
1
3
1
1
2
0
0
0
0
1
0
1
2
0
0
0
1
0
1
0
2
1
0
1
1
0
2
2
2
1
0
2
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
2
1
0
3
0
1
0
1
0
2
0
0
0
1
1
1
0
0
4
0
0
0
2
1
0
2
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
2
1
0
0
0
2
0
1
0
1
1
0
0
1
3
2
2
1
2
2
0
0
1
0
1
1
0
1
0
2
0
0
0
0
1
2
0
0
2
0
0
2
0
1
1
1
0
0
0
0
1
1
1
1
1
0
2
0
1
0
0
1
0
0
1
0
1
1
2
1
0
0
0
1
1
1
1
1
2
2
0
1
1
0
0
2
1
2
1
1
0
0
2
0
1
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
2
2
2
3
1
0
0
0
3
0
1
0
0
1
1
0
0
0
0
0
2
1
2
1
0
3
2
0
0
1
1
1
0
3
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
2
2
1
0
1
0
0
0
1
1
0
1
1
0
1
0
0
0
0
1
2
0
0
3
0
0
0
0
2
2
2
0
0
1
2
1
1
1
0
1
1
0
0
1
1
1
1
2
4
0
0
0
2
0
2
2
1
0
0
2
1
0
1
1
0
0
1
0
1
0
0
1
1
0
0
0
0
1
2
0
0
2
0
1
1
2
1
0
0
1
0
0
0
0
0
1
2
1
0
2
1
2
0
2
1
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
2
0
2
0
0
2
1
2
2
1
0
1
2
2
1
2
0
0
3
1
0
0
0
1
2
2
1
1
0
1
1
2
1
1
0
2
2
0
0
0
2
1
0
1
2
0
0
0
1
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
3
1
1
1
1
1
1
0
1
2
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
2
2
0
0
0
1
2
0
0
1
2
0
0
0
2
0
1
1
1
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
2
2
0
0
2
2
0
1
2
0
0
0
0
0
0
1
1
2
0
0
0
2
2
1
0
1
1
0
0
2
0
0
2
1
0
0
3
1
0
0
0
0
0
2
0
2
2
2
1
2
1
0
1
1
0
0
1
0
1
2
2
0
1
0
0
0
1
1
0
0
1
0
3
0
0
0
0
1
1
0
2
2
0
0
3
0
2
1
0
0
1
0
0
1
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
2
0
1
2
0
0
0
0
2
2
0
0
1
2
1
1
0
2
1
1
0
1
2
2
0
0
2
0
2
1
0
0
1
1
2
0
0
1
0
2
2
2
1
0
1
1
0
0
1
0
0
0
1
2
1
2
0
1
4
0
0
0
1
0
2
2
2
1
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
1
0
1
1
1
0
1
0
0
0
0
2
0
1
2
1
1
0
2
0
1
0
1
0
0
1
2
0
0
0
0
1
1
0
0
3
1
0
0
1
0
1
2
3
2
0
1
0
1
0
1
1
1
2
1
0
0
1
2
0
2
0
0
1
0
0
2
2
0
0
0
0
0
2
1
0
1
1
1
0
2
1
0
0
1
2
0
0
0
0
1
1
1
2
0
1
1
0
0
0
1
0
0
0
0
2
1
0
3
1
1
1
0
1
0
1
0
0
2
1
0
2
1
0
0
2
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
2
0
0
0
1
0
1
0
0
0
1
1
1
1
0
1
0
1
1
0
2
0
2
0
2
0
0
0
2
1
2
1
1
0
1
0
0
0
2
1
2
0
0
1
0
0
0
0
2
0
1
0
2
0
1
1
0
2
0
0
0
0
1
1
0
2
0
1
0
2
0
0
1
0
1
2
1
2
0
0
1
0
0
0
0
4
0
2
1
0
1
0
0
0
1
1
0
1
2
0
2
1
2
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
2
1
2
1
4
1
1
1
0
1
2
1
0
1
2
1
0
3
0
0
1
0
0
0
0
0
0
0
1
2
0
2
0
2
2
2
0
1
0
1
0
0
1
0
1
0
0
0
1
2
2
0
0
1
0
0
2
0
1
1
1
1
1
1
0
1
1
0
2
0
0
1
1
1
2
0
0
1
0
2
0
1
1
0
0
2
1
0
1
0
0
0
2
2
0
2
2
0
0
0
0
0
0
1
1
0
1
0
2
1
2
0
1
0
0
2
0
0
1
0
0
2
0
0
0
2
1
1
0
0
0
0
1
0
0
4
1
0
0
2
0
0
2
0
0
0
1
2
1
0
1
1
0
2
2
2
1
0
1
1
1
0
0
2
0
0
0
1
0
2
0
1
0
2
2
2
1
0
0
1
0
0
0
0
1
1
3
0
1
0
2
0
0
1
2
2
0
1
1
2
0
1
1
1
0
3
2
1
0
0
0
0
2
0
0
0
0
1
1
1
0
2
0
0
3
0
2
0
0
0
1
0
2
0
1
0
0
1
0
2
1
1
0
0
0
0
2
1
0
2
1
1
0
2
0
0
0
1
0
0
2
0
1
0
0
0
0
1
0
0
1
1
1
0
1
0
1
0
0
0
1
1
1
2
0
0
1
2
0
1
2
0
1
1
2
0
0
2
0
1
0
0
2
1
0
0
0
1
2
0
0
0
1
1
0
0
2
1
1
1
0
0
0
1
2
1
0
2
2
0
2
1
0
1
0
1
0
0
0
0
1
1
1
1
2
0
9
2
0
1
2
1
0
1
1
1
2
0
2
1
0
0
0
0
1
2
1
1
0
1
2
1
2
0
0
0
1
2
1
1
2
0
0
0
0
2
2
0
2
1
0
1
0
0
1
1
0
2
2
1
2
1
1
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
1
1
0
0
0
1
2
0
1
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
2
2
0
2
0
1
1
0
0
0
1
0
0
1
2
0
2
0
0
1
3
0
0
0
1
0
1
1
0
0
1
0
2
0
2
1
1
1
2
0
0
1
1
1
0
1
0
2
1
1
1
1
1
0
1
2
0
1
1
0
1
1
0
0
0
0
3
0
2
0
1
0
1
0
1
0
0
1
0
0
0
0
2
2
0
0
0
0
3
0
0
2
1
0
0
3
2
0
1
1
0
0
0
0
0
0
0
1
0
1
3
0
4
1
0
0
2
1
0
0
0
1
0
2
1
1
1
0
0
2
5
1
1
0
0
2
0
0
0
1
0
0
0
4
1
1
0
2
0
0
0
0
0
0
1
1
2
2
2
2
1
1
0
0
0
0
0
0
1
2
2
1
1
0
1
0
0
2
1
0
2
2
0
0
1
0
2
0
0
1
2
0
2
1
2
2
0
0
1
2
0
0
0
1
1
0
2
1
0
0
0
0
1
1
0
2
2
0
0
0
3
1
1
0
0
0
2
0
2
2
2
0
0
0
2
1
1
0
1
0
0
2
2
0
0
0
0
0
0
0
2
2
1
2
0
1
0
3
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
1
0
2
0
1
0
0
0
0
0
1
1
2
1
0
1
1
1
0
0
0
0
1
0
0
0
1
0
0
2
0
1
1
2
1
2
0
1
0
0
0
2
0
2
1
1
0
0
0
2
0
0
0
0
1
0
3
1
0
0
0
1
0
0
0
2
0
1
0
0
0
0
2
0
2
2
0
1
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
2
2
1
0
0
1
1
0
2
3
0
0
2
0
0
0
0
1
0
2
1
0
0
3
2
1
1
0
0
1
1
2
1
2
0
1
0
0
0
0
2
0
0
1
1
0
0
2
0
1
2
1
1
1
2
0
1
0
2
1
1
1
0
2
0
6
0
0
2
0
0
0
0
1
1
1
0
1
0
1
1
1
1
0
0
2
1
1
0
1
1
0
2
0
1
2
0
1
0
0
0
2
1
1
0
1
0
7
2
0
1
1
0
1
0
1
2
1
2
0
0
2
0
0
0
0
1
0
1
0
1
0
1
1
2
2
1
1
1
0
1
1
0
1
1
0
0
1
0
2
0
0
1
1
2
1
2
1
2
2
1
0
2
3
0
0
0
0
1
3
0
0
0
0
2
0
2
1
1
0
0
0
0
1
1
0
0
0
0
1
2
2
2
0
4
0
0
0
1
1
0
0
3
0
1
0
0
1
2
1
0
0
1
1
0
0
1
1
1
2
1
0
0
0
1
1
0
0
0
2
2
2
0
0
0
1
0
1
1
0
0
5
0
2
2
0
1
1
0
0
1
0
0
0
1
1
1
0
0
3
0
0
0
1
0
2
1
0
1
0
1
1
1
1
0
2
0
2
0
1
1
0
0
1
0
2
0
1
1
0
3
0
0
3
0
2
1
2
1
1
1
1
1
0
1
0
1
1
0
1
1
1
2
0
0
0
0
1
2
0
0
0
0
2
1
0
1
0
0
2
2
0
0
2
0
0
1
1
2
0
1
2
2
0
0
1
2
0
0
1
2
1
1
0
1
1
0
2
2
1
0
1
1
0
0
1
0
0
2
1
0
2
1
1
0
0
1
0
2
0
0
1
1
2
0
2
2
0
0
1
0
1
1
1
0
2
2
1
0
0
1
1
0
0
2
0
0
0
1
2
0
0
0
0
0
1
1
2
2
1
0
0
2
2
0
0
0
2
1
0
0
0
0
0
0
1
1
0
1
0
0
2
0
0
0
1
2
0
0
2
0
1
0
0
0
0
0
0
1
1
0
1
0
3
0
2
3
0
2
1
1
1
1
0
2
2
0
4
0
0
0
0
3
0
0
2
0
0
0
1
0
1
1
0
1
0
2
0
0
0
1
0
1
2
0
0
0
1
1
0
0
1
0
0
0
0
0
1
2
2
0
0
1
2
1
1
1
1
0
2
0
1
0
0
1
3
0
2
2
1
2
1
1
1
1
0
1
0
0
1
0
0
2
1
0
0
0
0
1
1
1
2
1
1
0
2
0
0
0
0
0
2
1
1
0
2
1
0
0
0
0
2
2
0
0
2
1
0
1
1
0
1
1
0
0
0
0
1
1
0
0
0
0
0
2
0
1
0
0
0
2
1
0
2
0
0
1
1
1
0
0
2
2
0
1
1
2
0
1
2
0
1
2
0
0
2
0
2
1
0
0
1
0
0
0
2
0
0
1
2
2
0
2
1
2
2
2
0
0
0
0
1
0
1
1
0
0
0
0
0
1
1
0
0
0
2
1
0
0
2
2
0
0
1
0
0
0
0
0
1
1
2
2
0
0
2
0
2
0
1
0
1
2
0
2
1
2
1
0
2
2
0
1
1
1
0
0
0
1
2
1
0
0
1
2
0
0
1
0
2
1
0
0
0
0
0
1
0
1
0
2
0
0
0
0
2
1
1
0
0
0
2
2
4
1
1
1
0
0
0
2
2
0
0
2
0
2
2
0
0
1
0
2
0
1
1
0
0
2
0
0
1
2
0
1
0
2
0
0
1
0
1
0
0
0
1
1
0
0
1
1
0
0
2
0
1
2
1
1
1
1
2
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
1
1
1
1
0
0
1
2
0
1
0
1
0
1
1
1
2
0
2
2
0
0
2
2
0
1
0
0
2
2
0
0
3
2
1
0
2
0
0
1
0
2
1
1
0
0
0
1
0
1
0
0
0
1
1
0
1
0
0
0
0
1
0
0
2
0
0
1
1
0
0
0
1
2
0
0
0
0
1
0
1
0
2
0
1
2
0
0
0
2
0
1
2
2
0
1
0
0
1
0
0
0
1
0
0
0
2
0
0
2
0
1
1
1
0
2
1
2
0
2
1
1
6
0
2
0
0
0
0
0
0
1
0
0
1
2
1
0
1
1
1
2
0
0
0
2
1
0
2
0
1
0
0
2
0
2
2
0
0
2
1
0
0
1
0
2
2
0
0
1
1
0
1
1
0
1
0
0
1
0
2
2
0
0
4
0
2
0
1
0
0
0
0
0
1
1
0
2
1
2
1
0
2
0
0
1
0
0
0
0
0
0
1
2
0
1
1
1
1
0
0
1
2
4
0
2
1
0
0
3
0
1
0
1
2
0
0
0
0
2
1
2
0
1
0
1
1
0
0
0
0
1
0
0
2
0
1
2
0
1
1
0
0
2
1
0
0
2
1
0
0
1
0
1
2
0
0
0
0
0
0
0
2
0
1
1
0
0
1
0
0
0
2
0
0
1
0
1
2
0
1
0
0
2
0
0
0
0
2
1
1
2
0
0
2
1
0
2
2
0
1
0
2
0
2
0
2
1
0
2
1
0
1
0
2
2
1
1
2
0
3
1
0
0
2
2
1
0
0
2
0
0
1
0
0
1
1
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
2
0
1
0
0
1
1
1
0
1
3
0
0
0
2
2
1
1
0
1
0
2
1
2
0
1
0
2
1
1
1
0
0
0
2
0
1
0
2
2
0
0
2
1
0
1
0
1
0
1
0
2
1
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
2
2
2
0
1
2
0
0
1
0
0
2
0
0
1
0
0
0
1
1
1
0
1
2
0
2
0
1
1
0
1
0
3
0
1
1
0
1
3
0
2
0
1
2
1
0
0
0
0
0
0
0
1
1
0
2
0
2
1
0
0
0
0
6
1
1
1
1
0
0
0
0
0
0
0
2
1
0
1
1
3
3
0
1
1
1
0
1
2
1
0
1
2
0
0
0
0
0
2
0
1
0
2
2
0
0
1
0
2
0
0
1
0
2
2
1
0
1
1
0
0
0
0
1
1
2
0
0
1
1
0
1
2
1
0
1
0
0
1
0
0
2
2
0
0
1
2
0
0
0
1
1
2
0
0
1
1
0
0
1
0
2
2
0
0
0
0
1
1
0
2
2
1
1
0
1
1
0
1
0
0
0
0
0
0
0
2
0
1
0
0
2
0
1
0
1
0
2
0
0
0
2
2
2
1
1
2
2
1
0
0
1
0
0
1
2
0
1
1
3
0
0
2
1
6
1
1
0
2
0
0
2
0
0
2
0
1
0
2
1
0
1
0
1
0
0
0
0
2
0
2
2
0
1
0
0
2
1
0
2
2
0
0
2
1
1
2
1
1
2
0
2
1
1
2
0
1
2
1
0
0
0
0
0
0
1
1
0
1
1
2
2
2
2
0
1
1
1
0
0
1
1
2
2
0
1
2
0
0
0
0
3
1
1
1
2
0
0
0
1
2
1
2
3
0
0
2
2
2
1
0
2
0
0
0
0
0
0
2
0
2
2
0
1
2
2
1
1
1
1
1
1
2
2
2
2
0
1
2
2
1
2
2
2
1
1
1
2
1
2
0
0
0
0
1
1
0
1
0
1
0
0
0
1
0
0
1
0
0
0
1
1
0
1
1
0
1
1
1
0
0
0
1
0
2
3
0
0
0
2
2
0
0
0
1
1
2
0
1
0
0
0
2
0
2
0
2
0
0
0
1
0
2
1
2
0
0
1
0
2
2
2
1
0
0
0
2
0
1
0
0
0
0
0
2
2
1
0
2
2
1
1
0
1
0
2
0
1
1
1
0
1
2
2
0
0
2
1
0
0
1
2
2
0
0
1
0
0
0
1
0
2
0
1
0
1
2
0
0
1
0
0
0
2
0
1
0
1
0
0
0
0
0
1
1
0
0
2
1
0
0
3
0
1
0
0
0
2
0
0
1
0
2
2
0
0
1
0
1
0
0
0
1
2
1
2
1
0
0
0
0
0
4
2
0
1
1
0
0
0
2
0
1
0
0
0
1
0
2
1
1
1
0
1
2
1
0
2
2
1
0
1
0
0
1
2
0
1
2
2
0
0
2
0
1
0
0
1
1
0
0
0
1
0
1
1
0
2
1
1
0
1
0
1
0
0
0
2
0
2
0
2
0
1
0
1
1
0
0
0
1
2
0
0
1
1
2
0
1
1
1
0
0
0
0
1
2
2
2
0
0
1
1
1
4
1
0
1
2
0
1
2
0
1
2
0
1
0
0
0
2
0
1
1
0
0
0
1
1
0
0
0
0
1
0
2
0
2
0
1
0
0
0
1
0
2
0
2
0
0
1
0
0
0
1
0
1
1
0
0
1
0
0
0
0
1
0
1
1
0
0
1
2
0
0
0
0
1
1
1
0
2
2
0
0
1
0
1
0
0
0
0
0
0
1
1
1
1
0
0
1
1
0
0
1
1
0
0
2
0
2
2
0
1
0
0
0
0
0
0
2
1
3
0
1
2
0
0
0
2
1
0
0
0
0
2
3
0
0
0
1
0
0
1
1
0
2
0
1
0
1
0
0
1
1
2
1
0
0
2
0
2
2
1
0
1
0
0
0
0
1
0
1
1
0
1
0
1
2
0
0
0
0
1
0
0
2
2
0
0
2
0
2
0
1
0
0
0
1
1
2
1
1
0
0
0
1
0
0
1
1
2
0
0
0
0
1
1
1
2
1
1
2
0
0
0
0
0
1
1
0
0
1
2
2
1
1
2
1
1
3
0
0
0
1
0
2
1
0
0
2
0
2
0
1
0
0
0
0
0
2
1
2
1
2
0
2
0
0
0
0
1
1
0
0
2
0
2
1
0
1
0
1
0
0
0
1
2
2
0
0
1
0
0
1
1
1
1
2
0
0
1
0
1
0
0
1
0
1
1
1
0
0
0
2
2
0
3
0
2
0
1
0
0
0
1
2
0
0
1
0
2
0
0
1
0
1
0
0
0
1
1
1
0
2
1
0
2
0
0
2
2
2
0
0
0
0
1
2
1
0
0
1
1
1
0
1
0
0
0
0
2
0
2
0
0
0
1
2
0
1
2
0
0
1
1
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
2
1
1
0
2
2
0
0
0
0
0
1
0
1
2
0
0
1
2
0
0
0
1
1
0
1
0
0
0
0
2
0
1
0
1
0
0
2
0
0
0
1
0
1
0
2
2
0
0
0
0
0
2
0
0
2
1
0
2
1
0
0
0
0
1
1
0
2
0
0
1
1
0
1
0
2
2
0
1
0
1
0
0
0
0
4
0
1
0
2
2
0
1
0
1
0
1
2
0
0
1
0
2
0
2
1
0
1
2
1
0
0
1
2
0
0
1
2
0
0
0
1
0
1
0
2
0
2
2
1
0
1
0
0
0
0
1
1
0
1
0
0
0
2
0
0
2
0
0
2
0
0
0
1
1
0
0
0
2
0
0
0
1
1
0
2
0
1
1
0
0
1
0
1
1
1
0
1
1
1
0
0
0
0
2
0
1
0
0
1
2
0
0
0
0
1
1
2
2
1
0
2
2
1
2
0
0
0
1
0
2
3
0
1
1
1
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
2
0
1
1
1
0
0
0
0
0
0
1
0
0
2
2
2
0
1
0
0
2
0
1
0
1
1
0
0
2
0
1
2
0
1
0
2
1
1
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
1
1
0
2
0
0
1
0
1
2
0
2
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
1
0
2
0
1
0
0
0
2
2
2
1
1
1
0
2
2
0
0
3
0
1
1
3
0
0
0
1
0
2
2
0
0
1
0
0
1
1
0
1
0
0
0
0
1
2
0
2
1
2
1
1
1
0
0
0
0
0
2
1
0
0
2
2
1
0
2
2
1
1
1
0
0
0
2
1
1
0
1
1
0
0
1
0
0
0
1
2
1
0
1
0
0
1
0
0
1
0
0
0
0
2
1
0
1
0
1
1
2
0
2
2
0
0
0
3
1
1
0
1
0
0
1
0
1
0
1
2
2
2
0
2
0
1
0
2
1
2
2
0
0
0
1
1
3
2
2
1
0
0
2
0
0
1
1
2
2
0
0
2
1
2
0
1
1
1
2
0
0
1
1
2
2
0
1
0
0
0
2
0
0
1
2
0
1
0
2
0
1
0
1
2
4
0
0
0
1
0
0
0
2
1
0
1
0
0
2
4
2
1
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
2
0
2
1
1
0
2
0
0
0
2
0
0
0
2
1
0
3
1
0
0
1
1
0
2
0
0
0
0
1
2
0
2
1
0
2
0
0
0
2
0
0
0
0
2
0
0
2
1
0
0
0
0
1
0
0
2
1
2
1
2
1
1
0
0
0
0
1
0
0
3
0
1
0
0
0
1
0
0
2
0
0
1
0
0
0
1
0
2
1
0
1
2
1
2
0
0
0
1
2
1
0
1
0
0
0
2
1
2
1
0
0
1
1
0
0
0
0
1
1
2
0
1
1
0
1
0
2
2
0
0
1
0
0
1
0
0
0
0
1
0
1
0
1
2
2
0
0
0
0
1
1
0
1
1
0
0
0
0
1
0
0
0
2
2
1
0
0
1
2
0
1
0
1
1
3
1
0
0
0
1
1
0
0
2
0
0
3
0
0
1
1
0
1
1
3
1
2
0
1
2
1
1
2
1
0
0
0
0
3
1
1
2
2
1
1
1
1
0
1
1
1
0
1
0
0
1
1
0
2
0
2
0
2
0
1
1
0
0
2
0
0
0
1
2
2
2
1
2
2
0
0
0
0
0
0
0
0
0
2
0
2
1
2
0
1
0
0
0
0
0
0
0
0
2
0
2
0
2
2
3
0
0
0
1
0
1
0
1
1
3
1
0
0
1
0
1
0
2
0
0
0
0
2
1
0
0
2
0
2
1
1
2
0
0
1
2
0
0
1
0
2
2
0
0
0
0
1
1
2
2
0
0
1
2
1
0
1
1
0
1
2
0
0
2
2
0
0
2
0
0
0
0
0
0
2
2
1
0
1
0
0
1
1
2
2
1
0
2
0
0
1
0
0
0
0
0
1
1
0
2
0
0
0
6
0
1
0
0
0
1
0
0
0
1
0
0
1
1
1
0
1
2
1
0
2
0
1
1
0
1
0
1
2
1
0
2
1
1
2
1
1
1
0
0
1
1
2
1
1
0
1
2
1
0
0
0
0
0
1
2
0
0
0
1
2
1
1
0
1
0
0
0
0
1
2
0
2
0
0
0
0
2
0
1
0
0
0
0
1
0
1
0
0
0
1
3
1
0
2
1
2
0
0
1
1
1
2
1
4
2
1
0
0
0
2
0
0
0
0
1
1
2
0
2
0
0
2
0
0
0
0
1
2
0
0
2
0
2
3
0
0
0
0
1
2
1
0
1
0
2
0
1
1
0
2
1
0
1
2
0
2
0
1
1
0
0
0
2
1
1
1
1
1
0
0
0
0
0
0
0
1
0
0
2
1
2
0
2
0
1
1
0
0
0
2
2
1
1
0
0
0
1
2
0
1
0
2
0
0
0
1
0
1
2
1
0
1
1
1
1
2
0
0
0
0
0
0
1
0
1
3
0
0
0
0
1
1
1
0
0
1
2
0
0
0
0
0
1
1
2
0
0
1
2
0
2
2
0
0
2
2
0
0
0
0
2
2
1
0
2
0
1
0
0
0
1
0
1
0
1
2
0
1
0
1
0
3
0
2
1
2
2
1
0
0
0
0
0
0
0
1
4
1
2
0
0
0
0
0
0
0
0
0
1
1
2
0
2
0
0
2
0
2
2
1
1
0
0
0
0
0
2
2
0
2
2
0
0
0
0
0
2
3
2
0
1
2
1
3
1
1
1
1
0
1
0
0
0
2
1
2
1
0
2
0
1
0
0
1
1
0
2
0
2
0
1
1
0
0
1
1
0
0
0
0
2
1
0
1
1
0
0
0
1
0
0
0
0
0
2
1
2
0
0
0
1
2
0
0
1
1
1
2
0
0
0
1
0
1
1
2
2
1
3
2
1
0
0
1
0
2
1
1
0
2
1
0
2
0
0
2
0
0
0
2
0
2
0
0
2
3
0
0
0
1
0
0
1
0
2
0
1
0
1
1
2
2
0
0
0
0
2
1
1
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
1
2
0
0
2
0
1
2
0
0
0
0
2
0
1
1
0
0
0
2
1
1
0
0
1
1
2
2
1
2
0
0
1
0
0
0
2
2
0
0
0
0
0
1
1
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
1
0
2
2
0
2
2
0
0
0
0
1
0
0
0
2
0
0
0
2
0
1
0
0
1
0
0
2
0
0
1
1
2
1
0
2
0
1
0
0
1
0
1
0
2
1
1
1
3
1
0
0
1
0
1
1
0
1
1
1
0
0
0
0
0
2
0
0
1
1
1
2
1
1
2
0
2
0
2
3
0
2
2
1
1
0
2
0
0
0
2
0
2
0
0
1
2
1
0
0
1
0
1
1
0
2
4
0
0
0
2
0
2
0
2
1
0
4
0
1
0
0
2
2
1
2
1
0
0
2
0
1
0
0
4
0
0
1
2
1
2
0
2
2
0
0
1
0
1
0
0
2
1
0
0
0
0
0
0
0
1
1
1
1
0
1
0
1
2
0
0
0
0
1
0
2
0
0
1
1
2
0
1
0
0
1
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
4
2
0
0
0
0
0
2
0
2
2
0
0
0
1
0
1
1
0
0
1
0
1
0
0
1
0
0
2
1
0
0
0
1
0
1
0
2
0
0
2
0
2
0
0
0
1
1
0
0
0
0
1
0
0
2
0
1
1
1
2
1
1
2
1
0
0
1
0
1
0
2
0
2
0
2
0
0
1
1
2
0
2
0
0
0
2
0
0
0
1
1
0
2
0
0
2
1
1
1
2
0
0
1
2
0
0
0
1
0
2
0
1
0
2
0
0
1
0
1
2
1
2
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
1
0
1
1
0
0
1
0
0
1
0
0
1
1
0
0
3
2
0
1
0
0
0
0
0
0
1
0
1
0
2
2
1
0
0
0
2
2
2
0
1
2
0
0
1
2
1
0
0
2
1
0
1
1
2
2
2
1
1
2
0
1
2
1
1
0
1
1
8
1
0
3
1
0
0
0
1
0
0
2
0
1
0
0
0
0
1
0
0
0
0
1
0
3
0
0
0
0
1
0
1
0
0
1
0
0
1
0
1
0
1
2
0
0
1
0
1
0
0
0
1
0
1
0
1
0
0
1
2
1
0
0
1
0
1
0
4
1
1
1
0
2
1
0
2
1
0
2
2
0
2
0
1
0
0
1
3
2
2
1
1
0
0
1
1
1
0
0
0
3
1
0
0
0
0
2
0
0
2
0
2
0
0
0
1
0
0
1
0
1
0
0
2
2
0
1
0
2
0
4
0
0
0
0
0
2
1
0
0
2
2
1
0
0
0
2
2
1
2
1
2
0
0
2
2
1
0
0
0
1
2
2
2
2
1
0
2
0
1
1
0
1
1
0
0
2
0
1
0
0
5
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
1
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
1
2
0
1
0
0
0
2
0
11
0
0
1
0
1
1
2
0
0
0
3
2
0
0
1
0
1
2
0
0
1
0
0
1
1
1
1
0
0
2
0
2
1
2
2
2
1
2
2
0
0
0
2
1
2
2
2
0
0
0
3
1
0
0
0
1
0
1
0
2
2
0
1
1
1
0
1
0
1
0
0
2
0
0
1
1
1
0
0
2
1
0
1
2
0
0
0
1
2
0
0
2
0
1
0
2
2
0
0
0
1
0
2
2
0
0
1
0
1
1
3
0
0
0
3
0
0
0
2
3
0
0
0
1
1
0
1
0
0
2
1
0
0
1
1
1
1
0
2
1
0
1
1
1
0
0
0
1
2
2
2
2
0
0
0
2
2
2
0
0
1
1
1
2
1
0
1
0
1
1
2
1
1
1
1
2
1
1
2
0
2
1
0
0
0
0
0
0
1
2
1
5
0
1
0
2
2
1
0
0
2
0
0
2
1
1
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
2
0
0
0
1
0
0
1
0
1
1
0
1
2
0
0
0
2
2
1
0
2
1
2
0
1
0
1
0
0
2
2
0
0
1
0
1
0
1
0
0
2
0
2
2
2
1
1
0
0
1
1
0
0
0
0
0
2
0
1
2
0
0
0
2
2
0
0
0
2
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
2
1
0
1
2
1
0
1
0
2
1
2
0
0
1
0
0
0
1
1
0
1
2
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
1
0
0
0
2
0
1
0
1
2
1
0
1
1
2
0
0
2
0
0
0
0
0
2
0
0
0
2
2
0
1
1
0
1
0
1
0
2
1
2
0
0
2
0
2
2
1
1
0
1
1
0
1
1
1
0
2
0
1
5
1
3
1
1
2
0
1
1
0
2
1
2
0
2
0
1
2
1
2
1
0
0
1
1
2
1
2
1
0
1
1
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
1
1
0
0
2
1
0
0
0
0
0
2
0
3
0
0
0
0
2
2
1
2
2
1
0
2
0
1
0
1
0
0
1
2
0
3
1
1
1
0
0
1
0
0
2
1
2
0
0
1
0
0
1
1
0
1
0
2
0
1
3
0
1
0
0
1
0
1
1
2
1
0
1
0
1
2
0
1
0
0
2
1
0
0
0
1
2
1
1
1
0
0
1
2
1
1
1
0
0
0
1
0
0
0
0
2
1
0
1
0
1
0
0
0
2
0
0
1
2
0
1
0
1
1
0
0
2
0
0
0
2
0
0
1
0
2
0
0
2
0
2
1
1
2
1
1
1
0
2
2
2
0
0
0
1
1
0
0
0
0
0
0
2
1
2
0
0
0
0
0
2
0
0
1
0
1
0
0
0
2
2
0
0
2
2
1
1
1
1
1
0
0
1
0
0
1
1
2
2
1
0
0
1
1
0
0
2
1
1
1
1
1
0
1
1
0
2
0
2
1
1
2
1
2
2
2
0
0
0
0
1
0
0
2
1
2
2
0
1
0
0
0
1
0
0
1
1
1
2
0
2
1
0
1
1
0
0
2
1
1
0
0
3
1
1
2
2
0
1
2
1
0
2
0
0
0
2
0
1
0
0
1
2
2
2
1
2
0
0
1
2
0
0
2
0
0
1
0
0
1
0
2
1
0
1
2
0
1
0
2
0
0
0
0
0
0
1
1
2
1
1
1
0
0
1
0
2
1
0
0
0
1
4
0
2
0
2
1
2
0
3
1
2
0
0
0
1
0
0
1
2
3
1
1
0
1
0
1
1
1
1
1
0
2
0
1
1
2
0
0
2
0
1
0
1
1
1
1
1
1
0
2
0
2
0
0
1
1
1
1
0
2
1
2
0
0
1
2
1
0
1
0
3
0
0
2
2
1
2
2
0
1
1
1
0
0
1
1
0
2
1
0
2
2
0
2
0
0
1
1
1
2
0
0
0
0
1
0
1
0
0
1
2
2
1
3
1
0
3
1
2
0
0
0
0
2
0
2
2
0
1
2
1
2
1
2
0
1
0
0
1
0
0
2
0
0
1
0
3
0
0
1
1
1
1
2
0
1
2
1
0
0
0
0
1
0
0
0
2
0
0
0
2
1
0
1
0
0
0
0
0
2
1
0
0
2
0
0
0
0
1
1
1
0
2
2
1
0
1
1
1
2
2
0
0
1
1
1
1
1
0
2
0
0
0
1
1
0
0
0
1
1
0
0
1
0
0
0
0
1
0
1
1
1
1
2
0
1
2
2
0
0
0
0
2
2
1
1
0
2
1
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
2
0
2
1
0
0
1
1
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
2
0
0
1
1
0
2
1
0
2
1
0
0
2
0
0
0
0
2
2
0
0
2
0
0
2
1
1
0
1
0
0
1
0
0
0
0
2
1
0
0
1
0
2
0
2
1
1
0
0
0
0
1
0
1
1
0
0
1
1
2
0
0
2
1
2
1
1
2
0
1
2
2
0
2
0
0
0
0
0
1
2
0
0
1
2
1
1
2
0
0
0
2
1
0
0
0
0
0
2
0
0
1
1
0
0
0
1
1
0
0
1
0
0
0
0
2
0
0
2
2
0
1
0
0
0
0
0
0
0
2
2
0
0
1
0
1
0
0
1
0
2
2
1
0
1
0
0
0
2
0
0
1
1
0
0
0
0
0
2
0
0
1
0
0
1
0
0
1
0
1
2
2
0
1
2
1
0
2
1
2
0
2
1
1
0
1
0
0
1
1
1
0
1
2
1
1
0
1
0
1
0
1
0
0
0
0
1
0
0
0
2
0
2
2
0
0
1
0
2
2
2
1
0
0
2
1
0
0
0
2
0
1
2
0
1
0
1
1
0
1
2
1
1
0
0
1
2
1
1
0
0
1
3
0
1
0
2
0
1
1
0
2
1
0
0
1
2
0
0
3
0
2
0
2
0
1
1
1
0
1
0
2
0
0
2
0
2
0
0
0
0
0
1
2
0
1
0
1
0
2
0
2
0
0
1
4
0
1
2
0
0
1
0
1
0
2
1
1
0
0
1
2
0
0
2
0
1
1
0
2
2
3
0
0
3
1
2
1
1
0
2
0
2
1
0
0
1
1
2
0
0
0
0
0
0
0
3
0
1
0
0
1
2
0
1
0
0
0
2
1
1
1
2
1
0
0
0
2
2
0
0
0
1
1
0
1
1
3
0
3
1
0
1
0
1
0
1
2
0
0
1
0
2
0
1
0
0
2
1
0
2
0
0
2
2
2
2
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
2
2
1
0
1
0
1
2
0
1
1
0
2
1
0
0
0
0
1
1
1
2
1
1
0
1
1
0
3
1
0
2
0
2
1
0
1
1
1
0
0
0
2
2
1
0
3
0
0
0
0
1
1
0
1
1
0
0
1
1
0
0
1
1
0
1
1
1
2
0
2
0
2
1
0
2
2
1
1
1
0
0
0
0
2
0
1
0
3
1
1
1
0
2
0
1
0
2
1
0
0
2
2
0
0
0
1
1
2
1
1
2
0
1
1
1
0
2
0
1
0
1
1
1
0
1
1
2
0
0
2
0
0
2
0
1
1
0
0
0
2
0
0
0
0
2
1
2
1
0
0
0
1
1
1
0
0
0
0
1
0
0
2
0
1
0
0
0
2
0
0
1
1
0
2
1
2
2
1
0
0
2
1
1
0
1
1
0
2
0
0
0
1
1
1
2
3
3
2
1
0
0
1
1
1
0
0
0
1
0
0
2
1
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
1
1
1
1
5
1
2
2
2
0
1
0
1
0
1
1
0
0
0
2
1
2
1
0
0
0
1
1
1
3
1
1
0
2
0
0
0
0
2
2
0
0
0
0
0
3
1
2
0
1
2
2
3
0
1
0
1
0
1
1
1
0
2
1
0
0
1
0
0
1
1
1
2
0
0
0
1
0
0
1
0
0
2
0
0
1
0
1
0
1
1
0
1
0
0
0
0
0
2
2
0
0
0
2
2
0
0
1
0
0
1
1
0
0
0
0
0
2
1
1
1
0
1
0
1
2
1
0
0
0
0
0
2
2
0
0
2
0
1
0
2
1
2
1
1
1
4
1
1
0
1
0
0
0
3
1
0
3
2
1
0
1
1
0
2
0
1
1
0
0
0
0
1
1
0
1
2
0
1
2
2
2
0
0
1
1
1
0
0
0
1
3
2
2
2
0
0
1
2
0
0
1
0
1
2
2
0
1
0
1
0
1
0
0
2
0
0
1
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
2
0
0
3
0
0
2
0
2
1
0
0
2
1
0
2
2
0
0
0
0
2
2
0
1
0
0
0
1
2
0
2
2
0
0
2
2
0
1
1
1
0
0
0
2
0
2
1
1
0
0
1
0
2
0
1
1
1
2
1
0
0
1
2
0
0
2
0
2
2
0
1
0
1
1
0
0
0
3
3
0
1
0
1
1
0
0
0
2
0
0
0
0
0
0
0
1
2
3
1
0
0
1
0
1
1
0
1
1
2
0
2
2
0
1
0
4
5
0
2
2
0
1
0
0
0
2
1
0
1
0
2
1
1
0
2
0
2
1
1
1
0
0
0
1
0
0
0
0
0
0
0
1
2
1
0
2
0
1
1
0
0
0
2
1
1
0
1
0
0
2
1
2
1
0
0
1
1
0
2
0
2
2
0
2
0
1
0
1
0
2
0
1
0
1
0
1
0
1
0
0
2
1
0
2
0
0
2
1
0
1
2
2
0
1
1
1
0
1
1
0
0
2
2
2
0
0
0
2
1
2
1
1
1
0
0
2
2
2
2
2
0
0
0
2
0
2
0
1
0
1
1
0
1
2
1
1
0
0
0
0
0
1
2
2
0
0
1
2
0
0
1
0
2
0
0
1
1
1
0
0
2
0
1
0
2
0
1
2
1
2
0
0
0
0
2
2
0
0
0
0
0
2
1
3
1
0
0
0
2
1
1
0
0
2
0
2
1
0
2
1
1
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
1
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
1
0
1
1
2
0
0
0
0
1
1
0
0
0
0
0
2
1
0
0
1
0
1
0
2
0
0
1
3
1
0
1
2
0
4
1
0
1
0
0
0
0
0
1
1
0
2
2
2
2
0
0
0
0
0
0
0
2
0
1
2
0
0
2
1
0
0
1
0
0
0
0
0
1
1
1
0
1
1
0
1
0
0
0
1
0
0
0
0
2
0
1
1
2
1
1
2
2
0
0
0
3
0
2
0
1
0
2
1
0
2
1
2
2
2
1
0
2
1
1
1
1
2
1
0
0
0
1
1
1
2
0
0
2
1
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
2
2
2
0
0
0
0
0
0
2
0
1
0
2
2
0
0
1
1
2
0
0
2
1
0
1
1
1
1
2
0
2
2
0
0
1
2
1
0
0
0
1
0
0
0
1
1
0
0
1
0
0
1
2
0
0
0
1
0
1
6
0
1
2
0
1
1
1
1
1
1
2
1
1
1
1
0
2
2
0
2
0
0
0
0
0
3
0
2
0
1
0
1
3
1
2
2
0
0
2
2
0
1
0
0
0
1
1
0
2
0
0
0
1
1
1
0
1
0
1
0
0
1
1
0
0
1
2
2
3
1
1
4
0
1
0
0
2
0
0
0
2
3
1
2
0
0
1
1
1
1
1
0
0
0
0
1
0
2
1
0
0
1
1
2
0
1
1
1
0
2
0
0
2
1
1
0
0
0
2
0
2
0
2
1
0
0
0
0
2
1
4
0
3
2
0
4
0
0
2
2
0
2
0
0
0
0
0
2
0
2
1
0
0
0
1
0
0
2
0
0
1
1
0
1
0
1
1
0
1
0
0
0
0
1
1
1
1
2
1
0
2
0
0
1
3
0
1
2
1
0
2
1
0
1
2
2
1
0
0
1
1
1
0
2
0
2
1
1
0
0
1
0
0
1
1
2
2
1
0
2
0
0
0
2
0
3
0
0
3
0
0
0
0
0
0
0
1
2
2
0
1
1
0
1
0
0
0
0
1
1
0
0
1
1
2
0
1
2
1
0
2
1
2
0
1
0
1
0
1
1
0
2
0
0
0
2
0
0
0
2
2
0
1
1
0
1
0
1
2
0
1
0
2
0
0
0
0
1
2
2
0
1
2
1
3
0
1
0
2
2
2
1
0
1
0
0
0
2
1
1
0
0
0
1
1
1
1
0
1
0
0
1
0
2
0
1
1
0
1
0
0
0
1
0
1
1
1
0
1
1
1
0
2
1
1
0
2
0
0
1
1
0
0
2
0
1
0
0
1
2
0
1
2
2
0
0
2
1
0
0
1
0
0
0
2
0
0
2
0
2
0
0
0
0
1
0
1
1
0
2
0
1
0
2
1
0
1
0
0
0
2
1
0
0
0
0
1
0
0
1
0
0
0
1
0
2
0
0
2
0
0
0
2
0
0
0
2
0
1
3
1
0
2
0
0
2
0
2
0
0
1
1
2
0
1
1
0
0
0
1
0
1
0
1
2
1
2
0
0
1
0
2
1
1
0
0
2
2
0
0
1
0
0
0
1
1
0
2
2
2
0
1
0
2
0
1
2
1
1
1
2
0
0
0
0
0
2
0
0
0
0
1
0
0
2
2
1
0
0
0
1
1
2
1
1
0
0
0
1
0
0
1
0
0
1
1
0
2
0
0
0
1
0
1
0
0
0
1
1
1
0
1
1
1
1
0
0
2
0
2
0
1
2
1
1
1
0
1
1
2
0
2
1
0
1
0
1
0
1
7
1
0
1
1
0
1
0
0
0
2
0
1
3
2
1
1
1
1
1
1
0
1
1
1
0
1
1
1
0
1
0
2
1
2
0
0
0
0
0
0
1
0
1
3
2
0
0
2
0
1
1
1
0
1
1
0
2
0
0
0
1
1
0
0
0
0
0
1
1
2
2
1
0
5
0
1
0
0
2
1
0
1
2
2
0
0
0
0
0
1
0
0
2
1
0
3
1
0
0
0
1
0
0
0
1
1
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
1
1
0
1
0
2
0
0
0
0
1
2
0
2
1
1
1
0
0
0
1
0
0
0
2
0
1
1
0
0
1
1
0
1
0
0
2
1
1
1
2
1
2
0
2
0
0
2
2
0
2
0
1
0
2
1
1
2
2
1
0
1
0
0
1
2
2
0
0
2
0
0
1
0
2
1
1
0
0
0
1
1
1
0
1
2
0
0
1
1
1
1
0
0
2
2
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
1
2
0
0
0
0
0
3
1
0
1
2
0
0
0
0
3
2
2
1
0
0
0
2
0
1
0
0
0
1
0
2
0
0
0
0
1
2
1
1
0
0
0
0
1
0
1
2
1
2
2
0
2
0
2
2
0
0
0
2
0
1
0
2
1
0
2
0
4
0
1
1
1
1
2
2
1
0
0
2
1
0
0
0
1
0
0
1
0
0
1
1
0
1
0
1
1
2
0
0
0
0
2
0
0
0
1
0
1
0
2
0
0
0
0
0
0
1
0
0
0
1
1
2
0
0
0
2
0
1
0
0
0
1
0
0
0
2
2
0
0
1
2
0
0
1
0
0
1
0
2
0
2
1
2
2
0
0
2
2
3
2
1
0
1
0
1
0
0
2
0
0
0
1
0
1
1
0
0
0
1
0
1
0
0
1
2
2
1
1
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
2
0
0
1
2
1
0
1
4
1
2
0
2
0
0
0
6
1
0
0
2
1
1
1
0
2
0
0
0
0
2
0
0
1
1
1
1
0
1
0
0
0
0
1
0
0
0
2
2
1
1
0
1
2
0
1
1
1
0
0
0
0
0
1
2
0
0
2
0
0
0
1
0
0
2
0
1
2
4
1
0
0
2
2
0
0
1
1
2
0
0
0
2
2
2
5
2
2
0
0
0
1
1
0
0
2
1
2
1
0
0
0
1
2
1
2
1
0
2
2
1
0
0
1
0
1
0
2
1
0
1
0
0
2
1
0
1
0
2
0
1
0
0
0
3
1
0
0
1
0
1
1
1
1
0
0
0
2
0
0
0
0
1
0
2
0
3
0
0
0
0
1
1
2
2
2
1
0
0
0
1
0
2
0
2
1
2
1
2
0
1
2
0
1
0
0
0
2
3
0
0
1
0
0
1
2
0
2
0
0
2
0
0
2
2
0
0
0
3
1
0
0
2
1
1
3
2
1
0
1
1
1
0
1
0
0
1
0
0
1
0
0
0
0
3
2
0
0
1
0
0
0
0
2
1
2
0
2
1
2
1
0
0
0
1
0
1
0
1
0
0
1
0
2
2
2
2
0
0
0
0
2
0
0
0
0
0
0
2
0
3
0
0
0
0
0
1
2
0
1
0
0
1
0
0
3
1
0
1
2
0
1
0
0
0
2
1
0
0
1
1
0
2
1
0
2
1
0
2
0
1
2
0
1
1
1
0
2
2
0
0
2
4
0
0
2
0
1
1
0
1
0
1
0
0
0
1
1
1
1
1
1
2
2
1
1
1
1
0
0
0
1
0
0
1
0
2
1
0
1
1
0
2
2
1
0
2
2
1
0
1
1
1
0
0
0
0
1
2
2
2
2
1
1
1
0
1
2
0
0
0
1
1
0
1
0
2
0
3
1
0
2
0
2
0
0
3
2
0
0
0
2
0
0
1
1
0
1
2
1
1
0
2
0
1
0
0
1
2
0
0
3
0
1
1
2
0
0
2
0
1
0
0
1
1
0
1
0
0
1
1
3
0
0
0
1
1
1
1
0
0
0
1
2
0
0
1
0
2
0
1
1
2
0
2
0
0
1
1
0
2
0
0
0
0
2
2
2
2
0
0
2
0
1
2
2
0
2
0
1
2
1
3
2
2
1
1
0
1
0
0
1
1
1
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
1
1
0
0
1
1
1
0
2
0
0
0
0
2
1
0
0
0
0
2
0
0
2
1
1
1
2
0
1
0
0
1
0
0
2
1
1
2
0
1
2
0
2
1
1
0
1
0
1
2
0
2
1
2
0
0
0
2
1
2
2
0
1
0
0
1
0
1
0
2
0
0
0
0
0
0
2
1
1
1
1
0
2
0
2
1
0
1
0
0
1
0
1
1
1
2
0
0
0
0
1
0
1
1
2
0
0
0
2
0
0
2
1
0
1
0
0
0
1
1
1
0
1
1
2
0
0
1
0
2
0
2
1
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
1
0
0
0
2
1
1
0
0
2
0
0
0
0
0
0
0
1
1
1
2
0
0
0
0
0
0
0
0
1
1
0
0
0
2
1
1
1
0
1
0
1
0
2
0
2
2
1
1
7
0
0
2
1
0
0
2
1
0
1
2
2
1
0
0
1
1
1
2
0
2
2
4
1
0
1
1
0
0
1
0
0
0
1
1
1
0
0
0
1
2
0
1
2
0
0
1
0
0
0
2
2
1
0
1
1
1
0
0
0
0
1
2
1
1
2
0
1
1
0
0
2
0
0
0
3
1
0
2
2
0
1
0
1
0
2
0
0
0
0
0
0
1
2
2
0
0
1
0
1
0
0
2
0
2
2
0
0
1
2
1
0
0
0
0
0
0
1
0
1
1
2
1
0
0
3
1
2
0
1
1
0
1
0
1
2
0
1
0
2
1
0
2
0
2
1
0
1
0
0
0
1
2
0
0
0
0
1
2
0
1
0
0
2
0
1
0
1
2
1
1
0
1
2
1
0
1
1
2
2
1
1
1
1
1
0
1
0
1
0
2
0
1
1
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
1
2
2
0
1
0
0
1
2
2
0
0
0
3
2
2
0
0
0
0
0
0
0
4
0
0
0
2
0
0
1
1
0
0
0
0
0
1
4
1
0
2
0
0
0
1
0
3
0
3
0
0
0
0
2
0
0
0
1
1
0
1
1
2
0
2
1
1
1
0
0
0
1
1
0
0
2
2
1
1
0
1
2
1
2
1
2
1
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
2
0
0
3
0
1
0
2
1
1
1
0
3
1
0
0
0
1
1
0
0
2
0
2
0
1
0
2
1
0
0
0
0
3
0
3
0
2
2
2
1
0
1
1
1
1
0
2
1
2
0
0
0
1
2
2
0
0
2
0
1
1
0
0
1
1
2
2
0
0
1
0
2
1
0
1
2
0
1
1
1
0
1
1
1
1
1
2
0
2
0
0
0
0
0
2
1
2
1
1
0
0
1
0
2
2
1
0
0
0
2
0
2
0
2
1
0
1
0
0
2
1
0
1
0
0
0
0
1
2
0
1
1
0
0
1
1
2
0
0
1
1
0
1
2
2
1
1
0
2
0
0
3
0
1
2
0
2
0
0
2
0
2
0
0
2
0
1
1
1
0
2
0
0
0
1
1
1
0
1
2
0
0
0
1
2
2
1
1
2
0
0
1
1
0
0
0
2
1
1
0
0
0
2
1
1
0
0
2
1
2
0
2
0
0
0
0
0
1
1
0
0
0
0
1
0
2
1
0
0
0
0
0
0
1
2
2
2
1
1
0
1
0
2
1
1
0
2
2
0
0
1
0
0
1
1
1
0
0
0
0
1
3
2
0
0
0
3
0
0
3
0
0
1
1
0
0
1
1
1
0
0
0
1
1
0
0
0
0
0
1
1
2
0
1
0
1
0
2
0
1
2
0
1
0
0
0
0
1
3
1
1
0
2
0
0
0
0
1
0
0
1
0
0
2
0
1
1
1
0
1
0
2
0
1
2
1
0
1
1
1
1
1
0
3
0
0
1
2
2
0
0
2
1
2
1
2
0
2
0
3
1
0
2
0
0
0
1
1
1
1
1
2
0
0
2
1
2
0
1
0
1
0
1
1
2
0
1
1
2
0
1
2
0
2
1
1
1
0
1
0
0
0
1
2
2
1
1
2
0
0
1
3
2
0
0
0
0
2
1
0
0
2
2
0
0
2
2
0
0
2
0
0
0
0
0
0
2
1
0
0
2
2
1
1
0
1
1
0
1
0
1
2
0
0
0
2
1
0
2
2
0
0
2
2
2
1
2
3
0
0
1
0
1
0
0
0
0
0
0
1
1
1
0
2
0
0
1
2
0
0
0
2
2
0
1
2
0
1
0
1
2
0
1
0
0
0
1
0
0
0
0
0
0
2
2
0
1
2
0
1
1
0
0
0
1
1
2
0
1
0
2
1
1
0
1
0
0
1
1
2
0
0
1
2
0
0
0
0
1
0
1
1
0
2
0
1
0
1
0
1
2
2
0
0
2
2
0
0
0
0
0
2
1
1
0
1
1
1
0
1
2
0
0
0
1
0
1
1
0
0
3
1
0
0
0
1
2
1
0
2
0
0
2
0
1
0
2
2
0
0
2
2
0
2
1
2
2
0
1
1
0
0
1
0
1
2
1
0
0
0
2
0
1
1
0
0
0
2
1
1
2
2
2
2
1
1
1
1
0
2
2
1
2
0
3
1
1
1
0
1
0
0
1
0
0
1
0
1
0
2
0
2
0
0
1
2
0
2
3
3
1
0
1
3
2
1
2
0
0
0
0
0
2
1
0
0
0
0
0
2
0
1
0
1
0
1
0
2
4
0
0
1
2
2
0
0
0
2
2
0
0
1
2
0
0
1
0
0
1
1
1
1
2
2
1
0
1
2
1
1
0
0
1
2
1
0
1
1
1
0
1
2
1
1
2
0
2
0
0
1
1
2
1
0
0
1
0
0
1
1
2
0
0
0
1
0
0
1
0
0
1
0
2
2
2
1
1
0
0
1
0
1
2
0
1
1
2
0
0
0
1
1
0
2
0
0
0
1
2
1
0
2
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
2
0
0
2
2
0
0
1
2
0
1
0
1
1
0
2
0
0
0
1
0
0
2
2
3
2
0
1
1
0
0
1
0
0
0
2
2
2
1
1
1
2
1
0
0
0
0
1
0
0
2
0
0
0
0
1
1
2
0
0
0
1
1
0
1
1
0
0
0
2
0
1
1
0
0
2
2
0
0
0
1
1
0
1
2
2
0
2
2
0
1
2
0
1
1
1
0
2
0
1
0
1
0
2
1
0
3
2
2
0
0
0
1
1
2
0
0
0
2
2
2
0
0
1
0
2
2
1
0
0
0
2
0
1
1
0
0
2
2
1
1
0
0
0
2
3
0
1
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
2
0
1
1
0
1
0
0
2
1
1
0
1
0
0
2
0
1
1
1
0
0
2
2
1
0
0
0
0
1
1
0
0
2
1
0
0
0
1
1
1
0
2
1
0
2
2
0
2
0
2
0
0
0
0
1
0
0
2
0
0
0
1
0
1
0
0
1
1
0
2
0
0
1
1
0
0
0
1
2
0
1
2
0
0
0
1
1
0
2
0
0
1
3
0
1
0
2
0
1
0
2
0
1
1
0
0
3
0
1
2
0
0
0
1
2
0
0
0
0
2
3
0
0
0
0
0
0
0
1
0
0
0
1
1
0
2
1
0
0
0
0
1
2
2
2
1
0
0
2
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
2
0
0
0
0
1
0
1
1
2
1
0
2
0
1
2
2
2
0
3
0
0
1
0
1
0
1
3
3
1
0
1
1
2
3
0
0
1
1
0
1
0
2
0
0
0
1
2
0
0
0
0
0
0
2
1
2
0
1
0
2
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
2
2
0
0
0
0
1
1
1
1
1
1
0
0
0
0
1
1
1
1
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
1
2
1
1
0
2
1
0
0
0
2
0
0
1
0
1
0
2
2
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
2
1
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
2
2
1
0
1
0
0
0
2
0
0
0
0
2
0
0
2
1
0
0
0
2
0
1
1
1
0
1
1
0
1
1
0
0
0
0
0
1
4
0
2
0
1
2
0
0
0
2
2
0
1
0
1
0
0
1
1
0
1
2
1
0
2
3
1
2
2
0
2
1
1
2
3
2
0
1
1
2
1
0
1
1
0
0
2
0
1
1
0
2
1
1
2
2
0
3
0
0
2
0
0
1
1
0
2
2
1
1
0
0
2
0
0
0
1
0
2
0
2
1
0
2
1
1
0
0
0
0
0
0
0
2
0
0
1
0
1
2
0
1
1
1
1
0
1
1
2
0
0
1
0
0
1
0
1
1
0
1
0
1
1
0
0
0
2
0
1
0
2
2
0
1
0
0
0
0
1
0
0
0
1
1
1
0
0
2
0
0
0
2
0
0
2
2
1
2
1
0
1
1
0
1
0
0
2
0
1
4
1
1
0
2
0
0
1
0
0
3
1
1
0
0
2
0
0
0
0
2
2
0
1
2
0
2
0
1
2
0
0
2
2
1
0
1
1
1
0
2
0
0
2
0
2
2
1
1
2
0
0
1
2
0
0
0
2
1
2
2
2
1
0
1
1
2
0
1
1
0
0
0
0
0
0
1
0
0
0
0
3
1
2
2
2
0
1
0
2
0
1
0
2
1
0
1
1
0
0
1
0
1
0
1
0
1
1
2
0
0
1
2
1
0
0
0
1
1
3
0
0
0
0
0
0
1
1
8
0
4
1
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
2
0
0
2
0
1
0
2
1
2
1
1
2
0
2
1
0
2
0
0
1
3
1
0
2
1
0
0
0
0
0
0
1
0
1
0
0
1
1
1
2
0
1
0
2
1
0
1
2
0
2
2
0
0
2
1
1
0
0
0
1
2
0
1
0
0
2
0
0
1
2
2
2
0
0
1
1
0
2
2
2
1
0
1
0
2
1
0
0
3
1
0
1
0
0
1
1
0
2
0
0
2
0
1
2
0
2
0
1
0
0
1
2
2
1
1
1
0
0
0
1
1
0
1
1
0
1
0
0
2
0
0
0
1
2
0
0
2
3
1
0
0
1
2
0
1
1
0
1
2
2
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
1
0
1
0
1
2
0
1
0
0
0
0
0
0
0
2
0
0
1
0
1
1
2
0
0
2
0
0
2
2
1
0
2
0
0
2
2
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
2
1
1
0
1
0
2
1
1
0
0
1
2
2
2
0
0
0
0
1
1
0
0
1
1
1
2
0
0
0
2
2
2
0
1
1
0
0
2
0
1
0
1
0
1
1
0
1
1
1
1
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
2
2
1
2
1
0
0
0
0
0
0
1
0
0
1
0
1
1
1
1
0
2
1
0
0
0
1
0
2
0
0
1
0
0
1
2
0
0
1
1
1
0
2
1
1
1
1
0
1
2
2
1
0
0
0
1
1
0
0
0
1
0
0
1
2
1
2
1
0
2
2
6
0
2
1
2
2
2
3
1
0
0
1
1
2
0
0
2
0
0
0
1
0
0
2
1
0
1
0
2
0
1
1
2
0
0
0
0
0
1
1
1
0
0
1
2
0
0
2
0
2
1
2
1
0
1
0
1
1
0
0
2
0
1
1
1
2
0
2
0
1
2
2
2
0
2
0
2
0
0
0
1
0
2
2
0
0
1
1
1
0
3
0
3
0
0
1
0
0
1
2
0
0
0
1
0
0
1
0
0
1
0
0
2
2
2
1
1
1
1
0
2
1
0
0
0
2
0
0
2
1
1
1
1
0
2
1
0
0
0
2
0
0
1
0
1
0
0
0
1
1
2
1
2
0
1
1
2
3
2
0
0
1
0
1
2
2
2
0
1
2
1
0
0
0
0
0
1
0
1
2
0
0
0
0
2
1
3
1
0
1
0
0
0
0
1
0
2
0
0
2
2
0
0
0
1
0
2
1
2
1
1
1
1
1
1
0
0
0
1
0
0
1
0
0
2
0
1
2
0
1
0
2
1
1
0
0
0
0
0
2
0
0
0
1
0
0
2
0
1
1
3
1
0
0
2
0
0
1
1
0
0
0
1
1
0
1
2
1
2
0
0
1
0
3
2
1
1
1
0
2
0
0
0
0
0
0
1
1
1
2
1
1
0
0
1
2
2
0
1
2
0
0
0
0
0
0
1
0
0
1
1
2
1
0
0
3
2
2
0
0
0
1
0
2
0
0
0
2
0
2
2
0
2
0
2
1
1
2
0
0
0
0
2
1
2
1
1
1
1
2
2
2
1
1
0
2
0
0
0
0
0
2
0
0
2
2
0
0
0
2
2
0
1
2
0
3
0
1
2
2
0
0
0
0
1
2
0
0
1
1
0
2
1
2
1
0
0
1
1
0
2
2
1
2
1
0
1
1
0
0
0
2
0
0
3
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
2
0
3
0
0
1
0
0
2
2
1
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
2
0
1
1
0
0
2
2
1
0
1
0
0
0
3
3
2
2
0
2
1
0
0
0
0
0
0
1
0
1
1
1
0
1
0
1
2
1
0
1
0
2
3
0
0
2
1
0
0
2
0
3
2
1
0
0
0
1
2
1
2
0
0
0
0
2
0
0
0
0
2
2
1
1
0
1
3
1
0
2
2
0
0
0
0
0
1
2
0
0
2
1
0
4
0
1
0
2
0
2
2
1
0
1
0
2
1
0
2
0
0
0
0
1
1
0
2
1
2
0
2
2
1
0
1
0
1
2
0
0
2
2
1
2
2
0
0
2
0
0
1
0
1
1
0
1
0
0
2
2
1
1
0
0
1
0
2
1
0
2
2
0
1
0
1
1
0
0
1
2
0
2
2
0
0
0
0
0
2
2
0
0
0
1
0
1
1
1
0
2
1
1
0
0
0
2
0
1
1
0
0
1
0
0
2
2
2
0
1
0
1
0
0
1
1
1
2
0
0
2
1
1
0
1
1
0
0
0
0
0
0
2
0
1
1
1
0
0
1
2
0
0
0
2
0
2
0
0
0
0
2
1
2
1
1
0
2
4
1
2
0
2
0
1
0
0
2
0
0
0
1
2
1
0
1
1
1
1
0
0
0
1
0
0
1
0
1
0
1
1
0
1
2
3
3
1
0
0
0
0
2
0
2
1
1
1
2
0
0
0
2
0
1
2
0
2
2
1
0
1
0
0
1
1
2
1
0
1
1
2
1
0
0
0
0
0
2
2
1
2
1
0
0
1
0
0
1
0
0
1
1
0
2
2
1
0
0
1
0
0
1
2
0
2
1
0
1
0
0
1
0
1
0
1
2
0
1
2
0
2
3
2
0
1
0
1
0
1
0
0
2
0
1
2
1
0
0
2
3
0
0
2
0
0
1
2
2
2
1
1
0
1
2
0
2
1
1
0
0
1
1
2
0
0
1
1
2
0
2
2
1
0
0
2
0
1
0
1
1
0
0
1
2
2
2
0
0
1
0
2
0
1
1
0
0
0
1
1
0
0
0
1
1
0
1
0
0
0
1
1
0
2
0
0
0
0
0
2
0
0
0
1
2
0
0
1
0
0
0
1
2
2
0
1
0
0
1
1
0
2
1
0
3
1
2
2
0
0
0
1
1
1
0
2
0
2
1
0
0
2
0
0
1
0
1
1
0
0
0
0
1
1
2
8
2
0
0
1
1
0
0
0
1
2
0
0
0
1
0
0
1
2
0
1
2
2
0
0
0
3
0
1
1
2
2
1
2
1
2
2
2
0
0
3
0
1
0
0
1
0
2
0
0
0
0
2
2
0
2
1
0
2
1
0
1
0
2
0
0
1
1
1
2
1
2
0
1
2
0
0
2
0
1
3
0
0
2
2
0
1
1
0
0
0
0
2
1
0
0
0
2
0
1
0
1
2
0
1
2
0
0
0
1
0
2
0
0
1
0
0
2
1
1
0
1
1
0
1
2
2
0
1
0
0
0
0
1
2
2
0
1
1
1
0
1
1
1
0
0
1
2
1
0
4
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
1
1
1
1
2
2
1
1
2
1
0
0
0
2
0
0
2
1
2
0
0
1
0
0
1
1
0
1
1
1
2
0
2
0
1
1
1
1
3
1
1
1
1
0
0
0
1
1
0
1
1
2
0
1
1
1
1
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
2
1
0
3
0
0
1
0
1
0
2
1
0
0
0
1
1
0
1
0
1
0
1
0
2
1
0
0
2
0
1
0
2
0
0
1
0
0
2
0
2
1
0
2
1
2
1
0
2
2
1
0
0
0
0
1
0
1
1
0
0
0
2
1
1
1
0
2
0
0
4
1
1
0
2
2
4
0
0
0
1
0
0
2
0
1
0
0
0
2
2
2
0
0
0
0
1
2
1
2
1
0
1
1
1
0
2
2
0
2
1
0
1
2
0
0
2
0
0
2
0
3
0
1
0
0
1
2
2
0
0
1
1
2
1
2
0
2
1
0
1
0
1
1
0
1
0
0
1
1
2
0
2
0
0
0
0
0
1
0
1
1
1
0
0
2
0
0
0
1
1
1
0
0
0
0
0
0
0
1
2
0
1
0
2
2
2
1
1
1
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
2
2
1
1
0
1
0
1
0
2
0
1
1
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
1
2
0
0
1
2
0
0
0
0
0
3
0
0
0
0
0
1
1
1
0
0
0
1
2
0
0
1
0
0
0
1
1
0
2
1
1
2
5
0
0
1
1
2
1
0
1
0
1
0
5
2
0
2
0
0
2
2
1
2
0
2
0
0
0
0
1
2
1
1
0
1
1
1
0
0
1
1
1
2
2
2
0
0
0
0
1
1
0
2
0
1
0
1
0
0
0
0
2
2
3
2
0
0
2
2
1
1
1
0
1
1
0
2
0
0
0
1
0
1
0
2
0
2
0
0
0
0
2
0
1
1
0
1
1
0
1
2
2
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
2
1
1
0
0
1
1
0
0
2
2
1
2
2
2
1
0
2
2
2
2
1
0
0
2
1
1
0
0
1
0
0
1
3
0
0
0
1
1
1
0
1
1
0
0
0
0
2
0
1
0
0
0
2
2
0
0
0
0
3
2
1
1
1
0
2
1
2
0
0
2
0
0
2
1
0
2
1
2
0
1
0
0
0
2
0
2
0
4
0
2
0
3
0
0
1
0
0
0
0
2
0
0
1
0
0
2
2
0
0
0
2
0
0
2
2
2
1
2
1
2
2
1
2
0
1
1
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
1
1
2
1
0
2
2
0
0
0
0
0
0
1
0
2
2
1
2
0
0
1
1
1
2
0
0
0
0
0
0
2
2
0
0
2
2
0
1
2
0
1
0
1
2
0
0
2
0
0
0
2
2
1
0
1
0
0
1
1
1
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
2
0
3
0
1
2
2
2
0
0
0
0
2
0
1
0
0
2
1
0
1
0
2
0
2
0
0
0
0
0
0
1
0
2
0
0
0
2
0
1
0
0
2
0
0
1
1
0
1
2
2
1
2
0
0
1
0
1
0
0
0
2
0
2
1
2
0
0
1
2
0
0
0
0
1
2
1
1
0
0
0
0
1
0
0
2
0
0
1
1
0
0
1
0
2
1
0
0
0
0
0
2
1
0
0
0
3
0
1
2
2
0
1
0
0
0
0
2
0
2
0
2
0
1
0
1
0
0
2
2
1
2
0
0
1
1
0
4
0
2
2
1
1
1
2
0
2
2
0
1
3
1
2
0
0
0
0
0
1
0
0
0
1
0
0
0
2
2
1
0
1
1
0
0
0
0
0
1
0
2
2
1
1
1
0
2
0
1
0
0
0
2
0
2
0
0
1
1
0
2
0
2
2
0
1
0
0
1
1
0
0
2
1
0
1
0
0
1
0
0
2
1
1
1
2
1
1
0
1
1
2
1
0
0
0
1
2
1
0
2
0
1
0
1
0
0
1
0
1
1
0
0
0
1
0
1
1
0
0
2
2
1
0
1
0
3
0
2
1
2
1
2
1
1
1
0
2
0
2
0
0
1
1
1
1
0
0
0
1
0
2
0
0
0
2
1
0
0
2
0
1
1
0
0
0
1
1
2
1
1
1
2
1
1
2
1
2
0
0
2
0
1
0
1
0
1
2
0
1
0
1
0
2
1
1
0
0
1
0
0
1
1
1
0
5
0
2
1
1
1
1
0
1
0
3
1
2
1
2
0
2
0
0
0
4
1
2
1
0
0
0
2
2
0
1
0
0
0
2
1
0
0
0
3
1
0
1
2
1
0
0
1
0
2
0
2
0
0
2
1
1
2
0
1
0
1
0
0
1
0
0
0
0
2
0
1
2
0
1
2
0
0
0
0
1
0
1
0
2
2
0
2
0
0
2
1
0
1
0
1
0
0
1
0
0
1
2
0
1
0
1
2
0
1
1
3
1
1
1
2
1
1
1
2
2
0
1
0
0
1
0
0
1
1
0
0
1
2
1
2
1
0
1
1
0
2
1
1
0
0
0
0
1
0
0
1
0
1
0
0
0
2
1
0
1
0
1
2
1
0
0
1
0
0
0
0
2
2
1
0
1
2
1
1
1
0
1
2
0
0
1
0
2
0
1
0
0
0
2
0
1
0
0
0
1
0
0
0
1
1
0
0
1
1
1
0
0
2
0
0
0
1
0
0
1
0
1
0
0
0
0
1
2
0
1
1
3
0
0
0
1
0
0
1
0
0
0
1
0
1
1
3
2
0
1
1
1
1
0
0
2
0
1
0
1
0
1
1
0
0
0
0
0
0
0
1
0
2
1
1
0
0
0
1
0
0
0
0
1
0
2
0
0
2
2
1
0
1
0
0
0
0
1
0
0
1
0
3
0
0
1
0
0
0
0
1
1
0
2
0
1
1
2
0
2
1
2
0
1
2
0
0
2
2
2
1
2
0
1
0
1
0
0
2
0
0
1
1
0
1
2
1
1
1
1
2
0
2
1
2
1
0
0
1
2
0
1
0
1
0
0
1
0
0
3
1
0
0
1
2
0
2
0
0
1
0
0
0
0
0
1
0
1
1
0
2
1
2
2
0
0
0
2
1
0
1
1
0
2
2
1
1
0
2
2
2
0
0
2
0
0
2
0
2
1
0
2
0
0
0
0
2
2
1
0
1
0
1
1
1
0
0
2
0
0
1
0
0
0
0
0
0
0
1
2
2
1
0
1
1
1
2
1
0
2
1
0
1
1
0
2
0
2
3
0
2
0
0
1
0
1
1
0
0
0
1
1
0
2
0
1
1
0
0
0
1
0
0
0
0
0
1
2
2
3
2
0
1
0
0
2
1
0
3
2
0
2
0
0
0
0
2
0
1
0
1
1
0
0
1
0
2
0
0
0
0
0
1
1
0
0
0
2
2
1
2
1
2
1
0
2
1
0
0
2
0
2
0
1
2
2
0
2
2
0
1
1
1
0
0
1
1
0
0
2
0
2
0
1
1
2
2
0
0
2
0
0
2
0
0
0
1
0
2
2
0
1
0
0
0
2
2
0
1
2
1
0
0
2
0
1
2
2
2
2
0
1
1
0
0
0
1
0
0
3
0
2
1
1
0
2
1
1
0
0
0
0
1
0
0
1
0
0
1
2
0
2
1
0
1
2
0
0
1
0
0
0
0
0
1
1
1
3
1
1
2
2
0
0
0
3
0
1
1
1
1
2
0
0
0
2
1
0
1
1
0
2
3
0
0
2
0
1
0
1
0
0
1
0
1
1
0
1
0
1
0
0
2
0
0
0
1
0
0
0
1
1
0
1
3
0
2
0
0
0
0
2
1
0
0
0
1
2
1
1
0
0
0
1
1
1
0
0
0
2
2
0
2
0
0
0
1
1
2
0
1
0
0
0
1
1
2
1
1
0
0
0
1
1
1
1
1
0
0
1
1
0
0
1
1
0
1
0
0
0
1
0
3
1
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
2
2
2
0
0
1
4
0
0
1
1
2
1
1
0
0
1
1
0
1
0
1
0
1
0
1
2
0
1
2
1
1
2
0
1
0
1
0
0
0
2
1
1
1
0
0
1
0
0
1
1
1
2
2
0
1
0
1
2
0
2
0
0
0
1
1
0
0
2
1
2
1
1
0
0
0
1
0
0
1
1
0
0
0
1
0
2
0
2
1
0
2
0
2
1
1
0
1
0
1
0
2
0
2
0
2
2
2
0
1
1
1
1
0
0
0
2
3
0
0
2
1
1
1
1
0
0
0
1
0
0
0
1
1
0
0
0
1
1
2
1
2
0
2
1
0
2
0
1
1
0
0
1
0
2
0
1
0
1
1
0
0
1
2
0
0
1
0
0
2
2
0
0
1
2
2
1
0
0
2
1
0
1
2
1
0
0
2
2
2
1
1
0
2
0
1
2
3
1
5
1
1
0
0
1
0
0
1
0
0
1
2
1
2
0
0
1
0
2
2
0
2
1
0
5
0
0
1
1
1
1
0
0
3
0
1
3
1
2
0
1
0
1
0
0
2
2
0
2
2
0
2
1
0
1
1
1
1
1
0
1
0
1
2
1
3
0
0
0
0
1
0
0
0
0
0
4
0
1
1
0
0
2
1
0
0
0
0
1
2
1
2
2
1
0
0
3
1
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
2
0
0
1
1
0
0
2
2
1
1
2
0
2
1
0
0
0
0
1
1
1
1
1
0
2
0
1
1
0
1
0
0
1
1
0
1
1
0
0
0
0
0
0
2
0
0
1
1
0
2
1
1
1
0
1
1
1
2
1
1
3
0
2
0
0
0
1
0
0
0
0
1
2
2
0
0
0
0
1
2
2
0
0
0
2
1
0
1
2
0
0
0
1
1
0
2
2
0
1
0
0
0
0
0
0
2
2
3
1
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
2
0
0
1
2
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
2
2
2
0
0
2
0
2
0
0
0
1
0
1
1
0
0
2
0
0
1
2
0
4
0
0
0
1
0
0
0
1
1
0
0
2
2
0
0
0
0
0
1
0
1
2
1
2
1
0
0
1
0
1
1
0
0
1
2
0
2
0
1
0
1
0
2
0
1
0
0
2
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
1
2
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
2
1
0
2
0
1
1
2
2
2
1
0
0
0
0
2
1
0
2
1
2
1
2
0
0
2
0
1
1
2
1
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
1
2
0
0
2
0
0
0
0
1
2
2
1
1
1
1
1
0
1
5
0
1
0
1
2
1
1
0
1
0
0
0
0
0
1
1
0
0
0
2
1
1
1
1
0
1
1
1
1
0
1
0
1
2
1
1
0
0
1
1
2
1
2
0
0
0
0
2
1
2
1
2
5
1
0
0
1
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
1
1
0
1
2
1
0
1
1
0
0
0
0
1
1
0
0
1
3
1
4
0
2
0
0
0
2
1
1
0
1
1
0
0
1
0
1
2
1
1
0
1
2
0
1
1
2
2
2
0
0
2
0
1
1
0
1
1
2
0
2
0
0
0
3
2
2
2
1
0
1
1
0
2
0
1
1
2
0
0
2
1
2
0
1
0
0
1
1
0
1
0
0
1
0
0
0
2
2
0
0
2
1
1
1
1
2
0
2
0
1
0
0
1
1
0
1
0
2
0
2
1
0
1
0
0
1
1
1
0
2
0
0
0
1
0
1
1
2
0
0
1
0
0
0
3
0
1
3
1
2
0
0
0
1
0
0
0
1
2
0
0
2
0
0
1
1
2
2
1
2
2
2
2
0
0
1
1
0
1
0
0
0
0
0
0
0
0
3
1
1
2
0
0
1
1
1
0
1
1
1
0
2
0
0
2
0
0
0
2
0
0
2
1
0
0
1
2
0
0
0
2
1
0
1
1
0
2
0
0
0
2
1
2
2
1
2
0
2
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
1
0
0
1
0
0
1
0
0
2
1
2
1
2
1
0
1
0
1
0
0
0
1
2
0
0
0
0
2
0
2
2
2
0
1
2
0
1
0
0
0
0
0
2
0
0
1
2
1
1
2
0
0
0
1
0
1
4
0
1
2
2
0
2
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
1
1
1
1
1
1
1
1
1
2
0
2
0
2
0
1
0
0
0
0
2
1
1
1
0
0
0
3
0
0
0
1
0
1
0
1
0
0
1
0
0
1
0
0
2
2
0
0
1
0
0
0
2
0
0
0
1
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
1
1
0
2
0
0
2
0
0
2
0
1
2
2
0
2
0
1
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
1
1
0
1
3
1
0
0
0
2
2
1
1
0
1
0
1
2
0
1
1
1
1
0
0
0
1
0
2
0
1
0
1
0
2
1
1
0
1
0
0
0
1
0
1
1
1
1
2
1
1
0
0
0
0
2
2
0
0
0
1
2
0
2
1
2
2
0
4
1
0
0
0
2
0
1
1
1
2
0
1
1
0
0
2
0
0
2
0
0
0
0
1
0
0
1
1
1
1
0
1
0
2
1
0
0
1
2
0
0
1
0
3
1
1
1
2
2
1
1
1
0
0
0
0
0
0
1
0
0
1
0
0
1
2
0
0
0
0
2
0
1
1
0
0
2
2
0
2
0
2
0
1
0
0
0
0
0
1
0
0
2
1
1
0
0
0
0
0
1
2
0
0
1
0
1
2
2
1
1
2
2
3
0
2
0
0
4
0
1
2
1
0
2
2
1
0
2
1
1
1
1
1
0
2
0
0
2
0
3
2
1
0
0
1
1
0
2
2
0
1
0
0
1
1
2
0
2
2
0
0
0
0
2
0
0
0
0
0
3
1
0
0
1
0
0
0
0
2
1
0
0
0
2
0
1
0
2
0
2
0
0
1
0
3
2
1
0
1
0
2
2
2
1
1
0
1
2
1
1
1
2
0
2
0
0
1
2
0
1
0
2
2
1
0
0
2
1
0
0
0
2
0
1
0
0
1
1
0
0
1
1
0
0
1
0
0
2
1
1
0
2
0
2
0
1
0
2
0
0
0
2
1
1
0
1
2
1
1
2
0
3
0
1
1
0
0
0
1
2
0
1
1
2
0
0
2
0
0
1
3
0
1
0
0
1
2
0
2
0
2
2
0
1
2
1
0
0
2
2
1
2
1
0
0
0
0
0
0
2
0
1
1
0
1
2
1
2
0
2
2
0
0
2
2
0
0
0
1
1
1
0
0
2
2
1
0
2
0
2
2
1
0
0
0
0
0
0
2
1
0
2
1
0
0
2
2
1
2
1
0
1
1
0
0
0
5
1
1
1
1
0
2
1
0
2
0
1
0
0
0
2
0
1
1
1
0
0
0
0
0
1
1
2
1
1
2
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
2
0
1
0
2
1
2
2
1
0
0
2
0
2
1
2
0
1
3
1
1
2
0
0
2
1
2
2
1
0
1
2
1
2
0
2
1
0
0
1
2
0
2
1
0
0
1
0
1
3
0
1
0
0
0
2
2
0
1
0
2
1
1
0
2
0
0
1
0
2
0
1
0
0
0
1
0
0
0
1
2
0
2
1
1
0
0
0
1
2
2
2
1
0
0
0
0
2
0
0
0
0
1
0
1
0
0
1
0
2
0
1
1
0
2
0
0
2
2
1
0
2
2
1
0
0
0
2
2
0
0
0
2
1
0
2
2
1
0
2
0
1
2
2
3
1
2
1
0
1
0
2
0
0
0
0
1
0
2
1
0
1
0
0
1
0
1
0
0
0
1
1
1
1
2
0
0
1
1
2
3
1
0
0
0
2
1
0
0
0
2
1
1
0
1
2
0
0
2
1
0
1
3
1
1
1
0
0
1
0
0
0
0
1
1
1
2
1
1
0
0
0
1
0
1
2
1
1
2
0
1
2
0
0
0
0
0
0
0
2
2
2
1
1
2
0
1
2
1
0
1
0
1
1
0
0
1
0
0
0
1
0
2
0
1
1
1
0
1
0
0
0
0
1
0
1
2
0
1
1
0
2
0
1
0
2
0
0
1
0
0
1
2
0
2
2
1
3
0
1
2
1
1
0
1
1
0
2
0
0
1
0
0
2
2
2
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
2
0
0
0
1
1
2
0
1
1
1
1
0
0
0
0
0
2
2
0
0
2
2
1
0
1
3
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
1
2
1
3
2
0
1
0
0
1
0
0
1
1
2
1
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
2
1
0
2
0
0
0
1
0
1
1
0
1
1
0
1
0
0
1
0
0
2
1
0
0
1
4
0
0
1
0
2
0
2
2
2
0
2
2
1
2
0
2
3
0
1
1
1
0
0
0
1
1
2
0
1
2
0
0
0
0
1
0
1
2
0
2
1
1
1
0
1
0
1
0
0
2
0
1
0
1
1
1
0
0
1
0
1
0
0
1
1
0
0
0
1
0
0
1
0
1
1
0
2
2
1
0
1
2
1
1
0
1
2
0
0
0
1
2
0
1
0
0
0
1
0
1
1
2
0
1
0
1
1
0
0
2
0
0
0
0
2
1
0
2
0
0
1
2
1
0
2
2
1
2
0
0
0
0
0
2
1
1
2
2
0
0
0
0
0
0
2
0
2
0
1
2
2
1
2
0
0
1
1
1
0
2
0
1
0
0
1
0
1
1
0
0
1
1
2
0
0
1
0
2
2
0
0
1
1
2
1
1
1
0
0
1
3
1
0
0
1
1
1
2
1
0
0
0
1
1
0
1
0
0
0
1
0
1
1
0
1
3
1
0
1
2
2
1
0
2
1
1
0
0
1
2
2
1
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
1
1
2
0
2
0
2
3
3
0
0
2
0
0
1
0
1
0
1
2
0
0
2
2
1
1
2
1
0
0
2
0
6
1
0
0
1
0
1
1
0
2
0
1
1
0
1
0
1
0
0
0
0
0
1
2
0
1
0
0
0
1
2
0
0
2
2
0
1
1
2
0
0
2
1
0
1
2
2
0
0
0
1
0
0
2
2
0
0
1
1
2
0
0
2
0
0
0
1
0
0
2
2
2
0
0
0
0
0
0
1
1
1
2
0
0
1
0
0
4
2
2
2
0
0
2
0
0
1
0
1
2
2
2
0
6
0
2
0
0
2
0
1
0
0
0
4
0
1
3
2
0
0
0
1
2
2
2
2
1
0
0
2
2
1
1
1
0
1
2
2
0
0
1
0
2
0
0
2
0
0
1
0
1
2
2
0
1
1
0
1
1
3
1
0
0
0
1
0
0
1
0
1
2
2
0
0
0
2
0
0
2
2
0
1
0
2
0
2
0
0
0
0
2
0
2
0
2
1
2
2
0
2
0
1
2
1
1
1
1
0
0
0
5
1
1
1
1
1
0
1
1
0
2
1
0
4
0
1
0
0
2
0
0
1
0
1
1
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
1
0
1
0
4
2
2
2
1
0
0
2
2
2
0
0
0
1
0
0
0
1
0
2
1
1
0
2
1
0
2
0
0
1
1
2
1
0
1
0
1
1
1
0
0
1
0
1
3
1
1
1
0
2
0
0
1
1
1
2
0
1
1
1
0
1
0
0
2
1
0
2
1
1
2
1
0
2
1
0
0
1
1
0
0
3
1
0
2
0
1
0
1
2
1
0
0
0
2
0
2
2
0
0
0
0
0
2
0
0
0
0
1
2
2
1
1
1
0
2
1
0
1
2
0
2
1
2
2
2
1
2
1
1
3
0
0
1
1
0
0
0
1
0
0
3
2
1
2
2
1
1
1
1
2
1
0
0
1
2
0
1
1
2
0
0
0
0
0
1
0
0
1
0
2
2
0
0
0
1
2
1
2
1
2
1
1
1
1
2
0
0
0
0
0
1
1
2
2
0
2
1
0
1
1
0
2
1
0
0
1
1
1
1
1
1
0
1
0
4
2
1
2
2
1
0
0
1
0
0
2
2
1
0
2
1
1
1
1
1
2
3
2
2
2
0
2
0
2
1
1
0
0
4
2
1
0
1
0
0
2
0
1
0
2
0
0
1
0
2
1
0
1
0
0
0
1
1
0
0
1
1
0
0
0
1
0
1
0
0
1
1
1
0
0
0
0
2
1
1
1
1
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
2
0
0
4
0
2
0
0
0
0
1
0
0
1
1
0
0
4
1
0
0
0
0
0
0
2
1
2
1
1
1
0
2
0
0
0
2
0
1
0
0
2
0
0
2
1
2
1
2
0
0
1
0
0
0
2
1
1
1
2
0
1
0
0
2
0
1
0
2
0
1
1
2
2
1
1
2
1
0
3
0
0
0
0
1
1
0
2
1
2
0
0
0
1
0
0
0
2
2
2
2
2
0
0
1
0
0
2
2
2
1
0
0
0
0
1
0
1
1
0
0
0
1
0
2
0
0
2
1
0
1
1
0
0
0
2
0
2
0
2
0
1
0
0
0
0
2
0
0
0
1
1
2
0
0
1
1
0
1
2
0
0
0
0
0
2
0
1
1
1
1
0
1
0
0
0
0
0
1
1
2
1
0
0
0
1
0
0
0
3
0
0
1
0
1
2
0
2
0
0
0
0
1
2
3
2
2
1
0
0
1
2
0
1
0
1
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
2
0
2
1
0
0
1
0
2
0
2
0
1
1
0
1
1
0
0
0
0
1
0
2
1
0
0
0
0
1
0
0
1
0
0
0
2
0
1
2
0
2
1
1
1
2
1
0
2
2
1
1
2
0
0
3
2
1
1
1
1
0
1
0
0
0
2
1
0
0
1
0
1
0
0
0
0
3
0
1
2
0
2
0
0
1
0
1
1
1
1
0
2
1
1
1
0
0
0
0
1
1
1
0
1
2
2
0
0
0
1
0
0
2
2
0
3
1
0
0
0
0
0
2
1
1
2
0
0
0
2
1
2
0
0
0
0
0
3
0
0
1
1
0
0
2
1
2
1
1
0
0
2
1
0
0
0
2
1
0
1
2
0
1
0
1
1
2
0
1
1
1
2
1
1
0
0
0
0
0
3
0
0
1
1
2
1
1
1
1
2
1
0
0
0
1
1
2
0
0
1
0
0
0
1
2
0
0
0
1
0
1
0
1
1
0
0
1
0
1
1
1
1
1
2
0
2
1
0
0
0
1
0
0
2
2
0
1
0
1
2
1
1
0
0
0
0
1
0
2
0
0
1
0
0
0
1
0
1
1
1
2
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
2
1
4
0
0
0
0
0
0
2
0
1
0
1
0
1
0
2
1
2
1
1
2
2
2
1
0
2
0
0
1
1
0
0
0
0
0
1
0
0
1
0
2
2
2
2
1
2
0
2
0
0
1
0
0
0
2
0
1
0
1
1
0
1
1
0
1
0
0
0
2
1
2
3
0
0
0
0
0
1
0
2
1
0
1
0
2
0
0
0
1
2
0
1
0
0
0
0
0
2
1
2
1
0
0
0
0
0
2
1
1
1
1
1
1
1
2
2
1
1
0
0
0
1
0
0
0
0
1
1
0
2
1
0
0
2
2
0
0
0
0
2
2
0
0
2
0
0
0
2
1
0
2
1
0
0
1
0
2
0
0
0
0
1
1
2
0
0
1
1
1
0
2
2
2
0
0
0
0
0
2
1
0
0
1
0
0
1
0
1
0
0
2
0
0
2
1
0
0
0
0
2
0
2
0
0
0
1
2
1
2
3
0
2
1
0
2
2
0
2
1
1
1
0
1
0
1
1
0
2
1
1
3
0
0
0
2
1
0
0
0
0
1
0
0
2
0
1
1
0
0
0
0
2
1
1
0
2
1
0
0
1
2
2
2
0
0
1
0
2
0
2
0
2
0
1
1
2
1
0
0
1
1
2
1
0
2
1
0
0
0
1
2
0
0
1
0
2
2
2
1
0
1
2
0
0
2
1
1
3
0
0
1
0
0
0
0
1
0
0
2
1
2
0
1
0
1
0
1
0
0
0
2
2
0
1
1
2
1
2
0
0
0
1
0
0
0
0
0
1
2
0
1
0
0
0
1
0
0
2
0
1
0
2
0
0
0
0
0
0
0
3
1
1
0
2
1
0
0
0
1
2
1
1
0
1
1
2
0
0
2
0
0
0
1
0
1
0
0
1
0
1
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
1
1
0
1
1
1
1
2
1
0
0
0
0
1
1
2
0
0
0
0
1
1
1
2
0
0
2
1
0
1
2
0
1
1
0
2
0
0
0
2
0
0
0
0
1
2
1
1
2
1
0
1
0
0
1
0
1
1
0
0
0
1
0
1
0
0
1
1
2
0
1
0
0
0
1
0
0
1
0
1
1
0
0
0
2
1
1
1
0
2
1
0
0
2
2
1
0
1
2
1
0
2
1
0
0
1
0
0
0
0
2
0
0
1
2
1
0
0
1
1
0
2
2
2
1
0
1
0
1
1
0
0
1
1
1
0
1
0
1
1
0
0
1
2
0
1
0
2
0
0
2
0
0
0
1
2
0
2
1
0
1
0
0
0
1
1
2
2
2
0
2
1
2
0
0
2
1
1
1
0
0
0
1
0
0
2
1
2
0
3
2
0
2
1
0
2
1
0
0
0
0
1
0
0
5
0
0
0
0
1
1
0
1
0
1
2
1
1
0
2
0
0
0
0
2
0
2
0
1
0
2
1
1
2
2
1
1
2
1
3
0
0
0
0
0
0
1
0
1
1
1
1
1
0
0
1
2
3
2
0
2
0
0
2
0
0
2
0
0
1
0
0
2
1
2
1
2
2
1
0
0
1
1
1
0
1
0
1
0
1
1
2
1
0
1
1
1
1
0
1
0
1
1
1
1
1
0
0
1
0
2
0
4
0
2
0
1
0
1
0
1
2
0
2
2
0
0
0
1
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
1
0
2
0
0
1
1
1
0
1
0
2
0
0
1
0
2
1
1
1
1
0
1
2
1
2
2
0
0
0
0
1
0
1
2
0
1
0
0
1
2
1
1
0
1
0
0
1
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
1
0
1
1
1
1
0
0
0
1
0
0
0
0
2
0
2
1
0
0
1
0
2
1
0
0
1
0
0
0
0
0
0
2
0
2
1
1
0
0
1
0
2
0
0
0
1
0
0
0
1
0
0
0
2
0
1
1
1
2
1
1
1
1
0
1
0
1
1
0
2
0
1
1
0
0
1
1
0
0
1
1
0
1
2
2
2
0
1
1
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
2
1
0
1
1
0
0
0
0
0
1
1
2
0
2
2
1
3
2
1
3
0
1
2
2
2
0
0
2
0
1
0
0
0
1
0
1
0
0
0
1
1
1
0
0
1
2
2
0
1
1
1
13
0
0
1
1
0
0
0
0
0
0
0
1
1
2
1
1
0
1
2
1
2
1
0
0
0
1
0
0
1
0
1
2
2
0
1
0
2
0
1
0
0
2
2
0
1
0
0
0
1
0
0
0
2
0
1
0
2
1
1
0
1
0
0
1
2
1
2
0
0
0
0
0
0
1
1
1
1
1
2
1
0
2
0
0
0
1
2
1
1
0
0
0
0
0
0
1
1
2
1
1
0
0
2
0
0
2
1
1
0
0
2
0
3
2
2
1
2
0
0
0
3
1
0
4
1
0
0
0
1
2
0
1
1
0
0
1
0
0
1
1
1
1
1
0
1
0
0
0
1
0
3
3
1
2
1
0
0
0
1
1
1
0
0
0
2
1
1
0
1
2
2
0
2
1
0
2
1
1
0
1
1
0
1
0
0
1
0
0
1
1
0
1
1
1
3
0
0
0
1
1
0
0
0
2
1
3
0
1
2
2
2
1
0
1
1
0
0
0
3
1
1
1
1
0
1
0
1
0
2
2
0
2
1
0
1
2
0
2
2
2
0
0
3
0
2
0
0
0
1
1
0
2
1
0
0
2
2
0
0
2
0
1
0
0
1
0
1
2
0
0
0
0
1
0
1
1
2
1
1
1
2
2
0
0
1
2
1
0
0
0
2
2
1
2
0
1
1
3
0
0
0
0
0
0
2
0
1
3
1
0
1
1
1
0
1
1
2
0
0
1
1
0
0
1
0
0
0
2
0
0
1
0
0
1
2
0
0
2
2
1
2
0
1
0
0
2
0
0
3
0
1
1
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
1
2
1
3
0
0
0
0
0
1
0
0
1
2
1
0
1
0
0
0
0
2
2
0
0
0
0
0
1
0
1
0
0
1
0
0
1
1
2
0
0
0
2
0
0
0
2
1
0
3
1
0
1
0
0
1
0
1
0
1
2
0
0
2
0
2
1
2
0
2
1
0
1
1
0
1
0
0
2
0
0
1
1
0
2
0
0
0
2
0
0
1
2
3
2
0
0
2
0
1
3
2
0
0
0
1
1
0
0
1
2
0
0
0
0
2
0
2
0
2
0
0
0
0
0
2
1
0
0
0
3
0
0
2
0
1
0
3
1
2
1
1
0
0
0
0
0
2
0
1
2
1
0
2
0
2
0
2
1
0
0
2
0
0
2
1
4
2
0
0
1
2
1
1
1
0
0
3
3
11
1
0
1
1
0
0
2
0
2
0
1
1
1
0
0
0
0
1
0
0
1
1
0
1
2
1
1
0
0
0
1
2
1
0
1
0
2
0
2
0
0
1
1
1
0
0
0
0
2
2
3
0
0
1
0
1
0
2
0
1
2
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
3
0
1
0
0
1
0
1
0
1
1
0
0
0
2
2
0
1
1
1
0
0
0
1
2
2
2
1
0
2
0
0
0
0
1
0
2
0
1
0
0
1
0
0
1
0
2
0
1
1
1
1
0
2
2
2
0
0
2
2
0
1
0
0
0
1
1
0
1
2
1
0
1
0
0
2
1
2
1
0
0
2
1
0
0
0
0
2
1
0
0
1
0
0
0
0
0
2
2
0
2
0
0
1
0
1
0
1
2
0
1
0
0
0
1
0
0
0
0
0
2
0
0
1
0
1
1
0
0
1
0
1
0
2
1
0
1
1
0
1
0
1
0
0
2
1
0
0
0
1
0
0
1
1
1
1
1
0
2
1
1
1
0
0
0
2
0
0
1
0
0
0
0
0
0
1
2
0
2
2
0
2
0
0
1
0
0
1
1
1
0
2
0
0
0
1
1
1
2
2
2
0
1
0
0
0
0
1
1
1
5
0
0
0
0
2
0
2
0
0
0
2
1
0
0
1
1
0
0
2
0
0
2
1
2
0
0
1
1
1
0
1
1
0
2
0
1
0
0
2
1
1
0
2
2
1
0
0
1
1
1
0
0
1
1
0
2
0
2
0
2
0
0
1
1
1
0
0
0
0
0
0
0
1
0
2
0
1
1
1
1
1
3
0
1
0
1
1
2
0
1
1
2
1
2
1
2
0
0
1
1
2
1
1
0
1
1
2
0
1
0
0
0
0
1
0
1
0
3
1
0
2
1
0
1
0
0
0
2
1
0
0
1
1
1
0
1
2
2
0
1
0
2
2
1
1
0
0
0
1
0
0
1
2
2
1
0
1
0
0
3
1
2
1
2
1
1
0
1
2
2
0
1
1
1
1
0
2
0
1
0
0
2
2
0
1
0
2
0
0
0
1
0
1
1
2
6
1
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
1
2
1
2
0
1
0
2
0
2
0
0
0
2
2
2
0
1
0
0
0
2
0
2
2
2
0
3
0
2
1
0
1
0
0
0
0
1
5
1
1
1
2
2
0
0
2
1
0
2
0
1
0
0
0
2
2
1
2
0
0
0
1
0
2
0
1
0
2
1
0
2
0
0
0
2
1
2
0
0
1
1
2
0
2
2
1
0
0
1
1
1
0
1
0
1
1
0
0
0
1
0
4
0
2
0
0
2
2
1
1
0
1
0
1
0
0
2
1
0
0
1
1
1
2
0
0
1
0
1
0
1
0
0
2
1
0
2
0
0
0
0
3
0
0
1
1
1
0
1
2
1
1
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
2
1
0
1
1
0
0
2
2
0
1
1
0
2
2
0
0
0
0
1
0
0
1
1
0
1
1
0
0
0
2
0
2
1
0
0
0
0
0
1
1
1
1
1
0
1
1
2
0
2
0
0
0
0
1
0
1
2
2
2
1
1
0
3
1
0
0
2
2
0
0
0
0
2
1
2
0
1
0
0
0
0
0
0
1
2
0
0
1
0
0
2
0
1
0
0
0
1
2
0
0
0
1
1
0
0
0
0
0
0
1
1
0
1
0
0
2
0
0
2
0
2
0
0
0
0
0
2
1
1
0
1
2
0
2
0
2
2
0
2
0
0
0
0
0
0
1
0
1
1
0
0
1
2
1
2
0
2
0
0
0
2
1
1
0
0
1
1
1
1
2
1
1
1
0
0
1
0
0
1
1
1
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
1
0
1
0
0
0
0
0
1
0
0
0
2
1
2
1
0
1
0
1
1
0
1
0
2
1
2
2
2
2
2
0
1
2
1
2
0
0
0
2
0
2
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
2
0
1
2
0
2
3
2
2
0
1
0
0
1
0
0
1
1
1
1
2
0
2
2
0
2
1
0
0
0
2
1
0
1
1
1
2
2
2
1
0
0
0
1
0
2
1
1
1
0
2
0
1
1
1
0
2
1
2
0
0
0
0
2
0
0
1
0
1
1
3
0
2
2
1
0
0
1
0
0
1
0
1
1
2
0
2
2
2
2
2
1
1
0
1
0
1
0
1
0
1
2
2
0
1
0
1
0
0
1
2
1
0
2
0
2
0
2
3
2
2
0
0
0
0
2
0
1
0
2
0
1
0
3
0
0
1
2
0
2
0
1
0
0
0
2
2
2
0
2
1
1
0
0
0
0
0
0
0
0
0
1
0
1
1
1
2
1
1
0
2
0
1
0
0
0
1
0
1
0
0
1
0
1
1
1
1
1
0
1
2
1
0
3
0
1
2
0
2
0
1
1
2
2
0
0
2
0
0
0
1
0
1
0
1
1
1
2
2
1
0
2
1
1
1
2
1
0
1
0
1
0
1
1
1
1
2
2
0
0
0
1
2
2
1
0
2
2
1
0
0
0
2
1
2
0
2
1
1
0
1
0
3
0
2
0
0
0
2
1
1
0
2
0
2
0
1
1
0
2
0
2
0
0
0
0
1
1
4
1
0
0
0
1
1
1
1
0
4
0
0
1
2
7
0
1
1
0
0
0
0
2
0
1
2
2
1
0
2
0
0
1
0
2
0
1
0
1
1
2
1
0
2
10
0
1
0
1
0
0
0
0
1
3
2
1
0
0
0
0
1
0
1
0
0
1
1
0
2
0
0
1
2
1
1
0
1
2
2
1
1
1
0
0
1
0
0
1
0
0
0
1
2
0
1
0
0
2
2
0
0
1
1
2
0
0
2
0
0
0
1
1
0
0
0
2
0
0
0
0
1
1
0
2
0
0
2
1
1
1
0
1
1
1
0
2
0
0
1
1
1
0
1
0
0
2
0
2
2
1
0
0
2
2
2
1
2
1
0
2
0
0
0
0
0
1
1
0
1
0
0
1
2
2
1
2
3
0
0
2
0
1
0
1
1
1
0
0
0
1
1
1
1
1
1
0
0
3
2
0
2
1
2
0
0
1
0
0
0
2
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
1
1
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
1
0
0
1
2
2
1
0
2
0
1
0
0
0
1
2
2
2
0
0
1
2
0
0
0
1
2
0
3
1
1
0
0
0
2
0
0
1
2
0
0
1
0
1
1
0
0
1
0
1
0
0
1
1
0
1
2
2
1
0
0
0
1
1
0
0
0
0
0
1
2
0
0
0
1
2
1
1
0
1
2
0
0
0
0
2
1
0
1
0
0
1
1
0
0
2
2
0
0
2
1
0
1
1
0
0
1
0
0
2
0
1
1
2
0
0
0
0
0
0
0
0
4
1
0
1
1
1
0
0
2
2
1
0
2
1
2
2
1
0
2
2
2
2
2
0
1
2
0
0
2
2
1
1
1
2
1
0
2
0
1
1
1
1
0
0
0
1
1
1
1
1
0
0
0
0
1
0
1
0
0
1
0
0
0
2
0
1
1
2
0
0
2
0
1
2
2
0
1
0
2
1
2
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
1
2
3
1
0
0
2
3
3
0
0
0
0
1
1
1
0
2
1
0
1
0
1
0
2
1
1
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
2
0
2
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
1
1
0
0
2
2
0
1
2
2
0
0
1
1
2
1
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
2
2
0
0
1
2
0
2
0
0
0
1
0
0
2
2
0
0
1
2
2
1
2
0
0
0
1
0
2
0
1
0
1
1
1
0
0
0
2
0
0
0
3
1
0
0
2
1
2
0
2
2
0
0
0
0
0
0
2
2
1
0
0
2
2
0
1
1
1
1
2
4
0
0
0
0
1
2
0
0
1
1
2
1
0
0
1
1
1
1
0
2
1
0
0
2
0
0
2
0
1
0
0
0
0
1
0
1
1
1
1
0
0
1
0
0
2
1
1
0
2
0
0
1
2
0
2
1
0
2
2
4
1
0
0
2
0
0
1
0
2
0
1
1
2
0
1
0
0
0
1
1
1
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
3
4
0
2
0
0
0
1
4
0
1
0
0
2
2
5
0
2
0
0
0
0
2
0
0
0
0
0
2
5
1
0
0
0
1
0
2
1
0
0
0
1
2
0
1
0
0
1
1
0
0
1
1
0
0
1
2
0
1
1
0
0
1
1
0
2
0
1
0
1
1
0
0
0
0
1
1
1
0
0
0
1
2
0
0
0
1
1
0
0
1
1
3
1
0
2
0
1
1
1
0
1
1
0
1
0
1
2
0
2
1
0
2
1
1
0
2
1
2
0
2
2
0
1
1
1
0
0
1
2
1
1
1
0
0
1
1
0
0
2
0
0
2
1
3
0
1
0
1
2
0
1
0
0
0
1
1
0
2
0
1
1
1
1
4
0
0
0
0
2
0
1
1
0
1
2
0
0
0
0
1
2
0
2
0
0
0
0
2
0
0
0
0
1
1
1
2
2
0
1
1
0
1
0
0
2
1
1
1
2
0
0
1
1
0
2
1
0
0
0
0
1
0
1
0
3
0
1
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
1
0
0
1
0
0
0
1
2
0
2
0
0
1
0
2
2
1
2
0
1
0
1
2
1
0
1
0
0
0
0
2
0
0
2
1
1
4
0
0
2
0
1
1
1
0
0
0
1
0
1
0
0
0
2
0
1
0
2
0
2
2
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
1
0
2
0
0
0
0
1
0
0
1
0
3
0
1
0
2
0
1
0
2
0
1
1
0
0
1
1
1
0
0
0
1
0
0
0
0
1
0
0
0
2
1
1
0
2
0
2
0
1
0
0
2
1
1
1
2
0
0
0
3
1
1
1
2
0
0
0
1
1
0
0
0
0
2
0
0
0
2
0
1
0
1
2
1
0
2
0
1
0
1
0
1
0
2
1
0
0
1
2
2
0
1
0
0
0
2
0
0
2
0
1
0
2
0
2
2
0
2
0
2
0
0
0
2
1
0
0
1
1
0
0
1
0
0
1
1
2
0
0
1
0
1
2
0
0
1
1
0
0
2
1
1
2
0
1
1
1
1
2
0
0
1
0
0
0
0
1
2
1
0
2
1
0
2
0
2
2
0
2
0
1
0
2
2
1
2
0
1
0
0
0
1
1
1
2
0
1
0
3
0
2
1
3
0
2
0
1
2
1
0
0
0
1
1
1
0
2
0
0
0
0
2
3
1
1
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
1
0
1
1
2
2
0
0
2
2
1
1
1
1
1
2
2
1
2
1
1
0
0
0
0
2
2
2
0
0
1
0
1
0
1
2
1
0
0
1
2
0
0
0
0
0
0
1
0
0
0
10
3
0
0
1
1
0
2
1
1
1
1
0
0
0
0
0
0
1
1
0
1
0
0
1
1
0
0
0
0
1
0
2
1
2
1
1
1
1
1
0
1
1
0
2
0
1
1
2
0
1
0
1
0
1
0
1
0
1
1
0
1
1
0
1
0
1
0
1
3
0
2
1
0
1
0
0
2
0
1
0
0
1
2
1
2
1
1
0
0
0
0
2
0
0
0
1
2
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
1
1
1
1
1
0
1
0
0
0
1
1
0
0
2
1
2
0
0
0
0
0
3
0
1
0
0
0
0
1
0
4
0
0
1
1
2
1
1
1
0
0
1
1
1
0
1
0
2
1
2
1
0
0
0
2
0
0
2
0
0
2
1
2
4
2
1
1
1
0
0
0
0
0
2
0
1
2
2
1
1
0
2
0
2
1
0
2
0
1
0
0
1
2
1
1
0
0
0
0
0
0
1
0
1
2
1
1
0
1
0
2
0
2
0
2
0
2
1
1
0
2
0
1
0
2
1
1
0
2
1
1
2
0
1
2
0
2
1
0
2
2
1
0
1
1
0
0
0
0
0
1
0
2
0
1
2
1
2
0
0
1
1
2
2
2
0
0
0
0
2
1
0
1
0
0
0
1
0
0
2
2
0
0
0
1
0
1
0
1
1
1
0
0
1
1
1
0
0
0
2
0
1
1
2
0
0
0
2
0
0
1
0
2
1
0
0
0
1
1
0
3
0
0
0
2
0
1
0
1
0
0
2
0
2
1
0
0
0
1
1
1
0
0
0
0
1
0
1
1
0
0
0
1
0
1
1
4
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
1
1
2
1
0
0
1
0
1
1
0
0
1
0
1
1
1
0
0
2
0
1
0
0
0
0
1
1
0
1
1
0
1
0
0
2
0
0
0
1
1
2
0
2
1
2
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
2
0
1
2
0
2
0
2
0
2
2
2
0
3
1
1
1
1
1
1
2
2
0
2
0
2
2
1
0
0
0
0
0
1
1
0
0
0
1
2
0
0
1
0
0
0
1
0
0
1
0
0
0
2
1
3
0
1
1
3
0
1
1
2
0
0
0
0
1
4
2
0
1
0
0
0
1
0
1
2
1
0
0
0
1
0
1
0
2
2
2
0
1
0
1
1
0
0
0
0
0
0
0
2
1
2
0
1
2
0
0
2
0
0
0
0
0
0
2
1
0
0
2
0
2
2
0
0
1
0
1
2
1
2
1
0
1
2
0
1
0
0
0
0
2
1
2
0
1
2
0
1
1
0
0
1
1
0
0
2
2
0
0
0
0
2
1
1
1
1
0
0
0
0
0
0
2
0
1
0
0
0
2
2
2
0
0
1
0
2
1
1
2
2
0
0
0
1
1
3
0
0
2
0
2
1
1
1
1
0
0
0
0
2
3
0
0
2
1
0
0
0
1
0
2
0
0
0
1
0
0
1
1
0
2
0
0
1
0
1
0
0
0
0
0
0
1
2
1
0
1
0
2
0
0
1
1
0
1
3
1
1
2
0
0
0
2
1
1
2
0
1
0
1
0
2
0
0
1
1
0
2
1
2
0
1
0
0
0
0
1
0
2
1
1
0
0
1
0
1
0
1
1
2
2
0
1
0
0
1
3
0
0
1
0
0
0
1
0
0
0
2
0
2
1
2
0
2
2
1
0
1
0
0
0
0
1
1
0
2
0
0
0
1
0
2
0
0
2
0
0
2
0
1
0
2
0
1
1
1
0
0
1
1
0
2
0
0
0
1
1
1
1
0
2
1
2
2
0
0
0
0
2
1
1
0
0
0
0
0
2
0
0
1
1
1
0
0
2
0
2
0
1
1
0
0
0
2
0
0
0
0
0
2
1
0
3
0
0
0
0
0
0
0
1
0
0
1
1
0
0
2
0
0
2
2
0
2
1
1
0
1
1
1
2
2
0
0
1
2
1
1
0
1
0
0
1
2
1
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
1
2
1
0
0
0
1
2
1
1
0
1
0
0
0
2
2
0
0
0
2
0
0
0
2
0
0
0
2
0
0
1
0
0
0
1
1
1
0
2
2
0
0
0
0
1
1
2
0
2
0
0
1
2
0
0
2
3
1
2
2
0
1
0
0
0
0
0
0
0
2
1
1
0
0
1
1
1
1
1
0
0
0
2
2
0
1
1
0
1
0
0
1
1
0
1
0
0
1
2
2
2
1
2
2
0
2
1
0
2
1
3
2
0
0
0
1
2
0
1
0
1
0
1
0
2
1
2
2
0
0
0
0
2
2
1
2
2
1
0
2
2
2
2
0
1
0
0
0
1
0
0
2
2
2
0
1
0
1
0
1
0
2
0
1
0
0
0
1
2
0
0
0
0
3
3
0
2
2
0
2
1
0
0
0
1
1
2
1
2
1
0
2
1
0
0
2
0
2
1
1
1
1
0
1
0
2
2
1
2
0
2
0
2
1
0
0
0
0
0
0
1
1
2
0
0
0
1
0
0
2
0
0
0
1
0
1
1
0
0
1
0
1
1
0
1
0
1
1
0
0
0
0
0
2
1
1
0
0
0
1
0
1
2
0
0
0
1
1
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
2
3
2
2
0
0
0
1
1
1
3
0
0
1
0
0
0
1
0
1
0
0
0
2
0
0
1
1
0
1
0
0
1
0
0
1
1
1
1
0
2
0
1
1
1
0
0
1
0
0
0
2
1
1
0
1
0
1
0
2
0
0
1
1
1
1
1
1
2
0
1
0
0
1
0
1
0
0
2
1
1
0
0
4
3
2
0
0
2
0
0
0
0
1
2
0
1
2
1
0
1
1
0
0
2
0
0
0
2
2
2
1
1
1
1
0
0
0
1
2
2
0
2
0
1
1
1
0
0
1
1
0
0
2
0
1
0
0
2
0
0
1
2
2
0
2
0
0
2
1
0
2
1
1
3
3
0
0
2
0
2
1
2
1
2
1
0
1
0
0
0
0
1
0
0
4
0
0
0
1
0
0
1
0
1
0
1
0
0
0
1
1
0
0
0
0
1
1
0
0
1
0
1
0
0
0
2
0
2
0
2
1
0
0
0
1
2
2
0
2
1
1
1
1
1
0
0
1
2
6
1
1
1
0
0
1
2
0
1
1
1
0
1
1
0
2
0
1
2
1
0
0
0
0
1
0
0
1
1
0
2
0
0
0
0
0
2
1
1
0
1
0
2
0
2
1
1
1
0
0
0
0
0
0
1
1
0
0
2
0
1
2
0
0
1
0
0
1
0
2
1
0
0
1
3
1
1
0
0
0
0
1
0
0
3
0
2
0
2
1
2
0
1
2
1
0
1
0
0
1
2
1
0
2
1
1
0
0
0
1
1
1
1
1
1
0
1
0
2
2
0
0
0
1
0
0
0
0
0
1
0
1
2
0
0
1
0
0
0
0
1
6
0
1
0
1
2
0
0
1
1
0
1
1
1
2
2
1
4
1
2
2
1
1
3
1
1
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
2
1
3
0
0
1
0
0
1
0
0
0
2
1
3
0
0
1
0
0
2
1
1
0
0
3
0
0
2
0
0
0
0
0
1
0
0
1
0
1
2
2
0
1
1
0
0
0
0
0
3
1
0
2
1
1
0
0
2
2
0
2
2
2
1
2
0
0
2
1
1
1
2
1
1
0
0
2
2
1
1
0
1
0
1
1
0
0
1
0
0
1
1
1
0
1
0
0
0
1
2
1
0
0
0
0
0
1
0
1
0
2
1
2
2
2
1
1
1
0
0
0
0
1
1
0
2
0
0
0
0
0
2
1
1
2
1
1
0
1
0
2
0
1
2
1
1
1
0
0
1
0
0
0
0
0
1
1
1
1
2
0
0
1
2
0
0
1
0
0
0
0
2
1
0
0
2
0
0
0
1
2
2
0
1
0
2
1
0
0
0
0
1
2
2
0
0
0
0
1
7
0
0
0
0
1
1
1
2
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
2
0
1
2
0
2
0
0
0
1
0
1
1
0
2
1
1
0
2
0
1
0
2
0
1
2
2
2
2
2
1
0
0
2
1
1
1
0
0
0
0
0
1
2
0
0
2
0
1
0
1
2
2
0
2
0
0
0
2
0
1
1
0
0
0
1
0
2
0
0
0
1
0
1
2
0
2
2
1
2
0
1
0
0
0
1
2
1
1
0
0
2
1
0
0
0
0
0
0
0
0
1
0
2
0
1
1
1
0
0
0
1
0
1
2
0
1
0
0
1
0
0
0
2
0
1
1
1
1
1
1
0
0
1
0
0
1
1
0
1
2
1
0
2
1
0
1
0
0
0
0
1
2
0
1
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
2
2
0
0
0
1
0
1
0
0
0
2
0
2
2
0
0
1
1
0
0
0
0
1
4
0
0
0
0
2
2
1
0
0
2
0
1
0
0
1
1
0
2
0
1
2
2
2
0
1
0
1
2
1
1
1
2
0
0
2
2
2
1
0
6
0
1
0
0
1
1
1
1
0
0
0
2
0
0
0
1
0
0
0
1
1
2
2
1
0
1
0
1
2
0
1
1
0
2
1
0
0
0
2
0
1
0
0
1
2
1
0
1
5
0
2
0
1
1
0
2
0
0
1
2
0
0
0
1
2
1
1
1
1
1
0
1
0
1
0
2
1
0
0
0
1
2
0
0
0
0
0
2
1
0
0
1
0
2
0
1
2
1
0
2
0
0
0
0
2
2
0
1
0
0
0
2
0
0
0
0
2
0
2
2
0
1
0
0
1
2
0
2
0
0
2
0
1
0
2
1
0
0
0
0
0
1
0
2
2
0
0
1
1
2
0
0
0
2
0
0
0
0
0
0
2
1
1
1
0
2
1
0
2
1
1
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
2
2
1
0
0
0
0
0
1
0
0
0
0
1
0
2
1
0
2
0
0
2
2
2
2
1
0
0
0
0
1
0
1
0
0
0
2
0
0
1
0
0
0
0
0
2
0
1
0
1
0
0
1
0
1
0
0
2
0
2
2
1
1
0
0
1
0
1
1
1
0
2
0
2
0
1
1
0
0
0
1
0
3
0
2
0
0
1
1
0
0
3
0
1
1
3
1
1
2
0
0
0
0
0
1
0
0
0
1
0
1
0
2
0
0
1
1
0
2
2
1
1
0
0
2
2
3
1
0
1
0
1
0
0
0
0
0
2
0
0
0
2
0
1
0
2
1
0
1
2
1
0
2
0
1
0
1
0
0
0
1
0
1
0
0
1
2
3
0
0
0
1
1
0
1
0
1
0
1
0
2
0
0
0
0
1
2
0
0
0
1
1
2
1
0
2
0
1
1
2
1
0
0
0
1
1
1
1
0
0
1
0
2
0
2
1
0
1
0
1
0
0
2
0
0
0
2
0
0
0
0
0
2
1
0
2
2
0
1
2
1
1
1
1
0
1
2
0
1
2
1
1
0
1
1
1
2
2
0
3
1
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
1
0
2
0
1
1
2
0
1
0
2
3
2
0
0
1
1
1
1
0
0
1
0
2
0
0
0
2
1
2
0
2
2
2
1
1
1
2
1
0
2
0
1
1
2
1
0
0
0
0
0
0
1
0
2
0
0
1
1
0
1
0
0
0
1
2
0
0
0
2
0
2
0
1
2
0
0
0
1
1
1
0
1
0
0
0
0
1
0
1
0
2
0
1
0
1
0
0
0
0
0
1
0
0
2
0
0
1
1
0
0
0
0
0
0
2
0
1
0
0
3
0
1
0
0
0
4
2
2
0
0
0
1
0
0
1
1
0
1
0
3
3
0
1
1
2
0
1
2
0
1
1
0
1
1
2
1
2
0
1
0
1
0
1
2
1
0
0
2
1
1
0
1
1
0
1
1
0
1
1
0
0
0
1
0
2
2
1
0
1
0
2
0
2
0
0
2
2
0
2
0
0
0
0
0
0
0
0
1
1
0
1
1
2
1
1
1
0
2
0
1
0
0
0
0
1
2
1
1
0
0
2
0
1
1
0
1
0
0
0
2
0
0
0
2
1
0
2
2
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
1
2
1
2
1
2
0
2
0
2
2
0
0
0
1
1
2
0
1
0
1
0
0
2
0
0
0
1
2
0
1
0
1
0
0
2
1
2
2
0
1
1
0
1
3
2
0
1
1
0
1
2
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
2
0
2
1
0
1
0
2
1
0
0
0
0
0
1
0
2
0
1
1
0
0
0
2
0
1
2
0
0
1
2
0
2
1
1
2
2
0
2
0
0
1
0
2
0
1
0
1
2
0
1
1
0
1
1
1
2
1
2
1
1
0
0
2
0
0
2
0
1
1
0
1
2
1
0
1
2
2
0
0
0
0
0
0
2
0
2
2
2
0
0
0
2
1
0
1
2
2
0
1
1
0
0
0
0
2
1
0
1
2
1
1
1
0
3
0
0
0
1
0
0
0
2
1
0
0
0
0
2
2
0
0
2
0
0
3
1
0
1
1
0
1
0
0
0
2
0
0
2
0
0
0
1
0
2
2
1
2
0
1
0
2
0
1
0
2
1
1
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
1
2
1
0
2
1
2
2
0
0
1
0
0
0
1
0
0
2
1
1
0
0
1
0
2
1
0
0
0
2
2
0
2
0
0
1
2
3
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
2
2
0
0
2
0
0
0
1
2
0
0
0
0
1
2
0
0
0
0
0
0
1
2
2
0
1
0
0
3
0
1
0
1
5
1
3
0
0
2
0
0
0
1
1
0
2
0
0
0
0
1
0
2
0
1
0
1
0
0
2
1
0
0
0
1
2
1
2
0
1
2
4
0
1
2
0
0
1
0
1
2
0
2
0
1
1
0
0
0
0
1
1
0
2
0
0
0
0
1
0
0
0
0
2
0
1
2
0
2
0
1
0
1
0
1
0
0
0
0
0
2
0
0
2
0
0
1
0
0
2
2
0
0
2
0
1
0
0
0
1
0
0
1
0
0
1
0
2
1
0
1
2
1
3
1
4
1
0
1
0
1
3
0
0
0
0
0
1
0
0
0
1
2
2
1
2
2
3
0
2
1
0
0
0
0
0
2
0
1
1
1
1
2
1
0
0
2
0
0
1
1
0
1
1
0
1
0
2
1
0
0
1
0
2
2
0
1
1
1
1
1
5
4
3
2
1
1
0
1
0
0
0
2
2
3
3
0
2
0
0
2
0
0
0
2
1
0
0
0
0
0
1
1
2
1
0
0
1
1
1
0
1
0
1
0
0
3
1
1
2
2
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
2
2
0
2
3
1
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
1
2
0
1
2
1
0
1
0
0
0
2
0
0
0
0
1
0
2
1
0
2
1
0
2
1
0
0
2
2
0
0
2
0
1
0
1
1
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
2
0
2
1
1
0
1
0
2
2
0
0
1
1
0
0
0
0
1
1
1
0
1
0
1
0
1
3
2
2
2
0
2
2
0
0
2
0
0
2
0
2
2
0
0
1
0
0
0
2
2
0
1
2
1
1
1
2
6
0
0
2
0
0
1
0
1
0
0
1
0
1
2
1
2
0
1
0
0
0
1
0
2
0
2
0
0
2
1
1
0
2
0
0
2
0
1
0
0
2
0
1
1
1
0
0
0
0
2
0
0
0
1
1
0
0
0
2
2
0
0
0
0
1
2
1
0
0
2
0
1
0
2
0
0
2
2
2
1
0
1
0
0
1
1
1
0
2
1
1
0
2
0
2
2
1
0
1
1
0
1
2
0
1
1
1
2
2
2
2
1
0
1
2
0
0
1
2
0
0
1
1
0
0
0
0
1
0
1
2
0
0
0
1
0
0
2
0
2
2
1
0
0
1
0
0
2
2
2
0
1
1
0
3
2
0
0
0
0
1
1
2
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
2
1
2
1
2
2
0
0
0
1
0
2
0
0
0
2
1
0
1
2
2
0
0
1
1
0
1
0
1
2
9
4
1
1
1
1
0
2
1
2
1
0
0
1
0
1
0
0
2
0
2
2
1
2
0
0
0
1
1
1
1
1
0
0
1
0
1
1
1
1
0
1
1
1
2
0
0
2
2
0
1
2
2
0
0
0
2
0
0
1
2
2
1
0
1
1
0
0
1
0
1
0
0
0
2
0
1
1
0
2
0
1
0
1
1
0
2
0
1
0
0
2
1
0
1
2
2
0
2
0
1
1
0
4
1
2
1
0
0
2
0
0
1
0
0
2
0
1
2
1
1
0
2
1
0
0
1
0
1
0
0
0
1
2
2
1
1
2
0
0
1
0
1
1
0
0
1
1
0
0
1
1
0
2
1
2
1
1
0
1
1
1
1
1
1
1
0
0
0
2
1
0
2
0
0
2
0
1
1
1
1
0
0
2
1
2
1
1
1
0
1
1
0
0
1
0
1
0
2
0
2
0
1
0
0
1
1
2
1
1
1
1
4
1
2
2
0
0
2
0
0
0
0
0
2
0
2
2
2
1
2
0
2
1
1
0
1
0
0
0
2
1
1
0
0
0
0
0
1
1
0
2
0
2
1
0
1
0
3
0
0
0
0
0
0
0
1
1
1
0
2
1
0
2
0
1
1
0
3
1
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
1
2
1
0
0
1
3
0
0
0
0
0
2
0
1
2
0
0
0
1
0
1
2
2
0
1
4
0
1
0
1
0
1
1
2
0
0
0
1
0
0
1
2
1
0
2
0
2
0
2
0
0
0
1
0
0
1
2
0
0
1
0
2
0
1
0
2
1
2
0
0
0
1
0
2
1
2
1
0
0
0
0
1
2
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
3
2
0
0
1
0
1
2
0
1
0
0
0
0
1
0
1
0
3
0
0
0
0
0
0
1
0
1
2
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
1
0
2
1
2
2
1
0
1
0
2
2
1
0
0
0
2
3
1
2
2
0
0
0
0
0
1
0
1
2
0
0
0
2
0
0
1
0
2
5
0
1
0
0
1
0
0
2
6
1
1
0
0
0
1
1
0
0
2
1
2
0
2
0
0
1
1
1
1
0
0
0
1
1
2
0
0
0
0
1
2
0
2
1
0
1
0
0
1
0
0
1
0
0
2
0
2
2
0
0
1
0
1
0
1
0
0
1
0
0
2
1
2
1
0
0
0
0
1
0
0
0
1
0
0
1
0
2
0
4
0
0
0
0
0
1
1
2
1
0
1
1
1
1
0
2
0
1
0
2
0
0
2
1
0
0
0
2
1
0
0
0
1
4
2
2
2
0
3
2
2
1
0
0
1
2
1
0
1
0
0
1
0
1
0
2
2
0
0
1
1
0
0
1
1
0
0
2
1
2
0
1
1
1
1
2
0
2
0
0
1
1
2
1
1
1
0
0
1
1
3
1
1
0
0
0
0
0
2
4
0
1
0
0
1
2
1
0
2
0
2
1
0
0
2
1
1
2
0
1
2
0
2
2
0
2
0
0
2
0
0
0
0
0
0
1
0
1
2
0
1
2
0
0
1
0
1
0
1
2
2
1
0
2
2
1
2
0
1
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
2
0
1
1
0
0
0
0
2
2
1
0
1
1
0
0
2
2
0
0
1
0
0
0
0
2
0
0
1
0
2
1
2
0
2
1
2
0
0
2
1
0
0
0
0
1
0
1
0
0
0
2
0
0
1
1
0
1
0
2
1
0
2
2
0
2
1
0
0
2
0
0
3
1
2
1
0
1
0
1
0
0
0
2
2
0
2
2
0
1
0
2
0
0
1
1
2
3
1
0
0
0
1
2
1
0
0
0
1
0
1
1
1
0
1
1
2
2
0
1
0
0
2
0
1
0
0
1
2
0
0
0
1
1
1
1
1
3
2
0
0
1
1
0
0
2
1
2
2
1
0
1
0
0
0
1
0
0
0
1
1
0
0
0
2
1
1
0
0
0
1
0
1
1
0
1
0
1
2
2
0
1
2
2
0
0
0
1
0
2
0
1
1
1
0
0
1
0
0
0
1
1
0
1
1
0
0
1
0
2
0
0
2
0
0
1
1
0
1
1
2
2
1
0
2
1
0
2
1
0
0
1
1
1
1
0
2
2
2
1
0
0
0
2
3
1
0
0
0
0
0
0
0
1
2
0
0
2
0
2
0
2
0
0
0
0
0
1
0
0
1
2
0
0
2
1
2
0
0
0
0
0
2
1
2
1
2
2
0
1
2
2
0
1
1
0
1
1
2
0
0
2
1
0
0
0
0
0
2
2
0
0
0
0
0
1
0
5
0
2
1
0
2
0
1
2
0
0
0
0
0
0
1
1
0
0
2
0
1
0
0
0
2
1
1
2
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
2
2
1
2
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
1
0
1
1
2
0
0
1
2
0
4
2
1
0
1
1
0
0
0
2
1
0
2
0
1
2
0
0
0
0
0
0
1
1
1
0
0
1
0
1
0
0
1
1
2
1
0
2
2
1
0
1
0
1
0
0
3
2
1
0
0
0
1
0
0
0
0
3
1
1
2
0
0
1
0
0
0
0
0
2
3
1
2
0
2
2
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
1
2
2
0
0
0
1
1
0
1
0
0
1
0
0
0
1
1
1
1
0
1
2
0
1
0
0
0
0
1
1
2
1
0
0
0
3
0
0
0
1
0
1
0
1
0
0
2
0
0
1
1
2
1
2
3
2
1
0
1
2
0
1
1
2
0
1
0
0
1
0
0
1
1
2
2
0
0
1
0
0
1
0
0
1
1
1
0
2
0
0
1
1
1
0
0
1
0
2
0
1
0
0
1
0
2
0
0
0
1
1
0
2
2
0
1
1
2
1
1
0
0
1
1
2
2
0
0
0
1
1
0
0
2
0
2
1
2
1
1
0
0
3
1
1
1
1
0
1
0
0
1
0
1
1
2
1
0
0
1
1
0
2
1
0
1
1
1
1
1
0
0
0
0
2
0
0
1
0
2
0
0
1
1
0
0
1
0
1
0
1
0
4
0
0
2
1
0
0
1
1
1
0
1
0
2
0
1
0
1
1
2
0
0
0
2
0
1
3
0
1
2
1
2
1
1
0
0
0
1
1
0
1
1
0
0
2
0
1
0
3
2
0
1
1
0
2
2
2
0
0
1
1
0
0
0
2
2
0
1
0
1
1
0
2
0
1
0
0
0
0
2
1
1
0
1
1
0
1
0
0
0
1
0
2
0
0
2
1
1
2
1
1
2
1
0
0
2
1
1
0
0
0
0
0
1
2
0
0
0
0
0
1
0
1
2
0
0
0
2
0
2
0
1
2
1
2
1
0
0
1
2
0
0
2
0
0
1
0
2
1
0
2
0
1
0
0
1
2
1
2
0
0
2
0
1
0
0
2
0
0
1
0
0
2
0
0
2
1
0
0
0
0
1
0
1
0
0
1
0
0
0
1
1
2
2
1
0
2
0
0
0
0
2
2
1
1
2
1
1
1
1
0
1
2
1
1
1
0
0
0
0
1
1
0
0
1
0
1
2
1
7
2
0
0
1
0
2
0
0
0
2
1
0
0
4
0
1
0
0
0
2
1
0
1
0
2
2
2
1
0
0
0
1
2
0
3
0
0
0
0
0
0
0
0
0
1
1
1
0
2
2
0
2
0
1
0
0
0
2
0
1
0
1
0
2
0
0
0
2
0
0
0
2
0
0
0
1
0
2
0
0
0
2
0
1
0
0
0
0
0
0
2
1
2
1
1
0
1
1
2
0
0
0
0
0
0
0
0
1
1
0
0
1
1
1
1
1
3
7
1
1
0
1
0
0
1
2
0
2
0
0
1
1
1
1
0
1
0
0
1
0
2
0
2
1
0
1
1
0
1
1
1
2
0
1
1
1
0
0
0
0
2
0
1
0
1
1
2
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
2
0
0
1
1
0
3
2
2
0
0
0
2
1
0
1
2
1
0
0
0
2
1
0
0
2
1
0
0
2
1
2
1
1
0
1
2
0
1
2
2
0
0
0
1
1
1
4
1
2
1
0
0
1
1
0
2
0
2
0
1
0
0
0
1
0
2
2
2
1
0
0
0
0
1
1
0
2
0
0
2
0
0
2
1
0
0
1
0
1
0
1
0
1
0
2
0
0
1
1
0
0
1
0
0
1
0
1
0
1
1
1
0
2
3
1
0
1
0
1
0
0
0
0
3
0
1
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
1
0
1
1
0
0
0
2
1
1
0
2
1
0
0
1
0
1
0
0
0
1
1
0
0
0
2
2
0
0
2
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
2
0
1
1
2
0
0
0
0
0
0
0
0
2
2
0
0
1
1
1
0
2
1
0
0
0
1
0
1
0
0
0
2
0
0
2
0
1
0
1
1
0
1
0
2
0
0
0
0
1
1
0
1
0
0
2
0
0
0
0
2
0
1
0
0
0
0
1
0
0
3
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
1
2
0
1
1
2
0
0
1
0
2
2
2
0
1
1
0
2
2
3
2
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
2
1
2
2
0
2
0
0
1
2
2
1
0
0
0
2
0
2
1
2
2
1
0
1
1
1
1
1
1
0
2
0
0
1
1
0
2
0
1
1
2
1
1
0
1
0
2
5
0
0
2
0
1
0
2
0
0
0
1
0
0
0
1
0
1
0
2
0
0
0
0
1
2
0
2
0
0
0
0
2
0
0
0
0
0
0
2
2
2
2
2
1
0
1
0
1
0
1
0
0
0
0
2
1
1
1
2
2
0
1
2
0
0
0
0
0
1
0
0
0
2
0
1
0
2
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
2
1
5
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
1
0
1
0
1
1
0
1
1
1
2
0
2
1
0
0
0
1
0
1
1
0
0
0
1
1
0
0
1
0
0
0
0
1
0
1
2
2
1
1
0
1
0
2
0
0
0
1
1
1
1
2
0
0
2
0
1
2
2
0
0
1
1
0
1
0
1
0
0
1
1
1
1
0
1
2
1
2
1
2
3
1
0
0
1
1
1
0
0
2
0
0
1
0
0
2
1
1
0
0
1
2
2
1
2
0
1
0
1
0
0
0
2
1
0
0
1
0
2
1
0
0
0
0
1
2
1
0
0
0
1
0
1
2
0
0
2
2
0
0
1
0
0
1
3
0
1
2
2
0
0
1
0
0
1
1
1
2
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
1
1
0
0
0
0
1
1
0
0
1
0
0
1
2
2
0
0
0
1
3
0
0
0
1
0
0
1
2
0
0
1
2
0
0
0
0
2
0
1
0
1
2
2
2
0
0
0
0
2
0
0
2
0
2
0
0
1
0
2
0
0
2
0
1
0
0
0
0
1
1
0
2
1
0
0
0
1
2
0
1
1
0
2
0
0
1
0
0
0
1
0
0
2
0
1
1
0
0
2
0
0
1
0
0
1
1
0
2
0
2
1
2
0
0
1
0
0
0
0
0
1
2
1
0
0
1
0
0
1
0
0
2
2
3
0
0
1
0
0
0
0
0
0
2
1
0
0
0
1
1
2
3
2
2
2
0
1
1
2
1
0
2
2
0
1
0
1
0
0
2
0
1
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
1
1
1
1
0
0
0
0
1
2
1
0
0
0
2
1
2
2
0
0
1
1
2
0
1
2
1
0
1
1
0
1
1
0
1
0
1
0
1
2
0
2
0
0
2
0
0
0
2
0
0
2
2
0
0
0
1
1
0
2
0
0
2
1
0
1
0
1
2
0
1
0
0
1
1
0
1
0
0
0
2
0
0
0
1
1
0
2
0
2
0
0
0
1
1
2
2
2
0
0
2
0
0
1
1
0
3
1
1
0
0
0
2
0
2
1
2
0
1
0
0
0
0
0
0
0
1
6
1
2
2
2
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
1
1
1
1
1
0
1
1
1
0
4
4
1
1
1
1
2
2
1
0
0
1
2
2
2
1
0
1
2
1
1
1
0
1
1
2
0
0
0
0
1
1
0
1
2
1
0
0
1
1
1
1
0
1
0
0
2
3
0
1
2
0
1
1
2
0
1
1
0
1
0
0
2
0
1
1
1
1
0
0
0
0
1
0
1
0
0
1
1
2
1
2
0
1
1
2
0
0
0
0
1
1
1
1
0
0
1
1
2
0
0
1
2
0
1
2
0
0
0
1
0
1
1
0
1
3
1
2
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
1
1
0
1
0
2
0
1
0
0
2
0
0
0
1
1
2
1
2
1
2
0
0
0
2
1
1
1
0
2
1
0
1
0
2
1
1
0
1
1
0
1
0
0
0
2
0
2
2
1
0
0
2
2
2
0
1
2
0
0
2
0
0
1
0
0
0
0
0
1
1
2
1
0
1
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
1
2
0
0
0
2
1
0
0
1
0
0
0
1
1
2
0
0
0
0
0
0
1
1
2
2
0
3
0
0
0
0
0
1
1
1
1
0
1
2
1
0
1
1
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
3
0
2
3
0
0
0
1
2
0
0
0
0
0
2
2
2
0
0
2
1
2
0
0
0
0
1
2
0
0
2
0
0
2
2
0
1
0
2
3
1
2
1
2
2
0
2
2
0
0
0
0
1
1
2
2
1
2
0
1
2
0
1
0
0
0
0
0
0
2
2
0
1
2
0
1
0
0
0
0
1
0
1
0
2
0
0
2
1
0
1
1
2
1
0
0
0
0
1
0
2
0
0
2
1
2
0
0
0
2
1
1
1
0
1
1
0
1
0
1
0
1
0
1
0
0
0
0
0
2
0
2
0
0
0
1
1
0
0
0
2
0
0
1
1
2
0
2
2
2
2
0
1
0
0
2
0
2
1
2
1
0
0
0
2
0
0
0
1
1
0
0
1
2
0
0
0
3
2
0
0
0
0
0
0
2
0
1
1
0
1
2
1
2
0
1
0
1
1
2
0
0
1
2
0
0
1
0
2
0
2
1
0
2
0
0
0
0
1
1
2
1
0
1
0
1
0
2
1
2
1
0
1
0
1
0
2
0
0
1
0
2
0
2
0
0
0
1
0
1
0
0
0
0
0
3
0
2
0
2
1
1
0
2
1
1
0
0
0
0
0
0
0
1
2
1
1
0
1
2
0
2
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
7
0
0
2
2
0
1
0
2
0
0
3
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
2
2
0
0
0
0
0
0
1
1
2
1
2
1
0
2
1
2
2
0
1
2
0
1
2
0
0
1
1
0
1
2
0
0
0
1
2
1
0
0
1
1
1
2
0
3
0
1
2
0
0
0
1
2
0
0
1
1
2
1
0
2
1
0
0
0
0
1
0
2
0
0
2
1
1
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
1
0
3
1
1
0
0
2
0
0
0
1
1
0
0
0
1
0
1
0
1
1
1
0
0
1
1
2
2
0
1
1
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
1
2
0
0
1
0
0
2
2
2
2
0
1
0
0
1
0
0
0
0
0
1
2
1
2
1
1
1
2
0
2
1
0
0
0
2
0
1
0
2
0
0
1
2
2
2
0
1
0
1
0
0
1
2
0
2
1
0
2
1
0
2
0
0
1
1
2
0
0
2
2
2
0
2
2
2
0
0
0
0
1
2
0
0
1
0
2
1
1
0
0
1
2
1
0
2
2
0
2
0
0
2
1
1
1
1
0
0
0
2
0
2
0
2
0
1
0
1
0
0
1
2
1
0
1
2
0
0
0
2
2
2
0
0
1
1
3
3
1
0
0
2
2
2
0
0
1
0
0
1
0
0
0
0
1
0
2
1
0
0
1
1
0
2
0
0
1
0
0
1
2
1
0
0
0
0
0
1
0
2
1
2
1
1
0
2
1
1
0
0
1
0
0
0
2
0
1
1
0
1
1
1
1
2
2
0
0
0
2
0
1
0
2
0
2
0
1
1
0
0
0
1
1
2
0
3
1
1
1
0
0
0
2
0
0
0
0
2
2
1
2
1
1
1
0
1
1
3
0
0
1
1
0
1
0
2
1
2
4
2
1
2
1
1
0
1
1
1
0
0
1
1
1
2
0
0
2
0
1
1
1
0
0
0
1
0
0
1
1
1
1
1
1
0
0
1
0
1
1
2
0
2
0
2
0
0
0
2
0
2
0
1
0
0
2
1
2
2
2
2
1
0
0
2
0
0
1
0
0
1
0
1
2
0
0
0
0
1
0
0
1
1
2
1
2
1
0
2
0
0
1
1
0
2
2
2
0
0
0
0
1
1
1
0
1
1
2
2
2
1
0
0
0
0
0
0
1
0
1
0
2
0
2
1
1
1
0
0
1
1
3
2
1
1
3
5
0
1
1
0
2
2
0
2
2
2
0
0
1
0
0
2
0
0
0
0
0
2
0
2
0
0
2
0
2
0
2
0
0
2
0
1
2
1
1
1
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
2
2
0
1
0
2
2
2
1
2
0
0
0
0
1
0
0
1
2
0
0
2
0
0
1
0
1
0
2
0
1
0
2
2
0
2
0
0
0
1
0
0
0
0
0
1
3
1
1
0
1
1
0
2
1
1
2
2
0
1
2
1
1
0
0
0
0
0
0
2
2
0
1
0
1
2
2
0
0
0
1
1
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
2
0
0
0
1
2
0
1
0
0
1
1
0
0
3
1
0
1
0
0
0
1
0
0
2
1
1
2
0
1
0
1
0
0
2
0
2
0
0
1
1
2
0
0
0
1
0
0
1
1
0
0
0
0
1
0
2
0
1
2
0
2
1
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
1
0
1
0
2
0
2
1
1
0
0
1
2
0
1
0
0
2
0
2
1
0
0
0
2
0
0
0
0
1
2
2
1
0
1
1
0
1
2
0
2
2
2
1
0
5
0
1
0
1
1
2
0
0
2
1
0
2
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
4
1
0
0
0
1
1
0
2
1
0
0
0
0
0
1
0
2
0
0
1
0
0
1
0
1
0
0
0
0
0
2
1
2
1
1
2
0
0
0
0
2
1
0
0
1
2
1
1
0
0
0
0
0
2
1
2
1
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
2
1
0
1
1
0
0
0
1
3
0
0
3
0
2
2
0
2
0
2
1
0
1
1
1
1
0
1
2
1
1
0
0
2
1
2
0
2
0
0
2
0
0
3
2
0
2
0
0
0
3
2
1
0
0
2
0
0
0
2
0
1
0
0
0
1
0
1
2
1
2
0
0
2
2
0
0
0
2
0
2
1
0
1
2
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
2
0
0
1
0
0
0
1
0
1
2
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
2
0
2
0
1
1
1
0
1
0
1
0
0
2
0
2
0
6
2
1
1
2
0
0
0
0
1
1
1
2
0
0
0
2
2
1
2
0
0
1
0
1
2
0
1
1
0
0
1
1
2
0
0
0
0
1
0
2
2
0
2
1
1
0
0
1
0
1
0
1
0
0
1
2
1
0
2
1
0
0
0
2
1
0
1
2
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
3
1
2
1
0
0
0
1
2
0
0
2
2
1
0
1
0
0
0
0
2
1
0
0
1
2
2
0
1
0
1
0
3
1
0
0
0
2
2
1
1
0
1
0
2
1
1
0
1
1
1
2
0
1
1
0
1
1
2
2
0
1
1
2
2
0
1
2
0
0
0
0
2
2
0
0
1
1
0
1
0
0
2
0
0
1
0
1
0
0
2
1
0
2
1
0
2
1
1
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
1
3
1
0
2
1
1
0
2
2
1
1
1
0
1
0
1
0
0
2
2
1
1
0
2
2
1
1
2
0
0
0
2
1
0
2
0
0
1
1
0
0
0
1
1
0
0
2
2
0
0
2
1
2
0
0
1
0
1
0
1
0
0
0
1
0
2
0
1
0
2
3
1
1
1
0
0
0
2
0
4
0
0
2
2
0
2
0
0
1
0
1
2
1
0
1
0
0
1
1
0
1
0
0
1
3
0
0
1
0
1
0
2
0
2
0
0
1
1
1
1
1
1
0
3
0
1
3
2
2
0
0
0
0
1
1
0
0
1
1
0
1
0
2
1
2
2
0
1
2
0
0
2
1
0
1
0
1
4
0
0
0
1
0
3
0
0
3
0
2
0
0
1
1
0
1
0
2
1
0
4
0
1
0
1
0
0
0
0
1
0
1
0
1
0
0
1
0
0
4
0
1
1
0
1
0
0
0
2
1
0
2
0
0
0
1
1
0
0
1
0
2
2
0
0
1
0
0
0
0
0
2
2
0
2
0
1
0
1
2
1
0
0
1
1
0
0
1
0
0
0
1
0
1
1
0
2
0
2
1
2
0
0
0
1
0
0
3
1
1
2
0
2
0
0
0
0
2
0
2
2
2
0
0
2
1
3
1
2
0
2
2
1
1
1
0
0
0
0
1
0
1
0
0
0
1
0
1
1
0
1
2
0
0
1
0
1
2
0
0
0
0
1
0
0
0
0
0
2
0
0
2
2
0
0
0
1
2
0
1
3
0
1
0
1
2
0
0
0
0
2
0
2
0
0
0
0
0
1
1
0
2
1
0
0
1
3
0
0
0
1
2
0
2
1
0
0
1
0
0
0
0
0
2
0
0
0
2
0
1
2
0
0
1
0
0
2
0
0
0
0
0
1
0
2
0
2
0
0
2
1
0
1
1
1
2
2
1
0
0
1
0
1
1
0
1
0
0
1
0
1
0
1
0
1
0
0
0
0
0
1
0
1
0
0
2
0
1
2
0
0
1
2
1
0
2
0
0
0
0
2
1
0
0
2
2
0
0
1
0
2
0
0
0
0
1
1
0
0
2
1
0
1
0
1
0
2
3
1
0
2
0
1
0
2
1
0
0
2
1
1
0
0
2
1
0
1
1
0
1
2
0
0
0
1
0
4
0
1
0
1
0
0
1
1
1
1
2
0
1
2
0
1
0
0
0
1
0
0
0
2
0
0
1
0
1
0
0
2
1
2
0
2
1
1
1
0
2
0
1
0
2
0
0
0
0
2
0
0
0
1
1
1
2
0
0
0
1
2
2
0
0
0
2
0
0
0
1
0
2
0
0
2
0
0
2
2
1
0
0
2
3
0
2
0
0
0
0
0
1
2
1
2
1
0
1
2
0
1
0
0
0
0
1
1
0
2
0
2
0
0
1
0
1
1
0
1
1
0
1
1
0
1
1
1
1
1
2
2
0
0
1
0
1
0
0
1
0
0
0
0
2
0
2
2
1
1
0
1
0
1
2
1
0
0
0
1
0
0
0
0
2
2
0
1
1
2
1
1
1
2
0
0
0
1
0
1
0
1
2
1
1
2
1
1
1
0
3
2
2
0
0
2
0
1
3
0
4
1
0
0
2
0
1
0
2
0
0
1
1
1
0
1
0
0
0
2
1
2
2
0
2
1
0
0
1
0
0
1
0
0
1
0
1
2
0
0
1
1
2
1
2
8
0
0
1
1
0
0
0
2
1
2
1
1
0
0
1
0
1
0
0
0
1
1
0
1
2
1
0
1
0
2
0
1
2
1
0
2
0
0
1
0
2
1
0
1
0
2
0
0
0
0
0
1
0
2
0
0
2
1
2
2
1
1
0
5
0
2
2
2
1
1
0
0
0
2
1
0
1
1
2
1
1
0
0
1
1
0
2
2
0
0
0
0
0
0
1
2
0
1
0
0
1
1
0
2
0
2
1
1
2
0
1
2
0
2
0
0
0
0
0
1
1
0
0
0
0
2
3
0
2
0
0
0
0
0
1
0
0
2
1
0
1
0
0
1
1
3
1
0
2
0
1
3
0
0
0
0
0
1
0
0
2
0
1
0
2
1
2
0
1
0
0
0
2
1
0
0
1
0
0
0
0
2
1
0
2
0
1
1
0
0
0
0
0
0
2
2
2
0
0
2
0
1
1
2
0
0
0
0
0
1
2
0
0
1
2
0
1
0
2
1
1
0
0
1
0
0
0
2
1
2
2
0
0
0
2
1
2
1
1
0
2
0
0
0
0
1
1
0
0
0
0
1
0
2
0
1
0
0
2
1
0
2
1
1
1
0
2
2
0
0
1
0
0
0
1
0
1
0
0
1
2
0
0
1
0
0
1
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
1
1
1
2
2
0
1
0
0
0
2
1
0
1
1
0
1
1
0
0
0
0
0
1
1
5
1
0
1
2
0
0
0
0
1
1
1
3
1
1
1
0
2
4
0
2
0
0
1
2
0
0
0
2
2
2
0
0
0
2
2
4
0
0
0
0
0
0
2
2
2
0
0
1
0
0
2
0
2
0
0
2
1
1
0
1
0
0
0
0
2
1
0
1
3
1
0
0
1
0
2
2
1
2
0
1
0
1
0
1
1
0
1
1
0
0
1
2
0
0
1
0
0
1
0
2
1
3
3
2
1
1
1
1
0
2
0
0
2
1
2
0
0
0
0
0
0
0
1
1
2
4
1
0
2
1
3
0
1
0
0
0
0
2
0
0
2
1
0
1
2
2
0
0
2
2
1
1
1
2
2
2
0
2
1
2
1
0
0
1
0
2
1
1
0
1
2
0
0
0
1
1
0
0
0
0
0
2
0
0
0
2
1
0
1
2
2
0
2
0
2
1
2
1
1
2
1
2
0
0
3
0
0
1
0
0
0
1
0
0
1
0
0
0
0
3
1
1
1
1
0
2
0
0
0
1
0
0
1
0
1
0
2
2
1
0
2
1
0
1
1
1
1
1
1
5
0
0
2
0
0
2
0
2
1
0
1
0
1
0
0
0
2
0
0
0
0
0
2
1
0
0
1
0
0
1
1
1
3
1
0
2
0
1
0
1
0
0
0
0
0
0
0
1
0
1
2
0
2
2
0
0
1
0
0
1
0
1
2
1
1
0
0
3
1
1
2
0
0
0
0
3
0
2
0
1
1
0
1
0
1
1
0
0
2
0
0
0
0
1
0
0
0
2
0
0
1
1
0
1
0
0
1
0
1
1
0
1
0
1
0
1
0
2
0
1
2
2
1
0
2
2
0
2
1
1
2
1
1
1
2
1
2
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
1
1
0
0
0
2
1
0
0
1
0
0
0
1
0
0
0
1
1
1
0
1
1
1
0
0
0
1
0
0
1
0
0
1
2
2
2
2
1
0
0
1
1
1
1
2
2
1
1
0
1
0
0
0
0
0
1
0
1
1
0
0
1
0
0
2
0
2
0
1
0
1
1
0
2
2
2
0
2
1
2
1
1
2
1
0
0
0
1
0
2
0
1
1
2
0
2
1
3
0
0
1
0
0
0
2
0
1
0
1
0
1
0
2
0
0
1
0
0
0
2
1
3
2
1
0
3
0
1
0
0
2
2
0
1
0
2
0
0
2
0
1
4
0
0
1
2
0
2
0
0
0
2
0
1
0
1
0
2
2
0
1
2
2
1
1
1
0
0
0
1
0
0
1
0
0
0
0
2
1
1
0
1
0
1
2
1
0
0
0
0
2
1
0
0
0
2
0
0
1
1
0
1
1
0
1
1
0
1
1
1
1
2
0
0
1
1
2
0
0
0
1
1
0
0
1
0
1
0
1
1
0
1
2
2
2
2
0
2
2
0
0
0
0
0
2
0
0
2
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
1
0
0
0
2
0
0
0
1
2
1
0
0
0
0
2
0
0
0
1
2
0
2
0
1
0
0
2
1
0
0
2
0
0
0
0
0
1
0
0
1
1
1
1
2
2
2
0
1
1
1
1
0
0
0
1
0
0
0
2
0
1
1
1
0
2
0
0
1
0
1
0
2
0
1
0
0
1
0
2
1
2
0
0
0
1
3
0
2
1
0
2
0
0
1
0
0
1
0
1
0
0
0
0
0
2
2
1
1
2
0
1
0
0
2
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
2
2
1
1
0
0
2
2
2
1
1
0
1
2
1
1
0
1
1
1
0
0
0
0
6
2
0
1
2
0
1
1
0
0
0
0
2
1
0
0
0
0
2
0
2
1
0
2
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
2
2
2
0
0
3
0
0
2
2
1
0
2
0
1
1
2
0
0
2
0
0
1
1
1
0
1
0
0
0
0
0
1
0
0
1
1
1
1
2
0
0
0
0
1
2
1
0
0
0
0
0
1
0
3
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
1
1
0
1
0
1
1
0
0
1
1
0
0
1
2
1
2
1
1
0
0
1
0
1
3
2
2
0
0
0
0
0
0
1
0
0
1
2
1
0
0
1
2
2
0
1
1
0
1
0
1
0
2
0
0
2
0
2
1
1
0
1
0
1
1
1
0
0
0
2
0
2
0
0
0
2
1
0
1
2
1
1
1
1
0
0
2
0
2
1
0
1
0
1
2
0
1
0
0
1
0
1
1
0
0
2
1
0
0
2
0
2
0
1
0
2
0
1
0
0
2
0
1
1
1
0
1
0
0
0
1
1
1
1
1
2
1
0
2
1
0
2
0
0
1
0
1
0
0
0
1
1
1
2
0
0
4
2
0
0
0
1
2
2
1
0
2
1
1
1
0
0
0
0
0
0
1
2
1
0
0
0
0
1
2
0
2
0
0
0
0
2
2
1
0
1
3
1
0
0
3
1
0
1
1
0
0
4
1
1
0
1
2
0
0
0
0
0
1
0
1
0
0
1
0
0
0
3
1
1
5
0
2
0
0
2
2
0
0
0
2
0
1
0
1
1
0
0
0
1
0
0
1
2
1
0
2
1
0
0
2
0
2
0
0
1
1
1
2
1
2
0
0
0
0
1
1
2
2
2
0
2
0
2
0
0
0
0
2
2
2
0
0
2
2
1
0
1
2
0
0
0
0
0
2
0
1
0
2
2
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
2
1
0
1
1
0
0
1
2
0
1
0
1
2
2
2
0
2
0
2
0
0
2
1
2
1
1
1
0
2
1
1
0
0
0
2
2
0
0
1
0
1
2
1
2
2
0
0
0
0
2
0
0
1
1
1
0
1
1
0
0
0
0
0
0
1
0
0
1
2
1
0
2
0
0
0
2
1
0
1
0
1
2
0
0
0
0
0
0
2
0
1
0
1
0
2
3
0
0
2
1
0
2
3
0
1
2
0
1
2
1
0
2
2
0
0
2
0
0
0
0
0
2
2
1
3
0
1
2
1
0
1
4
2
0
2
1
1
2
1
2
1
1
1
1
1
1
2
0
1
2
1
0
0
1
1
0
0
2
1
2
2
2
0
0
0
1
1
0
1
0
2
1
0
0
0
2
1
2
0
1
0
0
0
0
1
0
2
2
1
0
1
3
0
0
0
1
0
0
2
0
2
2
0
2
0
1
2
1
0
1
1
1
1
0
0
0
0
1
0
0
2
1
2
0
0
2
2
1
0
0
1
0
0
0
1
1
2
0
1
1
1
1
0
0
1
0
0
1
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
2
0
1
2
1
2
0
0
0
3
0
0
0
1
2
2
0
0
0
0
0
1
0
2
1
1
2
1
1
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
2
0
0
2
0
1
0
1
0
2
0
0
2
1
0
0
1
0
1
1
0
0
0
2
0
2
1
0
2
0
2
1
2
1
0
1
1
0
0
0
2
1
0
0
2
0
0
0
2
0
0
2
0
0
1
0
2
0
1
2
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
1
2
1
0
2
0
0
1
0
0
1
0
0
2
0
0
2
1
2
1
0
1
0
2
0
1
2
2
0
1
0
0
1
2
1
1
2
0
2
0
0
1
1
0
1
1
2
2
1
0
1
2
0
0
0
1
1
0
0
1
0
0
2
1
1
1
1
0
1
0
2
0
0
0
2
0
2
1
0
0
1
2
0
0
0
0
0
0
0
2
1
1
0
0
0
0
1
1
2
0
0
0
1
1
0
0
0
0
0
1
0
1
2
1
0
1
1
2
0
0
1
1
0
0
1
0
2
1
0
1
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
1
1
0
0
1
0
2
0
2
2
1
3
0
0
1
2
2
0
0
1
1
1
0
2
0
0
2
0
0
1
0
2
3
1
1
0
2
0
1
0
1
0
0
3
0
0
2
0
0
1
1
1
1
1
3
0
1
0
1
0
0
0
2
1
1
0
0
1
0
3
0
4
0
2
0
1
0
2
2
1
1
2
0
1
0
2
0
0
0
0
1
2
1
0
2
0
1
0
0
0
0
0
1
2
0
1
1
1
0
2
0
1
0
0
1
0
0
0
1
1
2
0
1
0
0
0
0
0
0
0
1
0
1
1
1
0
0
1
0
0
0
2
0
1
1
0
0
1
1
0
0
1
0
1
1
0
2
1
1
1
0
1
0
0
0
1
0
1
0
0
0
1
2
0
0
2
2
0
1
1
0
0
2
0
0
2
0
0
2
1
1
0
0
1
0
0
0
2
0
0
0
2
1
2
0
0
2
1
2
1
2
0
2
0
0
1
2
0
0
0
0
1
0
0
1
1
1
1
2
2
0
0
2
1
0
1
0
0
1
1
0
2
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
1
1
2
1
4
2
0
1
1
1
1
0
2
0
1
1
0
0
1
2
1
0
2
0
2
0
0
1
0
0
0
2
1
1
0
0
2
0
0
1
0
2
1
0
1
0
0
0
0
1
0
2
0
1
0
0
0
1
2
1
1
0
2
1
1
0
2
2
1
0
1
0
0
1
1
1
2
0
1
0
2
0
1
0
2
0
1
0
2
0
0
0
0
0
1
0
2
0
2
1
1
0
0
2
2
0
2
0
1
0
2
0
0
1
1
0
0
1
0
0
0
0
2
0
0
0
1
1
1
3
1
0
0
0
2
0
2
2
0
1
1
1
0
0
1
0
1
0
0
2
1
1
2
1
1
2
1
1
0
0
1
1
1
1
0
2
1
3
0
1
0
0
0
0
0
0
2
1
1
0
0
1
1
0
2
1
2
1
0
0
1
1
1
0
1
2
1
0
0
2
1
2
2
1
1
2
0
2
0
1
0
1
1
0
1
0
1
2
2
0
0
1
1
1
0
1
2
2
2
2
0
0
1
1
0
2
2
0
1
1
2
0
1
1
1
2
0
3
2
1
0
0
1
2
0
2
0
1
0
1
1
2
0
2
2
0
0
0
0
0
0
0
2
2
2
0
1
0
0
1
0
0
1
0
8
1
1
2
0
0
0
0
1
1
2
0
1
0
0
0
0
0
0
0
1
4
0
0
1
0
0
0
1
0
2
0
0
0
1
0
1
0
1
0
2
2
1
1
1
1
0
0
0
0
4
0
0
0
2
0
2
1
0
2
0
0
1
0
0
0
0
1
1
0
0
2
0
1
2
1
1
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
1
0
1
2
2
2
0
0
1
2
0
0
2
1
0
1
2
1
0
0
1
0
1
1
0
2
1
0
1
0
1
2
0
0
0
0
1
0
0
0
0
1
1
2
2
24
1
0
0
0
0
0
0
0
4
1
0
3
0
1
2
0
0
2
0
0
0
1
0
2
2
0
0
2
1
1
0
2
1
0
2
0
1
0
0
0
0
3
1
2
0
0
2
1
1
0
1
0
2
2
1
0
0
2
0
0
0
0
1
0
1
2
0
0
0
1
0
0
0
0
1
0
0
2
0
2
0
1
1
1
1
0
2
0
0
1
0
0
0
0
0
3
0
0
0
0
1
0
0
0
1
1
2
2
2
1
0
2
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
1
0
2
1
1
0
2
1
2
1
0
0
2
1
1
2
0
0
0
0
0
2
1
0
0
0
1
0
0
1
0
0
1
0
0
2
0
1
0
1
0
0
2
1
0
0
2
1
2
0
1
1
0
0
2
0
0
0
0
1
1
2
0
2
1
0
0
1
0
0
0
1
2
2
1
2
2
0
0
1
1
0
2
2
0
1
1
3
0
0
2
1
1
0
0
1
1
1
0
2
1
1
0
0
0
1
2
2
1
1
2
0
0
2
0
0
0
0
1
0
1
1
0
0
1
0
2
0
2
0
1
0
1
0
0
0
1
0
2
0
0
0
0
1
2
0
2
1
0
0
0
2
2
1
1
1
0
1
0
1
1
2
1
1
0
0
0
2
0
1
0
1
0
1
0
2
2
1
0
0
2
0
0
0
1
0
0
1
0
1
2
2
0
1
2
0
1
1
1
2
0
0
0
0
0
2
0
1
0
0
2
0
2
0
0
2
1
0
2
0
2
0
1
0
0
0
2
0
0
1
2
0
0
0
2
2
0
1
1
0
0
0
0
1
0
0
0
0
0
2
2
0
2
1
0
0
0
0
0
2
2
0
1
1
1
0
0
1
0
0
1
1
1
0
1
1
1
0
2
0
0
1
1
2
0
1
0
0
1
2
1
1
1
2
1
2
0
1
0
0
0
2
0
0
0
3
0
1
0
0
1
0
0
2
0
2
2
0
0
1
0
0
0
1
0
1
2
1
0
0
0
0
0
4
2
2
1
0
0
0
0
1
1
0
0
0
1
3
0
0
1
1
0
0
2
2
1
0
2
0
0
0
0
2
0
0
1
0
2
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
2
1
1
0
2
0
1
1
1
0
0
2
0
1
0
2
1
0
1
1
2
0
1
0
2
0
0
1
0
0
0
0
1
1
1
1
1
2
0
2
1
0
6
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
2
0
2
0
1
0
0
0
1
0
1
1
1
2
0
0
1
0
1
1
0
0
1
2
0
0
2
0
1
2
1
0
2
1
0
0
1
2
0
2
0
0
2
1
1
0
1
1
0
0
2
1
0
2
0
1
1
1
2
0
1
1
3
2
0
0
0
0
0
1
2
1
2
0
1
1
1
0
0
1
1
0
0
0
1
2
0
0
2
0
0
0
0
2
1
1
0
0
1
2
2
2
2
1
0
0
1
0
0
1
1
0
1
1
0
0
0
1
0
1
0
1
1
0
1
0
0
2
2
0
0
0
0
1
2
2
2
1
1
1
1
1
2
0
1
0
2
1
2
1
1
0
0
1
0
2
0
1
0
0
0
0
0
2
0
0
1
0
0
1
1
1
1
1
1
2
0
1
1
2
0
1
1
0
1
2
0
1
1
0
0
0
2
2
0
2
0
0
2
0
0
0
0
1
0
0
1
0
2
0
1
0
2
0
0
2
2
1
0
0
2
2
0
0
2
0
2
0
0
2
2
1
0
0
3
0
2
0
0
1
0
0
0
2
0
2
2
0
0
1
0
1
0
1
1
1
0
2
0
0
0
0
0
0
0
1
0
0
1
0
2
1
3
1
0
1
3
2
2
0
1
2
3
1
3
0
1
0
1
0
1
1
2
0
1
1
0
0
0
0
1
1
2
1
0
2
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
2
0
2
1
1
0
0
0
0
0
0
0
1
2
1
2
0
0
0
0
0
0
1
0
1
0
1
1
0
2
0
0
0
0
0
0
0
1
2
0
1
0
0
0
2
0
2
0
1
1
2
1
1
2
0
5
2
0
0
2
2
2
1
0
0
0
2
2
1
1
0
0
0
1
2
0
0
3
1
0
0
2
0
0
1
0
2
2
2
0
1
2
1
2
1
1
0
1
1
2
0
1
1
0
1
0
1
0
1
0
0
0
1
0
1
0
1
0
1
0
1
2
0
0
1
2
2
1
1
0
2
0
0
1
0
0
0
0
0
0
2
2
0
1
1
2
1
0
0
0
0
0
1
2
0
1
2
1
2
1
2
0
0
0
0
1
1
1
0
1
2
1
0
1
0
2
2
0
2
0
1
0
0
2
1
1
1
2
2
1
1
0
1
2
0
1
1
0
2
0
0
0
0
2
2
0
0
1
0
1
1
0
2
0
0
0
0
1
2
0
3
1
0
1
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
1
2
0
2
1
2
2
2
0
0
0
0
0
2
3
2
0
0
0
0
1
2
1
0
2
1
0
0
2
0
0
0
2
0
0
1
2
2
1
0
0
0
0
2
1
2
0
1
1
2
0
0
0
1
2
0
0
0
0
0
0
0
1
0
1
0
0
1
0
2
2
0
0
1
0
0
1
2
0
2
1
1
1
0
0
1
1
2
0
0
1
2
0
0
1
0
0
0
1
0
0
1
1
0
0
1
1
0
2
1
0
0
2
0
1
1
1
2
0
3
0
0
0
1
0
1
2
1
1
2
3
1
1
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
2
2
0
1
2
0
0
2
0
0
0
2
1
0
1
1
2
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
1
1
2
0
1
0
0
0
2
1
1
2
1
0
1
0
2
1
0
0
0
0
0
1
0
1
2
2
0
0
1
0
0
2
0
0
0
1
2
0
2
0
2
0
1
2
1
0
0
0
0
0
1
0
0
3
0
0
0
3
0
0
0
0
0
1
1
0
1
0
1
1
0
1
4
2
2
0
1
3
0
1
0
0
0
1
1
1
1
1
1
1
1
1
0
1
1
0
2
0
1
2
0
0
1
2
1
0
1
1
0
1
1
2
3
1
0
0
1
0
0
0
2
1
1
0
1
0
0
0
1
2
0
0
1
0
1
1
1
1
2
0
1
0
0
1
2
0
2
1
2
0
2
0
1
0
0
1
1
2
1
0
1
2
0
2
1
0
0
0
0
0
1
0
1
0
2
1
0
1
1
1
2
1
1
0
0
1
0
0
0
1
1
1
0
0
1
0
1
0
0
2
0
0
0
0
0
1
1
1
0
0
2
0
1
1
0
1
2
2
1
0
0
0
1
0
1
1
0
1
0
0
0
0
1
0
4
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
2
1
0
1
1
1
0
1
0
0
1
0
0
0
0
2
1
0
0
1
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
1
1
1
0
1
0
0
1
0
0
0
1
1
1
0
0
0
0
0
1
1
0
1
0
2
0
0
0
0
0
1
0
2
1
0
2
0
0
0
0
2
0
0
2
0
1
2
1
2
0
0
0
0
2
0
0
2
0
1
1
1
2
1
0
0
2
2
1
0
0
2
1
2
0
0
2
0
0
1
0
0
1
1
0
1
1
0
1
2
0
0
1
1
0
2
1
0
1
1
0
1
0
0
0
0
1
0
1
0
1
0
3
0
0
0
0
0
2
1
2
0
0
2
2
1
1
2
0
0
0
1
0
1
0
0
0
1
0
2
0
0
1
0
3
0
0
1
0
0
1
0
0
2
0
0
0
0
2
0
0
0
2
1
2
0
0
2
1
0
0
2
2
0
0
0
0
1
0
1
0
1
1
2
2
0
1
2
0
1
0
1
2
0
0
1
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
1
1
0
1
0
1
2
2
1
0
0
1
0
0
1
0
1
0
2
1
1
1
1
1
2
2
1
0
1
0
2
2
2
2
0
0
0
1
0
0
2
2
2
1
0
0
1
2
0
0
1
1
0
2
1
2
1
0
1
1
1
0
1
1
2
0
1
7
0
0
2
0
0
0
2
0
1
0
1
3
0
3
0
1
1
0
1
0
0
2
0
2
0
2
2
0
2
0
1
1
1
1
1
0
2
0
0
1
0
1
1
0
1
1
0
0
0
3
0
0
2
0
2
0
1
0
1
0
0
0
0
0
2
0
1
2
0
0
1
0
0
1
3
0
1
1
0
0
1
0
1
0
1
0
2
1
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
1
0
2
0
2
0
0
2
1
0
2
1
0
0
2
2
1
0
2
0
0
1
2
1
1
1
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
2
3
1
0
1
0
1
0
0
0
1
0
1
1
0
0
0
2
1
0
3
0
2
0
2
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
2
1
2
1
0
2
2
1
1
1
0
1
0
1
0
1
0
2
0
0
1
0
2
1
2
0
1
0
0
1
1
6
0
0
1
0
1
0
1
1
2
2
0
2
0
1
0
0
0
1
0
1
0
2
0
2
1
0
0
0
1
1
0
0
1
0
0
0
2
1
1
0
2
2
1
0
0
2
2
0
2
1
0
1
0
2
1
0
2
0
2
0
0
2
1
2
0
0
1
2
0
1
1
0
0
3
0
1
0
0
1
0
0
0
0
1
2
1
1
1
0
0
0
0
2
1
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
1
0
2
2
1
0
0
0
1
0
0
2
2
2
1
0
0
2
0
2
2
2
0
0
0
0
1
0
0
0
0
1
3
0
0
0
0
1
1
2
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
1
2
0
0
2
0
0
2
2
1
1
0
2
0
1
1
1
0
2
1
2
0
0
1
0
0
0
0
0
1
0
1
0
2
1
2
0
0
0
0
1
0
2
0
0
1
0
2
0
1
0
2
1
0
0
0
0
2
0
1
0
0
2
2
2
0
1
1
1
2
0
3
2
0
0
2
0
1
1
1
1
0
2
2
0
0
3
1
1
1
0
1
0
1
0
0
0
2
2
0
6
0
0
2
0
0
1
0
0
0
2
1
1
0
1
0
0
1
1
0
2
1
2
0
0
1
0
0
1
1
4
1
0
0
1
0
0
1
2
0
2
0
2
1
1
1
1
2
2
0
2
0
1
0
0
2
0
0
1
0
0
0
1
1
0
1
1
1
1
2
0
0
1
1
0
2
0
0
2
0
1
0
0
1
2
0
1
1
0
0
0
0
0
0
2
2
0
0
1
0
1
0
0
0
0
0
0
2
0
2
1
1
0
1
0
0
2
0
1
0
0
2
2
2
0
1
0
1
0
1
0
0
2
2
1
2
0
1
0
0
0
2
1
0
0
0
0
0
2
2
2
0
0
1
2
2
0
0
0
0
0
2
0
0
0
1
2
0
1
0
1
0
0
2
0
1
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
1
1
1
2
1
0
2
0
1
1
0
2
0
1
1
0
2
1
0
0
1
0
0
0
1
0
1
1
1
1
2
0
2
2
1
0
0
1
0
0
1
1
0
0
1
0
1
1
1
0
0
1
0
1
2
0
0
0
0
0
0
0
0
1
1
0
1
1
0
1
0
2
1
2
1
1
1
1
0
1
2
2
0
0
0
0
1
1
0
0
1
0
1
0
0
1
2
1
2
1
0
1
1
0
0
1
2
0
0
1
2
1
2
1
0
0
1
1
1
0
0
1
0
1
0
1
1
1
0
2
1
1
3
0
1
2
0
1
0
0
1
0
2
0
1
0
1
1
1
0
1
0
2
1
1
1
1
0
1
1
0
1
0
1
0
1
1
1
0
2
1
0
0
0
2
1
0
0
2
1
2
0
0
0
0
0
0
0
0
1
1
1
0
2
0
2
1
0
0
1
1
1
0
2
1
0
1
0
0
0
0
1
0
0
2
0
2
0
0
0
0
1
0
1
0
0
0
1
1
1
0
0
1
0
2
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
2
1
1
1
0
0
0
1
0
2
1
1
0
0
0
0
0
1
0
0
2
1
1
0
1
1
0
1
2
1
1
1
0
0
2
0
0
2
1
2
1
1
0
0
2
2
0
2
0
0
0
0
1
0
0
2
1
1
2
2
0
2
0
0
2
2
2
1
0
0
0
2
0
1
0
1
0
2
2
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
1
1
1
0
1
0
2
1
0
1
0
0
0
0
1
0
0
1
1
2
1
0
0
1
0
1
1
1
0
0
2
0
0
1
0
0
1
0
0
1
1
2
0
2
0
1
2
0
2
0
1
1
1
1
3
1
0
0
0
0
1
0
0
0
0
1
1
2
1
0
0
0
1
1
2
0
0
2
0
0
1
4
0
0
1
0
2
1
1
0
0
0
2
1
1
0
0
2
1
1
1
1
0
1
0
1
4
1
1
1
2
2
1
2
2
2
0
0
0
0
0
0
1
0
0
0
0
0
1
1
2
0
0
2
1
0
1
0
1
0
1
1
0
1
1
0
0
1
2
0
1
2
1
0
2
0
2
1
0
0
0
2
0
2
0
0
0
1
0
0
0
3
0
0
2
1
1
0
0
0
1
0
2
2
1
2
0
0
1
1
1
1
0
0
0
0
1
1
0
1
2
1
2
1
0
0
0
0
1
1
0
0
1
2
0
1
1
1
2
0
0
1
1
0
0
1
2
1
0
0
0
1
2
2
0
1
1
1
0
0
0
0
0
1
1
0
0
3
1
0
2
2
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
1
2
0
1
1
0
0
0
0
2
2
0
1
2
0
0
3
0
1
1
0
0
1
1
1
0
1
0
1
2
0
1
1
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
1
0
0
2
1
0
0
2
1
1
2
0
0
2
2
0
0
2
2
1
0
0
0
1
2
1
2
2
1
2
1
0
3
0
0
0
1
0
1
2
0
1
0
1
0
0
0
0
1
0
0
3
0
0
2
1
0
0
1
2
2
0
2
0
0
0
1
1
0
0
1
2
1
2
1
2
2
1
0
3
2
0
0
0
1
0
2
0
2
0
0
0
0
1
0
0
2
1
0
1
0
0
0
2
1
1
2
2
0
2
0
0
0
0
0
0
0
1
0
2
1
0
0
2
1
0
2
0
0
1
0
0
0
2
0
2
1
2
2
1
1
1
0
2
1
2
1
1
1
2
0
0
0
0
1
2
2
0
0
1
0
1
1
0
0
2
2
1
1
2
2
0
0
0
1
0
1
2
2
2
2
1
1
2
1
1
1
1
1
0
0
1
0
2
0
1
1
0
1
0
0
1
0
2
0
0
0
0
0
0
0
1
1
1
0
0
0
0
2
2
1
2
0
1
0
0
0
1
0
0
2
2
0
0
2
0
1
0
2
1
1
0
0
1
0
1
2
0
2
1
2
1
0
0
0
2
2
0
0
0
1
0
1
2
0
1
2
2
0
0
0
0
3
0
2
0
0
0
0
0
1
2
1
1
0
1
1
0
0
0
0
1
0
1
0
1
1
0
1
0
1
1
2
0
2
2
1
0
0
0
0
5
0
2
0
1
0
1
0
0
0
1
0
1
1
2
1
1
1
0
0
1
2
2
0
1
0
1
1
0
0
2
1
0
2
3
2
2
1
0
2
1
0
2
0
1
1
1
0
0
0
1
2
1
2
0
2
1
0
0
0
1
0
1
2
0
0
1
2
0
0
0
3
1
0
0
0
1
2
0
0
1
2
1
1
2
2
0
2
1
0
1
0
1
0
2
0
1
1
1
2
0
1
0
1
0
0
1
0
1
1
0
0
1
2
0
1
0
2
0
0
0
1
2
0
0
1
0
0
1
1
0
2
0
2
0
0
2
0
0
1
2
0
0
3
1
1
1
1
3
1
2
2
1
0
0
0
0
0
2
1
1
0
1
1
0
0
1
1
1
0
0
2
0
0
2
0
0
1
2
0
0
0
1
1
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
1
0
1
2
0
0
2
2
1
0
1
0
1
3
0
2
0
3
1
0
0
2
1
1
0
2
0
0
0
0
1
1
0
0
2
0
2
0
0
1
2
0
0
2
1
2
0
0
0
1
0
0
0
0
2
0
1
0
0
1
0
2
0
2
0
0
3
2
1
0
0
0
1
0
1
0
2
1
2
1
0
0
0
0
0
1
0
5
1
2
0
0
2
2
1
0
0
0
2
1
1
2
1
0
0
0
0
2
2
0
1
2
4
1
0
2
1
2
0
0
0
1
2
1
0
0
2
0
0
2
2
0
0
1
2
2
1
1
1
2
0
1
0
0
0
0
0
0
0
0
2
2
1
1
0
1
2
2
3
0
1
2
2
0
1
2
2
0
1
2
0
0
1
1
0
0
0
0
1
0
1
1
0
0
2
0
1
0
2
2
1
1
1
2
1
2
1
1
0
0
3
0
1
0
0
1
0
1
0
0
0
2
0
0
0
1
0
0
0
1
0
2
2
0
3
1
1
0
0
0
0
0
2
0
3
0
0
0
2
2
2
0
1
1
1
2
1
0
2
1
2
2
1
0
0
0
1
2
1
1
2
0
2
0
0
0
0
0
1
0
0
0
1
0
0
2
0
2
0
0
0
0
1
1
2
0
1
2
2
0
1
1
1
0
0
0
0
0
0
2
1
0
0
1
0
1
1
1
0
2
0
0
2
0
1
1
0
1
1
0
1
2
1
0
0
0
0
2
0
0
1
0
2
0
2
0
1
2
0
0
0
0
2
2
0
2
1
0
1
2
0
2
2
0
0
0
0
0
2
2
0
1
1
2
0
0
2
0
2
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
1
0
1
1
0
1
0
0
1
0
0
0
2
1
0
0
1
1
1
0
0
2
1
0
0
0
0
0
1
0
1
0
1
2
1
0
0
0
0
0
0
2
0
1
2
0
1
2
1
0
1
2
2
0
0
2
1
1
0
0
1
4
1
3
1
1
0
0
0
0
1
0
1
2
0
1
0
0
1
0
0
0
0
2
0
0
1
3
0
0
0
0
1
0
0
0
0
0
1
0
3
2
2
1
2
1
0
0
2
0
1
0
0
0
0
0
1
2
0
0
0
0
2
1
1
1
1
0
2
0
0
0
0
2
1
0
0
0
0
0
3
1
0
0
0
1
1
1
0
2
0
1
2
2
2
1
2
0
0
0
0
1
2
0
1
1
1
0
2
2
2
1
0
1
1
2
0
2
0
3
1
0
0
1
1
0
2
1
1
1
2
0
2
1
0
1
1
0
0
4
1
2
2
0
0
0
1
0
0
0
2
2
1
1
2
0
0
1
0
0
0
1
1
0
1
0
1
0
0
0
0
1
2
1
0
0
2
0
0
0
1
2
0
1
2
2
2
2
0
1
0
0
0
0
2
0
0
0
0
2
2
1
1
0
1
1
2
0
0
0
1
0
1
0
1
1
0
1
1
1
2
2
1
2
1
2
0
2
1
1
2
2
0
0
0
0
1
0
0
0
2
0
0
1
2
0
2
0
2
1
0
1
1
3
0
0
1
2
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
6
0
2
1
0
1
1
2
0
0
0
0
0
1
1
1
0
1
0
0
0
1
2
1
2
2
0
0
2
0
1
2
1
0
0
2
1
2
1
2
1
1
0
1
0
0
0
2
2
2
0
2
0
1
1
1
2
0
1
2
1
0
0
2
1
0
1
2
0
0
0
1
0
1
2
2
2
2
0
0
0
2
2
1
2
1
0
1
0
1
1
0
0
0
0
1
0
0
1
0
0
1
0
3
3
0
1
1
0
0
0
0
0
1
2
3
0
0
0
1
1
0
0
1
0
1
2
1
1
2
2
2
0
0
2
1
1
0
2
2
0
0
0
1
0
0
0
1
2
5
0
0
2
1
2
1
3
1
0
0
1
1
1
1
2
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
2
1
1
2
0
1
0
0
0
0
0
0
2
0
1
1
0
1
0
0
0
0
0
0
0
0
1
1
0
1
2
0
1
1
0
2
0
0
0
0
2
2
1
1
1
2
1
1
0
0
1
0
1
1
0
0
1
0
2
0
0
0
1
0
0
2
1
0
0
0
2
1
0
1
0
2
0
0
0
1
0
0
2
1
0
0
1
1
0
0
1
0
0
1
0
2
0
0
1
1
0
0
2
2
6
0
2
0
2
0
1
1
0
0
1
0
2
1
1
0
0
0
2
2
1
0
1
1
1
1
1
0
1
2
0
2
0
2
0
1
1
2
0
0
1
1
1
2
2
0
2
2
0
0
0
1
0
0
0
1
0
0
0
1
0
2
2
1
2
2
1
0
2
1
2
0
1
0
0
1
1
0
0
0
2
0
1
0
1
2
2
0
1
0
0
1
2
1
1
2
0
0
2
2
0
0
1
1
0
0
1
0
0
0
0
0
2
2
0
2
0
1
2
2
1
1
0
1
2
2
0
2
0
1
1
1
0
2
1
1
1
0
0
2
0
0
1
0
1
1
1
2
0
0
0
0
0
0
0
2
3
0
0
2
2
2
1
1
2
0
0
0
2
0
0
0
0
1
1
0
1
0
0
2
3
1
1
1
0
0
1
3
2
0
0
1
1
1
1
0
1
2
0
0
0
0
2
1
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
1
2
0
1
0
2
0
1
0
2
0
1
1
0
4
0
1
1
0
0
0
2
2
1
0
0
1
1
0
0
8
0
0
0
0
1
0
0
1
0
2
1
0
0
1
0
0
1
0
9
0
2
1
0
0
0
0
0
1
1
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
2
1
0
0
0
2
1
0
1
2
0
2
1
0
0
0
2
1
1
0
0
1
0
1
1
1
0
0
1
1
0
0
0
0
0
1
2
0
1
1
1
1
1
1
0
2
1
0
3
0
0
1
1
1
0
0
0
0
0
0
2
1
0
2
0
2
0
1
0
1
0
2
2
0
2
0
0
0
1
1
0
1
2
1
1
1
0
1
1
1
0
1
1
1
0
2
0
0
2
0
1
1
1
0
1
1
0
2
0
0
0
0
1
0
0
0
1
0
1
0
0
1
1
0
1
1
0
1
0
0
0
1
1
1
0
0
0
0
1
0
2
0
2
0
1
0
0
1
1
2
2
1
0
1
0
1
0
0
0
0
0
0
0
0
2
0
1
1
0
0
1
0
0
0
0
0
2
1
0
0
2
1
0
0
0
2
0
0
2
0
0
1
2
0
2
2
0
0
0
1
0
1
0
1
0
0
0
1
0
1
1
0
2
2
1
1
1
0
0
0
0
0
1
1
0
1
1
0
2
2
1
1
0
0
0
0
2
2
1
1
1
1
0
0
1
0
0
2
4
2
1
2
0
0
0
1
1
0
1
0
1
1
0
1
1
3
2
2
1
3
0
2
0
0
2
0
2
0
0
0
1
2
0
0
2
0
0
0
0
0
1
0
2
0
1
1
0
0
0
1
1
0
1
1
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
1
0
1
0
2
2
0
2
2
3
2
0
1
0
0
2
1
0
1
1
0
0
0
0
0
1
0
3
1
0
1
1
0
1
0
0
0
2
0
0
0
2
1
0
0
4
2
1
1
1
2
1
3
1
1
0
0
0
0
1
2
2
2
2
0
0
0
3
0
0
0
0
0
2
0
0
0
2
1
0
2
1
1
0
1
0
0
0
1
0
0
0
0
0
1
0
2
1
0
0
1
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
1
1
0
1
1
0
2
0
1
0
0
1
0
1
2
2
1
0
0
0
0
0
1
1
2
2
0
1
0
0
1
0
0
0
0
2
1
2
2
0
2
1
0
1
0
1
1
1
2
0
1
1
1
0
0
2
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
2
2
0
1
0
0
0
1
0
0
0
0
0
1
1
0
2
1
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
2
1
1
2
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
1
1
0
2
0
1
0
1
1
2
1
2
0
0
0
0
1
0
1
2
1
1
0
0
0
0
2
0
0
3
0
0
1
0
1
1
1
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
2
2
0
1
1
2
0
2
1
0
0
1
2
0
0
0
0
0
1
2
0
0
0
2
1
2
1
0
0
2
0
0
1
1
1
1
1
1
0
0
0
0
0
0
2
0
1
2
2
0
0
1
1
1
1
0
2
0
1
0
0
2
2
0
2
1
1
1
2
0
0
1
1
1
0
1
0
0
0
1
1
0
2
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
1
2
0
3
1
0
2
1
2
1
0
0
0
1
2
0
0
2
3
0
2
0
0
1
1
0
2
1
0
2
0
1
1
0
0
1
1
1
0
0
1
0
2
0
1
0
0
0
0
0
0
1
2
0
0
1
1
2
1
0
2
0
2
0
1
0
1
1
2
1
0
1
0
2
0
2
0
0
0
0
1
1
1
0
0
0
2
0
2
2
0
0
2
1
1
0
0
1
1
2
1
0
0
1
1
0
0
1
1
0
1
2
0
0
0
0
2
0
0
1
1
0
0
1
0
0
1
0
0
2
1
2
2
0
1
0
1
0
0
0
0
0
1
0
1
1
0
1
1
1
0
2
1
0
2
2
1
2
1
1
1
1
1
0
0
0
0
2
2
2
2
1
2
0
2
1
0
2
0
0
2
1
4
0
1
0
0
0
2
0
0
1
0
0
1
2
0
2
1
1
0
0
0
2
0
0
0
0
1
1
2
1
1
0
1
0
2
0
1
2
0
0
1
0
1
1
0
0
2
1
2
0
2
0
1
1
1
0
2
0
0
0
0
0
2
2
0
2
1
0
2
1
2
1
1
2
2
1
0
1
0
2
2
1
4
0
2
0
2
2
0
2
0
0
0
0
0
1
1
1
1
1
1
1
1
0
3
0
3
0
0
2
2
1
0
1
0
1
1
0
0
0
0
2
0
0
0
1
0
0
2
1
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
2
0
3
0
0
1
0
0
0
2
0
0
2
0
0
1
1
1
1
2
2
0
0
1
0
1
0
0
1
0
0
2
0
0
0
2
1
2
1
2
0
0
2
1
0
2
2
0
0
0
0
1
2
2
0
1
0
3
1
2
1
0
2
0
0
2
1
0
1
1
2
0
0
0
2
1
0
2
1
0
3
0
0
1
0
0
0
1
2
1
1
0
0
0
2
1
1
1
0
0
0
1
0
0
0
1
1
1
1
1
0
0
0
1
2
1
1
0
2
0
3
0
2
1
1
1
2
0
0
1
0
0
0
2
1
2
0
1
0
1
1
0
0
0
0
1
1
0
0
1
0
1
0
1
0
0
2
0
1
0
1
0
1
3
0
0
0
2
1
2
2
0
0
2
0
2
0
1
1
2
2
1
0
2
0
0
2
2
0
0
0
2
0
1
2
0
0
0
1
1
0
0
1
0
0
2
0
1
0
1
0
1
0
1
2
0
0
0
1
0
0
1
1
1
1
0
3
0
2
0
2
2
1
1
0
0
0
0
2
0
0
3
0
0
2
0
0
0
2
2
1
2
1
1
0
0
1
1
1
0
2
0
0
2
2
3
1
2
0
0
2
1
1
1
2
0
4
1
2
0
0
0
2
0
0
1
0
0
1
0
1
0
2
0
0
2
1
0
1
0
0
1
1
2
1
2
2
2
0
1
0
1
1
0
1
0
0
0
0
2
2
1
0
0
0
0
0
1
1
0
1
0
0
0
1
2
0
0
2
0
0
2
1
1
2
0
1
1
0
0
1
0
1
0
1
3
2
0
1
0
1
3
1
2
0
0
0
0
0
1
0
1
1
2
1
0
0
0
2
1
2
2
1
0
2
0
0
0
0
1
0
0
0
1
1
1
1
0
2
2
0
2
0
0
0
1
1
3
0
2
1
1
0
1
1
0
0
0
1
0
0
0
2
2
3
0
0
1
0
1
0
0
1
1
1
1
1
0
0
0
0
0
2
2
2
1
0
1
0
0
0
0
0
2
2
1
1
2
1
1
0
1
1
2
0
2
1
0
1
0
0
1
2
1
1
0
1
0
2
0
1
2
1
0
0
2
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
2
0
0
2
1
2
2
1
0
1
1
2
0
0
2
0
0
2
0
0
0
0
1
0
2
0
2
2
0
3
0
1
1
1
2
0
0
0
1
1
1
1
1
1
0
0
1
0
2
2
1
2
2
1
0
1
1
1
0
0
1
1
1
1
0
2
0
1
3
0
1
3
0
2
0
0
1
1
1
1
0
1
0
1
2
0
1
0
0
2
1
0
1
0
1
1
1
0
2
1
0
0
2
2
2
2
0
0
0
0
1
2
1
0
0
0
0
2
0
2
0
1
0
1
3
1
0
1
0
0
2
1
0
0
2
1
0
1
0
1
0
1
2
0
1
0
0
0
0
1
0
1
0
1
0
0
2
0
1
3
0
0
2
1
0
2
0
1
0
1
1
0
1
2
0
0
3
1
1
0
0
0
2
0
0
1
1
2
1
1
0
2
0
0
1
1
0
0
0
0
0
0
2
1
0
1
0
0
2
0
0
0
2
1
0
1
1
0
2
1
0
0
1
2
1
1
1
0
2
0
0
0
1
2
1
0
0
3
1
0
0
1
1
0
0
2
2
0
0
1
1
1
0
0
1
1
1
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
1
2
0
1
5
0
0
2
2
1
0
0
0
0
1
0
2
0
3
0
0
1
2
0
1
0
0
0
0
0
1
0
1
0
0
1
0
1
1
3
2
1
0
0
0
0
1
1
0
1
0
2
0
0
3
3
0
2
2
0
0
1
2
0
2
1
0
2
0
1
0
2
2
1
4
0
1
1
1
1
1
0
0
0
0
1
0
0
2
1
0
0
1
2
1
0
1
1
0
0
1
2
0
0
2
2
0
0
0
0
1
2
2
1
1
0
1
1
1
0
2
0
2
2
0
0
1
1
1
1
0
1
0
0
0
2
0
0
0
0
0
2
2
2
1
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
2
0
0
0
1
0
0
2
0
2
1
2
0
0
2
1
0
0
3
1
1
0
2
2
2
0
1
3
1
0
2
1
2
2
2
2
0
1
0
0
1
0
0
0
1
0
0
1
0
1
2
0
2
2
1
1
0
0
0
4
1
0
2
1
2
0
0
2
2
0
0
2
0
0
2
0
2
1
2
0
2
2
1
0
0
0
1
0
2
0
2
2
0
2
0
3
2
0
0
1
0
0
0
1
2
0
1
0
1
0
0
0
1
1
2
1
1
2
0
0
2
1
0
0
0
0
1
2
1
2
1
2
0
1
0
0
2
0
0
0
0
0
1
0
0
2
2
0
1
0
1
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
2
2
0
1
0
0
2
0
1
2
0
1
0
0
0
1
6
2
1
0
0
0
0
1
0
0
2
1
0
2
1
0
0
0
0
0
1
2
1
0
2
1
1
0
2
1
0
1
0
2
0
2
1
0
0
0
1
2
0
0
0
0
0
0
1
1
1
2
0
1
2
1
1
0
0
1
1
1
0
1
2
2
0
1
1
2
0
2
0
0
2
0
1
1
1
2
0
2
0
0
2
2
0
1
2
0
2
0
0
0
2
2
1
1
2
1
2
0
1
0
1
3
0
0
2
2
0
2
0
0
1
0
1
0
0
1
1
0
0
2
0
0
0
0
2
1
0
1
1
1
1
1
0
0
2
2
2
1
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
1
0
2
0
1
1
0
1
3
0
0
1
3
0
0
0
0
0
0
1
0
0
0
2
2
0
2
2
0
0
0
1
0
1
1
2
0
2
0
0
1
1
2
1
2
1
1
0
1
0
1
0
0
0
2
1
0
0
1
1
1
1
2
1
0
0
0
0
0
1
2
1
1
2
0
0
1
0
0
0
0
1
2
0
0
1
2
0
1
1
1
0
1
1
0
0
0
0
1
0
1
0
1
2
0
1
2
0
0
0
2
0
1
1
2
1
0
1
0
2
3
0
0
0
2
0
2
1
0
0
0
1
0
2
1
1
0
1
1
2
1
1
0
0
0
0
0
2
2
2
0
0
1
1
0
3
0
1
0
1
0
1
1
1
0
1
2
0
0
1
2
0
0
0
1
0
1
0
1
1
1
0
1
0
0
1
0
0
0
1
0
0
1
0
1
2
0
0
1
0
0
0
0
2
0
0
0
2
0
1
2
0
1
2
0
0
1
2
0
1
1
0
0
0
2
0
0
0
2
0
2
1
0
1
2
1
0
0
2
0
2
0
1
0
0
0
0
2
0
1
1
0
0
1
0
0
1
1
0
1
1
0
1
2
2
0
0
2
0
2
1
0
0
2
2
0
0
0
2
0
0
2
0
0
4
2
0
1
0
1
1
0
1
0
0
0
0
0
1
2
0
1
2
1
1
0
0
2
0
1
3
0
1
0
1
0
2
2
1
1
1
1
0
2
0
0
2
2
0
0
1
0
4
1
2
0
2
1
2
1
0
1
0
0
1
0
2
0
1
0
2
2
0
1
0
1
2
0
1
0
0
1
0
1
1
0
1
2
1
2
2
0
2
0
1
1
0
0
1
1
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
2
2
2
0
0
1
0
2
0
0
1
0
1
0
0
0
0
2
2
2
0
0
0
0
0
1
3
2
1
1
2
2
3
0
0
0
1
0
2
2
1
0
2
0
0
0
0
0
1
1
1
1
0
1
2
0
0
1
1
1
0
0
1
0
2
1
2
0
1
1
1
0
0
2
0
0
0
0
1
0
0
2
1
0
1
1
0
3
0
2
2
2
1
1
0
0
1
0
1
0
2
0
0
2
1
0
0
1
2
1
1
3
1
0
2
0
1
0
2
1
2
0
0
1
1
0
0
0
2
0
0
1
1
0
0
0
4
1
2
0
1
0
0
0
0
0
1
1
1
3
2
0
1
0
2
0
0
0
0
1
0
0
0
2
1
0
0
1
1
2
1
1
0
1
0
2
1
3
1
0
1
1
2
2
0
2
1
0
0
0
0
1
0
0
0
2
0
0
2
0
1
0
0
1
2
1
0
0
1
2
0
1
0
0
0
0
0
1
2
0
0
1
1
1
0
0
1
1
0
1
0
0
1
0
2
0
0
0
1
0
0
2
2
1
1
0
1
2
2
1
0
1
2
0
0
1
2
0
1
2
1
0
2
0
0
0
4
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
2
0
0
2
0
2
0
0
0
0
2
1
0
0
1
0
1
1
0
1
0
1
0
1
0
0
0
1
0
1
1
0
2
0
1
1
1
0
4
2
0
1
1
0
0
1
0
2
1
1
0
1
0
2
1
0
1
2
0
2
0
0
1
0
2
1
1
1
2
0
1
0
0
1
2
2
2
2
1
1
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
1
0
1
1
2
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
1
1
2
0
1
0
0
1
0
1
1
2
0
0
0
2
1
1
2
1
0
0
1
1
2
0
1
0
1
2
1
2
2
0
0
0
0
2
0
2
1
2
0
1
2
0
1
1
2
0
0
0
1
0
1
0
0
2
2
2
0
0
2
0
2
1
2
1
0
2
0
0
2
1
0
2
0
0
0
0
0
0
0
1
1
0
2
3
0
0
0
0
1
0
0
1
0
0
1
0
1
1
2
0
0
2
2
0
3
0
0
0
2
1
1
1
1
0
2
1
0
0
0
2
0
0
0
2
1
0
2
0
0
0
0
1
0
0
0
0
1
0
1
0
6
0
1
0
0
1
0
1
1
1
0
0
0
0
0
0
1
0
0
0
2
2
1
1
0
0
0
0
1
0
0
2
0
0
1
0
1
1
2
1
3
0
0
1
0
1
0
2
1
0
0
1
1
0
0
2
0
1
0
1
1
0
0
2
2
0
1
0
0
0
0
0
1
2
1
0
0
2
1
0
1
1
1
0
1
1
0
0
1
0
1
1
2
0
1
2
2
0
0
0
0
0
6
1
0
0
0
2
0
2
1
0
0
0
2
1
0
0
1
1
2
0
1
0
0
0
0
2
1
0
1
0
1
0
1
0
0
0
1
2
0
1
1
1
0
1
0
0
1
1
2
2
1
0
0
0
0
0
0
1
2
1
1
0
2
0
0
1
0
0
2
1
2
1
0
2
0
2
2
1
0
0
1
1
1
1
1
1
0
0
0
1
0
0
0
0
1
0
1
1
1
0
0
1
0
0
1
1
2
0
0
1
2
0
0
1
2
2
0
0
0
2
0
1
0
0
0
0
2
1
1
0
1
0
0
0
1
0
1
1
0
1
0
2
0
0
1
0
0
0
0
2
1
2
2
2
0
1
0
0
1
0
1
1
0
0
0
2
0
0
0
0
0
0
0
1
2
0
1
2
2
0
0
0
0
1
1
0
0
1
2
0
1
1
0
0
1
0
1
0
0
2
0
2
1
0
1
2
1
0
0
0
0
0
1
0
1
1
1
1
2
0
1
0
0
0
0
0
2
0
0
2
0
0
1
0
2
0
1
2
2
1
0
0
1
1
0
0
0
1
2
0
2
0
1
1
1
2
1
0
1
1
1
0
1
1
1
0
0
0
0
0
1
0
0
2
0
1
0
2
0
0
0
1
2
2
1
1
0
1
1
1
1
1
0
0
0
2
1
0
0
1
0
2
0
1
1
0
1
0
1
1
2
1
0
0
1
0
0
0
1
0
2
0
0
0
2
1
1
0
2
1
1
0
0
1
1
0
2
2
1
1
1
1
0
2
1
1
2
0
0
0
1
0
1
1
0
1
1
0
0
0
1
0
1
0
1
0
0
2
1
2
2
0
0
0
1
0
0
1
0
0
0
1
2
1
1
0
2
0
1
2
2
1
0
0
0
0
0
0
0
1
1
1
1
0
0
1
1
0
0
0
1
0
2
3
1
0
0
2
1
1
1
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
2
2
0
3
0
2
0
0
0
0
1
0
0
0
0
1
4
1
1
1
1
1
2
1
1
3
0
1
1
1
2
0
1
0
0
0
0
2
1
0
1
1
1
0
1
2
1
0
1
1
1
0
2
0
0
2
1
1
2
2
1
1
1
0
0
0
1
2
0
0
0
1
0
2
2
1
0
1
0
0
0
0
1
1
0
1
1
2
0
0
0
2
1
0
0
0
1
0
2
1
1
0
2
0
1
0
1
0
1
0
2
0
0
2
1
0
0
0
0
2
0
1
0
0
1
1
1
2
0
2
0
2
1
0
1
0
0
0
1
0
2
0
2
2
0
0
0
0
0
1
0
2
2
1
0
1
2
3
0
0
1
0
0
1
2
0
2
1
0
0
1
0
2
2
0
1
0
1
3
0
0
0
1
0
0
0
0
2
1
0
0
1
2
1
0
0
1
0
1
1
2
0
1
1
1
1
2
1
1
0
0
2
0
0
1
0
0
0
0
2
0
1
2
2
0
0
1
0
2
0
1
0
3
0
0
1
2
0
2
0
0
2
0
1
0
0
0
2
1
2
0
0
0
2
0
0
2
1
0
2
1
1
1
0
1
0
0
2
0
0
0
0
1
2
0
1
0
0
1
0
1
2
0
1
1
2
0
0
0
0
0
2
1
0
0
1
2
0
2
0
1
0
1
0
0
0
0
1
1
0
0
0
2
2
0
2
1
0
0
0
2
0
0
4
1
0
0
0
0
1
0
1
0
0
6
0
1
2
0
0
2
1
0
2
0
3
2
0
0
2
0
0
0
0
0
0
2
1
0
2
0
1
1
0
0
1
0
2
0
2
0
0
1
1
2
1
2
0
0
2
1
0
3
2
1
0
2
1
1
1
0
2
1
0
0
0
1
0
1
1
1
1
0
3
0
1
0
1
1
2
0
3
1
0
1
0
2
0
0
0
0
1
3
1
1
2
0
2
0
0
1
0
1
2
1
1
0
0
1
1
0
2
0
0
0
1
1
1
0
0
3
1
2
0
0
0
2
1
0
2
0
0
1
1
2
0
0
2
0
1
1
1
0
2
0
1
0
0
1
0
0
0
0
1
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
3
3
1
2
1
1
0
1
1
0
2
2
1
0
1
1
1
0
0
1
0
5
0
1
1
1
0
0
2
0
2
1
0
0
0
0
0
1
3
0
0
0
1
0
2
0
1
2
0
1
0
1
1
2
0
2
2
2
0
2
2
0
0
2
1
0
1
2
0
0
2
1
1
1
0
0
0
0
2
1
0
2
0
1
1
1
0
0
1
2
0
1
0
0
1
1
0
2
0
0
0
1
0
1
1
0
1
0
0
2
0
0
1
2
0
1
2
0
2
0
1
0
0
1
1
1
0
0
2
1
2
0
0
0
1
0
0
2
1
0
2
1
1
1
2
0
1
2
0
1
0
0
0
1
0
0
0
0
1
0
0
0
2
0
1
0
2
0
0
1
2
1
0
0
1
1
2
1
1
0
2
2
0
1
2
0
1
0
0
0
0
2
0
2
2
0
2
1
0
0
4
0
0
1
2
2
2
2
1
1
1
2
0
2
1
1
2
0
1
0
0
2
0
2
0
2
1
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
1
0
0
2
2
1
1
2
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
2
1
1
1
0
0
0
0
2
1
0
2
1
0
0
1
0
1
2
1
1
0
0
1
2
0
0
2
1
0
0
2
0
1
0
1
2
1
0
2
1
1
0
0
2
0
2
0
0
0
0
0
0
0
1
0
2
8
0
1
1
2
0
1
1
2
1
3
1
1
1
0
2
0
0
0
1
2
1
0
2
1
0
1
2
0
2
1
2
0
1
1
0
0
1
1
2
1
2
0
2
0
2
1
1
1
0
0
1
0
1
0
1
1
0
0
2
0
0
1
1
0
0
1
1
2
1
0
2
0
0
2
2
2
0
0
1
0
0
2
2
2
0
1
0
1
0
0
0
0
2
0
1
1
2
0
0
0
0
2
1
1
0
0
1
2
1
2
0
1
1
0
0
1
0
0
0
1
2
2
0
1
0
1
0
1
0
0
0
1
2
1
1
1
0
0
0
1
0
2
0
0
0
2
0
1
1
2
0
1
2
0
0
1
0
1
0
2
0
1
0
1
0
1
2
0
1
2
0
2
0
2
0
1
0
0
0
0
1
1
2
1
0
1
0
1
0
0
2
0
0
2
0
2
2
2
0
0
1
2
2
0
1
0
0
1
1
0
1
1
1
0
2
0
1
1
0
0
0
1
1
2
0
1
0
0
1
1
0
0
0
0
0
2
1
2
0
2
2
0
0
0
2
0
0
0
1
2
2
1
2
2
0
2
0
2
0
2
0
0
0
0
1
0
1
0
0
1
0
0
0
1
1
2
0
1
0
2
0
2
0
0
1
0
0
1
0
1
0
2
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
2
2
1
2
0
0
1
1
2
2
0
0
1
2
0
0
0
2
0
2
0
1
1
2
1
2
0
2
0
0
0
2
0
0
2
2
1
0
0
0
1
2
0
2
1
1
1
0
2
2
0
0
0
0
0
2
0
0
1
1
1
1
0
0
0
2
1
2
1
0
0
2
1
1
1
0
0
1
0
1
0
3
0
2
0
3
0
1
2
0
2
1
2
0
2
0
1
3
2
3
0
1
1
0
2
2
4
0
1
0
2
1
1
0
0
0
4
1
1
2
0
2
0
1
0
1
0
2
1
0
1
0
0
1
2
0
2
2
0
0
0
0
0
1
0
1
1
1
0
1
1
1
0
0
1
1
0
0
1
0
2
1
0
0
1
0
0
0
2
0
0
2
1
0
1
0
2
0
2
1
1
0
1
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
2
0
1
2
1
1
1
0
0
0
0
0
1
0
0
2
1
0
2
0
0
0
1
1
0
1
0
0
0
2
0
2
0
0
0
1
0
0
1
0
2
0
1
2
0
0
0
0
2
3
1
2
0
0
0
2
0
0
1
2
2
3
0
2
0
0
0
0
0
0
0
0
2
2
2
2
0
1
2
2
2
0
2
1
2
0
1
2
0
2
1
0
0
0
1
1
2
2
2
0
1
2
0
0
0
1
0
1
0
0
0
0
0
1
2
0
2
1
0
2
0
2
2
0
0
2
0
0
2
2
1
0
0
1
0
2
0
2
1
0
2
0
0
0
0
0
1
0
1
1
2
0
4
2
0
2
1
2
0
2
1
0
1
0
2
0
0
2
1
7
1
2
2
1
1
1
0
2
1
0
0
0
1
1
0
0
1
0
2
0
0
0
1
1
0
0
2
3
1
0
1
0
0
0
1
0
2
0
0
1
0
0
1
0
1
2
1
0
1
1
2
0
0
2
1
0
1
2
2
3
2
1
0
1
2
1
1
2
1
1
5
1
1
1
2
1
3
0
0
0
0
1
1
0
0
0
0
1
1
0
0
2
2
0
2
3
2
1
2
0
1
0
0
1
0
1
0
1
1
1
2
0
1
1
1
1
2
0
1
0
2
1
1
1
1
0
0
1
0
1
0
2
2
0
1
0
0
0
2
1
0
1
0
1
0
1
0
0
0
0
2
1
0
0
1
2
2
0
2
2
2
2
0
1
1
2
1
0
1
2
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
1
2
0
0
2
1
0
0
1
0
0
0
2
0
1
1
1
0
0
1
1
0
0
2
1
2
1
1
0
1
1
1
2
3
1
0
1
0
2
1
0
1
2
1
0
2
0
0
0
2
0
0
0
0
1
0
0
0
1
1
1
1
2
0
0
1
1
0
2
0
2
1
2
0
0
0
1
0
1
2
2
1
0
1
1
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
1
0
1
1
1
1
0
2
0
0
0
2
1
2
0
0
0
0
1
0
0
0
0
1
2
1
0
2
2
2
1
1
1
1
0
0
0
2
1
1
1
1
0
1
0
0
0
1
1
0
2
0
1
1
2
0
1
1
1
1
0
0
1
2
0
0
0
0
2
2
0
1
2
0
1
0
0
2
0
0
0
0
1
2
0
1
1
0
0
1
0
0
1
1
2
1
1
0
0
1
0
0
0
1
1
0
1
0
1
2
0
1
0
0
1
1
2
0
0
0
1
2
1
2
1
0
0
0
0
0
0
0
2
0
0
5
0
2
2
1
0
0
1
0
0
0
2
1
0
1
0
0
0
1
1
0
0
0
0
1
0
1
2
2
0
0
1
2
2
1
0
0
0
2
1
1
1
0
0
0
0
0
2
1
0
0
0
4
0
0
0
0
0
0
2
1
0
0
0
1
2
4
0
1
1
1
1
1
1
0
0
1
2
1
0
2
1
0
2
0
1
0
2
1
0
1
0
1
2
1
1
0
0
1
0
0
1
1
0
0
1
0
2
3
0
0
0
1
1
0
2
0
2
1
0
0
1
2
1
0
0
2
0
2
2
0
0
0
0
0
1
0
3
2
0
0
0
1
0
1
0
0
0
0
2
2
0
0
2
0
0
1
2
1
1
0
0
1
0
2
0
0
1
0
0
0
2
0
1
2
0
0
0
0
2
0
2
0
0
1
2
0
0
1
2
1
2
0
1
0
1
0
0
0
2
1
0
1
2
0
0
1
0
2
2
1
1
1
2
0
1
1
0
0
0
2
1
0
1
1
2
0
2
2
0
1
0
0
3
1
0
0
0
0
2
0
0
0
2
1
0
1
0
1
0
2
1
2
0
0
0
0
1
0
0
0
0
1
1
2
2
2
1
1
0
0
1
1
2
0
3
2
1
0
0
0
0
2
4
2
2
0
0
0
0
1
2
0
0
0
1
2
1
0
1
0
1
0
0
2
3
0
0
2
0
1
2
1
5
0
0
3
1
1
0
0
0
1
2
0
0
0
0
0
1
0
2
0
0
2
1
2
2
1
0
1
1
2
0
0
1
1
1
0
0
2
1
2
0
0
1
1
1
1
0
2
1
0
0
0
1
2
0
0
0
1
0
0
0
0
1
2
1
2
3
2
0
1
0
1
0
2
1
0
0
0
0
0
2
1
2
0
1
2
1
2
1
1
0
0
1
2
1
0
2
2
1
2
0
1
1
1
0
1
1
0
1
0
0
0
0
1
1
1
2
1
1
1
0
0
1
0
2
1
0
0
0
1
2
1
0
1
1
0
1
0
0
2
1
0
0
0
1
0
1
1
1
1
0
2
0
0
2
2
0
0
1
0
1
0
0
1
0
0
1
0
1
0
2
0
1
0
0
1
2
0
0
0
0
1
2
5
0
1
1
2
0
1
0
3
3
0
1
1
2
1
1
2
0
0
1
1
2
0
0
0
0
0
0
1
0
1
0
0
0
0
2
2
1
0
2
2
0
0
1
2
6
0
0
0
0
0
0
0
1
0
2
1
0
2
1
1
1
2
0
1
1
0
1
2
0
1
1
1
1
1
2
0
0
2
0
0
1
0
0
2
2
2
1
0
1
1
2
0
0
0
0
2
0
0
0
0
1
2
2
0
0
2
1
2
2
1
2
2
2
2
2
1
1
2
0
1
1
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
2
2
0
0
0
2
1
2
0
0
1
2
0
0
2
1
0
1
0
0
0
2
0
0
0
0
1
1
0
1
0
2
1
0
0
0
0
0
1
0
0
0
0
1
2
0
1
0
1
0
2
0
0
1
0
2
0
2
2
0
2
0
0
0
0
0
0
0
1
1
1
0
0
0
0
2
1
1
0
1
0
0
1
2
1
2
0
2
1
0
0
0
2
1
1
0
1
0
0
1
1
0
1
0
2
0
0
0
2
1
2
0
1
0
0
0
0
0
0
0
0
0
1
0
2
2
1
1
1
2
0
0
1
0
1
2
0
0
1
1
1
0
1
1
1
1
0
2
2
0
2
0
0
1
1
0
0
2
0
2
0
0
1
1
2
0
0
0
1
1
1
2
2
0
0
0
1
0
2
1
0
0
1
0
0
1
0
1
0
2
1
2
1
2
1
1
1
0
0
0
0
0
4
0
0
0
0
2
1
0
0
1
1
1
1
2
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
1
1
1
1
1
0
1
1
1
2
1
0
1
0
1
1
0
0
1
2
2
2
1
0
2
2
0
0
0
1
0
3
1
1
2
0
0
0
0
0
0
0
1
0
1
0
1
2
0
0
0
1
0
0
2
0
0
2
1
2
1
1
0
1
2
0
0
1
1
3
0
0
2
0
2
0
0
0
2
2
0
10
0
0
0
1
2
2
1
1
1
0
0
0
0
1
2
0
1
1
0
0
0
0
0
0
2
0
1
1
1
0
2
0
0
0
0
2
1
11
0
0
1
0
2
0
0
0
0
2
2
0
0
0
1
2
1
0
0
0
0
1
1
0
1
0
1
2
1
2
0
0
0
0
0
0
0
2
0
2
1
0
0
1
0
0
0
2
0
6
2
0
0
2
1
0
0
2
2
2
0
1
0
1
0
1
1
1
0
1
0
0
0
1
0
3
2
0
0
1
0
0
0
1
2
1
0
1
0
2
1
3
0
1
3
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
1
2
0
0
0
0
12
0
0
0
0
2
1
0
0
2
0
1
1
0
0
1
0
0
0
2
2
0
0
0
2
1
0
0
0
4
1
1
0
0
0
0
1
0
2
0
0
0
2
0
1
0
0
0
1
0
0
0
2
1
0
1
0
2
0
0
0
0
0
1
0
2
0
2
2
1
2
1
0
0
2
1
2
0
0
0
1
0
2
1
0
0
1
2
1
2
4
2
0
1
0
0
2
1
0
0
0
1
2
0
0
1
1
0
0
2
0
0
0
2
0
0
0
1
1
2
0
3
1
2
0
0
0
0
1
1
0
0
2
1
0
0
2
1
0
1
2
2
0
0
1
1
1
2
1
0
2
0
2
1
1
1
0
2
2
0
3
1
2
0
2
0
1
2
0
1
2
0
1
1
1
0
1
1
0
0
2
0
0
1
0
2
2
0
0
1
2
1
0
1
0
1
1
2
1
0
1
0
1
1
1
2
1
1
1
5
0
0
8
2
0
1
1
1
0
0
0
2
0
3
1
1
1
0
0
0
1
2
3
2
0
0
1
1
1
0
2
2
0
0
1
0
0
0
0
1
0
2
0
0
0
1
1
0
0
0
1
1
0
1
0
0
2
0
2
2
0
3
0
1
0
1
1
1
1
0
1
0
1
0
1
0
0
0
0
4
0
1
0
2
1
2
3
1
1
0
1
1
0
0
0
2
1
0
1
0
2
1
3
1
0
1
0
0
1
1
2
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
2
0
1
2
1
0
1
0
1
2
0
0
0
0
0
1
1
1
0
0
0
0
0
1
1
0
0
0
2
1
2
1
2
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
1
2
2
3
2
2
0
0
0
0
1
2
0
0
0
0
1
0
1
0
1
1
1
0
0
0
1
1
0
0
2
0
2
1
0
1
0
0
1
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
1
0
0
1
1
1
0
1
3
2
2
1
1
1
0
1
0
1
1
0
0
0
0
1
0
1
0
0
1
2
2
0
0
2
1
1
0
1
2
0
0
2
0
1
2
0
1
1
2
1
1
0
2
0
2
0
2
0
0
0
0
1
2
1
0
0
0
0
2
1
0
1
1
0
1
0
0
0
1
1
1
1
0
2
1
2
0
0
2
0
0
2
2
0
0
0
0
0
1
2
2
0
0
1
1
0
0
0
0
0
0
0
0
2
1
0
0
0
2
1
2
3
1
2
1
0
1
0
0
0
1
2
3
0
1
0
0
0
1
0
2
0
0
0
0
0
0
5
1
1
0
0
1
2
2
0
1
0
0
0
1
0
1
1
1
3
0
0
1
0
0
2
1
0
2
0
3
1
0
2
1
0
1
0
0
1
0
1
0
2
0
0
1
0
0
0
2
1
0
1
1
0
2
0
2
0
0
0
0
1
1
1
1
1
1
0
0
0
0
1
2
1
0
0
2
1
0
0
1
1
0
0
1
2
1
0
0
0
1
0
1
2
1
2
1
0
0
0
1
1
2
1
1
0
0
0
2
0
0
1
0
1
1
2
0
0
0
2
0
0
3
1
2
1
0
1
0
0
0
0
0
1
0
1
1
1
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
1
0
1
0
1
0
2
1
0
0
3
1
2
0
1
1
1
0
2
0
0
0
0
0
0
0
1
0
1
2
0
0
0
2
1
0
1
0
1
2
1
0
1
0
1
1
0
0
1
0
0
0
1
2
0
1
0
1
0
1
2
0
1
0
3
1
1
0
1
2
1
0
1
0
0
1
0
0
0
0
1
0
0
1
2
1
0
0
0
2
0
0
3
2
0
1
1
0
0
0
1
1
0
1
0
2
1
2
0
0
1
0
0
0
0
1
2
0
1
1
0
1
0
2
0
0
0
0
1
1
1
1
2
0
2
1
2
1
0
0
0
1
1
0
0
1
2
1
0
1
0
0
2
0
0
1
0
0
0
0
0
0
1
1
2
1
0
0
1
0
0
0
2
0
2
0
0
0
2
2
1
0
0
1
2
0
0
1
1
0
0
2
0
2
0
0
1
1
0
0
0
2
0
0
0
1
2
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
2
2
1
2
0
0
1
0
0
0
0
2
0
1
2
0
0
2
0
2
0
2
0
1
0
1
1
2
2
1
0
1
0
1
0
2
0
1
2
2
0
2
1
0
1
0
1
2
2
0
1
1
1
1
2
1
0
0
1
0
0
3
0
2
0
1
0
0
0
0
0
3
0
2
0
0
2
1
0
2
0
0
2
0
0
0
0
1
1
0
1
0
2
1
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
3
2
1
0
1
1
0
1
0
0
1
0
0
0
2
2
0
0
0
1
0
1
0
0
0
2
0
1
2
2
1
2
1
2
0
0
0
0
1
0
0
2
0
2
0
2
1
1
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
2
1
1
2
0
1
1
1
0
0
1
1
0
0
1
0
2
1
2
0
1
1
1
2
0
1
1
0
0
1
1
1
1
0
0
0
0
0
0
2
0
0
1
2
1
0
2
1
1
0
2
1
2
1
0
1
0
0
0
0
0
3
0
1
1
1
0
1
0
1
0
1
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
2
2
1
0
0
0
3
2
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
2
2
0
2
0
0
2
2
0
4
1
1
1
2
0
0
0
0
0
0
0
0
0
1
0
0
1
2
1
0
1
1
2
1
0
1
2
0
1
0
0
2
1
1
1
0
2
0
0
0
1
0
0
2
1
1
0
0
1
0
0
0
1
2
0
0
0
2
0
2
1
0
0
1
0
0
0
2
2
2
0
1
0
0
0
0
1
1
0
1
0
2
1
0
0
0
1
0
0
1
0
2
0
1
2
2
1
1
1
0
0
0
1
0
0
0
1
0
0
1
1
0
2
1
0
0
0
0
0
1
1
2
1
0
2
1
1
1
1
1
2
1
1
1
0
0
2
0
2
1
0
1
1
1
2
0
2
2
0
3
0
0
2
2
2
0
1
1
0
0
2
0
0
1
2
0
0
0
0
0
2
2
1
1
0
0
0
1
1
1
1
0
1
0
0
0
1
1
2
1
1
0
0
0
1
3
1
0
1
0
1
1
2
0
1
1
2
1
3
0
0
0
0
2
2
0
1
0
0
0
2
0
0
0
0
0
2
0
2
0
1
0
0
0
0
1
1
2
1
2
2
0
1
0
2
2
0
2
0
2
1
2
0
2
0
0
0
0
1
0
0
0
0
1
3
0
3
0
0
0
0
2
0
0
0
1
1
0
2
0
0
0
2
2
1
2
2
0
0
0
0
0
0
0
0
1
1
0
2
2
1
1
0
2
0
1
0
1
0
0
1
0
0
2
1
1
2
0
1
0
0
1
0
1
0
2
1
2
1
2
1
1
1
0
2
0
2
0
2
1
2
1
0
0
3
1
0
2
2
2
1
1
1
1
1
0
1
2
0
0
0
1
0
0
0
1
1
2
1
0
2
2
1
1
2
0
4
0
1
0
3
2
3
0
1
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
3
2
0
0
0
0
1
0
0
0
1
2
2
0
0
0
0
1
2
0
0
0
2
1
2
0
1
2
0
1
0
1
1
2
0
1
0
2
0
0
0
1
0
2
0
1
1
0
2
1
0
1
0
2
0
2
1
1
1
2
0
0
1
1
1
2
2
1
0
0
0
0
2
0
0
0
1
2
0
0
3
0
1
2
0
0
1
0
0
0
1
2
0
0
2
2
0
0
1
0
0
0
2
0
0
2
1
0
0
0
2
0
1
0
1
0
2
1
3
0
1
0
0
0
0
1
2
1
5
1
0
1
2
0
1
0
1
1
0
0
0
0
1
3
0
2
2
0
1
1
0
0
1
0
2
2
0
0
1
0
0
0
0
1
1
1
2
2
2
0
1
1
0
0
1
2
0
2
0
1
0
1
0
0
2
0
0
0
0
0
0
2
0
0
1
0
1
1
2
2
0
0
2
1
0
0
2
2
0
0
0
0
0
1
0
0
0
1
0
1
0
0
2
0
1
0
0
1
0
4
2
1
1
0
0
1
2
0
0
0
1
0
1
2
0
0
0
2
0
1
2
1
0
0
1
0
1
2
0
2
0
0
1
1
0
0
0
0
1
0
0
2
0
0
1
1
0
1
2
0
1
1
0
0
0
2
0
0
0
2
0
1
2
2
0
0
2
1
2
1
1
2
0
0
0
0
0
0
1
2
1
2
0
1
0
2
0
2
0
0
0
1
1
2
2
1
0
1
1
2
2
0
1
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
1
2
0
2
0
3
1
1
3
2
1
1
1
0
0
0
1
2
1
1
0
0
2
0
0
0
1
1
1
0
2
2
1
0
0
2
0
0
0
1
0
0
1
2
2
0
1
0
0
2
0
1
0
0
1
0
1
2
1
0
1
0
0
0
1
0
0
2
0
1
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
3
1
2
1
0
1
1
2
0
1
0
0
1
1
1
1
1
2
2
1
0
2
2
2
2
2
0
0
0
0
1
2
1
0
0
2
0
0
1
0
0
0
1
1
0
0
0
1
0
2
2
0
0
0
1
0
0
2
0
0
1
1
1
0
0
2
1
1
2
0
0
0
0
1
2
2
0
0
2
2
1
1
1
1
0
2
0
0
2
2
1
1
1
0
0
2
2
2
3
0
0
1
0
0
0
0
1
2
0
0
1
1
5
2
0
0
0
1
0
2
0
0
1
1
0
1
2
1
0
0
1
2
0
1
2
2
0
0
1
1
1
0
0
0
2
0
0
1
1
0
1
0
2
0
0
1
0
0
0
0
0
0
1
0
2
2
1
1
0
1
0
1
1
1
0
0
1
1
0
2
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
2
0
0
0
1
3
1
0
0
1
0
0
0
0
1
0
1
1
1
0
2
0
1
2
2
1
1
0
2
1
0
1
2
0
2
0
1
0
0
1
1
1
1
0
0
0
0
1
1
2
2
1
1
0
0
1
2
1
0
2
0
0
0
2
1
1
1
0
2
0
0
2
0
2
0
0
2
1
0
0
2
0
0
0
0
2
0
1
1
0
0
0
1
0
0
0
1
0
1
1
2
1
2
2
0
2
1
2
0
1
0
0
0
0
0
1
2
0
0
0
1
1
0
1
2
1
1
0
0
0
0
1
0
2
1
2
0
0
0
1
1
0
1
1
0
0
0
0
1
0
0
0
1
2
0
0
0
2
0
1
1
1
2
3
0
0
0
0
0
1
0
1
0
2
1
1
0
1
0
1
0
2
1
1
0
1
0
1
2
0
1
0
2
1
0
2
1
0
1
2
0
0
0
0
2
0
0
0
1
1
2
1
0
2
0
1
1
4
0
0
1
1
1
1
0
0
1
2
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
1
0
1
1
0
2
2
1
0
2
0
0
1
2
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
2
0
1
0
0
0
1
0
0
2
0
1
0
2
0
0
0
1
2
1
0
1
0
1
1
0
0
1
0
0
0
0
0
2
0
0
2
1
0
0
1
1
0
0
1
1
0
2
0
1
2
2
2
0
2
3
2
0
1
0
2
2
2
0
0
1
2
0
1
1
0
2
0
0
0
1
0
0
0
0
1
0
1
0
1
1
3
2
1
2
0
0
2
0
2
0
0
1
0
1
0
1
2
0
0
0
1
0
2
0
0
3
0
2
2
1
0
1
2
1
2
0
1
2
2
0
0
1
0
1
1
1
2
2
1
1
1
1
1
1
0
1
2
0
0
1
0
2
2
2
1
0
1
0
0
0
2
0
0
1
0
2
0
1
2
1
0
2
0
1
3
2
0
1
2
0
2
0
0
2
0
1
1
0
1
2
0
1
1
2
1
2
5
2
2
2
0
2
0
2
0
0
1
1
1
2
0
0
0
0
1
1
1
0
0
0
1
0
2
1
0
0
0
3
1
0
1
0
0
2
0
2
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
1
0
1
1
1
1
0
0
2
0
1
0
0
1
2
2
0
0
2
0
0
0
0
0
0
0
1
1
2
1
0
2
0
2
0
0
0
1
1
0
0
0
2
1
1
0
1
1
1
1
1
1
2
2
0
0
1
1
1
0
0
1
1
0
1
0
2
0
0
0
2
0
0
1
2
0
0
2
0
2
1
1
1
2
0
1
0
1
0
5
0
1
1
0
0
0
0
0
2
1
0
1
0
0
1
2
1
0
0
2
2
0
1
0
0
2
0
1
1
1
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
1
0
1
1
1
1
1
0
1
0
1
1
1
0
0
0
0
0
1
0
1
4
0
1
0
2
0
1
4
0
2
0
0
2
0
0
2
1
2
1
0
1
2
2
1
2
1
4
0
2
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
2
1
0
2
1
1
1
2
0
1
0
0
0
0
1
0
0
2
2
3
0
1
0
0
0
0
1
0
1
0
0
0
0
0
2
0
1
1
1
2
0
1
1
2
2
0
1
2
1
2
0
0
1
2
0
0
0
0
0
3
1
0
2
3
1
2
2
1
2
0
1
0
1
0
0
2
1
0
1
0
0
0
2
0
1
0
2
1
0
0
0
0
2
0
0
0
0
1
0
0
1
1
0
0
0
1
0
1
0
0
1
2
0
0
0
1
0
0
1
1
0
0
0
1
0
1
0
2
1
1
2
0
1
2
0
0
0
1
0
1
1
0
1
0
0
2
1
1
0
0
1
0
2
0
1
3
0
0
1
0
2
0
1
2
0
0
1
1
0
1
0
0
1
1
0
1
1
1
1
0
1
1
1
2
1
0
0
1
0
0
1
1
1
0
0
1
0
1
1
0
2
0
2
2
0
2
1
1
1
0
0
1
1
0
1
0
2
1
0
0
2
2
2
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
2
2
0
1
1
0
0
0
0
1
1
0
1
2
0
1
0
0
1
2
0
0
1
0
1
0
0
0
0
2
1
0
0
0
1
0
0
0
0
2
1
0
1
1
1
1
1
0
0
0
1
1
1
0
2
1
1
0
0
2
0
0
2
0
2
0
0
1
0
1
0
1
1
1
0
0
1
0
1
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
2
1
2
1
0
0
0
0
2
1
0
2
2
1
0
0
0
0
0
2
0
0
2
0
3
2
1
2
0
2
2
0
1
1
0
0
2
2
0
1
0
0
0
0
0
0
2
1
0
2
0
1
0
1
0
0
0
1
0
2
0
1
0
1
0
1
1
1
2
0
1
2
3
0
1
0
0
2
1
0
0
0
0
0
0
0
2
1
1
0
0
0
5
0
0
0
0
1
1
1
0
1
0
0
1
2
1
2
1
0
0
1
0
1
1
3
0
1
1
1
0
0
2
0
0
2
1
0
1
0
0
0
0
0
0
2
1
0
2
0
2
0
1
0
1
2
1
0
0
0
1
0
1
1
0
0
0
1
0
2
2
0
1
0
0
1
2
0
0
0
2
2
0
2
0
1
0
0
0
0
2
0
2
1
2
0
1
1
1
0
1
2
0
1
1
2
1
0
2
2
0
1
2
2
1
0
1
1
1
0
2
3
0
2
3
2
0
1
0
2
2
1
0
1
0
1
1
1
0
1
0
1
0
1
1
0
1
0
2
0
1
0
0
2
0
0
2
3
0
0
1
1
2
0
2
0
2
0
0
0
1
2
0
2
0
0
0
1
0
0
0
0
0
0
1
1
0
1
1
0
1
0
1
0
4
0
1
1
1
0
2
0
0
0
0
1
2
0
1
0
2
0
0
1
2
0
1
0
1
2
0
1
3
0
2
2
0
1
1
0
1
1
0
1
0
0
1
2
0
0
1
0
2
1
1
0
0
0
0
0
1
0
1
0
2
1
0
1
1
1
1
2
0
0
1
0
2
1
2
1
0
2
0
2
0
0
0
1
0
1
0
0
0
0
0
0
2
0
2
0
0
6
0
2
0
0
0
1
0
1
1
1
2
0
0
1
1
0
2
1
1
1
0
0
0
1
0
2
0
1
1
1
1
0
2
1
2
0
1
0
1
0
0
0
0
1
0
2
1
0
2
0
1
0
2
1
0
0
0
2
2
0
2
1
0
0
1
1
0
1
1
2
0
0
0
0
1
0
0
2
0
1
2
1
0
1
0
2
0
0
0
1
0
1
0
0
2
0
0
0
2
1
0
0
0
0
2
0
1
0
0
0
1
0
1
1
0
0
0
0
2
0
2
1
0
1
1
0
1
1
0
2
1
0
0
0
0
1
0
0
0
1
2
1
0
1
1
0
0
1
0
2
0
1
0
0
1
0
1
2
1
1
1
0
0
1
0
1
2
0
0
1
0
1
0
1
0
3
0
2
1
0
0
1
0
0
0
0
0
2
1
0
0
1
1
0
2
2
0
1
0
1
1
2
0
0
1
0
0
2
0
1
1
0
0
1
1
1
0
2
2
1
2
2
1
1
1
2
2
0
4
0
0
2
0
0
2
0
1
0
1
1
0
0
0
2
4
0
1
0
1
0
0
1
0
1
1
0
0
2
1
2
1
1
1
0
0
0
0
2
2
0
0
2
1
1
1
0
1
0
1
2
1
1
1
0
1
0
0
0
0
0
0
2
1
2
1
2
0
0
0
2
0
0
1
1
0
0
2
0
0
0
2
3
1
1
3
0
0
1
0
1
2
2
0
1
1
2
0
1
0
2
1
2
2
1
0
0
0
2
0
1
0
3
0
0
0
0
0
0
2
5
0
1
0
0
1
0
2
0
0
0
1
0
0
0
1
2
0
0
0
1
0
1
0
2
0
0
1
0
1
0
0
0
1
2
0
0
0
1
1
1
0
1
1
0
1
0
1
0
0
2
0
1
1
1
0
1
0
3
1
2
0
1
0
0
1
2
0
0
0
0
1
0
2
2
0
0
1
0
0
2
2
1
0
2
0
2
0
0
0
1
2
0
1
1
0
0
0
0
0
2
2
1
0
0
2
0
2
0
0
2
1
1
1
2
0
1
0
2
1
1
2
0
2
2
0
0
2
0
1
0
2
0
1
0
0
1
2
0
2
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
1
1
1
0
0
2
0
0
1
2
1
2
2
0
1
2
0
0
0
1
2
2
0
1
1
0
0
1
2
2
1
0
0
0
1
2
0
0
0
1
0
1
2
1
1
2
0
1
0
2
0
1
0
0
0
0
2
0
2
0
0
0
1
0
2
0
2
0
0
0
1
2
1
1
1
1
1
2
0
2
0
2
0
1
0
1
1
1
0
0
2
0
0
1
1
1
1
2
0
0
1
0
0
0
2
0
0
2
0
0
1
1
1
0
0
0
1
1
1
0
1
0
2
0
2
1
1
2
1
2
1
2
1
0
1
1
2
0
0
2
0
0
1
2
0
0
0
2
1
0
2
0
0
0
1
0
3
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
2
2
1
1
1
1
0
0
0
0
1
0
1
2
1
0
2
1
2
0
2
1
0
0
0
0
2
2
2
0
0
0
0
0
1
0
0
0
2
3
2
1
1
2
1
0
0
1
2
2
0
1
1
0
2
0
0
0
1
1
0
1
2
1
0
0
1
0
1
1
1
0
2
0
0
1
1
1
0
0
0
0
0
0
0
4
0
2
0
0
0
0
0
1
0
0
0
0
2
1
1
1
1
0
0
1
1
2
2
2
1
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
1
1
2
2
0
1
1
0
4
2
2
1
1
0
1
1
0
1
1
0
0
2
0
0
1
2
0
0
0
2
0
0
0
0
0
0
2
0
1
1
0
2
1
2
0
2
0
1
1
0
0
1
1
0
0
0
1
1
2
1
0
1
0
2
1
2
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
1
0
1
0
2
1
1
1
1
0
0
0
0
1
1
0
0
0
2
1
0
0
0
0
0
0
1
2
0
1
0
0
0
0
1
2
0
1
1
0
1
2
0
0
0
0
0
1
2
0
1
0
1
1
1
2
0
2
0
2
2
1
1
2
1
1
0
3
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
2
2
1
0
1
0
0
0
0
2
2
0
0
0
2
0
0
1
0
1
1
2
0
0
0
0
0
1
0
0
2
0
0
1
1
1
0
1
0
0
0
0
2
1
0
0
0
2
1
0
0
0
2
1
1
0
1
2
0
2
1
0
1
0
1
1
3
1
2
0
1
1
0
0
0
0
1
0
2
1
2
0
0
1
0
1
2
0
0
1
2
1
0
0
0
2
0
1
0
0
0
0
1
0
2
0
2
0
0
2
0
0
0
2
2
2
0
0
1
0
1
1
2
0
2
1
0
1
0
0
0
0
1
2
1
0
2
1
2
2
1
1
0
0
1
2
2
2
0
0
2
1
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
1
2
1
0
2
1
2
0
2
1
1
0
2
1
0
0
0
0
2
1
2
0
1
3
2
0
2
2
0
2
2
1
0
0
1
1
1
1
0
1
0
0
2
0
0
1
0
1
0
1
2
0
1
2
1
1
0
1
0
2
2
0
0
0
2
2
0
0
1
1
0
1
2
0
1
1
0
3
0
0
3
0
1
0
2
2
0
2
0
1
2
1
2
0
0
1
0
1
1
2
0
0
1
0
1
2
1
1
1
1
0
2
3
1
1
0
1
1
1
1
0
0
0
1
0
1
2
2
1
0
1
2
1
2
2
1
0
0
0
1
1
0
1
0
1
0
2
0
1
0
0
2
2
1
3
0
2
0
1
0
0
1
1
0
0
2
0
2
1
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
2
3
0
2
0
0
1
0
0
2
0
0
0
1
0
0
0
0
2
1
1
1
1
1
0
2
0
0
0
2
1
0
1
1
3
1
0
0
0
2
0
0
2
1
3
0
0
0
2
0
1
0
1
0
1
1
2
0
1
1
0
0
0
2
1
1
1
1
1
2
0
2
2
0
0
0
2
2
1
0
1
1
0
0
0
2
1
0
1
1
0
1
0
1
0
2
0
0
1
0
0
0
1
2
0
1
1
2
0
1
2
0
1
1
0
2
2
0
1
3
0
1
0
0
0
1
2
0
1
0
0
1
0
0
0
0
0
1
1
2
2
1
2
2
0
3
0
1
1
1
1
1
0
1
3
0
0
1
0
1
0
0
1
1
2
2
2
0
1
0
1
1
1
0
0
1
2
0
1
0
1
1
0
1
2
0
2
1
0
0
1
1
2
0
2
4
0
0
1
2
1
1
2
0
0
0
1
3
0
1
1
0
1
2
2
1
2
1
2
0
1
1
2
0
1
0
1
0
0
2
2
1
1
0
0
1
1
2
0
1
0
0
0
1
0
1
0
0
0
0
1
2
2
1
1
0
1
1
0
0
0
0
2
0
2
1
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
1
0
1
0
0
1
2
1
0
0
1
0
2
1
2
1
0
2
0
0
2
2
1
1
0
1
1
2
0
1
0
1
1
1
0
1
0
2
2
2
1
2
1
0
0
0
2
1
0
1
0
0
0
1
0
1
2
0
0
0
1
0
1
1
2
0
0
0
0
0
1
1
1
1
0
0
0
1
1
0
0
1
1
1
2
0
0
0
1
1
1
0
1
2
0
1
0
1
0
1
1
2
0
2
1
0
1
2
2
1
3
0
1
0
2
0
0
2
0
1
0
0
2
0
2
1
2
1
1
1
1
0
0
1
0
0
0
3
0
0
1
0
1
1
1
2
0
1
1
0
1
0
2
1
2
2
1
1
0
2
0
0
0
1
1
1
0
0
0
0
2
0
0
2
2
1
0
1
0
0
1
1
1
0
0
1
0
0
0
0
0
1
2
0
0
1
1
1
1
2
0
1
0
0
0
1
1
0
0
0
0
2
2
1
0
0
2
0
0
0
0
1
1
0
0
1
2
1
0
2
0
0
1
2
2
1
1
0
0
1
1
0
1
0
0
0
0
1
1
0
2
0
1
2
0
0
0
1
0
0
2
0
1
1
0
1
1
0
1
0
1
1
0
1
0
1
1
0
0
0
2
1
0
1
0
0
0
2
2
0
0
2
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
2
1
1
1
0
1
2
0
3
0
1
1
1
0
2
2
2
1
0
0
1
1
0
0
2
1
1
0
0
3
2
0
0
0
2
0
2
0
2
0
1
0
0
2
0
1
1
0
0
0
0
1
0
0
0
1
0
0
1
2
1
1
1
0
1
1
0
2
1
0
1
2
0
2
1
0
1
1
0
1
2
0
1
0
1
1
2
0
0
0
0
2
1
0
0
0
1
2
1
2
1
0
0
1
1
0
1
0
0
1
0
1
2
0
0
1
3
2
1
0
1
0
1
0
2
1
1
1
0
1
1
2
1
0
0
2
0
1
2
1
0
2
0
0
0
2
1
2
1
0
0
0
0
0
0
0
0
0
1
1
1
1
1
1
2
1
0
0
0
0
1
1
0
0
1
0
0
2
2
0
0
1
0
1
0
2
1
1
2
1
0
1
2
0
1
0
2
0
0
0
0
2
1
0
0
1
1
2
0
2
1
0
1
0
2
0
1
0
0
0
2
0
1
1
1
2
1
15
0
0
0
2
1
0
0
0
0
0
0
1
0
1
0
0
0
2
0
3
1
0
0
1
0
2
0
0
2
0
2
3
0
1
1
0
2
1
1
1
0
2
0
2
1
1
0
1
1
2
1
1
0
2
0
0
2
0
0
0
3
3
1
1
2
1
1
0
1
0
1
0
1
1
1
1
0
0
0
0
1
1
0
0
1
0
2
1
0
1
0
0
1
1
0
0
2
0
2
0
2
0
1
0
0
0
0
0
1
0
1
1
2
2
2
1
0
0
1
0
1
0
1
2
0
1
0
2
2
0
0
0
1
0
0
1
0
2
2
0
1
1
1
0
0
3
0
1
0
1
1
0
0
0
1
0
0
2
0
1
0
0
1
2
1
0
2
2
0
0
1
2
0
1
0
1
0
2
0
1
0
1
0
0
2
0
0
1
0
1
2
0
2
2
1
1
1
1
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
1
1
0
2
0
1
2
2
0
0
0
2
1
0
0
1
3
1
0
0
1
2
0
1
3
0
0
1
0
2
0
0
0
2
0
0
1
1
0
2
0
0
0
1
2
2
0
2
0
0
2
0
0
1
0
4
0
0
2
0
2
0
1
0
0
0
0
0
1
0
0
2
0
1
0
0
1
2
2
1
1
2
0
0
1
2
1
0
2
2
0
0
0
2
3
0
1
0
0
0
0
0
2
0
2
1
1
1
1
0
1
2
2
0
1
0
1
1
2
2
2
0
0
0
0
0
1
0
2
1
1
0
1
1
0
1
1
1
2
0
0
2
0
2
0
0
2
1
1
2
2
0
1
0
1
1
0
0
0
1
0
1
0
2
1
0
0
0
0
0
2
0
0
0
0
1
1
0
0
1
1
1
1
0
1
1
0
2
0
1
2
0
2
0
0
0
2
2
1
1
0
0
2
0
1
2
0
1
0
0
2
2
2
1
1
2
2
2
1
1
0
0
0
0
0
1
0
0
2
0
2
1
0
3
0
0
1
1
2
0
2
0
0
1
1
2
0
1
1
0
1
0
0
0
3
2
0
1
1
1
2
1
2
0
1
0
0
0
0
1
0
0
2
0
2
0
0
2
1
0
0
0
1
0
0
0
1
1
1
0
0
1
1
1
0
1
0
0
2
0
2
0
0
0
1
0
1
1
2
0
1
0
2
3
1
0
1
2
0
2
2
2
0
2
0
1
2
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
2
0
1
0
2
0
0
0
0
0
1
2
0
1
1
2
1
0
0
2
3
0
0
0
0
0
1
0
1
1
2
0
1
2
1
0
2
2
0
0
0
0
0
1
1
0
0
2
0
0
2
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
1
1
2
1
0
0
2
2
2
0
0
0
1
0
0
1
0
1
0
1
2
1
0
2
1
0
0
0
0
0
2
0
2
0
2
2
0
0
1
1
0
0
2
2
0
2
1
0
1
0
3
2
1
0
2
0
0
1
0
0
1
2
1
1
1
3
1
0
1
2
1
1
1
2
1
0
1
1
2
0
0
0
1
1
0
0
0
2
1
1
0
1
2
0
0
0
0
0
2
1
2
0
2
0
1
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
1
1
1
2
0
2
0
2
1
0
0
2
1
0
0
1
1
1
1
1
0
0
0
2
1
0
2
0
0
0
0
0
1
1
1
0
0
0
0
1
2
1
1
1
0
2
2
1
2
0
0
0
0
0
2
1
0
1
0
0
0
0
1
1
0
0
2
1
0
0
0
0
0
0
0
2
0
1
0
2
0
1
0
0
1
2
1
0
0
0
0
0
1
1
0
0
0
0
2
0
4
0
0
0
2
1
2
1
0
1
1
0
0
1
1
1
1
2
0
1
0
0
1
0
1
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
2
0
1
0
0
0
1
1
0
0
0
1
1
0
2
0
2
0
2
1
0
0
1
2
0
2
1
1
2
1
0
2
0
1
1
2
0
0
1
2
0
1
1
0
4
0
1
1
0
0
0
2
2
1
0
0
0
1
2
1
3
0
2
1
1
0
0
0
2
0
0
1
2
1
0
2
1
0
2
1
0
3
1
0
1
0
1
1
1
0
0
2
1
1
2
0
0
2
0
2
1
1
0
2
0
3
2
2
0
1
2
1
1
0
1
1
2
1
1
3
0
0
2
0
0
1
0
1
2
1
0
0
0
1
0
2
0
0
1
0
2
0
1
1
1
0
0
1
0
0
0
2
1
2
0
2
1
0
0
2
1
2
3
1
1
0
1
0
1
2
0
2
1
2
1
2
1
1
0
0
0
1
0
1
0
1
0
1
2
2
0
0
1
1
0
0
1
0
2
0
1
0
0
1
1
0
1
0
0
2
1
0
0
1
0
1
0
0
0
1
1
0
0
1
7
1
0
0
1
0
0
0
0
1
0
0
0
1
2
1
1
0
0
1
0
0
0
0
1
2
0
0
0
1
3
0
4
1
1
0
4
1
0
2
1
0
2
1
0
1
2
0
0
1
1
0
0
1
0
1
1
0
0
0
2
2
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
2
4
0
2
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
1
2
1
2
0
2
1
0
1
1
0
2
2
2
2
0
0
2
0
2
0
0
0
2
2
0
2
1
0
0
1
1
0
0
1
2
0
0
0
0
0
2
0
0
2
1
0
2
0
1
1
0
2
1
1
3
0
0
0
1
1
0
0
0
1
0
0
1
1
0
0
2
3
0
0
1
0
0
0
2
1
2
1
2
0
0
2
0
0
0
0
2
0
0
0
1
0
1
0
1
2
0
0
1
0
1
0
1
2
0
2
0
1
0
2
1
0
1
0
0
0
0
0
0
0
1
2
2
1
0
2
1
2
3
2
0
0
1
1
0
0
1
2
0
2
1
0
2
0
3
0
0
1
0
0
2
0
1
1
3
0
0
2
0
1
1
2
1
2
2
0
0
2
0
0
2
1
0
0
0
2
1
1
1
0
1
1
2
1
0
0
0
2
1
0
2
0
0
0
0
1
2
1
1
2
0
0
0
1
0
1
0
2
0
0
0
2
1
0
0
0
0
0
1
1
0
1
0
1
0
0
1
0
2
0
0
2
0
2
0
0
1
2
1
0
2
2
0
1
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
1
2
1
2
1
0
1
0
2
0
1
1
1
0
0
0
1
0
0
0
0
2
1
1
0
2
0
3
0
0
0
0
1
1
2
0
0
3
1
0
2
2
1
0
0
2
2
0
1
0
2
1
1
1
2
1
1
1
3
1
1
0
1
1
2
1
0
0
2
0
1
0
0
0
1
1
0
2
0
1
3
0
0
0
0
1
1
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
2
1
1
2
1
0
2
0
1
0
1
0
0
3
1
0
1
2
0
1
0
1
0
0
0
0
1
1
1
0
0
2
0
2
2
0
1
1
0
2
1
1
0
1
1
1
0
2
1
0
0
0
0
0
2
1
4
1
0
1
1
0
2
1
1
1
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
2
0
0
1
0
4
2
1
0
2
0
0
0
2
1
0
1
1
0
0
0
0
1
2
0
1
0
0
0
2
1
2
0
1
0
0
0
2
0
1
1
1
2
2
1
2
1
1
0
0
0
0
0
1
2
0
2
0
2
2
0
2
0
2
0
1
1
2
1
2
1
0
0
2
1
2
1
1
0
2
0
0
0
2
1
2
0
2
0
1
2
0
0
0
0
2
2
0
2
0
2
0
0
0
2
0
0
1
1
1
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
2
0
1
0
0
1
0
1
2
1
2
0
2
0
1
1
0
1
0
1
0
1
1
0
0
0
2
0
0
3
1
2
2
2
1
1
2
0
0
0
0
0
0
1
0
1
1
2
7
1
0
0
3
0
1
0
0
2
0
0
1
0
0
0
0
0
1
2
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
2
0
2
0
0
2
1
3
2
0
2
0
0
1
0
1
0
1
0
2
0
0
0
0
0
1
1
0
0
3
1
0
2
1
0
0
1
0
1
0
2
0
1
2
1
0
0
0
0
0
0
2
2
4
0
2
0
1
0
0
1
1
1
0
2
3
1
1
0
0
1
0
0
0
0
0
0
0
1
1
0
2
0
0
0
2
0
1
0
2
0
1
0
1
0
0
1
0
0
2
0
0
1
2
2
0
0
3
2
0
0
1
1
0
2
1
1
0
1
0
1
2
0
0
2
2
0
1
1
2
1
2
0
2
1
0
1
2
2
0
0
0
1
0
1
0
1
1
0
1
1
0
0
0
0
2
1
1
0
2
3
1
0
2
2
0
1
0
2
0
0
2
0
0
0
1
0
1
0
0
2
0
1
0
0
0
1
2
1
0
0
0
0
2
0
0
2
2
0
0
0
2
2
0
1
0
0
2
0
0
2
0
1
0
0
0
0
2
2
0
0
2
0
2
1
0
0
0
1
0
2
0
1
0
1
0
0
1
1
0
1
1
0
0
2
0
2
1
0
0
2
2
0
0
1
0
1
1
1
1
1
0
0
1
2
0
1
1
1
0
1
0
1
0
1
2
1
0
0
2
1
2
0
2
2
1
0
2
1
1
0
1
1
2
0
0
2
2
1
1
0
1
0
0
0
0
2
0
2
1
2
0
0
0
0
0
1
1
1
0
2
0
0
2
0
1
0
2
0
0
1
0
1
1
1
2
0
1
0
0
1
0
1
0
0
0
1
0
2
1
0
1
0
1
1
2
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
1
0
0
0
2
0
0
1
2
2
2
0
2
1
1
0
0
0
1
0
1
2
1
2
0
1
0
0
0
0
0
0
0
1
0
2
1
1
1
4
2
0
0
0
0
1
0
1
2
0
0
1
0
2
1
0
1
1
0
2
1
0
0
1
1
2
2
0
0
0
1
0
0
0
0
2
0
3
0
1
1
2
0
2
0
1
2
0
0
1
1
2
2
2
0
0
1
0
0
2
1
0
0
2
2
0
1
0
0
0
2
1
2
2
3
0
1
1
1
1
0
0
1
0
0
0
0
0
0
0
1
1
1
1
0
1
0
0
1
0
2
2
1
0
0
0
1
0
0
0
0
0
1
0
1
2
0
1
0
0
1
2
0
0
0
0
1
2
1
4
0
0
2
1
1
0
0
0
1
0
0
2
0
1
2
2
1
1
2
2
2
0
0
0
0
1
1
0
1
3
0
0
0
1
3
0
0
2
2
2
1
0
1
1
0
1
2
0
0
4
0
2
0
1
0
1
2
2
1
0
0
0
0
2
2
0
2
2
0
1
2
1
0
2
0
1
0
0
0
2
2
0
1
0
1
0
1
0
1
2
0
0
0
2
0
0
1
1
2
2
0
0
2
1
0
2
1
0
0
1
0
1
2
1
0
0
1
0
1
0
2
0
0
0
1
0
0
2
1
1
1
0
0
0
1
0
2
0
1
2
0
2
1
1
0
0
0
0
2
1
0
0
0
3
0
1
1
1
1
0
0
0
1
1
2
2
2
0
1
1
2
0
0
1
0
1
0
1
2
0
0
1
0
0
0
1
1
0
1
1
3
0
0
1
0
0
0
0
0
0
0
0
1
0
3
0
1
2
1
0
0
2
1
1
1
1
2
0
0
0
5
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
1
4
1
2
1
1
1
0
2
0
1
0
2
1
1
0
0
0
1
1
2
1
1
3
2
0
0
0
0
0
0
1
0
0
1
2
0
0
0
1
0
2
0
0
0
0
0
3
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
1
1
0
0
2
0
1
0
0
0
0
0
2
3
1
0
1
1
0
2
1
0
0
1
0
1
1
1
2
1
2
0
0
2
1
1
0
2
0
2
0
0
0
1
1
2
2
0
0
0
1
0
0
0
1
2
1
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
1
2
1
0
0
1
2
0
1
2
2
2
0
1
0
0
0
1
1
0
0
1
1
0
0
1
0
2
0
1
1
0
0
3
1
0
0
1
0
0
1
0
0
2
0
1
2
1
1
0
0
0
0
0
0
0
0
1
1
0
0
2
2
1
8
0
1
0
1
3
1
1
0
0
1
0
0
2
2
0
0
0
1
1
1
0
1
0
0
0
3
0
1
1
0
2
0
0
0
0
1
1
1
0
0
1
2
1
2
2
1
1
1
0
2
0
0
1
0
2
2
1
0
0
0
3
0
1
1
0
0
0
2
1
0
1
0
0
0
1
0
2
2
0
0
1
2
2
0
1
2
2
0
0
0
0
2
0
0
0
0
1
1
0
2
1
1
1
1
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
1
0
2
0
1
0
1
0
0
1
0
0
1
0
2
0
0
2
2
0
0
4
1
0
0
0
0
1
0
1
0
1
1
2
0
2
0
1
1
0
1
1
2
0
1
2
1
1
1
2
1
0
0
1
1
1
7
0
1
0
0
2
1
0
1
1
0
0
0
2
0
1
0
0
0
2
1
0
0
0
0
1
0
2
0
2
2
0
1
0
0
2
2
2
0
0
0
0
0
0
2
1
0
1
0
1
1
0
0
0
1
1
0
4
0
1
1
0
0
1
1
1
0
1
1
1
0
1
0
0
1
2
1
1
2
2
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
2
0
2
1
2
0
1
0
2
0
1
2
0
0
0
0
2
1
2
1
0
1
0
0
1
1
0
2
1
0
1
1
1
2
0
1
1
1
0
1
1
1
1
0
2
0
1
0
0
2
0
0
1
2
0
1
1
1
2
0
0
0
2
0
1
0
1
1
1
0
0
0
1
1
2
0
1
1
0
0
1
0
0
0
0
0
1
0
3
0
0
2
0
1
1
2
1
1
1
1
0
2
0
0
0
0
0
1
0
2
1
1
0
2
1
2
2
1
0
2
1
1
1
0
0
0
0
0
1
1
0
2
0
1
2
0
0
0
0
0
0
0
0
1
0
1
6
2
0
2
0
1
0
0
1
0
0
2
0
0
1
1
0
2
0
1
1
0
0
1
0
2
2
0
2
0
0
0
0
0
0
1
0
1
1
3
0
0
2
0
3
3
0
0
2
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
2
1
0
0
1
1
2
2
0
1
0
1
0
1
1
0
0
2
1
1
0
1
0
1
0
1
0
2
0
0
2
0
3
0
1
0
0
2
2
2
0
1
0
0
0
0
0
1
0
2
0
1
0
2
0
2
0
0
2
0
0
1
0
2
1
0
1
0
1
0
0
3
0
2
0
0
1
0
1
1
1
1
0
1
0
0
1
1
1
0
1
1
2
0
0
1
0
0
0
0
2
2
1
0
0
0
2
0
1
2
0
1
1
0
1
0
0
0
0
0
0
1
1
0
0
1
1
1
0
0
1
0
1
2
1
1
2
0
0
1
0
1
1
0
1
2
0
0
0
0
1
0
2
2
0
1
0
1
0
2
0
0
0
1
2
0
0
1
0
0
0
0
0
1
0
1
1
1
0
2
2
0
1
0
0
2
4
1
0
0
2
0
1
0
2
0
0
1
1
0
0
1
2
1
2
0
0
2
0
0
2
0
0
0
0
1
1
0
0
0
1
0
1
0
0
1
1
0
0
1
0
2
1
2
0
1
2
0
0
1
0
0
0
1
0
1
0
2
0
0
1
2
1
1
0
3
1
2
2
1
0
1
1
0
1
0
0
0
0
2
2
0
2
1
1
2
0
0
0
0
1
1
1
3
0
0
0
0
1
1
1
2
0
0
3
0
0
2
2
3
1
0
0
0
0
0
1
1
0
2
1
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
1
0
0
0
0
1
0
0
3
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
2
0
1
1
1
0
1
2
1
2
1
1
1
1
2
1
0
2
2
0
0
1
0
2
0
7
2
0
1
0
0
0
1
1
0
0
0
0
2
0
0
0
0
1
0
0
1
1
2
1
0
1
0
1
1
0
1
0
1
1
1
2
1
2
1
1
0
1
2
0
0
0
0
0
0
0
1
1
2
0
2
2
0
1
0
0
0
0
1
0
0
1
2
0
1
2
2
0
0
0
2
0
0
2
2
1
0
1
1
1
2
2
1
0
1
1
1
0
0
1
0
1
0
2
0
2
1
0
2
1
0
0
1
0
2
1
0
2
1
2
0
0
0
2
0
0
0
0
2
1
1
0
0
0
0
0
2
0
0
1
1
0
1
0
2
0
1
2
0
2
0
0
1
0
1
0
0
2
2
1
1
2
0
2
0
1
0
0
1
0
0
0
1
1
1
0
1
0
0
1
2
0
0
0
1
0
0
0
1
1
1
0
1
0
0
1
0
0
2
0
0
2
2
2
0
1
1
1
0
2
0
0
0
0
1
2
0
1
2
2
2
0
0
2
1
1
1
0
1
1
1
0
0
1
3
0
0
0
1
0
0
2
0
0
0
1
1
2
1
0
0
0
1
1
2
0
2
0
0
1
0
0
0
1
0
0
2
2
2
1
0
2
2
2
3
1
1
0
0
1
0
0
1
2
0
2
1
1
0
0
1
2
0
1
1
0
2
3
0
2
2
0
0
2
2
0
0
3
0
0
3
1
2
0
0
1
1
0
0
0
0
0
0
0
0
2
0
1
1
0
2
1
0
0
2
1
1
0
0
0
2
0
1
0
1
0
1
1
0
0
1
0
0
0
2
2
2
0
0
0
1
0
1
0
2
1
1
0
1
1
1
2
1
1
1
1
0
1
1
2
1
1
2
3
2
1
1
2
1
0
0
0
0
1
0
2
2
1
0
0
0
0
5
2
0
0
2
0
2
2
2
2
0
0
0
0
3
2
2
0
2
0
1
0
0
0
0
0
0
1
2
0
2
0
2
1
1
0
1
0
4
0
0
1
0
1
2
0
0
2
0
1
0
0
1
0
2
0
2
0
0
2
0
0
1
0
1
1
0
1
1
0
0
0
1
0
0
1
2
0
0
1
0
0
1
3
0
0
0
0
1
0
0
1
2
0
0
1
0
4
2
0
1
0
1
0
0
0
0
1
2
1
0
0
0
1
2
0
1
0
1
1
1
0
0
2
0
0
1
1
0
1
1
0
0
1
0
0
0
1
2
1
2
0
0
0
2
0
2
1
0
1
1
2
2
0
1
1
1
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
1
1
2
1
0
2
1
0
0
0
2
2
1
2
0
0
1
1
0
0
0
2
1
1
1
1
1
1
1
1
0
0
1
1
2
0
1
2
1
0
2
1
0
1
1
0
1
0
0
0
1
1
0
0
0
1
0
1
2
0
0
2
1
0
1
1
0
0
0
2
0
2
2
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
2
0
1
0
1
1
0
0
1
1
0
0
1
2
0
1
0
1
1
1
0
1
1
0
4
0
0
0
0
1
0
0
0
2
3
2
1
0
2
0
1
1
1
0
1
2
2
0
1
1
1
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
2
1
2
2
0
0
0
0
1
4
0
0
0
2
0
0
1
1
2
1
1
2
1
2
1
2
2
0
0
1
2
0
0
1
1
2
0
1
1
0
1
0
0
1
1
3
0
0
0
1
0
2
1
5
1
0
0
1
1
0
1
0
0
0
1
2
0
1
0
0
1
0
2
0
0
0
0
1
2
0
0
0
2
0
0
1
1
2
0
0
0
0
1
3
1
2
1
1
0
2
0
0
1
0
1
0
1
1
0
2
1
1
0
0
0
0
1
0
1
0
0
1
0
0
2
0
0
0
0
0
1
1
0
1
0
2
1
0
1
0
2
2
2
0
0
2
2
1
1
1
1
1
1
2
1
1
0
0
0
0
1
1
1
1
0
2
2
1
0
2
2
2
1
0
1
2
1
1
2
2
2
1
1
1
0
0
1
1
0
0
0
1
0
1
0
2
0
0
1
0
0
2
0
2
1
0
2
1
1
2
0
1
0
0
0
0
1
0
0
0
1
0
0
2
0
2
1
0
0
2
0
0
1
1
1
2
2
2
1
0
1
0
0
2
0
0
0
0
0
0
1
1
2
1
1
0
2
1
1
1
0
0
2
0
3
0
2
3
0
0
0
3
4
4
1
1
2
0
0
1
0
1
3
0
2
0
0
0
1
0
0
2
2
3
0
0
0
0
0
0
3
1
0
0
2
0
1
1
0
0
2
1
1
2
0
1
0
0
0
2
0
2
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
1
2
1
1
0
1
1
1
1
2
2
1
1
0
2
1
1
1
0
2
0
0
2
1
0
1
0
1
0
2
2
0
0
0
1
0
0
1
0
0
0
1
2
1
2
0
0
0
0
0
2
0
1
1
0
0
0
1
0
0
1
0
1
0
0
1
0
2
0
0
2
0
2
2
1
0
2
2
0
0
0
1
0
1
0
1
2
2
2
2
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
2
0
0
2
0
0
3
0
2
0
2
1
4
2
2
1
0
0
0
0
0
0
0
4
1
1
0
1
2
1
1
1
1
0
1
0
2
0
0
1
0
2
0
2
0
1
0
0
0
1
2
0
1
2
0
1
2
0
2
2
0
0
0
0
0
1
0
0
0
1
1
2
1
2
1
0
4
1
0
3
1
1
1
0
1
0
0
0
0
2
0
0
0
2
2
0
2
1
1
2
0
2
0
2
0
2
0
0
1
0
0
2
0
1
1
0
0
0
0
0
1
0
2
0
2
2
1
0
1
1
0
0
0
1
0
0
1
0
0
1
0
1
0
0
1
0
0
1
1
0
1
0
0
1
2
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
2
1
0
1
1
0
0
0
1
2
0
2
1
6
1
0
0
0
2
0
0
3
0
1
1
0
0
1
2
0
0
0
0
0
2
0
2
0
3
0
2
2
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
2
0
1
1
0
0
1
4
0
0
0
3
0
2
2
1
2
2
1
2
0
2
0
0
0
0
2
1
1
0
1
0
0
0
3
0
0
0
1
0
0
0
1
0
0
0
2
1
2
0
3
1
3
1
0
1
0
2
0
0
2
0
0
1
1
0
0
3
0
3
0
1
1
3
1
0
1
0
2
0
1
0
0
1
0
0
0
0
1
0
1
2
2
2
0
0
1
4
0
0
1
2
5
2
2
2
1
0
2
3
1
1
1
1
0
1
0
1
1
0
2
0
1
1
0
0
3
1
0
0
1
2
0
0
1
1
1
2
1
2
3
1
0
0
1
0
1
0
0
1
1
0
2
0
0
1
2
0
0
0
2
0
0
1
0
0
0
0
2
1
2
0
3
2
0
1
0
0
0
3
2
0
0
1
0
1
1
1
0
2
0
2
0
0
1
2
0
2
0
1
2
1
1
0
1
1
0
0
0
0
2
2
0
1
0
3
0
2
0
2
1
0
0
2
0
0
0
0
0
1
2
2
0
0
0
0
2
0
0
0
1
1
1
1
0
0
0
1
1
1
0
0
0
0
1
0
2
1
0
2
0
0
0
0
0
0
1
1
0
1
0
1
0
1
1
1
1
2
0
1
0
2
1
0
0
0
2
0
2
1
0
0
0
4
0
1
1
1
4
0
0
2
2
2
0
0
0
2
0
0
1
1
2
0
3
1
0
0
0
1
0
0
0
1
1
0
2
0
0
2
0
0
1
1
2
2
1
0
0
0
0
0
1
1
2
1
0
0
1
0
1
0
1
0
2
0
0
1
0
0
1
2
0
1
0
1
2
0
1
1
1
1
0
0
0
0
1
2
1
0
2
0
2
0
0
0
2
0
1
0
0
0
2
1
1
5
0
0
0
0
2
0
0
0
2
0
1
1
3
0
0
0
2
1
0
2
1
2
0
2
0
0
1
0
0
0
2
1
0
1
0
1
0
0
0
0
1
0
1
0
2
1
0
0
0
2
0
2
1
0
0
2
0
1
0
2
3
1
0
0
3
0
2
1
0
0
1
0
1
0
2
1
0
2
1
2
0
0
0
3
0
0
0
1
0
2
0
2
0
2
0
0
2
1
1
0
1
2
0
1
0
1
2
0
2
0
2
1
0
0
2
0
0
2
1
2
0
1
0
1
0
0
1
0
0
1
1
1
1
1
2
1
0
0
0
1
0
2
0
2
0
0
0
0
1
1
0
1
0
0
0
2
0
2
3
1
0
2
0
1
0
0
0
1
1
0
0
2
0
0
2
2
1
1
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
2
1
2
2
1
0
0
0
0
1
2
2
1
1
0
1
2
0
0
1
0
1
1
1
0
1
2
1
0
0
0
1
1
0
0
0
1
0
1
0
1
1
0
0
0
0
0
2
1
0
2
2
2
0
1
0
0
0
1
2
3
1
0
0
1
0
0
1
1
3
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
1
2
0
1
0
2
1
0
1
2
0
0
2
0
0
0
1
2
0
0
1
1
0
1
0
0
1
2
0
2
2
0
0
0
1
1
0
0
0
0
0
1
2
0
0
0
1
2
0
1
1
0
0
0
0
0
0
0
2
1
1
0
2
2
0
0
1
0
0
0
1
2
2
0
0
0
0
2
0
0
1
1
0
1
0
0
0
1
2
0
2
1
1
2
1
2
1
0
3
2
0
0
1
1
0
0
0
2
2
1
1
2
1
0
1
1
1
0
0
1
0
2
0
0
0
0
0
0
1
12
0
2
1
0
0
0
0
0
1
2
1
1
1
0
0
0
0
2
2
0
0
0
0
1
2
1
0
0
2
0
1
1
0
0
1
0
0
2
2
3
3
1
0
0
5
2
2
2
1
0
0
2
0
0
1
0
0
2
0
0
1
0
3
2
1
1
0
0
1
2
0
0
2
0
1
1
0
0
0
1
0
0
0
1
0
0
1
2
0
2
0
2
2
0
1
1
0
1
2
2
1
0
2
1
1
1
0
0
3
0
1
0
1
2
1
0
0
0
1
1
1
2
0
0
2
1
1
0
0
6
1
0
0
2
3
0
1
1
0
1
0
0
0
0
1
2
1
0
1
2
3
1
0
2
1
2
1
0
0
2
0
0
0
0
2
1
0
0
2
2
2
0
1
1
0
2
3
0
1
0
2
0
2
2
2
0
0
0
0
0
2
1
1
0
0
1
1
0
0
2
1
0
4
0
0
1
1
0
2
1
1
2
0
0
1
2
1
0
0
0
0
0
0
2
2
0
2
1
0
0
2
0
2
0
2
0
2
0
1
1
0
1
0
1
0
0
0
1
2
2
0
0
1
1
2
1
1
1
0
0
2
0
2
0
2
0
1
0
0
2
0
0
2
2
0
2
1
0
1
0
2
0
0
0
0
2
1
2
0
0
2
0
1
2
1
1
1
0
0
0
1
1
0
1
0
0
0
1
0
1
1
1
0
0
2
0
0
0
0
2
2
0
1
0
0
2
2
0
0
0
0
0
1
0
1
0
2
1
1
2
0
0
1
2
0
0
4
1
2
1
0
0
0
1
0
2
1
2
0
0
0
1
2
0
2
2
0
0
1
2
1
1
2
0
1
1
0
1
0
1
0
1
2
2
0
2
0
0
0
0
2
1
0
1
0
0
0
0
1
1
0
1
1
0
0
0
1
2
1
1
1
0
1
0
1
0
2
1
1
2
0
1
0
1
1
0
0
0
1
0
0
2
2
2
0
2
1
0
1
1
0
0
1
2
0
2
0
1
0
0
0
2
0
0
1
2
0
2
2
1
1
1
1
1
2
1
0
1
2
0
2
2
0
1
2
1
2
0
1
0
0
1
1
1
1
1
2
1
1
0
0
2
0
0
0
0
0
0
0
1
2
0
1
1
0
2
0
0
3
0
2
0
1
3
1
2
0
0
0
2
2
2
1
0
1
0
2
1
0
0
3
1
0
0
0
2
0
0
0
0
0
0
1
0
0
1
2
0
1
0
2
2
0
0
0
2
1
2
1
1
2
1
0
2
0
0
2
2
1
0
1
1
0
0
0
2
2
0
2
1
0
0
0
0
0
1
0
1
0
0
0
1
1
0
1
2
1
2
2
2
0
1
2
2
0
1
0
0
1
0
1
0
0
0
1
0
0
0
1
1
1
1
1
0
0
1
0
0
1
2
0
1
1
2
0
1
0
0
0
1
0
1
1
2
2
2
2
0
2
1
1
0
0
0
2
0
0
0
1
0
1
1
1
0
1
2
1
0
1
0
1
0
1
0
1
2
0
1
1
1
0
0
0
1
2
0
2
2
2
2
1
1
0
0
1
0
1
0
1
0
0
0
1
0
0
0
1
0
0
1
2
0
2
2
2
2
2
0
0
1
0
0
0
4
1
3
1
0
0
1
1
2
1
0
1
0
1
2
0
1
2
1
3
1
2
0
2
0
0
3
1
0
2
0
0
0
0
0
0
0
2
2
1
1
0
2
0
0
1
1
0
0
2
0
2
2
1
1
0
0
0
0
0
0
2
2
0
0
2
1
2
0
0
0
1
2
1
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
1
1
1
1
0
2
1
2
1
2
0
0
1
1
0
1
2
1
0
1
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
1
1
2
0
0
1
1
0
1
3
2
0
0
1
1
0
0
0
2
1
2
8
0
1
0
2
2
0
4
1
0
0
0
0
0
0
0
0
0
0
2
2
1
1
0
0
1
1
1
0
0
2
0
0
1
0
1
0
2
1
2
1
0
1
0
0
2
0
0
2
2
2
1
1
2
0
0
0
1
1
1
2
0
1
0
2
1
1
1
0
2
1
1
0
1
0
0
0
2
0
0
0
0
2
0
2
1
0
0
0
3
1
2
0
0
0
0
1
2
0
1
0
1
0
2
1
0
0
0
1
0
0
0
2
0
2
1
0
0
1
1
0
0
0
0
1
0
0
0
1
0
3
1
0
1
0
0
1
2
0
1
1
2
0
1
0
1
1
0
0
1
2
2
0
0
2
1
1
0
1
0
2
2
0
0
2
2
0
1
0
1
2
1
1
2
1
0
1
0
0
0
0
0
1
2
0
2
0
1
1
0
0
0
0
0
0
1
1
1
0
1
1
1
0
1
1
0
2
1
0
0
0
0
1
0
3
2
2
2
0
1
0
0
0
0
1
0
0
1
2
1
0
2
2
2
0
0
1
0
0
0
2
2
0
0
0
0
1
1
2
0
1
0
0
2
0
2
1
1
1
0
0
0
0
1
0
0
2
0
0
2
2
2
2
0
0
1
0
0
2
1
1
1
0
1
2
1
0
1
0
2
0
1
1
0
2
1
1
1
2
0
0
0
2
1
2
0
0
2
0
2
0
0
4
1
0
0
1
0
2
0
2
2
1
0
0
2
1
1
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
1
0
1
2
1
2
0
1
1
1
0
2
1
2
1
0
0
1
1
0
0
2
2
1
0
0
2
1
1
2
1
2
1
0
0
2
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
1
0
1
0
1
0
0
0
1
1
2
0
0
0
0
1
0
2
0
0
0
2
0
0
1
1
1
1
2
0
0
0
0
2
0
1
2
1
1
1
0
0
0
1
2
1
0
0
1
0
2
2
0
0
0
0
1
1
0
1
0
2
1
1
0
0
1
1
1
2
0
0
0
0
0
1
1
1
1
0
1
2
1
2
2
1
0
1
0
1
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
6
2
0
1
2
0
0
0
0
2
1
2
0
0
0
1
0
0
0
2
1
2
2
1
2
1
1
0
0
2
2
1
0
1
2
2
1
2
2
0
1
2
1
0
0
0
0
0
2
1
1
2
2
2
0
1
2
0
1
1
2
0
1
2
0
1
1
1
2
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
1
1
0
1
2
0
2
1
3
0
1
0
2
1
2
1
0
2
0
1
2
0
0
2
0
1
0
0
2
2
0
1
0
0
0
0
1
1
1
2
0
0
0
1
2
0
2
0
1
0
0
1
1
1
0
0
2
0
0
2
0
2
0
2
2
2
0
0
1
2
0
2
2
0
2
0
1
1
0
2
1
1
2
1
0
0
2
1
1
0
1
2
0
0
0
0
1
2
0
1
0
2
1
2
2
2
0
1
2
0
2
1
0
0
2
2
0
0
0
2
0
0
1
0
2
0
1
2
1
0
0
2
0
0
0
1
2
0
0
0
2
1
0
0
1
0
1
1
2
0
0
2
0
1
0
1
1
1
0
0
0
2
2
0
1
0
0
1
0
1
1
0
1
2
1
1
1
2
1
2
1
1
0
1
0
0
2
0
2
0
0
2
2
1
0
2
1
1
0
0
1
0
1
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
1
1
1
2
0
2
2
1
1
1
2
2
0
0
0
0
1
0
0
1
0
1
0
2
0
0
1
0
0
1
0
0
0
1
2
0
0
1
0
1
0
0
1
2
0
0
0
0
0
2
1
0
0
1
2
2
0
2
0
0
2
2
0
0
0
1
1
2
0
0
2
0
1
2
2
1
2
0
2
0
2
0
0
0
0
1
1
0
2
1
0
2
0
0
1
1
0
1
0
0
0
0
0
1
0
2
2
0
0
1
0
0
0
0
0
1
2
1
1
0
2
0
1
1
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
1
1
1
2
0
0
0
1
0
1
1
2
0
0
0
4
0
0
0
1
0
0
1
0
2
2
0
1
0
0
0
3
0
1
0
0
2
1
1
0
1
0
2
0
4
1
0
1
0
2
0
1
0
0
2
0
0
0
1
0
0
1
2
1
2
0
0
0
0
2
2
2
0
0
0
2
0
0
0
1
1
0
0
1
1
3
0
2
1
0
1
2
0
0
1
2
1
0
1
0
0
0
0
2
0
0
1
0
0
2
0
0
2
2
0
0
0
0
2
2
0
2
0
0
1
0
2
0
3
1
1
0
2
0
2
0
0
2
0
1
0
0
0
0
2
3
0
0
3
0
1
1
0
2
1
0
0
0
0
1
2
0
0
2
2
0
0
1
0
0
2
0
1
1
0
0
1
1
0
1
0
0
0
1
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
1
1
1
2
2
0
0
2
0
0
0
1
0
0
1
0
0
0
0
1
2
0
1
2
1
0
2
2
1
3
0
2
0
1
1
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
1
0
2
0
0
1
0
0
1
2
2
2
1
0
2
2
2
0
2
1
2
0
0
2
0
0
0
1
0
0
0
1
3
0
0
1
0
0
2
1
0
0
3
3
1
0
2
1
0
0
2
0
2
2
1
2
1
0
2
0
2
1
1
0
2
1
1
2
4
1
1
0
0
2
0
1
4
0
1
1
0
0
0
0
0
0
0
0
2
2
0
1
1
0
1
0
2
1
0
1
1
1
1
1
1
1
2
1
1
1
1
2
0
1
2
0
0
1
0
2
1
1
1
0
0
1
0
1
1
2
1
2
0
0
0
2
0
0
0
0
1
0
1
1
0
0
2
2
2
2
2
0
0
2
2
0
0
1
1
0
0
1
0
0
3
2
2
2
0
1
2
0
1
1
0
2
2
0
0
0
0
1
1
0
1
1
2
0
0
1
0
0
3
0
1
1
1
0
2
1
0
1
1
1
0
1
0
1
0
0
1
0
0
2
2
2
0
0
0
1
0
1
0
2
1
0
0
0
1
2
0
2
0
1
0
0
1
0
0
1
2
2
0
2
0
1
1
2
1
1
0
0
0
2
0
2
0
0
2
1
0
2
2
1
1
1
0
2
1
0
1
0
1
0
1
0
2
1
1
0
1
0
0
1
0
0
2
0
2
2
1
2
2
0
1
1
0
1
2
2
0
0
0
1
2
1
0
2
0
0
0
0
0
2
2
2
0
1
0
0
0
0
0
0
1
2
2
1
1
2
2
2
0
0
0
2
0
0
1
1
2
1
0
2
0
0
0
1
1
1
0
0
1
0
0
0
0
0
1
0
2
1
2
1
0
2
0
1
1
0
1
1
0
1
0
1
0
0
1
0
1
1
2
0
0
1
2
0
1
1
0
0
1
1
1
1
2
2
0
0
1
0
1
0
0
0
0
2
0
2
1
0
1
0
2
0
2
0
1
0
2
0
0
1
1
0
0
1
0
0
0
0
1
1
1
2
0
0
1
0
1
2
0
0
1
2
0
0
0
0
0
0
1
0
0
2
0
2
0
0
2
1
1
1
1
0
0
0
2
0
2
1
0
1
0
1
1
0
0
0
0
0
0
0
0
2
3
0
1
2
2
2
2
1
0
0
1
1
0
1
0
0
0
0
0
0
0
1
2
0
1
1
0
0
1
1
2
1
2
1
0
0
1
1
1
3
1
0
0
0
1
0
1
1
2
1
2
0
0
1
2
0
1
0
0
0
0
4
1
1
0
2
1
0
0
2
2
1
1
1
1
2
1
0
1
0
2
0
0
0
1
0
0
1
2
0
0
0
2
0
0
1
1
1
2
0
2
2
1
0
0
1
2
1
0
1
1
0
0
0
2
2
1
0
1
0
1
2
1
2
1
0
1
1
0
2
0
2
0
3
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
1
1
0
0
1
2
1
0
0
0
2
0
4
0
2
1
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
2
2
0
0
1
6
1
0
0
2
0
0
2
0
0
2
0
0
1
2
0
0
0
0
1
1
1
0
0
0
0
2
0
0
0
2
2
0
1
1
2
1
2
1
1
1
0
4
0
0
0
1
1
0
2
0
0
1
0
0
2
0
1
0
0
1
2
0
0
2
1
1
1
2
0
0
1
2
1
1
0
1
0
3
0
1
0
0
1
1
1
0
2
0
2
0
2
1
0
1
1
2
1
0
0
0
0
0
2
1
0
1
0
1
2
0
0
0
2
1
1
1
0
1
0
0
0
1
1
0
0
0
0
0
1
1
0
1
0
0
0
2
0
2
0
0
0
2
2
1
2
1
0
0
1
1
0
0
1
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
1
0
0
2
0
0
0
0
1
3
1
0
0
1
1
3
1
0
1
1
0
2
0
0
2
0
0
1
0
1
1
1
1
2
0
1
2
0
1
0
0
2
0
0
2
0
0
0
1
0
0
1
0
1
0
2
2
0
1
1
2
1
1
0
0
2
1
0
1
0
1
0
0
0
0
0
1
1
1
3
0
1
0
1
1
2
1
0
3
3
0
1
0
0
0
1
0
3
2
1
0
0
0
2
2
1
1
2
2
0
0
1
0
0
1
1
1
2
1
0
0
2
0
0
1
2
0
2
1
1
1
0
0
1
2
2
1
1
0
0
0
2
1
0
1
1
1
2
0
1
1
0
1
2
1
1
0
0
0
0
0
0
2
1
2
0
2
1
2
1
1
0
0
1
0
0
1
0
1
2
1
0
0
1
1
1
0
1
0
0
2
1
0
0
0
0
0
1
0
2
0
2
1
0
1
2
1
1
0
2
1
1
0
1
0
1
1
1
1
0
1
1
0
2
1
0
2
0
0
1
0
1
1
0
1
1
1
0
2
1
0
0
2
0
0
1
0
2
0
1
0
0
0
0
1
1
2
0
1
1
0
0
0
0
1
0
0
1
3
1
0
1
0
0
0
1
2
2
1
1
0
0
0
0
2
2
0
1
1
3
2
0
1
2
1
0
0
1
0
0
0
0
0
2
1
0
1
2
0
1
0
0
0
0
1
1
2
1
1
0
0
0
2
2
0
0
1
1
2
0
2
2
1
1
1
0
0
2
0
1
2
0
1
2
0
0
0
0
3
0
0
0
0
1
0
3
1
0
1
1
1
0
1
2
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
4
0
1
2
2
0
1
0
2
1
0
0
0
1
2
0
0
0
0
2
0
0
0
1
1
1
0
0
0
1
0
2
0
0
1
1
0
1
1
0
0
0
0
0
1
0
1
0
3
1
0
0
0
1
0
2
0
2
2
1
0
1
0
1
1
1
2
0
0
1
2
0
1
0
0
1
1
0
0
1
2
1
0
2
0
2
1
1
1
1
1
1
2
0
1
1
0
0
0
0
1
0
0
2
1
0
1
0
0
3
1
1
2
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
1
0
0
0
1
0
0
1
1
1
1
1
1
1
0
2
0
1
0
0
0
0
2
0
2
3
1
1
0
1
2
3
2
0
1
0
0
1
2
0
1
1
2
2
0
2
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
2
1
0
2
1
1
0
0
0
2
0
1
2
0
2
0
2
1
0
1
2
1
0
1
0
0
0
0
0
1
0
1
2
0
1
1
0
0
1
1
0
0
1
0
0
2
0
2
0
0
2
0
2
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
1
2
0
1
0
1
0
1
1
1
1
0
1
1
2
0
1
1
1
1
1
0
2
2
0
0
1
0
0
1
0
0
0
2
0
0
1
0
2
1
1
4
0
0
0
0
0
1
0
1
0
0
1
0
0
2
0
2
2
0
2
0
0
2
0
2
0
0
0
0
0
1
0
0
2
1
0
1
1
2
2
1
2
1
0
1
0
2
2
1
2
1
2
2
2
1
2
1
1
0
0
1
0
0
1
2
0
2
0
0
0
2
1
1
0
0
0
2
0
2
1
0
0
1
0
2
0
0
0
1
0
1
0
0
1
0
1
2
0
0
1
2
1
2
0
2
2
0
1
0
0
1
0
0
1
0
0
2
2
0
0
0
1
5
0
0
0
1
0
1
0
2
1
0
0
0
0
0
0
0
0
2
2
2
0
0
0
2
0
0
1
0
2
0
2
2
1
0
0
0
0
0
0
0
1
1
1
0
1
0
0
1
2
1
0
0
0
0
0
1
0
1
0
1
2
0
0
0
1
0
2
0
1
0
0
0
2
2
0
1
2
0
2
1
1
2
2
0
0
0
0
2
0
2
1
1
0
1
1
0
0
1
0
1
1
0
0
1
2
1
2
2
1
0
1
2
1
0
0
1
0
2
1
2
1
0
0
1
1
0
2
0
0
2
2
1
0
2
1
0
0
0
1
0
1
0
0
1
2
2
0
1
2
1
1
0
0
0
2
2
1
1
1
1
2
2
0
1
0
2
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
2
0
1
1
1
0
3
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
2
1
1
2
1
1
0
0
1
1
2
0
2
1
1
2
0
1
0
1
1
2
1
0
0
2
0
1
0
0
0
0
0
0
0
0
1
1
0
2
2
2
1
0
0
0
0
0
1
0
0
1
0
1
0
0
1
1
1
2
2
2
1
1
2
1
0
0
2
0
0
4
2
1
1
1
0
0
1
3
1
0
0
0
0
0
0
2
0
0
0
1
2
1
0
1
0
0
0
1
0
0
0
1
2
1
0
1
1
2
1
2
0
2
0
0
4
0
1
0
0
0
0
0
2
2
0
0
2
1
1
0
0
1
0
1
1
0
1
0
1
0
1
2
2
2
0
0
0
0
0
0
0
0
0
0
2
1
0
1
2
1
0
0
0
0
0
1
0
2
2
1
1
1
0
0
1
1
2
0
0
2
0
0
0
1
2
2
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
1
2
0
1
0
0
1
0
1
2
0
0
1
0
0
2
3
1
0
2
1
2
0
0
1
0
0
1
1
1
2
0
1
2
2
1
1
1
1
1
3
1
0
1
0
0
2
1
0
2
1
0
0
0
0
0
2
1
1
0
1
0
0
1
2
0
1
1
1
0
0
2
0
1
3
0
0
2
1
1
0
0
0
1
0
1
2
1
1
2
0
2
2
3
1
0
0
1
0
0
0
2
1
1
0
2
2
2
1
2
0
0
0
0
0
0
1
2
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
3
0
1
0
1
0
0
0
2
0
0
0
0
1
1
0
0
2
1
0
2
0
0
2
0
1
0
1
1
2
0
2
0
1
0
1
0
2
0
0
0
1
0
2
0
0
2
2
0
0
3
1
0
0
2
1
1
1
1
0
0
0
0
1
1
0
0
1
0
2
2
1
2
2
0
1
2
0
0
3
0
0
2
2
0
1
2
0
2
0
0
0
0
1
1
1
0
0
0
2
1
1
0
0
0
1
1
0
0
2
2
2
1
2
2
0
2
1
2
1
0
1
1
1
0
0
1
1
0
1
0
1
0
0
2
0
2
1
0
0
0
2
1
1
0
1
1
0
2
1
2
2
1
0
0
1
1
2
0
3
2
0
2
0
0
1
1
2
0
1
1
1
0
0
1
2
2
1
1
0
0
1
0
1
1
2
0
0
0
2
0
0
0
0
1
0
0
1
0
1
1
1
0
2
0
0
3
0
0
0
0
1
0
0
1
0
0
0
1
1
2
1
1
0
1
0
0
2
1
1
0
1
2
0
0
1
0
0
0
1
0
0
0
0
0
1
1
2
0
2
4
0
2
0
0
0
1
2
1
0
0
1
1
0
0
0
3
0
0
0
1
0
1
1
3
0
1
0
0
1
0
0
0
0
1
2
0
0
0
2
0
0
0
0
1
2
1
1
0
0
1
0
2
0
0
0
0
2
0
2
2
0
0
0
1
0
2
0
1
1
0
0
2
0
2
0
1
0
0
1
1
2
0
1
2
0
2
0
2
1
2
2
1
1
0
2
0
0
1
2
1
0
0
1
0
1
1
2
1
2
2
2
0
0
1
1
1
1
2
0
1
1
2
1
1
1
0
0
1
1
3
1
1
1
1
0
0
0
2
2
0
0
2
0
1
2
0
0
1
2
0
1
1
0
1
1
2
0
2
2
1
2
0
1
0
1
2
0
0
0
0
1
1
0
1
0
1
2
0
0
1
0
2
0
2
2
1
1
2
0
1
0
2
0
1
1
0
0
1
0
0
2
1
1
1
1
0
2
1
1
2
2
2
0
4
0
0
1
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
2
1
0
0
0
2
0
2
1
1
2
1
1
2
0
0
1
1
2
0
0
0
1
1
0
0
0
0
3
1
0
0
1
1
0
1
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
1
0
0
2
0
0
2
1
2
1
1
4
2
0
1
0
0
0
0
2
2
3
2
1
0
0
1
2
0
2
0
0
0
0
3
2
1
1
2
1
2
1
2
1
1
1
0
2
1
1
2
0
0
0
2
2
0
0
1
2
1
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
1
1
0
2
0
0
1
0
0
0
0
0
0
0
0
2
1
1
0
2
0
1
0
0
0
0
2
0
0
0
1
0
1
1
2
2
1
1
0
2
0
1
1
0
1
0
1
1
0
0
1
1
2
0
0
1
0
1
0
0
0
1
2
1
1
0
2
0
1
0
1
1
0
1
1
1
0
1
1
2
0
1
0
1
0
0
1
0
0
2
1
0
1
0
2
2
0
0
1
2
0
0
2
1
0
0
2
0
1
2
0
1
0
2
2
1
2
0
3
0
1
0
0
0
1
0
1
0
0
2
0
0
2
2
0
3
1
0
7
2
2
5
2
1
1
0
1
0
0
0
1
1
1
0
2
2
1
1
2
0
0
0
1
2
2
2
2
0
0
1
0
0
1
1
2
0
0
0
0
1
0
1
0
0
2
1
0
1
3
2
1
2
0
0
0
1
0
0
1
0
0
1
0
0
0
1
2
0
0
0
0
0
2
3
1
2
0
0
0
0
2
1
1
1
0
1
0
0
0
0
1
1
2
0
1
0
0
0
1
0
1
2
2
1
0
0
0
0
0
1
0
1
0
1
0
0
0
1
1
0
1
1
1
0
0
2
2
0
0
0
0
1
0
0
0
1
0
0
2
3
1
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
2
1
0
1
1
0
0
0
3
1
2
0
1
1
1
1
0
0
0
0
2
1
0
1
1
0
1
2
0
0
2
0
2
0
1
0
2
1
3
0
1
0
1
0
2
0
2
2
0
2
0
0
0
1
1
0
1
0
0
1
2
1
2
0
0
0
0
0
1
1
2
1
0
1
2
2
1
0
2
4
1
1
2
0
1
2
1
0
0
1
1
2
2
0
2
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
1
1
1
2
1
0
2
0
2
1
0
2
2
2
2
1
0
0
3
1
0
0
2
0
0
0
0
2
0
0
1
0
0
1
0
0
0
1
0
2
0
0
2
0
1
0
2
0
2
0
1
2
1
0
0
3
0
1
1
0
0
1
0
0
1
0
2
0
0
1
2
0
1
2
0
1
0
1
2
1
0
2
1
0
0
1
1
1
2
1
2
2
0
2
0
0
1
2
1
2
0
0
1
0
1
1
0
1
2
0
0
0
0
1
1
0
2
1
1
1
1
0
0
2
0
2
0
0
0
0
0
2
2
1
0
0
0
0
0
0
2
0
0
1
1
1
1
1
0
0
0
2
1
2
0
0
0
0
0
1
2
0
1
2
1
1
2
1
0
1
0
0
1
0
1
0
0
2
1
0
2
0
1
0
0
2
0
1
0
1
1
2
0
0
0
1
0
2
1
0
0
2
1
1
1
0
1
2
0
0
0
2
0
0
2
0
2
1
1
0
2
0
1
1
0
1
0
1
0
2
0
0
0
1
0
0
0
1
2
1
0
1
1
2
0
1
0
0
1
1
0
1
1
0
2
0
0
0
1
0
0
1
0
1
1
0
2
2
1
2
0
0
1
0
2
1
2
1
2
0
2
2
1
0
0
1
2
2
0
0
0
0
0
0
1
1
1
0
0
0
0
2
2
0
0
2
1
0
0
0
0
1
0
1
2
0
0
0
2
1
0
0
3
0
0
0
1
0
0
2
0
2
1
0
1
1
0
2
1
0
1
1
0
0
1
0
0
1
0
1
0
2
0
2
0
1
0
2
0
1
2
1
2
2
1
2
0
0
0
1
0
1
2
2
1
0
2
1
0
0
1
1
1
0
2
0
0
1
2
1
0
0
2
1
1
0
1
2
0
1
2
2
1
0
1
2
1
2
2
1
1
2
0
2
2
0
1
2
0
0
1
2
0
0
1
1
2
2
2
1
1
0
0
1
0
0
2
0
0
1
0
0
1
0
2
1
0
2
1
2
0
0
0
0
1
1
1
0
2
2
0
1
1
0
1
0
0
1
1
0
1
1
0
2
0
1
3
0
0
2
0
1
1
1
1
2
0
0
0
1
0
1
0
2
2
0
1
2
0
0
0
1
1
0
1
1
2
0
0
0
0
0
0
4
0
1
1
1
1
1
0
2
0
2
0
0
0
0
1
2
0
0
1
2
0
1
2
0
1
0
1
0
2
1
1
1
0
1
0
0
1
0
0
0
2
1
0
2
1
0
1
1
2
1
0
2
0
0
2
0
0
0
2
1
1
0
0
1
2
1
2
1
0
2
2
0
0
2
0
2
0
0
0
1
2
1
0
1
0
0
3
2
1
0
1
0
1
1
0
2
2
0
1
1
2
1
1
0
1
0
0
0
0
1
1
2
1
0
2
0
1
1
1
2
1
0
2
2
2
2
1
0
0
2
0
2
1
0
0
2
0
1
0
0
2
1
2
0
1
0
2
0
0
0
2
1
1
0
2
2
2
0
1
0
0
0
0
0
0
2
0
0
4
1
0
0
0
1
1
0
1
0
0
0
1
2
1
1
0
2
0
1
1
0
1
1
2
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
3
1
2
0
1
0
0
1
1
0
0
1
3
1
0
2
1
3
2
1
1
2
0
1
1
2
6
2
0
2
0
2
0
2
0
1
1
2
1
0
0
0
0
0
2
0
1
1
0
1
0
0
2
2
0
0
0
0
2
1
1
2
1
0
0
0
0
2
0
0
2
1
1
0
1
0
3
0
0
0
2
1
2
0
0
1
1
0
1
1
0
1
0
1
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
2
0
0
0
0
0
1
0
0
0
2
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
2
1
0
0
2
0
1
0
0
0
2
1
0
1
2
0
0
0
0
0
0
2
2
2
1
1
0
1
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
1
1
0
0
0
0
1
1
2
2
2
1
2
2
0
1
1
1
2
2
0
0
0
0
2
1
1
2
2
0
1
0
2
1
0
0
1
1
2
0
0
0
0
0
0
1
1
1
1
0
1
0
1
0
0
0
0
1
1
0
0
2
1
2
0
0
1
0
0
0
0
0
1
2
1
1
0
2
0
0
1
0
0
0
1
1
0
0
1
0
0
0
2
0
1
0
0
1
2
0
0
0
1
0
0
0
0
1
0
1
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
2
1
0
1
0
1
0
0
0
2
0
1
0
0
2
2
0
0
0
0
0
0
1
0
1
0
0
1
1
1
1
0
2
2
0
0
1
0
0
2
1
0
0
0
0
1
2
0
1
1
0
0
1
0
1
1
0
2
0
0
0
0
0
0
1
0
0
0
2
1
0
1
0
1
0
0
2
0
1
0
1
1
1
1
0
1
2
2
1
0
2
2
0
0
2
2
2
1
0
1
0
1
1
1
4
1
0
2
2
1
2
0
0
2
1
2
0
1
0
0
0
1
2
0
2
0
0
0
0
1
0
0
1
2
0
1
2
0
1
0
0
0
0
1
2
0
3
0
0
1
2
0
2
0
0
0
1
0
8
0
2
2
2
1
1
0
0
1
2
0
2
2
1
1
1
1
0
2
0
2
1
0
0
2
0
0
1
0
0
1
0
2
0
1
0
0
1
2
1
1
0
2
0
1
0
1
1
0
0
0
0
0
0
0
1
4
0
1
1
0
0
1
0
2
1
0
2
1
0
0
0
1
0
2
0
0
0
2
0
1
1
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
1
0
2
0
0
2
0
1
0
0
2
0
1
0
0
0
0
2
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
2
0
0
1
1
0
2
2
2
1
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
2
1
2
1
2
0
0
1
0
2
2
2
1
0
1
1
2
1
0
0
1
2
0
2
2
0
1
1
0
0
1
2
0
2
1
1
0
0
1
2
0
0
1
3
0
2
1
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
2
0
0
0
2
0
1
0
0
0
0
2
1
0
0
2
0
0
1
2
0
1
0
2
0
1
1
0
2
0
0
0
2
1
0
2
1
1
0
0
0
0
1
2
4
0
0
0
1
0
1
0
1
2
1
0
0
1
0
1
0
1
0
0
0
1
0
2
1
1
0
1
1
0
0
0
0
0
0
3
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
3
1
1
2
2
0
0
2
0
3
2
0
0
2
0
0
1
0
1
0
1
0
2
0
0
1
0
0
2
1
1
0
0
0
0
1
1
0
1
0
0
0
0
0
2
0
0
2
0
0
1
0
2
0
1
1
1
0
1
2
2
0
1
0
0
0
1
2
1
2
0
0
1
0
2
0
1
0
0
0
2
2
1
0
2
1
0
2
0
0
1
0
2
0
1
0
1
0
2
0
0
2
1
1
0
1
0
0
2
0
0
0
1
0
1
2
2
0
1
0
2
0
2
1
1
1
5
0
1
0
1
0
0
0
2
3
1
1
2
0
1
0
2
2
1
0
0
0
0
1
3
0
1
0
3
0
2
2
1
1
1
0
1
1
0
1
0
1
0
0
2
4
2
2
1
2
0
1
0
0
0
0
0
1
1
0
0
3
0
0
0
0
2
1
0
1
1
0
2
1
1
0
0
2
0
2
0
0
0
1
1
0
0
2
0
1
1
2
0
1
2
0
0
1
1
2
2
1
0
2
1
1
0
2
1
2
0
0
0
0
2
0
0
1
0
0
0
1
1
2
0
2
1
1
2
0
0
0
1
1
2
0
0
2
1
1
0
0
0
0
0
0
2
0
1
0
2
0
2
0
1
2
0
0
1
0
1
0
0
0
2
1
1
2
1
1
0
3
0
1
1
1
0
2
0
2
1
0
1
1
0
0
0
0
0
0
3
0
2
2
0
1
2
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
2
2
0
0
0
2
0
1
2
1
1
1
0
0
0
1
0
0
1
0
1
1
0
0
2
0
0
1
2
0
1
0
1
0
2
2
0
2
0
2
0
0
2
2
2
0
1
0
0
0
0
0
2
0
3
1
1
1
0
0
0
0
1
0
1
1
2
0
0
0
0
0
1
1
0
1
0
0
0
0
2
3
0
0
0
0
2
1
0
0
0
1
0
0
0
3
0
0
3
0
1
1
1
0
1
0
0
1
2
0
0
0
0
0
0
0
0
1
0
1
2
2
0
2
2
0
1
0
1
0
1
0
0
0
1
0
2
1
0
0
0
0
0
0
4
1
0
1
0
0
0
0
1
0
0
1
0
1
0
1
1
0
1
0
0
1
0
1
2
1
0
0
2
0
0
2
0
0
1
0
0
3
0
0
0
0
0
0
0
1
1
1
0
0
2
0
2
0
2
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
1
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
2
4
1
2
1
1
1
1
0
0
0
3
1
0
1
0
1
0
0
2
0
1
1
0
4
1
0
0
2
0
0
1
0
2
1
0
1
0
1
3
2
0
2
0
1
0
1
3
0
0
0
2
0
2
0
0
0
0
1
1
1
1
0
0
1
2
0
0
0
0
1
2
2
1
0
0
3
0
0
0
1
0
1
1
2
1
1
2
1
1
0
1
0
2
2
1
0
2
0
1
3
1
1
1
2
0
0
0
0
1
1
0
0
0
1
0
0
1
0
1
0
0
2
0
2
0
1
2
0
1
2
0
1
0
0
2
0
1
0
1
0
2
0
2
0
1
1
0
1
0
1
2
0
0
2
0
1
2
2
0
1
0
0
1
1
0
1
0
0
0
0
0
2
0
1
0
2
0
1
0
0
1
1
0
1
1
0
1
2
1
1
0
0
1
0
0
0
0
0
2
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
2
1
0
1
1
0
0
1
2
0
2
1
1
1
1
0
2
0
2
0
1
0
1
1
0
0
1
0
0
0
2
0
0
0
2
1
1
1
2
0
1
2
1
1
0
0
2
1
2
1
1
0
3
5
0
1
1
1
0
1
2
0
0
2
0
0
1
2
1
0
1
0
1
2
0
0
0
5
1
1
0
0
3
0
1
2
0
2
2
2
0
0
2
0
2
0
0
0
2
0
0
1
0
2
0
0
0
1
1
1
1
2
1
1
2
0
0
2
1
0
3
0
2
0
1
0
0
1
0
2
0
0
0
2
1
0
0
2
0
0
1
1
0
0
1
1
1
0
1
1
0
1
0
3
0
0
0
2
0
0
2
1
1
0
0
1
1
1
1
0
0
1
1
2
1
1
1
3
0
0
2
0
2
1
2
0
1
2
1
2
1
0
2
3
0
1
0
0
0
0
0
0
0
0
1
2
0
1
4
1
1
2
0
1
0
0
2
0
0
0
1
1
0
1
1
0
1
0
2
1
7
1
0
0
0
2
2
3
1
0
0
0
0
1
0
1
0
1
2
0
0
0
0
0
1
1
1
1
0
0
1
1
0
1
0
0
2
1
1
2
2
0
0
1
0
0
0
0
0
1
1
0
1
2
0
0
0
0
2
0
0
2
1
0
2
0
0
1
1
1
0
1
1
1
0
2
2
0
0
1
0
0
0
4
1
0
0
0
0
2
2
0
0
1
2
0
1
2
0
0
1
0
1
0
1
1
1
1
2
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
3
0
2
1
1
1
2
0
2
0
2
1
1
2
2
1
1
2
1
1
2
1
5
2
0
2
1
2
0
0
1
1
1
1
0
2
0
2
0
2
2
0
1
0
0
0
0
0
3
0
2
0
0
2
1
2
1
1
1
2
2
2
0
2
1
0
2
0
0
0
0
0
0
0
3
2
0
1
1
0
0
0
1
1
6
2
1
2
0
0
0
0
0
2
1
1
1
0
1
0
2
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
2
1
0
0
2
0
2
0
1
1
1
2
0
0
2
0
0
0
2
0
0
2
0
0
2
0
1
2
0
0
0
0
1
0
0
0
1
1
1
0
1
1
0
0
0
1
0
1
0
0
0
0
2
0
0
2
2
2
0
0
0
0
0
0
0
2
2
3
0
1
1
0
0
0
1
1
1
1
0
0
0
0
2
4
0
1
0
0
2
0
1
1
0
0
1
0
1
1
0
0
2
0
0
0
1
0
2
1
2
0
2
0
0
2
2
1
2
0
0
1
0
1
2
2
1
1
2
0
0
2
0
1
0
1
0
1
0
0
2
1
1
1
0
3
1
0
1
0
0
1
0
1
0
1
0
1
0
1
0
0
1
0
0
1
2
1
0
0
2
1
0
0
0
1
2
0
2
1
0
0
1
0
0
2
0
2
0
1
0
4
1
0
0
0
3
0
0
1
0
0
0
0
0
2
2
1
1
1
0
1
0
0
0
1
0
1
2
0
1
0
0
0
1
2
2
1
0
0
2
2
0
2
0
0
1
0
2
2
0
0
2
2
0
0
0
1
0
0
2
0
2
0
0
0
0
1
1
0
1
0
0
2
1
0
1
1
1
0
0
0
2
0
0
1
1
1
0
0
0
0
0
0
2
0
1
1
1
0
3
1
2
1
1
1
0
0
1
0
1
2
1
2
0
0
0
1
0
2
0
1
0
2
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
2
0
0
1
1
2
0
1
0
1
0
0
0
1
0
0
1
0
4
0
2
1
3
0
1
1
0
0
0
0
1
1
0
0
0
1
1
1
2
1
0
1
1
0
2
2
0
0
0
0
0
0
1
0
2
4
1
0
2
0
0
1
2
0
2
0
1
2
3
2
0
1
1
3
2
0
1
1
0
1
0
0
0
1
2
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
1
1
2
0
0
0
1
2
0
0
1
0
1
1
2
0
2
0
0
2
0
1
1
5
0
0
1
1
1
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
3
0
1
2
0
1
0
2
0
0
1
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
1
0
1
1
1
0
2
1
1
1
1
0
0
0
1
2
2
1
1
0
2
0
2
2
0
0
1
1
2
3
2
1
0
0
3
0
1
0
1
0
0
2
1
0
1
0
0
0
1
1
4
0
1
0
1
1
0
1
1
0
0
0
0
0
2
0
0
1
1
0
0
1
0
0
1
1
1
0
2
0
0
2
2
1
0
2
0
0
1
2
0
0
2
0
0
0
0
0
1
2
0
2
1
1
1
2
1
2
1
1
0
0
0
1
1
1
1
0
2
1
0
1
3
1
0
1
2
0
0
0
3
0
1
0
1
2
1
2
0
0
2
2
0
1
0
1
2
0
1
0
0
1
1
2
1
2
0
0
2
0
2
1
2
0
0
1
1
0
2
0
1
1
0
0
2
0
0
1
0
0
1
0
1
2
1
0
0
0
1
0
0
1
0
0
2
0
0
1
2
0
1
1
1
2
1
0
0
0
0
1
0
0
1
1
3
0
0
1
1
2
0
3
2
1
0
1
0
0
1
2
0
2
0
0
0
0
0
0
0
2
2
0
1
2
1
2
1
0
1
1
1
2
3
1
0
0
0
1
0
2
0
0
2
0
0
1
1
0
2
0
0
1
2
1
1
1
0
2
0
0
2
2
1
0
0
2
0
1
0
1
1
1
1
2
0
0
2
1
0
0
1
0
2
1
1
1
2
0
2
0
0
1
0
0
1
1
3
2
1
0
2
1
2
3
0
1
1
1
0
0
1
0
1
0
0
0
2
0
0
0
0
1
0
1
2
0
1
1
0
2
0
2
0
1
1
0
1
0
1
2
0
1
2
1
0
1
0
0
1
0
0
1
0
0
0
2
1
0
0
1
2
2
3
3
0
2
0
1
0
0
1
2
1
2
0
0
2
0
0
2
0
0
2
1
0
0
1
0
1
2
0
1
0
3
1
0
1
3
0
1
2
1
2
1
0
1
0
0
0
0
2
0
1
1
0
2
5
0
0
0
0
1
0
0
1
0
1
0
0
2
0
0
1
0
0
0
0
2
0
1
0
2
0
0
2
2
0
1
2
1
1
0
0
1
1
0
1
1
0
2
0
0
2
0
2
0
1
0
1
0
0
1
3
0
2
2
1
0
0
0
0
0
1
0
1
0
2
0
2
1
0
0
0
1
1
2
0
2
0
0
0
0
0
0
5
0
2
0
0
0
1
0
0
0
1
2
2
2
0
0
0
1
0
1
0
1
0
1
0
0
0
1
1
1
1
2
1
0
2
2
4
2
0
0
1
2
2
2
0
1
0
0
0
0
0
2
0
0
2
2
0
3
0
2
0
1
1
0
2
1
1
0
0
0
0
0
0
0
0
1
0
1
1
1
2
0
2
2
0
2
1
3
2
0
0
0
0
0
1
1
2
2
0
1
0
0
0
0
1
2
1
2
1
0
1
0
0
2
2
0
0
1
2
2
2
0
2
2
2
0
0
2
2
1
2
3
2
0
2
0
0
1
0
3
0
0
0
2
0
0
0
2
1
1
0
2
0
0
2
0
2
1
0
0
2
0
0
0
1
0
0
2
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
1
1
0
1
2
0
0
0
1
1
0
1
1
0
0
0
0
4
0
1
0
0
0
3
0
0
1
0
0
3
0
0
2
1
0
0
1
0
1
1
0
0
0
3
0
0
0
1
0
0
0
2
1
0
0
2
1
1
1
0
1
1
1
0
0
1
0
1
2
1
0
0
0
0
2
0
0
0
0
1
1
0
2
0
0
0
1
1
1
0
0
1
0
0
1
0
2
2
1
0
0
1
0
0
0
1
3
0
1
0
0
0
0
0
1
2
1
1
0
2
0
0
1
1
2
1
2
1
1
1
1
2
1
0
1
1
0
1
0
0
2
0
1
0
0
1
0
1
0
0
0
0
0
0
2
2
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
1
2
2
1
0
1
2
2
0
0
0
2
1
0
3
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
2
1
0
2
2
0
0
0
0
0
2
2
2
0
1
0
0
1
0
2
0
1
0
2
2
0
1
1
1
2
0
1
1
2
2
0
1
2
2
2
4
1
0
1
0
0
1
0
0
0
1
2
0
1
0
0
2
2
0
0
0
1
0
0
2
0
1
1
0
0
0
0
1
1
0
1
0
2
1
2
1
1
1
0
2
1
0
0
1
0
1
1
1
0
1
1
0
0
1
0
0
1
0
0
1
1
0
0
0
2
0
0
1
2
1
2
0
1
0
1
0
0
0
0
1
0
1
1
1
0
0
0
0
0
1
2
3
2
0
2
1
0
0
2
0
1
0
0
0
1
1
2
0
1
0
0
2
2
0
0
2
0
0
0
2
0
0
0
2
0
0
0
1
0
3
1
0
1
2
1
2
1
1
1
0
0
1
0
1
0
2
0
2
2
1
0
2
0
0
1
1
0
1
1
0
1
0
1
2
0
0
0
1
1
5
2
0
2
0
2
0
0
0
1
1
2
1
0
0
0
0
1
0
1
2
1
0
4
0
1
1
0
0
0
0
0
1
0
0
2
0
0
0
1
1
1
0
1
0
0
0
0
1
0
2
1
0
0
2
1
0
0
0
0
1
0
1
1
2
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
2
0
3
0
0
1
0
0
1
1
1
1
0
1
0
0
0
1
0
1
2
1
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
1
0
1
0
1
2
0
1
2
1
0
2
3
0
2
0
0
0
1
0
2
0
0
1
1
0
1
1
2
0
0
0
2
0
0
2
1
1
1
2
1
0
0
1
0
2
0
2
1
2
1
1
1
0
0
0
0
2
0
1
0
1
0
0
2
2
3
0
2
1
1
0
0
2
2
4
1
3
1
0
0
1
1
0
0
0
0
0
1
2
1
1
0
0
2
1
2
0
2
0
0
2
0
0
0
0
3
2
0
1
0
2
0
0
0
2
0
0
2
1
0
1
3
1
0
0
0
1
2
2
1
0
2
0
1
0
0
1
1
0
0
1
0
0
2
1
2
1
0
0
1
0
2
1
1
1
2
0
0
0
0
1
0
3
0
0
0
2
0
2
0
1
1
2
2
0
1
2
0
2
2
1
1
1
0
2
1
2
1
1
1
2
0
0
0
0
0
2
0
1
0
0
1
2
1
1
2
2
2
0
0
1
1
0
0
1
0
2
0
0
0
6
1
0
0
0
0
2
1
1
1
2
2
0
0
0
2
1
0
0
0
1
0
0
1
1
1
1
0
0
0
1
1
1
2
0
0
1
0
0
0
0
0
2
1
1
0
2
0
0
2
0
1
0
1
0
2
1
1
0
0
1
1
0
1
1
1
0
3
0
0
0
1
1
0
2
1
1
0
1
0
0
0
1
0
1
0
1
1
1
1
2
0
0
0
2
2
0
0
3
0
1
0
1
1
0
0
0
0
1
0
0
1
2
2
2
0
1
2
0
0
0
2
0
0
1
0
2
2
0
0
2
2
0
0
1
0
2
0
1
0
0
0
1
0
2
1
1
0
0
2
0
0
1
0
2
1
0
1
1
3
1
1
1
1
0
2
0
1
2
1
0
2
1
0
2
2
2
2
1
0
0
1
1
2
2
0
0
1
3
2
1
2
1
2
0
1
1
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
1
2
2
0
0
1
0
1
0
0
0
1
1
1
0
1
1
0
2
1
1
2
0
1
1
0
0
1
2
0
0
1
0
2
0
0
1
0
1
0
0
0
1
0
2
1
0
0
1
1
1
1
0
0
0
0
0
0
2
0
3
2
1
2
0
0
1
0
1
2
1
0
0
0
1
0
2
0
0
0
1
1
2
0
1
0
0
0
1
2
2
0
0
1
0
1
0
2
0
1
0
1
2
0
0
1
0
0
1
2
0
0
0
0
2
2
0
4
0
0
0
0
2
0
0
1
1
0
1
0
1
0
0
1
0
0
0
1
1
1
1
0
0
3
1
1
0
0
3
0
0
0
0
0
0
1
0
0
0
1
1
2
1
0
0
2
0
0
0
0
0
0
4
2
1
0
0
0
0
0
0
0
0
0
1
0
2
1
0
1
2
2
0
0
1
0
3
1
1
2
0
2
2
2
2
0
0
1
0
0
1
0
0
0
0
1
0
0
2
1
2
0
1
0
0
1
2
2
0
1
2
0
0
0
1
1
2
0
1
1
2
0
1
0
2
0
0
2
1
0
2
1
0
0
0
5
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
1
1
0
0
1
2
0
1
0
0
0
1
1
1
0
1
3
2
2
0
0
2
2
0
1
1
0
1
0
0
0
0
3
1
1
2
3
0
0
0
1
1
0
0
0
1
1
0
1
1
1
1
1
1
0
1
0
0
0
1
0
1
1
2
2
0
0
1
0
1
0
1
1
1
3
0
0
1
2
2
1
0
0
0
3
0
1
1
3
2
1
2
2
2
2
0
1
0
0
0
0
1
1
0
1
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
2
2
0
1
1
0
0
2
1
0
0
2
2
0
2
0
0
1
1
1
0
2
0
1
0
1
0
2
1
0
1
0
0
0
0
1
1
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
1
0
0
2
0
3
0
1
0
1
0
0
1
2
1
0
0
0
0
0
0
2
0
1
0
1
1
2
1
0
1
1
0
1
0
1
2
2
0
1
0
0
1
0
0
1
2
0
2
1
0
2
0
0
0
0
0
1
2
0
1
1
1
3
0
1
0
2
0
0
0
1
1
0
1
0
0
0
2
1
0
1
2
0
1
1
1
1
2
0
0
0
1
0
1
0
1
2
1
0
2
2
0
2
0
0
2
1
0
1
0
0
2
2
0
2
2
0
0
0
0
0
1
1
1
0
0
0
1
0
0
2
0
0
0
1
1
2
0
1
2
1
1
1
2
0
0
0
0
0
0
0
2
3
1
2
0
4
1
2
0
1
0
0
0
1
0
0
2
1
1
2
1
0
1
0
0
0
1
0
0
0
0
1
1
1
1
2
1
1
1
2
1
1
0
1
0
0
2
1
0
1
0
0
1
2
0
2
0
2
3
0
1
2
0
1
1
4
2
0
1
1
0
0
0
0
0
2
1
0
2
0
1
1
1
1
2
1
0
0
0
0
0
1
2
0
1
0
1
0
3
0
0
1
1
0
0
1
0
0
0
1
2
0
0
0
0
2
1
0
1
0
1
0
0
3
0
0
2
0
4
1
0
1
0
0
0
0
1
2
0
0
2
0
0
2
1
1
0
1
1
2
0
0
1
0
0
1
2
1
0
1
0
0
1
1
0
0
0
2
1
1
0
0
2
0
1
2
0
2
0
1
1
0
5
0
0
1
0
1
0
2
0
1
0
0
1
0
3
0
2
0
2
0
1
4
0
2
0
0
1
0
0
0
2
2
3
1
0
0
0
2
1
1
0
2
0
2
1
2
1
1
1
0
0
1
0
0
1
1
0
0
2
2
1
0
0
0
0
1
2
0
0
2
1
0
2
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
2
0
4
0
2
0
0
0
1
2
0
1
1
1
0
0
4
2
2
1
1
0
0
1
0
1
1
0
0
1
3
2
0
0
2
4
0
1
0
1
2
0
1
0
0
2
0
1
2
3
1
0
1
2
0
1
0
0
2
1
1
0
1
2
2
1
0
1
0
1
0
1
0
0
0
2
1
1
0
2
0
1
0
0
2
0
2
1
0
2
1
0
0
0
0
2
1
0
0
2
0
1
2
0
3
1
1
1
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
1
0
1
1
0
2
2
0
1
0
1
0
0
0
0
1
1
0
0
0
2
0
0
2
0
0
1
1
2
2
0
0
1
1
1
3
0
0
0
0
0
1
1
1
0
0
2
2
1
2
1
2
0
2
1
0
0
0
1
0
1
1
2
0
4
3
2
0
0
0
2
0
1
0
2
0
0
0
0
1
0
0
0
2
0
1
1
2
0
2
0
0
0
0
0
1
2
0
0
1
1
1
1
1
0
2
0
0
0
1
3
0
0
0
0
1
1
2
0
0
0
1
1
1
2
0
2
0
0
0
0
0
0
2
0
2
1
0
0
1
2
2
0
0
1
2
0
0
2
0
0
1
1
1
1
1
1
2
1
0
0
2
0
2
0
2
1
0
2
0
1
2
2
0
1
1
1
2
1
0
0
0
1
0
0
2
0
2
1
3
4
0
0
1
2
1
0
2
0
0
2
0
1
2
2
1
1
0
0
0
0
0
1
2
0
0
1
0
1
2
0
0
2
2
0
0
1
0
1
0
1
0
0
1
1
2
0
2
0
0
0
0
1
1
0
2
1
0
1
1
2
1
1
0
1
1
2
0
1
2
1
1
0
1
1
2
1
2
1
0
2
2
2
0
1
2
1
0
1
1
0
0
2
1
0
2
0
2
0
1
1
1
0
1
2
0
2
1
1
0
0
0
1
0
0
0
1
2
1
1
0
1
2
1
0
0
1
0
2
0
0
0
0
2
2
1
0
0
0
1
0
0
0
0
1
2
2
0
2
0
0
0
0
0
0
0
2
0
2
2
1
0
1
0
1
0
0
2
1
0
0
1
0
1
0
0
0
2
1
2
1
1
1
3
1
2
0
1
1
0
0
1
0
2
0
0
0
0
2
0
2
1
1
1
0
2
1
1
0
0
0
2
0
1
2
0
2
0
1
0
0
1
0
2
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
1
1
2
1
0
0
0
0
2
2
0
0
1
0
1
1
0
0
0
0
0
0
0
1
1
0
2
1
0
0
0
2
1
0
0
0
1
0
1
2
0
1
2
2
1
0
0
0
2
1
0
0
1
0
2
2
0
0
0
1
0
1
0
1
0
0
2
1
0
2
1
0
0
2
2
1
0
0
2
3
5
2
1
1
0
2
1
1
0
2
2
0
1
0
0
1
2
0
5
2
1
0
0
0
2
1
0
0
0
0
0
2
0
1
3
1
2
1
0
0
1
1
1
0
1
2
0
0
1
1
0
1
2
0
0
0
1
2
0
0
1
1
2
0
2
0
0
1
2
1
2
2
3
0
0
0
1
2
0
0
0
1
1
1
2
2
3
0
1
1
2
0
0
1
0
2
1
0
0
1
1
0
0
0
1
1
2
0
0
1
2
0
0
0
0
0
0
2
2
0
0
2
2
2
0
2
1
1
1
1
0
0
2
1
1
1
2
0
2
1
0
0
1
2
0
2
0
2
1
0
0
0
2
0
1
0
1
2
1
1
1
0
2
0
2
2
2
2
1
0
2
4
2
1
2
2
0
1
1
1
0
2
1
1
1
0
2
2
0
1
1
1
1
0
1
1
0
0
2
0
1
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
2
1
2
0
0
2
0
0
1
0
0
1
0
0
1
1
2
2
1
1
2
2
0
3
0
0
0
1
1
0
0
0
1
0
0
0
1
1
1
1
2
0
1
0
0
2
0
1
0
3
2
1
2
1
0
1
0
1
2
0
0
0
2
0
1
0
2
2
0
0
1
1
0
2
1
0
0
1
2
1
1
0
0
1
1
0
0
0
1
1
0
0
0
1
0
1
1
1
1
0
2
2
0
1
1
0
0
1
1
1
0
0
1
0
1
2
0
2
0
0
0
1
0
0
1
1
0
0
1
1
1
0
2
2
1
2
1
2
1
0
0
1
0
0
0
0
0
0
1
1
0
1
2
1
2
0
0
0
0
2
0
0
0
0
1
1
1
0
2
1
0
1
0
0
0
3
0
1
1
1
2
1
1
2
0
0
0
2
0
2
0
0
4
2
0
0
1
0
0
0
2
1
1
1
0
0
2
2
0
0
2
1
0
2
0
2
0
0
1
1
4
0
0
0
0
0
1
1
1
0
0
2
0
2
1
1
0
0
0
0
1
1
0
0
2
0
1
0
0
2
0
2
0
0
1
0
1
0
0
0
1
2
0
1
0
0
2
0
1
1
0
2
1
1
0
0
0
1
2
2
2
0
1
2
0
2
0
0
0
1
1
0
4
0
0
2
1
1
1
2
1
1
1
0
0
0
0
0
1
1
0
1
0
2
0
0
2
0
2
2
0
0
1
1
2
0
0
3
0
0
3
0
0
0
1
1
1
0
0
0
0
0
0
1
1
0
0
2
1
2
2
0
0
0
2
1
1
1
0
1
1
2
1
1
0
1
1
0
0
0
0
0
1
0
0
1
0
1
0
1
0
1
2
1
1
0
0
0
2
0
0
0
1
0
0
0
2
0
0
1
0
1
2
0
2
1
2
1
0
2
0
0
0
1
0
0
2
3
2
1
3
0
0
1
2
0
0
0
0
1
1
0
3
1
0
1
2
0
2
2
0
0
0
1
1
1
0
2
1
2
1
0
0
2
0
0
0
0
0
0
2
0
1
1
0
0
0
1
2
0
1
2
0
1
1
2
2
1
1
0
1
1
1
0
0
1
2
0
2
0
1
1
1
0
1
1
2
0
0
2
0
1
0
0
0
1
1
0
1
0
0
1
2
1
2
0
0
0
1
0
2
2
0
0
1
1
0
3
1
1
0
0
1
2
0
0
0
0
0
1
0
0
2
1
1
1
0
2
0
0
0
0
0
0
2
2
0
0
1
0
0
1
1
2
0
0
0
1
1
0
0
1
0
1
0
0
0
0
2
2
0
0
1
0
0
2
1
2
2
0
1
2
0
1
2
0
2
0
0
0
0
1
1
1
1
0
1
0
0
0
2
1
0
1
0
0
1
1
0
2
2
0
0
0
0
1
2
1
0
2
2
1
2
0
1
0
2
1
1
0
1
0
1
2
0
0
1
2
1
0
0
0
0
3
0
0
0
0
1
0
0
0
1
2
0
2
0
0
0
0
1
2
2
1
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
2
0
2
0
2
2
0
1
1
0
0
1
1
1
0
1
2
0
1
2
0
0
0
0
0
0
1
2
2
2
2
1
0
0
0
1
0
1
0
0
2
0
2
1
2
0
0
1
1
2
0
0
0
2
2
0
2
0
1
2
0
1
0
0
0
2
0
1
1
1
1
2
1
2
0
1
1
1
0
0
0
2
1
0
0
1
2
0
1
0
2
1
2
0
0
0
2
1
2
0
0
0
0
2
2
1
1
3
2
3
0
0
1
1
0
1
0
0
0
2
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
1
2
0
0
1
2
2
1
1
0
0
0
1
0
1
1
0
0
0
2
0
2
1
0
1
0
0
0
2
1
0
2
2
1
1
2
0
1
0
0
1
2
1
0
2
1
2
0
0
1
0
0
0
2
0
0
2
0
0
0
1
2
0
1
1
1
0
1
0
0
1
3
1
2
0
0
9
1
1
3
2
0
0
5
0
2
1
2
0
1
1
2
1
1
0
1
0
0
0
0
0
1
0
0
0
1
2
0
0
0
1
2
1
1
0
1
0
1
1
2
0
0
1
1
2
1
1
0
0
1
1
1
2
3
0
0
0
1
1
0
1
0
0
0
0
0
1
1
2
2
2
0
4
0
1
0
2
0
0
0
0
1
0
1
0
0
1
1
1
0
2
0
2
0
1
0
1
2
1
1
1
0
1
1
1
1
0
0
0
0
0
2
0
0
2
0
0
0
2
1
0
2
0
0
2
1
1
0
1
0
2
1
0
2
1
1
0
2
0
0
1
1
0
0
2
0
1
0
0
1
0
2
0
2
0
0
2
1
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
2
0
1
0
1
0
0
1
2
1
2
2
3
2
0
0
0
2
0
0
1
0
3
0
1
1
1
0
0
2
1
1
1
0
2
0
0
1
0
0
1
0
2
0
2
1
1
2
0
1
0
2
1
0
0
0
0
0
0
0
1
0
1
1
1
2
0
1
2
1
1
0
0
1
1
1
2
0
1
0
1
1
1
1
0
0
0
2
2
1
0
2
2
2
0
0
2
0
1
1
0
0
0
1
1
0
3
0
0
1
0
1
1
1
1
1
1
2
0
1
1
0
1
2
0
1
0
0
0
1
0
1
1
0
2
2
1
1
0
1
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
1
0
4
0
2
0
1
2
1
0
0
1
0
0
0
0
0
0
0
0
1
2
3
0
0
1
2
0
0
1
0
2
0
2
0
0
1
0
1
0
2
1
0
0
1
0
2
1
2
1
1
1
0
2
1
0
1
0
1
0
2
1
0
0
0
3
0
0
0
1
1
0
2
0
1
0
0
0
1
1
2
0
0
1
0
1
0
0
2
3
0
0
0
2
0
2
0
0
0
1
0
0
0
0
1
0
1
2
0
0
0
2
2
2
0
0
0
1
2
0
2
1
0
1
1
0
0
1
0
1
1
2
0
0
2
0
1
0
2
1
1
0
1
1
2
0
0
0
0
2
0
1
1
0
0
0
2
0
0
1
2
1
1
0
0
0
0
0
0
1
0
2
0
0
1
1
2
2
0
1
0
0
2
1
0
0
2
2
0
1
0
0
2
0
0
1
0
0
1
0
0
0
2
1
1
0
2
0
0
1
1
0
0
0
1
1
1
1
2
1
1
0
1
1
2
0
0
2
0
1
1
2
0
0
0
2
0
1
0
2
2
0
1
0
1
0
0
1
2
1
0
0
0
0
0
2
3
2
0
1
0
2
0
0
0
2
0
2
0
1
2
2
0
0
0
1
0
0
0
0
1
0
2
2
2
0
0
1
0
2
1
0
2
1
0
0
0
2
1
0
0
0
1
0
1
2
0
1
1
2
1
0
0
2
2
2
2
0
0
0
1
0
0
1
2
0
0
2
0
0
2
1
0
0
1
0
0
0
0
1
2
1
0
1
1
1
2
2
0
2
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
2
0
1
1
1
2
1
1
2
0
1
1
1
0
0
0
2
0
2
0
1
1
1
0
2
1
2
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
1
0
2
1
1
2
0
0
1
1
0
0
0
0
2
1
2
1
0
0
0
2
1
0
0
1
1
1
1
0
0
1
2
2
0
0
0
1
0
0
0
0
2
0
0
1
0
1
1
2
2
1
2
0
2
2
1
1
2
0
0
3
1
0
0
1
2
0
0
1
0
0
1
1
1
1
2
0
0
1
1
0
2
2
1
1
0
0
0
0
0
1
1
2
2
0
1
1
0
0
0
1
2
0
0
0
1
0
2
0
1
0
0
2
0
2
0
0
0
1
1
1
0
0
0
2
0
1
0
0
0
0
1
0
1
1
0
1
0
0
2
2
2
2
1
0
0
1
1
1
0
0
0
2
2
0
1
0
0
1
0
2
1
0
0
0
0
0
0
2
1
1
0
1
0
0
1
2
0
0
0
2
0
0
2
1
2
0
0
0
0
3
0
0
0
0
0
2
0
0
3
0
1
0
0
2
2
1
0
0
1
1
0
3
2
0
4
1
0
1
0
1
1
0
1
0
0
0
3
1
0
0
2
0
2
0
1
1
0
0
0
1
0
0
1
2
1
0
2
2
2
1
2
1
0
0
0
0
1
1
0
0
1
2
0
0
1
1
0
0
0
0
2
4
1
1
0
2
0
1
0
1
0
0
1
0
0
1
0
1
1
1
0
2
0
1
1
1
2
0
0
1
0
2
0
0
0
0
0
0
3
0
1
1
0
1
0
1
1
1
1
2
2
2
0
0
1
2
1
0
1
1
2
0
1
0
2
1
0
1
0
1
0
2
0
2
1
0
0
1
0
2
1
0
0
0
1
2
0
2
1
2
1
0
2
0
0
0
1
0
0
0
2
0
1
1
1
0
1
0
0
0
0
1
1
1
1
1
1
1
0
1
1
0
0
2
0
0
1
0
2
1
2
1
0
0
1
2
2
0
2
1
0
0
0
0
2
3
0
2
0
0
1
0
0
2
0
2
1
0
0
0
0
0
0
0
0
2
1
0
2
0
0
2
1
0
0
1
0
1
0
3
1
1
1
1
0
0
0
0
0
1
2
0
2
0
1
0
0
0
0
0
2
1
0
0
0
1
0
2
1
0
1
0
2
2
0
1
0
2
0
0
1
2
0
1
1
0
1
2
0
0
0
1
1
0
1
0
0
1
0
0
0
1
2
0
2
0
0
0
1
2
1
0
0
2
0
0
1
1
0
2
1
1
0
1
1
0
0
0
9
1
1
0
0
1
0
0
1
1
1
1
2
0
0
0
2
1
0
0
1
0
1
0
0
0
0
0
2
0
1
0
0
0
0
1
3
0
0
1
2
1
2
0
2
0
0
0
0
2
2
0
0
2
0
0
1
1
0
0
0
1
0
0
2
1
0
0
2
0
0
0
2
1
0
0
1
0
0
0
0
2
1
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
1
0
0
1
2
0
0
2
0
1
1
2
0
0
2
0
2
1
1
0
2
0
0
2
0
2
1
2
0
0
1
3
1
1
0
0
2
0
0
0
0
0
1
2
0
0
0
1
0
1
2
4
0
0
1
1
0
1
2
2
0
1
0
1
1
0
0
1
1
0
0
1
1
1
1
0
0
2
1
1
0
1
2
1
1
3
0
2
2
0
0
0
1
1
1
2
3
0
0
2
0
1
1
0
0
1
1
1
1
1
0
0
1
2
1
1
2
0
0
0
2
0
2
2
1
0
2
0
0
0
0
2
0
2
0
0
12
2
0
2
1
0
1
0
1
0
0
3
0
3
1
0
1
0
2
0
0
1
0
0
0
0
0
1
0
1
1
0
0
1
2
0
0
0
1
12
0
0
1
2
0
1
0
3
1
1
1
1
0
0
0
2
2
0
2
1
2
1
0
0
0
0
2
0
1
0
0
1
0
0
0
0
2
0
0
0
0
1
1
0
1
1
1
2
1
0
0
2
0
2
0
2
0
0
1
0
1
1
1
0
0
1
1
1
0
0
1
0
0
2
0
0
0
2
2
0
2
1
0
0
1
1
0
0
2
2
2
0
0
0
1
0
0
0
1
3
1
0
2
2
0
1
2
0
2
2
1
2
0
1
1
0
2
1
2
0
0
0
1
0
0
1
1
2
0
2
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
1
1
2
1
0
2
0
1
0
0
0
1
0
0
0
1
1
0
0
2
0
3
0
1
0
1
0
1
0
1
1
0
0
0
0
1
0
0
0
0
1
0
2
0
1
0
0
0
0
1
2
1
1
1
0
1
0
1
1
1
3
1
0
0
0
1
2
0
0
1
0
0
0
2
1
0
0
0
2
0
0
1
1
1
1
0
3
0
2
1
1
0
0
1
0
1
0
0
2
0
1
0
1
0
0
1
2
0
2
0
2
0
0
2
0
0
2
0
2
1
0
0
0
1
2
2
0
0
0
1
2
1
1
11
2
2
0
1
1
2
0
0
1
0
1
0
0
1
0
0
1
1
0
0
0
0
1
2
0
1
0
0
0
2
2
2
0
1
2
0
1
0
0
0
2
0
1
0
1
2
0
1
0
2
0
0
2
0
2
0
2
1
2
1
1
1
1
2
0
2
0
0
0
1
1
1
2
0
0
0
2
2
0
0
0
2
0
0
1
0
2
0
0
1
0
2
1
1
1
1
0
2
2
1
2
2
0
2
0
0
2
2
0
0
2
0
0
2
0
0
0
0
0
0
1
1
2
0
0
0
2
1
2
0
1
0
1
0
0
1
0
2
1
2
0
1
0
0
0
1
0
0
0
0
1
1
2
0
1
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
1
2
0
1
1
0
0
0
1
2
0
0
0
0
2
1
1
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
2
1
0
2
0
0
1
4
1
0
0
0
1
0
0
0
1
0
0
1
2
1
2
1
0
0
2
0
0
2
0
0
2
2
0
0
0
0
0
2
0
1
1
2
0
1
1
1
1
1
2
0
0
0
0
0
3
2
0
0
2
1
1
2
3
1
2
0
0
2
1
2
1
0
2
1
1
1
1
1
0
2
0
0
2
0
2
2
2
0
2
1
5
0
0
2
2
2
0
0
2
1
0
0
1
2
1
1
0
1
6
0
2
1
1
0
0
0
1
1
2
0
0
1
0
0
1
1
1
0
1
0
0
0
1
0
2
1
0
0
0
0
0
0
2
0
0
1
2
0
0
0
1
0
2
0
0
2
0
0
2
0
1
0
1
2
0
1
1
0
0
1
0
0
1
1
0
1
0
0
2
0
0
2
2
0
1
1
0
0
0
0
1
0
0
0
0
0
0
2
1
2
3
1
0
2
2
1
0
2
1
1
0
0
0
1
1
1
1
1
0
0
0
0
1
1
2
1
2
0
1
0
0
0
1
1
0
1
2
2
0
0
0
0
1
2
1
1
0
0
0
0
0
1
2
0
1
0
0
0
1
1
1
1
0
2
0
2
0
0
0
0
1
0
1
0
0
1
1
0
0
0
1
0
0
2
0
0
0
0
2
0
1
1
1
0
0
0
1
0
1
2
1
1
1
0
1
0
0
1
1
1
0
2
2
0
2
0
1
2
1
0
1
1
0
0
2
2
0
0
1
1
0
0
3
2
1
1
0
1
0
1
0
0
1
0
0
3
0
1
0
2
0
0
1
0
1
1
0
0
1
0
0
0
0
0
1
2
2
1
1
1
0
0
0
0
1
0
0
2
0
1
0
0
1
0
0
1
2
1
1
2
1
1
0
1
1
0
0
1
1
1
0
3
0
2
0
2
2
0
2
0
0
1
0
1
0
0
0
2
3
1
0
0
1
0
1
1
0
1
0
2
2
0
1
1
0
0
2
0
0
0
0
0
1
1
2
0
2
0
0
0
1
0
2
0
0
0
1
0
1
1
1
0
2
0
0
1
0
1
0
1
0
3
1
2
2
1
0
0
0
0
0
0
2
0
0
1
0
0
1
1
0
0
0
0
1
0
2
2
0
0
0
0
0
1
1
1
2
2
0
1
2
0
0
2
0
1
3
0
0
0
1
1
0
0
0
0
0
0
2
0
1
1
0
0
1
2
1
0
1
0
2
0
1
0
1
0
2
1
0
0
2
1
0
0
1
0
1
0
1
0
0
0
0
2
1
2
1
0
0
2
2
1
0
2
0
0
2
0
1
0
0
1
1
3
2
0
0
0
1
1
3
1
1
0
1
2
0
0
1
1
0
1
0
1
1
1
0
2
1
0
0
1
2
0
0
2
2
2
2
0
1
1
1
0
0
0
0
0
0
0
2
0
2
1
2
0
0
0
1
0
2
0
0
1
3
2
2
3
2
1
1
1
0
0
0
0
1
0
1
0
1
2
0
2
0
1
1
1
0
2
0
1
1
3
0
0
1
0
0
0
1
2
0
0
1
0
2
1
1
0
0
0
0
2
1
0
0
1
0
0
1
1
1
0
1
0
1
0
3
0
0
2
1
0
0
2
1
0
0
2
0
2
2
1
1
1
1
0
0
0
1
0
0
0
0
2
2
0
0
0
0
1
2
1
1
0
0
2
0
0
0
2
1
1
0
0
1
2
0
0
2
1
0
2
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
1
0
1
2
2
0
1
2
1
1
1
2
2
2
1
1
0
0
2
1
2
1
0
0
1
1
1
0
3
0
0
6
0
2
1
1
2
1
1
0
0
0
1
0
1
0
0
0
1
0
1
0
1
0
0
2
0
0
1
0
0
0
0
1
1
1
0
0
0
0
1
0
1
1
0
1
1
0
2
0
2
0
0
0
1
2
2
2
1
0
2
0
2
0
0
0
0
3
0
0
0
2
1
2
2
1
2
2
0
1
1
2
2
0
2
0
2
0
2
1
1
2
0
0
1
2
2
0
2
0
1
1
1
0
1
0
2
0
2
2
0
2
1
0
1
1
3
1
0
0
2
3
0
1
1
3
1
2
0
0
1
1
0
0
0
0
0
0
2
2
2
0
0
1
1
0
2
0
0
1
0
0
1
0
0
1
0
1
2
2
1
1
0
0
1
0
0
1
0
0
0
1
1
0
2
0
1
3
1
0
1
1
0
2
2
1
1
0
2
0
3
1
2
1
1
2
1
2
1
1
1
2
0
1
2
1
0
0
0
2
0
0
2
1
0
1
2
2
0
0
0
1
2
1
1
2
0
0
1
1
2
1
0
0
1
0
0
1
0
0
0
0
2
2
2
0
2
1
0
1
1
1
0
0
0
0
2
1
0
1
1
1
0
2
2
0
2
0
0
2
0
1
0
1
0
0
0
1
1
2
0
0
1
1
5
1
0
1
0
0
1
1
0
0
0
0
2
2
0
0
0
0
2
1
2
1
0
0
0
2
0
0
0
0
1
1
2
2
1
2
0
0
2
0
1
2
1
0
0
0
0
0
0
1
1
1
0
1
2
0
0
1
1
0
1
1
0
0
2
1
0
2
1
0
0
1
1
1
0
0
0
1
0
0
0
2
1
1
1
1
1
0
0
0
0
0
0
1
0
0
2
0
1
1
1
0
2
0
2
2
1
2
1
0
0
1
0
1
0
0
0
0
0
1
1
0
1
2
1
1
0
0
2
2
0
0
1
0
2
0
0
1
1
1
2
0
0
1
0
1
0
1
1
0
1
2
0
2
0
0
1
0
0
2
0
1
0
0
2
1
1
0
2
2
1
1
2
0
0
0
3
0
3
0
2
1
0
1
0
3
0
1
0
0
0
0
2
2
1
3
0
0
1
0
0
10
0
1
2
2
2
0
1
0
0
2
2
0
1
0
0
1
0
1
2
0
0
0
2
2
0
3
0
0
2
0
1
1
0
1
0
0
0
1
1
1
0
0
0
2
2
0
0
2
2
1
0
2
0
0
2
2
1
1
0
1
2
0
1
0
0
0
1
1
0
0
0
1
0
1
2
0
2
2
0
1
0
0
0
2
0
0
1
1
0
0
0
1
1
1
0
1
0
1
0
1
0
2
0
1
0
1
1
0
0
0
0
1
0
1
1
0
0
2
2
1
4
2
0
1
2
1
0
1
2
0
0
0
0
2
0
2
2
2
0
0
2
0
1
0
1
0
1
0
0
2
1
1
0
0
2
0
0
1
1
0
1
0
0
0
0
1
1
0
0
2
2
0
1
2
0
0
0
2
2
0
1
0
2
0
1
1
0
2
1
0
0
2
1
9
0
0
2
0
1
0
0
0
2
2
2
2
1
1
2
1
0
0
0
1
0
2
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
2
1
2
2
2
0
1
1
1
1
0
1
0
0
0
1
0
0
2
1
1
1
0
1
0
1
1
2
1
1
0
1
0
1
0
1
1
1
3
2
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
2
0
2
2
0
1
2
1
0
0
0
0
0
0
0
1
2
2
0
2
2
0
0
2
2
0
0
1
0
2
0
1
0
0
2
0
0
0
0
0
4
0
0
2
0
2
1
2
0
0
0
0
1
1
0
1
1
0
0
1
0
0
3
0
2
2
0
0
0
1
1
2
4
0
0
1
2
9
0
0
0
1
0
2
1
0
1
1
1
0
2
0
1
2
1
0
0
2
0
0
1
0
1
1
1
1
0
0
0
1
2
2
0
0
1
0
0
0
0
1
2
1
0
0
1
0
1
0
1
2
1
0
2
0
0
1
0
1
0
2
0
0
0
1
0
0
2
0
0
0
2
0
4
0
0
1
0
2
0
1
1
1
0
1
1
1
0
1
0
0
0
2
0
0
1
0
2
2
0
2
0
0
1
1
0
0
0
0
1
1
1
1
2
1
2
0
1
0
0
1
0
1
1
0
1
2
2
0
2
0
1
1
0
0
2
0
0
2
1
0
0
2
1
0
0
0
2
1
2
2
1
0
2
1
1
2
0
0
0
0
0
1
0
0
1
0
0
1
0
2
0
0
0
1
1
2
0
0
0
1
1
2
0
1
1
0
1
0
2
1
0
2
0
0
0
1
0
0
0
0
2
2
1
1
0
0
0
0
2
0
1
0
1
0
1
0
0
1
1
0
2
0
1
0
0
0
0
0
2
0
2
2
1
0
2
0
0
0
0
1
0
0
1
1
2
1
2
1
1
0
2
1
0
1
0
1
1
1
2
1
1
0
0
0
0
0
0
1
0
2
0
1
1
0
1
0
2
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
3
0
2
0
0
0
2
2
2
0
0
0
0
0
0
1
0
0
0
2
1
2
2
0
0
2
3
2
2
0
0
0
2
3
0
0
1
0
0
0
0
1
0
2
1
2
1
1
1
2
0
1
2
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
2
0
1
2
0
1
0
0
2
0
0
0
0
2
3
0
1
2
1
0
0
1
0
0
1
1
0
0
1
2
3
2
0
1
1
0
1
0
0
0
0
0
1
0
0
0
2
1
1
1
1
0
2
1
1
2
0
1
2
0
0
2
1
1
0
2
1
0
0
0
1
1
2
0
0
0
0
0
2
2
1
2
1
2
0
0
0
1
0
0
0
0
3
0
2
1
0
0
1
1
0
2
2
0
2
1
0
0
0
1
0
0
0
2
1
2
0
0
2
0
2
1
0
0
0
0
0
0
1
0
0
1
0
2
1
0
2
1
0
0
1
0
2
0
1
2
0
1
1
0
1
1
2
0
0
2
0
0
0
0
0
1
1
0
0
1
0
2
2
2
1
1
1
2
1
2
1
3
1
2
2
1
1
0
0
0
1
0
0
0
2
0
1
0
2
1
1
3
3
2
0
0
0
0
0
1
2
0
1
1
1
2
0
1
2
0
0
1
0
0
0
1
0
1
1
1
2
0
1
1
0
2
0
0
0
0
1
0
0
0
0
2
1
1
1
1
0
3
0
1
0
0
2
0
0
0
1
1
0
0
1
1
0
1
0
0
0
5
1
4
1
0
1
1
0
0
0
1
0
0
0
0
1
0
2
1
0
1
0
2
1
2
0
2
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
1
2
1
0
0
2
2
2
1
1
2
1
0
0
2
0
1
1
1
0
0
1
0
1
0
2
2
1
0
1
0
0
1
0
0
1
2
2
1
2
2
0
0
2
1
1
0
0
1
1
0
0
2
0
0
0
1
1
1
1
0
0
0
0
2
4
0
1
2
1
0
0
3
0
1
1
1
2
1
0
2
0
1
0
0
2
0
0
0
1
2
0
1
1
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
1
2
0
1
0
0
1
2
0
2
2
0
0
0
0
0
1
1
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
1
1
0
0
2
1
2
1
0
1
0
1
0
0
1
3
0
2
1
1
1
0
0
0
0
0
2
0
1
1
0
0
2
2
0
0
0
0
0
1
0
0
1
2
1
2
0
1
0
0
0
1
0
1
1
2
0
0
0
0
3
0
0
3
0
0
2
0
0
1
0
0
0
0
0
1
1
0
4
0
2
0
1
0
1
2
1
0
1
1
1
0
0
1
1
0
2
0
2
0
0
1
0
2
2
1
2
0
0
2
2
1
0
0
0
0
0
0
1
1
1
0
0
0
0
2
0
1
0
1
3
1
0
1
2
1
0
1
0
1
2
1
2
4
1
2
0
0
0
1
0
0
0
0
2
1
1
2
0
0
1
2
0
1
2
1
0
2
0
0
2
1
2
1
0
0
0
0
0
3
0
0
0
2
2
1
2
1
2
0
0
0
0
1
0
0
0
2
0
1
0
0
2
0
1
1
1
1
0
2
0
0
2
0
0
1
1
0
1
1
0
1
0
1
2
1
1
0
1
2
0
1
2
2
1
2
0
0
1
1
1
2
0
1
1
1
0
2
2
0
0
0
0
0
0
0
0
0
2
0
1
2
1
0
1
0
0
1
0
1
1
1
0
2
1
2
0
0
1
2
1
1
2
0
0
1
1
1
0
0
0
1
1
1
1
2
0
0
1
0
0
0
1
0
0
0
3
1
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
2
0
2
1
0
1
0
0
0
1
0
0
1
1
0
2
0
0
0
0
1
0
2
0
0
2
0
2
1
0
0
2
1
0
0
0
0
0
0
2
1
0
0
0
0
2
0
1
2
0
0
0
0
0
0
1
0
1
0
2
1
0
2
1
1
1
0
2
0
1
2
2
0
1
1
1
1
1
0
0
1
0
0
1
2
1
2
2
0
0
0
0
0
1
1
2
0
0
0
2
1
0
0
0
1
0
1
1
1
2
0
1
0
2
1
0
0
1
0
4
0
0
2
1
1
0
2
0
0
0
2
1
2
0
0
1
1
2
0
0
1
0
0
1
1
0
0
1
1
1
0
0
0
1
1
0
1
0
1
3
0
0
0
2
0
2
0
0
0
0
0
0
1
2
0
1
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
2
1
0
2
0
0
2
0
1
0
0
1
2
1
1
0
0
0
2
2
0
2
0
1
1
0
2
2
0
1
0
1
2
2
1
2
0
0
0
1
0
1
1
0
0
0
0
2
0
1
0
0
0
2
0
0
2
1
0
1
2
0
1
2
0
0
0
1
2
2
0
0
1
1
1
1
0
0
7
1
1
0
2
2
2
3
0
0
0
1
2
0
2
0
0
1
3
0
0
1
1
1
0
0
0
0
2
0
0
0
1
1
1
0
1
0
0
0
0
1
2
1
1
1
1
0
0
1
0
0
0
0
1
0
0
2
0
2
0
0
0
9
1
1
0
2
1
1
0
0
0
1
0
0
0
0
1
1
2
2
0
1
0
1
2
1
0
1
0
0
0
1
2
0
0
2
0
1
0
0
2
2
1
1
2
0
0
1
1
2
2
0
0
1
1
1
2
0
0
1
0
2
0
2
1
1
1
0
0
2
0
0
1
0
1
1
2
1
1
1
2
0
1
1
2
2
1
1
2
0
1
0
0
0
2
2
0
1
0
0
0
2
1
1
2
0
0
1
0
1
2
0
2
2
2
0
1
0
1
0
2
1
1
0
0
0
0
0
1
0
2
0
1
1
1
1
1
2
0
2
0
1
1
2
2
1
1
0
0
1
1
1
1
0
0
0
2
2
0
1
0
0
0
1
0
0
0
0
0
0
2
1
0
2
0
0
2
1
0
0
3
1
0
2
1
0
1
2
0
0
0
1
0
2
3
1
2
1
0
0
1
1
2
1
0
0
0
0
1
0
0
1
0
2
2
0
1
1
1
2
0
1
0
0
0
1
0
0
0
0
0
1
0
2
0
0
2
1
2
1
0
2
1
0
0
0
0
0
2
2
1
0
2
1
0
0
0
2
0
0
2
2
0
1
1
1
0
2
0
0
2
0
0
0
0
0
1
1
1
0
1
1
0
0
0
1
2
0
1
1
1
0
0
0
0
2
0
2
2
2
0
0
1
0
2
2
0
2
1
0
2
0
1
0
2
0
0
3
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
2
1
0
0
1
0
2
0
1
1
0
1
0
2
1
4
1
1
0
2
0
1
0
1
1
2
0
1
1
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
1
1
0
0
2
2
2
0
3
2
0
0
1
1
1
1
0
2
0
1
1
2
1
2
0
0
1
2
0
0
2
0
3
0
0
0
1
0
1
0
1
1
0
0
0
1
1
1
3
1
2
1
0
1
0
1
1
1
0
1
2
1
0
0
2
0
1
0
1
1
0
1
0
2
0
0
1
0
0
2
0
0
1
0
1
0
1
0
0
1
1
0
1
0
1
0
1
0
0
1
0
0
1
0
0
0
1
0
1
2
0
0
2
1
0
1
0
0
2
0
1
1
0
1
2
2
2
1
0
0
0
2
1
0
1
1
2
3
2
1
1
0
0
0
1
2
1
1
0
1
0
2
0
2
0
0
1
1
2
0
2
1
0
0
1
2
0
2
0
0
0
1
0
0
2
1
1
1
2
2
2
0
0
1
0
0
0
0
0
0
0
0
2
1
2
0
1
2
2
0
2
2
0
2
0
1
0
0
0
0
2
1
0
1
0
1
1
1
0
1
0
0
0
0
1
0
0
1
0
1
1
0
0
0
1
2
1
0
0
1
1
1
2
0
0
1
1
0
1
1
1
1
0
0
0
0
0
0
1
0
1
2
2
1
2
0
1
0
0
1
0
0
1
1
2
2
0
0
1
1
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
1
1
2
0
1
0
0
1
0
1
1
1
1
1
0
1
0
1
2
1
1
2
1
2
1
1
0
1
2
0
0
0
0
2
1
1
0
1
1
1
0
1
1
1
0
0
0
1
0
0
0
1
0
1
1
0
0
1
0
1
0
1
1
1
1
0
1
2
3
2
1
2
0
1
1
1
0
1
1
0
0
0
2
0
0
0
1
2
0
0
2
0
0
0
2
0
1
2
0
0
1
1
0
2
0
0
0
0
1
2
0
2
1
0
2
0
0
0
0
0
0
0
1
2
0
0
0
1
1
2
2
0
1
1
2
0
0
2
2
0
0
0
0
0
2
1
2
2
1
0
2
2
1
0
2
0
0
0
2
1
0
0
0
1
0
1
1
1
0
1
1
2
1
0
2
1
0
0
0
5
1
2
1
0
1
0
0
0
0
0
1
1
0
1
0
0
1
2
2
2
0
2
1
0
1
0
0
1
2
0
0
1
1
0
0
2
2
1
0
1
0
2
1
2
0
1
1
1
0
0
2
0
2
0
0
2
1
1
0
1
0
0
0
0
1
2
0
0
0
0
2
0
0
1
1
0
0
0
1
1
0
0
2
1
0
2
0
0
0
0
1
0
1
2
0
2
2
0
0
0
2
0
1
0
0
0
1
1
2
2
0
2
1
2
1
0
0
0
0
2
2
0
1
0
0
0
1
0
0
2
1
1
2
2
1
0
2
1
1
0
0
0
1
1
3
1
1
0
0
2
0
0
1
0
2
0
1
2
0
0
0
1
0
0
2
1
1
0
0
2
1
1
0
0
1
0
0
0
2
1
0
8
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
2
0
1
0
1
2
2
0
1
1
0
2
0
0
2
1
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
3
2
1
2
2
1
0
1
0
2
1
1
0
0
0
1
1
2
0
1
2
0
1
0
0
0
4
2
2
0
0
1
0
1
0
1
1
1
0
0
0
1
1
0
1
0
0
2
2
0
0
1
0
2
1
0
0
2
2
0
0
0
2
2
2
1
0
1
2
1
1
0
2
2
0
2
0
1
3
2
1
2
0
0
1
1
2
1
0
1
2
3
1
1
1
2
0
0
1
0
1
0
0
0
1
1
1
2
0
1
1
1
1
1
2
1
0
1
0
2
0
0
0
1
0
0
1
1
0
1
1
0
0
0
0
2
1
0
0
0
0
1
0
0
1
0
0
0
0
0
2
2
1
0
1
1
0
0
0
0
2
0
1
0
2
2
1
0
1
1
2
2
2
0
1
0
2
1
1
1
0
2
0
0
0
1
0
1
0
0
0
1
0
0
0
1
1
1
0
1
1
0
0
0
1
2
0
2
1
2
4
0
0
0
2
1
2
0
0
1
2
0
2
2
0
0
0
1
2
0
2
0
0
3
1
1
0
0
3
0
0
0
0
2
2
1
1
0
0
2
2
1
0
1
0
0
2
2
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
1
1
0
0
1
0
1
1
1
0
2
0
2
1
1
0
2
0
0
1
0
0
1
1
0
0
1
6
2
2
1
0
2
2
0
0
2
1
9
2
0
1
2
0
1
1
0
2
0
0
2
1
0
0
0
0
2
1
2
2
0
0
0
0
1
1
0
1
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
3
1
0
2
0
0
0
1
2
2
0
2
0
0
1
0
2
2
1
0
0
0
2
0
2
0
2
0
2
0
0
2
0
0
0
0
1
0
0
1
0
0
0
1
2
1
0
0
0
1
1
0
2
0
1
1
0
2
2
2
1
1
0
0
0
1
1
1
0
1
0
1
0
1
1
0
2
0
0
1
1
0
0
1
2
1
2
1
1
1
0
0
0
0
1
0
0
0
0
2
1
0
2
2
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
2
0
0
1
1
0
2
2
0
0
2
2
2
0
0
1
0
0
0
1
0
0
1
0
0
1
2
1
0
1
1
2
2
2
1
2
0
1
0
1
1
0
0
0
1
0
0
2
2
0
1
1
1
1
1
0
1
0
0
0
0
0
0
0
0
2
1
0
1
0
1
1
2
1
0
0
0
1
1
2
0
0
1
0
0
2
0
1
0
0
0
0
1
0
1
1
0
1
1
0
0
1
1
0
0
1
2
1
0
1
2
0
0
2
0
0
1
0
0
1
1
1
2
1
2
1
1
1
0
0
0
1
0
1
0
2
0
1
2
0
0
1
0
3
1
1
0
0
0
2
0
1
1
1
1
1
0
1
0
0
2
0
1
0
0
2
1
0
0
0
2
0
1
0
1
0
0
0
0
1
2
0
0
0
1
1
0
1
1
2
0
2
1
0
2
0
2
1
2
1
0
0
0
2
2
2
0
0
0
0
0
0
0
0
1
0
2
1
2
0
0
1
1
0
0
0
0
2
2
0
0
0
2
0
0
0
2
0
1
2
1
1
0
2
0
0
0
2
2
1
0
2
1
4
2
0
0
2
2
0
2
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
2
1
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
1
1
0
0
0
0
2
0
1
1
0
0
0
1
0
0
1
1
1
0
0
2
0
1
2
1
0
0
0
0
1
1
0
2
0
0
0
1
1
0
0
1
0
1
0
2
0
1
0
1
0
0
1
1
0
1
1
0
1
1
0
2
1
1
0
0
0
1
1
1
0
0
0
7
2
2
2
0
0
1
2
0
0
0
0
0
0
1
0
2
0
1
0
0
0
2
1
1
1
1
0
2
3
0
1
2
2
1
1
1
1
2
1
1
1
0
2
0
2
1
2
0
0
1
0
0
2
1
0
2
0
4
3
0
1
2
2
0
0
2
1
0
0
2
1
0
0
0
0
1
2
0
0
2
0
1
0
1
0
0
1
0
0
0
2
0
1
0
1
1
0
3
1
1
1
1
2
2
0
0
1
0
1
0
0
0
0
0
0
1
1
1
0
1
1
1
1
1
1
0
0
0
1
1
0
0
0
0
0
0
2
2
0
3
1
0
1
0
0
1
2
0
0
0
1
2
2
0
1
0
2
2
0
2
0
0
1
0
0
1
0
0
2
1
1
1
1
1
1
0
1
1
0
1
0
1
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
2
1
0
0
0
1
1
1
0
0
2
1
0
0
0
0
0
1
1
0
0
1
1
0
0
0
1
2
1
1
2
0
0
2
2
1
0
0
2
1
2
0
1
0
1
0
2
0
1
0
0
0
0
1
0
1
0
0
1
1
0
3
0
1
1
0
1
2
0
0
1
0
0
2
2
0
0
2
1
0
0
2
0
2
1
1
0
2
2
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
3
1
0
2
1
1
0
0
1
2
0
1
0
1
0
0
1
1
0
2
1
0
2
0
2
1
1
0
1
1
0
1
0
0
0
0
0
0
0
1
0
1
2
0
0
1
1
1
2
1
1
1
3
1
1
0
0
0
1
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
3
1
1
0
1
0
1
0
0
0
0
0
0
2
0
0
3
0
1
0
0
0
0
0
1
2
2
1
0
0
1
0
1
1
0
1
0
1
1
2
1
2
0
1
1
0
1
0
0
0
2
0
2
0
1
0
1
2
0
0
1
0
0
0
2
0
1
1
0
0
1
0
0
2
1
2
0
1
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
1
1
1
0
1
0
1
0
2
0
1
0
0
0
0
2
1
1
1
1
1
0
1
0
0
0
1
2
0
0
1
2
0
1
0
2
2
0
2
4
1
1
2
1
0
0
0
2
2
1
2
0
2
1
2
0
3
0
0
0
0
0
0
0
3
0
0
2
0
1
0
0
0
0
1
2
3
0
1
0
0
1
0
1
2
0
1
2
2
1
2
1
0
1
2
0
1
0
2
2
0
1
1
0
0
2
2
1
3
0
0
2
2
0
0
1
0
1
1
1
1
1
0
1
1
0
0
0
0
1
2
0
1
1
0
1
0
1
0
1
2
0
0
0
2
0
0
2
1
0
2
0
2
0
0
1
0
1
1
2
0
0
1
2
0
1
0
0
0
0
2
0
2
1
1
1
0
3
0
0
0
0
0
2
0
2
2
0
0
0
0
1
1
1
0
1
0
0
1
0
1
0
0
0
6
0
0
2
1
1
0
0
0
1
1
1
2
1
1
1
2
0
0
0
2
2
1
0
0
1
2
2
0
2
2
0
1
3
1
0
0
0
0
1
1
0
0
0
1
0
2
1
1
1
1
0
0
0
3
1
2
0
0
1
2
1
0
2
0
0
0
2
0
2
0
0
2
1
1
1
0
0
0
0
0
1
1
1
3
0
1
0
1
1
0
1
1
1
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
1
1
1
0
0
0
0
0
0
2
1
0
0
0
1
1
0
2
0
0
1
0
1
2
1
2
2
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
2
1
1
0
0
1
0
1
1
2
0
0
1
0
1
0
0
0
2
2
2
0
1
1
0
0
0
0
0
1
0
0
1
1
0
0
5
2
1
0
1
0
0
0
2
0
2
2
0
1
0
0
0
0
0
1
0
2
1
0
2
0
0
1
1
0
0
0
2
0
0
1
0
0
0
2
0
1
1
0
0
0
0
0
1
0
1
0
1
1
0
0
2
0
0
1
1
2
1
0
2
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
2
0
2
2
0
0
1
1
0
0
0
1
1
0
2
4
1
0
1
0
1
1
1
0
1
0
2
1
0
4
2
0
1
0
0
1
2
0
0
1
2
0
1
2
1
3
1
0
1
2
0
0
0
1
0
2
1
2
0
0
0
2
2
1
0
0
1
0
0
0
0
2
0
1
0
0
0
2
1
1
2
1
1
0
1
2
0
2
0
1
0
0
0
2
0
1
0
0
0
0
0
2
1
2
1
0
1
0
2
1
1
0
0
0
1
1
0
1
0
0
0
1
0
0
1
1
2
0
1
0
1
1
1
2
2
1
1
0
0
0
0
2
1
0
0
3
1
1
1
2
0
1
0
0
0
0
0
0
0
0
2
1
0
0
2
2
1
0
0
3
1
0
2
2
1
0
0
1
2
0
0
1
1
0
0
0
2
0
1
0
0
1
1
1
2
0
0
0
2
0
1
3
0
1
1
0
0
0
0
0
0
0
0
1
2
0
1
1
1
2
2
3
0
1
2
1
0
1
0
2
1
0
0
2
1
2
1
0
2
0
0
1
1
0
1
2
0
0
2
1
0
0
0
1
0
2
0
0
0
1
2
1
1
2
1
0
0
1
0
0
0
0
0
0
1
2
0
0
1
0
0
0
2
2
0
2
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
2
0
1
0
0
0
0
0
1
2
1
1
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
2
1
1
1
2
1
1
2
0
0
2
0
0
1
1
1
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
1
0
0
2
0
1
0
2
0
0
1
0
0
0
1
2
1
1
2
2
2
1
0
2
0
0
2
1
0
0
0
0
1
0
1
1
1
0
1
0
1
0
1
0
0
0
0
0
1
0
0
2
3
0
0
0
0
2
1
0
0
0
2
1
1
0
0
2
2
0
2
0
0
0
1
0
1
1
0
0
1
0
2
0
3
0
0
0
0
0
0
0
0
0
1
2
1
1
0
1
1
1
1
0
1
2
0
1
0
1
0
2
0
1
0
0
2
1
1
2
2
2
0
0
1
0
2
1
0
1
0
0
1
1
1
0
1
0
0
0
1
0
0
0
1
2
0
0
1
0
2
0
0
1
0
1
0
0
0
0
0
0
2
0
1
0
2
2
0
2
0
0
0
0
0
2
2
2
1
0
2
0
0
1
1
0
0
2
1
2
2
0
1
1
2
1
0
0
0
0
1
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
3
0
0
1
2
0
1
0
1
0
1
2
0
3
0
2
1
0
0
2
0
0
0
0
0
1
2
2
0
0
0
0
1
1
1
0
0
0
2
0
0
2
0
0
1
0
0
2
2
0
1
1
1
1
1
2
0
0
0
2
2
1
0
1
0
1
0
2
2
1
1
1
1
0
1
0
2
0
0
1
1
1
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
1
4
0
1
0
1
0
1
2
0
0
1
0
0
0
2
2
0
2
2
0
1
1
0
2
1
0
2
0
1
0
0
4
0
2
1
0
0
0
0
0
0
0
2
0
0
3
2
1
0
0
0
0
0
1
0
2
1
1
0
0
0
1
2
0
0
0
0
1
1
0
0
0
1
0
1
1
2
1
2
2
1
2
0
1
0
0
2
2
1
0
1
1
0
1
1
0
0
0
1
0
1
0
0
2
0
0
0
1
2
2
1
0
2
0
0
0
1
1
2
1
0
0
1
0
0
1
2
1
1
1
1
0
0
1
1
0
1
0
1
0
0
1
1
0
1
2
1
0
5
0
2
0
0
0
1
2
0
2
1
0
0
0
0
2
0
1
2
0
1
2
0
0
2
2
0
1
0
1
0
1
0
2
1
1
0
1
4
1
1
0
0
0
0
1
1
1
1
2
1
0
2
1
0
1
2
0
0
2
3
0
1
0
0
0
0
2
2
0
0
0
1
2
0
1
1
2
0
0
0
0
0
2
1
1
0
1
2
0
0
1
0
3
0
1
1
0
2
1
2
1
0
0
0
0
0
0
2
0
0
1
0
0
2
0
2
0
2
1
1
0
1
0
0
0
2
0
1
0
0
1
0
2
0
1
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
1
1
2
1
0
2
2
0
0
0
1
2
0
0
2
0
0
2
0
2
2
0
0
0
1
1
1
0
1
1
0
1
2
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
1
0
0
0
1
1
1
1
1
0
0
0
1
0
2
0
0
0
1
1
1
0
0
0
2
2
1
0
1
1
1
3
1
0
1
0
1
1
1
0
2
0
1
2
0
2
2
1
2
1
1
1
0
2
1
1
0
0
0
3
2
1
0
0
1
0
0
1
0
2
1
1
1
0
2
1
0
1
2
2
2
2
0
1
2
2
0
0
2
0
0
1
0
2
0
2
1
1
0
0
0
0
2
2
0
2
1
0
0
2
2
1
0
1
0
0
2
1
0
1
2
1
1
1
2
0
2
0
1
0
0
1
1
0
0
0
0
1
0
0
0
1
0
2
0
1
2
0
0
1
0
0
1
2
1
1
1
1
0
1
1
3
2
0
0
0
0
0
0
4
2
1
0
0
2
0
0
0
2
2
0
0
2
0
0
0
1
1
1
1
1
1
1
0
2
1
1
0
1
1
1
0
2
0
1
0
0
2
2
0
2
0
0
0
0
0
3
2
2
0
0
2
0
1
0
0
2
1
2
0
0
0
0
1
0
2
1
0
0
1
1
0
0
1
0
1
0
2
0
1
0
0
0
1
0
0
0
0
0
0
2
1
0
1
0
2
0
2
0
1
2
0
0
1
1
1
0
2
2
0
2
3
1
1
0
0
0
0
0
0
0
1
0
0
1
1
2
0
2
0
0
1
0
0
1
1
1
0
0
1
1
0
1
0
1
1
1
1
0
0
2
1
0
0
0
0
0
0
0
2
1
1
0
1
0
0
1
0
0
0
0
1
1
0
0
2
0
0
2
2
0
1
0
1
2
2
1
2
0
0
0
2
3
0
1
0
2
0
2
2
0
0
2
1
4
0
2
1
1
0
1
2
0
2
2
0
2
0
0
0
0
0
2
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
1
2
0
1
0
0
1
5
1
1
1
0
0
2
1
0
0
1
0
0
0
1
1
0
0
2
2
2
1
0
2
1
1
1
1
0
0
1
2
0
1
2
1
0
2
0
0
2
0
1
1
0
0
1
0
0
0
0
1
1
2
2
0
2
0
2
1
1
0
0
0
1
2
2
2
0
1
1
0
2
0
2
0
0
0
0
2
1
0
1
1
3
2
1
1
1
0
0
2
2
0
3
0
0
0
1
0
5
1
0
0
0
0
0
1
1
2
0
0
0
2
0
2
3
0
0
1
0
2
2
2
2
0
0
1
0
0
1
0
0
0
1
0
2
0
1
0
2
1
0
0
1
1
1
0
1
0
0
1
0
1
1
1
3
2
0
3
3
0
0
0
1
1
2
0
0
1
0
0
1
0
2
1
0
1
2
0
0
2
0
0
1
0
0
0
0
0
1
1
0
0
0
1
2
0
0
1
1
0
1
0
1
1
2
0
1
2
0
3
2
0
1
0
0
2
0
0
0
1
0
0
0
3
2
1
0
1
0
2
0
0
0
1
1
0
0
2
0
1
1
1
0
0
1
1
2
1
0
2
0
1
0
1
0
0
1
0
0
2
0
0
0
1
0
2
0
1
0
3
1
0
2
1
1
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
3
0
2
2
0
1
0
1
1
1
1
0
0
1
2
1
1
0
0
1
1
0
0
1
0
2
1
0
2
0
1
1
0
0
1
1
0
2
0
1
2
0
1
0
0
2
2
1
1
2
2
0
2
0
0
1
1
1
1
1
0
0
1
1
0
2
0
0
0
1
2
3
0
0
1
1
2
0
0
0
1
1
0
1
1
0
1
0
0
2
0
0
0
0
2
0
2
1
0
0
0
1
0
0
0
0
0
2
2
0
1
0
0
1
0
2
0
0
0
2
0
0
0
0
1
2
1
2
0
2
3
0
1
1
2
0
0
1
1
0
2
0
1
1
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
1
2
1
0
0
0
0
0
0
1
0
1
0
0
1
0
2
0
2
0
2
0
1
0
1
0
2
0
0
2
2
1
2
0
0
0
0
0
0
0
1
0
1
0
1
1
1
1
2
0
0
2
0
0
0
0
2
8
0
0
0
0
1
2
3
1
0
0
0
0
1
0
0
1
2
2
1
0
2
0
0
2
0
0
0
2
0
0
2
0
0
0
1
0
1
1
1
1
0
1
2
0
1
0
2
0
0
1
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
2
0
0
2
1
1
1
0
0
1
0
0
0
1
1
1
1
0
2
0
0
0
1
0
1
0
0
0
1
2
0
1
2
0
0
0
0
1
2
2
1
4
2
0
1
0
0
2
1
0
2
1
0
1
0
2
1
0
1
0
0
0
2
0
0
0
0
2
2
0
0
0
2
0
2
0
0
2
2
0
1
1
2
1
0
1
0
0
1
1
0
2
0
0
0
2
0
2
0
1
2
0
0
1
0
0
2
2
2
0
1
2
0
1
0
0
1
2
0
0
3
3
1
1
1
0
0
0
2
0
0
4
1
1
1
1
1
1
1
2
1
2
0
1
0
0
1
1
0
2
1
0
0
0
1
0
0
0
0
0
0
1
1
1
1
1
0
0
0
1
0
0
0
0
0
0
6
0
2
2
0
0
0
1
0
1
1
1
1
0
1
1
2
1
0
0
1
0
1
2
0
2
0
2
3
1
3
2
0
0
1
0
0
2
1
1
1
1
0
0
0
2
2
0
0
2
0
0
1
2
0
1
0
1
1
0
0
1
1
0
0
2
0
0
0
0
0
1
0
0
2
0
0
1
0
2
1
2
1
1
0
0
0
1
2
1
1
0
1
0
1
2
0
2
0
0
0
2
0
2
0
0
0
1
0
1
1
1
2
0
0
1
1
0
0
1
0
0
2
1
0
1
2
0
0
2
1
2
2
2
0
2
0
1
0
0
0
0
0
0
2
0
2
1
2
0
0
2
0
0
0
2
2
0
0
1
1
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
2
2
0
0
1
0
0
0
1
0
1
1
0
0
0
1
2
2
0
1
0
0
1
0
1
1
1
2
0
1
2
2
1
2
0
2
1
1
0
0
1
2
0
1
1
0
2
0
1
2
2
0
1
0
0
1
2
1
1
0
0
2
0
0
1
0
1
1
0
2
0
2
0
1
1
1
1
2
0
1
0
0
2
0
2
1
1
0
1
0
0
0
0
0
2
2
1
0
0
0
1
2
2
0
1
1
1
0
2
0
1
0
0
0
1
1
0
0
0
1
1
0
0
1
1
0
0
1
2
2
0
0
2
0
2
0
0
0
0
2
1
2
0
0
1
0
1
1
1
1
1
0
0
0
0
2
0
0
0
0
0
1
1
2
1
0
0
0
0
0
1
1
1
0
2
0
1
1
1
0
0
0
1
1
0
0
0
0
4
0
0
0
0
0
1
1
2
2
2
0
1
3
0
0
1
1
0
2
1
2
1
0
1
2
0
0
1
0
0
0
1
0
1
1
1
0
0
0
2
0
1
0
0
0
1
0
0
1
0
0
2
0
0
1
0
1
0
1
0
1
0
2
2
0
0
2
1
0
0
1
0
0
1
1
0
1
2
2
0
0
0
2
2
2
1
1
1
0
0
2
0
1
0
0
0
1
1
0
1
0
2
1
0
0
0
1
1
1
1
2
2
0
0
1
0
0
0
2
0
2
0
0
0
1
0
2
4
1
0
2
2
0
0
0
1
1
1
0
1
2
0
0
2
2
1
2
1
0
1
1
0
2
0
2
0
1
1
0
1
1
0
0
0
0
0
0
0
1
0
1
0
2
2
1
1
1
2
0
2
2
0
0
0
1
0
0
0
0
0
1
0
1
2
0
0
0
0
2
3
0
1
3
1
1
1
0
2
0
0
2
0
1
0
1
2
0
0
0
0
0
2
1
1
2
0
1
2
0
0
0
0
2
0
1
0
1
1
1
0
0
0
0
0
2
2
0
0
1
1
0
1
0
0
2
1
0
0
1
2
2
0
0
2
1
1
2
0
0
1
2
2
1
1
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
1
0
0
0
2
0
3
1
0
1
0
0
0
0
2
0
2
1
2
0
0
0
2
2
0
0
1
2
2
1
0
0
2
0
0
0
2
1
0
0
0
0
0
0
3
0
2
1
0
0
3
1
0
0
1
0
1
2
2
1
0
3
0
1
2
1
0
1
1
0
0
1
0
2
0
0
0
2
0
0
0
1
0
1
0
2
1
1
0
1
1
0
1
0
1
1
2
2
0
0
0
1
2
0
2
0
1
1
1
1
1
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
2
1
0
0
0
1
1
1
2
0
0
0
0
5
1
1
0
2
1
1
0
1
2
3
1
0
2
1
0
0
2
2
1
0
0
1
1
2
2
0
2
0
1
1
0
0
2
0
3
0
0
5
0
1
0
1
0
1
2
0
0
2
1
1
0
0
1
2
0
0
1
0
0
1
0
0
0
1
0
0
0
3
1
1
1
1
0
2
1
0
1
1
0
0
0
0
0
0
2
1
0
0
0
0
1
2
0
0
0
2
0
2
0
1
0
1
1
2
2
1
0
0
0
1
0
1
1
1
2
0
0
1
0
1
1
0
0
0
0
0
2
1
0
0
1
0
2
2
0
2
0
2
0
1
0
1
0
2
1
0
0
1
1
2
0
0
0
0
1
0
0
2
1
1
0
0
0
2
0
0
2
0
0
2
1
2
0
0
0
2
0
1
1
1
1
0
2
0
0
1
2
0
2
0
1
1
0
0
1
0
2
2
2
1
0
2
1
1
0
0
1
1
2
2
1
2
1
2
0
1
1
0
0
1
0
3
1
1
0
1
0
1
1
0
2
1
0
1
1
2
2
1
0
1
2
1
2
2
0
0
0
3
0
0
1
0
1
1
0
0
0
0
3
1
1
1
0
1
2
0
0
1
1
0
1
0
0
0
1
1
2
2
1
1
2
0
0
0
1
2
0
1
3
0
1
0
1
0
0
2
1
1
0
2
1
1
1
0
0
2
0
1
1
2
0
1
2
0
3
1
0
1
0
1
0
0
2
2
2
1
2
0
1
1
0
2
2
1
0
0
1
0
1
2
3
1
0
0
0
1
0
1
0
1
0
1
0
2
0
0
0
0
2
1
1
0
0
2
0
2
2
0
0
0
2
2
0
0
0
0
0
0
0
1
1
0
1
0
2
0
1
1
1
1
2
0
2
2
0
2
2
3
2
1
2
0
0
2
1
0
0
3
0
2
2
2
0
0
1
0
0
0
1
0
0
2
2
1
2
0
0
2
1
1
1
0
1
0
1
1
2
0
0
0
1
0
0
1
2
0
1
0
0
1
0
1
0
0
0
0
1
0
0
1
1
1
1
0
0
1
1
1
1
1
1
1
0
1
0
0
0
0
2
0
0
1
1
0
1
2
0
1
2
2
3
2
0
0
1
0
2
0
1
2
1
0
2
1
0
0
1
0
1
0
0
2
0
0
1
0
1
0
0
0
0
0
2
0
2
2
1
0
3
0
0
0
2
0
1
2
2
0
0
0
0
2
0
0
1
0
0
1
1
1
0
0
1
1
1
2
1
1
0
0
0
1
0
2
1
2
1
0
0
1
0
0
2
1
0
0
0
1
0
0
2
0
1
0
1
1
1
0
0
0
0
1
0
1
0
0
2
1
1
2
2
0
1
2
2
1
0
0
0
3
2
2
0
0
2
0
0
0
4
1
1
2
2
2
1
2
0
0
1
1
1
1
2
0
2
0
1
0
0
0
1
1
0
1
1
1
3
0
0
1
0
2
2
1
1
0
0
0
1
0
0
2
2
0
0
0
2
0
0
0
0
1
2
1
0
0
0
0
0
0
0
1
1
1
2
2
2
0
0
1
0
1
0
0
1
0
1
1
2
0
2
1
0
0
1
0
2
2
0
0
1
2
1
0
2
1
0
2
2
0
0
2
0
0
1
1
2
2
1
1
1
0
2
0
2
1
2
1
0
2
3
2
0
2
0
2
1
0
0
0
1
2
1
0
1
2
1
3
2
2
0
0
1
0
1
0
1
2
0
2
2
1
0
0
0
0
1
0
1
1
0
0
2
0
2
0
2
1
2
3
0
1
2
2
1
1
2
0
2
1
0
4
0
0
2
0
2
1
2
1
2
2
0
1
0
0
0
2
0
2
0
2
0
0
0
2
0
0
1
0
1
1
0
1
1
0
1
0
1
0
0
0
2
2
2
1
0
2
3
0
0
0
1
0
2
0
1
1
1
0
0
0
0
0
2
0
1
1
1
1
0
1
1
1
1
0
0
2
0
0
2
0
0
0
0
1
1
0
2
2
1
0
0
1
1
0
0
1
1
0
0
1
0
2
0
0
2
1
1
0
0
1
0
0
1
0
2
2
1
1
0
0
0
2
0
2
0
1
0
2
1
0
0
0
0
2
1
0
0
0
1
1
0
2
0
0
1
1
0
1
2
1
1
0
0
0
0
1
0
0
0
2
1
0
0
0
2
2
0
0
0
0
0
0
0
1
2
0
1
0
1
0
0
1
0
0
0
0
1
0
2
0
3
2
1
0
2
1
0
1
1
2
1
1
0
1
2
0
0
0
2
1
0
0
1
0
0
0
0
0
1
2
2
0
0
1
1
0
2
2
1
0
0
1
1
1
0
2
2
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
1
0
1
2
2
0
0
2
0
2
1
0
0
1
1
0
2
1
1
1
2
2
2
0
2
1
0
0
0
0
2
0
1
1
0
1
0
0
1
1
2
0
2
0
0
1
1
0
1
0
2
0
1
1
1
1
1
2
1
1
0
0
0
0
2
0
5
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
1
1
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
4
0
2
0
1
0
0
0
0
0
0
1
0
2
1
2
0
0
1
0
1
0
2
1
0
0
0
0
0
0
2
0
1
4
1
0
2
1
2
1
2
2
0
1
1
0
2
0
0
0
0
0
0
0
0
1
1
0
2
0
2
0
1
1
0
1
1
1
0
1
1
1
2
0
2
1
2
2
1
2
1
0
0
0
2
0
3
1
1
2
0
1
0
1
2
0
1
1
2
2
0
1
1
0
0
2
0
0
0
2
0
1
2
0
0
2
0
0
1
0
1
2
1
0
1
0
1
0
0
0
2
1
2
0
1
0
3
0
1
1
2
1
3
0
1
3
1
2
0
0
0
1
1
1
0
0
1
0
0
2
0
1
0
0
0
1
0
0
0
1
0
0
2
0
0
1
1
0
2
0
1
0
1
0
1
2
1
0
0
1
1
2
2
0
0
0
0
2
1
0
2
0
0
1
1
0
0
0
1
1
1
0
1
1
2
1
1
1
2
0
6
2
0
2
1
0
2
0
0
0
1
1
2
1
2
1
0
0
1
0
1
1
2
2
1
0
0
2
0
1
2
0
0
2
0
2
0
2
0
0
2
1
1
0
1
0
2
0
0
0
0
3
2
0
0
2
2
1
0
1
0
0
0
1
1
0
1
1
0
2
0
0
2
1
2
0
2
0
0
1
0
2
0
0
1
0
1
1
1
0
3
0
0
0
0
0
0
0
1
0
2
1
1
0
1
1
2
0
0
0
0
0
2
1
1
2
2
1
1
0
1
1
0
1
2
0
1
1
1
1
0
0
0
0
0
0
0
0
1
2
0
1
0
2
1
2
0
1
0
1
1
0
1
0
0
1
1
2
1
0
0
0
1
1
1
0
1
0
1
0
0
1
1
0
0
0
0
0
1
1
2
0
1
1
0
0
2
2
3
1
1
0
1
2
0
1
0
2
0
0
1
0
0
2
1
0
2
0
0
0
0
0
1
0
2
0
1
0
1
1
2
0
0
0
2
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
1
1
0
0
0
0
3
2
0
2
0
1
1
3
1
0
1
1
2
2
0
1
0
1
2
1
0
0
3
1
0
2
2
1
2
0
1
1
1
0
0
1
0
0
0
0
1
0
0
0
2
0
2
0
2
0
0
1
2
0
0
0
0
2
0
2
1
1
0
2
2
0
0
0
0
0
0
2
1
0
1
1
0
1
0
0
1
1
1
2
2
0
0
1
0
1
0
0
0
1
0
0
1
1
1
0
0
0
0
1
2
0
2
1
0
0
0
1
2
2
0
1
1
2
2
0
1
0
1
1
0
2
2
0
0
1
1
0
2
0
1
0
0
1
0
0
1
0
1
1
1
1
1
0
0
0
0
1
0
0
0
1
1
1
0
1
0
2
1
0
0
1
2
3
0
0
1
3
0
0
0
2
1
0
1
0
0
1
1
2
0
2
0
0
0
2
0
0
0
1
2
0
0
1
0
1
1
0
3
0
2
1
0
1
1
0
0
0
1
1
0
0
0
1
1
2
1
2
5
1
2
1
1
0
1
1
2
0
0
0
2
2
0
0
2
0
2
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
1
1
0
0
0
1
0
1
1
2
0
0
0
1
1
0
0
1
1
2
0
0
2
1
2
0
2
1
0
0
0
1
1
1
1
1
2
1
1
0
1
2
1
0
0
2
2
0
1
0
2
2
1
0
2
1
1
1
0
2
0
0
2
0
1
1
0
0
0
0
2
0
0
0
0
0
2
0
1
0
1
0
0
1
0
0
0
0
0
2
1
0
1
2
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
2
1
0
1
0
0
0
2
0
0
0
0
1
0
0
1
0
1
0
1
1
2
2
0
2
0
0
0
2
0
1
1
0
0
1
0
1
0
0
1
0
0
0
1
2
1
1
0
0
1
0
1
2
1
0
0
0
1
1
1
0
2
1
0
0
0
0
0
1
1
1
0
0
2
0
0
2
1
0
1
3
1
1
0
0
1
0
0
0
1
1
0
1
1
0
1
1
0
1
0
0
0
0
1
1
0
0
0
1
2
1
1
0
1
2
0
0
0
0
0
0
1
0
0
1
0
0
1
2
0
1
1
0
0
0
1
0
0
2
2
1
0
1
2
1
0
2
0
1
0
1
2
1
0
0
0
0
2
2
0
0
1
0
2
1
2
1
3
2
0
1
1
0
0
0
2
0
0
0
0
0
1
0
1
0
1
2
1
1
1
1
0
1
1
0
0
1
0
1
1
0
2
0
1
1
0
1
0
1
0
0
1
0
0
2
2
0
0
1
0
4
0
1
1
2
0
0
1
2
1
0
0
0
0
3
0
1
6
0
1
1
1
0
0
2
0
1
1
1
2
0
0
1
0
1
0
1
1
1
1
1
0
0
0
1
2
1
1
2
2
0
0
0
2
0
0
2
0
0
0
0
0
1
0
1
0
0
1
1
3
2
0
0
0
1
2
0
2
1
1
0
0
0
0
2
2
1
1
2
0
1
0
1
1
0
0
0
2
0
2
1
0
1
1
0
0
0
1
0
0
1
1
0
0
2
1
1
0
0
0
0
0
0
0
0
2
2
0
2
1
0
0
1
1
0
0
0
1
1
1
1
0
0
0
0
1
1
1
2
1
0
0
1
1
2
0
1
1
2
1
0
0
2
0
0
2
0
0
0
2
1
1
0
0
0
0
0
3
2
0
0
1
2
0
2
1
1
1
1
0
1
1
1
0
1
1
0
0
0
0
2
1
0
0
1
0
0
2
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
2
2
1
1
0
0
1
0
1
2
0
0
2
0
0
2
0
2
2
1
2
1
0
2
0
1
1
0
0
1
1
1
1
0
0
1
1
2
0
2
1
0
0
1
1
1
2
0
2
0
2
2
1
2
0
1
1
1
0
0
0
2
0
1
1
0
0
2
1
0
2
1
0
0
0
0
1
1
0
1
1
0
2
1
0
1
0
1
1
0
0
2
1
0
1
0
0
2
1
0
0
0
1
0
1
4
0
2
1
1
2
0
1
1
2
0
0
0
2
2
0
1
0
4
0
1
0
0
1
0
0
1
2
0
1
1
2
0
1
0
0
1
0
0
1
0
0
0
0
1
0
2
0
1
2
0
1
1
0
1
2
2
2
1
1
0
1
2
1
0
1
1
0
1
0
1
1
2
1
2
1
1
1
2
1
0
0
0
0
1
1
1
2
0
0
2
0
0
0
0
0
1
0
1
2
0
0
1
0
0
0
0
0
0
3
2
2
0
1
0
0
0
0
1
1
0
1
0
1
3
0
1
0
0
2
0
1
0
2
1
0
2
0
0
2
2
0
0
0
1
2
1
1
2
1
2
0
0
1
4
1
1
1
2
0
0
1
0
0
0
0
2
0
3
1
0
0
2
0
2
0
0
0
2
1
0
2
1
0
0
1
0
0
0
0
2
0
1
0
1
0
0
0
0
2
1
1
1
2
0
1
0
0
0
0
0
0
0
0
1
1
2
1
2
1
0
0
0
0
0
0
1
1
2
1
0
0
1
0
1
1
1
1
2
0
1
0
0
0
0
2
2
0
1
1
0
2
0
3
1
2
0
1
1
0
0
3
2
1
2
1
1
3
1
1
2
2
1
0
2
0
0
2
1
1
0
1
1
0
0
1
0
1
0
1
0
0
0
1
3
1
1
0
0
2
2
0
0
1
1
0
0
0
0
1
1
2
0
0
1
1
1
4
2
0
0
1
2
1
1
1
2
1
1
0
0
1
2
2
1
0
1
0
0
0
1
1
2
0
1
1
2
0
0
1
0
2
2
0
0
2
0
0
0
2
1
2
1
1
0
4
1
1
0
0
1
0
0
0
0
2
0
1
0
0
0
3
2
0
0
0
0
2
1
0
1
0
2
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
2
1
0
2
0
0
0
1
1
1
2
0
0
2
0
3
2
0
1
0
2
2
0
0
2
0
1
2
2
2
0
1
1
1
2
1
1
3
2
0
0
0
0
1
0
0
2
0
1
0
2
2
0
0
0
2
1
1
1
0
0
0
1
0
1
0
1
0
0
1
0
1
0
1
1
0
0
0
0
0
0
3
2
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
2
2
0
1
0
0
2
0
0
1
0
0
1
0
1
1
2
1
0
0
0
1
1
1
1
2
0
0
0
0
2
2
0
1
0
0
0
0
0
1
0
2
2
0
3
2
2
1
0
2
0
2
0
3
0
0
3
0
1
1
3
2
2
1
0
1
1
0
1
2
2
0
1
2
2
2
1
1
1
0
1
0
0
0
1
1
1
0
0
0
1
2
0
0
0
0
3
1
1
0
2
2
4
0
1
1
0
1
0
1
0
0
0
1
0
0
1
1
2
1
2
4
2
0
2
0
0
0
1
1
2
0
1
1
1
1
0
1
0
1
2
0
0
0
2
0
2
2
1
0
1
3
1
0
1
2
0
0
1
0
0
0
0
1
1
0
0
1
2
0
1
1
1
0
2
1
2
0
0
0
0
0
1
1
2
0
1
3
0
2
0
1
2
1
3
0
0
0
2
0
0
0
1
2
1
0
1
2
0
0
1
0
2
0
0
1
0
0
1
0
1
1
1
0
1
1
0
0
0
1
0
1
0
1
1
1
0
2
1
2
2
0
0
0
0
2
2
0
2
0
2
0
0
1
0
0
2
0
0
1
2
1
1
0
0
1
0
1
1
2
2
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
2
1
0
2
0
0
0
1
1
1
0
1
2
2
1
1
2
2
3
0
2
1
0
0
0
0
2
1
0
0
1
0
2
1
2
1
1
1
1
0
0
2
1
2
1
0
0
0
0
0
0
0
1
1
1
1
2
1
0
2
0
1
0
5
0
0
2
0
1
1
0
0
2
1
1
1
0
1
0
0
3
0
1
0
0
0
2
0
2
2
2
0
1
0
0
1
2
0
2
0
1
1
0
2
0
1
1
2
0
2
0
0
1
1
0
1
0
0
0
1
1
0
0
0
2
0
0
2
2
1
1
0
0
0
1
1
0
0
1
0
0
2
1
0
1
0
2
4
3
0
2
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
1
0
1
0
1
1
2
0
0
2
0
2
2
0
0
0
2
1
2
2
2
0
2
0
1
0
0
0
0
1
2
0
1
0
0
2
0
0
0
2
0
1
0
2
0
0
1
0
2
2
0
0
1
1
1
1
2
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
1
0
1
0
1
0
0
1
1
0
0
1
0
1
1
1
1
0
0
1
0
0
1
1
0
0
1
0
1
1
0
2
1
0
1
0
0
0
1
0
1
1
1
0
2
0
2
4
0
0
2
2
0
0
2
0
2
0
1
3
0
0
1
1
0
1
0
2
1
0
1
1
1
0
1
1
0
0
0
1
2
0
1
2
0
0
0
1
0
0
2
0
0
1
1
2
0
0
1
0
2
2
0
0
1
0
2
0
2
0
0
1
2
0
2
0
0
0
2
0
3
0
0
2
0
2
2
1
2
2
2
0
2
0
0
1
0
2
2
0
1
0
0
2
2
1
1
2
0
0
2
1
2
0
0
0
1
0
1
1
0
2
1
0
1
0
0
1
0
0
1
0
2
1
1
2
1
0
1
0
0
2
1
0
0
4
0
1
3
1
0
1
1
1
1
0
0
1
1
2
0
0
0
2
0
0
2
1
2
0
0
0
0
0
1
1
2
0
2
1
0
2
1
1
0
2
0
2
0
0
0
0
2
0
0
1
1
0
0
0
2
3
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
2
0
1
0
2
0
2
1
1
1
0
1
0
2
1
1
0
0
0
0
2
0
0
0
2
2
0
2
0
2
0
1
2
0
0
0
2
0
0
2
0
0
1
2
2
1
1
3
2
1
1
1
0
1
0
1
2
0
1
0
0
0
2
2
1
0
1
0
2
0
2
1
2
0
2
0
1
0
2
1
0
0
0
1
0
0
1
1
1
0
0
1
0
0
0
1
0
0
1
0
0
1
0
1
0
0
1
0
1
0
0
1
0
0
0
0
2
0
1
2
1
0
2
0
2
0
3
2
0
0
2
1
1
4
0
0
0
0
1
0
0
0
1
2
2
1
2
0
0
1
2
0
0
0
0
1
0
1
0
0
0
2
0
0
0
1
0
0
0
1
1
1
2
2
0
1
0
1
0
2
1
2
0
0
0
1
2
1
2
1
0
0
0
0
0
2
1
1
0
1
2
1
1
0
0
0
1
0
2
0
1
1
0
0
0
0
1
1
1
0
0
2
1
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
1
1
2
1
0
0
2
2
2
0
0
1
1
1
0
0
2
1
1
2
0
1
0
2
0
0
0
0
0
0
2
1
2
1
1
0
1
0
0
2
3
0
1
0
0
0
0
0
1
1
0
0
1
0
2
0
1
3
0
0
1
0
0
1
0
0
1
2
0
0
0
2
0
1
2
1
1
0
1
0
1
1
0
0
0
2
0
0
1
2
0
0
0
1
0
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
2
0
0
0
1
0
1
0
0
1
0
0
1
0
1
0
1
2
0
0
2
1
1
1
0
0
1
0
0
1
0
0
0
0
2
0
0
0
1
1
0
0
0
2
1
0
0
4
1
1
1
0
0
0
0
4
0
0
0
0
0
1
1
1
2
2
1
0
0
0
1
0
0
3
0
0
1
0
0
2
0
0
1
0
0
2
0
2
0
2
1
0
2
0
1
1
2
2
0
0
2
0
0
0
2
1
0
0
0
0
0
2
1
0
2
2
1
0
2
1
2
0
1
0
1
1
1
0
1
0
0
1
2
0
1
0
1
1
3
0
0
2
0
2
2
0
2
1
0
2
0
0
0
1
0
1
2
0
0
1
1
0
0
0
0
0
1
0
1
0
1
1
2
1
2
1
1
1
1
1
2
0
0
0
1
1
0
1
2
2
0
0
1
0
2
0
2
2
3
0
0
2
0
0
2
0
2
0
0
1
2
2
0
1
0
1
0
0
3
2
0
1
0
0
2
1
3
0
1
0
0
2
2
0
1
0
0
0
1
1
1
1
0
1
2
0
0
1
0
0
1
2
2
1
0
0
1
2
0
0
1
0
0
0
1
0
0
0
0
1
0
1
2
0
0
0
0
0
1
0
0
1
1
1
2
0
1
0
1
0
1
1
1
0
0
0
0
1
1
2
1
1
0
0
0
0
0
0
1
2
1
0
4
0
0
1
2
0
2
0
0
1
2
0
0
1
0
1
2
2
0
2
2
1
1
0
2
1
4
0
2
0
2
1
1
3
1
4
1
1
0
1
2
2
2
1
0
0
0
2
0
0
0
1
0
2
0
0
0
0
2
2
0
2
2
1
2
1
1
0
1
1
1
1
1
3
0
2
2
0
0
0
2
0
0
1
0
0
0
2
1
1
1
0
0
1
1
0
0
0
2
0
0
1
2
2
0
2
4
0
2
0
1
0
0
0
0
0
1
1
0
1
1
1
0
0
0
5
1
1
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
1
0
1
1
0
0
1
3
1
0
1
1
0
1
2
1
0
0
0
0
3
0
1
0
1
0
2
0
1
1
0
0
0
1
2
1
0
0
1
2
0
2
0
0
2
1
1
1
2
0
1
0
2
0
0
0
2
2
2
3
2
0
0
0
0
2
0
0
0
0
0
0
0
1
1
2
0
0
0
1
0
1
2
0
0
1
1
1
3
0
0
0
0
0
0
2
0
1
0
0
2
2
1
0
2
1
1
0
1
1
1
0
2
0
0
1
2
0
1
1
0
0
0
1
2
0
2
0
0
1
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
1
1
0
1
1
1
0
0
2
0
0
0
1
0
1
1
0
1
0
0
1
1
0
0
1
1
1
2
1
0
0
0
0
2
0
0
1
0
2
0
0
1
2
1
3
2
1
0
2
2
0
2
1
0
0
0
2
0
0
2
0
0
1
0
0
0
2
0
2
0
0
0
1
0
1
0
1
1
2
1
2
0
0
0
2
0
1
0
1
0
2
2
0
0
0
2
2
2
0
0
0
0
1
2
2
4
2
2
1
1
0
0
1
0
2
2
2
0
1
0
1
0
0
9
0
0
1
0
1
1
0
0
0
2
0
0
2
1
0
0
2
0
0
1
0
4
0
0
0
0
2
1
1
2
2
0
0
0
0
1
2
2
1
0
0
0
0
0
0
2
0
1
1
0
1
0
3
0
2
0
0
0
0
0
0
0
4
1
0
2
0
0
1
1
1
0
1
0
5
1
1
1
0
2
0
2
1
0
1
0
2
2
1
2
0
0
0
2
2
0
1
1
1
1
2
2
0
1
0
1
0
1
0
1
2
0
0
1
0
0
0
1
0
1
0
2
2
0
0
0
0
0
1
2
0
1
0
0
0
1
2
1
0
0
1
1
2
1
0
1
1
2
0
1
0
1
0
1
0
0
0
0
2
0
0
0
0
1
2
1
1
0
0
1
0
1
2
2
1
1
2
0
0
1
2
0
0
0
1
1
0
2
1
1
0
0
1
1
0
0
1
0
1
0
2
2
0
0
2
0
2
1
0
0
0
2
2
2
0
2
0
1
1
0
1
2
0
1
1
2
1
0
0
0
1
1
0
0
2
0
0
0
0
2
1
0
1
1
0
0
0
1
1
0
2
0
2
1
2
0
2
2
0
1
2
0
1
0
0
0
0
0
1
0
0
0
1
0
1
1
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
2
2
0
1
2
2
0
0
0
1
1
0
0
1
2
0
0
1
0
1
0
1
0
1
0
1
1
0
0
1
4
1
1
2
0
0
1
1
0
0
0
1
1
0
0
1
0
0
0
1
2
0
0
1
0
0
0
0
2
0
0
0
0
2
2
0
0
1
0
0
0
1
2
0
0
0
0
1
0
0
3
0
0
1
1
0
1
1
0
1
0
0
2
0
0
0
2
1
0
0
0
0
1
1
0
1
0
1
0
2
0
1
0
1
0
1
2
2
0
2
2
2
2
1
0
1
2
1
2
0
1
0
0
0
1
1
0
0
2
2
2
0
1
0
0
1
2
0
1
3
0
1
0
0
3
0
2
0
1
2
0
0
0
0
0
1
0
2
0
2
0
0
0
2
0
0
1
2
0
0
0
0
1
0
3
0
2
0
1
1
2
2
2
1
2
2
1
1
0
0
2
2
0
2
1
0
1
0
0
0
0
0
1
1
1
1
0
1
1
1
0
1
1
0
2
1
0
0
1
4
0
0
0
1
0
1
0
1
1
0
2
3
0
0
3
0
1
1
0
1
2
1
0
2
0
0
2
1
1
1
0
1
1
0
0
0
0
0
0
0
1
1
2
2
1
1
1
0
1
1
0
0
1
0
0
0
2
1
0
0
1
1
0
0
0
0
2
0
0
0
0
1
0
1
0
1
0
0
1
0
1
0
0
0
1
2
2
0
0
2
1
1
2
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
2
1
2
0
0
0
0
0
2
1
1
0
0
0
0
0
1
1
0
0
2
1
1
2
2
0
2
1
1
0
2
0
0
0
0
0
1
2
0
0
1
2
0
0
2
1
0
0
1
1
1
0
0
0
0
0
1
0
2
2
0
0
1
0
1
3
0
1
0
0
0
1
1
1
0
1
0
1
3
0
0
1
0
0
0
0
1
1
2
0
0
1
0
1
0
1
2
3
0
1
0
1
0
0
1
1
0
2
1
2
0
0
2
1
0
2
0
1
0
2
2
0
1
1
0
2
1
0
0
0
1
1
0
0
1
0
0
0
2
0
0
0
1
0
2
1
0
0
1
1
2
0
0
1
1
0
2
0
2
2
1
0
0
1
1
0
2
0
0
1
1
0
0
0
1
0
0
2
0
2
1
1
0
0
2
0
1
0
2
2
0
1
0
1
0
2
0
1
0
1
1
1
1
0
1
0
0
2
1
0
1
2
1
1
1
2
0
1
0
0
2
0
1
0
0
2
0
1
3
0
0
0
2
2
0
0
1
0
1
2
2
0
0
0
2
2
0
0
0
1
0
0
1
0
1
0
1
1
1
0
0
2
0
2
1
2
2
0
1
0
0
1
0
0
1
1
1
0
2
3
1
0
0
2
0
1
0
1
2
1
0
2
1
0
1
2
2
2
1
0
0
2
1
0
0
2
1
2
0
0
0
1
0
0
0
2
0
0
2
0
2
0
0
0
1
0
1
1
0
0
2
0
0
0
1
2
0
1
2
0
1
2
0
2
1
0
1
0
2
0
0
0
2
1
1
0
1
1
0
0
0
2
1
0
1
0
2
0
0
1
3
0
0
0
0
0
1
0
0
1
0
0
0
2
0
1
0
2
2
1
2
0
2
0
0
2
1
1
0
0
3
2
2
0
0
0
1
2
1
0
1
0
0
0
2
1
0
1
1
1
2
0
1
2
0
1
0
0
0
0
0
1
0
0
2
0
0
1
2
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
2
5
1
2
0
0
1
0
0
1
0
1
0
0
0
1
1
2
0
1
1
1
0
1
3
2
0
0
0
0
2
0
0
1
2
0
0
0
1
0
0
0
1
1
2
0
2
1
1
1
1
2
1
0
0
0
0
0
2
0
0
2
0
0
3
0
0
1
2
0
1
0
2
0
2
1
0
0
0
0
0
1
0
0
2
0
0
0
1
0
2
2
1
1
2
1
0
0
1
0
0
1
0
0
0
2
0
0
0
1
2
0
2
2
1
0
0
2
0
1
0
2
0
1
0
0
0
0
2
1
1
1
6
0
0
1
2
0
2
2
1
2
0
2
0
0
0
1
0
0
2
1
1
1
0
2
1
1
1
1
2
1
0
0
2
0
0
2
0
1
0
0
2
0
1
1
0
0
0
0
1
0
1
0
0
1
2
0
2
0
1
1
3
0
0
0
2
0
1
1
0
1
0
1
2
0
1
0
2
1
2
0
0
1
0
2
1
2
1
2
2
0
1
0
0
2
0
0
1
0
0
1
0
0
0
0
1
2
0
3
0
0
0
1
1
1
0
2
0
2
2
1
0
1
1
0
0
1
1
0
1
2
0
1
0
1
0
1
0
0
2
0
1
0
0
2
2
0
2
2
3
0
1
2
1
1
1
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
2
2
2
0
0
2
0
1
0
2
1
0
0
1
0
1
0
1
1
0
2
0
0
2
1
0
0
0
0
2
0
2
0
0
0
1
0
1
0
0
2
0
0
4
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
2
4
0
0
1
2
1
0
2
0
0
0
0
1
1
0
0
0
1
0
0
1
1
0
0
1
1
2
0
0
0
0
2
1
0
2
1
2
1
1
0
1
2
2
0
0
0
0
0
0
0
1
1
0
0
2
2
1
0
1
0
2
1
0
1
0
0
0
1
1
1
0
0
1
0
2
0
1
2
0
0
0
1
0
0
0
0
2
0
1
1
0
0
1
1
2
0
1
0
0
0
0
0
0
2
2
0
0
0
1
1
0
0
1
2
0
1
1
1
0
2
4
1
0
2
2
0
0
0
0
0
0
0
1
1
1
1
0
0
1
0
2
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
3
0
1
0
0
2
2
2
0
1
1
0
2
0
0
0
0
2
1
0
1
0
3
1
2
1
0
1
2
0
0
1
0
0
0
0
0
1
0
2
0
1
1
2
1
0
2
2
2
0
1
0
0
2
2
0
0
0
2
2
0
2
0
1
0
1
0
0
1
1
2
0
0
0
1
0
0
0
1
0
1
3
2
1
0
0
0
0
0
1
0
2
0
2
1
1
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
1
1
2
0
1
0
0
0
1
0
0
1
2
2
0
0
0
1
2
2
2
1
0
2
2
1
1
0
0
2
1
2
0
0
0
0
1
0
1
0
0
0
1
1
1
1
0
0
2
0
0
0
2
2
0
0
0
0
0
1
1
2
1
1
2
1
1
0
0
1
2
0
0
0
1
0
0
0
0
0
2
1
1
0
1
0
2
5
2
2
1
2
2
0
0
0
0
0
0
2
1
3
0
1
2
0
1
0
1
1
1
0
1
1
0
0
0
1
2
1
1
2
1
1
2
1
0
2
1
0
2
0
2
2
0
0
0
0
0
1
0
0
3
0
2
0
0
1
0
0
1
0
0
0
0
1
1
0
1
0
0
1
1
0
0
1
1
2
0
0
1
0
0
0
0
2
2
0
2
2
1
0
1
1
1
2
0
0
2
3
1
0
0
2
1
0
1
2
1
2
1
1
2
2
2
2
0
1
0
0
0
1
0
0
1
1
1
1
0
1
0
0
0
0
1
0
0
2
0
2
2
1
2
2
0
2
1
0
2
1
1
2
4
0
0
1
0
0
1
0
2
1
2
0
2
0
2
0
1
2
0
3
1
0
1
2
2
0
0
1
1
0
0
1
0
2
2
1
1
1
1
0
1
1
1
0
1
1
1
0
0
1
2
1
0
0
0
2
2
0
1
2
0
0
2
0
1
2
2
1
0
0
1
2
0
1
1
0
0
1
2
1
0
0
1
0
0
0
1
2
2
2
1
1
0
0
0
1
0
2
1
1
1
1
1
0
2
0
0
0
1
0
0
0
2
0
1
2
0
3
0
1
1
0
0
0
1
1
2
2
2
0
1
0
1
2
1
2
0
2
1
0
0
2
0
0
0
0
1
1
1
0
1
2
0
1
1
3
0
1
1
0
0
0
1
1
2
0
0
0
2
1
0
2
1
0
1
0
2
0
0
0
2
2
0
0
1
1
0
2
1
0
0
2
3
0
2
2
0
2
0
0
2
1
0
2
0
0
1
0
2
1
1
2
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
2
0
0
0
1
1
0
0
1
1
1
0
0
4
0
5
1
1
2
0
0
0
0
0
0
0
1
0
1
2
1
0
0
0
1
1
0
1
2
0
2
0
2
0
1
2
1
0
1
0
0
1
2
0
0
1
1
1
1
2
0
0
1
0
0
0
1
0
2
0
1
1
1
1
1
2
0
1
1
0
0
1
1
0
1
0
2
0
1
0
0
0
1
0
0
0
2
1
1
0
2
2
1
0
1
1
1
2
2
0
0
0
0
2
0
1
1
1
0
1
1
1
1
0
2
2
0
0
0
2
1
0
0
0
0
0
0
1
0
2
3
1
1
0
1
1
1
0
1
0
0
1
0
2
1
2
0
2
1
1
1
0
1
2
0
0
0
1
1
0
0
0
1
1
1
0
0
0
1
0
2
0
1
0
1
0
1
1
1
1
0
0
0
0
0
0
2
1
0
1
0
0
0
0
1
2
0
2
0
0
1
0
3
0
0
1
0
0
0
2
2
0
0
0
0
2
1
3
0
2
0
1
0
0
0
2
2
1
1
1
1
0
0
2
1
2
1
0
0
0
2
2
2
1
1
1
0
1
0
0
2
2
0
0
1
1
0
1
0
1
1
2
0
1
1
0
3
2
1
0
0
0
2
0
1
2
1
0
1
1
2
0
0
0
0
0
2
3
0
0
3
1
1
0
0
1
1
0
1
2
0
0
1
0
1
0
0
0
1
2
0
2
0
1
0
0
1
0
1
1
2
1
1
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
2
0
1
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
1
1
2
3
1
2
1
0
3
0
0
1
0
0
2
0
0
4
2
1
2
0
0
1
1
2
1
0
3
0
1
0
1
1
1
0
1
0
2
0
0
0
2
0
0
0
3
1
0
2
1
0
1
2
0
0
1
0
0
0
0
0
0
0
1
3
2
1
0
1
2
1
1
0
0
0
0
2
1
0
2
0
2
1
0
2
2
0
0
0
0
1
4
1
1
2
1
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
1
1
1
0
0
0
1
0
0
0
2
0
0
1
2
0
0
0
0
1
0
0
2
0
1
1
4
0
1
1
0
0
1
0
3
0
2
0
1
0
0
1
2
0
0
1
2
2
2
1
0
1
2
0
2
0
0
2
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
2
1
1
0
0
1
0
0
0
0
0
2
4
1
0
1
1
2
1
2
0
0
0
0
0
1
0
2
0
0
1
0
1
1
0
1
0
0
0
1
1
1
2
2
0
1
1
0
0
0
1
0
0
0
1
0
1
0
1
0
1
2
0
0
1
0
1
2
0
1
1
2
0
1
1
0
2
0
0
0
0
2
0
0
0
1
1
1
2
0
1
0
1
0
1
0
0
2
1
2
0
1
1
0
0
0
0
1
1
1
0
1
0
0
0
2
2
0
0
0
0
0
0
0
2
2
1
1
2
2
0
2
0
2
2
0
0
0
1
0
0
0
0
1
0
1
0
0
2
0
1
0
0
0
0
1
2
0
2
2
1
2
0
0
0
2
0
0
1
2
2
1
0
0
2
0
0
2
2
1
1
0
0
2
0
1
0
0
3
0
0
0
0
2
0
0
3
0
0
1
0
1
1
0
0
0
0
1
0
0
0
4
0
1
0
0
2
0
1
0
1
2
0
0
0
0
1
0
0
2
2
0
1
0
0
0
1
0
0
1
2
0
1
2
0
0
1
0
1
1
0
0
2
0
0
0
2
0
0
1
2
0
0
1
2
0
0
0
3
0
1
2
0
0
1
0
0
2
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
2
2
2
0
1
2
1
0
2
0
1
0
2
0
2
2
1
1
2
3
0
0
0
0
2
1
0
0
3
0
1
1
2
0
1
2
1
0
0
1
0
0
1
1
0
0
1
1
0
0
1
2
0
2
0
0
0
1
0
1
0
0
2
1
2
0
0
1
1
2
1
1
0
1
0
1
3
0
0
1
2
0
1
2
1
1
2
1
0
0
0
0
1
2
1
2
0
0
2
0
0
1
0
2
0
0
1
2
1
0
0
0
1
2
0
2
0
2
0
1
0
1
1
0
1
2
1
2
1
0
2
2
1
0
2
0
0
1
2
0
0
1
2
2
0
0
2
0
1
0
0
2
1
2
0
2
1
1
2
0
0
0
0
0
0
0
2
0
0
0
1
1
0
2
2
1
0
1
0
0
0
0
0
1
2
2
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
2
0
2
0
1
0
2
2
1
2
0
2
1
1
2
1
0
0
1
2
1
2
2
2
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
2
1
2
1
2
0
2
1
0
1
0
1
1
1
2
0
1
2
2
0
1
2
0
2
0
1
1
0
0
2
2
1
2
2
0
1
2
2
0
0
2
2
2
0
0
1
0
0
2
4
0
0
1
0
1
1
0
1
2
3
1
0
0
1
0
2
1
1
0
0
1
0
0
0
2
2
0
2
1
1
3
0
2
0
2
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
2
1
0
0
2
0
2
0
1
2
1
0
1
0
1
0
2
2
0
2
3
1
1
1
0
0
0
1
1
0
0
0
3
0
2
1
2
2
0
0
2
2
2
0
0
0
1
1
2
1
2
0
1
0
2
1
1
1
0
1
1
0
1
2
1
0
0
0
0
0
2
1
0
4
0
1
1
2
0
0
1
1
0
2
2
0
1
0
2
0
4
0
1
0
0
0
1
1
0
0
2
1
2
0
1
0
0
1
1
2
2
0
2
1
1
1
0
1
1
0
0
1
0
2
0
0
0
1
1
1
1
2
2
1
1
3
0
0
0
1
0
1
1
0
0
0
2
0
2
1
0
1
0
2
2
0
2
2
2
0
0
0
0
1
1
1
0
2
0
0
2
1
2
0
0
2
0
0
1
0
0
0
0
0
0
1
1
1
0
1
0
2
0
2
1
0
2
1
0
1
1
1
0
1
2
0
0
0
1
0
0
1
3
2
0
0
2
0
1
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
3
0
2
0
1
2
0
0
1
2
0
2
0
0
0
0
0
0
0
1
0
1
2
0
0
2
0
1
0
0
1
0
0
0
0
0
0
1
3
0
2
0
1
2
0
0
1
1
1
2
0
1
0
1
1
0
2
2
0
1
0
0
1
0
0
1
2
0
0
2
2
2
2
0
0
2
2
0
1
0
1
2
0
1
0
0
2
1
1
0
0
0
0
1
1
3
0
1
0
2
0
2
1
1
1
1
0
0
0
1
0
1
2
0
0
1
0
1
0
0
6
2
1
2
0
0
2
2
1
0
1
1
0
7
0
0
0
0
1
0
0
0
2
1
0
2
0
1
0
1
0
1
1
0
1
0
0
1
0
0
1
1
1
1
0
0
1
1
1
0
0
0
0
0
2
0
0
2
1
0
1
1
0
1
2
1
0
0
0
0
1
2
2
0
0
1
4
2
0
0
0
0
1
1
0
0
2
0
1
1
0
0
1
0
1
2
1
1
1
0
0
1
0
1
0
4
1
0
0
1
1
2
2
2
1
0
0
1
0
0
0
0
2
2
0
1
1
2
0
0
0
2
1
0
0
0
0
1
0
0
0
1
0
1
0
1
1
0
2
0
2
1
2
0
0
0
0
0
2
1
1
0
3
0
2
1
0
0
0
0
0
0
2
0
0
0
1
1
0
2
1
0
0
0
1
0
1
0
0
0
0
0
0
1
2
0
1
1
0
1
0
0
0
2
0
0
2
2
1
0
4
1
0
1
2
0
1
1
1
0
0
1
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
2
1
0
1
0
1
1
2
0
0
1
1
0
0
0
0
0
0
0
2
1
0
0
1
0
0
1
0
0
0
1
0
1
1
0
2
2
0
2
2
1
1
2
2
1
0
0
2
0
0
2
0
2
2
1
3
3
1
1
0
2
1
2
0
0
1
1
0
0
2
0
0
0
0
2
0
0
3
1
0
0
2
0
0
0
0
2
1
0
0
0
3
0
0
1
1
1
0
0
0
0
1
0
2
0
0
2
2
2
0
2
1
0
1
2
1
0
2
2
1
0
0
1
0
1
0
0
0
0
1
0
2
2
0
1
0
1
0
2
1
0
1
0
1
1
1
0
1
0
1
2
1
0
2
0
1
0
2
0
1
2
1
2
0
2
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
2
2
0
2
0
0
1
1
1
1
1
1
2
0
2
3
2
2
1
2
0
0
1
0
2
2
1
0
1
1
1
0
1
1
0
1
0
0
1
2
1
0
2
0
3
1
0
2
0
0
0
1
1
4
1
1
0
1
1
1
0
0
1
1
2
0
2
0
0
0
1
0
0
0
1
0
2
1
0
0
1
0
2
0
0
0
0
1
2
3
2
0
0
0
0
1
1
0
2
0
0
2
0
2
0
2
0
1
1
1
2
0
0
1
0
0
2
2
1
1
0
1
2
2
0
0
1
0
0
0
0
1
2
0
0
0
0
1
2
1
0
1
0
1
0
0
0
1
0
2
0
0
1
0
0
0
1
0
1
1
0
0
1
1
2
0
1
0
0
0
1
2
0
2
0
0
1
2
0
2
1
0
2
0
3
0
2
0
0
1
0
0
0
0
1
0
1
0
2
0
1
0
1
0
2
1
0
0
1
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
1
2
1
1
0
1
0
0
1
0
2
0
0
0
0
1
0
2
2
0
2
2
2
0
2
2
0
0
0
1
0
1
3
0
1
0
1
2
0
0
0
0
2
0
1
0
0
0
2
0
1
1
2
2
0
0
1
0
0
0
0
1
2
1
0
1
1
0
1
0
2
1
1
1
0
0
2
1
1
0
0
0
0
1
1
0
2
1
1
0
1
0
0
0
1
1
0
0
0
0
1
0
0
1
1
0
0
1
0
1
0
1
1
1
0
0
1
0
0
0
1
1
2
0
0
0
0
1
1
3
2
0
2
0
0
2
2
0
1
2
0
1
0
1
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
1
2
0
0
1
8
0
0
1
1
1
0
0
1
1
1
0
2
1
2
0
0
0
0
1
1
2
0
2
2
0
1
0
1
2
0
1
0
1
2
1
1
0
0
0
2
0
0
0
1
0
2
2
1
0
2
2
0
1
1
1
0
0
1
0
0
4
2
1
0
1
1
0
0
2
0
1
0
0
0
1
0
0
0
2
2
0
1
1
1
1
2
0
1
1
0
1
1
0
0
1
0
1
0
0
0
0
2
1
4
1
0
0
0
0
2
2
0
1
0
0
2
0
0
1
2
0
1
0
0
1
0
0
2
0
1
0
1
0
0
1
1
1
0
1
2
2
0
0
1
0
0
0
2
0
0
2
1
2
1
0
0
0
1
0
0
0
0
2
0
1
0
1
0
0
0
2
1
4
0
2
1
1
1
2
2
0
0
1
1
1
2
0
0
0
0
0
1
1
0
1
1
0
2
0
0
2
2
1
1
0
1
1
0
2
1
2
2
0
0
1
1
0
2
1
0
0
2
0
0
2
0
2
0
0
1
0
1
0
1
2
1
1
0
1
0
0
0
0
0
1
2
0
0
1
0
0
2
1
0
0
1
0
0
2
0
0
0
1
0
2
0
0
2
0
0
1
0
0
0
0
0
1
0
0
1
2
1
0
1
2
0
0
1
2
1
0
1
1
1
2
0
0
2
2
1
0
0
0
1
1
0
0
2
0
3
1
0
0
0
0
0
0
0
2
0
1
2
0
2
0
1
0
1
0
1
2
1
0
1
1
0
0
1
0
1
2
1
0
1
2
1
1
2
0
0
2
0
0
2
1
1
1
2
0
0
0
1
0
0
1
2
0
0
0
1
0
0
2
1
0
0
1
1
0
0
0
2
0
2
1
0
1
2
1
1
0
0
0
1
1
0
4
1
1
0
0
0
1
1
0
0
0
1
0
2
0
1
0
0
2
1
1
0
1
0
0
2
0
0
2
2
0
2
0
2
0
2
1
1
0
0
0
1
0
1
2
1
0
0
0
0
0
0
0
2
2
1
0
2
0
6
4
0
0
0
1
0
1
0
2
0
2
0
0
2
2
4
0
2
1
2
2
1
1
0
2
2
2
0
2
0
0
1
2
0
2
0
0
1
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
1
2
1
1
1
0
1
0
2
0
1
2
0
1
0
0
0
0
1
0
2
0
0
0
1
1
1
3
2
0
0
1
1
2
2
0
0
1
0
1
0
0
0
1
0
0
3
1
1
1
1
2
0
0
0
1
1
1
1
0
1
0
2
0
0
0
2
2
0
1
0
0
2
2
1
2
0
1
1
0
2
0
2
1
0
1
1
1
2
0
0
0
0
0
0
0
1
0
0
0
1
3
0
2
0
0
0
2
0
2
0
2
1
2
0
0
0
0
0
1
2
0
1
2
0
0
1
1
1
0
0
2
2
2
0
0
0
2
0
0
0
2
3
0
1
0
0
1
1
0
2
0
2
2
0
0
0
1
0
2
0
2
1
2
1
1
0
0
2
2
0
2
0
1
0
1
1
0
0
3
1
0
0
1
0
0
1
0
0
0
2
1
2
0
0
2
2
0
0
0
3
2
0
1
0
1
1
0
3
0
2
1
1
2
0
1
0
0
0
1
0
0
0
2
1
0
0
1
0
2
1
1
0
0
1
1
2
2
0
0
2
0
0
0
0
3
0
1
0
0
0
1
2
0
0
0
2
0
1
2
0
0
0
0
2
0
2
0
1
0
0
0
2
1
0
0
0
0
2
2
0
1
1
1
1
0
0
0
0
2
1
1
0
1
2
2
0
0
0
2
0
1
2
1
2
1
2
1
0
0
0
2
0
2
1
0
0
1
0
1
1
0
0
0
2
2
0
1
0
2
0
2
0
2
2
2
0
2
1
2
0
1
0
0
1
0
1
0
1
0
0
2
0
0
2
1
0
0
1
0
0
2
1
0
0
0
0
2
2
0
0
2
0
0
0
2
1
1
4
0
0
1
2
1
1
0
0
2
1
0
0
0
1
2
0
0
1
0
0
0
0
0
0
1
2
2
0
2
1
0
2
0
0
0
3
0
1
1
1
1
7
1
0
0
0
0
1
0
0
1
1
1
2
0
2
0
0
1
0
0
1
0
0
1
0
1
1
1
0
0
2
2
1
2
0
2
2
1
1
1
2
1
0
2
1
0
0
2
0
0
0
0
1
0
1
0
0
2
2
1
1
0
2
2
1
0
1
0
0
2
0
0
0
0
1
1
0
0
1
2
0
1
0
0
0
0
0
1
0
1
0
0
0
2
2
2
0
2
2
0
1
0
0
0
1
0
2
1
0
1
1
1
2
3
0
0
0
1
2
0
0
1
2
0
0
0
1
3
1
3
2
0
1
1
2
0
2
1
0
1
0
1
2
2
0
2
1
1
2
2
0
1
1
1
0
1
0
1
0
0
0
0
0
1
2
2
2
1
0
1
1
0
0
2
0
0
0
0
2
1
4
1
2
0
2
0
2
1
1
5
1
2
1
2
0
2
1
2
0
1
0
2
0
2
0
1
2
0
1
0
1
2
0
1
2
0
1
3
0
0
2
0
0
1
0
0
2
1
0
0
1
0
0
0
1
1
0
1
1
0
0
0
0
1
1
1
0
0
0
2
2
0
1
2
0
2
0
0
0
0
2
0
0
1
0
1
2
2
2
1
0
1
4
1
1
0
0
1
0
1
0
3
0
0
1
0
0
2
0
3
1
0
2
1
2
5
2
1
2
0
1
0
2
1
1
2
1
0
2
0
0
1
0
0
0
2
0
2
0
1
2
0
0
0
1
2
1
0
0
2
0
0
0
2
0
0
0
1
0
2
0
2
0
1
1
0
0
0
2
0
0
0
0
2
1
0
1
0
0
1
0
0
0
0
2
0
1
2
0
0
0
2
2
1
2
0
1
2
1
0
0
2
2
1
4
1
2
0
0
1
1
0
3
1
0
0
0
0
0
0
2
0
1
1
1
0
1
1
1
0
1
1
1
0
1
2
0
1
0
2
1
0
0
0
1
0
1
1
0
1
0
1
0
2
1
1
0
0
0
1
0
0
1
1
1
1
2
0
0
0
2
1
2
1
0
1
3
0
2
0
2
1
1
1
0
2
2
2
1
0
0
0
1
2
0
1
1
0
2
1
2
0
0
0
2
0
1
1
2
0
0
1
1
0
0
0
0
5
0
1
0
2
0
1
0
0
3
1
0
0
1
1
1
0
0
1
0
2
1
0
2
0
0
1
1
2
0
1
0
0
1
1
0
0
2
2
2
1
1
2
0
0
0
0
1
1
0
1
0
0
0
0
2
0
0
1
0
0
0
1
0
0
3
1
2
0
0
0
3
1
0
0
1
1
2
1
0
0
2
0
0
2
1
1
2
0
0
0
1
2
1
2
0
0
0
1
1
0
1
0
0
2
0
1
0
1
2
0
0
0
1
1
2
0
0
1
0
1
0
1
0
0
0
0
1
2
1
1
4
3
2
2
1
2
2
0
1
0
1
1
1
0
1
0
1
0
0
1
0
2
0
0
2
2
0
0
0
2
2
2
1
1
0
2
2
1
0
0
1
0
3
1
0
0
1
1
2
1
0
0
1
2
0
0
0
0
2
1
0
0
1
2
0
1
1
2
1
2
0
0
0
1
1
2
0
3
1
0
1
0
1
0
1
3
1
2
0
1
0
0
0
2
1
0
0
1
0
0
0
1
0
0
2
1
2
2
1
0
0
2
2
2
0
1
1
1
0
0
2
2
1
1
0
2
2
2
0
0
1
1
1
2
0
1
1
0
0
1
0
0
1
0
0
0
0
2
1
1
0
0
1
1
0
0
2
0
1
1
1
0
2
0
2
0
1
2
1
0
1
0
0
1
0
1
1
2
2
0
2
0
0
1
1
0
1
0
2
0
0
1
1
0
2
1
0
2
2
0
0
3
2
0
1
1
2
0
0
1
1
1
0
1
0
1
1
0
2
1
0
0
4
0
0
0
0
1
0
1
2
1
1
0
2
0
0
1
0
0
2
0
2
1
2
0
0
0
1
1
1
1
2
1
1
3
2
0
0
0
0
0
0
0
0
0
1
4
0
0
1
0
0
0
3
0
0
1
0
2
1
1
1
0
2
2
1
0
0
1
0
1
0
0
0
1
0
2
2
0
1
1
0
1
0
0
2
0
1
1
2
1
1
1
2
0
0
0
0
1
0
0
1
1
1
1
1
1
1
2
1
0
2
0
0
0
1
2
0
0
1
1
0
3
1
1
1
2
1
0
2
0
1
1
0
2
0
0
1
2
1
2
1
0
2
1
0
2
2
0
0
1
0
0
0
0
2
0
2
0
0
1
2
0
1
1
0
2
1
1
0
0
0
1
0
2
0
0
0
1
0
2
0
1
0
0
0
1
0
1
1
1
1
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
1
1
0
2
1
1
0
0
1
3
2
0
1
0
1
0
2
0
2
0
2
1
1
2
2
0
0
2
0
0
0
0
0
0
0
1
2
0
1
1
0
0
0
1
0
1
1
2
0
1
1
2
3
1
2
1
0
0
1
1
1
6
0
0
0
1
0
2
0
0
0
0
0
1
0
2
0
0
1
1
0
0
0
1
2
1
0
0
1
0
1
2
2
0
1
0
0
0
2
0
2
1
2
0
1
0
0
0
0
0
2
0
0
1
0
0
1
0
0
1
2
0
0
0
1
1
1
2
1
1
1
0
0
2
0
0
0
2
1
1
1
0
1
1
1
2
2
2
0
2
0
1
0
1
2
0
0
0
1
1
2
1
2
0
0
2
2
0
0
1
0
1
0
1
0
0
0
0
0
0
1
2
2
0
2
0
0
2
1
1
0
0
1
0
0
2
0
1
2
0
1
0
1
2
1
0
1
1
0
2
1
0
0
1
1
0
1
0
3
1
1
1
0
1
1
1
2
0
0
0
0
0
0
0
1
0
1
0
0
1
1
2
2
2
2
1
1
1
0
1
0
0
0
0
0
1
1
0
0
1
2
2
0
0
1
1
0
2
0
3
1
0
0
2
0
0
0
5
2
1
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
3
2
1
0
0
1
1
1
0
1
0
0
1
0
0
0
2
1
1
2
0
0
0
2
0
1
3
2
1
0
0
0
1
1
0
1
0
0
0
2
0
2
2
1
0
1
1
0
3
2
0
0
1
0
1
0
0
0
1
2
1
0
0
2
0
2
1
1
2
5
0
0
2
1
0
3
2
0
0
0
0
1
2
0
1
0
1
2
0
0
0
0
1
0
0
2
1
1
0
3
2
1
2
0
1
2
1
2
2
0
0
0
0
1
0
0
2
0
1
1
0
2
0
0
0
0
0
0
0
2
0
0
1
1
0
1
1
1
0
0
1
0
1
2
0
1
1
1
2
1
2
0
1
3
2
0
0
1
1
1
1
0
1
0
2
0
0
2
1
0
0
2
0
1
1
0
0
1
2
2
0
0
0
2
0
0
1
0
1
1
2
0
0
0
2
2
0
0
1
0
2
0
0
0
1
0
0
0
0
0
2
1
1
0
1
1
0
0
0
0
0
1
0
0
0
0
1
2
1
1
0
1
0
2
2
0
2
0
0
1
0
0
1
1
1
1
0
0
0
2
0
0
0
1
0
0
2
3
1
0
1
1
0
0
1
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
2
0
1
1
0
0
0
1
0
1
1
4
0
0
0
0
0
2
0
0
2
0
0
1
1
1
2
1
0
1
0
0
1
0
1
1
0
0
1
1
1
0
1
3
0
0
1
0
0
1
1
0
0
1
2
2
0
0
0
0
0
1
1
1
1
0
0
2
0
0
2
1
2
1
1
0
0
0
0
0
1
0
2
2
0
0
0
2
0
0
0
0
2
0
1
2
1
1
1
2
0
0
2
0
1
0
1
0
1
1
1
0
0
1
0
1
1
0
1
2
0
1
2
2
3
0
1
0
0
2
2
2
0
0
0
0
0
0
1
2
1
3
0
0
2
0
0
0
0
0
0
2
2
0
0
0
1
0
2
0
0
1
1
0
1
0
2
1
0
0
1
2
0
0
0
0
0
3
2
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
1
1
0
0
2
2
2
0
0
1
1
0
0
0
2
1
0
1
0
1
2
0
0
1
0
2
2
1
0
2
4
2
1
1
0
0
1
1
0
0
1
1
1
0
3
0
1
2
0
1
1
2
1
0
1
2
0
0
1
0
1
0
0
1
1
0
0
0
0
1
2
2
1
0
2
1
0
0
0
2
0
0
1
0
0
0
1
0
0
0
2
2
0
3
3
2
0
0
1
1
3
1
1
0
0
2
0
0
2
0
1
2
2
0
0
0
0
0
1
2
0
0
0
0
1
2
0
0
1
0
0
2
2
2
0
1
0
1
1
2
2
0
1
1
2
2
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
2
1
1
0
0
0
2
0
1
1
0
0
1
2
0
1
1
0
0
0
0
0
2
0
0
1
1
1
2
1
1
1
0
1
0
2
2
0
2
1
0
1
0
2
0
1
0
0
1
0
1
0
0
0
2
2
1
1
0
0
0
1
1
0
0
1
1
0
2
1
2
2
1
0
0
1
2
1
0
1
1
0
0
0
1
1
0
2
0
0
1
0
2
2
2
0
0
1
0
3
0
3
0
0
0
0
0
0
0
0
2
0
0
0
1
1
1
0
0
1
0
0
0
0
1
2
2
2
2
0
0
0
2
0
0
0
0
1
2
1
1
0
0
0
0
0
1
2
1
0
0
0
0
1
1
0
0
0
0
1
0
2
1
4
0
0
1
0
0
0
4
0
1
1
3
0
0
0
0
0
1
1
0
2
1
1
0
0
2
1
1
1
0
1
0
0
1
0
0
1
0
2
0
0
1
1
0
0
0
0
2
1
0
0
2
0
1
1
1
1
1
1
2
0
1
0
0
0
0
1
0
2
0
1
2
1
0
0
0
0
2
2
2
1
0
0
1
1
1
0
1
0
0
0
0
0
1
2
0
0
0
0
2
1
0
1
1
0
1
2
2
1
2
2
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
1
0
1
0
2
1
0
0
0
1
2
1
2
1
2
1
0
1
1
0
0
2
2
1
0
2
2
1
0
1
1
0
1
2
2
0
1
0
1
0
0
0
2
2
0
0
1
0
1
1
0
2
0
1
0
0
0
0
3
0
0
0
1
2
1
0
0
0
2
0
1
1
0
1
2
0
1
0
0
1
0
1
0
0
0
2
0
2
1
1
1
0
0
3
0
2
2
0
1
1
2
0
0
0
0
1
0
0
0
0
2
1
2
0
0
2
4
0
1
2
0
0
0
1
4
1
2
1
1
0
1
0
0
2
1
0
0
0
0
0
1
0
0
0
1
1
0
2
2
5
1
0
1
1
0
0
2
2
0
0
0
2
0
0
1
0
2
0
0
0
1
0
0
0
2
2
1
2
2
0
0
0
0
2
1
2
2
1
0
0
1
1
0
2
0
1
1
0
1
1
1
0
0
0
1
1
1
0
0
0
0
0
0
0
2
0
2
0
1
1
3
0
0
0
1
0
0
1
2
1
2
0
0
1
1
1
2
0
0
1
2
0
0
1
0
2
2
2
1
0
0
2
1
0
2
0
2
0
0
1
2
2
0
2
1
1
2
0
5
0
1
0
0
3
0
0
1
2
0
2
0
1
0
0
2
3
2
0
2
0
0
1
0
1
0
2
0
0
0
2
1
1
0
0
0
0
1
0
0
0
1
0
2
0
0
1
2
0
0
0
0
0
1
0
2
0
0
1
0
1
0
1
0
2
1
1
1
1
0
0
0
0
0
2
0
1
2
2
2
1
2
0
0
1
1
1
0
0
0
1
1
0
0
2
1
0
1
1
0
1
1
3
2
0
2
0
0
1
0
0
0
0
0
0
2
0
1
1
1
3
0
2
0
1
0
0
0
1
2
1
0
2
2
0
0
0
1
0
1
2
0
0
0
0
0
0
1
0
0
0
1
2
0
2
0
0
0
1
1
0
0
1
0
0
0
2
1
1
1
0
0
1
0
1
0
0
1
0
2
1
2
2
1
0
1
1
3
2
0
0
1
0
0
0
0
0
3
2
0
0
2
1
1
2
1
0
0
1
0
0
0
1
0
1
0
1
0
1
0
0
2
1
1
0
2
1
0
2
0
1
1
1
0
0
0
3
0
1
1
0
1
1
2
0
1
0
0
1
1
0
2
2
0
0
0
0
0
0
0
1
0
2
0
2
1
0
1
0
2
1
1
0
0
1
1
0
8
0
0
1
2
2
0
1
1
0
1
0
2
2
0
0
2
0
1
3
2
2
0
0
2
0
1
0
0
0
1
0
1
0
1
1
2
1
1
2
0
1
0
2
2
0
0
2
1
0
1
2
2
0
0
1
1
0
0
0
2
0
2
0
2
1
1
1
0
0
1
1
2
1
0
1
0
0
1
1
0
0
1
1
2
1
1
0
0
1
1
0
1
2
0
2
0
0
1
0
1
1
0
0
1
0
2
2
1
3
0
1
0
1
0
2
0
0
0
0
1
1
2
0
1
0
0
1
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
2
0
0
1
2
2
1
2
0
0
0
1
1
0
1
0
1
0
0
2
0
2
1
0
1
2
0
2
0
1
0
2
2
0
0
0
0
1
2
1
1
2
3
0
0
2
1
0
0
0
2
0
1
2
1
0
0
2
0
0
1
1
1
1
1
3
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
1
1
0
0
2
0
1
0
1
0
1
0
0
2
0
1
2
0
1
0
1
1
1
0
2
0
1
1
1
2
1
0
2
2
0
0
0
2
1
0
2
0
1
0
1
0
1
2
1
0
0
1
0
0
0
0
0
0
1
0
1
0
2
0
2
2
1
2
1
2
1
0
3
3
0
2
0
0
0
1
2
1
0
1
1
0
0
1
2
2
0
1
0
1
1
1
0
1
0
0
0
1
2
0
0
1
0
4
1
1
0
2
1
1
1
0
0
1
1
1
1
2
1
1
0
0
2
3
0
0
0
0
2
1
0
1
1
0
0
1
1
2
2
1
1
1
1
2
2
0
2
0
1
0
0
1
0
0
0
0
1
2
1
1
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
1
1
1
0
1
1
1
0
0
0
2
0
2
2
1
0
1
2
1
1
2
1
1
0
0
2
0
1
0
0
1
2
0
0
0
1
0
2
0
1
0
0
1
0
0
1
1
0
0
1
0
0
0
0
1
2
1
0
1
1
0
2
0
1
0
1
0
1
0
1
1
1
1
2
2
0
1
1
0
0
1
1
2
0
0
0
2
1
0
0
0
0
1
6
1
1
0
1
2
2
0
0
2
0
1
1
1
1
0
0
1
1
1
2
1
1
0
0
0
1
1
0
2
0
0
0
1
0
0
0
0
2
2
2
0
0
1
0
2
10
0
1
0
2
1
0
1
1
1
1
0
1
1
0
2
2
2
0
0
2
0
0
1
4
1
1
0
1
0
2
0
1
0
0
1
2
0
0
2
0
0
0
0
1
1
0
2
0
2
0
2
0
0
0
0
2
2
2
0
0
1
1
0
0
0
0
1
1
0
1
0
0
1
0
1
1
2
3
0
2
1
0
1
2
0
2
1
0
2
1
0
1
1
3
0
1
1
2
0
0
0
0
2
0
2
0
0
1
2
0
2
1
1
0
0
0
1
0
0
1
2
0
2
2
0
1
0
1
2
1
1
0
0
0
0
2
2
0
1
0
2
0
0
1
0
0
1
0
2
1
0
2
0
2
2
2
1
0
2
0
0
0
1
1
1
0
0
1
1
0
0
0
2
2
0
0
1
1
0
1
1
2
1
1
1
2
0
0
2
1
2
0
0
1
0
0
1
0
0
2
1
0
0
0
0
0
0
0
1
1
0
2
0
1
2
2
0
0
2
0
2
1
0
0
1
1
2
0
0
0
1
1
2
0
0
0
0
0
2
2
1
1
2
2
2
1
1
0
0
1
2
1
0
0
0
2
0
2
0
1
1
0
2
0
0
0
3
0
1
2
0
0
0
2
2
1
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
2
1
3
0
0
1
1
1
0
1
0
0
0
1
2
1
1
0
0
0
0
1
2
0
0
2
2
0
0
2
0
0
1
0
0
0
2
1
1
1
2
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
2
0
1
0
0
0
0
1
0
0
0
2
1
0
2
1
1
1
0
1
1
0
1
1
0
0
1
0
0
2
0
0
0
2
0
1
0
1
0
1
2
1
0
0
1
2
2
0
2
0
0
1
1
0
2
2
0
0
1
1
0
1
2
1
0
1
1
1
1
0
2
0
0
1
0
0
1
2
0
0
0
0
0
0
1
0
2
0
0
2
1
1
1
1
0
0
0
0
0
2
4
0
0
1
0
0
1
2
0
0
2
1
1
0
1
2
0
0
0
2
1
0
0
2
0
0
0
1
0
1
0
0
0
1
2
1
2
2
1
0
1
0
0
0
0
0
0
0
1
1
0
2
0
1
0
1
0
1
1
1
0
1
0
1
0
1
1
2
0
1
0
1
1
2
2
1
1
1
0
1
0
2
0
0
0
1
0
1
2
0
0
2
1
1
2
0
0
1
2
1
0
0
1
0
1
2
0
0
0
0
1
0
1
0
1
0
8
0
0
1
2
0
0
0
0
0
1
0
0
1
0
0
3
1
1
2
0
2
0
1
0
2
0
2
0
0
0
0
1
2
0
1
0
0
1
0
1
7
1
0
0
2
2
0
1
0
2
0
0
0
1
0
0
1
0
0
2
2
0
0
1
1
1
0
0
0
0
2
0
2
1
0
0
2
0
0
0
0
1
1
0
1
1
2
2
0
0
1
0
1
1
2
2
0
1
0
1
1
2
1
3
1
2
0
2
2
1
1
1
1
0
0
0
1
0
0
2
0
2
0
0
0
0
1
0
0
1
0
0
1
1
0
1
0
0
0
0
1
0
2
0
1
2
1
0
0
1
0
2
1
2
1
0
2
0
2
0
0
0
0
0
1
1
2
0
0
0
2
2
0
0
1
1
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
1
2
2
1
2
1
2
0
0
0
2
0
1
0
0
2
1
0
0
2
2
1
0
1
3
0
0
0
1
2
0
0
1
1
0
0
1
2
1
1
0
2
1
0
1
0
0
1
0
2
0
1
0
1
0
0
1
0
1
0
0
0
0
0
2
1
0
1
1
2
1
0
0
0
0
2
0
2
1
0
1
1
0
0
0
1
2
1
0
1
1
2
1
0
0
0
1
0
3
0
1
0
1
0
2
1
0
2
1
1
3
1
2
1
0
0
1
3
1
0
2
0
1
0
1
0
2
2
2
2
1
0
0
1
1
1
0
1
0
0
4
2
0
0
1
1
0
0
2
2
2
0
2
0
0
2
2
1
0
0
0
1
1
1
2
0
1
2
0
2
2
0
0
1
1
0
2
1
0
2
1
1
2
1
0
1
1
0
1
2
0
1
2
0
0
3
1
0
3
0
0
2
0
1
0
0
0
1
0
0
0
0
3
1
0
0
1
1
0
0
0
0
0
1
1
1
2
0
1
0
1
1
0
1
0
0
0
1
2
0
0
0
0
0
2
0
1
1
2
1
0
2
2
0
0
0
2
0
2
0
2
1
0
0
0
1
0
1
0
2
2
1
2
1
0
1
0
1
2
1
0
1
2
0
2
2
1
1
0
0
1
0
0
2
1
0
1
0
1
0
0
1
0
2
1
0
0
0
0
1
0
2
2
0
0
0
2
1
2
0
2
0
0
0
1
0
0
0
2
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
1
4
0
0
1
0
0
0
0
2
1
1
1
2
0
0
2
0
0
0
1
1
1
2
1
0
1
0
0
0
2
1
0
1
0
0
1
2
2
1
2
2
0
1
1
0
2
1
1
0
1
3
0
2
1
0
0
2
0
0
1
0
1
0
1
0
4
1
1
0
2
0
0
0
2
0
0
0
1
1
0
1
2
0
0
1
0
1
0
2
0
0
0
2
0
1
0
0
0
0
0
2
0
1
2
0
1
0
1
0
0
2
0
0
0
0
1
1
0
0
0
0
1
1
1
0
2
2
0
1
4
0
3
1
0
2
0
1
0
1
1
0
0
0
0
1
0
2
0
1
0
3
2
0
1
1
2
0
0
1
0
0
1
0
1
1
1
2
0
2
2
1
0
1
1
0
0
1
2
0
0
1
0
2
0
1
0
0
2
0
1
0
1
1
0
1
2
2
0
1
0
1
0
0
1
2
1
1
1
0
0
1
0
2
0
1
0
0
2
1
0
0
4
0
1
4
0
2
0
0
1
0
2
0
1
0
0
2
1
2
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
2
1
0
1
0
1
0
1
2
2
0
0
0
0
0
1
0
1
1
1
0
0
0
2
1
1
0
0
2
1
0
0
2
1
0
2
0
0
0
0
2
2
0
0
1
2
1
0
1
1
0
2
1
0
0
1
0
2
1
2
1
0
0
1
2
0
0
0
1
1
1
1
0
2
0
2
0
0
1
0
2
2
2
2
0
0
1
2
0
1
1
0
2
1
0
1
0
0
0
1
2
0
2
1
0
0
0
1
1
0
2
0
2
2
4
1
1
2
2
0
1
2
0
0
1
1
2
0
1
0
1
3
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
1
2
0
1
1
1
1
1
0
2
0
0
2
2
0
1
1
1
0
0
1
1
0
1
2
1
0
0
2
2
1
1
0
0
0
2
0
0
0
2
0
1
0
0
1
2
1
1
0
0
0
0
0
2
0
2
1
0
2
1
2
1
0
0
0
0
2
2
1
2
1
0
1
0
1
1
0
0
0
1
1
0
0
1
0
2
1
0
0
2
1
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
1
2
2
3
0
1
0
1
2
2
1
0
2
0
1
0
0
0
1
1
1
1
0
0
2
1
0
0
2
2
0
0
0
0
0
1
0
1
0
2
0
2
1
0
0
0
2
0
2
2
2
1
0
0
0
0
0
2
0
1
1
0
1
1
0
2
2
2
2
0
0
1
0
2
1
0
0
0
1
0
1
1
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
2
2
0
1
2
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
2
1
0
1
1
1
2
0
1
0
0
0
2
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
1
1
0
0
1
1
1
1
2
0
1
1
0
2
1
0
0
0
0
0
2
0
1
0
2
2
0
2
0
1
1
1
2
0
2
0
1
2
1
1
1
0
0
0
0
0
0
2
0
1
0
0
1
1
0
1
0
0
1
0
1
2
2
0
0
0
0
0
1
0
1
2
0
0
0
1
2
2
8
0
0
1
0
2
1
0
0
2
2
3
1
1
1
2
2
0
1
2
2
1
1
1
0
0
2
0
0
0
1
0
0
2
2
1
3
1
1
0
2
1
0
0
0
0
0
1
1
1
1
0
0
0
0
1
3
2
2
0
0
0
0
2
2
1
0
0
0
1
2
1
1
2
4
1
1
0
2
1
0
2
1
1
2
0
0
1
0
2
0
1
0
2
0
0
2
1
0
2
0
0
1
2
0
1
1
2
1
2
1
2
0
0
0
1
0
1
0
0
1
1
0
1
0
0
2
0
0
1
1
0
1
0
2
0
0
0
0
0
1
2
0
0
1
1
0
1
0
0
0
0
0
0
1
1
1
2
1
0
2
0
1
1
0
0
0
0
0
1
2
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
1
2
1
1
1
1
0
0
0
0
1
0
1
0
0
1
2
2
0
0
0
0
1
1
1
0
2
1
1
0
2
2
2
0
3
0
2
0
1
0
0
0
0
1
0
2
1
0
0
1
0
0
1
1
0
0
2
1
0
1
2
2
2
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
1
0
0
0
1
1
1
0
1
0
0
1
0
0
2
0
0
0
0
0
2
3
0
2
1
2
0
1
0
2
0
1
1
0
1
1
1
0
0
0
0
0
2
1
0
0
2
2
0
0
2
1
1
1
1
1
0
1
1
0
0
0
2
1
2
1
2
1
4
2
0
0
1
2
0
0
0
0
1
0
2
1
1
1
1
0
1
0
1
0
1
1
0
1
1
0
2
1
0
1
0
0
1
1
0
1
1
2
2
0
1
0
0
0
0
2
1
0
0
2
3
0
1
1
2
0
1
1
0
2
0
0
1
1
0
1
2
0
0
1
0
0
2
0
0
1
1
0
1
2
1
0
2
0
2
1
1
2
2
1
1
2
0
2
0
0
3
0
0
0
0
1
0
1
0
0
1
0
1
1
0
0
1
1
1
2
0
1
1
0
0
0
1
1
0
1
1
0
2
1
0
2
2
1
0
1
0
2
0
0
1
1
2
0
0
0
1
1
0
2
2
0
0
0
1
0
1
0
1
2
0
1
0
0
1
0
0
2
1
0
0
0
0
0
2
2
0
1
1
0
1
2
1
1
2
0
0
0
2
0
0
1
1
13
1
1
2
0
0
0
1
1
1
3
0
0
0
0
0
0
1
0
0
0
1
0
1
2
0
0
1
0
1
0
2
0
2
3
0
0
1
0
0
1
0
0
1
0
1
0
2
0
2
1
2
0
0
1
0
1
0
1
0
2
0
0
0
2
2
2
0
0
0
0
1
0
2
1
2
1
2
1
0
2
2
2
2
0
1
2
2
1
1
0
0
1
1
0
0
0
1
0
1
0
1
0
2
0
2
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
2
1
1
0
1
0
0
0
2
0
2
1
1
0
0
1
0
0
0
2
1
1
0
2
2
0
0
2
1
1
0
0
0
0
0
0
2
0
0
1
2
0
0
1
1
0
1
0
2
2
2
1
0
0
0
0
0
0
1
1
0
2
0
0
1
3
0
0
1
1
0
0
2
1
0
0
2
1
1
0
0
1
2
0
1
0
1
1
1
2
2
1
0
0
0
2
1
0
0
1
1
0
2
0
1
2
0
1
2
1
2
2
2
0
0
0
1
1
0
1
2
0
1
1
1
2
0
0
2
0
1
1
0
1
0
2
2
3
0
3
0
1
0
2
0
1
1
0
0
0
0
0
0
2
0
2
2
2
0
0
1
0
0
0
1
0
0
0
0
2
0
2
0
0
0
1
2
1
1
2
0
0
2
1
0
3
2
0
2
2
0
2
0
0
0
1
1
1
0
1
1
1
0
3
1
1
2
1
1
1
0
0
2
2
1
3
2
1
0
0
0
0
1
1
0
1
2
1
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
2
0
1
0
0
0
1
0
1
1
0
0
0
2
1
2
0
2
2
1
0
1
1
0
1
1
1
0
0
0
1
2
3
0
0
0
0
0
0
1
0
2
0
0
1
1
0
1
2
1
0
1
0
0
1
0
1
0
2
0
0
0
2
0
0
0
0
0
1
1
2
0
0
1
2
1
0
2
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
1
2
3
1
1
0
0
1
0
0
0
2
1
2
2
1
0
1
2
1
1
0
0
3
2
1
0
0
1
1
0
2
1
0
0
0
1
1
3
2
0
2
2
0
0
0
0
1
2
0
1
0
0
0
0
2
0
1
0
2
0
0
0
0
1
1
1
2
0
2
0
0
0
4
0
0
2
0
1
0
3
0
1
0
0
2
2
2
0
1
1
1
2
0
0
0
1
0
0
0
1
0
0
0
0
0
2
1
0
1
1
0
0
2
0
0
2
0
1
0
1
0
1
1
0
1
0
1
1
2
0
0
1
4
0
1
1
0
0
0
1
0
0
0
0
2
1
1
1
2
0
0
0
2
0
0
1
0
1
0
1
0
1
0
0
0
2
0
2
0
0
0
0
1
0
1
2
1
0
1
1
0
0
1
0
1
1
2
1
1
2
1
0
2
0
0
2
0
1
0
0
1
2
1
0
1
0
1
1
0
0
0
0
2
1
0
2
0
0
1
1
1
0
0
0
0
0
1
1
0
1
1
1
2
0
0
1
1
0
1
0
2
1
1
0
0
0
1
0
1
0
1
0
1
0
1
0
0
1
0
0
0
1
0
1
0
0
0
1
1
0
2
1
2
2
0
2
2
2
2
0
1
1
1
0
0
1
1
1
1
0
0
1
2
2
1
0
0
2
0
1
1
1
0
0
1
0
0
1
2
2
0
0
0
0
1
0
1
0
1
2
1
2
0
2
0
0
0
2
0
2
1
2
1
1
0
1
0
2
1
1
1
1
1
0
1
1
0
1
2
1
0
1
0
1
0
1
0
2
1
2
2
0
1
0
0
1
1
0
1
1
1
0
1
2
0
0
1
0
0
0
2
0
0
0
1
3
2
0
2
0
1
0
2
1
1
2
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
2
1
1
0
1
0
2
1
2
0
0
0
1
0
0
0
0
1
1
1
2
1
0
3
1
3
0
1
1
1
0
2
0
0
0
2
0
1
2
1
2
0
1
0
0
0
2
0
0
3
1
0
0
0
1
2
0
1
0
0
0
1
1
2
2
1
0
2
1
1
2
2
2
2
1
0
1
0
0
1
2
1
1
2
0
2
2
2
0
0
0
0
0
0
0
1
1
1
0
1
2
0
0
0
1
0
1
0
0
0
1
2
0
0
1
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
2
1
1
0
2
0
0
0
0
1
0
0
1
2
0
0
1
2
1
2
2
0
0
1
0
2
2
0
2
1
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
2
0
0
1
0
0
1
0
1
1
0
1
0
0
0
0
0
1
1
1
0
0
0
1
2
4
0
0
2
0
1
0
2
0
1
0
0
1
0
1
0
2
2
0
0
2
0
2
0
2
0
2
0
2
2
2
0
2
2
2
0
0
1
0
0
0
0
0
1
0
0
2
2
0
1
0
0
0
0
2
0
1
0
0
0
0
3
0
2
1
2
2
0
0
2
1
1
1
0
0
1
0
1
0
1
1
2
0
0
1
1
1
2
1
0
1
2
0
0
0
2
0
2
0
0
0
0
1
3
0
1
0
0
1
1
1
1
1
3
0
2
2
1
0
2
0
4
0
0
0
0
0
1
1
0
1
2
2
0
0
2
2
0
0
0
0
1
0
2
1
1
0
1
0
1
0
0
2
0
1
3
0
2
1
2
2
1
2
0
1
0
2
2
2
0
0
2
0
1
1
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
1
0
2
1
2
0
2
0
1
1
2
1
0
0
2
0
0
2
0
1
1
0
1
1
1
0
2
1
2
0
1
0
1
1
0
1
1
2
0
0
0
0
0
2
0
3
0
0
2
0
0
2
0
2
2
0
1
2
0
0
1
1
2
0
0
0
1
0
0
1
1
2
1
4
2
0
0
2
2
1
0
1
0
1
0
0
2
0
0
1
2
0
2
1
1
1
0
2
0
0
1
0
0
2
0
2
1
0
0
0
1
0
0
0
0
5
0
0
0
1
0
11
0
1
0
1
0
2
1
1
0
0
1
1
1
0
0
0
0
1
1
2
2
0
0
1
0
1
1
0
2
0
0
0
1
2
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
4
0
1
1
0
0
0
0
1
0
0
1
0
2
0
0
0
1
0
4
0
0
2
1
1
0
0
0
1
0
2
0
1
2
0
2
0
1
0
0
0
0
1
0
1
2
1
0
0
3
0
2
1
2
0
0
0
3
2
0
2
0
1
0
1
0
2
1
0
3
2
2
0
0
0
0
0
0
1
0
2
0
0
1
0
0
1
0
0
1
1
1
2
1
1
0
1
2
0
0
0
1
0
1
1
0
1
2
0
1
0
0
2
0
2
1
1
0
0
1
0
1
0
1
2
0
0
0
1
1
0
2
0
0
0
0
0
0
0
2
1
1
2
1
2
0
4
0
0
1
2
0
1
0
2
0
0
0
0
0
2
2
2
0
1
1
0
1
0
1
1
0
2
0
0
1
0
0
0
1
1
0
0
0
1
0
0
2
0
0
2
1
0
2
3
0
2
1
1
2
0
0
0
2
0
0
2
2
1
0
1
0
0
2
0
1
1
1
1
0
0
2
0
1
2
1
0
2
1
3
0
2
0
0
0
2
0
2
1
0
1
0
2
0
2
0
0
2
1
1
0
1
1
0
0
1
1
1
1
2
0
0
0
1
0
2
1
0
1
2
1
0
1
0
0
0
0
1
0
0
2
1
0
0
0
0
1
1
0
0
0
3
0
0
0
2
1
0
0
0
0
0
0
2
2
0
0
1
2
2
1
0
1
0
2
1
0
1
0
2
0
0
1
0
0
1
2
1
0
0
1
0
1
1
1
1
2
1
0
0
0
4
0
1
1
0
0
0
0
1
1
0
1
0
1
0
3
0
2
4
1
0
1
0
0
0
2
0
1
0
2
0
0
1
1
1
2
1
2
2
0
0
2
0
2
2
0
1
2
0
0
0
0
1
0
1
3
2
2
1
1
0
0
0
0
0
0
3
0
1
2
1
1
0
1
0
0
0
1
0
0
0
2
1
1
0
0
1
0
1
0
2
2
1
2
0
2
0
1
1
2
0
4
0
0
2
0
0
0
0
0
0
0
1
1
1
0
1
0
4
1
1
1
2
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
2
1
0
0
0
2
1
0
2
1
0
1
1
0
0
1
0
0
1
0
0
1
0
1
2
1
1
1
0
0
0
1
2
1
2
0
0
0
0
2
1
1
0
0
0
0
1
1
0
0
2
1
0
0
1
0
1
1
2
10
0
0
0
0
0
2
0
2
2
2
0
1
2
0
0
0
0
1
1
3
0
1
0
0
2
0
1
0
0
1
0
0
3
1
0
1
0
1
0
0
0
1
0
0
1
1
0
2
0
1
1
0
1
0
0
1
0
2
0
0
1
1
1
1
1
1
0
2
2
0
0
1
3
0
0
0
0
0
0
1
1
1
0
1
1
1
2
0
0
1
2
2
2
4
0
1
2
0
2
0
0
0
1
0
1
1
2
2
0
0
2
2
0
1
2
0
0
0
1
0
0
1
2
0
2
2
0
0
2
1
1
2
1
0
1
1
2
0
1
0
3
0
0
1
0
1
1
2
0
0
0
0
1
1
0
2
0
2
0
1
1
0
1
0
1
1
0
0
1
1
1
1
0
0
2
2
1
1
2
0
0
0
0
1
1
1
2
0
2
1
2
0
1
2
0
4
0
0
1
0
0
1
1
0
1
1
1
2
2
0
1
1
0
1
2
1
2
0
0
1
1
2
0
0
0
1
0
0
0
2
0
0
0
2
1
1
1
0
2
1
1
0
3
1
0
0
2
0
0
2
1
0
1
0
1
1
0
0
0
0
1
0
0
1
0
2
2
0
1
1
1
1
0
0
0
1
0
2
0
0
2
0
1
1
1
0
0
0
2
0
0
1
2
0
0
0
0
2
0
2
0
1
0
1
1
0
2
2
0
1
0
0
1
2
0
0
0
2
0
0
0
0
1
0
1
1
1
1
0
0
0
0
0
1
1
1
0
2
0
1
0
0
0
0
0
0
0
0
0
1
2
1
3
0
0
1
0
0
2
2
0
0
2
0
2
2
2
1
1
2
2
0
1
0
2
4
0
1
0
2
0
0
0
0
1
2
0
1
1
2
2
2
1
2
0
1
0
0
2
0
1
0
0
1
0
1
0
0
0
2
1
2
1
0
0
0
2
1
0
0
0
0
0
0
1
1
1
3
1
0
2
1
0
0
1
0
2
0
0
0
0
1
1
1
1
0
0
0
2
0
1
2
0
2
0
2
0
1
1
0
0
1
1
2
2
0
2
0
0
0
1
0
2
0
0
0
0
1
1
0
0
2
0
0
1
0
0
1
2
1
2
2
0
1
0
1
0
0
0
1
0
1
0
1
0
1
1
0
1
2
0
1
0
4
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
2
1
0
2
0
2
0
1
0
1
1
2
0
0
2
1
0
1
2
0
1
0
2
2
1
1
0
2
0
2
0
0
2
0
1
1
0
3
0
0
2
1
0
2
1
2
1
0
1
2
1
0
1
2
0
0
0
1
1
1
0
2
0
0
1
1
1
0
0
0
1
0
1
2
1
0
0
2
0
4
1
0
0
1
1
1
2
0
1
0
0
2
0
0
1
0
0
1
1
0
0
2
0
1
0
0
1
0
2
1
2
1
0
0
3
2
2
0
0
2
2
1
0
2
1
0
0
0
1
1
1
0
1
1
0
0
1
1
0
1
0
2
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
2
2
1
0
1
0
0
1
1
0
2
0
0
0
2
2
0
0
0
0
0
1
2
0
1
1
1
2
0
1
2
1
0
0
0
0
1
1
1
1
0
2
0
0
1
0
0
0
2
1
1
0
2
1
0
1
2
1
1
0
1
0
0
1
1
0
0
1
0
0
1
2
2
1
0
2
2
0
0
0
0
1
0
1
0
1
3
2
0
0
0
2
0
0
0
1
1
0
1
0
0
0
0
1
1
2
2
0
0
1
1
1
0
2
0
0
2
2
1
0
2
0
3
1
0
0
3
1
0
1
2
0
0
0
2
1
2
0
0
0
1
0
0
1
2
3
2
1
0
2
2
1
0
0
0
2
1
0
0
0
1
0
0
1
0
2
2
2
1
0
1
0
1
0
1
2
1
1
1
1
1
2
0
2
0
1
0
1
1
2
2
1
1
0
2
0
1
0
2
0
0
0
0
0
0
1
1
0
1
0
1
2
2
0
0
0
2
0
1
0
2
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
1
1
2
2
0
0
0
0
1
0
0
1
1
2
1
2
0
0
0
0
2
0
0
2
2
2
0
0
1
0
0
1
1
1
0
0
0
0
2
2
0
1
0
0
0
3
1
2
1
0
0
0
0
1
1
0
1
0
1
2
0
0
0
2
0
1
0
0
0
2
0
2
0
2
1
0
0
1
0
0
1
0
2
0
2
2
0
0
2
1
2
0
0
3
2
2
2
2
0
1
0
0
1
1
0
2
2
1
2
0
1
0
1
1
0
0
0
1
1
0
0
0
1
0
0
1
1
2
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
1
1
0
2
0
1
2
2
2
0
0
1
2
0
0
0
1
1
0
0
1
0
0
0
3
0
2
0
0
0
1
0
1
2
0
0
1
0
0
0
0
0
4
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
1
0
1
1
0
2
1
1
0
0
0
2
1
1
2
0
2
1
1
0
0
0
2
0
1
0
2
0
2
0
0
0
0
1
1
0
2
0
2
0
0
1
0
1
0
0
1
0
2
1
1
0
2
1
0
0
0
2
1
0
0
0
0
2
2
0
2
0
0
2
0
0
0
2
0
0
0
0
2
1
1
2
0
1
1
1
0
0
1
1
1
2
3
1
2
1
4
0
2
2
1
0
1
1
0
0
0
0
1
2
0
1
0
0
0
2
0
0
1
1
2
2
0
0
0
0
1
0
0
0
0
2
1
1
0
2
2
0
0
0
2
1
1
3
2
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
1
1
2
0
1
2
0
2
0
1
2
2
2
1
0
0
2
0
0
0
1
0
1
1
0
0
2
0
0
0
0
0
0
1
2
0
0
1
0
2
0
2
0
1
0
1
0
0
0
0
3
2
1
1
0
2
0
0
2
2
0
0
1
0
0
1
1
0
0
1
0
0
2
2
0
0
1
1
1
1
2
0
0
2
1
0
1
1
2
0
0
1
1
0
2
0
1
2
0
2
1
0
0
0
1
1
0
0
0
2
1
2
1
0
1
2
0
3
0
1
1
1
0
0
1
1
0
1
1
0
0
1
1
0
0
1
0
1
2
3
2
0
1
0
2
1
0
0
0
1
2
1
0
0
0
0
2
0
1
1
0
1
0
1
2
0
0
0
0
0
2
3
2
0
0
1
1
0
1
3
0
1
0
1
2
0
3
0
0
0
0
1
1
0
1
16
2
0
2
1
0
2
0
0
2
1
1
2
0
0
2
0
0
0
3
0
2
2
4
1
2
0
1
1
1
1
1
0
0
0
2
0
2
0
0
2
1
1
0
1
2
1
2
0
0
0
0
0
0
1
1
1
0
1
0
2
2
0
0
0
0
0
1
0
0
2
1
0
2
2
2
0
0
1
0
0
0
1
0
1
1
1
1
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
3
0
1
4
0
1
2
0
1
2
0
0
1
0
0
1
2
0
0
0
0
1
0
2
0
3
0
1
0
2
0
3
2
1
0
1
2
1
2
1
0
0
0
0
0
2
0
3
0
1
0
1
3
2
2
0
2
0
1
1
0
1
2
0
1
1
0
1
0
2
0
0
0
1
1
2
0
0
2
0
1
1
1
0
0
2
1
1
0
1
2
1
0
0
0
2
1
1
1
2
0
0
2
0
2
0
1
1
2
1
0
1
2
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
2
2
1
0
0
0
1
0
0
2
3
0
0
0
2
1
1
0
1
1
0
2
0
0
1
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
2
1
2
0
0
0
0
1
0
0
1
0
2
0
0
3
0
0
1
0
1
2
0
1
2
2
0
0
2
1
0
0
2
0
0
0
0
2
0
1
0
1
0
1
2
0
1
0
0
1
1
1
0
1
0
0
1
0
1
0
1
1
2
1
0
1
1
1
0
0
1
1
1
3
3
0
1
2
0
1
0
0
0
1
2
0
2
0
1
0
2
0
0
0
0
0
1
1
0
1
0
0
1
1
0
0
1
1
0
2
1
0
2
0
2
1
1
1
0
1
3
1
1
0
0
2
2
1
0
1
2
1
0
0
1
1
0
0
0
0
0
0
0
1
0
1
2
2
0
1
0
0
2
0
1
0
0
2
0
1
0
1
2
0
0
2
0
0
3
1
1
2
1
2
0
0
1
1
0
1
0
0
0
1
0
0
1
1
0
0
0
1
1
0
0
1
0
0
2
2
1
0
1
0
1
2
1
0
2
0
0
2
1
1
1
1
1
0
0
1
2
0
2
0
0
0
0
0
1
0
2
1
2
2
1
2
0
2
1
0
2
0
0
2
1
0
2
0
2
1
0
0
0
0
0
1
2
1
1
0
0
0
0
1
2
1
0
0
2
0
1
2
0
1
2
2
0
2
0
2
1
0
1
2
1
0
2
0
0
2
1
0
1
0
3
0
1
2
0
1
2
2
3
0
0
1
0
0
0
1
1
0
1
0
0
0
1
2
2
0
0
0
1
0
2
1
2
1
1
1
2
2
1
0
1
0
1
2
1
0
2
1
0
0
0
1
0
0
0
0
2
2
0
0
0
0
2
0
1
1
1
0
2
2
3
2
1
0
2
0
0
1
0
1
0
1
1
1
0
0
0
2
1
0
0
0
1
0
2
3
0
0
1
1
1
0
0
1
1
2
5
0
2
0
0
1
0
1
0
0
0
0
1
0
0
0
3
0
3
2
2
0
0
0
2
0
0
1
2
0
2
1
2
0
0
2
1
0
0
2
1
0
2
1
1
0
0
2
0
2
3
1
1
0
1
0
1
2
1
0
1
1
1
2
2
0
1
1
1
1
0
0
0
0
1
1
2
0
0
0
0
0
0
1
2
1
2
0
2
0
0
0
1
0
1
0
0
0
1
2
0
1
0
0
0
2
1
1
1
2
2
1
2
2
2
0
2
0
1
1
2
1
2
0
1
0
2
0
1
0
0
2
2
0
1
2
0
1
0
0
0
1
1
1
1
0
2
2
0
3
0
0
0
0
0
1
0
1
0
1
0
0
1
2
0
0
0
1
2
2
1
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
2
1
1
0
0
0
1
2
0
1
2
2
1
1
1
2
1
1
0
1
2
0
0
2
1
0
0
0
2
0
0
2
0
2
0
2
0
2
2
0
0
0
0
1
2
0
1
1
1
1
2
0
0
2
0
0
0
1
0
0
0
3
0
1
2
0
0
0
1
1
2
1
2
2
0
0
1
0
1
2
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
1
0
2
3
0
1
1
2
1
2
0
2
0
1
0
1
0
0
0
2
2
0
1
2
0
0
0
0
1
0
1
1
0
0
0
0
1
2
1
0
0
1
0
1
1
0
0
2
0
2
2
0
2
6
0
0
0
0
1
2
1
0
0
0
1
0
1
2
0
0
2
0
0
1
0
2
1
1
1
0
1
0
0
1
0
0
1
1
0
2
0
0
0
0
0
0
3
0
0
0
0
1
2
1
3
0
0
1
0
0
0
0
0
2
1
1
1
0
0
1
1
0
2
0
1
0
0
1
2
0
0
1
0
0
0
0
0
2
1
0
0
0
0
2
0
10
0
2
2
1
2
1
1
2
3
2
0
0
0
0
0
1
1
0
1
2
0
2
2
1
0
0
1
0
0
2
0
2
0
1
0
0
2
0
0
1
2
2
0
1
1
0
1
0
0
1
0
0
3
2
0
0
0
2
0
2
0
0
0
1
0
0
0
0
1
1
2
0
0
0
0
2
0
1
2
1
0
3
2
2
0
0
0
0
0
4
1
1
2
0
0
0
2
1
0
0
0
2
2
1
0
1
0
0
2
0
0
3
1
2
1
1
2
0
2
0
2
0
0
1
1
0
2
1
0
0
2
1
0
0
2
0
0
0
1
0
0
1
2
1
0
2
2
1
7
1
2
0
0
2
2
0
1
2
2
1
2
1
0
1
0
2
1
0
1
0
4
1
0
2
0
0
0
1
1
0
2
0
0
0
0
1
0
1
1
1
0
0
0
0
0
3
0
0
1
2
1
2
1
2
0
0
0
0
0
0
1
0
0
2
1
0
1
0
0
0
0
0
0
2
0
2
0
2
3
1
0
1
1
0
1
0
0
2
1
0
0
0
0
2
0
1
1
2
2
0
1
0
0
2
2
0
1
3
2
2
0
2
0
1
0
2
0
1
1
0
1
0
0
2
1
0
2
2
2
0
3
2
0
0
2
2
1
1
0
1
0
3
0
0
1
2
0
0
1
2
0
0
0
2
0
1
1
1
0
0
0
0
2
1
0
0
0
0
1
0
1
1
0
0
1
0
1
1
0
0
0
1
2
0
0
2
3
1
3
0
1
0
2
0
1
1
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
2
0
2
2
0
0
0
0
0
3
0
2
1
0
0
1
0
2
0
0
1
1
2
1
1
1
0
1
2
0
1
1
2
0
1
2
2
0
0
1
0
2
0
0
1
2
1
1
1
0
0
0
1
1
1
0
2
2
0
1
1
3
1
1
1
0
0
0
0
1
0
0
1
0
2
3
0
0
1
2
1
2
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
2
2
0
0
1
0
1
2
0
1
0
2
1
1
1
4
1
0
1
0
0
1
2
1
0
2
1
0
0
1
0
0
2
1
2
1
0
1
1
1
0
0
0
0
0
3
2
0
0
0
0
2
1
0
2
0
0
0
1
0
1
1
0
1
1
2
1
0
0
0
0
1
0
2
0
2
0
1
1
0
0
0
2
2
1
1
0
1
2
1
0
0
0
0
0
0
1
0
1
0
1
3
1
0
1
1
1
0
1
1
2
1
2
0
0
0
0
1
1
0
2
1
0
0
2
1
0
0
0
0
0
0
0
0
1
0
2
0
1
2
0
0
0
2
1
1
0
2
1
1
0
0
0
0
0
0
2
0
0
1
1
0
0
0
2
0
2
0
0
0
0
1
1
1
0
2
0
1
1
1
0
1
2
0
0
2
0
0
0
1
0
1
1
1
1
0
1
0
0
1
0
1
2
0
0
0
1
2
1
1
1
1
1
1
1
0
0
1
2
1
1
0
0
0
1
0
1
0
0
2
1
0
1
2
0
1
2
2
1
1
1
2
2
0
0
0
0
0
0
1
0
0
1
2
1
1
2
1
0
1
1
0
1
0
1
1
2
1
0
1
3
2
1
0
0
0
1
1
0
1
0
0
1
0
0
0
2
0
1
0
2
0
0
0
2
0
0
0
2
2
1
1
1
0
0
0
1
0
2
0
0
0
1
2
2
0
0
2
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
2
0
0
1
0
3
2
0
2
1
0
0
0
2
0
2
2
0
0
1
0
0
0
0
1
0
0
3
0
1
0
1
0
0
0
1
0
0
2
2
2
1
0
0
0
0
0
2
0
0
1
1
1
0
1
1
3
1
0
0
0
0
0
0
0
0
0
1
0
2
1
0
1
1
0
0
0
2
0
0
0
3
1
0
2
1
1
0
0
1
1
1
0
1
1
0
1
0
0
1
1
2
0
0
0
0
0
0
1
0
0
1
2
2
0
2
1
2
0
1
0
0
0
0
0
1
1
1
0
1
1
0
0
2
0
0
0
1
0
0
0
0
1
0
0
1
0
0
2
0
1
1
1
1
0
0
0
1
1
1
0
4
0
0
0
2
0
0
0
1
0
0
3
1
2
2
0
0
3
1
0
2
0
0
1
0
2
1
1
1
0
2
2
2
3
0
0
0
0
1
1
2
1
2
0
0
0
0
0
0
0
0
0
2
0
0
2
1
1
1
0
0
0
0
0
0
0
0
0
1
1
2
2
0
0
1
2
0
1
0
0
2
0
1
0
0
0
1
0
1
2
2
1
0
0
1
1
0
0
1
0
0
1
1
0
0
2
1
2
1
0
1
0
0
1
0
0
0
1
1
2
1
0
0
0
2
1
1
0
0
1
0
0
0
1
0
0
1
2
1
0
0
2
0
2
0
1
0
2
4
2
0
0
0
0
0
0
2
2
0
1
2
0
0
1
0
1
1
1
2
1
0
1
0
2
2
1
2
0
1
2
0
0
0
0
1
0
1
1
0
2
2
2
0
2
2
1
0
0
2
0
0
1
0
1
2
2
0
0
2
0
2
0
1
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
1
0
1
1
3
1
0
0
0
0
2
0
1
1
0
0
0
0
2
1
2
1
0
0
1
0
0
1
0
0
1
0
0
2
0
0
0
0
1
0
2
0
1
2
1
0
0
2
0
0
0
0
0
0
1
0
1
1
2
0
0
1
1
1
1
0
2
0
0
1
1
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
2
1
1
0
0
0
0
2
0
2
1
0
0
0
0
0
1
2
0
1
1
2
1
0
0
2
0
0
0
0
0
0
0
2
2
1
0
0
2
0
0
0
1
1
1
1
1
0
0
0
0
1
1
2
1
0
1
1
0
0
0
0
1
2
1
2
0
0
2
2
1
2
0
2
0
0
1
0
0
2
1
0
0
1
2
0
0
2
2
1
1
1
0
1
1
1
1
2
2
1
1
1
3
1
0
0
0
1
1
0
0
2
1
1
0
0
0
0
2
0
0
0
0
2
2
0
2
2
1
1
2
1
0
7
2
1
1
2
0
0
1
0
3
2
0
2
2
2
1
0
2
1
0
0
2
1
1
0
0
2
0
0
0
2
0
1
0
0
1
1
1
2
2
0
2
1
2
1
1
1
1
0
1
0
0
0
0
2
0
1
0
1
1
0
1
1
1
1
1
2
2
1
0
1
0
6
2
0
0
0
0
1
2
0
1
0
0
0
1
0
2
0
0
1
0
2
1
1
0
0
1
0
2
0
0
1
0
2
0
1
2
1
2
1
2
0
1
0
2
2
0
0
2
1
0
1
1
0
0
0
0
0
0
0
1
1
0
0
2
0
1
1
0
1
2
1
0
0
0
0
2
1
1
0
0
1
2
2
2
1
0
2
1
0
2
0
1
1
0
0
0
1
2
0
1
1
0
0
0
2
1
1
0
1
1
0
2
2
0
2
0
1
1
1
1
0
0
0
0
1
1
2
0
2
0
2
2
0
1
1
0
0
2
0
4
1
0
0
0
0
1
2
0
0
2
0
0
3
0
0
0
1
1
1
2
0
1
0
2
0
0
2
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
1
0
0
0
0
0
0
2
2
0
1
1
0
1
0
1
1
0
0
1
2
2
0
2
0
0
0
0
2
0
2
1
1
0
0
1
0
2
1
3
2
0
2
0
1
0
1
0
0
2
2
0
1
0
0
2
1
0
2
0
0
1
0
0
1
0
0
2
0
1
1
2
1
1
0
0
1
1
2
0
1
0
0
0
2
0
0
1
1
0
0
0
2
0
1
0
0
0
0
1
1
0
0
2
1
0
1
2
0
0
0
1
0
0
0
2
0
1
0
1
0
1
2
0
0
0
1
2
0
0
0
1
0
0
1
0
2
0
0
0
0
1
0
0
0
0
2
2
0
1
0
0
1
1
0
0
2
1
0
0
0
0
0
0
0
2
0
2
0
1
2
0
0
1
2
0
0
3
2
0
0
0
0
1
1
0
0
0
0
0
0
2
2
1
0
0
0
2
0
1
2
0
0
0
1
0
1
0
0
0
1
0
1
0
1
2
0
0
0
4
1
2
1
1
0
1
1
0
0
0
2
2
0
0
0
0
0
0
0
2
1
0
1
2
0
2
1
2
0
2
0
0
2
0
1
0
0
0
0
0
2
2
1
1
0
0
1
0
0
2
0
2
1
1
0
2
0
2
1
0
2
2
1
1
2
0
0
2
2
0
1
0
0
0
1
0
1
0
1
1
2
0
1
1
2
1
2
1
1
0
1
0
0
0
0
2
0
0
1
0
2
1
1
0
1
0
0
2
0
1
0
1
0
0
0
0
1
0
0
0
1
2
1
0
0
1
2
2
1
1
1
2
0
0
0
0
0
0
0
1
2
1
0
0
0
0
1
0
0
1
0
2
0
0
0
0
1
2
1
3
0
1
2
0
0
0
1
1
0
2
0
1
0
0
0
2
0
0
2
0
0
0
0
0
1
0
2
1
0
2
0
2
0
0
2
2
2
1
1
0
1
0
0
2
0
0
1
2
1
0
1
1
0
0
0
2
0
1
0
0
2
2
2
0
2
1
1
1
1
0
0
0
1
1
0
1
2
0
0
0
1
2
1
1
2
1
0
0
2
2
1
0
0
1
1
1
2
1
1
2
1
2
0
0
0
1
1
0
0
1
0
2
2
0
0
0
2
2
1
1
2
0
1
2
1
2
0
0
0
1
2
1
2
2
0
0
1
0
0
2
2
2
2
0
1
1
0
0
1
1
0
2
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
1
0
2
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
2
0
2
0
1
2
0
2
0
0
0
0
0
1
1
0
0
2
0
0
1
0
2
0
0
0
0
0
2
2
1
0
0
1
2
0
0
2
1
1
1
1
0
0
2
2
1
1
0
1
1
1
0
0
0
1
0
1
0
0
0
0
1
1
0
1
2
2
0
0
1
2
2
0
1
1
2
1
1
1
1
1
0
2
0
0
2
0
1
1
0
0
2
0
0
0
0
1
0
1
0
1
0
1
0
2
2
0
0
0
2
2
1
2
0
2
0
0
0
0
0
1
2
0
0
2
1
1
0
0
3
2
2
1
0
0
0
0
0
1
2
0
3
1
0
2
0
0
0
0
0
0
1
0
1
0
1
0
2
0
1
1
0
2
2
0
0
0
1
0
1
0
0
1
0
2
1
0
0
1
0
0
0
0
0
0
2
1
1
0
2
1
1
0
2
0
0
2
0
0
2
0
1
1
0
3
1
1
0
0
0
1
1
3
0
0
1
0
1
0
1
0
1
0
0
0
2
0
0
0
1
0
0
1
0
2
1
2
0
1
0
2
0
0
2
0
0
2
4
0
2
0
2
0
2
1
2
1
1
1
0
0
0
1
1
2
0
1
1
0
1
0
2
2
0
1
1
0
1
1
1
0
0
1
1
0
0
1
1
0
1
2
2
2
0
1
1
0
0
0
1
2
0
1
2
2
3
1
0
0
1
1
1
0
1
0
0
1
1
0
1
0
2
0
1
1
1
1
0
1
0
1
0
0
0
0
1
0
2
0
2
0
0
3
1
0
2
0
0
0
0
1
2
1
1
1
1
0
0
0
0
0
2
1
0
0
2
1
2
2
0
2
1
2
0
1
2
2
2
2
1
1
0
0
0
0
0
0
0
1
0
0
2
0
1
1
0
0
1
1
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
2
0
1
0
2
0
1
0
0
2
2
1
0
1
0
0
2
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
1
0
1
0
1
0
1
2
0
0
2
1
1
0
0
0
0
1
0
4
0
0
0
1
0
0
0
1
0
2
0
1
0
1
0
1
2
0
0
0
2
1
0
1
1
1
0
2
0
0
1
1
1
0
1
0
1
0
1
1
0
0
0
2
1
1
0
2
0
0
2
1
0
1
0
1
0
1
0
1
1
2
0
2
0
1
0
0
4
3
2
0
1
2
0
0
2
2
0
0
0
2
2
0
1
0
0
0
0
1
0
0
0
2
2
1
1
1
1
1
0
2
0
1
1
0
0
0
0
0
1
0
0
2
0
0
0
2
0
2
2
0
0
1
0
0
0
2
1
2
0
2
0
0
0
0
2
0
1
1
2
3
0
3
0
0
1
0
0
2
1
2
3
0
0
7
0
2
1
1
0
0
0
0
2
0
2
0
0
0
3
0
0
1
0
1
1
2
0
0
1
1
0
0
1
0
2
2
0
0
0
1
0
2
1
1
1
2
2
0
0
0
1
0
1
0
1
2
3
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
1
1
2
1
1
0
0
0
0
1
3
1
1
3
0
1
1
1
2
1
3
0
1
0
1
0
1
1
2
4
0
0
0
1
0
2
0
2
0
2
1
1
0
0
0
0
2
0
1
1
0
0
0
1
0
1
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
2
1
0
1
0
2
2
2
0
1
2
0
0
1
2
1
0
1
9
0
0
1
0
0
1
1
0
4
1
2
0
0
0
0
0
0
1
0
1
0
0
2
1
0
2
1
1
3
2
2
0
0
0
0
2
1
1
1
1
2
0
0
1
0
1
2
1
0
2
1
0
0
0
0
0
1
1
1
0
0
2
0
0
0
1
0
0
0
2
0
0
0
1
0
0
1
2
1
0
0
0
1
1
2
0
0
0
1
0
0
2
0
1
2
1
2
2
0
2
0
0
1
0
1
1
0
2
0
1
1
1
2
2
0
3
2
0
0
0
1
0
1
1
1
1
0
1
1
2
0
2
0
0
1
0
0
0
1
2
2
1
0
0
0
2
0
0
0
0
1
1
1
0
0
0
0
0
2
3
1
2
1
1
3
0
0
0
2
2
2
1
0
1
3
1
0
1
0
1
0
0
0
1
1
0
0
0
1
1
2
0
0
2
1
2
0
0
1
2
1
1
0
0
0
1
1
2
0
1
0
0
2
0
0
0
2
3
0
1
2
1
0
1
0
0
2
0
0
1
2
1
0
0
1
2
0
2
0
0
2
0
0
0
0
1
1
2
0
0
1
1
0
2
0
0
0
0
1
2
0
0
2
1
2
2
0
0
1
2
0
0
1
2
2
0
1
0
2
1
0
0
0
1
0
0
0
0
1
0
0
0
2
2
0
2
0
1
0
1
0
0
0
0
0
0
1
0
0
1
1
2
1
1
1
0
2
1
3
1
0
1
2
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
2
0
2
2
2
0
0
2
0
1
0
1
0
0
0
0
0
2
0
2
1
0
0
2
2
1
1
2
0
2
2
2
3
0
0
1
0
1
1
0
0
0
1
2
1
1
1
0
2
2
0
1
1
0
2
1
1
0
0
0
0
2
1
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
2
0
1
0
2
0
1
1
2
0
0
0
0
3
2
0
0
0
2
1
0
0
0
0
1
0
0
1
0
2
1
3
0
1
1
3
2
2
1
1
0
1
0
1
0
0
0
0
2
0
2
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
3
0
0
0
0
1
0
0
1
1
0
1
1
0
2
0
2
0
1
0
1
0
0
1
0
2
1
0
0
0
0
0
0
1
1
2
1
1
0
1
0
0
0
1
0
2
2
0
0
0
1
0
0
2
0
1
0
1
0
2
1
0
2
2
1
1
0
1
0
1
0
0
1
2
0
0
1
2
0
0
0
0
2
0
0
0
2
1
0
0
1
1
1
2
0
0
0
1
2
0
1
0
2
2
0
1
2
0
0
2
1
0
0
0
2
2
0
2
0
1
0
2
1
0
0
2
0
2
0
1
1
1
2
1
1
0
2
0
2
1
0
2
2
1
2
1
0
1
0
2
0
1
2
1
2
2
1
0
0
0
0
2
0
2
0
2
0
1
0
1
2
1
4
1
1
2
0
1
1
1
0
2
0
0
0
0
0
1
0
1
2
1
0
0
0
0
1
0
1
0
2
2
0
0
1
0
1
0
0
0
1
1
0
0
2
0
0
2
0
0
0
0
0
2
0
2
0
1
2
2
0
0
1
0
0
0
1
2
1
0
1
2
2
0
1
2
2
0
0
0
1
1
2
0
1
1
0
1
0
0
2
0
2
2
0
0
2
0
0
0
0
0
0
1
2
0
0
2
0
0
1
1
0
0
0
1
0
0
2
0
0
1
2
3
1
0
1
0
2
2
0
0
2
2
0
1
2
0
2
0
0
0
1
1
1
2
0
1
0
0
1
1
0
1
0
0
0
2
1
2
1
0
0
0
1
0
1
2
1
1
1
0
0
1
0
1
1
0
0
0
0
0
0
3
0
0
0
2
0
0
2
0
2
3
2
1
1
0
1
0
1
1
1
1
1
2
2
1
1
1
0
1
0
2
0
0
1
1
0
0
1
0
1
2
2
0
0
0
1
2
0
1
0
0
2
1
2
2
2
1
1
1
0
1
0
2
1
0
2
0
0
2
0
0
0
0
2
0
2
1
0
1
1
1
2
2
2
0
0
0
2
0
0
1
0
0
1
3
2
0
0
0
0
2
1
0
0
0
0
2
0
2
0
1
0
1
0
0
1
0
1
0
2
0
1
0
2
1
0
1
2
0
3
0
0
0
1
1
0
1
1
0
1
2
0
1
1
1
0
1
0
0
1
0
0
2
1
2
2
0
1
2
0
1
4
0
2
1
1
1
0
2
1
0
4
0
1
0
2
0
2
2
0
0
1
1
0
0
0
0
1
2
0
0
0
2
1
4
1
1
1
0
2
0
0
0
0
0
1
2
2
1
1
2
0
1
1
0
2
1
2
0
1
0
2
0
0
1
0
2
0
2
0
2
0
0
0
1
1
0
0
1
0
0
0
0
0
1
2
0
0
0
4
1
0
2
2
0
0
1
1
0
0
1
2
0
1
0
0
1
2
1
0
0
0
1
0
1
1
0
2
0
1
1
0
0
2
2
1
0
2
0
2
1
0
0
0
0
2
1
0
1
0
0
0
1
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
1
0
2
1
0
0
1
1
0
2
0
2
1
1
1
2
0
0
2
0
0
0
2
2
1
0
1
2
0
3
0
0
0
1
0
0
1
2
2
1
1
0
2
1
0
1
3
0
0
0
1
0
0
0
0
2
6
0
0
0
1
1
2
0
0
1
0
0
2
1
2
2
0
0
0
0
2
0
1
2
2
2
2
1
1
0
2
0
0
0
1
0
0
0
0
0
0
0
2
1
1
2
0
0
0
1
2
0
0
0
3
0
1
2
0
0
0
0
1
0
1
2
1
2
0
1
1
0
3
2
1
1
1
1
1
0
1
0
0
2
0
0
1
1
0
0
2
2
1
1
1
1
1
2
2
0
2
0
4
2
0
0
0
2
0
1
2
0
0
1
0
1
0
0
1
1
0
0
0
1
0
2
0
0
0
1
1
1
0
0
1
2
0
0
0
2
1
0
1
0
1
0
0
0
2
2
0
1
0
0
2
1
0
0
1
1
1
1
0
1
2
0
1
0
0
1
0
2
0
2
1
0
0
0
0
0
0
2
2
2
0
0
0
0
0
2
1
0
0
1
0
2
0
0
1
0
2
1
0
2
0
0
0
0
0
1
2
0
1
1
1
1
2
2
0
1
2
3
0
1
1
1
0
0
0
0
0
1
0
1
1
1
2
0
0
1
2
2
0
0
0
2
1
0
0
0
1
1
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
1
0
0
0
1
1
1
1
0
1
2
1
2
0
0
0
0
0
1
1
0
0
2
2
0
1
2
1
0
2
0
1
1
1
0
1
0
1
0
2
1
0
0
2
2
1
1
0
0
0
0
2
2
1
0
0
2
0
0
0
1
0
1
0
1
0
2
0
2
0
1
0
0
0
0
2
0
2
1
1
0
1
0
2
0
1
1
0
1
2
1
1
1
1
0
0
0
1
0
2
0
0
0
1
0
0
0
0
2
2
2
1
0
1
1
0
0
0
0
0
0
1
0
3
1
0
0
0
0
0
2
0
2
0
0
0
2
0
0
1
0
1
0
1
2
1
0
0
0
1
2
3
0
1
0
1
0
1
2
0
0
0
0
0
0
1
0
0
0
0
1
0
2
1
0
0
2
0
0
1
0
0
2
0
2
2
2
1
0
1
1
1
1
1
1
1
0
1
2
0
1
2
2
1
1
3
0
0
2
3
1
0
1
0
0
0
2
1
0
1
0
1
2
1
0
0
2
1
1
2
1
0
2
0
0
1
0
1
0
0
1
2
0
2
1
1
0
2
0
0
1
2
2
1
0
3
0
0
1
2
0
0
2
2
0
2
0
0
1
2
2
0
2
1
0
1
0
0
4
0
0
1
1
1
0
1
0
1
1
1
0
1
1
0
1
1
2
2
0
0
0
0
2
0
0
0
2
3
1
0
1
0
2
0
0
2
2
1
0
0
1
0
1
0
0
1
1
1
0
1
0
0
0
1
0
0
2
0
1
0
2
1
0
1
2
1
1
0
1
1
2
2
0
0
1
0
0
0
1
0
3
0
0
1
1
0
2
2
1
0
1
0
0
2
1
2
0
1
0
2
0
2
0
0
2
2
2
0
0
0
1
0
0
0
1
2
2
0
0
1
1
0
1
3
0
1
2
0
0
1
1
1
0
1
0
0
1
2
0
0
0
1
2
0
1
0
2
2
2
0
0
0
0
0
0
1
0
1
2
0
1
2
0
0
0
0
1
0
2
0
1
1
0
1
0
1
1
1
1
0
2
1
1
2
0
0
0
1
2
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
3
0
0
1
0
1
1
0
0
0
1
1
0
2
0
0
0
1
2
1
1
0
2
1
2
1
0
0
1
0
1
0
3
0
0
0
2
2
1
1
2
1
2
0
0
1
2
0
2
0
1
1
0
0
0
0
0
1
2
0
0
1
0
1
0
0
1
0
2
1
3
0
1
1
1
2
1
0
1
2
1
0
2
0
1
2
0
1
1
0
1
2
1
2
0
1
2
0
0
0
0
0
2
1
2
0
0
2
2
1
0
2
0
1
0
0
0
1
2
0
1
1
0
0
0
0
0
1
1
0
1
2
0
2
2
0
0
0
0
0
2
1
0
1
2
2
1
1
1
0
0
2
4
0
2
1
1
0
0
0
2
2
0
0
0
0
0
2
0
0
2
1
0
0
0
0
2
0
1
0
0
0
2
7
1
0
0
0
1
2
2
1
2
1
1
2
2
1
2
0
0
1
2
0
0
2
0
1
0
0
1
0
1
1
1
1
0
0
1
0
1
0
2
1
0
2
0
1
0
0
2
0
0
2
0
1
1
0
0
1
1
0
1
0
0
1
2
0
0
0
0
1
0
1
2
1
1
0
2
0
0
1
0
1
1
1
2
0
2
2
0
3
1
0
0
2
1
0
0
1
1
2
0
0
0
0
0
0
1
1
1
0
2
0
0
0
1
0
1
0
0
0
1
2
2
1
3
0
0
0
0
2
1
0
1
2
0
2
2
0
1
0
1
1
1
2
1
0
0
1
1
0
0
1
0
0
0
1
0
0
0
1
1
0
2
0
0
0
0
1
0
1
0
0
0
1
2
1
1
2
0
0
2
1
0
1
2
0
0
1
0
2
2
1
1
0
0
2
0
0
1
2
2
1
2
0
1
1
0
2
1
1
1
1
1
0
2
1
2
1
2
1
0
1
2
2
0
2
0
1
2
0
0
0
0
2
0
1
2
1
0
2
2
1
2
1
0
1
1
0
1
2
0
0
0
0
0
0
0
2
2
0
2
0
3
0
0
4
1
0
2
0
2
1
1
2
1
0
2
1
0
1
1
0
1
0
1
0
0
0
0
2
0
1
0
1
2
2
0
1
2
2
1
0
0
1
1
1
0
1
2
1
1
0
0
0
0
1
2
2
1
0
2
1
0
0
0
0
2
2
1
0
1
0
0
0
0
0
0
0
1
1
2
2
1
3
1
0
2
0
2
0
1
2
0
1
0
1
1
1
0
2
1
0
2
1
2
0
2
2
2
1
1
1
0
0
2
2
0
0
1
1
2
2
0
1
0
1
2
0
0
0
1
1
0
1
2
0
0
0
1
2
0
0
1
1
2
2
3
0
2
0
0
2
0
2
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
2
0
0
0
1
1
0
0
0
1
2
0
2
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
1
1
1
0
0
0
2
0
0
2
2
0
1
2
0
0
2
1
6
1
2
0
0
1
0
2
0
2
0
2
1
0
0
0
1
2
1
0
0
0
2
1
0
0
1
1
2
0
2
2
1
2
0
0
1
0
0
0
2
2
0
1
0
1
0
2
1
0
0
1
0
0
1
1
1
1
0
0
0
1
0
0
0
1
0
1
0
1
1
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
2
0
0
2
0
0
1
0
0
0
2
2
3
0
2
1
0
0
1
2
1
1
1
0
1
2
2
0
1
2
1
0
1
1
1
0
0
1
0
1
2
2
0
1
1
3
0
0
1
2
1
0
0
2
0
0
3
0
0
1
0
0
2
2
0
2
0
1
1
0
0
2
1
0
1
0
2
2
0
2
1
2
0
2
1
1
1
0
0
1
0
3
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
1
0
1
2
1
1
0
1
2
1
1
2
2
2
1
2
1
2
1
1
2
1
0
2
0
0
2
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
2
1
1
0
0
1
0
1
1
2
1
0
1
0
0
2
1
2
1
1
1
2
1
2
0
0
0
2
0
0
2
1
1
0
0
0
1
0
2
2
0
1
0
0
1
0
0
1
2
2
2
0
2
2
2
0
2
0
2
2
2
2
1
0
2
0
1
0
0
1
0
1
0
0
1
0
0
1
0
1
0
2
1
0
0
1
0
2
1
0
0
3
0
0
1
0
0
2
1
4
0
0
1
0
0
0
1
2
1
1
0
0
1
0
1
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
2
0
1
0
1
0
0
1
0
0
2
1
0
0
0
1
1
0
0
2
2
1
0
2
1
0
2
2
0
1
0
0
1
2
0
1
0
1
0
0
0
1
0
2
0
0
1
0
1
0
1
1
1
1
3
2
0
1
2
1
1
0
0
2
0
0
2
0
0
2
2
0
0
0
0
0
0
0
2
0
0
2
2
2
0
1
1
2
1
1
0
2
0
2
0
0
2
1
0
0
0
2
1
1
1
0
3
0
2
0
1
0
0
2
0
1
0
0
0
1
0
1
0
1
0
1
1
1
2
2
0
3
0
0
1
0
0
2
0
1
0
1
1
1
0
1
1
1
1
0
1
2
1
2
1
1
0
3
0
0
0
0
0
0
1
0
2
0
1
0
1
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
1
0
1
1
1
2
2
1
1
2
2
0
0
1
1
1
0
2
1
1
1
0
0
0
1
2
0
1
1
0
2
1
0
0
2
0
0
0
1
2
0
1
3
2
0
0
0
2
0
2
2
0
2
1
1
0
0
0
0
0
0
2
1
1
0
0
0
0
1
1
0
0
0
0
1
1
0
2
1
3
2
0
0
0
2
0
1
1
1
0
0
0
1
2
1
0
1
1
1
2
1
0
0
1
1
0
1
0
1
2
1
1
0
0
1
2
0
0
2
2
0
1
2
0
2
1
0
1
1
0
0
0
1
1
0
0
0
0
1
0
1
0
1
0
0
2
0
1
0
0
1
1
0
1
0
2
0
2
2
0
1
1
1
0
3
0
2
1
1
0
0
1
0
2
1
2
0
0
0
0
2
0
0
0
0
2
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
1
1
1
1
1
2
0
2
1
1
2
2
1
0
1
1
0
2
0
2
0
1
0
0
2
0
0
0
2
0
2
2
2
0
0
0
2
0
0
2
0
2
0
2
2
1
0
0
2
0
0
4
1
1
0
0
2
1
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
1
0
0
2
0
1
2
0
0
0
0
2
0
2
0
0
0
0
1
0
0
1
0
0
1
0
0
1
1
1
2
2
1
2
0
2
0
2
1
2
1
2
1
0
0
0
1
1
0
2
2
0
0
1
0
1
2
0
1
0
0
0
0
2
1
1
2
1
0
1
0
2
0
0
0
2
0
1
0
2
0
1
2
1
1
2
1
1
2
0
1
0
1
1
2
1
2
0
1
1
0
1
0
0
0
0
0
0
1
2
0
2
0
1
1
0
0
0
1
2
0
2
0
0
0
0
0
0
2
3
0
0
0
0
1
3
0
0
1
1
0
0
2
2
1
1
1
0
0
1
1
1
0
0
0
0
1
0
2
1
4
0
0
1
0
1
1
2
2
1
1
1
0
2
4
2
0
4
2
0
3
0
3
0
1
1
0
2
2
2
1
1
1
2
0
1
0
1
1
4
1
0
3
1
0
0
0
0
1
2
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
1
1
1
0
1
1
0
0
1
0
0
0
2
1
0
1
0
0
1
2
2
1
1
2
0
0
2
2
0
0
2
1
0
0
1
2
1
0
1
0
0
0
0
0
2
2
0
2
0
0
0
2
2
1
0
0
1
2
2
0
1
0
1
1
0
2
1
0
0
0
0
0
0
2
1
0
0
1
2
0
0
2
2
0
0
0
2
2
1
2
0
0
1
2
0
0
0
1
1
3
2
0
1
1
0
0
1
1
0
0
1
1
0
2
0
0
1
0
0
0
0
2
0
2
1
0
1
2
0
1
0
1
0
2
1
1
0
3
0
1
0
0
0
2
0
1
1
2
1
1
0
0
0
0
0
0
0
0
1
2
1
2
0
0
0
1
0
2
1
0
2
1
0
0
1
0
2
0
2
1
1
2
0
0
2
0
2
3
0
1
1
0
0
2
0
2
1
0
2
2
1
0
1
0
1
2
0
1
0
2
1
0
0
0
0
0
2
2
0
3
0
1
0
0
2
1
1
1
2
2
0
2
2
0
2
0
0
0
1
2
2
1
2
2
2
1
0
2
2
0
0
1
2
0
3
0
2
1
0
0
1
1
1
1
0
0
0
0
1
1
0
1
1
0
0
3
0
1
0
2
0
2
0
0
1
1
0
0
0
0
0
1
0
0
1
0
1
0
2
2
0
1
1
1
1
0
1
1
1
0
0
2
0
2
0
1
0
1
0
0
2
2
1
0
0
2
0
0
1
0
0
1
0
2
1
0
0
1
0
1
2
2
0
0
0
1
1
1
1
1
1
2
2
0
0
2
2
0
0
0
1
1
0
1
0
0
0
2
0
1
0
0
0
0
1
0
2
2
0
3
0
2
1
2
0
1
0
0
2
1
0
0
2
0
0
1
1
2
0
1
0
2
0
1
0
0
2
0
0
2
2
1
0
1
2
4
1
0
0
0
2
2
2
0
1
1
1
0
0
2
1
0
1
0
0
0
2
1
2
0
2
1
0
0
0
2
0
1
0
1
0
0
1
1
0
0
1
0
2
0
1
1
1
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
2
0
2
2
0
0
0
1
2
1
0
1
1
2
0
2
0
2
0
0
0
0
0
3
0
0
0
1
1
1
0
1
1
1
0
0
2
1
5
0
0
1
2
2
0
2
2
0
1
3
1
0
1
0
0
1
0
0
0
0
1
0
0
0
2
1
1
1
0
1
0
1
0
1
2
0
0
0
0
1
0
1
2
1
0
1
0
2
1
0
2
0
0
1
2
2
1
0
2
0
0
0
0
1
0
1
0
0
0
0
0
2
2
1
1
0
0
0
2
0
2
1
0
2
0
1
0
1
0
1
1
0
0
2
1
0
0
0
2
0
2
0
2
2
0
0
1
0
0
0
1
0
0
1
1
1
0
0
1
2
1
1
0
1
1
1
0
0
2
2
0
0
1
1
1
1
1
2
2
0
0
0
0
0
0
1
1
1
0
0
2
0
0
0
3
0
1
1
1
2
0
1
1
0
2
1
1
0
1
1
1
0
1
2
0
0
2
1
0
1
2
1
1
2
0
1
1
1
0
0
0
2
0
0
2
1
0
0
0
0
2
1
1
2
2
0
0
0
1
1
0
1
0
0
1
1
0
1
0
1
0
0
1
0
2
2
0
0
2
0
0
2
0
0
2
1
0
1
2
1
0
1
0
0
0
2
0
2
2
2
0
0
0
1
2
1
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
1
1
1
0
1
1
1
2
0
0
0
0
1
2
1
1
0
1
0
2
0
0
0
0
0
1
0
0
0
1
2
0
1
0
0
1
0
2
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
1
0
2
1
0
1
1
1
0
1
0
1
0
2
0
0
1
2
1
0
0
1
0
2
0
1
1
0
1
0
0
2
1
2
2
0
1
0
2
0
0
2
0
0
0
0
0
1
2
1
1
1
0
0
0
2
2
1
1
1
0
0
1
1
0
0
2
2
3
0
0
2
1
0
1
0
0
0
0
2
1
0
2
1
0
0
1
0
0
1
0
2
1
0
0
2
2
0
1
0
1
1
2
2
4
0
0
0
2
0
1
1
0
0
1
0
0
0
0
0
0
0
1
1
1
1
1
0
1
0
3
0
1
0
1
1
1
1
0
2
1
2
2
0
2
0
2
0
1
0
1
1
0
2
4
2
0
0
1
2
0
0
0
1
1
0
0
0
1
1
0
1
1
1
0
0
0
1
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
2
1
1
2
0
2
1
0
1
0
2
2
0
2
0
0
0
2
0
2
1
0
0
1
2
0
2
2
0
3
1
2
1
0
0
1
0
1
1
0
0
2
0
4
0
1
0
1
0
1
0
1
0
0
1
0
0
1
0
0
2
2
0
0
0
1
3
0
0
2
1
0
1
0
1
1
0
0
1
2
1
0
0
2
0
1
1
1
0
0
2
0
1
1
0
1
1
0
0
0
0
2
1
0
2
1
1
0
2
0
1
1
0
1
0
2
1
1
0
0
0
0
0
0
1
1
0
0
2
2
0
1
1
0
1
1
1
0
0
1
0
0
1
2
1
1
1
0
0
2
0
1
1
2
0
0
1
0
1
0
1
0
0
1
1
1
1
0
1
0
1
1
1
0
0
1
0
2
2
0
0
0
4
0
0
2
2
2
1
0
2
1
0
1
2
2
0
1
1
1
0
1
1
0
0
0
1
0
2
0
1
0
1
0
2
2
2
0
1
0
0
2
1
0
1
0
0
2
0
1
1
2
5
1
2
1
2
0
0
1
0
1
0
2
0
1
0
1
0
0
1
0
0
0
0
2
2
0
1
0
0
1
0
3
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
2
1
1
1
1
2
0
2
1
0
2
1
1
0
0
0
0
0
0
1
0
1
0
1
0
1
0
1
0
2
1
1
1
0
2
0
0
1
1
2
1
2
0
0
2
3
2
0
0
0
0
0
2
2
0
2
4
1
0
2
4
0
0
1
0
1
1
2
1
0
2
2
1
3
0
0
1
0
1
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
1
0
2
2
2
1
1
1
0
0
1
0
0
1
1
1
1
1
0
0
2
0
0
0
1
1
1
0
1
2
1
1
1
1
1
0
0
0
1
2
0
0
1
2
0
1
1
1
0
0
2
1
2
1
0
0
0
0
0
0
2
2
1
0
0
1
1
0
1
1
0
0
1
1
0
1
0
1
1
0
1
0
0
0
1
0
0
1
1
0
0
0
1
2
1
1
1
0
2
0
0
0
0
0
1
2
2
0
2
1
1
0
0
0
1
0
0
0
0
0
2
1
2
1
0
2
0
0
1
1
2
0
2
0
0
1
0
2
0
0
1
0
0
0
0
0
1
0
1
1
0
2
1
0
2
0
2
2
0
0
0
2
0
0
0
1
3
1
0
0
0
2
1
0
0
2
1
1
2
1
0
0
1
0
1
2
0
1
1
1
1
0
1
3
2
1
1
1
1
3
0
0
1
0
0
0
2
2
1
0
2
1
0
0
1
2
0
1
2
0
0
0
2
0
2
2
0
2
2
0
1
0
1
0
0
1
1
0
0
1
1
0
1
3
0
2
2
3
1
1
2
0
2
0
2
1
0
0
0
2
2
0
0
0
1
1
0
2
0
2
1
0
0
0
1
1
1
0
0
0
0
2
0
1
1
2
2
2
1
2
1
1
2
1
1
3
2
1
0
0
1
0
0
0
0
1
1
0
1
1
1
2
1
0
0
0
0
2
0
0
0
2
0
1
1
0
0
0
0
1
2
2
0
0
1
0
0
2
0
1
1
0
0
0
1
1
0
0
0
1
0
0
3
1
2
1
0
2
1
1
0
1
0
0
0
2
2
1
0
2
1
1
0
0
1
0
0
0
0
0
0
0
1
1
0
1
2
0
2
2
1
1
2
0
0
1
0
0
0
2
1
0
2
0
1
2
0
0
1
1
2
0
1
0
1
0
0
2
0
0
0
0
2
2
0
0
0
2
0
2
1
0
2
0
1
1
1
0
0
0
1
0
1
1
1
0
1
0
1
1
1
2
0
1
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
2
2
1
2
1
0
2
1
0
0
1
0
2
0
1
0
0
0
1
2
1
0
1
3
2
0
1
1
0
4
1
0
0
1
1
3
0
2
1
1
1
0
1
0
1
0
5
2
1
0
1
0
1
1
1
1
0
0
0
0
1
2
0
1
0
1
1
2
0
2
0
0
0
2
0
0
0
0
0
0
1
1
2
0
1
2
2
1
1
0
0
2
1
2
0
1
0
1
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
1
2
0
1
2
0
0
1
0
0
0
2
1
2
1
2
2
0
4
0
0
0
0
1
0
0
0
1
2
0
0
0
2
0
0
0
1
0
2
0
1
0
1
2
0
2
0
1
2
0
2
0
2
1
3
1
0
0
0
0
0
0
0
0
1
1
0
0
2
0
2
0
2
1
1
0
2
0
2
2
1
0
0
2
0
0
2
1
2
1
0
2
0
1
0
2
1
1
2
0
0
2
1
0
0
1
2
3
0
1
1
0
0
2
1
0
2
2
1
0
0
0
0
1
2
2
1
0
1
1
2
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
2
2
2
2
0
0
0
1
1
2
0
2
1
2
2
1
2
0
0
0
0
1
0
0
2
2
0
1
1
0
0
1
1
2
0
0
0
0
0
1
0
2
2
0
1
1
2
0
0
1
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
2
0
1
0
2
0
1
1
0
0
2
0
1
1
1
2
0
0
2
0
1
0
2
0
0
2
1
1
1
0
0
0
1
0
1
0
0
2
0
1
0
1
2
1
1
0
0
0
1
0
0
0
1
2
2
2
1
3
1
0
2
0
1
0
0
0
2
1
1
0
0
2
0
2
1
3
2
0
0
0
2
1
2
2
0
2
0
1
0
0
0
1
1
0
1
1
1
1
1
2
0
0
1
0
0
0
0
1
0
2
0
0
2
1
0
2
3
0
2
0
2
0
2
1
3
1
0
1
0
2
0
1
1
2
1
0
1
0
2
0
0
0
1
0
1
0
2
1
0
0
1
2
1
0
4
0
1
1
1
0
1
0
2
0
1
0
2
0
0
1
0
1
0
1
0
0
0
1
2
2
1
2
1
0
2
1
1
1
0
2
3
1
1
0
0
1
1
1
0
1
2
1
1
0
0
0
0
1
1
1
1
1
2
1
2
1
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
1
2
0
2
1
0
1
0
0
0
1
0
1
2
0
1
0
1
2
0
2
0
0
2
0
2
1
1
0
2
2
2
0
0
1
0
0
2
1
1
0
0
1
1
0
2
0
1
0
1
0
1
0
1
1
2
0
2
0
2
1
2
0
0
2
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
1
1
1
0
0
2
1
0
2
2
0
0
0
1
0
0
1
1
0
2
2
0
2
1
1
1
0
0
2
1
1
3
0
0
2
1
0
0
2
1
0
2
0
2
1
1
2
0
0
0
1
0
0
1
1
2
1
0
2
1
2
2
2
2
0
2
0
2
1
1
0
0
2
0
0
2
0
1
1
1
0
0
1
0
0
0
0
1
0
1
0
1
0
0
2
1
1
2
0
1
0
0
1
0
0
1
3
2
1
2
2
0
1
2
0
0
0
1
2
3
0
2
0
1
2
0
0
0
2
0
0
2
2
2
0
1
0
2
0
1
2
0
1
0
1
2
1
2
1
1
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
2
0
0
1
0
1
2
2
4
1
2
2
0
1
0
1
4
0
0
1
0
2
0
0
1
0
1
1
2
2
0
0
0
2
2
0
0
0
0
1
2
2
0
1
1
0
0
0
2
0
0
0
1
2
2
0
2
1
2
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
2
0
0
0
8
2
1
0
0
0
0
0
0
1
1
1
1
0
2
0
0
0
2
1
0
0
0
2
0
0
0
1
1
0
0
0
1
0
1
0
2
0
0
0
0
0
0
2
0
2
3
0
1
0
0
1
0
2
1
0
0
0
2
1
4
0
1
0
0
2
2
1
4
1
1
0
0
0
1
0
0
0
0
1
2
0
1
0
0
1
1
0
0
0
1
0
0
2
1
0
2
1
0
0
0
0
1
0
0
0
2
3
1
0
0
1
1
1
2
0
2
0
2
0
1
0
0
1
0
0
0
0
0
1
0
1
1
1
1
1
0
0
0
0
3
0
2
1
1
0
0
1
0
0
1
2
0
0
0
2
0
2
0
0
0
0
0
0
2
0
2
2
1
1
0
1
0
1
0
0
0
0
0
0
3
1
2
1
0
0
2
0
0
0
2
0
1
1
2
0
1
0
0
1
0
0
0
1
0
2
0
1
2
2
3
4
0
0
1
4
0
0
1
0
2
2
1
0
1
1
0
1
1
0
1
2
2
0
0
1
0
1
2
2
0
1
0
0
0
1
1
1
2
0
0
0
1
0
2
0
1
0
0
0
2
1
0
2
0
2
1
0
0
0
1
1
1
0
0
3
0
0
0
0
0
0
2
1
0
1
0
1
0
1
0
0
0
1
0
1
0
1
2
2
2
1
0
1
1
2
1
1
0
1
0
1
0
0
0
2
0
0
2
1
2
1
0
0
0
2
3
0
3
1
0
1
1
1
0
1
0
2
0
2
0
0
0
0
1
0
0
0
1
0
2
0
1
2
2
2
0
0
1
1
1
0
1
0
0
1
0
1
0
1
1
0
1
2
1
0
2
1
1
0
0
1
0
2
0
0
1
3
1
2
0
2
1
0
1
3
1
2
2
0
1
0
2
0
1
0
0
1
0
2
2
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
2
1
1
2
0
0
1
1
0
2
3
1
0
1
2
1
2
0
2
1
1
2
0
2
1
2
1
0
0
1
2
0
0
0
0
0
2
1
1
0
0
1
0
1
0
0
2
0
1
1
0
1
0
1
0
1
0
2
2
1
0
0
1
0
1
2
1
2
2
0
1
0
1
0
1
2
0
0
1
0
2
0
2
1
0
0
0
1
0
0
1
0
0
0
1
1
1
0
1
1
2
2
0
0
1
1
0
1
0
0
4
0
0
0
0
2
0
2
1
1
0
1
0
0
1
0
0
2
0
2
1
1
2
0
2
0
0
3
0
1
0
2
0
0
0
1
0
0
1
1
1
0
0
2
2
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
2
0
5
0
5
1
0
1
1
1
1
0
0
2
1
0
0
0
0
0
0
1
2
2
2
0
2
0
2
0
0
0
1
3
0
0
0
0
0
2
0
1
0
0
2
2
2
2
2
1
2
0
0
2
0
1
0
1
0
1
0
0
0
0
2
0
0
1
2
1
0
2
1
1
2
0
1
0
1
1
0
0
0
2
0
0
2
0
0
1
1
1
1
0
0
0
1
0
4
0
0
0
1
0
0
2
1
2
1
0
1
1
0
0
2
0
1
2
0
1
1
2
1
0
1
0
1
2
2
0
0
1
0
1
0
0
1
1
1
1
1
0
0
0
0
1
0
2
0
0
0
0
2
1
3
2
1
1
0
0
0
0
1
1
2
0
2
0
0
2
0
0
0
0
0
0
1
0
1
1
2
0
1
2
2
2
0
1
1
0
0
0
2
2
1
1
2
0
1
0
1
1
1
1
2
1
0
2
1
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
2
1
1
0
2
2
1
0
0
1
0
0
2
1
0
0
3
0
3
1
0
0
2
2
0
0
1
0
0
1
2
2
0
0
2
0
0
0
0
0
1
1
0
0
1
0
0
3
1
0
0
1
0
1
1
0
2
0
1
1
1
0
2
0
0
0
0
0
3
0
0
1
0
1
2
2
0
1
1
0
1
1
2
1
0
0
0
1
2
1
1
0
2
0
0
0
0
2
1
0
2
2
0
2
2
2
0
1
0
0
0
1
0
0
2
0
0
0
0
1
0
2
0
0
0
0
1
2
1
0
0
0
0
0
1
1
0
1
0
1
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
2
1
0
1
2
0
2
2
0
0
1
0
2
0
1
2
1
0
1
1
0
0
1
0
0
1
1
1
1
0
1
1
2
0
3
0
0
0
0
0
2
1
1
0
1
0
2
0
0
2
2
0
2
1
0
0
1
1
0
2
1
0
0
1
1
2
1
0
2
0
0
2
0
0
2
0
1
0
0
2
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
2
0
0
0
0
1
2
1
2
0
1
1
0
1
1
1
1
1
1
1
0
0
0
0
1
2
2
1
2
0
0
2
1
0
1
1
0
2
0
2
0
0
2
0
0
1
1
2
2
0
0
0
1
1
0
1
1
0
2
0
2
0
1
0
0
0
0
0
0
1
0
2
0
0
1
0
1
1
0
1
1
0
0
1
0
1
1
2
0
2
2
1
0
1
0
1
1
0
2
1
0
1
2
2
0
2
2
1
1
1
1
1
0
0
1
0
2
1
0
0
0
1
0
0
0
0
0
1
2
0
0
2
1
1
0
1
0
1
1
1
1
0
0
2
1
1
0
2
1
1
1
0
0
0
2
0
0
0
1
0
0
3
0
1
2
1
0
2
1
0
0
0
0
1
0
1
0
0
2
1
0
0
0
0
0
2
1
2
0
1
0
0
1
0
0
0
1
0
2
0
1
0
1
2
1
0
1
0
2
0
2
3
0
0
0
0
2
0
1
0
0
0
2
0
1
1
0
0
0
0
1
0
2
0
1
1
2
1
0
0
0
0
0
2
2
0
0
1
0
1
0
0
1
2
0
0
2
1
0
0
0
1
0
0
0
1
2
0
3
1
1
0
0
0
2
0
2
1
0
2
0
2
2
1
0
2
1
1
2
1
1
1
2
0
2
0
0
2
2
0
0
0
2
2
1
1
0
1
0
0
1
2
0
0
0
1
1
2
1
0
1
2
1
1
0
0
0
1
2
0
0
1
1
0
0
2
1
0
2
0
2
0
2
0
0
1
1
1
2
1
0
1
0
2
2
1
2
1
0
1
2
0
1
0
0
2
2
0
1
1
2
2
0
1
0
4
0
2
2
0
0
0
3
0
0
0
0
4
2
0
1
0
0
0
0
0
1
2
0
0
0
0
0
1
0
1
0
0
2
0
0
2
1
0
0
0
0
2
0
0
2
0
0
1
2
1
2
1
1
0
2
0
0
1
0
1
2
0
1
0
0
1
1
2
1
2
1
0
1
0
0
1
0
0
1
2
2
1
0
2
0
2
1
1
1
1
2
2
0
0
0
0
1
1
2
1
0
1
0
2
0
0
0
0
0
0
1
1
0
1
1
2
1
0
0
1
0
3
1
0
1
0
1
4
0
0
0
2
3
0
2
1
0
1
1
1
0
1
0
0
2
0
0
0
1
0
2
2
1
2
1
2
0
1
0
2
0
2
0
0
1
0
0
1
1
0
2
3
0
0
2
1
0
0
0
1
0
2
1
0
1
1
0
2
0
2
1
1
1
0
0
0
0
2
0
0
0
0
2
0
0
1
0
1
0
0
1
2
1
1
2
0
2
1
0
0
0
0
0
0
2
2
2
0
2
1
2
0
0
0
2
1
2
0
0
0
4
0
1
2
0
0
0
0
1
0
0
0
0
1
0
1
0
3
1
1
2
0
0
1
3
2
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
2
0
2
2
1
2
2
0
1
0
0
1
1
0
2
0
1
1
1
0
1
1
0
0
0
1
0
0
1
1
1
0
1
0
0
0
2
0
1
1
0
0
0
1
3
0
0
2
0
0
1
1
0
0
0
0
0
1
0
2
0
1
0
0
1
2
0
2
2
0
0
0
0
2
0
2
1
0
1
0
1
2
0
1
0
0
0
0
1
0
2
1
2
0
3
2
0
0
2
0
1
0
0
0
0
0
1
2
2
1
3
1
2
2
0
2
0
0
0
0
1
1
1
0
0
1
0
0
0
0
1
1
0
1
0
0
2
0
0
0
1
0
0
0
2
1
1
0
0
2
2
0
2
0
1
1
0
1
2
0
1
2
1
0
0
0
2
2
0
0
0
3
0
1
1
2
1
0
1
0
1
0
3
1
0
1
1
0
0
1
0
1
1
1
0
0
1
0
0
1
1
1
1
2
1
2
0
2
0
0
2
1
2
1
2
2
1
0
0
1
0
0
0
1
0
2
1
1
0
1
0
1
1
1
0
0
0
1
0
0
0
2
0
0
0
1
1
1
1
2
0
0
2
1
0
1
2
0
0
1
1
1
1
0
2
0
0
2
1
1
2
0
0
0
1
0
0
0
1
0
1
0
4
0
2
2
1
1
1
0
2
1
1
2
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
1
3
0
1
0
2
1
0
0
2
2
1
0
0
2
1
0
1
0
0
1
0
0
0
1
0
1
0
0
1
1
0
0
0
2
1
0
1
0
0
2
2
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
1
0
2
0
0
2
1
0
3
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
1
1
3
2
2
0
2
2
0
2
2
0
1
0
0
0
0
0
1
2
0
1
1
3
0
2
0
0
0
0
2
3
2
0
2
1
0
0
0
0
1
0
2
1
2
0
1
1
2
0
2
0
0
0
0
0
2
2
2
1
0
0
1
2
0
1
2
0
0
1
0
2
0
1
0
0
0
0
1
0
0
0
1
0
0
0
2
0
1
0
0
1
1
1
0
1
0
0
1
0
0
1
0
0
0
0
1
0
2
0
0
0
0
1
1
0
1
0
0
1
1
0
1
2
0
2
0
2
0
0
1
1
2
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
1
2
1
0
0
0
0
1
0
1
2
3
0
0
0
2
2
0
0
0
0
2
0
1
0
1
1
0
0
1
1
0
0
0
1
0
1
0
3
1
0
1
0
1
0
0
1
1
2
1
2
3
1
2
2
1
0
1
0
0
2
1
0
0
0
1
1
1
1
1
0
1
1
0
0
1
2
1
0
1
0
2
2
0
0
0
1
0
2
4
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
1
0
1
0
1
0
1
0
2
0
0
1
0
0
1
0
0
0
3
2
3
0
0
0
1
0
2
1
0
0
1
2
0
1
0
2
0
0
0
0
2
0
1
0
1
0
0
0
2
1
0
1
2
0
0
1
1
0
0
1
1
0
2
0
1
2
0
1
0
1
0
0
0
2
5
2
1
0
0
1
1
0
2
1
0
1
0
2
2
0
2
1
0
0
0
1
1
0
0
0
0
0
0
0
0
2
1
0
1
1
0
0
1
0
0
0
2
3
2
0
0
1
0
1
0
0
1
1
0
0
0
0
0
2
1
0
0
3
0
0
0
2
1
0
0
0
1
2
0
0
0
1
0
0
0
2
2
2
2
0
1
1
1
0
0
0
1
2
0
0
1
0
0
1
0
0
0
0
1
1
1
0
0
0
2
2
1
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
1
2
0
0
0
1
0
2
1
1
0
0
1
1
0
0
1
0
0
1
0
0
1
1
1
0
0
0
1
0
0
0
2
0
1
1
0
0
0
1
0
2
1
0
2
0
0
1
2
0
1
0
2
1
1
1
0
2
2
2
0
0
2
1
0
1
2
1
1
0
0
0
2
0
0
2
2
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
2
2
0
1
1
0
0
1
0
0
1
2
2
0
2
1
0
1
2
2
1
1
1
1
1
0
0
1
0
0
1
0
0
0
0
0
0
2
2
2
0
2
2
0
1
0
1
0
0
0
1
1
2
2
1
0
0
0
0
0
2
0
1
1
1
1
0
1
0
0
1
0
2
0
2
0
0
0
0
0
1
1
0
1
0
0
2
2
0
0
0
1
0
3
0
1
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
1
2
1
0
2
0
0
2
0
0
3
1
0
2
0
2
1
0
2
2
0
0
0
0
2
1
1
0
0
2
0
0
0
1
1
2
0
2
0
0
2
1
1
0
1
0
2
0
0
2
0
0
2
2
2
2
1
2
1
3
1
1
1
0
0
0
0
0
1
0
5
0
1
1
0
2
0
1
2
0
1
1
1
1
1
2
1
0
1
0
2
2
0
0
0
0
0
0
0
1
2
0
0
1
0
1
0
0
2
1
0
2
0
1
0
0
1
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
1
0
1
2
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
3
0
1
0
1
0
1
0
1
0
0
5
0
0
0
0
2
0
2
1
0
1
0
1
1
2
1
0
0
1
2
2
0
0
0
0
2
2
0
0
0
0
1
0
2
2
0
2
1
1
0
1
0
3
0
1
1
0
0
0
0
1
2
1
1
0
0
0
0
1
2
2
1
0
0
2
1
0
0
1
1
1
0
2
0
0
1
0
2
2
1
1
1
1
0
2
0
0
0
0
1
0
2
0
1
0
1
2
0
0
1
0
1
0
0
2
0
0
0
1
1
1
1
0
0
0
0
0
2
0
1
1
0
1
0
0
1
1
2
3
2
1
2
2
1
1
1
0
1
0
0
0
0
0
1
1
1
1
1
1
0
2
0
0
1
1
0
1
0
2
0
0
2
0
1
3
1
2
1
1
1
4
1
0
1
2
0
4
2
0
2
2
1
0
0
2
1
1
0
1
0
2
0
1
2
2
2
0
0
2
1
1
1
0
3
2
1
0
1
0
2
2
0
0
1
1
2
1
0
0
2
0
2
2
2
2
0
1
0
0
0
0
1
0
2
0
0
1
0
1
0
2
1
0
0
1
1
0
0
0
2
0
0
4
0
2
0
0
0
2
0
0
2
0
1
0
1
1
2
1
1
2
0
0
0
2
1
0
0
0
0
0
2
2
0
0
2
0
2
1
0
0
1
0
0
2
1
0
1
0
1
2
0
2
1
0
1
1
0
0
0
1
1
0
0
1
3
2
0
0
0
0
2
1
0
0
2
0
0
1
0
0
0
0
2
2
1
0
1
0
3
2
2
1
0
0
1
1
0
1
0
2
0
1
1
0
0
0
1
2
4
2
2
1
2
2
0
0
2
1
0
0
0
0
1
0
2
0
0
0
0
1
1
1
1
0
0
0
1
0
0
2
0
0
1
2
0
2
1
0
0
1
1
1
1
1
2
0
3
1
2
0
0
2
1
0
2
0
0
0
2
0
0
0
0
1
0
0
1
0
3
0
1
2
0
1
2
0
0
0
1
2
1
1
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
1
0
1
1
1
0
1
0
2
1
0
2
1
0
0
1
2
0
0
0
1
2
0
2
0
0
0
0
0
2
0
0
1
1
0
0
2
1
0
0
0
0
2
0
1
2
0
0
1
2
0
2
0
1
0
1
0
2
1
0
1
0
0
0
1
0
2
1
0
0
0
0
0
0
0
1
0
2
1
0
1
1
0
0
1
0
0
2
0
2
0
1
1
1
0
2
2
0
1
1
1
2
0
0
0
1
1
0
0
0
1
0
1
0
1
2
0
2
0
0
0
0
2
2
2
0
0
0
0
1
1
0
1
0
1
1
2
1
2
0
3
1
1
0
0
2
1
1
2
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
2
0
2
0
0
0
0
0
2
2
2
1
1
0
1
0
0
0
0
0
0
0
0
0
2
1
1
3
1
0
0
0
1
1
0
0
0
1
0
1
2
0
1
0
2
2
1
2
2
1
0
2
1
2
2
0
1
1
0
1
1
1
0
0
0
1
0
1
0
0
0
0
0
1
2
0
1
2
0
0
6
0
1
2
1
0
2
0
0
0
1
1
0
2
1
0
2
0
2
1
2
0
1
0
3
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
2
0
2
0
2
1
1
1
0
2
1
2
0
0
0
0
0
2
0
0
1
0
1
1
0
0
1
0
1
0
1
1
0
2
1
0
1
0
2
2
0
2
1
0
0
0
2
0
0
0
0
0
1
1
0
1
0
1
0
1
0
1
0
1
1
0
1
0
0
1
0
1
2
1
1
0
0
0
0
2
1
0
1
0
1
0
1
1
0
1
1
1
0
1
0
0
0
0
1
1
2
0
0
2
0
0
0
2
0
1
1
1
0
0
1
2
0
0
1
0
0
0
0
1
0
0
1
0
2
1
0
1
1
1
1
1
1
0
0
0
1
1
0
2
0
2
1
0
0
2
0
0
0
1
0
0
1
0
2
1
2
1
0
0
1
1
1
0
0
0
1
1
0
0
1
2
1
1
0
0
2
1
0
1
0
0
1
1
1
2
0
0
3
0
0
2
0
1
0
0
2
1
1
0
1
1
0
2
1
1
0
0
1
1
0
2
0
2
0
2
1
1
0
0
1
1
0
1
2
0
2
0
1
1
0
0
0
0
1
1
0
2
0
0
1
2
2
0
0
0
1
0
2
2
1
0
1
0
1
1
1
1
0
0
2
1
0
1
0
0
0
1
1
2
0
1
3
1
1
2
2
2
1
0
2
2
0
0
7
0
0
0
2
0
1
0
0
1
1
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
1
2
2
1
0
1
1
3
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
1
2
1
0
1
1
1
0
0
0
2
0
1
1
0
2
1
0
1
0
0
2
2
0
0
0
0
0
0
1
2
0
1
2
0
1
2
0
1
0
2
2
2
0
0
2
1
1
0
2
2
1
2
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
3
0
0
0
0
1
0
1
1
1
0
3
1
1
2
1
0
0
0
1
0
0
1
2
0
0
1
2
1
1
1
0
0
0
1
2
1
1
1
0
1
1
2
1
0
0
0
2
2
0
2
2
1
2
0
2
0
2
3
1
2
0
0
1
2
1
2
0
2
0
3
2
2
2
1
1
0
0
0
0
2
0
1
1
3
0
0
1
2
0
0
0
1
0
0
0
0
0
0
2
1
2
0
2
0
0
0
2
1
1
1
2
0
2
0
0
0
1
0
0
0
1
1
0
0
3
0
0
1
0
0
1
1
1
0
0
1
0
0
0
1
0
1
1
1
0
1
0
0
0
2
0
1
2
2
1
1
0
0
0
0
2
2
1
1
1
0
0
1
5
1
0
0
0
5
2
0
2
0
0
2
1
0
2
2
0
1
5
1
0
1
2
0
0
1
0
1
2
1
0
1
0
1
2
1
0
0
0
1
0
1
2
0
1
1
0
0
1
0
0
1
0
1
0
0
0
1
1
0
1
0
1
2
2
0
1
1
1
0
1
1
1
0
1
0
0
0
2
2
0
0
1
0
2
0
1
1
0
2
0
0
0
0
0
1
0
1
0
0
0
1
1
2
1
1
1
0
0
0
2
0
0
1
0
1
1
0
0
2
2
0
1
0
0
0
2
2
0
0
0
0
0
0
0
2
1
2
0
1
0
3
2
4
2
2
2
4
0
1
0
0
1
1
0
0
0
1
0
2
3
0
2
1
0
1
1
2
1
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
2
2
0
0
1
1
2
2
1
2
0
2
2
1
1
2
1
0
0
1
0
2
2
1
0
1
0
0
0
0
0
1
4
2
2
2
0
1
1
0
0
1
0
0
0
0
1
2
0
0
0
0
1
0
0
1
1
0
0
2
0
0
2
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
2
0
0
1
1
0
1
1
0
2
1
2
1
1
1
0
1
0
1
1
0
0
0
0
2
1
0
0
1
0
0
1
1
0
0
2
0
1
0
2
0
2
0
1
0
1
0
0
0
1
2
1
1
1
0
1
0
1
0
1
2
2
0
1
1
0
1
2
0
1
1
1
0
0
0
2
0
0
0
0
2
1
3
1
0
2
2
1
2
0
0
0
0
1
1
0
1
2
4
1
2
2
1
1
2
1
1
2
2
1
0
0
0
1
0
2
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
3
2
2
0
2
0
0
1
1
1
0
0
0
2
1
0
1
1
0
0
2
0
1
0
0
0
0
1
1
0
0
2
2
0
1
0
0
0
1
1
0
1
2
0
4
0
0
2
2
1
1
1
0
2
2
0
0
0
2
1
0
2
0
0
1
1
0
3
0
0
1
0
2
0
0
0
1
0
0
0
1
0
2
0
2
0
0
0
1
0
1
0
1
0
2
0
1
1
2
0
0
1
1
1
0
0
4
2
1
2
0
0
1
1
2
2
0
1
0
0
0
2
0
2
0
0
2
0
1
0
2
0
0
2
0
2
0
0
1
2
0
2
0
2
1
2
2
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
2
1
0
0
0
2
0
1
1
1
0
1
0
0
1
0
0
2
0
1
2
0
1
2
0
0
0
0
2
1
0
1
2
1
2
1
0
0
0
1
0
3
3
0
2
2
0
0
0
2
1
2
0
0
2
1
2
2
2
0
0
1
6
0
0
1
0
1
0
4
0
1
0
0
2
0
0
1
1
0
0
1
1
0
0
0
0
2
4
1
0
0
0
0
0
1
1
0
1
1
0
0
1
1
0
1
0
0
0
1
0
2
1
1
1
0
1
0
1
0
0
1
0
1
0
0
0
0
1
0
0
3
0
1
1
0
0
1
0
0
0
2
0
1
0
0
0
1
2
1
2
2
0
0
0
2
1
1
2
2
2
1
1
0
0
2
2
0
0
0
0
1
0
1
0
1
0
1
0
2
0
1
0
0
0
0
2
1
0
1
2
1
0
1
0
1
0
1
0
1
0
0
0
1
0
1
0
3
2
0
0
0
0
0
0
2
1
1
1
0
1
1
0
0
1
1
0
0
1
0
1
2
0
2
1
1
0
1
1
0
1
1
1
0
3
0
0
2
0
1
0
2
0
0
1
0
0
2
0
1
0
1
0
1
1
4
0
1
0
0
1
1
1
0
0
2
0
3
1
0
0
0
0
0
2
1
0
1
2
0
2
2
1
1
1
0
1
2
1
0
1
1
0
0
2
1
0
2
2
1
1
0
0
1
0
2
1
1
0
1
0
1
2
1
0
1
1
0
1
1
2
2
0
2
0
1
0
0
0
0
0
0
2
0
0
1
0
1
0
1
1
2
0
0
0
1
2
0
2
0
0
0
1
2
1
1
1
0
0
1
1
1
0
1
1
1
2
1
2
0
1
2
2
0
0
1
0
1
1
1
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
3
0
0
1
0
2
0
0
2
3
1
1
1
1
0
0
1
0
0
0
1
1
1
1
2
0
2
0
1
2
0
1
1
0
0
0
0
1
2
0
0
0
2
1
1
0
0
1
0
0
0
1
1
2
0
1
0
2
0
0
2
0
1
0
2
0
0
2
0
0
0
1
2
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
1
0
0
1
2
0
0
0
0
1
0
1
0
1
0
0
1
2
0
1
1
1
0
2
0
0
0
0
1
0
0
0
1
0
1
0
1
1
0
0
0
1
0
0
1
0
1
2
0
0
3
0
2
1
2
0
3
1
2
0
1
2
1
0
0
0
1
1
1
0
0
0
1
0
2
2
3
1
3
2
0
1
0
0
1
0
2
1
1
0
1
2
2
2
0
1
2
1
1
0
1
0
1
0
0
0
1
0
1
0
1
3
0
0
2
0
0
2
2
2
0
0
0
2
0
1
1
0
2
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
2
2
3
2
1
0
0
0
2
0
0
0
0
1
1
0
1
0
3
0
0
0
1
2
1
0
1
0
0
3
1
0
1
0
0
2
1
0
0
0
0
2
0
0
0
2
1
0
0
3
0
0
1
0
1
0
2
0
2
1
0
2
0
2
0
0
0
1
0
0
0
2
0
1
0
1
0
0
1
2
0
2
0
2
1
0
1
0
0
0
0
0
2
1
2
2
0
0
1
2
2
2
0
2
0
1
1
2
0
2
0
0
2
0
0
0
2
0
2
2
0
0
2
0
0
2
2
3
0
1
1
2
0
0
0
2
2
1
0
2
1
1
0
3
2
2
0
0
1
2
2
0
0
2
2
0
0
0
1
2
1
0
0
2
0
0
0
1
0
0
1
2
1
1
2
0
2
2
0
1
0
1
2
0
1
2
0
2
0
0
0
2
2
1
0
0
2
0
1
3
0
1
1
1
1
1
1
0
0
0
0
0
2
0
1
1
2
0
0
1
1
1
0
1
2
1
1
0
0
0
1
2
0
0
0
1
0
1
2
2
0
3
0
1
0
3
1
0
0
0
2
0
0
2
0
2
2
1
1
0
1
1
2
0
2
1
1
1
0
1
2
0
1
1
0
0
2
1
2
0
2
2
1
0
1
0
2
1
1
0
0
0
0
1
0
1
0
2
2
1
1
0
0
2
0
0
1
0
2
0
0
0
2
0
1
2
1
1
0
2
1
0
2
0
0
2
1
2
0
1
1
0
1
2
2
0
0
0
1
0
0
2
2
2
1
1
0
1
0
0
2
0
2
0
0
1
2
0
2
0
1
0
0
1
1
0
1
0
2
1
0
1
0
2
1
2
1
0
0
0
0
1
0
1
2
0
0
0
0
0
0
1
3
0
2
1
0
0
0
0
1
0
0
0
2
1
0
1
2
0
0
0
1
1
0
0
0
0
0
2
1
1
2
0
1
0
2
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
2
1
0
0
0
2
0
0
1
0
0
1
1
2
2
0
1
1
2
2
1
3
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
2
0
0
1
1
0
1
0
0
1
2
1
1
0
1
2
0
1
2
1
1
1
0
0
0
0
0
0
1
4
2
0
0
0
0
0
0
0
2
1
1
0
2
1
2
0
2
2
2
2
1
0
0
1
0
0
0
2
0
1
1
1
1
0
2
1
0
1
1
2
0
0
2
0
2
2
0
2
1
0
1
1
2
2
0
0
1
0
0
1
2
2
2
1
1
0
0
0
2
1
10
1
0
0
0
1
1
0
0
2
1
0
1
0
1
0
0
0
1
0
2
2
0
0
2
1
2
0
1
0
0
2
2
1
2
2
2
0
1
0
2
1
1
1
1
2
0
0
0
0
2
0
1
0
0
0
0
1
0
0
1
1
0
2
2
2
1
0
1
0
0
1
1
2
2
0
2
0
0
1
0
2
0
2
2
1
1
0
2
1
1
0
0
2
0
2
1
1
1
0
0
2
0
0
2
0
2
0
1
0
0
0
2
2
0
0
2
1
1
0
0
0
0
2
0
2
0
0
2
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
1
0
2
1
2
2
0
0
1
1
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
1
0
3
0
2
1
0
0
1
0
1
1
0
0
0
2
0
0
0
0
2
0
0
0
0
1
2
0
0
2
0
1
2
2
1
1
1
1
2
1
2
1
1
2
1
1
0
2
1
1
2
2
1
0
0
2
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
2
2
0
1
1
1
0
0
0
1
1
0
0
0
0
0
1
2
1
1
2
0
3
2
1
2
0
1
1
1
0
0
1
0
1
1
0
2
0
1
2
2
0
2
1
4
0
1
2
1
2
0
1
0
0
1
1
2
1
2
0
1
0
2
2
0
1
2
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
1
2
2
0
1
1
0
1
1
1
0
0
3
0
0
0
0
1
0
1
0
2
1
0
0
0
1
0
0
2
3
0
1
2
2
0
0
0
1
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
1
0
0
2
1
2
0
1
0
3
0
1
1
1
0
0
2
1
2
2
1
0
0
0
0
0
0
2
0
1
0
1
1
0
1
1
2
0
1
0
0
0
1
1
0
0
1
0
1
0
2
0
0
0
1
1
0
0
0
2
1
0
2
0
0
0
0
1
0
2
1
0
1
1
1
1
2
0
2
0
0
0
1
1
1
0
2
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
3
1
0
2
1
1
0
1
2
1
2
2
1
2
2
1
0
0
0
0
2
0
1
2
0
0
0
1
1
0
0
0
0
1
2
1
2
0
1
1
1
2
2
0
2
1
1
1
0
0
0
0
0
1
1
2
2
2
1
0
0
0
0
2
0
1
0
0
1
1
1
0
1
0
2
1
2
0
2
1
2
1
1
2
2
2
0
1
2
1
0
0
1
0
1
0
0
2
0
2
2
2
1
0
0
1
2
0
0
1
2
1
0
1
1
1
0
0
1
0
2
0
0
0
0
2
0
0
0
2
1
0
0
1
0
2
0
1
4
0
1
1
2
2
1
2
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
2
0
1
0
1
2
1
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
2
0
1
0
0
0
1
0
0
1
2
1
0
2
0
1
0
1
1
0
1
1
2
0
0
2
0
0
2
0
0
1
0
1
1
0
2
2
1
0
1
0
1
2
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
2
0
0
1
0
1
1
1
0
0
1
0
0
0
1
0
0
0
0
0
5
2
2
0
0
2
1
0
0
0
0
0
0
3
0
0
1
2
2
0
2
1
2
0
0
0
1
0
1
2
1
2
1
2
2
0
0
1
0
1
2
2
2
1
0
0
0
0
0
0
1
1
1
0
2
1
1
0
1
0
0
1
0
0
2
1
0
0
0
1
1
2
0
2
0
0
2
0
0
0
1
0
1
0
2
0
2
0
0
0
3
1
1
0
0
0
0
0
1
0
2
0
0
1
0
2
1
2
0
2
1
0
0
1
0
0
0
0
1
1
2
0
1
0
0
0
3
0
0
0
1
0
1
0
0
0
1
1
0
1
1
0
0
3
2
1
0
0
1
1
2
3
0
1
1
0
0
1
0
0
1
1
1
0
1
0
1
2
1
0
2
0
0
0
0
0
1
1
2
1
2
0
0
0
0
1
0
0
1
0
0
2
0
0
0
2
1
1
0
2
5
0
0
0
1
0
0
2
2
0
0
2
1
0
0
0
0
0
1
0
0
1
0
1
2
1
0
1
2
4
1
0
2
1
0
1
1
1
0
0
2
0
0
0
1
2
0
2
0
0
0
0
0
2
1
0
0
2
1
0
2
0
0
2
1
0
0
0
2
0
1
1
1
2
3
0
0
1
0
1
0
0
0
1
0
1
0
1
2
0
1
2
0
0
1
0
0
0
1
0
1
0
1
0
0
1
1
2
1
2
1
1
0
1
0
2
2
0
0
1
0
1
2
2
1
2
0
1
2
0
1
2
0
2
1
0
0
0
0
0
0
2
0
3
0
0
0
0
2
0
2
1
1
0
0
2
1
1
1
0
0
0
2
1
0
0
0
1
0
1
1
0
3
0
0
0
0
0
0
0
0
3
3
1
1
2
0
0
1
1
0
0
1
1
2
0
1
0
1
0
0
1
2
1
0
1
0
2
1
3
2
2
1
1
1
0
1
0
0
0
1
0
2
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
1
1
0
0
1
2
0
0
0
1
1
2
1
2
0
0
0
0
0
2
1
0
0
0
0
2
0
1
1
0
0
1
0
1
2
2
0
2
0
3
1
1
0
1
1
4
2
0
0
1
1
1
1
0
0
0
1
1
1
0
0
1
1
0
1
0
0
0
2
1
2
0
0
2
2
0
2
1
0
2
2
2
0
1
0
1
1
1
2
1
0
0
0
1
0
2
1
2
0
1
1
0
1
2
0
0
0
1
1
1
1
0
0
3
0
1
0
0
0
2
0
2
0
1
2
0
2
0
1
0
0
1
0
0
0
0
1
2
0
0
1
2
0
2
0
0
0
2
0
1
0
2
2
1
1
0
0
0
1
0
0
0
0
0
3
1
1
0
0
0
0
1
2
0
0
1
1
0
1
0
1
0
1
2
2
2
0
1
2
0
0
0
0
0
2
2
0
1
0
1
2
0
0
1
0
0
2
2
2
1
1
1
1
1
0
2
0
0
0
0
1
0
1
1
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
2
0
1
0
1
0
1
1
0
0
0
1
1
1
0
0
0
0
1
0
0
1
1
0
2
0
0
1
0
1
2
0
1
0
0
2
1
1
0
3
1
1
1
0
0
2
0
2
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
1
0
0
1
0
0
1
0
0
1
2
2
0
0
2
1
0
1
0
2
0
1
0
2
1
0
1
1
1
0
0
1
2
1
1
1
1
2
2
1
1
0
1
0
0
0
0
1
0
0
2
0
3
0
1
0
0
0
1
2
0
0
0
0
0
1
0
2
1
2
0
0
1
0
0
1
0
2
0
1
0
2
0
1
1
2
2
0
0
1
1
2
0
2
0
4
0
0
0
2
1
0
0
1
0
0
1
2
1
2
0
0
0
1
0
1
1
2
0
1
1
0
1
0
0
1
1
1
0
1
0
0
0
1
2
0
2
1
1
0
0
1
0
1
2
0
0
2
1
0
3
0
1
0
1
1
0
0
4
1
1
0
0
2
1
0
1
2
0
1
1
1
0
0
0
0
2
0
1
1
0
3
1
1
1
0
2
1
2
0
0
0
2
3
1
2
1
0
2
0
3
3
0
0
0
1
1
0
3
2
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
1
1
2
0
1
0
0
1
2
0
0
0
1
2
2
0
2
0
0
1
1
0
2
0
1
0
1
0
0
1
0
0
1
0
0
0
1
0
1
1
3
2
0
0
0
0
0
1
2
0
1
0
2
0
3
1
2
1
1
1
0
1
1
2
0
0
1
1
0
0
0
0
0
0
2
3
0
0
1
1
0
0
0
1
1
1
0
1
0
0
0
2
0
1
1
1
0
2
1
0
2
1
0
0
0
2
0
1
1
0
2
1
2
2
0
1
2
0
1
2
0
0
0
0
2
0
1
0
2
0
1
1
1
1
0
0
0
0
2
2
7
0
0
1
1
2
0
0
1
1
1
0
0
0
0
0
1
0
0
3
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
2
0
1
0
0
0
0
1
2
1
0
0
0
1
0
1
2
2
0
0
0
1
1
0
1
1
1
2
1
2
1
0
1
0
0
2
2
0
0
0
0
2
0
1
2
0
1
1
2
0
0
1
0
0
0
2
0
0
0
0
0
2
1
1
1
0
1
1
1
1
0
1
0
0
0
1
0
1
0
0
2
2
1
0
0
0
0
0
2
0
2
0
1
1
0
1
0
0
0
0
2
1
0
5
0
1
2
1
2
0
0
2
1
2
0
0
1
0
2
1
0
2
0
0
2
2
0
2
2
0
1
1
1
0
0
0
1
1
1
2
0
0
0
0
0
2
1
1
0
2
1
0
1
3
2
1
1
0
1
0
1
0
0
1
1
1
1
3
0
2
0
0
0
1
0
1
1
1
0
1
0
1
2
0
2
0
0
0
2
1
1
2
1
1
1
0
0
1
0
0
2
1
1
1
1
1
0
2
2
1
2
1
2
0
0
0
0
2
2
2
0
1
2
0
0
0
0
0
2
0
1
1
0
0
2
2
1
0
0
2
1
0
0
0
3
0
0
2
0
1
1
0
1
3
2
2
0
0
0
0
1
2
0
1
0
1
1
1
1
0
0
1
1
1
1
0
1
0
0
1
0
1
0
2
2
0
1
2
1
2
0
1
1
1
0
2
0
0
1
0
1
0
0
1
1
1
0
0
1
0
0
0
3
2
2
1
1
1
0
0
1
1
1
0
2
0
1
0
0
1
0
1
1
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
5
0
1
1
0
2
0
1
1
1
0
0
0
1
0
0
0
0
1
0
0
2
1
3
1
1
0
1
0
1
1
1
2
0
0
1
1
0
1
1
0
0
1
0
0
0
0
1
0
0
0
2
1
0
0
0
2
1
0
0
1
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
2
2
1
0
2
2
0
0
1
2
2
1
0
0
0
1
0
1
1
1
0
0
0
0
0
2
0
0
1
1
1
0
2
1
0
2
2
0
1
2
0
1
2
0
0
0
0
1
0
1
1
0
1
0
0
0
0
2
0
1
0
0
1
0
4
0
1
0
0
0
1
0
1
0
2
0
0
0
0
1
0
0
0
0
2
0
2
2
1
0
1
2
0
2
0
0
0
1
2
1
0
0
2
1
0
2
2
2
0
2
0
1
0
0
2
0
1
2
2
0
0
0
0
1
0
0
0
2
0
1
0
1
1
1
1
0
0
0
1
1
0
1
0
1
0
1
1
2
0
0
2
1
0
0
0
0
1
0
1
0
2
1
0
2
1
2
0
0
1
0
1
0
0
1
0
0
0
1
1
2
0
0
0
0
1
0
0
0
2
2
2
1
1
0
0
0
0
0
2
1
0
0
0
0
2
2
2
0
1
0
0
2
2
2
2
2
0
1
1
0
0
0
1
0
1
0
0
2
0
1
1
0
2
2
1
0
0
2
0
1
0
0
2
0
0
1
0
1
1
2
1
0
1
2
1
1
0
0
0
1
2
0
0
0
1
1
0
2
0
2
0
0
2
1
0
0
0
1
0
0
0
1
0
0
0
1
0
2
0
0
2
1
1
10
0
1
1
1
1
1
1
0
1
0
0
1
1
3
0
1
2
0
2
0
2
0
0
0
0
0
1
1
1
0
0
3
1
1
0
0
2
1
3
1
0
0
0
0
4
0
1
0
1
0
1
0
1
1
2
0
1
2
0
0
2
0
0
1
1
0
0
2
0
1
0
2
2
0
0
0
2
3
0
1
1
2
1
0
1
0
0
0
0
2
0
0
1
1
1
1
3
1
0
0
0
0
0
1
1
1
0
2
0
1
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
1
1
2
0
0
2
2
1
1
0
0
1
0
1
0
2
0
0
0
0
0
1
1
0
1
1
0
1
0
0
1
0
0
1
1
0
0
1
2
2
0
0
2
0
2
2
0
0
0
0
0
2
0
1
0
2
0
1
1
1
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
1
0
0
0
2
0
0
0
1
2
2
0
0
1
0
0
0
0
2
0
2
1
1
2
2
0
0
0
0
2
0
0
3
0
1
1
1
1
0
0
0
2
0
0
2
1
0
0
2
0
0
0
2
0
2
0
0
1
2
0
0
0
0
2
1
0
2
1
0
0
1
2
1
0
1
2
0
1
1
0
0
1
0
2
0
0
0
0
0
2
2
2
0
2
2
1
1
0
1
0
0
2
2
1
2
0
2
1
1
0
0
0
0
1
1
0
0
1
0
2
1
0
1
1
0
0
0
0
3
2
0
1
0
0
0
3
1
0
1
0
0
0
4
0
1
0
2
1
0
1
0
2
0
0
1
1
1
1
2
1
1
8
0
2
0
1
1
1
0
0
0
1
2
1
0
0
2
1
1
0
1
0
1
1
0
1
0
0
1
1
0
1
1
1
0
1
0
2
1
0
0
0
0
0
1
0
0
0
1
2
1
0
0
1
1
2
1
0
0
0
0
0
0
2
1
2
1
0
2
1
1
0
0
0
1
0
0
1
0
1
0
0
1
1
1
2
2
0
0
2
0
0
0
0
2
2
6
0
0
0
2
0
2
4
0
0
0
1
2
0
0
1
1
0
1
0
2
0
0
1
2
0
0
0
1
2
1
1
1
0
1
1
0
1
0
2
1
0
1
2
2
1
0
0
0
2
0
0
1
0
0
2
0
1
0
0
2
0
0
1
0
0
0
0
0
1
1
1
1
1
0
0
0
0
1
0
1
1
0
0
2
1
1
2
0
1
0
1
0
1
0
0
0
0
1
3
2
0
0
1
2
0
2
1
2
0
2
2
1
0
0
1
0
2
1
0
0
1
0
1
1
0
2
0
1
0
1
1
0
0
1
0
1
2
1
0
0
1
0
1
0
0
2
2
0
1
0
0
1
0
1
0
2
0
2
0
1
1
0
1
0
0
0
3
0
1
1
4
1
0
1
0
0
0
2
0
0
4
2
2
2
0
0
1
1
2
1
1
0
2
1
0
2
1
1
1
0
2
0
2
0
0
1
0
0
0
0
1
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
2
3
0
0
0
2
0
1
0
0
0
1
1
1
0
0
0
2
1
1
0
0
1
1
0
0
1
1
2
0
0
2
1
2
1
1
0
0
0
2
1
0
0
1
1
0
0
0
1
2
0
1
0
0
2
2
0
2
1
0
2
1
0
0
0
0
2
3
1
0
2
0
2
1
0
1
0
0
0
0
0
1
2
0
0
0
0
1
2
1
0
1
0
1
0
2
0
2
1
0
1
1
1
0
2
2
0
2
1
2
0
1
0
0
0
0
2
0
0
1
2
1
0
1
1
0
2
2
1
1
0
0
0
0
0
0
3
1
4
1
0
0
0
0
1
2
1
0
1
2
0
0
2
0
0
0
2
2
0
0
0
2
2
2
0
2
1
0
2
0
1
0
0
0
2
0
0
0
1
0
1
0
0
2
0
0
0
0
1
0
0
0
4
2
2
0
1
1
1
2
0
2
0
0
0
0
2
1
0
2
1
2
0
0
1
1
0
0
0
0
0
0
2
0
0
0
1
1
0
1
0
2
2
0
0
1
1
1
0
1
2
3
2
2
0
0
0
0
2
0
7
0
1
3
0
0
2
0
4
0
1
0
0
0
2
0
1
0
0
1
0
2
2
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
2
0
0
1
1
1
0
2
0
1
1
0
1
1
1
0
1
0
0
3
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
1
0
0
2
2
0
1
0
2
1
0
0
1
2
0
2
0
0
0
1
0
1
0
0
1
1
0
2
0
1
2
1
2
0
0
1
2
0
0
0
0
2
0
1
1
0
2
0
1
0
0
1
1
0
2
1
0
0
2
0
2
0
0
2
1
0
2
1
1
0
1
0
1
1
1
1
2
1
4
0
1
1
0
0
1
2
0
1
0
1
0
0
2
2
0
0
1
0
0
3
2
1
0
1
3
3
2
1
1
1
4
2
0
2
0
0
8
1
0
1
1
2
2
1
0
1
1
2
1
0
0
0
1
1
2
1
0
1
0
1
1
0
0
0
0
0
0
1
1
0
1
0
0
1
2
0
0
1
0
0
0
0
2
0
2
2
2
0
0
0
0
1
1
2
0
0
0
0
0
0
2
0
1
0
1
2
1
0
1
0
0
1
0
1
2
0
2
0
1
1
2
1
0
1
0
0
0
0
1
2
1
0
0
1
0
1
2
1
0
1
0
1
1
1
0
1
2
0
0
0
1
4
1
0
0
0
0
1
0
0
0
1
3
2
0
0
0
2
1
0
2
0
0
1
1
2
2
0
1
1
0
0
1
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
2
2
0
0
0
0
1
2
2
1
1
2
1
0
2
0
2
0
2
0
0
0
2
2
0
1
0
0
1
1
1
0
4
2
1
0
2
0
0
2
0
1
0
0
2
1
1
0
1
1
2
1
1
0
0
0
1
0
0
1
1
0
2
0
0
1
0
0
0
2
0
2
0
1
0
1
2
0
0
0
0
1
4
1
0
1
1
2
0
0
1
0
1
0
0
1
0
2
0
1
1
0
1
0
1
0
2
2
0
0
1
0
1
0
0
0
1
0
0
2
2
2
1
1
2
3
1
2
0
0
2
0
0
0
1
0
0
0
1
2
0
1
2
1
0
0
1
0
0
0
0
1
2
2
0
0
2
1
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
2
0
0
0
0
3
0
2
0
1
0
0
2
2
0
2
0
1
0
2
0
1
0
0
0
1
1
0
0
1
1
0
2
0
0
0
0
1
0
0
2
0
2
2
0
0
0
1
0
1
1
0
0
2
0
2
0
0
1
1
0
2
1
0
1
2
3
1
0
0
1
0
0
0
2
1
2
0
2
1
2
2
2
1
1
0
1
1
0
0
1
0
0
0
0
2
1
2
0
0
2
0
0
2
1
1
1
0
0
0
2
0
0
2
1
2
0
0
0
2
0
0
0
2
0
0
2
1
0
0
0
2
0
0
1
0
0
0
3
2
2
1
0
2
0
2
0
0
0
0
0
0
0
2
1
0
0
2
0
2
0
0
3
0
0
1
1
0
0
1
0
0
1
3
1
0
0
0
1
2
0
2
1
1
1
1
0
0
0
0
1
2
1
2
1
0
2
0
2
0
2
0
2
0
0
0
1
0
0
2
0
0
0
1
1
2
1
0
0
2
0
1
2
0
1
1
5
0
1
0
2
2
0
2
2
0
2
0
1
2
1
0
1
0
0
1
1
0
0
0
1
0
1
0
1
0
2
1
2
0
0
0
1
2
1
2
0
0
0
0
2
0
2
0
1
1
1
0
0
1
1
1
3
2
2
0
1
2
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
1
0
1
2
2
1
2
0
0
1
1
0
0
0
2
2
0
0
0
2
1
0
0
2
2
1
0
0
0
1
2
1
0
1
0
1
1
0
0
1
1
0
0
0
1
0
0
0
0
0
2
2
2
1
2
1
0
1
1
2
0
0
1
0
0
1
0
1
0
0
1
0
0
2
2
1
1
0
2
0
0
2
0
1
3
2
0
0
2
2
0
2
0
1
0
0
0
0
1
2
0
2
2
0
0
1
2
0
2
1
2
0
2
1
1
1
0
0
2
0
0
1
0
1
0
1
0
2
2
0
2
0
0
1
0
2
1
0
0
2
0
2
0
0
0
0
0
0
1
0
2
0
2
0
1
1
2
2
0
1
1
0
1
2
2
2
1
4
1
1
0
0
2
0
1
9
0
2
1
2
0
0
2
0
2
0
0
0
0
0
2
1
0
0
0
2
2
1
1
0
0
1
0
0
0
2
0
1
0
0
0
2
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
1
1
0
0
2
0
3
2
0
0
3
0
1
1
0
0
1
0
0
0
0
0
1
1
0
2
0
1
0
1
2
0
1
0
1
1
0
1
1
0
0
0
0
3
0
0
2
0
0
0
1
0
1
1
2
2
1
2
0
2
0
0
1
3
1
0
0
0
1
2
0
2
2
2
1
0
1
1
2
1
1
0
0
0
0
0
0
1
1
2
0
0
1
1
1
1
0
0
0
0
0
0
1
1
2
0
1
0
0
0
0
0
1
1
1
0
0
0
1
2
2
0
2
1
2
0
0
0
2
0
2
2
1
0
0
0
0
0
0
2
0
0
2
2
0
0
1
1
2
1
2
3
0
0
1
1
0
1
1
0
1
2
0
0
2
2
0
1
0
0
0
1
1
1
0
2
0
1
1
0
1
0
0
0
0
0
2
0
1
0
0
1
0
0
0
1
2
0
1
0
0
0
2
1
1
0
0
0
2
0
0
0
3
2
0
3
0
0
2
4
2
0
0
0
0
0
0
0
1
2
1
2
0
1
2
0
1
0
0
2
0
0
0
1
0
1
0
0
1
2
0
0
0
1
0
0
0
1
0
2
1
0
0
0
1
1
1
0
2
0
2
0
0
0
1
2
0
0
0
0
0
0
3
1
0
1
0
0
0
2
0
2
0
1
1
0
0
0
2
1
0
2
0
1
0
0
0
2
2
0
0
2
1
0
2
1
1
0
0
2
1
2
1
0
0
1
0
1
2
2
1
0
2
0
1
4
1
1
0
0
1
2
2
0
1
1
1
1
0
0
1
0
0
1
1
2
1
0
0
0
1
1
1
3
0
0
0
1
1
1
2
2
0
0
1
2
0
0
0
1
1
1
0
0
0
0
0
0
0
2
2
0
1
2
0
0
1
0
0
0
1
2
2
2
0
2
1
0
2
0
0
1
1
0
0
1
3
0
2
0
2
0
1
2
0
0
0
2
2
1
1
0
0
1
0
0
0
0
0
0
2
1
0
0
0
1
2
2
2
0
1
2
1
0
1
1
2
0
1
1
1
0
0
1
0
2
2
0
1
2
0
2
1
0
0
3
1
0
0
1
1
0
2
0
2
0
3
1
0
1
1
1
1
2
0
0
2
1
2
0
1
0
2
2
1
1
0
0
0
2
0
2
0
1
1
0
2
1
0
2
0
0
0
0
0
1
1
1
0
0
2
0
1
0
1
0
2
0
2
0
1
0
0
0
0
1
0
2
0
1
0
2
0
0
0
0
0
1
2
1
0
2
0
0
1
0
1
0
1
0
2
0
2
0
0
2
1
1
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
1
0
2
0
0
1
1
0
2
1
0
1
2
0
2
1
1
1
0
0
1
1
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
3
1
0
1
1
0
0
2
1
0
1
2
1
1
0
0
0
0
0
1
0
2
1
2
0
0
0
0
1
1
0
0
0
2
2
2
0
1
0
0
2
0
0
0
1
0
1
1
0
0
1
0
2
2
0
1
0
0
1
1
0
2
1
0
2
0
2
0
0
2
2
0
0
0
0
0
0
1
0
0
1
1
1
0
0
1
1
0
0
0
1
1
0
2
0
0
1
0
1
3
1
0
2
0
0
2
1
1
0
2
0
2
1
2
0
1
0
0
2
0
0
1
1
0
0
1
0
0
0
2
0
1
0
1
0
2
1
1
1
1
1
2
2
1
1
0
2
0
3
1
3
2
0
1
1
0
2
0
1
2
0
0
0
1
1
1
0
0
1
2
2
1
1
0
0
2
1
0
0
1
0
3
0
2
1
1
0
1
1
0
0
0
0
2
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
2
0
7
0
2
1
0
0
0
0
1
2
0
1
2
0
0
2
2
2
0
1
0
2
0
0
0
0
0
1
2
0
1
2
0
0
0
1
0
1
1
1
0
1
0
2
2
1
0
0
0
1
0
2
1
0
0
1
0
1
0
1
0
1
0
0
2
0
2
0
1
0
2
1
0
0
0
1
1
1
0
1
1
1
1
0
1
1
0
0
1
0
1
0
1
0
1
0
0
0
0
1
0
1
1
0
0
1
0
1
0
0
0
0
0
1
4
2
0
1
1
0
0
0
0
0
0
2
0
0
2
2
1
0
1
0
0
0
1
1
0
0
1
0
2
0
3
2
0
3
0
0
0
1
0
0
1
1
0
2
2
2
0
1
1
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
1
1
0
1
1
0
1
0
2
0
2
3
1
2
0
0
0
1
0
0
1
2
0
0
2
0
0
1
0
0
0
0
0
2
0
1
0
0
1
1
1
0
2
2
2
1
0
1
0
0
2
0
0
3
1
0
1
2
1
1
2
1
0
2
0
0
1
1
0
0
0
0
0
1
2
1
2
1
0
1
0
3
0
0
0
1
0
1
0
1
1
0
0
0
2
1
1
0
2
1
1
2
2
0
2
2
1
2
1
0
3
2
0
1
3
2
0
0
0
2
0
0
0
1
0
2
1
0
2
0
1
0
2
0
2
2
0
0
0
0
2
1
2
0
0
2
1
1
0
0
0
1
1
1
2
0
0
2
1
1
0
0
3
0
1
0
0
3
1
0
1
1
0
1
1
0
0
0
0
3
2
1
0
1
0
1
1
0
0
2
0
1
2
1
1
0
1
2
2
0
0
0
1
0
0
1
2
0
0
1
0
0
1
1
2
2
0
1
0
0
0
2
0
0
2
0
0
2
2
0
1
0
0
2
0
1
2
1
2
0
0
2
0
1
0
0
2
0
0
2
0
0
1
2
0
0
0
1
0
1
0
2
1
0
1
1
0
0
1
0
0
0
2
0
0
1
1
0
1
0
0
0
0
0
0
1
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
1
2
2
0
0
0
3
1
0
1
0
1
0
1
3
2
2
1
0
1
0
1
0
0
0
0
0
1
2
2
1
0
0
0
0
0
0
4
2
0
3
1
0
2
0
2
1
1
0
0
0
2
1
0
0
1
1
2
2
1
2
0
0
0
0
0
0
0
0
1
1
1
0
1
2
0
1
2
0
0
0
2
2
0
1
2
0
0
0
0
1
1
0
1
7
0
0
0
0
0
2
0
0
1
0
1
0
1
4
0
0
0
0
2
1
1
0
1
1
2
2
0
0
2
1
0
1
0
1
1
2
0
0
2
0
1
2
3
4
0
1
1
2
0
2
0
3
2
2
1
0
0
0
1
0
2
0
1
1
0
1
2
1
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
2
2
0
1
0
0
0
1
1
0
1
0
2
2
2
1
2
1
0
0
1
3
1
1
3
0
1
3
2
0
2
2
0
2
0
1
0
1
2
0
0
1
2
1
1
1
0
1
1
1
0
2
1
1
0
0
0
0
1
0
0
0
0
2
0
0
0
1
1
0
1
0
1
0
0
1
0
1
2
0
2
2
0
0
2
1
1
0
2
1
0
0
1
0
2
2
0
2
0
0
0
0
0
1
0
0
0
0
1
1
1
0
1
0
0
1
2
0
0
2
1
2
1
1
1
0
4
0
1
0
0
1
1
1
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
2
2
0
1
0
1
1
2
0
0
0
0
0
2
0
0
0
1
0
0
2
2
1
1
0
1
1
0
1
2
2
0
1
1
0
0
0
1
0
1
0
1
1
2
2
0
1
3
2
3
0
2
1
2
1
2
0
0
2
0
0
1
1
0
0
2
0
0
1
1
0
1
2
1
1
2
1
0
0
0
1
0
2
2
0
0
3
1
1
2
1
0
2
0
3
0
2
1
0
0
0
1
1
1
0
0
0
2
1
1
0
1
1
1
1
7
0
0
1
0
1
2
0
1
0
1
0
1
0
0
0
0
2
0
2
1
1
1
0
2
2
1
0
0
1
1
0
0
2
0
2
1
1
0
1
0
1
1
0
0
0
0
0
0
0
0
2
1
0
1
2
0
1
2
2
0
1
2
0
1
1
1
0
0
2
1
2
1
0
0
2
1
0
0
0
2
1
0
1
0
1
0
1
2
0
0
0
0
2
0
0
0
2
2
0
2
0
0
1
1
2
2
2
0
0
0
1
1
0
0
1
1
0
1
0
2
2
2
0
2
0
1
1
0
2
2
0
0
0
1
0
1
1
1
0
0
0
2
2
0
1
0
0
0
0
1
0
0
1
2
0
1
0
2
2
0
0
2
4
3
0
0
0
0
2
2
0
0
2
1
0
0
3
0
0
0
0
2
0
0
0
1
1
2
2
0
0
1
2
0
0
2
0
0
0
2
1
1
0
2
0
1
0
1
1
0
2
2
2
0
2
1
0
0
2
1
1
1
1
0
3
1
0
0
0
0
0
1
0
1
2
0
1
2
1
1
0
0
1
1
1
1
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
2
2
1
2
0
1
1
1
0
0
0
1
0
2
1
2
0
0
2
0
0
0
2
0
1
2
0
0
0
1
0
0
2
2
0
1
1
2
1
1
0
0
0
0
0
0
1
0
0
2
1
1
0
0
0
2
0
0
0
1
1
0
1
0
2
1
4
0
0
2
1
0
0
2
0
0
2
0
1
0
0
3
0
2
1
1
2
1
2
2
0
0
1
1
2
1
1
0
0
2
0
1
0
0
1
0
1
2
0
1
1
2
0
0
2
1
1
0
0
1
0
0
2
0
0
2
0
1
1
1
2
0
1
1
0
1
0
2
3
1
0
0
2
0
1
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
2
1
1
0
0
2
0
0
0
1
0
1
0
0
0
3
1
0
0
0
0
2
0
2
1
0
0
1
1
0
1
1
0
0
1
2
0
0
0
0
2
1
2
1
1
0
0
1
1
1
2
1
1
0
0
2
1
1
0
2
2
1
2
0
0
2
1
2
0
1
2
0
0
1
1
0
0
0
1
1
1
0
1
0
0
2
1
2
1
0
1
2
2
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
1
0
1
0
2
2
2
0
1
1
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
2
2
1
0
0
1
1
0
0
2
2
2
2
1
0
0
1
1
0
0
0
1
0
0
2
1
1
0
0
0
1
2
1
1
2
1
2
0
0
1
0
1
1
2
1
0
1
1
1
1
1
1
1
2
0
0
1
0
1
0
0
1
1
1
1
0
0
0
1
3
0
1
0
0
1
0
2
1
1
0
1
0
2
0
0
0
0
0
0
2
1
2
0
2
0
2
1
0
0
2
0
0
0
0
0
0
2
0
2
1
0
2
0
1
0
0
4
2
2
0
1
0
1
1
1
3
0
0
0
0
2
0
1
2
2
3
2
0
2
2
0
1
0
1
0
1
1
1
2
1
0
1
0
1
1
0
0
0
0
2
2
0
1
0
1
0
0
1
2
1
0
0
0
0
2
0
1
1
0
0
0
1
0
2
2
0
1
1
1
0
1
0
0
0
2
0
0
1
0
1
2
0
1
0
1
0
3
0
0
0
0
0
2
1
0
0
0
1
2
0
1
0
1
2
1
0
0
2
0
2
1
1
0
0
0
0
0
1
0
0
0
1
1
1
1
0
0
2
1
4
0
1
0
0
0
0
0
2
0
0
1
2
0
0
2
0
0
2
1
0
0
1
0
1
0
1
0
0
1
0
2
1
1
4
0
0
3
2
1
0
0
0
2
1
0
0
1
2
0
1
1
0
0
1
2
1
1
0
0
2
2
2
1
1
0
0
2
0
0
0
0
2
0
0
2
1
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
2
0
0
0
1
1
1
1
1
0
2
0
0
1
0
1
0
0
1
2
0
1
0
1
0
0
0
0
0
3
0
1
1
3
0
1
2
0
0
0
2
1
2
0
2
0
2
0
0
1
0
0
0
0
0
2
2
1
1
0
0
0
1
2
1
1
0
0
2
1
0
0
0
2
3
1
1
0
2
1
0
0
0
1
2
0
1
1
0
0
2
1
0
0
2
0
0
1
0
0
0
1
0
2
0
2
3
1
0
0
0
0
1
0
1
2
1
1
1
0
0
1
0
0
0
2
0
2
1
2
2
0
0
0
0
1
0
2
2
0
2
0
2
0
1
0
0
0
0
1
0
0
0
1
3
0
2
1
0
0
1
1
0
1
2
0
0
2
1
2
0
0
1
0
4
0
0
1
2
5
1
0
0
2
1
1
1
2
1
0
1
0
0
0
0
0
0
1
0
0
2
0
2
0
0
1
2
0
2
0
1
2
0
0
1
1
1
1
1
0
0
0
0
0
0
0
0
0
2
2
2
1
2
1
0
0
2
1
2
3
0
2
0
0
0
1
0
0
0
2
0
2
2
1
2
2
2
0
1
0
1
2
1
0
0
0
2
0
0
2
1
1
2
0
0
2
3
0
2
0
0
0
1
2
0
0
3
1
0
1
1
1
0
2
0
0
0
0
1
0
1
0
0
2
2
0
0
1
1
3
0
0
0
2
0
2
0
1
0
0
1
2
0
2
0
1
0
0
2
0
0
0
0
1
0
2
0
0
0
1
1
1
0
0
1
0
1
0
1
0
0
1
1
0
0
0
0
0
1
2
1
0
1
1
0
0
0
1
2
0
2
0
0
0
0
1
2
0
2
0
0
0
2
1
1
0
0
0
2
0
0
0
2
1
1
0
1
2
1
2
0
1
2
0
0
0
0
2
0
1
1
0
1
0
0
0
1
1
0
1
0
2
0
1
2
0
1
5
2
1
0
2
0
2
0
1
2
0
2
0
2
1
2
0
0
1
1
2
0
0
0
1
2
1
1
0
0
1
1
1
2
1
0
2
1
2
0
0
1
0
0
0
0
1
0
0
2
1
0
0
1
1
0
0
1
2
1
2
2
0
0
0
2
0
0
0
0
0
0
2
2
1
1
1
2
0
1
2
1
2
0
1
0
0
1
1
0
0
1
1
2
0
1
0
0
0
0
0
1
0
0
0
2
0
1
0
2
0
2
1
0
1
1
0
1
0
0
0
1
1
0
0
2
0
0
1
1
0
0
0
0
0
1
1
0
0
1
2
0
1
0
1
2
0
0
0
0
2
1
0
1
0
1
2
1
0
1
1
0
1
2
1
1
0
1
1
0
2
0
2
0
2
2
0
3
0
0
0
2
1
0
2
3
1
2
0
0
1
1
0
0
3
0
0
2
0
0
1
1
1
0
0
1
0
0
0
1
1
0
0
1
2
0
0
2
0
0
2
1
1
0
1
0
1
1
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
1
1
1
2
1
0
0
0
0
1
1
0
2
0
0
0
1
0
1
2
0
1
1
1
0
0
2
1
0
1
0
0
0
0
0
1
0
0
2
2
1
0
1
1
0
0
1
0
1
0
0
0
0
0
2
1
0
0
0
2
0
1
1
1
0
0
2
1
2
0
1
1
0
2
1
1
1
1
1
2
1
1
0
0
0
1
0
2
1
0
0
1
1
2
0
0
2
0
0
0
0
2
0
2
1
0
0
0
1
1
1
0
0
0
1
0
0
1
0
2
1
1
1
1
1
0
1
1
2
0
1
0
1
0
2
2
0
2
2
0
0
2
1
0
0
1
0
1
0
1
0
1
2
0
1
0
2
0
0
2
1
0
1
0
0
0
2
0
2
0
1
0
1
0
1
1
2
0
0
0
1
0
1
1
1
0
1
0
0
0
2
0
0
3
1
0
0
1
1
0
0
0
1
0
1
1
0
2
1
1
0
1
1
0
1
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
2
0
0
0
0
0
2
0
2
0
0
1
0
2
2
1
2
0
0
0
2
0
0
0
1
2
1
0
1
2
2
2
1
0
1
0
2
3
2
0
0
0
1
0
0
1
1
1
0
0
0
2
1
2
2
0
1
1
0
1
2
1
0
2
0
0
0
1
1
2
0
0
2
2
1
0
0
1
0
0
0
0
2
0
1
1
0
1
0
0
0
2
1
0
0
2
0
2
0
2
1
8
1
0
0
1
1
0
1
1
0
1
0
0
0
0
0
0
0
0
2
1
0
0
1
3
0
1
1
1
1
0
0
1
0
0
2
0
1
2
0
0
0
0
1
2
2
1
0
6
2
1
1
2
1
0
0
1
1
0
0
2
1
1
1
0
1
0
2
1
0
0
2
2
1
0
0
1
0
2
0
0
0
0
1
0
2
2
1
0
0
0
2
0
0
1
0
0
0
2
0
0
1
1
1
0
0
1
1
1
0
0
1
1
3
0
1
0
0
0
0
1
0
0
1
0
0
1
1
1
1
0
0
0
2
0
0
2
0
2
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
1
2
2
2
2
0
0
0
0
1
1
1
2
0
2
0
2
1
2
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
7
0
0
0
1
1
2
0
2
1
0
0
0
1
1
2
0
1
2
0
2
0
0
2
2
0
2
0
0
1
1
1
0
0
1
1
0
2
0
1
0
2
1
2
0
2
0
1
0
0
2
2
1
0
1
0
2
0
0
1
0
0
0
0
0
2
0
1
0
2
0
1
0
1
1
0
2
0
0
0
0
1
1
2
0
1
1
1
3
4
1
0
1
1
2
2
0
0
1
0
1
0
2
1
2
0
0
2
1
0
0
0
1
2
1
0
0
0
1
0
1
4
1
1
0
2
1
1
1
1
0
0
0
0
2
2
0
0
2
1
0
2
0
2
0
1
0
0
0
0
1
0
1
1
2
1
1
2
0
0
1
3
0
1
0
0
0
2
6
0
2
0
0
2
0
2
0
0
0
0
1
2
2
1
0
0
0
0
0
0
2
0
1
1
1
0
2
2
4
0
2
1
2
2
0
1
0
0
1
0
0
0
0
1
0
0
1
2
1
1
0
1
0
0
6
0
0
0
1
1
0
0
0
0
2
0
2
0
2
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
2
1
1
2
1
2
0
2
0
0
2
0
1
0
0
1
0
0
0
1
1
0
1
0
2
1
2
0
0
1
1
0
0
1
1
1
2
0
1
1
0
1
0
1
1
0
0
1
0
2
0
1
2
0
0
1
2
0
0
1
1
3
0
0
0
2
0
2
2
2
0
1
2
0
2
1
0
1
0
2
2
1
0
1
0
2
2
0
0
0
1
0
0
0
1
1
2
3
1
1
1
2
0
1
2
0
2
2
1
0
0
0
2
1
3
0
2
2
1
0
0
2
1
1
0
0
0
4
2
2
0
0
2
1
0
0
0
1
0
1
2
0
2
0
0
0
1
1
0
1
1
1
0
2
0
1
0
1
1
2
1
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
2
2
2
2
1
0
1
0
2
2
1
0
0
0
0
1
0
2
1
2
2
1
1
0
0
1
0
0
1
0
0
0
1
0
0
0
2
0
0
2
0
0
1
1
0
2
0
0
1
2
0
1
2
0
1
0
1
1
1
0
2
0
3
0
0
2
1
2
1
2
1
0
0
1
2
2
2
0
0
1
0
0
0
1
0
1
2
1
1
0
0
2
2
0
1
0
0
1
0
1
0
0
1
0
2
0
1
0
1
2
1
1
0
2
0
1
0
2
0
1
3
0
1
0
2
0
4
1
1
1
1
0
0
0
1
1
0
0
1
0
1
1
0
1
0
0
0
2
1
1
1
0
2
0
0
1
1
0
0
0
1
2
1
0
1
0
0
2
1
0
0
1
0
1
0
1
2
2
1
1
0
0
1
2
1
0
0
0
0
1
0
1
0
0
0
2
1
0
0
0
0
0
0
2
2
1
0
0
0
1
0
1
1
0
0
1
0
0
0
0
3
1
0
0
0
2
1
1
0
1
1
0
0
0
1
0
0
0
0
1
0
2
0
2
0
0
0
0
1
1
0
1
1
0
2
0
0
0
1
0
2
2
1
2
1
2
1
0
1
1
0
0
0
0
0
1
1
0
2
0
1
0
1
0
1
0
0
1
0
1
0
1
0
2
1
0
0
0
0
0
1
0
1
0
1
1
0
1
1
2
0
1
2
0
0
1
0
2
1
0
2
0
0
2
0
2
1
1
1
1
0
2
2
1
0
0
2
0
2
2
0
0
1
1
1
0
0
2
1
2
1
2
2
2
0
1
2
2
1
0
0
0
2
0
2
0
0
2
0
0
2
2
2
0
1
0
2
2
1
1
0
1
1
0
1
0
0
2
1
3
0
1
2
1
1
0
0
2
0
0
0
0
1
1
1
1
0
2
0
0
1
1
0
0
1
2
1
2
0
0
0
0
1
1
1
1
0
1
1
0
1
0
2
0
0
1
0
2
0
0
0
0
0
1
1
2
0
1
1
0
0
1
0
0
1
0
0
3
1
0
0
1
0
2
0
1
1
1
1
2
1
1
0
0
2
0
1
0
0
0
0
0
0
2
3
1
0
0
0
2
1
0
0
0
0
2
1
1
0
0
2
0
0
0
1
1
0
1
1
1
1
1
0
0
2
2
0
1
0
1
1
2
0
2
0
2
0
1
0
1
0
0
2
0
0
1
1
1
2
2
0
1
2
1
0
1
0
0
0
2
0
0
1
2
0
0
0
2
0
1
0
0
0
2
2
0
0
1
1
2
1
1
0
2
0
1
2
3
1
1
1
0
0
0
2
0
2
0
0
2
0
1
1
0
0
0
1
0
0
0
1
2
0
0
0
1
0
0
1
1
0
2
1
0
1
2
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
2
0
0
0
1
1
0
0
2
2
1
0
1
1
0
0
1
1
0
2
0
0
0
1
0
0
0
2
0
0
2
0
2
2
0
2
0
2
0
2
0
2
0
2
0
2
2
2
1
1
1
1
0
0
2
2
2
0
0
2
0
1
2
1
2
0
1
0
0
0
1
0
2
1
0
2
0
2
0
1
0
1
2
2
2
2
2
0
0
1
0
0
0
0
0
1
3
1
0
1
1
0
1
0
1
0
0
0
0
1
0
1
0
0
2
0
5
0
0
2
2
2
1
2
0
0
0
0
0
0
1
2
1
2
2
0
0
0
1
1
2
0
0
1
2
0
0
2
4
0
0
0
0
1
0
1
0
2
0
2
1
0
1
2
1
2
0
0
0
2
2
1
0
0
2
2
0
0
2
0
2
1
0
0
0
3
2
3
1
0
1
0
1
0
2
1
2
2
3
2
2
0
0
1
0
2
0
1
1
0
0
0
0
2
0
1
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
2
0
2
0
1
0
0
1
0
0
1
2
0
0
0
1
1
2
0
2
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
3
1
1
0
0
0
0
2
0
0
1
0
1
2
0
2
0
2
0
1
0
0
1
2
0
2
0
0
0
0
1
2
1
0
1
0
2
0
2
1
1
0
1
0
1
0
1
2
0
0
2
0
1
0
2
1
0
1
1
0
2
1
2
0
3
1
0
0
0
1
0
4
0
3
2
1
0
0
2
0
1
1
1
0
1
0
2
1
1
0
1
1
0
0
1
0
0
0
0
0
2
0
0
1
1
0
4
0
1
0
0
0
0
0
0
0
3
0
2
1
0
0
0
0
0
0
3
0
1
0
0
0
0
1
2
0
3
1
2
1
2
0
2
2
2
2
3
0
0
1
2
0
0
1
2
2
1
0
0
0
2
0
1
0
0
0
0
2
2
0
0
0
1
0
0
2
2
0
0
1
0
2
0
0
0
1
1
1
0
2
0
1
0
0
1
2
0
3
0
0
0
0
2
0
2
1
2
2
0
1
2
1
1
2
0
0
0
0
1
1
1
0
1
0
0
3
1
1
2
0
2
1
2
2
0
0
0
0
1
0
0
1
0
0
0
0
0
1
2
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
1
0
0
1
2
2
1
0
2
1
0
0
0
1
2
0
0
1
1
1
0
2
1
2
1
0
2
1
0
1
0
3
1
0
2
1
1
0
0
0
0
0
0
0
0
2
0
1
0
0
1
1
0
0
0
2
1
2
0
2
0
2
2
1
0
2
0
0
2
0
0
1
1
1
0
0
0
2
0
1
0
0
1
1
2
0
1
0
0
1
1
1
0
1
2
0
0
1
1
0
0
2
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
2
1
0
2
2
0
1
1
0
2
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
2
1
0
1
1
1
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
1
1
2
0
0
0
2
0
1
0
1
0
1
0
0
1
1
0
2
1
1
0
0
0
1
0
0
0
0
2
1
1
1
0
2
0
0
1
2
0
0
2
0
0
2
1
0
0
2
0
0
3
2
2
0
2
0
0
1
2
1
0
2
1
1
0
0
1
3
0
0
0
0
1
2
2
0
0
2
0
0
1
0
2
1
1
0
2
0
1
0
0
1
0
2
0
1
0
1
1
2
0
2
0
1
1
0
0
0
0
0
0
1
0
1
1
1
2
1
0
1
0
0
1
1
0
0
0
2
1
1
5
1
0
0
0
2
0
1
1
0
0
1
0
0
1
0
0
2
2
1
0
2
2
0
0
0
2
1
0
1
2
2
2
1
2
2
0
2
1
2
0
2
2
1
0
2
0
1
0
0
0
0
1
0
1
0
1
4
0
0
0
0
0
2
0
1
0
1
2
0
0
1
0
2
0
2
2
0
0
0
0
1
2
2
0
0
2
1
0
3
0
2
1
2
2
1
0
1
1
0
2
0
2
3
2
0
1
1
0
0
1
0
0
0
0
1
1
0
2
1
0
1
0
1
1
1
0
2
1
2
1
2
0
0
0
3
0
0
1
0
2
1
1
0
0
1
1
0
0
0
0
2
0
0
2
1
0
0
0
1
2
0
0
0
0
0
1
1
0
0
1
0
2
0
1
2
1
0
1
0
0
0
0
1
1
0
0
0
1
1
1
0
1
0
0
0
0
1
0
1
1
0
2
0
1
2
0
0
1
0
0
2
2
1
0
0
1
0
0
1
2
0
0
1
0
2
2
3
1
0
0
5
0
2
0
2
2
0
0
2
2
1
0
0
0
2
0
1
0
1
0
2
2
2
1
0
0
0
2
2
0
2
0
0
1
0
0
2
2
1
2
0
1
0
0
0
1
1
0
1
1
1
1
1
0
0
1
0
0
0
1
2
1
3
0
0
1
0
2
2
1
1
2
0
0
0
1
1
0
0
0
1
1
0
0
1
0
2
0
1
0
1
0
2
1
0
0
2
2
1
0
3
0
0
0
3
0
2
1
1
0
2
1
2
0
2
0
0
2
0
2
2
2
1
0
1
0
2
0
0
2
0
1
1
1
0
0
2
0
1
3
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
2
1
3
0
0
0
0
1
1
2
2
1
2
1
1
0
0
0
2
1
0
1
2
1
2
5
1
0
2
2
0
2
1
0
2
1
0
0
0
2
0
0
0
0
2
0
2
2
0
2
1
0
0
2
0
1
0
1
2
0
2
0
1
1
0
2
1
0
0
2
2
1
0
1
1
0
1
2
0
2
0
0
0
0
2
0
0
0
0
3
0
1
2
0
0
2
3
1
0
2
0
2
0
1
3
1
4
0
2
1
0
2
2
1
0
0
1
2
2
0
2
0
0
0
2
0
1
1
0
0
0
0
2
1
0
0
0
1
0
1
2
0
1
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
1
2
0
0
1
0
0
1
1
0
0
2
0
0
0
1
2
0
0
0
0
1
7
0
1
1
2
2
1
0
0
1
1
0
0
2
1
0
2
2
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
2
0
0
1
0
2
0
0
1
1
2
2
0
0
2
0
2
1
1
1
1
1
1
0
1
2
0
0
0
0
0
1
2
0
2
0
0
1
1
0
0
0
1
3
0
0
0
0
1
1
2
2
0
0
0
2
1
0
0
0
0
1
1
1
0
0
0
0
1
2
1
0
1
0
1
2
0
0
1
0
2
1
1
1
0
0
1
1
2
0
1
0
1
0
2
2
2
0
0
1
0
0
0
1
1
1
0
1
2
1
0
1
2
2
0
0
0
3
0
0
0
0
0
0
0
0
2
1
3
0
1
0
2
0
1
0
2
2
1
1
1
2
0
0
0
0
0
1
1
1
0
0
0
0
2
0
4
0
1
2
1
0
1
0
0
2
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
2
1
0
1
1
1
1
0
1
0
0
0
1
2
0
1
2
2
0
1
1
1
2
0
0
0
0
1
2
1
1
0
0
0
0
2
2
0
1
2
0
1
2
2
1
2
0
2
0
0
1
0
1
0
3
2
2
1
0
2
0
0
1
1
0
0
1
0
0
1
1
1
0
2
1
0
2
0
0
0
0
3
1
2
0
2
0
0
2
1
0
2
1
1
2
1
1
0
0
1
1
0
1
0
0
2
0
1
2
1
0
0
0
1
2
1
2
0
2
0
0
0
1
0
8
0
1
1
2
0
0
2
2
0
0
1
0
1
0
2
2
2
2
1
0
0
2
0
0
1
0
1
0
0
0
0
1
1
0
1
1
2
1
1
5
1
0
0
2
0
0
0
0
1
2
1
1
0
0
1
0
1
2
0
2
0
0
2
0
0
0
0
0
0
0
1
2
0
2
0
0
1
1
1
0
0
0
1
1
0
1
2
0
0
1
0
1
1
1
2
1
2
1
1
0
1
0
1
2
3
0
3
0
0
0
0
0
0
1
2
0
0
1
2
0
1
0
1
0
1
0
0
2
0
1
2
0
0
0
2
0
0
1
2
1
0
2
0
2
1
1
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
1
1
2
2
0
0
1
0
2
0
1
2
1
0
1
1
2
0
1
0
0
0
0
0
1
1
0
0
1
2
0
0
2
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
1
0
2
1
1
0
0
0
0
1
1
0
0
5
0
1
0
0
0
0
1
1
0
1
0
1
1
1
0
2
2
0
6
0
0
0
0
0
1
0
0
1
0
1
2
0
1
0
0
2
1
0
1
0
0
1
0
0
1
0
0
0
0
1
2
2
0
0
2
2
0
0
0
2
0
0
1
0
0
0
0
1
0
0
1
1
3
1
2
0
2
0
0
0
1
0
2
1
0
1
1
2
0
0
3
0
0
0
1
2
0
1
1
0
1
0
1
1
0
2
0
1
0
0
2
2
0
0
1
2
2
1
0
1
0
0
0
1
1
0
0
0
2
0
0
1
0
0
0
1
1
0
0
0
0
0
2
1
1
2
1
1
1
0
0
2
2
0
0
0
2
0
0
0
0
2
1
0
0
1
4
1
2
2
1
0
0
1
1
0
0
0
0
0
2
1
0
0
0
2
0
0
2
0
2
0
1
1
1
1
2
0
2
1
0
2
2
1
0
1
0
0
2
1
0
0
1
0
0
0
0
1
2
2
1
2
0
0
2
0
0
2
2
0
0
2
0
1
0
6
0
1
2
2
1
0
2
1
1
1
2
2
0
1
0
0
1
2
4
1
1
0
0
0
0
0
1
2
1
0
4
0
1
0
0
0
1
0
1
0
0
1
0
2
1
0
1
0
2
1
0
1
2
0
1
0
0
0
0
2
0
2
0
0
0
0
2
1
1
0
1
1
1
1
0
1
2
0
1
0
0
1
2
1
0
0
0
2
2
0
0
3
0
0
0
0
2
0
1
1
1
1
0
2
0
0
1
0
1
0
0
0
1
0
1
0
2
0
2
0
2
0
1
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
2
0
1
0
0
1
0
0
1
0
0
0
0
2
2
1
0
1
0
0
0
0
1
1
1
2
1
1
1
2
1
0
0
0
0
0
2
1
1
0
0
1
1
0
0
2
0
0
1
0
0
0
0
2
2
0
0
1
0
1
1
1
0
2
0
1
0
1
1
0
0
2
2
1
0
1
4
1
0
2
2
0
1
0
2
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
2
0
1
2
0
0
0
0
0
1
0
1
0
0
0
0
2
0
1
0
0
0
2
0
1
3
2
1
0
2
1
2
0
0
0
2
1
1
0
1
0
0
0
2
0
0
2
1
0
0
0
1
0
2
1
0
1
2
0
5
0
1
0
0
0
3
2
0
2
1
0
0
0
2
0
0
2
2
0
2
1
2
1
2
1
1
0
4
0
1
0
1
0
2
0
0
0
1
1
0
0
0
2
1
1
0
1
2
0
2
1
0
0
0
0
0
2
2
0
1
2
1
2
2
1
1
0
0
0
1
1
0
2
0
1
2
1
1
0
0
1
2
2
0
2
0
1
0
0
2
2
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
2
1
1
0
0
0
0
0
0
1
0
2
2
0
0
0
1
2
0
1
0
0
1
0
0
1
0
0
1
1
0
1
0
1
1
0
1
0
1
2
1
0
0
1
0
0
2
1
1
0
2
0
2
1
3
2
2
0
2
0
0
0
2
1
0
1
0
2
0
0
0
0
0
2
2
0
0
1
2
0
0
0
0
2
0
0
0
1
1
0
0
3
0
0
2
2
1
0
0
1
2
0
2
0
1
1
0
1
2
0
1
1
1
1
0
1
2
2
0
4
1
2
1
0
3
1
0
0
0
0
1
0
0
2
1
0
1
0
0
0
0
1
0
1
0
2
0
0
0
1
0
0
0
2
0
1
0
3
0
0
1
1
0
0
0
1
2
0
2
2
0
0
0
1
1
1
1
2
1
1
1
1
1
1
0
0
2
0
2
0
0
2
0
1
0
0
1
0
5
2
1
1
0
0
0
2
0
1
0
0
1
0
1
0
0
0
0
2
0
1
0
0
1
1
0
2
0
2
0
0
0
0
0
0
2
1
0
0
2
0
1
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
2
0
1
0
0
0
0
0
0
1
0
0
2
0
2
2
0
0
0
4
0
0
2
1
2
1
0
0
0
0
2
2
1
1
0
1
0
0
2
2
0
1
0
2
2
0
0
0
1
1
0
0
2
0
0
0
0
2
2
0
0
1
1
1
0
0
0
0
2
0
1
1
2
1
3
0
0
0
0
0
1
1
0
0
2
1
0
1
0
2
1
0
0
2
1
2
1
0
0
1
1
1
0
1
1
0
1
2
1
1
1
0
0
0
2
1
0
0
0
1
1
0
2
0
0
2
2
0
1
0
1
0
2
1
0
2
2
1
0
1
0
0
1
1
1
2
1
0
0
1
2
1
2
0
0
0
1
0
2
0
1
0
3
0
0
0
1
0
1
0
0
1
1
0
2
1
0
1
1
1
1
1
3
1
0
0
0
0
2
0
0
2
2
2
1
4
0
0
2
0
1
1
1
0
1
2
1
2
0
2
1
0
2
1
0
0
1
2
2
1
2
1
0
0
1
1
1
0
1
2
0
2
0
0
0
0
0
1
2
1
2
1
1
0
0
1
0
1
1
1
0
1
0
2
1
2
0
0
0
0
2
1
1
1
0
0
1
1
0
0
0
2
2
0
2
1
1
0
1
1
0
0
0
1
0
0
0
2
1
1
0
0
1
1
1
1
0
0
2
1
0
1
0
0
0
2
3
2
0
2
1
1
0
2
1
0
0
0
0
1
1
0
0
0
0
0
0
1
3
1
2
0
1
0
0
3
0
2
2
1
0
0
1
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
2
3
0
0
1
1
0
2
1
0
2
0
0
1
1
1
1
3
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
1
0
2
0
0
1
0
1
0
1
0
1
0
0
0
0
0
1
1
1
0
2
0
1
0
0
0
2
0
2
0
0
0
1
1
1
1
0
1
0
0
1
2
0
1
1
2
1
0
2
0
1
0
1
0
1
1
0
0
0
1
1
1
1
0
0
0
0
1
0
2
2
0
1
1
1
0
0
0
0
2
1
0
2
0
2
1
2
1
0
0
2
1
2
0
1
0
2
0
1
0
0
0
0
0
0
2
0
0
1
0
1
2
1
1
0
2
0
1
1
0
1
0
1
0
0
0
1
0
2
0
2
0
2
1
0
2
1
2
1
0
1
1
2
2
3
0
0
1
0
1
3
0
0
0
1
0
1
0
1
1
1
2
0
0
0
0
0
0
1
1
0
0
2
0
0
1
1
0
0
1
1
0
2
1
0
1
1
0
0
0
2
2
0
1
0
0
0
1
0
1
0
0
0
2
1
1
2
1
1
0
1
1
0
0
2
1
0
0
0
0
0
1
1
1
0
0
0
1
0
0
1
0
2
3
2
1
0
1
1
1
1
0
2
0
1
1
0
0
1
2
1
1
0
2
0
0
1
2
4
2
2
0
2
1
2
2
0
0
3
2
0
0
0
0
2
0
0
0
2
0
0
1
1
0
1
1
0
1
2
1
0
2
0
0
1
1
1
2
2
1
0
0
0
0
0
1
0
1
2
1
1
1
1
0
1
2
1
2
0
1
2
0
0
0
0
2
0
1
1
0
0
2
1
2
1
1
0
0
0
1
0
2
2
2
1
0
2
0
0
1
2
0
0
2
1
1
1
2
0
2
1
0
0
0
2
1
1
0
0
2
2
2
1
0
0
3
1
1
0
0
0
0
0
1
0
2
1
2
0
0
1
0
0
1
0
0
0
1
2
1
1
1
0
1
0
2
0
2
0
0
2
0
1
0
2
2
0
0
0
1
1
3
0
1
0
1
0
0
0
0
0
2
1
1
1
0
1
0
0
2
1
1
1
0
0
0
0
0
1
0
0
0
0
1
1
1
2
1
0
2
1
1
1
0
0
2
2
0
1
0
0
0
1
0
2
0
0
0
1
0
0
0
1
0
2
0
2
1
0
0
1
1
2
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
2
1
1
1
0
1
0
1
1
1
2
0
0
0
2
0
0
1
1
0
0
0
0
0
3
1
0
0
0
0
2
0
1
3
1
0
0
0
2
0
1
0
0
0
1
0
1
2
2
0
1
0
0
0
0
0
0
1
1
2
2
2
0
0
2
1
0
0
1
1
1
0
3
0
0
2
0
3
2
2
0
2
0
0
2
0
2
0
2
1
2
2
2
2
0
0
1
0
1
1
1
0
1
0
1
0
0
1
1
0
2
1
0
2
0
2
0
2
0
1
1
0
2
1
0
1
0
2
0
0
2
0
0
2
0
1
1
1
0
2
1
1
0
1
0
0
0
1
1
0
1
1
0
2
1
2
0
1
2
2
0
0
0
1
2
1
2
0
2
0
1
0
2
0
0
0
0
1
0
1
0
0
0
1
0
0
1
1
1
1
0
2
0
2
0
0
0
2
0
2
1
0
0
0
0
0
1
0
0
1
3
0
1
2
0
0
0
2
0
0
0
1
0
0
0
0
1
1
2
1
0
1
0
2
1
1
1
0
1
1
0
2
0
0
0
0
2
0
0
0
0
1
1
1
2
0
0
0
1
0
1
0
1
2
0
1
0
0
0
2
0
0
1
2
2
0
2
1
0
1
1
1
0
0
3
0
0
0
0
0
1
1
0
2
0
2
1
2
0
2
1
1
0
0
0
1
0
1
0
0
2
0
1
0
2
1
0
0
0
0
2
1
1
2
1
0
2
0
0
7
0
0
0
1
0
0
2
0
0
1
0
0
1
0
1
1
0
0
0
0
1
2
0
1
0
1
0
0
2
2
2
1
0
1
0
0
0
1
0
0
1
2
1
1
2
1
1
2
2
1
1
1
0
1
0
2
0
2
1
2
2
1
2
0
2
1
0
1
1
0
0
2
0
0
0
0
0
0
0
0
1
0
2
2
1
2
0
0
0
0
1
1
0
0
0
0
0
1
0
1
2
1
0
1
0
0
1
0
2
2
2
0
1
2
1
0
0
0
0
0
1
2
0
1
2
0
0
2
1
0
0
2
0
0
0
1
1
0
2
0
0
0
0
1
1
0
0
1
0
2
2
1
0
1
2
0
0
0
2
1
1
2
1
2
0
1
1
0
0
0
0
3
0
0
2
0
0
1
1
1
4
1
0
2
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
2
2
0
1
2
2
2
0
1
0
2
2
1
1
1
0
0
0
0
2
0
2
1
1
1
0
2
0
0
2
1
0
2
0
0
2
1
0
1
1
0
0
2
0
0
2
0
0
0
0
1
0
1
0
0
1
1
1
0
0
0
0
0
2
0
1
0
1
1
0
1
0
0
1
2
0
1
2
1
0
1
1
2
1
0
0
2
2
0
2
0
10
1
0
2
1
0
2
0
0
0
1
1
0
1
0
0
2
0
1
1
0
0
1
1
0
1
0
0
0
1
0
1
1
1
1
0
2
0
0
2
0
1
1
1
1
1
2
0
1
0
1
1
1
2
0
0
0
1
0
2
0
1
1
2
0
0
1
1
1
0
0
1
0
2
1
0
0
0
1
1
0
3
0
0
0
1
1
0
2
2
1
2
0
0
1
1
2
2
1
1
1
1
0
0
0
1
0
0
1
0
1
1
0
3
1
1
0
1
1
1
1
0
0
0
0
2
1
1
0
2
3
1
2
0
0
0
0
1
0
0
1
0
1
2
0
0
0
1
1
0
0
1
1
0
1
1
2
0
2
2
1
1
2
2
0
1
0
0
2
0
0
0
1
2
1
0
2
2
2
4
0
2
1
1
1
2
1
2
1
2
2
1
1
0
0
0
0
1
0
2
0
2
2
1
0
0
1
0
1
1
2
2
0
2
0
1
1
2
0
0
0
0
0
0
1
0
1
0
2
0
2
0
1
1
0
0
1
0
2
0
2
0
0
0
0
0
1
0
1
1
2
0
2
0
0
1
0
2
0
0
0
2
1
0
1
1
1
2
0
0
1
0
1
0
0
1
0
0
1
2
1
2
0
3
0
0
1
2
1
1
1
2
1
0
2
0
0
0
1
0
0
1
0
0
0
4
0
2
0
0
0
1
1
1
0
0
2
0
0
1
0
1
0
0
2
0
0
2
0
0
2
0
0
0
2
0
1
0
0
1
0
2
2
0
2
0
0
2
0
2
2
0
1
1
1
1
0
0
0
0
5
0
0
1
0
0
0
5
0
1
0
0
1
2
2
2
1
0
0
2
0
0
2
2
1
1
1
0
2
2
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
1
0
0
2
0
0
1
0
1
2
1
2
0
2
0
1
0
0
1
0
0
0
0
0
0
1
2
0
0
0
2
0
0
1
0
2
2
1
0
0
0
2
0
0
0
0
1
4
0
1
0
0
0
1
0
0
1
0
1
0
0
0
2
4
0
0
0
0
0
1
1
1
0
2
1
0
0
0
0
0
0
1
0
3
0
0
1
2
0
2
1
1
0
0
1
0
0
0
0
0
3
0
1
1
0
0
3
1
2
1
1
0
1
1
0
0
1
1
0
0
0
1
0
2
0
0
0
0
0
0
1
0
1
1
1
1
0
1
0
1
2
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
1
0
1
2
0
0
0
2
1
1
0
2
1
1
0
1
1
1
1
0
1
0
0
1
0
1
0
0
2
2
0
2
0
0
2
0
0
0
0
0
0
2
2
1
0
1
0
4
2
0
1
0
1
2
0
0
1
0
2
0
1
0
1
2
1
1
2
0
0
1
2
2
0
0
3
0
1
0
0
1
1
2
1
2
1
1
1
1
0
1
0
0
0
1
2
1
0
0
0
0
2
1
0
1
0
0
0
2
0
2
1
0
2
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
1
1
0
0
0
0
0
2
1
2
1
0
2
0
0
0
0
0
2
1
0
1
1
0
2
1
1
0
2
2
0
1
1
1
0
0
0
0
1
0
2
2
0
2
0
0
0
1
0
2
0
0
2
1
1
0
2
0
2
2
0
2
2
1
0
0
3
1
0
0
0
0
1
1
1
0
2
2
0
0
1
1
0
0
1
2
2
1
1
2
1
0
1
2
0
0
0
0
1
1
2
2
0
2
1
1
0
0
0
2
3
1
1
1
1
1
2
1
0
0
0
0
0
2
0
0
1
1
3
1
0
0
0
0
0
1
1
0
0
2
0
2
0
1
0
2
0
0
0
0
0
0
1
2
0
0
2
2
0
0
0
2
1
0
2
1
1
1
0
0
1
1
1
1
0
0
0
2
0
3
0
0
0
0
0
2
0
2
2
0
1
1
0
2
0
0
1
1
2
3
0
0
1
1
0
1
2
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
1
1
1
1
2
1
0
0
0
3
0
0
0
0
0
3
0
1
1
0
1
0
3
1
1
2
1
1
0
1
2
0
1
0
2
1
0
1
2
0
0
0
4
2
0
1
1
2
0
1
2
0
0
2
1
0
1
11
2
3
0
1
0
0
1
0
2
1
2
0
0
3
0
2
0
1
2
1
3
0
0
0
1
0
1
1
0
1
0
2
1
0
1
1
0
0
0
2
1
2
0
1
1
0
2
1
0
1
1
2
0
0
0
1
1
1
0
0
0
0
0
2
1
0
0
0
2
0
1
1
1
0
0
0
0
0
0
0
0
0
2
1
1
0
2
0
2
0
1
1
2
0
1
2
2
0
0
5
2
2
2
0
0
1
2
0
0
0
2
1
0
1
2
1
3
0
0
1
1
0
2
1
0
0
2
2
2
1
0
2
1
2
0
0
1
0
0
2
2
0
0
0
0
2
1
0
1
1
1
2
1
1
0
1
1
3
1
2
0
1
1
2
1
0
0
0
1
1
1
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
2
2
1
2
1
0
0
0
1
1
1
1
0
0
0
1
1
2
0
1
0
0
0
3
0
0
1
0
0
0
0
2
0
1
0
0
2
0
0
1
1
0
0
2
1
0
2
1
0
1
0
0
2
1
0
0
1
0
0
0
0
2
0
1
0
0
2
2
1
0
1
3
1
0
1
0
0
0
0
1
1
1
0
0
0
1
0
1
0
0
2
0
0
1
2
0
0
1
0
2
0
1
2
3
1
1
0
2
0
0
1
0
0
1
0
2
1
1
2
0
1
0
0
0
0
0
2
0
1
1
1
1
1
2
0
1
1
1
0
2
0
0
1
2
0
2
0
1
0
0
0
0
2
0
1
0
1
1
0
0
0
0
0
0
0
1
0
2
0
0
0
2
1
2
0
1
2
1
0
1
0
0
0
1
2
2
0
2
0
0
2
3
0
0
0
0
0
1
0
1
0
1
1
1
0
0
0
1
1
0
1
1
0
0
2
1
1
0
2
1
0
1
2
1
1
0
0
1
1
0
0
0
1
1
1
0
1
2
1
1
1
2
2
2
0
0
0
0
2
1
0
2
2
2
0
0
0
0
2
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
1
2
1
0
0
0
2
1
2
2
0
2
0
2
0
1
1
0
0
1
1
1
0
0
0
0
0
2
0
0
0
0
1
1
0
1
0
0
0
0
1
1
1
1
2
0
0
0
1
0
2
0
1
0
2
0
2
0
1
2
0
0
2
2
0
1
2
0
1
0
0
0
0
2
2
1
2
2
0
1
1
2
0
0
0
2
0
0
1
2
0
1
0
0
0
1
1
0
1
0
0
1
2
1
0
0
1
0
0
0
2
2
1
0
2
1
1
2
1
1
0
2
0
2
0
0
2
0
1
0
0
4
0
0
0
2
0
1
0
2
0
0
1
1
0
2
2
2
1
1
0
1
0
2
0
1
2
1
1
1
2
0
0
3
0
0
2
0
0
0
2
1
1
3
2
0
0
2
0
1
1
1
1
0
0
2
0
1
0
0
0
3
0
2
0
0
0
0
0
3
1
0
1
1
0
1
1
2
0
2
2
2
0
1
0
3
0
2
0
0
1
2
1
0
1
2
0
1
0
1
1
1
0
2
0
1
2
0
0
1
1
2
3
0
1
0
0
0
1
2
0
1
0
1
1
1
2
0
0
2
0
2
1
0
3
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
2
1
0
1
0
2
0
1
1
1
1
1
0
1
2
1
1
1
0
0
0
2
1
0
2
2
1
0
2
0
0
1
0
0
0
1
0
0
0
1
1
2
1
1
0
1
2
2
1
0
2
0
0
0
2
3
1
2
0
1
2
1
0
2
1
0
0
0
1
1
2
0
1
1
1
0
0
3
0
0
0
0
1
1
0
0
2
0
1
0
1
0
1
1
2
2
2
1
1
1
1
1
0
0
0
0
0
1
0
0
1
1
2
1
2
1
1
0
0
0
1
0
0
0
0
0
2
1
1
1
0
1
1
0
1
0
0
1
0
1
2
0
0
0
0
0
1
0
2
0
3
2
0
1
0
1
0
1
1
2
1
2
0
0
2
2
0
1
0
0
0
1
2
2
0
1
3
1
2
0
2
1
2
1
2
1
0
0
0
0
1
0
2
1
2
0
2
0
0
2
1
1
2
2
1
1
1
0
0
1
0
1
0
2
0
0
1
0
2
0
1
0
2
0
1
1
2
1
1
0
0
1
1
2
0
0
2
1
2
1
1
1
2
0
1
1
0
0
1
0
1
1
1
0
1
0
0
1
2
0
0
1
0
0
0
1
2
0
1
0
0
1
0
1
0
0
0
2
2
0
0
0
0
1
2
0
0
0
1
0
0
2
1
1
0
0
1
0
0
1
0
1
1
0
1
0
0
0
0
2
0
1
0
0
1
2
2
1
2
1
1
0
1
2
0
2
2
1
2
1
1
1
0
0
0
1
0
0
1
0
2
2
0
2
0
0
2
1
2
0
1
0
1
0
0
2
1
0
0
2
0
2
1
0
0
1
0
1
2
1
0
1
0
2
1
1
2
0
3
0
1
1
2
0
0
0
0
0
1
2
1
0
0
0
0
1
0
2
0
0
1
1
1
2
2
3
0
1
1
0
0
0
0
1
0
0
0
0
2
0
1
2
2
0
1
0
1
1
1
2
2
0
1
2
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
2
2
0
1
0
0
0
0
0
1
0
0
2
0
2
0
2
0
1
2
2
2
0
0
0
0
2
0
1
2
2
0
0
2
2
0
0
2
0
2
1
1
0
0
0
0
0
1
2
2
0
2
1
0
0
0
0
2
0
2
0
1
0
2
2
1
2
1
0
1
0
0
1
0
0
1
1
0
0
0
1
0
0
0
1
0
1
1
0
0
1
0
3
3
1
0
0
0
0
1
0
0
0
1
1
1
0
0
0
1
0
0
0
2
0
2
0
1
0
0
1
2
0
1
0
2
0
2
2
0
2
0
0
2
1
1
0
0
0
0
0
2
0
1
2
0
1
2
1
1
2
2
1
2
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
1
1
0
2
1
2
2
0
1
1
0
0
2
1
0
0
0
0
0
2
0
2
0
0
0
1
1
0
2
0
1
1
0
0
2
0
2
0
0
1
1
0
1
2
3
0
0
2
1
0
0
2
1
1
0
1
1
0
0
1
0
0
0
1
1
1
2
1
0
0
1
1
0
1
1
1
1
0
2
1
0
1
1
1
1
0
2
0
1
2
0
2
0
1
0
0
0
3
0
0
1
1
0
2
0
1
0
0
1
0
0
1
0
0
2
1
2
0
1
2
1
1
1
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
2
2
2
1
2
0
1
0
0
0
0
3
0
2
0
0
1
1
2
0
0
1
0
0
2
1
2
0
1
1
1
2
0
1
0
0
2
2
0
2
1
2
1
0
0
1
0
0
0
2
1
2
1
1
0
1
1
0
1
0
2
0
1
0
2
1
1
2
0
0
1
1
2
0
0
0
1
0
0
3
2
1
1
1
1
0
1
0
3
1
1
2
1
1
1
0
0
2
0
0
0
1
1
2
0
0
1
0
0
2
0
0
2
1
0
0
2
0
0
0
2
1
0
1
0
1
1
1
2
2
1
0
1
1
1
0
0
2
0
0
0
1
1
0
0
1
0
2
0
0
0
1
1
1
0
0
2
1
2
2
2
0
0
0
2
0
2
2
0
0
1
0
2
0
2
0
0
1
2
1
1
0
0
0
2
0
0
1
0
2
0
1
2
0
1
1
0
1
1
0
0
2
2
1
1
0
0
0
0
0
0
2
0
0
0
2
0
0
1
2
2
2
1
0
0
0
2
0
0
2
1
0
7
1
1
2
0
2
0
1
2
2
0
0
0
0
0
2
1
2
2
0
1
2
0
1
1
0
0
1
0
1
1
2
0
0
0
2
0
2
2
0
0
0
0
2
0
3
1
3
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
2
0
1
0
0
1
0
1
0
0
0
0
2
1
1
0
0
0
0
1
2
1
0
0
2
0
0
0
1
1
2
0
2
1
0
0
2
0
2
1
0
0
2
0
0
0
0
1
1
0
0
2
2
2
0
0
0
2
0
0
1
1
1
1
0
1
1
0
0
2
0
0
2
0
0
1
0
2
0
0
2
0
0
0
0
1
0
2
1
0
1
3
0
2
0
1
1
0
0
0
1
1
2
0
0
0
1
1
0
0
0
3
0
1
0
1
0
1
1
0
2
1
1
1
1
1
2
0
2
2
0
0
1
1
0
1
2
0
0
3
0
0
0
2
0
0
0
0
1
0
1
2
1
0
0
1
2
1
0
2
1
1
1
1
1
1
0
0
2
0
1
2
2
0
0
2
0
1
1
0
0
0
0
0
0
2
0
0
0
1
1
0
1
0
3
2
0
2
1
0
0
0
0
2
0
0
0
2
0
1
0
2
0
0
1
0
0
2
1
2
1
0
0
1
0
0
1
1
1
1
1
2
1
1
1
0
1
1
0
2
1
1
2
0
0
2
1
1
1
3
0
1
1
1
1
0
0
2
0
1
0
1
0
2
1
1
0
0
0
0
0
0
1
0
1
1
0
1
1
1
0
0
0
0
1
1
0
0
2
0
0
1
0
2
2
2
1
0
2
2
1
0
2
1
0
0
3
0
0
2
1
0
1
0
0
0
2
0
0
0
0
1
0
0
0
2
0
3
0
1
0
0
2
0
2
1
0
1
2
0
1
0
0
0
1
2
0
0
2
0
1
0
1
0
0
2
2
1
0
1
0
1
1
0
0
1
0
2
2
0
0
2
2
0
2
0
0
1
0
0
1
2
0
1
0
1
0
2
0
1
0
0
2
2
1
1
3
2
1
2
0
1
1
0
0
0
2
0
2
0
2
0
1
0
0
2
2
0
2
0
1
0
1
0
1
0
0
2
2
0
1
2
1
3
2
0
2
0
0
1
1
0
1
1
0
1
0
0
0
2
1
1
0
0
0
2
0
1
0
2
2
1
0
1
2
0
0
2
0
2
0
1
0
1
0
0
0
2
0
1
0
1
1
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
2
0
1
0
1
0
1
1
0
1
0
0
2
0
1
1
1
0
0
0
0
0
0
2
1
0
0
0
3
1
0
1
0
2
0
0
2
0
1
0
0
2
0
0
0
0
2
1
0
2
0
0
2
0
0
0
1
1
0
1
1
0
1
1
1
1
1
1
1
0
0
0
0
0
2
0
1
1
0
0
2
0
2
0
2
1
0
3
2
2
1
2
0
0
0
1
0
0
0
1
1
1
2
4
0
1
1
1
1
1
1
0
0
0
0
0
0
1
0
1
1
3
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
1
0
1
2
1
1
1
2
0
0
0
1
1
2
0
0
0
2
2
0
2
0
2
1
0
0
1
0
1
1
0
0
1
1
0
0
1
0
1
0
1
0
0
1
2
0
1
2
0
0
0
1
2
2
0
1
0
1
1
0
1
1
0
2
0
0
0
1
0
2
1
1
2
0
2
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
1
1
0
0
0
2
1
2
0
0
0
0
0
1
2
0
2
1
2
0
0
2
2
2
0
0
0
2
1
0
0
0
4
0
0
0
0
2
1
1
2
0
2
0
0
0
2
0
2
0
1
0
2
1
2
2
2
1
0
0
1
1
0
0
2
2
2
0
1
0
1
0
0
1
2
0
0
1
2
1
0
0
0
1
1
2
2
0
1
3
2
0
2
0
2
0
0
1
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
2
1
0
0
1
0
2
0
0
0
2
1
0
1
0
1
1
1
0
2
1
2
1
1
0
1
0
0
2
0
0
0
0
2
2
2
0
0
0
0
0
0
2
1
2
0
1
2
0
1
0
0
0
0
2
0
1
2
0
0
2
0
0
0
0
2
0
1
1
2
2
0
2
0
1
0
1
2
0
0
0
0
0
1
0
1
0
0
1
0
0
0
2
0
0
0
2
0
2
2
0
0
1
1
1
0
2
1
2
0
1
2
1
1
1
1
1
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
1
0
5
0
1
2
0
0
3
0
1
0
0
2
0
0
1
0
0
0
0
1
1
0
1
1
2
1
0
1
1
2
2
1
1
0
0
0
1
0
1
0
0
1
2
1
0
2
0
1
1
2
0
1
1
0
1
2
1
3
1
1
1
2
0
1
1
0
2
1
2
0
2
1
1
0
0
1
1
1
1
0
0
1
0
2
0
0
1
0
2
0
0
2
0
2
1
0
0
0
0
2
1
0
0
0
1
1
1
1
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
1
1
2
3
1
0
2
0
0
1
1
1
0
2
2
1
0
0
1
0
0
0
0
0
1
1
1
0
1
0
0
2
0
1
1
0
2
2
0
0
1
2
0
0
1
0
1
2
1
0
2
2
2
0
1
1
1
2
0
2
0
0
0
2
1
2
0
1
1
1
2
0
2
2
0
2
1
1
2
2
2
2
1
0
0
2
0
2
2
0
0
1
1
1
0
1
2
0
1
2
0
2
0
1
0
2
2
0
1
0
0
1
1
1
2
1
0
4
0
0
2
1
1
0
1
2
2
0
0
0
0
0
2
0
0
3
2
3
0
0
2
0
0
0
1
7
1
1
0
0
0
0
1
1
1
0
1
1
0
1
0
0
0
0
0
1
2
0
0
1
0
0
0
2
0
1
2
0
2
1
0
2
0
0
0
0
0
1
1
0
2
0
1
1
1
1
2
2
0
2
2
2
0
1
1
2
1
0
1
1
1
0
0
1
1
0
0
1
0
1
0
0
0
6
2
1
0
0
1
0
1
0
0
0
0
1
2
3
1
2
2
0
0
0
0
1
0
0
1
0
2
2
0
2
0
0
2
2
2
1
0
0
1
2
0
0
2
0
0
0
1
3
0
0
2
0
0
2
1
0
1
1
0
1
0
0
2
0
0
0
2
1
0
1
1
0
0
1
2
1
3
1
0
1
1
1
0
0
2
0
0
0
1
0
0
2
1
0
1
0
0
0
1
1
0
0
0
0
2
0
1
2
0
1
0
1
1
1
0
0
1
2
1
2
0
1
0
0
2
0
0
1
0
0
2
3
1
1
0
2
1
0
1
4
1
0
2
1
0
0
5
0
2
2
1
0
0
0
0
0
0
1
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
1
1
0
0
0
0
2
1
1
1
0
0
0
1
2
2
3
2
2
0
2
2
1
1
0
0
1
1
1
0
1
1
0
2
2
1
0
0
0
2
1
1
0
2
1
0
1
1
2
1
1
0
2
0
0
0
2
0
0
0
1
0
0
2
0
1
2
1
0
1
1
1
0
0
0
1
2
0
1
1
1
1
2
0
1
1
0
0
1
2
0
0
3
0
2
0
0
0
0
1
0
1
1
2
0
0
0
1
2
0
1
1
0
0
0
0
1
2
0
1
0
2
0
2
0
1
2
2
1
1
0
1
0
0
0
0
1
0
2
5
0
0
2
0
0
0
0
2
0
0
1
0
6
0
0
1
0
1
2
4
0
2
0
0
0
0
2
1
2
0
0
1
1
0
0
0
0
0
2
2
2
1
0
0
2
2
0
0
1
1
2
1
0
0
1
1
0
0
1
2
0
0
1
0
0
2
3
1
2
0
1
0
0
1
1
0
0
0
2
0
1
2
0
0
1
2
1
0
0
1
0
1
2
0
0
2
1
2
2
0
2
0
1
2
0
0
0
0
0
1
0
1
0
1
1
1
0
0
2
1
0
3
0
0
1
0
0
1
0
8
1
2
0
0
0
2
0
0
2
0
1
1
0
2
2
0
1
0
1
3
0
0
0
1
2
1
0
0
0
1
2
2
0
0
0
1
0
2
0
2
1
1
2
3
0
2
1
0
2
0
2
0
0
0
1
2
1
0
2
2
0
0
0
2
0
1
0
2
2
2
1
0
0
1
0
1
2
2
0
1
1
0
0
2
3
1
1
2
0
2
0
2
0
1
2
1
1
1
0
0
1
0
0
0
0
0
0
2
1
0
1
0
2
0
0
3
0
2
1
1
0
1
2
1
0
1
0
2
0
0
1
0
2
1
1
2
0
1
1
0
3
0
0
0
1
1
0
1
0
1
0
1
1
1
0
0
1
0
1
0
0
2
0
0
0
1
0
2
1
2
0
1
2
1
1
0
1
2
1
0
1
0
0
2
0
3
1
0
2
1
1
0
1
0
0
0
1
0
1
0
1
2
1
2
0
0
0
2
3
2
2
0
1
0
0
2
2
2
0
1
2
0
0
1
0
2
0
0
0
1
0
1
2
1
2
0
1
0
2
1
0
1
1
2
0
0
6
0
1
1
0
0
1
1
2
1
0
0
1
0
2
0
0
0
0
0
1
0
1
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
2
1
2
0
3
0
1
0
0
0
0
0
0
1
0
1
0
1
1
0
1
0
2
0
1
0
0
0
2
1
0
1
1
0
1
0
0
0
0
1
0
2
1
0
1
0
2
0
0
1
0
0
1
0
0
0
0
1
0
1
0
1
0
2
1
0
2
2
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
2
2
0
1
2
1
2
0
2
0
0
1
0
0
1
2
1
0
1
5
0
1
0
0
0
0
3
2
0
0
0
1
2
0
0
0
0
2
0
0
0
2
2
0
1
0
0
0
2
1
2
0
0
0
0
1
0
0
1
0
1
1
0
0
0
1
1
3
0
0
1
0
0
0
1
2
1
2
1
0
1
1
1
0
0
0
0
2
1
0
2
1
1
0
2
0
0
0
1
0
2
0
2
2
0
0
0
1
1
1
0
1
1
2
1
1
2
1
2
0
1
1
1
0
1
1
1
0
0
2
0
2
0
2
1
0
0
1
2
0
1
1
0
0
0
0
0
2
0
0
0
0
2
2
0
0
1
0
1
2
1
1
2
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
1
2
2
0
0
0
1
0
0
0
0
0
1
0
0
5
1
0
0
0
0
2
0
0
2
0
0
0
1
0
1
0
1
1
0
1
1
1
0
0
2
1
1
1
1
0
0
0
1
0
0
2
1
0
1
2
0
0
0
1
0
1
1
1
2
0
0
2
2
0
1
1
1
1
0
0
1
1
0
1
1
2
1
2
0
0
0
1
0
0
0
0
1
0
0
2
0
0
2
0
0
0
1
0
0
0
1
0
0
0
2
2
1
0
1
0
4
3
0
2
0
0
1
0
0
2
1
1
0
1
0
1
4
1
1
1
0
0
1
0
1
0
1
2
1
0
0
1
0
1
1
2
1
0
0
3
2
0
2
1
0
0
0
0
0
1
1
0
1
0
0
0
0
1
2
1
1
1
0
0
1
2
0
2
2
0
0
2
0
3
0
0
0
1
0
0
2
1
0
0
1
2
1
0
1
0
0
1
0
0
1
2
0
0
0
0
0
2
2
0
1
2
0
0
1
0
2
1
1
0
0
2
0
2
0
2
2
2
1
0
1
2
1
0
0
0
2
2
0
1
0
1
0
1
1
0
2
0
1
2
0
1
0
1
0
2
0
2
0
1
0
2
1
0
0
1
1
0
3
0
0
0
1
2
1
1
1
1
0
0
1
1
1
0
0
0
0
1
6
2
4
0
1
0
1
1
0
0
1
0
1
0
0
0
0
1
1
2
0
0
0
2
2
2
1
0
0
0
0
1
0
1
1
1
0
4
2
1
1
0
0
0
0
0
2
1
0
0
2
0
0
0
0
1
0
2
0
0
1
2
1
2
1
1
1
0
0
0
2
0
1
0
1
0
0
0
1
0
1
1
0
0
2
0
2
0
2
1
2
0
0
2
0
0
0
1
2
1
1
0
0
0
0
0
0
0
1
2
1
1
2
0
0
0
1
2
0
0
1
0
0
0
1
0
2
2
1
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
2
1
0
0
2
0
1
0
2
0
0
0
1
0
0
0
1
0
0
0
2
0
2
0
2
0
3
2
0
2
0
1
0
0
1
1
1
0
1
2
0
2
0
0
1
0
2
0
1
1
2
1
1
1
0
0
1
0
1
0
0
0
0
2
1
2
1
2
0
1
0
0
0
1
0
1
2
1
0
0
0
2
2
2
1
1
1
3
0
2
1
1
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
1
1
2
1
0
0
0
0
2
2
0
2
0
2
1
0
1
0
1
3
0
0
0
2
3
0
1
1
0
0
2
2
0
1
2
1
0
0
1
0
0
1
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
2
1
2
1
0
0
1
1
1
1
1
1
0
0
0
1
2
0
0
1
0
0
2
0
0
0
2
0
2
3
2
0
0
0
0
2
2
2
1
2
0
1
1
0
1
0
1
0
2
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
1
2
1
2
1
0
1
1
1
1
2
2
1
1
0
3
1
0
2
2
2
1
1
0
1
1
0
2
0
1
0
0
0
0
2
1
0
0
0
2
2
0
1
1
0
0
1
0
2
2
2
0
1
1
2
0
0
0
0
0
1
2
0
2
2
0
1
1
1
0
1
0
1
1
0
2
0
2
0
1
1
0
0
0
2
0
2
1
2
0
1
0
1
1
1
1
0
0
1
0
0
0
2
0
0
2
3
1
2
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
1
1
1
1
0
2
1
1
0
0
0
2
0
1
2
0
2
0
2
1
0
1
0
0
0
1
0
2
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
1
2
2
0
0
0
0
1
2
0
0
3
0
1
0
0
0
1
3
1
0
1
1
0
1
0
0
0
1
2
0
0
2
0
0
3
0
1
1
0
2
0
1
2
1
0
0
2
2
0
1
1
0
1
0
1
1
0
2
2
0
1
0
0
3
2
0
2
1
1
2
0
1
0
0
0
1
0
1
1
2
1
0
1
1
1
1
0
0
1
2
1
0
0
0
2
0
0
1
1
2
1
0
0
0
2
0
1
0
0
0
2
1
1
1
2
0
0
1
0
0
0
2
0
2
0
1
0
1
1
0
0
0
2
1
2
0
1
0
1
0
2
1
0
0
0
2
1
1
0
1
1
0
0
1
0
2
0
2
0
0
2
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
1
0
1
0
3
0
1
1
2
2
2
0
0
0
2
0
1
2
0
0
2
0
0
0
1
1
0
1
0
0
0
0
2
2
2
1
1
2
0
2
1
2
0
0
2
0
1
2
0
1
2
2
0
2
2
2
2
0
3
2
0
2
0
2
1
2
2
2
0
2
2
1
0
1
0
1
1
0
2
1
1
0
1
0
2
1
2
0
0
2
0
1
0
0
0
3
2
0
0
1
0
0
2
3
1
2
0
0
1
0
1
0
2
1
0
0
1
2
0
1
1
1
0
0
0
0
0
0
3
1
1
1
2
2
0
1
2
2
0
2
1
1
0
2
2
0
0
1
0
0
1
2
0
0
1
0
2
2
1
2
1
1
2
0
0
1
0
0
1
0
2
0
2
0
0
2
0
0
0
1
1
0
0
0
0
1
0
0
0
2
2
1
0
2
0
1
0
1
2
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
1
2
0
1
0
0
0
3
1
0
2
2
0
2
0
0
2
1
1
0
0
0
0
0
1
0
2
0
2
4
1
0
2
0
1
0
2
0
0
2
0
1
2
1
1
0
3
2
2
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
1
3
0
0
1
0
0
2
1
0
1
0
1
1
1
1
0
1
2
2
1
3
0
0
2
0
1
0
1
4
1
0
4
0
2
1
0
0
0
1
1
0
1
0
0
0
2
2
0
1
1
0
2
0
1
0
1
0
2
0
1
2
0
0
3
1
0
1
0
2
0
0
2
1
0
2
0
0
0
0
0
0
0
1
0
0
2
0
2
1
3
1
0
0
1
2
0
1
0
0
0
2
0
2
0
0
1
0
0
2
0
2
0
1
1
1
0
0
0
1
1
1
1
2
0
0
2
0
0
0
2
2
2
1
3
2
0
1
0
0
1
1
2
1
0
1
0
1
0
0
0
1
0
0
0
0
1
1
2
0
0
2
1
0
0
0
0
2
0
1
0
1
0
1
0
0
0
0
0
0
1
2
0
0
1
1
0
1
0
0
1
3
0
4
1
1
0
5
0
0
2
2
0
1
2
0
0
0
2
1
0
1
2
0
0
0
2
0
0
0
1
0
0
0
1
0
0
1
1
0
2
1
1
1
3
0
2
0
1
0
0
2
0
1
1
1
2
0
0
1
0
0
0
1
0
1
1
1
0
2
2
0
2
1
1
0
0
2
3
0
0
1
1
2
0
1
0
0
2
0
0
1
1
1
0
0
1
0
0
0
0
0
2
0
0
0
1
1
2
0
2
0
0
1
0
3
2
2
1
1
0
0
1
2
0
1
1
1
1
0
2
1
0
1
0
2
0
0
0
0
0
0
1
0
0
2
0
0
1
0
1
0
0
1
1
0
3
1
0
1
0
2
1
2
1
1
1
0
1
0
1
0
1
1
1
0
0
2
0
2
2
0
0
0
2
1
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
1
1
1
0
0
1
2
1
2
0
1
0
2
3
0
0
2
1
0
1
1
4
0
1
1
1
0
0
1
1
0
2
2
2
2
0
1
0
0
1
0
2
2
0
2
2
2
1
0
0
3
0
0
0
0
1
2
0
0
1
0
0
2
0
0
0
0
0
0
1
0
2
1
0
1
2
0
2
0
2
1
1
2
2
0
1
0
0
0
1
1
1
1
1
1
1
4
3
1
0
2
1
0
0
1
2
0
1
0
0
0
0
0
0
1
0
2
1
1
2
0
0
0
1
2
0
3
2
0
0
2
0
0
0
0
0
1
0
1
2
0
2
2
0
0
0
0
0
0
1
0
2
0
1
0
0
2
0
2
1
0
1
1
1
0
0
0
0
0
0
5
0
2
1
1
0
0
1
1
2
0
1
1
0
1
1
2
0
0
0
0
1
0
0
2
2
2
0
22
1
0
0
1
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
1
1
2
2
1
0
0
2
1
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
2
1
0
1
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
2
2
1
0
0
1
2
2
0
1
0
0
0
2
2
0
1
0
0
0
0
1
0
0
0
1
2
0
1
1
1
2
1
0
0
1
1
0
0
1
1
0
0
0
0
0
0
2
2
0
1
0
0
0
1
0
1
2
0
1
2
1
0
1
1
2
2
0
0
0
1
1
1
0
1
2
1
1
2
0
0
1
1
0
0
0
1
3
1
1
0
1
0
0
0
2
2
3
1
1
1
0
3
2
0
1
0
0
0
1
2
1
0
0
2
1
0
1
0
1
0
1
1
1
2
1
0
0
0
0
3
0
0
0
1
2
0
0
2
2
2
0
0
0
1
0
0
0
1
0
1
0
2
2
0
0
0
2
3
0
2
0
0
1
0
0
0
0
2
1
1
0
2
1
1
0
1
0
1
0
2
0
2
0
0
0
1
0
1
2
0
1
0
0
1
0
2
2
2
0
0
1
1
0
1
2
0
2
0
0
1
0
0
2
0
1
1
1
0
0
0
0
0
0
0
2
1
1
1
2
1
7
0
0
0
2
0
2
2
0
2
0
0
0
1
0
0
0
2
1
2
2
0
0
2
0
1
2
1
0
1
0
0
0
3
1
0
2
2
0
1
2
2
0
0
2
0
0
2
0
0
3
0
0
1
0
2
1
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
2
0
1
0
0
3
0
2
2
0
2
0
1
2
0
1
1
0
1
0
0
0
0
2
0
0
1
0
1
2
0
0
0
0
1
1
1
0
0
1
3
2
1
0
2
1
0
0
2
0
2
2
1
0
0
1
3
0
3
1
1
2
0
2
2
1
1
0
0
1
2
1
0
2
0
0
2
2
0
0
2
0
1
2
2
0
0
0
1
1
0
0
0
1
2
0
0
0
0
1
0
2
2
0
2
0
1
2
2
1
0
2
1
1
0
0
0
0
0
0
1
0
2
0
0
2
0
1
1
0
1
1
1
1
0
2
2
0
1
1
2
0
1
0
1
2
1
2
1
0
0
1
0
0
0
2
0
0
1
2
0
0
0
2
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
1
0
1
1
2
0
0
2
0
0
2
2
1
0
1
1
0
0
2
0
0
1
2
1
2
0
2
0
0
1
0
3
1
0
2
2
0
1
0
0
0
0
1
1
0
2
1
2
1
0
0
0
1
0
0
2
1
0
0
0
1
9
0
1
1
1
0
2
2
2
2
3
0
1
3
1
1
0
0
2
0
0
0
0
0
0
1
0
2
2
2
1
1
0
1
0
0
0
0
1
1
1
1
2
0
1
1
2
0
0
0
0
0
1
0
2
1
1
1
2
2
1
0
1
0
0
1
0
2
0
1
1
3
2
1
2
0
0
0
1
0
0
1
1
0
0
0
1
0
0
1
0
2
0
0
2
0
0
1
0
0
0
0
2
1
0
1
0
0
2
0
0
1
2
1
1
2
2
0
0
1
2
0
0
2
1
2
2
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
1
1
2
0
0
1
0
1
0
0
1
0
1
0
1
0
0
2
2
0
1
0
1
0
1
0
0
0
1
1
0
2
2
2
1
2
0
0
1
0
1
0
1
0
1
2
0
1
2
1
0
0
0
0
1
1
0
0
1
1
1
0
2
0
1
0
0
0
0
1
2
0
1
1
0
0
1
0
1
2
0
0
0
0
2
0
0
0
0
4
0
1
0
1
0
1
2
0
0
0
0
0
0
1
0
1
1
0
0
0
0
3
0
2
1
2
0
1
0
0
1
0
0
1
0
2
0
0
1
1
1
0
1
0
1
0
0
1
1
1
0
0
1
0
2
1
0
0
1
1
0
0
2
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
1
1
2
0
2
0
0
0
0
1
3
2
2
0
2
0
1
0
1
0
0
0
0
1
0
1
0
0
2
1
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
2
1
0
2
0
0
2
0
2
1
0
3
0
2
2
0
0
0
1
0
0
0
2
1
0
1
0
0
0
5
1
0
0
1
2
0
2
2
0
1
0
1
1
0
2
0
0
0
0
0
4
2
1
0
0
0
1
7
0
1
1
0
1
1
1
1
0
1
2
0
1
1
0
1
2
0
0
1
2
2
0
0
1
0
1
0
1
2
0
0
1
1
2
0
2
0
0
0
1
0
1
0
0
0
0
2
1
1
1
2
0
1
1
1
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
2
1
1
0
2
0
1
0
2
2
2
2
0
0
1
2
1
0
2
1
2
0
2
1
2
0
0
0
0
0
0
0
1
2
1
0
0
2
1
2
0
0
0
0
0
1
0
2
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
1
1
1
0
2
3
0
2
1
2
0
0
0
0
2
1
0
1
0
0
1
0
2
2
0
1
1
0
1
1
1
2
0
0
0
0
0
2
1
2
2
2
1
0
2
0
2
2
1
0
2
0
0
1
0
0
0
0
0
2
0
1
2
2
0
0
1
2
0
0
0
0
0
2
1
0
0
1
0
1
1
0
2
0
2
2
1
1
2
0
1
2
1
0
1
0
0
0
0
0
0
2
0
1
0
0
2
1
0
2
0
1
0
0
2
0
0
1
2
1
1
0
0
0
2
0
0
2
4
0
2
1
0
0
2
1
4
1
0
2
1
2
0
2
0
0
0
0
2
0
0
2
0
0
2
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
2
1
0
0
0
2
0
1
0
1
2
3
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
2
1
1
0
1
0
0
0
2
3
0
0
1
0
0
2
0
1
1
0
2
0
1
1
0
1
0
0
0
1
0
2
0
0
1
0
0
0
2
2
0
0
0
1
0
1
0
0
0
1
2
0
4
0
0
0
1
1
1
1
1
1
1
0
1
0
0
1
1
0
0
1
0
0
6
0
0
1
2
0
1
0
1
0
0
0
0
2
1
0
0
0
0
3
0
1
2
0
2
0
1
0
1
0
1
0
2
0
1
0
1
2
0
2
1
0
1
1
1
0
1
2
1
1
1
0
1
0
1
1
1
1
0
2
3
0
3
0
1
2
0
0
2
0
0
2
2
3
0
0
0
2
2
0
0
2
1
0
1
2
1
0
0
1
0
1
0
0
4
0
0
0
0
0
1
1
1
0
0
2
0
0
0
1
1
2
2
0
0
1
0
1
0
1
1
0
0
0
1
0
0
0
2
0
1
0
0
2
2
1
2
2
0
0
0
0
1
0
1
2
1
1
1
0
0
0
2
0
0
0
2
0
2
2
0
1
0
1
0
1
0
0
0
0
0
0
1
1
0
1
0
1
0
1
0
2
1
1
0
2
0
0
0
2
1
2
2
0
0
2
1
0
0
0
0
1
0
2
2
0
0
0
1
0
0
0
1
0
0
1
1
2
1
1
0
0
1
1
2
0
0
2
0
2
0
1
2
0
1
0
0
0
1
0
0
0
2
0
0
2
0
0
2
2
0
0
0
3
0
3
0
1
1
1
0
0
0
0
1
2
0
0
1
1
1
0
1
1
0
0
1
0
2
0
0
0
2
1
0
0
2
0
1
0
0
1
2
0
4
1
2
0
1
0
1
1
1
0
1
2
1
1
0
0
1
6
2
0
1
0
0
2
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
2
0
1
0
2
1
0
0
2
1
2
0
2
1
0
0
0
0
2
0
3
0
1
1
2
2
2
0
0
2
0
1
1
1
2
1
0
2
1
1
0
2
0
2
0
0
1
0
0
2
1
1
0
0
1
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
1
2
1
2
1
0
0
0
2
0
2
1
2
0
1
1
0
0
1
0
1
0
2
0
2
0
1
0
1
2
2
1
0
0
0
1
0
0
0
0
0
0
1
2
0
1
0
1
1
1
1
2
0
2
0
0
1
0
1
2
1
0
1
0
1
1
0
3
0
0
1
2
0
2
0
0
0
1
2
1
0
1
0
0
1
1
1
0
1
1
2
2
0
0
1
0
1
0
0
2
2
2
0
2
1
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
2
2
0
0
1
0
0
0
3
1
0
0
0
3
2
0
1
0
1
2
1
0
0
0
0
0
1
0
3
2
0
0
0
0
0
0
0
1
2
2
2
0
1
0
0
0
2
1
0
1
2
2
0
0
0
0
0
0
1
2
0
1
0
2
2
1
1
0
0
0
0
0
0
0
1
2
2
1
1
0
1
0
0
0
1
2
0
0
0
3
0
2
1
2
1
0
0
2
0
0
1
0
1
0
1
1
0
2
1
0
0
2
0
0
2
0
2
0
2
2
0
0
0
0
0
0
0
2
0
1
2
2
0
1
0
1
0
2
1
1
0
0
1
0
2
0
0
0
0
1
2
2
0
1
1
0
0
1
0
1
0
0
1
0
1
0
0
2
1
1
0
1
2
0
1
0
2
0
0
1
1
0
5
0
0
0
1
2
0
0
0
1
3
0
2
1
2
0
0
1
2
2
2
0
1
1
0
0
0
0
0
0
1
0
2
0
1
1
2
0
0
1
1
0
1
0
2
0
2
3
0
1
1
0
0
0
2
2
0
2
0
0
0
0
0
1
0
1
0
1
2
1
0
0
0
1
0
2
2
0
0
0
1
1
0
0
1
0
0
1
0
0
2
2
0
1
0
2
2
0
1
1
1
1
2
2
0
2
0
2
5
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
2
2
0
0
1
1
0
1
0
0
0
2
0
1
0
1
3
0
2
0
0
0
1
1
0
0
0
2
0
1
1
1
0
2
1
0
0
0
0
0
2
2
2
1
2
0
2
0
0
0
1
8
2
2
4
2
1
2
2
0
1
0
1
0
1
1
0
1
0
2
2
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
4
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
2
2
1
1
0
1
1
1
1
0
0
0
1
0
2
0
2
0
2
1
1
2
0
0
0
1
1
0
1
0
0
1
2
2
0
0
0
0
0
0
2
0
1
1
0
0
2
0
0
2
0
1
1
1
2
0
1
1
0
0
2
1
0
0
1
2
1
0
1
0
1
0
0
1
0
1
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
2
1
1
1
0
0
0
0
1
0
0
2
1
0
1
0
1
0
2
2
0
1
2
0
0
1
3
2
2
0
0
0
1
0
0
0
1
0
1
1
2
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
2
1
1
2
1
1
0
0
0
2
0
0
0
0
1
0
2
2
1
1
0
0
0
2
0
2
1
2
0
3
0
0
2
0
2
1
1
1
0
0
2
2
1
1
0
0
0
0
1
2
1
0
1
1
0
0
2
2
2
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
1
0
2
0
1
0
0
0
0
1
1
0
1
2
2
2
1
0
3
0
2
0
0
2
0
0
1
0
1
1
1
0
2
2
0
0
0
0
1
0
0
0
0
0
4
1
0
0
0
0
1
0
2
0
1
2
0
1
1
1
2
3
0
1
0
2
0
0
0
1
1
1
0
2
0
0
0
0
2
2
1
1
2
1
2
2
0
1
0
0
0
0
0
3
2
1
0
2
0
0
2
1
0
0
1
1
0
0
0
0
1
0
2
1
1
1
0
2
0
0
1
0
0
0
2
2
0
0
2
0
0
1
1
2
2
2
0
0
0
0
0
2
1
0
2
3
0
0
2
0
2
0
1
0
1
0
2
0
0
0
0
1
0
2
1
0
0
0
2
0
0
0
0
0
0
1
1
0
2
0
5
0
1
0
2
0
0
0
0
2
0
1
1
1
0
2
2
0
1
1
0
1
2
0
1
1
1
0
2
1
0
1
0
0
0
2
0
1
2
1
0
1
0
2
3
1
0
2
0
0
1
0
1
1
1
0
2
2
0
1
2
2
0
2
0
0
0
1
1
0
0
0
1
0
0
0
0
2
2
2
1
0
0
0
2
0
2
0
2
2
1
0
1
0
0
1
1
0
0
0
1
2
0
2
0
0
0
0
0
2
1
2
2
0
0
0
0
0
0
0
0
1
1
0
2
2
0
0
0
0
1
2
0
0
0
1
0
1
0
2
0
1
0
0
0
2
0
1
1
2
2
1
0
2
2
0
1
0
0
0
0
1
1
0
1
1
1
0
1
0
1
0
0
1
2
1
1
0
1
0
1
2
3
1
0
1
0
0
1
0
1
0
1
0
0
2
1
0
0
2
1
1
1
0
0
1
1
0
0
1
0
0
2
0
2
0
0
1
0
1
0
0
0
1
2
1
0
0
0
0
0
2
0
0
2
1
0
1
2
0
2
0
1
3
1
2
0
0
0
0
2
1
1
0
2
2
2
0
2
1
2
0
0
0
1
3
1
0
2
0
1
0
1
0
2
1
0
1
0
2
0
1
2
0
0
2
0
0
1
1
0
0
0
0
2
0
1
0
0
0
0
1
0
0
2
0
1
0
0
1
0
1
0
1
0
0
0
1
2
2
1
0
2
0
0
0
0
0
2
0
0
0
4
0
1
1
1
1
0
1
0
0
0
2
2
2
2
2
0
0
1
2
2
0
0
0
0
0
1
1
1
2
1
2
2
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
2
0
1
1
0
0
0
0
1
1
0
2
0
2
1
1
0
0
0
2
2
0
1
0
0
0
1
2
0
2
3
1
2
0
2
0
1
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
1
3
0
0
2
1
0
0
0
0
0
1
0
0
2
1
1
0
1
1
2
1
0
1
0
0
1
0
2
0
1
1
0
0
0
1
1
1
0
1
1
2
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
1
2
0
1
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
2
0
0
1
2
0
1
0
2
0
1
2
1
0
0
0
0
0
0
2
2
1
0
0
0
2
0
0
0
0
2
0
0
1
0
1
0
0
1
0
1
0
1
1
1
0
0
2
0
0
2
0
0
0
2
0
0
0
1
0
2
2
0
1
2
1
2
0
0
0
0
0
1
0
1
0
1
0
0
0
0
2
0
0
0
1
2
1
1
1
0
2
1
0
0
0
1
0
1
0
1
4
0
1
0
2
0
2
0
1
0
0
1
0
0
0
1
2
2
4
2
1
0
0
2
0
0
0
0
0
2
1
0
0
2
0
0
1
0
0
0
0
0
0
2
0
2
0
1
1
1
0
0
2
2
2
0
0
0
2
0
2
0
0
2
0
1
0
0
0
2
1
2
2
1
1
0
1
0
2
1
0
2
0
2
1
1
0
0
0
0
1
2
1
2
1
1
2
2
0
2
2
2
0
0
1
1
0
1
2
2
0
2
2
1
0
1
1
2
0
0
0
3
0
2
0
2
0
0
1
0
2
1
0
0
2
0
0
0
3
0
4
1
0
0
0
0
1
1
0
0
1
0
2
0
1
0
1
1
1
0
0
1
2
0
7
1
0
0
1
0
2
2
0
0
0
1
1
0
2
0
0
1
0
1
1
0
0
1
1
0
0
1
0
0
0
3
2
2
1
0
1
0
2
2
1
2
0
0
0
0
2
0
0
0
1
1
1
0
4
0
0
2
0
2
1
2
1
2
0
2
0
2
1
0
1
1
2
0
0
0
2
0
2
2
0
1
1
2
2
1
0
0
0
0
0
1
0
0
1
0
2
1
2
2
0
0
0
2
1
2
1
0
1
2
0
1
1
0
0
0
1
4
2
0
1
1
0
2
0
2
0
0
0
2
0
0
0
2
0
0
1
1
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
2
1
0
1
2
0
2
0
0
0
0
2
2
2
1
0
2
0
0
1
0
0
1
0
0
0
1
1
0
0
1
0
0
2
0
4
1
0
0
0
1
0
0
1
2
0
0
0
1
3
0
1
0
4
0
2
0
2
0
1
0
0
2
0
1
1
2
1
2
0
2
2
0
1
2
0
2
1
0
2
1
1
0
1
0
0
0
1
0
2
2
1
2
0
1
0
1
0
4
0
1
2
1
1
1
5
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
3
0
0
0
1
2
0
0
2
1
2
2
0
1
1
1
0
0
0
0
0
0
0
0
2
0
2
1
1
0
1
1
0
0
2
0
1
0
0
1
1
0
1
2
1
2
2
2
0
0
0
2
1
0
0
0
0
0
2
2
1
0
2
0
2
1
1
1
0
0
1
0
2
2
1
0
0
0
1
1
2
0
1
2
0
0
0
1
0
0
1
0
0
0
0
3
1
0
0
0
0
0
0
1
1
0
2
1
0
0
0
3
0
1
0
3
0
2
1
1
1
1
0
1
1
0
0
1
2
2
0
3
1
0
0
1
0
0
1
2
0
1
1
3
0
0
0
2
0
2
1
3
2
1
0
2
0
0
2
2
2
1
0
2
0
0
1
0
2
1
0
0
2
2
2
1
1
2
0
0
1
0
1
1
0
2
1
4
0
2
0
2
0
0
0
1
0
0
1
0
0
2
0
1
0
0
0
0
0
1
1
1
0
2
0
2
0
0
1
1
1
1
1
0
0
2
1
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
2
0
2
1
1
0
1
2
0
2
0
1
0
0
1
0
1
1
1
2
1
0
0
1
1
2
3
0
0
0
2
0
0
0
2
1
1
2
0
0
0
1
0
0
2
0
0
2
0
0
2
0
1
1
1
0
0
4
1
1
0
0
0
1
0
1
1
1
0
1
0
0
0
0
1
1
0
1
3
1
0
0
0
2
0
2
0
0
0
0
0
1
0
0
1
2
0
0
2
1
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
2
0
1
0
0
0
2
1
1
2
0
0
1
0
1
1
1
2
2
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
2
3
1
1
1
0
0
1
2
2
1
0
1
0
0
1
0
2
2
2
1
2
0
0
0
1
0
0
2
2
1
1
1
1
0
1
1
4
1
2
2
1
2
1
1
2
1
0
1
0
2
1
1
0
1
0
0
1
2
1
0
2
2
1
0
0
2
0
2
0
0
1
0
0
2
0
0
0
0
1
1
2
1
0
1
2
2
2
0
1
1
0
0
0
0
0
1
0
2
1
0
0
1
2
2
1
1
0
1
2
2
1
2
0
2
1
0
0
1
1
1
0
1
0
0
4
3
2
0
0
0
2
1
0
1
0
0
0
0
0
0
0
1
1
0
2
3
1
0
2
1
0
0
1
0
2
0
1
1
1
2
0
0
0
1
1
1
1
2
1
2
1
2
0
2
1
1
0
0
1
0
2
0
0
1
1
1
0
2
0
2
0
0
1
2
0
0
1
0
1
1
0
2
2
1
1
1
0
0
0
0
0
1
0
1
4
2
1
0
1
0
0
0
1
0
2
2
0
0
0
0
2
0
1
2
2
0
1
0
0
2
0
0
0
0
0
1
0
2
1
1
0
2
0
0
0
0
1
2
1
0
3
1
2
0
2
2
2
2
1
1
1
1
2
2
2
1
1
1
2
2
0
1
0
1
1
0
1
1
1
1
0
0
1
2
0
0
1
2
0
0
2
2
1
0
1
2
0
0
0
2
1
0
0
0
2
2
1
0
1
0
1
0
1
0
1
2
0
0
1
0
0
0
1
2
0
1
2
1
0
2
1
0
1
3
1
0
0
1
1
0
0
2
1
2
1
1
2
0
2
0
0
1
1
2
1
0
0
0
0
2
2
0
0
1
0
0
2
0
2
2
1
0
2
0
2
1
1
0
3
0
0
1
2
4
1
0
0
2
0
0
0
1
0
2
1
1
0
1
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
1
2
1
2
0
1
0
2
1
1
1
0
0
0
0
0
2
0
0
0
0
1
1
0
1
0
1
0
1
0
0
2
1
0
1
0
3
0
0
2
1
0
0
0
0
3
1
0
2
0
1
0
0
0
1
1
1
1
0
1
1
0
0
0
3
0
0
0
2
1
2
1
1
0
2
0
2
0
0
0
1
1
1
0
2
1
1
0
1
0
2
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
2
1
1
1
0
0
0
1
2
0
1
1
1
1
1
1
0
1
0
0
0
0
1
1
1
1
1
0
0
7
2
0
2
0
2
2
0
1
1
2
1
0
1
1
0
0
0
0
1
0
2
2
2
0
2
2
0
2
0
0
0
1
1
0
1
2
1
0
2
1
2
0
2
0
2
0
0
1
0
0
2
1
0
2
3
0
0
1
0
2
1
0
1
0
0
2
0
2
3
0
0
0
0
0
2
0
0
1
2
0
2
0
2
0
1
0
1
0
1
0
0
1
0
0
0
0
1
2
0
1
0
0
0
1
0
1
2
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
2
2
0
0
0
0
0
0
1
1
2
2
0
0
1
0
1
0
0
2
0
0
0
0
1
1
0
1
1
0
2
0
0
1
2
0
0
0
0
0
1
0
0
0
2
0
1
1
0
1
1
1
0
0
0
0
2
1
0
2
1
0
0
0
0
2
2
2
0
1
1
0
0
0
1
0
0
0
0
0
0
0
2
1
0
2
1
0
0
1
1
2
0
0
2
0
1
0
2
0
1
0
0
0
0
0
0
1
0
0
0
2
0
1
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
1
0
1
2
2
2
0
0
1
1
0
0
1
1
1
1
1
2
2
2
1
0
0
0
0
1
1
1
0
0
2
1
1
1
0
0
2
2
2
5
2
1
0
1
0
1
2
0
0
4
0
2
3
1
2
0
0
0
1
1
1
1
2
0
1
0
2
1
0
0
1
1
1
2
0
1
0
0
2
2
0
2
0
1
1
1
0
0
2
0
1
0
2
0
0
1
0
1
2
0
1
0
2
0
1
1
1
0
0
0
0
0
2
0
0
1
2
0
0
0
0
1
2
0
1
1
0
0
2
1
4
2
0
0
1
0
0
1
2
0
0
0
0
2
2
0
2
1
3
1
2
1
1
1
1
2
0
1
0
0
2
2
0
2
2
0
1
1
0
1
1
1
2
0
0
0
0
1
2
0
0
1
3
0
1
2
1
0
0
3
1
0
0
0
2
0
3
1
0
1
1
2
0
2
2
1
2
0
0
1
1
2
3
0
0
1
0
0
0
1
0
2
0
1
1
2
0
1
2
0
0
1
0
1
0
2
1
1
2
0
1
1
1
0
0
1
0
2
0
1
1
1
0
0
2
0
0
0
2
2
1
1
2
1
0
2
1
1
2
0
0
0
0
1
0
2
0
0
1
1
1
1
1
0
2
0
1
0
2
0
0
0
2
0
0
2
1
3
1
0
0
0
2
0
0
1
1
1
1
1
0
0
0
1
0
2
1
1
2
0
1
1
0
2
1
0
0
1
1
0
0
1
1
1
0
2
0
1
0
0
1
1
0
0
1
0
1
2
0
1
0
1
1
2
1
1
0
1
0
0
0
1
0
0
1
0
0
1
2
2
0
2
0
2
1
0
0
0
2
1
2
1
0
0
2
1
1
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
1
1
1
2
0
0
0
0
2
0
1
0
0
1
2
1
1
0
1
2
0
1
0
1
0
2
0
1
2
4
0
0
0
0
2
0
1
2
1
1
0
1
2
0
1
1
1
2
2
0
0
1
1
1
0
1
0
1
0
0
0
2
1
3
0
1
0
0
2
2
0
1
2
0
2
2
2
2
1
1
2
0
1
2
2
0
0
1
3
1
1
1
0
1
1
1
0
1
2
2
2
2
0
0
1
0
0
0
1
1
0
2
0
2
0
0
0
0
1
2
0
0
1
1
1
0
2
1
1
0
0
1
1
0
2
0
0
1
1
0
1
0
2
1
0
0
0
0
1
3
0
1
0
0
0
0
1
0
0
0
1
0
0
2
2
2
0
1
2
0
0
0
1
1
0
0
2
1
0
0
0
2
0
1
0
0
1
1
0
1
0
2
1
0
1
0
2
0
1
0
3
0
0
0
2
0
2
0
1
2
0
0
1
0
0
0
2
2
1
1
2
2
0
1
1
2
0
0
0
0
0
2
0
0
1
1
2
1
1
0
2
0
0
2
0
1
0
1
2
0
1
0
1
1
0
0
0
2
0
2
0
0
1
0
0
2
2
0
1
0
1
0
2
0
2
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
2
0
1
0
0
0
2
2
2
1
2
0
0
0
0
2
0
0
0
1
0
0
2
0
2
1
1
1
2
0
1
0
2
1
1
1
2
2
0
0
0
1
0
0
2
2
0
0
1
1
0
1
0
2
2
1
4
1
1
1
0
0
2
1
0
0
2
1
0
2
1
1
1
0
0
1
1
0
1
0
0
2
0
0
1
2
0
1
2
2
1
0
0
3
0
0
0
1
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
1
2
1
1
1
2
0
0
1
0
0
1
0
1
0
1
1
0
0
3
0
0
0
1
1
1
1
0
1
0
2
1
1
1
0
0
1
0
1
2
1
0
1
1
0
1
2
0
1
1
0
2
0
1
2
2
0
0
0
0
0
2
1
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
1
2
1
0
1
2
0
2
0
0
1
2
1
2
0
2
2
0
1
0
0
1
0
1
0
1
0
2
0
2
0
2
2
2
0
0
1
0
0
0
2
1
1
0
0
3
0
3
0
1
1
0
2
0
0
0
0
2
0
1
0
0
1
0
0
0
2
0
3
1
2
0
2
0
1
1
2
2
0
0
0
2
2
1
2
2
1
0
1
1
1
3
0
1
1
1
1
1
0
2
0
2
2
0
1
1
1
1
0
1
1
2
1
1
0
3
1
0
0
1
1
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
2
2
1
1
0
2
0
2
1
0
1
0
0
1
2
0
2
2
2
0
1
0
1
0
1
0
2
0
0
2
0
0
1
2
0
0
0
0
0
0
2
0
0
2
0
0
2
2
2
0
0
1
3
0
2
0
2
2
1
0
1
0
0
1
2
1
0
2
0
0
0
0
1
0
1
1
0
0
0
1
0
2
1
0
2
1
0
0
1
0
2
1
0
0
0
1
0
0
0
0
0
0
1
2
2
0
2
1
2
1
1
2
0
0
2
1
0
1
0
2
1
0
0
0
0
2
0
2
0
1
1
0
2
1
1
1
0
2
1
0
0
1
0
0
1
2
1
1
0
0
1
2
2
1
1
1
0
1
3
0
0
1
0
0
0
0
0
0
2
1
1
0
2
0
0
0
0
0
2
0
0
1
0
1
0
1
1
0
0
2
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
2
0
0
2
0
0
1
0
1
0
0
0
0
0
2
2
0
2
2
0
0
2
2
0
1
1
2
1
2
0
0
0
1
0
1
1
0
1
0
2
0
1
0
1
0
0
2
2
1
0
0
1
2
2
0
2
0
0
0
1
1
2
2
1
2
0
0
1
2
1
1
1
0
1
1
0
1
2
0
1
0
1
0
2
0
0
1
1
0
0
2
1
2
0
1
1
2
0
0
0
0
0
1
2
1
0
2
0
0
2
2
1
0
1
2
0
1
0
1
2
0
1
0
0
1
2
0
0
1
1
0
0
0
0
1
2
1
1
1
0
1
0
1
1
0
1
0
2
2
1
0
0
1
0
1
1
0
2
0
0
1
0
0
1
1
0
0
0
0
1
1
0
0
0
0
1
0
2
0
1
2
1
1
0
3
0
0
1
0
1
1
0
0
1
0
1
0
0
1
0
0
2
0
1
0
2
0
0
0
0
0
0
1
1
1
0
1
1
2
1
0
1
0
1
0
0
2
2
2
0
3
1
0
0
0
1
0
0
0
0
1
0
0
9
0
0
2
1
0
0
1
1
0
0
1
0
3
0
1
0
0
0
1
1
1
0
0
0
1
0
0
2
2
1
0
0
0
1
2
0
0
2
2
0
1
0
2
1
2
5
1
0
0
0
0
1
2
0
4
1
1
0
2
1
2
2
0
1
2
2
2
0
1
1
0
1
1
0
0
3
1
0
0
0
0
2
2
0
0
1
0
0
1
1
2
1
0
0
0
0
1
0
0
0
0
2
3
2
0
0
1
0
0
1
0
1
1
0
2
1
0
2
3
0
2
0
1
1
1
2
0
0
1
2
0
1
0
0
1
2
3
0
0
2
0
0
2
0
2
0
1
0
0
0
0
0
2
0
1
0
1
0
0
0
1
1
1
0
2
2
2
0
2
1
0
2
2
1
1
0
0
0
2
1
0
0
3
0
2
1
1
2
2
2
0
0
4
0
2
1
1
1
0
2
1
0
2
0
0
0
2
2
1
1
1
2
2
2
1
1
0
1
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
2
1
0
0
1
0
2
0
0
0
0
2
0
1
1
1
0
0
1
1
0
0
1
0
2
2
1
1
0
1
2
0
1
0
2
0
3
1
0
0
1
3
0
1
1
1
0
2
0
0
1
1
0
5
0
1
0
1
2
2
0
1
0
2
0
2
0
1
2
1
2
1
2
2
2
2
1
1
1
0
0
1
0
1
2
0
2
0
0
0
0
0
2
0
1
2
2
0
2
0
2
0
2
0
0
0
0
2
1
3
0
1
1
0
1
2
0
2
0
1
1
0
1
2
0
2
1
0
2
0
1
1
1
0
0
0
0
1
1
1
0
2
0
0
1
2
1
2
1
0
1
0
0
0
1
0
0
0
2
0
1
0
0
1
0
2
1
2
0
2
0
1
2
1
2
0
2
0
0
0
0
2
1
3
0
0
0
1
0
1
0
0
1
0
1
1
1
1
1
2
0
0
0
1
1
0
2
0
0
1
0
1
2
1
1
0
0
1
0
2
0
1
0
1
0
0
0
0
0
2
1
1
1
0
1
1
1
0
1
1
0
0
0
0
2
0
0
0
1
0
1
2
2
0
0
0
1
1
2
2
0
0
1
0
0
0
0
1
4
1
0
1
1
2
1
2
0
1
0
0
0
3
0
0
2
2
0
0
0
0
2
0
2
2
1
0
1
0
2
1
1
1
0
0
3
0
0
2
1
0
2
1
1
0
2
0
2
3
0
0
0
0
0
1
0
1
0
2
1
0
0
0
1
2
0
1
0
0
0
2
1
0
1
1
0
1
0
0
0
2
0
0
1
0
1
2
0
0
0
0
0
0
2
2
0
2
0
1
2
2
0
2
1
0
2
1
1
1
2
1
0
0
0
0
1
0
2
0
0
10
0
1
0
0
0
0
2
1
2
0
1
2
0
2
1
1
0
0
0
1
0
3
1
0
0
0
0
2
0
0
2
0
2
0
1
0
0
0
0
0
0
2
0
2
2
0
2
0
0
1
0
2
0
0
0
2
0
2
1
1
0
1
0
1
1
1
1
0
1
2
0
0
0
0
1
1
2
1
0
0
0
2
0
1
1
1
0
0
3
2
0
0
0
0
0
0
1
1
0
0
2
0
0
0
1
1
1
0
0
1
0
0
0
2
1
2
1
1
0
0
0
1
2
5
3
3
0
0
1
0
1
1
1
0
0
2
2
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
1
2
1
2
0
1
0
0
1
0
0
2
0
0
1
1
2
1
0
0
1
0
0
0
0
0
0
0
1
2
2
2
1
2
1
0
2
1
0
1
1
1
0
1
1
1
2
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
3
0
1
0
1
0
2
0
1
0
0
0
0
1
0
1
0
0
2
2
0
0
0
1
2
1
2
1
1
1
1
0
0
0
1
2
2
0
1
0
0
0
1
1
1
0
0
0
0
1
2
0
2
2
1
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
1
0
2
3
1
0
1
0
0
0
1
2
0
1
2
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
1
0
1
0
0
0
0
1
1
0
2
0
10
1
0
1
0
0
1
0
1
0
1
1
1
0
2
0
2
0
0
2
1
1
2
0
2
0
0
0
0
0
1
1
1
0
0
0
0
0
1
1
0
1
2
0
0
0
0
0
0
0
1
0
0
2
0
2
0
1
0
2
2
0
0
1
1
0
0
0
2
1
1
2
1
2
2
0
0
2
2
2
0
2
2
0
1
2
0
0
1
0
0
0
1
0
0
2
1
1
2
2
0
0
1
0
1
0
0
2
1
2
0
0
3
0
2
0
2
1
0
0
2
1
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
1
1
0
0
0
0
3
2
0
0
0
1
0
0
0
3
2
2
2
0
0
2
0
0
0
0
1
2
0
0
1
1
2
1
0
0
0
0
0
3
2
0
2
0
0
0
1
0
0
1
1
2
2
0
2
0
0
0
1
1
2
0
1
2
0
0
1
0
3
0
2
0
0
0
0
0
0
0
1
2
2
0
2
0
0
1
0
1
1
0
1
0
0
0
0
0
2
0
1
1
1
1
0
2
1
0
6
0
2
1
2
2
1
0
2
2
0
1
1
2
0
1
2
2
0
4
1
2
1
2
1
1
1
1
2
0
1
2
0
1
0
0
2
2
1
1
0
1
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
1
0
1
0
0
2
0
2
0
1
0
1
1
1
0
1
0
2
0
0
0
1
0
1
1
1
0
3
2
0
1
1
1
1
2
2
0
1
2
1
0
0
1
0
0
1
1
1
1
0
0
1
0
1
1
1
1
1
1
0
2
1
1
2
0
3
0
0
0
0
1
1
0
1
2
2
2
0
0
0
1
0
0
0
1
3
0
2
1
0
0
1
0
0
0
1
2
1
2
0
0
1
1
1
2
1
2
0
0
0
0
1
0
1
0
0
0
1
2
0
0
2
1
1
1
2
1
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
2
1
2
0
1
1
2
1
0
0
1
0
0
1
1
0
1
0
0
0
0
2
2
1
2
0
0
0
1
0
0
1
2
2
0
1
0
1
0
1
0
1
2
2
1
1
2
0
0
0
1
1
0
0
1
0
0
1
2
0
2
1
1
2
2
2
1
0
0
2
2
1
0
0
1
0
1
1
2
2
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
1
0
2
0
0
0
2
0
2
0
0
2
1
0
1
0
2
1
0
0
1
2
0
1
1
0
0
1
0
2
0
0
0
0
1
2
1
0
1
0
0
1
2
1
1
2
0
1
0
0
0
2
2
2
2
0
1
0
2
1
1
2
1
1
0
1
0
1
0
1
0
1
1
1
0
0
0
3
0
1
0
1
1
0
1
0
0
0
1
0
0
0
0
2
0
2
0
1
1
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
1
1
0
1
1
0
0
0
0
0
0
0
2
3
0
0
2
0
2
0
1
2
0
0
0
0
0
0
2
1
0
1
1
0
2
2
2
0
0
0
2
1
0
2
0
0
1
0
0
2
2
0
0
0
0
0
1
0
0
0
1
0
1
1
1
2
1
2
1
0
0
2
1
0
0
0
2
1
0
0
1
0
1
0
2
0
1
0
0
0
0
1
0
0
1
1
0
1
3
1
1
0
1
1
1
0
2
1
1
1
1
0
2
2
0
1
1
0
0
0
1
2
1
0
0
0
2
1
0
0
2
0
2
0
0
2
0
0
0
0
1
1
0
0
1
0
0
2
1
1
0
1
1
1
2
2
1
1
1
1
0
0
1
1
1
2
0
0
0
0
4
1
0
0
1
0
0
0
0
2
0
2
0
0
6
0
1
2
0
0
0
2
0
0
0
0
0
1
2
1
0
1
0
0
0
0
0
0
0
0
0
0
2
2
6
0
1
3
1
2
2
0
1
0
1
0
1
2
0
1
2
0
1
2
1
0
0
2
1
0
0
1
0
1
0
1
1
0
0
2
0
0
0
2
0
0
1
0
2
0
2
1
0
0
3
0
1
1
2
1
1
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
1
0
2
0
0
0
0
2
0
0
0
1
0
1
2
1
0
3
2
0
0
0
1
2
0
1
2
0
0
0
0
0
1
0
2
0
1
1
0
1
0
1
0
0
0
0
0
2
0
1
0
0
0
0
1
0
1
0
1
1
2
1
0
1
2
0
1
1
0
0
2
0
0
0
0
2
0
1
0
0
0
1
3
0
2
0
0
0
0
1
1
1
1
1
0
0
0
0
1
1
0
1
2
0
0
2
0
0
1
0
1
0
0
0
2
2
0
1
1
1
1
2
2
1
0
0
1
2
0
0
0
0
1
0
2
0
2
1
0
0
2
1
1
2
2
0
0
0
0
0
1
0
0
1
0
2
3
2
1
2
2
2
0
1
1
1
2
0
0
0
2
1
2
2
0
1
0
1
0
0
0
0
0
0
1
0
0
1
1
1
1
0
1
1
0
1
1
2
0
3
1
0
1
0
0
2
1
1
2
0
0
1
2
0
0
1
0
1
1
2
0
2
0
0
0
1
0
0
1
0
1
0
2
0
1
1
0
0
2
0
0
0
1
1
2
0
1
0
1
5
0
1
1
0
0
1
1
0
0
2
0
1
1
2
0
0
2
0
2
2
1
2
0
2
0
1
2
2
2
1
0
1
1
0
1
1
0
2
2
1
1
1
0
2
2
0
2
1
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
1
0
1
2
1
0
0
0
0
1
0
2
1
1
1
0
2
1
0
2
2
2
0
2
1
2
1
0
1
0
2
0
1
0
1
0
0
0
0
1
0
2
0
2
1
0
0
0
1
1
2
0
1
0
1
0
1
0
2
1
0
0
0
0
0
3
2
0
1
2
0
2
2
1
2
0
0
0
2
0
1
2
0
1
2
0
1
1
0
0
2
0
1
1
0
0
0
1
1
1
0
1
2
0
1
0
1
0
1
0
2
1
0
2
1
1
0
0
1
1
4
1
1
1
0
1
1
0
1
1
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
1
2
0
0
2
0
0
0
1
2
0
0
1
0
2
2
2
2
0
1
0
2
2
2
0
2
0
1
0
0
1
1
3
0
2
1
0
1
1
0
2
0
0
0
1
0
2
5
0
1
2
2
2
0
0
0
1
0
0
1
0
0
1
0
1
0
1
1
1
2
0
2
0
2
2
0
1
0
1
1
1
0
1
2
2
2
0
1
0
0
1
1
0
0
0
1
0
0
1
1
0
0
0
3
0
0
2
0
2
0
0
0
2
0
0
0
3
2
2
0
1
0
0
0
0
2
0
0
1
1
0
1
4
0
1
0
0
1
1
0
0
1
1
0
2
0
1
0
0
2
1
0
0
1
1
1
0
0
0
2
0
0
0
0
0
0
1
0
0
2
1
0
0
1
2
1
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
3
1
0
0
0
0
0
1
2
0
0
1
2
0
0
2
0
0
0
0
1
1
0
1
2
0
0
0
0
1
0
1
0
0
0
0
2
1
1
1
0
0
0
0
1
1
2
2
0
0
1
2
2
1
1
1
0
1
1
2
0
1
2
0
0
1
0
0
1
2
0
1
0
0
0
0
0
0
1
2
2
0
1
0
0
1
2
0
1
2
0
0
3
3
2
0
0
0
2
1
1
2
2
0
2
0
0
0
2
0
0
0
1
0
1
0
0
0
0
1
0
2
1
0
2
0
2
0
0
0
2
0
1
0
0
1
0
0
1
1
3
0
1
0
1
0
0
1
1
2
0
0
1
0
2
0
2
0
0
1
0
1
2
0
0
0
0
1
0
2
1
0
0
1
2
1
0
2
0
2
1
0
0
2
1
0
1
2
2
1
1
0
1
0
1
0
0
0
0
2
2
0
1
0
2
0
0
1
0
2
0
0
2
0
1
1
0
0
0
0
0
1
0
2
0
0
0
1
0
1
2
0
2
0
0
2
0
1
1
0
2
1
1
0
0
0
2
1
0
2
2
2
1
0
0
1
0
1
0
1
0
1
0
1
0
0
1
3
1
2
2
1
0
0
0
1
1
3
1
2
2
1
0
0
2
1
1
1
1
1
0
0
0
0
0
1
1
2
1
1
2
0
1
1
0
0
1
1
2
0
0
1
1
0
0
1
0
1
0
0
0
5
0
0
2
0
0
1
1
0
3
1
1
1
0
1
2
1
1
0
0
0
0
1
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
2
0
0
0
0
0
3
2
0
1
0
1
0
0
2
0
0
1
0
1
0
2
0
1
0
1
2
0
0
1
0
0
1
2
0
2
0
0
1
2
1
0
0
0
2
0
1
0
2
0
2
0
1
1
2
2
0
1
0
0
0
0
1
0
0
1
1
2
1
1
0
0
1
0
2
0
1
2
0
1
2
1
1
1
2
0
0
2
1
1
0
1
1
1
0
0
0
0
0
1
2
3
1
2
0
2
1
0
1
0
2
0
0
0
0
2
1
0
1
1
2
2
0
1
0
0
2
1
0
1
2
0
0
2
0
0
0
0
1
2
0
2
0
0
2
2
0
0
0
0
2
0
0
1
2
2
2
0
1
1
0
0
0
0
0
0
2
1
1
0
0
1
2
0
0
0
0
0
1
0
1
0
2
2
0
0
0
1
2
1
0
1
2
0
1
2
0
0
0
0
0
0
1
0
1
0
0
2
2
1
0
1
0
0
0
1
2
0
0
0
2
0
2
0
2
0
0
2
1
1
2
0
1
1
1
2
0
0
1
0
1
2
0
0
2
0
0
1
0
0
1
0
0
1
1
2
0
0
2
2
1
0
0
0
0
1
0
0
1
2
2
0
0
0
0
2
2
0
1
2
1
1
1
0
1
0
0
2
0
1
2
1
0
0
0
2
1
0
1
2
0
2
0
2
1
0
1
1
2
1
0
1
1
0
0
0
1
0
0
1
1
1
0
0
1
0
0
0
0
0
1
1
0
1
2
2
2
0
1
1
0
0
1
2
0
2
0
0
1
6
0
2
1
1
0
1
1
0
1
0
0
0
2
3
0
0
2
0
1
2
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
3
0
1
1
0
0
0
2
0
3
1
2
1
0
0
1
1
0
2
0
0
0
1
0
2
1
0
0
1
0
2
2
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
3
2
0
0
0
4
0
1
0
0
1
2
1
1
1
0
0
2
1
0
0
1
2
0
1
0
1
2
0
0
0
0
0
1
1
0
1
0
0
1
1
0
0
3
0
0
0
2
1
0
1
0
1
0
0
0
1
0
1
1
1
0
2
0
0
1
2
1
0
0
0
0
1
0
1
2
1
2
0
4
1
1
2
0
0
0
0
0
2
1
2
1
0
0
0
0
2
2
0
2
1
1
2
1
1
0
0
0
0
0
1
1
0
1
0
0
1
0
1
2
1
3
1
0
0
0
0
0
1
1
2
2
2
0
1
1
0
0
0
0
0
1
1
0
2
1
0
0
0
0
0
0
1
1
0
0
0
1
2
0
1
2
0
0
2
1
1
0
1
0
0
1
1
2
1
1
0
1
2
0
0
0
2
0
0
0
0
0
2
0
1
0
1
0
1
0
1
2
1
2
0
0
0
1
0
2
3
1
0
0
1
2
1
2
2
1
2
2
1
0
1
2
0
0
0
0
0
3
0
0
1
2
1
0
0
3
1
0
0
1
0
2
0
1
3
2
2
1
0
1
1
2
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
4
3
1
1
1
1
0
0
0
2
0
0
2
0
1
2
0
2
2
2
0
0
1
0
0
1
0
0
0
1
1
0
1
1
0
3
0
0
0
3
2
1
0
0
1
2
0
2
2
0
1
0
0
1
2
0
1
2
1
2
2
0
1
0
1
0
2
0
0
1
0
2
0
3
0
1
2
2
2
1
2
0
0
1
1
2
1
0
2
0
2
2
0
0
0
1
2
0
1
1
2
2
0
1
1
0
1
0
0
0
1
1
2
0
1
0
0
1
1
1
2
2
1
0
1
0
2
0
1
1
0
1
0
0
2
2
0
0
0
1
0
3
3
1
0
0
0
1
1
0
0
0
2
0
0
1
0
2
1
1
1
0
2
0
1
0
0
1
0
2
1
3
0
0
2
0
2
0
1
1
1
0
1
1
1
0
0
1
1
2
2
2
0
1
0
0
0
1
0
0
2
0
0
1
1
1
2
0
2
0
1
1
1
0
0
0
1
0
1
0
1
0
2
2
1
0
1
2
1
0
0
2
0
0
0
1
0
1
0
0
0
0
1
0
1
0
1
0
2
0
0
1
0
1
2
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
2
0
1
1
1
0
0
2
0
2
0
0
0
2
2
0
1
1
1
0
0
2
0
2
0
2
0
1
0
0
2
1
2
0
0
1
0
0
0
2
2
0
0
1
0
0
0
1
0
2
0
0
2
1
0
1
1
0
0
1
1
0
0
0
1
0
1
1
1
2
0
2
0
2
1
0
2
1
1
1
0
2
1
0
0
0
2
0
1
0
2
0
2
1
0
1
0
1
0
1
1
2
0
0
2
2
0
2
1
1
0
1
0
4
0
0
1
2
0
1
1
1
1
1
2
2
2
0
0
0
2
1
0
2
2
1
0
0
3
1
0
2
0
0
0
0
0
0
1
2
0
1
2
2
1
0
1
0
0
0
0
0
2
1
1
0
0
0
2
0
1
1
0
0
2
1
0
1
0
1
1
0
1
0
1
1
2
1
0
1
0
0
1
0
1
1
1
0
1
0
0
1
0
0
0
0
1
1
1
1
0
1
0
0
0
0
1
1
1
1
0
2
0
0
2
1
0
0
1
0
0
0
0
2
1
0
1
0
0
0
2
0
0
1
1
0
0
1
1
0
0
1
0
2
0
0
2
1
0
0
0
1
1
2
1
0
1
2
2
1
1
1
1
0
2
0
1
1
3
0
0
0
1
2
2
0
2
1
0
0
2
0
2
0
1
0
0
2
0
1
3
0
2
0
1
1
0
0
2
0
0
0
1
0
2
1
1
0
0
0
0
0
0
1
1
1
0
0
1
1
1
0
1
0
0
0
0
2
1
1
2
1
2
0
0
0
1
0
0
1
2
0
0
2
1
0
0
1
0
2
1
0
1
1
2
1
0
0
3
0
0
1
1
1
0
0
0
0
0
1
1
1
1
2
0
2
1
0
0
0
2
1
0
2
1
0
2
2
0
1
0
1
2
0
1
0
2
0
0
0
0
0
2
1
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
2
0
1
1
0
1
0
0
1
1
4
1
0
0
0
0
0
1
0
0
2
1
1
2
2
1
1
0
1
2
0
1
2
0
1
2
2
1
2
0
0
0
1
0
2
1
1
0
2
1
0
0
2
0
2
0
0
0
2
1
0
1
2
0
1
0
0
2
0
0
2
0
0
1
0
1
1
0
0
2
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
1
0
0
1
1
0
1
0
2
1
2
0
1
1
1
2
1
0
0
0
1
0
1
0
1
1
2
0
0
1
2
1
2
0
2
1
0
0
1
0
0
0
0
2
0
2
0
1
0
2
0
0
0
0
1
0
2
1
0
1
1
1
0
1
0
0
0
2
0
1
0
0
2
3
0
0
1
0
0
2
1
0
2
0
0
0
1
0
2
1
0
0
1
2
1
1
0
0
0
2
0
1
2
0
0
1
0
1
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
1
0
1
2
0
1
0
1
1
1
1
0
0
0
0
0
0
2
0
0
1
1
1
1
0
1
1
0
1
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
1
0
0
1
2
0
2
0
2
2
1
0
0
0
0
1
1
0
2
0
0
2
0
0
0
0
1
1
0
0
2
1
1
0
0
2
0
1
0
0
2
0
2
2
1
0
2
1
1
0
0
0
1
2
2
1
1
2
1
0
1
1
2
2
2
0
2
1
0
0
0
1
1
0
2
0
1
0
1
2
1
2
0
1
2
0
0
2
0
1
1
2
0
0
0
2
0
1
1
0
0
2
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
1
0
1
0
1
0
0
0
1
2
1
0
1
0
1
1
1
0
0
0
1
0
3
2
0
0
1
2
0
2
0
1
1
1
1
1
0
1
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
2
1
0
0
2
2
1
1
2
0
0
0
0
1
1
2
1
2
2
2
0
1
2
1
1
0
0
1
2
1
0
0
2
0
0
2
2
0
0
0
0
0
1
2
1
0
1
2
3
0
0
2
0
1
0
1
0
0
1
1
0
0
1
1
2
0
1
1
0
2
0
0
2
0
0
2
0
2
2
2
0
0
1
2
0
0
0
0
0
0
1
3
0
0
0
1
0
2
0
1
0
0
0
2
2
1
1
0
0
2
1
0
0
0
1
0
0
0
2
0
2
0
0
2
0
1
1
2
1
0
1
2
0
1
0
0
1
1
0
0
0
1
0
2
0
0
1
2
2
2
1
2
0
1
0
0
0
0
2
0
0
0
0
0
2
2
1
0
1
1
0
0
0
2
1
0
0
1
2
0
0
1
0
0
0
0
1
0
0
0
2
0
0
2
1
2
0
2
0
0
1
0
0
1
0
1
1
0
2
0
0
0
0
0
0
2
2
2
1
0
0
0
1
2
2
0
1
1
1
0
2
2
0
0
1
2
2
0
0
2
0
2
1
1
0
1
1
2
3
0
0
0
0
1
0
0
0
2
7
2
0
0
0
1
0
2
1
1
2
1
1
0
1
0
0
1
0
0
0
0
0
1
3
0
1
0
2
1
2
2
0
2
2
2
2
0
2
0
1
1
0
1
0
0
2
0
2
0
0
0
1
0
2
0
2
0
0
1
0
2
2
0
2
2
0
0
1
0
1
1
0
1
0
1
1
1
0
0
0
0
2
2
1
1
0
1
1
0
0
1
0
1
0
0
0
1
2
0
0
0
1
0
1
0
0
2
1
0
0
0
0
0
0
1
2
2
1
2
0
0
0
0
1
2
2
2
0
0
0
1
0
1
0
0
2
0
1
1
2
1
0
2
2
0
1
1
1
1
0
0
0
1
0
0
1
0
2
0
1
0
1
0
0
0
0
2
2
2
2
0
1
0
1
1
0
0
2
0
0
1
0
0
0
1
1
1
2
0
0
2
0
2
2
2
0
1
0
0
1
2
0
8
2
2
1
1
1
0
1
1
2
0
0
0
0
2
0
1
1
1
1
0
1
0
0
1
1
2
1
2
0
0
0
1
0
2
0
0
1
2
0
1
1
0
0
2
2
0
0
0
1
2
0
2
3
2
0
1
0
0
1
0
0
0
2
0
0
1
1
2
0
1
0
0
0
0
0
2
0
0
1
2
0
0
1
0
1
1
1
0
0
0
1
0
1
1
1
1
0
1
2
0
2
0
0
1
1
2
0
0
1
1
1
0
3
0
1
0
1
1
2
1
0
1
2
1
1
2
0
0
0
0
0
0
0
1
0
1
0
1
2
1
2
0
0
0
1
0
1
3
0
0
0
1
2
0
1
0
0
1
1
1
1
0
0
1
2
2
1
0
1
1
0
1
1
2
2
2
0
0
2
0
2
0
2
1
0
2
2
0
0
1
0
0
0
0
0
0
1
2
2
0
1
0
0
1
1
2
1
0
0
0
2
0
0
0
1
0
1
1
0
2
0
3
2
0
0
1
0
0
0
0
1
2
0
1
2
0
1
2
1
2
2
1
0
2
0
0
1
2
0
2
0
0
2
1
1
1
0
2
2
0
0
0
1
2
1
0
2
0
1
0
0
3
2
1
0
2
1
0
1
2
0
0
0
0
0
0
0
0
0
2
1
0
1
0
4
1
0
0
1
1
0
0
1
0
2
0
1
0
1
1
1
0
0
0
0
0
1
0
0
1
3
1
0
0
1
1
0
1
0
0
2
0
1
1
2
2
0
0
0
0
1
0
0
0
1
0
1
0
1
5
0
1
0
1
0
1
2
1
0
1
0
1
0
0
2
0
1
1
1
0
0
1
1
2
2
0
2
0
1
1
0
1
1
7
0
0
0
0
2
2
0
1
0
2
1
0
3
1
0
2
0
0
0
1
1
2
0
1
0
0
2
1
1
0
2
0
2
1
0
1
0
0
0
1
0
2
0
1
0
2
1
1
2
1
1
0
2
1
1
1
0
0
1
0
2
0
0
2
0
1
1
0
1
1
2
3
0
1
0
1
0
0
1
0
0
0
0
2
0
1
1
1
0
1
2
2
2
1
2
0
0
0
0
0
0
0
1
0
1
0
0
1
0
2
0
2
2
1
2
1
0
1
1
1
0
0
1
1
0
2
0
0
2
0
1
0
2
0
0
0
0
0
0
1
1
0
1
0
1
1
1
1
0
2
0
0
0
1
1
1
1
0
2
1
0
0
0
1
2
1
0
0
0
1
1
1
1
1
1
0
1
1
2
1
1
1
0
2
0
1
1
0
0
0
0
1
0
2
1
0
0
0
1
2
2
0
0
0
0
1
1
0
1
1
1
1
0
2
0
2
0
1
0
0
2
0
0
1
1
0
0
0
0
1
0
0
1
2
1
0
0
2
0
0
0
2
0
0
0
0
0
0
1
1
1
2
2
1
0
0
1
1
1
0
2
2
0
1
2
1
0
0
2
0
1
2
0
2
0
1
1
0
0
0
1
0
1
0
1
1
1
0
0
0
2
0
1
0
1
1
2
0
0
0
2
0
2
1
1
0
1
0
1
2
0
1
0
0
0
1
1
3
0
1
2
1
0
2
0
2
0
0
0
1
2
2
3
1
2
0
0
1
2
1
0
0
1
0
1
2
0
0
0
0
0
1
0
2
2
2
0
1
1
2
0
2
1
1
2
0
1
0
0
1
1
1
2
2
2
2
0
1
0
0
0
1
1
0
2
1
0
0
1
0
0
0
0
2
1
0
0
3
2
1
0
0
0
2
0
2
0
1
0
0
0
1
0
0
2
2
0
0
2
1
1
0
1
1
0
0
0
2
1
0
2
1
0
1
1
0
1
3
0
1
0
0
0
0
0
0
0
1
1
1
1
0
1
1
0
0
0
2
2
1
0
3
0
0
0
5
2
0
0
0
2
1
2
0
0
0
0
1
0
1
1
2
0
1
0
1
1
1
3
0
0
2
1
0
2
0
0
0
0
1
0
0
0
1
0
1
1
1
0
2
1
1
2
0
2
1
0
1
0
0
1
2
1
0
1
1
1
0
2
2
0
1
0
2
0
1
0
0
0
0
1
1
2
0
0
0
0
0
0
0
3
0
0
2
1
0
2
1
1
0
0
0
0
2
2
0
1
0
0
1
0
0
0
1
1
0
1
0
1
1
2
1
1
1
0
0
0
0
1
1
1
0
2
0
1
1
0
0
2
0
0
0
0
1
0
1
0
0
2
2
0
1
0
0
1
0
1
1
1
1
1
1
0
0
1
0
2
2
0
1
1
1
1
0
0
4
1
1
0
2
1
1
0
0
0
0
0
0
0
0
2
2
2
0
1
1
1
1
1
0
0
1
1
1
1
1
0
1
2
2
0
1
2
0
2
2
0
0
0
3
2
0
2
0
0
1
2
0
2
0
0
0
2
2
1
0
2
1
0
1
0
0
2
0
2
0
1
0
0
0
2
0
0
1
1
0
1
2
0
1
1
0
0
1
2
0
0
0
0
1
1
1
1
1
1
1
0
0
2
0
0
0
1
1
1
0
1
0
0
1
1
1
1
0
0
0
0
2
1
0
1
0
0
0
2
2
2
1
0
2
1
1
0
0
0
2
1
1
2
0
2
0
2
0
1
1
0
2
1
1
0
1
1
1
0
0
1
0
1
1
0
0
2
1
0
1
0
1
2
1
3
0
0
0
0
1
1
1
2
1
1
2
2
2
2
1
0
0
0
2
2
1
2
0
3
0
1
2
0
0
0
2
5
0
0
1
1
0
0
1
1
1
1
1
2
2
2
1
0
1
0
1
1
0
1
1
2
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
1
0
1
2
1
1
0
0
1
2
0
1
0
0
1
1
1
0
0
0
0
1
2
2
1
0
0
1
0
0
2
0
0
3
0
0
1
2
0
2
2
1
1
0
0
1
1
1
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
2
1
1
0
1
2
0
1
2
2
0
1
2
1
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
1
1
1
0
0
1
0
0
1
1
1
0
3
1
0
1
0
0
2
1
0
1
0
1
0
0
0
1
1
0
0
0
0
0
2
0
1
1
3
1
0
0
0
1
0
3
0
0
0
1
1
0
0
0
1
0
1
0
1
0
2
0
0
2
0
1
2
0
0
0
0
2
1
0
1
1
0
0
0
1
0
1
0
0
2
0
0
1
0
2
0
1
0
1
0
0
2
0
1
0
1
0
1
0
2
2
0
0
1
2
0
1
0
0
2
0
1
1
0
1
1
0
0
2
0
0
1
0
0
0
2
1
0
1
0
0
1
0
0
0
1
0
0
0
1
1
2
2
0
2
0
2
0
2
0
0
0
0
0
0
2
0
0
2
1
1
0
0
1
0
1
0
2
2
0
2
1
1
0
0
0
0
1
0
0
4
2
0
0
1
1
1
2
0
0
0
2
2
0
2
0
2
0
0
1
0
1
0
0
0
2
0
1
0
2
1
1
0
0
0
0
1
3
0
1
1
0
1
2
0
2
0
1
1
0
1
0
0
1
1
0
2
0
2
0
0
2
0
0
0
0
0
0
1
1
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
1
0
1
1
0
1
1
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
2
2
1
1
0
0
1
0
2
0
1
1
1
0
0
1
2
0
1
0
2
0
0
3
1
0
1
0
2
0
1
1
3
0
2
2
1
0
0
0
0
1
0
0
1
1
1
1
1
0
1
1
0
1
0
0
1
2
0
1
1
0
2
0
0
1
1
2
0
1
0
2
1
2
0
0
0
0
1
2
0
0
2
0
2
0
0
0
0
0
1
0
2
1
1
1
2
0
0
0
1
1
2
0
3
0
1
1
0
0
2
0
3
0
1
0
1
0
1
0
0
1
0
0
0
1
2
2
2
0
1
1
1
0
0
1
0
1
1
0
1
0
0
2
1
0
0
1
0
0
0
0
1
0
1
0
2
0
1
0
1
1
0
0
0
0
1
0
0
0
2
0
1
0
0
0
1
1
1
0
2
2
1
1
0
0
2
0
1
1
0
1
1
2
0
2
2
0
1
0
2
1
0
2
2
2
1
1
0
1
0
1
0
1
0
2
0
2
1
0
2
1
0
2
1
0
1
0
0
1
1
0
0
0
2
0
0
0
1
0
2
1
2
1
1
1
0
0
1
0
0
1
1
0
0
0
2
0
0
0
0
0
1
1
1
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
2
2
1
3
1
2
0
0
0
2
0
0
0
0
1
0
2
0
1
1
0
0
0
2
0
0
2
0
1
0
2
1
0
0
2
2
1
0
0
0
1
0
1
1
0
0
0
2
1
2
2
2
0
1
0
0
0
1
1
0
1
0
0
0
0
2
0
0
1
0
2
0
0
0
1
0
0
1
0
2
3
2
2
2
1
2
1
0
0
2
0
0
2
0
2
1
0
1
0
1
0
2
2
0
0
0
2
0
0
0
0
0
0
2
1
1
0
1
1
1
1
1
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
1
2
0
2
1
0
0
0
1
1
0
1
0
1
1
0
0
1
2
0
1
1
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
2
1
1
0
0
2
0
0
0
1
0
0
1
0
1
1
1
2
1
0
1
0
0
2
1
1
0
0
1
0
1
0
0
1
2
0
1
1
0
0
1
0
1
0
0
0
2
2
0
1
2
0
0
1
0
0
0
1
0
0
0
0
1
4
0
0
0
0
2
1
0
0
0
2
0
0
2
1
0
1
1
0
0
2
1
1
0
0
1
1
0
1
0
0
0
1
0
2
0
0
2
0
0
0
1
2
1
0
0
1
1
1
0
0
2
3
0
2
0
0
1
0
0
1
0
2
0
2
1
2
0
0
1
1
0
0
0
0
5
0
0
1
0
0
0
1
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
1
1
1
1
2
0
0
2
1
1
0
0
0
1
1
2
0
3
1
1
0
2
0
1
2
0
4
0
0
1
0
2
0
2
0
0
0
0
1
1
2
2
1
0
0
2
0
1
2
1
2
0
0
1
0
0
2
1
0
0
2
2
0
0
1
0
0
2
2
0
0
1
2
1
3
1
1
1
0
1
1
0
0
0
1
1
1
1
2
1
0
0
0
1
0
1
0
2
2
0
0
0
0
0
0
0
0
0
2
2
1
0
1
2
3
1
0
0
1
2
1
0
0
0
0
1
1
2
0
0
2
1
1
2
1
0
2
1
0
0
1
0
0
0
2
1
1
0
0
0
0
0
0
1
1
2
0
1
2
2
1
0
0
0
2
2
1
0
1
1
0
0
0
0
1
2
0
0
1
1
2
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
2
0
2
1
0
2
2
1
1
0
1
1
0
0
0
0
1
1
0
2
1
2
3
0
2
2
0
1
0
2
0
0
0
0
0
0
1
0
0
1
1
0
2
1
0
0
3
0
0
0
0
2
0
1
0
0
0
0
0
1
1
1
1
1
0
0
0
0
1
0
0
0
0
2
1
0
1
1
0
1
1
0
0
0
1
0
0
1
0
0
1
1
1
0
2
1
1
0
1
2
0
2
3
1
2
2
1
1
2
0
1
1
1
2
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
1
1
2
0
1
0
1
0
1
0
1
1
0
1
1
1
2
2
0
1
2
0
2
0
0
1
0
2
0
0
1
0
0
0
1
0
1
0
0
1
1
1
0
2
2
1
3
1
1
0
0
0
0
1
0
1
1
0
0
0
2
0
3
2
0
1
0
0
1
0
0
0
2
1
2
0
2
0
2
0
1
1
1
0
0
1
1
1
1
0
1
1
0
1
0
1
0
1
0
0
2
1
1
0
0
0
2
1
1
1
0
0
0
0
1
0
1
1
0
0
0
1
1
1
1
1
0
4
1
2
0
0
0
0
1
1
2
2
1
2
1
0
1
1
0
1
1
0
2
0
1
0
0
0
0
0
0
0
0
1
1
2
2
1
1
2
2
0
0
0
1
0
1
1
1
0
0
2
2
1
1
0
1
0
0
0
0
1
1
1
0
2
0
1
2
1
0
0
2
0
0
2
0
0
1
2
0
0
0
1
0
0
0
2
0
0
2
0
1
0
1
1
0
1
0
2
1
0
0
2
1
1
0
0
0
0
0
2
1
0
0
0
0
1
0
0
2
0
1
2
0
0
0
0
1
2
0
0
0
2
0
0
1
0
1
2
0
2
0
0
1
0
1
1
0
0
2
0
1
0
0
0
0
2
2
0
1
1
0
0
0
0
0
2
2
1
0
1
1
0
0
0
1
2
1
0
0
0
1
0
1
0
0
1
1
2
1
1
0
1
0
0
0
1
3
0
2
1
1
1
1
0
0
0
0
0
2
2
1
2
2
2
2
0
0
0
0
1
0
0
1
0
0
1
0
1
0
2
0
1
2
0
0
0
1
1
0
0
0
2
2
3
2
2
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
2
2
1
2
0
0
2
0
0
3
1
2
2
2
1
0
0
1
2
0
0
0
1
2
1
0
0
1
2
0
0
0
1
0
0
1
0
2
2
0
2
1
0
1
1
3
1
0
0
0
1
0
1
0
2
0
3
0
1
2
1
1
2
0
2
2
0
0
1
0
1
0
0
0
0
0
0
1
0
2
2
0
0
0
1
1
0
0
0
0
1
2
2
0
0
0
0
2
2
2
1
2
0
0
0
0
1
1
1
0
0
2
0
0
0
1
1
1
0
2
1
1
1
0
1
1
1
1
0
2
0
1
1
2
1
0
1
1
1
2
2
0
2
0
1
1
0
0
0
0
0
0
1
1
3
0
2
0
1
1
0
1
0
2
0
1
0
0
0
1
0
0
1
1
0
0
0
1
1
1
2
0
1
0
0
0
0
1
2
2
1
0
1
1
1
1
0
0
0
2
2
0
0
1
1
1
2
2
1
0
0
1
0
2
0
0
0
0
0
0
1
1
0
2
0
0
1
2
1
1
1
0
2
0
0
1
1
1
0
2
1
1
1
2
1
0
0
2
2
0
0
1
2
1
3
2
0
0
0
2
1
0
0
0
2
2
0
0
0
0
0
2
2
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
1
2
0
1
2
0
0
1
1
1
0
2
0
2
0
1
0
0
1
0
0
1
0
0
0
1
1
1
0
0
0
0
1
0
0
0
1
0
1
0
2
0
0
0
0
0
1
0
1
1
2
0
1
1
0
0
2
1
1
2
0
2
2
0
0
0
1
1
0
0
0
2
0
2
0
0
2
1
1
2
0
1
2
1
1
0
1
0
0
0
1
1
0
0
2
1
0
1
0
1
1
0
0
0
1
0
0
1
1
1
3
0
0
0
0
1
0
0
0
0
0
6
0
2
1
0
0
1
0
0
1
2
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
2
0
1
2
1
1
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
2
2
2
1
0
1
1
1
2
1
0
0
0
1
1
0
2
1
1
0
0
0
0
2
1
0
2
0
1
0
0
0
0
1
1
1
2
1
0
1
0
0
0
0
1
1
0
2
0
0
0
1
2
1
1
0
0
1
0
1
2
1
0
0
2
1
2
1
0
1
0
0
0
0
0
1
1
1
2
0
1
1
0
0
2
0
2
0
1
2
0
1
0
1
0
0
1
0
1
1
1
0
0
0
1
2
1
1
0
0
1
2
0
1
1
0
3
3
1
1
1
0
2
0
0
2
0
1
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
1
0
1
0
1
2
0
0
1
1
0
0
3
1
2
0
2
0
0
2
2
2
0
0
0
0
1
1
0
3
0
0
2
0
1
0
0
2
0
0
0
1
0
0
1
0
0
2
2
2
2
0
0
0
0
0
2
1
0
2
0
0
1
1
1
1
1
1
0
0
0
0
2
2
0
1
0
0
0
0
0
1
2
0
0
0
0
1
0
0
2
2
1
2
2
1
1
1
1
0
0
1
1
1
0
2
0
2
1
2
1
0
0
0
1
1
0
1
0
0
2
2
1
0
0
2
0
0
2
0
2
6
0
0
0
1
0
0
0
1
0
0
1
1
0
2
1
0
1
1
1
0
2
1
2
0
2
1
2
1
0
0
0
0
1
0
0
0
0
0
1
0
3
0
0
2
1
0
2
2
2
0
0
0
0
1
1
0
1
0
0
0
2
2
0
0
0
1
0
2
1
1
1
0
0
0
0
1
0
2
1
0
1
1
1
0
1
2
0
1
0
0
0
5
0
2
1
0
2
2
0
0
2
0
1
2
0
0
0
2
0
1
0
2
0
2
0
2
1
0
0
1
0
0
1
2
5
0
1
2
2
0
1
0
0
0
1
2
2
0
0
0
2
1
2
1
0
0
1
1
1
1
0
1
1
1
1
1
2
0
0
0
3
1
0
2
0
0
0
0
1
2
1
2
1
0
1
2
0
1
1
0
2
1
1
1
0
0
0
1
0
0
1
0
0
0
1
2
0
1
1
0
2
2
0
1
2
0
0
0
0
0
1
0
0
1
1
0
1
2
1
0
1
1
1
0
0
1
0
0
0
2
2
0
0
1
1
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
1
0
2
0
0
1
2
2
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
2
1
1
2
0
0
1
0
0
2
2
1
2
1
0
0
1
0
0
1
2
1
1
2
1
0
0
1
2
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
2
0
4
0
0
0
0
0
0
0
2
0
0
1
0
0
1
2
0
1
1
1
0
1
2
1
0
0
1
4
2
1
0
1
0
2
0
1
1
0
2
1
0
1
2
0
0
0
2
0
1
1
0
0
0
1
0
1
0
0
0
2
1
0
1
1
0
1
0
1
1
0
0
1
0
0
1
0
0
2
0
0
0
1
1
0
1
0
1
0
2
1
0
4
0
2
2
0
0
0
2
1
1
2
0
0
0
0
2
2
2
3
0
0
1
0
2
0
0
0
0
0
2
2
1
0
1
0
0
3
0
0
1
2
0
1
0
2
2
2
1
1
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
2
1
0
3
0
0
2
1
0
1
0
1
0
0
0
0
2
1
2
2
0
0
0
1
2
1
0
0
2
0
2
1
2
1
0
1
1
0
1
1
1
1
0
1
1
2
2
0
2
0
0
0
1
0
1
2
1
1
2
0
1
0
1
0
2
2
1
0
2
2
0
1
2
1
1
1
0
1
2
0
0
0
2
0
0
0
1
2
1
1
0
1
1
0
0
1
0
1
1
1
1
0
1
1
0
1
0
0
0
0
0
0
0
0
1
1
2
1
0
0
0
0
1
0
0
0
0
1
3
0
0
0
2
0
0
2
2
0
2
0
0
2
0
2
1
0
0
2
1
0
0
1
1
1
0
0
0
1
1
3
1
0
0
2
2
1
0
1
2
2
2
0
0
0
0
0
0
1
1
0
2
0
1
0
1
0
2
1
0
0
0
1
0
0
0
1
0
0
1
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
1
1
2
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
1
0
1
1
2
1
2
0
1
0
2
2
0
1
2
0
2
2
0
1
0
0
0
0
2
2
0
2
1
3
1
0
1
2
2
0
1
2
1
1
0
1
3
0
1
2
2
0
0
1
2
1
0
1
0
2
0
1
0
1
1
0
0
0
1
2
2
0
0
2
1
0
1
1
0
1
1
0
0
2
0
0
0
0
1
0
1
1
1
1
0
2
2
2
2
0
1
0
0
1
2
0
1
1
1
2
0
0
1
1
1
2
1
1
0
0
0
0
0
0
0
0
1
0
2
1
2
0
1
1
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
2
1
0
1
1
1
0
0
0
0
0
0
1
0
1
2
2
0
1
0
2
0
1
1
0
0
0
1
0
0
1
0
1
0
1
1
0
1
0
1
1
1
2
1
1
1
0
0
1
2
1
2
1
0
0
0
0
1
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
2
2
1
1
0
0
2
0
0
0
1
0
2
2
0
1
0
1
1
2
1
1
2
2
0
0
0
1
1
1
2
0
2
0
2
0
0
1
2
0
1
0
0
1
0
1
1
2
1
1
2
0
1
1
1
1
3
2
2
1
1
1
1
0
1
0
2
1
0
1
1
1
0
1
0
1
1
1
4
2
1
0
3
0
2
0
0
1
0
1
1
0
2
1
0
2
1
0
0
2
2
0
1
1
2
2
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
1
1
0
0
0
0
2
1
0
0
2
0
0
2
0
1
2
1
0
1
1
1
1
0
2
0
0
0
0
0
1
0
2
1
0
0
1
1
2
0
1
2
1
1
0
1
1
1
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
1
2
1
0
2
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
2
2
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
1
0
1
0
2
2
2
2
1
1
0
2
0
2
1
1
0
1
0
1
2
0
0
0
0
1
0
0
2
0
0
2
1
1
1
1
2
3
2
0
0
0
1
0
1
1
0
0
1
1
3
1
0
0
1
0
0
1
2
1
1
1
0
0
0
1
0
2
0
0
1
0
1
2
0
1
0
1
1
0
2
0
0
1
2
10
0
2
0
0
0
2
0
0
1
0
0
0
0
0
2
0
1
2
2
1
0
2
2
0
1
2
1
0
2
1
2
2
0
1
0
0
2
0
1
2
1
2
0
1
1
0
1
0
0
0
0
7
2
0
1
1
1
0
1
0
0
0
1
2
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
1
0
2
1
1
1
1
1
0
0
0
3
2
0
0
2
1
1
1
0
0
0
0
0
1
1
2
0
0
0
0
1
1
1
0
2
0
2
1
1
1
0
5
0
0
1
1
0
1
0
2
1
0
0
0
2
1
0
2
1
0
1
2
0
2
0
0
0
0
0
2
0
1
0
1
1
1
0
2
1
2
0
2
6
0
0
1
2
2
2
1
1
2
1
2
1
0
0
1
1
1
0
0
1
0
0
0
0
0
0
2
1
2
1
1
0
1
2
1
2
0
1
3
1
1
0
0
0
1
0
0
0
2
0
1
2
0
0
1
0
1
0
1
0
1
2
1
0
2
2
0
0
0
0
1
1
2
1
0
1
0
0
1
0
2
2
3
0
1
0
1
1
1
2
0
1
0
0
1
0
0
1
2
0
0
1
1
0
0
1
2
0
1
0
2
0
1
0
0
0
0
1
0
2
0
0
0
2
1
1
1
0
0
0
0
0
1
2
0
0
1
0
1
0
2
0
2
2
1
2
0
0
1
2
0
1
2
0
1
0
1
2
0
0
2
0
0
0
1
2
1
2
2
1
1
1
2
0
1
0
1
0
0
1
0
0
3
1
0
1
2
2
1
0
0
0
0
0
0
1
0
0
0
3
0
1
0
2
2
0
0
1
1
2
2
0
0
2
0
0
1
0
0
2
0
1
1
0
0
0
0
2
2
0
0
1
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
3
0
0
2
0
0
0
1
1
1
0
1
1
2
0
2
2
1
0
1
0
1
1
0
0
2
0
0
0
0
1
2
3
2
0
0
0
2
2
2
2
0
0
1
0
1
0
1
7
0
1
0
0
1
0
1
2
2
1
1
0
0
2
0
2
0
0
2
4
0
0
2
2
0
0
1
0
2
0
1
0
0
1
0
0
2
1
0
0
0
0
1
1
0
1
2
1
0
0
0
1
0
1
1
2
1
0
1
0
0
1
1
2
1
1
2
1
0
0
0
1
2
4
2
0
2
0
1
0
1
0
2
0
16
0
0
2
1
2
0
0
0
2
2
0
0
0
0
0
0
0
2
0
3
0
3
0
1
1
0
1
0
0
1
0
0
0
1
2
0
0
0
0
0
1
2
1
1
0
1
0
0
1
3
1
2
1
1
0
0
2
2
1
5
0
2
0
1
0
0
0
0
2
2
0
0
1
0
0
1
1
2
0
2
0
3
2
0
2
2
0
1
2
0
1
0
0
0
3
1
0
0
0
1
1
1
1
1
0
2
1
1
1
1
0
0
0
1
0
2
1
0
1
0
1
0
0
2
2
1
0
1
2
1
1
1
1
0
1
0
1
0
1
0
0
0
2
0
2
1
1
0
0
1
1
2
2
0
0
0
2
0
0
0
0
1
0
2
1
1
0
2
0
2
1
0
1
0
1
2
0
2
0
0
1
1
2
0
0
0
0
0
0
2
0
0
1
0
2
0
1
1
0
0
0
2
1
1
2
2
2
2
1
0
0
1
1
0
1
2
0
0
1
2
1
0
2
1
1
1
1
0
0
0
2
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
2
1
2
1
0
1
0
1
1
0
2
1
2
0
0
2
2
1
0
2
0
1
0
1
0
0
1
1
0
1
2
0
0
2
2
0
0
0
1
1
1
0
1
2
2
0
0
1
2
1
0
0
0
2
0
0
1
2
0
0
2
1
2
2
1
0
0
1
1
1
1
1
1
0
0
0
2
1
2
2
0
0
0
1
0
2
0
1
0
2
0
3
0
0
2
1
1
0
0
0
0
0
1
0
0
2
1
1
1
0
2
0
1
2
0
2
1
1
0
0
1
0
0
0
1
1
0
1
2
6
0
0
0
1
0
0
1
3
0
0
1
0
2
1
0
1
1
0
0
0
2
1
2
0
0
0
0
1
0
0
1
2
0
0
1
1
0
1
0
0
1
2
2
0
0
1
1
1
1
0
1
0
2
0
0
2
0
1
1
0
1
1
0
0
1
1
1
0
0
0
1
1
1
1
1
0
0
1
0
0
1
2
0
2
2
1
1
0
2
2
0
1
1
0
1
0
3
2
0
0
0
0
2
1
1
1
0
2
2
1
2
1
2
1
1
0
0
2
1
2
1
1
0
0
2
0
2
1
1
1
2
5
1
0
1
2
0
0
2
0
0
1
0
0
0
0
1
2
1
2
1
2
0
0
1
0
2
0
1
0
0
2
2
1
2
2
0
0
2
2
0
1
3
0
0
0
0
0
2
1
2
1
2
0
0
1
1
1
0
1
2
2
0
2
0
2
0
0
0
0
2
0
0
2
0
0
0
1
1
2
0
1
1
2
1
0
0
0
1
2
0
0
0
0
2
0
0
1
2
1
0
0
0
0
1
2
0
2
2
0
0
0
1
0
1
1
1
0
2
1
1
0
0
0
2
0
0
1
1
1
2
2
3
1
0
0
1
0
0
2
0
0
0
2
0
1
2
1
0
0
1
2
2
0
1
0
1
0
0
2
0
0
2
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
2
1
0
1
1
1
0
0
2
0
0
2
0
0
0
0
1
2
0
1
0
0
0
2
1
2
1
2
0
0
1
0
2
2
1
1
0
0
2
0
1
0
0
1
0
2
0
3
0
2
0
0
2
0
1
1
0
1
0
1
2
0
1
0
2
2
0
0
1
2
1
0
0
0
2
1
1
0
0
0
0
2
2
2
2
0
0
2
0
1
1
1
0
0
2
0
1
0
0
2
2
0
2
0
0
1
0
0
0
0
0
1
2
2
1
5
1
1
0
1
1
3
0
0
2
0
0
1
1
0
0
0
1
2
1
1
1
0
0
1
2
0
2
1
1
0
0
1
0
2
0
0
0
2
0
2
1
0
2
0
1
2
1
1
2
0
0
1
2
1
1
2
1
0
2
2
0
0
1
1
0
2
0
0
2
0
0
3
0
0
2
0
0
1
0
0
1
0
2
1
0
1
0
1
1
1
1
1
0
1
0
0
1
2
1
0
0
1
2
2
0
2
0
2
0
0
0
0
0
0
0
1
0
1
2
2
0
0
0
0
1
1
1
2
0
1
1
0
2
0
0
0
1
0
2
0
0
0
0
2
2
0
1
0
1
0
1
1
1
2
2
0
0
2
0
2
1
0
1
1
0
0
0
0
0
2
0
0
0
1
0
1
1
1
0
0
0
2
1
0
2
0
1
0
0
0
0
0
3
0
1
0
0
0
0
1
1
0
0
0
0
0
2
3
2
1
0
1
0
2
0
2
2
0
0
0
0
0
0
0
0
1
0
2
1
2
0
2
2
1
0
1
0
0
0
2
0
0
0
1
1
1
0
1
0
2
1
0
0
0
0
1
1
0
0
3
0
0
0
0
2
2
1
2
1
0
2
3
0
0
2
0
2
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
2
0
1
0
1
0
1
2
2
1
1
0
1
1
2
0
0
1
0
2
0
0
1
1
5
0
0
0
0
1
0
0
1
0
1
1
1
0
0
1
0
2
0
2
1
0
0
0
1
0
0
2
1
0
2
0
1
0
0
0
1
0
2
1
0
0
0
2
2
1
0
0
2
5
2
1
2
0
0
1
0
1
0
0
0
0
0
0
3
0
0
0
1
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
1
1
1
3
1
1
1
0
0
0
0
1
1
2
2
0
0
0
0
1
1
2
1
1
2
0
0
1
1
1
1
0
0
1
1
0
0
0
0
1
4
1
1
0
1
2
2
0
2
3
0
0
1
0
1
0
0
0
0
0
2
2
2
1
0
2
0
0
0
0
1
0
1
2
2
0
2
1
2
1
1
1
0
2
0
1
0
2
0
2
0
0
0
0
1
0
1
0
3
2
0
1
1
1
1
1
0
2
0
0
2
1
0
1
2
2
2
0
1
0
1
10
1
0
1
2
1
1
1
1
1
1
2
2
0
0
1
2
0
1
0
1
0
0
0
2
1
0
1
0
0
1
1
0
2
0
0
0
0
0
0
1
2
1
0
0
1
1
1
1
2
1
2
0
0
0
0
0
0
1
0
0
1
1
0
1
2
1
1
0
1
0
2
0
1
0
3
0
1
1
0
2
1
1
1
0
2
1
0
0
0
1
2
1
2
1
1
0
1
0
0
0
0
0
0
0
1
1
1
0
0
2
1
0
2
1
1
2
0
2
1
0
1
1
1
2
2
1
0
0
0
0
0
2
0
0
1
0
1
0
0
1
0
1
0
1
0
0
0
1
2
0
2
1
1
0
0
2
1
1
2
0
1
0
0
1
2
0
2
0
0
1
1
0
0
0
0
1
1
2
0
2
0
1
3
2
1
1
1
0
0
0
0
0
1
2
1
2
1
0
2
0
1
2
3
0
2
0
0
1
1
1
1
0
0
0
0
1
1
1
1
1
1
0
1
2
0
1
0
2
0
2
1
0
1
0
1
1
2
1
0
0
1
0
1
0
2
2
0
1
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
1
2
1
1
2
2
1
2
0
1
1
1
1
2
0
1
1
0
0
6
1
0
0
0
0
1
2
1
1
0
0
0
1
2
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
2
2
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
1
0
1
2
0
1
1
1
1
1
1
1
0
0
3
2
3
0
1
1
2
2
0
1
0
0
1
2
0
0
1
0
1
0
0
1
2
0
1
0
2
0
1
1
0
1
0
2
0
2
0
2
3
4
2
0
0
4
2
1
4
0
0
0
1
0
0
2
0
0
0
0
2
0
0
2
3
2
1
2
0
1
2
0
4
1
0
2
1
0
1
0
1
0
0
0
0
0
0
0
1
2
0
1
1
0
1
2
2
1
0
0
0
0
0
0
1
0
0
1
0
0
1
2
2
3
0
0
1
2
1
0
0
0
2
1
1
1
2
0
1
0
0
2
1
3
1
0
1
0
1
0
1
0
0
1
1
0
0
0
2
0
1
1
0
1
1
0
0
1
1
0
0
0
0
0
0
1
0
1
2
0
0
0
1
2
1
0
1
1
1
1
1
0
1
2
2
1
0
1
1
0
2
0
0
2
0
1
0
1
0
2
1
1
2
1
1
0
1
0
0
0
2
1
0
1
0
0
0
1
2
0
1
0
0
0
1
0
0
0
1
0
1
1
2
2
1
1
2
1
2
2
1
0
2
2
0
1
2
0
2
0
2
1
0
1
2
1
2
0
0
0
0
0
0
1
2
0
1
0
1
0
1
1
0
0
1
0
1
0
1
1
1
2
0
0
0
2
1
0
0
3
0
1
4
2
0
0
0
1
3
0
1
2
1
2
0
0
0
1
2
0
0
2
1
0
2
2
2
1
1
0
1
0
0
0
0
0
0
1
0
1
1
0
2
0
0
1
1
0
1
1
2
1
2
0
0
0
0
2
2
0
0
0
3
3
0
2
1
1
0
0
0
1
0
0
2
2
0
0
1
0
0
1
2
0
0
0
2
1
1
0
0
0
1
2
0
0
0
0
0
1
0
1
0
1
2
0
0
0
0
0
2
0
0
0
0
0
1
2
2
0
2
1
0
2
0
2
2
0
2
2
1
0
0
2
2
2
0
1
0
0
0
1
1
0
2
0
0
2
0
1
0
0
1
1
2
0
0
2
1
0
1
0
0
3
1
0
1
0
1
0
2
0
0
1
2
0
2
1
2
1
0
0
0
1
0
2
1
0
0
1
1
0
0
0
0
1
0
0
0
2
0
1
0
0
0
1
0
0
0
1
0
2
0
0
2
1
1
3
0
2
2
0
1
0
0
1
1
0
1
0
2
1
0
0
0
1
1
0
0
0
1
0
0
2
0
1
0
0
2
0
1
2
1
2
1
0
0
0
1
1
0
1
1
2
0
1
0
2
0
0
2
0
1
0
0
0
1
0
1
0
0
0
0
0
0
2
1
0
0
0
2
2
0
0
0
1
0
1
1
1
4
1
2
0
0
1
2
2
2
0
1
1
0
0
0
1
1
0
1
2
0
0
0
1
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
2
1
0
2
2
0
1
1
1
0
1
0
1
6
2
2
1
0
2
0
1
1
0
2
0
2
1
1
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
2
1
1
2
8
1
2
0
0
2
2
0
1
1
1
0
0
0
3
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
2
1
2
1
1
1
0
0
0
1
0
1
0
2
0
0
2
0
0
1
0
1
0
1
0
0
0
0
1
1
0
0
3
1
0
3
0
2
0
1
1
2
1
1
0
0
2
0
0
0
1
0
0
1
0
2
0
1
2
0
0
0
0
0
0
1
0
1
2
1
2
1
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
1
2
0
1
0
0
1
2
0
0
2
2
0
0
0
0
1
1
4
0
2
1
0
0
1
0
2
0
0
0
3
0
2
2
1
0
0
1
0
2
1
0
0
0
0
0
1
2
0
1
0
1
0
0
0
0
0
2
0
1
0
2
2
0
0
1
0
2
2
0
0
0
0
1
0
0
0
3
2
1
2
0
0
0
0
1
1
1
2
0
0
0
1
1
2
1
1
1
1
2
2
0
0
2
0
1
2
2
0
0
0
2
0
2
1
0
0
2
4
0
2
1
2
2
0
0
0
1
0
1
2
0
1
0
0
0
0
1
1
0
0
0
1
0
0
2
1
0
0
0
1
1
0
0
0
0
2
2
0
0
0
1
0
0
0
1
2
1
0
0
2
0
0
2
0
1
0
0
0
4
0
1
1
0
1
1
0
2
2
0
0
0
1
2
0
1
0
2
2
1
0
1
2
1
1
1
1
1
2
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
2
0
1
2
1
1
1
0
0
1
0
0
0
0
2
0
0
0
1
4
0
0
1
0
0
2
1
0
2
3
1
1
1
0
0
0
2
2
0
2
1
1
1
0
0
0
2
1
1
2
0
2
0
2
1
2
1
0
0
2
0
0
1
0
0
0
3
0
1
0
2
1
0
2
0
0
2
2
1
2
0
2
0
0
2
0
0
1
1
0
0
0
2
1
2
0
0
0
1
1
0
1
2
0
1
0
1
2
2
2
1
0
2
0
0
0
1
2
0
2
1
1
0
2
0
2
0
0
1
0
2
0
2
0
2
1
0
0
1
2
1
8
0
0
1
0
1
0
0
0
0
1
2
1
2
2
0
1
0
1
2
1
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
1
0
1
0
2
2
2
0
1
0
2
0
1
0
1
1
0
1
1
0
0
2
0
0
1
1
2
0
0
2
1
2
0
0
1
1
0
1
0
1
2
0
1
2
2
0
0
0
0
1
3
1
0
1
0
1
2
1
0
0
0
0
0
0
1
1
2
0
2
0
1
1
1
0
0
0
2
0
1
1
0
1
0
0
0
0
1
0
1
0
0
0
2
2
0
2
0
1
2
0
0
0
1
2
1
1
1
1
2
0
1
0
0
3
0
1
2
1
2
1
1
1
0
1
0
2
0
0
1
0
1
1
4
2
1
0
3
2
0
0
1
0
1
1
1
2
0
0
0
0
0
0
2
1
1
1
0
0
0
1
1
1
2
0
0
0
0
0
0
2
1
2
0
2
0
0
2
1
0
0
0
1
0
0
2
2
1
2
0
1
2
0
0
1
0
1
0
2
1
0
0
0
1
1
1
0
0
0
2
0
0
1
0
0
0
2
0
2
0
0
0
1
0
1
1
1
0
0
2
1
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
1
2
0
0
1
1
0
0
3
2
0
0
2
1
0
2
0
1
0
1
0
0
0
0
0
2
2
0
0
1
2
0
2
1
1
0
2
0
0
1
0
1
2
1
2
0
0
0
2
0
1
0
0
2
0
0
0
1
0
0
0
0
2
0
0
1
2
0
0
0
1
0
2
0
0
0
0
0
2
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
4
2
1
0
2
1
1
2
2
2
0
0
0
0
2
2
0
0
0
0
1
2
0
0
0
1
1
2
2
3
1
1
2
0
0
0
1
0
2
0
1
1
3
0
0
0
0
1
1
2
1
1
2
1
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
4
2
1
3
1
1
0
0
2
1
0
0
0
0
0
1
0
1
0
2
0
0
1
1
1
1
2
0
0
1
0
1
2
0
1
2
0
1
2
0
2
3
1
0
1
0
2
1
0
0
2
1
2
1
0
1
0
2
1
1
2
0
1
0
1
2
2
0
0
3
1
1
0
0
0
0
1
0
2
2
0
1
1
1
0
0
1
2
0
2
2
0
0
0
0
0
1
2
1
1
0
2
1
2
1
1
0
2
0
1
2
2
0
2
2
2
1
1
1
2
1
1
1
0
0
0
0
0
0
0
1
0
3
0
0
0
1
2
3
0
1
3
2
0
0
2
0
1
2
1
1
2
4
1
0
0
1
2
1
1
0
1
0
0
2
1
0
2
0
0
1
1
1
2
1
2
0
1
0
2
0
0
2
3
0
1
2
0
0
2
3
0
1
1
0
2
0
2
0
0
0
2
1
0
2
1
1
2
0
2
2
0
0
2
1
1
1
5
0
2
0
0
2
0
1
1
1
1
1
0
2
0
1
2
2
0
2
1
1
2
1
0
1
0
0
0
1
2
0
0
0
1
2
2
0
1
1
1
1
1
0
0
1
1
1
1
2
0
1
2
0
1
0
0
1
1
1
1
0
0
2
0
1
0
1
1
0
0
1
0
0
2
0
0
0
1
0
1
1
0
2
0
1
2
1
0
0
1
0
2
2
0
0
1
0
2
0
2
0
1
1
2
0
0
1
0
0
1
2
0
4
2
1
0
1
1
0
1
1
1
0
1
1
1
0
2
2
0
1
1
0
1
0
0
0
0
0
1
1
1
0
0
1
0
0
1
0
0
2
2
0
0
0
0
0
1
0
0
0
2
1
0
0
0
1
0
0
3
1
0
0
2
1
0
0
0
1
2
1
1
2
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
2
0
0
0
3
0
0
0
0
0
2
0
1
1
1
1
2
0
0
0
1
0
1
1
1
2
1
0
0
1
0
0
0
0
2
2
2
0
0
0
0
2
0
0
1
0
0
2
0
1
2
0
1
0
1
0
2
1
1
0
0
0
2
1
0
1
0
0
0
2
1
1
0
0
2
0
1
0
1
1
0
1
1
0
1
1
0
0
1
0
0
1
0
3
0
0
2
0
1
0
1
2
0
0
0
0
0
2
0
1
0
0
0
0
2
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
1
2
0
0
0
1
0
0
0
1
0
0
1
0
1
1
0
1
0
0
0
0
1
2
1
0
3
0
1
0
1
1
0
0
1
0
1
0
1
2
0
2
2
2
2
2
2
1
0
0
1
2
1
1
0
0
2
1
0
0
1
0
2
0
1
1
0
1
0
0
0
0
2
2
0
1
0
0
0
0
1
0
2
1
0
2
0
0
0
2
0
0
0
2
0
2
1
2
1
2
0
1
0
0
1
2
0
0
2
1
1
1
0
0
0
0
2
0
0
0
0
0
1
1
1
2
0
0
1
1
1
0
1
1
0
0
1
0
2
1
0
1
2
1
0
0
1
2
0
1
0
0
2
1
0
1
2
0
2
1
0
1
1
1
1
2
0
3
1
1
0
1
2
1
1
2
1
2
1
1
0
1
0
0
5
0
0
2
1
1
0
1
0
1
2
1
1
0
0
1
1
2
1
0
0
2
2
1
0
0
0
0
0
1
0
0
1
1
2
0
1
1
1
0
1
1
1
0
2
0
2
0
2
0
0
0
2
3
1
1
0
1
1
1
2
0
0
0
6
2
1
1
0
2
1
1
0
0
1
0
1
0
2
0
0
0
0
1
1
0
2
0
1
1
1
0
1
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
2
0
2
0
1
1
2
2
2
1
2
1
0
0
0
2
0
0
2
1
2
0
2
0
0
0
0
2
1
1
0
4
1
1
0
1
0
2
1
0
0
1
0
0
2
0
0
1
1
2
1
2
2
1
1
1
2
0
0
0
1
2
2
1
0
0
0
1
0
2
3
2
0
1
0
0
0
2
0
2
0
0
1
2
2
0
2
2
2
0
0
2
0
1
0
0
1
2
2
1
0
1
0
1
1
0
0
2
2
1
1
0
2
3
0
0
0
1
2
1
0
2
0
0
0
1
0
0
0
0
1
0
1
1
6
2
2
0
2
0
0
0
2
0
2
0
1
1
0
0
2
0
0
2
2
0
1
0
1
2
2
1
1
3
0
0
2
0
2
0
1
0
1
0
0
2
1
1
2
1
1
2
0
1
1
3
0
0
0
0
0
1
1
2
0
2
2
0
1
0
0
0
1
0
1
0
2
2
0
2
0
9
0
0
0
1
2
3
0
1
0
1
0
1
1
1
1
0
2
1
0
1
2
0
0
0
2
0
0
2
1
0
2
0
0
2
0
0
0
1
2
0
2
0
0
2
2
1
0
0
2
2
1
1
0
0
0
0
0
1
0
1
1
0
2
2
1
2
2
1
2
0
0
0
0
0
2
0
2
0
0
1
1
0
3
0
0
1
2
0
0
0
1
1
0
1
0
0
2
0
0
2
0
0
0
2
0
0
0
0
4
0
0
2
0
0
0
1
2
2
1
3
2
0
0
0
2
1
2
2
0
1
0
0
1
0
1
0
2
0
0
2
0
0
1
0
0
1
0
1
1
0
1
2
0
1
2
2
0
2
0
0
0
0
1
0
0
0
2
2
0
0
0
0
2
0
0
2
1
1
2
0
1
2
1
1
1
1
0
2
1
0
0
1
2
0
1
2
0
0
0
0
0
0
1
2
1
0
0
2
0
0
2
1
1
0
0
0
2
1
0
0
0
2
1
0
0
1
1
0
0
1
0
3
2
1
1
2
2
0
1
0
1
0
0
1
2
1
3
1
0
0
0
0
2
0
0
3
1
2
0
1
0
1
0
0
1
0
0
1
0
0
2
0
1
0
0
1
0
2
1
0
0
1
0
0
1
0
0
1
4
1
1
0
0
0
0
2
0
1
0
2
2
0
1
2
0
0
1
0
1
0
0
2
2
1
1
0
1
0
2
0
0
1
0
10
0
2
0
1
1
1
0
2
1
0
0
0
1
2
0
0
1
1
0
1
0
1
0
2
1
0
1
0
1
1
1
1
0
0
0
0
0
0
1
0
2
2
1
0
0
0
0
1
1
1
1
0
0
0
1
0
0
0
1
0
2
0
0
2
2
0
1
0
0
3
0
2
1
1
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
1
1
1
1
0
2
1
0
0
1
0
1
1
0
0
0
1
0
0
1
0
0
1
1
1
0
0
2
0
2
0
2
0
0
0
0
0
1
0
1
1
0
1
2
1
0
0
0
2
0
0
0
0
0
0
0
2
2
2
1
2
0
0
2
0
0
0
0
2
1
2
1
1
1
0
0
2
0
0
0
0
2
3
0
0
0
0
0
1
1
0
0
2
0
0
2
0
1
1
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
1
0
2
0
1
0
1
1
2
0
0
2
2
1
0
0
0
1
0
2
0
0
0
0
0
1
1
0
2
0
0
2
0
0
0
2
1
0
0
1
4
3
1
1
0
0
1
0
0
1
0
1
0
1
0
0
1
2
2
1
0
1
2
1
1
1
1
0
0
1
0
2
0
0
0
2
1
1
0
1
2
0
2
0
1
0
1
1
3
0
1
0
0
0
0
1
0
5
0
1
2
2
0
1
1
0
1
1
2
0
3
1
2
0
1
2
1
2
2
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
1
2
1
0
3
0
0
2
0
2
2
0
0
2
2
0
0
0
0
1
0
0
6
0
1
1
0
0
0
2
0
0
0
1
2
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
1
2
0
0
2
2
0
2
1
0
0
2
1
1
0
1
0
0
0
0
0
1
1
0
2
0
1
0
2
1
0
0
2
2
1
0
1
0
1
0
0
0
0
0
1
1
0
0
1
1
2
1
2
0
0
1
1
0
1
2
0
3
2
2
0
0
0
0
1
0
1
2
0
0
1
2
1
0
0
1
0
2
1
2
1
0
1
0
0
2
1
1
0
0
1
1
0
1
1
0
2
0
0
1
2
2
1
1
1
0
0
0
1
0
2
2
1
2
1
0
1
0
1
1
0
1
1
0
1
3
0
0
0
2
1
0
0
0
1
0
0
0
2
2
2
1
0
1
0
0
2
0
0
1
1
1
3
1
0
1
0
1
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
1
1
2
0
0
0
2
1
2
0
1
1
2
1
0
1
1
1
0
0
0
1
0
0
2
2
1
1
2
0
1
0
0
2
2
0
0
0
0
0
3
0
1
0
0
1
1
0
1
0
0
3
1
2
0
0
2
1
0
0
1
1
1
2
0
1
1
0
0
0
0
1
1
0
0
0
2
4
0
0
1
1
0
2
1
1
0
0
1
0
0
2
0
1
0
1
1
1
1
1
0
1
0
0
0
0
1
2
0
0
0
1
1
0
1
2
2
0
1
0
2
2
0
0
2
1
1
1
1
1
0
2
1
0
0
0
0
2
0
0
1
2
1
1
2
2
1
0
0
1
2
1
1
0
1
1
0
0
2
2
1
0
0
2
1
1
1
0
0
2
0
2
2
1
0
0
3
0
1
1
0
1
0
1
2
0
0
0
1
1
0
1
0
0
0
2
0
2
0
1
2
0
0
5
0
1
0
1
1
1
2
1
2
0
1
0
0
0
0
1
0
1
0
0
1
0
0
2
0
3
1
1
0
2
1
0
0
0
0
2
0
1
1
1
0
0
0
1
0
2
1
1
0
1
0
1
1
1
0
0
1
2
0
1
2
1
0
2
0
2
0
0
0
2
0
1
0
0
0
1
1
1
1
0
0
1
0
0
0
2
2
1
1
0
1
1
1
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
1
0
1
1
1
0
1
2
0
1
0
2
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
3
2
3
0
2
1
0
1
0
1
2
2
1
0
0
1
2
1
1
1
1
2
1
1
2
1
1
0
2
1
1
0
0
1
1
0
1
0
1
0
0
0
0
1
2
2
0
0
0
2
0
1
1
2
1
1
1
0
0
0
0
0
0
1
2
1
0
1
1
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
1
1
0
0
1
0
1
0
1
2
0
1
1
0
0
1
1
0
1
1
4
2
0
0
0
0
0
2
0
2
0
0
0
1
0
2
1
0
0
0
2
1
2
1
2
1
1
0
0
0
2
4
0
0
1
1
0
1
0
1
0
0
0
2
0
1
2
0
0
0
1
0
0
0
0
0
0
0
2
1
0
2
0
0
0
2
2
2
3
0
0
2
2
1
0
1
0
1
0
0
1
2
0
2
0
2
0
0
0
0
2
2
1
0
1
1
1
1
0
2
0
0
0
1
0
2
0
0
1
0
2
0
0
0
1
1
0
0
0
1
2
2
1
2
0
0
1
0
0
0
0
1
1
0
1
0
2
0
1
0
0
1
2
0
2
1
1
0
1
1
0
0
1
0
0
1
4
1
0
0
0
1
0
2
1
0
1
1
2
0
2
1
0
1
0
2
0
1
0
2
0
2
0
1
2
1
0
0
0
0
0
0
1
2
0
0
1
1
2
2
0
0
2
1
0
2
0
0
0
2
0
0
0
1
2
3
0
0
0
0
0
0
0
2
0
0
1
0
1
3
0
1
1
0
2
0
0
0
0
1
0
0
1
0
2
0
0
0
1
2
1
2
0
0
1
0
2
1
3
0
2
0
1
2
1
1
3
2
0
0
0
0
2
0
1
0
0
0
1
0
2
1
1
3
0
0
1
0
2
2
0
0
0
0
3
1
1
1
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
1
0
4
0
0
1
0
0
1
1
2
1
1
0
1
0
0
2
0
2
0
0
0
1
0
2
0
0
0
2
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
2
2
0
0
1
1
0
2
0
0
1
0
0
2
0
1
0
1
2
0
2
2
1
1
2
0
0
0
0
2
0
0
0
2
1
2
1
0
1
1
2
0
1
2
0
0
0
1
0
2
0
1
0
0
1
2
0
0
3
2
0
0
0
1
0
2
2
2
2
1
2
0
2
0
0
0
0
1
0
0
2
3
0
0
1
0
1
0
0
1
0
0
1
0
2
1
1
0
1
0
0
1
3
1
0
0
2
0
0
0
1
2
0
0
0
2
0
0
0
0
0
1
1
2
1
0
0
0
0
1
0
0
0
2
0
0
2
1
2
2
0
0
0
0
0
1
0
1
2
0
1
0
2
0
1
1
0
1
2
2
0
1
0
0
0
0
2
0
1
2
0
1
1
1
2
0
0
0
0
0
1
2
0
0
0
0
1
2
3
2
0
1
1
2
0
0
0
0
0
1
0
1
2
0
1
0
0
0
0
1
1
1
0
2
0
1
0
2
2
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
2
2
1
2
0
0
0
0
1
0
0
1
0
2
0
2
0
2
0
0
0
1
3
0
1
1
0
0
2
1
0
0
0
2
2
2
0
2
1
2
1
2
0
1
1
0
0
1
1
0
0
0
3
0
0
0
3
1
1
0
2
1
0
0
2
3
1
0
0
2
0
1
0
1
1
0
1
0
2
0
1
1
1
1
0
0
1
0
0
0
1
2
2
0
1
1
0
0
0
0
2
1
1
3
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
1
0
0
0
1
0
0
2
0
2
0
1
1
1
1
0
0
1
1
0
1
3
0
0
1
1
0
0
1
0
2
0
0
0
0
1
2
0
2
0
0
0
1
0
2
0
1
0
2
0
0
1
1
2
0
2
0
2
1
0
0
1
2
1
0
0
1
0
1
0
0
0
1
0
0
1
0
2
0
2
1
0
2
1
2
2
1
0
0
1
1
2
0
0
0
1
0
0
0
0
0
1
0
0
0
1
2
1
2
2
1
2
3
1
0
1
0
0
0
3
0
2
2
0
1
0
2
3
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
2
1
0
2
2
0
0
2
2
0
0
1
1
0
3
0
0
1
1
0
2
0
0
1
8
1
2
0
0
1
1
2
1
1
0
0
1
1
0
0
0
0
2
2
2
2
2
0
1
2
1
0
2
1
1
0
2
0
5
0
1
1
0
0
2
1
0
1
2
4
1
2
1
0
2
2
0
4
1
2
0
3
0
0
2
0
2
1
0
1
1
7
2
1
0
0
0
2
0
0
2
2
2
2
1
2
1
1
4
2
0
0
0
0
2
1
0
1
1
1
1
1
0
0
1
2
2
1
0
2
1
1
0
2
0
1
2
2
1
2
1
0
0
1
1
0
1
0
0
0
1
0
2
0
1
1
1
1
0
1
0
0
0
1
2
0
0
0
2
0
0
2
0
2
1
0
2
2
2
0
0
0
0
1
0
0
0
1
1
2
0
1
0
1
0
1
2
1
1
0
2
0
1
0
2
0
0
2
1
0
0
1
0
2
2
0
1
1
1
0
0
2
1
0
2
0
2
0
0
2
1
0
0
4
1
1
1
0
1
0
1
2
1
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
4
0
0
2
0
1
0
0
2
1
3
1
0
0
0
2
0
2
0
2
0
1
0
1
1
1
0
0
0
0
1
0
0
1
0
0
1
0
1
3
1
1
0
1
0
0
1
1
0
4
1
2
1
0
1
0
0
0
1
0
0
0
0
0
0
1
2
0
1
1
1
1
0
0
0
0
1
2
1
0
1
2
2
0
0
2
2
0
2
0
0
0
4
2
1
2
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
3
0
0
1
2
2
0
1
2
4
0
0
0
1
2
0
0
0
0
1
1
0
1
2
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
2
0
1
2
1
0
2
2
0
0
0
1
0
1
0
1
1
0
2
0
0
2
2
2
0
1
0
1
0
2
2
0
2
0
0
0
0
0
1
0
0
0
2
2
0
0
1
3
0
2
2
2
0
0
1
0
0
0
0
2
0
0
1
0
2
0
1
0
0
1
1
1
0
2
2
1
0
2
2
0
0
2
2
2
1
0
0
1
1
2
0
1
2
0
0
1
2
2
0
2
2
0
0
0
0
1
0
0
0
0
1
0
1
1
2
0
2
1
0
2
0
0
0
0
0
1
2
2
3
1
0
0
1
0
2
2
1
0
1
1
1
1
0
0
0
2
0
1
0
0
2
1
0
0
1
2
2
1
0
1
0
2
1
1
4
1
2
0
2
0
0
0
0
0
0
0
2
0
3
0
0
2
0
0
3
0
0
1
1
0
2
0
2
1
0
1
0
1
0
2
2
1
0
0
1
0
0
0
0
1
1
0
1
1
1
1
1
0
0
0
0
1
1
0
0
0
2
1
0
1
2
2
0
3
1
0
1
0
0
0
0
0
1
0
1
1
0
0
2
2
2
1
1
3
0
0
0
0
1
1
1
2
0
1
1
0
0
0
2
0
1
1
2
1
0
1
1
2
4
1
0
3
1
0
0
0
0
2
0
1
1
2
1
1
0
0
2
0
0
2
1
0
0
0
2
0
0
0
0
1
0
0
2
0
2
2
0
0
1
0
2
0
0
1
0
0
0
0
2
1
1
4
0
0
0
0
0
0
0
0
1
0
2
1
0
2
2
0
0
1
1
0
2
1
0
1
1
2
0
2
1
1
0
1
0
0
0
0
0
2
1
1
1
0
2
0
1
2
0
0
1
0
0
1
0
1
1
1
0
0
2
2
2
0
1
0
1
1
2
0
1
2
0
1
0
1
6
2
0
1
2
2
0
1
0
0
1
0
0
1
0
0
1
2
1
0
0
2
0
0
0
1
0
1
2
1
1
0
0
1
1
0
1
0
0
1
3
2
1
0
0
1
0
0
1
0
0
0
0
1
0
2
0
1
2
1
0
2
0
0
2
0
0
0
0
1
0
2
2
1
0
0
0
1
0
0
0
0
0
1
0
0
2
1
2
0
1
0
1
1
1
0
0
0
0
0
3
1
2
2
2
1
0
1
2
1
1
0
0
0
1
0
2
1
2
2
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
1
2
0
2
1
0
2
2
0
0
0
1
2
2
0
0
0
1
0
0
1
0
0
0
2
2
1
1
1
0
2
1
2
0
2
2
0
0
0
1
0
1
2
2
3
1
0
1
0
2
0
0
1
0
0
0
0
2
2
1
0
0
0
1
0
1
1
0
0
0
3
0
0
1
0
0
1
2
1
0
0
0
1
0
1
1
0
0
0
2
1
2
0
2
0
2
2
0
1
2
0
0
2
0
0
1
0
1
2
0
0
2
1
0
1
0
0
2
2
0
2
0
0
2
3
0
0
0
0
1
1
2
0
1
0
1
2
1
2
0
0
0
1
11
2
0
0
2
1
1
0
0
0
1
0
1
0
2
0
2
0
1
0
1
0
0
0
1
1
2
0
2
1
0
0
1
0
2
2
2
2
0
0
2
0
1
2
2
0
0
0
0
0
0
0
0
2
3
0
1
0
1
0
1
0
1
2
2
1
1
0
2
0
1
2
0
1
0
0
0
0
1
2
2
0
0
1
2
1
0
0
2
0
1
1
0
2
0
0
0
2
0
1
0
0
2
2
0
0
1
0
1
1
0
0
2
2
0
0
2
2
0
2
1
0
6
1
0
0
1
0
0
0
2
0
1
1
4
0
0
0
0
0
0
1
0
2
0
2
0
0
1
1
0
0
0
1
0
0
2
9
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
1
1
1
0
0
1
2
2
1
2
0
0
2
0
0
1
0
0
1
1
0
2
0
1
2
0
0
2
0
1
1
1
0
0
2
2
1
0
0
2
0
2
0
1
1
1
1
1
0
1
0
1
1
1
1
0
0
0
0
1
0
0
0
2
1
0
0
0
1
0
0
0
0
1
1
1
1
1
2
1
0
5
1
2
0
2
1
1
1
0
3
0
2
0
0
0
0
0
0
2
1
0
0
2
1
2
1
1
1
1
2
0
0
0
2
0
2
1
1
0
0
1
0
0
1
0
0
3
0
3
0
1
2
0
1
0
1
0
2
0
2
6
0
1
0
2
2
2
2
1
0
2
2
0
0
2
1
1
0
0
2
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
1
0
0
2
0
0
1
1
1
0
0
0
2
0
1
2
1
0
0
0
0
0
1
1
0
2
1
1
1
0
0
1
0
0
2
1
2
0
0
0
0
2
1
1
1
0
1
1
1
0
0
0
0
0
1
0
1
2
0
1
0
2
1
1
0
0
0
1
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
3
0
2
0
0
3
0
2
2
1
0
1
0
1
2
1
0
2
1
0
1
0
1
0
1
0
1
1
2
0
1
0
1
0
2
0
1
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
2
1
1
1
1
2
1
0
0
0
0
1
1
1
0
0
1
0
0
0
1
2
0
0
1
2
0
1
0
1
0
0
0
2
0
0
1
2
2
1
1
1
0
0
1
0
0
1
1
1
0
1
0
0
2
0
0
2
2
1
0
0
1
0
0
2
0
1
0
2
2
0
0
0
0
2
1
0
0
0
1
1
3
0
1
2
2
0
3
0
0
0
2
2
0
0
1
3
1
1
1
0
1
0
0
0
0
2
1
1
0
0
1
0
0
0
2
1
1
0
2
1
1
1
0
1
1
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
1
3
1
1
0
2
3
0
2
2
1
0
0
0
2
1
1
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
1
1
0
0
1
1
2
0
0
0
2
2
0
0
1
1
1
3
2
2
2
2
0
2
0
1
2
0
0
3
2
0
0
1
0
0
2
2
0
2
1
2
0
0
2
1
2
1
0
0
0
0
0
2
1
1
2
2
0
1
0
0
1
0
0
1
1
2
0
2
2
1
0
0
0
2
0
0
1
0
1
3
1
0
0
2
3
0
0
0
2
2
1
1
2
0
0
0
1
0
1
0
2
0
0
2
1
0
2
0
0
2
0
0
0
2
2
1
0
0
1
0
1
1
1
1
2
2
3
0
0
1
0
0
0
1
0
0
2
0
2
2
0
0
0
2
0
0
1
1
0
0
1
1
2
0
0
1
1
0
1
0
2
0
0
0
0
0
2
0
1
0
0
0
1
0
0
1
1
0
1
1
0
2
2
0
0
0
1
1
0
1
1
0
0
2
0
0
1
0
0
0
1
2
1
0
0
2
2
0
1
1
0
0
0
2
0
0
0
2
1
1
1
0
2
0
1
0
1
2
0
2
1
0
0
0
1
1
1
2
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
2
2
0
0
1
2
0
1
1
0
0
0
0
1
0
2
0
1
0
0
1
0
1
1
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
1
1
0
0
0
0
2
1
0
2
5
2
2
0
0
2
2
0
1
2
0
1
3
0
0
0
2
0
1
1
0
0
1
0
0
0
1
1
0
0
1
0
2
1
0
1
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
1
1
2
2
0
1
0
0
1
0
2
1
1
0
2
1
2
2
0
1
1
1
0
2
2
0
0
0
4
0
2
0
2
0
1
1
1
0
2
0
0
3
0
0
2
1
2
2
3
1
0
0
2
2
0
0
2
1
1
0
1
1
1
1
2
0
2
0
1
1
2
1
0
1
1
0
2
2
1
0
1
1
0
2
0
0
0
0
2
1
2
1
1
1
2
0
0
0
2
0
0
0
1
1
2
0
1
1
0
2
1
1
1
0
1
0
2
1
2
1
0
1
1
0
1
2
0
0
0
0
0
2
2
1
2
0
0
1
1
1
1
0
0
2
0
0
4
1
0
0
0
2
0
2
1
2
0
2
0
0
0
0
0
1
0
1
2
0
0
0
1
2
0
1
0
0
1
0
0
0
0
1
1
0
0
2
0
1
0
1
0
2
0
1
2
0
0
2
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
2
0
1
0
2
0
2
0
0
0
0
0
1
1
0
3
0
2
1
0
0
1
1
2
1
1
2
1
1
0
0
0
1
1
2
2
1
0
1
0
1
0
0
0
0
1
0
2
2
0
1
0
0
0
0
2
1
2
0
2
1
1
1
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
1
0
2
1
1
1
0
0
2
0
1
0
0
0
2
0
0
0
1
1
0
0
1
0
0
2
1
2
2
0
2
1
1
2
3
1
0
0
0
1
0
2
0
0
0
2
1
2
0
2
1
0
1
0
1
0
1
1
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
1
0
2
2
1
0
0
2
0
4
1
0
2
0
1
2
2
1
0
2
3
1
1
2
1
1
2
0
2
0
2
1
0
0
0
0
0
2
0
2
1
1
1
0
0
1
0
0
1
0
0
0
0
0
2
1
2
0
0
0
1
0
0
1
2
2
1
1
2
0
0
1
0
1
0
1
2
2
1
0
0
0
0
2
1
2
0
1
4
2
0
1
2
0
0
1
0
1
2
0
2
0
0
0
0
0
0
0
1
1
0
0
2
0
1
0
1
0
0
1
1
1
1
1
2
0
0
1
0
0
1
0
2
0
1
0
0
2
0
1
0
0
1
0
1
1
0
1
1
0
1
0
0
0
0
1
3
0
1
2
2
0
0
0
1
0
0
0
1
1
0
1
2
0
0
2
1
0
2
1
0
0
0
0
0
0
1
1
0
2
1
2
2
2
2
2
1
0
0
0
2
0
0
2
0
2
0
0
1
0
3
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
2
2
2
3
0
0
1
1
0
0
0
0
2
0
1
1
0
0
2
0
0
1
1
1
1
0
0
0
0
1
2
2
0
0
0
0
3
0
0
1
1
3
0
2
0
0
0
1
0
1
0
2
0
2
2
0
0
0
0
2
0
0
0
1
1
1
1
0
2
1
0
0
0
0
0
2
2
1
1
0
0
1
2
1
0
1
1
0
0
0
1
0
2
0
0
1
1
2
2
0
0
1
0
2
0
0
0
0
1
1
0
1
0
0
0
6
3
1
0
0
0
3
1
1
0
0
3
1
1
1
2
1
2
2
0
0
0
0
1
0
0
2
2
0
2
2
2
1
2
0
0
0
1
0
0
0
0
1
1
1
1
0
2
0
0
2
0
2
0
1
0
0
2
0
1
1
1
0
0
1
2
0
0
2
0
0
1
0
0
0
2
2
1
0
1
0
2
0
1
1
2
1
2
0
0
0
0
1
0
2
0
0
1
1
0
4
0
0
1
2
1
2
1
0
2
0
2
0
1
0
0
0
0
0
1
0
2
1
3
0
0
2
0
2
1
2
1
1
1
0
0
1
0
0
0
0
2
1
2
2
0
0
0
0
0
2
1
0
1
1
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
2
2
1
1
0
0
0
0
1
1
4
0
1
0
2
0
0
1
1
0
0
0
0
0
2
0
2
0
1
1
2
0
0
0
0
1
1
2
0
0
1
2
0
1
2
0
1
2
0
1
1
2
0
0
2
1
0
0
0
0
2
1
0
3
0
0
3
0
0
0
1
2
0
0
1
1
0
0
1
0
2
2
0
0
0
0
2
2
1
0
2
2
0
1
0
1
1
2
2
0
0
0
0
3
1
0
1
0
0
0
1
1
1
0
0
1
0
1
0
2
3
2
2
0
0
2
1
0
1
0
1
0
2
0
0
1
1
1
2
0
1
1
0
2
0
2
2
0
0
0
0
2
2
1
0
1
1
0
1
0
1
0
0
2
0
0
0
1
0
2
0
0
1
2
1
1
1
0
0
0
0
3
1
0
0
0
1
0
1
0
2
0
0
0
0
2
4
2
0
1
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
2
1
0
0
0
0
1
9
1
0
2
1
0
0
0
0
0
0
2
1
2
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
1
2
0
0
1
2
1
0
0
0
1
0
1
2
0
0
3
0
0
2
0
0
2
1
0
2
1
0
0
0
0
1
2
0
0
0
2
2
1
0
0
0
3
0
1
2
0
1
0
0
0
2
1
2
0
2
1
1
2
1
1
1
1
0
1
0
2
0
0
1
3
1
0
2
1
0
2
1
0
0
1
0
2
0
2
1
0
2
2
0
0
0
0
0
0
0
0
2
0
1
1
2
0
1
1
0
0
1
2
1
1
1
1
2
1
0
0
0
2
0
1
1
1
2
0
1
1
1
0
0
1
1
0
1
0
1
0
0
2
1
2
0
1
0
2
1
0
0
1
0
3
1
2
1
1
1
0
1
0
2
1
2
1
2
0
1
0
1
0
0
0
0
1
1
1
0
0
0
2
0
1
0
0
0
2
0
0
1
1
1
0
0
0
1
0
0
0
1
0
0
0
2
1
0
1
0
0
0
1
0
1
0
2
0
2
0
0
1
0
0
0
0
2
2
0
0
0
1
0
2
2
3
2
3
0
0
2
0
1
1
0
2
1
0
0
0
1
2
1
0
0
1
2
0
1
0
1
1
1
0
0
0
0
0
0
0
1
1
0
1
0
2
2
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
1
0
1
0
1
2
1
0
0
0
1
0
0
0
2
0
2
0
0
1
2
1
2
1
2
0
1
2
0
2
1
2
1
0
2
2
1
0
0
0
0
1
0
1
1
1
0
0
0
2
1
2
1
0
0
0
1
0
1
2
2
1
2
2
0
2
0
0
0
1
2
1
0
0
0
2
1
2
0
1
2
1
1
1
0
1
1
0
2
0
2
1
0
1
2
0
1
1
0
2
1
0
0
2
1
1
2
2
1
0
1
0
2
0
1
1
0
0
0
0
1
3
1
0
1
1
5
0
1
1
0
0
0
0
2
0
1
1
0
0
0
1
1
0
1
0
0
0
0
0
2
0
3
0
1
2
0
2
2
0
0
1
0
1
0
1
1
0
1
0
0
1
6
0
0
1
0
2
1
0
0
0
2
2
2
0
0
0
0
1
2
0
1
0
2
0
0
0
2
0
2
1
1
1
2
0
0
0
0
2
0
0
0
0
1
0
0
0
2
2
1
1
0
1
1
0
0
1
1
1
2
3
0
0
1
0
1
0
0
2
2
2
1
0
2
0
0
0
0
0
2
0
0
2
1
2
1
1
0
0
0
1
0
2
7
0
0
1
0
3
2
2
0
0
0
1
0
1
2
0
1
0
1
0
2
2
1
1
0
2
0
1
0
2
2
1
0
0
1
0
0
2
0
0
1
0
1
0
0
1
1
0
0
0
2
0
0
1
2
0
0
0
1
0
0
1
0
1
3
1
1
2
2
1
1
1
1
2
1
0
2
1
0
2
2
0
2
0
0
0
2
2
1
1
1
4
1
2
0
0
0
0
1
0
0
1
2
0
0
0
1
3
1
1
0
2
1
0
1
2
1
1
0
2
1
2
0
0
2
0
1
0
0
2
0
1
0
0
2
1
2
0
2
0
2
0
0
1
1
0
0
0
1
0
2
1
0
0
1
0
2
2
0
0
0
1
1
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
2
2
2
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
5
1
0
0
1
0
1
0
0
0
0
1
1
0
0
0
1
0
0
1
0
3
1
2
3
0
0
2
1
0
1
0
2
0
0
0
0
1
2
0
1
0
2
0
0
0
0
0
1
1
1
0
2
0
0
0
1
0
1
2
2
0
1
0
1
2
2
0
1
1
4
0
0
1
2
1
0
2
0
1
1
1
0
1
0
2
2
1
1
1
0
1
1
0
1
1
0
0
0
0
1
0
0
2
0
0
0
1
0
1
1
2
2
1
2
0
0
0
1
0
1
0
0
2
0
2
1
0
2
1
1
0
1
1
2
1
2
0
0
2
0
2
0
0
1
2
1
1
1
1
2
1
1
0
0
1
0
2
0
0
0
1
0
1
0
1
0
1
0
2
1
0
1
2
0
0
0
2
0
0
0
0
0
0
0
2
0
1
1
0
0
0
1
3
0
0
0
0
0
2
0
0
1
0
0
1
0
0
1
1
0
2
1
0
2
1
1
0
0
0
2
0
3
2
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
2
2
2
1
0
0
2
0
0
1
4
2
0
1
1
0
2
2
0
1
0
0
2
0
0
3
0
0
2
2
1
0
0
0
2
0
1
1
0
0
3
0
0
1
0
0
0
0
0
2
0
0
1
2
2
0
0
0
1
0
0
0
1
0
1
1
0
0
11
0
0
2
1
0
1
1
2
1
2
1
1
1
0
0
0
2
1
2
0
1
0
0
0
2
2
1
0
0
1
0
1
1
1
0
0
1
1
0
0
1
0
2
2
0
0
1
2
0
2
0
0
0
0
1
0
0
0
1
1
1
0
1
0
1
1
2
0
0
1
0
1
1
1
0
1
0
0
0
1
1
0
1
2
1
0
0
0
0
1
2
1
0
0
1
2
0
0
0
0
1
0
0
0
1
0
0
2
0
0
2
0
1
2
2
0
0
0
0
0
1
1
0
2
1
1
0
2
1
0
2
0
0
0
1
2
1
4
1
0
0
1
4
0
0
0
1
0
2
1
1
1
3
1
1
0
0
1
0
2
1
0
0
0
2
0
2
0
2
2
1
0
1
0
1
1
0
0
0
1
2
1
0
0
1
1
0
2
1
1
1
3
2
1
0
2
1
0
1
0
0
2
2
1
1
0
1
1
0
0
2
2
0
0
0
0
1
1
0
0
0
0
2
3
2
1
0
1
0
0
2
0
0
0
1
0
1
1
0
1
2
0
0
3
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
1
1
0
0
0
1
2
0
0
1
1
1
0
0
0
0
0
1
0
0
0
2
1
1
0
0
2
0
0
1
0
0
0
0
2
2
1
1
0
1
2
1
1
1
2
2
1
2
1
1
0
1
2
1
2
1
1
0
2
0
1
0
1
0
2
1
1
2
2
1
1
0
0
1
1
2
2
1
0
0
0
1
1
1
0
0
0
2
1
1
0
0
0
0
0
1
2
0
2
1
1
0
0
0
0
1
2
0
0
2
1
0
0
0
0
0
1
0
0
0
0
2
0
2
0
1
0
0
0
1
0
0
0
2
1
0
1
1
0
0
1
0
1
0
0
3
0
1
0
1
2
0
2
0
2
0
1
2
1
2
0
0
1
1
0
0
2
2
0
0
0
0
1
0
1
2
1
0
0
2
0
1
2
0
0
2
0
0
0
0
2
1
2
1
0
1
0
0
2
0
1
1
0
2
0
1
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
2
0
2
0
2
0
0
2
0
0
0
2
0
1
1
0
2
2
2
1
1
1
0
2
0
0
2
2
0
0
0
2
0
0
0
0
0
1
1
2
0
1
0
0
0
0
2
3
1
1
0
2
2
0
0
0
1
1
2
0
2
0
1
1
0
0
0
0
2
2
0
1
2
0
2
1
1
0
1
0
1
0
2
1
1
0
0
2
0
0
1
0
0
1
0
0
0
1
1
0
2
2
0
0
2
0
1
0
0
1
1
0
3
2
2
2
0
1
0
0
0
1
0
1
1
0
1
2
1
0
0
0
0
1
1
2
0
0
0
2
1
0
2
2
0
1
1
2
0
0
0
2
0
0
0
2
1
1
0
0
1
0
0
0
1
1
0
0
1
1
0
0
0
1
2
1
0
2
1
2
2
0
0
1
0
1
2
0
0
1
1
1
1
0
0
1
1
2
0
0
2
0
0
1
0
0
1
0
0
0
0
0
1
0
1
1
1
0
1
1
0
1
1
0
1
0
1
0
0
0
0
0
1
0
2
1
1
0
0
0
1
0
0
2
0
1
2
0
1
1
1
0
0
2
0
1
0
0
0
0
2
2
0
0
2
0
0
0
1
2
1
2
2
1
1
0
1
0
0
0
0
0
0
0
2
2
0
1
0
2
0
1
0
2
0
2
0
0
0
1
0
1
0
1
0
1
2
0
0
0
1
1
2
0
0
0
0
1
2
1
1
0
1
0
2
1
2
0
1
0
0
0
2
0
0
2
1
1
1
1
0
0
1
0
1
0
0
2
1
0
0
2
2
1
0
2
2
0
1
0
0
1
1
0
2
0
2
2
0
2
0
1
1
0
0
0
0
0
2
1
1
3
0
1
0
2
0
0
0
0
1
2
0
2
0
2
1
1
1
0
1
0
1
0
2
0
2
0
0
1
1
0
0
0
0
1
0
1
0
2
0
2
1
0
0
0
0
0
0
2
1
0
1
1
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
1
1
0
1
2
0
1
2
0
2
0
0
0
1
0
0
1
2
0
0
1
1
0
0
0
2
1
0
0
5
0
1
0
0
2
1
0
0
1
2
0
0
0
1
1
0
0
2
1
0
0
1
0
1
1
0
1
0
0
0
1
0
0
0
0
0
1
1
1
0
1
2
0
1
1
2
1
0
0
2
1
0
1
0
1
1
0
1
0
1
2
3
0
0
1
0
1
2
0
0
1
1
0
2
1
0
2
0
0
0
0
0
0
0
1
0
1
0
2
0
0
1
1
0
1
0
0
1
1
2
0
0
1
2
0
2
1
1
2
1
0
0
1
1
0
0
0
1
0
2
1
0
0
0
0
0
0
0
2
1
0
2
0
2
0
0
1
2
0
1
0
1
0
1
0
1
0
0
1
0
1
0
0
2
2
2
0
2
1
1
1
2
1
2
1
2
1
2
0
0
0
0
2
2
1
0
2
1
0
1
1
1
0
2
1
1
1
0
0
1
1
2
1
2
1
1
1
0
2
0
0
1
2
0
2
0
2
0
1
1
0
0
1
0
1
0
0
0
0
2
1
1
0
0
2
1
2
2
0
0
1
0
0
0
0
0
2
0
2
1
0
0
1
0
1
0
0
1
0
1
1
1
1
1
2
0
0
0
0
0
0
1
2
0
1
2
0
1
1
0
1
2
0
0
3
0
0
0
2
0
0
1
1
2
1
1
0
0
0
0
0
1
0
2
1
1
1
0
0
1
1
2
1
0
0
0
0
0
1
1
0
0
2
5
0
0
1
0
0
2
0
0
2
1
0
0
1
0
1
0
0
2
0
0
1
0
1
2
2
0
0
2
0
0
1
2
1
0
0
2
0
0
1
2
0
7
2
0
0
1
2
0
0
1
2
0
0
2
1
0
1
2
2
0
0
1
1
2
0
2
0
6
2
1
2
3
0
1
0
0
0
0
1
1
0
1
0
2
2
1
3
0
1
0
0
0
2
0
1
2
0
0
2
0
1
1
1
1
2
0
1
0
1
0
0
2
0
0
1
1
0
1
0
0
2
2
0
0
2
1
2
2
0
1
0
1
0
0
0
2
1
0
1
1
0
0
2
0
0
0
2
0
1
4
0
0
0
0
0
0
0
2
2
0
1
0
1
0
1
0
0
0
1
0
1
0
1
1
1
0
0
1
0
1
1
0
0
2
0
2
0
0
0
0
1
1
1
0
1
0
0
0
1
1
1
2
2
1
0
1
0
0
0
1
2
0
2
1
1
2
1
0
0
0
1
0
1
0
1
0
1
1
1
0
1
0
0
0
0
1
2
1
1
0
0
0
0
2
0
1
3
1
0
1
1
0
2
1
1
2
0
0
1
2
2
0
2
0
2
2
1
0
1
1
1
1
0
0
0
1
2
1
1
5
0
0
0
2
0
0
1
1
1
2
1
0
0
0
1
2
0
0
3
0
1
2
0
0
0
0
2
0
4
0
0
0
0
1
1
1
0
0
1
0
2
1
1
2
0
0
2
1
1
1
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
4
0
1
1
1
0
2
1
2
1
0
0
1
2
0
0
2
1
0
1
1
0
0
0
0
0
0
2
0
1
1
1
1
0
1
0
0
0
0
2
1
0
0
2
1
0
2
1
3
2
1
1
0
2
0
2
2
2
1
0
1
0
1
2
0
2
1
0
0
0
0
2
0
0
1
0
2
4
0
1
0
0
1
0
2
0
1
1
1
1
0
1
0
0
0
0
1
0
0
0
0
2
3
0
0
1
2
4
1
2
0
0
0
1
1
0
0
0
1
0
0
1
1
2
0
0
1
0
0
2
1
0
2
0
0
2
2
2
2
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
1
1
0
0
1
0
0
0
0
0
1
1
0
0
2
0
2
1
1
1
0
0
0
1
0
0
3
1
1
0
0
1
1
0
1
1
2
1
2
0
0
1
1
0
2
1
0
1
2
0
1
2
0
3
2
0
0
2
1
0
0
2
7
1
2
2
0
0
0
1
2
2
0
1
1
1
1
0
1
1
0
2
0
0
2
0
2
0
2
2
0
1
1
0
2
0
2
1
0
0
0
0
0
1
1
0
2
2
0
1
1
2
0
0
3
1
0
0
2
0
0
0
2
1
0
2
1
1
1
0
1
1
0
0
0
0
2
2
2
2
0
0
0
2
2
1
1
0
1
0
0
1
1
1
1
0
2
2
0
1
0
0
0
1
1
2
2
0
0
1
0
2
2
0
1
2
0
2
1
1
0
1
0
0
2
0
1
0
1
1
2
0
1
0
0
0
2
0
1
0
2
0
2
0
1
1
1
1
0
1
2
0
0
4
2
0
0
1
1
0
0
1
0
1
0
0
2
1
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
3
0
2
1
0
0
5
1
0
2
0
0
0
0
1
1
0
1
1
1
0
0
1
0
0
1
1
1
0
2
0
1
1
2
0
2
0
2
1
0
1
2
4
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
3
0
1
0
1
1
0
1
2
0
1
0
0
4
0
1
0
0
0
0
0
1
1
1
1
0
2
1
1
2
1
2
0
0
0
1
0
0
0
0
1
0
1
1
0
1
0
2
0
0
1
0
0
0
0
1
2
0
0
0
0
1
0
1
1
0
1
1
1
2
0
1
2
1
0
0
1
0
1
1
2
1
1
0
0
0
2
0
1
2
2
2
0
0
2
0
1
1
0
0
0
2
0
0
3
1
0
0
0
1
1
1
0
1
0
0
0
0
4
0
0
0
0
0
4
0
0
1
1
0
2
0
1
1
0
2
1
0
0
0
0
0
2
1
2
0
0
0
2
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
1
2
2
0
1
0
0
0
2
2
0
0
0
2
1
0
0
0
0
1
2
2
0
1
0
1
0
1
1
1
1
0
0
0
1
0
5
1
2
1
0
2
0
0
1
2
0
0
1
0
0
0
0
0
0
0
1
0
2
2
1
0
2
0
2
2
0
0
1
1
0
1
1
0
0
1
0
0
2
0
0
1
2
0
2
2
0
2
0
1
0
0
2
0
2
1
2
1
0
0
3
1
0
2
2
0
1
0
1
1
0
2
2
0
0
0
0
0
1
1
0
3
2
2
0
0
1
2
2
2
1
1
0
0
0
1
0
1
2
2
1
0
1
0
2
0
0
0
2
0
1
2
3
0
1
0
2
2
1
1
0
1
1
1
1
0
0
2
1
0
0
2
2
1
0
1
2
2
0
0
1
0
0
1
1
1
0
1
1
1
0
0
0
1
0
0
0
1
0
0
1
1
1
1
2
0
0
1
0
0
0
2
1
0
0
1
2
2
1
2
0
1
0
1
1
0
2
0
1
0
0
0
2
1
0
0
1
2
2
2
0
0
0
1
2
0
0
0
0
0
0
0
0
1
1
2
0
2
0
0
1
0
2
0
0
2
2
1
0
2
2
0
2
0
1
1
0
1
0
1
2
1
0
2
2
0
1
1
1
2
0
0
0
0
1
1
0
0
0
0
1
1
0
0
1
1
0
0
3
2
1
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
2
1
0
2
1
1
1
1
1
0
0
2
2
0
0
0
0
1
0
2
1
1
0
2
2
0
1
0
0
0
2
1
0
1
2
1
1
0
1
2
0
0
0
2
1
1
0
0
2
2
0
0
0
1
4
0
0
0
0
0
1
0
0
1
0
0
1
2
1
2
1
2
1
0
0
2
0
0
1
0
0
0
2
0
0
0
1
4
0
2
1
1
2
0
1
2
1
0
0
0
1
0
0
0
0
2
2
0
2
0
1
1
0
0
0
0
0
0
0
0
0
1
3
0
2
0
0
0
2
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
2
2
1
0
1
2
1
0
0
0
2
2
0
0
0
2
0
1
1
1
0
2
2
0
2
2
0
2
0
2
2
0
1
0
1
0
0
1
0
1
0
2
0
0
1
1
0
1
1
1
0
1
1
0
0
2
2
0
0
0
1
1
2
0
2
0
1
0
1
1
0
2
0
2
1
1
1
0
0
1
0
0
1
0
0
0
0
1
0
1
0
2
1
0
1
0
0
0
0
0
0
0
0
2
0
1
0
2
1
0
0
1
0
1
0
0
1
0
1
0
2
1
1
0
2
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
1
1
1
0
2
1
1
2
0
1
0
0
2
0
1
2
0
0
0
0
1
1
2
0
1
0
0
0
0
0
1
3
1
0
1
1
1
0
0
1
0
0
3
0
0
2
0
0
1
1
1
2
0
0
2
1
0
0
0
0
0
2
2
1
1
0
1
0
0
2
1
0
1
2
1
0
1
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
3
0
0
1
1
0
0
1
1
1
1
1
1
0
2
1
1
1
1
0
0
0
0
0
0
1
0
0
1
0
0
3
0
2
2
2
1
0
4
0
1
2
0
0
0
1
2
0
2
0
2
0
1
0
2
0
0
2
0
1
2
2
1
0
1
0
0
0
0
2
0
1
0
2
0
2
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
1
1
2
0
0
0
2
1
2
0
2
0
2
1
0
1
0
0
1
0
1
1
2
1
2
1
2
0
0
0
2
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
2
0
1
1
0
0
0
0
0
2
2
0
2
0
0
2
1
2
1
2
0
0
0
1
0
0
1
1
1
0
0
0
2
2
1
1
0
1
0
0
3
1
2
0
1
2
0
3
0
1
2
1
0
0
1
0
1
1
0
0
2
2
2
0
2
1
0
1
1
0
2
1
0
0
0
2
1
1
1
0
1
1
3
2
1
0
2
0
2
2
1
0
1
1
1
0
0
1
0
0
0
0
2
2
1
0
1
0
0
2
1
2
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
2
1
1
0
0
1
2
0
1
0
2
0
0
2
0
2
1
0
0
2
2
0
1
2
1
1
2
0
0
0
0
2
0
1
0
0
1
1
0
0
0
0
0
0
2
2
0
0
2
1
0
2
0
6
1
2
1
0
1
0
0
0
0
1
0
1
3
0
1
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
1
0
1
1
2
0
2
0
0
1
0
0
0
0
0
1
2
2
0
1
2
0
0
2
2
1
0
0
1
2
1
2
0
2
3
1
0
1
0
0
1
2
3
0
0
2
0
0
0
0
0
0
3
0
1
0
0
1
1
0
1
0
1
2
0
0
0
1
0
1
0
0
0
2
1
0
0
2
2
1
0
0
0
2
1
2
0
0
0
1
0
1
0
0
0
1
0
0
0
0
2
0
1
0
1
0
2
2
0
1
0
2
2
2
2
0
0
0
3
1
0
2
0
0
2
1
2
0
0
1
2
0
0
0
0
0
1
0
0
0
0
2
1
0
2
0
0
0
1
2
2
0
2
0
2
0
2
2
1
0
0
0
2
0
0
0
2
0
1
1
1
2
1
1
0
0
1
0
0
1
1
2
1
2
1
0
0
0
2
0
2
1
1
0
0
2
1
1
0
2
1
0
0
0
4
0
2
0
0
1
0
1
0
1
0
2
0
1
0
2
0
1
0
2
0
2
0
2
1
2
2
0
0
2
1
0
0
2
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
2
2
0
2
0
0
1
0
0
1
2
0
2
1
0
0
1
1
2
0
1
1
1
2
0
0
0
0
1
1
0
0
0
2
1
1
0
0
0
0
2
1
2
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
2
2
1
0
1
1
1
1
1
1
1
2
2
2
1
1
0
1
1
0
0
0
1
2
2
2
0
1
3
0
0
1
1
1
0
2
0
0
0
0
0
1
0
1
1
2
0
2
0
2
0
1
2
1
1
0
1
0
2
1
2
0
0
0
0
1
0
0
0
0
1
2
0
0
0
1
2
1
0
1
2
0
0
0
0
1
2
0
0
0
0
2
1
0
0
2
0
0
2
2
1
1
0
0
1
1
1
0
0
1
0
1
1
0
1
0
0
1
0
0
2
2
1
3
1
0
1
0
0
0
0
1
1
1
0
0
0
0
0
1
1
0
1
0
0
0
1
0
1
2
1
1
0
0
0
0
0
0
1
0
2
1
2
2
1
0
3
0
0
2
0
0
1
1
1
0
2
1
0
1
2
1
0
2
0
1
1
1
2
0
0
0
1
1
0
0
0
0
4
2
0
0
2
2
2
0
0
0
0
1
1
1
0
0
2
2
1
2
0
0
1
0
2
1
2
0
1
2
0
0
0
0
0
0
1
0
1
4
0
1
1
2
2
0
0
0
0
2
1
0
0
2
0
0
0
1
1
0
1
0
0
0
0
3
0
2
1
0
0
3
0
0
0
0
1
1
2
0
2
2
1
0
1
0
1
0
2
1
0
0
1
0
4
2
0
1
0
0
0
0
1
1
0
1
1
0
0
2
0
0
0
0
1
0
0
0
2
0
0
1
2
2
0
0
0
0
1
0
0
0
1
0
0
0
0
2
4
0
2
1
0
2
0
0
0
2
2
0
2
0
2
1
0
0
1
0
0
0
2
0
0
0
1
1
0
1
2
1
0
0
1
0
0
3
0
2
1
0
1
0
0
3
2
1
0
2
1
0
2
0
0
0
1
0
0
1
0
0
0
3
1
1
0
1
0
2
0
0
3
0
0
1
2
1
1
2
0
1
1
3
0
2
2
0
0
0
1
2
0
0
1
0
0
0
3
1
1
1
0
0
1
1
2
1
0
0
1
0
0
0
0
1
0
1
0
2
0
0
2
1
0
4
1
0
2
0
0
1
2
1
0
0
0
0
1
1
1
1
1
0
0
2
2
2
0
0
1
1
0
0
0
1
2
1
1
0
0
0
1
1
0
1
0
1
1
0
1
0
6
2
0
0
2
0
1
0
1
0
0
0
0
1
1
0
2
0
0
1
1
1
3
0
2
0
1
0
2
0
1
0
1
0
3
2
0
0
0
1
0
1
0
1
1
2
1
0
0
1
0
0
1
0
1
2
1
0
1
1
2
1
0
0
3
0
0
1
2
0
2
3
0
1
1
0
0
2
1
0
0
4
1
0
0
0
1
1
0
1
0
0
1
0
0
0
2
0
0
1
0
7
0
2
0
0
1
2
0
2
5
1
2
2
0
0
1
0
0
0
0
0
2
0
1
1
0
1
0
0
0
2
1
0
0
1
1
2
0
1
1
0
0
1
2
0
0
0
0
1
1
0
0
1
0
0
2
0
1
1
2
0
2
1
1
0
0
0
0
2
1
0
2
0
0
0
3
2
1
0
0
0
0
0
0
1
0
1
2
1
0
0
0
1
0
1
1
1
1
0
0
2
2
0
2
2
1
1
0
1
1
2
0
0
1
0
1
2
1
0
0
0
0
2
0
0
1
0
2
2
0
0
1
0
1
0
2
2
1
1
0
2
1
0
1
1
2
1
2
0
1
0
1
2
1
0
2
0
2
0
0
0
0
1
2
1
1
0
1
0
1
1
0
0
0
2
0
1
0
1
0
0
2
2
0
1
1
1
0
1
2
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
2
0
1
0
1
0
0
1
0
1
1
0
0
1
2
1
0
1
0
0
1
4
1
0
2
0
0
1
2
0
1
2
2
0
0
1
1
0
1
0
2
0
2
0
1
2
0
0
1
0
0
0
0
2
0
2
0
1
0
1
0
0
1
2
2
1
2
0
2
1
0
0
0
1
0
1
2
0
0
2
0
0
0
2
0
1
0
0
1
1
1
1
1
0
0
1
2
2
0
0
0
0
1
0
0
0
1
0
2
2
0
0
1
0
1
2
2
0
2
0
2
0
2
2
0
0
1
1
2
0
0
1
0
0
3
0
2
2
0
0
1
0
1
0
2
1
0
0
0
0
0
1
0
0
0
3
2
0
1
0
1
0
0
0
1
1
2
2
2
0
1
1
2
1
0
2
1
2
0
2
2
1
1
0
0
1
0
0
0
0
0
1
0
0
2
1
3
2
0
2
0
2
0
1
0
1
1
2
1
4
2
0
2
1
0
0
0
0
1
1
1
1
0
1
0
0
2
1
1
2
0
1
0
1
0
2
0
0
2
1
2
1
0
0
2
0
1
0
1
1
0
0
0
1
2
0
0
0
0
0
0
2
1
1
0
1
1
0
0
0
1
1
3
2
1
1
0
1
2
0
0
2
0
1
1
0
1
1
0
0
3
0
0
2
0
0
0
0
0
0
0
2
1
1
1
0
0
0
0
1
0
6
1
1
1
1
2
1
0
0
5
0
1
0
0
0
0
0
1
2
0
0
0
0
1
2
0
0
0
2
10
1
0
1
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
2
0
0
2
1
0
1
0
2
2
0
2
1
0
5
0
1
0
0
1
2
0
0
1
2
0
2
1
1
1
1
2
1
2
2
2
2
1
0
2
0
1
0
1
2
0
0
2
2
0
2
1
1
1
1
0
0
0
2
2
0
1
1
0
0
1
0
0
1
0
1
1
2
0
2
2
0
0
0
0
1
0
2
0
0
0
1
0
0
2
2
0
0
2
2
2
1
0
0
1
1
0
0
1
0
0
0
1
1
0
0
2
0
0
1
0
0
1
2
0
0
1
1
0
2
2
0
2
0
0
0
0
2
0
2
0
0
1
2
0
0
0
2
0
0
0
0
1
0
2
0
0
1
1
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
1
0
2
0
0
1
1
1
1
1
0
0
1
0
1
1
2
2
2
0
0
1
1
0
0
1
0
0
3
0
0
0
1
3
0
1
0
1
0
1
0
0
0
0
0
5
1
0
1
0
0
3
0
0
0
2
0
0
0
1
1
2
0
0
1
0
0
1
1
0
1
1
3
1
1
2
0
0
0
3
0
0
1
0
0
0
1
0
0
1
0
3
1
1
1
0
0
1
1
0
0
0
0
1
4
2
1
0
1
1
1
2
1
1
2
3
0
1
1
0
0
1
1
0
0
2
1
1
0
0
1
0
2
0
2
0
0
1
1
1
0
0
0
0
0
0
0
1
1
0
1
2
2
0
2
1
1
1
1
0
2
1
0
0
2
1
0
1
1
0
0
0
0
0
0
0
1
1
2
0
1
0
0
1
0
1
0
1
0
0
0
0
2
0
0
0
1
1
2
1
0
2
1
1
0
1
0
1
0
0
1
0
0
1
0
2
2
0
2
1
1
2
0
0
0
0
2
2
0
2
2
0
0
1
1
0
0
2
2
1
1
1
0
0
0
0
0
2
1
1
0
0
0
0
2
0
1
0
1
1
0
0
0
1
1
2
1
1
1
0
0
0
1
2
0
1
1
0
2
1
2
4
0
0
1
0
1
1
2
1
0
0
1
1
1
2
1
1
0
1
2
0
9
1
0
1
1
0
0
1
0
0
0
0
0
0
1
1
2
0
0
0
2
0
0
0
1
4
1
0
0
0
0
1
1
0
1
1
1
0
0
0
0
0
1
1
2
1
0
0
0
0
0
1
1
0
1
1
0
0
0
1
2
0
1
0
0
0
2
2
0
0
0
0
0
2
1
0
0
0
0
0
2
1
0
1
1
0
2
1
2
0
0
0
1
0
2
0
1
0
2
1
1
2
0
1
0
1
0
1
1
0
1
1
1
1
3
2
0
1
1
2
0
1
0
2
1
0
2
0
1
0
0
0
0
2
2
2
1
1
0
0
1
2
0
1
2
0
2
2
0
1
0
1
2
1
0
1
0
1
2
0
1
1
3
0
1
0
0
0
2
0
0
2
1
2
1
2
0
2
0
0
0
1
3
0
2
0
0
0
0
3
2
0
0
1
0
0
2
0
0
2
0
2
0
1
0
0
0
1
0
2
2
1
1
2
0
0
1
0
1
2
1
0
2
0
0
3
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
2
3
0
0
2
0
0
0
0
0
0
0
1
1
0
0
1
3
2
1
0
0
2
2
1
0
0
3
0
0
0
1
2
0
2
0
2
0
0
1
0
1
0
2
1
1
1
2
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
3
0
1
2
3
0
1
2
0
1
0
2
1
2
1
1
2
2
0
0
2
0
0
0
0
1
1
0
2
2
0
2
2
0
1
1
2
1
1
0
0
0
2
2
1
1
1
2
0
1
1
0
0
0
2
1
1
2
1
0
0
1
0
1
1
1
1
0
2
0
1
2
0
0
2
1
1
2
2
0
2
1
1
0
0
2
1
1
0
2
0
1
1
1
0
0
1
0
1
2
1
0
1
0
0
0
1
0
1
3
1
0
0
0
0
0
1
1
0
0
1
1
1
0
0
0
0
0
2
0
1
0
3
0
1
2
0
1
0
0
1
1
2
2
2
1
1
1
0
1
0
2
2
0
0
0
2
1
0
1
1
0
0
1
1
0
0
0
2
1
1
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
1
0
0
2
1
1
0
0
1
0
0
0
0
2
1
0
3
0
0
0
2
0
0
2
1
0
0
1
1
0
2
0
0
0
1
0
1
0
3
0
1
0
1
2
2
1
1
2
0
1
0
2
0
1
0
2
1
1
1
1
0
1
0
0
0
2
0
0
1
1
0
1
1
0
1
0
1
0
2
1
2
0
1
1
2
2
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
2
0
0
2
0
3
0
2
2
0
2
0
0
0
0
1
0
2
2
1
1
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
2
0
2
0
2
2
0
2
0
1
2
1
0
1
2
2
0
0
1
1
0
1
0
2
0
2
0
1
1
0
1
2
0
0
0
0
1
0
2
1
1
2
0
1
0
2
0
1
1
3
3
2
0
1
0
2
1
1
1
0
0
1
0
1
1
1
0
0
1
2
0
1
1
0
1
0
1
2
0
0
1
0
0
0
2
1
0
2
5
1
1
0
0
0
0
1
0
1
1
0
0
0
1
0
2
1
0
0
2
0
0
1
2
1
0
0
0
1
0
2
0
2
0
0
2
2
0
0
2
3
1
1
0
0
0
0
0
1
2
0
0
1
1
1
0
0
2
0
0
0
0
0
0
0
2
1
0
1
0
0
1
0
1
2
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
2
0
1
3
0
0
0
0
2
0
0
2
0
1
0
0
0
1
2
2
0
0
0
0
1
1
1
1
2
1
2
1
1
1
1
0
0
3
1
1
2
0
1
0
1
0
1
0
0
2
1
1
0
2
0
0
1
0
1
1
1
1
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
2
0
1
0
1
1
1
1
1
0
0
1
0
2
0
1
0
1
3
1
0
1
1
2
0
2
1
0
0
0
0
2
1
2
0
1
0
0
0
0
0
0
0
1
2
0
1
1
2
1
1
1
0
0
1
0
1
2
1
0
2
0
0
1
3
2
2
1
1
1
2
1
1
1
2
0
0
2
0
1
3
0
1
0
0
2
1
1
1
0
1
1
1
2
0
0
0
0
0
0
0
0
1
0
0
1
2
1
0
0
2
0
1
0
1
0
0
2
0
2
0
1
0
1
1
0
1
0
1
1
1
1
1
0
0
1
2
0
2
1
1
1
2
1
0
1
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
2
1
0
0
0
2
0
0
0
0
0
0
3
1
0
1
1
0
0
1
2
0
0
2
0
2
0
0
0
0
0
2
1
3
1
0
0
1
2
0
0
1
0
0
1
1
0
1
2
3
0
2
1
0
2
0
0
0
1
0
1
2
0
0
0
0
2
0
1
1
0
0
1
0
2
0
2
0
0
2
0
2
0
0
0
0
2
0
0
2
2
0
1
0
2
1
0
0
0
0
1
0
0
1
2
2
0
1
0
0
1
0
0
1
0
1
2
2
1
1
0
1
0
0
0
0
1
1
1
0
2
0
0
2
0
0
0
0
1
2
1
1
2
2
1
4
0
1
2
2
1
1
1
0
0
0
1
5
0
2
0
0
1
1
2
0
3
0
1
1
2
2
0
1
2
1
1
1
1
1
0
2
2
1
0
0
0
2
0
2
1
0
0
1
1
1
1
1
0
2
2
0
0
2
1
6
2
1
0
0
0
0
2
1
0
0
1
1
1
1
1
0
0
0
2
1
2
2
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
1
0
2
1
0
1
1
0
0
2
1
1
0
1
0
2
1
2
0
2
1
0
0
0
5
0
0
1
0
1
1
0
0
0
3
0
2
0
2
0
0
2
2
0
0
0
1
1
0
2
1
1
0
0
0
1
0
0
1
1
0
1
0
0
2
0
0
1
0
0
2
2
0
1
0
0
0
1
0
1
2
2
0
0
0
0
0
0
5
0
0
1
0
0
1
1
1
0
0
0
1
0
1
1
0
2
0
0
0
0
2
1
1
0
1
0
0
1
3
1
1
0
0
0
2
0
0
0
0
2
1
0
1
0
0
2
1
0
0
2
1
1
1
1
0
0
2
1
1
0
0
1
1
0
0
0
0
1
2
0
1
0
0
2
0
2
0
1
0
2
1
0
2
2
1
0
0
0
0
0
1
0
1
2
1
2
2
0
0
0
2
0
1
0
0
1
1
0
2
0
1
0
0
0
1
0
0
0
2
1
0
1
2
0
0
0
1
1
0
0
2
0
2
2
2
2
0
0
1
2
0
1
0
1
1
0
2
0
0
1
0
0
0
0
0
1
0
2
0
1
0
0
1
0
1
1
0
0
1
2
0
1
1
1
1
2
1
0
1
2
0
1
2
1
0
2
0
0
1
0
0
0
1
0
1
1
0
2
1
1
2
0
2
1
0
0
0
2
0
1
0
1
1
2
0
0
2
1
0
2
1
1
0
0
0
1
0
0
0
0
0
0
2
0
0
2
1
2
0
1
1
0
0
2
0
0
2
0
0
1
0
0
0
1
2
1
1
2
0
2
0
0
1
0
2
1
2
1
1
1
1
2
0
0
1
0
1
1
0
0
0
1
1
2
1
0
1
0
0
1
0
0
0
0
1
2
1
2
2
0
0
1
1
0
0
1
0
1
2
1
2
0
2
1
0
1
2
0
1
1
0
0
0
0
1
2
1
2
0
1
0
0
1
2
2
0
2
1
1
2
1
1
2
0
0
0
0
2
1
2
0
1
1
0
1
1
0
2
0
0
1
1
0
1
0
3
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
2
0
0
0
0
3
0
2
0
2
2
1
2
0
2
0
0
2
0
1
1
2
0
0
0
0
1
0
1
1
0
0
0
0
1
1
2
2
2
0
1
1
2
1
0
1
1
0
0
0
1
2
1
0
1
1
0
1
0
0
0
1
0
2
0
1
1
2
1
0
4
2
0
1
2
0
0
2
1
0
2
0
1
0
0
2
2
0
0
0
3
0
0
0
0
0
0
2
0
1
1
1
0
0
1
1
2
2
0
2
2
2
1
0
0
2
3
0
1
1
1
1
0
1
0
0
0
2
2
0
1
1
0
0
0
0
2
0
0
0
0
1
2
0
3
0
1
0
0
1
2
2
2
0
0
0
0
2
1
0
1
1
2
0
0
1
2
1
0
0
0
0
2
0
1
1
1
0
1
2
1
2
0
2
1
2
2
0
2
1
0
2
1
1
1
1
2
0
3
1
2
1
0
1
0
0
0
1
1
2
1
0
1
0
1
0
1
1
0
2
2
1
2
0
0
1
1
1
0
1
1
0
0
2
1
2
2
0
1
0
1
1
3
0
0
0
0
0
2
0
1
1
0
2
0
0
1
1
0
3
2
0
0
0
1
0
0
0
1
2
1
0
1
0
2
0
1
0
1
2
1
0
2
1
0
0
2
1
0
0
0
2
0
2
0
0
0
0
0
2
2
2
4
1
0
0
1
1
0
1
0
1
2
0
0
2
1
0
0
0
0
0
0
1
1
0
1
2
0
0
0
0
2
0
1
0
0
1
2
2
1
2
0
0
0
0
0
1
2
2
0
0
0
0
1
4
2
0
1
0
0
2
0
0
1
0
0
1
0
1
0
1
1
0
1
4
3
0
0
2
1
0
1
1
2
2
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
2
2
0
0
1
2
1
0
1
0
1
0
0
0
0
0
2
1
0
0
1
0
0
2
0
2
7
0
0
2
0
2
2
2
0
0
2
0
1
0
0
0
2
1
0
1
0
1
0
0
1
0
2
2
2
0
0
1
0
1
1
0
0
0
1
2
0
0
1
1
0
1
2
0
0
1
0
0
1
0
1
2
0
0
1
0
0
2
1
0
0
2
1
0
1
2
0
0
0
0
2
0
2
1
1
1
0
1
2
0
0
2
2
1
0
0
2
2
0
0
2
0
1
1
0
2
0
0
2
1
2
1
1
2
0
1
0
0
2
0
0
0
2
0
2
0
1
0
2
2
0
1
2
1
2
0
2
1
2
0
0
1
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
2
0
2
0
0
0
3
1
0
1
1
1
1
2
2
2
1
0
1
0
2
0
2
2
0
0
0
2
0
2
1
0
1
0
0
1
0
0
1
0
2
0
1
2
0
0
0
0
2
0
1
1
0
0
1
0
1
0
2
0
0
2
0
0
0
0
1
0
0
0
3
2
0
6
3
0
0
1
1
0
0
0
2
2
1
2
1
2
1
2
1
2
1
0
2
1
2
0
0
0
1
0
2
0
1
0
0
0
0
2
2
0
1
0
0
1
0
0
0
0
0
1
0
1
1
0
2
1
0
0
0
0
0
1
0
0
0
2
2
2
2
0
1
2
0
1
2
2
0
0
0
0
0
0
1
1
2
1
0
2
3
0
0
1
0
0
1
2
2
1
1
0
0
2
1
2
0
0
1
0
1
2
0
0
2
2
0
1
1
0
1
1
0
0
2
0
0
1
2
0
1
1
2
1
3
1
0
1
0
0
2
0
2
0
1
2
1
0
1
1
0
0
1
3
1
2
0
0
0
1
0
0
0
0
1
2
2
0
1
0
2
0
2
1
0
2
0
0
0
2
2
0
2
0
3
0
0
0
2
2
1
0
2
0
1
0
3
0
0
0
1
1
0
0
0
0
1
0
2
1
0
1
0
0
0
0
0
1
1
0
1
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
1
2
0
0
1
1
1
0
2
1
2
0
1
1
2
1
2
0
2
1
0
0
0
0
1
0
0
0
1
1
2
2
0
0
0
0
0
1
1
1
0
0
0
1
1
0
2
1
2
0
0
1
1
2
0
0
4
2
0
0
3
0
2
0
1
1
0
2
1
0
1
0
1
0
1
0
2
0
2
2
0
3
1
2
0
0
0
0
1
0
0
1
3
1
0
0
1
2
1
1
1
1
1
0
0
1
0
1
0
0
1
0
2
0
3
0
1
0
0
1
2
1
3
0
0
0
2
2
1
1
0
0
0
0
2
0
1
1
2
1
3
0
0
1
0
0
0
0
0
1
0
2
4
2
0
1
2
2
0
0
0
0
0
0
2
1
2
3
0
0
0
1
1
1
1
0
0
1
2
0
0
2
0
1
1
0
0
1
1
0
2
1
0
1
0
0
1
0
0
0
0
2
0
2
2
2
0
0
0
1
1
2
0
0
0
1
0
2
1
1
0
2
0
0
2
0
2
2
2
1
0
0
0
1
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
1
0
2
0
0
0
0
1
0
1
0
0
1
2
1
0
2
1
0
1
1
0
1
2
0
2
0
0
0
0
1
0
0
1
1
2
0
1
1
3
2
1
1
0
0
2
2
0
0
1
1
5
0
0
2
0
0
1
1
0
1
0
1
2
0
0
0
1
0
1
0
0
2
2
0
1
0
0
0
2
0
2
2
1
1
0
0
2
0
2
0
0
1
1
0
3
0
3
0
2
0
0
0
2
0
0
0
0
2
0
3
0
2
0
0
1
0
1
0
1
1
2
1
1
3
1
0
0
1
2
2
1
0
0
1
1
1
0
2
1
1
2
2
1
1
1
0
0
3
1
1
1
0
0
3
2
1
1
0
1
0
1
1
1
2
0
2
0
1
0
2
1
0
0
3
1
0
1
0
1
1
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
3
1
0
0
1
0
0
2
1
0
0
0
1
1
0
0
0
0
0
0
1
0
2
2
1
0
0
1
2
0
2
0
1
1
4
1
0
2
1
2
1
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
1
1
0
1
0
0
1
2
1
0
0
0
0
0
0
2
1
0
2
1
1
0
1
2
1
1
2
0
0
0
1
0
0
0
2
0
1
1
0
1
2
0
1
1
0
0
2
1
2
2
0
2
1
0
2
1
2
0
1
1
1
2
1
1
0
2
0
0
2
0
0
0
2
2
1
2
0
1
0
0
1
0
1
1
0
0
0
2
2
2
1
0
1
0
0
0
1
1
2
0
0
0
0
2
0
2
2
1
1
0
1
0
1
0
0
1
1
2
1
2
0
2
0
1
0
0
1
2
0
2
0
1
0
0
0
1
1
0
0
0
0
0
0
2
1
0
0
1
3
0
0
0
0
2
1
0
0
2
1
1
0
0
0
0
0
2
2
2
0
2
0
0
2
0
0
2
0
0
1
1
0
1
1
2
0
2
1
0
2
0
0
1
0
0
0
0
2
0
0
1
1
0
2
5
1
0
0
2
0
0
2
0
0
0
0
0
1
1
0
1
3
1
0
1
1
0
0
1
0
0
1
0
0
2
2
0
0
4
1
1
0
1
1
0
2
1
1
0
1
1
0
2
1
0
0
1
2
1
0
1
2
0
0
0
1
0
2
0
0
3
0
0
0
2
1
2
0
2
0
0
2
0
1
0
0
1
0
0
0
1
0
1
0
1
0
2
1
1
0
1
0
0
0
0
2
1
3
1
2
0
1
2
0
1
0
1
0
0
0
1
0
0
0
0
1
1
0
1
2
2
0
1
3
0
2
0
0
1
2
0
2
1
0
1
2
0
0
0
0
0
2
0
1
1
2
0
2
2
0
0
2
0
0
1
0
0
1
0
1
0
2
0
2
2
0
1
2
0
2
0
0
1
0
0
1
0
0
1
1
1
1
0
1
2
0
2
0
2
0
2
1
2
2
0
1
1
2
1
2
0
0
0
2
0
1
0
0
0
2
0
0
0
1
0
0
2
0
2
2
0
0
0
3
2
0
0
0
1
2
1
2
2
0
3
0
1
0
0
1
0
0
1
2
0
2
0
0
1
0
1
1
0
0
1
0
0
0
2
0
0
0
1
2
2
2
0
2
0
2
1
1
1
1
2
3
1
0
0
2
2
1
1
1
1
1
0
0
0
1
0
0
2
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
4
0
1
1
0
0
0
1
0
0
0
0
5
1
3
0
2
1
1
2
2
0
1
0
1
0
1
0
0
1
0
2
0
3
0
1
0
0
2
1
0
1
1
0
0
1
2
0
0
0
0
2
1
0
2
1
0
1
1
1
1
2
1
0
4
0
0
0
0
2
2
2
1
0
0
2
0
0
0
0
0
1
1
1
0
0
2
0
2
0
0
1
0
2
0
0
1
1
0
0
0
2
2
0
1
1
0
2
1
0
2
1
2
2
0
0
2
0
8
2
1
1
1
0
1
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
1
2
1
0
1
0
0
0
0
2
0
0
2
0
0
1
0
2
0
0
0
1
1
2
0
0
0
0
1
1
0
1
0
0
0
0
0
2
1
2
0
0
2
0
1
0
0
2
1
0
0
2
2
3
0
0
0
0
0
2
0
0
1
0
0
2
0
2
0
1
1
2
1
2
2
2
0
0
0
2
0
2
1
1
0
0
0
0
0
0
0
2
2
0
0
0
1
0
1
0
2
1
1
0
1
0
1
0
0
2
3
1
0
0
1
0
0
2
1
1
0
0
0
0
2
2
0
1
0
0
1
0
0
1
1
2
1
1
0
1
0
0
0
0
1
0
0
2
0
1
0
0
0
0
1
2
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
1
0
1
2
1
0
0
0
2
3
0
1
1
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
1
0
1
1
0
0
0
2
2
2
0
0
3
0
1
1
0
0
2
1
0
0
1
2
2
1
2
1
2
1
0
2
1
0
0
0
1
2
1
0
2
0
0
0
1
0
1
0
2
0
0
1
2
1
0
0
0
1
1
0
1
0
1
1
0
2
0
1
1
1
1
1
1
0
0
0
1
0
0
1
0
1
0
0
1
0
1
1
0
0
0
2
0
1
0
0
2
2
2
0
1
0
0
0
1
1
2
2
0
0
1
2
1
0
1
0
0
1
0
1
0
0
1
1
0
1
2
1
0
2
2
2
2
1
1
1
2
1
3
3
2
1
0
2
1
0
1
1
0
1
1
0
1
0
0
1
0
0
1
0
0
2
0
0
0
0
2
0
2
4
2
2
0
0
2
0
0
1
0
0
0
0
2
0
1
1
1
1
1
0
2
1
1
1
2
1
0
0
0
0
1
3
1
0
0
2
1
0
0
0
0
1
0
0
0
0
1
1
1
1
3
1
1
1
1
1
1
2
0
2
1
0
0
2
0
0
1
0
1
2
1
0
0
1
1
1
2
0
0
1
0
0
0
0
1
1
0
1
1
0
0
2
0
3
1
0
0
0
0
0
0
0
0
0
1
2
0
1
1
0
1
1
0
1
2
2
1
0
2
1
0
1
0
0
2
0
2
2
0
0
0
0
0
2
1
2
2
0
0
0
0
1
0
2
1
3
2
2
0
1
2
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
2
0
1
0
1
0
0
1
1
0
0
0
0
2
2
1
0
0
0
0
0
2
1
1
1
1
0
0
0
0
0
4
2
1
0
0
2
2
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
3
0
0
0
1
2
2
1
1
0
2
0
2
0
2
1
2
0
0
0
0
1
2
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
1
2
1
1
0
1
1
0
3
2
2
0
0
1
0
2
2
1
0
1
1
2
0
0
0
1
1
2
1
1
2
0
0
1
0
1
4
1
0
0
0
0
1
1
0
0
0
0
2
0
2
0
0
0
2
1
0
1
1
0
0
0
0
0
3
2
2
0
0
0
0
0
2
0
0
2
0
1
1
1
0
0
2
1
1
0
0
2
0
1
1
1
2
0
2
1
3
1
2
0
0
0
1
2
0
0
0
0
1
1
1
0
0
0
1
2
0
3
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
2
0
0
1
0
2
0
1
0
0
1
0
0
2
0
1
2
0
0
0
0
2
0
1
2
0
0
0
0
0
2
1
0
2
0
1
1
0
0
0
1
1
1
0
0
0
0
0
0
1
0
2
0
0
1
1
0
0
1
0
1
0
1
1
0
0
1
2
0
2
0
1
3
0
0
0
0
0
2
2
1
1
1
2
0
0
1
2
0
0
2
2
2
1
1
1
0
0
1
0
0
0
0
6
2
0
0
0
0
2
1
0
0
1
1
0
2
1
0
0
0
1
1
1
0
1
2
1
0
2
0
0
2
0
2
0
2
1
3
2
0
0
0
1
0
1
0
0
1
0
0
2
0
1
0
0
0
1
1
1
0
1
1
2
0
2
3
2
0
0
0
2
0
1
1
0
1
1
2
1
0
1
0
4
0
0
3
1
1
1
0
1
0
2
0
0
1
1
0
0
0
2
0
1
0
2
0
2
1
1
1
1
2
2
1
1
0
1
1
0
0
1
0
2
1
0
0
0
0
1
2
0
0
2
0
1
0
0
0
1
1
0
1
2
1
2
0
0
1
1
1
0
0
0
0
1
2
1
0
0
2
1
0
2
1
2
2
0
0
1
3
0
0
0
0
2
2
0
0
1
0
0
0
0
0
1
1
0
1
2
0
2
0
0
0
1
2
0
0
0
1
1
0
0
2
0
0
1
1
0
0
2
1
1
0
0
1
2
1
2
1
1
0
1
3
0
0
0
0
0
1
2
0
2
0
0
0
0
0
2
0
1
1
1
1
2
1
0
2
0
0
0
0
0
0
0
1
1
2
0
2
1
0
1
2
2
2
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
1
1
1
1
1
0
1
0
2
1
1
1
1
0
0
1
1
0
0
0
0
1
1
0
0
1
2
0
0
0
0
0
0
1
0
1
0
1
1
1
2
0
2
2
0
0
0
1
1
2
2
1
0
1
2
0
0
2
2
2
1
1
0
2
0
0
1
0
1
0
1
2
1
1
1
0
0
1
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
2
2
0
0
2
0
0
1
2
1
0
0
2
1
0
0
0
1
2
0
0
0
0
0
0
2
1
2
1
0
1
2
0
0
0
2
1
0
0
1
0
3
2
1
1
2
1
0
1
1
0
0
0
1
1
0
0
0
1
1
2
0
0
0
0
0
0
1
1
0
2
1
0
1
0
0
0
0
1
1
2
1
1
0
0
0
2
1
1
0
1
1
0
1
0
1
0
0
0
1
1
0
0
2
1
0
0
0
0
2
0
0
1
0
0
1
1
1
1
0
0
0
0
0
0
2
0
1
0
0
1
2
0
1
0
2
2
2
2
2
0
0
1
1
0
0
1
0
0
1
1
1
1
1
0
1
2
1
1
1
0
1
1
0
2
0
1
0
1
1
2
0
1
2
1
2
0
0
1
0
1
0
1
2
1
2
1
1
1
1
0
1
0
2
2
0
1
0
2
0
0
0
0
1
1
2
1
2
2
1
0
1
1
1
0
0
2
0
1
0
1
0
1
0
1
0
1
0
0
1
2
2
0
2
1
2
1
2
0
0
0
0
0
0
1
1
0
0
1
2
0
0
1
1
1
0
2
1
0
1
0
0
2
0
1
0
0
1
1
0
0
0
0
1
0
1
2
0
2
0
2
1
0
2
0
0
2
0
1
0
1
0
1
0
0
2
0
0
0
1
0
3
1
1
2
0
0
2
1
0
0
0
2
0
0
0
1
0
1
0
2
2
2
0
2
0
1
2
1
0
2
1
2
2
1
0
1
0
0
1
0
0
0
1
1
1
0
0
0
0
1
0
1
1
2
0
0
2
0
2
1
0
0
2
1
2
1
2
1
0
2
0
0
0
2
0
0
2
3
0
1
2
1
2
1
0
0
1
0
0
1
1
0
1
0
0
1
0
0
1
2
2
0
1
2
0
1
1
1
2
0
2
1
0
0
1
1
0
0
0
1
1
1
0
0
1
1
0
0
0
0
2
0
1
4
0
0
0
0
1
0
0
2
0
0
0
0
0
3
1
0
2
1
0
0
1
1
0
1
1
0
0
0
0
1
1
1
2
0
0
2
0
0
1
1
1
0
2
1
0
2
0
1
1
0
0
0
1
0
1
1
1
0
2
2
0
1
2
0
2
1
2
2
0
1
1
1
0
0
2
1
1
0
1
0
0
2
1
2
0
0
0
0
0
0
1
2
0
0
0
0
3
1
1
0
1
2
0
0
0
2
0
0
0
2
2
2
0
1
0
0
1
1
1
1
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
1
2
0
1
1
1
2
3
2
2
1
2
2
1
0
1
0
1
2
2
2
0
1
0
0
0
1
0
0
0
1
0
2
2
1
1
0
0
4
0
0
0
0
0
0
2
1
0
0
1
0
0
2
0
0
0
1
1
2
1
1
0
1
0
0
1
1
1
2
3
0
0
1
2
1
0
0
1
0
1
0
1
1
1
1
1
1
2
1
0
0
0
0
0
0
0
0
1
1
1
1
0
0
2
0
2
0
0
4
1
0
0
3
1
0
0
1
1
2
2
0
1
0
0
0
1
2
0
0
1
1
1
1
2
1
0
0
1
1
0
0
2
0
0
1
0
0
0
2
0
0
2
0
1
0
1
0
0
0
1
1
0
0
1
2
1
0
0
2
0
0
1
0
2
1
0
0
0
0
0
2
1
0
0
0
1
0
1
0
2
1
0
0
1
1
0
1
0
0
2
1
2
1
2
0
1
1
0
1
1
2
5
1
2
0
0
0
1
1
1
0
0
2
1
0
1
1
0
1
1
0
0
1
0
0
2
2
0
1
2
0
1
0
1
1
0
0
2
2
0
0
1
0
2
2
0
0
0
2
0
0
1
1
2
0
0
0
0
1
1
1
0
2
1
1
0
0
0
0
2
1
0
0
2
0
2
0
0
1
0
1
1
2
2
0
1
1
1
0
0
0
2
1
1
1
2
0
2
1
0
1
1
1
0
1
0
1
0
0
1
0
0
0
1
1
2
0
1
2
0
0
1
2
2
0
0
2
0
2
0
0
1
0
2
0
0
2
0
0
1
0
1
3
1
0
0
1
1
1
2
2
0
1
0
0
0
0
1
1
2
2
0
1
0
0
1
0
0
0
0
1
0
2
3
0
2
2
0
0
0
0
1
2
1
0
2
0
0
0
0
0
1
0
2
0
0
0
1
0
3
0
0
0
0
2
1
1
1
2
0
1
1
2
0
2
1
2
1
1
0
1
1
0
0
1
0
0
0
0
1
2
1
0
0
0
0
2
1
0
0
0
0
0
1
0
2
0
1
1
1
1
2
3
0
0
0
1
0
2
0
2
0
0
1
0
2
0
0
1
0
0
0
0
1
1
1
0
0
2
0
3
1
0
0
0
1
1
2
0
2
0
2
1
1
0
0
0
1
0
1
0
0
0
0
0
1
1
0
2
2
0
0
0
2
0
0
1
0
0
0
0
2
1
2
0
0
1
2
1
0
1
0
1
4
1
2
2
1
1
0
2
0
0
0
0
2
2
0
1
2
0
0
0
1
0
1
1
1
0
1
0
0
0
0
0
0
1
2
2
0
0
2
1
2
0
0
1
0
0
0
0
2
1
1
1
0
0
1
0
2
1
2
0
0
2
1
1
1
1
1
2
0
0
0
1
0
0
1
1
0
2
1
1
2
2
0
2
1
0
2
1
0
0
0
0
0
1
2
0
1
1
0
2
0
1
1
2
3
1
0
2
1
0
1
1
0
2
1
2
1
0
1
0
2
0
0
0
1
1
2
1
2
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
2
1
1
0
1
1
2
1
0
0
1
0
1
2
2
2
0
0
0
0
2
0
0
0
4
0
2
0
1
0
1
0
0
0
0
2
1
0
1
1
1
0
2
0
1
2
0
0
0
0
1
0
0
1
1
0
1
0
1
2
0
1
2
0
0
1
2
1
1
0
1
0
0
0
0
0
2
1
0
1
2
2
0
0
2
0
0
2
1
1
2
0
1
0
0
2
1
1
0
0
0
0
1
2
1
0
1
2
1
0
2
1
0
2
1
0
0
0
0
0
3
2
0
2
0
2
1
2
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
2
1
0
0
0
2
2
1
0
5
1
0
2
0
1
1
0
0
1
0
0
1
1
0
1
0
1
1
1
0
1
0
1
1
0
0
0
0
1
0
0
1
0
1
1
1
2
1
1
2
0
2
1
0
2
4
1
0
2
1
1
1
0
0
0
0
0
0
0
0
0
2
0
0
1
1
1
1
1
0
2
1
1
1
0
0
0
0
1
0
0
1
0
1
0
2
1
0
1
0
2
0
0
2
0
0
2
0
0
0
0
0
0
2
1
2
1
0
0
0
1
1
1
0
0
0
1
1
1
0
1
2
0
1
1
3
0
0
1
0
2
0
0
0
2
1
1
0
0
0
2
1
0
0
1
1
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
1
1
1
0
0
0
2
1
0
0
3
1
0
1
3
0
1
1
2
1
1
0
0
0
0
2
0
1
1
0
5
1
0
2
1
1
1
1
1
0
0
1
0
4
2
0
2
0
0
1
0
0
1
1
0
0
0
1
0
2
1
1
0
2
1
0
0
0
0
0
0
0
0
1
1
0
2
1
2
1
1
1
0
0
1
0
1
2
0
1
0
0
2
0
0
2
0
1
2
1
0
0
0
2
0
0
0
0
0
0
2
0
1
1
2
0
1
2
2
0
1
0
1
0
0
1
1
1
0
0
0
0
0
7
0
1
0
0
1
2
1
0
2
0
2
0
0
1
2
1
1
1
1
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
2
0
0
2
1
0
1
2
2
2
0
1
1
1
0
1
0
2
1
0
1
1
2
2
0
2
2
0
0
1
2
0
2
1
0
2
1
1
0
0
0
1
1
1
1
2
2
1
0
0
2
0
1
2
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
4
1
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
2
0
2
1
1
0
2
2
1
2
2
1
1
0
2
0
1
1
2
0
1
2
0
2
1
2
0
0
1
3
2
0
0
0
1
0
0
2
1
0
1
1
0
0
0
0
0
0
1
1
1
0
1
1
0
0
0
2
0
2
0
2
2
0
0
2
2
2
0
2
0
0
1
0
2
2
2
0
1
1
0
0
2
1
1
0
0
2
1
0
0
0
0
2
0
3
0
2
0
1
0
0
1
1
0
0
2
0
1
2
0
0
0
1
0
0
0
0
1
1
2
2
0
1
0
1
0
2
1
1
0
0
0
1
0
1
2
3
2
2
1
2
1
1
1
3
1
0
0
1
1
1
0
1
0
1
0
1
0
0
0
2
3
0
1
2
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
1
0
0
1
0
1
1
0
0
1
0
0
0
0
0
1
0
0
2
1
0
1
0
0
2
0
0
0
0
0
1
2
1
2
8
1
0
0
0
0
0
0
1
1
1
1
3
1
0
0
1
0
1
0
2
1
1
2
0
2
0
2
0
2
0
2
0
1
1
2
2
1
1
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
1
0
1
1
2
2
0
1
0
1
0
0
3
2
1
0
2
1
0
0
3
0
0
2
2
0
1
1
0
0
2
1
1
0
0
0
0
0
1
0
1
0
0
1
1
0
1
0
0
2
1
1
0
0
2
0
2
1
0
1
0
0
3
1
0
1
0
0
1
1
2
0
0
3
0
0
0
2
1
1
1
2
1
1
1
0
0
0
0
0
1
0
1
2
0
0
0
2
2
0
0
2
2
1
1
0
1
1
0
1
1
0
0
0
0
3
0
1
1
1
0
0
0
1
1
0
1
1
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
2
0
2
1
0
0
2
2
0
2
1
0
0
3
0
0
0
1
1
2
1
0
0
0
1
1
1
0
2
0
0
1
1
0
0
1
0
0
0
2
1
2
0
0
1
0
0
2
0
0
0
0
0
1
1
0
0
2
2
1
0
0
0
2
1
0
0
1
1
0
1
0
2
1
2
2
0
0
0
1
2
1
1
3
2
2
2
0
0
1
1
4
1
2
1
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
1
1
0
0
0
1
0
0
1
0
0
2
1
0
0
1
1
0
2
0
3
0
0
2
1
1
1
0
0
2
1
0
1
1
0
1
0
0
0
2
0
1
0
2
0
2
2
1
0
1
2
0
1
0
1
0
2
1
1
0
1
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
1
0
1
0
0
0
0
2
0
1
1
0
0
1
0
2
0
0
0
2
0
2
1
2
0
1
0
0
1
0
1
2
0
1
0
3
0
0
1
0
2
0
2
1
1
0
1
1
1
0
0
2
0
2
0
1
0
1
0
1
2
0
1
0
0
0
1
1
0
0
2
0
1
2
0
1
0
2
0
1
0
0
0
2
1
2
0
0
0
2
2
0
2
0
0
1
3
0
0
2
0
0
0
0
2
2
2
0
0
1
1
2
0
1
0
2
1
2
0
0
2
1
0
0
0
0
2
1
1
1
2
1
0
0
0
0
0
2
1
1
0
1
0
1
1
0
1
0
0
1
1
0
1
0
1
1
0
1
1
0
1
0
0
2
2
0
0
0
2
1
3
1
2
0
2
0
0
1
0
0
0
1
0
2
0
0
0
1
2
1
0
2
0
0
0
0
2
0
1
2
1
0
0
1
2
11
1
1
1
1
0
1
2
0
0
0
1
0
1
0
0
1
0
1
2
0
0
1
0
0
0
3
0
0
0
0
0
2
2
0
2
1
0
0
0
1
0
0
0
2
0
2
2
1
1
1
2
1
0
0
1
0
0
2
0
0
0
0
1
0
0
2
3
3
2
0
3
1
1
0
0
0
2
0
1
0
0
0
0
0
1
1
2
1
3
0
1
1
0
2
1
1
0
1
1
0
0
0
1
1
0
1
0
0
0
2
0
1
0
1
3
0
0
0
2
1
1
1
0
0
0
0
0
0
3
0
1
0
0
0
2
0
0
1
0
1
2
1
1
0
1
2
0
0
1
0
0
1
2
1
1
1
0
0
2
0
1
0
0
1
1
0
2
0
0
0
0
0
1
1
2
1
0
0
1
0
1
0
0
0
0
2
0
2
1
2
0
1
2
1
1
2
2
1
0
1
0
0
2
0
0
0
2
2
0
1
0
0
0
1
0
0
2
1
2
0
1
2
1
0
0
0
0
1
1
0
2
1
2
0
0
0
0
1
0
0
2
0
5
2
3
1
0
1
0
0
0
2
0
2
1
0
2
1
0
0
0
2
1
1
1
0
1
0
0
2
0
0
0
2
2
0
0
1
1
0
1
2
0
0
0
2
0
1
1
0
0
1
2
1
1
2
0
0
2
2
0
1
2
1
0
0
1
0
0
2
1
0
1
1
1
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
2
1
2
0
0
0
0
0
0
2
0
1
2
0
1
0
0
0
0
1
2
0
0
0
1
0
0
1
2
1
3
1
0
2
2
0
3
0
1
0
1
0
2
1
1
0
1
0
0
0
2
0
2
2
1
1
0
2
2
3
0
0
0
2
1
0
1
0
2
0
1
0
1
0
1
1
0
0
0
0
1
0
2
0
1
1
0
0
1
0
1
1
2
1
1
0
1
0
0
0
1
1
0
0
0
1
0
2
0
0
0
0
1
0
0
1
0
2
1
0
1
1
1
2
4
2
1
2
0
0
1
1
1
0
0
0
0
1
0
1
1
0
3
1
0
1
1
0
0
2
2
2
0
2
1
2
0
1
1
0
0
2
0
0
1
0
2
1
0
2
0
0
1
1
0
1
0
0
1
1
0
0
1
1
0
1
0
1
1
0
0
1
0
0
0
2
1
0
1
1
0
1
0
1
0
2
0
0
2
0
0
2
1
1
1
0
2
1
1
3
0
1
0
0
1
2
0
0
2
1
2
0
0
0
2
0
1
1
1
0
1
2
0
2
0
1
1
0
1
3
1
2
3
0
1
1
0
0
1
1
0
1
0
1
0
1
0
1
0
0
1
0
0
1
0
0
1
1
1
0
2
1
0
1
1
0
1
2
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
2
0
1
2
0
0
0
1
2
2
0
2
0
1
0
0
2
0
2
1
0
2
2
2
0
1
1
0
1
0
1
0
2
2
0
2
0
0
1
2
0
0
0
0
2
0
0
2
2
0
0
0
1
0
0
0
1
0
0
2
0
0
0
2
0
1
1
2
1
0
1
0
1
0
1
2
0
0
0
1
2
1
2
0
1
1
1
0
1
1
0
0
1
0
2
0
0
1
0
1
0
1
0
0
0
0
1
1
1
0
1
0
2
0
1
1
0
2
0
2
2
0
2
0
0
0
0
2
1
0
1
2
1
2
1
0
0
2
0
0
0
0
1
2
1
0
0
1
2
0
0
0
2
0
2
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
3
0
0
0
0
1
0
2
1
0
0
2
1
0
0
1
0
0
2
0
0
0
1
1
0
2
0
1
0
0
1
1
2
2
1
0
2
2
0
1
2
0
0
0
0
2
1
0
1
0
2
1
0
0
5
0
0
1
1
0
0
0
0
1
2
0
0
1
2
0
0
0
1
2
0
1
0
0
1
0
0
0
0
2
0
1
1
2
1
0
2
0
1
8
0
0
2
0
1
2
1
1
1
0
1
3
0
0
1
0
0
2
1
0
1
2
0
2
1
0
1
0
1
0
0
1
0
0
1
0
0
1
0
2
0
3
1
2
0
0
0
1
0
0
2
2
0
1
0
1
0
1
1
0
0
1
1
0
2
2
1
0
1
1
1
1
0
0
0
0
1
2
2
0
1
0
1
0
0
2
2
2
0
1
1
1
1
1
0
0
0
2
0
0
2
2
1
0
1
2
2
2
0
0
2
1
1
1
1
0
1
0
2
4
2
0
2
0
0
1
0
0
0
1
3
0
1
0
0
1
0
1
0
3
2
2
0
0
1
0
1
0
0
1
2
1
2
1
0
0
1
2
0
0
0
0
1
1
2
1
0
0
2
1
0
0
1
2
0
1
0
0
2
1
0
0
2
1
2
0
3
1
4
2
0
0
1
2
1
0
0
1
0
2
0
0
1
2
0
2
2
1
0
1
0
1
2
1
0
0
0
2
1
0
0
1
2
0
0
2
2
0
0
0
0
2
0
0
1
2
0
1
1
0
0
0
0
0
0
1
0
1
2
3
0
0
0
3
0
2
2
1
0
2
2
2
1
0
0
2
1
0
2
1
0
0
1
1
1
1
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
2
2
1
0
2
0
0
0
1
2
1
0
0
1
1
1
2
0
2
2
1
1
1
0
1
0
2
2
0
2
0
0
0
2
0
0
0
0
1
1
0
1
1
0
2
1
0
0
2
2
0
1
1
1
0
0
0
0
0
0
0
1
0
2
6
0
0
0
2
1
0
2
0
2
0
1
2
1
0
2
0
1
0
0
0
1
0
0
1
0
2
0
0
1
0
0
3
1
1
0
1
0
0
0
0
2
2
0
0
1
2
0
0
1
0
0
0
2
2
1
0
1
1
0
1
0
1
2
0
1
1
0
0
2
0
0
1
0
0
0
1
1
1
0
2
1
0
1
0
0
0
0
0
0
0
0
2
0
2
1
2
0
0
0
0
0
2
2
1
1
0
1
1
0
2
1
0
2
0
0
1
0
0
0
1
2
1
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
1
2
0
0
0
2
0
0
2
0
1
0
0
2
0
0
0
1
2
0
0
2
1
1
0
0
0
0
0
2
0
0
0
1
2
2
2
4
1
0
0
1
3
2
1
0
0
0
2
1
0
0
0
0
0
0
1
1
0
3
7
0
2
0
1
2
1
1
0
0
0
0
0
2
2
1
1
2
1
2
3
1
0
1
0
1
2
0
0
2
0
1
0
1
1
2
0
0
0
0
0
0
1
0
2
1
0
0
0
2
1
0
2
1
1
1
1
2
0
2
1
2
1
0
0
1
1
1
1
1
2
0
2
0
0
1
2
0
1
1
1
3
0
0
0
0
3
2
1
0
0
1
0
2
0
0
0
0
0
1
1
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
2
1
4
0
0
0
2
0
2
1
2
0
2
2
1
0
0
1
1
2
0
0
0
2
0
5
2
0
0
0
2
0
1
1
2
1
2
0
0
1
2
0
0
0
1
0
2
0
2
0
0
1
0
1
0
2
1
2
0
0
1
1
0
2
4
0
0
0
0
1
0
2
0
2
0
2
1
1
0
0
1
0
0
0
0
1
0
2
1
0
0
0
0
0
1
0
0
0
1
0
2
2
0
2
1
1
0
1
0
1
1
3
2
1
0
0
0
1
0
0
2
0
0
0
0
1
1
0
0
1
1
4
0
0
1
0
2
0
0
0
1
2
2
1
0
1
0
0
2
0
2
2
2
0
0
0
2
2
3
0
0
1
0
1
1
0
1
0
1
0
0
1
1
0
0
1
0
0
1
0
2
0
0
1
2
1
1
1
1
0
0
6
0
0
2
1
5
1
0
0
1
1
0
1
0
2
13
0
0
0
1
0
1
0
0
1
1
0
0
2
2
2
1
0
2
0
2
0
0
1
1
2
1
1
1
0
1
2
0
0
1
1
1
2
0
1
0
1
2
0
0
0
1
1
2
0
1
0
0
1
1
0
1
1
2
0
0
0
0
0
0
2
1
0
1
0
0
0
1
0
0
1
2
2
1
0
1
1
2
1
0
0
2
2
2
0
0
1
0
1
0
1
0
0
0
1
0
1
0
2
0
0
0
0
0
0
1
0
0
1
2
1
2
0
1
1
0
0
1
1
0
0
0
0
0
0
0
1
1
1
0
1
1
1
0
2
1
1
2
0
0
1
1
3
0
0
1
1
0
1
1
0
1
2
0
1
0
1
1
0
0
0
2
0
0
2
0
1
1
0
2
1
0
1
0
1
2
0
0
1
0
0
0
0
2
1
0
1
0
2
2
0
2
0
0
2
1
0
0
2
0
0
0
2
2
2
0
1
1
1
0
1
0
1
1
2
0
1
1
0
1
0
1
2
2
1
0
1
2
1
1
0
2
0
0
2
2
1
0
1
0
0
1
0
2
0
0
0
2
0
1
0
1
1
0
0
1
0
1
0
1
1
0
0
2
1
3
2
1
2
1
0
0
1
0
0
1
1
0
1
2
1
0
0
0
2
0
1
1
1
0
0
1
2
0
2
0
1
0
0
0
1
1
1
0
0
1
1
1
0
0
0
0
0
0
0
1
0
1
1
0
2
0
1
2
0
2
2
0
1
0
2
0
1
1
0
0
1
1
1
1
0
2
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
2
1
2
1
1
0
2
1
2
0
0
0
0
0
1
0
0
0
0
0
2
1
0
2
4
2
1
0
1
2
0
1
0
0
1
0
0
2
2
2
0
1
4
0
3
0
0
0
0
0
2
2
0
0
2
0
1
1
2
2
0
0
0
1
0
0
0
2
1
1
0
0
1
1
1
1
0
0
0
0
0
2
1
0
0
0
0
1
2
0
1
1
1
2
1
1
1
0
1
0
0
2
0
0
1
0
1
0
1
0
0
0
1
0
2
1
2
1
1
1
2
1
2
0
0
1
0
0
2
0
1
0
0
0
1
0
1
1
0
1
0
0
1
1
1
1
0
2
2
0
0
0
0
0
2
2
0
0
0
0
1
2
1
2
0
0
0
0
0
0
1
1
0
2
0
1
0
0
0
0
1
2
1
0
2
0
0
0
1
2
0
1
0
2
1
0
0
1
2
1
2
1
1
0
0
0
2
1
1
0
3
1
0
1
0
1
1
0
0
0
1
0
2
0
0
1
0
0
0
0
0
2
2
2
0
2
0
1
0
0
0
0
0
2
0
1
1
1
1
1
1
1
0
0
0
0
1
1
0
1
0
1
0
2
1
1
0
0
1
0
0
0
0
0
0
0
0
2
0
1
1
2
0
3
0
2
2
1
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
1
1
1
0
1
0
0
0
1
0
1
0
2
0
0
1
0
0
2
0
2
0
0
1
0
1
0
0
1
0
0
0
2
0
0
2
0
2
2
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
1
0
2
1
1
1
1
0
2
1
2
0
2
0
1
0
1
0
1
2
0
0
1
2
2
0
1
0
1
1
1
1
1
1
0
0
0
1
2
1
2
0
2
2
1
0
1
0
0
2
0
0
2
2
1
1
0
0
0
1
0
2
2
2
1
0
1
2
5
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
1
1
1
1
1
1
2
0
0
0
1
0
0
2
1
0
1
1
2
0
2
0
0
2
1
2
0
0
0
1
1
1
3
2
2
1
0
2
0
0
3
0
2
2
1
1
1
0
0
0
1
1
3
1
0
0
1
1
0
1
2
1
0
1
1
0
1
2
0
1
1
0
0
0
0
1
2
1
2
0
2
2
0
1
1
0
2
0
2
1
1
1
0
0
0
0
1
1
1
0
0
2
0
2
0
3
0
2
1
0
1
0
1
0
1
0
2
0
2
2
1
0
0
0
2
0
0
1
0
0
1
2
2
0
2
1
0
1
0
0
1
5
0
0
1
1
0
0
1
0
0
1
1
0
1
2
0
0
0
0
2
0
0
0
0
1
1
1
1
0
0
1
2
0
2
0
1
1
1
0
1
0
0
1
1
0
2
1
0
0
0
1
0
2
1
1
0
0
0
2
1
0
2
1
1
1
0
1
2
2
2
0
0
0
2
2
0
1
0
0
1
1
2
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
2
0
1
0
2
0
0
0
0
0
0
2
0
0
0
1
2
2
0
2
2
1
0
1
0
2
0
0
1
0
1
2
2
0
1
0
2
0
1
2
0
0
1
1
0
0
0
2
2
0
2
0
2
1
1
2
2
2
0
0
0
1
2
0
0
1
0
0
0
2
0
1
0
0
2
0
1
0
0
1
2
0
0
0
0
2
0
0
1
2
2
0
0
0
0
2
1
0
0
0
0
2
1
1
1
0
0
1
1
0
0
0
2
1
0
0
0
0
0
1
2
0
2
1
0
2
0
1
0
2
0
0
2
2
1
0
1
2
2
0
1
1
0
1
1
1
0
1
1
1
2
0
2
1
0
0
0
1
1
0
0
1
1
1
0
2
1
1
0
3
0
2
0
1
0
1
1
1
1
0
0
2
1
0
1
1
0
1
1
1
1
0
1
1
0
0
0
0
1
2
0
2
1
2
0
0
0
0
1
1
0
1
0
0
1
1
0
0
0
1
0
1
2
0
1
1
0
0
0
0
0
1
1
1
1
0
0
0
1
2
0
2
0
0
2
2
0
0
0
1
0
0
1
2
2
2
0
2
0
0
0
0
0
1
1
0
1
2
1
2
1
2
0
0
0
2
2
2
0
1
0
1
0
2
0
0
0
0
2
1
0
1
1
0
1
2
2
2
0
0
2
2
0
2
0
0
2
2
1
2
0
0
2
2
2
0
2
2
1
1
0
2
1
1
0
2
0
0
0
1
1
0
2
1
0
2
2
0
2
0
2
0
0
1
0
0
0
1
1
1
1
1
0
0
0
2
2
1
0
0
0
1
1
0
2
0
2
2
0
0
0
2
1
1
2
0
1
2
2
0
1
0
1
0
3
2
0
1
2
0
1
1
1
2
0
0
2
1
1
2
0
0
1
0
2
1
0
2
0
2
0
0
1
0
0
0
1
0
0
1
0
0
2
1
2
2
0
1
0
0
0
3
1
0
0
2
2
1
1
0
1
1
1
2
3
2
3
1
0
0
1
2
0
0
0
0
1
0
1
0
0
1
0
0
1
1
0
1
0
3
2
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
2
1
0
0
1
1
0
1
2
0
0
3
2
1
0
1
1
1
0
1
1
2
2
0
2
0
1
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
1
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
2
2
1
0
0
2
1
2
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
1
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
1
0
1
0
2
1
0
0
1
0
2
0
1
1
0
1
1
0
2
1
1
0
1
1
0
0
0
0
1
1
1
0
1
0
2
3
0
1
0
1
0
0
0
0
1
1
0
0
0
1
2
0
2
1
2
0
0
0
2
1
2
0
0
1
0
0
0
2
2
1
1
2
0
1
0
0
4
0
2
1
0
0
0
3
2
0
1
0
2
0
2
2
3
2
0
0
1
1
2
1
0
1
0
0
0
1
1
0
0
1
1
1
0
1
0
1
0
2
1
4
1
1
2
0
0
0
0
2
1
0
1
0
1
0
0
0
2
0
1
1
0
0
2
0
1
0
3
0
0
0
1
1
0
0
2
0
1
1
1
0
2
1
0
1
1
1
0
1
0
0
2
0
2
0
0
0
1
1
2
2
2
0
2
0
2
0
0
0
1
0
1
1
0
0
1
3
0
1
0
0
1
1
0
0
0
2
0
0
2
1
0
2
1
0
1
0
0
0
1
0
0
1
0
0
1
2
0
0
2
1
0
0
0
1
1
1
4
0
3
2
2
0
1
3
0
1
2
0
0
1
0
0
2
1
1
2
0
0
1
0
1
0
2
2
0
0
1
0
0
0
0
2
0
2
1
2
1
1
0
1
2
0
2
2
0
1
1
1
1
1
0
0
0
2
1
0
2
0
0
0
0
0
2
2
2
0
1
1
0
1
0
1
0
0
0
0
0
0
2
2
2
0
0
0
0
1
2
2
2
1
1
2
0
0
0
0
0
0
1
0
2
0
0
1
0
1
2
2
0
0
1
0
1
0
0
1
1
1
0
2
1
1
0
0
0
2
0
0
2
2
0
0
0
0
1
1
0
0
0
1
0
2
1
0
1
2
1
0
0
0
0
2
3
0
1
1
0
2
0
1
0
0
0
1
0
1
1
2
0
2
2
0
0
1
0
1
0
1
2
1
1
1
2
1
0
0
2
2
0
4
2
0
0
0
1
0
0
2
0
0
0
2
0
1
0
8
2
0
2
0
0
0
2
1
1
2
0
0
0
0
1
0
0
0
1
2
1
0
0
2
2
0
0
0
1
1
0
1
1
0
0
2
0
1
2
0
0
0
1
0
2
0
0
0
2
2
0
1
3
2
0
1
1
2
1
0
2
2
1
3
1
0
0
0
2
0
0
1
1
1
2
0
1
0
1
0
0
0
0
2
0
0
1
1
1
2
1
2
0
1
2
1
0
0
2
2
2
2
0
1
2
0
2
0
1
0
1
1
0
0
0
0
0
1
0
1
2
0
1
0
2
0
0
1
1
0
0
0
1
1
0
1
0
1
1
0
0
1
2
2
2
2
0
1
0
0
1
0
2
1
3
2
1
1
2
0
1
2
0
2
0
0
0
1
0
2
0
0
1
0
0
0
1
4
1
2
1
2
0
0
0
0
0
2
1
2
2
0
0
0
0
1
1
2
2
0
0
1
2
0
0
0
0
2
0
0
0
1
1
1
3
0
1
0
4
0
0
1
0
1
0
0
0
2
0
2
0
1
2
3
1
1
0
1
1
1
0
0
0
1
1
1
0
0
0
2
0
0
1
1
2
0
2
0
0
0
1
0
1
1
1
0
0
1
2
1
1
2
0
2
0
0
0
1
1
0
0
2
1
1
0
0
2
0
0
0
0
2
1
0
1
2
1
0
2
0
0
1
0
0
2
1
2
0
0
2
0
1
0
0
0
0
0
2
2
2
0
0
2
0
0
3
3
2
0
0
0
1
0
0
0
0
1
0
0
1
2
1
1
1
1
1
0
0
0
0
0
1
1
1
2
1
0
0
1
0
0
2
3
0
0
0
1
0
0
0
0
2
0
0
1
1
1
1
0
0
2
1
2
0
2
0
1
0
1
1
0
2
2
0
0
2
0
0
0
4
1
0
2
2
0
3
1
0
0
0
2
1
0
2
1
1
1
0
4
2
1
2
1
0
0
2
0
2
2
0
0
0
1
1
0
0
0
1
1
1
0
0
1
0
2
0
2
0
0
0
0
0
0
1
2
1
0
2
2
0
0
1
2
1
0
0
2
2
1
0
1
2
1
0
0
3
0
1
0
1
1
1
1
1
1
2
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
1
0
0
1
0
0
1
3
1
2
1
0
1
1
0
1
0
0
0
2
1
0
1
0
1
1
1
1
0
0
0
0
4
0
1
1
1
0
2
1
0
2
1
0
0
1
0
4
1
0
0
0
0
0
0
0
2
0
1
2
2
0
0
1
0
0
0
0
0
1
0
1
1
0
1
2
2
1
0
0
1
1
0
2
1
0
0
2
1
1
0
0
2
0
2
2
0
1
1
1
0
0
2
0
0
2
1
1
1
0
0
0
2
1
1
2
0
0
0
2
0
0
2
1
2
0
1
1
0
0
0
2
2
0
0
3
0
5
0
0
0
0
1
1
1
0
1
1
1
0
2
1
1
2
1
2
1
0
2
1
0
0
0
1
0
0
0
0
1
1
0
0
0
2
0
0
2
0
1
4
0
1
1
2
1
1
0
2
0
0
0
2
1
1
1
0
0
2
1
0
0
1
1
2
1
1
0
0
2
0
2
1
0
0
0
1
0
1
0
2
0
0
0
0
1
2
0
1
0
1
1
0
6
2
0
0
1
3
2
0
2
1
1
0
2
0
1
1
2
1
0
0
0
2
2
2
0
1
1
0
0
0
3
0
2
1
1
1
1
0
2
0
2
2
0
0
0
0
0
2
2
0
1
0
0
1
2
0
2
2
2
1
0
0
2
1
0
2
2
0
0
0
0
0
1
1
2
0
0
2
0
2
2
1
1
0
0
2
1
0
0
0
0
0
0
1
0
2
2
0
1
0
2
0
0
0
1
0
2
2
0
2
0
1
1
0
0
2
0
1
0
0
2
0
0
2
0
0
1
0
0
0
2
2
0
1
0
2
1
0
3
0
0
2
2
1
0
0
1
0
1
0
2
0
0
0
0
0
1
1
0
2
0
0
1
2
2
0
1
0
1
2
0
0
1
1
1
1
2
0
0
0
0
1
2
0
0
0
0
1
1
1
1
1
0
0
2
1
1
0
0
0
1
0
1
0
1
2
2
1
0
1
0
1
0
1
0
0
0
1
0
3
0
0
1
0
1
1
0
0
2
0
1
2
2
0
2
0
1
2
0
1
0
0
0
1
0
0
0
0
3
2
0
1
0
0
1
3
0
1
1
0
1
0
0
1
2
0
0
1
1
0
0
0
0
0
0
1
2
0
0
0
0
2
1
1
1
0
1
0
0
0
0
2
0
1
2
1
0
1
1
0
0
1
1
0
0
0
2
2
2
2
2
2
1
1
0
0
0
1
2
1
0
2
0
1
2
1
0
2
0
0
2
1
0
0
0
2
1
0
1
2
1
0
0
0
0
0
5
1
0
0
1
0
2
0
0
2
2
0
0
0
2
2
1
0
0
0
2
1
2
0
2
1
1
0
0
1
1
0
1
0
0
1
1
1
2
0
0
0
0
2
0
1
1
2
0
0
1
0
0
2
1
0
1
1
0
1
0
1
0
1
0
4
1
0
0
0
2
0
0
0
1
1
1
1
1
0
2
2
1
2
0
2
0
0
2
0
2
1
0
2
1
0
1
0
0
0
2
2
1
2
2
0
0
1
2
0
1
2
0
0
2
0
1
1
1
2
0
1
2
0
0
1
0
0
0
1
0
0
1
1
2
2
3
0
1
0
1
0
0
2
0
1
1
0
0
0
0
0
2
0
2
1
0
0
0
1
2
0
1
1
3
2
0
2
1
0
0
0
2
0
1
1
0
0
2
0
1
2
2
2
1
0
2
0
0
0
2
0
0
0
0
0
1
1
0
1
0
0
1
0
2
2
0
0
0
0
3
0
0
1
0
1
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
2
1
2
0
0
2
1
0
0
1
1
1
1
1
0
0
0
1
0
0
0
0
0
0
1
1
0
2
1
2
2
1
0
1
0
1
0
0
0
0
0
2
1
0
2
0
0
0
1
0
0
0
1
0
2
1
0
0
1
0
1
0
1
0
1
0
0
0
0
2
0
1
1
2
0
2
0
0
0
1
0
0
2
0
1
0
0
0
1
1
1
0
2
0
0
1
1
0
1
0
2
2
0
0
1
2
0
2
0
1
1
2
0
0
0
1
1
3
0
0
0
1
2
1
0
0
0
0
1
0
0
2
0
1
1
0
2
0
2
0
0
0
0
0
1
2
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
2
0
0
0
2
0
0
1
2
1
2
0
0
0
0
1
2
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
1
1
1
1
0
1
0
2
2
1
1
2
0
1
1
0
0
0
1
2
2
0
0
0
2
1
0
3
0
0
0
1
0
0
2
0
0
3
2
1
0
0
2
2
2
0
0
2
2
2
2
0
0
0
2
2
0
1
1
0
0
0
0
2
2
2
0
1
2
0
3
2
0
1
3
1
0
1
0
3
1
0
0
1
0
0
1
0
0
0
1
0
0
1
0
2
0
8
0
2
1
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
2
1
1
0
0
2
1
1
0
0
1
0
0
1
0
2
1
0
0
0
2
2
2
0
0
1
1
1
0
1
0
3
0
1
1
2
0
2
0
2
0
2
0
1
1
0
2
0
1
1
1
0
0
0
0
1
2
0
1
0
0
1
0
2
0
1
0
0
1
1
1
1
0
1
2
1
2
0
2
0
0
1
0
0
2
0
2
2
2
0
1
0
0
1
0
1
0
2
2
1
2
0
1
0
2
0
2
1
2
0
1
1
0
0
2
0
1
2
1
1
1
0
1
0
0
0
0
5
2
0
2
1
1
0
1
0
0
1
1
1
0
0
0
0
1
2
1
0
0
1
1
1
1
2
0
0
1
2
1
0
0
1
0
2
0
0
2
0
1
1
1
0
0
0
0
1
0
0
1
1
0
0
0
0
3
1
0
0
2
0
0
1
0
0
2
1
2
0
0
0
0
1
0
0
1
3
1
1
2
0
3
0
2
2
2
0
0
2
2
0
1
0
1
1
0
0
0
0
0
2
2
1
3
1
0
2
1
2
0
1
1
0
2
1
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
2
1
2
0
0
1
1
0
1
0
0
2
0
1
2
2
0
0
0
0
0
1
0
0
2
1
1
2
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
2
0
0
2
1
1
0
1
0
2
2
1
2
1
0
2
0
1
0
1
0
2
1
1
1
1
2
1
0
0
0
2
2
0
0
0
2
0
2
0
1
1
0
0
4
0
0
1
0
2
2
0
2
1
0
2
0
0
0
0
1
1
0
0
0
0
2
2
3
2
0
1
0
1
1
4
0
1
1
1
1
0
1
2
1
2
1
1
1
2
0
0
1
1
2
0
0
0
0
1
0
0
1
1
2
0
1
0
1
0
1
0
2
2
2
0
0
1
2
1
0
2
1
2
0
0
1
1
1
2
0
0
1
0
0
1
1
0
2
0
0
0
1
0
0
0
1
2
2
2
1
0
2
0
2
0
1
1
1
0
2
0
1
0
1
0
2
0
2
1
0
0
1
2
0
0
1
1
0
2
2
2
0
0
1
3
2
1
2
0
1
0
1
2
2
1
0
0
2
1
0
0
0
0
0
2
0
2
0
0
1
0
3
0
1
1
0
0
0
0
0
1
0
1
0
0
1
0
0
2
0
1
0
1
0
0
1
2
0
0
2
1
1
0
1
0
1
0
0
0
2
0
2
0
1
0
1
0
0
0
2
1
1
1
0
2
0
0
1
0
2
0
1
0
0
1
0
2
0
2
0
2
0
1
1
1
1
0
1
0
0
2
0
0
1
0
2
0
3
2
0
1
0
1
2
2
0
1
0
0
1
0
0
1
1
1
0
0
0
1
1
0
1
1
3
1
0
1
1
0
0
1
0
0
2
0
0
1
1
0
3
1
0
0
1
1
1
0
0
2
0
1
1
1
1
0
1
0
0
1
0
0
0
0
2
1
1
1
1
4
2
0
0
1
1
0
1
1
0
1
1
1
0
0
0
2
0
0
1
0
0
1
2
0
0
0
2
0
1
0
2
0
0
0
0
1
1
0
0
1
2
2
0
0
0
2
1
1
1
0
1
1
1
0
0
1
2
0
0
1
0
0
0
2
0
1
0
4
0
1
0
2
1
1
2
4
0
1
0
0
0
1
0
2
0
0
0
1
1
2
0
2
1
0
0
2
0
0
1
2
1
1
1
0
1
0
0
0
1
1
1
0
0
0
0
0
2
2
1
2
2
0
0
1
2
0
1
0
2
0
0
0
0
0
2
0
7
2
1
0
0
0
0
0
2
0
0
2
2
1
1
1
2
0
0
1
2
0
0
0
0
1
0
0
2
2
1
0
1
1
1
0
2
0
2
2
0
1
0
2
0
0
0
0
1
1
0
1
1
0
1
2
1
2
2
0
0
0
2
2
0
0
0
0
1
0
0
1
0
7
1
1
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
1
1
0
0
1
1
2
0
0
2
1
1
1
0
0
1
0
1
1
1
2
2
0
1
0
0
0
2
2
0
0
2
2
0
3
0
0
1
0
2
1
0
2
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
2
0
1
2
0
0
1
1
0
1
0
1
2
0
2
0
1
1
1
0
0
0
2
1
0
2
0
1
0
0
1
1
2
0
2
1
1
0
4
0
2
0
3
0
0
0
1
1
0
0
1
0
0
1
1
1
0
0
2
1
0
1
1
0
2
0
0
0
1
0
0
0
0
0
1
1
2
0
2
0
0
3
1
1
2
1
1
2
2
2
0
0
0
1
1
2
2
1
0
1
2
0
0
1
2
0
0
1
0
1
1
0
1
3
3
1
0
0
1
1
1
0
1
0
0
0
0
0
0
1
2
2
1
1
2
1
0
1
0
0
2
0
1
0
0
1
0
1
1
0
2
0
0
1
1
2
0
1
2
2
1
0
1
1
1
1
1
0
0
2
1
0
0
2
1
1
0
0
0
0
0
1
0
3
1
2
0
0
1
0
2
1
0
0
2
0
1
2
0
0
1
0
0
0
1
0
0
1
0
0
0
2
1
1
1
0
0
0
0
0
0
0
2
2
1
0
1
1
0
1
1
2
1
1
0
1
1
0
0
2
0
0
1
0
0
1
2
1
0
2
0
0
0
0
2
0
2
0
1
0
0
0
1
2
1
1
2
1
2
0
1
1
1
1
2
2
2
0
0
0
2
0
1
1
2
1
0
0
1
0
2
1
0
1
0
0
1
0
0
0
0
0
0
3
0
0
2
0
0
2
1
2
1
2
0
0
0
1
1
0
0
2
0
0
1
0
1
0
0
0
0
0
3
1
0
0
0
5
0
0
2
1
2
0
0
0
2
1
1
0
0
0
0
0
1
0
1
1
2
1
1
0
0
0
2
1
0
0
0
1
3
1
2
2
0
1
1
0
1
0
0
1
0
1
1
0
1
0
0
1
0
2
0
2
1
1
1
0
0
0
0
0
1
0
1
0
1
4
0
0
2
0
0
0
0
0
2
0
0
0
1
1
0
1
0
0
1
2
1
1
2
0
0
2
0
1
2
0
0
2
0
3
0
0
2
1
0
2
2
0
1
2
0
2
0
2
0
0
0
2
2
0
0
2
0
1
1
2
0
2
2
0
0
1
1
0
0
0
0
0
1
2
1
0
1
1
0
1
0
0
0
2
0
0
2
1
1
0
0
0
1
1
0
1
1
0
2
1
0
0
0
0
0
0
0
0
0
3
0
2
0
0
1
1
2
0
0
0
0
0
0
2
1
2
2
1
1
0
0
2
0
2
1
3
2
0
2
0
1
0
0
2
1
0
1
1
2
0
0
2
0
1
0
1
1
2
0
1
1
0
0
0
1
2
1
1
0
2
0
1
2
2
2
0
0
1
0
0
1
0
0
1
2
2
0
2
0
1
2
0
0
2
0
0
1
1
0
1
1
2
0
2
0
2
0
1
0
0
1
0
1
0
0
2
0
1
2
0
1
2
1
1
0
0
0
2
0
2
2
0
1
1
1
2
0
1
0
0
0
0
0
0
2
0
0
2
0
2
1
0
0
2
1
0
0
0
2
0
2
2
0
0
2
0
2
0
1
0
0
1
1
1
1
0
1
0
0
2
1
1
2
1
2
0
0
0
1
2
4
0
1
0
1
2
1
1
0
0
1
1
2
0
0
0
1
2
0
0
0
1
0
0
2
0
2
1
2
0
2
1
1
0
0
0
2
0
1
1
4
2
0
0
0
4
2
2
2
1
2
1
2
0
2
2
0
0
0
1
0
0
0
1
0
2
0
2
0
0
0
0
0
1
0
0
2
0
0
1
2
0
1
0
2
1
0
0
1
1
0
0
2
0
0
0
0
1
1
0
0
1
0
0
0
2
1
2
1
2
1
1
0
1
0
2
0
0
0
1
0
2
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
2
1
1
0
0
0
1
0
0
1
2
1
0
2
2
1
2
0
0
2
1
1
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
1
1
1
1
2
1
0
1
1
1
0
1
1
0
0
0
1
0
0
0
0
1
1
2
2
0
1
0
0
0
0
1
1
2
0
1
0
0
1
2
0
0
1
1
0
1
0
0
0
0
0
0
1
2
0
0
2
1
0
1
0
1
0
1
1
1
1
2
0
1
0
0
0
0
1
1
1
0
2
1
0
0
0
1
0
1
1
2
0
0
4
0
1
0
2
0
0
1
0
2
0
5
2
0
0
0
2
2
0
1
0
1
0
2
1
0
2
0
0
2
0
0
1
2
3
1
0
0
0
1
1
2
1
2
3
2
0
1
0
0
0
1
1
2
0
3
2
1
0
0
0
1
0
1
1
1
2
0
1
1
0
0
0
2
2
1
1
0
0
0
1
1
0
1
0
0
1
1
0
0
1
1
2
2
1
0
0
0
0
0
0
1
2
0
1
2
0
1
1
0
2
0
0
0
0
0
0
0
0
1
0
2
0
2
0
2
0
2
2
1
2
1
2
1
2
2
0
3
1
1
1
0
1
1
0
1
0
2
4
2
0
0
2
1
0
0
2
0
0
0
1
2
0
0
1
3
1
0
0
1
0
1
1
0
1
0
1
0
2
3
1
2
0
0
0
1
0
2
1
1
1
2
0
2
0
1
2
1
1
1
0
0
1
0
1
2
0
2
0
0
1
0
0
0
0
2
1
0
0
0
0
1
2
1
2
0
0
0
0
1
0
1
0
2
0
1
2
1
3
1
0
0
0
0
1
0
0
1
0
0
1
1
1
2
1
1
0
2
0
1
1
1
2
0
1
3
1
0
0
0
4
1
3
0
2
2
0
0
0
0
0
0
0
1
2
0
1
0
1
2
0
1
1
1
1
0
1
0
0
1
0
2
1
2
0
0
2
0
1
0
0
3
2
0
0
2
0
0
0
0
0
2
1
0
1
0
2
0
2
0
2
0
1
0
0
1
1
0
1
1
1
0
0
1
2
0
1
2
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
1
2
1
0
0
0
1
1
0
1
1
0
0
2
0
0
1
0
0
2
2
0
1
1
0
1
0
1
2
1
0
1
3
0
1
0
2
1
0
0
0
0
1
1
1
0
0
1
0
1
1
1
0
0
1
0
1
1
1
0
0
2
0
1
0
1
2
0
0
2
2
1
1
1
1
1
0
2
1
3
0
2
0
0
0
0
0
2
1
0
0
1
2
3
0
1
1
0
0
0
0
0
1
2
0
0
1
1
1
0
0
0
1
0
1
0
1
1
1
0
0
0
0
0
0
1
0
2
0
1
0
0
1
0
0
0
0
1
0
2
0
1
0
1
2
1
0
2
2
1
1
1
0
2
0
0
1
1
1
2
0
0
0
0
1
0
1
2
0
0
2
1
0
0
1
0
0
2
0
0
0
1
1
0
0
2
2
0
0
1
0
2
2
0
0
0
2
0
0
0
1
2
0
0
0
1
1
0
2
3
0
0
1
1
1
0
0
0
0
0
0
1
0
0
1
0
0
2
2
0
2
0
0
0
0
0
0
1
2
0
2
2
1
1
1
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
1
0
1
2
0
0
0
1
0
2
2
0
0
0
0
1
0
1
0
2
2
0
0
0
0
2
1
2
0
1
1
0
1
1
1
2
0
0
2
0
0
0
0
0
0
1
2
0
1
0
1
0
1
1
0
0
0
2
2
0
0
0
2
0
0
0
1
0
1
1
0
2
1
0
0
0
1
3
2
1
1
1
1
1
2
0
1
1
0
0
0
2
0
0
1
0
0
2
2
0
0
0
0
1
1
1
1
0
0
1
0
0
2
0
0
0
0
0
1
1
0
0
1
1
1
0
1
0
0
3
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
2
0
2
1
1
1
2
0
0
1
0
0
0
3
1
0
1
0
0
2
1
1
0
1
0
1
1
0
2
2
0
2
0
0
2
1
2
0
0
0
1
1
0
0
0
2
0
2
1
0
0
1
0
1
0
2
0
1
0
2
0
2
0
1
2
2
0
0
1
0
2
1
0
1
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
2
2
1
0
0
0
1
3
1
0
0
1
2
1
2
2
1
2
0
0
1
2
0
1
0
0
1
0
0
1
0
2
2
0
2
0
0
0
0
1
1
0
1
7
0
1
0
2
2
0
1
0
0
0
2
2
1
0
1
0
0
0
2
0
0
2
2
0
0
2
0
2
3
1
0
0
1
0
0
1
0
2
1
0
0
2
0
0
0
1
1
1
2
1
0
0
1
1
0
0
0
2
1
0
1
0
0
2
1
0
2
2
2
0
1
0
2
2
1
0
0
0
2
0
0
1
0
0
1
2
1
2
0
1
2
2
2
2
1
0
0
2
1
1
1
1
1
1
0
0
1
1
0
1
2
1
2
0
1
0
1
1
1
0
0
2
0
1
0
0
0
1
0
0
0
1
1
0
3
0
1
0
2
0
1
0
1
1
1
0
1
2
0
0
2
0
0
1
1
0
1
0
2
1
0
1
1
1
1
0
1
2
0
1
0
0
1
0
0
0
1
0
0
1
2
0
0
2
0
2
1
1
2
1
1
0
0
1
1
2
2
1
0
0
2
0
0
0
0
1
0
2
1
0
0
1
0
2
0
0
2
1
2
0
3
0
1
1
0
0
0
0
0
2
2
1
1
2
0
0
0
2
0
1
0
0
2
1
0
2
2
0
0
1
0
2
0
2
0
2
0
1
0
0
0
0
1
1
0
1
0
1
0
0
2
2
2
1
1
0
0
0
0
2
1
1
1
1
0
0
3
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
1
0
1
2
0
0
0
0
0
1
1
0
1
0
0
0
0
2
0
1
1
2
1
0
0
1
0
0
4
1
0
1
3
0
0
0
0
1
1
2
0
1
0
0
2
0
2
0
1
2
0
1
1
0
0
0
0
1
0
0
1
1
0
1
0
0
0
1
1
0
2
0
0
2
0
0
0
0
1
0
1
2
2
1
2
0
1
0
1
1
0
2
2
1
0
0
0
1
1
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
2
1
1
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
2
2
2
1
0
0
1
1
0
0
0
1
1
2
1
2
0
1
0
0
2
0
0
2
0
0
0
2
0
0
2
0
1
1
1
0
1
2
2
2
1
1
1
0
2
2
2
1
0
0
0
1
1
1
1
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
1
1
0
0
2
0
1
1
1
0
1
0
1
2
1
1
0
0
0
2
2
0
1
2
0
1
2
1
0
0
2
1
2
0
0
2
1
1
1
0
2
0
1
2
0
1
0
0
0
2
2
1
2
0
1
1
0
0
1
0
0
0
1
0
0
1
0
1
2
2
2
2
1
2
2
0
1
2
1
1
0
1
0
0
1
0
1
0
0
2
1
1
2
0
0
0
1
0
2
0
1
1
2
0
1
0
0
1
0
2
0
2
2
0
1
0
0
0
1
2
1
1
0
0
0
2
1
3
2
0
0
0
2
0
3
0
0
0
1
2
0
0
2
0
2
0
2
0
0
1
0
1
0
2
1
0
0
2
0
2
0
2
1
0
1
0
0
2
1
0
2
1
0
1
2
0
0
1
0
1
1
0
0
1
0
1
1
1
2
2
0
2
1
2
0
0
1
0
0
1
0
0
0
1
2
0
0
0
1
0
3
1
0
2
1
1
0
0
0
2
1
0
0
0
0
1
0
2
1
2
1
0
6
0
1
0
2
0
0
0
0
0
0
0
1
0
0
1
0
2
1
0
0
0
1
0
1
1
2
0
0
0
1
1
0
0
0
2
5
1
1
0
0
1
2
1
1
0
0
0
1
0
1
2
0
2
0
1
0
1
1
0
0
0
0
2
0
0
2
0
0
2
0
0
2
0
0
1
0
1
0
2
1
1
1
3
0
0
0
2
1
2
0
0
2
2
1
1
0
3
1
0
1
1
0
2
1
1
1
0
1
0
0
0
2
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
3
0
0
0
1
0
1
3
1
2
0
1
2
0
1
0
2
0
2
2
0
1
0
0
0
1
1
0
0
1
2
1
1
0
0
0
2
0
0
1
2
1
0
2
0
1
1
1
0
1
0
0
1
0
2
0
2
0
0
1
0
1
2
0
0
0
0
1
0
0
0
1
0
0
3
0
0
1
0
0
0
1
1
2
2
1
2
2
1
0
2
1
0
1
0
1
0
0
2
0
0
2
1
0
2
0
0
1
1
0
1
1
2
0
0
0
0
0
2
0
1
2
0
1
0
2
2
1
1
0
0
2
2
0
0
1
0
1
2
1
2
1
0
1
1
0
1
1
0
2
8
2
0
3
2
2
0
2
0
2
1
1
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
2
1
0
3
1
1
0
0
0
0
0
0
2
1
1
1
2
0
0
0
0
1
0
0
0
0
1
2
1
1
0
0
1
0
2
1
0
0
1
0
0
2
0
1
1
0
1
0
0
2
1
2
2
1
1
1
1
1
2
1
1
2
0
2
1
0
2
0
2
0
0
2
0
0
0
0
1
1
1
0
1
2
0
0
1
0
0
2
1
2
1
0
1
0
0
0
1
1
2
0
0
1
1
0
0
0
0
1
0
1
0
0
1
0
0
2
1
0
0
1
0
1
0
0
1
1
0
0
2
0
0
1
1
1
1
0
2
0
0
1
0
0
1
0
2
4
1
0
1
2
2
0
2
0
0
1
0
0
0
1
2
0
1
1
1
1
0
0
0
0
0
2
1
1
0
0
0
0
0
1
1
2
0
2
2
0
0
0
0
2
0
1
1
2
0
0
1
0
2
0
0
0
1
0
0
1
0
0
0
2
0
2
0
2
0
1
0
2
0
2
0
1
1
0
2
2
1
1
2
0
2
2
1
0
0
1
2
1
0
2
2
0
1
2
0
1
0
0
0
0
0
2
1
0
1
2
0
0
0
1
0
1
0
0
0
0
2
1
0
1
0
0
1
0
1
1
1
0
0
0
2
2
0
0
0
1
2
0
0
1
0
1
0
0
0
1
0
0
1
1
0
2
0
1
0
0
0
0
0
0
0
2
2
1
2
0
1
2
0
2
1
1
0
0
2
1
1
0
0
0
1
1
1
0
2
2
2
2
1
1
0
1
0
1
1
1
2
2
0
0
0
2
0
0
0
0
0
1
1
0
2
1
1
0
0
2
1
0
2
0
2
1
0
0
1
0
1
1
0
0
0
1
0
2
0
2
2
3
2
1
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
2
0
0
2
0
0
0
2
2
0
2
0
2
0
0
0
0
0
2
0
1
0
1
2
0
2
0
1
1
0
0
1
0
0
0
1
2
1
0
2
2
2
1
2
2
0
0
0
1
1
0
0
2
0
0
0
0
0
1
1
0
2
0
1
1
0
0
0
1
0
0
0
0
2
1
0
0
0
1
0
0
1
2
1
0
0
0
1
0
0
0
0
0
0
0
1
1
1
2
1
0
0
0
0
0
0
1
1
0
2
0
2
0
0
0
1
0
2
2
1
0
1
0
2
0
0
0
1
0
0
1
1
2
0
1
0
1
2
0
0
1
0
1
0
1
1
2
1
0
2
0
0
0
1
1
5
2
0
0
0
1
2
0
1
0
0
2
2
1
0
0
2
2
0
0
2
0
0
1
2
0
2
0
0
1
0
2
2
0
0
0
1
1
1
1
2
0
2
0
0
1
1
2
0
2
2
0
0
0
1
0
1
1
0
1
0
0
0
0
0
2
1
2
1
0
0
0
1
1
0
0
0
1
3
1
1
0
2
1
0
0
2
0
1
0
0
0
1
1
0
0
2
2
0
1
0
1
3
0
0
1
3
1
1
2
2
0
4
0
0
1
1
1
0
0
1
0
1
0
1
0
0
1
0
1
0
0
1
1
0
2
0
1
1
1
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
1
0
1
0
1
1
1
0
1
0
0
0
1
2
0
0
1
2
0
1
1
0
0
0
2
0
0
0
2
2
1
0
0
0
1
2
0
2
1
0
2
0
1
2
0
0
1
0
1
1
0
0
2
0
0
1
0
2
0
1
1
0
1
1
1
1
1
0
1
1
1
2
1
5
0
0
1
0
1
0
0
0
1
0
0
0
0
1
2
2
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
1
2
0
0
1
0
0
1
1
0
0
0
2
0
1
1
0
2
0
0
1
2
0
0
0
0
2
2
2
1
0
1
0
2
1
0
1
2
2
0
0
3
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
2
2
1
1
1
1
1
1
1
0
2
0
1
0
1
1
0
0
1
0
2
1
1
1
0
0
0
1
0
1
0
1
1
1
2
2
2
0
2
2
0
0
0
0
2
0
0
2
0
2
2
1
0
2
0
1
0
2
0
0
2
1
0
3
0
0
0
1
0
2
0
1
4
0
0
0
0
1
0
0
4
0
2
1
2
0
2
0
2
3
2
0
2
0
1
0
2
1
2
1
2
1
0
0
2
1
0
1
0
1
1
2
0
0
1
0
0
0
0
1
2
2
0
0
2
2
2
2
1
0
0
0
0
0
2
4
0
0
0
2
2
1
2
0
1
2
0
0
2
0
1
1
2
1
1
0
0
0
0
1
0
2
2
1
1
1
0
0
0
2
2
2
0
1
0
1
2
0
1
0
0
1
1
1
1
0
0
1
1
1
1
1
2
1
1
0
0
0
1
1
2
0
0
1
1
1
1
1
1
2
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
1
1
0
1
0
1
1
1
0
1
3
0
2
2
1
2
1
0
1
2
0
0
0
0
0
0
0
1
0
0
2
1
2
2
0
2
0
1
0
0
0
0
2
0
0
0
0
2
3
1
2
1
2
1
2
2
0
2
1
0
1
2
1
2
0
1
0
1
0
2
1
2
0
1
1
0
1
0
2
0
0
1
0
2
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
2
3
0
2
2
0
0
1
0
0
1
2
0
0
2
0
0
2
1
0
0
0
2
2
0
2
0
1
1
1
1
0
0
2
1
0
0
0
0
0
0
1
1
0
1
0
2
2
0
0
0
1
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
2
2
0
0
2
0
2
2
0
0
0
0
2
0
0
2
1
1
0
3
2
0
1
1
0
2
0
0
0
0
1
0
1
0
0
1
1
2
0
1
0
1
0
0
0
3
0
0
1
1
0
3
0
0
0
1
1
0
1
0
0
1
0
1
2
2
2
0
0
0
1
2
0
1
0
0
1
1
0
2
1
0
1
2
1
0
2
0
0
1
0
1
2
0
3
0
0
2
1
0
0
2
0
1
0
0
0
2
0
1
0
0
2
1
1
2
0
1
0
0
0
0
0
2
0
0
1
0
0
1
2
1
1
0
0
0
0
0
2
0
1
1
0
0
1
0
2
1
2
1
0
0
0
2
1
0
1
0
1
0
2
1
0
1
0
1
0
0
1
0
1
2
2
0
0
0
0
0
1
1
2
1
0
1
0
2
2
0
1
1
0
1
0
0
0
0
2
1
0
1
0
1
2
0
0
0
0
0
0
1
4
0
1
1
0
0
0
1
1
0
1
0
0
2
2
0
1
1
2
1
1
0
0
0
2
2
1
0
2
1
1
0
0
0
1
1
1
1
0
0
1
0
0
2
0
1
0
0
0
0
0
2
2
1
1
0
1
1
0
2
0
1
0
1
0
1
0
2
2
1
1
1
0
0
2
0
1
2
2
0
0
0
0
0
0
0
0
1
2
0
1
1
0
0
0
1
1
0
1
2
2
0
0
0
0
0
0
2
0
0
0
1
2
0
1
0
0
2
1
1
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
2
0
0
0
0
1
1
0
0
0
1
0
2
0
0
0
1
1
0
2
0
1
0
2
1
0
1
1
2
2
0
0
1
2
0
1
0
0
0
1
1
1
2
1
1
2
0
1
0
0
0
1
0
0
0
0
1
0
0
2
0
1
0
0
0
0
1
1
2
0
0
2
0
1
0
0
1
0
1
1
1
0
0
1
0
1
0
0
2
1
0
0
0
0
2
2
2
1
1
2
0
0
1
0
2
2
0
1
0
0
0
2
1
0
0
0
0
0
0
2
0
0
2
1
2
1
2
0
2
2
1
2
0
0
0
0
1
1
0
1
0
1
0
1
1
0
0
1
2
0
2
0
0
0
2
1
1
0
0
0
0
0
2
1
1
0
1
3
2
0
2
0
1
0
2
1
0
2
15
0
1
2
2
0
1
0
2
2
0
1
1
0
1
0
1
0
0
0
0
0
1
0
0
1
0
2
0
0
0
1
0
0
1
1
0
0
0
0
0
2
0
1
0
2
0
1
2
1
0
2
0
0
0
0
0
0
0
1
1
1
2
0
1
0
2
0
1
2
0
1
0
1
1
1
0
1
0
0
2
2
2
2
1
0
1
2
2
2
0
0
0
0
0
0
0
0
1
1
0
1
2
0
0
2
1
0
1
2
0
1
0
0
2
1
1
0
2
1
2
0
0
2
2
2
0
2
0
0
1
0
1
6
1
2
4
0
1
2
1
2
0
0
0
0
2
0
0
1
1
0
0
2
1
0
0
0
2
2
0
0
1
1
0
1
1
4
0
1
0
2
1
0
1
2
0
0
0
1
0
0
1
0
0
0
0
1
0
2
1
3
0
2
0
0
0
0
0
1
1
1
0
0
0
0
0
0
2
2
1
1
2
0
2
1
1
0
0
2
0
1
3
1
0
1
1
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
2
0
3
0
0
0
0
2
0
0
1
3
0
2
1
0
0
1
1
2
0
0
0
2
0
0
0
0
0
2
3
0
2
0
2
8
0
2
0
1
1
0
0
0
2
0
2
0
2
0
1
2
0
0
1
0
0
0
0
0
3
1
0
0
1
0
1
0
0
0
2
2
2
1
0
2
1
2
1
0
0
0
1
2
0
0
1
1
1
0
2
0
1
0
2
1
3
1
1
2
0
1
3
0
2
0
0
0
2
1
0
0
1
1
1
2
1
0
0
0
0
1
2
0
1
1
0
0
2
1
1
1
3
0
1
1
2
0
0
2
0
2
1
2
1
6
1
0
2
1
0
2
0
1
0
1
0
0
2
0
0
2
0
1
1
1
0
1
1
0
0
1
0
2
0
2
0
1
1
0
2
2
1
0
0
0
1
0
1
0
0
0
1
1
0
2
0
0
1
1
0
2
0
1
0
0
1
1
0
0
0
2
0
1
1
1
0
1
2
0
0
1
0
0
1
0
1
0
0
1
0
1
1
2
0
2
0
1
0
1
2
1
2
0
0
1
0
1
2
0
0
2
1
0
2
0
1
0
0
1
1
0
0
1
1
0
0
2
0
0
0
1
0
0
0
0
1
2
0
0
2
1
1
0
1
2
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
3
3
1
2
0
0
2
0
0
0
1
2
1
0
1
1
0
2
1
1
1
0
1
1
0
0
1
0
1
0
0
1
2
4
0
0
0
3
4
1
1
1
1
0
1
0
1
2
2
0
1
0
0
0
1
0
0
1
2
1
1
2
1
0
3
2
1
0
0
0
0
0
0
1
1
1
0
2
0
1
0
2
1
1
1
1
1
1
0
0
0
1
0
1
0
0
1
0
1
0
2
0
2
3
1
0
0
1
0
1
0
0
1
1
0
1
2
1
0
2
0
0
2
0
0
0
0
1
2
1
1
1
1
2
2
1
1
1
0
2
0
0
1
0
0
2
1
0
0
2
1
0
0
0
0
1
0
0
1
1
0
1
1
0
0
2
0
0
0
0
2
2
0
0
1
1
0
0
1
1
1
0
1
2
0
0
0
2
1
0
2
0
0
2
0
0
0
0
0
1
1
2
2
4
1
0
1
1
3
1
2
0
3
0
0
2
0
0
1
0
0
0
1
0
2
0
1
1
1
1
1
2
0
2
1
3
0
0
1
1
0
1
2
0
0
0
2
0
0
2
2
0
1
0
3
1
0
1
0
0
0
0
1
0
0
1
2
2
2
2
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
1
2
0
2
0
1
0
1
1
1
1
0
2
0
0
2
0
0
1
1
0
1
1
0
2
1
2
0
1
0
1
1
0
1
2
0
0
2
0
1
0
2
0
0
1
0
0
2
0
1
0
2
1
1
1
0
0
0
0
0
1
2
2
0
2
0
0
0
0
0
0
0
2
1
0
2
0
3
2
1
0
1
2
2
0
1
2
1
1
1
0
0
1
0
1
0
3
0
1
1
2
2
2
2
0
0
1
1
0
0
2
0
2
2
0
1
2
2
1
2
1
1
1
0
1
0
0
1
1
0
1
0
0
0
2
2
1
2
2
0
0
1
0
1
1
0
0
0
7
1
0
0
1
0
1
1
1
0
2
0
0
0
2
0
0
2
2
0
0
2
0
2
2
1
0
0
2
1
0
1
2
2
0
1
2
2
0
2
2
1
2
0
1
0
2
0
2
2
0
0
1
1
2
0
0
2
0
0
0
0
2
0
1
1
0
2
0
1
0
0
1
1
0
2
0
2
0
0
1
0
1
1
1
0
1
1
0
0
2
2
2
1
1
0
0
0
0
0
0
0
1
0
1
0
2
1
0
1
2
0
1
2
2
0
2
0
0
1
2
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
1
1
1
0
0
2
2
1
0
1
0
0
0
1
2
0
2
2
0
1
2
0
1
1
0
0
0
1
2
0
0
2
0
1
0
2
2
0
0
0
2
0
1
2
0
0
0
2
1
2
1
0
0
1
2
1
0
0
0
0
1
0
0
0
0
2
1
0
2
1
0
1
0
1
1
1
0
0
2
3
0
0
1
2
0
0
0
0
0
2
2
2
1
0
0
1
0
0
0
2
0
0
0
1
1
1
0
0
2
1
1
0
0
0
1
0
2
0
0
0
1
0
0
1
0
0
0
1
0
0
0
2
0
1
0
1
1
1
0
1
0
1
2
2
2
0
0
1
1
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
2
2
0
0
1
0
1
0
0
1
1
2
0
2
1
0
2
0
0
1
1
2
1
0
2
0
0
1
0
2
0
2
0
0
1
0
1
1
0
1
1
1
1
1
0
1
0
1
0
1
0
0
0
1
1
1
3
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
1
0
0
1
1
1
1
0
0
2
0
0
3
0
0
1
0
1
0
0
0
0
1
1
1
0
1
0
2
0
1
1
1
0
1
0
0
3
0
2
0
0
1
0
0
0
2
0
0
3
0
0
1
0
0
0
0
0
0
0
3
0
2
1
2
1
2
1
0
0
2
0
2
1
0
0
1
0
1
1
0
0
1
2
0
1
2
0
0
5
0
1
0
5
0
2
0
0
1
0
0
2
3
0
0
0
1
1
0
1
0
1
0
3
0
0
1
0
1
2
1
0
0
2
0
0
0
1
2
2
0
2
0
0
2
2
0
2
2
1
1
1
0
0
2
0
1
0
2
1
1
1
0
0
0
1
0
1
0
2
2
1
1
1
0
1
0
1
0
1
1
2
0
2
1
0
1
1
0
1
1
0
0
1
0
0
2
0
0
1
1
0
1
0
0
2
1
0
1
0
2
0
0
0
0
2
1
0
0
1
1
1
0
2
1
1
1
0
1
1
2
0
2
0
0
2
2
2
0
2
0
1
0
2
2
0
2
0
1
0
2
2
2
0
0
2
1
1
0
0
0
0
0
0
0
1
1
1
2
2
0
2
0
0
1
0
1
2
1
1
0
0
1
0
0
1
1
2
1
0
0
1
0
0
0
1
0
1
0
1
0
1
1
2
0
1
4
1
0
1
0
2
1
1
0
0
1
1
0
0
1
0
0
0
2
2
2
1
0
0
0
1
1
0
0
2
0
1
0
0
1
1
0
0
0
0
1
0
0
2
1
1
0
0
0
0
0
0
1
0
1
0
0
2
2
0
1
2
0
0
0
0
0
0
1
0
0
0
1
2
1
0
1
0
0
1
2
0
0
0
1
1
0
1
1
0
0
2
0
0
0
0
1
1
0
0
0
0
0
2
1
1
1
1
0
1
0
2
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
1
1
2
1
0
1
1
2
1
0
0
0
0
2
0
2
2
1
0
0
0
0
0
2
0
1
2
2
2
0
0
2
0
0
0
2
2
1
2
0
0
0
1
0
0
1
2
2
0
1
0
0
0
1
2
0
2
1
0
1
2
2
5
0
0
0
1
0
2
0
1
0
1
0
2
0
0
0
1
0
0
1
2
0
0
0
0
0
1
0
2
2
0
1
2
1
0
0
2
0
2
0
1
2
1
0
1
1
0
1
0
0
1
2
1
0
0
2
1
0
2
0
0
1
1
0
5
0
1
0
1
0
0
2
0
2
1
2
1
0
2
1
0
1
0
0
0
0
1
1
1
1
0
2
1
1
2
2
0
2
0
2
3
2
1
1
2
1
0
0
1
0
0
0
0
1
0
0
1
1
0
1
1
0
2
2
1
1
0
0
2
0
1
0
0
0
1
0
0
1
2
2
0
0
3
1
2
0
0
1
2
0
1
2
1
1
0
1
2
0
2
1
0
1
0
1
2
2
0
2
0
1
3
0
0
2
2
0
2
0
0
2
0
1
0
0
0
0
1
0
0
1
0
0
1
1
2
0
2
1
2
0
0
0
0
1
0
0
2
0
0
1
0
1
0
1
0
1
0
0
0
1
0
1
2
1
0
3
1
0
1
0
2
0
3
1
1
2
0
0
1
0
0
0
2
1
0
1
0
2
1
1
0
2
0
0
0
0
0
1
0
0
1
1
1
1
0
0
0
2
1
2
0
0
2
1
0
0
0
1
0
0
0
2
0
2
2
1
2
0
3
1
0
3
1
0
1
0
2
1
2
0
0
2
1
0
1
1
0
1
0
3
0
0
1
2
0
0
1
0
0
0
0
1
0
2
1
0
0
0
0
1
0
0
1
0
2
2
0
0
0
0
0
1
1
1
0
0
1
0
1
1
1
2
0
1
1
0
1
0
1
1
2
0
1
2
1
0
0
0
2
1
0
2
1
2
0
1
2
0
1
0
0
2
0
3
1
1
0
2
0
0
2
1
0
0
1
0
0
1
1
0
0
0
1
0
1
1
2
1
0
1
0
0
0
2
2
1
2
0
2
0
1
0
0
2
1
0
0
0
2
0
1
0
0
1
2
0
2
2
0
2
1
0
1
2
0
3
0
2
0
1
0
0
1
0
2
0
0
2
1
1
1
0
0
0
3
0
1
1
1
2
1
0
2
0
0
1
2
2
2
2
0
1
2
0
3
1
1
1
0
0
0
1
0
2
2
0
0
1
1
2
1
0
0
1
4
0
1
0
0
2
1
1
0
2
1
0
0
0
0
0
2
0
0
0
2
1
0
1
1
1
0
0
0
0
1
1
0
1
0
1
2
1
1
0
1
0
2
0
0
0
0
1
0
0
2
1
0
1
0
0
0
2
1
1
0
0
1
1
1
0
0
0
0
1
0
0
0
3
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
1
2
1
1
0
0
0
1
0
2
0
2
1
0
0
0
2
1
0
0
0
0
1
2
0
2
0
1
3
0
0
0
0
2
1
1
1
1
0
1
1
1
2
1
1
2
1
0
1
1
1
0
1
2
0
2
1
0
0
2
0
1
0
0
0
2
2
1
1
0
0
2
1
0
0
0
0
1
0
1
1
0
1
0
2
1
1
0
0
2
0
0
0
0
0
0
0
1
0
1
2
0
0
0
1
0
0
2
0
0
1
2
0
1
3
2
0
1
0
0
6
0
2
0
0
2
0
2
0
0
0
0
0
1
0
1
0
0
2
0
0
3
2
1
0
1
2
0
0
0
1
1
0
1
1
1
1
0
0
0
2
0
0
2
2
0
1
1
1
0
0
2
0
0
0
0
1
1
1
0
0
0
0
0
1
1
2
2
0
0
2
0
0
1
0
0
0
0
2
0
2
0
0
0
0
1
1
0
0
0
0
0
2
1
0
1
0
0
0
3
0
0
0
0
1
1
0
0
0
2
2
1
1
0
1
1
1
0
1
2
0
1
2
1
0
1
1
1
1
0
0
0
0
1
5
1
2
0
2
1
1
0
0
0
0
0
3
0
0
2
1
0
0
0
2
0
0
0
1
2
0
0
2
0
0
1
1
0
0
0
0
1
2
0
0
0
0
2
0
0
1
0
0
0
0
0
1
1
1
0
2
2
0
2
3
1
0
1
1
3
1
2
0
1
2
0
0
0
1
0
1
0
0
1
0
2
1
1
0
0
1
1
0
4
1
0
1
1
2
2
0
0
2
1
0
0
0
0
0
1
1
0
0
0
2
0
0
1
0
2
0
0
1
0
0
0
0
1
0
0
0
0
1
3
0
0
0
0
2
0
0
0
0
1
1
0
1
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
2
0
1
1
0
2
0
0
2
0
0
0
0
1
0
1
0
1
0
1
0
0
0
2
0
2
0
2
0
1
0
0
1
1
1
2
2
2
0
0
1
0
0
0
1
0
2
0
0
1
0
0
0
2
1
0
2
0
0
0
0
1
1
2
2
0
0
0
0
0
1
1
0
0
0
0
1
0
1
2
0
0
0
0
0
1
0
1
2
1
0
1
0
2
0
0
1
0
2
2
1
0
2
2
0
3
0
2
2
0
0
0
1
0
0
1
1
1
0
1
1
1
2
0
0
0
0
0
0
0
1
0
1
0
1
1
1
0
1
0
0
0
0
1
1
1
0
0
0
0
2
2
1
2
0
0
0
0
1
1
0
1
0
1
2
0
0
0
0
2
0
0
0
0
2
1
1
0
0
0
2
0
1
0
0
1
1
2
2
0
0
1
0
0
1
2
0
1
0
1
0
0
1
2
0
0
1
0
1
0
0
0
0
2
2
0
1
2
0
1
1
0
1
1
1
1
0
0
1
1
0
1
0
0
0
0
1
4
2
1
1
2
0
0
2
0
1
0
0
3
0
2
2
0
0
1
0
1
0
0
2
1
0
2
0
1
0
1
3
1
0
1
1
1
0
1
1
0
0
2
1
2
1
0
0
0
0
0
1
0
2
2
0
0
0
2
0
0
0
1
0
0
0
0
0
1
2
0
1
0
0
0
1
1
1
2
0
0
1
2
0
0
2
0
1
3
1
1
0
0
1
1
0
2
0
0
1
0
0
0
0
0
0
2
0
0
1
1
0
0
1
0
0
0
1
0
0
0
1
2
0
0
0
1
2
0
2
1
7
1
0
2
0
1
0
0
1
1
1
0
2
2
0
0
0
0
1
0
1
2
2
1
2
2
2
1
2
1
1
1
1
0
2
2
1
1
1
0
8
0
1
0
1
1
2
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
1
2
0
0
0
3
1
1
1
0
0
0
2
0
1
0
1
1
0
0
2
0
0
0
0
1
0
2
2
0
0
2
1
0
0
0
2
1
0
0
1
0
0
0
0
0
0
1
2
0
0
0
2
1
1
0
2
1
0
2
1
0
0
1
0
0
0
1
0
1
1
1
0
0
2
2
2
0
2
1
2
1
0
0
0
0
0
0
2
2
0
1
3
2
0
2
2
0
0
0
0
1
0
0
2
1
0
2
2
0
0
0
1
2
2
1
1
1
0
0
2
5
1
2
1
2
1
0
0
0
2
0
2
0
1
0
0
1
1
1
2
1
2
1
2
1
2
2
0
1
0
1
2
2
0
0
1
0
2
1
0
2
0
0
0
1
0
2
2
2
2
0
0
1
2
1
0
0
0
0
0
0
9
0
0
2
1
4
0
2
2
0
0
2
0
2
2
0
0
4
0
0
1
0
2
0
0
0
0
1
0
0
1
2
2
1
1
1
0
1
1
2
2
0
2
2
0
1
0
0
1
1
1
0
0
0
1
0
0
2
0
1
1
1
0
1
0
1
1
0
0
0
2
0
0
0
0
1
1
1
0
0
0
1
1
1
2
1
0
1
1
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
2
1
0
0
0
1
0
2
2
1
1
2
2
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
2
1
0
0
0
2
0
0
1
2
0
1
0
1
1
0
0
2
1
1
0
0
0
1
5
0
0
0
1
0
0
1
2
0
0
0
1
2
1
0
2
2
0
0
0
2
1
1
0
2
0
2
2
0
1
1
1
1
2
0
1
0
0
2
0
2
0
0
2
0
0
0
1
0
2
0
1
0
2
0
2
1
0
0
1
0
0
1
0
0
1
0
1
0
1
0
0
0
1
0
2
1
1
0
0
0
0
2
0
0
1
1
1
2
0
2
1
0
1
0
1
2
0
0
0
1
2
0
0
0
1
0
0
1
0
0
0
1
0
1
1
0
0
1
2
0
1
1
2
1
0
2
2
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
1
0
1
2
1
0
1
0
0
0
0
0
0
1
0
1
0
1
1
1
0
0
1
1
0
2
0
0
1
2
0
0
1
1
1
0
1
0
1
1
1
0
0
0
0
1
0
0
0
0
2
0
0
1
0
1
1
1
0
1
0
1
1
1
1
2
0
0
0
1
0
0
0
2
0
2
0
1
2
0
0
2
1
1
0
0
0
0
2
1
0
2
0
0
0
6
0
0
0
0
1
1
1
1
1
2
2
1
0
0
0
1
2
1
2
0
2
0
1
2
0
0
0
0
1
1
0
2
0
1
0
0
0
2
1
0
0
1
1
0
2
0
1
0
0
0
0
1
0
0
0
2
2
0
0
1
1
0
0
1
0
0
1
2
2
0
1
0
1
1
0
0
0
0
0
0
2
0
0
1
0
2
0
2
1
0
0
2
1
0
1
1
2
0
1
2
1
0
0
0
2
0
1
0
1
0
2
1
2
2
1
0
1
1
0
0
0
1
0
0
0
0
3
1
0
0
1
2
0
0
1
0
0
0
0
0
0
2
0
2
0
1
1
0
0
1
0
0
0
1
2
1
1
0
1
0
1
1
1
2
2
1
1
1
0
0
0
0
0
1
0
2
1
0
2
1
1
0
0
2
2
2
2
0
2
0
1
0
0
1
2
2
1
0
2
1
0
0
1
2
2
0
1
0
2
0
0
2
0
0
1
1
1
0
0
0
1
0
2
1
1
1
0
2
0
0
1
0
0
1
2
3
0
1
2
1
0
0
1
0
1
2
0
1
2
1
0
0
1
0
0
0
0
2
2
1
2
1
1
1
1
0
1
1
2
0
2
1
2
2
0
1
0
0
0
1
0
1
0
0
2
0
0
0
1
0
1
0
0
2
1
0
0
1
0
1
0
0
0
0
1
2
3
1
0
1
1
0
2
1
0
0
0
0
0
1
2
0
0
0
2
1
0
2
0
1
0
1
1
1
1
0
1
0
0
1
0
0
1
0
2
0
2
1
1
1
0
0
1
0
2
1
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
1
2
2
1
0
2
0
1
1
1
1
1
0
0
2
2
1
0
2
0
1
0
2
2
1
0
0
1
4
0
0
0
0
0
1
2
0
1
2
1
0
0
0
1
0
0
0
2
0
1
0
1
0
1
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
1
1
0
1
0
0
0
0
2
0
1
0
1
1
0
0
1
1
0
4
0
0
2
0
0
0
1
0
0
1
1
2
0
0
2
1
0
0
0
0
1
0
0
1
1
0
0
0
0
1
1
2
0
1
0
0
1
0
1
1
1
0
0
1
1
1
0
2
1
0
1
1
0
2
0
1
2
0
0
0
1
1
0
0
0
0
0
2
1
1
0
0
2
0
1
3
0
0
0
2
1
0
0
3
0
0
0
0
2
2
2
2
1
2
2
0
1
0
2
0
0
0
1
0
0
2
0
0
2
0
2
2
1
0
0
1
2
1
2
1
2
0
0
2
2
0
0
0
2
1
0
1
1
2
2
0
0
0
0
0
1
0
0
0
2
2
0
0
0
1
1
3
0
0
1
0
1
0
0
0
0
2
2
1
1
1
0
2
0
0
1
1
0
0
0
2
2
0
1
2
2
0
2
0
2
0
0
1
0
0
1
0
1
0
0
0
3
1
0
0
0
0
2
0
0
1
1
2
0
0
0
2
0
2
0
0
1
0
2
0
0
2
0
2
2
2
0
2
0
0
1
1
0
0
1
0
1
2
1
0
2
0
0
3
0
0
1
1
1
1
1
2
0
2
1
1
0
0
0
0
0
2
1
1
0
2
0
0
1
1
2
1
0
0
4
2
1
0
0
2
0
3
2
0
1
2
0
0
2
0
0
0
1
0
1
0
0
0
1
0
1
2
0
0
2
1
0
3
2
1
2
2
1
0
3
0
0
2
1
0
2
2
0
1
2
1
0
1
1
0
2
1
3
0
2
1
2
2
1
0
0
0
2
1
1
0
1
2
0
0
3
0
1
0
2
0
1
1
2
0
0
0
0
0
0
0
0
2
1
1
0
0
2
1
0
1
2
1
0
0
0
0
0
2
0
2
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
2
2
2
0
0
1
2
1
1
2
0
1
1
1
2
0
0
0
0
0
0
3
1
0
0
0
1
1
1
2
1
0
0
0
0
1
2
0
0
2
2
0
0
0
0
0
1
1
2
0
1
0
2
0
1
0
0
1
0
2
1
2
2
0
1
1
0
0
1
1
0
1
2
2
1
2
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
4
0
1
1
0
0
0
0
1
0
1
1
0
0
0
2
3
0
0
0
0
0
2
0
1
2
1
2
2
0
0
0
3
2
0
0
0
0
1
2
1
0
1
0
0
1
0
1
2
2
0
1
2
2
1
0
2
0
0
0
1
1
1
4
0
0
1
0
1
1
1
1
2
2
1
2
1
1
1
0
2
1
1
0
1
2
1
0
1
2
2
1
1
0
1
2
0
0
1
1
1
1
2
1
3
0
2
0
1
0
0
0
0
2
2
0
1
1
0
0
0
0
2
0
2
1
0
1
0
2
0
0
2
0
0
0
1
1
2
0
1
1
1
1
0
2
0
1
1
1
0
1
0
0
0
0
2
0
1
2
0
2
1
0
0
2
2
0
0
1
1
1
0
0
2
2
3
1
3
1
0
1
0
2
0
2
1
1
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
1
4
1
2
0
1
1
2
2
2
1
0
2
0
1
0
0
0
2
0
0
0
2
0
1
1
0
0
1
2
0
0
0
0
1
2
1
1
0
1
1
0
1
1
0
0
1
0
0
0
1
0
0
0
1
0
0
2
0
0
0
2
2
0
0
1
1
1
0
3
0
1
0
0
0
1
0
2
1
5
3
0
2
0
0
2
0
2
0
0
1
0
2
4
0
0
0
2
0
0
0
0
1
1
2
0
2
0
1
1
2
0
0
1
0
1
1
0
0
1
2
2
0
1
1
1
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
2
1
1
2
0
1
1
0
1
2
4
0
0
2
0
2
1
1
0
2
1
0
1
1
1
0
0
0
2
0
0
1
0
1
1
2
0
1
0
2
1
0
0
1
1
0
1
1
0
1
2
0
0
0
2
2
0
1
0
0
0
2
0
0
0
0
2
1
2
0
0
2
2
1
0
0
1
0
1
3
1
0
1
0
2
0
0
0
2
0
2
0
0
2
2
0
0
1
1
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
1
1
0
1
0
1
0
0
0
1
3
1
0
2
1
0
1
0
0
0
1
1
2
0
2
0
0
2
0
2
1
1
2
0
1
2
1
1
0
0
0
0
1
0
2
1
0
0
2
0
0
2
4
0
0
1
0
1
1
0
0
0
0
0
0
2
2
1
0
0
2
2
1
0
0
0
1
0
2
0
2
1
1
0
0
1
1
2
2
1
0
2
1
0
0
1
0
1
1
0
0
0
0
1
0
0
1
2
1
0
0
0
0
1
1
0
0
1
1
1
0
2
2
6
2
0
1
2
0
1
1
2
0
1
0
3
0
2
1
0
2
1
1
1
1
2
2
0
1
0
0
3
0
1
1
1
0
2
1
0
1
2
0
1
0
0
2
0
1
0
2
0
0
0
1
0
1
0
0
0
0
1
0
0
0
2
1
0
2
2
2
2
2
1
0
2
1
1
0
0
0
0
0
1
2
1
0
3
2
0
0
0
0
0
0
2
0
1
0
1
0
2
0
0
0
1
2
0
0
0
0
1
0
2
2
0
1
0
2
1
1
0
0
2
2
0
1
0
0
0
1
0
1
0
2
0
2
3
2
1
0
0
0
1
1
1
2
1
0
0
1
2
0
1
2
0
0
0
0
1
0
1
1
2
2
0
0
1
0
0
1
2
0
2
0
1
0
2
1
1
1
1
0
0
1
1
0
0
0
0
0
0
0
1
2
2
1
1
0
1
2
1
0
0
1
0
2
1
0
1
1
2
0
1
0
1
0
1
0
0
1
1
0
0
0
0
1
2
1
1
2
0
2
2
2
0
0
0
2
0
1
0
2
1
0
0
2
0
1
0
0
0
0
1
2
0
0
0
0
1
0
2
1
0
1
0
0
1
0
3
2
0
1
1
1
2
2
0
1
2
0
0
1
0
1
0
1
0
1
0
2
1
0
0
2
2
1
1
2
0
0
1
2
0
1
0
0
2
0
1
1
0
0
0
1
1
1
3
0
0
2
1
2
4
2
1
0
0
0
0
0
0
2
1
1
0
0
2
0
1
0
0
0
1
0
0
0
0
2
1
2
0
0
0
0
2
2
1
0
0
2
2
0
0
0
0
1
2
1
2
0
0
1
2
2
0
0
1
1
1
1
2
0
1
2
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
2
1
0
16
2
2
1
1
1
1
0
0
0
0
0
0
0
1
2
2
1
0
1
0
2
1
0
0
2
0
2
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
1
0
0
0
0
2
0
1
1
1
0
2
1
0
0
0
1
0
0
0
1
1
1
1
0
0
0
1
0
1
1
2
0
0
3
0
1
2
0
0
1
0
2
0
0
1
1
0
1
2
1
0
1
0
0
2
0
0
2
1
0
0
0
2
0
2
1
0
2
0
0
0
2
0
2
1
1
3
1
0
0
0
2
0
0
1
0
2
0
2
2
0
0
0
2
1
0
1
2
0
0
0
1
1
1
2
0
1
1
0
2
0
0
2
0
1
0
0
1
0
0
0
0
2
0
0
1
2
2
1
0
1
0
1
0
1
1
0
1
2
1
2
0
1
0
1
0
1
0
1
0
1
3
1
1
0
0
1
1
1
0
3
2
0
2
0
0
2
0
1
2
1
0
0
0
0
0
1
2
0
3
0
0
0
1
0
0
0
3
1
0
1
2
1
1
2
2
2
0
0
1
0
1
0
2
0
2
1
0
0
0
4
2
1
0
0
0
0
0
4
0
1
0
0
0
0
0
0
1
0
0
2
0
1
0
1
0
1
2
0
0
0
0
2
2
0
0
0
1
0
1
1
0
0
0
3
0
0
0
1
0
1
0
1
1
1
1
0
1
2
1
1
0
0
1
2
0
1
2
0
1
0
0
0
0
1
0
1
0
1
1
1
1
0
0
0
1
0
0
2
0
1
1
0
1
0
0
2
2
1
1
2
1
1
2
0
0
0
1
1
2
1
1
0
1
0
1
0
0
0
1
0
1
1
1
0
1
0
0
2
0
0
0
1
0
0
0
0
2
0
1
0
1
1
1
1
1
1
0
1
0
0
1
1
0
0
1
1
1
0
1
0
1
0
2
0
1
2
1
0
0
0
0
1
0
0
2
1
1
1
1
1
0
2
0
0
0
1
1
2
2
1
0
0
1
1
0
1
0
1
0
2
4
1
0
0
0
1
1
0
0
2
0
2
0
1
1
2
1
1
1
0
0
0
0
1
1
2
1
0
1
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
1
1
0
2
2
0
1
0
2
0
0
0
1
2
0
0
1
0
1
1
1
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
1
2
0
1
2
2
0
1
1
9
1
0
2
1
1
0
0
1
0
0
0
0
1
3
0
1
0
2
0
0
1
1
1
1
0
2
0
0
0
0
2
2
1
0
0
2
1
0
0
0
1
0
1
0
0
1
0
1
0
2
1
0
0
2
1
0
0
0
0
2
1
2
0
0
1
0
1
1
0
1
0
0
0
0
0
1
0
0
0
1
1
0
1
0
1
2
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
1
1
2
1
1
0
1
2
0
1
0
1
0
1
1
1
3
0
0
2
0
1
0
0
0
1
1
1
1
0
1
2
2
0
1
0
2
0
0
1
0
0
3
0
0
0
1
0
1
2
1
0
2
0
0
1
0
2
0
2
0
0
0
1
0
0
0
2
0
1
1
2
1
2
1
0
1
1
1
1
0
1
1
0
2
0
2
1
0
2
2
2
0
0
0
1
1
0
1
2
1
1
0
0
1
2
2
1
2
4
4
0
2
0
1
0
0
1
2
0
1
0
2
5
1
0
0
2
0
0
0
1
0
1
4
1
0
2
1
0
2
0
1
2
0
2
0
0
1
0
0
1
2
2
2
0
1
0
1
2
2
1
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
1
3
1
0
1
2
1
1
0
1
0
0
0
0
1
2
0
0
0
2
0
0
1
4
1
1
2
2
4
0
1
1
1
1
0
1
0
0
1
0
0
0
1
1
0
1
0
0
0
0
2
1
2
1
0
1
1
0
0
1
0
2
0
2
0
1
2
1
0
0
1
2
0
1
1
1
1
0
1
0
0
2
2
1
2
0
0
0
1
0
1
1
2
0
1
1
2
1
1
0
2
0
1
1
0
1
1
0
0
0
1
0
1
2
2
0
2
0
0
0
0
0
1
0
2
1
1
2
1
1
0
3
1
0
0
0
0
0
2
1
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
1
1
2
2
1
0
0
0
2
2
2
1
1
0
0
2
0
2
1
0
0
0
1
0
0
0
0
0
2
2
0
2
0
1
0
1
0
0
2
1
2
0
0
0
0
1
0
0
2
2
1
1
0
1
2
1
2
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
2
1
0
1
0
0
0
1
1
0
0
0
0
1
0
1
0
1
2
0
0
0
2
1
1
2
0
1
1
0
2
1
2
1
0
1
0
1
0
0
1
3
0
0
0
0
1
1
1
0
1
0
1
0
0
2
0
1
1
1
0
2
1
0
2
1
2
2
1
0
2
2
0
0
0
1
1
2
0
1
2
2
0
0
2
0
1
0
1
3
0
0
0
1
0
1
1
2
0
0
0
0
1
0
1
0
0
1
1
0
0
1
0
1
0
2
2
1
0
1
2
1
0
1
2
0
1
0
1
1
1
0
0
2
1
1
1
1
1
1
0
0
0
0
1
0
1
1
0
2
2
0
2
1
0
1
1
0
1
1
0
2
1
2
0
0
1
0
0
0
0
0
1
1
2
2
1
1
2
1
1
0
0
1
0
1
0
0
1
2
2
1
0
0
2
0
0
0
2
0
0
1
1
1
0
1
0
1
2
1
0
0
0
2
0
2
0
0
1
1
0
0
1
0
0
1
0
0
2
0
1
0
0
0
1
0
0
1
0
2
1
0
1
0
1
1
0
0
0
0
2
0
0
0
2
1
0
1
1
3
0
1
1
0
0
0
2
0
1
0
1
1
1
0
1
0
1
1
0
0
1
2
1
0
0
1
0
1
2
1
0
0
1
0
1
1
1
1
0
0
0
0
2
0
1
0
1
2
0
0
0
2
0
2
1
2
0
0
0
1
1
2
0
1
0
0
0
1
0
0
1
0
1
2
0
0
0
0
1
1
2
0
2
2
1
0
0
0
2
0
0
2
0
1
0
0
1
0
1
2
0
1
1
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
2
1
0
1
1
0
0
1
2
0
1
1
1
0
0
1
1
0
2
0
1
1
1
0
0
1
1
0
1
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
1
1
2
6
1
1
0
2
0
0
2
0
0
0
2
0
2
0
0
1
1
0
1
2
1
0
1
0
1
1
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
2
1
1
2
0
1
0
0
0
0
0
2
0
0
1
0
2
2
0
1
2
2
0
0
1
0
0
2
1
0
1
0
2
0
0
0
1
1
0
0
1
0
0
1
2
0
1
0
0
0
2
0
0
1
0
2
0
0
0
2
0
1
0
2
0
1
1
0
0
1
0
2
1
1
0
0
0
0
2
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
2
0
1
0
1
0
0
0
0
1
0
2
2
1
1
0
0
1
0
0
1
1
0
2
0
2
0
0
0
0
2
0
1
1
1
0
1
1
1
0
0
0
2
2
0
0
1
1
0
0
0
1
0
3
0
0
1
2
0
0
2
0
1
1
1
0
0
1
1
2
1
2
2
2
0
1
0
1
2
1
1
1
2
1
0
1
0
0
0
0
2
0
1
0
2
2
0
1
1
2
1
1
1
0
0
0
0
1
0
0
2
0
0
1
0
2
1
1
0
1
0
0
1
2
2
0
1
1
0
2
1
0
0
0
0
0
2
0
0
0
1
1
2
1
1
0
0
1
1
2
1
0
0
1
2
0
2
0
1
0
0
1
0
0
0
5
0
1
0
1
0
0
2
0
0
0
0
1
0
1
1
2
1
0
1
1
0
0
0
1
1
2
0
1
2
2
1
2
1
3
2
0
1
1
1
2
0
1
0
3
1
3
0
2
0
0
0
3
1
0
0
2
2
0
0
2
0
1
0
1
2
0
1
1
0
4
0
1
0
2
0
1
0
1
1
2
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
1
0
1
0
0
1
1
1
2
0
0
2
0
0
0
1
1
0
2
0
2
2
0
1
0
1
1
1
1
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
1
0
0
0
0
1
2
2
2
1
0
2
0
0
0
0
0
1
0
0
1
2
2
3
0
0
0
0
0
1
1
1
3
1
0
0
3
2
2
0
1
1
2
0
2
0
0
0
0
0
1
0
2
0
1
0
2
2
0
2
0
0
2
0
0
0
0
2
0
0
0
2
1
0
0
2
0
2
0
1
0
2
1
0
2
0
1
0
3
2
0
3
1
1
0
0
0
0
1
3
0
2
0
0
2
1
0
0
0
0
1
1
1
1
0
2
0
0
2
2
1
0
1
0
0
0
0
0
0
2
3
0
0
1
1
0
0
0
1
0
2
0
1
2
1
1
0
1
1
1
1
1
1
2
2
0
0
0
2
1
0
0
0
0
0
2
1
1
0
1
1
0
2
1
1
1
1
2
0
2
0
0
0
0
0
0
0
3
0
2
1
0
0
0
1
1
2
0
2
0
2
0
2
0
1
2
1
1
0
0
0
0
0
1
0
2
0
0
2
0
0
1
2
0
1
0
0
2
2
0
0
1
0
0
1
1
0
1
3
2
0
1
0
1
1
0
1
0
0
2
0
1
2
0
0
0
0
2
0
0
1
2
0
0
0
1
1
1
2
1
0
0
1
0
1
2
2
1
0
1
0
1
0
2
0
0
1
1
1
1
0
0
0
2
0
0
0
1
0
0
0
0
1
2
0
0
0
0
1
0
0
0
1
2
0
2
1
2
1
0
1
1
1
1
0
0
0
0
2
4
2
0
2
1
1
0
0
0
0
0
0
0
0
2
1
1
0
0
1
1
2
0
4
0
1
1
1
0
0
2
0
2
0
2
3
0
2
0
0
2
0
0
2
2
1
2
0
2
0
1
2
0
0
0
0
1
2
0
0
2
2
0
0
2
0
1
1
0
0
0
0
0
1
1
0
1
1
1
0
0
3
0
0
0
0
1
1
0
0
0
2
2
0
0
1
1
3
2
1
2
1
2
0
0
4
2
0
0
0
1
1
1
2
1
1
0
0
2
1
0
0
1
1
1
2
0
0
2
1
0
1
0
2
0
2
2
0
0
0
1
0
2
1
2
0
1
1
1
2
2
0
0
0
9
0
0
1
2
0
1
0
1
0
0
0
1
1
0
0
0
0
1
0
2
3
0
1
0
1
2
0
1
1
3
0
0
1
3
0
0
0
1
1
2
0
0
0
0
2
0
0
1
2
0
0
1
0
2
2
0
1
0
0
1
1
0
3
0
1
1
0
0
0
0
0
2
0
2
0
0
1
1
1
0
0
0
2
1
0
2
0
1
0
2
1
1
1
0
1
2
2
2
0
2
0
0
1
2
1
2
2
2
1
0
1
2
1
0
1
2
1
0
2
1
4
0
0
0
0
0
1
2
3
0
0
0
2
0
1
0
1
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
2
1
0
2
1
5
0
0
0
0
0
0
0
1
2
2
0
0
2
0
0
0
0
1
0
1
0
0
0
0
1
3
0
0
0
0
1
0
2
0
2
0
1
2
0
0
1
0
0
2
0
0
2
0
0
2
1
0
0
2
0
0
2
0
0
0
0
0
0
0
5
2
0
2
1
1
1
1
1
0
1
2
0
1
0
2
0
0
2
1
0
2
2
0
1
0
0
1
0
0
0
0
0
0
0
1
1
1
1
1
0
1
1
0
2
0
0
3
0
1
0
2
0
1
0
1
0
0
0
2
0
2
2
0
0
0
1
1
0
0
1
2
0
2
1
2
0
1
2
1
0
0
0
0
0
4
1
1
0
0
1
2
0
1
1
0
1
0
0
0
0
1
3
2
0
0
0
0
1
1
0
2
0
0
2
0
1
0
2
1
0
0
0
1
1
2
0
1
0
1
0
0
0
1
0
1
0
1
2
1
2
0
0
0
1
2
2
0
0
0
0
1
1
0
0
1
0
1
0
2
0
0
1
0
0
0
2
0
2
0
0
0
2
2
0
0
2
0
2
1
1
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
2
0
1
0
1
1
0
0
0
0
0
1
0
1
1
0
1
0
1
0
0
1
0
0
0
0
1
0
1
0
0
2
0
2
0
0
2
2
2
0
2
0
0
2
1
2
0
1
0
0
2
0
0
3
0
0
1
0
1
0
0
0
0
1
0
2
0
0
2
0
0
0
1
1
0
0
1
1
1
0
0
0
0
0
1
0
0
0
2
0
1
1
0
2
2
0
4
0
1
0
1
0
0
1
1
0
0
0
0
0
0
2
1
1
1
2
2
0
1
2
1
0
0
0
2
1
0
0
0
0
1
1
2
1
1
1
0
1
1
2
0
0
1
0
1
2
1
0
0
2
1
0
0
5
0
2
0
2
0
0
0
1
2
0
0
1
2
2
0
2
1
0
0
1
2
0
2
0
2
2
2
0
1
2
0
4
1
0
0
0
1
1
2
0
0
1
1
1
1
0
0
0
0
0
1
0
1
2
1
2
0
1
1
0
1
2
0
1
1
6
2
2
0
1
0
0
2
2
0
1
1
2
0
0
1
2
2
1
0
1
2
0
0
1
1
0
0
1
1
1
0
0
2
1
0
0
1
0
1
2
3
0
0
2
2
2
1
0
0
1
0
0
0
1
0
2
0
2
1
1
0
1
2
0
0
2
0
0
2
11
0
2
0
1
2
0
3
0
1
0
2
0
0
0
0
1
1
1
1
0
0
0
1
0
2
1
1
0
3
1
1
0
2
1
0
1
0
0
2
0
0
1
0
2
0
1
2
0
2
0
2
1
1
0
1
1
1
0
0
0
1
0
0
1
1
0
0
0
0
1
2
0
2
1
3
0
2
1
0
1
1
0
2
0
1
0
0
0
0
2
0
1
2
2
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
2
2
1
1
1
0
0
0
1
1
2
0
2
0
2
2
0
1
1
2
0
2
2
0
1
0
3
2
0
0
1
0
0
2
1
0
2
1
2
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
2
0
2
0
0
2
2
2
0
0
0
1
1
0
0
1
2
0
1
0
4
2
2
0
0
0
2
2
0
1
1
3
0
1
0
0
0
0
1
2
1
0
0
0
2
2
0
2
0
0
1
2
2
3
0
0
0
2
0
1
1
2
0
2
0
1
1
1
0
1
2
0
0
0
1
1
0
2
0
0
1
1
2
0
1
0
0
2
1
2
2
0
2
0
1
1
0
1
2
1
2
2
0
1
0
2
1
0
0
0
0
0
11
1
0
0
1
1
1
1
0
0
1
2
0
0
0
1
0
2
0
1
2
0
0
0
2
1
2
0
1
1
0
1
0
0
0
2
1
2
0
2
1
0
1
1
1
0
0
1
0
0
0
1
1
0
2
2
1
0
0
2
2
0
1
0
0
1
0
3
2
1
0
0
0
1
0
2
2
0
2
4
0
0
1
0
1
2
0
1
0
1
5
0
0
2
1
0
1
1
0
0
2
2
0
0
0
2
0
2
1
1
1
0
0
1
1
0
0
0
1
0
2
2
1
2
0
0
0
0
0
2
1
0
2
1
0
2
1
3
0
1
0
0
0
2
2
2
1
0
2
0
2
1
1
1
0
0
2
2
1
0
2
1
1
0
1
0
1
2
2
1
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
2
2
0
2
0
1
0
1
0
1
1
1
1
0
2
0
0
2
0
1
0
0
0
0
1
2
0
2
0
0
2
1
0
0
2
1
0
1
0
2
0
0
1
2
0
1
1
0
1
1
0
1
1
1
2
1
2
0
2
2
0
0
0
3
1
0
0
1
1
1
0
1
0
1
2
1
0
0
2
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
2
2
0
0
1
1
0
0
0
2
0
1
2
1
0
1
1
1
1
2
1
0
0
2
1
2
0
2
1
0
0
1
0
0
3
2
0
0
0
1
2
0
1
2
1
1
0
1
0
0
1
2
0
0
1
0
1
0
0
1
0
1
0
0
0
1
1
1
1
0
1
1
2
0
1
1
1
1
0
0
0
0
0
1
1
1
1
2
1
1
0
0
1
0
1
0
2
0
0
1
0
3
0
2
0
1
1
0
1
0
2
0
1
2
0
1
1
0
0
1
1
0
1
0
0
1
0
0
3
1
0
0
0
2
0
0
0
2
2
2
0
3
0
0
1
0
1
0
0
2
0
1
0
1
0
0
1
2
2
0
1
0
2
1
0
0
0
0
1
0
1
0
1
0
0
0
0
2
0
2
1
0
2
1
0
1
0
2
0
0
1
0
0
0
0
0
1
0
1
0
0
0
2
2
0
0
0
0
3
2
0
1
0
0
3
1
0
1
0
1
1
0
2
0
0
1
2
2
2
1
1
0
2
3
4
2
2
1
0
0
0
0
1
1
0
2
0
1
0
1
1
0
0
0
2
2
2
1
0
0
0
0
1
2
0
5
2
1
0
0
3
2
0
2
1
0
1
0
1
0
0
0
0
1
0
2
1
5
0
1
0
0
1
0
1
1
0
1
0
1
3
2
0
2
0
0
2
1
0
0
2
1
1
2
2
1
0
0
2
2
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
2
1
2
0
1
0
1
2
2
1
2
0
2
2
1
0
1
0
0
1
0
0
2
2
0
0
0
0
1
0
0
1
2
2
1
1
0
1
1
1
0
0
0
0
2
0
0
0
0
1
0
1
0
0
1
0
1
0
1
0
1
1
0
0
1
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
1
1
0
0
0
3
2
0
2
1
0
2
1
1
1
2
2
1
0
0
2
0
0
0
0
0
0
1
2
0
0
1
0
0
0
1
2
0
1
0
2
0
0
1
1
0
0
0
2
0
2
0
1
1
0
0
1
0
0
0
0
2
0
0
2
1
0
1
0
2
0
2
2
0
0
0
1
1
2
2
0
0
0
0
1
0
0
0
0
0
2
2
2
0
1
0
3
2
0
2
0
0
1
1
2
1
2
0
1
2
2
3
2
1
0
2
1
0
0
0
9
1
1
0
0
0
1
1
1
1
1
2
0
0
0
1
1
1
2
0
3
1
0
0
0
0
0
0
0
2
0
0
1
1
1
0
0
1
2
0
0
0
2
0
0
2
0
1
0
0
0
2
1
2
0
0
0
0
0
3
0
1
1
3
0
0
2
1
0
2
0
0
1
1
1
0
0
1
0
0
0
0
2
2
2
0
0
2
3
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
1
1
0
1
0
1
0
0
0
1
0
2
0
0
0
0
1
1
0
1
0
0
1
1
1
0
1
1
3
0
0
1
2
2
0
1
1
2
0
0
0
1
1
0
0
0
0
0
1
1
0
0
1
1
1
0
1
0
0
0
2
2
2
2
0
1
0
0
1
1
1
1
2
0
0
2
0
0
2
1
0
2
0
1
0
1
2
1
0
1
0
0
0
0
0
0
0
0
2
2
1
0
0
1
3
1
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
2
0
0
1
0
2
0
0
1
2
0
2
0
0
0
3
1
1
0
0
0
0
0
1
1
0
3
4
2
3
0
0
0
0
1
0
1
1
1
2
2
2
0
0
0
0
1
0
1
2
1
1
1
2
0
1
0
0
1
1
2
0
1
1
0
2
1
1
0
1
1
1
1
1
0
2
1
0
0
1
0
4
2
2
1
1
1
0
1
0
1
2
1
2
0
1
2
1
0
1
0
0
0
2
0
1
0
1
0
0
0
3
0
0
0
1
0
2
0
2
2
0
0
2
0
0
0
1
1
2
2
2
0
1
2
2
2
0
0
0
1
2
0
1
0
1
0
0
0
1
1
0
0
0
2
2
3
2
1
0
1
2
0
0
0
0
1
1
0
0
0
0
0
0
1
1
1
0
0
2
0
1
0
1
0
0
1
2
1
1
1
0
1
1
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
1
0
1
1
1
1
0
0
0
0
2
1
0
1
0
1
0
1
1
0
0
0
2
1
1
2
0
0
4
0
1
1
1
1
0
0
2
1
1
0
1
0
1
0
0
2
0
0
0
1
0
1
2
1
1
0
0
0
0
0
0
1
0
2
1
2
1
0
0
0
0
0
2
2
1
0
0
0
0
2
1
1
1
2
0
1
1
2
2
2
0
0
0
0
1
0
1
1
1
0
1
0
2
1
1
1
0
1
0
1
0
0
2
2
1
0
0
2
0
1
2
1
2
0
0
0
0
0
0
1
1
0
2
1
0
0
0
1
0
0
0
2
0
2
2
1
1
2
1
1
0
0
1
2
1
0
1
2
0
0
1
0
1
3
1
0
0
0
1
0
2
0
0
1
1
0
1
0
0
1
3
0
0
2
0
0
0
2
0
0
0
2
0
1
1
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
3
2
2
0
1
0
0
1
0
0
0
1
1
0
0
0
1
0
1
0
1
1
0
1
0
0
0
2
2
1
2
0
0
0
0
0
0
1
1
0
1
1
1
1
0
2
2
1
1
2
1
0
2
0
0
0
1
3
1
0
0
0
2
1
0
0
0
1
1
0
0
1
0
1
0
2
0
1
0
0
0
0
1
0
0
0
0
0
2
1
1
0
0
0
0
0
0
1
1
0
0
2
1
1
2
0
0
0
0
0
2
2
1
0
0
0
0
2
0
1
1
1
0
1
1
1
1
0
0
1
0
0
1
2
0
2
0
0
2
2
0
0
1
0
1
1
0
0
1
0
1
1
0
1
0
3
1
2
2
2
0
0
1
0
0
1
0
1
2
1
0
0
1
1
0
3
0
1
0
0
0
2
1
1
0
1
0
1
0
0
0
1
1
0
2
0
1
0
0
1
0
1
0
1
2
0
2
2
0
0
0
0
0
0
1
0
0
2
0
2
4
0
2
0
2
2
0
1
0
0
0
0
0
1
0
0
1
0
0
0
2
1
0
0
1
2
0
0
0
0
1
2
0
0
0
1
2
0
0
0
2
0
1
0
0
0
2
1
0
1
0
2
0
2
2
0
0
0
1
0
2
1
2
0
1
2
2
0
2
0
0
0
0
1
1
0
1
2
1
2
0
2
1
2
2
0
0
1
1
1
1
3
2
1
0
2
0
2
0
1
1
1
0
0
0
0
0
0
0
2
1
0
2
0
2
1
1
0
0
1
0
1
0
2
0
2
0
0
0
2
0
1
2
1
0
0
1
0
0
2
0
2
0
2
0
0
1
1
1
0
0
2
1
0
1
1
1
0
2
2
0
0
0
1
2
2
0
0
0
1
0
0
1
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
2
0
0
0
1
1
0
3
2
0
1
1
0
0
0
1
1
0
2
0
0
0
0
0
0
1
0
1
1
2
2
0
0
0
2
0
0
0
1
0
0
4
1
1
0
1
2
2
0
0
1
1
2
0
1
2
0
0
0
0
1
0
0
2
1
2
0
0
1
2
1
1
0
0
1
2
0
1
1
0
0
0
2
2
1
0
0
0
2
1
0
1
2
1
1
0
1
0
1
1
0
2
0
0
1
0
0
1
0
2
1
1
0
0
0
0
0
1
2
1
0
3
2
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
2
1
2
0
0
0
0
1
2
1
1
0
2
0
1
0
0
0
0
0
0
1
2
0
0
0
0
1
4
0
1
2
2
0
0
2
2
0
2
2
0
1
2
1
0
1
1
0
0
0
2
2
2
0
1
0
0
0
2
0
2
0
2
7
2
2
1
0
1
0
0
1
2
2
0
2
1
0
1
0
1
2
0
0
0
0
0
2
1
0
0
1
1
0
0
2
0
1
2
2
2
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
2
0
1
0
2
0
1
0
1
1
2
0
2
0
4
0
2
0
2
2
0
0
0
0
1
1
0
0
1
0
1
0
0
1
0
0
0
0
1
2
0
2
2
0
0
2
0
2
0
0
0
1
2
1
1
0
0
0
1
1
2
0
1
0
2
0
1
0
1
0
3
1
0
1
0
0
1
0
2
0
1
2
3
1
1
2
0
0
2
0
0
2
1
2
1
0
1
0
1
2
5
2
1
1
2
0
0
1
2
1
0
1
0
0
0
0
1
2
0
1
2
1
0
0
0
1
0
1
1
1
0
0
0
2
0
1
0
2
0
1
2
2
1
1
0
0
2
1
0
2
0
0
0
1
1
0
2
0
0
0
2
0
0
0
1
0
0
1
0
2
1
0
1
1
2
1
2
0
2
4
1
0
0
1
1
1
0
2
1
0
2
0
0
1
0
2
3
1
1
0
2
0
0
3
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
1
2
1
2
1
0
0
0
0
2
0
2
0
1
0
0
1
0
0
0
0
3
1
0
0
0
0
2
1
0
0
2
1
2
2
2
1
2
0
0
0
0
0
0
3
0
1
0
1
0
0
0
1
0
0
1
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
2
0
1
0
0
0
0
2
1
0
0
1
0
0
1
2
1
0
1
1
0
1
0
2
2
1
0
0
0
2
3
1
0
0
0
1
1
3
0
1
0
0
0
2
0
1
0
0
1
1
2
0
0
2
1
1
1
1
0
0
1
0
0
0
0
1
0
2
0
0
0
4
1
2
1
2
2
0
0
0
1
1
0
1
0
1
1
1
1
2
1
2
1
0
1
2
1
2
0
1
0
0
0
0
0
1
0
1
1
0
1
0
2
1
2
0
1
0
2
1
0
1
0
2
0
3
0
1
0
0
1
0
0
1
1
0
1
1
0
2
0
0
0
0
1
0
2
1
1
2
1
2
2
0
0
0
0
0
1
0
1
0
3
2
0
3
0
1
0
1
0
1
1
1
0
0
0
0
0
1
1
1
0
0
0
2
0
1
0
1
0
0
3
1
0
0
0
0
1
2
1
1
1
0
1
0
0
0
0
0
0
2
0
3
0
2
0
2
1
0
2
2
2
0
0
0
2
1
0
1
1
1
0
0
0
1
0
0
0
1
1
0
0
1
0
0
3
0
2
0
0
1
0
2
0
0
0
1
0
1
0
0
1
6
1
1
0
0
2
1
0
0
1
1
0
2
1
1
0
2
0
2
0
0
0
1
2
0
3
1
0
1
1
2
2
0
1
0
0
2
2
0
1
1
0
1
1
0
0
0
0
0
2
0
2
2
0
0
0
0
1
1
0
1
0
1
2
1
0
2
1
2
2
0
1
1
0
2
0
2
0
1
2
2
1
1
2
1
1
0
1
0
0
2
2
1
1
1
1
1
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
1
1
0
1
0
0
2
0
1
2
2
0
0
0
0
0
0
1
3
1
1
2
0
0
2
1
2
0
1
2
0
2
1
1
0
0
1
0
3
1
0
1
2
0
0
0
0
0
1
0
1
2
1
1
1
0
1
1
2
0
2
0
1
0
0
0
1
0
1
1
0
1
0
0
0
2
0
1
1
1
0
0
0
1
0
2
0
0
1
0
0
0
1
0
2
1
2
1
1
2
1
0
0
0
1
0
1
2
0
0
0
1
1
1
0
1
0
2
0
2
0
2
2
1
0
1
0
0
1
2
0
1
1
1
1
2
0
1
1
0
1
0
0
0
0
0
1
1
2
0
0
2
1
1
1
2
0
0
0
1
2
1
2
3
2
1
2
0
0
0
0
1
1
2
0
0
3
1
0
0
3
0
0
1
1
0
0
1
1
1
1
0
0
0
1
1
2
0
1
0
0
1
0
1
0
0
1
2
0
1
1
3
2
1
1
0
1
1
1
0
3
0
0
2
1
2
0
1
1
3
1
0
2
2
0
2
0
0
0
0
1
0
0
3
1
0
0
0
2
1
1
0
1
0
2
1
1
0
0
0
0
0
2
1
2
0
1
0
0
0
0
2
2
0
1
1
0
0
0
0
0
1
0
0
0
2
0
0
1
2
1
0
1
0
2
2
1
2
2
2
0
3
0
2
0
0
0
0
0
1
1
1
0
0
2
0
1
0
2
3
0
6
0
1
0
0
1
0
0
0
0
1
1
0
1
1
3
2
0
0
0
0
1
1
1
3
2
0
3
0
0
0
2
0
0
0
1
0
1
1
0
0
0
0
1
0
0
1
0
2
0
3
0
0
1
0
2
0
1
0
2
0
1
0
2
1
1
0
0
1
1
2
2
0
0
1
0
1
2
1
2
2
1
2
0
2
2
0
1
3
0
0
0
0
0
1
2
2
0
1
2
2
0
0
0
1
1
0
2
1
0
0
0
2
0
1
1
0
2
1
0
1
0
2
1
0
0
0
0
1
2
1
0
0
1
2
0
0
1
0
1
0
0
0
0
3
3
0
0
0
0
0
2
0
2
1
2
2
0
1
2
1
0
0
0
3
1
1
2
2
1
0
0
0
2
2
3
0
0
0
0
0
0
2
2
2
1
0
1
1
2
1
2
0
2
1
2
1
2
2
1
1
0
0
2
1
1
0
1
0
0
2
0
1
1
0
0
0
1
1
2
1
1
0
0
0
0
1
2
2
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
2
0
2
1
2
2
1
0
0
1
0
0
1
0
0
1
0
2
0
1
0
2
0
1
0
0
0
1
1
2
2
3
2
0
2
0
0
0
0
1
1
1
0
1
2
1
0
1
0
1
1
0
0
0
0
0
0
0
0
1
1
1
0
2
1
0
1
1
1
0
1
1
0
2
0
0
0
0
2
1
1
2
1
0
2
2
2
2
0
0
0
1
0
0
1
1
1
0
0
0
2
0
0
0
0
1
1
2
1
1
1
0
1
1
0
0
0
1
0
0
1
0
2
1
1
0
0
1
2
0
4
0
0
0
1
1
0
0
0
0
1
0
1
0
2
1
0
0
0
1
0
1
2
0
1
1
1
2
0
4
0
0
0
1
0
2
1
1
1
0
1
0
2
1
0
2
4
1
1
1
4
0
1
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
2
0
0
1
0
0
0
1
0
2
1
1
1
0
1
2
0
0
1
1
0
0
0
0
1
1
0
0
1
2
0
0
1
2
0
1
1
0
1
1
1
2
0
2
0
1
1
0
1
2
0
2
1
2
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
1
0
2
0
1
1
2
2
0
1
0
0
1
0
2
0
0
2
2
1
1
0
2
1
1
0
2
0
1
0
0
0
0
1
0
1
0
0
0
2
0
2
1
0
0
0
0
1
0
0
0
0
0
2
0
0
1
1
0
0
2
0
1
1
0
0
0
1
0
0
1
0
1
0
1
2
0
1
2
1
0
1
1
0
0
0
0
0
1
0
2
0
0
0
1
1
1
0
0
2
0
0
2
0
1
1
0
2
0
1
2
0
2
2
1
0
2
1
0
0
0
0
1
0
0
1
1
1
0
1
0
2
1
1
0
1
2
2
2
0
0
1
1
2
0
1
2
0
0
2
0
0
2
1
0
1
3
1
1
0
1
1
2
0
2
2
2
1
0
2
0
2
0
1
1
0
0
1
0
0
2
0
1
2
2
1
2
0
0
1
1
0
2
1
0
2
1
0
1
2
0
0
2
0
2
2
2
0
1
0
0
0
0
1
0
0
0
2
2
2
0
1
0
0
2
0
0
1
1
3
0
1
0
0
0
1
0
1
0
0
0
1
2
2
0
0
0
2
2
1
0
0
0
1
1
0
0
2
2
0
0
1
0
0
0
0
1
0
0
1
0
0
0
2
0
1
0
0
2
0
0
0
0
1
1
0
2
1
1
3
0
1
0
0
1
2
0
2
1
1
1
1
2
0
1
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
1
0
2
0
1
1
0
0
2
0
2
1
0
0
1
1
0
1
0
0
3
0
0
2
1
0
0
3
0
0
0
0
0
0
1
0
0
3
0
2
2
1
2
0
1
0
0
1
0
1
1
1
0
0
0
0
1
0
0
0
0
2
3
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
2
0
0
2
3
0
2
1
0
1
1
0
0
1
2
1
1
1
0
1
2
0
0
0
1
0
1
0
2
2
1
2
0
0
0
0
0
2
0
0
1
1
1
1
0
0
0
2
1
0
2
0
2
2
1
0
1
0
0
2
1
1
0
1
0
0
2
0
0
1
0
0
2
0
0
0
1
1
1
1
2
2
2
1
0
1
0
0
0
2
1
2
0
0
1
1
0
0
0
1
2
0
0
2
0
0
0
0
1
2
0
0
1
1
0
2
1
0
1
0
0
0
2
1
0
2
3
0
0
1
0
1
2
0
3
0
0
1
2
1
0
1
0
0
0
0
0
1
2
0
0
0
0
2
1
2
1
0
0
1
1
1
0
0
2
1
1
2
0
1
0
1
2
0
1
2
2
0
0
0
1
3
0
0
2
2
0
0
1
0
1
1
1
1
0
0
0
0
0
1
0
0
0
2
2
1
0
2
2
0
0
2
0
0
0
2
0
1
0
1
0
0
1
0
1
0
2
2
1
1
0
1
0
0
0
1
0
1
1
1
0
0
0
0
0
0
1
0
3
2
0
2
2
2
0
0
0
2
2
1
0
1
2
0
0
1
2
0
0
2
1
3
0
1
0
1
2
1
0
0
2
1
0
1
0
0
0
0
1
0
0
1
0
0
1
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
1
1
0
0
0
2
1
0
0
0
0
0
0
1
0
1
2
2
0
1
0
0
3
2
0
1
2
0
1
0
0
0
0
4
2
2
0
0
1
1
0
1
1
1
0
0
2
1
2
0
1
0
1
2
0
0
0
2
0
1
0
1
1
1
2
0
1
0
1
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
2
0
2
1
0
1
0
1
1
0
0
0
0
2
0
3
1
1
1
0
0
2
1
0
0
0
0
1
1
0
0
0
0
0
2
0
2
2
2
2
0
2
1
1
1
0
2
1
0
2
1
0
1
0
0
0
2
0
0
0
1
2
0
2
2
1
0
1
0
0
0
0
0
1
0
2
1
0
2
1
1
1
3
2
0
0
0
1
1
0
0
1
0
0
2
0
0
1
0
1
1
0
2
4
0
0
0
0
1
0
1
0
0
0
0
2
1
2
2
2
0
1
0
1
0
2
1
0
1
0
2
1
2
0
0
0
0
0
0
2
1
1
1
2
0
1
1
0
0
0
2
0
1
1
2
0
2
0
0
0
2
2
1
0
0
0
0
2
0
0
1
0
1
0
0
1
2
0
2
0
0
0
0
0
0
2
0
0
0
2
2
2
1
1
1
1
2
0
0
4
0
1
0
2
0
0
1
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
2
0
2
1
1
1
2
0
0
1
0
1
0
1
2
1
0
0
3
0
1
0
0
1
1
2
1
1
0
0
0
2
0
0
0
1
1
1
0
1
1
1
2
0
1
0
0
1
0
0
1
0
0
1
0
0
0
1
1
2
0
0
2
0
1
2
0
0
1
3
1
1
1
4
0
0
2
0
0
0
0
1
1
0
1
1
0
1
0
0
0
1
0
0
1
1
0
2
0
0
0
0
0
0
2
0
1
0
0
1
1
1
1
0
2
0
2
0
1
0
3
0
0
0
1
1
1
2
2
2
0
0
0
0
1
1
0
0
0
1
2
1
2
1
0
0
0
0
0
0
0
0
2
1
0
1
0
1
1
0
2
1
1
0
1
2
2
1
0
0
0
0
3
0
0
0
0
0
1
1
2
1
0
2
0
1
2
0
2
1
0
0
0
2
2
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
1
1
0
1
1
0
0
2
0
1
1
0
2
2
0
1
0
1
0
1
9
1
0
0
1
0
0
1
1
0
2
0
3
0
1
0
1
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
2
0
0
0
0
0
1
1
0
0
0
1
0
2
0
1
0
0
0
4
0
0
2
0
1
0
0
1
1
0
0
0
0
0
0
0
2
0
0
1
0
2
2
1
0
0
0
1
1
1
0
2
1
1
0
0
0
0
0
0
1
3
2
1
0
0
0
0
1
1
1
1
0
1
1
0
1
0
1
0
0
1
2
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
1
2
0
2
0
1
0
1
2
0
1
0
0
2
0
1
0
1
0
0
1
2
0
0
2
1
1
0
1
0
0
1
1
1
0
0
2
0
2
0
0
0
0
1
0
2
1
2
1
0
0
0
0
1
0
0
0
1
1
1
1
0
0
0
1
2
0
2
0
2
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
1
1
0
2
0
0
0
0
0
1
2
0
2
2
0
2
2
1
0
1
1
0
0
0
1
1
2
1
1
0
1
0
0
0
0
2
0
1
0
2
1
0
0
0
2
0
1
2
1
1
1
1
0
1
2
0
1
0
1
1
0
0
1
0
1
2
1
1
1
2
2
0
2
0
2
2
0
3
0
0
2
0
0
0
0
2
0
0
3
0
2
0
0
1
0
1
0
2
0
2
1
1
0
3
0
0
0
0
1
2
0
0
0
0
0
1
2
0
1
2
0
0
0
0
2
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
3
0
0
1
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
2
2
0
1
2
2
1
2
0
1
1
0
0
1
0
0
2
0
0
1
0
0
0
1
0
0
1
2
1
1
2
0
0
1
2
0
2
1
2
2
1
1
0
1
0
1
2
1
2
2
2
0
1
0
0
0
1
0
0
0
0
2
1
1
1
0
2
0
1
2
1
1
1
0
0
1
2
0
3
1
2
1
0
3
0
1
0
0
0
0
2
0
2
0
3
2
0
2
2
2
0
1
1
0
1
2
0
1
0
0
2
1
1
0
1
1
1
1
1
1
0
2
1
0
0
1
0
1
2
1
1
0
0
2
1
0
0
1
0
1
1
0
2
0
0
0
0
2
0
1
2
1
1
1
2
0
0
0
0
4
0
0
0
2
2
0
1
0
1
0
0
2
1
1
0
1
1
0
0
1
0
2
1
2
0
1
0
0
0
2
1
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
2
1
1
1
2
0
1
0
3
0
1
0
2
0
1
0
0
0
0
0
2
0
0
1
0
0
1
0
2
0
1
1
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
2
1
0
1
0
0
0
2
0
1
1
2
0
0
1
0
0
1
0
0
0
0
0
0
0
2
1
0
0
1
2
0
3
0
2
2
2
2
1
1
0
0
2
1
3
0
1
2
0
3
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
2
2
0
0
0
0
1
0
1
0
2
1
0
0
0
0
0
0
1
0
2
2
1
2
0
0
2
1
0
2
0
2
0
2
0
0
2
0
0
0
2
0
2
0
2
0
0
2
0
1
2
2
0
0
1
0
0
1
2
0
0
1
3
0
2
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
1
2
2
2
2
0
1
2
0
0
1
1
1
0
0
1
0
1
0
1
2
1
0
0
1
1
1
1
0
1
2
1
0
2
2
1
2
2
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
1
0
2
0
0
1
0
1
0
0
1
0
0
1
0
1
0
1
0
0
4
0
0
0
2
2
2
0
0
2
0
0
2
1
0
1
0
1
2
1
0
1
2
0
2
2
0
0
0
2
2
0
2
1
2
0
0
0
0
2
2
0
0
0
1
1
2
0
2
1
0
1
0
0
0
2
1
1
0
1
0
0
1
0
2
1
1
1
1
1
0
1
0
0
1
0
1
0
2
1
1
1
2
1
0
0
2
1
1
2
1
1
0
0
1
0
0
2
1
0
1
0
0
1
1
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
2
0
1
0
2
0
1
2
2
1
2
2
0
0
0
2
1
0
0
0
2
0
2
2
0
0
1
0
0
1
1
1
0
1
0
2
2
0
1
1
2
0
1
1
0
2
0
1
1
1
1
2
1
1
0
0
0
1
0
1
0
2
2
2
1
1
1
0
0
1
1
1
1
2
0
2
1
0
2
2
2
0
2
1
2
2
0
0
0
1
0
0
0
1
1
1
0
1
0
2
1
0
1
0
0
2
1
2
1
2
0
0
1
0
0
0
1
1
1
0
0
1
0
1
0
1
2
0
0
1
1
1
1
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
2
0
1
0
0
3
2
0
1
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
1
3
1
2
1
0
0
0
1
1
1
2
2
1
0
1
0
0
0
1
0
1
0
0
1
1
2
0
1
2
0
0
0
0
2
2
1
0
0
2
2
0
2
1
0
0
0
2
0
2
1
1
2
0
0
0
1
1
1
0
1
0
2
0
1
2
1
1
0
1
2
0
0
0
0
0
1
0
2
0
2
0
1
2
1
0
2
0
0
1
1
0
1
0
0
1
0
1
0
0
0
2
1
3
0
0
0
1
0
0
0
0
2
0
1
0
1
0
1
2
1
2
1
0
1
1
0
0
0
2
0
0
0
0
2
1
0
4
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
1
0
0
1
2
1
2
0
0
0
1
2
1
2
1
1
1
4
2
0
1
1
0
0
2
0
1
3
0
0
2
0
0
0
0
2
2
0
0
1
0
1
1
3
2
1
0
0
0
1
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
1
1
0
2
0
0
0
1
0
1
1
0
0
0
1
2
0
0
0
2
0
0
2
0
2
1
0
1
0
0
0
0
1
1
1
2
1
0
1
0
0
2
2
0
1
2
3
0
0
2
2
0
2
1
1
2
1
0
1
1
1
1
0
1
2
0
0
0
0
0
2
0
1
0
2
1
1
0
1
0
1
0
0
0
1
1
0
2
0
0
2
1
0
1
0
0
2
3
2
0
0
1
1
0
2
1
0
0
2
0
0
0
0
0
1
0
0
1
1
1
1
1
1
0
0
5
1
1
1
1
1
1
0
1
2
0
0
0
2
2
1
0
0
0
0
2
2
0
1
0
0
2
1
0
1
0
1
0
0
0
0
0
2
2
0
2
0
1
1
1
0
0
1
1
0
1
0
1
2
0
0
1
2
0
1
1
0
2
1
1
1
1
0
0
2
1
0
1
2
1
2
1
1
0
0
1
0
0
0
0
1
1
0
2
0
1
1
0
0
0
0
0
1
0
1
0
0
1
0
2
2
0
0
1
0
1
0
0
1
0
0
1
0
0
2
1
0
2
0
0
0
1
2
0
1
0
0
0
0
1
5
0
0
1
2
0
0
2
0
0
0
1
2
1
1
2
0
0
2
1
0
0
1
2
0
0
2
1
1
2
0
0
0
2
2
2
0
6
0
1
2
0
1
0
0
0
0
1
1
1
0
0
2
1
1
1
0
1
1
0
2
3
2
0
1
0
0
0
2
2
4
2
0
0
0
2
0
1
2
0
0
0
0
0
1
2
2
0
3
1
2
2
0
1
0
1
1
1
0
1
0
0
0
2
2
0
0
0
0
1
0
1
0
1
0
0
1
1
0
2
0
1
1
1
0
1
0
1
1
2
1
0
1
1
0
1
2
1
1
1
2
0
1
1
0
2
1
0
1
1
1
1
0
1
0
1
0
0
2
1
2
0
0
2
1
0
2
2
1
0
1
2
0
4
0
2
0
2
1
1
1
0
1
0
0
0
0
3
0
0
1
2
0
0
2
0
0
0
0
0
1
1
0
1
0
0
0
1
1
1
0
0
2
2
1
0
0
1
1
0
1
0
0
0
0
0
0
2
0
2
1
1
1
0
0
1
0
2
0
1
1
1
0
0
1
0
0
2
2
1
0
1
1
1
2
1
1
0
2
1
0
0
2
1
0
0
0
1
2
2
1
0
0
2
2
0
0
1
0
0
1
0
1
0
0
2
0
0
1
0
0
0
0
2
0
1
2
1
1
1
1
1
0
0
1
2
0
1
2
2
0
1
2
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
3
1
1
2
0
1
2
0
2
2
0
0
1
1
0
2
0
0
1
4
0
2
2
2
0
0
0
1
1
0
0
3
2
0
0
0
2
2
2
0
0
1
0
2
0
1
0
0
1
2
0
2
1
0
0
2
2
0
0
0
1
1
3
2
0
0
0
2
2
0
0
0
0
0
1
1
0
2
0
2
1
0
0
1
0
0
0
0
1
1
1
0
0
2
0
0
2
2
1
0
0
1
1
1
0
0
1
1
3
0
0
0
0
0
2
0
2
2
1
1
2
2
0
0
3
0
0
0
0
1
0
2
1
0
0
2
0
0
0
5
0
1
1
1
2
2
2
1
0
0
0
0
0
0
0
1
0
1
0
0
1
2
1
0
0
1
0
2
1
1
4
8
1
2
1
0
1
0
2
0
2
0
1
2
0
1
2
0
2
2
2
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
2
1
1
0
2
0
0
0
1
2
0
2
2
0
0
1
0
0
4
1
1
0
0
2
0
2
1
1
0
0
2
0
0
0
0
2
1
2
0
1
4
0
1
0
1
1
1
0
2
1
0
0
0
0
2
0
1
0
0
1
0
1
0
0
0
1
1
0
2
0
1
0
0
1
1
2
1
2
0
0
1
0
1
0
2
0
0
0
0
2
2
2
2
3
0
1
1
2
0
0
1
1
1
2
2
1
0
1
0
0
1
0
1
0
0
1
0
0
2
1
1
0
1
1
0
0
0
0
2
0
0
0
2
0
2
0
0
2
1
1
0
1
0
0
2
1
0
0
1
0
0
0
0
1
0
0
1
0
2
1
1
1
2
1
1
0
0
1
1
2
1
0
1
2
2
1
2
2
0
1
0
0
0
0
1
0
1
0
0
2
1
0
1
2
2
1
0
0
2
0
0
1
2
0
2
1
1
0
1
1
0
4
1
0
0
2
0
0
2
0
0
1
0
2
0
1
1
1
0
2
2
0
0
0
0
0
2
0
1
0
0
2
0
1
1
1
0
1
2
1
1
0
0
2
0
1
0
2
0
0
0
0
2
1
1
1
1
2
2
0
0
2
1
0
1
1
0
1
0
1
1
1
0
1
1
0
2
0
1
1
1
1
0
0
1
1
2
0
0
2
2
0
0
1
1
1
0
1
2
0
0
1
0
0
2
1
0
1
0
0
0
2
0
0
2
1
1
0
1
1
2
0
0
0
0
0
0
1
2
2
2
1
2
2
3
0
0
0
1
1
0
1
0
0
2
2
1
1
1
0
0
1
1
0
0
2
0
1
0
0
0
1
0
0
0
0
0
2
2
0
1
2
0
0
1
0
0
0
0
2
1
0
0
0
0
1
0
0
2
0
0
0
0
1
1
2
0
1
0
0
2
1
0
1
2
1
1
0
0
0
1
0
0
1
2
1
1
2
1
0
2
0
2
2
1
0
0
2
0
2
1
2
2
2
1
2
6
0
1
0
0
1
0
0
1
2
1
0
1
0
2
0
2
0
2
1
0
0
2
2
0
3
0
2
2
0
1
0
2
2
0
1
2
3
1
0
1
0
2
0
2
2
2
0
1
0
3
0
3
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
1
0
2
0
3
1
1
0
1
2
2
0
0
0
0
2
0
1
0
0
0
0
2
0
1
0
0
0
0
1
0
2
1
0
0
1
0
0
2
2
0
1
1
2
1
0
1
0
1
0
2
0
1
2
0
0
0
2
2
2
1
1
2
0
0
0
0
0
0
3
1
1
0
0
0
2
0
1
1
1
2
1
1
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
2
1
2
0
0
2
1
0
1
0
1
0
1
0
1
2
0
1
1
0
0
0
2
0
0
0
0
3
1
0
0
1
0
2
1
0
0
4
1
1
1
1
2
1
2
0
0
0
1
0
1
1
2
1
1
1
1
2
0
0
2
0
1
0
1
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
2
0
1
0
0
1
1
2
1
2
0
1
0
0
0
1
0
1
0
1
2
1
1
2
2
1
1
1
0
0
1
0
0
1
1
1
0
1
0
0
3
0
0
2
2
1
0
1
1
0
1
0
1
1
2
0
2
1
0
1
0
2
3
1
0
0
0
0
2
1
0
0
0
0
2
3
0
0
1
0
2
1
2
0
0
0
1
0
0
0
2
0
2
1
3
2
0
0
1
2
0
2
0
0
1
0
2
1
1
0
1
1
0
2
1
0
0
1
1
2
1
1
0
2
2
0
2
0
2
0
0
0
2
0
0
1
0
2
0
0
1
1
1
0
0
0
0
0
1
1
0
2
0
0
1
0
0
0
2
0
1
2
1
0
0
0
1
0
1
0
0
2
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
1
2
0
1
1
1
0
1
0
2
2
2
0
0
1
0
0
4
0
1
0
2
0
3
0
1
0
0
0
1
1
2
2
1
0
0
0
0
1
0
0
0
2
1
0
1
0
0
0
2
1
0
2
0
0
0
0
1
1
2
0
2
1
0
2
0
1
0
1
0
0
0
1
2
1
1
1
1
0
0
0
1
0
0
1
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
2
2
1
1
1
0
1
1
0
0
1
0
0
0
1
0
0
2
0
0
0
0
1
0
2
1
2
0
0
1
1
0
0
1
0
2
1
0
0
1
0
0
0
1
0
0
0
2
1
2
0
2
1
1
1
0
0
2
2
3
0
0
1
0
0
2
2
1
0
0
2
0
2
0
1
1
0
0
0
0
1
0
0
1
0
0
0
1
2
2
2
0
0
0
2
1
1
1
0
2
0
1
0
1
0
0
2
1
0
1
0
0
0
2
1
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
1
2
0
1
0
0
0
0
1
1
0
1
1
0
0
0
1
0
1
0
1
1
1
0
0
0
0
2
0
0
0
0
1
3
0
0
1
0
0
1
0
2
0
0
0
0
0
1
1
2
0
1
0
2
1
1
0
2
1
2
0
0
1
2
2
8
1
0
1
2
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
2
1
1
1
0
0
0
1
0
0
1
0
2
1
0
0
0
1
1
0
1
2
2
2
2
0
0
2
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
1
3
0
1
0
0
1
0
1
1
0
2
0
0
1
0
2
0
0
0
0
1
0
0
2
0
1
0
0
1
1
1
2
3
0
0
2
1
0
3
0
1
0
1
1
0
1
0
0
0
0
2
0
0
1
0
1
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
1
0
1
2
1
0
3
0
0
0
0
4
0
0
0
1
0
2
1
0
0
1
0
0
0
1
0
0
0
0
0
2
1
2
0
0
1
0
0
0
1
0
0
0
1
3
0
0
0
2
2
2
2
0
0
2
0
1
2
1
1
1
0
0
0
0
0
0
2
2
2
0
1
0
0
0
0
1
0
2
0
0
0
0
0
2
2
0
0
1
2
0
0
1
0
1
1
0
0
0
0
0
0
0
0
2
0
1
2
0
1
0
0
0
0
1
0
0
3
1
2
2
0
2
0
0
0
2
1
2
2
0
2
3
1
1
2
1
0
0
0
0
0
0
2
0
0
0
1
0
1
2
2
0
1
0
0
0
0
2
1
0
2
0
0
3
0
0
0
2
1
2
0
1
0
0
2
1
1
1
0
1
1
1
0
0
2
2
2
0
1
1
2
0
0
0
2
0
1
0
0
1
2
1
2
0
2
1
0
3
1
0
2
0
0
0
0
0
2
2
0
1
0
0
0
2
0
2
4
1
2
0
1
0
0
1
0
1
1
1
1
0
1
0
0
1
2
2
2
0
0
0
1
2
0
0
0
1
1
1
1
1
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
2
0
2
0
0
0
2
0
0
0
0
2
0
2
0
0
1
0
1
1
0
1
1
1
1
2
0
2
2
0
1
0
2
2
1
1
2
2
0
0
0
0
0
2
1
2
0
0
0
2
1
1
2
0
0
0
0
1
1
0
2
1
0
0
1
2
0
1
1
0
0
0
0
0
0
0
0
2
1
0
1
0
0
2
0
0
0
0
0
2
0
1
1
1
1
0
0
0
0
2
0
2
0
0
1
0
0
2
2
0
2
1
0
0
1
0
0
0
0
1
0
2
0
0
1
0
0
0
1
0
0
2
0
2
3
1
2
0
0
0
0
0
0
0
0
2
2
0
2
2
0
1
0
1
2
1
0
1
1
1
0
0
1
0
3
0
2
1
1
0
0
2
0
0
2
2
1
0
0
0
1
0
0
0
1
0
0
2
1
2
0
2
0
1
4
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
1
1
1
0
1
2
0
0
0
2
1
1
2
2
0
2
0
0
1
2
1
0
2
1
1
0
0
0
2
0
0
1
0
2
1
1
1
0
2
1
2
0
0
2
2
2
1
1
0
1
0
0
0
0
1
0
0
2
0
2
0
2
0
1
0
1
0
0
2
2
0
0
0
1
0
0
2
0
1
1
0
0
0
2
0
0
2
0
0
1
2
1
2
0
1
2
0
2
0
0
2
1
0
0
0
0
1
0
0
0
1
1
2
2
1
1
1
0
4
2
0
0
2
2
1
1
1
0
1
0
0
2
0
1
1
1
0
2
2
1
0
1
2
3
1
0
0
2
0
1
2
2
2
0
0
0
0
0
0
0
1
0
0
1
2
0
2
0
2
0
0
4
0
0
2
2
2
1
1
0
0
0
0
1
1
2
0
2
1
1
3
1
0
1
0
0
1
1
0
1
0
1
0
2
1
2
0
0
1
2
1
2
1
0
0
0
1
1
0
1
0
0
1
0
2
0
1
0
1
0
0
0
0
0
0
2
0
2
0
1
0
1
0
3
0
0
2
0
0
5
2
0
0
1
1
1
0
2
1
2
0
0
0
0
0
0
1
1
1
0
0
1
0
2
1
0
1
2
0
1
2
0
0
0
1
0
2
2
1
0
0
0
1
1
2
2
0
1
1
1
0
2
0
0
3
1
2
1
1
1
2
2
0
0
1
0
0
1
0
2
0
0
2
2
0
1
2
1
2
0
2
1
0
0
2
0
1
0
1
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
2
0
1
0
2
2
0
1
1
1
1
0
0
0
0
0
0
0
1
2
1
0
2
0
0
1
1
0
0
2
1
2
2
1
1
1
2
0
1
0
0
2
2
0
1
9
2
4
2
0
2
0
1
0
1
1
2
0
1
0
2
0
0
2
0
1
0
0
1
0
2
1
1
1
1
0
0
0
0
0
0
0
1
1
2
1
1
0
0
1
0
0
2
0
1
0
0
2
1
1
1
0
0
1
0
0
2
2
1
0
1
0
0
0
1
0
0
1
2
0
0
2
1
0
3
0
0
0
1
0
1
0
1
0
0
0
1
1
0
1
0
0
1
2
0
1
0
2
2
1
1
0
3
0
0
2
0
0
0
0
2
1
0
0
1
0
1
0
0
0
1
0
1
0
0
1
1
0
1
1
0
0
1
1
0
0
0
0
0
1
1
2
0
0
0
1
1
2
0
1
0
0
0
2
2
0
0
0
0
2
2
2
0
0
1
1
0
0
0
3
0
0
0
0
0
2
0
0
0
1
1
0
2
1
0
0
0
0
0
0
2
1
2
2
1
4
0
0
0
0
0
2
0
0
2
2
0
1
1
2
0
1
1
1
0
1
0
0
2
0
1
0
2
2
2
0
0
0
2
1
1
0
1
2
0
1
2
0
1
3
1
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
1
1
2
1
1
2
0
0
0
1
1
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
2
3
0
1
0
0
2
2
0
0
1
0
0
0
1
0
0
1
0
1
1
2
1
0
1
0
7
1
1
2
0
0
2
1
0
0
1
2
1
0
0
0
2
0
0
2
1
3
3
1
1
1
1
2
1
0
0
2
0
0
0
2
1
0
1
0
2
0
0
0
1
0
1
0
2
1
1
2
1
1
1
2
0
0
1
2
2
0
0
0
0
1
0
2
2
0
0
0
0
1
1
0
1
0
2
2
2
0
0
0
0
0
1
2
1
0
0
0
0
0
0
1
2
0
2
0
2
2
1
0
2
0
0
0
1
0
2
0
1
0
0
1
1
0
2
2
0
2
0
0
0
0
1
0
1
0
1
1
2
1
1
2
1
1
1
1
1
0
0
2
0
1
1
0
1
1
0
1
1
1
2
0
0
1
1
0
0
1
1
1
1
0
3
1
0
1
0
0
0
2
0
0
1
1
1
2
4
0
0
2
3
1
0
1
0
0
0
2
0
1
0
2
2
0
0
0
2
1
0
0
1
1
1
2
0
2
0
0
1
0
0
1
0
0
0
0
1
2
1
0
2
2
0
1
0
1
2
0
0
1
3
2
0
1
0
1
0
3
1
0
1
1
0
0
2
1
0
0
1
2
0
1
0
0
2
0
0
0
0
2
1
0
0
0
0
1
0
3
0
1
1
0
3
2
1
0
1
1
1
0
2
0
0
0
1
1
0
2
0
2
0
1
0
1
0
1
2
1
0
0
0
0
1
2
0
1
1
0
1
0
0
2
0
2
2
1
1
1
0
0
0
0
0
1
1
1
0
0
0
1
0
1
0
1
1
0
0
1
0
0
0
2
0
0
0
0
2
0
1
0
1
0
0
2
0
0
0
0
0
2
1
0
2
0
1
1
0
1
2
0
2
0
0
0
0
1
0
1
1
0
1
0
0
2
1
0
1
0
0
1
0
1
2
0
1
0
2
0
0
0
1
0
0
2
0
0
1
2
2
0
2
0
0
0
2
0
0
1
1
0
1
0
0
2
0
2
0
0
0
0
1
0
0
1
1
2
0
0
0
1
0
0
1
1
0
2
1
0
0
1
2
0
2
1
0
1
2
1
2
0
0
1
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
1
0
0
0
0
0
2
0
1
2
0
0
1
0
1
0
0
0
2
0
2
1
0
1
1
0
0
2
1
1
1
2
0
0
2
0
0
0
2
0
0
1
0
2
0
0
0
2
2
1
1
0
0
0
0
2
1
0
2
3
0
0
1
0
0
0
1
1
2
0
0
0
4
2
0
0
1
0
1
0
0
1
1
2
0
0
0
1
2
1
1
1
0
2
0
0
1
0
1
0
0
0
2
2
1
0
0
0
2
2
1
2
0
1
1
0
0
1
1
1
0
0
2
0
1
2
0
0
1
0
1
0
2
1
0
0
0
2
2
2
2
2
0
0
1
0
1
2
1
1
0
2
1
0
2
1
1
0
1
1
0
1
0
0
1
0
2
0
1
2
0
0
0
0
2
2
0
0
1
1
0
0
0
0
0
0
1
1
0
0
2
2
1
0
1
0
1
0
0
0
0
1
3
1
1
0
1
2
1
2
0
0
0
0
1
1
0
0
0
1
0
2
0
2
2
0
0
5
1
0
0
2
0
1
0
0
0
2
0
0
0
0
1
1
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
3
2
0
1
1
0
0
0
1
1
0
0
5
1
1
2
0
0
1
1
0
1
0
1
1
0
0
1
1
2
2
2
0
1
0
0
0
0
1
0
0
0
1
0
2
1
0
0
1
0
3
0
2
0
2
0
0
0
0
1
1
0
0
0
1
0
2
0
0
0
1
1
3
2
2
2
0
0
0
0
2
0
1
0
0
0
1
0
1
0
2
0
1
1
2
0
0
0
0
0
0
1
2
0
1
1
2
1
1
0
2
0
0
2
1
0
2
2
1
4
0
0
2
2
0
0
1
0
0
1
0
2
2
0
0
0
0
0
0
0
1
0
0
2
1
1
2
0
2
2
0
0
2
4
0
0
1
0
1
0
1
0
2
0
1
0
1
2
0
0
1
1
1
2
1
1
0
0
0
0
1
0
0
2
1
0
2
2
2
0
0
0
2
0
0
0
1
0
2
1
1
1
0
0
1
0
0
1
2
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
2
3
0
1
3
1
0
1
0
3
2
2
0
2
0
0
1
1
0
1
0
0
2
1
0
0
0
0
0
2
1
0
0
0
0
3
0
0
2
1
1
2
0
0
0
1
1
0
2
1
2
2
0
0
2
1
0
1
1
0
1
0
0
1
1
1
3
0
0
0
0
0
0
1
2
0
0
0
1
1
2
2
0
0
0
0
2
0
2
0
0
0
1
0
1
0
0
0
2
2
0
2
0
2
0
1
1
0
0
0
0
0
1
2
0
2
1
0
2
0
2
0
1
2
0
0
1
2
0
1
2
0
1
0
1
3
0
1
1
4
0
0
0
1
2
1
0
0
1
2
1
0
0
3
0
2
0
0
0
1
3
1
1
1
1
0
0
1
3
1
1
0
1
2
0
1
1
0
1
0
2
2
2
1
2
2
0
1
0
0
0
2
2
0
0
2
0
0
1
1
0
0
0
0
1
0
1
2
3
2
0
1
1
1
0
0
1
0
2
3
0
1
0
1
2
0
0
2
0
1
1
0
1
2
0
0
1
0
0
0
1
1
0
1
0
1
0
0
0
2
1
0
0
0
0
2
0
2
0
0
1
1
0
0
2
0
1
0
1
1
1
2
2
1
1
0
0
0
0
0
0
2
0
2
0
1
0
1
2
2
0
1
2
0
0
0
0
1
2
2
2
1
2
0
2
1
0
1
3
2
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
1
1
2
2
2
0
0
1
1
2
1
2
1
0
2
0
0
2
0
2
0
2
0
2
0
0
0
3
1
0
1
0
0
1
0
0
0
2
0
1
0
0
1
1
2
2
0
1
3
3
1
0
0
0
0
1
2
0
1
0
0
1
2
3
2
0
1
0
2
2
2
0
0
2
1
2
1
0
1
0
2
0
0
0
2
2
1
1
1
2
0
2
0
0
0
0
0
1
0
1
0
2
1
0
1
0
2
1
0
0
2
1
0
0
0
0
0
1
2
1
1
0
0
0
1
2
1
0
0
1
0
1
1
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
3
1
2
7
0
0
0
2
1
1
1
1
0
0
0
2
1
6
0
0
1
0
0
2
0
0
1
2
0
0
1
1
0
1
2
0
2
1
0
2
0
0
0
0
0
2
0
2
2
0
2
1
1
0
1
0
1
0
2
1
0
1
1
2
1
0
0
0
1
0
1
0
1
1
2
0
0
0
0
0
0
0
1
3
1
1
0
0
2
1
0
2
0
0
0
0
2
2
1
2
0
2
0
2
0
0
0
0
2
0
0
1
1
2
1
1
0
1
0
2
1
0
0
1
2
0
1
0
2
2
1
0
1
2
1
0
0
1
0
0
0
2
0
1
2
1
3
1
1
1
0
2
0
0
2
0
0
2
1
1
0
2
1
1
1
1
2
1
0
0
0
1
2
1
0
1
1
0
1
1
1
0
0
0
0
1
2
0
1
0
0
1
1
1
2
0
0
1
0
1
0
2
2
0
2
2
0
0
0
1
2
0
1
0
1
2
1
1
0
2
0
1
0
1
0
2
0
1
0
0
0
1
2
0
1
0
1
1
2
0
0
1
4
1
0
0
1
1
1
0
1
0
2
0
1
0
1
0
3
0
0
0
2
0
2
2
2
0
0
0
0
1
2
1
2
1
0
0
2
3
0
2
1
1
0
1
1
0
1
0
0
1
0
1
0
0
0
0
1
0
0
1
1
0
0
1
1
2
1
0
2
2
1
0
0
2
1
0
0
1
0
1
0
0
0
2
0
0
0
0
2
0
1
2
1
0
0
2
0
1
0
2
1
0
1
1
0
1
1
0
0
0
0
1
1
0
1
0
2
1
1
0
2
1
1
0
1
0
0
0
0
1
1
2
1
2
0
1
1
3
1
0
2
1
1
3
0
0
0
1
0
0
0
0
1
0
0
0
1
1
3
1
0
0
2
1
0
1
0
1
2
1
0
1
0
0
0
0
2
0
1
2
2
1
2
0
0
1
0
0
1
0
0
2
0
0
1
0
0
0
0
0
1
0
1
0
2
0
2
0
1
2
0
0
1
0
2
2
0
1
0
1
0
2
0
0
1
0
0
0
1
0
1
1
0
0
3
0
0
0
1
0
3
1
0
0
0
1
1
2
1
0
0
0
2
0
3
1
0
2
2
0
2
1
0
0
2
1
1
0
2
1
1
2
0
2
0
2
1
1
2
0
0
1
1
1
2
1
1
2
2
0
1
1
1
0
2
1
0
2
1
0
0
3
1
0
0
2
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
8
2
0
0
0
1
1
1
1
0
0
1
0
1
1
2
2
0
0
0
0
2
0
0
1
3
1
2
2
0
2
0
0
0
0
0
1
0
0
0
0
2
1
0
1
2
2
0
2
1
0
2
0
2
0
1
1
1
0
0
1
0
0
2
2
0
0
2
0
0
0
0
0
1
1
0
1
2
1
1
1
0
1
1
0
1
0
0
1
0
0
0
0
2
1
2
0
0
1
2
2
0
0
0
2
0
1
2
1
1
0
2
0
0
0
1
1
0
0
1
0
2
0
0
0
1
2
1
0
0
0
0
2
0
4
0
0
2
0
0
2
1
1
1
0
0
0
0
0
0
1
2
2
2
1
0
0
0
0
0
2
0
0
0
0
0
2
1
1
0
0
1
0
3
1
0
1
0
0
0
0
0
0
0
0
0
2
1
0
1
1
0
2
2
1
0
3
0
1
1
0
0
0
0
1
1
1
0
0
0
0
0
1
2
0
1
1
1
1
2
0
0
2
1
1
1
0
0
1
1
0
0
0
2
2
1
2
1
1
1
0
1
2
1
2
2
0
1
1
1
0
3
0
1
2
0
3
2
2
0
2
3
0
0
2
1
1
0
0
0
1
1
0
0
1
0
2
0
2
0
1
1
1
2
1
0
3
0
2
0
1
0
1
1
0
3
0
2
1
0
0
0
2
4
0
0
0
0
1
2
0
0
2
0
1
2
0
2
0
0
1
0
1
0
0
1
2
0
3
1
0
1
1
1
1
0
1
1
0
1
1
1
3
0
0
1
1
0
0
0
0
2
0
1
1
0
1
0
0
2
2
2
0
1
0
1
0
0
0
2
0
1
0
0
0
0
1
0
2
0
0
0
2
1
0
0
0
0
1
1
1
0
0
0
0
0
0
2
0
1
0
1
0
1
0
0
0
2
2
1
0
1
1
1
1
1
0
0
0
0
0
0
0
1
0
2
0
1
0
1
0
0
1
2
0
2
1
0
1
0
0
1
1
1
0
0
2
1
0
0
0
1
0
0
1
0
3
1
0
0
0
0
1
0
0
2
2
0
0
1
1
0
2
0
1
1
0
0
0
0
0
1
1
1
0
0
1
2
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
2
0
1
1
0
1
1
0
0
2
0
0
0
0
0
0
0
2
1
1
2
2
3
0
2
0
1
2
0
4
0
0
0
0
2
0
0
0
1
0
1
0
1
2
0
2
0
0
1
0
1
0
0
0
0
0
1
0
0
1
1
0
2
1
0
1
0
1
2
0
1
1
1
0
0
1
1
0
0
0
0
0
0
0
0
2
0
2
2
2
1
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
2
0
0
1
0
0
2
1
0
0
0
1
2
1
0
0
1
0
2
0
0
0
1
1
0
2
0
0
2
0
0
2
1
0
1
0
0
0
1
1
0
0
1
0
0
0
0
1
0
1
0
1
2
0
1
0
2
1
1
0
1
1
2
0
0
1
0
1
2
1
0
3
0
1
0
1
0
2
1
1
0
1
0
2
1
1
1
2
1
0
4
1
0
0
0
0
1
2
1
0
0
0
2
0
1
1
0
1
1
1
0
0
1
2
0
1
2
0
1
1
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
2
1
0
0
1
1
3
0
2
1
1
0
2
0
0
0
0
2
0
0
1
2
1
6
0
2
0
1
2
1
0
1
0
0
0
0
0
2
0
1
1
0
2
2
0
0
1
0
1
2
4
2
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
1
1
2
1
0
2
1
2
3
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
2
2
0
2
1
0
0
1
2
1
0
0
0
0
1
0
0
1
1
1
0
0
1
1
0
1
1
0
2
0
0
0
2
0
1
1
1
0
0
1
0
1
1
1
0
1
2
0
0
0
1
1
1
1
1
0
0
1
0
0
2
0
2
1
1
2
2
0
2
2
0
1
0
0
2
0
2
0
0
1
2
2
2
0
0
1
0
0
0
2
0
2
0
3
0
0
2
0
0
2
0
0
0
0
0
0
0
2
1
1
2
1
0
2
0
2
1
1
0
2
1
1
1
0
2
0
0
0
0
0
0
1
2
1
0
1
1
1
2
0
0
2
1
0
1
1
0
1
0
1
0
1
1
2
0
0
0
2
1
0
0
0
0
0
0
1
1
1
0
1
2
1
0
1
0
2
0
0
0
0
2
2
0
1
0
1
1
2
1
2
1
0
1
1
1
1
0
0
2
2
0
0
0
1
0
1
0
1
2
1
2
1
1
1
1
0
0
0
0
0
0
2
0
1
0
1
1
1
0
2
0
0
1
1
2
2
1
0
0
2
1
1
0
0
2
1
1
0
2
2
0
1
1
1
0
0
1
0
2
0
2
0
0
1
1
0
0
1
0
2
0
1
0
0
1
0
0
1
0
1
1
0
0
2
0
0
2
1
0
0
2
1
0
2
1
0
0
0
1
0
1
2
0
3
0
0
0
1
0
0
1
0
0
0
0
0
0
4
0
1
1
2
1
0
0
0
0
0
2
2
1
0
0
0
2
0
0
0
2
0
0
0
0
0
1
1
2
2
0
0
1
0
0
3
0
2
1
0
1
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
2
1
0
2
1
1
1
0
2
1
2
1
1
0
1
0
1
0
0
1
1
1
2
1
0
0
1
1
2
1
3
1
2
0
1
0
0
1
0
1
0
3
1
0
1
1
1
0
0
0
0
0
2
0
1
2
0
0
0
0
1
0
2
1
0
0
0
1
0
0
0
1
0
0
0
2
0
2
0
1
1
2
2
0
0
1
0
0
0
0
0
0
1
2
0
0
2
1
1
1
0
1
0
0
0
0
0
0
0
2
0
1
0
1
1
0
0
1
2
0
2
0
2
2
2
1
1
0
0
2
0
2
0
0
0
2
0
0
0
0
1
2
0
1
0
1
1
1
2
0
1
1
2
1
0
0
1
2
1
0
1
2
1
0
1
0
1
0
1
2
1
1
2
0
0
0
2
1
0
0
0
1
0
0
1
0
2
1
2
2
2
0
2
2
2
1
1
0
1
1
1
0
1
0
1
2
0
0
0
0
0
3
0
2
0
0
1
0
1
2
1
0
1
1
0
0
0
0
1
0
2
0
0
0
2
2
1
0
2
1
0
0
1
1
0
1
0
2
0
0
0
1
1
0
0
1
2
0
0
1
2
2
1
2
1
1
0
0
0
1
0
0
0
1
3
1
0
0
0
0
1
0
1
1
3
0
0
0
2
1
2
0
0
2
0
1
2
0
1
0
0
0
0
1
1
2
1
1
0
0
0
0
1
2
0
2
2
1
0
0
0
0
1
1
0
1
1
1
0
1
0
3
3
2
2
0
1
1
1
0
0
0
1
0
0
3
1
0
0
2
1
4
0
0
0
2
0
0
1
2
2
0
0
0
0
0
0
2
0
0
0
1
2
2
0
1
0
1
1
0
2
0
0
0
1
1
0
2
1
2
1
1
0
2
0
0
0
1
0
1
2
1
0
0
2
0
1
1
0
0
2
0
0
0
1
1
1
1
2
0
1
1
0
1
2
0
0
0
0
0
0
0
0
2
0
0
6
0
0
0
0
2
0
1
0
0
0
0
2
3
1
3
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
2
0
0
1
0
0
0
1
0
0
0
0
2
0
0
1
1
0
1
0
1
2
0
2
1
1
0
0
1
1
0
1
1
1
1
0
1
1
2
0
2
0
2
2
2
2
1
1
0
1
2
0
0
1
0
1
0
0
0
0
2
1
0
0
1
1
0
0
0
1
1
1
2
0
1
0
0
1
0
2
0
0
2
1
0
0
0
1
0
1
0
0
0
2
0
2
1
0
0
1
1
1
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
1
2
0
0
0
0
1
0
1
1
1
0
1
1
1
1
2
0
0
1
2
0
1
0
2
0
0
0
1
0
0
0
0
0
2
1
0
0
1
0
1
1
0
0
1
0
1
5
1
2
1
1
1
0
2
1
0
0
3
2
0
1
1
0
2
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
2
1
1
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
1
2
0
1
2
0
3
2
0
0
0
2
0
1
0
0
0
0
0
1
0
0
1
0
0
0
2
1
0
1
1
0
0
0
1
2
0
0
0
2
1
0
1
1
1
0
2
0
0
0
1
1
0
1
1
2
1
1
0
0
1
0
0
1
0
2
1
1
0
0
0
1
0
0
0
2
0
0
0
1
1
1
0
2
0
1
0
0
0
0
2
0
0
0
1
3
0
0
1
1
0
2
0
1
0
1
2
1
2
0
0
2
0
0
0
3
2
0
1
2
1
0
0
2
0
0
2
0
0
1
0
0
1
0
0
0
2
2
2
2
1
1
1
1
2
0
0
1
1
2
0
0
0
1
2
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
1
2
3
0
0
1
0
0
0
0
0
0
1
2
1
0
1
0
0
0
0
0
2
2
2
2
1
0
1
2
2
0
0
0
0
1
0
0
2
0
0
4
1
2
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
2
1
1
1
1
1
0
2
0
0
0
0
0
0
0
3
0
0
0
2
0
1
0
2
1
0
1
0
0
0
1
1
0
2
0
1
2
1
2
0
2
0
1
0
2
2
2
1
0
1
1
0
0
0
1
0
1
0
0
0
1
0
2
0
2
0
0
0
0
0
0
1
0
0
1
1
0
2
0
3
2
2
1
0
0
0
1
0
1
2
0
0
0
1
0
0
1
0
1
0
0
2
1
0
1
0
1
0
0
1
2
0
2
0
1
0
0
0
0
1
0
1
0
2
0
0
1
2
1
0
1
0
1
2
1
0
2
2
1
1
2
0
1
0
3
0
0
2
0
0
0
0
2
0
2
1
3
0
0
0
0
1
0
0
1
0
2
1
1
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
2
1
1
1
2
0
0
0
0
0
3
1
0
0
2
2
1
0
1
1
1
0
2
0
0
1
1
0
1
1
1
0
1
0
0
2
0
1
0
1
1
0
0
0
1
1
0
0
0
2
0
1
0
0
1
0
1
3
2
1
1
1
0
1
0
0
1
2
0
0
2
0
0
0
0
2
1
0
0
1
1
0
0
0
0
0
1
1
1
2
0
0
1
0
0
1
0
2
2
0
2
0
0
0
1
1
0
2
0
0
1
1
1
0
2
0
1
0
2
0
1
0
1
0
0
1
1
2
0
0
2
1
2
0
0
1
0
1
2
0
0
1
0
0
2
0
0
0
0
0
1
2
0
2
2
0
0
0
1
1
1
0
0
0
0
1
0
0
1
2
0
0
0
0
2
2
0
2
2
0
0
0
0
2
1
0
0
2
1
2
0
2
2
2
1
1
1
2
1
1
0
0
0
0
1
1
0
0
0
2
2
1
0
0
0
0
0
2
0
2
0
0
0
1
2
2
2
0
2
2
0
0
0
0
0
0
0
2
3
1
0
0
2
1
0
1
2
1
0
1
1
0
1
0
0
0
0
1
1
1
0
2
0
2
2
2
0
1
0
0
1
0
0
2
1
1
3
0
0
1
0
2
1
0
0
1
2
0
0
0
1
1
1
0
2
1
0
2
0
2
1
1
1
1
2
1
0
0
0
0
0
1
0
1
0
3
0
1
2
0
1
1
2
1
2
1
0
2
0
0
2
0
2
2
1
1
1
0
1
0
0
0
0
1
1
1
1
0
2
1
0
0
0
1
0
1
2
0
0
0
0
0
1
0
0
0
3
0
2
1
2
0
0
0
1
1
1
1
2
0
0
3
0
0
2
2
0
0
0
0
0
0
0
1
0
1
1
0
0
0
2
0
1
0
0
2
0
2
3
1
0
0
0
0
1
2
1
2
0
0
1
0
3
0
0
0
1
0
2
1
1
0
0
1
1
0
0
1
2
1
2
1
0
0
1
0
3
1
2
1
2
0
1
1
1
3
0
1
2
1
0
1
0
1
0
2
0
0
2
2
3
1
0
0
2
2
0
1
0
2
0
1
0
3
0
2
0
0
1
1
0
0
0
0
0
1
0
0
2
1
0
1
1
1
2
1
2
1
2
1
0
2
0
1
1
2
0
0
0
0
0
0
0
2
0
2
0
1
0
1
0
0
1
0
1
2
1
0
0
0
0
0
1
1
0
1
0
0
0
0
2
0
2
2
0
0
1
1
2
0
0
2
2
0
1
0
1
0
0
0
2
2
1
3
0
0
2
2
0
0
1
1
1
1
0
2
0
2
0
0
2
1
0
0
1
2
0
0
2
0
0
0
0
2
1
1
0
0
1
0
1
1
1
0
0
2
0
1
0
0
1
0
0
0
0
0
1
1
2
0
2
0
1
3
0
0
1
3
0
1
0
0
2
0
0
3
0
2
0
0
2
2
0
2
0
0
0
0
1
1
0
1
1
2
1
2
1
2
1
0
0
0
1
0
1
0
1
0
2
0
1
0
1
0
2
1
1
1
1
1
0
2
1
0
1
0
2
2
1
2
1
0
0
0
0
0
0
0
0
1
3
0
1
1
1
1
1
2
0
0
1
0
1
0
1
0
0
2
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
2
2
2
0
0
4
0
0
0
0
0
2
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
2
1
2
0
1
2
0
0
1
2
0
0
0
1
1
0
1
0
1
0
0
0
2
1
0
2
1
1
1
0
2
1
0
0
0
2
0
1
1
2
0
0
2
1
0
1
1
0
0
0
0
4
1
0
2
0
0
1
0
0
2
2
1
0
0
1
1
0
2
0
0
0
0
2
1
0
1
1
1
0
0
2
0
0
1
0
0
1
0
0
0
1
0
1
0
1
1
0
0
0
1
1
1
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
1
2
0
0
0
0
1
2
0
2
0
1
0
2
0
1
0
4
1
0
0
1
1
0
0
0
1
2
0
0
0
1
2
5
1
0
0
1
0
1
0
2
1
0
2
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
1
0
1
0
2
2
0
0
1
1
0
0
0
1
0
0
1
1
0
1
0
1
0
0
1
3
0
0
1
0
1
0
0
0
0
0
0
0
1
1
1
2
1
0
1
1
0
2
1
0
0
0
1
2
1
0
1
1
1
0
0
0
0
2
0
0
0
2
0
1
0
1
0
0
0
0
2
1
0
1
0
0
0
0
1
0
1
0
1
1
0
0
0
1
2
1
0
1
2
0
1
0
1
0
2
1
0
1
0
0
0
1
0
1
1
0
0
0
1
1
2
2
1
0
0
1
0
2
1
1
1
2
1
1
1
2
0
0
0
0
0
1
0
1
2
1
2
0
1
1
2
0
2
2
0
0
2
0
2
0
0
0
0
3
1
0
1
0
2
1
0
0
2
0
0
0
0
1
1
2
0
2
1
1
1
2
0
1
1
0
0
1
1
1
1
2
2
2
1
0
2
3
0
2
0
2
2
1
1
0
1
2
1
1
1
2
1
0
0
1
2
0
2
1
2
1
0
0
3
0
1
0
0
2
0
1
0
0
1
1
0
2
0
1
2
0
1
1
1
1
0
1
0
0
0
1
0
0
2
1
1
1
0
1
0
0
0
0
0
0
1
1
1
0
0
0
1
0
1
0
1
1
0
2
0
3
0
1
1
2
0
0
0
0
0
1
1
1
0
1
1
0
1
2
0
0
1
0
0
2
0
0
3
1
0
0
0
2
2
0
1
1
0
1
2
1
0
0
0
0
1
2
2
0
0
0
1
2
2
2
1
1
2
1
2
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
2
1
1
1
0
0
1
2
0
2
2
0
0
0
0
0
2
1
0
0
1
0
1
2
2
2
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
1
2
1
0
1
0
0
1
0
2
0
1
0
0
2
1
1
2
0
2
1
2
0
1
0
0
1
0
1
2
1
1
1
1
0
2
1
0
1
0
0
1
0
1
0
0
0
0
0
1
1
1
2
0
1
0
2
1
0
0
1
1
0
1
0
2
2
1
2
0
0
0
0
2
2
0
0
0
0
2
0
1
2
0
0
1
1
3
1
0
2
0
0
1
0
1
0
0
1
0
1
2
2
0
0
2
1
2
0
2
2
1
0
0
0
0
0
2
0
0
1
2
0
1
1
0
2
0
0
1
0
0
2
0
2
0
0
1
2
1
2
0
1
1
2
2
2
2
0
2
0
0
1
0
0
3
0
2
2
1
1
2
1
1
1
0
0
0
0
0
2
1
0
0
1
0
0
0
1
1
0
0
0
0
1
2
2
0
0
0
0
3
0
0
0
1
0
1
1
0
1
0
1
1
2
0
2
1
1
1
2
0
0
0
2
0
2
2
0
1
1
1
1
0
1
0
1
0
0
0
0
1
1
0
1
1
0
1
1
2
1
0
1
1
0
2
1
2
1
1
0
0
0
0
3
0
0
1
2
0
1
1
0
2
0
0
0
1
1
0
1
2
0
0
1
0
0
2
1
1
0
0
0
0
2
1
0
2
2
0
0
0
0
1
0
0
0
0
0
1
1
0
0
2
0
1
2
1
1
2
2
0
1
0
0
0
0
0
3
0
0
2
1
1
2
0
1
1
2
0
1
1
2
0
1
1
1
2
0
0
0
2
2
2
1
0
1
1
0
1
2
0
3
0
0
0
2
0
0
1
1
1
1
0
2
2
1
0
3
0
2
0
0
0
1
0
0
0
1
2
0
0
1
0
0
1
3
0
0
0
1
1
0
2
0
1
0
1
2
0
0
0
1
0
2
0
0
1
1
1
0
1
0
2
2
2
1
0
0
1
0
0
1
1
0
0
0
2
0
0
0
2
1
0
0
1
0
0
0
0
0
0
2
0
2
0
1
0
0
1
0
1
1
0
0
1
1
0
0
0
0
2
0
0
2
1
2
1
0
1
1
2
0
1
1
1
0
0
0
2
0
1
0
1
1
0
0
2
1
1
0
0
0
1
2
1
0
0
0
1
0
0
0
1
1
2
0
0
2
2
2
2
0
0
2
0
2
0
0
0
0
0
0
0
0
3
2
1
2
0
0
2
1
0
1
1
0
0
0
0
1
0
2
2
0
2
0
0
0
0
1
0
0
2
1
0
2
0
1
0
0
1
0
0
1
0
1
0
1
1
1
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
1
1
0
2
2
1
1
0
1
1
2
0
1
1
1
2
0
0
1
0
1
2
1
0
0
1
0
3
0
1
2
0
0
1
0
0
0
0
0
0
0
1
1
2
1
0
0
1
2
0
1
0
2
1
1
1
0
0
2
0
1
2
1
0
0
2
0
0
1
0
1
2
1
2
1
0
1
0
0
1
0
0
1
2
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
1
0
1
0
1
0
0
1
2
0
1
0
2
1
0
1
2
1
1
2
2
1
1
1
0
0
0
1
1
2
1
1
1
0
0
0
2
0
1
0
0
1
2
0
3
1
1
0
1
2
1
1
2
1
2
1
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
1
0
2
0
1
2
2
1
1
0
0
2
0
1
0
1
0
0
2
0
1
0
2
0
1
1
1
0
0
1
1
1
1
0
0
0
0
1
1
1
2
2
0
1
1
0
1
1
0
2
0
2
1
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
1
0
2
1
0
1
0
0
1
1
0
2
0
0
1
0
2
0
1
0
1
1
0
1
1
1
1
1
0
0
1
1
1
0
0
0
0
3
1
0
1
1
2
0
0
0
1
2
1
1
0
0
2
0
2
2
0
0
1
0
0
2
0
0
0
0
2
0
2
0
1
1
3
2
0
1
0
2
0
1
1
2
0
0
0
1
1
1
0
0
0
0
2
1
1
0
1
0
1
3
0
1
0
0
1
1
1
0
0
0
1
0
0
2
0
2
0
1
2
2
0
0
0
1
0
0
1
0
1
1
1
2
0
0
0
0
1
0
1
2
2
0
0
0
0
0
0
0
0
1
0
1
0
2
0
1
1
1
2
1
1
0
2
0
2
2
2
1
1
2
0
3
1
0
0
3
0
1
2
0
0
0
0
1
0
0
1
0
0
0
0
1
0
2
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
2
0
0
2
0
0
1
2
2
1
2
1
2
0
2
1
1
1
1
0
1
0
0
0
1
1
0
1
1
0
1
1
0
1
0
1
1
0
0
0
1
1
0
1
0
0
0
3
0
1
2
0
0
1
1
0
0
2
0
1
0
2
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
2
2
1
1
1
1
2
1
0
2
0
1
2
2
2
0
1
2
0
0
0
0
0
0
0
1
2
0
1
2
0
2
2
1
1
0
2
2
3
1
1
0
1
0
0
1
2
0
0
0
1
1
3
2
2
1
0
1
1
1
1
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
1
0
1
2
0
4
0
2
0
0
1
1
0
0
2
2
2
1
0
1
0
0
0
1
0
2
0
1
0
0
0
1
2
2
0
1
0
2
0
2
0
0
1
0
1
0
1
1
0
0
1
0
1
1
0
1
0
2
0
2
0
2
0
0
1
1
0
3
1
1
1
2
0
0
0
1
1
0
0
0
0
0
0
2
0
3
0
0
0
0
1
1
1
0
2
1
2
3
1
1
0
0
0
0
1
2
2
0
0
0
1
0
0
0
1
0
0
0
2
1
0
1
1
0
4
0
1
1
2
0
0
1
1
0
2
1
0
0
0
0
1
0
0
0
0
3
0
0
0
1
1
0
0
0
0
0
0
1
0
2
0
0
0
2
1
0
0
0
0
0
1
0
0
0
2
2
0
0
1
0
0
1
2
0
0
0
0
1
0
1
0
0
2
0
0
2
1
0
0
0
1
2
0
0
1
0
2
2
0
0
1
1
1
1
2
0
0
0
2
0
0
0
1
1
2
0
1
3
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
2
2
2
0
1
1
1
0
2
0
1
0
2
0
2
2
2
2
0
1
0
1
0
2
1
1
1
0
0
0
1
0
2
1
0
0
0
0
2
1
1
3
2
2
2
0
0
1
0
2
0
1
1
0
2
0
2
1
0
0
0
0
0
0
2
1
1
1
1
1
2
0
1
0
2
0
1
0
0
0
1
0
0
1
2
2
2
0
2
0
0
0
0
1
0
1
0
1
0
1
1
2
0
0
0
0
1
1
1
0
1
0
3
1
0
2
0
1
1
0
2
1
1
2
0
1
1
1
1
0
0
0
2
0
0
1
1
2
0
0
1
1
0
0
0
0
0
1
0
2
1
0
2
0
2
1
2
1
1
0
0
0
0
0
0
0
3
0
0
0
0
1
0
1
0
0
0
0
1
1
2
0
0
1
2
3
1
0
1
2
0
0
2
2
0
1
1
0
2
1
0
0
1
2
0
1
0
0
0
2
0
1
1
0
1
0
2
0
0
1
0
0
2
0
0
3
1
0
0
1
0
0
0
0
0
0
1
0
1
1
3
0
1
1
1
0
0
2
0
1
0
0
1
1
0
2
2
1
0
0
2
1
2
1
0
0
0
0
0
0
1
1
0
2
0
0
1
1
0
0
2
0
0
1
0
1
0
1
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
2
1
2
2
2
2
0
0
1
0
1
1
0
0
2
1
0
2
0
0
2
1
0
0
2
0
0
2
2
1
1
0
0
0
2
1
0
3
0
1
2
1
2
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
2
3
2
0
0
2
0
0
0
2
1
0
1
1
0
0
0
0
0
1
1
0
2
1
1
5
0
0
1
2
0
0
0
2
0
0
0
2
2
0
1
0
0
1
0
2
0
0
0
0
0
0
2
0
3
0
1
1
0
0
0
2
0
1
0
1
1
0
2
1
2
3
0
0
1
2
1
1
1
0
0
1
0
3
0
1
0
0
0
0
1
2
0
0
1
1
2
2
0
0
2
0
1
3
0
0
0
1
0
0
0
1
1
0
0
0
2
1
0
0
1
0
3
0
1
0
2
2
0
0
1
0
0
2
1
1
1
0
1
0
0
1
1
1
2
1
1
0
1
1
0
1
0
0
0
0
2
0
2
1
1
0
0
0
2
2
1
0
0
1
0
0
0
0
1
1
0
0
0
1
1
0
1
0
0
2
0
0
2
0
2
0
2
0
1
1
2
0
0
1
0
1
2
1
0
1
1
0
0
1
1
0
0
1
0
2
0
1
0
1
1
1
1
0
1
1
0
2
0
0
1
2
1
1
0
2
2
0
1
0
0
0
1
1
0
1
0
0
0
4
0
1
0
0
0
0
2
2
1
0
0
1
2
0
2
2
0
0
0
2
0
0
3
2
0
0
0
1
1
0
2
0
2
1
0
2
1
2
1
0
1
0
0
2
2
1
0
0
0
1
0
0
0
0
0
0
1
0
1
2
1
2
2
2
1
0
0
2
0
2
1
1
0
4
0
2
0
1
0
0
1
1
0
0
0
0
1
0
0
1
1
1
0
2
2
0
0
2
1
2
0
0
0
0
1
1
0
0
2
3
0
1
1
1
2
0
1
0
2
1
0
0
0
0
2
0
1
0
1
2
0
0
2
0
1
2
0
2
2
1
1
0
0
1
1
0
1
0
0
1
1
1
0
5
0
1
2
1
0
1
2
2
0
0
0
0
0
0
0
2
0
1
1
1
0
1
1
0
0
0
1
1
0
0
2
0
0
2
2
1
0
0
0
1
1
1
1
0
1
1
0
2
1
1
0
0
0
0
2
1
2
0
0
2
1
1
2
0
2
0
0
1
2
1
0
1
1
0
1
2
0
0
0
2
0
1
0
1
0
1
0
0
1
3
0
0
1
0
2
1
0
0
1
2
0
0
0
2
0
2
0
0
0
1
1
0
0
2
1
1
0
2
1
1
0
0
2
1
0
2
1
0
0
1
2
0
0
1
2
1
0
1
0
1
1
1
2
2
1
0
2
0
1
1
0
2
2
0
0
1
1
2
1
0
0
1
0
0
2
0
0
0
0
1
2
0
0
0
0
2
0
1
2
1
0
0
1
0
1
0
2
2
0
0
1
1
0
2
1
2
2
0
2
1
2
0
0
1
0
1
1
0
1
2
2
0
1
0
0
2
2
0
1
1
2
1
0
3
1
1
1
0
1
0
0
0
2
0
0
2
2
0
2
1
0
3
0
0
0
0
0
2
2
1
1
2
1
1
0
1
0
2
0
2
2
1
1
2
2
0
3
0
0
1
0
1
0
0
0
2
1
0
0
0
0
0
1
2
2
1
0
2
0
0
1
2
3
1
0
0
0
1
0
0
0
1
0
1
1
2
0
1
0
0
1
0
0
2
2
0
1
0
0
0
2
0
1
0
0
0
2
0
1
0
1
1
0
1
0
2
0
1
0
1
0
2
2
1
1
0
2
1
2
1
2
0
0
2
0
0
0
2
1
0
1
0
0
1
0
2
1
0
0
1
0
2
2
2
0
0
0
1
2
0
2
0
0
1
0
1
1
1
0
1
0
1
0
0
0
0
2
0
1
2
0
1
1
3
0
1
2
0
1
0
0
2
2
1
2
1
0
2
0
1
0
1
1
1
0
0
2
0
2
1
2
2
1
0
1
1
0
0
1
2
2
0
1
1
2
0
1
2
3
0
0
2
3
1
0
2
0
0
2
2
0
0
0
1
1
0
1
1
0
0
0
1
1
0
1
0
1
0
0
0
0
0
2
2
1
0
0
1
0
1
1
1
0
1
0
0
0
1
1
0
0
0
2
1
1
0
0
2
2
0
1
0
2
1
0
1
2
2
0
0
2
1
0
2
0
0
2
2
2
2
0
0
0
0
1
0
0
2
1
0
1
1
0
1
0
2
1
0
0
1
1
0
0
2
1
0
2
1
1
0
1
2
3
0
0
0
1
3
2
0
1
2
3
0
0
0
0
0
0
2
0
0
0
2
0
1
0
1
0
1
1
0
0
0
1
0
1
0
0
0
2
2
0
0
0
1
2
2
2
0
2
1
0
2
0
3
1
0
0
9
0
2
1
0
1
0
0
2
0
0
1
1
1
1
3
1
2
0
3
1
0
1
1
0
1
0
0
1
0
0
1
1
1
0
0
0
0
2
0
1
0
2
2
2
0
1
0
1
0
1
1
1
1
0
0
0
2
0
2
0
0
0
1
0
0
0
1
0
2
1
0
1
0
0
0
0
1
1
1
2
0
1
0
0
2
0
1
0
3
2
1
0
0
0
0
1
1
0
0
2
0
0
0
3
0
0
0
0
0
0
2
0
1
2
1
0
1
2
0
0
1
3
0
0
1
3
2
2
0
0
0
2
0
0
0
0
0
2
1
2
0
2
0
4
1
0
0
0
0
2
1
1
0
0
1
0
0
1
9
0
1
0
0
2
1
1
1
0
0
1
0
0
2
0
2
0
2
1
0
0
1
2
1
1
0
2
2
2
2
1
0
0
1
1
0
2
2
0
0
1
2
0
0
2
0
0
1
1
0
0
0
0
1
1
2
0
0
1
1
0
2
0
2
1
0
1
0
1
1
1
0
0
1
2
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
1
1
0
1
0
1
1
0
1
0
1
0
0
0
0
1
1
2
0
0
1
0
2
1
1
0
0
1
1
2
0
0
1
0
0
1
1
3
0
2
0
2
2
1
2
2
1
2
2
0
0
1
1
1
1
0
1
0
0
2
0
2
2
0
2
2
0
2
1
0
0
0
0
1
0
0
1
1
2
0
0
1
0
1
0
1
0
0
0
1
1
0
0
0
1
1
1
0
0
2
0
0
0
1
1
0
1
0
2
0
1
2
1
2
0
2
2
0
0
0
0
0
2
2
0
2
0
0
0
0
0
2
2
0
2
1
1
1
2
1
0
2
2
1
0
0
2
2
1
2
1
2
0
0
1
1
1
0
0
0
0
1
2
2
2
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
1
1
0
1
0
2
2
3
0
1
0
0
0
4
0
2
0
0
1
2
1
0
0
0
1
2
0
0
0
0
1
0
0
0
2
3
0
0
1
1
2
0
1
1
1
1
1
1
1
0
1
1
0
1
0
0
1
0
0
1
1
0
4
0
0
0
0
1
1
1
0
1
0
0
0
2
1
1
0
1
0
1
0
0
1
0
0
0
0
1
0
1
0
1
0
0
1
1
1
0
0
0
0
1
1
0
1
0
2
0
1
1
2
2
2
0
1
0
0
0
2
1
2
1
2
0
1
2
2
0
0
0
0
1
2
2
0
2
0
1
1
1
1
2
1
0
1
2
2
0
1
2
2
3
0
2
2
0
2
1
0
1
2
1
2
0
0
0
0
2
1
1
0
0
2
2
1
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
1
2
0
2
1
1
1
1
0
1
1
0
0
2
2
0
2
0
1
1
1
2
0
0
1
0
5
1
0
1
0
2
0
0
0
0
0
1
0
2
1
0
1
1
0
2
0
1
2
1
1
0
2
1
0
1
0
1
1
2
0
2
2
0
0
1
0
0
1
0
1
0
1
2
0
0
1
0
1
0
0
0
1
1
1
0
1
0
3
0
1
2
0
1
0
0
0
1
0
2
1
0
0
3
0
0
3
2
0
2
2
1
0
2
0
1
0
0
1
0
2
0
0
2
1
3
0
0
0
0
1
1
2
1
0
1
0
0
1
1
0
1
0
1
1
1
2
0
0
1
0
2
1
1
1
2
0
1
0
2
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
1
0
1
2
1
0
1
2
0
0
0
2
0
0
2
1
2
1
2
0
0
0
2
1
0
0
2
0
0
0
0
1
1
0
2
3
2
0
2
1
2
2
0
1
0
0
0
1
0
0
0
1
0
1
1
1
2
2
0
1
2
1
0
0
0
2
0
0
2
0
2
2
2
1
0
1
1
3
1
2
1
0
2
0
0
0
2
0
0
0
1
0
1
0
1
0
1
0
2
1
0
2
0
0
0
0
0
2
0
0
2
1
2
1
1
0
1
0
2
0
1
1
2
0
0
0
2
0
2
1
1
0
2
1
0
1
0
0
0
0
2
1
0
2
1
2
1
0
0
0
1
1
0
1
1
1
1
1
0
0
1
0
1
2
0
0
0
0
0
4
0
0
0
1
1
1
0
0
0
0
0
1
1
0
0
0
0
0
1
2
0
2
0
1
2
0
0
0
0
1
1
1
0
2
2
2
1
1
1
0
0
2
1
0
2
0
2
0
1
2
2
0
2
1
0
0
1
3
1
0
0
1
0
1
1
2
1
0
2
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
1
1
0
1
1
1
0
0
1
0
2
1
2
2
0
0
1
0
2
1
1
0
2
1
0
2
0
0
0
0
0
1
2
0
0
0
0
1
0
2
0
0
2
2
1
0
1
0
1
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
2
0
1
0
4
0
0
0
0
1
2
0
0
2
1
0
1
0
0
1
2
0
1
0
0
1
1
0
1
1
0
2
0
0
0
1
0
1
2
1
2
2
0
1
1
0
1
2
1
1
0
1
0
1
1
2
0
2
1
0
0
1
1
1
2
1
1
0
1
0
3
2
0
1
0
0
1
2
0
0
2
0
2
0
2
2
0
1
0
1
0
1
0
0
1
1
2
0
0
0
1
0
1
2
1
1
0
0
0
5
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
2
0
0
1
0
1
2
2
2
0
0
0
1
0
1
0
0
1
0
0
1
0
2
0
0
2
1
1
0
0
0
0
2
0
0
0
1
0
0
0
1
1
0
0
0
0
2
1
2
0
1
0
2
0
1
0
0
2
1
0
0
1
0
0
0
1
0
2
2
0
0
1
0
0
1
1
1
0
1
1
2
3
0
7
2
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
2
0
0
2
1
1
0
1
2
3
0
2
0
1
1
0
1
1
3
2
1
0
0
0
0
0
0
0
2
1
0
0
0
1
2
0
1
0
0
0
0
0
1
0
1
0
0
1
1
0
1
1
2
0
0
0
2
1
1
0
2
0
2
1
0
1
1
0
0
0
1
3
0
0
1
2
1
2
2
0
2
0
1
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
1
0
2
0
1
0
0
1
0
0
0
0
0
1
2
2
1
2
2
1
0
0
0
0
1
2
2
3
1
0
1
1
2
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
2
0
0
0
0
1
0
2
0
1
1
0
0
1
1
0
2
1
0
0
2
2
2
4
0
0
0
1
0
0
0
1
1
2
0
0
2
1
1
0
1
0
0
1
2
0
2
1
0
0
0
2
0
0
0
1
0
2
1
2
0
0
0
0
0
2
0
0
2
0
2
0
0
1
0
2
2
2
2
2
1
2
1
3
0
1
0
0
1
0
3
0
1
0
0
0
2
1
2
0
3
1
0
2
2
1
1
1
3
1
1
0
0
0
0
2
2
0
0
1
0
1
1
2
1
2
2
2
1
0
0
0
1
0
2
0
0
2
0
0
2
3
0
1
2
1
0
0
0
2
0
1
2
1
0
1
2
1
0
0
0
1
0
2
0
0
0
0
2
1
2
1
1
1
2
0
0
0
2
0
0
0
0
2
3
5
0
1
2
0
0
3
1
2
0
0
0
1
1
1
1
2
0
1
0
0
2
0
0
0
0
1
0
0
0
3
1
0
0
1
0
0
0
1
0
0
3
1
0
1
2
0
2
0
2
0
1
0
1
0
2
0
1
0
0
0
1
0
0
2
0
0
0
0
3
0
0
1
0
0
0
1
0
2
1
0
0
0
2
0
1
1
0
0
1
0
0
1
0
1
0
1
0
1
0
0
2
0
1
2
2
0
1
1
0
1
1
0
3
0
1
0
0
0
0
2
0
0
1
2
0
2
0
0
1
1
3
1
0
0
1
0
2
2
0
2
2
1
0
1
0
0
1
0
0
0
2
2
2
0
0
0
0
1
0
1
1
1
1
0
0
0
0
2
0
0
2
2
3
0
2
1
0
0
1
0
3
1
0
0
0
0
0
1
1
1
0
0
2
1
1
2
1
0
0
0
1
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
1
2
1
1
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
2
1
2
0
0
1
1
1
2
1
0
2
2
2
0
1
2
0
2
0
2
1
1
2
0
0
0
2
0
1
1
0
1
2
0
2
0
0
1
1
0
2
0
0
1
1
0
2
0
0
2
1
0
2
0
1
1
2
2
1
1
1
2
1
0
0
4
1
1
1
1
2
0
2
0
1
2
0
2
2
2
0
1
1
1
0
0
0
1
1
0
2
2
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
1
0
2
0
0
1
5
1
0
0
0
1
0
0
0
0
0
1
1
1
0
1
0
0
1
1
1
0
0
1
2
1
0
0
1
0
0
1
1
0
0
1
0
0
2
1
0
1
0
0
1
1
1
0
2
2
0
2
2
0
0
2
1
0
0
1
2
0
1
1
1
0
0
0
0
0
2
2
0
2
1
0
2
0
0
1
0
0
1
1
2
2
1
0
1
2
1
5
0
0
0
2
1
0
1
1
1
2
1
1
2
0
0
2
0
1
0
1
1
1
0
0
1
2
1
1
0
1
1
0
0
0
1
1
2
1
0
1
0
0
1
0
0
0
1
1
0
0
1
0
1
0
2
1
2
1
0
1
2
0
0
0
0
0
1
0
1
1
0
0
3
0
0
0
2
0
0
0
0
0
3
0
1
1
1
0
0
3
1
1
2
0
1
0
2
0
0
2
2
3
0
1
0
1
2
0
1
3
1
1
0
1
2
0
0
0
0
0
0
0
1
0
1
0
0
1
1
2
1
0
0
0
2
0
1
1
0
1
0
1
1
0
1
0
1
2
1
0
2
2
0
0
2
1
0
0
0
2
0
0
0
2
2
2
3
2
1
0
1
0
0
1
0
1
1
1
2
0
0
0
0
1
2
2
1
0
0
0
1
0
3
0
1
0
0
1
2
2
2
2
1
1
2
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
3
0
0
1
0
0
1
1
0
0
0
1
1
2
0
0
1
2
1
1
0
0
0
0
0
1
0
0
1
1
1
0
1
2
1
0
2
1
3
1
1
0
0
1
0
0
2
0
1
0
1
1
1
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
1
0
1
2
3
2
0
1
1
1
0
0
0
0
3
1
1
2
1
0
2
0
1
0
0
0
1
2
1
0
0
0
1
1
2
0
2
0
0
0
1
1
2
0
0
0
0
0
0
2
0
0
0
1
1
2
2
0
1
0
2
0
0
1
1
1
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
2
2
0
0
2
1
1
1
0
2
0
0
1
2
0
1
2
0
2
0
0
0
1
0
0
2
0
0
0
0
2
0
1
0
0
0
2
1
1
1
2
3
0
0
2
0
2
0
2
2
1
2
0
0
0
0
2
0
2
0
0
1
2
0
1
0
1
0
1
1
1
2
0
0
1
1
0
1
0
1
0
1
0
1
0
2
0
1
2
0
2
0
0
1
2
1
1
1
0
0
0
0
0
1
1
0
0
0
2
0
0
0
2
0
4
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
1
0
2
0
1
0
2
1
1
0
1
0
1
0
2
1
1
0
1
1
0
2
1
0
0
1
0
1
1
0
2
0
0
0
2
0
0
0
1
0
1
0
1
1
0
0
2
2
0
0
2
2
0
0
0
0
2
2
1
0
0
0
0
0
1
1
0
2
0
1
0
1
0
0
1
1
0
1
0
0
1
1
3
2
0
2
0
2
0
1
1
1
1
1
2
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
2
2
0
1
4
0
1
1
0
0
1
1
0
1
0
0
1
2
0
2
1
2
0
2
0
1
1
0
0
1
0
0
0
2
0
0
0
1
2
0
0
2
0
1
0
0
0
0
3
0
1
2
1
2
0
1
0
1
0
0
0
2
0
1
1
0
0
1
0
1
0
0
0
0
0
2
1
0
0
2
0
0
0
1
2
1
0
1
2
0
4
0
1
0
0
1
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
2
2
1
2
2
0
0
2
2
2
2
2
0
1
2
0
0
2
2
0
2
0
0
0
0
1
1
0
0
1
0
0
2
1
0
2
0
0
2
0
0
0
0
2
0
0
2
1
1
1
1
1
0
0
1
0
0
2
2
2
0
0
0
0
1
0
2
1
1
0
2
0
2
1
1
2
0
0
0
0
2
0
1
2
2
7
0
1
1
1
1
0
0
1
2
0
0
0
0
1
3
0
1
0
1
0
2
0
0
2
1
0
0
1
0
3
0
1
1
1
2
2
0
0
0
2
2
0
1
0
0
0
0
3
1
0
1
0
0
0
1
0
1
1
0
2
0
0
1
0
1
0
0
0
0
0
2
1
1
0
0
3
1
1
0
1
1
1
0
1
2
0
1
0
2
1
0
2
2
0
0
0
1
1
2
1
0
0
1
0
0
0
1
0
0
1
0
2
0
3
1
0
1
0
2
0
2
1
0
1
2
1
0
2
2
2
0
1
0
1
0
0
0
0
2
1
0
1
0
1
0
0
1
0
0
0
2
2
2
2
0
0
1
1
0
0
0
0
1
0
0
1
0
1
0
2
0
0
0
2
0
0
0
1
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
1
2
0
2
1
0
2
0
1
0
1
0
2
1
1
0
0
0
0
1
1
1
1
0
2
1
0
1
1
0
1
0
2
0
1
0
2
0
1
0
0
1
0
0
0
2
1
0
1
0
0
0
2
1
0
0
0
0
1
2
1
0
0
0
0
0
2
2
0
0
0
1
1
0
0
2
0
1
1
0
0
1
0
1
1
2
1
2
2
0
0
4
0
0
0
1
0
1
1
0
0
2
0
0
0
1
0
0
1
2
1
0
0
2
1
0
2
1
0
1
1
1
1
1
2
0
1
0
1
2
1
0
0
1
0
0
0
2
1
0
2
0
0
1
2
2
0
2
0
2
1
0
2
0
2
1
0
2
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
2
0
0
2
1
3
0
2
1
1
0
2
0
2
0
0
1
1
0
1
0
2
0
1
2
2
2
1
1
0
0
0
1
0
1
0
2
2
2
0
4
1
0
1
1
1
2
2
2
1
2
1
1
1
1
0
1
2
1
0
1
2
1
1
0
0
0
1
2
2
1
0
0
1
2
0
0
0
0
0
0
0
2
1
1
2
0
0
0
0
0
0
0
1
1
1
2
1
0
0
2
0
2
1
2
2
0
0
0
0
0
0
1
0
1
0
0
1
0
0
2
0
1
1
1
1
0
1
0
0
1
0
2
1
0
2
1
0
0
2
3
0
0
0
2
2
2
1
0
0
1
0
2
0
1
0
0
2
0
2
0
2
0
0
0
1
0
0
2
0
1
0
0
0
0
1
2
1
1
2
0
0
2
1
2
0
0
2
0
0
2
0
2
2
0
3
1
0
0
0
1
1
0
0
2
0
1
1
0
1
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
1
1
1
0
2
0
1
0
0
0
2
2
2
0
2
0
0
0
0
2
2
2
0
0
0
0
0
2
0
1
0
1
0
1
0
1
0
1
1
0
0
2
3
2
2
0
1
0
2
0
2
0
0
0
1
0
0
1
0
3
1
0
0
1
2
0
1
0
3
0
1
1
1
0
1
0
0
0
0
2
0
0
0
2
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
2
1
1
1
2
0
1
0
1
0
2
0
0
5
1
0
0
2
2
0
1
0
1
2
0
0
0
0
0
0
2
1
2
1
0
0
0
0
2
0
2
2
1
0
2
2
1
1
0
2
2
1
0
0
1
0
0
1
0
0
2
2
1
2
0
0
0
0
0
2
0
2
2
0
1
1
3
1
0
0
0
0
0
2
2
0
2
1
0
0
0
0
1
1
0
0
3
0
1
0
0
0
2
1
0
0
1
1
1
0
2
2
1
0
1
1
2
2
0
0
1
0
0
1
1
0
0
0
1
1
0
0
0
2
2
0
0
2
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
2
2
2
1
1
0
0
0
0
2
0
0
0
1
2
0
0
1
0
0
1
0
1
0
1
1
0
1
2
0
1
1
1
0
0
0
0
0
0
0
1
1
1
0
1
2
2
0
2
0
0
0
0
0
2
0
0
2
2
1
0
1
0
1
0
0
1
0
0
1
3
1
0
0
2
1
1
2
0
1
0
0
0
1
2
2
2
1
1
0
0
0
1
0
2
0
1
2
1
0
3
0
2
1
1
0
1
0
0
1
0
0
0
1
1
0
1
0
0
0
0
1
2
2
2
0
0
1
1
0
0
0
1
0
1
1
1
0
0
0
0
2
0
0
0
0
0
2
1
1
1
1
1
2
3
0
0
1
0
2
0
2
0
2
1
0
2
0
0
0
2
1
0
1
2
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
1
0
1
1
1
0
0
0
0
2
0
0
0
2
0
1
0
0
0
1
2
3
1
0
0
0
2
2
0
2
1
1
1
4
0
1
2
2
1
0
1
0
0
0
1
1
0
0
0
0
0
0
2
1
1
1
2
0
0
0
0
1
2
2
1
0
2
0
0
0
0
1
0
1
0
0
0
1
0
1
0
1
3
0
1
0
0
0
2
0
0
1
0
1
2
0
0
0
0
0
0
1
1
1
2
0
1
0
2
0
2
0
0
0
0
2
2
1
0
1
0
2
0
2
0
0
1
2
1
2
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
1
2
2
1
2
2
0
0
0
1
1
0
1
0
0
1
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
1
0
2
2
2
1
0
0
1
2
0
0
0
0
0
3
0
2
0
2
0
1
0
1
0
0
0
2
0
0
1
1
2
2
0
0
0
2
0
0
1
2
2
1
2
0
0
0
0
0
1
0
0
1
2
1
1
0
1
0
0
1
1
0
0
2
0
0
1
0
0
0
0
2
0
2
0
1
0
2
2
0
1
2
0
1
2
1
0
0
1
1
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
1
0
0
0
1
0
0
2
1
1
0
1
1
0
0
2
0
0
1
3
0
0
1
1
2
0
2
0
0
1
1
0
0
0
0
2
2
3
0
1
2
1
1
0
0
0
0
0
2
0
1
3
0
0
0
1
2
0
0
0
1
0
0
1
0
0
0
2
0
1
0
0
1
1
0
1
2
0
0
0
0
1
0
0
0
0
0
2
1
2
2
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
1
0
1
1
0
2
0
0
0
2
0
1
3
0
1
1
0
0
0
2
0
1
0
1
0
0
1
0
0
0
1
2
0
0
0
1
1
1
0
0
1
2
1
1
2
0
2
1
1
2
1
0
0
0
2
0
2
0
2
1
0
1
1
1
0
0
2
1
0
1
0
0
2
1
0
1
0
0
0
0
0
2
3
0
1
0
1
0
1
2
0
0
0
1
1
0
1
1
0
0
1
0
1
0
0
2
0
2
1
2
0
2
0
1
1
0
4
0
1
1
0
1
1
1
0
1
0
2
0
0
1
1
1
1
2
2
0
1
0
1
0
1
0
0
2
1
0
3
1
1
1
1
0
2
3
0
1
0
0
0
0
0
2
0
0
2
0
0
1
1
0
2
0
0
0
0
1
2
1
0
0
1
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
2
1
0
2
1
0
2
0
1
1
1
0
0
1
0
2
1
1
0
0
1
1
0
0
0
1
2
2
0
0
0
2
1
2
0
1
2
0
2
2
1
0
1
2
2
0
1
0
2
2
0
0
1
3
1
2
1
1
2
2
0
1
1
1
1
1
1
1
1
0
0
1
1
2
1
0
1
1
0
0
0
1
1
0
0
2
1
1
1
0
1
0
0
0
0
1
0
0
0
0
1
1
0
2
0
0
2
1
1
1
0
2
0
0
1
1
2
0
0
1
1
0
0
0
0
1
0
0
1
1
2
0
0
2
1
1
1
1
1
2
0
0
1
2
0
0
2
1
0
1
0
0
0
0
0
0
1
0
2
2
1
2
1
2
2
1
1
2
0
0
0
0
0
1
0
0
1
2
1
1
0
1
2
2
1
0
0
1
2
1
0
1
0
2
0
0
1
0
1
0
0
0
0
2
1
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
1
0
2
0
1
0
2
0
2
1
1
2
0
2
0
0
0
0
2
2
2
0
0
0
0
2
0
0
0
1
0
2
1
0
0
0
1
2
0
1
1
1
2
1
3
1
1
0
0
1
0
0
0
0
0
1
0
2
2
2
0
0
1
0
2
0
2
0
1
0
0
2
0
0
1
0
2
2
1
0
0
0
2
0
0
1
0
0
2
0
0
1
0
1
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
1
0
0
1
0
1
0
1
0
0
0
1
0
0
2
0
0
2
0
1
1
0
1
0
0
0
1
0
0
2
0
2
1
0
1
1
0
1
0
1
1
1
1
1
2
2
0
2
0
2
0
0
0
2
0
1
0
1
0
0
2
0
2
0
2
1
1
1
0
0
0
0
0
2
0
1
1
1
0
1
0
1
2
1
0
1
0
0
0
0
0
1
2
1
1
0
0
0
1
1
0
2
0
1
1
1
0
0
0
0
1
0
0
2
0
0
0
2
1
0
0
0
2
0
2
2
0
0
0
1
0
0
1
0
0
0
1
0
0
1
1
2
0
0
1
2
0
0
0
1
0
1
1
0
1
2
0
1
0
0
2
2
1
1
0
0
0
0
1
2
0
3
0
0
1
0
1
0
0
0
0
2
1
0
0
1
1
0
1
0
1
2
0
0
1
2
2
0
0
0
1
2
2
2
0
1
1
0
0
0
1
0
0
2
0
2
0
2
1
1
0
0
0
0
1
0
1
0
1
0
2
0
0
0
0
0
0
2
2
0
1
1
0
0
1
0
1
1
2
1
1
0
2
1
0
0
1
1
0
0
1
0
2
1
0
0
0
0
1
0
0
2
0
0
0
2
0
1
1
2
0
2
0
1
1
1
0
2
0
0
1
0
0
2
2
0
1
1
0
0
2
0
0
0
2
0
0
0
1
2
1
0
2
2
1
0
0
2
0
0
1
1
1
0
0
0
0
2
0
2
2
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
1
0
2
2
0
0
0
0
1
0
0
0
2
1
0
1
0
0
0
2
1
1
2
2
0
1
3
1
1
1
2
1
3
0
1
0
0
2
1
1
1
0
1
1
1
1
1
1
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
2
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
3
0
1
0
2
1
0
0
0
2
1
2
3
1
0
0
2
1
0
6
1
1
1
2
2
2
1
0
1
0
1
1
2
0
2
1
0
0
3
0
1
1
0
2
0
1
0
0
0
0
1
0
0
2
0
0
1
2
1
0
0
2
2
1
0
0
0
1
2
0
0
0
0
0
1
1
2
1
2
0
1
2
0
2
1
1
1
2
1
2
1
1
1
0
2
2
2
1
1
0
0
2
2
0
3
0
0
0
1
2
0
1
0
1
0
0
0
1
1
0
0
1
1
1
0
0
0
2
0
2
0
1
0
0
0
1
1
0
1
2
2
4
1
1
1
0
0
1
1
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
1
0
0
2
1
0
0
0
0
2
0
1
1
2
0
2
2
0
0
1
1
1
1
0
1
1
1
1
0
0
2
1
0
2
0
1
2
0
1
0
2
1
0
1
0
1
0
0
2
1
4
1
1
2
0
0
0
0
0
2
2
2
0
1
1
1
0
1
1
0
0
0
0
1
1
2
1
0
2
2
2
2
1
0
1
2
1
0
0
1
0
0
1
2
0
1
0
0
1
0
1
1
2
0
0
2
0
0
1
1
1
1
1
0
0
2
0
1
0
1
1
0
1
1
1
0
1
0
0
1
0
3
0
0
0
2
1
0
0
1
0
1
0
1
0
0
1
0
1
2
2
2
1
0
0
0
0
0
2
0
0
0
1
0
1
2
1
0
2
2
1
2
2
0
1
0
0
0
1
1
2
1
0
2
1
0
0
2
1
0
2
0
0
0
0
1
0
2
1
1
0
2
0
1
2
0
0
2
0
2
0
0
0
0
0
1
1
0
2
1
1
2
0
1
0
0
2
2
0
0
0
0
2
1
1
0
1
2
1
1
2
0
0
0
1
0
0
1
0
1
0
0
1
1
1
1
1
1
1
2
0
2
0
0
0
0
0
0
0
1
0
1
1
1
0
1
1
1
0
0
0
0
2
1
0
2
0
0
0
0
0
2
2
1
2
1
1
2
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
2
1
1
2
0
0
0
1
0
0
1
0
0
0
0
0
2
2
0
1
1
2
0
0
0
0
1
0
0
1
2
0
1
0
0
0
1
1
0
1
0
0
0
0
1
1
2
2
0
0
1
0
0
0
0
2
0
0
2
1
0
1
2
0
1
2
1
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
2
1
2
2
2
1
0
0
1
2
1
4
0
0
0
0
1
1
0
0
0
0
2
0
0
3
0
1
0
2
0
1
0
0
1
2
1
0
0
0
1
0
0
0
0
4
1
0
1
0
2
0
0
2
0
1
0
3
2
0
0
0
1
0
2
0
1
0
0
1
0
0
1
1
2
1
2
0
1
0
0
2
0
3
0
0
0
0
0
2
0
0
0
1
2
0
2
1
2
0
0
2
1
0
0
0
1
0
0
0
2
0
1
0
0
0
0
1
0
1
1
2
1
1
2
0
0
0
0
1
0
1
0
0
0
3
2
0
1
1
1
1
2
3
0
0
1
1
2
2
0
0
4
1
0
0
0
2
2
1
1
2
0
2
0
2
0
2
0
2
0
0
1
0
2
0
1
0
2
0
2
1
0
0
0
1
0
0
0
2
0
1
0
0
1
0
0
1
0
0
2
1
0
1
0
0
1
1
2
1
1
0
1
0
0
0
0
0
1
0
0
0
0
4
2
1
0
0
0
0
0
2
1
1
0
0
0
0
2
2
0
1
2
0
0
1
1
0
2
1
2
0
0
1
2
2
2
2
0
1
1
1
1
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
10
1
2
1
1
1
0
2
0
0
0
0
0
0
1
0
0
1
0
0
1
2
1
1
1
0
0
6
1
0
0
0
2
1
2
0
2
1
0
2
1
0
1
0
3
0
0
1
2
1
1
2
2
1
2
0
0
0
0
0
2
0
1
0
0
1
1
1
2
2
1
0
1
1
1
2
1
0
1
1
1
1
1
1
1
0
0
0
0
0
2
0
0
0
1
0
0
0
2
1
0
0
1
1
2
0
1
0
0
1
1
1
0
0
0
0
0
0
2
2
1
0
1
2
2
0
2
1
2
0
1
0
2
0
0
0
2
0
2
0
1
2
0
0
0
1
1
2
2
0
0
1
0
0
1
2
2
1
0
0
1
0
2
0
1
0
0
1
1
1
0
0
1
1
0
0
0
1
1
1
2
3
4
0
1
2
1
2
0
1
2
0
3
0
2
1
0
2
1
1
2
0
0
2
2
1
1
2
0
2
0
0
2
2
2
1
1
0
1
0
2
0
2
1
1
1
0
0
1
0
0
0
0
0
0
0
2
1
1
2
2
0
2
1
0
0
2
3
1
0
0
0
2
0
1
0
0
0
0
0
0
0
1
2
0
0
0
1
0
1
1
2
1
1
0
0
0
1
1
0
2
0
1
0
0
0
0
1
0
0
2
1
1
0
0
1
2
1
0
1
1
0
2
0
0
0
0
0
2
1
0
1
2
0
0
0
1
1
0
2
0
2
2
2
0
1
1
2
1
1
0
0
0
1
0
1
0
0
0
0
0
1
0
2
1
0
0
0
2
0
1
1
0
0
1
0
2
0
1
1
1
1
0
0
2
2
1
0
0
1
0
0
1
1
0
0
2
2
2
1
0
0
2
1
0
0
0
1
2
2
0
1
1
0
1
0
0
0
0
1
1
2
0
1
0
0
1
0
1
0
0
1
0
0
1
0
2
1
0
0
1
1
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
2
2
0
1
1
0
1
0
0
1
2
0
0
3
0
0
0
1
2
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
3
2
0
0
0
0
0
1
3
0
1
0
0
0
0
0
2
1
0
0
6
0
0
0
0
1
1
2
2
0
0
2
0
1
0
0
0
0
2
0
2
1
2
0
0
0
1
2
2
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
1
1
1
1
0
1
0
0
0
0
1
0
1
0
0
0
0
2
1
0
1
0
2
0
0
0
2
2
2
0
0
1
1
2
0
0
1
2
0
1
1
1
1
0
0
2
2
0
0
2
0
0
0
0
1
0
1
1
1
1
2
1
0
0
2
3
0
0
0
0
0
1
2
1
0
2
0
1
2
0
2
2
0
0
1
0
1
1
0
2
1
0
2
1
4
0
2
0
3
0
1
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
2
0
2
0
0
3
0
0
2
0
1
1
0
1
1
0
0
0
2
0
2
0
1
0
2
0
0
1
2
2
2
1
0
1
1
1
1
0
0
0
1
1
0
0
0
2
0
1
1
2
1
0
0
0
0
0
1
15
0
0
1
0
1
0
0
0
0
0
0
2
0
2
1
1
1
2
1
0
1
0
0
0
2
0
0
0
1
0
0
0
2
1
0
0
1
3
0
0
0
1
2
1
0
1
0
0
0
0
1
1
1
0
1
0
0
0
2
2
0
0
1
1
1
1
0
1
0
2
0
0
2
2
1
1
0
1
2
0
0
1
1
0
2
0
1
0
0
0
2
1
1
1
1
1
0
0
0
0
0
2
1
2
0
0
0
2
0
2
0
1
0
0
2
0
1
0
1
1
0
2
0
0
1
0
0
1
1
2
2
0
1
0
0
2
0
2
2
1
1
1
0
0
0
0
1
0
3
0
0
0
1
1
1
0
1
0
0
0
2
0
2
2
2
0
3
0
1
2
2
1
2
0
0
0
0
1
0
0
1
1
0
0
0
0
0
2
0
0
0
2
0
0
0
1
1
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
2
2
0
0
0
0
1
2
2
2
1
0
0
0
2
0
1
2
1
1
0
2
0
1
1
2
0
0
1
0
1
0
2
1
1
0
1
1
1
1
2
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
1
0
0
1
0
0
0
0
1
0
2
1
2
1
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
2
0
1
3
0
1
1
2
0
2
1
0
1
1
0
1
2
0
2
2
0
2
0
2
2
2
0
0
2
1
0
0
0
0
0
0
0
2
2
2
2
2
0
1
0
1
0
2
2
0
1
0
1
1
2
0
0
0
0
0
1
0
1
0
0
0
2
2
0
1
0
0
3
0
1
1
2
0
11
1
0
2
0
1
0
0
1
0
2
1
0
0
0
1
0
0
0
3
0
0
0
0
1
0
0
0
2
0
2
0
1
0
2
0
1
1
0
2
0
2
0
3
2
2
2
1
1
0
1
0
0
0
1
0
2
1
0
0
1
0
1
0
2
1
3
0
0
0
0
1
0
0
1
0
1
2
1
2
0
1
0
2
0
0
1
0
1
2
1
2
1
1
1
0
0
2
3
2
1
3
0
0
1
1
0
2
1
0
0
1
0
1
0
1
1
2
0
1
0
1
0
0
0
1
1
2
1
0
2
1
1
1
0
1
0
2
0
0
1
0
2
1
2
1
1
0
0
1
2
2
0
0
2
0
0
0
1
0
0
1
1
0
0
1
1
0
0
0
1
0
1
0
0
0
2
2
3
1
0
2
0
0
3
1
0
1
0
0
0
0
2
1
1
2
0
1
2
2
0
2
1
0
1
0
1
2
0
1
1
0
0
0
0
0
0
1
0
1
1
1
0
0
3
2
0
1
0
2
2
0
0
1
0
2
0
2
0
1
2
0
1
0
0
0
0
1
0
0
0
2
1
2
1
0
0
1
0
1
0
0
0
0
0
1
0
0
1
1
2
1
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
2
0
0
0
0
1
0
0
1
0
1
2
0
0
1
1
0
0
0
0
1
1
2
2
0
2
1
0
1
0
0
2
2
2
2
0
1
1
0
2
0
1
0
0
0
1
0
0
0
0
0
1
0
0
2
1
0
2
1
0
1
1
2
1
1
1
1
1
0
0
1
0
1
1
2
1
1
0
0
0
0
2
0
1
1
1
0
1
0
1
0
0
0
0
0
0
1
0
1
1
1
1
1
0
2
0
2
0
1
2
1
0
0
1
0
0
0
1
0
0
2
1
1
2
0
1
1
1
0
3
1
1
2
0
0
2
0
0
0
1
1
2
2
0
0
1
2
2
0
0
1
2
0
0
1
1
0
0
0
1
0
0
0
0
0
0
2
0
1
2
0
0
1
1
0
0
1
1
0
0
0
0
0
0
1
2
0
0
0
1
1
0
0
0
1
0
0
1
0
0
1
0
1
0
1
1
1
2
0
0
0
2
0
1
2
0
2
0
1
0
1
0
1
1
2
1
1
2
0
0
1
1
1
2
1
0
2
2
0
0
0
1
1
0
2
1
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
1
2
0
0
1
1
1
0
1
0
0
2
0
0
1
1
0
0
1
0
2
1
0
1
0
1
3
1
0
0
0
1
0
1
2
0
2
2
1
2
1
0
0
1
0
0
0
1
0
2
1
0
1
0
0
1
0
2
1
0
1
0
1
0
0
0
0
3
2
0
2
1
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
3
1
0
0
2
0
1
0
1
2
0
1
1
2
0
1
0
1
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
2
0
0
2
0
2
0
0
0
0
2
0
3
0
1
1
0
0
0
1
0
2
0
0
1
0
0
0
0
0
1
0
0
0
2
2
1
2
1
1
1
0
0
0
0
0
1
1
0
1
1
0
2
0
0
0
0
1
0
0
2
0
1
3
0
2
1
0
1
0
0
2
2
0
2
0
0
2
1
2
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
2
0
2
2
1
2
0
2
1
2
0
1
1
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
0
2
2
2
0
1
0
0
1
1
1
1
0
2
1
2
0
1
0
3
0
0
1
0
2
0
0
0
0
2
0
0
0
0
1
1
1
0
2
0
0
2
1
2
0
1
0
2
2
0
1
2
0
0
1
0
1
0
0
0
0
1
1
1
1
0
1
1
1
1
1
2
0
0
0
0
1
0
1
0
1
0
0
0
7
0
1
0
1
0
0
0
0
2
0
2
0
1
1
0
0
0
0
1
0
2
0
2
1
0
1
0
0
1
0
1
0
1
1
2
1
0
0
0
0
2
1
1
2
1
0
0
0
0
0
1
1
2
1
2
0
0
1
0
0
2
0
2
0
0
0
1
0
0
1
0
2
1
1
2
0
0
2
3
2
0
2
0
0
1
2
0
1
2
1
0
2
1
2
1
0
1
2
0
0
0
0
1
0
0
2
1
1
1
1
2
1
2
0
2
4
1
1
0
0
0
0
0
2
1
0
0
2
1
1
1
1
0
0
2
1
0
2
0
2
1
1
2
1
2
0
2
2
1
1
1
0
0
0
0
1
2
0
0
2
0
0
0
1
1
2
1
3
2
0
2
1
0
1
0
0
2
0
0
1
2
1
0
1
1
0
1
1
0
2
1
1
0
2
0
0
0
0
1
1
3
0
0
0
1
1
0
1
0
2
0
2
1
0
0
1
2
2
0
1
2
0
1
0
0
0
1
3
1
0
0
1
1
2
1
1
1
0
2
1
1
0
0
0
2
4
0
2
2
0
2
1
1
0
0
0
1
0
0
3
0
2
1
0
0
0
0
1
0
2
0
2
0
2
1
1
0
1
2
0
0
5
2
0
2
1
2
0
0
2
0
0
1
1
0
1
0
0
2
2
1
1
0
0
1
0
0
0
2
2
1
0
0
1
0
2
0
0
0
0
1
1
0
1
1
1
0
1
2
0
1
1
1
2
0
2
2
0
0
1
0
0
1
0
1
2
6
2
0
0
1
0
2
0
1
0
2
0
0
1
0
1
1
0
0
1
0
0
0
1
1
0
0
1
1
0
0
0
1
0
0
0
1
0
1
0
0
1
2
1
2
3
1
2
1
2
0
2
0
1
0
0
1
0
0
0
1
0
0
1
0
0
2
0
0
2
0
0
0
1
2
0
0
0
0
1
2
1
1
0
1
0
0
1
2
0
0
1
0
1
1
0
0
0
2
0
2
1
2
0
0
0
0
1
0
0
1
2
1
1
1
2
3
2
1
0
1
1
1
1
0
0
0
0
2
0
0
0
1
0
2
0
0
0
2
1
0
1
2
0
0
1
0
0
0
0
1
0
2
1
1
2
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
2
1
1
1
0
1
2
0
0
2
1
1
0
2
2
1
0
0
0
0
0
0
0
1
1
0
0
2
2
0
0
2
0
0
0
1
1
0
2
1
1
0
0
2
2
0
2
0
0
0
0
0
2
2
2
1
0
1
2
0
0
0
0
1
0
0
0
0
1
0
1
0
0
2
0
1
1
0
1
2
1
2
0
0
2
0
1
1
0
0
3
0
0
1
0
2
0
0
2
1
1
0
2
0
0
0
4
0
0
1
2
0
0
0
0
1
0
0
1
1
0
2
0
1
0
2
0
0
0
1
1
0
0
2
0
1
0
0
1
0
0
2
2
0
0
1
2
1
1
1
0
1
0
1
0
1
0
0
0
2
1
1
2
1
3
0
0
0
0
1
3
0
1
0
0
0
0
0
0
2
0
2
2
0
1
2
0
2
0
1
1
0
2
0
0
0
0
1
1
2
0
0
0
2
1
0
0
0
0
1
1
0
0
1
0
0
1
0
1
2
0
0
0
2
0
0
2
1
0
3
0
2
0
0
0
1
1
1
1
1
0
0
1
4
0
1
2
0
2
1
1
0
1
1
0
1
2
1
1
0
2
0
2
1
1
1
1
0
1
1
2
2
0
1
1
2
0
2
1
1
0
2
2
1
1
0
2
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
1
0
0
0
1
0
1
0
0
1
0
0
1
0
0
1
1
0
1
1
1
0
0
1
2
1
1
2
1
0
2
2
0
0
2
0
1
0
2
0
0
0
3
2
0
2
1
1
2
1
0
0
0
3
1
2
0
1
0
0
2
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
2
2
1
0
0
1
1
2
2
1
0
0
2
0
0
1
0
2
2
0
1
2
2
0
2
2
2
0
0
0
1
1
2
1
2
2
1
1
1
2
0
1
0
0
1
1
0
1
1
0
2
1
0
3
2
0
0
0
0
1
0
0
0
0
1
1
1
2
1
0
0
0
1
2
3
2
1
2
1
0
7
0
1
1
0
0
0
1
0
1
0
1
1
1
0
1
0
1
2
2
1
0
0
0
0
1
0
2
2
0
0
4
2
0
0
0
2
0
2
0
2
1
0
0
1
1
2
2
0
0
1
1
0
0
3
0
0
2
0
0
2
1
2
0
1
2
1
0
0
0
0
3
4
0
0
0
0
0
2
0
2
0
0
0
1
0
1
1
0
1
1
2
0
2
0
0
0
1
1
2
0
1
2
1
0
0
1
2
1
1
0
2
0
0
1
0
2
1
0
1
0
0
0
1
1
2
2
0
2
1
0
0
2
0
0
1
0
0
0
0
1
0
1
0
2
0
0
0
1
0
1
0
0
0
2
0
2
1
2
2
0
1
0
0
0
1
0
1
1
1
0
0
1
1
0
0
1
0
2
0
0
2
4
0
0
1
1
0
0
1
1
0
0
0
1
2
0
2
1
0
1
0
2
1
1
0
0
2
1
0
1
1
2
0
1
1
0
0
1
0
0
2
2
0
1
1
2
2
0
1
2
3
3
0
2
5
1
1
0
0
0
1
1
0
0
0
0
1
1
1
0
0
2
0
0
2
0
1
0
1
0
0
1
2
2
0
1
2
1
2
2
1
0
0
1
2
0
1
1
0
0
0
0
3
0
0
0
0
1
1
1
2
0
1
0
0
2
0
2
0
1
0
0
0
0
2
2
2
1
2
1
1
1
1
0
0
0
0
0
0
1
0
0
2
0
1
0
0
1
2
1
0
1
0
0
1
1
0
2
0
1
0
0
0
0
2
1
2
1
0
0
0
2
0
1
0
0
0
0
3
1
2
0
2
2
0
1
0
0
0
0
0
1
1
2
0
0
0
0
0
0
1
1
0
0
2
1
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
2
1
1
1
1
2
1
2
1
0
1
0
1
0
2
1
2
0
1
1
0
2
1
0
1
2
2
0
1
2
1
0
1
0
0
1
2
1
0
2
0
2
2
0
1
1
0
0
0
2
1
0
0
2
2
2
0
1
0
2
2
1
2
0
1
1
0
1
0
1
0
0
0
0
1
2
2
1
3
1
0
0
0
0
1
1
1
1
1
0
0
0
1
0
2
0
2
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
6
1
0
0
0
0
0
0
1
0
1
0
0
0
2
0
1
0
0
1
2
0
0
0
2
2
0
2
1
0
2
0
0
0
1
0
1
0
0
0
2
2
0
1
0
0
0
0
1
0
2
2
0
0
1
1
1
2
0
1
0
1
2
1
0
2
0
0
0
1
0
0
1
0
2
2
1
2
0
0
0
0
1
0
2
2
2
0
0
1
0
2
1
2
1
1
0
0
1
1
1
1
2
1
2
0
1
1
0
1
0
0
0
1
0
0
0
0
0
2
3
0
2
2
1
1
1
0
1
0
0
0
2
2
2
0
0
1
0
2
1
0
0
0
0
0
0
2
0
2
0
0
1
2
0
1
1
1
2
1
0
0
1
1
0
0
2
0
0
0
0
0
1
1
1
0
2
0
1
1
2
0
1
1
0
1
0
1
0
0
0
0
2
2
1
0
0
1
1
0
1
0
0
1
2
0
0
0
1
0
0
2
1
0
0
1
0
1
0
1
1
0
2
0
0
0
0
0
0
2
2
0
0
0
1
1
0
2
0
0
0
1
1
0
2
2
2
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
1
0
2
0
2
1
0
0
0
0
4
1
0
0
0
0
1
2
1
1
1
2
0
0
0
0
1
0
0
2
1
1
1
2
1
0
2
0
1
1
2
2
2
1
0
0
2
0
2
0
1
1
0
2
3
0
1
0
0
0
0
0
2
1
3
1
0
1
0
1
0
0
2
0
2
0
0
2
2
0
0
0
0
1
0
0
1
0
1
1
2
2
0
1
0
2
0
0
2
0
2
1
0
1
1
1
0
0
1
1
0
1
0
0
1
0
1
2
1
2
0
1
0
0
2
1
1
1
0
1
2
0
0
2
0
0
0
1
0
2
0
1
1
0
2
1
1
0
2
0
2
1
1
0
2
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
1
1
0
2
2
1
0
2
0
0
1
0
0
1
0
0
2
0
1
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
2
4
1
1
1
1
1
0
1
0
2
1
1
1
0
1
0
0
0
0
1
1
0
2
1
0
0
0
0
2
1
1
1
1
2
1
0
0
0
0
2
1
0
0
2
1
0
0
0
0
2
0
0
0
0
2
4
0
0
2
3
1
0
0
1
2
1
2
0
0
0
0
1
1
1
0
1
0
0
1
1
2
5
0
0
0
0
1
0
0
0
0
2
0
2
0
0
1
0
0
2
0
2
0
0
0
0
1
2
1
0
0
0
0
2
1
0
0
1
1
0
2
2
1
0
0
2
0
1
1
0
1
1
0
2
1
2
1
1
0
0
1
0
2
0
1
0
3
1
0
1
1
0
2
0
1
2
1
1
1
0
0
2
1
1
2
2
2
1
2
1
1
2
0
0
1
1
1
0
1
2
0
0
0
1
0
0
1
0
2
1
0
2
1
0
2
0
1
1
1
0
0
1
0
0
5
0
0
0
2
0
0
0
3
1
1
1
0
1
1
0
1
1
2
1
1
1
3
3
0
2
1
1
2
0
0
0
0
0
2
1
4
0
0
0
1
0
2
0
2
1
1
0
0
2
0
2
1
1
2
1
0
1
2
0
3
0
0
2
0
0
0
1
1
0
0
1
0
1
0
1
0
0
1
0
0
0
1
0
1
2
0
0
1
0
0
1
1
2
5
1
0
1
0
2
0
1
1
2
0
1
1
2
2
1
0
0
0
0
0
0
0
0
0
3
0
2
1
1
2
4
1
0
0
0
0
1
0
0
1
0
1
1
1
1
2
4
0
0
0
1
0
1
0
0
1
1
0
0
2
0
0
0
1
1
1
0
1
0
2
2
0
0
2
1
0
1
0
0
1
0
2
1
0
0
0
0
0
0
1
3
1
0
0
0
3
0
0
0
2
0
0
2
0
0
1
1
0
0
0
0
2
2
0
3
0
2
0
0
1
0
2
0
0
1
1
1
0
0
1
0
0
0
2
0
3
1
0
2
1
0
2
0
0
0
0
2
1
0
1
2
0
0
0
2
1
0
0
0
0
1
1
0
1
0
0
0
1
2
6
1
1
2
0
0
1
0
0
1
0
1
2
0
0
0
3
1
3
0
2
2
1
1
1
1
2
0
0
2
0
1
0
1
2
2
2
1
1
1
0
1
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
1
2
2
1
0
0
0
2
0
0
2
1
0
0
0
0
1
1
1
2
1
0
2
1
1
2
2
0
0
1
1
1
0
0
0
0
1
0
2
0
2
0
2
1
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
1
1
2
0
0
0
0
1
1
2
0
1
1
0
1
1
2
1
0
0
0
0
0
2
1
0
1
0
0
0
0
0
1
2
0
0
0
1
0
0
1
0
2
1
0
0
0
0
0
1
1
1
2
9
0
0
0
2
2
0
2
1
2
0
0
0
0
2
2
0
0
1
1
0
0
1
2
0
1
1
2
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
1
1
0
1
0
2
2
2
1
2
0
0
2
0
0
4
0
1
1
2
0
0
2
0
0
0
0
3
0
0
2
0
1
2
2
0
0
0
0
1
1
1
1
1
0
0
1
0
0
2
0
0
0
1
1
1
1
1
1
1
0
0
0
0
0
4
2
0
0
0
1
0
2
1
2
0
0
1
2
0
1
0
2
0
1
0
2
0
1
1
1
0
1
0
0
1
2
0
0
0
3
0
0
2
0
0
0
2
1
2
0
0
0
2
0
1
0
0
1
0
0
1
0
1
1
1
0
0
2
2
1
2
0
3
0
0
5
0
2
0
0
0
1
1
1
2
1
0
2
0
2
0
0
0
0
0
1
1
0
0
2
2
0
0
1
0
2
1
0
0
0
0
1
0
0
0
0
1
1
0
1
1
1
0
0
2
0
0
0
0
0
1
2
1
1
1
0
1
2
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
2
1
2
2
0
0
0
1
1
2
0
0
1
0
2
0
1
0
0
1
0
1
0
0
1
1
1
0
1
1
0
0
2
1
0
1
2
0
1
0
0
0
2
0
0
1
0
1
2
0
1
0
1
1
0
1
0
0
0
2
4
0
1
1
2
2
0
0
1
1
1
0
1
0
0
0
2
0
2
2
0
0
2
0
0
1
2
0
1
2
1
0
0
0
2
2
3
2
0
2
0
2
2
1
0
1
1
1
0
2
2
0
0
0
0
1
2
3
0
0
0
0
2
1
0
0
1
1
0
3
0
0
2
0
2
2
0
2
0
0
0
2
1
0
1
1
1
0
3
2
2
1
1
1
1
0
0
0
1
2
0
2
1
0
0
2
0
1
0
1
2
1
2
0
1
0
1
6
2
0
0
2
0
0
0
0
1
0
1
1
0
1
1
0
1
0
1
0
2
0
0
1
2
0
2
1
0
0
0
0
0
0
0
2
1
0
0
0
0
2
2
1
0
1
1
1
0
2
2
0
0
1
0
2
1
1
0
3
0
1
2
1
0
2
1
0
1
0
2
2
2
0
2
0
1
0
0
2
1
0
2
2
1
1
0
1
1
1
1
0
0
1
2
0
1
0
2
2
0
2
0
2
0
2
2
1
2
0
0
2
0
1
0
0
2
0
0
0
2
2
0
1
1
0
0
2
0
0
0
2
0
1
1
1
0
0
0
1
0
0
0
1
2
1
1
2
1
0
3
0
1
1
1
0
1
2
1
1
2
0
1
0
0
0
1
0
1
1
1
0
2
0
0
0
0
0
1
0
1
0
0
0
1
0
0
2
0
0
0
1
2
1
2
1
1
0
0
2
1
0
0
1
1
0
1
0
1
1
1
1
1
0
2
2
0
0
1
1
1
0
0
0
1
0
0
0
1
2
1
1
2
0
1
1
0
2
1
2
1
0
2
0
0
2
0
0
2
0
0
1
0
0
2
1
1
1
1
0
0
1
2
0
0
1
2
1
1
0
2
0
1
0
1
0
1
0
1
1
2
0
0
1
0
2
0
1
0
0
0
1
1
1
0
0
2
1
1
1
0
2
2
0
2
0
0
1
0
1
0
0
0
2
0
0
2
1
0
2
1
1
1
0
0
0
2
0
0
0
0
2
0
0
0
1
2
2
2
1
1
1
1
1
0
0
0
0
0
2
0
0
0
1
0
1
1
0
1
2
0
1
0
0
0
0
0
0
2
1
0
1
0
2
0
1
0
0
1
0
0
1
1
2
0
0
0
0
0
1
1
0
1
0
0
0
2
1
0
2
0
1
1
1
0
2
1
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
2
1
1
0
0
1
0
1
0
1
1
0
0
0
0
1
4
0
0
0
0
0
3
2
0
0
2
0
1
0
2
0
1
0
0
0
2
2
0
0
0
1
1
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
3
0
0
2
0
1
0
2
2
0
1
1
0
1
0
1
2
0
2
2
1
0
0
3
1
0
0
0
0
0
1
1
1
1
0
2
0
2
0
0
4
1
0
1
0
0
0
1
1
0
1
1
0
0
1
1
0
2
1
0
0
1
0
2
3
1
1
0
1
0
0
1
0
1
2
1
0
1
0
1
0
1
0
0
0
1
0
0
0
0
1
1
2
0
0
1
0
2
0
0
0
1
2
0
0
2
1
1
2
0
0
0
0
1
0
1
1
1
1
1
1
1
0
0
2
1
0
2
0
0
0
0
2
1
2
3
0
2
2
0
1
0
1
0
0
2
1
0
0
0
0
0
1
0
0
1
0
2
1
0
0
0
2
0
2
1
0
2
0
1
2
0
0
1
2
0
2
1
1
0
0
0
0
1
0
1
0
2
0
0
0
0
2
0
0
2
0
2
2
1
0
2
0
2
0
0
0
1
1
0
2
2
0
0
0
1
0
1
0
0
0
1
1
1
0
3
1
1
1
1
0
0
1
0
0
0
0
1
0
0
2
0
1
0
0
1
0
0
1
0
0
2
1
0
0
1
0
1
0
0
1
2
0
0
1
1
1
3
1
0
0
1
1
2
0
2
2
0
0
1
0
0
0
0
1
2
0
2
1
0
1
0
0
1
3
0
0
0
1
0
0
0
0
2
0
0
2
0
2
3
0
0
1
0
2
1
0
0
0
2
2
0
0
1
2
2
0
1
1
0
0
0
0
2
0
2
1
2
0
1
0
0
1
0
2
0
4
2
0
0
0
1
1
1
1
1
0
2
0
0
2
0
2
1
0
0
0
1
2
0
0
0
0
2
3
0
1
1
0
0
2
1
1
1
1
0
2
1
0
1
1
1
2
1
2
0
0
0
1
0
1
2
2
0
2
0
0
0
0
1
2
0
1
1
1
0
1
1
1
0
0
2
0
1
0
0
0
0
0
0
0
0
2
2
1
1
0
0
1
0
0
2
1
3
1
2
1
0
0
1
0
1
0
1
0
0
2
2
0
0
1
1
0
1
1
1
0
0
0
0
1
2
2
0
1
1
0
2
2
0
0
2
0
0
1
1
0
1
0
0
1
2
1
1
0
2
0
0
0
2
1
1
0
2
1
0
2
2
1
0
0
2
1
1
0
0
0
1
1
0
1
2
2
1
0
0
2
0
1
1
2
0
0
0
1
0
1
2
1
1
1
0
1
1
2
3
0
0
0
1
2
0
0
0
2
2
1
0
0
0
1
2
2
1
1
0
0
2
0
0
0
2
2
1
1
2
2
1
2
0
0
2
0
2
1
2
2
0
2
2
0
0
0
2
2
1
0
1
4
6
0
0
1
5
0
2
0
1
0
1
0
1
0
1
0
0
2
0
2
1
1
0
1
0
2
2
0
0
0
0
0
0
0
0
2
2
1
1
1
0
1
0
0
0
1
0
1
2
0
1
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
1
0
0
0
2
0
0
2
1
2
1
0
3
3
0
0
0
2
1
0
1
1
0
1
0
2
1
0
0
11
2
0
0
0
1
3
0
1
0
0
1
1
0
2
1
0
0
3
1
1
3
0
0
1
0
0
0
0
2
0
0
1
0
2
1
0
2
0
0
0
1
0
0
2
1
1
1
1
1
0
0
0
1
0
0
0
1
2
1
0
2
1
1
1
0
0
2
1
0
0
0
4
1
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
2
1
0
0
0
0
2
2
3
0
1
0
2
0
2
1
0
1
1
0
2
2
3
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
1
2
0
3
1
0
2
1
0
2
1
1
1
1
0
2
0
0
1
0
1
0
2
0
0
1
1
1
0
2
0
2
0
1
1
0
1
0
0
0
2
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
1
0
1
0
0
2
0
0
2
0
2
1
0
0
2
1
0
0
1
2
0
1
1
0
2
1
2
0
0
0
0
1
1
0
0
2
1
0
1
0
0
0
2
2
1
0
0
0
4
0
1
2
0
2
1
1
0
0
0
1
2
1
0
1
1
2
0
1
1
1
1
1
0
2
2
0
2
0
1
0
0
0
2
1
2
0
1
2
3
0
1
1
1
2
2
2
0
0
0
0
2
0
0
1
1
0
0
0
2
0
1
0
1
0
2
0
0
0
2
0
1
3
1
1
2
0
0
0
0
0
0
0
0
0
2
4
4
1
0
0
2
4
1
2
3
1
0
1
2
0
0
0
0
2
1
0
0
2
0
0
1
0
0
0
0
1
0
0
0
1
2
2
1
1
2
0
0
0
1
0
0
0
1
0
0
2
0
2
0
1
0
1
1
2
0
0
2
1
0
0
0
2
1
0
1
1
1
2
1
1
0
0
1
2
0
1
0
2
2
0
0
0
0
1
2
0
1
1
5
1
1
0
1
1
0
0
0
0
0
1
2
1
0
0
0
1
1
2
0
2
0
2
0
1
2
1
1
0
1
0
0
1
2
3
1
0
0
1
1
0
0
0
2
2
1
2
0
0
0
1
1
0
1
0
0
1
3
0
1
1
0
0
0
1
0
0
1
0
0
1
0
1
0
1
0
0
1
1
1
0
0
3
1
1
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
3
0
1
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
2
2
0
2
0
0
2
1
2
1
0
1
0
3
0
2
0
0
1
1
1
0
0
0
0
1
0
0
1
2
0
0
0
1
1
0
1
0
0
0
1
2
0
0
1
1
0
0
1
2
2
0
1
5
2
0
0
0
2
0
0
2
1
1
0
2
1
0
0
0
1
0
0
0
1
2
0
0
0
0
0
2
1
1
1
0
0
0
1
0
1
2
0
0
1
0
0
2
2
0
1
1
1
1
1
1
0
0
0
0
0
0
0
1
1
2
0
0
2
2
0
0
2
0
0
1
1
2
1
1
1
0
2
1
1
1
2
0
1
0
2
0
2
0
1
2
1
1
2
2
1
2
0
0
1
0
0
0
0
1
0
2
0
0
1
1
1
0
0
1
1
1
0
1
1
2
1
1
0
3
1
1
2
1
1
1
1
1
1
0
1
1
0
1
1
2
0
1
0
2
1
1
0
1
1
2
2
0
2
1
0
2
2
2
0
0
1
0
0
2
0
1
1
0
1
0
0
0
1
1
0
2
1
1
0
2
1
1
0
0
0
1
2
2
0
1
0
0
0
0
0
2
1
0
1
3
0
1
0
0
0
0
0
0
0
3
0
3
1
0
1
1
2
2
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
1
0
2
0
1
1
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
2
2
0
1
1
2
1
1
2
0
0
2
2
2
0
2
1
1
2
2
2
2
2
1
0
1
1
0
0
1
1
1
1
0
1
2
1
0
0
0
0
4
3
2
0
0
2
0
0
0
0
0
2
0
2
1
0
1
2
2
1
1
0
2
0
1
0
2
2
0
1
2
2
0
1
0
2
0
0
0
0
0
0
0
4
2
1
2
2
0
0
1
1
0
0
2
0
2
1
0
1
2
0
0
0
1
1
1
0
0
1
1
1
2
1
2
0
1
1
2
1
1
1
0
1
2
0
0
2
2
0
2
0
0
1
0
1
0
1
0
1
1
0
2
1
2
0
2
0
2
0
2
0
1
0
2
0
2
0
0
0
0
1
0
1
2
1
0
0
0
0
0
0
1
2
2
0
1
0
0
2
1
0
2
2
0
2
2
0
0
0
1
0
2
2
2
1
0
0
0
2
0
2
0
1
0
0
0
1
1
0
1
1
0
3
0
1
1
0
2
0
0
1
0
0
2
0
0
1
0
0
0
0
2
0
0
0
1
0
1
2
3
1
1
2
0
0
2
2
1
0
1
2
0
1
1
0
0
0
0
1
1
1
0
0
0
0
1
1
3
0
1
2
0
0
0
0
0
1
1
1
0
0
0
1
2
0
0
0
2
0
2
0
0
2
0
2
0
2
2
0
0
1
0
2
0
0
2
1
2
1
2
0
0
1
0
1
0
0
0
2
1
2
0
0
2
1
1
0
1
0
1
1
0
1
2
3
0
0
0
2
0
0
1
0
1
1
1
0
0
2
0
0
0
1
0
1
0
0
1
2
0
2
1
0
1
1
0
0
0
0
0
0
1
1
2
0
2
1
0
1
0
0
0
2
0
1
2
1
2
0
1
0
0
0
0
0
1
1
3
0
2
1
0
0
1
0
2
0
0
0
1
0
0
1
0
1
1
0
2
2
3
0
2
0
0
0
1
0
0
0
1
0
1
1
0
1
1
2
0
2
2
0
0
1
1
1
2
1
0
2
0
0
0
2
2
2
0
0
0
0
1
1
0
2
3
0
0
0
0
0
1
1
0
0
2
1
0
0
1
0
0
0
1
0
0
2
0
2
0
0
0
0
2
0
2
2
0
0
0
1
0
0
0
0
1
1
1
0
0
1
0
0
2
1
2
1
1
1
2
1
2
0
0
2
0
0
1
2
0
1
0
2
0
1
0
1
4
2
0
0
0
0
0
0
2
2
0
2
0
0
0
2
0
2
0
1
0
0
0
2
0
1
0
1
0
0
1
2
1
0
0
0
2
1
0
0
0
0
0
0
1
2
0
0
0
1
2
0
0
2
1
1
0
0
0
2
0
1
0
0
2
0
0
2
2
1
0
0
1
0
0
1
0
1
1
1
1
1
0
0
0
1
1
1
1
1
0
2
0
0
0
0
1
0
1
0
0
3
1
0
0
0
1
0
2
1
1
0
2
0
0
0
0
1
1
0
0
0
0
0
0
2
0
1
1
0
0
0
2
0
1
1
1
1
0
0
2
2
0
0
1
0
0
0
2
1
0
0
0
0
0
1
0
1
1
0
1
0
0
1
0
0
2
0
2
0
0
0
0
1
1
0
2
2
0
0
0
0
0
2
0
2
1
0
2
1
1
1
1
0
1
2
0
1
1
1
1
0
3
0
0
1
0
0
0
1
0
1
0
2
1
0
0
0
1
0
3
1
2
1
0
2
3
0
2
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
1
1
1
0
1
1
0
2
0
2
0
1
1
0
2
2
0
1
2
0
1
0
0
0
1
0
0
1
2
0
0
2
0
0
0
1
0
1
2
2
0
2
0
2
2
1
2
0
2
2
2
0
2
0
1
1
1
2
0
0
1
0
2
1
1
3
0
0
2
0
0
2
2
1
0
0
1
1
2
0
0
0
1
0
0
2
0
2
0
1
2
1
2
0
2
2
0
2
0
0
0
0
2
2
2
2
2
0
1
1
1
0
0
0
2
1
2
0
0
0
0
2
0
0
0
1
1
2
1
0
1
0
1
1
1
0
1
2
1
0
0
2
1
0
0
1
1
0
1
0
1
0
1
1
3
0
0
0
1
0
1
1
1
1
2
1
2
1
0
0
0
0
0
0
0
2
1
0
2
2
0
0
1
0
1
0
1
0
0
0
1
0
0
1
2
0
0
0
1
2
1
2
0
0
2
2
0
1
0
1
0
1
0
0
0
1
0
1
1
1
1
0
0
0
2
2
1
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
1
0
2
0
2
1
2
0
0
1
1
2
1
0
0
0
0
0
2
0
2
3
2
1
2
2
1
1
1
0
0
2
2
0
2
2
0
0
0
1
0
0
0
0
1
2
0
2
2
0
1
1
1
1
2
1
2
0
2
1
1
2
0
2
1
0
2
1
0
0
2
2
0
2
0
3
0
0
1
1
1
0
2
0
1
0
3
1
2
1
0
1
2
1
1
0
1
2
0
5
0
2
0
2
1
0
1
1
2
0
0
0
0
1
1
2
2
0
2
1
0
1
0
0
0
2
0
1
2
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
1
0
1
0
0
0
1
0
2
0
0
2
1
0
0
0
1
1
1
1
2
0
1
1
0
2
0
1
0
0
0
0
2
1
1
0
2
2
1
3
1
0
1
0
0
0
1
0
0
2
1
0
0
0
0
1
1
1
0
2
0
1
0
0
1
2
0
2
0
1
0
2
1
1
4
1
1
1
0
1
0
0
0
0
2
0
1
2
0
0
1
2
1
0
0
0
1
1
2
0
0
2
1
1
1
1
1
1
1
0
2
2
1
0
0
0
1
0
0
1
2
0
1
1
0
0
1
1
0
2
0
0
2
1
0
1
1
0
2
1
0
0
0
0
2
2
2
2
1
2
1
0
3
0
1
1
2
2
0
2
1
1
2
2
0
1
2
0
0
0
0
1
0
2
0
3
0
2
1
1
0
1
2
2
3
0
0
1
2
0
0
1
0
0
1
0
2
2
2
2
1
2
2
1
0
2
0
1
0
0
0
0
1
0
1
0
1
0
0
1
1
0
0
0
1
1
0
2
2
2
0
0
0
0
0
0
0
0
2
1
1
0
1
1
2
0
2
2
2
2
2
1
2
1
0
1
1
0
0
1
0
1
0
2
1
0
1
0
0
1
0
0
1
1
0
1
0
0
0
0
0
1
1
0
0
0
0
1
2
1
1
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
2
1
1
1
1
0
2
2
0
0
1
1
0
0
1
0
0
0
0
0
0
3
1
0
0
2
2
0
0
2
0
0
0
1
0
0
2
0
1
0
2
2
0
0
1
0
0
0
1
0
0
0
0
0
0
2
1
0
2
0
0
2
0
2
0
2
0
0
1
2
1
0
2
1
0
0
0
0
2
0
1
2
0
0
0
0
0
0
2
0
0
2
1
2
0
3
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
1
2
0
2
0
0
1
1
0
2
1
0
1
0
2
0
1
1
1
1
0
2
0
1
0
0
2
0
0
0
1
0
0
2
0
0
1
1
1
2
2
1
0
2
0
0
1
2
1
0
0
0
2
1
0
0
2
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
1
0
1
0
2
0
1
1
0
0
2
0
1
1
1
2
2
0
0
0
0
1
0
2
0
2
0
0
2
0
0
0
1
1
2
1
1
2
1
1
0
3
0
0
2
1
0
2
2
0
0
2
0
0
0
2
2
1
0
0
0
0
0
2
2
0
0
0
0
1
2
2
0
0
0
2
0
0
1
1
0
1
2
0
0
1
0
0
2
0
0
0
2
0
0
0
1
0
0
2
0
1
0
1
0
0
1
0
0
1
0
0
1
1
2
2
1
2
0
2
0
0
0
0
0
0
3
0
0
1
2
2
2
2
1
0
0
0
0
1
3
0
2
0
1
1
0
1
1
0
2
0
0
0
1
0
0
2
1
0
1
0
1
1
1
2
0
2
0
2
2
3
0
2
0
0
2
3
1
0
0
1
0
1
1
0
2
2
0
0
2
2
0
1
2
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
2
0
2
2
1
0
3
0
0
0
0
2
1
2
1
0
2
0
0
1
0
0
1
2
2
1
1
0
1
0
1
1
1
0
0
0
1
1
1
1
2
2
1
0
0
0
0
1
1
1
3
0
2
0
0
1
1
0
1
1
1
0
0
2
2
2
2
0
0
0
0
0
2
1
2
0
1
0
1
0
0
1
0
2
0
0
2
1
2
3
1
3
1
1
2
2
2
1
1
0
2
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
1
1
0
0
0
0
1
3
1
2
2
0
0
0
0
1
1
1
2
0
2
0
1
0
0
0
0
0
2
0
0
2
0
0
1
1
1
1
0
1
2
0
2
0
3
0
0
1
0
0
0
1
0
1
0
1
0
0
2
1
2
2
0
2
1
2
0
1
1
1
2
0
0
0
0
0
1
0
1
2
2
2
2
0
2
1
0
0
2
1
1
0
0
2
1
0
0
2
0
2
1
0
1
0
0
1
1
0
2
0
0
0
0
1
0
0
0
0
2
1
0
2
2
0
1
0
0
1
0
1
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
2
0
1
0
3
0
1
1
2
0
1
1
0
1
0
1
0
0
0
2
1
1
2
0
0
0
1
0
0
2
2
1
2
1
3
0
4
8
0
2
0
0
2
2
1
1
0
2
0
0
0
1
4
2
0
0
0
0
1
0
0
1
0
0
1
0
1
0
1
2
2
0
0
2
0
1
0
0
1
2
0
0
2
0
2
2
1
0
0
0
0
0
1
1
1
1
0
0
1
2
0
2
1
0
1
0
0
1
0
2
0
1
1
1
1
0
0
1
0
1
1
0
0
1
1
1
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
2
0
2
0
0
1
0
0
0
0
2
0
2
2
0
2
1
1
2
0
1
1
0
0
1
2
2
1
0
0
0
1
0
1
0
0
2
1
0
0
3
0
0
0
0
0
2
0
1
0
1
0
1
1
2
0
0
0
0
0
2
0
0
1
0
0
0
2
2
0
0
2
0
1
1
0
1
2
5
2
1
0
2
0
0
1
0
1
1
1
1
1
1
4
0
0
2
0
0
1
0
0
1
1
1
1
0
0
0
2
0
1
2
0
1
0
0
1
1
0
0
2
0
2
0
0
0
1
1
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
1
1
1
1
1
0
1
2
2
1
0
0
1
0
0
1
0
1
0
1
0
1
0
1
0
1
0
0
1
0
0
0
0
0
2
0
0
2
1
0
0
0
3
2
2
1
2
0
2
0
1
0
1
0
1
2
2
0
2
0
0
0
2
0
0
1
1
1
1
1
0
1
2
0
0
0
2
1
1
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
1
2
1
0
0
0
1
1
0
2
0
1
1
1
2
0
1
0
0
1
1
0
0
2
2
0
0
0
0
1
1
0
1
1
0
0
2
1
0
2
2
0
0
1
0
2
0
0
1
1
2
0
1
1
0
2
2
0
2
0
2
1
0
0
0
2
1
2
1
0
1
0
1
0
1
1
0
1
0
0
0
0
1
0
2
2
2
2
1
1
1
0
1
0
0
1
1
0
0
0
0
0
1
2
0
0
0
0
0
1
1
1
1
2
2
0
0
1
2
0
0
1
2
3
1
1
0
0
0
0
0
1
0
1
2
1
0
0
0
0
3
0
2
0
0
0
0
1
1
0
1
0
2
0
0
0
0
2
0
1
0
1
0
0
2
0
0
1
0
0
0
1
0
1
1
0
2
0
1
1
3
3
0
0
0
2
2
1
2
2
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
1
0
1
0
0
1
1
1
1
0
0
0
0
2
0
0
1
2
0
1
2
0
2
0
1
0
0
1
2
0
1
0
1
0
0
1
0
0
1
0
0
2
0
0
2
0
1
2
2
1
0
1
0
1
1
1
0
2
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
2
0
4
0
0
3
0
0
2
0
1
2
1
0
0
2
0
0
1
2
1
2
1
0
0
0
0
0
6
0
2
2
2
0
0
1
2
1
2
1
1
0
0
0
2
0
0
2
2
0
2
3
0
0
0
0
0
1
1
0
0
0
2
0
2
2
1
0
0
0
0
3
1
0
0
1
2
1
1
0
0
0
1
2
0
0
0
2
1
0
0
0
0
0
0
1
3
1
0
2
2
0
0
1
1
0
1
1
2
0
1
0
0
1
0
4
1
0
1
0
0
0
2
2
0
0
1
0
0
2
0
0
2
2
2
0
1
0
0
1
1
1
2
0
2
0
1
1
1
2
0
1
2
1
2
1
1
1
0
1
0
1
2
1
2
0
0
1
0
0
0
2
1
2
0
1
1
2
1
0
2
1
0
0
1
0
1
2
2
1
2
0
1
1
0
1
2
4
0
2
0
0
1
0
0
0
0
0
0
1
1
0
0
2
2
0
0
2
0
2
0
2
0
2
1
0
1
0
2
1
1
0
0
1
0
2
2
0
0
0
2
2
2
1
1
1
0
0
0
0
3
2
1
0
0
2
0
0
1
0
2
2
0
0
2
1
0
1
2
2
0
2
0
1
0
0
1
0
0
0
1
1
0
1
0
2
0
1
0
1
3
0
1
0
0
0
0
0
0
0
2
0
1
0
2
0
2
1
1
1
0
1
1
0
1
1
0
2
1
0
0
2
1
1
1
2
2
0
3
0
1
0
0
0
0
0
0
0
1
0
1
2
2
0
1
2
0
1
1
0
1
2
2
0
0
1
0
0
0
2
1
1
0
1
0
0
1
2
1
0
0
2
0
0
2
2
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
1
0
1
1
0
0
0
0
2
0
1
2
1
1
1
0
0
1
0
0
0
2
1
0
2
0
2
1
0
0
0
1
2
0
4
0
0
0
1
2
2
0
0
1
1
0
0
2
0
0
1
0
1
0
0
2
0
2
1
2
2
0
0
2
0
3
1
1
0
0
1
0
0
0
3
1
1
0
0
0
0
0
2
1
2
1
0
0
1
0
0
1
0
3
1
0
0
0
0
0
2
1
0
1
4
1
0
0
0
1
0
1
0
0
1
0
0
1
1
0
1
0
1
0
1
0
2
0
2
0
0
0
0
0
2
0
0
0
0
2
1
1
2
0
0
0
0
0
0
0
1
0
1
0
2
2
0
0
1
0
0
1
2
0
0
1
1
2
0
0
1
0
2
0
1
0
0
1
1
1
0
1
0
0
1
2
2
0
0
0
0
0
0
1
2
1
1
0
0
1
2
1
1
2
1
0
2
0
0
0
0
0
2
0
1
0
1
0
2
2
1
2
0
1
1
0
1
0
2
1
1
1
1
1
0
2
0
1
2
1
0
0
2
2
2
0
1
1
1
0
0
3
0
0
0
0
1
1
0
0
0
1
1
0
1
0
1
1
1
0
1
1
0
1
1
0
0
0
2
0
2
0
0
1
0
0
2
1
0
0
2
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
2
2
1
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
3
0
2
0
1
2
1
0
0
1
2
0
1
1
1
2
0
2
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
1
2
0
2
0
0
1
0
0
1
0
2
2
2
0
0
1
1
0
2
5
0
0
3
1
0
2
2
0
0
0
0
0
1
0
0
3
3
1
0
1
2
2
1
0
1
1
1
2
0
0
2
1
0
1
2
1
2
0
1
0
2
0
0
1
2
1
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
1
2
0
0
2
2
0
0
0
2
1
1
0
0
0
0
0
0
1
3
0
0
1
1
1
2
0
2
1
2
1
0
2
0
2
0
0
2
0
1
0
0
1
1
2
2
0
1
1
0
2
0
2
2
0
2
0
0
0
2
1
0
1
0
2
0
1
0
0
2
0
0
0
1
1
0
0
0
1
1
1
1
1
1
1
0
0
2
1
0
1
1
0
0
2
0
2
2
1
1
1
0
1
3
0
0
3
1
0
2
2
0
3
1
1
0
1
1
1
1
0
0
2
2
1
0
1
1
0
0
0
3
1
0
0
0
3
0
1
0
1
3
0
1
0
1
1
0
0
2
2
0
0
0
0
0
0
1
1
1
2
0
0
0
1
2
1
1
1
1
0
8
3
1
2
3
2
0
0
1
0
1
0
2
2
0
1
0
2
2
0
0
0
2
1
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
2
1
1
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
2
0
2
2
0
1
0
0
0
0
1
1
0
0
1
1
0
1
0
2
2
1
0
2
2
1
1
1
2
2
2
1
2
1
1
1
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
1
1
2
2
0
1
1
0
2
1
7
2
0
0
0
1
2
1
2
1
0
1
2
0
2
0
1
3
0
0
1
0
3
0
0
0
0
2
1
0
1
1
2
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
1
1
0
1
0
2
1
1
1
0
0
1
0
0
2
1
1
1
0
0
1
3
0
0
0
0
0
1
2
0
0
3
0
1
0
1
2
0
0
1
0
0
0
2
1
1
1
1
1
1
0
1
0
0
0
1
0
2
0
0
1
1
1
1
0
0
0
0
2
1
1
2
2
0
2
1
2
0
4
0
0
1
2
1
0
2
0
0
1
0
0
0
1
0
0
2
1
0
1
1
0
0
1
0
0
3
1
2
1
1
0
1
1
1
0
1
2
0
0
1
2
2
0
1
0
0
2
0
2
0
0
0
1
2
1
1
0
1
1
1
0
1
0
2
1
2
0
0
2
0
0
0
0
1
1
2
1
0
0
1
0
1
1
1
2
2
1
0
0
0
1
2
1
0
0
1
1
1
0
0
1
1
3
0
0
0
0
2
1
1
0
0
0
1
0
0
1
1
1
0
0
1
0
0
1
2
1
0
1
0
0
2
1
1
2
0
1
2
0
0
0
2
0
1
0
0
5
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
1
1
2
0
1
2
1
0
1
0
1
0
0
1
1
1
0
0
0
0
2
1
2
0
0
1
0
0
0
0
1
1
1
1
0
0
0
2
0
0
0
2
0
0
1
0
0
0
1
2
1
3
0
1
2
1
1
1
1
0
1
0
2
2
0
0
0
0
0
2
1
0
1
0
2
1
0
0
0
0
1
1
2
0
0
2
0
0
0
0
0
0
2
1
1
0
1
0
1
2
0
1
1
0
1
1
1
2
1
1
0
3
1
0
0
0
1
1
1
2
0
0
0
2
0
3
1
1
2
2
2
1
2
0
0
1
1
0
2
1
0
0
1
1
0
2
0
0
1
0
1
0
1
1
1
1
1
1
2
0
1
1
2
0
1
0
1
0
0
0
2
0
1
0
2
0
1
0
3
1
0
0
0
0
2
1
1
2
0
2
2
0
1
0
0
1
0
1
0
0
1
1
0
0
0
2
2
0
2
0
1
1
0
1
1
1
0
1
0
2
0
0
0
0
1
2
1
0
1
1
0
1
0
2
1
1
2
0
0
0
0
2
0
0
0
0
1
0
0
1
1
2
1
2
2
2
0
1
1
3
1
0
1
0
2
1
0
0
0
1
2
1
0
2
1
1
3
0
0
0
1
2
0
1
2
2
1
0
2
0
1
1
1
1
1
1
2
0
0
1
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
2
0
0
1
1
2
1
0
0
2
1
1
0
0
0
1
0
0
1
0
0
0
2
0
0
0
1
1
0
0
1
0
0
2
0
0
2
0
2
1
0
0
1
2
0
3
1
0
0
1
1
2
0
1
0
2
0
4
0
1
0
0
0
1
0
2
3
1
0
0
1
1
0
0
0
2
0
2
1
1
0
0
1
1
1
2
0
1
0
1
0
2
1
0
0
0
2
2
1
2
0
2
3
1
1
0
0
0
0
0
0
0
1
2
1
0
2
1
1
0
1
0
1
1
2
0
0
0
0
1
0
0
2
0
0
0
2
1
0
0
0
0
0
2
0
0
0
2
0
1
1
0
3
1
0
0
1
2
0
0
0
0
2
1
0
0
1
1
1
1
0
0
2
1
2
2
0
0
0
0
1
1
2
1
1
0
0
1
2
2
1
0
2
1
1
1
2
0
1
1
2
2
2
1
1
0
0
0
0
1
2
0
2
0
1
0
0
0
0
0
0
2
0
0
0
1
2
1
1
2
0
1
0
0
0
2
0
0
0
1
2
2
0
0
0
2
0
2
0
0
0
0
1
0
1
0
0
0
1
0
4
2
0
0
1
0
1
0
0
0
2
2
0
0
1
1
1
1
0
1
2
0
0
1
0
0
0
1
1
2
0
0
2
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
2
0
2
2
0
0
0
2
1
1
0
1
1
1
0
2
0
0
0
1
1
1
0
0
0
0
2
0
0
1
1
1
0
0
1
1
1
1
1
2
1
1
2
0
2
0
1
2
0
0
0
2
1
2
1
0
0
1
0
2
0
0
0
0
0
1
1
0
1
0
2
0
2
2
2
0
1
1
1
0
1
1
1
0
1
1
1
0
0
0
0
0
2
0
1
0
1
2
0
1
0
2
0
0
0
0
0
1
2
0
0
0
2
0
0
2
2
1
0
0
2
2
0
2
2
0
1
0
2
0
2
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
1
0
2
0
0
0
1
1
0
0
1
1
0
0
0
2
1
0
2
1
1
0
0
1
1
0
2
0
0
0
2
0
0
0
2
0
0
2
0
0
0
2
2
3
0
2
0
2
0
0
0
2
2
1
1
0
2
0
0
1
1
2
0
0
0
2
0
0
0
0
1
1
0
0
1
0
1
1
2
0
1
1
2
2
1
0
0
0
0
1
0
0
2
0
0
1
0
1
0
1
0
1
2
1
1
2
1
1
1
0
1
0
0
2
0
1
1
1
0
0
1
0
1
0
1
0
1
0
1
1
2
1
0
2
0
1
0
0
1
0
1
1
1
0
1
0
2
0
1
2
0
0
0
2
1
0
0
2
0
2
1
2
0
2
4
0
2
0
0
2
3
0
0
2
0
0
0
2
0
0
2
3
1
0
0
1
1
1
0
0
1
0
1
2
2
0
1
2
1
1
1
0
0
1
2
2
0
1
1
2
0
0
1
0
2
0
1
2
0
0
1
1
2
2
0
1
0
0
1
2
1
1
2
2
1
0
1
1
0
1
0
0
1
2
0
0
2
2
0
1
0
1
2
0
0
1
0
2
1
0
0
2
2
1
0
2
2
0
1
2
0
0
2
2
1
1
0
0
1
2
0
1
0
0
2
0
1
0
2
1
3
0
0
1
9
1
0
1
1
1
1
0
3
1
1
0
0
0
2
0
1
2
1
0
0
1
1
0
0
0
0
0
2
1
1
0
1
0
0
1
1
2
0
2
1
0
1
1
1
2
1
1
2
2
1
2
1
0
1
0
0
0
0
0
0
0
1
1
0
2
2
0
0
1
5
1
1
0
0
2
0
0
2
2
0
2
0
0
1
0
3
0
1
2
0
1
0
1
2
1
2
0
0
0
0
0
1
0
0
0
2
1
1
0
1
1
1
1
1
0
0
0
2
0
1
1
0
0
0
1
2
1
1
0
1
0
2
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
1
2
0
1
1
0
0
0
2
1
1
0
0
1
0
0
0
2
1
0
0
0
2
0
2
1
0
1
1
0
1
2
2
1
0
2
2
0
0
2
0
1
1
2
2
3
2
1
0
2
1
1
1
0
1
0
0
2
1
1
1
0
1
1
2
1
0
0
0
2
1
0
0
0
0
2
0
2
0
2
1
1
1
0
0
0
2
2
1
3
1
0
1
1
0
0
0
0
0
0
0
2
0
0
0
3
2
1
0
1
0
1
0
2
0
0
3
0
0
0
0
0
1
2
0
0
0
2
0
0
1
1
2
1
0
2
2
1
0
2
0
0
0
1
0
0
0
0
1
1
0
0
2
1
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
1
2
0
1
0
1
0
1
0
0
0
0
0
1
2
2
1
1
0
0
0
2
0
0
0
0
1
1
2
0
1
0
0
1
0
0
0
2
0
1
0
1
0
0
0
2
0
0
1
0
1
0
0
0
2
0
0
1
2
2
0
0
0
1
0
2
2
2
1
2
0
1
1
0
1
1
2
0
1
1
1
1
1
2
2
1
0
1
2
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
7
2
2
0
1
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
1
1
1
1
0
3
0
0
1
2
1
1
0
0
1
0
2
2
0
0
2
0
1
1
1
0
0
0
1
0
2
1
0
2
1
1
0
1
1
2
2
2
1
1
2
0
2
0
1
1
1
0
0
0
1
0
1
1
0
2
1
2
0
2
0
0
1
2
1
2
0
2
0
2
0
0
2
0
2
2
2
1
2
1
0
0
1
1
1
1
0
0
1
0
0
0
1
2
1
0
0
1
1
1
1
2
0
1
0
0
0
0
0
1
0
2
2
2
0
1
2
2
1
2
1
1
0
2
0
0
0
1
2
0
2
2
1
1
0
0
1
0
0
0
1
4
0
0
0
0
1
0
0
1
2
0
0
2
0
2
0
0
0
2
1
1
2
2
1
1
1
1
1
1
2
0
1
2
1
1
1
2
0
0
0
0
0
2
1
4
1
0
0
0
0
2
0
0
0
2
0
0
2
2
2
0
1
2
1
0
1
0
1
2
0
0
1
1
1
1
2
2
1
0
0
0
0
1
1
0
1
1
0
1
1
0
1
0
0
0
2
0
1
0
0
0
1
1
0
0
1
1
1
0
0
0
1
0
0
0
1
2
0
0
0
2
0
1
2
0
0
0
1
1
0
1
1
0
2
0
2
0
2
1
1
0
0
0
1
1
0
0
0
2
0
0
1
2
1
0
0
2
2
1
2
1
1
1
1
1
2
0
0
0
0
0
0
1
0
2
0
1
1
0
1
0
2
2
0
0
0
2
0
1
2
0
0
2
1
1
2
0
2
1
2
0
0
0
0
1
2
1
1
1
1
0
1
0
1
0
1
0
2
0
0
0
2
1
1
0
2
3
0
0
2
2
1
1
0
0
2
2
1
1
1
1
0
0
0
0
1
0
1
1
1
1
1
1
0
0
0
0
2
1
2
0
0
2
1
1
1
0
2
2
0
2
1
0
0
0
1
1
1
0
1
0
0
2
0
0
1
0
1
1
1
1
0
3
1
1
1
0
0
1
0
2
1
1
0
2
0
1
0
0
0
2
0
1
2
0
0
2
0
2
2
2
1
2
2
2
0
1
0
1
1
0
1
0
0
1
0
3
0
2
0
0
1
0
0
0
1
0
0
2
0
0
1
0
0
1
0
1
2
2
0
4
0
0
1
2
0
0
2
0
0
1
0
0
1
2
0
0
1
0
0
1
0
0
2
0
1
0
0
1
2
2
0
1
2
2
1
1
0
1
2
1
1
0
2
2
1
0
1
2
0
3
5
1
1
0
1
2
1
2
0
2
2
0
1
1
0
1
2
0
2
0
2
1
0
2
1
1
0
0
1
0
2
1
0
1
0
1
0
2
2
0
0
0
0
1
0
0
1
0
1
2
3
4
0
0
0
1
2
3
0
0
1
2
0
1
1
1
1
2
2
0
0
0
0
0
1
0
1
0
0
2
0
1
0
1
0
2
0
0
2
0
1
1
2
0
1
0
1
0
1
2
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
1
0
0
0
1
0
2
0
1
0
2
3
2
1
0
0
0
0
2
3
1
1
0
0
0
1
2
1
1
1
0
0
0
1
0
1
2
0
0
1
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
1
0
1
2
0
0
0
0
0
0
0
1
1
2
0
1
2
0
4
1
0
0
2
0
0
1
0
0
0
1
0
2
0
0
2
1
1
0
0
2
0
3
0
0
1
0
0
1
1
0
2
2
4
0
2
2
2
0
0
2
0
1
1
1
0
0
1
2
1
2
1
2
1
2
0
1
2
0
0
1
1
0
0
1
1
1
0
1
1
1
0
1
1
0
0
1
1
0
0
0
2
2
0
0
0
0
2
0
0
1
1
1
1
0
0
0
0
0
0
2
0
1
1
2
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
1
1
0
0
0
1
0
1
1
1
0
2
0
0
2
1
0
1
0
0
1
2
1
1
1
0
3
0
1
3
0
0
2
2
0
2
2
0
0
1
0
1
1
0
1
0
1
0
0
1
0
2
0
0
0
0
0
2
1
0
2
1
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
1
1
0
0
1
2
0
0
1
0
2
0
1
0
4
1
1
0
0
1
1
2
1
0
1
0
0
2
2
0
1
2
0
0
0
1
0
1
0
0
0
0
2
0
0
0
1
1
1
0
0
0
0
0
2
0
0
1
0
0
0
1
1
1
1
0
2
2
1
0
0
1
0
1
2
1
0
1
0
1
1
0
0
0
1
0
2
0
1
0
0
0
0
0
1
1
4
1
0
0
1
1
0
2
1
0
1
0
0
1
1
0
2
0
2
1
0
0
1
1
0
1
2
0
2
0
0
0
2
0
2
0
1
2
2
2
2
2
2
0
0
1
2
0
1
2
1
0
0
1
1
1
1
0
0
0
1
0
0
0
0
1
2
1
0
0
2
0
0
0
1
1
1
0
0
1
0
0
0
2
1
0
4
1
1
0
0
0
2
1
2
0
0
0
1
1
2
2
2
0
1
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
1
2
2
0
1
2
1
0
0
2
1
0
1
1
1
1
0
0
0
0
1
2
0
2
0
0
2
1
0
0
0
1
2
0
0
0
2
2
2
1
0
0
0
1
0
2
0
2
0
0
0
0
0
0
1
2
1
2
1
0
1
0
2
1
0
1
0
2
0
2
0
2
0
0
2
0
2
0
1
1
2
1
1
1
1
0
0
0
1
0
0
0
0
0
1
0
2
1
1
1
1
0
2
1
0
2
1
0
2
1
2
0
0
0
0
3
1
1
0
1
1
0
0
1
0
0
1
0
0
0
1
0
2
0
0
1
1
2
0
1
0
1
0
0
2
2
1
2
4
1
0
0
0
0
1
1
1
2
0
0
1
0
0
0
0
0
0
0
2
1
2
1
1
1
2
1
3
1
1
1
2
0
1
0
2
2
0
0
0
0
1
0
1
0
1
1
0
2
0
3
1
1
1
1
2
1
0
1
0
0
0
1
1
0
0
1
0
2
2
0
2
0
2
0
2
0
0
0
1
1
0
1
1
0
0
2
2
0
1
0
0
2
0
0
2
0
2
0
0
1
0
2
2
1
0
0
1
2
1
0
1
0
1
1
1
0
1
0
1
2
0
0
0
0
2
0
2
1
0
1
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
2
1
0
0
2
2
0
0
0
0
0
1
1
0
2
1
0
0
0
0
2
1
0
2
1
0
1
1
0
1
1
2
0
0
0
3
2
0
1
2
0
1
1
0
2
3
1
0
1
0
1
1
0
0
0
0
2
0
1
0
0
0
1
2
1
2
2
1
0
0
2
0
1
0
0
0
1
2
0
0
1
1
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
1
0
2
0
2
1
1
0
0
1
1
1
1
2
1
1
0
0
1
1
0
5
0
2
2
0
0
1
1
2
1
0
2
0
0
1
1
1
1
0
1
0
0
1
0
0
0
0
0
1
3
1
0
2
1
0
2
0
2
0
1
1
0
0
2
1
0
0
0
1
1
1
1
1
0
0
0
2
2
0
0
0
1
0
0
0
1
1
2
0
0
0
1
1
1
2
1
1
0
0
2
0
0
1
1
0
0
1
1
7
0
1
2
0
0
0
2
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
2
1
2
0
2
1
1
2
2
2
1
0
1
3
1
0
0
1
1
0
0
1
2
0
0
1
0
0
2
1
0
0
1
0
0
1
0
2
0
1
0
1
1
0
0
2
0
1
8
0
1
1
1
0
2
2
0
1
0
2
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
1
1
1
1
2
1
0
2
1
0
1
2
1
0
0
1
0
0
2
1
2
2
0
0
2
0
0
0
1
0
2
0
1
0
2
0
1
2
1
2
0
2
0
1
1
0
1
1
0
4
0
1
0
0
0
2
1
1
1
2
1
2
1
1
0
2
0
2
1
0
0
3
1
0
0
0
3
0
0
0
2
2
1
1
0
0
1
1
0
0
1
2
2
0
1
1
0
0
4
0
1
0
0
1
2
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
1
1
0
1
1
2
0
1
2
1
0
1
2
1
0
1
1
0
2
2
1
0
0
1
2
0
1
1
2
0
0
0
2
2
2
0
0
0
0
2
1
0
1
0
0
1
0
1
0
1
0
2
2
5
3
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
2
0
0
1
2
0
0
1
0
0
1
2
0
0
0
1
0
0
0
1
2
0
0
1
0
0
0
0
1
1
2
0
0
1
2
3
1
0
0
0
0
0
0
2
1
0
2
1
2
0
2
1
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
2
0
1
2
0
1
1
0
0
0
1
0
0
1
1
0
1
0
0
2
1
0
1
1
0
0
0
0
0
1
1
0
2
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
1
2
0
2
0
1
1
0
2
0
0
0
0
0
2
0
0
0
1
1
0
1
0
1
0
0
0
0
2
0
0
1
2
1
0
1
1
0
0
1
1
0
2
0
0
0
0
2
1
0
0
1
0
0
0
2
1
1
2
0
0
1
2
2
1
2
0
0
1
0
0
2
1
2
0
0
0
2
2
0
0
1
2
1
0
0
0
0
0
2
1
1
0
1
0
0
0
1
1
0
2
0
0
1
1
2
1
1
1
0
1
0
0
2
2
1
1
1
2
1
0
1
1
0
1
2
0
2
2
0
1
1
0
0
1
0
0
1
2
0
0
2
0
2
1
0
2
1
0
2
1
2
1
1
1
0
2
2
0
1
1
0
2
2
1
1
0
1
0
1
0
0
0
1
1
2
1
0
0
0
0
1
0
2
1
0
1
1
2
2
1
0
1
2
0
0
1
2
0
2
2
0
0
1
0
1
1
0
1
0
0
1
1
0
0
1
2
1
1
1
1
0
0
1
1
2
0
2
2
0
0
2
0
1
0
0
0
0
1
0
0
0
2
1
0
2
1
0
0
2
2
0
2
0
0
1
1
2
0
0
3
2
1
0
1
2
0
2
0
0
0
0
1
1
0
2
1
0
0
1
1
0
0
0
1
1
1
2
0
1
1
0
2
1
0
0
0
2
0
0
1
1
0
0
1
0
2
0
0
1
0
0
2
0
0
1
2
1
1
0
1
0
1
2
1
2
1
1
0
2
1
0
1
2
1
2
1
0
0
2
2
0
1
0
1
0
0
2
2
2
0
1
1
0
0
0
3
0
0
0
1
2
1
0
2
0
0
2
3
2
0
0
1
1
3
0
1
1
2
2
0
0
0
0
0
1
2
2
3
0
2
0
0
0
1
0
5
0
2
2
3
0
0
0
1
1
1
2
0
2
0
0
0
1
1
0
0
1
0
0
1
1
0
1
0
1
1
2
1
0
2
1
5
0
0
1
0
0
0
1
2
0
1
0
0
0
0
0
0
1
2
0
1
0
1
0
1
2
2
1
1
0
0
1
0
2
0
0
0
1
1
0
2
0
0
0
2
0
3
1
1
2
3
0
2
1
0
2
1
0
1
1
2
2
0
0
0
2
0
0
1
0
2
2
0
1
1
1
0
0
2
1
0
0
1
2
0
1
0
2
1
0
0
1
0
1
2
1
0
0
1
0
0
0
1
1
1
1
0
0
0
2
1
2
1
0
1
0
1
1
1
1
2
1
0
2
1
1
0
1
0
0
0
2
0
1
0
1
1
0
1
1
0
0
1
0
1
2
1
0
0
2
2
2
0
0
2
0
0
1
0
1
0
1
1
1
1
0
1
2
1
0
2
0
0
1
1
2
1
1
2
0
1
1
0
1
0
1
0
0
1
1
0
0
0
2
0
1
0
1
0
3
0
0
1
2
0
0
1
0
2
2
0
0
1
0
0
2
1
0
0
1
1
0
2
0
0
0
2
0
0
0
1
0
1
2
1
1
0
0
1
1
0
2
0
0
0
0
0
0
0
1
0
2
1
1
1
0
0
0
1
2
0
0
0
0
0
2
1
0
1
0
1
0
0
1
0
0
1
2
1
0
1
0
3
0
2
1
2
0
0
0
0
1
3
1
0
0
2
0
0
2
2
2
0
0
1
0
0
1
0
0
0
0
0
1
0
2
1
0
1
1
4
0
0
0
2
0
0
0
0
1
0
0
1
0
0
2
1
2
1
0
0
0
1
2
1
1
1
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
2
0
0
0
0
3
2
0
0
1
0
1
0
0
1
0
1
2
1
2
1
0
0
0
0
2
0
0
0
0
1
2
0
1
0
0
1
1
1
1
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
1
1
0
1
0
2
0
2
0
1
1
0
1
0
0
2
2
1
0
1
1
1
1
0
2
0
0
0
0
0
0
1
1
0
0
2
0
0
2
0
1
1
2
0
0
1
2
0
0
2
2
2
1
2
1
0
2
0
2
1
1
0
1
2
1
0
0
1
0
0
0
1
0
1
1
0
1
2
1
2
0
1
0
3
1
3
2
0
0
0
1
1
1
0
1
2
0
0
0
0
2
0
2
0
2
0
0
2
0
2
1
0
1
1
0
0
0
1
0
0
3
0
1
1
1
0
2
2
2
0
0
2
1
2
1
1
0
1
2
0
1
0
2
0
1
0
0
1
0
1
0
1
0
0
1
1
0
2
0
1
1
0
2
2
0
0
2
0
1
0
0
1
0
2
0
0
3
1
1
0
0
0
2
0
0
0
0
2
2
0
1
0
0
1
0
1
0
0
1
0
0
0
1
2
1
0
2
1
1
1
0
1
2
0
2
0
0
1
0
2
1
0
0
1
1
0
1
0
2
1
2
1
2
2
0
0
0
2
2
0
2
0
0
0
0
0
2
1
2
0
0
1
0
1
0
0
2
0
1
1
2
0
2
0
0
0
2
0
1
1
1
0
0
2
2
0
0
2
0
1
0
0
3
1
2
0
2
2
0
1
0
2
0
0
2
3
1
1
1
1
0
2
0
1
1
2
0
1
0
1
0
2
1
2
1
0
1
1
0
1
2
2
1
0
2
0
2
2
1
1
0
0
0
2
2
1
2
0
0
2
0
0
1
1
0
2
2
2
1
0
0
0
1
0
0
0
1
1
1
0
1
1
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
2
0
2
2
1
1
4
0
2
0
2
0
2
0
1
1
2
0
0
2
1
0
2
2
0
0
2
0
0
0
1
0
0
0
2
1
2
1
0
0
2
2
1
0
1
0
0
1
0
0
2
0
1
2
0
2
0
2
0
0
2
2
0
1
2
0
1
2
0
1
0
2
0
0
0
0
0
1
2
0
0
2
0
2
1
1
1
2
0
2
2
0
0
0
1
0
0
2
0
0
0
0
1
2
2
1
2
0
0
0
0
1
2
1
1
0
0
1
0
1
0
0
3
0
0
0
2
0
0
1
0
0
0
0
0
0
2
2
0
1
0
0
1
1
0
1
0
0
1
0
0
2
1
1
1
0
2
0
2
1
1
0
1
0
1
0
2
0
0
2
2
0
2
0
0
0
0
0
1
0
2
0
0
0
0
3
0
2
0
0
0
2
2
0
0
2
1
0
0
0
0
0
1
1
0
2
0
0
2
0
1
1
1
0
0
0
1
2
0
0
0
2
1
0
1
0
0
1
0
0
0
2
2
2
0
1
0
1
0
1
0
1
1
0
3
1
0
0
1
1
0
1
1
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
1
2
0
0
2
0
0
0
2
1
2
1
0
0
1
0
0
1
1
1
1
2
1
0
0
0
0
2
0
2
0
0
0
3
0
0
0
1
0
1
0
0
0
0
1
2
0
1
0
1
1
2
0
0
0
0
1
0
0
3
1
0
0
0
1
2
2
0
0
0
2
0
2
0
0
2
1
0
1
0
0
1
1
0
1
0
1
1
0
0
0
2
1
0
2
0
0
1
1
0
2
0
0
1
2
0
1
1
0
0
0
1
2
1
2
0
2
0
0
0
1
0
2
0
1
0
1
1
1
1
0
0
0
0
1
0
1
2
1
0
0
2
0
1
2
0
0
2
1
1
1
0
2
2
1
1
0
1
2
2
1
0
2
0
0
0
0
0
0
3
1
2
2
0
1
2
1
2
1
2
2
0
2
0
1
0
0
1
2
1
0
2
1
0
1
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
2
0
0
1
2
1
2
2
0
0
0
1
1
0
2
0
0
2
0
1
0
2
2
0
0
2
1
0
2
0
1
1
2
2
0
1
0
0
1
1
0
0
0
0
0
2
2
1
1
2
1
1
0
2
2
1
1
0
1
2
1
2
0
0
1
2
4
0
2
0
0
0
1
1
0
1
1
0
0
0
0
1
2
0
0
2
0
0
2
0
0
0
2
0
0
0
1
0
0
1
2
0
2
0
2
0
0
0
2
0
1
0
0
1
0
2
0
1
0
1
2
0
1
1
0
0
1
1
2
0
0
0
0
2
1
0
1
1
2
0
0
2
1
0
0
0
2
2
0
0
0
0
2
0
0
1
2
0
0
0
2
2
1
0
0
1
0
2
0
0
0
1
1
0
2
0
0
0
1
0
0
0
2
0
2
0
0
0
2
0
0
4
1
0
1
1
1
1
0
3
0
1
0
0
0
1
1
1
1
1
1
2
0
0
0
0
1
0
1
0
2
0
0
0
2
2
0
3
2
0
0
2
0
1
1
1
1
0
3
0
2
0
0
1
1
0
1
1
1
0
2
1
0
0
2
1
2
1
0
0
2
0
2
0
0
0
0
0
3
0
1
0
1
0
0
1
0
0
2
2
0
1
1
1
0
1
0
0
0
0
0
0
2
1
0
1
0
0
1
0
0
0
1
1
2
1
2
2
0
0
0
0
0
0
1
1
0
1
0
2
1
1
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
1
0
1
0
1
0
1
1
1
2
0
1
1
1
0
0
0
0
1
1
0
1
1
1
3
0
1
0
2
0
0
0
2
0
0
2
2
0
0
2
1
2
1
0
0
2
2
2
1
0
1
0
2
1
2
0
3
1
0
0
0
0
2
2
1
0
1
1
3
0
0
0
2
0
0
1
3
2
2
0
0
0
0
0
1
0
1
2
2
0
2
0
1
0
0
0
0
0
0
2
1
1
0
1
0
2
0
0
1
1
0
0
2
0
2
1
0
1
2
0
0
0
0
1
0
1
0
0
0
0
0
1
1
1
0
1
2
1
0
0
0
0
1
2
0
0
1
1
1
0
0
0
1
1
2
2
1
0
1
1
0
0
1
1
1
0
2
0
0
1
0
0
2
1
2
0
2
2
0
1
2
1
0
1
0
0
2
1
1
1
2
0
0
0
0
0
2
3
1
1
1
1
1
2
0
0
1
2
2
4
0
0
1
2
0
2
0
1
1
1
0
0
0
2
0
0
0
2
2
0
0
0
1
1
2
2
1
1
1
1
0
0
1
0
0
1
2
1
0
1
2
2
0
0
0
2
0
4
0
1
0
1
1
0
2
1
0
2
2
2
0
1
1
0
0
0
2
0
0
2
2
1
0
1
0
0
2
2
1
2
0
0
0
2
1
2
0
1
0
1
0
2
2
0
0
1
2
1
0
2
1
2
0
1
0
2
0
0
2
1
0
0
1
0
0
0
0
1
0
1
2
0
0
1
0
0
2
1
0
0
2
0
0
1
2
0
0
0
0
2
2
2
0
0
2
0
0
1
0
1
0
2
1
1
1
2
0
0
1
4
0
0
2
0
0
1
1
2
2
1
0
0
2
2
2
0
0
0
1
2
1
1
2
0
0
1
0
0
0
0
2
0
0
0
1
2
0
1
0
1
0
0
1
0
0
3
0
0
1
3
0
0
0
1
0
1
0
0
0
2
2
0
0
1
0
1
1
0
3
2
1
1
0
1
1
0
0
2
0
1
0
0
1
0
0
1
1
1
0
1
1
2
1
1
1
0
2
0
2
0
0
1
0
2
2
1
2
2
1
2
0
0
1
0
0
2
1
0
0
1
0
0
0
0
2
0
1
0
2
1
2
0
2
1
0
2
0
0
1
1
0
2
0
2
1
0
0
0
0
2
2
0
1
0
1
0
1
0
0
0
2
1
0
0
1
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
1
2
1
2
1
0
2
0
2
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
1
2
0
1
0
2
0
1
0
1
0
0
1
1
1
0
1
0
1
0
0
1
1
0
0
1
0
0
0
2
0
0
2
2
0
0
0
0
2
2
0
2
2
1
1
2
2
2
2
1
0
0
1
1
0
1
0
0
0
0
0
2
1
1
1
0
1
0
0
0
0
0
0
2
1
0
0
1
1
2
0
1
0
1
0
2
0
2
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
1
1
0
1
0
0
0
0
1
0
0
1
0
1
2
0
1
0
0
0
2
0
2
0
0
1
0
0
0
2
0
2
1
2
0
0
0
0
0
1
0
0
5
2
0
0
0
0
1
1
1
2
0
2
0
0
0
0
1
0
2
0
0
0
0
2
0
0
1
0
2
2
2
1
0
0
2
1
1
0
0
0
2
1
2
2
1
0
0
0
0
2
0
2
1
1
1
2
2
0
0
1
0
2
1
1
0
1
0
0
0
1
0
2
2
2
1
0
0
0
2
0
1
0
0
1
1
1
0
2
1
0
1
2
0
0
0
1
1
0
0
0
0
0
1
2
2
5
0
0
0
0
0
2
0
2
1
1
1
2
0
0
0
1
2
1
1
0
1
0
0
1
2
2
2
1
0
1
2
0
1
1
0
3
1
2
1
0
0
0
1
0
1
0
0
0
2
0
1
2
1
0
1
0
0
1
1
1
0
0
2
0
3
2
0
0
0
0
0
0
2
0
1
2
2
0
1
0
1
0
1
3
0
0
2
1
2
1
0
0
0
0
1
0
0
1
0
2
1
1
0
1
1
2
1
0
0
1
0
0
0
1
2
1
1
0
2
0
1
0
2
2
0
1
1
1
2
1
0
2
0
0
0
1
0
0
0
2
0
0
1
1
1
1
1
2
1
0
2
0
0
1
1
0
2
2
0
2
2
0
0
2
1
2
0
0
0
1
0
0
0
0
1
0
2
0
2
0
0
2
1
0
0
2
0
2
1
2
2
2
0
1
1
0
2
0
0
2
2
1
1
0
1
0
2
1
1
0
2
0
0
0
1
2
1
2
1
0
2
3
1
1
0
2
0
1
2
0
0
1
0
3
0
2
2
0
1
2
0
2
0
1
0
0
0
0
1
0
1
1
1
1
0
0
1
2
0
1
0
0
0
1
0
2
0
0
2
2
0
0
2
0
2
0
2
0
1
1
1
2
0
0
1
0
0
0
1
1
0
1
0
2
0
2
2
1
0
0
2
1
2
0
2
0
0
0
2
0
0
1
0
2
0
0
0
0
1
1
0
2
1
0
2
1
0
0
1
2
0
0
1
2
1
0
1
0
0
0
2
2
0
1
0
0
0
0
0
0
1
0
1
7
1
2
0
0
0
0
0
1
0
0
2
0
2
0
2
0
0
0
0
0
1
2
0
1
0
2
1
1
0
1
0
0
1
0
1
1
0
0
0
1
1
0
1
2
0
1
0
0
1
3
0
0
0
0
0
2
1
0
2
0
0
1
1
1
1
1
0
0
2
1
0
1
1
0
0
1
1
1
0
0
1
0
0
1
2
0
0
2
0
0
0
0
0
2
1
0
0
2
1
0
2
1
2
1
1
0
0
1
1
0
2
0
0
2
1
1
0
1
2
2
0
1
0
0
0
2
1
0
2
1
1
2
0
0
0
0
1
1
0
0
0
0
0
1
2
1
1
0
0
0
1
1
2
2
0
0
2
2
0
0
1
2
0
0
0
1
0
1
1
0
1
0
1
3
0
1
1
0
0
0
3
0
1
1
0
2
0
0
1
0
0
1
0
0
1
1
0
0
3
0
1
1
2
1
0
0
2
0
0
1
0
3
0
0
0
0
0
0
0
1
2
1
0
0
0
0
2
0
1
1
0
1
1
1
1
1
0
1
2
0
1
0
1
2
2
0
0
2
1
1
0
2
3
0
0
1
0
0
1
2
2
1
1
1
1
1
1
1
1
1
1
0
0
0
0
0
2
2
0
1
1
0
2
0
3
3
1
2
0
1
1
0
1
0
0
1
2
2
1
2
4
1
1
0
0
1
0
1
1
0
1
0
1
0
0
0
0
1
1
2
0
0
2
2
2
1
1
2
1
0
2
0
2
4
0
2
0
2
1
2
0
0
2
0
0
3
0
2
1
1
1
2
0
0
0
0
2
0
0
0
1
2
2
0
0
1
0
1
1
0
1
2
1
0
0
1
0
0
2
1
0
1
1
0
0
2
0
1
1
0
0
0
0
1
0
0
1
0
0
0
2
1
2
0
2
2
1
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
2
2
0
0
1
3
1
0
0
0
1
2
2
1
0
2
2
0
0
0
1
2
1
0
1
1
2
0
1
0
0
0
0
2
1
2
0
0
1
2
3
0
1
0
2
1
1
1
0
1
1
1
0
2
0
0
2
0
0
2
2
0
0
2
2
0
1
2
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
2
1
1
1
0
1
0
2
1
0
2
2
1
1
0
2
2
1
2
0
0
1
0
1
0
1
0
0
0
0
0
1
1
1
1
0
2
0
0
0
0
0
0
1
0
0
1
1
0
0
0
2
0
3
0
2
6
1
2
1
1
0
2
2
1
1
1
1
1
0
1
1
0
1
0
0
0
0
1
1
1
0
1
0
0
1
0
1
0
1
0
1
1
1
0
0
0
0
2
2
2
0
0
1
0
0
0
0
0
2
1
3
2
0
2
0
2
1
0
0
1
1
0
0
0
1
2
1
0
2
0
1
0
0
0
0
1
0
1
1
2
0
1
0
1
0
0
0
0
2
0
0
1
1
2
1
0
0
0
0
1
2
0
0
0
1
1
0
0
0
1
2
2
0
0
1
0
0
0
1
0
0
1
0
0
1
0
2
0
0
1
1
0
0
1
0
0
0
1
1
0
1
2
0
2
0
1
0
0
1
1
0
1
0
2
0
0
2
1
0
0
2
0
1
2
1
1
0
0
1
1
1
1
0
1
3
1
3
2
0
0
0
0
0
1
1
1
0
1
1
0
2
0
0
0
1
1
2
2
1
0
2
2
1
0
0
2
1
1
1
1
0
2
0
0
0
0
2
2
1
1
0
0
0
0
2
1
1
1
0
1
0
0
0
1
0
1
1
0
0
1
1
1
1
1
6
0
1
0
0
0
0
0
0
2
1
1
1
0
1
2
1
0
2
1
2
0
0
1
1
1
2
1
1
3
0
1
1
0
0
0
1
0
1
1
0
0
1
2
2
0
0
0
1
2
2
1
2
1
2
1
0
2
1
0
0
0
2
1
0
0
0
1
2
0
0
1
1
1
0
0
0
0
2
1
1
1
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
2
2
0
0
1
1
1
1
0
0
0
1
0
2
0
2
2
1
0
1
1
1
1
0
1
0
0
2
0
2
0
2
4
0
1
0
0
1
2
0
0
0
1
1
0
2
1
3
0
0
2
0
2
0
2
0
2
1
0
0
0
2
1
0
1
1
0
0
0
1
2
2
2
2
1
0
0
2
0
0
2
0
2
1
2
0
2
1
1
0
2
1
0
1
0
2
0
2
2
0
1
1
1
1
1
0
0
1
0
0
2
3
2
0
2
1
0
1
2
0
2
1
1
0
0
1
1
0
0
0
0
0
0
1
1
0
2
2
0
1
1
0
1
1
2
0
1
1
0
0
1
0
0
0
0
0
0
1
3
0
1
1
1
0
0
2
0
0
2
0
0
1
1
2
2
0
0
0
0
0
2
0
0
0
0
0
1
4
2
2
2
0
0
0
0
2
0
2
2
0
1
0
1
0
1
0
1
1
0
2
0
1
1
1
0
0
2
2
0
0
1
1
0
1
1
2
0
0
0
0
2
0
2
2
2
2
1
1
0
2
2
0
1
0
0
0
0
2
2
0
1
1
0
0
2
2
0
0
0
2
1
0
2
0
2
1
0
0
1
0
0
0
2
1
0
2
2
2
2
1
0
3
1
0
2
0
0
0
0
1
1
1
2
1
2
1
0
0
2
0
2
2
0
1
2
0
3
0
2
0
2
0
2
0
1
2
2
0
1
0
0
3
0
0
1
2
1
1
2
0
2
0
0
0
2
0
1
1
2
2
2
2
0
0
0
2
0
2
2
0
1
0
1
1
1
2
1
2
0
2
0
0
0
1
1
2
0
0
1
0
2
1
1
0
0
0
1
1
0
1
0
0
1
2
2
2
0
1
0
2
0
1
0
1
0
1
1
2
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
1
2
0
0
0
0
1
0
0
2
1
0
2
1
0
0
1
1
1
1
2
0
0
0
4
2
1
2
1
0
0
0
1
2
2
2
0
1
1
2
0
1
0
1
1
1
0
1
2
0
2
0
0
1
3
1
1
1
0
2
8
2
2
0
0
0
0
1
1
1
0
2
0
1
0
1
1
0
0
0
1
1
1
0
0
2
1
1
1
1
1
1
1
0
1
1
1
0
2
2
0
0
1
1
0
0
2
0
1
0
0
2
0
0
2
1
0
1
1
2
1
2
0
2
0
0
3
0
1
0
2
0
1
1
0
0
0
1
1
1
1
1
0
2
1
1
0
0
2
2
0
0
1
0
0
1
1
1
0
0
0
1
0
0
1
0
1
0
0
2
0
0
0
1
2
0
2
2
1
0
0
0
1
2
1
0
0
0
0
1
1
0
2
1
0
0
1
0
3
1
2
0
0
2
1
1
0
1
0
0
0
2
1
2
1
0
0
1
2
1
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
2
4
2
2
1
0
0
0
1
0
0
0
1
1
0
2
0
1
0
0
2
0
1
0
0
0
1
0
2
2
2
2
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
2
0
2
1
1
0
2
1
0
0
1
0
0
1
0
1
0
2
0
2
0
2
0
2
2
0
0
2
2
0
2
0
0
1
0
2
0
2
0
0
0
1
2
1
1
2
2
1
2
2
1
1
1
0
1
0
0
2
1
0
0
0
0
0
2
2
0
1
0
0
0
0
1
1
0
2
2
2
1
1
1
2
0
1
0
0
2
0
1
3
4
0
2
1
0
0
0
1
2
0
0
2
0
1
2
2
1
0
0
1
0
0
1
0
0
0
0
0
1
0
2
0
3
1
0
0
0
0
0
1
2
1
1
0
0
2
0
0
0
1
1
0
2
2
1
0
1
2
0
2
1
1
0
0
0
2
2
0
1
0
1
0
0
0
0
0
0
1
1
0
0
2
1
0
1
1
0
1
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
2
1
2
0
1
0
3
0
1
2
3
0
1
0
1
0
2
2
0
1
1
0
1
1
0
0
2
1
2
0
2
1
2
1
0
2
0
3
0
3
1
2
3
2
0
0
0
1
0
1
0
2
0
2
2
1
2
1
1
0
1
2
1
2
1
1
1
2
0
0
1
2
0
0
1
2
0
0
1
0
0
0
2
0
0
2
0
0
1
1
1
0
1
2
1
0
0
2
0
0
1
0
0
2
0
0
1
2
2
2
2
2
2
0
0
0
1
0
1
0
0
1
2
1
0
0
0
0
1
0
0
0
0
2
2
0
1
2
1
0
2
0
0
0
0
2
0
1
0
0
0
1
0
3
2
0
0
1
0
2
1
1
2
3
2
0
1
2
1
1
2
1
0
2
1
2
0
0
0
1
0
1
1
0
0
1
0
1
2
0
2
1
1
2
1
2
2
2
2
0
2
1
2
0
0
0
1
2
1
1
0
0
2
1
2
0
1
1
1
2
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
1
0
1
0
2
0
0
0
1
0
0
0
0
1
1
0
1
2
1
2
0
0
3
2
0
0
1
0
0
1
1
0
1
2
0
2
1
0
0
2
1
0
1
1
0
0
0
2
1
2
0
0
0
0
2
0
1
0
1
0
1
0
0
2
1
1
0
0
0
2
0
2
1
0
0
1
1
0
0
0
1
2
0
0
0
2
2
0
0
0
0
0
2
1
1
2
1
0
0
2
3
1
1
0
0
0
0
1
1
2
0
0
0
0
2
0
1
0
1
1
1
0
1
0
0
0
0
1
1
1
0
1
1
1
0
0
1
0
0
2
0
0
0
0
2
0
0
2
0
0
1
2
2
0
1
1
0
1
0
2
1
0
0
0
2
1
0
0
0
0
2
2
0
2
0
0
0
0
1
0
1
1
0
0
0
1
0
0
2
0
2
0
1
3
1
0
0
1
1
3
0
2
0
0
1
0
0
2
0
0
0
1
0
2
1
0
0
0
0
0
0
2
0
1
2
0
0
0
1
0
2
0
0
0
1
1
0
3
0
0
0
2
2
0
2
0
1
0
0
3
1
2
0
2
0
1
2
0
0
0
1
0
0
2
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
1
2
1
0
0
1
0
2
0
1
1
1
1
0
0
2
1
1
0
2
2
0
2
1
0
0
0
1
5
2
1
0
1
2
0
0
2
0
4
0
0
0
0
2
2
0
0
2
1
1
2
0
1
0
0
2
1
0
2
2
2
0
1
2
0
1
0
2
0
1
1
0
0
1
0
0
1
1
0
1
0
2
0
2
1
1
3
0
0
1
2
4
0
0
3
0
2
1
0
3
1
2
0
0
0
0
1
0
1
2
0
1
0
1
1
2
0
0
0
0
1
0
0
1
0
1
2
1
0
0
0
1
1
1
0
0
0
0
0
0
2
0
2
0
1
1
0
0
0
3
2
0
2
0
1
0
1
0
0
0
0
0
0
2
1
0
0
0
3
2
1
0
2
1
0
0
0
0
0
1
1
1
1
0
2
1
0
0
0
2
0
2
1
1
0
1
2
0
2
0
0
1
1
0
0
0
1
0
1
0
0
1
0
0
0
1
0
1
0
0
1
1
2
0
11
0
1
1
2
3
0
1
1
0
1
0
0
1
1
0
1
1
0
0
0
0
0
0
2
1
2
0
1
1
1
2
2
3
0
0
0
0
0
0
0
1
2
1
2
1
1
0
0
0
0
1
2
1
1
1
1
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
2
2
2
1
0
2
0
0
0
2
3
0
0
2
0
0
0
0
1
1
0
0
0
2
0
2
0
0
0
1
2
0
0
1
0
0
2
0
0
0
2
2
1
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
2
1
0
0
1
2
1
2
2
1
0
2
1
0
2
1
0
0
1
0
0
0
2
2
0
0
0
2
0
1
1
1
1
3
1
1
2
0
2
1
2
1
0
0
1
0
0
1
1
2
0
0
1
2
2
1
0
0
0
0
0
0
2
1
1
1
0
1
1
1
2
1
0
0
0
1
0
1
1
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
1
0
0
1
0
1
2
0
0
0
0
1
2
0
0
2
1
0
2
1
2
1
0
2
0
0
0
1
0
1
2
2
1
0
0
1
2
1
0
0
0
1
0
0
1
2
0
1
0
2
0
1
2
1
2
0
0
0
0
0
0
0
1
2
2
0
0
1
1
3
0
2
2
0
0
0
2
1
0
1
2
1
2
2
1
0
0
1
1
1
0
1
2
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
1
0
1
0
1
1
0
0
1
0
1
0
0
1
1
2
1
0
0
1
2
3
0
0
1
2
0
0
0
1
0
1
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
3
0
2
2
2
0
2
0
2
0
0
0
1
1
0
0
1
0
0
2
1
2
1
0
0
0
1
2
0
0
0
0
0
1
0
2
1
0
1
0
0
2
2
2
0
0
2
3
0
2
0
1
0
0
1
0
1
0
2
0
0
0
2
1
1
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
2
1
1
1
0
0
2
3
3
1
0
0
0
2
1
2
0
0
2
2
2
0
2
0
1
1
0
0
2
0
0
1
1
0
0
2
0
0
2
0
0
2
0
2
2
0
0
0
0
0
1
0
1
0
2
0
0
2
0
0
0
1
2
2
0
1
0
1
0
0
0
0
0
2
1
0
1
2
2
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
2
2
0
0
1
0
0
0
1
2
0
0
2
2
0
0
0
1
1
0
0
0
0
0
1
2
0
0
0
2
0
2
1
1
1
1
2
2
0
1
1
1
0
1
1
0
1
2
0
0
2
2
0
2
0
2
0
0
0
0
0
0
0
2
1
1
2
0
0
1
0
1
1
3
0
2
1
2
0
0
0
1
0
0
1
0
1
2
1
1
0
1
2
2
0
0
1
0
2
0
0
0
0
0
1
1
0
1
0
2
0
0
3
1
1
1
0
2
0
0
1
1
1
0
2
1
2
1
1
2
0
2
1
0
0
0
0
1
0
1
0
1
1
0
0
0
0
2
0
3
1
1
1
0
0
0
1
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
1
2
1
1
2
0
0
0
1
0
0
0
0
0
1
0
2
0
2
1
0
0
2
0
1
0
2
0
0
1
0
0
0
1
1
0
1
1
1
1
0
0
0
2
1
1
0
0
0
0
2
1
0
0
0
2
0
0
0
0
1
2
1
0
0
1
1
1
2
0
2
0
0
1
1
1
0
1
0
2
0
1
1
0
0
0
0
0
0
2
0
0
0
1
1
1
0
1
0
2
2
0
1
3
1
0
0
1
0
2
1
1
0
2
0
2
1
1
2
0
0
2
1
2
0
0
1
1
0
0
2
0
1
0
0
0
2
1
0
1
0
0
1
2
0
2
0
1
1
0
2
0
0
0
0
2
0
0
0
0
1
1
2
1
0
0
1
0
0
0
0
1
0
0
1
0
2
1
0
1
0
0
1
2
1
0
0
2
0
0
1
0
0
0
0
0
0
1
2
2
0
1
0
1
1
0
0
2
0
1
1
2
2
2
0
0
0
1
0
2
0
0
2
2
0
0
0
1
1
0
1
1
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
1
1
0
1
0
1
0
0
1
1
0
0
1
1
1
0
0
0
0
1
0
2
0
1
1
2
1
1
0
1
0
2
1
1
0
2
1
1
0
0
2
0
0
0
0
2
1
0
0
0
0
1
1
2
2
0
1
2
2
2
0
1
1
0
1
1
0
2
0
1
2
0
1
1
0
1
2
2
0
1
2
0
1
0
0
0
0
0
0
1
1
1
2
0
0
0
1
1
0
1
0
1
2
0
0
1
0
1
2
1
0
1
2
0
1
0
3
0
1
0
1
0
2
0
1
0
0
1
1
0
0
4
1
0
2
0
2
0
3
2
0
1
2
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
2
1
2
2
0
0
0
0
0
1
1
0
0
0
0
1
2
0
0
0
2
0
2
0
1
2
0
0
0
1
0
0
2
0
1
1
2
0
0
1
1
0
2
0
0
1
1
2
1
1
1
1
2
1
0
2
1
0
2
2
0
0
1
0
1
1
0
0
1
1
0
1
0
1
1
2
2
0
1
1
2
2
2
0
0
1
0
0
1
1
0
1
2
0
0
1
1
0
2
2
1
0
0
0
1
1
0
0
0
0
1
2
4
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
1
0
1
0
1
2
0
2
0
2
0
0
1
1
1
1
0
0
0
1
2
0
1
0
0
1
0
0
2
1
0
1
2
0
2
2
1
0
0
1
1
0
1
0
0
0
0
0
1
2
0
2
2
2
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
1
2
2
1
0
0
0
0
0
2
0
1
1
0
0
5
0
0
2
3
0
0
1
0
0
1
1
0
1
2
2
2
1
1
2
0
0
0
1
2
1
0
1
0
2
0
1
0
0
2
2
2
0
1
1
0
1
1
0
1
0
2
0
2
1
0
1
1
0
0
2
1
0
1
3
1
1
0
1
0
0
0
2
3
0
1
0
0
0
1
0
1
1
1
0
0
0
0
2
1
2
1
3
2
0
2
0
0
0
1
0
2
0
2
0
2
0
1
1
0
0
2
0
1
0
1
0
2
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
1
0
0
4
0
2
0
2
0
0
0
0
1
0
2
2
0
1
1
1
0
0
2
0
1
0
1
1
0
0
0
0
0
3
2
0
2
2
1
2
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
1
1
1
1
0
0
2
1
1
0
0
1
1
1
1
1
2
3
0
0
1
0
1
1
0
0
0
3
1
0
2
0
0
0
0
0
1
0
1
0
0
0
1
4
0
0
1
0
0
2
2
2
0
0
0
1
2
1
0
2
4
0
1
1
0
1
0
2
0
1
0
0
0
1
0
0
0
0
1
0
1
0
1
1
0
0
0
2
0
2
1
1
0
1
1
0
0
2
0
0
1
0
1
1
0
1
0
0
1
2
1
1
0
0
1
2
1
0
0
2
1
0
0
1
1
1
1
0
1
1
1
2
2
1
0
1
0
0
2
1
0
0
0
0
1
1
0
0
1
1
1
1
0
0
0
0
2
0
1
2
2
0
1
0
1
0
0
1
0
0
0
0
2
0
0
2
0
1
0
0
0
0
2
0
0
5
2
0
0
0
0
1
1
1
2
1
1
0
0
0
1
1
0
0
4
1
0
0
0
0
0
0
1
0
0
0
1
1
1
0
2
1
0
0
0
1
0
2
2
0
0
2
0
0
1
1
1
0
0
0
2
1
2
0
0
0
0
1
1
2
1
2
1
0
3
0
1
0
2
0
0
0
1
0
1
0
0
2
1
2
1
2
0
0
0
0
1
0
0
0
0
2
1
1
0
0
1
1
0
0
2
0
2
0
0
2
1
0
1
1
0
0
1
1
0
1
1
1
0
1
0
1
1
0
0
0
2
2
0
0
1
0
1
1
1
0
0
0
2
0
1
2
1
2
1
0
2
0
1
1
2
1
0
1
2
0
0
1
0
0
0
0
0
2
0
0
1
1
0
2
0
2
1
0
0
0
2
1
0
0
2
0
1
0
1
1
1
2
2
1
1
0
0
0
0
0
1
1
1
1
1
2
0
1
2
1
2
1
0
1
0
0
1
1
2
0
1
2
0
2
1
1
0
2
2
1
1
2
0
0
0
2
0
0
2
0
0
1
1
1
0
0
1
1
0
1
0
0
0
0
0
0
2
1
2
2
0
0
1
0
1
2
2
2
2
1
2
0
2
1
0
0
2
2
1
0
1
0
0
0
0
2
2
0
0
0
2
2
0
0
1
1
2
0
2
1
0
2
0
0
0
2
0
0
0
0
1
0
0
0
1
1
1
1
1
2
1
0
2
0
0
2
0
0
0
3
1
0
0
0
0
1
1
1
1
0
0
0
0
1
0
1
1
0
0
1
1
2
0
0
0
0
2
0
0
0
0
1
0
1
1
1
0
2
0
0
0
1
0
0
2
1
0
0
0
1
0
0
3
2
1
2
0
1
2
1
1
2
2
1
0
0
1
8
1
0
0
0
0
1
0
1
1
2
0
0
0
2
1
0
0
4
0
1
0
1
2
0
2
0
1
0
0
1
1
1
2
0
0
0
1
0
1
2
0
1
1
2
0
1
0
0
0
1
0
1
0
0
0
1
1
0
3
2
2
0
2
1
0
0
0
0
0
1
0
1
2
0
0
1
0
0
2
1
1
0
3
2
0
0
0
2
0
0
0
1
0
1
1
0
0
1
0
1
0
1
1
1
1
0
2
1
0
0
0
2
1
0
1
0
0
2
2
1
1
1
0
0
0
0
0
1
0
0
0
0
1
1
1
2
0
1
0
2
0
2
2
0
2
1
0
1
0
1
1
2
0
0
1
0
2
0
1
0
0
0
2
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
2
0
2
0
0
2
0
0
1
0
0
1
2
1
0
0
0
0
1
0
1
1
0
0
1
1
0
2
0
2
0
1
0
0
0
0
0
2
1
0
1
2
2
0
1
2
1
1
1
1
0
0
0
1
0
0
0
0
4
2
0
1
1
1
2
2
0
1
1
0
2
0
0
0
2
2
1
1
0
0
1
1
1
1
0
0
2
1
1
2
1
2
2
2
1
2
1
2
0
0
1
2
0
0
1
1
0
1
0
1
0
1
0
0
0
1
0
2
0
0
0
0
0
0
2
1
2
0
2
0
0
2
1
1
0
1
1
0
0
1
0
2
0
0
0
0
0
1
0
2
2
0
2
1
0
2
0
0
1
0
0
0
2
1
2
0
2
0
0
0
0
2
0
2
0
1
1
0
1
1
2
2
2
0
1
1
0
2
1
0
2
0
1
1
1
2
0
0
0
1
0
0
1
1
1
0
0
2
0
2
1
0
1
0
0
0
1
0
0
2
0
0
1
0
1
0
2
0
2
0
1
2
1
1
1
1
2
0
1
0
0
2
0
1
0
1
0
0
0
1
0
1
0
2
0
0
1
0
0
1
0
1
2
0
1
0
0
0
0
1
2
0
0
0
2
1
0
1
1
1
3
0
0
0
2
0
0
1
0
1
2
0
0
0
2
0
0
2
0
2
0
1
0
0
0
2
0
1
2
0
0
1
1
1
0
0
2
0
2
0
1
1
1
0
2
0
2
0
0
0
0
1
1
1
0
2
0
2
2
2
0
0
0
2
0
1
1
2
0
0
1
0
2
1
0
2
2
1
0
0
0
0
1
0
0
0
1
0
0
1
1
0
2
0
1
0
0
2
1
1
0
0
0
2
0
1
2
0
0
0
0
0
2
3
2
0
1
2
0
0
1
1
3
0
1
2
0
0
0
1
2
0
2
0
0
0
2
1
1
0
0
2
0
0
2
1
0
0
0
1
0
0
0
0
1
0
1
0
0
2
1
1
1
0
1
0
0
0
0
0
0
1
0
0
0
1
2
0
1
0
0
1
2
0
2
1
2
0
2
0
2
0
2
1
0
1
2
0
1
1
0
1
0
0
0
0
0
1
2
0
0
1
0
2
1
2
0
0
2
0
0
1
0
0
2
0
2
0
0
1
2
2
2
0
1
0
1
0
2
0
0
0
0
2
1
1
0
0
0
1
2
2
2
1
1
0
0
1
0
0
3
0
0
0
1
0
2
1
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
2
0
2
1
1
0
1
2
2
2
0
1
2
1
1
0
0
2
0
1
0
2
0
2
1
2
0
0
0
2
0
3
0
0
0
0
1
0
2
0
0
0
2
0
0
0
3
3
0
1
1
0
1
0
0
0
1
2
1
0
1
0
1
2
0
2
0
1
0
1
0
0
1
1
1
0
0
0
2
0
1
1
0
0
1
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
4
2
1
0
0
0
1
1
0
0
2
2
0
0
1
0
1
1
0
0
0
0
1
1
1
2
0
0
0
0
0
1
0
0
0
2
0
1
0
2
0
1
1
0
1
2
1
0
2
1
1
2
0
0
0
1
1
0
0
1
1
8
0
2
1
2
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
1
2
2
0
0
0
2
0
1
0
2
1
0
0
0
0
2
0
1
0
0
2
2
0
1
1
0
1
1
0
0
2
2
0
1
1
0
0
2
0
0
1
0
0
0
2
0
1
0
0
1
1
0
1
0
1
2
0
2
0
0
0
0
0
2
2
0
1
0
0
1
0
2
0
0
1
1
1
0
0
1
0
1
1
2
0
2
0
0
0
2
1
1
4
2
0
0
2
0
0
0
0
2
1
0
1
0
0
0
1
0
2
2
1
1
1
0
0
1
0
1
2
1
0
0
3
1
0
0
1
0
1
1
0
0
0
0
1
1
1
0
1
0
1
0
0
0
5
2
0
1
1
3
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
1
1
2
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
1
0
0
0
0
1
1
1
0
2
0
0
0
1
0
1
0
1
0
0
1
0
0
1
1
1
1
0
0
2
0
1
2
0
0
0
0
2
2
0
0
1
0
1
0
0
1
1
2
2
0
2
0
0
1
0
0
0
0
1
2
0
0
0
2
1
0
0
0
0
1
1
2
0
2
0
0
1
2
1
1
0
1
0
0
1
0
0
0
2
2
1
2
2
1
1
0
0
0
2
1
2
1
1
0
1
0
1
1
1
2
0
1
0
2
1
1
0
1
2
0
2
0
0
0
0
0
1
2
0
0
0
1
0
4
1
1
2
2
0
0
0
0
2
0
2
0
0
1
0
1
0
1
1
1
0
2
2
1
2
1
0
1
0
0
0
0
0
1
1
1
2
0
0
0
1
0
0
2
0
0
1
1
0
0
0
0
0
2
0
1
1
1
0
0
0
0
0
4
1
0
1
1
1
0
0
0
1
0
2
0
1
0
2
1
2
0
0
1
2
0
1
1
1
1
0
0
2
0
2
1
0
1
0
0
0
1
1
1
0
1
1
1
0
1
3
0
1
2
3
1
0
0
2
0
2
0
0
0
0
0
1
0
2
0
1
0
2
0
0
1
2
2
1
0
2
2
0
0
0
0
0
0
0
1
1
0
1
3
0
0
2
2
0
0
2
2
0
1
0
2
0
3
0
2
0
0
1
2
0
2
0
0
1
0
2
0
1
0
2
2
0
0
1
2
0
2
0
2
2
1
1
0
0
1
1
2
0
1
0
1
1
0
0
1
1
0
0
0
0
1
1
0
1
0
0
2
3
0
1
0
0
0
0
2
0
0
0
2
2
0
0
0
1
1
0
1
0
0
0
0
1
1
1
2
0
0
3
0
1
0
1
1
0
0
2
0
2
0
1
0
1
2
1
4
1
2
0
1
2
1
1
1
0
2
2
0
0
2
2
1
2
0
0
1
0
0
2
0
1
0
1
2
0
0
2
0
2
1
0
1
0
0
1
2
0
2
0
2
0
0
1
2
1
1
1
0
0
3
1
1
1
0
0
2
1
0
1
1
2
0
3
0
0
1
0
1
0
0
1
2
0
0
0
0
2
0
0
2
2
0
2
1
1
0
0
0
2
0
1
2
0
0
0
0
0
0
1
2
1
2
1
0
2
0
0
1
1
2
1
0
1
0
2
0
2
0
0
0
2
2
1
1
0
2
1
1
1
2
0
0
0
2
1
0
2
0
0
1
0
0
0
2
1
2
0
0
1
0
0
0
0
1
1
1
0
0
0
3
1
0
1
1
2
0
0
0
0
0
2
2
0
0
0
1
1
1
1
2
1
0
0
1
2
1
0
0
0
0
0
2
2
2
2
1
0
0
0
1
1
2
2
2
2
1
1
2
2
1
0
1
2
1
2
2
0
2
0
0
0
0
2
0
0
1
2
1
1
2
2
2
0
1
0
0
0
1
1
1
1
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
2
0
1
0
1
3
2
0
3
1
2
2
3
2
2
2
2
0
0
1
1
2
0
0
1
2
0
0
0
2
0
0
0
0
1
1
3
1
0
0
0
2
2
2
0
2
0
1
2
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
2
1
1
0
0
1
1
1
0
0
2
0
2
1
0
0
0
0
2
2
0
1
1
1
0
0
0
0
2
8
0
0
0
0
1
0
2
0
0
2
2
1
1
2
0
0
0
0
2
1
0
2
1
1
0
1
0
1
0
2
0
0
1
0
2
0
0
2
0
0
2
0
0
1
0
1
0
2
0
1
0
0
1
0
1
0
1
0
0
1
0
2
0
0
0
1
0
2
0
0
2
1
1
1
0
0
1
2
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
1
0
2
0
1
0
0
0
2
2
2
1
1
0
0
2
1
1
0
0
2
0
0
0
0
0
2
0
0
2
0
2
0
1
2
2
0
1
0
0
1
1
0
2
1
2
1
0
2
0
0
0
2
2
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
2
1
1
0
1
1
2
0
1
0
1
0
1
1
0
1
1
1
2
1
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
1
0
1
0
1
0
2
1
1
0
0
1
1
0
1
0
0
1
0
0
0
1
1
0
1
0
0
1
0
0
0
0
1
2
0
0
1
1
3
0
0
0
0
1
0
0
2
0
0
2
0
2
1
0
0
2
0
0
2
1
2
2
2
0
0
1
1
0
2
0
1
0
0
0
1
1
1
0
1
2
3
1
1
1
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
1
1
0
0
1
1
2
2
1
2
0
1
0
0
1
1
1
0
0
0
0
2
0
0
1
0
0
0
1
0
1
1
0
0
1
0
1
0
1
0
2
0
0
2
0
4
1
1
2
1
2
0
0
1
0
0
0
0
0
0
0
1
0
2
0
2
0
3
0
2
0
0
3
0
2
0
1
1
1
1
0
0
0
0
1
0
0
2
0
1
1
0
0
2
0
2
0
1
0
0
0
1
0
0
2
0
2
2
0
1
1
0
0
2
0
0
0
2
0
0
1
0
1
1
1
0
3
1
0
0
0
1
0
1
0
0
0
3
1
1
1
0
1
1
2
0
0
2
0
0
1
1
2
2
0
0
5
0
2
2
2
0
2
1
0
1
0
0
0
2
1
1
1
0
0
0
2
2
1
1
1
0
0
0
2
0
1
1
0
2
2
0
2
1
0
0
1
2
2
0
0
0
1
1
1
0
1
1
2
0
0
0
0
0
0
0
1
2
1
3
1
0
1
2
2
1
1
1
2
0
1
1
0
5
0
1
0
0
1
0
1
1
1
0
2
0
2
2
2
1
0
0
2
0
0
0
0
0
1
2
0
1
1
1
2
2
0
1
0
3
1
0
1
0
1
0
1
0
0
0
0
0
1
2
2
3
0
0
1
0
0
1
1
1
1
0
0
2
0
1
2
0
1
1
0
1
2
0
0
1
0
1
0
0
2
0
0
0
1
0
0
4
0
0
2
1
0
0
0
1
0
0
2
2
2
2
0
0
1
1
1
0
0
1
0
2
0
0
0
0
2
0
1
0
0
0
0
1
1
1
0
3
0
1
2
0
0
0
1
0
0
0
1
0
2
1
0
0
0
0
0
0
0
1
0
0
1
1
1
1
0
0
0
2
2
0
1
0
0
2
1
0
0
0
2
1
0
1
1
2
2
0
0
0
1
1
0
0
0
1
0
1
1
0
0
0
1
1
0
1
1
0
1
0
0
0
0
1
0
2
1
0
1
1
0
0
2
0
0
0
0
0
0
0
1
2
0
0
1
2
2
1
1
0
0
0
2
2
2
0
1
1
1
3
0
1
0
2
1
0
2
0
0
0
7
0
0
0
2
1
0
1
0
1
1
1
0
2
2
0
0
1
1
0
0
2
0
0
0
1
0
0
0
1
3
0
1
2
0
0
0
2
1
0
0
1
1
2
0
0
0
1
1
1
1
1
0
0
2
1
1
1
0
0
2
1
1
0
0
0
2
2
1
1
1
0
0
1
0
0
1
0
2
0
0
0
0
2
2
2
0
0
0
0
0
2
1
1
1
0
0
0
0
0
0
3
0
3
0
2
0
1
0
0
0
0
0
0
1
2
1
1
0
1
0
0
2
1
0
4
0
2
0
0
1
0
1
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
1
0
1
0
0
1
0
1
1
0
1
1
1
1
1
2
0
2
2
0
1
0
0
2
0
0
0
0
2
2
1
0
0
0
0
0
0
0
2
0
0
1
1
0
1
0
0
3
0
0
0
0
1
1
1
0
2
1
0
1
1
1
1
0
2
0
0
0
2
0
1
0
1
0
1
0
2
1
0
0
2
0
1
0
2
0
0
0
1
1
0
3
0
1
0
1
1
0
0
1
2
1
1
2
1
0
0
2
1
0
1
0
0
0
0
1
0
1
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
2
2
0
1
1
0
1
2
1
2
0
2
0
1
1
2
2
0
1
0
1
1
1
1
0
0
2
0
0
0
0
0
0
1
0
0
2
2
0
1
0
0
0
0
1
0
2
1
0
0
0
0
0
2
2
1
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
1
1
1
0
1
2
2
0
2
0
0
2
0
0
1
0
1
2
1
1
0
0
2
2
1
1
1
1
1
0
2
0
1
1
2
0
0
0
0
1
2
1
0
3
0
1
2
0
0
1
0
0
0
0
0
0
1
0
1
0
1
1
1
2
0
1
0
2
0
1
1
0
0
0
0
0
2
0
2
2
1
0
1
2
0
0
1
1
0
1
0
1
1
2
1
0
1
0
1
1
2
3
0
0
0
1
0
1
2
2
0
2
0
0
0
1
0
0
0
3
0
1
0
0
0
0
2
0
2
0
0
0
2
0
1
0
1
0
0
0
0
2
1
0
1
0
2
0
0
0
1
1
0
2
0
0
2
1
2
1
0
2
1
0
3
1
0
1
1
1
0
0
0
0
2
2
2
2
0
0
2
2
2
0
0
0
1
0
0
2
2
0
0
1
1
0
2
0
0
1
1
2
0
0
1
4
1
1
0
0
0
1
1
2
0
1
0
2
1
0
2
1
0
1
1
1
0
0
0
2
2
2
1
2
1
2
0
2
1
0
0
2
0
0
1
3
1
1
2
0
1
0
0
1
1
2
0
1
0
1
0
2
1
1
0
2
1
1
2
1
0
1
1
0
1
0
0
0
1
1
0
1
0
1
1
1
0
1
0
0
2
2
2
2
0
1
0
0
0
1
0
0
1
0
0
2
3
0
0
2
0
0
3
2
0
1
0
1
1
1
0
1
2
0
0
2
1
2
0
0
0
0
0
1
1
0
1
0
0
1
2
1
3
2
2
0
0
0
0
1
1
0
2
2
0
0
1
0
0
0
1
0
3
2
0
0
1
2
0
0
2
0
0
1
0
2
2
1
0
0
1
1
0
2
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
2
0
0
0
0
1
1
1
0
0
5
2
0
0
0
1
0
0
0
2
0
0
0
0
1
1
0
0
2
2
2
2
0
1
0
1
0
1
0
0
2
0
2
0
0
0
0
2
2
0
0
0
2
2
0
1
0
1
1
0
1
2
1
1
2
1
1
1
0
2
1
2
0
1
0
1
1
0
2
0
0
1
0
2
1
0
1
0
2
2
0
1
1
1
0
0
1
0
2
1
2
0
1
1
0
0
0
0
0
0
3
3
0
2
1
1
1
1
0
2
1
0
2
0
1
2
0
2
2
0
0
0
1
2
0
0
0
2
0
0
2
0
0
0
3
2
2
1
0
2
0
1
0
1
2
0
1
2
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
1
1
1
0
1
3
0
0
0
1
0
2
0
0
0
0
1
1
2
0
0
0
0
0
2
2
1
0
0
0
0
2
0
0
0
2
1
0
0
2
0
0
1
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
3
1
0
0
2
2
2
0
0
1
1
0
1
2
2
0
3
1
1
0
2
2
1
1
1
0
0
2
2
0
0
0
0
1
0
2
0
2
1
1
1
0
2
1
3
0
0
0
0
0
0
0
0
0
2
0
1
2
1
0
1
0
1
0
1
1
2
0
0
2
0
0
2
2
0
0
2
0
2
1
2
1
2
2
0
1
0
1
1
0
2
0
1
0
0
1
0
0
0
0
2
1
1
0
2
0
0
0
1
1
0
0
0
0
2
1
0
1
2
1
1
2
0
2
2
3
0
1
0
0
0
2
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
1
1
1
0
1
1
2
2
2
0
2
2
0
1
0
0
1
0
1
2
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
2
1
1
0
2
0
0
0
1
1
1
2
2
0
2
2
0
1
0
2
0
0
0
0
1
0
1
2
1
0
0
0
0
0
2
1
2
0
0
1
1
0
2
2
0
2
0
0
1
1
1
2
0
0
0
0
0
1
2
0
0
0
1
2
0
2
0
0
0
0
0
1
1
1
0
2
2
1
0
4
0
2
0
0
2
0
1
0
1
1
0
0
0
0
1
0
0
2
1
2
0
0
0
0
2
0
2
0
2
0
1
0
0
1
2
3
0
0
2
0
0
0
0
0
0
1
1
0
1
1
2
0
2
0
0
0
1
0
1
1
2
1
0
1
1
0
1
2
1
1
0
0
4
0
1
2
2
1
0
0
2
1
1
0
0
0
0
0
1
2
2
2
2
0
0
0
0
2
0
1
0
0
0
0
0
1
1
2
0
0
1
0
0
1
2
0
1
0
1
1
0
1
0
0
1
2
0
1
3
1
0
0
0
1
1
1
0
0
0
0
2
0
0
1
0
0
1
0
1
1
0
1
0
1
2
1
0
1
0
1
0
1
1
1
2
1
0
2
2
0
2
2
2
0
0
0
0
4
0
1
0
0
0
3
1
1
2
0
0
2
0
2
0
2
2
0
0
0
0
0
1
1
0
0
1
0
2
0
1
1
0
2
2
0
1
1
0
0
3
1
0
0
1
1
2
0
2
0
0
1
0
0
1
1
1
0
2
1
0
0
0
0
1
2
0
2
2
0
0
0
1
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
1
2
0
0
0
2
0
0
0
0
10
0
0
1
1
0
2
0
1
1
2
2
1
0
0
1
2
1
1
1
1
0
0
2
0
1
2
0
0
0
0
0
0
2
1
2
0
0
1
0
0
1
0
0
0
0
1
2
0
0
0
0
0
1
0
0
2
2
0
1
0
0
1
0
0
0
2
2
0
0
1
0
0
0
0
0
1
0
2
0
0
0
2
0
0
2
0
2
1
0
0
0
0
2
0
0
1
2
1
1
0
2
0
0
1
0
2
2
0
0
2
1
0
2
1
0
2
2
2
0
1
1
3
0
0
1
0
0
1
0
0
1
0
1
0
3
0
1
0
0
0
1
1
1
0
2
1
2
0
2
0
4
0
0
1
1
0
0
2
0
1
2
1
2
1
0
0
1
2
0
1
0
1
0
0
0
0
0
0
1
0
1
0
1
1
2
1
0
0
0
0
0
0
1
2
0
0
0
0
2
1
1
1
1
0
2
0
1
2
0
0
1
0
1
1
2
2
2
0
0
1
0
0
0
0
0
0
0
3
1
0
2
0
1
2
0
1
0
0
2
0
0
1
2
0
1
2
2
0
0
2
0
0
1
0
0
0
2
0
0
2
0
0
0
1
0
1
1
1
0
0
1
1
0
1
0
2
0
0
2
0
0
0
1
0
1
1
1
0
2
1
0
1
1
0
0
1
1
0
0
0
1
0
2
0
0
0
0
0
1
1
3
2
1
0
0
0
2
0
1
2
1
2
1
2
2
0
3
0
1
1
2
1
0
1
1
1
1
0
1
1
1
0
0
0
1
0
0
1
0
0
2
2
1
2
2
0
0
0
2
1
1
0
0
2
2
0
1
1
3
0
1
2
1
1
1
0
0
2
1
0
0
0
2
0
1
0
1
1
2
0
2
0
1
0
2
0
2
1
2
3
0
2
1
0
1
0
1
0
0
1
0
1
0
0
0
1
1
0
0
1
0
2
1
1
0
0
0
2
0
2
2
1
0
1
1
1
0
0
2
1
1
0
2
1
0
0
0
1
0
3
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
1
0
1
0
1
2
0
2
0
1
4
0
0
0
1
1
0
1
1
0
0
0
0
0
1
1
0
6
0
1
0
0
1
2
0
0
1
0
0
0
0
2
0
0
1
2
0
2
2
1
0
0
1
1
0
1
0
1
2
3
0
2
0
0
1
0
1
0
0
2
1
1
0
0
2
1
0
0
0
0
2
0
1
0
2
0
1
0
0
1
2
0
0
1
0
2
0
0
0
0
0
1
1
0
1
0
1
2
1
0
6
2
0
0
0
0
1
1
1
1
1
1
2
0
0
0
0
1
1
1
2
0
1
2
1
1
0
1
0
0
1
0
1
0
1
1
2
0
0
0
0
2
1
1
0
0
0
0
0
1
4
0
1
1
2
1
2
1
1
1
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
2
2
3
2
0
0
2
1
0
2
2
1
0
0
1
0
1
0
0
0
1
0
0
2
0
1
1
0
0
0
0
0
0
2
2
1
0
1
2
0
0
0
0
1
0
0
2
1
0
1
1
2
0
0
1
0
1
2
0
1
0
1
2
2
0
3
0
1
0
2
0
0
1
2
2
3
1
1
1
2
1
0
1
2
0
0
0
0
2
2
2
0
0
1
1
2
3
0
1
0
0
0
2
0
2
0
1
2
0
0
3
2
1
0
2
1
2
0
1
0
1
3
1
0
0
2
1
0
1
3
0
0
0
0
2
2
0
1
1
0
2
3
0
0
2
1
0
0
0
2
1
1
1
1
0
1
0
0
2
0
0
0
1
2
0
1
0
1
0
0
2
0
2
0
1
0
0
2
0
1
0
1
1
3
1
0
1
0
1
0
1
0
2
0
1
1
0
0
0
1
2
1
1
1
0
1
0
1
1
0
0
3
0
3
2
0
0
0
1
1
0
0
1
0
1
1
0
2
2
0
1
0
0
1
2
1
2
2
0
0
0
0
1
0
1
1
2
0
1
2
1
1
3
0
0
0
0
2
0
1
1
1
1
1
2
0
2
0
1
0
2
0
0
0
3
1
0
1
1
1
2
2
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
2
2
0
1
1
0
1
3
0
0
0
0
3
2
0
1
1
1
0
2
2
0
0
1
2
2
1
1
0
0
1
0
0
0
0
2
0
1
1
0
0
0
0
0
1
2
1
2
1
0
1
0
0
2
1
0
0
1
0
1
1
0
1
1
1
1
0
1
0
0
0
2
2
0
0
0
3
1
2
1
2
0
2
0
2
1
1
1
2
1
0
2
0
1
1
2
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
2
1
0
1
0
1
2
1
2
2
0
1
0
0
2
1
0
0
1
1
2
2
1
1
0
3
1
0
2
0
2
1
1
0
0
0
0
2
1
1
1
0
2
1
0
0
1
0
0
0
2
0
2
0
0
0
1
0
0
1
1
0
0
1
2
2
0
0
1
0
2
2
2
1
0
0
2
1
0
1
0
1
2
1
0
1
0
2
2
2
0
0
1
1
2
0
2
2
1
0
0
0
2
0
1
2
2
0
0
1
1
0
2
2
0
0
0
1
0
0
0
1
1
2
2
2
1
0
2
0
0
1
0
0
0
0
2
1
0
1
0
2
2
2
0
2
2
1
0
1
0
0
1
1
0
1
2
1
2
0
1
1
0
2
0
0
1
0
1
1
2
2
2
1
0
0
2
0
0
2
0
2
2
0
1
0
2
1
1
0
0
1
1
1
1
0
1
0
0
2
0
0
0
0
0
0
0
2
1
0
0
1
0
2
1
0
0
2
1
0
2
2
0
1
0
1
1
0
1
2
2
0
2
1
0
1
0
2
0
1
1
0
2
0
1
1
1
2
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
1
0
1
2
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
2
0
1
2
0
0
1
1
1
0
1
0
1
2
1
0
0
2
0
2
0
2
1
1
2
1
2
2
0
0
1
0
0
1
0
0
1
1
1
2
0
2
0
2
0
0
0
2
2
1
2
0
0
0
2
0
1
1
0
0
0
0
1
0
1
1
2
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
2
0
0
0
2
1
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
2
0
2
0
0
1
0
0
2
0
0
0
0
1
2
0
1
0
0
1
1
0
1
0
1
2
0
0
0
1
1
0
2
0
1
1
1
2
0
0
0
2
0
0
1
0
0
1
1
1
1
1
2
1
0
1
1
0
2
0
1
1
0
1
1
0
0
1
0
0
0
0
0
0
1
1
0
2
0
1
0
0
1
0
1
0
0
1
0
0
1
1
2
0
0
0
1
1
2
0
1
2
0
0
0
0
1
0
2
0
0
1
2
2
2
2
0
3
0
0
1
1
2
0
2
1
0
1
0
1
0
2
0
0
2
0
0
2
2
0
2
0
2
1
2
0
2
1
0
0
1
0
2
0
1
0
2
0
1
0
0
1
0
2
0
2
0
2
1
1
1
0
0
0
1
2
0
0
1
2
0
2
0
0
0
0
0
0
0
2
1
0
1
0
0
1
1
0
1
0
0
0
2
1
1
0
2
2
0
0
0
0
1
0
0
0
1
2
1
1
0
0
0
0
0
2
2
0
1
1
1
2
2
3
0
0
1
1
0
2
0
0
2
0
0
0
0
0
0
0
1
0
2
2
1
0
1
2
0
2
1
0
2
0
0
1
0
1
0
0
1
1
1
0
2
2
2
0
1
0
1
0
0
1
1
0
1
0
0
0
1
1
1
1
1
0
0
1
0
1
0
1
1
1
2
2
0
1
1
1
2
0
1
2
0
0
2
1
0
2
2
1
0
1
2
2
0
2
0
1
1
2
0
1
0
0
0
1
1
2
1
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
2
0
1
0
1
1
1
0
1
2
2
1
0
0
0
0
1
1
1
1
1
0
0
1
0
1
0
0
0
0
0
1
1
2
0
1
1
0
0
0
1
2
1
0
0
0
2
2
0
2
1
1
0
2
0
0
0
2
1
2
1
0
6
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
2
2
0
2
1
0
2
0
0
0
0
0
2
2
2
0
0
1
2
0
0
0
2
1
0
1
1
1
1
2
1
1
1
0
1
0
0
0
0
0
0
1
1
0
2
1
0
0
1
0
2
0
0
2
0
1
0
1
0
1
2
1
1
0
0
0
1
0
1
0
0
0
2
0
0
1
1
0
0
1
2
2
0
1
0
1
0
1
0
2
0
0
0
2
1
0
2
0
0
3
1
1
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
1
0
2
1
2
0
0
2
1
2
2
2
0
0
0
1
2
1
2
0
0
1
3
1
0
0
0
0
0
2
0
2
2
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
2
0
0
0
1
2
0
1
0
1
0
0
1
0
1
0
1
4
0
0
0
1
1
0
1
0
1
0
1
0
0
1
1
1
2
0
0
1
0
0
0
2
0
0
1
0
1
0
2
0
0
0
2
1
0
2
2
0
0
1
0
0
0
1
0
1
2
0
0
2
2
1
0
0
0
0
0
0
1
0
0
2
1
1
1
0
0
0
1
2
0
0
0
3
0
2
0
0
2
0
0
2
0
2
0
1
0
0
2
2
0
0
0
1
0
0
2
1
1
0
1
0
2
0
2
0
0
2
2
0
0
0
0
2
0
1
0
1
0
0
3
0
0
1
0
0
0
2
0
1
0
0
0
2
0
2
0
0
2
0
0
0
2
1
0
0
2
1
0
0
0
1
1
1
2
0
0
0
2
0
2
2
2
1
0
1
1
1
0
0
0
2
0
2
0
2
0
1
0
1
0
0
0
0
0
2
0
2
1
1
0
2
2
0
1
1
0
1
0
0
2
1
2
2
0
0
3
0
0
0
0
1
0
0
0
1
0
2
2
2
1
2
2
2
1
2
1
1
1
1
2
0
1
1
2
0
1
1
2
1
2
2
0
0
0
0
2
1
0
0
0
1
1
0
0
2
1
1
0
0
1
0
0
0
1
2
0
2
0
1
1
2
0
0
2
0
0
0
0
0
1
1
2
1
0
2
0
2
0
1
1
0
1
0
1
2
2
1
2
1
2
0
0
2
0
0
1
1
0
0
0
2
1
0
0
1
1
0
1
0
1
0
2
0
2
1
1
2
1
0
0
1
2
0
3
0
0
1
1
0
2
0
0
1
0
0
1
1
1
0
0
0
0
0
2
1
1
1
0
1
0
1
0
1
1
0
0
0
0
0
1
0
2
2
2
0
1
0
1
0
1
0
1
1
2
2
6
0
0
0
1
0
0
2
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
2
2
0
1
1
1
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
1
2
0
2
1
1
1
1
1
1
0
0
3
1
1
0
1
0
0
1
0
0
2
2
1
0
1
0
1
1
0
2
1
0
0
1
0
0
0
1
0
1
2
2
1
0
0
2
0
0
1
1
2
1
1
2
2
1
2
2
0
0
0
0
0
0
1
2
2
1
1
1
0
4
1
2
2
1
2
1
1
2
3
3
2
0
1
0
2
1
0
2
2
1
0
0
3
0
1
0
2
1
0
0
0
0
2
0
0
0
0
0
2
1
1
0
0
0
0
0
0
1
0
0
2
0
1
2
1
0
0
0
1
2
0
0
2
0
3
0
0
0
0
1
1
0
0
0
0
1
1
0
3
3
2
0
0
0
0
3
1
2
0
2
0
1
1
1
0
0
0
0
0
0
1
0
0
1
0
2
0
1
0
0
1
0
0
0
1
0
1
2
0
2
1
0
2
1
3
0
1
1
0
1
0
0
2
1
1
1
1
0
0
2
1
0
1
2
0
0
0
0
0
2
1
1
0
1
2
0
0
1
0
2
2
2
1
1
2
0
1
1
2
1
2
2
0
0
0
3
0
1
1
1
2
0
1
1
2
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
1
2
2
0
2
2
0
0
0
1
2
0
2
1
0
0
0
0
1
0
0
0
2
1
0
0
1
1
0
0
1
1
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
1
1
1
1
1
1
1
0
2
1
0
0
0
0
0
0
0
0
1
2
0
2
2
0
0
1
2
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
2
0
2
1
1
2
0
1
0
0
0
1
1
1
1
2
0
0
0
0
0
0
0
0
0
2
2
1
2
1
1
1
1
0
0
1
2
0
0
1
0
1
1
1
0
1
0
2
1
0
3
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
1
2
2
0
0
0
3
2
1
2
6
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
1
0
1
0
0
1
0
0
2
0
1
0
1
0
0
2
1
1
1
2
2
0
0
1
1
1
0
0
1
0
1
1
1
0
0
0
1
2
0
3
1
2
1
2
1
1
2
0
1
0
2
1
0
2
2
0
0
0
2
0
0
1
2
0
2
0
1
0
0
1
1
0
2
0
2
2
1
2
1
0
0
0
1
0
2
0
0
1
0
1
0
0
2
0
1
0
1
0
2
0
0
0
0
0
0
2
1
1
0
0
0
2
2
1
0
3
1
1
3
2
1
0
0
3
0
0
1
0
1
0
0
2
2
0
0
2
0
1
1
1
2
0
3
0
0
1
0
0
1
0
1
0
2
0
1
0
1
1
0
0
2
2
1
0
2
0
2
0
0
2
1
0
0
2
1
1
0
0
2
0
0
2
1
2
1
0
0
1
1
1
0
1
0
0
2
0
2
2
0
1
0
1
2
2
0
1
0
0
0
4
2
0
1
1
1
1
0
0
0
0
0
1
0
2
2
0
0
0
2
1
0
0
0
0
1
0
1
0
1
1
1
0
0
2
2
3
1
1
2
0
2
1
1
0
2
0
0
0
2
1
1
0
1
2
0
2
0
0
2
0
0
1
0
1
0
0
1
4
2
0
1
1
1
2
0
0
2
1
2
1
0
1
1
0
2
0
0
1
2
1
2
0
0
0
2
0
1
0
0
0
2
0
0
1
1
0
0
1
0
1
1
1
0
0
1
0
0
1
1
0
0
0
1
0
0
1
2
1
0
1
2
1
1
0
2
0
2
0
0
0
0
0
0
0
2
0
2
2
1
0
1
0
1
1
2
0
2
1
2
0
1
1
0
0
1
1
2
1
2
3
2
1
1
1
1
0
0
0
0
0
1
2
1
1
0
1
0
0
0
0
1
0
0
0
1
1
0
1
1
1
2
2
1
0
0
2
2
0
0
0
0
0
1
2
1
0
1
1
2
0
1
1
0
2
2
1
1
1
1
0
0
0
1
0
1
0
0
1
0
0
2
2
2
1
1
0
2
2
0
0
0
0
0
1
1
0
0
0
1
0
1
0
1
0
0
0
0
0
2
1
0
2
1
0
1
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
2
0
2
0
8
1
0
0
1
1
1
1
1
0
2
2
0
1
1
2
0
0
0
2
1
2
1
1
0
0
0
0
0
0
1
0
0
0
0
2
0
1
2
2
0
0
0
1
0
1
0
0
0
0
0
1
1
2
0
1
0
2
1
0
0
1
1
0
1
2
0
0
0
0
0
2
1
0
3
0
0
0
0
2
1
1
2
1
2
0
0
0
2
0
1
0
2
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
2
3
1
0
0
0
1
0
4
1
2
1
0
0
0
2
0
0
1
1
0
2
0
0
0
0
1
0
2
1
0
2
2
0
0
0
1
0
2
1
1
0
2
1
2
1
2
0
3
0
1
1
1
1
0
0
2
0
0
2
2
2
1
1
1
0
0
1
0
1
3
0
1
0
1
2
1
0
0
2
0
0
0
0
1
0
0
1
0
2
1
0
1
1
0
0
0
2
2
1
1
2
2
0
0
0
0
0
0
1
0
1
1
0
0
1
2
1
1
2
1
2
0
2
0
1
0
0
0
2
0
0
0
0
0
1
2
0
0
0
3
1
4
2
1
0
0
1
0
2
0
0
2
0
1
2
1
0
1
0
1
0
2
1
2
0
0
0
2
0
0
0
1
1
2
1
0
2
1
0
0
1
0
0
1
0
1
2
0
0
0
2
1
1
0
0
0
1
1
0
0
0
0
0
0
2
0
2
0
3
1
0
1
0
2
0
0
2
1
0
2
1
1
1
0
0
2
0
0
0
1
1
0
0
0
1
0
0
1
1
2
1
2
0
0
0
0
1
0
0
0
0
2
1
1
0
1
0
1
1
2
2
1
0
1
0
2
1
2
0
0
0
0
0
2
0
1
0
1
0
2
0
0
0
1
1
1
1
0
2
0
1
0
1
2
0
0
0
1
0
1
0
1
1
0
0
0
1
0
2
0
0
0
4
0
1
0
1
0
2
0
1
2
0
0
0
0
1
0
1
1
0
2
1
0
0
3
2
0
0
0
1
1
2
2
0
0
0
0
0
1
1
0
1
0
2
1
1
0
0
1
3
4
1
1
0
1
0
1
0
0
2
0
1
1
4
0
0
0
2
2
0
0
3
0
0
1
1
2
0
0
0
1
0
0
1
0
2
0
0
1
4
1
0
2
0
0
2
2
3
0
0
0
1
0
0
1
0
0
1
0
2
1
0
2
0
0
1
0
0
0
0
1
0
2
2
0
1
2
2
1
1
1
1
1
0
2
0
2
0
1
1
1
0
0
0
0
1
1
1
0
1
0
0
0
1
0
1
1
0
0
0
0
0
1
0
1
1
0
2
0
2
2
2
0
2
0
0
0
1
0
1
1
0
0
0
2
0
0
0
2
0
0
1
0
2
0
1
0
1
0
0
0
1
1
1
1
0
0
4
0
1
1
3
0
2
1
0
0
2
2
0
3
1
2
0
4
0
0
1
2
0
1
0
2
2
2
0
2
2
1
1
0
0
0
0
0
0
1
3
1
0
2
1
0
0
2
0
0
1
1
2
0
2
2
0
0
1
2
1
3
2
0
0
0
1
0
1
1
1
0
1
0
2
0
0
2
2
1
3
2
0
1
1
0
1
0
0
1
0
2
1
1
0
0
1
2
0
1
1
0
2
1
0
2
2
0
1
0
0
0
1
1
0
1
1
0
1
2
1
0
0
1
2
1
2
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
1
1
2
2
1
0
0
0
2
0
0
2
1
0
0
2
0
1
0
0
0
0
2
2
2
2
0
0
1
3
0
0
2
2
0
0
0
2
0
1
2
1
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
1
0
2
1
1
0
0
0
2
1
1
0
0
0
0
2
1
1
1
1
0
0
0
0
0
2
2
0
2
1
3
0
0
1
0
3
1
0
1
2
0
0
0
0
0
0
2
2
6
1
0
0
0
1
0
0
2
0
2
0
0
0
0
0
2
1
2
0
2
0
1
0
0
1
1
1
0
2
3
2
1
0
0
1
1
0
0
0
2
2
2
0
1
0
1
2
2
0
0
0
0
3
1
2
1
1
1
0
1
1
2
0
0
0
2
1
3
0
0
0
0
2
1
0
1
4
1
1
2
2
0
1
0
2
1
0
1
0
1
2
0
0
0
0
2
2
0
0
0
2
0
1
1
7
0
3
2
0
2
2
1
0
0
2
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
2
0
1
0
1
0
0
0
0
0
1
1
0
1
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
1
2
3
2
0
1
2
1
1
0
2
2
1
1
1
0
0
0
2
2
2
0
0
0
0
1
1
1
1
0
0
0
2
0
0
1
0
0
1
1
1
0
2
1
1
0
0
2
1
1
0
1
0
0
0
2
2
0
1
1
0
4
0
1
2
1
0
2
0
3
1
0
2
0
0
1
0
0
0
0
1
2
1
0
1
0
1
0
1
0
0
2
2
2
2
1
0
0
0
1
1
0
0
1
2
1
1
0
2
1
0
0
1
0
0
0
0
1
0
2
1
0
2
1
0
1
1
1
0
1
1
2
1
3
0
1
0
1
1
0
1
1
0
2
0
2
0
0
2
2
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
1
1
1
0
0
2
2
0
2
0
1
1
0
0
0
0
2
0
0
2
2
2
0
0
0
2
0
2
0
0
0
0
2
0
1
2
1
1
0
0
1
0
0
1
0
0
0
2
0
2
1
0
0
2
0
0
0
0
2
0
0
0
1
0
2
1
0
1
1
2
0
2
0
1
4
2
1
1
2
0
0
0
0
1
1
0
1
2
0
0
0
2
0
3
0
0
1
0
2
2
1
2
0
0
1
0
0
2
0
0
1
0
2
0
0
1
1
1
0
1
1
0
2
0
0
0
2
0
1
1
0
0
0
2
0
0
1
1
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
1
0
2
0
1
2
2
1
0
1
0
0
0
1
0
0
1
2
0
1
2
0
1
1
0
2
2
0
2
1
2
0
0
2
0
1
2
1
0
0
0
0
0
1
0
3
1
1
1
1
0
1
0
0
0
0
1
1
1
0
0
1
0
2
0
1
2
0
1
1
0
1
0
0
0
0
1
1
0
1
0
0
0
0
1
1
2
0
0
0
0
1
1
1
0
1
1
1
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
2
2
2
1
2
0
2
1
1
0
1
0
2
0
0
1
0
0
2
0
1
0
2
0
1
1
0
1
1
2
1
2
2
1
0
2
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
3
1
2
1
0
1
2
0
1
0
0
3
1
2
2
0
0
2
2
1
0
1
2
1
0
2
3
0
2
2
1
3
1
2
0
1
0
0
0
0
0
0
0
1
2
0
1
0
0
1
0
0
1
2
0
1
2
0
1
0
1
2
0
1
2
1
2
0
3
0
0
1
2
0
1
0
2
0
5
0
0
2
0
0
0
2
0
1
2
0
0
0
2
0
2
1
1
2
1
1
2
0
2
0
2
0
1
0
1
0
1
1
0
1
1
2
0
0
1
2
1
2
1
0
2
1
0
0
0
1
1
0
1
0
0
0
0
0
1
2
1
1
1
0
1
0
1
1
2
0
1
0
0
1
2
2
2
1
0
2
0
0
0
1
0
0
0
0
2
3
0
2
0
2
0
0
1
0
0
1
0
0
1
0
0
0
0
0
2
0
0
2
2
0
2
1
0
0
0
2
0
0
1
1
3
1
0
0
1
2
0
0
0
2
1
0
0
0
1
2
0
0
1
1
0
0
1
1
2
0
0
2
0
0
1
3
1
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
3
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
1
0
0
0
0
1
1
1
1
1
3
0
0
0
0
1
2
2
1
1
1
0
0
2
0
0
0
0
1
0
2
0
0
1
1
2
0
1
1
1
2
0
2
2
3
0
1
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
1
0
0
2
2
0
3
1
0
0
0
1
0
2
0
2
0
2
1
0
1
1
0
0
0
0
0
3
0
2
2
2
0
0
0
0
0
1
1
0
2
1
1
2
1
1
0
1
1
0
2
0
0
2
0
1
0
1
1
0
1
0
1
2
1
0
2
1
1
0
0
0
1
1
0
0
0
0
2
1
0
2
0
0
0
0
1
2
0
1
0
1
0
1
0
0
1
0
0
1
2
1
0
0
1
2
0
2
0
1
2
0
0
0
2
1
2
1
0
1
0
1
2
3
2
1
0
1
0
0
1
0
2
0
1
2
0
0
1
0
0
1
0
0
0
0
1
3
1
1
1
0
2
1
0
0
1
1
0
2
2
0
1
0
0
2
0
3
0
0
1
0
1
0
2
0
1
1
1
1
2
1
2
1
0
0
0
2
1
2
0
0
1
3
1
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
1
1
7
2
0
0
0
2
1
2
1
0
2
0
1
0
1
1
2
2
2
1
1
0
0
1
0
0
1
1
2
0
2
1
0
1
0
1
0
1
0
0
1
1
1
0
3
0
0
2
0
0
0
0
0
0
0
1
1
1
0
0
0
2
0
0
0
1
0
0
0
0
2
2
2
2
1
1
0
1
1
1
2
0
0
1
0
0
0
2
0
1
2
1
0
0
1
0
1
2
2
1
2
2
1
0
2
2
2
0
1
1
2
2
0
0
2
1
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
2
0
0
1
1
0
1
0
0
2
0
0
1
0
0
1
0
0
1
1
1
0
0
0
1
1
1
0
0
0
1
0
0
1
2
1
0
0
0
0
0
1
4
0
0
0
0
0
0
1
1
2
0
2
1
0
1
1
0
0
3
1
0
0
0
0
1
1
2
0
0
0
1
2
0
1
0
2
0
2
0
1
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
4
0
0
2
1
2
0
0
1
0
2
2
0
0
2
0
1
0
0
1
0
1
1
0
2
1
0
0
1
1
0
2
0
1
1
0
1
0
0
0
1
0
2
0
0
2
2
2
1
0
2
0
3
2
2
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
2
0
1
0
4
0
1
0
1
1
0
0
0
3
0
0
2
0
0
0
0
0
0
1
0
2
2
1
1
2
1
4
0
1
1
1
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
2
1
0
0
0
1
1
1
0
1
0
0
0
1
1
0
0
3
0
0
0
2
1
0
0
0
2
0
1
0
2
0
3
1
3
2
1
0
0
0
1
0
0
0
2
0
1
0
0
1
1
2
0
2
0
1
0
2
0
2
2
0
1
0
0
0
1
0
0
0
1
2
2
0
0
2
0
1
0
0
0
0
2
0
0
1
1
0
0
0
1
1
0
1
0
0
0
0
0
1
0
2
1
1
0
0
1
0
2
0
0
2
1
0
0
1
0
0
0
0
1
0
0
0
1
0
1
2
0
0
0
2
1
1
0
2
1
0
1
0
1
0
0
0
0
1
1
1
2
1
2
0
1
0
2
1
0
0
1
0
2
1
1
1
0
0
1
2
2
3
1
0
2
0
0
1
1
1
2
1
0
1
1
0
0
1
1
2
0
1
2
2
2
0
0
0
0
0
2
2
1
0
1
0
1
0
0
0
2
2
0
0
1
2
0
1
0
2
0
0
2
0
2
2
1
1
1
0
0
0
0
2
1
2
2
1
2
1
2
0
1
0
1
2
2
1
0
2
0
1
0
0
2
1
2
0
0
1
0
0
2
2
0
0
1
1
1
0
0
1
1
0
1
2
2
2
1
0
1
0
2
0
0
1
1
0
0
2
1
0
0
0
0
0
2
0
0
2
0
2
1
1
1
1
1
1
1
1
0
2
0
2
2
0
2
0
1
0
0
0
0
0
1
2
0
0
0
0
0
4
1
0
1
0
1
2
4
0
1
2
2
0
2
2
0
1
0
2
0
1
0
1
0
1
1
2
2
0
2
1
1
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
1
0
1
1
0
1
0
0
0
2
0
2
0
1
2
1
1
0
0
0
6
0
1
0
0
0
0
0
1
0
0
2
0
0
1
2
0
1
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
1
2
2
2
0
0
0
0
2
0
1
1
1
0
1
1
0
2
1
0
0
0
1
0
0
1
0
2
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
2
1
1
0
1
0
1
1
0
0
0
2
0
0
0
1
1
0
1
1
0
1
0
0
0
0
2
0
1
0
0
1
1
1
0
1
2
0
0
0
0
2
0
2
0
0
0
2
1
0
0
1
0
1
1
0
0
2
0
0
1
0
1
2
1
0
0
0
0
2
1
0
0
0
0
0
0
8
0
0
0
1
0
2
0
0
0
2
2
1
0
0
0
2
2
0
0
2
0
2
0
0
0
1
2
1
1
1
0
0
0
1
1
2
1
0
2
0
0
0
0
0
0
2
0
1
2
0
2
1
0
2
0
1
1
0
1
0
1
0
0
0
4
0
0
1
2
0
0
0
0
1
1
2
0
0
1
1
0
2
1
2
1
3
2
0
0
1
1
1
0
0
0
2
2
1
0
1
2
1
2
0
1
2
1
1
2
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
2
1
0
0
1
1
1
1
0
1
1
2
0
0
2
1
0
0
2
1
0
1
3
0
0
0
0
0
0
0
1
1
1
0
1
0
0
3
0
1
0
2
0
0
1
2
0
0
0
0
0
2
0
2
2
0
2
0
2
1
1
2
1
1
0
1
0
1
0
1
0
0
2
0
2
0
2
0
2
1
0
0
3
0
0
2
0
1
2
0
0
0
1
0
0
0
1
2
0
0
2
0
1
0
2
1
0
1
1
1
0
2
2
0
0
2
0
2
0
0
0
1
0
1
1
2
1
1
1
0
0
1
0
0
1
0
0
2
1
0
0
1
0
0
1
0
2
0
2
2
2
1
0
0
4
0
0
2
2
0
2
1
0
0
0
0
2
0
1
1
0
1
1
1
0
0
1
0
0
0
0
3
1
2
1
0
3
0
2
0
1
0
1
0
0
2
0
0
2
0
0
0
2
1
0
0
0
1
0
1
2
0
0
0
0
0
0
2
0
0
1
0
1
1
0
0
0
1
2
2
0
1
2
1
2
2
0
0
2
1
0
1
0
1
1
1
0
2
1
0
2
1
0
1
0
0
0
0
2
1
1
0
1
0
2
0
0
0
0
2
0
0
0
0
1
1
1
1
0
1
2
0
2
0
0
2
0
1
1
2
2
0
2
0
7
1
2
1
0
1
0
1
0
0
2
2
0
0
1
0
2
1
2
0
0
0
1
2
2
1
1
2
0
0
1
2
2
0
1
1
0
0
0
0
0
0
2
1
0
1
0
1
1
0
1
1
1
0
0
0
2
0
0
2
1
2
0
0
0
2
0
0
0
0
0
0
3
1
0
0
0
1
1
1
2
2
0
0
3
0
8
2
0
0
1
3
0
0
0
1
1
1
1
2
0
2
1
1
1
2
2
2
0
0
2
2
0
0
0
1
0
1
0
0
1
0
0
2
1
0
2
0
2
1
1
1
2
0
1
0
1
1
1
0
1
4
0
0
1
0
1
0
2
0
0
0
1
0
0
1
0
1
2
0
0
0
1
0
2
2
0
0
1
1
0
2
2
1
0
0
2
0
0
0
2
1
0
1
0
0
0
0
0
2
1
0
1
1
1
0
1
1
0
0
0
0
2
1
0
0
0
0
0
2
0
2
0
0
1
2
0
1
0
0
1
1
0
0
0
0
0
2
1
0
0
1
2
0
0
0
1
1
1
2
1
3
1
2
0
2
2
0
1
3
1
1
0
0
2
0
0
0
0
0
1
1
0
0
0
2
0
1
1
1
0
0
0
3
2
0
1
0
1
1
0
1
1
0
2
1
2
0
0
1
2
2
0
0
0
1
2
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
1
1
0
2
1
1
0
1
0
1
0
0
1
0
0
1
0
1
2
0
0
1
1
1
0
0
0
0
1
0
0
1
3
1
0
1
0
2
2
2
2
0
0
0
0
1
0
1
0
0
0
2
0
0
3
0
0
1
1
2
2
0
0
0
1
1
0
0
4
0
0
0
0
0
1
2
0
1
1
0
0
1
1
0
0
0
0
0
2
2
0
2
1
0
2
0
0
1
2
1
0
1
1
0
0
0
0
2
3
0
1
1
0
1
0
2
0
0
0
0
1
2
0
1
0
0
0
2
0
1
2
0
0
1
1
0
0
2
1
1
0
1
6
1
0
0
1
1
2
0
0
0
1
0
1
0
1
1
0
1
2
0
2
0
1
1
2
2
4
1
2
0
2
1
1
0
2
0
0
0
0
2
0
1
7
1
1
0
1
0
0
0
1
2
3
0
1
0
1
1
0
2
0
0
2
1
1
0
0
2
0
0
2
0
0
0
2
1
0
2
0
0
0
0
0
0
1
0
0
1
2
2
0
2
2
1
0
1
0
0
2
0
0
0
0
2
0
1
1
0
0
0
0
1
4
1
0
2
0
0
0
2
2
0
2
0
0
2
0
0
1
1
1
0
1
0
2
0
2
1
1
4
0
0
2
1
0
1
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
2
0
1
1
1
2
0
0
2
2
1
0
0
0
0
1
1
1
2
0
2
0
0
2
1
2
1
2
1
2
0
1
0
0
0
2
0
0
0
2
0
0
0
0
1
1
0
0
0
1
2
0
2
1
0
1
0
0
2
0
2
1
1
1
0
0
0
0
1
1
0
2
2
1
2
0
2
0
0
1
1
1
1
0
1
0
0
1
0
0
1
1
0
0
2
0
0
0
1
0
1
0
2
0
0
0
0
2
0
1
0
2
1
0
2
2
1
0
0
0
2
4
0
1
0
2
0
2
1
0
1
0
1
2
0
0
1
0
1
2
0
1
1
0
0
0
0
0
2
1
1
3
0
0
0
0
1
0
2
2
2
0
0
0
2
0
1
2
2
0
0
0
1
1
0
0
0
2
0
0
2
1
1
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
8
1
1
0
0
0
0
1
2
1
0
1
2
1
0
1
1
0
0
2
0
0
0
1
0
0
1
2
0
0
1
0
1
0
2
2
0
0
0
1
0
1
0
1
1
1
2
1
2
1
1
1
0
0
2
0
1
0
1
2
1
7
0
0
2
2
1
2
0
1
0
1
1
2
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
3
1
1
0
0
0
2
2
0
0
2
1
2
2
0
0
2
0
1
4
1
0
0
1
1
1
0
0
1
0
2
0
2
0
1
2
1
0
2
0
0
1
0
0
1
0
0
0
2
0
1
1
0
1
2
0
2
0
1
1
0
0
0
3
1
0
1
3
0
0
1
1
0
1
1
2
0
0
0
2
0
0
1
2
0
0
0
0
0
0
2
0
1
0
1
0
2
1
0
0
2
0
1
1
1
3
0
2
0
1
2
1
1
1
2
2
0
0
0
0
0
2
2
2
1
0
0
1
1
0
2
0
0
1
2
0
1
1
1
0
0
0
0
0
4
1
0
0
0
2
3
2
0
1
0
0
1
0
1
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
1
1
0
2
2
1
2
1
0
2
3
0
0
1
0
0
0
0
0
2
0
2
0
0
0
1
1
1
0
0
1
0
0
1
0
0
0
2
2
1
1
0
2
4
0
0
0
1
1
2
1
0
2
2
0
3
1
0
0
0
0
1
0
1
0
1
2
0
1
0
0
0
2
2
0
1
1
0
2
2
1
1
1
0
1
1
0
1
0
0
0
0
0
0
1
1
1
0
2
3
1
0
2
0
0
0
0
1
1
1
0
0
0
2
0
0
1
1
2
2
0
0
12
2
1
2
0
2
1
0
0
0
1
0
0
0
2
2
1
1
1
2
0
1
0
0
0
2
2
1
0
0
0
0
1
2
0
0
0
1
1
1
0
0
2
0
1
0
1
1
0
2
0
0
0
1
1
2
1
0
1
0
2
0
1
1
2
0
0
2
0
1
1
2
2
1
1
0
0
0
1
0
2
1
0
0
0
0
0
0
4
1
1
0
0
0
1
0
1
2
0
1
2
0
1
1
0
1
2
0
0
0
1
0
1
0
3
0
0
0
1
0
2
0
0
0
0
1
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
1
4
1
0
1
2
0
1
2
1
0
0
0
0
0
1
2
0
0
3
1
1
1
1
0
0
0
1
0
1
1
3
1
0
0
1
0
1
1
0
2
0
2
0
2
2
0
0
0
2
0
0
0
0
1
0
0
1
0
1
1
1
1
0
0
2
0
1
1
0
0
0
0
0
2
0
2
0
1
0
0
0
2
0
1
0
2
2
0
0
2
2
0
1
0
0
0
1
0
1
1
0
1
1
1
3
1
0
1
2
0
2
0
0
2
2
2
0
0
2
2
1
0
4
0
0
1
0
0
0
2
0
0
0
3
1
0
0
0
0
2
0
1
0
2
2
0
1
0
2
1
1
3
1
1
2
0
0
2
1
1
0
1
2
0
0
0
2
1
1
1
1
1
1
2
1
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
2
2
2
2
0
0
1
0
1
0
0
1
1
0
1
2
1
1
1
2
0
1
1
1
0
0
0
0
1
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
2
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
5
2
0
2
0
0
2
4
0
0
2
1
0
0
1
2
1
1
0
0
1
1
1
1
2
2
2
2
2
0
1
2
2
2
1
1
0
1
0
0
1
3
0
0
0
0
0
1
0
0
2
0
2
2
1
1
1
2
0
0
0
0
0
1
0
2
0
0
0
0
1
0
1
1
2
0
0
1
1
1
0
2
0
1
1
1
1
0
1
1
1
1
1
0
0
2
2
1
1
0
0
0
0
0
1
1
0
1
0
1
2
0
1
0
1
0
1
2
0
1
2
1
0
2
0
2
0
0
0
0
0
0
1
0
1
0
2
2
1
2
2
1
0
2
1
1
2
7
0
0
0
0
0
2
2
1
0
1
2
2
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
1
0
0
1
2
0
1
2
0
0
0
1
0
1
0
2
1
1
1
0
1
0
2
0
2
1
1
0
0
0
0
2
1
2
1
0
1
0
0
1
0
0
0
2
0
0
1
2
0
2
2
0
0
2
1
1
0
0
1
2
0
1
2
0
0
0
1
2
2
1
0
0
2
1
2
0
1
0
1
2
0
2
0
2
1
0
0
2
0
1
0
0
1
1
1
1
2
0
0
1
2
0
0
3
0
0
2
2
0
0
0
2
1
1
4
0
2
1
1
1
0
1
0
2
0
2
2
0
1
1
0
0
0
0
2
2
1
1
1
0
0
1
2
2
1
2
0
2
0
1
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
2
0
0
1
0
0
1
0
1
0
2
1
0
2
2
1
3
0
1
2
0
1
2
0
0
1
0
0
2
2
0
1
0
0
2
2
2
1
0
0
1
0
1
1
1
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
1
0
1
1
4
0
2
1
2
2
0
1
1
0
1
1
0
0
0
0
0
0
1
2
0
0
2
1
1
0
0
0
1
0
1
1
2
1
2
0
1
0
1
0
0
0
2
0
1
0
0
0
1
2
1
0
0
1
0
0
2
0
1
0
0
2
1
0
1
0
1
0
0
1
1
1
1
2
0
0
0
0
0
0
0
1
1
2
0
1
0
2
0
0
1
1
1
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
1
0
1
0
1
1
0
2
0
1
2
2
1
1
2
1
0
0
1
0
2
3
0
2
0
3
0
0
0
2
0
1
0
2
0
0
1
0
1
0
1
1
1
2
0
0
0
1
0
1
1
0
2
1
1
1
0
0
2
0
1
2
0
0
1
0
0
0
0
0
0
0
1
2
1
2
0
0
2
0
0
1
2
1
0
2
0
0
0
0
0
0
2
0
1
0
1
1
0
1
1
0
0
0
0
0
1
1
2
0
0
2
0
1
1
1
0
0
0
0
1
0
0
1
2
1
0
0
0
0
2
1
0
0
0
0
1
1
0
1
1
1
1
0
0
0
1
0
0
1
1
2
1
2
2
1
2
1
0
1
0
2
1
2
0
1
1
0
0
1
0
0
0
1
0
2
0
2
1
0
1
0
0
0
0
2
0
0
1
2
0
2
1
0
3
1
0
0
2
2
0
0
0
2
0
0
0
1
0
0
2
2
0
1
1
0
2
1
1
0
0
0
1
1
0
1
0
1
0
0
1
1
0
0
1
0
0
0
0
1
1
1
0
1
1
5
1
0
0
0
1
1
0
3
2
1
1
1
0
0
2
2
0
0
1
1
1
0
1
2
0
0
2
0
2
0
0
1
1
1
0
1
0
0
2
0
0
1
1
0
2
0
2
1
0
2
0
1
1
0
0
2
0
1
0
0
0
1
1
0
1
0
1
2
3
0
0
0
0
1
1
0
2
0
0
0
1
0
0
1
2
0
2
1
1
2
0
0
0
0
1
0
2
0
1
0
0
0
2
0
1
0
0
0
2
1
0
0
1
0
0
2
2
1
0
0
1
2
1
1
0
0
0
2
0
2
1
0
1
2
2
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
2
2
1
0
1
1
1
0
1
0
0
1
2
0
3
0
1
0
0
0
0
1
2
1
0
0
1
0
2
0
1
1
1
1
0
0
0
0
2
0
0
1
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
1
2
0
2
1
0
0
1
0
0
0
0
0
0
2
1
3
0
0
0
0
1
0
1
2
1
0
0
0
1
0
4
0
0
0
1
0
2
0
0
0
2
0
2
0
1
1
2
0
0
0
0
0
0
0
2
0
0
1
0
2
2
0
1
0
0
1
0
0
1
0
1
5
1
0
2
1
0
0
1
0
0
0
0
2
1
0
1
0
1
1
1
0
1
1
2
2
0
0
1
1
5
1
0
0
0
0
1
0
0
1
0
2
1
0
0
1
0
0
0
0
2
1
0
0
0
2
1
1
0
2
0
1
0
0
0
2
0
0
0
1
0
0
2
3
1
1
0
0
0
1
0
1
1
1
0
1
0
2
1
1
0
0
1
0
0
1
2
3
1
2
1
2
2
0
2
2
0
0
0
2
1
0
2
0
0
0
1
1
0
0
2
2
0
1
2
1
0
1
1
0
2
1
1
0
2
1
0
0
1
0
2
1
0
0
6
1
2
0
0
1
2
2
1
1
0
0
1
0
0
1
0
2
2
2
1
1
0
2
1
1
1
0
1
1
0
0
0
1
0
1
0
2
0
0
1
0
2
1
2
0
0
0
2
2
0
2
0
0
1
0
0
1
2
0
0
0
2
0
0
1
1
0
0
2
0
0
0
1
0
0
0
2
1
0
0
1
2
1
0
0
0
0
2
0
1
0
0
0
0
1
0
0
2
0
2
1
1
1
0
1
0
0
1
2
2
0
1
0
0
1
2
0
0
1
2
0
0
2
0
0
1
0
1
0
0
0
2
1
0
0
0
0
0
1
2
0
0
2
1
2
1
0
0
0
0
0
0
2
0
2
1
1
0
0
1
1
0
1
2
2
0
0
0
0
2
0
2
1
2
1
0
2
0
0
1
2
0
2
0
0
1
0
0
0
1
0
0
0
0
2
1
0
0
1
1
0
0
1
1
1
4
0
1
0
0
0
0
0
0
0
0
1
1
1
0
2
0
2
0
1
1
1
0
0
0
0
0
1
0
3
2
1
0
1
1
0
1
6
3
1
0
2
0
1
2
0
1
0
0
0
0
2
0
2
0
2
2
2
2
2
0
2
0
1
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
1
1
1
1
0
1
2
0
0
0
0
1
1
1
1
1
0
0
1
1
1
2
0
0
1
0
0
1
2
0
0
1
2
3
0
1
0
0
2
1
0
1
0
2
0
0
2
2
0
0
2
0
0
0
1
0
0
2
1
2
1
1
2
1
1
1
0
0
0
1
1
1
1
2
1
0
0
0
0
1
2
1
2
1
0
1
0
1
1
0
0
1
1
1
2
2
2
1
0
2
0
0
0
1
3
0
3
2
1
1
2
0
0
0
0
0
2
0
0
1
1
0
0
3
0
2
0
0
1
0
2
0
0
1
2
1
0
1
2
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
2
0
0
0
0
1
2
0
0
2
3
0
1
0
0
0
2
0
0
0
1
0
0
2
1
0
1
0
2
0
1
0
0
0
1
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
3
0
2
2
2
0
0
2
1
2
0
0
2
0
1
1
0
1
0
0
0
0
2
2
0
1
2
0
2
0
1
1
0
2
1
2
0
0
2
0
2
1
1
1
1
0
1
1
0
0
0
1
0
0
1
1
0
0
1
0
2
1
0
0
1
1
2
2
0
1
0
1
2
2
2
1
0
0
0
0
1
0
1
1
1
0
1
2
0
0
1
2
1
2
0
2
0
1
1
0
1
1
0
1
1
1
0
2
1
0
1
0
0
1
1
2
1
0
1
0
1
2
2
1
0
1
0
0
2
0
2
0
2
0
0
2
0
0
1
2
0
1
0
1
1
1
0
1
1
0
1
0
0
2
2
1
0
1
1
0
1
0
0
1
0
0
0
0
1
2
0
0
2
0
0
1
0
1
0
0
2
0
2
2
2
2
2
2
5
1
1
0
0
1
2
2
0
2
0
1
1
0
3
2
1
2
1
0
0
0
0
0
0
2
0
2
0
0
0
2
1
1
2
1
1
2
1
1
0
0
0
0
0
0
1
1
2
3
1
1
1
0
1
0
0
2
2
0
0
2
1
0
0
1
1
0
1
1
0
1
0
1
1
0
1
0
2
1
1
2
1
0
0
0
0
0
1
0
2
0
0
1
0
1
1
0
1
0
1
1
0
0
0
0
1
0
2
0
0
1
1
0
2
1
0
2
1
0
0
0
0
2
0
2
1
2
2
2
0
0
1
1
1
1
1
2
0
0
2
0
1
2
0
2
1
1
1
1
1
1
2
1
2
0
1
1
2
1
2
0
1
1
1
0
0
2
0
2
0
1
1
0
2
1
0
1
0
1
1
1
0
0
1
0
0
0
0
0
2
1
1
0
1
2
0
1
2
2
1
2
2
1
0
0
2
0
0
1
0
0
1
1
0
0
1
1
1
2
0
1
2
1
0
2
1
1
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
3
0
0
0
1
0
1
0
0
0
0
2
1
0
1
0
2
0
1
0
0
2
0
2
0
2
0
0
0
1
0
2
0
1
2
2
0
1
1
0
0
1
2
0
0
0
0
1
0
0
1
2
0
1
0
0
1
0
0
0
0
0
2
0
1
0
2
1
1
2
2
0
1
1
1
0
0
3
2
0
0
0
1
1
1
1
0
0
0
0
0
1
0
1
2
0
0
1
0
0
2
1
0
0
1
0
1
1
0
2
1
0
0
2
2
1
1
0
1
2
2
1
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
1
0
1
1
1
1
0
0
0
0
1
1
0
1
0
0
1
0
1
0
1
0
1
2
0
0
1
0
0
0
0
0
3
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
2
1
1
1
0
0
0
0
0
0
2
2
2
0
1
0
1
0
1
0
1
0
2
2
1
1
2
0
0
1
0
0
2
0
1
0
0
0
0
2
0
0
2
2
0
0
1
0
1
1
0
0
1
0
2
1
2
1
0
2
2
0
0
1
2
0
0
1
4
2
0
1
1
0
1
0
1
0
2
0
0
1
0
0
2
2
2
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
1
0
0
1
1
1
1
0
2
1
1
1
1
0
0
2
0
1
0
0
1
0
0
0
2
2
1
0
0
1
0
0
0
0
0
2
0
1
0
2
1
0
2
1
3
1
0
1
2
0
2
0
1
1
1
0
2
3
0
0
2
0
2
2
0
0
1
0
1
1
2
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
2
0
0
1
1
0
0
2
1
2
2
1
0
0
2
1
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
2
0
1
0
0
0
2
0
3
2
0
1
0
3
1
1
1
0
0
1
0
1
0
1
0
1
1
1
1
0
2
0
2
0
2
0
1
0
2
0
2
2
2
1
1
0
1
1
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
1
2
1
2
0
0
2
0
1
0
2
0
1
0
2
1
3
0
1
1
2
1
1
2
2
1
2
1
1
0
1
0
2
0
0
1
0
0
0
1
2
1
2
1
0
0
1
0
1
2
0
2
0
1
1
1
2
1
0
0
2
1
0
2
2
0
1
0
0
4
3
0
0
2
0
0
2
0
1
1
1
0
0
0
1
0
0
2
2
3
2
1
0
1
2
1
0
2
0
0
2
1
1
1
1
0
0
0
0
2
0
2
0
0
2
0
1
2
0
0
0
0
0
1
0
0
1
3
1
0
1
0
1
0
0
2
1
1
0
0
0
0
1
0
0
1
3
2
2
1
1
1
1
1
1
2
0
0
0
2
1
0
2
1
0
1
0
0
1
0
2
0
0
0
0
0
1
2
3
1
1
0
1
0
2
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
1
1
1
0
0
0
0
1
0
1
2
1
0
2
1
2
0
0
2
0
0
0
1
0
0
1
2
2
0
1
0
2
0
0
1
1
0
2
1
1
0
0
2
2
0
0
1
2
1
1
3
2
2
1
1
2
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
2
0
2
0
0
1
2
1
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
2
1
0
1
2
1
0
0
1
1
0
1
0
0
0
1
0
0
0
0
1
0
1
1
1
1
0
0
1
2
1
0
0
0
0
0
0
0
0
1
0
1
0
1
2
0
0
1
2
1
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
2
0
1
2
0
0
0
1
0
0
2
0
0
0
2
1
0
0
1
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
1
2
0
3
2
1
2
1
0
1
1
0
1
1
0
0
2
1
1
0
1
0
0
0
0
0
1
2
0
0
0
0
2
0
1
0
1
0
2
1
1
1
1
2
3
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
2
1
0
0
0
2
0
1
0
0
2
2
0
0
1
0
1
0
0
0
0
2
2
0
0
0
2
0
0
0
2
0
1
0
2
1
1
0
0
0
1
0
0
0
0
2
1
1
0
0
0
2
0
0
1
1
0
1
1
0
0
2
3
0
1
1
0
2
0
0
2
1
0
0
2
4
0
0
0
1
1
0
1
0
0
0
2
1
2
2
1
2
0
2
1
2
0
0
2
0
0
0
1
0
0
2
2
0
1
0
0
0
1
2
0
2
0
1
0
0
2
0
2
0
1
1
1
0
0
0
0
1
2
0
1
0
0
1
1
0
0
2
0
0
1
1
0
1
0
2
0
0
1
1
2
1
0
1
0
1
1
2
0
0
0
1
1
0
0
1
0
0
0
2
0
0
0
0
1
2
1
0
0
1
0
1
1
2
2
1
0
2
0
0
2
1
1
1
0
1
0
1
2
1
0
1
1
1
0
2
1
2
1
0
2
2
0
0
2
0
1
1
0
0
1
1
6
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
2
1
0
0
1
0
1
1
3
2
1
0
1
0
0
2
0
1
0
1
2
2
0
1
1
2
0
0
1
1
1
0
2
0
2
0
0
1
1
0
2
0
1
1
2
0
0
0
0
2
1
0
0
0
2
1
1
2
2
1
1
1
1
0
0
3
1
0
1
0
2
0
0
0
0
2
2
0
0
2
0
0
1
0
1
0
0
0
0
0
0
2
0
2
0
0
2
1
0
1
2
1
1
0
0
2
0
0
1
1
0
1
0
1
2
0
2
2
0
2
1
0
1
2
0
0
0
2
0
0
1
0
0
2
1
0
1
0
0
1
0
0
0
2
3
0
0
1
0
0
0
0
0
1
1
2
0
0
0
0
1
0
5
1
0
0
2
1
0
0
4
3
0
1
1
0
0
0
0
0
1
1
1
0
0
0
2
1
1
0
3
2
1
0
0
0
0
0
2
0
0
2
1
1
2
0
1
2
2
0
2
1
1
1
0
2
3
0
0
2
1
3
0
0
0
1
2
1
1
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
1
0
0
1
0
1
0
0
2
2
1
1
0
0
2
2
0
0
1
2
0
0
2
0
0
2
0
2
2
0
1
0
1
1
2
2
1
2
0
0
0
0
0
2
1
1
1
1
0
2
0
0
1
0
0
1
2
0
2
0
0
0
0
0
0
1
1
1
1
0
2
0
1
0
2
0
0
0
2
1
0
1
2
1
0
0
2
0
2
1
1
2
0
1
1
1
0
2
2
2
2
0
0
1
0
1
2
0
1
0
0
0
1
2
0
2
0
1
1
2
0
0
0
0
1
0
0
1
2
1
0
0
0
0
2
1
0
1
1
0
1
0
2
1
1
1
4
3
0
0
0
2
0
2
1
1
2
1
0
0
1
1
0
0
1
2
0
0
1
1
1
0
0
0
1
1
0
3
0
0
2
1
0
1
3
1
0
1
2
0
0
0
0
0
0
2
2
1
0
1
0
0
0
4
1
0
0
1
2
0
1
1
1
1
1
1
0
0
0
1
2
1
1
0
0
0
2
0
1
0
1
2
1
0
2
0
2
1
2
0
0
2
0
0
1
0
2
2
1
0
1
0
2
0
0
1
0
0
0
2
2
0
1
1
1
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
2
2
0
1
0
0
3
0
0
0
2
0
1
2
2
0
2
0
2
2
3
0
2
1
1
1
0
1
1
2
2
0
0
0
0
2
0
2
0
0
2
2
0
1
1
0
0
0
1
0
0
0
0
2
2
0
0
0
0
2
2
0
1
3
3
0
0
2
0
1
2
0
4
0
0
2
0
0
0
0
2
1
2
2
1
1
0
1
0
0
0
0
2
1
0
1
1
1
0
0
1
1
1
0
2
0
0
0
0
0
0
1
0
2
2
0
2
0
0
0
0
2
2
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
2
0
4
0
0
3
0
0
2
2
1
1
0
0
2
1
1
1
0
0
1
0
1
0
0
1
0
2
2
2
0
1
0
1
0
0
1
2
1
0
0
1
1
1
0
0
2
0
2
0
0
0
0
1
0
0
2
1
0
2
1
0
1
1
1
0
1
1
0
0
0
0
0
1
1
1
1
1
2
2
0
1
2
1
0
1
2
0
2
1
0
2
2
0
2
1
1
2
2
0
1
0
2
0
1
1
2
1
0
4
1
1
1
1
0
0
0
2
1
0
1
0
0
2
0
2
0
0
0
1
0
0
0
2
0
0
1
0
0
2
0
0
1
0
1
2
0
0
1
0
0
1
1
0
3
0
2
1
0
2
0
1
0
0
0
0
1
0
2
0
0
1
2
1
0
0
0
2
0
0
0
1
0
0
0
0
1
0
1
1
1
0
1
1
1
0
0
1
2
2
1
0
1
0
2
1
0
0
0
0
0
0
1
0
1
0
2
0
2
0
1
1
2
1
0
0
0
0
1
1
0
0
0
1
2
0
1
2
1
2
0
0
1
2
2
0
1
2
2
0
1
0
2
1
0
0
2
0
0
3
0
0
0
2
0
0
1
2
0
0
0
0
0
0
1
1
0
1
0
0
1
0
1
2
2
0
0
2
0
0
1
0
0
0
0
0
1
1
0
0
1
1
0
0
0
1
0
0
1
0
0
0
1
2
0
1
0
1
1
0
0
2
2
1
1
1
0
0
0
0
1
0
0
0
0
1
0
0
2
1
0
1
1
3
0
2
1
1
1
0
2
2
0
0
0
2
1
3
0
1
0
0
1
0
2
1
0
0
0
1
2
0
1
0
0
0
0
1
1
0
0
2
1
0
1
1
0
0
0
0
2
1
2
2
0
0
2
2
1
0
1
0
0
0
1
2
2
0
2
1
0
0
0
1
0
0
0
2
0
0
2
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
2
0
1
0
0
0
0
0
0
2
2
1
0
2
2
0
0
2
1
1
0
1
0
0
0
0
0
0
2
0
2
0
1
2
0
0
1
0
2
1
0
2
0
1
3
0
3
0
0
0
2
0
2
1
0
1
0
0
0
3
0
2
1
0
0
2
1
1
1
0
1
0
0
1
2
1
1
0
1
1
2
0
1
2
2
1
2
1
2
1
0
2
2
2
0
1
1
1
1
0
1
0
1
0
0
0
1
2
3
0
0
2
0
1
0
0
0
1
2
0
0
0
1
1
0
2
0
1
0
0
0
1
1
2
1
1
0
1
0
0
2
3
3
1
0
0
2
1
2
0
0
0
1
2
0
0
0
1
1
0
1
1
0
0
0
1
2
0
3
1
1
0
1
0
2
0
0
1
0
0
1
0
1
0
1
0
0
1
0
2
0
2
0
0
2
1
1
0
0
1
1
0
0
0
0
2
1
0
0
0
0
1
0
1
1
0
0
2
2
1
0
0
1
0
2
0
0
1
2
1
1
0
0
3
0
0
0
0
4
1
1
1
0
2
2
1
0
1
0
1
0
0
1
0
0
0
0
3
2
2
1
1
0
1
0
2
0
0
0
0
0
2
1
0
1
2
2
0
0
1
2
0
2
0
0
0
0
1
1
0
2
2
0
0
0
0
0
2
2
2
0
0
0
1
6
0
0
0
0
1
0
1
0
2
2
1
0
5
0
1
0
0
0
0
7
2
0
0
2
0
1
1
0
0
1
2
0
0
1
2
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
1
2
0
0
2
1
0
2
1
0
2
0
0
0
3
0
0
5
1
2
1
1
2
0
0
3
1
1
0
1
1
0
2
1
0
1
1
1
0
2
0
1
1
1
0
0
1
0
1
0
0
1
0
2
0
2
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
2
2
0
0
2
2
0
0
1
1
0
0
1
0
1
0
2
2
1
0
2
0
2
2
0
1
0
0
1
3
1
2
2
2
0
2
0
1
0
0
1
0
1
0
1
0
1
1
0
2
2
2
1
0
0
2
2
1
0
1
1
0
0
1
0
2
1
2
0
2
0
1
0
0
2
1
1
1
1
1
0
2
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
2
0
0
2
0
1
1
0
0
0
0
0
1
0
2
0
0
0
1
0
0
1
3
2
0
0
0
2
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
1
0
0
0
1
1
0
2
2
1
1
0
0
1
0
0
0
1
0
2
4
1
1
0
0
1
0
0
3
0
0
0
2
0
2
1
0
2
0
0
0
3
0
3
1
0
2
1
1
0
1
4
1
0
0
0
0
0
0
2
1
2
1
1
0
1
1
0
1
0
0
2
2
0
0
2
1
2
0
0
0
1
0
0
0
4
0
0
0
3
0
0
0
0
2
1
0
0
1
2
0
2
0
0
0
2
1
0
0
0
1
2
0
0
0
2
0
0
0
2
1
2
1
0
0
0
0
2
1
0
2
1
1
0
0
1
0
1
1
1
1
0
0
1
0
2
1
2
0
1
0
1
0
1
0
2
0
0
1
1
2
0
0
0
2
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
1
2
2
1
0
2
2
1
0
0
1
0
0
2
0
1
0
1
2
0
0
2
2
2
0
0
1
0
1
0
1
0
0
2
2
0
0
1
0
1
1
0
2
0
2
0
0
2
0
0
0
1
0
1
1
0
1
1
2
0
0
2
2
1
2
2
2
0
0
0
2
1
0
0
0
0
1
2
1
2
1
1
2
2
0
0
0
2
2
3
0
0
0
0
0
2
4
0
0
1
1
2
0
0
0
2
0
4
2
0
2
2
0
0
1
0
0
2
0
2
0
0
1
1
3
0
1
1
0
2
0
2
0
1
0
0
0
0
0
1
0
0
0
1
1
1
1
1
0
0
0
0
2
0
1
1
1
3
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
4
0
1
2
0
1
2
0
1
0
0
0
2
2
2
2
0
0
3
0
0
0
0
2
1
0
0
2
2
2
0
1
1
0
2
2
0
1
1
0
2
2
1
0
1
0
0
1
0
0
0
2
4
0
1
1
2
0
1
2
0
0
0
0
0
0
2
0
1
1
0
1
3
0
0
0
0
2
0
1
0
0
3
0
2
0
1
0
0
0
0
2
0
2
1
2
0
2
0
1
1
1
1
0
0
1
0
1
2
0
2
1
0
0
2
2
0
0
2
0
0
2
1
0
0
1
0
0
0
2
1
3
0
1
1
2
1
2
1
2
2
2
0
0
2
2
2
0
1
0
2
1
0
2
0
0
0
2
2
0
0
0
2
2
1
2
2
0
0
0
2
1
0
0
0
0
1
1
0
3
0
2
1
2
0
0
0
1
2
0
2
1
0
0
0
2
0
1
0
1
1
2
0
1
0
0
0
0
0
0
1
0
1
1
2
2
0
1
1
0
2
1
1
0
1
1
0
0
0
1
1
0
2
2
0
0
1
1
1
1
1
2
3
0
0
0
0
1
2
0
0
0
1
0
1
0
0
0
1
1
0
2
2
0
0
0
2
1
1
0
0
5
1
1
2
2
1
1
0
0
0
0
2
1
0
2
0
0
2
0
1
0
0
0
0
1
1
2
1
1
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
1
0
2
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
1
1
2
1
0
0
1
1
0
0
0
1
0
0
0
1
1
0
0
0
0
1
1
0
2
2
0
1
1
1
0
0
1
0
2
1
2
2
0
0
0
2
2
3
0
0
0
0
2
1
0
0
0
2
0
0
0
0
2
0
0
2
2
2
2
1
1
1
0
1
0
1
1
0
1
1
1
0
0
0
2
0
0
1
0
0
0
0
0
1
2
2
2
0
1
0
0
3
0
0
1
2
1
1
0
0
2
1
1
0
2
0
2
2
0
1
0
1
0
2
0
1
0
0
1
0
0
0
1
1
1
1
2
0
1
1
1
1
1
1
2
2
0
0
1
2
1
1
1
2
0
1
1
1
0
0
0
1
2
0
1
0
1
2
1
2
0
1
0
0
2
2
2
0
2
0
1
1
2
0
2
2
0
1
2
0
1
0
1
0
0
0
2
0
0
0
1
0
1
2
1
0
2
0
1
0
0
1
0
2
0
0
2
1
0
0
1
0
0
1
1
1
2
1
0
1
0
1
0
1
0
1
1
0
1
1
0
0
0
0
2
1
1
0
0
0
0
2
1
1
1
2
1
2
2
2
0
0
0
0
0
0
1
1
0
0
1
1
0
1
0
0
1
0
0
0
1
0
0
2
0
6
1
0
2
1
2
2
2
0
0
0
0
0
1
2
1
1
2
1
1
0
1
0
0
0
0
2
0
0
1
1
0
0
2
0
0
1
2
1
0
0
1
0
2
0
0
0
1
2
2
0
2
0
0
2
0
0
0
2
2
1
0
0
1
0
0
1
0
0
2
2
2
0
0
1
2
0
0
2
2
0
0
0
2
0
1
0
2
0
2
1
0
0
0
1
0
1
0
1
0
0
1
0
1
1
0
1
2
0
0
2
2
1
0
1
0
1
0
2
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
2
0
2
1
1
0
2
2
0
0
1
0
0
0
2
1
0
1
1
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
2
0
1
1
1
1
0
1
2
0
0
2
0
1
0
1
2
2
0
1
0
0
0
1
1
1
1
2
0
1
0
1
0
0
0
0
1
2
2
0
0
1
0
1
1
2
1
0
0
1
1
1
0
0
0
2
1
2
1
0
0
1
0
1
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
3
2
0
0
3
0
0
0
0
0
0
0
2
0
1
0
1
1
1
2
0
1
3
3
0
0
2
1
1
2
0
2
0
2
0
0
0
0
0
1
0
0
1
1
0
1
1
1
0
1
0
2
3
0
1
1
1
2
1
0
0
2
0
0
3
0
0
2
3
0
0
0
1
1
0
1
1
1
0
0
0
1
0
1
1
1
0
0
0
2
0
2
2
0
0
0
1
2
2
2
2
1
0
0
1
0
2
1
0
6
0
0
1
0
0
0
1
0
0
1
1
1
1
0
2
0
0
1
0
2
1
1
1
0
1
1
4
2
0
1
0
0
1
0
1
1
0
2
1
2
1
2
0
2
0
2
0
0
1
0
0
0
2
1
0
0
1
2
0
0
1
1
1
2
0
0
0
1
0
0
0
0
2
0
1
1
0
1
2
2
2
0
1
0
2
3
2
0
1
0
1
2
0
0
2
0
5
0
1
0
0
1
1
0
1
3
3
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
1
1
1
0
3
1
0
0
2
0
0
3
1
0
0
0
1
0
0
0
1
1
2
0
4
0
0
0
0
0
1
1
0
1
0
0
2
1
1
0
1
0
1
0
0
0
2
0
2
0
2
2
0
2
0
2
0
0
1
1
2
0
1
2
0
0
0
0
2
2
1
2
1
0
0
0
0
0
1
0
1
1
0
1
1
2
0
1
0
0
0
0
2
0
3
1
1
0
1
0
1
2
1
2
0
0
2
2
0
1
2
1
0
1
1
0
1
0
1
2
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
1
0
0
0
1
0
1
0
1
1
0
0
1
0
0
2
0
0
0
1
0
0
2
2
0
2
2
2
0
0
1
0
1
1
0
2
1
0
2
0
0
0
1
1
0
0
1
0
2
0
1
0
1
0
0
0
1
2
4
2
0
1
1
0
1
1
2
0
0
0
1
1
0
0
0
0
2
1
0
2
1
0
0
2
0
1
1
0
0
0
2
0
3
1
0
1
0
2
1
1
0
0
0
2
1
0
1
2
2
0
2
0
1
2
0
0
0
0
0
2
1
1
1
2
1
0
0
0
2
3
1
0
0
2
0
1
0
0
2
2
0
0
0
2
0
0
0
0
0
0
2
2
2
0
0
2
0
0
0
0
1
0
0
1
0
2
0
1
0
1
1
0
6
1
0
1
0
0
0
2
0
0
0
0
1
2
0
2
1
0
1
2
1
0
0
2
0
0
2
0
1
2
2
0
1
1
2
1
0
0
1
0
0
2
1
0
1
1
2
0
0
1
1
0
0
0
1
1
0
0
0
1
1
0
1
0
1
0
0
0
1
0
0
2
1
2
0
0
0
0
1
0
1
0
0
2
0
0
0
2
1
2
0
1
1
0
1
2
0
1
1
0
0
2
2
2
1
0
0
0
0
0
1
0
0
2
0
0
2
1
1
1
1
0
0
1
0
1
1
2
0
1
1
2
2
0
2
1
0
1
1
2
0
0
0
0
0
1
1
2
1
1
1
0
0
0
2
0
0
1
1
1
0
0
0
1
0
0
0
0
0
2
2
2
1
0
0
1
1
0
2
0
0
3
0
0
2
0
1
0
0
0
1
0
0
0
0
0
2
0
0
1
0
1
1
2
0
0
3
0
0
4
0
0
0
1
3
1
0
2
0
0
4
0
0
1
0
2
0
0
0
0
0
0
1
2
0
1
0
1
1
0
2
0
0
1
2
0
0
1
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
2
0
2
2
0
1
0
0
3
0
0
1
1
0
2
0
0
0
0
2
0
2
0
0
1
0
0
1
1
1
1
0
2
1
0
0
0
0
2
0
1
0
0
2
2
0
1
0
1
0
2
1
0
0
1
1
1
0
0
2
1
0
0
0
0
0
0
0
0
2
0
1
1
1
1
2
0
1
0
0
1
1
2
1
0
0
0
0
1
2
0
1
1
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
1
2
2
0
1
1
2
2
0
1
1
0
0
0
2
1
1
1
2
1
1
1
0
1
1
2
0
0
0
0
0
1
2
4
2
0
1
0
0
0
0
2
0
0
2
1
0
1
0
1
0
0
1
0
1
5
0
0
0
0
0
2
1
0
0
0
0
3
0
2
0
0
1
2
1
2
0
0
2
2
1
0
2
0
0
0
0
0
1
2
1
2
0
1
0
1
0
0
2
0
0
1
5
1
1
1
0
2
1
1
0
0
2
0
2
0
1
3
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
1
2
0
0
1
0
0
2
1
0
2
1
0
0
1
1
2
0
0
0
1
1
0
0
1
2
0
0
0
3
0
1
0
1
0
2
1
0
0
0
1
2
2
2
0
1
2
0
0
0
2
1
0
0
0
1
1
1
0
0
2
0
1
0
1
0
1
2
0
1
2
1
1
0
2
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
2
0
1
0
1
0
0
0
0
0
0
1
1
0
0
1
1
1
0
0
2
0
2
2
0
1
1
1
2
1
2
0
2
0
0
1
2
0
0
0
1
2
0
0
1
0
1
1
0
0
0
0
0
0
10
0
0
1
3
1
1
1
0
0
1
0
2
0
0
0
0
2
0
0
1
0
0
1
0
1
1
1
0
0
2
2
1
0
1
2
0
1
0
1
0
3
0
0
0
2
1
1
1
1
2
0
2
2
0
1
2
2
0
0
0
1
2
1
0
0
2
2
1
0
0
0
1
0
0
0
1
1
2
0
0
2
1
2
2
0
1
0
0
0
2
0
0
0
0
0
2
1
2
0
0
2
0
1
0
0
1
2
0
0
0
0
0
2
0
2
2
0
0
0
0
1
0
0
1
0
0
1
2
1
0
0
2
1
0
2
1
2
2
1
3
0
1
0
2
0
0
0
0
1
0
0
1
0
1
0
1
0
1
0
1
2
0
2
1
1
0
0
1
0
1
1
1
0
1
2
0
0
0
1
1
1
1
1
1
0
0
2
0
1
0
1
2
0
0
0
2
0
2
1
0
0
0
0
1
1
0
1
1
0
0
0
1
1
7
0
2
0
0
2
1
1
0
0
1
1
1
2
2
1
0
0
1
0
1
1
1
1
1
1
0
0
0
1
0
2
2
2
0
2
1
1
0
0
2
1
0
0
1
2
0
2
1
0
0
0
2
1
1
0
0
0
1
0
1
2
1
1
0
0
0
2
2
0
1
2
2
0
0
0
2
1
1
0
2
1
0
2
0
2
1
1
2
0
1
0
2
0
1
0
0
1
0
0
0
1
2
0
0
0
2
1
0
1
1
0
0
2
2
2
2
0
1
0
0
2
1
2
1
0
1
1
0
2
1
1
0
1
1
1
1
0
2
0
0
0
0
1
2
1
1
0
0
2
2
0
0
0
0
2
0
1
0
2
1
1
1
0
0
1
0
0
0
0
1
0
2
0
0
0
1
2
0
0
6
2
1
1
1
0
0
1
0
2
0
0
0
1
0
2
3
0
2
1
1
0
2
1
0
0
2
0
1
1
1
0
1
1
1
1
0
1
1
1
1
0
0
2
0
1
0
0
1
2
0
0
0
2
0
1
0
1
0
0
1
2
0
0
0
0
1
1
1
0
2
1
0
2
1
0
1
1
2
1
1
0
0
0
1
0
1
0
1
1
1
0
2
1
0
2
1
1
0
1
0
0
2
2
1
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
1
0
0
0
1
1
3
2
2
1
0
0
1
0
0
2
0
2
0
1
1
0
2
2
0
0
1
3
1
2
1
0
0
2
2
1
1
0
4
0
0
1
2
1
0
1
0
0
2
0
1
0
0
0
3
0
0
2
0
2
0
1
0
0
2
0
0
2
0
0
2
0
1
2
0
0
2
0
1
0
0
1
1
4
0
0
0
1
0
1
1
1
0
0
2
0
1
1
2
2
2
0
0
2
0
1
1
0
0
0
0
0
2
1
0
1
0
0
1
0
0
1
2
0
1
1
0
2
1
1
2
2
0
0
0
2
0
1
2
0
0
2
1
0
1
1
1
1
2
1
2
0
2
1
0
1
1
0
1
4
0
2
1
0
2
0
0
0
1
1
0
0
2
0
1
1
1
0
1
1
2
1
0
2
1
1
0
0
2
2
0
0
0
0
0
1
0
1
1
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
2
1
1
1
0
1
0
0
2
2
2
2
1
0
0
1
2
1
3
0
0
0
0
0
1
1
0
2
2
1
1
0
1
2
0
0
1
0
0
0
1
0
2
0
0
1
2
0
2
1
1
1
1
0
2
0
1
0
0
0
1
2
0
1
1
2
2
2
1
2
0
1
1
0
1
0
1
2
0
0
0
0
0
1
0
1
1
2
1
1
0
0
1
1
0
1
2
1
2
1
2
0
2
0
0
1
1
0
2
1
0
0
0
0
0
1
1
0
0
0
0
2
0
2
2
1
0
0
1
1
0
0
2
2
0
0
1
0
0
1
0
0
0
0
0
1
0
2
1
0
2
0
1
1
1
0
0
2
1
0
2
1
2
4
0
3
2
1
0
1
0
0
0
1
2
2
1
0
2
2
0
0
0
0
2
3
0
2
0
0
0
1
0
2
0
0
0
1
1
0
1
1
0
1
0
0
0
1
0
0
1
0
2
0
0
1
0
0
2
0
1
1
1
2
1
0
0
1
0
0
1
0
2
0
0
2
1
1
0
1
0
1
1
1
0
1
1
0
0
1
2
0
0
1
0
0
2
0
0
0
0
1
0
2
0
0
0
1
1
2
2
1
0
2
0
0
3
1
2
0
0
2
0
1
0
1
1
1
1
1
1
0
1
0
0
0
0
0
0
0
1
1
0
0
1
2
0
1
2
0
2
2
0
1
0
0
1
0
1
1
0
0
0
2
1
2
0
0
2
1
0
0
0
1
2
0
2
1
1
1
0
0
1
0
0
1
0
0
0
0
1
2
1
2
1
1
1
2
1
0
1
0
2
0
0
2
2
1
1
0
2
0
1
0
0
0
2
2
0
1
0
0
0
0
0
1
1
0
0
1
1
0
1
1
0
0
0
0
0
1
0
0
0
1
2
3
0
2
0
2
1
0
1
0
1
1
2
0
0
2
0
0
1
0
2
0
1
1
0
0
1
0
1
0
1
1
0
0
1
2
1
1
0
0
1
0
0
0
0
0
0
1
1
1
0
1
0
2
0
0
1
1
0
1
0
0
0
0
0
2
0
2
2
2
2
1
0
2
2
0
0
2
0
1
1
0
0
0
0
0
0
2
0
1
1
1
1
0
1
0
1
0
1
1
0
2
2
0
0
2
1
1
0
0
1
1
0
1
0
1
0
2
0
1
0
1
1
2
2
0
0
1
1
0
0
1
0
0
3
2
1
0
0
2
2
2
2
1
1
1
1
2
2
2
2
0
1
2
1
0
0
1
2
0
1
2
1
0
2
0
0
0
1
0
0
0
2
0
1
0
1
0
1
1
1
2
2
1
0
1
1
1
0
0
1
0
1
0
1
1
2
1
0
2
1
0
0
1
0
0
2
0
0
2
0
1
0
1
3
1
1
1
0
3
1
0
1
1
0
0
0
0
2
2
2
4
0
0
0
0
0
2
1
0
0
0
1
1
0
0
0
2
0
0
0
0
0
2
1
1
0
0
0
1
2
1
0
0
0
0
1
2
0
3
2
1
2
1
0
0
0
0
1
1
0
2
0
1
2
2
2
0
1
0
2
0
0
2
1
1
2
4
0
2
0
3
0
2
0
1
1
0
0
0
0
1
2
0
1
0
2
1
0
1
0
2
0
2
1
3
0
1
2
2
1
1
1
0
0
0
1
0
0
0
2
0
1
0
1
0
0
2
0
0
0
2
0
0
1
0
2
0
0
0
2
0
0
1
1
0
1
2
0
0
0
2
1
0
0
1
1
0
0
0
2
1
2
1
1
1
0
2
0
0
2
3
0
0
0
2
1
1
1
2
1
1
0
0
0
0
2
2
0
1
2
2
0
0
1
2
0
0
1
0
0
0
0
2
2
0
0
0
0
2
0
1
1
1
0
1
1
2
0
0
0
0
0
0
2
1
1
0
0
0
0
1
1
0
1
2
2
0
2
0
1
0
1
1
1
0
1
1
0
1
2
2
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
2
0
0
0
0
1
1
0
0
2
2
0
0
1
2
0
2
0
1
0
2
0
0
1
0
0
1
0
1
0
0
2
0
0
2
1
0
1
0
1
0
2
1
2
0
0
5
0
0
1
1
0
2
0
1
0
1
2
1
3
1
1
1
1
0
0
2
0
1
0
1
0
0
0
2
0
1
0
1
0
2
1
0
2
1
1
1
1
0
0
0
1
0
2
0
0
1
1
0
0
2
0
0
0
1
1
1
0
0
1
3
1
0
0
0
1
1
0
0
2
1
2
1
1
1
0
1
0
0
0
0
0
1
1
0
1
0
0
1
1
0
0
0
0
0
2
1
1
3
0
2
0
0
2
2
1
0
1
2
0
3
0
1
0
1
0
1
1
0
1
2
2
0
1
1
2
2
0
0
1
1
0
0
1
0
1
1
2
1
0
0
0
1
2
1
1
2
1
0
1
2
1
1
0
2
0
2
0
0
0
1
0
1
1
2
0
1
0
2
1
2
0
1
1
0
0
1
1
0
1
0
1
0
1
1
0
1
2
1
0
0
0
1
2
2
0
3
1
1
0
1
0
0
2
0
0
0
0
1
2
0
1
1
0
0
0
2
2
0
1
0
0
0
1
0
1
0
0
0
1
1
1
1
0
0
0
2
2
0
1
1
1
0
2
0
0
0
0
0
2
0
2
0
1
0
1
0
0
0
0
2
1
1
1
2
0
1
1
0
0
2
0
1
0
0
1
0
1
1
0
0
0
3
0
0
1
0
1
1
1
2
2
0
0
0
0
1
1
0
0
0
0
2
0
1
2
1
1
1
1
1
1
0
0
0
2
0
0
0
1
1
2
1
0
2
0
1
0
0
3
0
1
3
0
1
1
0
1
0
0
1
2
0
0
2
1
1
0
1
0
2
2
1
2
1
1
0
0
2
0
1
1
0
0
1
1
2
1
1
0
0
0
2
0
0
0
1
0
0
0
0
1
1
0
1
0
0
1
0
2
0
2
1
2
1
1
2
1
0
1
0
0
0
0
0
0
0
2
1
2
1
1
0
2
1
0
2
0
0
2
0
2
2
0
1
1
0
1
0
0
1
0
2
0
1
0
2
1
2
2
0
1
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
2
2
0
3
0
1
0
1
0
1
1
0
1
1
0
0
0
2
0
0
2
0
2
1
0
0
0
2
1
0
0
2
3
1
0
1
0
2
2
0
1
0
0
1
2
0
1
0
2
2
1
2
0
1
2
0
2
0
0
0
0
0
1
0
0
0
0
1
1
0
2
0
0
0
0
1
0
0
1
0
2
2
0
0
5
0
0
1
1
2
1
2
3
1
2
2
2
0
3
1
0
0
0
1
2
0
0
2
2
0
1
0
1
0
0
0
1
0
0
0
2
2
1
2
1
0
2
0
0
0
1
2
0
2
2
0
1
2
0
1
0
1
2
0
3
2
0
1
1
0
1
1
0
1
0
2
1
2
1
0
1
0
3
1
0
1
0
1
0
0
0
1
0
0
2
0
0
1
0
0
0
1
0
1
1
0
1
1
0
0
0
4
8
1
0
0
1
0
1
2
0
0
1
0
1
2
1
0
0
0
0
2
1
1
0
0
0
0
0
1
1
0
2
1
2
0
1
0
1
0
1
0
0
0
1
6
2
1
0
2
1
1
1
2
0
1
0
0
2
0
1
2
0
0
0
0
3
0
0
2
1
1
0
1
0
0
2
0
1
0
1
0
1
2
0
1
0
1
0
0
1
1
0
2
0
2
1
1
0
0
0
1
0
0
0
2
2
0
2
1
2
1
0
1
0
0
0
1
4
1
0
0
1
1
0
2
0
0
1
0
2
1
1
0
2
1
1
2
2
0
0
0
2
2
1
2
0
0
0
0
1
1
1
0
2
0
0
0
0
1
0
0
2
2
0
2
0
0
1
0
1
2
1
0
1
0
1
0
1
2
0
0
2
0
0
0
2
2
0
0
2
0
0
0
2
0
0
0
0
1
1
2
0
0
2
0
2
1
0
0
0
0
0
1
2
2
2
1
1
0
0
0
0
2
0
1
1
2
1
1
2
0
2
0
0
0
2
2
0
2
2
2
1
0
0
0
1
2
0
2
0
1
0
1
0
0
1
0
1
7
0
1
0
1
3
1
1
2
2
1
1
0
2
2
1
0
1
0
0
0
0
0
0
0
2
0
0
0
2
2
1
0
0
2
0
0
1
0
2
0
0
1
1
1
0
0
0
3
0
1
0
1
0
2
2
0
0
1
0
1
0
0
0
0
2
0
1
0
0
0
0
0
2
1
0
2
0
0
0
1
0
0
0
2
1
2
0
0
0
1
0
2
0
0
3
2
1
1
1
1
0
3
2
0
2
2
0
0
0
1
2
0
0
1
0
2
1
0
0
0
0
2
0
1
1
7
0
1
0
1
1
2
3
0
1
0
2
1
0
1
0
2
0
1
0
2
2
0
1
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
2
2
0
0
0
0
0
2
0
0
1
1
0
2
0
0
1
0
2
2
1
2
2
1
1
1
0
1
8
0
2
0
1
1
0
0
1
0
2
0
0
0
2
2
1
2
1
0
1
0
1
0
0
0
0
2
0
0
1
1
1
0
1
0
1
1
0
1
0
1
0
1
0
0
0
1
0
0
0
2
1
1
0
0
1
1
0
0
0
2
0
0
2
0
1
1
0
0
0
0
2
0
0
1
1
0
1
1
0
0
0
0
0
1
1
1
1
0
2
0
0
1
2
0
0
2
0
0
1
0
1
1
1
0
0
0
2
3
2
2
0
1
0
0
0
0
0
2
1
1
2
0
0
1
1
2
0
0
0
0
0
0
1
2
1
0
1
0
1
1
0
2
1
0
0
1
0
0
0
1
1
2
1
0
0
0
1
0
0
1
1
0
0
1
0
0
1
0
1
1
2
0
1
1
2
1
0
0
1
0
0
0
0
0
2
1
1
1
1
1
1
1
1
2
0
2
1
1
0
0
2
0
0
0
1
0
1
1
1
0
1
0
0
2
2
0
0
0
0
2
0
1
0
2
1
0
2
1
0
1
1
0
1
0
1
1
0
1
0
0
2
0
2
0
2
0
0
1
2
1
0
0
0
1
0
1
1
2
0
2
0
0
0
0
1
0
0
1
2
0
0
1
2
0
0
0
1
5
2
3
1
0
1
1
0
1
1
2
0
0
0
0
0
0
0
1
1
2
0
0
1
1
1
1
1
1
2
1
3
0
0
0
0
0
0
1
1
0
2
1
0
1
0
0
2
0
2
0
0
0
0
0
2
2
2
2
1
0
0
1
1
0
2
0
0
1
0
0
1
0
0
0
2
0
0
2
2
1
0
0
0
0
0
0
0
1
0
0
2
2
0
0
1
0
1
0
0
0
0
0
0
1
0
0
2
0
1
1
0
1
1
0
1
1
0
0
3
0
1
2
0
1
0
2
1
0
2
0
1
1
2
0
1
1
0
0
0
0
0
0
0
0
0
0
1
4
1
2
0
1
1
2
0
2
2
0
0
1
2
0
1
2
1
0
0
1
0
1
1
2
2
1
1
0
2
0
1
0
0
1
0
1
0
1
0
2
0
0
0
0
0
1
0
1
0
1
0
0
1
3
2
2
1
1
0
0
1
0
0
2
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
2
0
0
0
1
0
1
0
0
2
0
0
2
2
0
1
2
0
0
2
2
0
1
1
0
1
0
0
1
1
2
0
0
0
0
1
2
2
0
0
2
1
1
0
1
0
0
2
0
0
1
0
2
0
0
2
0
2
0
0
2
0
1
0
2
3
0
1
0
0
2
0
0
0
0
0
2
0
2
0
1
1
0
2
0
1
1
1
1
0
0
3
0
2
0
1
1
1
0
0
0
0
2
2
0
2
1
0
0
2
1
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
2
2
2
0
1
0
1
0
0
0
0
0
0
1
1
2
0
0
0
0
1
1
0
2
0
0
1
0
1
2
2
1
1
0
3
1
0
2
0
1
1
1
0
1
0
0
0
2
0
0
1
1
0
1
0
1
2
2
1
2
1
0
0
1
1
1
5
0
1
1
3
0
0
2
1
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
2
0
1
0
0
1
1
2
2
1
1
0
1
0
0
5
2
1
1
2
0
0
0
0
1
0
1
2
1
0
1
0
1
1
0
1
2
2
0
2
0
1
0
1
2
1
1
1
1
1
1
2
1
0
0
1
0
0
1
1
3
1
0
0
1
1
2
3
0
0
2
0
0
0
2
2
0
0
0
0
1
0
0
1
1
0
1
0
0
0
1
1
1
2
0
1
1
1
0
1
1
2
1
1
0
1
2
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
2
0
3
2
0
1
2
0
1
1
1
2
2
2
0
1
0
1
1
3
0
0
0
0
0
0
1
1
2
2
0
0
0
1
1
2
0
0
1
2
2
4
0
1
1
0
2
1
1
0
1
0
2
0
0
1
1
0
2
0
0
1
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
2
0
0
0
2
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
2
0
2
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
1
2
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
2
2
0
1
1
0
1
0
2
0
1
2
2
1
2
0
0
0
1
0
0
1
0
2
0
1
1
0
1
2
1
0
0
2
0
2
1
0
0
3
0
2
0
0
0
0
2
1
0
0
1
0
0
0
2
0
0
0
0
0
0
1
1
2
0
1
0
2
0
0
1
2
0
0
1
0
0
1
1
0
2
0
0
0
1
0
1
0
0
2
0
2
1
3
0
3
0
0
1
2
4
1
2
0
0
1
0
2
1
2
1
0
2
0
0
2
2
0
0
1
1
0
0
2
0
1
1
1
0
0
1
3
0
0
0
2
1
0
4
2
0
0
0
0
0
4
2
1
0
0
1
1
0
0
1
1
1
0
1
3
2
0
2
2
1
0
0
0
3
0
2
0
2
2
1
0
0
0
0
1
0
0
0
1
3
0
0
0
0
0
1
1
1
0
2
0
0
0
1
0
0
2
0
1
2
2
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
3
2
1
0
0
0
2
0
1
1
0
0
1
0
2
0
0
0
0
0
2
1
0
0
0
1
2
1
2
0
0
0
0
1
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
1
1
0
2
1
0
0
1
1
0
0
0
2
1
1
0
0
1
0
1
0
0
0
2
2
1
0
2
1
2
1
0
0
1
0
0
0
0
0
1
0
1
0
1
2
0
1
0
0
2
11
1
0
0
1
1
1
0
0
1
1
1
1
0
1
2
0
1
1
1
0
1
2
0
0
0
1
0
1
2
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
2
2
0
2
1
0
0
0
0
2
2
0
2
1
0
2
0
0
1
0
2
2
0
2
1
0
0
2
1
1
0
1
0
0
1
2
0
0
0
1
0
1
0
0
0
0
1
0
3
0
1
1
0
0
0
0
0
1
1
0
2
0
1
0
0
0
1
3
0
1
1
2
6
0
0
1
0
1
0
0
0
1
1
1
0
1
0
0
1
1
1
0
2
1
0
1
2
2
0
1
1
0
0
0
1
0
1
0
0
4
2
1
1
1
0
3
1
0
1
1
1
1
1
0
2
1
0
0
0
2
0
0
2
0
0
1
0
0
0
0
1
0
0
1
1
0
2
0
0
1
1
0
0
1
2
0
0
0
0
0
0
0
2
0
1
2
0
0
0
2
3
3
0
0
2
1
0
0
0
0
1
1
0
1
0
2
1
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
2
2
1
0
1
2
0
0
2
0
1
2
2
0
1
1
1
0
1
0
0
2
0
0
1
0
0
0
0
0
2
2
0
1
0
0
0
0
1
3
0
0
0
1
1
0
0
0
3
1
2
1
0
3
0
1
1
1
1
0
1
1
1
1
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
1
0
0
0
2
0
3
1
0
0
1
1
2
1
0
0
0
1
1
2
0
0
1
1
1
0
0
0
0
2
2
0
0
0
1
0
1
0
1
2
1
0
0
1
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
1
0
0
0
1
2
2
2
1
0
0
0
1
1
1
0
1
2
0
0
0
0
1
1
0
1
1
0
1
2
1
2
2
1
1
2
0
0
2
1
0
1
0
0
1
0
1
0
0
0
0
2
1
0
1
0
0
0
1
0
1
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
1
0
2
1
0
0
0
0
0
1
0
1
0
0
1
0
2
0
0
0
1
0
2
1
0
0
2
0
2
1
0
2
0
0
1
1
1
2
2
0
0
2
0
2
2
2
1
2
3
1
2
0
1
1
1
1
0
1
1
1
1
0
2
1
1
1
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
2
0
1
0
1
0
0
1
1
2
0
3
0
3
0
0
0
3
0
1
2
2
1
1
1
1
1
0
1
1
0
1
0
1
2
0
1
0
0
0
0
0
0
1
0
0
0
0
2
2
1
2
2
2
0
2
2
0
2
2
0
0
0
1
0
1
0
0
0
3
0
0
2
2
3
2
0
0
2
0
0
1
0
1
0
2
0
1
0
2
0
0
1
0
0
0
2
1
0
0
1
0
0
2
0
0
0
0
1
0
0
0
2
0
1
0
1
0
1
0
0
0
0
1
2
0
0
2
2
1
1
0
2
2
1
0
1
0
1
0
0
1
2
1
1
2
2
1
0
1
0
2
0
0
1
0
0
2
0
0
1
1
0
2
0
0
0
1
1
1
0
2
1
0
2
0
1
1
0
1
0
0
0
2
1
2
0
1
0
1
2
1
0
2
0
0
0
1
1
2
1
0
0
1
0
2
1
2
0
0
0
1
1
0
0
2
0
0
1
1
2
0
0
1
2
1
0
2
0
3
0
0
1
0
0
0
2
0
2
2
1
0
1
0
1
2
2
1
0
7
0
1
0
2
2
0
0
0
1
0
2
1
0
1
1
0
0
2
0
0
1
2
0
0
2
2
1
0
0
0
2
0
2
0
1
1
1
2
0
1
1
0
0
2
2
1
0
2
1
2
0
2
2
1
0
0
0
2
0
1
0
2
0
1
1
1
3
0
2
1
0
0
1
2
3
0
1
2
0
0
0
0
0
2
0
0
0
1
0
0
2
0
1
0
1
1
1
0
0
2
1
1
0
1
0
0
1
0
1
0
1
0
0
5
1
0
1
1
1
1
1
0
0
0
1
1
1
2
0
0
0
1
1
0
2
0
1
1
0
0
0
1
0
0
0
3
2
0
0
0
0
2
2
0
1
1
2
0
0
1
1
1
0
0
2
0
0
0
1
0
0
2
0
2
3
1
0
0
1
0
0
1
1
0
0
0
2
0
1
1
0
0
1
0
0
1
1
0
2
0
1
0
1
1
0
2
0
2
1
1
0
0
0
0
0
0
0
1
0
1
2
2
2
1
2
0
0
2
1
0
0
0
0
0
0
2
1
0
0
1
1
2
0
0
0
0
0
1
2
2
1
1
0
0
0
1
0
0
0
0
0
0
2
0
1
2
1
0
0
0
0
1
1
1
0
2
1
1
2
2
1
0
1
0
2
0
0
0
2
0
0
1
2
2
0
1
0
2
0
1
0
2
0
0
1
2
0
1
1
2
0
0
0
2
0
0
2
0
1
1
0
1
1
2
0
0
0
1
1
0
1
0
1
1
0
2
0
0
2
1
0
2
0
0
0
2
2
1
1
1
0
2
0
1
0
3
1
3
2
0
2
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
2
0
1
1
1
1
1
0
0
0
1
2
0
0
2
2
2
1
1
0
0
0
0
0
0
0
0
1
0
1
0
1
2
0
0
0
0
0
1
2
0
2
1
2
0
1
0
0
0
0
2
1
2
2
1
0
0
1
2
0
0
1
0
1
0
0
1
0
1
2
1
1
2
2
0
0
1
0
2
0
0
0
1
0
0
2
0
0
0
2
0
0
1
0
2
1
0
0
0
0
2
2
2
0
1
0
0
2
0
1
0
1
0
2
0
1
2
2
0
3
0
1
0
0
1
1
2
2
0
2
0
0
1
4
0
0
0
0
0
0
0
3
0
2
3
0
1
0
0
2
0
0
1
1
2
2
1
0
0
1
1
0
2
2
0
2
1
0
0
1
1
1
0
0
2
0
1
0
1
0
0
1
0
0
2
0
0
0
0
0
1
1
0
1
1
4
1
2
0
0
1
1
1
0
1
0
2
1
1
0
0
0
3
2
2
0
1
0
0
0
0
1
0
0
2
0
0
2
0
1
0
1
0
0
0
1
2
0
0
0
1
2
1
1
0
1
1
0
0
1
0
0
2
3
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
1
1
0
0
0
3
1
3
0
1
1
2
1
2
1
3
1
2
0
2
1
1
0
1
0
0
0
1
1
0
0
1
0
0
1
1
2
0
1
0
0
5
0
2
0
0
2
0
0
1
2
1
1
0
1
0
0
0
0
2
0
0
0
0
1
1
2
2
0
0
1
0
0
1
2
0
0
2
2
0
0
1
0
0
0
1
0
1
1
0
0
0
2
1
1
0
3
0
2
0
1
1
0
2
2
0
0
0
2
0
0
2
0
2
2
2
0
0
1
1
0
0
0
0
1
0
2
2
0
0
0
1
1
0
1
0
0
2
2
0
2
1
2
2
0
1
0
0
2
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
3
1
3
0
0
1
2
0
0
1
0
0
0
0
2
2
1
1
3
0
0
0
0
0
2
0
0
1
2
2
0
1
1
0
0
1
0
0
0
0
2
1
2
0
0
0
2
0
2
1
0
0
1
0
0
2
0
0
0
1
1
3
0
0
0
0
0
0
2
2
1
0
1
0
1
1
1
0
0
0
0
1
1
0
2
0
0
1
1
3
1
1
0
0
1
0
0
1
0
2
1
0
0
0
1
0
0
0
0
0
2
1
2
0
1
2
0
2
0
0
1
10
1
1
1
1
0
2
0
1
1
0
1
0
0
2
0
2
0
0
0
2
1
1
0
0
2
2
2
0
1
0
0
0
0
0
0
1
0
1
1
0
2
0
1
0
0
0
0
3
2
0
1
1
0
1
2
4
0
0
1
1
2
0
2
2
0
2
0
0
0
1
0
0
1
0
2
2
1
0
0
2
1
0
2
1
0
0
0
2
0
1
1
0
0
0
1
2
0
1
0
1
1
1
0
2
1
1
2
2
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
1
1
0
1
1
2
0
0
2
1
2
1
0
0
0
1
0
2
2
0
0
1
2
0
0
0
2
0
0
1
0
1
2
0
0
1
1
0
1
1
1
0
0
0
0
1
0
0
2
0
2
1
0
0
2
1
2
0
0
1
2
0
0
2
1
2
2
1
0
1
0
1
3
1
3
0
2
2
0
1
0
0
0
2
0
2
0
1
2
0
0
2
5
1
2
2
1
0
2
2
1
1
0
1
0
1
0
0
2
2
0
2
0
0
0
1
2
2
0
1
0
0
0
2
2
1
1
0
0
0
0
2
1
1
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
1
1
2
1
0
1
1
2
1
1
0
0
0
1
0
0
2
2
0
1
2
2
1
0
2
1
0
1
0
1
1
1
2
1
0
1
0
1
1
2
1
1
0
1
0
0
0
1
0
1
0
1
2
0
7
0
0
1
2
0
1
0
0
0
2
0
1
2
3
0
0
1
1
2
1
0
2
0
1
2
0
1
1
0
2
0
0
2
2
2
1
0
1
1
0
1
0
0
1
0
0
2
0
0
1
1
2
2
0
2
0
0
2
0
0
6
2
0
1
2
3
0
0
0
0
1
2
1
0
1
1
0
2
2
0
2
2
2
2
2
1
1
0
0
1
1
1
0
0
0
1
2
0
1
0
2
2
1
2
0
1
1
2
2
0
1
2
0
0
1
2
0
1
0
1
2
0
0
0
0
0
1
0
1
0
1
0
1
0
2
0
2
0
0
1
2
0
0
2
2
0
2
0
0
0
0
2
2
0
0
0
0
2
2
1
1
1
1
0
1
0
1
1
2
0
1
1
0
0
0
0
1
0
2
1
0
1
1
0
1
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
2
0
1
2
0
0
0
1
2
1
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
1
0
2
0
0
1
2
2
0
3
0
0
0
3
0
1
0
2
2
2
0
0
2
0
0
0
0
0
0
2
0
1
0
1
0
1
0
2
0
1
2
1
0
0
2
0
0
0
1
0
2
1
2
0
0
0
1
2
0
2
1
0
1
1
1
2
2
1
0
1
0
2
0
0
2
1
1
0
1
0
1
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
1
1
0
0
0
1
1
0
0
0
2
2
1
0
1
0
2
0
2
1
0
0
2
0
0
2
0
1
0
0
0
1
0
0
0
0
1
0
2
1
0
0
0
2
0
1
1
1
2
2
1
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
1
1
1
1
1
0
0
0
1
1
0
1
2
1
0
2
2
0
0
1
0
2
1
1
2
1
2
0
1
1
0
0
0
2
1
2
1
1
0
1
2
1
0
0
0
0
1
0
0
0
2
3
0
0
2
2
0
1
0
0
0
0
1
1
1
1
2
1
0
1
0
0
1
1
1
0
0
2
0
2
1
0
2
0
2
1
1
1
0
0
0
0
2
1
1
1
0
1
1
0
0
0
1
0
1
1
1
1
0
0
2
1
0
1
0
1
2
2
0
0
0
1
0
1
2
1
0
2
2
0
1
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
1
2
2
0
0
1
0
2
0
0
0
0
0
2
1
1
0
0
0
0
1
1
2
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
1
2
0
0
2
0
2
0
1
1
1
0
1
2
1
0
0
1
1
1
3
2
0
1
0
1
0
2
0
0
1
1
0
1
0
1
2
0
1
2
2
1
2
1
0
0
0
0
0
0
0
1
0
1
1
1
1
1
3
1
1
0
0
1
0
1
0
1
1
0
0
1
0
0
1
2
2
1
0
3
1
0
1
2
1
0
2
0
0
0
0
0
2
1
1
0
1
1
0
1
0
0
1
0
0
1
0
1
0
4
2
1
0
1
1
0
0
0
0
2
1
0
0
0
1
2
1
1
0
0
0
2
2
1
0
1
0
2
0
0
1
2
2
1
0
1
0
2
1
2
1
2
0
1
0
0
1
0
0
2
0
0
2
0
3
0
2
3
0
0
1
1
0
0
0
0
2
1
2
1
0
0
2
0
1
0
1
1
0
3
0
2
0
2
2
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
1
0
0
1
1
1
1
0
0
2
0
1
0
1
1
0
1
0
0
2
0
0
2
1
1
0
0
0
0
1
0
0
1
0
3
1
2
0
2
0
0
0
0
2
1
1
0
0
1
2
0
0
0
0
1
2
0
0
1
1
0
2
1
2
1
2
1
2
0
0
2
0
2
1
2
0
0
1
0
1
0
2
0
0
1
0
1
0
2
1
0
0
2
0
1
0
2
1
2
2
0
0
1
0
0
1
2
1
1
1
2
0
0
0
1
1
1
2
2
1
1
2
0
0
1
2
0
0
1
1
0
0
0
0
2
0
1
2
1
1
0
0
0
1
1
2
1
0
3
0
1
1
1
1
1
2
1
0
1
2
1
0
0
1
4
2
1
2
0
0
1
2
1
2
0
3
1
0
0
1
1
0
3
0
1
0
1
0
1
1
0
0
0
1
0
2
1
2
0
1
2
3
2
0
2
0
0
0
0
0
0
0
1
0
1
2
0
2
1
1
2
0
0
0
1
0
0
0
3
3
2
1
0
0
0
0
0
0
5
0
0
1
1
2
0
0
1
2
2
1
0
0
1
2
0
1
0
0
1
1
1
1
0
1
0
0
1
1
1
0
0
2
3
0
0
1
0
2
1
0
0
0
2
0
2
0
1
0
1
0
2
2
2
0
1
0
2
0
0
0
0
0
1
2
1
0
0
0
3
0
0
0
0
0
2
2
1
1
0
0
0
3
0
0
2
4
2
1
1
1
3
2
1
0
0
2
0
3
1
1
0
2
2
0
0
0
1
1
2
1
1
1
0
0
0
0
1
0
1
0
2
0
2
0
0
0
3
0
0
0
0
1
0
1
0
0
0
1
1
2
1
1
1
0
1
2
0
1
0
0
3
0
1
0
0
0
0
1
1
0
0
1
0
2
0
1
1
0
2
1
1
0
0
1
0
0
0
1
2
0
2
1
1
0
1
1
1
0
0
3
0
0
2
2
2
3
0
0
2
0
2
0
0
0
0
0
1
5
2
0
0
1
2
1
0
1
2
0
0
0
0
0
0
2
0
2
0
2
0
0
0
1
0
2
1
0
0
0
1
0
0
2
0
0
0
1
1
2
0
0
2
0
1
2
2
0
0
2
0
0
0
0
2
1
2
0
0
0
2
1
0
0
0
0
2
5
0
1
2
1
1
2
1
1
0
0
0
0
2
0
0
0
0
0
1
2
2
2
0
1
0
1
2
0
0
1
0
0
0
0
1
1
1
1
1
1
0
0
2
0
4
0
0
2
0
0
0
0
1
0
0
0
1
0
2
1
1
0
1
2
0
0
1
1
0
1
1
0
1
1
0
0
0
2
1
0
2
1
0
1
2
0
4
0
0
0
0
2
0
0
0
1
1
1
2
0
1
0
2
1
3
0
0
0
0
1
0
1
0
0
1
0
1
0
1
2
0
1
0
0
0
2
1
0
0
1
1
1
0
1
0
0
2
2
1
1
2
1
0
1
1
1
2
0
0
2
0
2
2
1
0
0
1
0
0
0
0
1
1
0
1
0
2
2
0
0
1
1
0
0
2
2
1
0
1
0
2
0
1
0
2
0
0
0
1
0
0
0
0
0
0
1
0
1
1
2
1
0
2
1
1
1
1
2
0
0
2
0
1
2
0
1
0
0
0
1
0
2
2
0
1
0
0
0
0
0
0
1
2
2
2
1
0
2
0
0
2
0
0
2
2
1
2
2
0
0
0
1
0
0
0
1
0
1
2
0
2
1
1
0
0
1
1
0
0
0
2
2
2
0
0
0
0
0
0
2
0
0
1
2
0
0
1
0
1
0
0
0
0
0
0
0
0
2
2
2
2
1
0
2
2
0
0
1
2
0
1
0
2
1
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
1
1
0
0
2
0
0
2
2
0
1
1
0
2
2
0
0
0
0
0
0
0
2
0
1
0
1
2
0
1
2
0
0
0
2
0
1
2
0
0
1
0
0
2
1
1
1
1
0
0
1
0
0
1
1
0
0
0
1
2
2
2
1
0
2
0
2
1
1
2
1
1
0
1
1
2
0
1
1
1
2
0
0
0
1
2
0
2
0
0
0
0
0
1
1
1
0
2
4
0
0
2
0
0
1
0
0
2
0
0
1
0
0
2
2
0
5
1
1
1
0
0
1
1
1
1
1
1
1
0
1
1
0
0
2
1
1
0
3
0
2
1
0
1
0
0
1
0
0
0
2
1
0
0
2
0
2
0
2
1
1
2
3
1
2
0
0
1
1
1
2
0
1
0
0
0
1
1
0
2
1
0
2
0
1
1
0
0
1
1
0
1
1
0
1
2
0
1
1
0
0
2
1
0
0
1
1
0
1
1
1
1
0
1
1
0
0
1
1
1
0
2
0
0
2
0
1
0
1
2
3
2
0
2
0
0
1
0
2
1
3
0
2
0
0
0
1
2
0
2
1
0
2
0
0
0
0
1
2
0
1
1
0
0
1
1
0
0
0
0
0
1
1
2
2
0
1
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
2
0
0
0
1
1
2
0
0
1
2
0
0
2
2
1
0
0
0
0
1
0
2
1
0
2
0
1
0
2
2
0
0
1
2
0
1
1
1
1
1
2
0
2
0
2
0
2
3
0
3
1
2
2
0
3
0
2
3
1
2
2
0
0
2
0
2
1
0
0
2
0
0
0
0
0
2
0
2
1
0
0
1
1
0
0
0
2
1
1
1
1
1
1
1
0
0
2
0
0
1
0
0
1
0
3
0
1
0
0
0
2
1
0
0
0
2
0
1
0
1
1
0
1
0
1
0
0
0
1
0
1
1
2
0
0
1
1
2
0
1
1
2
0
1
1
0
0
1
0
1
2
2
2
2
2
2
2
1
0
0
1
1
0
0
1
1
0
1
0
2
0
0
0
0
2
0
0
2
1
0
2
1
0
1
0
0
0
1
1
0
0
1
0
1
2
1
1
1
1
0
0
2
1
2
0
0
2
0
2
0
0
1
2
1
2
0
0
1
0
0
0
0
1
0
1
1
0
2
0
0
1
0
0
0
0
1
1
1
1
0
1
1
0
2
3
1
2
0
0
0
2
1
1
1
1
2
0
2
2
2
0
1
2
1
0
0
0
1
0
1
0
3
0
2
2
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
2
1
0
0
2
2
0
2
1
0
2
2
1
0
0
1
2
1
2
0
0
1
1
0
1
1
0
0
1
0
0
1
0
1
1
0
1
1
0
0
0
0
1
0
1
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
1
4
0
1
2
1
0
0
0
2
0
2
1
1
2
1
0
2
1
0
0
0
0
1
1
0
0
1
0
1
0
1
2
3
2
2
2
0
2
1
0
0
0
1
0
1
2
2
2
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
4
0
1
1
0
0
1
0
0
0
0
1
4
1
2
0
1
1
0
1
0
0
1
1
1
0
2
0
0
2
1
1
4
0
0
0
0
1
1
0
2
1
2
1
0
2
2
0
0
1
2
0
1
0
0
1
2
0
0
1
0
2
0
0
0
1
1
0
2
0
0
1
0
1
1
4
1
0
0
1
0
2
0
0
1
1
0
0
2
1
2
0
0
0
1
0
1
0
0
1
2
0
2
0
0
0
0
2
0
2
0
1
1
1
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
2
0
1
1
1
1
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
1
2
0
2
1
0
1
1
1
0
1
2
1
0
0
1
1
0
1
2
1
0
0
1
0
2
0
1
0
0
3
2
2
0
0
1
0
0
0
1
1
0
1
1
0
1
0
1
0
2
1
1
2
1
3
3
1
0
0
0
0
0
1
0
0
0
0
2
1
2
0
2
1
0
2
2
2
0
0
0
0
0
1
0
0
1
0
0
2
0
2
0
2
2
0
0
3
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
1
0
0
2
0
1
0
0
1
1
0
1
2
2
2
0
1
1
0
0
1
0
1
2
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
1
1
0
0
0
1
2
0
0
0
1
2
0
2
0
0
0
1
1
1
1
0
1
2
1
0
1
0
2
0
0
1
0
1
0
0
0
1
1
2
0
0
2
0
1
0
2
0
0
1
0
2
2
0
1
2
0
1
0
0
1
2
0
2
1
0
0
0
0
2
1
0
0
1
2
0
1
0
1
2
0
2
2
0
1
0
1
0
0
1
1
0
0
2
2
1
2
1
0
0
0
0
1
0
0
0
2
2
0
0
2
1
1
1
0
0
0
0
0
2
0
1
0
0
0
0
0
1
1
0
0
3
2
1
0
1
0
1
2
2
0
0
3
0
1
0
0
0
2
1
1
0
1
0
2
1
0
0
1
0
0
0
0
0
2
2
0
1
0
1
2
1
2
0
1
0
0
0
0
1
0
1
0
1
0
2
1
1
0
0
1
0
2
1
1
1
2
2
0
1
2
0
0
1
2
1
1
1
1
1
1
1
0
3
1
0
1
0
0
0
1
0
1
2
0
2
1
1
1
0
0
0
0
2
0
0
2
2
0
1
2
1
0
3
0
1
0
1
2
1
1
0
2
0
0
5
0
2
0
4
2
2
1
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
1
1
1
0
0
1
0
1
4
1
0
1
0
1
1
2
1
0
3
0
0
1
0
1
2
0
2
1
0
2
0
1
1
2
2
3
0
0
1
2
0
0
0
0
0
0
0
0
2
2
1
2
0
0
0
3
2
1
0
0
0
0
0
2
0
0
0
2
1
2
0
0
0
2
0
3
1
0
0
0
0
0
0
2
1
1
1
0
2
0
1
1
2
0
0
1
2
0
1
0
1
0
0
0
1
0
1
2
1
0
0
2
1
0
2
0
1
2
0
1
0
1
2
0
1
0
0
0
2
1
0
0
2
2
1
0
0
2
0
0
2
2
0
0
0
0
1
0
1
2
2
1
1
1
1
2
0
0
1
1
0
0
1
2
0
0
1
1
1
0
0
2
0
2
0
1
1
1
0
1
0
1
1
1
0
0
0
2
0
0
0
0
0
0
1
0
2
0
1
1
0
0
1
1
1
0
1
0
0
0
0
1
0
0
2
1
0
0
0
1
1
0
2
2
0
1
0
0
0
1
0
2
0
1
0
1
0
0
1
0
0
0
1
2
0
1
0
0
0
0
0
1
1
1
2
1
0
0
1
0
0
1
2
0
1
0
1
2
0
2
2
0
0
1
2
0
2
0
0
0
0
0
2
1
1
0
1
1
1
1
0
0
2
2
2
0
0
1
0
2
0
0
0
1
0
2
1
2
2
2
0
1
1
1
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
1
0
1
0
0
0
2
1
0
0
0
0
0
0
1
0
1
2
1
0
0
1
2
1
2
0
0
0
0
3
0
0
0
1
2
0
1
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
2
0
1
1
2
2
1
0
0
1
1
1
0
0
2
1
1
2
1
1
0
0
0
2
1
2
3
4
2
1
2
1
0
1
1
1
1
0
0
0
2
1
0
2
2
0
3
0
0
0
1
2
1
1
0
0
1
1
1
0
1
0
1
1
0
0
1
0
1
1
0
1
0
0
1
0
0
0
2
1
0
0
1
0
1
2
0
0
0
1
1
1
0
1
0
1
0
0
0
2
0
0
0
1
1
0
2
2
1
0
0
0
2
1
0
0
0
2
1
0
0
0
0
1
0
0
1
1
1
2
1
0
0
0
1
0
0
1
0
0
1
0
0
0
2
1
0
2
2
1
0
1
2
2
2
0
2
0
2
0
1
2
1
0
0
1
1
0
2
2
0
2
0
1
0
1
0
1
1
0
0
2
0
1
0
0
0
0
0
0
2
1
2
2
1
1
0
0
2
1
0
1
0
0
1
0
2
0
0
2
0
0
0
2
0
2
2
0
0
0
0
0
1
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
1
2
0
2
0
0
2
0
1
0
1
1
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
1
1
1
0
1
2
0
0
1
1
0
1
0
0
1
0
1
0
0
2
2
0
2
1
1
0
2
1
0
0
1
1
0
3
0
0
0
0
0
0
0
2
0
2
1
1
0
0
0
1
0
2
2
0
2
1
2
2
1
1
1
0
1
0
0
0
2
0
0
0
1
0
0
1
0
2
1
2
1
0
0
1
2
0
1
2
1
1
1
2
1
3
1
0
0
2
2
0
1
0
0
0
0
2
0
0
0
1
0
1
1
1
7
1
0
0
0
0
1
2
0
1
1
0
1
0
0
0
1
2
0
0
1
2
0
0
2
1
1
0
2
0
0
0
1
1
1
0
0
2
0
0
1
1
0
1
2
1
0
1
1
0
2
0
0
1
0
2
0
0
1
1
2
1
0
0
1
1
0
0
1
0
0
0
0
3
1
2
0
1
0
0
1
0
1
1
0
0
0
1
1
0
0
1
1
1
1
2
1
0
1
2
1
1
0
0
2
0
0
2
2
5
1
2
4
2
1
1
0
0
0
0
1
0
0
2
2
0
1
0
0
0
1
1
2
1
2
1
0
1
1
2
0
0
1
1
1
2
2
0
0
1
1
4
1
0
0
1
0
0
0
0
2
0
1
0
0
2
1
1
2
0
1
0
0
2
2
2
0
2
9
0
0
1
2
0
0
1
0
1
1
2
1
1
1
1
0
0
2
0
1
2
0
0
1
1
0
0
0
0
1
1
0
1
1
1
0
0
1
2
2
1
2
1
0
0
0
4
0
2
1
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
2
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
2
0
0
2
0
0
0
0
1
0
0
2
0
0
2
2
2
1
0
0
2
1
0
1
0
0
2
0
0
2
2
0
1
2
0
1
1
0
0
1
3
0
1
0
0
0
0
2
0
0
1
0
1
0
1
0
0
0
1
0
1
0
2
2
0
0
0
1
1
0
2
2
2
0
2
0
1
0
0
2
0
1
0
2
0
0
0
2
1
0
0
1
0
0
2
0
0
0
1
1
0
2
0
0
1
2
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
1
2
0
3
1
0
1
1
0
1
0
1
0
2
0
0
2
0
0
0
1
0
0
0
1
2
2
0
0
0
0
1
0
2
0
0
0
1
0
0
2
0
2
1
0
2
2
0
0
1
0
2
0
2
4
2
0
0
1
0
0
0
1
0
0
2
2
0
0
1
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
2
1
1
0
0
1
1
1
0
5
2
0
0
2
0
0
0
1
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
2
1
2
0
1
2
2
2
0
1
1
1
1
0
1
2
1
1
0
2
0
0
0
2
1
1
0
0
2
0
0
0
0
0
0
0
1
2
1
0
0
2
0
0
1
1
0
0
3
2
3
0
0
0
1
0
2
2
0
0
2
0
0
0
0
0
1
0
0
0
1
0
1
1
0
2
0
0
1
2
0
1
1
2
0
0
0
2
0
0
0
0
2
0
0
2
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
2
0
1
0
2
2
2
1
0
0
2
0
1
0
0
1
1
0
0
1
1
2
0
0
0
6
1
0
0
2
0
0
1
0
1
0
2
2
0
1
1
1
0
2
0
0
1
0
0
2
0
0
0
2
0
0
2
1
1
1
1
0
0
2
1
0
0
1
0
0
0
1
0
2
0
1
0
0
0
1
2
2
0
1
0
2
1
1
0
1
0
0
2
1
1
0
0
0
2
0
0
0
0
2
2
0
1
3
0
0
1
1
0
1
0
0
1
1
0
0
1
0
1
0
1
0
1
0
1
1
0
1
0
1
0
1
0
0
0
0
2
1
2
0
1
1
0
0
0
1
0
2
0
1
0
0
0
0
1
0
2
1
1
1
0
0
0
0
0
0
0
1
0
0
0
1
1
4
0
2
1
0
0
0
1
1
0
1
0
0
0
0
2
0
2
2
0
1
0
0
0
1
0
0
1
0
1
2
2
3
0
2
1
0
1
1
0
2
1
2
1
0
0
0
1
0
1
2
1
1
1
1
0
0
0
1
0
1
2
0
2
1
1
1
1
1
2
0
2
1
0
1
1
3
0
0
3
1
1
2
0
1
2
0
2
2
1
0
0
1
1
2
1
0
2
1
0
2
0
0
2
2
1
0
0
0
1
0
2
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
1
0
2
0
0
0
0
2
0
1
2
0
0
0
1
0
0
3
1
1
3
1
1
0
0
0
2
2
0
1
0
1
0
2
1
0
1
0
1
2
1
0
2
2
0
2
1
0
0
2
1
1
0
0
1
0
2
2
0
0
0
1
0
0
0
0
2
0
2
0
1
0
0
0
2
1
0
0
1
0
0
0
0
0
0
1
0
1
1
1
0
2
2
0
2
0
2
0
2
1
2
1
1
0
1
0
1
1
0
3
1
0
0
0
2
7
0
1
0
2
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
2
1
1
1
0
0
2
0
0
2
0
0
1
2
0
1
2
1
2
0
0
0
0
1
0
1
1
2
0
0
1
0
0
0
0
1
0
0
1
2
2
1
0
1
1
2
3
0
0
1
2
1
0
1
1
0
0
1
0
0
0
0
1
0
0
1
0
2
0
2
0
0
2
0
4
0
0
0
2
2
0
0
0
0
0
2
1
0
0
1
1
1
1
0
0
0
1
1
0
0
0
1
2
1
1
0
2
0
1
2
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
3
0
0
2
0
0
0
4
0
0
0
1
2
0
2
0
0
0
0
0
1
0
0
1
2
1
0
0
2
2
0
2
0
1
0
0
0
0
2
2
2
0
1
1
3
1
0
2
1
2
0
2
2
0
0
0
2
0
1
1
0
0
2
1
0
1
0
1
2
2
0
1
0
0
1
1
0
0
1
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
2
1
0
2
1
0
0
2
1
1
7
0
0
1
1
0
0
0
0
2
0
2
1
1
0
1
0
0
0
0
0
2
1
1
1
0
0
0
2
0
2
2
1
0
2
0
4
0
2
1
0
2
2
2
1
2
0
1
2
0
2
0
1
2
0
0
0
0
1
1
0
2
1
0
0
1
0
0
3
1
0
2
1
2
0
2
0
1
1
0
0
2
1
2
1
1
1
0
0
2
0
0
0
2
0
1
0
2
0
3
0
0
0
1
2
1
1
0
1
1
0
0
2
1
0
0
0
2
0
0
0
2
0
0
2
1
2
2
1
0
0
2
2
0
0
1
2
1
0
3
3
2
0
0
0
1
0
1
0
2
2
2
2
1
0
1
1
0
0
1
1
2
0
0
0
1
1
2
0
0
0
2
0
0
0
1
1
0
1
2
0
1
0
0
0
2
1
0
1
0
2
1
0
2
0
0
1
0
0
0
2
1
1
0
1
1
1
0
3
0
0
1
0
2
1
2
2
0
0
1
0
0
0
1
2
0
0
0
2
0
0
1
2
0
0
0
0
2
0
0
0
0
0
1
0
0
2
1
1
2
1
1
3
0
0
0
2
2
0
1
0
0
1
0
2
1
0
2
1
0
0
0
1
0
0
2
0
1
0
2
2
0
0
0
2
2
1
0
1
1
1
0
0
1
0
0
0
0
1
0
2
2
9
1
0
2
1
1
2
0
3
2
1
0
0
0
2
0
2
1
2
1
1
0
1
1
0
1
1
2
0
0
1
2
0
1
0
0
0
0
0
1
1
0
0
0
3
0
0
0
0
0
0
1
0
2
1
0
0
1
0
0
0
1
0
1
2
1
1
0
0
0
2
0
1
0
3
0
0
0
0
1
0
0
0
0
0
0
2
2
1
2
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
1
1
0
1
2
3
2
1
0
2
2
1
1
2
0
0
1
0
0
0
1
0
0
0
0
2
1
0
0
2
0
1
0
1
1
0
0
0
0
2
1
1
1
0
1
0
1
1
1
0
1
0
2
1
0
0
1
1
1
1
0
1
2
2
0
1
2
2
1
1
0
0
0
0
1
2
0
1
2
0
2
1
1
0
2
1
0
0
1
1
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
2
2
1
2
1
1
0
0
0
2
1
2
1
3
0
2
1
1
0
1
0
0
3
0
0
0
0
1
2
0
2
0
0
0
3
1
1
0
0
2
2
1
0
1
1
2
0
0
2
0
1
1
0
2
3
1
0
0
0
1
3
0
0
0
1
2
0
1
0
0
0
1
2
0
1
2
0
0
2
2
0
1
1
1
1
2
3
2
1
0
1
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
2
0
1
1
2
1
1
0
0
1
0
1
2
2
1
0
0
0
2
3
1
0
0
0
2
1
1
0
3
0
0
1
0
0
1
0
0
1
1
0
0
0
2
2
1
0
0
0
0
0
0
0
3
2
1
0
3
2
2
1
0
0
0
1
0
0
1
1
0
2
0
1
2
2
2
0
0
0
0
1
2
0
0
0
0
0
1
0
2
2
1
0
2
1
2
3
0
0
0
0
2
0
1
0
1
0
1
0
0
2
1
0
0
0
1
2
1
1
2
2
1
0
2
0
0
0
0
3
1
1
1
2
0
1
1
0
2
0
1
0
0
2
0
0
1
0
1
0
0
0
0
1
2
0
2
2
0
0
1
1
2
1
1
0
1
0
1
1
1
0
0
0
0
0
2
0
2
2
2
0
1
2
0
2
1
1
0
0
0
1
0
0
0
0
1
2
1
2
0
0
0
2
1
2
2
0
0
0
2
2
1
0
1
1
1
0
1
1
0
0
1
0
0
0
1
2
1
2
1
1
0
0
0
0
0
1
2
0
0
3
1
1
0
0
2
0
2
0
0
2
0
2
0
0
0
0
0
0
0
2
1
0
0
0
1
0
2
1
0
1
0
1
2
1
0
1
1
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
2
1
1
0
0
1
0
0
1
0
0
0
2
0
0
1
1
0
2
0
1
0
0
1
1
0
0
0
0
2
0
3
0
0
0
0
2
3
0
2
0
1
0
0
1
2
0
0
1
1
0
0
1
0
0
1
1
0
0
1
1
1
1
2
2
0
1
1
2
2
3
0
1
0
1
0
2
1
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
4
0
1
0
0
1
1
1
0
1
2
2
0
2
2
0
0
0
0
0
0
1
2
2
0
0
0
0
0
1
2
1
0
0
1
0
1
1
0
1
2
0
0
0
0
1
1
0
2
0
2
1
0
0
1
2
1
2
2
2
1
1
0
0
0
0
0
0
1
0
1
0
2
1
1
2
1
1
2
1
0
0
0
0
1
2
0
1
2
2
1
1
1
2
1
1
1
0
1
2
0
0
0
1
2
0
0
2
0
0
2
0
1
0
2
1
0
1
0
2
0
1
0
2
1
0
1
0
1
2
1
2
0
1
0
1
0
2
1
2
1
1
0
1
0
0
1
2
3
0
0
2
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
1
0
1
1
0
0
0
1
2
2
0
0
0
0
1
0
0
1
0
2
1
0
0
0
9
0
0
0
1
1
2
0
0
1
0
0
2
0
2
0
0
0
0
0
2
1
0
0
0
1
0
0
1
0
2
0
2
1
2
1
0
0
1
1
0
2
0
0
2
0
2
0
1
0
1
0
0
1
0
0
1
0
0
0
0
1
3
0
0
1
0
1
0
2
1
0
0
0
2
0
0
0
1
2
0
0
0
1
0
0
0
0
1
0
2
0
0
0
1
2
1
0
1
0
2
1
0
1
0
0
0
0
1
4
0
2
1
1
0
1
0
0
1
0
1
4
1
1
0
2
2
0
2
0
0
2
0
1
0
2
1
1
0
2
0
0
0
0
0
1
0
1
0
0
1
2
0
1
2
3
0
0
2
2
0
2
0
2
1
0
1
0
1
0
2
0
0
0
1
0
0
1
1
1
2
0
3
1
0
1
0
1
2
2
2
0
0
2
0
0
1
0
0
1
2
1
1
0
1
1
2
1
1
2
0
1
0
0
2
0
2
2
1
1
1
0
0
3
0
3
3
0
0
2
0
0
1
2
0
0
1
0
0
0
2
0
1
1
1
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
2
1
0
2
0
2
1
3
2
0
0
2
1
0
0
2
0
2
1
1
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
1
1
0
1
0
1
0
1
0
1
0
2
0
1
0
2
2
0
0
1
0
1
1
0
0
0
0
0
1
2
0
1
1
1
2
1
1
0
0
1
0
2
0
0
1
1
0
0
1
0
1
1
0
0
0
0
2
0
1
1
0
1
0
1
0
0
3
1
0
0
2
1
0
2
0
0
0
0
2
1
0
1
1
0
1
2
0
0
2
0
1
1
1
0
0
2
2
0
0
1
0
0
0
0
1
0
1
2
1
0
2
1
1
0
2
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
2
0
0
2
2
2
1
0
1
3
0
1
0
0
2
0
2
2
2
2
0
1
1
1
0
0
0
0
0
0
0
2
1
1
2
0
1
0
1
2
0
0
2
0
2
0
1
0
0
0
1
2
1
2
2
1
0
2
1
2
0
1
0
0
1
2
0
0
1
0
0
0
0
2
1
0
2
4
2
2
1
0
2
0
0
2
1
0
0
1
0
1
1
2
1
1
0
1
2
0
0
1
2
0
0
0
1
0
0
1
0
0
2
1
0
0
1
0
0
0
2
0
0
1
2
1
0
0
2
2
2
1
1
1
1
0
2
2
2
1
0
1
1
2
0
0
0
1
1
0
0
1
3
0
0
0
1
1
0
0
2
1
2
0
0
0
0
2
0
0
1
2
1
0
1
0
0
1
2
1
0
1
0
1
0
1
0
0
2
0
2
0
0
2
0
1
2
2
1
2
1
0
1
0
0
2
1
0
0
0
0
0
0
1
2
0
3
0
1
0
1
1
0
1
0
0
1
1
0
0
1
2
1
1
0
2
0
1
2
0
1
1
0
1
0
0
0
1
0
0
1
2
1
2
0
0
1
0
1
0
2
0
0
1
0
1
1
1
0
0
2
0
0
0
1
2
0
1
0
0
0
0
2
2
0
0
0
2
0
1
1
0
0
0
0
0
0
1
1
0
1
1
1
0
2
2
0
0
0
2
0
1
0
0
0
1
2
0
2
1
1
0
1
1
1
2
2
0
1
1
0
1
0
0
1
0
1
2
0
1
2
0
0
2
0
0
0
1
2
0
0
0
1
2
0
0
2
0
0
2
1
0
0
0
0
2
2
2
1
0
0
2
0
0
1
0
0
0
0
2
0
1
1
2
0
1
0
1
2
1
0
1
0
0
0
1
2
2
1
1
0
3
0
1
0
0
1
2
1
1
1
0
0
0
0
1
0
0
2
0
1
1
1
1
0
0
0
0
1
0
0
0
1
0
0
1
1
0
1
2
0
0
1
0
0
0
0
0
1
2
0
1
0
2
1
1
2
1
2
4
0
0
1
1
1
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
1
0
0
0
0
1
2
1
0
0
0
0
0
0
2
0
2
1
0
0
0
0
2
0
1
0
0
0
0
0
1
1
1
2
0
1
1
0
0
1
1
1
1
1
0
2
2
0
0
0
0
2
1
0
2
1
0
0
1
0
0
2
0
1
1
0
0
1
0
0
3
1
0
1
1
1
2
0
2
1
2
1
0
0
1
0
0
1
0
0
0
2
2
0
2
2
2
0
2
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
1
0
0
0
0
2
3
0
0
2
0
1
1
1
0
0
0
1
0
1
1
0
0
0
0
0
1
1
2
2
0
0
2
0
0
1
2
0
1
1
2
0
1
0
1
0
1
0
2
0
0
1
0
1
2
0
1
0
2
0
1
3
1
1
1
0
0
0
2
0
0
0
2
1
2
0
1
0
0
2
0
0
0
0
1
2
0
0
0
2
0
0
2
2
0
0
0
0
0
1
0
0
2
1
0
0
2
1
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
1
0
2
1
0
1
0
1
2
1
0
0
0
0
0
2
0
1
0
0
1
2
0
0
0
1
1
0
3
0
0
2
1
1
2
1
0
0
0
1
2
0
0
1
0
0
0
0
0
0
1
1
0
3
1
1
0
0
0
2
1
2
0
3
1
0
1
1
0
1
1
0
1
0
1
0
0
0
2
14
0
0
0
2
0
1
0
1
2
0
0
1
2
1
0
2
0
2
2
2
1
0
1
0
0
2
2
0
0
0
1
0
0
2
1
2
3
2
1
1
2
1
2
0
0
1
1
1
2
0
3
1
0
1
0
0
1
2
0
0
2
1
0
1
0
0
0
2
0
2
2
1
2
1
0
0
2
1
0
1
2
1
0
1
0
0
0
0
1
0
1
1
0
2
0
2
0
1
2
0
1
2
0
2
0
1
0
1
1
1
0
1
0
0
1
0
1
0
0
1
1
0
0
2
0
2
3
1
0
0
3
2
1
1
0
2
0
0
0
0
0
0
0
2
0
1
2
2
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
2
0
1
2
1
0
0
0
1
0
1
0
0
0
2
1
0
1
0
0
0
0
0
2
1
0
1
0
1
0
2
1
0
0
2
1
1
0
0
2
0
0
0
0
2
0
1
1
2
0
0
0
1
0
0
5
1
2
0
2
0
0
2
0
0
2
1
0
1
0
0
0
1
1
0
0
2
2
0
0
0
0
1
1
0
1
2
0
0
1
0
0
1
2
2
1
2
1
2
0
0
1
0
0
2
1
2
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
1
0
1
2
3
2
1
2
0
0
1
2
2
0
4
1
0
1
0
2
0
2
1
0
0
0
0
1
0
2
0
0
1
1
0
1
1
0
0
0
0
2
0
18
1
0
0
0
0
0
2
0
0
0
1
1
1
1
2
0
0
2
0
1
2
0
0
0
1
0
0
2
0
0
2
0
2
2
2
2
2
0
0
0
0
0
0
2
1
1
0
2
0
2
2
0
0
0
2
0
1
0
1
1
3
0
1
1
1
1
2
2
1
1
3
0
0
1
2
0
1
2
1
0
0
2
0
1
0
1
0
0
1
1
1
0
0
0
0
1
1
2
1
0
0
0
0
2
0
0
0
1
2
0
1
0
1
0
2
0
0
0
1
0
0
0
0
1
1
0
2
2
0
1
1
0
1
0
0
0
4
0
2
0
2
0
0
2
2
1
2
0
0
1
0
1
0
0
0
1
0
1
1
0
0
0
0
0
2
2
0
0
0
0
0
5
1
0
2
2
0
1
1
1
1
0
1
1
1
1
1
3
0
0
0
2
0
1
1
0
0
2
1
1
0
1
0
0
1
1
2
1
0
1
0
0
0
1
2
2
0
0
1
1
2
0
0
0
0
2
2
1
0
2
1
1
0
4
0
1
1
1
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
2
0
2
0
1
1
0
0
0
0
2
0
1
0
1
2
0
0
0
0
2
1
2
0
0
0
0
1
1
0
0
1
0
0
2
2
2
1
2
1
2
1
1
0
1
0
1
1
0
0
2
1
1
2
1
1
0
1
1
1
2
2
1
0
0
0
1
1
0
1
1
0
0
0
0
1
0
0
0
1
0
0
1
1
1
2
0
0
1
0
2
1
0
2
0
0
0
0
1
0
1
1
0
0
1
1
0
1
0
0
1
1
1
0
0
1
0
1
1
0
0
1
0
0
2
2
0
0
1
1
0
2
2
1
0
0
1
0
0
0
0
1
0
1
1
1
0
2
0
1
0
1
0
1
0
0
2
1
0
0
0
0
0
2
0
2
2
0
0
2
2
1
0
1
0
2
1
0
0
2
0
2
0
0
1
0
1
0
1
2
0
0
0
0
1
1
1
0
2
1
0
2
1
2
0
1
1
1
0
0
0
2
0
1
2
2
0
0
0
0
1
0
1
1
0
0
1
0
0
1
1
0
0
1
0
0
1
2
0
0
0
1
0
2
0
0
1
0
1
2
2
0
1
0
2
0
1
1
2
2
2
0
1
0
0
1
0
2
1
0
0
0
2
1
1
2
0
0
0
1
1
2
1
2
0
1
1
0
0
0
0
0
1
0
0
1
1
2
1
2
0
0
1
0
0
1
0
1
0
0
0
0
2
0
1
1
1
1
3
0
1
1
1
1
2
2
0
0
2
1
2
0
2
0
0
0
0
0
0
1
2
1
0
1
0
0
0
0
1
1
0
0
1
0
1
1
0
1
2
0
0
1
1
0
0
2
0
2
2
1
0
4
1
1
1
0
2
1
2
1
2
0
0
1
0
0
1
2
2
2
0
0
0
0
1
0
1
2
1
1
1
0
0
0
0
0
0
1
1
1
1
0
2
0
0
0
0
2
0
0
1
2
3
0
0
0
0
0
2
1
0
2
0
1
0
1
0
0
1
0
0
1
2
0
2
0
1
0
0
0
0
1
2
0
1
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
1
0
0
0
2
1
1
0
0
3
0
2
0
2
3
0
0
0
1
0
0
3
0
1
1
1
2
0
1
1
0
0
1
0
0
0
2
0
0
0
1
0
1
0
1
1
0
2
1
1
0
0
0
2
3
0
1
1
1
1
2
1
1
0
1
0
1
0
1
0
1
1
2
0
1
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
2
1
2
1
0
2
0
2
0
3
2
1
2
0
1
0
0
0
1
1
0
2
1
1
0
0
0
0
1
0
1
0
0
0
0
1
0
2
2
1
1
0
1
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
1
1
0
0
6
2
1
1
1
1
3
3
0
1
0
0
0
2
2
1
0
2
2
2
1
2
0
1
0
1
0
0
1
1
0
0
0
0
0
1
3
1
0
1
0
2
2
1
0
0
1
2
1
1
0
0
1
1
0
0
0
2
1
0
0
1
1
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
1
1
1
0
0
0
2
0
1
1
1
0
2
1
0
0
2
0
0
1
0
0
1
1
1
0
1
0
1
0
1
0
0
0
2
0
0
2
0
0
0
1
2
1
2
2
0
1
0
1
1
0
2
0
0
1
0
0
0
1
0
1
1
0
0
0
2
2
0
0
1
0
2
0
1
1
0
0
2
2
0
0
0
0
3
2
1
0
2
0
2
1
0
0
0
1
1
1
0
2
1
1
0
2
0
0
2
1
0
1
0
1
2
1
0
0
0
1
0
0
0
2
1
0
1
0
0
0
2
2
1
0
2
0
0
2
1
2
1
1
1
0
1
0
0
0
0
0
0
2
2
0
2
1
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
2
1
1
0
0
2
0
0
1
1
0
1
0
2
1
0
1
0
2
2
1
0
0
1
0
1
0
0
0
1
2
0
1
1
0
1
2
1
0
0
1
0
1
0
0
0
2
1
0
0
0
0
1
1
0
0
0
2
0
0
0
2
0
1
1
1
1
0
0
2
0
0
1
2
2
1
1
0
0
0
0
0
1
1
0
0
0
0
2
0
1
0
1
2
0
1
2
2
0
1
0
2
0
0
1
1
1
1
0
2
2
2
0
0
1
0
0
0
1
1
0
0
2
0
1
1
3
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
1
2
1
0
1
0
1
0
0
1
1
1
1
1
2
0
0
2
1
2
1
0
1
0
1
0
1
0
1
0
0
0
1
1
1
1
1
1
0
1
0
1
0
0
3
1
0
1
0
2
0
2
2
0
1
0
2
1
2
1
0
0
0
0
2
1
1
3
0
2
1
0
0
1
0
0
0
0
2
0
1
1
0
0
0
0
0
1
0
0
0
1
1
2
0
0
0
1
1
0
1
0
1
4
0
0
0
0
1
0
3
1
1
2
1
0
2
1
0
2
1
0
1
1
1
2
0
1
0
1
0
0
2
0
0
0
1
2
0
2
1
0
2
0
1
0
0
0
0
0
3
0
2
1
1
0
2
1
2
1
1
1
1
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
1
0
2
2
1
0
1
0
1
2
0
0
0
1
1
0
1
2
1
1
0
1
0
2
0
0
0
1
0
0
1
2
1
0
1
0
2
0
2
0
0
0
1
0
1
0
0
2
1
0
0
1
0
1
1
1
1
0
0
1
3
3
0
1
0
0
3
1
1
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
2
1
0
1
1
1
1
1
0
1
0
0
1
0
0
0
0
0
2
0
1
1
1
1
0
1
1
0
0
0
1
3
0
1
0
2
0
1
1
0
3
1
5
5
1
0
2
0
3
1
1
0
0
0
0
0
0
1
2
0
0
1
2
0
0
1
0
0
0
0
0
0
1
1
1
0
1
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
2
0
1
1
0
0
0
0
1
1
0
0
1
0
1
1
1
0
2
0
0
0
0
0
1
0
0
1
0
1
2
0
1
0
2
0
2
0
2
1
1
0
2
0
0
0
2
0
0
2
0
0
0
0
1
3
0
2
0
0
2
0
2
1
0
0
0
2
1
1
2
1
0
0
3
0
1
1
0
1
0
1
0
0
0
1
1
1
2
1
1
1
1
2
1
1
1
0
0
0
0
2
1
0
0
1
1
0
2
1
0
4
0
0
0
0
1
0
0
2
3
2
0
1
1
0
2
0
0
0
0
0
0
2
2
2
0
0
2
2
2
2
1
0
1
2
1
1
1
1
0
1
0
1
1
0
2
2
1
0
0
0
0
1
2
2
0
0
0
2
0
1
2
0
0
1
0
2
0
0
0
0
0
2
2
1
1
0
0
1
0
0
0
2
0
1
0
0
1
2
1
0
0
0
2
2
1
1
0
0
0
0
0
0
0
0
0
2
2
2
1
1
0
0
1
0
0
1
2
0
0
2
1
1
3
0
2
1
0
1
1
0
0
0
2
1
1
2
1
0
1
1
0
0
2
2
0
0
0
1
0
1
0
0
2
0
1
0
0
0
2
2
1
2
0
1
2
1
2
0
0
0
0
1
2
0
0
0
0
1
0
0
1
1
1
0
0
0
1
0
0
1
0
1
0
1
0
0
2
0
0
0
0
2
0
2
0
0
5
0
0
0
0
0
1
0
0
0
2
0
1
0
0
1
1
0
0
0
2
2
1
0
0
0
0
2
1
0
2
2
0
1
0
1
0
0
1
0
0
0
0
1
1
2
0
0
0
0
1
1
1
0
0
0
0
2
1
2
1
2
0
1
2
1
0
0
0
2
0
0
3
0
1
0
2
0
0
1
2
0
2
2
1
1
0
1
1
0
0
0
2
0
0
0
1
1
1
0
0
0
0
0
0
2
0
1
2
0
1
0
1
0
2
0
2
0
2
0
1
1
1
1
0
2
1
0
0
0
2
1
0
0
0
0
0
9
1
2
1
2
0
2
1
0
0
0
1
0
0
1
1
0
0
1
0
1
0
0
0
1
0
1
0
1
2
0
0
3
0
1
2
0
0
0
0
0
0
2
1
0
1
1
3
3
0
1
0
0
2
0
0
1
1
0
2
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
2
1
0
0
0
1
1
2
1
0
0
2
0
0
0
1
0
1
2
0
0
0
0
0
0
1
1
0
2
1
0
0
2
1
0
1
0
1
1
1
0
1
0
3
1
2
1
0
2
1
0
2
0
0
0
3
1
2
1
0
0
2
0
0
1
0
0
0
0
0
0
2
0
1
0
2
0
1
2
2
1
0
1
0
1
0
1
0
0
2
2
0
0
0
1
1
1
1
0
2
1
1
1
0
0
0
1
1
0
1
0
1
0
7
0
1
1
2
2
0
2
1
1
0
1
1
0
0
2
2
1
2
0
0
2
0
3
3
0
4
0
0
1
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
2
0
1
1
0
0
5
2
0
0
1
1
1
0
0
0
1
2
0
1
0
0
1
0
1
1
2
1
0
1
1
0
1
2
0
2
0
1
0
2
3
1
0
3
0
0
2
1
0
0
0
0
1
1
0
0
1
0
2
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
2
1
1
2
2
0
0
0
1
0
0
1
2
0
0
0
1
0
1
0
2
1
1
2
1
0
0
0
0
0
0
1
1
0
0
1
0
1
0
2
2
1
2
1
0
2
1
2
2
0
0
1
1
0
0
0
0
3
0
1
0
0
0
2
0
0
0
1
1
2
2
2
1
2
2
0
0
2
0
0
1
1
0
0
1
0
2
0
0
1
0
3
0
0
0
0
1
2
3
0
1
0
2
0
0
0
2
1
0
1
1
0
1
1
0
0
1
1
1
2
3
2
1
1
0
0
0
0
1
1
1
2
0
0
0
0
0
0
1
1
0
0
0
3
1
0
0
0
1
0
2
1
1
2
0
2
0
0
0
0
2
2
1
0
0
1
2
0
0
2
1
0
0
1
5
0
2
0
0
1
2
1
0
0
0
0
2
3
1
0
0
0
1
2
0
0
2
0
0
0
0
2
1
0
0
1
0
2
1
0
0
0
0
1
2
2
0
1
2
2
0
1
0
0
2
0
0
0
0
1
0
1
1
2
1
0
1
0
2
0
3
0
3
0
0
0
0
1
1
1
1
1
0
2
0
1
1
2
1
2
0
0
2
1
2
0
1
1
0
0
1
0
0
2
1
0
1
2
2
2
0
1
0
0
2
2
0
0
1
0
1
0
0
1
0
1
0
3
1
2
2
0
1
10
2
1
1
1
0
1
0
0
0
0
2
1
1
0
1
1
0
1
2
1
2
2
0
1
0
1
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
1
2
0
2
2
0
0
0
1
0
0
1
2
1
0
0
0
3
0
0
2
0
0
2
0
1
0
0
0
0
0
2
0
0
0
1
0
0
1
1
1
1
0
0
0
1
1
0
0
2
1
0
2
0
2
0
1
1
2
1
1
1
0
0
1
1
0
1
3
2
0
1
1
1
1
2
0
0
1
1
1
0
0
1
2
0
0
2
0
0
0
1
2
0
1
0
2
1
2
1
2
1
1
2
2
1
1
1
1
0
0
2
0
1
0
2
0
1
2
0
0
1
2
0
1
1
2
0
1
2
1
0
0
1
0
0
1
0
0
0
0
0
0
1
4
0
0
0
2
1
2
0
2
0
1
1
1
0
0
0
2
1
1
2
2
0
4
0
0
0
0
1
6
0
0
0
0
0
0
0
1
2
0
0
2
2
0
0
1
0
1
0
0
0
1
0
0
1
0
0
2
0
0
1
0
0
2
3
0
0
0
0
0
1
1
0
0
1
3
1
0
2
3
2
0
1
0
1
1
1
1
4
1
1
0
0
2
1
0
1
1
2
1
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
1
1
5
1
0
2
0
0
0
2
0
0
1
1
0
2
1
1
0
0
2
2
0
0
0
0
0
3
0
1
0
0
0
2
0
0
0
1
2
0
0
1
2
0
0
0
1
1
0
0
2
0
0
1
0
0
0
2
0
1
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
2
0
1
1
1
0
0
1
1
1
0
2
0
1
0
0
0
1
0
0
0
2
0
2
0
0
1
1
0
0
0
2
0
0
0
1
0
1
0
0
0
2
1
1
1
0
0
0
0
0
0
1
1
1
1
0
0
1
0
2
0
2
2
0
1
0
2
0
1
0
2
0
0
2
1
0
0
1
2
1
2
2
0
0
2
0
0
1
0
1
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
1
1
1
0
2
0
1
0
0
1
0
0
1
0
2
0
0
2
0
0
1
2
2
0
0
2
1
1
2
0
0
0
2
2
0
1
1
0
0
1
0
1
0
0
1
2
0
2
2
1
0
0
1
0
0
0
0
0
0
1
0
1
2
2
0
1
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
1
0
1
2
0
0
0
1
0
0
2
0
1
0
1
0
0
1
2
0
2
0
1
0
1
1
0
1
0
1
3
2
2
1
2
0
1
2
1
1
2
0
0
2
0
1
1
0
1
0
0
2
2
1
2
0
2
0
2
0
1
0
1
0
1
0
2
2
0
2
2
1
1
1
2
1
0
2
0
0
1
0
1
1
0
0
0
1
0
0
0
1
0
1
1
0
1
0
0
0
2
0
1
0
0
0
2
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
2
1
1
0
0
0
0
0
0
2
2
2
0
1
1
2
0
0
0
1
0
2
0
1
2
1
0
1
1
0
0
0
2
0
1
2
0
0
1
6
2
0
0
0
1
0
1
0
1
0
1
2
0
1
0
1
2
0
2
2
2
0
0
0
2
1
2
2
0
1
1
0
3
2
0
1
0
1
0
2
0
1
1
0
0
1
0
1
2
3
0
2
0
0
0
0
0
1
0
2
1
2
1
0
0
1
0
0
0
0
1
0
0
2
0
2
2
1
1
0
1
2
0
0
1
0
0
0
2
1
1
2
1
0
2
1
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
1
3
2
0
1
2
1
0
0
0
0
0
0
1
2
0
0
1
2
1
2
0
1
1
1
0
2
0
1
0
0
1
0
1
2
2
1
0
0
1
1
0
2
0
0
0
2
1
0
0
0
0
2
2
0
0
1
1
1
0
1
2
2
0
1
0
1
0
1
2
1
1
1
0
0
1
0
0
2
0
1
0
1
0
2
0
0
0
1
0
0
0
0
0
0
2
0
2
2
1
2
0
1
2
0
0
0
0
1
0
3
0
0
2
0
2
0
1
2
1
2
0
0
0
0
2
1
0
0
0
2
0
1
0
0
0
0
0
0
2
2
0
1
0
0
3
0
0
0
0
0
0
1
2
0
0
0
0
2
1
1
0
0
2
2
1
2
0
0
1
1
0
0
0
1
0
1
1
0
0
1
1
0
0
2
1
0
0
0
1
2
1
0
1
0
0
1
0
1
1
1
0
0
1
1
1
0
1
0
1
2
0
0
1
0
1
1
1
0
1
2
0
2
1
0
0
1
1
2
0
0
0
0
0
1
0
2
2
0
1
0
0
2
1
0
1
1
1
1
0
0
0
1
0
0
1
1
0
0
2
0
1
2
0
0
0
1
2
2
0
1
2
0
0
1
2
1
1
1
0
2
2
1
0
1
2
2
0
2
0
2
0
1
0
1
0
0
2
1
0
0
1
1
0
0
1
0
2
1
0
0
1
2
1
0
0
0
0
0
2
0
0
0
1
0
2
0
2
0
0
1
1
0
2
1
2
0
1
0
1
0
2
1
0
2
0
1
2
0
1
0
0
1
2
0
0
2
0
1
0
1
1
0
1
0
0
1
1
0
1
0
1
1
0
2
2
0
0
2
1
0
1
0
0
0
1
0
0
0
0
0
1
0
1
1
1
1
1
0
2
0
0
0
2
0
2
1
0
0
2
1
0
0
0
0
2
1
0
0
2
1
1
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
2
0
0
0
0
0
2
1
0
0
1
0
1
2
2
0
1
0
0
0
0
1
1
1
0
2
0
1
0
0
0
0
0
1
2
2
0
3
2
0
0
0
0
0
3
0
0
0
0
0
1
0
2
0
0
2
0
0
2
0
0
1
0
1
1
0
0
0
4
0
2
1
0
2
0
1
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
2
0
0
2
0
2
0
1
1
1
0
0
1
0
0
0
0
1
0
1
0
0
2
0
3
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
2
0
1
1
0
1
3
0
1
1
1
2
2
2
1
4
1
4
2
0
2
3
1
0
1
2
1
2
2
0
0
0
0
0
1
1
2
2
0
1
1
0
1
1
0
2
2
0
0
1
0
0
0
0
1
0
2
0
0
1
2
2
0
0
1
0
2
0
0
1
0
0
0
0
0
1
1
1
0
3
1
0
0
1
0
0
1
0
0
0
1
1
3
4
0
1
0
1
2
0
0
2
1
2
0
1
0
0
2
2
1
0
2
1
0
0
1
0
2
0
1
1
1
1
2
0
0
2
0
2
1
2
1
1
0
2
0
1
2
0
0
1
1
2
4
0
2
0
0
1
0
0
0
2
2
2
1
1
1
0
0
1
1
2
0
1
0
3
1
0
1
1
2
1
1
0
0
2
2
1
2
0
2
2
1
2
0
0
2
0
1
1
1
1
0
0
0
2
0
0
0
0
0
0
1
2
2
2
0
1
1
1
2
2
0
1
1
1
2
0
0
0
0
0
0
0
0
2
1
2
0
2
2
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
1
2
0
0
1
2
2
1
0
0
2
0
0
0
0
0
1
2
3
0
1
0
0
0
2
0
0
2
2
0
0
1
0
1
1
1
1
0
0
1
1
0
1
0
0
0
0
1
0
0
1
0
2
0
1
0
2
0
0
1
2
2
1
2
2
1
1
1
0
0
0
2
0
1
0
0
0
1
2
0
2
0
2
0
0
0
0
2
2
0
1
2
1
1
0
0
0
2
0
0
0
2
1
0
6
1
0
0
0
0
1
0
0
0
1
1
2
0
0
0
0
1
1
0
0
0
0
0
0
0
2
1
1
0
2
1
0
2
1
0
2
2
1
0
1
0
0
0
0
0
1
0
0
2
1
2
0
0
0
0
0
1
2
1
0
0
0
0
1
2
1
2
0
0
0
0
1
1
0
0
0
0
1
0
0
0
2
2
2
0
0
2
0
3
0
0
0
0
2
1
0
1
1
0
2
2
0
1
1
2
2
1
0
1
1
0
0
1
2
2
0
1
0
2
0
0
0
0
0
2
0
0
0
1
1
2
0
3
0
1
0
0
1
1
1
2
0
0
0
1
0
0
1
0
0
2
2
1
0
2
1
1
1
0
0
2
0
0
1
0
2
0
0
0
0
1
2
1
1
2
2
5
2
0
1
1
0
0
0
0
0
0
2
1
0
2
0
0
0
1
0
0
2
0
0
2
2
0
1
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
2
0
0
0
0
1
1
0
0
0
2
2
2
1
1
1
1
0
1
0
0
0
2
1
1
1
2
0
0
0
2
2
1
0
0
0
0
1
0
0
1
0
2
1
2
0
0
0
0
0
0
0
1
1
0
1
0
2
0
0
0
1
0
2
1
0
1
1
1
1
2
1
2
1
0
0
0
2
1
1
0
0
1
0
1
1
0
0
1
2
1
1
0
0
1
1
1
2
2
2
1
0
1
1
0
0
0
0
0
2
1
0
2
2
1
1
2
2
0
0
2
2
1
0
0
0
0
0
0
2
1
1
0
2
1
1
0
0
1
0
2
1
2
0
1
1
1
1
1
1
1
0
2
0
2
2
1
0
1
2
0
1
0
1
0
0
5
2
0
1
1
0
0
2
1
0
0
0
0
2
0
0
1
3
1
1
2
0
2
2
0
0
0
1
0
1
0
2
0
0
0
1
0
2
1
1
0
0
2
0
0
0
0
1
0
0
0
1
0
2
0
0
1
0
0
0
0
1
0
0
2
1
2
0
1
0
0
1
0
1
0
0
0
0
0
0
0
2
0
1
0
0
1
0
1
3
2
1
1
0
0
1
5
0
0
3
1
2
0
2
1
0
0
0
0
2
1
0
2
1
1
1
0
1
1
0
0
0
1
0
1
1
0
2
1
1
0
1
1
0
1
0
1
0
0
0
0
0
2
1
2
0
2
1
1
0
2
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
2
1
0
0
2
0
0
0
5
0
1
1
0
2
0
0
0
0
1
0
1
0
0
0
1
0
1
2
0
2
0
1
0
2
0
0
1
1
1
1
0
1
1
2
0
1
0
1
0
0
1
1
0
2
3
0
0
0
1
1
2
0
0
0
1
0
0
1
0
2
0
1
1
0
1
1
0
0
1
2
0
0
2
1
0
1
2
2
1
1
0
2
0
0
1
2
2
0
0
0
2
1
1
2
2
0
0
2
1
0
0
0
0
1
2
0
2
1
0
2
1
1
1
2
1
1
2
0
1
0
0
1
2
0
2
2
2
1
1
1
0
0
0
4
1
2
0
0
0
0
0
1
2
0
0
2
0
2
2
2
0
1
1
3
2
0
1
0
1
2
0
0
1
0
2
0
0
1
0
1
0
0
2
1
1
1
2
1
2
0
1
0
1
1
0
1
1
2
2
0
0
0
0
2
0
1
1
0
2
0
1
2
2
2
1
0
0
0
0
2
1
1
1
1
0
0
0
2
2
0
0
0
0
1
0
1
2
0
1
1
2
0
0
0
0
1
0
1
0
1
0
0
1
1
0
0
2
2
0
1
0
1
0
0
1
0
2
0
0
1
0
2
1
0
0
5
0
0
0
3
0
0
0
1
1
1
1
0
1
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
2
2
0
1
2
0
2
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
2
1
0
2
0
0
1
0
1
1
0
0
2
0
1
1
2
1
0
1
1
0
1
1
0
0
0
2
0
0
0
1
0
0
2
2
0
1
0
1
0
0
1
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
2
2
0
2
1
2
1
0
1
0
1
0
1
2
2
1
2
2
1
2
2
0
2
1
1
0
0
0
0
1
1
1
0
0
0
0
1
1
0
2
2
0
0
0
0
1
1
0
0
1
0
2
1
0
0
0
1
1
0
2
0
0
2
0
0
1
0
1
2
3
0
0
0
1
1
0
1
1
1
0
0
1
1
2
1
0
0
0
0
3
0
2
0
0
1
1
0
3
0
0
0
0
1
0
1
2
1
0
2
0
1
2
0
0
0
2
1
0
2
2
1
1
0
0
0
2
2
0
0
1
0
0
1
0
2
2
4
2
1
2
0
0
0
0
0
1
0
2
1
0
0
0
2
2
0
1
1
2
0
1
0
1
1
0
1
0
0
0
0
0
0
3
0
1
1
0
0
0
1
1
2
0
1
1
1
0
1
2
2
0
1
0
2
1
2
1
2
0
1
0
0
0
5
0
1
0
2
1
1
0
3
0
0
1
0
2
3
0
2
0
0
0
2
1
0
0
2
0
0
0
2
0
2
0
1
0
1
0
0
2
0
2
0
1
0
0
0
0
2
2
0
1
0
0
1
1
0
0
1
1
1
2
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
3
1
0
1
0
0
0
0
2
0
1
0
1
2
0
0
1
0
2
2
1
2
2
1
0
1
0
1
3
0
2
1
0
0
1
0
0
2
2
0
2
2
1
1
0
0
0
1
1
1
2
0
1
2
0
2
0
2
1
1
1
0
1
2
1
0
3
0
1
1
0
0
2
1
0
0
1
1
0
2
0
2
0
0
0
1
2
0
0
1
0
0
1
0
0
2
0
0
1
2
0
0
0
4
1
0
0
2
0
1
0
2
2
0
2
15
1
1
0
2
0
2
0
4
0
0
1
1
2
0
2
1
0
0
0
4
1
1
1
1
0
2
0
1
2
1
2
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
2
1
0
2
0
0
1
1
0
0
2
0
1
0
0
1
0
0
2
2
1
0
0
0
0
0
2
1
1
2
0
0
1
1
0
2
0
1
0
1
2
2
1
2
1
1
0
0
0
2
1
0
1
0
0
1
3
1
0
0
0
1
0
1
2
1
0
1
2
1
0
1
0
1
0
2
1
0
0
1
1
1
1
1
2
1
0
1
0
1
0
1
0
0
2
2
1
0
1
1
1
2
0
0
2
0
1
1
0
0
2
0
2
1
0
3
0
2
1
3
0
2
0
0
0
1
1
1
1
0
2
2
0
1
1
1
1
0
1
0
1
1
0
2
0
2
1
0
0
2
2
1
2
0
0
0
1
1
1
0
2
0
1
0
0
0
2
2
2
0
0
0
2
2
0
0
2
1
0
1
2
0
1
2
0
2
2
1
0
1
2
0
1
0
0
1
0
1
0
2
0
1
1
1
2
0
2
1
1
1
1
0
0
0
0
2
0
1
1
0
0
0
1
0
0
0
0
0
0
1
1
1
2
0
1
1
1
0
0
3
2
2
1
0
1
1
0
0
1
1
1
1
1
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
3
0
0
1
1
1
0
2
0
0
0
2
2
0
0
0
0
1
2
1
1
2
0
1
1
2
2
0
0
0
0
2
1
0
3
1
2
0
1
1
2
1
1
0
0
0
0
1
1
2
0
1
2
0
2
1
0
0
1
0
0
0
0
0
0
1
0
2
0
2
0
0
2
0
0
1
0
0
0
2
2
0
0
2
0
0
2
0
0
2
1
1
0
1
0
2
0
0
0
1
1
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
2
1
0
0
0
2
0
2
0
1
1
0
1
1
1
0
0
2
0
0
1
0
1
0
1
1
0
1
0
2
0
0
1
0
0
0
2
1
0
0
0
2
0
1
2
2
2
0
0
2
1
1
1
0
2
0
0
2
0
0
2
0
0
0
1
0
1
0
1
1
1
1
2
0
0
0
0
1
0
2
2
2
0
1
2
0
0
1
2
2
1
1
1
0
0
0
2
1
0
1
2
2
0
0
0
1
0
2
0
1
0
2
0
1
0
1
1
0
0
0
3
1
0
0
1
0
2
0
0
0
0
1
0
2
0
2
0
1
1
2
0
0
0
1
2
0
0
2
2
1
1
2
0
0
0
2
0
2
0
1
0
1
0
0
2
0
2
2
3
1
0
1
2
0
1
1
2
0
2
2
3
2
0
0
2
2
3
2
1
0
2
0
2
1
0
0
0
0
1
2
2
2
0
2
1
2
1
2
0
1
0
0
1
0
9
1
2
0
0
0
0
1
0
0
0
0
2
0
0
3
0
2
1
0
2
0
1
0
0
1
2
1
0
1
0
0
0
2
0
0
1
2
0
2
1
2
2
0
0
0
2
0
0
2
1
0
0
1
0
1
0
1
1
1
0
0
0
0
0
2
2
2
0
2
0
10
1
2
1
1
0
0
0
0
0
1
0
2
1
0
2
2
1
0
2
0
0
1
1
0
0
1
1
1
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
2
3
0
0
1
2
0
1
0
0
0
1
0
0
1
2
0
0
0
0
1
0
2
0
1
1
0
1
3
4
0
2
1
2
0
1
0
2
3
2
0
0
0
0
0
2
0
2
1
2
0
1
1
0
1
0
1
0
0
0
1
0
2
0
0
0
0
0
1
1
0
0
1
0
2
0
1
0
0
3
2
0
0
1
1
0
1
1
2
1
0
1
1
1
0
1
0
0
1
2
0
1
1
0
0
0
0
0
0
2
2
1
1
1
1
1
1
1
0
0
0
0
0
0
1
0
0
1
0
2
0
0
1
0
0
0
0
1
0
0
0
2
0
0
2
1
0
1
1
2
0
0
2
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
3
0
1
0
0
0
1
0
0
2
3
0
1
1
2
0
2
0
0
2
0
2
0
0
1
2
0
0
0
0
0
2
0
0
1
0
1
0
3
1
2
0
2
0
0
2
1
1
0
1
2
2
0
0
0
0
0
0
1
0
2
1
0
2
0
2
0
1
0
1
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
2
2
0
2
2
0
0
0
1
0
0
2
0
0
1
3
0
0
0
0
1
2
2
0
0
0
1
1
0
1
2
0
0
0
0
0
1
0
1
0
2
3
2
0
2
1
2
0
1
1
1
1
0
0
3
0
1
2
0
0
2
0
1
0
0
1
1
0
2
1
0
0
0
0
1
0
1
1
0
0
1
0
0
1
1
2
1
2
1
0
1
0
0
1
2
1
0
2
1
0
2
2
0
1
0
2
0
0
2
1
1
0
3
2
2
1
2
0
0
0
0
0
0
0
0
0
1
1
1
4
1
2
3
0
2
0
1
1
0
0
0
1
0
0
0
1
2
0
0
2
0
1
1
0
2
1
0
0
0
1
0
1
1
2
1
1
0
0
0
2
0
0
0
1
1
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
2
0
0
3
0
1
0
1
0
1
2
0
2
1
1
0
3
1
1
2
0
0
2
0
0
0
0
1
1
0
0
0
1
0
0
1
1
1
1
0
1
2
0
1
0
2
1
2
0
0
0
0
0
2
0
1
4
2
0
0
2
2
1
1
0
0
0
1
0
0
2
0
0
0
3
1
2
1
0
0
2
0
0
0
1
0
1
1
1
1
1
0
1
1
2
1
2
2
1
0
2
0
0
2
1
0
0
1
2
0
2
1
2
0
0
2
0
0
0
1
0
0
1
0
0
1
0
1
0
1
0
1
0
0
1
0
0
0
1
1
0
2
1
1
2
0
1
0
1
1
0
0
2
1
0
2
1
0
0
1
0
1
0
0
0
2
0
1
1
1
0
2
0
0
1
0
1
1
2
0
2
0
0
0
2
0
1
0
0
0
1
0
1
0
0
0
2
0
0
1
0
2
0
2
0
2
2
0
0
1
0
2
1
0
0
0
1
0
2
1
4
1
1
0
0
0
1
0
1
0
0
0
1
1
1
1
1
0
0
1
2
0
0
2
0
2
0
2
0
0
2
1
1
0
1
0
2
0
1
0
0
0
2
0
2
2
2
0
1
0
0
0
0
0
2
1
0
0
0
0
1
1
0
0
1
1
0
1
0
1
0
2
0
2
1
3
1
0
0
0
1
6
1
1
0
1
2
0
0
2
2
0
4
1
0
1
1
1
0
1
0
0
1
1
0
2
1
1
1
2
0
0
2
1
2
1
0
0
0
0
2
1
3
2
0
2
1
2
0
2
2
1
0
2
0
3
0
1
1
0
0
0
1
0
0
1
2
0
0
1
0
1
0
0
0
2
1
1
0
0
0
0
1
0
2
0
0
1
0
0
1
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
2
0
0
1
0
1
1
3
2
2
2
2
1
5
1
0
1
0
0
0
2
0
0
0
1
1
2
0
0
0
1
0
0
3
1
0
0
4
1
1
1
0
2
0
0
2
2
0
1
0
2
0
0
0
0
1
2
1
1
0
0
0
1
2
0
1
0
0
2
0
1
2
2
0
0
1
2
2
0
0
6
1
2
0
1
2
0
1
1
2
1
0
1
2
0
2
2
2
1
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
1
2
0
2
2
2
0
2
2
2
0
2
2
1
0
2
1
0
2
0
2
1
0
1
1
0
2
0
2
0
0
1
2
0
1
1
0
2
2
0
1
0
1
1
0
0
0
1
2
0
2
0
1
0
1
0
0
0
1
1
2
1
0
2
2
1
0
0
5
1
0
0
2
0
0
0
0
0
1
1
0
1
1
2
1
1
2
2
0
0
0
0
1
0
1
1
0
0
0
0
2
1
0
0
0
1
1
0
2
1
0
1
0
1
2
0
0
0
0
0
2
2
2
0
2
2
1
1
0
0
2
1
0
0
0
1
2
1
0
0
1
2
0
0
0
0
0
0
0
0
0
1
2
0
1
1
3
0
0
1
2
2
1
0
0
2
0
0
0
0
0
0
0
0
1
1
1
6
1
1
2
0
1
2
2
1
0
2
1
1
1
1
0
1
0
0
0
0
2
0
0
1
2
3
2
1
0
2
0
2
2
2
2
0
0
1
0
1
0
0
2
1
2
1
0
2
1
2
2
0
0
2
2
2
0
3
2
1
2
0
1
0
1
1
1
1
0
2
0
2
0
0
1
0
2
0
0
0
0
0
0
0
1
0
1
2
2
3
1
2
2
0
0
1
0
1
0
1
0
0
1
0
0
0
1
0
0
1
2
2
0
2
1
1
0
0
0
0
0
1
0
1
1
0
1
0
1
2
0
1
0
0
0
1
1
0
1
0
0
0
1
2
0
0
1
2
2
1
2
0
1
2
1
1
0
1
1
0
2
1
0
1
0
1
1
3
1
0
1
0
0
0
0
0
2
1
0
2
1
1
0
1
1
1
2
0
0
2
0
1
2
1
0
1
2
0
0
0
1
2
2
1
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
2
1
2
0
1
0
2
0
1
1
2
0
0
1
0
1
1
2
0
0
0
0
1
0
2
0
2
3
0
1
0
1
0
0
1
0
2
2
1
0
1
1
0
0
1
0
2
2
1
2
0
2
1
0
0
0
0
0
0
0
2
1
1
1
0
1
2
0
2
1
1
0
2
0
0
0
0
0
2
0
1
0
0
0
0
1
0
1
1
4
1
2
1
0
0
1
0
0
2
0
0
0
0
1
1
1
1
1
0
2
0
2
1
1
1
0
1
0
0
2
1
2
0
1
0
1
0
1
2
0
2
0
3
1
2
2
0
1
0
0
2
0
0
0
2
1
1
0
0
2
2
0
1
0
0
0
0
0
0
1
0
1
0
0
1
3
1
0
1
0
2
0
0
0
2
0
1
1
0
1
0
2
0
0
0
0
0
0
2
1
1
0
0
5
1
2
0
0
2
0
0
0
0
1
2
3
2
0
2
0
2
1
0
0
2
1
0
2
1
0
0
1
0
0
1
0
0
2
1
1
0
0
1
0
2
1
0
1
0
2
2
0
0
2
0
0
0
0
1
2
0
1
1
0
2
0
1
0
3
0
0
0
0
1
1
1
0
0
1
2
1
2
1
0
0
1
0
1
0
2
1
0
0
1
0
0
0
2
0
0
3
0
0
0
2
0
1
2
0
0
0
2
0
0
2
1
0
0
0
0
0
2
1
1
2
0
0
2
2
0
1
1
0
0
0
0
2
0
0
0
2
2
0
13
2
0
1
1
1
1
1
2
0
0
0
0
6
0
0
0
3
0
0
0
1
2
0
0
0
2
0
0
0
2
2
0
0
1
0
1
1
0
0
0
2
0
0
0
0
0
1
2
0
3
0
2
2
0
1
2
0
1
1
0
0
0
0
0
2
2
1
0
2
1
2
1
2
0
0
0
0
1
1
0
0
1
0
4
0
2
0
3
3
0
0
1
1
1
0
0
1
2
1
0
1
0
0
0
1
3
1
1
1
0
1
0
1
0
1
0
1
0
2
2
0
1
1
1
0
0
1
0
5
0
0
0
0
3
1
0
2
0
1
0
2
2
1
1
0
2
0
0
0
0
0
2
0
1
0
2
1
0
0
0
1
0
0
2
0
0
0
2
0
0
2
0
0
0
1
2
0
0
0
2
0
0
0
0
2
1
2
0
0
1
1
0
0
0
0
0
0
0
1
2
1
0
1
2
0
2
0
0
0
1
0
0
2
0
0
0
0
0
1
2
2
0
2
0
1
1
2
0
1
2
0
2
0
1
1
0
0
0
0
2
0
1
0
0
0
2
2
1
0
0
0
2
1
0
0
0
0
0
1
0
2
1
2
0
0
1
2
1
0
2
0
0
0
2
0
1
0
0
0
4
2
0
1
1
1
2
0
1
0
0
0
1
0
2
2
1
0
0
1
1
0
0
0
2
0
0
0
3
0
0
0
3
1
0
0
1
0
0
0
0
0
0
0
2
1
4
10
0
0
0
2
0
0
0
0
1
0
2
0
0
1
0
0
0
1
1
0
0
0
1
2
1
1
0
2
1
2
0
0
1
1
1
0
2
1
0
1
1
1
0
2
0
2
1
0
1
0
1
1
2
1
0
0
1
1
2
2
0
1
1
1
0
1
0
0
0
0
0
0
1
1
2
0
0
0
0
0
2
2
2
1
0
0
0
0
2
0
0
0
2
1
0
0
1
1
0
0
1
0
0
0
0
0
1
1
1
2
0
0
1
2
2
1
0
0
1
1
0
1
0
0
0
1
0
0
2
0
0
0
1
2
1
1
2
0
3
0
0
0
0
1
1
2
1
2
0
0
0
0
0
0
3
0
1
4
1
0
1
1
0
1
0
1
2
0
0
0
0
0
2
0
0
1
2
2
2
1
1
1
1
2
0
1
1
1
0
0
2
1
0
1
1
1
2
1
0
2
3
0
3
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
1
2
0
1
1
2
1
0
1
0
0
0
0
2
0
1
0
0
0
0
1
0
0
1
2
2
2
1
2
1
0
0
0
0
1
2
0
1
10
3
0
1
0
0
1
0
1
1
0
0
0
0
2
0
0
0
1
2
0
1
0
1
0
0
0
1
1
1
1
1
0
1
1
2
2
2
2
0
0
0
1
1
0
1
2
0
2
0
0
1
1
0
2
1
1
2
0
0
1
1
1
1
1
0
1
2
2
0
1
0
0
1
1
0
0
2
0
6
0
0
1
1
0
0
2
0
0
1
0
2
0
0
2
1
2
2
1
1
1
2
0
1
0
0
0
1
0
1
1
0
0
2
0
0
1
1
1
2
0
2
3
0
1
0
0
0
0
3
2
0
0
1
0
0
0
2
2
0
1
0
0
1
0
2
0
0
1
1
2
0
2
1
2
0
0
1
1
3
1
0
1
0
2
0
2
9
0
0
0
1
0
0
0
1
2
0
2
1
0
0
0
0
1
2
0
2
1
2
1
2
2
1
2
1
0
2
0
2
2
1
0
0
1
0
0
1
0
1
0
0
1
1
1
2
2
0
2
0
1
0
0
2
0
0
0
2
0
0
3
0
0
1
1
0
0
1
1
2
1
0
1
2
1
1
0
1
2
0
2
0
0
1
1
0
0
0
0
1
2
1
0
0
0
1
0
4
1
0
0
2
1
1
1
0
0
2
1
0
0
1
0
0
0
1
0
0
0
0
0
0
3
2
1
1
0
1
1
6
2
3
0
1
0
0
1
3
2
2
0
0
0
0
5
1
1
2
0
0
0
1
0
1
0
2
0
0
0
2
0
0
2
0
1
0
0
0
2
2
0
2
0
4
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
1
1
0
1
2
1
0
1
2
1
0
0
2
0
2
2
0
1
2
2
1
1
0
0
1
0
1
0
3
0
0
0
0
2
1
0
2
0
0
1
0
1
2
0
0
1
1
2
0
1
1
0
1
1
0
1
0
2
2
1
0
0
0
0
0
0
1
0
1
2
0
0
0
1
1
0
1
0
2
0
0
1
2
1
1
1
2
0
0
0
0
1
0
1
0
1
0
0
3
1
2
2
3
1
0
0
1
0
2
0
2
2
0
1
0
0
2
0
1
1
0
0
1
0
0
0
0
1
2
1
0
1
0
0
0
1
0
1
0
1
1
1
1
0
0
1
0
0
2
0
1
2
1
2
1
1
1
0
1
0
1
0
0
0
1
2
0
0
0
2
2
2
0
2
0
0
0
2
1
0
3
1
2
0
0
0
1
0
1
1
2
0
1
0
1
1
0
0
2
2
1
2
2
0
2
1
0
2
0
2
1
0
0
0
0
4
1
0
1
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
3
1
0
2
0
0
0
0
1
0
1
0
0
0
1
0
1
1
2
2
0
0
2
0
1
0
1
0
1
0
0
0
2
0
1
2
2
0
3
2
1
0
0
1
0
0
1
2
1
1
1
0
0
0
0
1
0
1
1
2
1
0
0
1
0
0
2
2
3
2
1
0
0
0
0
1
0
1
1
0
1
0
1
2
0
1
1
0
0
0
1
1
0
0
5
0
2
0
0
0
1
1
0
0
1
0
2
2
0
0
0
0
0
2
0
2
2
0
1
0
0
2
2
0
0
0
2
1
2
1
0
1
0
0
0
0
0
0
1
1
0
1
0
2
0
1
0
1
0
2
0
0
1
1
0
0
0
0
1
0
2
0
0
0
2
0
0
0
2
0
1
0
2
1
0
1
2
2
1
1
1
0
0
0
0
1
1
1
2
2
1
1
0
1
1
0
0
1
0
0
2
0
0
1
2
0
2
0
0
0
0
1
1
0
1
1
1
0
1
0
0
2
1
0
2
0
3
1
0
1
0
0
1
0
1
2
0
2
0
1
0
0
0
1
2
0
0
0
0
0
2
1
2
1
0
0
2
1
2
0
2
0
2
0
2
0
0
2
0
1
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
2
2
0
1
0
0
1
0
0
0
1
2
1
1
0
0
1
0
2
2
0
0
0
1
0
0
2
0
0
1
2
0
0
0
0
2
2
3
0
0
1
2
0
2
2
4
2
1
3
3
1
1
0
2
0
0
1
1
0
0
0
1
1
1
0
0
2
2
0
0
0
1
1
2
1
0
0
1
0
1
1
0
0
1
1
1
1
1
1
3
1
1
0
2
0
0
1
0
1
2
0
1
0
1
0
2
0
0
2
0
1
1
0
0
1
1
1
0
1
0
0
4
2
1
1
1
0
1
2
0
1
0
1
0
1
0
1
1
0
0
0
0
2
0
2
1
0
1
1
0
0
0
0
0
0
0
1
3
1
0
1
1
1
0
2
1
2
0
0
2
1
0
0
1
0
1
1
1
0
0
0
1
0
1
0
0
0
0
0
1
2
1
0
0
0
2
1
1
0
0
0
2
2
0
0
0
0
0
1
0
0
0
3
0
0
2
0
1
1
1
1
1
0
0
0
0
0
1
0
2
2
1
1
0
2
0
0
0
1
1
0
1
1
1
0
0
0
2
1
0
1
2
1
1
0
1
2
1
0
2
0
0
1
2
0
1
0
1
1
0
0
0
3
1
0
1
0
2
2
1
0
1
0
2
1
2
0
0
0
1
0
2
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
1
0
0
1
0
0
1
0
2
0
3
1
1
2
1
0
0
1
0
1
0
1
0
2
0
0
1
0
0
1
0
0
1
2
2
2
1
1
0
0
1
0
1
0
0
3
0
0
0
2
0
2
0
2
2
2
0
0
1
0
0
1
1
0
0
0
2
2
1
1
2
1
1
0
0
1
0
0
0
0
0
1
1
1
1
1
1
1
0
0
1
1
0
2
0
0
1
0
1
1
2
0
1
0
2
2
1
0
1
1
0
2
2
0
0
0
1
3
0
1
0
2
0
0
0
0
2
0
1
0
2
3
0
0
1
0
0
1
0
1
0
1
0
1
0
0
0
2
1
1
2
1
0
0
1
0
1
0
0
1
0
0
0
1
0
0
1
0
0
1
1
0
1
0
2
1
0
0
2
0
2
0
7
0
3
1
0
1
0
1
0
1
1
0
1
0
1
0
0
0
0
1
0
1
2
2
2
1
2
1
0
0
1
1
0
2
2
1
0
1
0
0
1
2
1
0
0
1
0
1
0
0
3
0
1
0
2
2
0
1
2
0
2
0
0
0
0
0
1
0
1
0
1
1
1
1
0
0
0
1
2
0
1
0
2
0
1
1
1
1
0
1
1
0
1
0
0
0
0
0
1
0
1
0
4
0
1
1
2
0
0
0
0
2
2
2
1
0
0
0
1
1
0
2
2
0
0
0
2
0
1
1
2
1
0
0
0
4
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
2
0
0
0
1
0
1
1
2
1
0
0
0
1
0
1
2
2
2
2
1
1
0
1
1
0
2
2
1
0
0
0
2
2
0
2
3
0
1
0
2
0
0
0
1
1
1
0
0
2
1
0
0
1
2
0
2
0
0
2
2
1
0
0
1
0
2
2
1
2
2
1
0
2
0
2
0
0
0
1
0
0
0
1
0
1
0
0
1
1
0
2
1
1
1
1
0
0
1
0
0
0
0
0
0
1
0
0
1
2
2
0
0
1
0
0
0
3
2
1
0
1
0
1
1
0
0
3
0
1
0
0
1
0
0
1
0
2
4
0
1
0
1
0
1
0
2
2
0
0
2
0
2
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
2
0
1
1
1
2
0
1
1
0
0
1
3
0
1
0
1
0
1
0
1
0
1
0
2
0
0
2
1
0
0
1
1
1
0
0
1
0
1
3
0
0
1
0
3
1
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
2
0
0
1
1
1
0
0
1
0
2
0
2
1
1
0
1
0
1
1
0
0
0
0
1
1
2
2
2
0
0
0
1
1
0
1
0
1
0
1
1
1
0
2
0
1
0
1
1
0
2
0
0
0
2
2
0
0
0
0
1
0
0
1
0
2
0
1
0
1
2
2
0
0
2
0
0
0
2
2
0
2
1
0
2
3
1
0
1
0
0
0
0
2
2
1
0
1
0
0
2
0
1
0
2
1
0
1
1
0
2
0
0
0
0
0
0
0
2
0
0
1
0
2
2
1
0
1
0
0
0
0
0
1
1
2
2
1
0
0
1
1
1
0
1
1
1
0
2
0
0
0
1
0
0
1
0
1
2
2
0
0
1
0
0
1
0
0
2
0
0
2
0
1
0
0
0
0
1
0
1
1
1
0
2
0
0
0
0
2
1
1
1
0
0
2
0
1
0
0
0
0
2
0
2
0
0
0
2
0
0
1
1
0
2
0
1
0
0
2
0
1
0
1
1
2
0
0
2
0
1
0
0
0
1
0
2
0
0
0
2
0
1
0
1
2
0
0
0
1
1
2
0
2
1
0
0
2
2
1
1
5
0
2
0
0
2
0
0
3
1
1
1
1
0
1
2
0
2
0
1
4
1
0
0
2
0
1
3
0
1
1
0
0
0
1
0
0
0
2
1
0
0
0
2
0
2
0
0
2
0
1
0
0
2
0
1
1
2
0
1
0
2
1
1
1
0
0
0
0
1
1
0
0
2
0
0
1
0
1
1
1
0
2
2
0
0
0
2
1
1
1
1
0
3
1
2
0
1
0
0
0
2
0
2
0
0
2
1
0
0
0
1
0
2
2
0
0
1
0
1
0
0
1
0
0
1
0
2
1
0
0
2
1
2
0
0
2
1
0
1
0
2
1
0
2
0
0
0
0
2
0
0
1
0
3
1
2
2
1
0
0
2
0
1
1
0
0
1
2
2
0
0
0
0
0
3
1
2
0
1
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
1
1
1
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
1
2
1
0
1
0
0
2
2
0
1
0
0
0
4
0
0
0
1
2
1
0
3
0
0
0
0
1
0
0
2
0
1
1
0
1
2
1
2
2
0
0
2
1
2
1
2
0
0
0
2
1
0
0
2
2
0
0
0
0
1
0
1
2
0
1
2
0
1
1
0
2
0
1
2
1
2
1
1
0
0
0
0
2
0
1
0
0
0
0
2
0
1
2
1
0
0
2
1
0
0
0
0
0
1
1
1
1
2
1
1
0
1
2
0
0
0
1
1
2
2
1
0
0
2
0
0
0
0
0
1
0
2
2
2
2
1
1
0
0
1
1
0
2
1
0
1
1
2
1
0
0
0
0
1
0
1
2
1
0
0
0
1
0
1
0
0
1
0
2
1
2
0
2
0
2
0
0
0
1
0
2
0
1
0
0
2
0
0
1
2
0
0
0
0
1
0
2
2
0
0
0
0
2
0
1
0
0
0
3
1
0
1
1
0
0
0
3
0
2
1
1
1
2
1
0
0
1
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
1
1
2
2
1
1
0
1
1
0
0
1
0
2
0
0
0
2
0
1
1
1
0
0
1
0
0
1
2
0
0
0
2
1
2
4
1
2
0
0
2
0
2
1
0
2
0
0
0
3
0
0
1
2
2
2
1
0
0
1
2
1
0
1
0
2
2
0
0
0
0
2
1
1
0
0
0
0
1
0
0
2
0
0
0
0
3
0
1
2
0
3
2
1
1
0
1
2
1
1
1
0
0
1
0
1
0
0
0
2
2
0
2
1
2
1
2
1
0
1
1
0
4
1
2
0
1
0
0
0
0
2
0
0
1
2
2
2
1
0
2
0
0
2
0
2
0
0
0
0
0
2
2
2
0
1
2
1
1
2
0
0
1
2
0
0
0
0
2
0
2
0
0
1
2
2
0
0
0
1
2
1
0
3
2
1
0
2
0
2
2
0
0
2
0
2
1
1
1
0
2
0
0
2
0
1
0
0
0
1
1
1
1
1
2
2
0
1
2
0
1
1
1
0
0
0
1
0
0
1
1
1
0
1
0
1
0
1
2
1
0
1
1
0
2
2
2
0
1
0
0
2
2
0
1
0
0
1
0
2
0
2
1
1
3
1
2
1
0
0
0
2
0
1
0
0
0
0
0
0
1
1
2
2
1
0
0
0
1
0
2
2
0
1
1
0
0
0
1
0
0
1
0
0
2
0
1
0
0
0
2
2
0
1
0
0
1
0
1
0
1
1
2
0
0
0
1
0
0
1
0
0
0
2
1
2
0
1
0
1
1
0
2
0
0
0
2
2
1
0
0
1
0
0
0
3
1
1
0
1
1
2
1
0
1
2
2
1
1
2
0
0
0
0
1
1
0
2
2
2
0
0
0
4
1
0
1
2
2
0
1
1
0
2
1
0
1
2
1
1
1
1
1
2
0
0
1
2
0
2
0
1
2
2
1
0
1
1
0
0
2
1
0
1
0
1
1
0
0
0
0
0
2
1
1
0
1
0
0
2
2
2
4
1
1
1
1
2
0
0
1
1
0
0
0
1
2
1
0
1
2
1
0
1
0
2
0
2
0
2
1
0
2
0
2
0
1
0
0
0
0
1
1
0
0
2
0
2
0
0
0
3
2
2
2
0
1
0
2
0
2
3
1
0
0
1
1
1
1
1
1
2
0
1
0
0
1
0
2
1
0
1
0
1
0
0
1
0
1
1
2
0
2
1
0
0
0
2
0
0
0
1
0
1
1
1
0
0
1
1
0
2
0
2
2
0
1
2
1
2
0
1
1
0
0
1
2
1
0
0
0
1
0
0
1
2
0
1
0
0
0
1
2
1
0
1
1
0
0
1
3
1
1
0
1
1
0
1
0
0
1
0
2
1
0
0
0
0
2
0
0
0
0
0
0
1
0
1
1
0
1
0
1
0
2
3
0
1
0
0
2
1
0
1
0
1
0
1
0
0
1
0
1
0
0
0
1
0
1
0
2
2
0
1
1
1
0
0
2
2
0
2
1
0
0
2
1
0
0
0
0
2
1
1
1
2
0
0
1
1
1
1
0
2
2
2
0
0
0
1
2
0
2
2
0
2
1
1
0
0
2
0
0
0
1
2
0
2
2
0
1
1
1
1
0
1
0
0
2
2
0
2
0
1
1
0
0
1
2
1
1
2
2
1
0
0
1
2
1
1
1
0
0
0
0
2
0
1
0
1
2
0
1
0
1
0
0
2
1
0
0
1
0
2
0
0
0
2
1
3
0
1
2
1
2
1
0
0
1
0
0
0
1
1
0
2
0
1
2
0
0
0
0
0
0
1
2
2
0
2
1
1
0
0
0
1
1
0
0
2
0
1
2
0
0
0
2
2
0
3
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
2
1
0
0
2
0
0
0
1
1
0
0
0
1
0
1
1
2
0
0
2
1
0
0
0
0
1
0
1
0
3
0
1
1
0
1
1
0
0
4
0
1
1
1
1
0
1
0
1
1
2
1
0
2
1
0
1
1
2
2
1
0
1
1
1
1
2
0
0
0
0
1
1
2
1
1
0
0
1
0
0
2
1
0
0
1
0
1
0
0
1
1
1
0
0
0
1
2
1
1
1
0
0
2
1
0
0
0
0
1
0
0
1
1
2
1
1
0
0
0
1
1
2
0
0
1
2
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
2
0
0
0
1
2
2
2
2
1
0
2
1
0
0
2
1
1
2
0
0
3
1
0
2
1
1
2
2
0
0
0
0
2
2
2
1
0
0
0
2
1
0
1
1
0
0
1
0
1
1
1
1
0
0
1
2
1
0
0
0
0
1
0
1
1
2
0
1
0
0
2
1
0
1
2
0
0
0
0
0
1
1
0
1
0
1
0
1
1
0
0
3
0
1
0
1
2
2
2
1
2
4
0
1
0
0
0
1
2
0
0
1
0
2
0
0
1
2
0
1
0
0
0
0
1
0
2
1
1
1
0
0
2
0
2
0
1
1
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
2
2
0
1
2
0
0
1
1
2
0
0
1
2
3
0
3
1
0
1
0
0
0
2
1
0
0
1
1
1
0
1
0
0
0
0
0
1
0
0
2
2
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
2
1
0
1
2
1
0
0
2
1
2
0
1
2
2
0
0
1
1
2
0
1
0
2
0
0
1
0
0
0
2
0
2
1
1
0
2
0
1
0
0
1
1
1
0
1
2
0
1
0
0
1
1
0
1
2
2
0
1
0
2
2
2
1
0
1
2
0
1
0
0
1
2
0
2
1
5
0
1
1
1
5
0
0
1
0
0
2
0
2
1
0
2
2
0
1
1
0
0
0
0
0
0
0
1
0
1
2
0
1
1
1
0
1
0
0
0
1
0
1
1
1
0
0
0
3
0
0
1
0
0
2
0
1
1
3
1
0
0
1
1
2
0
0
0
2
0
2
0
1
0
1
0
0
2
1
1
0
0
1
2
0
0
1
1
0
2
0
2
1
0
1
0
1
2
1
2
2
0
0
1
3
1
0
0
0
0
0
1
0
0
1
3
0
0
1
0
1
0
1
1
1
0
0
0
0
1
0
2
0
0
0
2
0
1
2
0
2
0
1
0
0
1
0
1
0
0
0
0
0
0
5
0
1
0
1
1
2
2
0
1
0
1
2
1
1
1
0
2
2
0
2
0
0
0
2
1
0
0
2
1
0
0
0
1
1
2
1
0
0
1
2
1
1
0
0
0
0
2
2
1
2
0
0
0
0
1
1
0
0
0
2
1
0
0
1
0
0
0
0
0
1
1
1
0
0
5
0
1
1
0
0
1
0
0
1
0
1
3
1
0
1
2
0
2
2
0
0
0
2
1
2
0
0
1
2
1
2
1
0
1
1
0
3
0
1
0
2
0
1
2
1
1
1
1
0
1
0
0
2
1
0
2
0
2
0
0
0
0
2
0
0
2
0
3
1
0
1
2
0
0
1
0
2
2
1
1
1
1
1
2
1
1
0
1
0
0
0
2
2
0
0
0
1
0
0
2
0
0
1
0
0
0
0
2
2
1
2
2
3
1
0
0
3
0
0
0
2
0
2
0
1
0
1
0
2
0
0
2
1
1
0
1
0
0
2
1
1
2
0
0
2
0
1
1
0
0
0
0
0
0
1
1
0
1
1
4
0
2
0
2
2
0
1
1
0
1
0
0
1
0
0
1
2
1
2
1
0
1
2
2
0
0
0
0
0
1
0
1
0
1
1
0
1
0
0
0
0
1
0
0
0
3
0
2
1
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
1
5
1
1
0
0
1
1
2
1
1
0
1
1
2
0
0
1
1
1
1
1
0
1
2
2
0
2
0
1
2
0
0
3
0
0
0
2
1
0
1
1
2
2
0
1
1
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
2
0
2
1
0
0
2
0
0
0
0
0
1
0
0
1
1
1
1
0
0
1
0
2
1
1
2
1
1
0
2
2
0
0
0
1
3
1
0
1
0
2
0
4
0
1
2
0
0
2
2
0
0
1
0
0
2
0
1
2
0
0
2
1
2
0
0
1
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
1
1
2
2
0
2
2
0
0
2
0
2
1
0
2
2
2
1
0
1
0
0
0
0
1
1
0
2
0
1
0
2
0
0
1
0
2
2
2
0
2
0
0
0
1
0
0
0
0
2
0
0
1
0
1
1
2
1
1
2
0
1
1
1
1
0
0
1
2
0
2
1
0
2
2
0
2
0
1
1
2
2
2
1
0
0
0
0
3
1
0
0
2
0
0
1
0
2
1
5
2
2
2
1
0
0
0
1
1
0
0
2
2
0
0
0
2
0
1
0
1
0
1
1
2
0
1
0
0
0
0
0
1
0
2
0
0
2
0
0
2
0
2
0
0
2
0
0
0
1
0
2
1
1
0
1
0
2
0
1
2
0
1
0
1
0
5
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
2
1
0
0
1
4
2
1
2
1
2
1
0
0
2
0
2
0
0
2
0
0
0
0
2
0
0
1
1
0
1
1
0
0
2
0
1
1
0
1
0
0
2
0
0
2
0
2
0
2
0
0
2
1
2
0
1
0
0
0
0
0
0
0
2
2
0
0
3
1
1
2
0
0
1
1
0
0
0
1
1
1
1
0
0
0
1
0
1
0
1
1
0
1
2
0
0
2
0
0
0
0
2
0
1
0
0
0
0
2
2
2
2
1
0
1
0
2
1
1
2
0
0
0
3
0
2
0
1
1
0
0
1
0
2
0
2
1
0
0
0
2
0
1
1
0
0
0
0
1
0
1
0
2
2
0
1
0
2
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
1
0
1
0
0
1
0
2
2
1
0
0
0
0
0
0
0
1
0
0
1
0
1
1
2
0
0
0
1
0
1
0
0
0
2
1
0
1
0
2
0
0
0
1
0
2
0
0
1
1
0
1
0
1
3
1
0
0
0
3
2
2
1
0
0
2
0
0
3
0
2
2
0
1
1
1
4
1
1
0
2
1
2
0
0
2
0
3
0
0
0
1
0
0
1
1
0
2
1
2
0
2
0
2
0
1
1
0
0
0
2
2
1
0
2
0
2
1
0
0
0
0
1
2
0
0
0
0
1
0
1
0
1
0
0
3
1
0
0
2
1
0
1
2
0
0
2
0
1
1
0
1
1
0
0
0
0
2
1
1
0
2
0
0
1
1
1
0
0
1
1
0
0
1
0
0
1
1
0
0
1
3
0
2
0
1
1
0
0
1
0
0
0
1
1
2
1
2
0
1
2
0
2
0
0
0
0
2
0
1
1
1
0
0
0
1
2
2
0
0
0
1
1
2
0
0
0
0
1
1
2
1
0
2
0
0
1
2
0
0
2
0
2
1
1
1
0
0
0
2
0
1
0
1
2
1
0
2
1
1
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
3
0
1
0
1
0
1
0
3
2
0
1
1
0
0
0
0
1
0
1
1
1
0
2
0
1
0
0
0
0
0
2
0
1
0
2
0
0
1
2
1
0
2
0
0
0
0
2
1
1
1
2
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
2
0
0
0
1
0
0
0
0
2
1
0
0
2
1
0
1
0
0
0
0
0
2
1
2
2
0
0
0
1
1
0
2
2
2
0
0
0
0
1
2
0
1
0
2
0
0
0
0
0
2
1
1
0
0
4
0
0
2
0
2
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
1
0
2
1
2
2
2
0
0
0
2
1
1
0
0
1
1
1
1
1
0
0
0
1
0
0
0
1
0
0
1
1
1
1
0
0
0
1
0
0
0
0
2
0
0
2
0
1
1
0
2
1
0
0
4
2
1
0
2
1
2
2
0
0
1
0
2
0
1
0
0
2
0
0
1
2
0
0
2
1
1
2
1
2
1
2
2
1
2
0
0
2
1
0
2
1
1
0
0
1
0
0
1
0
0
3
1
0
0
1
2
2
1
1
1
0
0
0
2
2
0
1
2
2
0
2
1
1
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
1
0
1
0
0
0
0
0
2
1
0
1
0
1
2
1
0
0
0
1
0
0
1
1
0
4
1
0
2
1
0
2
1
1
0
2
0
1
0
0
0
1
2
0
2
2
0
0
1
0
2
4
0
1
1
2
1
2
1
0
1
0
1
0
0
0
1
1
1
0
0
1
2
2
2
1
1
2
2
1
2
2
0
2
0
2
0
0
0
0
2
2
0
0
0
0
2
1
0
1
1
0
0
0
0
1
1
0
0
1
1
2
2
0
1
0
2
1
0
1
1
2
0
0
2
0
0
0
1
1
0
0
2
0
0
0
2
0
1
2
0
0
2
0
2
1
1
1
2
2
1
3
1
1
0
0
2
0
2
2
2
1
0
0
0
2
1
0
2
0
0
2
0
1
2
1
2
0
0
0
1
0
0
1
2
1
0
0
3
2
2
0
0
2
2
2
0
1
4
0
0
1
0
0
0
2
0
2
0
0
2
0
0
0
2
0
0
0
0
1
0
1
1
0
0
2
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
2
0
2
0
1
1
1
0
1
0
0
1
0
0
0
2
2
2
0
1
1
1
1
1
1
1
1
1
0
1
0
0
0
1
0
0
0
0
1
0
1
2
0
2
0
0
2
1
1
2
0
0
0
2
0
2
2
0
1
2
1
0
0
1
0
0
0
3
0
0
1
0
0
0
3
0
0
1
3
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
2
0
2
2
0
0
2
2
0
2
2
0
1
0
0
1
1
2
0
2
0
2
0
2
1
0
1
1
0
2
2
0
0
2
0
0
0
1
0
0
0
2
1
1
2
3
2
0
1
1
0
1
1
1
2
1
0
2
1
0
3
1
2
0
2
0
2
1
1
0
1
0
0
1
0
2
0
0
0
0
0
2
2
1
1
2
1
0
0
1
1
2
2
1
1
1
1
1
0
0
2
0
2
1
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
2
1
0
0
0
0
0
1
0
0
0
1
1
0
2
0
1
0
0
2
1
2
0
0
2
1
1
0
0
1
0
0
0
1
1
0
0
2
0
1
0
1
2
2
0
0
0
1
0
1
0
2
0
0
0
2
1
0
1
1
2
0
0
0
2
2
2
2
1
0
0
1
0
0
0
2
1
0
2
1
2
0
2
0
1
0
1
0
1
0
1
4
0
1
1
2
0
0
0
2
1
1
2
0
1
1
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
2
2
1
0
1
0
0
1
0
0
1
2
0
1
0
0
2
0
2
0
1
0
0
1
0
0
0
2
1
0
2
0
2
1
1
0
1
0
2
2
2
2
0
1
1
0
0
0
0
0
0
0
0
0
2
2
1
1
1
1
1
0
2
2
0
1
1
1
0
2
2
0
0
2
1
3
2
0
0
0
2
0
1
0
0
1
1
2
1
2
0
0
2
0
5
1
1
2
1
1
1
2
0
1
2
0
0
1
0
1
2
3
3
1
0
0
0
2
2
2
0
1
0
0
0
0
0
0
2
1
1
2
0
0
0
0
0
1
2
0
1
1
1
2
2
0
0
0
0
2
0
0
0
3
0
2
1
0
1
1
2
0
0
0
2
0
0
3
0
2
0
2
1
0
0
1
0
0
2
2
1
1
1
2
1
0
2
1
1
2
3
0
1
0
3
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
1
1
0
2
2
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
1
1
0
2
0
0
1
0
0
0
1
0
2
0
0
2
0
1
1
2
0
0
1
2
0
0
0
0
3
0
1
0
1
2
0
0
0
1
1
1
2
0
0
3
1
1
1
1
2
2
0
0
1
2
2
1
0
0
0
1
2
1
2
0
1
0
2
0
0
2
4
1
2
0
1
1
0
2
2
0
1
0
0
0
1
0
1
0
3
0
0
1
0
0
0
0
2
0
1
0
1
2
0
2
0
0
0
2
1
0
0
0
2
2
2
0
1
0
0
2
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
2
0
1
1
0
0
8
1
0
0
1
0
1
2
0
1
1
0
1
2
1
0
2
0
1
0
0
0
2
1
1
0
0
0
2
1
2
0
0
0
1
1
0
0
1
2
2
1
1
1
1
0
1
0
2
0
3
0
1
1
0
3
0
1
0
0
0
1
0
1
0
0
1
0
4
1
1
0
0
1
0
1
1
0
2
1
0
3
0
1
2
2
2
1
0
1
0
1
1
0
1
1
0
0
0
0
0
0
2
2
2
0
3
0
0
2
1
0
2
2
0
0
1
2
0
0
0
1
0
1
2
0
0
1
1
0
2
2
0
1
0
1
0
2
0
0
2
0
0
0
1
3
2
1
0
0
1
0
2
2
0
0
0
1
0
2
0
1
0
2
2
2
1
0
0
1
0
1
0
0
1
0
2
0
1
0
0
2
2
0
1
2
1
3
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
4
0
0
1
0
0
2
0
0
2
2
1
2
1
0
1
0
0
0
1
0
0
1
0
2
0
0
0
0
1
2
1
0
0
1
1
0
1
0
2
0
0
1
0
2
3
1
3
0
0
1
0
1
0
0
0
2
1
1
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
2
2
3
0
0
0
2
0
0
0
1
0
0
1
1
1
0
0
1
2
0
3
1
1
3
0
1
0
0
0
0
2
1
0
0
2
0
2
0
0
1
2
0
0
1
2
1
1
0
0
0
0
1
0
1
1
0
2
2
2
0
2
0
0
1
0
1
1
0
2
0
0
0
0
2
0
0
1
1
0
1
2
1
2
0
0
0
2
2
0
1
1
2
2
1
2
0
0
0
0
0
1
2
0
0
2
1
2
1
0
0
1
0
0
0
0
2
1
0
1
1
0
0
0
1
0
0
2
0
1
0
2
1
0
0
2
1
2
0
0
0
0
1
0
2
0
1
2
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
1
1
1
0
1
3
1
2
0
1
0
0
0
0
2
1
1
2
1
0
0
0
0
2
1
1
0
0
0
2
0
1
0
0
0
0
0
2
1
1
0
1
0
1
0
0
2
0
0
0
0
0
0
2
2
0
2
0
0
1
0
1
1
1
2
1
2
2
0
0
1
2
1
2
0
2
1
0
0
0
2
0
0
0
0
0
2
0
1
1
1
2
0
2
1
1
1
0
2
2
0
1
3
0
1
2
0
1
1
0
0
2
0
0
0
2
0
1
1
1
3
0
0
0
0
1
0
0
2
0
0
0
1
1
0
0
0
2
2
0
1
0
0
0
0
0
0
1
0
2
0
1
0
0
1
2
1
1
0
2
0
2
0
2
2
1
0
0
1
0
0
3
0
1
0
0
2
0
0
0
2
1
1
0
2
0
0
2
0
0
2
0
0
2
0
0
2
2
0
1
1
0
1
1
1
0
0
2
0
2
0
2
3
0
0
0
0
1
3
1
2
0
0
1
0
1
2
0
0
0
0
2
1
1
0
2
2
2
2
0
1
0
0
0
1
0
0
0
0
1
2
2
2
1
1
1
1
0
0
2
2
1
5
1
0
0
0
2
1
2
2
2
1
0
0
0
0
1
2
1
0
1
0
0
0
1
0
1
1
1
2
1
0
1
2
0
1
0
0
0
2
0
2
1
0
0
2
0
2
2
0
1
0
1
1
0
0
0
1
1
0
1
1
0
0
2
1
0
1
1
0
0
0
1
2
2
0
2
0
1
2
0
1
2
2
0
1
1
1
0
0
0
0
2
1
0
0
1
0
2
0
0
1
2
1
1
1
1
0
0
1
0
0
0
1
1
0
1
0
2
0
0
0
1
1
1
2
0
1
0
1
1
1
0
2
1
2
2
0
1
1
0
0
1
2
1
0
0
1
0
2
0
2
0
2
0
0
0
0
1
1
0
0
1
0
1
0
0
0
2
0
2
0
2
0
0
0
0
0
2
3
0
1
1
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
1
2
1
0
0
0
0
0
1
1
1
0
1
0
1
0
0
0
0
1
0
1
2
2
0
1
1
2
0
0
2
2
0
2
0
0
0
1
2
2
2
0
0
1
1
0
1
0
0
1
2
0
2
0
0
0
0
1
2
1
0
1
0
2
0
1
1
0
0
0
7
0
1
1
0
1
1
0
0
0
0
1
1
0
0
1
4
2
0
1
0
0
2
0
0
0
2
2
0
1
0
1
0
2
0
1
2
0
0
0
1
0
0
2
0
2
1
0
2
0
1
1
2
1
0
0
0
1
1
1
0
1
0
2
2
1
0
1
2
2
2
2
1
1
1
0
0
0
1
0
1
0
0
2
0
1
0
1
0
1
0
0
0
1
0
0
0
2
1
2
0
0
2
2
0
0
2
0
3
0
1
2
2
0
0
1
0
0
0
2
0
0
0
2
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
2
0
0
2
0
2
2
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
1
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
1
1
0
1
0
0
2
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
2
1
0
0
1
1
0
1
2
1
0
1
2
1
0
0
2
0
0
0
0
0
1
1
2
2
1
0
1
2
1
0
0
0
0
3
0
1
0
1
0
0
0
3
0
1
1
2
1
0
0
2
0
0
0
2
0
1
0
2
0
0
2
0
2
0
0
0
0
0
1
1
1
2
2
1
0
1
0
3
2
0
1
0
2
1
0
0
0
3
1
1
0
2
2
0
0
0
1
2
0
0
0
1
0
0
2
0
1
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
2
0
1
0
1
0
2
0
0
0
0
1
1
0
2
2
0
1
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
1
2
1
1
0
0
2
2
1
0
1
0
0
0
2
0
1
0
0
0
2
0
0
0
0
2
2
1
0
2
0
0
1
2
1
2
2
0
0
2
1
6
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
2
0
0
1
0
1
0
0
2
0
0
0
1
1
0
1
2
0
0
1
1
1
0
0
0
0
2
1
1
1
0
2
2
3
0
0
2
0
2
1
2
1
2
2
1
1
0
0
0
0
2
2
2
1
1
0
1
2
1
1
0
2
2
0
0
2
1
0
1
2
1
0
0
0
2
1
2
0
0
0
1
2
0
1
0
3
1
0
0
1
1
0
0
1
1
2
1
0
0
0
2
0
1
0
0
5
0
0
0
1
1
1
0
1
0
0
1
1
1
0
0
0
0
2
0
0
1
2
1
2
0
1
0
0
0
3
2
0
0
0
0
0
0
0
2
0
0
1
3
2
1
2
2
1
2
1
0
1
0
0
1
0
1
1
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
1
1
1
1
1
2
0
0
2
1
0
2
0
1
0
0
0
0
0
2
2
1
0
2
0
2
0
1
1
2
1
0
2
1
0
0
1
0
2
0
1
0
0
1
0
0
2
1
0
0
0
0
1
1
0
2
2
1
0
0
0
1
1
0
1
2
0
3
0
2
0
0
1
0
2
0
1
0
1
0
2
0
0
2
4
0
1
0
0
0
0
0
0
2
1
0
0
0
0
2
2
1
1
1
2
2
0
2
0
1
1
1
1
0
0
2
1
0
1
2
1
0
1
0
1
2
2
0
2
2
0
0
0
1
0
0
2
0
0
2
0
0
1
0
1
0
0
2
0
1
1
0
0
2
0
0
1
1
1
0
0
1
0
0
0
0
1
0
0
0
2
0
1
1
0
0
1
0
0
0
3
1
0
1
0
0
0
1
0
1
0
1
0
0
1
0
2
0
1
2
0
0
1
2
0
1
1
2
0
0
2
1
0
0
2
1
1
2
1
1
2
0
0
1
0
0
0
0
1
0
0
0
0
1
0
2
0
2
0
0
0
0
2
0
1
0
1
0
0
2
2
1
1
1
0
2
0
0
0
2
1
2
0
0
0
1
1
0
0
0
2
2
1
0
0
1
1
1
0
0
1
1
2
0
1
0
2
0
2
2
1
0
0
0
0
2
0
2
0
2
2
0
1
0
0
1
0
2
1
1
0
1
1
2
0
0
0
1
1
0
0
1
1
0
0
2
0
1
3
0
2
1
0
2
0
2
0
0
0
0
0
0
0
0
0
1
1
3
0
2
1
0
1
2
0
0
0
1
1
1
0
1
0
1
0
1
0
0
1
0
2
0
0
0
2
0
2
0
0
0
0
1
1
0
0
0
0
1
3
0
1
0
0
1
0
1
2
0
2
0
0
2
0
0
1
1
2
1
0
0
2
0
0
0
1
0
0
2
0
0
2
1
1
0
0
2
0
1
2
0
2
2
2
0
1
1
0
1
3
2
1
0
1
2
0
1
3
0
2
1
1
0
0
1
0
0
0
0
2
1
0
1
0
0
2
2
0
0
0
0
0
2
0
0
0
2
1
2
1
1
0
0
0
1
1
0
1
0
1
2
0
0
1
1
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
1
2
0
2
2
0
0
1
0
3
0
0
0
0
0
1
0
2
0
0
1
0
1
2
2
2
0
2
3
1
0
1
0
0
0
1
1
0
0
1
2
2
0
1
1
1
1
0
0
0
0
0
0
1
0
1
0
0
2
2
0
0
0
2
1
0
0
0
1
0
1
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
3
0
0
1
1
1
1
0
1
0
0
1
2
1
0
0
2
0
2
5
0
0
0
3
1
2
0
0
2
0
2
1
0
0
0
0
0
0
2
1
0
1
1
0
0
0
1
1
1
1
0
1
1
1
2
2
0
0
0
1
0
0
2
2
2
0
0
1
0
0
2
2
1
0
1
0
0
0
0
0
0
0
0
1
1
2
0
0
1
2
1
0
2
2
1
1
0
0
2
0
2
0
1
0
0
1
2
1
0
2
1
2
0
2
0
2
2
2
0
2
0
1
1
2
0
0
0
0
0
0
1
1
0
2
0
0
2
0
2
3
1
0
0
0
0
1
1
0
2
1
0
1
0
0
0
1
1
0
7
0
1
1
0
0
2
1
1
1
1
0
0
1
2
1
1
0
0
1
0
1
0
0
0
1
2
2
1
0
1
1
0
2
0
0
2
0
2
1
1
1
3
1
1
0
0
0
2
1
1
0
0
1
1
1
1
0
1
1
0
0
0
0
1
0
1
1
3
2
2
0
2
2
0
1
2
4
1
0
0
0
0
0
0
0
0
0
1
0
1
2
1
0
0
0
1
0
0
2
0
1
1
1
0
2
1
0
1
2
0
0
1
2
2
2
0
1
2
2
2
0
1
2
0
0
2
2
2
0
0
0
0
2
1
0
2
0
2
1
0
0
0
0
0
0
2
1
0
0
2
2
2
0
0
0
1
2
0
1
0
0
0
2
1
0
2
1
1
1
0
2
0
0
1
0
0
2
1
1
0
0
0
0
1
0
2
0
1
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
2
1
2
1
0
1
1
0
0
0
0
0
0
1
1
0
2
2
2
0
2
2
1
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
2
1
2
1
1
2
0
2
0
0
0
0
0
1
0
1
0
1
0
0
1
1
0
0
0
0
0
1
2
0
1
2
2
0
2
1
0
0
1
0
0
0
2
1
1
1
0
2
0
1
2
0
1
1
0
0
3
0
0
2
2
1
2
0
0
0
0
1
0
2
1
2
0
0
2
0
0
2
0
0
1
2
2
0
1
0
2
0
0
0
0
2
0
1
0
2
1
0
0
3
1
0
1
0
0
0
1
2
1
2
0
0
2
0
0
1
0
0
2
1
0
0
0
1
0
0
1
0
1
0
0
0
2
0
0
1
2
1
0
0
2
0
1
2
2
0
0
0
1
0
2
2
1
2
2
1
1
0
2
2
1
0
1
0
2
1
0
0
2
2
0
2
0
2
0
0
0
0
0
0
0
0
1
0
1
2
0
0
2
0
1
0
0
0
2
0
1
1
0
0
1
3
2
2
0
3
1
1
1
1
2
0
0
0
1
0
0
1
2
0
0
0
0
0
0
2
0
4
2
1
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
1
2
1
0
0
0
1
0
0
1
0
2
0
0
0
1
0
0
2
2
0
1
2
0
0
0
1
1
1
0
0
2
1
1
1
4
1
1
2
0
2
1
1
0
0
1
2
2
0
0
2
0
1
0
2
0
0
0
1
1
1
2
0
2
2
1
0
0
2
1
0
0
1
0
1
1
0
0
0
2
0
0
0
0
2
1
1
3
0
1
3
2
0
0
1
0
1
0
0
1
1
0
1
1
0
2
0
0
0
1
0
0
0
0
2
1
0
0
0
2
2
0
0
0
2
1
0
2
2
2
0
1
1
0
0
0
1
2
1
1
0
1
1
0
0
1
2
0
0
1
0
2
0
1
0
2
0
2
1
0
1
0
1
1
0
0
1
0
0
1
0
0
1
1
0
0
0
1
3
0
2
0
2
1
1
0
1
0
1
0
1
0
2
0
0
2
1
0
2
1
0
0
2
0
2
1
0
1
0
2
2
0
1
2
0
1
0
0
1
0
1
2
0
1
2
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
1
2
0
0
0
2
0
1
0
1
1
0
0
1
0
1
0
1
0
1
1
0
0
0
1
2
0
0
1
0
0
2
1
0
1
0
1
0
1
0
1
1
1
1
2
0
0
2
0
1
0
1
1
0
0
0
1
1
1
0
2
0
0
2
1
1
1
0
1
0
2
0
0
0
0
2
2
0
0
1
0
1
0
2
0
1
2
2
0
0
0
1
0
1
2
2
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
2
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
1
0
2
0
1
2
0
0
1
1
2
0
0
1
0
1
1
0
0
0
0
3
0
0
1
0
0
1
0
1
1
0
0
0
2
2
0
0
1
1
1
1
1
0
0
0
2
1
1
0
1
1
0
0
1
0
1
0
0
0
0
1
0
1
2
0
1
2
0
1
2
0
0
1
0
2
0
0
0
0
1
0
2
0
2
1
1
0
1
0
0
2
0
0
1
0
0
2
0
0
0
0
2
0
1
0
0
0
2
1
0
0
0
1
2
3
1
0
0
1
2
1
0
1
1
0
0
0
1
0
0
1
2
0
1
0
1
1
0
0
1
0
2
0
2
1
0
0
0
0
0
1
0
1
0
0
0
0
0
2
1
1
2
0
1
0
1
1
0
1
0
2
1
0
0
0
0
1
1
1
2
2
0
0
0
2
0
0
0
0
0
1
1
0
1
0
3
1
2
0
0
1
1
1
0
0
2
0
0
0
2
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
1
0
2
0
1
1
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
2
1
0
0
2
3
0
1
1
1
0
2
1
0
0
1
0
0
0
0
0
0
0
1
1
0
2
2
3
0
0
0
1
1
0
1
2
0
2
0
0
0
1
1
1
0
2
0
0
0
1
4
0
1
0
1
0
0
0
2
0
0
1
1
0
0
2
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
2
0
1
0
2
0
0
0
1
1
1
2
0
0
0
2
1
1
0
1
0
0
1
0
0
2
0
1
1
0
0
0
0
0
0
2
1
0
0
0
0
1
1
0
1
1
1
3
0
1
0
0
0
0
1
2
0
0
0
0
0
1
1
2
1
0
0
0
2
0
2
1
0
1
1
0
0
1
2
0
0
0
2
2
0
1
0
1
0
0
1
1
0
0
2
1
0
2
0
0
2
0
1
0
2
1
0
0
0
2
0
2
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
4
2
0
2
2
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
1
1
1
0
0
1
0
1
1
0
2
1
0
0
1
0
2
0
0
2
1
0
1
0
0
2
1
0
2
0
1
1
1
0
1
0
1
1
2
1
0
0
0
2
2
0
1
0
1
0
2
1
0
0
1
2
0
1
0
0
2
1
1
0
0
1
0
0
1
2
1
0
0
0
1
2
2
0
0
1
1
0
2
0
2
2
1
1
0
0
0
0
0
0
2
0
2
1
2
0
2
1
2
2
0
1
0
2
0
0
0
0
0
0
0
0
1
0
1
1
0
1
1
0
1
0
0
1
0
1
0
0
1
2
0
0
0
1
1
3
1
0
0
2
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
2
1
1
2
0
1
0
1
2
1
1
2
0
0
0
1
0
0
0
0
0
0
2
0
0
1
2
0
0
0
2
1
1
1
0
0
0
1
0
1
1
1
0
1
1
0
2
0
0
2
1
0
2
0
1
0
0
1
0
1
1
0
1
2
0
0
0
0
2
3
0
0
2
0
0
2
0
0
1
0
1
1
1
1
0
0
1
0
1
1
1
0
3
0
0
0
0
0
0
0
0
1
0
2
1
2
0
0
0
0
1
0
2
1
2
2
0
0
0
0
0
0
1
1
2
0
0
1
0
1
1
0
1
1
1
0
1
0
0
3
0
0
0
2
1
2
0
1
0
0
2
0
0
0
1
0
3
0
0
1
0
5
0
0
0
1
2
1
1
0
0
1
0
0
0
1
2
0
0
2
1
2
0
1
2
2
1
0
1
0
2
0
2
2
0
2
2
0
0
2
0
0
2
1
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
1
2
2
0
2
0
1
2
0
0
0
1
0
2
0
1
0
2
0
2
2
0
0
0
2
0
0
1
1
0
0
2
2
2
2
2
2
1
0
1
0
1
1
1
1
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
1
2
1
0
2
0
0
0
1
1
0
0
2
0
1
1
2
2
0
0
1
0
2
0
0
2
0
1
1
0
0
0
1
0
0
0
1
2
1
1
0
1
2
1
0
0
1
2
0
0
2
0
1
0
0
0
1
0
0
0
0
1
0
0
0
2
0
2
1
1
0
1
1
0
1
3
1
1
0
0
1
2
1
0
0
0
2
0
0
0
2
3
0
0
2
0
2
0
0
3
1
0
0
1
1
0
1
1
0
1
1
2
1
0
1
1
2
0
1
0
0
0
2
0
2
0
1
2
0
0
1
0
0
1
0
2
0
1
2
0
2
0
0
0
0
2
0
1
1
0
1
0
0
1
0
1
2
0
0
1
1
2
1
0
2
2
1
0
3
1
1
0
2
1
1
0
1
0
0
0
0
1
0
1
3
1
1
2
1
1
2
1
2
0
1
0
1
1
1
0
0
1
0
1
0
0
0
1
0
0
1
1
1
1
1
2
0
0
1
1
1
0
1
3
1
0
0
0
1
0
1
2
1
0
0
1
2
0
7
1
2
1
0
1
0
1
2
2
0
0
0
0
2
2
0
0
1
0
1
0
1
0
1
2
1
3
2
0
2
0
2
2
1
1
3
0
2
1
2
0
0
0
0
2
0
0
0
1
2
1
0
2
0
2
0
0
3
0
0
2
0
2
1
3
1
0
2
0
1
2
2
2
0
1
4
0
0
2
1
1
0
1
1
0
1
0
1
1
2
0
2
2
3
1
0
2
1
1
0
0
0
2
0
2
0
1
0
2
0
0
2
0
0
0
2
1
0
0
0
0
1
2
1
0
1
1
0
0
0
0
0
1
1
2
0
0
0
1
0
2
1
0
0
2
1
0
1
0
2
0
2
1
0
0
0
0
0
2
0
1
0
0
1
2
0
0
0
2
0
2
1
2
0
0
2
2
1
3
2
0
1
0
0
1
0
2
0
1
1
1
0
1
2
1
2
0
1
0
1
1
0
2
1
2
0
2
1
2
1
3
1
0
1
0
2
2
0
0
1
0
0
1
1
0
1
0
1
1
0
0
1
0
0
0
2
1
0
2
1
1
0
0
0
0
0
2
0
0
0
2
0
2
0
1
0
2
1
0
0
0
0
2
2
2
2
1
0
1
0
0
0
0
2
1
0
1
1
0
0
0
3
0
1
0
0
3
0
2
0
2
0
0
2
0
2
2
0
0
2
1
0
0
0
1
0
0
2
1
0
1
3
1
1
1
0
0
0
2
1
0
2
2
0
0
0
1
1
1
1
0
0
0
2
0
1
0
0
0
2
0
0
0
2
0
2
0
1
1
1
1
5
0
2
0
1
1
2
3
2
2
2
0
1
2
2
2
0
0
2
0
1
0
1
0
0
0
0
0
1
2
1
0
0
3
0
3
1
1
1
1
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
1
1
2
0
0
2
0
2
2
0
0
3
3
0
2
1
1
1
1
1
1
1
1
1
2
0
0
0
1
0
1
2
0
0
1
2
1
0
0
1
0
0
1
2
0
1
0
2
0
0
1
0
2
0
0
0
0
2
3
0
1
1
0
1
0
0
0
1
0
1
1
1
1
2
1
1
0
2
0
0
0
1
2
1
0
2
1
0
1
2
1
1
0
0
2
2
0
1
1
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
1
2
0
2
0
0
0
1
0
0
2
0
0
1
0
0
3
2
1
2
2
0
1
2
7
0
2
1
0
1
2
1
2
0
0
1
0
0
2
0
1
1
1
0
0
0
0
2
2
2
0
1
1
1
0
0
1
0
0
0
1
0
0
2
1
1
0
1
0
1
0
0
1
0
0
0
0
2
2
0
1
0
0
2
2
2
1
1
1
2
3
1
0
0
0
1
1
0
2
2
2
1
0
0
1
1
2
1
0
0
0
0
1
1
0
0
4
0
2
2
0
0
1
0
2
0
0
0
0
2
1
1
2
0
0
0
1
0
0
0
2
1
1
2
4
2
1
2
2
1
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
1
0
0
4
1
2
1
0
2
2
1
0
1
0
1
1
1
0
1
1
1
1
2
1
1
2
1
1
1
0
1
0
2
2
0
2
0
0
1
0
1
2
0
0
1
2
0
1
0
0
2
0
1
2
0
0
0
0
2
0
2
2
1
1
0
2
2
1
0
2
2
0
0
0
0
0
0
0
0
1
1
2
1
2
1
0
0
2
0
1
1
2
2
0
0
4
0
2
2
1
1
2
1
0
2
1
1
2
0
2
2
0
0
3
0
1
0
0
1
1
1
0
0
1
1
1
1
0
0
0
1
0
0
2
0
0
2
0
0
1
0
2
0
0
1
4
1
1
2
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
1
2
0
1
0
0
1
2
1
0
1
0
2
0
0
1
0
0
1
0
4
1
0
0
1
0
0
2
0
0
0
0
2
2
0
1
0
0
0
2
1
1
1
0
1
1
1
1
0
2
0
1
2
0
0
1
0
1
1
2
0
1
0
0
0
2
1
0
1
3
0
0
0
3
1
0
0
0
2
2
0
0
1
4
0
0
0
2
0
0
2
1
1
2
0
3
0
0
0
0
0
0
2
0
3
0
2
1
0
3
3
0
0
0
0
2
1
4
1
1
0
1
1
0
0
0
1
0
1
0
0
2
0
0
0
1
1
0
0
2
1
2
0
1
0
2
0
0
0
2
2
3
2
0
1
2
2
1
0
0
2
1
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
2
2
0
1
1
1
0
1
1
2
2
0
0
0
1
1
2
0
0
2
0
0
1
2
2
2
0
1
1
1
0
1
0
1
1
0
0
0
0
0
0
0
1
2
1
2
0
0
0
1
0
1
0
2
2
2
2
0
2
0
2
0
0
1
2
0
2
2
0
2
2
1
0
0
1
1
0
1
2
1
2
0
1
2
0
2
2
0
0
1
3
2
1
2
0
1
2
1
0
0
0
2
2
0
1
0
0
1
2
0
1
2
1
1
0
0
0
1
1
1
0
2
2
2
0
0
0
0
0
0
1
0
0
1
0
0
1
1
1
0
0
0
2
4
1
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
3
0
2
2
0
1
1
0
0
0
1
1
1
1
1
0
1
0
2
2
0
1
2
1
0
1
0
0
0
1
0
1
1
1
0
0
0
2
1
0
1
0
0
0
0
2
2
3
2
1
0
0
0
2
0
1
1
2
1
0
0
0
0
2
1
0
0
1
0
0
0
1
0
1
0
2
0
0
1
0
0
2
1
0
1
2
0
0
2
1
1
0
0
0
1
1
0
1
0
1
1
1
3
1
0
2
0
1
1
0
1
1
0
0
1
2
2
1
2
1
2
0
1
0
0
1
0
2
2
1
1
0
0
0
1
1
0
1
2
1
2
1
1
1
0
1
0
4
1
0
1
0
0
0
0
2
1
0
0
1
1
1
0
0
2
0
1
0
0
1
3
2
2
1
2
0
0
0
0
1
2
1
0
1
0
0
0
0
0
0
1
0
0
2
1
1
3
2
2
0
2
0
1
1
1
0
1
0
0
0
0
3
0
0
0
1
2
0
1
2
3
0
0
0
1
2
0
1
0
0
0
1
0
0
2
1
0
0
1
1
1
0
0
0
1
1
0
1
1
0
2
0
2
2
0
0
0
1
0
2
0
1
1
1
1
0
2
1
0
2
1
2
2
1
2
0
0
2
0
1
0
1
0
0
2
1
2
0
0
2
0
0
0
1
0
1
1
0
0
1
1
0
1
0
0
2
0
1
0
2
0
1
3
0
0
1
1
0
1
0
1
0
1
0
1
1
0
1
0
1
2
2
0
0
2
1
0
2
0
0
0
0
0
1
1
2
1
1
2
1
1
2
0
0
0
1
1
1
2
0
2
0
1
0
0
0
0
1
2
1
0
0
0
0
2
1
1
1
0
1
0
1
0
0
0
1
0
1
0
0
0
1
2
0
2
0
0
1
0
1
1
1
2
3
0
0
0
2
2
0
2
0
0
0
0
1
1
0
1
0
1
2
1
2
0
1
0
4
0
0
2
0
2
0
0
1
1
2
0
2
0
1
2
0
0
1
1
1
2
2
1
2
2
0
1
3
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
1
1
1
0
2
2
0
2
2
1
1
0
1
2
0
5
1
2
0
2
0
0
0
1
1
0
0
0
1
0
1
0
2
0
2
0
0
2
2
1
0
1
2
0
2
1
0
1
0
0
0
0
2
0
0
1
0
0
1
1
0
4
0
3
0
0
2
2
2
2
1
1
0
2
1
5
1
0
0
0
2
2
1
1
1
1
2
2
0
4
0
0
1
0
0
2
0
1
0
0
0
0
0
1
1
0
2
2
0
0
0
0
0
1
0
0
1
0
1
8
1
1
0
0
0
3
0
1
2
2
0
0
0
0
2
2
0
1
2
1
1
0
0
0
0
2
2
0
0
0
0
0
0
1
2
2
0
1
2
0
0
1
1
0
1
0
0
1
0
0
0
0
1
2
1
1
1
2
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
1
1
1
0
0
1
2
0
2
0
0
1
2
0
0
1
1
0
1
1
2
2
0
0
0
3
2
1
1
0
2
0
0
2
2
1
2
0
0
2
0
2
0
2
1
0
2
2
2
2
0
2
0
0
0
0
1
1
1
0
0
2
2
1
0
1
1
0
1
2
1
1
0
2
0
2
0
0
2
0
1
1
1
1
2
1
1
2
2
1
0
1
0
0
0
2
3
0
2
0
1
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
1
0
2
1
0
1
2
0
2
2
1
0
1
1
0
1
1
1
0
1
0
1
1
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
3
0
0
0
0
1
1
2
1
0
0
0
1
0
2
0
0
2
0
2
1
2
2
2
2
0
0
0
2
0
2
0
1
1
2
1
2
2
2
2
0
2
1
0
2
0
0
2
0
0
0
2
2
0
2
0
2
0
1
1
0
1
0
0
1
0
0
2
1
0
0
0
0
2
1
0
1
0
0
0
2
1
0
0
1
0
0
1
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
3
1
0
0
0
0
1
1
1
0
2
1
0
0
2
0
0
0
1
0
0
0
1
2
0
0
2
3
1
1
0
0
2
0
0
2
2
0
2
2
0
0
0
0
2
2
0
0
1
0
0
1
0
4
0
1
11
1
2
1
2
1
2
1
0
2
0
0
2
0
1
0
1
1
0
1
1
2
1
2
1
1
1
1
1
2
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
1
0
1
1
0
2
0
1
2
0
2
0
0
0
1
1
0
1
1
1
0
0
0
0
1
2
2
2
0
0
0
2
1
0
2
0
0
0
0
0
2
0
0
2
0
0
1
1
0
2
2
2
0
1
0
1
0
1
1
0
0
2
1
0
1
2
1
1
1
1
0
5
1
0
1
0
0
2
0
2
0
2
1
0
0
0
0
0
0
2
1
0
0
0
0
2
2
0
0
0
2
2
1
0
0
0
1
2
1
2
0
1
0
0
2
0
0
0
2
0
2
0
2
0
0
0
1
0
1
0
0
2
1
2
0
0
0
6
1
2
0
2
0
0
2
1
0
2
0
2
0
0
0
1
0
0
0
2
1
1
2
1
0
1
0
2
0
0
1
0
1
0
1
1
0
1
0
1
2
0
2
0
2
0
2
2
0
1
3
1
1
0
0
1
2
0
0
0
0
2
1
2
0
0
2
1
2
0
1
2
1
2
0
0
2
0
0
0
1
0
0
0
2
0
0
1
0
1
1
2
3
1
2
0
1
1
2
0
0
1
0
0
1
0
0
1
1
0
1
0
1
0
2
0
1
2
0
1
0
1
2
0
2
0
0
2
0
0
1
1
2
0
1
0
0
2
0
2
0
1
0
3
1
2
1
0
3
0
0
1
1
1
0
0
2
0
1
0
0
0
2
1
1
0
0
0
0
0
0
2
1
0
2
1
0
2
2
1
2
2
1
0
0
0
1
2
1
1
1
0
1
2
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
2
0
0
0
1
1
0
1
2
0
0
2
0
1
0
0
0
2
0
2
1
1
0
1
2
0
1
0
0
0
1
1
0
0
0
2
2
1
0
5
1
1
0
2
1
0
0
2
1
0
1
2
0
0
1
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
2
0
2
3
0
1
1
0
1
0
1
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
1
0
0
0
2
0
1
2
0
2
1
1
0
1
2
0
2
0
1
2
0
0
0
0
1
2
1
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
1
2
1
0
2
1
0
1
1
0
1
1
3
1
1
1
1
0
1
2
0
0
2
2
1
2
1
0
1
0
0
1
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
1
1
0
2
0
2
1
0
1
0
0
0
1
2
2
2
2
1
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
1
1
0
0
1
0
1
1
0
2
1
2
0
0
1
1
1
2
0
0
1
0
0
0
1
0
1
0
0
0
0
1
1
0
0
2
0
1
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
1
0
0
2
2
0
0
1
2
0
2
1
0
2
1
2
0
0
2
0
1
0
0
1
0
0
0
0
1
1
0
2
2
0
2
1
0
1
1
2
1
1
1
3
0
2
2
1
0
0
0
0
1
1
2
1
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
4
0
2
1
0
2
0
4
0
1
0
0
0
1
2
2
0
5
1
0
0
0
1
1
1
0
0
0
0
1
2
2
1
0
0
0
1
0
0
0
0
0
1
1
0
1
1
0
1
0
0
2
1
2
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
1
2
0
0
1
2
0
0
0
2
1
0
3
0
0
1
0
1
1
1
0
0
1
1
0
0
1
1
0
0
0
3
2
0
0
0
0
1
2
0
2
1
1
0
0
0
1
2
3
0
2
0
0
2
2
1
0
2
1
2
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
1
2
1
0
1
1
2
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
1
0
0
0
1
0
0
0
1
2
0
0
2
0
0
0
1
0
1
1
2
1
2
0
1
2
1
0
0
3
1
2
1
1
1
0
0
1
0
2
0
0
1
2
0
1
0
0
0
0
1
0
0
0
2
0
2
1
0
1
0
0
2
7
0
1
2
1
0
2
1
1
1
1
0
0
3
0
0
1
0
0
0
0
0
1
0
0
1
0
2
1
0
0
0
1
0
0
2
1
1
0
0
0
2
1
1
2
0
1
1
2
1
0
1
0
0
2
1
0
0
1
0
0
0
2
0
0
1
0
1
0
1
1
0
0
1
1
0
0
0
2
1
0
2
0
1
1
1
0
1
1
1
0
0
0
0
2
0
1
2
0
1
1
1
2
2
0
1
0
1
1
0
1
1
2
2
0
0
1
0
0
0
0
1
0
1
2
2
2
1
1
0
0
0
0
1
2
2
1
0
2
2
2
0
3
1
0
0
1
0
1
0
0
0
2
0
0
1
1
0
2
0
1
0
1
1
0
1
1
1
0
0
1
2
2
0
2
1
2
0
1
2
1
2
0
0
2
1
1
1
0
0
1
1
2
2
0
0
1
0
0
0
1
1
1
0
0
4
0
1
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
2
1
1
0
0
1
0
1
1
0
1
0
0
0
2
2
0
2
2
0
2
0
1
1
1
0
1
0
2
0
3
0
0
0
2
0
0
1
2
0
0
0
1
2
0
1
0
0
2
1
1
1
0
1
1
0
0
0
2
1
2
2
0
0
1
1
0
0
0
0
0
0
1
2
1
0
1
0
0
1
0
1
1
0
2
1
1
1
2
1
0
0
0
1
0
0
0
0
0
0
0
0
2
3
0
0
0
0
1
1
1
0
2
0
0
1
1
0
3
0
0
2
0
1
1
2
1
1
0
0
0
2
0
1
0
1
0
0
1
0
0
0
0
0
0
1
1
2
0
0
0
0
0
1
1
0
1
1
2
2
0
0
2
0
1
2
0
2
1
1
2
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
2
0
2
2
1
0
0
1
1
0
0
0
1
1
2
0
1
1
1
0
0
0
2
2
0
2
0
0
1
1
0
2
1
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
1
2
0
1
2
0
1
0
0
1
0
0
0
0
0
1
1
1
0
2
0
3
2
0
3
1
0
0
0
1
1
0
0
0
0
2
1
2
0
1
0
1
0
2
1
0
1
0
2
0
0
1
1
0
1
0
0
1
0
0
0
0
0
1
2
1
0
0
2
1
1
1
1
1
0
0
2
0
1
0
1
0
0
0
1
2
1
0
0
0
0
1
1
0
1
0
0
0
1
1
0
0
2
1
0
0
1
0
1
0
0
0
0
0
0
2
1
1
0
1
0
1
2
2
0
0
1
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
1
1
2
2
0
0
1
0
1
0
0
2
0
0
2
0
2
0
0
1
2
1
0
0
4
0
1
0
2
1
0
0
2
1
0
0
0
0
2
0
0
2
3
0
1
0
1
0
0
1
0
0
2
0
1
1
0
0
0
0
0
2
4
2
1
2
1
0
2
0
1
2
2
0
1
2
1
0
2
1
0
1
0
2
0
2
0
2
1
2
1
0
2
0
0
0
1
0
0
0
1
2
0
1
0
2
2
0
2
2
1
1
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
2
1
1
0
1
0
0
1
0
0
0
0
2
0
2
1
1
0
0
1
1
1
0
2
0
0
0
1
1
1
1
0
0
0
0
1
0
0
3
2
1
1
0
2
1
0
0
1
0
0
1
0
0
2
0
0
1
0
0
2
2
2
0
2
0
0
0
2
2
1
1
2
1
2
0
0
1
0
0
0
2
0
0
1
2
0
1
0
0
0
0
1
0
1
1
1
0
0
2
2
1
2
0
0
1
2
1
0
1
1
2
0
0
1
0
1
1
0
0
1
0
0
1
0
1
0
1
2
2
0
0
1
0
1
1
0
1
0
2
2
1
0
2
0
0
1
2
2
1
0
0
2
0
1
0
1
1
1
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
1
1
0
1
2
0
0
0
2
2
0
0
5
0
0
0
1
1
2
0
1
0
0
3
1
0
0
2
2
0
1
1
2
0
0
1
0
1
0
0
0
2
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
1
2
1
1
0
2
0
1
0
2
0
2
3
0
0
1
1
0
1
0
0
2
0
0
2
0
0
0
0
0
0
2
1
0
0
0
2
2
2
2
1
1
1
1
1
1
0
2
2
1
1
2
0
1
0
1
0
1
0
0
2
2
0
0
0
3
0
0
0
0
1
2
0
0
1
0
0
1
2
0
2
0
0
2
0
0
1
0
2
0
0
2
1
0
2
1
2
0
2
2
0
1
2
0
1
1
0
0
3
0
0
0
1
0
1
2
3
1
1
2
1
0
0
0
2
0
2
0
2
0
2
2
0
1
1
0
2
0
5
0
2
0
3
1
2
2
1
0
0
0
2
2
0
2
0
2
2
2
1
1
1
1
1
1
0
0
2
0
0
0
2
0
2
1
0
0
0
0
2
0
1
2
1
0
0
1
0
0
0
2
1
1
0
2
0
2
1
0
1
0
0
0
1
0
1
0
0
2
0
0
2
2
0
0
1
2
0
0
0
0
0
0
0
2
1
0
0
0
3
0
0
0
2
0
3
1
0
0
0
2
0
0
1
2
1
0
2
0
0
2
0
0
0
0
0
0
2
0
0
1
0
1
2
1
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
1
2
1
1
0
1
2
2
1
2
0
0
2
0
1
1
3
1
0
1
1
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
1
2
1
1
0
0
0
1
0
1
1
0
1
1
0
1
0
2
0
2
1
0
0
3
1
0
0
1
0
0
3
1
0
0
4
0
0
1
3
0
1
1
1
1
0
1
0
0
1
1
0
1
2
1
2
0
1
3
1
3
0
0
0
2
1
0
2
1
0
4
2
1
1
1
0
0
0
0
0
1
3
0
1
1
0
4
0
0
0
0
1
2
0
1
0
3
0
0
0
1
2
1
2
0
1
1
1
0
1
2
1
0
0
2
2
1
0
0
0
1
0
0
2
2
0
0
1
0
1
2
0
0
0
1
0
1
2
2
0
1
1
0
0
0
0
0
1
1
0
1
0
0
0
1
1
1
2
0
1
0
2
1
1
1
0
0
2
0
1
0
0
0
0
0
1
2
1
1
0
0
3
0
0
0
0
3
2
2
1
1
2
2
0
0
2
0
1
0
1
0
2
0
0
1
1
0
0
0
1
1
2
2
2
1
1
0
0
0
0
1
0
2
0
0
2
1
1
0
0
0
1
0
2
2
0
1
1
2
0
1
1
0
0
1
0
1
2
4
0
0
2
2
1
2
0
2
1
0
2
1
0
0
2
1
0
0
1
2
0
2
1
0
0
2
0
0
1
1
1
0
1
1
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
2
1
1
2
1
0
1
2
0
0
0
1
0
3
0
0
3
0
0
0
0
0
0
2
0
1
0
1
0
0
1
0
0
1
0
1
1
0
2
0
0
0
1
3
0
0
0
2
0
2
0
2
0
0
0
1
0
0
0
0
0
2
1
0
2
1
0
0
1
0
1
0
0
0
1
1
0
1
1
1
1
0
3
1
0
0
1
1
2
1
1
2
0
2
2
1
2
2
1
0
0
0
2
0
0
0
2
0
0
2
0
2
2
2
1
2
0
1
0
0
1
1
0
2
0
1
1
3
0
1
1
0
0
0
1
0
0
1
0
2
1
2
0
2
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
2
0
2
0
1
1
1
0
0
1
2
0
0
2
1
0
2
1
1
0
1
1
2
1
1
2
2
0
1
0
0
1
1
1
1
0
0
0
0
1
0
1
1
2
2
0
2
0
1
2
1
2
1
1
0
2
1
1
0
2
0
0
1
0
1
0
2
2
0
0
2
2
1
0
0
2
1
0
0
0
1
3
0
2
0
0
1
0
0
0
1
3
0
0
1
2
0
0
1
1
2
2
0
0
0
1
0
0
0
0
0
1
0
0
1
2
1
2
0
2
0
0
0
2
0
3
0
1
0
0
2
1
0
0
1
1
0
1
0
1
1
1
0
0
2
0
1
1
0
0
0
1
1
1
0
2
0
0
1
0
0
1
0
0
0
2
2
2
0
0
0
0
1
1
0
1
0
2
0
0
0
1
1
1
0
1
2
1
0
2
0
2
0
0
1
0
0
0
1
0
0
1
2
1
2
1
1
0
2
1
0
1
0
1
0
0
0
0
1
0
0
0
1
1
0
1
0
0
1
1
2
1
0
2
1
0
1
1
1
2
1
2
1
0
0
1
2
0
0
0
1
1
1
0
0
1
1
1
1
0
0
0
1
2
1
3
1
1
0
0
1
2
0
0
0
0
1
1
0
0
2
1
0
0
2
0
0
0
2
0
1
0
1
2
2
0
0
1
0
0
0
1
0
1
1
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
2
0
0
0
1
0
4
1
0
2
1
0
0
0
0
0
1
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
6
1
0
1
2
1
0
2
1
0
0
0
2
2
0
0
1
2
1
0
0
0
0
1
1
0
0
1
1
1
1
1
1
1
0
1
0
3
1
1
0
0
0
2
2
0
1
1
0
0
0
2
2
1
0
0
1
0
1
2
0
1
1
0
0
1
0
2
1
0
1
3
0
3
0
1
2
0
0
3
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
1
1
0
1
2
0
0
2
1
2
0
0
0
1
0
0
3
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
1
2
0
1
0
0
1
3
0
1
0
1
1
2
0
0
1
2
0
1
0
3
0
2
2
1
0
2
0
2
0
1
1
0
0
0
1
1
0
2
0
0
0
0
2
0
0
2
1
2
0
2
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
1
1
0
1
0
0
0
1
2
0
0
0
0
1
0
1
2
1
1
1
0
1
0
0
0
1
0
2
0
2
2
0
0
2
0
0
2
2
1
3
2
2
0
0
1
0
1
0
0
1
2
2
0
0
1
0
0
1
0
2
1
3
0
3
1
1
3
1
1
0
1
1
1
1
0
0
0
0
0
0
0
0
0
1
1
2
2
0
1
1
1
0
1
0
2
0
0
2
2
0
0
0
0
0
1
1
1
0
0
1
0
0
1
2
0
2
3
1
0
0
3
0
1
1
0
0
2
2
0
0
1
0
1
2
0
1
1
0
0
2
0
2
0
0
0
2
1
1
0
1
0
0
0
0
2
2
0
0
0
1
2
0
0
0
0
2
1
0
2
0
0
0
1
1
2
0
2
0
1
1
0
0
2
2
0
2
0
0
0
2
1
0
1
5
0
0
2
0
1
2
2
1
0
1
0
0
1
2
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
2
1
0
1
1
2
1
0
0
1
0
2
0
3
1
1
0
0
1
0
9
0
2
1
0
1
2
1
0
1
1
0
1
1
0
2
1
1
1
2
1
2
1
0
0
1
0
2
1
1
1
2
0
2
2
1
0
1
0
1
1
2
0
1
0
0
0
2
0
1
1
0
0
0
1
0
2
0
1
1
2
0
0
0
1
0
0
0
2
1
2
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
1
2
1
1
1
2
0
1
0
0
1
1
0
0
0
0
1
2
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
3
1
1
0
2
0
0
0
2
0
0
0
1
1
2
1
1
2
0
0
0
0
2
0
0
0
2
2
2
1
2
2
2
0
1
0
2
0
2
0
0
2
2
0
1
0
1
0
1
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
2
0
2
0
0
2
0
1
0
1
0
2
1
1
0
1
0
0
0
2
0
1
2
0
5
0
1
1
1
2
1
2
1
0
1
0
0
0
1
1
0
1
1
1
2
1
1
1
0
0
0
0
2
0
0
0
2
1
1
2
2
0
2
0
0
1
0
1
0
0
1
1
2
0
1
2
3
1
0
0
1
1
1
3
1
0
1
1
0
0
1
0
0
0
0
1
2
0
0
2
1
2
3
1
1
1
1
0
1
0
2
0
1
0
0
2
2
1
2
0
2
0
2
1
0
1
1
0
0
0
2
2
1
1
0
0
0
0
0
0
0
2
1
1
0
2
0
1
0
2
0
1
1
2
0
1
0
0
1
0
1
1
0
2
0
0
1
1
0
3
1
0
0
0
1
0
0
1
0
0
2
0
1
0
2
2
4
0
4
0
0
1
0
3
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
2
0
0
0
2
0
0
1
1
0
0
1
0
1
1
1
2
0
0
0
1
0
0
0
2
1
1
0
1
1
0
0
1
1
0
1
0
2
1
1
0
2
0
1
0
0
0
0
1
0
1
2
1
1
0
0
2
0
2
2
0
1
2
1
0
2
0
0
0
1
3
0
0
0
1
1
1
0
0
0
0
0
2
1
0
0
1
1
0
1
0
1
0
0
0
1
1
2
0
1
0
0
0
1
0
0
0
1
0
2
1
0
1
2
1
1
1
1
1
0
1
0
0
0
2
2
2
1
0
0
0
0
0
2
0
1
1
1
1
1
0
2
0
1
2
0
1
2
2
2
1
1
1
2
2
0
2
0
0
1
2
2
2
2
0
0
2
0
0
0
2
2
1
2
0
0
1
1
0
1
0
2
1
1
1
0
0
0
2
0
0
2
2
1
0
2
1
0
0
0
2
0
0
2
0
0
2
1
0
0
0
0
0
0
2
2
1
0
0
1
0
0
1
0
1
1
0
1
1
1
1
1
1
0
0
1
1
1
0
1
0
1
0
0
1
2
2
0
2
0
0
1
2
0
1
1
0
0
2
2
0
0
1
0
0
0
1
2
0
0
0
0
1
0
0
2
1
0
1
0
2
1
2
0
0
0
0
2
0
0
1
2
2
0
0
0
2
1
0
1
1
1
2
0
0
0
2
2
0
0
2
2
1
1
0
1
0
0
2
3
0
1
0
1
0
0
0
2
1
1
0
1
0
0
2
2
0
2
1
0
1
1
0
1
2
1
0
0
1
0
1
0
0
1
0
1
1
1
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
1
1
0
0
1
1
1
0
1
0
0
2
1
0
1
0
0
1
0
2
2
0
1
1
0
2
0
1
0
2
0
0
1
0
0
3
0
2
0
1
2
2
0
0
0
1
0
0
1
0
1
2
1
1
0
0
1
2
0
2
1
1
0
0
1
0
2
1
0
0
0
0
2
0
0
0
0
0
1
1
2
1
0
0
2
0
0
0
0
1
0
1
1
3
0
0
2
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
2
3
0
1
0
1
1
0
0
0
0
2
2
1
0
1
0
1
1
1
4
2
0
2
2
0
0
1
0
1
0
1
0
0
0
2
1
1
0
1
0
2
1
1
1
0
0
0
2
1
3
1
0
0
1
0
1
0
0
1
1
0
1
0
2
0
0
0
1
0
0
2
0
0
0
1
2
1
2
0
1
1
0
2
0
0
1
0
0
0
1
1
1
2
2
0
1
2
1
0
0
0
1
0
2
0
1
0
1
0
0
0
1
2
1
1
1
1
1
1
1
0
2
1
0
1
0
1
0
0
1
0
1
1
0
1
1
1
0
0
0
2
0
0
1
1
0
1
1
2
1
0
0
0
0
0
2
2
0
0
0
0
1
2
0
1
0
0
1
0
1
0
0
0
0
2
2
1
1
0
2
1
0
1
0
0
0
2
1
1
0
0
1
0
0
2
1
0
0
0
0
0
0
1
0
2
1
0
0
1
0
1
0
0
0
1
1
0
2
2
0
0
2
1
0
0
0
3
0
1
0
0
0
0
2
0
2
0
1
1
1
1
1
0
1
1
2
0
0
0
0
1
0
0
1
2
2
0
0
1
0
2
2
2
0
2
2
1
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
2
2
2
1
0
1
2
1
0
2
1
0
1
0
0
1
0
0
2
1
0
1
2
0
1
0
0
1
0
2
0
0
0
1
1
0
2
2
0
0
2
0
1
1
1
0
1
0
0
0
1
1
2
2
0
2
2
0
2
1
1
1
0
1
2
0
1
1
2
2
0
0
0
1
1
2
2
2
0
0
0
2
1
1
1
1
2
0
0
2
0
1
1
2
0
0
0
0
0
2
0
0
2
1
1
1
2
0
0
0
2
1
0
0
1
2
1
2
1
0
2
0
1
0
0
1
0
0
1
0
0
2
0
2
0
0
2
0
0
0
0
2
2
2
0
1
0
1
1
5
0
0
2
1
1
2
0
0
4
1
0
1
0
1
0
1
0
0
0
0
0
0
2
1
0
0
2
0
1
1
2
1
1
0
0
2
0
3
0
2
1
1
2
0
1
2
1
0
0
0
0
1
1
0
0
2
0
1
1
0
2
1
1
0
0
2
1
0
0
2
0
0
0
1
0
1
0
1
2
1
0
0
0
1
0
0
0
1
0
1
0
0
2
2
2
1
0
2
0
2
0
1
2
2
2
1
3
0
0
0
1
0
2
1
0
0
2
2
0
1
0
0
1
0
2
2
1
0
1
0
0
2
0
2
0
1
2
2
0
1
0
0
0
0
1
0
2
1
1
0
2
0
0
0
0
2
0
1
1
0
0
2
0
0
0
1
2
2
2
0
1
0
0
0
2
1
1
0
1
0
0
0
1
0
0
0
1
2
0
0
0
2
0
0
1
2
0
0
0
2
2
2
1
1
1
0
1
1
2
1
0
1
2
0
0
0
0
0
1
0
0
2
0
2
0
1
0
0
2
1
1
0
2
0
1
0
0
2
0
0
0
0
0
1
2
0
0
0
3
0
1
1
2
0
2
1
1
0
0
0
2
0
0
0
2
1
2
0
1
0
0
2
1
0
1
1
0
2
0
1
0
0
0
2
0
0
0
1
0
1
1
2
0
1
1
1
1
0
0
0
0
1
0
1
2
0
1
0
0
2
0
1
0
2
2
2
0
2
1
2
0
2
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
2
0
2
0
2
1
2
1
0
0
0
0
0
2
0
2
2
2
0
0
0
3
0
1
0
0
0
1
2
2
1
0
0
0
1
0
0
0
2
1
0
2
1
0
2
0
0
0
0
0
0
0
1
1
2
1
0
2
1
2
0
0
3
0
0
1
1
0
0
1
2
1
2
1
1
0
1
2
0
0
0
2
0
0
1
0
1
0
0
0
2
1
1
1
0
0
0
0
0
0
2
5
1
1
3
1
0
4
1
0
0
0
0
1
0
0
2
2
0
1
0
2
2
1
0
0
0
2
0
2
0
0
0
2
1
0
0
0
0
0
0
2
0
1
1
0
1
0
1
1
0
0
2
0
1
0
0
1
0
1
2
3
0
1
0
2
2
1
1
2
1
1
0
2
0
0
1
0
1
0
2
0
0
1
1
1
0
0
1
0
0
1
1
0
0
8
2
2
2
2
1
2
0
1
0
0
0
0
0
2
1
0
1
0
0
2
0
0
2
1
0
2
0
1
1
1
1
0
2
2
0
2
0
1
0
0
2
1
0
2
0
0
2
0
1
0
1
0
0
1
0
0
0
2
0
1
0
2
2
0
0
1
2
1
1
0
0
0
0
2
1
1
2
0
2
0
0
2
0
0
0
0
0
1
1
1
0
1
0
0
1
0
3
1
0
0
0
2
0
1
0
1
1
0
0
0
1
0
1
2
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
1
1
2
2
2
0
0
1
1
0
0
1
1
2
0
2
0
0
0
1
1
0
2
0
2
1
0
1
2
0
0
2
3
1
1
1
1
0
0
0
0
2
1
2
1
1
0
0
0
1
2
0
0
0
1
0
0
1
3
0
1
1
0
0
1
0
1
1
0
0
2
1
0
2
1
0
0
2
0
0
0
0
3
0
2
2
1
0
1
1
0
0
2
2
0
2
0
1
0
2
0
0
0
1
0
0
0
0
0
2
2
1
2
1
0
0
2
1
0
1
0
1
0
2
0
2
0
0
2
2
0
4
2
0
1
0
1
1
0
1
0
0
2
0
1
1
1
1
2
1
0
1
1
0
2
0
1
0
0
2
0
1
0
0
0
0
1
0
0
2
0
0
1
2
2
1
0
0
1
3
0
0
1
0
0
0
1
0
1
0
0
0
4
1
0
1
0
1
2
1
1
0
0
0
1
1
0
2
0
0
0
1
0
0
0
1
0
1
0
2
1
1
0
2
0
0
2
2
0
2
1
0
0
0
1
0
0
0
1
3
0
1
1
2
2
0
1
0
2
2
0
1
2
1
3
0
2
2
1
0
1
2
0
0
2
2
1
2
2
2
2
0
0
1
0
1
1
1
0
1
2
1
1
0
1
2
3
1
0
1
1
0
1
1
0
1
0
1
2
0
2
2
0
0
1
0
0
2
2
2
0
2
0
0
1
1
1
2
2
0
2
0
1
0
0
0
0
1
0
1
2
0
2
1
0
0
0
0
0
0
0
2
2
0
0
0
1
0
2
2
0
0
0
0
2
1
0
0
0
0
0
0
3
0
1
1
0
1
2
0
0
1
1
0
0
2
0
2
1
0
0
0
1
0
0
2
0
0
1
1
1
0
1
1
0
2
1
2
0
0
2
1
0
0
0
0
0
2
1
0
1
0
2
0
0
1
1
1
0
2
2
1
0
1
2
0
0
0
0
0
1
1
0
0
2
0
1
3
1
2
0
0
0
0
1
2
2
1
2
0
2
1
0
1
0
0
2
0
1
0
0
1
0
1
0
1
0
0
1
2
0
0
0
1
1
1
2
0
0
0
0
1
0
1
0
1
0
1
1
0
2
1
1
0
0
0
0
0
1
0
0
2
2
1
0
1
0
1
0
0
0
1
1
0
2
0
2
0
0
3
0
1
0
0
2
0
0
0
0
0
1
0
1
2
0
0
0
2
1
0
1
2
0
0
0
0
2
0
2
2
1
0
0
0
0
2
0
0
1
1
1
0
0
0
1
1
1
1
0
0
2
2
2
0
0
0
1
0
2
0
0
0
2
1
0
0
1
1
1
0
0
1
0
0
1
0
1
2
1
2
0
1
1
1
0
1
0
0
1
1
0
0
0
0
0
0
1
1
0
1
3
2
2
0
1
0
0
1
1
1
1
1
0
0
0
1
0
0
0
0
1
3
2
0
0
0
0
2
2
0
0
0
0
1
0
4
2
0
2
0
0
1
2
1
0
0
0
0
0
1
0
0
2
2
1
1
1
0
0
1
0
0
0
0
1
0
0
0
3
0
0
2
0
0
2
2
1
0
2
1
2
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
2
1
6
1
1
1
0
0
0
1
2
1
0
2
2
0
0
2
0
0
0
0
0
1
1
2
2
1
1
0
1
1
1
1
1
1
0
0
1
1
1
1
0
0
0
0
2
0
0
0
2
2
0
2
1
0
2
1
0
0
0
1
0
1
1
0
0
0
0
0
1
2
0
1
1
0
1
1
0
0
1
0
0
0
0
0
1
2
0
2
1
0
0
1
2
0
1
3
0
0
0
0
3
0
1
1
0
0
1
1
0
1
0
1
0
0
0
1
0
1
0
2
2
1
1
1
0
2
1
2
0
0
0
0
2
2
0
2
2
1
0
0
0
1
1
2
0
0
0
1
1
0
1
0
0
1
2
0
0
0
1
0
0
1
0
0
0
0
2
1
2
0
2
0
2
0
2
0
1
1
0
1
0
0
0
0
1
1
1
0
2
1
1
0
1
2
0
0
0
2
1
1
1
2
0
1
0
1
0
0
0
1
0
1
0
2
0
1
0
0
2
2
0
1
1
1
1
1
0
0
0
2
1
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
1
1
2
1
0
0
0
0
0
2
2
0
1
0
0
1
1
1
2
0
1
3
0
0
1
2
0
0
0
1
2
1
1
2
0
0
0
0
0
0
0
2
1
2
0
0
2
1
0
0
0
1
0
0
0
1
1
0
1
0
1
0
1
3
0
1
0
1
1
0
0
0
2
0
0
2
0
0
0
1
2
2
1
2
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
1
3
0
0
1
1
2
0
1
0
2
0
2
0
0
1
0
0
0
0
0
1
1
2
0
0
0
1
0
1
1
2
2
2
0
2
0
1
0
0
2
2
1
0
0
0
1
0
2
2
2
0
1
1
0
0
1
0
0
0
0
1
0
0
0
2
0
2
1
2
0
1
1
1
0
2
1
0
0
2
2
0
1
2
1
1
2
2
1
2
2
2
1
0
1
0
2
1
0
0
0
0
1
2
0
1
0
1
1
0
0
1
0
2
0
1
2
2
1
0
1
0
0
2
0
0
2
0
0
1
0
2
0
2
2
0
0
1
0
2
0
0
0
0
0
2
1
1
2
0
0
0
0
0
0
1
0
0
0
2
0
0
2
2
2
0
2
1
0
1
1
0
0
1
1
0
0
3
0
1
0
1
2
2
1
0
0
1
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
1
1
0
2
1
0
0
7
2
0
0
1
1
1
0
1
1
0
0
0
0
2
1
1
0
2
2
1
0
0
2
2
0
1
2
1
2
2
1
2
1
3
4
0
0
3
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
2
5
1
0
2
1
0
1
1
0
0
2
0
0
0
0
2
0
0
1
1
0
2
0
1
2
1
0
2
0
0
0
1
0
0
0
2
2
0
2
0
1
1
1
0
0
0
2
0
2
0
0
0
2
0
0
2
1
2
0
0
0
1
0
1
0
1
1
0
1
1
0
2
0
0
0
0
0
1
2
1
1
0
1
0
0
0
1
0
0
1
0
0
2
2
2
2
2
2
0
4
2
0
1
0
0
2
0
0
1
0
0
1
0
0
2
1
0
2
1
1
2
0
0
0
2
0
0
1
0
2
0
0
2
0
1
3
2
2
1
0
0
0
0
2
1
0
1
1
2
1
1
0
1
2
1
0
0
0
0
0
0
0
0
2
2
0
2
2
1
0
0
0
0
0
0
1
0
2
0
0
1
2
2
0
0
0
2
1
2
1
2
2
0
0
0
0
1
2
0
0
2
0
1
0
1
0
2
0
0
0
2
0
1
0
1
0
1
0
2
2
0
0
0
1
0
2
0
2
0
2
0
0
2
1
2
0
0
0
1
1
0
0
0
0
2
2
2
0
2
0
2
0
2
0
2
0
0
2
0
0
0
0
0
0
2
0
2
1
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
2
2
0
0
0
0
0
0
2
1
0
1
0
5
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
2
1
1
1
1
2
2
1
0
2
1
0
0
2
2
1
0
0
0
1
2
6
0
1
2
2
0
1
1
1
0
2
1
0
0
0
2
0
1
0
0
0
2
0
0
2
0
0
0
2
0
0
1
0
0
0
1
0
2
0
1
0
2
1
1
2
0
0
2
2
1
1
0
2
0
1
2
0
2
0
2
0
0
1
0
0
0
1
1
2
0
2
2
2
0
1
0
0
0
2
1
0
0
3
1
0
1
0
2
2
2
2
1
2
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
1
3
0
2
2
0
0
0
0
1
2
0
0
0
0
2
0
1
2
0
0
0
2
1
0
2
1
0
2
1
1
0
1
2
1
0
1
0
1
0
0
1
1
0
0
2
0
1
2
2
1
2
0
1
2
1
0
0
1
0
1
0
0
0
0
1
0
0
0
2
2
1
0
1
0
0
1
0
0
1
0
2
1
0
0
1
2
2
2
0
1
0
1
1
1
0
1
0
1
1
2
0
0
1
1
2
0
0
0
0
3
2
0
1
1
0
0
2
0
0
0
0
1
0
1
1
1
1
0
1
0
1
1
1
0
0
1
1
1
1
0
0
0
0
0
0
0
1
2
0
0
1
0
2
1
1
0
1
0
1
1
0
0
0
0
0
1
0
0
3
1
0
0
0
0
1
0
2
0
2
1
2
3
2
0
1
0
2
2
1
0
2
3
0
2
0
0
0
1
0
1
1
1
1
0
0
1
0
0
2
0
0
0
2
3
1
0
0
1
2
1
0
0
1
0
1
0
2
1
1
0
0
2
1
2
0
0
2
1
0
0
0
2
1
2
2
0
1
0
4
2
0
2
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
1
0
2
1
0
2
0
2
0
2
0
0
1
2
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
1
1
0
1
0
1
1
0
5
2
1
0
0
1
0
0
1
2
2
0
0
0
1
0
0
1
0
1
0
0
1
2
0
1
1
1
1
1
1
2
2
2
0
2
0
0
0
0
1
1
0
1
0
1
0
0
1
1
2
0
0
1
0
2
2
0
1
0
0
0
0
0
1
2
2
2
1
2
0
0
0
1
0
1
0
2
2
0
0
2
2
0
0
0
0
2
2
0
0
2
1
0
1
0
0
0
1
1
0
0
1
2
0
2
0
1
1
0
1
1
2
1
0
0
0
0
1
0
0
1
1
1
2
0
0
0
2
1
2
0
1
1
2
0
0
0
0
1
0
0
0
0
1
1
0
1
1
1
1
4
1
0
1
0
0
0
1
1
2
1
2
2
2
1
2
0
2
2
0
0
2
0
0
0
2
0
1
1
0
2
2
0
1
1
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
2
1
0
2
0
0
0
1
0
0
0
2
1
0
0
0
2
1
0
0
1
1
0
0
0
1
0
1
1
1
2
0
2
0
2
1
0
0
0
0
2
1
1
1
0
0
1
1
0
0
0
2
0
0
0
1
1
2
1
0
0
0
1
1
1
0
0
0
0
0
1
0
0
3
0
0
1
2
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
2
0
0
1
2
0
0
1
0
0
1
1
0
2
0
0
0
1
4
0
0
2
1
0
1
1
0
0
1
0
0
1
0
0
2
1
0
0
2
0
1
0
0
1
2
0
0
0
0
0
2
0
2
1
1
1
0
0
1
2
0
0
1
0
1
0
1
1
1
2
1
1
0
1
0
0
1
1
1
0
1
0
1
0
1
0
2
3
1
0
1
2
1
1
0
0
1
0
0
1
1
1
0
0
0
1
2
0
1
2
2
1
0
0
0
0
0
1
2
4
2
0
1
1
0
0
4
2
0
2
1
0
0
2
0
1
2
0
1
1
0
0
1
1
0
0
0
1
0
0
0
1
0
0
2
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
2
1
1
0
2
2
0
1
0
1
0
2
0
1
2
0
0
0
0
1
1
0
0
0
1
1
0
1
0
1
0
0
1
0
2
2
0
0
1
2
0
0
0
2
1
0
1
2
0
0
0
0
1
0
1
0
1
1
1
2
0
1
2
0
0
3
1
1
2
2
2
1
0
0
1
1
0
0
2
0
0
0
0
0
1
1
0
0
0
1
1
0
0
1
1
0
2
1
0
0
0
1
0
0
0
0
2
0
1
1
0
3
1
1
0
1
3
1
1
0
1
0
0
0
1
0
0
2
0
2
0
0
0
2
0
1
0
1
1
1
2
1
1
1
1
1
1
2
0
0
0
0
0
1
2
1
1
1
0
0
1
1
0
0
0
0
1
0
1
0
0
0
2
0
0
1
0
0
1
1
0
2
3
0
0
0
2
0
1
1
0
0
0
1
0
1
0
3
0
0
0
0
2
1
0
0
0
2
2
0
1
1
0
2
1
4
1
4
0
0
0
1
1
0
0
1
0
0
1
0
0
0
2
0
1
2
0
0
0
4
0
0
2
1
2
1
0
1
2
0
0
2
0
3
1
3
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
1
1
3
0
1
1
1
0
0
0
1
0
0
1
1
0
2
0
3
1
0
0
2
1
0
0
0
2
0
0
0
1
0
0
0
4
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
2
1
0
0
0
1
2
0
0
1
0
1
0
0
0
1
1
0
0
0
1
0
0
2
1
0
3
0
1
2
0
1
0
0
2
0
1
0
0
2
0
0
1
2
1
2
0
1
1
1
1
0
1
2
2
0
2
0
1
2
0
0
0
1
1
0
0
0
0
1
0
0
2
0
0
1
2
1
1
1
0
0
0
0
1
2
0
1
0
1
0
0
2
1
1
1
0
0
1
0
0
2
0
0
0
0
0
0
1
2
0
0
1
0
6
0
1
0
0
0
0
0
0
1
1
0
1
0
1
3
1
1
0
0
1
1
0
0
2
0
0
0
0
0
0
2
1
0
2
0
13
0
0
0
0
0
0
2
2
0
1
0
2
1
1
0
1
1
0
1
2
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
1
0
1
2
1
1
0
1
1
0
0
1
0
2
0
0
0
0
0
1
2
0
1
0
0
2
1
2
0
2
7
0
0
0
2
2
2
0
0
2
0
3
2
2
0
3
0
0
0
2
0
0
0
0
0
0
0
1
1
2
0
0
0
0
1
20
1
0
0
0
1
0
1
0
0
1
0
0
0
2
1
0
1
1
0
2
2
0
0
0
2
2
0
1
2
0
0
1
1
1
2
1
0
1
0
0
0
1
2
0
4
0
2
2
1
0
0
0
1
0
1
0
1
0
2
2
0
0
0
0
1
0
0
1
1
2
0
2
1
0
2
0
0
1
1
1
0
0
0
1
1
2
0
0
1
0
1
1
2
1
0
1
0
0
2
2
0
1
1
0
1
0
1
0
0
0
1
2
1
0
2
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
4
0
1
2
2
0
2
0
2
1
0
0
2
0
1
0
0
2
1
1
2
0
0
0
1
0
0
1
2
0
0
2
2
0
3
0
2
0
0
0
3
2
0
2
1
1
1
2
0
0
0
2
0
0
2
0
1
0
1
0
1
1
0
0
1
0
2
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
2
3
1
0
1
0
4
3
0
0
1
0
2
1
1
0
1
0
0
2
2
0
0
0
1
3
0
0
1
2
1
0
0
2
0
0
2
2
1
0
2
1
0
2
2
1
3
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
1
1
1
0
1
0
1
0
0
0
1
0
0
2
2
0
1
0
0
2
2
1
0
0
1
0
0
0
2
0
2
0
2
0
0
1
0
0
1
1
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
1
1
0
1
1
0
1
1
0
0
0
3
0
0
0
1
2
1
0
0
0
1
3
0
0
0
0
1
2
0
0
0
3
0
1
0
1
2
1
2
0
0
2
1
1
2
0
1
1
0
1
1
0
0
1
1
2
1
1
0
0
0
0
1
0
2
1
1
0
1
0
1
1
0
2
2
0
1
1
1
2
2
0
0
1
0
0
0
1
0
1
0
0
1
0
0
1
0
1
1
2
0
0
2
0
1
0
1
2
0
3
2
0
2
2
2
0
0
0
0
0
0
4
1
0
1
1
0
0
0
0
3
1
0
2
0
2
0
0
1
0
0
1
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
2
1
2
0
1
0
0
1
2
1
1
1
0
0
2
0
1
1
0
1
0
0
0
2
1
1
1
1
2
2
0
0
0
2
0
1
0
1
0
0
0
1
1
1
2
1
0
0
1
0
0
0
2
0
0
1
2
0
1
2
2
1
1
0
2
0
1
0
0
0
0
0
0
0
2
1
2
0
2
3
0
3
1
0
1
1
1
0
0
0
0
2
2
1
0
0
1
2
0
1
0
0
1
0
0
1
3
2
2
0
2
0
2
0
1
0
0
0
0
0
2
0
1
0
0
2
1
0
2
2
1
1
0
2
2
1
2
0
0
0
1
0
1
0
1
0
1
0
0
1
2
2
0
3
2
1
2
0
0
0
0
2
1
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
1
0
0
2
1
1
3
0
0
1
0
0
0
1
1
0
0
0
0
2
0
0
2
0
0
0
3
1
0
0
2
2
0
1
0
2
1
0
2
0
2
2
0
1
1
0
0
2
1
2
0
0
0
0
0
0
1
0
1
1
2
0
0
2
1
0
1
0
0
0
2
1
1
3
0
2
0
2
3
1
0
1
2
1
0
1
1
0
0
0
1
0
0
0
2
1
2
0
0
0
0
0
2
2
2
1
0
2
1
1
1
1
0
1
2
0
2
2
0
0
1
0
0
0
2
0
1
0
2
1
0
0
1
1
1
2
2
1
0
3
0
1
1
1
0
1
0
0
2
0
1
2
3
1
0
0
0
0
0
1
1
2
0
0
0
0
2
0
2
2
2
1
0
1
0
2
0
0
2
1
1
1
0
0
1
1
1
2
1
0
0
1
0
1
2
0
0
0
2
1
0
0
0
1
2
2
0
1
1
1
2
2
0
0
0
1
2
0
0
2
4
0
1
0
0
0
2
2
0
2
0
2
1
1
1
1
1
0
2
0
0
0
1
2
0
1
1
2
0
0
0
0
0
1
1
2
1
0
2
0
0
2
0
2
0
2
2
0
1
1
0
2
0
1
0
2
1
0
1
0
1
2
0
0
0
0
0
0
0
1
1
0
2
1
1
1
1
2
1
2
3
0
0
0
0
0
0
0
1
1
1
0
0
1
1
2
1
0
2
0
2
2
0
0
1
0
3
1
0
0
1
1
0
1
1
0
1
1
0
1
1
0
2
0
0
0
1
0
2
0
1
1
1
0
2
0
2
0
0
0
2
2
2
0
1
1
0
1
0
1
1
0
0
2
1
0
2
0
0
0
1
1
0
2
0
1
0
0
2
2
2
0
1
0
0
0
1
0
0
0
0
2
0
1
0
1
1
1
1
0
0
0
0
0
2
0
0
1
1
1
0
0
0
0
1
1
1
1
0
0
1
0
1
0
0
0
2
0
1
0
1
0
2
0
0
1
0
2
0
1
1
1
2
0
2
0
3
0
0
0
1
0
0
2
5
1
0
2
1
1
0
1
1
2
1
0
2
1
0
2
2
1
0
1
2
0
0
5
0
1
0
0
0
1
0
0
1
0
2
0
0
0
1
0
0
2
2
0
3
1
2
1
0
1
0
2
1
2
0
0
0
0
0
0
0
1
0
2
2
2
1
0
0
1
1
0
0
0
0
1
0
1
0
3
1
0
1
2
2
1
0
0
0
0
2
4
0
1
1
0
0
1
2
1
0
0
0
0
0
0
2
2
1
0
1
1
1
2
0
0
0
1
1
2
1
2
1
0
2
3
0
1
1
0
2
0
1
2
0
0
0
1
0
1
0
0
0
1
0
2
1
3
0
0
2
0
1
2
2
0
0
1
1
1
0
0
0
0
1
1
2
1
2
1
2
1
0
0
2
3
0
1
0
2
2
0
1
1
2
0
0
0
0
0
2
1
1
0
1
2
0
2
1
0
0
2
2
2
1
0
0
1
1
0
0
3
2
0
1
1
0
2
0
0
0
0
1
0
0
1
1
0
1
0
0
0
2
0
1
0
0
0
2
0
0
2
2
0
0
2
0
0
1
0
0
0
2
2
2
0
1
0
1
0
1
0
0
1
1
0
1
1
0
0
1
3
0
0
2
0
0
2
2
2
0
0
2
0
1
1
1
1
0
6
0
1
2
0
0
2
0
1
0
1
2
0
3
2
0
2
2
1
5
2
2
2
1
3
1
0
0
0
1
1
0
0
0
0
0
1
1
3
1
0
1
0
2
0
1
1
2
0
1
1
1
2
1
0
1
0
2
2
1
1
1
1
2
0
2
2
2
0
1
2
1
2
1
0
2
0
0
2
0
0
1
2
0
0
0
1
0
0
1
0
1
0
0
0
1
2
1
1
2
1
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
2
0
0
1
0
1
1
0
2
1
2
0
0
2
2
1
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
4
0
0
0
0
1
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
1
0
2
0
0
0
2
0
2
0
0
2
0
1
0
0
1
0
2
0
0
0
1
0
1
0
0
2
0
1
0
1
0
0
1
0
2
2
0
1
1
0
1
2
2
0
0
0
0
0
4
2
1
0
0
2
1
1
0
1
2
0
0
1
1
1
1
0
0
0
0
0
1
0
0
3
0
0
1
1
2
1
2
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
1
1
0
1
0
2
1
0
0
0
0
0
0
2
1
2
0
2
0
0
1
1
0
0
2
0
1
2
0
0
0
1
1
2
0
0
1
0
4
0
2
1
1
0
0
1
2
1
0
1
2
1
1
0
1
1
1
0
1
2
0
0
0
1
1
0
0
0
2
1
2
0
1
0
2
1
0
1
0
0
0
1
2
0
1
2
1
0
0
0
0
2
3
0
0
0
0
0
1
1
0
2
2
0
0
0
0
2
2
0
0
2
0
2
2
1
0
0
1
0
1
0
0
0
0
1
0
1
0
1
0
1
0
1
0
0
1
3
2
3
1
0
1
0
0
1
0
1
0
2
0
2
1
2
0
2
0
0
1
0
1
0
0
0
1
0
0
2
0
1
1
2
0
2
1
0
0
0
1
0
1
0
2
0
0
1
1
0
0
2
0
0
2
0
2
0
0
1
1
0
0
2
0
1
0
0
7
0
0
2
0
1
0
2
0
3
0
2
2
1
2
1
0
2
0
1
0
1
0
2
0
0
0
3
0
0
1
1
0
0
1
1
0
1
0
0
2
0
1
0
2
0
0
1
0
0
0
3
1
1
1
0
0
0
0
1
0
2
2
0
2
1
0
2
0
1
1
2
0
2
2
1
1
0
0
2
0
2
1
2
2
1
1
0
1
0
0
0
2
0
0
1
1
1
0
0
0
1
2
1
2
0
2
0
0
0
2
1
0
2
2
0
0
1
0
2
0
1
0
1
1
1
0
1
1
1
1
0
0
0
2
1
0
0
1
1
0
0
1
0
1
0
1
2
2
1
1
1
0
1
0
0
0
1
1
0
0
2
2
0
0
0
0
1
0
0
1
0
0
1
0
2
1
0
0
1
2
0
3
0
1
1
2
0
2
1
0
0
1
2
1
0
1
0
1
2
2
2
0
0
0
1
1
1
0
2
1
2
0
0
0
0
0
2
4
1
2
0
0
1
0
0
2
0
2
1
1
0
1
1
1
2
1
0
0
2
1
0
1
0
1
0
1
0
0
0
2
1
2
1
0
3
0
0
0
0
0
1
0
2
0
0
1
1
1
0
2
0
1
0
1
2
0
0
2
0
0
0
0
2
0
0
2
1
2
2
0
1
0
0
1
1
1
0
1
0
2
2
1
0
2
0
1
0
1
0
1
1
1
0
1
0
1
2
1
2
0
0
0
0
1
0
1
2
0
2
2
1
0
1
1
1
0
1
2
0
0
0
1
0
1
0
1
1
0
2
2
2
1
1
0
1
0
1
2
0
0
2
0
1
2
0
0
0
0
0
1
0
1
0
0
1
2
1
0
2
0
1
0
1
0
0
1
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
1
0
1
4
0
0
2
0
1
0
1
3
3
1
2
0
0
0
0
0
0
1
1
0
1
1
1
2
0
1
0
2
0
0
2
0
1
0
0
0
0
1
0
1
0
1
0
1
0
0
0
4
2
2
2
1
1
1
2
1
2
1
1
2
1
0
0
0
0
0
2
2
3
0
0
1
1
1
0
0
0
0
2
0
1
2
0
0
1
1
0
0
0
0
2
1
1
0
0
0
0
0
0
4
2
0
0
0
1
0
0
0
1
0
0
2
1
9
1
1
0
1
1
1
0
6
0
1
0
0
0
1
1
1
0
1
2
0
2
2
0
0
0
1
0
1
2
1
2
0
1
0
1
0
0
1
1
0
0
0
0
1
0
2
0
1
0
2
1
0
0
1
1
0
3
0
1
2
0
1
0
0
1
1
1
1
2
0
1
2
0
2
0
1
1
0
1
2
2
2
2
2
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
1
0
1
0
0
1
1
2
1
0
0
1
2
0
1
2
2
1
1
2
0
1
1
4
1
2
1
1
0
1
1
0
1
0
2
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
2
1
1
1
1
0
0
0
2
1
2
0
0
0
2
2
2
1
0
0
1
0
0
2
1
0
0
1
2
1
2
1
0
2
0
0
2
0
0
1
0
1
2
2
1
0
0
2
1
0
1
1
0
1
0
0
0
0
0
0
1
0
1
1
0
2
4
1
1
0
1
0
0
0
2
2
0
1
1
1
0
0
2
1
2
1
0
1
0
0
1
0
1
0
1
0
0
1
0
0
0
1
0
0
0
2
1
0
2
1
1
0
0
1
2
0
0
2
1
0
1
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
2
0
2
2
1
1
0
0
1
4
2
2
0
1
0
0
0
2
0
0
1
0
0
2
1
0
2
1
0
1
2
0
0
1
0
0
0
0
0
0
0
3
2
0
1
0
0
2
1
0
1
1
2
0
0
0
0
1
1
0
0
1
0
1
1
1
0
0
1
0
1
0
1
1
0
2
2
0
1
0
2
2
0
0
0
0
1
1
0
3
2
0
1
1
1
0
1
0
0
1
1
2
1
2
0
1
2
0
0
0
0
0
0
1
0
2
0
0
2
0
0
1
0
2
1
0
0
0
0
0
1
0
0
2
0
0
1
2
0
1
0
0
0
0
2
2
0
3
0
1
0
2
2
0
1
1
1
0
1
0
2
0
0
0
1
0
0
0
2
2
0
2
1
0
0
1
1
0
1
0
0
0
0
0
1
0
1
2
11
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
2
2
1
0
2
0
0
1
1
0
2
1
1
0
0
0
0
2
1
0
2
2
1
0
2
0
0
0
2
1
0
1
2
2
1
0
0
0
1
0
0
2
0
2
3
1
0
0
1
0
0
2
0
0
1
2
0
1
1
0
0
2
0
0
0
0
0
1
1
2
0
1
0
0
0
0
3
2
0
2
0
0
0
2
2
0
0
1
0
4
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
2
1
0
1
2
0
2
1
0
0
0
1
1
2
1
0
0
1
0
0
0
1
0
1
0
2
0
1
0
0
1
0
0
1
0
1
2
2
0
2
1
0
0
0
0
1
0
0
1
0
2
2
1
1
1
2
0
0
2
2
0
0
0
2
2
1
0
0
1
1
1
2
1
1
2
1
2
0
3
0
2
0
0
2
1
2
0
1
1
3
1
1
2
1
0
7
0
0
1
2
2
1
0
0
1
0
1
1
0
0
1
0
0
2
1
1
1
2
0
1
0
2
2
1
3
1
2
1
0
0
0
0
1
1
0
0
5
0
3
0
0
0
1
2
0
0
0
2
1
1
1
0
0
1
1
1
0
0
0
0
2
1
1
1
2
1
1
1
2
1
2
0
2
0
0
2
2
0
0
2
1
2
0
1
0
0
1
2
2
0
1
1
0
2
0
0
2
0
0
0
0
1
0
2
0
1
1
2
0
0
0
0
0
2
1
0
1
2
1
0
0
1
0
2
0
1
1
0
0
0
2
0
0
1
2
1
0
0
0
0
0
2
0
1
1
0
1
0
1
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
1
2
0
0
1
4
0
0
1
0
0
1
2
1
0
2
1
1
0
2
1
3
2
1
0
0
1
0
0
0
0
2
0
1
2
0
0
2
2
0
0
0
1
0
0
1
0
0
1
0
0
1
2
0
2
0
0
1
0
0
1
2
0
3
1
0
1
0
1
1
0
0
1
1
0
2
1
1
0
0
1
0
1
1
1
2
2
3
0
0
2
0
2
1
0
0
0
1
0
0
0
2
0
2
2
1
2
0
1
1
1
1
2
0
2
1
1
1
0
1
0
2
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
2
0
1
1
1
0
0
0
0
0
0
0
2
0
0
1
1
2
0
1
1
2
0
0
0
0
1
0
0
2
0
2
2
2
1
1
1
0
2
0
1
0
1
1
1
2
1
0
0
0
0
0
0
0
0
1
2
2
2
2
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
1
2
0
1
1
1
2
0
2
3
2
0
1
3
1
1
0
0
0
0
1
0
2
2
0
0
2
2
0
0
1
1
0
0
0
0
1
0
0
2
0
0
1
2
2
0
1
0
0
2
0
1
0
0
1
1
1
1
1
0
0
2
0
0
0
0
1
0
2
1
1
0
0
2
0
0
0
1
1
1
2
1
1
1
1
1
1
0
0
0
0
2
1
0
0
0
0
0
1
0
2
1
1
2
2
1
1
0
0
0
2
0
0
0
1
1
0
1
1
1
2
2
0
2
0
0
1
1
1
0
0
1
1
0
1
1
1
0
0
0
0
1
0
1
2
2
2
1
0
0
0
0
2
1
0
0
1
2
1
0
1
0
2
0
0
2
1
0
2
0
2
0
2
1
0
2
2
1
1
0
1
0
0
0
1
0
2
2
2
1
2
2
0
1
0
2
1
0
0
0
0
0
1
0
2
0
0
2
0
1
0
0
1
1
0
0
0
0
0
0
2
1
1
0
1
1
0
0
0
5
2
2
2
0
1
1
4
2
0
1
1
2
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
2
0
3
0
2
1
2
0
0
0
0
0
2
2
2
1
2
1
2
1
2
1
0
2
0
0
0
1
1
2
0
0
0
0
1
0
0
0
1
1
0
0
3
0
0
1
1
1
1
0
0
1
1
1
2
1
0
2
0
0
0
0
0
0
0
0
2
1
2
0
0
1
1
1
1
1
0
2
0
0
2
1
0
1
0
0
1
0
0
0
1
0
1
0
0
0
3
0
0
1
0
0
0
1
2
1
0
0
1
0
1
0
0
2
0
1
2
0
1
2
0
0
0
1
1
0
0
1
2
1
0
1
0
0
1
1
0
0
1
2
1
1
2
0
2
0
2
0
0
0
1
1
0
0
0
1
0
1
1
1
0
0
0
0
2
0
1
0
0
1
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
2
1
0
0
0
0
2
2
0
0
1
1
0
2
0
2
0
1
0
1
3
1
2
1
2
1
0
0
2
1
0
0
0
0
1
0
1
0
0
2
0
1
0
0
2
0
2
1
0
2
2
1
0
0
3
0
0
1
2
0
0
0
2
0
0
1
0
0
0
1
2
2
2
0
0
2
1
0
2
0
0
1
1
3
1
0
1
1
1
1
1
1
0
1
0
2
0
0
2
3
1
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
4
0
2
0
0
2
1
0
0
1
0
2
1
1
1
1
0
2
1
0
2
1
1
0
0
0
0
0
0
1
0
1
1
0
2
0
0
0
1
0
0
0
0
1
1
2
0
0
1
2
0
4
2
0
1
1
1
2
0
2
0
1
0
0
2
1
0
1
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
6
0
2
0
0
2
0
2
0
0
0
0
1
1
0
2
0
2
0
1
0
0
2
1
2
0
1
1
0
0
1
2
0
0
2
2
1
0
1
0
0
2
0
2
1
2
1
3
1
2
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
1
2
0
0
0
2
2
2
0
0
1
0
0
2
0
1
2
2
0
0
3
1
0
1
0
1
1
2
0
0
3
2
2
0
2
1
0
1
2
2
0
1
0
2
0
0
2
1
0
2
1
1
1
4
0
3
2
1
2
2
0
0
0
2
0
1
0
0
0
1
2
1
2
1
2
0
0
2
0
0
0
0
0
2
1
2
0
2
0
2
1
2
1
1
0
0
0
0
1
0
1
0
0
1
2
1
0
0
1
0
2
0
2
2
2
1
0
1
0
0
0
2
2
0
2
0
1
2
2
1
1
1
0
0
1
1
0
1
1
1
0
2
0
2
1
1
0
0
1
0
1
0
0
0
1
0
0
1
0
3
1
2
0
1
0
1
1
0
1
0
1
0
2
2
0
0
0
0
0
1
0
1
0
2
0
0
0
0
1
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
1
2
1
0
1
1
1
0
0
0
1
2
2
0
0
0
0
0
3
0
1
0
1
1
0
4
2
2
0
0
0
1
2
1
0
3
2
0
0
1
0
0
0
1
2
2
3
1
0
1
0
0
16
0
0
1
1
1
0
0
0
1
1
0
0
1
0
0
0
1
1
2
2
1
0
0
0
0
1
0
1
1
0
1
1
2
2
0
1
2
0
2
0
2
2
2
0
0
0
2
4
2
0
0
0
0
0
0
1
0
0
0
1
0
1
0
2
0
0
0
0
0
1
0
0
2
0
0
2
1
0
0
1
1
0
3
1
1
1
0
0
0
0
1
0
1
3
1
0
2
0
2
0
1
0
0
0
0
0
0
1
1
0
0
2
1
2
0
0
0
0
2
5
0
1
1
0
2
2
0
1
0
0
0
2
0
0
2
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
1
2
0
0
1
0
0
0
0
0
2
2
0
2
0
2
2
0
0
0
1
1
0
0
1
0
0
1
0
0
0
2
1
2
1
2
0
0
2
0
0
1
1
1
1
2
1
0
0
2
2
0
2
0
0
0
1
0
0
1
0
0
2
0
1
2
0
1
0
0
0
4
2
1
0
0
0
2
0
2
2
2
0
0
0
1
0
0
0
1
1
0
0
0
0
2
2
1
0
0
0
3
0
1
0
2
1
0
0
0
2
2
0
0
1
2
0
0
2
0
0
0
0
0
0
1
0
0
1
1
0
2
0
0
0
0
0
0
0
1
0
2
3
2
0
2
0
0
3
2
2
1
0
0
1
0
2
1
0
1
1
2
1
0
0
0
0
0
0
0
1
0
1
2
0
1
0
1
0
1
2
4
1
1
0
1
0
0
0
2
0
1
0
0
0
0
0
1
0
1
0
1
0
2
0
1
0
1
0
3
0
2
1
1
0
0
1
0
0
2
0
2
2
1
1
0
0
2
1
0
2
0
0
1
1
1
0
0
2
1
2
2
1
1
1
1
1
1
1
0
0
0
0
2
2
2
0
2
0
2
0
0
1
2
1
0
1
0
2
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
1
1
1
1
1
0
1
2
2
0
0
1
0
2
3
2
1
0
1
0
0
1
2
1
0
1
0
0
0
1
2
1
1
1
1
0
0
0
0
2
0
1
2
1
1
1
0
2
1
0
1
0
1
1
2
1
1
0
0
0
1
1
1
0
0
1
0
0
0
1
0
2
2
1
1
2
1
0
0
0
2
1
0
0
2
0
1
0
0
0
0
0
1
0
0
1
1
2
0
2
1
0
2
1
1
0
0
3
0
0
0
0
2
0
0
2
1
0
2
0
0
0
0
2
1
1
1
2
0
2
0
2
2
2
2
1
1
2
0
0
0
1
0
0
2
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
1
1
1
1
0
2
0
0
1
1
0
0
1
2
0
2
0
1
0
0
1
0
0
2
0
1
0
0
0
1
1
0
0
3
1
2
2
1
1
0
0
0
1
1
2
0
1
1
0
4
2
1
2
0
2
2
2
0
0
1
1
0
1
0
2
1
0
0
0
0
0
0
0
1
1
2
1
1
0
2
0
0
1
1
1
1
1
2
0
1
0
1
1
1
1
2
0
0
0
0
0
0
0
1
0
1
0
2
2
0
0
1
1
0
0
0
1
1
2
2
0
0
0
0
2
0
0
1
1
1
1
2
1
2
0
2
0
0
0
0
2
0
0
0
1
1
0
2
0
1
0
1
2
0
1
0
0
0
1
0
1
0
1
1
1
1
1
0
2
1
2
0
2
0
0
0
0
1
1
0
0
2
0
0
0
2
1
2
0
1
0
1
1
3
0
0
0
1
0
0
0
1
0
0
3
0
0
0
0
0
0
1
2
2
2
2
1
0
2
1
2
1
1
0
1
1
2
0
1
0
1
0
0
0
0
0
1
0
1
1
2
1
1
2
0
1
0
0
0
0
1
2
0
2
1
0
0
0
0
3
0
0
3
1
0
4
2
1
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
2
0
1
0
0
1
0
0
1
0
0
1
0
2
0
0
0
0
1
2
1
1
0
1
0
1
0
0
0
1
0
0
2
0
1
2
1
1
1
0
2
1
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
1
0
0
0
1
0
2
0
0
1
0
0
1
0
1
0
0
2
2
1
2
0
1
0
1
0
1
0
0
0
0
0
0
1
1
1
1
2
0
1
1
1
0
0
1
0
1
2
0
2
0
0
0
0
3
0
0
0
2
0
0
0
0
2
0
2
1
2
1
0
0
0
2
1
0
0
0
2
1
1
0
2
0
0
0
2
0
0
0
2
1
0
0
2
2
1
0
1
1
0
2
1
0
0
1
2
3
1
0
1
0
2
3
2
1
0
1
1
2
0
0
1
0
2
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
1
0
1
2
1
0
1
1
0
0
2
1
1
0
0
2
0
1
2
2
0
0
0
2
0
1
1
0
0
1
1
0
1
2
2
0
0
2
0
1
0
1
1
0
2
0
2
0
1
0
0
0
0
1
0
0
0
2
0
1
1
1
0
0
1
0
1
0
1
1
0
1
0
2
0
2
0
0
0
1
1
0
0
0
1
2
0
1
0
0
0
2
2
0
1
1
0
0
0
1
0
0
1
1
0
0
1
0
1
0
1
0
0
0
0
1
2
0
0
0
0
1
0
1
3
2
0
1
0
0
1
0
1
0
0
0
1
0
0
2
0
1
1
1
1
0
2
0
0
2
1
0
0
1
0
0
0
0
0
2
0
0
1
1
3
0
1
4
2
0
1
0
2
2
0
0
0
2
1
2
0
1
0
1
0
1
0
2
0
1
0
2
0
1
0
0
0
0
1
0
2
0
1
0
1
2
2
0
0
1
0
2
2
0
0
0
2
2
2
1
0
0
0
0
0
0
1
1
0
0
1
0
1
0
1
0
1
0
1
1
0
2
1
1
0
1
2
0
0
2
1
0
0
0
0
0
2
0
0
1
0
0
1
0
1
1
0
2
1
1
0
2
0
1
2
0
0
1
7
0
0
1
1
0
0
0
2
0
0
0
1
2
1
2
1
0
2
0
1
1
1
1
2
0
1
1
3
0
0
0
0
0
2
0
0
0
0
2
0
2
2
0
0
0
0
0
1
1
0
0
0
1
1
1
2
0
0
2
2
1
0
1
0
2
0
0
1
1
1
2
1
0
0
1
2
0
0
0
0
0
1
0
2
1
1
0
1
2
0
0
0
1
1
1
2
1
0
2
0
0
1
1
0
0
2
0
0
0
2
1
1
0
2
0
0
0
2
1
2
0
0
1
2
0
2
2
0
1
2
2
0
2
1
0
2
1
0
1
2
0
0
0
1
0
0
0
1
2
1
0
0
2
0
1
0
0
0
1
1
0
1
0
0
2
0
0
0
0
2
2
3
1
0
1
1
2
0
0
0
0
2
1
0
0
0
2
0
0
1
0
0
1
0
1
0
3
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
2
1
0
0
1
0
3
0
1
0
0
2
1
1
2
0
0
0
2
0
1
0
2
1
2
0
2
0
1
1
2
1
1
2
0
1
1
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
1
1
0
2
0
1
0
2
0
2
0
1
0
2
1
2
0
0
1
0
0
0
1
0
0
0
2
0
3
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
1
0
0
2
2
1
2
1
0
0
3
1
0
2
0
0
1
0
1
2
0
1
2
1
1
1
2
0
1
1
0
1
1
1
0
0
0
0
0
0
0
1
2
2
1
0
0
1
1
0
1
1
0
1
1
0
2
1
2
1
2
2
1
2
2
0
0
0
2
0
0
1
0
1
0
0
1
0
1
1
1
1
5
2
0
1
2
1
0
0
1
0
0
2
2
0
1
1
2
2
1
0
0
1
0
0
1
0
2
1
1
2
2
0
2
0
0
0
1
0
1
3
1
0
0
0
1
2
0
1
0
1
0
0
1
0
1
1
1
2
4
0
2
2
2
1
0
0
1
2
1
0
1
1
1
0
0
2
0
0
2
1
0
0
0
0
2
0
0
2
0
0
1
0
0
1
1
0
3
0
1
0
0
0
0
0
0
0
1
1
0
2
0
2
1
0
0
2
1
0
2
0
0
1
1
0
0
0
2
1
0
1
1
2
0
1
2
0
0
2
0
0
0
0
0
2
0
0
0
0
2
1
2
2
4
0
6
2
2
1
2
0
2
0
1
0
2
0
0
0
2
2
1
0
0
2
0
0
0
0
2
2
1
2
0
1
2
1
0
1
1
1
0
2
1
2
1
1
1
0
0
0
0
0
0
1
0
0
0
0
2
2
2
0
3
0
2
1
0
0
1
2
1
0
1
0
1
0
0
1
0
0
2
0
0
0
2
0
1
0
0
0
0
1
0
0
2
2
1
2
0
2
0
0
2
0
3
2
2
0
0
0
2
0
0
1
0
0
1
0
1
2
0
0
2
1
2
2
0
1
1
0
2
0
1
1
0
2
3
2
2
1
1
0
1
0
2
0
0
0
1
0
1
2
2
0
1
0
0
0
2
0
2
0
0
0
1
0
0
0
1
2
0
0
2
0
1
1
0
0
0
2
1
0
0
0
0
0
2
0
1
0
1
0
0
1
0
0
1
0
0
2
1
1
0
1
0
0
0
0
2
1
0
1
2
0
0
0
0
1
0
1
0
0
0
1
0
1
2
0
1
0
1
0
0
1
1
0
0
0
2
0
0
1
2
2
1
0
0
0
0
0
0
0
1
0
0
1
0
1
1
2
0
1
1
0
0
2
2
0
1
0
1
0
0
2
0
2
1
0
0
0
1
2
0
0
2
2
1
0
0
0
0
0
0
2
2
0
0
1
0
3
1
1
1
0
1
2
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
2
1
0
0
1
2
0
0
1
0
1
2
0
1
1
2
1
1
0
1
0
0
2
0
0
2
0
0
0
2
5
2
0
2
1
0
0
0
0
1
0
1
0
1
0
1
1
1
0
0
1
1
1
0
1
1
1
0
0
0
0
0
3
2
0
2
0
2
0
0
0
0
0
0
1
1
0
0
1
2
1
0
1
2
1
0
2
1
0
0
3
1
1
1
1
0
1
0
0
0
1
0
1
1
2
0
0
1
0
1
0
0
2
0
0
0
0
2
0
0
0
0
2
0
1
1
3
0
2
0
1
0
2
1
2
0
0
1
1
1
1
0
1
1
1
1
0
2
3
2
1
1
0
1
1
0
2
0
1
2
1
0
1
2
0
0
2
0
0
1
1
0
0
0
2
0
2
0
1
2
0
0
1
1
0
0
1
0
0
0
2
3
1
0
2
0
2
1
0
0
2
1
1
1
2
1
0
0
1
1
0
1
2
2
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
2
1
0
0
0
1
0
0
0
1
0
4
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
1
0
0
0
0
1
0
1
0
2
1
0
1
1
0
0
2
0
0
1
0
1
0
0
2
0
2
0
0
0
2
1
2
0
0
0
0
1
7
2
1
0
1
0
0
1
1
0
0
0
2
0
0
1
0
2
2
1
0
0
0
0
0
0
4
0
2
0
1
0
0
2
0
1
0
1
0
1
1
0
2
0
0
2
0
0
2
1
1
0
0
0
2
0
0
1
0
0
2
1
2
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
1
2
0
0
2
1
0
1
1
0
2
3
0
1
1
0
2
0
1
0
0
1
0
1
0
2
1
1
0
0
0
0
2
0
0
2
0
0
0
0
1
1
0
0
1
1
0
2
0
0
2
1
2
1
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
1
0
1
1
1
2
2
2
0
0
0
2
0
0
1
0
0
1
0
1
1
0
2
1
1
0
2
4
2
2
0
0
1
0
0
1
0
1
0
1
0
0
0
1
0
0
0
1
1
0
0
0
1
3
0
1
0
0
0
0
1
1
2
2
0
2
1
1
0
1
1
0
0
0
0
2
1
0
2
0
0
1
2
1
0
0
0
2
0
0
0
1
0
0
2
0
0
2
1
2
0
0
0
0
2
0
2
0
0
1
1
0
2
0
0
1
1
2
2
0
0
1
0
0
1
2
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
2
2
0
1
2
3
1
0
0
0
1
0
2
1
0
1
0
4
0
0
1
1
2
0
1
1
0
2
0
2
1
0
2
0
1
2
0
0
1
2
0
1
0
1
0
1
0
1
0
1
0
0
0
2
2
0
1
1
0
3
0
0
0
1
0
0
0
0
3
1
0
2
2
1
0
0
2
2
2
2
1
2
5
2
2
2
1
0
0
0
1
1
0
1
0
2
0
3
0
1
0
0
2
2
0
0
2
0
0
2
0
0
0
1
1
0
0
1
1
1
0
1
0
2
0
0
0
2
0
2
0
0
0
1
0
1
1
1
1
1
0
0
0
0
0
0
2
1
1
0
0
1
0
1
2
1
0
1
2
1
1
1
0
1
1
0
2
1
1
0
1
1
0
0
2
0
0
1
1
0
0
0
3
3
0
1
2
0
1
3
0
2
0
1
2
0
1
0
0
1
2
0
2
0
0
1
2
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
1
2
0
0
2
1
3
0
0
0
1
1
2
0
0
2
1
0
1
0
1
1
0
2
1
2
1
0
0
0
1
0
1
0
0
0
0
3
1
1
1
1
0
0
1
1
1
0
0
1
0
2
1
2
0
0
0
2
2
1
0
1
0
0
0
1
1
0
0
0
0
0
0
2
1
0
0
1
1
1
0
0
1
2
0
0
2
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
2
0
0
2
1
0
1
0
0
0
2
2
2
1
0
0
0
0
2
1
1
1
2
2
4
2
1
2
2
2
1
2
1
1
1
0
2
2
1
0
1
0
1
0
0
2
0
0
1
1
1
2
1
2
0
1
0
0
1
1
0
0
1
0
1
0
0
0
1
0
0
2
1
1
1
0
1
2
2
1
0
0
0
1
0
0
1
0
1
1
0
1
0
2
0
2
0
4
0
0
0
1
1
0
1
2
0
1
1
2
1
2
2
1
0
2
0
0
1
0
2
1
1
0
0
1
3
2
0
4
2
0
0
3
0
0
0
0
2
0
2
0
0
0
2
2
1
2
2
0
1
1
1
2
1
0
1
2
0
0
0
2
1
2
0
1
1
0
0
2
0
1
2
0
1
2
2
0
1
2
0
2
1
0
0
2
1
2
0
1
2
0
1
0
0
1
2
0
0
0
1
1
2
0
0
1
1
2
0
0
0
0
1
1
1
0
2
0
0
0
2
0
0
0
1
1
1
0
0
0
1
2
2
0
1
0
0
0
0
2
0
1
1
1
0
0
0
2
0
0
1
2
0
3
2
1
0
0
0
1
1
0
2
0
3
1
0
0
0
1
1
0
0
1
0
0
0
1
1
1
1
0
0
0
1
0
2
0
1
2
1
0
0
1
1
0
1
1
1
0
0
0
2
1
0
1
0
2
0
0
1
1
1
2
0
0
1
1
2
0
1
0
2
0
2
2
0
1
1
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
1
1
1
1
1
0
3
0
1
0
0
1
0
0
1
0
0
0
1
2
2
1
1
0
1
0
0
3
0
2
1
0
2
1
2
0
0
0
2
0
2
2
0
2
0
0
0
0
0
0
1
0
0
0
0
4
1
0
0
0
1
1
0
2
1
0
1
1
0
2
0
1
0
1
1
0
2
0
1
0
1
2
0
0
0
1
0
1
1
0
0
0
0
2
2
0
1
0
2
2
1
1
1
0
0
0
0
0
0
0
0
1
1
1
2
1
0
2
1
0
1
1
1
1
2
2
2
1
1
1
1
1
2
0
0
2
1
0
2
0
1
1
0
2
0
1
0
0
0
0
0
2
0
0
0
0
1
0
1
2
0
2
0
0
0
1
0
0
1
1
1
0
2
1
0
0
1
0
1
0
0
1
0
2
1
0
1
2
1
0
2
1
0
0
1
2
0
1
1
2
0
0
0
0
1
2
0
1
0
1
1
2
0
0
0
3
0
0
1
0
1
0
0
0
0
0
1
1
0
1
2
0
1
2
0
0
1
0
0
1
0
0
1
1
0
0
2
1
0
2
1
2
1
0
0
1
2
0
0
0
2
1
0
1
1
0
2
0
2
1
1
0
0
1
0
0
0
2
1
0
1
0
1
1
0
0
1
0
0
2
0
0
0
1
0
0
2
0
0
0
1
0
0
0
1
5
1
2
0
2
0
2
0
3
2
0
0
0
1
0
0
1
1
2
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
1
0
0
2
0
0
0
0
1
0
1
0
2
0
1
1
2
0
0
1
2
1
0
1
1
1
2
0
0
0
2
0
0
0
1
1
3
0
0
1
0
2
2
2
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
1
2
2
0
0
0
2
1
2
0
3
0
1
0
2
0
1
1
1
0
1
1
1
2
0
0
1
1
0
2
1
0
2
0
2
0
0
0
1
2
0
0
0
2
1
1
2
2
2
2
0
0
0
1
0
2
0
2
2
1
1
1
2
1
0
0
2
2
2
0
0
0
0
0
0
0
0
1
0
0
0
1
1
2
0
0
0
0
0
1
0
0
0
2
2
2
0
2
0
0
3
0
1
1
0
0
3
2
0
0
0
0
1
2
1
0
1
1
1
2
0
2
1
1
0
0
2
0
1
0
0
3
0
0
0
0
0
1
1
0
2
1
1
1
2
2
0
0
1
0
0
2
0
1
0
2
0
0
0
0
2
0
0
0
2
1
0
0
0
1
0
1
2
0
2
0
0
2
0
1
0
0
3
0
1
0
1
1
1
0
1
1
0
1
2
1
0
1
2
1
0
0
0
0
2
0
1
1
1
0
2
0
0
0
0
0
3
0
2
2
0
2
1
0
1
1
0
2
2
0
0
0
1
0
0
0
1
1
1
2
0
0
0
1
0
0
2
0
0
2
0
1
0
0
0
1
1
0
0
2
0
0
1
1
2
0
0
0
0
2
2
2
1
0
0
2
1
1
2
1
5
0
1
0
1
1
0
2
1
0
0
2
2
1
0
1
4
2
0
1
1
1
0
0
2
0
2
1
1
0
0
0
2
1
1
3
0
0
0
2
0
2
2
2
0
2
0
0
2
0
0
2
0
0
0
0
1
2
1
2
1
0
1
2
0
1
1
1
0
0
0
0
2
1
0
0
0
0
0
0
1
2
1
2
0
0
0
2
1
0
0
1
2
0
0
0
1
1
0
2
2
0
2
1
1
1
0
0
2
2
1
0
0
0
0
2
0
1
0
2
0
0
2
1
1
2
0
0
4
0
0
0
1
0
1
2
0
4
1
0
1
1
1
2
0
0
0
0
1
1
1
2
2
0
0
1
1
1
0
1
0
1
2
1
0
0
1
1
1
0
0
2
0
2
0
1
0
0
0
0
1
1
0
0
0
2
2
0
0
1
0
1
1
0
0
2
0
1
0
0
1
0
1
0
0
0
0
2
0
0
1
2
1
2
0
0
1
1
11
0
2
1
0
1
2
0
2
2
0
2
0
1
0
1
0
0
0
1
0
1
1
0
2
2
2
1
0
1
2
0
2
2
1
3
0
0
1
2
0
2
0
0
0
0
0
1
0
1
2
2
1
2
1
1
0
0
0
0
1
0
2
0
0
0
0
4
0
1
0
1
0
1
0
1
0
1
0
0
2
1
1
0
2
0
2
0
0
0
0
1
1
1
1
0
0
1
0
0
2
2
0
1
0
1
2
0
0
0
0
1
0
1
0
0
0
0
2
1
0
1
1
1
1
1
0
1
0
1
1
2
1
2
2
1
2
1
0
1
0
0
0
1
0
0
0
2
0
2
0
0
1
0
0
2
2
1
1
2
1
1
2
1
0
1
0
0
0
1
0
0
1
1
2
0
0
0
1
0
2
1
1
1
2
0
2
0
0
0
2
0
0
1
1
2
0
0
0
2
0
0
0
2
1
0
0
0
0
1
2
2
1
0
0
1
0
1
0
1
1
0
2
1
0
1
0
2
2
0
0
1
0
0
3
0
2
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
2
1
3
1
2
0
0
0
0
2
2
0
1
0
0
0
0
2
2
2
0
2
2
0
1
1
2
0
1
0
1
0
2
0
0
0
1
0
4
2
3
1
2
0
1
0
1
0
1
2
2
1
1
0
2
0
0
0
0
1
1
2
2
1
2
2
1
0
0
0
1
0
0
1
0
0
0
2
1
0
0
0
3
1
1
0
1
1
0
0
0
1
2
0
0
0
0
1
0
1
1
2
0
0
1
1
0
0
2
2
3
1
0
1
1
1
1
0
1
3
2
1
0
0
1
1
1
0
1
0
1
2
2
2
0
2
2
0
0
0
2
1
1
2
1
0
2
0
1
3
1
1
1
2
0
0
2
1
2
0
0
0
2
1
0
1
2
0
0
1
2
0
0
1
1
0
0
0
0
2
2
2
1
0
0
0
2
1
2
0
2
0
0
0
1
0
2
1
0
0
0
0
1
0
0
1
1
0
1
1
0
1
1
0
0
0
0
0
0
0
0
3
0
0
0
2
2
0
1
0
0
0
1
0
0
0
1
2
0
0
2
0
0
2
1
0
1
2
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
3
1
2
0
0
2
0
0
1
0
0
0
1
2
1
0
0
0
1
0
0
0
0
1
2
1
2
0
1
1
1
2
0
0
2
0
0
0
2
2
1
0
2
0
0
2
2
0
1
0
0
0
0
0
0
1
0
0
1
2
0
0
1
0
1
1
0
0
2
2
1
1
0
2
1
0
0
1
1
2
0
0
0
0
0
0
2
2
0
0
4
2
0
2
1
0
0
0
2
0
0
0
1
2
1
0
3
1
0
1
2
2
2
2
0
1
2
0
1
1
0
0
3
0
0
0
1
0
0
0
0
2
1
0
2
1
2
1
1
1
3
0
2
1
1
0
0
1
2
1
0
2
0
1
1
2
2
1
0
1
2
0
1
0
1
1
0
1
2
1
2
0
0
0
0
1
1
0
3
1
1
2
0
0
0
0
2
0
1
1
1
0
1
0
0
1
2
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
2
0
0
0
1
0
0
2
0
0
1
2
0
0
0
1
0
1
1
1
1
2
0
2
1
1
2
2
0
0
1
0
1
0
0
0
0
1
1
0
0
2
1
1
2
0
0
0
0
0
0
0
2
2
0
1
0
1
2
0
0
0
0
1
0
0
1
0
2
0
0
0
1
0
1
1
1
1
0
0
0
0
1
1
2
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
1
0
0
1
1
0
1
1
2
2
2
1
0
1
0
1
2
2
2
0
1
0
0
1
1
0
0
2
2
0
0
2
1
0
0
0
2
0
0
0
0
0
2
2
0
2
0
1
0
0
2
0
0
2
0
2
0
2
0
1
0
2
1
0
1
2
0
0
1
2
0
2
1
1
0
1
1
0
0
0
2
0
2
2
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
2
0
0
1
2
2
1
0
1
1
0
1
0
1
1
2
0
1
0
0
2
0
1
0
0
1
1
0
1
1
1
0
1
2
0
2
0
0
0
0
0
0
1
0
0
1
1
0
1
2
2
0
1
0
2
0
1
0
0
1
0
1
0
1
1
0
2
0
0
0
1
1
2
1
0
0
0
0
0
2
0
0
1
0
1
0
0
1
2
0
1
0
2
0
2
1
0
0
0
0
0
1
0
2
1
0
0
2
1
0
0
0
0
0
1
0
2
3
1
0
1
0
2
0
0
0
0
1
0
1
1
0
3
0
1
0
2
1
1
0
0
2
0
2
1
0
0
2
1
0
0
1
0
0
0
0
2
0
0
0
1
0
0
1
1
2
0
0
1
0
2
1
0
0
2
2
0
2
1
0
1
0
1
0
1
0
1
0
0
0
0
2
0
0
0
0
1
0
0
3
0
3
0
2
0
2
0
0
0
2
2
0
0
2
2
1
1
2
2
1
2
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
2
1
0
0
1
0
1
2
0
0
0
0
2
0
2
0
1
1
1
0
0
0
0
1
0
0
2
0
1
1
0
0
2
0
0
2
0
2
0
2
1
0
0
1
2
0
7
0
1
0
0
0
0
2
1
2
0
0
0
1
0
2
2
1
0
0
1
0
1
2
0
0
1
0
0
0
1
0
0
0
1
1
1
1
0
2
0
1
0
2
1
1
1
2
0
1
1
0
2
1
2
0
1
0
0
0
1
1
0
0
2
1
2
0
0
0
0
1
0
0
1
0
0
0
2
0
0
9
1
1
0
1
1
0
0
0
0
0
2
1
0
0
0
1
1
0
2
1
0
0
1
1
1
0
0
2
0
0
2
1
0
1
1
0
0
1
0
0
0
0
0
1
1
1
1
1
2
1
0
0
0
1
0
0
1
0
1
2
0
0
0
0
1
3
1
2
2
0
0
1
0
2
1
0
1
0
2
0
0
1
1
0
1
0
1
1
0
1
1
0
0
0
0
0
0
2
0
0
2
3
2
0
0
0
2
2
0
2
1
3
2
1
1
1
1
1
1
0
0
1
0
0
1
0
0
1
0
1
1
1
2
1
0
0
1
1
0
0
2
0
0
0
4
0
0
1
0
2
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
1
0
1
1
0
0
0
2
0
2
1
0
0
0
0
1
2
2
2
0
0
1
2
0
1
0
0
1
0
0
2
1
0
2
0
0
0
0
0
1
0
1
0
0
0
2
1
4
2
0
0
0
1
1
1
0
2
1
1
1
0
2
0
2
2
0
2
1
0
0
1
2
0
0
1
1
2
0
1
2
1
0
0
1
0
0
2
0
2
0
0
0
1
0
0
0
1
1
1
1
0
0
0
0
0
0
0
2
1
1
0
0
0
0
1
1
2
0
0
0
5
1
0
1
1
1
0
0
2
0
1
0
1
0
0
1
0
1
1
0
0
0
0
1
2
0
0
1
1
1
2
0
1
0
1
2
1
1
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
3
0
2
1
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
2
1
1
2
0
1
2
0
0
0
1
0
0
0
1
0
1
0
1
0
0
1
0
2
2
3
2
1
0
1
0
0
6
0
0
1
0
2
0
2
1
0
0
1
1
0
2
0
2
0
1
1
0
0
1
0
0
0
0
1
2
2
0
1
0
0
2
1
0
2
1
0
0
0
0
2
0
0
1
2
2
1
2
0
0
2
1
2
0
0
2
0
1
0
2
0
0
2
0
1
1
0
0
1
1
0
1
1
2
1
0
2
1
2
1
0
0
0
1
0
0
1
1
1
2
0
2
0
0
1
0
0
1
0
1
0
2
1
0
0
0
0
2
0
2
1
2
1
0
2
1
1
1
1
1
1
0
0
0
1
1
2
0
0
1
0
2
0
2
2
0
2
1
1
0
1
1
2
0
2
1
0
0
0
0
1
1
0
0
0
1
0
0
1
2
0
0
0
0
0
1
1
0
1
1
0
1
1
0
0
1
0
0
1
1
0
2
0
2
2
1
0
0
1
0
1
3
1
1
1
0
1
0
1
0
0
0
0
0
1
1
2
2
2
1
0
0
0
0
0
2
0
0
0
1
0
1
0
2
2
0
1
0
1
3
0
0
1
0
0
0
0
1
1
1
0
1
0
1
1
1
0
0
3
2
2
0
0
0
0
1
0
0
1
1
0
0
1
1
0
0
1
0
0
2
0
2
2
0
2
0
2
0
0
0
0
0
0
2
0
0
1
0
2
0
2
2
0
0
0
0
0
1
0
2
1
1
0
1
0
1
2
2
2
0
1
1
1
2
0
0
2
0
1
0
1
1
1
0
1
0
1
2
1
0
1
0
0
0
2
0
1
0
0
1
2
1
2
0
3
0
2
1
0
2
1
0
0
0
1
1
0
2
2
0
0
1
2
1
2
0
0
0
2
0
0
0
1
2
0
2
0
0
1
1
0
0
0
1
2
2
2
0
0
2
0
0
2
0
0
0
0
0
1
1
0
1
0
0
2
1
1
0
0
2
0
1
0
0
0
0
0
1
0
0
0
2
1
0
2
2
0
1
0
0
1
0
0
0
0
0
0
2
1
0
1
0
0
1
0
1
0
0
0
0
0
1
1
0
1
2
2
1
2
1
1
0
2
0
0
0
1
1
0
1
0
0
1
1
1
2
1
0
1
1
2
1
0
0
0
0
1
1
0
1
0
0
1
1
2
1
1
2
0
1
2
0
1
0
2
0
2
0
2
2
0
2
0
1
1
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
2
1
1
0
0
0
2
1
0
0
0
2
2
1
1
1
0
0
0
0
1
1
0
2
0
0
2
1
2
0
0
2
1
0
0
1
1
0
0
1
0
0
3
1
0
1
2
1
2
1
0
0
1
0
1
0
0
1
1
0
0
0
2
1
0
1
0
1
0
0
0
0
0
2
0
1
1
2
3
1
1
2
6
0
1
0
1
0
0
1
1
1
0
2
0
2
0
1
1
2
3
0
0
0
1
0
1
2
0
2
0
0
2
0
0
2
2
0
0
1
2
0
0
0
2
0
2
0
1
2
0
0
1
1
0
2
0
0
0
0
2
0
0
0
0
0
0
2
1
0
1
0
0
1
0
1
0
0
1
0
1
0
2
1
2
1
0
0
1
0
2
2
2
0
0
0
1
0
0
1
0
2
0
1
0
0
0
2
1
1
0
0
2
4
0
0
0
2
0
1
1
1
2
0
1
1
2
0
0
0
0
1
2
0
2
0
0
1
2
1
2
0
0
0
0
2
0
0
0
2
2
1
0
1
0
0
0
1
1
0
1
1
0
0
2
1
4
1
0
2
0
1
0
1
0
0
2
2
1
0
0
1
1
0
0
1
1
2
0
2
0
0
2
2
0
0
1
0
0
0
0
0
0
1
1
1
2
1
0
0
1
1
0
0
1
2
0
2
0
1
0
2
0
0
0
1
2
4
0
1
0
1
0
0
2
0
0
1
0
2
1
2
1
3
1
0
1
0
2
0
2
0
1
0
0
0
0
0
1
1
1
1
1
1
2
0
0
0
0
1
0
2
0
1
2
0
2
0
1
0
2
1
2
0
0
3
0
2
2
2
1
1
0
2
0
2
0
2
0
0
1
0
2
0
1
0
1
2
1
2
1
2
2
1
0
3
1
1
2
0
2
2
2
1
0
0
1
1
1
1
1
0
0
0
0
0
1
0
3
1
0
0
2
0
1
0
1
2
0
1
1
0
1
1
0
0
1
1
2
0
1
0
0
2
2
0
1
0
2
0
0
0
1
1
0
0
0
0
1
1
1
2
0
0
0
0
0
0
2
0
3
2
2
0
0
1
0
0
0
1
1
1
2
0
2
2
1
2
0
1
2
1
1
3
3
0
0
0
0
1
2
0
2
0
0
0
0
2
1
1
0
0
0
1
3
1
1
1
1
2
2
0
0
1
2
1
1
5
2
0
2
2
1
0
1
2
0
0
0
1
1
2
1
0
1
1
0
1
0
0
1
0
2
0
1
1
0
0
2
2
1
0
0
1
1
0
2
1
1
0
0
2
0
1
0
2
1
0
2
2
0
2
1
0
0
0
1
2
0
0
2
1
1
0
2
4
1
4
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
1
1
0
1
0
1
2
0
2
1
0
0
1
0
0
0
0
1
2
0
1
1
2
1
0
0
1
0
1
0
0
0
0
0
0
3
0
0
2
0
1
2
3
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
2
1
2
1
0
2
1
0
2
1
2
0
1
0
0
1
1
0
1
2
2
0
0
0
1
0
2
1
0
0
1
1
0
1
0
0
0
1
0
2
0
2
2
0
0
2
0
3
0
2
0
0
0
0
0
1
0
0
0
0
0
1
1
0
2
2
2
0
0
2
0
1
2
0
2
0
2
1
0
1
0
0
0
1
0
0
2
0
0
1
0
0
1
1
2
0
0
0
1
1
0
0
0
0
0
1
0
2
0
0
1
0
0
0
2
0
0
2
2
2
0
0
2
1
0
1
1
1
4
1
1
1
0
0
0
2
0
0
2
0
0
1
0
1
2
1
1
0
0
1
1
1
1
2
2
0
0
1
2
0
2
0
0
0
1
0
0
1
2
1
0
2
0
0
2
0
0
1
0
1
0
0
1
0
2
0
1
1
1
0
1
2
0
2
0
2
1
0
2
2
2
2
0
1
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
1
0
1
4
1
2
2
0
0
0
1
1
0
0
0
0
1
0
1
0
1
11
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
1
0
0
0
2
0
1
0
3
0
7
1
0
2
1
0
0
2
0
2
1
1
2
1
0
0
0
2
0
0
1
1
1
1
0
1
2
2
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
1
1
0
0
2
0
1
0
2
1
0
1
0
0
0
1
2
2
0
0
1
0
2
1
1
2
2
0
1
0
2
1
1
2
0
2
0
0
0
0
0
0
0
0
1
0
1
2
1
1
0
1
1
2
1
1
1
0
1
0
0
2
1
2
1
1
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
1
2
0
0
0
0
1
0
1
1
0
0
0
1
0
0
1
0
0
2
1
0
0
2
2
1
1
1
0
0
0
0
1
3
0
1
2
1
2
0
1
0
2
0
1
0
0
0
2
1
1
0
2
1
1
1
1
0
0
1
0
1
1
2
0
0
1
1
0
0
2
1
0
0
2
0
0
1
0
0
0
2
2
2
1
0
3
4
0
1
0
1
0
1
2
2
1
0
0
1
2
2
2
2
2
2
2
0
0
0
1
0
1
0
0
1
1
1
0
1
2
0
2
1
2
0
0
2
1
1
2
0
1
2
0
0
0
1
0
0
1
0
0
0
0
1
3
0
1
2
0
1
0
1
2
0
0
1
0
1
2
1
0
1
3
0
1
1
0
2
0
0
2
0
1
0
0
0
2
0
0
0
0
2
0
1
1
0
0
3
1
0
1
1
1
0
2
0
0
1
1
0
0
2
0
1
0
3
0
1
0
0
2
2
0
2
0
1
0
0
0
0
0
1
0
0
1
2
0
0
0
0
2
0
1
1
1
0
0
0
0
1
1
1
1
2
2
0
0
0
1
1
1
0
1
3
1
0
0
2
1
0
0
1
0
0
1
0
2
0
1
0
0
1
1
1
0
2
0
1
1
2
0
2
0
1
0
0
0
2
0
0
1
2
1
0
1
2
0
3
0
2
0
1
0
0
0
0
0
0
1
0
2
0
0
0
2
2
0
2
2
0
1
0
0
0
0
1
0
1
0
1
2
2
1
2
1
2
0
1
1
1
0
2
1
0
2
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
2
1
1
2
1
0
0
0
0
1
1
0
0
1
2
0
1
0
1
0
1
0
1
1
0
0
0
0
0
1
1
0
3
0
0
2
1
0
0
0
1
2
0
0
1
1
0
1
0
2
0
2
0
1
0
1
0
0
2
1
0
2
0
0
2
1
0
0
2
1
1
0
1
0
3
1
1
0
1
2
0
2
1
1
1
1
2
0
0
0
0
2
3
1
2
1
0
0
0
0
0
1
2
0
1
0
0
1
2
0
0
0
0
0
2
2
3
2
0
1
0
1
0
1
1
0
0
0
1
2
0
0
1
1
2
1
0
0
2
1
0
0
1
3
0
0
0
1
0
1
2
0
0
0
1
2
1
1
0
0
0
0
0
0
0
4
0
1
0
1
1
0
0
0
0
2
0
0
2
2
1
1
0
1
1
0
0
0
2
1
0
0
0
0
2
0
1
2
1
0
3
2
0
0
0
1
0
0
1
0
0
0
0
1
1
1
2
2
1
1
0
2
1
2
0
2
1
0
1
0
0
0
0
0
1
0
0
1
2
0
2
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
1
1
1
0
1
0
1
1
1
0
2
1
2
0
0
1
0
2
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
1
0
2
1
0
0
0
1
0
0
0
1
1
3
0
0
2
0
0
0
0
0
0
0
2
2
1
1
1
1
1
1
2
1
0
1
1
0
0
1
2
1
0
0
0
1
0
1
2
2
0
1
2
2
0
1
0
2
0
0
0
2
0
2
0
2
0
0
1
2
0
0
2
0
0
2
0
1
0
0
1
0
0
2
0
0
1
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
1
0
1
3
0
0
1
0
2
0
0
0
1
0
0
0
0
2
0
0
0
1
1
0
1
1
0
1
0
2
1
0
1
1
2
2
1
1
0
1
2
0
1
0
2
1
2
0
2
1
2
2
0
1
1
0
2
0
0
1
0
0
0
0
1
0
2
1
1
1
0
0
2
0
0
1
0
1
0
2
0
1
0
2
1
1
0
1
0
1
0
1
0
0
0
1
0
2
1
0
0
0
2
0
1
0
1
2
1
1
0
2
1
0
0
2
1
0
0
1
2
0
0
0
2
0
1
1
0
0
0
1
2
2
0
0
0
0
0
1
0
0
2
2
0
2
1
0
1
1
1
1
1
0
1
0
0
0
0
1
2
2
2
0
1
0
0
0
1
2
2
0
0
0
0
0
0
1
1
1
0
0
0
1
0
1
0
1
1
0
0
0
1
0
1
0
1
0
1
1
2
0
0
2
0
1
0
1
0
0
2
0
0
2
1
0
0
1
1
1
2
0
0
0
1
0
0
0
0
0
3
0
0
3
2
0
0
2
0
1
0
2
1
2
2
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
1
1
0
1
2
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
1
0
0
0
2
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
1
1
2
0
0
1
1
1
0
0
0
1
1
0
1
0
1
0
2
2
0
2
1
0
1
0
2
1
1
2
0
0
0
1
1
0
2
0
0
0
2
2
0
0
0
2
2
2
2
0
0
0
0
0
0
0
2
0
1
1
2
1
0
0
0
1
0
1
0
2
0
0
2
1
1
1
1
0
0
0
2
0
1
0
0
1
0
0
2
0
0
0
0
1
1
0
0
2
0
1
0
0
2
2
1
0
1
1
0
3
0
0
2
2
0
1
0
3
1
2
0
0
0
0
0
1
2
0
1
2
1
1
2
3
2
0
0
0
1
0
0
1
4
0
0
1
1
0
1
0
2
3
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
2
2
0
1
2
1
1
0
1
0
0
2
2
0
0
2
2
0
1
1
1
1
1
0
0
1
2
0
1
0
0
0
0
2
1
0
2
0
1
2
1
0
0
2
0
0
1
1
2
0
0
0
1
1
0
0
1
0
2
0
1
2
1
1
2
0
0
0
0
0
1
0
0
1
1
2
0
0
1
1
2
2
1
0
0
1
1
1
2
0
0
1
2
1
1
0
2
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
2
2
0
1
0
0
1
0
3
2
2
0
1
0
1
2
1
0
1
2
2
1
0
1
0
2
1
1
1
1
0
1
1
0
2
3
2
0
1
1
1
2
1
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
2
1
1
1
1
0
1
0
2
1
0
1
2
2
2
0
0
0
0
0
1
0
3
1
0
1
0
1
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
2
1
2
0
2
0
0
0
2
1
1
0
0
1
1
1
0
0
1
1
0
2
1
0
1
0
0
0
0
0
1
0
2
0
2
1
1
0
2
0
0
0
1
0
0
1
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
1
2
1
0
0
0
0
0
1
0
2
1
1
2
0
2
1
0
1
0
0
0
2
1
1
0
0
0
0
1
0
0
2
1
0
0
1
0
1
1
0
0
2
0
0
0
1
0
0
0
0
1
1
0
1
1
0
0
2
1
1
0
1
1
0
0
0
0
0
1
0
2
0
0
1
1
0
0
1
1
0
2
0
2
0
0
11
2
0
1
2
1
0
0
0
0
2
0
1
1
1
0
2
1
2
1
0
1
2
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
1
1
1
1
0
0
2
0
0
1
1
1
0
1
2
2
1
1
0
0
0
0
1
1
0
0
0
0
0
2
0
2
1
0
0
1
0
0
1
2
0
2
1
0
1
0
0
0
0
1
0
1
0
2
1
2
0
0
0
0
0
0
0
1
0
2
0
2
1
0
0
2
1
0
3
1
0
2
0
2
0
1
1
0
2
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
1
2
2
0
0
0
0
0
1
2
1
0
1
1
2
0
0
1
0
1
1
5
0
1
2
0
1
1
9
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
2
0
0
1
0
2
0
1
1
0
1
0
0
0
1
1
0
0
0
2
0
0
1
0
2
0
3
1
0
0
0
1
3
0
1
2
1
2
1
0
2
1
1
1
3
0
0
2
1
0
1
0
0
0
0
0
1
2
0
0
0
2
1
2
0
2
0
1
0
1
0
0
2
1
0
0
0
0
1
1
0
2
0
2
0
0
0
1
2
2
0
0
1
2
0
0
1
1
0
1
0
0
1
0
0
0
3
0
0
1
1
1
0
1
0
0
2
0
0
0
1
2
1
1
0
0
0
1
0
0
1
1
2
1
1
0
5
1
0
1
0
1
2
2
0
0
0
2
1
0
1
1
0
0
2
0
0
1
0
1
2
1
1
0
0
1
0
0
0
2
0
1
2
0
0
0
1
0
1
0
0
2
0
0
1
0
1
2
0
0
1
1
1
0
0
0
0
2
1
0
1
1
0
2
2
1
0
1
0
2
0
1
0
0
0
0
2
0
2
0
0
0
1
0
1
2
2
0
3
2
0
0
2
2
0
0
0
2
0
0
0
2
1
1
2
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
2
1
0
1
0
0
0
1
0
1
2
1
1
0
0
0
0
0
1
0
0
0
0
2
2
0
1
2
0
3
2
2
0
2
0
2
0
0
2
0
0
0
0
0
0
0
2
1
0
0
2
1
2
0
2
0
0
1
1
0
1
2
0
0
1
0
2
0
0
2
1
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
3
0
0
0
0
2
2
1
1
0
1
1
2
1
0
1
1
2
2
0
2
1
0
0
0
1
2
0
0
2
1
0
0
0
1
2
1
0
2
0
5
3
1
3
1
1
0
0
1
2
2
0
1
2
1
0
0
0
1
4
1
0
0
0
0
0
0
2
0
1
1
2
0
0
0
0
0
0
1
0
2
0
1
0
0
1
0
0
0
0
2
0
2
1
1
0
1
0
0
2
2
2
0
0
0
0
2
2
0
0
0
0
2
0
1
1
2
2
0
1
2
0
0
0
1
0
0
0
1
0
0
2
1
2
1
0
2
0
0
0
0
0
0
1
0
2
2
0
0
1
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
2
0
0
1
0
3
0
0
1
0
1
0
0
0
0
0
0
2
0
2
0
1
2
0
2
2
0
2
0
0
0
2
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
1
1
0
1
1
3
0
0
2
3
1
0
1
0
1
0
0
0
0
0
2
0
0
1
2
0
0
2
0
2
1
0
1
0
1
2
0
1
1
0
0
0
0
0
0
0
0
2
0
2
0
2
1
0
0
1
0
0
0
1
2
0
1
0
0
1
1
2
1
1
2
1
1
2
0
1
1
0
0
0
1
0
2
0
0
1
0
2
0
1
0
0
1
2
0
0
2
1
1
0
1
1
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
2
0
2
0
2
0
1
0
1
0
0
0
2
0
2
0
0
0
2
0
0
2
2
0
3
0
0
0
2
0
0
2
2
0
0
0
0
1
0
0
0
0
0
2
1
0
2
0
0
1
0
2
0
0
2
1
0
0
1
0
0
0
0
0
1
1
2
1
1
0
1
4
0
0
2
2
1
0
1
0
0
0
0
0
0
0
1
0
1
1
0
1
3
0
0
2
0
0
0
0
2
0
0
1
0
1
1
2
0
3
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
3
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
2
1
1
0
0
1
0
2
0
1
0
1
1
1
1
0
1
0
0
0
0
0
1
1
0
2
2
0
0
0
2
0
0
1
1
1
1
1
1
0
2
3
1
4
1
2
0
0
2
2
2
0
0
0
1
1
0
1
0
1
0
0
1
0
0
0
0
1
0
0
1
0
2
1
0
2
2
2
0
0
0
0
1
0
1
1
2
0
1
0
0
2
0
1
2
0
1
0
2
1
2
0
0
2
0
0
0
0
0
0
2
1
1
0
2
1
2
1
2
1
0
0
0
2
0
1
0
2
0
1
0
2
0
0
1
4
0
0
2
2
2
2
2
0
2
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
1
0
1
1
1
1
1
0
0
0
2
1
2
0
1
0
0
1
1
1
1
0
1
1
1
0
1
1
0
1
0
2
0
0
0
1
0
1
0
2
0
0
0
2
0
0
0
0
0
2
1
2
0
1
0
0
2
0
1
0
0
0
5
0
2
0
0
1
1
1
1
0
1
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
2
0
1
0
1
0
1
0
0
2
1
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
2
1
2
1
2
1
0
1
0
0
0
2
1
1
0
2
2
2
2
0
2
0
3
2
1
1
2
1
1
1
1
1
0
2
0
1
0
2
2
1
0
1
0
1
0
0
0
0
1
0
0
2
1
1
2
0
2
1
0
2
0
1
2
0
0
0
0
1
0
1
0
1
1
0
0
1
1
0
0
3
1
4
0
1
0
0
2
1
0
1
2
2
2
3
1
2
0
1
2
0
3
0
0
0
1
2
2
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
2
1
0
1
1
2
2
1
1
2
0
2
1
0
3
2
2
1
1
0
0
1
1
1
2
1
1
0
1
1
0
0
0
2
1
0
0
0
0
1
1
0
2
1
0
0
0
1
2
1
1
0
2
0
1
0
0
2
0
2
0
0
0
0
2
0
0
1
0
2
3
1
1
0
1
0
0
2
2
0
0
0
1
3
0
1
2
0
0
2
0
0
0
1
0
0
0
0
2
1
2
1
2
1
0
1
1
0
1
7
1
0
0
0
0
0
1
0
1
3
1
1
1
1
0
2
0
1
0
0
2
0
1
2
2
0
0
1
0
0
2
0
0
2
2
1
0
0
1
0
0
0
0
0
0
2
1
2
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
1
0
2
0
0
2
1
0
0
3
0
1
2
0
0
0
0
0
2
0
1
0
1
1
0
2
0
0
0
1
0
0
1
1
1
2
1
1
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
1
0
0
0
2
2
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
2
1
0
0
0
2
2
1
0
0
0
0
1
0
2
0
2
1
2
0
0
2
0
0
1
0
0
1
0
1
1
0
0
1
1
1
1
0
0
0
2
2
0
0
1
2
1
1
0
0
0
1
0
0
0
2
0
2
0
1
0
1
0
2
1
2
0
1
0
0
1
2
2
0
2
2
0
1
2
0
2
0
1
0
1
2
2
0
1
0
0
1
2
0
1
1
0
0
3
1
0
0
1
0
2
0
1
0
0
0
0
1
0
1
0
1
0
2
1
1
1
1
1
0
0
0
2
2
1
0
0
1
1
0
1
0
0
2
2
2
1
1
2
1
0
0
0
1
0
2
1
0
0
0
0
1
1
0
2
1
3
1
0
2
0
1
0
0
0
1
0
2
0
3
1
1
1
0
2
2
0
0
1
0
1
1
1
4
2
0
1
2
0
0
2
1
1
0
2
2
0
3
1
1
0
0
0
5
1
1
1
1
0
2
0
0
0
0
1
1
1
0
0
1
0
1
0
1
2
0
0
0
2
0
1
0
2
1
1
0
1
0
2
0
1
1
0
0
0
1
2
1
0
0
5
1
1
0
2
2
0
3
3
1
2
0
2
2
0
3
1
1
2
2
2
0
0
1
1
1
1
2
0
2
2
1
2
2
0
1
1
1
1
1
1
1
0
0
0
0
0
0
1
2
1
2
0
0
0
1
0
1
2
0
0
0
1
1
0
2
1
0
0
2
1
3
2
0
1
0
0
0
1
1
1
0
1
0
0
1
1
1
1
0
2
1
2
0
2
0
0
0
0
0
1
1
2
2
2
1
0
0
2
2
2
2
0
0
1
2
0
0
2
0
0
1
1
0
1
0
1
0
0
2
1
1
2
2
2
0
0
1
0
1
2
0
2
2
2
2
2
2
0
0
3
2
1
1
1
2
0
0
2
1
0
6
0
0
0
2
2
0
0
1
2
1
0
0
1
0
1
0
0
0
0
0
1
0
2
1
0
1
2
0
1
2
1
0
0
0
2
2
0
2
1
0
0
2
0
0
1
1
2
0
0
0
1
2
0
1
0
0
0
0
1
0
1
1
0
0
0
2
0
0
0
2
0
0
2
1
1
1
0
0
2
1
1
1
0
0
0
0
1
0
2
0
0
0
1
1
2
0
1
0
1
1
0
2
1
2
2
0
0
1
2
0
0
0
1
0
1
0
0
2
0
2
1
0
0
0
1
1
0
1
0
0
2
0
0
1
2
0
0
2
0
0
1
1
0
2
0
1
0
1
1
0
0
1
0
0
1
0
2
1
1
0
0
2
0
1
3
1
1
2
0
3
0
0
1
2
0
1
2
0
1
3
0
1
1
2
3
0
0
1
0
2
0
1
0
0
2
0
2
1
0
2
0
2
2
0
1
1
0
0
2
0
0
1
2
1
0
1
2
1
1
2
0
1
4
0
1
1
1
2
1
0
2
1
0
0
1
0
2
1
0
0
2
1
2
2
0
1
0
1
1
0
0
0
2
1
3
1
0
0
0
1
0
0
1
1
4
0
0
1
0
2
1
1
1
2
0
0
0
2
0
0
2
2
2
1
0
0
1
1
2
1
0
1
2
1
1
1
0
0
3
0
1
1
0
2
0
1
2
0
0
0
0
0
0
0
1
1
1
0
2
1
2
0
1
0
1
1
0
0
0
2
1
0
0
1
0
2
0
0
2
0
0
0
1
2
0
1
0
2
3
3
0
1
0
0
0
0
1
1
1
1
1
0
0
0
0
0
0
0
0
0
1
2
0
1
0
1
1
2
1
0
2
2
0
1
2
0
0
1
0
0
2
1
1
1
0
2
0
0
1
0
1
0
1
1
2
2
1
0
2
1
0
2
1
1
1
0
1
0
2
3
0
2
2
2
0
0
0
2
0
0
0
0
2
2
0
1
1
3
0
3
0
1
0
0
1
1
1
0
1
0
0
3
1
0
0
1
0
2
1
1
0
0
0
0
3
0
1
1
1
1
0
2
0
0
0
1
2
0
0
0
1
1
1
0
2
1
2
0
1
0
0
1
0
0
0
0
0
0
1
2
1
1
0
2
0
1
1
0
2
1
1
0
2
0
0
2
0
2
0
0
0
1
0
1
2
0
1
0
2
2
0
1
0
1
1
1
1
0
2
2
2
0
0
0
1
1
2
0
0
1
2
0
1
0
1
2
1
0
0
0
0
0
4
0
0
0
2
1
1
0
2
1
0
0
0
2
0
0
1
1
0
0
1
2
3
0
0
1
4
1
0
2
0
0
1
1
1
1
0
1
0
1
2
1
2
2
2
1
0
2
0
2
1
2
1
1
0
0
1
0
1
2
2
0
1
0
1
1
1
0
2
2
1
0
0
1
0
0
0
1
0
2
0
1
2
0
1
0
3
0
0
0
1
0
0
1
0
0
0
0
0
2
0
2
2
0
0
1
2
0
0
1
1
1
0
1
1
2
0
0
0
1
0
1
1
0
2
2
1
0
0
1
0
2
0
0
0
0
0
0
2
2
0
0
2
2
1
2
0
2
0
0
0
1
2
0
0
0
0
1
2
3
0
2
0
0
0
0
1
0
0
1
1
2
0
0
0
1
0
0
0
2
2
0
0
0
1
0
1
1
2
1
0
4
2
1
0
1
0
0
1
0
2
1
0
0
1
1
0
0
4
0
0
0
0
0
2
0
2
1
1
1
1
0
0
1
0
2
0
0
0
1
1
1
0
1
0
2
0
1
1
0
2
0
0
0
0
0
0
1
1
0
0
1
0
1
0
1
1
1
2
2
1
0
0
1
2
1
2
0
1
0
2
2
4
2
1
2
0
1
1
1
1
2
0
0
0
0
2
2
0
1
1
2
0
0
0
0
0
0
1
2
0
0
0
3
2
2
1
3
3
0
0
2
1
2
1
0
0
2
2
0
0
1
1
0
0
2
0
1
1
0
0
0
1
0
1
0
0
0
1
0
0
2
1
1
1
2
4
1
0
2
0
0
1
0
0
0
2
0
1
3
1
0
2
0
0
0
1
0
1
0
0
2
2
1
0
0
0
1
1
0
2
1
1
0
0
0
1
1
1
0
0
0
1
0
0
1
0
0
0
2
1
0
0
0
0
0
2
0
1
2
1
0
0
2
3
0
1
2
2
2
1
0
0
0
2
0
1
0
2
1
0
0
0
1
1
0
1
0
1
0
0
1
0
1
1
2
2
2
3
1
0
2
2
0
0
1
2
1
1
1
2
2
0
2
0
0
0
2
0
1
0
1
2
2
0
0
0
1
0
0
1
1
2
0
0
2
0
0
0
0
0
0
2
0
2
1
2
0
0
2
0
1
1
1
2
2
2
0
2
0
0
2
0
1
1
2
2
0
0
1
2
0
0
0
2
0
0
0
2
1
1
1
0
0
0
1
3
0
0
0
3
0
0
0
0
0
1
0
1
0
5
2
1
0
1
0
0
1
3
1
1
1
0
1
1
0
0
1
1
2
2
1
0
0
0
0
0
0
0
2
0
1
1
0
2
1
2
1
0
2
2
2
2
0
0
1
1
1
0
0
2
0
1
0
1
0
1
0
1
1
2
0
1
1
1
0
0
2
0
1
1
1
0
1
0
0
0
2
0
1
0
1
1
0
2
0
0
2
2
0
1
2
1
0
2
0
1
0
0
0
2
0
1
0
2
0
1
1
0
2
2
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
2
1
0
0
0
0
0
3
2
0
0
0
0
1
0
1
2
2
0
2
0
1
0
0
0
1
0
0
2
0
0
0
1
1
0
0
1
1
0
0
1
0
0
2
0
0
1
1
0
0
0
0
0
2
1
0
0
0
2
2
0
1
0
1
1
0
0
1
2
0
1
2
0
0
0
0
2
2
1
1
0
2
0
1
1
1
2
0
1
2
0
1
0
2
0
3
1
0
0
0
0
1
0
1
2
0
1
0
0
1
0
0
1
0
1
1
0
0
0
2
0
0
1
2
1
1
1
1
2
1
0
0
0
0
0
3
0
2
0
1
0
0
1
2
1
0
0
3
1
0
1
0
1
1
0
1
0
2
0
1
1
1
3
2
2
1
0
0
0
2
1
1
2
2
2
0
0
1
0
0
1
0
1
0
0
0
2
0
3
0
2
2
0
1
0
0
0
1
2
2
2
1
1
1
2
1
0
1
0
0
1
0
0
0
2
1
2
0
1
0
0
0
0
0
1
0
1
2
0
0
0
0
0
1
1
0
1
1
1
1
1
1
0
0
1
1
0
2
0
0
2
0
0
1
1
2
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
1
1
2
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
1
0
0
1
0
1
0
2
2
0
1
2
2
1
1
0
1
2
0
0
0
0
0
1
0
0
2
0
4
2
1
0
1
0
0
1
1
0
0
1
1
2
0
1
0
0
2
1
2
1
2
0
2
1
0
0
0
0
1
1
0
2
0
0
1
1
2
1
0
1
2
0
1
0
0
0
0
2
0
0
2
0
0
0
1
1
0
0
2
1
2
0
2
1
0
0
0
0
0
1
2
2
0
0
1
1
0
0
1
0
1
0
0
0
2
1
1
0
0
0
1
2
0
0
1
2
0
1
1
1
1
0
1
2
0
1
1
0
1
0
0
0
0
0
1
0
4
2
0
2
1
0
2
2
2
1
2
2
1
0
1
2
2
0
1
2
0
0
2
0
1
1
1
0
0
0
1
0
0
2
2
2
0
2
1
0
0
2
0
2
2
2
1
17
2
1
0
0
1
1
2
0
0
0
0
0
0
0
2
0
2
2
0
1
0
0
0
1
1
0
1
0
0
1
0
0
1
0
2
0
1
1
0
0
1
0
1
0
2
1
1
1
2
1
0
0
0
0
2
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
2
2
0
1
1
0
1
0
1
1
3
1
0
1
0
0
1
1
0
2
0
2
1
1
0
0
1
1
0
2
0
3
2
1
1
0
0
0
2
2
1
1
0
0
1
0
0
1
0
1
2
0
1
2
2
2
1
0
0
0
2
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
2
0
0
0
1
0
2
0
0
0
3
3
0
0
1
0
0
0
0
2
2
0
0
0
0
0
1
0
0
2
0
1
0
1
0
2
0
3
1
0
2
2
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
2
0
0
0
1
1
0
0
0
2
2
0
0
0
0
2
2
2
0
0
0
1
0
2
1
0
0
2
1
1
1
0
1
1
0
0
1
0
0
0
1
0
2
0
3
1
0
2
1
0
0
0
2
0
0
2
1
0
1
0
1
0
0
1
2
0
1
2
0
0
0
0
2
0
0
1
1
2
0
0
0
1
0
0
0
1
1
1
2
0
0
0
0
0
0
0
2
0
0
0
1
1
0
2
2
2
1
4
2
1
0
0
0
2
0
0
0
2
1
0
2
1
0
0
2
0
1
0
0
1
1
0
0
0
0
1
2
0
0
3
1
0
0
1
1
0
0
0
2
1
0
1
2
0
1
1
0
1
1
0
0
0
0
0
1
3
0
0
2
2
1
1
0
1
0
1
0
1
1
2
8
0
1
2
0
0
1
2
2
0
1
0
1
0
0
0
0
1
1
1
0
0
0
1
1
0
3
2
0
1
1
0
0
1
1
1
1
2
2
2
0
2
1
0
1
1
0
1
1
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
1
2
0
0
0
2
0
0
0
1
1
1
0
0
0
2
1
2
2
0
0
0
1
0
0
1
0
0
0
1
2
0
0
1
0
0
0
0
2
2
1
0
2
1
1
2
2
0
2
0
0
1
1
1
1
1
0
0
1
0
0
1
0
0
1
1
0
0
0
0
1
2
1
0
0
1
0
0
0
2
3
1
0
1
1
2
0
2
0
1
4
1
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
1
0
1
1
0
1
1
0
0
2
1
0
0
0
2
0
1
0
1
1
1
1
1
0
0
0
0
1
2
0
1
0
0
1
1
0
0
0
0
0
0
2
0
1
2
2
2
0
1
0
1
1
1
1
0
0
1
1
1
1
1
2
1
1
0
0
1
0
1
1
2
0
0
0
3
1
0
2
0
2
1
1
2
1
2
0
1
0
0
0
1
1
0
0
0
0
2
0
1
2
0
0
0
0
1
1
0
0
1
4
2
0
2
2
0
2
2
0
0
0
0
1
0
0
0
2
0
1
2
0
0
0
2
1
0
0
0
1
2
1
0
2
1
0
2
0
0
2
1
0
1
0
0
1
2
0
0
1
0
0
2
1
0
0
0
2
2
0
0
0
0
0
1
2
0
2
0
0
1
0
2
0
0
1
0
0
1
1
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
2
1
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
1
0
0
0
2
0
0
2
0
0
1
0
0
2
1
0
2
1
1
0
0
1
0
1
0
0
0
1
1
2
1
1
2
1
0
2
0
1
0
1
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
1
1
0
0
1
0
0
1
3
1
1
0
0
2
0
0
1
1
0
2
2
0
1
2
2
0
0
2
3
0
0
2
2
0
2
1
0
0
2
0
0
2
0
1
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
1
0
0
0
0
0
1
2
0
1
1
0
2
0
1
0
0
0
1
1
0
0
0
1
2
0
0
1
2
0
0
0
0
1
0
1
2
0
0
0
2
0
2
2
0
1
0
0
2
0
0
0
0
0
2
1
0
2
0
0
1
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
1
2
1
0
1
0
2
0
1
1
0
0
1
1
2
2
0
2
1
2
2
0
0
1
2
1
0
1
1
0
1
0
1
2
0
0
6
0
0
1
0
0
0
0
0
1
0
3
3
0
1
2
2
0
1
0
0
2
1
1
0
0
2
1
1
0
1
0
2
2
0
1
1
1
2
1
1
0
1
2
0
0
1
1
2
0
0
0
2
0
1
0
0
1
0
1
1
2
2
2
2
1
1
1
0
1
1
1
0
1
1
0
0
2
1
2
0
0
2
0
0
1
0
0
1
2
1
0
0
0
0
1
0
0
1
1
2
0
1
0
0
0
1
2
0
0
1
1
0
0
2
0
0
0
1
0
1
1
2
0
1
1
1
1
1
1
0
2
2
0
0
0
0
0
0
1
1
2
1
3
1
1
1
1
1
2
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
1
2
2
1
2
0
0
1
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
1
1
1
1
0
2
0
1
0
0
0
0
2
2
2
0
0
1
4
1
0
2
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
1
2
2
0
1
0
0
1
1
0
1
2
0
0
0
1
0
1
0
0
1
0
0
0
2
1
2
1
2
2
1
1
1
0
1
0
0
1
1
1
1
0
2
1
1
1
2
2
0
1
0
0
1
0
1
1
3
2
2
0
2
0
1
0
2
0
1
0
1
1
0
0
0
2
2
2
1
0
1
0
0
0
7
0
0
1
1
0
0
0
0
2
2
0
2
0
0
1
1
0
1
0
0
0
2
0
0
0
1
2
2
0
2
0
1
2
0
2
2
1
1
1
2
0
1
0
0
0
2
1
3
0
0
1
1
0
0
2
1
2
1
0
0
1
2
0
0
1
1
2
1
2
0
0
0
0
3
1
1
1
2
1
1
2
0
1
2
1
0
0
2
1
0
0
2
0
2
2
0
2
1
0
2
1
1
0
0
0
1
0
1
1
2
0
1
1
0
1
0
1
0
1
1
1
1
1
2
0
1
2
0
0
2
1
2
0
0
0
1
1
0
0
0
1
2
1
0
2
0
1
3
0
0
1
0
0
0
1
2
1
0
2
1
1
0
0
1
0
0
1
0
2
0
0
1
0
1
1
1
1
1
2
0
0
2
0
1
0
0
0
3
1
0
0
1
0
2
1
1
0
0
0
1
0
0
0
0
1
1
6
0
0
2
0
1
1
0
0
1
1
0
2
2
0
0
0
0
1
0
0
0
2
1
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
3
0
1
1
0
1
0
1
0
2
1
2
0
0
0
0
1
2
0
2
2
1
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
1
2
0
1
0
0
2
0
1
2
0
2
1
2
0
0
1
0
2
0
0
1
0
2
0
0
0
0
2
2
0
2
1
0
0
1
0
2
2
0
0
2
0
2
0
1
0
0
1
1
0
0
1
0
2
0
1
0
1
0
0
0
1
2
0
0
0
1
1
2
2
0
0
1
2
0
2
2
1
1
1
0
0
0
1
0
1
0
1
0
0
1
1
3
0
0
0
2
0
0
0
0
1
0
0
0
1
2
1
1
2
0
2
1
0
1
0
1
0
1
1
0
0
1
2
1
0
1
1
0
0
0
1
1
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
2
0
1
1
0
2
2
1
1
1
0
0
2
0
0
0
2
2
0
0
1
0
1
1
2
0
1
1
1
1
0
1
1
0
2
1
1
0
4
2
0
0
1
0
0
0
1
2
0
0
0
0
2
0
0
0
0
1
0
1
0
2
0
0
0
1
1
0
0
2
1
2
2
2
0
2
2
2
1
2
0
0
1
0
2
0
2
0
0
1
1
0
0
1
0
1
0
1
0
2
0
0
1
0
2
2
1
1
2
0
0
1
0
0
2
0
2
2
1
2
0
0
0
0
0
0
2
0
0
0
1
1
0
0
2
0
1
2
2
0
1
0
0
2
0
0
0
1
0
0
2
0
1
1
1
1
0
2
1
0
1
0
1
0
2
0
2
0
1
0
0
2
0
3
0
2
2
0
1
0
1
1
1
0
0
0
0
2
1
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
2
0
2
1
0
0
2
2
0
0
0
1
0
1
0
1
1
0
2
0
0
0
2
1
0
7
0
0
1
0
0
1
1
0
1
2
1
1
0
0
0
0
2
0
1
0
0
0
0
1
2
1
0
0
1
0
0
0
2
0
2
2
0
2
0
0
0
2
0
0
0
1
1
1
1
2
2
0
0
1
0
2
1
0
1
1
1
0
0
1
2
1
0
1
1
1
0
1
0
0
0
2
2
0
2
1
2
0
2
0
1
0
2
0
1
0
1
0
1
1
0
2
1
0
2
1
0
3
0
0
2
0
0
2
1
0
3
0
2
2
1
0
1
0
2
0
1
0
1
2
0
1
2
0
0
0
1
2
0
1
0
2
0
0
0
0
0
0
1
0
0
0
1
1
2
2
0
1
0
0
0
0
0
2
1
1
0
2
0
0
2
0
0
2
0
0
3
0
0
0
0
0
0
1
2
2
0
0
0
0
0
2
0
3
0
1
0
1
0
2
2
2
0
0
2
0
0
0
2
0
1
2
1
1
0
0
1
0
0
0
0
0
0
0
2
0
1
1
0
0
1
0
1
1
0
2
0
0
2
2
1
0
0
0
3
1
0
2
1
1
2
0
1
1
0
2
2
0
0
0
1
1
1
1
0
2
0
1
1
0
1
1
0
1
2
1
0
0
0
1
0
2
0
1
0
2
0
1
1
1
1
0
0
2
2
1
0
0
0
0
1
0
2
0
0
1
1
1
0
1
0
1
0
1
0
0
0
0
1
1
0
1
2
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
1
2
3
1
0
1
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
2
0
3
0
0
1
0
3
1
3
0
0
1
1
2
0
0
1
0
0
0
0
2
3
1
1
0
0
0
1
1
0
0
0
3
0
0
2
1
0
0
0
1
0
1
1
0
1
2
1
0
0
1
1
7
0
0
1
3
0
0
0
1
0
0
0
0
2
0
1
0
1
0
1
1
0
2
2
1
2
1
0
2
0
0
1
0
0
0
1
1
0
1
2
1
0
1
2
1
2
0
2
2
0
1
1
0
0
2
0
1
1
0
1
0
2
1
2
2
0
0
0
0
2
0
1
1
1
0
0
1
0
2
1
0
0
0
2
1
0
0
0
0
1
0
3
0
1
0
2
1
0
0
1
1
1
1
2
0
0
0
2
0
0
1
0
2
2
0
2
1
0
2
0
1
1
1
0
0
1
1
1
1
0
0
0
0
0
0
1
2
0
0
0
2
0
1
0
1
0
3
2
0
0
2
1
0
1
0
1
0
3
2
0
0
0
1
2
0
1
0
1
0
0
0
0
2
0
0
0
0
1
1
1
0
1
2
2
0
0
1
0
2
0
0
3
1
0
0
2
1
0
0
0
0
0
0
0
1
2
1
2
1
1
2
1
1
0
0
2
2
0
0
2
1
1
0
1
1
0
0
0
1
0
2
0
0
1
0
1
1
2
0
0
1
1
2
1
0
1
1
2
2
1
2
0
0
0
1
0
1
2
0
0
0
0
1
2
0
0
0
2
0
1
1
0
0
1
0
0
0
1
0
1
2
0
2
1
2
2
0
0
2
1
1
0
0
0
0
1
0
0
2
0
1
2
0
0
1
0
2
0
0
0
1
1
0
0
0
1
0
1
0
1
1
2
0
1
0
0
2
2
0
0
0
2
0
1
0
1
0
0
0
1
2
0
0
0
0
0
4
0
0
0
0
0
1
2
0
0
0
0
0
0
1
2
0
0
2
2
1
1
0
1
1
0
0
3
0
1
0
0
0
1
2
0
0
1
2
0
0
1
0
0
2
2
3
0
2
2
1
0
0
0
0
1
1
0
0
0
2
0
0
1
0
1
2
0
0
1
0
0
0
0
1
1
0
1
0
1
0
2
0
0
1
0
1
2
2
2
0
0
2
2
0
0
1
0
0
1
2
1
0
2
3
1
0
2
1
1
0
0
0
2
1
0
0
0
1
2
2
0
1
0
0
0
0
0
1
0
1
2
0
0
1
0
0
0
2
2
1
1
2
0
0
1
1
0
2
0
1
2
0
1
0
1
0
1
0
0
0
0
1
1
1
4
2
0
1
0
0
2
1
0
0
0
3
0
2
1
2
0
0
0
1
0
0
1
1
2
1
0
2
0
1
1
0
1
0
0
0
0
1
1
0
2
2
3
2
1
0
0
0
1
1
0
0
1
2
0
0
1
0
0
1
0
1
0
0
3
0
0
1
2
0
0
1
1
1
0
0
2
0
0
0
2
0
0
2
1
1
0
1
0
0
0
1
0
1
2
0
0
0
1
0
2
0
1
0
1
1
0
2
2
1
0
1
1
2
0
0
1
1
0
0
0
0
0
1
0
0
2
0
1
0
2
1
0
0
2
1
2
0
0
0
1
0
1
1
1
2
2
0
0
1
1
2
1
0
1
2
0
3
0
0
0
1
0
2
1
2
0
0
0
1
0
1
0
1
1
2
0
0
0
0
1
1
0
1
1
3
2
0
0
1
0
2
1
2
1
0
0
1
2
0
2
1
1
1
0
1
0
1
0
1
1
0
1
2
1
2
0
0
0
1
0
1
1
2
1
0
0
0
1
2
1
1
1
0
0
1
0
1
2
1
2
2
1
1
3
0
0
0
2
0
0
0
0
1
0
0
2
1
2
0
0
0
2
2
0
1
2
2
1
1
3
1
0
0
0
1
0
1
0
0
0
1
2
1
0
0
0
0
0
2
0
0
1
0
0
0
0
1
1
2
2
2
1
0
1
2
2
0
0
2
0
1
0
0
0
1
1
3
0
1
0
1
0
1
1
0
0
0
0
0
0
1
2
2
3
1
1
1
2
1
2
3
1
0
0
2
0
0
2
0
0
2
0
1
1
0
0
1
0
1
0
0
4
2
0
0
0
0
1
0
1
2
0
1
0
0
0
1
2
0
1
1
1
0
0
0
1
0
2
0
5
2
0
0
2
2
0
2
0
0
0
0
0
0
1
0
1
0
0
0
1
1
1
0
0
0
0
0
1
0
1
0
1
1
0
0
1
0
1
0
0
1
0
1
2
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
2
2
2
1
1
0
0
0
2
0
0
1
1
1
0
1
1
2
1
1
0
1
1
1
0
0
1
0
1
0
2
3
0
1
2
3
1
0
0
2
1
0
0
1
1
0
1
1
2
2
1
0
1
2
0
2
1
1
0
2
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
1
0
1
1
1
2
4
0
1
0
0
0
1
2
1
1
2
0
0
0
1
2
1
0
0
0
0
2
1
0
2
0
0
0
0
1
1
2
0
0
3
1
0
0
2
0
0
0
0
0
1
2
0
0
0
1
0
0
1
1
0
1
0
2
1
0
1
1
0
1
1
1
0
0
1
2
2
1
2
2
1
1
1
2
0
1
2
0
1
1
1
1
0
1
2
0
1
0
0
1
0
2
2
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
1
0
1
0
0
2
0
0
2
1
0
1
0
2
1
0
0
2
0
0
0
2
0
1
2
0
2
0
0
0
0
2
2
1
0
1
0
0
2
0
0
1
1
0
2
2
1
0
0
0
1
0
1
1
0
1
0
1
1
0
2
0
0
0
1
0
2
0
1
2
0
0
1
0
2
2
0
1
0
0
2
2
0
1
0
1
0
0
1
2
1
2
1
1
1
2
2
2
0
0
0
0
0
0
1
2
0
1
0
0
2
1
1
1
1
1
0
0
1
1
1
0
0
0
1
0
1
1
2
2
0
1
0
2
1
2
1
1
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
1
2
0
1
0
1
1
2
0
0
0
1
0
0
0
0
0
1
2
2
0
0
1
0
0
3
2
0
2
1
1
2
0
0
2
1
2
0
0
1
0
1
0
1
0
0
0
1
0
1
0
1
2
0
2
0
2
1
1
1
0
1
2
2
1
2
1
1
1
1
0
1
0
0
1
1
0
0
2
1
0
1
0
1
1
1
0
0
1
2
1
1
2
1
1
0
0
0
0
0
5
0
0
2
0
0
0
1
2
1
0
1
0
0
0
1
0
2
0
0
1
0
0
0
0
0
1
1
1
0
0
2
0
2
1
0
0
2
1
2
0
0
1
1
0
0
0
1
1
0
0
1
2
0
0
0
0
2
0
0
0
0
0
2
2
1
1
1
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
1
0
2
0
1
2
1
0
1
0
2
0
0
1
1
0
2
1
1
1
0
0
1
1
1
0
0
1
2
0
0
0
2
2
1
1
0
2
2
0
1
0
1
2
1
0
2
0
2
0
2
1
0
0
1
0
1
0
1
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
1
1
1
0
0
1
1
2
1
0
0
0
0
1
0
2
1
1
0
0
0
2
0
2
1
0
0
1
3
0
2
2
1
1
0
2
1
1
0
0
0
1
1
1
2
3
2
0
0
0
0
0
0
0
0
0
2
0
2
1
1
1
0
0
1
1
1
0
0
2
0
1
0
1
2
1
0
0
2
0
2
0
0
0
1
1
0
1
0
1
0
3
1
2
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
1
0
1
1
0
1
0
3
2
0
1
1
0
0
0
2
2
1
2
0
0
0
1
1
2
2
0
3
0
0
0
0
0
0
0
1
0
1
2
0
0
1
0
1
0
1
0
0
2
0
0
0
0
0
2
0
2
0
0
1
0
0
0
1
2
2
0
0
0
0
1
0
3
1
0
0
2
1
1
1
0
0
0
0
1
1
2
1
0
0
0
2
1
0
0
1
0
0
0
1
0
1
0
0
0
0
1
1
1
0
0
2
0
0
0
0
1
0
2
1
1
1
2
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
1
1
1
0
3
0
0
2
1
2
2
2
2
1
2
0
1
1
1
1
0
0
2
1
0
0
1
0
0
0
0
1
1
1
2
1
0
0
0
0
2
1
1
1
0
1
0
0
0
2
1
2
0
0
1
1
0
2
0
1
0
5
0
0
3
0
0
0
0
2
1
1
0
1
2
0
2
3
0
1
2
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
2
1
1
1
0
0
1
1
0
0
0
2
2
1
1
0
1
0
1
0
1
0
0
0
0
0
1
2
0
1
1
1
0
1
1
1
1
0
2
0
2
0
0
1
0
1
2
0
1
1
1
0
1
1
2
0
1
2
3
0
0
0
0
0
2
0
2
0
0
1
0
1
0
0
0
2
0
1
0
2
1
0
0
0
0
0
0
0
0
1
0
2
2
1
1
0
1
1
1
3
3
2
0
0
0
1
2
2
1
1
1
0
0
0
1
0
1
0
0
0
2
0
2
0
0
0
1
2
2
2
0
2
0
0
0
1
1
0
2
0
2
0
0
2
1
0
2
1
0
0
2
1
1
1
1
2
2
0
2
2
0
1
1
1
1
1
1
1
1
1
1
1
0
1
0
0
0
0
2
2
0
1
0
1
0
2
0
1
1
0
0
2
0
2
0
0
0
0
0
2
1
1
1
0
1
1
1
1
0
0
1
0
2
2
0
0
0
2
1
2
0
2
0
1
0
0
2
2
2
0
0
1
0
0
0
0
0
0
2
2
0
1
2
2
1
1
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
1
1
0
0
1
0
1
0
1
2
3
1
1
0
1
2
1
4
0
1
0
0
1
0
2
0
0
0
0
2
0
0
2
0
4
1
2
1
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
1
0
0
0
0
1
0
1
1
0
2
0
1
0
0
2
2
0
2
1
1
1
0
0
0
1
3
1
1
0
2
1
1
0
1
1
1
0
0
2
2
1
0
1
1
1
2
0
2
1
1
0
1
0
0
0
1
0
0
0
0
1
2
1
1
0
0
1
1
2
0
0
1
1
2
0
0
1
0
0
0
0
0
2
2
0
0
0
0
1
1
0
0
0
2
1
0
0
2
1
2
0
2
2
1
0
2
2
1
0
0
1
0
0
2
0
0
1
2
1
1
1
2
0
1
1
1
0
0
0
1
1
0
0
1
0
0
2
1
0
0
2
0
0
0
0
0
2
2
0
0
0
1
0
1
2
0
2
0
2
1
1
1
1
5
0
0
1
2
1
1
0
0
2
0
0
1
0
0
0
0
0
2
0
0
1
2
0
2
0
0
2
2
1
0
0
2
1
2
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
2
4
1
0
0
2
0
2
2
1
0
2
1
0
1
1
2
1
0
2
2
1
0
1
0
2
0
1
1
0
0
0
0
0
2
1
2
1
0
2
2
1
0
0
0
0
0
0
0
1
0
0
2
2
0
2
0
0
2
0
1
0
1
0
0
1
2
1
1
1
0
0
0
0
1
1
0
3
0
2
0
1
2
0
0
1
0
0
0
2
0
1
1
0
0
0
4
1
0
1
0
2
0
0
0
1
0
1
0
1
1
1
1
1
2
0
1
2
2
1
0
0
0
0
0
2
0
0
2
2
0
0
0
1
1
0
0
0
1
0
2
2
1
0
0
0
0
1
0
0
0
0
2
0
1
0
3
1
1
2
1
1
0
1
0
7
0
0
2
2
0
2
1
0
3
0
0
0
0
4
0
0
2
2
0
0
0
1
0
0
0
1
1
0
2
1
1
1
1
2
2
0
0
1
0
3
2
1
0
1
1
1
0
2
0
0
0
0
2
1
0
2
0
2
1
1
1
0
0
0
0
0
1
2
0
2
2
1
0
0
0
1
1
1
0
0
1
0
0
0
2
1
2
1
1
1
1
1
0
1
1
1
0
2
2
2
0
0
0
0
2
1
0
0
1
0
0
1
0
0
0
1
1
1
1
3
2
2
2
0
0
2
0
0
0
0
3
0
0
1
1
1
0
1
1
2
0
0
1
0
1
0
1
2
1
0
0
0
0
1
2
1
1
1
2
0
2
0
0
0
0
2
2
2
0
0
0
0
0
1
0
0
0
0
1
2
1
1
2
0
0
0
1
0
2
0
2
1
0
2
1
0
1
0
0
0
0
2
0
2
0
8
2
0
0
0
2
0
1
1
2
3
1
2
1
1
0
0
0
1
2
1
1
1
0
0
1
2
0
1
0
0
0
1
1
0
2
0
1
2
1
2
1
1
2
0
1
0
2
1
1
0
0
2
0
2
0
2
1
0
0
0
1
0
0
0
0
1
1
2
4
1
2
0
2
0
0
0
0
1
1
0
0
0
2
1
2
1
2
1
0
2
0
2
2
0
1
2
1
0
0
2
2
0
2
0
4
0
0
1
2
0
0
0
1
0
3
0
0
0
1
0
3
1
1
0
1
0
1
0
0
2
2
1
1
1
0
1
1
1
0
0
1
2
0
0
1
1
2
0
1
1
0
0
2
2
1
1
1
0
1
1
0
2
0
0
0
1
1
0
0
0
0
0
2
1
1
0
0
0
2
2
0
0
0
2
2
2
1
0
1
1
2
0
0
0
0
0
1
0
0
0
0
0
1
1
2
2
0
0
2
0
1
2
0
0
1
0
0
1
2
1
0
0
1
0
2
3
0
0
2
1
0
2
0
0
1
1
0
0
0
0
0
2
0
2
0
2
0
0
0
2
0
0
2
0
2
2
0
0
0
0
1
0
0
2
2
1
1
0
1
2
1
1
0
2
0
2
0
0
1
1
0
0
0
1
0
0
0
0
0
5
2
0
1
1
1
4
2
2
1
0
1
0
0
0
1
1
1
1
0
0
0
1
1
1
0
0
0
2
0
0
2
1
0
2
1
2
0
0
0
0
1
1
1
2
0
0
2
1
0
3
3
2
0
0
1
1
2
0
1
0
0
1
0
1
0
0
1
0
2
1
0
1
1
0
2
2
0
2
1
1
0
0
1
0
0
0
0
0
1
2
2
0
1
0
1
0
0
2
0
0
1
1
0
1
0
0
0
2
0
2
0
1
0
0
0
1
0
1
0
0
0
2
0
0
0
0
2
1
1
1
0
2
1
1
2
1
0
3
1
0
2
0
1
0
0
1
1
0
0
0
0
2
2
2
0
2
0
0
0
1
0
0
1
1
0
2
0
1
0
1
0
2
1
3
0
0
2
0
2
2
2
1
0
1
0
1
0
0
0
0
2
1
2
2
0
2
0
2
0
2
1
1
1
2
2
1
1
0
2
0
0
2
1
0
1
2
1
2
0
1
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
2
0
2
1
0
1
0
0
0
0
0
1
2
1
3
2
0
4
0
0
1
0
0
1
1
1
1
1
2
1
0
0
0
2
1
1
1
2
0
0
0
0
1
1
1
4
1
0
0
2
0
2
0
1
0
1
2
0
1
0
0
1
0
0
0
2
0
2
2
0
0
2
2
0
0
2
2
0
1
1
1
2
0
0
1
2
2
1
2
1
1
1
1
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
1
1
2
1
0
1
1
0
1
1
0
1
1
0
2
0
2
2
0
0
0
0
2
0
0
1
1
1
2
0
0
1
1
0
1
0
1
0
3
2
2
0
0
0
1
1
1
0
0
0
0
1
0
0
2
3
0
0
1
0
2
1
1
0
0
2
0
0
1
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
1
1
2
2
1
2
2
2
0
2
2
1
1
2
1
0
1
0
0
2
0
2
0
1
1
0
1
0
1
2
0
1
0
0
0
0
0
1
2
2
1
0
0
0
0
0
1
2
0
0
1
1
0
0
1
1
0
2
0
2
0
0
0
0
0
0
0
2
2
1
1
0
2
1
2
0
0
2
0
0
0
0
0
1
2
1
1
1
3
1
2
0
0
1
0
1
1
0
2
0
1
2
0
1
2
0
0
2
0
0
0
0
0
1
2
0
1
0
2
2
2
0
0
1
0
1
1
0
1
0
0
0
1
0
0
0
1
2
0
0
1
1
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
2
1
1
1
1
0
0
3
0
2
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
2
0
1
2
0
2
0
0
0
0
0
2
0
1
0
1
0
2
1
0
0
0
2
0
2
0
0
0
2
0
2
0
0
0
2
0
0
3
1
2
0
2
2
0
1
2
0
0
0
2
0
2
4
2
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
2
1
0
1
1
1
1
0
1
2
0
1
3
0
0
1
0
1
0
0
0
0
1
0
0
0
1
1
0
1
3
2
0
0
0
0
1
0
0
1
2
0
1
5
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
2
2
2
0
0
0
2
0
0
0
0
2
1
1
0
1
2
0
2
0
1
1
2
0
0
0
1
0
1
0
0
0
1
1
2
0
0
0
0
1
0
2
2
2
0
0
0
0
1
0
2
0
2
0
0
0
1
1
0
2
0
0
1
1
1
0
0
0
0
1
0
1
1
0
0
5
0
0
0
0
0
0
0
2
0
1
1
0
0
0
1
0
0
2
0
1
1
2
1
0
0
2
0
0
0
1
2
1
0
1
0
0
1
1
1
0
0
3
0
2
1
1
1
2
0
0
0
0
2
1
1
0
2
0
1
0
2
2
0
0
1
1
0
1
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
1
0
1
0
4
2
1
1
1
1
0
1
0
3
0
0
3
2
1
2
0
0
0
0
0
1
2
1
1
2
1
2
0
1
0
0
1
1
0
1
2
0
0
0
1
2
2
0
0
2
1
1
0
0
0
0
0
0
0
1
1
2
0
0
0
0
2
2
2
0
0
1
3
0
0
2
3
2
2
1
0
1
0
1
0
1
0
0
0
0
0
12
0
0
1
1
0
0
0
0
1
2
2
2
0
2
0
2
0
0
0
1
2
1
0
1
0
0
0
0
1
0
0
0
1
0
2
0
1
0
2
1
0
1
0
1
1
1
0
0
1
0
1
0
1
2
0
1
3
1
1
1
0
2
1
2
2
0
1
2
0
0
1
1
0
0
0
0
0
1
1
0
2
0
0
2
0
1
0
2
1
1
2
0
0
0
4
1
0
0
1
1
1
1
0
0
0
1
0
5
2
2
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
1
1
1
0
0
1
2
0
2
1
0
1
0
0
2
1
0
0
2
0
0
2
1
0
2
0
0
0
0
0
0
1
1
0
1
2
3
2
1
0
0
0
0
0
0
1
0
3
1
0
0
1
1
0
2
1
0
2
0
0
0
1
0
1
0
0
2
2
0
1
0
0
1
1
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
2
1
1
1
0
0
0
2
2
0
0
2
1
2
2
2
0
0
0
1
1
1
0
0
0
2
0
0
0
2
0
0
0
1
1
2
1
0
0
0
0
0
1
0
0
1
0
1
0
2
2
0
0
0
0
1
0
1
2
0
0
2
1
0
1
1
2
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
2
2
0
0
0
1
1
0
0
1
0
0
0
0
0
1
2
0
2
1
2
0
0
1
0
2
1
0
1
0
0
1
2
0
1
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
2
2
0
1
0
0
0
1
2
0
0
0
0
2
2
0
0
2
1
0
0
0
0
1
1
2
0
2
0
0
0
1
0
0
2
0
0
0
1
2
0
2
1
2
0
1
0
0
0
0
2
0
1
2
0
2
2
1
0
2
0
0
2
9
0
2
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
2
1
0
2
2
0
0
1
0
0
1
0
1
0
2
0
1
2
1
0
2
0
0
2
0
2
1
2
1
0
2
0
1
0
0
0
3
2
2
2
2
0
0
0
1
1
1
2
2
2
0
1
0
0
2
0
0
0
0
1
1
0
2
0
1
0
2
0
0
1
1
0
0
0
2
1
1
1
0
0
0
1
2
2
0
2
0
0
1
2
0
0
1
1
0
0
1
0
0
0
0
0
1
1
3
0
0
0
0
2
2
1
2
2
0
0
0
1
0
0
0
2
1
0
0
0
0
0
1
1
2
0
1
2
0
1
1
2
0
2
1
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
3
0
1
2
0
0
0
1
0
2
2
2
2
1
2
1
1
0
1
0
0
0
2
0
0
0
2
0
0
0
0
1
0
2
2
0
2
2
1
1
1
1
0
0
1
0
2
1
0
1
1
2
0
2
0
1
1
2
0
1
1
0
0
2
1
2
0
2
0
2
1
0
0
2
0
0
0
1
2
2
0
1
1
2
0
1
0
0
0
0
2
1
0
4
0
0
1
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
1
2
0
0
0
0
2
1
1
1
1
1
0
1
1
0
2
0
0
0
5
1
1
0
2
0
1
2
1
1
0
0
2
0
0
2
0
0
0
0
1
0
0
0
1
2
2
2
2
1
2
0
2
0
3
0
0
2
0
0
1
0
1
2
2
0
1
1
0
0
1
2
0
0
1
0
0
0
0
1
0
0
1
2
2
0
1
0
0
0
0
0
1
0
1
0
1
2
1
0
1
0
0
1
2
0
1
1
1
1
1
0
0
0
0
0
1
0
2
1
1
1
2
0
0
1
0
1
1
0
0
2
1
0
0
0
0
2
0
1
0
0
0
1
0
1
0
0
0
2
0
0
2
0
2
1
0
1
1
2
0
0
2
2
2
2
0
1
0
0
0
1
0
0
1
0
0
0
0
1
1
0
2
2
0
0
0
0
1
0
0
0
1
1
0
2
1
0
0
0
2
1
0
0
1
0
0
0
0
1
1
1
1
0
1
2
1
0
0
1
1
0
1
0
2
0
2
0
0
0
0
0
1
0
1
2
1
2
1
0
2
0
0
2
1
1
1
0
0
0
2
0
1
2
1
2
0
4
0
0
0
0
0
1
1
1
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
1
1
0
2
1
0
0
1
1
1
0
0
0
0
0
2
2
0
0
0
0
0
1
2
1
0
1
1
1
0
3
2
1
0
0
0
2
1
2
0
1
1
2
0
0
0
1
0
0
0
1
0
0
1
0
2
0
0
1
0
0
1
1
0
0
1
2
1
2
2
2
0
2
2
1
1
0
1
0
0
2
1
0
0
0
1
1
0
1
0
5
0
0
1
1
0
2
0
2
1
0
0
0
2
0
0
0
2
1
1
1
2
2
0
0
0
1
0
0
7
0
1
2
4
0
2
0
1
0
0
1
0
0
1
2
1
1
1
0
0
1
0
3
2
0
1
0
0
0
1
0
0
0
0
1
1
2
2
0
0
1
0
1
2
2
2
0
0
2
0
0
2
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
4
0
1
1
2
0
1
2
0
0
0
1
1
0
1
0
0
2
3
1
0
0
1
0
1
0
0
2
0
0
1
0
1
0
0
1
2
2
1
2
1
2
3
2
0
2
1
2
1
0
1
1
0
1
2
0
0
0
0
0
1
1
0
0
2
0
0
0
0
1
0
0
3
1
1
0
0
0
2
0
2
2
2
0
4
1
1
1
2
2
1
0
1
0
0
0
1
0
1
1
0
1
1
0
0
0
0
2
1
1
2
1
2
0
2
0
0
0
3
1
0
2
1
3
1
0
0
1
0
1
1
1
1
1
2
0
0
2
0
2
0
1
1
3
2
0
2
1
2
1
0
1
1
1
0
2
0
2
1
1
0
4
2
0
3
0
1
0
0
2
1
1
0
1
1
0
1
1
1
1
1
0
0
5
0
0
0
0
0
2
2
0
1
1
0
0
1
0
0
1
1
2
2
1
2
0
1
0
2
1
2
0
1
0
1
0
2
0
2
2
0
2
0
1
4
2
0
0
2
0
2
1
0
0
1
2
0
1
2
2
0
0
0
0
1
2
0
0
0
2
0
0
0
2
0
1
1
2
0
3
0
0
1
0
0
1
0
0
0
1
2
1
0
0
0
2
0
2
1
1
0
0
1
1
1
0
0
0
0
0
1
1
0
1
1
0
0
2
0
2
2
2
1
1
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
2
1
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
1
0
0
2
1
0
1
2
0
0
2
0
0
1
5
1
1
0
2
0
1
1
2
0
0
2
2
0
0
1
0
0
2
0
1
1
2
0
2
1
0
2
1
1
1
0
0
1
0
0
0
2
0
2
0
0
1
2
0
1
0
1
0
2
0
1
0
0
2
0
0
2
0
0
0
2
2
2
0
0
0
2
2
0
2
0
1
2
1
1
0
0
1
0
2
0
0
0
3
0
1
1
0
1
0
0
0
2
2
2
3
0
0
0
2
0
0
0
0
1
0
0
1
1
0
0
2
0
2
1
0
0
0
0
2
1
1
0
1
1
0
0
1
1
0
0
1
1
1
0
1
1
1
0
2
0
0
1
0
1
1
0
0
0
2
0
0
0
1
2
2
0
1
2
2
0
0
1
2
0
0
1
0
2
0
1
2
1
0
1
0
2
0
1
2
2
0
2
0
1
0
1
2
0
1
1
0
1
1
1
0
0
2
1
0
0
0
0
0
1
1
0
1
0
2
0
0
1
0
0
2
0
5
2
0
1
1
0
0
1
0
0
0
1
0
2
1
0
2
1
0
3
0
2
1
0
2
0
0
1
2
0
0
0
2
0
2
0
0
0
1
0
2
0
2
1
0
0
0
2
0
2
0
0
0
1
0
0
1
2
0
0
0
1
0
1
1
1
1
1
2
2
2
0
2
0
2
1
2
1
2
0
0
1
2
0
2
0
1
2
2
2
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
1
1
1
1
0
0
0
0
0
2
0
0
2
0
1
1
0
2
0
0
2
2
1
2
2
0
2
0
0
0
0
0
2
1
0
0
2
0
0
1
0
2
0
0
0
1
1
0
0
0
2
0
0
2
1
1
1
1
2
2
0
1
2
2
0
0
1
0
2
0
2
1
2
0
3
2
0
0
2
1
0
0
0
0
2
2
2
2
0
0
1
2
0
1
1
1
0
1
1
0
2
2
2
2
0
3
0
0
0
0
2
0
0
2
0
1
0
0
0
0
2
1
1
2
2
1
1
0
0
2
0
2
0
0
1
2
1
1
0
0
0
1
1
1
0
2
1
0
0
2
2
3
2
2
0
1
1
1
3
0
1
0
0
0
2
2
0
1
0
0
2
1
0
0
2
0
1
1
2
0
1
0
1
1
1
1
0
1
0
0
0
3
0
0
2
1
1
0
1
0
0
2
3
1
1
2
1
1
0
0
0
0
1
1
0
1
0
0
0
1
1
2
2
2
0
0
1
0
1
0
0
0
1
0
1
2
3
1
1
0
0
0
0
1
0
0
2
0
1
2
2
1
0
1
0
2
0
3
1
0
3
1
2
1
0
2
0
0
0
2
0
0
1
2
0
0
2
2
1
1
0
0
2
0
2
0
1
1
1
0
1
0
1
2
0
1
1
0
0
1
1
1
0
0
0
1
0
1
0
0
0
1
1
0
0
1
0
0
0
1
2
0
1
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
2
0
0
0
2
0
0
0
0
1
2
2
0
2
0
0
0
0
0
2
1
1
1
1
1
2
1
0
2
0
0
2
0
1
2
0
0
0
0
1
0
0
1
0
0
1
0
1
0
2
2
0
0
0
0
0
0
0
0
2
2
0
1
0
0
1
0
4
0
0
1
2
2
0
0
2
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
1
2
1
2
0
0
1
1
2
0
1
0
2
1
1
0
0
3
0
0
3
1
0
0
0
0
0
1
1
1
2
0
0
1
0
1
0
2
0
1
1
0
1
0
0
1
1
0
1
0
1
1
1
0
1
0
0
1
0
1
0
0
0
0
0
0
2
1
0
0
1
2
1
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
1
0
3
0
0
0
0
4
1
1
1
0
0
0
0
0
0
1
0
0
2
1
0
1
0
0
0
0
0
0
0
2
0
2
0
2
0
2
1
0
2
2
0
1
1
1
2
2
0
0
0
2
0
0
0
2
1
0
3
0
1
2
1
0
3
0
0
0
2
2
2
0
1
0
0
0
0
0
1
0
1
0
1
1
2
1
1
0
1
0
2
0
1
0
0
1
1
0
0
0
1
0
0
0
0
1
1
0
0
2
1
0
1
0
0
0
1
1
1
1
0
0
2
1
0
1
0
1
2
2
2
0
1
1
0
0
1
0
0
0
1
1
0
2
3
2
0
2
1
0
1
1
0
1
2
0
0
1
0
0
2
2
2
2
0
0
0
0
0
1
1
0
2
0
2
0
2
0
1
0
0
0
2
0
0
2
2
1
0
2
1
0
0
2
0
1
1
3
0
1
2
0
1
0
1
2
0
1
0
0
1
0
2
0
0
0
1
2
0
2
1
2
0
0
0
2
3
0
1
1
0
2
2
0
0
0
1
0
2
0
0
0
0
1
1
0
0
0
0
4
0
1
2
0
0
0
1
0
0
1
1
0
0
1
0
0
1
4
2
0
0
0
1
2
0
1
0
0
2
0
2
1
0
0
0
1
0
1
2
0
1
1
0
1
1
0
0
0
1
0
2
1
2
0
0
2
2
0
1
0
0
0
2
1
0
0
1
0
2
0
1
2
0
0
2
1
0
2
0
2
1
1
0
0
0
2
0
2
1
0
1
2
1
1
1
0
1
2
0
2
1
0
1
0
2
1
1
0
0
2
0
0
0
1
1
0
0
2
0
0
0
1
1
1
0
2
0
1
0
1
1
0
0
0
1
0
1
0
1
0
0
1
0
2
0
2
1
0
0
0
1
0
1
1
1
0
0
2
0
0
1
1
1
1
0
1
0
0
0
1
2
1
2
0
1
2
0
1
4
1
1
0
3
1
1
0
2
1
1
0
1
2
2
0
1
0
1
0
0
2
0
0
0
2
0
1
0
1
0
2
0
1
0
0
1
0
0
0
1
0
2
0
0
1
0
2
0
1
2
0
1
0
0
0
1
1
0
0
0
2
1
0
2
3
1
2
0
0
1
3
1
0
2
2
2
0
1
0
1
1
1
2
0
0
0
0
0
0
0
3
2
0
0
0
0
0
1
1
1
0
0
1
0
2
0
0
1
0
1
0
1
0
1
0
0
1
0
1
2
1
2
0
3
0
0
0
0
1
1
1
0
0
0
1
0
0
0
2
1
1
2
0
3
0
0
0
1
2
1
0
0
2
1
0
0
1
1
2
0
0
2
0
1
1
2
0
1
0
2
0
2
0
0
1
1
0
1
0
0
2
0
3
0
1
0
0
1
6
1
1
1
1
2
2
0
1
1
2
1
1
1
1
0
2
1
1
0
0
0
0
1
1
2
2
1
1
1
2
0
1
0
0
2
1
0
0
0
0
2
1
2
2
1
0
0
1
1
2
0
1
1
3
1
1
0
0
2
0
1
1
1
0
0
0
2
1
0
2
0
1
2
0
0
0
2
0
2
2
1
0
1
0
0
1
0
0
0
0
1
1
1
2
0
0
0
0
2
0
0
1
0
0
0
0
2
2
0
0
2
1
1
0
1
1
1
0
0
2
1
1
0
3
0
0
0
1
0
0
0
0
0
1
1
2
0
0
0
0
0
0
2
0
0
0
0
1
1
1
0
0
0
0
2
1
0
0
0
2
2
1
2
2
2
2
2
0
1
0
2
0
0
0
2
2
0
2
7
2
0
0
1
0
0
1
0
0
0
0
2
2
2
1
0
0
2
0
1
2
0
0
0
0
0
0
1
0
0
2
0
0
0
2
1
2
0
2
1
2
0
2
0
0
0
1
1
0
1
0
2
0
0
2
2
0
1
0
1
2
0
1
0
0
1
2
0
0
0
1
0
1
1
2
1
1
0
2
0
0
0
0
1
0
2
0
1
2
2
1
2
2
2
1
0
1
2
0
1
0
0
0
0
0
0
2
0
0
1
2
0
1
0
0
0
0
0
2
0
1
2
0
3
0
2
1
0
1
0
0
0
2
0
1
2
2
2
2
2
0
0
0
3
0
2
1
0
1
0
1
1
0
2
0
1
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
2
1
0
1
2
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
2
0
0
0
0
2
2
0
0
1
1
0
0
0
1
2
0
2
0
0
0
0
0
0
2
2
2
0
0
0
0
2
0
0
0
0
0
2
1
0
1
0
2
1
1
0
0
2
2
0
0
2
2
0
2
1
1
0
2
1
0
0
1
0
1
1
0
0
0
0
0
2
1
2
1
2
1
1
0
1
1
0
0
1
2
0
2
1
0
2
1
1
1
0
0
1
2
1
1
0
2
1
1
0
0
0
1
0
1
2
1
1
0
1
1
0
0
0
2
0
0
1
0
0
0
0
1
1
0
0
1
0
1
2
1
2
2
1
2
0
1
2
2
2
2
0
2
1
0
0
2
1
1
0
1
2
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
2
0
1
0
0
2
3
0
0
0
2
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
1
0
2
1
1
0
2
0
0
1
1
2
0
1
1
1
1
2
0
2
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
2
2
2
2
1
0
2
1
0
1
1
2
0
0
1
2
0
2
1
0
0
0
0
2
0
2
2
1
0
2
0
1
0
0
0
2
1
0
2
0
0
0
2
0
2
0
2
0
2
0
0
1
0
2
1
0
2
0
0
0
0
1
1
0
0
0
1
1
0
0
1
1
0
1
0
1
0
0
2
2
1
0
0
0
2
2
0
1
0
0
0
0
0
0
1
1
0
2
2
0
0
0
2
0
0
2
0
0
1
1
1
1
0
0
1
10
2
1
0
0
1
0
0
1
0
0
1
0
0
1
1
0
0
2
0
1
1
1
2
0
1
2
1
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
1
1
0
0
1
2
0
0
0
1
0
2
2
0
1
1
1
0
1
1
2
1
4
2
1
0
0
2
0
1
1
0
0
2
0
2
2
0
1
2
1
0
0
2
0
2
1
1
0
0
2
0
1
0
2
0
1
0
0
0
2
2
0
0
0
0
0
1
0
2
0
0
1
1
0
2
1
0
2
0
0
0
2
1
2
1
0
1
2
4
0
0
1
0
0
0
0
1
1
2
2
0
1
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
1
0
0
1
1
2
0
2
1
1
2
0
2
0
2
1
0
0
1
1
2
0
0
1
0
0
0
0
0
0
1
1
2
0
0
2
0
0
0
0
1
3
1
1
0
0
2
2
0
2
2
0
0
0
0
0
2
0
1
0
0
0
1
0
1
0
4
2
0
1
0
0
0
1
0
0
0
3
7
1
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
2
0
2
4
2
0
0
0
0
0
2
2
0
2
0
2
3
1
2
0
2
1
0
0
0
0
0
0
1
1
1
0
0
2
1
1
1
0
1
0
0
0
0
0
0
0
2
1
1
0
2
0
1
1
0
0
0
0
2
1
2
2
3
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
3
1
0
0
1
0
0
1
0
0
0
1
1
2
1
0
1
1
2
0
0
2
0
1
0
2
2
2
2
2
0
0
2
0
1
1
1
0
1
0
0
2
1
0
1
2
1
0
1
1
2
1
0
0
0
1
0
1
2
0
0
0
0
2
1
1
1
1
0
0
0
1
0
0
1
2
0
0
0
2
2
0
0
2
2
1
0
1
3
1
0
1
0
2
1
2
2
2
0
1
2
0
0
1
2
1
0
1
1
1
2
0
1
0
0
1
2
0
0
0
2
0
0
2
0
0
0
3
2
0
1
0
0
1
1
2
1
0
0
0
1
2
0
2
1
0
2
1
1
1
1
1
1
1
1
1
2
0
1
2
0
2
3
1
0
0
0
1
1
0
2
1
2
1
1
1
0
0
0
2
0
0
3
0
2
0
0
0
0
0
2
1
0
0
1
0
2
0
0
0
1
0
0
1
0
1
1
0
1
1
0
2
1
2
0
2
2
2
0
0
0
1
0
0
1
0
1
0
0
0
1
2
0
1
1
0
2
1
0
0
0
2
0
2
0
0
1
1
2
2
1
0
2
0
2
2
0
1
1
2
2
0
0
0
1
0
2
0
2
0
2
1
3
0
0
0
2
0
0
1
0
1
1
0
0
2
0
2
1
0
1
0
0
1
2
1
0
1
2
0
0
0
2
1
1
2
0
1
0
0
0
0
3
0
1
2
0
1
0
0
4
0
0
1
0
1
0
0
1
2
0
0
0
1
0
2
0
0
1
1
1
0
2
1
2
2
0
0
2
1
1
1
0
2
0
1
0
1
1
1
2
4
0
1
1
1
0
1
2
1
0
1
0
0
0
1
1
0
2
0
2
0
1
0
1
0
0
0
1
2
0
1
1
2
2
0
0
0
0
1
0
0
2
0
2
2
2
0
0
0
1
0
2
2
0
1
2
2
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
2
2
0
0
0
0
0
0
1
1
0
1
3
0
0
0
2
0
1
1
0
2
0
1
0
0
2
0
2
2
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
1
0
1
2
0
1
2
2
0
1
1
1
1
0
1
1
0
2
1
0
0
1
1
2
0
0
1
0
1
1
0
3
1
1
0
0
0
0
1
1
0
0
2
1
1
1
0
0
1
2
2
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
1
1
1
1
0
0
0
1
2
1
0
1
0
1
0
0
0
0
2
2
1
0
0
1
0
0
1
1
1
1
0
2
2
0
0
0
1
2
0
1
0
0
1
0
1
0
0
0
1
0
2
1
1
0
1
0
1
2
0
0
2
1
0
1
1
2
1
0
0
2
0
0
1
0
0
1
1
2
1
2
1
1
0
0
0
0
0
2
0
0
0
0
2
1
0
1
1
2
0
1
1
0
1
1
0
1
0
1
0
0
0
0
2
0
0
1
1
0
1
1
0
2
0
0
2
0
0
0
2
0
0
0
2
0
2
0
1
0
2
0
0
0
1
2
0
1
0
0
1
0
0
1
0
1
1
2
2
0
2
0
2
2
0
1
0
0
0
2
1
1
2
0
1
0
0
1
2
0
0
3
2
0
2
0
0
0
0
0
0
1
2
1
0
1
2
1
0
0
4
0
0
3
1
1
1
0
1
2
1
0
0
1
0
0
0
2
0
1
0
0
0
2
0
1
2
0
0
1
2
0
2
0
0
1
0
2
2
1
0
0
2
0
1
0
1
0
0
1
0
0
1
0
1
0
0
0
1
1
1
0
0
0
2
0
0
2
2
0
1
1
0
0
0
2
0
0
2
2
2
0
2
0
2
2
0
0
0
0
0
0
0
2
2
0
1
0
0
0
2
1
0
0
1
1
0
0
0
0
0
2
1
0
1
0
1
3
1
0
2
0
0
1
2
1
0
0
1
2
0
3
2
0
0
2
1
2
0
1
0
0
0
1
2
1
1
1
0
0
1
0
0
0
1
0
2
3
1
0
0
0
0
2
0
1
2
0
3
0
2
1
0
0
1
1
2
0
0
2
3
1
1
0
0
1
0
0
0
0
0
1
0
0
1
0
2
0
0
0
2
1
0
1
1
0
2
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
1
1
0
1
1
0
0
1
0
1
2
0
0
2
2
0
0
1
1
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
1
0
2
1
0
0
0
1
1
0
1
2
1
0
0
1
2
1
2
1
1
0
2
2
2
0
2
0
0
0
0
0
2
1
2
1
0
2
0
0
0
0
0
1
1
0
0
1
2
1
0
1
0
0
2
0
1
1
0
1
1
0
0
1
2
1
1
0
2
4
1
0
2
2
2
0
0
0
2
1
0
1
0
0
1
0
0
1
0
0
0
0
1
1
2
0
1
2
0
2
0
0
0
0
1
0
1
1
0
1
1
1
0
1
1
0
2
1
0
2
0
1
0
2
0
1
0
0
1
0
0
1
0
1
0
2
0
2
2
1
0
3
0
2
0
0
1
0
0
1
1
0
0
0
2
0
0
0
2
0
1
0
0
2
0
0
1
1
1
2
0
0
0
1
0
0
0
0
1
0
1
1
0
1
0
0
0
3
0
1
2
1
0
0
2
1
0
1
2
1
1
0
0
0
1
1
1
0
1
0
1
1
0
2
0
2
0
0
1
1
0
0
0
2
1
0
2
0
1
1
0
0
2
0
0
0
0
1
0
1
1
2
1
1
0
1
1
0
0
0
2
2
2
1
0
0
0
0
0
0
0
2
0
2
0
0
0
1
2
6
0
2
1
0
0
0
1
2
0
0
1
2
0
1
0
0
2
2
0
0
2
2
2
2
1
2
0
1
2
2
2
0
1
0
1
0
1
0
0
0
1
2
2
2
2
0
0
0
0
0
0
1
0
1
0
0
0
3
0
2
1
0
0
0
2
0
2
2
2
1
1
2
0
1
0
0
1
1
1
0
0
0
1
0
2
0
2
2
0
1
0
1
1
0
2
1
0
0
0
0
2
2
0
1
0
2
0
1
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
1
0
0
0
0
2
1
2
2
1
0
2
0
0
0
0
1
0
0
0
1
2
1
0
0
2
1
2
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
1
0
0
1
1
0
2
2
1
1
0
0
0
3
1
1
0
2
0
2
1
0
0
2
0
2
0
0
1
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
1
3
0
2
1
4
1
0
0
0
0
0
1
0
2
2
0
1
0
2
0
0
2
3
0
0
2
2
0
0
1
2
0
2
0
0
2
0
0
0
0
1
0
2
2
1
1
0
2
2
0
0
0
2
2
2
0
0
0
1
0
1
0
1
2
1
1
0
0
0
1
0
1
2
0
0
1
1
1
2
0
1
2
1
1
1
2
2
1
1
2
1
1
0
1
0
0
2
0
1
0
2
2
3
1
0
1
0
0
0
1
1
1
0
0
0
0
1
0
1
0
1
0
0
2
3
2
2
1
0
1
2
0
2
1
0
1
1
1
0
1
0
1
0
1
0
0
0
1
0
1
2
1
1
0
0
0
0
1
2
1
0
1
2
1
2
2
2
2
0
2
2
0
3
0
0
2
1
1
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
1
0
0
2
0
2
1
0
1
0
0
0
0
0
0
1
1
2
1
2
1
3
0
1
1
0
2
0
1
0
2
0
0
0
0
0
0
1
0
1
2
1
2
0
0
1
1
0
1
1
2
1
0
0
2
0
0
1
2
0
1
0
0
1
1
0
2
0
2
0
0
0
0
1
1
0
2
2
0
0
0
0
2
2
0
0
0
1
1
0
0
0
0
2
1
0
1
1
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
1
0
2
0
0
0
0
2
0
3
0
0
0
0
0
0
0
1
1
1
1
1
0
0
1
0
1
3
0
2
0
0
0
0
0
0
0
0
1
1
0
1
0
1
1
3
2
2
1
1
0
2
0
0
1
1
0
3
0
0
0
1
1
1
2
1
1
0
0
0
0
2
0
1
0
1
2
0
0
2
2
1
0
1
0
0
2
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
2
2
1
0
1
0
0
2
0
0
0
2
0
0
0
3
2
0
0
0
2
1
2
2
0
0
0
3
1
2
1
0
1
1
1
2
2
0
0
1
0
2
0
0
1
0
0
1
2
0
0
0
1
0
0
2
1
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
2
0
1
0
2
1
0
0
1
2
2
0
0
0
1
1
0
2
0
1
0
1
0
0
0
1
0
0
2
1
2
0
2
0
1
0
1
1
4
0
0
2
2
1
0
0
2
1
0
0
2
2
0
0
0
2
0
0
0
0
0
1
2
1
1
0
2
2
0
0
2
0
2
0
0
0
1
1
1
0
0
2
0
2
0
1
0
0
0
1
2
2
3
0
0
0
0
1
0
0
1
0
0
2
2
1
0
1
0
1
2
0
0
0
0
1
2
2
0
0
2
1
0
0
0
0
2
2
2
0
0
0
0
2
0
1
2
0
0
0
4
1
1
0
0
1
1
0
2
0
0
0
2
1
1
2
2
0
1
0
1
1
0
2
0
2
0
0
0
1
1
0
1
0
1
0
1
2
0
0
1
0
0
2
1
0
1
0
0
2
2
1
0
2
2
0
0
0
0
2
0
0
2
1
2
0
2
0
0
2
1
1
0
0
0
1
2
1
0
4
0
1
0
3
0
2
3
0
0
2
0
1
0
2
1
1
2
0
0
2
2
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
2
2
1
0
0
2
1
0
1
0
0
0
3
2
0
1
1
1
1
1
2
2
0
0
0
1
0
2
0
2
0
1
0
0
0
1
1
2
1
3
0
1
2
1
0
1
1
0
0
1
4
1
0
0
0
0
0
2
2
0
0
0
2
0
0
0
1
0
2
1
0
1
0
1
0
2
1
0
1
2
1
0
1
0
1
1
0
1
0
0
0
1
1
1
0
1
2
0
2
1
0
1
2
3
0
0
2
1
0
0
0
1
0
1
2
2
1
1
0
0
1
3
2
1
0
0
0
0
1
0
1
1
2
0
0
2
1
2
1
0
1
0
1
0
0
1
1
0
1
0
0
0
2
0
0
2
2
0
1
0
0
1
1
1
0
2
0
0
1
2
0
0
2
0
0
2
0
0
0
1
1
0
1
0
1
1
1
0
0
2
0
1
0
1
0
0
0
2
1
0
0
2
4
2
2
2
0
2
0
5
1
0
1
1
1
0
0
1
0
1
1
2
0
1
0
0
0
2
0
0
1
2
0
0
1
0
1
1
2
1
0
1
0
1
0
0
2
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
2
0
1
2
0
0
1
1
2
2
1
0
1
0
0
0
0
0
2
0
0
1
0
0
1
2
0
3
2
1
0
0
0
0
1
2
0
1
1
1
0
1
0
0
1
1
2
1
0
0
0
0
0
2
0
0
2
0
1
0
1
0
0
0
2
0
0
1
0
1
2
0
2
0
0
1
0
0
0
2
0
1
1
2
1
2
1
0
1
0
1
1
0
1
0
0
1
0
0
2
0
0
0
1
2
0
0
0
0
2
2
1
0
0
0
2
1
1
1
1
1
1
0
2
1
1
1
0
1
0
0
1
2
1
0
1
0
0
2
0
0
0
3
0
1
1
0
0
2
2
2
1
3
0
1
1
0
2
1
0
0
2
1
0
0
0
2
0
0
0
1
0
0
1
1
1
0
2
2
0
2
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
2
1
0
1
1
0
3
1
2
0
1
1
0
0
1
0
0
0
0
2
1
0
0
2
1
0
1
0
1
2
1
1
0
0
0
2
0
1
2
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
1
0
0
1
1
0
0
1
0
0
1
0
0
1
1
0
1
1
0
1
0
1
0
3
0
1
0
0
0
0
1
1
1
0
0
2
0
0
0
2
0
2
0
1
1
1
0
1
2
0
2
0
0
1
0
1
1
0
0
0
2
1
0
1
0
1
0
2
0
0
2
1
1
0
1
2
0
0
0
0
1
0
2
0
2
1
1
0
0
2
0
0
0
0
1
1
0
2
1
2
0
0
0
0
1
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
2
2
1
2
0
2
0
2
0
0
0
0
2
2
2
1
0
0
0
0
2
2
0
2
1
1
1
1
2
0
2
1
0
1
0
1
0
1
2
0
1
1
0
0
0
2
0
2
2
0
1
1
0
0
0
1
0
0
0
2
2
1
0
1
2
0
1
0
0
2
0
1
0
1
0
0
0
2
2
0
0
0
1
1
1
0
0
0
0
0
0
2
0
1
0
0
0
0
2
1
2
0
0
1
0
0
1
1
0
2
1
0
1
2
0
2
0
0
0
0
0
1
0
0
0
2
0
0
1
0
1
0
0
3
0
2
2
1
0
1
0
0
1
2
1
2
0
2
0
1
2
0
1
1
0
0
2
0
0
1
1
0
2
0
4
1
0
0
0
2
0
1
0
1
2
2
3
0
0
2
2
2
0
1
0
2
0
1
0
0
0
0
1
0
0
1
1
0
2
0
0
0
1
1
0
2
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
1
0
3
0
0
0
0
2
1
1
2
0
0
0
2
1
2
1
1
0
2
1
1
0
1
1
2
0
1
2
0
0
0
1
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
1
1
1
1
1
1
2
1
1
0
1
2
1
0
1
0
1
2
0
2
1
2
1
0
0
2
0
0
0
1
1
1
0
0
2
3
0
0
0
2
0
0
0
1
2
0
0
0
2
0
0
2
2
0
3
2
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
1
0
1
0
2
2
0
0
1
1
1
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
2
0
0
1
0
0
1
2
1
0
2
0
0
0
0
2
0
1
1
2
1
1
0
0
2
0
1
0
0
0
3
1
0
1
2
0
3
2
0
0
1
1
3
2
1
0
2
1
1
0
0
1
1
1
2
2
0
0
0
0
2
0
0
0
1
1
1
1
1
2
1
0
0
2
0
2
0
2
2
0
2
0
0
0
2
1
2
2
1
2
1
0
0
2
1
0
0
2
1
0
2
0
0
0
1
0
0
0
1
0
0
0
2
0
2
1
0
2
0
0
2
0
2
1
0
2
2
0
0
1
0
2
0
1
1
2
0
0
0
1
2
0
2
1
1
1
2
1
0
0
0
0
1
2
0
1
1
0
0
0
1
0
0
0
0
2
1
0
0
1
0
0
1
1
0
2
0
1
0
1
0
2
1
1
1
2
0
0
2
0
0
0
1
1
0
0
2
0
1
0
2
0
1
0
1
1
0
1
1
0
2
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
1
2
0
2
0
0
0
1
2
2
0
0
1
0
0
2
2
0
0
2
1
1
2
0
2
0
2
0
0
0
0
0
0
0
2
1
1
2
0
0
2
2
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
2
0
1
0
0
0
0
0
2
0
0
1
0
0
1
0
2
0
0
2
2
0
0
2
0
1
1
0
1
0
0
0
0
1
0
1
2
0
0
1
2
0
1
1
0
1
1
0
0
1
0
0
1
2
1
0
0
0
1
1
0
0
1
0
1
1
2
0
0
0
0
1
1
1
0
0
1
1
1
1
2
2
0
0
1
0
2
2
0
2
0
2
3
0
0
1
0
0
1
0
1
0
0
2
1
1
1
1
0
0
0
0
0
1
1
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
2
1
0
2
2
1
0
1
1
0
3
1
2
0
1
1
0
0
0
0
0
2
0
0
0
1
0
0
0
1
1
3
1
0
0
1
1
1
2
0
0
0
2
1
1
0
1
1
1
1
2
1
0
2
2
2
2
2
0
1
2
0
1
0
0
2
2
1
2
2
2
0
0
0
1
0
1
0
2
2
0
0
1
3
0
0
1
2
0
1
1
0
0
1
0
2
0
2
0
2
1
0
1
0
0
0
4
0
0
0
0
0
1
0
0
2
1
0
1
0
0
0
2
1
1
0
2
2
2
1
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
1
2
2
0
2
0
1
1
2
0
2
0
0
0
1
0
0
2
1
1
1
0
0
0
1
2
0
1
1
0
7
1
0
0
0
2
1
1
0
0
1
1
0
2
1
1
1
0
0
0
1
1
0
1
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
2
0
0
1
0
0
1
0
1
0
0
1
1
0
0
1
1
2
1
1
1
1
0
0
0
1
0
2
0
1
0
3
1
0
0
0
1
2
0
0
2
0
0
0
0
0
1
1
1
0
2
1
1
2
0
1
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
1
2
1
2
3
0
2
0
0
1
0
1
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
1
1
2
0
0
0
1
2
1
0
0
1
2
0
1
1
1
0
1
0
2
0
0
0
0
0
2
0
2
2
1
0
0
1
0
2
0
0
2
1
0
1
1
0
1
0
0
0
1
1
0
1
0
1
2
0
0
4
3
1
5
0
0
1
0
1
0
2
1
0
1
1
0
2
0
0
0
1
2
1
0
2
0
0
2
0
0
0
0
0
2
0
1
1
0
0
1
1
1
1
1
0
0
0
0
2
1
1
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
2
0
0
2
1
0
0
0
2
0
0
2
1
3
4
0
0
2
0
1
2
0
0
0
1
1
1
0
0
0
0
0
1
0
1
2
1
2
1
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
1
1
1
1
0
3
2
0
1
0
0
1
1
0
2
0
1
0
0
1
0
1
0
0
1
0
0
0
2
1
1
1
0
1
1
2
0
1
1
0
1
2
0
0
1
0
0
0
0
2
0
1
0
0
2
0
1
0
2
1
0
3
0
0
0
0
0
0
0
1
2
1
12
2
2
0
7
2
0
0
0
1
1
1
0
3
2
2
0
1
1
0
4
2
1
0
2
0
0
0
1
0
0
0
1
3
1
1
0
1
0
0
1
0
0
0
0
1
0
1
2
0
2
1
0
2
0
1
1
0
0
0
1
0
1
0
2
4
0
3
1
0
1
0
0
1
0
1
0
0
0
1
0
0
1
1
0
0
0
1
0
0
2
2
0
0
0
1
0
0
1
6
0
0
0
1
0
1
0
0
0
0
2
0
0
1
2
0
0
0
1
0
0
1
1
0
2
0
0
2
0
1
1
0
1
1
0
1
2
0
1
2
0
0
0
0
1
0
2
1
2
0
0
2
0
2
1
0
2
2
0
1
0
0
0
1
0
0
0
2
1
0
0
1
2
0
1
2
0
0
0
0
0
0
2
0
1
1
1
0
0
2
0
0
2
1
0
2
0
0
0
0
0
2
0
0
0
2
1
2
0
0
0
0
1
0
1
0
0
0
0
1
1
1
2
0
0
1
0
1
0
0
2
2
0
0
2
1
2
0
1
2
2
2
0
0
0
0
2
2
1
2
2
2
0
1
2
0
2
1
0
2
0
0
0
1
0
2
0
0
1
0
1
2
0
1
2
0
0
2
0
2
0
2
0
0
2
2
2
0
0
0
0
0
0
0
0
0
1
0
1
1
1
1
0
0
2
0
1
2
2
0
1
1
0
1
1
0
2
1
1
0
1
0
0
0
0
2
0
0
2
0
0
1
0
1
1
0
2
2
0
0
1
0
0
0
0
2
2
0
3
0
1
0
0
0
1
0
2
1
0
0
2
0
0
0
2
0
0
0
0
0
0
4
0
2
0
1
0
1
1
2
2
0
1
2
1
1
1
1
1
1
2
1
1
2
2
1
2
2
2
4
1
2
0
1
0
0
1
0
0
1
0
0
2
0
0
2
0
2
0
1
0
0
0
1
0
0
0
2
0
1
4
0
1
1
1
1
2
1
1
0
0
0
0
0
0
1
2
1
0
2
1
0
4
0
1
0
1
0
0
0
2
1
1
0
0
1
1
0
1
0
0
1
0
1
3
0
0
0
0
2
1
0
0
2
2
0
0
0
1
0
1
2
0
0
1
1
2
2
0
0
0
1
0
2
3
1
2
2
1
2
0
1
1
0
1
1
0
0
0
2
0
2
1
2
2
0
3
1
0
0
2
0
2
0
1
0
0
1
4
1
1
2
0
2
0
1
1
0
0
2
2
2
0
2
0
1
0
0
2
0
2
2
0
0
0
0
0
0
1
1
1
1
0
0
0
2
0
1
1
0
1
0
0
3
0
1
0
0
0
0
2
2
1
2
2
0
1
0
0
1
0
1
1
1
1
0
0
0
0
1
2
0
2
2
0
1
0
2
0
2
0
1
1
2
1
2
0
1
1
1
0
0
1
2
2
0
1
2
0
0
0
1
0
1
0
2
0
1
0
0
0
2
1
0
8
1
1
2
2
0
1
1
3
2
1
1
0
1
0
1
1
0
2
0
2
2
1
1
1
0
0
0
0
1
1
2
2
1
0
1
1
0
1
0
1
0
0
1
1
1
1
0
1
1
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
1
2
2
1
0
1
2
3
1
2
1
0
2
1
2
0
1
2
0
0
0
0
0
0
2
0
1
0
0
2
0
1
0
0
0
1
1
0
3
0
0
2
2
2
1
1
2
1
0
2
1
2
2
2
0
0
2
0
0
0
1
1
0
2
0
0
2
2
1
2
1
0
1
0
2
2
1
2
0
0
0
0
0
0
0
1
2
0
0
1
7
0
2
3
2
0
2
2
2
1
0
0
0
0
0
0
2
2
1
0
1
2
1
0
0
1
1
1
0
1
0
2
0
0
0
1
2
0
2
3
2
1
2
0
0
1
0
0
0
0
2
1
0
2
2
0
0
1
2
0
0
0
2
0
1
0
1
0
0
2
3
0
2
2
0
1
1
0
0
3
1
1
0
0
0
1
2
2
0
0
0
0
2
2
0
1
0
0
3
1
1
1
1
0
0
0
0
0
0
2
1
0
0
1
0
2
2
2
0
0
0
0
1
1
2
2
1
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
1
0
1
0
0
2
1
0
0
2
2
2
2
1
2
0
0
2
0
1
0
2
0
1
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
2
0
2
2
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
1
3
0
0
0
0
0
2
0
1
1
2
1
1
1
1
0
0
1
0
1
1
1
0
2
0
1
1
0
2
2
1
2
1
2
0
2
0
0
0
2
1
0
1
1
1
0
1
2
1
0
1
1
0
0
0
1
0
0
0
0
0
2
0
1
2
2
1
0
0
0
2
0
1
0
0
1
1
1
2
1
1
0
0
0
1
1
0
1
1
1
0
1
1
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
1
2
0
2
2
1
2
2
1
1
2
0
1
0
0
0
1
1
1
0
0
1
0
2
0
0
0
0
0
2
1
0
0
2
1
1
1
0
0
0
0
1
1
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
1
0
0
2
0
2
2
1
5
0
1
2
0
0
0
0
0
1
2
1
1
2
2
0
0
2
0
0
2
2
0
0
1
0
2
2
2
0
2
1
0
2
2
2
0
2
2
0
2
1
0
0
2
1
0
0
2
1
2
2
0
0
1
0
1
1
2
1
1
0
0
0
1
0
2
2
2
1
1
0
0
0
0
0
2
2
1
1
0
1
3
0
2
0
0
0
0
2
2
1
0
1
0
0
2
0
0
1
1
0
1
0
2
1
0
1
1
0
1
0
2
0
0
1
2
0
1
0
4
0
2
0
1
1
1
0
0
0
1
0
0
1
0
0
2
0
1
0
1
1
0
1
0
0
1
2
1
3
0
1
0
0
0
1
0
0
0
1
1
2
0
1
0
0
2
0
0
1
0
0
0
1
0
2
1
1
1
0
1
1
2
2
0
0
1
0
0
1
0
0
2
1
1
0
1
1
1
2
0
0
1
2
1
0
0
1
0
2
0
0
1
1
0
1
2
0
1
0
0
2
0
0
1
2
0
0
1
1
0
0
0
2
0
2
1
1
2
1
0
0
0
0
0
1
0
1
0
1
1
2
2
0
2
0
0
1
1
1
0
2
1
0
1
1
0
0
1
0
5
1
1
0
0
1
2
0
0
0
2
2
0
0
0
2
1
2
2
1
1
0
0
0
0
0
2
0
0
1
0
1
1
0
0
0
2
0
1
0
1
0
0
0
0
1
0
1
0
2
0
1
0
0
2
1
0
1
2
0
0
1
2
1
1
1
2
0
1
2
1
2
1
0
0
1
7
2
2
0
2
1
1
2
0
1
0
0
1
0
2
0
0
0
0
2
0
0
0
2
0
0
0
1
0
1
1
1
0
0
2
1
1
2
0
0
2
0
0
0
1
2
0
0
0
0
1
0
1
1
1
1
2
0
1
2
0
0
0
2
0
0
1
1
2
2
0
0
1
0
1
1
0
1
3
2
0
2
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
2
1
0
0
2
1
1
2
1
2
0
0
0
4
0
1
0
2
0
0
0
2
1
0
0
0
1
0
1
2
2
2
2
0
2
2
2
0
0
2
0
0
0
2
1
0
1
0
0
0
2
0
1
0
4
0
0
1
1
2
0
0
0
0
2
1
1
0
1
0
2
1
0
1
1
0
2
0
2
1
0
0
0
2
0
2
1
2
0
0
0
1
1
2
2
1
1
0
0
0
0
1
0
0
0
2
0
0
1
0
2
1
1
0
0
0
1
1
0
0
1
2
1
2
1
1
0
0
1
0
0
2
0
0
5
1
0
0
0
0
1
1
0
0
0
1
2
1
0
0
0
2
0
1
2
1
0
2
1
3
1
1
1
0
0
2
1
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
2
0
2
2
0
0
0
0
3
1
2
1
0
0
0
0
0
0
2
0
2
2
2
0
0
0
1
1
0
3
1
2
1
2
0
0
0
0
1
1
0
0
0
1
2
0
0
0
0
1
1
0
0
0
2
0
2
1
2
1
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
1
2
0
0
1
2
1
1
0
0
0
1
0
0
0
0
1
0
0
2
0
1
1
0
2
0
3
1
0
1
1
1
2
1
2
5
0
1
0
0
1
0
0
0
0
2
0
2
1
2
0
2
0
0
1
0
0
0
1
0
2
1
2
0
1
0
1
1
1
0
1
0
0
1
0
2
0
0
0
1
2
1
1
0
1
0
2
0
2
1
1
0
2
0
0
3
0
2
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
2
1
0
0
0
0
1
0
1
0
1
0
2
1
0
0
0
2
0
0
1
1
2
0
0
0
0
2
2
0
1
0
2
0
2
0
2
0
0
1
0
0
0
0
2
0
0
1
2
0
0
0
0
0
1
1
1
0
5
0
0
1
1
1
0
2
2
1
1
0
0
1
1
0
0
2
0
1
0
1
1
2
2
2
0
2
1
0
2
1
1
1
2
1
0
1
1
1
2
0
0
0
1
2
3
1
0
1
2
0
0
2
1
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
1
0
0
0
1
2
0
1
1
1
0
2
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
3
0
0
2
1
0
1
0
0
2
0
1
2
0
0
2
2
2
0
1
0
0
0
1
2
1
2
0
3
2
0
2
0
2
1
0
2
0
1
0
2
1
0
1
0
0
0
1
0
0
1
0
2
2
1
0
0
1
0
2
2
1
1
1
0
2
0
2
2
1
1
1
0
0
1
0
0
0
1
0
0
1
1
0
2
0
0
1
3
0
0
2
1
0
0
0
2
0
0
0
1
4
1
0
2
0
1
0
0
1
1
2
2
0
0
2
1
1
4
2
2
2
0
0
1
0
0
0
0
1
3
0
1
0
0
1
0
0
0
0
1
0
2
0
1
2
0
12
1
0
0
0
2
0
0
0
0
2
1
1
1
0
1
2
0
2
0
1
2
0
0
1
0
0
0
2
0
1
0
3
1
2
1
1
0
1
2
2
2
1
1
1
1
1
5
0
0
2
0
0
0
2
2
1
2
0
0
0
0
0
1
0
0
0
1
0
2
0
0
2
2
0
3
0
2
0
2
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
3
1
1
0
1
1
0
0
0
0
0
1
0
0
0
0
2
2
0
10
1
0
0
1
0
0
2
1
1
2
0
1
0
0
0
0
1
2
2
0
1
2
0
0
1
0
0
0
0
0
1
2
2
2
0
0
0
0
1
2
2
0
0
1
1
1
0
0
1
0
2
2
1
1
0
2
0
1
0
1
0
1
1
2
0
0
0
0
0
2
0
0
1
2
0
1
2
0
0
0
1
0
1
1
0
0
0
0
2
1
1
0
2
1
0
0
2
0
3
0
0
1
0
1
0
0
0
1
0
0
1
0
2
2
4
0
1
1
0
2
0
1
0
0
2
2
0
0
2
1
1
1
1
0
0
3
0
2
1
2
0
1
2
1
0
1
0
1
2
0
0
1
0
2
0
0
0
2
0
2
0
0
0
1
3
1
1
0
0
1
2
0
3
0
0
2
0
1
0
0
0
0
1
0
0
0
2
0
1
2
0
0
2
1
1
1
2
0
0
2
0
0
2
0
1
0
2
2
0
0
0
0
0
1
0
0
0
2
1
1
0
0
1
1
1
0
1
1
0
2
3
0
0
0
0
1
0
1
0
1
0
2
3
1
2
1
1
0
2
0
2
0
0
0
0
1
0
0
2
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
1
1
0
2
1
0
1
2
0
0
0
2
0
1
0
0
0
0
2
0
2
0
1
1
2
1
2
1
0
2
0
1
2
0
1
5
0
1
1
0
0
1
0
0
0
0
2
1
0
1
1
1
0
0
1
2
0
2
2
1
1
0
1
1
0
0
0
2
0
0
0
1
1
0
1
1
1
1
0
0
0
0
1
0
0
3
0
2
0
2
1
0
2
0
2
0
0
1
0
0
2
0
0
2
0
1
0
0
2
0
0
0
0
0
1
0
0
1
2
0
0
1
1
0
1
1
0
0
1
1
0
0
0
0
1
1
1
0
0
1
0
0
1
0
1
2
0
0
0
1
0
1
1
0
0
0
2
2
0
0
0
0
0
2
0
0
1
1
0
1
1
0
1
0
0
1
0
1
1
0
0
0
3
1
2
2
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
2
1
0
0
2
0
1
2
1
3
0
0
0
2
0
2
0
0
0
1
1
0
4
2
0
1
0
0
2
1
0
0
0
1
2
1
0
0
2
0
1
2
1
1
2
0
1
2
2
0
0
0
0
1
1
0
2
1
1
0
1
0
0
2
1
2
0
1
1
0
1
0
0
0
0
1
2
1
1
1
0
0
0
2
2
2
1
0
0
1
0
2
0
0
0
0
0
0
0
2
1
0
0
2
0
1
1
0
1
1
2
2
1
0
1
2
1
0
0
0
0
0
1
0
1
0
0
2
2
1
2
0
1
0
1
2
2
0
0
0
0
0
2
1
1
2
1
0
0
0
2
0
0
0
0
1
2
1
0
0
0
1
0
0
0
1
0
0
2
2
0
0
1
1
0
1
0
1
0
0
2
1
0
1
0
0
1
1
0
0
1
0
0
3
2
0
1
0
3
0
1
2
0
1
0
2
0
0
1
1
1
1
1
1
1
1
0
0
0
1
0
1
0
0
1
2
0
1
1
0
0
1
0
0
0
8
0
0
1
2
1
0
2
1
1
1
0
1
0
1
1
0
2
2
0
0
0
1
0
0
0
0
0
0
2
1
1
0
0
0
1
1
1
0
1
0
4
1
0
2
0
2
0
0
0
1
2
0
1
1
3
0
0
2
1
3
0
1
0
0
0
1
0
0
0
0
1
2
0
3
2
2
0
0
1
0
0
2
0
1
0
0
0
1
0
1
0
0
1
1
0
1
0
1
0
0
1
2
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
2
2
0
0
1
0
0
0
1
0
0
2
1
0
1
0
0
2
1
1
1
0
0
0
1
1
0
2
1
2
0
0
1
0
1
0
1
1
0
0
1
0
0
0
0
2
1
0
1
0
1
2
1
0
0
2
0
2
0
0
0
0
1
1
0
2
0
2
0
0
1
0
0
0
0
1
2
1
0
1
1
1
2
0
1
0
0
1
2
0
1
1
0
1
2
0
0
0
0
2
1
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
2
1
0
0
0
0
0
1
1
1
1
0
1
1
0
0
0
0
1
0
2
0
2
2
0
0
0
2
0
0
1
0
0
2
0
1
0
0
0
1
0
0
0
1
0
0
0
1
1
0
1
1
0
1
0
0
0
2
2
2
0
0
1
2
1
1
1
1
1
0
0
0
0
0
2
2
0
0
2
1
0
3
1
1
0
0
1
0
2
1
2
0
0
0
0
0
1
0
1
0
2
0
0
0
2
0
1
0
0
2
2
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
1
1
2
0
0
1
1
0
1
0
2
0
0
1
1
0
1
2
2
0
1
0
1
2
0
1
1
0
0
1
1
0
2
0
0
0
0
0
0
1
1
1
0
2
0
0
2
0
2
1
1
0
1
1
1
0
1
1
0
0
0
0
0
2
3
1
2
2
0
0
0
0
0
0
2
0
2
1
1
0
1
0
0
1
0
0
0
2
0
0
0
1
0
2
0
0
2
0
1
0
0
0
0
1
1
0
2
0
2
0
0
0
0
0
1
2
2
1
1
0
1
2
0
2
1
1
1
1
2
0
0
1
0
1
0
1
2
0
1
1
0
0
0
2
2
0
0
0
2
1
0
1
0
2
2
1
1
0
0
2
2
0
0
0
0
0
1
1
0
0
1
2
1
1
0
2
0
1
0
2
0
0
0
0
0
0
1
0
0
0
1
1
2
2
0
2
0
1
0
1
0
0
0
2
0
2
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
2
1
0
2
0
0
0
2
1
0
1
1
1
0
0
0
1
1
2
0
0
0
0
0
2
0
0
2
1
1
2
2
1
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
2
1
1
0
0
1
0
0
0
0
2
0
2
1
2
0
1
0
2
1
1
2
0
0
0
1
0
2
0
2
0
0
0
1
1
0
1
0
0
0
1
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
4
0
0
2
0
0
1
0
0
1
1
1
2
0
0
1
1
1
0
0
2
1
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
2
2
0
2
1
2
0
3
0
1
0
1
0
2
0
0
0
0
1
0
1
1
1
1
0
0
0
0
2
0
0
1
0
2
0
0
2
0
0
0
0
1
0
1
0
1
1
1
0
0
0
1
0
2
1
4
1
0
2
2
2
1
1
0
2
0
0
2
0
0
1
0
1
0
0
1
1
0
0
0
0
1
0
0
2
1
3
0
1
1
2
1
2
1
1
0
0
0
1
2
1
1
1
2
0
3
3
0
2
1
2
0
1
0
1
2
1
1
1
0
0
3
1
3
0
0
1
1
0
0
1
0
0
1
1
1
0
1
1
2
2
2
1
2
0
1
0
2
1
1
0
2
0
0
2
0
0
0
1
0
1
0
0
2
1
1
1
2
1
1
2
0
0
1
0
1
2
0
0
0
2
1
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
1
2
0
2
1
2
0
2
0
0
0
2
1
1
2
0
1
0
2
0
0
1
0
1
0
0
2
0
0
0
2
2
0
2
2
2
0
1
1
3
0
0
0
0
2
0
0
0
0
1
0
0
2
2
2
1
2
2
0
0
0
0
0
0
0
2
2
1
3
0
1
2
2
1
1
0
2
2
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
3
1
0
0
1
0
1
1
1
0
2
1
2
0
0
1
0
0
2
1
0
1
0
0
1
1
1
0
1
1
0
0
3
2
0
1
1
0
0
2
0
0
2
0
0
2
0
1
0
0
1
0
0
0
0
0
2
2
3
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
1
1
0
0
2
0
0
1
0
0
1
0
0
1
0
1
1
0
2
2
1
0
0
0
0
0
1
0
2
0
0
0
0
1
2
0
0
2
0
1
1
0
0
1
0
0
0
0
0
2
0
2
0
0
0
1
2
2
1
0
2
1
0
1
1
0
2
1
0
1
0
0
1
0
0
0
1
1
0
0
1
2
3
1
1
0
1
0
0
0
1
0
1
2
2
0
2
0
0
1
2
1
0
1
2
0
1
2
0
0
0
0
0
1
0
1
0
1
0
2
1
1
1
1
1
2
0
1
0
1
1
2
0
1
3
1
2
0
2
1
1
2
0
2
2
0
3
1
1
2
2
2
1
1
0
1
2
2
0
0
2
1
0
1
2
1
0
0
1
0
0
0
1
0
1
0
1
1
0
1
0
0
0
0
0
1
0
1
2
1
0
0
0
1
0
0
0
0
2
0
1
1
1
0
0
1
0
0
0
1
0
2
0
0
0
0
1
3
0
2
2
2
0
0
2
1
1
0
0
0
0
0
1
1
1
1
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
1
1
0
2
2
0
1
1
0
0
0
0
2
0
0
0
2
2
1
0
0
2
0
1
1
0
1
2
0
0
1
0
0
2
0
1
0
0
2
0
2
0
1
0
0
2
0
0
2
1
0
1
1
0
0
1
1
0
2
0
0
0
1
1
0
0
0
2
2
2
1
1
0
0
2
1
1
0
0
0
2
1
0
2
1
0
0
1
0
2
2
1
1
0
1
1
1
1
1
1
2
1
2
1
1
0
0
1
0
1
0
0
3
1
0
3
2
1
1
1
0
0
2
0
1
0
0
2
0
2
0
1
2
0
0
0
0
1
0
1
2
0
0
0
1
2
1
0
0
1
0
0
1
2
0
2
0
2
1
0
1
2
0
1
0
0
0
0
0
1
1
0
1
1
1
0
1
0
1
2
0
0
2
1
1
1
2
0
0
2
0
0
2
2
1
1
0
0
0
0
1
1
1
2
1
1
0
0
0
3
0
0
2
1
0
1
0
2
1
0
2
2
0
1
0
0
0
0
0
0
0
0
0
1
1
1
1
1
2
1
0
1
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
2
0
0
2
0
1
2
0
1
1
1
2
1
1
0
0
2
0
0
3
0
0
0
2
1
1
0
2
0
0
0
0
1
0
0
0
2
2
0
1
0
0
2
2
2
1
0
2
0
1
2
0
1
0
0
1
3
1
2
0
1
1
0
2
2
0
2
2
0
0
0
1
1
1
1
0
2
0
1
0
0
0
1
0
0
3
1
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
1
0
0
2
2
0
0
2
1
0
1
1
1
0
0
0
1
2
0
1
2
0
0
1
2
2
0
2
0
0
0
0
2
0
1
0
0
0
0
2
2
0
0
0
2
0
1
0
0
2
0
1
1
0
2
0
0
0
1
2
0
1
1
0
0
1
1
0
1
2
1
0
0
1
0
1
0
0
1
1
0
0
2
1
0
1
0
0
2
1
1
1
0
0
0
2
1
2
0
1
0
0
0
0
1
1
0
1
1
0
0
2
0
0
1
2
0
0
0
2
1
2
0
1
0
1
0
0
2
0
1
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
2
1
1
2
0
2
0
2
0
1
0
0
0
2
2
1
1
0
0
0
0
0
2
0
0
2
2
2
0
0
1
0
2
2
0
0
0
1
1
1
1
1
2
1
1
0
0
0
0
1
0
0
2
1
1
0
0
1
0
2
2
0
0
1
2
0
0
0
1
0
0
2
0
2
0
0
0
2
0
0
1
0
2
1
0
0
2
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
1
2
2
0
0
0
0
3
1
1
1
0
0
0
2
0
0
0
2
0
0
2
0
0
2
0
1
2
2
1
2
0
2
0
1
2
0
0
2
0
2
3
0
1
1
2
1
0
0
2
2
0
0
0
0
0
0
1
1
0
1
1
0
0
1
0
1
1
0
0
0
0
0
1
0
2
1
0
0
1
0
0
1
1
0
1
2
0
1
0
0
2
2
0
0
2
1
0
2
0
1
1
0
0
2
1
0
0
1
2
0
0
2
1
0
0
0
2
0
0
2
2
0
1
1
2
1
0
0
0
0
1
0
0
1
0
2
1
1
0
2
2
1
2
2
1
1
0
2
2
1
3
0
1
2
1
1
2
0
0
1
0
1
0
2
2
0
0
0
0
1
0
2
0
2
0
0
2
1
0
0
0
0
1
2
3
0
0
3
2
0
1
1
2
0
1
1
2
0
1
0
0
1
2
0
2
1
0
0
0
1
2
0
0
0
0
2
0
1
0
1
0
1
2
0
0
0
0
0
2
2
1
0
0
2
2
2
0
2
0
0
0
0
1
1
1
0
1
0
0
1
3
1
0
1
0
0
0
1
1
0
0
1
0
0
1
0
2
1
0
2
0
1
1
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
2
1
0
0
1
2
0
1
0
0
0
0
1
0
0
0
0
2
0
2
2
0
0
3
1
2
2
0
2
0
1
0
0
0
0
2
0
1
0
1
1
1
0
0
2
0
2
1
1
0
0
1
0
2
0
1
2
1
0
0
2
0
0
1
2
0
0
0
0
2
1
2
1
0
0
0
2
2
0
0
0
1
0
1
2
0
0
1
1
0
2
0
0
2
0
0
0
1
0
0
2
0
2
1
0
0
2
0
0
2
1
0
0
2
0
0
2
0
2
0
0
1
0
0
0
1
1
2
0
0
1
1
0
0
0
1
1
2
2
0
0
1
1
0
0
0
2
0
0
1
1
1
0
1
2
0
0
0
0
0
0
0
0
3
0
0
0
0
2
2
0
1
0
0
0
2
1
0
1
2
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
2
1
1
1
1
1
1
0
0
1
1
0
0
0
0
3
0
1
2
0
1
1
1
0
3
2
2
0
0
1
1
2
3
1
0
1
0
2
1
2
0
0
0
2
0
0
1
2
0
1
0
0
1
1
0
0
2
0
0
0
0
1
2
0
0
2
1
0
1
1
0
2
1
1
1
1
0
0
0
0
1
0
1
2
0
3
0
1
0
0
2
2
0
1
0
2
1
0
1
0
1
2
2
3
0
1
1
0
0
1
1
0
0
1
2
2
1
1
1
0
0
1
1
1
0
2
2
0
0
2
0
0
0
1
1
2
1
2
0
0
2
1
0
0
0
0
1
0
0
0
1
2
1
0
2
1
2
0
2
0
0
2
2
2
2
0
1
0
0
1
2
0
2
1
0
0
0
1
1
0
1
2
0
1
0
0
0
1
1
2
2
0
0
0
1
0
1
1
2
0
2
0
0
1
1
0
2
1
3
0
2
2
2
2
0
2
2
1
1
1
0
0
2
0
0
0
1
1
1
2
1
1
0
1
1
1
0
1
0
0
1
1
2
0
1
0
1
1
1
1
0
1
1
1
2
1
0
0
0
1
2
0
1
1
0
1
1
1
1
0
1
0
1
0
0
1
1
1
1
0
1
0
1
1
2
1
1
0
1
0
0
2
0
0
0
0
0
2
2
0
2
0
1
1
1
2
0
3
1
2
0
1
1
0
0
1
0
0
1
1
0
2
0
0
0
0
0
0
1
2
0
0
2
0
0
2
2
0
1
1
0
0
1
6
0
1
0
1
1
0
0
0
0
1
2
0
2
1
1
0
0
0
4
0
2
0
0
0
2
0
1
2
0
2
1
1
1
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
1
0
0
1
1
1
0
0
2
0
1
0
1
0
2
1
0
0
3
2
1
0
0
0
0
1
1
0
0
0
0
2
1
0
0
2
0
0
1
0
2
1
1
0
0
0
2
0
1
1
0
0
2
0
0
2
0
1
0
0
1
0
2
2
0
0
1
2
1
0
0
1
0
0
1
0
0
1
0
0
1
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
1
1
0
0
1
2
0
0
0
1
0
0
2
1
1
2
2
1
0
0
2
0
0
1
1
0
2
0
2
1
2
1
0
1
2
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
2
1
0
2
3
0
1
0
2
1
0
1
1
0
1
1
1
1
1
2
0
3
0
1
2
0
0
1
0
0
1
3
0
0
0
0
0
0
1
0
0
0
0
2
1
0
2
0
0
1
0
0
1
2
0
0
0
0
0
0
1
2
2
1
0
1
0
2
0
1
0
2
0
0
0
0
1
1
0
0
0
0
1
2
0
2
0
0
1
0
0
0
1
0
2
1
0
0
0
1
0
1
1
0
1
0
0
1
2
0
0
1
2
1
0
0
0
0
0
0
0
1
0
1
0
2
0
0
1
2
0
0
1
1
0
2
2
0
0
0
0
2
1
1
0
1
2
1
0
2
0
0
1
2
0
0
0
0
0
0
2
3
2
0
1
0
0
1
2
2
1
0
1
2
0
1
0
1
1
2
0
0
0
1
0
2
1
0
3
0
0
0
3
1
1
1
2
2
2
1
0
0
2
0
0
0
1
0
0
0
0
0
1
0
1
2
1
1
2
0
2
2
0
2
1
0
1
0
1
2
2
1
0
1
0
0
0
0
0
0
0
1
0
1
2
3
1
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
1
3
1
1
0
1
0
1
1
2
1
1
1
2
0
0
0
1
0
1
1
0
2
1
2
0
1
2
1
0
1
1
1
0
0
1
2
0
0
1
0
0
0
0
0
0
0
1
1
2
0
2
1
0
1
2
1
2
1
0
0
0
0
0
2
1
0
1
0
0
0
0
1
0
1
2
2
1
2
0
0
2
0
0
0
1
0
0
0
1
0
1
0
1
0
2
0
0
0
1
0
2
0
1
2
1
1
0
0
1
0
0
0
0
0
0
1
1
0
2
0
0
0
2
0
0
0
0
0
2
0
1
0
2
0
1
0
2
1
1
0
1
1
1
1
0
0
3
0
0
0
0
0
0
1
2
1
0
0
2
3
1
2
0
0
1
1
0
0
0
0
0
0
1
0
3
0
0
1
0
2
0
2
3
1
2
1
0
0
1
0
0
0
1
1
1
1
0
0
0
0
2
0
1
1
0
0
0
1
1
0
3
1
1
1
2
2
0
1
0
1
0
0
0
0
2
1
0
4
1
0
2
1
0
3
0
0
0
1
1
0
0
0
1
0
2
2
0
2
2
2
0
2
0
1
0
1
2
2
0
2
0
1
2
0
0
0
2
0
1
4
1
0
1
2
0
1
0
1
0
1
0
0
1
0
0
1
0
1
0
1
0
0
0
1
0
2
0
0
1
0
0
1
3
0
0
0
2
0
0
1
1
3
0
1
0
0
1
2
0
1
0
0
0
3
0
3
2
1
1
0
2
0
0
2
0
0
0
0
1
0
1
0
2
0
0
1
1
0
1
0
2
2
0
3
0
1
1
1
0
0
0
2
1
2
0
2
0
1
0
1
0
1
0
0
1
1
0
2
2
0
1
0
0
2
2
1
0
0
0
0
0
0
0
1
1
1
2
0
0
0
2
0
2
1
2
0
1
0
0
1
0
0
2
1
2
0
0
2
0
1
2
2
0
1
0
1
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
1
1
4
0
0
1
1
1
0
0
1
0
0
2
1
2
0
0
0
1
2
2
2
0
1
3
0
2
1
0
0
0
0
1
1
2
0
1
0
0
1
0
1
2
0
0
0
1
0
1
1
1
0
1
1
0
0
0
1
0
0
1
0
2
1
1
1
0
0
2
0
2
1
1
0
1
0
0
1
0
0
0
2
1
0
0
1
2
2
2
1
0
2
2
0
0
1
0
0
0
1
0
2
0
1
1
1
0
1
0
0
0
0
0
2
0
2
2
0
2
1
1
0
0
0
0
1
0
1
1
0
0
0
1
0
2
2
2
1
1
1
0
0
1
2
1
1
0
1
0
0
2
2
1
1
0
0
0
0
0
0
0
0
1
0
1
2
0
2
2
0
0
0
2
0
0
0
1
1
0
0
0
1
1
0
0
1
1
2
2
2
1
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
1
1
1
1
1
0
0
0
0
0
1
2
0
0
2
2
0
3
0
2
2
0
0
0
0
0
0
1
0
3
0
1
0
0
1
0
2
1
0
0
1
0
0
1
0
0
0
1
0
0
0
2
1
1
0
1
1
0
0
0
0
0
0
0
1
2
0
1
0
0
1
0
0
2
2
0
0
1
0
1
0
2
0
2
1
2
1
0
0
1
0
0
1
1
1
1
2
0
0
1
0
0
1
1
1
1
0
2
0
2
0
0
0
2
0
1
0
2
0
0
1
2
1
0
0
0
0
0
0
2
2
1
1
0
2
2
1
0
1
0
2
0
2
1
0
2
0
1
0
1
0
1
0
0
2
1
0
0
1
0
0
0
1
0
0
0
0
2
0
0
1
1
0
1
2
1
0
1
1
2
0
1
1
2
2
1
0
0
0
0
1
1
0
0
0
0
1
2
0
1
0
1
2
1
0
0
0
0
0
2
2
1
0
2
0
0
1
1
1
0
0
2
0
1
1
0
2
1
0
2
0
2
1
1
0
1
2
0
0
0
0
1
1
0
2
0
2
0
2
1
0
0
1
0
0
2
0
0
1
0
2
3
0
0
1
1
1
0
2
0
0
0
0
3
1
1
0
0
1
0
1
0
2
0
1
0
0
1
1
1
0
2
1
0
1
2
1
2
1
0
2
1
0
1
0
0
1
2
1
0
1
2
1
0
1
0
1
1
0
2
2
1
1
0
0
2
1
0
0
1
0
1
0
0
1
0
2
0
0
0
2
1
1
0
1
0
1
1
0
1
2
0
0
0
2
0
0
0
0
0
1
0
0
1
0
1
0
1
2
0
1
1
1
0
1
1
0
2
0
2
0
0
0
1
0
0
0
2
2
2
2
2
0
2
0
2
0
0
0
2
0
1
2
0
0
0
1
1
1
0
2
1
1
0
2
2
0
1
0
0
0
1
1
2
0
0
0
0
1
2
0
1
0
1
0
0
0
1
0
4
1
0
2
1
0
0
2
2
0
0
0
0
0
0
0
0
2
1
1
1
0
0
1
0
0
0
0
0
1
2
0
0
3
0
1
1
1
0
0
2
0
2
2
0
0
0
3
2
0
0
1
0
0
2
0
0
2
1
0
0
0
0
0
0
1
1
0
0
2
1
2
0
1
0
0
1
0
1
0
0
0
1
1
1
0
0
1
1
0
1
0
2
0
1
2
0
2
2
0
2
0
2
1
0
0
0
2
1
0
2
0
1
2
0
0
5
1
0
1
2
0
0
2
2
1
2
1
2
0
3
1
0
0
1
3
0
2
0
1
2
0
1
0
2
1
1
1
0
0
0
1
1
2
2
2
1
0
0
0
1
1
0
1
2
0
1
0
1
0
0
0
0
0
2
1
0
0
3
1
0
0
1
1
2
2
1
0
0
2
5
0
0
2
0
1
2
1
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
2
0
0
1
1
2
0
1
3
0
2
0
2
0
0
0
2
2
0
0
0
1
0
0
1
0
0
1
1
1
2
1
0
0
2
1
0
0
0
2
1
0
1
0
0
0
0
0
2
2
0
1
1
1
2
1
0
2
2
1
0
0
1
3
2
1
1
2
2
1
0
2
0
0
1
0
0
2
2
0
1
1
1
0
0
1
0
0
1
0
0
0
1
0
2
1
2
2
0
0
3
0
0
1
1
0
0
0
0
1
1
0
0
1
2
1
0
0
2
0
2
0
2
2
2
2
0
2
0
0
1
0
1
0
1
2
0
1
0
0
2
1
0
0
2
0
0
1
2
1
2
0
1
0
0
0
0
1
1
1
0
1
2
1
0
1
0
0
2
1
1
2
0
1
1
0
1
1
1
0
0
1
0
1
0
0
0
1
2
2
0
0
1
0
0
3
0
2
0
0
1
0
1
0
0
2
0
2
1
2
0
0
0
1
0
0
0
0
0
1
0
1
1
2
0
0
0
2
2
1
0
0
1
0
2
1
0
1
0
3
1
1
2
0
0
0
0
2
0
0
0
1
1
3
0
0
0
0
0
0
0
2
2
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
1
2
0
2
0
1
0
0
2
0
1
0
0
1
2
1
1
1
1
1
0
0
2
1
2
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
2
0
0
2
3
0
2
0
0
0
2
1
1
0
2
0
2
0
0
0
2
1
2
1
2
2
0
5
0
0
1
0
0
0
1
2
0
0
0
0
1
1
2
1
0
2
0
0
0
0
1
0
0
0
0
0
2
1
1
1
0
2
2
0
2
0
0
1
1
0
1
0
1
0
0
1
0
0
1
0
1
0
2
0
1
1
1
1
0
0
1
0
0
1
1
2
0
1
2
1
1
0
2
0
2
1
0
0
0
0
0
1
0
1
0
1
0
0
0
2
1
2
1
0
0
0
1
0
0
0
2
1
2
2
0
0
0
0
0
0
1
0
0
0
0
2
0
2
1
0
0
3
0
2
0
0
1
3
2
0
2
2
1
0
2
0
1
1
2
0
0
0
0
0
0
1
1
2
0
2
0
1
2
0
0
2
1
0
2
1
1
1
1
0
0
0
1
0
2
0
0
0
2
1
2
0
0
1
2
0
2
1
2
2
3
1
1
0
0
1
0
0
1
3
2
1
0
1
0
0
1
1
2
0
2
0
1
2
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
1
2
0
0
0
3
0
0
2
2
1
0
2
0
1
1
1
1
2
1
1
0
2
1
3
2
0
0
2
0
2
1
1
2
2
2
2
0
0
0
0
0
1
2
0
4
0
1
2
1
2
0
0
0
0
1
1
1
2
0
0
2
2
0
0
1
0
2
1
3
0
0
0
1
1
1
0
0
1
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
1
1
1
4
1
0
0
2
1
2
0
1
0
0
1
1
0
0
0
0
1
0
1
0
0
1
2
0
1
1
0
2
1
0
1
0
0
0
1
2
0
1
0
2
0
2
2
0
2
0
0
0
2
0
0
1
1
0
1
2
0
0
1
2
0
0
0
0
2
2
1
0
1
0
1
1
0
1
1
1
2
1
2
0
0
2
0
1
1
0
1
1
2
1
0
1
0
2
0
0
0
0
2
0
1
0
0
1
0
2
2
0
1
0
0
1
2
0
0
0
0
0
2
2
2
2
1
3
0
0
0
0
1
0
2
2
1
3
2
1
1
0
1
0
0
2
2
1
1
7
1
0
0
0
1
0
0
0
1
0
2
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
2
0
1
0
0
0
2
1
0
1
2
1
1
2
0
0
2
1
0
0
1
0
0
1
0
0
2
0
3
0
0
1
1
2
0
0
1
0
1
0
0
0
0
3
2
0
1
0
0
2
1
0
2
0
0
0
0
2
2
0
1
1
0
1
0
1
0
0
2
2
4
1
2
0
0
0
0
1
0
0
1
1
0
0
0
2
1
0
0
0
1
2
1
0
0
0
1
1
0
1
1
2
0
1
0
1
0
1
0
1
0
0
0
2
0
0
0
1
0
2
0
2
1
0
0
0
1
0
0
0
2
4
0
2
0
0
1
1
1
2
1
0
2
1
2
1
0
5
2
2
2
0
1
0
1
0
0
0
2
2
0
2
0
1
0
1
0
0
1
2
0
1
0
4
1
1
2
3
0
0
2
1
1
0
0
0
0
0
5
0
1
0
2
1
2
1
0
1
0
0
1
0
0
0
1
1
3
1
0
0
0
1
0
2
2
0
0
0
0
2
0
1
1
1
1
2
1
3
0
1
2
0
2
0
0
1
0
1
0
0
0
1
0
2
1
0
0
0
1
2
0
0
0
2
1
1
1
0
2
0
0
0
2
1
0
0
2
2
3
1
0
0
0
0
0
0
0
1
2
0
1
0
1
0
1
0
0
2
0
1
2
0
1
0
0
1
0
1
0
2
0
0
0
2
0
0
0
0
1
0
2
0
1
0
0
0
1
1
1
1
0
2
0
0
1
0
0
0
2
1
1
1
0
1
1
2
0
2
0
2
1
0
2
0
0
3
1
0
0
0
0
0
1
0
2
0
0
1
0
1
0
1
0
0
1
2
2
1
0
1
2
1
0
1
0
0
1
0
0
0
0
1
2
1
2
2
1
2
1
1
1
0
2
1
0
0
1
0
0
0
1
0
1
2
0
0
0
0
1
0
0
1
3
0
0
1
1
0
2
0
0
2
0
1
0
1
0
1
0
1
2
0
2
0
2
0
1
1
2
0
0
0
2
1
0
1
1
0
0
1
1
2
0
2
1
0
2
0
0
2
1
0
1
2
1
2
1
0
2
1
1
0
0
0
1
0
0
0
1
0
1
1
0
2
0
1
2
1
1
0
0
0
2
1
0
0
2
0
2
1
3
0
1
1
0
1
2
1
0
0
0
1
0
0
1
1
0
4
1
2
0
1
1
1
1
2
0
2
0
0
0
2
2
2
0
1
2
2
0
2
2
0
2
0
0
0
0
1
1
0
0
2
1
0
0
0
1
0
2
1
0
0
2
1
1
1
3
2
1
2
1
1
1
2
1
0
0
1
0
0
3
1
0
0
1
2
0
1
1
1
0
0
0
0
2
1
0
0
1
1
1
0
1
0
0
0
1
0
0
2
1
0
2
1
2
2
0
2
0
0
2
1
1
1
2
1
0
2
2
2
0
1
1
0
1
0
1
0
1
0
1
1
0
2
0
1
0
1
1
1
0
0
2
0
0
0
2
2
0
2
2
2
0
0
0
0
0
1
2
0
0
1
1
1
0
0
0
0
1
1
0
1
1
2
0
0
1
1
2
0
1
0
0
0
1
1
2
0
1
0
0
1
1
1
2
1
0
1
1
0
3
0
1
2
0
1
0
1
0
2
1
1
1
2
0
0
1
1
1
1
0
1
0
0
4
0
2
1
0
0
0
2
2
0
0
0
0
0
2
1
0
1
0
0
1
0
0
1
0
1
1
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
2
2
1
0
2
2
0
0
0
0
1
0
1
0
2
0
0
2
0
0
0
1
1
0
0
1
0
2
1
0
0
0
2
1
2
1
1
1
0
2
1
1
2
1
1
2
1
0
1
0
0
1
2
1
1
2
1
0
0
0
2
2
0
2
0
0
1
0
0
0
1
0
0
0
0
1
0
2
2
0
0
2
0
1
0
1
1
0
0
1
0
0
0
0
2
1
2
2
0
0
2
1
0
2
0
2
1
2
0
0
0
0
0
1
0
0
0
0
0
1
4
2
0
0
2
0
0
0
0
1
0
1
1
0
0
0
0
1
1
0
2
0
0
0
0
5
0
0
1
2
1
0
0
0
0
1
0
1
1
0
1
2
0
0
1
0
0
0
6
0
0
1
1
1
3
0
0
1
2
0
1
1
2
1
1
1
0
1
1
0
0
1
2
2
0
0
0
0
1
2
3
0
0
1
0
0
0
2
2
0
0
1
0
0
1
2
2
2
0
0
0
2
0
1
0
0
2
0
1
2
0
2
0
0
0
0
1
0
1
2
2
2
1
0
0
0
0
3
0
0
1
0
0
0
0
0
3
1
2
0
0
2
0
0
0
0
0
1
0
0
1
0
1
2
0
0
1
3
0
1
1
1
2
0
0
0
1
0
2
0
4
1
1
1
1
1
0
2
5
2
0
1
1
0
2
1
2
1
2
0
2
0
0
1
4
1
0
1
0
0
1
0
1
1
0
1
0
0
0
2
0
1
1
1
1
1
0
0
0
2
1
2
0
0
1
1
0
1
0
0
0
0
1
2
1
1
2
1
0
3
2
0
0
0
0
1
0
2
0
0
1
0
0
0
2
2
1
1
1
1
0
1
0
2
1
0
3
1
0
1
0
1
0
0
0
0
0
0
1
0
1
0
2
1
0
0
3
2
2
2
1
1
2
0
1
1
3
0
0
0
1
5
0
0
2
1
2
0
0
0
1
0
0
1
1
2
0
1
0
0
0
2
2
0
0
1
2
1
2
1
0
1
2
0
2
0
0
1
0
0
0
2
1
0
0
0
1
1
1
0
1
1
1
0
0
0
2
0
0
0
0
2
0
1
0
2
1
0
0
0
2
0
3
0
2
1
1
1
2
1
0
0
2
1
2
2
3
1
2
0
0
1
1
0
0
0
1
1
0
2
2
1
0
0
1
1
2
0
1
0
0
1
1
1
0
0
0
9
2
1
0
2
0
0
0
0
2
1
0
0
0
1
1
3
1
0
0
0
2
0
1
0
0
1
0
0
1
0
1
0
1
2
0
0
0
1
2
2
0
1
0
0
2
0
0
0
1
1
1
0
2
0
0
1
1
0
2
1
0
1
0
2
1
0
0
0
1
0
0
0
1
2
1
0
0
1
0
1
1
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
1
3
1
1
0
0
1
1
0
1
0
1
1
0
0
1
0
0
1
0
0
0
0
2
1
0
0
1
0
1
0
1
1
2
0
1
0
0
2
3
2
1
0
0
0
2
0
2
5
1
2
0
0
1
0
0
1
0
1
0
0
2
1
0
0
1
0
0
1
0
2
2
0
0
0
1
0
0
1
1
2
1
2
2
0
1
0
0
2
0
0
2
1
1
1
0
0
1
0
0
0
2
1
0
0
0
1
1
0
1
0
1
1
1
0
0
1
0
0
0
0
2
0
0
1
1
2
1
2
0
0
2
0
1
0
0
1
0
1
2
0
2
0
1
0
2
2
0
2
2
0
0
0
0
0
0
0
2
0
0
1
0
1
1
1
1
1
0
1
2
0
1
0
0
0
0
0
1
2
0
0
2
1
0
0
0
1
1
0
0
2
0
0
1
0
0
0
1
0
2
1
0
0
1
2
0
2
0
1
0
0
0
0
0
0
0
3
0
1
0
0
2
1
0
2
1
1
1
2
0
0
1
1
1
0
3
1
0
0
1
0
0
1
0
2
0
0
1
2
1
0
0
0
1
0
0
1
2
2
0
0
1
0
1
1
1
0
1
2
0
1
2
0
0
0
2
0
0
0
0
2
0
1
1
0
0
1
4
3
0
0
1
1
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
2
0
0
2
0
2
1
1
1
2
1
0
0
0
1
0
0
1
2
1
0
2
0
0
0
2
0
0
0
0
1
1
0
2
1
0
1
2
1
0
0
0
0
1
1
4
1
0
1
0
0
0
0
0
0
0
2
1
0
1
1
1
0
4
1
0
2
0
0
0
1
0
0
2
0
0
0
2
0
1
1
1
0
0
1
2
0
1
2
1
0
0
0
2
1
0
0
0
0
1
1
0
1
1
0
0
1
0
1
0
2
2
2
0
1
2
2
1
2
1
0
0
0
1
1
1
1
1
0
0
0
2
0
0
0
1
1
1
0
2
0
0
0
0
0
0
2
0
1
1
0
2
1
0
2
2
2
1
0
1
0
1
0
0
1
2
2
0
1
2
0
1
0
0
2
0
3
0
2
2
1
0
0
3
1
1
0
0
0
1
1
1
0
1
0
1
0
0
1
0
0
1
0
0
2
1
0
0
0
0
0
2
0
0
0
1
2
1
1
2
2
0
0
1
0
0
2
0
1
2
2
1
0
0
0
1
0
0
0
1
0
1
0
2
0
1
0
1
1
0
0
0
0
0
0
1
0
1
1
0
0
2
0
1
2
1
0
0
0
1
0
2
1
0
0
0
0
0
2
1
0
0
2
1
0
0
2
2
1
0
2
0
0
1
1
1
2
0
2
0
2
0
0
2
0
0
0
1
0
0
2
0
2
0
0
1
0
0
0
1
0
1
2
1
0
2
2
0
1
0
1
1
0
0
0
1
0
1
0
0
2
0
1
1
2
0
1
0
1
1
1
0
0
2
0
1
0
0
1
1
0
1
2
1
1
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
1
1
1
1
1
3
0
0
2
3
1
1
3
1
0
2
1
0
0
0
1
2
1
0
2
2
1
1
2
0
1
2
0
1
0
0
2
2
0
0
1
0
1
0
1
0
1
0
0
2
1
0
0
0
1
0
0
0
0
1
0
1
2
1
1
0
1
0
0
0
0
1
0
2
2
1
2
2
0
0
0
1
0
2
1
0
0
1
1
0
0
2
1
0
1
2
0
0
1
0
0
1
0
0
4
3
3
0
0
0
0
2
2
1
0
2
0
0
1
0
0
0
0
0
1
1
1
2
0
0
0
1
1
0
0
0
0
2
0
0
1
0
0
2
0
0
1
1
0
1
1
0
1
0
0
1
1
0
1
0
0
2
0
2
2
1
0
0
0
0
2
1
0
0
0
2
0
0
2
1
0
2
2
0
0
2
1
1
2
2
0
0
1
0
2
1
0
0
0
0
0
0
0
2
0
1
0
1
1
0
2
0
1
2
0
2
1
0
1
1
0
1
1
1
0
4
0
0
1
0
0
0
0
1
0
0
0
2
0
0
1
1
0
1
1
0
1
0
2
0
2
2
2
1
0
2
3
2
2
0
2
0
0
1
0
0
1
0
0
1
0
0
0
0
0
3
1
0
1
1
2
0
2
0
0
0
0
2
1
1
0
0
0
2
1
2
1
0
0
1
0
1
0
0
1
1
2
0
0
2
0
1
2
1
0
1
0
0
0
0
0
2
2
1
2
0
0
0
1
2
2
2
1
2
1
2
1
0
1
0
1
0
0
0
0
2
0
2
1
0
1
0
0
0
0
1
2
0
0
0
0
0
0
2
0
3
0
0
1
1
1
0
2
1
1
0
0
1
0
2
0
2
1
2
2
0
0
1
0
0
1
0
0
0
1
2
1
0
0
0
1
0
2
0
1
2
1
0
1
1
1
0
0
1
2
0
1
2
1
0
2
0
1
0
0
0
0
0
2
1
1
1
1
2
0
1
0
0
0
2
0
1
1
1
1
2
1
0
2
0
2
0
0
0
2
1
0
3
1
0
2
2
0
0
0
0
1
0
1
2
1
1
0
0
1
1
2
1
1
0
1
0
2
1
0
1
1
2
2
0
0
0
1
1
0
2
0
0
1
1
0
0
1
0
1
0
2
0
1
0
0
1
0
0
1
0
2
0
0
0
0
0
1
0
2
2
0
1
0
0
0
1
1
0
0
1
3
2
0
0
1
1
0
1
0
1
0
2
1
2
0
2
0
0
0
2
1
0
0
0
0
0
1
0
1
1
0
0
0
0
2
1
0
2
2
1
1
0
2
2
1
1
0
0
0
1
2
2
2
2
1
1
0
0
0
0
0
0
0
0
2
1
0
0
2
1
0
0
2
2
2
1
0
0
0
0
2
2
1
0
2
1
0
6
0
1
2
0
1
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
2
0
1
1
0
3
0
1
2
0
1
0
1
1
2
1
0
1
2
0
0
1
0
1
0
2
0
1
1
1
0
1
0
0
0
0
0
1
1
0
0
4
0
2
1
1
2
0
1
1
2
0
1
0
5
0
2
1
0
2
0
2
1
1
1
0
1
2
1
0
2
1
0
4
0
0
0
0
0
2
0
0
2
0
3
0
2
1
5
1
1
1
1
0
1
1
1
1
2
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
1
1
1
0
1
1
0
0
0
2
4
0
0
1
0
1
2
3
0
0
1
1
1
1
2
1
0
0
2
1
0
0
0
1
1
0
0
1
0
1
1
2
0
1
0
2
0
0
0
0
1
2
2
0
0
3
0
0
2
0
0
0
0
1
0
1
1
2
2
2
1
1
0
2
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
1
3
2
0
1
2
0
2
0
1
0
2
0
0
1
1
2
0
0
1
0
1
0
2
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
2
0
3
1
0
1
0
1
0
0
3
0
1
1
1
0
0
1
0
0
2
0
0
0
0
1
1
1
0
1
1
0
2
0
1
2
1
0
1
0
2
0
0
1
0
0
0
1
0
0
2
1
0
0
0
2
2
2
2
0
0
0
0
1
0
0
1
1
1
1
1
0
0
0
0
2
0
0
0
3
1
0
1
0
0
0
1
1
0
2
1
0
1
1
0
0
0
1
0
2
2
2
2
0
2
1
1
0
0
1
0
1
0
0
0
0
1
2
2
0
0
0
0
1
1
0
0
0
0
0
2
2
2
0
3
1
0
0
0
2
0
1
2
0
3
1
1
0
0
0
0
1
1
1
0
2
0
0
0
1
0
0
0
2
0
0
2
1
2
0
3
2
1
0
0
2
0
0
2
2
0
0
0
2
1
1
1
2
1
0
2
0
2
0
1
0
0
0
0
0
0
2
1
0
0
2
0
0
1
2
2
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
2
0
1
0
0
2
0
0
1
1
0
2
0
1
0
0
0
0
0
1
1
0
0
2
0
1
0
0
1
2
0
2
3
0
0
0
1
2
1
1
1
0
2
0
0
0
1
0
0
0
3
0
0
0
3
2
2
0
0
2
1
0
0
0
1
0
2
0
1
0
1
0
0
0
0
0
1
0
1
0
1
0
0
1
1
0
1
2
0
2
1
1
0
0
2
2
1
3
1
1
0
2
0
1
0
1
0
1
1
0
2
1
2
0
0
1
1
2
0
2
1
2
0
1
0
2
0
1
2
1
0
1
0
0
0
0
2
2
0
0
1
0
0
1
1
1
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
2
1
2
2
1
1
1
1
0
0
2
1
0
2
0
1
0
0
0
2
1
0
1
0
0
0
2
0
2
2
0
0
0
1
2
1
0
2
0
0
0
1
1
0
0
0
0
0
0
0
1
1
1
0
1
2
0
2
3
2
0
0
1
4
1
1
1
2
2
0
0
1
0
0
1
1
0
0
1
0
1
0
0
1
1
0
1
0
1
1
1
0
1
0
0
0
0
0
1
2
1
2
1
0
0
0
1
0
0
2
1
0
0
0
0
2
2
0
0
1
1
0
2
1
0
0
0
1
0
3
2
0
0
1
2
1
0
2
2
0
1
2
2
0
0
1
0
2
0
1
2
0
2
0
0
1
0
0
1
0
2
1
0
0
0
0
1
1
1
0
0
2
0
2
1
2
1
0
0
2
1
0
3
1
2
1
0
2
0
2
2
0
0
3
1
0
2
0
1
1
2
1
0
2
0
1
0
0
2
1
2
2
0
2
2
2
2
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
1
0
1
0
2
2
2
0
0
1
0
1
0
2
2
0
2
0
0
2
1
0
0
1
2
2
0
0
1
0
1
0
2
0
1
1
0
0
0
0
0
0
2
0
0
1
0
0
0
1
1
2
0
1
1
0
0
1
0
0
0
3
0
0
0
1
0
1
0
0
2
0
1
2
0
2
0
2
0
0
2
0
0
0
2
0
0
2
0
0
1
0
0
0
1
2
3
0
0
0
2
0
2
0
0
1
0
2
0
0
1
0
1
0
1
0
1
1
0
1
2
2
1
0
1
0
0
0
0
0
0
2
1
0
0
0
1
1
1
1
0
1
0
0
0
5
0
0
1
1
0
2
0
1
1
0
2
1
0
2
0
1
1
0
1
2
0
2
2
1
0
2
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
1
1
2
0
0
1
0
0
0
2
2
0
1
2
0
0
0
2
0
0
0
0
2
1
0
1
0
0
0
2
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
2
2
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
1
0
0
2
1
1
1
0
1
0
0
2
1
0
0
1
1
0
2
1
0
1
1
0
0
2
0
0
0
1
1
1
0
1
0
0
2
1
0
2
1
0
0
2
1
0
0
0
2
0
2
3
2
0
1
0
0
0
3
1
2
1
1
1
0
1
2
2
1
0
1
0
0
2
0
1
1
0
2
0
3
1
2
1
1
1
2
1
1
1
2
1
0
0
2
1
1
0
1
1
1
1
0
0
0
1
0
0
1
1
0
0
2
0
0
2
1
0
1
1
2
1
1
0
0
2
1
2
1
2
0
0
0
1
1
0
0
0
0
1
1
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
1
2
0
1
0
0
2
1
2
3
1
0
1
0
1
1
0
0
1
2
1
0
0
1
0
1
0
2
0
0
0
2
0
1
1
2
0
1
1
1
1
0
1
2
1
2
1
1
0
1
0
0
0
0
0
0
0
1
2
1
0
0
1
1
2
0
1
1
1
0
1
0
1
2
1
0
2
0
1
1
0
0
1
3
0
1
0
0
1
0
1
1
0
0
0
2
1
1
1
0
0
3
0
2
1
0
0
0
1
0
0
2
1
2
0
2
1
0
1
1
0
0
0
1
2
0
3
2
2
1
1
0
0
2
0
0
0
0
0
2
0
1
0
0
1
0
2
1
1
0
0
1
1
2
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
1
0
1
1
1
1
0
0
0
1
0
4
1
2
2
0
2
0
0
0
1
3
1
0
0
1
2
0
0
1
0
1
0
2
1
0
2
2
1
0
1
2
0
0
0
2
1
0
0
2
1
0
1
0
0
2
1
1
2
0
2
2
1
2
0
0
1
0
1
0
2
0
0
1
2
1
0
1
2
0
1
1
1
0
1
0
0
2
1
0
0
0
0
0
0
0
2
1
1
2
1
1
2
2
2
0
1
0
0
0
0
1
2
0
0
0
0
0
2
1
1
2
0
0
1
4
1
2
2
0
0
0
0
1
2
0
1
0
0
1
1
2
0
0
2
0
1
0
1
2
2
0
1
1
0
1
0
2
0
1
0
0
0
2
1
1
2
3
1
1
1
0
1
1
3
0
1
1
0
1
0
0
0
0
1
0
0
2
0
1
2
0
0
0
0
1
0
0
2
0
2
1
1
0
0
0
0
0
0
0
2
1
0
0
0
2
1
1
0
1
1
1
1
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
2
1
1
3
2
0
2
0
0
1
0
2
0
0
0
0
1
0
0
1
0
0
0
0
2
3
0
0
0
0
1
1
0
0
0
0
0
1
0
1
2
1
1
1
2
2
0
1
0
0
2
0
0
0
0
0
1
0
2
1
1
1
1
2
2
0
2
1
0
1
0
2
1
2
0
0
0
0
2
1
0
1
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
2
0
2
1
0
0
2
2
1
1
0
1
0
0
2
1
2
1
0
0
2
1
1
0
0
2
0
0
1
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
1
0
2
0
0
1
1
2
0
0
1
0
1
2
0
0
0
0
2
2
0
2
1
1
1
2
1
0
0
0
2
0
0
0
0
1
0
0
1
1
0
0
2
0
2
1
1
1
0
2
2
0
2
0
1
0
0
1
2
2
2
1
1
2
0
0
2
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
1
0
0
0
0
2
0
1
1
0
0
2
1
2
0
0
0
3
1
0
0
1
0
2
0
3
2
1
0
0
1
0
2
1
1
2
0
1
0
1
1
1
0
1
1
0
0
0
0
0
1
0
2
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
2
1
0
0
1
0
0
0
0
3
1
1
0
1
0
1
2
2
1
0
0
2
2
0
3
0
0
0
1
0
1
1
0
0
0
1
0
2
0
0
0
0
0
0
2
1
0
1
0
1
0
0
0
0
1
0
1
0
0
0
2
0
0
2
2
0
0
0
2
0
2
0
0
1
1
1
0
0
0
1
2
1
1
0
1
1
0
1
1
2
0
1
0
2
2
0
0
0
2
5
1
0
2
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
2
0
1
1
2
2
0
1
0
2
1
0
0
0
2
1
0
0
0
0
0
1
2
2
1
0
0
0
0
0
0
1
0
0
2
2
0
0
1
0
2
0
0
0
0
1
0
1
2
0
0
0
0
0
0
2
0
1
2
0
0
0
0
1
0
0
0
0
3
0
1
0
1
2
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
2
1
1
0
1
1
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
1
1
1
1
0
2
0
1
0
0
0
1
0
2
0
0
2
1
0
1
0
1
0
0
0
2
2
1
0
0
0
1
1
1
0
0
0
0
1
1
1
2
0
2
0
2
2
0
0
2
0
0
0
2
0
0
2
0
1
0
3
1
1
1
0
0
0
1
2
1
1
0
0
0
0
1
1
0
2
0
0
1
1
0
2
0
3
1
0
1
0
0
0
1
0
0
0
1
0
2
1
1
0
1
2
0
0
0
0
2
0
0
2
0
1
2
0
1
0
2
0
0
2
1
2
2
0
2
2
1
0
0
0
0
0
1
0
0
1
0
3
1
1
2
2
0
0
0
2
2
0
2
1
0
0
1
1
1
0
0
0
0
0
0
1
2
0
0
2
0
0
2
1
1
0
2
1
0
0
1
2
2
0
1
1
2
0
1
0
0
2
1
0
0
0
2
0
0
0
0
2
2
2
0
1
0
1
0
0
0
1
1
1
2
0
2
1
1
2
0
1
0
0
1
2
1
2
1
0
0
0
2
0
0
2
0
0
0
1
2
0
0
0
1
1
0
0
2
1
2
0
0
4
0
2
0
2
0
0
0
2
1
0
3
3
1
2
0
2
0
0
0
2
0
1
0
1
0
2
1
2
1
1
1
2
0
0
0
2
4
1
0
1
1
1
2
0
0
0
0
0
2
0
0
0
0
3
0
0
2
0
0
0
1
0
1
0
0
0
1
1
0
1
1
0
0
2
0
0
0
0
0
1
1
1
2
2
0
0
0
0
0
1
2
0
0
0
2
0
0
1
0
2
1
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
2
0
1
0
2
3
1
1
1
0
1
4
2
0
2
0
0
2
1
1
2
2
2
0
1
0
2
1
2
2
1
0
0
2
0
1
0
0
1
1
0
0
2
1
2
0
1
2
1
0
1
1
3
1
0
0
0
1
1
2
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
2
1
1
2
2
1
1
1
1
1
2
0
3
1
0
0
1
1
1
1
0
2
1
0
1
0
0
1
1
2
1
0
1
1
2
2
0
2
1
0
2
2
0
2
0
2
1
1
1
0
0
2
2
2
1
3
2
1
0
2
1
0
0
0
1
0
0
0
2
1
2
1
0
1
1
2
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
2
0
1
1
0
2
0
2
2
0
0
0
0
2
0
1
2
1
1
4
1
0
0
0
2
0
0
2
0
0
0
0
0
2
1
0
1
1
1
1
0
1
0
0
2
0
2
0
1
0
0
1
0
2
0
1
1
2
2
1
0
2
2
2
2
0
1
2
1
0
1
0
0
2
1
1
1
0
2
2
0
0
2
1
2
1
0
0
0
0
1
0
0
2
0
2
0
1
1
1
1
1
0
0
2
0
1
0
0
2
0
0
1
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
1
1
1
1
0
0
0
1
1
0
0
2
1
2
0
0
0
0
0
0
0
0
1
1
0
2
1
0
0
1
2
2
0
0
1
0
2
1
1
0
2
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
1
2
0
2
0
0
2
3
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
2
1
0
0
2
2
3
2
1
0
0
2
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
1
1
1
1
0
1
1
0
0
0
0
2
1
1
0
1
0
1
1
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
2
0
2
0
2
2
0
2
0
0
0
2
0
0
1
0
0
1
1
2
0
0
1
0
1
0
2
1
1
1
0
0
2
0
2
1
2
1
1
0
2
1
2
0
0
0
2
0
1
0
1
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
1
2
1
0
0
1
0
2
0
1
1
0
2
2
0
2
4
0
0
0
0
1
2
3
1
1
2
0
1
1
0
2
2
0
2
1
2
2
0
0
2
2
2
3
0
0
0
1
0
2
0
1
1
0
1
0
2
1
0
5
0
0
2
0
2
0
1
0
1
2
1
2
0
0
0
1
0
0
0
1
1
0
2
1
1
1
2
1
0
0
0
2
0
2
0
2
0
1
0
1
2
0
0
1
2
1
1
1
0
1
1
1
0
0
0
2
0
0
0
2
1
1
1
1
0
2
2
0
1
2
1
0
1
1
0
2
4
0
0
0
1
0
0
0
0
0
1
1
1
0
0
2
1
0
0
0
0
1
1
2
1
1
2
1
2
0
0
1
2
1
1
1
1
1
0
1
0
0
0
0
0
1
1
0
0
1
1
1
0
1
0
0
1
0
2
2
0
1
0
1
0
0
3
0
2
2
0
1
2
0
0
0
1
1
0
4
0
3
0
0
2
0
1
0
0
1
2
0
2
0
0
1
1
2
0
0
1
0
2
0
0
0
0
0
0
1
1
1
3
2
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
2
0
0
0
0
2
2
0
2
1
1
2
0
1
0
1
2
0
1
1
0
0
1
1
0
1
0
1
1
1
0
0
1
2
2
1
0
0
1
0
1
1
2
0
0
1
1
0
1
1
2
0
0
1
2
0
1
0
1
0
0
0
1
0
0
0
1
1
2
1
0
2
2
0
0
0
0
2
0
2
2
1
0
0
0
0
0
0
1
1
2
0
0
0
1
0
2
1
0
0
1
1
0
0
0
0
0
1
0
0
1
1
2
1
0
1
1
0
0
1
1
0
0
0
0
2
1
2
1
0
2
1
0
0
0
2
0
1
0
1
1
0
0
1
1
2
0
0
0
0
3
2
1
1
1
0
1
1
2
1
0
1
0
0
1
1
0
1
0
0
0
0
1
2
1
0
1
0
0
2
1
0
2
1
1
0
3
0
1
1
0
0
2
1
1
1
0
0
2
2
1
2
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
2
0
2
0
1
0
1
0
0
0
0
1
0
4
2
0
3
0
0
1
2
1
0
0
2
0
0
2
0
0
0
1
0
0
0
0
1
0
1
0
0
2
0
0
1
0
0
0
2
2
1
0
0
0
1
0
0
1
1
2
1
1
0
0
2
0
1
1
2
1
1
1
1
0
1
3
0
2
0
0
0
2
0
1
2
1
1
0
1
1
0
0
2
3
0
0
0
1
1
2
0
1
1
1
0
0
0
0
1
0
0
1
2
2
2
0
0
1
0
0
0
2
0
1
0
2
2
0
1
0
0
0
2
0
0
0
1
0
0
0
0
2
0
1
2
0
0
1
0
3
0
4
2
1
1
0
2
0
1
0
2
0
0
2
0
0
0
1
0
2
0
0
0
0
2
0
0
0
2
2
2
2
8
2
0
1
0
2
0
1
1
2
0
0
0
0
1
2
0
1
1
2
2
1
0
0
0
0
1
0
0
2
2
0
2
1
0
0
0
0
2
0
2
0
0
1
0
1
0
1
0
0
0
2
1
0
1
1
0
1
0
1
0
0
0
1
5
1
2
0
0
1
0
0
2
2
0
0
0
0
2
0
1
0
0
1
0
0
0
0
2
0
1
1
0
2
0
1
2
0
0
2
0
0
0
0
0
2
0
1
1
2
0
0
0
1
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
1
2
2
1
2
0
0
2
0
1
2
0
1
2
2
0
2
0
0
0
0
1
0
1
4
0
2
3
2
2
0
1
0
1
0
1
2
0
0
0
0
4
1
0
1
0
0
2
0
0
1
1
1
0
0
2
0
1
0
0
1
0
2
2
1
1
2
0
1
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
2
0
0
1
1
0
0
3
0
0
0
0
2
1
0
0
0
0
1
0
2
2
0
3
0
2
0
0
0
0
0
0
0
2
2
0
7
1
1
0
0
0
0
1
0
1
0
0
2
0
1
0
1
0
0
0
0
0
2
0
0
0
0
1
2
0
1
2
0
0
1
0
0
0
1
0
0
0
0
1
1
2
1
0
2
1
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
1
0
0
0
1
0
1
2
0
0
0
2
0
1
0
1
2
2
2
2
0
0
0
1
0
2
2
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
2
0
1
0
0
0
2
0
1
0
1
0
1
2
0
0
1
0
0
2
1
0
2
0
0
0
0
0
1
1
0
0
1
0
1
2
1
0
1
0
0
0
1
1
1
0
0
1
0
3
2
1
0
0
0
0
0
0
0
0
0
5
1
2
0
1
0
1
2
0
0
2
2
0
1
0
0
1
5
0
0
1
1
0
0
0
1
2
2
2
0
2
2
2
0
0
0
2
0
0
0
1
1
2
0
2
1
1
1
0
2
1
2
1
0
0
0
0
1
2
0
1
0
1
0
1
2
0
0
1
1
2
0
0
1
2
0
0
0
0
0
0
0
1
0
2
2
0
6
1
1
1
0
2
1
0
2
3
1
1
1
0
0
1
2
1
0
0
0
2
2
0
1
0
0
2
0
0
1
0
0
0
3
1
1
0
0
1
0
2
0
0
0
1
0
1
0
0
1
2
0
2
1
0
2
0
2
1
1
1
2
0
1
1
1
2
1
2
0
3
2
0
0
0
0
2
0
0
0
0
0
0
1
1
1
1
0
0
0
2
0
2
1
0
0
2
0
0
0
0
0
1
0
0
0
2
2
0
0
2
0
0
1
2
0
0
1
0
2
0
1
0
1
0
1
0
0
0
1
0
1
3
1
2
0
1
2
1
0
0
0
1
0
0
2
0
1
1
0
0
0
0
0
2
1
0
0
1
2
0
0
1
1
0
0
0
0
2
0
0
1
0
2
0
1
0
2
2
0
0
0
0
1
3
0
1
2
1
2
0
0
0
2
1
0
1
1
0
0
1
0
1
0
1
2
2
0
0
0
0
1
0
1
1
0
0
0
0
2
0
0
2
0
0
1
1
0
0
1
1
0
0
0
0
1
2
0
0
0
2
2
0
0
0
0
2
0
0
2
2
1
0
1
1
0
2
1
2
0
0
0
1
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
2
0
1
1
0
1
0
2
1
2
0
0
1
0
2
0
0
0
0
0
2
2
0
0
2
0
2
1
1
1
1
0
1
0
1
0
0
0
1
1
0
1
2
1
0
1
0
0
1
0
1
4
0
0
0
1
1
0
2
2
0
0
2
1
2
2
2
1
0
0
1
1
1
0
0
1
0
1
0
1
1
0
0
2
2
1
0
0
0
2
0
0
1
1
2
0
0
0
1
0
0
0
1
0
1
1
0
1
0
2
1
0
1
1
1
2
0
1
2
1
0
2
0
1
1
0
3
0
2
0
2
2
1
2
3
1
0
1
0
0
2
2
1
1
0
2
0
0
0
1
1
4
0
0
0
0
3
0
0
0
0
2
1
1
1
0
2
1
1
0
2
1
1
1
0
1
2
0
1
0
0
0
0
0
0
1
1
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
3
2
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
2
0
0
2
0
0
0
0
0
4
1
1
0
1
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
1
0
2
0
4
1
1
2
1
0
0
0
0
0
1
2
1
0
0
1
0
1
2
0
1
0
1
0
1
0
0
1
0
0
0
2
0
0
1
1
1
3
1
0
0
1
0
0
0
1
1
0
0
2
2
1
0
2
0
1
1
1
1
0
0
0
0
0
2
0
1
0
2
0
1
1
1
2
0
1
0
2
0
2
0
2
0
2
1
0
0
0
3
1
2
0
0
0
2
1
2
0
1
0
1
0
0
1
2
2
0
0
0
0
1
1
0
1
0
1
1
0
1
0
2
1
0
0
1
1
0
3
0
0
0
0
0
1
0
0
0
2
1
2
0
0
0
0
1
0
0
3
0
2
0
2
0
2
1
1
0
0
2
0
0
2
1
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
2
1
0
2
2
0
1
0
0
4
1
0
1
1
2
0
0
0
0
2
0
1
2
2
0
0
2
0
1
1
0
0
0
0
1
1
0
1
3
0
2
1
0
0
0
0
2
0
1
1
2
1
1
1
1
1
0
0
1
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
1
1
0
1
2
2
0
2
0
1
0
0
0
0
0
0
0
1
0
1
2
1
1
0
0
0
0
1
1
0
0
2
0
2
0
1
1
4
0
2
0
0
0
1
1
1
0
0
1
1
0
1
1
0
1
0
0
1
1
1
0
0
0
1
1
0
2
2
0
1
2
1
0
1
2
1
0
0
0
2
2
0
0
0
0
0
1
1
0
1
1
0
0
0
2
1
0
2
1
2
2
1
1
0
2
2
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
1
1
2
0
2
1
0
0
0
0
0
1
0
0
0
1
0
0
2
1
0
1
0
2
2
0
0
3
1
0
1
0
2
0
1
2
1
0
0
1
2
0
2
1
0
1
0
0
0
1
0
1
0
0
2
1
0
0
2
0
1
0
0
0
0
1
2
0
0
0
1
0
0
1
0
0
1
0
0
0
2
2
2
2
0
0
0
2
2
0
0
0
0
0
0
1
2
1
0
2
1
1
0
1
0
0
3
1
1
0
0
1
2
0
1
0
1
0
0
2
1
0
0
1
0
0
0
0
1
1
0
0
0
2
1
1
0
0
0
0
1
2
0
0
3
1
0
0
1
0
1
1
0
1
0
1
3
0
2
1
0
0
1
0
1
2
2
1
0
1
1
0
0
0
1
0
0
1
2
0
2
0
2
1
2
2
2
1
0
2
0
0
2
0
1
1
1
0
0
2
0
0
0
2
0
0
0
1
0
0
1
0
0
1
2
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
1
1
0
2
0
0
0
0
1
0
0
0
2
2
0
0
2
2
0
2
2
1
2
0
3
2
1
0
1
0
1
2
0
1
2
0
0
2
2
1
0
2
0
0
1
2
0
0
1
1
0
1
0
1
1
0
1
0
0
0
1
0
1
0
1
1
0
1
0
1
2
1
2
1
0
1
2
1
0
0
2
0
0
0
0
0
0
0
0
1
0
1
2
2
1
2
0
0
0
0
1
2
0
1
0
2
1
0
1
1
0
3
1
0
1
0
0
1
1
1
1
0
0
2
0
0
0
1
1
2
0
0
0
2
0
1
1
0
4
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
2
0
0
1
2
0
1
1
1
0
2
0
0
2
2
0
0
0
0
1
0
2
2
1
0
3
1
0
0
1
1
0
2
0
1
2
0
4
2
2
1
0
0
1
0
0
2
1
0
2
0
0
1
0
0
2
0
0
0
0
0
1
1
0
0
1
1
0
0
0
2
1
0
1
3
2
2
0
0
0
1
1
1
0
2
1
2
2
0
0
2
0
0
0
2
3
0
0
2
0
2
2
0
0
1
0
0
1
1
0
1
0
0
0
2
2
1
1
2
0
0
0
2
2
2
1
1
0
0
1
0
0
0
2
1
0
0
0
2
0
0
2
0
0
0
0
2
1
1
0
0
4
0
2
0
0
1
2
0
1
1
2
1
1
0
0
1
2
0
0
0
0
1
0
0
0
2
0
1
1
1
2
2
0
2
0
1
1
1
1
1
0
0
0
0
0
0
0
0
2
0
0
1
0
2
2
0
0
0
2
2
0
0
2
0
2
0
0
0
0
0
0
1
1
0
1
0
1
1
0
0
0
2
0
0
2
0
0
0
0
0
1
2
0
0
1
0
0
1
2
3
1
2
0
0
0
1
0
0
0
2
0
0
2
1
2
1
1
1
0
2
0
1
0
0
3
3
2
1
1
2
1
2
0
2
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
1
0
2
0
0
0
0
0
0
2
2
2
1
1
1
0
0
0
2
0
2
0
0
0
0
1
0
2
0
1
1
0
0
1
2
0
2
0
1
0
0
2
0
0
1
0
0
2
0
2
0
1
1
0
0
0
2
1
1
1
1
2
1
1
1
0
2
0
2
0
1
2
0
2
1
2
1
0
0
1
0
1
2
0
0
0
0
0
1
0
2
0
2
2
0
0
0
1
0
2
0
0
0
0
1
0
0
3
0
0
0
0
0
0
2
2
2
0
1
2
1
1
0
1
2
0
1
0
0
0
0
0
2
0
0
0
0
1
2
1
1
1
2
0
0
1
4
0
1
0
0
1
0
0
1
0
0
3
0
0
0
2
0
1
0
0
0
2
0
1
2
0
1
0
1
0
0
1
1
0
2
1
1
1
1
0
1
0
0
0
0
0
1
0
0
0
2
1
0
2
0
2
0
0
2
0
0
0
0
2
0
0
0
0
2
1
1
0
0
0
2
2
3
1
0
1
1
0
2
0
1
0
1
1
0
0
1
1
0
0
2
0
0
1
2
1
0
1
0
0
2
0
1
0
2
2
2
0
1
1
0
1
2
2
2
0
2
0
0
2
1
1
2
0
1
1
0
0
1
0
0
2
1
1
0
1
0
0
0
1
0
1
0
3
2
1
1
0
2
0
2
0
1
0
0
0
0
1
2
0
0
0
0
1
1
0
2
0
1
0
0
1
1
0
1
1
2
1
0
2
2
0
1
1
0
0
1
0
0
0
2
2
2
0
0
0
1
0
0
1
0
2
2
2
3
0
1
0
2
0
2
2
2
0
2
0
0
1
1
1
0
0
1
0
1
4
0
1
2
1
0
0
1
1
2
1
2
1
0
0
2
0
1
0
2
0
0
2
1
0
2
2
0
2
2
2
3
1
1
0
1
0
2
1
2
1
2
2
1
0
0
2
1
2
2
1
0
0
0
1
0
1
0
2
2
0
1
0
0
0
0
2
1
0
0
1
2
1
2
5
0
0
0
2
0
1
2
2
0
2
1
0
2
0
0
1
2
1
2
0
1
2
1
3
3
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
1
1
0
2
2
0
1
1
1
0
0
2
0
0
2
0
1
0
0
2
2
1
0
2
0
0
2
0
0
0
1
0
0
0
2
0
2
0
0
2
1
2
0
0
2
0
0
1
1
0
1
2
0
1
0
0
2
1
0
0
0
1
2
0
2
1
0
0
0
0
0
1
1
0
0
0
0
1
2
1
2
0
0
2
0
2
1
0
0
1
0
0
0
0
0
0
1
1
1
1
2
1
2
1
1
2
1
2
0
2
1
0
1
0
2
0
2
1
0
1
0
0
0
1
1
2
1
2
1
0
1
1
0
3
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
2
0
1
1
2
0
0
0
1
2
0
2
2
0
1
0
0
0
2
2
0
0
2
0
1
2
0
2
5
0
0
2
2
2
0
1
0
2
0
1
0
1
1
2
1
0
0
0
1
1
1
0
2
1
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
2
0
0
1
2
0
1
2
1
0
0
0
0
1
0
0
0
2
1
2
1
0
0
0
0
0
0
0
1
1
1
0
0
2
1
0
2
2
2
1
0
2
1
1
1
0
0
0
2
2
0
0
0
0
0
1
4
1
0
0
0
0
0
0
0
0
2
1
0
1
2
2
1
0
1
0
0
0
0
0
2
2
0
1
3
0
0
0
1
0
2
1
1
0
1
2
2
0
0
1
3
0
0
0
0
1
0
2
1
0
2
3
0
0
2
1
0
1
1
1
0
0
0
1
2
0
0
0
2
0
0
3
0
1
0
3
2
0
1
0
1
1
2
2
3
2
1
0
0
0
4
1
0
0
0
1
1
0
1
1
0
1
0
2
1
0
0
0
1
0
1
0
0
0
0
1
2
1
1
0
1
1
0
0
1
0
1
2
0
1
0
1
1
2
0
0
0
1
0
0
1
2
2
0
2
1
2
0
1
2
0
2
2
1
0
1
1
1
0
0
0
2
3
0
2
1
0
0
1
1
2
0
2
2
2
2
0
0
1
2
2
0
1
2
0
1
0
0
2
1
2
2
0
0
1
1
1
2
0
2
2
0
2
0
0
0
2
1
0
2
2
0
2
0
0
1
1
1
2
0
0
1
0
1
1
0
0
0
2
1
1
1
0
1
1
3
1
0
0
1
1
0
1
0
0
1
2
0
2
1
2
0
2
2
0
2
1
0
0
1
2
0
0
5
2
2
1
0
1
1
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
1
0
1
2
1
2
0
0
0
0
0
0
1
0
0
1
1
0
2
2
1
2
1
0
1
0
1
0
0
0
1
0
0
0
0
2
3
2
0
1
2
1
2
1
1
0
2
0
2
2
1
0
0
0
0
2
2
0
0
2
1
1
0
2
0
0
0
2
1
0
0
1
2
0
1
0
2
0
2
0
0
2
2
0
0
1
2
2
0
0
1
1
1
1
0
0
0
0
3
1
0
2
1
0
0
2
0
0
1
1
2
1
0
1
1
1
0
1
0
0
2
2
0
0
0
1
1
1
1
0
1
1
2
0
0
0
0
0
1
1
0
0
1
1
0
0
2
0
1
0
0
1
1
2
1
0
2
0
2
0
1
0
0
2
2
0
2
1
0
0
0
0
0
2
0
1
0
0
1
0
0
2
0
0
1
0
1
0
4
0
0
1
2
0
1
0
0
1
1
2
0
0
1
1
2
1
3
0
2
0
0
1
0
0
2
2
0
1
0
0
0
2
1
1
2
1
2
2
0
0
0
1
3
0
2
0
0
1
0
0
0
1
0
0
0
1
1
0
1
0
2
1
1
0
2
0
0
1
1
1
0
2
2
0
0
1
1
0
0
0
1
0
1
2
1
2
0
0
0
0
0
2
0
1
0
2
0
0
0
2
2
0
0
1
1
0
0
0
0
2
1
1
0
0
0
1
1
2
0
1
1
0
0
0
0
1
0
1
0
0
0
0
1
1
1
0
2
2
1
1
0
0
0
3
0
2
1
0
0
1
2
2
0
2
2
0
0
2
0
0
1
0
2
0
0
2
2
2
1
0
1
2
0
4
1
0
0
0
2
0
0
1
1
1
0
0
0
0
1
0
0
1
1
0
1
1
0
0
1
1
0
0
1
2
2
1
2
1
1
2
1
0
0
0
2
0
1
0
1
0
1
0
2
2
1
1
0
0
0
0
0
0
3
0
1
1
2
1
0
2
1
0
0
2
4
1
0
2
0
0
1
0
2
2
2
1
2
0
0
0
4
0
1
1
1
0
0
0
1
2
0
2
1
0
2
1
0
0
1
0
2
0
1
0
0
0
1
0
1
1
0
0
1
0
0
0
1
2
0
1
1
2
0
0
0
1
0
0
1
1
0
0
1
0
0
3
1
0
0
0
1
1
0
1
2
0
1
0
2
0
0
0
0
0
1
1
0
1
1
2
0
0
0
1
0
1
0
0
0
1
0
0
0
0
3
1
0
2
0
1
0
1
0
1
2
0
0
4
2
1
1
0
0
1
1
2
1
2
0
1
0
2
2
0
0
0
0
0
1
0
0
2
0
2
0
4
0
2
0
0
0
2
0
0
2
1
0
0
1
0
2
1
0
2
0
2
1
2
0
3
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
2
0
0
1
1
1
2
0
0
1
0
1
0
0
1
2
0
1
0
0
1
0
1
1
2
0
3
0
0
0
0
2
1
1
0
2
0
1
1
1
2
0
0
1
0
2
0
1
0
0
0
2
2
1
0
2
1
1
1
0
0
0
0
1
0
0
1
0
0
0
1
2
1
2
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
2
1
2
2
1
0
0
1
2
0
3
0
2
0
2
0
2
1
0
0
0
0
1
2
0
1
0
1
1
1
0
3
2
1
1
0
0
1
2
1
0
2
1
1
2
0
0
2
0
0
0
0
1
0
3
1
1
0
1
1
1
0
2
0
0
0
0
0
0
1
0
0
1
0
0
8
2
1
0
0
1
0
2
1
1
0
0
0
0
0
0
2
1
0
0
2
0
2
0
2
1
1
2
1
0
0
1
0
1
0
0
0
1
0
1
2
2
0
1
1
0
0
3
0
0
1
0
0
1
1
2
0
0
1
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
2
2
1
0
0
2
0
0
0
0
0
2
2
0
0
1
1
0
0
0
1
0
2
2
0
2
0
0
0
0
0
1
0
0
0
0
1
0
1
1
1
1
1
0
0
0
1
0
2
0
0
1
0
0
0
2
0
1
2
2
1
1
1
0
1
1
1
1
0
0
1
0
1
1
1
0
3
0
0
1
0
0
2
0
1
1
0
0
1
1
1
2
2
0
1
1
0
1
0
1
0
1
2
1
2
0
0
0
2
0
0
2
1
2
2
0
1
2
0
2
1
0
0
2
0
1
0
1
2
0
1
1
0
0
1
0
0
1
0
0
0
0
0
2
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
1
2
0
2
0
5
0
0
2
0
0
2
3
0
0
1
0
0
0
1
0
0
1
0
1
2
0
2
1
2
1
0
0
1
2
0
0
2
2
2
0
1
1
0
0
1
0
1
0
1
1
0
1
0
2
0
0
1
0
0
0
0
1
1
0
4
0
0
0
2
1
0
1
0
2
1
3
1
1
0
0
0
1
1
2
1
1
1
0
0
0
0
1
0
0
1
0
2
1
0
0
1
0
1
0
1
0
1
2
0
0
1
0
2
2
1
0
1
0
1
0
0
0
2
0
1
1
0
0
2
0
0
1
0
0
1
1
0
0
0
0
0
2
2
3
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
4
1
0
1
2
1
0
1
1
0
2
1
0
0
1
0
0
2
0
1
1
0
0
1
1
0
0
1
1
0
0
0
1
1
3
0
0
2
1
2
1
0
0
0
1
1
0
2
0
0
0
0
0
0
1
1
0
2
0
1
0
2
1
0
0
0
0
0
0
2
0
2
0
2
2
1
1
2
1
0
3
2
2
0
0
0
1
2
0
0
0
0
0
1
2
2
0
0
5
2
1
1
0
1
0
0
0
0
2
0
0
1
1
2
0
0
2
1
0
0
2
1
3
1
0
1
1
2
0
0
0
3
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
2
1
2
1
2
2
1
0
0
1
1
0
2
1
0
0
0
2
0
2
2
1
1
0
2
1
0
2
0
2
0
0
2
1
0
0
2
0
0
2
1
2
0
0
2
0
1
0
1
1
0
1
1
0
1
1
2
0
1
1
2
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
3
0
2
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
2
4
0
0
2
1
1
1
2
0
0
0
3
1
0
0
0
0
2
0
1
0
0
1
0
1
0
2
0
1
0
0
1
1
0
0
1
0
1
0
1
1
0
2
3
0
1
0
0
1
1
0
1
0
2
0
1
0
0
2
0
3
0
0
2
1
0
1
0
1
1
1
1
1
0
1
0
2
0
2
0
0
2
2
0
1
0
0
1
2
2
1
1
1
0
2
1
2
0
0
1
2
2
1
0
1
0
2
0
1
0
1
0
0
0
0
1
1
0
1
1
2
0
0
0
0
1
2
0
0
2
2
1
2
0
0
2
2
0
1
0
0
2
2
1
1
3
0
1
0
1
0
0
2
0
0
0
1
1
0
1
1
1
2
1
1
1
1
1
2
0
0
1
0
0
1
1
2
0
1
1
1
1
0
0
0
0
0
0
2
0
1
2
2
0
0
0
1
0
2
1
1
0
0
2
0
0
0
1
0
1
1
0
0
2
2
1
0
1
0
1
1
1
0
0
0
0
0
2
0
0
0
0
3
1
2
1
1
0
2
2
0
0
2
0
0
1
0
0
1
0
0
1
2
2
0
1
0
0
2
0
1
0
1
0
0
2
0
0
0
1
0
1
1
0
0
2
2
0
1
0
1
0
0
0
0
2
1
0
0
2
1
2
2
0
0
2
0
0
1
2
0
1
2
0
1
1
0
0
1
0
4
0
2
1
1
1
0
0
0
0
1
0
0
3
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
1
0
1
0
1
0
0
0
2
0
0
1
0
1
0
0
0
1
1
1
2
0
0
2
0
0
0
2
0
0
2
1
0
0
0
0
1
0
0
1
2
0
2
2
1
1
1
1
1
1
1
1
0
1
0
1
1
2
0
1
0
2
1
1
0
0
0
0
0
1
1
1
1
0
0
0
0
0
2
0
1
1
0
2
1
2
1
0
0
0
2
2
2
0
2
0
1
2
2
0
0
1
1
2
0
0
0
1
0
1
0
1
0
2
0
0
2
2
0
1
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
1
2
0
1
1
0
0
0
0
0
1
0
1
0
2
0
0
0
2
2
2
0
2
0
0
1
0
1
0
2
0
1
0
1
2
0
0
0
0
2
1
1
2
1
1
1
2
0
0
1
0
0
2
0
1
0
0
1
0
0
1
0
1
0
0
0
1
0
0
1
1
0
2
1
2
1
2
1
1
0
0
1
2
0
0
2
1
2
2
1
1
0
0
1
0
0
1
2
1
1
0
2
1
1
0
1
3
0
0
3
1
0
0
0
0
0
0
1
4
0
0
2
0
0
0
0
1
0
1
0
0
0
1
0
1
1
0
1
3
0
1
0
2
1
0
0
2
1
0
2
0
1
0
0
1
0
1
1
0
2
0
1
1
0
1
1
1
1
2
0
0
1
1
2
0
1
0
3
1
1
1
0
2
0
3
1
0
0
1
0
0
0
1
0
0
2
1
0
0
0
0
2
0
0
1
1
0
2
2
0
0
1
0
0
1
0
0
1
2
0
2
1
0
0
1
0
0
1
0
0
2
0
0
0
0
1
0
0
1
2
0
1
1
0
0
0
0
0
1
0
2
0
1
0
2
0
0
1
0
1
0
1
0
0
1
1
1
0
2
0
0
1
2
2
0
0
0
2
2
1
1
2
1
0
0
1
1
2
0
2
0
0
1
2
2
3
0
2
1
2
0
1
1
1
0
1
2
4
1
2
0
1
2
3
1
2
0
2
0
2
1
1
1
1
0
0
2
1
0
0
0
0
1
1
0
0
2
0
1
0
0
2
0
1
0
1
1
0
0
1
0
1
0
0
0
3
0
1
0
0
1
0
1
2
2
2
0
2
0
1
2
2
2
0
0
0
1
1
0
1
0
0
1
2
2
0
1
0
4
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
1
1
1
0
0
1
2
0
0
0
0
0
2
0
1
0
2
1
0
2
2
2
1
0
0
0
2
1
0
0
0
0
2
1
0
2
1
0
0
0
0
1
0
1
1
2
1
1
0
0
1
2
0
0
1
3
0
0
0
0
2
0
0
0
1
1
0
1
2
2
0
0
1
0
0
1
0
0
1
0
0
1
2
2
0
0
0
0
0
1
2
2
2
0
0
1
0
0
0
0
0
1
1
1
1
0
1
1
1
0
2
1
0
0
0
2
1
0
1
4
0
2
2
1
0
0
1
2
0
1
1
1
1
0
1
1
0
1
1
0
0
1
0
2
2
0
1
1
0
2
0
0
0
1
1
0
0
2
2
0
2
1
1
0
2
0
0
0
0
2
1
0
0
0
0
1
1
0
0
0
1
0
3
0
1
1
1
0
0
2
0
2
1
0
0
1
0
0
0
1
0
0
2
0
0
2
0
1
2
1
0
0
1
1
0
1
2
0
0
1
3
1
0
0
1
0
0
0
0
2
0
0
1
1
1
0
0
0
0
0
1
2
2
0
0
0
0
0
1
0
2
1
0
0
1
2
2
0
1
0
2
2
0
1
0
0
0
2
0
0
0
1
1
0
1
0
0
2
0
1
0
0
1
2
1
1
1
2
0
0
1
1
0
1
0
2
1
1
0
1
0
1
1
0
0
0
0
0
1
0
0
2
2
0
0
2
0
2
0
2
2
0
1
1
2
0
0
0
0
2
2
1
1
0
3
1
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
2
2
0
0
1
0
2
2
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
2
1
0
0
2
1
0
1
0
0
3
0
1
0
1
3
1
2
0
0
0
2
2
1
0
1
1
0
1
0
1
0
0
0
1
0
1
7
0
0
1
0
0
2
1
0
1
1
1
0
0
1
1
1
0
0
0
0
0
2
1
3
0
2
2
0
2
0
0
1
1
0
1
0
2
0
1
1
1
0
0
2
0
0
0
0
1
1
0
1
0
0
1
1
1
1
0
1
0
1
3
0
1
0
1
0
0
0
2
0
2
0
0
1
3
1
0
1
0
1
0
0
0
0
2
0
1
1
0
0
0
0
1
1
0
0
0
0
2
1
0
1
1
1
1
0
0
0
2
0
0
0
0
1
0
1
2
1
2
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
1
1
1
0
0
1
1
1
0
0
1
0
2
1
0
2
0
0
1
0
2
0
0
1
0
1
2
0
0
0
1
0
1
1
0
0
0
0
1
2
2
0
0
2
1
0
2
2
0
0
1
0
0
0
1
3
0
1
1
0
0
1
1
0
1
2
2
0
1
0
0
0
1
2
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
2
0
2
0
1
0
1
0
0
0
2
1
0
0
1
0
0
1
0
1
1
0
0
0
2
1
2
1
1
1
0
0
0
2
0
0
0
0
0
1
0
1
0
2
1
0
0
0
0
2
1
2
3
2
1
0
1
0
1
0
0
0
2
0
0
0
0
0
1
2
0
2
1
2
3
0
2
0
0
0
1
0
0
1
1
0
0
0
0
1
1
1
1
1
2
1
1
1
1
0
2
1
2
0
0
0
1
0
1
2
0
1
0
1
1
0
2
1
0
1
1
1
0
1
1
1
1
2
1
2
2
1
2
3
2
4
0
1
0
0
0
2
0
1
1
1
0
0
4
0
0
1
2
2
0
1
0
0
2
0
0
2
0
4
0
0
0
1
1
0
4
0
0
1
0
0
1
1
0
0
1
0
1
1
1
1
1
0
1
0
1
0
0
0
0
1
0
0
1
2
2
2
1
2
0
0
1
0
2
1
2
0
0
0
0
1
1
0
0
1
0
0
2
1
1
2
0
1
2
0
2
0
0
0
0
2
0
1
1
1
0
2
2
0
0
2
0
0
0
1
2
0
1
0
0
1
1
0
0
0
2
1
0
1
1
1
0
1
1
1
0
2
1
2
3
2
1
1
0
0
0
0
1
1
0
1
1
1
1
1
2
1
0
1
2
1
1
1
1
1
1
1
2
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
2
2
1
0
1
1
0
1
1
0
0
1
1
2
2
1
2
2
0
1
2
0
1
0
1
2
0
0
2
0
0
2
1
0
1
2
0
1
0
0
0
0
1
1
0
1
1
1
1
0
1
1
2
2
0
1
1
0
1
2
0
2
0
0
0
0
1
2
0
0
0
0
0
2
2
2
2
0
1
0
1
1
0
0
1
0
2
1
2
0
0
1
0
2
1
0
1
1
2
0
2
1
2
0
0
0
1
0
2
2
0
2
2
1
0
1
3
1
0
2
0
0
0
0
0
0
2
1
1
0
0
3
0
0
1
0
0
0
1
2
0
0
2
1
0
1
3
0
1
1
1
0
2
1
0
0
1
3
0
1
0
0
2
2
0
0
0
4
0
1
0
0
0
1
0
3
2
1
2
0
1
1
1
0
0
1
0
0
1
0
1
0
1
2
1
0
3
0
0
2
0
0
0
1
1
0
0
0
1
0
0
2
0
1
0
1
0
0
1
2
0
1
0
0
0
0
1
2
1
0
0
0
2
1
1
5
0
1
0
1
2
2
0
2
0
0
0
1
0
1
0
1
0
2
0
2
2
0
0
0
1
2
0
1
0
0
0
1
1
2
1
0
1
0
1
2
0
0
0
1
1
0
0
2
2
2
0
1
2
1
0
2
0
0
0
2
1
2
1
0
0
2
0
2
0
0
0
0
0
0
0
2
2
1
2
0
1
2
0
0
1
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
1
0
0
1
2
0
0
0
1
1
0
1
0
0
1
2
2
1
1
0
1
0
2
1
0
0
1
0
0
1
1
0
0
3
0
1
1
0
2
0
2
1
0
1
2
0
2
0
0
2
0
0
1
0
1
1
1
0
1
1
0
1
2
1
0
1
2
2
0
1
2
1
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
2
2
1
0
2
0
0
0
0
0
0
2
3
0
2
1
0
1
1
0
0
2
2
1
0
0
0
2
2
0
5
0
0
2
1
1
0
1
1
0
0
1
0
0
1
0
2
0
2
2
0
1
0
1
0
0
1
0
2
0
1
0
2
2
0
0
2
1
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
1
1
0
1
2
1
0
0
1
0
0
2
1
0
1
1
2
1
1
0
0
0
1
2
1
0
0
2
2
2
2
1
1
0
0
0
0
0
2
1
0
2
0
0
2
0
0
2
2
1
1
1
0
0
1
1
0
0
2
2
0
0
0
0
0
0
0
1
0
1
0
3
0
2
2
2
0
0
0
0
0
2
0
6
0
0
2
1
0
0
0
1
0
2
0
0
0
0
0
1
0
1
3
0
0
0
0
2
1
2
0
2
1
0
0
0
2
0
0
2
1
0
0
1
0
2
0
1
0
0
1
2
2
0
0
2
2
0
1
0
6
0
0
3
0
0
1
1
1
3
0
1
2
2
0
1
1
1
0
1
0
2
2
1
0
0
2
0
0
0
1
2
2
0
0
1
0
1
0
2
2
0
0
1
0
0
2
1
2
0
0
0
2
1
0
1
0
0
0
1
2
0
0
0
2
4
0
0
0
1
0
1
1
0
0
1
0
0
1
0
0
1
1
0
2
0
0
0
0
2
2
1
2
1
1
0
0
2
2
1
1
0
0
1
0
0
2
1
0
0
2
0
1
1
0
3
0
1
1
0
0
1
0
3
0
0
1
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
1
2
1
0
1
1
0
1
0
1
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
1
1
0
2
2
2
0
2
1
0
0
0
1
0
0
1
0
1
1
0
1
1
0
2
1
0
0
1
0
2
0
0
0
0
1
1
4
2
2
2
2
0
2
0
0
0
2
0
0
2
0
0
1
0
1
0
2
1
1
0
1
0
1
0
0
0
2
2
1
2
0
2
1
0
2
2
0
2
1
0
0
0
0
1
0
0
0
1
1
0
1
0
0
1
0
1
2
1
3
0
0
0
2
2
2
3
2
2
0
1
0
0
0
2
0
2
1
0
0
0
1
2
2
1
0
0
2
1
2
1
2
1
0
0
0
1
0
2
1
0
0
0
2
1
1
0
1
1
0
1
1
1
1
1
0
0
1
0
1
0
0
1
1
1
0
1
0
3
0
3
1
0
1
2
0
1
0
0
0
1
0
2
0
1
0
2
1
2
0
1
2
1
1
1
0
2
0
0
2
0
0
2
0
1
0
2
2
0
0
0
0
1
2
1
1
1
1
0
0
0
0
0
0
0
1
0
3
1
2
1
0
0
2
1
0
0
1
0
0
0
0
2
0
1
0
0
1
0
2
0
2
0
0
0
0
1
1
2
1
1
1
0
1
1
0
0
0
0
0
0
2
0
0
0
1
0
0
2
3
0
1
0
0
2
1
1
1
2
1
0
0
0
1
1
1
0
1
0
0
2
2
2
2
1
0
2
1
2
1
2
0
0
1
1
1
1
0
0
2
0
1
1
1
1
0
2
2
0
1
0
2
0
0
3
2
2
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
2
0
0
0
1
1
0
3
2
0
1
0
1
2
1
0
0
0
1
1
1
2
0
2
0
0
1
1
1
0
0
0
0
1
2
1
2
2
0
1
1
0
0
1
0
0
1
0
0
0
2
0
0
0
0
2
0
0
1
0
0
1
2
2
2
2
2
1
0
8
2
1
1
1
0
0
2
1
0
0
1
0
1
1
0
1
0
1
1
1
1
0
1
0
0
2
0
2
1
0
0
0
1
1
3
0
1
0
2
0
0
1
0
2
0
0
0
0
0
1
1
0
0
2
0
0
2
0
1
0
0
0
1
0
1
2
2
0
0
1
0
0
2
0
1
1
0
0
1
0
0
1
0
1
0
1
0
1
0
0
1
1
1
1
0
0
2
2
0
0
2
2
0
0
2
0
1
0
0
0
1
2
0
0
2
0
0
1
1
1
0
0
1
1
1
1
2
2
1
2
0
2
1
1
0
0
2
0
1
0
1
0
0
0
0
1
1
1
2
0
0
0
0
0
0
1
1
0
0
2
1
1
1
1
1
0
0
0
1
1
0
3
0
0
0
1
0
1
2
4
2
0
0
0
0
2
1
0
1
0
0
1
0
0
2
1
0
2
1
1
0
0
0
0
0
0
2
0
2
1
2
1
0
0
3
1
0
1
0
0
1
0
1
1
0
1
2
1
2
0
1
1
1
2
1
1
0
1
0
0
2
0
0
2
2
0
0
0
0
2
2
1
0
1
0
1
2
0
2
2
0
0
0
2
1
0
0
3
0
0
0
0
0
0
1
1
0
0
0
0
1
0
2
1
0
0
0
0
1
1
1
1
1
2
2
0
0
0
0
1
2
0
1
0
1
1
0
1
0
1
1
0
2
1
0
0
0
1
1
1
0
0
0
0
3
4
2
0
2
0
0
1
0
3
0
0
0
2
0
1
0
0
0
1
1
0
2
1
0
2
0
2
3
1
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
2
1
2
0
0
2
0
0
0
1
0
0
2
1
0
1
0
0
0
1
1
1
0
2
1
0
0
1
0
1
0
0
0
2
0
1
2
2
2
0
2
1
0
1
1
0
1
0
2
1
0
0
0
2
1
1
0
0
0
1
0
1
1
0
2
0
0
1
2
0
1
2
3
0
0
4
1
1
0
0
0
0
3
1
1
0
0
0
0
0
0
2
0
2
1
1
1
0
0
2
0
1
0
0
1
1
2
1
0
2
0
1
0
0
0
0
2
0
1
1
1
2
0
0
1
0
1
1
0
0
1
0
2
0
0
0
2
0
0
0
2
0
0
0
2
3
1
2
0
2
1
0
2
1
0
0
0
1
0
2
0
0
2
1
0
0
1
2
0
1
0
0
2
2
1
1
0
0
2
0
1
2
1
1
0
2
0
2
0
0
2
2
0
2
2
0
0
1
1
0
0
0
3
1
0
2
2
0
1
2
1
2
2
0
0
0
2
2
2
1
0
0
2
0
0
2
2
0
2
1
2
1
0
0
0
1
1
1
0
0
0
0
0
1
1
0
2
0
0
2
0
2
0
0
2
3
2
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
1
0
0
1
2
1
1
0
0
0
1
2
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
1
1
1
0
1
0
1
1
0
0
0
1
0
1
1
0
1
0
2
0
0
2
2
2
3
0
0
1
2
0
1
2
1
0
0
0
2
0
2
0
0
0
0
1
2
1
0
1
1
0
0
2
1
0
0
0
1
1
1
1
1
0
0
0
0
0
1
2
2
3
2
1
2
2
1
0
2
0
1
0
0
3
0
1
0
2
1
1
0
2
0
0
1
1
2
1
0
0
1
0
2
1
1
0
0
0
2
0
0
0
0
1
0
0
2
1
0
1
1
1
0
0
0
1
1
0
0
0
2
0
1
0
0
0
1
2
0
0
0
0
1
0
0
0
1
2
1
1
2
1
2
4
0
1
2
0
1
1
2
0
1
0
3
0
0
0
0
0
1
0
0
2
0
0
2
1
0
0
1
0
2
0
0
0
0
2
0
0
1
0
1
2
0
0
2
1
2
2
1
1
0
2
2
0
1
2
0
1
4
2
1
0
0
2
0
2
2
0
1
0
1
0
0
0
1
2
0
0
2
0
0
2
0
1
2
0
0
0
1
0
2
2
1
1
2
0
0
0
1
2
1
1
0
0
0
0
1
1
2
1
0
2
0
0
1
2
1
1
0
0
0
1
0
2
2
1
0
1
0
0
0
1
1
0
1
2
0
1
1
2
0
2
2
1
1
1
1
1
0
0
1
0
0
0
0
1
2
2
0
1
0
2
1
0
1
1
2
2
0
1
2
0
0
2
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
2
1
2
0
1
0
0
1
0
2
0
1
0
1
2
2
1
0
3
1
1
1
0
1
1
0
1
0
3
0
2
0
0
0
0
2
2
0
1
0
1
0
1
0
0
1
0
3
2
0
0
2
1
1
2
0
0
0
0
0
0
0
1
3
2
0
2
1
1
0
0
2
1
1
1
0
1
1
0
0
1
1
1
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
2
0
1
2
1
0
0
0
2
0
1
0
0
1
1
0
1
2
0
2
1
0
2
1
0
0
0
0
0
1
0
2
0
0
0
0
3
1
1
2
1
2
2
0
1
1
2
0
0
0
0
2
0
0
0
2
1
0
2
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
1
2
2
0
0
0
0
1
1
2
0
1
2
2
0
0
2
0
1
0
0
0
1
0
1
0
0
1
2
1
0
1
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
2
2
2
0
0
0
0
2
1
1
1
0
0
0
2
2
2
1
2
2
0
1
0
0
0
2
0
1
0
2
1
2
1
1
0
0
0
1
1
0
1
2
1
0
1
0
1
0
0
2
0
2
0
0
0
3
1
0
0
1
1
0
1
0
0
1
1
0
2
0
1
1
1
0
1
1
0
0
1
0
0
0
2
1
1
0
0
0
2
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
1
0
2
0
3
0
0
0
1
1
0
1
0
0
2
1
1
0
0
0
3
1
0
0
2
0
1
2
2
2
2
1
0
2
1
0
0
0
1
1
0
0
3
0
0
0
2
1
0
2
2
1
0
1
1
0
0
2
0
0
0
1
1
0
2
0
0
0
0
0
2
0
1
0
0
1
2
0
0
0
1
1
1
0
0
0
0
0
0
0
2
1
2
2
1
2
2
0
0
0
1
2
0
1
0
0
2
0
0
0
2
1
0
1
3
3
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
1
2
0
0
1
0
1
1
1
0
0
2
0
1
2
2
2
2
0
1
2
2
1
1
4
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
1
1
0
0
0
2
0
0
2
2
2
0
1
2
0
2
0
2
1
0
1
0
0
1
0
0
1
0
0
0
0
1
2
2
1
0
0
1
0
1
1
1
1
0
2
0
0
0
1
2
3
2
0
0
0
1
1
1
1
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
2
1
2
0
0
1
0
0
1
0
2
2
0
0
0
0
0
2
2
1
2
0
2
1
0
0
0
0
0
2
0
2
0
0
0
1
0
2
2
0
1
0
0
0
1
1
0
1
0
0
1
1
1
0
0
1
1
0
0
1
2
2
1
0
1
0
0
0
0
1
0
2
1
0
1
0
1
1
0
2
0
1
2
2
0
0
0
0
0
0
1
0
3
0
0
2
0
0
2
1
1
1
0
2
0
0
1
2
2
2
0
0
2
2
0
0
2
1
0
1
0
2
0
2
0
2
2
1
0
0
0
1
2
1
2
1
1
0
0
1
0
0
2
0
1
1
1
2
2
0
0
0
1
3
0
1
0
1
2
1
0
0
1
1
0
0
2
6
0
1
1
0
0
4
2
1
2
0
1
1
3
1
1
2
1
2
0
1
0
0
0
0
1
1
2
0
2
3
2
0
2
2
2
0
0
0
0
0
0
2
2
2
2
0
0
0
0
0
2
0
0
1
0
2
1
1
0
2
0
1
1
1
0
0
0
1
0
0
0
0
2
2
2
1
0
1
1
1
1
1
0
0
1
0
2
0
0
2
0
1
0
0
1
1
0
0
0
0
2
0
0
1
0
1
0
0
1
0
0
2
0
2
1
0
0
1
1
0
1
1
0
0
2
1
0
1
0
0
0
2
0
1
1
0
1
0
0
0
1
1
1
2
1
0
0
0
0
2
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
2
1
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
1
0
4
1
1
0
0
1
0
0
0
0
0
1
2
1
1
1
1
0
0
0
0
0
0
0
2
2
0
0
1
0
2
1
1
0
0
1
0
1
0
2
0
1
1
2
0
1
1
2
0
0
1
0
2
1
1
1
7
2
0
0
1
1
2
0
0
0
1
2
0
0
0
0
2
0
2
0
2
0
1
1
1
0
1
0
1
0
0
0
1
1
0
1
0
0
0
1
0
2
0
0
2
1
0
2
0
0
1
0
1
0
0
1
2
1
2
1
1
0
2
0
1
3
0
1
2
0
0
0
3
1
0
2
0
0
1
0
2
0
2
0
2
1
2
0
1
1
0
2
0
2
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
1
1
0
2
2
0
1
2
2
2
2
1
0
0
1
0
1
0
1
0
0
0
1
0
1
2
2
0
0
0
0
1
5
0
1
3
0
2
1
0
0
1
0
0
0
0
1
1
1
0
2
0
0
1
0
2
0
0
1
0
1
0
0
1
0
1
1
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
1
0
0
2
0
1
1
1
1
2
0
2
0
1
1
0
1
3
1
0
0
2
0
0
0
1
2
0
2
0
1
1
0
0
0
0
2
1
0
1
0
1
0
0
0
0
0
0
2
0
1
1
0
2
0
2
1
0
1
1
0
0
0
1
0
2
0
0
1
0
1
1
1
2
1
1
2
1
0
0
1
0
0
0
1
1
1
0
1
0
2
1
2
0
1
0
0
0
1
2
1
1
1
0
0
1
0
1
0
0
2
0
2
0
0
2
2
0
0
0
1
2
1
0
0
0
0
0
2
1
0
2
2
0
0
1
2
2
0
1
0
1
1
0
0
0
1
1
0
1
1
2
0
0
0
0
0
0
0
2
2
1
0
1
0
2
1
0
0
1
0
0
1
0
0
1
1
1
0
1
2
0
2
0
0
0
1
2
1
1
2
0
2
0
2
1
0
0
0
1
2
1
2
0
1
2
1
0
1
4
0
1
0
1
0
2
0
0
3
2
0
1
0
2
2
0
0
0
0
0
0
0
1
0
0
2
2
2
2
1
1
1
0
0
0
1
0
2
0
2
0
0
2
2
0
2
1
0
1
2
0
0
1
0
1
1
2
1
3
0
0
0
1
1
0
0
0
1
1
0
2
0
0
2
0
0
1
1
0
1
1
1
1
0
2
0
2
1
1
2
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
1
0
0
0
2
1
0
0
1
0
0
0
2
2
0
1
2
0
0
0
0
1
1
2
2
0
2
1
0
2
1
0
0
0
2
0
1
2
0
2
1
0
0
0
2
2
0
2
0
0
0
0
0
0
1
1
2
0
0
2
1
0
1
0
2
0
1
1
0
0
2
2
1
0
1
0
2
2
2
1
0
1
2
0
3
0
0
1
1
2
1
0
0
0
0
2
0
1
1
0
0
0
1
0
2
1
2
2
3
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
1
1
1
1
1
0
1
0
2
1
0
1
0
0
0
0
1
1
2
1
2
1
2
1
0
2
2
0
0
0
2
0
1
3
2
3
0
3
1
1
2
0
0
3
3
0
2
0
0
2
2
0
1
0
2
2
1
0
0
1
2
1
1
0
1
0
0
5
0
0
1
0
0
2
1
0
0
2
0
1
0
0
1
1
1
0
1
1
1
0
1
0
0
1
0
0
0
0
0
2
0
0
1
1
2
2
0
1
0
2
0
2
2
0
0
2
0
2
0
1
2
0
2
0
0
0
1
0
0
1
1
1
2
2
2
0
0
0
0
0
0
0
2
2
1
0
0
8
0
0
2
0
0
1
2
0
1
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
2
0
0
1
2
0
1
0
0
0
0
0
0
1
0
2
0
0
1
1
1
1
0
0
0
0
2
0
0
1
0
1
1
1
3
1
2
0
1
1
2
2
4
1
4
1
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
1
1
1
1
0
1
0
0
0
0
0
1
1
2
0
0
1
0
2
0
0
0
0
0
0
0
0
2
1
3
1
0
1
1
0
1
0
0
0
0
2
0
0
1
0
0
2
2
2
2
0
0
1
3
1
1
2
2
1
0
1
2
0
1
1
0
0
1
0
1
0
1
2
0
1
2
2
0
1
0
0
0
1
0
0
0
2
0
1
0
2
0
0
1
1
2
1
1
3
0
0
1
1
0
1
2
2
0
0
2
1
0
1
0
0
3
2
1
0
0
2
1
0
0
0
1
2
0
1
2
0
0
2
2
2
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
1
0
0
0
2
2
0
0
0
0
1
1
0
0
0
2
1
0
1
0
0
2
1
2
0
0
2
1
1
3
2
2
0
1
0
2
0
3
2
0
0
0
2
0
2
0
0
2
1
0
2
1
0
2
0
0
1
0
1
0
0
0
0
0
2
1
0
3
0
2
0
1
0
0
0
1
0
2
2
0
1
0
5
2
0
1
0
1
1
0
1
0
2
0
1
0
2
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
1
2
0
1
0
1
1
0
1
0
0
1
0
0
1
2
2
0
1
0
2
0
1
0
2
0
1
2
0
0
1
0
2
1
0
0
1
1
1
0
0
0
16
0
0
0
1
0
2
0
2
0
0
2
0
0
1
1
0
0
1
2
0
0
2
1
1
2
1
1
2
1
0
0
1
0
0
1
1
1
2
1
1
2
0
1
0
2
1
0
0
0
0
0
2
0
0
0
0
2
0
2
0
3
1
0
1
0
0
0
1
2
1
0
0
1
2
0
1
1
1
1
1
2
0
0
0
1
2
0
2
2
2
1
0
1
2
2
0
0
0
0
0
0
1
0
2
0
2
3
0
2
0
1
0
1
1
0
0
1
0
3
0
1
0
2
1
2
0
2
0
1
1
0
2
0
1
0
0
1
3
0
0
1
2
0
1
2
0
2
2
2
0
0
1
2
2
0
0
1
0
0
1
0
0
0
2
0
1
1
0
0
0
1
2
2
0
1
1
0
2
1
0
0
0
0
0
0
0
0
1
1
0
0
2
0
1
1
0
0
0
0
2
0
0
0
2
0
2
0
0
1
2
1
0
2
0
0
2
0
2
2
2
1
0
0
1
0
0
3
0
0
1
0
0
0
0
0
0
0
0
1
1
5
0
2
0
2
1
0
0
2
1
2
0
0
1
2
0
0
1
1
1
1
0
0
0
1
1
2
0
1
2
1
0
2
1
0
2
0
0
2
2
0
2
0
0
0
0
0
2
2
1
1
0
2
2
0
1
1
2
2
0
0
1
0
1
0
1
2
0
1
2
2
0
2
0
0
0
1
2
2
1
2
0
2
0
2
4
0
1
0
1
0
0
0
0
0
0
2
0
1
2
0
0
1
0
0
2
1
1
2
0
0
0
2
1
0
2
2
2
0
1
1
0
0
2
0
2
0
1
0
0
0
0
1
3
2
1
0
0
0
0
2
2
0
2
1
1
1
0
0
2
3
0
0
2
0
1
0
2
0
0
0
2
1
1
1
0
2
1
1
1
2
2
0
1
0
1
2
2
1
1
0
1
0
0
2
1
1
0
1
3
1
1
0
0
1
2
1
0
1
0
2
2
0
0
1
1
2
2
2
0
0
0
0
0
0
0
4
1
0
0
0
0
1
0
0
2
0
1
0
1
0
2
1
0
0
1
1
0
1
1
2
1
0
0
0
0
2
0
1
2
2
1
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
2
1
0
0
1
0
1
0
1
0
0
1
2
1
0
1
0
1
0
2
0
2
0
2
1
1
2
2
4
1
0
1
2
0
0
0
2
0
2
0
0
2
1
0
0
2
0
3
1
1
1
2
1
0
2
2
1
0
0
2
0
2
1
0
0
0
1
1
2
1
2
1
0
0
1
0
0
0
0
0
1
0
1
0
0
1
1
2
0
1
0
2
0
4
0
0
2
0
2
0
2
1
0
0
0
1
1
0
0
4
0
0
0
1
1
0
1
1
0
2
2
0
0
0
0
1
0
0
0
1
1
0
1
1
0
0
0
2
0
1
0
4
0
0
0
0
1
0
0
1
2
1
0
2
1
0
1
0
1
1
1
0
0
1
0
2
1
0
0
2
0
1
0
0
1
1
0
0
0
1
2
0
2
0
1
1
2
1
1
2
0
1
0
0
2
0
2
1
1
0
0
0
0
2
0
2
1
1
0
1
1
1
1
3
0
2
2
0
0
2
0
1
1
0
0
1
1
2
2
0
2
0
1
1
0
2
2
2
2
0
0
1
3
0
2
0
0
1
0
1
0
0
1
2
0
1
1
2
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
3
2
1
2
0
0
0
2
0
1
2
0
3
0
0
0
1
0
0
1
0
1
0
2
0
0
0
0
0
1
0
0
1
1
0
2
3
0
0
0
1
0
2
2
0
2
0
1
0
0
0
0
1
1
2
1
0
0
0
0
1
2
0
1
0
0
1
0
0
0
1
1
0
0
7
0
0
0
1
1
0
1
1
0
4
0
0
0
2
0
1
1
1
1
2
1
0
2
0
1
1
3
2
1
2
2
1
0
1
3
2
1
0
1
1
2
2
2
1
0
2
0
0
0
2
2
0
1
0
0
0
2
2
0
0
0
3
1
1
1
2
0
0
1
0
2
2
0
1
1
2
1
0
1
0
0
2
2
0
0
0
1
0
0
2
0
1
0
2
2
2
1
1
0
0
1
0
0
1
4
0
0
0
1
2
1
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
1
1
0
2
2
1
0
1
0
0
0
0
0
2
0
0
1
1
0
0
0
1
1
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
2
1
1
0
1
0
1
1
1
2
0
3
0
1
0
0
2
1
2
0
0
0
0
0
1
1
2
0
2
1
0
1
2
2
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
2
2
1
3
1
0
1
0
0
0
2
0
0
0
0
2
0
0
0
2
4
2
0
3
1
0
2
0
0
0
0
0
1
2
1
1
1
1
1
1
0
0
0
0
1
1
0
1
2
1
0
0
2
0
0
1
0
2
2
2
0
0
0
1
1
2
1
1
0
1
0
0
0
1
0
2
1
0
0
2
1
2
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
2
0
2
0
0
1
0
2
0
2
0
1
2
2
0
0
0
0
0
1
1
1
1
0
1
1
2
1
2
1
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
1
2
0
0
0
3
0
0
2
0
2
1
0
3
1
2
0
1
0
2
2
0
1
2
2
1
0
0
1
0
0
1
1
0
2
2
0
1
0
2
0
0
0
1
0
1
1
0
1
0
0
3
0
0
2
0
1
0
0
0
0
1
0
0
2
1
2
0
1
1
1
0
0
0
3
0
0
2
0
0
0
2
2
1
2
0
3
0
0
0
1
0
0
0
1
2
1
2
0
0
2
0
0
1
2
1
1
2
0
1
0
2
0
0
1
1
0
1
0
0
0
1
0
1
1
0
1
0
2
2
0
1
2
0
0
0
2
2
1
0
0
1
1
0
0
2
0
0
1
2
0
0
2
1
2
2
0
2
1
1
0
0
0
2
1
0
0
0
0
0
0
0
0
1
1
0
2
2
1
2
1
0
0
1
2
2
0
0
1
1
1
0
1
0
2
1
1
1
1
1
0
2
2
2
1
1
0
0
1
1
0
2
0
0
0
2
0
0
1
2
0
0
0
1
0
3
0
0
2
0
0
0
0
0
0
0
1
1
1
1
0
0
2
0
2
2
2
0
0
0
1
1
0
0
1
1
4
0
0
1
0
2
2
1
0
0
1
0
0
0
0
0
1
0
0
0
1
1
1
0
2
0
0
0
1
1
1
1
0
1
0
2
0
2
1
1
2
1
0
1
0
0
1
2
0
1
4
2
0
0
0
1
0
2
0
0
0
2
0
0
0
1
1
0
2
0
0
0
1
0
0
1
1
0
0
1
1
2
2
0
1
2
1
1
0
1
1
2
0
2
0
1
0
0
0
0
1
0
0
1
0
2
0
0
1
0
1
2
4
0
2
0
2
1
0
0
1
0
0
1
2
0
0
1
1
0
2
0
0
0
0
0
0
1
2
0
0
0
0
2
2
0
1
2
0
0
3
1
1
0
0
1
1
0
1
2
0
1
0
0
0
0
0
1
0
1
0
0
1
2
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
2
1
1
0
0
6
3
2
2
0
2
1
1
1
0
0
0
0
0
0
1
0
2
1
0
0
0
1
0
0
1
2
1
1
1
0
1
1
2
0
2
1
0
0
1
2
0
1
1
0
0
2
1
0
0
1
0
0
1
1
0
0
0
0
0
1
2
0
1
2
2
0
1
2
0
0
1
2
1
0
0
4
0
0
0
0
1
0
2
1
0
0
2
0
1
0
2
0
1
1
1
0
0
1
1
2
1
0
2
1
1
0
0
2
0
1
0
1
3
0
0
1
0
0
0
0
0
1
2
2
3
2
0
2
2
0
2
0
0
2
1
1
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
3
0
1
1
2
1
0
1
0
2
2
2
0
1
0
1
1
2
1
1
1
0
1
0
1
0
2
0
0
2
0
0
0
1
1
0
0
2
0
0
0
0
2
0
0
2
0
0
0
1
0
0
2
0
2
0
0
4
0
1
1
1
1
0
0
0
0
1
0
2
1
1
0
0
2
2
0
0
3
2
0
0
1
0
1
0
1
1
2
1
5
1
1
0
2
0
0
2
1
0
2
2
0
2
2
0
0
0
0
0
0
1
2
0
0
1
0
0
2
0
2
0
0
1
3
0
0
1
0
2
1
2
0
0
0
0
1
1
0
0
0
1
1
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
1
0
0
2
2
0
0
0
0
0
0
1
1
0
2
0
0
0
0
2
2
1
0
2
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
1
0
2
0
2
0
0
0
1
1
0
1
1
0
1
1
0
1
2
1
2
0
0
1
0
1
0
1
1
1
1
2
0
1
0
2
0
1
1
2
1
1
1
0
1
1
0
0
0
1
2
0
1
0
0
3
2
2
1
2
0
0
0
1
2
2
0
0
0
1
2
1
0
0
1
0
0
0
0
1
0
2
2
1
0
2
0
1
0
1
0
0
0
2
2
1
0
1
2
0
0
1
1
0
0
1
0
2
2
0
1
1
0
2
0
1
2
1
1
0
0
0
2
0
2
1
2
0
0
0
0
0
0
1
1
2
0
1
0
1
2
0
1
1
0
0
0
0
0
2
1
1
2
3
0
0
0
1
0
0
0
0
2
1
0
1
0
0
1
1
0
2
0
0
0
2
1
1
0
0
0
2
0
1
0
0
1
0
1
0
2
1
0
0
2
1
0
0
0
0
1
0
2
1
0
1
0
2
1
0
1
2
1
1
1
2
0
0
0
1
2
1
0
1
2
2
1
2
0
2
1
1
2
0
0
1
0
2
0
1
0
1
0
0
0
0
1
0
0
0
2
0
2
2
0
1
0
3
0
1
2
1
2
0
2
2
1
0
1
0
0
0
2
2
2
2
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
1
0
1
2
1
0
2
1
0
1
1
0
0
1
2
1
1
0
1
2
0
3
2
3
1
0
0
0
0
0
1
1
0
0
1
1
0
0
0
2
2
1
1
1
1
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
2
1
0
3
1
1
2
1
0
1
1
2
0
1
0
0
0
1
1
1
0
2
1
1
2
1
0
1
2
0
1
0
2
1
0
1
1
1
0
1
0
0
0
0
0
1
0
1
0
2
1
0
1
0
1
1
2
1
0
0
0
2
0
1
1
0
1
0
2
0
0
0
0
0
0
1
2
2
1
2
0
0
0
0
1
0
0
0
1
0
2
2
0
0
1
1
0
0
0
0
2
2
1
1
0
0
1
1
2
2
1
1
1
2
0
1
1
1
1
0
0
1
0
0
0
1
0
3
0
0
0
4
2
0
1
0
0
0
0
0
0
2
1
0
0
0
2
2
1
1
2
0
0
1
0
1
0
0
0
2
2
0
2
2
1
1
0
1
1
2
0
0
0
1
2
2
0
2
2
0
2
0
1
0
1
0
0
1
1
0
2
0
2
0
0
1
0
1
2
2
2
1
2
0
1
0
1
2
0
1
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
3
0
1
0
0
1
0
1
2
2
2
1
1
1
1
3
0
2
0
1
0
0
1
0
0
0
1
0
2
1
0
0
0
2
2
1
0
0
0
2
0
0
2
0
2
0
0
0
0
1
0
2
1
0
0
2
0
2
1
0
1
0
1
0
0
0
0
0
1
0
0
2
2
1
1
0
0
1
1
1
0
0
0
0
0
1
0
1
2
0
1
0
2
2
2
0
1
1
3
1
0
2
0
1
0
1
1
1
0
0
0
0
2
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
6
1
2
0
1
0
0
0
2
1
0
2
2
0
0
2
0
1
0
1
2
2
0
2
2
0
0
2
0
2
1
0
0
0
0
1
2
2
0
1
0
0
1
1
1
0
0
0
1
1
1
3
0
0
0
1
0
2
1
2
0
0
2
0
0
0
2
1
0
0
2
2
2
1
0
0
0
0
0
1
2
2
0
0
0
0
0
2
0
2
1
0
1
0
0
3
0
0
0
1
1
2
2
0
1
2
0
0
0
0
1
0
0
0
1
2
1
0
0
1
0
1
2
0
0
0
0
0
0
0
0
1
2
1
0
0
1
1
1
0
0
0
1
0
0
0
1
2
1
0
1
0
2
0
0
1
0
3
2
0
2
0
2
0
0
0
2
0
0
1
0
0
2
0
1
4
1
0
0
2
0
0
0
0
1
2
0
0
1
1
2
1
1
1
0
1
1
1
2
3
1
1
0
2
2
2
1
0
1
1
2
0
2
0
1
2
0
1
0
1
0
1
0
0
0
1
0
1
1
1
0
0
0
0
1
0
0
2
1
2
0
0
0
0
1
1
2
0
0
0
0
0
2
2
0
0
0
1
2
0
0
0
0
1
0
0
2
1
2
1
0
0
0
2
0
2
0
0
1
0
1
1
2
0
2
0
0
1
1
1
0
1
0
1
2
0
2
4
2
0
0
0
0
1
0
2
2
0
1
0
1
1
2
0
1
0
1
2
0
0
1
0
0
1
1
0
0
0
0
0
1
1
0
0
1
0
1
2
2
0
2
0
0
2
2
1
2
2
0
1
0
0
0
1
1
0
0
0
0
0
1
1
2
0
0
1
0
1
2
1
2
1
0
2
0
0
1
2
0
0
3
2
2
1
1
0
1
0
0
0
0
0
1
0
0
2
0
2
1
0
1
0
0
2
0
2
2
0
2
1
0
1
2
1
3
1
0
2
2
2
1
0
0
0
1
0
2
0
1
0
1
2
2
2
1
2
0
1
2
1
1
0
1
1
0
1
2
1
1
1
0
0
0
2
1
0
0
1
0
3
0
0
0
2
0
1
0
0
0
1
1
3
2
0
0
1
0
2
0
2
1
1
2
2
0
0
0
0
0
0
0
1
1
0
2
2
0
0
3
0
0
0
0
0
0
1
3
0
0
1
0
1
0
0
4
1
0
0
0
2
0
0
2
2
1
0
0
0
0
2
0
0
1
2
1
0
1
0
0
0
1
1
0
0
0
0
0
1
1
0
2
0
0
0
0
1
0
2
2
0
0
0
1
2
2
1
0
1
0
0
1
0
0
1
0
1
1
0
0
0
2
2
0
0
0
0
0
1
1
0
1
1
0
0
1
1
2
2
1
0
2
1
1
0
0
3
2
1
2
0
1
1
1
2
0
0
1
4
0
0
0
2
1
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
1
1
0
2
0
0
0
4
0
0
0
2
2
0
0
3
1
1
2
0
0
1
2
1
0
0
0
2
0
0
0
1
2
1
0
2
2
0
1
0
0
2
0
1
0
1
1
0
2
0
0
1
1
0
0
1
4
1
0
1
2
1
0
2
0
0
1
0
1
1
1
1
0
0
0
1
5
0
0
0
1
2
0
0
0
0
0
1
2
0
2
1
0
2
1
1
2
0
2
0
0
0
2
0
0
1
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
1
0
1
0
1
2
0
0
0
1
2
0
1
0
0
2
0
2
2
0
0
1
2
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
1
2
1
0
2
1
0
0
2
2
2
2
2
1
0
1
0
0
1
2
2
1
0
0
1
0
0
0
1
2
0
0
2
1
2
2
0
0
1
0
1
0
0
1
0
1
1
2
1
0
1
0
2
1
0
2
1
0
1
0
2
0
0
1
1
2
0
0
2
2
0
1
1
0
1
1
1
0
0
0
1
0
0
0
2
0
1
0
0
3
2
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
3
0
1
1
0
0
2
2
1
1
1
0
0
0
1
0
1
0
0
2
2
1
1
1
2
1
0
1
0
2
0
1
0
1
0
0
1
0
1
0
0
1
1
0
1
0
2
0
2
2
1
0
0
0
2
0
1
1
0
0
0
0
1
0
0
1
0
1
0
0
1
1
2
2
2
1
2
0
0
0
2
1
0
0
2
0
0
0
0
0
1
1
1
1
1
2
0
0
3
2
1
0
2
2
0
0
1
1
0
3
2
0
0
2
1
0
0
2
2
0
2
0
2
2
2
0
1
0
1
0
0
0
1
1
0
0
0
2
1
1
0
0
2
0
1
0
0
0
0
0
1
0
1
0
3
0
0
0
0
0
0
0
2
1
0
0
1
0
1
1
0
0
0
2
1
0
0
1
0
2
2
0
1
1
1
2
0
1
2
1
1
0
1
0
0
0
0
2
2
1
1
0
2
1
0
0
1
0
0
0
0
0
1
0
1
1
0
1
2
0
0
0
0
0
2
1
0
2
1
0
1
0
2
1
0
2
1
1
0
0
0
1
0
1
2
0
2
1
3
2
0
2
0
1
2
0
0
1
1
1
0
0
0
0
1
2
3
1
1
0
1
1
2
1
2
0
0
0
0
1
1
0
0
0
2
0
0
1
0
0
0
1
0
2
1
2
1
2
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
1
0
1
0
1
0
2
0
1
1
1
1
0
1
1
1
0
0
1
1
1
0
0
0
1
0
0
1
1
2
3
2
0
0
3
0
0
1
0
3
0
1
0
0
2
0
0
2
0
1
0
1
0
0
2
1
0
1
0
0
0
0
1
0
2
1
0
0
1
0
2
0
1
0
1
0
0
0
0
0
1
2
3
2
1
1
0
2
0
0
0
2
0
0
2
0
0
0
1
0
0
0
2
1
0
1
0
2
0
2
0
0
1
1
0
0
0
2
2
0
0
0
2
0
0
2
2
0
0
0
0
1
1
1
0
2
2
1
2
0
2
0
0
0
1
1
0
0
0
0
0
1
2
2
0
0
0
0
0
0
1
0
2
0
1
1
1
0
0
0
0
0
2
3
1
2
0
0
2
1
0
0
2
0
2
2
0
0
2
2
0
1
0
0
1
0
0
0
0
0
0
0
0
2
1
2
0
1
0
0
1
2
2
0
1
0
3
2
1
0
0
0
0
0
0
0
1
1
2
0
1
2
1
0
2
1
0
0
1
1
0
0
1
1
0
0
1
1
0
0
1
2
1
1
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
1
1
3
2
1
1
2
0
0
2
2
0
0
1
1
1
0
0
0
1
0
1
1
0
3
1
0
0
0
0
0
0
0
2
2
2
1
4
0
0
0
0
1
0
0
1
1
1
2
0
1
2
4
7
2
0
0
2
1
1
1
0
0
2
0
0
1
1
2
1
1
0
0
2
0
1
1
1
0
0
0
1
0
1
0
1
2
0
0
0
0
0
0
0
1
1
0
2
1
0
2
2
0
1
1
0
0
0
2
0
0
0
1
0
1
0
2
0
1
0
0
0
1
1
1
2
1
3
2
1
1
0
0
0
2
1
2
1
0
2
0
1
0
1
0
0
0
0
2
0
3
0
1
0
2
1
0
0
0
0
3
0
0
2
0
0
1
0
1
0
0
0
0
1
0
1
1
0
1
1
0
2
2
0
1
0
2
1
0
0
0
1
2
1
2
1
1
2
0
0
2
0
0
0
2
0
1
1
2
1
0
1
0
0
0
2
1
0
2
2
1
1
2
1
0
1
0
0
0
0
1
0
1
0
2
0
0
1
0
1
1
0
1
0
0
0
2
1
0
1
2
0
0
1
2
2
1
3
1
0
1
0
0
2
2
0
2
0
2
0
0
1
1
2
1
0
2
0
1
2
1
0
1
0
0
1
1
2
0
1
0
0
1
2
1
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
1
0
0
2
0
0
1
1
0
0
1
0
0
0
1
2
0
1
0
2
1
1
0
0
0
3
0
1
0
1
1
1
1
2
1
0
1
0
0
0
1
2
2
0
0
0
1
1
2
1
1
0
0
0
1
0
0
0
1
2
0
2
2
0
0
0
0
0
0
1
0
0
0
1
1
0
2
0
1
0
0
0
1
0
0
0
0
0
0
1
0
2
0
2
1
2
2
1
2
2
0
1
2
0
1
0
1
1
1
2
0
0
1
1
1
1
0
0
0
0
2
0
2
0
1
0
1
1
0
0
2
2
0
1
1
1
1
0
0
1
0
1
1
0
1
1
0
0
0
2
1
1
0
1
2
0
0
2
0
1
0
1
2
1
1
1
2
0
0
2
0
2
0
0
1
1
0
2
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
2
3
0
1
1
2
0
0
0
0
1
1
0
0
0
2
1
2
0
1
0
2
0
0
2
1
2
1
0
2
3
0
2
0
1
0
0
0
2
0
1
1
1
1
0
0
0
0
0
2
2
0
1
0
0
2
0
2
1
3
1
0
0
0
0
0
1
2
1
0
0
0
2
0
1
1
1
0
0
0
2
0
0
0
1
0
1
1
0
2
0
0
0
0
2
2
0
2
0
1
0
0
0
0
2
1
1
0
1
2
0
0
0
1
0
1
0
1
2
0
0
0
0
1
3
0
1
0
1
2
2
2
1
1
0
2
1
0
3
0
1
0
2
0
2
1
0
1
1
1
2
1
0
0
0
0
0
0
1
1
2
2
0
0
1
1
2
1
1
1
3
0
0
1
3
0
0
2
0
1
0
1
2
1
1
1
0
0
0
1
1
1
0
0
2
0
0
1
0
1
0
0
0
2
2
0
2
1
1
0
1
0
0
1
1
0
0
1
0
1
0
0
0
0
2
0
1
0
1
0
0
0
1
0
1
0
1
1
1
0
1
1
0
2
0
1
3
0
0
0
2
0
2
1
2
1
0
2
0
2
1
1
0
2
0
2
2
0
0
2
2
0
0
2
0
0
1
0
0
0
0
1
1
0
0
2
1
0
0
0
0
1
1
1
2
2
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
2
1
1
0
2
0
1
0
0
0
0
0
1
0
1
1
0
1
0
1
0
0
1
1
0
0
0
0
2
0
3
0
1
2
1
0
0
2
0
2
0
0
2
0
0
0
2
1
0
2
0
0
2
2
1
0
1
1
0
2
1
0
0
1
4
0
0
0
0
2
0
0
2
0
6
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
1
0
1
0
0
2
1
0
1
1
0
0
0
0
0
2
0
0
0
1
1
1
0
0
0
0
0
0
0
2
0
0
0
1
2
0
1
0
0
2
0
0
0
2
2
1
1
0
2
0
0
0
1
2
0
0
2
0
2
1
2
1
0
3
2
0
1
1
1
1
1
2
0
2
0
0
2
2
1
1
1
3
2
0
0
2
0
1
1
3
2
2
1
0
1
2
2
0
0
0
0
0
0
0
0
3
0
2
0
0
0
1
1
0
1
0
2
1
0
0
0
0
0
1
0
2
2
1
0
0
0
2
1
0
0
0
0
0
1
0
1
1
0
1
0
0
2
1
0
0
0
0
0
0
3
2
1
0
0
4
1
0
3
1
2
2
1
2
0
0
0
0
0
3
0
0
1
0
0
0
0
1
1
3
0
1
0
0
2
0
1
1
0
0
2
0
0
0
1
0
3
2
0
0
0
0
1
1
1
2
0
0
2
0
0
0
1
0
0
1
0
1
0
1
0
2
0
1
2
2
0
2
2
0
2
0
1
0
0
1
0
0
0
0
0
1
0
1
1
1
0
0
1
2
2
0
1
0
1
0
1
1
1
1
4
1
0
1
1
2
0
0
1
0
0
0
1
1
0
1
0
0
0
1
0
1
0
2
2
0
2
1
1
0
1
1
0
1
0
0
0
1
2
2
0
0
1
0
4
0
0
0
0
1
0
0
1
1
0
0
0
0
1
1
0
2
0
0
2
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
2
0
2
1
0
1
1
0
0
0
0
2
0
1
0
1
0
2
0
2
0
0
0
1
0
0
0
2
0
2
0
0
2
0
1
1
0
0
1
0
0
1
1
3
2
1
0
0
0
0
1
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
1
0
2
1
0
0
0
1
2
5
0
0
3
0
1
0
0
0
0
1
1
0
0
0
1
0
0
2
0
0
3
2
2
0
0
0
0
0
1
0
0
1
2
0
0
0
1
0
0
0
2
0
0
0
2
0
1
3
0
1
1
1
0
0
2
1
1
0
0
2
4
0
0
2
1
1
0
2
1
0
2
0
0
1
2
2
1
0
0
3
2
0
1
1
2
2
1
0
0
2
2
0
2
1
1
1
0
0
0
0
0
0
1
1
0
0
0
1
4
1
0
0
1
0
0
0
1
0
0
1
2
0
0
1
1
1
2
1
1
3
1
0
0
1
2
0
1
1
0
2
1
2
0
1
0
0
1
1
0
0
0
5
0
2
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
1
1
0
0
1
0
0
1
2
2
4
0
0
2
1
2
1
0
1
0
1
1
0
2
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
1
0
2
0
2
0
0
0
0
0
1
1
1
0
0
0
0
2
0
0
0
1
0
2
0
1
0
1
2
0
0
2
0
0
2
1
1
2
1
0
0
0
0
1
0
1
1
0
1
0
0
0
2
0
2
0
0
1
1
2
1
0
1
3
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
1
0
2
0
0
1
1
1
1
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
1
0
0
2
2
1
0
1
1
1
0
2
0
1
0
1
0
0
1
0
2
0
1
0
1
0
1
0
0
1
2
1
1
1
0
2
2
1
0
1
0
1
0
0
1
0
0
1
0
0
1
0
2
0
0
2
0
0
1
1
0
0
0
0
1
0
0
1
0
1
2
0
0
0
0
1
0
0
0
2
1
0
1
1
2
0
3
2
0
0
1
1
0
0
0
1
3
1
0
1
0
2
0
0
2
1
1
2
5
0
0
0
1
2
0
0
1
0
1
1
0
1
1
0
0
4
2
3
2
0
0
0
1
2
0
0
0
1
0
0
1
1
0
0
0
2
0
0
0
1
0
0
0
0
0
7
3
1
2
0
0
0
1
0
1
1
1
0
2
0
2
0
0
0
1
0
0
1
2
0
0
1
1
2
0
2
3
0
0
2
0
1
1
0
1
1
0
2
1
0
2
1
0
0
1
1
0
0
0
1
0
0
0
1
0
0
2
2
1
0
1
0
0
0
1
0
1
1
2
1
1
1
0
0
1
0
1
0
0
2
2
1
2
0
0
1
0
0
0
1
2
0
1
1
0
1
0
1
0
1
1
2
0
0
1
2
0
1
1
1
0
2
2
0
2
0
2
1
2
2
0
0
0
1
2
2
0
2
0
0
0
0
1
0
0
2
1
0
1
1
0
0
1
0
1
2
2
1
0
2
2
0
0
0
2
1
1
1
0
2
1
0
0
2
2
0
1
2
0
0
0
0
1
0
0
0
2
1
2
0
1
0
1
0
0
2
1
0
0
1
2
1
3
1
0
0
1
0
0
1
2
0
2
6
1
0
2
2
1
0
0
0
0
0
2
1
0
1
1
0
0
0
2
1
0
0
1
1
0
0
0
0
0
1
0
2
0
2
0
0
2
2
0
1
1
2
2
1
2
0
1
0
0
1
3
0
0
1
0
2
2
2
0
0
1
2
0
1
1
0
2
0
1
2
0
0
0
0
2
0
0
0
0
1
1
1
1
1
2
1
1
1
1
0
0
0
1
1
1
0
2
2
2
0
0
1
2
1
0
0
0
0
0
2
1
1
2
0
2
1
0
1
1
1
0
0
2
0
0
0
0
0
0
1
0
2
0
1
2
1
2
1
0
1
2
0
0
2
0
0
0
1
2
0
0
1
3
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
3
2
1
1
2
0
0
1
0
1
0
1
1
3
0
2
0
1
0
2
0
2
2
0
0
1
0
0
0
1
2
1
1
0
0
0
2
0
1
0
2
0
0
0
2
0
0
1
0
0
1
0
1
0
0
0
1
2
0
1
0
0
0
1
1
0
0
2
0
1
2
1
0
0
0
0
1
2
0
1
2
0
1
1
0
1
2
0
1
0
0
0
2
1
1
0
2
0
0
0
0
0
1
0
1
0
0
2
0
1
1
3
1
0
0
0
0
0
1
0
1
2
1
2
1
2
0
1
1
0
0
0
0
0
0
0
2
1
1
2
0
1
1
1
0
1
0
0
0
0
2
2
2
0
2
1
0
3
2
1
1
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
2
0
0
0
1
0
1
1
0
1
0
0
2
0
0
1
2
1
2
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
5
0
1
1
1
1
2
1
2
0
0
1
1
1
0
0
0
1
0
0
1
0
1
1
0
1
0
2
1
0
0
0
0
0
0
2
2
2
0
0
0
0
2
0
1
2
3
1
0
0
1
0
1
0
1
0
0
1
0
0
2
0
2
0
1
0
1
2
1
0
0
0
0
2
1
0
1
1
0
0
0
1
0
0
1
1
1
2
0
2
2
3
0
2
0
0
2
0
1
0
0
1
0
2
0
0
0
0
0
2
0
2
2
1
1
0
0
1
0
1
0
1
0
1
0
1
1
1
0
1
0
0
2
0
0
0
0
0
3
0
1
0
0
1
0
0
0
0
0
0
1
2
1
0
2
0
0
1
0
0
0
0
1
3
0
2
1
0
0
1
1
0
0
2
0
0
0
1
0
1
0
1
1
2
1
0
0
1
0
0
1
0
1
1
0
1
2
1
0
0
0
0
0
1
1
1
1
2
1
0
1
0
0
0
0
2
0
0
0
1
2
0
0
0
2
2
1
0
0
0
0
2
0
0
2
1
0
2
1
0
1
1
0
0
1
2
0
0
1
0
1
0
2
0
0
0
1
2
2
0
0
2
1
1
2
2
1
0
0
0
1
0
2
0
1
1
0
0
0
0
2
2
2
2
0
1
1
2
0
0
2
0
0
1
0
2
0
1
2
0
0
2
1
0
0
0
1
2
0
2
0
0
2
1
0
1
2
2
2
0
1
1
2
2
0
0
2
0
2
2
0
2
0
0
0
1
1
0
2
0
1
0
0
2
1
0
2
0
2
2
1
0
0
0
2
0
0
1
2
2
1
1
1
0
0
1
3
0
1
0
3
2
2
1
1
0
0
2
0
1
2
1
0
0
1
0
1
0
0
0
2
1
1
1
2
2
2
2
0
1
1
0
1
1
1
0
2
0
0
1
0
0
0
2
0
0
0
1
0
0
0
1
0
0
1
0
0
0
2
1
0
0
0
0
1
0
2
0
2
2
0
1
1
2
1
1
0
0
2
1
1
1
0
1
0
1
0
1
0
2
0
1
0
0
1
0
2
0
2
0
2
0
0
1
1
2
0
0
2
0
0
0
1
0
2
0
2
1
0
0
0
1
2
0
0
0
1
1
0
2
0
1
0
2
0
1
2
0
1
0
1
0
2
0
0
0
3
0
0
0
0
2
0
0
0
2
2
1
0
2
2
0
0
0
0
0
1
0
2
0
1
2
0
0
0
1
1
0
1
1
2
0
0
0
0
0
2
1
2
0
1
0
1
0
1
0
1
0
2
1
2
0
0
1
0
0
2
0
0
0
0
3
1
2
1
0
0
0
2
1
0
1
0
2
2
1
2
0
2
1
0
4
0
2
2
1
1
1
0
2
1
0
1
0
1
0
1
0
0
1
1
1
0
0
0
1
0
0
0
0
0
1
0
2
1
2
1
0
0
0
0
0
0
1
0
0
0
1
0
0
2
2
0
1
2
3
2
0
0
1
2
0
1
1
0
1
1
2
2
1
0
2
0
2
0
2
1
0
0
0
2
0
0
1
2
2
0
0
1
0
0
0
1
2
0
1
0
1
0
1
1
2
0
2
1
1
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
2
0
0
0
0
1
0
0
1
1
1
0
1
0
0
0
2
1
0
0
2
2
3
1
0
2
2
2
2
2
0
2
1
0
1
2
0
1
1
0
0
2
0
0
1
0
3
0
0
0
0
2
1
0
1
1
1
0
0
1
1
0
0
2
0
1
1
2
0
1
1
0
1
0
1
1
1
2
1
0
0
0
1
0
0
0
2
0
2
1
0
0
1
0
2
0
0
0
1
3
0
0
2
1
0
0
1
0
0
2
1
0
0
1
1
1
0
1
0
0
0
0
0
0
1
0
0
2
1
0
1
0
0
2
1
0
0
2
0
1
2
0
1
1
1
0
2
1
0
1
0
1
0
1
0
0
2
0
0
0
0
1
2
0
0
0
0
0
1
1
0
0
1
0
0
1
1
0
2
0
0
0
0
4
0
2
0
0
2
0
0
1
0
0
1
1
1
0
0
0
1
1
0
0
0
2
2
0
0
2
0
0
1
0
0
0
2
2
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
1
0
1
0
1
1
0
0
2
0
1
0
0
0
1
2
1
0
2
0
0
2
0
1
0
1
0
1
2
0
0
2
1
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
1
1
2
2
0
1
1
1
0
0
1
1
2
0
0
0
0
1
0
0
2
0
1
3
1
1
0
0
4
0
0
0
0
0
0
1
1
0
7
0
0
2
0
0
0
0
0
0
2
2
0
0
0
1
0
1
2
1
1
0
2
2
0
1
0
2
1
2
1
1
1
0
1
0
0
0
0
1
0
0
0
0
1
2
0
2
0
1
2
0
0
0
2
2
3
1
0
2
2
2
0
0
0
0
1
2
2
1
0
0
0
2
0
0
1
2
0
0
0
2
0
1
0
1
0
1
0
0
0
0
0
1
1
0
0
0
2
1
0
2
0
0
1
0
2
1
2
1
2
0
2
0
2
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
1
0
0
0
0
2
1
1
0
1
0
0
0
2
2
2
2
1
1
0
0
0
0
1
1
0
1
0
2
0
0
0
0
1
1
2
0
1
0
2
2
1
1
0
2
0
2
1
1
1
0
0
0
0
0
1
0
1
0
1
0
2
0
1
1
2
1
0
0
1
0
0
2
0
0
0
0
2
0
0
2
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
1
4
2
0
0
2
0
1
0
0
0
2
0
1
0
2
0
0
1
1
0
0
1
1
2
2
0
0
0
1
0
0
1
1
0
1
1
0
0
0
2
1
1
2
2
1
1
0
0
1
0
1
2
1
2
1
0
0
2
0
2
3
0
0
0
0
0
1
2
1
2
0
1
0
1
0
1
2
2
0
0
2
0
0
0
0
2
0
2
1
0
1
2
2
1
0
1
2
0
0
0
0
0
0
2
0
1
0
0
2
0
2
1
0
1
0
0
1
1
0
0
0
0
0
1
0
0
2
2
0
0
0
0
1
1
2
0
3
0
0
1
0
0
0
2
1
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
2
0
1
2
1
2
1
2
0
1
1
1
0
0
1
0
1
2
0
0
1
1
0
0
0
2
2
1
0
0
1
1
2
1
0
1
2
0
0
0
1
0
0
0
2
0
0
2
1
1
0
1
0
0
0
2
1
0
1
0
2
0
1
0
2
1
0
2
0
2
0
3
1
0
2
1
0
0
2
2
0
0
0
0
1
1
1
1
0
0
0
0
2
0
0
0
0
1
0
1
2
2
1
0
1
0
0
0
0
0
0
0
1
0
2
2
0
1
0
0
2
1
1
0
1
1
0
0
0
3
0
0
0
0
2
2
0
1
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
1
1
1
0
1
1
1
0
0
0
1
2
0
2
0
1
1
0
0
4
2
2
0
2
0
1
0
0
0
2
0
1
2
1
0
0
0
0
0
0
1
2
2
1
2
2
1
0
0
0
0
0
0
1
1
1
1
2
1
1
0
1
2
2
1
0
0
1
2
0
1
2
0
0
1
1
0
0
0
0
0
1
1
1
0
0
0
1
0
1
0
0
1
1
0
0
2
0
0
2
0
0
0
3
1
0
1
1
0
0
1
0
0
1
1
2
0
0
1
1
0
0
2
0
2
0
0
0
2
2
0
0
2
1
0
1
2
2
0
1
0
0
0
0
1
2
1
2
1
0
1
0
0
2
0
0
2
0
1
0
0
1
0
0
0
1
0
0
0
1
2
0
0
0
1
0
0
1
1
7
0
0
0
1
2
2
0
1
2
0
1
1
0
2
1
0
0
0
0
2
2
2
0
0
1
1
0
2
2
0
0
0
0
1
0
1
2
0
0
0
1
1
2
1
0
1
1
0
0
1
2
0
0
0
0
2
1
0
1
0
1
0
0
2
4
2
2
0
1
1
0
1
0
0
0
1
0
0
0
1
0
2
1
0
0
0
0
1
1
0
0
2
2
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
1
0
1
0
2
1
0
4
0
1
0
2
0
1
0
1
0
1
1
0
1
1
2
2
0
0
1
0
0
0
0
2
0
0
2
1
0
0
2
1
1
0
0
2
0
0
2
0
0
0
1
0
1
0
0
2
0
1
2
0
0
2
0
1
1
1
2
2
1
0
0
0
0
1
0
2
0
1
0
1
1
1
0
1
1
2
0
2
1
0
2
1
0
0
0
1
0
0
2
1
2
1
1
0
0
0
0
2
1
0
1
0
0
0
1
1
1
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
1
1
1
2
0
1
0
1
0
0
0
0
2
1
1
1
0
1
2
2
1
0
1
0
0
2
0
1
1
1
3
2
0
0
1
2
0
0
1
0
0
1
0
0
2
0
0
2
0
2
0
1
0
2
1
1
2
0
0
0
0
0
1
0
1
0
0
2
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
1
1
2
2
0
1
0
2
0
0
0
0
1
2
2
2
2
0
0
1
2
0
1
0
0
0
0
0
2
2
2
0
1
0
2
0
0
0
0
2
0
2
1
1
2
0
0
1
2
2
2
0
1
1
1
1
0
3
0
0
1
1
1
0
0
1
2
1
0
1
1
1
0
0
2
1
1
2
0
1
2
0
0
2
1
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
2
1
1
1
1
0
0
2
0
0
0
0
0
1
0
0
3
1
0
1
2
1
1
0
1
2
1
0
0
1
0
1
1
0
0
3
2
0
1
1
0
2
0
1
0
2
2
2
1
0
1
0
1
0
0
2
1
2
0
0
0
3
0
0
0
0
0
0
0
1
2
0
0
2
0
1
3
0
0
2
0
2
1
0
0
1
2
5
0
0
2
2
2
0
0
1
0
0
0
2
1
0
1
0
0
0
1
0
0
5
0
0
0
1
0
1
1
0
0
2
2
1
0
2
0
2
0
1
2
0
2
1
0
0
1
0
1
1
1
0
1
1
1
2
0
0
1
1
0
2
0
2
0
1
0
2
0
0
0
2
0
1
0
1
0
1
0
0
0
0
0
1
0
0
2
0
0
0
2
0
1
0
0
0
0
1
0
2
0
0
0
0
1
2
0
0
2
2
2
0
0
1
0
2
2
0
1
0
2
1
2
1
0
1
0
0
2
1
0
1
0
2
2
0
0
2
1
0
0
0
1
2
1
0
0
1
0
0
0
0
1
1
0
0
1
1
0
1
0
2
1
3
0
0
0
0
2
0
2
1
0
2
1
1
1
0
1
0
0
0
2
1
2
2
1
0
2
0
1
1
1
2
0
0
2
1
0
0
1
0
0
0
0
1
1
2
1
0
0
0
1
0
0
0
2
0
1
1
2
2
2
1
0
0
0
0
0
2
2
1
0
0
0
2
0
1
0
0
1
0
2
1
2
1
0
2
0
1
0
0
0
0
1
0
0
1
0
2
1
1
2
1
2
1
0
1
1
0
0
1
0
1
0
0
2
0
0
1
2
0
1
0
0
0
2
0
0
1
0
1
1
1
1
0
0
0
0
1
0
1
2
1
0
0
0
2
0
0
2
2
0
0
1
1
0
1
0
1
2
0
0
0
1
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
2
0
1
1
0
2
0
0
1
0
2
1
1
0
0
1
0
0
0
1
1
2
2
1
1
0
0
0
0
0
0
0
1
0
0
2
2
0
0
1
0
0
0
0
0
1
1
0
3
0
0
2
1
1
1
2
0
0
1
1
2
1
0
1
2
1
1
2
1
0
1
0
0
1
1
0
2
0
0
2
2
1
1
0
0
2
2
0
0
0
1
1
0
0
1
1
0
2
2
1
1
1
0
2
0
1
1
0
1
0
2
0
1
1
2
0
0
0
0
1
1
2
0
0
0
1
1
1
0
1
3
1
0
0
1
0
0
0
0
1
2
1
0
2
2
1
0
2
0
1
0
2
0
1
5
1
0
2
0
0
0
0
3
2
2
0
2
2
1
0
0
1
2
0
1
1
1
0
1
0
1
2
0
0
0
1
0
9
0
1
2
2
1
0
0
0
1
1
0
2
0
1
1
1
1
0
2
1
2
0
3
0
0
1
0
0
2
0
1
6
1
2
0
1
0
2
0
1
3
0
1
0
1
1
0
2
2
1
1
1
0
0
0
1
0
1
2
0
0
4
0
1
2
1
1
5
0
1
1
0
0
2
0
0
2
0
0
2
0
0
2
0
2
0
1
1
1
0
0
1
1
0
2
1
0
0
0
2
2
1
0
0
1
2
0
2
1
0
0
0
1
2
1
1
0
1
2
0
0
0
2
2
1
1
0
1
0
1
0
1
1
1
0
0
0
1
0
0
3
0
0
0
1
1
1
0
7
0
1
0
1
1
0
0
1
0
1
0
2
1
2
2
1
0
1
0
0
0
2
0
0
1
0
1
2
2
1
0
2
2
2
2
0
1
1
0
1
0
2
1
0
1
0
1
0
0
2
0
0
1
1
1
1
0
0
2
1
1
1
1
0
2
1
0
2
0
1
0
1
0
1
0
0
0
0
0
1
1
0
0
2
1
0
0
0
0
0
0
1
1
0
1
1
2
0
2
1
0
0
0
1
1
0
2
1
2
0
1
1
1
1
1
0
0
0
0
0
1
2
1
0
1
1
1
0
5
1
1
0
0
1
0
0
0
0
1
1
0
0
1
1
1
0
1
0
1
1
0
0
0
0
1
2
1
0
0
0
0
0
1
2
2
2
0
1
0
1
2
1
0
2
0
2
1
1
0
2
1
1
0
1
0
1
0
0
1
0
0
2
2
0
0
0
1
0
0
0
0
0
0
2
0
0
1
1
0
0
1
0
2
1
1
2
1
0
1
2
2
1
0
0
0
1
0
0
2
2
1
1
0
1
0
3
0
1
0
0
0
0
1
0
1
2
1
1
0
2
1
0
1
0
0
1
0
0
1
1
1
2
2
0
0
0
0
0
2
0
1
0
0
0
0
2
0
2
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
2
1
1
0
2
2
0
0
0
1
0
0
1
0
1
0
0
1
0
3
2
2
0
0
0
2
1
0
2
0
2
1
0
1
2
2
1
0
2
2
1
2
0
0
2
0
1
0
1
0
2
2
1
0
2
3
0
0
2
0
1
0
1
2
0
0
2
0
0
1
2
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
2
0
0
2
0
1
0
2
0
0
1
1
0
3
1
2
4
0
1
0
2
0
0
2
0
2
1
0
5
2
4
1
0
1
0
0
1
1
0
0
0
3
0
1
2
1
0
1
1
1
0
1
0
0
9
0
1
2
0
0
1
0
1
0
0
0
1
1
0
0
0
0
1
0
0
1
0
1
0
2
1
2
1
1
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
1
1
1
10
0
2
0
1
0
0
0
2
0
2
0
2
0
0
2
0
0
1
0
1
1
0
0
2
0
0
2
1
2
1
0
0
1
1
0
0
0
0
2
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
1
2
0
1
0
0
0
2
2
1
1
0
0
1
0
1
0
2
2
2
0
0
1
1
1
0
1
0
0
1
2
2
0
0
1
8
0
0
0
0
0
2
0
0
0
1
0
1
0
1
4
1
2
2
0
0
1
2
0
2
2
0
0
1
0
2
2
0
1
1
1
0
0
2
1
1
1
0
0
1
0
1
0
1
1
2
0
2
2
0
0
0
1
0
0
1
2
1
1
0
0
1
0
1
0
2
3
1
2
0
0
0
0
2
1
0
0
2
0
1
0
0
1
1
0
0
2
0
1
0
0
1
1
2
0
1
0
1
0
0
1
0
1
1
0
0
2
0
0
1
1
0
0
2
1
0
2
1
1
0
1
0
1
0
1
1
0
0
0
0
1
0
1
0
0
2
2
0
1
0
0
1
0
1
0
2
0
1
0
1
0
1
2
1
1
0
0
0
0
2
0
0
0
2
0
1
2
2
2
1
0
1
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
1
0
1
0
2
3
0
1
0
0
1
0
2
1
2
0
1
2
0
1
1
1
0
0
1
2
2
0
2
0
0
0
0
1
2
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
2
0
2
2
0
0
0
1
0
2
1
0
1
2
0
0
2
0
1
0
0
0
1
0
0
2
0
0
1
0
0
0
1
0
0
1
3
1
1
2
2
2
0
1
0
1
1
1
1
0
0
0
0
2
0
0
1
0
1
1
0
2
1
1
2
0
1
0
0
2
1
1
0
0
1
0
2
1
0
0
1
2
1
2
0
2
1
0
0
1
1
0
1
0
1
0
0
0
1
0
0
2
1
0
1
0
2
2
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
1
0
2
1
2
0
2
0
2
0
1
0
1
0
1
0
1
0
0
1
3
1
1
0
2
0
0
0
1
1
0
2
0
0
1
0
0
1
1
0
0
1
1
2
0
0
2
1
0
1
0
1
2
0
0
1
2
0
0
1
2
0
1
0
0
1
1
1
0
2
0
0
0
0
2
4
1
0
1
0
2
2
1
0
0
1
0
1
0
0
0
2
0
0
0
0
1
2
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
1
1
0
1
0
1
0
0
1
1
1
0
1
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
1
0
1
0
1
0
1
0
2
0
2
0
0
0
1
0
1
0
2
0
1
0
2
2
2
1
2
0
1
1
1
0
2
1
2
0
2
1
0
2
0
0
0
2
2
3
0
0
1
0
4
1
2
2
3
3
0
0
2
2
0
0
1
1
0
0
0
0
3
0
0
2
0
0
1
0
2
0
0
1
2
1
0
1
0
0
1
1
1
1
2
1
0
0
0
1
0
1
0
2
0
3
0
0
1
0
2
1
2
2
1
2
0
2
1
2
0
2
0
0
0
1
0
0
0
2
1
0
0
1
1
0
1
1
1
2
0
0
0
0
0
2
0
2
1
0
0
1
0
1
0
1
5
0
1
1
0
0
0
0
0
1
1
1
1
0
1
0
1
1
2
0
2
3
0
1
1
1
2
1
2
2
0
0
1
0
2
1
1
2
0
0
1
1
0
1
1
0
0
0
1
2
0
1
0
2
0
2
1
1
0
0
1
1
2
0
0
0
1
0
0
0
0
0
0
1
1
0
1
1
2
2
0
0
2
0
0
2
1
1
0
1
1
2
2
2
0
0
0
0
0
1
1
0
1
0
2
1
1
1
1
0
0
2
1
1
0
0
0
0
0
3
0
1
0
1
0
0
1
1
0
0
3
0
0
0
1
1
0
0
2
0
0
2
2
0
0
1
0
2
2
1
0
0
1
0
1
1
1
2
1
1
1
1
0
1
1
0
0
1
1
2
1
2
0
2
3
1
1
1
2
0
2
2
1
1
2
0
0
0
0
0
2
1
0
0
1
1
1
0
1
2
1
0
0
0
0
0
1
1
0
0
0
1
2
1
0
2
0
1
0
1
0
2
0
0
1
1
0
0
0
2
2
1
0
0
1
2
0
0
1
2
0
1
1
1
1
0
0
0
0
2
0
0
1
1
0
8
1
0
0
1
2
0
1
0
1
1
0
2
0
0
2
0
0
2
0
2
2
1
1
0
0
1
1
1
0
0
1
1
1
1
0
0
0
0
0
0
0
3
1
2
2
0
0
2
0
2
1
1
0
1
0
0
2
0
1
0
0
1
0
0
3
2
0
1
1
1
0
0
2
1
1
2
2
0
2
0
1
0
0
1
1
1
0
3
2
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
1
1
0
2
1
0
0
1
1
1
0
2
0
0
2
1
0
0
0
0
1
0
1
3
2
1
0
1
0
2
0
0
1
0
0
0
0
0
0
2
2
0
0
2
0
1
1
0
0
2
0
3
0
1
2
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
3
0
1
1
0
0
0
2
1
0
1
2
0
1
0
0
1
2
1
1
1
0
1
0
0
1
1
0
1
1
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
1
0
0
2
2
2
1
1
0
2
1
0
0
0
2
0
0
1
0
2
6
1
0
2
1
2
0
0
1
0
2
0
2
0
0
3
1
2
0
0
1
2
0
0
0
2
2
1
1
1
2
1
0
2
1
1
2
0
0
0
1
2
2
0
0
2
0
2
2
1
0
1
0
2
0
0
1
8
0
0
0
1
2
0
0
1
1
0
2
1
2
1
1
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
2
2
2
0
0
0
0
2
0
0
0
0
1
2
2
2
2
0
0
1
0
1
2
0
1
0
0
1
2
0
1
0
2
1
1
2
4
0
0
0
0
2
2
0
0
2
2
0
0
0
0
2
2
2
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
2
2
0
1
2
0
1
1
1
0
2
0
1
0
0
0
0
2
2
2
0
1
1
0
1
1
0
2
1
0
1
0
0
0
0
0
0
0
1
2
0
1
0
0
2
2
0
0
0
1
2
1
0
0
0
0
0
2
0
0
2
2
0
1
1
0
0
1
0
0
0
0
2
0
1
0
0
0
2
1
1
1
0
0
1
1
0
2
0
1
1
3
0
2
0
0
1
1
0
0
0
1
2
0
0
2
2
0
1
2
3
0
0
0
1
2
2
0
1
0
0
0
1
0
1
0
0
2
1
0
2
0
0
2
2
2
1
0
0
0
0
0
0
1
0
2
1
0
1
0
0
1
1
1
0
0
0
0
0
1
2
0
1
3
0
2
1
0
0
2
1
2
1
0
2
0
0
1
1
0
0
0
0
0
2
1
0
1
2
2
1
2
2
0
0
2
0
0
1
2
1
0
2
0
3
0
0
0
0
1
0
0
2
1
1
1
1
4
1
2
1
2
0
2
0
0
1
2
0
2
1
1
0
0
1
0
0
0
0
1
1
0
2
0
1
2
0
2
0
0
0
0
0
0
0
1
0
2
2
0
1
2
1
1
1
1
0
2
0
0
1
2
0
0
1
0
1
1
2
0
2
1
1
1
0
0
0
0
2
0
2
1
0
0
3
2
1
0
2
2
0
0
0
3
1
1
1
0
1
1
0
5
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
1
1
1
0
1
1
0
2
2
0
0
2
0
0
0
3
1
0
0
1
0
0
1
0
0
0
0
0
0
1
2
8
0
2
0
1
0
0
4
0
0
0
1
0
0
0
0
2
0
2
1
0
0
1
1
0
2
2
0
2
0
3
1
0
1
1
2
1
1
1
0
0
0
0
2
0
2
1
4
0
0
2
1
1
0
0
1
0
1
2
0
0
0
1
0
0
2
2
2
0
2
3
1
0
0
2
0
0
0
0
2
0
2
0
2
3
1
0
0
0
0
0
1
2
1
2
1
0
0
0
0
0
0
1
0
1
1
1
1
1
0
0
2
0
0
0
2
1
2
0
0
0
1
0
0
0
1
0
1
1
1
2
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
1
0
0
1
0
0
1
0
1
1
1
0
4
2
0
0
1
0
2
1
2
0
0
2
2
0
0
0
1
1
0
1
0
4
1
2
0
1
0
0
1
0
1
1
1
1
0
1
2
0
1
0
2
0
1
3
1
1
0
1
0
2
0
1
0
0
2
0
0
0
1
2
0
2
1
0
2
2
0
1
1
0
0
0
1
2
0
0
0
0
1
2
1
2
0
2
0
1
0
0
3
0
1
0
2
0
3
0
2
1
2
2
0
0
0
0
0
0
1
3
2
0
1
0
0
0
0
0
2
0
3
1
0
1
0
0
0
1
0
0
3
1
0
0
2
2
0
1
0
0
2
1
0
0
2
0
0
0
0
2
0
0
0
2
0
2
1
1
0
3
1
0
2
3
2
0
2
1
0
0
1
2
0
2
0
0
0
1
0
0
1
0
0
0
2
2
0
0
0
1
0
0
0
1
0
0
2
1
0
2
0
0
0
1
0
0
0
0
2
0
0
1
2
0
1
0
1
0
0
1
1
1
2
2
1
1
0
0
1
0
0
1
1
0
1
1
0
2
1
0
0
0
0
0
3
1
1
1
2
0
2
0
1
1
0
0
0
3
1
0
2
2
2
0
1
0
0
1
1
0
1
2
1
1
2
1
0
0
0
2
0
1
0
1
1
0
0
0
0
2
0
0
0
0
1
1
1
3
0
1
1
0
0
1
1
2
0
0
2
0
4
0
5
3
0
1
0
0
2
0
2
0
1
1
1
0
2
0
1
0
2
0
0
0
0
0
2
1
2
0
2
3
0
1
2
0
0
2
1
1
0
0
0
2
0
0
2
0
1
0
0
1
0
2
0
0
0
2
0
1
1
0
0
0
0
2
0
0
0
0
0
1
0
0
1
1
0
1
0
0
1
0
1
0
0
0
0
1
0
2
1
0
0
0
0
1
2
0
1
0
2
0
1
0
1
2
1
2
0
2
0
1
0
0
0
1
2
0
1
2
0
1
2
0
2
1
2
0
0
1
1
0
2
0
0
1
0
0
1
0
1
1
2
0
0
0
1
2
0
1
0
1
0
1
2
0
2
1
0
0
1
0
2
1
1
1
1
0
0
0
2
0
0
0
0
1
0
0
0
2
0
2
0
2
1
1
0
1
0
0
1
1
1
1
0
0
1
2
0
2
0
1
2
0
1
0
3
2
1
1
1
0
1
1
1
1
0
1
2
0
2
2
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
5
0
2
0
0
0
0
0
0
0
1
3
2
2
0
2
0
0
0
2
2
0
0
2
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
2
0
1
1
1
2
0
2
1
0
1
1
0
1
2
0
1
0
0
0
2
0
0
2
0
0
1
0
0
0
3
1
1
1
0
0
0
1
0
2
0
1
1
0
2
0
1
2
1
0
0
2
0
2
2
0
0
2
0
0
0
0
2
2
0
0
0
0
1
0
0
0
2
2
0
0
1
0
1
1
1
2
1
2
1
0
1
0
0
0
0
2
0
0
0
2
2
2
2
0
2
0
0
0
0
1
0
0
1
2
0
1
2
1
2
2
0
0
1
1
0
0
2
2
2
2
0
0
0
0
0
0
1
0
1
0
1
0
2
0
0
0
0
0
0
2
0
1
2
2
0
0
1
0
0
0
1
1
2
2
1
1
2
0
2
0
0
1
0
1
1
0
0
0
0
1
0
2
0
0
0
2
0
2
0
0
1
0
4
1
0
1
1
1
1
0
1
0
1
1
1
1
0
0
1
0
2
2
1
0
2
0
2
0
0
2
2
1
0
0
0
1
0
0
2
1
1
0
1
1
0
2
0
0
1
1
0
0
0
1
1
1
2
2
2
2
2
1
0
2
0
1
0
1
0
1
0
2
0
0
2
1
0
1
0
1
2
1
0
1
0
0
0
1
1
2
0
1
2
1
1
1
1
3
0
2
2
0
7
1
1
1
1
0
1
1
1
1
2
1
1
1
0
1
0
0
1
1
2
0
2
1
0
1
0
2
1
0
0
0
0
1
1
1
0
2
0
1
0
1
3
1
0
0
0
1
0
1
1
0
2
2
2
1
1
1
1
1
0
0
0
1
0
1
0
0
1
1
0
2
0
1
2
1
2
1
1
1
3
0
1
0
0
0
0
0
1
1
2
0
0
0
1
1
1
2
2
0
1
0
1
2
0
1
3
2
0
0
0
0
0
2
0
2
0
0
2
1
0
0
0
2
0
0
0
0
0
1
0
2
3
2
2
2
0
1
1
2
0
2
1
0
0
3
1
0
0
0
1
1
1
0
2
2
1
0
0
1
0
0
1
2
2
1
2
1
1
2
2
0
1
0
0
2
0
0
0
2
2
1
0
2
0
0
2
2
1
2
2
0
1
1
0
2
0
0
1
1
0
0
1
1
1
0
1
2
2
1
1
0
2
0
1
0
0
1
1
0
0
0
0
2
1
0
1
0
1
2
1
2
2
0
1
1
0
0
3
2
1
0
0
1
0
0
0
0
2
1
0
0
0
0
1
2
1
0
1
0
0
1
1
0
1
0
0
1
1
2
2
0
0
2
0
0
1
0
0
0
0
0
0
0
1
1
2
0
2
1
0
2
1
0
1
0
0
1
1
1
0
1
0
0
0
2
2
0
3
0
2
2
0
0
1
1
0
0
0
0
1
1
0
0
0
1
0
1
1
2
1
0
0
1
0
3
0
1
2
1
1
2
0
0
1
0
2
3
0
0
0
0
1
0
0
0
0
2
1
0
1
0
2
1
2
0
1
2
2
0
1
0
0
3
2
0
0
0
1
0
0
2
0
2
0
1
0
1
0
2
0
0
1
2
0
1
2
0
1
1
0
1
1
1
2
2
2
0
1
0
2
1
2
0
1
2
2
2
1
2
0
2
1
1
0
2
2
0
1
1
0
0
0
0
1
1
0
0
1
2
0
1
1
1
1
0
3
0
1
0
2
2
2
2
2
1
1
0
0
1
2
1
0
0
2
0
0
1
0
1
0
2
4
0
2
0
0
1
0
2
0
0
1
2
2
1
0
1
0
1
1
1
1
0
0
0
0
2
0
1
1
0
0
2
1
0
1
0
1
0
0
2
2
0
0
1
0
0
2
0
1
1
2
0
0
2
0
0
2
2
0
0
1
1
1
1
1
1
1
0
1
0
0
2
0
3
0
0
0
1
2
2
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
2
2
1
1
1
0
4
2
0
3
0
0
2
0
0
2
1
0
0
0
0
2
2
0
2
0
0
0
0
2
0
2
0
0
0
1
2
0
0
1
0
2
0
0
0
1
2
1
0
1
0
1
1
0
0
0
1
2
0
1
2
1
1
1
0
0
1
0
1
0
0
2
0
1
0
0
1
2
2
0
0
0
0
0
0
0
0
2
0
1
0
0
2
1
2
2
0
0
0
0
1
0
1
1
0
0
2
0
1
0
0
1
2
0
0
0
0
2
1
2
2
0
0
0
0
1
1
1
0
2
1
0
1
2
0
0
2
2
0
1
0
0
1
0
1
0
1
0
0
2
0
1
0
0
2
2
0
0
1
0
1
1
2
1
0
0
0
1
1
0
0
2
1
1
1
1
0
1
2
1
0
0
0
1
2
0
0
0
0
0
1
0
2
1
1
2
1
0
2
0
2
2
1
2
2
0
0
2
0
0
1
1
0
0
0
0
0
1
0
1
1
1
2
0
0
1
1
0
0
0
2
0
0
2
2
1
0
0
2
0
0
1
0
1
0
2
2
2
0
1
1
0
4
1
0
0
0
0
2
0
0
2
2
2
0
0
1
2
0
0
0
0
0
0
0
2
2
0
2
0
0
2
1
0
0
1
0
0
1
2
0
1
1
1
1
2
2
2
2
0
0
2
1
2
2
0
1
0
0
0
1
1
0
2
1
1
0
0
0
0
2
2
1
0
2
1
2
0
0
1
0
0
0
1
0
1
0
0
0
2
2
1
2
1
0
1
1
1
0
0
1
2
3
1
1
1
1
0
2
0
1
0
2
0
1
1
0
0
0
0
0
0
0
0
1
0
0
2
1
1
0
0
0
1
2
0
0
0
1
0
1
2
0
0
2
0
1
0
0
1
1
2
0
0
0
1
2
0
2
1
0
0
0
0
0
0
2
0
1
0
0
2
1
0
1
0
0
0
1
2
0
0
0
0
1
2
1
0
2
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
2
0
0
0
1
0
2
0
1
1
0
1
0
1
0
1
1
1
0
1
2
2
1
0
0
1
1
0
1
1
0
0
1
1
1
2
0
0
0
0
2
1
0
0
0
1
1
1
0
0
0
0
0
0
0
2
2
1
2
1
0
0
1
1
1
0
0
2
1
0
1
0
0
0
1
2
1
1
1
0
0
0
0
1
1
0
2
2
0
2
0
0
2
2
0
0
0
2
0
1
2
0
1
2
0
0
0
2
0
2
2
0
1
0
0
0
0
2
2
0
2
2
0
0
1
0
0
0
1
2
1
0
0
0
0
0
1
0
0
0
0
0
3
1
0
1
2
1
0
1
0
0
0
3
2
0
2
1
0
1
0
2
1
2
0
1
1
2
2
3
0
1
0
1
0
1
0
0
2
2
2
1
0
1
0
0
0
0
1
2
0
0
0
1
0
1
2
0
1
0
0
0
1
0
2
2
0
2
0
0
1
1
1
0
1
2
0
2
1
0
0
0
0
1
1
2
1
0
0
0
1
1
0
2
1
0
0
1
0
0
2
0
0
0
0
2
1
1
1
0
0
2
1
0
0
0
2
0
1
0
1
0
2
0
2
0
0
0
1
0
0
1
0
0
2
0
0
0
0
2
0
2
0
0
1
2
0
2
0
1
0
1
0
0
3
0
1
2
1
0
2
1
0
2
0
3
1
2
1
1
0
1
0
0
2
0
1
1
4
0
0
0
2
2
0
0
1
1
0
1
1
0
0
1
0
0
0
0
1
0
1
0
0
1
2
0
2
0
1
0
1
1
0
0
0
4
2
0
1
0
0
0
0
1
1
0
1
1
0
0
1
0
1
1
0
2
0
0
2
0
1
0
1
1
1
0
1
1
1
0
0
1
0
2
0
0
2
0
2
1
0
1
1
0
2
0
1
2
0
1
1
0
0
0
1
0
1
1
0
2
0
1
0
0
1
1
1
0
2
0
0
1
0
1
1
0
1
1
1
0
0
0
1
2
0
0
0
1
1
1
1
2
0
0
2
1
0
0
2
1
0
1
0
0
0
1
0
0
0
0
0
0
2
0
2
2
0
0
1
1
2
0
2
0
2
0
0
0
0
0
0
0
2
2
1
1
1
1
2
0
1
2
1
0
0
1
2
4
0
2
1
0
0
1
2
1
0
2
1
0
2
1
0
0
0
0
0
0
2
0
2
2
0
1
0
0
0
1
1
0
0
1
1
2
2
1
2
0
0
2
2
0
1
0
0
1
1
1
0
0
1
1
0
0
0
0
0
1
2
0
4
0
0
2
0
2
0
0
0
0
1
0
0
0
1
0
0
1
1
0
1
0
2
1
0
0
0
1
1
0
0
0
0
0
1
0
1
1
1
1
0
0
2
2
0
2
0
1
0
3
0
2
1
1
1
0
2
0
0
0
2
0
2
1
1
2
1
0
0
0
1
0
2
4
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
3
0
0
2
1
0
0
0
1
1
2
1
2
0
1
1
2
0
0
2
1
0
0
2
2
3
2
0
1
1
0
2
0
0
0
2
0
0
0
0
0
0
2
1
2
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
2
2
2
1
1
1
0
2
0
2
2
0
1
2
0
0
1
2
2
1
0
3
1
2
0
3
0
0
1
0
0
0
0
0
0
1
0
0
0
1
2
0
1
0
1
2
0
0
0
2
2
0
1
0
0
2
2
2
2
2
2
0
0
0
1
1
2
2
0
2
1
1
0
0
1
1
0
0
2
0
1
0
0
0
0
1
0
0
0
2
1
1
0
1
0
0
1
0
1
0
0
0
1
2
1
1
1
0
0
0
2
2
0
0
0
2
0
0
1
1
0
0
1
0
0
1
0
0
0
0
1
1
1
0
0
0
0
1
0
1
0
2
0
1
1
0
2
0
0
2
1
2
1
0
1
0
0
6
1
0
1
0
4
0
2
1
0
1
0
0
0
0
0
0
0
2
0
2
0
1
2
1
0
0
0
0
2
1
0
0
0
1
0
2
0
2
2
1
1
0
1
0
1
0
0
0
0
0
1
1
0
1
0
0
0
1
0
1
2
2
0
2
0
1
0
0
0
4
2
0
1
0
2
2
0
0
0
1
1
1
0
1
0
1
2
1
1
1
0
2
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
2
4
2
1
0
0
2
2
1
1
1
0
0
0
0
0
2
0
0
1
0
2
1
0
2
0
0
0
1
0
1
0
2
0
0
0
0
2
2
2
0
0
1
0
2
0
1
0
0
1
0
1
0
1
0
1
0
1
1
2
2
0
0
0
1
1
1
0
0
1
3
0
1
0
0
0
0
1
0
0
0
0
1
2
0
1
0
0
1
2
0
1
2
1
1
0
2
0
1
1
1
1
2
1
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
1
1
1
0
1
1
0
0
0
0
0
3
0
0
0
0
1
0
1
0
2
0
1
0
0
2
1
1
1
2
1
1
0
0
2
1
0
0
0
0
0
0
1
1
1
5
0
0
0
1
0
0
2
1
1
0
0
0
1
2
1
1
2
1
0
1
2
2
1
0
0
0
0
0
0
0
1
0
1
2
1
1
0
1
0
1
0
0
2
0
1
1
2
1
0
1
0
1
1
1
1
3
0
1
0
0
1
1
1
0
1
1
2
1
0
1
0
1
0
0
0
0
1
0
1
1
1
0
0
1
0
1
0
2
2
3
0
0
0
2
1
0
1
0
1
2
1
1
0
0
0
1
0
0
0
4
1
1
2
3
0
1
0
2
0
2
2
1
0
1
2
1
1
1
2
0
3
1
0
1
0
0
2
0
1
0
1
2
0
1
2
1
2
1
0
2
1
0
1
2
0
1
1
0
0
1
0
1
1
0
1
0
2
2
1
0
2
0
1
2
0
0
0
0
1
1
2
0
1
1
1
0
1
1
2
1
1
1
0
1
1
0
0
2
1
0
2
0
1
0
2
0
1
0
2
0
0
0
0
2
2
0
1
0
1
0
1
1
2
2
0
1
2
0
1
0
1
0
0
1
1
0
0
2
0
2
0
0
1
0
0
0
2
1
2
0
0
0
1
0
0
0
0
1
1
0
0
2
2
0
1
0
1
2
0
1
3
1
1
2
2
1
1
1
1
1
1
0
1
0
2
1
1
0
0
1
3
2
2
1
0
1
1
1
2
0
2
1
1
0
0
0
1
2
1
0
2
0
2
2
0
1
1
1
0
0
1
2
0
0
1
2
1
1
0
1
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
1
2
0
0
0
2
1
0
1
0
1
0
2
0
1
0
0
1
1
0
1
2
0
1
0
1
0
0
0
2
0
1
0
1
1
0
0
1
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
2
1
1
4
1
0
0
1
0
1
0
0
1
1
0
0
2
2
2
0
2
1
0
1
0
2
0
0
0
1
1
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
2
1
1
0
0
1
2
0
0
1
0
2
0
0
9
1
0
2
1
0
2
1
2
2
0
0
2
0
0
0
0
1
1
1
1
0
0
2
1
1
2
1
2
1
2
0
0
0
0
1
2
0
1
0
1
2
0
0
1
2
0
0
0
1
0
0
2
0
0
0
2
0
2
0
1
0
1
1
0
0
3
0
1
1
0
1
1
1
1
2
2
1
0
1
0
0
1
1
1
0
1
2
0
0
0
1
2
2
2
0
0
2
1
2
1
0
1
2
1
0
2
1
0
0
1
2
1
1
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
3
0
1
1
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
2
0
0
2
1
0
0
0
0
1
0
0
2
0
2
2
1
1
0
0
1
1
0
0
0
0
0
1
0
0
1
1
2
0
1
0
0
0
1
0
1
0
1
0
1
0
1
1
0
1
0
2
0
0
0
0
1
2
1
0
0
0
1
0
0
2
0
1
0
0
0
1
1
2
0
0
0
0
2
2
1
0
0
1
0
0
0
0
1
1
0
0
0
0
2
0
0
0
2
0
2
1
1
0
0
0
1
1
0
0
2
0
0
0
0
0
0
1
1
2
2
1
2
2
0
1
0
1
1
0
1
0
0
1
0
0
1
0
1
2
3
2
2
1
0
0
0
1
0
2
1
2
2
1
0
0
1
0
0
0
0
2
0
0
0
0
1
2
0
2
2
0
1
0
0
1
0
0
0
0
1
1
0
2
1
0
0
1
0
1
0
0
1
0
1
1
1
1
1
0
1
0
2
2
0
2
1
2
2
1
2
0
0
2
1
1
0
0
0
0
0
0
0
2
1
0
1
1
2
0
0
1
0
1
1
1
0
0
2
0
1
1
0
0
1
5
1
0
0
1
0
2
1
0
0
0
1
0
0
0
1
0
0
0
2
0
1
0
2
0
1
0
1
0
2
0
0
0
1
0
1
0
2
1
1
0
0
2
0
1
0
1
0
1
2
1
0
1
0
0
1
0
0
0
1
0
0
1
0
2
1
0
0
0
2
1
2
1
1
1
0
1
2
0
2
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
2
1
0
2
0
0
1
1
1
1
1
0
0
0
4
2
1
2
0
1
0
0
1
2
2
0
0
1
1
2
2
2
0
1
0
0
1
2
1
2
0
2
0
1
0
0
1
0
0
0
0
0
2
3
0
0
2
1
0
2
2
1
1
0
0
0
2
1
2
1
0
2
0
1
0
1
1
0
0
0
0
1
0
0
2
2
0
0
0
0
1
1
0
2
0
0
3
0
1
2
0
1
1
0
0
1
0
0
0
2
2
2
1
0
0
0
1
0
1
2
0
0
1
1
0
0
0
1
1
1
1
1
0
0
0
0
0
1
1
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
1
0
0
0
2
1
0
2
4
1
0
2
0
2
0
1
2
0
2
0
2
2
0
1
3
0
1
0
1
1
0
0
0
1
0
2
2
0
0
0
1
1
1
0
0
0
1
2
1
0
2
1
1
1
0
0
0
0
2
0
1
2
3
2
0
0
0
2
1
1
0
0
0
2
1
2
0
1
1
1
2
0
2
0
0
1
2
0
0
2
0
1
2
1
1
1
0
0
2
1
1
0
1
1
1
1
0
2
1
0
1
2
0
2
2
2
2
0
1
0
0
0
3
1
1
1
2
0
2
0
0
1
0
0
0
1
1
1
0
0
1
1
0
0
1
2
0
0
0
0
1
1
1
0
0
0
1
1
1
1
0
0
0
1
1
2
1
1
0
1
2
0
1
1
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
2
1
0
0
1
2
2
1
0
1
2
0
1
1
1
0
1
2
0
1
2
0
0
2
0
1
0
1
0
0
2
1
0
1
1
0
0
1
1
0
0
1
1
0
0
3
1
0
0
0
1
2
2
0
1
1
1
0
1
0
0
2
0
0
2
1
0
0
1
0
1
1
1
1
2
0
0
1
2
0
0
0
1
0
2
2
1
2
2
2
0
1
0
0
1
0
0
0
1
0
0
1
1
1
0
0
1
1
0
0
0
0
2
1
0
0
0
2
1
0
0
1
1
2
0
1
1
0
3
0
0
0
2
0
1
1
0
1
2
2
0
2
2
1
0
0
0
1
1
2
1
0
1
0
0
2
1
0
1
2
0
0
0
0
0
0
0
2
2
0
1
1
0
0
0
1
0
0
0
0
2
0
1
1
0
0
1
0
2
2
1
1
0
1
1
1
2
1
2
2
0
0
0
1
1
0
1
2
0
1
2
2
0
1
0
0
2
2
0
1
5
0
0
0
2
0
2
1
0
1
0
0
1
2
1
2
0
1
0
1
1
2
2
0
2
3
0
0
0
0
0
0
0
0
1
2
2
2
2
0
1
0
0
1
0
0
1
0
1
2
0
0
2
0
0
0
1
2
0
0
0
0
1
1
1
0
1
1
2
0
0
1
0
2
2
0
3
2
0
0
1
0
0
2
0
0
2
0
2
0
0
2
2
0
2
1
11
3
0
1
2
0
2
1
0
0
0
0
0
1
1
0
2
2
2
0
1
1
0
0
3
0
0
0
2
2
1
1
0
0
0
0
1
1
1
1
1
0
1
1
0
0
0
3
0
1
0
1
0
1
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
2
1
1
1
1
0
0
3
0
2
1
0
0
2
0
0
1
0
0
0
2
1
1
1
0
0
0
2
2
1
2
1
0
2
0
3
1
1
0
1
2
1
1
2
2
0
0
3
1
1
0
0
1
0
1
0
0
2
0
0
0
1
0
1
2
0
0
1
2
2
1
3
2
0
0
0
1
0
0
2
1
0
2
0
0
2
0
0
1
1
1
0
1
1
0
2
0
0
0
2
0
0
0
1
0
0
2
0
2
0
0
1
2
0
0
0
0
1
1
0
0
0
2
1
0
1
2
0
0
2
1
0
1
1
0
1
0
0
1
0
2
1
0
0
0
0
0
2
0
2
0
0
2
0
1
1
0
0
0
2
0
0
1
1
2
0
0
2
0
0
0
2
1
1
2
1
0
1
0
0
1
0
2
0
1
0
1
0
2
0
2
1
0
0
1
1
3
0
1
0
2
1
0
0
2
1
1
0
0
1
2
1
2
0
0
0
2
1
0
2
2
1
1
0
0
0
1
1
2
2
2
0
0
1
0
0
2
0
0
2
1
1
0
0
1
0
2
0
0
1
1
1
0
2
1
0
0
0
0
0
1
0
0
2
2
0
1
0
2
0
1
0
0
0
0
1
1
0
2
0
2
0
1
1
0
0
2
0
0
2
0
1
2
0
1
0
1
1
1
0
2
2
0
0
0
2
0
2
2
0
0
0
1
1
2
0
1
2
0
2
1
0
0
2
1
0
0
0
0
2
2
2
1
0
0
0
0
0
1
0
0
2
1
0
2
2
1
0
0
0
0
0
1
0
2
0
0
0
2
0
1
0
2
0
2
2
2
2
1
1
0
0
0
0
1
0
3
1
2
1
0
0
0
0
0
2
0
0
0
2
1
0
0
2
4
2
0
0
2
1
0
1
0
1
0
2
1
0
1
0
1
0
0
1
0
2
1
0
2
0
0
2
0
1
2
0
2
2
2
0
2
0
1
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
1
1
0
0
0
2
1
0
0
1
2
1
0
2
1
0
0
0
0
1
0
3
2
0
0
2
1
1
3
1
0
1
0
2
2
1
1
0
0
0
2
0
0
2
2
1
0
0
0
2
2
2
0
0
1
1
1
1
0
2
0
0
0
2
0
0
0
1
0
1
1
1
0
2
1
0
3
2
1
2
0
2
0
0
2
1
2
0
0
1
2
0
0
0
0
1
0
1
0
0
2
0
2
1
1
0
0
2
1
0
2
1
1
1
2
0
0
1
1
0
0
2
8
2
1
0
0
2
0
1
0
0
0
4
0
1
1
0
0
1
0
2
0
2
0
1
0
1
2
4
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
1
0
1
1
0
0
0
3
2
2
0
0
1
0
1
1
1
2
0
1
0
1
0
1
1
1
1
0
1
0
0
0
0
1
0
1
0
4
0
2
1
0
0
1
1
1
0
0
1
0
0
1
0
0
2
0
1
2
0
0
1
1
0
0
0
1
0
0
4
1
2
1
3
0
0
0
1
0
0
2
1
0
0
2
1
2
0
2
0
1
2
1
0
0
0
0
0
0
1
1
2
0
0
0
0
2
0
3
0
0
0
0
2
2
0
2
1
0
2
1
2
0
0
1
0
1
0
2
0
0
3
0
2
1
0
0
0
0
0
0
1
0
0
0
0
2
2
0
2
2
0
0
1
1
1
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
3
0
0
2
1
2
0
0
1
1
1
0
1
1
0
2
1
0
0
0
1
1
0
0
2
0
1
0
0
0
0
0
1
1
0
2
0
1
1
1
1
1
0
2
2
2
1
2
1
0
0
1
0
1
0
2
0
2
1
1
0
0
0
1
0
0
1
0
2
0
0
2
0
0
2
4
0
1
0
0
2
1
1
2
0
1
0
0
0
0
0
1
1
1
2
1
0
2
1
1
2
0
3
0
1
2
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
2
0
0
0
2
0
1
0
0
0
1
2
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
1
0
0
6
2
0
2
0
0
3
0
0
2
0
0
1
2
1
0
2
0
0
0
1
1
0
1
0
0
0
0
0
0
1
1
1
2
0
0
0
1
0
0
1
0
0
1
1
2
0
1
0
0
0
0
2
2
0
0
0
0
0
1
0
2
0
0
0
0
1
0
1
0
0
1
2
0
0
2
0
0
0
0
0
0
2
0
0
0
9
1
1
2
2
0
1
0
0
0
1
2
0
0
0
1
0
0
1
0
0
1
0
0
0
0
2
1
1
0
2
1
0
1
2
0
0
0
2
2
4
0
2
1
0
1
0
0
2
1
0
1
0
2
0
0
0
2
0
1
0
0
0
2
0
1
2
0
0
0
0
0
0
0
2
1
2
0
0
2
2
0
0
0
0
0
2
0
2
1
1
0
1
2
1
1
0
0
1
1
1
1
1
1
2
1
0
2
0
1
0
0
1
1
0
2
2
0
1
1
0
0
1
0
0
0
2
1
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
1
1
0
2
1
1
2
0
0
0
0
2
0
0
0
0
1
0
3
0
0
1
0
1
1
0
0
0
0
1
1
1
0
0
2
0
2
0
0
1
0
2
2
1
2
1
0
0
3
0
0
2
0
0
1
2
2
1
2
2
0
0
0
2
0
1
1
0
1
0
2
0
0
0
1
0
1
0
1
2
1
1
0
0
0
2
1
2
0
1
2
0
2
1
0
2
1
0
3
1
1
9
0
0
0
1
0
1
1
1
1
2
0
1
0
0
3
1
2
0
2
0
2
1
0
1
0
1
0
2
1
2
0
1
2
0
0
0
0
0
2
0
0
2
1
2
1
0
2
0
0
1
0
0
1
1
0
1
0
0
1
2
1
2
0
0
1
1
0
1
0
0
0
0
0
2
0
0
1
1
0
1
1
0
0
0
2
1
0
1
0
0
0
2
0
0
0
1
2
2
0
0
0
0
0
0
1
0
0
0
1
0
2
1
2
0
0
2
0
1
1
0
2
1
2
2
1
1
0
0
0
1
2
1
0
2
0
0
0
0
1
0
0
1
1
0
1
0
1
0
0
2
1
2
0
1
1
1
2
1
2
0
1
2
1
0
1
6
1
1
3
0
0
0
0
1
1
1
0
2
0
0
0
0
1
1
1
2
1
0
1
0
1
2
0
1
0
1
0
0
0
1
1
0
1
1
1
0
0
1
0
0
2
0
2
1
0
0
0
2
0
0
2
2
0
2
1
0
2
2
2
3
0
0
0
0
1
0
1
1
0
0
1
0
1
0
1
0
2
2
0
2
0
0
1
0
0
0
0
0
0
2
2
0
0
1
0
0
0
3
1
0
1
1
0
1
0
1
2
1
0
0
0
1
1
0
1
1
0
0
0
0
1
2
1
1
0
2
0
1
0
1
1
2
1
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
1
1
0
2
3
0
1
0
1
1
0
2
0
0
0
2
0
0
0
0
1
1
0
2
0
0
0
0
0
2
1
0
1
0
2
0
0
2
1
2
2
0
2
0
0
1
1
0
1
1
1
0
0
2
0
0
1
0
1
0
0
0
0
0
0
1
0
0
2
2
1
2
1
0
1
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
1
0
2
2
1
4
0
2
1
2
0
2
0
0
2
0
0
2
1
1
0
2
1
3
0
2
0
0
2
0
0
1
0
0
1
1
0
1
0
1
0
0
0
2
2
0
3
2
1
1
1
1
0
1
1
0
0
1
0
0
1
1
0
0
0
0
2
0
0
2
0
0
2
0
0
2
1
1
1
1
0
2
0
1
0
2
2
0
1
2
0
0
0
0
1
0
0
0
2
1
0
1
0
2
0
1
0
0
2
0
0
0
0
0
2
0
0
1
0
2
1
0
0
0
0
1
0
0
2
0
1
2
0
2
1
0
0
0
0
0
2
1
2
1
2
0
0
0
1
0
0
0
1
1
2
0
0
1
0
0
1
0
1
1
0
0
1
0
3
0
0
1
0
0
0
2
0
0
0
0
2
0
1
2
5
2
2
1
0
0
1
0
0
2
0
0
0
0
0
2
0
2
0
1
1
0
0
0
1
2
1
2
2
0
2
1
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
1
3
1
1
1
1
0
2
2
0
0
1
0
0
1
0
2
0
0
1
1
2
2
2
2
2
0
2
0
0
2
1
3
2
2
1
6
1
0
2
0
0
0
1
2
0
1
0
2
2
0
0
2
2
1
1
2
0
0
1
1
2
2
0
0
1
1
0
2
0
3
1
0
0
2
1
2
1
0
1
3
0
2
1
2
1
1
2
0
0
0
0
0
0
2
0
0
0
1
0
0
3
2
0
1
0
0
1
1
2
0
0
2
2
0
1
1
0
0
3
0
0
0
2
0
2
1
0
1
0
1
0
0
1
0
1
2
0
0
2
2
2
2
1
0
3
3
0
1
1
0
0
2
0
1
0
2
1
1
2
0
1
3
0
2
0
2
1
0
0
0
0
1
1
0
2
2
2
0
0
1
0
2
2
0
0
1
0
0
2
0
0
3
1
2
1
0
0
0
0
1
2
0
0
3
0
1
1
0
2
1
0
0
1
1
2
0
0
0
3
0
2
1
2
0
0
1
0
0
1
1
2
2
1
1
0
0
0
2
0
1
0
0
2
0
0
0
0
0
2
0
2
0
0
1
0
0
1
2
0
1
1
0
0
2
0
1
1
0
0
0
1
1
0
1
0
0
1
0
0
0
1
1
0
0
0
2
0
0
1
0
1
1
0
1
0
0
0
2
2
0
0
1
1
1
3
0
2
0
0
2
1
0
0
2
1
1
1
0
2
0
1
0
0
2
0
3
0
0
0
2
0
2
2
0
2
1
2
0
2
0
2
0
1
2
0
1
1
0
2
0
0
1
0
1
0
0
0
2
0
3
2
0
1
0
0
0
0
2
3
0
0
0
0
0
1
0
0
0
4
0
0
0
0
2
1
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
1
2
1
1
2
1
0
1
0
1
1
1
2
0
1
0
0
0
1
2
2
0
0
0
1
0
2
0
0
0
0
2
1
1
0
2
1
0
2
0
0
0
1
0
0
1
0
0
0
0
0
1
2
2
1
2
1
0
0
0
0
0
1
1
0
1
2
2
2
1
2
0
0
0
0
1
1
0
0
1
0
0
0
0
2
1
0
1
0
1
0
1
1
0
0
2
4
0
0
0
1
0
1
1
1
0
1
1
0
0
1
0
1
1
1
0
3
0
1
0
1
2
0
0
0
0
2
2
1
2
2
0
0
2
1
2
0
2
0
0
2
3
2
2
0
1
0
0
0
0
1
2
0
2
0
1
1
0
2
0
1
0
3
0
2
0
3
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
2
1
0
0
0
1
8
1
1
2
0
1
2
0
0
0
2
0
2
2
0
0
1
1
0
1
1
1
3
1
0
0
1
0
0
1
2
0
0
0
1
0
0
0
2
0
0
0
1
0
3
1
1
2
1
0
1
1
0
1
2
0
0
2
0
0
1
2
1
0
0
2
0
0
0
0
0
0
0
1
2
0
1
2
0
0
2
2
1
1
1
2
0
2
1
0
0
0
2
0
1
1
1
0
0
0
1
0
1
1
0
0
0
0
2
1
0
0
1
1
1
0
0
3
0
0
0
2
0
1
2
0
2
1
1
0
0
1
0
1
1
2
1
1
2
0
0
0
0
2
0
0
0
1
0
1
2
1
2
1
0
1
0
1
0
0
0
0
0
2
2
0
0
0
1
0
2
3
2
0
1
2
1
1
0
2
0
1
0
0
2
1
1
1
0
0
0
2
0
1
1
0
0
0
0
2
0
0
0
0
1
1
1
0
2
0
0
2
0
2
0
1
0
0
0
0
1
0
0
1
1
1
2
1
2
0
1
0
1
3
0
0
0
0
0
0
0
1
2
0
1
2
0
0
0
2
1
0
0
2
0
1
0
0
0
2
2
2
0
0
0
0
2
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
1
1
0
1
2
0
0
0
2
1
1
1
0
1
0
2
0
1
1
0
0
0
0
1
2
0
0
0
0
2
1
0
0
0
0
0
6
0
1
0
1
0
1
2
2
2
1
0
1
2
1
0
2
0
0
0
0
0
4
1
1
2
3
2
0
2
1
0
2
0
1
2
0
0
1
0
1
1
2
0
0
1
1
1
0
0
0
0
1
1
3
0
1
0
0
0
0
0
1
0
1
2
0
1
0
0
1
0
0
3
2
0
1
1
0
0
0
0
2
0
1
1
1
0
0
1
0
1
0
2
0
1
0
1
1
1
2
0
0
1
0
1
1
1
0
1
1
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
1
1
0
0
1
1
2
2
0
1
0
1
0
2
0
2
0
0
2
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
2
2
2
0
0
0
2
0
1
0
2
0
1
2
1
1
0
2
1
1
0
3
1
1
0
0
0
0
0
2
0
0
1
2
0
2
2
2
0
0
0
1
1
0
0
0
0
2
0
0
0
2
0
2
0
0
4
0
1
2
1
1
0
0
1
1
1
0
0
0
0
0
1
0
1
0
0
0
1
2
0
0
0
0
0
1
0
0
2
2
2
0
0
0
1
2
1
0
1
2
1
1
0
0
0
2
0
1
2
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
3
0
1
1
1
0
0
0
2
0
2
0
0
2
1
0
0
2
0
0
2
2
0
1
2
1
2
0
2
1
2
0
1
1
0
3
0
0
0
1
0
0
1
0
1
0
1
1
1
2
0
1
0
1
1
2
1
0
0
1
0
1
0
0
2
0
1
2
1
0
1
1
1
1
2
2
0
1
3
0
0
0
0
1
1
0
1
1
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
1
1
1
2
1
2
0
1
2
0
0
2
2
0
0
1
0
1
0
0
0
0
2
0
0
1
1
0
2
0
1
0
2
0
0
1
2
2
1
0
2
0
3
0
0
1
2
0
0
1
1
0
0
0
0
1
0
0
1
2
0
0
2
0
1
2
1
0
0
2
2
0
2
2
0
1
0
0
1
2
2
3
0
2
2
1
0
1
1
0
1
0
0
2
0
1
0
1
1
1
0
0
1
0
0
0
0
0
1
1
0
1
1
0
0
1
0
0
0
1
2
2
1
0
2
0
0
0
0
0
2
2
2
0
0
2
0
1
1
0
0
2
0
2
2
0
2
1
0
1
2
1
2
0
0
2
1
1
0
2
0
1
1
2
2
1
2
1
1
1
0
0
0
2
2
0
2
0
1
1
1
0
1
1
1
1
1
1
0
4
2
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
1
2
1
0
0
0
2
1
1
0
0
2
1
1
0
2
0
0
0
1
0
0
1
0
2
2
2
1
0
1
1
0
1
1
0
2
0
1
1
0
0
2
0
0
1
2
3
0
0
1
0
0
1
1
1
1
0
2
2
0
2
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
2
0
1
2
0
0
1
0
0
1
0
1
14
0
1
0
2
1
0
1
0
2
2
1
2
1
0
2
2
1
1
0
1
2
0
1
2
0
3
0
0
1
0
0
0
1
1
0
0
0
0
2
2
1
0
0
0
0
0
2
0
3
1
0
0
0
0
0
1
0
2
0
1
2
0
0
0
1
0
1
2
2
0
1
1
2
2
0
2
1
0
0
1
0
1
2
1
0
0
3
0
0
0
1
0
2
1
0
0
1
2
0
1
2
0
0
1
0
0
0
2
0
1
0
1
0
2
1
0
3
2
2
0
0
1
0
1
0
2
0
2
0
3
1
1
0
1
3
0
0
0
1
1
1
0
0
0
2
1
1
1
2
0
0
0
3
0
1
0
0
0
0
1
0
1
0
2
0
0
0
1
1
1
2
0
2
1
1
0
3
0
2
1
1
0
1
1
0
2
2
0
1
0
2
1
1
0
0
0
1
0
1
0
2
2
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
2
1
0
1
0
0
0
1
0
3
0
0
0
2
2
1
1
1
0
0
2
1
0
0
1
1
2
2
0
1
2
1
2
0
0
0
2
1
2
0
1
1
1
1
0
0
0
0
3
1
0
1
1
0
1
0
1
1
2
0
0
0
0
0
0
0
2
0
2
0
0
1
1
0
0
1
0
0
2
0
0
0
1
2
1
2
0
0
1
0
2
1
0
0
2
0
1
0
0
0
0
0
0
2
0
2
0
0
1
1
0
0
1
2
2
1
0
1
1
0
1
1
0
0
2
1
2
0
1
2
0
1
1
3
0
0
2
0
0
0
0
2
2
0
0
0
2
0
0
0
0
2
1
2
0
0
2
0
0
0
2
0
0
6
1
1
0
1
1
1
0
2
2
1
0
0
0
0
1
2
2
2
1
2
2
1
2
1
1
2
1
1
1
1
0
0
0
0
1
0
0
0
0
1
0
1
1
1
0
1
0
1
0
0
0
0
1
0
0
0
1
1
2
0
0
1
0
2
0
1
0
0
0
0
1
1
0
2
2
1
0
1
0
0
0
1
2
0
2
2
1
1
0
2
0
1
0
2
2
0
0
2
0
1
2
0
0
0
0
0
0
1
1
2
0
2
1
0
0
1
1
1
0
1
0
1
1
0
3
1
0
0
1
0
2
1
0
0
0
1
0
0
0
1
0
0
0
2
2
2
1
0
2
1
2
1
0
0
0
0
2
1
1
0
2
2
0
0
1
1
2
2
1
0
1
0
0
0
0
1
0
1
2
2
2
2
0
1
0
0
0
2
0
0
1
0
0
1
2
0
1
0
1
2
3
2
0
1
0
0
0
0
1
0
0
1
0
0
2
1
0
2
1
2
0
1
2
0
1
1
0
1
2
1
0
1
1
0
1
1
1
2
0
0
2
0
0
0
0
0
0
0
0
1
2
2
1
0
0
1
0
0
2
0
0
2
2
0
3
1
2
0
1
1
1
0
0
2
1
1
0
0
0
0
3
1
0
0
0
0
2
0
0
0
0
0
3
1
1
0
0
2
2
2
0
1
1
1
2
3
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
1
0
1
0
2
3
2
2
1
0
0
0
1
1
0
1
0
2
0
0
2
2
2
1
0
2
0
1
1
0
2
1
2
1
4
0
1
1
1
0
0
1
1
2
0
2
1
0
0
2
0
0
0
1
0
0
0
2
2
0
2
1
0
0
0
0
1
1
0
2
1
2
1
0
0
2
1
0
0
2
0
2
1
0
1
2
0
0
6
0
2
2
0
0
0
1
0
1
1
0
0
2
0
0
1
0
0
0
3
3
1
2
1
0
0
1
1
1
0
0
0
0
2
1
1
1
0
0
0
0
2
1
0
0
0
1
1
0
0
0
0
0
2
0
1
0
1
0
2
0
2
0
0
2
0
0
2
0
1
1
2
0
1
0
4
0
1
0
2
2
0
1
2
2
1
1
2
1
4
0
3
0
0
2
1
0
0
3
0
0
0
1
0
0
0
0
0
2
3
0
0
0
2
1
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
1
2
0
1
0
0
0
1
0
2
2
1
2
0
0
0
1
0
1
0
1
1
1
0
2
0
1
0
0
4
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
2
4
0
0
0
0
0
0
2
0
2
0
1
1
0
2
2
1
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
1
1
0
0
1
1
2
0
0
2
0
2
0
1
1
0
3
1
0
1
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
1
1
1
2
1
1
0
1
2
0
0
2
0
0
1
1
0
2
0
1
2
1
0
0
0
0
0
0
2
1
0
1
1
0
0
0
0
0
1
3
0
1
0
0
0
0
0
0
2
0
0
1
1
1
0
0
0
0
0
2
0
2
0
1
0
0
0
1
0
2
2
0
0
1
2
1
0
0
1
1
1
1
0
0
0
0
0
0
2
1
0
1
2
1
1
0
0
3
0
2
0
0
1
0
1
0
0
0
0
0
2
3
0
0
0
0
1
0
1
1
0
1
0
1
0
1
1
0
2
1
1
0
2
1
2
0
1
0
0
1
2
1
1
1
1
0
1
0
2
0
1
0
0
0
0
0
2
2
1
0
0
0
1
0
0
2
1
0
0
0
0
1
1
1
0
2
0
0
0
0
1
0
0
1
0
2
1
0
0
0
0
0
0
0
1
2
0
2
0
1
0
0
2
1
1
0
0
0
0
2
1
0
0
1
2
1
2
5
0
0
0
0
0
1
1
2
0
1
1
1
0
0
0
1
1
0
0
1
2
1
1
1
0
0
0
0
1
2
0
1
1
0
0
0
0
1
0
0
0
1
1
2
0
1
0
1
0
2
1
2
1
0
1
0
1
1
0
0
0
0
0
2
0
1
1
2
0
2
0
0
0
0
0
1
2
1
0
1
0
0
0
0
0
0
0
1
2
0
1
0
0
0
2
0
2
2
2
3
2
2
1
1
2
2
3
0
1
2
1
2
0
1
1
0
1
1
1
0
2
0
0
1
0
0
0
1
0
1
0
1
0
1
0
1
0
0
0
0
2
0
1
1
0
0
0
1
2
3
0
0
1
2
1
1
2
0
0
2
0
0
2
0
0
1
3
1
1
0
2
0
2
0
1
2
2
1
0
2
0
0
0
3
1
2
0
0
1
2
0
2
0
1
2
0
1
0
0
1
1
1
0
2
0
0
1
1
1
0
0
0
1
1
1
0
2
0
0
0
0
1
0
0
1
0
0
0
0
2
0
3
1
1
1
0
1
0
0
1
1
0
0
1
0
0
1
0
0
0
0
1
1
2
0
2
2
3
1
0
2
0
1
1
1
1
0
0
1
0
1
1
0
1
0
0
0
1
0
5
2
2
0
1
1
1
1
0
1
0
2
1
1
0
2
0
0
0
0
0
2
0
0
0
1
0
0
1
2
1
1
0
1
0
0
2
0
0
2
1
1
0
1
2
2
0
1
0
0
0
1
0
0
1
1
0
0
0
0
2
0
0
1
1
0
0
0
0
5
2
2
0
1
0
2
1
0
3
2
1
0
1
0
0
0
0
0
0
0
2
3
1
0
0
0
1
0
1
2
1
1
1
0
1
1
0
1
0
1
0
0
0
1
0
1
0
0
2
0
0
2
0
1
2
0
1
0
1
0
0
0
0
1
0
1
0
1
1
2
0
0
0
1
0
2
0
1
2
0
1
0
1
0
2
0
1
0
0
0
0
0
0
0
0
2
0
1
1
1
1
1
0
0
0
0
0
0
0
1
0
2
1
2
0
0
0
0
2
0
0
1
2
0
0
1
2
0
2
0
1
1
0
0
0
1
0
0
1
0
0
1
1
0
2
2
0
0
0
2
0
1
0
0
2
0
2
0
0
0
1
0
1
0
0
2
0
0
0
0
1
1
2
1
0
1
2
0
2
1
1
0
0
0
0
0
1
0
1
2
0
0
1
1
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
2
0
2
2
0
0
0
0
1
2
0
0
2
0
0
4
0
1
0
1
0
0
1
2
3
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
2
0
0
0
0
1
0
1
0
2
0
0
2
2
2
1
1
0
0
1
1
1
2
0
0
0
0
2
0
1
0
0
0
1
1
1
0
1
0
0
2
0
0
0
0
1
0
0
1
0
2
0
2
3
0
0
0
0
1
0
1
1
1
0
0
1
3
1
2
0
3
1
2
1
1
0
3
1
1
0
1
0
1
1
0
0
2
1
0
1
0
1
3
0
0
2
0
1
0
0
2
2
1
0
2
0
0
0
2
0
0
0
0
0
1
2
1
0
2
1
0
1
1
0
0
0
0
1
1
2
1
1
1
0
0
1
0
2
2
0
1
2
1
0
2
1
0
0
2
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
1
2
1
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
1
0
1
0
1
2
2
2
1
0
1
1
0
0
0
0
0
1
0
0
1
0
1
0
3
0
2
0
1
2
1
0
2
1
1
0
2
0
0
1
0
1
0
1
2
0
1
0
2
1
2
0
0
1
2
0
2
0
1
1
2
0
1
0
2
2
0
0
1
1
2
2
0
0
1
0
0
0
0
0
1
0
0
1
2
0
1
1
0
0
1
0
0
0
1
2
0
2
0
0
1
1
1
0
0
2
0
0
2
0
1
0
2
0
0
0
1
0
2
0
0
0
2
1
1
1
2
2
0
0
0
2
0
0
2
1
2
1
1
2
2
2
1
0
2
0
0
2
1
0
0
0
2
0
0
2
1
0
2
1
1
0
2
0
0
0
2
1
0
2
0
0
2
0
0
1
1
0
0
1
1
2
0
0
2
0
1
1
1
0
2
0
1
1
0
1
0
0
0
1
0
1
1
1
0
0
0
1
0
2
1
0
0
1
2
0
0
1
1
0
2
1
1
0
0
1
2
2
0
1
2
0
0
1
0
1
1
2
0
3
0
1
1
0
1
0
1
0
1
2
1
2
1
0
1
1
1
0
1
1
2
0
0
0
0
0
0
1
0
0
0
2
1
1
0
1
0
0
1
2
0
2
2
1
2
0
1
0
0
0
1
0
0
1
0
1
1
0
1
1
1
1
1
2
0
1
0
0
0
2
1
1
2
2
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
2
2
1
0
1
2
0
1
1
0
0
0
1
1
2
1
1
1
2
1
1
0
0
0
0
0
1
0
2
2
0
2
0
2
0
1
1
0
2
0
2
0
2
0
1
0
1
0
0
0
0
0
1
2
0
0
0
1
0
2
1
1
0
2
0
0
0
0
1
2
1
0
0
1
0
0
0
1
1
1
1
0
1
2
0
1
1
0
0
0
0
0
0
2
2
1
0
0
1
0
1
1
0
2
0
0
0
1
1
2
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
1
1
2
1
0
1
0
2
0
0
1
0
0
0
0
0
2
2
2
1
1
2
1
1
0
2
0
1
1
0
0
1
2
1
1
3
1
0
2
2
0
1
1
0
1
0
3
1
0
1
2
0
1
1
1
0
0
0
3
0
1
2
0
1
2
0
0
0
0
1
1
0
0
2
0
0
3
0
0
0
0
1
2
1
0
2
2
1
0
1
0
2
2
0
1
0
0
1
0
0
2
2
0
0
2
1
3
0
0
0
0
0
0
0
0
1
0
0
1
3
4
0
2
0
0
0
1
1
2
1
0
0
2
0
2
1
1
0
0
0
1
0
1
0
0
0
0
2
0
0
2
0
3
1
2
2
0
2
2
0
1
1
2
2
0
0
1
2
1
0
0
1
0
2
0
0
1
0
1
1
0
2
2
0
1
0
2
1
0
2
0
4
0
0
1
1
0
2
0
2
2
0
3
0
2
0
2
0
2
2
0
1
1
0
0
1
0
1
2
2
1
1
2
0
0
0
0
0
1
1
0
3
0
0
2
0
1
2
1
0
0
1
1
2
0
1
0
0
0
1
0
0
0
0
0
0
2
1
1
2
2
0
0
0
1
3
0
0
2
0
2
0
0
0
1
0
2
0
0
0
1
0
2
0
0
0
1
1
0
1
3
1
0
0
2
1
0
1
3
1
0
0
0
0
2
0
0
0
2
0
1
3
2
2
0
0
2
1
2
0
2
2
0
2
1
0
2
0
0
0
1
1
5
0
1
1
2
1
2
1
2
1
0
0
2
1
0
1
0
1
0
2
2
2
1
0
2
0
0
1
0
0
2
2
0
0
1
0
0
0
0
0
0
2
0
2
1
2
2
0
0
0
0
5
3
0
0
1
2
0
2
2
1
2
1
0
1
1
2
0
0
1
0
1
0
2
0
0
0
1
0
2
0
0
1
0
0
0
0
0
2
0
2
2
2
0
0
2
3
0
0
1
0
0
0
1
1
2
0
0
0
0
2
1
1
0
0
1
2
1
1
2
1
0
0
1
0
2
2
0
1
0
0
2
0
2
0
3
2
0
2
1
0
0
0
0
2
2
0
2
1
2
0
0
0
1
0
1
2
1
3
1
3
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
1
2
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
2
0
0
1
2
0
2
2
1
1
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
2
0
0
1
2
1
3
6
0
0
1
0
1
2
0
1
2
0
0
1
1
2
0
2
1
2
0
2
1
1
0
1
1
1
2
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
2
1
1
1
2
2
1
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
1
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
1
1
0
0
0
0
0
0
2
0
2
1
0
1
2
1
1
1
0
0
0
0
0
0
1
0
1
2
0
0
1
1
1
0
2
0
1
0
1
0
0
1
1
0
1
0
0
2
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
1
0
1
2
0
2
2
0
0
1
0
1
0
2
1
0
0
1
3
1
0
0
0
0
2
0
0
1
0
2
2
2
0
0
2
0
2
1
2
0
1
0
1
0
1
2
0
2
1
0
0
1
0
1
0
0
0
0
1
1
0
2
0
1
1
0
0
0
2
1
0
0
1
1
1
1
2
0
1
2
2
2
1
0
0
0
1
0
2
0
0
1
0
0
0
0
3
1
0
1
0
0
0
1
1
1
0
0
0
0
2
0
0
0
0
0
1
1
1
2
0
0
2
0
3
1
0
0
1
0
2
0
0
2
0
2
2
0
2
0
0
1
2
1
0
0
1
0
0
0
1
1
2
0
0
1
1
0
2
0
2
2
0
0
0
0
0
0
1
0
0
0
0
1
2
0
1
1
2
1
0
0
0
1
1
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
2
0
0
0
3
0
1
2
2
1
2
1
0
1
0
2
0
1
0
0
2
0
1
0
1
0
1
0
0
0
1
0
0
1
0
0
0
1
0
2
0
0
0
1
0
0
5
0
2
1
1
2
0
1
0
2
1
2
0
2
1
0
2
0
1
0
3
0
1
0
2
1
0
0
2
0
1
0
1
0
2
0
2
0
1
1
1
1
0
0
0
1
1
1
2
0
1
0
0
0
0
2
0
1
1
0
1
2
2
0
1
0
0
0
1
0
1
0
0
0
0
0
2
0
2
1
1
0
0
0
0
0
0
2
1
1
0
1
0
2
0
0
1
1
1
0
1
2
1
2
0
0
2
0
0
2
0
2
0
0
0
2
2
1
0
0
1
0
0
0
2
0
0
0
2
1
0
2
3
0
0
1
1
1
0
1
0
2
0
0
0
1
2
0
0
1
0
1
1
0
1
1
1
0
0
0
0
1
1
1
1
1
0
0
0
2
2
2
0
1
0
0
0
1
1
0
0
0
2
2
0
2
0
1
3
0
0
2
1
0
1
1
0
1
2
2
1
0
0
0
0
1
1
1
1
1
0
0
2
0
0
1
0
2
1
2
0
0
1
0
0
1
2
3
0
2
0
0
2
0
0
0
0
0
1
1
2
0
2
0
0
2
0
0
2
0
0
0
1
2
2
0
0
0
1
0
0
1
0
0
0
2
0
0
0
1
1
2
2
2
1
2
1
1
1
3
2
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
1
0
1
0
0
1
0
0
0
2
1
1
1
0
1
0
1
1
0
0
2
0
0
0
1
2
0
0
2
1
1
0
1
0
0
1
1
2
0
2
0
0
0
1
0
0
1
1
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
1
1
2
0
2
0
2
2
0
2
0
0
0
0
0
1
0
1
1
1
2
2
1
0
0
1
0
0
1
1
1
5
0
0
0
0
0
2
2
1
0
0
1
2
1
2
1
1
2
2
0
0
0
0
7
1
2
1
1
0
0
1
1
0
0
0
0
0
1
0
1
2
2
2
0
0
1
1
0
1
0
4
0
0
2
2
0
0
0
0
0
1
1
0
1
0
1
0
1
0
2
0
0
1
2
1
0
1
0
0
0
1
0
0
0
0
1
0
2
0
2
2
1
0
1
0
1
0
2
2
0
0
2
0
2
0
0
2
1
1
1
2
1
2
2
2
0
0
1
0
0
0
2
1
0
1
0
2
0
1
0
1
1
0
1
0
0
1
0
1
2
2
0
0
1
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
2
1
1
0
2
0
3
0
1
1
1
1
0
0
1
0
0
0
2
0
1
2
2
0
2
0
0
0
2
0
0
1
0
0
0
1
1
1
2
0
1
1
0
0
0
1
1
0
1
1
0
0
1
1
0
1
0
0
2
2
0
0
1
5
0
2
0
0
1
2
2
0
2
2
0
3
0
0
1
0
0
1
1
0
2
1
0
3
0
2
0
2
2
2
0
2
0
2
0
0
0
1
0
0
1
2
1
1
2
1
1
0
1
0
1
2
0
1
1
0
2
0
0
2
0
1
0
0
0
0
0
1
1
2
1
0
0
0
1
1
2
1
0
0
0
1
0
0
0
2
0
1
2
0
1
4
0
0
2
1
0
2
1
1
0
0
0
2
0
2
0
0
0
1
0
1
2
0
0
0
0
0
1
1
0
1
0
1
1
0
1
1
1
0
1
2
2
1
1
0
0
1
1
0
1
2
0
0
1
0
0
0
1
2
1
1
2
2
0
0
0
0
1
2
2
2
0
0
0
2
0
1
1
1
0
0
0
0
1
0
0
0
0
1
1
0
2
2
3
1
2
2
1
1
0
2
1
0
0
1
2
0
2
0
0
0
0
2
0
2
2
2
0
0
0
0
2
2
0
1
1
2
0
0
1
0
0
0
0
2
0
2
0
3
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
2
0
1
0
1
0
1
2
2
0
0
2
0
0
0
1
0
1
0
1
0
1
0
2
1
0
0
0
1
0
2
2
3
0
0
1
0
0
0
1
1
0
1
2
0
1
2
0
0
2
0
0
2
1
0
0
0
2
2
0
0
1
0
0
0
0
2
0
0
0
0
1
1
1
0
0
2
0
4
1
0
0
0
0
2
1
0
1
1
0
0
1
1
1
2
0
1
0
0
0
0
1
1
0
0
2
2
2
0
0
1
0
0
1
1
0
0
0
1
2
1
0
0
1
0
0
0
1
0
0
2
2
0
0
1
0
2
0
1
0
0
0
0
2
1
1
1
2
3
2
0
0
0
1
0
0
1
1
0
0
2
0
0
1
2
0
0
2
0
2
2
2
1
2
0
0
0
0
0
2
2
0
0
0
2
0
1
2
0
1
0
1
0
0
0
0
0
1
1
1
2
2
0
1
1
0
0
2
1
0
0
0
0
1
0
0
1
1
0
1
1
1
2
1
0
0
3
1
1
0
0
1
0
0
2
0
0
0
0
2
0
2
2
0
1
0
2
0
0
0
1
2
2
0
0
0
5
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
1
1
1
0
0
1
0
0
2
1
0
0
0
0
0
1
2
1
0
2
0
0
0
0
0
1
1
2
0
0
1
1
2
2
1
0
0
0
0
0
0
1
1
0
0
0
1
1
1
0
0
0
1
1
1
2
0
0
1
1
0
2
0
2
0
2
1
1
2
1
2
0
1
1
1
1
1
0
1
1
1
1
1
0
1
0
2
0
0
0
0
0
0
2
0
1
0
0
2
0
2
0
0
2
1
1
2
0
0
0
0
1
0
0
0
0
2
2
0
2
0
2
1
0
1
0
0
0
1
0
0
0
0
0
1
2
1
0
2
0
0
2
1
0
1
0
1
0
0
0
0
2
0
0
4
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
1
1
0
1
0
0
2
1
2
0
0
5
1
0
0
0
0
0
0
0
0
0
1
0
1
2
0
2
2
0
2
0
1
0
1
0
0
0
1
0
2
1
0
1
0
0
0
0
0
0
0
1
2
0
1
2
0
2
1
0
0
1
3
1
1
2
0
0
0
1
1
2
2
1
2
1
0
0
0
2
1
2
2
2
1
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
2
1
1
1
1
4
0
0
2
1
0
0
0
1
2
1
1
0
1
1
0
2
2
0
1
0
1
1
1
0
3
0
0
0
0
1
0
0
2
1
2
0
1
1
1
0
2
1
0
1
0
1
1
1
0
0
1
0
1
0
2
1
0
2
0
0
0
0
0
1
0
2
0
0
1
2
0
2
2
0
2
0
1
2
0
1
0
0
2
0
2
1
1
0
0
0
2
0
2
2
1
0
0
0
2
0
0
0
0
0
0
2
1
1
2
0
2
0
2
2
0
2
6
1
1
1
0
0
1
0
0
0
1
0
0
2
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
1
0
0
1
0
1
0
0
2
0
1
1
1
1
0
1
1
0
0
0
0
0
1
0
0
2
0
1
2
0
2
1
0
0
2
0
0
0
2
1
0
0
2
0
1
0
0
2
0
2
0
0
0
1
0
0
2
0
0
1
0
0
1
0
1
0
2
1
0
2
0
1
0
0
0
0
0
1
2
1
0
0
0
1
2
1
0
2
0
2
0
2
0
0
1
1
0
1
1
2
0
3
0
0
2
1
6
1
2
2
1
0
0
1
0
2
0
1
2
1
1
0
0
1
0
2
0
0
1
1
1
1
0
2
0
0
0
1
1
1
2
0
1
2
3
0
1
1
1
2
1
0
0
1
2
0
0
2
2
1
0
1
2
2
2
0
0
0
5
0
0
1
2
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
1
0
2
1
0
0
2
0
2
0
1
0
1
0
0
0
0
0
2
0
2
0
1
0
1
0
2
1
3
0
0
0
1
0
1
0
3
0
1
0
0
0
1
0
1
0
2
1
1
2
1
0
2
0
1
0
0
0
0
0
4
0
2
1
1
1
0
3
1
0
2
1
2
2
0
0
0
0
2
0
1
1
1
3
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
2
1
0
2
0
1
0
0
0
0
0
2
0
5
1
1
0
1
0
1
0
0
0
0
2
4
0
0
1
0
0
0
0
0
3
1
1
0
1
1
0
0
0
0
1
0
0
0
2
2
1
0
2
0
0
2
0
0
0
2
0
2
0
0
0
0
1
1
0
0
2
2
1
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
1
2
2
0
1
0
1
0
0
2
1
0
0
0
0
0
1
2
2
2
0
0
0
2
1
0
2
1
2
0
2
8
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
3
0
0
0
1
2
0
2
0
2
1
1
0
0
1
1
2
0
2
0
2
1
0
0
0
1
1
1
1
0
1
0
1
1
1
2
1
0
1
0
0
0
0
0
0
0
2
1
0
2
0
0
1
2
1
2
1
2
0
0
0
0
0
1
1
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
1
0
2
0
1
0
0
1
1
0
1
0
0
0
0
1
0
0
1
1
0
2
1
0
0
1
0
2
0
0
1
2
0
2
0
2
1
2
2
0
0
2
0
1
0
2
0
2
1
0
0
1
0
2
0
1
2
0
1
1
0
0
0
0
2
1
0
0
0
1
1
3
2
0
2
2
0
0
3
0
2
1
1
1
0
2
0
0
0
2
0
0
0
0
1
2
0
1
1
1
0
0
1
2
0
0
0
2
1
1
0
0
0
1
0
0
1
0
1
2
2
0
0
0
1
0
2
2
1
1
0
2
0
0
4
0
1
0
0
0
0
1
2
1
0
0
0
0
1
0
0
0
1
2
0
1
0
0
1
0
0
0
0
2
1
1
2
0
0
0
2
0
2
1
0
1
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
2
2
0
0
1
0
1
0
1
2
2
0
2
2
2
0
0
0
0
1
2
0
1
0
2
0
0
0
1
2
1
2
0
0
1
2
1
1
0
0
0
0
0
0
1
1
2
2
1
1
2
2
2
1
1
0
1
1
0
0
0
0
0
0
2
0
0
0
0
2
2
0
1
2
0
1
1
1
0
0
0
1
0
2
0
0
2
1
1
0
0
3
0
1
1
0
1
0
1
2
0
1
1
0
2
1
0
1
0
1
0
0
0
0
0
1
2
0
2
0
0
2
1
1
2
0
1
0
1
0
0
1
1
0
2
1
2
1
1
0
0
2
0
1
0
2
1
0
0
1
2
1
0
0
1
1
2
0
2
2
2
0
3
2
1
0
3
2
0
2
0
1
1
0
1
2
1
0
0
0
0
0
1
0
1
2
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
2
1
0
2
0
0
1
0
0
0
1
2
2
2
4
2
1
0
0
2
1
1
0
0
0
0
3
0
1
2
1
0
1
0
0
1
1
1
0
2
1
1
0
1
0
0
0
0
0
1
2
0
2
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
1
2
0
0
1
1
0
2
1
0
0
2
1
0
1
1
0
2
2
2
0
0
2
0
0
2
1
1
1
0
0
0
0
1
2
1
1
0
0
2
0
0
0
1
2
1
0
2
1
1
2
2
0
0
2
2
0
0
0
0
0
0
0
0
1
2
1
0
1
0
0
1
0
1
1
2
1
0
1
0
0
0
1
0
0
0
2
2
0
2
0
0
0
0
0
1
0
0
0
1
0
2
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
1
1
0
2
0
1
1
0
1
2
0
2
1
1
0
0
0
0
0
2
2
2
0
0
0
0
0
1
0
2
0
1
2
0
0
1
1
0
0
2
0
2
0
0
1
2
2
2
0
2
2
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
2
0
1
2
0
0
2
0
0
0
1
2
0
1
2
1
0
1
2
1
0
1
1
1
1
1
2
0
0
2
2
1
0
0
0
1
1
0
2
0
0
1
1
0
0
2
1
0
0
0
0
2
1
2
0
2
1
2
1
0
1
0
2
0
0
0
1
1
2
2
2
1
0
2
0
0
2
0
1
0
1
2
1
0
1
2
0
2
1
0
1
0
0
0
1
0
0
1
1
0
1
0
0
1
1
0
0
0
0
1
0
0
2
0
1
3
1
2
1
1
0
3
0
0
0
1
0
0
2
0
2
0
0
1
0
2
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
3
1
0
0
0
1
0
1
2
0
0
0
0
2
3
1
0
0
1
1
3
1
1
2
0
1
0
2
2
0
0
0
0
0
0
0
1
0
1
2
0
1
0
0
1
0
2
0
0
0
0
2
1
0
1
1
0
0
0
1
0
1
2
0
0
1
1
0
0
0
1
0
0
0
0
0
2
2
0
0
1
1
0
0
1
2
0
1
0
0
1
2
1
1
0
1
1
1
1
0
0
0
1
0
0
1
0
0
2
2
0
1
2
1
1
1
0
1
0
2
1
1
0
0
0
0
1
0
2
1
2
1
0
0
2
0
0
0
1
2
2
1
1
0
0
2
0
0
1
2
2
2
0
0
0
2
0
2
0
1
0
1
1
0
0
0
1
0
0
0
0
2
2
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
1
0
1
0
0
0
1
1
1
2
2
0
0
0
0
0
2
0
2
0
1
0
1
0
0
1
0
1
1
1
2
0
0
0
0
1
0
0
0
2
2
1
0
1
0
0
1
2
0
0
0
1
0
0
2
1
0
2
0
1
0
0
1
0
0
0
2
0
0
1
1
0
0
2
0
0
0
2
1
1
0
2
0
2
0
2
0
0
1
0
1
3
0
2
0
0
1
0
1
2
1
1
1
1
0
1
1
1
1
0
1
1
2
1
0
0
2
2
0
0
2
0
0
2
0
0
1
0
2
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
1
1
2
1
0
2
1
0
0
1
2
0
3
0
0
1
0
1
0
2
2
1
0
1
0
1
0
2
1
2
0
0
2
1
0
0
0
0
1
0
0
1
1
0
1
3
2
0
0
0
0
0
1
2
2
0
2
0
0
2
0
0
2
0
0
0
1
1
2
0
1
1
0
2
0
0
1
1
2
0
3
2
0
1
0
2
2
0
1
2
0
1
0
0
2
0
0
0
0
1
2
0
0
2
0
1
0
0
0
0
0
0
2
2
0
2
1
1
0
2
0
1
0
2
0
1
1
1
1
1
1
0
0
0
0
1
1
0
0
1
2
1
3
1
0
0
0
0
0
0
0
1
2
0
2
2
1
1
1
1
0
1
2
0
1
0
0
0
0
1
0
1
1
0
0
0
2
1
1
2
1
0
2
0
0
0
0
2
2
0
2
3
0
0
1
0
0
2
0
0
0
1
1
0
1
0
1
3
1
0
0
0
0
0
1
0
1
0
2
1
0
0
0
2
0
0
1
1
0
1
0
0
0
0
0
0
0
1
1
3
4
0
1
0
0
2
0
2
1
1
0
2
0
0
0
0
1
2
0
1
1
1
1
1
0
1
1
0
0
0
1
0
0
0
1
3
0
0
2
2
2
2
1
0
2
0
2
0
2
0
0
1
1
0
1
0
0
1
0
0
0
0
1
1
2
1
2
0
0
0
0
0
0
1
2
0
1
1
0
0
1
1
1
0
0
0
1
0
0
0
2
0
0
1
0
1
0
0
2
2
0
1
1
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
2
2
1
0
0
1
2
1
2
2
0
0
0
0
1
1
1
1
1
1
0
1
1
0
0
0
0
0
0
1
1
0
0
1
2
0
0
0
1
2
0
1
1
0
2
0
0
0
1
1
0
2
0
0
0
0
1
2
0
0
0
1
1
1
0
0
1
2
2
0
0
2
0
0
2
1
1
2
1
1
0
2
2
2
0
0
1
1
2
2
1
1
0
0
0
0
1
2
0
0
0
1
0
1
2
1
1
0
1
3
0
1
1
0
1
1
2
0
1
1
2
0
0
2
0
0
1
2
0
1
0
0
0
1
0
0
1
1
2
0
0
1
1
3
1
1
1
2
2
0
1
1
1
0
0
0
1
0
2
0
0
0
2
1
0
1
2
1
1
0
0
2
0
1
0
0
1
1
0
0
0
0
0
1
2
3
1
1
0
2
1
2
1
2
0
1
0
1
0
1
0
1
2
0
0
0
2
1
1
0
1
0
0
0
1
1
0
0
0
1
0
1
4
0
0
2
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
2
1
1
3
0
0
1
2
1
1
1
0
1
1
0
1
0
2
0
1
1
0
1
1
0
2
0
0
0
0
1
1
1
0
0
0
0
2
1
1
1
0
0
0
0
2
0
0
4
0
2
1
1
2
0
1
0
0
0
1
0
1
0
0
0
2
2
0
0
0
0
1
1
0
1
0
0
2
0
1
0
1
1
1
0
0
0
1
1
1
0
1
0
0
1
0
0
1
2
2
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
1
3
1
0
2
0
2
0
0
0
0
1
0
0
0
1
1
0
2
2
0
0
0
0
0
1
2
0
0
0
0
1
0
1
0
2
0
4
0
2
0
2
1
2
1
2
0
2
1
0
0
2
1
1
0
0
0
1
0
0
1
1
0
3
1
0
1
0
0
0
1
0
1
0
3
0
0
1
0
0
0
0
1
0
0
0
0
0
1
2
2
0
0
2
0
0
1
0
0
2
0
0
2
2
0
0
1
0
2
1
2
0
1
0
0
0
1
0
0
0
1
1
0
0
2
2
0
1
2
0
0
1
0
0
1
0
0
1
0
0
0
1
0
1
0
2
2
2
0
1
1
1
3
0
0
0
0
0
0
2
0
1
1
1
0
0
2
1
0
0
0
0
0
0
0
2
0
2
2
0
0
0
2
0
0
1
1
0
0
2
0
0
0
1
0
0
1
1
0
0
1
0
0
1
1
1
0
0
1
0
2
0
0
0
0
0
1
0
0
0
2
0
0
1
0
1
0
2
2
1
1
1
1
0
0
0
2
1
2
1
0
1
0
0
1
1
2
2
0
3
2
2
2
0
2
1
0
0
1
0
3
5
0
0
0
0
1
0
0
2
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
1
1
1
0
0
1
0
0
2
1
2
0
1
1
1
1
2
0
1
0
1
0
1
0
2
2
2
1
1
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
1
1
0
1
1
0
1
0
0
0
0
0
1
1
0
1
0
1
1
2
0
0
0
1
2
0
2
2
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
5
0
0
0
0
1
2
0
0
1
0
3
5
1
1
6
0
1
0
0
1
2
1
1
0
0
1
0
0
1
1
3
3
0
1
2
0
0
1
1
2
1
1
0
0
2
2
0
1
1
0
0
0
0
2
2
0
0
0
1
2
2
1
1
2
2
1
0
2
0
0
2
0
1
0
0
0
1
0
1
2
1
0
2
0
2
1
0
2
2
0
2
2
0
1
0
0
2
1
1
1
0
0
1
0
1
0
2
0
0
2
0
0
0
2
1
0
0
2
0
0
1
2
2
0
0
3
0
0
0
0
0
1
0
2
2
2
1
2
0
1
1
0
1
1
0
2
0
6
0
2
0
1
1
1
0
0
0
0
2
1
1
0
0
0
0
0
0
1
0
0
1
0
0
1
1
1
2
4
0
1
0
0
0
2
2
0
2
1
0
1
0
0
1
1
2
0
0
2
2
0
0
0
1
2
0
0
2
1
2
0
0
1
2
0
0
0
1
0
1
0
1
0
1
0
2
0
2
0
0
0
0
2
2
1
2
1
2
0
0
1
0
0
1
2
0
0
0
1
0
1
1
2
3
1
0
2
2
2
2
1
2
0
1
1
2
0
2
0
0
0
4
2
0
0
1
0
0
1
0
0
1
0
0
2
2
0
2
1
0
1
0
1
1
0
1
0
1
0
0
1
1
2
1
0
0
2
0
0
2
0
2
1
0
0
0
2
1
2
0
2
2
0
0
1
0
3
0
2
2
1
0
1
0
0
2
2
0
1
2
2
1
0
0
0
1
1
1
1
0
0
1
1
1
0
2
0
0
0
1
2
0
2
1
1
1
0
0
0
0
0
3
0
1
1
0
0
0
0
1
0
1
3
2
1
0
1
0
0
0
0
2
1
3
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
5
1
3
0
0
1
0
0
2
1
1
0
0
0
1
2
0
0
2
2
2
0
0
0
0
2
2
1
2
1
1
2
0
0
0
0
0
1
1
0
1
2
1
2
0
0
1
0
2
0
3
1
0
0
1
1
0
1
0
0
0
2
1
1
2
1
1
0
1
3
1
2
0
1
1
1
2
1
1
1
1
1
0
1
1
0
3
1
2
0
2
0
0
1
1
1
0
0
2
2
0
0
1
0
1
0
0
0
0
2
1
1
0
0
2
3
1
1
2
0
0
0
2
0
0
1
0
2
0
2
0
0
1
0
1
0
2
0
2
1
0
1
2
1
1
0
0
1
1
0
1
0
1
3
0
3
0
2
2
2
0
2
0
1
0
0
1
0
0
1
1
5
1
1
1
1
2
1
0
1
2
1
1
1
1
0
2
2
1
1
1
0
1
1
2
1
0
0
0
2
0
0
1
1
0
0
0
1
0
0
1
1
1
0
2
1
1
1
0
0
0
0
2
0
0
1
1
0
0
0
1
1
2
1
1
2
1
0
0
0
0
0
2
0
1
0
0
1
0
0
0
1
3
2
1
1
0
0
0
0
1
0
2
0
0
2
0
0
0
0
1
1
0
0
0
2
1
1
1
0
0
1
1
1
0
1
0
2
1
0
0
2
2
0
0
2
0
0
0
2
1
0
2
1
0
0
1
0
0
2
0
1
0
0
1
2
0
0
1
0
0
1
1
0
1
0
0
2
0
0
0
0
2
2
0
1
2
0
0
0
0
0
0
2
0
0
2
2
1
0
2
1
0
1
0
0
2
0
0
2
1
0
2
0
2
0
0
2
1
2
0
1
1
1
0
1
0
1
0
1
2
0
2
1
0
1
1
0
0
1
0
1
2
2
0
2
2
0
1
0
0
1
0
0
0
0
2
0
1
1
2
2
0
0
1
1
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
1
0
1
1
0
1
2
1
0
0
0
0
0
2
1
0
1
2
0
1
1
0
1
2
1
1
0
1
1
1
0
0
3
1
0
0
3
0
1
1
0
0
1
1
1
0
0
0
0
1
0
1
0
0
0
1
0
2
0
2
2
2
1
0
0
0
1
2
1
0
1
0
1
1
1
0
0
1
0
1
2
2
2
2
1
1
0
3
1
2
1
1
1
1
2
0
0
0
0
2
0
4
0
2
0
1
0
2
1
0
0
0
0
0
2
0
1
3
0
0
1
0
1
1
0
0
0
0
0
1
0
0
1
1
2
0
1
0
0
2
2
1
1
1
2
0
0
2
2
2
0
1
1
0
0
0
1
0
1
0
0
4
0
2
0
0
0
0
0
0
0
1
3
0
2
0
2
1
1
0
1
2
2
0
1
0
1
1
1
0
2
0
2
0
1
0
0
0
2
2
0
1
0
0
2
0
2
0
2
0
2
2
0
0
2
2
0
1
0
1
2
0
1
0
0
1
2
0
0
0
0
0
0
0
2
1
0
6
0
1
0
2
0
1
0
1
2
1
0
2
0
1
2
0
1
1
1
0
0
0
2
2
1
2
2
0
0
3
2
0
0
5
0
0
0
0
0
1
0
1
0
1
1
2
1
0
0
0
0
3
0
0
0
1
0
0
0
0
2
1
2
0
2
0
0
3
0
2
1
2
0
0
0
0
0
2
0
0
0
2
4
2
0
1
1
0
1
2
0
2
2
1
0
1
0
0
0
0
0
2
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
1
1
0
0
0
0
2
0
1
0
2
1
2
1
0
1
2
1
0
0
0
2
1
0
1
2
1
2
2
0
0
2
1
0
0
0
2
0
0
0
1
1
0
1
0
0
3
1
0
0
0
1
0
0
2
0
1
2
0
0
1
0
0
0
0
1
0
2
1
2
1
0
0
0
0
2
1
2
1
1
0
2
0
1
1
2
0
0
0
3
1
1
0
1
0
0
1
1
0
0
1
2
0
0
1
0
1
0
0
1
0
2
1
0
2
2
0
1
1
1
1
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
2
2
0
1
1
2
0
1
1
0
2
2
0
0
0
0
0
1
0
2
6
2
0
2
1
0
2
0
1
0
1
0
2
0
0
2
0
0
2
0
0
0
0
1
0
2
1
2
0
0
1
1
1
0
1
1
2
1
2
0
0
0
0
1
0
0
1
1
1
0
1
0
0
0
2
2
0
2
0
0
0
1
1
0
0
0
2
1
1
0
0
0
1
1
0
0
2
0
1
0
0
1
1
0
1
0
0
1
0
0
0
2
1
0
2
0
0
0
2
0
2
0
0
2
0
0
1
1
0
0
2
1
1
1
1
1
1
2
1
0
0
2
2
0
0
2
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
2
2
2
0
0
0
0
0
0
0
1
0
0
1
2
2
0
0
0
1
0
2
0
0
2
2
0
1
0
6
0
1
0
0
2
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
1
1
0
1
1
1
0
0
0
2
0
0
1
0
0
2
0
1
1
3
0
2
0
0
0
1
0
0
1
2
0
1
1
2
0
0
0
1
0
2
0
0
0
0
0
0
0
1
1
3
0
1
1
0
1
1
1
2
2
2
2
0
2
0
1
0
0
0
0
1
2
0
1
1
0
0
0
1
1
2
0
0
0
1
0
1
0
0
0
1
1
0
1
1
0
2
1
0
2
0
0
2
0
1
2
0
1
1
0
0
1
2
0
1
0
0
0
0
2
0
0
0
1
1
2
0
0
0
0
1
1
0
0
0
2
2
1
0
0
0
2
1
0
2
2
0
1
1
0
2
0
0
0
0
0
0
2
2
0
0
0
2
2
2
0
0
0
1
1
0
0
1
0
1
2
1
1
0
1
1
0
0
0
0
2
0
1
0
0
2
2
1
0
0
0
1
0
0
0
0
1
2
1
0
1
0
2
0
2
0
0
1
0
0
1
2
1
0
1
2
1
1
0
1
0
0
0
0
2
0
2
0
2
0
2
0
0
2
0
1
2
0
1
4
1
2
2
0
0
2
1
0
1
0
1
0
1
0
1
1
2
0
1
1
0
0
1
1
1
0
2
2
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
1
0
1
1
1
0
1
1
1
2
0
0
0
2
2
1
0
2
0
2
0
0
0
0
0
2
0
0
0
1
1
1
1
0
0
2
0
1
1
0
2
0
0
1
0
1
0
0
0
5
2
2
0
0
0
1
1
1
1
1
1
0
3
1
0
2
2
0
1
0
2
1
0
0
2
0
0
0
1
1
0
1
0
0
0
1
1
1
1
1
0
1
2
2
1
1
1
0
1
2
1
0
1
0
2
1
2
2
0
1
0
0
1
0
0
1
1
1
1
2
1
0
0
7
0
0
2
1
0
0
0
2
0
1
0
0
0
1
0
0
0
2
1
2
0
0
1
1
1
1
1
2
0
0
1
2
1
0
0
0
2
2
1
1
2
1
4
0
0
1
0
0
0
0
0
1
0
2
2
0
1
0
0
0
2
4
0
1
1
0
2
0
0
1
0
1
0
0
0
2
0
0
1
2
2
0
0
1
2
0
1
0
0
1
0
0
1
1
0
0
0
1
0
0
0
3
1
0
1
1
0
0
0
0
1
2
1
2
1
0
1
0
0
2
0
1
2
2
2
0
1
2
0
1
0
0
2
2
2
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
1
2
0
0
0
2
2
1
1
1
6
0
0
1
2
0
0
1
1
0
1
0
0
1
1
0
0
1
1
0
1
0
2
7
1
2
1
0
0
2
0
1
0
0
1
1
0
0
2
1
2
2
1
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
2
2
1
0
2
1
1
0
0
1
0
0
0
2
2
1
1
2
0
0
0
0
0
0
1
0
1
0
0
1
1
2
1
1
2
0
1
2
0
0
1
2
2
0
1
1
0
0
2
0
0
1
0
2
1
1
1
0
2
1
1
1
2
1
2
2
2
1
0
1
2
2
0
0
1
0
1
2
0
1
1
0
1
1
1
0
2
0
0
2
3
0
2
2
0
2
1
0
0
1
1
0
0
0
0
0
0
0
1
1
2
0
1
1
0
1
2
0
1
0
3
1
0
2
0
1
0
0
1
2
1
0
0
1
0
1
1
0
0
0
1
1
0
2
1
0
1
1
2
0
1
1
0
0
0
0
0
0
1
0
2
1
0
0
0
1
0
0
3
0
2
0
0
1
4
0
1
0
0
2
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
2
2
1
1
0
0
2
1
2
0
2
0
1
1
0
2
1
3
0
1
2
0
1
2
1
0
1
0
0
0
2
0
0
0
0
1
0
1
0
0
1
0
0
0
2
1
0
1
0
1
1
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
2
0
2
0
1
3
0
0
0
1
0
1
2
0
1
0
1
1
1
2
0
0
1
2
3
0
0
1
2
1
0
0
0
0
0
0
0
2
2
0
1
0
2
0
1
2
0
3
0
1
1
2
0
3
0
2
2
1
2
2
1
0
2
1
2
0
0
1
0
0
1
0
0
2
0
0
1
0
2
7
2
0
1
0
0
1
1
0
1
0
0
1
1
0
1
0
0
2
0
2
2
0
0
1
2
0
0
0
0
1
2
2
2
0
1
1
0
2
2
1
0
1
0
2
2
0
2
1
0
2
0
0
1
1
2
1
2
2
2
0
1
1
2
0
0
1
2
1
2
2
1
0
1
0
0
0
1
1
0
0
2
1
2
0
0
0
1
0
0
0
2
0
1
0
1
0
1
2
0
2
0
0
0
2
1
1
1
2
1
0
1
1
2
1
0
0
0
0
0
3
2
0
2
0
0
0
0
0
0
0
2
1
0
0
0
2
4
1
0
0
0
1
0
0
0
2
0
1
0
0
0
0
1
1
2
0
2
1
1
0
0
0
0
1
0
1
1
0
0
1
0
2
0
0
0
2
1
4
0
2
0
1
2
0
0
1
0
1
1
0
2
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
1
1
0
2
1
1
0
1
0
2
0
0
1
2
2
1
0
1
0
2
0
0
1
1
1
0
2
1
1
0
5
0
0
2
0
0
2
1
0
1
0
0
0
1
1
1
0
1
0
1
1
0
0
1
0
0
1
0
0
0
0
2
0
1
0
0
2
2
0
0
2
0
0
2
2
0
2
0
0
1
1
1
1
1
0
0
0
1
2
1
1
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
1
0
2
0
2
0
0
2
1
3
1
1
1
0
0
0
0
1
1
1
0
0
1
1
0
0
1
0
0
2
1
1
2
2
1
2
0
0
2
0
1
1
0
2
0
0
1
1
1
0
0
0
1
1
0
2
0
0
1
0
0
1
2
1
0
0
1
1
2
2
0
0
1
1
1
1
0
1
1
1
2
2
0
2
2
1
1
1
2
0
1
0
1
0
2
1
2
0
0
2
2
0
0
2
0
0
0
2
0
0
1
1
0
2
4
0
0
2
2
2
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
2
1
0
0
0
0
0
0
2
0
0
2
1
2
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
1
1
1
2
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
1
0
2
0
1
0
0
0
1
1
1
1
0
2
1
2
1
0
2
0
1
0
1
0
0
1
2
0
4
0
0
0
0
0
1
4
2
0
0
1
1
3
1
1
1
0
2
0
0
1
1
0
0
1
1
0
1
2
0
0
0
1
1
0
0
2
0
1
0
1
0
0
1
0
1
0
2
0
0
2
0
0
1
0
0
0
0
1
2
2
0
2
1
0
2
0
1
0
0
0
0
2
2
1
0
1
1
0
1
0
1
0
0
2
1
0
1
0
3
0
0
2
0
1
1
2
0
1
1
1
0
2
0
2
2
1
0
0
0
0
0
1
0
1
0
1
1
1
0
0
1
0
2
1
0
1
0
2
1
0
1
0
0
0
0
0
1
0
2
0
2
2
0
0
2
0
0
0
0
0
0
1
2
0
0
2
2
0
0
1
1
3
0
0
2
1
2
0
2
0
1
1
0
1
0
0
2
1
2
1
2
0
1
0
2
0
1
0
1
2
0
0
1
0
0
0
0
1
1
1
0
0
2
1
0
0
0
0
0
0
0
0
1
1
2
1
1
0
0
1
0
0
0
0
2
1
0
2
2
0
1
0
1
3
1
1
0
2
1
0
0
1
1
1
1
0
2
1
0
0
0
0
2
2
0
0
0
0
0
3
1
0
0
1
0
2
0
0
2
1
0
0
1
2
0
0
0
0
0
0
1
1
0
1
0
3
0
0
0
0
3
0
2
0
0
0
2
0
2
1
0
4
2
0
1
2
0
1
0
0
1
0
2
0
0
0
0
2
1
0
0
3
1
2
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
1
0
1
0
0
1
2
0
0
0
2
1
1
2
0
2
1
2
1
0
0
2
2
1
0
0
0
1
0
0
0
0
1
1
2
0
0
1
0
1
1
2
0
0
1
0
0
2
2
1
1
2
1
2
0
0
0
1
0
0
1
1
1
2
0
0
1
2
0
2
2
2
0
1
2
2
0
2
1
2
1
0
0
1
2
0
1
1
1
2
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
2
2
1
0
0
1
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
3
0
1
2
0
0
2
1
1
1
0
2
1
0
1
0
2
1
1
2
1
0
2
0
2
0
0
0
0
2
0
1
0
2
0
0
0
3
2
0
1
2
0
0
1
4
2
0
1
0
0
0
0
1
1
1
1
1
1
1
1
0
1
1
3
1
2
0
0
0
0
2
4
0
1
0
0
2
1
0
1
1
2
1
0
0
1
0
1
1
0
0
1
3
0
0
0
2
0
0
0
2
2
1
1
0
1
0
1
0
3
0
0
2
1
0
2
0
0
0
3
0
2
2
1
0
0
0
0
1
0
2
0
2
2
6
0
0
0
0
2
2
0
0
0
0
2
1
0
0
0
1
2
0
0
0
1
1
1
1
0
0
2
0
0
2
1
0
0
2
1
0
0
0
0
2
0
2
0
1
1
1
1
1
1
0
1
0
2
1
0
1
0
0
0
2
0
2
1
0
2
2
0
0
2
1
1
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
1
1
0
2
0
0
1
2
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
1
2
0
0
2
1
0
1
0
0
2
0
2
1
1
0
0
1
0
0
2
1
2
1
1
2
0
1
2
0
1
0
1
0
0
0
0
1
3
2
1
0
0
2
1
1
2
2
2
0
3
1
3
0
1
0
1
2
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
1
1
0
0
0
1
1
1
0
1
0
0
0
0
1
2
0
1
0
0
1
0
0
1
1
0
1
0
1
0
1
1
1
2
0
2
1
0
0
1
0
2
0
1
0
1
0
2
0
0
0
1
0
0
2
2
1
0
0
0
2
1
0
2
2
0
3
1
0
1
2
1
2
0
1
2
0
2
0
0
0
1
2
0
0
1
0
2
1
0
0
2
1
2
0
0
0
0
0
0
2
1
2
1
2
0
1
0
0
0
0
0
2
1
2
1
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
2
2
0
0
2
0
2
1
0
2
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
2
2
0
1
2
1
1
0
2
0
0
1
1
0
0
0
1
0
0
0
2
0
0
1
2
0
1
0
0
1
0
1
0
1
0
2
2
0
1
1
0
2
0
2
2
0
0
1
0
0
0
2
1
0
1
0
1
0
0
0
1
2
0
2
1
0
1
1
1
1
2
0
1
0
4
2
0
0
2
0
1
1
2
0
0
1
1
1
2
0
0
2
1
1
1
1
1
1
1
1
0
0
0
2
0
0
2
0
1
0
0
1
0
2
2
0
0
2
0
2
2
1
0
0
1
2
0
0
0
2
0
0
1
0
3
0
0
0
1
0
1
1
0
2
2
2
0
0
1
0
0
1
2
2
1
2
1
2
0
0
1
0
0
1
0
2
2
2
1
1
0
0
1
0
2
0
2
0
0
1
0
2
0
0
0
0
4
0
2
0
0
1
1
1
0
0
1
0
0
0
0
0
2
1
2
1
2
0
0
3
1
0
2
1
0
1
3
1
1
2
1
1
0
0
0
0
2
2
1
0
2
8
2
1
0
1
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
1
1
3
2
0
0
0
0
0
2
1
1
2
2
0
1
0
0
3
0
0
0
0
0
1
2
0
0
0
0
1
1
0
0
1
1
0
0
0
2
1
0
1
1
1
0
3
2
1
1
1
1
2
2
0
2
0
0
1
2
1
1
1
5
0
0
1
0
1
0
0
1
1
1
0
1
0
0
0
0
1
0
0
3
1
1
0
0
0
1
1
0
0
1
2
1
0
0
0
1
0
2
1
1
1
1
2
1
2
0
1
2
0
0
0
0
0
0
1
1
2
0
0
0
0
2
0
0
1
0
2
0
0
2
0
3
1
1
0
1
0
0
2
0
0
1
1
1
0
1
2
1
1
0
2
2
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
1
2
1
1
0
2
2
2
0
0
2
0
1
0
0
0
2
1
0
0
2
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
3
1
2
1
1
1
0
0
0
0
0
3
0
0
0
1
1
1
0
0
2
2
0
1
2
0
1
2
0
0
2
1
0
0
0
0
0
0
0
0
1
3
0
0
1
2
1
0
0
0
0
0
1
0
1
1
0
1
0
0
1
0
1
0
1
0
0
1
1
0
0
3
0
1
2
1
0
1
1
0
0
1
0
0
0
0
0
2
0
1
1
2
0
0
0
2
1
1
0
1
2
0
0
2
0
1
1
0
0
1
1
2
1
2
0
0
2
0
1
0
0
2
0
0
2
0
1
1
0
0
0
1
0
3
0
1
0
0
0
0
0
2
1
4
2
0
2
1
2
1
0
0
2
2
1
1
2
0
0
0
2
1
2
0
1
2
0
0
2
0
2
1
1
0
0
0
1
1
2
1
1
1
1
0
0
0
2
2
2
0
0
2
0
0
0
0
0
1
0
1
1
0
2
0
1
0
1
0
1
0
1
0
1
2
1
1
1
1
1
0
1
0
2
0
0
1
0
1
2
0
0
1
0
0
0
0
1
0
2
0
0
0
3
0
2
0
1
1
2
1
2
1
0
0
1
1
1
0
0
0
1
1
0
1
1
0
1
0
0
1
0
0
2
1
1
0
0
2
0
2
0
0
1
1
0
2
2
1
2
1
0
0
1
0
0
0
2
1
0
2
2
0
1
0
2
0
1
1
1
0
1
2
1
0
2
1
2
1
1
0
0
0
2
1
0
1
1
2
1
0
1
0
0
1
1
0
0
0
0
1
1
1
0
2
1
0
2
2
1
1
0
1
0
1
0
0
3
2
1
2
0
0
1
1
0
0
2
2
2
2
0
0
1
2
0
0
1
0
0
0
0
1
1
0
0
1
1
1
1
0
0
1
0
0
0
2
0
0
2
2
3
1
1
2
3
1
1
1
2
1
2
2
1
0
0
0
2
1
0
1
0
1
2
2
0
1
0
1
0
2
1
1
0
0
2
0
0
1
1
0
1
2
1
1
0
2
0
0
2
2
1
0
2
2
0
0
0
0
1
0
0
0
0
0
2
1
0
1
0
0
0
4
0
2
1
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
1
0
2
0
2
0
1
0
1
1
0
1
0
0
0
2
1
2
1
0
1
0
1
0
0
0
1
0
1
1
2
1
1
0
1
0
2
0
0
1
0
4
2
1
1
0
1
1
0
1
0
0
1
0
0
0
1
0
1
2
0
1
0
0
0
1
1
0
0
0
0
0
2
2
1
2
2
0
0
0
1
0
1
1
1
1
2
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
1
0
2
0
1
0
0
1
2
2
2
0
1
0
1
0
2
0
0
1
0
1
1
0
0
1
1
0
1
0
1
1
0
2
2
0
2
0
0
0
0
0
0
1
0
2
0
1
1
0
1
1
2
0
1
1
0
0
0
0
0
0
2
0
0
0
4
2
0
0
2
1
1
2
0
1
0
0
1
1
5
1
1
3
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
2
0
1
0
0
1
0
1
0
0
1
0
2
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
1
0
2
0
0
1
2
1
1
2
0
0
1
1
0
0
3
2
0
0
0
0
5
2
0
2
0
1
0
2
2
2
0
0
2
1
0
1
2
0
1
2
0
0
1
1
0
2
1
0
0
0
1
0
2
0
3
2
0
2
2
0
0
0
1
1
0
2
2
1
0
1
0
1
2
3
1
1
2
2
1
2
2
0
2
1
0
0
0
0
0
1
2
0
0
1
0
0
2
1
0
0
0
0
4
3
1
1
1
0
1
0
1
1
2
0
0
0
2
2
1
0
1
2
0
1
1
1
0
0
1
1
1
1
3
0
0
0
0
2
1
2
0
2
0
0
0
2
2
2
1
0
0
1
1
3
0
2
0
0
0
2
0
0
1
1
1
1
1
1
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
2
1
0
0
0
1
2
1
2
1
1
2
1
0
2
0
0
0
0
1
1
0
0
0
1
0
1
0
2
2
0
0
0
1
0
2
0
0
2
1
1
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
6
0
0
2
0
2
0
0
0
1
1
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
2
0
2
1
0
0
0
1
2
1
0
0
2
0
0
2
0
1
0
0
0
0
2
1
0
2
0
0
0
0
4
2
2
2
0
2
2
0
1
1
5
1
2
1
2
0
1
0
2
0
0
1
0
2
1
0
2
1
2
1
0
2
1
0
2
0
0
2
0
0
1
1
0
2
2
1
0
1
1
1
0
1
0
1
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
2
2
1
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
3
2
1
0
1
0
1
0
1
1
1
0
1
2
2
1
2
2
2
0
1
1
1
0
1
0
2
0
0
0
0
1
2
2
2
0
1
0
2
0
2
1
1
0
1
2
2
0
0
0
0
0
1
1
0
0
0
1
0
2
0
1
0
0
1
2
0
1
1
0
0
2
0
0
2
0
2
0
2
0
1
0
0
1
1
0
2
1
1
0
0
0
2
0
1
0
2
2
0
2
0
1
1
2
1
0
0
0
0
1
2
2
0
0
1
0
1
0
0
1
1
0
0
2
2
0
0
2
2
1
2
0
1
0
0
1
2
1
0
2
3
0
0
0
1
1
0
2
1
1
0
2
1
0
0
0
3
2
1
1
0
2
0
0
0
2
0
1
2
5
1
0
0
2
0
5
3
1
0
0
1
2
1
1
0
0
0
0
0
2
1
1
0
0
0
1
1
0
0
0
1
2
1
0
0
0
1
2
0
2
0
0
1
0
0
0
1
2
0
2
1
2
0
0
1
0
0
0
0
1
1
1
1
2
0
2
0
0
0
0
2
2
1
1
0
1
3
5
1
0
0
0
0
0
2
0
1
0
1
1
1
0
2
0
1
2
0
0
1
1
1
2
1
4
0
1
1
0
1
2
1
1
0
2
1
2
1
0
2
0
0
1
0
2
1
0
0
1
1
2
1
2
0
0
3
1
2
2
0
2
1
1
1
1
1
0
0
0
2
2
1
2
2
0
1
2
0
0
2
2
0
0
0
1
0
1
1
1
0
1
2
0
0
0
1
0
0
1
0
0
2
0
0
0
1
2
2
4
0
0
0
1
2
1
0
2
2
0
1
0
0
1
2
1
1
0
1
0
1
0
2
0
0
1
0
1
0
2
0
1
0
0
2
2
0
0
0
1
0
0
2
2
1
1
0
2
0
2
0
1
1
2
0
0
1
2
0
3
2
0
1
1
0
2
1
2
0
0
0
0
0
0
2
0
0
1
0
2
1
0
0
0
0
1
0
2
0
1
1
0
1
1
1
2
0
1
2
1
1
1
2
2
1
2
0
0
0
2
0
1
0
0
2
1
2
2
0
0
2
0
2
0
0
0
1
0
2
2
2
1
2
2
0
2
0
0
1
0
0
2
0
2
1
0
1
0
1
1
0
1
1
2
1
0
0
1
0
0
1
1
2
1
0
2
1
1
0
4
1
0
0
0
0
0
0
0
0
1
0
1
2
2
0
0
0
1
0
2
2
0
1
1
0
0
1
1
1
4
0
0
0
0
0
0
1
1
2
1
1
2
2
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
2
1
1
0
2
0
1
0
0
0
2
1
0
2
6
1
1
0
0
1
1
0
0
0
0
1
2
0
0
0
0
1
1
0
3
1
1
0
2
1
1
0
1
0
4
5
0
0
0
2
1
1
0
1
1
0
0
1
0
0
0
1
0
1
1
0
0
1
0
0
0
0
1
0
1
0
0
1
0
1
2
0
0
0
2
0
0
0
0
0
1
1
1
0
0
0
2
2
0
0
1
1
0
0
0
1
1
0
1
2
0
0
1
2
1
0
2
1
1
2
0
0
0
1
0
5
1
0
1
0
2
0
2
2
0
0
2
0
0
0
2
1
0
0
0
0
2
2
0
0
2
1
0
1
0
0
0
1
0
1
1
0
0
0
1
1
0
0
0
0
1
1
0
2
2
2
0
0
0
3
0
1
0
0
0
0
4
2
2
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
2
0
1
1
0
1
0
0
1
1
1
2
2
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
1
1
1
0
0
1
2
0
0
0
0
2
2
1
0
0
1
0
1
0
0
2
1
1
3
0
2
1
1
0
0
0
1
2
0
0
0
0
0
2
2
1
0
1
2
0
0
0
0
0
2
0
0
2
0
0
1
1
2
0
0
1
0
0
1
0
1
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
2
1
0
0
0
0
1
0
1
0
0
2
1
1
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
2
0
4
2
0
1
0
2
1
0
0
2
0
1
3
3
1
0
0
2
0
1
0
1
1
0
0
0
2
0
2
1
0
1
2
0
1
1
1
1
0
0
2
0
0
3
0
0
0
0
2
1
2
0
0
2
1
2
0
0
0
0
0
1
2
0
0
0
0
2
3
0
0
1
2
2
0
2
1
3
0
2
1
0
1
2
2
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
2
1
2
1
1
2
1
1
2
1
0
0
0
0
0
0
0
0
2
0
1
1
0
0
3
0
1
0
0
1
0
0
1
0
0
2
2
1
1
1
1
0
1
0
1
1
1
0
2
2
2
0
1
0
0
2
1
1
0
1
1
1
0
2
0
0
0
2
3
1
3
1
2
3
0
0
1
0
0
0
0
0
1
2
0
0
1
0
1
0
2
0
0
0
1
0
0
2
1
1
1
1
0
1
2
2
2
0
0
1
2
1
0
0
1
0
1
0
2
0
1
0
0
0
0
2
1
1
0
0
1
0
1
3
0
0
0
0
1
0
0
1
0
1
1
1
0
1
0
1
1
0
1
1
2
0
1
2
0
2
0
0
0
0
1
1
0
1
0
0
0
0
2
0
0
1
0
1
1
0
1
0
0
0
1
0
2
3
1
1
1
0
1
1
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
2
2
1
1
1
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
1
2
0
0
1
1
0
2
0
0
0
0
2
2
2
0
0
1
0
0
0
1
2
0
0
2
0
1
1
1
0
2
0
0
1
1
0
2
1
0
2
4
0
2
0
2
0
0
2
0
1
2
0
0
1
0
2
0
2
2
2
0
0
1
2
0
1
2
1
0
1
0
0
0
1
0
0
1
1
1
0
1
2
1
1
0
1
0
0
0
1
0
1
0
2
0
0
2
2
0
0
2
3
0
0
2
0
2
0
1
1
2
0
0
0
0
0
5
1
0
0
1
0
0
0
1
0
0
0
0
2
2
0
2
0
0
0
0
2
0
0
1
1
1
1
2
0
0
2
1
0
2
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
1
1
2
2
2
0
1
0
1
1
2
0
1
2
0
0
0
2
0
0
0
1
1
2
1
0
1
1
0
1
1
1
2
0
2
0
1
0
0
0
0
0
2
1
0
0
0
1
2
0
0
1
0
2
0
0
0
1
0
2
0
2
1
3
2
1
1
0
1
0
0
2
0
1
0
2
0
0
1
1
2
0
3
0
0
0
2
0
2
1
2
1
0
0
0
0
2
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
1
1
0
2
0
1
0
0
1
0
3
1
0
0
2
1
0
0
0
0
1
1
1
1
2
0
1
0
0
0
1
1
2
1
0
0
2
1
0
2
2
2
1
0
0
0
1
1
1
0
1
1
1
0
3
0
0
0
0
2
1
0
0
0
2
0
0
1
0
0
3
1
0
0
2
0
0
1
0
0
0
0
1
2
0
0
0
0
2
0
1
0
2
2
0
2
0
0
2
2
2
1
0
1
1
1
0
1
1
2
1
1
1
0
2
2
0
2
0
0
1
0
2
0
0
0
1
0
0
1
1
0
0
0
2
1
0
1
1
0
0
1
1
1
0
1
0
0
1
0
0
0
1
4
0
1
2
0
2
0
1
1
0
0
0
1
0
2
0
0
2
0
1
0
0
0
0
1
0
1
0
3
0
2
0
0
0
0
1
0
2
0
0
0
1
0
1
0
2
0
0
1
0
0
0
2
2
0
0
0
2
1
0
0
0
0
2
0
0
1
0
0
0
2
2
2
1
0
0
2
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
2
1
0
0
0
2
0
0
1
0
0
2
1
0
0
0
2
0
2
0
0
1
2
0
0
0
2
1
0
1
0
1
0
1
2
2
1
2
0
1
2
0
1
0
0
2
1
1
0
0
2
0
1
0
2
1
0
0
1
0
0
2
1
2
0
0
1
1
1
1
2
0
1
0
1
0
4
2
0
2
2
2
2
0
0
0
1
1
0
1
0
0
0
4
1
0
1
1
0
2
0
0
0
0
0
0
2
0
1
1
0
0
2
0
1
1
0
0
0
0
1
0
0
0
1
0
2
1
0
1
0
2
0
0
2
2
2
1
1
1
0
1
2
0
0
0
0
1
0
1
1
4
0
0
2
0
4
1
0
1
0
0
0
0
1
1
2
1
1
2
0
0
2
0
1
0
0
0
2
0
0
2
0
2
1
0
0
1
2
0
0
2
2
1
1
0
0
0
0
2
1
1
1
0
2
0
1
3
1
0
1
2
1
0
2
2
1
0
2
1
0
0
1
2
0
0
1
0
1
0
2
1
1
0
0
1
1
0
1
0
0
0
0
2
0
0
2
0
0
2
2
0
0
0
0
1
0
1
0
1
0
0
2
2
0
0
0
1
1
0
2
0
0
0
0
0
1
0
1
1
0
0
0
0
3
2
1
1
0
1
1
2
2
0
1
0
1
0
0
2
0
1
1
0
2
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
2
1
0
1
0
0
0
0
2
2
0
1
1
1
0
0
0
1
0
1
2
0
1
0
1
2
1
0
3
0
2
1
0
0
1
2
1
1
2
1
0
1
2
0
1
0
0
0
0
1
1
2
1
0
0
1
1
1
2
1
0
0
0
2
2
2
2
2
0
2
0
1
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
1
1
0
0
0
1
0
0
0
2
0
1
0
0
2
0
1
2
1
0
0
0
0
2
0
2
0
1
0
0
1
0
0
2
0
0
0
1
0
2
2
1
2
1
2
0
1
0
0
2
3
0
1
2
0
0
0
1
2
1
0
2
0
2
1
0
1
2
1
2
0
0
2
0
0
0
0
1
0
0
0
1
2
1
1
1
0
0
2
1
1
0
1
0
0
0
0
0
2
0
1
0
0
2
0
5
0
0
0
1
1
0
1
3
1
2
2
9
0
0
0
1
0
0
1
1
0
0
0
2
0
1
0
0
0
2
0
2
0
1
1
0
0
2
1
2
0
0
1
0
1
2
0
2
0
0
0
1
0
0
1
1
0
1
0
2
0
2
0
2
0
0
2
0
0
0
0
1
0
1
1
1
1
2
0
0
1
0
1
0
2
0
0
0
0
2
2
2
2
2
1
2
0
2
0
0
0
1
2
1
0
1
0
2
1
0
2
0
2
0
0
1
0
1
2
1
1
1
0
3
1
0
2
1
0
0
0
1
2
0
0
0
2
0
0
0
0
0
1
0
3
2
1
2
1
1
0
0
1
0
3
0
1
1
1
0
0
0
2
2
0
0
1
0
0
0
2
0
1
0
1
0
3
0
0
1
0
3
0
0
0
2
1
0
2
1
2
0
0
0
2
1
0
0
0
1
0
1
0
2
0
1
2
0
1
0
0
0
0
2
0
2
1
3
1
6
2
0
2
0
2
0
0
3
1
2
1
2
0
0
0
2
0
0
0
0
1
1
1
0
2
0
0
2
1
0
0
0
1
1
2
0
0
0
0
1
0
0
2
0
0
0
1
0
2
1
0
0
0
1
2
0
0
0
1
0
1
0
0
1
0
0
0
2
1
0
3
0
1
0
1
0
0
0
0
1
0
0
0
1
2
1
1
0
2
0
0
1
2
1
0
2
0
0
0
0
0
0
3
1
0
1
1
1
0
1
3
1
2
1
0
1
0
0
0
1
1
2
1
1
0
0
0
0
2
1
0
1
2
0
0
2
1
2
0
0
2
0
0
0
0
0
2
0
2
2
0
0
1
0
3
1
1
0
1
0
0
0
2
2
0
0
0
1
2
0
0
2
2
1
1
0
1
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
2
1
0
2
2
1
2
2
0
1
2
0
0
0
0
2
2
2
0
2
1
0
2
0
0
2
0
0
1
0
1
2
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
1
0
2
2
1
0
1
1
1
0
1
2
0
3
0
2
0
0
1
3
0
0
0
1
1
1
1
0
1
0
0
1
1
0
0
1
1
1
0
1
1
3
0
0
0
0
0
0
1
1
0
0
2
1
0
2
2
1
1
2
2
1
0
1
0
0
3
0
0
0
1
0
0
0
2
0
2
1
0
0
2
0
0
1
0
0
3
0
0
1
0
0
0
1
0
0
0
1
0
2
0
0
2
0
2
1
0
2
0
1
2
0
2
0
1
2
2
2
1
4
0
0
0
1
1
2
0
2
0
0
2
1
0
2
2
0
0
1
0
0
0
1
0
0
0
2
2
4
0
0
1
1
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
1
0
2
0
0
0
0
1
0
0
0
0
1
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
2
0
2
0
2
2
11
0
0
0
1
0
2
1
2
2
0
2
0
0
1
1
2
1
0
2
2
0
0
2
0
0
0
1
2
0
0
0
0
2
1
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
1
0
1
2
0
0
0
1
1
0
1
1
1
0
0
0
0
2
0
0
1
0
0
1
0
2
2
0
0
1
0
0
0
2
2
0
2
0
0
0
1
1
1
0
0
2
0
0
2
0
0
0
0
4
0
2
0
1
1
0
0
0
1
2
1
0
1
1
0
0
2
0
0
2
1
5
1
2
0
1
2
1
0
0
2
0
0
0
1
0
0
0
0
0
0
3
1
1
0
0
0
1
0
1
1
1
2
1
0
1
1
0
0
2
0
0
1
1
2
1
0
1
0
2
2
2
1
1
4
2
2
2
0
0
0
0
1
2
0
1
0
0
1
2
0
0
0
0
0
0
2
1
1
2
1
1
1
1
2
1
0
1
0
0
0
0
0
3
3
1
2
0
0
0
2
1
0
2
1
0
0
0
2
1
1
0
1
0
0
4
0
1
2
1
0
1
0
2
2
0
0
0
0
0
0
2
2
0
0
1
2
2
0
0
5
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
2
0
0
0
2
0
1
0
0
0
0
5
2
0
0
2
0
0
0
0
2
2
0
0
1
1
0
0
0
1
0
0
1
1
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
2
1
0
0
2
0
0
2
0
0
2
2
2
0
0
0
0
1
0
0
0
2
0
1
0
2
1
0
0
0
0
2
1
1
2
0
0
1
2
1
1
1
0
1
0
4
0
0
2
2
1
2
2
0
0
1
0
0
2
1
0
1
2
0
0
0
1
1
0
0
0
1
1
2
0
0
1
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
1
1
0
2
0
0
0
1
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
2
0
2
0
0
1
0
1
0
2
0
2
1
2
0
1
0
1
2
2
2
0
0
2
1
1
0
1
2
0
1
1
2
2
2
1
1
0
3
0
0
0
2
0
1
2
2
0
0
0
2
0
0
0
0
1
2
0
0
2
1
0
0
1
2
2
0
0
0
0
1
0
0
1
2
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
1
1
1
1
0
1
0
1
2
0
2
1
0
0
1
0
1
3
0
2
0
2
0
3
1
2
1
2
0
0
1
0
2
0
1
0
2
0
0
0
0
0
2
1
0
1
0
0
0
2
0
1
2
1
2
0
0
0
0
1
0
0
2
1
2
0
0
0
0
0
1
0
14
0
0
1
2
1
0
1
2
0
1
2
1
2
0
1
0
0
0
0
4
1
0
0
0
0
0
2
1
1
2
1
0
0
2
0
0
2
2
0
0
0
1
0
0
1
1
0
0
0
1
0
2
0
0
1
0
1
1
1
2
0
0
0
2
0
2
0
0
0
2
2
2
1
1
0
0
0
0
0
2
1
0
1
0
0
0
0
2
0
0
0
0
1
0
2
1
2
2
0
1
2
1
2
0
0
2
0
0
0
0
1
0
0
2
2
0
1
0
2
1
0
0
0
0
0
1
0
3
0
2
2
0
1
1
2
0
1
0
2
1
0
0
0
0
2
0
0
0
1
1
0
0
0
2
0
1
0
0
2
2
2
0
0
0
2
0
1
0
0
1
2
0
0
1
1
3
2
0
0
1
1
0
1
1
0
0
1
2
1
0
1
0
0
0
2
2
2
0
0
0
0
3
2
0
0
0
0
0
2
0
0
1
2
0
0
2
1
0
1
1
1
0
0
1
0
0
1
0
0
2
1
1
2
1
1
0
1
2
1
1
0
0
0
1
2
0
1
0
0
2
2
1
0
0
1
1
1
0
1
0
2
2
1
0
1
1
2
1
1
0
2
0
0
2
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
1
0
0
2
2
2
1
2
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
1
2
0
0
1
0
0
0
0
0
0
0
1
0
0
2
2
1
2
0
1
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
1
0
1
1
0
1
0
0
2
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
1
0
0
0
1
1
0
0
1
1
2
0
0
0
1
1
2
0
0
4
0
0
0
0
0
0
1
1
0
0
1
1
1
2
1
1
3
0
0
4
0
1
0
0
0
0
1
0
0
1
0
1
0
0
2
0
2
2
0
4
1
0
2
2
0
0
0
1
0
1
1
1
0
1
2
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
2
1
1
0
2
0
0
1
8
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
2
1
1
2
2
1
0
1
0
1
2
1
2
0
0
2
1
2
1
0
2
0
0
1
0
0
1
0
0
0
0
0
2
0
1
0
1
1
2
0
2
0
1
1
0
2
1
0
3
0
1
0
2
0
0
1
0
2
0
0
0
2
0
2
0
2
0
0
0
0
2
0
2
0
0
1
1
2
1
0
1
2
0
1
0
1
0
0
0
1
1
1
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
2
0
1
0
3
1
0
0
3
1
1
1
0
2
1
0
2
2
1
0
1
1
0
2
3
1
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
1
1
1
1
0
1
0
1
2
0
1
0
0
0
1
1
2
1
0
2
1
2
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
4
1
0
2
1
2
0
6
0
0
0
3
0
0
2
1
1
1
2
0
4
0
0
1
0
0
0
0
0
2
1
0
0
1
1
1
1
1
0
0
2
0
0
0
2
1
0
1
0
0
0
1
0
0
1
2
0
1
0
1
0
2
0
1
0
1
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
1
2
1
2
2
0
1
1
1
1
2
1
0
1
0
0
2
4
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
2
2
0
1
0
3
2
1
0
0
1
0
1
0
1
2
0
1
2
1
3
0
2
0
0
2
1
1
2
5
2
1
0
0
1
0
1
2
1
4
2
2
0
2
1
0
0
0
2
0
2
0
1
1
1
2
1
2
2
0
0
2
0
2
0
0
0
2
2
0
0
1
1
0
0
1
1
0
0
0
1
1
0
0
1
0
2
4
0
2
1
1
0
1
0
0
2
0
0
0
2
0
0
0
0
0
1
1
1
2
3
0
1
2
0
0
1
0
0
1
2
0
1
2
5
2
0
0
0
0
1
0
0
0
1
1
1
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
2
4
0
0
0
1
0
0
0
0
1
1
0
1
1
0
0
2
1
0
0
0
1
1
1
0
1
0
2
2
1
0
0
1
1
0
2
2
0
0
0
0
1
0
2
1
2
1
1
0
0
2
0
0
0
0
0
1
1
2
2
2
2
2
2
0
2
0
2
0
1
1
0
0
2
0
1
0
2
2
1
1
4
2
0
0
1
1
2
0
0
2
6
1
0
0
0
0
1
0
2
2
1
1
2
2
0
0
1
0
0
1
1
0
2
1
2
0
0
0
0
0
2
2
2
2
0
0
2
0
0
0
2
2
1
0
1
1
2
0
0
2
3
0
0
2
0
2
2
0
1
0
2
4
2
0
2
0
1
0
2
1
1
0
0
1
0
0
1
2
1
0
0
0
2
2
1
1
0
1
0
0
0
0
0
1
0
2
0
0
1
1
1
1
2
1
2
1
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
2
1
1
0
0
2
0
2
0
0
0
0
2
0
3
0
0
2
0
0
1
1
1
1
1
1
2
2
1
1
0
1
0
0
0
0
2
0
2
0
1
1
0
0
0
0
1
1
0
2
3
0
0
1
0
0
2
1
2
0
0
1
1
2
0
0
0
0
0
0
0
0
2
2
2
0
3
1
2
2
2
1
2
1
0
0
0
2
2
2
2
0
0
0
2
0
0
1
0
0
1
2
2
0
1
2
1
0
1
0
0
0
1
0
0
1
1
1
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
2
0
0
0
0
0
1
0
0
0
1
2
0
2
0
1
0
0
0
1
0
0
0
2
0
1
2
1
2
2
0
1
0
0
2
1
2
0
0
2
1
1
1
1
1
0
2
1
1
0
1
2
1
5
0
0
1
2
0
1
0
1
0
1
1
0
0
2
1
0
1
1
1
1
0
0
2
2
1
0
0
0
2
2
2
1
0
1
0
0
0
0
0
2
2
1
1
2
0
1
0
0
0
1
0
0
1
0
1
1
0
0
0
2
0
2
0
2
0
2
2
0
1
1
0
1
0
0
0
1
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
2
0
2
0
1
2
1
1
0
1
0
1
1
0
0
0
0
0
0
0
1
0
1
1
1
0
0
1
0
0
2
0
1
1
0
1
0
0
0
2
1
0
1
2
2
1
0
1
2
2
2
0
0
2
0
0
2
0
3
2
0
1
0
2
1
1
0
1
0
0
1
2
0
0
0
2
3
1
0
2
0
1
0
2
1
1
2
1
1
0
0
2
0
0
0
2
2
2
0
1
2
0
0
0
2
0
3
0
2
1
0
1
0
1
2
2
2
2
0
1
0
1
2
0
0
0
1
0
0
1
0
1
0
1
0
0
0
1
0
0
2
0
1
2
0
0
0
0
2
1
0
1
0
2
2
1
1
1
2
0
0
0
0
2
1
2
0
0
0
0
1
0
1
0
2
0
0
1
2
2
2
0
1
0
0
0
0
1
1
0
0
2
0
0
0
2
2
1
2
1
2
0
2
2
1
1
0
2
0
0
0
3
0
0
0
2
0
0
0
2
0
2
1
2
0
0
1
0
0
2
1
1
0
1
0
2
1
1
2
0
0
0
0
2
0
2
0
1
0
0
3
0
1
2
1
0
0
0
0
1
0
2
2
1
1
0
1
2
0
0
1
0
1
0
0
0
0
2
0
2
2
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
2
1
0
2
2
1
2
0
3
0
0
0
0
0
2
1
0
0
0
0
2
2
1
1
3
1
3
1
0
0
0
1
0
0
1
0
1
2
0
1
0
0
3
2
1
3
0
0
2
2
0
0
2
1
0
0
1
0
1
1
0
2
0
0
0
1
2
0
2
1
0
0
0
2
0
1
2
1
2
0
0
2
0
0
2
0
0
2
1
0
1
2
2
1
0
1
0
0
2
1
2
1
0
1
1
1
0
2
1
0
1
3
1
2
1
2
0
0
2
1
0
0
2
1
1
0
0
1
1
1
0
1
3
2
0
0
0
0
0
0
2
1
0
0
1
1
1
2
0
0
1
1
0
1
0
0
0
2
0
1
2
2
2
1
0
1
1
0
0
2
1
2
4
0
1
1
0
2
0
2
0
0
2
0
0
0
0
1
4
1
1
1
1
1
0
1
1
2
0
2
2
0
0
0
0
2
1
0
0
2
3
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
2
1
2
0
1
0
0
1
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
2
2
0
1
1
1
1
2
0
0
0
0
1
0
2
0
1
0
2
0
0
1
1
1
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
1
1
1
0
1
2
1
2
0
2
2
2
0
0
1
0
0
2
0
0
1
2
1
0
0
0
0
1
0
0
1
1
0
0
1
2
2
2
0
0
2
1
0
0
2
0
1
1
2
2
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
2
0
2
2
0
1
1
0
0
0
2
0
2
0
0
0
0
0
3
0
0
0
2
2
0
1
0
1
0
1
1
1
0
0
0
1
1
0
1
1
0
1
0
0
0
1
0
2
0
0
0
2
1
1
1
1
1
0
0
0
2
0
1
2
2
0
0
0
1
1
1
0
2
0
0
0
0
2
0
0
1
0
1
1
0
2
0
3
0
2
1
0
0
4
0
0
0
0
0
0
2
1
0
1
1
0
2
0
0
2
0
1
0
0
2
0
0
2
0
0
1
1
1
0
2
0
0
2
0
0
0
0
2
0
2
1
0
0
2
0
0
0
0
1
1
2
3
2
0
1
2
0
1
0
0
0
0
0
2
0
2
1
0
0
1
1
1
0
1
3
1
1
0
2
0
2
1
1
0
0
1
2
0
2
1
1
1
2
0
0
0
0
1
1
0
0
1
0
0
1
0
2
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
1
1
0
2
2
0
0
0
1
0
1
1
0
1
0
0
0
2
0
0
0
3
2
0
2
0
0
0
0
0
2
0
2
2
2
2
2
2
2
0
0
1
2
0
2
0
1
0
2
1
0
0
1
1
4
1
1
0
1
2
1
1
1
2
3
2
0
1
2
1
1
1
1
0
1
0
0
0
2
0
2
1
1
2
0
1
0
0
0
0
0
0
2
1
1
1
0
0
0
1
0
0
2
1
0
0
1
1
0
1
2
0
0
1
2
0
1
1
1
2
0
0
0
0
2
0
0
1
0
0
2
2
1
2
2
0
1
0
2
1
0
0
0
1
2
2
2
0
2
2
0
1
0
1
1
2
1
0
1
0
2
0
2
0
0
0
3
1
0
1
0
0
1
1
2
0
0
0
1
1
0
1
0
1
0
1
2
1
0
0
1
0
2
0
0
1
0
0
1
1
0
1
0
2
1
1
2
0
3
1
0
1
2
0
1
0
1
3
0
1
0
5
1
2
3
0
0
0
0
0
1
1
0
2
1
0
0
2
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
2
0
1
0
1
1
0
1
0
0
0
2
2
0
1
2
2
0
2
0
2
0
0
1
0
0
1
2
0
2
3
0
1
0
1
0
2
0
2
2
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
1
0
2
0
0
0
0
2
1
0
2
0
0
2
2
1
1
0
0
2
0
0
0
0
2
0
2
1
0
0
0
0
1
0
1
1
0
1
0
0
1
0
0
1
1
0
0
1
0
1
0
1
4
0
0
0
1
1
2
0
2
2
2
1
2
1
2
1
2
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
1
0
1
0
0
2
2
0
0
0
1
0
2
0
0
0
2
0
0
1
2
0
0
0
2
1
1
1
0
3
1
0
0
0
0
0
2
0
0
2
1
1
0
2
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
1
2
0
0
0
0
0
1
0
1
1
1
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
1
0
2
0
2
0
1
1
0
0
1
0
0
0
1
0
1
0
0
0
0
1
1
0
1
0
0
1
2
0
2
1
1
2
1
0
0
0
1
0
0
1
2
2
0
1
1
0
1
1
1
0
0
1
2
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
2
1
0
0
1
0
0
1
2
0
0
2
2
0
1
0
0
0
2
1
2
0
0
3
3
2
1
1
0
0
0
0
1
1
1
2
0
2
2
0
2
1
1
0
0
0
1
1
1
0
0
0
0
0
2
0
1
0
2
0
0
0
0
2
1
2
0
0
2
0
1
0
2
0
1
0
2
0
2
0
0
0
0
1
1
2
0
0
0
0
0
0
2
2
2
0
0
1
1
2
2
2
1
1
0
0
0
2
0
2
0
1
1
0
0
0
1
0
2
3
2
1
1
2
0
1
1
2
1
0
2
0
0
1
0
1
0
0
1
0
2
0
0
0
1
0
0
0
0
0
2
0
0
3
2
1
1
0
2
1
0
2
0
2
0
2
0
1
1
0
0
0
2
0
2
0
0
2
0
0
0
2
0
2
0
0
0
1
2
0
2
2
0
1
0
0
2
0
2
0
0
0
0
0
1
0
2
0
1
0
0
2
0
0
0
1
0
0
1
0
0
1
0
1
0
0
1
0
2
0
1
0
0
0
0
0
1
2
0
0
0
1
2
0
1
0
0
2
2
1
2
0
2
0
1
1
1
1
0
0
1
0
1
0
1
0
0
2
2
2
1
0
2
0
1
1
0
1
2
0
1
0
0
0
0
0
1
2
0
2
0
1
0
0
1
0
0
1
0
1
1
0
2
0
0
0
1
0
2
2
2
2
0
1
2
0
2
0
1
1
1
2
2
1
0
0
0
0
2
0
0
0
1
0
2
0
1
1
0
1
2
0
1
1
0
2
1
0
0
0
0
0
0
2
0
0
2
1
1
1
2
2
0
0
0
0
0
0
0
2
0
0
1
1
0
0
2
1
0
0
1
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
2
1
2
2
1
0
0
0
0
2
1
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
3
1
1
3
0
2
0
1
0
2
2
0
0
0
0
2
0
0
2
0
2
0
2
0
0
0
0
0
0
2
1
2
0
0
0
2
0
0
2
2
0
1
0
0
0
0
1
1
1
0
3
2
2
0
2
0
1
2
0
0
2
1
0
1
0
0
0
0
1
1
0
0
0
1
0
1
1
2
0
2
0
1
1
0
0
0
0
1
0
0
5
0
0
0
1
0
2
2
1
0
2
0
2
2
2
0
1
0
0
0
1
1
1
9
0
0
1
2
0
0
2
1
1
2
0
0
0
1
1
0
0
1
1
1
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
2
0
0
0
0
2
0
0
1
0
0
1
0
0
1
2
0
1
1
0
1
2
2
0
1
0
1
0
0
1
0
2
1
0
1
1
1
1
0
1
0
2
0
2
0
1
0
0
0
0
1
0
2
0
0
0
1
1
0
0
0
0
0
1
2
1
0
1
4
2
1
1
2
1
0
1
1
1
2
0
1
0
1
0
2
0
1
2
2
1
2
1
2
0
3
0
1
0
2
0
0
0
0
1
2
0
1
1
2
0
1
0
0
2
0
1
0
0
1
0
0
2
0
1
0
0
0
1
0
1
1
0
2
0
0
0
1
3
0
0
1
0
1
1
1
1
0
1
0
0
2
1
1
0
0
3
0
3
1
2
0
3
2
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
2
1
0
1
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
2
2
2
1
0
0
3
0
1
0
0
2
1
2
2
1
0
1
2
2
8
2
2
0
1
1
0
0
0
2
1
0
2
1
0
0
2
1
0
0
1
0
1
0
1
2
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
1
1
2
2
0
1
1
0
0
2
1
0
0
0
0
0
2
1
1
0
1
0
2
2
0
2
1
1
1
1
0
1
0
1
1
1
0
0
0
2
1
0
0
1
0
1
3
0
2
0
1
1
2
0
1
1
0
0
1
1
0
0
0
0
1
1
0
1
1
2
0
2
0
0
2
2
0
1
0
0
1
1
0
0
2
3
2
0
0
1
0
1
0
0
0
1
2
1
0
0
0
0
0
0
2
2
0
2
0
0
2
2
0
0
0
2
1
0
1
2
1
0
1
1
3
0
0
1
1
1
3
1
0
2
1
1
1
0
0
0
0
0
0
0
1
1
0
2
0
2
0
0
1
2
0
0
2
1
0
0
1
2
0
0
0
1
0
1
1
1
0
1
1
0
1
1
1
1
0
0
1
0
0
1
2
1
0
0
2
1
1
0
1
1
0
0
1
0
0
3
1
0
0
0
1
2
2
0
2
1
2
2
1
1
2
2
0
0
1
0
0
2
0
0
0
1
0
0
0
0
1
1
0
1
2
0
1
0
0
1
1
1
1
1
0
3
1
0
0
0
2
1
0
0
0
0
0
1
1
0
2
0
0
1
0
0
1
1
1
0
2
2
1
0
1
1
2
0
0
2
1
0
0
0
1
0
0
2
0
1
2
0
0
4
2
1
1
0
1
0
2
1
0
0
0
1
2
0
0
0
1
0
0
0
1
1
0
1
1
1
0
0
0
1
0
1
0
0
1
1
1
0
0
2
1
0
1
1
2
1
0
0
2
1
2
1
0
2
2
1
0
0
0
1
1
2
1
2
1
0
2
0
1
0
1
1
0
2
2
0
2
0
2
1
0
0
1
1
2
0
1
0
4
1
1
0
1
0
1
0
0
1
2
0
0
0
0
1
1
0
1
1
2
1
0
1
0
2
2
2
1
1
1
0
0
1
0
2
0
0
0
0
2
0
0
1
0
0
2
0
2
0
0
0
0
1
1
0
0
0
1
0
2
0
1
0
0
0
2
2
0
0
0
1
0
0
1
1
0
2
0
0
1
0
1
1
0
1
1
1
0
2
2
0
0
0
0
0
0
0
0
1
1
1
3
0
2
0
1
2
0
2
1
0
0
0
0
0
2
0
3
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
1
1
0
1
0
0
2
0
1
0
0
0
0
2
1
0
1
0
0
1
1
1
1
2
2
0
2
0
1
0
2
0
0
0
2
1
0
1
1
0
2
2
2
1
1
0
0
1
1
1
1
0
0
2
1
0
2
1
1
0
2
0
0
2
0
2
0
2
0
0
0
1
1
0
2
0
0
1
0
2
3
0
2
2
0
0
0
2
1
0
1
1
2
1
0
2
0
0
0
1
2
1
1
1
0
1
0
0
0
0
1
0
0
1
1
2
4
0
0
0
1
2
1
0
0
2
2
2
0
0
0
0
0
5
0
0
0
0
2
0
0
2
0
2
0
0
2
0
2
1
0
0
0
1
2
0
1
1
0
1
0
0
3
2
1
0
0
0
2
0
0
2
1
1
1
2
0
1
0
0
1
1
1
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
1
2
1
1
1
2
2
0
0
2
0
0
1
0
0
1
1
1
2
0
1
0
0
1
1
2
0
0
1
0
0
0
2
4
2
0
0
2
0
2
0
0
2
0
0
0
1
0
0
0
0
1
0
2
1
1
0
1
1
1
2
1
0
2
0
0
1
0
2
4
1
0
0
2
2
2
0
1
2
0
0
2
4
1
1
3
0
1
1
0
0
0
0
1
2
2
1
0
2
0
1
0
1
0
0
1
0
1
1
1
1
1
2
0
1
6
0
2
2
0
0
1
2
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
1
1
1
0
1
2
0
2
2
1
0
1
0
0
0
1
0
2
0
1
0
0
0
2
2
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
1
0
2
0
1
1
0
1
1
0
0
1
1
2
0
0
1
1
1
1
0
0
2
0
0
1
3
0
2
0
2
0
0
0
2
0
0
0
2
0
0
2
2
0
0
0
1
0
0
1
0
0
1
0
0
1
2
0
4
1
1
0
0
0
2
0
1
2
2
0
1
2
0
0
1
2
0
1
2
0
0
0
2
0
0
1
1
0
2
0
0
0
5
1
2
0
1
2
1
1
1
0
1
1
0
1
0
0
2
1
2
2
1
0
1
0
1
0
1
0
1
1
0
0
0
0
2
0
1
0
0
1
0
1
2
0
2
0
1
0
0
0
2
1
0
0
0
4
1
2
0
0
1
1
0
2
0
2
0
3
1
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
1
2
2
0
0
0
2
1
0
0
2
2
0
0
1
1
0
0
1
0
2
1
0
0
2
1
2
0
2
2
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
1
0
1
0
3
1
0
0
1
2
0
0
0
1
1
1
0
1
0
1
0
0
0
1
1
0
2
1
0
1
2
3
0
2
1
0
0
0
0
0
1
2
2
2
0
0
0
0
2
2
1
1
0
0
1
2
0
0
1
0
1
2
1
0
1
1
2
2
2
2
1
2
0
0
0
1
1
0
0
0
0
0
2
1
0
0
0
0
1
0
2
1
2
1
2
1
1
0
2
0
1
0
2
0
2
0
0
0
0
0
2
1
0
0
0
0
1
2
0
1
1
0
2
0
0
1
0
2
0
0
2
1
1
0
0
0
2
0
1
1
2
1
1
0
0
0
0
3
0
1
0
2
1
0
0
1
2
0
0
1
2
0
0
0
2
2
0
1
0
1
1
0
2
0
0
0
0
2
0
1
0
1
0
2
1
0
0
1
2
0
3
0
0
0
0
4
1
0
1
0
1
3
1
2
0
0
0
2
0
0
1
1
1
0
2
0
3
1
2
2
0
0
2
1
0
0
0
0
1
1
1
1
0
0
0
2
1
0
0
2
0
0
0
1
2
2
0
0
0
1
0
0
1
2
2
1
0
2
0
2
0
0
0
0
2
0
0
2
0
1
1
0
1
0
2
0
0
0
0
0
2
2
2
2
1
1
0
1
1
0
0
1
1
1
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
1
1
1
1
1
0
0
0
2
0
3
0
0
2
1
0
0
0
0
0
0
1
1
2
0
0
0
0
2
2
0
1
1
1
1
0
2
1
0
0
0
4
2
0
0
0
2
0
0
0
0
4
3
1
0
0
0
0
0
1
2
0
0
2
1
0
0
1
0
2
0
1
0
0
0
0
1
2
0
0
1
0
0
0
2
3
0
2
2
0
2
1
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
1
1
2
0
0
1
0
0
2
0
1
2
0
1
1
0
0
1
0
0
2
0
0
1
2
2
0
0
2
0
1
0
0
1
0
2
0
1
1
1
2
0
0
0
1
1
1
1
1
0
3
1
1
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
2
2
0
0
3
2
0
1
1
0
2
2
0
0
0
2
0
1
0
2
0
2
2
1
0
1
0
0
0
2
0
0
0
1
1
0
2
2
0
1
2
0
0
0
2
2
1
0
0
0
0
0
2
1
0
1
1
0
2
0
0
1
0
1
1
1
0
0
4
0
0
1
2
1
0
0
1
2
1
2
0
1
0
1
1
2
1
0
2
0
1
0
0
0
0
1
1
2
1
2
2
1
2
0
2
0
0
0
1
1
0
1
1
0
1
0
0
0
1
1
0
0
0
1
0
1
1
1
0
1
0
0
1
1
0
2
2
2
0
2
1
0
0
1
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
2
0
1
1
2
0
0
1
0
0
0
3
1
1
1
0
1
3
1
2
1
2
0
1
0
0
2
0
1
2
0
0
3
1
0
2
0
3
0
0
0
2
1
2
0
2
1
0
2
0
0
0
1
0
2
0
0
0
2
0
0
0
2
1
1
2
0
0
0
2
0
0
1
1
0
0
2
2
0
1
1
1
0
0
0
1
0
0
2
2
0
2
0
0
0
0
0
0
0
1
0
0
2
0
1
1
0
0
0
1
0
0
1
1
1
1
2
2
1
0
0
1
0
1
2
2
1
1
1
0
0
0
1
0
2
1
1
1
0
0
1
0
0
1
0
0
2
0
1
2
0
0
2
0
0
1
1
0
0
0
1
0
1
0
0
1
1
0
1
0
1
0
0
1
0
1
0
0
0
2
0
0
2
1
2
0
3
2
0
2
0
2
0
0
0
0
1
0
1
1
1
0
0
0
0
1
2
0
0
0
0
2
2
0
1
0
0
0
3
0
0
0
0
1
2
0
0
2
2
1
3
0
0
0
2
2
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
2
0
2
2
0
1
0
2
2
0
1
0
0
1
1
0
0
1
0
0
2
0
0
0
0
0
1
0
1
1
0
2
0
0
0
0
1
1
0
2
0
0
0
1
2
2
0
1
1
1
0
0
2
2
0
2
2
2
1
2
1
0
2
0
0
0
1
1
1
2
0
1
0
2
0
0
3
0
1
1
1
1
0
0
0
2
0
2
0
0
0
1
1
0
2
0
1
0
0
1
0
2
2
2
0
1
0
0
1
0
1
1
0
0
1
0
1
0
1
0
1
0
0
1
0
2
0
0
2
0
4
2
2
1
0
2
2
0
2
1
0
1
0
0
1
2
0
0
2
0
1
1
0
0
1
1
0
0
2
0
2
0
2
0
0
0
0
1
0
2
1
2
0
0
1
1
0
0
1
1
1
0
1
2
0
1
2
0
1
2
0
0
1
0
0
0
0
1
2
2
1
1
0
0
0
2
0
1
1
0
0
0
0
1
2
0
1
2
2
0
2
1
0
2
1
0
2
1
1
0
0
1
0
0
0
1
0
0
0
1
2
1
0
2
1
2
1
0
4
1
2
0
0
1
0
3
0
0
0
2
1
2
0
0
1
1
0
0
1
0
0
0
1
0
1
1
2
2
0
0
0
0
0
2
2
1
0
0
1
0
1
1
1
1
0
0
2
0
1
0
1
0
0
0
0
1
0
1
1
2
0
1
0
1
0
0
1
2
0
0
0
0
2
0
1
2
1
0
0
3
2
2
2
0
4
1
1
0
1
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
4
0
1
1
1
2
0
0
2
0
0
0
0
0
0
1
0
0
1
1
0
1
2
2
5
1
2
1
1
0
2
0
0
0
0
1
1
2
2
1
0
1
1
0
0
0
0
1
1
0
1
0
2
0
1
0
0
0
0
1
2
2
0
0
1
1
1
1
2
1
2
0
2
1
0
1
2
0
1
1
2
2
0
0
2
0
0
0
0
0
2
0
1
1
1
1
1
1
0
0
0
0
0
1
2
0
1
0
1
0
0
2
4
2
2
1
2
0
0
0
1
2
0
0
0
1
0
1
2
0
2
0
0
0
2
2
1
2
0
0
0
1
0
2
2
1
2
0
1
1
2
2
2
1
1
0
1
0
1
0
0
0
0
2
1
2
0
0
0
0
0
1
2
0
2
2
2
2
0
2
0
1
0
0
0
0
2
0
0
2
1
1
0
1
2
0
1
0
0
0
1
0
0
1
1
0
0
2
1
0
1
0
0
2
2
1
2
1
1
2
2
2
1
0
2
2
0
1
0
0
2
0
1
0
1
1
0
0
2
0
0
0
0
1
0
2
1
0
0
0
1
1
3
2
1
0
1
0
0
2
2
1
1
1
0
0
1
1
0
0
0
2
3
2
1
4
2
0
0
0
1
2
1
2
0
0
0
0
2
2
2
2
2
0
0
1
1
0
3
1
2
0
0
0
1
0
2
1
2
0
1
0
1
2
2
2
0
0
2
1
0
0
0
0
1
0
1
2
0
2
1
2
2
0
0
0
0
0
1
1
1
0
2
0
0
1
0
1
1
0
0
1
0
1
0
0
2
2
0
0
1
1
0
1
2
2
2
2
0
2
1
1
0
1
0
1
1
2
1
1
0
0
0
1
1
0
0
0
0
0
0
2
0
0
2
1
0
0
1
1
1
1
2
0
2
1
1
0
1
1
0
2
0
0
0
1
0
1
0
2
3
0
0
1
3
0
0
1
1
1
0
2
0
1
1
2
1
1
1
2
0
0
2
1
2
0
0
2
2
2
1
0
1
2
0
0
2
0
2
1
0
0
0
1
1
1
2
2
1
0
0
1
1
1
1
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
2
1
2
2
2
0
0
0
1
0
0
2
2
0
0
1
0
1
0
3
0
1
2
1
0
1
0
0
2
0
0
0
0
2
0
1
0
1
0
0
0
1
0
0
2
2
2
2
0
0
0
1
2
0
0
0
0
0
0
1
1
2
1
0
1
0
0
1
0
1
2
0
0
1
2
0
2
2
2
0
0
2
0
0
1
1
0
0
0
2
1
1
2
0
1
1
0
1
0
1
0
0
1
2
0
2
0
0
0
0
2
0
2
0
1
0
0
0
2
0
0
0
0
0
1
2
0
0
1
0
0
1
0
0
0
0
1
0
1
2
0
0
0
0
1
0
0
1
1
0
1
1
2
2
2
1
3
0
0
1
0
0
2
0
1
0
0
1
0
1
0
0
0
0
1
1
0
1
2
0
0
1
1
0
0
0
2
0
2
0
0
2
2
0
0
2
0
2
1
0
3
1
1
0
0
1
1
2
2
1
0
1
0
0
0
0
0
0
2
1
0
1
2
1
1
1
2
0
0
0
3
0
0
0
0
1
2
1
0
0
0
0
1
0
2
0
1
1
1
0
1
1
1
0
1
0
1
0
0
0
0
0
0
1
0
0
1
2
0
1
0
1
0
0
2
0
0
0
2
0
1
1
0
2
2
1
1
1
0
0
0
0
1
2
0
0
1
1
0
0
1
1
2
0
0
2
1
1
1
0
2
0
0
0
0
2
2
2
2
0
1
1
0
2
2
1
1
1
1
0
1
0
0
2
0
2
1
1
0
0
1
0
1
0
1
2
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
1
2
2
0
1
0
0
1
1
2
2
8
1
0
0
0
0
1
0
2
1
0
1
1
2
0
0
1
2
2
2
2
0
1
2
1
1
1
0
0
0
2
0
0
1
2
1
1
1
0
2
2
0
1
0
2
0
0
0
0
1
0
0
2
2
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
3
1
2
1
0
0
0
1
1
2
0
0
0
3
1
0
0
0
2
0
0
1
1
0
0
2
0
1
1
1
0
4
2
1
1
1
0
2
0
1
1
0
0
1
1
1
3
0
1
0
0
0
0
2
3
2
0
0
1
0
0
1
2
0
0
1
2
0
0
1
0
0
1
0
1
0
0
3
0
0
1
1
2
0
1
1
0
2
1
0
1
1
0
0
0
0
0
0
1
1
2
0
0
0
0
0
2
2
2
1
2
0
0
1
0
0
0
1
0
1
1
0
1
2
0
0
0
0
1
1
2
0
2
1
0
0
0
0
0
1
0
2
1
0
0
0
0
0
2
2
0
0
0
0
1
0
0
2
2
1
0
0
3
0
0
0
0
0
1
1
1
1
2
1
1
0
1
3
2
0
1
1
2
2
1
0
1
0
1
0
0
0
1
1
0
1
1
0
1
0
0
0
2
0
1
2
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
1
1
2
0
0
2
1
2
1
0
2
0
1
0
1
1
0
2
0
3
1
0
0
0
0
1
0
0
0
2
0
1
0
1
1
1
1
0
2
0
1
1
0
1
1
2
0
0
0
2
1
0
0
0
0
0
1
0
1
1
2
0
2
0
2
0
0
3
0
0
2
1
0
1
2
2
1
1
1
0
0
1
0
1
0
0
2
2
0
1
2
1
1
2
2
1
0
2
1
0
2
0
0
1
1
0
1
0
1
1
2
1
2
1
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
3
0
0
1
0
1
0
0
1
1
0
1
3
0
0
0
0
2
2
1
2
1
0
1
1
2
0
0
0
0
1
0
2
0
2
1
0
0
0
0
0
0
1
0
2
1
1
2
2
0
1
1
1
1
2
2
0
0
1
0
1
1
1
0
2
1
1
0
2
1
1
1
5
1
0
1
2
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
1
2
0
0
0
0
1
1
2
0
1
0
1
0
1
0
1
0
0
1
0
3
0
1
0
0
0
0
0
1
0
2
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
2
0
0
0
0
1
1
1
0
2
2
1
0
0
0
0
1
0
0
1
2
0
3
0
0
0
2
0
0
0
2
0
1
0
1
2
0
0
0
0
0
1
0
1
0
2
2
2
1
0
2
0
1
2
0
1
1
0
0
0
2
0
1
0
0
1
2
1
1
1
2
2
2
0
3
0
1
2
1
0
0
0
2
0
1
2
1
0
0
1
2
0
0
1
0
2
0
1
0
1
1
2
2
2
2
0
0
0
1
1
0
2
0
2
2
0
0
1
0
0
1
0
0
1
1
2
2
1
2
1
0
1
1
0
0
1
0
2
0
1
1
0
0
0
1
0
0
0
2
1
2
0
0
1
2
0
3
2
1
2
0
0
2
1
1
0
1
0
1
1
0
1
1
1
0
0
0
0
1
1
1
1
0
0
1
1
2
0
1
1
0
2
0
0
0
0
2
0
0
0
1
1
2
0
2
1
0
2
1
1
2
0
0
1
0
0
0
0
1
2
1
0
1
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
1
0
2
2
1
0
0
0
2
1
1
0
1
0
0
0
0
0
1
0
2
0
1
1
0
0
1
0
0
2
0
0
5
0
2
0
0
0
1
1
3
1
0
1
0
3
1
1
1
3
1
0
0
1
0
2
1
0
0
0
2
0
2
1
2
0
0
0
1
0
0
0
0
1
1
2
0
0
1
0
1
2
1
1
0
2
1
3
2
3
0
2
0
0
2
1
0
0
1
0
1
0
1
2
1
1
1
1
0
2
1
1
1
2
0
0
0
1
1
0
0
2
1
1
0
2
1
2
1
0
0
2
0
1
2
1
0
0
0
1
0
0
1
0
1
0
1
1
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
2
2
1
2
1
2
0
0
0
4
0
1
2
1
1
1
2
0
0
0
0
1
0
2
0
0
2
2
0
0
2
2
1
2
0
1
2
1
0
0
0
2
0
0
2
1
3
1
1
1
1
0
2
0
0
1
0
0
0
1
2
2
2
1
0
0
1
1
1
0
0
1
1
0
1
0
0
1
0
0
3
2
0
1
1
0
0
0
0
1
1
1
0
2
0
0
0
2
1
0
0
0
0
1
0
2
0
0
2
1
0
1
0
0
0
0
1
0
0
0
0
1
1
0
3
0
2
1
0
0
1
0
0
0
1
0
1
0
0
0
1
3
0
0
0
0
0
0
0
0
0
1
1
2
2
1
0
0
1
0
0
1
2
1
0
1
0
0
2
1
2
1
0
0
1
2
2
2
2
1
0
0
0
2
0
1
2
0
3
2
1
0
2
1
0
2
1
0
0
3
0
1
3
1
0
0
0
0
0
1
1
1
1
2
1
1
2
1
0
0
0
1
2
1
0
0
0
2
1
2
1
2
0
4
1
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
1
1
0
1
0
0
0
2
2
1
0
1
1
1
0
1
0
1
0
1
0
1
2
0
0
2
1
0
0
1
2
2
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
3
0
0
2
0
2
1
0
0
2
0
1
2
1
2
0
0
1
0
2
2
1
0
2
2
1
0
1
1
1
1
0
0
0
1
0
0
2
0
2
0
0
2
2
0
1
1
0
0
2
1
1
0
2
2
0
1
0
1
1
1
0
0
0
2
1
1
2
2
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
1
1
0
1
2
1
4
2
1
0
0
0
0
1
2
1
1
2
0
0
2
3
0
0
0
1
1
0
0
2
0
0
0
0
1
0
1
2
0
0
1
1
0
1
0
2
0
1
1
1
1
0
1
2
0
1
2
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
1
1
2
0
0
1
1
0
0
0
2
2
2
0
1
0
2
3
1
1
0
0
0
2
1
0
2
2
1
2
1
0
0
0
0
1
0
0
2
0
1
0
0
0
0
1
2
1
2
2
0
0
2
0
0
4
1
0
2
1
0
1
1
2
0
0
3
1
0
1
0
1
3
0
0
0
1
1
0
1
0
0
1
1
0
2
0
0
2
0
0
0
0
1
1
0
0
1
3
0
1
0
2
2
1
0
0
0
0
0
0
0
0
2
1
1
2
0
2
0
2
2
2
0
2
1
0
2
2
0
0
0
2
0
0
0
1
1
4
0
1
1
1
2
1
0
0
0
0
1
0
0
0
2
0
1
0
1
0
0
0
1
2
0
0
0
0
1
0
0
0
1
2
1
0
2
0
0
1
0
0
1
2
1
2
0
2
0
2
0
1
1
2
1
1
1
0
2
2
1
1
1
2
0
0
0
1
2
0
2
2
0
1
0
2
1
1
0
0
1
0
2
0
0
0
0
0
1
1
1
0
1
2
1
0
2
0
1
0
1
1
0
1
0
2
0
0
0
0
0
0
1
1
0
2
1
2
0
1
1
1
1
2
0
1
2
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
1
1
2
0
1
1
1
0
0
0
1
0
2
0
0
0
0
0
2
2
1
1
1
1
2
0
0
0
0
1
0
1
2
0
2
2
0
2
1
2
0
0
0
2
2
0
0
0
1
0
2
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
2
2
0
0
0
0
1
4
0
1
0
1
0
1
0
1
1
2
0
2
2
0
0
0
0
1
0
1
1
0
1
1
1
0
2
0
1
2
2
1
1
2
1
1
2
0
2
0
2
0
1
3
0
1
1
0
0
2
1
0
0
1
1
0
0
2
0
2
0
2
1
0
2
0
2
0
0
0
2
0
0
2
2
2
0
0
0
0
0
0
1
2
1
1
0
0
0
0
0
1
1
0
2
1
0
0
1
2
1
2
2
0
0
0
0
2
2
0
0
2
0
0
2
0
0
0
1
2
1
1
2
1
1
0
1
0
0
0
0
1
2
0
1
0
0
1
0
2
1
3
1
1
0
0
2
0
0
1
0
1
1
1
2
1
2
0
0
0
1
2
1
1
2
0
2
0
0
0
2
2
1
1
2
0
1
2
0
1
1
0
0
2
2
3
0
1
1
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
4
0
0
2
2
2
2
0
0
1
1
1
2
1
2
1
0
1
2
0
1
0
0
1
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
1
1
0
0
0
2
1
3
0
2
2
0
2
2
1
0
1
3
1
2
0
0
4
1
0
0
1
0
1
1
1
0
0
1
1
1
0
0
2
1
0
1
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
1
0
1
2
1
1
2
0
1
2
1
0
2
1
1
0
1
0
0
1
0
0
0
0
2
1
2
0
1
2
3
1
0
0
0
2
1
0
1
1
0
0
0
0
0
0
1
2
1
0
0
1
0
0
1
2
0
2
0
1
0
1
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
1
0
0
2
1
1
1
2
0
2
1
0
0
0
2
1
1
1
0
0
0
2
0
1
2
2
0
0
0
0
1
0
2
1
1
2
0
0
0
1
0
2
0
2
0
0
0
1
1
0
1
0
0
2
1
0
0
1
0
0
0
0
1
2
1
1
0
0
0
1
1
0
0
0
2
0
2
1
2
0
0
1
0
1
0
0
1
0
0
0
0
1
0
3
0
0
0
2
0
2
0
1
0
1
0
0
3
0
0
0
1
1
0
0
2
2
1
0
3
2
1
2
1
0
1
1
0
2
0
0
1
1
1
0
0
1
0
0
0
1
0
2
0
2
3
1
1
2
0
2
0
2
0
0
2
0
2
2
0
0
1
0
1
2
0
0
0
0
2
0
1
3
1
0
0
0
1
0
2
0
0
1
0
1
2
0
1
1
0
1
0
2
0
1
1
0
2
0
0
1
0
0
0
1
2
2
2
2
2
0
1
0
1
1
2
1
2
0
0
0
2
2
0
1
2
1
2
1
0
0
2
1
0
1
0
1
1
1
0
0
0
2
1
1
2
0
2
1
1
0
2
1
1
2
0
0
2
1
0
1
1
1
0
1
2
2
1
1
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
2
0
0
0
1
1
0
1
0
0
0
0
0
0
0
2
1
0
0
1
0
1
0
0
0
0
1
0
1
0
0
1
2
0
2
0
2
2
0
3
1
1
0
0
1
0
1
1
2
0
1
2
1
2
2
1
1
0
1
2
2
2
2
0
0
1
0
1
0
1
0
0
0
2
0
1
1
1
0
0
7
0
0
0
1
0
0
0
1
1
2
0
0
1
1
1
0
0
0
2
0
0
2
2
0
0
1
0
1
2
0
2
1
0
0
1
1
0
2
2
0
0
2
0
1
0
0
1
2
0
0
1
2
2
1
2
0
0
3
0
1
0
1
0
1
0
0
2
1
0
0
0
0
0
0
0
1
1
0
0
2
2
1
2
1
0
2
1
1
0
1
2
1
1
1
2
0
2
1
2
0
0
1
2
0
0
0
0
1
3
4
0
0
3
2
0
0
2
0
1
3
1
0
1
0
2
0
1
0
1
0
0
2
2
1
0
0
0
0
1
0
0
0
2
0
2
2
2
0
1
1
0
1
2
0
0
0
2
2
2
0
0
0
0
1
0
2
0
0
2
1
0
1
2
0
0
1
2
0
1
2
1
0
0
2
2
0
0
1
4
2
1
0
0
2
3
0
0
1
1
0
0
0
1
1
0
1
1
0
0
2
2
2
0
0
0
1
0
0
2
0
0
0
1
0
1
0
1
2
2
0
1
1
2
1
2
0
0
3
1
1
0
0
1
2
1
0
0
2
1
0
0
0
1
0
0
1
2
2
3
0
0
1
2
1
1
0
0
1
1
0
0
0
1
2
0
0
2
1
2
0
2
0
2
1
1
2
0
0
1
0
2
0
1
0
2
2
1
0
1
0
0
0
1
2
2
0
0
0
2
0
0
1
0
2
0
3
1
1
0
1
0
0
0
0
2
0
0
1
1
0
0
2
0
2
0
1
0
2
0
0
1
0
0
1
0
1
0
1
0
0
1
1
2
0
1
2
2
2
1
1
0
0
2
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
1
0
1
2
1
2
0
1
1
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
1
1
2
1
0
1
1
0
1
0
2
2
0
2
1
0
0
0
0
2
0
2
1
2
2
1
0
1
0
2
1
2
2
0
0
1
0
0
0
0
2
1
0
0
0
3
2
0
0
1
1
2
1
0
0
1
0
0
0
1
0
2
2
2
3
0
1
0
1
0
1
0
0
1
2
3
0
0
2
1
1
0
2
2
2
1
1
2
0
0
0
1
0
1
1
1
1
1
0
1
1
1
1
0
2
1
0
0
0
1
0
1
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
2
0
2
1
0
0
0
2
0
0
2
0
1
0
0
2
0
0
0
1
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
2
0
2
0
0
2
0
1
0
2
2
1
0
0
0
1
0
1
1
1
0
2
1
1
0
1
2
2
0
0
0
0
2
2
2
0
1
0
2
0
0
1
1
1
2
0
0
1
2
0
0
0
1
0
0
0
1
1
1
2
0
0
2
0
0
2
0
0
0
1
1
0
2
2
0
0
0
2
1
1
0
2
0
0
1
1
1
0
3
0
2
0
0
0
1
0
1
0
0
1
2
0
0
1
1
1
2
1
2
1
0
1
0
2
2
0
0
1
2
0
0
1
2
0
0
2
1
0
2
1
2
1
0
1
0
0
0
0
2
0
1
0
0
1
2
0
0
0
2
0
0
0
0
1
2
0
1
2
2
0
0
0
1
1
1
2
0
0
1
0
0
1
0
2
2
0
0
0
0
1
0
0
0
2
1
2
1
0
2
2
2
2
0
0
1
1
2
0
1
2
1
0
2
1
2
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
1
1
2
0
0
2
1
1
0
1
0
0
2
2
2
1
1
0
2
1
0
0
2
1
2
1
0
1
0
2
2
0
2
2
1
0
0
0
2
1
0
0
0
0
2
0
2
1
0
1
0
2
1
2
0
1
2
2
2
1
2
0
0
2
0
0
0
2
0
1
0
0
0
0
1
2
0
1
1
0
1
0
1
0
2
2
2
0
0
0
1
0
1
2
1
2
0
0
1
0
1
1
1
2
0
0
3
1
0
2
0
1
1
0
0
0
0
2
0
2
1
0
2
1
0
1
1
0
0
0
2
2
0
2
1
2
1
1
1
0
1
0
1
2
0
1
0
2
0
2
2
1
4
1
1
0
2
1
2
2
0
2
2
0
0
0
1
1
0
1
2
0
0
0
0
1
0
0
4
2
0
1
0
0
0
1
0
1
0
0
2
2
0
0
0
1
0
1
1
1
0
1
0
2
12
0
0
1
1
2
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
1
0
2
0
0
2
0
1
0
3
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
1
0
2
0
0
1
1
0
0
0
2
1
0
0
0
0
0
0
0
2
3
1
0
2
2
2
1
2
2
0
1
2
2
0
1
2
2
1
0
0
0
0
0
1
2
0
0
2
1
0
0
0
0
0
2
1
0
0
0
0
4
2
1
2
2
0
0
1
0
2
2
1
0
0
2
0
2
0
1
0
0
0
0
1
1
1
0
1
0
1
0
0
0
0
1
0
3
0
0
0
2
0
0
0
1
1
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
2
0
2
2
0
0
0
0
2
0
1
0
1
0
0
2
1
0
2
1
0
2
1
0
0
2
3
2
1
0
2
0
1
0
2
4
1
0
1
0
0
1
1
2
3
0
0
0
2
0
1
2
1
0
0
1
0
0
1
0
0
0
1
0
0
0
2
0
0
1
2
0
1
0
2
1
0
1
0
1
1
0
1
1
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
2
0
1
0
2
0
0
3
0
2
0
2
1
0
1
2
0
3
1
1
2
0
0
0
0
1
2
0
0
1
2
1
0
2
1
0
0
0
1
3
0
0
0
2
0
2
0
2
1
0
1
0
2
1
0
2
1
0
0
2
0
1
0
1
2
0
0
1
0
1
1
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
2
0
2
2
0
1
1
1
1
0
0
1
0
0
2
0
1
2
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
1
0
2
1
0
0
1
0
0
0
1
0
2
1
0
2
0
3
2
0
0
0
0
0
0
0
0
2
0
0
0
1
1
2
1
1
0
1
1
0
0
1
1
1
4
1
2
0
0
1
1
1
0
0
2
0
1
0
0
0
1
1
1
0
1
0
2
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
2
0
3
1
0
0
0
0
2
0
1
0
2
0
0
1
3
1
0
0
2
2
1
1
1
0
0
0
0
0
0
2
0
1
0
0
1
0
0
1
0
0
0
0
1
2
2
1
0
0
0
1
0
1
0
0
0
0
1
3
1
0
0
0
0
0
1
2
0
0
0
0
0
1
1
0
0
2
1
0
1
1
0
1
1
0
0
0
1
1
0
0
0
3
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
1
0
0
1
1
1
0
2
0
1
0
1
0
1
0
1
1
0
0
0
0
1
1
2
2
2
0
1
1
0
1
0
0
2
1
2
0
0
0
1
0
0
0
0
0
0
1
2
2
1
1
0
0
0
1
3
1
1
0
1
0
0
0
0
0
2
0
2
0
2
0
0
0
2
0
2
1
0
0
0
1
3
2
1
1
1
1
2
1
0
1
1
0
0
0
0
3
2
0
1
1
0
1
0
1
0
0
1
2
0
0
1
0
2
0
0
1
1
1
2
1
1
2
3
0
0
0
1
0
2
0
0
2
2
1
0
1
1
2
2
0
0
0
1
0
1
0
0
1
0
0
1
0
0
2
2
0
2
1
1
4
1
0
0
1
2
2
1
0
2
2
2
0
0
1
0
3
1
0
0
0
0
1
1
1
0
0
1
1
1
1
1
0
1
2
0
1
1
0
0
0
0
0
1
0
0
1
1
1
0
2
2
0
2
2
0
0
2
2
1
2
0
1
2
0
0
0
0
2
0
2
0
0
0
0
2
1
2
0
1
1
1
0
1
2
0
2
1
0
0
0
0
2
0
1
1
2
0
0
0
0
0
1
3
0
2
2
1
0
0
1
0
0
2
0
2
0
0
1
0
1
1
0
1
0
0
2
0
2
1
0
1
0
0
1
0
0
0
0
1
1
0
0
0
2
0
1
0
2
2
1
0
0
1
0
0
0
0
1
0
1
1
0
0
0
1
2
1
1
1
0
2
2
2
1
2
2
2
0
1
0
0
0
0
4
1
0
1
0
1
0
1
1
0
0
0
0
0
2
0
1
0
2
2
0
1
2
1
2
0
1
1
0
0
0
0
0
0
0
1
3
0
0
2
0
2
0
0
0
0
0
1
3
0
1
0
0
2
1
1
0
2
0
2
2
2
0
0
1
0
0
2
1
1
1
0
1
2
0
1
1
1
0
1
0
0
0
1
0
0
1
1
1
0
2
0
0
0
2
1
2
2
0
1
0
1
0
1
0
1
1
0
2
1
0
2
2
2
1
0
2
2
2
1
0
0
2
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
2
0
2
2
0
1
1
0
1
2
0
0
0
0
0
1
2
2
0
2
0
0
1
1
0
0
0
0
1
0
0
4
1
1
1
0
2
0
1
1
1
0
2
0
2
2
1
2
1
0
1
2
0
2
0
1
1
1
0
3
0
0
2
0
1
0
0
0
0
0
0
0
1
0
1
0
2
1
2
1
1
0
2
1
1
0
0
0
0
0
1
1
1
0
1
2
0
1
1
1
0
2
0
0
0
2
2
2
0
0
1
1
2
0
2
0
0
0
0
1
0
1
0
1
2
0
1
2
0
2
1
0
0
2
2
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
2
1
0
2
0
2
0
0
1
1
1
0
0
2
0
0
0
2
1
0
2
1
0
0
1
2
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
2
2
0
1
2
2
2
2
0
1
0
0
0
0
2
0
0
2
1
0
0
2
0
0
0
1
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
2
1
1
0
0
2
1
1
2
1
0
0
2
1
2
0
1
1
1
0
0
0
0
0
0
2
1
1
2
0
0
1
2
0
1
2
1
0
3
1
1
1
1
1
1
0
2
0
1
0
1
2
2
1
0
0
0
1
2
0
0
1
0
1
1
0
0
0
0
3
0
0
0
0
1
0
0
0
1
0
0
2
2
0
2
0
3
1
0
0
0
0
1
0
0
2
0
1
1
2
0
0
0
0
1
1
0
0
0
1
0
2
0
1
1
0
2
1
0
1
0
0
0
1
1
1
0
0
0
1
0
2
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
2
1
0
2
2
2
2
0
1
0
1
0
2
0
0
0
1
0
0
1
0
1
1
0
0
2
2
1
0
1
1
1
0
2
0
1
0
0
0
1
1
2
2
0
0
2
0
1
0
0
0
2
2
2
2
2
2
1
0
0
1
1
0
0
2
1
1
0
0
1
1
0
0
0
0
2
1
0
0
2
2
2
2
2
1
1
1
0
0
2
2
1
0
0
0
0
0
0
0
0
2
1
1
1
0
0
1
1
0
1
0
1
0
1
0
1
0
1
0
2
2
2
1
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
2
1
0
3
0
2
3
0
2
1
1
0
0
1
0
2
0
2
0
0
0
1
1
3
0
1
0
0
0
2
1
0
0
1
0
2
0
3
0
0
0
0
1
0
1
1
1
0
2
0
2
2
2
0
1
0
2
0
1
0
0
1
0
0
0
2
1
0
5
1
1
0
0
0
0
2
0
1
1
0
3
0
2
2
0
1
2
0
2
1
0
0
0
2
0
0
1
0
2
0
0
1
1
0
0
0
2
1
0
2
0
2
2
2
0
1
1
0
1
2
1
0
0
1
0
0
0
1
1
1
0
2
0
0
0
2
0
3
0
1
0
0
1
0
1
0
0
3
1
0
2
0
1
0
2
0
0
0
1
3
2
0
0
2
3
0
2
0
0
1
0
1
0
1
2
0
1
0
0
3
1
1
0
2
1
0
0
1
2
0
0
0
1
1
2
0
2
1
2
1
6
0
1
1
0
1
0
2
0
1
1
0
1
3
2
1
2
0
1
0
0
1
0
0
0
0
0
0
0
2
3
0
0
0
0
1
0
0
2
1
0
2
0
2
2
0
0
0
1
1
1
2
0
0
1
1
0
1
1
0
2
1
0
1
1
2
1
2
1
1
1
1
0
0
0
1
2
2
0
0
1
0
0
0
1
1
2
1
1
0
2
1
1
1
1
2
0
2
0
1
0
0
0
0
0
1
0
1
1
0
1
0
0
0
1
1
0
1
0
0
1
1
1
0
1
0
0
1
1
0
0
2
0
0
0
0
1
0
0
0
0
0
2
1
0
2
0
1
1
0
0
0
1
1
0
0
2
0
1
0
0
0
1
2
2
1
0
1
3
2
2
0
1
0
2
2
2
2
1
1
1
0
0
0
0
2
0
1
0
0
0
0
2
0
0
1
2
2
2
0
0
0
0
2
1
0
2
0
1
1
0
0
3
2
1
0
0
0
0
1
0
0
0
1
1
0
1
0
2
0
1
0
1
0
0
1
0
1
2
0
0
1
1
1
0
1
0
0
1
0
0
1
1
2
1
2
0
0
2
1
2
2
0
3
2
3
0
1
0
1
0
2
0
0
0
1
0
2
0
2
2
0
0
0
0
2
1
0
1
1
0
2
3
1
1
0
2
0
1
1
0
1
0
2
0
2
0
1
0
0
1
0
1
1
1
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
2
0
1
2
1
0
2
0
0
0
0
0
1
0
0
0
2
1
2
2
0
0
1
1
2
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
2
1
1
0
0
1
0
0
1
2
1
0
0
0
0
0
0
0
1
0
0
2
2
3
0
0
1
1
0
1
2
0
0
2
1
1
0
2
1
0
0
0
1
2
1
1
1
2
0
2
0
2
0
0
2
2
1
0
0
1
1
0
0
1
1
0
0
0
2
1
0
0
0
0
1
0
0
2
0
0
1
0
2
0
1
2
1
2
1
3
1
0
0
1
1
0
2
2
0
2
1
0
2
1
2
0
0
0
2
0
0
0
0
2
1
1
1
0
0
0
2
2
0
0
0
0
1
0
1
1
1
2
0
0
0
1
1
0
2
0
1
0
1
0
4
0
1
0
2
1
2
1
1
0
0
0
0
1
0
2
0
0
3
0
2
0
2
1
2
2
1
7
1
0
0
1
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
1
2
0
1
0
1
0
2
1
0
1
0
1
0
0
0
0
0
1
1
0
0
2
1
0
2
1
1
2
0
0
0
2
0
2
0
1
0
2
1
2
2
1
1
1
0
0
1
0
0
3
0
2
0
2
3
0
0
2
1
2
6
0
0
0
0
0
1
2
0
0
1
1
2
1
0
0
2
0
0
1
0
0
2
1
2
2
2
1
1
0
0
0
1
0
2
0
0
0
1
1
0
2
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
5
2
0
0
0
2
0
0
0
0
0
0
0
2
2
2
2
2
1
1
1
0
2
2
0
6
0
0
0
1
0
2
0
2
0
1
1
1
2
4
0
0
0
0
1
0
2
1
0
0
0
1
0
0
3
2
0
0
0
0
0
1
0
0
1
0
1
1
2
0
1
0
1
2
1
0
2
0
1
0
0
2
0
0
1
0
1
0
0
0
1
1
0
1
0
0
1
1
0
0
0
3
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
3
2
1
4
1
1
0
2
1
1
0
0
0
2
2
2
0
3
3
0
0
1
0
0
1
1
2
1
2
0
1
0
1
1
0
0
0
2
2
0
0
0
1
2
1
0
0
1
0
0
2
0
1
2
1
2
1
2
0
0
1
1
3
1
0
2
0
0
2
1
0
0
0
0
2
1
1
0
0
0
2
1
2
0
1
2
1
0
2
1
2
0
1
0
1
0
0
0
2
1
0
3
2
0
2
1
0
2
0
1
2
0
0
0
1
0
0
1
0
0
2
0
0
1
0
0
0
1
1
1
2
0
1
0
3
1
2
0
0
0
0
0
2
0
1
0
0
1
1
0
1
0
0
0
2
1
0
0
1
1
1
0
0
1
2
1
1
1
1
0
0
1
0
0
2
1
0
2
1
0
0
0
0
0
1
0
2
1
0
0
2
1
1
1
2
0
2
1
0
1
0
0
0
0
1
0
0
1
1
1
0
1
0
0
0
1
2
2
1
1
0
1
1
0
1
2
0
0
2
0
0
2
2
0
0
0
1
0
0
1
1
1
0
1
1
0
1
0
1
1
0
0
0
2
0
2
0
0
0
0
0
0
1
2
0
4
2
1
0
0
1
2
0
2
1
1
0
0
0
2
0
1
2
0
0
1
1
4
1
0
1
1
1
1
1
0
0
0
1
0
1
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
2
2
1
2
0
1
0
0
0
0
0
1
2
0
1
0
0
0
1
2
2
1
0
1
1
0
0
0
1
1
2
0
0
0
1
1
0
1
2
0
0
3
0
1
0
2
1
1
0
1
0
2
0
0
1
0
2
0
0
0
3
0
0
0
1
0
1
0
0
0
2
1
0
0
0
0
2
0
0
1
1
2
2
0
0
0
0
0
0
2
1
0
0
0
1
0
0
1
2
0
0
1
1
0
0
0
0
0
2
2
0
2
1
0
0
0
1
0
0
0
0
0
1
1
1
0
0
2
0
0
1
2
0
0
0
0
0
0
1
0
2
2
0
2
1
1
0
0
0
1
0
1
0
1
0
2
2
1
0
1
0
0
1
0
0
2
2
1
0
0
0
2
0
4
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
2
2
2
0
1
0
0
0
1
0
0
1
2
0
2
0
1
2
2
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
1
1
0
2
1
0
0
1
0
0
0
2
0
0
1
0
1
2
0
0
1
2
0
0
1
1
0
1
1
0
1
0
2
0
1
0
0
0
2
0
2
1
1
0
2
0
1
1
1
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
1
1
1
2
0
0
0
0
0
1
1
1
1
0
2
2
0
2
1
2
0
0
2
1
0
0
0
2
0
0
1
1
0
2
2
0
1
2
0
0
0
2
1
2
2
2
0
2
0
0
0
0
0
1
1
1
0
1
0
1
0
1
0
0
1
1
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
2
0
2
2
0
2
1
0
1
2
1
2
1
0
2
0
0
0
2
1
0
0
2
0
0
1
0
0
1
0
2
0
0
3
1
2
2
2
0
0
0
0
1
0
0
0
0
0
2
1
0
4
0
2
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
1
0
1
2
1
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
2
1
0
0
0
2
0
0
0
1
0
0
2
2
2
0
2
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
3
0
1
1
0
0
2
0
0
0
1
0
0
0
1
0
0
0
2
0
2
0
2
2
0
0
0
1
0
1
2
2
1
2
2
0
1
1
0
1
0
2
0
0
1
0
1
2
1
1
0
1
0
2
2
2
0
2
0
2
1
1
1
0
0
0
1
0
2
0
0
1
0
0
0
0
2
0
0
2
1
0
0
0
1
2
0
0
2
0
0
1
0
2
1
0
0
0
0
0
0
0
2
0
0
1
0
2
7
0
0
1
1
0
2
0
2
1
0
0
1
2
0
0
2
1
0
0
0
0
0
0
0
1
0
0
2
3
0
2
1
0
1
0
0
0
0
0
0
0
2
0
1
1
0
0
0
1
1
0
1
0
1
0
1
1
2
5
1
0
0
0
0
0
0
1
2
0
1
1
2
1
3
1
1
0
0
1
1
1
2
0
0
1
0
1
0
1
0
0
2
0
0
1
0
1
1
1
1
0
2
0
0
2
1
0
0
2
0
0
0
0
2
2
2
2
0
0
0
1
2
2
0
2
1
0
2
0
0
2
1
1
0
0
0
0
1
2
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
1
1
1
2
2
0
1
1
0
0
0
0
2
2
0
2
0
0
4
1
0
0
0
0
1
2
0
2
1
0
0
0
0
0
1
0
1
0
1
0
1
0
0
2
0
1
0
0
1
2
0
2
2
0
2
0
0
0
0
1
2
0
0
2
0
0
0
1
0
0
2
1
2
0
0
0
0
2
1
2
0
3
0
2
0
0
2
1
0
2
0
0
1
1
0
0
2
1
1
2
2
1
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
2
0
1
0
0
0
1
2
0
1
0
2
1
2
2
1
0
0
1
0
0
0
0
1
3
0
1
2
1
0
0
0
1
2
0
0
1
2
0
1
0
1
0
1
1
1
0
0
0
1
0
0
3
0
2
2
0
1
0
0
2
0
0
0
1
2
1
0
1
0
0
1
1
0
0
0
0
1
1
0
0
2
1
1
1
0
1
2
0
0
0
1
1
0
0
0
0
0
1
1
0
0
1
1
3
0
1
2
2
1
0
0
0
2
1
0
2
1
1
0
2
0
2
2
1
1
2
1
0
1
1
0
0
2
0
0
0
0
0
1
0
1
0
1
0
0
1
1
0
1
0
2
2
1
1
2
0
0
0
0
2
2
1
0
0
0
0
2
3
1
1
2
0
1
1
1
2
0
1
2
1
2
0
0
1
0
2
0
1
1
2
0
1
0
1
2
2
2
0
2
7
1
1
2
0
1
1
1
1
0
2
0
0
1
1
0
1
1
0
1
4
0
0
0
2
0
1
0
1
0
2
0
1
2
2
2
2
2
0
1
1
0
0
2
0
2
1
1
1
2
0
0
0
0
2
2
0
0
0
0
1
2
1
2
0
1
0
1
0
1
0
1
2
0
0
0
1
2
2
2
1
1
1
0
1
1
1
2
0
1
0
1
1
2
2
0
1
2
0
0
1
2
1
0
2
1
0
2
1
0
1
0
2
2
0
0
0
2
3
1
0
0
0
0
0
0
1
0
0
0
2
2
0
1
1
2
1
4
1
0
0
0
2
2
0
0
1
2
7
1
2
0
2
1
1
0
1
0
0
1
0
0
1
0
0
1
0
2
1
2
0
0
1
0
1
1
0
0
2
1
0
1
1
0
0
1
0
0
2
2
0
0
0
1
0
2
0
0
1
1
1
1
0
0
2
1
1
0
2
2
0
0
0
0
1
2
0
1
1
1
1
0
1
0
0
1
2
2
0
0
2
2
0
0
0
0
2
1
2
0
0
2
0
2
0
1
2
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
1
0
2
0
2
2
2
0
0
2
0
2
1
0
0
0
1
0
0
0
2
0
1
1
2
0
2
0
0
1
2
1
0
1
0
1
1
1
0
0
2
0
0
0
2
2
1
0
1
1
0
2
2
1
2
2
0
0
0
0
2
1
0
2
0
0
0
0
2
2
1
1
0
1
0
0
0
1
0
0
0
1
0
1
0
1
2
0
2
2
0
0
2
2
2
0
1
0
2
0
1
2
3
0
1
1
0
0
0
1
1
1
0
1
0
0
3
3
0
0
0
1
0
0
2
0
1
0
0
0
1
2
1
0
0
1
1
0
0
1
0
0
2
0
1
1
0
0
1
0
0
1
0
0
0
0
1
2
1
1
0
1
1
1
1
0
1
2
0
0
2
0
0
0
0
1
1
0
1
1
1
1
0
0
1
1
0
1
0
0
2
2
0
0
1
1
2
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
2
0
2
0
2
1
0
0
1
0
1
2
1
1
0
0
0
0
2
2
0
1
0
2
0
1
0
0
0
1
2
0
1
2
1
1
1
0
0
0
0
0
1
0
0
0
2
2
0
1
1
1
1
2
0
0
0
0
0
0
0
0
1
0
0
0
1
2
1
0
0
0
0
0
0
2
2
0
1
0
0
2
0
0
1
0
1
1
2
0
0
0
2
1
1
2
0
1
0
0
2
0
1
0
2
0
0
0
1
0
0
0
1
0
0
1
1
1
2
2
2
1
0
2
0
0
1
0
2
0
1
1
1
0
0
1
1
1
2
0
0
0
0
1
0
2
0
0
0
1
1
2
2
0
2
0
1
1
0
0
0
0
1
1
1
0
0
1
1
0
0
2
1
1
1
1
1
0
1
0
2
0
0
1
0
1
0
1
0
1
0
0
0
0
0
1
0
0
2
0
2
0
0
0
2
0
1
3
0
1
0
2
0
0
0
1
1
2
0
0
0
0
0
2
0
2
0
0
1
1
0
0
2
1
0
0
1
2
0
1
2
0
0
0
2
1
2
0
1
0
1
0
0
2
1
0
0
0
1
1
0
1
1
0
1
0
1
1
2
0
1
0
1
1
0
0
1
1
2
0
2
1
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
1
2
0
1
0
0
1
0
1
0
0
2
0
2
1
1
0
1
0
0
1
2
1
0
1
0
2
2
0
1
2
0
1
0
1
0
1
0
2
2
1
1
0
2
1
1
3
0
2
1
0
1
0
2
0
1
0
0
2
2
0
0
2
0
2
0
0
0
0
1
0
1
0
0
2
2
0
2
0
2
0
0
0
1
0
0
0
2
2
0
1
1
1
2
2
0
1
0
0
0
2
2
0
1
0
0
1
2
0
1
0
2
0
0
1
1
0
0
0
0
0
0
1
0
2
1
0
0
2
1
1
1
1
1
0
0
2
0
1
1
0
2
2
0
0
0
0
1
0
1
2
0
0
2
0
0
1
1
2
0
2
0
0
0
1
2
2
2
0
2
0
0
0
2
1
0
0
0
1
0
1
0
1
0
2
0
1
3
1
2
0
0
0
1
2
0
0
1
0
0
2
0
1
2
2
1
1
2
2
1
1
1
0
0
0
0
2
0
0
0
0
1
3
2
0
1
2
1
0
0
0
1
0
0
0
0
1
0
0
2
1
0
0
2
2
1
2
1
1
1
1
0
0
1
0
1
2
0
0
2
0
2
1
1
2
0
0
1
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
2
2
0
1
0
0
0
2
3
2
1
1
1
0
0
2
1
0
1
0
1
0
1
0
1
0
0
0
2
0
0
0
1
2
1
1
3
0
0
0
1
2
1
1
1
2
0
3
0
2
0
2
0
1
1
1
0
1
2
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
2
1
1
0
0
2
0
2
1
0
0
1
0
1
4
1
2
0
2
0
2
1
0
1
1
1
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
1
2
1
1
0
1
0
2
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
1
1
2
2
1
1
0
2
0
0
1
0
0
1
0
0
2
1
0
1
0
1
0
0
0
0
1
0
0
0
0
2
1
2
1
1
0
0
2
1
0
2
3
0
2
1
0
0
2
0
1
1
0
2
0
2
1
0
1
0
3
0
2
0
1
2
1
2
1
0
1
0
1
0
0
1
1
0
2
2
0
0
0
1
1
0
0
1
1
0
0
2
3
1
0
0
1
0
1
1
0
1
2
0
0
2
0
3
0
0
0
1
2
2
1
1
1
0
0
2
1
1
2
2
1
0
2
2
1
0
1
2
1
1
1
2
0
4
0
1
0
0
1
2
1
0
0
0
0
0
2
2
0
1
1
2
0
0
0
1
2
1
0
0
0
1
0
1
0
0
0
0
2
2
1
2
3
0
0
0
2
1
0
1
0
0
1
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
1
1
0
0
2
0
0
2
0
0
1
1
1
0
0
0
0
1
0
0
1
0
2
0
1
1
2
1
1
1
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
1
1
0
1
0
2
1
0
0
0
2
0
2
2
0
0
4
0
0
0
2
3
0
0
0
0
0
1
1
0
0
2
2
0
1
0
0
2
0
0
0
1
3
2
2
0
0
0
1
0
2
0
2
1
1
1
3
1
0
1
2
2
0
1
0
0
1
0
2
0
0
1
2
1
1
2
2
1
1
0
1
0
1
2
0
1
0
1
0
1
0
0
0
1
1
2
0
0
0
0
0
1
0
0
0
0
0
3
2
0
0
1
2
2
0
1
1
0
2
1
0
0
1
2
2
2
0
1
1
0
1
0
0
1
1
1
0
1
1
1
0
1
0
0
0
1
1
1
0
0
0
2
0
0
1
0
5
1
0
0
0
3
0
2
0
0
2
2
2
2
0
1
0
0
1
2
1
2
0
0
1
0
1
0
1
0
1
0
2
2
0
2
1
1
0
0
1
0
2
1
1
0
1
0
0
2
0
0
2
0
2
1
0
0
0
0
2
0
1
1
0
0
3
0
2
0
1
0
0
0
0
2
0
2
1
0
1
1
1
0
0
2
1
1
0
2
3
0
0
1
1
1
1
0
2
1
0
2
2
0
0
2
1
0
0
1
2
2
0
2
0
2
1
0
1
1
2
1
0
0
0
0
1
1
2
0
1
2
1
0
1
0
3
1
1
0
2
0
0
0
0
1
0
2
2
0
0
2
2
1
1
0
1
0
2
2
2
2
1
0
2
0
2
0
1
2
0
0
0
0
2
0
0
1
0
0
1
1
1
0
0
2
0
1
1
2
0
1
1
1
1
0
0
0
1
2
1
0
0
0
0
0
1
0
0
0
0
2
1
0
2
0
1
0
2
1
0
2
0
0
2
2
2
1
1
1
0
0
0
1
0
0
0
0
1
0
2
1
1
0
1
0
0
2
0
2
0
1
2
1
0
0
1
2
1
1
0
0
2
0
0
0
2
0
0
1
2
1
2
0
1
0
2
0
0
0
0
1
0
2
0
1
0
0
2
2
1
0
1
0
1
2
0
0
3
1
2
1
0
2
2
2
1
0
0
0
0
0
0
1
0
0
2
0
1
0
0
1
0
0
1
2
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
1
1
0
2
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
2
2
1
0
0
0
0
2
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
2
2
2
0
2
1
0
2
0
0
1
0
2
0
1
2
0
0
0
0
0
0
0
2
2
2
0
1
1
1
1
0
1
0
0
2
0
0
1
2
1
2
0
2
1
0
2
1
2
1
1
0
2
0
2
1
1
0
0
1
1
2
1
1
1
0
1
2
2
2
1
1
0
2
0
0
0
0
0
0
1
2
0
0
0
0
1
2
0
1
0
0
2
0
0
1
2
0
2
0
2
0
0
0
0
1
0
1
2
1
0
2
0
0
0
0
1
0
2
0
1
1
0
0
0
2
0
0
0
0
2
2
0
0
0
1
2
1
1
1
0
1
1
2
2
0
1
3
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
1
1
0
2
0
0
1
0
1
0
0
0
1
0
0
1
0
5
0
0
0
0
2
0
1
2
0
2
0
1
0
0
1
0
0
0
1
0
0
2
2
1
0
0
2
0
0
2
0
0
1
0
2
1
0
0
0
0
0
0
1
2
0
0
0
1
0
0
1
0
2
0
2
2
1
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
2
1
0
2
0
0
2
0
0
0
0
0
0
3
0
2
0
1
2
1
0
0
0
2
1
2
0
0
1
0
1
2
0
1
1
0
1
0
1
0
1
0
1
0
2
0
1
1
0
0
0
2
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
2
0
0
2
1
1
0
0
1
2
0
0
1
0
0
0
0
2
0
3
0
0
0
6
0
1
1
1
0
0
0
0
0
1
1
1
1
0
0
0
2
1
2
0
2
2
1
1
0
2
1
1
1
0
0
1
1
0
0
0
0
1
1
2
0
1
2
2
2
1
0
0
2
1
2
1
0
2
1
0
1
0
1
3
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
1
0
1
0
1
0
0
0
2
0
0
2
0
1
1
0
0
1
1
1
3
0
0
0
0
1
1
0
1
0
2
0
0
0
0
1
2
2
1
2
0
0
2
0
1
0
1
2
2
0
1
0
4
1
0
1
1
1
0
1
1
1
0
2
4
0
0
0
0
0
0
2
0
1
0
1
0
0
1
1
1
1
1
0
0
1
0
2
0
0
2
1
0
2
1
2
0
3
0
2
2
1
2
0
1
0
0
2
2
0
0
0
1
2
1
0
0
0
1
0
0
2
3
0
0
0
1
0
2
0
0
1
0
0
1
1
0
1
0
1
1
9
2
2
1
1
0
0
0
0
1
1
1
0
2
1
2
0
2
2
0
3
0
1
0
0
0
2
2
0
1
2
1
0
0
0
0
1
0
1
0
1
0
0
2
1
0
0
0
1
0
1
1
0
2
0
2
0
2
2
2
2
2
1
1
2
0
0
0
0
1
1
0
2
0
1
1
2
1
1
0
0
2
1
1
3
0
0
0
0
0
2
1
1
0
0
4
0
0
0
1
0
2
1
0
2
1
0
0
2
0
3
1
0
1
0
1
1
1
0
1
0
0
0
0
0
1
0
2
2
0
1
0
1
1
0
2
0
1
2
1
0
0
2
0
2
1
0
2
2
1
2
1
0
1
1
0
0
1
2
0
1
1
0
1
2
0
0
0
2
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
2
1
0
1
2
0
1
1
0
0
1
1
0
1
0
0
1
1
2
0
1
1
2
1
2
2
2
0
1
2
1
0
0
2
1
2
2
1
1
1
2
0
0
2
0
2
1
0
1
2
0
1
0
2
0
1
2
0
0
0
1
0
1
0
0
2
2
2
0
0
2
0
0
0
1
0
3
1
0
0
2
0
0
2
1
0
1
2
2
1
1
2
0
0
1
0
0
0
2
0
0
1
0
2
1
1
0
1
5
7
2
2
0
1
0
0
1
1
0
1
4
0
0
1
0
2
0
0
0
1
0
1
2
0
2
2
1
0
1
0
0
3
0
0
0
0
2
0
1
1
0
2
1
0
0
1
2
0
2
0
4
1
1
1
0
0
0
0
0
0
0
2
0
0
4
0
1
0
0
1
0
2
0
2
1
0
0
1
0
2
2
2
0
1
0
0
0
1
2
1
0
0
0
2
2
0
0
1
0
5
0
0
1
1
1
0
0
1
2
0
0
0
2
0
3
0
0
3
0
0
1
0
2
0
2
0
1
1
0
0
0
0
2
1
3
0
2
0
1
0
0
2
1
0
0
2
0
0
2
0
2
1
0
0
1
0
0
1
1
0
0
0
2
1
0
0
0
1
2
1
0
2
0
0
1
0
2
0
1
2
1
2
2
2
1
1
1
1
3
0
0
2
1
0
2
2
1
0
1
1
0
1
0
1
0
1
1
4
2
0
0
1
1
3
0
2
0
3
1
2
0
0
0
1
1
0
1
2
1
1
0
1
0
0
2
0
2
0
0
0
0
2
0
1
0
1
0
2
0
2
2
2
0
0
1
1
0
1
0
0
1
0
0
0
5
0
0
1
0
0
0
1
1
3
2
0
0
0
2
1
1
0
1
0
0
0
1
0
0
0
1
1
2
0
0
0
0
2
1
1
1
0
2
1
1
0
0
1
0
0
0
0
0
1
0
2
2
0
1
0
0
1
1
1
0
2
0
1
0
1
0
0
2
1
1
1
1
1
0
0
1
1
2
0
0
0
0
0
0
1
1
0
2
1
0
0
1
0
1
2
0
0
4
0
2
2
0
2
0
0
1
1
0
0
0
0
1
1
1
0
0
1
2
2
2
0
2
0
2
6
0
1
1
3
2
0
1
0
0
1
0
0
1
2
0
2
0
2
0
0
0
0
0
0
2
1
1
0
1
0
1
2
1
0
0
2
0
2
1
1
0
0
2
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
1
0
2
0
0
0
1
1
0
0
2
2
0
2
0
0
3
0
1
1
2
0
0
3
0
2
0
1
0
0
0
0
2
1
0
1
2
0
0
2
1
0
0
0
2
2
0
0
1
2
0
1
2
0
0
0
1
0
0
1
0
2
0
0
0
0
1
1
1
2
0
0
0
0
0
1
1
0
2
1
2
0
1
0
1
1
2
1
3
0
1
2
0
1
0
0
0
1
2
1
1
0
0
2
1
0
0
0
1
0
0
1
2
1
1
2
0
0
3
0
0
0
0
2
2
0
0
0
2
1
1
1
0
1
1
0
1
0
0
0
0
0
2
2
0
0
2
0
0
3
0
0
0
0
0
1
0
1
2
2
3
2
0
2
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
1
0
1
0
1
0
0
0
1
0
0
1
2
0
0
0
2
0
0
0
0
0
0
1
0
2
1
2
0
1
1
2
0
0
1
2
0
1
0
0
0
1
0
1
0
0
1
1
1
2
1
2
1
2
0
1
1
0
1
0
0
2
0
0
0
1
3
2
0
0
0
0
1
1
0
1
1
0
1
1
1
1
1
0
0
2
1
0
1
1
0
1
1
0
2
0
1
1
1
1
0
2
0
4
0
0
2
0
0
2
2
1
0
0
0
1
2
2
0
0
2
0
2
0
1
1
0
2
0
2
0
0
0
0
1
1
1
2
1
1
0
0
0
2
0
0
1
2
0
0
2
1
0
2
1
1
2
2
2
0
2
2
1
0
0
2
2
1
0
0
0
0
0
0
1
2
0
1
1
1
0
1
0
0
2
2
1
0
0
0
0
2
8
0
0
0
0
1
2
2
0
3
2
0
0
1
1
0
0
1
0
0
1
2
0
1
0
2
0
1
0
2
0
0
1
2
0
0
0
1
0
0
2
1
0
2
1
2
0
0
2
1
0
2
0
0
1
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
1
1
4
0
0
0
0
2
2
0
1
0
0
1
1
0
0
2
1
0
1
0
1
1
0
0
0
2
0
0
2
0
2
1
0
1
1
0
0
0
0
0
1
2
0
0
2
0
0
0
0
2
0
0
1
2
0
0
0
0
2
0
0
2
2
1
2
1
1
1
2
0
0
2
0
1
1
1
0
2
1
0
0
1
0
0
0
1
0
0
1
1
0
1
0
2
3
0
2
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
2
0
1
0
0
0
0
1
1
1
0
0
8
0
0
0
0
0
0
0
2
2
4
2
0
1
1
0
1
0
1
0
0
0
0
2
2
2
0
1
0
0
1
0
1
0
1
0
1
0
0
1
0
1
1
2
0
2
2
1
0
1
1
1
0
1
2
0
0
0
0
0
0
0
0
1
0
2
0
2
1
0
1
0
1
0
0
0
1
0
0
0
0
1
2
0
1
0
0
0
0
0
1
1
0
0
2
0
2
2
2
0
0
0
0
0
1
0
0
0
3
3
2
2
1
0
0
0
0
2
1
1
0
0
0
1
2
0
1
0
2
1
0
1
2
1
1
1
2
0
0
1
2
0
1
0
1
0
2
2
2
1
0
0
1
1
1
1
0
1
0
0
0
2
2
0
0
0
2
2
0
0
0
0
0
1
0
0
1
1
2
0
0
2
1
0
2
1
0
1
0
1
2
1
1
1
0
0
1
1
0
0
0
2
0
2
1
0
0
0
0
1
2
0
1
1
1
2
1
0
0
0
0
1
1
0
0
2
0
1
3
0
2
0
2
0
1
2
0
2
0
1
0
1
0
1
1
1
0
0
1
1
0
0
1
0
0
0
0
1
3
0
0
3
0
0
0
0
3
0
1
1
0
2
0
0
0
0
1
0
0
1
0
2
0
0
0
1
2
1
1
0
0
1
1
0
0
1
2
0
1
0
2
0
0
2
0
0
0
1
2
0
2
1
1
0
0
1
1
2
1
0
0
1
2
1
1
3
1
0
1
0
0
2
1
1
0
1
1
1
0
0
0
2
1
0
0
0
1
2
1
1
0
1
1
0
2
0
0
0
2
0
0
0
1
0
3
0
0
0
0
0
0
0
1
0
1
2
1
0
0
0
0
0
1
1
2
0
0
0
1
0
0
0
0
0
2
0
2
1
0
0
2
1
2
2
0
0
2
1
1
2
1
1
2
0
0
1
0
0
2
0
0
0
0
0
0
2
1
0
0
1
2
0
0
0
1
5
0
1
1
0
0
2
0
1
4
0
1
0
0
1
0
2
0
1
0
0
1
2
2
1
2
0
0
1
0
2
1
2
0
1
0
0
0
1
0
1
1
2
1
0
0
0
1
0
1
0
0
0
0
1
1
0
0
1
0
1
0
0
0
2
1
0
2
3
0
1
0
0
1
1
0
1
0
0
0
1
0
1
1
0
2
0
2
2
0
0
0
2
0
0
0
0
0
2
1
1
1
1
1
0
1
0
2
0
0
0
0
0
0
2
0
0
1
0
2
0
0
1
1
0
0
0
0
2
0
5
1
2
0
0
0
0
1
1
0
1
1
1
0
0
1
1
1
0
0
0
0
1
2
1
0
0
0
2
1
0
1
0
2
0
0
0
0
2
0
0
1
0
1
2
0
0
1
0
0
0
0
0
1
2
0
0
2
0
0
2
0
0
2
0
0
2
0
1
1
2
0
1
0
0
1
1
1
0
1
2
1
0
0
0
1
1
2
0
0
1
0
2
0
2
2
1
2
2
2
1
1
1
0
0
2
0
0
2
0
0
0
1
0
0
1
0
0
4
0
2
0
1
1
0
0
0
0
2
0
0
0
0
1
0
0
2
0
2
0
1
1
0
1
0
0
1
2
1
1
0
1
1
0
0
1
0
0
0
0
2
1
2
0
2
1
3
1
0
0
0
1
0
0
0
0
0
4
0
0
2
1
0
1
1
0
1
0
0
0
0
0
0
2
0
0
2
1
0
0
1
0
1
0
0
0
1
1
2
0
0
0
0
2
0
1
1
0
0
1
0
1
3
0
2
0
4
1
0
1
0
1
0
1
0
1
1
0
0
0
0
1
1
2
2
0
0
1
1
0
1
2
1
0
1
1
0
1
0
0
6
0
0
0
0
1
2
0
0
0
1
0
0
3
0
1
1
0
1
0
1
2
2
0
0
1
0
1
2
0
2
0
0
0
1
1
1
0
0
0
0
0
0
0
2
0
2
0
0
2
0
1
0
0
0
0
3
1
0
0
2
1
2
2
2
0
2
2
2
1
1
2
1
0
1
0
1
2
0
1
0
1
2
0
1
0
0
0
1
0
0
0
1
0
0
1
0
1
1
0
2
0
0
1
0
1
0
0
0
2
0
2
2
2
1
0
2
1
0
0
1
1
2
1
1
0
2
1
1
0
0
2
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
1
3
4
1
0
2
1
0
1
0
0
3
1
1
0
2
0
0
1
0
1
0
0
2
0
0
0
0
2
1
2
2
0
2
2
2
1
1
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
1
0
0
1
2
1
0
0
0
2
2
2
1
1
0
0
0
0
0
0
0
0
3
0
1
0
0
0
1
1
0
1
1
0
0
1
0
2
0
2
2
0
0
1
1
0
2
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
2
0
2
0
1
0
0
1
1
2
0
1
0
0
2
0
1
0
0
0
0
2
0
0
0
2
3
1
1
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
1
1
0
2
0
0
1
1
1
0
3
0
0
0
1
0
2
0
1
0
0
0
0
0
1
2
1
0
1
0
0
2
0
0
0
0
0
0
1
1
2
3
0
0
0
1
0
2
0
2
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
1
0
1
0
0
2
2
1
0
1
0
0
1
0
1
0
2
0
2
0
2
0
0
0
0
0
0
1
0
1
1
0
1
1
0
0
1
2
0
0
1
1
1
0
2
0
0
0
0
2
1
1
0
4
1
1
1
2
1
2
2
1
0
1
2
2
3
2
0
0
0
0
1
0
0
0
0
1
1
3
2
1
1
2
0
2
0
0
2
0
2
0
0
0
3
1
2
0
1
1
0
1
2
1
0
1
0
1
0
0
1
0
1
1
0
2
2
0
0
1
2
1
1
2
1
0
1
1
0
0
1
2
0
1
0
2
1
0
0
0
1
0
0
0
2
0
1
2
2
2
0
1
0
1
1
2
0
2
0
0
0
1
0
0
0
0
1
1
0
1
2
0
0
0
1
2
0
0
1
0
0
2
1
1
0
1
0
0
0
0
0
0
0
2
2
0
0
1
0
0
1
2
0
0
0
0
0
1
0
0
2
0
0
2
1
1
1
1
2
0
0
1
0
1
0
0
0
2
0
0
1
0
1
2
1
0
0
1
1
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
2
1
0
1
0
0
0
0
0
2
2
2
0
2
0
0
2
1
0
1
0
0
2
0
0
1
1
1
0
0
0
0
0
0
1
2
0
0
1
1
0
0
1
2
1
0
0
0
1
2
1
1
1
1
1
0
0
0
0
1
1
0
2
0
0
2
0
1
2
0
3
0
0
2
0
0
2
0
0
0
1
0
0
0
1
2
0
0
0
1
2
2
1
2
1
0
0
0
0
1
0
0
1
1
0
0
2
0
1
0
0
1
1
2
0
0
2
0
1
0
0
0
0
1
2
0
0
0
2
2
1
0
1
0
1
1
1
1
2
0
0
1
0
1
1
1
2
1
2
2
2
1
0
1
2
0
2
3
0
0
0
2
0
1
1
2
2
0
0
2
2
1
1
1
0
2
1
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
3
1
3
0
1
1
2
1
0
0
0
0
1
0
0
1
0
0
1
0
0
2
0
0
1
0
0
0
0
2
2
0
1
0
1
0
0
0
1
1
1
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
2
0
0
0
2
2
1
0
1
0
1
2
2
2
0
0
2
1
2
2
1
0
1
0
1
2
2
2
1
0
1
0
2
3
1
0
0
0
0
1
1
2
1
0
2
2
3
1
2
1
1
0
2
0
0
1
2
1
2
2
0
1
0
0
0
0
0
2
0
0
0
1
0
2
1
0
0
1
0
2
0
2
1
2
2
0
0
0
0
1
1
0
0
1
1
2
0
1
2
0
0
1
1
1
2
0
2
0
0
2
0
1
2
0
0
0
0
0
1
0
1
0
2
0
0
1
0
2
0
2
0
1
2
0
0
3
2
1
0
0
2
2
2
0
1
2
0
2
0
1
1
2
0
0
1
0
1
0
2
2
0
1
1
0
0
2
0
2
0
1
1
0
0
2
0
1
0
0
0
0
0
1
0
1
2
0
1
0
1
0
0
0
0
1
0
0
1
1
2
1
0
0
0
2
0
1
2
0
2
2
0
0
2
1
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
2
0
0
0
1
0
1
0
3
1
0
1
0
0
3
0
2
1
0
1
0
1
0
0
1
1
0
1
0
0
1
0
0
2
0
0
0
0
1
1
0
0
0
2
0
0
1
0
1
0
1
0
0
3
1
1
0
0
1
0
0
0
1
2
0
0
1
1
1
1
0
0
2
1
2
1
0
1
0
1
1
1
0
2
0
1
1
1
0
1
0
0
0
1
0
0
1
0
2
1
1
1
0
1
1
0
2
0
2
0
0
0
0
0
1
0
0
0
1
0
2
1
0
0
0
2
0
0
1
0
1
2
2
2
2
2
0
1
1
1
2
1
0
1
0
1
1
1
2
1
0
0
0
0
0
1
2
1
1
0
0
0
2
0
2
1
1
2
1
0
4
0
2
1
0
0
1
1
2
0
2
0
0
1
0
0
2
2
0
2
0
1
1
0
0
3
0
0
2
1
0
0
0
0
1
0
0
0
2
0
0
0
1
1
0
2
1
0
1
0
0
0
1
0
0
2
2
0
0
1
0
1
0
2
2
2
0
1
0
2
0
1
2
0
1
0
2
1
0
0
0
0
1
0
0
0
0
2
0
0
0
2
1
2
0
2
2
2
2
1
0
1
0
2
0
0
0
0
2
2
0
1
1
2
1
2
0
2
0
1
1
0
1
0
0
2
0
0
1
0
0
1
2
1
1
0
0
2
1
1
0
0
7
1
0
0
0
0
2
1
0
0
1
2
0
0
1
0
2
0
1
0
0
0
0
2
0
2
0
0
0
2
0
1
1
0
0
1
1
0
0
2
1
0
0
2
1
1
0
2
2
0
1
0
0
0
1
0
1
0
2
1
1
0
1
0
0
2
1
2
0
0
0
2
7
1
1
0
1
1
0
0
2
2
0
0
2
1
3
0
2
1
3
1
1
1
1
0
0
0
1
2
1
0
1
0
0
0
0
0
0
2
1
1
1
0
0
1
1
1
0
1
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
1
1
2
0
2
1
0
0
0
2
0
0
0
2
3
2
2
1
1
0
0
0
0
0
0
1
1
1
1
2
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
1
0
2
1
1
0
0
3
1
0
2
0
0
0
1
3
1
2
0
2
0
0
0
1
2
0
0
1
0
0
0
2
1
1
1
2
0
1
1
0
2
0
0
1
0
0
1
0
0
0
1
2
2
1
2
0
1
2
0
1
1
0
0
0
1
0
2
1
1
1
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
1
0
0
1
2
0
2
2
0
2
1
2
0
2
2
0
1
0
0
1
2
0
0
0
0
0
0
0
2
0
1
0
0
1
0
1
1
1
0
1
0
1
1
0
1
2
0
0
1
0
2
2
1
0
0
1
0
0
0
0
2
1
2
0
0
0
1
1
0
0
2
0
2
0
0
0
0
1
1
0
3
0
1
2
0
1
1
0
2
2
1
0
0
0
1
0
2
0
1
0
0
0
3
0
1
2
2
1
0
2
1
2
0
1
0
0
1
1
0
0
2
1
3
0
0
1
0
0
0
1
0
0
1
1
0
1
0
1
0
0
0
1
0
1
0
2
1
0
0
2
0
0
1
2
2
0
2
1
1
2
0
1
0
1
0
2
1
0
0
1
1
0
0
0
4
2
0
0
0
1
1
2
1
0
0
1
2
0
1
0
0
0
0
2
0
0
1
0
1
0
1
1
1
0
1
2
0
1
0
2
1
0
2
0
0
1
2
0
0
2
0
0
0
0
0
2
0
2
0
2
0
0
1
1
1
0
1
1
2
2
0
3
2
0
1
2
1
1
0
0
2
0
0
0
2
0
1
1
2
0
2
0
0
2
0
0
0
2
2
0
1
0
0
1
2
0
1
0
1
1
0
0
2
1
0
0
0
1
2
0
2
0
0
2
1
0
0
1
0
1
3
0
0
0
1
0
0
0
0
5
2
1
1
0
3
2
1
0
1
0
0
0
0
0
2
0
0
0
1
1
1
1
1
0
0
1
0
1
0
0
1
0
0
0
0
0
1
2
0
1
0
1
1
0
2
2
0
0
0
2
2
0
1
0
2
2
1
2
2
0
0
1
2
0
0
0
2
3
1
0
1
0
0
0
0
0
0
0
0
1
1
3
0
0
0
1
0
1
2
0
0
2
0
1
1
0
0
1
1
0
0
1
1
0
2
0
0
2
0
0
0
1
2
2
2
2
0
0
2
0
2
2
0
2
1
2
1
0
1
1
0
2
2
0
1
2
0
1
0
1
0
0
2
0
1
0
0
2
2
0
2
0
0
1
2
0
1
0
2
0
2
0
0
2
1
2
0
1
0
1
2
1
0
1
0
2
0
0
1
0
1
1
2
0
1
0
0
0
2
1
2
0
0
0
0
2
2
1
0
0
0
3
0
0
2
2
0
0
0
0
0
2
0
2
1
1
0
0
0
0
0
0
2
0
1
0
0
0
2
1
1
1
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
2
2
0
1
0
0
1
2
0
0
2
0
0
1
2
4
1
0
2
2
0
0
0
0
0
2
0
0
0
1
0
1
2
2
1
0
0
0
0
2
1
0
1
1
1
2
0
1
2
1
1
0
1
1
1
0
0
0
2
0
1
1
0
1
1
1
2
2
2
1
0
0
3
0
0
1
0
1
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
1
1
2
1
2
0
2
0
0
0
2
0
2
2
1
2
2
1
0
1
0
0
0
2
1
0
0
0
1
2
0
1
2
0
0
1
0
2
1
0
1
1
0
2
2
1
0
1
1
0
0
1
0
2
2
0
1
0
2
0
0
2
0
2
1
2
3
1
1
1
0
1
0
0
2
1
2
1
0
2
1
0
2
0
0
0
2
2
1
0
2
0
0
3
1
0
2
2
0
0
2
2
0
1
0
0
0
3
0
0
2
2
0
0
2
0
0
0
1
1
1
1
0
1
1
0
0
1
0
0
1
0
1
1
0
2
0
0
2
0
0
0
1
0
0
0
0
1
1
1
1
0
0
1
4
3
0
0
0
2
2
0
1
0
0
2
0
1
0
1
0
0
3
0
0
0
0
0
0
0
2
1
0
1
0
2
0
0
2
0
2
2
2
0
2
0
1
0
1
2
1
0
3
1
0
1
2
1
0
1
1
0
1
0
4
1
0
0
0
0
0
1
1
0
2
0
2
1
0
1
0
1
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
1
0
2
1
2
1
0
0
0
2
2
0
2
0
2
0
2
2
1
0
0
1
0
2
1
0
3
0
0
2
1
0
1
1
1
0
0
0
0
0
1
1
1
0
0
2
2
0
1
0
0
0
0
1
0
2
0
1
0
2
2
2
2
0
0
0
0
0
1
3
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
1
2
1
0
0
1
0
0
0
2
0
0
0
2
1
0
1
0
2
1
1
0
1
0
3
0
1
1
2
2
2
0
1
0
1
1
0
3
0
2
0
0
0
2
1
0
0
0
2
0
2
2
0
3
1
0
1
0
1
2
0
2
0
0
0
0
0
2
0
0
1
1
0
1
1
2
0
1
2
0
1
1
2
1
2
0
1
0
1
1
1
0
1
1
0
2
1
0
2
1
1
0
1
1
0
1
1
0
2
1
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
3
2
0
0
0
1
0
0
0
0
0
1
0
1
0
0
2
0
0
2
0
1
3
1
1
0
2
1
1
0
0
1
0
0
0
1
1
1
1
0
0
2
1
1
2
1
2
0
1
2
1
0
2
2
2
2
0
0
1
1
0
0
0
2
0
1
0
0
2
0
0
0
0
1
0
0
2
1
0
0
1
0
1
0
0
1
1
0
1
2
0
1
1
0
0
2
0
2
0
1
2
0
0
0
2
1
0
1
1
0
2
2
4
0
0
1
2
0
0
0
1
1
1
1
1
0
2
1
0
0
1
0
2
2
2
0
0
0
1
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
2
0
1
0
0
1
1
2
0
0
0
2
2
0
0
0
0
2
2
0
0
1
1
1
1
0
0
0
2
1
1
0
1
2
0
0
3
1
0
1
2
1
0
1
0
1
2
0
1
1
1
1
0
0
1
0
0
1
0
0
0
1
0
2
1
0
0
2
0
0
0
2
0
3
1
0
0
1
2
1
0
1
2
0
0
1
1
0
3
0
0
1
1
0
1
0
0
0
0
0
1
1
0
1
0
0
1
1
1
0
0
0
0
0
4
2
1
0
2
0
0
0
0
0
0
1
0
0
1
0
2
0
0
2
1
1
0
2
1
0
0
0
2
2
1
1
0
1
1
2
0
2
1
0
0
0
2
0
0
0
0
0
3
1
0
1
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
7
0
0
1
0
1
0
0
1
1
0
0
1
2
1
0
2
0
0
2
0
1
1
0
0
3
0
0
0
0
1
8
1
0
0
2
1
0
0
0
1
0
0
0
1
1
2
1
0
0
1
2
1
2
2
0
0
0
2
0
0
1
0
2
0
0
1
0
2
0
1
0
0
0
1
0
1
0
1
1
1
0
1
0
0
1
1
0
1
2
2
0
2
1
2
2
1
1
3
0
0
2
1
0
0
0
2
0
1
0
2
2
0
0
0
0
0
2
1
0
1
2
0
1
2
1
1
0
0
0
1
0
0
1
0
1
0
0
0
2
0
1
2
0
0
2
0
0
0
0
0
0
1
1
1
1
1
1
2
2
1
1
0
1
0
0
1
2
0
1
1
2
0
2
0
1
1
1
0
2
2
1
1
0
0
0
0
0
1
0
1
1
2
0
1
0
0
0
0
0
1
1
0
0
0
2
1
0
1
0
0
2
0
1
0
2
2
0
0
1
0
1
1
0
1
1
1
0
0
0
1
2
1
1
0
0
1
1
0
0
2
2
0
0
1
0
1
0
0
0
0
2
0
0
1
0
1
1
0
0
0
1
1
2
1
0
1
1
2
0
0
0
0
1
1
0
1
2
1
2
1
1
1
0
2
0
0
0
0
1
2
1
1
1
0
0
0
1
2
0
0
0
1
1
1
1
0
0
1
1
2
0
4
0
0
1
0
1
0
0
2
0
0
1
0
0
1
1
2
2
0
0
1
1
0
0
0
0
0
1
1
2
0
2
0
1
2
1
0
1
1
2
1
2
0
0
2
0
0
2
0
0
1
0
2
1
0
1
2
1
1
0
2
1
0
1
2
1
2
1
0
0
0
0
2
2
1
2
0
0
0
1
0
1
1
0
1
0
1
0
0
2
0
0
0
1
1
0
1
0
2
0
0
0
0
1
2
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
2
0
1
0
0
2
0
1
1
1
0
0
2
0
0
0
0
0
1
0
0
0
1
1
0
2
0
2
0
2
0
0
2
1
2
1
0
0
0
0
1
2
0
1
0
1
0
1
1
1
1
0
2
1
1
0
0
2
0
0
2
2
1
4
1
1
0
2
0
0
0
2
0
0
2
0
1
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
3
0
0
2
1
1
0
0
0
2
0
2
2
0
0
2
2
2
0
3
2
1
0
1
2
0
0
0
2
0
0
2
1
0
1
2
1
3
2
0
1
0
0
2
0
2
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
2
0
1
0
1
0
1
2
0
1
0
0
0
0
2
0
1
2
2
1
1
2
0
1
1
0
2
0
1
2
2
0
0
1
1
1
3
0
0
0
2
0
0
1
2
0
2
0
0
2
2
0
0
0
0
1
2
1
0
1
0
0
0
0
0
0
0
2
1
1
2
2
1
1
0
1
2
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
2
0
0
2
0
1
0
0
0
0
1
0
2
0
0
1
0
0
0
2
0
1
1
0
1
0
0
0
1
0
1
0
0
0
2
2
0
0
1
0
0
1
1
0
2
0
2
0
2
1
1
2
0
0
1
2
0
1
1
1
2
1
1
0
0
2
1
0
2
1
1
1
2
0
0
1
0
1
0
0
2
0
0
0
1
1
1
1
1
2
2
0
1
1
1
0
0
0
0
0
0
1
1
2
0
0
0
2
0
0
1
0
0
2
1
0
0
2
2
0
0
3
2
0
1
1
0
0
0
1
1
0
0
0
2
1
2
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
2
3
0
0
2
2
1
0
1
0
1
2
0
0
0
0
0
2
0
4
1
1
0
1
0
0
0
0
0
0
1
0
0
0
1
2
0
1
2
0
1
0
0
1
1
0
0
2
1
1
1
0
1
3
0
1
1
0
0
2
2
3
2
1
0
1
0
0
2
0
0
1
2
0
0
0
1
0
0
1
0
1
0
1
1
2
1
1
2
1
2
0
2
0
1
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
2
0
1
0
1
0
0
2
1
0
2
0
0
2
0
2
0
0
0
0
0
0
0
2
0
2
3
2
0
2
0
2
2
0
0
0
1
1
2
2
0
0
1
2
2
0
2
0
2
2
1
1
0
1
0
1
1
2
0
1
1
1
0
1
0
4
1
0
0
2
0
0
0
1
1
0
1
1
2
0
1
0
0
0
0
2
2
1
1
0
1
2
0
1
0
1
0
2
1
0
1
1
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
1
0
1
1
1
0
3
2
1
0
3
0
0
3
0
2
0
4
0
0
0
1
1
0
2
2
0
0
0
0
0
0
0
0
0
1
2
1
2
1
0
1
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
3
2
0
0
3
2
1
0
0
1
0
2
0
3
1
0
0
0
0
1
0
0
1
0
0
2
0
0
1
0
2
0
0
0
1
0
0
1
2
2
2
1
0
1
0
0
2
0
0
1
1
2
0
4
1
1
1
2
0
0
1
2
1
0
1
2
1
0
2
2
0
2
3
0
0
0
0
1
2
1
0
2
1
1
2
0
1
1
0
0
0
1
1
0
0
2
0
2
0
0
0
0
0
0
0
2
2
0
1
0
2
0
0
0
1
0
1
2
1
0
0
0
1
0
2
0
0
0
1
2
2
0
1
0
2
0
1
1
0
1
0
1
0
0
1
1
1
0
2
0
2
2
0
0
2
0
2
0
2
1
1
0
1
0
2
0
0
1
1
1
0
1
1
0
1
2
0
1
2
1
1
2
2
0
1
1
1
1
0
2
2
0
0
1
1
2
1
2
0
1
0
1
1
3
0
0
0
2
0
0
0
0
0
4
2
0
2
0
0
0
0
2
1
1
1
1
2
0
2
2
0
1
9
2
0
0
1
1
0
2
1
0
2
0
0
0
2
1
0
0
0
0
1
0
1
1
1
0
1
0
0
1
1
1
3
1
0
0
0
0
0
1
1
0
0
2
1
0
0
0
1
1
2
0
1
0
0
1
0
1
0
2
0
0
0
2
1
1
0
0
2
2
0
0
0
0
0
0
0
1
1
1
0
1
1
0
0
0
0
0
0
0
1
1
0
1
2
0
1
2
0
1
2
1
0
1
2
0
0
0
0
1
0
1
1
0
1
2
0
0
0
0
0
0
0
1
1
0
2
0
2
0
5
1
0
1
0
0
0
3
1
0
1
0
0
0
1
0
0
0
1
0
2
0
0
0
0
1
1
0
2
0
1
1
2
0
0
1
3
0
0
0
1
2
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
1
2
0
0
3
2
1
1
1
0
1
0
2
2
0
2
1
0
0
1
0
1
0
2
0
2
0
1
0
3
0
0
1
0
0
0
0
1
1
0
1
2
0
2
0
0
0
2
0
1
0
0
0
0
0
1
1
0
1
1
0
0
2
3
1
0
1
1
2
0
0
0
1
3
0
2
2
1
0
1
0
2
0
0
2
0
1
0
2
1
0
1
2
0
1
0
0
1
0
0
6
0
1
2
0
1
1
0
3
0
0
1
1
1
2
0
0
1
0
2
0
2
0
0
0
0
1
2
1
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
2
0
0
0
2
1
0
2
1
2
0
1
2
0
2
0
1
2
1
1
0
2
0
3
1
2
0
0
0
1
0
0
0
1
1
1
0
1
0
0
0
2
0
0
1
2
1
2
0
0
0
2
1
2
2
2
1
1
0
2
0
0
2
0
1
1
1
0
0
0
2
0
0
0
0
2
2
2
3
0
0
0
0
2
2
0
0
0
0
0
2
0
1
0
1
1
1
0
0
0
0
1
0
2
1
0
1
1
1
1
1
0
2
1
1
2
1
0
0
2
0
0
0
2
0
0
0
1
2
3
1
1
2
0
0
2
0
0
0
0
1
2
0
0
0
2
0
1
0
0
1
0
1
1
0
0
1
0
0
1
0
1
0
0
3
3
2
0
0
0
0
1
0
2
0
0
2
1
0
0
0
0
2
1
0
1
0
1
0
0
0
2
1
1
1
0
3
1
1
2
2
0
0
1
1
2
4
1
1
1
0
2
2
2
2
0
2
0
1
0
0
0
2
1
1
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
1
1
0
2
1
0
1
0
0
2
0
0
1
1
2
0
0
0
2
1
0
1
1
0
1
0
1
1
0
1
2
1
1
0
0
1
2
1
0
2
0
1
1
0
0
1
3
2
0
0
1
0
0
0
0
0
1
2
0
2
0
2
0
0
0
0
0
0
0
2
2
1
1
0
2
2
1
0
2
0
0
0
1
0
0
0
0
1
0
1
1
2
0
0
1
1
2
1
1
1
0
2
0
1
0
0
2
0
2
1
1
0
1
0
2
2
1
2
0
1
0
0
0
0
0
1
0
1
1
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
1
2
2
0
2
1
2
0
0
0
0
2
0
2
2
1
1
0
0
2
1
0
0
1
0
2
0
1
0
1
0
0
1
0
2
2
1
1
0
1
0
1
1
0
0
0
0
0
0
2
0
0
0
0
1
2
0
1
2
2
0
2
1
0
0
2
0
1
0
1
2
0
0
0
1
0
1
0
1
0
2
0
2
0
1
0
2
0
2
0
0
0
2
1
0
0
1
1
2
0
3
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
1
0
0
1
0
1
0
0
2
1
1
1
2
1
1
0
0
2
0
0
1
0
2
0
1
0
2
1
0
0
0
0
2
0
2
1
1
1
0
0
0
1
0
1
0
0
0
1
0
0
1
1
0
0
0
1
1
4
0
2
0
2
0
2
1
1
0
2
0
0
1
1
2
0
1
1
2
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
2
2
0
2
0
0
1
0
2
2
2
0
0
2
1
0
0
0
2
0
3
1
0
0
0
1
0
2
2
0
0
0
1
1
1
2
0
0
0
0
0
0
1
0
2
2
0
0
0
0
1
1
0
0
0
1
0
2
1
0
0
0
0
0
1
0
1
2
0
0
0
1
0
0
1
0
1
2
2
0
1
0
0
1
2
0
1
0
1
1
2
1
1
1
0
0
1
2
1
0
1
1
0
0
0
0
4
0
2
1
1
2
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
1
0
1
1
0
0
1
2
0
0
0
1
1
0
2
0
0
0
2
1
0
2
0
1
1
0
2
1
1
0
0
2
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
1
1
2
1
0
0
2
0
1
2
2
1
0
1
2
2
2
2
0
0
0
2
1
1
2
0
2
0
0
1
2
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
2
2
2
1
0
1
2
0
0
0
0
1
1
0
2
1
0
0
0
0
0
1
1
1
2
1
1
0
0
0
1
0
1
0
1
2
0
1
0
0
1
0
2
0
2
0
0
1
0
1
2
1
1
0
0
1
0
1
0
1
0
0
1
1
0
1
1
0
0
2
1
1
0
1
0
2
1
2
0
0
0
0
1
0
0
2
0
1
2
2
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
2
2
1
1
1
1
0
2
1
1
0
1
1
0
1
1
2
1
1
1
0
0
0
0
2
0
0
2
0
2
0
0
2
3
2
1
0
0
2
1
0
0
2
0
0
0
1
1
0
0
0
0
0
2
1
1
1
0
1
1
1
0
0
0
0
0
2
2
0
1
0
0
2
1
3
0
1
0
0
0
0
2
0
1
3
0
3
0
0
0
0
1
0
1
0
0
1
1
12
2
1
1
2
0
1
0
2
0
1
2
0
0
0
2
1
0
2
0
0
0
0
0
1
1
2
0
2
2
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
2
1
1
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
1
0
1
0
1
2
0
0
2
2
1
0
2
0
0
1
1
1
0
0
0
2
2
0
0
0
2
2
2
0
0
0
1
0
2
1
0
8
0
0
1
1
0
0
2
1
0
1
0
0
0
0
2
0
2
0
2
2
1
0
1
1
0
0
0
1
2
2
2
0
0
0
0
0
0
1
0
2
0
0
0
1
0
1
0
2
0
0
1
0
1
1
0
2
1
0
0
1
0
0
0
2
2
2
0
0
0
0
2
0
1
0
2
0
0
2
0
2
0
2
4
0
1
1
0
0
0
1
1
0
1
2
0
2
1
0
1
1
2
0
2
2
2
1
0
0
1
0
1
0
0
2
2
2
0
0
0
0
1
2
1
0
2
0
0
0
0
1
0
0
1
0
0
1
1
0
1
1
0
0
2
1
1
2
2
2
2
1
0
0
1
0
1
2
0
0
1
0
1
1
1
0
0
2
1
1
1
0
0
1
1
0
1
1
0
0
2
0
0
0
0
2
1
1
0
0
0
1
0
0
0
1
2
0
1
1
2
3
0
3
2
0
1
3
1
1
0
1
2
2
0
0
0
0
0
0
3
0
1
2
0
0
2
1
0
0
1
1
0
1
0
2
1
0
0
0
1
0
1
1
1
0
1
0
1
2
0
0
0
1
1
0
1
0
0
0
0
2
0
1
1
1
0
2
0
0
0
2
0
1
0
0
1
2
0
0
0
2
1
2
0
0
2
0
0
1
1
0
2
1
0
0
0
1
0
1
2
1
1
0
0
2
2
0
0
1
2
2
0
0
0
2
0
0
0
0
1
2
0
1
3
0
2
0
0
0
2
0
1
0
0
1
0
2
2
0
2
2
0
1
0
0
1
1
0
0
1
1
0
2
3
1
0
0
1
1
0
0
0
0
2
0
0
0
0
2
0
1
0
2
0
2
0
1
0
0
0
2
0
0
2
0
2
3
0
1
0
0
0
0
0
0
1
2
0
1
0
2
0
0
0
2
0
0
0
1
2
0
0
0
1
1
1
0
2
1
0
0
0
1
2
0
0
0
1
0
1
0
2
1
2
2
0
2
0
0
1
2
2
0
1
0
2
1
1
0
0
0
0
0
2
0
1
0
1
1
0
1
2
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
2
1
1
1
0
1
2
0
1
0
2
0
1
0
0
2
0
1
2
0
0
1
2
2
0
1
0
2
2
0
1
0
1
0
0
1
0
0
1
0
0
0
0
2
0
0
0
3
1
1
0
0
2
2
1
0
0
0
0
0
2
0
0
1
1
1
0
1
0
1
2
0
1
2
2
0
0
0
1
0
2
0
2
0
2
1
0
0
0
1
0
0
1
2
3
2
0
1
0
0
1
0
1
0
2
0
0
0
1
0
0
1
0
2
0
1
1
2
0
2
0
0
2
0
2
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
2
0
2
1
1
2
0
0
0
2
0
2
1
0
0
2
0
0
2
0
0
0
0
2
0
1
1
1
0
1
0
1
0
0
2
0
0
1
0
3
0
1
0
3
0
0
0
0
1
1
1
1
1
2
0
2
0
0
1
1
0
0
0
2
0
1
0
0
0
0
0
0
2
0
2
2
2
1
1
0
2
1
0
0
0
2
1
0
0
0
2
0
0
1
2
2
2
2
1
0
2
1
3
0
2
1
0
0
1
2
0
2
1
1
2
2
2
0
2
0
0
1
2
0
1
4
2
2
0
0
0
0
1
0
2
0
0
0
0
0
1
1
2
0
0
3
1
0
0
0
0
0
1
1
0
2
0
0
2
2
0
1
0
1
0
0
0
0
2
0
0
2
0
1
0
1
0
0
1
2
0
0
2
1
1
0
2
1
1
2
2
0
2
1
2
1
0
0
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
1
0
0
0
0
1
2
0
1
1
0
0
0
1
0
1
0
0
2
0
0
0
1
0
0
0
1
1
2
1
2
1
0
0
2
0
0
1
1
1
2
0
0
2
0
0
0
2
0
0
2
0
1
0
1
1
0
0
0
1
1
1
0
0
2
0
1
2
0
2
0
1
1
1
1
0
0
1
0
2
0
2
0
1
1
0
1
0
2
1
2
0
0
1
1
1
0
0
0
2
0
0
0
0
1
1
0
1
2
0
1
0
1
0
2
0
0
0
0
0
2
2
0
2
0
2
2
3
0
0
1
2
0
0
0
0
0
1
0
2
0
1
0
0
0
2
0
0
0
2
0
0
1
1
0
3
0
2
1
1
0
1
0
0
1
0
0
2
0
0
1
0
2
0
0
0
0
1
1
0
2
1
1
1
0
0
2
0
0
0
1
1
0
2
1
0
1
1
4
0
1
0
0
1
0
1
1
0
0
1
0
0
0
1
1
0
2
1
0
2
0
1
0
1
1
0
0
0
0
1
2
1
1
0
1
0
0
0
1
1
1
1
0
0
0
4
0
0
0
0
2
1
0
2
1
0
0
0
0
0
2
2
1
0
0
0
0
1
2
0
0
1
1
0
2
0
2
0
1
2
0
2
1
0
2
2
1
2
0
1
1
0
0
1
0
1
0
1
2
0
0
2
2
2
0
1
0
0
1
1
0
0
0
1
2
0
2
0
1
2
0
1
0
1
0
1
0
1
0
2
1
1
1
1
2
1
1
2
1
0
1
1
0
1
1
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
1
0
0
3
0
0
0
3
2
1
2
0
0
1
2
0
1
0
1
3
1
0
0
1
0
0
1
0
2
0
2
2
0
2
0
0
0
0
1
0
2
1
2
2
1
0
0
0
1
2
0
0
2
0
2
0
1
0
2
0
2
0
0
0
0
0
3
0
1
0
1
2
0
0
1
0
1
0
1
1
1
0
1
0
2
0
0
0
0
2
0
0
0
1
2
0
1
1
1
2
0
0
0
2
1
0
0
1
1
1
0
0
0
2
0
0
2
0
0
0
0
3
0
2
2
0
0
0
0
0
2
1
2
1
2
0
0
0
0
0
2
0
0
3
1
1
2
1
1
0
1
0
1
0
0
0
1
2
2
0
2
2
0
0
2
0
1
0
0
2
0
0
4
0
1
2
0
2
0
0
0
0
0
1
0
0
0
2
1
0
1
1
1
1
1
1
0
2
1
0
1
2
1
2
2
0
0
0
1
3
0
0
0
2
2
0
1
2
0
0
0
0
0
0
4
1
0
1
1
0
2
0
2
2
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
1
0
0
0
2
2
0
0
0
0
2
0
1
0
0
1
2
0
1
0
0
0
3
2
0
0
0
1
0
1
2
0
1
2
0
0
0
1
1
2
0
0
1
0
1
0
0
0
0
2
0
0
2
1
0
1
0
0
1
0
1
0
0
0
1
1
1
0
0
2
0
2
1
0
0
0
3
0
2
3
0
0
2
0
1
2
0
0
1
1
2
0
2
0
1
2
0
0
0
1
1
1
0
0
0
2
0
3
0
1
1
0
1
1
0
0
0
0
0
0
0
2
1
0
0
1
1
1
1
0
1
2
2
0
2
1
1
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
2
2
0
1
0
1
0
0
1
0
1
0
2
1
0
0
0
0
2
2
0
0
2
1
1
2
0
1
2
0
0
0
1
0
2
1
2
0
0
0
0
1
1
0
2
2
0
2
2
1
0
0
2
2
1
0
0
0
1
1
2
2
0
2
0
3
1
0
1
1
1
3
0
2
0
0
2
0
1
1
0
1
0
0
1
0
0
0
2
1
1
0
0
0
0
1
0
0
0
1
0
1
2
1
2
0
0
0
2
0
0
2
1
0
0
0
0
1
1
2
1
1
0
1
0
0
2
0
0
2
0
2
0
2
1
2
0
3
5
1
0
0
0
0
3
0
1
2
0
0
0
0
0
1
0
0
1
2
0
1
0
0
0
0
0
1
2
0
0
0
2
0
1
0
2
0
0
2
0
0
1
0
0
0
1
0
1
1
0
0
0
2
1
0
1
0
0
0
1
1
2
1
0
2
0
1
2
2
1
0
0
1
0
2
3
1
1
1
0
2
1
0
0
1
0
1
0
2
0
2
0
2
2
0
1
0
1
0
0
1
0
0
2
0
0
0
0
1
1
1
0
4
0
2
3
0
0
0
1
2
1
0
1
0
1
0
1
0
2
1
2
1
0
2
0
1
0
1
0
1
0
0
0
0
0
1
0
1
2
2
2
1
1
0
0
1
0
2
0
0
1
1
0
0
0
0
0
0
0
2
0
1
1
0
2
0
1
0
0
2
2
1
2
2
0
1
0
1
0
0
0
1
0
2
0
3
2
2
2
0
0
0
2
1
0
1
2
2
1
2
0
0
0
0
0
2
2
0
1
0
1
0
0
2
1
0
0
1
1
0
1
0
0
0
1
2
0
0
3
0
2
1
0
0
1
2
1
1
0
0
0
0
0
0
3
1
1
1
0
1
1
2
1
1
1
0
0
0
1
0
0
0
2
0
2
2
0
0
1
1
1
1
2
0
1
1
2
1
0
1
2
1
0
1
1
1
0
2
0
0
0
1
1
0
0
0
2
1
0
0
1
1
1
1
0
2
0
1
0
1
2
0
1
2
0
1
0
0
0
0
1
2
0
0
2
0
0
1
1
0
1
1
0
1
0
0
2
2
0
2
0
2
0
2
0
0
0
1
1
0
0
0
1
0
2
0
2
0
1
0
2
2
1
0
2
1
2
2
1
0
0
0
2
0
0
0
0
1
1
2
0
1
0
2
0
2
0
0
0
0
0
2
0
0
0
1
0
1
0
0
1
2
1
0
2
1
1
1
1
1
1
2
1
1
2
0
0
1
0
0
0
0
2
2
1
0
0
0
0
2
1
1
1
0
0
0
0
0
0
0
0
2
1
1
1
0
1
0
1
1
1
1
0
0
1
0
1
0
3
1
0
0
2
0
0
0
0
0
3
0
1
0
0
1
0
0
1
1
2
0
1
0
2
1
0
1
0
0
0
0
2
2
0
0
1
2
0
0
2
0
1
0
1
0
1
2
0
2
1
1
0
0
0
3
0
1
0
0
2
1
0
1
0
2
0
0
0
1
1
0
1
0
0
0
2
0
0
1
2
2
0
2
0
0
0
3
2
0
0
2
1
0
2
2
0
1
2
1
1
2
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
1
3
2
0
0
0
2
1
0
0
1
1
0
1
1
0
0
2
2
2
2
0
0
0
3
2
0
0
2
0
0
0
0
1
1
0
1
1
0
2
2
2
1
0
0
2
0
1
0
0
2
1
0
0
0
0
2
0
2
1
1
1
2
0
1
0
1
0
1
0
0
1
0
1
1
2
0
0
2
1
2
0
1
0
1
1
2
2
0
0
1
1
2
0
0
2
2
2
1
0
0
0
0
2
7
0
0
2
0
0
0
1
0
2
0
0
0
2
0
0
1
0
2
0
0
0
1
1
0
3
0
1
0
0
1
3
1
1
2
3
1
2
1
1
0
1
0
1
0
0
1
0
2
2
2
0
0
1
1
0
0
2
0
2
2
2
0
0
0
1
1
1
1
0
1
2
0
2
0
1
0
0
0
0
2
2
2
2
0
0
0
2
0
2
2
0
1
0
0
0
1
0
2
2
0
2
0
1
1
0
0
0
0
1
1
2
1
0
0
0
1
0
0
0
0
2
0
0
2
2
0
2
0
0
0
0
1
1
2
1
2
0
0
0
1
2
2
2
0
2
0
1
0
1
0
0
0
0
1
0
0
0
3
0
0
2
2
1
1
0
2
1
1
0
0
1
0
0
1
1
1
1
0
0
1
0
0
0
0
0
0
0
0
2
0
1
2
1
0
1
0
2
0
1
0
1
2
0
1
3
2
0
1
1
1
2
1
1
1
0
0
2
0
2
1
1
0
0
0
1
0
1
0
1
0
1
1
0
0
0
1
0
3
1
1
1
0
2
1
0
1
0
1
0
2
1
0
1
0
0
0
1
0
0
0
2
1
0
0
2
0
2
1
1
0
1
2
2
0
0
2
1
2
0
0
0
0
0
1
0
0
1
0
1
0
1
0
1
1
1
0
2
1
1
0
1
0
0
0
1
2
0
0
3
2
1
0
1
0
2
0
1
0
0
1
1
1
2
0
2
1
1
1
1
2
2
0
0
0
1
0
0
1
0
1
1
1
0
2
1
0
0
0
1
0
0
1
2
0
2
0
2
2
2
0
0
0
0
2
1
0
0
1
0
2
0
2
1
1
0
1
1
2
0
0
1
0
1
0
0
2
1
0
0
0
2
0
0
0
1
0
0
0
2
2
0
1
1
0
1
1
0
0
1
0
2
0
0
1
3
0
2
0
0
0
1
1
2
0
2
0
0
0
1
0
2
3
0
0
0
0
0
0
2
1
2
1
1
1
0
0
2
0
0
2
1
8
0
3
0
0
0
0
1
0
1
0
1
2
0
2
0
2
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
1
1
0
0
0
2
0
2
0
0
1
2
0
0
0
0
0
5
0
2
2
2
0
2
0
0
2
0
1
2
1
1
0
2
0
0
2
0
0
0
0
0
1
1
0
2
0
1
1
2
0
0
2
2
0
0
0
0
2
2
1
2
2
1
2
0
2
0
0
0
2
0
2
1
0
0
2
1
1
0
0
0
1
0
0
2
1
0
0
2
1
0
1
0
0
0
2
0
1
0
0
2
1
0
0
0
1
0
1
1
0
0
2
1
0
0
1
0
1
0
5
0
0
0
0
0
2
0
1
0
0
0
0
1
0
1
2
0
1
0
2
0
0
0
0
2
2
3
0
3
1
0
0
0
1
0
1
1
2
0
2
1
0
2
0
1
1
2
0
1
1
0
1
2
0
0
0
1
0
1
0
0
1
0
1
2
0
0
0
1
1
2
1
0
0
0
0
1
1
2
0
0
1
1
1
0
0
0
2
2
1
0
0
1
0
0
0
0
2
0
1
0
0
1
2
0
0
1
1
1
0
1
1
1
2
2
2
0
2
2
3
0
2
0
0
0
0
0
0
1
0
0
2
2
0
0
0
1
0
3
1
0
2
0
1
0
2
0
0
0
0
1
0
0
3
0
0
0
1
0
0
1
0
0
1
0
2
0
0
0
0
1
1
2
2
0
1
0
0
3
0
1
1
2
0
0
2
1
2
1
1
1
0
0
0
0
0
1
0
0
1
3
1
0
3
2
2
0
0
0
0
0
0
0
0
2
0
0
1
0
2
2
2
0
0
0
1
1
1
1
2
1
1
3
0
1
0
1
2
0
1
0
1
1
0
1
2
0
1
0
1
0
1
0
0
1
1
1
1
0
1
1
2
0
0
2
1
1
0
2
1
0
0
1
2
0
1
1
1
2
0
0
0
0
0
0
0
0
0
1
2
2
2
0
2
3
2
0
2
0
1
0
1
1
2
0
1
0
0
2
2
2
0
0
0
1
1
0
1
0
1
2
1
1
0
0
0
1
0
0
1
0
2
0
0
0
2
3
0
0
2
2
2
2
1
0
0
2
1
2
1
1
1
2
1
1
0
1
1
0
0
1
0
2
2
2
2
0
0
1
0
2
2
2
1
0
1
0
0
0
2
1
1
0
1
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
3
0
0
0
0
0
1
0
0
0
3
0
2
1
2
0
1
2
0
0
1
2
1
1
0
2
2
0
1
1
1
2
2
0
1
0
1
2
1
1
2
2
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
2
0
3
1
2
0
2
0
1
0
0
2
0
0
3
0
0
1
2
1
2
1
0
0
1
0
2
0
0
0
1
0
2
1
0
1
1
3
0
0
2
2
4
0
1
2
0
1
0
0
2
0
1
2
1
0
0
1
1
0
0
3
0
1
0
2
0
1
0
0
2
0
0
0
0
0
0
0
2
1
1
2
1
0
1
1
0
2
1
0
0
1
0
0
0
0
1
0
0
2
1
1
2
1
1
0
0
0
2
0
0
0
0
0
1
1
0
1
1
2
2
0
0
1
1
0
2
0
0
2
0
0
1
2
0
0
1
0
1
0
0
1
1
0
2
1
0
2
0
1
0
0
1
0
1
0
0
0
2
0
0
2
1
0
1
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
1
2
2
1
1
0
0
2
2
0
0
0
1
0
2
2
0
0
2
2
1
0
2
1
1
0
0
0
2
2
2
0
0
2
0
2
1
0
1
1
1
2
1
0
0
2
2
0
0
2
0
2
1
2
1
0
3
0
2
2
12
0
2
0
0
1
0
0
0
1
0
4
1
0
0
2
1
0
1
0
2
0
1
0
0
0
2
0
0
0
0
1
2
1
2
0
0
2
1
1
0
2
0
0
1
0
0
0
2
1
2
1
0
0
0
4
2
0
0
0
1
1
1
1
2
0
1
0
2
0
3
1
0
0
1
0
0
0
1
2
3
0
1
2
4
1
1
0
2
1
0
2
0
1
2
0
0
0
0
0
1
1
0
0
3
1
2
0
0
0
2
0
0
1
0
2
0
4
1
2
1
2
1
2
0
1
0
1
1
0
0
2
1
0
0
0
1
1
2
1
1
0
0
2
0
2
2
1
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
2
2
0
2
0
1
1
0
2
1
0
0
1
1
0
1
0
1
0
0
2
0
0
1
1
0
0
1
1
2
2
1
0
0
1
0
0
1
0
0
0
1
0
0
2
0
2
1
1
0
0
0
1
1
2
1
2
0
0
0
1
2
1
1
2
2
0
0
2
2
1
0
2
1
0
2
2
0
0
1
1
0
1
0
2
0
2
1
0
1
1
0
2
1
0
1
0
2
4
0
0
0
0
0
2
0
2
0
0
1
1
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
2
0
1
0
2
0
0
0
2
1
1
1
0
0
1
0
0
0
0
0
4
1
1
2
1
0
0
0
2
0
0
4
1
1
0
2
0
0
0
0
0
0
1
1
2
2
0
0
0
0
0
0
1
0
2
0
0
1
0
2
0
1
3
0
0
1
0
1
0
1
0
0
0
0
0
1
2
2
1
0
2
0
2
0
0
2
1
2
2
0
0
0
1
2
2
0
0
2
0
1
1
0
0
0
0
1
2
0
1
0
1
1
1
2
1
0
2
0
0
1
1
0
0
0
0
0
1
0
1
2
2
2
0
2
1
0
1
0
0
0
2
2
2
0
2
1
1
2
0
0
0
2
1
2
0
1
0
0
0
1
1
0
0
1
0
0
1
3
1
2
2
0
3
2
1
0
1
1
1
1
0
0
0
1
0
1
2
1
0
0
2
1
0
0
0
1
0
0
2
0
2
0
0
1
1
1
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
1
2
1
0
2
0
1
0
1
2
2
1
1
2
0
0
2
0
1
1
1
0
2
2
2
0
0
2
2
2
2
0
0
0
0
0
0
2
2
0
2
2
0
1
0
1
0
2
1
0
0
0
1
2
0
1
1
0
0
1
0
0
0
4
0
0
1
2
4
0
2
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
2
0
1
1
0
2
0
2
1
0
0
0
0
0
1
0
0
0
0
0
2
1
1
2
2
0
0
1
2
0
0
0
1
3
1
2
1
0
2
0
0
1
0
0
1
0
0
1
0
2
1
2
2
0
3
2
0
3
0
2
0
0
0
1
1
0
2
0
0
0
2
0
0
2
1
0
2
1
0
1
1
2
0
0
1
0
2
1
0
0
1
0
1
0
0
0
0
0
1
1
1
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
2
0
2
0
0
0
1
0
0
2
0
0
1
2
1
2
1
1
0
2
0
1
1
0
1
0
0
1
0
0
1
0
1
1
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
1
0
1
2
1
0
0
0
0
0
3
1
2
0
1
2
0
2
0
0
0
1
0
2
1
0
2
1
0
2
1
1
1
0
1
2
0
0
0
0
0
1
0
0
0
0
1
0
7
1
0
0
1
0
0
0
1
1
0
0
1
0
2
1
2
0
0
0
1
1
0
0
0
0
0
0
2
2
0
0
3
2
2
1
0
0
2
1
0
1
0
1
3
0
2
0
0
0
0
0
0
1
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
2
2
0
1
2
2
0
0
1
0
1
1
2
2
0
0
0
0
1
0
1
0
2
0
0
0
0
2
1
0
0
0
0
1
2
0
0
0
0
1
2
0
0
2
1
2
0
1
0
2
0
2
1
0
1
1
2
0
1
1
1
1
2
0
1
0
0
2
1
0
0
0
1
1
0
1
0
0
2
0
1
0
2
0
1
0
1
0
0
1
0
1
0
0
1
0
2
0
0
1
0
0
0
0
2
0
1
0
2
2
1
0
1
1
2
0
0
0
0
1
2
1
0
1
0
1
0
1
1
0
0
1
2
1
2
2
1
2
2
1
1
1
0
0
1
1
0
1
2
0
0
2
0
0
1
0
0
0
2
1
0
2
1
0
1
0
1
1
2
2
1
0
3
0
2
0
1
1
1
0
0
2
2
0
0
2
1
0
2
2
2
1
0
2
1
2
1
0
2
0
1
1
1
1
0
0
2
1
0
0
2
0
0
2
0
1
0
2
0
0
0
0
2
0
0
0
0
2
0
1
1
0
0
0
0
0
2
0
0
2
0
2
1
1
1
0
0
0
2
1
1
1
0
0
0
2
0
0
2
1
1
5
0
2
0
1
0
0
1
2
0
2
0
1
0
1
0
0
1
0
1
2
1
1
1
0
2
3
2
0
0
0
0
1
2
0
1
1
1
0
1
1
1
2
2
1
2
1
0
1
1
0
0
4
1
0
0
0
0
1
0
1
1
0
0
1
0
2
0
0
1
0
2
0
3
0
1
0
0
0
1
1
0
2
1
2
1
0
0
1
1
1
0
0
0
2
1
2
2
0
0
0
1
0
1
1
0
0
1
0
2
2
2
0
2
0
0
2
0
0
0
0
0
0
1
1
1
0
2
0
0
2
3
2
2
0
0
0
0
1
1
0
1
1
0
0
1
0
0
2
0
2
3
0
0
2
0
0
2
0
0
0
1
0
2
0
1
3
0
0
1
0
0
1
1
0
1
1
1
0
1
1
0
0
0
2
1
1
1
1
0
0
0
0
0
0
2
1
1
0
1
3
2
0
1
2
1
1
3
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
1
2
1
0
2
2
2
0
2
1
1
0
2
0
1
3
0
1
0
0
2
1
0
1
0
0
0
0
0
1
1
2
0
0
0
0
2
0
0
1
0
0
1
1
2
2
0
1
2
0
2
0
0
2
2
0
1
0
0
0
0
1
1
1
0
2
1
1
1
2
1
1
2
0
0
2
0
0
7
1
2
2
0
2
0
1
0
0
1
1
0
2
1
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
1
1
0
0
0
2
0
0
1
2
1
0
3
5
0
2
0
0
0
1
0
0
1
1
0
0
1
2
0
1
2
0
0
0
0
1
2
0
1
3
1
0
1
2
0
1
0
1
0
0
0
0
2
1
2
0
0
1
0
0
1
2
0
3
2
0
0
2
0
0
2
1
0
0
0
0
0
1
0
1
0
2
0
1
1
1
1
1
1
0
0
1
0
0
2
0
0
1
2
1
0
1
1
2
0
0
0
0
1
0
0
2
1
0
0
2
1
0
0
0
1
0
1
0
0
1
1
1
2
1
0
2
1
2
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
2
0
1
0
2
0
2
0
0
2
1
0
1
0
2
2
1
1
1
2
0
2
0
0
0
2
0
2
2
2
3
0
1
0
1
0
0
2
0
0
1
0
0
0
2
0
1
0
2
0
1
1
9
1
0
0
0
2
0
0
1
2
1
0
0
5
0
0
0
3
0
0
0
0
1
0
3
0
0
0
1
1
0
0
3
0
1
0
1
0
2
2
0
3
0
0
0
0
0
0
1
0
0
2
0
2
1
0
0
1
1
1
2
2
1
0
2
2
0
1
2
2
0
0
0
1
0
3
2
0
1
0
2
0
2
0
0
1
0
1
2
0
1
0
0
0
1
0
1
2
0
1
0
0
1
1
0
2
0
0
0
2
2
0
2
0
0
0
0
2
0
0
2
0
0
1
2
1
0
1
1
0
1
0
0
2
0
3
0
1
2
1
0
0
0
0
2
0
0
1
1
1
0
0
1
0
2
1
0
0
1
2
1
1
0
2
0
1
0
2
1
0
0
1
1
0
1
0
0
2
0
3
0
4
0
1
0
0
0
0
0
1
0
2
0
2
0
3
1
1
1
2
2
3
0
0
2
0
0
0
1
2
2
2
1
0
0
0
0
0
2
0
2
2
0
0
3
0
0
2
0
2
0
1
0
0
3
2
2
1
1
0
2
0
1
0
0
2
0
2
0
0
0
1
1
2
2
1
0
0
0
2
2
0
0
1
2
0
0
1
0
0
2
2
0
1
0
1
1
0
1
0
0
0
1
0
1
0
1
1
2
0
0
2
1
0
1
1
2
1
1
1
1
1
0
2
0
0
0
1
0
0
1
2
1
0
0
0
2
2
2
1
1
0
2
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
2
0
1
1
1
1
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
1
0
2
0
2
0
0
1
0
1
1
0
0
0
1
1
0
1
0
2
1
2
2
2
3
0
0
0
0
0
0
0
0
0
3
0
2
1
0
4
0
0
0
0
2
3
1
2
1
1
0
0
2
0
1
0
1
0
1
0
2
1
0
1
2
0
1
4
0
2
1
0
0
0
2
0
0
0
1
2
3
1
0
2
1
1
1
0
2
1
1
0
0
0
0
1
0
1
0
1
1
0
2
0
1
0
0
2
2
2
1
1
1
1
1
0
0
0
0
0
0
1
2
0
0
2
0
1
1
2
2
0
0
0
0
1
0
0
1
2
0
7
1
3
1
0
3
0
3
2
0
0
0
0
0
2
1
2
1
0
0
0
0
1
1
0
1
2
2
1
0
4
3
1
0
0
2
0
0
2
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
1
1
0
1
2
0
1
0
1
1
1
0
0
1
2
0
1
1
0
2
0
0
2
2
0
0
1
1
1
2
1
1
1
0
1
2
2
2
1
1
0
0
1
2
0
1
1
2
2
0
0
2
5
0
0
0
0
2
2
0
1
2
2
0
1
0
1
1
1
2
0
0
1
0
2
0
0
0
0
0
0
1
0
1
2
1
0
2
0
1
0
0
0
2
0
0
1
2
1
0
1
1
0
0
1
2
0
0
0
0
1
0
1
2
0
1
1
1
1
0
1
0
2
2
0
2
0
1
1
2
1
2
2
0
0
0
2
2
1
2
2
0
0
2
0
1
1
1
1
0
1
2
0
2
0
0
2
2
1
2
2
2
0
2
1
1
2
0
0
2
0
2
1
0
0
0
2
0
0
2
1
1
3
0
0
2
2
1
1
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
3
1
1
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
1
0
0
2
2
2
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
2
0
0
1
0
0
1
0
0
0
0
1
1
1
0
0
2
3
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
2
2
1
0
0
1
0
1
1
1
1
2
2
0
1
2
0
1
1
2
0
2
1
0
2
1
2
6
0
0
0
0
0
0
1
1
0
3
2
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
2
2
3
1
1
1
0
0
3
0
0
2
0
1
1
1
0
2
0
0
1
0
0
0
2
0
0
0
0
1
0
2
0
0
1
1
2
2
1
0
0
0
2
0
0
2
0
0
1
1
2
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
2
1
1
0
1
0
0
1
0
2
2
2
0
1
0
0
1
1
1
0
1
2
0
1
0
2
1
1
0
1
0
0
1
0
2
0
2
0
1
0
0
0
0
2
0
0
1
1
2
0
0
1
1
0
0
0
2
0
1
1
0
1
1
1
0
2
1
0
0
1
2
1
1
0
0
1
0
1
2
0
2
2
1
0
0
1
2
0
0
2
2
0
0
1
0
1
0
2
0
1
1
2
0
0
1
1
2
1
2
1
1
2
1
1
1
0
0
1
1
0
1
0
1
0
0
0
2
0
1
2
2
0
0
0
1
0
1
1
1
0
2
0
0
0
2
0
0
0
0
2
1
0
1
0
0
0
0
0
0
2
0
0
0
1
1
1
1
0
0
1
1
1
0
2
0
1
2
2
2
1
2
1
2
0
0
0
0
0
2
2
2
1
2
0
3
3
1
0
1
0
0
0
0
0
0
1
2
1
1
1
0
0
1
0
0
0
1
0
1
0
0
2
0
0
1
0
1
0
0
0
2
2
2
0
0
0
1
0
0
2
1
0
0
0
1
1
0
0
1
1
0
0
1
2
1
0
0
2
2
0
1
0
2
0
0
0
1
2
2
0
2
1
2
2
1
1
0
0
0
2
0
2
0
1
1
0
0
0
2
2
0
0
0
0
2
2
0
0
2
1
1
0
1
0
1
0
0
0
0
0
1
2
0
0
2
0
0
2
1
1
1
1
2
0
0
2
1
0
0
0
6
1
2
1
0
2
1
2
2
0
0
0
0
0
1
0
0
1
0
1
0
1
2
1
1
0
0
0
0
1
0
0
1
0
0
2
2
0
0
1
1
0
0
2
1
0
0
0
2
2
4
2
1
0
1
1
1
0
0
2
0
0
0
2
0
0
2
0
0
1
0
0
0
2
2
1
0
0
2
0
0
1
0
2
0
0
0
0
0
2
0
0
0
2
0
3
1
2
2
1
2
0
0
2
2
0
0
0
0
2
0
0
2
1
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
2
2
0
0
1
0
2
1
0
0
2
1
0
0
0
2
2
1
0
2
0
0
0
0
2
3
2
1
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
1
1
1
1
0
2
0
0
2
1
1
1
1
1
0
0
0
1
2
1
2
1
0
0
0
0
0
0
0
2
1
1
0
1
0
0
2
0
1
0
1
1
0
2
0
1
0
3
0
2
2
1
1
1
2
0
1
0
1
0
0
0
0
0
2
2
0
1
0
0
0
2
0
2
2
0
0
2
0
0
2
0
0
0
0
0
1
1
2
1
1
0
1
1
0
2
0
2
2
1
0
2
3
2
0
0
0
1
1
2
1
1
1
1
1
0
0
2
1
0
1
1
3
2
0
0
0
2
0
1
0
0
0
2
0
0
1
0
1
0
0
2
0
0
1
0
1
0
1
0
0
1
1
2
0
1
0
0
0
0
1
1
0
1
1
2
2
1
0
1
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
1
0
2
1
1
0
2
2
0
2
0
0
2
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
4
0
0
1
0
1
1
0
1
2
0
2
0
1
2
1
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
1
0
1
2
0
4
0
0
1
0
0
2
2
2
0
2
1
0
0
0
0
3
0
2
1
0
0
0
0
2
0
1
2
0
1
0
1
1
0
0
1
2
1
0
0
1
2
1
0
0
0
1
0
0
1
0
0
1
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
3
0
2
2
0
0
2
1
0
1
0
0
0
0
2
2
1
0
2
0
0
1
2
0
0
2
0
1
1
0
0
1
1
0
0
1
0
1
0
2
2
0
0
0
0
1
1
2
1
0
0
1
0
1
0
1
0
0
0
2
0
0
0
1
2
0
2
0
1
0
1
0
2
0
2
0
1
1
2
2
0
0
0
2
0
0
0
2
2
0
2
2
1
2
1
0
2
1
1
0
0
2
0
0
2
0
0
1
0
0
0
1
1
0
0
2
0
1
0
1
0
1
1
2
2
0
1
0
0
0
0
0
1
2
0
1
0
3
2
2
0
2
1
1
0
2
1
0
1
1
1
0
1
1
2
1
1
0
0
0
1
2
1
0
2
0
0
2
0
1
0
0
2
1
0
0
2
0
0
1
0
0
1
0
2
0
2
1
1
1
1
0
2
0
0
0
2
1
0
0
0
0
1
0
2
0
1
2
1
1
0
1
1
2
0
0
0
0
1
1
2
0
2
0
1
0
0
1
0
0
0
0
0
1
1
0
1
0
2
2
1
2
0
0
2
0
0
0
1
0
0
2
0
1
1
0
0
0
0
0
1
0
0
0
2
1
0
0
0
2
2
2
0
2
0
0
0
2
2
0
1
0
0
0
0
1
0
2
0
0
0
0
0
3
0
2
2
0
0
0
1
2
2
0
0
0
0
1
0
2
0
0
2
0
0
2
0
0
1
0
0
3
0
1
1
1
1
1
0
1
1
2
1
1
2
1
0
1
1
0
2
1
0
2
0
0
1
2
0
2
0
2
2
0
0
0
2
1
0
0
2
1
2
2
0
2
2
0
2
2
1
0
0
2
1
1
2
1
0
0
0
1
2
1
0
2
0
1
2
2
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
2
0
2
0
0
0
0
2
0
1
0
0
2
1
0
1
0
2
1
0
1
0
2
1
1
0
0
1
2
0
0
2
0
0
0
2
0
0
0
1
2
0
0
0
1
0
0
0
0
0
1
0
2
0
2
2
2
0
0
0
1
0
1
0
0
1
0
0
2
2
2
1
2
0
1
0
1
2
0
0
1
1
0
0
2
1
1
0
1
0
1
0
3
0
2
2
0
0
0
2
1
2
0
2
0
1
0
0
1
0
0
0
0
1
3
0
0
0
2
0
0
2
2
0
1
0
1
0
0
2
2
1
2
0
0
2
1
0
1
0
1
1
1
1
3
1
0
0
0
1
0
0
1
2
0
2
1
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
1
0
1
2
0
1
0
0
0
1
0
2
1
2
0
0
2
0
0
2
0
2
0
1
1
2
1
1
0
1
0
3
0
2
1
0
1
1
2
1
1
2
1
0
1
0
0
2
1
2
1
0
2
0
0
0
0
2
0
0
1
0
0
2
0
0
2
2
2
2
2
1
0
2
0
2
1
0
0
0
1
0
2
2
0
1
0
2
0
0
0
0
0
1
1
0
1
0
1
1
0
0
2
3
0
1
2
1
0
0
1
0
0
0
0
0
0
0
2
0
2
1
1
2
2
2
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
1
1
1
2
1
0
0
1
0
1
2
1
2
0
1
4
0
0
0
2
0
1
1
0
2
2
2
0
0
2
0
1
0
0
2
0
0
1
0
0
2
0
1
0
2
0
0
1
0
0
1
1
1
1
0
2
1
1
0
3
1
1
2
0
0
0
0
2
0
0
1
0
0
1
1
0
1
0
1
1
0
2
1
2
1
0
0
2
2
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
1
2
2
1
1
1
0
1
0
1
0
1
0
0
0
0
0
1
1
1
1
1
1
0
0
1
3
1
0
0
2
2
0
2
0
1
0
0
1
1
2
2
0
0
2
2
1
1
0
1
0
2
0
2
1
2
0
1
0
0
1
0
0
2
0
0
1
1
1
0
0
0
0
1
0
0
0
1
2
1
0
0
1
0
0
1
0
2
0
2
1
1
0
1
0
0
0
0
1
3
3
1
0
1
0
0
2
0
0
1
1
0
0
0
0
0
0
2
0
1
1
0
0
2
1
2
0
2
0
0
0
0
0
2
1
2
0
0
2
0
0
0
0
0
1
2
0
1
1
0
2
1
1
0
0
1
2
2
0
0
1
1
0
0
1
0
0
1
0
2
2
2
1
0
0
0
0
2
0
0
2
1
0
0
1
0
1
2
0
0
2
0
0
1
0
1
2
0
0
0
0
1
0
1
0
0
0
3
1
3
2
1
1
2
0
2
0
2
1
1
1
1
0
1
1
2
3
1
3
0
0
1
0
0
0
0
0
0
1
1
2
2
1
0
1
1
2
0
1
1
0
0
2
1
0
0
0
0
0
1
2
0
0
2
0
0
1
0
2
2
1
1
1
0
2
1
1
1
0
2
1
2
1
1
2
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
1
1
1
2
2
1
0
1
0
0
1
2
0
0
2
2
0
1
0
1
1
1
0
1
1
0
0
2
0
0
1
1
1
0
0
0
1
2
2
1
1
0
1
5
2
0
2
1
1
0
0
1
1
1
1
0
3
0
2
0
0
1
2
0
1
2
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
2
0
0
0
2
1
0
1
0
0
2
2
0
1
0
0
0
0
1
0
0
0
2
0
0
1
0
1
2
0
1
0
0
3
0
1
2
1
0
0
1
0
1
0
0
2
0
1
1
1
0
0
2
1
0
1
1
1
1
2
1
2
0
1
1
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
1
0
1
0
2
0
0
1
2
1
2
2
1
0
1
1
1
1
1
0
3
2
1
0
0
1
0
0
0
2
0
7
1
2
2
0
0
1
1
0
1
0
0
2
2
0
0
2
1
2
0
2
2
1
2
0
2
1
1
0
0
2
1
1
2
2
0
0
0
1
1
1
1
0
2
2
0
1
0
2
0
1
1
1
2
0
0
1
1
2
0
0
1
2
0
1
0
2
3
0
0
1
1
0
0
1
0
0
1
0
3
1
2
2
0
1
1
0
0
0
2
0
0
2
0
0
1
0
0
1
1
0
2
1
1
0
0
0
0
0
0
1
2
0
1
1
2
0
0
1
2
2
2
0
0
0
0
0
0
0
1
0
1
0
2
1
1
0
0
2
0
0
2
3
1
3
1
2
0
2
0
2
1
1
1
0
2
0
2
1
0
0
1
0
0
1
0
1
0
0
1
2
0
0
0
0
0
0
2
0
3
0
0
1
1
1
2
2
1
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
2
1
0
0
0
0
2
1
1
2
1
0
1
1
1
2
2
0
2
1
0
0
0
1
0
0
1
2
0
1
1
0
1
0
1
0
1
0
1
0
0
2
1
0
1
0
0
0
1
0
0
0
1
0
1
1
0
1
2
1
1
0
0
0
0
1
0
1
0
0
1
2
2
1
1
1
1
0
1
0
1
1
1
0
0
0
1
0
1
0
0
2
2
1
0
2
1
1
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
1
0
0
2
0
0
1
3
0
0
0
0
0
0
2
2
0
1
0
2
1
0
0
0
1
0
1
1
0
2
2
0
2
2
1
0
0
2
0
2
1
1
0
1
0
1
2
1
0
0
1
0
0
1
1
2
0
2
1
0
0
1
0
0
0
2
0
0
0
1
2
3
2
0
2
2
1
2
2
0
0
1
0
0
1
2
1
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
2
1
2
2
0
1
0
1
0
1
0
0
1
1
0
0
0
0
2
0
2
0
2
0
0
0
0
0
4
1
0
0
0
3
0
0
0
1
0
1
1
0
0
0
1
0
1
0
1
0
1
2
0
0
1
1
2
2
0
1
2
1
2
2
0
0
0
2
0
0
1
2
0
0
1
0
0
2
1
2
0
0
1
3
2
0
0
1
0
2
0
0
0
0
3
2
0
1
0
2
0
0
1
2
0
0
0
0
0
0
0
0
1
0
2
1
0
1
0
0
2
0
0
2
1
1
2
0
0
0
2
0
0
2
0
0
0
0
0
3
3
0
2
1
0
0
2
0
1
0
1
0
1
1
2
1
0
0
0
0
0
0
0
1
1
2
1
1
1
0
3
1
0
1
0
0
0
2
2
1
4
1
1
1
1
0
0
0
0
0
1
0
0
2
0
0
0
3
0
0
1
1
0
0
0
1
1
0
2
1
2
2
2
3
0
0
0
4
0
2
1
1
0
2
1
0
2
1
0
0
1
2
0
2
1
1
0
0
0
0
1
0
0
1
1
0
2
3
0
1
4
1
0
0
2
2
2
0
2
1
0
0
0
0
2
0
0
2
1
0
0
0
0
1
0
0
0
1
0
0
0
2
0
2
0
1
2
0
0
1
0
1
2
1
1
2
0
0
0
1
0
0
0
3
1
2
2
0
0
2
0
3
1
1
2
0
2
1
0
1
0
0
1
0
0
4
0
0
0
0
2
2
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
2
0
0
1
1
0
2
0
0
2
1
0
0
0
0
1
0
1
1
2
1
1
0
0
1
2
0
1
0
2
0
0
0
2
3
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
1
3
2
2
1
0
1
0
1
0
0
0
1
0
2
0
0
0
0
0
1
2
1
1
0
3
0
1
0
0
1
0
2
0
1
0
1
0
1
0
0
0
2
2
2
0
2
2
2
1
0
0
2
2
0
2
0
0
1
0
0
0
2
0
0
1
1
1
0
1
0
0
2
2
0
0
0
1
0
1
2
1
0
0
0
0
1
0
1
3
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
2
2
0
0
3
1
0
2
0
0
0
0
2
2
1
0
0
2
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
3
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
1
0
0
2
0
1
1
0
0
0
1
3
1
0
0
1
2
0
0
2
1
2
2
0
0
0
0
0
0
2
0
0
0
1
1
2
0
1
1
4
1
3
1
1
1
2
2
2
0
3
2
0
0
0
0
1
0
0
0
1
0
2
0
1
0
0
0
0
1
0
1
1
0
1
0
0
0
2
1
1
2
0
0
2
1
0
0
0
0
0
1
1
0
1
0
0
0
2
0
0
1
1
0
2
0
2
1
0
0
0
1
1
0
2
1
0
0
1
0
1
0
2
0
0
1
1
1
2
1
0
1
2
1
1
0
1
2
1
0
1
0
2
2
0
1
0
1
1
1
0
1
1
0
0
0
0
0
0
0
1
0
2
1
0
2
0
0
0
0
0
0
1
1
0
0
2
5
2
1
0
1
1
1
0
0
0
0
1
2
0
4
0
0
0
0
1
0
0
0
0
2
1
1
2
0
1
0
0
2
2
1
0
0
0
2
0
1
1
2
0
1
0
2
0
1
0
2
0
0
1
1
2
0
1
1
0
0
0
0
1
1
1
0
0
0
2
1
1
1
0
0
1
1
0
0
0
0
0
0
1
0
1
2
0
2
0
2
2
0
2
0
0
0
2
0
0
1
1
3
0
0
2
2
0
0
0
2
0
0
0
0
2
0
1
2
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
3
0
2
1
0
2
0
0
2
1
2
2
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
1
0
0
0
1
2
1
2
0
1
0
2
0
1
2
2
0
0
1
1
0
1
1
1
0
0
1
0
2
2
0
0
1
1
0
2
0
2
0
1
2
1
0
1
2
1
1
0
1
0
0
1
2
1
0
0
0
0
1
1
2
0
0
1
0
1
2
0
2
1
0
0
0
0
0
0
0
0
1
3
1
0
2
0
2
0
1
3
0
0
1
0
0
2
2
0
2
1
0
0
3
2
0
1
0
2
0
1
0
2
1
1
2
0
1
1
1
0
0
0
1
0
1
1
1
1
2
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
1
1
1
0
0
1
0
1
1
1
2
1
0
0
2
0
0
0
1
0
1
2
1
1
0
0
0
3
2
0
0
0
1
2
0
1
0
0
1
0
2
0
2
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
1
2
0
1
0
1
1
0
0
2
1
0
0
2
1
0
0
0
0
0
1
2
0
2
2
0
1
0
0
2
0
2
2
2
1
0
2
0
1
0
2
0
1
0
1
8
1
2
0
0
2
0
1
2
0
1
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
1
0
0
1
0
1
1
0
2
0
0
2
2
0
2
0
0
0
2
0
0
2
0
0
1
0
0
2
0
0
1
0
0
1
0
2
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
1
0
0
2
1
1
0
0
0
0
0
0
0
1
0
1
1
1
1
1
0
0
0
1
0
0
1
0
1
1
1
1
0
1
0
1
0
2
1
0
0
1
0
2
0
0
0
0
1
1
2
0
3
1
0
1
0
1
0
1
0
2
2
0
1
1
0
1
0
2
0
1
0
1
2
0
1
1
0
0
1
2
3
2
0
1
2
1
0
2
1
2
0
2
0
0
0
2
1
1
1
1
0
2
1
1
0
2
1
1
1
1
0
0
0
1
1
0
2
0
2
2
0
2
1
2
1
2
2
2
1
2
0
1
2
0
0
0
1
0
0
2
0
0
2
0
1
0
0
0
0
2
0
0
0
2
1
1
0
1
0
0
0
1
2
2
2
1
0
0
0
2
4
0
1
1
0
1
0
0
0
2
1
1
1
1
0
0
1
2
0
1
1
1
0
0
1
1
0
0
1
1
0
0
1
2
0
0
2
2
0
0
2
0
2
0
2
1
2
1
1
0
0
1
0
0
0
1
1
2
2
1
0
0
1
1
2
1
0
1
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
2
0
0
0
0
2
0
0
0
1
0
1
1
2
1
0
0
0
0
0
1
2
0
1
2
1
1
0
0
2
1
0
0
0
0
0
2
0
1
0
1
0
0
2
1
0
1
0
2
0
0
0
2
0
1
1
0
2
0
1
0
0
0
2
2
0
2
0
0
2
1
0
1
0
1
1
0
0
0
3
0
1
1
0
0
0
0
1
0
2
1
0
1
2
0
1
0
0
1
1
0
1
0
2
0
1
0
0
1
0
0
1
0
1
1
0
0
1
1
2
1
1
0
1
0
3
1
2
1
0
1
2
1
1
0
0
0
1
1
1
2
0
0
0
2
0
2
0
0
0
1
0
0
1
2
1
2
2
1
0
0
1
1
2
2
0
2
0
1
2
1
1
1
1
1
0
0
1
7
1
0
0
0
0
0
1
1
0
1
2
0
0
0
2
1
2
0
1
0
0
1
2
2
2
1
0
0
1
0
0
2
0
0
1
1
0
2
0
0
2
0
0
1
2
3
1
0
0
0
0
1
2
0
0
0
2
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
3
0
2
0
2
1
0
0
1
1
2
0
1
0
2
2
1
2
0
0
0
2
0
1
2
0
3
0
1
0
0
1
2
0
0
1
0
1
0
0
0
0
0
0
1
2
2
0
0
1
0
0
2
1
0
0
0
0
0
0
1
0
2
0
1
0
2
1
2
2
0
0
0
1
0
2
0
0
1
2
0
1
0
1
1
2
2
0
1
2
0
2
0
0
0
2
1
0
1
1
0
1
1
0
0
1
2
0
1
1
0
0
0
1
1
1
0
1
3
3
2
1
0
2
0
1
1
2
2
0
2
1
0
0
2
0
0
1
3
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
1
0
0
2
0
2
1
0
1
1
0
4
2
0
0
0
0
1
0
2
0
0
1
2
6
0
1
1
1
2
1
0
0
0
1
0
2
2
0
0
0
2
2
0
0
0
2
0
1
0
0
6
0
1
1
0
0
2
0
0
0
1
2
2
1
0
0
0
0
0
1
0
1
2
1
2
2
1
0
0
1
0
1
2
0
0
0
1
0
1
2
0
0
0
0
0
3
2
0
1
0
0
2
1
0
0
0
0
2
2
0
2
0
1
2
3
0
0
1
2
2
0
0
2
1
2
1
1
0
0
0
0
1
0
1
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
2
2
1
1
1
1
1
1
1
1
1
1
0
0
0
2
1
1
1
1
0
2
0
1
2
1
2
1
0
2
1
0
0
2
1
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
3
0
0
1
2
1
1
1
1
1
1
1
1
1
0
0
2
0
0
2
0
2
0
0
0
1
0
0
0
0
2
0
1
0
1
1
2
1
1
0
0
0
0
1
0
1
2
1
1
1
1
2
2
1
0
3
0
0
0
2
0
2
1
1
1
1
0
1
1
1
0
1
2
3
2
1
1
0
2
1
0
0
1
2
0
2
1
2
2
2
0
1
1
2
0
2
0
0
4
2
0
0
0
0
1
0
0
0
1
1
0
1
1
1
0
2
2
1
0
2
1
0
0
0
0
1
1
0
0
0
0
0
0
3
2
2
0
0
0
1
1
0
3
1
1
0
1
2
0
3
0
0
2
2
1
0
4
0
0
2
0
0
0
0
1
0
0
1
2
0
0
1
0
0
0
1
0
0
0
1
1
1
0
3
0
0
1
1
0
1
2
0
0
0
0
3
0
1
0
0
1
0
0
0
2
0
0
1
1
2
2
1
3
2
0
0
2
0
0
2
2
2
2
0
2
0
0
2
0
0
2
0
0
0
0
0
0
2
0
1
0
0
2
1
0
0
0
1
0
0
1
0
1
0
1
2
1
1
1
1
2
1
1
2
1
0
2
2
0
2
0
0
0
0
0
0
1
1
1
1
0
1
1
1
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
1
0
2
0
0
0
1
0
1
2
0
2
0
0
1
0
0
0
1
0
0
0
0
2
0
1
0
0
0
2
2
3
1
0
0
0
0
1
0
1
0
0
0
2
0
1
0
0
0
1
1
0
1
2
1
2
0
0
1
1
0
0
2
0
0
2
0
0
0
0
2
0
4
1
0
0
0
2
1
1
0
2
1
0
1
2
0
2
1
1
2
1
1
0
2
0
0
3
0
0
0
2
2
1
2
1
0
0
1
0
1
0
0
0
1
0
1
0
2
1
0
0
0
2
1
0
2
0
0
0
1
0
2
2
0
1
0
0
2
0
0
2
0
2
1
2
1
0
1
1
1
0
2
0
1
0
1
2
1
0
0
2
1
1
0
0
1
1
0
0
0
0
2
2
0
0
1
0
2
1
0
1
0
0
1
0
1
0
0
2
0
1
0
0
0
0
0
1
2
1
1
0
0
0
0
0
1
0
0
1
1
1
0
2
0
1
2
1
2
2
1
1
0
1
1
0
2
2
0
0
0
3
0
0
0
1
0
0
0
1
8
7
0
0
0
1
2
0
0
2
1
1
0
2
2
1
1
0
2
0
0
1
0
2
0
2
1
2
0
1
1
1
0
2
2
0
0
1
1
0
1
1
1
0
2
0
1
0
0
0
2
1
2
1
0
1
0
0
0
0
2
0
1
0
2
0
2
0
0
1
1
1
1
2
1
0
3
0
6
0
2
1
2
0
0
0
2
1
0
1
0
1
0
0
2
0
0
0
0
1
2
0
0
2
0
2
0
1
0
1
0
1
0
0
0
1
0
2
3
0
0
0
0
1
0
2
0
1
1
2
1
0
0
1
0
0
2
1
0
0
2
0
0
0
0
1
0
0
0
1
1
0
0
2
2
1
1
2
0
0
0
0
0
0
1
0
1
2
0
2
0
0
1
1
1
0
0
0
1
0
0
1
0
0
0
0
1
2
2
0
0
0
2
1
1
3
0
2
2
0
2
1
1
2
0
0
2
0
2
0
2
0
1
0
1
1
0
0
3
0
0
1
1
1
0
1
0
0
2
2
0
1
1
2
1
0
0
2
1
1
0
2
0
0
1
0
1
1
1
2
1
1
0
0
5
0
0
0
0
7
1
2
1
0
1
0
2
0
1
0
1
2
1
1
0
2
0
2
0
1
0
0
2
1
0
2
3
0
0
0
0
2
0
1
0
2
2
0
1
1
0
1
0
1
0
2
0
0
0
1
0
1
1
3
2
1
1
1
0
1
0
0
2
1
1
2
2
2
2
1
0
1
0
0
0
1
1
0
0
0
0
2
0
0
1
2
0
1
1
0
4
0
2
0
2
0
3
0
1
2
0
2
2
0
2
1
4
1
0
1
0
0
0
1
1
1
1
0
0
2
2
2
2
0
0
0
2
0
1
2
2
0
0
0
2
0
0
1
0
0
2
2
1
0
1
2
0
2
1
2
1
0
0
0
1
0
0
1
2
0
0
2
3
0
0
0
0
1
0
0
0
0
1
0
1
3
0
0
2
0
0
0
2
2
0
0
0
0
0
1
0
0
2
2
0
0
1
1
1
0
1
0
0
0
1
1
0
2
0
2
0
1
0
0
0
1
1
0
1
0
0
0
0
2
0
0
3
0
2
0
1
0
2
2
0
5
1
0
0
0
0
2
0
1
0
0
2
0
2
1
0
0
0
0
1
2
0
1
2
2
2
2
1
1
2
0
0
0
0
3
1
1
0
1
2
0
0
1
0
0
0
1
0
0
2
0
0
1
1
0
0
0
0
1
1
0
0
0
1
1
0
1
1
0
0
0
2
0
0
0
2
1
0
0
0
1
1
0
0
2
0
1
1
0
0
2
2
1
2
1
1
1
0
1
2
0
0
1
1
1
2
0
0
1
1
1
2
2
0
0
0
1
2
1
0
1
1
2
0
0
0
1
1
0
1
0
0
1
0
0
0
0
1
1
0
1
0
2
0
0
0
0
1
0
0
1
2
2
2
0
0
1
0
0
2
0
2
2
2
1
4
0
3
2
0
2
0
0
0
0
0
0
1
3
1
0
2
2
2
1
0
2
2
1
0
0
0
1
0
1
0
2
1
2
0
1
2
0
0
1
0
2
2
0
2
1
1
0
1
0
2
3
1
0
1
2
0
2
1
1
0
0
1
0
1
1
1
1
0
1
1
0
1
0
0
0
1
0
0
2
0
0
2
2
0
0
0
1
1
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
2
0
2
0
0
0
1
0
0
0
2
1
0
2
1
1
1
0
0
0
2
1
2
0
2
1
0
0
0
0
1
2
0
3
1
0
1
1
1
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
1
0
0
2
0
1
0
2
1
2
2
2
0
2
3
0
1
1
0
1
0
0
0
1
1
2
2
0
0
0
2
1
2
1
0
0
1
0
0
1
0
0
0
0
3
0
3
2
0
0
0
0
2
0
0
0
2
1
0
1
1
0
2
2
0
2
0
0
0
1
2
1
0
1
0
1
0
0
0
0
2
1
0
1
0
0
1
0
0
2
0
1
1
0
0
1
0
1
0
0
0
1
0
0
0
1
1
2
1
1
0
1
0
2
0
0
2
2
0
1
0
1
2
0
1
1
0
0
0
1
3
0
3
0
1
0
2
0
3
2
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
1
1
2
0
0
0
1
2
1
0
2
2
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
1
0
0
1
1
1
0
0
1
1
0
0
1
2
0
2
0
0
0
0
2
2
1
2
0
0
0
2
1
0
2
1
0
2
2
2
3
1
0
1
0
0
1
0
2
0
0
0
2
2
0
0
1
0
1
0
0
0
2
0
0
0
2
0
0
1
0
1
0
0
0
0
1
2
0
0
0
0
1
0
1
0
0
1
2
0
0
1
0
2
1
0
0
0
1
1
0
2
0
0
1
0
1
1
0
0
0
0
1
0
0
0
1
0
3
2
0
1
0
0
2
0
1
4
1
0
0
0
0
0
0
0
2
2
0
4
2
0
1
0
0
2
0
2
1
2
1
1
0
2
1
3
0
0
1
1
1
0
0
2
2
0
0
0
0
1
2
0
1
2
0
0
0
0
1
2
2
0
0
1
0
0
1
0
1
0
0
1
0
1
0
0
0
1
0
0
0
2
0
1
0
1
1
2
2
0
1
0
0
0
2
0
1
0
0
1
1
0
5
0
0
0
1
0
0
2
2
1
2
1
0
1
1
0
0
0
0
2
1
0
0
0
0
1
2
0
1
0
0
2
0
0
0
0
2
2
1
0
1
1
0
0
0
0
0
1
0
1
0
0
0
1
0
1
1
2
1
1
0
0
2
0
0
0
0
2
0
0
0
1
1
0
0
0
1
2
0
2
1
0
1
0
1
1
1
0
0
0
0
5
0
0
0
1
2
0
0
0
0
1
0
0
0
1
0
1
0
3
1
0
0
0
0
0
0
0
0
0
0
1
2
0
2
1
2
1
0
1
1
0
0
2
2
0
0
1
0
0
2
1
2
0
2
0
0
0
2
1
1
0
2
0
2
0
0
0
0
1
0
0
2
2
1
0
0
0
4
0
1
0
1
0
0
0
0
0
1
2
1
0
1
2
1
0
2
0
0
2
2
0
0
0
2
0
1
1
0
0
1
1
1
0
0
0
3
0
0
2
0
0
0
0
0
1
1
1
1
0
0
0
1
0
2
1
1
2
2
1
2
0
0
3
1
0
0
0
2
0
1
1
0
1
1
2
0
1
0
0
0
0
2
1
0
2
3
0
1
2
0
1
1
1
0
2
3
1
1
2
0
1
1
0
2
0
0
1
0
0
2
1
1
2
0
0
0
0
1
0
0
0
2
2
1
0
2
0
0
0
2
0
0
0
0
2
0
0
1
2
1
2
0
1
0
0
2
1
0
0
0
0
0
0
0
1
2
1
2
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
1
0
2
1
2
2
0
0
2
0
2
1
2
1
2
1
0
0
0
0
0
0
2
1
0
1
0
1
0
2
2
1
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
2
3
2
1
0
0
1
1
2
0
0
0
0
0
1
1
1
1
2
0
0
2
1
0
0
1
2
1
0
1
0
2
3
0
0
2
0
1
1
0
2
3
0
0
0
0
0
0
2
1
0
1
0
0
1
2
0
2
0
4
0
0
2
1
0
0
0
0
0
0
2
0
1
0
0
1
2
5
0
0
2
0
2
1
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
3
1
0
1
3
2
0
1
0
1
0
2
0
2
2
0
0
2
0
2
2
0
2
0
2
0
1
0
0
3
0
0
2
0
0
0
2
0
0
1
4
0
0
1
0
0
2
1
0
2
1
1
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
2
0
2
1
0
0
0
1
0
0
1
0
0
0
1
0
2
0
2
1
0
0
0
1
0
2
1
0
0
0
0
1
0
2
2
1
0
0
0
2
2
0
1
1
3
0
0
0
0
0
0
1
0
1
2
2
1
0
0
0
2
0
1
0
0
1
0
0
0
1
0
0
2
2
0
0
0
0
2
0
0
1
0
1
1
2
1
3
3
2
0
2
0
0
1
0
0
2
0
0
0
2
1
0
1
1
2
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
1
1
1
1
0
0
0
1
0
0
2
1
1
0
2
0
1
2
0
0
0
0
0
1
2
0
1
0
0
2
0
0
3
2
2
0
2
0
1
2
0
0
0
2
1
0
0
1
0
0
0
1
2
1
0
0
0
0
0
1
1
0
1
0
0
2
0
0
0
0
2
0
1
1
15
1
2
2
0
1
1
1
2
0
0
2
1
0
0
2
0
1
0
2
2
3
0
1
0
3
0
0
1
0
1
2
1
1
1
0
0
0
2
0
1
1
0
1
0
2
0
2
0
0
0
1
0
0
0
1
3
0
1
0
0
0
0
0
1
1
1
1
2
0
0
2
2
0
1
0
0
0
0
0
2
2
1
0
0
1
2
1
2
2
0
0
0
2
1
1
2
1
0
2
0
0
1
1
0
2
0
0
0
1
0
0
0
1
0
0
1
0
0
0
2
1
2
0
0
0
0
1
0
0
1
2
2
0
2
1
1
0
1
1
2
0
0
0
1
0
0
0
0
2
0
0
2
0
0
2
2
0
0
0
2
0
1
3
0
0
1
1
0
1
0
2
1
0
1
1
0
0
1
0
0
0
2
0
1
1
0
0
0
4
1
0
0
2
0
1
2
1
0
0
2
0
0
1
1
1
0
1
1
0
1
1
0
0
1
0
2
3
1
0
0
0
0
0
1
1
0
0
0
3
0
1
0
2
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
2
1
1
3
0
0
0
0
0
1
2
0
0
2
2
1
0
0
1
1
0
0
1
0
2
0
0
0
0
2
1
0
0
0
1
2
0
0
2
0
1
1
0
0
2
0
0
0
0
0
0
1
2
0
6
0
0
1
0
2
0
1
1
0
0
1
2
0
0
0
0
1
2
0
2
1
1
0
0
0
0
0
2
0
1
1
0
2
0
0
4
0
2
1
0
0
1
2
1
1
2
1
0
1
0
1
1
1
0
1
1
0
0
2
0
1
2
0
2
6
0
2
2
0
1
2
1
0
0
0
1
1
1
1
1
1
0
0
2
0
6
2
0
1
1
0
1
1
1
1
0
0
2
0
1
1
0
0
1
0
0
0
0
0
0
0
4
2
1
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
1
1
0
0
1
2
2
2
1
0
2
2
2
0
1
0
1
0
0
0
1
0
0
2
1
1
1
0
2
2
1
0
2
2
0
0
1
0
1
1
2
2
0
0
0
1
1
2
0
0
0
1
0
2
2
2
1
1
0
0
0
0
1
1
2
1
0
2
0
1
1
0
1
0
1
1
0
0
2
1
0
0
0
2
0
0
1
2
0
0
1
2
1
0
0
0
0
1
1
1
0
2
2
0
2
0
0
1
2
1
3
2
1
0
0
2
0
1
1
0
0
1
1
0
2
0
2
2
1
1
2
2
1
2
2
2
1
0
0
1
0
0
0
1
2
0
1
0
2
2
0
0
0
1
0
0
2
1
1
2
0
0
0
0
0
0
0
0
0
1
1
1
0
1
1
0
1
1
2
1
1
2
0
2
0
0
2
1
0
1
0
0
0
1
0
0
0
1
0
0
1
0
2
2
0
2
1
2
1
0
0
0
0
0
0
2
1
0
0
1
0
2
0
2
1
1
1
0
1
1
1
0
1
1
1
0
0
2
2
0
1
1
0
1
1
2
0
0
0
0
0
1
1
1
1
0
0
1
2
0
0
2
0
0
0
1
0
2
2
0
1
1
0
2
1
1
0
0
1
0
0
0
0
0
1
0
0
1
2
1
0
0
0
2
1
2
0
2
1
2
2
1
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
1
1
0
2
2
0
1
0
3
0
2
2
1
0
1
0
0
0
2
0
1
0
2
0
0
1
1
0
0
2
0
1
0
1
2
2
1
1
1
0
2
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
1
2
1
2
0
2
1
2
2
0
4
0
1
0
0
0
0
0
0
0
1
0
0
1
1
2
0
1
1
1
0
0
0
0
0
1
0
1
1
2
0
0
0
0
1
1
1
1
0
1
0
0
0
0
2
2
1
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
2
0
1
2
1
0
1
2
2
0
0
1
2
2
1
1
2
0
1
0
2
2
0
0
1
2
0
1
1
0
0
1
2
0
0
0
0
1
3
0
2
1
0
0
1
0
1
2
0
0
2
1
0
2
1
1
0
2
1
0
0
0
1
1
2
3
2
2
0
0
0
0
0
2
0
2
0
1
0
0
0
1
0
1
1
0
1
2
2
1
0
2
2
1
1
0
2
0
1
2
1
0
0
0
1
0
0
1
2
0
2
1
0
0
0
1
2
2
0
2
1
0
2
0
0
0
1
0
1
1
0
0
0
0
0
0
0
2
1
1
0
0
0
0
2
1
2
1
0
2
0
1
0
1
4
0
2
2
0
0
2
0
2
0
0
0
0
1
0
0
2
0
1
0
1
2
0
2
0
0
1
1
0
0
2
1
0
0
0
0
0
0
1
1
0
2
1
2
0
1
1
2
0
0
0
1
0
0
0
0
0
2
0
1
0
2
0
2
1
0
1
1
1
1
1
1
1
1
1
1
1
0
0
2
0
0
0
2
1
2
1
4
2
0
0
1
2
1
1
2
0
0
1
0
1
2
1
1
0
2
0
1
2
0
0
1
0
1
3
0
2
0
0
1
0
1
1
1
0
0
0
1
1
0
0
0
0
0
0
2
2
0
0
0
0
2
2
2
1
0
2
0
2
0
0
0
0
0
0
2
1
1
1
2
0
0
1
2
0
0
0
0
0
0
0
0
1
1
1
0
0
2
1
0
2
1
1
2
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
1
0
1
0
0
0
0
0
1
0
1
1
0
1
0
1
5
1
1
2
0
2
0
0
1
0
2
2
2
1
0
1
0
0
1
0
2
1
0
0
0
0
0
1
0
0
2
2
1
0
0
1
0
1
0
3
2
1
0
2
2
0
0
0
0
0
1
0
0
2
1
0
0
2
0
1
0
1
0
0
0
0
1
0
2
0
0
2
0
0
1
0
0
2
1
0
2
0
0
0
0
1
0
0
0
0
1
0
2
0
1
1
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
2
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
3
1
0
1
0
2
0
1
0
1
0
0
0
2
0
1
0
0
1
1
0
1
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
1
2
2
1
0
2
0
2
0
0
1
0
1
2
0
2
0
0
0
0
0
2
0
1
0
2
1
0
1
0
0
2
1
1
0
2
1
0
1
0
1
2
0
0
1
0
0
0
0
2
0
2
0
1
1
0
1
1
0
2
1
0
1
0
1
0
0
0
0
0
1
2
1
1
0
1
0
0
2
2
0
0
0
0
2
1
0
0
0
1
0
2
0
1
2
1
0
0
2
0
1
0
0
0
2
1
1
0
1
0
1
1
1
0
0
0
1
1
1
0
0
0
0
0
1
1
1
1
2
0
2
1
3
1
0
1
0
2
0
1
2
0
0
0
0
0
1
1
0
1
3
2
4
0
1
2
0
0
0
0
1
1
0
7
0
1
2
3
2
0
1
0
0
1
2
1
0
2
2
0
0
2
0
1
2
2
1
0
0
0
1
0
0
0
4
1
2
0
0
0
2
1
0
0
0
1
0
2
2
0
2
0
1
0
0
0
0
0
1
0
0
3
1
2
1
0
1
0
0
0
0
0
3
1
0
1
1
1
1
0
0
0
2
0
1
0
1
2
0
0
1
0
0
1
0
0
1
0
0
0
2
2
2
1
1
1
1
0
2
2
0
2
0
1
0
0
0
1
2
1
0
1
0
0
0
0
0
1
0
0
0
1
2
0
2
0
1
0
2
0
0
0
2
1
2
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
1
0
2
1
1
1
0
1
1
0
1
0
0
1
2
1
0
0
0
1
0
1
1
1
1
0
0
0
1
0
0
0
1
2
0
1
2
0
1
1
0
0
2
0
1
0
1
0
0
0
2
2
0
0
0
2
2
2
0
0
2
1
0
0
1
2
2
1
0
1
1
2
1
1
0
2
0
1
1
1
0
0
0
0
0
0
2
2
1
1
0
1
0
1
0
0
0
2
1
2
0
1
1
0
1
0
1
1
0
0
1
0
1
0
2
1
1
0
0
1
0
2
1
0
1
0
0
2
1
2
0
2
2
0
1
0
2
2
1
0
0
0
0
0
1
2
2
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
2
1
0
1
1
1
1
1
2
2
5
1
0
0
0
1
1
0
1
2
0
2
0
0
0
0
1
1
1
0
2
0
0
1
0
0
0
0
1
0
0
1
1
1
2
0
0
0
2
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
2
1
2
0
0
1
0
0
2
0
0
1
0
1
0
0
0
2
0
2
0
1
0
2
0
0
0
1
3
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
2
0
2
2
2
0
0
2
0
0
2
0
2
0
1
0
1
0
0
1
1
2
0
2
0
0
2
2
0
0
0
1
0
0
0
0
1
2
1
3
2
0
0
1
1
0
2
0
2
6
1
0
0
0
0
2
0
1
0
0
1
0
1
2
0
2
0
0
2
1
1
1
0
2
0
0
1
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
1
1
0
0
1
0
2
1
0
1
1
0
0
2
0
1
0
2
0
2
2
0
2
0
0
0
2
1
0
0
1
0
0
2
0
1
0
0
2
1
0
1
0
0
1
0
2
0
0
0
1
2
0
1
0
0
2
2
1
0
0
0
1
1
0
0
1
0
0
0
4
0
0
0
1
0
0
1
2
0
0
0
0
1
2
0
0
1
0
0
1
0
1
0
0
1
1
0
1
0
0
0
2
0
1
1
0
0
1
2
0
0
0
0
1
1
1
0
0
1
1
2
0
2
1
1
1
0
1
0
0
1
1
0
0
1
0
0
2
0
2
2
2
0
0
1
0
1
2
0
0
2
0
0
0
0
0
0
0
2
0
2
0
1
0
1
0
1
0
0
1
0
1
1
0
0
4
0
2
0
0
1
1
2
0
0
0
2
1
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
1
0
1
0
1
2
1
2
0
1
0
5
0
0
0
2
2
3
0
0
0
1
1
0
0
1
2
1
4
1
0
1
1
0
2
6
0
0
2
2
0
1
2
2
0
0
2
0
0
0
0
1
0
1
0
0
9
1
0
0
2
1
0
0
2
2
1
2
2
0
0
0
1
0
0
2
1
1
2
1
1
0
0
1
1
0
0
1
1
0
0
0
2
1
0
0
1
0
1
2
1
0
2
0
1
0
2
0
0
2
1
0
0
0
4
0
0
0
1
1
2
2
0
0
2
1
1
0
1
2
4
0
0
1
2
0
2
1
1
2
1
6
0
0
0
2
2
0
0
0
0
0
0
2
2
0
0
0
1
1
2
0
0
0
1
0
1
0
2
2
0
2
0
3
2
1
0
0
1
0
1
0
1
0
0
1
1
1
0
0
0
0
0
0
0
1
2
1
0
1
2
1
0
0
2
1
0
0
2
2
0
0
1
0
0
0
0
1
0
0
1
1
1
0
2
1
0
1
2
0
0
0
2
0
1
0
1
1
0
0
0
2
0
0
0
2
0
2
0
1
0
0
0
0
1
0
0
0
2
0
2
0
1
0
2
2
0
2
2
2
2
0
1
1
0
0
0
4
1
0
0
2
0
0
2
2
2
2
1
0
0
2
1
0
0
0
1
2
1
2
1
0
0
2
0
0
1
1
0
0
0
1
2
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
3
0
1
2
0
1
6
1
0
1
0
2
0
2
2
1
0
1
2
0
0
1
1
0
2
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
3
1
0
2
1
0
1
1
0
1
1
2
0
2
1
0
1
1
1
0
0
0
0
0
3
2
1
0
0
0
0
3
0
2
1
0
3
0
1
0
2
1
2
0
0
1
0
0
1
0
1
2
2
0
2
0
1
2
1
0
2
2
0
0
0
0
1
0
2
0
0
2
0
1
1
1
0
0
0
0
2
0
2
1
0
0
0
1
0
1
0
0
0
0
1
2
0
1
1
1
0
1
1
0
2
1
1
2
0
0
2
1
0
0
0
0
2
2
1
0
1
0
0
0
2
1
1
0
0
0
0
2
0
1
0
1
0
1
0
2
0
2
0
2
2
0
1
1
1
2
0
1
2
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
2
0
0
0
1
0
0
2
0
1
0
0
0
0
1
0
0
0
2
1
0
0
0
2
0
2
0
2
0
0
1
0
1
2
1
1
2
0
1
1
0
0
0
0
1
1
1
1
1
0
0
1
2
0
0
1
0
0
0
1
0
1
0
0
2
0
2
4
2
2
0
1
1
1
0
0
1
2
0
0
0
0
1
2
0
0
0
0
1
1
0
2
0
0
2
1
1
0
0
0
1
1
1
0
0
0
0
2
0
0
1
0
0
1
2
0
1
0
0
1
1
1
0
0
0
0
1
1
0
2
1
1
0
1
0
0
1
1
0
0
1
1
1
1
0
0
2
0
0
0
0
0
1
2
1
1
1
0
0
1
0
0
2
0
0
2
2
0
2
0
2
2
0
0
3
1
2
2
0
0
2
2
1
1
2
0
0
0
0
0
1
0
2
0
0
1
0
2
2
0
1
0
0
1
0
1
0
0
2
1
0
1
1
2
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
2
0
0
0
0
2
1
0
2
1
0
0
0
0
5
1
0
1
1
0
1
2
0
0
0
0
0
2
0
1
1
2
2
0
1
0
0
1
0
0
0
0
1
0
1
0
1
2
1
1
0
1
1
0
1
0
0
1
2
0
1
3
0
0
0
1
2
0
0
0
0
2
1
1
0
2
2
0
0
1
2
1
2
0
0
0
1
0
2
1
0
1
0
3
2
0
0
0
0
2
0
1
1
0
1
0
0
0
1
0
0
2
1
1
1
1
0
0
1
2
1
1
0
2
2
1
0
1
0
0
2
1
1
0
0
2
0
0
0
1
0
1
1
1
1
0
1
0
0
0
0
1
1
0
1
1
0
1
1
1
1
1
1
0
0
0
0
0
0
0
1
0
1
0
4
2
0
3
0
2
2
0
1
1
1
2
1
2
1
2
0
2
0
1
0
1
0
0
0
2
1
0
0
1
2
1
0
1
2
1
0
2
1
0
1
2
1
1
2
1
0
0
0
0
2
0
0
3
0
3
1
1
0
0
3
1
0
0
0
0
1
2
0
2
2
0
0
0
1
1
1
3
3
1
1
1
0
2
2
0
0
0
0
0
1
2
0
2
0
0
2
1
0
0
0
0
0
0
0
0
2
0
2
2
2
1
2
0
0
1
2
2
0
1
0
1
0
0
1
2
1
0
0
1
1
2
2
2
0
0
2
1
0
0
0
2
0
0
2
0
0
0
1
1
0
2
0
1
1
2
1
1
2
1
1
0
0
0
2
2
2
0
1
1
0
0
2
1
2
1
2
2
1
1
0
0
1
0
0
0
0
2
0
2
1
1
2
2
2
2
0
0
2
0
2
2
0
0
0
1
1
1
2
2
0
0
0
0
1
0
1
0
2
0
0
2
0
1
2
1
0
0
0
0
0
2
0
1
0
0
0
2
0
2
1
1
0
0
0
1
2
0
0
2
4
0
1
1
1
0
1
0
1
2
1
0
1
0
0
1
0
0
2
0
2
0
0
1
3
1
0
1
0
1
2
0
0
1
0
0
0
2
1
0
1
0
0
0
1
0
2
0
0
2
2
1
2
0
0
0
0
0
2
0
0
0
1
1
0
1
0
2
1
2
0
1
1
1
0
0
0
0
0
0
0
1
1
1
0
1
2
0
1
0
2
0
0
2
1
2
0
2
0
1
0
2
0
0
1
0
0
0
0
0
1
2
0
2
0
0
0
2
0
1
0
2
2
0
0
1
0
2
0
0
0
1
0
1
1
1
0
1
1
2
0
1
0
1
2
0
2
0
0
0
1
1
0
1
2
0
2
0
2
1
0
2
1
1
0
1
0
0
0
2
1
3
1
0
2
1
0
2
2
2
0
1
0
1
1
0
0
0
0
0
1
1
0
1
0
0
2
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
2
0
0
0
1
0
0
0
0
0
1
0
0
0
1
2
0
2
0
2
1
0
0
0
0
2
0
2
2
0
2
1
0
2
0
0
0
1
0
2
0
0
0
2
0
0
1
0
1
2
1
0
0
0
0
0
1
0
2
2
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
2
2
1
0
0
1
0
1
0
0
1
2
2
1
1
1
0
0
1
1
2
0
2
1
1
2
0
0
0
0
1
0
1
0
1
0
2
2
0
2
0
0
0
2
1
0
1
1
0
0
1
0
0
1
0
0
1
0
1
0
2
1
0
0
0
2
0
0
2
2
1
0
1
0
1
1
0
2
0
1
0
0
1
0
0
3
0
2
3
0
0
2
0
1
0
2
0
0
0
0
0
2
0
0
0
2
2
0
0
1
3
0
0
0
2
0
0
0
1
2
2
1
1
1
0
1
0
0
1
0
1
0
0
1
1
0
0
0
1
1
0
0
0
0
0
1
2
2
2
0
2
0
2
0
0
4
0
1
2
2
0
1
0
1
0
2
0
1
0
0
0
2
0
1
0
1
0
2
2
1
2
1
0
2
1
1
0
0
2
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
1
1
2
1
0
1
1
1
1
0
1
1
0
1
0
1
2
2
0
1
1
1
0
1
1
0
2
1
0
0
0
1
0
0
0
0
0
1
2
2
1
1
1
0
1
1
0
0
0
0
0
1
1
0
0
0
2
0
1
0
0
0
1
1
2
2
0
0
1
0
2
0
1
0
1
1
0
0
2
0
1
0
2
2
1
0
0
3
1
1
1
1
2
1
1
2
0
0
1
0
1
0
1
0
0
0
1
6
0
0
0
0
2
1
0
1
2
1
1
0
0
0
0
1
0
2
3
4
0
1
2
0
1
2
1
0
1
1
0
1
0
2
1
2
1
1
2
0
0
0
2
1
0
2
0
2
1
0
1
2
1
1
0
0
0
1
0
2
0
2
0
1
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
1
0
2
2
0
1
1
2
2
0
0
1
2
2
0
1
0
1
1
0
0
0
0
1
0
2
2
2
1
0
2
0
0
0
0
1
0
1
0
0
2
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
2
0
0
0
1
2
0
2
1
0
2
1
2
2
0
1
1
0
0
0
1
1
3
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
1
2
0
1
0
0
1
2
0
2
1
0
0
0
1
2
2
2
1
0
1
0
1
0
2
0
0
0
1
0
0
1
1
2
0
0
0
0
2
1
2
0
0
0
0
0
1
0
2
1
1
0
2
2
2
1
2
1
1
0
1
0
0
2
0
1
0
0
0
0
0
1
2
2
1
1
0
1
3
0
2
0
1
0
0
2
0
1
1
1
2
0
2
1
0
1
1
2
0
1
1
0
1
0
2
0
2
0
1
0
0
2
0
2
0
2
0
0
0
0
0
0
2
1
1
1
0
2
0
0
1
0
0
1
0
1
1
1
1
3
0
0
1
0
0
3
1
1
1
0
1
0
1
1
1
0
1
0
0
0
1
1
2
2
0
0
0
1
2
1
2
0
1
1
2
1
0
0
0
1
2
0
0
0
0
1
0
1
1
0
0
0
3
0
2
0
0
2
1
0
1
0
0
2
2
0
0
0
2
0
0
1
1
2
1
0
2
0
0
3
6
0
0
1
1
1
0
1
2
0
1
0
0
2
2
1
1
0
0
1
0
0
2
2
0
0
2
1
0
1
0
0
1
0
3
0
1
0
0
0
0
0
1
1
1
2
2
0
0
0
2
0
3
0
1
2
0
0
2
0
0
0
0
2
0
1
0
0
1
1
2
1
0
2
2
1
0
0
0
0
1
0
1
0
1
4
0
0
2
1
0
0
0
0
2
1
2
2
0
0
0
0
2
0
0
2
1
1
0
1
1
2
1
2
0
2
0
1
1
0
0
1
0
2
1
0
0
1
0
0
0
2
0
1
2
0
1
1
0
2
0
0
0
1
0
0
2
0
1
0
1
0
2
0
0
1
0
1
1
2
0
1
0
1
2
2
1
1
1
1
0
1
0
0
0
2
2
0
0
0
0
0
3
0
0
1
0
0
0
1
1
0
1
1
0
1
0
1
0
1
2
1
1
1
1
0
1
2
1
0
1
0
1
0
0
0
2
1
1
0
0
0
1
0
0
1
1
2
2
1
2
1
0
2
0
0
0
1
0
1
0
0
0
0
0
1
1
0
2
1
0
3
0
1
0
0
1
1
1
0
2
2
1
0
0
2
0
0
1
1
0
2
0
2
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
2
1
2
1
0
1
0
0
0
2
0
1
2
0
0
0
2
3
0
4
4
0
1
0
0
0
0
2
1
0
0
1
0
2
0
1
1
2
0
0
1
0
0
0
0
3
0
2
2
0
0
1
0
3
2
0
0
0
0
0
0
1
2
0
0
0
1
2
1
0
0
0
0
1
2
0
1
2
1
2
0
0
0
0
0
0
1
1
1
1
0
0
0
1
0
0
1
0
0
1
0
0
2
0
0
1
0
1
4
0
2
2
0
0
0
1
4
0
0
0
2
0
1
0
0
0
2
0
1
2
0
2
0
1
2
0
2
2
0
0
1
0
0
0
0
0
1
0
1
1
1
1
1
1
2
1
0
1
0
2
0
0
2
0
0
1
1
2
0
1
2
0
1
0
1
2
1
0
1
2
1
0
0
0
0
0
0
1
0
0
2
0
1
0
1
2
1
0
0
1
2
0
0
2
0
0
0
2
2
0
0
0
1
1
2
0
2
0
1
0
2
0
4
2
0
0
1
2
0
1
2
0
0
0
0
0
1
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
1
1
1
0
0
1
1
0
2
0
0
0
0
0
1
2
1
1
0
0
1
1
3
2
1
0
0
2
0
1
0
4
1
0
0
0
1
0
0
0
0
2
2
1
0
0
0
1
0
0
0
1
0
0
0
1
2
2
2
1
0
1
0
2
0
0
0
2
0
2
2
0
0
1
0
1
0
0
2
2
2
1
2
0
2
1
0
1
1
1
2
2
1
0
2
2
0
0
1
1
0
0
0
2
1
0
2
2
2
1
0
0
2
0
0
2
2
2
0
2
0
0
0
2
1
0
2
0
1
0
1
2
1
0
1
1
1
0
0
0
2
0
0
1
0
0
0
1
0
2
0
0
1
1
1
1
0
1
0
1
0
0
2
1
1
0
1
0
2
0
0
0
2
1
1
1
2
0
0
2
1
0
1
1
3
0
1
0
0
0
2
0
0
0
0
2
2
1
0
0
1
2
0
0
0
0
3
0
2
1
0
0
3
0
0
0
0
0
0
1
2
0
1
1
0
1
2
0
1
0
0
1
2
2
0
2
1
0
1
0
0
0
1
1
2
1
0
0
0
1
1
0
1
2
2
0
2
0
0
1
0
1
2
1
1
1
0
1
1
2
3
0
2
1
1
1
1
1
0
2
1
1
1
2
1
2
2
0
2
0
0
1
0
2
0
0
0
0
2
0
2
0
0
0
3
0
2
1
1
1
0
1
1
0
1
0
1
0
1
0
0
2
0
0
0
1
0
2
0
3
0
0
0
0
0
1
0
1
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
2
2
2
0
1
2
2
0
1
1
1
0
0
0
1
1
2
1
0
0
0
1
0
1
1
1
0
2
1
1
0
1
0
2
0
0
0
0
1
2
1
1
0
1
2
1
1
2
2
2
1
2
1
0
2
0
0
0
2
1
0
0
2
2
2
0
2
2
2
2
0
0
0
0
1
2
0
0
0
0
0
0
2
4
0
0
0
0
1
0
0
0
0
1
0
0
1
0
3
0
0
0
0
0
1
0
0
2
3
0
0
2
2
1
1
0
0
0
0
2
0
0
0
0
2
1
2
1
2
0
0
2
2
0
0
1
0
2
1
2
0
1
0
0
2
0
0
2
0
1
2
0
2
1
1
2
0
2
0
1
2
2
0
1
0
1
0
0
0
1
0
0
1
2
1
2
1
0
0
0
1
3
0
0
2
0
2
2
2
0
0
0
2
0
1
0
1
1
0
1
1
2
0
2
0
0
0
2
1
2
1
2
0
0
1
0
2
2
0
0
0
1
0
0
2
0
3
1
1
0
2
0
2
1
0
0
0
1
2
2
0
1
0
0
0
0
0
0
0
1
4
2
2
1
1
0
0
2
0
0
0
0
1
0
1
0
0
0
0
2
0
1
0
0
0
2
0
0
1
2
0
1
0
1
0
0
0
2
0
1
0
0
2
1
1
0
0
2
2
1
0
0
1
1
0
2
0
2
2
1
2
1
2
0
2
2
1
0
1
0
0
2
1
1
1
0
0
1
2
0
1
0
0
0
0
0
0
1
0
7
1
1
1
0
1
0
2
0
0
2
1
1
1
0
1
2
2
0
0
0
0
0
1
0
0
1
2
0
0
1
2
2
0
2
0
0
0
0
0
2
1
0
2
1
0
0
0
0
0
1
2
0
1
0
2
1
0
1
1
1
2
1
0
1
2
1
0
2
0
0
1
0
0
0
3
1
1
2
2
1
0
2
2
0
0
1
0
1
1
0
0
2
1
2
0
1
1
0
1
0
2
1
2
0
4
0
2
2
1
0
1
0
1
0
0
0
1
0
2
0
0
1
1
1
0
4
0
0
0
1
0
2
0
5
0
0
1
3
2
0
0
0
1
0
0
2
1
0
2
0
0
1
0
1
1
0
0
1
1
0
0
0
0
0
1
2
0
0
1
2
0
2
0
1
1
0
1
0
0
0
2
0
2
2
0
2
0
0
0
0
2
1
1
2
0
0
0
0
0
2
0
2
2
0
2
0
2
2
0
1
1
1
2
1
0
0
1
2
0
1
1
0
2
0
0
2
2
1
0
2
0
1
1
0
0
0
3
0
2
2
1
2
0
2
5
0
2
0
2
2
0
0
2
1
0
4
0
1
0
1
1
2
0
2
0
0
1
1
2
2
0
2
1
0
1
0
0
1
0
0
1
0
1
0
0
2
0
2
0
0
1
0
1
1
0
0
0
0
1
2
0
0
0
1
0
0
0
0
1
2
0
1
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
2
2
0
0
0
1
1
2
2
1
0
0
0
0
2
1
0
0
0
1
2
1
1
0
1
0
0
1
2
2
1
2
0
0
0
1
0
1
0
0
0
1
2
0
1
0
0
0
1
2
2
1
1
0
0
1
2
0
2
1
1
1
0
0
0
1
1
1
0
0
0
2
0
0
1
1
0
0
0
0
1
1
0
0
1
0
2
2
1
0
2
1
0
2
0
1
1
0
0
1
0
2
0
0
0
1
0
0
1
1
2
1
2
1
0
0
0
2
0
0
0
0
0
2
0
1
2
1
0
0
0
0
0
0
1
0
0
0
0
2
0
3
0
0
1
1
3
0
1
0
2
0
0
0
0
2
1
1
1
0
1
1
0
1
0
0
2
2
1
0
2
2
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
1
1
1
1
1
2
1
0
0
0
0
0
1
1
1
0
1
2
2
0
0
0
1
1
1
0
1
0
0
0
0
2
0
2
0
0
2
1
0
0
0
0
0
0
1
1
0
2
0
0
2
0
2
0
1
1
0
1
2
0
0
0
1
0
2
2
0
0
0
2
0
1
0
2
1
0
0
1
0
0
0
0
2
1
2
2
0
1
1
1
3
1
0
0
0
2
0
0
0
0
1
2
2
0
0
0
1
0
2
0
0
5
1
0
1
0
0
1
1
2
2
1
0
0
0
0
0
2
0
1
2
2
0
0
2
2
1
0
0
0
0
0
1
0
0
1
0
1
2
1
0
2
0
0
2
0
0
3
1
0
0
0
0
0
2
0
0
1
1
0
1
0
1
1
0
0
1
2
0
1
1
0
2
1
0
0
0
0
2
0
0
0
0
0
0
1
2
2
0
1
0
0
0
0
0
0
2
2
2
0
0
0
2
1
1
0
0
0
0
1
3
2
0
2
1
1
0
2
1
1
3
1
0
0
1
0
0
0
1
1
0
1
1
0
2
0
0
1
1
0
1
0
0
2
0
2
0
1
2
0
0
0
1
0
1
1
0
0
0
1
1
2
3
0
3
1
1
0
1
2
2
2
0
1
1
0
0
1
0
0
0
0
1
1
1
0
1
2
0
1
1
0
0
0
1
1
0
0
1
0
1
2
2
0
1
0
2
0
2
1
1
0
3
1
2
1
0
0
1
1
0
1
1
0
3
0
1
0
2
0
0
1
0
0
1
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
2
0
1
2
1
0
0
0
0
0
0
2
2
2
1
0
2
2
1
0
1
1
1
1
1
2
1
4
1
0
0
1
7
1
1
0
0
1
2
0
2
2
2
3
0
0
1
0
0
0
1
0
2
2
0
1
0
0
0
0
2
1
0
3
2
2
1
1
0
1
2
0
1
2
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
3
2
2
2
2
2
1
0
0
2
1
0
0
1
1
0
0
0
1
2
0
1
0
0
1
0
2
1
0
2
0
1
1
2
1
2
0
0
1
0
1
0
0
2
2
0
0
2
2
1
1
2
2
1
1
1
0
0
0
0
1
0
0
0
0
2
1
0
2
1
2
0
0
0
1
0
1
1
2
0
2
0
2
0
2
1
2
1
0
0
0
0
3
0
0
1
2
0
1
1
2
0
0
1
0
0
1
0
0
0
0
2
2
0
0
2
1
2
1
2
0
2
0
0
1
0
0
0
0
1
1
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
1
2
0
1
2
2
2
1
0
1
0
2
2
1
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
1
1
2
0
2
1
0
0
1
0
2
1
1
0
0
0
0
1
0
0
0
2
2
1
1
2
0
0
0
0
0
2
2
0
0
1
0
2
2
0
1
1
1
0
1
0
2
1
0
0
2
2
1
0
2
0
0
0
0
0
1
2
0
2
1
2
2
2
1
2
2
1
1
1
0
1
0
2
2
1
1
0
2
1
0
0
0
0
2
1
0
1
0
1
0
1
2
0
1
0
1
0
2
0
2
0
5
0
1
0
1
0
1
0
0
0
1
0
0
1
1
0
0
2
1
0
1
1
0
2
0
0
1
2
0
0
0
0
1
1
2
1
2
2
0
1
1
4
1
0
1
0
0
0
1
1
0
0
0
2
0
1
0
2
0
0
2
1
1
0
1
1
1
2
0
1
0
0
0
0
1
1
2
1
0
2
1
1
2
1
0
0
0
1
0
0
0
0
0
1
2
1
0
0
2
0
1
0
0
2
0
0
0
2
1
0
0
0
0
1
0
2
1
2
0
0
0
0
1
1
2
0
1
2
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
2
1
1
0
1
0
0
1
0
1
0
0
0
1
0
1
0
1
0
2
1
3
1
1
0
2
0
0
2
2
1
2
0
2
0
1
2
0
1
0
2
2
0
0
0
1
2
0
1
1
2
1
0
3
1
0
1
0
2
0
1
0
2
0
0
0
0
2
2
1
0
0
2
1
2
1
1
0
1
1
1
1
0
1
2
0
0
0
1
1
2
0
1
1
1
1
1
0
1
0
0
0
2
0
1
0
0
1
0
2
1
0
0
0
0
0
0
1
0
1
2
0
1
1
0
0
0
1
1
0
1
1
2
0
0
0
0
3
0
6
1
1
3
1
0
1
0
0
0
1
1
0
1
0
0
2
0
0
0
1
2
1
2
2
0
3
0
1
0
1
0
0
0
0
1
2
0
0
0
0
1
0
1
0
2
0
2
0
0
0
2
1
0
0
0
2
0
2
0
0
0
2
0
2
1
0
3
1
0
2
0
0
1
7
0
2
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
2
0
0
0
1
1
2
0
0
0
0
1
0
0
7
0
1
0
2
0
0
0
3
1
2
0
2
0
3
0
0
0
0
0
1
2
0
1
0
2
2
1
0
0
2
1
1
0
0
0
1
2
0
0
2
0
1
3
0
0
0
4
0
3
0
0
1
1
0
0
1
1
2
0
1
1
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
2
1
0
0
0
0
2
2
1
2
0
2
1
0
0
0
0
2
1
1
2
0
1
2
3
1
1
2
1
0
0
2
2
0
0
0
1
2
0
0
0
1
0
1
2
2
1
2
2
0
2
0
1
0
0
1
1
1
0
2
0
0
1
2
0
1
1
0
0
1
0
0
0
2
1
0
1
1
0
2
0
2
2
2
0
0
2
0
1
1
0
0
0
2
1
1
1
0
0
1
0
0
0
1
0
1
1
0
1
1
0
1
2
0
1
0
2
2
0
0
1
2
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
2
2
2
0
1
1
0
0
0
0
1
0
2
1
1
0
1
0
2
0
1
1
0
0
0
2
1
0
1
2
0
0
2
1
2
0
2
0
0
2
0
1
0
0
0
0
0
0
1
1
2
4
0
2
0
1
2
0
1
0
0
0
1
0
2
1
0
0
0
0
0
0
2
0
0
2
0
2
1
0
2
2
2
2
2
1
2
0
0
2
1
1
0
0
0
0
1
2
0
2
0
0
0
3
1
2
1
1
0
1
1
2
1
1
0
1
0
0
0
0
0
1
3
0
0
0
0
1
1
1
0
2
1
0
1
0
1
0
0
2
0
0
0
1
1
0
3
2
1
1
0
0
2
0
0
1
0
0
2
1
2
0
0
0
2
1
0
2
1
1
3
0
0
1
2
0
0
3
2
0
1
0
1
0
0
0
0
0
2
0
1
1
0
0
3
0
2
0
1
2
0
2
0
0
0
1
0
0
0
1
0
1
1
1
2
2
0
0
0
2
0
1
2
0
0
1
1
1
1
2
1
0
0
0
0
2
8
0
0
0
1
2
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
2
2
0
0
0
2
0
1
1
2
2
0
0
2
1
0
1
1
0
0
0
0
1
0
1
1
0
0
0
1
1
0
2
1
0
1
0
1
1
2
0
0
1
1
0
0
2
1
0
0
0
0
2
2
0
2
2
0
2
0
0
2
1
0
1
0
1
2
0
0
0
0
1
1
1
1
0
0
2
2
1
1
2
0
0
1
0
2
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
1
3
0
5
1
0
0
5
0
0
0
0
1
1
0
1
2
0
1
0
1
2
0
1
0
0
2
0
0
2
0
2
0
0
0
2
0
2
1
0
2
2
0
0
1
0
0
0
2
0
0
0
0
1
0
2
0
1
1
2
0
2
1
1
0
0
1
1
0
1
2
1
1
1
2
0
0
1
1
0
0
0
1
0
1
4
2
0
1
0
1
0
0
3
2
1
2
0
0
0
0
0
0
0
2
0
0
2
1
1
0
2
2
2
0
1
0
0
2
3
1
2
1
1
0
0
0
1
2
0
2
0
0
0
2
2
0
0
1
0
0
0
2
0
2
1
1
1
0
0
0
1
1
0
3
0
0
1
2
0
0
2
0
1
1
0
1
2
0
2
2
2
1
1
2
0
0
1
0
0
2
0
1
0
0
0
1
0
2
0
0
0
0
1
0
2
0
1
0
0
1
0
0
1
1
0
2
1
0
0
2
0
1
1
1
1
1
0
1
1
0
0
2
1
0
2
1
0
2
3
2
0
0
0
0
2
1
0
0
1
1
0
0
1
2
0
1
0
0
1
1
0
2
0
2
0
1
1
0
2
1
1
0
0
0
0
0
0
0
0
2
2
0
1
0
0
1
0
2
2
1
0
0
0
0
1
2
2
1
0
0
2
2
0
0
1
1
0
2
0
0
3
0
2
1
1
2
0
0
0
0
2
1
2
0
2
0
0
2
1
0
0
0
1
1
0
0
1
2
0
0
0
2
1
0
1
0
0
1
2
0
3
1
0
2
0
1
0
0
0
0
0
2
0
0
1
1
0
0
0
0
2
0
1
2
2
0
2
1
0
4
1
0
1
0
0
1
1
1
1
0
1
2
0
2
0
0
0
1
1
2
0
0
0
0
1
0
0
0
2
0
1
0
0
0
1
0
0
2
1
0
2
0
1
2
0
1
0
2
0
1
2
0
1
0
1
2
2
1
1
2
2
1
0
0
0
1
2
0
0
1
0
1
2
1
2
1
3
1
0
0
0
3
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
2
0
1
1
1
2
2
1
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
2
0
0
1
0
0
0
0
2
0
2
2
3
1
0
0
3
0
1
0
0
0
2
3
1
1
1
2
0
0
0
1
2
0
0
1
2
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
2
1
2
1
1
0
2
1
0
0
2
3
0
0
0
0
2
0
1
0
0
0
1
1
2
0
0
0
0
1
2
0
2
2
2
1
2
0
0
0
0
0
0
0
1
0
2
1
1
0
0
1
1
0
1
2
1
0
0
2
0
2
3
0
2
2
1
2
2
1
0
2
2
0
0
1
0
0
2
2
0
1
1
1
0
0
0
0
0
2
0
1
0
1
1
0
1
1
1
0
0
0
0
1
0
1
1
2
0
0
0
2
0
1
2
1
0
1
2
0
0
0
1
0
2
0
4
0
0
0
2
0
1
2
1
0
0
1
1
0
1
1
1
1
0
1
3
1
0
1
0
1
1
0
0
1
2
1
0
0
1
0
0
1
1
1
1
0
2
0
0
0
0
0
2
1
0
1
0
0
1
0
2
1
1
0
0
1
0
0
1
1
0
0
0
0
2
0
0
1
2
1
1
0
0
0
1
0
1
0
0
2
2
0
0
0
1
1
0
0
2
2
0
2
0
4
1
1
0
1
1
0
2
2
1
2
0
0
1
1
1
2
2
0
2
1
1
2
2
1
0
2
0
1
0
0
1
1
2
1
1
1
2
1
1
1
0
2
0
1
0
0
1
3
1
0
0
0
1
0
0
0
1
0
1
0
0
2
3
0
2
3
0
2
2
0
1
0
2
1
0
0
0
0
0
1
1
1
0
0
1
0
0
2
2
0
0
2
1
2
1
0
0
0
0
0
0
1
0
4
0
0
0
0
1
0
0
1
2
1
0
0
2
1
2
0
0
0
1
2
1
1
0
0
1
0
0
0
3
0
0
2
0
0
1
0
1
0
1
0
0
1
0
0
0
0
2
0
1
0
0
2
0
0
1
1
2
1
1
0
2
0
0
0
0
0
1
1
1
2
0
0
0
0
0
0
0
0
0
0
1
0
1
2
1
1
0
0
0
0
2
1
0
0
3
0
0
1
2
2
0
0
1
1
0
0
0
0
1
1
1
1
0
0
0
2
1
1
2
0
0
0
3
2
0
2
0
1
1
1
0
1
0
0
0
0
1
0
0
1
0
2
2
0
0
0
0
2
1
0
1
0
0
2
0
0
0
0
2
2
1
0
0
0
2
2
0
2
1
0
1
1
0
2
0
0
0
0
0
0
2
0
1
0
2
0
0
0
1
0
2
0
0
2
2
1
2
0
0
1
1
1
1
1
2
1
2
0
0
0
0
0
0
2
1
1
0
0
0
0
0
1
1
0
2
2
1
0
0
1
0
0
0
0
0
2
1
1
0
0
2
0
2
0
0
0
0
0
1
0
1
1
0
1
1
2
2
0
1
0
0
1
1
1
0
0
1
0
1
0
0
0
0
0
1
1
1
0
0
1
2
0
0
2
0
0
0
0
0
1
1
1
2
0
0
1
1
2
0
2
1
1
1
0
1
1
0
1
0
1
2
0
1
2
1
0
1
1
0
1
0
0
2
0
1
0
1
0
0
0
0
1
1
2
0
0
0
1
0
0
0
0
2
2
1
0
0
0
0
0
0
1
1
1
0
2
0
0
0
0
2
3
0
0
2
0
0
0
1
0
2
1
0
1
1
2
1
0
2
0
0
2
1
2
0
1
2
0
2
1
2
0
1
2
1
0
0
0
1
0
0
1
0
0
1
2
0
0
0
1
2
1
0
1
0
0
0
2
2
0
1
1
0
1
0
0
0
2
0
1
1
3
2
1
0
0
2
0
0
0
1
3
0
0
2
1
2
0
2
1
0
0
2
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
1
0
0
2
0
1
0
0
2
0
0
2
2
0
0
0
0
1
0
1
0
1
0
1
2
2
1
0
0
2
0
1
1
0
2
1
1
0
1
0
0
0
1
0
2
1
0
1
1
0
1
1
2
0
0
1
1
0
2
0
0
1
0
0
2
1
2
1
0
2
1
0
1
0
2
1
1
0
1
0
1
0
0
0
2
0
2
2
0
0
0
0
1
1
1
2
1
1
3
0
1
0
0
0
1
1
1
1
0
1
1
2
0
0
0
1
0
0
2
0
0
0
0
1
0
0
1
0
0
1
2
0
1
1
0
0
1
0
1
1
1
1
0
1
2
0
1
1
1
1
1
2
1
2
0
2
0
0
2
0
0
3
0
0
1
1
0
2
0
1
0
1
0
0
0
1
1
1
1
0
1
2
3
1
1
0
0
1
0
2
0
3
1
0
0
2
0
0
2
1
0
0
1
0
2
1
1
0
2
1
0
0
0
2
0
2
0
1
0
2
0
0
1
1
1
1
0
2
0
1
2
0
1
1
1
0
1
0
1
2
2
1
1
2
0
1
0
1
0
1
2
1
0
0
1
3
1
0
0
0
0
0
2
0
0
1
0
1
1
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
1
0
0
0
2
2
0
1
1
2
1
1
2
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
2
2
4
0
0
1
0
0
0
1
0
1
1
0
0
2
0
1
0
1
0
0
0
1
0
0
2
2
1
2
1
1
0
2
0
2
1
0
0
1
1
0
0
1
0
0
1
2
2
1
2
2
1
0
1
0
1
0
0
0
3
1
0
0
1
2
0
1
1
0
0
0
0
1
0
3
1
0
3
0
0
1
2
1
0
1
0
2
0
2
0
0
0
0
1
2
1
2
1
1
0
2
2
1
0
2
0
0
2
0
0
1
0
2
0
0
1
1
0
2
1
0
0
1
1
0
1
1
0
1
0
0
1
1
0
0
2
2
5
0
0
1
2
1
1
0
0
1
0
0
0
2
1
1
0
2
0
0
0
2
0
2
1
1
0
1
0
0
0
2
0
0
0
1
1
0
0
0
2
0
0
3
2
2
1
1
0
1
2
2
2
0
2
0
1
1
0
1
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
1
0
1
2
0
2
0
0
0
2
1
1
1
0
0
1
1
1
1
0
2
0
0
1
0
0
1
0
0
1
1
0
1
0
2
0
1
0
0
0
2
0
1
0
0
0
0
1
0
2
0
0
0
1
2
0
0
0
0
0
0
1
2
2
0
3
0
1
2
2
1
1
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
1
0
2
0
2
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
2
2
1
1
0
1
1
0
2
1
0
3
2
0
0
0
0
0
0
2
0
0
1
2
0
0
1
0
0
2
0
3
2
0
3
0
0
0
1
0
1
0
0
0
1
1
0
1
0
0
1
0
2
0
0
1
1
0
1
0
0
0
1
0
3
1
0
0
1
0
0
1
0
2
1
0
1
2
0
0
2
0
1
1
0
2
2
0
1
2
0
1
1
0
2
1
0
2
3
2
2
0
0
2
1
1
0
1
0
2
0
0
2
2
2
1
1
0
3
2
0
0
0
0
1
0
2
0
1
0
2
0
2
1
0
2
0
0
2
0
0
0
0
1
2
0
1
0
0
0
2
1
2
0
0
0
0
0
0
1
0
1
2
4
0
1
2
1
0
1
0
0
0
0
0
1
0
2
0
0
1
0
1
0
2
1
2
2
0
0
2
0
1
1
0
3
0
1
1
0
0
2
1
1
1
2
0
0
2
0
0
1
0
1
0
2
0
2
1
0
1
0
1
1
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
1
2
1
0
2
0
0
1
2
1
0
0
0
0
1
1
1
1
0
0
1
1
0
1
0
0
0
2
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
1
1
0
0
0
0
1
2
1
1
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
2
2
0
0
1
1
1
0
2
2
0
1
0
1
2
0
1
0
1
0
1
0
0
0
0
0
2
0
1
2
2
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
1
2
0
0
1
1
1
0
1
0
2
2
0
2
2
1
0
1
0
0
0
2
0
0
1
1
0
0
0
1
2
2
0
0
1
2
2
2
0
0
1
1
2
2
0
0
0
2
2
1
0
0
0
1
0
0
0
1
0
0
2
1
1
2
2
0
1
0
0
3
2
2
1
0
0
0
0
2
1
0
2
0
1
0
0
0
0
1
0
0
2
0
2
1
2
2
1
1
2
1
0
1
2
0
1
2
2
1
0
0
2
2
0
0
2
3
0
0
2
1
2
0
2
1
0
0
1
0
0
0
0
2
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
2
0
0
1
1
0
1
3
1
0
1
0
0
0
1
0
2
0
0
0
0
0
2
1
0
0
2
1
2
0
0
0
0
1
0
1
1
0
0
0
0
2
0
2
1
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
2
1
2
0
2
2
2
0
1
0
0
1
0
0
0
1
0
1
2
0
1
0
2
0
0
1
1
0
3
1
0
0
2
2
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
2
1
0
2
0
0
2
0
0
0
2
2
1
2
1
2
1
1
2
0
1
2
0
1
2
1
1
2
1
0
0
2
0
0
0
0
2
1
0
0
1
1
0
2
3
0
0
1
2
0
1
1
1
0
1
1
1
0
2
0
2
1
0
0
0
3
2
0
1
0
0
2
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
1
1
0
1
0
1
0
1
2
1
1
2
0
0
0
1
0
0
2
0
1
2
1
1
1
0
2
0
1
1
0
1
1
0
0
1
0
2
2
1
0
1
1
1
0
0
0
0
2
0
0
0
0
1
1
1
0
0
2
1
0
2
0
0
0
0
1
4
0
0
0
0
3
1
0
1
1
0
0
0
1
1
2
0
0
0
0
2
0
2
1
1
0
0
1
1
0
2
1
1
1
0
2
1
0
2
0
1
0
0
1
2
2
0
0
0
2
0
0
0
1
2
0
2
2
0
0
1
0
0
0
0
0
1
2
1
1
0
1
0
0
0
2
2
2
0
0
0
0
0
1
0
1
0
2
1
0
0
1
2
1
1
0
1
0
0
0
3
1
2
1
0
0
2
2
0
0
0
0
1
1
1
2
0
0
1
0
1
0
0
1
0
1
0
1
0
1
1
1
0
0
0
2
1
2
2
0
1
0
2
0
1
1
0
0
0
0
2
1
1
2
2
0
0
3
0
1
2
0
0
2
0
2
0
0
0
0
1
1
2
0
0
0
2
2
0
2
1
2
0
0
0
1
3
0
1
1
0
2
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
2
1
1
1
0
2
2
0
0
0
0
1
0
0
0
1
2
1
1
2
1
1
0
2
0
2
2
1
0
0
0
0
1
1
0
1
0
1
1
2
1
0
2
1
0
1
0
0
1
1
1
1
0
2
1
0
0
1
2
2
0
1
0
0
2
0
0
1
1
1
0
2
1
0
0
2
0
0
0
0
2
0
1
2
1
1
0
1
2
1
2
0
0
0
2
1
0
1
0
0
1
0
2
1
1
2
1
2
2
1
0
1
1
0
2
0
0
1
8
0
0
1
4
0
0
1
0
0
2
0
0
2
1
2
1
0
1
0
0
0
2
0
0
0
1
0
2
0
0
0
1
2
1
1
2
0
0
0
2
0
1
1
1
0
2
0
0
2
0
2
1
0
0
1
0
0
0
1
1
0
1
0
0
2
0
2
0
0
1
2
0
1
2
1
1
0
0
2
1
0
0
2
0
0
0
0
2
1
2
0
2
0
1
0
1
0
0
0
2
2
0
1
1
1
0
1
0
0
1
1
0
1
0
0
1
0
0
1
2
0
2
1
0
0
0
0
0
2
0
4
2
2
0
0
1
0
0
2
2
0
1
0
1
0
2
0
0
2
4
0
1
0
2
0
1
0
0
1
0
2
1
0
0
0
3
0
0
0
2
1
0
0
0
0
0
1
2
1
0
0
3
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
1
2
2
1
0
0
0
1
1
0
1
1
1
0
1
0
0
1
0
0
0
4
2
0
1
1
1
1
0
2
2
0
0
2
0
0
1
0
0
2
0
0
0
0
1
1
0
2
0
2
1
0
2
0
0
0
2
2
2
1
1
0
0
2
2
0
0
2
0
0
2
0
0
0
0
0
1
2
1
1
0
0
1
1
2
0
1
1
0
0
1
0
0
2
3
0
1
1
0
2
0
1
1
0
1
1
1
1
0
0
0
0
1
0
1
0
2
0
1
0
2
0
0
0
0
0
0
2
1
0
0
0
1
1
1
0
1
0
2
0
1
0
1
1
0
0
0
0
3
0
0
0
0
0
0
0
1
2
0
0
0
1
2
2
1
0
0
0
0
0
2
1
0
0
1
2
0
0
1
1
2
2
2
0
1
0
0
0
2
0
2
2
0
0
2
2
1
1
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
2
1
1
1
0
0
0
2
0
0
0
0
0
3
0
1
2
1
1
1
0
2
1
1
2
2
2
0
0
0
2
0
1
0
1
0
1
1
0
0
0
1
0
2
1
1
0
2
0
1
0
2
1
0
0
2
0
1
2
0
0
1
1
0
2
0
0
1
0
2
2
0
2
0
1
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
2
1
2
0
2
0
1
0
0
6
0
0
1
0
1
0
2
0
0
0
0
1
1
0
0
2
0
1
0
0
2
0
0
2
0
0
1
1
2
0
1
2
2
1
0
2
0
0
0
2
0
0
0
0
2
0
0
0
1
0
1
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
1
2
1
1
1
1
1
0
2
2
0
0
0
2
0
0
1
1
0
0
0
0
2
1
2
0
1
0
0
0
0
1
1
0
2
1
0
0
2
1
0
1
2
2
1
1
0
1
1
2
2
1
0
1
1
0
0
0
0
0
0
0
0
0
0
2
1
0
2
2
2
0
0
0
1
0
0
2
1
1
0
1
0
1
1
1
0
0
1
1
2
2
2
1
1
3
0
0
1
2
1
4
0
2
2
0
0
2
1
0
0
2
0
0
2
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
2
0
1
1
0
1
0
2
0
0
0
1
2
0
1
0
0
0
0
1
2
1
1
1
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
1
2
2
0
0
1
1
0
2
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
3
2
0
0
2
3
1
0
2
2
0
1
0
1
0
2
0
0
0
0
1
0
2
1
2
1
2
0
0
0
0
2
0
0
0
2
0
0
1
0
2
0
2
0
0
0
1
1
0
1
0
0
1
0
2
2
0
0
1
2
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
1
0
2
0
1
0
0
1
1
0
0
2
1
0
2
0
2
2
1
0
0
0
0
1
2
0
0
0
2
1
2
0
0
0
0
0
2
1
2
0
2
2
2
1
0
2
0
0
1
0
0
2
1
0
0
0
2
2
0
1
0
2
2
2
0
1
2
1
1
1
1
0
0
1
1
0
2
2
1
2
1
0
0
0
1
1
1
2
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
2
1
2
0
2
0
0
1
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
1
0
0
2
2
1
1
1
0
3
0
1
1
0
2
1
2
2
0
1
0
0
1
0
0
2
2
1
0
0
0
1
2
1
2
1
0
0
3
0
1
1
2
0
0
0
0
1
0
0
0
2
0
1
0
0
0
1
0
0
1
1
0
2
0
0
0
0
0
1
0
1
1
2
0
0
2
2
1
0
1
1
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
1
2
2
2
1
2
0
0
1
2
0
1
0
1
0
2
2
0
1
0
0
0
1
1
0
0
1
1
0
0
2
0
0
1
2
1
1
1
0
2
0
0
0
1
0
2
0
0
0
1
3
2
0
0
2
0
2
0
1
1
0
0
2
0
0
0
0
2
0
1
1
0
1
0
2
2
1
0
0
0
1
2
2
1
1
0
0
0
2
2
2
0
0
0
0
2
0
1
0
1
2
0
1
2
1
0
0
0
1
1
2
0
0
0
1
0
1
1
0
2
1
0
0
0
1
1
0
0
0
0
0
0
2
1
0
0
2
2
2
0
2
0
2
0
1
1
3
0
1
1
0
0
2
2
2
0
1
1
1
2
0
0
1
0
0
2
1
2
1
2
2
0
0
1
1
0
0
1
1
0
0
0
1
0
0
0
2
0
0
2
1
2
0
0
2
0
0
1
1
0
2
2
1
0
2
0
0
2
0
0
4
2
0
1
0
2
0
0
1
1
2
0
2
0
1
1
2
2
0
1
0
0
1
2
1
1
1
2
0
0
0
1
1
0
2
1
0
0
0
0
0
0
1
5
2
0
1
0
0
0
1
1
0
0
2
0
1
1
1
1
0
0
2
1
1
0
1
1
0
2
0
1
0
0
0
0
0
2
1
1
1
2
0
1
2
1
0
0
0
0
2
1
0
2
0
1
2
1
2
1
0
2
0
1
1
0
1
0
1
1
0
0
1
0
0
0
0
2
0
0
1
2
1
2
0
0
0
0
1
2
3
1
0
2
0
0
2
1
0
2
0
0
0
0
0
0
0
1
1
2
0
1
3
0
2
2
1
2
1
2
0
0
0
0
1
2
0
1
0
2
1
2
1
2
0
2
0
0
2
1
1
0
0
0
0
2
0
0
2
1
2
0
1
0
0
0
2
0
1
1
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
1
2
1
0
3
0
1
1
1
2
0
1
1
0
2
2
0
0
1
1
0
1
0
1
0
1
2
0
2
0
1
2
0
1
0
1
0
0
0
1
0
2
1
0
0
1
0
1
0
1
1
0
0
1
1
0
0
2
0
2
1
0
0
0
1
0
1
2
1
2
1
2
1
2
0
0
0
2
0
1
0
0
2
2
0
1
2
0
2
1
1
0
1
1
0
1
0
0
5
1
0
2
2
0
2
2
0
0
1
0
0
1
0
2
0
0
0
2
1
2
0
1
1
1
0
1
0
0
1
1
1
2
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
2
0
1
2
2
0
0
0
0
1
2
0
0
1
1
2
0
0
0
0
2
0
0
1
0
1
0
0
0
1
0
0
1
0
1
0
0
1
0
1
8
2
2
2
1
0
1
1
1
0
2
2
0
0
1
1
1
0
4
1
0
0
0
0
0
0
0
2
3
0
2
0
0
1
1
1
1
1
1
0
1
1
0
1
2
1
0
1
0
1
0
0
1
0
2
1
0
1
0
0
0
1
1
0
0
0
2
0
2
0
0
0
0
0
0
2
1
0
2
0
0
1
1
0
0
1
0
1
1
0
0
2
0
0
0
2
0
2
1
0
0
0
2
2
0
0
0
2
2
0
2
0
1
0
1
0
2
0
5
0
0
1
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
2
0
1
0
2
1
2
1
2
0
1
0
1
2
0
1
1
3
0
0
0
0
2
1
1
1
1
1
0
0
2
2
1
2
1
1
2
0
0
0
2
1
2
1
0
2
2
2
4
1
1
0
0
0
1
1
0
1
0
0
3
2
1
0
0
0
0
0
2
0
0
1
0
2
0
1
1
1
0
0
0
1
1
1
0
1
0
2
0
0
0
3
0
2
0
0
2
2
0
0
0
1
0
1
0
0
2
1
0
0
0
1
0
0
2
0
1
0
0
0
1
1
1
0
2
1
1
0
1
2
0
2
0
0
1
1
4
2
0
0
0
0
0
1
2
1
2
1
0
0
0
0
2
0
2
0
0
1
2
1
0
0
0
1
0
0
2
0
0
0
0
0
1
1
2
0
2
0
0
1
0
0
2
1
0
0
0
0
1
2
1
0
0
3
1
0
1
1
0
0
2
1
1
1
0
1
2
0
1
1
0
0
0
0
2
1
3
0
0
0
1
2
1
1
0
1
1
2
0
2
2
0
0
0
0
1
1
0
0
1
1
0
0
1
0
1
1
2
0
2
0
1
1
2
0
0
0
0
0
0
2
2
2
0
0
0
0
1
1
0
1
0
0
0
0
0
2
0
0
0
2
0
1
0
0
1
0
0
0
1
0
0
1
0
2
1
2
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
2
1
2
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
1
1
0
1
0
0
0
1
2
0
1
0
0
2
1
1
0
0
2
2
0
1
0
0
2
0
0
0
1
0
2
0
1
1
0
0
0
1
0
3
0
1
0
0
0
1
1
0
0
2
2
3
1
2
0
0
1
0
0
0
2
1
2
0
2
2
2
0
3
0
0
2
0
0
0
1
2
1
2
1
1
1
2
2
2
0
1
0
3
2
0
0
0
1
1
1
2
1
0
2
2
0
1
1
1
1
2
1
12
0
2
1
0
0
1
0
0
0
0
2
0
2
1
0
0
0
2
0
1
1
0
0
0
1
0
2
0
2
0
0
0
0
0
1
1
1
0
0
2
0
2
0
2
0
2
0
0
0
0
0
2
1
0
1
2
0
0
1
0
0
0
2
0
0
0
1
0
2
0
0
0
0
1
0
0
1
1
0
2
0
0
0
0
1
0
0
1
0
0
0
0
1
2
0
0
1
0
1
1
2
0
0
2
0
0
0
0
1
0
0
1
0
1
0
2
1
2
0
1
0
1
0
1
0
0
1
0
2
1
1
0
2
0
0
3
0
0
1
1
1
1
1
0
0
0
0
0
0
0
1
0
2
1
2
1
0
0
0
1
3
0
0
0
1
0
0
0
0
1
1
0
4
0
2
0
0
2
0
0
0
1
0
2
1
0
1
0
0
0
2
0
0
0
3
0
0
0
0
1
1
1
2
0
0
0
1
2
2
0
1
1
0
0
0
1
1
2
0
2
0
1
0
0
2
1
2
0
0
0
0
1
0
0
2
1
0
0
1
1
0
1
0
2
1
0
0
1
0
0
0
0
2
3
2
0
0
0
0
2
1
1
0
2
0
1
2
0
1
0
0
0
2
0
0
2
0
0
2
1
0
2
1
1
0
1
0
0
1
1
1
1
1
0
1
1
1
1
2
0
2
1
0
0
1
1
0
2
0
0
1
1
2
0
2
2
2
3
0
1
1
0
1
0
0
2
1
1
2
0
1
0
0
2
0
2
0
0
2
2
0
2
1
0
2
1
2
1
0
2
2
2
0
0
2
1
1
1
0
0
2
0
1
0
2
2
0
1
2
3
0
0
0
0
0
0
0
0
3
0
0
0
1
0
1
1
1
1
1
1
0
0
2
1
0
3
0
2
0
0
1
0
1
0
0
2
0
1
0
1
1
0
0
0
0
0
0
2
0
2
3
1
2
1
1
0
0
1
0
1
1
0
0
1
1
0
0
2
1
0
1
0
0
0
1
0
5
2
2
2
0
0
0
0
1
0
0
0
2
0
1
2
0
1
1
1
0
2
0
0
0
1
2
1
0
1
2
0
1
0
0
1
1
0
2
1
2
2
2
1
1
0
0
2
1
0
1
0
0
1
0
0
0
0
0
0
0
1
1
1
0
2
2
2
2
0
1
0
1
1
1
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
1
0
2
1
0
0
1
1
0
0
2
0
0
2
2
0
0
0
2
0
2
0
1
0
1
1
0
0
0
1
0
1
0
2
0
0
0
1
0
0
0
1
2
1
2
1
0
1
1
2
0
0
0
0
2
1
1
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
1
0
0
0
1
1
1
0
1
0
0
0
0
0
0
2
0
1
0
0
0
1
1
0
1
1
2
4
0
0
0
0
0
0
2
1
3
0
0
2
0
1
2
1
0
0
0
1
1
0
0
1
1
0
3
0
1
1
0
0
1
1
5
2
0
2
0
2
0
2
0
2
0
0
1
0
1
0
1
1
2
0
0
1
0
1
0
0
2
0
1
0
0
0
0
0
7
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
2
2
1
2
1
0
1
0
0
0
0
0
1
0
0
0
2
0
3
2
1
0
2
0
2
2
0
2
0
0
2
0
2
2
0
2
0
3
0
0
0
2
1
0
0
0
2
2
0
1
0
2
1
1
1
1
0
0
2
0
0
1
0
0
2
0
0
0
0
2
0
0
0
2
2
0
1
1
0
0
0
0
0
1
0
1
0
1
2
0
0
1
2
1
1
1
1
1
1
0
0
2
3
0
1
1
0
3
1
0
0
1
2
1
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
2
0
0
0
2
0
0
0
1
1
2
1
1
1
0
1
1
0
1
1
0
0
1
0
0
0
0
2
2
0
1
1
2
0
1
0
0
1
2
1
1
1
2
2
2
1
0
0
0
0
2
2
2
0
0
0
1
2
0
2
2
1
1
1
0
1
1
0
0
0
1
1
0
0
0
0
0
0
2
3
1
1
1
0
1
1
2
0
0
0
2
1
0
0
0
2
0
0
1
0
0
2
1
3
0
1
0
2
0
2
2
1
0
2
0
2
0
1
0
1
2
1
0
0
1
1
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
1
0
1
0
0
1
1
1
0
1
0
0
0
1
0
1
1
0
1
2
0
0
0
3
0
2
0
1
1
0
0
0
0
2
0
0
1
1
0
0
0
0
2
0
0
0
2
0
0
1
1
0
0
0
0
2
1
2
0
2
1
1
0
0
0
1
3
1
0
0
2
1
0
0
0
1
0
2
0
0
0
0
2
0
2
0
2
0
0
0
1
0
0
1
0
0
2
0
1
1
0
0
1
1
1
1
0
0
0
2
1
0
1
0
2
0
0
1
0
0
1
1
2
0
1
1
2
1
0
0
1
1
0
0
1
0
0
0
0
2
0
1
7
2
0
1
1
0
0
1
2
0
0
0
1
0
0
1
0
1
1
1
0
2
1
0
0
0
1
0
0
0
1
0
1
2
0
0
0
2
1
0
1
0
1
1
0
2
0
0
1
1
0
1
1
0
0
0
0
2
1
0
1
2
0
0
1
1
1
0
2
1
2
2
0
0
0
0
2
0
0
2
1
2
0
1
0
0
0
1
1
0
0
1
3
1
0
0
2
1
1
0
2
2
0
0
2
0
1
1
0
4
0
0
1
0
1
0
0
1
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
1
2
1
1
0
0
2
0
0
1
1
0
2
0
2
0
2
2
1
1
1
2
1
3
0
0
1
0
2
0
0
0
4
0
1
2
1
1
0
0
0
0
0
2
0
1
1
1
0
1
1
0
1
0
2
0
1
0
0
0
1
0
0
3
1
2
2
1
1
1
0
0
1
0
0
2
2
2
1
0
0
0
1
0
1
0
0
2
1
2
0
2
1
1
0
1
0
0
2
0
1
0
0
1
1
1
2
2
0
1
2
0
0
1
1
1
2
2
1
0
3
2
1
2
0
1
0
0
0
2
0
1
2
1
2
1
1
0
2
0
1
1
1
0
0
0
0
1
1
1
0
0
2
0
2
0
1
0
0
0
1
0
0
0
1
1
5
1
1
0
0
1
2
0
0
0
0
3
0
1
1
0
0
0
2
0
2
0
0
0
0
1
0
0
0
1
0
2
1
0
2
0
1
0
0
0
2
1
0
0
0
0
2
1
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
1
1
1
0
2
1
2
1
1
2
2
0
0
0
1
0
1
1
2
2
0
0
0
0
1
2
0
0
1
1
0
0
1
2
0
0
0
0
0
2
1
1
0
2
1
0
2
2
0
0
1
1
2
0
0
1
0
0
2
2
1
0
1
2
2
1
0
2
0
1
1
0
1
0
2
1
0
0
1
2
0
1
0
0
2
0
0
2
0
1
2
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
2
0
0
0
0
2
0
0
2
1
1
0
0
0
2
0
1
0
2
2
2
1
1
2
1
0
1
1
0
1
0
0
2
0
0
0
2
0
0
0
0
1
0
6
2
2
0
1
0
0
0
0
1
0
0
2
1
0
0
2
0
0
2
0
1
0
1
0
1
0
0
0
1
0
0
2
2
0
0
0
0
1
0
0
1
1
0
2
3
0
2
2
0
0
0
0
1
0
0
0
0
1
1
2
0
1
2
2
1
1
0
0
0
1
1
0
0
0
0
0
1
0
2
2
1
0
2
2
0
2
0
0
0
0
2
1
1
1
1
0
1
1
2
2
0
0
0
0
2
0
0
1
0
0
0
1
0
1
2
0
0
1
1
0
1
2
0
1
0
0
1
0
0
1
1
2
1
2
3
2
0
2
0
1
0
0
1
2
2
2
0
1
0
1
1
0
1
1
0
0
0
0
0
2
1
0
0
0
2
2
1
0
1
0
0
2
0
0
0
1
0
0
1
2
0
0
0
1
0
2
0
3
0
2
2
2
0
1
0
1
1
2
1
2
0
0
1
2
0
2
0
2
0
2
2
0
2
0
1
0
1
0
1
0
0
1
2
2
0
0
2
0
0
2
1
0
1
0
0
0
0
2
1
4
1
2
1
1
2
0
1
2
0
0
0
1
0
0
2
0
1
0
1
2
0
0
0
0
0
0
2
1
0
1
0
1
0
0
0
0
2
0
2
3
2
2
1
0
0
1
0
0
1
0
0
2
1
0
0
2
0
0
0
1
2
0
2
1
0
1
0
0
0
0
0
1
0
1
0
1
1
2
1
0
0
0
0
0
0
3
2
1
0
1
0
1
2
0
2
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
1
1
0
2
0
0
2
1
3
2
0
0
0
2
2
1
1
2
0
1
2
0
0
0
1
2
1
0
0
1
2
1
0
1
0
1
0
1
0
0
1
0
0
1
1
0
0
0
1
0
1
0
0
2
0
1
2
0
0
0
0
2
0
1
2
0
1
1
3
0
0
0
0
0
1
1
0
0
0
1
0
1
2
1
0
1
2
0
0
1
1
0
1
2
0
0
2
0
0
0
0
1
2
0
0
0
1
1
0
1
2
1
1
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
1
0
2
1
0
0
2
0
0
2
1
0
0
0
1
0
2
0
0
1
1
2
2
0
0
0
0
1
0
1
0
0
2
1
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
2
1
2
1
1
0
0
1
0
0
0
0
1
1
0
2
0
0
0
1
1
0
1
0
0
2
0
0
0
0
0
1
0
3
2
1
0
0
2
2
2
0
0
0
0
0
2
0
1
1
2
0
0
1
1
0
1
0
1
0
0
0
1
2
0
0
0
0
1
0
0
2
2
0
0
2
0
0
2
2
0
0
2
0
0
0
2
0
1
0
1
0
0
0
1
1
1
2
1
0
2
0
0
2
1
1
0
0
1
0
1
2
0
0
0
0
1
2
1
1
0
2
1
0
0
0
1
2
1
2
0
1
0
1
0
1
0
0
2
3
1
0
2
0
2
0
2
1
0
1
0
0
1
4
1
2
0
0
0
0
1
2
0
1
2
1
0
3
1
0
0
2
1
1
0
0
0
1
1
2
0
1
0
0
0
3
0
0
0
2
0
1
2
1
0
2
1
1
0
0
0
0
0
0
1
0
2
1
0
0
2
2
1
0
2
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
1
3
1
1
0
0
0
1
0
0
1
0
1
0
0
2
2
1
0
1
1
1
2
1
2
2
3
1
1
0
0
0
1
0
1
2
1
1
0
1
2
0
1
0
2
0
0
0
1
1
0
1
1
0
1
0
2
2
0
2
0
0
0
0
0
3
1
1
0
0
1
1
1
2
2
1
2
1
0
0
0
1
0
1
2
2
0
0
0
4
1
0
2
2
1
1
0
0
1
1
1
0
0
2
1
1
2
1
1
0
0
0
1
0
0
2
0
1
1
0
0
0
2
0
1
2
0
2
1
1
1
2
1
2
1
2
0
0
0
1
2
0
1
2
2
0
0
0
2
0
0
1
0
0
2
1
0
2
2
0
0
0
1
0
1
0
1
0
2
0
0
2
0
1
0
1
0
0
0
0
1
2
0
3
0
1
0
0
2
2
2
1
2
1
1
2
0
2
2
1
0
0
0
0
0
1
2
2
2
0
1
0
2
1
0
1
0
2
0
0
1
2
0
1
0
1
0
0
1
0
1
1
1
0
0
0
1
3
0
0
0
0
0
0
1
1
0
2
1
0
0
0
1
2
2
0
1
0
1
2
0
2
4
0
0
0
0
1
1
1
1
1
0
1
0
0
0
1
2
0
0
1
0
0
1
0
0
0
1
0
0
0
1
1
2
1
0
1
0
0
1
1
0
0
0
0
2
2
1
1
0
2
0
0
0
0
2
2
1
0
0
1
1
0
2
0
2
0
0
1
0
0
2
0
0
1
2
2
1
0
0
1
0
1
0
1
1
2
2
1
0
2
1
0
0
1
1
0
0
0
0
0
0
1
2
0
0
2
0
0
1
1
2
0
0
2
2
2
0
0
0
2
1
1
0
0
1
0
0
0
1
1
0
2
2
2
0
0
0
2
0
0
0
0
0
2
0
1
0
2
2
1
2
1
0
0
0
0
1
0
0
0
2
2
1
0
1
1
0
0
2
1
1
1
0
0
0
2
0
0
0
2
0
2
0
2
0
0
0
1
0
1
1
2
1
0
2
0
0
0
0
2
1
1
0
0
2
0
2
0
2
0
0
1
1
2
0
0
1
1
1
0
0
2
1
0
0
0
0
1
1
0
0
1
0
2
0
1
0
2
0
0
0
0
0
0
0
3
1
1
1
0
0
2
0
1
0
1
2
0
2
0
0
1
0
1
0
0
0
0
1
2
2
2
0
1
1
1
1
0
2
0
0
0
0
0
0
2
0
0
0
0
1
2
0
1
0
2
2
0
2
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
1
2
0
2
0
1
1
0
2
0
0
1
0
2
1
1
0
1
1
0
2
1
0
1
1
1
1
1
0
2
2
0
0
0
0
0
0
0
1
2
2
1
0
2
2
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
1
2
1
3
2
1
1
0
0
0
1
0
0
0
2
1
0
0
0
0
1
0
1
2
0
0
0
1
0
0
1
0
1
1
1
0
0
0
2
1
2
1
1
2
1
2
0
1
0
0
0
2
2
0
0
1
2
1
0
2
0
1
0
1
0
0
0
0
0
0
1
1
0
2
1
0
0
1
0
0
2
0
1
1
0
0
0
1
1
0
2
3
0
0
1
0
0
2
1
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
1
0
0
3
1
1
0
2
1
1
0
0
0
0
0
1
0
0
0
1
0
0
2
0
1
0
0
1
1
1
0
0
0
0
2
1
0
2
0
0
0
1
0
0
0
0
1
0
1
1
1
1
0
1
0
1
2
0
2
1
0
1
0
0
1
1
1
0
0
1
0
0
1
2
0
1
2
0
1
2
0
3
0
2
0
0
1
1
0
0
1
0
1
1
0
0
2
0
0
0
0
1
0
0
2
0
0
2
0
1
2
1
1
0
0
0
0
0
0
0
2
0
0
1
0
2
0
3
0
0
0
3
2
1
1
0
0
0
1
0
2
0
1
1
1
0
0
2
2
0
1
0
0
1
0
0
2
6
2
0
0
0
0
0
0
0
1
2
1
0
0
1
0
0
0
0
1
0
0
1
1
1
2
1
0
1
2
0
0
0
1
1
2
0
0
2
1
1
0
0
0
1
0
2
1
1
0
1
1
2
2
2
0
1
3
1
2
0
2
0
2
0
0
0
2
1
0
1
0
2
2
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
2
0
4
0
1
2
0
0
0
0
0
1
0
0
2
2
0
1
2
0
2
1
2
1
2
0
1
0
1
1
1
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
2
0
1
0
0
0
0
0
0
0
2
0
1
0
1
0
1
0
2
0
2
0
1
0
2
0
2
1
0
0
0
2
2
2
1
0
1
0
0
0
1
1
1
0
0
0
0
0
0
2
0
0
1
1
3
0
0
0
0
1
2
0
2
1
2
0
0
2
0
0
1
3
1
1
2
0
2
0
0
1
0
0
2
0
0
0
0
0
1
0
1
0
1
0
1
1
0
1
0
0
1
3
0
0
0
1
1
0
0
0
2
0
1
0
2
0
0
1
0
1
1
0
1
0
0
1
0
2
0
0
0
0
1
1
2
1
0
0
0
0
0
0
2
2
1
0
2
0
0
2
1
0
1
1
2
1
0
1
0
2
0
0
0
0
0
1
0
2
2
0
2
0
1
0
1
0
0
1
0
1
0
0
1
3
2
0
0
2
1
0
2
0
0
1
0
2
1
1
0
0
0
2
2
0
0
0
0
0
0
0
1
2
0
1
0
0
0
1
2
0
0
1
0
1
0
0
2
0
0
0
0
0
2
1
2
1
2
0
0
3
2
0
2
0
0
1
2
1
2
0
0
1
2
0
2
0
2
1
1
0
1
0
0
0
0
0
0
1
0
1
0
4
1
1
0
1
1
0
0
1
0
2
0
0
2
0
0
1
1
2
2
0
1
1
1
0
2
0
2
2
1
0
1
0
0
0
2
1
0
0
0
0
0
0
2
3
0
1
1
1
0
0
3
2
1
0
1
0
1
0
1
0
0
2
0
1
1
1
0
0
2
2
2
0
0
0
0
1
0
0
1
2
1
0
0
0
2
0
1
1
0
0
0
0
0
2
1
1
0
0
0
1
2
2
1
1
2
2
1
1
0
0
0
1
2
0
1
2
0
1
0
0
2
0
0
0
2
0
1
0
1
2
0
2
0
0
0
1
0
2
2
0
1
1
1
1
0
0
0
0
2
2
0
1
0
0
1
0
0
0
2
0
1
0
2
0
0
0
0
1
2
1
2
1
2
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
3
2
0
0
1
1
0
0
2
0
2
0
0
0
1
2
0
0
0
0
1
2
1
1
0
0
1
0
0
0
0
3
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
1
0
1
0
1
0
2
2
1
1
1
2
2
0
0
0
1
2
0
0
0
0
0
1
0
0
1
1
2
0
1
1
0
1
1
0
2
2
1
1
1
0
0
1
2
2
0
2
0
0
2
0
0
1
1
0
0
0
0
0
0
1
0
0
2
0
1
0
0
3
0
2
0
2
2
0
0
2
1
4
1
0
1
1
0
0
1
2
2
1
0
1
1
1
0
0
0
0
0
1
0
1
1
0
0
0
1
1
0
0
0
0
2
1
4
0
2
0
1
0
0
0
0
0
2
2
0
1
3
0
0
0
1
1
0
2
1
1
1
2
0
1
0
1
0
2
0
0
1
1
1
1
2
1
0
1
0
1
1
1
0
1
2
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
3
0
0
0
0
2
2
0
0
1
0
1
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
2
2
1
1
1
1
0
0
0
2
0
1
1
1
2
0
1
0
0
2
0
1
1
2
0
1
1
1
0
0
0
0
0
1
0
0
2
1
2
0
2
0
1
1
1
1
1
2
1
1
0
0
1
0
0
0
0
0
1
1
0
1
0
0
2
0
2
0
0
1
0
0
0
2
0
1
1
2
0
0
0
0
2
0
1
0
2
2
0
0
0
1
0
1
1
0
1
0
2
2
3
0
1
0
2
2
0
0
2
0
0
0
0
0
0
2
1
0
0
0
2
1
1
1
2
0
2
0
1
0
0
0
2
1
0
0
1
0
0
0
0
0
0
1
1
0
2
1
0
0
1
0
1
0
1
1
1
1
0
0
2
0
1
0
0
2
1
0
0
0
1
0
2
0
0
1
0
0
1
0
0
0
2
0
2
0
0
0
0
0
2
2
1
1
0
0
0
1
1
0
0
2
0
0
1
1
0
1
2
1
1
0
0
2
1
1
2
2
1
0
1
0
0
2
0
1
0
0
1
2
0
0
0
0
2
1
2
2
2
0
0
0
1
2
0
2
3
0
2
0
2
2
1
1
1
1
0
2
0
1
0
2
2
0
0
0
0
2
0
0
0
1
0
2
1
1
1
2
0
2
2
2
0
1
0
0
0
0
0
2
0
0
2
2
1
0
0
0
1
1
2
0
1
1
0
1
0
0
0
0
1
0
2
0
1
2
1
0
2
1
0
0
0
1
0
2
4
0
0
1
1
1
0
1
1
1
0
2
0
0
1
0
0
0
1
0
0
1
0
1
0
2
1
2
0
0
0
0
2
2
1
2
1
0
2
0
1
1
2
0
0
0
2
1
2
0
0
1
1
1
2
1
0
0
2
0
2
2
1
1
3
1
0
0
0
2
0
0
1
0
0
2
0
1
1
0
0
0
2
1
0
0
0
2
1
1
2
1
0
2
0
1
2
0
2
2
0
0
1
1
0
1
0
0
1
2
0
0
3
2
0
0
0
1
1
2
2
0
2
0
1
1
2
2
0
1
0
0
3
0
0
0
1
0
0
0
1
0
0
0
1
2
0
0
2
0
1
0
1
0
0
0
0
2
0
2
2
1
1
0
0
0
1
0
1
1
0
1
0
0
0
0
0
1
2
0
1
1
1
1
2
0
0
1
1
2
0
1
3
0
1
1
1
0
1
1
3
0
2
3
1
0
1
1
0
0
0
1
1
1
1
0
0
1
2
0
1
2
2
2
2
2
2
2
0
1
1
1
1
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
2
0
2
1
1
0
2
2
1
0
0
0
0
0
2
0
0
0
2
3
2
1
0
1
1
0
1
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
3
1
0
1
1
0
0
0
0
2
2
2
2
1
0
0
0
1
0
1
2
1
0
0
0
1
1
2
2
1
1
1
0
1
1
2
1
0
1
1
0
0
1
2
0
0
0
0
1
0
1
2
1
0
2
2
0
1
0
0
0
2
0
2
0
0
0
2
0
1
1
1
0
0
1
0
1
0
0
0
0
1
1
0
0
0
2
0
1
0
2
1
2
1
1
2
0
1
0
2
0
0
1
1
0
1
1
4
0
0
2
0
1
1
2
2
2
1
1
1
1
1
0
1
2
0
0
0
0
2
1
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
1
3
2
0
0
0
2
1
0
0
0
2
0
0
0
0
1
1
0
0
0
1
0
0
0
2
0
1
0
0
1
0
0
0
0
0
2
0
0
1
1
0
1
1
3
0
0
1
0
2
0
0
0
1
0
2
1
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
1
0
2
2
2
1
0
1
0
0
1
2
1
1
0
2
0
0
0
2
0
2
0
1
0
1
0
0
1
0
1
2
2
0
0
1
0
0
0
0
0
1
0
0
2
1
0
0
1
1
0
1
2
2
2
0
0
0
0
0
1
0
3
0
2
0
0
1
0
1
2
0
0
0
0
0
0
0
1
0
2
1
0
1
0
0
3
2
1
4
1
0
1
1
0
0
0
1
0
2
2
1
1
0
0
1
0
3
0
0
0
2
0
0
1
3
0
0
0
3
1
1
0
1
1
1
2
0
1
2
1
2
2
0
0
0
1
0
2
0
1
2
2
0
0
1
2
2
0
1
1
1
1
2
0
0
0
1
0
1
1
1
1
1
0
1
0
1
1
0
0
0
0
1
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
2
0
0
2
0
3
2
2
0
2
0
2
0
0
0
0
0
0
0
2
2
0
1
0
0
1
1
1
0
0
0
1
0
0
0
0
1
0
0
1
0
2
0
1
2
0
1
1
0
2
1
0
0
0
1
2
0
0
0
0
0
0
2
1
1
1
0
2
2
0
1
1
1
1
2
1
2
0
0
1
2
2
2
0
0
2
2
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
2
2
0
0
1
0
1
1
0
0
1
0
1
0
2
0
1
0
0
0
2
0
2
1
0
1
1
0
0
2
1
1
1
0
2
0
2
0
0
0
1
0
0
1
0
0
0
0
1
0
2
2
1
0
1
2
0
1
0
2
2
2
2
1
1
1
1
0
2
0
0
2
0
1
0
0
0
0
0
3
1
1
0
0
2
0
1
2
3
0
2
1
0
0
0
0
1
0
1
2
0
0
0
2
0
2
2
3
0
2
0
0
0
0
0
0
1
0
0
1
1
2
0
0
1
0
1
0
0
1
0
1
2
0
1
0
0
1
1
1
0
1
1
0
0
0
1
1
0
1
0
2
0
0
1
0
0
1
0
1
0
0
1
0
2
0
0
1
0
2
0
1
1
1
1
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
2
2
0
1
1
0
1
0
1
0
2
0
0
1
0
0
1
0
2
0
0
3
0
0
2
3
3
1
0
1
0
2
2
0
0
0
0
0
0
0
0
1
1
2
1
0
0
1
1
0
0
0
2
1
0
3
0
0
0
0
0
0
0
0
0
0
3
0
0
0
3
0
0
1
0
0
2
1
5
0
2
1
2
0
1
2
0
0
2
1
0
0
0
1
0
0
0
1
1
0
2
0
2
1
2
0
0
2
0
0
2
2
0
0
0
0
1
2
0
0
0
2
1
0
0
1
2
1
1
1
2
2
2
0
2
2
1
0
2
0
2
0
0
1
0
2
0
0
2
0
2
0
0
0
1
2
1
2
0
0
2
0
1
1
0
0
2
0
1
3
1
2
0
2
1
2
1
1
3
0
0
2
1
1
0
1
2
2
0
0
0
0
1
0
2
0
1
2
2
0
2
0
0
0
1
0
1
0
0
2
0
0
0
1
1
1
0
0
1
2
0
1
1
0
0
2
0
2
2
2
0
1
0
2
0
0
2
0
0
0
0
1
0
0
2
1
1
0
1
0
1
0
0
1
2
0
2
1
0
0
0
0
1
1
2
2
1
2
2
2
0
0
1
0
0
0
1
1
0
1
0
1
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
1
3
1
0
2
0
0
0
3
0
0
0
2
0
1
0
2
2
0
0
0
2
1
1
0
0
0
0
0
1
0
0
2
1
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
1
1
0
1
2
2
2
0
0
0
2
0
0
0
0
2
1
0
0
0
0
2
2
0
0
2
2
0
0
1
1
0
2
0
0
1
2
2
0
1
2
0
2
0
0
1
1
2
1
0
0
0
0
0
0
1
1
0
0
2
0
0
2
0
1
0
0
0
0
2
0
0
2
1
0
0
0
0
0
1
2
2
0
1
0
0
0
4
1
3
0
1
1
0
1
0
2
2
0
0
0
2
3
0
0
0
2
1
0
2
0
0
1
2
0
0
0
3
1
0
1
0
2
1
1
0
0
2
0
0
1
0
2
2
0
0
2
1
0
2
0
1
0
0
2
2
1
1
0
1
0
2
0
2
0
0
0
2
1
1
1
1
1
0
0
2
0
0
1
1
2
1
0
0
1
2
0
0
1
2
1
0
1
0
1
0
0
0
1
0
2
1
1
0
1
1
0
0
0
1
0
1
1
0
1
1
1
5
1
0
0
2
1
2
1
1
0
0
0
0
1
0
1
0
0
0
0
2
0
2
2
1
0
0
1
2
0
1
3
0
2
0
2
0
2
1
1
1
1
2
1
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
6
2
0
1
0
0
0
1
2
2
0
1
2
1
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
1
0
0
2
2
1
2
0
0
0
0
0
0
0
2
1
2
1
0
2
1
0
1
0
3
2
0
0
0
2
0
1
0
0
1
0
2
0
1
0
0
1
0
1
0
2
0
1
2
0
1
2
1
0
0
1
2
2
1
0
2
3
0
0
0
1
0
0
1
2
1
0
0
2
1
0
2
0
1
2
1
0
2
1
1
1
0
0
2
2
1
2
1
0
1
1
1
1
0
0
2
1
1
0
0
1
1
1
1
0
0
2
0
1
0
0
2
1
1
0
0
2
0
0
0
1
0
0
0
1
2
1
0
3
0
0
2
0
2
2
1
0
1
0
1
0
1
1
1
1
0
0
1
5
1
3
2
1
2
0
0
2
1
2
0
3
2
0
0
1
0
0
2
2
0
1
1
0
0
0
1
1
1
0
0
1
0
0
0
1
0
0
0
0
0
1
2
1
2
0
2
0
1
1
0
0
1
0
0
0
0
1
1
0
1
0
2
1
2
0
1
0
2
0
0
0
2
0
0
2
0
2
0
0
1
2
2
0
1
1
0
0
0
1
2
0
1
0
0
0
0
2
0
0
2
2
1
1
2
0
1
2
0
0
1
2
0
0
0
1
1
1
0
0
2
0
0
0
0
0
1
2
1
1
2
1
2
2
2
0
0
1
1
0
0
3
0
1
1
1
0
2
0
0
0
0
1
0
3
0
0
2
0
2
2
0
1
2
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
2
0
0
1
1
1
1
1
0
2
0
3
0
1
0
1
1
0
0
2
0
0
0
1
1
2
0
1
0
1
1
1
1
0
2
3
0
2
0
2
1
0
0
0
1
0
1
0
0
1
1
1
1
0
0
2
0
0
2
0
1
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
2
1
0
0
0
2
0
2
0
0
1
2
1
1
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
2
1
2
1
1
2
1
1
1
0
0
0
2
1
0
1
0
1
2
0
1
1
1
0
0
0
0
2
2
0
0
0
3
2
1
0
2
0
1
1
0
0
1
1
0
2
0
2
1
0
1
1
0
2
0
0
2
0
0
1
0
2
2
1
0
0
0
0
0
2
0
0
2
2
0
0
1
0
1
0
1
1
2
2
0
1
0
2
2
0
1
0
1
0
2
1
2
0
2
0
2
1
0
0
0
1
2
0
1
4
0
1
0
1
0
0
0
0
3
1
0
0
0
0
1
0
1
0
0
0
2
1
0
1
2
0
2
1
2
1
1
0
0
1
2
0
0
0
0
1
1
0
0
2
0
1
1
0
0
2
0
0
1
1
1
0
0
0
0
4
1
2
0
1
0
1
0
0
0
0
0
0
0
0
0
1
2
0
1
0
2
0
0
1
2
1
0
3
0
0
1
0
0
1
2
0
0
0
0
0
1
0
0
0
2
1
2
0
1
2
0
0
0
1
1
0
1
1
0
2
1
0
1
1
1
1
0
1
1
1
1
0
2
0
0
2
0
1
0
2
0
0
0
1
1
2
0
0
0
1
0
2
2
0
0
2
1
1
1
0
1
0
1
1
0
0
0
0
2
0
1
0
0
0
0
1
1
2
1
0
0
2
0
0
0
0
0
1
1
0
2
0
1
0
0
0
0
0
0
3
1
0
0
1
2
0
2
1
2
2
1
3
2
2
2
0
2
2
1
0
1
1
2
1
1
1
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
2
0
2
2
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
1
0
1
0
0
0
0
2
0
2
1
0
0
1
0
1
1
0
8
0
0
0
1
0
2
0
1
2
2
0
2
0
2
0
0
1
2
0
0
0
0
0
2
2
2
0
2
0
1
0
2
1
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
2
2
0
2
0
0
1
0
1
1
2
0
0
1
0
0
1
1
2
0
0
2
0
0
0
0
0
2
0
2
1
1
1
0
0
0
0
0
0
0
0
1
1
2
1
1
0
1
0
2
1
2
0
0
0
1
0
1
2
2
1
0
0
0
0
0
0
0
0
2
1
0
1
2
1
0
2
1
2
2
0
1
1
1
0
0
2
2
1
2
0
2
0
1
0
0
0
2
1
0
0
0
0
0
1
0
1
2
1
1
2
0
1
3
0
1
0
0
1
1
1
0
0
0
2
0
2
0
0
0
0
0
1
0
1
0
2
1
0
0
1
2
1
1
2
1
2
0
2
0
0
0
0
1
0
1
0
1
2
0
1
1
0
1
0
0
0
1
0
0
1
2
1
2
1
2
0
1
0
2
2
1
0
2
0
2
1
1
1
0
1
0
0
0
0
0
1
0
1
1
0
1
1
1
2
0
1
2
1
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
1
0
0
2
2
1
0
0
1
1
2
2
0
0
1
0
0
0
0
1
2
0
0
0
0
0
1
1
0
1
0
0
0
1
2
1
2
1
0
0
3
0
0
1
2
2
1
0
2
0
2
0
1
0
2
1
2
1
1
1
1
0
1
2
1
0
0
0
2
1
1
1
1
1
0
0
0
0
1
0
0
0
1
2
0
1
2
2
2
0
1
1
2
0
2
1
1
0
0
0
1
0
1
2
1
0
1
1
0
3
0
0
1
0
2
1
0
1
1
0
2
0
0
0
2
1
0
0
2
0
0
0
2
2
0
0
0
0
0
1
1
0
0
0
0
2
2
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
1
1
0
0
0
1
0
1
1
1
2
1
0
0
0
0
2
0
0
0
1
2
2
1
1
1
1
0
1
1
1
0
0
1
2
2
1
0
1
0
0
1
1
1
1
0
0
1
1
0
0
1
0
0
0
0
1
2
1
0
0
2
1
0
0
2
0
1
1
2
0
0
1
1
0
0
0
2
0
0
1
0
1
1
0
1
0
1
1
0
2
2
1
0
0
1
2
1
3
0
0
3
1
1
2
0
0
0
0
0
0
0
0
0
1
0
0
2
1
1
0
0
0
2
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
1
1
1
0
0
0
2
0
0
1
3
2
1
0
2
2
2
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
2
0
0
1
2
4
0
1
1
0
1
1
2
0
1
0
2
0
0
2
0
2
0
1
2
1
2
0
0
1
1
2
2
1
2
0
1
2
1
0
1
0
0
0
0
1
1
1
1
0
0
0
5
0
0
0
1
0
2
2
1
0
0
1
0
0
1
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
1
1
0
2
2
0
1
0
3
0
0
1
0
0
1
0
0
0
1
0
2
0
1
1
2
0
1
1
0
1
2
0
0
0
1
0
0
1
0
0
2
0
1
0
0
1
1
2
2
0
0
1
0
2
0
2
0
0
0
0
1
0
0
1
0
1
2
0
0
0
0
2
0
1
2
1
2
1
0
0
0
2
0
0
1
1
2
1
2
0
0
0
0
0
2
0
1
1
0
0
2
1
0
2
2
0
0
0
0
1
1
0
2
1
0
0
0
0
2
0
0
2
0
0
2
1
0
0
0
1
0
1
0
0
1
1
0
0
0
1
1
0
1
0
0
1
0
1
0
1
2
0
0
0
1
1
0
0
0
2
0
1
1
0
1
0
0
0
2
0
0
0
1
0
1
2
0
0
1
1
0
0
1
0
2
1
1
0
2
2
0
1
1
2
1
1
2
0
1
1
1
2
0
2
2
0
0
0
2
1
0
1
1
0
0
0
2
0
1
0
1
2
2
0
2
1
0
0
0
2
0
1
0
2
0
2
2
2
0
0
1
0
0
0
2
1
0
0
0
0
1
1
0
0
0
1
1
1
2
1
2
0
1
0
2
1
2
0
0
0
1
3
0
2
0
0
0
2
2
1
0
1
1
1
2
0
1
0
1
0
0
0
0
0
0
1
0
0
2
1
3
2
0
0
0
0
0
1
2
1
2
0
2
0
0
0
2
1
1
0
0
7
1
1
0
1
2
0
2
0
1
2
1
0
2
0
1
1
0
1
2
0
2
1
2
1
2
0
2
1
0
0
0
1
2
0
0
0
0
1
1
0
0
0
1
1
1
0
2
0
2
0
2
1
0
2
0
1
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
2
1
2
0
1
0
0
1
1
1
1
0
1
1
0
0
0
0
2
2
2
3
1
0
1
0
1
1
0
0
1
1
2
1
0
2
0
1
2
0
2
2
2
0
1
1
0
0
2
1
1
0
2
1
0
0
0
0
1
0
0
0
0
1
0
0
1
2
0
0
2
0
0
3
0
0
1
0
2
2
2
0
2
1
3
0
0
0
2
1
1
1
0
2
0
2
0
1
0
0
1
2
0
0
0
0
2
0
0
1
0
1
1
0
2
0
0
0
1
0
1
0
0
0
0
0
1
2
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
1
2
2
0
0
0
2
2
0
1
0
0
0
0
1
1
1
0
1
0
0
2
0
0
2
0
2
1
2
1
0
0
0
1
0
0
2
1
0
0
0
1
0
0
1
2
1
1
0
0
2
0
0
1
1
5
0
0
2
2
2
0
1
2
0
2
1
2
2
1
1
0
1
0
0
2
1
0
2
0
2
1
1
0
0
0
0
1
0
0
0
1
1
0
1
1
1
3
0
2
1
0
0
0
0
1
1
1
0
1
1
1
0
1
0
0
0
1
0
2
0
2
1
1
0
0
0
0
0
1
0
0
1
0
1
1
1
1
2
0
1
0
0
0
2
0
0
1
2
0
1
2
1
0
3
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
1
1
0
0
2
1
0
2
2
0
0
0
1
0
1
0
0
0
1
0
1
0
1
2
2
2
1
2
0
0
0
1
0
2
0
0
0
1
1
5
0
1
5
1
2
0
1
0
2
0
0
0
0
2
2
1
0
0
0
1
0
1
2
2
2
2
1
0
2
0
0
2
1
2
2
0
2
0
2
0
0
1
1
0
0
1
1
0
1
0
2
1
0
1
0
2
1
0
0
0
0
0
1
1
0
0
0
1
1
2
1
1
0
2
2
2
1
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
2
0
0
0
1
1
0
2
1
1
1
0
2
0
0
2
1
0
2
0
0
1
0
1
2
0
1
2
0
1
0
0
0
0
2
0
0
0
1
1
0
0
0
2
0
1
2
1
1
1
0
2
0
1
1
1
3
2
1
2
0
1
0
0
0
3
0
0
0
0
0
0
0
1
1
2
0
1
1
2
1
0
1
0
0
0
2
0
0
0
2
0
1
2
0
0
0
0
0
1
1
0
0
1
1
1
0
0
0
2
0
1
0
2
2
2
0
0
0
1
0
1
2
1
2
2
1
0
0
1
0
0
2
0
0
0
0
0
0
0
1
2
0
2
0
2
2
0
2
1
0
1
1
1
0
1
0
0
0
1
0
2
1
0
0
0
1
0
0
1
1
0
1
2
0
0
0
1
0
0
2
2
0
1
1
0
2
2
2
3
2
1
0
1
1
0
0
0
1
0
2
1
1
0
0
0
2
1
2
0
0
0
2
1
0
1
1
1
0
0
1
1
0
0
1
0
2
1
0
0
0
2
2
2
2
0
1
1
0
0
2
0
0
2
2
0
0
0
0
1
2
0
2
1
2
2
2
0
0
0
2
2
0
0
1
0
0
1
2
0
1
2
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
2
0
1
1
1
0
0
7
1
0
2
2
1
1
2
1
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
3
0
0
2
1
0
0
0
2
0
1
0
0
0
2
0
0
0
0
1
0
2
0
3
0
0
0
0
0
0
1
0
2
1
0
1
0
1
1
2
0
0
1
2
2
0
0
1
0
2
1
0
0
1
1
1
0
0
0
1
1
0
2
0
1
1
0
0
1
0
0
2
2
0
0
0
0
6
1
0
1
2
0
1
1
2
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
2
0
0
2
2
1
1
1
0
0
2
1
1
1
0
0
0
1
1
0
0
1
1
0
0
0
0
2
2
1
1
2
0
2
0
3
0
1
2
0
1
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
1
2
0
1
0
1
1
0
1
1
2
1
1
0
1
1
0
0
2
0
1
0
0
0
1
0
0
1
0
0
0
0
1
1
0
2
1
0
0
1
0
0
0
0
0
0
2
2
2
0
2
1
0
0
1
0
1
0
0
0
1
0
0
1
0
0
2
0
2
1
1
2
1
2
1
1
2
0
0
2
1
0
1
0
0
1
0
1
2
0
1
0
1
0
1
0
2
0
0
0
0
0
1
0
0
0
0
1
1
2
0
0
1
0
1
0
0
0
0
2
2
0
0
2
0
0
1
2
1
2
1
1
0
0
1
2
2
0
0
2
0
0
1
1
3
1
2
0
0
1
2
1
4
0
2
0
0
0
2
3
0
0
0
0
1
0
0
1
1
3
0
2
0
0
0
1
0
0
2
0
0
2
1
1
2
1
0
0
2
3
0
0
0
0
2
0
3
0
0
2
0
1
0
2
0
0
1
0
0
0
0
0
0
2
1
0
0
1
0
0
2
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
2
1
2
3
0
1
2
1
2
1
2
0
1
2
2
2
0
1
0
0
0
0
0
1
1
1
2
2
0
0
0
2
0
0
0
0
1
0
2
1
2
1
0
2
0
0
1
0
0
0
1
1
0
2
0
0
0
2
1
2
4
0
1
0
2
1
2
1
1
1
1
3
0
0
2
1
1
2
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
1
0
0
2
0
1
0
1
2
0
0
0
0
1
2
1
0
0
2
0
2
1
2
0
1
0
0
1
1
2
1
2
0
2
0
1
1
0
0
0
0
1
0
2
1
1
0
0
2
1
0
0
0
1
2
1
0
0
0
0
0
2
1
0
0
0
0
1
1
0
2
0
3
0
1
0
0
1
2
1
0
1
0
2
0
0
1
1
0
0
1
0
1
1
1
0
0
0
1
1
0
2
0
0
0
0
2
0
0
0
2
2
2
0
0
0
1
0
1
0
0
1
1
0
0
1
2
2
1
1
0
2
2
0
1
0
2
2
1
1
1
0
1
0
1
1
0
3
0
0
0
0
2
0
1
2
1
1
1
0
0
0
2
1
1
1
1
2
0
2
1
0
0
4
1
0
0
0
0
1
2
0
0
1
2
1
2
1
0
0
0
1
1
0
2
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
2
0
0
1
1
0
1
0
2
0
1
2
1
3
1
0
0
2
0
2
2
0
1
2
0
1
0
1
0
0
0
1
0
2
0
0
0
2
0
1
0
1
0
0
1
0
2
2
0
0
0
0
0
2
0
1
1
1
1
2
1
0
0
1
2
0
1
2
0
0
1
0
0
0
2
0
1
2
0
1
0
1
0
0
0
0
2
0
0
2
0
1
1
1
0
0
2
2
1
0
2
1
0
0
2
1
0
2
2
1
0
2
0
0
0
1
2
2
3
1
0
1
0
0
2
0
1
1
0
2
0
1
0
0
2
2
0
2
0
0
0
1
2
0
2
0
0
2
1
0
1
1
2
1
0
0
1
1
2
0
0
0
0
0
2
1
0
1
1
1
2
1
2
2
0
2
1
2
0
0
0
0
2
1
3
0
0
0
0
1
2
2
0
0
0
2
1
1
3
1
1
0
2
2
1
1
2
2
0
0
0
0
1
0
1
0
1
0
0
3
0
1
0
0
0
2
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
1
1
1
0
0
0
0
0
2
2
2
0
1
1
1
1
0
3
2
0
2
0
0
0
1
2
1
0
2
0
2
2
0
3
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
1
0
0
2
2
0
0
1
0
1
2
0
1
0
0
1
2
0
1
1
2
1
2
0
1
1
0
1
1
0
1
1
1
0
1
0
0
0
1
0
0
0
1
0
0
1
1
1
0
2
2
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
2
0
0
2
2
0
0
2
1
0
1
1
0
0
1
2
2
0
0
2
0
1
1
0
2
1
0
0
2
1
1
3
0
1
2
0
3
1
1
2
0
0
1
0
1
1
2
0
1
0
2
0
0
2
1
0
2
1
1
0
1
2
0
0
0
0
2
0
1
1
0
1
0
0
1
0
1
2
0
0
0
0
2
0
2
8
0
1
0
0
1
1
0
0
0
0
1
1
2
2
0
0
1
1
0
3
2
1
2
0
2
2
0
0
1
2
0
0
0
1
2
1
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
1
1
2
0
0
1
0
2
2
2
2
3
0
0
0
2
1
1
0
2
0
0
0
0
0
1
0
0
0
0
1
1
1
2
2
1
0
0
1
2
0
1
0
0
2
0
2
0
0
2
0
2
2
1
0
2
0
0
0
0
0
0
1
0
2
0
2
2
0
0
1
0
2
1
1
0
1
0
0
2
2
0
1
0
0
0
0
1
2
0
0
1
0
0
1
2
2
1
0
2
0
2
1
0
2
1
0
1
0
0
1
0
0
0
1
1
1
1
0
0
2
0
2
1
1
0
1
1
0
1
0
1
0
1
0
1
0
0
2
0
0
1
0
0
1
1
0
1
1
0
0
2
2
0
0
2
0
1
1
0
2
0
0
2
1
0
1
0
0
2
0
0
2
0
1
0
0
2
0
0
2
1
0
0
0
2
0
1
2
0
1
1
0
0
1
2
2
0
1
0
2
3
1
1
2
1
0
0
1
0
0
0
0
1
1
0
1
0
2
0
0
0
0
0
1
2
1
0
2
1
0
0
0
0
2
0
0
1
0
1
2
1
0
1
2
0
0
2
2
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
1
3
1
1
1
0
0
0
1
0
1
0
0
0
2
0
1
0
0
0
0
1
0
0
1
0
0
0
1
3
2
0
2
0
1
1
2
2
0
0
0
1
2
0
0
0
0
1
0
1
0
0
0
1
0
0
0
2
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
2
0
1
0
1
1
0
2
2
0
0
0
0
2
1
0
1
0
0
0
0
2
3
1
2
2
0
2
1
0
0
2
2
0
0
2
0
0
0
0
1
2
0
1
2
1
0
2
2
2
0
0
0
2
0
0
2
2
0
0
2
0
2
2
0
0
1
1
0
0
0
0
0
2
2
1
2
1
2
2
0
0
0
0
0
0
0
1
1
3
0
0
1
0
0
0
1
0
0
2
0
1
2
1
2
1
0
0
0
1
0
0
0
0
2
0
2
2
0
2
2
0
0
0
1
0
0
0
1
0
0
1
0
0
2
1
2
0
0
0
1
3
1
3
1
2
0
0
3
2
2
1
1
0
0
0
0
1
2
3
0
0
0
1
0
0
2
1
0
2
0
0
1
1
1
0
0
2
2
0
0
0
0
1
0
1
1
1
0
2
0
0
0
0
0
0
2
0
1
0
0
0
1
0
2
0
0
2
0
2
0
0
0
1
0
0
2
1
0
0
0
0
0
0
3
0
1
2
0
0
1
2
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
1
2
0
0
1
1
1
0
1
0
0
1
0
0
0
0
2
1
2
2
1
0
1
0
2
0
1
1
1
0
1
0
0
2
1
1
0
0
0
0
0
1
2
3
0
0
2
1
1
1
1
2
1
2
0
0
2
0
0
2
2
1
3
1
1
2
1
1
1
0
1
1
1
1
1
0
1
4
0
0
0
1
1
0
0
0
0
2
0
1
1
2
2
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
1
0
0
0
0
1
0
2
0
1
1
0
1
0
0
1
0
0
3
1
1
0
0
1
1
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
1
1
2
0
2
2
2
1
0
0
0
0
0
0
0
0
2
2
2
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
2
0
3
0
3
2
1
0
2
2
0
0
2
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
1
1
2
0
0
0
0
0
0
0
0
0
0
0
2
2
1
1
0
0
0
0
0
0
0
2
0
0
2
1
1
2
1
0
2
0
1
0
1
1
0
1
1
0
0
0
0
3
1
1
2
0
1
0
0
0
0
0
1
1
1
2
2
2
2
0
2
1
0
1
0
0
1
0
2
0
1
0
0
0
1
2
1
0
1
2
2
2
0
0
0
0
3
0
0
0
2
0
0
1
2
0
1
1
0
1
2
0
1
1
0
2
0
1
1
0
0
0
0
0
2
0
1
0
0
0
1
2
1
1
2
2
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
2
0
1
0
1
1
0
0
1
2
0
2
0
0
0
0
2
8
2
0
0
0
0
2
1
0
0
2
0
0
0
1
2
0
2
0
1
1
0
1
2
0
1
1
3
0
1
0
0
0
2
0
0
1
0
3
2
0
0
0
2
1
0
0
0
2
1
0
0
1
2
4
1
2
0
2
0
0
0
0
0
0
0
1
0
1
2
0
2
2
1
0
2
0
0
0
0
0
1
1
0
2
2
0
0
0
2
0
4
0
1
0
0
2
1
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
1
0
2
0
0
2
0
2
0
1
2
1
0
0
0
1
1
1
0
0
0
1
3
1
0
0
0
1
0
0
1
1
1
0
2
1
1
0
0
0
1
1
1
0
0
3
1
1
0
0
0
2
0
0
0
0
1
1
1
2
0
1
2
0
0
0
0
2
0
0
1
0
1
0
2
0
1
1
1
1
0
1
0
1
0
1
0
1
1
0
0
2
2
0
2
0
0
1
0
2
2
0
0
0
0
0
2
1
1
0
1
1
0
0
0
2
2
1
2
0
0
0
0
0
0
0
2
0
0
2
1
0
0
1
2
2
0
1
0
1
0
0
0
0
0
0
0
1
0
2
1
0
2
0
6
2
0
1
0
0
2
0
2
0
0
1
2
0
1
1
0
1
1
0
0
0
0
1
3
1
0
0
1
1
1
0
1
1
0
4
1
2
0
0
1
1
0
0
1
1
2
0
1
0
0
2
2
0
1
0
0
1
2
0
1
1
2
1
0
1
0
0
5
0
2
0
1
0
0
0
1
0
0
2
0
0
0
1
0
1
1
0
0
0
0
1
3
1
1
1
2
2
2
2
3
2
0
0
0
1
1
1
2
0
0
0
2
1
0
0
1
0
0
1
0
0
1
2
0
1
0
0
0
0
2
1
1
2
1
1
1
1
0
0
0
2
0
2
1
0
2
1
2
0
1
1
0
2
2
1
0
1
1
0
0
1
0
2
1
1
1
1
0
0
1
0
2
10
2
0
0
0
1
1
0
0
2
1
1
1
1
0
1
1
2
3
0
0
1
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
1
0
2
2
0
1
1
3
0
0
0
2
3
2
1
2
1
0
2
1
1
1
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
2
0
0
1
0
0
0
2
1
0
1
0
1
2
0
2
1
0
0
1
2
2
0
1
0
1
0
1
0
0
2
1
2
0
2
2
0
0
0
2
0
1
1
0
1
0
2
0
0
0
0
0
2
1
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
2
3
2
0
0
0
0
1
1
0
2
0
1
1
0
0
0
1
0
2
0
1
0
1
1
1
0
1
2
0
1
2
2
0
1
0
0
1
1
2
0
0
2
0
0
2
0
1
1
1
0
1
1
1
3
0
0
2
1
1
0
1
0
0
1
3
4
1
1
1
1
0
0
2
1
0
1
1
1
0
1
0
1
1
0
0
1
0
0
0
1
0
2
0
3
0
2
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
1
2
1
0
0
2
3
0
2
1
0
1
2
2
0
2
0
1
2
0
0
0
0
2
1
0
2
2
0
0
1
0
0
1
0
2
0
3
2
0
1
1
2
0
0
1
0
1
0
0
0
0
0
2
1
0
0
0
0
1
1
1
0
2
2
0
0
2
3
0
2
0
2
2
0
0
2
0
0
0
2
2
1
1
0
0
2
0
2
0
1
0
1
2
0
0
0
0
0
2
1
0
0
0
0
1
1
1
2
1
0
0
0
0
2
1
1
0
1
0
1
0
2
0
2
0
0
3
0
1
1
1
1
1
1
2
0
0
0
2
1
2
0
0
0
0
1
0
0
2
1
0
1
0
0
2
4
0
2
1
0
2
1
2
0
1
2
1
0
1
1
1
2
2
0
0
2
1
0
0
1
1
1
0
1
0
2
1
1
1
0
2
2
0
0
0
1
0
1
1
0
0
2
0
0
0
0
1
1
0
0
0
2
1
1
2
1
1
0
0
1
1
0
0
0
3
2
1
0
1
0
0
1
1
2
0
0
0
0
1
0
0
0
1
0
0
1
2
2
0
1
2
0
0
1
0
1
1
0
3
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
2
1
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
1
3
0
1
1
0
0
1
1
1
0
0
2
1
3
1
1
1
0
2
2
1
1
0
0
0
2
0
1
2
1
0
0
0
2
0
0
0
1
1
0
1
0
0
0
1
0
0
1
1
1
0
0
2
1
1
0
2
0
0
1
0
0
2
1
1
1
0
0
1
0
2
3
0
1
0
0
0
0
0
0
0
1
2
2
0
1
0
2
2
2
0
0
0
1
1
0
0
0
0
0
1
1
0
2
0
0
1
1
0
0
0
1
0
0
2
1
2
0
2
2
2
0
0
2
1
0
0
1
2
1
0
2
2
1
2
1
0
0
0
0
1
0
1
0
1
0
0
0
1
0
2
0
0
0
0
2
0
0
1
3
0
0
2
1
2
1
1
2
0
0
1
1
1
4
1
0
1
0
1
0
3
2
1
0
1
2
0
0
1
0
1
1
0
1
0
2
0
0
2
0
0
0
0
0
0
2
2
0
1
0
1
0
0
1
0
1
0
2
2
1
1
1
1
0
0
2
0
1
1
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
1
0
2
0
0
1
3
0
2
1
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
2
0
1
0
2
0
0
2
2
1
1
0
0
0
1
1
1
0
0
1
1
1
1
0
0
0
2
0
0
0
1
1
0
0
0
1
1
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
1
2
0
1
0
1
2
1
0
0
0
1
0
1
2
2
0
0
6
0
2
0
0
0
2
2
0
0
0
1
0
0
1
1
1
2
2
1
0
2
0
0
0
0
0
2
0
1
1
0
2
2
1
0
0
1
1
0
0
0
0
0
1
2
0
1
1
0
0
1
2
0
0
2
2
2
0
0
1
0
1
2
0
2
0
0
1
1
0
0
0
1
1
2
2
2
1
0
0
0
1
0
0
1
2
0
1
0
1
0
0
1
1
0
0
1
3
0
0
0
1
0
0
0
1
0
1
0
0
0
1
1
0
0
0
1
0
2
1
0
0
1
0
0
1
0
0
1
2
0
0
0
0
0
2
0
2
0
0
0
1
2
1
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
1
1
0
0
2
0
0
2
0
0
0
2
0
0
1
0
0
1
1
0
1
0
0
0
2
0
1
1
0
1
2
1
0
0
0
0
0
1
2
1
0
0
0
1
0
0
1
1
0
0
0
1
1
2
0
0
0
1
0
0
1
1
0
1
1
1
1
1
1
1
2
1
2
1
0
0
0
1
0
1
1
2
2
0
0
0
2
1
1
1
0
1
3
2
0
0
0
0
0
1
3
1
0
1
1
0
0
2
1
0
1
1
1
0
0
1
0
1
2
0
0
2
0
1
0
1
3
0
1
1
0
0
1
0
2
1
0
0
1
2
2
0
0
2
1
0
0
0
0
2
0
0
0
2
0
0
2
0
0
1
0
1
0
2
1
0
1
0
0
0
0
1
2
2
0
1
1
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
2
0
1
0
2
0
1
1
0
2
1
2
2
1
0
0
0
2
1
2
0
1
0
1
2
1
0
0
0
2
0
0
0
0
0
0
0
2
2
0
1
2
0
0
0
1
1
1
1
1
0
2
0
0
1
0
0
0
0
1
1
5
1
3
0
4
0
1
1
0
2
0
0
0
2
0
0
0
0
0
2
1
0
1
0
0
0
0
0
2
0
2
0
0
1
0
1
0
0
2
1
3
0
0
2
2
1
0
0
0
2
0
0
1
0
2
3
2
0
2
0
2
0
0
1
0
0
1
0
0
2
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
1
1
0
1
1
2
0
0
2
0
0
0
1
0
2
1
0
0
1
0
0
0
0
2
0
1
0
0
1
1
1
0
0
1
2
0
0
1
1
3
0
0
1
0
1
0
0
3
2
0
0
1
2
0
0
1
0
0
0
0
2
0
0
0
0
0
1
1
2
0
0
1
0
4
0
2
2
0
1
0
1
0
0
1
1
1
2
0
0
0
2
0
2
1
2
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
1
1
2
0
0
1
0
1
0
1
0
0
2
1
1
0
0
0
0
2
0
1
0
0
3
0
0
0
1
0
1
1
0
1
0
2
0
0
0
1
0
0
1
0
2
0
1
0
0
0
2
2
2
1
1
1
2
1
1
1
1
0
0
0
2
3
0
1
1
1
1
1
0
3
0
0
0
0
0
2
2
2
1
0
1
0
1
0
1
1
2
0
1
0
0
0
0
0
0
2
1
0
2
0
1
1
0
3
2
0
2
0
0
1
1
3
0
0
0
2
0
1
2
0
0
0
1
0
0
2
2
1
1
2
0
0
0
4
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
2
1
0
0
0
0
0
2
1
2
0
1
0
0
0
1
2
0
0
2
0
0
0
2
0
0
1
2
0
0
1
1
2
0
0
2
1
0
1
0
1
1
0
0
0
1
1
2
3
0
2
0
3
2
1
1
0
0
0
1
1
5
2
1
1
1
0
0
1
1
1
2
1
0
0
1
2
0
0
0
0
1
0
3
1
0
2
0
1
0
0
0
2
0
0
0
2
0
1
0
1
2
0
0
0
0
1
0
1
0
1
1
1
0
1
0
1
1
0
1
2
0
0
1
0
2
0
2
0
0
0
2
0
0
0
1
0
0
0
0
1
0
1
0
0
0
2
1
2
2
1
0
1
0
1
0
0
2
0
0
1
0
1
0
0
0
2
2
1
0
2
2
0
2
0
0
0
2
1
1
1
1
0
0
0
0
2
0
1
0
1
2
0
1
2
2
0
0
1
1
2
1
1
2
1
1
1
0
0
0
1
0
0
0
0
0
1
0
0
2
0
1
2
2
2
0
0
1
0
1
0
1
2
1
1
0
1
0
0
0
1
1
1
2
2
1
2
2
2
1
0
2
0
0
1
1
0
0
1
0
0
2
0
0
0
0
0
2
1
1
0
0
0
0
1
2
2
0
0
0
0
2
0
0
0
0
1
0
1
1
0
0
2
2
0
0
0
1
1
0
1
0
1
0
0
0
1
0
2
0
0
1
0
1
2
1
0
2
2
1
1
1
1
0
2
1
2
0
1
0
1
2
0
0
1
0
0
0
1
1
3
0
2
1
0
1
0
0
0
2
2
0
0
1
1
0
0
2
2
1
0
1
0
0
0
2
2
0
0
0
1
1
1
2
1
1
1
0
1
2
1
0
1
0
1
0
0
0
0
0
0
2
1
0
0
0
0
1
2
0
0
0
1
0
0
2
1
0
1
0
1
0
0
0
0
1
2
2
2
2
0
0
1
5
0
0
1
1
3
1
1
2
0
0
0
0
1
1
1
1
1
0
2
0
0
1
0
1
1
1
2
0
1
1
0
1
0
1
2
2
2
2
1
2
0
1
2
2
0
0
2
2
1
1
0
1
0
0
0
0
1
1
0
0
2
0
1
0
0
1
2
2
1
2
2
0
1
2
0
1
0
0
0
0
1
0
0
1
0
0
2
0
0
2
0
2
0
0
2
1
0
1
0
0
1
1
2
1
0
1
2
0
1
0
2
0
0
0
1
2
1
0
0
1
0
0
0
0
2
0
2
1
0
3
1
0
0
0
1
2
1
2
0
3
0
0
0
1
1
1
1
0
0
1
2
2
0
2
1
0
1
1
0
0
1
0
0
1
0
1
1
0
0
1
1
2
1
0
0
0
1
0
0
1
1
0
2
0
0
1
1
2
0
2
0
2
1
1
1
2
3
2
0
0
1
0
0
0
0
1
0
3
2
0
2
1
0
0
1
2
0
0
1
2
1
2
1
0
0
0
1
0
2
0
0
0
2
0
0
1
0
0
1
1
0
0
0
0
1
2
0
2
1
1
2
1
2
0
0
1
2
3
2
2
2
0
0
1
1
1
3
1
1
0
1
0
2
2
1
2
0
0
2
0
2
2
0
1
0
2
0
2
1
1
0
1
2
1
3
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
2
2
1
0
1
0
1
1
0
1
1
0
0
0
1
2
2
0
0
0
0
0
0
1
1
0
2
0
0
1
1
0
1
0
0
0
0
2
1
0
1
2
2
0
1
0
0
1
1
1
1
1
1
1
0
0
0
1
2
2
0
0
2
0
2
0
0
2
0
2
0
1
2
1
0
1
2
0
0
0
0
3
2
1
0
0
1
2
2
0
1
0
1
0
0
0
1
0
0
2
0
0
2
2
2
2
2
0
0
0
0
0
1
0
0
0
2
0
2
1
0
2
2
0
0
1
0
0
1
1
0
1
0
1
0
2
1
2
1
0
2
0
0
0
0
1
0
0
0
2
1
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
1
2
1
1
1
2
0
2
0
2
0
2
1
1
2
1
0
1
1
2
2
0
0
1
1
2
0
2
0
0
4
2
2
0
0
2
2
0
1
1
0
0
1
0
1
0
2
1
1
0
2
0
0
0
1
1
0
1
3
2
0
0
0
1
0
0
0
1
1
0
2
0
2
0
1
0
0
2
0
1
1
1
0
1
1
2
2
0
0
1
0
0
2
0
0
0
1
1
1
2
0
0
1
2
0
1
1
3
0
0
1
1
2
0
0
2
0
0
1
0
0
0
0
0
1
2
1
0
0
1
0
1
1
0
1
2
0
1
0
0
1
1
0
2
1
0
0
2
1
0
9
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
1
0
0
1
2
0
0
0
0
0
0
0
1
2
0
2
0
1
0
2
1
2
0
0
1
0
2
0
0
1
0
2
1
2
0
0
2
0
0
0
0
2
1
0
0
1
1
2
2
0
2
2
1
1
0
3
0
1
0
1
0
1
0
0
1
0
0
0
1
0
1
0
2
1
1
1
0
1
0
1
0
0
1
1
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
2
2
1
2
2
0
1
2
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
2
1
2
0
0
0
0
0
1
0
1
1
2
1
1
1
0
1
1
2
2
3
0
0
1
0
0
0
0
0
0
1
0
2
1
1
0
0
0
0
1
2
1
2
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
1
0
1
0
0
1
2
1
0
0
0
1
0
1
0
0
1
1
0
1
0
2
1
0
0
1
1
2
1
0
1
1
2
1
1
0
1
1
2
0
0
0
0
0
2
0
0
2
0
1
2
2
1
1
0
1
1
3
0
1
1
2
1
1
1
0
0
0
0
0
0
1
0
0
0
2
1
0
1
1
1
0
2
2
1
0
0
0
0
0
1
0
0
0
2
1
2
2
2
1
2
2
0
5
1
1
2
1
0
1
2
0
2
0
2
0
2
0
0
0
0
2
0
0
0
1
1
0
0
0
0
1
0
0
2
0
2
1
1
2
2
1
0
0
2
0
1
0
1
0
1
2
1
1
0
0
1
0
2
0
0
2
3
1
0
2
0
0
0
0
1
0
0
0
0
1
0
0
1
1
1
0
1
2
0
0
0
2
1
0
0
1
0
0
0
2
2
1
0
1
0
0
1
1
0
0
0
0
2
1
0
1
0
0
0
0
0
0
1
2
0
4
0
0
0
1
1
1
0
0
0
1
2
0
2
0
0
0
1
1
0
0
0
3
1
0
0
0
0
1
0
1
0
1
4
0
0
0
0
1
1
0
0
0
1
1
1
1
2
2
0
0
0
0
1
2
1
0
0
1
0
0
1
0
0
0
0
2
0
1
0
0
2
1
0
0
1
0
1
1
1
0
1
1
0
2
3
2
1
1
0
2
0
2
2
2
1
0
0
0
0
0
1
0
2
2
0
2
2
0
2
1
4
2
0
1
1
1
1
2
2
2
0
0
1
2
0
1
0
0
1
0
0
2
1
2
0
0
2
1
3
2
1
2
0
0
0
0
2
0
1
1
2
2
0
0
0
0
2
0
0
1
0
0
0
1
1
0
0
1
0
0
2
2
2
0
2
0
1
0
0
1
0
0
1
1
2
0
0
4
2
0
0
0
0
2
0
0
1
1
1
2
2
0
0
0
0
0
0
2
0
2
0
2
2
2
0
2
1
0
1
0
3
1
0
0
0
1
0
1
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
1
0
2
1
1
0
1
1
1
0
0
0
0
0
2
1
1
1
0
0
0
1
1
3
0
0
1
0
2
0
1
1
0
1
2
2
2
2
1
1
1
2
2
0
0
0
2
2
0
1
0
0
1
2
3
2
0
0
1
0
0
0
1
0
0
5
2
1
2
1
0
1
0
0
2
2
0
0
1
0
0
0
0
1
0
1
1
2
0
0
0
1
2
1
2
2
0
2
0
2
0
2
0
0
1
3
0
1
0
0
0
2
1
1
0
2
0
0
0
0
0
1
1
0
2
0
0
2
0
2
1
0
0
0
0
1
1
0
0
0
0
2
0
2
0
0
1
1
1
0
1
0
2
0
0
0
2
1
2
0
0
0
0
0
0
2
0
1
1
2
2
2
3
0
0
0
1
1
0
0
0
4
0
2
0
2
4
0
1
0
0
0
0
0
2
0
0
0
1
1
1
2
0
1
2
0
0
0
1
0
0
2
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
2
0
1
0
0
2
0
0
1
0
0
0
1
0
2
1
3
0
0
1
0
1
1
0
1
1
2
1
1
0
1
0
0
2
2
0
0
1
0
1
0
2
2
0
2
2
1
0
1
6
0
0
1
2
0
2
1
0
0
5
2
0
0
2
2
1
0
1
3
2
0
1
0
2
0
0
0
0
0
1
0
0
1
0
1
1
2
2
0
0
0
2
0
0
0
0
3
0
0
0
0
2
1
0
1
1
2
2
2
0
0
0
1
0
0
0
0
2
1
0
1
0
0
0
2
0
0
1
2
0
0
1
2
1
1
1
2
0
2
1
0
0
0
0
1
1
0
0
2
2
1
0
1
0
0
3
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
2
3
2
0
1
1
0
0
0
0
2
0
0
0
0
2
1
0
0
2
1
0
0
0
0
0
0
2
0
2
2
0
1
0
2
0
0
2
0
0
2
1
0
0
0
0
2
1
0
0
1
2
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
1
1
0
1
0
0
3
1
2
0
0
0
0
1
0
0
0
2
2
0
1
0
0
0
0
1
0
0
0
0
1
2
2
1
1
0
2
2
0
0
0
0
0
1
0
2
1
2
0
0
2
2
0
0
1
0
0
1
2
1
0
0
0
2
0
0
0
1
1
0
2
2
1
0
0
0
2
1
1
1
1
0
1
1
1
0
0
0
0
1
0
1
0
1
1
0
0
1
2
6
0
0
0
1
0
1
0
1
0
0
0
2
1
0
2
0
1
0
2
0
1
2
0
1
0
0
1
1
1
1
0
2
2
0
0
2
1
2
0
0
0
0
0
1
0
1
1
0
0
0
2
0
2
0
2
0
0
2
1
0
0
1
1
0
0
2
1
0
1
0
1
0
0
1
0
0
0
0
1
0
2
1
0
0
2
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
1
0
0
0
2
0
1
0
0
0
2
0
1
0
1
0
2
1
1
2
0
0
0
1
1
0
0
2
0
0
2
1
2
3
0
2
1
2
0
0
0
1
0
0
0
0
1
0
0
0
1
0
2
2
1
2
0
0
0
0
0
0
0
0
0
1
1
1
0
1
2
0
1
2
1
1
1
1
0
3
1
2
0
1
0
2
1
0
0
0
0
1
1
1
1
2
1
0
2
0
0
2
2
1
0
1
2
2
0
1
1
2
0
1
0
0
0
1
2
1
0
0
0
1
1
0
0
2
1
0
1
1
2
1
0
1
1
0
0
0
0
0
0
2
1
1
0
0
0
1
2
0
1
0
0
0
0
1
2
0
1
2
0
0
0
1
0
2
0
0
1
2
1
0
2
2
0
0
2
0
0
1
1
0
0
1
0
1
0
0
4
9
1
1
0
0
1
1
0
0
0
0
0
1
0
3
1
2
1
2
0
0
1
1
0
2
0
2
0
0
1
2
1
2
2
2
0
1
2
0
1
0
0
0
0
0
2
2
1
0
1
0
0
0
1
2
1
2
1
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
0
1
0
0
0
1
2
2
1
0
0
1
0
0
2
1
2
0
1
1
1
0
2
0
1
0
2
0
0
2
0
0
2
1
0
2
1
0
2
2
0
1
1
0
0
2
0
1
0
0
1
1
0
1
1
1
1
0
1
2
1
1
0
1
1
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
1
1
1
2
0
0
2
1
0
2
2
0
2
1
2
0
2
2
1
0
0
0
0
1
2
1
1
0
0
1
2
1
2
1
0
1
0
1
1
0
0
1
0
1
2
2
2
0
0
0
1
1
1
2
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
1
0
1
0
0
0
1
2
2
1
0
0
2
0
1
2
0
1
0
1
0
0
2
0
0
2
1
1
0
0
2
0
0
2
0
1
0
0
1
0
1
1
1
0
0
1
0
2
0
1
0
0
0
1
1
1
1
1
0
2
0
3
0
0
2
0
1
0
2
2
1
0
1
0
0
2
0
1
0
0
1
0
0
2
1
1
0
2
1
1
1
0
1
0
0
0
0
1
0
0
2
0
0
2
1
1
1
0
1
1
2
0
0
0
0
0
2
0
2
1
1
0
1
0
2
1
0
2
2
1
0
2
0
1
1
0
0
7
1
0
0
2
2
0
1
0
0
2
1
2
0
0
0
3
0
1
1
2
1
2
0
1
2
1
0
0
0
2
2
1
1
2
1
1
0
0
0
1
1
0
0
0
0
0
1
0
1
2
1
0
2
0
0
0
0
0
1
0
0
2
1
0
1
0
0
0
1
1
0
2
2
1
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
7
2
1
1
2
2
1
1
1
1
1
1
0
1
1
1
0
3
2
0
0
0
1
0
0
0
1
1
0
2
2
2
0
0
1
0
0
2
0
2
1
5
0
0
0
0
2
2
1
2
2
2
1
0
0
0
1
0
1
2
2
1
2
1
1
0
1
1
1
1
4
1
2
0
8
1
1
0
1
0
1
0
0
0
0
0
1
1
0
1
1
1
0
0
2
1
0
0
2
0
0
2
0
0
1
2
0
0
1
1
0
2
2
0
2
1
0
1
0
0
0
2
1
1
0
0
0
1
0
1
1
0
2
1
2
0
2
0
0
2
0
0
1
1
0
0
1
2
2
0
1
0
0
1
2
0
0
1
0
0
2
1
1
1
0
0
0
1
0
1
1
1
0
0
1
2
1
1
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
2
0
1
1
2
1
2
1
1
0
1
0
0
1
0
3
1
0
0
1
0
0
2
1
0
0
0
0
1
1
0
1
1
0
1
2
0
0
2
0
0
0
0
8
2
2
0
2
1
2
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
2
2
0
0
2
1
0
1
2
1
2
1
3
0
0
0
0
1
0
1
0
1
0
1
0
0
0
1
2
1
2
1
0
0
1
0
0
0
2
2
0
2
1
0
0
0
0
2
2
1
1
2
0
0
0
2
0
1
2
0
1
2
1
2
1
0
0
1
2
1
1
1
2
0
0
1
0
1
2
0
0
1
2
0
2
0
0
0
2
0
2
0
2
0
0
0
2
0
0
1
2
2
0
0
0
0
0
1
0
0
0
0
1
2
0
2
1
0
2
2
1
3
0
0
1
1
1
1
0
0
3
0
0
1
0
1
2
0
2
0
0
0
1
3
2
2
1
2
0
0
1
1
0
0
2
2
1
0
0
0
0
1
0
2
0
1
0
1
0
2
0
0
0
0
2
1
0
0
2
1
2
2
0
0
0
1
0
1
2
0
0
2
0
2
1
1
1
1
1
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
1
3
0
0
0
0
0
2
0
2
0
0
0
0
0
3
0
2
0
0
0
0
2
2
1
3
1
3
0
1
0
1
0
0
1
2
0
0
0
1
1
0
1
1
0
0
0
2
0
0
0
1
0
0
0
2
0
2
1
0
1
2
0
0
2
0
1
0
0
2
0
0
0
0
1
0
2
2
1
1
1
0
1
1
2
3
0
0
3
0
0
0
0
2
2
0
2
1
2
1
0
2
1
1
0
2
2
2
1
0
1
1
0
2
0
1
0
2
0
0
0
2
0
1
0
0
0
0
0
2
1
0
2
0
2
2
1
1
0
0
1
0
1
0
0
0
0
2
0
1
1
0
1
0
2
1
0
2
1
1
2
0
2
2
0
0
0
1
0
0
2
2
1
2
0
1
1
1
0
0
0
0
1
0
1
1
0
1
0
1
1
2
1
1
0
1
1
0
0
2
0
0
0
2
1
0
0
0
0
0
2
1
0
0
3
0
0
0
1
0
0
0
2
1
1
0
1
0
0
2
0
1
0
0
2
1
2
0
1
1
0
0
2
1
1
1
0
0
0
0
1
2
2
1
1
1
0
0
1
0
2
0
0
1
2
1
0
1
0
2
0
1
0
0
0
0
2
2
2
1
0
1
0
0
1
2
0
1
1
0
1
0
1
2
0
2
2
0
0
2
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
2
0
2
0
1
2
2
0
0
1
0
0
1
1
0
0
0
1
0
1
2
1
0
2
1
0
2
2
2
1
1
2
1
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
2
2
0
0
0
1
1
1
2
0
0
0
0
0
2
2
2
2
1
0
1
6
0
1
1
1
0
0
2
1
2
1
2
0
0
0
0
0
2
0
0
1
0
0
2
2
0
2
0
0
0
1
0
1
0
2
0
0
2
0
0
0
2
0
3
0
2
0
1
2
1
2
0
0
2
1
0
0
0
0
1
2
1
0
2
2
0
0
0
2
1
2
0
1
2
1
2
2
1
0
0
0
1
0
1
2
0
1
1
1
0
0
3
2
1
2
0
3
2
1
1
2
1
0
1
0
0
1
2
1
0
0
2
0
1
0
1
1
1
0
1
0
0
1
0
0
0
0
1
0
0
1
1
1
0
1
0
1
1
0
0
0
1
1
0
0
0
0
2
1
1
0
0
0
0
2
0
2
0
2
2
2
0
1
2
0
0
0
2
0
0
0
0
2
1
1
0
0
0
1
1
1
2
0
0
0
1
2
1
2
3
1
1
1
2
0
1
3
2
0
2
0
0
0
0
2
1
1
1
0
1
0
1
0
0
0
2
0
1
1
0
1
0
1
0
3
0
0
0
0
0
0
2
0
0
0
0
2
0
2
2
0
2
0
1
1
0
0
1
2
0
0
0
0
0
1
2
0
0
0
0
2
0
2
2
0
1
2
4
1
1
0
2
0
1
1
1
2
0
1
0
0
0
0
1
1
1
0
2
2
0
2
0
0
0
0
1
2
1
2
0
0
0
0
0
0
0
1
0
0
1
2
0
0
1
0
1
1
1
0
0
1
0
1
2
0
2
0
0
0
1
1
0
1
0
1
1
2
1
0
2
1
1
0
2
1
0
2
1
1
0
0
1
3
2
1
0
0
2
0
2
1
0
2
0
0
1
0
1
0
0
0
0
0
1
1
1
0
0
1
1
0
0
2
0
0
2
0
2
0
2
0
1
1
0
0
0
2
1
0
1
0
0
2
0
0
0
2
2
1
0
0
1
2
2
1
0
2
2
0
5
0
0
1
1
1
2
2
1
2
0
3
0
1
2
2
0
1
0
0
2
1
0
2
1
0
0
0
0
1
1
0
2
1
1
1
0
2
0
0
0
0
0
0
1
2
1
1
0
1
2
1
1
2
0
1
1
1
2
2
2
0
0
0
2
0
0
1
2
2
2
0
1
0
1
0
0
2
2
1
1
1
1
1
1
2
0
4
1
0
0
2
0
0
1
2
2
0
1
1
0
0
3
0
0
0
1
0
1
0
1
0
0
0
0
1
0
1
1
1
1
0
1
0
0
2
1
1
2
1
2
0
0
0
2
0
1
1
0
2
0
3
2
0
0
2
1
1
0
0
2
0
0
0
0
1
1
2
2
0
1
1
1
1
0
0
0
2
2
0
2
1
1
0
0
1
2
1
2
2
1
1
0
0
1
0
0
0
1
0
0
1
2
0
0
0
2
1
1
0
0
1
0
2
1
0
0
0
1
0
0
1
0
1
0
1
1
0
1
2
0
0
0
0
2
2
2
2
1
0
0
1
0
1
1
2
2
1
0
0
0
0
1
2
1
0
1
0
0
0
2
0
0
1
5
0
0
2
2
1
2
0
1
0
0
0
2
1
1
2
1
2
0
1
0
1
1
1
1
0
2
0
0
2
0
0
0
1
0
1
1
1
2
0
0
1
1
1
2
0
1
1
0
0
2
1
0
2
1
0
0
1
2
1
2
0
0
0
0
0
0
1
2
1
1
1
0
2
2
0
1
0
2
1
1
2
0
1
2
1
0
2
0
0
0
0
1
2
1
2
0
1
1
0
1
0
0
2
0
0
2
1
0
0
0
0
2
1
2
2
1
1
0
2
3
0
1
0
2
4
0
0
0
0
2
0
1
0
0
0
1
0
0
0
1
4
3
0
0
0
1
1
1
0
1
1
2
0
1
0
0
1
0
0
0
0
1
2
0
0
1
1
0
0
0
3
0
1
0
0
2
0
0
0
1
0
1
0
1
1
2
1
2
0
1
0
2
0
2
1
0
0
0
0
2
0
0
0
0
1
0
0
0
1
2
0
0
2
0
1
2
5
0
1
1
0
1
2
0
1
0
1
0
2
0
0
1
1
1
1
5
1
1
0
0
2
0
1
0
0
1
1
1
0
2
2
0
2
2
0
2
1
0
0
1
2
0
2
0
2
0
0
1
2
1
0
1
2
1
0
1
0
1
1
0
0
0
0
1
0
2
0
2
0
2
1
2
0
0
0
5
0
1
1
0
0
2
0
2
1
2
1
2
2
1
1
0
2
2
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
2
0
1
1
0
1
1
1
2
2
2
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
3
1
0
2
0
1
0
2
0
2
0
1
0
2
1
1
2
0
2
2
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
3
0
0
2
1
0
0
0
1
0
1
0
0
0
0
0
0
2
1
1
1
1
2
0
5
1
0
2
2
2
1
0
1
0
1
0
0
0
1
0
2
1
1
0
1
1
2
1
2
2
2
0
3
1
1
0
0
2
0
0
0
0
1
1
1
0
0
0
1
0
2
1
0
1
0
0
0
2
0
0
0
0
2
3
0
0
1
0
0
2
1
0
0
2
1
2
0
0
0
0
0
2
2
1
1
1
1
0
0
0
0
1
0
0
2
0
0
2
1
0
2
2
0
0
0
1
0
1
0
2
0
1
1
2
0
1
1
0
0
1
1
0
0
2
2
1
0
0
1
2
1
0
1
2
0
2
1
1
1
2
2
1
1
0
0
0
0
2
0
1
0
0
1
1
0
0
1
2
0
0
2
0
1
2
0
1
0
0
1
0
1
0
2
0
0
2
0
1
0
0
1
1
0
1
2
0
1
0
1
1
0
1
4
0
0
1
0
0
2
0
0
0
1
0
1
0
1
1
1
0
0
0
0
0
1
1
0
2
0
2
2
2
0
2
1
2
0
1
0
2
2
2
1
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
1
2
2
2
0
0
0
0
1
2
0
1
2
1
2
9
1
2
0
1
0
0
1
0
0
0
0
1
0
2
0
1
0
3
1
0
1
0
1
1
0
1
1
2
2
0
0
0
0
2
0
1
3
1
0
0
2
1
1
1
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
2
0
0
2
0
1
1
0
0
1
0
0
1
1
1
1
0
0
0
0
0
0
1
2
0
2
2
0
2
0
1
2
1
0
2
2
0
0
0
2
1
0
0
2
0
1
3
0
0
0
0
1
1
0
2
0
0
0
1
0
0
0
0
0
1
1
2
2
2
0
1
1
0
1
0
0
0
2
0
1
1
2
0
2
0
0
0
0
2
2
2
1
1
0
0
2
1
0
0
1
0
1
1
0
1
0
1
1
1
2
2
2
1
2
1
0
1
2
1
1
1
1
2
0
2
1
2
0
0
0
0
0
1
1
1
0
2
0
0
1
0
1
0
0
0
1
1
1
0
1
0
2
0
0
1
0
1
0
2
1
1
1
0
1
0
0
2
0
1
0
2
0
0
2
0
2
0
1
0
0
1
0
1
2
0
2
0
0
0
1
2
2
1
2
0
1
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
1
1
3
2
0
2
0
1
0
0
1
1
0
2
2
0
0
2
0
2
2
0
0
0
1
1
1
2
0
0
0
1
0
0
1
1
1
2
0
1
1
0
0
0
1
0
0
2
0
0
2
0
0
0
0
2
1
0
1
1
2
0
0
0
0
1
0
2
0
1
1
2
1
2
0
2
1
2
0
1
0
0
2
2
2
0
1
0
0
1
1
0
0
2
2
0
0
0
1
1
0
2
0
1
1
0
0
1
0
1
1
0
0
1
0
0
1
3
0
2
0
1
1
2
0
0
3
0
0
2
1
0
0
1
0
0
1
0
0
1
1
0
0
1
1
2
1
0
0
0
2
0
0
0
0
0
1
0
1
1
0
3
0
0
3
0
2
2
1
2
1
0
0
0
1
0
0
0
1
0
0
1
0
0
1
1
0
1
0
1
0
1
0
4
0
0
1
0
0
1
3
2
1
0
1
1
0
1
0
0
0
2
1
1
0
2
2
0
0
1
2
1
0
1
5
0
1
0
1
1
1
0
2
0
0
1
1
2
0
0
0
2
2
0
2
2
0
1
1
2
0
2
0
0
1
0
2
1
0
0
0
4
0
1
2
0
2
2
0
1
2
0
2
3
0
1
0
0
0
0
2
0
2
0
2
0
1
0
2
0
0
1
2
0
0
1
0
0
0
0
0
0
2
2
1
0
2
1
0
1
0
0
2
0
2
1
2
0
0
0
0
0
2
0
2
2
0
0
0
1
1
0
0
2
1
2
0
1
2
1
0
0
2
0
0
0
2
0
0
1
0
0
0
0
1
2
0
1
2
2
2
0
2
0
0
1
0
0
0
0
2
0
0
2
0
1
2
0
0
1
1
1
0
1
1
0
0
0
0
0
0
2
4
0
2
0
0
0
0
1
1
1
1
0
0
0
0
1
0
0
0
0
2
0
0
2
0
1
2
0
0
2
0
1
0
0
1
0
2
1
1
1
0
1
3
0
0
1
2
0
1
0
2
0
2
3
1
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
1
0
1
0
1
0
1
0
1
0
0
0
1
0
2
3
1
2
1
1
1
0
1
0
1
2
0
0
2
0
0
0
0
1
1
0
0
0
1
1
2
2
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
1
0
0
1
0
1
2
0
3
2
0
2
0
2
2
1
1
0
0
0
0
2
1
1
0
1
2
0
0
0
1
2
0
0
0
1
0
2
0
1
0
0
0
1
2
2
1
0
0
2
1
1
1
0
0
0
0
1
0
0
0
2
0
2
2
2
0
0
1
0
1
2
1
2
0
2
0
0
0
0
2
0
0
1
1
0
0
0
1
0
0
2
0
1
2
0
0
1
1
2
2
2
1
0
2
0
2
1
0
1
0
1
0
0
0
1
0
1
1
2
0
1
4
0
1
1
1
1
1
0
2
0
0
2
1
1
0
1
1
1
0
2
0
0
2
1
1
0
0
0
0
1
0
0
5
0
1
0
0
1
2
1
0
0
1
0
0
2
0
0
2
0
0
3
0
2
1
0
1
0
2
0
0
1
1
0
0
0
0
1
0
2
1
0
2
0
0
2
1
1
0
0
0
0
1
1
1
0
0
0
1
0
2
0
1
2
1
1
0
0
0
2
1
2
2
1
2
0
0
2
1
1
0
1
0
1
2
1
0
1
1
0
0
0
2
1
1
1
0
2
1
2
0
1
0
2
2
0
1
0
0
2
0
0
0
0
0
0
1
0
0
1
1
0
1
1
0
0
1
0
0
1
0
2
0
1
0
1
0
1
1
2
0
0
0
1
0
0
1
3
0
2
2
1
0
0
1
2
0
0
2
0
1
1
2
1
1
1
0
0
2
2
0
0
0
0
1
0
2
1
0
0
1
0
2
3
1
0
0
2
1
1
0
3
0
1
0
1
0
0
2
0
0
1
0
0
0
0
0
0
1
0
1
2
0
0
0
0
1
1
0
1
2
1
1
0
3
1
1
0
2
2
0
2
0
1
0
1
1
0
0
0
0
0
2
0
0
2
0
1
0
1
2
0
0
0
0
0
0
0
1
1
0
1
1
0
1
0
0
3
0
0
3
1
2
0
0
0
2
0
1
0
1
2
2
0
2
0
1
0
2
1
0
0
2
1
2
0
3
0
0
1
0
0
0
1
0
1
2
0
0
1
0
0
2
2
1
0
0
0
0
0
1
1
0
2
0
1
1
0
0
0
1
1
1
1
1
1
1
0
0
0
1
2
0
0
0
1
0
2
2
1
1
0
0
0
1
0
0
2
0
0
0
0
1
4
0
0
0
2
1
0
1
2
1
0
1
0
0
2
1
0
0
2
0
2
0
2
0
1
0
1
2
0
0
0
1
2
0
0
0
2
0
0
0
2
2
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
2
2
1
0
0
0
2
2
1
0
1
1
0
0
0
1
0
2
1
2
0
0
0
2
2
0
0
1
1
1
0
1
2
0
1
1
0
0
1
0
0
2
0
0
0
0
0
1
0
1
0
0
2
2
2
3
0
1
0
0
0
2
1
2
0
0
0
2
0
0
0
1
2
1
1
0
0
0
0
2
1
2
2
0
0
0
3
0
0
0
1
0
1
0
0
2
0
2
0
0
0
1
2
1
0
1
1
1
1
0
0
1
0
0
0
1
1
1
0
3
0
0
2
0
0
1
0
1
0
0
1
1
2
0
0
0
0
0
1
2
0
0
1
0
0
1
1
0
3
1
1
0
0
2
0
0
0
1
0
2
2
0
1
0
0
1
0
0
2
0
0
0
1
1
0
0
0
1
0
2
1
0
2
1
0
0
0
0
0
0
0
2
2
0
0
0
2
1
0
2
0
1
0
0
1
0
2
0
0
2
0
1
1
0
1
1
0
1
1
0
0
1
1
0
1
0
1
2
0
0
0
2
1
2
0
0
1
0
0
0
0
1
2
0
0
0
1
1
0
0
0
0
1
0
1
0
0
1
0
0
2
1
0
1
1
2
0
1
0
0
0
1
3
1
1
1
2
0
1
0
1
0
3
2
0
0
0
2
0
0
1
1
0
2
1
1
2
0
0
1
0
1
0
0
2
0
1
1
0
0
1
0
1
0
0
3
0
0
0
0
0
0
2
0
0
1
2
0
1
0
2
0
0
0
0
0
0
0
1
2
1
0
0
0
0
1
1
0
0
1
0
0
1
1
1
2
0
0
2
2
1
1
1
2
0
2
0
2
2
0
0
1
0
2
1
2
0
1
0
0
2
1
1
1
0
1
0
2
0
0
0
0
0
0
0
1
0
0
1
1
0
1
2
0
0
0
0
2
0
0
2
2
2
1
0
2
1
2
0
0
0
1
0
0
0
5
1
2
1
1
1
2
0
1
1
1
0
1
0
0
0
0
2
0
0
1
0
2
0
0
0
1
0
0
1
2
2
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
1
1
1
0
0
1
0
0
2
0
1
2
2
2
1
0
0
2
0
0
1
0
2
0
0
1
1
0
0
0
1
0
2
1
2
0
1
1
0
1
2
0
0
1
0
2
0
1
0
0
3
1
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
1
2
0
1
0
2
0
0
0
0
1
1
1
0
0
0
0
1
1
2
0
2
3
0
0
0
2
0
0
2
2
0
1
1
2
1
0
0
1
0
1
0
1
0
2
0
0
1
0
1
0
1
1
1
0
1
0
1
0
1
1
0
0
0
0
0
2
2
1
1
0
1
1
0
0
0
0
1
0
2
0
0
1
1
0
0
0
0
1
2
2
1
1
3
0
2
0
1
0
1
2
2
0
0
1
2
2
0
1
1
1
1
0
2
0
0
0
0
0
0
0
1
1
0
0
2
0
0
2
2
2
0
3
0
2
1
0
0
2
3
1
0
2
1
1
1
0
0
0
1
0
0
2
0
1
0
0
2
0
1
2
1
0
1
1
0
0
0
2
1
2
0
0
0
2
2
1
0
2
0
1
2
2
0
0
0
0
0
0
0
1
0
1
1
1
1
2
0
0
0
1
0
0
0
0
0
0
1
2
1
2
0
2
1
2
2
0
0
0
0
0
1
0
0
0
0
1
2
2
0
0
0
0
2
1
1
2
1
0
4
0
0
0
0
0
0
2
1
1
1
2
4
0
0
1
0
0
1
0
0
2
1
0
1
0
1
0
0
2
0
1
0
1
0
1
1
0
0
0
1
0
0
0
1
0
2
1
2
1
0
0
0
0
2
1
2
0
1
0
2
0
1
0
0
2
2
2
1
0
0
0
2
0
1
2
0
0
0
2
1
0
1
2
0
1
1
0
1
0
0
0
0
1
2
2
1
2
0
1
1
1
0
0
1
0
0
0
0
0
2
0
1
1
0
0
0
1
0
0
0
0
1
0
0
1
0
2
0
1
1
0
0
0
1
0
1
0
1
0
0
1
1
2
0
1
1
2
0
1
0
1
0
0
1
0
1
0
0
0
2
1
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
1
2
0
0
0
1
0
1
0
0
0
0
2
0
2
1
0
0
0
0
1
2
0
0
2
0
1
0
0
0
0
1
0
2
0
0
1
2
0
0
2
1
2
1
0
1
0
1
1
1
0
0
0
1
1
0
1
0
1
1
4
2
2
1
0
1
0
2
0
0
0
2
2
2
0
0
1
0
2
0
3
0
2
0
0
0
0
1
1
0
2
0
1
1
0
1
0
2
1
0
0
0
2
1
0
0
0
1
0
0
0
1
1
2
1
0
0
0
1
1
0
1
1
2
0
0
2
2
0
0
0
2
0
1
2
1
0
2
0
0
1
0
0
0
0
0
0
1
0
0
1
1
2
2
0
2
2
1
1
0
1
1
2
1
0
2
0
0
2
0
0
1
0
0
2
0
0
1
0
1
1
0
1
1
1
1
6
2
0
0
1
1
0
0
1
2
2
1
0
1
0
1
2
1
0
1
0
0
1
1
1
0
1
0
0
0
6
1
0
1
2
0
1
0
0
0
2
3
0
0
0
0
0
2
0
0
3
0
0
2
1
0
0
2
0
1
1
1
4
0
0
0
2
1
2
0
2
0
0
0
0
0
0
0
0
1
0
0
1
2
1
0
0
0
0
2
0
0
2
1
1
0
0
1
1
1
0
1
1
0
0
1
0
2
0
0
0
0
2
0
0
0
0
2
2
1
1
0
1
1
0
1
0
1
3
0
0
1
1
1
1
0
1
1
0
1
1
1
0
1
0
0
2
0
1
1
1
0
1
0
0
2
1
0
1
2
0
1
1
0
0
2
0
2
2
1
1
2
1
0
2
0
0
0
0
1
1
0
2
2
1
2
0
0
0
0
0
0
2
0
2
2
1
2
1
2
0
1
2
0
0
2
2
2
1
1
2
0
0
0
0
1
0
2
0
1
0
0
2
1
2
0
0
0
1
1
1
0
0
0
1
0
1
2
0
0
0
1
1
0
0
0
1
0
1
0
1
1
1
1
1
1
0
2
0
0
2
0
0
1
1
0
1
1
0
2
0
0
0
1
0
1
0
1
0
2
0
0
2
0
1
0
1
2
0
2
0
1
1
2
0
0
1
0
2
0
0
0
1
1
2
0
1
1
2
2
0
0
2
0
2
0
0
0
1
1
2
0
0
0
1
0
0
1
0
2
1
0
2
0
1
1
1
0
0
0
0
0
0
0
1
1
1
0
2
2
1
0
0
2
3
0
1
0
1
0
1
0
0
2
4
2
2
0
2
1
1
0
0
0
0
2
1
0
0
2
0
0
2
2
0
0
0
0
1
0
3
1
2
1
0
1
2
3
0
0
0
0
0
1
1
0
1
1
1
0
0
0
0
0
0
0
0
1
0
1
2
1
1
2
2
0
1
1
0
2
1
2
0
2
0
0
0
2
2
0
1
3
0
0
1
2
0
0
2
0
1
0
0
0
1
2
0
0
0
0
0
1
2
0
2
2
1
2
0
1
2
0
2
6
0
1
2
1
1
0
0
0
2
2
1
2
0
1
0
0
0
1
1
0
0
0
2
1
0
0
0
0
1
0
0
1
0
0
1
0
1
2
3
0
0
0
0
0
1
0
1
0
0
2
1
2
1
2
2
2
0
1
2
2
0
1
0
0
0
2
0
0
0
0
0
0
1
1
0
2
0
1
0
0
0
1
1
0
0
2
0
0
0
0
2
0
1
0
2
1
1
0
0
2
0
2
2
1
0
2
1
0
0
0
2
0
1
0
0
0
2
0
0
3
0
0
2
0
0
1
0
2
1
4
1
1
0
2
1
0
0
0
0
0
1
0
0
0
1
2
0
2
1
1
0
0
0
4
2
1
1
0
0
1
0
0
0
0
1
1
0
0
1
2
0
0
0
2
0
0
1
1
0
0
0
1
0
1
0
0
0
1
0
0
2
0
1
1
0
0
0
1
0
1
3
0
0
0
0
1
0
2
0
0
0
2
0
1
1
2
0
1
2
0
2
2
2
1
2
0
0
0
3
1
0
0
0
2
0
0
2
1
2
0
2
0
1
1
2
2
2
1
0
2
0
2
0
0
0
1
2
1
0
0
0
2
2
2
0
0
1
1
2
2
2
0
1
1
2
1
0
0
0
0
0
0
0
1
1
0
0
2
2
0
0
1
0
0
3
0
1
0
0
0
1
0
2
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
2
2
1
2
2
1
0
0
0
0
0
1
2
0
1
0
2
0
0
2
2
0
0
2
2
1
0
3
0
0
1
1
0
0
1
0
1
0
0
0
0
3
0
2
0
1
0
1
0
2
0
1
0
0
2
1
0
2
2
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
1
3
1
0
1
0
1
0
2
0
0
1
2
1
2
0
0
0
0
0
1
0
2
0
0
0
0
1
2
1
0
1
0
0
0
2
1
2
2
1
0
0
1
0
0
0
1
0
2
0
0
1
1
1
1
0
1
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
1
1
0
1
1
1
0
0
1
0
0
0
1
0
1
1
1
1
0
3
1
2
0
1
0
0
1
0
0
0
3
0
2
0
2
3
0
0
0
0
0
2
0
2
0
1
2
0
1
0
0
2
0
1
1
1
0
0
2
1
0
1
0
2
2
1
1
1
0
1
0
0
2
1
0
1
1
0
0
0
2
2
1
1
1
3
0
0
1
1
1
1
1
0
2
2
1
0
1
1
0
0
1
2
1
2
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
2
1
2
1
1
0
2
0
1
2
0
0
0
0
2
0
1
0
0
0
0
2
0
0
1
2
0
1
2
1
0
0
0
0
1
2
2
1
1
1
0
1
1
1
0
0
2
0
1
1
0
1
0
0
1
1
2
2
1
0
0
0
0
1
0
0
0
0
2
0
1
0
2
2
1
2
1
1
0
0
0
0
0
0
0
0
1
2
2
0
0
2
0
1
1
0
1
1
1
0
2
0
1
1
0
1
0
2
0
0
2
3
0
1
0
1
2
2
1
0
2
2
3
0
1
0
0
0
2
0
0
0
2
0
0
0
0
1
2
1
0
1
1
1
0
1
0
2
0
1
1
1
0
0
0
0
1
1
0
2
0
2
1
0
0
2
1
1
1
0
0
0
2
1
1
0
0
0
1
3
0
0
2
0
1
2
1
0
0
0
1
1
3
0
1
2
1
0
1
1
2
0
0
0
0
1
0
1
2
0
0
2
5
1
1
2
1
0
0
0
0
0
2
1
0
2
0
0
0
2
0
2
0
0
2
0
1
0
2
0
2
1
1
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
2
1
0
0
1
3
0
0
2
0
1
0
0
2
2
2
1
2
1
0
0
0
0
0
1
0
0
2
0
0
1
0
1
1
2
3
1
0
0
2
1
0
0
0
0
0
2
1
0
0
2
0
2
1
0
1
1
0
2
0
0
0
2
0
2
0
0
1
0
1
2
2
2
1
0
1
0
0
0
0
0
1
5
1
2
0
0
0
1
1
0
1
0
1
1
2
2
1
0
0
1
0
0
0
1
2
1
0
2
2
1
0
0
1
2
0
2
0
0
1
0
0
1
0
0
0
1
0
2
0
1
1
0
0
1
1
1
1
0
0
0
1
1
2
0
0
1
2
1
3
0
1
0
1
0
1
0
0
1
0
0
0
1
2
0
1
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
2
1
0
0
2
1
0
0
0
0
2
1
1
1
0
0
1
2
2
0
0
0
0
3
3
0
0
2
1
1
1
2
0
1
0
0
1
0
2
0
0
0
0
2
1
1
1
0
2
1
0
2
2
1
0
0
2
2
1
2
0
2
2
0
0
0
0
1
0
1
0
2
2
1
1
0
2
0
0
0
2
1
2
1
1
2
0
0
3
0
0
1
0
1
0
0
0
1
0
0
1
0
1
1
1
0
0
0
1
1
0
1
2
0
1
1
0
0
1
1
1
2
0
2
2
0
0
3
2
1
2
0
0
0
2
2
0
0
0
2
1
2
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
1
1
0
3
0
1
0
3
0
1
1
1
0
2
0
0
1
0
1
2
1
0
2
0
0
0
0
0
1
1
0
0
1
2
0
0
1
1
2
1
1
1
0
0
1
2
0
4
0
0
0
0
0
1
0
0
0
1
3
2
1
1
2
1
0
1
1
0
1
0
1
2
1
1
0
2
1
1
0
0
1
1
1
2
0
0
0
0
0
1
0
2
1
2
0
0
0
0
0
1
1
1
1
0
1
1
0
2
1
0
0
1
0
2
0
1
0
1
0
2
0
2
0
1
0
1
1
0
0
1
1
0
0
0
2
1
2
2
1
3
1
1
0
1
2
1
0
0
0
0
1
1
1
1
1
0
0
1
0
0
2
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
1
4
0
0
2
0
0
0
0
1
2
0
1
0
1
0
2
2
0
0
0
1
1
2
0
0
2
0
1
0
1
0
0
0
2
0
0
1
1
1
0
1
0
0
2
0
2
0
0
0
0
0
1
0
0
2
1
0
1
2
0
0
2
1
1
1
1
2
1
1
1
0
3
1
0
3
2
1
1
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
1
1
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
1
0
0
1
0
2
2
1
0
1
2
0
1
1
0
2
2
1
0
0
0
1
0
0
2
1
0
2
2
0
1
0
0
1
2
0
0
1
0
0
1
1
0
0
0
0
0
1
2
0
0
2
0
0
1
0
1
0
1
1
2
2
1
1
1
0
2
0
0
1
2
0
0
0
0
1
0
2
0
1
1
0
2
0
1
1
0
0
2
0
0
0
2
0
1
0
1
0
2
0
0
1
0
0
0
1
0
0
1
1
1
1
0
1
0
2
0
1
0
0
0
2
2
1
0
2
0
0
0
0
3
0
2
2
0
0
2
2
1
1
1
0
0
0
0
0
0
1
2
0
0
0
0
2
1
0
2
0
0
2
2
0
0
1
1
0
2
0
0
1
0
1
0
0
1
0
0
1
1
1
0
1
1
0
1
1
0
0
1
0
0
0
0
0
1
2
0
3
1
0
1
1
1
0
0
1
1
0
0
1
2
1
0
2
0
2
1
0
2
2
1
1
0
1
0
0
1
1
1
2
0
0
0
0
0
1
1
0
0
0
0
1
0
2
2
0
0
1
0
0
1
0
1
1
0
1
1
0
1
0
0
1
2
2
1
2
0
1
1
1
2
2
0
0
1
0
0
1
0
2
0
0
2
0
0
1
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
2
1
0
2
1
0
0
1
1
2
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
2
0
1
0
0
0
1
0
1
0
0
1
0
1
1
0
2
0
0
2
0
1
0
1
1
1
2
2
0
0
1
2
1
0
2
0
1
1
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
2
2
0
3
0
0
0
0
1
1
2
0
0
0
0
1
0
1
0
1
0
0
0
0
6
0
0
2
0
2
0
0
0
2
0
1
0
0
2
0
1
1
0
2
4
0
1
2
1
0
0
0
0
0
0
0
1
2
1
1
1
0
0
1
2
2
0
0
1
4
1
2
2
0
0
0
2
0
1
2
0
1
1
0
0
2
0
0
1
0
0
0
1
0
2
0
0
0
3
1
0
2
2
1
0
0
1
0
2
1
0
0
1
0
1
2
0
1
0
1
1
0
1
2
1
1
0
0
2
0
2
0
0
0
1
0
1
0
0
0
0
2
1
0
1
1
0
1
0
0
2
0
0
2
0
1
0
0
1
0
1
0
1
0
0
0
1
2
0
1
0
1
3
2
0
1
0
0
0
1
1
0
1
2
2
0
2
0
1
0
1
1
2
0
1
0
0
0
0
0
1
0
0
1
2
0
0
2
0
0
0
2
0
0
2
3
2
0
1
1
0
0
0
0
3
0
0
2
0
0
0
1
1
3
0
0
0
1
0
0
0
0
0
2
0
1
0
0
1
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
1
1
0
2
0
0
1
0
3
0
0
2
2
0
0
0
0
0
1
1
1
2
1
2
1
0
0
0
1
1
0
2
7
2
0
2
0
0
2
0
0
0
0
2
2
1
0
1
0
0
1
2
0
0
0
0
0
2
0
2
0
0
1
3
0
0
1
2
1
0
5
2
0
0
2
2
1
0
0
1
0
1
0
1
0
0
1
0
0
2
2
2
2
2
0
0
0
1
0
2
0
0
1
1
0
1
0
1
2
0
1
0
2
1
0
1
0
0
2
0
0
0
0
0
2
2
2
0
0
0
1
1
1
1
0
1
1
2
0
1
0
0
2
0
0
0
0
2
0
2
2
0
0
0
2
1
2
1
0
1
3
1
0
1
0
1
0
1
0
0
1
0
1
1
0
2
2
0
2
1
1
1
2
0
1
0
0
2
1
1
0
0
0
0
2
0
4
1
2
0
1
0
1
2
0
0
0
0
2
1
0
0
0
0
0
0
1
1
0
0
1
0
0
2
0
0
0
0
2
2
1
1
2
1
2
1
0
0
2
2
0
0
2
1
1
0
1
0
1
0
1
1
2
2
0
0
1
1
0
0
2
0
0
3
0
0
0
2
0
0
2
0
2
1
1
1
0
0
2
2
1
0
0
0
0
2
0
1
2
0
1
0
0
2
0
2
1
0
2
1
0
0
2
0
0
1
0
2
1
2
1
1
0
1
2
2
1
0
1
2
1
2
0
0
1
1
0
0
2
1
0
0
1
2
2
0
0
2
2
2
3
2
0
0
1
0
0
2
1
3
0
2
1
1
1
1
0
1
1
0
1
1
0
1
1
1
0
0
0
0
1
0
0
0
1
0
0
2
1
2
0
0
2
0
1
1
0
0
0
2
0
0
0
1
1
1
1
1
2
1
1
1
0
1
0
2
1
2
0
0
0
2
1
0
1
1
1
1
2
0
0
1
0
2
1
0
2
1
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
2
2
0
0
2
1
0
1
0
2
0
0
0
0
0
1
1
0
1
1
0
0
2
0
0
0
0
1
0
2
0
2
2
0
0
0
0
1
0
0
1
0
3
2
2
1
2
1
2
2
0
0
0
1
1
2
0
0
1
1
1
0
1
2
2
0
0
0
2
1
0
0
0
0
0
0
0
1
1
2
0
1
0
1
0
0
1
1
1
0
0
0
1
1
0
1
0
0
1
0
0
2
1
0
0
4
0
0
2
0
1
1
2
0
0
1
1
2
0
1
1
0
1
0
0
0
0
1
0
1
0
2
2
0
2
0
0
1
1
1
0
1
0
2
0
1
2
1
1
0
2
2
2
0
2
2
0
2
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
1
1
0
2
1
0
0
1
2
2
0
1
0
0
0
0
2
0
2
0
0
0
0
1
1
0
0
0
7
0
0
0
0
2
1
0
1
0
2
0
2
0
0
0
0
1
2
0
1
0
0
0
1
0
1
2
1
1
1
3
1
2
0
0
0
0
1
1
0
0
1
2
0
2
1
1
1
1
1
1
1
0
1
0
1
0
1
2
2
2
0
0
1
1
1
0
0
1
2
0
0
0
1
2
0
2
1
2
1
1
0
0
1
1
0
0
2
0
1
2
2
2
2
0
1
2
0
1
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
2
2
1
1
2
1
1
2
0
1
1
1
2
3
0
1
0
2
2
0
1
1
0
0
0
0
1
0
0
0
0
2
1
1
0
0
0
0
2
1
2
0
1
0
2
0
0
0
1
1
1
0
0
1
0
0
2
0
0
1
0
0
2
0
1
1
1
0
0
0
0
2
2
0
3
2
2
0
0
1
0
3
0
0
1
2
0
1
2
1
2
2
2
1
0
1
0
1
0
2
1
2
0
0
1
1
0
1
2
1
2
0
2
0
0
0
1
0
1
0
1
1
0
0
0
2
0
1
2
2
2
1
1
0
0
0
1
0
0
0
2
2
0
1
0
0
0
0
1
2
1
0
0
1
3
1
0
0
0
0
0
1
2
0
0
0
0
1
2
0
0
0
1
2
1
1
2
0
0
4
0
0
1
0
0
2
1
0
2
0
0
0
0
0
1
0
1
0
2
0
1
0
0
1
0
0
0
0
0
2
1
2
0
1
0
0
1
0
2
0
1
1
1
1
0
1
0
1
1
0
0
2
0
0
2
0
0
0
0
0
0
1
1
1
1
1
0
0
2
2
2
0
1
2
0
2
1
0
0
1
0
1
1
0
2
0
0
0
1
0
1
2
0
0
1
1
1
1
0
0
2
0
1
1
1
1
2
2
0
2
2
0
1
2
0
2
1
0
0
0
0
2
0
0
1
0
2
0
2
1
2
0
1
2
2
2
0
0
2
1
0
1
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
2
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
2
0
2
2
0
1
1
1
0
1
2
1
0
2
0
1
0
0
2
0
2
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
1
2
0
2
0
1
0
2
0
0
1
1
0
1
3
2
2
0
2
0
1
2
0
0
0
1
0
1
2
3
0
0
2
0
2
2
0
0
0
0
0
2
1
2
0
0
1
2
0
1
2
1
0
1
0
0
1
1
5
1
1
2
0
0
1
1
1
0
0
2
0
0
0
0
1
0
2
0
1
0
1
0
0
1
0
0
2
1
0
0
0
0
1
0
1
0
0
2
1
1
1
0
0
0
0
0
2
2
4
0
1
2
2
1
1
1
0
0
0
0
2
0
1
1
1
0
0
0
1
0
2
0
0
0
2
2
0
1
1
0
0
1
0
0
0
2
0
0
0
0
0
1
0
1
1
0
3
2
0
1
1
0
1
1
0
0
0
0
1
0
2
1
0
0
0
1
0
1
1
2
0
0
0
1
2
0
0
1
2
0
1
0
1
0
0
0
0
2
2
0
2
0
1
0
1
0
2
1
1
0
1
1
0
1
0
0
0
0
0
3
1
0
1
1
2
0
2
0
0
0
2
1
0
1
1
1
0
1
1
0
1
0
1
1
1
2
0
0
0
0
2
0
0
1
1
2
1
1
2
1
0
0
0
0
2
0
1
2
0
0
0
0
2
0
2
2
0
0
0
2
2
1
0
0
1
1
0
1
0
1
0
0
0
1
2
0
2
1
0
0
1
1
2
0
0
1
0
3
3
0
1
0
0
0
1
0
0
2
0
0
0
0
2
1
1
1
1
0
0
0
0
3
0
1
0
2
0
0
1
1
0
0
0
1
2
1
0
0
2
1
0
0
0
0
2
2
0
0
1
0
0
0
1
0
2
0
0
0
2
1
0
2
0
0
1
0
0
0
0
0
1
0
2
1
2
2
2
1
0
0
2
2
0
1
0
0
0
1
0
0
1
1
0
0
0
0
1
1
0
1
0
1
0
0
0
0
1
1
0
0
0
0
2
0
0
0
1
1
0
0
0
0
1
2
0
0
0
0
2
0
1
0
1
0
1
2
0
1
3
2
0
1
0
0
0
0
0
2
1
0
1
0
0
2
0
0
0
1
0
0
2
2
0
1
1
1
0
0
2
0
0
1
0
1
1
0
2
1
1
1
1
1
2
2
2
1
2
0
1
2
0
1
0
1
0
2
1
2
0
0
2
0
0
0
0
1
1
0
0
1
0
0
0
2
2
2
0
0
2
1
0
1
1
1
0
0
1
0
0
0
0
1
2
2
0
2
0
2
2
2
1
1
0
0
1
1
0
0
0
1
2
1
1
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
2
0
0
0
2
2
0
1
1
2
0
0
0
0
0
1
3
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
2
0
0
1
0
1
0
0
2
1
2
0
0
1
0
1
2
1
2
2
2
0
0
1
0
0
0
1
0
0
1
2
0
0
0
0
1
0
0
2
1
2
1
0
0
1
0
0
2
2
0
0
1
2
2
0
1
0
0
6
0
6
1
2
0
0
1
1
1
1
0
0
2
0
1
0
3
0
0
1
0
0
1
0
3
0
1
2
0
2
1
0
2
0
1
1
2
1
1
1
0
0
0
0
0
3
0
0
1
2
1
11
0
1
2
0
0
1
1
1
0
0
1
1
0
0
2
0
2
2
1
1
0
1
0
1
0
1
0
0
0
2
2
1
4
0
0
0
0
2
2
0
0
2
0
2
0
1
0
0
1
1
1
0
2
2
1
1
3
3
0
0
0
0
0
2
2
2
1
0
2
3
2
0
2
0
2
1
1
1
0
1
2
0
0
1
2
1
0
0
1
1
1
0
1
0
1
1
0
3
0
1
1
1
0
0
2
1
0
0
0
0
0
0
1
0
1
2
1
2
0
1
1
0
2
3
2
2
2
0
0
1
0
0
1
2
0
1
0
0
2
1
0
2
0
1
2
0
0
0
0
2
2
0
1
0
1
2
2
2
0
1
0
2
0
1
0
1
1
0
2
1
0
2
1
1
2
0
0
0
1
0
1
0
1
0
1
0
0
2
1
2
2
0
0
1
0
2
2
1
1
1
2
0
1
0
1
0
0
0
0
2
1
0
1
0
0
0
1
2
1
0
1
1
1
0
0
0
0
1
0
1
1
1
0
0
0
0
0
2
1
0
0
0
1
1
0
0
1
0
1
1
3
0
0
1
0
2
0
0
1
2
1
0
1
1
1
1
1
2
2
0
0
1
1
0
2
0
2
1
0
0
0
1
0
1
1
0
1
2
0
0
1
2
2
0
1
1
1
2
1
0
0
0
2
1
0
1
0
0
1
0
0
0
2
0
1
2
0
0
0
0
0
1
1
0
0
0
1
0
2
0
0
0
1
2
0
0
0
0
0
2
1
0
2
0
1
0
0
0
0
0
1
1
0
0
0
1
0
2
1
1
1
1
2
0
0
0
0
1
0
0
0
2
0
2
2
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
1
0
1
2
2
2
0
1
2
3
0
0
2
0
0
2
1
0
0
0
2
0
1
0
1
1
0
0
0
1
1
1
0
1
2
0
0
0
0
1
0
1
0
1
1
0
1
0
2
0
1
0
1
1
1
2
0
0
0
3
0
0
0
0
0
2
0
0
1
0
2
2
1
2
1
2
0
0
0
1
0
2
0
1
0
1
0
0
0
1
1
1
1
0
0
1
0
0
1
1
0
0
0
2
2
1
0
0
2
0
1
0
0
1
0
0
0
1
0
0
0
2
1
0
2
1
0
1
2
1
1
0
0
1
0
0
1
0
0
2
0
0
0
2
0
0
0
2
1
2
1
0
0
1
0
0
2
0
1
0
1
2
1
0
1
0
0
0
0
2
0
0
0
0
2
1
2
0
0
1
0
0
0
2
0
2
0
2
0
0
1
0
0
0
2
1
0
1
0
1
1
0
1
0
0
0
3
1
0
2
0
1
0
0
3
1
2
0
0
0
0
1
2
0
1
1
0
0
0
0
0
1
1
0
2
0
2
0
1
0
2
1
0
1
0
0
2
0
0
5
0
0
2
0
1
0
2
0
0
0
2
2
1
1
1
1
1
0
1
1
0
0
1
1
0
0
0
1
1
0
0
0
2
0
0
1
0
0
1
1
1
1
1
0
0
1
2
0
2
0
1
0
1
2
1
0
2
0
2
1
1
0
1
1
0
2
0
2
1
0
0
1
1
1
1
1
1
0
0
2
1
1
0
0
0
0
0
2
2
2
1
0
0
1
1
0
2
1
0
1
2
2
0
2
0
1
0
0
1
2
1
0
1
2
1
1
1
0
0
0
2
1
0
1
0
0
0
1
0
0
2
0
1
0
2
1
0
0
0
1
0
0
0
1
0
0
1
0
0
1
2
1
3
2
0
0
0
2
3
0
0
0
1
0
1
0
1
1
0
2
1
0
0
0
0
2
1
0
0
1
1
1
0
1
2
1
1
2
0
1
1
3
1
0
2
1
0
0
0
0
0
2
0
0
0
2
1
2
2
1
0
0
0
2
3
0
0
0
1
0
0
0
0
0
1
0
0
0
2
1
0
1
0
0
1
1
1
1
0
0
1
1
1
2
0
1
0
2
1
0
1
1
1
0
1
0
2
0
1
1
0
0
0
0
0
0
2
1
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
1
1
0
1
1
2
2
2
1
1
1
0
2
0
0
0
2
1
0
1
0
0
0
2
3
0
0
0
0
1
0
2
1
2
1
2
0
0
0
0
0
0
0
0
2
1
0
5
0
1
2
0
1
1
0
0
0
2
0
0
0
0
2
0
0
1
0
4
0
0
0
2
2
0
0
0
1
0
2
1
2
0
0
1
0
0
2
0
1
1
0
0
0
2
1
0
0
0
2
0
2
0
1
0
0
0
3
0
0
0
2
0
2
1
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
1
1
1
0
0
0
1
0
0
1
2
0
2
1
0
2
1
2
0
1
0
1
1
0
1
0
0
0
0
0
1
2
0
0
1
2
1
0
1
2
0
1
0
1
1
1
0
1
1
0
0
2
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
1
0
1
1
0
0
1
2
1
3
0
0
0
1
0
0
1
0
0
1
1
1
0
0
2
0
0
0
1
0
0
0
0
0
1
3
1
0
1
2
2
1
1
0
2
2
0
0
1
2
0
0
1
2
0
0
0
2
2
0
0
1
0
0
1
1
0
0
1
1
0
2
1
0
2
2
1
1
0
0
1
2
2
0
1
1
0
1
2
0
1
0
0
2
0
3
2
1
0
0
2
0
1
1
1
0
1
1
2
1
0
2
0
2
1
0
0
0
1
0
0
1
2
2
1
0
0
1
0
1
0
0
0
1
0
0
1
1
0
0
1
1
1
2
0
3
0
1
0
1
0
1
1
0
2
2
0
0
0
0
1
0
0
0
1
1
0
1
1
2
2
2
2
2
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
2
0
0
0
2
0
1
0
1
1
0
0
0
0
1
1
0
1
0
3
0
2
0
1
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
1
2
2
0
2
1
0
1
2
0
1
2
0
0
1
0
0
0
3
0
2
0
0
1
2
0
1
0
0
0
2
2
2
0
0
1
0
0
0
0
0
0
0
0
1
2
2
0
0
2
1
0
1
0
0
0
0
0
1
0
2
0
0
2
1
1
2
0
2
0
2
0
2
0
2
2
1
0
0
1
0
1
0
0
0
5
1
0
2
1
0
1
2
1
0
1
0
1
0
0
0
1
0
1
1
2
1
0
2
0
1
1
0
2
1
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
2
2
0
2
1
1
2
0
1
0
0
1
2
0
1
0
1
1
2
0
0
2
0
1
0
0
0
0
0
2
1
0
0
1
1
2
0
0
0
2
0
1
0
2
3
1
0
1
0
3
1
0
1
0
0
0
1
1
1
0
1
1
0
1
0
0
2
0
2
0
0
0
0
0
0
1
0
1
2
0
1
0
2
2
1
0
1
1
0
0
2
1
1
0
0
0
2
0
0
0
0
2
0
1
0
0
0
1
1
1
0
0
1
2
1
0
1
2
0
1
0
2
1
0
1
1
0
0
1
0
1
1
2
1
0
1
0
1
0
1
1
1
0
0
0
1
0
2
0
1
2
0
1
1
1
2
1
0
0
1
0
0
1
2
1
0
1
1
1
0
1
1
0
0
0
1
2
0
0
0
0
1
0
1
0
1
1
0
2
1
1
1
0
0
2
0
1
0
1
0
2
2
0
0
4
0
0
3
0
0
1
1
2
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
4
0
0
1
0
1
1
0
1
2
0
0
1
2
0
2
2
0
1
0
0
0
0
2
0
2
1
2
0
0
0
0
0
2
1
3
1
0
1
2
0
0
0
0
0
0
1
2
1
1
1
1
2
0
0
0
0
0
1
0
1
0
1
0
1
1
2
1
1
0
0
1
0
2
0
1
0
0
0
2
0
0
1
0
0
0
2
0
1
0
1
0
0
0
1
1
3
0
0
0
1
0
0
0
0
2
2
1
2
0
0
1
1
0
0
0
1
0
0
1
0
1
1
1
0
2
0
0
1
0
2
0
2
0
1
2
2
0
0
4
2
1
2
0
2
0
0
1
1
0
0
1
1
2
0
0
4
2
0
0
1
2
0
1
0
0
0
3
0
0
0
0
0
2
1
0
2
2
0
0
0
1
0
0
1
0
0
0
2
1
0
1
2
0
1
1
0
2
0
2
0
0
0
2
0
0
0
1
2
1
0
0
0
0
0
0
0
0
2
2
2
2
0
0
2
0
0
1
2
1
0
0
0
2
1
2
1
0
2
0
1
2
1
0
1
0
1
1
0
3
1
0
0
0
0
1
0
0
0
2
2
1
0
1
1
0
2
0
1
0
0
0
0
2
0
2
2
0
1
1
1
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
1
0
1
1
2
1
1
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
2
0
1
0
2
2
0
0
0
0
2
2
2
1
1
1
0
1
0
0
0
0
2
0
0
0
1
0
0
0
1
2
1
1
0
0
0
0
0
1
2
0
1
1
0
0
0
0
1
2
0
1
2
0
1
1
0
0
0
0
2
0
1
0
1
0
1
2
1
0
0
1
2
1
0
0
0
2
0
1
0
1
0
0
2
0
1
0
2
0
0
0
0
2
0
0
0
1
0
0
0
2
2
0
0
2
0
2
0
0
0
2
1
1
0
1
0
0
1
2
2
0
0
0
0
1
2
0
0
1
1
1
0
0
3
0
1
0
0
1
2
2
1
0
0
0
0
0
0
0
0
0
2
2
1
2
1
1
2
1
0
3
2
0
2
2
0
1
0
1
0
0
1
1
0
1
0
0
0
0
2
1
2
0
2
1
0
2
0
0
0
1
0
0
1
0
2
0
0
0
2
1
0
2
0
1
0
0
0
1
1
0
1
2
0
0
1
1
0
1
0
2
0
0
0
1
2
1
0
1
1
1
0
0
2
2
0
0
0
2
4
1
0
2
2
0
0
0
0
0
1
0
0
1
0
1
0
2
2
2
0
1
0
1
0
0
0
1
2
0
1
1
0
1
2
2
0
0
0
0
1
2
1
1
2
2
1
0
0
0
2
1
2
2
0
0
0
0
2
0
0
1
0
0
0
2
2
0
2
0
2
2
2
0
2
0
0
1
0
1
0
0
0
0
0
2
4
2
0
0
0
2
0
2
0
0
0
1
0
0
2
2
2
1
0
0
0
1
2
0
0
1
0
0
0
0
2
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
2
1
1
4
1
2
5
0
1
1
3
2
0
1
2
0
0
0
0
0
3
2
2
0
0
0
1
1
0
1
2
1
0
0
0
1
0
2
0
0
1
0
2
0
1
0
3
0
0
2
1
0
0
0
0
2
0
0
0
0
3
2
0
1
0
0
0
0
0
0
2
0
1
0
1
1
1
0
0
2
0
1
2
1
1
0
0
0
0
1
0
0
1
1
0
1
1
1
0
2
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
2
2
1
0
0
3
2
0
0
2
1
2
1
0
0
2
1
2
0
0
1
0
2
0
2
2
0
0
0
0
0
0
0
0
2
1
1
3
0
1
2
0
2
0
0
3
0
0
1
1
0
0
0
0
0
1
0
0
1
2
0
1
1
1
0
2
0
0
1
3
1
0
4
0
0
0
2
1
0
0
0
0
1
2
2
1
0
0
0
1
1
1
1
2
0
1
3
2
0
2
0
1
0
1
0
0
1
0
2
0
0
1
0
0
1
0
0
1
1
0
0
2
2
1
1
0
0
2
1
2
1
0
1
0
0
1
0
0
2
1
1
1
0
0
1
2
2
0
6
1
0
0
0
3
1
1
0
0
0
2
2
1
0
0
1
1
0
0
0
0
0
2
0
1
1
4
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
1
2
0
1
2
0
0
2
0
1
1
1
1
2
1
1
2
0
0
2
2
1
2
0
1
1
0
2
2
0
1
0
2
1
0
1
2
0
2
0
1
1
0
1
1
2
5
0
0
2
0
2
2
1
0
0
2
0
0
0
0
1
1
2
1
0
0
2
1
0
0
0
1
2
0
2
1
0
1
1
1
2
0
1
0
0
2
0
0
0
0
1
0
2
0
1
2
2
2
2
0
0
2
1
0
2
2
0
0
2
2
0
3
1
0
0
0
0
2
0
0
1
1
1
1
0
2
2
1
0
1
0
1
0
0
2
0
0
1
1
0
2
0
1
0
0
2
1
0
1
0
1
1
2
0
0
0
3
1
0
2
2
0
1
2
0
4
0
1
2
1
1
2
0
1
0
1
1
1
2
0
2
1
0
0
2
2
1
0
0
1
0
0
0
0
0
0
1
0
0
0
2
1
1
1
1
1
2
0
0
0
1
0
2
0
0
0
0
0
0
1
0
1
0
0
0
1
2
1
1
2
0
1
0
1
0
1
1
1
0
0
0
0
0
2
2
0
0
2
0
0
0
2
0
0
2
0
0
0
0
2
2
0
1
0
0
0
0
0
2
1
1
1
0
3
0
0
2
1
0
0
0
2
0
0
2
2
1
0
1
1
0
0
0
0
2
3
0
2
1
0
0
2
1
2
0
0
2
1
0
1
1
0
1
0
1
0
2
1
0
2
1
1
0
1
0
0
0
0
1
1
1
0
1
1
0
2
1
1
0
0
3
0
1
2
0
0
0
2
0
0
0
1
1
1
2
0
0
1
0
2
0
0
1
0
0
0
1
2
4
2
1
2
0
0
0
2
0
0
0
1
2
2
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
1
0
1
0
0
0
1
2
0
1
1
0
2
0
0
0
1
1
1
0
1
1
0
1
0
1
0
0
0
0
2
0
0
1
1
1
2
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
1
2
0
1
0
0
0
1
1
0
1
0
2
0
0
2
1
0
0
1
1
1
0
1
1
2
0
0
0
0
1
0
1
1
0
1
0
0
1
1
0
0
2
0
1
0
2
0
1
0
0
1
0
1
2
0
0
0
0
0
0
2
1
0
0
0
0
3
1
0
1
2
0
1
1
0
0
0
2
0
0
2
0
1
1
0
0
1
1
0
2
0
2
1
2
1
1
2
0
0
0
0
0
1
4
0
1
1
0
2
0
0
0
1
2
1
1
5
0
1
2
0
1
2
1
1
0
2
0
1
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
1
1
2
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
2
0
1
2
2
1
0
1
2
1
1
0
0
0
0
2
1
0
2
3
1
1
2
2
1
0
0
0
1
0
2
0
0
1
2
0
1
0
2
0
1
2
1
0
0
2
1
1
1
2
0
1
0
2
1
2
1
0
0
0
1
0
2
1
1
0
0
0
1
1
1
2
2
1
0
1
1
2
0
1
0
0
0
0
0
3
1
0
0
0
1
2
1
2
0
0
1
1
2
2
2
0
0
1
0
2
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
1
2
2
0
0
1
0
1
0
2
1
0
0
1
1
0
1
0
0
0
0
1
2
0
0
1
3
0
2
1
1
0
1
0
1
1
1
0
1
2
0
3
0
0
1
1
1
0
2
2
0
2
0
2
1
0
0
0
0
1
0
2
2
0
2
1
0
0
2
1
1
1
0
2
1
1
1
0
1
0
1
0
0
0
0
1
0
1
1
1
1
2
1
1
0
1
1
1
0
0
1
1
0
0
2
0
0
0
2
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
1
2
1
0
1
0
2
2
1
1
2
1
2
1
0
2
0
0
1
0
0
0
1
1
0
1
0
2
2
0
1
2
1
0
6
0
1
2
2
1
0
0
1
0
0
0
1
1
0
1
1
0
2
0
0
1
1
0
0
0
0
0
1
0
1
2
0
0
0
0
2
1
0
2
1
0
0
0
0
2
0
0
0
2
0
0
1
1
1
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
2
0
0
2
1
1
0
1
0
1
1
0
0
0
2
0
2
1
0
0
1
1
2
0
2
2
1
1
2
0
2
0
0
0
0
0
0
2
1
0
0
0
1
1
1
0
0
1
0
0
0
2
0
0
1
0
2
0
0
0
0
1
0
0
1
0
1
1
0
1
1
2
0
2
2
0
0
0
0
0
1
0
2
0
1
1
0
0
1
0
0
2
0
2
5
0
1
0
1
1
0
1
0
0
0
0
1
0
0
0
1
1
0
1
1
0
2
0
2
0
0
1
0
0
2
0
2
1
1
1
1
1
1
0
2
0
2
2
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
2
1
0
2
2
1
0
0
2
2
0
1
0
0
1
0
1
0
2
2
0
0
2
0
1
1
2
0
3
0
1
0
2
0
2
1
0
0
1
0
0
4
0
0
1
1
0
1
1
1
1
0
0
2
0
0
2
1
0
2
1
2
0
0
1
0
2
0
1
1
0
1
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
1
1
0
0
2
1
0
1
1
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
1
1
0
1
1
0
1
0
0
1
0
0
1
2
1
0
1
2
2
1
1
0
0
0
1
0
0
2
0
0
0
2
1
0
0
0
1
0
0
1
2
1
2
0
0
2
1
2
2
0
0
2
0
0
0
2
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
2
0
0
1
0
1
0
2
0
0
0
1
1
1
1
0
0
2
0
0
0
0
0
1
1
0
1
0
0
0
2
0
0
0
0
0
1
0
1
0
1
0
1
0
1
0
2
1
2
2
2
1
0
0
0
2
1
0
0
0
0
0
2
0
2
2
0
1
0
0
0
2
0
0
0
1
1
0
1
2
1
0
2
1
1
0
0
0
1
2
0
1
2
2
2
3
2
0
2
0
0
0
1
1
0
1
2
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
1
0
2
0
1
0
1
0
2
0
2
0
0
0
0
0
1
1
0
0
0
0
0
3
2
2
0
0
1
1
2
1
0
2
1
0
0
0
1
1
0
0
0
1
0
2
1
1
0
0
2
1
1
0
2
2
0
2
1
0
2
0
0
0
0
0
1
0
0
1
2
0
2
1
2
2
1
2
1
2
0
0
0
1
0
1
0
0
0
0
2
1
0
2
2
1
2
2
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
3
1
2
0
2
1
0
4
0
0
0
0
2
0
0
3
0
0
1
0
1
3
1
2
2
1
0
0
1
1
2
2
2
1
0
0
0
1
0
1
1
0
0
0
0
2
1
2
0
2
0
0
0
0
1
0
2
0
2
0
1
2
0
0
1
0
0
2
0
0
2
0
0
1
0
0
0
1
1
1
0
0
2
1
1
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
2
2
0
1
1
2
2
1
1
0
1
0
1
1
2
1
2
0
0
0
1
0
0
1
1
0
2
0
0
0
0
0
1
0
0
0
0
1
0
2
2
1
0
0
2
0
0
0
1
0
1
0
0
3
0
1
2
0
1
2
0
2
2
0
0
0
1
0
0
0
4
0
0
0
2
2
1
2
1
0
1
0
2
1
1
0
1
2
0
1
0
0
1
0
1
2
1
2
2
2
1
2
2
0
2
0
0
0
1
2
2
0
0
0
0
0
0
0
1
0
2
1
0
2
6
0
0
1
0
1
0
0
1
1
2
0
1
1
0
2
0
0
0
1
0
0
1
1
0
1
1
1
0
1
1
0
1
2
0
0
2
0
1
2
2
0
2
0
0
0
1
2
1
0
1
0
2
0
2
1
1
1
0
0
2
0
2
0
0
1
2
1
1
0
0
1
0
1
0
1
0
1
0
0
1
1
2
2
0
0
1
1
1
1
0
0
1
0
0
1
0
2
0
2
1
2
1
2
1
2
0
2
1
0
0
2
1
2
1
2
0
1
1
2
0
0
0
0
1
0
0
2
0
1
0
0
0
2
1
1
2
1
0
1
1
0
1
0
0
0
1
1
0
1
0
0
0
0
1
0
0
1
0
2
1
0
1
2
2
1
1
0
1
0
0
0
0
1
0
1
1
1
0
2
0
1
0
1
1
2
1
0
0
2
1
0
2
0
0
0
0
0
0
1
1
1
0
0
0
3
0
1
0
1
2
0
0
2
0
0
0
0
0
1
2
0
0
1
0
0
0
0
1
3
0
0
2
2
0
0
1
0
1
4
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
1
2
1
2
0
0
0
0
0
1
0
2
1
0
2
2
0
2
2
0
0
0
2
1
1
1
2
0
1
0
0
0
2
0
2
2
0
0
0
0
0
0
2
2
2
0
1
0
0
0
0
2
0
1
1
0
0
0
0
0
0
2
2
0
2
1
0
2
0
0
2
0
2
1
1
1
0
0
1
0
0
0
0
3
0
0
1
0
2
0
2
0
2
1
0
1
1
0
1
0
2
1
2
0
1
0
1
0
0
0
0
1
2
0
3
0
2
0
0
1
0
0
2
1
1
2
2
0
1
1
1
0
1
0
0
3
1
0
1
0
1
1
1
0
2
1
0
1
0
0
0
1
3
0
0
1
0
0
2
0
0
2
0
0
0
2
2
0
0
0
0
0
0
2
3
1
0
0
1
1
0
0
0
1
0
2
2
0
0
0
0
0
1
0
2
0
1
1
0
0
2
0
1
1
1
0
0
1
0
0
0
2
0
0
2
1
0
2
2
2
0
0
1
0
1
1
2
0
3
1
0
2
0
0
0
2
1
0
0
1
0
3
1
2
1
0
1
1
2
1
0
2
0
1
0
0
1
1
0
0
2
0
0
0
1
0
0
2
0
0
0
1
2
1
2
2
0
0
0
0
1
0
2
2
1
0
0
0
1
0
1
0
0
2
0
2
0
0
2
1
0
2
1
1
0
0
2
1
1
0
0
2
0
1
0
0
1
0
2
0
0
0
1
1
0
0
2
0
0
0
0
2
1
0
1
0
1
0
2
0
0
0
0
0
2
1
1
0
0
1
2
0
2
2
0
0
1
2
2
0
0
2
1
0
1
0
1
1
1
3
0
0
1
0
1
0
2
0
2
2
1
0
2
0
0
0
1
0
0
0
0
1
0
0
3
1
0
2
0
0
0
1
0
2
0
0
1
0
1
0
0
1
1
0
1
0
1
4
1
0
2
0
1
2
0
2
0
0
1
1
0
2
2
1
2
2
1
1
0
0
2
0
0
2
0
1
2
0
0
1
1
0
3
1
1
1
2
1
0
1
2
1
0
0
1
2
1
0
1
2
1
2
2
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
2
1
1
0
0
0
2
0
0
0
0
2
0
0
0
2
0
2
0
2
2
0
0
0
0
2
1
1
0
0
2
1
1
1
0
1
1
0
1
1
0
2
0
0
0
0
1
1
0
1
2
0
1
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
1
1
0
2
0
0
0
0
1
0
0
0
1
1
0
1
1
0
2
2
1
0
1
0
2
1
0
2
0
0
0
0
0
1
1
1
0
2
1
1
2
0
1
0
0
0
2
1
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
2
1
2
1
1
1
0
1
2
0
0
1
2
0
1
1
1
0
2
1
2
1
2
1
0
2
2
1
2
1
1
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
1
0
0
0
0
1
1
0
2
1
0
3
0
0
0
1
1
2
2
1
0
1
2
0
1
1
0
1
1
0
2
1
1
0
0
2
1
1
0
0
0
3
0
0
2
2
1
0
1
1
0
1
2
0
2
1
2
2
0
2
2
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
2
1
1
0
1
2
0
1
2
0
0
1
1
3
0
1
5
0
0
2
0
2
0
0
1
0
2
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
2
1
0
0
2
1
0
1
1
0
0
0
1
0
2
1
0
2
1
1
0
1
0
0
0
0
1
2
3
1
1
0
1
1
0
0
2
1
0
2
1
0
0
0
0
1
0
1
0
0
1
2
0
0
0
1
0
3
1
1
1
0
0
2
2
0
2
2
2
2
2
0
1
0
1
1
0
0
0
2
0
1
2
0
1
0
1
0
0
2
0
1
0
1
2
2
1
0
2
0
0
1
1
0
0
0
0
0
1
0
0
0
2
2
1
1
0
0
2
1
0
0
0
2
1
0
0
2
0
0
0
0
1
0
1
0
0
0
1
0
2
0
3
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
2
0
1
1
2
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
1
0
4
1
0
1
3
0
1
2
1
1
0
1
1
0
1
2
1
2
3
0
1
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
1
1
0
0
0
0
0
1
0
2
0
0
2
1
2
1
0
2
0
0
2
0
2
1
2
2
1
1
1
1
0
0
0
2
1
2
2
2
0
0
1
2
1
1
0
0
0
1
0
1
1
1
1
2
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
1
0
1
0
0
2
0
0
0
2
2
0
2
2
0
2
0
1
0
1
0
2
1
1
2
1
0
0
2
0
1
1
1
2
1
1
1
1
1
2
2
2
2
2
1
0
0
1
0
3
0
0
0
2
0
0
2
1
0
1
1
0
0
1
0
1
1
1
0
0
0
0
0
1
0
0
0
2
0
0
2
2
1
0
2
0
0
0
0
1
0
0
1
0
2
2
0
0
0
1
0
0
2
0
0
0
2
2
0
0
0
1
0
2
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
2
1
0
1
2
0
1
0
1
1
0
2
1
0
0
2
0
0
0
0
0
0
0
0
2
2
2
3
1
2
1
1
2
0
0
2
0
1
1
0
0
0
2
0
1
0
1
2
0
1
0
0
1
0
2
2
2
0
0
0
2
1
1
2
0
1
1
0
0
0
0
0
3
0
0
1
2
0
1
2
0
1
0
0
0
0
0
1
0
0
2
1
0
0
3
0
0
1
0
0
2
0
0
2
1
0
2
2
1
2
0
0
0
0
2
0
2
2
0
1
0
1
0
2
0
0
0
0
2
0
1
0
1
2
1
1
0
0
0
2
1
0
0
0
1
2
0
1
1
2
0
0
0
2
0
0
0
0
0
0
1
0
0
1
2
0
0
2
1
2
1
0
6
2
1
0
1
1
0
0
0
0
1
0
1
2
0
0
0
1
0
0
0
2
2
2
0
0
0
0
0
0
0
0
2
0
1
1
2
0
0
4
1
0
2
0
0
0
2
1
1
0
1
0
2
2
0
0
0
0
1
2
1
0
0
0
0
0
1
2
1
3
1
1
1
2
2
0
0
2
1
1
0
0
0
0
1
1
1
0
1
2
2
1
1
2
0
0
0
1
0
0
0
0
2
1
1
0
4
0
0
1
2
0
2
2
1
0
1
0
0
0
1
2
0
0
1
0
0
0
0
1
2
2
1
0
2
0
0
2
0
2
2
0
2
0
0
1
2
2
0
2
0
1
0
0
2
1
0
1
0
0
0
1
0
2
0
0
1
2
0
2
0
0
0
2
2
0
0
1
0
2
1
0
3
0
0
0
1
2
1
2
0
1
1
0
0
0
0
0
0
1
0
0
1
1
0
2
0
1
0
0
2
1
1
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
2
1
1
2
0
1
1
0
0
1
1
2
1
1
2
0
0
1
3
0
0
2
0
0
2
1
1
0
1
2
3
0
0
0
1
1
0
1
1
0
2
0
0
2
2
1
0
1
1
1
0
0
0
0
2
0
0
0
0
1
1
1
0
2
0
2
1
2
0
1
1
0
1
1
1
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
1
2
1
0
0
0
1
1
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
3
0
0
1
1
2
1
1
2
1
0
1
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
2
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
2
0
2
0
1
1
2
0
2
0
2
2
0
0
1
1
1
2
2
1
1
2
1
0
1
1
0
2
0
2
3
0
2
0
0
0
1
0
0
0
1
0
2
2
1
0
1
1
0
1
2
0
0
6
0
2
0
0
1
8
0
1
0
0
0
2
1
0
0
0
1
2
0
0
0
0
1
1
0
0
0
0
1
1
0
0
1
1
0
0
2
1
2
0
2
0
0
2
0
1
1
0
0
1
0
0
0
1
1
0
1
1
0
0
1
0
1
2
0
0
0
3
1
3
0
1
0
0
0
0
0
1
0
1
1
0
1
0
0
1
0
0
1
2
0
1
0
0
1
0
1
1
0
0
0
2
0
1
2
0
2
0
2
2
1
1
1
0
2
0
2
0
1
1
3
1
0
1
2
0
2
2
0
1
0
0
0
0
0
0
2
0
1
1
1
1
0
0
0
0
1
1
1
1
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
1
1
0
1
1
1
0
1
2
0
0
0
1
0
0
0
2
0
0
2
0
1
1
1
0
0
2
1
0
0
0
2
0
0
2
2
0
1
1
2
0
2
5
2
3
0
0
0
1
2
0
1
0
0
3
1
2
0
0
0
0
0
2
1
1
1
1
1
1
0
0
1
0
0
1
0
1
2
0
1
2
2
0
0
2
0
1
2
4
2
2
3
1
1
1
0
2
0
0
2
2
2
0
1
0
0
0
0
1
0
0
2
0
0
2
1
0
0
0
0
2
1
0
0
1
1
1
2
2
2
0
2
1
2
0
0
0
1
1
2
0
0
0
1
0
1
1
2
0
0
2
0
2
2
0
2
2
0
2
4
0
1
1
0
2
0
0
0
1
1
0
1
1
0
0
2
0
0
1
1
1
1
2
0
0
0
0
2
0
0
2
0
0
0
2
1
2
2
0
2
0
0
0
1
1
2
0
2
0
0
2
0
0
0
0
0
2
2
0
0
1
0
1
2
0
0
0
1
2
1
2
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
3
0
2
0
1
1
0
0
1
0
2
0
2
0
1
0
0
2
3
1
0
1
0
2
2
2
1
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
1
2
1
0
1
0
1
0
0
1
0
2
1
0
0
0
0
0
0
0
0
2
1
0
0
1
0
2
2
0
0
1
1
1
0
0
0
0
1
0
0
1
2
1
0
1
0
1
2
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
1
0
1
0
2
0
0
0
2
3
1
0
2
0
0
0
1
1
0
0
1
0
2
1
0
2
2
1
0
0
0
0
0
0
0
2
1
0
0
1
0
1
0
1
2
1
0
0
1
1
1
0
0
0
0
2
0
0
0
0
1
2
0
2
2
0
1
2
1
0
2
2
0
1
2
0
2
1
1
2
1
1
2
0
0
0
1
1
0
0
2
5
0
1
1
1
0
3
0
1
0
1
1
0
1
1
1
0
3
2
2
1
0
1
2
0
0
0
2
1
1
1
0
1
0
1
0
0
0
2
0
1
1
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
2
0
1
1
1
2
2
0
1
0
1
2
2
0
0
1
3
2
0
0
1
2
2
1
1
0
0
2
0
1
0
0
0
0
0
1
0
0
2
0
0
1
1
0
1
0
0
2
1
2
2
2
0
1
0
1
0
1
0
1
0
1
1
1
2
0
1
2
0
0
2
2
0
1
2
1
1
1
1
1
0
0
1
1
2
0
0
0
1
0
0
0
0
0
2
0
0
1
1
0
2
2
2
0
0
0
1
0
2
0
1
1
2
1
0
0
2
0
3
0
0
1
0
1
0
0
0
1
2
2
0
1
2
3
0
0
0
1
0
0
0
0
1
0
2
0
1
0
2
0
1
0
0
1
0
2
0
2
1
0
1
0
1
0
1
0
0
0
1
0
1
1
1
1
1
0
2
0
0
1
3
1
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
2
1
0
0
2
1
0
1
0
1
0
0
2
0
2
1
1
1
2
0
0
1
2
1
0
0
1
0
0
1
1
0
0
2
0
2
2
1
1
2
0
0
2
2
0
2
0
0
2
1
0
0
0
0
1
0
2
0
0
0
3
0
0
0
0
0
2
0
1
2
2
1
1
1
2
0
1
1
0
0
1
0
1
0
1
0
0
0
0
0
6
0
1
2
0
0
0
1
2
1
1
0
1
0
0
0
0
0
1
0
4
0
0
0
2
0
1
0
0
2
0
0
0
1
2
0
0
0
0
0
2
0
0
2
0
0
0
3
0
2
1
0
2
0
2
2
1
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
2
0
0
0
1
1
0
0
1
0
0
0
1
1
1
0
1
1
0
2
1
4
2
1
0
0
1
0
0
0
0
1
0
1
2
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
2
0
0
1
0
0
0
0
2
2
1
0
0
2
0
2
1
1
0
0
0
1
2
0
2
0
0
2
0
1
2
0
0
1
1
0
0
0
0
2
3
0
1
0
2
2
1
1
0
0
1
0
0
0
0
0
2
2
2
1
1
0
0
1
0
0
0
1
0
1
0
0
3
1
0
2
2
0
2
0
1
2
1
0
1
0
2
0
1
1
0
0
0
1
2
1
0
2
0
0
1
0
0
1
0
1
1
1
1
0
2
2
2
0
0
2
2
1
0
2
1
1
0
2
1
0
0
0
1
1
2
0
0
1
2
1
0
2
1
0
0
1
0
1
2
2
0
2
0
1
0
2
0
0
0
0
2
0
0
3
0
0
0
0
0
0
1
0
0
1
2
1
0
2
0
0
0
0
2
1
0
0
0
1
0
0
0
1
1
1
1
0
1
0
0
1
0
0
2
1
0
1
2
0
2
0
2
0
0
2
1
0
1
0
1
0
0
0
1
0
2
1
0
0
0
0
1
2
0
2
0
0
0
0
0
0
2
1
0
0
0
1
1
1
2
3
1
1
0
2
1
0
0
0
0
2
0
2
0
2
1
0
2
0
0
0
1
0
1
1
0
1
0
0
0
1
0
2
2
0
2
2
0
2
2
2
2
0
0
2
2
3
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
2
2
0
1
2
0
0
1
1
1
1
0
2
1
0
0
0
1
2
0
0
1
0
1
0
1
0
1
0
0
2
0
4
1
0
0
2
2
2
1
0
2
1
1
0
0
2
1
1
1
2
2
0
0
0
0
2
1
1
1
1
1
1
0
0
0
1
2
0
0
1
0
2
2
1
1
0
2
2
0
2
0
1
2
0
1
0
1
0
0
2
0
0
0
0
1
0
0
2
1
0
1
0
0
0
0
0
2
0
0
1
0
2
2
1
0
0
1
2
2
0
0
0
0
0
0
3
0
0
0
1
1
0
2
0
0
0
0
0
1
0
1
0
2
1
0
1
0
1
0
0
1
1
1
0
0
1
2
0
2
1
0
0
0
0
2
1
2
2
1
0
0
0
0
2
0
2
2
1
0
0
1
1
2
0
0
1
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
1
0
2
2
2
0
1
1
0
0
0
2
0
1
0
2
0
2
2
1
0
0
0
0
0
0
0
0
1
1
0
2
2
2
0
0
0
1
2
3
0
0
1
2
1
0
0
1
1
1
0
0
1
0
2
0
1
0
0
0
1
2
0
0
0
0
0
1
0
1
2
0
0
2
1
1
2
0
0
0
0
0
2
0
0
1
1
0
0
0
0
2
0
2
2
0
1
2
0
0
1
1
2
0
1
0
0
0
0
2
1
0
0
0
1
1
0
0
1
0
1
1
1
0
0
2
2
0
0
0
2
0
1
3
0
0
1
0
0
0
2
0
0
1
0
0
0
1
0
2
2
2
1
1
0
0
0
1
2
2
0
0
0
1
0
0
1
0
3
2
0
1
0
0
0
0
0
1
0
2
1
0
1
0
5
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
2
4
0
0
1
0
1
0
2
1
2
1
0
2
2
0
1
0
0
2
0
0
1
0
2
0
1
0
0
2
2
1
0
0
1
1
0
0
1
2
0
0
1
0
0
0
0
1
1
2
0
0
0
2
2
2
0
0
2
3
0
3
0
2
0
1
0
0
0
1
2
0
1
1
0
1
1
0
0
0
0
0
0
0
2
1
1
2
0
0
1
0
2
2
2
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
1
2
2
0
2
0
0
0
2
0
2
0
0
2
0
2
1
1
0
1
1
0
0
0
1
0
1
1
0
0
1
0
0
0
1
1
0
0
1
0
2
1
1
3
0
0
2
0
2
0
0
0
2
0
1
0
0
1
1
1
1
1
0
1
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
2
2
2
0
0
0
1
0
0
1
2
0
0
2
0
1
2
1
3
1
0
1
3
0
0
1
1
0
1
1
3
3
3
0
1
0
0
0
1
1
1
0
0
0
1
0
1
1
1
0
0
0
2
0
0
2
0
0
0
0
3
2
1
0
1
1
1
0
0
0
1
1
1
0
0
2
0
0
1
1
0
0
2
0
2
2
1
1
1
0
0
0
1
2
0
0
0
1
1
0
2
1
0
0
1
1
0
0
0
2
0
2
1
1
2
0
2
1
0
2
1
0
0
1
0
0
1
1
0
2
2
1
0
2
0
0
2
0
1
2
0
0
0
2
0
0
1
1
1
1
3
1
2
2
0
0
0
2
2
1
1
0
1
0
1
3
2
0
0
0
0
0
0
1
1
0
1
0
1
0
2
1
0
0
2
0
0
0
1
5
0
2
1
2
0
1
0
0
2
1
2
2
0
0
2
2
0
0
2
0
0
0
0
1
3
1
2
1
0
1
0
0
0
2
0
1
0
2
2
1
0
0
0
2
1
2
0
1
0
0
1
2
1
0
0
0
2
0
2
0
0
2
1
0
1
2
0
0
0
0
0
2
0
1
0
0
0
1
1
0
0
0
0
1
2
1
2
0
0
2
1
0
1
0
2
0
2
0
0
0
0
1
2
2
0
1
0
1
0
1
0
0
0
1
0
2
2
0
1
2
2
1
0
0
1
1
1
2
1
2
0
0
0
1
1
1
0
1
0
2
0
0
0
2
0
1
0
1
0
0
1
1
0
1
0
1
0
2
0
0
2
1
0
1
1
0
1
0
1
0
0
1
0
0
1
2
0
0
2
1
1
1
2
1
0
1
0
0
2
0
2
1
2
1
0
0
1
2
1
2
2
0
0
1
1
2
1
1
0
0
2
0
0
0
1
2
0
2
0
1
0
0
1
0
1
0
0
0
1
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
1
1
1
0
0
1
1
2
0
2
0
0
0
2
2
0
1
2
1
2
0
0
0
0
1
1
0
2
0
2
1
1
2
0
0
0
1
2
0
0
1
2
2
0
3
1
2
3
2
0
0
0
0
1
0
0
1
2
1
0
1
0
2
2
1
2
0
1
1
0
1
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
2
1
2
0
0
1
2
0
0
0
0
0
0
0
2
1
0
1
3
2
1
2
0
1
0
4
1
2
2
0
0
0
2
1
0
1
1
1
1
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
1
1
1
0
1
1
0
0
1
2
0
1
2
2
0
2
1
0
1
0
0
0
1
1
0
1
0
0
0
1
0
2
2
1
1
1
0
0
0
0
1
2
0
2
1
0
0
1
1
0
0
0
0
0
1
0
0
0
1
1
1
0
1
0
0
0
2
0
0
0
0
0
3
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
2
1
3
2
1
0
1
0
1
0
1
0
1
1
0
0
0
1
1
1
2
1
0
1
0
2
2
0
0
2
2
0
1
0
0
0
2
1
0
0
0
0
2
0
1
0
1
1
0
1
0
1
1
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
2
0
1
0
1
2
0
0
1
2
2
1
2
0
1
0
2
0
1
0
1
2
1
0
0
0
0
0
0
1
0
1
0
1
1
2
0
0
0
0
0
1
0
1
1
0
1
2
2
2
0
1
1
0
0
1
1
0
2
2
0
0
0
1
0
1
0
1
0
1
0
1
0
1
0
1
1
0
0
1
0
0
0
2
0
1
2
0
2
1
2
2
0
0
0
0
1
0
0
2
0
2
0
1
2
1
3
0
0
1
0
0
0
1
1
1
1
0
0
1
1
2
0
2
0
1
0
0
1
0
1
0
2
1
0
0
0
1
0
1
0
2
0
0
1
2
1
0
0
0
0
1
1
1
0
2
0
0
0
0
1
1
1
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
3
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
1
0
2
2
1
4
1
2
2
0
2
0
1
0
0
1
1
1
2
1
0
0
0
0
0
0
0
1
1
1
2
0
0
0
0
0
2
0
1
0
0
1
0
0
2
0
0
1
0
3
0
1
0
0
1
2
2
1
1
1
1
0
0
2
0
1
0
0
2
1
2
0
3
0
0
2
0
1
0
2
0
0
2
0
0
0
0
2
0
1
2
0
0
0
1
2
0
1
1
2
1
0
2
0
2
0
0
0
0
1
1
2
1
2
0
2
0
0
0
0
0
2
2
1
2
4
2
1
0
0
2
2
2
0
0
0
0
0
1
0
1
1
3
2
1
0
0
0
1
0
0
0
1
0
1
2
1
0
0
2
3
0
1
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
1
2
0
0
2
0
1
1
0
2
2
0
0
0
1
0
0
0
1
0
1
0
0
2
0
0
1
1
1
0
1
1
0
2
1
0
2
2
1
1
0
0
1
0
1
1
0
0
1
0
2
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
2
3
2
0
0
2
2
0
1
0
1
1
2
0
0
2
0
0
0
0
0
0
0
0
1
1
2
1
1
0
0
0
2
1
0
0
1
0
2
0
0
0
0
2
1
1
0
1
0
1
2
0
0
2
0
2
1
3
0
0
2
2
0
1
2
2
1
2
0
1
2
0
0
1
1
0
0
1
1
0
0
1
0
1
1
0
1
1
3
0
0
1
1
0
0
2
1
2
0
1
1
0
0
0
0
1
2
2
0
2
2
1
1
2
3
1
0
2
0
0
0
2
1
0
4
0
0
1
0
2
0
0
1
0
0
3
1
0
2
0
0
1
0
2
0
0
0
0
2
0
0
1
2
3
2
1
0
0
0
1
1
0
1
0
0
2
1
2
0
2
1
0
0
1
0
0
1
0
2
1
2
1
1
1
2
0
1
0
0
2
0
1
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
3
1
1
1
0
0
2
0
1
0
2
1
1
2
1
2
2
0
1
0
0
1
0
0
0
2
0
0
0
2
0
2
1
0
1
2
0
0
0
0
1
2
0
1
1
1
1
0
0
2
0
1
1
1
2
1
0
0
3
1
0
0
0
2
1
0
1
1
1
0
2
1
0
1
1
1
0
0
0
0
0
2
2
0
0
0
1
0
1
2
0
0
0
0
0
2
1
0
0
0
0
0
1
1
4
0
0
2
0
0
0
2
2
2
1
1
1
1
0
1
1
0
0
2
0
1
0
0
0
1
2
1
2
0
0
2
1
0
1
2
1
0
1
2
1
0
2
2
1
1
0
2
2
0
0
0
0
0
2
0
1
0
2
0
1
0
2
2
2
0
2
0
1
0
2
0
0
0
2
0
2
0
1
0
0
1
0
0
1
0
1
2
0
1
1
0
1
1
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
1
0
1
1
2
0
2
0
2
0
0
0
0
1
1
2
0
0
0
2
1
1
0
0
0
2
2
2
1
1
1
2
1
1
0
1
0
0
0
0
1
2
2
1
0
0
0
2
1
0
1
0
1
0
0
0
0
1
0
2
0
0
0
1
0
1
1
2
2
0
0
0
1
0
2
1
1
2
2
1
0
1
0
1
1
2
1
2
3
0
0
1
0
1
0
1
1
0
0
0
0
2
0
1
2
1
2
0
0
0
0
2
0
2
0
0
2
0
1
2
1
0
0
2
0
0
1
2
2
0
2
1
0
3
1
1
0
0
0
0
0
1
2
0
2
2
0
1
1
0
0
1
0
1
0
1
0
0
1
1
0
0
0
1
0
0
2
1
2
0
0
0
1
1
2
0
0
1
0
1
0
0
0
1
1
1
0
0
0
0
2
1
1
0
0
2
0
1
0
0
1
1
2
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
2
1
1
0
0
0
2
2
0
0
0
0
1
1
0
0
1
0
1
2
0
1
0
0
0
2
2
1
1
0
0
0
1
0
2
0
0
1
0
0
2
0
2
0
1
2
2
2
0
0
0
1
1
2
0
0
0
0
1
2
1
1
1
0
2
0
1
2
0
0
0
1
0
2
0
0
2
1
2
2
0
2
0
0
0
1
0
1
0
0
2
2
0
2
0
0
1
1
4
0
0
0
1
2
1
0
0
0
2
0
1
0
1
0
2
0
1
1
0
1
1
0
1
0
0
1
2
0
0
0
2
0
0
0
0
0
3
1
0
0
1
1
2
1
1
0
0
0
0
1
1
1
0
0
0
1
1
2
0
0
0
2
2
1
0
0
1
2
2
0
1
2
2
0
0
0
3
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
1
1
0
0
0
2
0
0
0
1
1
2
1
2
2
2
2
1
1
0
0
1
1
2
0
1
2
0
1
0
0
1
1
2
1
0
0
0
0
2
2
0
0
1
0
0
1
1
1
1
0
1
2
1
0
2
1
0
1
1
0
1
1
2
0
3
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
1
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
2
0
0
0
2
0
0
0
1
2
0
0
2
1
0
1
1
0
1
1
2
2
2
0
0
2
0
0
0
0
2
0
1
0
0
0
2
0
0
0
2
0
0
2
0
1
0
0
0
2
0
1
3
2
1
1
1
1
0
0
0
2
0
1
1
0
1
0
0
2
1
2
0
0
1
0
2
0
1
0
2
2
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
2
0
1
0
0
1
1
0
0
2
1
1
1
2
1
3
0
2
1
2
0
3
1
0
1
0
0
0
2
1
0
2
2
3
1
1
2
1
0
2
1
0
0
0
2
1
1
2
1
0
1
0
2
1
2
0
0
1
1
0
0
0
1
2
0
1
0
4
1
3
0
0
2
0
0
0
2
0
0
2
0
1
2
2
0
2
0
1
0
2
0
0
0
0
2
0
1
0
1
0
0
2
2
1
0
0
2
0
0
1
1
3
0
0
0
1
1
1
3
0
0
0
1
0
2
2
2
0
1
0
2
0
0
2
1
0
0
1
0
0
0
2
0
2
0
1
0
1
0
2
2
0
0
2
1
1
0
1
0
0
1
2
0
2
0
1
0
2
0
2
1
1
0
0
2
0
0
0
2
0
0
1
1
2
1
0
1
1
0
1
0
0
2
0
1
1
0
0
1
0
1
0
0
1
0
1
2
0
0
2
1
0
0
1
0
0
1
0
0
2
2
0
0
2
0
2
1
2
0
1
2
0
2
1
0
1
0
2
0
0
1
0
0
1
2
1
0
0
1
0
2
0
0
0
0
2
1
1
0
0
0
0
2
3
0
0
1
0
0
1
0
2
0
1
2
0
0
0
0
0
0
0
0
1
1
2
0
1
0
0
0
1
1
2
1
1
0
2
1
0
1
2
0
2
1
0
0
2
1
1
1
0
0
0
0
0
0
0
4
2
0
1
1
1
1
2
0
1
0
0
2
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
1
1
1
1
1
1
0
0
0
0
1
1
3
0
1
1
1
0
0
2
0
0
0
2
0
1
1
2
0
1
0
2
2
1
2
1
1
1
0
0
0
1
0
2
1
2
0
1
0
0
0
1
0
0
3
0
1
0
0
1
2
2
2
0
0
1
1
0
2
1
2
1
2
0
0
1
0
2
0
1
1
2
1
1
2
0
1
0
2
1
2
2
3
0
1
2
1
1
1
2
0
0
2
1
0
1
0
2
1
0
0
2
7
0
1
0
2
0
0
0
2
1
0
0
1
1
1
0
1
1
1
0
1
0
1
1
1
2
0
2
0
0
2
2
2
0
2
1
0
0
2
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
2
0
1
0
1
0
0
0
2
0
1
0
0
0
2
1
2
1
0
0
6
1
0
2
1
0
0
0
0
2
0
0
1
0
1
0
1
1
2
1
1
2
2
1
2
0
0
0
0
1
0
0
1
0
0
0
0
0
2
3
2
2
0
1
0
1
0
0
1
0
3
1
1
2
0
2
0
2
0
0
1
0
1
0
0
0
1
0
1
0
3
0
0
0
0
1
0
2
0
2
0
0
0
1
1
2
0
1
1
1
1
2
1
2
2
0
1
2
0
1
0
0
0
1
3
1
1
0
2
1
1
0
0
2
0
1
1
0
0
0
0
0
0
0
1
1
0
0
1
0
1
1
1
0
2
0
0
1
1
0
2
1
1
2
1
1
0
0
2
0
1
0
1
0
0
0
0
0
0
0
2
1
0
0
1
2
3
0
0
0
0
0
1
1
2
2
0
1
0
0
3
2
0
2
3
1
0
0
2
0
0
1
2
2
4
1
1
1
0
2
2
0
1
0
0
0
0
1
0
0
1
2
0
0
1
0
0
2
1
3
0
1
0
2
0
1
1
0
2
0
0
0
2
1
0
1
0
0
0
2
0
3
0
0
0
2
0
2
1
1
1
0
2
2
1
0
0
1
1
2
1
0
2
0
1
0
1
1
2
0
1
0
0
0
0
0
1
1
0
3
2
2
0
3
2
0
2
0
0
1
0
0
1
0
1
1
0
0
0
1
0
2
1
0
0
0
1
1
0
0
1
0
0
1
1
1
0
0
0
2
2
2
1
2
0
0
0
1
1
2
1
2
2
0
0
0
0
1
0
2
0
1
3
0
1
2
0
2
0
0
1
2
0
0
3
2
1
1
2
2
1
1
0
2
2
2
2
1
0
1
2
0
0
1
0
1
1
0
1
1
0
0
1
3
0
0
2
2
2
2
0
0
0
0
2
2
0
0
1
1
0
3
2
0
1
1
0
0
0
2
3
1
2
0
1
2
1
0
1
0
0
0
2
0
2
0
0
0
1
1
1
0
1
0
0
2
1
2
1
0
0
0
1
2
0
2
0
0
1
0
2
1
0
0
0
2
0
0
1
2
1
0
1
0
1
0
0
5
0
2
2
2
1
2
2
2
1
0
0
0
2
1
1
0
0
0
0
6
1
0
0
0
1
0
0
0
0
0
0
1
1
0
2
0
1
0
2
2
1
0
0
0
2
2
0
1
0
0
0
0
0
0
2
2
0
1
0
1
2
3
0
0
0
2
1
0
0
1
0
0
1
4
2
2
2
0
2
0
0
0
0
0
1
1
2
0
0
0
0
0
2
1
1
2
0
1
0
0
0
0
0
3
1
0
2
1
0
0
0
0
0
0
0
1
0
1
0
1
0
2
0
1
0
2
1
1
0
1
0
1
1
2
0
0
6
2
1
2
1
0
2
0
1
0
1
0
0
0
1
2
0
2
1
1
2
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
2
0
0
1
0
0
0
1
2
0
1
0
1
0
0
0
1
0
2
0
0
1
1
0
2
0
2
0
0
1
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
2
1
0
0
0
1
1
4
2
0
2
0
1
2
1
0
0
0
0
1
0
0
2
0
0
3
1
0
0
1
1
1
1
0
0
0
0
0
2
0
0
0
2
1
1
1
0
0
0
0
0
2
1
1
0
0
2
1
0
1
1
0
1
1
0
0
0
0
1
1
0
2
2
0
2
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
2
0
0
1
1
0
0
2
1
0
1
0
1
2
1
2
0
2
1
1
0
1
1
0
2
0
0
0
0
0
1
0
0
0
1
2
1
0
0
0
0
0
0
0
2
1
0
0
2
1
2
2
3
0
0
0
0
0
1
0
1
0
0
1
1
2
0
1
0
3
0
0
2
2
1
0
1
1
0
0
1
2
2
0
1
1
0
0
1
0
0
0
2
0
0
1
1
0
2
0
0
0
2
2
0
2
0
1
0
0
1
0
0
0
0
1
1
1
2
0
2
0
1
0
0
0
0
0
0
0
0
1
0
1
2
0
2
2
0
0
0
0
2
1
1
1
1
0
1
1
0
1
1
0
0
0
0
2
1
0
0
0
0
1
0
1
0
1
0
0
0
0
1
1
0
2
1
1
1
0
0
1
2
0
3
0
2
1
1
0
0
0
1
0
0
0
0
2
0
1
0
1
1
2
1
1
1
1
0
1
2
0
2
0
1
0
1
1
0
3
1
0
2
1
0
0
2
2
0
0
1
1
0
0
3
2
1
1
1
1
0
0
0
1
2
0
0
0
2
0
2
1
0
0
0
1
0
0
1
3
1
0
0
2
1
1
1
0
1
0
0
2
2
2
0
2
0
1
0
2
0
0
2
0
2
1
0
0
0
2
1
0
0
2
1
0
0
1
0
1
0
0
0
1
2
0
1
0
1
0
1
1
6
0
2
0
0
1
2
0
0
0
1
0
0
2
1
0
1
0
0
0
0
2
0
0
0
1
1
1
0
0
0
2
0
0
0
2
1
1
0
2
0
1
1
1
0
0
0
0
0
0
2
2
0
0
1
0
1
1
2
2
1
1
1
0
2
0
1
1
0
0
2
0
2
1
0
0
1
0
2
1
0
1
2
0
0
0
2
0
1
3
0
1
0
2
0
0
0
0
0
2
5
0
2
0
1
0
1
1
0
0
3
1
1
2
2
0
1
0
0
2
0
1
2
0
2
0
0
1
2
2
1
2
0
3
0
0
2
1
1
1
0
0
2
0
0
0
1
1
2
1
2
1
1
2
1
2
0
1
2
1
1
1
1
0
0
2
1
2
0
1
1
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
1
1
0
2
1
1
1
0
0
0
0
2
2
1
0
1
2
0
1
1
2
0
1
0
1
2
2
0
0
1
1
1
1
0
2
1
0
1
0
1
2
1
2
0
0
0
1
2
1
2
0
0
0
0
1
0
1
2
0
2
0
0
0
1
1
2
1
2
2
1
2
1
2
2
1
0
2
0
2
1
1
0
0
3
0
0
0
1
0
2
0
0
0
0
1
2
2
0
0
0
2
0
0
0
0
2
2
0
1
3
1
1
0
1
1
2
2
2
1
2
1
1
1
4
0
0
0
0
2
1
1
0
1
1
0
0
1
1
0
1
0
0
2
0
1
0
1
1
1
0
0
2
0
0
1
0
1
0
0
2
2
1
1
2
1
1
1
1
2
1
1
1
0
1
0
0
0
4
2
1
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
2
0
1
1
1
1
0
1
1
2
1
1
1
1
0
2
1
2
0
2
1
2
0
1
0
0
1
0
2
1
1
2
1
1
0
0
2
2
2
2
0
1
0
0
0
0
0
1
0
0
2
0
1
0
1
0
2
1
0
1
2
0
2
0
0
0
1
2
1
1
0
0
0
0
2
0
0
2
1
1
0
0
0
2
0
0
0
2
0
2
2
0
1
1
0
2
0
0
1
0
2
4
1
1
0
0
0
0
0
2
0
1
0
0
1
2
0
2
0
1
0
0
0
1
2
1
1
3
3
1
0
0
0
0
0
0
2
0
2
2
1
0
0
1
1
1
0
0
1
0
1
2
0
1
3
1
0
1
0
0
0
1
2
3
1
1
0
0
1
2
1
2
1
1
2
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
1
3
0
2
1
1
0
1
0
0
1
1
0
0
2
1
0
0
0
0
0
1
1
0
3
0
0
0
0
0
0
0
2
2
0
0
0
2
0
2
0
2
2
1
2
1
0
0
2
3
0
0
0
0
2
1
3
0
2
0
1
2
0
0
0
1
0
1
0
1
1
0
1
2
2
0
1
1
0
0
0
1
1
0
1
0
1
0
0
2
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
1
1
0
1
2
2
1
1
0
0
2
0
1
0
0
1
0
2
2
0
1
1
0
1
1
0
2
2
0
0
0
2
2
0
0
1
1
1
0
1
1
0
2
0
0
0
1
1
1
0
0
0
2
0
0
0
0
1
1
0
1
0
2
2
2
1
0
0
0
1
0
0
0
2
0
2
2
0
0
0
2
1
0
1
0
1
2
2
1
2
0
1
1
1
0
0
1
2
0
1
0
0
0
0
1
2
1
0
1
1
0
0
0
2
1
0
1
1
1
2
0
2
0
1
1
0
2
0
0
2
0
0
2
2
0
0
1
0
0
1
1
0
1
0
1
2
2
0
0
2
0
1
1
2
1
0
1
2
0
2
0
1
1
1
0
1
0
1
1
0
0
0
2
1
0
0
1
0
0
0
1
2
2
1
2
1
1
1
2
1
1
2
0
2
0
1
0
1
0
1
1
2
0
0
0
0
2
2
2
0
0
1
1
1
0
3
0
0
2
2
1
1
1
0
1
0
0
0
1
0
1
1
1
2
2
1
0
2
0
0
0
2
1
1
1
2
0
0
0
0
1
0
2
0
0
0
1
0
1
1
7
0
1
3
0
0
0
1
0
1
2
1
0
2
1
2
1
2
0
1
0
0
0
1
0
1
0
1
0
0
1
2
0
1
1
0
0
0
1
0
0
2
0
0
2
1
1
1
3
0
1
2
0
1
0
0
2
1
1
0
3
0
0
1
0
2
2
1
1
0
0
0
1
2
1
0
0
0
1
1
1
1
0
0
1
1
1
0
1
0
1
0
0
1
2
1
0
0
0
1
0
0
1
1
1
0
0
0
0
0
2
0
2
1
2
0
0
2
1
0
0
0
0
2
0
1
0
0
0
0
2
1
0
1
0
0
2
0
1
0
0
1
0
2
0
2
0
1
1
1
0
1
1
0
1
1
0
0
0
1
0
2
2
0
0
0
2
2
0
0
1
0
1
0
1
0
0
2
0
0
0
2
0
0
1
1
0
1
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
1
0
0
0
1
1
0
0
0
1
0
1
0
0
3
1
0
0
2
0
0
2
0
0
1
1
0
0
0
1
2
0
0
0
2
0
1
0
0
1
0
0
0
2
0
0
2
1
0
0
3
0
0
0
1
0
1
1
1
1
0
1
0
1
2
0
0
0
2
0
1
1
0
0
0
0
0
0
2
2
0
1
1
1
0
1
0
0
0
0
0
2
2
1
1
0
2
0
1
1
0
1
1
0
2
0
0
1
1
0
2
2
0
0
0
3
0
2
1
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
2
1
0
1
2
1
0
2
1
0
1
2
2
0
2
0
2
2
0
1
0
2
1
0
0
0
2
1
1
1
0
1
0
2
2
2
0
0
2
2
3
0
0
1
2
2
3
2
0
2
0
1
0
0
0
1
0
1
0
1
0
0
2
0
2
0
0
0
1
0
0
0
2
0
2
0
0
1
2
2
0
1
2
1
2
0
1
0
0
2
2
1
1
0
2
2
0
2
2
1
0
0
1
1
2
0
1
1
1
1
3
2
1
2
2
1
1
0
1
0
1
2
0
2
2
0
1
0
1
1
2
0
0
0
0
2
1
1
3
2
2
1
0
0
2
2
0
2
2
1
0
0
0
1
0
0
0
1
3
0
1
0
1
1
0
0
1
4
0
0
1
1
3
2
1
0
0
0
0
0
3
0
3
1
0
2
0
3
0
0
0
2
0
2
0
0
2
2
0
0
2
0
2
3
1
2
1
0
0
0
0
0
1
1
1
0
1
0
0
0
0
2
1
1
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
1
2
1
1
1
0
1
0
2
0
0
0
2
0
0
0
0
1
2
0
0
0
2
3
1
1
2
0
1
0
2
1
1
0
0
1
1
0
1
0
0
0
2
0
0
0
2
0
2
0
2
0
0
1
1
0
0
1
0
1
1
2
0
0
0
0
2
2
0
2
1
1
2
2
1
1
2
0
1
2
0
1
1
1
0
0
1
1
1
0
0
0
1
2
1
1
0
1
0
0
2
1
0
1
0
2
1
1
0
0
1
0
1
1
2
1
0
0
0
0
1
2
1
0
0
0
0
1
2
1
0
0
0
2
2
0
2
2
0
0
1
0
0
2
1
0
2
1
2
2
1
1
3
1
3
0
2
4
0
0
0
0
2
0
0
0
2
1
0
0
0
0
1
0
1
0
2
1
0
0
1
0
1
0
0
1
3
0
2
0
0
0
2
0
0
0
2
2
1
0
1
1
1
0
1
0
1
3
0
3
0
0
1
0
0
2
0
1
1
0
2
0
0
1
1
3
0
0
1
0
1
0
0
0
0
1
2
0
1
2
1
0
2
1
0
0
0
0
2
1
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
2
2
2
1
0
0
0
2
0
0
1
0
0
0
2
0
1
0
0
0
2
0
0
1
1
0
2
0
0
0
1
3
0
2
1
0
0
2
0
0
1
0
1
2
1
1
2
0
0
2
2
2
2
2
1
3
2
0
1
0
0
1
0
1
2
0
0
0
0
2
0
0
0
1
2
1
0
2
0
1
1
0
2
0
1
0
1
2
2
1
0
1
2
1
1
1
0
0
3
0
0
0
0
0
1
0
2
1
0
1
1
1
0
0
0
0
0
1
2
2
1
0
0
1
0
1
0
0
2
0
1
1
0
0
0
0
1
1
2
0
1
0
0
1
1
1
1
0
1
1
1
0
0
0
0
0
2
0
0
2
1
0
1
0
0
0
1
1
1
1
1
1
0
0
2
0
0
0
1
2
0
1
1
1
0
0
1
0
1
0
0
0
0
1
0
1
2
0
3
0
0
0
2
2
2
1
0
0
1
0
0
2
0
0
2
0
0
0
1
0
2
0
2
1
1
0
1
0
0
2
1
1
1
2
0
2
0
0
1
0
0
1
2
0
0
0
2
1
0
0
0
0
0
0
1
1
1
2
0
1
3
0
1
0
0
1
2
0
1
1
1
0
1
0
0
0
2
1
0
0
0
1
0
2
2
1
4
2
1
2
0
2
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
2
1
1
0
0
0
0
0
0
0
0
2
2
1
0
1
1
0
2
2
2
0
0
2
2
1
0
2
2
1
0
2
0
0
1
1
2
0
0
1
1
1
1
0
1
1
0
0
0
0
1
0
1
0
0
2
0
0
1
2
0
2
3
0
1
0
1
0
0
0
2
0
2
0
0
0
1
0
1
1
1
2
0
1
2
2
0
0
0
0
0
0
1
0
1
5
0
0
1
3
1
3
0
0
1
0
2
2
2
1
0
1
0
3
0
0
0
2
1
0
1
2
0
2
4
0
1
2
1
0
1
0
0
0
0
2
0
0
2
2
0
1
2
0
0
0
0
0
0
2
0
1
0
0
2
2
1
1
0
1
2
0
1
4
0
1
0
1
0
2
0
0
0
0
1
2
0
1
1
0
0
0
0
3
0
0
3
0
4
0
1
2
1
0
0
2
0
0
0
0
0
0
2
0
1
0
1
3
1
2
1
0
1
4
0
0
1
1
2
0
1
1
0
1
0
0
0
1
0
0
1
1
3
0
1
1
1
1
0
0
1
2
0
1
2
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
1
0
2
0
0
3
0
1
3
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
1
0
0
1
1
0
0
2
0
2
0
2
1
2
2
0
1
1
0
1
0
1
1
0
1
0
0
2
0
2
1
1
0
1
0
1
1
0
2
1
1
1
0
1
0
2
0
0
0
0
1
2
0
1
1
1
0
1
0
0
2
2
0
1
0
0
0
0
1
0
1
0
1
2
4
2
0
0
0
2
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
2
1
1
0
2
2
0
3
1
0
1
1
1
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
2
2
0
2
1
2
6
0
1
1
1
0
2
1
2
2
2
1
2
0
0
2
0
2
0
1
0
1
1
0
0
2
2
0
0
0
1
1
0
0
0
1
2
1
2
1
1
1
0
0
2
2
0
0
1
2
0
2
2
2
0
0
2
0
1
1
2
0
0
0
0
0
0
1
1
0
2
0
0
0
0
2
0
0
0
0
0
1
2
1
0
2
2
0
2
0
2
2
2
1
0
0
2
0
2
2
3
2
0
2
3
0
0
0
2
0
1
0
2
1
1
1
1
0
0
0
1
0
2
1
0
0
0
1
1
1
1
0
0
0
1
1
0
0
2
2
0
2
1
1
1
1
1
0
0
0
0
1
0
2
0
1
0
1
2
1
1
1
0
1
0
0
1
0
0
0
1
3
1
1
0
0
0
0
2
1
0
2
0
1
0
1
2
0
1
2
0
0
0
0
2
0
0
0
2
0
0
0
0
1
1
2
1
0
1
0
0
0
0
0
0
1
0
1
1
1
1
1
1
5
0
1
0
0
0
2
1
0
0
0
0
0
0
1
1
1
0
2
2
0
2
2
1
0
1
0
0
1
0
0
0
1
0
1
0
2
2
0
2
1
1
4
2
0
1
0
1
0
0
0
0
0
0
1
1
0
2
2
0
1
0
1
2
0
1
0
0
0
0
2
0
1
0
4
1
0
0
1
0
1
2
1
0
0
1
1
0
0
1
1
1
0
0
0
1
1
1
1
2
2
0
1
0
2
1
1
1
0
0
0
0
1
1
0
2
1
3
1
0
1
1
0
1
1
0
3
2
2
1
0
0
2
0
0
2
0
0
0
1
0
0
1
0
1
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
2
0
1
1
1
0
0
2
2
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
3
1
2
0
1
0
0
2
0
2
1
0
1
2
1
1
1
1
2
0
0
0
0
3
0
1
0
0
0
1
1
0
0
2
0
2
0
0
1
0
0
6
1
2
0
0
0
2
1
0
0
0
0
1
1
2
1
0
0
0
2
0
0
0
0
1
0
0
1
0
2
0
0
1
0
0
0
2
0
0
2
0
3
0
2
2
0
0
1
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
2
2
0
0
2
1
0
1
2
3
0
0
0
0
0
2
1
0
0
0
0
2
0
1
2
2
1
2
1
0
0
0
1
0
1
0
2
1
1
2
1
1
1
0
0
2
0
1
0
0
0
2
1
1
0
0
0
1
2
0
1
0
2
0
1
1
2
0
0
1
0
0
1
0
2
0
1
0
1
0
1
0
3
0
2
0
1
0
2
3
0
2
0
2
0
1
1
1
1
0
1
1
0
0
0
0
1
2
1
0
1
2
2
1
2
1
2
0
0
0
1
1
0
3
0
1
2
1
0
1
2
1
0
0
0
0
2
1
0
1
0
0
0
2
0
2
1
1
2
1
0
0
1
2
0
1
0
0
1
0
1
2
0
2
2
0
2
3
2
2
0
0
0
0
0
0
1
1
0
0
0
0
1
1
1
0
0
1
0
0
0
1
0
1
0
2
0
0
0
1
1
0
2
0
0
1
1
0
0
0
2
1
0
1
0
2
1
0
0
0
0
1
2
1
0
2
1
2
1
0
1
0
2
0
1
0
1
1
2
0
0
2
1
0
0
0
2
3
0
0
2
0
2
0
2
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
3
3
1
2
1
0
1
0
0
2
0
0
2
2
0
0
2
1
1
2
0
3
0
2
0
0
1
0
1
1
0
0
2
1
0
1
2
0
1
0
2
2
2
1
0
0
0
2
2
0
0
1
2
0
2
1
3
1
0
0
0
0
2
0
0
2
0
2
1
0
0
1
1
2
0
1
3
1
0
1
2
0
0
0
0
0
0
0
0
0
1
1
0
5
0
0
0
2
1
1
1
0
0
1
0
0
0
0
0
0
2
1
1
0
0
0
0
1
1
0
1
0
0
1
2
1
1
2
2
0
0
1
0
1
2
0
2
2
0
1
0
0
1
0
0
2
1
1
2
0
1
0
1
0
0
0
0
2
1
0
0
1
1
1
1
0
0
2
0
3
0
0
2
1
1
2
1
0
1
0
2
0
1
0
2
1
1
1
0
1
0
1
1
1
1
0
0
2
0
0
0
1
2
1
0
2
1
1
0
0
1
0
0
1
2
0
0
1
1
0
2
0
0
1
1
0
2
0
1
1
1
1
2
1
1
2
1
0
0
2
1
0
0
0
0
1
1
0
0
1
0
2
0
1
3
0
0
0
2
1
0
0
0
1
0
0
0
0
1
0
0
2
0
1
1
0
2
0
2
1
0
2
2
0
1
0
0
0
1
0
2
2
0
1
0
0
2
1
1
1
2
1
0
0
0
2
2
0
0
2
3
2
2
0
0
1
2
1
0
2
0
2
2
0
0
2
1
1
0
2
0
0
0
1
3
1
1
1
0
0
0
0
0
0
1
1
2
2
0
0
0
0
3
0
1
1
0
1
0
1
1
0
2
1
2
2
0
1
0
2
0
2
0
0
0
1
1
1
1
0
0
1
1
0
1
0
1
1
0
0
1
0
0
1
0
0
2
0
2
0
0
1
0
0
1
1
1
2
0
1
1
0
0
0
0
0
0
2
0
2
0
0
0
1
1
0
0
1
1
1
2
1
0
0
0
3
1
1
0
1
0
1
1
3
0
1
0
0
2
0
1
1
1
0
0
2
0
2
0
0
0
1
0
0
1
0
0
0
0
0
3
0
0
1
1
1
1
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
4
2
0
0
1
0
0
2
1
3
0
1
1
0
1
0
0
1
0
0
2
1
0
2
0
1
0
1
2
1
1
2
0
1
1
0
0
1
0
1
1
0
0
0
1
0
0
1
2
0
1
1
1
1
1
0
0
1
1
1
0
2
1
2
1
0
2
0
1
1
2
0
2
5
2
0
1
0
2
2
0
0
0
0
0
0
0
2
0
2
2
1
0
1
1
1
0
1
1
0
0
2
0
3
0
2
2
2
2
3
0
1
2
2
0
1
0
1
0
1
1
0
3
1
2
1
0
3
0
0
0
0
0
0
0
0
0
2
2
0
1
0
1
0
1
1
1
1
0
2
2
1
1
0
1
0
0
2
2
0
1
2
2
1
1
1
1
0
0
0
2
0
0
0
0
2
0
0
0
2
2
1
0
0
0
0
0
2
0
0
0
0
1
1
0
2
2
0
0
1
0
2
1
1
2
0
2
0
0
2
2
0
2
0
2
0
1
0
1
0
0
0
1
0
2
0
0
0
0
0
1
2
0
0
2
1
1
2
0
0
0
2
1
0
0
1
0
2
0
1
0
2
0
1
0
0
1
0
2
0
1
0
0
1
0
1
2
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
1
2
0
1
0
1
2
0
2
0
0
2
0
0
0
0
0
0
1
0
2
0
1
0
1
0
0
1
2
0
1
0
1
0
2
1
1
1
0
1
0
0
2
2
0
0
0
0
2
1
0
0
0
0
0
0
0
1
1
2
1
2
0
1
1
0
0
2
1
0
0
2
1
0
1
1
0
0
0
0
1
1
0
1
0
0
0
1
0
2
0
2
0
0
0
0
0
1
2
1
0
0
0
0
0
2
0
2
0
0
0
0
0
2
2
1
1
2
0
1
1
2
3
1
2
0
0
0
0
1
0
2
0
2
2
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
1
2
1
0
0
1
2
0
0
1
0
1
2
0
1
2
2
1
0
1
1
1
0
2
0
0
2
0
0
0
1
2
1
0
0
1
0
1
2
2
1
0
0
0
0
1
0
2
2
1
0
2
0
2
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
2
2
1
0
0
0
0
2
2
0
0
1
1
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
2
0
1
0
0
1
2
1
1
0
0
1
0
2
0
1
1
0
0
0
0
0
0
4
0
0
1
0
0
1
1
0
0
0
1
2
0
1
2
0
0
0
2
1
1
2
2
2
2
1
0
1
1
1
0
1
1
1
0
0
0
0
0
0
0
0
2
1
0
4
1
2
0
0
2
2
2
1
1
0
0
0
1
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
1
1
1
3
1
1
1
0
2
0
0
0
1
2
1
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
1
1
1
0
0
2
0
1
1
0
0
0
2
1
2
0
0
2
1
0
1
2
1
0
0
2
1
2
0
1
1
1
1
0
0
0
0
2
0
0
2
0
2
0
0
0
1
2
1
1
0
0
0
0
2
0
1
2
0
0
0
0
0
2
0
2
0
1
0
1
0
0
0
2
1
0
0
0
2
2
1
0
0
0
2
1
0
2
3
0
1
0
1
1
0
1
1
0
1
1
2
1
0
2
0
0
1
0
0
2
0
0
0
0
1
1
0
2
0
2
0
0
0
2
0
0
0
1
1
0
2
1
2
1
0
0
0
0
1
0
0
2
1
1
0
1
1
2
2
0
0
0
0
1
1
0
2
1
0
1
0
1
0
0
0
1
1
0
0
1
0
2
2
0
1
1
0
0
0
1
0
1
1
0
0
2
0
2
2
0
3
0
0
0
1
1
0
0
1
0
0
0
2
0
3
0
0
0
0
1
0
1
0
1
0
0
1
3
1
1
0
0
0
1
0
1
0
0
1
0
2
0
0
0
2
2
0
0
0
0
1
2
2
0
1
1
1
2
1
0
2
2
1
1
0
0
2
0
3
2
2
1
2
3
0
0
1
0
0
1
0
0
0
1
2
0
3
0
1
2
1
2
1
0
0
2
0
2
1
2
0
1
0
2
2
0
9
0
0
1
0
0
2
0
2
0
0
0
1
0
2
2
0
0
0
0
0
0
1
0
0
0
1
2
0
1
2
0
1
0
1
0
0
0
0
1
0
2
2
2
1
0
1
0
0
0
0
1
0
2
0
1
0
1
0
0
2
0
0
0
3
0
0
1
0
1
0
0
1
0
0
1
0
0
2
2
0
0
2
0
0
1
2
2
2
0
1
0
3
1
2
1
1
0
2
0
2
2
0
1
0
0
1
2
2
0
2
0
0
0
1
0
0
2
1
0
1
0
0
0
2
0
0
1
1
0
1
2
0
0
1
0
2
1
1
1
1
0
1
1
0
1
0
0
1
0
1
2
1
1
0
0
0
0
1
0
0
0
0
1
2
0
3
1
0
1
0
0
0
1
2
2
0
1
0
0
0
1
2
0
1
0
0
2
5
0
0
2
1
0
1
0
0
2
0
2
2
1
0
1
0
1
0
2
2
0
0
0
2
0
0
2
0
1
1
0
0
0
1
0
0
1
2
0
0
2
1
0
0
1
1
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
1
0
1
0
0
4
0
2
1
0
1
0
0
2
0
2
0
0
0
2
0
2
0
0
1
0
1
0
0
4
2
0
0
0
0
2
0
2
2
1
0
2
0
1
0
3
1
1
2
1
0
0
1
1
2
0
0
1
1
1
0
0
1
0
1
1
0
2
1
0
0
0
1
2
2
0
2
0
0
1
2
0
1
0
0
1
1
1
0
0
0
0
2
0
2
0
1
1
1
0
2
0
1
1
0
0
0
0
2
0
2
0
0
1
0
2
0
1
0
0
0
2
0
0
1
0
0
0
1
0
1
2
0
1
0
2
2
0
0
2
0
1
3
1
0
1
1
0
1
0
2
0
1
0
0
0
1
0
2
1
2
0
0
0
0
1
0
1
1
1
0
2
2
0
1
0
0
0
2
0
0
1
0
1
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
1
0
2
0
0
0
1
0
1
0
1
2
0
0
0
0
0
1
1
2
2
0
1
0
0
0
1
1
2
2
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
2
2
0
0
1
0
0
0
2
1
1
0
1
0
1
1
1
1
2
0
2
0
0
1
0
1
0
0
0
0
1
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
2
2
0
0
3
1
0
0
0
0
1
0
1
0
2
2
1
0
1
0
2
0
2
0
1
0
0
0
0
0
1
2
0
0
0
2
1
0
0
1
2
1
0
0
0
2
0
0
2
0
2
2
0
1
0
0
0
0
1
1
0
0
1
2
0
0
0
0
1
0
0
2
0
0
2
0
2
0
1
1
0
0
0
0
0
2
2
1
1
0
1
1
1
3
1
0
2
1
1
0
0
0
2
0
0
1
0
0
1
2
0
0
0
2
0
0
0
1
0
4
1
1
0
0
0
0
0
0
1
0
3
1
0
0
0
2
0
0
0
0
2
1
0
0
1
2
0
2
0
0
0
2
0
1
1
0
2
2
2
0
1
3
0
0
1
0
0
2
0
2
2
0
1
0
1
0
1
0
2
0
0
0
0
1
1
0
2
0
1
0
0
1
1
1
0
0
0
1
1
0
0
0
0
2
1
1
2
0
0
1
1
0
1
1
0
0
2
0
0
1
1
1
0
1
0
1
0
1
1
0
1
1
1
1
1
1
0
0
0
1
2
1
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
1
0
1
2
1
0
0
0
2
0
0
2
0
0
1
1
1
2
1
0
2
0
0
0
0
2
0
0
1
2
0
0
2
1
0
1
0
1
1
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
2
0
0
1
0
2
1
0
1
0
1
0
2
0
2
0
1
2
1
0
0
1
2
0
2
2
3
0
0
0
0
0
2
0
2
1
0
1
1
0
1
1
1
0
0
0
0
1
1
1
2
0
0
1
0
0
1
0
1
0
0
0
2
1
2
2
0
1
0
3
2
2
1
2
1
1
2
0
0
0
0
0
2
0
0
0
1
0
1
2
0
0
1
0
2
0
0
0
0
2
2
0
0
1
0
2
2
1
1
0
0
2
2
4
0
0
0
0
0
0
2
2
1
2
2
1
1
1
0
0
0
0
4
0
1
0
1
2
1
0
1
2
0
2
1
1
0
0
1
0
1
0
0
1
0
1
0
0
1
2
0
1
2
0
1
2
1
0
1
1
0
0
1
1
0
0
0
2
1
0
0
0
2
0
4
2
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
2
1
0
0
1
0
0
0
2
0
2
1
1
0
1
2
2
2
1
1
0
0
0
1
1
2
0
0
2
2
0
1
2
2
0
1
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
1
2
2
0
0
0
1
2
0
0
1
2
0
0
0
1
1
1
2
1
2
2
1
0
0
1
2
2
0
0
1
0
2
0
2
1
2
0
1
0
0
0
2
1
0
0
0
0
2
0
0
0
0
2
0
1
0
2
0
2
3
0
0
1
0
0
0
1
2
2
2
2
0
2
0
1
2
1
0
0
1
0
1
1
2
1
1
1
0
1
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
1
2
0
2
1
0
1
0
0
0
0
0
0
1
0
1
0
2
1
1
0
0
0
2
0
1
2
1
1
0
1
2
2
0
0
0
0
2
0
0
1
0
0
0
0
0
1
1
2
0
0
0
0
2
2
0
0
0
0
0
1
1
1
2
0
0
0
1
1
2
1
0
0
0
2
2
1
0
0
0
2
0
0
0
1
2
0
0
0
1
0
0
0
2
1
2
0
1
1
0
0
0
0
0
0
2
1
1
0
0
0
2
0
1
2
0
2
0
0
0
0
1
0
2
0
1
1
1
0
1
0
2
1
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
2
0
1
0
0
2
1
0
2
2
0
0
0
0
0
0
0
2
2
1
0
2
0
0
1
0
0
0
1
3
1
2
0
1
0
1
1
1
0
2
1
0
0
0
0
1
2
1
1
1
0
2
0
0
0
1
2
1
1
2
0
0
0
0
0
1
0
1
2
0
1
1
2
0
1
0
0
0
1
0
0
0
2
0
0
1
0
0
1
0
2
0
1
2
0
1
0
0
1
0
0
0
0
2
0
0
0
2
1
2
0
1
2
2
1
2
0
0
0
1
0
2
0
0
2
0
0
0
2
2
0
1
1
1
0
0
1
5
2
2
0
1
2
0
1
0
1
0
3
0
0
1
0
2
1
1
2
0
0
1
1
0
1
1
0
0
1
1
0
2
0
2
1
2
0
0
0
1
0
3
0
1
1
0
2
0
0
2
0
2
0
0
0
0
1
1
0
1
0
1
0
0
2
4
1
0
2
0
3
1
0
0
0
2
0
2
0
2
3
2
1
1
1
0
1
0
2
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
2
2
1
1
1
2
0
1
2
0
0
0
0
0
0
4
1
0
1
0
0
0
1
0
2
0
0
0
0
2
0
0
0
2
1
0
2
3
2
1
1
2
1
1
2
0
2
0
1
1
1
0
2
0
2
0
2
0
0
2
1
2
0
1
1
0
0
0
0
0
0
1
1
2
0
2
7
0
0
1
0
0
2
1
1
0
0
2
0
2
1
0
2
0
1
0
2
0
1
0
2
2
0
0
2
1
1
1
0
0
0
2
1
2
2
1
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
1
2
2
0
1
0
2
0
0
0
2
1
0
0
1
0
0
1
1
2
0
1
1
2
0
1
1
1
2
0
0
1
0
3
2
0
0
2
2
0
1
0
0
1
2
0
1
0
0
0
0
1
1
1
0
0
1
0
0
1
0
1
1
0
1
0
1
0
0
2
0
1
2
2
0
0
1
0
0
0
0
2
2
0
2
1
0
2
0
1
0
0
2
1
3
0
0
2
2
0
0
0
0
0
0
1
2
0
1
2
0
4
0
2
0
2
1
0
1
1
0
0
2
1
0
0
2
1
0
0
2
0
2
1
2
1
2
2
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
2
1
0
1
1
3
0
2
0
2
2
0
2
0
1
0
0
1
0
0
0
1
0
1
0
1
1
1
2
0
1
1
0
1
2
0
1
0
0
2
0
0
0
1
2
0
0
0
0
0
2
1
0
0
1
0
0
0
1
0
2
1
2
0
0
2
0
1
0
0
3
0
0
0
0
0
0
1
2
2
2
0
2
0
0
1
0
2
0
0
0
0
0
0
1
2
3
0
1
1
0
2
0
0
0
0
1
3
2
1
1
0
0
1
1
3
0
2
0
0
3
1
0
1
1
0
2
2
1
2
0
0
0
1
0
0
0
1
1
2
0
1
1
0
2
1
1
0
0
0
0
1
0
0
1
1
0
1
1
2
2
2
2
0
1
1
1
1
0
0
1
1
1
1
1
2
0
1
2
2
1
3
1
2
0
2
0
1
0
1
0
0
2
1
2
0
0
0
0
1
0
1
0
0
4
1
1
2
2
1
2
1
0
0
0
1
0
0
1
1
0
0
1
1
2
1
0
2
2
0
0
1
2
0
0
0
0
1
1
1
2
0
0
0
0
1
0
1
0
1
3
0
3
0
0
0
1
2
1
0
0
0
1
0
0
1
1
0
0
2
1
0
0
0
1
0
0
3
1
1
2
0
1
2
3
0
0
2
1
1
1
0
0
1
1
0
1
1
0
1
0
0
1
1
2
2
0
0
0
1
0
2
1
2
0
1
0
2
1
0
2
1
1
0
0
2
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
1
0
2
2
1
2
1
0
1
0
2
0
0
0
0
0
0
1
2
0
1
1
2
0
0
1
0
0
0
1
1
2
0
1
0
1
0
2
2
1
2
1
1
0
2
1
0
0
2
0
1
0
1
1
0
0
2
0
1
0
3
2
1
0
0
1
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
1
1
2
3
0
0
2
2
0
2
3
0
0
0
0
2
1
2
2
1
0
2
2
2
0
0
0
0
0
0
0
2
0
1
3
1
0
0
1
1
0
1
0
1
0
2
1
1
0
2
1
0
0
2
0
0
2
0
0
0
0
2
1
0
1
0
1
0
1
3
1
1
0
1
0
0
2
2
1
1
2
0
2
1
0
1
0
1
0
3
0
0
0
2
0
1
0
1
2
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
3
2
2
0
1
0
7
1
0
1
1
2
0
2
1
0
0
1
1
1
0
1
2
1
0
1
1
1
0
0
1
0
1
0
0
0
3
1
0
2
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
2
1
0
1
0
0
1
1
0
2
1
0
0
0
0
0
2
2
0
0
1
2
2
2
1
0
1
0
0
0
0
1
1
0
1
0
0
1
1
0
2
0
1
0
0
1
0
2
0
1
1
2
1
1
0
1
0
3
0
0
1
0
0
0
0
1
0
0
1
0
1
1
0
0
0
1
1
0
0
0
0
0
1
1
1
1
2
0
1
2
2
0
0
2
0
0
0
1
1
2
0
2
1
0
1
1
2
0
0
0
1
1
1
0
2
1
2
0
0
0
2
0
0
1
0
1
1
0
0
2
2
1
0
1
2
1
0
0
0
0
2
0
0
0
0
2
0
1
0
0
1
0
1
2
0
2
1
2
0
0
0
2
0
0
2
1
0
2
1
0
0
0
0
1
0
1
0
2
1
2
0
2
1
0
2
0
0
0
1
2
2
0
1
1
0
1
1
1
0
2
0
0
2
1
1
0
0
0
2
0
1
1
1
0
2
2
0
0
0
1
0
1
2
0
0
0
1
1
0
2
0
2
2
1
0
0
1
0
0
1
0
1
1
0
1
0
0
0
0
2
2
2
0
2
1
2
0
2
0
1
0
0
0
0
1
1
0
2
1
0
0
0
0
0
0
0
1
1
1
0
0
2
1
1
0
0
0
0
2
0
1
0
2
0
2
0
2
0
0
1
0
0
0
2
1
0
0
0
1
0
3
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
2
0
1
1
1
0
0
1
1
1
2
1
0
2
2
0
3
0
0
0
0
1
0
0
0
2
2
0
1
0
0
0
0
1
0
1
1
1
0
1
1
1
1
1
0
2
0
0
0
0
1
0
1
0
2
0
0
1
1
0
0
0
2
2
0
2
0
2
0
0
0
2
1
0
1
1
2
1
2
2
1
0
2
1
0
0
2
0
0
2
2
1
1
0
1
1
0
0
1
1
0
1
2
0
1
2
0
4
0
0
1
1
0
0
0
1
2
0
1
2
2
0
3
1
2
0
0
0
0
1
0
1
1
0
2
1
0
1
0
0
1
1
2
2
0
2
0
0
0
1
0
0
0
0
1
0
1
1
0
0
4
2
0
0
2
0
1
2
0
0
0
2
1
0
0
1
4
1
0
0
2
2
0
2
0
0
1
2
1
0
1
0
1
2
1
0
2
2
0
0
1
2
0
2
0
0
0
0
0
1
0
1
0
0
1
1
1
1
0
0
1
0
1
1
0
0
2
0
2
0
0
2
0
2
0
0
1
0
4
1
0
0
0
0
1
1
0
2
0
0
0
2
1
0
0
1
0
1
1
0
1
0
1
0
1
2
1
2
0
2
2
0
1
1
0
1
0
2
0
0
1
1
1
0
0
0
2
2
0
1
0
1
0
0
1
0
1
2
1
1
1
0
1
0
2
1
0
2
1
3
2
0
0
1
1
0
0
0
1
2
2
0
2
0
0
1
1
1
0
2
0
0
0
0
1
2
0
1
1
2
1
0
0
1
0
1
0
0
0
1
0
0
0
1
1
0
0
0
2
0
2
0
5
1
1
1
2
0
0
0
2
0
0
0
0
2
2
0
0
1
2
0
0
1
3
0
0
0
0
3
0
0
0
0
2
2
0
0
1
2
0
1
2
1
1
0
0
0
1
0
0
0
1
2
0
0
0
0
1
0
0
2
1
0
3
1
2
1
0
0
1
2
1
0
0
1
2
2
1
0
0
3
2
0
0
1
2
0
3
0
0
2
0
2
1
0
0
2
2
0
1
1
2
1
1
0
2
2
1
0
2
0
1
1
1
2
0
0
0
0
2
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
2
1
0
0
0
2
1
2
0
2
0
1
2
2
1
0
2
1
1
0
0
2
0
1
0
1
1
2
0
0
0
0
0
2
0
0
0
0
2
1
2
0
0
0
0
0
0
0
2
0
0
1
2
3
1
0
1
0
1
1
2
0
0
2
0
0
0
2
1
1
2
0
2
1
1
2
0
0
0
1
1
0
0
1
1
2
2
0
0
1
0
0
1
2
0
0
2
1
0
2
2
0
0
0
2
0
1
0
0
0
2
0
0
2
0
0
1
2
2
2
1
2
0
1
1
2
1
0
0
0
1
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
3
2
1
1
0
0
1
1
1
0
0
0
0
0
2
0
1
1
0
1
0
0
0
1
1
1
0
0
1
2
0
2
2
0
0
0
0
0
2
2
0
2
2
0
1
1
0
0
0
1
2
0
1
2
0
2
1
0
0
0
1
1
0
0
0
0
1
3
2
1
1
0
0
0
1
0
0
1
1
2
1
1
1
1
0
0
1
0
0
0
0
0
2
2
0
0
0
1
0
2
0
1
0
0
2
0
1
0
2
2
1
1
2
0
1
1
1
2
0
0
0
0
2
1
0
1
0
0
1
0
2
0
0
0
2
2
1
3
1
0
0
0
0
0
0
1
0
0
1
1
0
0
2
0
2
0
1
1
0
0
2
0
2
2
2
0
1
1
0
1
1
0
2
0
1
1
2
0
0
0
0
0
1
2
0
0
1
0
0
2
0
1
0
0
2
0
2
1
1
1
1
2
1
1
0
1
0
1
1
0
0
2
0
0
0
2
0
0
0
2
0
2
2
1
1
0
0
1
0
0
0
1
2
1
0
2
0
0
2
0
0
0
1
2
0
0
0
0
0
0
1
2
1
1
0
0
1
1
0
0
0
2
2
1
0
0
0
0
0
0
1
1
1
3
0
1
0
0
0
2
0
2
0
0
2
1
0
3
0
0
2
0
2
3
0
2
1
2
2
1
1
2
1
1
0
2
1
0
0
1
1
0
0
0
2
2
2
0
2
0
1
2
1
0
2
0
0
3
1
0
0
1
0
2
1
4
0
1
1
0
2
2
1
0
3
1
0
1
1
0
3
2
0
0
0
0
1
2
0
1
0
0
2
0
0
0
0
1
0
1
0
0
1
2
0
0
1
0
0
2
0
0
0
0
0
0
0
2
2
1
0
2
1
2
2
1
0
0
2
0
2
1
0
0
0
2
1
0
0
0
0
0
2
1
1
1
2
0
1
0
0
0
0
0
1
2
3
0
1
0
0
0
0
0
1
1
0
3
0
0
3
2
2
4
0
2
0
0
2
0
0
0
0
1
1
0
1
2
1
1
0
0
2
0
0
0
2
0
0
0
0
3
0
1
0
1
2
1
1
0
0
2
0
0
2
0
0
0
2
2
1
0
2
1
0
1
1
1
0
1
0
0
1
0
0
1
2
2
0
0
1
0
0
0
0
1
0
0
1
2
0
1
1
1
0
2
0
0
0
2
1
0
0
1
1
1
0
0
0
0
2
0
1
2
1
1
0
0
0
1
2
0
0
0
0
1
1
1
2
0
0
0
1
0
0
0
2
2
0
0
0
0
1
0
0
1
0
1
1
1
0
0
1
1
3
0
0
0
0
1
1
1
0
1
0
0
2
0
1
2
1
1
0
0
0
2
0
1
0
2
0
2
1
0
0
2
2
1
0
1
2
0
1
2
0
0
1
1
1
0
0
2
2
0
0
1
2
2
3
1
0
2
1
0
1
0
1
0
1
2
0
4
1
0
1
2
1
1
0
0
2
1
1
0
0
0
0
0
0
1
0
2
1
0
0
2
1
2
0
0
1
1
1
0
1
0
1
0
0
0
1
0
0
0
0
0
2
0
2
0
1
0
1
2
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
1
0
1
0
1
0
0
2
0
0
1
0
0
2
0
2
2
0
0
2
0
1
0
0
1
1
0
0
2
0
2
2
0
1
1
1
0
1
2
0
0
1
2
0
0
1
1
0
0
0
0
2
1
1
1
2
0
0
1
2
0
1
2
3
0
1
1
1
1
1
2
0
0
1
1
1
0
1
1
3
0
0
0
1
1
0
1
2
1
0
2
2
2
1
2
0
0
0
0
0
1
1
0
0
0
0
1
0
0
2
0
1
1
0
1
2
0
1
1
0
1
1
0
0
2
0
0
1
1
0
0
1
2
0
0
0
1
0
1
2
0
0
2
0
1
0
2
1
0
0
1
2
0
1
2
1
0
0
1
0
0
2
1
1
3
1
1
2
2
0
0
1
2
1
2
1
0
0
3
0
2
1
2
0
1
1
0
0
0
1
2
1
1
0
1
0
0
2
2
0
0
2
0
3
1
1
0
2
1
1
0
1
0
0
0
2
1
2
1
0
0
2
0
1
1
1
0
2
0
1
0
0
2
2
0
1
1
0
0
0
0
0
0
3
3
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
1
1
0
1
1
1
2
0
1
0
2
0
0
0
0
0
0
0
1
2
1
2
2
0
0
2
0
1
0
3
2
0
0
0
0
2
2
0
1
1
2
1
2
0
0
0
0
1
1
0
1
2
2
2
0
1
3
2
0
1
0
3
3
0
0
2
0
0
1
1
0
0
2
0
0
0
1
1
1
2
0
1
2
1
1
0
0
1
1
2
1
1
0
2
0
1
0
0
1
0
0
1
1
2
0
0
0
2
2
0
0
0
2
2
2
0
1
0
1
0
0
2
1
2
1
0
1
1
0
0
0
2
0
1
1
0
0
2
1
1
0
0
1
0
1
2
1
2
1
0
0
0
1
2
3
2
0
1
0
1
0
0
1
2
1
2
1
1
1
3
1
0
2
0
0
0
0
0
1
1
0
1
0
0
0
0
2
0
1
2
1
1
1
0
1
0
1
0
0
0
0
0
1
0
0
0
2
0
1
2
2
1
0
0
0
0
0
2
0
1
0
1
0
0
1
0
0
0
1
2
0
1
0
0
0
1
1
2
0
2
1
0
0
0
0
2
0
0
0
0
1
1
1
2
1
1
1
0
2
2
0
1
0
2
0
0
1
0
2
0
0
2
0
0
0
0
0
0
1
2
1
0
1
0
0
1
2
0
0
3
0
2
0
0
0
0
0
2
1
11
1
0
1
1
1
2
1
1
0
0
1
3
0
0
0
1
0
0
0
2
0
1
0
1
1
0
1
2
2
0
1
1
2
0
1
1
1
1
1
0
1
1
0
1
0
0
0
1
0
0
2
0
3
2
0
0
1
0
2
0
2
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
1
0
0
1
1
0
1
1
1
0
0
0
0
0
0
0
2
1
2
0
2
2
0
0
2
0
0
1
1
0
0
0
1
1
0
0
0
2
0
2
0
0
2
0
2
0
0
0
1
2
1
0
0
0
0
1
0
1
1
0
0
1
0
0
0
2
0
2
0
1
0
1
2
0
2
0
0
0
1
0
0
2
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
1
1
1
3
0
0
0
2
1
0
0
0
0
2
1
0
1
2
0
0
0
0
1
0
2
2
0
2
2
2
1
0
2
0
0
0
0
2
0
0
0
2
1
0
0
0
1
1
0
0
1
0
0
2
0
0
0
0
0
0
0
1
1
1
1
1
0
2
0
0
0
0
0
1
1
0
1
0
1
0
1
2
1
0
0
1
1
0
1
2
1
0
3
1
1
2
1
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
1
0
1
3
1
0
0
0
0
0
2
0
1
1
3
0
0
0
0
0
0
1
2
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
2
2
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
1
0
2
0
0
1
0
0
1
1
1
2
2
1
0
2
0
1
1
1
0
2
1
0
0
0
0
0
0
0
2
0
1
0
0
2
1
0
0
0
0
0
1
2
0
0
1
0
2
2
0
2
0
0
1
1
0
1
1
0
0
0
0
2
1
2
1
2
0
2
1
0
0
1
0
2
0
1
0
0
0
0
0
2
1
0
1
0
0
0
0
2
0
1
0
0
0
2
1
2
3
1
0
0
1
1
2
0
1
0
1
0
2
0
0
4
2
1
0
0
2
3
0
1
0
0
1
0
0
0
1
0
1
1
2
0
0
1
1
1
0
0
2
0
1
1
1
0
0
0
1
0
1
0
1
0
1
2
1
0
0
0
2
0
0
0
0
0
0
2
0
1
2
0
0
0
2
0
1
0
2
0
1
2
2
1
0
1
1
0
3
1
1
0
0
0
0
0
2
0
0
3
2
0
1
0
1
0
0
2
0
0
0
0
0
1
1
1
0
0
0
1
0
0
1
1
0
1
0
1
0
2
2
2
2
0
0
2
2
2
0
0
2
1
0
1
1
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
1
1
0
1
0
1
0
3
0
0
1
2
0
1
1
2
0
2
0
1
1
2
2
3
0
1
0
0
0
1
1
1
1
1
0
2
2
0
0
0
0
0
2
0
2
1
0
1
0
1
2
0
1
2
1
1
1
0
2
2
1
0
2
0
0
2
0
0
0
1
0
1
1
0
1
0
0
0
1
2
1
2
2
0
2
1
2
1
0
1
0
1
0
2
0
0
1
3
0
0
1
0
0
2
0
0
2
1
1
1
1
0
1
2
1
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
2
1
0
1
2
0
2
0
0
1
0
0
0
0
2
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
1
0
1
2
1
0
2
0
1
2
0
0
1
1
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
4
0
3
1
0
1
1
0
0
0
1
2
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
1
1
0
0
0
0
1
0
1
1
0
2
1
0
1
0
0
0
0
2
1
2
2
1
2
0
0
0
0
0
0
1
0
1
1
0
1
1
0
2
0
2
0
1
1
0
0
1
2
0
0
1
1
0
0
2
2
0
1
0
1
0
2
2
0
2
0
1
0
0
0
2
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
2
2
0
1
0
0
0
0
1
2
2
1
0
1
0
0
1
2
0
1
2
1
3
1
2
2
0
0
0
0
1
1
0
2
1
0
0
0
2
2
0
2
2
0
0
2
0
0
0
0
1
0
0
0
1
0
0
1
0
2
0
2
1
0
2
2
1
2
1
0
5
2
2
0
1
0
1
0
2
0
0
1
0
0
1
0
1
0
2
0
0
2
0
1
1
1
0
0
1
1
0
1
1
0
0
0
0
0
0
1
1
1
1
2
0
1
1
0
0
0
1
0
2
0
2
0
0
1
0
0
0
0
0
1
1
2
0
0
0
1
0
0
0
2
0
0
0
0
1
2
1
1
0
2
0
0
0
0
0
1
0
0
2
1
0
2
0
2
0
2
0
0
0
0
1
0
0
2
1
1
1
0
0
0
2
0
0
1
0
0
1
2
1
1
0
1
2
1
0
0
2
1
0
0
0
0
2
1
0
2
0
2
0
1
2
3
1
2
0
2
1
0
0
1
0
0
1
2
0
0
0
2
1
0
1
1
0
0
0
0
1
0
0
2
0
0
1
0
0
2
0
0
2
1
1
1
2
1
1
2
0
0
1
0
0
0
0
1
0
0
0
2
1
0
2
2
0
1
0
0
0
1
0
1
0
1
0
1
0
0
2
1
1
3
2
0
1
0
0
0
2
0
2
2
0
1
1
1
1
1
0
0
2
1
0
1
2
0
0
0
2
3
0
2
2
1
2
0
0
0
1
0
0
0
0
1
0
2
2
0
2
2
0
3
1
0
2
0
0
2
0
1
1
2
1
0
1
1
2
1
2
2
2
0
2
0
1
2
1
0
1
0
0
2
1
0
1
2
1
0
0
1
2
2
1
0
2
2
0
2
2
1
1
0
2
0
0
1
1
0
0
1
1
1
1
0
1
1
1
2
0
0
1
1
1
2
0
0
1
0
1
2
0
2
0
0
1
2
1
1
0
1
0
3
2
2
1
0
0
2
2
2
0
0
1
2
1
0
1
0
0
2
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
2
0
2
0
1
2
1
0
0
1
0
1
0
1
1
1
1
1
0
1
0
0
1
0
0
0
1
0
1
2
1
0
0
0
0
0
2
2
2
1
2
1
0
1
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
1
1
1
1
1
1
0
0
0
6
0
0
1
1
1
2
0
0
0
0
0
0
0
2
1
0
1
1
0
0
2
0
0
1
0
0
1
0
1
0
1
1
0
2
1
0
1
2
1
1
1
2
2
0
1
2
0
2
0
0
1
2
0
1
1
0
0
1
1
0
0
1
0
1
0
1
1
0
0
1
1
1
0
0
2
0
0
1
2
0
0
1
2
0
0
2
0
0
2
1
0
2
2
0
0
0
0
0
0
0
1
0
2
0
7
2
1
0
0
1
0
0
1
0
1
0
0
0
0
0
3
1
1
1
2
0
2
2
0
0
0
1
2
0
1
0
0
1
1
2
1
0
0
0
2
0
0
2
0
5
0
0
0
0
2
0
0
0
2
1
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
2
0
1
0
2
0
0
0
0
2
2
3
1
0
0
2
0
1
0
2
0
0
2
1
1
0
0
0
1
2
0
0
0
1
0
2
1
0
1
0
0
0
0
0
1
0
2
1
0
1
3
2
0
0
0
0
1
0
0
0
0
0
1
2
0
1
1
2
0
1
1
2
0
0
0
1
0
0
0
0
0
0
2
1
0
0
2
1
3
0
1
1
0
0
0
1
0
0
0
0
0
0
2
2
0
1
1
0
0
0
1
2
1
0
1
0
0
0
0
0
1
0
1
2
1
1
0
3
2
1
1
1
2
1
2
0
2
0
0
0
1
0
0
4
2
0
1
0
0
2
0
2
0
0
0
1
0
0
2
2
0
0
1
2
2
0
2
0
0
2
0
1
1
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
2
0
2
0
0
1
0
2
1
0
1
2
2
0
0
0
0
0
1
0
0
1
2
2
2
0
1
2
1
0
0
2
0
2
0
0
1
0
0
1
0
1
3
2
2
1
0
0
0
2
2
1
0
0
1
0
0
1
2
0
0
0
2
2
1
0
2
2
1
2
0
0
0
0
1
3
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
2
0
1
0
1
1
0
0
2
0
1
0
0
0
1
1
2
0
0
0
0
0
0
0
2
2
2
1
5
1
0
0
1
0
2
0
1
1
1
0
0
0
0
1
1
0
0
0
0
1
2
1
0
0
1
2
1
0
1
1
0
0
0
0
1
1
2
0
1
0
2
0
0
5
0
0
2
2
1
0
2
0
1
1
0
1
1
0
1
1
0
0
1
1
2
2
0
2
1
2
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
1
0
2
1
0
2
1
1
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
1
1
1
2
1
1
1
0
0
0
0
0
0
0
2
2
1
0
1
0
0
1
0
2
0
0
1
2
1
0
1
0
2
0
0
2
1
0
2
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
2
0
1
0
1
2
0
0
0
0
0
1
0
2
0
0
2
0
0
0
1
0
0
0
1
1
0
2
1
0
1
1
0
2
2
0
1
0
2
1
2
0
0
2
1
1
2
1
2
0
2
0
0
1
0
0
1
0
0
0
0
0
2
1
1
2
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
1
2
1
1
0
1
0
1
2
2
3
0
0
0
0
0
0
2
0
1
0
1
0
0
3
1
1
1
0
0
0
0
0
2
2
0
2
0
1
0
0
1
2
1
1
2
1
1
0
0
1
0
0
0
0
0
0
2
2
1
0
2
0
0
0
1
0
0
1
1
1
2
0
3
0
4
3
2
0
0
2
0
0
0
0
2
1
2
0
1
0
0
0
1
0
2
2
0
0
1
0
0
0
0
0
1
0
1
0
0
1
1
1
2
0
2
0
0
2
0
0
0
1
0
0
1
1
0
1
1
0
0
0
1
0
1
1
1
3
0
0
0
2
0
0
1
2
0
1
0
0
0
1
0
1
1
1
2
0
1
0
0
2
0
1
0
0
2
0
1
1
0
0
0
0
0
0
1
0
0
1
2
1
2
0
1
0
1
0
0
0
1
0
2
0
0
1
1
1
0
0
0
0
0
1
2
0
0
1
1
0
0
1
1
0
0
1
1
1
0
2
0
1
1
2
1
0
0
0
1
1
0
0
3
0
2
2
0
1
0
2
1
1
0
1
2
0
0
0
0
2
0
1
0
0
0
1
0
0
1
2
0
0
1
1
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
2
0
0
2
0
0
1
0
0
1
2
1
2
0
0
2
2
0
0
1
0
0
0
0
0
2
0
0
1
2
1
0
2
1
0
0
2
0
1
2
0
1
1
1
0
1
1
1
2
5
0
0
0
2
0
0
2
0
1
1
0
0
0
2
0
2
0
1
2
1
0
1
0
0
1
1
0
0
0
1
2
3
1
0
0
0
1
0
1
0
1
1
0
0
1
0
0
1
0
0
0
0
0
1
1
2
1
0
1
2
0
0
0
2
0
2
0
2
1
1
1
2
0
0
0
0
1
1
2
0
2
1
0
0
2
0
1
0
2
0
0
0
0
1
2
0
0
1
0
1
0
0
1
2
1
2
0
0
1
0
2
1
1
0
0
1
0
3
0
1
0
0
1
1
0
1
1
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
1
2
0
1
1
2
0
0
2
1
2
0
1
3
0
1
2
0
0
0
0
0
0
2
0
1
0
2
1
1
1
1
2
0
0
1
0
0
1
1
2
1
0
0
0
0
1
1
3
0
0
0
2
0
0
2
0
2
0
0
0
2
0
2
0
0
1
1
0
2
3
0
0
0
1
1
1
0
0
2
0
0
1
2
0
0
1
2
0
0
1
2
1
0
2
1
0
1
1
1
2
0
0
2
2
0
1
2
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
1
2
1
0
1
0
2
0
0
1
1
1
2
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
2
0
0
2
0
0
2
0
3
0
0
2
2
0
0
0
2
1
0
0
2
1
1
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
1
3
0
0
0
1
1
1
2
0
2
0
1
2
0
2
0
1
1
0
0
3
0
0
0
0
0
1
0
2
0
0
0
2
0
0
2
2
0
1
1
1
0
1
0
2
0
0
0
2
1
0
2
1
1
0
0
1
0
0
1
0
0
0
1
1
0
2
2
2
2
1
3
0
0
2
1
0
1
0
1
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
1
0
1
1
1
0
1
2
2
1
0
0
1
0
2
2
1
0
0
1
2
0
1
0
0
0
0
0
2
1
1
0
2
2
0
0
0
2
1
1
2
0
0
1
1
1
1
0
1
0
0
1
2
4
1
0
0
0
0
0
0
0
1
1
1
1
1
1
1
0
0
2
0
3
1
0
0
0
0
0
1
0
1
1
1
0
1
0
0
0
0
2
2
2
1
1
0
1
1
1
0
0
2
1
0
2
0
2
0
1
0
1
0
2
0
0
0
1
0
2
2
0
1
1
2
1
1
0
1
2
0
1
0
2
0
0
0
0
1
0
1
0
0
0
1
0
2
1
0
2
0
0
1
2
1
4
0
0
2
0
0
0
2
2
2
0
2
1
0
0
0
1
0
2
0
2
0
1
1
1
2
0
1
0
2
0
2
0
1
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
1
0
0
1
3
0
0
1
0
1
0
1
0
0
0
1
1
1
0
2
1
0
1
1
0
0
0
0
0
0
2
2
0
4
1
0
0
0
0
0
2
2
0
1
0
0
1
0
1
0
1
0
0
2
1
0
0
1
2
1
1
0
2
0
0
0
0
1
1
1
2
0
1
0
2
1
0
0
0
1
0
1
1
1
0
0
0
2
1
4
1
0
0
0
0
1
1
2
0
0
0
0
1
0
0
0
0
1
1
2
2
1
0
2
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
2
2
0
1
0
2
0
1
0
2
0
0
0
0
1
0
2
0
0
0
1
2
0
1
0
0
1
0
1
1
0
0
0
1
1
1
1
0
0
0
2
0
0
0
0
1
0
2
2
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
1
1
1
0
1
0
0
3
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
1
2
0
1
0
1
2
1
1
0
0
1
0
0
1
1
2
0
0
0
0
0
0
1
0
0
2
0
0
3
2
2
0
0
2
2
2
0
1
2
4
0
0
1
0
2
2
1
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
1
1
0
3
0
1
1
2
0
1
0
1
1
0
0
0
0
0
0
1
0
2
0
2
2
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
2
1
2
1
0
2
1
2
2
0
0
2
0
0
0
0
0
0
2
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
2
1
2
3
0
0
2
2
0
1
0
3
1
0
1
2
0
0
0
0
0
2
0
0
2
0
0
0
1
1
1
2
0
1
0
1
0
2
1
2
0
0
0
0
0
1
2
1
0
1
1
1
2
1
0
1
0
1
0
0
1
0
1
0
0
0
1
2
0
1
0
0
0
0
0
1
1
3
1
2
1
0
0
0
2
0
1
0
0
0
2
0
2
1
2
0
1
0
3
0
1
0
0
0
2
2
2
2
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
5
0
2
0
2
2
1
0
2
1
1
2
0
1
2
0
1
0
0
0
1
0
2
0
2
0
1
0
1
1
2
0
2
3
0
2
0
0
2
0
1
2
1
0
1
0
0
0
0
1
0
0
0
0
0
1
2
1
4
0
0
1
1
1
1
1
0
1
1
0
1
0
0
2
0
0
2
1
2
0
1
3
1
2
0
1
0
1
0
1
1
2
0
1
1
0
0
0
2
0
1
1
0
1
1
0
0
0
0
0
0
0
2
2
0
0
0
1
5
1
1
1
0
3
0
0
0
1
0
0
0
2
0
1
0
0
2
0
0
0
0
2
2
2
1
1
0
1
0
1
1
0
2
0
0
0
1
1
1
2
1
0
0
1
2
0
0
2
0
0
1
1
1
0
2
0
1
0
1
2
2
2
0
0
0
1
2
0
1
0
0
2
0
0
0
1
1
0
2
0
2
0
1
2
3
2
2
0
0
0
0
1
1
0
0
1
0
0
2
0
2
1
0
0
0
0
1
1
0
1
0
0
2
0
0
0
1
0
1
0
2
0
0
1
2
2
1
0
0
2
2
0
2
0
0
0
1
0
0
0
0
0
1
2
0
0
0
1
0
1
1
0
0
0
0
0
0
1
2
2
0
0
0
2
0
0
0
0
0
3
2
0
0
0
4
1
0
1
2
1
2
0
1
2
0
0
1
1
1
2
0
1
1
2
0
0
0
1
0
1
0
3
2
2
0
0
1
0
0
0
0
0
0
0
1
2
2
2
0
0
0
1
1
0
2
2
2
0
0
1
2
0
2
0
1
1
0
1
3
0
1
0
2
0
0
2
2
1
1
0
2
1
0
2
1
0
1
0
0
0
0
0
1
2
0
1
3
0
0
0
0
0
2
2
0
0
1
2
1
0
1
1
2
0
2
1
0
1
0
0
0
0
1
0
3
1
0
1
0
3
2
1
0
0
1
0
1
0
0
3
2
2
2
0
2
2
0
0
0
2
0
1
1
0
0
4
0
1
2
0
0
0
1
1
0
2
1
0
1
1
0
0
0
0
1
1
1
2
1
1
3
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
2
1
0
0
0
1
0
0
0
1
0
2
1
0
1
2
1
2
1
2
1
2
0
0
0
2
2
1
0
0
0
2
0
0
2
0
3
1
0
1
0
1
0
1
0
2
0
1
1
1
0
0
0
2
0
1
1
0
2
0
2
1
1
1
2
0
1
1
1
0
1
0
2
0
0
2
1
0
2
0
0
3
0
0
0
0
0
0
1
0
2
1
2
1
0
1
0
2
0
1
0
1
1
2
2
1
0
0
2
0
0
1
0
0
2
2
2
2
0
1
2
2
2
0
0
1
0
0
0
0
3
1
0
0
0
1
2
1
0
1
2
2
2
0
0
0
0
0
2
1
0
0
0
1
0
1
0
2
0
1
0
0
0
0
2
0
2
2
2
2
0
0
0
0
2
0
0
2
0
0
0
1
0
0
1
0
0
2
2
3
0
1
0
1
2
0
2
1
0
1
2
3
0
0
0
0
1
1
3
0
0
0
2
0
2
0
0
0
2
0
0
1
0
0
1
1
1
0
0
1
1
0
1
1
1
1
0
0
2
0
1
2
2
0
1
2
0
2
1
0
2
2
1
2
0
0
1
0
1
0
2
0
1
2
0
1
1
1
1
2
0
0
1
0
0
1
2
1
0
2
2
1
0
2
0
0
1
0
1
1
0
0
3
1
1
1
0
0
0
2
0
2
1
1
0
0
0
2
0
1
3
1
0
2
0
1
0
0
0
2
0
1
0
0
0
0
1
1
2
0
0
0
0
1
0
0
3
0
1
0
2
1
1
0
1
0
0
0
1
0
1
2
0
0
2
1
1
2
1
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
1
1
1
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
2
0
0
1
0
0
1
0
0
0
0
0
0
2
1
1
0
0
1
1
1
1
2
0
0
1
1
0
1
0
0
2
2
0
0
2
0
0
2
0
0
2
1
2
2
0
2
0
0
0
0
0
6
0
0
1
0
1
0
1
0
2
1
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
1
1
0
0
2
0
2
0
1
0
1
0
1
0
0
1
0
0
2
0
0
1
2
0
2
0
1
2
0
1
0
0
2
0
2
0
2
0
0
0
0
0
1
2
0
1
0
0
0
2
2
0
0
0
2
0
0
2
0
0
1
2
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
2
1
1
0
1
2
0
0
1
0
1
1
0
0
0
2
2
2
0
0
2
1
1
0
0
0
1
0
0
2
3
2
1
0
0
0
0
1
0
0
0
1
0
0
1
2
0
0
1
0
0
0
0
0
2
1
0
1
1
1
0
0
0
1
2
0
1
0
0
0
0
0
2
2
0
0
0
1
0
1
0
1
1
0
1
1
2
0
0
1
0
0
0
2
0
2
0
0
1
1
0
0
3
1
2
5
0
0
0
0
0
1
1
0
1
1
1
1
2
0
1
0
0
0
2
0
0
0
2
1
0
0
1
0
2
1
0
2
1
2
2
2
0
0
0
2
1
1
0
1
2
2
0
0
2
0
0
0
1
1
1
7
0
0
1
2
1
0
1
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
1
1
2
0
1
0
0
1
2
0
0
2
1
2
1
1
1
1
0
0
2
2
0
1
0
0
2
0
2
0
0
0
1
1
0
2
0
2
1
0
2
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
1
2
1
2
3
0
0
2
0
0
0
0
1
2
2
2
0
0
2
0
2
1
0
0
2
0
0
2
1
0
0
2
0
0
0
0
2
0
0
1
2
2
0
1
1
0
0
1
0
0
0
0
0
1
2
2
1
1
1
0
1
2
0
1
0
1
0
1
0
1
2
3
0
1
2
0
0
2
0
2
0
0
0
0
1
1
2
2
0
1
0
1
0
0
2
1
0
1
0
0
1
1
1
0
0
1
0
0
0
1
1
0
0
1
1
1
2
1
0
1
1
1
0
0
1
1
0
0
0
1
2
1
0
1
0
0
1
2
0
2
0
2
2
3
0
1
0
0
1
1
1
2
1
0
0
0
0
0
0
0
1
0
0
2
0
1
0
1
1
0
1
2
0
0
2
0
0
0
0
0
0
0
0
2
1
2
1
2
2
3
2
0
0
0
0
1
0
1
3
0
0
1
2
0
2
0
2
0
0
0
1
0
0
1
1
1
1
0
1
0
1
1
2
0
2
1
2
0
0
1
0
0
1
0
2
2
0
2
2
1
0
0
3
0
2
0
0
0
1
2
2
2
0
2
1
0
1
2
1
1
2
1
0
0
0
1
2
0
0
1
3
0
0
2
0
1
0
1
0
3
1
0
0
0
0
0
1
0
2
1
0
1
0
0
0
2
0
0
0
1
0
0
1
0
0
1
0
0
1
1
2
1
0
2
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
3
2
2
2
1
0
2
1
1
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
2
2
3
0
1
0
2
0
1
2
1
1
2
1
0
0
0
0
2
1
2
0
0
1
1
2
1
2
2
1
1
0
2
1
0
2
0
1
2
0
1
1
2
2
1
0
2
1
0
0
0
0
1
1
1
0
2
0
0
1
2
2
0
3
1
0
0
0
0
0
1
1
0
2
1
1
1
4
1
1
0
2
1
0
1
1
2
1
2
1
1
0
0
0
3
0
0
1
1
1
1
2
0
0
2
0
0
0
0
1
2
0
4
1
1
0
0
0
2
2
0
1
0
3
0
0
0
2
1
0
1
0
0
2
3
1
1
1
0
1
0
0
3
0
0
1
0
1
0
1
1
0
0
0
1
1
0
1
1
2
0
0
0
2
0
0
0
0
1
2
0
0
0
1
2
0
1
2
0
0
0
0
1
0
0
1
0
0
0
1
0
0
2
1
0
1
0
2
0
3
0
2
0
0
0
2
0
2
1
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
3
1
1
0
0
0
2
0
1
0
0
2
1
2
0
0
1
1
1
2
0
0
2
1
0
2
1
0
1
0
0
1
0
0
0
0
2
0
1
2
1
2
0
0
0
3
2
2
0
1
1
0
0
0
0
1
0
2
0
1
0
0
1
1
0
0
0
1
0
2
0
0
1
0
1
0
2
2
0
2
1
0
0
2
2
0
0
1
2
1
1
0
0
0
0
2
2
0
2
0
0
0
0
2
2
2
2
0
1
0
1
1
0
1
2
0
2
0
0
1
2
2
3
0
2
2
3
0
1
2
0
1
1
0
0
2
0
2
0
1
0
0
1
0
2
2
2
2
0
1
1
4
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
3
0
0
0
1
0
0
1
1
0
0
0
0
2
1
1
2
2
0
1
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
1
0
1
0
0
1
1
0
0
0
0
2
1
2
1
0
1
0
0
0
1
0
2
0
1
0
0
1
1
1
1
0
0
0
2
2
0
0
1
0
0
1
0
0
0
1
2
0
0
2
2
0
0
0
2
0
1
0
1
0
0
0
0
0
2
1
0
0
0
1
0
0
2
0
1
2
0
2
0
3
1
0
0
0
2
1
2
0
0
1
1
1
2
1
1
0
0
1
0
0
2
0
2
0
0
0
2
1
5
0
2
0
1
1
1
1
0
1
0
2
0
1
0
0
1
0
0
0
1
1
1
1
0
2
2
0
0
1
0
1
0
1
0
0
0
2
0
0
1
0
1
0
0
0
1
0
2
1
2
1
1
1
2
0
1
0
1
2
0
1
0
2
0
0
0
1
0
0
0
1
0
0
1
3
1
0
1
2
1
2
0
0
0
1
0
0
1
0
1
0
1
0
0
0
2
0
2
0
0
2
0
0
1
2
0
2
2
1
3
0
2
1
1
1
1
3
1
0
2
1
2
1
1
0
0
0
2
0
4
1
1
1
1
1
0
2
3
1
2
2
1
0
0
0
2
0
0
2
0
0
1
0
0
2
1
1
1
0
0
0
2
2
1
2
0
2
2
2
0
1
0
1
3
5
1
2
2
0
1
1
0
2
2
1
0
2
0
2
2
2
2
1
2
1
1
0
1
0
0
0
1
1
0
2
0
0
2
0
1
1
2
0
0
0
0
2
0
2
0
0
1
0
0
1
1
1
2
0
2
1
1
1
1
0
1
1
2
0
0
0
0
0
1
0
2
1
4
0
0
0
0
1
2
1
0
0
1
1
1
0
1
1
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
2
1
0
1
3
0
0
2
0
0
0
0
0
0
1
0
2
1
0
1
2
1
0
0
1
2
0
0
2
0
0
2
1
2
0
1
1
1
2
0
1
0
1
1
0
5
2
0
1
0
1
0
0
0
1
0
2
2
2
1
1
0
0
1
2
0
1
0
0
0
0
1
2
1
1
0
0
0
2
1
1
0
0
3
2
0
0
1
1
0
2
1
0
0
0
1
0
1
0
0
1
0
0
1
2
1
2
0
2
5
0
0
0
0
1
2
1
0
0
0
0
1
0
0
2
2
0
0
2
0
2
2
2
1
2
0
0
2
0
0
2
0
0
1
0
1
2
0
1
1
0
0
0
1
0
0
1
4
1
0
0
0
0
1
2
1
0
0
1
1
1
0
0
0
1
0
0
2
2
0
4
3
2
0
0
0
0
1
0
0
0
0
3
0
0
0
2
1
1
1
0
0
4
2
1
1
2
1
0
0
0
2
2
0
1
0
0
0
0
1
0
2
3
1
1
0
1
0
2
0
0
6
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
3
0
0
0
0
0
1
0
1
0
2
0
1
0
1
1
1
1
1
1
0
1
1
0
2
0
2
1
0
0
0
1
1
1
1
0
0
0
2
0
0
2
0
0
4
1
0
1
0
0
2
0
0
0
2
2
1
1
0
1
1
2
2
0
1
1
2
2
0
0
0
0
1
2
2
0
2
0
2
0
2
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
2
2
0
0
0
3
0
1
1
1
0
2
2
0
2
2
1
0
0
2
2
0
0
0
2
0
0
0
1
2
0
2
0
0
2
0
0
0
1
2
2
2
1
1
1
0
0
2
2
0
0
2
2
0
2
2
0
0
0
1
1
1
0
2
0
0
2
1
2
0
1
1
0
1
0
2
0
0
0
1
0
0
0
2
0
1
0
1
0
1
1
1
0
1
1
1
0
1
0
2
0
0
0
1
0
2
0
0
1
2
0
1
1
0
0
0
0
0
1
0
2
3
0
2
2
0
0
1
0
1
0
0
2
0
0
0
3
1
1
2
0
2
0
0
0
2
1
0
1
1
0
0
1
1
1
0
2
2
1
0
1
0
2
3
0
1
0
0
0
1
0
0
0
0
0
1
1
0
1
0
3
0
0
0
2
1
1
0
0
0
0
0
0
0
2
1
2
1
0
1
2
1
2
2
1
0
0
1
2
1
0
2
1
1
2
0
0
0
0
0
3
2
0
0
1
2
0
0
1
0
0
0
2
1
0
0
1
0
0
0
0
0
0
2
1
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
1
2
0
2
0
0
1
2
1
1
1
0
0
0
2
0
0
0
0
2
0
1
0
16
0
2
0
1
1
2
2
3
0
0
2
1
1
2
0
2
0
2
1
0
0
2
0
0
0
1
2
0
0
0
0
0
1
2
0
0
0
0
0
1
0
2
0
2
0
0
1
0
0
0
0
0
3
1
0
2
1
0
0
0
0
0
2
2
1
1
0
2
2
0
1
1
2
0
2
0
0
1
3
0
2
2
0
2
0
1
2
2
0
0
2
0
0
1
0
0
0
2
0
0
0
2
2
2
0
0
2
0
0
2
0
1
2
1
0
0
2
2
1
0
0
1
2
2
0
1
0
0
0
0
0
1
1
0
0
1
2
0
2
0
0
2
2
0
1
0
1
0
0
0
3
1
0
0
0
1
0
0
0
2
0
1
1
0
0
2
0
1
1
1
1
2
0
1
1
1
1
1
0
1
2
0
1
1
2
1
0
0
2
0
1
0
0
2
0
1
0
0
0
0
2
0
2
2
2
0
0
2
2
1
1
0
2
0
2
0
0
0
1
1
0
0
2
1
0
1
1
0
0
2
1
1
0
2
2
1
0
1
0
0
0
0
1
0
0
0
2
1
1
0
2
0
2
0
3
2
0
1
2
0
0
0
0
1
1
2
0
0
1
1
0
0
2
1
0
1
2
0
0
1
0
2
0
2
0
1
0
1
1
1
1
2
0
2
0
0
3
0
0
1
2
2
0
0
1
1
1
3
0
1
1
1
1
1
0
0
2
0
1
2
0
2
1
0
0
2
0
0
2
0
0
2
0
1
2
2
0
2
0
2
1
0
1
0
0
1
0
2
1
1
1
1
3
1
1
1
0
1
1
0
1
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
1
2
1
0
0
0
2
0
0
2
0
0
1
0
1
1
0
2
1
0
0
2
0
1
0
1
0
0
2
1
2
1
1
2
2
2
0
0
1
0
2
0
2
0
1
0
0
0
1
2
0
3
0
1
0
1
1
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
1
2
0
0
0
2
1
0
0
2
0
0
2
2
0
0
1
0
1
2
1
0
0
2
1
1
1
2
0
2
0
3
2
0
0
0
1
0
1
1
2
0
0
0
0
0
2
0
0
0
2
0
1
1
1
1
0
0
0
2
0
0
0
1
0
2
0
0
1
2
0
0
2
2
0
1
0
0
2
2
3
0
0
0
2
2
1
1
0
0
0
0
0
0
0
0
0
1
0
1
2
2
0
2
0
0
1
1
2
0
4
0
0
0
2
0
0
1
2
1
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
2
2
2
2
1
1
0
2
2
0
1
1
0
0
1
2
0
2
0
2
1
0
0
0
0
1
0
2
2
0
0
2
1
2
0
2
0
0
1
0
0
2
2
1
0
0
1
2
1
1
1
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
2
1
2
3
0
0
0
2
0
0
2
0
0
1
0
2
1
0
1
0
1
0
1
0
1
1
2
0
1
0
0
0
0
2
0
0
0
1
2
0
0
1
2
0
2
0
0
1
2
1
0
2
0
0
2
0
0
0
1
0
0
1
2
1
0
1
0
1
1
2
0
0
1
2
1
2
1
2
0
1
0
0
0
2
0
0
1
2
2
0
0
0
0
2
0
1
0
0
1
0
0
2
2
1
0
0
1
0
0
3
1
1
1
1
0
1
0
2
0
1
0
1
0
0
0
2
0
0
0
2
1
1
1
1
0
0
0
2
2
0
0
0
0
2
1
0
0
2
0
0
0
0
2
0
0
2
2
1
0
0
1
0
1
0
2
2
0
1
1
1
2
1
2
0
0
0
2
0
2
0
0
1
2
0
0
0
0
1
3
0
1
0
0
0
0
2
0
0
0
1
2
1
1
1
0
0
0
0
0
2
0
0
1
0
0
5
0
1
0
0
1
1
2
2
2
1
1
1
1
0
1
1
2
2
1
0
0
0
1
2
1
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
2
2
1
0
1
2
0
1
1
0
0
0
0
1
2
1
0
0
1
0
0
2
1
0
2
0
1
1
1
0
2
2
0
1
2
1
2
2
1
2
0
0
0
0
0
1
2
2
1
0
0
0
0
1
0
1
0
2
0
0
0
1
0
0
2
2
1
1
0
0
2
1
0
0
0
2
0
3
2
0
0
4
0
1
2
0
0
0
0
0
1
2
0
1
3
0
2
0
1
1
0
0
0
1
0
1
1
1
1
1
2
1
0
4
0
1
0
1
1
2
2
2
0
0
0
0
1
0
0
2
2
1
0
2
2
0
1
0
4
0
0
2
2
0
0
1
2
2
0
2
0
0
0
0
3
0
0
0
1
1
1
0
1
0
0
1
0
3
0
2
0
2
0
3
1
1
2
0
1
2
0
0
2
2
0
2
0
0
1
0
2
1
0
2
1
2
0
0
0
0
0
1
0
1
0
1
1
3
1
0
0
0
2
0
0
2
1
2
0
2
0
1
1
0
1
0
0
2
2
1
0
1
1
2
2
2
0
1
0
1
2
1
1
0
1
1
0
0
0
1
2
2
2
1
2
3
0
1
0
0
1
0
0
0
1
1
0
0
2
1
0
1
1
0
0
0
1
1
0
0
2
0
0
2
0
1
0
0
1
2
0
0
0
0
0
0
2
1
3
2
2
0
0
2
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
1
0
1
0
0
0
1
2
0
1
0
0
1
0
2
2
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
2
0
0
1
1
0
2
0
0
0
2
0
0
2
1
1
0
1
0
1
0
0
1
1
2
0
2
0
0
0
0
0
2
0
0
0
1
1
0
1
1
0
2
0
1
0
0
0
0
1
0
0
2
2
0
1
0
1
0
1
0
0
0
2
2
0
0
1
2
1
1
0
2
0
0
0
0
0
0
2
0
1
0
2
1
0
0
1
1
2
2
0
0
1
2
0
1
1
0
1
0
0
1
0
0
0
0
0
0
2
2
0
0
0
2
2
2
1
0
0
1
2
0
0
1
0
0
0
1
0
2
1
1
0
0
0
0
0
0
1
2
2
0
1
2
1
2
0
0
2
0
0
0
1
1
1
1
0
0
1
1
2
1
0
0
0
1
0
0
2
1
0
3
0
0
0
0
2
2
1
0
0
1
0
0
0
1
1
1
0
0
0
0
0
2
0
2
0
1
0
4
2
0
0
2
0
2
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
2
0
2
2
1
1
0
2
0
1
2
0
0
1
1
1
0
1
1
1
4
0
2
1
0
0
0
0
0
0
0
1
0
1
2
1
0
1
0
1
1
1
0
0
1
2
0
0
0
0
1
2
1
1
1
2
1
2
1
0
0
0
0
1
0
0
0
0
2
1
0
0
0
2
0
0
1
1
0
0
0
1
0
0
0
1
0
1
1
0
2
1
1
1
1
1
1
0
0
2
1
1
0
1
0
4
2
1
2
1
0
0
0
2
0
1
1
1
1
0
1
1
2
1
0
0
1
2
2
0
0
1
0
0
0
0
0
2
0
2
2
0
1
1
1
0
1
0
0
1
0
0
0
1
0
1
1
2
2
0
0
1
0
2
0
2
0
0
1
1
1
2
0
0
0
2
1
0
0
1
1
0
0
0
1
0
0
1
0
0
0
2
0
1
0
0
1
1
1
1
1
1
0
0
4
2
0
2
1
0
0
1
0
1
0
1
0
2
0
0
0
1
0
0
0
1
2
0
3
1
1
2
2
2
0
1
0
2
0
2
0
0
0
0
1
0
1
0
0
0
1
0
0
0
2
1
1
1
0
2
0
1
1
0
0
0
0
2
0
1
0
2
0
0
1
0
0
0
0
1
2
1
2
2
1
2
0
1
0
2
0
1
1
0
1
1
0
0
0
0
1
0
2
2
0
0
1
2
1
4
0
0
1
2
0
2
2
2
0
0
2
1
0
0
0
0
0
0
0
2
0
1
0
2
0
0
2
2
1
0
0
0
1
2
1
2
0
0
2
2
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
1
2
0
0
0
1
0
1
1
0
2
0
2
0
1
1
1
2
2
0
0
0
1
1
0
2
0
0
1
0
1
1
1
0
0
0
2
0
0
0
2
2
1
2
0
0
0
1
2
1
0
2
0
2
0
0
2
1
1
1
2
4
0
0
0
1
2
2
0
0
1
0
0
0
0
2
1
1
1
2
2
0
2
0
0
0
0
0
0
1
0
3
0
0
2
0
2
0
0
0
0
2
0
1
1
0
0
2
0
1
1
0
1
0
0
0
0
0
2
2
0
0
2
0
0
0
2
2
0
0
0
2
1
0
0
2
2
2
0
0
0
0
0
0
1
1
1
1
1
1
0
1
0
2
2
0
0
2
0
1
0
0
0
0
1
2
0
4
2
0
0
0
0
0
1
0
2
2
0
0
0
0
1
3
0
0
1
1
1
2
2
0
0
0
1
0
2
1
0
0
2
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
1
1
0
2
1
0
0
2
0
1
0
0
0
0
0
0
0
0
1
2
0
0
2
3
0
1
0
1
0
0
2
2
1
2
1
1
1
0
0
2
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
4
0
1
0
0
0
2
2
1
0
0
0
2
1
2
1
0
0
0
2
0
2
0
0
0
1
0
1
2
3
1
1
0
0
1
0
2
2
0
0
1
1
2
0
0
0
2
0
0
1
0
0
2
3
1
0
0
0
2
2
0
2
1
2
2
1
0
0
2
0
0
3
0
2
0
0
0
1
1
1
0
5
0
0
1
0
0
0
2
1
0
2
0
2
0
1
0
1
0
1
2
0
0
2
0
1
1
0
2
0
0
0
2
1
0
1
1
0
2
1
0
0
1
0
0
0
1
7
0
0
0
1
0
2
0
0
2
2
0
1
0
2
2
0
2
0
1
0
1
2
1
0
2
0
1
0
0
2
2
0
0
0
1
0
0
0
1
1
0
1
0
2
0
0
2
0
1
0
0
0
2
2
2
1
2
0
2
1
0
0
2
0
0
0
1
0
1
0
0
0
1
2
2
0
2
2
0
2
1
0
1
0
1
0
1
2
2
0
0
0
1
1
0
1
2
0
1
0
1
0
5
0
1
2
0
0
0
2
2
0
0
2
0
1
2
0
3
0
1
1
2
0
0
0
2
1
0
0
2
2
0
2
1
1
0
1
0
1
0
0
0
0
1
1
2
0
0
2
0
0
0
1
0
0
0
2
0
2
0
2
0
0
1
2
1
0
0
1
1
1
0
0
0
0
1
0
2
1
0
0
0
2
0
0
1
0
1
0
1
2
0
0
0
3
1
0
0
1
0
6
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
1
0
1
1
2
3
0
1
0
1
2
1
2
0
2
2
2
0
2
1
2
1
0
1
0
0
0
0
1
2
2
1
0
2
1
0
1
0
1
2
1
0
0
2
2
1
0
0
0
1
2
0
0
0
1
0
0
0
0
0
1
0
0
2
2
0
2
2
1
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
1
1
0
1
1
3
1
1
0
2
1
1
0
0
0
1
1
3
0
0
0
0
1
2
2
0
1
2
0
0
0
0
2
0
0
0
0
0
2
4
1
2
2
1
2
0
0
0
0
2
0
1
0
0
0
1
0
0
0
1
0
2
2
0
2
1
0
1
2
0
0
1
2
0
0
0
2
0
1
0
0
1
1
1
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
1
0
0
2
0
0
0
1
1
0
1
1
0
0
0
0
0
0
1
0
2
2
2
0
1
0
0
0
1
0
0
0
1
2
0
2
4
0
0
2
0
2
0
0
2
0
2
2
0
2
1
1
0
2
0
1
0
2
0
0
0
0
1
0
0
1
0
0
3
2
2
0
0
1
0
0
2
2
2
1
2
1
0
0
1
0
1
0
0
0
0
2
2
1
0
2
0
1
0
0
2
1
0
0
0
0
2
1
0
1
2
0
1
0
0
0
1
1
0
0
0
1
1
0
2
1
0
0
0
0
0
0
0
1
2
0
2
0
1
0
1
0
0
0
2
1
0
0
1
2
0
0
1
2
0
0
1
0
0
2
1
2
7
0
1
0
2
1
0
0
3
2
1
1
0
1
0
0
0
0
0
0
1
0
1
0
1
2
0
0
0
3
1
2
2
2
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
2
3
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
1
0
2
1
1
0
0
1
0
1
0
2
1
0
0
0
2
2
0
1
0
2
1
1
2
2
0
0
0
1
1
1
0
0
1
2
1
1
2
2
0
2
0
0
0
0
1
1
1
0
1
2
0
0
2
1
0
0
0
1
0
0
0
0
2
1
1
1
1
0
0
3
2
0
3
3
2
2
1
3
0
0
2
1
1
0
2
1
1
2
0
0
0
1
2
2
0
2
1
0
0
0
2
0
3
0
2
2
1
0
1
0
2
2
0
0
2
1
1
1
0
0
2
0
2
1
1
0
0
0
0
0
0
1
0
1
2
1
0
0
1
1
0
1
0
1
0
1
1
2
0
0
1
1
2
0
0
0
2
0
1
0
1
0
1
0
2
0
1
0
0
0
0
1
0
2
0
1
1
1
0
2
0
0
1
0
1
0
0
2
0
2
0
3
1
0
0
0
1
1
0
0
1
0
2
0
0
0
2
0
0
0
0
2
0
0
1
0
0
1
1
0
0
2
0
1
1
2
2
0
1
2
0
0
1
1
1
1
0
2
1
0
0
1
0
1
1
1
0
2
0
0
0
0
0
0
1
0
2
2
1
0
0
0
2
1
0
0
1
1
2
1
1
1
0
0
0
0
0
2
2
0
0
0
1
0
1
2
0
2
0
0
0
1
5
0
1
2
2
0
2
0
0
0
2
0
0
2
2
0
1
1
1
1
2
1
2
1
0
1
0
0
1
0
2
2
0
1
2
0
1
1
2
1
1
2
0
1
0
0
0
1
2
0
0
1
0
1
0
0
0
1
0
1
1
0
2
0
0
0
2
2
0
0
1
1
1
1
0
0
0
1
0
2
1
0
1
1
1
0
2
0
0
0
2
2
2
0
0
2
1
0
0
0
1
0
1
0
0
0
0
1
2
0
1
1
1
0
0
2
0
2
0
0
2
2
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
1
0
1
0
1
0
0
1
0
0
0
1
2
1
0
1
0
2
1
2
2
0
1
0
1
2
1
2
1
1
1
1
0
0
0
4
3
1
0
0
0
2
0
0
2
0
0
0
2
0
1
0
2
0
2
1
1
1
2
1
2
1
2
2
0
1
1
2
0
0
0
2
0
0
0
0
1
2
1
2
1
2
0
0
0
0
2
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
2
2
2
0
0
0
0
0
2
0
2
2
0
0
0
2
1
0
1
1
0
0
2
0
0
0
0
1
1
1
0
2
0
0
1
1
0
2
0
1
0
0
1
0
1
1
0
0
1
0
2
1
0
0
0
2
1
0
1
0
2
0
1
2
1
2
3
0
0
0
0
0
0
0
2
0
1
0
0
1
1
1
0
0
2
1
0
0
2
0
0
2
0
1
0
1
1
1
1
0
0
0
2
0
1
0
1
0
0
1
0
0
1
0
1
0
0
0
1
0
2
0
0
1
2
1
0
0
2
0
0
1
1
0
0
1
3
0
0
0
0
1
0
0
0
0
1
1
1
1
0
0
0
0
0
2
1
1
0
2
1
2
2
0
1
0
1
0
4
1
0
1
0
0
0
3
0
0
1
0
0
1
1
0
0
0
2
0
0
0
0
2
2
0
2
2
0
0
0
1
0
0
1
0
0
1
0
1
0
1
0
0
2
1
0
0
0
1
0
2
0
1
0
1
0
1
1
1
0
0
2
1
1
1
0
1
2
1
2
0
1
1
0
0
0
1
0
2
1
0
2
0
0
1
0
2
1
2
1
0
0
2
0
0
0
0
1
2
2
0
2
2
1
0
0
0
1
0
1
0
0
3
0
1
0
0
0
1
2
0
2
0
0
2
1
0
1
0
0
0
2
0
1
1
0
2
2
0
2
2
2
0
0
0
0
0
0
1
0
0
0
2
2
0
0
1
0
0
0
0
1
0
1
2
0
1
0
0
1
2
1
1
0
2
2
2
0
2
0
0
0
2
0
1
0
0
0
0
1
1
2
1
0
0
1
0
0
1
0
2
0
4
1
1
0
0
1
0
0
2
0
1
0
0
0
2
0
0
0
2
2
0
0
0
1
1
1
2
1
0
0
2
1
0
1
1
0
0
1
0
0
0
0
2
4
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
1
1
1
0
1
0
2
0
0
2
1
1
0
0
2
2
2
1
2
0
2
2
1
2
1
2
1
0
1
0
2
0
2
0
2
0
2
0
1
0
2
2
0
1
1
2
1
0
0
0
0
2
2
1
3
1
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
2
0
3
1
0
1
3
1
2
0
2
0
2
0
0
1
1
0
2
2
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
2
1
2
0
0
0
2
0
0
4
0
2
0
1
0
0
0
3
1
1
0
0
0
1
2
2
1
2
0
0
1
1
2
2
0
1
1
0
0
0
3
0
0
0
1
0
0
0
0
1
0
2
0
1
0
1
0
0
0
2
0
0
0
1
1
3
0
0
0
2
0
1
1
0
0
1
0
0
2
1
0
0
1
0
1
0
1
1
1
2
0
0
1
2
1
0
0
0
0
0
0
0
0
2
1
1
1
0
1
2
0
0
0
2
2
0
0
2
1
2
0
0
0
1
0
0
2
0
2
2
2
1
0
3
2
0
0
0
1
0
1
1
1
1
1
2
6
0
1
2
0
0
0
0
0
1
1
0
1
1
0
0
0
2
0
0
1
1
1
1
1
2
1
1
2
0
2
2
2
0
1
0
0
0
1
0
1
0
1
1
2
0
2
2
2
1
0
0
0
1
2
0
2
1
0
2
2
0
1
3
1
1
1
0
0
0
1
0
1
0
2
0
1
0
1
0
1
2
0
2
0
0
1
0
2
1
2
1
0
1
2
1
0
0
0
0
0
1
2
0
0
1
2
0
0
3
1
0
1
1
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
2
1
1
1
2
2
3
1
1
2
1
1
1
2
1
1
1
0
2
0
1
0
0
1
0
0
1
0
1
0
2
1
0
0
0
2
0
1
2
0
2
0
1
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
2
3
0
1
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
2
0
0
1
0
1
0
0
0
1
2
0
0
0
2
2
0
0
1
0
0
0
2
0
0
0
0
1
2
1
0
1
0
2
2
1
0
0
1
2
0
0
1
0
0
0
0
0
2
2
0
0
0
0
2
1
1
1
0
0
0
0
2
0
2
0
1
1
2
0
0
0
2
2
2
0
0
0
0
0
0
1
1
3
1
2
0
0
1
2
2
1
0
1
1
0
0
0
1
0
1
0
0
0
1
1
0
0
1
1
0
2
1
1
2
1
0
0
0
1
2
1
1
0
0
0
0
1
1
1
1
0
0
1
1
0
0
0
1
1
2
0
0
0
1
0
0
0
2
0
2
0
0
0
2
1
0
0
0
1
0
0
1
1
0
0
0
0
1
2
0
1
1
0
1
0
1
2
0
0
0
1
1
0
0
2
2
0
0
2
1
0
0
0
0
0
0
1
1
0
1
2
2
0
1
1
0
1
3
0
2
3
0
2
0
0
0
0
2
1
0
1
0
0
1
0
1
0
0
0
2
2
2
1
0
2
0
2
0
0
2
0
0
1
1
0
2
1
0
2
1
0
2
1
1
0
2
1
0
2
0
0
0
1
1
1
1
0
1
0
0
0
3
1
2
0
0
0
2
1
0
0
1
0
1
2
2
1
0
0
0
1
1
1
1
1
0
0
0
1
1
1
2
0
0
1
2
1
2
2
0
2
0
1
2
0
2
0
0
0
0
2
3
0
0
0
1
0
1
1
0
0
0
2
1
1
0
0
0
0
0
0
1
1
0
0
0
0
2
2
2
0
2
0
2
2
0
1
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
2
2
0
0
0
1
0
0
1
1
0
2
2
0
0
1
1
0
1
2
1
0
0
3
0
0
0
1
2
2
1
0
0
2
1
1
1
1
0
0
0
0
1
1
1
1
0
1
0
1
1
0
0
0
2
1
1
0
0
2
0
1
0
0
0
1
2
0
0
2
0
1
2
1
0
1
0
0
2
0
0
1
1
1
1
2
0
1
0
2
0
1
2
1
0
0
0
0
2
0
0
1
1
0
0
0
2
0
0
1
0
2
2
1
2
0
2
2
1
0
2
1
2
0
2
1
0
0
1
1
1
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
2
2
1
0
2
2
0
2
0
2
2
0
0
2
0
1
0
0
1
1
1
1
1
0
2
2
2
0
0
0
2
0
0
2
0
0
1
0
0
2
2
0
0
0
2
0
1
0
0
2
1
0
1
1
1
2
1
0
0
0
2
1
1
0
3
1
0
2
1
1
0
0
0
1
0
0
4
2
1
2
0
0
0
1
0
0
2
0
0
2
2
0
0
2
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
3
0
1
0
1
0
1
1
0
1
0
0
0
0
1
1
0
1
1
1
1
1
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
1
1
1
0
0
2
2
2
0
0
2
0
1
1
1
0
2
1
0
0
0
0
0
1
2
0
2
1
0
1
0
0
0
1
1
2
1
1
0
0
1
1
1
0
0
2
1
0
2
0
0
1
1
0
0
0
0
1
0
1
0
0
1
1
0
0
1
0
0
0
2
0
1
0
2
0
0
0
0
0
2
0
0
2
1
0
0
1
0
1
1
0
0
0
1
2
2
0
0
2
0
0
1
0
0
1
0
0
0
2
1
1
0
0
1
1
1
2
2
1
2
0
0
2
0
1
0
1
0
0
2
0
1
0
1
3
0
0
0
0
0
2
0
1
2
0
0
1
1
1
2
0
1
0
0
0
1
2
0
0
2
2
1
0
1
1
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
2
1
0
1
1
0
0
1
0
1
0
0
2
2
0
0
0
0
0
0
0
0
1
1
0
1
0
1
1
2
0
2
0
1
1
1
1
2
0
2
0
1
1
0
2
0
2
0
0
2
1
3
0
2
0
1
2
2
1
1
1
2
0
0
2
1
0
0
2
5
1
1
0
0
0
1
0
0
1
1
0
0
0
1
0
0
1
0
5
0
1
2
0
0
1
1
3
1
0
1
0
1
0
0
0
0
0
1
0
1
0
0
2
1
1
0
0
0
2
0
1
1
0
3
1
2
1
2
2
0
0
0
0
1
2
2
1
0
0
1
1
2
0
1
2
0
3
1
2
0
0
0
2
0
0
0
0
0
1
2
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
2
0
0
0
0
0
2
1
0
1
2
0
1
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
1
0
1
0
0
2
0
3
2
0
2
1
1
0
0
1
0
0
2
0
1
1
1
0
1
1
0
0
1
1
0
0
0
2
0
0
0
0
0
2
0
2
2
0
0
0
1
1
1
2
0
4
0
0
2
0
0
0
0
0
1
2
0
2
0
0
0
0
2
0
0
1
0
0
0
1
3
0
1
1
0
0
0
2
1
2
0
0
0
0
1
0
0
0
0
2
0
2
2
1
0
0
0
0
0
0
0
1
0
0
0
0
2
1
2
1
2
2
0
1
2
2
0
0
0
0
0
0
1
1
1
1
1
0
0
0
0
1
1
0
0
1
1
2
2
1
0
0
0
1
0
2
2
0
1
1
0
2
0
0
1
0
2
0
0
2
0
2
1
0
1
0
1
1
2
0
2
0
1
2
1
0
0
1
1
0
0
0
0
1
1
0
1
1
1
1
0
1
2
0
2
1
0
0
0
2
2
0
1
0
0
1
0
0
0
0
0
0
0
1
0
2
0
1
2
2
0
0
1
1
1
0
1
1
0
0
2
0
0
0
1
1
0
3
1
3
0
1
1
0
0
1
0
1
0
0
1
2
0
1
2
0
0
0
1
0
1
0
2
1
0
0
1
1
0
0
1
2
0
0
0
2
0
0
1
0
0
0
0
0
2
0
2
0
4
2
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
1
1
0
1
1
0
0
1
0
0
0
0
1
0
0
2
0
2
0
0
0
1
0
0
1
0
0
1
1
0
0
1
2
0
0
0
0
2
0
2
1
1
0
1
1
0
0
0
1
2
1
2
0
1
2
0
0
1
0
0
0
0
0
2
0
3
0
1
0
0
4
0
2
1
1
0
0
0
0
2
2
0
1
0
2
0
0
0
1
0
2
1
0
0
0
0
1
0
0
1
0
1
1
2
0
1
1
0
0
2
0
1
0
0
1
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
1
0
1
0
1
2
0
2
0
1
2
0
0
0
2
2
1
0
2
1
1
0
2
1
2
0
0
1
2
0
1
0
2
0
1
2
0
2
0
0
0
0
2
0
0
0
0
0
1
0
1
0
1
0
0
1
0
1
0
2
0
1
0
0
2
1
1
0
2
0
0
1
2
2
2
0
1
0
2
1
1
0
0
2
0
0
2
1
0
0
0
1
0
0
0
0
2
2
2
1
1
0
0
0
2
0
1
0
0
2
1
1
0
0
1
0
1
1
1
0
2
1
0
0
0
0
2
0
0
2
0
0
2
2
0
0
0
0
0
0
2
0
0
3
0
1
0
2
3
0
0
0
1
1
0
2
0
2
0
0
2
0
0
1
1
0
0
2
2
1
1
0
0
0
0
1
0
0
0
0
3
0
2
2
2
1
1
0
1
1
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
1
2
2
0
0
3
1
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
2
0
1
2
0
0
0
1
1
1
1
1
0
2
2
3
0
1
1
1
1
1
0
0
2
2
0
1
0
0
0
0
1
1
0
1
2
1
1
0
0
1
1
0
0
2
0
1
1
0
1
2
1
1
2
0
1
0
0
1
2
0
0
0
0
3
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
1
0
0
0
1
0
4
2
1
0
0
0
0
1
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
1
2
0
0
0
4
1
2
2
0
0
1
1
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
1
1
0
2
2
2
4
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
2
0
2
0
3
1
0
1
1
0
1
0
2
2
0
1
1
0
0
2
2
1
0
1
0
0
2
0
0
1
1
0
0
0
0
1
1
2
0
2
1
0
2
1
0
0
1
0
2
1
0
1
0
1
0
1
1
0
2
0
2
1
2
0
0
1
1
1
0
0
0
0
0
0
2
0
0
1
0
1
2
0
2
0
1
0
2
1
1
1
0
1
0
0
2
0
1
1
1
2
1
2
0
0
0
0
0
0
2
1
1
1
0
3
1
1
0
0
2
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
2
1
0
0
1
0
2
1
1
0
1
1
0
0
1
0
0
2
0
2
1
0
3
0
0
0
1
2
0
1
0
2
0
1
0
0
0
0
1
0
0
1
0
0
2
1
2
0
1
0
0
0
0
0
0
1
4
1
0
1
0
2
0
0
0
0
1
0
0
0
2
1
1
0
0
0
2
0
0
0
1
0
0
1
0
1
0
0
0
2
2
0
2
1
0
0
1
1
1
0
2
0
1
1
0
0
1
0
2
0
0
1
0
2
0
0
2
0
0
0
1
1
0
2
0
2
1
0
0
1
0
0
1
0
1
1
1
0
5
1
1
0
2
1
2
2
0
1
1
4
0
1
2
2
1
0
0
0
0
0
0
2
0
0
1
1
0
0
2
0
0
3
1
0
0
0
0
2
1
2
2
1
1
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
2
0
0
1
1
1
2
1
2
0
1
1
2
0
2
1
1
0
0
0
0
0
1
0
1
3
2
1
0
0
1
1
0
0
3
2
0
0
0
2
3
0
1
3
2
0
2
2
1
0
0
0
1
0
1
0
0
2
0
0
2
2
0
2
1
0
2
0
0
2
2
2
0
1
1
0
0
0
0
0
0
0
1
1
1
4
0
1
1
2
2
1
1
0
1
1
0
1
2
0
0
0
2
0
1
0
3
1
0
1
1
0
1
0
2
4
0
0
0
0
0
0
1
1
2
1
1
2
1
2
1
2
1
0
2
1
0
0
1
0
1
2
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
1
0
1
0
1
1
2
2
0
0
0
1
0
1
2
1
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
1
0
0
0
1
2
1
2
0
0
0
0
0
2
0
0
0
2
0
1
0
1
0
1
2
0
1
0
2
1
1
2
0
1
0
2
1
0
0
0
2
1
1
0
0
0
2
2
0
0
2
0
0
2
2
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
2
0
2
0
2
2
2
0
0
2
1
0
2
2
2
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
2
1
1
0
1
1
2
2
1
2
2
1
2
1
0
2
0
2
0
0
0
1
3
0
0
3
0
0
0
0
2
2
1
0
0
1
0
1
2
0
1
0
1
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
1
1
0
1
0
1
0
0
0
1
1
1
1
3
1
1
2
0
0
0
2
1
1
1
0
1
0
0
2
1
2
2
2
0
1
1
0
0
0
1
0
1
1
2
1
1
0
0
0
0
2
1
0
3
1
0
1
0
0
2
0
0
0
1
2
0
1
1
0
0
0
2
0
0
0
0
1
2
2
2
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
2
0
1
0
0
1
0
0
0
1
2
1
2
0
1
1
0
0
0
2
0
0
0
0
0
0
1
0
2
1
0
0
2
2
1
0
1
0
0
1
1
0
2
0
0
0
0
1
0
0
2
0
1
0
2
0
1
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
2
0
0
2
1
1
0
2
1
0
0
0
1
3
0
1
0
0
0
0
0
0
2
0
1
1
1
0
2
2
0
0
1
0
0
0
0
2
1
0
1
0
0
2
0
0
1
1
0
1
1
6
1
1
0
0
1
0
0
0
1
1
1
0
1
1
1
0
1
0
1
0
2
2
2
0
1
2
2
0
2
0
0
1
0
0
1
2
0
1
1
3
2
1
2
2
1
2
1
2
0
0
0
0
0
2
0
0
0
0
1
0
0
2
1
2
1
0
0
1
2
3
0
0
2
0
1
1
1
0
0
1
1
0
2
1
3
0
0
1
1
0
4
2
2
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
2
1
2
1
0
0
0
2
2
0
0
2
0
1
0
0
1
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
2
1
0
2
4
0
2
1
2
0
0
0
1
0
0
0
1
2
0
1
0
0
2
1
0
0
1
0
1
0
0
2
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
1
1
1
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
1
0
0
1
0
0
2
2
0
9
1
0
0
1
0
2
0
0
3
1
1
0
0
0
2
1
0
0
0
3
1
2
0
0
0
1
0
1
0
3
2
0
2
0
1
0
0
2
2
2
0
3
0
1
1
1
1
1
0
0
0
0
0
1
2
2
0
1
2
0
0
0
1
1
2
1
0
0
3
0
2
1
0
1
1
1
0
1
1
0
0
1
0
1
2
0
1
1
0
1
1
0
0
1
0
1
2
2
1
1
0
1
0
2
0
2
0
0
2
1
1
2
0
0
1
0
1
0
0
0
1
0
2
1
0
1
0
0
0
0
0
2
1
1
0
0
2
1
0
1
0
2
1
1
0
2
1
0
2
2
0
2
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
2
1
0
1
2
0
1
1
0
1
1
0
1
0
1
0
2
1
2
2
0
0
1
2
1
1
0
0
0
2
2
2
0
0
2
2
2
0
0
0
0
2
0
2
2
0
1
2
0
2
1
2
2
2
0
0
1
0
0
1
0
0
0
0
1
1
0
0
1
0
1
0
2
1
0
1
0
2
0
0
2
2
0
0
2
0
0
1
1
0
0
1
0
0
0
2
0
0
2
2
0
1
0
0
0
1
2
0
0
1
0
2
1
0
1
0
0
2
1
2
1
0
2
0
1
1
0
0
0
2
0
3
2
0
0
0
0
2
0
1
0
1
0
0
1
0
2
2
1
0
1
0
0
1
0
0
0
1
0
1
2
0
0
2
0
0
2
0
2
3
1
0
2
0
1
1
1
2
0
0
1
2
0
1
0
0
0
0
1
1
1
0
0
1
0
2
2
2
0
1
2
2
0
2
2
2
0
1
0
0
1
0
0
1
0
0
2
0
2
0
0
0
0
0
2
1
0
0
1
1
0
0
1
2
0
2
1
0
0
0
0
2
0
0
2
1
0
1
2
0
0
0
1
1
1
0
2
0
2
2
1
2
1
1
0
0
1
0
2
1
1
0
2
1
0
1
1
1
0
0
0
1
0
0
2
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
2
2
2
1
1
1
0
0
0
0
0
1
0
3
1
1
1
0
0
0
0
1
2
0
0
1
1
1
1
1
1
1
0
0
0
1
2
0
0
1
1
2
0
0
0
0
0
0
1
2
0
0
1
0
1
1
0
0
2
0
0
0
0
2
0
2
0
2
2
2
0
1
0
0
1
2
0
0
1
1
1
0
0
0
1
0
0
2
0
2
1
0
0
0
1
2
2
0
0
2
1
0
0
0
0
1
3
2
0
1
0
1
0
1
0
2
4
0
0
1
0
1
1
2
0
1
0
1
2
2
0
1
0
0
1
1
0
0
0
2
1
0
1
1
0
0
1
0
2
3
0
2
1
2
0
0
0
2
0
0
0
2
0
0
0
1
2
0
0
1
1
1
1
1
0
0
0
0
0
0
0
0
0
2
1
0
1
1
2
0
2
0
2
0
3
0
1
0
1
0
0
0
0
0
0
0
2
0
0
1
0
3
2
1
2
0
1
0
0
2
0
1
1
0
2
0
1
0
2
0
2
0
0
0
0
1
1
1
0
2
2
0
0
3
0
0
1
1
0
2
2
0
2
1
0
0
2
0
0
0
2
1
0
1
1
0
0
0
0
0
0
0
2
0
0
1
1
1
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
1
2
0
1
0
0
0
0
0
1
0
0
1
1
0
0
2
0
2
1
0
2
1
0
0
0
0
1
0
1
0
2
1
1
1
0
0
0
0
0
0
0
1
0
1
2
0
0
1
0
2
0
0
2
0
0
7
0
2
0
1
0
0
0
0
1
0
1
1
0
0
0
1
0
0
1
1
1
0
2
1
0
0
0
0
1
3
0
1
2
0
1
2
0
2
0
1
2
0
1
2
0
0
2
0
0
2
0
0
0
1
1
1
0
1
1
3
2
0
1
1
1
0
0
0
1
1
2
0
1
0
1
0
0
1
1
2
2
0
1
0
0
1
2
1
0
1
1
1
0
0
0
0
2
0
0
2
0
4
2
2
2
0
0
1
0
0
0
1
1
1
1
1
1
2
0
0
2
0
0
0
3
1
0
3
0
0
1
0
0
1
1
0
1
2
1
0
1
2
0
1
0
0
0
0
0
1
2
0
0
2
0
1
1
2
1
2
2
2
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
1
2
0
2
0
0
2
2
0
1
0
0
2
4
2
0
2
0
1
0
0
0
0
0
0
0
0
0
1
2
0
1
1
2
3
1
0
2
1
1
0
0
0
0
4
1
1
2
0
1
0
1
0
1
0
1
0
1
2
0
0
1
2
1
0
0
0
1
1
0
1
0
0
0
1
2
1
0
0
1
0
2
1
1
0
3
2
2
0
0
1
2
0
0
1
0
2
1
0
0
2
3
1
0
0
0
2
0
0
0
0
1
1
2
0
0
0
2
1
0
1
1
1
0
0
0
0
2
0
2
0
0
1
2
1
2
0
0
0
2
0
0
2
2
2
1
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
3
0
2
1
0
2
2
1
1
1
2
0
2
0
1
2
0
2
2
0
2
0
0
1
0
0
1
2
1
3
0
5
0
0
0
0
1
0
1
0
1
0
1
0
0
1
0
0
0
1
0
0
1
2
0
1
2
0
1
1
0
1
0
1
0
1
0
1
1
2
1
0
2
1
0
1
1
2
0
2
1
0
0
0
2
2
1
1
0
0
1
0
0
0
2
0
1
0
1
0
0
1
0
0
0
1
2
1
0
0
1
2
0
2
0
0
0
0
0
1
1
2
0
0
3
2
1
0
0
1
0
0
0
0
1
1
2
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
2
0
2
1
0
1
2
1
0
0
0
0
1
2
1
2
0
0
0
2
2
0
0
1
0
0
0
0
1
0
2
0
2
2
0
0
0
0
0
0
2
0
2
0
0
1
0
0
1
0
1
0
0
0
0
1
1
2
2
2
1
0
1
2
2
1
1
2
0
2
0
0
2
0
1
1
2
1
1
0
2
0
0
2
2
0
0
1
2
2
0
0
1
0
0
1
0
0
1
0
0
2
0
1
0
0
2
1
0
0
0
1
0
1
0
1
1
0
0
1
2
0
0
0
2
0
0
2
0
0
0
0
0
1
0
2
0
0
1
0
1
2
2
0
1
2
2
0
0
2
0
1
2
0
0
0
0
1
1
0
2
2
1
0
0
0
1
1
0
0
0
1
0
2
2
0
0
0
0
0
0
1
4
2
0
1
2
2
1
0
1
3
0
0
1
0
0
1
0
0
0
2
0
0
2
2
1
1
0
0
1
7
1
0
0
2
0
0
0
1
1
0
0
0
1
0
0
0
2
1
0
2
0
2
2
1
1
0
0
1
0
0
1
2
2
0
0
2
0
1
0
0
0
0
2
1
0
0
0
0
0
1
1
1
2
0
0
0
0
1
0
0
1
0
1
1
2
0
0
0
1
2
0
0
1
0
2
0
0
0
0
0
2
0
2
1
2
0
2
1
1
1
2
1
1
0
0
0
1
0
0
1
1
0
1
1
2
1
1
1
1
0
0
2
1
0
0
0
2
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
1
1
1
2
1
0
2
0
0
2
0
1
0
0
1
2
1
2
0
0
1
0
0
0
0
1
0
0
0
2
0
2
2
0
0
0
0
2
0
2
1
0
1
2
0
0
1
0
0
2
1
0
0
2
0
0
0
1
0
0
2
0
0
0
1
2
2
1
0
0
1
1
1
0
2
2
1
2
0
1
2
0
0
1
0
1
0
0
2
0
0
1
0
1
1
1
2
1
0
0
1
1
0
0
0
2
0
2
1
1
1
1
2
1
0
0
0
1
0
0
0
0
0
2
0
0
2
2
2
2
1
2
0
0
1
0
0
0
0
2
1
0
0
1
1
1
0
0
2
1
0
0
3
0
2
0
0
0
1
1
0
2
1
0
0
1
1
0
1
0
2
0
0
0
0
0
2
0
0
1
0
2
0
2
1
0
1
0
1
1
1
2
2
0
0
0
1
2
2
1
0
0
2
0
1
1
1
1
2
1
1
0
2
1
0
1
0
0
1
1
0
2
0
0
0
0
0
2
0
2
1
0
0
2
2
1
1
0
1
0
2
2
2
0
0
0
0
0
2
0
1
0
0
0
0
1
0
2
1
0
0
0
2
0
2
0
0
0
1
0
3
1
2
1
2
0
2
1
0
0
2
0
1
2
0
1
0
0
2
0
0
0
0
0
2
0
0
2
1
0
1
0
2
0
1
0
0
0
0
3
1
0
0
0
0
2
1
1
0
1
1
1
1
1
1
2
2
0
1
0
3
0
1
2
1
1
2
0
1
0
2
0
0
1
0
2
0
1
1
2
0
0
0
0
1
2
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
1
0
1
0
1
1
0
1
0
1
2
1
0
2
2
2
2
0
0
0
2
0
1
1
1
1
1
0
2
1
1
1
0
2
2
1
0
1
1
1
1
0
1
1
1
1
1
0
0
2
0
0
0
0
2
1
0
2
0
1
0
0
1
0
2
0
1
3
0
1
1
2
1
0
0
3
0
0
2
0
0
0
2
2
2
0
0
3
0
0
1
1
0
1
0
2
1
4
1
0
0
0
1
0
0
0
1
1
1
1
3
0
0
0
0
0
0
0
2
2
1
1
0
1
2
0
0
1
0
0
0
1
1
1
0
0
0
0
0
1
1
2
0
1
1
0
0
0
0
2
0
1
0
1
0
3
0
0
2
0
0
1
2
0
1
1
1
1
0
0
1
0
1
0
0
0
2
2
3
1
0
2
0
1
0
1
1
0
2
0
0
0
1
1
0
0
1
0
1
0
2
1
1
0
2
2
0
2
0
2
0
1
2
2
0
1
1
0
2
1
0
0
2
0
0
0
0
2
1
0
2
2
0
1
0
1
0
2
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
2
2
0
0
0
0
0
3
0
0
2
2
0
2
2
0
0
2
1
0
2
0
0
0
0
0
0
0
0
1
1
2
0
1
0
0
1
2
2
0
0
1
2
2
2
0
1
1
2
1
1
0
0
1
2
0
1
0
0
2
0
2
0
0
0
0
0
2
1
0
1
1
1
2
1
0
2
2
0
2
0
2
1
1
0
0
2
0
2
0
1
0
0
0
0
2
0
2
0
2
0
0
0
0
1
0
0
0
2
0
0
1
0
2
0
2
0
1
0
0
0
2
0
1
1
0
1
2
2
0
1
0
3
0
1
0
0
2
2
1
1
0
2
1
0
1
1
0
0
1
6
0
0
1
1
0
3
1
0
1
0
2
0
2
2
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
1
0
2
0
1
2
2
3
1
0
0
2
0
0
1
1
0
0
1
1
0
3
0
0
2
0
0
0
1
0
1
1
0
0
0
0
1
0
1
0
1
0
2
0
0
0
0
0
0
1
2
1
0
2
1
0
0
1
2
0
1
2
0
1
0
0
0
0
0
0
1
2
0
0
2
0
1
1
2
1
2
1
0
2
2
6
0
0
0
0
0
0
2
0
2
0
0
0
1
2
0
0
0
1
0
1
0
2
0
1
0
1
0
1
0
2
0
1
1
1
2
0
2
2
1
0
0
0
1
2
0
2
1
0
0
2
0
0
1
0
1
0
2
0
0
1
0
1
0
0
1
1
0
0
1
1
1
0
3
0
0
2
2
1
0
2
1
0
1
1
0
0
1
1
2
1
1
2
0
2
0
0
0
1
1
0
2
0
2
2
1
1
2
1
1
0
2
2
0
0
0
0
0
1
0
0
1
2
1
0
1
0
2
0
1
0
2
1
1
1
1
2
2
0
2
2
0
0
0
1
0
1
0
2
0
0
0
0
1
2
0
1
1
0
2
4
1
0
0
0
0
0
1
3
0
3
0
0
1
0
0
0
0
1
1
1
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
2
0
2
2
1
1
1
0
1
1
1
0
1
0
0
0
1
0
0
0
0
2
0
0
2
2
0
0
0
0
0
2
1
2
0
2
2
1
0
1
0
2
0
0
0
0
0
0
0
1
0
2
0
0
2
1
1
0
0
0
1
1
0
0
0
2
0
2
0
0
3
0
2
1
0
3
0
1
2
1
2
0
0
1
3
2
1
0
0
1
1
0
1
0
1
0
0
1
1
0
1
1
2
0
1
2
2
0
0
2
0
0
1
0
0
0
2
2
0
1
0
0
0
0
2
2
0
2
0
0
2
0
1
0
1
1
0
0
0
0
0
2
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
1
0
0
2
3
1
0
0
0
2
1
1
0
1
2
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
2
2
0
1
1
0
1
1
0
1
2
1
1
2
2
0
2
1
0
3
1
0
1
1
0
0
0
1
1
0
0
0
0
0
1
0
1
0
1
2
0
0
2
2
1
2
0
0
0
1
0
1
2
0
1
0
1
2
2
1
1
0
0
0
0
1
0
2
0
1
0
1
2
2
1
0
0
0
2
0
0
1
0
0
1
0
1
1
2
0
0
0
0
1
1
2
1
2
1
0
0
0
0
0
0
2
1
0
0
0
0
0
3
3
3
0
1
2
1
0
1
1
2
0
0
2
1
1
2
2
0
0
3
1
0
0
0
1
0
2
0
0
0
1
0
0
1
0
1
0
0
1
2
1
0
0
3
1
0
0
0
1
2
1
1
1
0
0
2
0
0
2
1
0
2
1
6
1
0
1
0
2
0
2
0
1
2
1
2
1
0
3
0
0
0
1
0
1
0
0
1
0
0
0
0
2
0
2
1
1
0
0
0
1
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
2
1
0
2
1
2
2
2
0
0
0
0
1
2
0
0
2
0
1
0
1
1
1
0
1
0
1
0
0
1
2
0
0
1
1
1
0
1
0
1
0
0
1
0
0
1
0
0
2
1
0
0
1
2
0
0
1
1
2
2
0
0
1
2
1
0
1
0
1
0
2
2
2
1
2
1
1
0
0
1
0
2
0
1
0
0
3
0
1
0
0
1
0
1
0
0
2
0
1
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
2
2
0
0
0
0
2
1
0
4
0
2
1
2
1
2
2
2
1
2
0
2
0
1
0
0
0
0
0
2
0
1
0
1
0
0
1
2
1
0
1
1
1
2
2
2
1
2
1
0
0
1
2
0
1
2
0
1
0
1
0
0
0
2
1
1
2
2
0
2
2
0
2
0
0
2
1
0
0
2
0
1
2
0
0
0
1
2
0
0
0
0
2
0
0
1
1
0
0
0
1
0
1
0
1
2
0
2
0
2
0
0
0
2
0
0
1
0
2
0
0
1
0
2
0
0
0
2
2
0
1
0
0
1
0
0
0
1
2
1
0
1
1
0
3
2
3
0
1
0
0
2
1
2
2
0
2
1
1
0
2
1
0
1
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
1
6
1
1
2
2
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
1
2
1
0
0
1
2
0
1
1
1
0
0
1
2
0
1
0
2
1
1
0
0
1
0
0
3
2
2
1
0
1
2
0
1
0
2
0
2
2
2
1
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
1
0
2
1
0
0
1
0
1
1
2
0
0
0
2
0
1
1
0
1
0
2
2
2
0
0
2
0
0
0
2
1
0
2
1
2
1
0
0
1
0
0
1
0
2
0
0
1
0
0
2
1
2
1
1
0
0
2
0
1
1
1
0
0
2
0
1
1
1
2
0
1
2
1
0
0
0
1
2
2
0
2
0
0
0
1
0
1
0
2
1
2
2
1
2
2
0
0
0
2
2
2
2
1
0
0
0
0
0
1
0
2
1
0
2
0
2
2
0
1
0
1
1
0
0
2
1
2
0
0
2
0
0
0
2
0
0
1
0
1
1
1
0
0
1
0
0
0
0
1
0
1
0
2
1
1
0
3
3
1
2
0
0
1
0
0
1
1
0
1
0
1
0
0
0
0
0
0
3
0
0
2
5
1
0
0
2
0
2
1
0
1
1
0
1
0
1
1
0
0
1
0
1
0
0
1
1
1
0
3
2
2
1
0
2
2
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
2
1
0
0
0
0
2
0
2
1
1
0
0
0
0
0
0
1
0
1
2
2
0
2
3
2
1
1
1
1
2
1
1
8
3
0
2
2
0
1
1
2
0
0
0
4
0
0
0
0
0
1
3
2
1
2
1
1
2
1
3
1
0
0
1
2
0
1
1
0
0
0
2
1
0
2
2
0
0
2
0
1
0
0
2
2
2
0
1
0
1
1
0
2
0
0
0
0
0
2
4
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
1
3
0
0
0
0
1
0
1
0
1
1
1
0
1
0
4
0
1
2
0
0
0
0
1
2
2
0
2
0
1
2
1
0
0
2
0
2
0
1
1
1
1
0
0
0
1
3
0
1
0
1
0
2
2
0
1
1
0
0
2
1
2
2
0
0
1
1
0
1
1
0
0
1
2
0
2
0
0
0
0
1
0
1
0
0
2
0
1
1
1
1
0
0
0
1
1
0
0
1
3
1
0
1
0
2
1
1
0
2
0
0
2
1
0
0
0
0
1
3
0
2
0
2
0
1
0
0
0
0
0
2
1
0
1
1
0
1
0
0
1
1
0
2
1
0
1
1
0
1
0
0
2
1
0
0
0
0
0
2
2
1
0
0
0
1
0
0
2
2
1
0
2
2
0
3
2
0
1
0
1
0
0
0
0
2
0
0
2
1
1
0
0
0
1
0
1
2
0
1
2
0
2
0
1
0
2
0
0
1
0
0
0
0
2
0
0
2
1
0
1
1
0
2
1
0
2
0
1
2
1
1
0
1
0
0
0
1
0
2
1
0
0
1
2
0
1
0
2
0
0
0
2
0
1
0
0
2
1
1
0
1
1
2
2
0
0
1
1
0
0
0
0
0
1
0
0
0
2
0
2
1
2
0
2
0
1
0
0
0
1
0
1
1
1
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
3
0
0
0
0
3
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
2
1
2
1
0
2
2
0
0
2
0
2
0
0
0
0
0
2
2
2
0
0
0
0
2
1
3
0
0
1
0
0
2
1
2
2
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
1
1
0
0
1
1
0
0
0
0
2
0
0
0
1
0
1
0
2
1
1
2
2
1
0
2
0
1
0
0
0
0
1
0
2
1
0
2
2
1
0
1
0
1
0
1
1
0
0
2
1
0
0
0
0
0
1
0
1
0
1
0
2
2
0
0
0
1
0
0
2
1
0
2
1
0
1
3
0
0
3
0
0
0
0
2
1
2
0
0
1
0
1
0
0
2
0
1
0
2
0
1
0
0
0
1
0
1
0
0
4
0
0
0
0
2
0
2
2
0
0
0
1
2
2
0
0
1
4
2
0
1
0
0
0
1
1
0
0
1
0
0
0
2
2
1
1
0
0
2
1
1
0
0
0
0
0
0
1
1
0
1
0
2
0
1
0
1
1
2
1
1
2
0
0
0
3
0
2
1
1
0
2
0
0
0
2
1
2
0
1
1
1
0
0
0
0
2
2
2
1
0
1
2
0
2
1
2
1
2
1
1
0
1
0
1
0
0
1
2
2
0
0
1
2
1
1
1
2
1
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
2
2
0
1
1
2
0
0
2
1
1
1
1
0
0
0
0
1
2
0
1
0
1
0
1
0
1
2
0
0
1
2
0
1
1
0
1
1
0
0
1
0
1
1
2
3
0
0
1
1
0
0
1
2
0
0
3
2
1
0
0
1
1
3
0
0
0
2
0
0
1
1
2
1
0
0
1
0
3
0
0
0
0
0
1
1
0
0
0
2
2
0
1
2
0
0
0
0
0
0
3
0
0
0
2
1
1
2
0
0
0
2
0
0
0
0
0
0
4
0
0
0
1
0
0
1
1
1
3
0
4
2
0
0
0
0
2
1
0
4
0
0
0
0
1
0
0
0
1
0
2
2
2
2
1
0
0
1
2
1
1
0
0
0
0
2
1
2
2
0
1
0
0
0
0
2
0
0
0
0
1
1
0
1
1
0
1
0
1
1
1
0
0
1
0
0
0
1
0
2
2
0
0
0
0
1
0
2
1
0
2
1
2
0
1
1
1
2
0
1
1
0
2
1
0
0
0
0
1
1
2
2
1
0
2
0
1
1
2
0
2
2
2
2
0
1
0
0
0
2
0
1
0
0
1
2
2
0
2
2
0
0
0
0
1
1
2
0
0
1
1
1
0
1
1
0
2
0
2
1
1
0
0
1
1
0
2
0
0
2
3
0
0
1
0
0
0
0
1
2
0
0
0
1
0
0
0
0
1
1
0
0
2
1
1
0
2
2
0
1
2
1
1
2
0
0
0
0
1
2
0
1
1
2
1
1
0
0
1
0
0
1
0
1
1
0
1
0
0
0
2
2
0
1
1
4
2
0
1
1
1
0
0
0
1
1
1
0
0
0
1
1
0
0
1
0
0
1
2
0
2
0
0
1
1
0
1
0
2
0
3
2
0
1
0
1
0
1
0
1
0
2
2
2
0
1
0
0
0
0
0
0
1
0
2
1
2
0
2
3
1
0
0
2
0
0
1
1
2
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
1
2
0
0
2
1
0
2
0
2
0
1
0
1
2
1
2
0
0
2
0
2
0
0
0
1
0
0
0
0
0
1
1
0
1
1
0
1
3
0
0
0
0
2
1
0
0
1
4
0
1
2
0
2
0
0
0
1
1
2
0
1
0
1
0
0
2
0
1
0
1
0
0
1
0
0
1
1
0
1
1
0
0
0
2
1
0
1
0
1
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
1
1
2
1
0
1
0
0
1
1
1
2
0
1
2
0
0
0
3
2
0
0
2
1
2
1
1
0
0
0
1
0
0
0
2
1
1
0
0
2
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
1
1
0
3
0
2
1
0
0
0
1
0
0
1
1
1
0
0
0
2
2
0
0
1
1
0
0
0
1
0
0
0
0
2
1
1
1
1
0
1
1
0
1
2
1
0
0
2
0
1
0
1
0
0
0
0
2
1
2
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
3
0
1
0
0
0
2
0
0
2
0
0
2
2
2
1
0
0
2
1
2
0
0
1
0
0
0
0
0
2
0
0
2
1
2
2
0
2
2
1
0
0
0
0
1
0
0
1
1
0
1
0
0
0
1
0
2
1
2
1
1
0
1
0
2
1
2
0
2
0
2
2
1
1
0
0
0
2
0
0
0
0
0
1
0
0
0
2
1
0
0
0
2
1
0
0
1
2
0
1
0
0
1
0
0
2
1
2
2
0
0
1
0
0
0
0
1
0
0
2
1
1
1
2
0
0
0
2
0
0
1
0
0
0
0
2
1
1
0
1
0
1
0
1
0
2
1
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
2
1
0
0
0
0
0
0
1
0
0
0
2
1
0
1
0
1
1
1
0
2
0
0
2
0
2
2
1
0
1
1
0
2
0
1
0
2
0
0
0
1
0
2
0
2
0
0
0
1
0
0
0
1
1
0
1
0
2
0
2
0
1
1
2
0
1
1
0
3
1
2
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
2
2
2
0
0
2
1
1
0
0
0
1
2
0
2
1
1
1
1
1
1
0
0
1
1
0
1
1
2
2
2
0
0
1
1
2
0
1
2
1
3
0
0
0
1
0
0
0
2
0
1
1
0
2
0
1
0
0
1
0
1
0
0
0
0
2
1
3
2
2
1
0
0
0
0
2
2
0
0
1
1
2
0
0
0
2
0
0
0
0
0
1
0
1
0
0
1
0
0
2
0
1
1
1
0
1
3
1
0
3
0
0
3
0
0
0
0
1
7
2
1
2
3
3
0
0
0
0
2
0
0
1
1
0
2
0
0
0
1
3
1
0
0
2
1
1
1
3
1
0
1
1
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
1
2
0
0
0
0
1
0
1
0
2
0
1
0
2
1
0
1
0
2
0
2
0
0
0
1
0
0
0
3
0
0
0
1
0
0
2
0
0
0
1
2
1
1
0
0
0
0
2
1
2
0
0
0
0
0
2
1
0
0
1
0
1
2
0
0
1
1
0
1
0
0
0
1
0
0
1
2
2
1
0
2
1
0
0
1
0
3
1
1
0
1
2
1
0
2
1
2
2
0
0
0
0
1
0
0
1
0
0
0
0
1
2
0
2
2
1
2
0
0
0
2
1
0
1
0
0
2
3
0
0
0
0
1
0
0
2
2
1
0
2
2
0
1
0
1
2
1
1
0
2
1
0
0
2
2
1
0
0
0
0
0
0
2
1
0
0
2
0
1
1
1
1
1
0
0
2
1
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
3
0
3
0
2
2
0
1
2
2
0
0
3
1
1
2
1
1
1
1
2
0
1
1
0
1
2
0
0
1
0
2
1
0
0
1
2
1
2
1
0
0
2
0
1
1
2
0
1
1
1
0
0
0
1
1
0
0
0
1
2
2
2
0
2
0
2
0
0
2
0
0
1
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
1
1
1
0
1
1
0
1
0
0
1
0
0
0
1
0
1
0
1
2
1
0
1
1
0
0
0
2
0
0
1
0
0
1
2
0
0
2
0
1
1
0
1
1
0
0
2
2
1
0
3
0
1
0
0
4
1
1
0
0
2
0
0
0
1
0
0
1
1
0
1
1
1
2
0
0
1
1
0
0
0
0
1
1
1
2
0
1
0
0
0
1
0
0
0
1
2
0
0
0
2
0
0
1
0
0
2
1
0
0
2
1
1
0
0
0
0
2
0
1
1
1
2
0
0
3
1
0
0
0
0
1
3
2
2
0
2
0
0
0
1
2
0
0
2
1
2
1
0
0
0
0
0
1
1
1
0
0
0
0
1
0
1
2
1
2
0
1
1
2
0
1
1
2
0
0
1
0
1
0
1
1
0
2
0
2
2
0
2
1
2
1
0
2
0
2
1
1
1
0
1
1
0
2
0
0
1
1
0
2
1
2
2
0
0
2
0
0
0
1
0
0
0
3
0
0
2
0
0
2
0
0
0
3
2
0
0
2
0
0
2
3
1
1
2
1
0
0
0
1
2
0
1
0
0
0
1
0
0
1
0
1
0
1
1
1
1
1
1
1
0
1
0
0
2
0
0
0
0
0
2
2
0
2
0
0
2
2
0
0
0
0
2
0
0
0
0
0
2
2
0
2
2
0
2
0
1
2
2
2
0
0
0
0
1
0
0
0
0
1
2
0
0
1
0
2
0
0
0
1
1
0
1
1
0
0
0
2
0
0
0
0
0
2
2
1
0
0
2
1
0
1
1
1
2
0
1
1
0
2
0
1
1
0
0
0
1
1
0
1
0
1
0
0
2
0
0
1
1
0
1
2
0
0
0
2
2
0
2
4
1
1
0
1
2
2
0
1
2
1
2
2
1
0
2
1
0
0
0
0
2
1
2
0
0
0
1
0
1
2
2
0
3
1
0
0
0
2
3
0
2
0
0
0
0
0
0
0
0
1
0
0
1
1
1
1
1
1
0
2
0
0
0
1
3
2
1
0
0
1
0
0
0
1
2
1
2
1
0
1
1
0
1
2
2
1
1
1
1
0
0
1
2
1
0
0
0
0
0
0
1
0
1
1
1
1
1
0
1
0
0
2
0
2
2
2
2
0
0
0
1
1
0
1
0
1
1
1
2
1
1
1
2
0
0
1
1
0
0
2
0
2
0
0
0
0
1
1
1
0
0
0
3
2
0
2
1
0
0
0
2
2
0
2
0
1
0
0
0
1
2
1
0
0
2
0
0
0
2
1
2
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
1
1
1
1
0
1
0
1
2
0
0
0
0
0
0
2
0
0
1
0
1
2
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
3
1
2
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
1
1
1
0
2
1
0
0
0
0
0
0
0
0
1
2
2
0
2
2
2
1
0
0
0
1
0
0
3
2
0
2
0
1
1
0
0
0
1
0
0
0
0
0
0
1
1
0
2
2
1
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
1
3
0
2
1
0
1
3
0
0
0
0
0
2
0
0
2
0
1
0
0
1
0
0
0
0
3
0
1
0
0
0
0
1
0
0
1
0
0
1
2
1
1
0
0
0
0
0
0
0
0
1
1
0
1
2
0
0
1
1
0
0
0
2
0
1
0
1
0
2
0
0
2
0
0
2
0
1
2
1
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
1
0
0
2
2
1
0
1
0
0
1
1
0
0
0
0
0
1
2
2
1
0
2
2
0
0
0
1
0
1
1
2
1
2
3
1
0
2
1
10
0
0
0
0
1
1
1
1
0
3
0
1
0
0
1
1
2
1
3
0
2
0
0
0
0
0
0
0
1
0
0
0
2
2
1
2
2
0
0
1
2
0
0
1
2
0
1
2
1
0
0
2
0
1
1
0
0
0
1
0
2
0
2
1
4
2
1
1
1
1
1
1
0
0
0
0
2
0
0
0
1
2
2
0
0
0
0
0
0
2
0
0
0
1
1
0
0
1
0
2
0
1
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
2
1
2
1
2
0
0
0
0
0
1
1
1
1
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
2
0
3
0
3
2
0
0
0
0
0
0
0
0
1
2
0
0
3
2
0
1
0
4
0
2
0
1
0
1
2
0
0
0
2
0
0
0
0
0
1
0
1
0
0
1
2
0
0
0
3
1
0
0
1
3
0
2
2
0
0
0
2
1
0
0
0
0
0
0
2
1
0
2
0
1
2
1
0
0
0
2
0
0
0
0
1
1
0
2
0
1
0
0
0
0
1
0
2
2
2
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
1
1
0
0
2
0
0
2
0
0
0
1
1
1
3
0
0
0
0
2
1
2
2
0
0
0
0
2
2
0
0
0
1
2
0
1
1
0
0
2
1
0
2
0
1
0
1
0
1
0
0
1
0
2
0
1
0
2
2
1
0
3
0
1
1
2
0
0
1
0
1
1
0
0
0
0
0
1
2
0
0
2
1
1
0
0
1
1
0
1
0
2
0
0
0
1
0
0
2
1
0
0
2
2
1
2
2
2
0
1
0
0
1
1
1
0
0
2
1
1
0
0
1
0
0
0
0
2
2
0
1
2
1
1
2
1
0
0
0
0
0
1
1
0
2
1
2
1
3
0
2
4
3
0
0
2
0
0
0
1
1
1
1
0
1
0
0
1
0
2
0
0
1
0
1
0
1
0
2
1
1
0
0
2
0
2
0
1
4
1
0
0
1
0
0
0
2
1
0
2
0
0
2
2
2
0
0
0
0
1
0
1
1
2
0
1
2
0
1
1
2
0
0
2
1
0
2
0
1
0
1
0
0
0
0
0
1
1
2
1
0
0
0
0
2
4
0
0
0
0
2
1
1
0
0
0
0
1
3
1
0
0
0
0
1
0
0
0
0
1
1
0
2
2
1
0
0
1
0
1
0
1
1
0
0
0
2
0
0
0
1
1
2
0
0
1
1
0
2
0
2
0
1
0
0
0
1
1
0
0
1
2
0
1
1
0
2
2
2
0
0
2
0
1
1
0
0
0
0
1
1
0
2
1
0
1
0
0
0
1
0
0
0
2
1
2
1
0
0
1
1
1
0
2
0
0
2
0
2
0
0
0
1
5
2
0
1
1
2
1
2
0
0
2
0
1
2
0
0
0
1
2
0
0
0
0
0
2
0
0
1
1
1
0
0
0
2
1
0
0
1
0
0
0
0
0
0
3
1
0
2
0
0
1
2
1
0
0
0
0
2
0
0
2
0
1
0
1
0
0
2
1
0
2
1
0
1
1
0
0
1
1
1
1
0
1
0
0
0
0
1
0
2
0
1
1
1
0
2
0
0
1
0
2
0
1
0
2
1
1
0
2
2
1
0
0
0
1
1
0
1
1
0
3
2
0
0
0
0
1
0
0
2
0
2
2
0
0
0
0
3
2
0
0
2
0
0
0
1
1
2
2
1
0
2
0
0
2
1
1
1
0
0
1
2
2
0
1
2
1
0
0
0
0
0
1
1
2
2
1
0
0
0
1
1
0
1
0
1
1
1
0
0
0
0
1
0
0
1
1
0
0
0
0
1
2
1
2
1
0
0
0
1
2
1
2
0
0
2
0
2
1
0
0
2
1
1
0
0
0
1
0
2
1
2
1
2
1
0
2
2
0
0
1
0
0
1
2
2
0
0
1
0
1
1
1
0
2
0
1
0
2
0
0
3
2
0
1
2
0
0
0
0
0
2
1
2
1
1
1
2
0
1
0
0
1
1
1
1
2
0
1
2
0
1
0
0
2
0
1
2
0
1
0
1
1
0
1
1
2
0
1
2
0
0
0
0
0
2
1
0
1
1
1
0
0
2
0
0
1
1
1
0
0
0
0
0
0
0
2
1
1
0
1
1
0
2
1
0
0
1
0
2
1
0
0
0
0
0
0
4
0
1
1
1
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
2
1
2
1
0
2
1
0
2
0
0
0
1
1
1
0
1
0
1
0
1
0
0
1
1
1
2
1
0
0
0
0
1
2
0
0
0
0
1
0
1
0
0
0
0
0
1
1
1
1
2
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
1
1
0
1
0
0
2
0
0
1
0
0
0
1
1
0
0
1
0
0
0
2
0
2
1
0
0
0
1
1
0
2
1
1
2
0
0
0
0
1
1
2
0
0
1
1
0
0
0
0
1
0
1
1
0
2
0
0
0
3
0
0
0
1
0
2
1
2
0
1
2
0
1
0
2
0
2
2
1
2
0
1
0
0
2
1
0
0
1
0
1
2
0
2
2
0
1
3
0
0
1
2
1
0
1
2
0
0
1
0
1
1
2
0
0
0
0
1
0
0
0
0
2
1
2
1
0
0
2
0
0
0
1
1
0
0
0
1
0
2
1
0
0
0
2
0
0
0
0
0
1
0
0
2
2
0
1
2
0
0
0
1
0
0
1
1
0
4
0
1
1
1
0
0
2
0
0
0
0
1
1
3
2
0
0
0
1
0
1
2
2
0
0
0
0
2
1
1
1
1
0
1
1
0
1
0
2
0
2
2
0
3
0
2
0
0
1
1
2
1
2
1
0
0
0
1
0
0
0
1
0
1
1
0
0
0
2
0
0
0
0
1
1
0
2
4
2
0
0
1
0
0
1
0
1
0
0
1
2
2
1
0
0
0
1
0
0
0
0
0
1
1
2
2
1
1
3
0
0
0
2
2
2
0
0
0
2
0
0
0
2
2
0
1
2
0
0
4
2
0
1
0
0
2
1
1
0
0
0
0
0
2
1
1
0
1
1
2
0
2
1
1
0
0
0
0
2
0
1
1
0
0
0
1
0
0
2
1
0
2
0
0
0
0
2
0
0
1
1
0
2
0
2
6
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
2
0
0
1
2
0
2
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
3
0
1
1
0
2
0
2
0
0
2
1
0
3
0
0
0
2
0
0
0
1
0
2
1
1
0
0
1
1
0
0
0
1
1
2
1
1
2
0
1
0
1
1
1
3
0
0
1
2
1
1
0
0
2
0
2
0
2
1
0
2
0
1
0
0
0
1
1
0
2
1
1
1
2
1
2
1
0
0
1
3
1
0
0
0
0
1
1
1
1
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
1
3
0
0
1
0
1
1
0
1
1
0
1
0
0
0
0
0
0
2
2
1
0
0
1
0
0
1
0
0
2
0
0
0
2
1
0
0
1
0
0
1
0
1
0
1
1
0
0
0
1
0
0
0
2
0
0
0
0
0
2
1
2
1
1
2
0
4
1
0
0
0
0
0
2
0
2
1
2
0
0
0
0
2
0
0
1
1
1
1
0
0
2
1
0
0
3
2
1
0
0
0
0
0
0
0
1
0
0
1
0
0
2
1
1
0
0
1
1
2
1
1
2
2
1
0
0
2
1
1
2
0
0
1
1
0
0
0
2
0
0
0
1
2
0
2
0
0
2
1
2
2
0
1
1
0
2
0
2
1
0
1
1
1
2
0
0
1
1
1
0
0
0
1
2
1
0
0
0
2
1
1
0
3
0
0
0
0
2
0
0
0
0
0
1
2
2
1
1
0
0
2
0
1
2
1
0
0
0
1
1
0
2
0
2
0
0
0
1
0
1
1
2
0
1
1
1
2
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
3
0
1
1
0
2
0
2
0
0
1
1
2
0
0
0
1
0
0
1
0
0
1
1
0
2
0
0
2
0
2
0
0
0
0
2
2
0
0
0
0
0
1
1
0
0
1
1
1
0
0
1
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
1
2
1
0
3
1
1
2
0
0
1
6
0
0
0
0
1
2
1
2
0
1
0
2
1
0
0
0
0
1
0
1
0
0
2
1
2
0
0
1
0
1
2
1
0
1
5
0
0
0
1
0
3
2
0
0
1
1
1
2
1
1
0
2
3
0
0
1
1
2
0
0
0
1
0
0
0
1
0
1
0
1
0
2
0
0
2
1
1
2
1
0
0
0
1
0
0
1
2
0
2
0
1
0
0
1
0
1
0
1
2
0
0
0
0
0
1
0
2
1
0
2
2
0
0
1
0
2
2
1
2
1
2
0
0
0
2
1
1
1
2
0
1
1
2
0
0
0
2
0
0
2
1
0
2
0
1
1
1
0
5
1
0
0
0
1
0
0
0
1
1
1
1
0
0
1
0
0
1
1
0
2
0
4
1
1
0
0
0
2
0
4
0
0
2
0
0
2
3
1
1
0
0
0
1
1
2
1
0
0
0
0
2
1
0
0
1
0
0
1
0
1
0
0
1
0
1
0
0
1
0
0
0
1
0
0
2
0
0
2
0
1
1
0
3
0
0
0
0
0
1
0
0
1
0
0
2
3
0
0
0
1
1
0
2
0
0
1
0
2
0
2
1
1
2
0
1
0
1
0
0
1
0
0
0
2
0
1
0
0
0
1
0
0
2
2
2
1
2
1
0
0
1
2
0
0
2
0
0
1
0
0
2
1
1
1
0
0
0
2
2
0
2
0
2
3
2
0
1
0
0
0
1
0
2
1
2
0
0
0
0
1
0
0
2
1
0
2
0
0
1
0
0
0
0
1
0
0
1
1
0
1
0
1
2
1
0
0
2
1
0
1
0
2
0
0
1
1
0
1
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
2
1
0
2
1
0
1
2
0
2
0
0
0
2
0
2
2
1
0
0
0
0
1
1
0
0
1
2
1
1
0
0
0
0
0
1
2
0
2
2
2
0
0
0
2
2
2
1
1
0
0
0
0
0
2
2
2
0
1
0
1
0
2
1
1
0
0
0
0
4
0
2
2
2
1
0
0
0
0
0
0
1
1
2
2
1
2
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
1
0
2
0
0
0
2
1
0
0
2
1
0
0
1
2
0
0
2
2
0
1
1
1
0
1
0
1
2
0
2
0
2
1
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
2
2
1
2
1
0
0
1
2
0
0
1
1
0
0
2
2
0
1
0
2
0
0
1
1
0
0
0
0
0
1
0
0
1
2
2
0
0
0
0
2
0
0
2
0
2
0
0
0
0
1
0
1
0
0
0
3
0
1
0
1
0
0
1
3
0
1
0
0
0
1
0
0
1
1
2
2
0
0
3
1
2
0
0
2
0
0
1
0
0
1
1
1
2
1
0
2
1
1
2
4
2
0
0
1
1
0
0
0
0
0
1
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
1
2
0
2
0
2
2
2
2
0
0
3
2
4
1
1
0
1
0
0
0
1
0
1
0
2
2
0
1
1
1
1
1
0
0
0
1
0
1
1
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
2
1
0
2
0
0
0
0
1
0
2
0
0
2
1
0
0
0
0
0
0
2
1
1
0
2
2
1
1
1
1
0
0
1
0
0
0
1
2
1
1
0
3
5
1
2
0
1
1
0
0
1
0
5
0
1
0
3
2
0
1
0
0
1
2
0
0
0
0
0
2
0
0
0
0
2
0
1
2
0
1
0
0
2
1
0
0
1
1
0
0
2
2
0
2
0
0
0
0
1
0
1
3
0
2
0
0
1
1
0
0
0
2
0
1
1
0
0
1
0
0
0
1
1
0
2
2
1
1
0
1
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
1
0
0
1
0
0
2
0
2
2
2
0
0
0
0
1
0
2
2
2
0
0
1
0
2
2
0
2
0
1
1
0
0
0
0
1
0
1
1
0
0
0
0
2
1
1
2
1
1
1
2
0
0
1
1
2
1
0
0
1
2
2
0
2
0
2
2
2
0
2
2
0
0
1
1
0
0
2
1
0
1
1
2
1
0
0
2
0
0
1
1
0
0
2
1
0
0
2
0
0
2
3
2
0
0
0
1
0
0
0
0
0
2
3
2
2
0
1
2
0
1
2
1
0
2
2
0
1
0
0
1
0
0
0
1
0
1
0
1
2
0
0
0
0
2
0
0
0
0
0
0
2
2
1
2
0
2
0
2
0
0
2
1
0
1
0
1
1
0
0
0
4
0
1
1
0
0
0
1
0
0
2
1
1
1
0
0
0
2
2
2
0
0
0
2
2
1
1
1
0
0
0
0
0
0
2
0
0
2
0
2
1
0
2
1
0
0
1
0
2
0
0
0
0
0
1
0
1
1
0
2
1
2
0
2
0
1
2
1
0
2
2
1
0
0
0
1
1
1
0
0
0
1
1
0
2
2
0
2
0
1
1
1
0
2
1
0
0
2
0
0
2
1
0
0
0
2
5
2
0
0
0
1
0
0
0
2
0
0
1
1
1
1
1
0
0
0
2
0
0
4
2
1
2
0
0
2
1
1
0
1
1
1
0
0
1
0
2
2
0
1
2
0
0
1
1
2
1
2
0
0
2
2
0
0
0
2
2
2
0
0
0
0
1
0
0
0
1
2
1
0
1
1
1
0
1
0
2
0
0
2
2
0
2
1
0
2
0
0
0
0
1
0
1
0
0
0
2
0
2
4
1
0
1
0
1
0
0
1
0
0
0
2
1
1
1
0
0
0
1
0
0
3
0
0
1
1
0
0
0
2
0
2
1
2
1
2
2
0
2
0
2
0
2
0
0
0
2
0
1
1
0
2
0
0
0
3
1
2
2
0
0
2
1
2
0
0
0
0
2
1
0
2
0
1
0
2
0
0
1
0
0
0
0
0
0
0
1
1
1
2
2
2
2
0
0
0
0
0
0
0
0
0
1
2
0
1
2
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
1
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
1
0
1
1
0
1
0
3
1
1
2
2
1
2
0
0
0
0
3
2
0
1
0
4
1
1
1
0
1
0
0
1
0
0
2
1
1
1
0
0
2
1
0
0
0
2
0
0
0
4
2
0
2
2
0
0
2
1
2
2
0
1
0
0
0
1
0
0
1
0
2
0
0
0
1
0
1
0
1
0
2
1
0
1
0
0
2
0
0
2
0
0
0
1
2
1
0
2
0
0
0
1
1
1
0
0
1
1
0
0
1
2
0
1
0
1
1
0
1
1
0
0
2
0
1
0
1
2
0
0
2
0
1
1
1
1
0
1
2
1
0
0
3
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
1
0
0
1
1
2
0
1
1
5
2
0
0
2
1
2
1
0
2
2
0
1
0
2
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
2
2
2
0
2
1
0
1
0
0
1
0
0
1
0
0
2
0
0
4
1
0
0
0
1
0
0
0
2
0
1
1
0
1
0
0
2
3
1
0
1
0
2
2
0
1
0
2
2
0
0
0
0
0
0
1
1
2
1
0
1
1
2
1
1
0
0
2
0
2
1
2
0
0
2
0
0
0
2
1
0
2
1
0
2
0
3
0
1
0
2
1
1
0
0
0
0
0
2
0
1
0
1
2
2
1
0
1
0
1
0
3
0
2
0
0
1
2
0
0
2
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
2
0
2
2
1
0
0
0
1
0
0
0
1
2
0
0
0
1
1
0
4
0
2
2
0
0
0
1
1
0
0
1
1
0
0
2
1
0
0
0
1
1
1
0
0
0
1
1
1
0
2
2
0
0
0
1
1
1
0
0
2
3
1
0
2
2
2
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
2
2
0
0
3
0
1
0
0
0
0
1
2
1
0
0
2
0
0
0
0
0
0
1
2
0
2
1
0
2
2
0
0
1
2
1
0
2
0
1
2
2
2
0
1
0
0
0
1
2
2
0
1
0
0
3
1
0
0
0
0
2
1
0
2
0
0
0
2
0
0
2
1
1
0
0
1
0
0
1
1
1
0
0
0
0
0
0
2
1
2
1
1
1
2
0
0
0
1
1
0
1
0
0
0
1
2
0
0
2
0
2
0
0
0
2
0
2
0
0
1
0
2
1
0
2
0
1
0
1
2
0
2
1
0
2
0
2
2
0
0
0
1
0
0
0
1
1
0
0
2
0
2
0
1
0
0
0
2
0
1
0
0
0
3
1
0
2
1
1
0
1
0
1
1
0
0
1
2
1
0
1
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
3
0
0
1
1
0
1
0
1
0
0
2
1
1
0
1
0
2
0
0
1
1
0
1
0
0
0
0
0
1
1
1
1
1
2
0
1
2
0
1
2
0
0
3
1
0
2
2
0
0
2
0
1
1
0
0
2
2
2
2
0
0
0
1
1
0
2
2
1
0
1
0
0
0
0
0
2
2
2
1
0
0
0
1
0
0
0
1
0
1
1
1
0
0
2
0
0
0
2
3
1
2
1
1
1
0
2
1
1
0
1
2
1
0
1
2
2
0
0
2
2
3
0
1
1
0
1
0
1
1
0
0
0
0
0
1
1
1
2
1
2
1
1
0
0
0
0
0
0
2
2
0
0
2
0
2
2
0
0
0
1
1
0
0
0
0
0
1
1
1
2
2
1
2
0
2
1
0
0
1
0
0
2
1
0
0
1
0
1
2
1
2
0
2
0
0
2
2
0
2
1
0
0
0
0
3
0
0
2
1
0
1
1
0
1
0
0
1
1
0
2
1
0
0
0
0
0
0
1
1
0
1
0
0
3
0
1
2
0
0
1
2
0
1
1
2
1
0
1
2
0
0
0
1
0
0
2
1
1
0
0
0
1
1
2
0
0
0
0
1
0
3
1
1
1
0
1
0
2
0
0
2
2
0
1
0
2
0
2
0
1
2
1
0
1
1
0
0
0
0
1
0
1
0
2
0
1
0
0
0
0
2
0
1
2
0
1
0
0
0
1
0
1
0
1
0
0
0
1
1
0
3
0
1
0
0
2
1
0
1
0
0
1
0
2
2
1
0
1
0
0
1
0
2
0
2
0
2
2
1
1
0
2
1
0
2
1
1
0
2
0
1
1
0
0
0
0
1
0
0
0
3
2
2
0
1
0
0
1
0
0
0
0
1
0
1
0
1
1
0
0
1
0
0
1
2
2
0
1
0
1
0
1
1
0
1
1
0
1
1
1
0
2
2
2
0
1
2
2
2
1
1
2
0
2
0
0
2
0
3
0
2
2
2
1
1
1
0
0
0
0
1
0
2
2
0
1
1
2
2
0
0
0
1
0
2
1
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
2
2
0
1
1
1
0
0
2
1
0
0
1
0
1
2
0
0
1
0
0
2
1
0
0
1
0
0
0
0
0
2
0
1
1
0
1
2
0
0
1
0
1
0
2
1
0
0
1
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
2
2
0
0
1
2
0
2
1
0
2
0
1
1
2
0
2
0
1
0
1
0
1
1
0
0
1
0
1
0
0
0
2
0
0
2
1
0
0
0
1
2
0
0
0
0
1
0
2
0
0
1
0
1
0
2
0
1
0
0
2
1
0
1
0
1
0
3
2
2
1
0
0
1
0
1
0
1
1
0
1
2
0
1
2
0
2
1
2
0
1
0
2
1
0
2
0
1
0
0
0
0
2
0
1
0
0
2
3
0
0
0
1
0
0
0
1
0
0
0
2
1
1
0
0
3
0
0
0
0
1
0
2
0
0
1
1
0
1
0
0
0
1
0
0
1
1
1
0
0
0
1
0
1
2
1
0
0
1
0
1
0
0
2
0
0
0
0
1
0
0
1
1
0
1
1
1
1
0
0
0
1
1
1
0
2
1
1
1
1
0
0
1
0
1
0
2
2
1
1
1
1
1
0
0
1
1
2
2
0
1
2
1
1
1
0
0
0
1
1
0
0
1
2
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
3
0
0
1
1
1
0
0
5
0
2
0
1
1
2
1
0
0
0
1
1
2
0
1
2
2
1
2
0
1
1
1
2
0
0
0
0
2
0
0
0
2
2
0
2
0
1
0
2
0
0
0
0
0
2
0
0
1
2
0
2
1
1
4
0
0
0
2
0
1
0
0
1
0
0
2
1
0
0
2
2
0
0
2
1
1
0
2
0
0
1
0
0
0
1
0
1
0
0
1
0
1
0
1
0
0
0
2
0
0
0
1
1
0
1
0
0
1
2
2
1
2
0
2
0
0
1
0
1
1
2
0
1
1
0
0
2
1
2
0
0
1
0
1
0
2
0
0
2
2
0
0
0
0
0
0
1
3
0
1
0
2
1
1
2
2
0
0
0
1
1
2
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
1
1
1
2
1
1
2
0
0
0
2
1
1
1
1
0
0
0
2
1
0
0
1
0
0
0
0
0
0
1
0
0
1
2
1
0
0
2
0
2
0
0
0
1
2
0
0
0
0
2
1
0
2
0
0
0
0
0
2
2
0
1
2
1
1
0
1
0
0
1
1
1
2
1
1
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
2
1
0
1
1
2
1
1
0
0
1
2
1
0
0
1
0
0
1
0
1
0
0
1
0
0
2
0
0
0
0
1
0
1
1
3
0
2
0
0
0
0
2
2
0
1
0
0
0
0
2
1
0
0
2
0
0
0
0
0
1
2
0
0
0
1
2
0
1
0
0
1
2
0
2
0
1
2
2
2
0
1
0
1
2
0
0
0
0
2
1
0
0
0
0
1
1
2
2
0
0
0
2
0
1
0
1
1
3
0
0
0
0
2
0
2
0
0
1
0
0
0
2
0
2
0
0
1
0
0
1
0
1
2
0
1
1
1
0
0
1
2
0
1
0
0
0
2
0
1
2
2
1
2
0
0
0
0
0
1
0
0
0
0
0
2
1
1
0
1
0
1
0
2
1
1
0
1
2
1
1
1
0
2
1
1
2
1
0
2
2
2
0
2
0
0
1
0
1
2
2
0
0
0
1
0
2
0
0
2
0
1
0
0
0
1
2
1
0
2
2
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
1
0
2
1
0
1
0
1
0
0
1
0
2
0
1
0
1
1
0
1
0
2
1
0
0
0
0
2
1
1
1
0
2
0
0
0
0
2
0
2
0
4
1
0
2
0
0
0
0
1
1
0
1
2
1
1
1
0
2
0
2
0
0
0
1
0
1
2
1
0
0
0
2
1
2
2
0
0
1
1
1
1
0
2
0
0
0
2
0
1
1
0
1
0
0
0
0
2
0
2
0
0
1
1
0
0
0
0
1
0
0
0
1
0
1
2
0
1
1
0
0
0
1
1
0
0
0
1
2
0
2
0
0
0
2
2
1
2
0
1
0
2
0
1
0
0
1
1
2
0
0
1
2
0
2
1
0
2
2
1
0
2
0
2
0
1
1
0
0
0
0
2
1
1
1
1
0
0
2
0
0
0
1
0
2
1
0
2
1
1
1
0
1
0
0
1
0
2
2
0
0
0
0
1
0
2
1
1
1
0
2
0
1
1
2
2
0
1
0
2
0
0
0
0
0
0
2
2
1
1
1
0
0
0
2
0
2
1
0
1
1
1
0
3
1
1
0
2
0
0
1
0
1
0
0
0
0
0
0
2
1
0
1
1
0
0
0
1
0
0
0
1
0
2
0
0
2
1
0
1
0
0
0
1
1
0
0
1
2
0
0
2
1
0
1
2
1
2
0
0
2
0
1
0
0
0
0
1
2
0
2
0
1
1
0
1
1
2
0
0
0
0
0
1
0
2
1
0
1
0
0
0
0
0
0
0
2
0
0
3
1
1
1
2
0
1
0
0
0
1
0
1
2
2
1
0
0
1
1
0
0
2
0
0
0
0
0
1
2
0
0
1
1
2
0
0
1
0
0
0
0
2
2
0
1
1
0
1
3
0
1
0
0
0
0
1
1
1
1
0
0
2
1
2
1
0
1
1
1
1
0
0
0
1
0
2
2
1
0
1
1
0
0
1
0
1
2
1
0
2
2
2
0
1
0
2
0
1
1
0
0
0
1
3
1
2
0
1
0
0
2
0
0
0
1
0
1
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
2
1
0
1
1
1
0
1
0
2
0
0
1
0
2
2
2
2
0
0
2
1
1
0
0
1
1
1
1
2
1
2
1
0
1
0
1
0
0
0
1
2
0
0
1
0
0
0
2
2
1
1
1
1
1
0
2
3
0
1
1
3
1
2
0
0
2
2
0
0
1
0
0
0
2
1
3
0
1
1
1
1
1
0
2
1
0
2
1
0
1
2
0
1
0
0
0
2
2
0
0
2
1
1
1
1
0
2
0
1
2
0
0
0
0
1
0
0
1
0
0
1
0
2
0
2
0
2
0
0
0
0
1
0
2
0
0
0
1
0
0
2
0
2
0
0
0
2
1
0
0
0
0
2
2
2
0
0
0
1
0
1
0
0
2
1
0
4
2
2
0
0
0
0
2
1
0
1
2
2
1
1
1
2
1
0
0
0
1
2
1
0
2
2
1
1
0
2
1
0
0
1
0
2
0
2
0
0
0
0
1
0
1
4
0
0
0
0
0
1
0
2
0
0
2
0
2
1
1
1
2
2
1
1
0
0
1
1
1
1
0
2
1
1
1
0
0
1
0
1
0
0
0
0
0
3
2
1
0
1
1
0
2
1
1
0
2
0
2
0
1
1
2
0
0
2
0
0
2
0
0
0
1
1
0
1
0
1
0
0
0
0
1
0
2
0
1
2
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
2
0
0
2
1
1
2
0
1
1
0
0
1
2
1
0
0
1
1
1
1
0
3
0
0
0
1
1
0
0
0
0
0
2
0
1
1
0
0
0
1
2
2
0
0
0
2
0
3
0
2
0
0
0
1
0
1
1
0
0
1
1
0
0
1
0
0
0
2
1
2
1
3
1
1
1
2
3
0
0
0
1
3
0
2
2
1
1
2
1
0
0
0
0
0
0
0
0
2
1
0
2
0
1
0
2
0
2
0
0
1
0
0
0
2
0
1
0
2
0
2
0
1
0
0
2
1
0
1
2
2
1
1
1
3
0
2
1
2
0
2
1
0
0
0
0
0
1
1
1
3
0
1
0
1
2
1
2
2
1
0
1
0
0
1
2
2
1
1
0
1
2
0
0
0
0
1
1
0
0
1
0
0
0
1
0
1
1
1
1
1
2
1
0
0
0
1
2
0
0
0
2
1
0
1
3
1
0
1
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
2
2
2
0
1
0
0
2
0
0
1
2
1
2
0
1
1
0
2
2
1
0
0
0
0
1
1
2
1
2
2
1
0
2
2
2
1
0
2
0
2
0
0
2
1
0
1
2
1
0
1
0
2
0
0
1
1
0
0
0
1
2
2
2
0
2
0
0
0
0
1
0
2
0
1
0
1
1
0
0
0
0
1
2
1
1
0
2
1
1
2
0
0
0
1
0
0
1
1
2
0
1
0
2
0
0
1
1
1
0
0
0
0
2
0
1
0
0
0
1
0
2
2
2
3
0
0
0
2
0
1
0
0
0
2
0
1
0
0
0
1
0
1
1
1
1
0
3
2
0
3
0
0
3
0
0
0
2
1
0
0
2
0
0
0
0
0
2
0
0
2
0
1
0
0
0
2
0
2
0
2
0
0
0
0
1
0
0
2
2
0
0
0
1
0
0
2
1
1
0
0
2
0
0
0
0
1
0
0
0
0
1
2
0
1
2
0
0
2
1
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
3
0
2
1
2
2
0
1
0
2
0
0
0
0
0
3
0
1
1
0
1
0
0
0
2
2
0
1
1
1
0
0
1
2
1
0
2
1
1
1
0
2
1
0
0
0
1
2
2
0
0
1
0
0
0
1
0
1
3
2
1
1
1
1
0
0
2
0
0
2
1
0
0
2
2
2
0
1
1
0
0
0
1
0
2
0
0
0
1
1
0
1
0
1
1
0
0
1
1
1
0
2
0
1
0
0
1
0
0
2
0
2
0
1
2
0
1
2
0
1
0
1
2
0
1
0
1
1
0
1
0
1
1
2
0
0
0
0
0
1
1
4
2
1
0
2
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
1
0
1
1
2
2
0
0
2
0
0
1
1
1
1
2
1
1
0
0
0
0
0
0
0
0
1
0
3
0
2
1
2
2
0
1
0
0
0
1
0
0
2
1
0
1
0
0
2
0
0
0
0
1
2
0
2
0
1
2
1
0
0
1
0
1
0
0
0
0
0
0
0
2
2
1
1
1
2
0
2
2
0
0
1
0
0
0
1
1
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
1
1
1
0
2
0
3
0
0
1
0
0
1
1
0
0
1
2
2
2
2
1
1
2
0
0
0
0
0
1
2
1
2
0
2
0
0
0
0
1
1
0
1
0
0
2
0
1
1
1
0
0
1
0
2
0
0
1
0
0
0
0
0
1
2
0
0
2
0
0
0
2
1
0
1
0
1
0
2
2
0
2
0
0
0
0
0
0
1
0
3
0
1
0
1
0
1
2
2
2
2
0
2
0
0
3
0
0
0
1
2
0
0
0
2
2
1
1
0
11
2
0
2
0
2
0
0
0
0
0
0
0
1
1
2
0
0
0
2
0
3
1
2
4
1
1
1
2
0
0
2
0
0
2
0
2
1
2
0
2
2
0
0
2
1
0
4
0
2
0
0
0
1
0
2
2
0
1
1
0
0
0
0
2
2
0
1
0
0
0
0
0
1
0
1
0
0
5
0
0
3
1
0
1
0
0
1
0
1
0
0
1
1
2
1
2
1
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
2
0
0
1
2
0
2
2
0
1
0
2
2
1
2
0
0
2
0
0
1
0
1
0
2
1
2
0
1
0
0
2
0
0
1
2
3
1
0
0
2
1
0
0
2
5
1
0
1
2
0
0
1
0
2
0
1
1
0
0
2
3
2
2
1
0
0
1
0
2
0
1
2
2
0
0
1
2
0
0
0
1
3
1
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
1
0
1
0
1
2
2
0
2
0
2
2
2
1
0
0
0
2
0
0
1
0
3
0
0
0
0
0
1
0
1
0
1
1
0
0
1
1
0
0
2
1
0
2
0
3
0
0
2
0
0
0
2
2
2
0
1
0
2
3
1
0
0
0
0
1
1
0
0
3
2
1
0
1
2
1
2
0
1
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
2
0
0
1
0
0
1
0
1
1
0
0
1
1
0
0
0
1
0
0
1
0
1
0
0
1
2
1
0
2
0
2
0
0
1
1
0
1
0
2
1
0
1
0
2
1
0
2
2
0
0
0
1
1
0
2
2
0
1
0
1
1
0
0
0
3
0
0
1
0
0
1
0
0
1
1
0
3
0
0
0
2
0
0
1
1
0
0
1
0
0
1
0
1
0
0
0
2
0
2
1
2
1
0
0
1
2
2
0
0
0
0
2
0
1
1
1
0
2
1
1
2
0
1
0
0
1
0
1
0
0
1
0
2
1
0
1
2
2
1
1
1
0
0
2
0
2
0
2
1
0
0
1
0
1
0
0
1
1
0
0
2
2
1
0
1
0
0
2
1
0
0
2
1
1
0
0
0
2
2
0
3
1
1
1
1
0
0
0
2
2
0
0
0
0
2
0
0
1
0
1
0
0
1
0
2
1
0
0
2
0
0
1
2
0
1
0
1
0
0
0
2
0
0
1
2
0
4
0
2
2
2
0
2
0
0
0
2
0
2
0
0
1
0
0
1
0
0
0
1
2
2
2
1
0
1
0
0
1
1
0
2
0
1
0
1
0
0
0
2
2
0
1
0
2
0
0
2
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
1
1
0
1
1
1
0
0
0
2
0
1
0
2
0
0
1
1
0
1
1
0
2
1
2
2
1
0
0
0
1
2
0
0
0
3
2
0
0
3
0
0
1
0
1
0
1
0
2
0
0
0
2
0
0
0
0
0
1
0
1
0
2
0
1
1
1
0
0
0
0
0
1
0
0
2
0
1
2
2
0
1
2
2
1
1
2
0
2
1
2
2
3
0
0
0
0
2
2
0
0
0
2
2
0
2
0
1
1
2
0
0
2
0
0
2
0
0
0
2
1
2
0
1
0
2
1
1
0
0
1
1
0
0
0
1
0
0
0
2
0
2
1
0
2
1
2
2
1
2
0
1
1
0
1
2
0
1
1
2
0
2
2
0
0
0
2
0
0
0
0
2
1
1
0
2
0
0
0
0
1
1
0
0
1
0
1
2
2
1
0
0
0
1
0
1
0
2
1
1
1
0
1
1
0
0
1
0
1
0
1
0
0
1
0
0
2
2
0
0
0
0
1
1
1
1
0
0
0
2
1
2
2
2
0
2
0
2
1
2
0
1
0
2
0
1
1
2
0
0
2
0
1
2
5
0
0
1
3
0
0
1
0
1
0
1
0
1
0
0
0
0
0
1
1
2
1
2
0
1
1
0
1
1
0
1
2
0
1
0
0
1
1
2
2
1
0
0
0
3
1
0
2
0
0
0
0
0
0
1
0
1
0
1
1
0
1
1
1
1
0
1
0
0
1
0
1
0
1
0
1
1
0
0
0
0
1
1
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
2
1
2
0
0
0
2
0
1
2
0
0
0
0
0
1
0
2
0
0
0
0
1
1
1
0
0
0
2
0
0
2
2
0
2
0
0
1
2
1
0
2
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
2
0
1
0
1
1
2
0
0
0
0
0
2
1
2
1
0
1
1
1
1
1
0
0
1
0
0
0
2
2
0
2
0
0
1
7
0
2
0
0
0
1
2
0
0
0
2
0
2
3
0
0
2
0
0
0
0
0
0
0
2
1
2
2
1
0
0
1
0
0
2
1
1
2
0
1
0
1
0
2
0
0
1
1
0
2
1
2
0
0
0
0
3
0
1
2
0
0
0
0
2
1
1
0
0
2
1
1
0
2
0
2
0
2
0
1
2
0
2
0
0
0
0
1
0
0
1
0
1
0
0
0
0
2
1
1
2
1
0
1
0
1
2
1
0
0
0
1
0
0
0
0
0
0
2
3
0
2
1
0
2
1
0
0
0
0
1
1
1
0
0
0
2
1
0
0
0
0
1
0
2
1
0
1
0
0
0
1
0
0
1
0
0
0
0
2
0
0
2
1
1
0
0
0
2
2
1
0
0
1
0
2
0
0
3
0
0
0
1
0
0
0
0
0
1
2
2
2
1
0
0
1
2
4
0
0
1
0
1
2
0
2
0
0
0
0
2
1
0
0
3
0
0
1
1
0
0
0
0
1
2
1
1
2
1
1
1
0
0
1
0
0
1
1
2
0
1
2
2
0
1
3
1
1
0
0
1
0
0
0
0
0
0
0
0
2
0
2
1
1
2
2
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
1
0
1
1
2
0
1
0
2
0
0
1
0
0
1
0
0
0
0
2
2
0
1
0
0
1
0
0
2
0
1
1
0
0
0
0
1
1
0
2
2
1
1
0
0
2
0
1
0
0
0
0
0
2
0
1
1
2
1
0
1
1
1
0
1
2
3
0
2
0
0
1
2
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
1
1
0
0
0
1
0
0
0
2
0
0
0
2
1
0
1
0
0
0
1
1
2
0
1
0
2
2
1
0
1
2
1
0
0
0
1
0
0
0
1
0
1
1
0
2
0
0
0
0
1
3
0
0
2
2
1
1
1
0
0
0
0
0
0
1
0
8
1
2
2
0
0
0
1
0
1
0
2
1
1
0
2
0
0
0
0
0
0
2
0
1
0
1
0
1
1
0
1
2
2
0
2
1
0
2
0
1
2
0
0
2
0
0
3
0
1
2
0
1
0
0
2
2
0
0
1
0
1
2
2
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
1
1
0
2
1
0
0
2
0
2
1
0
2
0
0
1
0
0
0
0
0
0
2
1
0
1
0
0
0
2
0
0
1
1
2
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
3
1
0
1
0
0
0
1
0
0
0
0
3
2
2
0
0
1
1
1
0
0
2
0
0
0
2
0
2
0
0
0
1
0
0
2
0
2
2
2
1
1
1
0
1
2
2
2
0
0
0
1
0
0
0
0
2
2
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
5
0
0
0
0
1
1
1
0
1
1
1
0
2
1
0
0
1
0
0
4
1
1
2
0
2
2
2
1
0
1
0
0
2
2
0
0
0
0
0
1
0
0
0
0
2
0
3
2
1
3
0
0
1
0
0
0
0
0
1
1
2
0
1
1
1
0
0
1
0
0
0
0
3
0
0
1
1
6
0
0
2
1
1
2
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
1
2
0
2
1
0
0
0
2
4
0
1
1
0
1
0
0
0
0
4
2
3
0
1
1
1
0
0
0
0
2
1
0
1
0
0
1
0
0
0
3
0
0
2
1
0
0
2
0
1
1
1
0
0
0
5
1
0
0
2
0
0
0
0
0
2
0
1
1
0
0
0
0
1
1
2
1
0
2
0
2
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
2
2
1
1
0
0
1
0
0
1
0
2
0
0
2
0
1
1
0
0
0
2
2
0
0
1
2
0
1
0
0
0
1
0
2
1
1
1
0
2
2
0
1
0
2
0
1
0
0
1
0
1
1
0
0
0
0
0
1
2
0
1
0
0
0
0
2
0
0
0
0
0
3
1
2
0
3
1
0
0
0
1
3
2
0
0
1
0
1
2
1
2
0
2
0
0
0
1
1
1
1
0
2
1
0
0
1
0
1
0
1
0
5
0
2
0
1
1
0
0
2
0
1
2
1
2
2
0
1
0
0
0
0
1
2
0
0
2
0
0
1
1
1
0
1
2
0
1
0
1
4
0
0
0
0
0
0
2
2
1
1
0
0
0
0
0
0
1
0
0
2
0
1
0
1
2
0
0
1
0
2
0
1
0
0
1
1
0
2
0
2
0
0
0
2
0
0
0
2
2
0
0
0
1
0
1
0
1
2
0
0
1
2
1
0
0
0
0
1
0
1
0
0
1
0
0
0
1
2
1
0
1
1
0
0
2
0
1
0
2
0
1
0
2
1
1
0
1
0
0
0
1
2
2
1
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
2
1
1
2
0
1
2
3
1
0
0
0
1
1
2
0
1
0
0
0
0
1
1
0
2
0
2
1
2
1
0
1
0
0
3
0
3
2
0
0
1
1
2
1
2
1
0
0
1
1
1
0
0
1
0
1
2
2
0
0
1
2
0
2
0
0
0
0
0
1
1
2
0
1
2
1
2
1
1
2
0
0
1
0
1
0
0
0
1
1
3
1
2
4
1
1
1
1
0
1
0
1
0
1
0
0
2
2
2
5
0
1
0
0
1
1
0
0
1
0
1
2
0
0
2
0
0
0
1
2
0
2
1
1
0
0
0
0
1
0
0
2
0
0
0
0
1
2
0
0
2
1
2
2
0
0
0
0
2
0
0
2
1
1
0
0
0
0
2
2
2
1
0
0
1
2
0
1
0
0
3
1
1
2
0
0
0
1
1
0
0
0
3
0
2
0
0
0
1
1
1
0
0
1
1
0
1
0
2
1
0
0
0
0
0
2
1
0
1
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
1
1
1
1
2
0
0
2
2
0
0
1
2
2
0
1
1
1
0
0
1
1
2
1
3
0
1
1
0
1
0
2
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
1
2
1
1
0
0
1
1
1
2
0
1
0
2
0
0
0
2
2
1
0
1
0
1
0
1
1
2
1
0
1
0
0
0
0
0
5
1
0
0
1
0
0
2
1
1
0
1
0
1
0
0
2
2
0
0
2
2
1
2
0
2
0
0
0
1
1
2
0
1
0
1
1
4
0
1
0
1
1
1
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
1
0
3
1
0
0
1
1
2
2
1
0
2
0
0
0
0
0
1
0
0
0
0
1
2
1
1
0
0
1
1
0
1
1
0
1
0
0
1
1
0
1
1
1
1
0
1
1
1
0
1
1
0
2
0
2
0
2
0
0
0
0
2
1
2
0
1
0
1
0
0
2
1
2
5
2
0
0
1
0
0
1
0
0
0
0
0
1
2
0
0
2
1
2
0
1
2
0
1
1
0
0
0
1
2
1
0
1
0
0
1
2
1
1
1
2
0
2
1
0
0
0
2
2
0
1
0
2
0
1
1
0
0
0
1
0
1
0
2
2
2
2
1
1
0
1
1
0
0
2
0
1
0
0
2
0
1
0
1
2
3
1
0
0
0
0
0
0
1
1
0
0
0
1
0
2
0
0
0
0
2
1
1
2
1
2
0
0
1
2
1
0
1
0
2
0
1
1
0
0
3
0
0
0
0
2
0
0
1
0
0
2
1
0
2
0
0
0
0
1
0
2
1
2
4
2
2
1
1
0
0
0
0
0
0
0
2
0
1
0
1
2
1
2
2
1
0
2
0
2
2
2
2
0
0
1
1
0
0
0
0
0
0
2
0
0
2
2
2
3
1
0
2
0
0
0
4
1
1
0
0
0
2
2
1
2
0
1
1
2
2
0
2
2
0
0
0
1
0
0
1
1
0
0
1
1
1
1
1
1
0
2
0
0
1
0
1
0
0
0
2
2
0
0
3
0
2
2
0
0
0
2
0
0
0
1
1
2
0
5
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
1
2
1
0
0
0
0
0
0
1
1
0
2
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
2
1
0
1
2
3
0
0
0
0
0
0
0
1
1
0
2
0
1
0
0
1
0
0
1
1
1
0
0
0
2
0
0
1
2
1
0
0
0
0
0
1
0
1
0
1
0
0
0
2
1
2
2
1
1
1
0
2
0
0
0
0
1
0
1
3
0
1
2
2
0
0
0
0
1
0
0
0
1
1
2
0
1
1
0
1
1
0
0
0
0
0
2
0
2
0
0
2
2
0
2
0
1
0
0
0
0
2
0
0
2
2
1
1
2
1
1
1
0
1
1
0
1
1
0
0
2
0
0
0
1
0
1
0
4
1
1
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
2
2
0
0
2
1
0
0
0
0
0
0
0
1
0
1
0
0
1
1
1
0
1
0
2
0
0
0
0
1
0
2
2
2
2
2
1
2
1
0
0
2
1
2
0
0
1
0
0
1
0
0
1
0
1
2
1
0
0
0
2
0
1
0
2
0
0
0
0
2
1
0
0
0
2
1
1
2
0
1
2
0
1
0
1
0
2
0
0
0
0
3
0
0
0
0
1
0
0
2
0
0
0
0
1
0
2
1
2
0
1
1
0
3
0
1
0
1
0
0
3
0
2
0
0
1
0
0
0
0
2
1
1
2
1
0
5
0
2
0
0
0
2
2
2
0
1
2
0
1
3
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
2
2
0
0
0
0
1
2
0
0
0
1
0
1
0
2
2
1
2
3
2
1
0
3
1
0
1
2
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
1
0
0
0
1
0
1
2
1
0
0
1
0
1
1
2
0
0
2
0
1
1
0
0
0
0
1
2
0
0
0
0
2
0
2
2
1
0
0
0
1
1
0
0
2
0
0
2
1
0
0
2
0
1
2
0
0
0
0
0
2
1
0
0
0
1
1
0
0
2
1
0
1
0
1
0
0
0
1
1
0
2
1
1
0
0
1
0
0
0
0
0
2
2
1
0
2
0
0
2
0
1
0
0
0
0
2
0
0
1
0
2
2
0
0
1
0
1
1
1
0
0
1
0
1
0
0
0
1
0
1
0
1
0
1
2
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
2
1
2
0
0
0
0
2
1
2
0
0
0
0
1
0
1
2
0
2
1
0
0
1
0
0
0
0
1
2
2
0
2
0
0
0
2
0
0
2
1
3
0
0
0
1
1
0
1
0
0
0
0
2
1
0
1
1
1
0
0
2
1
0
1
0
0
0
1
1
1
2
0
1
1
0
1
0
0
0
2
0
0
2
1
0
1
0
0
2
1
1
0
0
0
1
1
0
0
2
2
0
4
0
1
0
0
2
0
2
1
2
1
1
0
1
0
0
1
1
2
0
1
0
1
0
1
0
0
0
0
1
0
1
0
0
1
1
0
1
0
0
1
0
0
0
1
1
0
0
2
1
0
0
1
0
0
2
1
0
0
0
0
2
3
2
2
1
1
0
2
1
1
0
1
0
0
0
2
1
0
1
0
0
2
1
1
2
2
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
1
1
3
0
1
1
2
0
1
0
0
0
2
2
2
0
0
2
0
0
0
1
1
1
0
0
0
0
2
1
0
0
1
0
3
1
0
0
2
0
2
0
0
0
2
1
1
2
0
1
2
0
0
2
0
0
0
0
0
0
0
1
0
1
2
0
2
0
0
0
2
2
1
0
0
1
2
1
1
0
1
0
1
1
0
0
2
0
1
0
4
0
2
0
0
2
0
1
0
0
1
0
1
3
1
0
2
0
0
0
1
1
2
1
0
1
1
2
0
1
2
0
0
1
0
2
1
2
0
1
0
0
0
2
1
0
0
0
3
2
1
0
1
0
0
1
4
0
1
1
0
0
1
2
1
0
2
0
0
0
1
0
2
0
0
0
1
0
0
0
1
0
2
0
1
1
1
2
0
2
0
0
0
0
1
6
1
2
2
2
2
2
0
1
0
0
2
2
0
2
0
0
1
1
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
2
2
2
0
2
2
2
0
0
0
2
2
0
0
2
1
1
0
0
2
0
1
1
0
0
1
1
0
0
0
0
2
0
1
0
2
1
1
1
2
1
1
1
1
2
1
4
0
1
1
1
0
1
1
1
1
0
0
1
1
1
0
0
0
0
0
0
0
0
3
0
2
2
1
0
0
1
0
0
2
0
1
0
2
2
1
0
1
1
1
0
0
0
1
0
1
2
0
0
0
0
1
1
1
0
2
0
0
0
2
0
1
2
0
0
1
0
0
2
2
2
0
1
0
1
0
2
0
1
1
0
0
1
3
1
0
1
0
2
2
0
2
2
0
0
0
0
2
2
1
0
0
0
0
0
0
2
2
0
2
1
1
0
2
1
0
0
2
0
0
0
0
1
1
1
0
0
2
4
0
2
0
1
1
0
2
0
0
1
0
1
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
1
0
0
1
1
3
1
1
2
1
2
0
0
0
2
0
1
0
1
0
1
1
1
2
0
0
0
0
2
2
0
1
0
2
0
0
0
0
0
2
1
3
0
0
0
1
2
0
0
1
0
2
0
0
1
0
1
0
0
0
1
0
0
0
0
2
1
1
0
1
1
0
0
3
1
0
0
2
1
0
2
1
0
2
1
2
0
1
1
1
0
0
0
0
0
2
0
6
0
0
0
2
0
1
0
1
0
0
0
0
0
3
1
1
0
1
1
0
0
0
2
0
0
0
1
0
0
2
2
2
2
0
1
0
2
1
0
1
1
1
1
1
0
0
0
2
0
2
0
0
1
0
0
0
0
0
2
2
0
0
1
2
3
1
0
0
2
1
1
0
0
2
0
0
1
1
1
1
2
1
0
0
0
0
2
0
0
0
1
1
0
0
1
0
2
0
0
0
1
0
2
2
4
1
0
0
3
1
0
1
2
0
0
0
2
0
0
2
1
0
0
1
1
2
0
0
0
0
2
0
0
2
0
6
0
2
0
0
2
0
2
0
0
0
0
2
0
5
1
2
2
0
0
0
1
1
0
2
0
1
0
0
0
2
4
1
0
0
1
0
0
2
0
0
0
0
0
1
2
0
1
0
1
2
1
2
2
1
0
1
0
1
1
0
0
0
1
4
1
0
0
1
0
0
0
1
2
0
2
0
1
0
1
0
0
0
1
1
2
0
1
1
1
1
0
0
0
0
0
2
0
0
1
1
1
1
2
0
4
2
0
3
0
2
0
1
1
2
0
0
0
2
1
1
2
1
2
1
0
0
2
2
0
0
0
0
1
1
0
2
1
0
1
2
2
1
0
1
0
0
0
1
0
1
2
1
0
0
3
2
1
0
2
0
1
2
2
0
2
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
2
1
0
0
2
2
0
0
0
0
0
0
0
0
0
1
3
1
0
2
1
0
0
1
0
2
0
2
3
0
0
0
0
1
0
0
0
1
0
2
2
0
1
1
1
0
0
2
0
0
0
0
0
2
0
0
0
2
2
0
0
2
0
0
0
1
2
2
0
1
0
1
1
1
0
0
0
0
1
0
1
0
1
1
1
0
0
1
1
0
0
0
2
1
1
0
3
0
0
0
2
0
1
0
0
0
2
0
3
1
0
2
2
0
0
0
2
2
1
2
2
2
3
2
2
2
0
0
3
2
2
1
0
0
1
1
0
0
2
0
2
0
0
1
0
1
0
0
1
0
1
0
0
2
1
0
2
3
0
0
0
2
2
2
1
0
1
2
0
0
1
0
0
2
0
0
0
0
0
2
2
0
1
0
2
0
1
1
0
2
1
0
1
1
0
1
0
1
0
1
1
2
2
0
0
1
0
0
0
0
1
0
2
0
1
2
0
1
0
0
1
1
0
0
2
0
2
1
0
3
2
2
0
1
2
0
2
0
2
0
0
0
1
0
2
2
4
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
2
0
0
0
0
1
1
1
0
0
2
0
0
1
0
1
1
2
0
1
0
1
1
0
0
3
1
0
0
0
2
0
0
1
3
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
2
2
0
1
1
1
0
1
1
0
0
1
0
0
3
1
1
2
1
0
0
1
2
2
2
0
1
2
0
0
0
0
0
2
0
1
0
0
0
0
1
0
1
3
1
0
0
2
1
0
2
0
0
0
1
3
2
1
0
0
0
2
0
2
2
1
1
0
0
2
0
0
1
1
0
1
2
2
2
2
2
2
0
2
1
0
1
0
0
0
0
1
2
1
1
0
0
0
0
1
0
0
2
1
2
1
0
0
0
2
0
0
0
0
0
2
0
0
1
1
2
0
0
0
2
0
1
0
0
2
0
0
2
2
0
0
0
1
2
1
1
2
1
1
0
0
0
1
0
1
0
0
2
2
0
0
0
0
0
3
0
0
0
2
0
0
0
1
1
1
1
0
0
2
3
3
1
2
2
1
1
0
2
0
2
1
0
2
1
0
0
1
0
2
0
0
0
1
1
0
1
2
0
0
1
1
0
0
1
2
1
0
2
1
1
0
0
1
1
1
0
1
1
0
1
0
0
2
0
0
0
1
0
0
1
5
1
2
0
0
0
0
0
0
0
2
0
2
2
2
0
0
2
0
1
0
0
2
1
0
2
1
0
1
0
2
0
2
1
0
1
0
1
0
1
0
0
2
2
1
0
2
2
0
1
1
0
2
2
1
0
3
2
1
2
1
0
0
0
1
0
1
2
2
0
3
1
1
1
0
1
1
0
0
1
0
0
1
0
0
2
1
1
0
0
0
0
0
0
1
1
2
0
0
2
0
0
1
0
1
0
0
0
0
0
1
0
3
7
1
0
0
0
1
0
2
1
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
1
0
0
0
0
2
0
2
0
1
0
1
2
1
0
0
2
1
0
1
0
2
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
2
1
1
1
1
0
0
1
2
0
2
2
0
0
0
2
0
1
0
2
0
0
2
2
1
0
1
0
2
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
1
1
0
0
2
2
0
1
0
0
1
3
1
1
2
0
1
0
1
0
0
1
0
1
0
1
1
0
0
0
0
2
0
2
1
0
0
2
2
3
0
0
0
2
0
0
2
2
2
2
0
1
1
1
0
1
0
0
0
2
1
2
1
0
1
1
2
1
0
1
2
0
0
0
1
0
1
1
1
3
1
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
2
1
0
1
2
2
0
2
0
0
0
2
1
2
2
0
2
0
1
0
2
1
1
0
2
0
1
1
2
1
4
0
0
0
0
2
1
1
1
0
2
0
1
2
2
1
0
2
0
4
2
0
1
0
0
1
2
0
0
2
1
1
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
1
1
0
1
2
0
0
1
1
0
0
1
1
1
0
1
1
2
0
2
0
1
0
2
2
0
0
0
0
0
1
0
0
2
0
1
2
0
0
1
2
0
1
2
0
1
1
2
0
1
1
0
0
0
1
2
0
0
0
0
2
0
1
0
1
0
1
1
0
0
0
0
0
1
1
0
1
1
1
0
1
0
2
1
0
1
0
1
1
1
0
1
0
1
0
0
2
0
0
1
0
0
2
0
0
0
1
0
1
1
0
2
1
2
0
0
0
0
1
0
2
0
0
1
1
2
0
2
2
0
0
0
2
1
3
0
2
0
0
0
1
0
2
0
0
2
1
1
2
2
0
0
1
0
0
0
0
1
2
0
1
1
0
0
1
2
0
0
1
1
0
1
0
2
0
1
1
4
0
0
1
1
2
1
0
1
1
0
1
1
0
0
1
1
2
1
1
0
2
1
2
1
0
0
0
1
0
0
0
0
2
2
0
0
1
1
1
2
0
2
2
2
1
0
2
0
0
0
2
0
1
0
2
0
0
0
0
2
2
0
0
1
1
2
0
0
1
1
0
1
0
0
0
0
0
1
0
3
1
0
0
1
3
1
0
2
2
1
0
2
0
0
1
2
0
1
2
0
1
0
1
0
0
0
0
0
1
0
0
1
2
0
0
1
0
1
1
1
1
0
0
2
0
0
0
1
0
0
2
0
2
1
0
2
0
0
1
2
1
0
2
1
0
0
2
0
0
2
0
0
2
1
0
2
1
1
1
0
0
0
2
1
0
0
0
0
4
0
2
1
0
1
1
0
1
0
0
2
0
1
1
1
0
0
0
0
2
1
0
0
2
2
2
2
1
0
1
1
1
0
0
1
0
2
0
0
1
2
1
0
2
0
0
1
0
2
1
0
0
1
0
1
0
0
1
1
1
0
0
2
2
1
1
1
1
0
5
1
0
0
0
1
0
0
0
1
1
0
1
1
0
1
2
2
0
0
1
0
0
0
2
2
0
0
0
1
1
0
2
2
0
1
0
2
2
0
1
2
1
0
1
1
1
0
0
1
2
1
0
0
0
1
0
2
0
1
0
0
1
0
0
0
2
0
1
1
1
0
2
0
0
1
0
2
1
0
0
1
0
0
1
2
0
0
2
0
0
0
0
1
0
2
1
0
0
0
2
1
0
2
0
0
0
0
2
2
0
0
1
0
0
0
0
1
1
0
2
0
1
1
0
1
1
2
0
2
2
1
1
0
0
1
2
0
2
1
0
1
0
0
0
1
1
0
1
0
1
0
0
0
1
1
0
0
2
4
0
0
2
1
1
0
2
2
0
1
0
1
0
0
0
1
1
0
0
0
0
2
0
0
2
1
1
0
0
1
1
0
1
1
0
0
1
0
2
0
0
2
2
0
0
1
0
0
0
2
2
1
0
0
2
0
0
0
1
0
0
2
0
0
2
0
0
0
3
2
0
2
0
1
0
0
0
1
0
2
2
0
0
2
0
0
0
1
0
0
1
1
3
1
0
0
1
1
1
0
1
1
1
1
3
1
0
2
3
1
0
0
3
0
2
0
1
1
1
1
2
0
1
1
1
0
1
0
2
0
1
0
0
2
0
0
0
2
0
2
3
0
1
1
0
0
0
1
0
1
0
0
2
0
2
2
0
1
2
0
0
0
2
0
0
0
2
3
1
0
1
0
0
0
1
0
0
0
1
0
0
2
2
1
1
2
0
1
1
0
0
0
0
1
0
1
1
0
0
0
0
1
0
2
2
0
0
1
0
0
2
2
2
0
0
1
0
0
0
1
0
0
0
1
0
2
0
1
0
0
0
0
2
2
0
1
0
3
1
0
0
0
1
0
0
2
3
2
0
0
1
0
0
2
2
0
2
0
2
1
0
0
1
0
2
0
1
1
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
1
1
2
2
1
2
0
1
0
1
2
0
2
2
1
0
0
0
0
1
1
0
0
0
2
2
0
1
2
0
0
2
0
0
1
1
2
1
1
0
2
2
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
2
2
1
2
0
1
0
2
2
0
2
1
0
1
0
0
0
0
0
0
2
2
0
2
2
0
0
0
0
1
0
1
1
0
0
0
1
0
0
2
0
1
2
0
0
0
0
2
2
0
0
0
0
0
2
1
0
0
0
0
1
1
1
0
0
0
0
1
2
0
2
2
0
1
1
0
0
0
2
2
1
0
1
0
1
0
1
0
0
2
0
1
1
0
1
0
0
1
0
1
0
1
1
0
0
0
0
0
1
0
0
0
1
4
1
0
3
1
0
0
1
0
0
0
1
0
1
1
1
1
2
1
0
1
0
0
1
2
1
0
1
2
0
0
2
2
0
0
2
2
0
3
0
0
2
2
1
0
7
2
1
1
1
2
0
1
1
1
2
2
0
2
2
0
1
0
0
0
0
0
2
2
0
2
0
0
0
2
1
0
0
1
0
0
1
2
0
0
1
1
1
2
2
0
0
1
0
2
0
0
0
0
2
0
2
1
1
0
0
0
0
1
1
0
0
1
1
0
1
2
0
2
1
1
2
1
0
0
1
0
1
1
0
0
0
0
2
2
2
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
2
0
0
1
2
0
0
1
0
0
0
0
1
1
0
1
2
0
1
0
2
0
0
2
2
1
1
0
0
0
0
0
2
0
2
1
1
0
0
1
0
0
2
1
0
2
1
2
1
0
1
0
2
1
2
1
0
1
1
1
1
0
0
2
0
0
1
0
6
2
3
0
0
0
2
0
0
1
0
1
0
0
2
1
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
2
0
0
2
0
0
2
1
1
1
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
1
0
0
0
0
0
1
1
0
4
1
2
1
1
1
0
2
1
2
0
0
0
0
0
0
0
1
1
0
2
0
1
1
0
0
0
0
2
1
0
0
1
0
2
1
1
0
0
0
2
1
0
1
0
2
1
1
0
0
0
1
1
2
1
1
0
1
0
1
2
1
0
1
2
0
2
0
0
2
4
2
0
1
4
2
2
2
0
0
0
2
1
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
2
2
2
0
0
0
1
1
0
0
2
1
2
0
0
2
0
1
1
0
0
0
0
1
0
2
2
0
0
0
0
0
2
1
0
0
2
1
2
0
1
1
0
1
2
0
0
2
0
0
0
1
1
0
0
2
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
1
2
0
0
0
0
2
1
1
2
1
2
2
0
2
0
1
2
0
0
0
0
1
0
2
1
1
1
0
2
0
0
0
0
0
0
0
0
1
1
2
0
1
1
1
0
0
0
0
0
2
0
0
2
1
0
0
1
1
2
0
1
0
2
1
0
2
1
0
1
2
1
1
0
1
0
1
1
0
1
0
2
0
1
0
0
0
2
1
0
2
1
2
1
3
0
2
0
1
0
0
1
1
0
0
0
1
0
0
1
1
1
2
0
0
0
1
2
0
0
0
1
0
0
1
1
0
0
0
0
0
2
1
1
0
0
0
0
2
0
0
0
0
2
0
0
1
2
2
0
2
1
1
0
0
0
2
2
0
0
2
0
2
1
1
0
0
2
1
0
1
2
2
0
0
0
0
0
2
2
0
2
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
2
0
0
1
1
0
2
2
0
0
1
0
2
1
1
0
1
0
2
0
0
1
1
0
1
0
1
1
2
0
0
2
0
0
0
1
0
0
0
0
2
2
2
0
1
0
0
0
0
1
0
1
1
0
0
1
2
0
0
0
1
0
2
1
4
1
0
2
2
1
0
0
1
2
1
0
0
0
0
0
0
2
0
1
2
2
2
2
0
0
1
2
2
1
1
0
2
1
0
2
0
0
0
0
3
1
0
0
0
0
1
1
2
0
0
0
0
1
0
1
0
2
1
0
0
1
0
2
0
0
0
1
0
2
0
0
3
1
2
0
0
0
0
0
1
2
0
0
0
1
0
0
1
0
2
0
1
0
0
0
1
0
0
1
1
0
0
1
1
0
0
0
1
0
0
0
0
2
1
1
1
1
0
1
1
2
1
0
0
0
2
0
0
0
3
4
1
1
0
1
1
2
0
0
1
1
0
1
0
2
0
2
0
0
4
1
0
0
0
2
0
2
0
1
1
0
1
0
0
1
1
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
1
1
2
1
0
0
0
1
0
0
0
1
6
0
2
1
2
1
2
2
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
3
2
2
2
1
3
0
2
1
0
3
0
1
1
0
2
0
2
0
1
11
1
1
0
0
1
0
1
0
0
0
2
1
1
0
0
0
0
2
1
0
0
0
0
1
1
2
1
1
1
0
0
0
0
0
0
1
0
0
0
1
1
1
2
1
0
0
1
1
1
2
0
1
0
0
2
0
1
0
0
1
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
1
0
2
1
1
1
0
2
0
1
0
0
0
0
0
1
0
0
1
0
1
2
1
2
0
0
0
2
2
0
0
1
1
0
2
1
2
1
2
2
1
0
1
0
1
0
0
0
2
2
0
1
1
0
0
0
1
2
2
2
0
1
0
1
1
1
0
1
0
1
2
2
1
0
0
2
0
0
1
0
0
0
2
0
2
2
0
0
3
0
3
0
1
2
1
0
0
0
0
1
2
2
0
1
2
2
2
0
0
0
0
0
2
3
0
0
0
2
1
1
1
0
0
0
1
0
0
1
1
1
1
0
0
0
0
2
0
0
1
0
0
0
2
0
1
0
0
2
0
0
2
2
1
1
1
1
1
2
0
0
0
0
0
0
0
0
2
0
1
0
2
1
2
1
1
0
0
1
0
0
1
0
0
0
0
1
1
0
0
1
1
1
1
0
0
0
1
1
0
0
1
0
0
1
1
0
0
0
2
2
0
0
0
1
1
1
0
0
1
0
2
3
2
0
2
1
1
2
0
0
1
1
0
3
0
0
2
0
0
1
0
1
0
2
0
0
1
0
0
2
2
0
0
0
2
0
2
0
1
0
0
0
1
0
0
1
1
1
0
0
0
0
2
1
0
0
0
0
1
1
1
1
3
1
1
0
0
0
0
1
1
0
1
1
0
1
3
1
0
0
0
0
3
7
1
0
2
0
0
0
0
1
0
1
0
0
1
1
2
0
1
0
0
0
2
0
2
0
1
0
1
2
0
0
2
1
0
2
2
0
0
1
0
0
0
1
0
0
0
0
1
0
1
2
0
2
5
2
2
2
0
0
2
0
0
1
0
2
1
0
0
1
2
0
0
1
1
0
0
0
1
2
0
0
0
0
1
2
0
2
1
0
0
0
0
0
2
1
2
1
0
0
1
2
0
0
1
1
1
1
1
0
0
0
0
2
0
0
2
1
1
0
0
1
0
0
0
0
0
2
1
2
0
0
0
1
0
1
2
0
0
0
0
0
1
0
0
0
1
2
1
0
0
1
0
2
1
0
0
1
0
0
2
2
2
0
2
0
0
2
0
0
0
1
2
0
2
0
2
0
2
1
0
0
1
0
0
0
1
0
1
0
2
0
2
1
0
0
3
0
1
1
0
0
1
0
0
2
2
2
2
0
2
0
1
0
1
2
2
2
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
1
0
0
1
3
2
0
1
3
0
1
3
4
1
0
0
1
0
0
0
0
1
1
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
2
1
1
1
0
1
0
2
1
0
0
0
1
5
0
0
2
0
0
1
1
2
1
0
0
1
2
0
2
2
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
2
0
0
0
0
0
0
0
0
2
1
0
0
1
1
2
0
0
1
1
2
0
0
0
2
0
2
0
0
0
0
0
2
0
1
0
4
2
0
2
3
0
0
2
1
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
2
0
0
1
0
2
1
2
0
0
2
1
0
1
0
2
1
0
0
1
0
3
2
2
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
1
0
1
1
0
0
0
1
0
0
2
0
1
0
2
0
1
0
2
2
2
1
0
0
0
0
2
2
0
1
1
2
3
0
2
2
2
0
0
0
1
1
0
0
1
3
0
0
0
0
0
0
0
1
2
1
2
0
0
1
1
1
2
0
0
1
0
1
0
2
1
0
2
0
2
0
0
1
2
0
0
0
1
0
2
1
0
0
2
0
0
2
0
1
0
2
1
1
1
0
0
0
0
1
2
0
1
0
0
1
2
0
0
0
3
2
0
0
0
2
0
2
1
0
1
1
0
1
3
0
0
2
0
1
3
1
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
2
0
1
2
0
0
1
0
0
0
0
1
1
2
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
1
1
1
0
0
2
1
0
1
1
0
2
0
1
2
0
0
2
1
0
0
0
1
0
1
0
4
2
1
0
0
2
0
0
0
0
0
0
2
1
0
0
2
0
0
7
1
1
4
2
1
0
0
2
3
5
0
2
0
1
0
1
2
0
0
1
1
1
0
0
0
1
0
4
0
0
0
1
0
5
0
1
0
0
0
1
2
3
2
0
1
0
4
0
1
1
0
1
0
1
0
0
0
1
2
0
2
2
1
1
2
1
2
0
0
0
0
2
0
0
2
0
2
2
2
1
0
0
0
0
0
1
0
0
1
0
1
0
0
2
0
1
0
0
2
2
1
2
0
0
0
0
1
1
0
2
0
1
0
0
0
0
1
1
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
1
1
1
1
1
2
0
1
1
0
2
0
0
0
1
0
1
0
1
4
0
1
1
1
0
0
2
0
0
2
0
3
0
1
2
0
2
3
0
0
1
0
1
0
2
2
0
1
1
0
0
0
1
0
0
0
2
0
1
2
0
0
0
0
2
0
1
0
1
4
2
2
0
0
0
1
1
1
1
1
2
0
0
2
1
2
0
0
10
2
0
0
2
2
0
0
0
1
2
0
2
3
2
1
2
2
0
2
0
0
1
0
0
1
0
1
3
2
1
1
0
1
0
1
0
0
1
1
0
0
0
0
2
1
0
0
0
1
0
0
1
1
0
1
1
1
2
1
0
0
0
1
0
0
3
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
1
0
0
1
2
0
0
1
1
2
2
1
0
0
1
1
0
0
0
0
2
0
2
1
3
1
1
0
0
1
1
1
2
2
1
1
2
3
1
2
0
1
2
0
0
0
0
0
0
0
1
0
0
0
1
2
2
2
1
0
2
2
2
0
0
0
1
1
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
2
0
2
0
2
1
0
0
0
0
0
2
1
1
0
0
0
1
1
1
1
1
1
0
1
0
1
0
0
1
1
0
1
0
0
1
2
0
2
0
0
3
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
2
0
1
1
1
0
0
0
0
2
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
2
1
0
2
2
1
1
0
0
1
0
1
0
1
0
1
2
0
1
2
0
0
2
1
0
1
0
0
0
2
2
1
2
1
1
0
1
2
0
0
1
0
0
0
0
0
0
2
3
0
2
1
0
0
2
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
1
1
1
1
1
0
0
1
0
0
0
1
1
0
0
1
0
1
0
0
0
1
0
0
1
2
0
0
2
0
0
1
0
2
2
0
1
0
2
0
0
0
1
2
1
1
0
1
1
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
1
0
1
1
2
5
1
1
1
1
0
2
0
0
0
0
0
2
2
0
0
0
0
0
2
0
1
0
0
3
0
0
1
1
2
0
1
1
2
0
0
1
1
0
2
1
0
1
1
0
0
0
1
2
0
2
0
1
0
1
0
0
0
2
0
1
1
0
0
0
0
0
0
0
1
1
0
1
2
2
0
1
0
0
1
1
2
2
2
2
1
0
1
0
1
0
0
0
0
0
1
1
1
2
0
0
0
0
2
0
1
0
2
1
0
0
0
0
2
0
0
0
0
3
0
1
0
0
0
2
2
0
2
0
3
1
2
2
0
0
0
1
0
0
1
0
0
1
0
0
2
1
0
0
2
0
1
0
0
0
0
0
3
0
0
1
1
0
1
1
0
1
0
2
1
0
1
0
2
1
0
0
0
0
0
3
0
1
2
1
2
0
0
0
2
0
0
0
0
1
2
2
0
0
2
0
1
2
0
1
0
1
1
0
1
1
0
0
0
0
1
1
2
1
1
2
0
0
0
2
2
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
2
0
2
1
0
2
2
0
2
1
1
0
1
0
2
0
1
1
0
0
1
0
1
0
2
0
0
0
1
2
0
0
0
0
2
0
0
0
0
3
0
2
0
2
1
0
1
2
1
2
0
0
1
1
0
0
2
2
0
0
1
0
0
1
0
0
2
2
0
1
0
1
1
0
1
1
1
2
0
2
0
0
1
2
0
2
0
0
0
1
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
2
1
1
0
0
0
1
0
0
1
0
1
1
2
1
0
0
2
0
2
0
0
0
0
0
1
1
0
1
2
2
0
0
0
0
0
0
1
1
0
1
1
0
2
2
2
2
1
2
0
2
0
1
1
1
2
0
2
1
1
2
0
0
2
2
1
0
0
2
0
1
4
0
1
1
0
0
2
2
0
2
0
1
0
1
0
5
0
2
0
0
2
0
0
0
0
1
0
2
2
0
1
1
2
2
1
1
0
0
0
2
0
1
0
0
1
0
0
0
3
2
0
0
0
0
0
0
1
0
2
2
0
2
0
0
1
3
1
0
1
0
1
2
1
0
2
3
2
0
0
0
0
1
1
1
2
0
0
2
0
2
1
0
0
0
2
0
1
0
1
1
2
1
1
2
2
0
0
1
1
0
2
2
1
1
1
0
2
1
0
0
1
0
0
0
1
2
0
0
0
2
0
0
1
2
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
3
0
0
3
0
2
2
0
1
1
1
0
1
0
0
0
0
1
3
0
1
1
0
1
0
1
2
0
0
0
2
0
1
0
0
0
1
1
2
0
0
0
1
1
5
0
0
0
1
2
0
0
1
1
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
2
0
1
1
0
2
0
2
2
1
1
2
0
0
1
0
2
1
0
0
0
1
0
1
0
0
3
0
0
2
0
1
0
1
0
2
1
1
2
0
0
0
0
1
0
1
1
1
0
2
0
1
1
1
2
0
0
0
1
2
1
0
0
0
2
0
4
1
0
1
0
1
0
2
1
1
0
0
1
0
1
0
0
1
0
0
1
1
2
0
2
1
0
0
0
3
0
0
0
0
0
1
1
0
0
0
0
1
2
1
0
0
1
0
1
1
2
0
2
1
1
1
1
0
2
1
1
0
0
0
1
2
0
0
1
1
0
0
2
0
2
1
0
1
0
1
0
0
2
0
1
0
0
2
1
2
0
0
0
0
1
0
0
2
0
0
1
0
0
1
0
0
0
0
2
2
0
2
2
0
0
0
2
0
1
1
1
1
0
0
2
0
0
0
2
0
2
1
0
1
1
0
1
0
0
0
1
0
0
6
0
2
0
0
2
1
0
2
0
0
1
1
2
1
1
0
1
1
1
2
5
0
2
1
1
0
2
1
2
0
0
1
0
1
1
0
2
1
1
1
0
1
1
2
0
0
1
0
0
0
0
0
1
1
0
1
1
0
1
0
0
0
1
0
1
1
2
0
0
2
1
0
0
0
2
0
1
1
1
0
1
0
0
0
0
1
1
0
2
3
0
2
3
1
1
1
2
0
1
4
0
1
0
1
0
0
1
0
1
0
0
0
2
0
0
2
0
0
0
1
0
1
1
1
1
1
2
0
0
0
0
1
0
1
0
1
0
2
0
2
0
0
0
0
1
0
0
2
0
0
3
1
0
0
1
0
0
0
2
2
0
1
0
0
1
1
0
2
2
0
3
0
0
2
2
0
0
0
0
1
0
1
0
2
0
0
0
1
1
1
0
2
2
0
0
0
0
0
0
3
2
0
0
1
1
0
0
0
0
1
2
0
2
0
1
1
1
0
1
0
1
0
0
1
0
2
3
0
1
1
2
0
0
2
0
0
0
0
2
0
2
1
1
1
0
1
0
1
0
1
4
0
0
0
1
2
0
1
0
0
1
0
2
2
1
0
2
0
0
2
0
0
1
0
0
0
1
0
2
0
1
1
1
0
2
1
2
2
2
3
0
1
0
0
0
1
0
0
2
1
0
2
0
2
1
0
2
0
0
1
1
0
2
0
1
0
0
1
1
0
1
1
0
2
2
1
1
1
1
1
0
0
0
0
0
3
0
2
1
0
0
2
2
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
3
0
2
0
0
1
0
0
2
0
2
1
1
7
1
1
0
0
2
0
0
1
0
2
0
0
2
0
0
2
0
0
1
2
0
2
2
1
0
0
0
3
1
2
1
0
2
0
0
2
0
1
2
0
0
0
0
2
0
2
0
2
2
0
1
1
0
1
0
2
0
0
0
0
0
2
1
2
2
0
1
0
0
2
1
0
0
0
1
2
0
1
2
0
3
2
2
1
0
0
0
0
1
4
0
0
4
2
1
0
1
1
1
0
0
0
0
1
0
0
2
2
4
0
0
2
0
0
0
0
0
1
0
1
0
0
2
0
2
1
3
0
0
1
0
0
0
0
0
1
2
1
1
1
0
0
1
0
1
0
0
1
2
0
0
0
0
1
0
0
1
0
1
1
1
0
2
0
2
1
0
1
0
0
1
2
0
0
0
1
2
2
0
0
0
0
0
1
1
0
0
1
0
1
0
2
0
1
0
1
2
2
1
0
2
0
1
0
1
0
0
3
3
0
1
1
1
0
0
1
1
2
0
0
3
1
0
1
0
0
0
1
0
0
1
0
1
0
0
1
2
0
0
0
2
2
0
1
0
0
1
0
2
1
2
1
2
0
1
0
1
0
1
0
2
0
0
1
1
0
2
0
0
2
2
0
2
0
1
2
1
2
1
0
2
0
0
2
0
0
0
2
2
1
1
0
2
0
1
2
1
1
0
2
0
2
0
0
3
1
0
1
0
2
2
0
2
1
0
0
1
0
2
0
0
0
1
1
0
1
1
0
0
1
1
0
2
1
0
0
2
2
2
0
0
1
0
1
1
1
0
0
0
2
1
0
1
2
1
0
0
1
1
0
0
2
2
2
0
2
0
3
0
2
0
1
1
0
0
2
0
1
0
0
0
1
0
2
2
0
0
1
0
1
1
2
0
1
1
1
0
0
0
0
2
2
1
0
0
1
0
0
1
1
1
0
0
0
1
1
0
0
1
0
0
1
1
0
0
0
0
0
2
0
0
0
1
1
1
0
0
0
0
2
2
0
3
0
0
1
1
0
0
1
2
0
0
0
0
0
0
2
0
2
2
1
0
0
0
1
1
0
1
0
1
0
0
2
1
2
1
0
2
0
0
0
0
2
0
0
1
3
2
0
1
2
0
0
2
0
0
1
0
1
2
0
2
1
0
0
1
0
0
1
1
3
0
0
0
0
0
1
1
3
1
0
0
1
0
0
1
2
1
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
1
0
0
1
2
2
0
1
1
0
1
2
0
0
1
1
0
0
0
1
2
0
1
0
2
0
2
2
0
0
1
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
2
0
0
1
1
0
4
1
0
1
1
2
0
0
2
1
0
0
0
0
0
2
1
0
1
1
1
0
0
0
0
1
1
2
2
1
0
0
1
0
0
2
1
0
0
0
0
1
1
1
0
1
0
0
1
1
1
2
2
0
2
0
0
0
0
0
0
1
0
0
1
2
0
0
1
2
0
2
0
0
0
1
1
1
2
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
2
1
0
0
0
0
1
0
2
0
0
1
1
2
0
1
0
0
0
0
1
1
0
2
0
1
0
1
0
2
1
0
2
0
1
1
2
0
0
0
1
0
0
0
1
1
0
3
0
1
1
1
0
0
0
2
2
0
0
0
0
2
1
0
2
0
1
1
1
2
1
0
0
0
0
0
1
0
2
5
0
0
1
1
1
0
0
2
1
0
1
0
1
2
0
1
1
0
1
0
0
1
1
0
0
0
1
0
0
0
0
1
2
0
0
1
1
1
0
0
1
0
0
1
0
0
0
0
2
1
1
0
0
1
0
0
0
2
1
0
0
1
0
2
2
0
1
3
1
0
1
2
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
2
1
2
2
1
1
1
0
1
0
2
1
1
1
0
0
2
2
0
0
0
2
0
0
1
0
1
0
1
1
1
6
0
0
1
2
1
1
0
1
1
2
0
0
7
0
1
0
0
0
2
1
1
0
0
0
0
1
0
2
0
0
1
1
1
0
1
1
0
0
2
0
1
1
2
0
2
1
0
0
1
0
0
0
2
0
0
0
2
3
0
0
2
1
1
0
2
4
0
2
0
0
0
0
1
0
0
0
0
0
0
3
0
1
4
0
2
2
0
2
0
0
0
2
0
1
0
1
0
1
2
1
0
0
1
0
0
0
2
1
0
1
2
1
1
2
0
0
1
1
1
0
0
0
2
2
3
2
0
1
1
0
0
2
0
0
2
0
0
0
0
3
0
1
0
1
0
0
0
0
2
0
2
0
0
2
1
1
0
1
2
2
1
1
1
1
0
0
2
0
0
0
0
1
0
0
1
1
1
1
0
0
1
2
0
2
4
1
0
0
0
1
2
1
0
0
0
0
2
2
1
0
2
1
0
2
0
0
2
1
0
1
0
2
2
1
1
1
1
2
0
0
0
1
0
2
1
1
0
0
0
1
2
0
0
1
2
0
1
0
0
2
0
1
0
2
0
0
2
0
0
2
0
2
0
2
2
0
0
2
2
1
1
0
0
0
0
0
0
1
0
2
0
2
2
0
0
1
0
0
0
2
1
0
0
0
2
1
0
0
2
0
1
0
0
0
0
1
2
1
0
0
1
1
1
0
1
2
1
1
1
0
1
0
2
1
0
2
0
1
0
0
0
2
0
0
0
0
1
2
1
0
2
2
0
0
0
1
0
0
2
1
2
1
0
1
1
1
2
1
1
4
0
2
0
1
1
2
1
1
2
0
1
2
0
1
1
0
1
1
2
2
0
1
4
0
1
0
3
0
0
2
0
1
2
1
2
1
1
0
0
0
0
0
1
2
0
0
1
0
3
0
0
2
0
0
1
0
0
1
1
1
0
2
2
0
1
1
2
1
2
1
0
0
2
0
0
0
1
0
0
1
2
0
0
0
1
2
2
0
0
1
0
2
0
2
1
1
0
2
0
0
1
2
1
1
0
0
1
0
0
1
0
1
0
2
0
1
0
1
0
0
0
1
0
1
1
0
0
0
1
1
1
1
2
1
0
1
0
1
2
1
0
2
0
1
1
0
0
1
1
2
1
1
0
0
0
1
0
0
2
3
0
2
2
1
1
0
0
2
1
0
0
1
2
0
0
2
0
1
0
1
0
0
0
1
0
2
1
0
0
0
0
1
0
2
2
2
0
0
0
2
1
0
1
2
0
0
2
2
0
0
0
2
1
0
1
0
0
0
0
1
0
1
0
0
0
0
1
1
1
0
0
2
1
0
1
1
1
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
1
1
0
0
0
0
0
2
1
0
1
0
0
0
2
1
6
1
1
1
0
1
0
1
1
2
1
0
1
1
1
5
0
1
2
0
1
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
2
1
2
1
0
2
1
1
1
1
0
1
1
0
0
0
1
1
0
1
0
2
2
1
1
1
0
0
0
2
5
1
0
0
0
1
1
2
0
0
0
1
2
0
2
0
1
2
0
1
0
0
0
1
2
0
3
1
2
0
1
0
1
2
1
1
0
0
1
2
0
2
0
1
1
0
0
0
1
2
1
1
0
0
1
0
0
2
2
0
2
0
1
2
1
0
0
0
1
0
1
2
0
1
0
0
2
0
0
0
1
1
0
0
1
0
1
0
2
0
0
2
1
0
2
0
0
2
1
0
0
2
2
0
3
0
0
0
0
2
0
0
0
0
0
3
1
0
0
0
2
1
2
0
0
2
0
0
0
0
0
1
2
2
0
0
0
0
0
0
2
0
0
2
0
2
0
1
0
1
2
1
0
0
1
0
0
2
0
2
0
1
1
0
0
1
3
1
0
0
2
0
2
2
1
0
0
0
1
1
2
0
0
0
2
2
0
0
0
0
1
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
6
0
0
0
0
1
2
0
1
0
0
2
0
0
0
2
1
2
0
1
2
0
1
0
1
0
2
2
0
2
1
1
1
1
0
2
0
0
2
0
3
0
0
0
0
3
0
0
0
0
1
1
0
0
1
2
1
2
2
0
0
1
1
0
0
1
0
2
0
1
0
0
1
2
1
0
2
0
0
1
2
0
2
0
1
1
1
1
2
0
2
2
0
0
0
0
2
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
1
0
0
0
0
0
1
0
1
0
2
2
0
0
0
1
1
1
0
0
0
1
2
0
1
0
0
1
0
1
1
2
1
2
0
2
0
1
0
2
1
1
1
0
0
1
0
0
0
0
0
1
1
0
1
1
0
0
1
2
0
1
2
0
2
1
0
2
1
0
0
2
1
1
1
0
1
0
0
0
0
1
0
1
0
1
0
1
0
1
0
2
2
0
2
1
2
0
0
2
0
0
2
1
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
4
0
0
0
0
1
0
1
1
1
0
2
0
0
6
0
0
0
0
2
0
1
0
0
3
2
1
1
2
0
2
0
0
1
1
1
2
2
0
0
2
1
1
1
0
1
1
0
0
2
0
0
0
0
0
1
0
0
0
2
2
0
1
1
1
0
0
2
0
0
1
2
1
2
2
2
1
0
1
0
0
1
0
1
1
1
2
0
1
2
0
1
0
0
0
0
1
0
0
0
2
2
0
0
1
2
1
1
1
2
0
0
0
0
1
1
3
0
0
2
0
1
0
1
1
0
1
1
0
3
1
1
2
0
0
1
2
2
0
2
0
0
0
1
0
0
0
2
1
0
0
2
2
0
0
1
0
0
0
0
2
1
1
0
0
1
0
0
1
1
0
0
0
1
0
2
2
0
0
2
1
1
1
1
0
3
0
0
2
2
4
0
1
0
1
1
0
0
0
0
1
0
1
1
0
0
0
1
2
1
0
0
0
0
0
0
1
1
1
0
0
0
1
0
2
3
0
0
0
1
0
1
1
1
2
1
2
0
2
0
1
1
0
2
1
1
2
0
2
0
2
0
0
0
2
2
1
0
2
1
0
0
0
0
0
0
0
2
0
2
0
3
1
2
2
1
0
2
1
1
0
0
2
0
2
0
2
1
0
0
0
2
0
0
2
2
1
0
2
0
3
0
1
0
0
1
1
1
0
1
0
2
2
2
2
2
1
2
1
2
1
2
2
0
2
2
0
0
1
2
1
0
2
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
2
5
0
2
1
0
1
1
1
2
0
1
1
0
0
0
1
0
0
0
2
3
1
0
2
1
0
1
0
1
0
0
1
1
2
0
2
0
3
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
1
2
1
0
0
0
2
0
0
0
0
2
1
0
0
0
2
0
1
0
0
2
1
1
0
0
0
0
0
0
0
2
1
2
1
1
2
0
1
1
1
0
0
2
0
0
0
0
1
0
0
1
2
1
0
0
0
0
0
0
2
0
0
0
0
0
1
1
1
1
3
1
0
2
2
0
0
1
0
1
2
0
1
0
0
4
0
2
0
0
1
1
0
0
1
0
2
1
0
0
0
2
1
1
1
0
0
0
0
0
0
0
0
2
3
0
2
3
2
1
0
1
1
0
1
0
0
1
1
0
0
0
2
0
0
1
1
0
1
2
0
0
1
0
1
0
2
0
1
2
0
0
0
2
0
0
2
0
1
0
1
2
0
2
2
1
2
0
1
0
2
1
0
1
2
0
2
2
0
0
0
0
2
0
0
1
1
0
0
2
0
2
0
1
0
1
3
2
2
0
1
0
2
0
0
0
0
0
2
0
1
0
2
1
1
2
1
2
0
2
1
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
2
2
1
0
2
1
2
2
0
1
0
1
2
0
1
2
0
0
0
1
3
0
1
2
2
0
1
1
1
1
1
0
2
2
0
0
0
0
0
2
0
0
3
2
2
1
1
0
1
0
1
2
1
0
0
0
0
0
1
0
2
0
0
0
1
1
0
3
1
0
0
2
0
1
0
2
1
2
0
0
0
0
2
0
0
0
1
1
2
0
3
2
2
0
1
2
0
3
0
2
0
1
0
0
0
0
1
2
1
2
0
0
0
2
0
0
1
0
0
2
0
0
1
0
0
0
2
0
0
0
0
1
2
1
0
2
0
2
2
1
2
0
0
1
2
0
1
0
0
0
2
1
2
0
0
0
1
0
0
2
0
1
0
0
1
1
2
0
0
0
1
1
0
2
0
0
1
0
0
0
0
1
0
2
0
2
0
1
1
0
0
1
1
1
2
1
1
0
2
0
1
0
2
0
1
1
0
0
1
0
0
0
0
1
2
1
2
0
0
0
1
1
0
1
2
0
1
1
0
0
1
0
0
0
0
2
0
0
2
0
1
0
2
1
1
0
0
0
0
0
0
0
2
0
2
1
0
2
0
1
0
1
0
0
1
2
0
0
0
1
2
2
2
0
0
0
0
1
3
0
0
0
2
1
0
2
1
0
1
2
1
1
1
1
0
1
1
1
0
0
0
0
0
1
0
1
1
2
0
1
1
1
0
2
0
1
1
1
2
0
0
1
0
0
1
1
1
0
1
0
1
1
2
0
2
0
0
0
3
2
0
2
0
2
0
0
0
1
2
0
3
0
1
2
2
0
1
0
1
0
2
0
0
0
2
0
1
1
2
0
0
0
0
1
0
2
0
1
0
2
0
2
1
0
1
1
1
2
0
3
1
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
1
0
1
0
3
1
1
1
1
1
2
1
3
1
0
0
0
1
0
1
3
0
0
1
0
1
0
0
2
0
1
0
0
1
0
1
0
1
0
0
1
1
0
0
1
1
0
2
0
0
0
0
0
0
1
0
0
1
3
2
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
3
1
0
0
0
1
1
1
0
0
0
2
0
0
2
0
0
0
1
2
0
3
1
0
0
3
0
0
0
0
0
0
0
0
2
2
0
0
0
2
2
0
1
0
0
1
2
2
1
1
0
0
1
1
2
0
3
0
0
0
1
1
1
1
0
2
0
0
0
0
2
1
1
2
0
0
2
1
0
0
0
0
2
0
1
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
1
1
1
0
0
0
0
1
0
2
1
1
1
2
0
1
0
1
1
0
0
2
1
1
0
2
0
0
1
0
0
0
1
0
1
1
1
0
0
2
0
2
0
2
0
0
0
1
0
1
0
0
0
1
1
1
2
0
2
0
0
1
2
0
2
2
0
1
1
0
2
2
0
1
2
1
0
2
3
2
0
1
1
1
0
0
2
0
0
2
1
1
1
0
2
0
1
1
0
0
2
2
2
2
0
0
2
1
2
0
1
1
0
0
0
1
2
1
1
0
0
2
0
0
1
0
1
0
2
0
3
1
0
0
0
1
0
2
0
0
2
0
2
0
0
2
2
1
1
2
2
0
0
0
2
1
1
0
0
0
1
0
1
0
2
0
1
1
1
1
1
0
1
2
0
0
0
0
0
1
1
1
1
2
0
1
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
1
2
1
0
0
0
0
1
0
1
1
1
0
0
0
0
1
1
0
1
1
0
0
1
0
2
4
0
1
0
0
0
0
2
0
1
0
1
0
1
1
2
0
0
1
1
1
2
1
0
1
0
2
2
0
0
0
2
2
1
0
2
0
0
1
0
1
1
0
1
0
0
2
2
0
0
0
1
1
0
1
3
1
2
0
0
2
1
0
0
0
0
1
2
0
0
1
0
1
0
1
2
1
0
1
2
1
0
1
1
0
1
1
1
1
0
1
0
1
0
1
1
0
0
1
0
0
0
1
2
0
1
0
1
0
0
0
1
0
0
1
1
0
1
3
0
1
2
0
4
0
0
0
2
2
1
1
1
1
1
0
1
1
1
4
1
1
1
0
0
3
1
0
1
1
1
0
1
0
0
0
0
1
1
0
1
1
0
1
0
0
2
0
1
1
0
2
0
0
1
0
0
1
0
0
1
2
1
0
1
2
2
2
2
0
1
0
2
0
0
0
1
2
0
0
0
0
0
0
0
1
0
2
2
1
1
0
1
2
1
0
0
0
0
1
0
2
0
4
1
1
0
2
2
0
2
0
0
0
1
0
0
2
2
2
1
0
0
0
0
1
1
0
1
1
2
0
0
2
2
0
0
2
0
2
2
0
2
0
0
1
1
0
1
2
2
0
0
0
0
3
0
1
1
0
2
2
0
0
2
0
0
0
2
1
0
0
0
0
1
0
0
0
0
2
0
0
0
2
1
2
0
2
2
0
0
2
1
1
1
2
1
0
2
2
1
0
2
0
2
2
0
2
0
0
0
2
0
0
1
2
0
2
0
2
0
0
1
0
2
0
0
1
2
1
1
0
0
0
1
0
0
2
1
0
1
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
2
1
0
0
0
2
0
0
0
1
0
0
1
0
0
1
2
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
2
0
1
0
0
2
2
1
0
2
1
2
1
0
1
0
0
1
2
0
1
0
2
0
0
0
0
3
1
1
2
2
2
0
0
0
1
0
0
1
0
1
1
0
0
0
0
2
2
1
0
2
2
1
1
0
1
0
2
0
1
2
0
1
0
0
2
1
0
2
2
1
1
0
2
1
1
0
0
6
0
0
1
0
0
2
0
0
0
2
2
0
1
0
0
0
0
0
1
2
0
1
1
6
0
0
0
1
1
0
0
2
0
0
1
2
2
1
0
0
1
1
0
1
1
1
0
0
0
0
2
1
0
1
1
0
0
0
0
0
0
3
0
0
4
2
1
2
0
1
0
0
0
1
1
1
0
2
2
2
0
0
1
0
2
2
0
0
0
0
0
3
0
0
1
0
2
0
2
2
0
0
1
1
2
0
1
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
2
1
1
1
1
0
0
0
2
1
0
1
0
1
0
0
1
0
2
2
3
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
2
1
1
0
0
1
0
0
1
1
1
2
2
0
1
0
2
0
0
2
1
2
1
1
0
0
0
2
2
1
0
0
0
2
0
2
2
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
1
0
0
2
1
2
7
0
0
0
0
0
0
0
0
0
0
1
1
0
2
2
2
1
1
1
2
2
1
0
0
2
2
0
1
1
2
0
2
0
0
2
0
2
2
1
2
0
0
0
0
1
0
2
0
2
1
0
0
0
1
0
1
0
0
2
0
2
0
0
0
0
1
2
0
2
0
2
0
2
2
2
0
0
1
0
0
2
1
0
1
0
1
0
0
1
1
0
2
1
1
1
2
1
0
2
0
0
0
0
0
0
0
2
1
0
0
1
0
1
0
2
1
0
2
0
0
2
1
1
1
0
2
2
0
2
0
0
2
0
0
0
1
0
1
2
0
1
0
0
2
0
1
2
0
1
1
2
0
1
1
0
2
1
0
0
0
0
0
0
2
2
0
1
0
1
0
1
0
0
0
0
2
2
2
2
2
0
2
0
0
1
1
0
0
0
0
1
1
1
0
0
1
1
1
1
2
1
0
2
1
1
0
1
0
2
0
0
0
1
0
1
1
1
1
2
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
1
0
1
0
0
1
0
0
2
1
0
0
0
1
0
1
1
1
0
0
0
1
2
2
2
0
1
1
2
0
2
2
1
0
0
2
0
0
1
0
0
1
1
0
2
0
0
1
2
0
1
0
1
0
1
0
0
0
1
0
0
0
2
0
2
0
1
2
0
1
0
0
0
0
0
0
0
2
2
2
0
0
0
0
3
0
0
1
2
0
0
2
1
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
2
0
2
2
0
2
1
1
2
0
1
0
0
0
2
0
0
0
2
1
1
1
2
0
2
0
0
0
0
1
1
1
0
0
2
1
1
0
3
2
2
0
1
0
1
0
0
0
1
2
0
0
0
0
2
0
2
0
0
0
0
0
0
1
1
1
1
1
0
0
1
0
0
6
2
0
0
1
0
0
0
0
0
2
0
2
0
0
1
0
2
0
2
2
0
1
0
1
0
1
0
2
0
3
0
0
2
0
1
2
2
0
1
0
2
0
2
1
1
0
2
0
1
0
0
0
1
1
0
0
0
0
1
0
1
0
1
2
1
2
0
2
1
0
2
2
1
1
0
1
1
2
0
1
2
0
0
2
0
0
1
2
0
0
2
0
1
0
3
0
0
0
0
0
0
2
0
1
1
0
1
2
0
0
0
0
0
0
0
1
0
1
2
2
1
0
0
0
0
1
2
1
0
2
1
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
1
0
0
2
0
0
1
0
2
1
2
1
2
1
0
1
2
2
0
2
0
0
4
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
2
0
0
2
1
1
1
0
2
0
0
0
1
0
2
2
1
1
0
0
0
1
3
0
1
2
0
0
1
1
0
2
1
0
0
0
0
1
1
0
2
1
0
2
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
2
1
0
1
0
0
0
1
0
0
0
0
1
1
0
1
0
0
2
1
1
0
2
0
0
0
0
1
2
1
0
1
1
0
2
2
0
0
1
0
2
0
1
2
1
0
2
2
0
0
2
1
0
0
1
0
0
0
0
0
0
0
2
0
2
0
2
2
0
0
0
0
0
0
2
1
1
1
0
0
0
3
2
2
0
1
2
0
1
3
1
0
1
0
1
0
0
1
0
1
1
1
2
0
0
0
1
0
0
3
0
3
3
1
2
2
2
1
0
0
2
0
1
1
1
0
0
1
1
1
0
0
0
0
0
1
2
0
0
2
0
1
1
0
1
0
2
1
0
0
1
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
1
2
0
1
2
1
0
0
3
1
0
2
1
1
1
1
0
1
1
0
0
0
1
1
0
1
0
0
1
1
0
0
0
1
1
0
1
0
0
0
2
1
2
1
2
1
0
0
2
0
0
1
1
2
1
2
0
0
0
2
2
1
1
0
2
1
0
0
2
0
1
1
0
0
0
2
0
2
0
0
1
2
1
0
0
1
0
2
1
1
0
2
0
1
0
2
0
0
0
3
0
1
0
2
0
1
2
1
0
0
1
0
0
2
0
1
0
1
1
0
0
0
0
0
0
0
2
1
1
4
1
0
1
1
0
1
0
1
2
0
0
0
2
1
0
1
0
0
0
0
2
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
1
0
2
2
0
0
2
2
0
1
2
0
0
0
2
0
2
0
1
0
1
1
0
1
0
1
0
0
3
0
0
0
0
0
0
0
0
2
0
1
2
0
1
0
1
0
0
0
0
1
0
0
1
0
3
2
2
0
2
1
1
1
0
1
0
0
0
0
0
1
1
0
2
0
1
0
0
0
2
0
1
1
0
2
0
0
0
1
0
1
1
0
0
0
0
1
0
2
1
0
2
0
1
2
0
1
0
1
0
0
2
0
1
2
1
0
1
0
0
0
2
2
1
0
0
1
1
0
0
1
0
1
0
1
0
0
0
0
2
0
0
0
1
1
0
1
2
0
0
1
2
2
1
1
1
0
1
2
4
0
0
1
2
0
0
0
0
1
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
2
2
0
1
2
2
2
1
0
0
0
2
1
2
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
1
0
0
3
2
0
1
3
2
0
0
2
1
2
0
2
2
0
1
0
0
1
0
1
1
0
1
0
0
2
1
1
1
2
0
1
0
0
0
0
2
1
0
0
0
3
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
1
0
0
1
0
0
3
2
0
2
2
0
1
1
1
1
1
0
0
0
0
0
1
0
0
0
0
1
1
2
0
2
0
0
2
1
0
2
0
1
1
0
0
0
0
2
2
1
0
0
0
0
1
0
0
1
0
0
0
2
1
0
1
1
0
0
1
0
3
0
1
1
1
0
0
1
0
2
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
1
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
2
0
0
0
1
1
0
2
1
1
0
0
0
2
2
1
1
2
2
0
0
0
1
2
0
0
0
0
3
0
0
2
0
2
0
1
0
0
0
0
0
2
0
0
0
1
1
0
0
1
0
2
0
0
1
0
0
2
1
2
1
0
0
0
0
0
0
0
0
1
0
5
0
0
0
2
0
1
0
3
0
0
0
1
0
1
2
0
1
1
1
0
2
1
0
2
2
0
3
0
1
2
0
1
0
2
2
1
1
0
1
1
2
0
0
0
0
1
0
1
0
2
1
0
1
2
2
0
1
0
1
1
1
0
2
2
2
2
1
0
1
2
2
2
0
2
1
1
0
1
0
1
0
0
0
0
0
0
2
2
0
2
2
0
0
2
0
0
2
0
1
1
0
1
2
1
0
0
0
1
1
0
0
0
1
0
2
2
2
1
0
0
0
1
0
0
1
0
2
2
0
0
1
0
0
0
2
1
1
1
1
2
0
1
1
3
0
1
0
0
0
2
0
0
0
2
2
1
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
2
0
2
1
1
0
1
0
1
2
2
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
1
2
0
1
0
4
0
0
0
0
0
1
2
0
1
1
0
1
2
0
2
0
0
0
0
1
0
0
0
1
2
0
0
1
1
0
2
2
2
2
0
0
0
2
1
0
1
1
2
0
0
0
0
2
1
0
1
0
1
2
0
0
0
0
0
0
2
1
2
3
2
1
1
0
0
0
0
2
0
0
2
1
0
0
1
2
2
0
0
2
0
0
1
0
1
0
2
0
0
1
0
2
2
0
1
0
0
1
0
2
2
0
0
0
1
2
0
1
0
2
1
0
2
2
1
3
1
0
0
2
2
0
2
2
2
1
2
2
1
0
2
2
0
3
0
0
0
0
1
0
2
1
0
1
3
0
0
0
1
1
0
2
0
0
0
1
2
1
1
0
1
1
0
0
2
0
1
1
0
1
1
0
0
0
0
0
5
2
0
0
2
0
0
0
0
2
2
0
0
1
0
1
2
1
0
0
2
4
0
0
2
0
1
0
1
1
0
0
1
0
1
2
2
0
1
0
0
1
2
1
0
2
2
2
0
0
2
0
1
2
0
1
0
0
0
2
0
2
0
0
1
0
0
0
0
2
2
0
0
2
0
0
0
0
0
2
1
2
0
0
0
1
0
0
1
2
0
0
2
0
0
1
1
0
1
1
0
1
2
0
0
2
1
1
0
0
2
2
0
2
2
0
2
0
2
0
0
0
0
0
0
0
1
2
1
0
0
2
1
1
0
0
0
0
1
1
0
0
1
0
0
0
0
1
2
1
0
0
2
0
0
1
0
0
0
1
0
1
1
2
2
0
0
1
1
0
1
0
1
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
3
1
0
0
0
0
0
0
1
0
0
2
0
1
2
0
0
1
0
0
0
1
0
1
0
0
1
1
1
2
0
1
0
0
1
0
0
0
2
1
1
0
0
0
0
2
1
1
0
1
1
1
0
1
0
1
1
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
2
2
0
2
0
0
2
0
0
0
1
1
2
0
0
1
4
1
0
0
2
1
1
1
0
0
0
1
0
0
0
0
1
0
2
1
0
0
1
0
0
0
0
0
1
0
0
1
1
1
2
0
0
2
0
2
2
2
2
0
1
0
2
2
0
0
1
2
0
0
0
1
2
1
0
2
0
0
2
0
0
0
0
1
1
0
1
0
1
2
0
1
0
1
1
0
1
0
2
0
2
0
0
2
2
0
2
1
0
0
0
0
0
2
0
0
1
2
3
2
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
2
2
1
1
4
0
1
1
0
1
0
0
1
1
2
0
0
0
0
0
0
3
0
1
0
0
1
1
1
0
0
0
2
0
2
2
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
2
1
0
2
0
0
0
0
1
0
2
0
0
0
0
2
2
1
1
0
0
0
0
1
1
0
1
1
0
2
0
1
2
1
1
1
0
1
1
2
0
1
1
0
0
0
1
0
0
0
0
0
1
1
0
2
2
0
2
0
0
2
1
0
0
1
1
2
0
1
0
0
0
0
1
0
0
2
1
1
1
2
0
0
0
1
0
3
1
2
0
2
2
1
0
1
0
0
2
1
0
2
0
0
0
2
0
2
0
1
2
2
1
0
1
1
1
0
1
0
4
1
1
0
1
1
2
0
0
0
0
1
0
0
2
0
3
0
1
0
2
0
2
1
2
0
0
0
0
0
2
0
0
0
1
0
2
1
2
1
0
2
1
0
0
2
1
2
1
0
1
1
0
0
0
0
2
2
1
1
0
2
1
0
2
0
0
0
0
1
2
0
1
2
0
2
0
0
2
3
0
2
0
0
0
0
0
1
0
1
1
0
0
0
1
2
0
2
1
2
0
1
0
1
0
1
2
0
2
1
0
1
0
2
0
1
0
2
1
0
2
0
1
1
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
1
2
1
2
2
0
2
0
1
0
0
1
2
0
0
0
2
0
0
0
0
2
1
2
0
0
0
2
1
0
1
2
1
1
2
1
0
0
0
0
0
3
1
1
1
1
0
0
2
3
2
0
1
1
0
2
2
0
1
0
1
1
0
1
0
0
0
0
0
1
2
0
0
0
0
1
0
3
1
1
0
0
0
2
0
0
0
0
1
1
0
2
2
0
1
0
1
0
1
0
0
0
1
0
0
2
1
0
0
2
0
1
0
0
2
0
0
0
1
1
0
0
0
0
1
0
0
0
1
1
0
0
2
0
1
0
0
0
0
0
1
1
2
1
1
1
0
1
0
1
1
0
0
0
2
0
1
2
0
0
1
0
0
1
1
2
0
2
0
1
2
1
1
2
0
1
0
1
1
0
2
1
3
1
2
1
4
2
0
1
0
0
1
2
1
0
0
1
0
0
0
2
1
1
1
1
2
0
0
1
1
0
0
1
1
0
0
1
0
0
1
1
2
0
0
0
0
0
0
1
1
2
0
1
0
0
0
2
1
1
0
0
0
1
0
0
1
1
0
0
1
2
0
0
2
0
0
0
0
1
1
0
0
0
0
0
2
1
0
0
1
2
2
1
2
1
1
2
0
0
1
1
0
2
1
0
0
0
1
0
1
0
1
1
2
2
3
0
0
0
0
2
0
2
1
1
1
1
0
2
2
1
7
0
1
1
1
0
0
1
2
0
0
0
2
2
0
0
0
0
0
1
0
0
0
2
1
2
0
1
2
4
1
2
0
0
1
0
1
0
2
1
0
0
0
2
1
0
2
1
1
0
0
2
1
1
1
0
2
0
3
0
0
0
1
0
1
0
0
0
2
1
1
1
0
2
0
2
0
1
0
1
0
0
0
1
1
1
1
2
1
0
0
1
0
0
0
0
1
0
0
2
0
0
1
1
0
0
1
2
0
0
0
2
0
0
1
0
1
0
1
1
2
2
2
0
0
0
1
0
2
0
2
2
1
0
0
0
2
1
0
0
1
2
0
0
1
1
0
0
0
2
0
1
3
0
0
0
0
0
1
0
0
1
1
0
1
2
0
0
0
2
0
0
0
1
1
2
0
1
2
2
1
2
0
1
2
0
1
2
2
0
4
0
0
2
2
0
0
0
0
0
0
2
0
2
0
1
1
0
1
1
0
1
0
0
1
0
2
0
2
0
1
0
0
0
0
1
1
1
2
1
0
1
1
0
2
0
0
0
0
1
0
1
0
3
0
2
0
0
1
0
0
0
2
1
1
1
2
0
0
1
0
1
0
1
0
2
1
2
1
0
0
0
2
2
1
2
0
1
1
2
1
0
0
0
1
0
0
1
0
0
1
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
1
1
1
1
3
0
0
0
2
0
1
2
0
0
0
0
2
1
0
2
1
1
0
1
1
1
0
0
0
0
1
2
2
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
2
0
1
2
2
1
1
0
0
2
0
1
2
2
0
0
2
1
2
0
1
2
0
0
1
2
1
0
1
1
0
2
1
1
0
2
0
1
2
2
0
2
2
2
0
0
2
1
1
0
0
0
1
2
0
1
0
0
0
0
0
0
2
0
3
0
1
1
1
0
1
0
2
2
0
2
1
0
1
0
2
1
1
0
2
1
2
0
0
0
0
1
2
0
0
0
0
1
0
1
0
1
2
1
1
0
2
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
2
4
0
0
0
2
1
2
2
2
0
2
1
1
0
1
1
1
1
0
1
2
2
0
0
2
1
0
0
0
2
1
0
0
1
2
1
1
1
0
0
2
0
2
2
0
1
0
2
0
1
0
0
2
0
0
0
0
2
2
2
0
3
0
0
0
0
0
0
0
0
2
0
0
2
1
2
2
1
0
0
0
2
0
1
2
0
1
1
0
1
1
2
2
1
0
0
1
0
3
0
2
1
1
0
1
1
0
0
2
0
2
1
1
0
0
0
0
2
0
2
0
2
2
0
5
0
0
0
2
0
2
0
1
0
0
0
1
0
0
1
0
0
1
1
1
2
1
2
2
2
0
0
0
1
0
0
0
2
0
2
1
0
0
0
1
0
1
0
0
0
0
2
1
0
1
1
0
0
2
0
2
1
2
2
1
2
0
1
1
0
0
0
2
1
1
0
2
0
0
2
1
2
0
0
0
0
1
1
1
0
1
1
0
1
0
2
0
1
0
1
2
0
0
3
0
0
1
1
0
0
0
1
0
2
2
0
0
0
0
1
2
0
0
1
3
1
1
0
0
0
1
2
0
0
1
2
0
2
2
0
2
0
0
0
4
1
1
1
0
0
0
0
0
1
1
1
0
1
1
0
1
0
2
0
0
1
0
1
0
1
0
0
1
1
0
1
1
0
1
0
0
1
0
0
0
0
2
1
1
3
0
2
1
0
0
0
0
1
1
2
0
1
1
0
1
0
1
1
0
0
1
0
1
0
0
0
1
0
1
2
0
0
1
2
1
0
1
1
0
0
0
0
0
0
0
2
2
1
0
0
0
0
1
0
1
1
1
1
1
0
0
0
0
1
0
1
1
0
0
2
0
0
2
2
2
0
0
1
0
2
1
1
0
0
0
0
0
1
1
2
0
1
1
0
0
1
0
1
0
0
0
0
1
1
2
1
1
0
2
0
2
0
0
2
1
2
0
2
0
1
0
1
0
2
1
1
0
0
2
0
2
0
1
0
0
2
0
1
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
3
0
0
2
1
1
2
2
1
2
0
1
0
0
1
1
0
2
0
1
0
2
0
0
1
1
0
0
3
0
0
1
0
1
0
0
1
0
0
1
1
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
3
2
0
0
2
1
2
0
2
0
0
2
1
0
1
2
0
0
0
1
1
1
0
0
0
2
0
2
2
0
2
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
2
1
1
2
0
0
1
1
0
0
0
1
0
0
0
2
2
1
0
1
0
0
1
1
2
0
0
2
2
2
0
2
1
1
1
2
0
1
0
1
0
4
0
0
2
2
0
1
0
0
0
0
2
1
1
0
0
0
1
0
5
1
1
0
2
0
0
0
0
0
2
0
1
2
2
0
0
2
2
3
0
1
2
2
0
0
1
2
0
1
0
0
2
0
1
2
0
2
0
1
0
0
0
2
0
0
2
1
0
0
2
2
0
2
0
2
0
0
0
2
0
0
2
2
3
0
0
0
0
1
1
0
1
0
1
2
1
0
0
2
0
2
1
1
1
0
0
1
0
2
0
1
0
2
0
2
0
0
2
0
0
2
2
1
1
1
1
2
0
2
0
4
1
0
0
0
1
2
1
0
0
0
0
1
0
1
0
0
2
0
0
1
1
2
2
3
0
1
0
0
0
2
0
0
0
1
4
0
1
0
2
1
0
0
2
1
0
1
0
1
2
1
1
1
1
0
0
0
0
1
1
1
0
0
0
2
0
1
2
0
2
1
0
1
2
0
0
0
0
0
0
0
0
2
0
2
3
2
0
0
0
0
1
1
2
2
0
0
0
0
1
1
0
1
0
1
1
1
0
0
0
0
1
0
2
0
0
2
1
0
0
1
1
0
2
0
2
0
0
2
0
0
1
0
2
0
0
0
1
1
1
0
1
0
0
0
1
0
1
1
1
1
0
0
1
0
0
2
2
2
1
1
0
0
0
1
1
2
0
0
0
1
2
1
1
0
2
3
0
2
0
0
0
0
0
1
1
1
0
0
2
0
0
0
0
2
0
0
2
0
0
1
2
0
2
0
0
1
1
2
2
0
1
1
1
1
1
0
1
2
0
2
1
0
2
0
0
0
3
0
2
0
1
2
1
1
1
0
1
0
1
1
0
1
0
2
0
0
1
2
2
0
0
0
1
1
0
0
0
0
2
2
0
0
1
0
1
2
0
1
0
0
1
0
0
2
1
1
0
2
0
0
0
1
1
1
2
0
1
2
1
2
1
2
1
0
0
0
0
2
0
0
1
1
0
0
1
1
2
2
0
1
0
0
0
0
2
2
1
0
2
0
2
1
1
0
2
0
2
1
2
2
2
1
1
0
2
1
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
1
0
0
0
1
0
0
0
0
1
1
3
1
1
0
1
0
0
1
2
0
2
0
0
1
1
2
1
1
1
2
0
2
1
2
0
0
0
2
0
1
1
0
0
0
2
1
0
0
2
2
2
0
0
1
0
0
2
0
1
0
1
2
0
1
0
0
0
0
1
1
1
2
1
1
1
0
0
0
1
1
2
1
0
0
2
0
1
2
0
0
0
1
0
2
2
1
0
1
2
1
0
0
1
0
2
0
1
1
0
1
3
0
0
1
2
2
1
0
2
2
3
2
1
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
2
2
3
0
2
0
2
0
1
0
0
0
1
2
0
0
1
0
1
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
1
0
1
0
2
0
2
0
1
0
0
1
2
0
0
0
2
0
0
0
0
2
1
0
0
2
1
0
0
2
1
0
0
1
2
2
0
1
0
0
0
0
1
1
1
0
1
0
0
1
1
1
0
0
1
0
1
0
2
0
0
0
2
0
1
2
0
1
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
2
0
1
1
0
0
0
2
0
1
0
0
1
1
2
0
1
1
0
0
0
1
0
2
0
0
0
0
1
2
0
2
0
0
2
2
1
2
0
1
1
2
1
1
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
1
1
1
0
1
2
1
1
0
0
0
0
0
1
0
0
1
0
2
0
2
1
1
1
0
3
0
1
0
1
0
0
1
2
0
0
0
0
1
0
1
0
0
0
1
0
0
1
2
2
0
2
1
1
0
1
0
0
2
0
0
0
0
1
1
2
0
1
0
1
0
1
2
1
0
2
0
2
1
2
0
1
1
0
2
2
0
2
0
1
1
0
1
1
1
0
1
2
0
2
1
0
0
1
1
1
0
3
2
2
0
1
0
2
0
0
2
0
0
0
0
1
1
1
3
0
0
1
2
1
2
0
2
0
3
1
1
0
2
1
2
0
0
1
0
0
0
0
0
0
2
0
1
1
3
0
1
0
4
0
0
2
1
0
2
0
0
1
0
1
1
0
0
0
0
1
0
0
1
1
0
2
0
1
0
6
0
2
2
1
0
2
2
0
2
0
0
0
2
0
0
0
1
2
0
1
2
1
0
2
1
0
0
1
1
0
0
0
0
0
1
1
0
7
0
2
2
1
1
0
0
1
0
2
1
2
2
0
1
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
2
0
0
1
2
0
1
0
0
2
0
1
0
1
2
2
0
0
0
0
1
0
1
2
2
1
0
0
3
0
1
0
0
1
0
0
0
1
0
0
0
0
1
2
1
0
1
2
0
0
0
0
0
0
2
0
0
1
1
2
0
1
0
0
1
1
0
0
0
1
0
0
1
2
1
0
0
1
0
0
1
2
0
1
0
1
2
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
1
0
0
1
0
0
1
1
0
0
0
1
1
0
1
2
0
0
0
0
0
2
2
0
2
0
0
2
0
0
1
1
0
0
1
0
0
1
0
1
0
0
2
0
1
0
0
2
0
0
1
0
1
3
0
0
1
2
0
0
0
0
0
0
1
0
1
1
0
1
0
0
2
0
0
0
0
0
2
2
0
1
0
1
0
0
0
1
2
0
1
2
1
1
0
0
0
2
2
0
0
1
0
1
0
0
1
0
2
2
0
1
0
1
1
1
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
2
1
0
1
1
1
2
3
2
0
0
0
0
2
1
1
0
0
0
0
0
0
1
1
2
2
0
2
0
1
0
1
2
2
1
2
0
1
1
2
0
2
0
1
1
1
1
2
0
1
2
0
0
0
0
0
2
2
0
0
2
0
0
0
0
1
2
0
0
0
1
0
2
2
1
2
4
0
0
1
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
1
0
2
1
0
0
0
0
0
2
1
1
0
0
0
2
0
0
1
0
0
2
0
1
1
0
1
1
0
2
2
1
0
0
0
0
0
0
1
1
1
1
1
0
0
0
2
0
1
3
1
1
0
1
0
1
1
0
1
0
0
0
2
1
1
1
0
0
0
2
0
0
0
1
0
1
1
1
0
1
0
0
0
0
0
0
2
1
0
1
1
2
0
1
2
0
1
0
2
1
1
2
0
0
0
1
0
1
2
0
0
1
1
0
0
1
2
0
0
1
0
0
0
0
0
0
0
1
1
1
1
2
0
0
0
2
1
0
0
1
0
0
0
2
1
0
0
2
2
0
0
0
0
2
0
1
2
1
0
0
3
2
0
0
1
1
2
2
0
0
1
0
0
2
1
0
2
0
1
0
0
1
2
1
3
1
4
1
2
4
0
1
1
0
0
0
0
0
3
1
0
0
1
1
2
0
3
0
2
4
0
0
1
0
0
0
0
0
1
0
3
1
0
2
0
0
1
2
0
1
0
1
0
0
1
1
0
0
1
1
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
1
1
0
1
1
0
2
0
0
4
1
1
0
2
0
0
2
0
1
0
1
0
0
1
2
1
0
2
0
0
2
0
0
2
0
1
2
0
1
1
0
1
1
5
0
0
0
0
2
0
0
0
1
2
0
0
2
2
1
2
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
2
1
1
0
2
0
0
1
0
0
1
0
1
1
0
3
0
0
0
0
0
1
0
1
1
1
2
0
2
2
2
0
0
2
0
2
1
1
0
0
2
0
0
1
2
0
0
0
0
0
1
0
3
1
0
0
1
2
1
1
1
3
0
0
1
1
0
1
2
0
4
1
0
0
1
0
0
1
0
1
2
1
0
6
2
0
4
1
0
0
0
0
0
0
0
2
0
1
0
0
0
2
1
1
0
3
1
0
0
2
1
2
0
2
0
0
1
0
1
0
0
0
0
1
0
0
2
0
2
1
2
0
0
0
0
0
2
1
0
0
0
1
2
0
0
0
2
0
1
2
9
0
0
1
0
2
1
1
1
2
0
2
0
0
0
2
1
1
0
0
1
0
1
2
2
2
2
0
0
0
0
0
0
0
0
2
2
1
0
1
0
1
2
0
0
1
1
1
0
1
0
1
1
2
2
0
0
0
0
2
1
1
2
2
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
3
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
2
0
2
2
2
1
1
1
0
1
1
0
2
0
1
1
0
0
1
0
0
0
0
0
2
2
3
2
2
0
2
0
2
0
1
3
2
0
0
0
2
1
0
0
2
1
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
1
2
1
2
0
1
1
0
2
1
0
1
1
1
0
0
0
0
1
0
0
2
0
1
0
1
1
1
0
1
1
0
0
2
1
1
0
0
1
0
2
0
0
0
2
2
0
1
0
0
0
2
1
2
1
1
1
0
0
1
1
0
0
2
0
2
1
0
1
0
1
2
0
2
2
0
0
0
0
0
2
0
1
1
0
0
0
0
2
0
0
0
1
2
2
2
0
2
1
0
2
0
1
0
0
1
0
1
0
2
0
0
1
0
0
0
2
0
0
1
0
2
2
0
1
0
0
0
1
3
0
2
1
1
0
1
3
2
0
0
1
1
0
0
0
1
1
0
0
0
1
0
0
1
4
1
1
2
1
0
1
1
2
1
1
0
0
0
1
0
1
0
0
0
0
0
1
1
2
0
3
4
0
0
0
0
1
0
0
0
1
1
0
0
1
0
2
0
0
1
0
2
2
0
1
1
1
0
0
1
0
0
0
2
2
1
1
1
0
0
1
1
0
1
0
1
2
2
1
0
1
1
1
2
0
0
2
0
0
2
0
0
3
2
2
1
0
1
1
0
0
0
0
0
0
1
1
1
2
3
1
0
0
0
2
2
2
0
0
1
0
0
2
0
1
0
1
1
1
2
1
1
1
1
2
1
0
0
0
0
0
2
1
0
1
0
0
0
0
1
0
0
0
1
0
1
0
1
2
0
0
1
0
2
3
0
0
2
1
1
0
0
0
3
1
0
0
1
2
1
0
4
2
0
0
0
1
2
0
0
1
1
0
2
0
0
1
0
0
2
1
4
2
0
2
0
1
2
1
0
0
0
1
0
0
1
0
0
1
2
0
4
0
1
2
0
0
0
0
2
2
0
1
0
4
2
1
1
0
0
0
1
0
1
1
0
0
0
0
1
0
1
0
0
0
1
0
1
2
0
0
2
0
0
2
1
1
3
0
2
0
0
1
2
2
0
2
0
2
0
0
1
0
2
0
1
1
0
0
2
1
0
0
2
1
2
0
2
0
0
1
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
1
2
2
2
0
0
1
2
0
1
2
3
0
2
1
1
1
2
2
0
3
1
0
0
2
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
1
0
2
1
2
1
1
0
1
0
1
0
0
0
0
1
2
1
0
0
0
2
1
0
1
0
2
0
0
2
2
0
4
0
0
0
2
0
0
2
0
2
2
1
0
0
2
0
1
0
0
1
1
0
0
0
0
1
0
1
1
1
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
2
1
2
0
1
1
1
1
2
2
0
0
1
0
0
2
0
0
0
0
0
1
1
0
0
1
0
2
0
1
2
1
0
1
2
3
0
2
1
2
0
1
0
0
1
0
1
1
1
0
2
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
2
1
0
0
0
0
1
0
0
1
1
0
2
0
2
0
0
0
1
0
0
2
0
0
2
0
1
0
1
2
0
1
2
0
0
2
2
0
0
2
0
2
1
1
2
0
1
1
0
1
1
0
2
0
0
1
0
0
0
1
0
1
2
1
2
1
2
0
0
1
1
0
1
0
1
1
0
0
0
0
2
2
0
0
0
0
1
1
2
0
0
0
1
1
0
2
3
1
1
1
2
0
1
2
2
0
9
2
1
2
2
1
1
0
0
0
0
1
0
0
2
0
2
0
1
1
0
1
0
1
0
3
2
0
0
0
1
0
3
1
0
0
0
1
2
0
0
0
1
0
1
0
0
0
1
0
0
1
2
2
0
1
0
2
0
1
1
2
0
0
0
0
1
0
1
1
2
0
1
0
0
1
2
0
0
1
0
0
0
2
2
0
0
0
2
0
0
1
0
2
1
1
0
2
1
1
2
0
0
0
3
2
0
1
0
0
0
1
1
0
2
1
2
0
2
1
2
0
0
2
1
1
2
1
0
1
0
0
0
2
1
0
0
0
1
1
1
1
0
0
0
2
2
0
0
0
0
2
1
1
1
2
2
1
1
0
2
0
2
1
0
0
1
0
0
1
0
1
2
0
1
0
2
2
1
0
0
0
2
1
2
0
2
0
0
1
0
0
0
0
1
2
0
0
2
0
2
2
0
1
0
2
1
0
0
0
0
0
2
0
1
2
1
0
1
0
0
0
1
0
2
1
0
0
1
1
2
0
0
1
2
0
2
0
2
0
2
0
1
1
0
0
0
0
0
0
0
2
1
2
2
1
0
0
1
1
0
2
0
1
0
1
1
0
0
0
2
0
0
0
0
2
1
0
2
1
1
0
1
0
0
2
0
1
0
0
0
0
1
1
2
0
0
0
1
2
0
2
1
2
0
1
0
2
1
0
0
0
2
0
4
1
0
0
1
0
0
0
0
0
0
2
1
2
1
0
0
1
1
1
1
0
0
1
0
0
0
0
0
0
2
3
2
2
2
1
0
0
1
0
1
3
1
1
0
4
1
1
0
0
1
0
1
1
0
1
1
1
0
0
2
0
0
0
2
0
0
1
0
0
0
0
1
1
0
0
1
2
2
0
0
0
0
0
0
0
0
2
4
1
1
1
1
1
1
2
2
1
1
0
0
3
2
0
0
2
1
0
3
2
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
1
1
2
0
0
3
2
0
1
3
2
0
0
2
1
0
1
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
2
1
0
2
0
1
0
1
3
0
0
1
2
1
1
0
3
0
1
0
0
1
0
0
0
1
1
1
0
1
0
2
1
0
0
1
2
2
0
0
0
1
0
2
0
0
0
3
1
0
0
1
1
0
0
2
1
2
0
0
2
0
2
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
2
1
1
2
0
0
1
0
0
0
1
3
0
0
1
0
0
0
0
1
0
1
2
1
2
0
0
0
1
0
2
1
0
0
0
1
0
2
0
0
2
0
0
1
1
0
1
0
0
0
2
2
2
2
1
3
0
2
0
0
1
0
1
0
2
2
0
1
2
0
1
2
0
1
0
1
0
0
0
2
1
1
1
0
1
0
0
0
0
0
1
0
5
1
2
0
1
0
2
1
1
1
0
0
0
1
1
0
0
0
0
1
0
0
1
1
2
1
0
0
1
1
1
3
2
1
0
1
1
2
0
1
0
0
0
1
0
0
0
0
0
2
0
1
1
1
1
0
2
0
0
1
1
0
0
2
0
6
0
0
1
2
1
2
0
1
1
0
0
1
1
1
0
0
0
0
2
1
1
0
0
0
6
1
1
0
0
1
1
2
0
1
0
0
1
0
2
0
2
0
1
1
3
2
0
0
1
4
2
0
1
0
0
0
0
1
2
0
1
1
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
1
2
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
1
1
1
0
0
2
1
0
1
0
0
2
0
0
1
1
0
3
0
1
0
1
1
0
0
0
2
0
3
0
3
0
0
0
0
3
0
0
2
2
0
2
1
0
0
1
0
1
1
0
1
2
2
1
1
2
0
0
0
0
0
0
0
0
1
2
1
0
0
0
2
0
0
0
1
0
2
2
1
3
1
0
1
1
0
2
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
1
0
2
0
0
0
1
1
3
0
1
2
2
1
2
0
1
0
2
0
0
0
0
1
0
0
0
1
1
1
2
1
0
0
0
0
0
1
0
1
0
2
1
0
2
0
2
0
2
0
0
1
0
0
0
0
1
0
1
1
2
2
0
0
1
0
0
1
3
1
2
1
1
0
0
1
1
3
2
2
0
1
0
0
2
0
2
0
2
1
2
1
1
0
0
1
1
2
1
1
2
0
2
0
3
1
2
0
2
2
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
1
0
0
0
0
1
1
1
0
2
1
0
0
0
1
0
0
0
0
1
1
2
0
0
0
0
0
2
0
2
1
0
0
1
2
1
1
0
0
1
3
0
2
0
2
2
0
0
0
2
0
1
2
2
1
0
2
2
1
1
0
0
0
2
0
1
0
0
2
2
2
0
1
0
0
0
0
1
1
2
0
2
2
1
1
1
0
1
1
1
1
4
1
0
1
1
2
0
1
0
0
0
1
0
2
0
2
0
1
1
1
1
1
0
1
3
0
0
0
1
2
1
0
1
0
0
0
1
0
0
1
1
0
0
1
0
2
1
0
2
0
0
2
1
2
2
0
2
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
1
1
2
0
1
2
0
1
1
1
0
1
0
1
1
1
0
1
0
0
2
0
0
2
0
1
1
0
1
0
0
0
2
0
0
0
1
0
2
0
0
0
0
1
0
1
0
0
1
2
1
0
2
0
0
0
0
1
2
0
0
1
1
1
1
0
0
0
0
0
0
0
1
1
1
1
2
1
0
2
0
0
1
1
0
0
0
1
0
1
0
0
1
0
2
1
0
2
1
0
2
0
1
0
0
2
0
1
0
0
1
0
2
0
1
0
1
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
2
0
0
2
1
0
1
2
0
0
2
0
1
1
1
1
2
1
1
1
2
0
1
0
2
2
2
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
4
1
1
1
4
0
1
2
2
0
2
0
2
0
0
1
0
0
1
0
0
1
0
2
0
2
1
1
0
0
2
0
0
0
1
0
2
3
0
1
1
1
3
0
1
0
1
2
1
0
1
2
2
1
2
0
0
0
4
0
0
0
1
2
2
0
0
1
0
0
2
0
0
0
1
0
1
0
2
2
2
1
0
1
0
1
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
2
0
1
0
0
1
0
0
2
0
0
0
2
1
0
2
0
1
0
0
1
1
1
1
3
1
1
0
1
1
0
2
0
2
0
1
2
2
1
0
0
1
1
0
0
1
2
2
1
0
0
0
0
0
0
0
3
0
0
1
2
2
1
1
2
0
0
2
1
2
2
0
0
1
1
1
2
0
0
1
1
1
2
0
0
0
0
1
2
1
1
0
0
2
0
0
0
1
0
2
0
1
1
0
0
1
0
0
1
0
0
0
4
3
0
0
2
2
0
2
0
1
0
0
1
2
0
1
1
0
0
2
2
0
0
1
0
0
0
0
1
0
0
2
0
1
0
0
1
2
0
0
1
0
2
2
2
1
0
1
1
0
1
0
0
1
0
0
0
0
0
2
2
1
2
0
0
1
0
1
1
2
2
3
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
2
2
1
2
2
0
0
0
2
2
0
2
1
0
0
0
2
1
2
0
1
1
1
2
0
0
1
1
0
0
1
0
0
0
1
2
0
0
1
2
0
0
1
2
0
4
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
2
2
2
0
1
0
0
1
2
0
1
0
1
0
1
0
2
1
0
1
1
1
2
2
1
0
0
1
0
0
1
0
1
1
1
0
0
1
0
0
2
0
0
2
0
2
0
0
2
2
1
0
0
2
2
0
2
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
1
0
2
0
0
0
0
2
0
0
0
0
1
1
0
1
0
0
0
0
0
0
2
0
0
2
2
1
0
2
2
0
0
2
1
0
2
2
2
0
2
0
0
0
0
0
2
1
2
2
0
1
0
3
2
1
0
0
1
2
0
0
0
2
0
0
1
1
2
0
0
1
1
1
2
1
1
0
1
0
0
1
0
1
0
0
0
2
1
1
0
0
1
1
2
1
0
1
2
0
2
1
0
0
1
1
1
0
0
1
1
0
0
0
1
2
2
0
0
0
2
2
0
2
3
0
0
0
0
0
0
0
0
2
0
0
0
1
1
1
1
0
0
0
0
1
1
0
1
0
0
0
1
0
2
1
2
0
0
1
1
0
0
1
1
0
0
2
2
1
0
2
0
0
1
1
0
2
0
2
0
0
0
2
0
1
0
1
0
1
1
2
0
0
0
1
1
2
1
1
2
0
0
1
1
0
0
1
2
0
1
0
1
1
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
1
1
1
0
1
1
0
2
1
0
0
0
0
0
1
0
1
1
0
0
1
2
2
0
0
0
0
0
0
1
3
0
1
1
1
2
2
1
1
1
0
1
1
0
0
2
0
1
0
1
2
0
0
0
0
2
0
2
0
2
0
0
1
1
0
0
2
1
1
1
1
1
1
1
0
0
2
0
1
1
1
0
2
2
0
0
0
1
1
1
2
0
2
1
0
2
0
2
0
0
0
0
0
0
1
0
0
0
2
2
0
1
2
2
0
0
1
0
0
0
1
1
1
0
0
1
0
1
1
3
0
1
0
1
2
1
0
0
0
2
0
1
0
1
0
0
0
2
0
0
1
0
0
2
0
1
1
0
2
0
0
0
2
2
0
0
0
2
0
0
2
2
1
2
1
2
0
2
2
0
2
0
0
0
0
0
0
2
1
0
0
1
0
1
1
0
0
1
0
1
0
0
0
1
0
0
0
1
0
1
1
2
0
2
0
0
1
1
2
1
0
0
0
0
0
0
0
5
0
3
0
0
2
0
0
0
0
0
3
0
1
1
0
0
0
0
0
0
0
0
0
0
3
1
0
1
2
1
0
0
0
1
0
1
0
0
0
0
3
0
0
1
4
2
0
1
0
0
0
0
0
1
1
1
1
0
0
0
1
1
1
0
2
1
2
2
0
0
0
0
1
0
0
1
2
2
0
0
2
0
0
0
0
0
0
1
0
2
1
1
0
0
0
0
0
2
1
0
0
2
1
0
0
0
0
1
0
1
1
0
2
1
0
0
0
0
0
2
3
3
1
1
1
0
1
2
2
2
1
1
2
1
0
1
0
0
2
2
0
3
0
2
0
1
2
0
2
0
0
0
2
0
1
0
2
1
0
1
0
1
1
1
1
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
1
0
1
1
2
2
1
0
0
0
0
1
0
0
2
0
0
0
1
1
0
1
1
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
1
0
2
1
0
2
1
1
2
2
1
2
1
0
0
2
1
1
0
1
2
2
0
0
1
2
0
0
0
1
0
0
6
2
0
0
2
0
0
0
0
0
1
2
0
0
1
0
1
0
2
0
2
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
1
0
0
1
0
1
1
0
2
2
0
0
2
1
0
2
0
2
1
0
0
0
0
1
1
0
2
0
2
2
1
0
1
1
0
2
0
1
0
1
0
0
0
0
0
0
1
0
2
0
2
2
2
2
0
1
1
2
0
0
0
2
1
1
1
1
1
0
0
2
1
1
1
1
1
2
2
2
1
0
0
0
1
1
1
0
2
2
2
0
1
0
1
0
2
1
0
0
0
0
0
1
0
0
2
0
0
2
1
0
1
0
2
0
0
0
0
0
2
1
1
0
0
1
0
0
1
0
0
0
3
2
2
1
2
1
0
0
2
2
2
1
0
2
2
0
0
0
0
0
2
0
0
0
2
0
1
1
1
1
1
2
1
1
0
1
0
2
0
0
1
0
0
2
2
1
1
0
0
1
2
1
2
2
1
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
1
0
2
0
1
0
0
1
0
0
1
1
0
1
0
2
0
3
2
0
1
2
0
0
1
0
0
0
0
3
0
1
2
0
1
0
1
4
2
0
1
0
2
2
1
0
0
0
0
0
2
0
0
2
1
0
0
1
2
0
2
0
0
0
3
1
0
1
1
0
1
0
0
0
0
1
0
2
0
0
0
0
1
2
2
2
0
0
0
1
0
0
1
2
0
1
1
1
0
1
3
0
1
1
2
1
2
0
2
2
0
2
1
0
2
1
2
1
1
0
0
2
1
0
2
0
1
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
1
1
2
1
1
2
0
1
2
1
0
1
0
1
0
1
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
1
0
1
2
0
0
2
1
1
0
0
1
2
1
1
2
0
1
1
0
1
0
1
0
0
0
1
2
0
2
1
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
1
0
2
1
0
0
1
0
2
1
3
0
2
0
2
0
0
3
0
1
1
0
0
0
0
2
1
0
2
1
0
0
0
2
0
0
1
2
2
0
0
0
1
2
2
0
0
0
1
0
0
0
0
0
3
1
2
2
0
1
1
0
1
1
1
1
0
0
1
1
0
0
0
0
1
0
0
0
3
1
1
1
0
1
0
0
0
2
0
0
1
3
3
1
0
1
2
1
0
0
0
2
0
0
1
1
0
2
1
0
0
0
1
1
1
0
0
0
0
1
2
2
0
1
1
1
0
1
1
0
0
1
2
1
0
1
0
2
0
0
1
1
1
0
0
1
2
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
2
2
2
0
1
1
2
0
1
0
2
1
0
2
2
0
1
0
1
0
0
0
1
0
0
0
0
1
1
3
0
1
0
1
2
1
2
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
1
2
2
0
2
1
1
0
0
1
2
0
1
0
0
0
0
2
0
1
2
1
0
0
0
0
2
0
2
2
0
1
3
0
0
0
0
2
0
1
1
1
1
0
0
2
1
2
0
1
1
1
1
2
2
1
1
1
0
1
1
1
3
0
0
0
2
0
2
0
0
0
1
0
0
0
3
1
0
0
0
0
0
1
2
0
0
2
1
0
2
0
0
1
2
2
0
0
1
2
2
0
1
2
0
1
0
0
0
0
0
0
1
2
0
0
0
0
2
0
1
0
0
1
1
1
2
0
1
1
0
0
0
2
2
0
0
0
0
0
0
0
1
0
1
1
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
2
0
1
1
0
2
2
0
1
1
2
0
0
0
4
2
1
0
0
0
0
2
0
0
3
1
2
0
0
0
0
0
2
1
0
8
0
0
2
0
0
2
1
1
0
2
0
0
0
0
2
0
2
1
0
0
0
0
2
0
0
2
1
1
0
0
0
0
1
0
0
2
5
3
2
2
2
0
0
1
1
3
1
0
0
0
0
2
0
1
0
0
0
1
0
1
1
2
2
1
2
0
0
3
0
0
2
0
2
0
1
0
2
0
0
2
0
0
0
0
0
1
1
0
2
1
1
2
0
0
1
0
0
2
1
0
2
0
0
0
0
0
1
0
1
0
2
0
1
3
2
1
0
0
2
0
1
1
0
1
2
1
0
2
1
2
1
2
0
0
1
2
0
1
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
1
2
0
1
0
3
2
2
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
1
1
2
0
0
0
0
1
2
0
1
0
0
1
2
0
0
0
0
2
0
0
0
1
1
2
2
0
2
0
2
2
0
1
3
0
0
1
1
0
2
0
0
2
0
1
0
0
2
0
0
1
0
1
2
2
4
0
1
0
0
3
0
0
1
0
1
0
0
1
1
0
2
0
0
0
0
0
1
2
2
0
1
1
0
2
3
0
2
1
0
0
2
0
0
1
2
0
1
1
0
1
0
1
0
1
0
0
0
0
0
2
1
0
1
0
0
1
0
2
1
1
1
1
0
0
0
2
1
0
0
2
2
1
0
0
1
0
2
0
1
1
1
0
0
0
0
0
2
0
2
0
2
0
2
1
0
0
0
1
2
0
2
2
2
1
2
0
0
1
1
0
0
0
0
0
2
2
0
0
0
0
1
0
1
0
2
0
1
0
4
0
1
0
0
0
0
2
2
0
0
1
0
1
1
0
0
1
0
0
0
0
0
1
2
0
2
2
0
0
1
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
2
1
0
0
2
0
0
2
0
0
1
0
0
0
2
2
0
0
0
1
1
0
0
6
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
3
2
0
1
0
0
0
0
0
1
0
2
2
1
0
0
1
0
0
1
5
0
2
0
0
2
1
0
0
0
1
2
1
2
0
0
2
0
0
1
0
0
2
0
1
0
0
2
0
0
1
1
2
0
0
0
0
0
2
0
0
0
1
0
1
1
0
1
2
1
0
0
1
0
2
1
0
1
1
4
0
0
0
1
0
0
2
2
0
2
2
0
2
0
1
0
1
0
1
1
2
0
0
1
1
0
0
0
0
0
1
0
2
1
0
0
0
10
0
1
0
1
0
1
0
0
0
2
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
2
2
2
0
2
1
0
0
2
1
2
0
1
0
0
0
2
0
1
1
1
1
2
1
0
1
1
1
2
0
0
1
0
2
1
1
0
0
2
0
1
1
1
0
1
0
0
0
2
2
1
0
4
1
2
0
0
0
0
0
0
1
0
1
1
2
0
2
0
2
1
2
1
0
0
3
1
2
0
2
2
2
2
1
1
1
1
0
1
0
0
0
0
0
1
1
0
1
2
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
1
2
0
0
2
1
1
0
1
0
1
0
2
0
2
1
2
0
0
2
0
0
1
2
0
0
0
1
0
0
1
0
0
1
1
0
0
2
1
0
1
0
0
1
0
2
1
2
1
0
0
1
1
0
2
1
0
1
0
1
0
0
0
0
1
2
1
0
2
2
1
0
0
0
0
2
0
1
2
0
1
0
1
0
0
3
0
0
1
2
0
0
0
1
0
0
2
1
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
2
1
1
1
1
2
1
1
0
0
3
2
1
0
0
0
2
0
1
2
0
0
0
0
1
2
0
2
0
0
0
1
2
0
3
0
0
0
2
0
0
0
2
0
2
0
1
2
0
1
1
1
0
0
2
1
0
1
0
1
2
0
2
0
2
1
2
1
2
2
0
1
0
0
0
1
0
0
0
2
2
1
2
0
0
0
0
2
0
2
2
1
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
2
0
1
1
2
0
0
0
1
2
1
0
0
0
0
0
0
1
0
1
1
1
1
0
2
3
2
0
1
0
0
0
1
2
0
0
1
2
1
2
1
0
2
0
0
0
2
2
0
1
0
0
0
1
0
0
1
0
1
2
0
0
1
1
2
1
1
0
0
1
0
0
0
1
2
1
0
0
2
2
0
0
2
0
1
2
0
1
0
0
1
0
1
2
0
2
0
2
0
2
1
0
2
0
1
1
0
0
0
0
2
0
0
1
3
1
0
0
0
0
1
1
2
0
0
2
0
0
1
0
0
1
2
0
0
1
1
1
2
1
0
0
1
2
1
0
1
0
2
0
0
2
0
0
0
0
0
3
1
2
0
0
0
0
2
0
4
0
2
0
0
1
2
0
1
0
0
1
0
2
0
1
2
2
0
1
0
0
1
2
0
0
1
0
1
1
0
2
1
0
0
0
0
2
0
0
0
2
0
2
2
0
1
0
0
1
1
1
1
2
0
1
0
1
0
0
0
2
1
1
1
1
0
0
1
1
1
2
0
0
0
1
1
0
4
1
0
2
2
0
0
0
0
2
2
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
1
0
0
0
2
2
0
2
1
0
0
2
0
2
0
1
0
0
2
0
0
2
2
2
0
0
1
0
0
2
1
2
0
0
2
1
2
0
1
1
1
1
1
1
0
2
1
0
1
0
2
0
0
0
0
0
0
1
1
1
1
1
1
0
0
5
0
1
0
1
1
0
1
2
2
0
2
1
0
0
0
1
2
1
0
0
2
0
0
0
0
2
0
0
0
1
1
0
1
0
0
0
1
2
1
1
2
1
1
0
0
0
1
2
1
0
1
2
1
1
0
2
1
1
1
0
2
0
1
0
1
1
0
0
2
0
0
0
1
1
0
0
0
1
0
3
2
0
0
0
0
1
1
1
0
0
1
0
10
0
1
0
2
0
0
0
0
0
1
0
2
2
0
1
1
1
1
0
1
1
0
0
2
0
0
1
2
0
0
2
0
2
0
1
2
2
2
0
1
0
0
1
2
0
0
0
1
0
1
0
2
1
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
2
1
0
1
0
0
1
0
2
0
1
0
2
0
0
1
0
0
0
0
0
3
2
1
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
1
2
0
1
0
1
0
0
1
0
1
0
3
1
1
2
0
0
1
0
0
0
2
1
1
2
0
1
0
1
3
0
0
2
1
0
0
2
0
0
0
0
2
2
0
0
1
0
0
0
1
2
1
1
0
0
0
0
0
0
0
1
1
0
1
2
3
2
2
2
0
0
0
1
2
0
2
2
0
0
1
1
0
0
2
0
0
0
0
0
1
0
0
2
0
2
0
1
0
2
1
0
0
0
3
2
0
0
0
0
2
0
0
0
2
0
1
0
0
1
1
0
1
0
0
0
0
2
3
1
2
1
1
1
0
0
0
1
1
2
0
2
2
0
2
1
0
0
0
1
0
1
0
0
0
1
2
1
0
0
0
1
0
0
2
1
2
0
1
0
0
2
0
2
0
0
1
0
0
1
0
1
1
2
0
0
2
0
2
0
1
2
2
0
0
0
2
1
0
0
2
0
1
2
1
0
1
1
1
0
0
2
0
0
1
0
1
1
1
4
3
0
0
1
2
0
1
1
1
0
1
0
0
0
0
0
1
2
0
2
1
0
0
2
0
0
0
1
0
1
1
0
1
3
1
0
0
0
2
0
1
0
1
0
0
2
0
2
0
2
0
1
0
2
1
1
2
1
0
0
3
0
0
0
0
1
0
1
2
0
0
0
1
0
2
0
1
1
2
2
0
2
0
1
0
2
2
1
2
1
2
1
1
0
0
0
1
1
0
1
0
0
1
2
1
0
1
2
0
1
0
0
0
2
0
2
0
0
1
0
0
2
1
0
0
0
2
2
1
1
0
0
2
2
0
2
0
0
0
1
0
1
1
0
1
0
2
2
1
0
2
0
0
1
0
1
1
0
4
1
0
2
0
0
1
0
1
1
1
2
1
1
0
2
0
0
1
0
0
2
1
1
1
1
0
0
2
0
0
0
1
2
2
1
0
0
0
2
1
2
0
1
2
0
0
1
0
1
2
1
0
1
1
2
0
0
0
2
1
2
1
0
1
0
2
1
1
0
2
0
1
1
0
0
0
1
1
1
0
1
0
0
0
0
2
1
0
0
0
0
1
1
2
1
0
1
1
2
0
0
0
0
0
0
2
0
1
1
0
1
1
0
0
1
0
2
0
0
0
0
0
0
1
3
0
1
1
0
0
1
2
0
2
0
0
2
1
0
0
0
2
0
1
0
1
0
2
0
1
0
0
2
0
0
3
0
0
0
0
0
0
1
2
0
1
0
0
0
2
2
0
0
2
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
2
2
0
1
1
2
1
1
0
2
3
2
0
0
1
0
0
1
2
1
2
0
2
0
0
0
4
0
1
1
0
2
2
1
1
0
2
1
1
0
1
2
2
1
1
0
1
0
0
0
0
0
1
1
2
0
2
1
0
0
0
1
0
0
0
0
0
2
1
0
1
2
1
0
2
0
0
0
0
0
0
0
1
1
0
2
1
1
0
3
0
0
0
1
0
2
0
2
0
0
0
0
0
2
0
1
1
2
2
2
0
1
0
1
2
2
0
0
0
0
1
0
1
1
2
2
1
2
0
1
0
0
2
0
0
0
0
0
2
1
0
0
1
0
1
0
1
2
0
0
0
0
0
1
1
2
2
0
1
0
0
1
2
0
0
2
2
2
0
1
0
0
1
1
0
0
1
0
0
0
1
2
0
1
0
0
0
1
1
0
0
1
2
1
0
1
0
1
1
0
0
0
0
0
0
1
2
0
0
0
0
1
0
2
1
2
1
0
0
0
1
0
5
0
0
0
2
0
1
0
2
0
3
2
0
1
0
0
1
1
1
1
1
0
0
0
0
0
2
1
2
0
1
1
2
2
1
0
1
0
0
0
2
0
0
0
1
2
1
1
0
0
0
0
2
0
1
0
0
2
0
0
1
0
2
0
1
1
0
2
0
1
0
0
1
0
1
0
1
0
0
0
0
0
2
0
1
0
0
2
2
0
0
2
1
0
0
0
2
0
0
1
2
1
0
2
1
1
2
2
0
0
2
0
1
0
0
0
2
0
0
0
1
2
0
0
2
0
1
2
2
1
0
0
1
0
0
0
0
0
0
2
0
0
0
2
1
0
0
2
0
0
1
0
0
0
1
0
2
2
2
0
0
1
0
1
1
0
0
2
0
0
0
0
0
1
0
0
0
1
1
0
0
1
1
1
2
0
0
2
1
1
0
0
0
4
2
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
2
1
2
0
1
0
0
1
1
1
0
2
2
0
0
0
1
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
2
0
2
2
0
1
0
0
0
2
1
2
0
1
0
0
1
0
0
1
0
1
0
4
0
1
0
1
1
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
2
2
1
1
0
0
1
0
1
2
2
0
0
0
1
1
0
3
0
1
0
1
0
2
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
2
0
0
0
1
0
2
0
0
2
2
1
1
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
2
0
1
1
0
1
1
2
1
2
1
1
1
1
2
1
0
2
2
1
1
1
1
0
2
0
1
0
1
2
0
1
2
0
0
0
0
0
0
0
0
1
0
1
0
1
2
2
0
1
1
0
0
0
1
2
1
0
0
0
0
1
1
2
2
2
0
0
0
1
0
2
0
0
0
0
2
0
2
2
0
0
1
1
0
0
0
0
0
2
0
2
0
0
0
2
0
1
2
0
2
0
2
0
0
2
0
0
2
2
1
0
1
1
0
0
0
1
0
1
0
0
0
1
1
0
0
1
2
0
2
3
0
1
0
2
0
1
1
1
0
1
0
1
0
1
1
0
0
1
2
0
2
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
2
0
2
0
0
1
1
1
1
0
0
0
2
1
0
1
0
0
1
2
1
1
2
1
0
1
0
0
0
0
0
2
1
0
0
1
0
1
0
0
0
1
0
1
3
0
1
1
0
0
1
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
1
1
2
0
2
2
1
1
1
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
1
2
0
1
1
0
0
0
2
0
3
2
2
0
0
1
2
1
0
1
0
0
1
0
0
0
1
1
0
2
1
2
1
0
1
2
1
2
2
1
0
2
0
1
4
0
1
0
0
0
0
0
0
1
0
1
2
0
2
0
2
1
0
0
0
0
0
2
0
1
1
2
0
0
2
0
1
1
2
2
1
1
0
2
2
5
0
0
2
0
0
0
2
1
2
0
2
0
1
1
1
2
0
0
0
0
0
0
2
2
0
1
0
0
0
0
1
1
0
0
1
1
0
1
0
1
0
1
2
0
0
2
0
0
2
1
2
0
1
0
0
3
1
0
2
2
1
1
0
2
0
2
1
1
2
1
1
1
1
2
0
1
1
1
1
0
0
1
1
0
2
2
0
0
1
0
2
1
1
0
2
1
1
0
0
1
2
0
0
0
0
2
0
1
2
0
0
1
0
0
1
2
2
10
0
0
1
1
0
0
2
3
2
0
1
0
0
0
1
0
1
0
1
0
2
2
1
0
0
1
2
0
0
2
2
1
0
0
0
1
1
2
0
1
0
1
0
0
0
2
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
2
1
0
0
1
0
2
0
0
0
1
0
1
0
0
1
1
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
3
1
2
0
0
1
0
0
1
0
0
0
2
0
1
0
0
2
0
1
1
1
0
2
1
0
0
1
1
1
0
1
0
0
1
0
0
2
0
0
1
2
1
0
2
0
0
0
1
0
2
0
1
1
0
2
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
1
1
2
1
1
1
0
2
0
1
1
2
0
0
2
1
0
2
1
0
0
1
0
1
0
0
2
1
1
1
1
0
0
0
1
0
1
0
0
1
1
2
1
2
0
0
1
0
0
0
0
1
0
2
2
2
0
1
0
0
1
1
0
2
1
2
0
1
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
1
0
1
0
4
2
0
1
2
1
0
0
1
2
2
0
0
1
0
0
0
0
0
0
1
2
0
0
2
0
0
0
2
0
0
1
0
1
2
0
0
0
1
1
2
0
0
1
1
1
1
2
1
1
0
0
0
0
2
0
0
0
0
1
0
0
1
0
2
0
2
0
0
0
0
0
0
0
1
0
1
2
1
0
0
5
2
1
0
0
0
0
0
1
2
1
0
0
1
1
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
1
2
0
0
0
0
0
1
1
1
2
2
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
1
1
2
1
1
3
0
1
0
0
0
1
1
2
2
0
0
2
0
0
0
0
2
1
0
2
1
0
2
2
1
0
0
0
0
4
4
2
0
0
0
1
0
0
1
0
0
1
0
1
0
2
1
0
0
0
0
0
0
0
2
0
1
0
2
1
1
1
2
0
0
4
1
7
0
0
0
2
0
1
1
2
2
2
1
2
1
1
1
0
1
1
0
0
3
2
1
1
0
2
1
1
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
2
1
0
0
0
1
0
2
0
0
0
3
1
0
0
0
1
2
2
1
2
1
1
0
0
1
0
2
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
2
0
2
2
2
0
0
1
1
2
2
0
1
2
0
0
2
2
1
2
0
0
0
1
1
1
2
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
2
0
0
2
0
2
2
0
1
1
0
1
0
2
2
0
2
0
1
0
0
0
0
0
1
0
0
1
1
0
0
1
2
2
0
2
0
1
0
1
0
0
0
1
2
1
2
0
2
3
1
0
0
1
1
1
0
0
0
0
3
0
1
2
0
1
0
0
1
1
0
1
0
2
0
1
0
0
0
0
0
2
1
0
0
1
1
0
0
0
2
0
2
2
1
1
1
0
0
0
1
0
0
1
2
0
1
1
0
0
1
0
0
0
1
2
1
0
0
1
0
0
1
2
0
0
1
1
1
0
2
1
1
3
2
0
0
1
2
0
0
2
0
0
0
0
1
0
0
0
0
2
4
1
0
1
0
2
2
1
1
0
0
2
2
2
0
0
1
2
0
1
0
0
0
1
0
0
3
0
1
0
0
1
1
1
0
0
0
2
1
0
1
1
2
0
0
2
1
0
0
1
0
0
0
1
0
0
1
0
0
0
2
0
1
0
0
0
0
2
0
0
1
0
0
2
0
1
0
1
0
1
2
2
0
0
2
0
0
0
0
3
2
1
1
6
2
0
2
0
2
1
2
1
2
0
0
1
0
1
0
2
0
0
2
1
1
0
1
2
0
0
0
2
1
1
1
2
2
1
0
0
0
1
0
2
0
0
0
0
1
1
0
1
0
1
0
2
0
1
2
0
2
0
2
5
1
1
1
0
0
0
1
0
0
0
1
2
1
1
0
0
0
2
0
0
1
0
1
1
3
2
1
2
2
1
0
0
1
1
0
0
1
0
0
1
0
0
1
1
1
0
0
0
1
1
1
1
2
0
2
0
1
0
2
0
2
0
0
1
1
1
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
1
0
2
0
3
1
1
2
0
2
1
0
1
1
1
0
0
0
2
0
1
0
1
1
1
3
0
1
1
0
1
0
0
0
0
1
0
2
2
0
2
1
2
1
0
0
1
0
1
0
2
0
1
1
0
1
1
1
0
0
1
1
0
1
3
0
2
2
1
1
2
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
1
2
0
0
0
1
0
2
0
1
0
2
0
0
0
2
1
1
0
0
1
1
1
0
2
0
0
1
0
1
0
0
0
0
1
1
0
0
1
1
0
0
2
0
2
0
1
0
2
0
0
0
1
0
1
3
0
0
2
2
0
2
0
0
1
1
1
0
2
1
2
0
1
2
1
1
0
1
1
0
2
0
2
2
0
1
1
0
0
0
0
2
1
0
0
0
2
0
1
1
1
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
3
2
1
1
1
0
2
0
0
1
0
0
0
0
1
0
3
2
0
2
1
0
0
2
2
2
1
0
1
0
0
2
0
1
2
0
0
2
2
2
1
1
2
2
1
0
0
2
2
2
0
0
1
0
1
1
0
0
0
0
0
2
0
0
1
1
2
0
1
0
0
0
0
1
0
0
1
3
1
1
0
0
0
1
0
1
1
0
1
1
5
0
2
0
0
0
1
0
0
1
1
0
1
1
1
0
1
2
0
0
1
2
0
0
0
5
2
2
0
1
0
0
2
2
0
2
2
1
1
1
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
2
3
0
1
0
0
2
0
1
0
0
2
0
0
1
0
0
0
0
0
1
0
1
0
1
1
0
0
2
0
4
0
0
0
1
0
0
0
1
3
1
1
2
0
0
2
1
0
0
1
2
2
2
2
0
1
1
0
1
1
1
0
0
1
1
0
0
1
0
2
1
0
0
1
1
1
2
0
2
2
0
1
0
1
0
0
2
1
0
1
0
1
0
1
0
0
1
0
0
1
0
1
0
0
0
2
2
3
1
1
0
0
2
0
1
2
0
0
0
2
0
1
1
0
1
2
2
2
1
0
1
0
0
0
0
2
0
1
0
0
0
2
2
0
0
1
1
2
0
1
0
0
1
1
2
0
1
0
1
1
0
0
2
0
1
0
2
1
0
0
2
1
1
0
1
1
1
0
0
0
0
2
1
1
2
1
0
0
0
2
1
0
0
0
2
1
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
2
1
0
2
2
1
0
1
2
0
2
0
0
0
0
0
0
0
1
3
0
2
0
0
1
0
0
0
0
0
2
0
0
1
3
0
2
1
0
1
1
0
0
0
0
0
0
2
2
1
0
2
0
5
2
2
0
1
0
2
1
0
1
0
1
0
0
0
1
2
1
0
0
2
1
2
1
0
0
2
0
0
2
0
0
2
1
0
0
0
0
2
0
0
3
1
0
1
0
1
1
0
1
0
1
0
0
0
1
1
1
1
2
1
1
1
0
0
0
1
0
1
1
0
0
1
0
2
0
1
0
1
2
0
1
0
2
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
3
1
0
2
1
1
0
2
0
0
0
0
0
0
0
1
1
0
2
1
0
2
2
2
0
0
1
0
0
0
1
2
1
1
0
1
2
0
0
1
0
1
1
2
0
1
0
0
1
0
0
0
0
0
1
2
0
0
2
0
2
2
0
1
0
1
0
0
0
0
2
1
2
1
1
2
2
1
0
0
0
0
1
1
0
0
1
0
0
0
2
1
0
2
0
1
0
0
0
0
0
2
0
0
2
1
0
0
0
0
1
2
0
2
0
2
1
0
0
2
1
0
0
0
0
0
1
1
1
2
0
0
1
1
0
0
1
0
1
0
1
0
2
0
1
1
0
2
2
1
2
1
2
2
0
0
0
0
1
1
0
0
0
2
1
0
0
2
0
2
2
1
0
0
1
0
2
1
1
1
1
0
0
0
1
0
0
2
1
0
0
2
0
0
2
0
1
1
1
0
2
0
0
1
1
3
2
0
0
1
1
0
2
2
0
0
0
1
1
2
0
1
2
0
0
1
2
3
0
1
2
2
2
0
1
0
0
0
2
2
2
1
0
0
1
2
3
1
0
2
0
0
0
0
3
0
2
1
1
2
3
2
1
2
2
1
0
2
1
0
2
0
0
2
0
1
0
1
0
2
3
0
0
2
0
0
0
0
0
1
0
0
1
1
1
1
0
0
0
1
1
0
1
1
2
1
1
0
2
2
2
0
0
2
0
1
0
2
1
0
0
0
1
0
2
1
1
0
1
0
0
2
1
1
0
0
0
0
1
0
0
0
0
2
1
2
0
0
1
0
1
0
2
1
2
1
0
1
2
1
0
1
1
1
2
0
1
1
1
2
0
0
0
2
0
0
2
1
1
3
1
0
0
0
0
0
1
1
2
0
1
2
1
0
0
0
0
1
0
1
0
0
1
0
0
2
1
0
2
0
1
2
3
1
0
1
1
0
0
1
2
1
2
0
0
1
0
0
0
0
0
2
0
0
1
0
2
2
0
0
2
2
0
2
0
1
1
0
2
1
0
2
0
0
1
1
0
0
0
2
0
0
2
2
1
0
0
2
0
0
0
1
0
0
2
0
2
0
1
2
2
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
2
1
0
0
1
0
0
0
1
0
0
2
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
1
0
0
2
2
0
0
0
2
0
1
0
0
2
0
0
0
2
1
0
0
0
1
2
0
1
2
1
1
0
1
0
0
0
1
0
1
2
0
2
0
0
1
2
1
0
1
0
0
1
2
2
0
2
0
0
0
0
1
0
0
0
0
1
1
2
2
0
0
0
0
1
2
0
0
0
0
0
1
2
0
0
1
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
3
0
0
2
1
0
0
1
1
2
2
1
0
0
5
1
1
1
0
2
0
2
1
2
2
1
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
1
0
0
3
0
0
1
2
0
1
0
0
0
0
1
0
2
0
0
1
0
0
2
1
2
0
0
2
0
0
0
1
1
0
0
2
0
0
2
1
0
0
2
0
0
1
1
0
1
8
1
2
0
0
0
0
0
1
2
2
1
1
2
1
0
1
2
0
0
2
0
0
0
1
0
0
3
1
0
1
0
2
0
0
1
0
0
1
0
1
0
0
2
0
0
0
1
0
0
0
0
3
1
1
1
0
2
0
2
0
0
2
2
0
0
0
0
1
1
2
0
2
2
1
1
2
1
2
2
1
1
0
0
1
1
0
0
0
0
0
2
0
1
2
1
0
0
0
0
0
2
0
0
1
1
0
0
2
3
1
0
1
1
1
0
0
1
0
1
0
0
0
1
0
2
0
1
2
0
1
0
1
1
1
1
0
0
1
0
1
0
0
0
1
2
1
0
0
1
0
0
0
0
1
0
1
2
2
0
0
0
0
2
0
1
0
1
2
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
1
0
2
0
0
2
1
0
2
0
0
1
1
0
2
0
1
0
0
0
1
1
0
1
1
2
0
0
1
0
0
0
0
1
0
1
2
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
1
0
0
0
2
1
1
0
1
0
0
1
0
0
1
2
0
0
2
1
0
1
2
0
0
0
0
3
0
2
1
2
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
4
0
0
0
0
0
1
1
0
0
0
0
1
1
0
1
0
0
1
0
2
0
1
0
1
0
1
0
0
0
2
2
0
0
2
2
0
2
0
1
1
2
1
0
0
0
2
1
1
0
0
1
2
0
0
2
0
2
1
0
2
0
1
1
1
0
0
0
1
0
2
1
2
0
1
1
1
2
2
0
2
0
0
1
3
1
1
1
0
1
2
0
0
2
1
1
2
0
1
0
1
0
0
0
1
0
0
0
1
3
1
2
0
1
0
1
2
0
1
1
0
0
0
1
0
1
0
0
2
0
2
0
1
0
1
1
0
1
0
1
0
2
1
0
2
1
1
0
0
1
0
0
2
1
0
0
0
1
0
0
0
2
0
0
2
0
0
1
1
2
1
2
1
2
0
0
2
0
1
0
0
1
2
0
2
0
2
0
1
0
0
1
1
1
1
0
1
1
1
1
0
0
3
1
0
0
0
0
0
0
2
1
0
0
0
0
1
0
2
1
0
2
0
1
1
1
0
0
2
0
1
4
1
0
0
0
2
0
0
1
1
0
0
0
0
0
2
2
1
0
0
0
0
0
0
1
0
2
0
0
0
2
1
0
0
0
1
0
0
0
0
1
1
1
2
0
4
1
2
0
0
0
2
0
0
2
0
1
0
1
0
0
2
1
1
0
0
4
0
0
1
0
0
0
0
0
1
1
0
1
0
1
3
1
1
1
1
0
0
1
1
0
1
2
2
0
0
1
0
0
0
1
0
1
2
2
0
0
0
1
1
0
0
1
1
3
0
0
0
1
1
2
0
2
1
0
1
0
1
0
0
0
0
1
3
2
1
2
0
8
0
0
1
1
0
0
2
1
0
0
0
2
0
0
1
0
0
1
0
1
0
0
2
1
2
2
0
0
2
2
2
1
0
0
0
0
3
2
0
1
0
1
1
2
1
2
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
1
0
0
1
0
2
0
1
1
0
2
1
0
1
0
0
0
0
0
2
0
0
0
1
0
1
0
0
1
2
2
0
1
1
0
2
2
0
3
1
1
0
0
1
0
0
2
1
2
0
1
0
0
0
2
0
0
1
0
0
0
1
0
0
1
1
0
0
0
1
2
0
0
0
0
0
2
1
1
1
1
0
0
2
0
1
1
2
1
2
0
0
0
0
1
1
0
2
1
0
1
2
0
1
0
2
1
2
0
1
0
0
1
0
2
0
0
0
0
1
0
0
1
2
0
2
0
1
5
1
0
2
2
1
0
0
0
2
0
0
1
2
2
1
0
1
1
2
1
0
0
0
0
0
1
2
0
0
0
2
2
0
2
0
1
0
0
0
1
0
1
1
1
2
0
1
0
0
1
1
1
2
1
2
0
2
0
0
1
1
1
0
0
0
0
0
0
1
1
2
2
0
2
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
2
1
2
1
0
1
1
2
2
2
2
0
0
0
0
0
2
0
0
2
0
0
0
1
1
1
0
1
2
1
1
0
2
0
0
1
0
0
0
2
1
1
2
0
1
0
0
1
0
0
0
1
1
0
0
1
0
0
1
1
1
0
0
1
1
0
1
1
1
0
1
0
0
2
1
0
0
1
2
1
0
1
0
0
1
0
1
1
0
1
2
1
0
0
2
2
1
1
1
0
2
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
1
1
1
0
2
0
0
1
0
0
1
2
2
0
1
2
0
2
0
2
0
0
0
1
2
0
2
2
2
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
1
1
0
4
1
2
0
2
0
1
0
1
1
0
1
2
2
0
0
2
0
0
2
2
2
0
2
0
2
2
1
0
1
2
0
1
0
2
0
1
2
0
1
0
0
0
1
2
1
0
2
0
1
1
0
2
0
2
2
1
0
2
1
0
0
0
0
1
1
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
2
2
1
0
0
0
0
0
0
1
0
0
0
2
0
1
2
1
1
1
0
1
0
0
1
2
0
0
1
2
1
4
0
0
1
1
2
1
0
0
0
0
1
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
2
0
0
1
0
1
0
1
2
0
1
1
2
0
1
3
0
2
2
0
0
0
0
2
0
3
0
2
0
1
1
0
3
0
2
0
0
1
3
2
0
1
0
2
0
0
2
1
3
0
0
2
2
2
1
0
0
0
0
1
0
0
2
1
1
0
1
0
1
0
0
0
0
0
0
0
2
2
0
1
0
1
0
0
0
0
2
0
0
1
1
1
0
1
0
0
2
2
0
0
0
0
0
0
0
0
1
0
1
1
1
0
2
1
1
0
0
0
0
0
0
1
1
1
1
0
1
1
0
0
1
2
1
0
0
0
2
0
1
1
1
0
0
1
1
1
2
0
1
3
0
2
1
0
0
1
0
1
0
2
1
1
2
0
0
0
0
1
3
0
0
0
1
0
0
0
0
0
2
1
1
0
0
0
3
0
1
0
0
1
2
2
0
3
0
1
2
2
1
0
0
2
1
1
0
0
2
1
1
1
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
1
0
1
0
1
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
1
2
0
0
0
1
2
0
0
2
2
1
0
2
0
0
0
2
2
0
2
2
1
1
2
1
1
2
2
0
1
2
0
0
0
2
0
0
0
0
1
1
0
2
0
0
2
0
1
2
2
0
1
0
0
1
0
1
0
0
0
0
1
0
2
0
0
0
2
2
1
0
0
2
2
0
0
0
0
1
0
0
0
2
0
0
0
1
1
2
0
0
0
1
0
0
0
2
1
0
1
3
0
1
0
0
0
2
1
0
2
0
1
0
0
2
2
1
2
2
1
1
1
0
1
2
3
0
0
1
2
2
2
1
1
0
0
2
0
2
2
2
0
1
1
1
2
0
0
0
2
0
0
0
1
0
0
2
0
1
0
1
0
0
0
0
2
0
0
0
1
2
0
0
0
0
2
1
0
1
1
2
0
0
0
2
3
0
1
1
1
0
2
2
2
0
0
0
2
0
2
1
0
1
0
0
1
2
0
1
1
1
0
1
0
1
0
0
0
0
0
2
0
1
1
0
1
2
1
1
0
0
0
0
0
0
1
2
2
1
2
2
2
0
0
2
0
2
0
1
1
0
2
0
1
0
1
1
2
0
0
0
2
1
0
1
1
1
1
2
0
2
0
0
0
0
2
0
1
0
1
2
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
2
0
0
1
0
3
1
0
1
0
0
0
1
0
2
1
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
2
0
2
0
0
1
2
0
1
2
2
0
0
2
1
0
0
2
0
0
0
3
1
0
1
1
0
2
0
0
2
1
0
1
0
2
0
2
1
1
2
0
0
0
1
0
2
1
1
0
0
1
0
0
0
1
0
1
0
1
1
2
1
1
2
2
0
0
0
1
1
1
0
2
0
1
2
0
0
2
1
0
1
0
0
0
0
1
1
2
0
1
0
0
1
0
0
1
2
1
2
0
1
2
1
0
1
0
0
0
1
1
0
1
1
0
0
2
1
1
0
2
0
2
0
0
0
7
1
2
1
2
1
1
2
1
1
2
1
0
1
2
0
0
0
2
0
1
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
2
0
0
0
1
0
0
2
0
1
1
0
2
0
3
0
1
2
0
1
0
1
1
2
1
0
0
1
0
0
0
2
0
0
0
0
2
0
1
1
2
0
0
0
0
0
0
1
0
0
0
0
0
2
1
2
2
0
2
3
2
5
0
0
0
0
0
1
2
2
0
0
1
0
0
0
0
1
0
1
0
0
0
2
1
0
0
0
2
0
0
1
0
1
2
2
0
2
1
2
2
1
1
0
1
0
0
0
0
0
1
2
1
1
0
2
1
1
1
0
0
2
0
0
1
3
0
1
1
1
0
0
0
0
2
0
2
1
1
1
0
0
1
0
2
1
0
2
0
1
2
2
1
1
0
0
0
1
1
0
0
0
2
1
0
1
0
0
2
0
1
0
0
0
1
2
0
2
0
0
0
2
1
2
2
1
1
3
1
1
2
0
1
1
2
2
1
1
2
2
0
1
2
0
1
0
1
2
2
0
0
0
0
0
0
0
0
2
1
0
1
0
2
0
2
1
1
2
0
1
1
0
0
2
1
0
0
0
2
0
1
2
1
2
0
0
0
2
1
1
0
2
2
3
0
1
0
1
2
1
0
0
1
2
1
2
0
0
1
0
0
0
1
4
1
0
0
2
1
0
2
1
1
2
1
2
1
0
0
1
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
2
0
2
1
3
1
0
2
0
0
0
1
1
1
0
1
0
1
0
1
0
0
2
1
2
2
0
0
1
1
0
0
2
1
0
2
0
1
1
0
1
3
1
1
0
2
0
0
2
1
1
0
2
0
2
2
1
3
1
0
1
0
0
0
0
1
2
0
3
1
3
0
0
0
1
3
1
0
0
2
2
0
0
0
0
0
0
1
0
0
2
0
0
2
1
0
0
2
0
1
0
2
0
0
0
0
0
1
0
0
0
2
2
0
1
0
0
3
0
1
0
1
0
0
1
0
0
0
1
1
0
0
0
1
0
0
2
0
1
1
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
2
2
1
1
1
2
0
1
1
1
0
2
1
0
2
0
3
0
0
0
2
0
1
1
0
3
0
2
2
2
0
0
0
2
2
2
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
2
0
1
0
1
1
0
0
2
0
0
0
2
2
1
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
1
1
2
1
0
0
0
0
0
2
1
0
0
3
2
0
0
1
0
2
0
0
3
1
0
0
0
0
0
0
0
2
0
3
0
0
1
0
0
1
1
1
2
0
2
0
0
0
0
0
2
0
0
2
2
1
1
1
0
0
1
2
0
0
2
0
0
2
0
0
1
2
1
1
1
0
0
0
1
0
0
1
2
2
0
0
2
1
0
1
1
2
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
1
1
1
0
1
0
0
2
1
2
0
2
0
0
0
0
0
0
2
0
0
1
2
1
0
2
0
2
1
0
1
0
0
1
2
1
1
0
1
0
2
1
1
0
0
1
0
0
0
0
1
1
1
0
0
1
0
1
0
2
2
0
0
0
1
0
0
2
2
0
2
0
1
1
0
1
2
1
0
1
0
0
1
2
2
2
0
0
2
0
0
2
1
1
1
1
0
1
0
0
0
3
1
0
0
2
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
2
2
1
0
2
0
0
1
2
1
0
0
0
0
0
0
1
1
1
2
1
0
0
0
0
0
0
2
2
1
1
2
2
0
2
0
0
2
1
0
0
1
0
0
0
0
0
2
2
0
1
1
0
1
0
0
0
2
0
0
0
0
0
2
2
2
0
2
1
1
3
4
0
2
2
2
0
0
1
1
1
1
0
2
0
2
1
0
1
2
1
2
2
0
2
0
2
0
0
1
1
1
2
0
1
2
0
1
2
1
1
0
0
2
0
2
2
1
0
0
0
2
2
0
0
1
8
1
5
1
0
2
1
1
1
1
1
0
0
0
0
1
2
1
3
2
1
0
0
0
1
0
0
0
0
1
0
1
0
1
0
1
1
0
0
0
1
0
1
2
2
1
2
0
2
0
0
1
1
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
1
1
2
4
2
1
0
2
2
0
0
0
0
0
0
1
2
0
1
0
0
0
0
1
1
0
0
1
0
0
1
2
0
0
1
1
0
2
2
3
0
2
0
2
2
1
0
2
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
2
1
0
1
2
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
1
1
4
1
0
2
0
0
0
0
0
0
0
0
1
1
1
2
1
1
0
1
2
0
0
2
0
0
1
1
2
1
1
0
2
2
1
0
2
0
0
1
0
2
0
1
0
0
0
1
0
0
1
1
0
1
1
1
0
0
0
0
2
1
2
0
0
1
2
1
1
2
0
0
0
0
2
2
2
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
1
2
2
0
1
1
1
0
0
0
0
0
0
1
2
1
2
0
1
0
1
1
0
0
1
0
0
0
1
0
0
2
0
1
0
0
1
0
0
0
0
1
1
1
1
2
1
0
0
1
0
0
0
0
0
0
0
0
1
2
0
2
0
0
1
1
0
2
2
0
0
0
0
2
0
4
1
1
2
0
2
1
0
1
0
0
0
0
0
0
1
0
1
2
0
0
2
2
2
2
0
0
2
5
2
1
0
1
1
2
1
1
0
2
0
1
1
1
0
2
1
0
0
0
2
0
2
1
1
1
0
0
3
1
0
2
1
2
1
0
0
0
0
0
0
2
2
0
0
1
0
0
2
1
0
1
2
0
0
0
0
1
0
2
0
1
0
0
1
1
4
0
1
0
1
0
1
0
0
0
1
2
1
0
0
0
0
0
0
0
0
2
0
2
1
1
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
2
0
1
2
0
0
2
2
0
0
1
2
0
4
0
0
0
2
0
2
2
0
0
0
0
0
2
1
0
0
1
1
1
2
1
0
0
1
2
1
0
0
0
1
0
2
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
2
0
0
1
1
1
0
2
2
0
1
2
0
0
2
0
0
2
2
1
1
0
0
2
0
0
1
2
0
1
0
1
1
1
1
0
0
0
1
1
2
3
2
2
0
1
0
0
0
2
0
2
0
2
1
4
0
1
0
2
1
1
0
0
1
1
1
1
0
0
2
2
1
0
0
1
0
1
2
0
0
1
0
2
1
2
2
0
2
2
0
0
2
0
1
0
1
2
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
3
2
0
1
1
1
0
0
2
2
0
1
1
2
0
1
1
1
1
0
0
2
0
1
1
2
0
2
0
2
1
2
0
0
1
2
1
0
2
0
0
0
3
2
0
1
0
2
1
0
0
1
2
0
0
2
1
0
1
1
2
0
1
0
0
1
2
0
0
2
1
0
0
0
1
0
2
1
0
0
2
1
0
2
0
3
0
2
0
0
0
1
0
0
0
0
0
0
1
2
0
2
0
0
0
2
2
0
1
0
2
0
0
0
0
0
1
2
2
0
0
2
0
0
0
1
3
0
2
0
0
1
0
0
1
0
0
2
2
2
2
0
0
0
1
2
1
1
0
2
0
0
2
2
0
1
0
0
0
0
0
1
2
1
0
0
2
0
2
0
0
1
2
1
2
0
0
0
2
2
1
1
0
0
0
2
0
2
0
2
0
2
0
1
0
0
0
2
1
2
0
3
2
0
1
0
0
2
0
0
2
1
0
0
1
0
0
1
0
0
0
1
2
0
0
0
0
0
2
1
0
0
2
0
0
1
2
0
0
1
2
1
2
0
0
1
1
0
0
1
0
1
0
1
0
0
0
1
1
0
1
1
0
1
1
0
0
0
2
1
1
0
1
2
0
0
0
0
0
0
2
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
2
2
1
1
0
0
0
1
1
2
2
1
0
1
2
0
3
0
0
1
2
0
3
0
1
2
1
1
0
0
0
6
1
2
0
2
0
0
0
0
1
1
0
0
1
0
0
0
2
1
2
3
0
0
1
0
0
1
0
2
2
0
2
1
2
1
0
2
2
0
2
1
0
1
1
0
2
0
0
1
3
0
0
2
0
1
1
0
0
0
2
0
2
0
0
2
0
0
0
1
1
1
0
1
1
0
1
2
0
0
0
0
0
0
1
1
0
0
1
2
1
0
0
2
1
0
2
2
1
0
0
0
0
2
0
0
0
0
1
2
2
1
2
2
1
0
0
0
1
1
0
1
0
0
0
1
2
0
1
1
0
1
2
3
0
1
1
0
0
0
0
2
1
2
0
1
1
1
0
0
1
0
0
1
0
0
0
0
1
2
1
1
0
0
2
0
0
0
2
0
1
0
1
1
2
1
1
0
0
1
1
0
1
2
0
0
0
2
0
0
2
2
0
1
1
0
2
1
2
0
0
1
1
2
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
2
0
0
1
0
2
1
0
1
1
1
1
0
1
2
1
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
2
0
1
1
1
0
0
0
0
1
0
1
0
2
0
0
0
2
2
0
0
2
0
0
1
1
1
1
0
1
0
0
0
0
0
0
1
1
0
1
2
2
0
1
2
0
2
0
0
0
0
2
1
0
2
0
2
0
1
1
0
1
0
0
0
1
0
1
0
1
0
2
1
1
0
0
1
0
0
0
0
1
1
2
2
0
2
1
0
0
1
0
0
0
0
2
0
1
2
0
0
0
1
0
2
1
0
1
0
1
2
1
0
0
2
2
1
0
0
0
1
1
0
0
0
2
0
1
0
0
2
0
2
1
1
2
0
0
1
1
1
0
2
0
1
0
0
0
0
0
0
2
1
0
1
2
1
2
0
0
1
1
0
0
0
0
2
0
2
2
5
1
1
0
1
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
2
0
0
2
0
1
1
0
1
0
0
0
1
1
1
2
2
0
0
0
0
2
0
2
0
2
2
0
2
0
0
1
2
0
0
1
0
0
2
0
0
0
0
1
0
0
1
2
0
0
0
2
2
0
0
0
2
1
0
0
1
1
0
1
0
0
2
1
0
1
2
0
1
0
2
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
1
0
2
2
2
0
0
0
2
0
0
5
1
0
1
1
1
0
0
0
0
1
0
0
1
0
2
0
0
1
2
1
2
1
1
0
0
2
1
2
1
0
2
0
2
1
0
2
1
0
0
0
0
1
0
2
0
0
0
1
0
1
0
0
1
0
1
0
2
0
0
0
0
2
2
0
1
0
1
1
2
0
0
0
0
1
0
2
0
1
2
1
0
1
1
1
0
0
1
2
1
2
0
4
2
0
2
1
0
2
0
0
2
0
0
0
0
1
0
0
0
2
1
1
0
0
0
2
1
3
0
1
1
0
1
0
0
1
0
0
1
2
1
0
1
1
1
0
1
2
2
0
1
0
0
0
1
1
0
1
1
1
0
0
1
0
0
0
0
2
1
3
0
0
0
2
2
0
0
1
2
0
0
0
0
0
1
2
0
0
0
0
1
1
3
1
2
1
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
1
2
0
2
0
2
0
0
0
0
0
0
2
1
0
2
0
1
0
0
2
1
1
1
0
1
0
0
0
0
3
1
2
1
0
2
0
0
0
0
3
1
1
0
0
2
1
2
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
1
1
2
3
0
0
2
0
2
1
0
0
2
0
2
0
0
0
0
1
1
0
2
0
0
1
1
1
1
0
2
2
2
0
1
0
1
1
3
0
0
0
2
0
0
0
2
0
1
1
0
2
0
1
0
1
0
1
0
0
0
0
1
2
1
0
0
0
1
0
1
0
1
1
1
2
2
1
0
1
1
0
1
2
2
2
0
0
0
0
2
0
1
1
0
2
2
1
2
1
1
2
2
1
0
2
0
0
3
3
1
0
0
1
1
0
2
0
0
0
2
2
0
2
2
0
0
1
3
1
2
0
1
1
2
2
1
1
2
0
2
2
0
1
0
0
0
0
0
2
0
0
2
0
0
0
1
0
2
0
1
1
0
1
2
0
0
0
1
2
0
1
1
1
1
0
2
0
0
0
10
1
0
0
1
0
0
2
1
0
0
1
0
1
0
0
0
2
0
0
0
2
0
2
2
1
0
0
0
1
0
0
0
2
0
0
1
0
0
0
1
1
0
2
1
1
0
1
0
1
0
0
0
2
0
0
0
1
0
1
2
0
0
2
0
0
1
0
0
1
0
2
2
2
0
1
0
2
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
2
2
0
0
1
1
0
1
1
0
0
0
1
0
1
0
1
0
0
2
0
3
0
0
3
0
1
0
0
2
1
0
1
0
2
1
0
0
1
0
1
0
2
0
1
0
1
0
2
0
0
0
2
2
0
0
1
0
2
1
1
0
2
0
2
2
1
0
0
0
2
0
1
0
0
0
2
1
2
0
1
0
0
0
2
0
0
5
3
0
1
2
2
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
2
2
0
0
1
1
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
2
0
0
2
1
0
2
0
1
0
2
2
1
0
2
0
1
0
2
0
2
2
0
1
0
1
0
0
3
0
0
2
2
0
1
0
1
0
0
0
1
1
0
0
4
0
0
1
0
1
1
0
1
0
1
1
0
1
2
0
0
1
1
0
2
2
2
2
1
0
1
1
0
1
1
0
1
1
2
1
0
0
2
0
0
2
0
0
2
0
1
2
2
0
1
1
0
0
2
2
0
2
1
1
0
2
0
1
1
0
0
0
4
0
1
0
1
0
2
1
1
2
0
1
0
0
1
0
0
0
0
0
2
0
2
0
1
0
3
2
0
0
0
1
0
1
1
1
1
1
1
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
2
2
2
0
0
1
0
0
0
0
1
0
0
2
0
0
1
1
0
0
0
1
1
3
0
2
2
0
0
1
2
1
0
1
0
0
1
0
0
2
0
0
2
0
0
0
1
0
5
1
1
2
1
0
2
1
0
3
1
0
0
1
0
0
2
2
1
1
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
1
1
1
1
0
0
0
0
0
0
0
1
2
3
0
0
0
1
1
0
0
2
2
0
2
2
0
1
0
0
2
1
1
2
2
2
0
2
0
1
0
2
0
0
0
1
2
0
0
2
0
2
0
0
2
0
0
1
2
1
1
0
1
2
0
0
2
2
0
0
2
0
0
0
0
1
0
2
3
3
0
0
0
0
3
0
2
2
0
0
1
1
2
0
0
2
1
0
0
0
2
0
0
0
0
1
0
3
1
2
0
0
0
3
0
0
0
1
2
0
2
0
0
0
0
0
0
0
2
2
0
1
0
0
0
2
0
0
2
0
1
2
0
0
0
1
0
1
2
1
0
0
2
1
0
2
0
0
2
0
0
0
0
0
2
1
2
1
0
0
0
1
1
0
1
0
2
2
2
0
2
0
1
0
0
3
1
0
1
0
0
1
1
1
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
2
1
1
1
1
0
0
1
0
2
2
0
2
0
1
0
0
3
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
2
0
2
2
1
0
1
2
0
2
0
1
0
0
1
0
0
0
0
2
1
0
1
0
1
1
0
1
2
1
1
0
2
1
0
2
0
1
1
0
0
1
0
1
1
0
2
1
0
1
3
0
0
1
1
0
2
1
1
2
2
0
1
0
0
2
0
0
3
2
0
0
0
0
1
1
0
0
1
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
2
0
0
1
1
0
0
1
2
0
1
1
1
0
0
1
1
1
1
0
0
0
0
3
0
0
0
4
0
1
2
2
0
2
1
0
0
2
0
2
0
1
0
2
2
0
0
1
0
0
1
2
1
1
4
0
1
0
2
1
1
1
0
0
1
0
0
1
0
0
2
1
1
1
1
0
2
0
1
0
1
1
0
1
1
0
0
1
2
2
1
2
0
2
2
0
0
2
0
0
0
2
1
2
1
2
0
0
0
0
1
0
0
2
2
2
2
2
0
2
1
2
0
0
0
2
0
0
1
1
2
2
0
0
3
1
2
0
2
2
0
0
1
0
0
0
0
2
2
0
2
2
2
1
0
1
0
0
0
0
1
0
0
0
2
2
0
0
1
2
1
1
2
0
2
2
2
2
1
0
2
0
1
1
1
0
1
2
0
0
1
0
0
0
2
1
2
1
0
0
1
0
0
2
0
1
1
0
1
0
0
0
0
0
0
0
0
2
2
2
0
0
1
2
1
0
0
0
1
0
0
0
0
1
0
0
1
2
2
0
0
1
0
0
0
1
1
0
0
1
0
1
2
2
1
0
1
0
0
0
0
1
1
2
1
0
0
1
0
0
1
0
0
1
2
1
0
0
0
0
1
0
1
3
2
0
2
0
2
1
1
2
0
0
0
1
0
0
4
1
0
3
1
1
1
2
0
1
2
0
3
0
0
0
0
0
1
0
2
1
0
0
1
0
2
1
0
1
0
0
1
0
0
0
1
2
0
0
1
1
1
0
1
2
0
0
0
5
2
0
2
0
0
0
1
0
1
2
1
1
0
2
1
1
0
0
0
2
2
0
0
2
2
0
0
0
1
2
0
0
1
0
0
1
0
2
1
2
0
0
1
1
0
1
2
2
0
0
0
0
2
0
3
1
3
1
1
1
2
0
1
0
0
2
0
1
0
1
1
1
2
2
0
1
0
0
2
0
0
1
0
3
1
0
2
1
0
0
0
0
2
1
0
0
1
1
0
1
1
0
2
1
2
0
0
1
0
1
0
2
2
0
0
1
0
0
3
0
2
0
1
2
1
2
1
0
0
1
0
0
0
0
2
0
2
1
0
0
0
2
1
0
1
1
1
1
2
2
1
2
0
0
0
1
0
2
3
1
0
2
1
0
0
0
2
0
1
0
1
1
2
2
1
0
0
1
1
2
0
1
0
0
3
3
0
0
2
0
0
1
0
2
0
1
0
0
3
1
1
0
0
1
0
0
1
0
2
0
2
1
0
0
1
0
1
2
3
1
0
0
0
2
2
0
1
2
1
1
0
8
0
0
2
0
1
0
0
0
0
0
1
0
1
0
0
1
2
4
0
0
0
0
1
0
2
1
0
0
2
0
0
1
0
1
0
1
0
0
0
1
1
0
0
2
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
3
2
0
0
1
3
0
0
0
1
0
0
0
1
2
1
2
1
2
0
2
0
2
0
2
2
0
1
1
2
0
1
1
0
0
0
0
1
0
0
0
4
0
0
0
2
1
1
0
0
0
1
1
1
1
2
0
3
2
0
0
2
0
2
0
0
0
0
0
2
0
0
1
0
0
0
1
2
2
0
1
1
0
0
2
1
0
0
0
0
0
2
1
0
1
0
0
2
0
0
1
1
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
2
0
1
2
0
0
1
1
1
1
2
1
2
1
0
1
2
1
1
0
0
2
2
1
1
1
2
1
0
0
1
0
2
0
2
0
2
0
1
1
2
1
1
2
2
3
1
2
0
0
0
0
0
1
0
2
2
0
1
0
0
0
0
0
0
2
0
3
0
0
0
4
1
0
2
0
1
3
1
1
2
1
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
1
2
1
1
2
2
0
1
2
0
2
0
2
0
0
0
1
1
2
1
1
1
0
2
1
1
2
0
0
0
2
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
2
0
1
1
2
1
1
0
0
0
0
2
1
0
0
0
1
2
1
0
0
0
0
0
0
2
1
1
2
1
0
0
0
1
0
4
2
0
1
0
0
0
0
0
2
1
0
1
1
2
0
0
0
2
1
1
0
1
0
1
0
0
1
1
0
1
1
2
0
0
0
1
1
1
1
0
2
4
1
0
2
1
0
2
0
0
2
1
0
0
0
0
0
1
1
1
0
0
0
0
2
1
1
1
1
0
0
2
2
2
0
0
0
3
1
0
1
1
2
1
2
1
0
0
0
2
1
0
2
0
0
1
0
2
0
0
2
0
2
2
4
1
1
2
2
1
1
0
0
0
0
0
1
1
2
0
2
2
0
2
0
0
1
0
2
1
1
1
0
0
0
1
0
0
0
0
3
1
0
0
1
0
0
0
1
0
2
1
0
1
0
2
2
0
2
0
0
2
0
0
0
1
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
1
3
0
2
0
0
1
0
1
1
2
1
1
1
3
2
0
0
1
0
0
0
1
2
0
0
1
0
0
0
0
1
0
0
0
1
2
0
2
0
0
0
0
0
0
0
2
2
0
2
0
1
1
2
2
2
2
0
0
2
0
1
0
3
0
2
1
0
0
1
0
1
2
0
0
0
1
1
0
0
3
0
0
0
1
2
1
0
0
1
0
1
0
0
0
1
0
4
0
1
0
0
2
0
0
0
1
2
0
0
0
1
0
1
1
1
1
0
0
0
2
1
2
0
2
1
0
0
0
1
2
0
0
0
1
1
0
0
0
1
2
0
0
0
1
0
0
0
0
2
2
0
1
1
0
1
0
2
2
3
0
1
1
2
2
2
0
0
1
0
1
0
0
1
1
3
0
1
0
0
1
1
2
0
1
0
0
0
0
2
2
3
0
2
2
0
1
2
0
0
0
1
0
1
2
0
3
2
2
0
0
1
0
2
0
2
1
0
2
1
3
0
2
2
5
1
0
2
1
1
0
2
0
0
0
1
1
2
1
0
0
0
0
0
1
2
1
0
0
0
0
2
1
1
0
1
2
0
2
2
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
1
2
1
0
1
0
1
1
0
0
2
0
1
2
0
0
0
0
0
0
0
3
2
1
1
0
2
0
0
2
2
3
0
2
2
3
1
1
2
0
0
0
0
2
2
0
1
0
1
1
2
1
0
4
2
0
2
0
0
1
0
0
0
3
0
1
1
1
2
0
2
1
0
0
1
0
0
1
2
0
0
0
0
1
4
0
2
0
1
0
1
0
0
0
1
1
3
0
1
1
0
0
2
0
0
0
0
1
2
0
1
0
1
0
0
0
1
0
0
1
0
0
1
0
2
1
1
0
0
0
1
0
0
0
2
1
2
0
0
0
0
0
0
2
0
2
0
0
1
2
0
2
0
0
1
2
1
0
0
1
0
0
2
0
0
2
0
1
0
0
1
0
0
0
1
1
0
2
2
1
0
0
0
0
0
0
0
0
0
1
0
2
2
0
2
0
1
2
2
1
2
0
0
0
3
2
3
2
0
1
2
0
1
0
1
0
0
0
1
2
1
2
1
1
0
1
2
2
1
2
0
1
1
2
1
0
1
0
2
1
0
0
0
1
2
0
0
1
0
1
1
0
2
0
0
1
0
1
0
0
0
1
1
0
0
1
1
0
0
1
0
1
1
2
1
1
1
0
0
1
6
0
0
1
0
2
0
1
0
0
2
0
2
0
1
0
0
0
1
0
2
1
1
0
0
2
0
0
0
2
0
1
2
0
1
1
1
2
1
1
2
0
2
1
0
1
1
1
2
2
1
1
1
1
0
0
0
0
0
2
0
0
0
1
1
1
1
0
0
0
0
2
0
0
0
0
0
2
2
2
2
1
1
0
0
2
0
0
3
0
1
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
1
1
0
0
0
0
2
1
0
0
1
2
2
0
1
1
2
1
1
0
1
0
0
0
0
0
2
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
2
0
1
0
0
0
1
1
0
0
0
1
4
0
0
0
0
0
1
1
2
1
0
1
2
2
0
0
0
0
0
0
0
2
1
1
0
0
0
1
0
1
0
0
1
0
0
1
1
1
0
0
0
0
2
2
0
0
0
2
2
0
1
2
0
1
1
1
0
2
0
1
0
0
1
1
0
0
0
0
2
0
2
1
0
1
1
2
2
1
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
1
0
0
0
0
2
1
1
0
0
2
0
1
1
0
0
2
2
0
0
1
0
0
1
0
0
2
2
0
1
1
1
1
2
0
0
0
2
1
1
0
2
0
0
1
0
1
0
0
0
0
0
1
0
1
2
2
1
0
1
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
2
1
1
0
0
0
2
1
2
0
0
0
0
0
0
1
0
1
2
0
1
0
0
0
2
2
1
0
1
1
0
1
0
2
0
1
1
0
0
0
2
1
1
1
0
0
0
0
1
2
2
0
1
3
0
2
0
1
1
1
0
2
1
2
1
0
0
1
0
1
0
1
2
2
1
0
0
3
1
2
2
0
1
0
0
0
0
2
1
1
3
2
0
2
1
1
2
0
1
1
0
1
0
0
1
1
5
0
2
0
2
0
0
0
1
0
0
0
1
0
0
1
1
1
1
0
3
0
0
0
1
1
0
2
0
0
1
1
2
0
0
1
0
0
0
1
2
1
2
1
2
2
0
0
1
0
2
0
0
0
1
2
0
2
0
0
3
1
0
0
2
1
0
2
0
1
1
1
0
0
1
0
2
0
0
0
1
0
0
0
0
2
1
0
0
0
1
1
2
0
1
2
0
0
1
0
0
0
1
2
0
0
0
0
1
2
0
2
3
0
1
1
1
0
1
5
1
1
0
1
1
2
1
0
1
0
1
1
0
0
2
1
0
0
0
3
1
0
1
0
0
0
1
1
2
0
1
0
0
1
1
2
0
0
0
1
0
0
1
2
1
0
0
1
0
0
0
2
1
0
2
0
1
0
0
0
0
0
4
1
1
0
0
0
2
2
1
1
2
0
2
2
1
0
0
1
2
1
1
1
2
0
0
3
2
1
0
2
0
0
2
1
0
0
0
0
0
2
2
0
0
0
2
1
1
2
0
1
0
0
0
0
2
2
0
0
2
1
0
0
0
2
1
1
0
0
2
0
0
0
0
0
0
1
0
2
0
1
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
1
1
1
0
2
0
1
2
2
0
2
1
1
0
1
2
2
1
0
0
1
0
1
1
1
0
0
2
2
1
0
0
2
0
0
0
2
1
1
0
2
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
2
0
2
0
1
1
1
0
1
1
0
1
1
1
1
1
0
0
2
0
1
0
1
1
1
2
2
0
0
0
0
1
2
1
1
0
0
0
0
0
1
1
1
1
1
1
2
0
0
2
1
0
1
0
0
1
0
0
0
0
1
0
1
1
0
0
0
3
0
2
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
1
0
1
1
0
0
0
1
2
0
1
2
2
1
1
0
0
0
2
2
0
2
1
0
1
0
2
1
0
1
0
1
1
0
1
0
1
0
0
0
0
2
0
0
1
1
0
0
0
0
2
2
0
1
0
1
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
2
2
1
0
1
1
0
1
0
2
4
5
0
3
0
0
3
0
0
0
0
0
0
0
1
2
2
0
2
1
1
0
0
0
0
0
1
0
1
2
0
1
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
2
0
1
1
1
0
0
0
1
1
2
0
1
2
0
0
1
1
0
2
0
2
0
1
0
0
0
1
0
1
0
1
0
0
0
0
2
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
2
1
0
2
0
0
0
0
0
2
0
0
2
2
0
0
0
1
2
2
0
0
0
0
2
1
1
2
1
2
1
2
0
0
0
0
0
1
0
0
2
0
2
0
0
1
0
0
0
2
0
0
0
0
0
1
1
0
0
1
0
0
0
0
2
0
2
0
0
0
2
2
1
0
0
0
1
0
2
0
0
0
0
2
2
1
1
1
1
2
1
1
0
0
1
0
0
2
0
1
1
1
0
2
2
1
2
2
2
2
1
0
0
1
0
1
0
2
0
1
0
1
0
1
2
2
2
0
1
2
1
0
0
0
1
0
0
1
1
1
0
2
2
0
2
2
2
0
0
2
1
1
0
0
2
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
2
2
0
1
1
2
1
0
0
0
1
0
1
1
1
0
3
0
3
0
0
0
2
2
0
0
0
0
2
0
2
1
0
0
1
1
2
2
2
0
0
0
1
0
0
2
0
1
0
0
1
0
0
1
3
0
2
0
0
0
0
2
0
0
2
2
0
1
2
0
3
0
2
1
2
0
0
1
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
2
1
1
0
0
0
1
1
0
0
0
3
1
0
1
0
1
0
0
1
0
0
0
2
1
0
2
1
1
3
2
2
0
1
0
2
0
1
0
0
0
2
1
1
1
1
0
1
1
1
0
2
1
0
1
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
2
2
1
2
1
0
0
0
1
2
1
2
0
0
1
0
1
2
0
0
1
4
1
2
1
0
2
2
0
2
0
0
0
1
0
2
2
1
1
0
0
1
0
2
0
2
1
1
0
2
3
1
2
0
1
0
0
0
1
0
2
1
0
1
0
0
0
0
1
0
2
0
0
2
2
0
0
0
3
1
2
0
2
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
2
0
0
0
1
0
1
0
0
0
1
0
0
1
1
0
0
1
0
0
0
1
0
1
3
0
0
1
2
2
1
0
2
0
2
0
2
0
2
0
0
0
0
1
0
0
0
1
0
1
1
2
1
0
2
0
1
1
0
2
0
0
2
1
0
0
1
1
2
0
0
1
0
1
0
2
0
2
0
1
0
0
1
1
2
0
1
1
0
0
0
0
0
0
0
1
1
3
0
1
0
2
1
0
1
0
0
0
1
1
1
2
0
0
0
0
0
2
3
0
0
2
0
0
0
2
0
3
0
1
1
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
4
0
0
2
0
0
0
2
1
0
0
2
0
2
2
0
3
0
0
0
0
0
1
2
0
0
0
0
0
0
6
1
1
1
0
0
1
1
0
1
2
2
0
1
0
1
0
1
0
0
2
1
2
1
1
2
0
2
0
0
3
2
0
2
1
0
0
0
0
1
0
0
2
1
2
0
1
0
0
0
2
1
2
2
0
0
0
1
0
1
0
2
1
0
0
0
2
0
2
1
1
0
0
1
2
1
0
1
0
0
0
0
1
2
1
1
2
0
0
0
2
0
2
0
1
0
0
0
1
1
1
1
1
0
1
0
1
1
1
0
1
0
0
0
0
0
0
1
1
1
2
0
0
1
1
1
0
0
0
0
1
1
0
2
1
0
2
1
3
0
0
0
0
2
0
2
0
0
3
0
1
0
2
2
0
0
0
1
1
0
1
1
2
0
0
0
0
2
2
0
1
0
2
0
1
0
1
1
1
1
0
1
0
0
0
2
3
1
0
1
1
0
0
2
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
1
2
2
2
1
2
1
2
0
0
0
0
0
0
2
0
0
1
0
3
0
1
0
0
0
1
0
0
0
1
2
1
1
0
0
2
0
1
0
2
0
2
0
1
0
1
1
2
1
1
2
1
2
2
1
1
0
1
2
1
0
0
0
3
0
0
1
0
2
2
0
2
0
1
0
2
0
0
1
1
2
0
0
0
1
2
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
1
2
0
1
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
2
1
0
0
1
0
2
1
0
0
1
1
1
2
0
0
2
1
2
0
0
1
0
1
0
1
0
1
0
0
0
1
0
1
0
0
1
0
0
0
1
3
0
0
1
1
0
2
0
1
1
0
3
0
0
2
0
0
1
0
2
2
1
0
2
1
1
0
0
1
2
0
1
0
1
2
1
0
2
5
0
0
2
1
2
0
0
0
0
0
0
1
0
1
7
1
0
0
1
0
1
0
1
1
2
1
0
0
0
0
0
0
0
1
0
1
0
0
1
1
1
2
1
0
0
0
0
0
1
0
1
1
0
0
0
0
2
2
0
1
0
0
2
0
0
0
0
1
1
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
2
2
1
0
0
0
1
3
2
1
2
1
0
0
0
1
2
1
1
1
0
0
1
0
0
1
0
2
0
0
0
0
1
1
1
0
0
0
0
1
0
2
2
0
0
0
2
0
0
0
1
1
0
0
1
0
0
0
3
0
1
0
0
0
0
2
0
0
0
0
2
1
0
1
0
0
2
0
0
0
1
0
2
1
1
1
0
0
0
0
2
0
0
0
0
2
0
1
0
0
1
1
0
0
2
0
0
2
2
0
0
2
0
1
0
0
1
0
2
2
0
3
2
0
2
0
1
0
0
0
1
0
0
2
0
2
2
2
3
0
1
0
0
0
2
2
1
0
0
1
0
2
2
0
2
1
0
2
2
0
0
0
0
0
0
0
0
0
2
2
2
0
1
0
1
1
2
2
0
0
2
1
0
0
0
0
0
0
1
3
2
1
1
0
0
0
0
2
0
0
0
2
3
1
0
1
0
0
0
0
0
0
2
1
0
1
0
2
0
1
1
1
1
2
1
1
3
1
0
2
0
1
0
0
1
1
0
2
0
1
0
2
1
2
0
1
0
1
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
2
1
3
0
1
2
2
2
0
2
0
0
1
0
0
1
0
0
2
0
0
1
0
0
0
2
0
1
0
0
0
1
0
0
1
0
1
0
1
1
2
2
1
0
0
1
2
1
2
1
1
0
0
1
1
0
0
0
0
0
0
0
1
0
2
1
2
1
0
2
0
2
1
0
3
0
0
0
0
1
0
0
0
0
2
0
0
0
3
0
1
0
0
2
0
1
0
0
2
0
1
0
1
0
1
0
0
2
0
3
0
0
2
0
1
0
1
2
0
2
1
0
0
1
1
2
2
0
0
0
2
0
2
1
1
0
0
1
2
0
1
0
1
0
0
2
0
1
0
0
2
0
0
2
0
0
0
1
2
1
0
0
0
2
0
0
0
1
1
1
2
0
2
1
0
0
0
2
2
0
2
0
2
0
1
2
0
0
0
2
0
1
0
0
0
2
1
0
1
0
2
0
0
2
0
0
0
2
2
2
1
1
1
0
0
1
0
2
2
0
2
0
1
1
1
0
1
1
0
0
0
1
0
1
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
4
0
2
2
0
2
2
1
2
0
1
0
0
0
0
1
0
0
0
3
0
0
0
0
2
1
1
1
0
2
0
0
2
0
0
0
0
1
2
0
0
0
0
2
1
1
1
0
0
0
0
2
2
0
2
1
1
1
0
2
1
1
1
1
1
1
0
0
2
1
0
2
2
2
1
0
1
2
0
0
0
0
1
0
1
0
0
1
1
1
1
3
1
0
0
0
2
0
0
0
0
0
2
1
0
1
2
1
1
1
2
0
0
2
0
2
1
1
0
0
0
1
0
0
0
2
0
3
0
0
0
1
1
0
1
0
1
0
0
1
1
1
0
2
0
2
0
0
2
1
0
1
1
1
1
4
1
1
2
2
1
0
2
0
1
0
0
0
2
1
0
3
2
0
0
0
0
1
1
1
0
0
1
1
0
1
1
0
0
0
1
0
2
0
2
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
2
0
0
2
1
2
2
0
0
1
0
2
2
0
0
0
0
1
2
2
1
0
0
0
2
0
1
0
1
1
2
0
0
0
0
0
0
1
2
1
1
2
2
1
0
1
3
1
0
1
0
0
2
1
2
2
0
0
1
0
2
1
2
0
0
1
1
1
0
1
0
2
0
2
1
1
0
0
2
0
3
0
0
0
3
2
2
0
0
2
2
0
0
1
0
0
1
0
1
2
1
2
1
0
1
0
2
0
2
6
2
0
0
0
1
1
1
1
0
2
1
1
2
0
1
0
3
0
0
1
0
1
1
0
2
0
2
1
0
0
2
0
0
2
0
0
1
1
0
0
4
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
2
0
1
1
1
0
0
0
1
0
0
0
1
1
0
0
1
0
2
0
3
2
0
1
2
1
1
1
1
0
2
0
4
2
1
0
2
0
0
1
1
0
0
0
2
0
1
0
0
1
1
2
2
0
1
0
2
0
0
2
0
0
2
0
3
0
0
7
1
0
0
0
0
0
0
1
0
0
1
2
4
0
0
2
1
0
2
0
0
1
3
1
0
1
2
0
2
1
1
0
0
0
1
0
2
1
1
0
0
0
2
3
0
0
0
1
1
0
0
0
0
2
1
2
0
0
1
2
0
1
0
2
1
0
0
0
1
1
0
0
1
1
0
1
1
0
0
2
1
0
0
0
1
1
1
1
0
2
0
0
2
0
0
1
0
0
1
1
2
0
1
0
1
1
0
2
0
1
1
0
2
1
2
0
0
0
1
0
2
0
0
0
2
0
0
0
0
2
0
1
0
1
1
1
0
0
3
1
0
0
2
0
0
1
1
0
0
1
1
2
0
1
3
0
2
0
0
0
2
0
0
2
1
0
3
0
0
0
0
0
0
1
2
0
2
0
0
1
2
1
0
0
2
3
1
0
2
0
4
1
0
0
1
0
3
0
1
2
0
1
1
0
1
1
0
0
2
0
0
2
2
2
0
0
0
0
0
2
1
2
2
2
2
1
2
0
1
0
2
2
1
0
2
3
0
0
0
0
1
0
1
1
0
0
0
0
2
0
0
2
3
2
2
1
0
0
1
0
0
0
0
2
2
0
1
0
1
0
0
2
0
0
0
0
2
0
1
0
1
1
0
2
1
2
0
2
1
0
0
0
0
2
0
1
1
0
1
2
2
2
2
2
0
0
0
0
1
1
0
0
3
0
2
2
0
0
1
1
0
1
2
0
2
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
2
1
1
1
2
0
0
0
1
0
0
0
1
0
1
0
0
1
0
1
1
2
0
0
0
0
0
1
2
2
0
0
0
0
2
3
1
0
0
2
0
2
2
0
0
0
2
0
0
0
0
1
0
0
0
0
2
1
1
1
1
0
0
1
0
0
0
0
0
0
2
1
1
1
2
2
0
0
0
0
0
0
1
0
1
3
0
1
2
1
1
2
0
2
0
0
1
3
1
1
0
1
2
1
2
2
2
1
1
2
0
0
1
0
2
1
1
0
0
1
0
1
0
0
0
0
2
0
1
1
2
2
0
1
0
1
0
1
0
0
1
0
0
0
1
1
0
1
0
0
0
1
0
2
1
0
1
0
3
1
0
1
2
2
0
0
1
2
0
2
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
1
2
0
1
2
0
0
0
0
0
1
1
0
0
2
0
0
1
1
1
2
3
0
0
0
2
1
1
3
0
0
1
1
1
1
0
1
0
1
0
1
1
2
0
0
0
0
0
2
1
0
0
1
0
2
2
1
2
2
0
2
1
1
1
2
3
1
0
1
2
1
2
0
0
2
1
0
2
1
2
0
1
0
0
2
0
0
1
0
0
0
0
1
0
0
0
4
1
2
0
0
1
1
0
0
1
0
1
0
0
2
0
0
0
0
1
0
1
2
1
0
1
0
0
0
0
0
1
0
0
0
1
1
0
2
0
1
0
0
1
2
1
1
1
0
0
0
0
0
0
2
0
0
0
1
1
0
1
2
1
1
0
2
1
0
1
2
1
2
1
2
0
0
0
2
0
2
0
0
1
0
0
0
1
1
0
3
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
1
0
1
0
1
1
0
2
1
1
2
1
1
0
1
3
0
1
0
1
0
1
1
1
0
2
1
2
0
2
0
1
0
0
1
1
0
1
0
2
2
1
0
1
1
2
1
3
2
1
0
0
0
0
0
0
0
2
2
1
0
0
0
2
1
1
2
3
0
0
1
1
0
0
1
2
1
1
0
0
1
0
1
2
0
0
1
0
0
0
0
0
1
1
2
1
0
0
0
1
0
1
1
0
0
2
0
0
0
0
1
0
2
2
3
0
2
0
2
2
2
0
0
1
1
0
0
0
0
0
0
1
1
1
1
2
0
0
2
2
0
0
1
0
2
0
0
0
3
0
2
0
0
0
1
0
0
1
2
1
0
0
1
1
0
2
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
2
0
2
2
2
2
0
0
0
0
0
0
1
2
0
2
1
2
0
1
1
0
0
1
1
1
0
0
0
1
0
2
1
0
0
0
0
1
2
0
0
0
3
0
2
2
0
2
0
0
2
0
1
1
2
0
0
0
2
0
0
1
1
1
2
1
1
0
2
0
0
2
1
2
0
0
2
0
0
0
2
2
2
0
0
0
1
2
1
0
1
2
0
2
2
0
1
0
0
1
0
2
0
1
0
0
0
0
2
1
1
0
0
0
2
2
1
0
1
1
2
2
0
0
3
1
0
1
0
0
0
0
1
0
3
1
1
0
0
0
0
0
1
0
0
1
0
2
2
2
2
1
1
0
1
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
2
1
0
0
0
2
1
2
0
0
1
2
1
0
0
0
1
0
2
6
3
1
0
0
2
0
0
0
1
0
1
0
1
0
0
1
0
0
1
0
1
1
2
1
2
0
0
2
1
1
0
3
0
1
1
2
0
1
1
2
1
0
1
1
0
1
0
1
1
5
0
1
1
1
2
0
2
0
0
1
0
2
3
2
1
0
2
0
1
1
3
2
2
1
0
2
0
0
0
0
4
0
0
1
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
1
2
1
0
0
0
1
1
1
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
2
1
2
1
2
1
0
2
0
0
1
2
0
0
2
1
0
2
0
0
0
2
0
0
2
1
1
1
1
0
0
1
0
0
1
0
0
1
2
0
0
2
0
1
1
1
0
1
1
2
2
2
0
0
0
1
2
0
0
1
0
0
0
2
1
0
0
4
0
0
1
0
1
2
0
1
3
0
2
0
2
0
0
0
0
2
0
2
1
0
2
0
0
0
1
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
1
0
1
0
0
0
1
2
0
0
1
0
1
1
0
2
1
0
1
2
1
0
1
1
2
2
0
0
2
0
3
2
2
0
1
0
0
0
1
2
0
2
0
1
3
1
1
1
1
0
1
1
0
0
2
1
1
1
1
2
2
0
0
0
0
1
1
0
2
0
3
2
0
0
1
0
2
1
2
0
1
0
0
0
2
0
0
2
0
0
0
0
1
2
2
0
1
1
2
1
0
0
1
0
1
1
1
0
1
2
0
0
0
1
2
0
2
1
1
0
0
0
2
0
2
0
0
0
1
0
1
2
2
1
0
1
2
0
0
0
0
2
0
0
0
1
0
0
0
1
0
1
0
1
0
1
0
2
1
1
0
1
1
0
0
0
0
2
2
1
1
0
2
0
1
0
0
0
0
2
2
0
0
0
0
0
1
0
1
0
2
0
1
1
0
2
1
0
0
1
2
5
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
3
0
2
2
0
2
0
0
1
0
0
0
1
0
0
1
2
0
1
1
0
2
0
2
1
2
2
3
0
0
0
2
1
1
0
2
2
0
2
2
1
1
0
0
0
1
0
0
1
1
0
1
1
1
3
0
1
0
0
0
3
1
1
2
0
0
0
0
1
2
0
0
2
0
0
0
1
2
0
1
1
1
2
1
1
1
0
0
1
2
2
0
0
0
0
0
4
2
0
2
0
0
1
0
0
1
0
0
0
2
0
0
0
0
2
1
0
0
0
0
1
0
0
1
2
0
1
2
1
0
2
0
0
0
1
1
0
1
0
0
1
2
1
0
1
2
1
1
1
1
2
0
0
0
0
2
0
0
0
1
1
0
1
0
0
0
0
0
2
0
0
1
2
4
0
0
2
1
0
0
3
0
1
1
0
0
1
0
2
1
1
0
0
0
1
0
0
0
0
0
2
2
1
1
2
1
1
0
0
0
2
0
3
2
1
0
0
0
0
2
0
2
0
0
0
1
0
0
0
1
0
2
0
0
2
0
0
0
0
1
0
0
1
0
1
0
2
1
1
1
0
0
0
2
0
0
1
1
0
2
1
1
0
0
0
0
2
0
0
2
0
2
2
0
0
0
0
1
0
0
2
0
2
2
0
1
0
2
1
2
1
1
0
2
1
1
0
1
0
0
2
1
1
0
0
1
0
2
0
0
0
1
1
1
0
1
2
1
2
1
0
0
2
1
1
0
0
0
0
2
0
2
0
0
0
2
0
0
0
1
2
0
1
1
3
0
1
0
1
2
3
2
1
0
0
0
0
2
0
1
0
1
1
0
0
1
0
1
0
3
2
1
1
2
1
2
2
1
2
0
0
0
1
0
1
1
0
0
0
2
0
0
0
1
0
1
2
1
2
0
0
0
0
0
1
0
0
2
3
1
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
1
0
0
0
0
1
2
0
0
2
1
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
2
0
1
0
0
1
0
0
2
1
0
2
1
1
2
0
0
0
0
1
0
0
0
1
0
0
3
0
0
0
0
0
1
1
1
1
1
1
1
0
0
0
2
0
2
1
1
0
1
0
1
2
1
0
0
0
0
1
0
0
1
1
0
1
2
0
2
0
0
1
2
0
0
1
0
0
0
0
1
0
3
0
0
0
1
2
0
0
0
0
1
0
0
1
0
0
2
0
0
0
2
1
1
1
0
2
6
0
2
2
1
2
2
1
0
2
4
0
1
2
1
0
1
1
0
1
2
1
2
0
0
0
3
0
0
1
1
1
1
1
3
0
0
0
2
0
0
0
1
0
0
1
0
0
0
1
2
0
0
1
0
1
0
2
1
2
2
2
2
1
2
1
1
2
0
0
2
0
0
3
2
2
1
1
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
6
0
0
2
1
1
0
1
0
0
2
0
1
1
1
2
0
2
2
2
0
2
1
1
0
2
1
0
1
0
0
1
0
1
0
0
1
2
1
2
4
0
1
0
2
2
0
1
2
1
2
0
2
0
0
1
0
0
1
2
1
0
2
0
0
0
2
0
1
1
2
1
0
0
0
2
2
0
2
0
2
0
0
0
0
0
1
3
1
0
2
1
0
1
0
0
0
1
0
0
1
1
0
2
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
2
2
2
0
0
0
0
1
0
1
1
1
0
2
0
0
1
0
1
0
2
0
1
0
0
0
0
2
0
0
1
2
0
0
0
2
1
0
2
1
0
1
0
2
2
2
0
2
1
1
2
0
0
0
1
0
0
0
0
0
1
1
0
1
1
0
1
0
1
0
1
1
1
1
0
0
2
2
0
1
0
1
0
0
2
0
2
0
1
0
2
2
1
0
0
1
3
1
2
1
0
2
2
0
0
0
0
3
1
2
0
2
2
2
1
0
2
2
0
0
0
1
2
0
1
0
0
1
2
0
0
2
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
1
1
7
3
1
0
0
0
2
0
0
0
1
0
2
0
1
0
0
1
0
2
1
2
2
0
1
0
2
1
0
1
2
3
0
0
1
0
1
0
2
0
0
1
0
1
2
1
0
1
0
0
0
0
1
0
0
0
2
0
1
0
0
2
1
0
0
0
0
1
1
2
1
0
1
1
2
0
1
1
0
0
0
0
1
0
0
1
0
2
0
1
1
0
0
0
0
1
1
2
1
2
0
0
1
0
0
1
0
2
0
1
0
2
0
1
0
0
1
0
0
2
1
2
1
0
0
2
1
2
2
0
0
0
0
1
0
0
0
0
0
1
1
2
0
0
0
1
1
1
1
1
0
2
1
0
1
0
0
1
1
1
0
0
1
0
0
1
0
1
2
0
1
0
2
1
0
0
3
0
1
0
2
1
0
0
0
1
0
1
0
1
0
2
0
0
1
0
0
0
2
2
1
1
0
2
0
0
1
2
0
1
1
2
0
0
1
2
0
0
1
1
0
1
0
0
0
2
0
0
1
0
0
3
0
0
2
1
2
1
2
0
0
1
1
0
2
0
1
0
0
2
1
0
1
0
1
2
0
2
0
0
1
0
0
2
0
0
0
1
0
0
1
1
2
1
0
0
0
0
2
0
1
0
1
0
1
0
1
2
1
0
1
0
0
0
0
1
0
0
2
1
0
0
1
0
0
0
0
0
0
0
1
1
1
1
1
1
1
2
0
0
0
0
1
2
0
1
0
0
0
2
0
2
0
0
2
0
0
0
0
1
1
1
1
0
1
1
0
1
0
0
0
1
0
2
0
0
0
1
2
2
1
1
1
0
0
0
0
2
0
0
1
0
1
0
1
0
1
2
0
0
1
0
2
1
1
1
0
2
0
1
0
0
2
0
2
0
2
0
1
0
3
0
0
0
0
1
1
1
1
2
2
2
0
0
1
0
0
0
2
3
1
0
0
0
0
2
1
3
0
2
1
1
1
1
0
2
0
0
1
0
0
1
1
1
1
0
3
0
0
1
0
0
2
0
2
0
1
0
0
0
0
0
1
2
0
1
0
1
0
0
0
0
1
1
9
0
0
1
1
2
2
2
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
1
1
0
0
2
0
0
0
1
0
0
0
2
2
2
1
0
1
1
0
1
1
0
0
2
0
1
0
0
2
0
2
1
0
2
0
0
2
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
2
0
0
3
0
1
1
0
1
0
0
0
0
0
0
2
0
1
1
1
0
1
0
0
1
1
2
1
3
2
0
0
0
1
0
0
2
0
0
0
2
0
0
1
0
0
0
2
1
2
1
0
2
1
1
1
0
0
0
1
0
0
0
1
0
0
0
1
0
2
1
0
2
2
1
0
2
0
2
0
0
2
0
2
0
1
1
2
0
1
1
0
1
0
2
1
2
0
0
0
1
2
0
0
1
0
0
0
0
0
2
2
0
2
0
1
0
0
1
2
2
2
0
0
1
0
0
1
0
2
1
1
0
1
0
1
0
1
0
1
0
1
2
1
2
1
1
0
0
1
2
2
0
1
0
0
2
0
1
0
0
0
0
0
1
0
0
4
4
2
0
1
0
0
0
0
2
0
1
0
1
1
1
1
2
1
0
1
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
1
1
0
0
1
0
2
1
1
0
2
0
0
1
2
0
0
0
1
0
1
1
1
0
0
1
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
2
1
1
1
1
1
1
0
0
0
0
0
1
1
0
0
1
0
0
1
0
2
2
1
0
1
0
1
0
1
0
2
1
0
0
1
1
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
2
0
1
2
2
1
0
2
1
0
1
1
1
0
0
0
0
1
1
2
2
2
0
2
0
0
0
1
1
2
0
0
0
0
0
0
3
0
1
1
1
2
1
1
0
0
0
2
1
1
0
0
0
2
3
2
0
0
0
1
0
3
2
0
0
1
0
0
0
1
0
0
0
1
0
0
2
0
4
0
1
1
0
1
0
1
1
0
1
2
2
1
0
1
0
0
1
2
2
0
0
2
1
0
1
1
0
2
2
0
0
0
1
0
1
0
1
0
1
0
1
2
0
2
2
0
0
2
2
2
0
1
1
6
0
1
0
2
0
1
1
0
0
1
1
0
1
1
0
0
2
2
0
1
1
0
0
0
0
2
0
2
3
1
2
0
0
0
0
1
1
1
1
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
2
0
0
2
2
0
0
2
0
1
0
1
0
0
1
0
1
2
2
0
0
0
2
0
0
0
2
1
1
0
0
2
0
0
2
2
0
0
1
1
0
1
1
0
2
1
1
1
2
2
1
1
2
0
1
1
1
0
0
1
0
1
1
1
0
0
1
0
1
1
2
1
0
1
0
2
1
0
0
2
0
1
3
0
0
2
1
0
2
4
0
0
0
2
1
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
2
2
0
0
0
1
0
1
0
0
0
0
0
1
2
1
2
2
1
2
2
1
1
0
0
0
2
3
2
0
0
1
0
0
0
2
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
2
3
0
0
0
2
1
1
1
1
0
2
1
1
0
0
1
1
1
1
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
2
0
0
2
0
1
2
0
2
0
0
2
1
0
0
2
1
0
0
1
4
1
2
1
1
1
0
0
0
1
0
0
0
2
0
0
0
2
3
0
1
0
0
1
0
1
0
0
0
0
2
0
0
1
2
0
1
1
0
1
0
1
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
5
1
0
2
0
0
0
0
2
0
0
3
0
1
0
2
0
2
1
0
1
0
0
2
2
0
0
0
1
2
1
1
1
1
2
1
0
2
1
1
1
1
2
0
0
0
0
0
0
1
0
1
3
1
0
0
3
2
0
0
0
0
0
0
1
0
0
1
4
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
2
2
2
1
2
1
0
1
0
0
2
2
0
0
0
0
2
1
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
1
0
1
0
0
0
2
0
0
0
3
2
0
1
1
2
0
1
0
0
2
1
2
0
0
0
1
0
2
0
0
0
1
2
0
1
1
0
2
0
0
1
0
0
0
0
2
2
1
2
1
0
2
1
1
2
2
1
2
0
0
1
0
0
2
2
1
0
2
1
1
0
0
0
1
1
1
0
1
0
0
0
1
1
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
1
0
1
1
0
1
0
1
6
1
2
0
1
0
1
0
0
0
2
0
0
1
0
0
0
1
1
1
1
2
1
0
2
0
0
2
2
2
0
2
1
4
1
2
0
0
0
1
1
0
2
0
0
0
2
1
0
2
1
1
2
1
1
1
0
0
2
1
1
0
0
1
2
2
1
0
0
1
2
2
0
0
2
0
0
0
1
0
1
1
0
1
0
0
2
1
1
1
2
0
2
0
2
0
2
1
0
2
0
0
0
2
1
2
0
0
0
1
0
2
2
0
2
0
1
2
0
0
0
2
0
1
0
0
1
0
2
2
2
0
0
2
0
0
1
0
0
0
2
1
0
0
2
2
1
0
3
0
0
2
0
1
1
1
1
2
1
0
2
0
1
1
0
0
0
2
1
0
0
1
0
0
2
1
0
0
1
0
0
1
0
1
0
0
2
1
1
3
0
1
2
1
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
1
1
0
1
0
1
1
0
1
2
1
0
0
0
0
0
0
0
1
0
0
1
0
1
1
2
0
2
0
0
0
0
0
1
1
0
0
1
1
1
0
0
2
1
0
1
0
0
1
1
1
3
0
0
2
1
2
2
0
1
1
0
2
0
1
0
1
1
2
1
2
2
2
1
0
1
0
0
0
0
1
1
2
1
0
0
1
0
2
0
0
1
0
2
2
1
0
0
0
0
0
1
0
0
2
1
0
0
0
2
1
0
0
0
2
1
1
3
0
0
0
1
1
2
2
2
0
1
0
0
0
0
1
2
1
1
2
1
3
0
0
0
1
0
0
0
0
1
0
0
1
0
2
0
2
2
2
0
0
0
0
0
1
0
1
2
0
2
0
0
0
0
1
0
1
2
0
1
0
1
0
0
2
1
0
0
1
0
1
0
0
1
0
0
6
0
0
1
1
0
1
2
2
1
0
0
3
1
0
1
0
1
1
0
0
1
0
0
1
1
1
2
2
0
2
0
2
0
0
2
1
0
0
0
0
2
0
2
1
1
2
0
1
2
0
1
1
1
0
1
0
0
1
1
0
1
0
0
1
1
6
1
2
0
0
1
0
1
0
1
1
0
0
1
0
1
0
0
0
1
0
1
0
2
2
1
0
2
0
0
0
2
3
1
0
2
2
0
1
0
5
1
0
1
0
3
0
1
0
0
0
2
0
0
0
2
0
0
0
0
2
1
0
1
0
2
0
0
0
0
2
1
0
0
0
0
2
0
0
0
1
0
0
2
2
2
4
0
0
0
0
1
2
0
2
0
0
2
0
0
0
0
1
0
0
0
1
2
0
0
2
1
1
0
2
2
0
0
0
0
1
0
2
0
1
0
1
1
0
0
2
0
0
0
0
0
0
1
2
1
2
0
1
1
0
1
0
2
1
2
1
0
0
2
0
0
0
0
1
0
0
1
2
2
0
0
0
0
1
2
0
0
1
0
1
0
0
0
1
0
0
2
0
1
0
0
1
1
0
2
1
0
2
0
0
0
0
0
0
1
0
1
1
1
0
2
0
0
0
0
1
0
2
0
0
0
0
2
1
2
1
1
2
0
0
0
2
2
0
1
2
0
0
1
0
0
0
2
0
0
0
1
1
2
1
2
1
2
0
1
0
2
0
1
1
0
1
1
0
0
0
0
2
0
0
2
2
0
2
1
0
1
1
0
1
1
0
0
2
2
0
2
0
2
1
1
0
1
3
0
0
0
3
2
0
0
0
0
0
0
3
1
0
1
0
0
2
0
1
0
1
1
1
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
2
0
2
1
0
1
1
1
0
0
1
2
0
0
0
1
0
1
0
1
0
0
0
1
1
0
1
2
0
1
0
0
0
0
1
2
2
0
1
0
2
0
1
0
1
2
1
2
0
0
0
0
1
0
2
1
0
1
0
2
0
1
3
2
1
2
1
1
0
1
0
1
0
2
1
2
1
0
1
0
0
2
1
0
0
0
2
1
0
0
0
0
0
2
2
2
0
0
0
1
1
0
2
0
1
2
1
0
0
1
2
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
1
0
3
0
0
2
0
0
2
0
0
1
1
1
0
1
4
0
1
1
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
1
1
4
0
1
1
1
0
0
1
1
1
1
0
0
0
0
1
3
2
0
0
0
1
0
1
3
0
0
0
0
0
0
0
2
0
2
1
0
2
0
2
2
2
1
0
2
1
1
2
1
0
0
0
1
1
0
1
0
0
0
2
2
1
2
0
0
0
0
0
3
0
2
1
4
1
1
2
0
0
1
0
0
0
2
1
1
1
2
0
0
0
2
1
0
0
2
1
0
1
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
1
2
3
1
1
2
0
2
0
0
0
0
0
0
0
0
0
2
2
0
1
1
0
1
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
2
1
0
1
2
0
1
0
1
2
0
0
0
0
1
0
1
0
0
1
0
2
2
2
1
0
1
0
2
0
2
0
1
4
1
1
2
1
1
2
1
2
0
0
0
1
0
0
1
1
0
2
0
2
1
1
1
0
0
1
2
1
3
1
0
2
0
0
1
0
2
0
0
1
0
0
1
0
1
1
0
0
2
0
0
0
2
0
1
0
1
0
1
0
0
2
0
1
1
1
2
0
1
0
0
1
1
1
2
0
0
1
0
0
1
0
1
0
0
1
0
2
1
2
1
0
0
0
2
0
1
0
1
1
0
0
2
1
0
1
2
1
2
1
0
0
0
0
0
0
2
0
1
0
0
0
2
1
2
2
2
0
0
0
0
0
0
1
0
2
1
2
2
2
2
1
2
2
1
0
2
0
0
2
1
0
0
1
0
0
1
0
1
0
0
2
1
0
0
1
2
0
2
2
0
0
0
0
2
0
1
1
2
0
2
0
2
1
0
1
1
1
1
1
0
1
0
0
0
0
2
2
2
0
3
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
2
1
0
0
0
2
1
0
0
0
0
0
0
1
1
1
1
0
1
0
0
0
1
0
0
0
2
1
1
1
0
2
0
0
0
0
1
0
0
0
1
0
0
1
0
2
0
0
1
0
0
1
0
0
0
2
0
0
1
3
2
3
0
0
1
2
0
2
0
2
1
1
2
1
0
0
0
0
1
0
0
1
2
0
2
2
0
0
0
0
0
1
1
0
0
1
2
0
1
1
2
1
1
0
1
2
2
0
2
1
1
2
2
2
0
2
0
0
1
0
1
1
0
1
1
1
2
1
0
0
0
1
1
0
0
0
0
1
2
1
1
1
1
2
0
0
16
0
1
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
2
1
0
2
4
2
0
3
0
0
2
0
1
1
0
2
0
1
0
0
0
0
2
0
1
2
0
0
2
0
1
0
0
1
0
0
0
0
0
1
0
0
2
0
1
1
2
0
0
1
2
1
0
0
1
0
0
0
1
0
2
1
0
0
0
0
1
0
0
1
0
1
0
2
1
2
0
0
0
2
2
0
0
2
0
0
0
2
0
1
2
0
0
0
0
0
1
2
0
1
2
1
0
0
0
2
0
2
0
2
2
1
0
1
0
1
2
1
1
0
2
4
1
1
2
2
0
0
0
0
2
1
1
1
0
1
0
1
0
0
2
0
1
0
1
2
2
1
2
1
0
0
0
1
0
0
4
2
0
2
0
2
0
2
0
1
1
1
1
0
2
0
0
0
1
1
0
0
1
1
2
2
1
0
3
2
1
1
0
0
0
1
0
2
1
0
0
0
0
2
1
0
1
0
1
1
1
2
2
0
1
0
1
0
1
0
0
1
0
3
1
2
1
1
3
2
0
0
0
1
0
2
2
0
0
0
0
0
1
2
0
0
0
0
2
2
1
0
0
0
1
0
1
0
1
1
0
2
0
1
0
0
0
2
0
1
0
1
0
1
0
0
0
0
1
1
0
0
2
0
1
1
1
0
1
0
1
0
2
1
0
1
0
0
1
0
1
0
1
2
1
0
1
0
0
1
0
0
0
1
1
2
0
0
0
0
0
0
1
1
0
2
0
0
0
1
1
1
1
2
0
1
1
0
1
1
0
1
2
0
1
2
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
1
1
0
1
0
1
0
2
1
0
0
4
0
0
0
2
0
2
0
1
0
0
2
2
0
1
0
1
0
0
3
2
1
1
2
2
0
0
3
1
0
1
0
0
1
0
0
2
0
1
1
0
0
0
2
2
0
2
0
2
0
0
0
0
0
0
2
3
0
1
0
1
2
0
2
1
1
1
1
0
2
1
2
1
4
0
0
0
0
2
0
0
0
1
1
2
1
1
1
0
2
1
2
0
0
2
2
1
2
0
1
1
1
1
1
0
0
1
0
0
1
1
1
0
2
2
1
1
1
0
0
1
2
0
0
0
1
0
0
1
1
2
1
1
1
1
1
0
1
1
0
0
1
1
2
0
0
0
1
0
0
0
2
0
1
0
1
2
1
1
0
2
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
2
0
2
0
2
1
3
0
2
2
0
0
0
2
3
0
0
2
1
0
0
1
1
2
2
1
2
1
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
1
2
0
2
0
0
2
2
0
0
0
1
0
3
0
0
0
0
0
2
2
1
0
2
1
1
0
2
1
0
1
1
2
0
2
1
1
0
2
2
0
1
1
2
1
0
0
0
1
0
1
0
1
0
0
1
0
1
3
0
1
0
3
0
2
2
1
2
2
0
1
0
0
0
1
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
2
0
2
1
0
2
1
0
0
0
2
0
0
0
2
0
0
3
0
0
1
0
0
2
0
0
0
0
2
2
0
0
1
1
0
1
1
1
0
0
2
0
0
2
0
2
0
1
2
0
2
2
0
1
0
1
0
0
0
2
0
0
0
1
0
0
0
0
1
1
2
0
0
1
0
1
0
0
0
1
1
0
0
0
0
1
2
2
2
1
1
2
1
0
0
1
0
1
3
2
1
0
0
0
2
0
0
0
0
4
0
1
0
0
0
0
1
1
0
1
0
0
2
0
0
2
1
2
1
1
0
1
1
2
0
0
0
0
0
3
0
1
1
0
1
2
1
1
2
0
1
2
0
2
1
0
3
0
1
0
0
1
2
0
0
2
0
2
2
2
0
2
0
0
2
0
1
0
1
0
2
0
2
0
1
2
1
0
1
0
1
1
0
0
1
2
2
1
0
0
0
0
2
3
1
0
0
1
0
1
0
1
1
2
1
0
1
1
2
0
0
0
0
1
1
0
0
0
1
1
1
0
1
0
0
4
0
1
0
0
2
2
0
0
0
0
0
1
1
0
2
1
2
1
1
0
2
0
0
0
0
2
1
0
0
0
0
2
0
0
0
1
0
1
2
0
0
0
1
0
0
1
0
0
0
0
1
0
1
2
0
2
1
0
0
3
0
0
2
0
0
0
1
2
1
0
0
1
1
2
2
0
0
0
0
1
0
2
1
1
0
0
2
0
0
0
2
2
1
0
0
0
2
2
2
0
0
0
1
0
0
0
0
1
1
0
1
1
1
0
0
1
1
1
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
2
1
0
0
0
0
0
2
1
1
2
0
1
0
0
1
2
0
0
1
1
1
1
0
0
0
1
0
4
0
2
0
2
0
0
2
0
0
1
0
1
2
1
0
0
0
0
0
0
0
2
0
0
1
0
1
1
1
2
1
1
1
0
2
0
0
2
0
2
0
0
1
1
0
0
1
1
0
0
0
0
0
0
2
0
3
0
2
0
0
3
1
0
1
0
0
0
0
1
0
0
2
1
1
1
1
2
2
2
1
0
2
0
0
2
1
2
2
2
0
0
0
0
2
0
0
1
1
3
2
0
0
0
0
0
1
2
0
1
0
0
0
1
1
2
0
0
1
0
0
1
0
1
0
2
0
0
2
1
0
0
2
2
1
0
1
1
1
1
0
2
0
0
1
0
0
1
0
0
3
1
0
0
2
0
1
0
1
2
2
1
1
1
2
2
0
2
1
0
0
0
0
0
1
3
1
0
1
1
1
0
1
0
1
0
2
1
0
2
0
1
0
4
0
0
2
0
0
1
1
0
0
0
1
0
0
3
2
1
0
0
0
0
0
1
0
2
1
1
0
0
1
0
1
0
0
0
2
0
2
0
1
1
1
0
2
2
0
0
1
0
1
0
1
1
1
0
1
0
0
1
1
1
0
0
0
1
2
0
1
0
0
0
1
1
1
2
2
0
1
1
0
2
0
0
2
1
0
0
0
0
0
0
0
2
2
1
1
2
0
0
0
1
2
0
1
1
2
0
0
2
2
2
1
0
0
1
1
1
1
2
1
0
0
2
1
1
0
1
1
2
1
0
0
2
1
1
2
0
0
2
0
4
1
0
2
0
0
0
1
1
0
2
0
3
2
0
1
0
1
0
0
0
0
2
1
0
2
1
2
1
2
0
1
0
2
1
0
1
1
2
0
0
1
0
2
1
1
0
0
1
1
2
0
1
0
2
0
2
1
0
0
0
0
0
2
0
1
1
0
0
2
2
0
1
0
0
0
2
1
0
0
2
0
0
0
0
0
0
1
0
1
0
1
2
1
1
0
1
0
0
0
1
0
0
1
0
2
0
0
0
1
0
2
0
0
2
1
0
0
1
0
1
2
2
2
2
0
3
4
1
0
0
1
0
0
2
1
1
0
2
2
0
1
2
1
2
2
1
1
2
0
2
0
0
1
0
2
0
0
2
2
0
2
2
0
2
2
2
0
0
0
2
1
1
2
1
1
0
2
0
1
0
0
4
0
0
0
3
2
0
0
1
1
1
0
0
0
2
0
0
0
1
1
2
2
0
0
2
0
0
0
0
2
0
0
0
1
2
0
0
1
1
2
0
2
0
1
0
1
1
0
1
2
0
0
2
0
1
0
1
0
0
2
2
1
0
2
2
0
2
1
0
1
0
1
1
1
2
0
1
0
1
2
0
2
0
0
0
0
2
2
1
0
0
0
2
2
0
0
0
1
1
0
2
0
1
0
0
1
0
2
0
0
1
2
0
1
0
0
0
0
2
0
1
3
0
1
1
0
1
3
0
1
1
0
1
0
1
0
2
1
0
2
0
0
0
0
0
2
0
0
2
0
0
0
1
1
0
0
0
0
1
0
0
0
0
2
0
1
2
2
0
1
1
0
3
1
0
0
0
2
1
1
1
2
2
0
1
0
2
0
2
2
1
1
0
0
0
0
0
1
0
0
0
1
1
0
1
1
0
2
1
0
1
1
1
1
1
1
0
2
0
2
0
2
2
2
3
2
1
2
0
1
0
2
0
2
0
0
0
0
2
1
2
1
1
0
0
0
0
0
2
0
0
1
1
2
0
0
1
0
0
1
0
0
1
1
2
1
0
0
0
2
1
2
0
1
2
1
0
2
0
2
0
1
1
1
0
1
2
0
1
3
0
0
1
1
1
1
1
1
1
2
0
0
0
1
0
2
2
0
0
0
0
0
0
2
0
2
1
0
0
0
2
2
0
0
2
2
0
1
2
0
0
1
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
3
1
0
0
1
0
0
2
2
0
0
1
0
0
0
0
0
1
1
1
0
1
0
0
0
0
3
0
0
0
1
0
1
1
2
0
1
1
0
0
0
0
1
0
1
0
2
0
1
0
2
2
0
1
0
0
2
0
1
1
3
1
2
0
0
0
1
2
1
2
0
0
0
0
0
0
0
1
2
1
1
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
1
0
1
0
0
0
2
1
0
0
2
1
0
1
1
1
1
0
1
0
1
0
1
1
0
2
0
2
1
2
1
1
1
0
1
2
1
1
2
1
0
1
0
1
1
1
2
1
2
0
2
0
2
1
1
1
1
1
2
1
1
0
0
0
4
2
1
0
0
2
0
0
0
0
1
1
1
2
0
2
2
0
0
0
0
1
1
2
0
0
0
0
2
2
1
1
0
1
0
0
0
1
2
2
0
1
0
4
1
1
0
2
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
2
0
0
0
2
0
1
11
2
1
0
0
0
2
1
2
3
1
0
2
2
2
0
0
0
2
0
0
0
2
1
1
1
0
0
0
0
1
1
0
0
0
2
1
1
1
0
1
0
2
0
2
1
1
1
0
1
3
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
1
1
2
0
2
1
1
0
0
2
0
1
0
0
2
1
0
0
1
0
1
0
2
0
1
0
0
1
1
1
0
1
1
1
2
0
2
2
0
1
0
0
1
1
0
0
2
0
0
1
1
0
1
0
1
0
2
1
0
0
0
1
1
1
0
7
3
1
0
1
2
1
0
0
0
1
0
1
0
2
3
1
0
0
1
1
2
1
1
2
1
1
2
1
0
1
1
1
2
4
2
0
0
1
1
0
0
2
1
1
0
0
2
1
0
2
1
0
1
2
1
0
0
2
0
2
1
2
2
1
2
1
0
2
0
1
2
0
0
0
0
0
0
0
0
0
1
1
0
2
2
1
1
2
0
0
0
2
1
4
0
0
1
0
2
0
0
0
0
1
0
0
1
0
0
1
0
0
1
2
0
1
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
1
0
1
0
1
0
0
0
2
2
1
0
1
0
0
0
0
2
1
2
0
0
0
4
2
1
1
2
1
2
0
1
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
1
0
0
1
0
1
0
0
1
0
2
3
0
0
0
0
1
1
0
2
1
2
0
0
1
0
0
0
0
0
1
0
2
1
0
2
0
0
0
0
0
1
0
2
2
1
1
2
0
0
0
0
2
2
2
0
3
2
1
0
2
0
2
1
1
2
1
0
0
1
1
0
0
0
0
1
1
0
0
1
1
1
0
0
2
2
0
0
1
0
0
2
0
2
0
1
2
1
2
1
0
0
1
0
0
2
2
0
1
2
2
2
3
1
2
0
0
0
1
2
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
1
2
0
0
0
1
1
0
1
1
1
0
0
0
3
0
0
1
0
0
0
2
1
0
2
1
2
0
0
0
1
0
1
1
1
1
0
2
2
2
2
0
0
0
1
2
1
0
0
1
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
1
1
0
1
3
0
1
0
0
2
0
0
0
2
2
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
2
2
1
4
0
0
2
2
0
1
1
0
1
0
2
0
0
0
1
0
1
0
3
1
1
1
1
0
2
0
0
2
1
0
0
1
2
0
0
1
0
2
1
2
2
0
2
2
0
1
1
0
1
0
0
0
0
1
1
1
1
2
1
0
1
0
1
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
2
1
3
2
1
1
1
1
2
0
1
0
1
0
0
2
2
0
1
0
1
0
0
0
2
0
0
2
0
1
2
1
0
0
2
0
0
0
1
2
0
0
1
1
0
1
0
1
0
0
2
0
0
1
2
0
0
0
1
2
2
1
0
3
0
1
0
1
0
0
1
0
2
2
1
0
1
0
2
0
1
1
0
2
2
0
1
0
0
1
0
1
0
0
0
0
1
1
2
1
1
2
2
2
1
1
0
1
3
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
2
2
2
1
0
1
2
1
2
1
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
1
0
2
2
2
1
1
0
1
1
0
0
0
0
0
1
0
2
0
0
1
2
2
0
0
1
2
2
1
0
0
0
0
0
1
0
1
0
0
2
0
2
0
0
2
2
1
1
2
0
1
0
1
0
0
0
0
0
0
2
2
0
2
1
2
0
0
1
2
0
3
1
0
0
2
1
0
1
0
0
0
0
1
0
0
0
0
2
1
0
1
2
2
0
0
2
1
1
1
0
0
0
0
1
0
0
2
1
0
4
3
0
1
2
2
0
0
1
0
1
1
0
0
0
1
0
1
0
0
0
0
1
0
0
2
0
6
1
0
2
0
0
2
0
0
0
2
0
0
1
0
2
0
0
1
0
0
2
0
0
1
0
1
1
0
1
1
1
2
1
2
0
0
2
1
0
1
1
1
0
2
2
0
0
0
0
1
2
0
2
1
2
1
0
0
4
1
0
2
1
0
0
1
0
1
0
2
0
1
1
1
1
0
1
0
0
0
0
0
1
1
2
2
1
2
1
0
2
0
2
0
0
0
2
0
0
0
1
1
1
1
1
0
0
1
0
1
1
0
1
1
0
0
0
0
0
1
1
0
1
2
0
2
0
0
2
1
2
1
2
0
1
0
0
0
1
1
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
3
2
1
0
3
0
2
1
1
1
0
0
0
1
0
2
0
0
1
1
2
0
0
2
0
2
0
0
1
1
0
1
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
2
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
1
1
0
1
0
2
0
2
0
0
1
0
0
1
0
1
5
1
2
2
2
0
1
2
0
1
0
1
2
0
0
1
0
0
2
0
0
0
1
0
2
2
0
2
0
1
2
0
0
0
1
0
0
2
0
1
2
1
1
0
0
0
0
0
0
0
0
0
0
3
1
1
3
0
1
1
1
0
0
0
1
2
0
1
0
0
2
3
0
0
0
2
1
0
1
0
2
1
0
1
1
0
1
1
2
0
0
1
2
1
1
0
1
0
0
0
2
0
1
1
1
0
1
1
0
0
0
0
0
2
0
0
0
1
0
1
1
0
2
0
1
0
0
1
1
0
2
0
0
0
0
1
2
0
1
1
2
0
1
3
0
3
1
0
0
0
1
0
0
2
0
0
1
2
0
0
1
2
0
0
0
0
0
1
0
0
0
1
1
2
2
0
0
2
0
0
3
0
0
0
0
1
0
0
2
0
0
2
1
1
1
2
0
0
0
1
2
0
1
1
0
1
0
0
0
1
0
0
0
0
2
0
3
2
2
0
0
1
0
0
0
0
0
0
2
2
1
1
1
2
0
0
2
1
1
0
2
1
2
1
1
0
0
1
1
1
2
0
1
2
1
0
2
1
0
1
0
0
2
0
0
2
1
2
1
0
0
1
0
2
0
0
0
1
2
0
1
2
1
1
3
0
0
1
0
1
2
0
0
1
0
1
1
0
0
2
0
0
0
0
0
1
0
3
1
1
1
2
2
0
2
0
1
0
2
0
0
0
1
1
0
1
2
1
0
1
1
0
1
0
0
2
2
1
0
0
1
0
1
1
0
1
0
1
1
0
2
0
0
1
2
2
2
1
0
0
1
0
0
1
2
2
0
0
0
1
2
1
2
1
1
1
1
3
0
0
0
1
1
0
0
1
2
0
1
0
1
2
0
0
0
2
0
0
0
0
0
2
0
2
1
0
1
1
0
0
1
0
0
1
0
0
1
0
1
0
0
1
0
0
1
1
0
2
1
0
0
0
0
0
0
0
0
2
1
0
1
0
2
0
0
3
1
2
0
0
0
2
0
1
0
1
2
0
2
0
0
0
0
1
0
2
1
1
0
0
1
0
1
0
0
1
0
0
2
1
2
0
1
0
0
0
1
1
0
0
0
3
0
2
2
0
0
0
1
0
1
0
2
2
0
0
0
0
0
1
0
1
1
0
0
0
1
1
2
2
1
0
2
0
0
2
1
1
2
2
0
0
0
0
0
0
3
1
2
0
0
1
1
2
2
1
0
1
0
2
2
0
0
1
0
1
0
1
0
2
0
0
1
2
0
1
1
0
0
0
2
0
1
0
0
2
0
4
0
1
1
2
0
0
0
0
0
2
1
0
1
1
1
0
1
0
3
0
1
2
0
2
1
2
1
1
1
0
0
0
0
0
0
1
1
1
2
0
2
0
1
2
0
2
0
0
0
1
1
2
1
0
0
0
0
3
0
1
3
0
0
0
0
0
0
0
0
0
0
1
2
1
0
1
0
0
1
2
0
0
2
1
1
2
1
0
1
0
2
1
0
0
0
0
2
1
2
2
0
0
1
0
0
1
0
1
0
2
1
2
2
0
1
0
0
2
0
0
0
0
1
2
1
0
0
1
0
0
3
0
1
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
4
1
0
2
1
0
0
1
0
2
0
1
2
2
1
0
0
1
2
0
1
0
0
2
1
0
0
0
2
0
1
0
0
0
1
1
2
0
0
0
0
1
0
1
0
0
1
1
0
0
1
0
1
0
0
0
1
2
1
0
0
0
0
2
0
0
0
2
0
1
0
3
0
0
3
2
2
0
0
0
0
0
1
1
1
0
2
2
0
2
1
0
0
1
0
0
0
0
2
2
0
1
0
0
0
0
0
1
1
0
1
0
1
1
0
0
0
2
0
0
2
0
1
0
1
2
2
0
2
0
1
0
0
1
1
0
0
1
0
2
0
0
4
1
1
0
0
0
2
0
0
0
2
1
2
0
1
1
1
0
0
0
0
0
0
0
0
2
1
2
1
0
1
1
1
1
0
0
0
0
1
0
0
0
1
0
0
2
1
2
0
1
0
0
2
0
1
1
2
1
1
0
0
2
0
0
0
0
0
0
0
1
0
2
2
0
2
0
0
2
2
1
1
0
0
2
1
1
0
0
2
1
1
0
0
1
0
1
1
0
0
1
2
1
0
2
0
0
1
0
1
2
2
1
0
0
0
1
0
1
0
2
1
0
1
1
0
2
0
0
1
1
1
0
0
0
1
0
1
0
1
2
0
0
0
0
0
1
1
4
0
1
2
1
1
0
1
2
0
0
1
1
0
0
0
0
2
0
0
0
2
0
0
0
1
2
1
0
0
1
0
1
1
1
1
0
1
0
2
1
2
2
0
0
1
2
2
0
0
0
2
1
0
1
0
1
1
0
0
2
0
2
1
0
4
1
0
2
0
2
2
2
0
0
0
0
2
1
1
0
1
2
0
1
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
1
2
2
2
1
1
0
0
0
1
0
0
0
0
2
0
0
0
2
1
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
2
1
0
0
2
0
3
0
0
2
0
0
2
1
1
0
4
1
1
2
0
0
2
1
0
2
2
0
0
2
1
1
1
0
2
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
1
2
0
1
1
0
0
0
1
2
2
0
2
1
2
1
0
0
4
0
0
1
0
0
0
0
0
2
1
2
1
0
2
0
3
0
1
1
0
2
0
0
1
1
2
0
1
0
2
1
0
1
2
0
1
0
0
1
1
1
2
1
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
1
1
2
1
1
2
3
0
2
0
2
0
0
0
0
0
0
2
1
0
1
1
0
0
0
1
0
1
2
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
2
2
1
0
1
0
0
1
0
1
1
0
0
1
0
1
2
0
0
2
0
0
1
0
1
1
4
0
0
0
0
0
0
1
0
0
1
0
0
1
1
3
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
2
1
0
0
3
2
0
2
1
0
0
1
1
1
0
2
2
1
2
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
1
0
3
0
0
2
0
0
1
0
0
0
1
2
0
1
0
2
2
1
2
0
0
0
0
2
2
1
0
0
1
0
0
0
2
2
0
1
1
2
0
1
1
0
1
0
2
0
2
2
0
2
0
0
0
0
1
0
1
1
0
0
1
2
0
0
1
0
1
0
0
0
0
0
0
2
1
1
1
0
1
0
2
0
2
0
0
1
0
0
1
2
2
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
2
0
1
2
0
2
0
0
2
0
2
0
1
0
2
0
0
2
0
2
1
0
2
1
1
0
0
0
0
0
1
1
0
2
1
1
1
0
1
2
1
1
0
2
3
0
2
0
1
1
1
2
0
0
2
0
0
2
0
0
0
1
1
2
0
1
0
0
1
0
1
2
0
0
1
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
3
0
0
0
2
0
0
2
1
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
2
1
2
0
1
0
2
0
0
0
0
1
0
0
1
2
1
1
1
0
1
0
0
1
1
0
2
1
1
3
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
2
0
2
0
1
1
0
0
0
1
2
2
0
1
0
0
0
1
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
2
1
1
0
0
1
1
1
1
1
2
1
0
1
1
0
0
1
0
0
2
0
1
0
1
0
0
0
0
1
1
0
1
2
0
1
0
0
1
1
0
2
0
0
1
0
0
2
0
2
2
0
1
0
0
3
0
0
1
3
2
0
1
1
2
0
0
1
0
1
2
0
0
0
0
1
3
1
0
1
2
0
4
1
0
0
0
2
0
0
1
0
0
0
0
0
2
0
2
2
1
1
1
0
0
4
0
0
0
0
6
0
0
1
1
1
1
0
1
2
0
2
2
0
1
2
0
0
0
0
0
1
0
2
1
4
0
0
1
2
0
0
1
2
2
1
2
0
1
1
0
2
1
0
0
0
1
2
2
2
1
0
0
2
1
1
0
0
0
1
1
1
2
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
1
1
2
1
0
0
0
0
0
0
2
0
1
1
0
0
2
0
1
0
0
0
1
2
1
0
2
0
2
0
1
0
0
0
1
2
2
0
1
0
2
1
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
2
0
1
2
0
1
0
1
3
1
2
0
2
0
1
0
0
0
0
0
2
1
0
0
0
1
1
0
1
1
1
0
0
1
1
0
1
0
2
0
2
3
1
1
2
0
2
1
1
0
0
1
1
1
0
0
1
1
0
1
0
0
1
2
0
0
0
2
0
1
1
1
2
0
0
1
2
2
2
0
0
0
3
0
1
1
0
0
2
0
1
0
0
1
2
0
0
0
0
0
0
0
0
1
2
1
2
2
0
0
1
0
0
0
0
1
2
0
1
1
2
1
0
0
0
0
0
2
0
0
0
3
2
1
1
0
2
0
1
0
1
0
0
0
2
0
0
0
0
2
1
2
1
0
2
1
0
4
0
0
0
0
2
1
2
2
0
1
1
0
0
0
2
1
1
2
0
1
1
1
0
2
0
2
2
0
0
0
0
1
1
0
0
0
0
2
0
0
1
2
2
1
2
0
0
0
0
0
1
2
0
1
0
0
0
2
2
0
4
1
1
1
0
1
2
2
2
0
0
0
1
1
1
0
2
0
3
0
0
1
1
0
2
2
2
0
0
3
2
0
1
0
1
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
2
1
1
1
1
1
2
2
0
0
2
1
2
1
0
1
1
0
1
0
0
0
2
0
0
1
0
2
0
2
1
0
1
1
1
0
1
0
0
1
1
0
1
0
0
0
2
0
1
0
2
0
1
1
0
1
0
1
0
0
1
0
1
2
1
0
2
2
0
2
0
0
2
1
2
0
0
1
1
1
2
1
0
1
0
0
2
0
0
2
1
0
0
0
1
2
2
0
0
2
2
0
2
0
0
0
1
0
0
2
4
0
1
0
2
1
2
2
0
0
2
0
1
1
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
2
0
1
1
0
0
0
1
0
1
0
2
0
1
1
0
1
2
0
1
0
1
0
2
0
0
0
0
2
0
0
1
0
1
0
1
0
1
1
0
0
0
2
0
0
0
0
2
0
1
0
2
0
0
0
3
1
0
1
1
2
0
1
0
0
1
2
2
1
2
1
2
0
1
0
1
0
1
0
0
1
1
0
0
1
1
0
1
0
2
2
1
2
2
0
1
0
0
0
1
0
2
1
2
0
1
1
3
0
2
0
0
0
1
0
0
1
0
1
1
1
0
1
0
0
0
0
0
0
0
0
1
0
1
2
3
0
0
0
0
0
2
1
0
2
0
2
0
0
0
0
2
0
2
1
0
0
0
2
1
0
0
1
0
0
0
2
1
1
1
2
1
1
2
1
0
1
0
0
0
0
2
0
0
2
2
2
0
0
0
0
0
2
3
0
0
0
1
0
0
0
1
0
0
0
1
2
0
0
1
0
2
0
1
0
0
2
0
1
1
1
1
1
1
2
1
0
0
1
0
2
0
1
0
1
0
1
1
0
1
2
0
0
0
0
0
1
1
0
2
0
0
2
0
0
0
1
0
0
2
2
0
0
0
0
0
1
0
1
0
0
0
2
0
0
2
0
1
0
0
0
1
2
2
2
1
0
0
1
2
1
1
0
0
0
1
1
0
1
1
1
0
0
1
0
1
2
0
1
1
1
1
0
0
0
0
0
0
0
1
3
3
2
0
2
0
1
1
0
0
1
0
0
1
1
0
2
1
0
0
2
2
1
1
1
1
1
2
0
0
0
1
0
0
2
0
0
2
0
2
0
1
1
1
0
0
0
0
0
5
0
2
0
0
0
1
0
1
0
1
1
0
0
0
0
0
1
2
1
0
0
1
1
0
0
0
0
1
2
0
0
2
0
2
0
0
1
0
0
0
0
0
1
0
1
1
2
1
2
1
1
2
2
0
2
0
0
0
1
2
2
1
1
0
0
0
0
2
0
1
0
2
1
0
0
0
0
0
0
2
0
2
0
1
1
0
0
0
0
0
2
1
0
0
1
1
0
0
0
0
2
0
1
0
0
1
0
0
1
0
0
0
0
0
2
1
1
2
0
0
1
0
0
2
0
0
3
0
0
2
0
1
2
0
1
0
0
0
1
0
0
2
2
0
1
0
2
0
0
0
0
0
0
1
1
2
0
0
0
1
1
2
0
1
0
0
0
0
0
0
0
0
1
0
0
2
1
0
1
2
0
0
1
0
0
2
0
2
0
1
1
0
0
1
2
0
0
0
2
0
0
0
1
0
0
2
2
1
2
0
0
0
2
3
0
2
0
0
1
1
0
0
1
0
0
0
1
2
0
0
2
2
1
0
0
0
0
1
2
0
2
0
0
3
2
0
1
1
1
2
2
1
0
0
2
0
0
1
0
0
0
0
0
0
1
0
1
0
1
1
1
0
0
3
0
1
1
0
1
2
3
1
0
0
0
0
0
0
1
2
0
1
2
1
2
0
0
0
1
2
1
0
0
0
0
2
1
0
0
2
0
0
1
1
0
0
0
2
1
1
0
1
0
0
1
1
2
0
0
0
1
2
0
2
0
2
1
3
1
0
3
2
0
0
0
0
2
1
2
1
1
0
1
2
2
0
2
0
1
2
0
0
4
0
0
0
1
1
2
1
2
0
0
0
1
1
2
1
1
1
0
2
0
0
0
1
4
0
1
0
0
0
0
0
0
1
0
0
1
0
2
2
2
0
1
0
0
2
0
1
1
0
0
0
2
3
2
1
0
0
0
0
1
0
1
0
1
2
2
2
1
0
0
1
2
2
0
1
1
2
0
0
0
1
0
1
1
1
0
3
0
0
2
0
0
0
2
1
2
0
0
0
3
2
0
0
0
1
1
1
1
0
1
0
1
2
2
2
1
1
2
1
1
0
1
2
0
0
1
0
1
0
0
1
0
0
1
0
1
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
2
2
1
0
1
0
2
0
1
2
0
0
1
1
1
2
0
0
1
2
2
0
0
1
0
0
1
0
2
1
1
2
0
0
0
0
1
1
3
0
1
1
0
1
0
1
0
0
0
0
1
0
2
0
2
0
0
1
2
1
1
1
1
0
0
0
1
0
0
0
1
0
1
2
1
0
0
2
0
0
0
1
1
0
2
0
0
2
2
0
2
1
2
0
2
2
0
2
1
1
1
1
1
1
0
0
0
0
0
2
1
2
0
0
0
0
2
0
1
2
0
0
1
0
0
1
1
0
2
2
0
2
0
0
0
0
1
2
0
1
0
1
0
1
0
0
0
1
0
0
2
1
1
1
0
0
0
0
0
1
0
1
0
0
1
0
2
0
0
1
2
0
1
1
1
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
1
1
0
1
0
1
0
2
1
0
3
0
0
1
2
1
0
0
1
0
1
0
2
0
1
0
0
2
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
1
2
0
0
0
2
1
1
1
2
0
2
3
0
0
2
0
1
1
1
0
1
2
0
2
1
2
1
1
0
0
0
0
1
0
2
0
2
0
0
3
1
0
0
0
0
2
1
0
1
0
0
0
0
0
0
2
0
2
0
1
3
1
1
0
0
2
0
2
2
0
1
0
2
0
0
1
0
0
1
0
2
0
2
1
1
0
0
1
0
1
2
2
1
2
2
0
0
0
0
0
0
0
0
1
2
0
1
0
2
0
2
0
0
1
0
2
1
2
0
1
1
0
1
1
0
2
2
2
2
0
0
0
2
0
0
1
0
1
2
1
0
2
2
1
1
0
2
3
1
0
1
0
0
2
0
1
1
0
1
0
0
1
2
0
0
0
0
2
0
0
1
1
1
0
0
1
5
1
2
0
0
2
2
3
1
0
0
2
1
0
0
2
0
0
2
3
1
2
0
1
0
1
0
3
0
2
1
0
2
0
0
0
1
0
2
1
1
3
0
2
1
0
2
0
1
1
1
2
1
1
1
0
0
1
2
0
1
1
0
0
1
1
0
0
1
0
2
2
1
2
2
1
0
0
0
0
1
0
2
1
1
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
1
1
1
0
0
0
1
0
1
1
0
0
0
0
2
1
4
2
1
0
0
2
2
0
3
2
0
1
1
1
1
0
0
0
0
0
0
0
1
2
1
0
1
0
0
0
2
0
0
0
0
1
2
0
2
2
0
2
2
0
1
1
1
1
0
0
0
1
1
2
1
0
1
0
0
0
2
1
0
0
0
1
0
0
1
0
0
0
2
0
1
2
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
1
0
1
0
0
1
2
0
0
0
0
0
2
0
0
0
0
2
1
0
1
2
2
1
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
3
2
0
1
0
0
1
1
1
1
0
0
2
1
4
0
0
0
2
0
2
0
0
1
1
1
3
1
2
0
0
0
2
0
0
0
0
2
0
1
0
2
2
1
1
0
0
1
2
0
0
0
0
0
2
0
0
1
1
0
0
1
1
1
2
2
2
0
0
0
1
2
0
0
2
0
2
0
0
2
1
0
0
0
0
1
1
2
2
0
2
0
0
0
1
1
1
1
1
2
0
1
2
2
0
1
0
0
1
0
1
1
3
1
0
2
0
0
2
0
0
0
0
2
0
1
0
1
1
2
0
0
0
2
0
1
3
0
0
0
2
2
0
0
1
0
2
1
0
1
0
1
0
0
1
1
0
2
2
1
1
0
1
0
0
0
0
1
1
1
1
0
2
1
1
0
0
0
1
0
0
2
1
1
1
1
1
0
1
2
2
1
1
1
2
1
0
0
0
0
0
0
1
1
1
1
1
1
2
0
0
2
0
0
0
1
3
0
2
2
1
2
0
1
0
0
0
3
2
3
0
1
0
2
0
0
0
1
2
1
0
0
1
0
0
0
1
1
0
2
1
1
1
0
0
1
2
2
1
1
0
0
1
1
1
2
1
1
2
0
2
1
3
0
0
0
2
0
0
0
1
1
1
2
0
1
0
1
1
1
1
0
1
0
1
1
2
0
0
1
0
0
2
0
0
0
0
0
0
4
1
2
1
0
0
0
0
2
0
1
1
0
0
0
2
3
1
0
1
0
0
1
1
1
0
0
1
0
2
0
0
0
2
2
0
1
0
0
0
2
0
1
2
2
1
0
0
1
1
0
0
0
0
1
2
1
1
1
1
0
0
0
1
1
0
1
1
1
0
0
0
0
3
1
0
1
1
2
1
1
1
0
1
2
1
2
0
1
0
0
1
0
1
0
1
0
0
1
2
2
2
0
0
1
0
1
5
1
0
2
1
0
1
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
1
2
0
2
0
0
0
0
1
2
0
1
0
1
0
0
0
0
1
0
0
1
0
0
2
1
1
1
1
2
0
0
0
0
0
1
0
0
0
1
2
0
2
0
0
5
0
3
0
0
1
2
1
1
1
1
2
1
1
1
0
1
0
2
0
0
0
0
1
0
0
4
0
1
2
1
1
0
1
2
2
1
2
0
0
0
0
0
2
0
0
0
0
2
1
2
1
0
1
0
0
1
0
0
1
0
2
0
0
0
0
1
0
2
0
2
0
1
0
1
1
1
0
0
2
0
1
0
0
0
0
0
2
1
1
2
0
0
0
0
0
1
0
0
0
1
1
3
2
1
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
3
0
2
1
1
2
4
0
1
2
0
2
0
0
1
0
4
0
2
2
1
1
1
0
1
0
2
1
1
1
0
0
1
0
2
2
0
2
2
0
2
2
0
0
2
1
1
0
3
1
2
0
1
2
2
0
1
0
0
1
0
0
0
1
1
0
0
0
2
2
1
1
0
2
0
1
1
3
0
0
0
0
0
1
2
2
2
2
0
2
1
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
1
0
0
1
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
1
1
2
0
0
0
1
0
1
2
0
0
0
1
0
0
0
1
1
0
2
2
0
0
1
0
0
1
1
0
1
2
0
0
0
0
2
2
2
0
0
0
0
0
1
0
1
2
1
2
2
1
1
0
2
0
1
0
1
0
1
2
0
2
0
1
2
2
0
1
1
0
0
2
2
2
0
1
1
0
1
1
2
2
2
0
2
1
0
0
0
2
0
1
1
1
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
2
2
1
1
1
0
0
1
0
0
0
2
1
1
2
0
0
0
1
0
0
0
0
1
1
0
1
1
1
2
2
0
0
0
1
1
1
0
1
0
1
1
2
1
0
3
0
0
1
0
0
0
1
1
1
1
0
0
0
0
0
0
1
2
1
2
2
1
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
1
1
2
1
1
1
2
0
0
2
0
2
2
0
1
1
0
1
0
2
1
0
1
1
2
1
0
0
6
0
1
0
1
1
2
0
1
0
0
0
0
1
0
0
0
0
2
0
0
2
0
1
2
2
1
0
2
1
0
1
0
0
1
0
0
2
0
0
0
0
2
1
1
2
0
0
0
1
0
1
2
2
0
2
2
0
1
1
1
0
1
0
0
0
0
0
1
0
1
1
1
0
0
1
0
1
2
1
2
0
0
0
1
2
0
0
0
0
0
1
0
0
1
2
1
0
1
0
0
0
3
1
1
0
0
0
0
0
4
1
1
0
0
1
1
2
4
0
1
0
0
0
0
0
2
0
2
1
2
0
0
3
0
0
1
1
0
0
2
0
0
2
1
1
2
0
0
1
1
1
0
1
3
1
0
0
2
2
1
0
2
0
0
0
1
3
0
2
2
1
2
0
0
1
1
2
2
0
0
2
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
2
0
2
1
1
0
0
1
1
0
0
1
2
2
0
0
0
0
0
2
1
1
1
1
2
3
0
1
0
0
0
1
0
0
0
0
0
1
2
2
0
1
0
0
1
0
1
0
0
1
0
2
1
1
0
0
0
1
0
0
2
1
0
0
1
0
0
1
1
0
0
2
0
1
0
2
0
3
1
0
0
0
1
0
0
0
2
2
0
0
0
0
1
0
0
2
0
0
2
2
0
0
2
0
0
0
0
0
1
0
1
1
0
0
0
2
2
0
1
2
1
1
0
1
0
1
1
1
0
0
0
2
2
0
0
2
0
2
2
0
2
1
1
1
0
0
0
0
0
1
0
1
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
1
2
2
0
1
1
0
0
0
0
1
0
0
2
0
2
1
1
1
0
0
1
0
0
0
1
2
0
2
0
2
0
0
2
2
2
0
0
1
0
1
1
0
0
0
1
1
0
1
1
0
0
0
2
3
1
1
0
0
12
0
2
1
2
1
0
0
0
1
0
0
1
1
2
1
0
1
2
0
0
3
0
2
0
1
2
0
1
3
0
1
1
2
2
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
1
1
0
0
2
1
2
0
0
1
2
0
0
0
0
2
0
2
0
2
2
0
1
1
0
0
0
0
2
2
2
1
0
0
1
1
1
2
0
0
0
1
0
0
1
2
2
2
2
0
3
1
0
1
2
0
0
0
2
0
1
1
2
0
1
0
0
2
2
0
1
0
3
1
1
0
2
2
1
0
1
2
1
2
2
0
2
2
2
1
0
0
0
1
2
1
0
0
1
0
0
0
1
2
0
2
0
2
7
0
0
0
0
3
2
0
0
0
0
0
3
1
0
0
1
0
0
0
1
1
0
1
2
1
1
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
1
2
2
0
1
1
0
2
0
1
0
0
0
2
0
1
0
0
0
3
0
0
2
0
0
3
0
0
0
1
1
2
2
0
0
0
1
0
2
0
2
0
1
0
1
0
0
1
1
1
0
0
1
0
0
1
0
0
1
0
2
0
1
2
2
0
1
2
2
0
0
1
2
0
2
1
0
2
0
1
2
0
1
0
0
0
0
0
0
0
0
1
1
2
0
1
2
0
3
0
0
1
1
0
0
1
0
0
0
1
0
0
2
2
0
2
0
1
1
0
0
0
2
1
2
0
0
0
0
0
0
0
1
1
1
3
1
1
0
0
0
2
1
0
2
0
2
2
0
3
1
0
0
2
0
0
0
0
2
1
0
0
0
2
0
0
0
1
0
2
1
0
1
0
2
1
0
2
1
0
1
0
0
0
0
5
1
0
0
0
2
1
0
2
3
4
2
2
0
3
0
1
0
0
2
0
0
2
2
1
0
0
0
0
0
0
1
0
0
2
0
1
1
2
2
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
1
1
1
0
1
2
2
1
0
0
0
1
2
3
0
1
0
0
0
1
1
0
0
1
1
0
0
0
1
1
1
0
2
0
0
1
1
0
1
0
1
0
0
0
0
0
0
1
0
0
1
2
2
0
0
1
2
2
1
0
0
1
1
0
0
2
1
2
0
2
2
1
2
1
0
1
2
0
0
2
0
0
2
1
0
1
0
1
2
0
0
1
0
2
0
1
0
2
2
0
0
0
0
0
0
0
2
2
0
2
0
1
0
2
0
0
0
0
0
0
0
2
0
0
1
0
2
1
0
0
0
0
1
0
0
0
1
4
2
1
1
0
1
0
1
1
1
2
1
0
0
0
0
1
1
0
0
0
2
0
2
2
1
2
0
0
1
1
2
0
0
0
0
1
0
0
0
2
0
3
0
0
1
0
1
1
2
1
1
0
2
0
2
2
1
0
0
3
1
1
0
2
0
2
0
1
0
12
0
0
0
0
1
0
1
2
1
2
0
0
2
1
0
2
1
1
0
2
2
2
1
0
0
1
0
3
0
1
2
0
1
1
0
0
0
0
1
2
1
1
2
1
0
2
1
0
0
0
0
1
1
1
0
0
1
2
0
2
2
0
1
2
2
0
1
2
0
0
0
0
0
3
0
1
0
2
2
0
1
0
2
2
2
0
1
0
0
2
2
1
0
2
0
0
0
0
1
1
0
1
0
0
0
1
0
2
2
1
0
3
0
2
2
2
0
2
1
1
0
2
1
1
0
0
0
0
0
0
0
0
1
0
0
0
3
0
1
0
1
2
1
1
2
0
0
1
2
0
0
0
2
1
1
1
0
2
1
1
2
1
2
0
0
2
0
1
2
0
1
1
1
0
0
2
0
0
0
1
0
1
1
1
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
1
0
3
2
0
1
1
2
1
0
1
1
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
4
2
1
0
2
1
1
2
1
2
2
0
2
1
0
0
0
1
0
1
2
1
0
2
0
1
0
0
0
0
0
1
1
1
0
0
0
1
0
2
0
0
1
0
1
0
0
0
1
1
0
0
0
2
0
1
1
2
1
0
2
2
2
0
0
0
1
1
4
1
1
1
0
1
2
1
0
0
1
0
0
2
2
1
1
0
1
1
0
0
2
0
1
1
0
4
1
1
1
0
1
0
2
0
3
0
1
1
0
0
2
1
1
0
3
0
0
1
0
1
1
1
2
0
1
1
0
0
0
2
2
1
1
0
2
0
1
1
0
0
0
0
0
1
0
0
0
1
2
1
1
2
0
1
0
0
0
1
0
0
2
0
1
0
1
0
0
1
0
1
2
1
0
0
1
0
0
1
1
0
0
2
2
0
0
0
0
0
2
1
1
1
1
2
1
0
0
0
0
0
0
0
1
2
1
0
1
1
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
1
2
0
0
1
0
2
2
2
0
0
0
1
0
0
0
1
0
2
2
1
2
2
0
1
0
0
0
0
2
1
2
0
1
0
0
0
2
0
2
0
0
3
0
1
0
2
2
0
0
0
0
2
1
0
0
2
1
0
0
0
0
1
0
1
1
1
4
1
0
1
1
1
0
0
0
1
2
2
1
0
0
0
1
2
0
1
2
1
2
0
0
2
0
1
1
0
1
0
1
2
2
0
2
1
0
3
2
0
0
1
0
2
1
0
0
0
0
2
1
0
0
0
1
1
0
2
0
1
0
0
0
2
2
0
0
0
0
2
2
2
0
0
0
6
0
0
2
2
2
0
0
0
1
2
2
1
1
2
2
0
0
0
0
0
0
0
0
2
0
2
2
0
1
0
2
0
1
0
2
0
0
0
1
0
1
2
0
0
2
0
0
0
2
0
0
3
0
1
0
1
1
0
1
1
1
0
1
2
0
0
0
0
1
0
1
2
0
0
1
0
1
0
0
0
0
0
1
2
0
0
0
0
0
3
2
0
2
1
0
2
0
0
2
0
3
0
0
2
2
1
1
2
1
1
0
1
0
0
2
0
1
2
0
0
0
0
1
1
0
0
0
0
1
0
2
2
1
1
0
1
0
0
2
0
0
0
1
0
1
1
2
7
0
0
0
2
0
1
2
0
1
1
1
1
2
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
2
1
0
0
0
1
0
0
1
0
2
0
0
0
1
0
0
1
1
1
2
2
1
1
0
0
1
0
0
1
0
1
2
1
0
0
0
0
1
1
0
0
2
0
0
1
1
0
2
1
2
0
0
0
0
1
0
0
1
2
0
0
2
2
0
1
0
0
0
1
0
2
2
0
2
0
0
1
1
2
0
2
1
0
0
0
0
0
3
2
0
2
1
2
0
0
0
0
1
0
0
0
1
1
0
1
1
0
1
0
0
0
2
2
2
2
0
2
0
1
0
0
0
0
1
0
0
0
1
0
0
1
1
1
1
2
0
2
2
0
3
2
0
0
1
0
0
0
0
0
2
3
1
0
0
0
0
0
0
1
2
0
3
1
0
1
2
1
2
0
0
1
1
0
0
2
0
0
2
0
0
0
2
1
2
3
1
1
0
0
0
2
0
1
0
1
1
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
3
0
5
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
2
1
0
0
1
1
0
1
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
4
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
2
0
1
0
0
2
2
0
2
2
1
0
1
1
2
1
1
0
1
1
1
2
0
0
0
1
2
0
0
2
0
0
0
0
2
0
1
0
1
0
1
0
1
0
1
0
0
0
1
1
0
2
0
1
2
2
0
0
0
0
1
0
0
1
0
2
0
1
2
2
1
1
0
2
1
1
0
2
0
0
2
0
0
1
0
5
0
2
1
0
1
0
0
2
0
2
0
1
1
3
1
0
1
0
0
0
0
0
1
0
1
1
0
0
2
1
0
1
1
0
1
0
0
0
2
1
0
2
1
0
0
0
1
0
0
2
0
1
1
2
2
1
1
0
0
0
0
1
1
0
0
2
0
1
2
0
3
0
0
0
0
0
0
1
3
0
2
0
0
0
0
0
0
0
1
2
0
2
2
0
0
0
0
1
0
3
1
2
2
1
0
0
0
0
2
0
0
0
1
2
0
0
1
0
1
1
2
2
0
1
1
3
0
0
0
0
2
2
0
2
0
0
0
0
2
0
0
0
0
1
0
0
1
1
0
1
0
0
0
2
1
1
0
0
0
0
0
0
1
1
2
2
0
0
1
0
0
1
1
0
0
0
1
1
0
0
0
0
1
0
0
2
1
0
2
1
0
0
0
1
1
0
2
0
2
1
1
2
0
1
2
0
1
2
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
2
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
1
2
0
0
1
0
1
0
1
0
1
1
0
2
0
0
1
0
0
0
1
0
2
0
0
1
0
1
2
1
2
0
1
0
2
0
0
0
0
0
2
1
0
0
0
2
1
2
2
0
2
2
0
2
0
1
1
1
1
1
0
1
2
2
0
2
0
2
0
0
2
1
0
1
1
1
0
0
2
0
0
1
0
0
2
0
0
2
0
0
0
0
2
1
1
1
0
1
1
1
0
0
0
0
2
0
1
0
0
1
0
1
0
1
0
0
1
0
2
0
1
2
1
0
0
0
1
2
0
1
0
0
0
0
1
1
0
0
0
0
1
2
0
0
0
1
1
1
0
1
0
0
0
0
1
1
0
1
1
1
2
0
0
0
0
0
0
2
2
2
0
0
0
0
1
1
1
0
2
0
2
1
2
1
0
1
0
0
0
0
0
2
0
0
0
0
1
0
2
0
3
1
0
1
1
1
1
1
0
1
1
0
1
1
0
0
1
1
1
0
0
0
0
0
1
1
0
2
2
0
2
0
2
0
0
0
0
0
1
0
0
1
0
0
2
1
1
0
2
1
0
4
0
2
1
1
0
0
0
0
2
0
0
2
1
2
1
0
0
1
1
2
2
1
0
1
1
1
1
1
1
0
1
0
0
0
2
0
2
0
1
1
2
2
0
2
0
0
2
2
0
2
1
0
0
0
0
0
1
0
0
1
1
1
2
0
0
1
0
1
2
0
0
2
0
2
1
2
0
0
0
0
3
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
2
1
1
0
0
1
1
0
1
0
2
1
1
1
0
1
0
0
1
0
0
5
0
0
0
2
0
1
1
0
2
2
0
1
0
0
0
2
0
1
2
2
2
1
0
0
4
0
0
0
0
1
2
0
1
2
1
0
2
1
1
0
0
0
0
2
2
2
0
0
0
1
2
0
0
0
2
0
1
0
0
0
0
1
0
2
3
0
0
2
0
2
2
0
1
0
0
1
0
0
0
2
0
1
1
0
1
0
2
2
0
2
0
0
0
3
2
0
0
1
0
0
0
2
0
0
1
1
0
0
1
0
1
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
2
2
0
2
0
1
1
0
0
2
1
3
1
1
0
1
0
0
0
0
1
0
1
0
1
2
1
1
0
0
2
0
1
2
2
0
0
1
0
1
0
1
1
1
0
0
0
0
2
0
0
1
2
2
1
0
2
0
0
1
0
0
0
0
2
0
3
0
1
0
2
2
2
2
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
2
1
0
2
2
0
1
0
1
1
0
1
1
0
0
1
1
1
1
1
0
0
0
0
0
0
2
0
0
2
0
0
1
2
0
1
2
2
1
1
2
0
1
0
0
1
2
2
1
1
0
1
2
0
0
1
0
0
0
0
0
5
0
2
0
2
3
0
0
2
1
1
0
2
2
1
2
0
1
1
3
0
0
0
0
0
2
0
1
0
0
1
2
0
1
0
4
2
1
0
0
2
0
0
3
3
1
0
1
2
0
1
2
0
1
0
0
0
0
1
0
2
1
1
0
1
0
2
1
0
0
2
0
0
1
1
1
0
1
0
0
0
1
1
0
1
2
0
2
0
0
0
1
1
1
2
0
0
2
0
1
1
2
1
0
0
0
0
0
1
1
1
2
0
0
2
1
1
0
0
2
2
1
0
0
0
2
0
2
0
0
1
1
2
2
1
0
0
1
0
2
0
1
0
1
0
0
3
0
0
0
2
2
0
2
3
2
0
0
0
0
1
0
0
1
1
1
2
2
0
2
0
2
0
0
0
2
0
0
0
1
2
0
2
1
0
0
0
1
0
7
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
1
0
1
0
2
0
2
0
0
2
0
2
0
2
2
1
0
0
1
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
2
0
0
0
0
1
2
0
0
3
0
2
2
0
0
1
0
0
2
0
1
5
0
0
0
0
1
2
2
0
1
0
1
1
0
0
1
2
2
2
0
0
1
0
0
1
0
2
1
0
1
0
0
0
0
0
0
2
2
0
1
0
1
0
1
1
0
0
0
2
0
0
0
0
0
2
4
2
1
0
1
1
0
1
2
0
0
0
0
1
1
0
1
0
0
2
0
0
1
1
0
1
2
2
0
1
0
1
0
0
0
0
0
0
0
0
2
1
1
2
1
1
0
0
2
1
1
0
0
0
2
0
0
1
1
0
0
1
0
0
0
0
1
1
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
2
1
1
1
2
2
2
0
1
1
1
1
0
0
0
0
1
1
0
1
0
0
0
1
0
2
0
1
0
0
0
0
1
1
0
2
5
0
1
1
0
2
0
1
0
2
0
0
1
0
1
2
2
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
2
0
0
2
0
0
2
0
0
0
0
2
1
0
0
0
1
0
2
2
0
1
0
2
0
1
2
0
0
2
1
0
0
1
0
1
2
1
0
1
1
1
2
0
1
2
1
0
1
0
2
0
2
1
0
1
0
0
0
0
0
1
0
2
0
1
1
0
1
0
1
0
1
0
1
0
0
1
0
0
0
1
1
1
0
1
0
2
1
2
1
0
0
0
0
2
0
0
2
0
3
1
0
1
2
1
1
0
2
0
0
0
1
1
0
0
0
1
2
1
0
1
2
1
2
2
0
2
0
0
1
0
1
1
1
0
1
1
0
0
1
0
1
0
0
2
1
0
1
1
0
2
2
0
2
0
0
3
1
1
1
0
5
0
1
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
1
0
2
0
1
0
2
0
0
0
0
1
0
0
2
1
2
1
0
0
0
1
2
0
0
1
0
0
0
1
0
3
0
0
0
0
0
0
1
0
1
1
1
1
1
0
1
0
0
1
2
0
0
0
0
2
0
2
0
1
1
0
0
0
0
0
1
1
1
0
1
1
2
0
2
1
0
0
2
0
0
2
1
2
0
1
0
0
0
2
2
0
1
0
2
0
2
0
2
0
1
0
0
2
1
1
2
2
0
0
2
1
2
1
0
0
1
1
0
1
0
0
0
0
0
1
0
1
1
1
0
0
0
1
0
2
2
1
0
2
0
0
0
2
2
1
0
2
0
0
0
1
0
0
0
1
0
0
2
0
2
0
1
1
0
1
0
1
0
2
0
1
0
1
0
1
0
0
0
0
2
3
0
1
0
0
0
0
0
0
0
2
2
0
1
0
0
2
0
0
0
1
0
0
0
0
1
0
1
0
0
1
2
1
1
2
2
0
2
0
0
1
0
0
0
1
1
0
0
0
0
2
0
1
1
1
0
0
2
1
2
2
1
0
2
0
0
1
0
2
1
2
1
1
0
0
0
0
0
0
1
0
0
0
2
2
2
0
0
0
2
2
0
1
1
1
0
0
0
0
0
0
1
1
1
0
1
0
1
0
0
0
1
0
2
1
4
0
2
1
0
0
3
1
0
1
0
4
1
2
2
0
0
2
0
0
0
1
1
1
1
0
1
2
2
0
0
0
1
0
0
1
1
2
0
1
0
1
1
2
0
0
2
2
0
1
1
1
1
0
0
1
0
0
1
0
0
2
1
0
0
1
0
0
1
2
0
1
0
0
2
1
1
1
1
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
1
1
0
2
0
0
1
1
0
3
1
2
0
0
1
0
0
1
0
1
3
0
0
1
1
0
0
0
0
1
0
0
2
2
1
0
0
0
1
0
0
0
1
1
0
2
1
2
0
0
1
0
1
1
1
0
1
0
1
0
1
2
2
1
3
1
0
0
0
0
0
0
1
0
0
1
0
2
1
0
0
0
1
0
1
1
0
1
0
0
0
0
0
1
2
0
0
1
0
1
0
0
1
0
0
0
1
0
2
1
0
0
2
1
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
1
6
1
1
0
2
0
4
1
1
1
0
2
1
0
0
1
2
1
1
1
0
2
0
0
1
0
0
1
2
2
0
2
0
1
0
1
1
2
2
1
0
0
3
0
0
0
0
2
0
1
3
1
0
2
1
0
0
1
3
1
0
1
1
0
0
0
0
1
0
0
0
1
1
0
1
0
2
0
0
0
0
1
1
0
0
1
2
1
0
0
0
1
0
2
0
2
1
1
0
2
0
0
0
0
0
0
1
1
0
2
0
1
2
2
0
1
1
1
0
0
0
2
0
1
0
1
1
0
0
0
0
2
1
1
3
2
0
1
0
0
1
1
0
2
1
0
1
0
1
0
0
1
0
0
1
2
1
1
1
0
1
1
0
2
0
4
1
0
1
2
0
0
1
1
2
0
2
0
2
1
0
0
0
1
0
0
0
2
1
2
0
1
0
0
1
1
0
0
0
0
2
2
0
1
0
0
0
0
0
0
2
2
2
0
2
0
1
0
2
0
2
1
0
1
1
2
0
0
0
1
2
0
1
1
0
1
2
2
0
0
2
2
2
1
1
0
1
1
1
0
0
2
1
0
2
2
2
0
0
3
2
1
0
0
1
0
0
0
0
0
1
2
0
1
0
0
2
0
0
0
1
1
1
1
1
0
1
0
1
0
1
0
0
1
1
0
2
1
0
0
0
0
1
2
0
0
2
2
2
0
2
0
0
0
2
2
0
0
0
1
0
0
0
1
0
0
1
1
1
0
2
0
0
0
1
1
2
0
1
1
1
0
0
0
0
1
1
0
1
2
0
0
0
1
2
0
0
2
0
0
0
0
2
2
0
0
1
0
2
1
1
2
2
1
1
2
0
1
0
0
0
1
0
2
0
0
0
0
1
0
1
0
0
1
1
0
0
2
0
0
0
1
0
1
2
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
1
1
1
2
1
0
0
1
0
1
1
2
0
0
0
0
0
0
1
1
1
0
0
1
0
1
1
2
0
2
1
0
1
0
2
1
1
1
1
1
0
2
0
0
3
1
2
0
0
0
2
0
1
0
1
1
2
1
1
0
0
1
0
0
2
1
0
3
0
0
2
1
0
1
1
0
1
0
1
1
0
2
0
1
0
2
0
0
2
0
0
0
0
2
2
0
1
2
1
1
2
0
1
0
0
0
1
0
0
0
0
0
1
1
2
2
2
0
1
1
0
0
1
0
2
1
0
0
1
2
3
0
1
2
1
0
1
0
1
0
2
0
0
1
1
0
2
1
1
0
0
1
1
1
0
0
0
1
1
0
1
1
0
1
0
1
0
1
0
0
0
0
0
1
2
1
0
1
0
0
0
0
0
1
0
1
2
2
0
0
0
0
1
0
0
2
2
2
0
2
0
2
0
3
0
1
1
0
0
1
1
0
2
0
0
0
0
2
1
0
0
0
1
0
2
0
2
2
0
0
2
2
2
1
1
0
2
2
0
1
1
1
0
0
1
1
1
1
2
0
2
0
0
1
0
3
1
0
1
0
1
0
0
1
0
2
1
0
0
2
2
0
0
1
1
0
3
1
2
0
0
1
1
0
0
0
2
1
3
0
2
1
0
0
0
0
1
3
1
0
1
0
0
0
0
0
1
2
2
1
0
2
2
0
6
0
1
2
0
0
0
1
0
1
0
1
0
0
0
2
0
0
2
0
0
1
0
1
3
1
1
2
0
2
0
3
2
0
0
0
1
0
0
0
0
1
2
0
2
0
0
0
0
1
0
0
0
2
1
1
2
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
1
0
2
0
0
0
1
2
2
2
8
2
1
1
1
2
0
0
0
1
3
0
0
0
1
0
2
0
0
1
1
0
0
0
2
0
1
0
2
1
0
1
0
0
1
0
0
2
0
0
0
0
1
2
0
0
1
0
0
0
0
1
2
0
2
0
0
0
0
1
2
0
1
1
2
0
2
2
2
0
2
0
0
0
0
1
0
1
2
0
0
0
1
1
1
0
1
1
0
0
1
1
2
1
0
0
1
1
0
0
2
0
1
1
0
0
2
0
2
0
2
0
0
1
2
0
0
2
0
0
1
1
2
1
0
1
0
0
0
0
4
0
2
0
0
2
0
2
2
2
1
0
0
2
0
0
1
1
2
3
2
2
0
1
0
0
2
0
2
2
0
1
0
2
1
0
0
0
0
2
1
1
0
0
2
2
0
2
0
0
2
0
0
1
0
1
1
2
1
0
0
1
1
0
0
0
1
0
2
0
1
0
2
0
0
0
0
1
0
4
0
0
2
1
0
0
2
1
1
1
0
2
0
0
2
1
1
0
1
0
0
0
1
0
3
0
0
0
1
3
0
2
0
0
0
1
0
0
0
2
2
1
0
0
1
1
1
2
1
1
1
1
0
1
0
0
1
0
0
0
1
1
2
1
1
0
1
2
1
2
1
0
0
1
0
2
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
2
2
0
1
0
1
11
0
0
0
1
2
1
1
0
1
1
1
1
0
2
0
0
0
1
1
1
1
1
0
0
2
0
3
1
2
0
2
0
0
0
1
1
0
0
0
2
1
0
2
0
1
0
0
0
1
2
0
0
0
0
2
2
0
1
1
0
1
2
0
0
0
1
1
0
1
0
0
1
0
3
1
1
0
0
1
1
2
2
2
0
0
0
2
0
0
0
2
0
1
0
0
0
2
0
2
1
2
0
1
0
2
0
1
0
0
0
0
0
1
0
0
1
1
2
3
0
1
0
1
0
0
1
2
1
0
3
0
2
1
0
1
2
2
0
0
2
0
2
1
0
1
2
1
0
0
0
1
1
1
0
2
0
0
0
0
1
1
2
0
0
0
0
2
0
0
1
1
1
0
0
1
1
1
1
1
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
1
1
0
2
1
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
2
1
2
0
2
0
0
0
1
1
0
1
1
5
1
0
3
2
0
1
2
0
1
0
2
1
1
1
1
0
0
0
1
0
0
0
0
0
1
1
0
2
0
0
0
0
0
1
2
2
0
1
2
0
0
0
1
0
0
0
1
1
1
2
0
3
2
0
0
0
0
3
0
1
0
1
0
1
0
0
1
1
2
0
1
1
1
2
0
1
1
1
1
2
0
0
1
0
0
2
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
1
2
0
1
0
1
0
2
0
2
2
0
0
1
1
0
1
0
0
2
1
2
2
1
0
0
0
0
2
2
1
1
2
2
1
0
0
0
1
0
0
1
0
0
0
1
1
1
0
0
0
0
0
2
0
3
1
0
0
0
0
0
1
0
1
1
0
0
0
2
0
0
0
2
0
0
2
0
1
1
0
2
4
1
2
1
0
1
0
0
1
1
2
0
2
1
1
0
0
0
0
0
2
0
0
0
2
1
0
1
1
2
2
1
1
0
0
0
1
1
1
1
0
0
1
2
0
0
0
2
0
1
1
2
0
0
0
0
0
1
1
0
0
2
0
2
0
0
0
0
0
0
2
0
0
1
0
1
0
3
0
0
0
2
0
0
0
1
0
2
0
2
2
0
2
0
0
2
0
0
1
2
1
0
1
0
0
2
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
2
1
0
1
2
0
0
0
2
0
2
0
0
2
0
1
2
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
1
1
0
1
0
1
2
2
0
0
1
2
0
2
0
0
2
1
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
2
0
1
0
0
2
1
1
0
0
1
2
1
2
0
0
0
1
2
0
0
0
0
2
1
2
1
2
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
1
1
2
2
0
0
0
0
1
1
0
0
2
1
1
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
2
2
0
1
1
1
0
0
0
1
1
2
1
1
1
0
1
1
0
1
1
2
1
0
0
0
0
1
1
1
0
0
2
0
0
0
2
1
0
1
2
0
0
2
1
1
1
0
0
2
1
0
0
0
3
2
0
2
0
1
0
0
2
1
1
2
0
0
0
1
0
0
1
0
1
1
1
0
0
1
1
2
2
0
1
0
0
2
3
0
0
0
1
0
1
0
2
0
2
0
0
0
2
0
0
0
1
0
0
2
2
2
1
0
0
1
1
0
0
2
2
2
2
0
1
0
0
0
0
0
1
1
0
0
2
0
1
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
1
0
0
0
0
2
2
1
2
0
1
0
2
0
1
0
0
2
0
1
1
0
2
2
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
1
1
0
1
3
0
0
0
0
2
1
2
0
2
0
0
0
0
0
2
0
2
1
1
0
0
0
2
1
0
0
1
1
0
2
0
1
0
0
0
0
0
1
0
2
1
0
0
1
0
1
0
1
1
1
1
0
0
0
2
2
1
3
1
1
1
0
0
1
0
0
0
0
1
0
0
0
2
3
0
0
2
0
0
1
2
0
1
0
0
1
2
1
2
2
1
2
1
0
0
1
0
1
0
5
0
0
0
0
1
0
0
1
0
0
1
1
2
1
0
0
0
3
0
0
2
0
0
2
0
0
2
1
0
0
1
0
2
0
0
0
0
2
0
2
2
0
1
0
0
0
0
1
0
1
0
0
1
1
2
1
2
1
2
2
1
0
2
0
0
1
1
0
1
1
0
2
2
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
3
0
0
0
0
0
1
0
0
1
1
0
1
1
1
0
0
0
1
3
0
2
1
1
0
0
2
0
0
1
2
2
1
0
1
0
1
0
2
1
2
1
0
1
2
0
0
2
1
1
0
1
0
0
1
2
2
0
0
1
0
2
2
0
1
0
2
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
2
1
0
2
0
2
1
0
6
1
0
1
2
0
0
0
0
1
1
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
1
2
1
7
0
0
1
0
2
2
2
2
0
0
2
2
1
0
0
1
0
0
0
1
0
1
1
1
1
0
0
1
0
0
2
0
0
0
0
0
2
1
1
0
1
0
0
1
0
3
0
2
1
1
0
2
0
1
0
2
0
0
2
0
1
2
0
1
0
1
0
0
0
0
1
2
0
0
1
2
0
1
0
1
0
0
1
0
2
2
0
1
0
0
0
1
0
0
0
0
0
2
0
2
0
0
2
2
0
0
0
0
0
0
2
0
0
2
0
1
1
1
0
1
1
1
2
2
0
1
2
0
1
0
0
0
2
1
0
1
0
0
0
2
2
0
1
1
2
0
0
1
0
2
1
0
0
1
0
1
2
2
1
0
2
3
0
0
2
2
0
0
0
0
1
2
1
2
0
0
1
1
1
2
0
0
0
0
3
0
0
1
1
1
2
2
1
0
1
0
1
1
0
0
0
1
1
0
0
2
0
1
1
1
0
0
1
1
0
0
1
1
0
1
0
3
1
0
0
1
0
0
0
2
0
0
2
1
2
2
0
0
0
2
0
1
0
0
1
0
1
2
0
2
1
0
0
1
1
0
1
0
1
2
0
1
1
0
0
1
0
1
0
1
1
2
0
0
0
2
1
0
0
0
1
1
1
0
0
0
1
1
1
0
0
0
0
3
1
1
1
0
0
2
2
2
1
0
1
0
0
1
0
0
0
0
0
1
2
0
2
0
0
1
0
2
2
0
0
0
2
2
0
0
1
0
1
0
0
0
2
1
1
0
1
0
0
0
0
2
0
1
0
1
1
1
1
0
0
0
1
1
0
0
0
0
2
0
0
2
1
1
2
2
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
2
2
1
2
2
1
2
0
1
0
1
0
0
1
1
0
1
0
1
0
0
0
1
1
2
3
1
0
0
0
0
0
0
2
0
1
0
0
1
1
2
0
0
0
0
1
0
0
1
2
0
0
1
1
2
0
0
0
2
2
2
1
1
0
0
0
0
0
0
1
1
1
0
1
0
0
2
0
0
0
2
2
1
2
0
0
0
2
1
0
2
0
0
0
1
2
0
0
2
0
0
0
1
0
0
1
2
0
1
1
1
1
1
0
0
0
2
0
0
1
2
0
2
0
2
0
1
1
0
1
0
0
0
2
0
0
1
1
2
1
2
2
1
2
0
0
2
0
1
0
1
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
2
4
0
0
0
2
1
1
2
0
2
1
1
0
0
1
2
0
0
1
1
1
0
0
0
1
1
1
0
0
0
1
2
1
0
0
0
0
0
2
1
1
1
3
1
0
0
0
2
1
0
1
0
2
0
0
0
2
0
0
0
1
1
0
1
1
0
0
0
0
0
1
2
0
1
1
1
2
0
1
3
0
0
0
2
1
0
1
0
2
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
2
0
0
1
1
0
0
0
0
2
2
1
1
0
1
0
1
0
0
1
1
2
0
0
0
0
2
0
0
0
1
0
2
0
1
1
2
0
2
0
0
0
1
0
2
1
1
2
1
1
2
2
0
1
0
1
1
0
1
1
2
1
1
2
0
0
0
1
1
1
2
6
2
1
1
0
2
1
2
0
2
0
0
2
1
0
1
1
0
0
0
1
0
2
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
2
2
3
2
2
2
1
1
1
2
0
1
0
0
0
1
1
0
2
0
2
2
1
2
1
0
2
2
2
1
1
2
1
0
3
0
0
1
0
2
0
3
2
0
0
0
1
2
0
0
1
0
0
0
3
0
2
3
1
2
1
0
1
1
2
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
1
1
0
1
1
0
1
0
0
1
0
1
0
1
0
1
0
0
0
1
2
2
2
2
0
1
0
0
2
0
0
2
1
0
0
0
1
1
1
1
2
1
2
0
0
0
0
1
2
1
0
0
0
3
0
0
0
0
1
2
2
0
2
2
0
0
0
2
1
0
1
0
1
1
0
2
1
1
2
0
2
0
3
0
0
0
1
1
2
1
0
1
2
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
2
2
0
0
0
1
1
2
0
0
0
1
0
2
1
0
1
0
2
0
0
0
0
2
0
1
0
1
2
1
1
2
0
0
0
0
0
0
0
2
0
2
0
2
0
2
1
0
2
0
2
2
0
1
2
1
0
0
3
0
2
1
2
0
1
1
0
0
1
0
0
1
0
2
0
0
0
2
0
0
0
0
2
0
1
3
0
0
1
0
2
0
1
1
0
0
1
2
0
2
2
0
0
1
2
1
0
1
0
2
0
1
0
2
0
0
0
0
0
2
0
0
0
1
0
2
1
0
0
1
0
0
0
1
0
7
1
1
0
2
0
0
0
1
0
0
2
0
0
0
0
2
0
2
0
0
1
1
0
0
0
1
1
2
0
2
0
2
1
2
1
0
0
0
0
0
1
0
2
0
0
1
0
2
0
2
0
0
0
1
1
1
2
0
0
1
2
1
7
1
1
0
0
2
1
0
0
4
0
1
1
2
0
1
0
0
0
0
1
0
1
0
0
1
0
2
0
0
2
1
1
2
2
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
2
1
0
0
1
1
0
2
1
0
0
1
2
2
1
3
0
1
0
2
2
1
0
3
1
0
1
0
1
1
0
1
0
0
0
0
2
1
2
0
1
0
0
0
2
2
1
0
1
0
0
1
1
2
1
0
0
2
2
0
0
0
0
0
1
1
0
0
1
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
1
2
1
2
0
0
2
2
3
1
2
0
0
2
0
1
1
0
3
1
2
2
0
0
0
0
1
2
2
1
1
1
0
0
0
0
0
2
0
2
0
2
0
0
0
2
0
0
2
0
0
0
0
0
1
1
1
0
0
0
0
0
0
3
1
0
0
0
0
2
0
0
2
1
1
0
0
1
0
1
0
1
0
0
1
2
1
1
2
0
2
1
1
2
0
2
1
2
1
0
0
0
0
2
0
0
0
1
1
0
0
0
1
0
0
2
0
0
0
1
2
1
0
0
0
1
1
0
0
0
2
1
2
2
1
0
2
2
1
1
2
1
0
1
1
0
0
0
0
1
0
2
0
1
0
1
0
2
2
1
0
1
0
1
1
0
2
0
1
2
1
1
2
0
2
0
0
2
1
1
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
2
2
0
1
0
0
2
0
0
0
2
0
0
0
0
0
1
1
0
1
1
1
0
0
2
0
1
1
1
0
1
0
1
1
0
1
1
0
0
0
2
1
0
0
1
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
2
1
0
0
2
0
0
2
0
0
0
1
0
0
2
0
1
2
0
0
0
0
0
0
0
0
2
2
1
2
1
2
0
1
0
0
1
1
0
2
0
1
1
1
2
2
13
1
0
0
1
0
1
0
0
1
1
1
0
0
1
1
2
0
1
1
0
0
0
2
0
0
2
0
0
2
1
2
1
1
0
0
0
0
1
0
0
0
1
1
0
0
1
1
0
1
1
1
0
0
1
0
1
0
0
0
1
0
0
0
2
1
0
1
0
0
1
0
2
0
2
0
0
2
0
0
2
0
0
2
0
0
2
0
2
0
0
1
0
1
0
0
0
0
0
3
0
2
2
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
2
1
2
0
1
2
2
0
1
2
0
0
0
1
0
0
0
1
0
2
0
0
0
1
2
1
1
1
0
1
0
0
1
0
1
2
0
1
0
0
1
1
0
0
0
0
1
1
2
2
1
2
0
0
2
0
2
1
1
1
0
0
0
2
1
1
0
2
0
0
0
0
1
1
2
0
0
1
0
1
0
1
0
1
0
1
1
2
2
0
0
0
0
2
0
0
1
0
0
0
1
2
1
2
0
0
1
0
2
1
2
0
0
0
0
2
0
2
2
0
1
0
0
1
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
1
0
0
1
1
2
1
1
0
0
0
2
2
0
2
3
3
1
1
0
1
2
1
0
0
1
4
1
0
0
0
3
2
2
1
2
0
0
0
2
0
2
1
2
2
1
0
0
1
0
1
2
1
0
2
0
2
2
1
1
0
0
3
0
0
2
1
1
2
2
1
0
0
3
0
1
0
0
1
0
2
1
2
1
2
1
0
0
0
0
1
0
0
2
1
0
1
1
0
1
0
1
0
0
1
0
0
2
2
0
0
0
2
0
2
1
1
0
1
0
1
2
0
1
1
1
0
1
0
0
1
0
0
1
2
2
0
0
0
2
2
2
1
0
0
2
1
0
0
0
0
0
1
2
0
1
0
2
0
0
0
2
0
2
0
0
0
1
1
1
0
0
1
0
2
0
0
1
0
2
2
1
0
0
2
0
1
1
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
1
0
2
2
1
0
1
3
0
0
1
1
1
1
0
0
1
0
0
5
2
2
1
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
1
0
0
0
0
0
1
0
1
3
1
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
1
0
1
1
1
2
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
2
0
1
2
1
0
0
0
0
0
3
0
2
0
2
1
0
2
1
1
2
1
2
2
2
2
1
1
1
2
0
1
2
0
0
1
2
0
0
1
1
1
1
3
0
2
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
1
1
2
0
10
0
1
0
0
0
0
2
1
0
1
2
1
0
2
1
0
1
0
2
2
0
2
1
2
0
0
1
0
2
1
0
2
2
0
2
2
2
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
1
2
0
0
0
0
0
0
1
1
0
2
0
1
2
1
0
2
0
0
1
1
0
0
0
2
1
0
0
2
0
9
2
1
1
0
0
3
1
0
1
2
2
1
0
0
0
1
0
2
0
1
0
0
2
1
1
1
0
0
2
3
2
2
2
1
2
1
4
0
2
0
0
1
1
2
1
0
0
0
2
1
0
1
0
2
0
0
0
0
0
0
0
2
0
2
0
1
2
1
0
1
1
0
0
2
0
0
3
1
1
1
2
0
0
2
0
0
0
0
1
0
2
1
2
1
0
0
1
0
2
0
0
1
2
2
0
1
2
1
0
0
0
2
0
0
0
1
1
1
1
2
0
0
1
1
1
2
0
1
0
1
0
1
1
0
0
1
3
1
0
3
1
0
0
0
2
3
0
0
1
0
0
2
2
0
0
0
0
1
0
1
0
2
2
0
1
0
2
0
0
2
0
0
0
0
0
1
0
0
1
0
2
0
0
0
1
0
1
0
1
2
0
2
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
2
2
0
2
0
0
2
0
2
2
0
2
2
0
2
0
1
0
0
1
1
0
2
1
0
0
0
1
0
1
2
4
0
2
2
1
1
1
1
1
1
1
0
1
0
0
0
0
0
0
0
3
2
2
1
2
0
0
0
0
3
1
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
1
1
2
1
0
0
2
2
0
1
0
0
2
0
0
2
0
3
0
0
0
2
2
0
1
0
0
0
0
0
1
1
1
0
1
0
1
0
1
0
1
0
0
1
0
0
1
1
4
0
1
0
0
0
0
0
0
1
2
0
0
0
1
2
1
0
0
1
2
2
0
0
1
0
1
0
1
1
1
0
0
2
0
1
2
0
1
0
1
1
0
1
0
1
0
1
0
0
0
0
1
2
1
1
3
1
1
0
1
1
0
0
0
0
1
0
0
1
2
2
0
0
0
2
2
0
0
0
1
0
1
2
0
0
1
3
0
0
0
1
1
4
0
1
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
1
2
2
0
1
1
0
0
0
1
1
1
1
1
0
1
0
0
0
0
0
1
0
1
0
1
3
1
1
2
0
2
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
2
2
1
1
1
1
2
0
2
0
0
0
2
1
0
1
1
0
0
2
1
0
1
1
0
0
1
1
1
0
0
1
0
0
0
2
2
1
0
2
2
1
0
1
1
0
1
0
0
0
0
0
0
1
0
2
0
1
2
0
2
1
1
1
2
0
2
0
1
0
0
1
0
2
0
1
0
2
1
2
0
0
0
1
1
2
2
0
0
1
0
1
3
2
0
1
1
1
2
1
0
0
0
0
0
1
2
0
1
2
2
1
1
1
0
0
2
2
0
2
1
3
0
0
0
2
0
2
0
0
0
0
0
0
2
2
0
1
0
0
0
1
2
1
1
2
1
2
0
3
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
1
2
0
0
1
0
1
3
0
1
1
0
2
0
0
2
1
1
1
2
2
1
1
0
0
2
0
0
0
0
0
0
0
2
2
2
2
0
2
0
2
1
0
0
0
2
2
0
0
0
2
0
3
0
0
0
0
2
0
0
1
2
0
0
2
0
0
2
0
1
1
0
0
0
1
1
2
2
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
1
2
1
1
0
0
1
1
0
2
1
2
0
0
1
2
1
0
1
0
0
0
2
0
2
1
1
2
0
2
0
0
0
0
2
0
0
1
0
0
0
0
1
1
1
2
1
0
1
2
0
4
1
0
0
0
2
0
1
0
1
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
1
1
2
1
0
1
1
0
0
0
0
0
0
1
0
1
0
2
2
2
0
1
2
0
1
0
0
2
0
1
0
1
0
0
1
0
0
0
1
2
0
0
0
2
1
0
0
0
0
0
0
1
0
2
0
1
2
1
1
0
0
1
0
0
0
0
0
2
0
0
0
4
0
2
1
1
2
2
2
2
1
1
2
0
0
2
0
2
0
3
0
2
1
0
0
1
0
0
0
0
0
2
0
0
2
1
2
2
2
0
0
0
2
0
1
1
1
2
2
0
2
0
0
1
1
0
0
0
0
2
0
1
0
2
0
1
0
0
0
1
0
1
1
1
0
1
1
0
0
2
4
0
1
0
0
1
2
1
0
0
1
0
1
1
0
1
2
0
1
1
1
0
1
1
2
0
0
1
2
1
0
1
0
0
1
0
0
2
1
0
0
0
0
1
2
2
0
1
1
0
0
1
0
0
0
1
1
0
0
0
1
2
1
5
1
0
2
1
0
0
1
2
1
2
0
1
1
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
1
1
0
0
0
0
0
0
2
0
0
2
0
2
0
2
1
1
0
2
2
0
1
2
2
2
0
1
0
0
0
1
1
0
0
1
0
0
0
2
1
1
1
0
2
0
1
0
0
0
0
2
2
2
0
0
1
2
2
1
0
0
0
1
0
0
0
0
0
2
2
0
1
0
0
0
1
1
0
4
2
0
0
1
0
0
2
0
1
0
0
0
0
1
0
0
0
0
2
1
0
0
2
2
0
0
1
0
0
1
2
0
0
2
1
0
0
0
0
0
1
0
1
0
1
0
0
1
1
1
0
2
2
0
2
3
0
2
0
0
0
0
0
0
0
0
1
1
0
1
0
3
2
0
0
0
0
1
1
0
1
0
2
0
0
2
0
0
0
0
0
0
1
1
1
0
0
0
0
2
0
0
0
0
0
2
1
2
1
1
0
2
0
0
0
0
2
1
0
1
1
1
1
0
2
1
1
0
0
0
2
0
1
0
0
2
0
1
1
0
0
0
0
2
2
1
0
2
1
2
1
0
1
0
0
0
0
2
2
0
1
2
0
1
0
0
1
2
1
0
0
2
0
0
0
0
2
0
2
1
0
0
1
1
2
0
2
0
1
2
0
2
0
2
0
0
0
0
2
0
0
0
0
0
1
0
1
1
0
3
0
0
0
0
0
0
3
0
0
1
1
0
1
0
2
0
1
0
2
2
0
0
0
1
0
1
2
2
1
2
0
0
2
2
1
1
1
1
1
1
0
0
0
0
0
0
0
1
0
0
1
0
2
1
2
3
0
2
0
2
0
1
0
0
1
0
1
0
0
2
0
1
2
1
0
0
3
2
1
0
0
0
2
0
1
1
2
0
0
0
0
1
0
2
0
1
0
0
2
2
0
0
2
0
2
0
0
0
1
0
1
0
1
0
0
0
0
0
0
2
1
0
1
1
0
1
2
2
1
0
1
0
0
1
0
0
0
2
2
0
0
0
2
2
0
0
1
2
0
0
0
1
2
1
0
0
1
1
2
2
0
1
1
2
1
1
0
0
3
1
1
2
0
3
0
2
0
0
0
0
0
2
1
2
1
0
0
1
2
0
0
0
0
1
1
0
0
1
1
0
0
0
0
1
2
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
2
0
0
1
0
0
0
1
2
1
0
1
0
2
0
2
0
0
1
0
1
1
0
2
1
0
0
0
1
3
1
1
1
0
2
0
0
1
1
0
1
0
1
0
0
2
9
0
1
0
0
0
3
0
0
0
2
2
0
0
1
2
0
1
0
2
1
1
0
0
2
0
2
0
2
1
0
1
0
1
0
1
0
0
2
0
3
1
0
0
0
1
0
0
1
1
0
0
5
0
2
1
2
0
0
2
1
0
0
0
2
3
0
0
0
0
0
0
1
1
1
0
0
1
0
2
1
0
0
0
0
0
2
1
2
2
0
1
0
0
2
0
1
1
2
1
1
0
2
2
0
1
0
1
1
2
0
0
2
2
0
1
0
0
0
0
0
0
1
0
0
0
0
2
2
2
0
1
0
0
1
0
2
0
0
0
1
0
2
0
0
3
0
1
0
2
0
1
0
2
0
1
2
1
0
1
0
2
2
2
1
1
0
2
0
0
1
1
1
0
2
1
0
0
2
0
2
2
1
0
0
0
1
1
0
1
2
0
0
0
0
2
1
1
0
1
0
0
0
2
2
2
2
1
1
0
1
0
0
0
0
0
2
0
0
1
1
2
1
0
0
0
0
0
0
2
1
1
1
0
1
0
0
0
0
1
2
0
0
0
1
0
0
0
1
0
1
0
0
3
0
0
0
1
2
1
1
0
2
1
2
0
2
1
0
0
1
2
0
1
1
1
2
2
0
1
1
0
2
0
1
0
1
0
2
2
1
0
0
0
2
2
0
1
0
0
1
0
2
0
0
1
1
1
2
0
2
0
1
2
0
2
0
0
0
1
0
2
0
0
1
1
0
0
0
0
0
2
2
1
0
4
2
0
0
0
2
2
2
0
0
1
0
1
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
2
0
0
2
1
0
2
1
1
2
1
1
2
1
0
2
0
2
0
1
0
2
3
1
0
1
0
0
1
2
0
2
0
0
0
1
0
1
2
0
1
0
0
1
1
0
0
0
2
0
0
0
1
1
0
1
0
1
0
0
1
0
0
2
1
0
0
2
1
0
0
0
3
0
2
2
0
2
0
2
2
1
0
0
1
0
0
2
0
2
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
2
1
1
0
0
2
0
0
1
0
0
0
1
0
0
0
1
1
1
2
0
0
0
0
0
0
2
2
1
1
0
1
0
0
1
1
0
1
2
0
0
1
2
1
3
0
0
0
0
1
0
0
1
0
0
1
1
1
2
0
0
2
1
1
1
0
0
1
0
0
1
1
0
0
0
2
0
2
0
0
0
1
2
1
0
0
2
0
0
0
0
0
2
1
0
2
2
0
2
0
0
0
0
0
0
0
0
1
1
2
2
0
1
0
2
0
0
0
1
0
0
0
0
3
2
1
0
0
0
0
1
1
1
1
0
2
0
2
2
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
1
0
1
2
0
1
0
0
0
0
2
0
2
1
0
2
0
1
1
1
1
0
1
1
0
0
1
0
1
0
2
1
0
0
3
1
0
1
1
0
0
0
1
0
1
0
2
0
0
1
0
0
1
0
1
0
0
0
2
0
0
2
0
2
1
1
0
0
2
1
0
0
0
1
0
1
0
1
0
1
2
0
0
1
2
0
2
0
0
0
1
2
1
0
1
0
2
0
1
1
0
1
1
1
0
1
2
1
0
1
2
2
0
2
0
0
1
0
0
0
0
0
1
1
1
0
0
1
2
0
1
0
1
0
0
0
1
1
2
1
0
0
2
1
1
0
1
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
1
0
2
0
2
2
1
1
0
0
0
0
2
0
0
0
2
0
0
0
1
0
2
2
0
0
1
2
1
0
0
0
0
2
1
2
0
0
2
2
0
2
1
2
0
1
1
0
1
3
0
2
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
1
1
0
0
2
2
0
2
0
0
0
0
0
1
1
1
2
0
0
0
0
0
2
0
0
1
1
1
0
2
1
1
2
0
1
0
2
1
1
2
1
2
0
0
1
1
2
0
2
0
0
0
0
0
1
0
3
0
2
1
2
0
0
1
0
1
0
1
1
1
0
2
2
0
1
2
1
1
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
2
1
0
2
0
2
1
0
3
0
1
2
0
2
0
1
0
2
0
1
0
0
1
1
0
0
1
1
0
0
1
1
2
2
0
0
0
0
1
2
0
0
0
0
1
0
0
1
0
0
0
1
0
1
2
0
2
0
0
0
0
0
0
0
2
2
0
0
0
1
2
0
1
2
0
0
0
1
0
2
1
1
0
0
2
0
0
2
2
1
2
2
2
2
1
0
0
0
0
0
1
0
0
1
2
1
0
2
0
0
2
0
0
0
2
1
0
1
0
1
2
0
0
1
3
0
0
2
1
0
0
0
2
2
0
0
2
2
2
0
0
1
0
0
0
0
2
0
2
2
0
0
0
0
1
1
1
0
1
0
1
2
0
3
2
1
3
0
2
0
1
2
2
2
0
1
2
0
0
1
0
0
0
2
2
0
1
2
0
0
1
0
7
0
1
2
1
0
0
0
0
1
1
1
1
1
0
0
1
1
1
0
0
1
1
1
2
0
2
1
0
1
0
0
1
0
2
0
2
1
0
0
0
0
1
0
2
1
0
0
0
2
1
0
1
0
0
0
1
1
1
0
0
0
2
1
0
0
0
2
2
1
0
1
2
0
0
0
1
2
0
0
1
2
0
0
1
1
1
1
2
1
2
2
1
0
0
1
0
0
1
1
0
0
2
0
5
0
0
0
0
0
3
1
0
2
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
3
1
0
0
0
1
1
0
1
0
0
0
0
1
1
2
1
0
2
0
2
0
0
0
2
1
0
0
2
0
0
1
3
2
0
0
0
0
0
0
1
0
2
0
1
0
2
0
2
0
0
0
1
0
1
1
0
0
2
2
2
0
2
0
0
0
0
0
2
1
0
0
2
0
1
1
2
1
0
1
0
1
0
0
1
0
1
0
0
0
2
0
2
0
1
2
1
2
2
0
0
1
0
0
0
2
1
0
1
1
0
0
2
2
2
0
0
1
0
2
0
0
0
0
0
2
1
1
2
1
0
2
0
0
1
0
2
1
0
0
3
0
0
1
0
0
0
2
0
0
0
0
0
0
1
3
0
2
1
0
1
0
2
0
0
0
2
0
0
2
0
0
1
1
0
0
0
0
0
0
1
1
1
1
1
2
1
0
1
0
0
1
0
0
0
0
2
0
1
2
1
2
0
0
1
0
0
0
0
1
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
1
1
0
0
1
1
2
0
2
0
0
0
0
0
1
0
1
2
1
0
1
2
0
1
1
1
1
0
0
0
2
0
0
1
0
2
0
0
0
0
0
1
2
1
0
2
1
0
2
2
2
0
0
1
0
2
2
0
1
0
2
0
0
0
0
0
1
1
0
0
0
0
1
0
1
1
0
1
1
1
1
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
1
2
0
1
0
1
2
0
3
1
2
0
2
2
1
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
3
0
0
0
2
2
2
1
1
1
1
1
0
0
1
1
1
1
1
2
0
3
0
0
0
1
1
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
1
2
0
1
0
0
1
1
0
3
2
2
1
2
0
2
0
0
0
0
5
2
1
0
0
0
0
0
0
3
0
0
0
0
2
0
0
1
2
0
0
1
0
0
0
1
1
0
0
1
1
2
0
2
0
2
2
0
0
2
0
1
0
0
0
1
0
2
0
1
1
0
0
2
1
1
1
1
0
0
2
0
0
2
0
2
0
1
1
3
2
1
0
1
1
2
2
0
1
0
0
0
2
0
0
0
1
0
0
1
0
1
2
1
1
2
0
0
2
0
1
0
1
0
0
0
2
2
2
2
1
0
1
0
0
1
0
2
0
0
0
1
0
0
0
2
1
1
0
0
0
1
0
2
1
1
0
2
1
0
1
2
1
2
0
2
2
0
0
0
0
1
1
0
0
0
2
1
0
2
0
0
0
2
1
0
0
0
0
2
0
2
0
1
0
0
0
1
1
0
0
0
1
0
0
2
1
2
1
3
1
1
2
0
0
0
0
1
0
0
0
0
1
1
1
1
2
1
0
0
0
1
0
2
0
0
1
0
0
1
0
1
1
1
0
0
0
4
2
0
1
2
2
0
1
0
0
2
0
0
1
0
1
0
1
0
0
1
2
3
1
1
0
2
0
0
1
1
1
0
2
0
0
2
1
3
0
0
0
0
2
1
2
0
0
1
0
0
2
2
1
0
2
0
1
1
0
0
0
0
2
2
0
0
1
1
1
1
2
1
1
2
2
0
0
0
0
1
1
1
0
2
0
0
1
2
1
0
0
1
1
2
2
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
2
0
1
0
0
0
1
0
0
1
0
0
0
1
2
0
0
0
1
1
2
0
0
0
1
0
4
1
1
2
2
2
2
1
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
1
2
0
1
0
1
0
0
0
1
1
0
1
0
1
0
0
2
0
0
1
1
0
0
1
0
1
1
0
0
1
0
2
1
1
0
2
2
3
2
0
0
1
2
0
0
1
2
2
0
5
1
0
1
2
1
2
0
1
0
0
0
1
0
2
1
2
2
1
0
2
0
1
0
0
1
0
1
1
0
0
1
1
0
2
0
0
0
0
0
1
1
0
1
2
2
1
0
0
0
0
1
1
0
0
0
0
2
0
0
2
0
0
1
0
0
0
1
1
1
0
0
0
2
0
0
2
0
2
1
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
1
0
0
1
0
1
0
2
0
1
2
0
1
1
2
0
2
0
0
0
2
2
2
1
2
0
1
0
0
0
1
1
0
1
0
0
0
0
0
2
2
1
1
0
1
1
2
1
0
0
0
1
1
0
1
2
0
0
0
0
0
0
0
2
0
1
0
1
0
2
1
1
1
1
0
2
0
0
0
2
0
0
2
1
2
0
0
0
2
0
0
0
2
1
0
1
0
1
0
0
0
2
1
1
0
0
0
2
0
1
2
2
1
0
2
2
2
1
0
1
1
1
0
1
4
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
2
0
1
0
0
0
1
1
2
0
2
2
0
2
0
0
0
2
2
0
0
0
1
1
1
0
0
1
1
0
4
0
0
0
2
0
0
0
1
0
2
0
0
0
0
1
1
0
0
0
0
0
0
2
2
4
0
0
1
1
2
1
2
0
0
2
1
0
2
0
1
3
1
0
0
0
1
3
0
0
0
0
1
0
0
1
1
1
0
2
1
2
1
0
0
0
0
0
1
0
1
0
0
0
0
1
3
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
4
1
1
0
2
0
2
1
0
0
1
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
2
1
1
0
0
2
2
0
2
1
0
1
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
1
0
1
0
0
1
2
1
0
1
0
0
0
0
1
0
1
0
2
1
0
3
1
0
2
0
1
0
6
0
1
0
2
0
2
0
0
1
0
1
1
1
0
0
1
0
1
0
0
0
0
2
0
1
0
1
0
0
1
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
1
1
1
0
0
1
2
0
0
2
2
0
1
1
0
2
0
2
2
1
0
0
0
0
0
2
0
0
0
0
1
1
0
1
1
1
1
2
0
2
0
2
2
2
0
0
0
1
0
2
1
1
1
1
1
0
0
1
0
1
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
2
1
0
1
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
4
2
2
1
1
3
1
0
0
1
0
1
1
1
0
0
1
0
0
0
0
0
2
1
1
0
2
0
1
1
0
0
0
1
0
0
1
1
0
2
0
1
2
0
0
1
1
1
1
0
0
0
1
1
1
1
2
1
1
0
1
0
0
0
0
1
2
0
5
0
0
0
0
1
1
0
0
1
1
0
1
1
1
0
0
1
1
0
2
0
1
0
0
1
0
1
1
2
0
1
0
2
0
0
0
0
0
0
0
0
1
2
1
2
0
0
2
1
2
2
1
0
2
0
0
1
1
0
0
0
4
0
0
0
0
0
0
0
1
1
1
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
1
0
0
2
0
0
2
1
0
0
0
1
1
0
2
0
1
3
0
0
0
1
1
1
1
0
0
1
1
0
2
1
0
0
0
2
0
0
0
1
0
1
0
1
0
0
0
1
0
1
2
1
0
0
1
0
0
0
0
0
0
3
0
0
1
2
0
1
1
0
1
0
1
0
0
0
0
0
1
1
2
0
0
2
2
0
0
0
1
0
0
1
0
1
0
0
1
1
0
2
1
0
2
2
2
1
2
0
0
0
0
0
0
1
0
1
0
1
0
1
0
1
2
1
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
1
1
2
1
2
0
2
0
2
1
0
0
0
0
0
0
1
1
1
0
2
0
1
0
1
0
0
0
2
0
0
1
0
0
0
0
2
1
1
2
2
0
0
1
0
2
1
0
1
1
2
0
1
2
0
0
2
0
0
0
1
1
2
0
1
0
0
1
2
1
1
0
0
2
2
2
0
0
2
2
1
0
1
2
0
2
2
0
2
2
1
0
2
0
2
1
0
1
1
0
0
0
2
0
0
1
2
2
2
0
2
0
0
3
2
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
1
2
2
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
2
1
0
0
0
5
0
1
0
1
1
2
1
0
0
1
1
0
2
0
0
1
1
0
1
1
0
1
1
0
0
0
2
0
2
0
0
0
0
1
0
1
0
1
0
1
1
1
0
1
0
2
1
0
0
0
0
1
2
0
0
0
1
0
0
1
2
0
1
1
1
1
2
1
0
1
0
2
2
0
2
1
1
1
0
1
0
1
1
0
0
3
0
0
0
0
0
2
0
0
1
0
0
0
0
1
1
0
0
1
0
0
1
1
2
1
0
0
1
1
0
0
2
0
1
2
1
1
0
0
0
1
0
0
1
1
3
0
2
1
1
1
0
0
0
3
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
1
1
2
1
1
0
0
1
0
0
2
0
2
0
1
0
0
2
4
1
0
1
1
2
1
2
0
0
2
1
1
1
0
3
2
0
0
0
1
0
2
1
0
0
0
1
0
2
0
1
0
2
2
0
0
0
0
0
2
2
1
1
0
0
0
1
0
0
0
0
1
0
2
1
0
2
1
0
2
1
0
1
2
0
1
2
0
2
1
2
2
0
3
0
0
0
2
1
0
2
0
2
0
0
0
1
0
0
0
1
0
0
1
1
1
1
1
1
0
0
0
0
0
2
0
0
3
0
0
0
0
2
1
2
2
1
1
1
1
0
2
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
3
0
0
1
0
1
2
0
2
0
1
0
0
0
1
0
1
1
2
0
0
2
0
0
2
2
1
0
2
1
0
0
0
0
1
0
1
0
2
0
2
0
2
2
0
1
0
0
0
2
0
0
1
0
1
0
0
2
2
0
0
2
0
1
2
0
0
0
0
0
1
0
0
2
2
0
0
0
0
1
0
0
0
1
0
2
2
0
1
1
0
0
0
0
2
2
1
1
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
1
2
0
2
0
0
0
0
1
0
0
1
1
2
0
1
0
0
0
0
2
0
1
2
2
2
2
1
1
0
0
1
0
2
1
0
2
0
2
1
0
0
1
0
0
2
2
0
1
0
0
0
2
1
0
1
0
0
0
2
0
2
1
0
2
2
0
1
3
1
1
1
2
2
0
2
1
1
0
1
1
0
2
0
0
1
1
0
0
0
2
0
2
1
1
2
2
0
4
0
0
0
2
1
1
0
0
0
0
1
0
0
1
1
0
3
1
0
0
0
1
2
1
0
1
0
2
1
1
0
3
1
3
0
0
1
1
1
1
2
1
2
2
2
0
0
0
1
1
2
1
0
0
0
0
1
2
0
1
0
0
0
1
0
2
0
1
0
0
1
2
1
1
0
1
1
0
0
2
1
0
0
0
0
0
1
1
2
0
1
1
1
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
4
0
0
1
1
2
2
0
2
0
1
0
2
1
0
0
1
1
1
0
2
2
1
2
0
0
1
1
0
0
0
1
0
0
2
1
0
0
0
0
1
1
0
0
2
0
0
1
0
1
0
1
2
1
1
0
0
0
1
0
2
0
2
0
0
2
1
0
0
1
0
1
2
0
0
4
0
0
1
1
0
2
0
0
0
0
0
0
2
0
0
0
1
1
1
1
2
2
0
0
1
1
1
1
1
0
0
1
2
2
0
0
0
0
1
0
0
2
0
1
0
1
0
0
1
0
3
1
1
0
0
2
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
2
0
1
1
2
0
0
1
3
0
0
2
0
0
2
4
0
0
1
1
0
0
1
1
0
1
2
2
0
0
0
2
0
0
1
3
1
1
0
0
0
0
1
1
2
0
1
0
0
1
0
0
1
0
0
0
1
1
2
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
2
2
2
5
2
0
0
0
0
0
0
2
2
2
0
0
1
0
2
1
1
0
1
0
0
2
1
2
1
0
1
0
0
0
0
0
2
0
1
0
2
0
0
1
1
0
0
1
0
0
0
0
2
1
1
0
0
1
2
1
1
0
0
0
1
0
1
0
2
2
2
2
1
2
1
0
2
0
1
0
0
2
0
1
1
2
2
1
0
2
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
2
1
2
1
1
1
0
0
2
1
2
0
2
1
0
0
1
0
0
0
1
2
0
1
2
1
1
0
1
2
0
1
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
1
0
1
2
0
0
1
0
0
2
0
0
0
1
0
0
1
0
3
2
1
1
4
1
1
2
1
0
1
2
0
0
0
1
0
0
0
2
2
1
0
2
1
0
1
0
0
0
1
2
0
0
0
0
0
1
0
1
1
0
1
0
0
1
0
0
0
0
0
2
0
1
1
0
1
0
1
2
2
0
2
0
0
0
2
0
0
3
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
1
2
2
1
1
0
0
1
1
0
5
0
2
2
2
1
0
0
2
1
0
2
1
1
1
0
1
0
2
2
0
2
1
0
0
1
0
0
0
0
0
2
0
1
1
2
0
2
2
0
1
0
0
2
2
1
0
0
0
0
2
4
2
0
0
2
0
1
2
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
1
0
2
0
1
0
1
0
0
0
0
0
2
3
2
0
0
0
0
1
2
0
1
0
2
0
0
0
0
2
2
0
0
0
0
2
0
0
2
1
0
1
2
2
2
0
0
1
0
0
0
1
2
0
0
2
1
0
0
3
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
1
2
0
1
2
1
0
0
0
2
0
1
0
0
4
2
0
1
0
0
0
1
1
0
0
1
0
0
2
2
0
0
2
0
0
2
1
0
2
0
1
1
0
2
0
0
1
1
1
0
1
1
1
0
0
0
0
1
0
0
2
2
0
2
1
0
2
0
1
0
0
1
0
1
1
3
0
0
0
0
1
0
2
0
1
1
1
1
1
1
0
0
1
0
1
1
0
0
0
0
0
2
0
1
0
1
1
0
2
3
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
1
2
0
0
2
2
0
0
0
0
2
1
1
2
1
0
2
0
0
0
0
0
0
0
1
0
1
0
1
1
1
2
0
1
0
0
0
1
0
1
2
3
0
0
0
1
0
0
0
2
1
2
0
0
2
2
0
2
0
1
0
2
0
0
0
1
1
1
0
2
2
2
1
2
1
1
0
0
2
2
0
0
0
0
2
0
1
0
0
1
1
1
0
0
1
1
0
0
0
0
0
0
0
0
2
0
1
0
0
1
2
1
1
0
2
1
2
1
0
0
0
1
1
0
1
1
0
2
0
0
0
0
1
0
0
1
1
0
1
2
0
0
0
2
2
1
0
2
0
2
0
0
1
1
0
2
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
4
1
0
0
0
0
0
1
0
1
3
1
0
0
0
1
1
1
2
2
1
3
2
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
1
1
3
0
1
0
0
1
2
2
0
0
1
1
0
0
0
2
2
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
2
0
1
2
2
0
0
1
0
2
0
0
0
1
4
0
0
0
0
0
0
2
0
0
1
0
2
2
0
1
0
0
1
0
2
0
0
1
1
0
1
1
0
0
0
1
0
2
0
2
0
0
0
0
1
0
1
1
0
4
2
0
0
0
0
0
0
0
2
0
1
0
2
0
1
1
0
1
0
0
2
2
0
0
2
2
0
2
0
0
0
0
0
1
0
0
0
0
2
1
1
0
1
2
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
2
0
0
0
0
1
1
0
1
2
0
0
0
1
1
2
1
0
0
1
1
4
0
0
0
1
2
2
3
1
1
0
2
0
1
0
2
1
0
1
0
2
2
0
0
1
0
1
0
0
0
0
0
0
1
0
0
2
0
1
1
1
0
0
2
0
0
2
1
1
0
0
0
0
0
0
0
1
2
1
0
0
0
1
1
1
0
2
2
0
0
0
0
1
0
1
5
0
2
2
2
1
2
0
0
1
1
2
0
2
0
0
1
2
0
0
2
0
1
0
0
0
1
2
1
0
2
1
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
2
0
0
1
1
2
0
0
1
0
0
3
1
2
0
1
0
1
0
1
2
2
0
2
0
1
0
0
1
0
0
1
2
0
1
0
0
1
2
1
1
0
1
0
0
1
0
0
2
2
1
0
2
0
0
0
3
0
0
1
1
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
1
2
2
0
1
1
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
3
0
1
1
0
2
2
0
1
0
2
0
2
0
0
1
0
1
2
0
0
1
2
0
1
0
0
3
0
0
0
1
1
0
0
2
0
0
0
0
1
0
1
0
0
2
0
1
1
2
0
0
1
2
0
2
0
2
0
1
0
0
1
0
1
1
2
0
0
2
1
0
1
1
1
1
0
1
1
2
0
2
0
0
2
2
2
1
1
0
2
0
0
0
2
0
2
0
1
1
0
0
1
0
0
0
0
1
1
2
0
1
0
2
0
0
0
1
1
1
4
2
0
1
1
2
2
1
0
3
1
1
0
0
1
1
0
0
1
0
0
0
1
1
1
0
1
1
0
1
1
0
2
1
2
2
1
0
0
2
2
1
1
0
0
0
0
1
1
2
0
0
2
1
2
0
1
0
2
2
0
2
0
1
3
2
0
1
1
0
0
0
0
1
1
0
1
0
1
1
0
0
0
2
0
0
2
2
0
0
2
1
2
2
1
0
1
0
0
0
0
1
2
0
0
0
0
2
0
0
1
1
2
2
0
2
2
2
2
0
1
1
0
0
0
0
2
2
0
0
0
0
0
2
2
2
1
0
1
2
2
2
1
0
0
5
0
0
0
1
0
0
0
2
2
1
0
0
0
1
2
2
0
0
0
1
2
0
0
1
2
0
0
1
0
0
1
0
1
0
1
2
0
0
0
1
1
1
0
1
0
0
0
0
1
2
1
0
1
0
0
0
0
0
0
0
1
1
1
0
2
0
2
0
0
1
0
0
0
0
0
1
1
0
2
0
1
2
0
1
1
2
0
0
0
1
0
1
1
0
0
2
1
0
0
0
0
0
2
0
1
2
0
0
1
2
0
0
0
2
0
0
1
0
0
4
0
1
2
0
0
0
1
0
0
1
2
0
1
0
0
0
2
3
2
0
1
0
0
1
0
1
1
0
2
0
2
0
0
2
1
0
0
0
0
1
2
1
0
1
0
2
0
0
2
0
2
0
0
3
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
1
2
0
0
0
2
1
1
0
0
1
1
1
1
1
0
2
1
0
1
1
0
0
1
0
1
0
1
0
1
2
0
0
0
0
0
1
0
1
0
1
0
1
2
1
0
2
0
0
2
1
0
0
0
0
0
2
0
1
1
2
0
0
1
0
2
2
2
1
0
0
0
2
1
0
1
0
2
1
1
1
0
1
1
1
0
0
0
0
2
2
1
5
2
2
0
0
0
0
4
0
0
2
1
1
0
0
0
0
0
0
1
0
0
2
1
0
2
1
0
4
0
2
0
1
0
2
0
1
1
1
2
2
1
0
0
1
1
1
0
0
0
0
0
0
2
2
0
0
2
2
0
0
2
0
0
1
0
0
2
1
0
1
1
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
2
2
0
0
0
0
1
2
2
2
0
3
0
0
1
0
2
2
1
2
1
0
1
0
0
0
0
0
1
1
0
2
1
1
0
1
0
0
0
0
1
0
0
0
3
1
1
1
0
2
0
1
2
0
0
0
1
0
0
0
0
0
1
1
0
1
0
1
1
1
1
1
0
0
1
0
0
1
2
0
0
2
0
1
0
0
0
0
0
1
0
0
1
0
0
1
2
0
0
1
0
0
2
0
2
0
0
1
1
2
1
0
2
0
1
1
2
3
1
0
1
0
2
2
2
2
1
2
1
0
0
1
1
0
1
1
1
0
1
0
0
1
0
0
0
0
0
3
1
0
1
1
2
1
1
0
0
0
5
1
0
0
2
2
0
2
1
1
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
1
3
2
1
0
2
0
1
1
0
0
1
0
2
2
1
2
1
2
0
2
0
0
1
0
0
2
0
0
1
1
0
1
0
0
1
0
2
3
0
0
1
1
0
1
1
1
0
0
0
0
0
2
1
0
0
1
0
0
0
0
2
1
1
1
2
1
1
0
0
1
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
2
0
0
3
1
2
1
0
1
2
2
2
0
0
1
0
1
0
2
1
2
0
0
0
2
2
0
1
2
1
1
1
0
2
0
2
1
1
0
1
0
1
0
0
0
1
3
0
0
0
0
1
2
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
2
1
2
1
0
2
1
1
0
0
0
1
1
0
0
2
1
0
0
0
1
1
0
1
0
0
2
0
2
1
2
2
0
3
0
0
1
2
0
0
0
0
1
1
0
0
0
1
0
0
0
3
1
0
0
0
1
1
0
2
0
2
0
2
0
0
6
0
1
0
0
0
0
1
0
0
2
2
1
2
0
1
0
0
1
1
4
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
1
0
1
2
2
3
0
0
0
0
1
1
0
0
1
1
0
2
4
3
0
1
2
0
1
0
1
1
0
0
0
2
0
2
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
1
0
1
1
0
0
0
0
2
0
0
0
1
0
0
1
1
0
1
0
2
2
0
0
1
1
0
2
1
0
1
0
1
0
1
0
0
0
2
1
0
0
0
1
0
0
1
2
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
2
1
0
0
0
0
2
2
1
0
0
0
2
0
2
1
0
0
0
0
1
0
1
1
0
0
1
1
1
2
2
0
0
0
2
0
0
0
2
1
0
0
2
1
1
0
0
2
1
1
1
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
2
1
0
1
0
2
1
0
0
0
0
0
0
0
1
0
0
1
0
0
3
1
0
0
0
1
0
0
1
0
2
0
1
1
0
0
0
1
2
0
3
1
0
0
0
2
0
0
0
2
1
0
0
1
0
1
1
1
1
2
0
1
2
0
2
0
0
2
2
0
0
1
0
0
3
0
0
0
0
0
2
0
0
0
0
1
0
1
0
1
1
0
2
0
0
0
1
0
0
2
0
2
0
0
2
1
0
0
0
1
0
1
1
0
0
0
2
1
0
0
1
0
1
0
1
0
2
0
2
2
0
0
0
0
0
1
1
0
0
5
2
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
4
0
0
2
0
0
2
1
1
0
1
1
2
0
0
0
0
7
0
2
0
4
0
0
0
2
0
0
2
1
0
1
0
0
1
0
0
1
1
0
0
0
1
0
1
1
1
0
0
1
1
2
0
1
2
0
0
2
2
0
0
0
0
0
2
2
0
0
2
1
2
0
0
2
0
0
0
0
1
2
0
2
0
0
1
1
2
0
0
2
0
1
1
2
0
1
0
0
0
0
2
1
0
1
0
0
0
0
0
2
2
2
2
0
0
1
0
0
0
0
0
0
2
0
0
1
1
0
2
0
2
0
0
0
0
0
1
0
0
0
1
0
1
1
0
1
2
0
2
0
0
0
2
0
0
0
2
2
1
1
2
0
0
0
0
0
2
2
2
2
0
0
2
2
0
1
0
0
0
1
3
1
2
0
1
2
2
0
2
1
2
2
0
1
0
1
2
1
1
0
1
0
1
0
1
0
0
0
0
0
1
0
1
1
3
0
1
0
3
1
1
0
1
2
1
1
2
0
1
1
0
1
0
1
0
1
0
0
0
2
0
0
0
2
1
1
0
0
0
1
0
0
0
0
1
0
0
0
2
0
3
1
0
1
0
0
1
1
0
2
1
0
3
0
0
0
2
0
1
1
0
1
1
0
2
2
0
0
0
0
1
2
0
0
1
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
1
0
1
0
0
1
0
1
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
3
1
0
0
0
1
1
0
2
0
0
1
0
0
0
1
0
0
1
2
0
0
1
0
1
0
0
0
1
0
1
0
1
0
0
0
1
0
2
1
2
1
0
0
3
0
0
1
2
1
1
1
0
1
2
0
0
0
1
0
0
0
2
0
2
1
0
0
0
0
1
0
0
1
1
2
1
0
0
3
2
0
0
0
0
2
2
0
7
2
1
0
2
1
1
0
0
0
0
0
2
0
0
1
2
0
0
0
2
0
5
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
1
1
5
0
0
0
2
2
0
0
0
0
1
1
0
0
1
0
0
1
1
2
0
1
1
2
0
0
0
0
0
0
0
1
1
1
0
0
0
2
0
1
1
0
1
0
0
0
0
0
0
2
0
1
0
0
2
1
2
0
0
1
0
2
0
2
0
0
1
0
2
0
0
0
0
0
1
1
1
2
1
0
0
1
0
0
1
0
3
1
2
1
0
2
0
0
1
0
0
1
0
0
1
1
0
0
2
1
1
1
0
1
0
0
2
0
2
1
1
2
0
1
2
1
1
0
2
2
0
1
1
1
0
1
2
1
0
0
2
1
5
0
2
0
0
0
0
2
2
1
0
1
1
1
0
0
1
0
0
0
0
1
1
0
2
1
2
0
0
1
1
0
1
1
0
0
2
1
2
1
2
2
1
0
4
2
3
0
0
2
0
0
3
0
0
2
2
0
4
0
0
1
0
2
0
1
0
0
0
1
2
0
2
2
0
1
0
0
0
0
4
2
0
0
1
0
2
0
1
0
0
0
1
1
1
2
1
0
0
0
1
2
1
0
0
0
2
2
11
0
2
1
0
0
0
0
2
0
0
1
1
0
2
0
1
1
0
0
0
2
1
0
2
1
0
0
0
0
1
1
2
2
0
0
0
1
2
1
1
2
0
1
0
1
0
0
2
1
1
0
0
6
1
2
1
2
0
1
0
0
0
0
1
0
1
0
1
0
2
1
0
2
0
0
0
0
0
0
1
0
0
2
0
2
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
1
2
1
2
1
1
0
2
0
0
0
1
0
2
0
2
1
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
1
0
1
1
1
0
0
0
1
0
0
0
2
1
3
2
2
2
1
1
0
2
1
1
0
1
2
0
2
1
0
0
1
1
2
1
0
3
0
0
2
0
0
2
0
0
0
2
0
0
0
1
3
1
0
0
0
1
2
1
1
0
0
0
3
2
0
0
1
0
0
1
0
1
0
1
2
0
2
2
0
2
1
0
0
0
0
0
1
1
3
2
1
1
0
0
0
0
1
2
4
1
2
0
0
1
2
0
0
0
0
0
1
1
0
2
0
0
1
2
1
0
1
0
1
0
1
0
0
0
0
0
2
0
1
1
0
1
0
0
0
1
1
0
0
2
0
0
1
1
0
0
0
2
0
0
0
1
1
0
0
1
1
0
0
0
0
1
0
2
2
0
1
0
0
2
0
0
1
0
0
0
1
3
2
0
2
1
3
0
1
0
0
0
0
0
3
0
1
1
0
0
0
0
1
0
0
1
3
2
0
1
0
1
0
2
1
0
0
0
2
1
0
2
0
2
0
1
0
1
0
0
0
1
1
4
0
4
1
0
0
1
0
0
2
0
0
0
1
0
0
1
0
1
1
2
1
0
1
0
2
0
1
0
0
0
1
0
2
0
0
0
1
0
1
0
1
0
0
1
2
2
2
2
0
1
2
2
0
0
0
0
0
1
0
0
1
2
2
0
0
0
2
2
2
2
0
0
1
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
2
1
1
0
2
0
0
1
1
1
1
0
0
2
0
1
1
2
0
1
1
3
1
1
0
0
0
0
0
2
0
2
0
2
1
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
1
0
2
0
2
1
0
1
1
1
1
1
0
0
2
0
0
2
2
0
1
2
0
0
0
0
1
0
1
1
1
0
0
2
1
0
0
0
1
2
2
0
0
0
0
2
0
2
0
2
1
1
1
0
0
1
0
0
0
1
2
1
0
1
2
1
0
1
2
1
0
0
0
0
1
0
0
0
0
2
1
1
10
3
2
2
0
0
0
0
0
1
1
1
1
0
0
1
0
1
2
2
3
0
2
0
0
1
0
0
0
0
2
0
2
1
0
0
1
2
0
1
0
0
1
2
1
0
1
1
1
0
0
0
0
2
1
0
0
0
1
1
0
0
1
2
2
2
0
0
2
2
1
1
1
0
0
0
1
0
1
0
2
0
0
1
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
2
1
0
0
2
0
0
1
1
1
2
1
1
2
2
0
0
1
0
1
2
0
2
0
0
2
0
0
2
0
2
1
0
2
2
0
2
2
2
0
1
1
0
0
0
0
0
1
2
0
1
2
0
0
0
2
0
1
2
1
0
0
0
0
1
0
0
2
0
2
0
0
0
1
0
2
1
2
0
1
0
2
2
0
0
0
2
1
0
1
0
1
0
0
2
0
0
0
1
0
2
0
0
0
1
0
2
2
0
0
1
0
1
1
0
0
0
0
0
2
1
2
1
0
2
0
0
1
0
2
0
0
0
0
0
0
1
0
0
1
3
0
1
0
1
0
0
0
0
1
0
6
2
1
0
2
1
0
1
2
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
2
0
1
0
1
1
0
0
2
0
1
0
0
2
0
0
2
2
0
0
1
0
2
0
0
0
0
0
2
1
1
1
0
0
2
0
0
2
0
0
0
1
1
3
2
0
0
1
0
0
0
1
0
2
0
1
0
1
1
0
0
1
1
0
0
0
0
2
1
0
4
1
0
0
1
2
2
0
0
0
0
2
1
0
0
0
0
0
3
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
2
0
2
2
2
1
0
2
0
1
0
1
0
1
0
0
0
0
3
0
0
0
0
1
1
1
2
2
0
2
1
1
2
0
1
0
1
0
1
0
0
1
0
1
1
0
0
1
2
0
0
0
1
0
2
0
0
2
1
2
0
0
1
0
0
1
0
1
2
1
0
0
0
0
2
2
1
2
0
2
0
0
0
0
0
3
3
2
2
0
0
0
2
0
1
1
0
0
0
0
1
1
1
0
2
0
1
0
0
1
1
2
2
0
0
1
1
0
2
2
1
3
0
0
2
1
2
2
0
0
0
0
2
0
0
0
1
1
1
0
1
0
1
2
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
1
2
0
1
2
0
0
3
2
0
0
0
1
2
2
2
2
0
0
2
0
0
0
1
1
2
2
0
1
0
0
0
0
0
0
0
1
0
2
0
0
2
0
7
0
0
1
1
0
2
0
0
1
0
0
0
0
1
0
1
0
0
0
2
0
0
2
1
0
1
0
1
3
2
1
2
0
1
2
0
0
2
2
1
1
0
0
0
0
1
0
0
3
1
0
1
0
0
0
2
0
0
1
0
1
0
2
1
0
2
1
1
1
2
2
1
0
1
1
0
0
1
0
0
1
2
2
1
0
0
2
0
0
0
1
0
0
3
1
0
4
0
0
1
0
0
1
0
0
0
0
0
0
1
0
2
1
2
2
1
0
0
1
1
1
0
1
1
1
1
2
1
0
0
1
1
1
0
0
0
2
0
0
1
2
1
1
2
0
0
2
1
0
0
1
0
2
2
0
0
0
0
1
0
1
0
0
0
1
2
2
2
1
0
2
1
0
2
0
0
0
2
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
2
2
1
0
1
0
2
2
0
3
2
1
0
3
0
2
0
0
0
0
2
2
1
0
0
0
0
0
2
0
3
2
0
2
0
0
1
1
2
1
2
0
1
2
1
1
2
0
1
2
0
0
0
0
0
0
0
2
0
2
2
0
1
0
1
2
1
0
0
0
0
1
0
0
0
0
1
0
2
0
0
1
1
3
2
0
2
0
2
0
1
1
2
0
1
1
2
1
3
1
1
0
0
0
0
0
2
1
2
1
1
0
0
0
0
0
2
0
1
0
0
0
1
0
0
1
1
2
2
2
2
1
1
2
0
0
1
0
0
0
2
3
1
0
0
1
0
2
1
0
0
1
0
1
1
1
2
1
0
0
0
0
2
0
0
0
0
2
1
1
0
0
2
1
0
0
0
1
2
0
1
0
0
0
0
2
2
0
0
2
0
1
0
0
1
0
1
0
1
1
0
1
0
1
0
1
0
0
2
0
2
0
0
0
0
2
0
1
0
0
0
1
2
0
0
0
0
1
0
2
2
1
0
0
1
0
2
0
0
0
0
0
2
0
2
0
0
1
1
1
1
1
1
2
0
0
0
2
2
0
2
0
1
0
1
0
0
0
0
1
2
1
4
0
0
1
0
0
0
0
1
1
1
1
0
0
0
1
0
2
0
1
1
0
2
0
0
0
1
0
1
0
0
0
2
0
0
2
2
1
2
1
1
0
0
2
0
1
2
0
1
0
2
0
2
2
0
1
1
2
1
1
0
2
0
0
1
1
0
0
1
2
0
0
0
0
1
1
0
0
0
2
0
2
2
0
1
0
2
0
0
1
2
2
0
0
2
1
2
0
0
1
0
2
2
0
0
3
1
1
1
1
1
0
0
0
0
1
1
0
2
0
3
2
1
0
0
2
0
0
0
1
1
0
2
2
0
0
0
0
2
0
0
0
2
1
1
2
1
0
1
0
2
2
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
1
0
1
1
0
2
0
0
1
0
0
1
0
0
0
1
2
2
0
2
0
1
2
0
0
0
1
0
1
0
2
0
2
0
0
1
0
1
1
1
1
1
2
1
0
1
0
1
0
2
0
1
1
0
0
2
0
0
0
0
1
0
0
1
2
1
1
0
0
2
0
0
0
1
1
2
0
2
1
0
2
1
2
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
3
0
0
1
0
1
0
1
0
0
3
1
2
1
1
1
0
0
1
0
0
1
2
1
0
1
2
0
1
1
1
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
4
1
0
2
0
0
2
1
0
1
2
2
2
2
0
1
0
2
0
2
0
1
0
0
2
1
1
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
2
0
0
0
1
1
0
1
1
0
1
1
1
0
0
1
0
2
2
2
2
1
2
0
1
1
2
0
0
1
0
3
0
0
1
1
2
0
1
1
2
1
0
0
0
1
2
0
1
1
1
0
3
0
0
0
0
1
2
1
0
0
0
2
0
1
1
1
0
0
1
1
2
0
1
0
1
0
0
0
0
3
1
2
0
0
0
0
1
0
0
1
2
1
2
0
0
0
0
1
1
0
0
1
0
0
1
0
1
1
1
1
0
0
0
0
0
0
2
1
1
0
0
0
1
1
0
0
2
1
0
2
1
0
1
1
1
0
0
0
0
0
0
0
5
0
1
0
0
2
0
2
0
1
0
2
3
1
2
0
1
2
0
0
2
1
1
0
1
0
0
2
0
1
0
0
0
0
2
0
0
1
0
0
0
0
2
0
2
0
0
1
1
2
1
2
2
0
0
0
0
0
1
1
0
0
2
2
1
1
0
0
2
1
1
0
2
1
0
2
0
0
0
0
0
0
2
2
1
0
4
0
1
0
2
0
0
1
1
0
0
0
0
1
0
0
0
1
1
2
2
1
0
0
1
1
1
1
2
1
0
0
0
0
1
1
1
0
1
1
2
2
2
1
0
2
0
0
1
1
1
0
2
2
0
0
0
2
0
0
2
0
1
0
2
1
0
1
2
2
4
2
0
0
1
0
1
0
1
1
0
0
0
0
0
0
1
0
0
2
0
0
0
2
2
2
0
0
1
0
1
2
0
0
1
0
0
0
1
1
0
0
1
2
0
0
3
1
0
0
1
1
0
0
2
2
0
2
0
1
1
0
2
1
2
0
0
0
0
0
0
0
5
0
0
0
1
2
1
0
0
1
2
1
0
2
0
0
0
0
0
1
0
2
1
0
0
1
0
0
0
1
0
0
0
1
2
2
0
0
2
1
0
0
0
0
1
0
0
2
2
2
0
1
0
0
1
0
0
0
1
1
0
2
2
0
2
2
0
1
0
2
0
1
0
0
0
0
2
0
0
0
0
0
1
1
1
0
0
2
1
1
0
0
0
0
2
1
2
2
1
0
2
1
0
0
0
0
0
0
0
0
1
2
2
0
0
3
2
2
0
0
0
2
0
0
2
0
1
0
2
0
1
2
0
1
1
2
1
1
0
2
1
1
1
0
0
0
0
0
2
0
1
0
0
0
2
1
2
2
0
1
2
1
1
2
0
0
1
0
1
0
0
1
0
0
0
0
1
0
1
0
2
2
0
0
0
0
1
0
1
0
0
1
2
0
1
0
1
2
1
0
0
1
2
2
1
0
2
0
0
0
2
0
0
1
0
0
2
1
1
1
0
0
1
0
2
0
0
1
0
1
2
0
1
0
0
0
0
0
0
0
0
1
0
0
1
2
2
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
3
0
0
0
0
0
0
0
1
2
0
2
0
2
0
0
2
0
0
0
0
0
0
2
1
0
0
1
1
0
0
0
1
0
0
0
1
0
0
1
3
0
3
2
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
1
1
0
0
2
1
0
1
1
0
1
1
0
0
1
1
1
0
2
1
0
0
1
0
1
0
1
1
1
1
1
0
2
0
1
1
1
0
0
4
1
2
1
0
2
1
0
1
0
1
0
3
0
0
0
0
1
0
2
0
0
0
2
0
0
4
0
1
1
0
0
0
0
0
1
0
1
1
2
0
2
1
2
0
0
0
0
0
2
1
1
1
0
1
0
0
1
0
2
2
1
0
3
1
1
0
0
2
0
1
2
0
0
2
0
0
1
0
0
0
1
0
0
2
1
0
2
1
2
0
2
2
2
0
0
0
0
0
1
0
1
2
2
0
0
2
0
2
0
1
0
1
0
0
0
2
1
0
2
0
2
0
1
2
1
2
1
1
0
1
3
0
0
0
0
2
0
1
2
0
2
0
0
2
2
1
0
2
2
0
1
2
0
1
0
0
0
1
0
0
1
1
0
0
0
2
0
0
3
0
1
0
0
1
2
0
0
0
2
1
2
2
1
1
1
1
1
0
2
0
1
0
0
0
0
0
1
2
0
2
2
0
2
1
2
0
0
0
0
0
0
0
0
2
1
0
1
1
1
0
0
2
1
0
0
0
0
0
0
1
0
0
0
2
2
0
0
2
0
1
0
0
2
3
0
0
0
1
1
0
1
0
0
2
1
0
0
0
0
0
2
0
1
1
2
0
2
0
0
1
0
0
0
0
0
0
1
2
1
0
0
2
0
0
3
0
0
0
1
1
1
2
2
0
0
1
0
0
0
2
0
0
0
0
0
0
3
2
3
2
1
1
1
0
2
0
0
0
0
1
0
2
0
0
2
0
0
0
2
1
0
0
0
0
0
0
1
1
1
0
0
0
1
1
2
0
0
0
1
1
0
0
1
0
2
0
2
0
0
2
0
2
1
1
2
1
0
1
0
1
0
1
0
3
1
1
0
1
1
0
0
2
2
0
1
0
0
1
0
2
0
0
1
0
2
0
0
1
0
0
0
2
0
1
0
0
0
0
1
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
1
1
2
0
1
0
0
2
1
2
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
1
0
1
2
0
1
1
2
1
1
2
0
0
0
0
0
1
2
0
0
2
1
1
0
2
1
0
0
2
0
0
0
1
2
1
0
2
2
0
0
0
0
0
0
0
2
2
2
2
0
3
1
1
0
2
0
2
0
0
2
0
1
1
0
2
2
0
0
1
0
2
3
2
1
2
0
1
0
2
1
1
1
0
0
0
2
0
2
2
0
0
0
0
1
1
2
0
0
1
1
2
0
0
0
0
1
1
1
0
2
0
0
1
0
2
0
0
1
0
0
0
1
0
0
1
0
0
0
2
2
2
0
1
1
1
1
2
0
0
1
0
1
1
1
0
2
2
0
1
0
0
0
2
0
2
0
0
0
0
3
0
1
0
1
0
1
2
2
1
0
1
0
1
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
2
0
2
0
0
1
1
2
0
2
1
0
0
1
0
0
1
0
0
1
0
0
0
2
1
1
0
0
0
0
1
0
1
0
2
0
0
1
1
2
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
2
1
0
0
1
1
0
1
1
0
1
0
0
2
1
0
0
0
2
1
0
0
1
0
2
0
0
2
1
1
0
4
1
2
1
0
1
0
0
0
0
0
1
0
0
0
2
0
0
1
1
1
2
0
1
1
0
2
0
0
2
0
0
0
1
0
0
1
0
0
1
1
7
0
1
1
2
2
1
2
2
0
1
0
1
0
0
0
1
1
0
1
1
2
1
1
1
1
0
2
1
0
2
1
1
1
1
1
5
0
0
1
1
0
0
0
0
0
0
1
0
0
2
0
0
1
1
2
1
1
0
0
0
1
2
2
1
0
0
0
0
0
0
1
2
1
0
1
1
0
0
0
0
0
2
1
0
2
0
0
1
0
1
0
0
2
2
0
0
1
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
1
1
1
1
2
1
0
0
0
2
1
0
1
2
1
0
0
0
2
0
0
2
0
1
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
2
1
0
2
0
1
0
2
0
0
0
0
0
1
0
0
2
0
1
1
0
0
1
0
0
2
0
1
1
0
1
2
1
0
0
2
0
0
0
0
0
0
0
2
2
1
2
1
0
0
2
1
0
1
1
0
1
2
0
2
0
1
1
1
1
0
2
0
0
1
0
0
0
0
2
0
0
1
1
0
0
2
0
1
0
0
2
1
0
0
1
0
2
1
0
2
1
0
0
0
0
1
0
0
0
0
2
1
0
1
0
0
0
1
0
2
0
0
0
1
2
3
0
1
0
1
0
0
0
2
0
1
0
1
1
1
1
0
0
2
0
0
2
0
0
2
0
0
0
0
1
1
1
0
0
1
0
2
1
2
0
0
0
2
1
0
2
3
1
1
2
0
2
0
1
1
1
0
0
0
2
0
2
1
1
0
0
1
0
0
0
0
2
0
1
1
1
1
1
0
0
2
3
0
0
2
3
1
2
0
0
0
0
0
2
0
0
2
2
0
2
1
0
0
2
2
0
0
0
0
1
1
0
2
1
2
0
1
2
2
0
0
2
0
1
1
0
2
2
0
0
0
1
1
0
0
0
1
0
2
0
0
2
0
0
1
2
0
0
0
0
1
4
0
0
0
0
0
1
0
0
0
0
2
1
1
1
0
0
2
0
0
2
0
0
1
1
1
0
0
0
0
4
1
0
2
0
0
0
0
0
2
1
2
0
0
1
0
0
0
1
0
2
0
2
0
1
1
3
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
2
2
0
2
1
1
0
0
2
2
0
3
2
0
0
0
0
0
1
2
0
2
0
1
0
0
0
1
0
0
2
0
0
0
0
1
2
2
0
0
0
2
1
1
0
0
0
0
0
1
1
2
2
0
0
1
0
0
2
2
1
2
1
0
3
2
0
0
0
1
0
2
3
1
0
2
0
0
1
1
0
1
1
1
1
1
2
1
2
0
1
0
0
0
0
1
1
0
2
0
2
0
2
0
2
2
1
0
0
1
1
1
2
0
0
2
1
0
0
1
1
1
1
0
2
2
1
2
2
2
1
0
1
0
1
0
2
0
2
0
0
0
0
1
3
3
0
0
0
0
2
1
1
0
2
0
1
1
1
1
0
3
1
0
0
0
0
0
2
1
1
2
2
1
0
1
1
0
0
1
0
2
0
1
2
0
4
1
0
0
1
0
2
2
1
0
0
0
3
0
0
1
1
2
1
0
0
1
1
0
0
1
3
0
1
2
1
0
0
0
0
0
2
0
2
1
2
0
0
0
0
1
0
0
1
1
0
2
1
0
1
1
0
0
2
1
1
1
2
1
0
2
0
1
0
1
0
1
1
0
2
0
0
4
2
0
1
0
0
0
1
0
0
0
1
1
1
0
2
2
2
1
2
1
0
4
2
2
0
0
0
1
0
1
0
2
1
1
1
0
1
1
0
0
1
2
0
0
0
0
0
2
2
0
0
0
1
0
2
0
1
1
1
1
0
0
0
2
1
1
1
2
0
0
0
0
0
0
1
0
0
1
0
2
1
1
0
3
0
1
0
0
0
0
0
0
1
2
2
2
1
0
0
2
1
1
1
0
2
1
2
1
0
0
0
1
2
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
2
3
0
2
0
1
0
2
1
0
1
0
0
0
1
2
2
0
0
1
1
0
0
1
2
0
0
0
0
2
2
1
1
1
0
0
0
1
1
0
3
2
0
2
2
6
1
0
0
0
1
0
0
0
1
4
1
0
0
3
1
0
2
0
1
0
0
2
1
0
0
0
0
0
0
0
0
2
0
1
1
1
0
1
0
1
1
0
1
0
0
2
0
0
2
2
0
1
2
0
0
0
0
3
0
0
0
1
1
1
0
1
0
0
1
0
1
0
0
2
0
0
1
1
1
0
0
0
1
2
1
0
1
0
0
0
0
0
2
0
1
1
0
1
0
1
0
0
2
1
0
0
1
2
2
0
0
2
1
0
0
2
0
0
0
1
1
0
2
1
0
0
0
1
0
1
1
0
1
1
2
0
0
0
1
2
1
1
2
2
0
2
1
1
1
0
0
0
1
3
2
1
0
2
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
2
0
0
2
1
0
0
2
0
0
0
1
0
1
0
2
0
1
0
2
1
2
0
2
0
2
0
2
2
1
0
0
0
2
0
0
0
0
2
0
1
2
0
0
1
0
1
2
0
0
1
5
0
1
1
2
2
2
0
2
0
2
2
0
0
0
0
2
2
1
0
2
2
1
1
1
1
1
0
0
0
2
0
2
0
2
0
0
2
1
0
1
0
1
1
1
2
1
0
0
0
2
1
0
2
1
1
2
1
1
0
0
0
2
2
2
1
0
0
2
1
0
0
0
1
0
0
0
4
2
0
0
0
1
0
1
3
0
0
2
0
1
0
0
0
0
2
0
0
2
0
0
0
1
0
1
0
1
2
0
0
2
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
2
2
2
1
1
3
1
0
1
2
0
0
1
1
1
1
0
2
0
2
2
0
0
0
0
1
1
0
0
1
1
0
0
1
0
1
0
0
0
0
1
2
1
1
0
0
2
2
1
4
0
2
2
1
0
0
2
0
1
2
0
2
0
0
2
0
0
0
0
0
0
0
1
1
0
0
1
2
0
0
1
0
0
0
0
2
1
2
2
0
0
0
1
1
1
1
0
0
0
0
0
2
0
0
0
2
0
2
1
0
0
1
2
0
0
0
2
0
0
0
0
2
1
1
0
0
1
2
1
2
0
1
2
0
0
1
1
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
2
2
1
0
2
2
0
2
2
2
1
1
0
0
1
0
1
1
0
0
0
2
3
0
1
0
4
2
1
1
0
0
0
2
2
1
1
0
2
0
0
0
0
0
0
1
1
1
2
0
1
0
1
0
0
3
2
1
0
0
0
3
1
0
1
1
1
1
2
0
0
0
0
0
1
0
2
0
1
2
0
0
0
1
2
0
2
0
0
1
1
2
1
1
0
0
0
1
0
1
1
1
1
1
0
0
1
2
0
1
0
0
0
0
1
1
0
2
2
0
2
3
1
0
0
0
1
0
0
0
1
0
1
2
0
1
0
0
2
0
0
0
1
0
0
1
1
0
0
0
2
1
0
1
1
2
1
1
1
2
2
1
2
0
2
1
0
2
2
0
2
1
0
1
1
0
0
1
0
0
0
1
2
1
0
0
0
1
0
1
2
1
2
2
1
1
2
2
2
1
0
0
0
0
0
0
0
0
1
1
0
1
1
1
1
2
2
2
0
1
1
0
0
2
1
2
0
1
0
0
2
0
0
2
1
0
4
2
0
2
1
3
1
0
1
1
0
0
0
1
2
2
0
1
0
3
2
0
2
1
1
0
0
1
0
1
1
0
1
0
2
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
2
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
1
0
2
0
0
2
0
0
1
1
0
1
2
1
0
1
0
0
0
1
2
2
2
1
1
1
0
0
1
1
0
0
1
2
1
0
2
0
1
1
0
0
0
2
0
1
0
0
1
2
0
0
2
0
2
0
2
1
2
0
1
1
0
0
1
1
1
1
2
0
2
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
2
0
0
0
1
0
1
0
1
1
1
1
0
2
1
3
2
0
0
0
0
2
1
1
0
0
0
0
0
0
1
1
0
1
0
0
2
0
4
1
0
2
0
1
0
0
1
1
0
1
0
0
1
1
0
0
1
2
1
0
0
0
0
0
0
0
0
1
1
0
2
1
0
0
1
1
0
0
2
0
2
3
2
2
2
2
0
2
1
1
1
1
0
1
1
3
0
1
0
0
0
1
0
0
0
0
0
0
2
0
1
1
1
0
0
0
0
0
0
1
0
0
1
2
1
1
1
1
1
1
0
0
0
2
0
1
1
0
2
2
0
0
2
0
1
0
0
0
0
1
3
0
1
1
1
0
2
0
0
0
1
1
1
1
0
2
0
0
1
2
4
0
0
1
0
0
1
0
1
0
2
1
1
0
1
0
2
0
2
1
1
2
0
1
0
0
0
1
0
1
0
0
0
0
0
2
2
1
0
1
1
0
1
2
1
0
1
0
1
2
1
0
1
3
0
0
0
1
2
0
1
0
1
2
2
4
0
0
1
0
4
0
0
1
1
2
0
0
2
2
0
2
2
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
3
2
1
0
1
1
2
1
1
0
1
0
0
0
1
0
0
5
1
0
0
1
1
1
0
0
1
1
1
0
1
0
0
0
1
1
3
0
0
0
1
2
0
2
0
2
0
1
0
2
1
0
3
2
0
0
1
1
2
0
2
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
1
0
1
1
2
1
0
0
1
0
1
1
2
0
1
2
0
0
0
3
0
0
1
0
1
1
0
2
0
1
1
1
1
2
0
2
1
0
0
1
2
0
0
0
0
7
1
2
0
0
0
0
0
1
1
3
3
1
0
0
1
0
0
2
0
2
0
2
1
0
0
0
1
1
0
2
1
2
0
1
1
0
1
1
1
2
0
0
0
1
0
2
1
1
0
2
0
0
1
1
1
0
0
2
2
0
0
1
1
0
0
0
0
0
1
2
2
1
0
0
1
1
0
2
0
0
1
2
0
0
1
2
1
1
3
0
0
1
3
2
7
0
0
1
1
0
1
0
0
0
1
1
0
1
0
2
0
0
4
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
1
2
1
0
1
0
1
0
1
0
1
0
0
0
0
2
0
0
2
1
0
0
1
1
0
2
0
1
0
0
2
0
1
0
6
0
2
0
1
0
1
0
0
0
0
1
2
2
1
2
0
1
2
4
0
1
3
0
1
0
0
0
2
0
1
0
2
1
2
1
0
1
0
2
3
0
2
2
1
1
1
0
0
1
0
0
3
2
0
0
0
0
1
2
2
0
1
2
0
1
0
1
1
2
0
0
0
0
2
1
0
2
0
1
1
0
1
1
0
0
2
0
3
1
1
0
0
0
1
1
2
2
0
0
1
1
1
0
0
0
2
1
0
1
1
1
0
1
2
0
0
2
0
2
0
0
0
0
0
2
0
1
1
0
1
0
2
0
0
2
0
2
1
1
2
2
2
1
0
0
0
0
1
0
0
0
0
1
0
0
0
2
1
0
1
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
1
0
1
0
0
2
1
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
2
0
0
2
2
0
1
1
1
1
0
1
0
2
2
0
0
4
2
0
0
0
0
1
1
2
0
0
2
0
0
1
0
1
1
1
3
2
0
0
2
0
1
0
2
0
0
0
0
2
1
0
0
0
1
0
1
1
1
0
0
3
0
0
0
0
0
2
0
0
4
0
0
0
2
1
0
0
0
0
0
0
0
0
1
2
1
0
1
0
2
0
2
2
0
1
1
1
2
0
2
0
0
0
3
1
1
1
0
0
0
2
2
0
0
1
3
1
2
0
1
1
0
0
0
0
0
2
0
0
0
1
2
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
1
2
1
1
2
2
0
0
2
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
3
1
2
1
1
0
2
0
1
1
0
1
0
0
2
0
2
2
0
1
2
0
0
0
2
0
2
0
3
2
1
0
1
0
0
0
0
1
0
1
1
2
0
2
0
2
2
1
0
0
1
0
1
2
0
1
1
2
0
1
0
2
1
2
0
0
0
2
0
1
2
0
0
2
0
0
0
2
0
0
0
1
1
2
1
2
0
0
1
1
1
0
0
0
0
0
2
0
1
1
2
2
1
0
1
1
0
0
0
2
0
0
0
1
2
0
1
2
0
0
0
0
2
0
1
1
0
2
0
0
0
0
0
0
0
0
1
2
1
1
2
1
2
0
1
1
0
1
0
0
1
0
1
1
2
0
2
0
0
2
0
0
0
0
0
2
2
2
2
1
0
0
0
0
1
1
0
2
1
2
0
0
2
1
0
0
0
1
0
2
0
0
0
0
2
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
2
0
3
0
2
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
1
1
0
0
1
2
0
2
1
1
0
0
0
1
2
0
2
0
2
0
0
0
1
2
2
0
2
1
0
0
1
2
0
0
1
0
0
0
0
2
1
2
2
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
2
1
2
1
1
0
0
2
0
2
2
0
0
2
0
2
1
3
0
1
0
3
1
1
0
1
1
0
0
2
0
0
0
1
0
0
0
1
1
0
1
2
0
0
0
1
1
1
0
0
1
1
1
0
1
2
2
0
0
0
0
0
2
0
4
3
0
0
0
1
1
0
2
0
1
0
0
0
2
2
1
2
0
0
2
2
0
0
2
0
1
2
0
0
0
0
0
1
1
0
0
0
1
2
2
0
2
1
0
1
0
0
0
2
1
1
0
0
2
1
0
1
1
1
0
0
0
0
0
0
1
1
1
1
0
1
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
1
1
0
0
1
0
1
0
3
0
1
0
2
2
2
2
2
0
0
0
2
0
0
2
0
1
2
0
1
1
1
0
1
0
0
0
2
0
0
2
0
2
0
1
1
1
2
1
0
2
0
0
2
0
1
0
2
2
0
1
0
0
0
2
0
0
1
1
2
2
2
1
0
1
0
2
1
1
0
2
0
2
0
0
0
0
0
2
0
0
1
0
0
0
1
0
2
0
1
0
0
0
1
3
1
1
0
1
1
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
1
1
1
1
0
0
1
2
3
1
0
0
0
1
0
2
0
0
2
2
1
0
1
0
0
0
1
0
1
1
0
2
0
0
0
0
0
2
0
0
1
0
0
0
1
1
0
1
0
1
2
3
1
1
2
2
0
0
0
2
2
0
0
0
2
0
0
1
3
0
0
0
0
0
1
0
0
1
0
2
1
2
0
1
0
2
0
1
3
2
1
0
2
6
3
2
1
0
2
1
0
1
0
2
1
2
0
1
1
0
0
0
1
1
2
2
0
0
0
1
1
1
1
3
0
2
0
0
2
0
0
2
0
1
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
1
0
0
1
0
1
0
2
1
0
1
1
0
2
0
1
2
0
1
0
0
2
0
0
2
0
1
1
0
1
2
2
2
2
2
0
2
0
0
2
1
2
1
0
1
0
0
0
3
1
1
1
2
1
0
2
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
2
2
0
0
2
0
0
0
0
2
1
2
0
1
1
1
1
0
0
0
2
0
2
0
0
0
2
1
2
0
1
0
2
0
0
2
0
0
0
0
2
1
2
1
0
2
0
0
0
1
0
0
1
0
0
2
1
0
0
2
1
1
0
2
0
0
1
0
4
0
1
0
0
0
2
2
2
2
0
1
0
0
0
0
0
1
2
1
1
0
1
0
2
2
1
0
0
0
1
0
1
0
3
1
2
0
0
0
0
0
1
2
0
1
0
1
0
1
0
0
0
2
0
0
0
2
0
1
0
1
0
1
2
0
1
0
0
2
1
0
1
0
1
1
0
2
1
0
1
2
2
2
0
0
1
1
0
1
3
1
0
0
0
1
1
2
2
0
2
2
2
1
0
0
0
0
0
0
0
1
3
0
0
1
2
1
0
2
1
1
0
1
2
1
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
1
2
0
2
1
0
0
2
1
0
0
1
3
1
1
2
2
1
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
2
1
0
0
0
0
0
2
0
0
0
2
1
1
2
0
0
4
0
2
0
1
1
0
2
2
1
0
1
1
1
0
1
1
1
1
0
1
1
3
1
2
0
0
0
1
1
1
0
0
1
0
2
0
0
0
0
2
1
0
0
0
0
2
0
2
2
0
0
1
1
3
2
2
1
1
1
1
2
1
2
0
1
1
0
2
2
1
2
0
0
0
0
0
1
0
2
2
0
1
0
0
1
0
0
0
1
0
1
2
1
0
1
0
0
0
0
0
0
0
2
2
2
0
0
0
2
1
0
0
0
0
1
1
1
2
0
2
1
2
1
0
2
0
2
2
0
0
1
2
1
0
2
0
1
1
2
2
0
1
1
0
1
1
1
2
0
1
0
1
0
2
1
0
0
0
0
0
2
2
1
1
2
2
0
2
0
0
0
1
0
1
2
0
0
1
0
0
0
0
0
0
0
1
1
2
1
1
0
0
1
2
0
1
1
0
2
2
0
1
0
0
2
2
0
0
2
1
0
0
2
1
0
0
0
0
2
0
1
2
0
0
0
0
2
0
0
2
2
0
0
2
0
2
0
0
4
0
0
0
1
0
1
2
2
0
7
1
1
1
0
0
0
1
2
1
2
0
0
0
0
1
2
2
1
0
0
0
0
0
2
0
1
1
0
1
1
0
0
0
2
0
0
3
2
1
0
1
0
0
2
0
1
0
1
2
1
0
0
2
1
0
1
0
3
0
0
1
3
2
2
0
2
1
1
0
1
2
2
0
0
0
1
0
1
1
1
1
3
2
2
1
0
1
1
0
2
0
1
1
2
1
2
1
2
1
0
1
0
0
1
0
2
0
1
0
0
0
1
0
1
0
0
0
2
0
1
1
0
0
0
2
0
1
2
1
0
2
0
2
0
1
1
0
0
2
0
0
1
2
0
0
0
2
0
2
0
1
0
0
0
2
0
1
1
0
0
0
0
2
0
0
1
0
0
0
1
2
0
0
1
0
0
1
1
0
0
1
2
2
2
1
0
0
2
0
0
2
0
2
2
0
0
0
1
1
1
0
0
1
1
1
0
0
0
2
0
0
0
0
0
1
0
0
1
2
0
0
0
0
2
0
1
0
0
1
2
1
0
1
1
2
0
1
1
0
4
1
0
0
0
0
3
1
1
2
0
0
0
0
1
2
1
0
1
0
0
1
0
0
1
0
0
0
0
1
2
2
1
1
0
1
1
0
0
1
0
1
1
2
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
1
1
0
0
1
2
0
3
1
0
0
2
1
0
1
0
2
0
2
1
0
2
0
0
2
1
2
1
0
0
0
1
2
0
0
0
1
0
0
1
1
1
0
1
0
0
1
1
0
0
2
2
0
2
0
0
1
0
1
1
2
1
0
0
3
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
2
1
1
1
1
0
2
5
1
2
2
0
0
0
1
0
0
0
0
2
2
1
1
1
0
2
1
0
1
0
2
1
0
2
1
1
0
2
0
0
0
0
0
0
0
1
1
0
0
0
2
0
3
0
2
0
10
0
0
0
0
2
1
1
0
0
0
0
2
1
0
2
0
2
2
2
0
1
1
0
0
2
0
0
0
0
0
0
1
2
1
1
0
0
2
0
1
1
1
1
0
2
0
1
2
0
2
2
2
2
2
2
0
1
0
0
1
1
0
1
0
0
0
0
1
0
3
1
2
2
0
3
0
0
0
0
1
0
1
0
3
0
0
0
0
1
1
2
0
0
1
2
0
2
1
2
1
2
2
1
1
0
1
0
0
0
1
2
1
0
0
1
0
0
1
2
3
1
1
0
0
2
2
2
2
1
1
2
2
0
2
0
2
2
0
0
0
1
2
1
0
2
0
1
1
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
2
1
2
1
0
0
1
0
0
1
0
3
0
0
1
0
0
0
1
2
0
1
2
0
0
0
0
0
1
0
0
1
2
2
2
4
0
1
0
1
0
2
0
0
2
2
1
0
1
0
0
0
0
0
0
1
3
0
0
0
0
0
0
3
2
0
0
1
0
1
2
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
1
0
2
1
0
0
1
2
0
0
0
1
0
2
1
0
2
0
3
1
1
1
0
2
0
2
2
1
1
0
0
0
2
0
1
0
0
0
2
0
2
0
3
1
2
0
2
1
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
1
1
1
1
2
2
0
0
0
1
0
0
0
1
1
0
0
0
2
2
0
0
1
1
2
0
0
0
0
1
0
0
0
1
1
0
1
2
0
0
0
1
5
0
2
0
0
4
1
0
0
0
1
0
1
1
0
2
0
2
2
2
0
2
0
0
1
2
1
0
0
0
0
1
2
1
1
0
1
1
1
0
0
0
0
0
3
1
2
0
2
2
0
0
1
1
0
0
2
0
1
1
0
2
0
1
0
1
0
0
1
1
1
1
0
1
1
2
0
1
0
1
1
0
2
1
2
0
0
1
3
2
0
1
0
2
0
0
2
3
2
1
0
2
0
0
0
0
2
0
1
0
1
0
2
2
2
0
1
2
0
2
1
1
0
0
0
0
0
0
2
0
1
1
1
1
1
1
1
0
2
2
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
2
1
0
1
1
1
1
0
0
0
2
0
0
1
0
1
0
3
0
0
0
0
2
2
2
1
1
1
1
0
1
0
0
0
1
1
1
0
0
0
0
0
2
1
1
2
2
0
1
1
2
0
0
0
0
0
1
0
0
3
1
0
0
1
2
1
1
1
0
0
1
1
2
1
3
2
1
0
1
3
0
1
0
1
0
0
2
1
0
0
0
2
0
1
2
2
2
0
1
0
0
2
0
1
0
1
2
1
1
0
1
0
2
0
2
0
0
1
0
1
1
1
0
1
1
0
0
0
0
2
0
2
0
1
1
0
0
1
2
0
2
0
1
1
1
2
1
1
0
2
1
0
2
2
1
0
0
0
1
2
2
1
0
0
1
0
1
1
1
2
2
1
0
3
1
0
2
1
0
0
3
0
0
0
0
1
0
0
1
1
0
2
1
0
0
1
0
0
1
1
1
2
0
0
1
2
0
0
0
1
1
1
0
2
0
0
0
1
0
1
1
3
1
0
1
2
1
2
1
0
0
0
1
3
0
1
0
1
0
1
1
0
0
3
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
2
1
2
0
1
2
0
0
0
1
0
0
1
1
1
1
0
2
0
1
1
0
0
0
1
1
0
0
1
1
1
2
1
0
2
0
0
1
2
1
2
1
0
1
0
2
1
0
0
1
1
0
0
1
2
0
0
0
0
1
1
2
2
1
2
0
0
0
1
0
2
0
2
1
0
1
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
2
2
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
3
2
0
1
3
2
0
0
1
0
1
1
0
1
0
1
0
0
0
1
2
0
0
0
1
0
0
0
1
1
1
0
1
0
0
0
1
1
0
0
2
2
0
0
0
0
3
0
1
1
0
0
0
0
2
0
0
1
0
0
0
1
0
0
1
1
1
2
1
1
2
1
0
0
6
0
1
0
1
0
0
2
1
1
0
1
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
1
0
0
2
1
0
0
2
4
1
0
0
2
2
1
2
0
2
2
0
2
1
1
0
0
0
2
1
1
1
2
0
0
1
0
0
1
0
1
0
1
0
0
1
3
1
1
0
1
1
0
0
0
0
2
0
2
1
1
0
0
1
0
0
0
0
1
0
0
2
2
1
0
0
2
1
1
0
0
0
0
0
0
1
1
0
0
1
0
2
1
0
0
0
0
2
1
2
2
0
0
1
1
2
0
0
0
2
0
0
1
2
0
0
0
1
0
2
0
0
1
0
1
0
1
0
1
0
2
2
0
0
0
0
1
1
1
1
1
0
1
1
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
2
2
0
2
0
2
2
2
0
0
1
1
0
0
0
0
1
3
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
2
3
1
1
0
0
1
0
0
0
1
1
0
2
1
3
0
1
1
1
0
0
0
1
2
1
1
1
1
2
0
3
2
0
0
1
1
0
0
2
1
1
0
0
0
2
1
0
0
1
1
0
1
2
2
1
0
0
2
1
1
0
0
0
0
2
0
0
0
0
1
0
0
1
2
2
0
0
2
0
1
2
1
0
0
1
0
2
0
2
0
2
1
0
0
2
3
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
2
0
0
0
2
0
0
1
1
2
0
1
1
0
1
2
0
0
1
1
1
1
1
0
0
0
0
3
0
0
0
3
0
1
2
1
0
0
0
0
0
0
2
1
2
0
0
0
1
2
4
0
1
1
1
1
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
1
0
1
1
1
1
0
0
1
1
1
2
1
0
0
2
0
0
0
2
1
0
0
1
0
0
0
2
1
2
1
0
1
0
1
0
0
0
1
1
0
0
1
0
2
0
1
1
0
0
1
1
1
0
3
1
1
2
1
0
1
1
1
0
0
1
0
0
0
2
2
0
2
0
0
3
0
0
0
1
0
0
2
3
1
0
0
0
1
2
1
1
0
3
0
2
1
0
0
0
0
0
1
2
1
2
0
0
0
1
1
0
0
0
1
0
0
0
1
0
1
0
0
1
0
1
0
0
2
0
2
0
2
0
2
2
1
0
1
2
0
2
0
0
1
2
0
2
0
2
2
1
0
0
0
1
0
1
0
0
0
1
0
2
2
0
0
2
0
0
0
2
0
0
1
0
0
1
0
0
1
0
0
0
2
1
1
1
0
1
0
1
1
2
0
1
0
2
0
1
0
0
0
0
1
0
0
1
0
0
0
2
0
0
1
0
2
2
0
1
0
1
0
1
0
2
0
0
1
0
2
1
0
2
0
0
0
0
1
0
2
0
1
2
0
2
2
0
2
3
1
0
0
2
0
2
2
1
0
1
0
0
0
2
0
2
1
0
1
1
2
1
2
2
1
2
1
2
0
0
0
1
2
0
1
0
2
1
0
0
2
0
1
2
0
0
1
2
2
0
0
1
0
0
0
2
0
0
0
1
0
2
2
2
0
0
1
2
0
2
0
1
0
1
1
1
0
2
0
1
1
0
0
2
1
0
0
1
0
0
0
2
1
1
1
1
0
0
0
1
1
1
2
0
1
0
1
2
1
3
0
0
0
2
0
1
1
1
0
0
0
1
0
2
3
0
0
2
2
0
0
0
0
0
0
0
0
2
0
1
1
0
0
1
0
0
1
2
1
2
0
0
1
0
0
0
3
2
1
2
2
0
2
1
0
0
2
1
0
1
2
0
1
0
2
0
0
0
0
0
1
0
0
0
0
2
1
1
0
0
0
2
3
2
0
0
0
1
0
0
1
2
1
1
1
1
0
3
0
2
0
0
1
1
2
0
0
1
2
2
0
2
0
0
0
0
0
2
0
0
3
0
0
0
1
0
2
2
0
2
1
0
0
2
2
1
0
1
0
1
0
0
1
0
2
1
0
0
1
2
0
0
0
0
0
1
2
2
1
1
0
0
0
0
0
1
2
0
0
0
0
1
1
0
0
0
0
0
2
0
0
2
2
0
1
2
0
0
0
0
0
0
1
1
0
0
0
2
1
3
1
0
0
0
0
2
0
0
1
1
2
0
2
0
0
1
2
0
0
1
0
1
0
0
0
1
0
0
0
2
1
3
4
1
0
0
2
0
0
1
0
0
0
0
1
0
1
1
0
2
2
1
0
0
3
0
0
1
0
2
1
0
0
0
2
0
0
0
0
1
0
0
0
1
2
1
3
2
0
2
1
1
0
2
1
2
1
1
2
1
0
0
0
0
0
1
0
1
0
1
0
1
0
0
1
2
1
0
1
0
0
1
2
0
0
0
0
1
1
1
1
2
0
1
0
0
1
2
0
0
1
2
1
0
0
1
0
1
2
1
0
2
0
2
2
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
1
2
1
0
1
1
0
1
1
0
0
0
1
0
0
0
1
1
1
0
0
0
0
1
3
0
0
1
0
0
0
0
1
0
2
1
0
0
1
1
0
0
0
0
0
0
1
2
1
0
0
2
1
2
1
0
1
1
0
1
0
0
0
0
1
1
0
3
2
2
2
2
0
1
0
1
0
1
2
0
0
0
0
1
0
2
2
1
1
2
0
1
1
0
0
0
0
2
1
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
1
1
0
0
0
1
1
2
0
0
2
1
1
0
1
2
2
1
0
0
0
2
1
0
0
6
1
2
2
2
0
0
0
0
0
2
1
2
1
0
1
0
2
0
0
1
0
0
1
0
0
1
2
3
1
1
2
0
1
1
0
0
1
0
2
1
1
1
0
0
1
2
0
0
1
0
0
2
0
0
0
0
1
1
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
2
0
2
1
2
0
0
0
0
0
2
1
0
0
0
0
1
1
1
3
1
2
2
2
0
0
1
1
0
0
0
2
0
1
0
2
2
0
1
1
1
1
1
1
0
2
0
0
0
0
2
0
0
0
1
0
0
0
2
2
0
1
0
2
0
0
1
0
1
1
0
1
0
1
3
0
1
0
0
1
0
3
1
2
0
0
0
0
2
0
0
0
1
0
0
3
1
0
1
0
0
5
0
0
1
1
1
1
2
2
2
1
1
1
0
0
2
5
4
0
1
1
0
5
0
0
0
2
1
1
2
2
0
2
2
1
1
1
0
1
0
0
0
0
1
0
0
0
0
0
1
1
2
0
0
0
1
2
0
1
0
2
1
0
2
0
1
2
1
1
0
2
2
0
0
0
0
1
1
1
0
1
2
0
0
2
0
1
0
2
1
0
1
2
2
0
2
0
0
2
0
0
0
1
1
0
0
1
0
0
1
2
0
0
2
0
1
0
0
1
1
0
0
0
2
0
1
0
2
0
1
1
1
1
0
2
1
2
0
0
1
0
2
0
1
0
0
1
0
2
1
2
0
1
1
0
1
2
1
0
0
1
2
0
0
2
0
1
1
0
1
2
0
1
0
2
0
0
0
0
0
1
1
2
1
1
0
0
1
1
1
2
2
0
2
1
2
0
0
0
1
0
2
0
0
0
1
0
2
2
2
0
0
0
3
1
1
0
0
1
0
2
0
0
1
1
2
2
2
1
0
0
1
1
0
2
1
2
1
2
3
1
0
1
0
0
2
0
0
2
0
1
1
0
0
0
0
0
0
1
3
0
0
0
0
2
1
0
2
1
1
0
0
0
1
2
1
1
0
1
0
1
0
1
1
0
2
0
1
1
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
1
1
0
0
2
0
2
0
1
0
0
0
0
0
0
1
0
1
0
2
1
0
2
0
2
0
2
2
1
2
0
1
0
2
1
0
2
0
0
0
1
1
2
0
0
0
0
1
2
0
0
0
2
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
3
2
1
0
1
0
7
1
2
0
0
2
1
0
2
1
2
2
0
2
0
0
0
1
5
1
2
0
0
0
2
1
0
1
1
3
0
2
0
1
1
0
1
0
1
0
1
0
0
0
2
0
0
0
0
2
0
2
1
0
1
0
0
0
2
2
0
0
2
0
1
0
1
2
0
0
1
0
0
1
0
3
1
1
2
0
0
1
0
0
0
1
0
2
0
1
1
1
1
0
1
0
2
1
1
0
1
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
1
0
0
0
2
1
1
0
1
1
1
1
0
2
1
0
2
1
1
0
0
1
0
1
2
0
0
0
0
1
0
0
1
2
2
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
1
0
2
1
0
0
1
0
0
1
0
0
0
2
2
2
1
2
0
0
1
0
0
0
0
0
2
1
0
0
3
0
1
0
2
1
0
2
0
0
0
2
1
1
0
0
3
0
0
2
0
0
2
2
0
1
1
2
1
2
0
0
2
0
0
1
0
1
5
0
0
0
2
0
2
2
0
0
2
0
2
0
0
0
0
0
0
1
0
2
0
2
0
1
1
2
1
0
0
1
1
0
1
1
2
3
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
1
1
0
0
1
0
1
0
0
0
0
0
0
3
0
0
0
0
0
1
1
0
0
1
0
0
2
2
0
0
2
0
0
0
1
0
2
2
1
0
1
2
2
0
2
0
0
2
1
1
1
1
0
0
0
0
2
0
1
0
0
2
0
0
0
0
1
2
1
1
1
1
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
2
0
2
2
1
0
0
2
0
1
0
0
2
0
1
0
0
1
2
0
1
0
0
1
2
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
2
2
0
0
0
1
1
0
0
0
0
0
1
2
2
1
2
2
0
2
1
0
0
0
1
0
0
1
1
0
1
2
1
0
0
1
0
0
2
0
0
1
1
1
1
0
0
0
0
0
0
1
1
1
2
0
0
2
0
0
0
0
0
1
1
0
1
0
0
0
0
0
4
0
0
2
0
0
0
0
2
1
2
1
2
1
0
0
0
1
2
0
1
0
0
0
0
0
2
0
0
1
1
0
0
2
0
0
0
2
0
0
2
0
1
0
2
0
0
2
1
1
0
0
2
0
0
0
2
1
0
0
0
0
2
0
0
1
1
0
2
2
0
1
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
2
0
1
0
0
1
2
0
0
0
0
2
0
0
0
0
0
1
0
1
0
1
0
1
0
0
2
1
2
1
0
1
2
0
2
0
0
2
0
1
0
0
0
0
2
0
0
1
0
1
1
0
0
2
0
2
2
1
0
0
2
0
0
0
0
2
0
0
0
0
1
0
2
0
2
1
2
2
0
2
0
2
1
1
2
0
2
0
1
0
0
0
0
2
2
1
1
2
1
1
0
1
0
1
0
1
0
0
0
0
2
0
0
0
0
1
1
2
1
0
1
0
2
0
2
1
2
1
2
0
2
0
1
2
1
1
2
0
0
0
0
0
0
1
1
2
0
0
0
1
0
1
0
0
2
1
1
0
0
0
0
0
1
0
1
2
1
0
0
0
2
1
1
0
1
1
0
0
0
2
1
0
1
0
2
0
0
2
1
2
1
0
0
1
0
2
1
0
1
2
2
0
2
0
0
1
0
1
0
0
2
0
1
0
1
1
2
0
1
0
1
0
3
0
0
0
0
0
0
1
0
0
1
2
0
1
0
2
0
2
1
2
1
0
2
2
0
0
0
0
2
0
2
2
0
0
2
2
2
0
1
0
0
0
1
1
2
1
1
0
1
1
0
2
0
0
0
1
1
0
1
0
2
0
0
0
0
0
1
1
0
1
0
2
2
1
0
0
2
2
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
2
1
2
0
1
0
1
0
0
1
1
1
0
1
0
2
0
0
0
0
3
2
0
0
0
0
0
0
1
2
0
0
1
2
0
2
0
0
2
2
0
2
0
0
0
0
0
0
0
0
1
1
1
1
2
0
0
0
2
2
0
0
0
0
0
1
0
0
1
1
2
1
0
0
0
1
1
3
0
0
0
0
2
0
1
0
0
0
1
0
0
0
2
3
2
0
0
0
0
0
1
0
0
0
0
1
1
1
1
1
1
1
0
0
0
0
2
2
0
0
1
1
0
0
0
2
3
0
2
0
0
0
1
0
2
1
2
0
0
0
0
1
1
1
2
0
1
1
0
2
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
2
0
2
0
0
0
0
1
2
1
1
0
0
0
0
1
1
2
0
1
0
2
1
0
1
0
2
2
0
0
2
1
0
0
0
1
1
1
0
0
0
1
0
0
0
1
2
1
2
1
0
1
0
0
2
0
2
2
6
2
1
0
2
1
1
0
1
0
2
1
2
1
1
0
2
0
0
2
0
0
1
0
0
2
4
0
1
2
2
0
0
2
2
0
0
0
0
1
0
0
0
1
3
0
1
0
0
1
0
0
2
0
2
1
1
1
0
2
0
1
1
1
0
0
0
0
2
2
0
1
2
1
1
1
1
0
0
0
1
0
0
1
2
1
1
0
0
0
1
0
2
0
0
3
0
1
0
2
2
0
1
1
1
1
1
1
1
1
1
0
0
0
0
0
1
1
1
0
1
2
0
0
2
0
0
0
1
2
0
0
2
0
2
0
0
4
1
1
2
2
0
1
0
0
2
0
2
0
1
0
2
0
1
0
2
0
0
1
0
0
0
0
1
2
1
1
2
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
1
1
0
1
0
0
0
0
1
2
0
0
1
1
2
0
2
3
0
0
0
1
1
1
1
0
1
0
1
1
0
2
0
0
2
2
0
0
0
0
2
2
0
1
0
0
1
0
0
0
0
0
0
2
0
2
13
0
0
0
2
2
1
1
1
0
0
0
0
1
0
0
1
1
2
2
0
0
0
1
0
1
0
1
0
0
0
0
2
2
1
2
2
2
0
1
0
3
0
0
0
2
0
2
0
1
0
0
0
0
0
2
0
0
0
0
2
1
1
2
2
2
0
1
1
0
1
0
0
1
2
0
0
0
0
0
0
0
0
2
1
2
1
1
1
0
2
2
3
1
0
3
1
1
0
0
2
0
0
0
0
2
2
0
0
0
0
0
2
0
2
0
1
0
2
0
0
0
1
0
1
1
0
0
0
1
1
0
1
2
1
1
0
2
0
1
1
1
0
0
2
0
1
0
0
2
2
0
2
0
1
1
0
0
1
0
2
0
2
0
1
2
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
2
0
0
1
0
0
0
1
2
1
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
1
1
0
0
1
1
0
1
0
1
2
0
1
2
0
1
1
0
0
0
1
0
0
1
1
1
0
3
1
0
2
1
0
2
1
0
1
0
0
1
0
2
1
0
0
0
0
1
1
2
1
1
0
0
0
0
0
1
0
0
1
0
1
0
0
2
1
0
2
0
0
0
1
1
0
0
4
0
0
1
1
0
0
1
0
0
0
1
0
0
0
1
0
2
0
2
1
0
1
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
2
0
1
2
0
0
1
0
3
2
2
0
1
2
0
0
0
0
1
2
1
0
0
2
1
2
1
1
2
1
0
0
1
0
0
1
0
1
0
0
1
1
1
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
2
3
1
2
2
0
0
0
1
1
2
0
1
0
2
0
2
1
0
0
1
0
1
1
1
1
0
0
0
2
0
0
1
2
1
1
0
0
0
1
1
1
0
0
0
0
3
1
1
1
1
0
0
2
2
0
2
1
1
2
0
2
1
1
0
0
2
0
0
0
0
0
0
0
0
1
1
1
1
0
0
1
1
0
1
1
0
0
1
1
1
1
0
1
2
2
1
1
1
0
0
0
2
1
0
1
2
0
1
0
1
0
2
0
0
1
0
1
1
0
0
2
0
0
0
0
2
1
0
0
1
1
1
0
2
2
1
1
2
1
1
0
0
0
1
0
0
4
2
1
0
1
0
0
1
0
0
2
1
1
0
1
0
0
2
0
0
0
2
0
2
1
1
0
0
0
1
2
1
1
1
2
2
0
1
1
0
0
1
0
0
0
0
0
0
0
0
2
1
1
1
0
0
0
0
2
2
1
0
1
1
0
2
0
2
1
0
1
1
1
0
1
2
0
1
0
2
0
1
2
2
0
0
1
0
2
0
0
2
0
1
0
0
0
2
2
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
1
1
0
2
2
0
1
1
1
0
1
1
2
0
0
1
1
0
0
0
1
1
0
0
1
0
2
0
0
0
0
0
2
0
1
0
1
1
0
0
0
2
0
0
1
0
0
0
0
1
2
0
0
1
2
2
0
2
1
2
1
1
1
0
0
2
0
2
0
1
0
0
1
0
0
0
0
0
1
1
1
1
2
1
0
0
0
0
3
0
1
0
0
1
2
0
0
2
0
0
1
1
0
0
0
0
2
0
2
1
0
2
5
1
1
0
3
1
0
0
2
0
0
0
0
1
0
2
0
0
2
1
0
0
0
1
0
1
0
0
0
1
1
0
0
1
1
3
0
1
0
0
2
1
3
0
2
3
1
0
0
0
1
0
0
1
0
1
1
0
1
2
0
0
2
0
0
0
0
0
0
0
0
2
2
1
1
0
2
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
1
1
1
2
0
2
0
2
2
0
1
0
0
0
2
0
0
0
1
2
0
1
0
1
1
1
2
2
1
0
2
1
0
0
0
0
0
2
0
1
1
1
1
0
1
0
0
0
2
1
1
1
2
0
2
1
0
0
0
0
0
1
4
2
0
0
0
1
1
0
1
0
1
1
0
1
0
1
0
0
2
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
1
1
1
0
0
0
1
1
0
0
1
1
0
1
0
0
0
2
1
2
0
0
0
2
0
1
2
0
1
2
1
1
0
0
0
1
0
2
2
0
1
1
1
1
2
0
1
1
1
1
0
2
1
0
0
1
1
0
0
1
1
0
2
1
0
0
0
0
0
1
2
0
0
0
2
2
0
2
0
2
0
0
2
2
2
0
1
1
0
3
0
0
2
1
0
0
1
2
4
0
2
0
1
0
2
0
0
1
1
0
0
1
0
0
0
1
1
1
2
0
1
0
0
0
1
2
0
0
0
0
0
2
0
0
0
1
2
1
2
1
1
2
0
1
0
1
0
0
1
0
0
2
1
1
0
0
1
0
0
1
1
1
0
1
2
0
3
1
2
0
1
2
0
2
0
0
2
0
1
0
0
0
1
1
2
1
1
0
0
0
0
0
1
2
0
2
1
0
0
1
0
0
0
0
0
2
1
0
1
0
0
1
1
1
1
0
2
0
2
1
2
0
1
0
0
2
0
1
0
0
1
0
0
0
0
1
0
0
0
0
2
1
0
1
0
0
1
2
0
1
0
2
2
0
2
0
2
2
0
2
2
1
1
1
0
0
1
0
0
0
0
0
0
1
0
1
1
0
2
0
2
0
0
0
0
1
0
3
0
1
3
1
2
1
0
0
2
2
1
1
2
2
2
0
2
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
1
1
1
2
1
2
0
1
0
0
0
1
0
0
0
1
2
2
0
2
2
1
1
1
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
2
0
1
1
1
0
1
0
1
0
3
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
1
0
0
0
1
2
0
0
0
1
0
2
1
2
0
0
1
2
2
1
0
0
0
1
0
2
1
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
1
0
1
1
0
0
1
1
2
0
0
0
0
2
0
2
2
0
0
0
0
0
0
1
1
0
0
1
2
1
0
0
0
2
0
1
0
1
2
1
0
2
1
0
2
0
0
2
2
0
2
1
0
0
0
1
1
0
0
0
0
1
0
2
0
0
2
1
0
0
2
0
0
1
0
0
0
1
2
0
0
1
2
0
0
0
2
2
0
2
2
2
2
0
0
0
2
1
1
0
1
0
0
0
0
1
0
1
0
0
1
2
2
0
0
0
1
0
2
1
0
0
1
0
0
1
2
2
0
1
0
2
2
1
2
3
2
0
2
1
0
0
0
0
0
0
2
1
1
0
1
0
0
0
2
1
1
0
1
2
1
0
1
0
0
1
0
1
0
0
1
0
0
2
0
2
0
0
2
1
0
2
1
1
1
0
2
1
0
0
0
0
0
0
1
0
1
2
0
1
0
1
0
0
0
2
0
2
0
0
1
0
0
2
2
3
2
0
0
0
3
0
0
2
0
0
0
1
0
1
1
0
0
0
1
2
0
0
1
0
0
0
1
2
0
0
0
1
0
0
2
3
0
1
1
2
0
1
2
0
1
0
2
1
0
0
0
0
0
0
1
1
1
0
0
1
1
0
2
2
2
1
0
0
0
2
2
2
2
1
1
1
0
0
2
1
1
2
2
0
2
3
0
0
0
1
1
2
0
1
2
2
1
1
2
0
0
1
1
1
2
2
0
0
1
1
0
2
0
0
2
1
1
1
0
2
0
0
0
1
0
0
0
0
1
4
0
0
0
0
1
0
1
0
0
0
2
2
1
0
2
0
0
0
0
1
0
1
0
0
2
0
1
0
0
0
0
1
1
0
1
1
0
0
1
2
2
2
1
1
1
1
0
0
0
1
1
1
0
0
1
0
2
0
0
4
0
0
2
1
0
2
1
1
0
1
0
0
1
0
2
1
0
0
0
0
0
0
0
1
1
0
1
1
0
0
1
0
2
1
3
0
2
0
0
0
0
1
0
0
1
1
1
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
1
1
3
2
1
2
1
0
1
0
1
2
0
0
0
1
2
0
2
0
1
0
2
2
0
0
0
1
2
1
0
0
2
0
2
6
1
1
0
2
0
0
0
0
1
0
0
0
1
0
5
0
0
2
0
0
1
3
0
2
1
0
0
4
0
1
0
0
1
1
1
2
2
1
0
0
2
0
1
2
0
2
0
1
1
0
0
1
0
0
0
2
2
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
2
3
2
1
0
0
0
1
0
0
0
2
0
0
0
2
0
2
0
1
0
0
0
0
1
1
2
0
1
2
2
1
0
1
0
1
2
1
0
0
0
2
2
1
2
0
2
2
0
1
2
0
1
1
1
0
1
2
1
0
1
2
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
1
1
0
2
0
2
0
1
1
1
2
0
2
0
0
1
0
2
0
1
1
0
0
0
0
0
0
0
2
0
0
0
1
1
0
1
0
1
0
1
1
1
2
1
2
0
0
0
1
2
0
0
2
1
0
1
0
0
1
1
1
1
2
0
0
2
0
1
0
0
1
1
2
0
0
0
0
0
0
0
1
1
1
0
1
2
0
0
0
0
0
1
0
1
0
0
1
2
0
0
1
0
1
0
0
0
2
1
0
1
0
0
0
1
0
2
0
0
1
0
1
0
0
0
1
1
2
2
1
1
1
0
0
1
0
0
2
2
0
0
0
0
0
0
0
2
2
2
5
0
2
1
0
2
2
0
0
0
0
0
1
0
1
1
0
1
2
2
1
1
1
0
2
0
0
1
2
0
1
0
2
2
0
2
2
0
1
0
0
1
0
0
1
0
0
1
0
2
0
2
1
1
0
0
3
2
1
1
0
1
0
2
1
2
0
0
0
0
0
2
0
2
0
2
0
1
1
0
0
1
0
2
1
0
1
0
2
0
2
0
0
1
0
1
0
1
0
2
1
1
2
2
2
0
0
0
0
0
1
0
1
1
0
1
2
1
1
0
0
2
0
0
0
0
0
0
0
1
2
1
1
1
0
1
0
2
1
0
1
0
1
0
0
2
1
1
0
0
1
1
2
0
0
2
1
0
1
3
1
2
0
1
2
0
1
1
0
1
0
1
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
1
0
1
0
1
0
1
0
1
0
0
2
1
0
0
0
2
0
2
0
3
0
0
0
0
0
2
0
1
2
1
0
2
1
0
2
0
1
1
0
0
2
2
0
1
1
1
0
0
0
0
1
0
0
1
0
0
2
2
1
0
0
3
0
1
0
0
0
2
0
0
1
2
0
0
2
1
1
0
1
2
0
1
0
1
0
1
0
1
1
1
2
0
1
2
1
0
1
0
1
1
2
0
0
2
0
0
0
0
2
1
2
1
2
2
0
2
0
0
1
2
0
0
2
1
0
2
0
0
1
0
0
0
1
1
0
2
0
2
1
1
0
2
1
0
0
1
1
0
0
0
0
1
0
2
2
1
1
0
2
0
2
1
0
2
2
0
0
2
2
0
0
1
1
0
1
2
2
0
0
0
2
2
0
0
0
0
0
3
0
0
1
1
1
2
1
0
0
0
0
1
2
0
0
1
0
1
0
0
2
2
0
2
0
0
1
1
0
2
0
2
2
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
1
0
1
2
0
1
1
0
0
0
0
0
1
0
0
2
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
1
0
0
2
0
0
0
1
0
1
0
2
0
1
0
3
2
2
0
2
2
0
1
0
0
1
0
0
0
0
2
2
0
0
0
3
1
0
0
0
1
0
1
0
2
0
1
0
2
0
0
0
0
1
0
1
0
0
2
2
1
0
0
0
2
0
1
2
2
0
1
2
2
0
2
0
0
0
1
1
0
0
1
1
0
0
0
2
0
0
0
0
0
2
1
0
1
0
0
1
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
1
0
0
0
2
0
2
1
1
1
1
0
0
1
1
0
1
0
0
0
0
2
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
3
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
2
2
2
0
0
1
0
1
0
1
0
1
0
0
1
0
2
2
1
0
1
0
1
0
0
0
0
1
0
1
0
1
1
2
0
0
2
0
2
2
0
0
1
2
0
0
0
1
6
0
0
1
0
0
0
0
1
0
1
1
2
0
1
0
0
2
0
1
0
1
1
2
0
2
0
1
2
1
0
0
2
1
0
0
0
1
0
0
0
0
0
0
2
0
1
2
1
0
0
0
1
1
0
0
0
0
2
1
0
1
0
0
2
0
0
1
0
0
0
0
1
0
2
0
0
1
1
2
0
0
0
0
2
2
0
0
0
0
4
0
0
0
1
0
1
2
0
0
0
0
2
0
1
0
0
0
1
0
0
1
1
2
2
0
2
0
1
1
0
0
0
0
0
0
1
2
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
2
1
0
1
0
1
0
0
1
1
0
2
0
0
0
1
1
1
1
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
1
0
0
0
0
1
2
0
0
2
0
0
1
0
1
0
1
1
2
0
0
2
2
1
0
1
1
1
1
0
0
0
0
0
0
1
1
1
1
0
0
0
0
2
1
2
1
2
0
1
1
2
0
1
1
1
0
1
0
0
0
0
1
2
0
0
1
1
0
0
0
2
1
0
2
1
2
1
0
0
0
1
0
0
0
0
0
1
0
1
2
0
1
0
0
1
0
0
0
0
0
0
1
0
2
1
2
0
0
0
0
0
1
1
0
1
0
0
0
2
0
0
1
0
0
0
2
2
2
0
0
1
1
0
2
0
0
1
1
1
0
1
1
0
0
0
1
0
0
0
2
1
0
1
2
0
2
2
0
0
1
0
3
0
0
0
2
0
1
1
0
0
0
0
1
2
1
1
0
2
2
0
3
1
0
2
0
0
1
1
3
0
2
0
1
0
0
1
1
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
2
2
0
0
1
0
0
1
0
2
0
1
0
0
1
1
0
0
0
1
0
0
2
0
1
1
0
1
0
0
1
2
0
1
0
0
0
0
1
1
0
2
0
1
0
1
1
0
0
2
0
2
0
0
0
1
0
1
1
2
0
0
0
1
1
1
2
0
0
2
1
0
1
1
0
1
1
0
1
1
2
0
1
2
2
0
0
0
0
2
0
0
0
2
1
0
1
0
0
2
2
2
1
0
1
0
0
2
1
0
1
0
0
0
2
0
0
1
0
2
1
1
0
0
0
0
2
1
0
1
1
2
0
0
2
0
1
2
2
1
0
0
4
2
2
1
0
0
0
1
1
1
2
0
0
2
1
0
0
2
0
1
0
0
0
0
1
2
1
0
1
2
2
0
0
2
0
0
0
2
1
2
0
0
1
0
1
0
0
0
2
1
0
0
2
2
1
0
1
1
2
0
0
1
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
2
1
0
2
0
3
0
0
2
0
2
1
1
0
0
0
1
0
0
2
2
2
0
0
0
0
2
1
0
1
0
1
1
1
1
0
2
2
1
0
1
0
0
0
0
0
2
2
0
0
1
0
1
1
0
1
2
0
1
0
1
2
0
0
0
1
0
0
0
1
3
2
0
2
0
0
2
0
13
2
0
1
1
0
0
2
2
1
0
1
0
1
1
1
2
0
1
0
0
0
1
0
0
1
0
2
0
1
0
3
2
2
0
1
2
0
0
0
2
2
3
2
1
0
1
0
0
1
0
2
3
0
3
2
0
2
2
0
0
0
3
0
1
2
2
0
0
1
2
0
1
0
2
1
0
0
2
0
1
0
1
1
1
2
0
1
0
1
1
1
0
0
1
1
1
1
0
2
0
0
6
0
1
1
1
0
0
1
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
2
1
2
0
2
0
0
1
2
2
1
2
0
2
0
4
2
0
0
0
0
0
1
0
0
1
2
1
0
0
1
0
1
1
2
0
0
0
0
2
0
0
0
1
0
2
0
0
1
2
1
0
1
0
1
0
0
0
0
1
2
0
0
0
1
0
0
0
1
0
2
0
1
2
2
0
1
0
1
0
2
2
0
2
2
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
2
0
0
0
2
2
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
2
0
2
0
1
0
0
0
2
1
0
0
0
0
0
1
0
1
1
2
2
0
0
1
0
1
1
1
0
0
2
2
1
1
0
0
2
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
1
0
1
2
3
1
0
0
1
0
0
2
0
1
0
0
0
2
2
0
2
2
0
0
1
0
0
0
0
0
3
0
1
0
0
1
0
0
2
0
2
0
1
0
2
0
0
1
1
2
0
2
1
0
1
0
2
0
1
0
5
2
0
0
0
1
2
1
0
0
1
1
0
2
0
1
0
0
0
1
1
1
0
0
2
0
0
0
0
0
0
2
0
0
1
2
0
1
0
0
0
1
0
2
1
0
1
0
2
0
0
0
0
0
0
0
2
2
1
2
2
2
0
0
0
1
1
1
1
2
0
0
0
0
3
0
1
0
0
0
0
1
0
0
0
0
2
0
2
2
2
0
1
2
0
0
1
1
0
1
0
2
0
2
0
1
0
0
0
1
2
0
2
0
0
2
0
2
0
2
1
1
0
0
1
2
0
0
2
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
2
2
2
0
0
1
1
2
2
0
0
0
0
0
2
2
0
0
1
2
0
0
2
0
0
1
0
1
0
1
2
1
2
0
0
1
1
0
0
1
2
0
1
2
0
2
1
0
1
1
0
0
2
2
0
0
1
3
2
0
1
0
1
0
0
0
0
2
2
0
0
0
2
1
1
0
1
2
1
1
0
0
0
2
0
0
0
0
0
0
2
2
1
2
0
1
2
1
2
1
1
2
2
0
0
0
0
2
2
0
0
1
0
1
2
1
0
0
0
2
1
0
2
2
0
1
2
1
0
1
2
1
1
1
1
0
0
0
0
0
0
1
0
0
1
0
2
0
1
1
1
0
0
1
0
2
0
0
0
0
1
1
0
0
0
1
2
0
0
2
1
0
2
1
0
2
0
1
1
0
0
0
0
1
0
0
2
1
1
0
0
1
2
2
0
0
1
0
0
0
0
0
0
1
2
0
1
0
0
1
0
2
0
1
1
1
1
1
0
1
0
0
0
0
2
3
0
1
2
1
0
0
0
1
1
0
0
0
2
2
0
1
2
1
0
2
2
1
0
0
0
1
0
0
0
0
0
1
2
1
0
0
0
1
0
0
0
0
2
1
1
0
1
0
0
1
2
1
0
0
1
2
1
0
0
0
1
1
1
0
2
1
0
2
1
1
0
0
2
0
1
0
0
0
0
1
0
0
2
0
0
2
2
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
1
1
1
0
2
2
1
2
1
2
0
2
0
0
0
0
0
1
0
1
0
1
2
2
0
0
0
1
0
2
1
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
2
1
1
0
2
0
0
0
2
0
0
0
1
2
2
0
0
1
1
0
1
0
1
0
2
1
0
2
1
0
0
2
2
0
0
0
0
2
0
1
1
2
1
2
1
3
2
2
1
1
0
1
2
0
0
0
0
0
1
0
0
2
0
2
1
0
2
0
1
1
1
1
0
2
0
0
0
1
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
2
0
1
0
2
0
0
0
0
0
2
1
1
0
0
0
3
1
0
0
0
0
0
0
2
2
0
2
0
0
1
1
0
0
0
0
3
0
1
2
0
1
1
2
1
0
0
0
2
2
2
0
0
1
1
1
0
0
0
0
1
0
0
2
1
1
0
0
0
0
1
0
0
2
0
2
0
1
0
1
2
2
1
1
0
0
0
0
0
2
0
0
0
0
1
2
1
1
1
1
2
1
1
0
1
1
1
0
2
1
2
0
1
2
0
2
1
1
0
0
0
1
1
0
0
0
0
2
1
1
2
0
2
1
0
0
0
0
0
0
0
0
1
0
1
0
1
1
1
0
2
0
2
2
0
0
0
0
1
0
0
0
2
0
2
0
2
1
1
0
1
0
2
1
1
0
0
0
1
2
0
2
0
0
1
0
0
0
2
1
0
1
0
1
2
1
1
1
2
0
2
0
1
0
0
0
0
1
1
0
1
2
1
0
0
2
0
0
0
3
0
2
0
2
0
1
0
2
1
1
2
1
1
0
1
0
0
2
2
1
0
1
0
1
0
2
0
0
2
2
1
1
1
0
0
1
1
0
0
0
1
0
2
0
2
2
0
1
0
0
0
0
2
0
5
0
0
0
0
2
1
2
0
0
1
1
0
0
2
0
0
0
1
0
1
1
2
0
0
2
1
2
3
2
0
2
1
0
1
0
0
0
0
3
0
2
0
0
3
2
0
2
2
0
0
1
0
0
0
1
0
0
0
2
0
1
2
0
1
0
0
0
2
2
1
0
0
0
1
0
0
1
2
0
1
2
1
1
1
0
0
2
1
1
1
0
1
1
1
0
1
2
1
2
0
2
0
0
1
3
0
2
2
1
0
0
1
0
1
0
1
2
1
0
0
1
0
2
2
0
0
0
0
1
1
0
0
0
0
0
1
0
1
1
0
1
0
0
2
0
0
1
0
1
1
1
1
1
1
0
1
1
0
2
0
0
0
0
0
0
1
0
1
0
1
0
1
2
0
0
1
1
1
0
0
1
2
2
0
2
2
0
0
0
0
1
1
0
1
1
2
1
1
2
2
2
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
2
1
0
0
0
3
0
1
1
0
0
0
0
0
0
0
1
0
3
1
0
2
0
2
0
1
1
1
0
0
1
2
0
0
0
0
0
0
1
2
4
2
1
0
0
2
1
0
0
0
2
1
0
1
0
1
1
0
0
1
0
1
2
2
1
2
1
0
0
1
0
0
0
0
1
1
0
2
2
0
0
0
2
2
1
1
1
1
0
1
0
0
1
0
0
2
2
2
2
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
1
1
0
1
1
1
0
0
1
0
0
0
0
1
2
0
3
2
0
0
0
2
0
1
1
1
0
2
1
2
0
0
0
1
0
1
2
1
0
0
0
1
0
0
0
2
2
2
0
0
0
0
0
0
2
2
1
0
1
0
3
0
0
0
1
0
1
0
0
1
0
0
0
0
2
0
0
1
1
2
0
1
0
2
0
1
0
0
1
1
0
1
0
2
0
2
1
0
1
1
1
0
13
2
0
1
1
2
1
1
0
0
0
1
0
0
0
0
0
2
1
0
0
1
0
1
0
1
2
0
1
0
0
0
3
1
1
1
1
1
0
5
1
0
0
1
2
0
3
0
2
0
0
1
0
0
1
1
0
1
0
0
0
1
0
0
2
0
2
2
2
2
0
1
0
0
3
0
1
2
0
1
0
2
1
1
1
0
0
0
1
0
0
2
1
1
1
0
1
0
1
1
0
0
0
0
0
2
0
0
0
0
1
1
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
1
2
2
3
0
0
1
0
0
2
0
0
1
1
0
0
0
1
2
0
0
2
0
0
0
0
1
1
0
1
0
0
1
0
0
2
2
2
0
0
0
2
0
2
0
2
0
1
0
0
0
1
0
0
0
1
1
2
2
0
0
2
1
1
0
0
3
0
0
2
1
0
0
1
2
1
0
0
0
1
1
0
0
0
0
2
2
0
1
2
1
0
2
2
1
0
2
1
2
1
1
0
2
1
1
1
2
0
2
1
1
0
2
0
2
0
0
1
0
0
2
0
2
0
1
1
1
0
2
2
7
0
0
2
1
0
1
2
0
0
0
0
0
2
0
0
2
1
0
0
1
0
0
1
0
1
0
0
0
1
1
0
1
0
0
0
2
0
1
0
0
0
0
1
0
2
1
0
0
1
0
0
0
1
0
0
1
2
0
0
1
0
0
1
2
2
2
1
1
1
1
0
0
0
1
1
1
0
0
0
0
0
1
1
0
2
1
2
0
1
1
2
0
1
1
1
1
0
2
2
2
2
0
0
0
2
1
0
1
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
2
0
2
1
0
1
0
1
0
2
2
0
1
1
2
0
1
1
0
2
0
0
2
0
4
2
0
4
4
2
1
1
2
0
0
2
0
0
0
0
1
0
1
0
0
0
2
0
1
0
2
2
0
2
2
0
1
2
2
1
0
3
0
0
2
2
1
1
0
2
1
1
2
1
0
1
0
1
2
1
0
1
3
0
0
0
0
0
2
0
0
2
0
1
3
0
0
2
1
0
2
2
1
0
0
0
2
0
0
1
1
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
2
0
2
2
1
2
2
0
0
1
0
1
2
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
2
2
0
2
0
1
0
0
2
1
0
2
2
2
0
0
0
2
1
2
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
1
2
2
0
2
0
0
1
2
0
2
1
2
1
2
0
2
1
2
1
0
1
2
1
0
1
1
1
1
1
2
1
2
0
2
1
1
1
1
0
2
0
0
0
2
2
0
0
2
0
0
1
1
0
1
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
2
0
2
1
0
1
0
2
0
0
0
1
0
1
0
1
0
2
0
0
0
0
0
0
3
1
1
1
1
1
1
0
0
0
2
1
0
2
2
0
2
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
1
1
2
0
0
0
1
1
2
1
0
0
1
0
3
0
2
0
0
0
0
0
0
2
2
2
0
2
2
1
1
1
0
1
0
2
1
2
2
1
0
0
2
1
2
0
2
0
0
0
1
1
0
0
2
2
2
1
1
0
1
0
0
0
1
2
0
1
1
1
0
0
0
0
0
0
2
0
2
0
0
2
0
1
2
0
0
2
0
0
0
0
0
1
1
2
0
0
0
2
0
1
2
0
2
0
0
0
0
0
0
0
0
0
1
1
1
0
1
2
1
0
2
2
2
0
0
0
1
0
0
0
2
1
0
2
1
1
0
1
2
0
0
2
0
0
0
0
1
1
0
1
2
2
0
1
2
0
1
2
2
0
1
0
1
0
0
2
0
0
2
0
0
1
0
0
2
0
0
1
0
0
2
0
0
0
0
0
1
1
2
0
0
0
0
1
1
0
2
2
0
2
2
1
1
0
0
1
2
2
6
3
0
2
1
0
0
0
1
0
2
0
2
0
0
2
0
4
0
0
0
2
0
0
0
2
0
2
1
0
2
1
0
0
1
1
1
0
0
2
0
0
0
0
1
1
2
1
0
1
0
1
2
3
0
1
2
2
0
1
1
0
2
1
0
0
0
1
2
0
0
2
2
2
0
1
1
1
0
1
2
0
1
0
0
0
1
0
0
2
1
0
1
0
1
0
0
2
2
1
0
0
2
0
0
0
0
0
0
0
0
0
1
1
1
1
0
7
3
0
0
0
0
1
2
1
1
2
1
0
1
0
0
0
0
0
1
0
2
1
2
0
1
0
1
1
0
2
0
0
1
0
1
0
0
0
1
0
0
1
0
1
0
1
0
2
1
0
0
4
1
2
0
0
1
0
0
1
0
2
0
1
0
0
0
1
0
1
1
0
0
0
0
1
2
0
1
0
0
1
0
0
1
0
2
0
0
2
0
0
0
1
2
2
0
0
2
0
1
0
0
1
0
0
0
0
2
2
1
0
1
3
1
2
0
1
1
0
2
0
2
1
0
2
1
2
1
0
1
0
2
0
2
0
0
0
1
1
0
1
1
2
3
0
0
0
0
1
1
2
0
0
1
0
2
0
2
0
0
1
0
2
1
0
0
0
1
0
0
0
1
1
0
0
1
1
0
0
0
0
2
0
1
2
1
3
1
1
0
0
0
0
0
0
0
1
0
2
2
2
2
0
0
1
1
0
0
1
0
1
2
0
1
1
0
0
1
0
1
2
0
2
2
0
0
0
1
0
1
0
0
0
0
2
0
2
1
2
0
2
0
0
1
2
1
0
0
1
0
0
2
2
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
2
0
1
1
2
0
1
2
1
0
0
0
0
1
0
0
0
1
1
2
1
0
3
0
2
0
0
0
0
2
0
0
2
1
0
0
0
1
0
1
0
1
1
0
2
2
0
1
2
0
0
0
0
1
1
0
2
0
0
2
2
0
2
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
2
2
0
0
1
1
1
0
0
1
0
1
0
0
0
0
1
0
2
4
6
2
0
0
0
0
2
1
2
1
1
0
0
2
1
0
1
0
1
2
1
2
1
2
1
2
2
1
1
0
0
0
0
1
0
2
0
2
1
3
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
3
3
0
0
1
0
0
2
0
0
0
0
1
2
1
1
2
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
1
2
0
1
1
1
2
3
1
0
0
0
2
0
1
0
2
1
1
1
0
0
1
0
0
0
2
5
1
0
0
0
2
1
0
2
0
0
0
2
1
1
1
1
0
0
1
2
2
2
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
2
2
2
1
2
1
2
2
0
2
0
0
0
1
2
1
0
2
1
2
0
0
0
0
2
2
2
0
0
1
0
0
0
0
1
0
2
1
0
0
2
1
1
0
1
0
0
2
0
0
1
0
2
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
1
1
0
2
0
1
2
0
1
0
0
2
0
2
0
0
1
0
1
2
2
1
0
1
0
1
0
0
0
0
0
1
1
2
0
1
1
0
0
0
3
2
0
0
1
1
1
1
0
0
0
0
0
1
2
0
1
1
0
0
0
0
2
1
2
1
2
1
2
2
0
1
2
0
2
0
0
2
1
0
1
0
1
1
0
0
0
0
0
2
1
3
0
0
0
1
2
0
0
0
0
1
0
1
0
2
0
1
0
0
0
2
2
1
3
0
0
0
0
0
0
0
0
2
0
1
2
1
1
1
2
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
1
0
2
1
1
1
3
0
0
0
2
2
0
0
1
2
0
0
1
0
2
0
0
2
0
1
1
1
0
0
2
0
1
2
2
1
2
0
0
0
1
0
0
0
2
2
1
2
0
1
0
0
2
1
0
1
0
1
2
0
2
0
1
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
1
1
0
2
0
1
0
0
1
0
1
1
0
2
2
0
0
0
0
0
0
1
1
1
1
0
2
1
1
0
2
1
0
0
2
1
0
0
0
0
0
0
1
0
2
0
0
0
0
2
2
0
1
0
0
2
0
1
1
0
0
0
1
1
1
0
1
0
0
1
0
1
0
0
0
2
2
0
0
4
1
1
1
1
0
1
0
0
0
0
2
0
1
0
0
2
2
0
1
0
2
1
1
0
2
0
1
0
0
0
0
2
0
0
0
1
2
0
1
1
0
0
0
2
0
2
0
1
0
0
0
2
0
0
1
0
2
0
1
0
1
1
0
1
1
0
1
4
0
0
0
0
1
2
0
2
0
2
1
0
0
3
0
0
0
0
1
0
1
0
1
0
1
1
0
0
0
1
1
0
2
0
0
2
0
0
2
6
1
0
1
0
0
2
0
1
1
0
0
1
0
0
2
2
0
2
0
1
2
2
0
1
0
0
0
0
0
1
2
0
2
2
1
1
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
1
2
1
0
1
1
0
0
0
2
1
0
0
2
1
2
0
0
2
2
1
0
0
1
2
0
0
2
0
1
0
1
0
1
0
0
0
2
0
0
1
0
2
0
0
2
0
0
1
0
1
1
0
0
2
1
0
0
0
2
1
0
1
0
0
3
0
1
2
0
0
0
0
0
2
0
3
0
0
2
0
2
0
0
0
0
1
0
0
0
0
2
1
2
2
1
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
2
2
2
0
1
0
0
2
0
1
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
2
1
0
4
0
1
0
0
1
0
0
0
1
0
1
2
0
1
0
2
0
3
0
0
0
3
1
0
0
0
0
0
0
1
1
0
1
3
1
0
1
0
0
0
0
2
0
0
2
1
0
1
0
2
0
1
1
1
2
1
2
0
0
0
1
1
1
1
2
0
1
0
1
0
1
1
1
2
2
1
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
1
0
2
0
2
1
0
0
1
1
1
1
0
1
2
1
1
0
1
2
0
0
0
1
2
1
2
1
0
2
0
0
0
0
0
2
0
0
0
0
2
0
4
1
1
0
1
2
2
0
0
0
2
2
2
1
0
2
1
0
1
2
0
0
0
0
0
0
1
2
0
0
2
1
1
1
0
2
0
0
1
0
1
1
0
0
0
0
0
1
1
1
2
1
0
0
2
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
1
1
2
0
0
0
1
0
1
0
0
2
0
1
2
0
0
0
2
2
0
1
1
1
0
2
0
1
0
2
0
1
0
0
0
1
0
2
2
0
0
1
1
2
1
1
1
0
1
2
0
2
2
0
0
1
1
0
0
1
0
0
2
2
2
0
0
0
1
0
0
2
2
4
2
0
2
0
3
0
1
0
1
0
1
0
0
2
0
1
0
1
1
1
1
2
0
2
1
0
2
1
0
0
1
0
2
0
0
0
0
0
0
1
0
2
2
2
0
0
0
0
10
2
0
1
2
1
0
0
1
1
2
0
1
1
2
2
1
0
3
0
0
2
1
4
0
3
0
0
0
1
2
0
1
0
0
0
0
0
1
1
1
1
1
2
0
3
0
0
0
0
2
0
1
0
1
2
0
0
2
0
2
2
2
0
2
2
1
0
0
0
1
0
1
0
0
1
1
1
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
2
1
0
2
1
0
0
0
1
2
0
2
1
0
1
1
1
2
1
0
0
0
0
1
1
1
1
2
2
0
2
2
3
1
2
0
2
2
0
0
1
1
0
0
2
2
1
0
0
2
2
2
1
1
3
1
1
2
3
1
1
0
0
1
0
0
1
2
0
0
1
0
0
2
1
1
2
2
1
1
0
0
0
0
0
0
1
0
2
1
2
3
2
0
0
0
0
1
0
1
0
0
1
2
2
1
2
0
2
0
2
10
0
0
1
0
0
0
0
0
1
2
0
0
1
1
2
0
3
2
1
0
0
0
0
0
0
2
0
1
0
1
0
0
0
2
0
0
2
1
1
0
1
0
0
0
0
1
0
0
0
1
2
0
1
2
1
2
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
4
1
0
1
0
1
2
0
0
1
2
0
0
0
0
0
2
3
0
5
0
0
1
0
0
0
0
0
1
1
2
0
0
2
0
0
0
2
2
1
0
2
1
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
2
0
0
1
1
0
1
1
0
1
0
0
1
1
1
1
1
0
0
0
2
1
0
0
0
3
0
0
2
2
1
2
0
2
0
2
0
0
1
0
2
0
0
0
0
1
1
4
0
0
0
1
1
1
0
0
1
2
0
1
1
1
1
1
0
0
2
3
1
1
1
1
0
2
2
1
0
0
0
0
1
0
1
1
0
2
0
1
0
1
1
0
0
2
1
0
2
0
1
1
1
0
0
0
1
0
2
0
0
0
1
1
1
0
1
2
1
2
0
2
0
1
1
4
2
0
0
2
0
0
2
1
0
1
0
0
2
1
1
0
0
1
0
0
0
2
2
0
1
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
2
0
1
0
0
1
1
0
0
0
1
0
1
0
0
1
2
0
1
3
1
0
0
0
0
0
0
1
1
0
0
1
1
0
1
0
0
1
1
0
0
0
2
1
3
1
0
1
0
0
2
0
0
1
0
0
1
1
0
0
2
1
0
1
0
0
2
0
1
0
0
1
0
0
1
0
1
0
1
1
2
2
0
0
0
0
0
2
2
0
1
0
0
2
1
0
2
1
1
0
0
1
0
1
1
1
0
0
0
0
2
1
0
1
0
0
0
0
1
0
0
1
2
3
0
0
0
1
0
0
0
0
1
2
1
0
1
0
0
2
0
2
2
2
1
0
2
1
2
0
2
0
0
0
0
2
1
1
0
1
0
3
0
0
0
1
0
1
0
0
0
1
0
2
1
0
2
0
2
1
0
2
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
1
0
3
1
0
1
1
1
1
1
0
1
1
2
1
2
0
1
0
0
0
0
0
1
0
2
2
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
1
1
2
1
2
0
1
0
1
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
2
2
0
0
0
2
2
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
2
2
0
1
1
1
0
3
2
1
2
1
0
1
0
1
2
1
1
2
0
1
2
0
2
0
0
1
2
1
0
0
0
2
0
0
0
1
0
0
1
2
2
0
0
0
0
0
2
0
0
1
0
0
2
2
0
1
1
1
2
0
1
0
1
1
2
0
0
0
2
0
2
0
2
0
0
0
0
0
0
1
0
1
1
1
1
0
0
0
0
0
0
1
2
1
1
0
0
0
3
1
0
2
1
0
1
1
1
0
1
0
1
1
0
0
0
2
0
0
0
0
0
1
0
2
0
1
0
1
0
0
2
0
0
0
2
1
0
0
0
2
2
2
0
0
1
0
0
2
2
0
0
1
0
0
2
2
1
1
2
0
0
1
2
1
2
0
1
1
0
1
2
2
0
3
0
1
0
0
1
3
1
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
1
2
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
5
0
1
0
1
0
0
0
0
0
1
2
1
10
0
1
0
1
2
1
0
2
2
1
2
0
1
1
2
2
1
2
1
0
0
2
0
1
0
2
0
0
0
1
0
0
0
1
0
1
2
0
1
1
0
2
0
0
0
0
3
0
0
1
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
1
2
0
0
2
1
0
0
0
1
0
1
2
1
0
0
0
1
1
2
0
0
3
0
2
1
0
2
2
0
1
0
0
2
0
1
1
6
0
0
0
1
2
0
2
0
0
1
1
1
2
0
2
0
2
0
0
0
0
1
1
0
1
0
0
0
1
1
0
0
1
2
2
0
0
0
1
0
2
0
2
1
1
0
1
2
2
1
1
0
0
1
0
1
1
1
0
0
0
0
1
3
2
2
0
1
0
2
1
0
0
0
0
2
1
2
0
1
2
1
1
1
0
0
2
1
0
0
0
1
0
1
1
1
2
0
1
0
2
2
1
2
0
1
1
0
1
0
2
0
0
0
0
2
2
0
2
0
0
0
0
0
1
0
0
0
0
0
2
1
0
2
1
2
0
0
1
2
1
0
1
2
0
2
0
0
0
2
2
0
3
2
2
1
0
0
0
0
0
2
0
0
1
1
0
1
0
1
0
1
1
0
0
0
1
0
2
1
2
0
0
2
0
1
1
1
1
1
1
2
0
0
3
2
2
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
2
0
0
0
0
3
7
2
0
2
1
2
0
2
1
1
0
0
2
1
3
1
2
0
2
0
1
1
0
1
0
0
0
0
1
0
0
1
2
0
0
2
0
0
1
0
0
0
2
0
0
1
0
1
1
0
0
0
2
2
0
0
1
0
0
0
0
2
1
0
0
0
0
0
3
2
0
0
5
2
1
0
0
1
1
0
0
0
1
0
3
0
0
0
2
0
1
2
1
1
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
2
1
1
0
0
2
1
2
1
2
0
1
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
2
2
0
2
0
1
2
0
0
0
0
2
0
2
0
2
2
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
2
0
1
0
0
1
2
0
1
1
1
0
0
2
0
1
0
1
0
2
2
1
0
0
1
2
0
0
1
1
1
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
1
2
0
1
0
2
1
0
0
1
2
0
2
0
2
1
1
0
0
2
0
0
2
0
2
2
0
1
0
1
1
1
0
1
0
2
1
2
0
2
5
3
1
2
2
0
1
0
1
1
0
1
2
0
0
0
0
1
2
1
1
2
1
0
1
0
0
3
0
0
1
0
0
1
1
1
0
1
0
0
0
0
1
0
0
1
1
1
0
0
2
0
1
0
0
2
1
0
0
2
1
0
0
2
0
1
0
1
0
2
0
0
0
1
0
0
0
0
0
3
1
1
0
0
0
2
1
0
3
0
0
1
2
1
0
2
0
0
0
1
0
2
1
0
0
1
1
1
0
2
0
0
2
0
1
2
0
2
0
1
1
1
1
0
2
0
1
0
2
0
0
0
0
2
0
0
1
0
0
2
1
0
0
2
1
1
0
1
1
0
0
2
1
2
0
0
1
2
2
2
1
0
1
1
0
1
0
2
2
1
0
1
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
5
1
2
0
0
1
2
1
2
0
0
0
0
2
1
1
0
0
3
0
0
1
0
0
1
0
1
0
1
0
0
2
1
1
0
0
1
2
0
0
1
0
2
0
0
1
2
0
0
0
1
0
0
0
1
0
0
0
2
0
1
2
0
0
1
0
0
0
1
2
0
1
1
1
0
0
1
1
1
2
0
0
4
0
2
0
1
0
0
0
0
0
1
0
0
0
1
0
1
1
0
2
2
0
0
0
2
0
0
2
2
0
0
0
0
0
0
1
0
2
2
2
0
0
0
0
0
0
1
0
0
0
2
1
0
2
0
0
0
2
2
0
0
0
0
0
2
0
1
0
2
2
2
0
0
1
1
0
1
0
0
0
0
0
0
1
1
1
1
0
0
2
5
0
0
0
0
0
2
0
0
3
0
1
2
2
0
0
1
1
1
1
2
0
0
1
1
1
1
2
6
2
2
0
3
0
1
2
1
1
0
1
2
0
0
1
2
0
2
1
0
0
2
0
3
0
1
0
5
3
0
0
0
1
1
0
0
0
0
0
1
1
0
1
0
2
0
2
1
0
0
0
2
2
2
0
0
2
1
1
2
0
0
1
4
1
0
3
0
2
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
2
1
1
1
0
1
1
0
0
1
2
0
2
1
0
0
0
2
2
0
0
0
2
0
2
2
1
1
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
1
0
3
0
0
1
2
2
0
2
0
0
1
1
0
1
1
0
0
0
1
0
0
0
2
0
0
1
1
0
0
3
0
1
2
0
2
0
1
0
0
1
1
0
1
0
0
1
1
2
1
2
0
0
2
1
0
1
2
2
2
0
0
1
1
0
1
1
0
2
0
1
1
1
0
2
1
1
0
1
0
0
1
1
1
1
0
2
1
1
0
0
1
1
1
0
2
2
0
0
0
1
1
0
0
1
1
2
2
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
1
0
1
0
0
0
1
2
1
0
2
0
1
0
0
0
3
1
0
1
0
0
2
0
3
0
0
0
2
1
0
0
0
0
1
0
0
1
0
1
2
0
0
2
0
0
2
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
2
0
0
0
1
3
0
2
1
0
1
0
1
0
0
2
2
0
0
1
1
2
0
2
0
0
1
2
0
0
2
1
0
1
0
0
2
1
2
1
0
0
0
2
2
4
0
1
0
1
1
0
1
1
1
2
2
3
0
0
2
0
1
0
1
0
0
1
2
3
1
1
2
2
0
0
1
2
0
1
1
0
0
0
0
0
0
0
0
0
2
2
2
0
1
0
0
1
0
2
0
1
0
1
1
0
2
0
0
2
0
1
0
1
0
2
0
2
0
0
1
1
0
0
1
1
1
0
1
0
0
0
1
1
1
0
0
1
2
0
1
2
0
0
0
0
1
3
1
1
2
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
1
0
1
2
0
0
0
2
0
0
1
2
0
1
0
1
0
0
1
1
0
1
0
1
0
0
0
2
1
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
2
0
0
1
2
0
1
0
0
0
1
0
2
0
2
1
2
0
2
0
0
1
0
2
0
1
4
1
1
1
0
1
1
2
1
2
0
1
1
1
2
0
1
1
1
0
2
0
1
0
0
2
0
0
1
0
2
0
0
0
1
1
0
2
0
1
2
1
0
0
2
2
1
3
0
0
3
0
0
1
0
2
0
0
1
0
1
2
1
0
0
0
0
0
0
1
1
1
1
1
0
0
0
0
0
1
0
0
0
2
0
0
0
1
1
0
1
0
0
0
1
1
0
1
2
0
1
1
0
2
1
1
3
0
0
2
0
0
0
0
0
2
1
0
0
0
0
1
1
2
0
2
1
2
7
0
0
1
1
2
5
1
1
0
0
1
0
2
1
2
1
0
1
0
2
0
1
2
1
0
1
0
1
2
2
1
2
0
0
0
0
1
2
0
0
2
2
0
0
1
1
1
1
2
0
0
0
1
1
0
1
0
1
0
2
1
0
1
1
0
0
0
0
1
2
6
0
0
2
0
0
1
2
1
0
0
1
1
0
0
0
2
1
0
1
0
0
1
0
0
0
2
1
0
0
1
2
0
1
1
0
0
0
1
1
2
0
0
0
0
0
1
2
2
0
1
0
0
0
0
2
0
0
2
1
1
0
0
0
1
2
1
0
0
0
0
0
2
0
1
2
0
0
2
0
0
0
0
2
3
1
2
1
1
0
1
2
0
2
2
2
2
0
2
1
0
0
0
2
0
0
0
1
0
0
0
0
1
0
3
1
0
0
0
0
0
2
0
0
2
1
0
2
0
1
2
2
0
2
2
2
2
0
1
0
2
2
0
2
2
2
1
0
1
2
1
0
0
0
0
0
1
1
0
2
2
1
1
1
0
1
0
2
0
2
0
0
2
1
1
0
2
2
1
0
1
0
0
0
2
0
0
0
0
0
2
2
1
0
1
1
1
0
2
0
1
1
1
0
1
1
0
1
0
1
0
2
0
0
0
0
1
0
0
0
1
0
2
1
0
0
2
1
0
1
0
0
1
0
0
2
0
2
0
0
1
0
0
0
2
1
0
0
0
0
0
0
2
1
2
1
0
0
0
0
0
0
2
0
2
2
0
0
2
2
4
2
1
2
0
0
1
1
0
0
1
0
1
0
2
0
0
1
1
0
1
1
0
0
1
0
0
0
0
1
2
1
1
1
1
0
1
2
1
0
1
1
2
1
0
0
1
1
0
0
0
0
2
0
0
0
0
1
2
1
0
0
2
0
0
0
1
0
1
0
2
1
0
1
0
0
0
0
0
2
0
0
0
0
1
2
0
0
2
2
1
0
0
0
0
1
1
2
2
0
0
0
0
1
0
2
2
1
0
1
0
0
2
0
0
1
0
0
0
2
0
0
2
2
2
0
0
0
2
0
1
0
1
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
2
1
0
2
1
0
0
0
2
0
0
6
0
2
1
1
0
0
0
1
1
2
1
0
0
1
0
1
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
3
1
1
2
0
0
1
0
4
1
0
3
0
2
0
0
1
1
0
1
0
0
2
1
1
0
1
1
0
0
0
0
0
2
3
0
1
2
3
0
0
1
0
2
2
0
0
2
2
0
2
1
2
0
1
0
0
2
0
1
0
1
1
4
2
0
1
0
0
1
2
1
1
0
0
0
2
0
1
1
0
2
2
1
0
0
1
1
0
0
0
1
1
0
1
0
0
2
1
1
0
2
2
0
0
0
0
1
1
0
0
0
0
0
2
0
0
3
0
1
0
1
0
1
1
1
2
2
0
1
0
0
0
0
2
1
0
0
1
2
0
0
0
2
0
2
1
2
0
8
3
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
2
1
1
1
2
1
0
0
2
1
2
0
1
1
0
0
2
0
0
0
1
0
1
2
0
1
0
0
1
2
1
0
0
2
0
1
0
1
0
1
2
0
0
0
2
2
0
0
1
2
2
1
2
2
1
0
1
2
0
2
1
0
1
0
0
2
1
1
0
0
0
1
1
1
0
1
0
0
0
2
0
0
1
2
1
0
1
0
0
1
0
0
0
0
0
0
1
2
0
0
0
1
0
0
2
0
0
1
2
2
2
0
0
2
0
0
1
2
0
1
2
0
0
0
1
0
0
0
2
1
1
0
2
1
2
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
3
0
1
0
3
0
2
0
1
0
2
2
0
1
0
1
2
1
0
1
0
1
1
0
1
0
0
0
2
1
0
1
2
2
0
0
0
0
0
1
0
2
0
0
0
1
0
0
1
0
1
1
0
3
0
1
0
0
1
0
0
2
1
0
1
0
0
0
2
0
0
0
1
0
1
1
1
0
1
0
2
0
0
2
2
0
0
1
1
0
0
1
1
1
1
2
0
0
0
2
0
0
0
2
2
1
1
0
1
0
0
0
0
1
0
0
1
3
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
1
1
2
0
0
0
0
1
0
1
1
0
3
1
0
1
1
1
1
1
2
2
0
0
2
0
1
0
0
0
2
0
0
0
1
1
0
0
0
1
2
0
0
2
2
1
0
2
0
2
1
1
2
5
2
0
1
4
0
0
2
0
2
2
1
0
1
0
0
0
0
0
0
2
1
2
0
2
0
1
2
0
1
1
2
0
0
1
2
0
1
0
0
0
2
0
1
2
1
0
0
1
1
0
2
0
1
2
1
1
0
0
1
0
0
0
2
0
2
2
2
0
0
0
0
2
2
0
0
1
2
2
0
0
2
1
0
0
0
1
0
0
0
2
0
0
1
0
1
0
0
2
2
1
0
2
0
1
0
1
0
1
0
0
2
2
1
0
0
1
3
0
1
2
2
0
2
0
1
1
0
0
2
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
1
2
2
0
1
0
1
0
0
0
2
1
1
0
1
2
3
1
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
2
0
2
0
0
1
1
1
0
1
0
0
0
0
1
1
1
0
1
0
0
1
1
1
0
0
2
0
0
1
1
1
2
1
0
0
1
0
0
0
0
0
1
1
2
0
2
0
0
0
2
1
2
0
0
0
2
0
2
1
0
0
0
0
2
0
0
1
1
2
0
1
0
0
2
1
0
1
2
0
0
0
1
0
0
1
2
2
1
0
2
1
0
2
0
2
0
0
1
0
1
1
1
0
2
0
1
0
1
0
0
0
0
0
2
1
1
1
1
1
1
1
1
1
0
0
1
0
0
1
0
1
0
6
2
0
2
0
2
1
0
0
2
1
1
0
0
2
0
0
2
0
2
2
0
1
2
2
1
1
2
2
1
2
1
0
2
1
2
2
2
0
1
0
2
2
0
2
1
0
0
1
1
2
0
1
0
1
1
0
0
0
2
0
0
0
0
2
3
2
1
0
0
1
1
1
1
1
0
0
1
1
0
0
1
0
2
0
0
1
2
0
3
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
2
1
0
1
1
0
2
0
0
2
0
1
0
1
1
0
1
1
0
1
0
0
0
0
0
2
2
0
2
2
0
1
0
2
0
2
0
2
4
1
0
0
1
0
1
2
0
0
0
0
1
0
0
2
0
0
0
2
0
1
0
1
0
0
0
0
1
0
2
0
0
2
1
0
1
0
0
1
0
1
0
1
2
0
0
1
0
1
2
0
0
0
2
2
0
0
0
1
0
0
0
0
2
2
1
0
0
0
1
2
0
1
0
0
0
0
1
0
0
1
0
1
0
2
0
0
1
1
2
1
2
0
1
1
2
1
0
1
0
2
11
0
2
0
0
2
0
3
1
2
1
0
0
0
2
0
0
0
1
2
2
1
1
2
1
0
1
2
1
2
2
1
0
2
0
0
1
2
1
0
1
3
0
1
0
2
1
0
2
2
2
0
2
0
1
0
0
0
0
0
0
1
0
2
2
0
0
0
0
2
0
0
1
2
0
0
2
3
0
0
0
2
0
0
2
0
0
1
2
2
1
0
0
2
0
1
1
1
2
0
0
0
2
0
2
0
2
1
2
0
0
0
2
1
0
0
1
1
1
1
0
0
0
0
1
0
0
1
1
1
2
0
0
1
1
2
1
0
0
1
0
1
0
0
0
0
0
0
2
0
0
1
0
1
0
2
0
0
2
2
0
1
0
0
2
0
1
2
2
1
0
0
1
0
2
1
2
0
5
0
2
2
1
2
0
1
1
2
1
2
0
0
1
0
0
0
0
2
2
2
0
2
1
1
2
2
0
1
0
0
1
1
1
0
2
1
0
0
2
1
0
0
2
0
0
2
1
1
0
2
0
1
2
0
0
2
1
1
2
0
1
2
0
2
0
0
0
2
1
1
1
0
1
0
0
2
2
0
0
0
0
1
2
1
1
0
1
0
1
1
2
0
1
0
1
2
2
0
0
2
2
0
0
2
0
2
1
0
0
1
1
2
0
0
1
0
0
1
1
0
0
0
0
0
0
4
0
2
1
0
0
0
2
0
0
1
1
0
0
0
0
2
0
2
0
1
2
2
0
2
1
1
0
1
0
0
1
0
2
2
0
1
0
2
1
0
2
5
0
2
0
0
2
3
2
1
1
0
0
0
0
0
0
1
1
0
1
1
1
2
0
0
0
0
0
0
0
1
1
0
1
3
0
0
1
1
0
0
1
0
1
1
1
1
0
1
1
0
0
2
1
0
0
0
0
0
0
2
0
0
1
1
0
1
0
0
0
0
1
0
0
0
1
1
0
0
1
0
1
1
3
0
2
0
0
1
1
1
0
0
4
1
0
2
2
0
0
0
0
0
1
2
2
0
0
2
1
1
0
1
2
0
0
0
0
1
1
0
1
1
0
1
0
1
3
0
1
2
2
0
1
0
0
1
3
0
0
0
2
0
1
0
0
2
0
1
0
1
1
0
0
1
1
1
1
2
0
3
0
0
3
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
2
0
1
0
0
0
0
1
1
3
2
1
0
1
0
2
0
1
0
2
0
0
1
0
1
0
0
0
0
2
2
1
0
2
0
2
0
0
1
0
1
1
0
2
0
0
1
0
1
0
1
1
1
1
3
1
0
2
1
0
1
0
1
2
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
1
0
1
0
2
2
0
2
2
0
1
2
0
1
1
2
0
0
2
0
2
0
0
2
0
1
2
1
0
2
0
1
2
0
0
3
1
1
1
1
2
0
0
1
0
0
0
0
2
0
1
1
2
1
2
0
0
0
0
2
0
0
0
0
1
2
0
0
1
2
0
0
0
0
1
1
1
0
2
0
1
1
0
1
1
2
2
0
1
2
0
2
0
0
0
0
0
2
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
2
0
2
0
1
1
2
1
0
0
0
0
1
0
1
2
3
0
0
1
0
0
0
2
4
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
2
0
2
4
1
1
0
0
1
0
0
1
1
0
1
0
2
1
0
0
2
0
1
0
2
0
0
2
2
1
1
0
0
1
0
0
0
0
2
2
1
0
0
1
0
0
3
0
1
2
2
0
1
1
0
1
2
0
2
0
1
0
1
0
0
1
0
0
2
2
0
1
0
1
0
1
2
0
3
1
2
0
0
2
1
2
0
0
1
1
1
0
1
0
2
1
0
1
2
0
2
2
1
2
0
0
0
3
1
0
0
0
3
0
0
0
2
0
1
0
1
0
0
0
0
1
0
0
1
0
0
1
1
2
2
1
0
0
0
0
0
0
1
2
2
1
1
1
1
0
0
2
2
0
0
1
0
1
3
0
1
1
2
2
1
0
1
1
0
1
0
0
2
0
1
0
0
1
2
2
0
0
2
2
0
1
0
0
2
0
0
2
1
2
0
0
0
0
2
0
0
0
2
2
0
0
2
1
1
0
1
1
0
1
1
2
1
0
1
0
1
1
0
0
0
0
0
1
1
0
2
1
1
1
1
2
0
1
0
0
0
1
0
1
0
0
0
1
0
1
2
0
0
1
1
2
2
2
1
0
2
0
1
1
0
1
0
2
0
0
2
0
0
1
1
1
1
2
1
2
1
1
2
1
0
0
1
0
0
0
2
1
0
1
0
0
0
0
1
2
0
2
1
0
0
2
2
2
0
0
0
1
0
1
1
2
0
1
0
2
0
0
2
0
2
1
0
1
1
0
2
0
1
1
1
0
0
2
2
0
0
0
1
0
1
1
0
0
2
0
0
0
0
0
1
1
0
0
0
4
1
2
2
0
2
0
0
1
1
0
0
0
1
0
0
0
0
1
0
2
0
1
0
1
1
0
0
0
0
1
1
2
0
1
4
0
0
0
1
5
2
1
2
2
2
1
0
1
2
0
3
1
0
1
0
1
0
1
5
0
1
2
0
0
0
1
0
0
1
0
0
0
0
1
0
1
1
2
0
1
0
1
2
2
0
0
0
0
0
0
0
0
2
1
0
0
1
0
2
0
1
1
1
0
0
2
1
2
0
1
0
0
0
0
0
2
2
0
2
0
1
2
0
0
2
0
0
1
0
1
0
1
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
1
0
0
0
1
0
2
0
0
0
0
2
0
0
0
1
0
2
0
2
1
0
0
1
0
1
1
2
0
1
2
1
1
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
2
1
2
0
0
2
1
0
1
0
0
1
0
0
1
1
1
0
2
2
2
2
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
1
0
1
0
0
2
2
3
0
1
0
2
0
0
2
0
0
1
0
0
0
0
1
0
0
2
0
0
2
2
2
0
1
0
0
2
2
2
1
0
1
0
1
1
2
0
1
0
2
1
0
1
2
2
0
2
0
2
1
0
2
2
1
0
0
1
0
1
1
0
1
1
0
0
2
1
0
2
2
1
2
2
2
0
0
2
1
1
1
2
0
0
0
0
0
1
2
1
0
0
0
0
1
1
0
2
0
0
0
0
2
0
0
2
0
0
1
0
2
0
2
1
0
0
0
2
0
2
1
1
0
0
0
1
0
0
1
1
1
0
1
1
0
0
0
1
1
1
0
2
1
1
0
0
0
1
2
0
0
2
0
0
2
0
0
0
2
0
0
0
2
0
0
1
0
0
1
1
1
1
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
2
1
0
0
0
0
1
0
0
1
1
0
0
0
0
2
2
0
1
2
0
1
1
0
0
1
0
0
0
0
0
2
0
0
0
3
2
1
0
0
1
0
0
2
0
2
0
2
0
2
1
1
0
2
0
1
0
0
0
1
0
0
1
0
2
1
2
1
0
2
1
1
2
0
2
0
1
1
1
0
1
0
0
1
1
2
0
0
1
1
1
2
1
1
0
1
0
0
1
0
2
2
0
1
0
0
1
0
0
2
0
2
1
0
2
1
0
1
0
2
0
2
1
2
0
1
1
1
2
2
1
0
0
2
1
0
0
1
1
1
2
2
2
0
1
0
0
0
2
1
1
0
2
0
1
0
0
0
0
1
0
0
2
0
1
0
0
0
1
0
2
2
0
0
1
0
0
0
0
1
1
1
0
0
0
0
1
3
1
1
0
2
0
1
1
0
1
2
2
1
3
0
1
2
0
0
1
0
1
1
1
2
1
3
1
1
2
1
1
2
1
1
0
2
1
1
0
0
0
0
1
0
1
1
1
0
2
0
2
1
0
0
0
2
2
1
2
1
2
0
0
0
1
1
0
0
1
0
0
2
1
1
0
0
1
2
1
0
2
0
1
0
0
1
1
1
1
0
0
2
0
1
0
0
0
0
0
0
0
2
0
2
2
1
3
0
2
1
2
1
1
3
0
0
0
1
1
0
0
0
0
2
2
0
2
0
0
3
0
0
0
0
0
0
2
0
2
0
0
2
0
1
0
0
0
1
1
0
1
0
2
1
1
0
1
1
1
2
1
2
0
1
0
0
0
0
2
1
1
1
3
0
0
1
1
1
0
0
0
2
0
0
3
2
0
1
1
0
0
0
0
2
0
0
0
0
1
2
0
0
1
0
1
0
0
0
1
0
2
1
0
2
2
1
0
0
0
1
2
0
0
0
0
0
1
0
0
2
1
0
0
1
2
3
1
1
3
3
1
1
0
2
0
0
2
2
0
0
1
0
0
0
0
1
0
0
0
1
2
1
0
1
2
0
0
2
0
0
0
2
0
4
1
0
1
0
0
1
0
0
1
1
1
1
0
0
2
0
0
1
0
1
0
1
1
1
1
0
2
0
1
1
2
1
0
0
0
0
0
1
0
2
0
1
1
0
0
0
2
1
1
1
1
0
0
0
2
2
0
1
0
0
1
1
0
0
1
1
2
0
0
2
1
0
0
0
0
1
5
0
1
1
2
1
0
1
0
2
0
1
0
1
2
2
0
0
2
0
1
0
0
0
1
1
1
0
2
0
0
1
0
2
2
0
0
0
2
0
2
1
0
1
2
0
2
0
2
2
0
0
1
3
0
0
0
0
1
1
1
2
2
1
1
2
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
2
1
1
1
0
1
2
0
0
1
3
0
0
0
1
1
0
1
2
0
0
1
0
0
1
0
1
1
0
1
1
0
0
2
2
0
1
0
0
0
2
1
1
2
1
0
1
0
2
1
0
0
0
2
1
0
0
2
2
0
1
0
1
0
1
2
2
2
0
0
0
1
1
0
2
1
0
0
2
1
0
2
1
2
0
2
0
1
0
1
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
1
2
0
0
0
1
1
4
1
0
1
0
2
0
0
1
1
2
3
0
1
1
1
0
0
0
2
0
0
0
1
1
0
0
0
1
1
0
0
0
2
1
2
0
0
1
0
2
0
2
0
2
1
0
1
1
1
0
1
2
0
1
0
1
0
2
2
0
0
0
0
0
0
0
0
0
2
2
0
0
2
1
2
0
1
0
2
2
1
0
0
0
1
3
0
0
1
0
2
0
3
1
1
0
1
2
0
1
2
1
0
2
0
0
1
0
1
0
0
0
0
0
0
1
0
2
2
0
1
2
2
0
0
0
0
1
0
0
1
0
1
1
1
2
1
0
2
0
0
0
2
0
0
1
0
0
2
2
2
0
0
1
0
0
0
0
0
1
0
1
0
1
0
2
1
2
1
0
0
2
0
1
0
0
0
0
0
2
0
2
1
1
0
0
0
0
0
0
2
1
0
0
0
0
0
2
1
0
2
3
0
2
2
2
1
0
1
0
2
1
1
2
0
2
1
0
1
2
1
0
0
1
0
1
0
0
1
0
0
0
2
2
2
2
0
2
3
2
0
0
0
0
2
0
0
1
1
0
0
0
2
2
2
1
0
0
1
0
0
0
0
0
0
1
1
0
2
0
1
1
0
0
1
0
0
0
1
2
1
0
1
0
2
1
0
3
0
2
0
1
2
1
1
0
1
2
2
2
0
1
2
1
1
1
1
2
1
1
1
2
2
1
0
1
1
3
1
0
2
0
6
0
0
0
0
0
2
0
1
0
1
2
0
0
0
0
2
0
0
2
1
0
0
0
0
3
3
0
2
0
2
5
0
2
2
2
2
1
0
1
1
0
2
2
0
4
1
1
1
0
1
0
0
1
0
1
1
2
1
0
1
0
1
1
2
1
0
2
2
0
2
2
0
0
0
2
2
1
0
1
0
0
0
0
0
0
3
4
0
1
1
0
1
1
0
1
0
0
0
0
0
2
1
0
3
1
1
1
0
2
0
0
1
1
0
1
0
0
0
1
0
0
0
1
0
0
2
1
0
0
0
2
0
2
0
1
2
1
1
2
1
0
0
0
0
0
0
0
2
0
1
2
1
0
0
0
0
1
0
0
1
0
0
3
0
0
0
1
1
1
1
0
0
0
0
0
0
1
1
0
1
0
1
0
1
1
0
0
2
2
1
0
1
1
1
1
1
0
0
0
3
2
0
1
2
0
1
2
0
0
0
0
1
1
1
1
0
0
0
0
2
0
2
1
2
0
0
0
2
1
0
2
0
2
2
0
0
1
0
2
0
2
0
0
0
1
3
0
0
0
0
2
0
0
0
2
0
2
0
2
2
0
0
2
0
0
3
0
0
0
1
2
0
0
2
0
2
1
0
1
2
0
0
2
2
1
0
2
1
1
1
0
0
1
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
2
1
0
1
0
0
0
3
0
0
0
0
1
1
1
0
0
2
2
2
1
2
0
0
0
1
2
0
2
0
0
2
1
1
1
1
2
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
3
0
1
0
1
1
0
2
1
2
1
0
1
2
0
3
0
2
0
0
0
0
0
0
1
0
1
1
2
0
0
0
0
0
1
1
1
1
1
0
0
0
0
0
1
2
0
2
1
0
0
1
1
2
1
0
0
1
0
0
0
0
0
0
0
0
2
2
0
2
1
2
3
1
2
2
0
1
0
2
0
0
0
2
0
0
2
0
0
0
0
1
1
0
0
0
1
2
2
0
1
0
1
0
0
2
1
1
0
1
0
2
0
0
0
0
0
2
1
0
0
1
0
0
0
1
0
0
0
4
0
4
0
0
2
1
1
2
1
1
1
0
0
0
1
2
0
0
1
1
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
2
0
2
1
0
1
1
1
0
0
1
0
2
0
1
1
4
1
1
0
2
1
0
1
0
1
1
0
2
0
0
0
2
0
1
0
0
0
2
2
0
1
2
0
0
0
0
1
2
2
2
7
0
0
1
2
0
0
0
0
0
0
0
2
0
2
0
1
1
1
0
0
0
0
2
2
0
1
1
0
0
0
1
1
0
0
0
5
0
2
0
2
0
1
2
2
0
0
0
0
0
2
1
1
0
0
0
0
0
2
0
1
0
0
2
1
1
2
0
0
0
4
1
2
1
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
2
2
2
0
0
1
1
0
1
1
0
0
2
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
1
0
1
0
0
2
0
1
2
1
0
0
0
3
0
1
0
1
1
2
1
1
1
0
0
1
1
0
0
0
0
3
2
0
0
0
0
0
0
1
0
0
1
2
2
0
0
0
0
2
0
0
0
1
0
0
1
2
0
0
0
0
1
1
1
0
1
1
0
1
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
1
0
1
1
2
0
3
2
2
0
1
1
1
0
0
0
0
0
2
0
1
1
0
1
0
0
0
2
2
1
2
0
1
2
0
1
2
2
1
0
0
0
1
0
0
1
1
2
1
1
0
0
1
0
0
1
1
1
0
3
0
0
2
2
0
0
2
2
2
1
2
2
0
0
1
0
2
0
2
1
0
0
0
2
1
0
1
1
2
1
1
0
1
4
0
0
3
0
2
0
0
0
2
2
0
1
2
1
0
0
4
0
0
0
0
0
2
1
0
0
0
0
0
1
0
3
1
1
2
1
0
1
0
1
0
2
1
0
0
1
1
0
0
0
1
0
2
2
0
1
1
0
1
0
1
0
0
0
0
2
0
1
1
1
0
0
1
1
1
0
0
2
0
0
0
0
0
0
0
1
1
0
1
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
1
0
2
2
1
0
0
0
1
1
2
0
0
1
2
0
2
1
0
0
0
0
2
0
1
1
1
0
0
2
0
1
0
2
0
1
1
0
0
1
2
0
0
0
2
1
2
0
0
2
0
1
1
1
0
1
0
2
0
1
0
0
1
0
0
3
0
2
0
0
1
1
2
2
2
2
0
0
0
2
0
2
0
0
0
0
2
1
1
1
0
1
0
0
0
1
3
0
0
0
0
1
0
0
0
2
0
0
1
1
1
2
0
0
1
0
1
1
1
0
1
1
1
1
0
2
0
2
0
0
2
2
0
1
1
1
0
2
1
0
1
0
2
1
0
0
2
1
0
0
1
3
0
0
1
0
0
3
1
3
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
2
2
1
0
1
0
0
0
1
0
0
0
2
0
0
1
0
1
2
1
1
1
1
1
0
1
0
0
0
1
1
0
0
2
2
2
0
1
1
0
0
0
2
2
1
0
0
0
1
1
0
0
2
2
0
0
1
0
2
1
0
0
0
1
0
1
1
1
1
0
0
2
1
1
0
1
3
0
0
1
1
1
0
0
0
0
1
2
0
0
0
1
0
1
1
1
0
2
2
0
2
2
0
1
1
0
2
2
0
1
0
2
2
2
0
1
0
0
2
0
1
3
1
0
2
0
0
0
1
0
2
1
0
2
1
0
0
0
0
2
0
0
1
0
2
1
0
1
0
0
0
1
0
0
0
1
1
2
2
1
2
1
1
0
0
2
1
0
0
0
0
1
2
0
1
1
0
1
0
0
1
0
1
3
1
0
1
0
0
0
0
1
2
2
1
0
0
0
2
2
0
0
0
0
0
1
0
2
1
0
2
0
1
1
1
2
0
2
0
0
1
1
2
0
0
1
0
0
0
0
3
2
0
1
1
2
0
1
0
0
1
1
1
0
0
1
1
0
0
1
0
1
2
0
3
2
0
1
0
0
0
0
0
0
2
0
0
1
1
2
0
2
2
1
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
1
2
0
0
0
0
0
1
0
0
2
0
0
0
2
1
2
0
1
0
1
0
1
2
0
0
1
1
1
2
1
1
0
2
0
0
0
0
3
2
1
0
2
0
1
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
2
0
0
1
2
0
0
1
0
1
0
0
0
1
1
2
3
0
1
0
1
0
1
2
0
1
1
2
0
2
2
0
0
2
1
1
1
0
2
0
0
2
0
0
2
1
0
1
0
0
0
2
0
0
0
0
2
1
0
0
0
2
0
0
0
2
2
1
0
0
0
2
2
0
0
3
0
1
3
1
2
2
1
1
3
0
1
2
2
2
1
0
0
0
2
0
0
0
0
2
2
2
0
2
1
0
2
1
0
0
2
0
0
0
0
1
2
0
0
2
2
4
0
0
1
1
2
2
0
2
4
0
2
2
0
0
3
0
0
1
0
1
1
2
3
1
0
0
0
0
1
0
0
0
0
1
2
2
2
0
0
2
0
1
0
0
1
2
0
1
2
3
2
1
0
0
0
2
1
2
0
0
2
0
2
1
2
2
2
0
1
2
2
0
0
0
2
1
2
2
0
2
0
0
2
1
0
2
0
0
0
0
1
0
2
2
2
0
1
1
2
0
1
0
1
0
3
0
0
0
0
2
2
0
1
0
0
2
0
1
1
0
0
0
2
0
0
1
1
0
0
1
0
0
1
1
0
1
0
0
0
0
2
2
0
1
0
2
2
0
2
0
0
2
1
1
2
2
0
2
0
1
1
2
1
0
0
2
0
2
1
1
0
0
2
0
0
2
0
0
0
2
1
0
4
0
0
2
0
0
0
1
2
2
2
1
1
1
0
2
0
1
1
7
0
1
2
0
2
0
0
1
0
0
0
0
0
0
1
1
1
0
0
1
0
0
1
0
2
1
3
2
0
0
1
0
0
2
0
0
0
0
0
0
0
1
2
0
0
2
1
0
0
0
0
0
0
2
1
1
1
0
0
1
0
1
1
0
2
1
1
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
1
1
0
3
0
1
2
0
0
0
0
1
2
0
0
1
2
2
1
0
3
0
0
0
1
0
1
1
0
0
1
2
1
1
1
1
1
0
0
4
3
0
2
0
0
1
0
0
0
0
0
2
2
2
0
0
1
2
0
0
2
2
0
0
0
0
1
0
2
1
1
0
3
1
2
1
1
0
0
3
1
2
1
2
0
0
0
0
0
0
1
0
1
1
2
0
0
0
2
0
0
1
0
1
0
2
0
0
0
0
1
1
1
1
0
1
0
1
2
2
0
1
0
0
0
0
0
3
1
0
2
2
2
2
1
1
0
0
2
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
1
0
0
0
2
0
1
1
1
2
2
0
0
0
1
0
1
0
1
0
0
2
1
0
0
1
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
1
2
2
1
1
0
2
1
0
2
2
1
0
0
1
0
2
2
0
1
2
0
0
0
0
3
0
0
0
0
0
0
0
1
4
3
1
1
2
1
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
2
0
0
0
1
0
1
2
4
2
5
1
0
0
1
2
0
1
0
1
1
0
2
0
0
2
0
1
1
0
2
0
1
0
0
1
2
1
0
0
2
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
2
1
2
0
0
0
0
1
0
1
2
1
1
0
2
0
0
0
0
0
0
2
0
2
0
0
2
1
0
1
2
2
2
0
1
4
0
0
2
0
0
0
1
1
0
0
0
0
0
1
2
0
0
0
0
1
3
1
1
0
0
1
2
0
0
0
0
0
1
1
2
2
0
0
1
0
0
0
0
0
1
2
3
0
0
1
0
0
1
0
0
1
3
0
2
1
0
2
1
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
2
0
1
1
2
1
0
0
0
0
2
1
0
0
1
0
0
1
0
0
0
1
1
1
0
0
2
1
0
3
3
1
2
0
1
0
1
0
2
1
2
0
2
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
1
1
0
2
0
1
0
0
0
0
0
0
0
0
2
2
2
0
1
1
0
1
0
0
0
0
0
0
0
2
2
0
1
0
2
1
0
0
1
2
2
2
3
1
0
1
1
1
1
1
2
0
0
1
1
2
1
1
2
1
0
1
1
1
1
0
0
1
0
1
0
1
0
2
0
0
1
2
1
0
0
0
1
1
1
0
1
0
0
0
1
1
0
1
0
1
2
0
0
2
1
0
1
0
0
0
0
0
1
1
1
2
2
2
0
0
1
0
0
1
1
0
0
2
0
1
1
0
1
2
0
2
3
1
1
0
0
1
0
0
2
1
0
0
0
1
2
1
1
2
0
0
2
2
1
1
1
1
0
0
1
0
0
0
1
0
0
1
1
1
0
1
2
3
0
2
0
0
0
1
1
1
1
1
0
1
0
1
0
2
1
0
0
1
0
0
0
0
0
1
0
4
0
0
1
0
0
2
0
2
0
0
0
0
1
1
1
2
0
2
1
0
0
1
1
1
0
1
0
1
0
0
3
0
0
0
1
0
0
2
0
0
2
1
0
0
1
0
0
1
0
1
2
2
1
1
0
0
0
0
0
0
1
2
0
0
2
2
1
1
0
2
0
0
1
3
0
0
0
1
2
1
0
1
2
0
0
0
3
2
1
1
1
0
2
3
0
2
0
0
0
2
0
2
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
2
0
1
1
1
2
1
1
0
0
0
0
0
1
2
0
0
0
2
0
1
2
0
2
3
2
2
0
0
2
2
0
0
1
0
0
1
2
2
2
1
1
0
1
2
2
0
0
0
1
1
0
2
1
0
0
0
1
0
0
1
1
0
2
0
0
0
2
0
2
0
1
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
1
1
1
1
0
0
0
1
2
0
0
1
0
0
2
2
1
1
2
0
0
0
1
2
1
2
0
1
2
0
0
1
2
0
0
1
0
1
0
0
2
2
2
0
2
2
0
3
2
0
1
2
0
1
0
1
1
0
2
0
0
1
3
0
1
2
1
1
1
0
0
0
0
0
0
0
0
0
0
1
2
2
2
0
2
0
1
2
2
0
0
2
3
1
1
0
0
0
0
1
0
0
0
1
0
1
0
2
0
0
1
1
1
1
1
0
0
2
0
0
0
2
1
1
2
0
1
2
1
0
1
0
0
0
2
1
2
0
1
0
0
0
0
0
0
0
0
1
2
0
2
2
1
0
2
2
0
0
1
0
0
0
1
0
0
2
0
2
2
0
0
1
0
0
2
1
0
2
1
0
0
0
1
1
0
2
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
1
1
2
1
0
0
1
1
0
0
1
1
0
0
0
0
0
0
1
1
1
2
1
0
1
0
1
1
0
0
2
0
1
0
1
1
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
1
0
0
2
0
0
0
2
0
1
0
1
0
2
0
0
0
1
1
0
0
0
0
0
0
2
1
0
1
0
0
1
0
2
1
0
0
0
0
0
0
0
2
0
1
1
0
0
2
1
0
0
0
2
0
2
0
1
6
2
1
0
0
0
0
1
0
1
0
4
1
2
1
1
1
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
2
0
1
1
2
0
1
1
0
0
2
3
0
1
2
0
0
0
1
0
1
0
0
1
0
1
0
2
0
0
3
2
1
0
1
2
0
0
0
1
0
0
0
3
0
1
1
0
0
0
0
0
2
1
0
0
0
2
0
1
0
0
0
2
0
0
0
0
1
2
1
2
0
1
0
2
1
1
2
0
0
1
0
0
0
1
0
0
2
1
0
0
3
0
2
1
2
0
2
1
1
0
1
0
3
0
0
0
0
2
0
0
0
1
1
4
0
0
0
0
1
1
0
1
2
1
1
2
1
0
0
0
2
1
0
0
1
1
0
1
0
0
0
1
0
3
0
0
1
0
0
1
0
2
1
0
0
0
0
2
1
1
0
1
0
2
1
0
1
0
0
2
0
0
0
1
1
0
0
2
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
1
1
0
0
1
1
0
1
2
1
0
1
2
2
0
1
1
0
1
0
0
0
0
0
4
0
2
1
2
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
1
0
0
2
2
0
0
2
0
0
0
1
1
0
0
2
1
0
0
1
2
2
0
0
1
0
0
1
1
0
2
1
0
0
0
0
2
2
0
2
1
0
2
1
0
0
2
2
1
0
0
0
0
1
0
0
1
0
0
2
0
0
2
0
1
0
2
1
2
0
0
1
1
0
0
2
0
2
0
0
1
0
0
0
0
2
2
0
2
0
2
1
2
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
1
2
1
0
0
0
0
2
0
1
0
2
0
1
2
0
0
1
1
2
0
0
1
1
0
1
0
1
2
0
0
0
0
2
0
0
0
3
1
1
1
1
0
1
2
1
1
1
0
1
1
0
1
0
1
0
0
2
0
1
0
0
0
1
0
0
1
1
0
0
1
0
0
1
0
0
2
0
0
1
0
2
2
1
1
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
2
1
1
0
1
2
3
1
0
0
0
1
0
1
1
2
0
0
1
1
0
1
0
0
0
1
0
1
0
0
2
0
1
0
0
1
0
0
0
0
0
0
2
1
0
0
0
4
0
0
1
2
1
1
2
2
1
0
1
1
0
1
0
1
2
0
0
2
6
2
0
2
0
1
1
0
1
1
0
1
0
2
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
1
2
0
2
0
0
0
0
1
0
0
1
0
0
0
0
2
1
2
1
1
2
0
2
0
1
3
1
2
0
1
0
2
1
0
1
0
0
1
1
1
0
0
0
0
2
0
0
1
0
2
0
2
0
2
1
1
1
1
0
1
1
0
1
1
1
2
2
0
0
1
0
2
2
0
0
1
0
2
1
0
2
0
2
1
0
2
1
1
2
0
0
2
1
1
0
2
1
0
0
0
0
0
0
2
0
0
1
0
1
1
0
0
0
0
0
1
0
0
1
1
1
0
1
0
0
0
0
1
0
1
0
2
0
0
1
2
0
2
2
0
2
0
0
0
0
1
2
0
2
0
0
0
0
0
0
1
2
0
1
0
0
1
1
1
0
0
2
1
0
0
2
0
0
2
0
2
0
0
1
0
1
0
1
1
3
0
0
0
0
2
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
1
1
0
0
2
0
1
0
2
1
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
2
0
2
0
0
0
0
1
0
2
0
0
1
0
0
1
0
0
1
0
1
2
1
1
2
1
0
2
1
0
0
1
2
0
0
2
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
1
0
0
1
1
0
0
2
0
0
0
0
2
2
0
1
0
2
0
2
1
0
1
2
1
0
3
0
0
1
1
0
0
1
0
2
1
0
3
0
1
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
3
1
3
0
2
4
3
0
2
0
0
0
2
1
0
1
1
1
2
0
0
0
2
2
2
1
1
1
2
0
0
2
1
0
1
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
1
1
1
2
0
0
0
0
2
0
2
0
2
1
0
0
0
3
1
0
2
0
1
2
0
0
0
1
0
2
1
1
1
3
0
0
1
0
1
2
1
0
0
0
0
3
0
2
2
1
0
0
1
0
0
1
1
0
0
0
0
2
1
1
0
0
1
2
0
0
0
2
1
0
0
2
1
0
0
0
1
1
0
1
1
1
2
0
1
3
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
2
0
1
0
1
0
3
1
0
1
5
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
1
3
0
0
0
0
0
1
0
3
0
1
0
1
0
2
1
0
0
0
2
1
1
0
1
2
0
0
0
2
0
1
1
2
1
1
0
1
1
1
1
3
0
0
0
0
1
0
0
2
1
0
1
0
1
2
2
2
0
1
0
2
0
2
1
2
1
1
0
1
0
0
0
0
1
1
0
0
1
1
1
1
0
0
0
1
1
0
0
2
0
0
1
0
0
0
2
0
2
0
0
1
1
2
0
2
1
3
0
0
0
3
0
0
0
0
0
0
1
1
1
3
1
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
2
2
3
0
0
1
0
1
1
2
0
0
2
1
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
2
2
2
0
0
1
0
0
1
0
2
1
1
0
2
1
1
0
0
1
1
0
0
1
0
1
0
1
2
0
0
4
1
0
0
0
2
0
0
2
1
1
1
2
1
2
0
0
0
1
1
0
1
1
0
2
1
0
0
0
1
0
2
0
3
1
0
2
2
1
0
2
2
0
1
0
2
0
0
0
0
0
2
1
1
2
0
1
0
1
0
1
1
1
0
0
1
0
0
0
1
0
0
1
2
0
0
2
2
2
0
0
0
0
0
0
1
0
2
0
0
2
1
0
0
0
0
1
2
1
1
2
2
2
1
0
2
1
0
1
0
0
1
2
0
2
1
2
1
1
2
1
0
0
1
2
1
2
1
1
0
0
2
0
1
1
0
0
0
0
0
2
0
1
0
0
1
3
0
0
2
1
2
0
1
0
1
0
0
2
1
2
2
0
0
2
2
0
1
1
0
2
2
2
0
0
0
0
0
0
0
0
0
1
2
0
2
1
0
0
2
0
1
1
0
1
2
0
1
1
2
1
1
0
2
0
0
1
0
0
2
1
0
0
2
1
2
0
2
2
1
2
2
0
2
2
3
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
2
0
1
1
0
1
1
0
2
0
0
3
0
1
0
0
0
0
1
2
1
0
0
0
0
2
4
0
0
1
1
0
1
0
2
0
1
0
0
1
2
1
0
0
2
0
0
0
2
1
0
1
0
1
0
2
1
1
0
0
2
0
0
1
2
0
0
2
1
0
1
0
0
0
0
2
0
1
0
2
2
1
2
0
2
2
2
0
0
0
0
0
2
1
1
1
1
0
1
0
0
3
1
0
0
1
0
1
2
0
0
0
1
0
0
1
0
1
1
0
2
0
1
2
2
0
1
0
0
1
1
0
1
0
0
0
2
0
0
0
1
1
2
1
0
0
4
1
2
2
0
1
0
0
1
0
0
0
0
2
1
0
0
0
1
0
0
0
0
2
2
2
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
1
0
0
1
2
2
0
1
0
0
0
1
1
0
0
2
2
0
0
1
0
0
2
2
0
0
3
0
1
2
2
1
0
1
0
0
0
2
2
1
1
2
0
0
0
2
1
0
1
0
2
1
1
2
0
0
1
0
3
0
0
2
1
0
1
0
0
0
0
1
3
1
2
0
2
1
0
2
0
1
1
1
1
0
1
0
0
1
0
1
2
0
0
0
2
2
0
0
2
1
0
0
2
0
0
2
0
1
0
0
1
1
1
0
0
1
0
0
0
0
0
2
0
0
0
2
1
0
1
0
1
0
0
0
0
1
2
0
1
1
0
2
2
2
2
0
0
0
0
1
1
1
0
2
0
2
1
0
2
2
0
0
0
0
2
1
0
1
0
2
0
0
1
1
0
0
0
0
2
0
0
0
1
0
0
0
1
1
1
0
0
0
0
2
0
0
0
0
0
1
2
3
2
0
2
0
1
1
0
0
1
1
3
2
0
0
5
0
7
1
0
0
1
1
0
0
1
0
0
0
2
2
0
2
1
0
0
1
1
0
2
2
1
0
1
0
1
1
1
2
0
1
1
1
1
0
1
0
0
0
0
0
1
1
0
0
1
3
1
0
0
0
0
2
1
1
1
0
2
0
0
1
1
2
1
1
0
2
1
0
1
0
0
0
1
1
2
0
2
0
1
2
0
0
1
0
1
1
0
0
0
0
1
1
1
1
0
0
1
2
0
0
0
0
1
0
0
0
0
1
1
3
1
1
0
0
0
0
1
0
0
0
0
2
1
2
0
2
1
0
1
2
0
2
0
3
0
0
0
1
2
0
1
0
3
5
1
0
0
2
0
2
0
0
0
1
4
2
0
1
0
0
0
0
2
1
1
2
0
1
0
1
0
0
0
1
0
1
0
0
0
2
1
1
0
1
0
0
0
0
1
2
0
1
4
0
0
0
0
1
0
1
3
1
2
0
0
3
0
2
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
2
0
2
0
0
0
1
2
1
0
1
0
1
1
0
0
0
1
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
1
1
0
0
0
2
1
1
0
1
1
0
0
1
2
0
0
1
0
0
0
4
2
0
0
0
1
2
1
0
0
2
0
1
1
2
0
2
0
2
2
1
1
0
0
0
1
1
0
0
1
0
0
1
1
1
0
0
1
1
2
0
0
0
1
1
1
0
0
1
1
0
0
1
0
0
0
0
0
3
2
0
0
2
0
0
0
2
5
2
0
1
0
0
1
0
2
2
0
2
2
0
1
1
2
1
0
1
0
1
0
0
0
1
1
0
2
1
0
0
0
2
0
2
0
0
0
0
0
2
4
0
0
0
1
2
0
2
2
0
2
2
1
1
0
0
0
2
0
2
2
1
0
1
2
0
2
0
1
1
2
0
1
0
0
0
2
1
2
2
3
0
2
0
0
2
0
0
2
0
0
0
1
0
0
0
2
1
0
2
1
0
1
1
1
0
0
1
2
0
2
2
1
1
1
2
0
0
1
0
1
2
2
1
0
0
1
2
1
0
0
0
0
1
2
0
0
1
0
1
0
1
0
2
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
1
1
1
2
3
0
0
2
2
2
0
1
1
3
0
1
0
0
0
1
0
1
1
1
0
2
0
0
0
0
1
0
0
2
0
0
2
0
1
2
0
2
1
0
0
2
1
1
0
2
2
0
2
2
1
1
1
0
2
0
2
0
2
0
0
0
1
0
1
1
0
0
0
2
0
2
2
2
1
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
1
0
0
1
0
2
0
0
0
2
1
2
2
0
1
1
2
1
1
0
0
1
1
1
1
1
2
0
0
1
0
1
0
0
0
1
0
0
2
2
1
1
0
1
0
0
1
4
0
1
0
2
2
0
0
2
0
0
0
1
1
0
0
1
2
1
0
0
2
0
1
0
2
2
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
2
1
0
1
0
1
0
0
1
0
1
0
0
2
0
0
0
2
1
1
1
0
0
1
1
1
2
2
0
2
0
0
0
2
2
1
0
0
1
0
1
0
1
0
2
1
0
0
0
1
1
0
0
1
1
0
1
1
2
0
1
1
1
1
1
0
0
0
1
0
3
0
0
0
1
0
2
0
1
0
2
0
0
0
0
2
0
0
1
1
0
1
1
0
0
1
0
1
0
1
0
2
2
0
0
2
0
1
0
2
0
0
0
1
0
0
0
0
2
0
0
1
0
2
0
1
1
0
0
2
0
1
0
0
1
0
0
0
3
0
2
0
2
1
0
1
0
1
0
1
2
1
0
0
0
1
2
0
0
0
0
0
0
1
1
1
0
3
0
2
1
0
2
0
0
2
1
0
0
0
0
0
2
2
0
1
1
2
2
1
0
0
2
0
0
0
1
1
1
0
1
2
0
2
1
2
1
0
3
0
2
0
3
0
0
0
1
0
2
1
0
0
0
1
0
0
1
0
1
0
2
3
2
1
0
1
0
0
0
0
2
0
1
1
0
0
1
0
0
0
2
0
0
0
1
0
0
0
1
2
1
0
0
0
1
0
2
0
2
2
1
2
0
1
0
0
2
2
2
1
2
2
1
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
1
0
1
0
1
2
0
1
3
2
0
4
0
2
0
1
0
2
0
2
0
2
1
0
1
1
0
2
0
0
0
0
0
2
0
2
2
2
1
1
0
1
1
0
0
2
0
1
2
0
1
1
0
0
0
0
0
1
0
0
2
2
1
1
0
0
0
0
0
1
0
2
2
2
1
0
0
0
1
2
2
2
2
0
1
0
0
0
0
2
0
1
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
1
0
2
3
1
1
0
2
0
0
1
2
0
2
1
0
0
2
0
0
2
0
3
0
0
1
1
1
0
0
0
1
2
0
1
0
0
0
2
2
2
1
2
1
0
1
1
0
6
1
1
1
1
0
4
0
0
0
1
1
2
0
2
2
0
0
1
1
0
0
1
2
1
0
0
1
2
1
4
1
0
0
1
0
1
1
0
0
0
2
2
1
1
0
1
1
0
0
2
0
2
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
2
2
1
1
0
0
0
0
0
1
0
1
2
1
0
2
1
1
0
0
0
1
0
0
2
1
0
0
0
2
0
0
1
2
1
0
0
0
2
0
1
0
0
2
0
0
1
0
1
1
1
2
1
0
0
0
3
1
0
1
1
0
1
0
0
2
0
0
0
0
0
2
0
0
0
1
1
1
0
0
0
1
0
0
1
2
0
0
1
0
3
0
1
0
0
1
0
0
0
0
2
0
2
0
1
2
1
1
1
1
0
0
1
0
1
0
0
1
0
2
0
1
1
1
1
0
0
2
0
0
2
2
0
1
0
0
0
2
0
0
3
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
3
0
2
0
2
0
0
1
1
0
0
2
1
2
0
0
2
0
0
0
0
1
0
1
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
5
1
1
0
0
2
0
1
0
0
1
1
1
1
1
2
0
0
0
1
2
0
0
0
1
1
0
0
0
0
0
0
0
1
0
2
2
2
1
0
1
1
1
1
1
1
1
1
2
0
0
0
0
1
2
1
0
1
1
2
2
0
0
1
0
0
0
1
2
2
2
0
0
0
2
0
2
2
1
1
2
0
0
2
0
2
0
2
5
0
1
0
0
2
1
0
1
0
1
0
0
1
0
0
1
0
3
2
0
0
2
0
2
0
0
0
2
1
0
2
1
0
2
0
0
0
0
0
1
2
1
0
1
0
1
0
0
0
1
0
0
1
1
0
1
2
0
0
1
1
2
2
0
2
0
1
0
1
2
0
0
2
0
0
0
1
1
2
0
1
2
0
1
1
0
0
0
1
0
0
1
0
2
1
2
0
2
2
1
2
0
1
1
0
2
0
2
0
0
1
0
1
0
0
2
2
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
3
2
2
0
1
2
0
1
0
0
1
1
0
0
2
2
0
0
2
1
0
1
0
1
1
0
0
0
2
2
1
1
1
0
1
0
1
0
0
2
2
2
1
0
0
1
0
1
2
1
1
0
1
0
1
2
0
0
0
0
2
0
1
2
0
0
1
0
0
1
1
0
0
0
2
1
2
0
1
0
1
2
4
0
0
0
1
1
2
0
0
2
1
1
0
5
2
0
0
2
0
0
0
0
0
1
1
1
1
2
0
0
1
0
2
1
0
0
0
0
1
0
1
0
2
1
0
1
2
0
1
0
0
1
1
0
0
1
0
0
0
1
2
0
0
0
2
1
2
0
0
2
0
1
0
2
1
0
0
1
2
1
1
0
0
0
2
1
0
0
0
1
2
2
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
2
2
1
0
0
0
0
1
0
0
0
1
1
2
1
1
1
0
0
0
2
0
1
0
0
1
0
0
0
3
2
0
0
0
2
1
1
0
0
0
0
0
1
0
0
0
1
0
2
0
1
1
0
0
1
4
1
0
1
0
0
2
1
1
1
2
0
1
2
0
0
0
0
1
0
0
1
1
0
1
1
2
2
1
0
1
0
1
1
1
0
1
0
0
0
0
0
1
0
0
1
2
0
1
3
0
0
0
0
2
0
0
0
0
0
3
2
1
0
1
2
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
1
3
0
0
1
0
1
2
1
0
0
1
1
1
2
2
2
0
1
0
2
0
1
0
0
0
1
0
1
2
0
2
0
1
1
0
0
2
1
0
1
0
0
0
0
0
0
3
0
1
1
1
2
2
2
1
1
1
0
1
0
2
0
0
0
0
0
2
0
0
0
2
2
2
0
1
0
1
0
3
0
1
2
2
0
2
1
2
1
3
1
1
1
2
3
2
0
0
0
1
0
0
0
0
1
0
0
2
0
1
3
2
2
0
2
2
2
1
2
1
1
0
0
1
0
1
0
1
0
1
1
0
0
2
0
0
0
0
2
1
2
1
2
0
0
0
2
0
1
0
0
1
0
2
2
0
2
2
0
0
0
2
2
0
1
1
0
0
1
1
1
0
0
2
1
2
0
0
0
1
2
0
0
0
2
1
0
1
1
0
3
0
0
2
0
2
1
1
0
2
0
2
2
0
2
2
0
0
0
2
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
2
2
2
0
0
0
0
2
0
0
2
0
2
1
1
2
0
1
0
0
6
0
1
0
0
0
2
1
0
2
0
0
0
0
0
0
3
1
1
1
1
1
0
0
1
0
1
1
1
2
0
1
2
0
0
1
0
2
1
0
1
0
0
0
0
1
1
2
0
1
1
0
2
0
2
0
0
2
0
2
1
0
0
0
1
0
0
0
0
2
1
2
2
0
2
0
2
0
1
0
1
0
0
0
0
0
2
0
0
2
2
0
0
1
1
0
0
1
2
0
0
1
0
0
1
0
0
0
2
0
2
0
1
2
1
0
0
2
2
0
0
2
0
2
1
3
1
1
0
0
2
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
3
1
0
0
1
0
2
0
0
0
2
0
1
2
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
1
1
0
1
1
0
1
0
0
2
0
0
2
1
1
0
1
0
0
0
1
0
0
2
3
0
0
0
1
1
1
2
1
1
0
0
0
0
1
0
0
0
0
0
1
1
0
2
0
0
2
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
1
1
2
1
0
2
0
1
0
2
1
1
0
0
0
0
1
0
2
2
0
0
0
0
0
1
1
0
1
0
0
0
1
1
0
0
0
0
0
0
1
2
0
1
1
2
0
1
0
2
2
1
1
1
1
0
0
0
1
1
2
2
0
0
1
0
0
1
2
2
0
0
1
0
0
0
0
0
1
0
1
0
1
0
1
0
1
2
0
1
1
2
1
2
0
1
0
0
0
0
2
0
1
0
2
0
1
2
1
0
0
2
2
0
0
0
0
0
0
2
1
0
3
0
2
0
0
0
2
0
0
1
2
1
1
0
1
0
0
1
1
0
0
0
0
2
0
0
2
0
0
1
1
0
0
0
2
0
0
0
0
2
2
1
0
2
0
2
1
2
3
0
0
0
2
0
0
0
1
1
2
0
2
1
1
0
1
0
2
0
1
0
2
0
2
1
0
0
1
2
0
1
1
0
0
0
1
1
1
0
0
0
1
1
0
0
2
0
0
2
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
2
1
1
3
0
0
3
0
1
1
0
0
3
1
4
2
2
0
0
1
0
1
1
1
2
2
2
2
1
2
2
1
1
2
1
1
0
1
2
1
1
1
0
2
0
1
0
0
0
1
1
1
1
1
2
0
1
0
0
1
3
0
1
0
2
1
0
0
0
2
1
2
1
2
0
2
2
0
1
0
0
2
0
0
0
0
0
1
0
0
4
0
0
1
0
2
2
1
2
0
0
0
0
0
0
2
0
0
1
0
2
0
2
2
1
1
1
1
1
0
0
1
0
0
0
1
1
1
1
0
1
0
0
0
2
2
2
0
0
0
1
0
1
0
0
0
0
2
0
2
1
0
1
1
3
0
0
1
2
0
2
2
0
0
0
1
1
2
0
1
1
2
0
0
1
0
3
0
1
2
2
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
2
0
2
0
0
1
1
0
2
0
1
1
2
10
0
0
0
0
0
2
0
0
2
0
2
1
0
0
1
2
0
1
0
0
0
0
0
2
1
0
0
2
1
2
2
1
0
0
0
1
1
2
2
1
1
4
0
0
1
1
0
1
0
0
0
1
1
2
0
1
2
0
0
2
0
1
1
2
0
0
1
0
2
0
1
2
1
1
0
0
0
0
0
0
1
2
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
3
1
0
0
0
0
2
2
1
2
2
0
0
0
0
0
0
0
0
1
1
0
2
0
1
1
1
2
1
0
0
2
0
0
1
2
1
1
1
1
0
0
0
0
1
0
1
0
2
0
0
2
0
0
0
1
2
2
0
1
1
1
0
2
1
1
0
0
0
2
2
0
2
0
0
2
0
0
0
0
0
1
2
0
2
0
0
1
0
0
1
0
0
0
1
0
3
0
1
0
2
2
1
0
0
0
0
0
0
1
0
0
2
0
3
0
2
1
0
1
0
1
1
0
0
1
0
2
1
1
0
1
1
0
0
0
0
0
2
0
1
0
2
0
0
2
1
0
1
0
1
0
0
0
1
0
1
0
0
2
0
1
1
0
0
1
0
2
0
2
0
0
2
0
2
2
0
1
0
1
1
0
1
2
0
0
1
0
1
0
0
1
1
2
0
2
0
0
1
0
0
2
0
1
0
2
3
0
1
1
1
2
2
0
0
0
2
1
0
0
1
1
1
0
0
1
1
0
0
2
2
0
1
1
2
0
1
0
0
1
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
1
2
0
2
1
1
0
0
0
1
0
0
0
0
0
1
3
0
2
0
0
3
0
0
1
0
1
2
0
2
0
1
0
1
0
1
1
0
0
1
2
0
0
0
0
2
0
0
0
1
0
1
0
0
0
2
1
0
0
0
2
0
1
0
0
1
0
0
2
1
0
0
0
1
0
0
1
3
0
2
2
0
0
0
0
0
0
0
1
1
2
0
0
0
0
1
0
1
1
0
1
0
0
0
2
1
0
2
0
0
0
0
0
2
0
0
0
0
2
1
2
0
1
0
0
0
1
0
2
0
0
0
2
0
3
0
0
2
0
1
0
2
2
1
0
1
2
1
0
2
0
0
0
2
0
1
2
1
2
1
1
1
1
0
1
1
0
1
3
0
1
0
0
0
0
1
0
1
2
0
2
1
1
1
0
0
0
1
0
1
0
0
0
1
0
0
0
1
1
1
0
0
0
1
2
2
0
0
0
0
0
0
1
2
1
0
0
5
2
0
0
1
2
0
0
0
0
1
1
3
1
0
0
2
2
0
0
1
0
0
0
0
0
2
2
2
0
1
1
0
1
0
2
2
0
2
0
0
0
0
0
0
0
0
2
0
0
1
1
1
0
0
1
0
2
0
0
1
1
1
0
1
1
1
2
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
2
2
1
0
0
0
0
1
4
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
2
0
0
0
6
2
0
2
1
1
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
1
0
0
2
0
1
1
1
2
0
0
2
0
1
1
0
0
0
0
0
0
1
2
2
2
0
1
0
0
0
1
0
0
0
1
1
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
2
0
2
0
2
0
0
1
2
1
1
1
0
0
2
0
1
0
1
0
0
2
0
2
0
1
0
0
0
2
0
0
1
0
2
1
0
0
0
1
1
2
0
1
1
0
0
0
1
0
0
0
0
1
2
1
0
0
0
0
0
0
0
2
0
1
1
0
0
1
2
2
2
0
1
0
0
4
1
1
0
2
1
1
0
1
1
2
1
1
0
0
1
0
0
0
1
0
0
0
0
1
0
2
0
0
1
1
0
0
2
0
2
0
1
0
1
1
2
0
1
2
0
0
1
1
1
2
0
2
0
0
0
1
1
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
1
2
0
2
0
0
2
2
2
2
0
1
0
3
2
0
1
1
2
0
0
0
1
0
0
10
1
0
2
0
0
0
1
0
0
2
0
0
1
0
1
1
0
3
0
1
0
0
1
0
1
0
2
1
1
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
2
0
1
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
2
1
0
3
0
2
1
1
1
1
0
2
0
0
1
1
0
0
0
1
0
0
2
1
0
0
2
0
1
2
2
0
0
1
2
0
0
0
0
1
1
1
1
3
2
0
0
0
2
0
1
2
0
2
1
2
1
0
2
0
1
0
0
0
0
2
0
1
0
2
0
2
1
0
1
0
2
0
0
1
2
0
1
0
0
0
0
0
2
0
0
1
2
2
2
2
1
1
2
2
2
0
1
1
0
2
2
2
2
1
0
0
1
1
1
0
1
0
0
0
1
1
0
2
0
1
0
1
0
0
0
0
2
0
1
2
1
1
2
0
1
0
1
2
0
0
1
0
0
0
1
0
0
1
0
0
0
1
2
0
1
0
0
2
2
0
1
2
1
0
1
0
0
0
0
1
0
0
1
2
1
1
0
2
4
1
1
1
1
0
1
0
1
2
0
0
0
2
0
0
0
1
0
1
2
3
2
2
0
2
1
1
2
0
0
0
3
0
0
2
0
1
0
0
1
1
0
1
0
2
0
0
0
1
0
0
1
1
2
0
0
0
0
2
0
1
0
1
1
1
0
1
1
2
0
0
0
1
0
2
0
2
0
1
0
1
0
0
1
1
0
1
2
0
0
0
0
1
0
0
1
1
0
0
0
1
2
0
2
1
0
2
0
0
1
0
1
3
0
0
0
1
2
1
1
0
1
0
0
2
1
0
0
2
2
1
1
0
0
2
0
0
2
0
1
1
1
2
0
2
3
0
0
2
1
1
2
0
0
0
2
1
1
1
0
1
0
1
1
2
1
1
2
2
1
2
1
0
0
0
0
1
1
0
2
1
1
0
2
0
0
0
2
0
0
1
0
2
2
0
0
0
0
1
0
0
2
1
2
1
1
0
0
0
1
2
0
1
0
2
0
1
1
0
0
0
0
1
1
2
1
1
0
2
2
1
0
0
2
0
1
0
1
2
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
4
1
0
0
0
0
1
1
0
1
2
1
0
0
1
1
1
0
2
0
2
1
0
1
1
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
1
1
0
0
1
1
2
0
0
0
1
0
0
2
1
2
2
0
1
1
0
1
2
0
0
0
1
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
2
2
0
2
2
0
0
2
2
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
2
0
1
0
1
2
0
0
1
0
1
0
0
0
0
2
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
1
1
0
0
0
0
1
1
1
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
1
0
1
2
2
1
0
0
1
0
0
1
1
0
1
2
0
1
1
1
2
1
2
0
0
2
0
0
1
0
0
1
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
1
0
1
0
1
0
2
0
1
0
0
1
1
0
1
0
0
2
2
0
0
0
1
0
0
2
2
1
1
0
1
0
0
0
0
0
2
1
0
0
1
0
1
0
0
1
0
1
0
0
0
0
4
2
0
2
2
2
0
0
0
0
2
0
0
0
1
0
0
2
1
0
1
2
0
2
0
2
0
1
1
1
1
0
1
0
1
0
0
0
0
2
0
1
0
2
1
3
0
1
1
1
0
1
1
0
2
0
1
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
1
0
2
0
1
0
2
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
1
0
1
1
0
0
2
1
1
2
1
1
0
0
0
1
0
0
1
1
2
1
0
0
2
1
1
2
1
0
1
0
2
0
2
2
1
0
1
1
1
1
2
0
2
1
1
0
0
2
1
2
0
1
2
0
0
0
2
0
1
1
1
2
1
2
1
1
2
0
1
0
0
4
2
0
1
0
0
0
1
2
0
0
0
2
2
0
1
1
0
2
2
1
0
0
1
1
0
0
0
0
3
1
1
0
2
0
1
1
2
0
0
1
0
2
0
0
1
0
0
2
1
1
2
1
1
0
0
0
2
0
0
0
1
1
1
2
0
0
0
0
0
2
1
0
0
0
2
0
1
0
0
0
1
0
0
1
0
0
1
0
2
0
0
2
2
1
2
1
0
0
2
0
2
0
0
0
1
1
0
0
0
2
1
2
0
0
0
0
0
0
0
0
2
1
0
2
0
1
0
1
0
0
0
0
0
2
0
2
0
0
2
0
1
2
1
1
1
1
1
1
2
0
2
0
0
0
1
0
1
1
0
0
3
0
0
1
0
1
1
0
0
2
0
2
1
1
1
1
1
0
0
0
0
1
1
0
0
0
2
0
0
1
2
0
0
1
0
0
1
0
2
0
0
1
0
0
1
1
0
0
1
2
0
0
1
0
2
0
1
0
0
1
2
0
0
0
1
2
0
1
1
2
0
0
0
0
0
1
0
0
0
0
1
2
0
1
0
0
2
1
0
0
0
0
0
1
0
0
2
1
1
1
0
0
1
2
1
0
2
0
0
0
2
1
1
0
0
0
0
1
2
2
0
1
1
0
1
4
0
1
0
1
0
0
0
1
0
0
1
2
4
0
1
0
1
0
0
0
0
0
1
3
0
1
0
0
2
0
0
1
2
2
2
1
0
0
1
1
0
1
1
2
1
0
0
1
0
0
1
0
2
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
3
0
0
1
1
0
2
2
1
0
2
2
1
2
2
2
1
0
0
0
0
1
0
0
0
0
0
2
2
0
2
0
0
0
0
0
2
0
0
0
0
1
0
1
1
1
0
1
1
0
0
1
3
2
0
1
0
2
0
2
2
0
0
0
0
2
1
0
1
1
2
0
0
2
0
2
1
1
0
0
0
1
1
1
1
0
0
2
0
1
0
0
0
0
2
0
0
1
0
0
0
0
1
0
1
0
2
2
2
0
0
0
0
1
1
0
2
0
1
2
2
0
0
2
2
1
1
1
2
2
0
2
0
0
0
0
0
0
2
0
0
2
1
0
1
2
2
0
0
0
1
1
2
0
1
0
1
1
1
0
1
0
0
1
0
1
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
1
1
2
0
2
1
0
1
2
1
0
2
2
0
1
1
2
1
0
0
0
0
0
3
1
0
1
0
1
0
0
0
1
1
0
2
0
1
0
2
1
1
0
1
0
0
0
2
2
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
1
2
0
0
1
1
1
2
1
2
1
0
1
1
0
0
1
1
0
0
0
1
2
1
2
0
2
0
0
0
0
0
1
0
1
0
0
0
1
0
1
2
1
0
0
0
1
2
1
1
0
1
0
1
0
0
0
0
2
2
0
0
2
0
2
0
1
1
2
0
0
0
1
0
1
0
1
1
0
0
0
0
0
1
2
0
1
2
2
2
2
1
0
0
0
0
0
1
2
1
2
1
1
1
1
0
0
1
0
0
1
2
3
0
0
3
0
0
2
0
0
0
1
0
1
1
1
0
0
0
0
2
0
0
2
1
0
2
0
0
0
1
0
0
0
2
0
0
1
2
0
1
2
1
2
1
1
1
1
1
0
1
1
0
2
0
2
1
2
2
1
0
0
0
0
0
0
2
2
1
2
1
0
0
2
2
0
2
2
2
0
0
1
2
1
0
0
1
0
2
2
0
1
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
2
1
2
0
0
0
1
0
1
1
0
2
1
0
0
0
5
0
1
2
0
1
1
0
0
0
1
0
0
2
0
0
3
0
0
1
1
1
0
0
2
1
1
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
2
2
2
1
1
0
0
0
1
1
0
0
1
1
0
1
0
0
2
0
3
1
1
0
1
1
0
0
0
1
1
2
0
0
0
0
0
2
2
0
0
1
2
0
0
0
2
0
1
0
1
0
0
1
2
0
2
1
0
1
0
0
1
0
0
0
2
0
0
0
0
1
1
0
0
1
2
0
0
0
2
0
0
2
1
0
0
2
2
0
1
1
0
0
0
0
0
2
0
1
1
1
1
0
4
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
1
1
1
0
1
1
0
0
0
0
0
2
0
0
0
1
2
1
0
1
2
1
1
0
0
0
0
0
1
1
0
2
2
1
0
1
1
0
2
2
0
0
1
0
1
1
1
1
0
0
2
1
0
1
0
0
0
2
0
0
3
1
0
0
2
3
0
2
0
2
1
0
0
1
2
0
0
0
1
0
2
1
0
1
0
0
0
0
0
0
2
2
2
0
0
1
0
0
2
0
2
0
0
1
2
1
0
0
0
1
0
1
0
0
0
0
1
0
0
2
1
0
0
1
3
2
2
0
1
0
0
0
1
0
0
1
2
1
2
0
0
0
2
0
0
0
1
1
2
0
0
0
0
0
0
1
2
0
0
2
0
1
0
2
2
1
2
0
0
0
1
0
2
0
0
0
1
2
1
0
2
0
2
0
0
0
2
0
0
0
0
0
0
1
1
1
1
2
1
1
2
2
0
0
2
0
0
0
0
1
0
2
1
0
0
0
0
1
0
2
0
3
0
0
0
0
1
0
0
0
0
1
0
0
1
0
2
1
0
0
0
0
1
1
2
0
0
0
1
0
1
2
0
0
0
0
3
0
2
1
0
0
0
0
0
0
1
0
1
0
1
3
1
2
0
1
2
0
0
0
0
1
0
1
0
2
0
1
1
0
0
2
0
1
0
0
2
2
0
1
0
0
0
0
0
2
0
1
1
0
1
0
1
0
1
1
0
1
0
0
0
1
0
2
1
1
0
0
0
1
1
0
2
0
0
0
0
0
1
0
0
0
2
2
2
0
0
0
1
0
2
1
0
0
0
0
0
2
2
0
1
1
2
1
0
0
2
2
0
0
0
2
0
2
2
2
1
0
2
0
1
1
0
1
2
2
1
4
0
2
2
1
0
1
0
1
2
0
0
0
0
2
1
1
0
2
0
1
0
2
2
0
0
1
0
2
2
1
2
0
1
3
2
1
0
1
1
2
2
0
1
0
0
1
1
0
0
0
2
1
0
3
1
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
2
1
1
0
0
3
0
0
2
0
2
2
0
0
0
1
2
0
2
0
0
0
1
0
0
3
0
0
0
2
2
1
0
2
2
0
0
0
2
1
2
0
0
0
1
0
1
0
2
0
0
1
1
2
0
0
3
1
0
0
0
0
2
0
1
0
0
0
1
0
0
0
1
0
1
2
3
0
0
1
0
0
0
2
1
0
2
1
2
1
0
1
0
0
0
1
2
0
0
1
0
0
2
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
2
1
0
2
3
0
1
1
0
2
2
0
0
0
1
0
0
0
2
0
1
1
1
0
0
1
1
1
1
2
0
0
0
0
1
3
2
2
2
2
2
3
1
0
0
1
1
0
1
2
0
1
1
0
0
0
0
1
0
0
2
0
0
2
7
0
1
1
0
1
0
1
1
2
0
0
1
1
1
1
0
1
0
0
1
0
2
1
0
0
1
2
1
2
1
1
1
3
1
0
1
0
0
1
0
2
0
0
1
0
1
2
0
0
3
0
0
2
0
1
1
0
0
2
3
0
0
0
1
0
0
2
2
2
1
2
1
1
1
1
0
0
2
0
0
2
1
0
1
0
2
0
0
0
1
0
0
1
1
2
3
1
0
3
0
0
0
2
0
0
1
1
0
0
0
0
0
1
2
2
0
1
1
0
1
0
0
0
2
0
0
0
0
1
0
0
2
0
1
0
2
0
0
0
2
0
2
0
1
2
0
0
2
0
1
1
0
0
0
0
0
0
0
2
1
0
0
1
1
0
0
0
5
0
0
2
0
1
1
2
2
0
1
2
0
1
0
1
1
1
1
0
1
0
1
0
0
0
1
1
0
0
0
1
0
1
1
2
0
0
0
1
1
0
2
0
1
0
2
1
1
2
0
0
0
2
0
0
1
0
0
2
2
0
0
1
1
0
0
1
2
1
1
1
2
2
1
1
1
2
2
0
0
0
0
1
0
1
1
1
0
2
0
1
0
0
0
0
0
1
0
2
0
0
0
8
0
0
0
2
0
0
0
3
0
2
1
2
2
3
0
1
0
2
0
2
0
0
0
0
2
0
1
1
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
2
1
2
0
2
0
2
1
0
0
0
0
1
1
1
2
0
0
1
0
0
0
0
0
0
1
2
0
1
1
2
1
2
0
0
2
0
2
1
0
0
0
2
1
2
0
1
0
0
0
0
0
0
0
0
1
2
2
1
1
1
0
1
2
1
0
2
0
1
1
1
0
2
1
1
0
2
0
0
0
0
0
0
1
0
1
2
1
2
1
3
0
0
0
0
0
0
0
0
1
2
1
0
1
2
0
2
1
2
0
2
2
1
0
2
0
1
2
0
0
0
0
1
2
3
0
1
0
0
1
0
0
1
2
1
1
0
1
0
2
0
0
2
0
0
1
1
1
0
2
0
2
0
2
0
1
1
0
0
0
1
0
0
0
2
2
1
2
2
0
0
0
2
1
0
0
0
0
1
2
0
1
0
2
1
0
0
1
2
0
0
0
1
0
0
2
0
2
0
1
2
2
2
2
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
1
0
0
1
1
2
2
0
1
0
0
2
0
0
0
0
0
2
0
2
0
2
1
0
0
0
2
0
2
2
0
1
2
0
0
2
2
0
0
1
0
0
2
1
1
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
1
0
5
2
0
0
0
1
1
1
0
1
1
0
2
1
1
2
1
2
1
5
0
1
2
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
1
2
0
2
0
3
1
1
2
0
0
1
0
1
1
2
0
1
2
1
0
1
4
1
0
1
1
0
1
0
2
0
0
1
2
1
1
0
0
0
0
0
0
0
2
0
2
1
1
1
0
0
0
1
2
0
2
2
0
2
1
0
2
2
1
0
0
0
2
1
1
1
0
1
2
0
2
0
0
1
0
0
2
1
1
2
0
0
1
0
2
2
0
0
0
0
1
1
1
2
0
2
0
0
2
0
2
2
0
1
0
0
2
0
0
0
0
0
2
2
0
2
1
0
5
0
0
0
0
1
0
2
0
0
1
2
2
0
0
2
0
2
4
0
1
1
0
1
0
2
1
1
0
1
0
2
0
1
0
0
0
0
1
0
2
1
2
1
2
1
0
2
2
0
2
0
0
0
1
0
0
0
2
1
0
0
1
2
0
0
2
2
0
0
0
0
1
2
1
2
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
2
0
2
0
3
1
1
2
1
0
0
0
1
0
2
2
2
0
2
1
0
0
1
2
0
0
0
1
1
0
2
1
0
1
0
0
0
2
0
0
2
2
1
0
1
0
0
0
0
2
0
2
1
0
0
0
1
1
0
3
2
0
0
0
2
0
0
0
3
0
1
1
1
2
0
0
0
1
3
0
2
1
0
0
0
0
2
0
0
0
1
0
0
2
2
2
0
0
2
0
0
0
3
3
2
1
1
2
0
1
1
1
1
0
0
2
1
2
0
0
2
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
1
2
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
1
2
1
0
0
1
3
2
0
2
0
0
0
1
2
0
0
2
1
2
0
0
2
2
2
2
1
1
0
0
0
2
1
0
0
0
2
2
1
1
0
0
1
0
2
2
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
1
2
0
1
0
2
0
0
2
1
2
1
0
1
0
0
0
0
1
2
1
0
0
0
0
0
2
1
0
4
0
0
1
2
1
0
0
2
1
2
0
0
0
0
0
0
1
0
1
3
0
0
0
0
0
0
1
0
0
1
1
0
2
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
2
2
0
5
0
0
1
1
0
2
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
1
2
2
2
0
0
2
0
1
0
1
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
1
0
2
0
1
0
0
1
0
0
1
0
1
0
0
0
2
1
0
0
0
0
1
0
1
1
1
2
0
0
2
0
0
0
0
1
1
1
1
0
2
0
1
0
2
0
1
1
2
2
0
0
0
1
0
1
1
1
2
2
1
0
2
0
1
1
0
1
0
0
1
0
2
2
0
0
0
0
1
0
1
1
0
1
2
0
0
0
0
0
1
2
1
0
0
0
0
2
1
2
2
2
0
0
1
0
2
0
2
2
0
1
0
2
2
0
2
1
0
0
7
1
2
1
1
2
0
1
0
1
2
0
0
0
0
0
1
0
1
0
0
1
0
1
1
1
0
2
2
1
2
2
2
0
0
0
1
2
0
0
0
2
0
1
0
0
0
2
1
2
2
0
0
0
0
1
0
1
0
1
2
7
0
0
1
2
1
0
0
0
1
0
0
0
2
0
2
0
0
0
1
2
1
1
2
0
1
1
0
0
0
0
2
1
0
0
2
0
1
0
2
0
0
2
1
0
0
1
0
0
2
2
1
0
0
1
0
1
1
0
0
1
1
0
0
1
0
2
1
1
1
0
0
1
1
0
1
1
0
1
2
0
0
2
1
0
0
1
2
0
1
0
0
0
1
0
2
0
0
3
0
0
2
0
0
0
0
1
0
0
0
0
0
2
1
1
2
2
2
0
0
4
0
1
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
1
0
1
1
0
1
1
1
0
1
2
0
1
1
1
2
1
0
0
3
1
0
0
1
2
0
1
0
1
2
0
0
0
2
2
1
0
0
0
2
2
0
1
0
0
0
0
0
1
1
1
0
1
1
0
0
0
0
2
0
2
2
0
0
0
1
1
1
1
2
2
0
1
0
0
1
0
0
1
0
2
2
0
0
2
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
1
1
0
1
0
1
0
1
2
0
0
0
0
0
1
1
0
0
0
1
0
4
2
0
0
0
0
3
0
0
3
0
2
0
3
0
0
1
0
0
1
1
1
0
2
1
0
2
0
0
0
0
0
1
1
0
0
0
2
0
2
0
1
0
1
2
2
0
2
1
0
0
1
1
1
0
2
2
0
0
2
0
1
1
1
2
0
0
0
0
2
0
2
2
1
1
2
1
0
0
0
0
1
1
0
1
0
0
1
1
0
0
2
1
0
2
0
3
0
1
0
2
1
1
2
1
0
0
1
2
2
0
1
2
0
0
0
1
1
0
0
1
1
1
1
2
1
0
0
0
0
0
1
0
1
0
0
2
0
1
0
0
0
0
2
0
1
0
0
1
0
2
0
0
0
0
1
0
1
0
1
0
1
1
0
0
0
0
0
1
2
0
0
1
2
1
0
0
1
0
0
0
1
0
2
1
0
0
0
2
0
1
0
1
0
2
1
1
1
1
0
0
2
0
0
0
1
0
1
0
1
0
2
0
1
2
1
2
0
0
1
1
0
0
1
0
2
0
1
0
2
2
0
0
1
0
0
1
2
0
0
0
2
2
2
1
2
0
0
0
0
0
0
0
0
0
2
0
0
1
1
4
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
3
1
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
2
0
0
0
2
1
0
0
0
0
1
0
0
0
1
0
2
0
0
1
0
4
2
2
1
2
0
1
1
0
2
2
0
0
2
0
3
1
1
1
0
0
2
0
2
0
1
0
0
2
1
0
0
0
2
0
0
1
0
0
0
1
0
0
2
2
0
0
0
1
1
0
2
0
2
2
0
0
0
1
0
2
3
1
1
2
0
1
0
1
0
2
0
1
1
0
0
2
1
1
2
1
0
0
1
0
2
1
0
0
1
2
0
1
1
0
1
2
0
0
2
1
2
0
0
2
2
0
2
0
0
1
5
1
2
0
1
1
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
1
0
0
2
1
1
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
2
0
1
0
0
0
0
3
0
2
0
0
2
0
0
0
2
1
0
2
1
0
0
0
0
0
1
1
0
0
2
0
1
0
2
1
2
2
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
2
4
1
1
0
0
0
2
0
0
2
0
2
0
0
0
1
0
1
1
1
0
1
0
1
0
1
0
2
0
1
0
0
1
0
0
2
1
0
0
0
0
0
2
2
2
3
1
1
0
0
1
1
2
2
1
1
2
0
1
2
1
1
0
1
1
2
2
1
1
2
0
0
1
1
0
0
0
0
3
1
2
1
0
0
0
1
0
2
0
0
0
0
2
2
2
2
0
1
0
1
0
0
2
1
0
1
1
2
0
0
0
0
1
0
0
0
3
0
1
0
2
0
0
0
0
0
5
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
2
2
0
1
0
2
1
0
1
1
0
1
0
0
0
1
1
2
0
1
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
2
0
1
2
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
1
0
2
2
2
0
0
1
2
0
1
0
0
1
0
0
1
0
0
0
0
0
0
2
1
1
0
0
0
4
1
0
1
0
1
0
1
2
0
2
1
0
0
2
1
0
1
2
1
1
0
1
0
1
0
0
0
1
1
0
2
1
1
0
2
0
2
1
0
0
2
2
1
0
1
2
0
1
2
2
1
0
0
1
0
0
1
0
1
0
2
2
0
1
1
1
0
1
2
1
1
1
2
0
0
0
0
0
0
0
0
1
0
0
2
1
1
0
1
0
2
0
0
0
0
1
0
1
2
0
0
2
0
1
0
1
0
0
1
0
0
1
0
0
0
2
0
1
0
0
3
0
1
1
0
1
0
2
2
0
1
0
0
2
2
2
1
1
0
0
0
0
0
2
1
0
0
1
0
0
1
0
0
2
2
2
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
1
2
0
1
0
0
2
1
2
1
0
0
0
0
1
2
2
0
2
0
0
0
1
1
0
0
2
2
0
0
1
0
0
3
0
0
1
0
0
0
0
1
3
2
0
0
0
2
1
0
1
0
1
0
1
0
2
1
0
1
0
0
2
1
1
0
0
1
1
2
2
0
1
0
0
0
0
3
3
1
0
4
0
0
0
0
1
0
0
2
0
1
0
2
0
0
0
0
1
0
0
0
0
0
1
1
0
1
2
2
0
0
2
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
1
2
0
2
0
0
0
0
0
2
0
1
1
0
2
0
0
2
0
1
0
0
2
2
2
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
1
0
2
1
1
1
0
0
1
0
1
0
1
1
0
0
0
0
1
1
3
0
2
1
0
1
0
1
0
0
1
2
1
0
1
2
1
0
3
2
1
1
0
1
0
0
2
2
1
1
0
0
0
0
2
1
1
1
1
0
1
0
2
1
0
1
1
0
1
0
1
1
0
2
0
0
1
2
2
1
0
0
2
3
1
0
1
0
0
0
0
2
1
3
0
0
0
1
2
1
1
2
0
2
0
0
0
1
0
1
0
2
0
2
0
0
1
1
2
1
2
0
2
3
0
2
1
2
0
2
1
4
2
1
2
2
0
1
0
0
1
1
1
1
0
1
0
0
1
0
3
0
0
2
0
2
1
1
0
2
1
0
0
0
1
0
0
1
1
0
1
0
1
0
1
0
0
0
2
0
0
2
2
2
1
0
1
0
2
0
1
0
2
0
2
0
0
0
2
1
2
0
1
2
0
0
0
0
0
2
0
2
0
2
1
1
0
1
0
0
0
1
0
3
0
0
1
0
0
0
2
0
2
2
0
2
1
0
2
1
1
2
0
0
1
0
0
0
0
0
1
2
2
1
0
1
0
2
0
0
0
0
0
1
1
2
0
0
2
1
0
1
0
0
0
0
0
1
2
2
0
0
2
2
1
0
2
2
2
0
0
1
1
0
1
1
0
0
0
0
1
1
2
2
1
0
1
0
0
0
0
0
0
0
1
1
2
0
0
0
0
1
1
2
1
1
2
1
0
1
1
2
2
0
1
0
1
0
0
0
0
2
1
0
1
0
1
3
2
0
1
2
1
0
0
2
2
1
1
2
0
0
0
1
1
0
2
2
0
2
2
2
1
0
0
0
0
0
1
1
2
0
0
0
1
2
0
2
0
1
1
0
0
0
0
0
0
0
0
2
0
2
2
1
0
2
0
0
0
1
0
2
0
0
2
1
0
1
3
2
0
1
0
0
0
2
0
0
1
1
2
2
0
1
1
0
2
0
0
0
1
2
0
0
1
2
1
2
0
0
2
0
0
3
0
0
1
0
0
1
0
0
0
1
0
1
1
0
2
2
3
0
0
0
1
2
2
1
3
1
1
0
0
0
1
0
0
0
0
0
2
2
1
0
1
2
1
2
0
0
0
0
0
1
0
0
0
3
0
1
0
2
0
0
1
0
0
2
0
0
0
1
1
1
0
1
0
0
3
0
2
2
0
0
1
0
0
1
0
2
2
1
1
0
0
2
1
0
0
2
0
0
0
1
1
0
2
0
0
0
1
0
2
0
1
1
0
0
2
0
1
2
0
0
1
1
0
2
2
0
0
2
1
1
0
2
2
0
2
1
1
0
0
1
0
1
0
0
0
0
1
2
1
0
0
0
0
1
2
1
1
1
2
8
2
0
0
0
1
0
0
0
0
0
0
0
1
2
0
1
1
2
1
0
1
0
0
1
1
0
0
4
0
1
0
1
0
0
0
1
0
0
2
0
1
1
0
0
0
2
2
1
0
1
3
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
2
0
0
1
0
2
1
0
0
0
2
0
0
2
0
3
1
1
0
2
1
0
0
0
1
1
1
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
2
0
2
1
1
0
0
0
2
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
1
2
0
2
1
1
0
0
0
2
1
1
0
1
0
0
0
0
0
1
0
0
0
2
0
1
1
0
0
0
0
2
0
0
0
1
0
2
1
2
1
1
0
0
0
0
0
0
0
0
3
2
0
0
2
2
1
1
1
1
0
1
0
3
0
0
0
2
1
0
0
0
2
0
1
2
2
2
1
0
0
0
0
1
1
0
0
0
0
0
2
0
0
1
0
1
0
1
1
2
1
1
2
0
1
0
0
0
0
0
0
2
0
0
2
0
1
1
1
1
0
2
0
2
0
1
0
0
0
0
0
1
2
2
1
0
0
0
2
1
0
0
1
1
2
0
1
1
0
1
0
0
2
1
0
0
0
1
1
1
0
0
0
1
0
1
0
2
0
2
2
0
3
1
0
1
2
0
1
0
3
1
0
1
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
1
0
0
0
0
1
1
0
0
0
2
2
0
2
0
0
1
0
0
0
0
0
1
0
1
0
2
1
1
2
1
1
2
0
2
2
1
0
0
1
0
0
2
0
2
1
2
0
2
1
0
0
3
0
0
0
1
2
0
1
0
2
2
3
1
0
0
0
0
0
1
0
0
0
2
2
0
1
2
3
0
0
0
2
2
2
1
0
0
1
1
1
0
0
1
0
0
0
0
1
1
0
2
1
0
1
0
0
0
2
0
1
0
1
0
0
1
0
0
1
2
0
2
0
0
2
2
2
0
0
2
1
2
3
0
0
0
1
0
3
0
2
0
1
0
0
1
1
0
0
1
1
0
0
0
0
0
2
2
3
0
0
0
0
1
0
2
1
4
0
0
1
0
1
0
0
3
2
1
0
0
2
0
0
1
1
0
2
1
0
1
0
2
0
3
0
1
0
1
2
0
4
2
1
1
0
0
0
0
0
1
2
2
0
1
0
0
0
0
0
1
0
0
2
0
3
0
2
0
0
0
0
1
0
2
0
1
0
2
0
0
2
2
1
0
0
0
2
0
0
1
1
0
0
1
1
0
0
0
2
2
2
0
1
0
2
0
1
2
2
0
0
2
0
1
2
0
0
1
0
2
1
0
0
0
2
1
0
0
0
2
1
0
2
0
2
1
2
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
4
0
0
1
2
0
1
1
0
1
0
0
1
1
0
1
4
0
2
0
2
0
0
1
2
2
1
0
1
0
0
1
2
2
0
0
1
1
0
1
0
2
0
1
1
2
0
1
0
2
0
1
1
2
0
2
1
2
2
0
0
1
0
1
2
0
2
0
0
2
0
0
0
2
0
0
1
2
0
0
0
0
1
0
2
0
0
1
2
0
0
1
1
1
4
2
0
3
0
1
0
2
0
1
2
2
2
0
0
0
2
1
1
0
1
1
1
1
1
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
2
0
0
1
0
1
1
0
0
2
0
2
0
0
0
1
0
2
3
1
1
2
1
0
2
2
2
0
2
2
0
0
1
0
0
0
1
2
0
0
0
2
0
1
2
1
0
0
2
2
1
2
1
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
2
1
1
2
1
2
0
2
0
0
2
1
0
1
1
0
1
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
2
1
0
1
1
0
1
0
1
0
2
0
0
1
2
0
0
0
2
0
1
3
0
0
1
2
0
0
1
0
0
1
0
2
1
0
2
0
0
0
2
1
0
4
0
0
0
0
2
1
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
2
1
0
1
1
2
1
1
1
1
1
1
0
0
0
1
0
0
1
0
0
1
0
0
0
2
0
2
0
1
0
0
1
0
1
2
1
1
0
0
0
2
0
1
1
1
1
0
0
2
0
1
0
1
0
1
1
1
1
1
1
1
1
2
2
2
1
0
0
2
1
0
0
1
1
0
2
0
0
1
0
1
2
0
0
3
2
1
1
1
2
0
0
0
2
1
1
1
2
0
0
0
1
0
0
1
1
0
1
0
1
2
0
0
0
0
0
1
0
2
0
0
0
0
0
2
1
0
0
1
1
1
2
0
1
1
0
2
1
0
0
0
0
2
1
0
0
1
1
1
2
0
0
0
0
1
1
2
1
1
0
2
2
0
0
0
0
0
0
0
0
1
2
0
0
1
1
0
0
2
1
0
0
1
1
1
0
0
0
3
0
1
0
0
0
0
0
1
2
0
0
0
2
0
1
1
1
1
0
0
2
0
1
0
0
2
2
0
0
0
1
0
0
2
0
1
1
2
1
0
0
0
1
0
1
1
0
0
1
1
2
0
1
1
0
2
2
2
2
1
0
1
1
0
0
2
0
0
0
0
2
2
2
0
0
2
0
2
0
1
0
1
0
0
0
2
2
0
0
2
0
2
0
0
2
0
1
0
0
0
1
1
1
0
1
1
0
0
0
1
2
1
0
1
2
2
0
1
1
0
0
1
0
0
1
0
0
0
0
2
1
0
1
0
0
2
1
0
0
0
0
0
0
0
1
2
1
1
0
1
0
2
1
2
1
0
2
1
0
0
0
0
0
2
0
0
0
0
1
0
1
0
1
2
2
1
2
0
3
1
1
0
1
0
2
1
1
0
2
0
1
0
1
2
0
1
2
2
0
1
0
1
1
0
0
0
0
0
0
0
3
2
0
0
1
0
0
1
0
1
0
0
0
0
1
1
2
1
2
0
2
1
0
0
2
1
1
0
0
0
0
0
2
0
0
1
0
1
0
2
1
2
2
1
1
1
0
1
2
2
1
0
0
1
0
0
0
2
1
0
0
0
2
0
0
3
2
0
0
1
0
2
0
2
0
2
0
0
2
0
0
0
2
1
2
2
0
0
1
1
1
1
0
2
0
1
0
0
0
0
0
0
2
0
1
1
2
0
1
1
1
0
0
0
0
0
1
1
0
2
0
0
0
1
1
1
2
1
0
1
1
0
1
0
3
2
0
0
1
0
2
0
0
2
0
0
0
2
1
0
0
0
1
0
1
0
1
2
1
0
0
0
0
2
0
2
1
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
3
0
2
2
2
1
0
1
1
0
0
0
0
2
2
2
0
2
1
2
1
0
1
1
0
1
0
2
0
3
0
1
0
0
0
2
0
0
2
0
2
0
0
0
5
0
1
0
0
0
2
2
2
1
0
0
2
0
0
3
0
0
1
0
0
0
2
0
0
3
0
2
1
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
2
2
0
2
0
1
1
0
0
0
1
0
0
0
1
0
0
0
1
1
1
0
0
1
1
0
2
1
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
3
1
1
0
0
0
2
0
0
0
0
0
0
0
1
1
0
2
2
1
0
0
0
1
0
1
0
0
0
6
2
1
0
0
1
2
2
0
2
2
1
1
0
1
0
0
1
1
1
0
0
0
1
1
2
1
0
1
2
0
0
0
1
0
0
1
1
1
0
2
0
0
0
0
1
1
0
2
0
0
1
2
1
2
2
1
0
1
1
1
3
0
0
1
2
0
0
0
0
0
0
1
2
0
1
1
0
2
1
1
0
0
0
0
0
0
1
2
0
1
0
1
2
2
1
1
0
0
0
0
1
0
0
2
2
2
0
0
0
2
4
1
0
0
0
0
0
0
0
0
0
2
1
1
0
1
2
1
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
1
1
2
0
0
0
2
2
0
1
0
0
0
1
0
0
2
0
0
0
2
4
1
0
0
2
1
1
0
2
2
2
0
1
1
0
0
0
1
0
0
0
0
1
2
0
0
2
1
0
0
1
1
0
1
0
1
0
0
1
2
0
2
0
0
0
0
0
0
2
0
1
2
1
1
0
2
1
1
0
0
3
4
1
1
0
0
0
1
0
0
2
0
0
1
1
0
0
2
1
0
0
0
2
2
1
2
0
0
0
0
0
0
1
0
1
0
3
1
0
1
0
0
0
1
2
0
0
2
2
0
2
0
0
0
2
1
0
0
5
0
1
1
0
0
0
3
1
1
0
1
0
0
1
0
0
2
1
0
0
0
2
0
0
1
0
0
0
1
0
1
0
2
2
0
1
2
3
0
0
1
0
1
2
0
0
0
1
1
0
1
1
2
3
0
1
0
0
2
0
3
1
1
0
1
0
0
0
0
0
1
0
0
1
1
2
2
2
0
0
2
0
0
0
1
1
2
1
2
2
1
2
0
1
0
2
2
0
0
0
0
1
1
0
2
2
1
1
0
0
0
1
0
2
2
0
2
0
0
0
0
2
0
1
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
1
0
1
1
0
2
1
0
1
2
1
1
2
1
2
0
3
1
0
0
0
0
0
0
0
0
2
1
2
2
0
2
0
1
1
0
0
0
0
2
2
0
0
0
0
0
1
2
0
0
0
0
0
2
0
1
1
0
0
0
0
2
1
1
0
2
0
2
0
1
1
2
1
0
2
0
0
2
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
1
6
0
2
1
0
1
0
2
2
1
0
1
1
0
1
0
0
2
1
1
2
0
1
0
0
0
0
1
0
0
2
0
1
1
0
2
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
2
2
1
2
0
2
2
1
0
0
0
0
2
0
0
1
0
0
0
2
0
2
0
0
0
1
1
0
1
0
1
0
0
0
0
1
0
1
2
0
0
1
0
0
0
0
0
0
1
0
0
1
1
2
0
1
0
2
1
0
0
0
0
0
1
0
2
0
0
1
1
0
1
2
0
0
1
2
1
0
1
1
1
2
0
1
0
0
0
1
0
2
0
0
2
0
0
0
0
0
1
0
2
1
2
0
1
1
1
1
0
0
1
2
0
0
0
1
1
0
2
1
2
2
1
0
0
0
3
1
0
0
1
1
2
2
0
0
0
0
0
0
0
0
0
4
2
0
0
1
0
1
1
1
0
0
0
1
2
2
0
2
0
1
0
0
0
2
0
0
2
2
0
0
0
0
0
0
2
0
0
2
1
0
1
0
1
1
1
0
0
0
1
0
2
0
0
0
1
2
2
0
1
1
2
1
1
3
1
1
1
0
0
0
1
0
2
1
1
2
0
1
1
0
0
0
3
0
1
2
2
1
1
1
3
1
1
2
2
0
1
1
1
2
0
0
1
2
2
2
2
1
1
0
0
1
0
0
0
1
2
0
1
2
2
0
2
1
0
2
2
0
0
1
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
2
1
0
1
1
1
0
1
0
0
0
0
0
1
1
1
0
0
0
2
0
0
0
0
0
1
1
0
0
3
2
1
1
1
0
0
1
0
2
1
0
0
1
1
1
0
0
0
0
2
1
0
0
0
0
0
2
2
0
2
0
2
3
0
2
0
0
1
1
0
4
1
1
2
0
0
0
1
1
0
1
1
1
1
2
2
0
1
2
0
1
0
2
0
0
0
0
2
0
1
0
0
2
2
0
2
0
1
0
1
0
0
0
1
0
1
0
0
0
1
1
1
2
0
0
0
0
0
2
0
1
0
1
1
0
0
2
2
0
0
1
2
5
1
0
0
1
0
0
2
1
0
2
0
1
1
1
1
0
2
1
2
1
1
2
1
0
0
2
0
1
1
1
0
0
1
2
0
0
2
0
0
1
0
0
0
1
2
2
1
0
1
1
0
0
1
0
0
0
2
0
2
0
2
0
2
2
3
1
2
0
2
2
1
2
1
1
0
0
2
0
0
1
1
0
1
3
0
2
0
2
0
1
0
1
1
1
0
0
0
2
2
0
3
2
0
0
1
1
2
1
0
2
1
2
0
1
1
0
0
2
1
0
2
0
2
0
1
2
1
0
2
1
0
4
0
2
0
1
1
0
1
1
0
1
2
0
0
0
2
0
0
0
3
1
0
1
1
0
2
1
1
2
2
0
2
1
2
1
2
1
0
3
0
1
1
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
2
0
0
1
0
0
0
0
1
1
0
0
0
2
0
0
0
0
1
0
2
0
1
0
2
0
2
0
1
1
0
0
2
0
0
0
2
1
1
1
0
0
1
0
0
0
1
2
0
0
2
2
0
1
0
1
0
0
1
0
0
2
0
1
0
0
1
0
3
2
2
0
0
0
2
0
1
0
2
0
1
0
2
0
1
2
0
2
2
3
0
1
2
0
2
2
0
0
1
0
0
3
1
0
0
0
0
1
0
0
2
1
1
0
0
0
2
0
0
0
1
2
0
0
1
0
0
1
1
2
1
0
1
1
2
2
0
2
0
0
0
1
2
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
2
2
1
0
0
1
0
2
0
0
0
1
0
2
1
0
1
0
0
2
2
0
1
1
1
0
0
0
1
1
0
0
2
1
2
0
0
1
2
0
1
2
0
2
0
0
1
4
2
2
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
2
0
1
0
2
1
0
2
0
2
1
0
1
1
0
1
0
0
1
1
1
1
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
1
1
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
2
1
0
1
0
2
4
0
0
2
1
1
2
0
0
0
0
0
0
1
0
0
0
1
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
2
1
1
2
2
1
0
1
1
1
0
0
0
1
0
2
0
1
2
2
1
2
0
0
1
1
0
0
0
0
1
0
1
2
0
2
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
1
2
0
1
2
0
2
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
1
0
1
4
0
1
0
2
1
0
0
0
1
2
0
0
0
1
1
0
0
2
0
1
1
1
0
1
0
1
1
0
1
2
0
0
0
1
0
1
1
1
0
0
1
1
2
1
1
0
1
0
0
0
2
0
2
0
0
1
0
0
0
0
0
1
1
0
0
0
1
2
0
0
2
2
1
2
0
0
1
0
1
0
2
2
1
1
0
0
1
1
0
2
0
0
2
1
2
0
2
1
0
1
3
0
1
0
0
1
0
1
1
2
0
1
1
2
0
1
0
2
2
1
0
2
2
2
1
2
0
0
2
1
0
0
1
0
0
3
0
1
1
1
0
2
0
1
2
2
1
0
0
2
2
0
0
1
0
0
0
0
0
0
2
0
1
2
0
1
1
0
0
0
2
0
1
0
1
0
2
1
0
1
1
0
0
0
2
0
0
0
0
2
0
0
1
1
1
1
0
1
2
2
0
0
0
0
0
1
0
0
0
2
0
1
2
2
1
1
2
1
3
0
0
0
1
0
0
0
1
0
0
0
0
2
2
0
0
2
1
0
2
0
2
0
0
0
1
2
1
2
0
0
0
0
1
1
0
1
0
2
2
0
0
0
0
0
0
2
0
1
1
0
0
2
0
0
0
0
1
0
0
0
2
0
0
2
0
2
1
1
2
0
1
0
0
0
1
1
1
0
1
1
2
0
1
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
3
0
0
1
3
0
0
0
0
0
0
1
1
0
2
0
1
1
1
1
0
0
1
0
1
0
0
2
0
1
0
1
0
4
1
2
2
1
0
1
2
0
0
0
1
0
0
0
0
0
0
1
2
2
1
2
3
1
0
0
0
2
2
1
0
2
0
1
0
1
2
1
0
2
1
2
1
2
1
1
1
0
0
2
0
0
0
0
1
0
2
2
0
1
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
2
2
2
1
1
2
0
1
1
0
0
2
1
1
2
0
2
1
1
0
1
1
3
1
0
1
0
1
0
2
3
0
0
0
0
1
0
0
1
0
1
0
1
0
0
2
1
0
0
0
1
0
1
0
2
0
1
0
0
0
1
2
0
0
2
0
2
0
0
2
1
2
1
1
2
0
2
2
1
0
0
1
2
0
0
0
2
0
2
1
2
0
2
1
0
2
0
0
2
0
0
1
0
0
0
0
1
1
0
0
1
0
1
2
0
0
1
2
3
2
1
1
0
2
0
2
0
0
2
0
0
1
1
1
2
0
0
0
0
1
0
2
0
0
2
0
0
1
4
0
0
1
0
0
5
2
1
0
2
2
1
1
0
0
1
1
1
0
0
0
2
0
0
2
1
3
5
0
0
0
1
2
4
0
1
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
2
5
1
2
1
1
0
2
0
0
1
2
0
0
0
2
0
0
1
1
2
0
0
2
2
2
0
0
0
1
0
2
0
0
2
2
0
2
0
1
0
2
1
1
3
0
0
0
0
1
0
0
0
0
0
3
0
0
2
1
1
1
1
2
1
1
1
0
1
2
0
0
0
0
0
1
0
0
2
0
2
2
0
1
0
0
0
1
0
1
2
0
0
0
1
2
1
1
2
2
0
1
0
1
0
2
2
0
3
1
2
2
0
0
1
0
1
1
0
0
3
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
2
1
1
0
2
0
1
0
0
1
0
1
2
1
1
0
1
0
2
0
0
0
1
1
2
0
2
0
1
1
0
1
1
0
1
1
1
1
0
1
0
1
1
0
1
1
0
0
1
2
0
1
1
0
1
0
1
0
0
2
0
1
2
0
1
0
0
1
0
0
1
0
0
1
1
0
0
0
1
1
0
0
2
0
2
1
1
1
0
2
1
1
0
0
0
1
3
0
2
1
2
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
1
0
1
1
0
2
2
0
0
0
0
0
1
1
1
0
2
0
1
0
0
1
1
0
2
2
0
0
2
0
2
0
0
1
2
1
0
0
1
0
1
1
1
2
0
1
0
1
1
1
0
1
0
1
0
1
1
0
0
0
0
2
0
0
1
0
0
0
0
1
2
0
0
0
1
0
0
1
1
1
1
1
0
1
0
0
0
1
3
0
2
1
0
1
1
0
3
1
0
1
0
1
0
1
2
0
2
0
1
0
0
1
1
0
0
2
0
2
0
1
1
0
2
2
1
0
2
0
0
0
1
2
1
0
0
0
0
0
0
2
0
0
0
1
1
0
0
2
2
0
0
1
2
0
2
2
3
1
1
1
0
1
0
1
0
0
0
0
1
0
2
2
1
0
0
0
0
1
0
0
0
0
1
0
0
2
2
1
1
1
1
2
0
0
2
0
1
0
0
0
0
1
2
0
0
1
0
0
0
1
2
1
0
0
1
0
2
1
0
0
1
1
1
0
1
0
2
1
1
1
1
0
1
1
0
0
0
0
0
3
3
2
0
2
0
2
0
0
1
0
0
2
0
0
0
0
2
2
0
4
2
1
0
1
0
0
0
0
0
1
2
1
2
0
2
1
0
2
1
0
0
1
1
0
1
0
1
0
2
0
2
0
0
1
0
0
1
2
0
1
1
0
1
0
0
0
0
2
0
0
1
0
2
0
1
0
0
1
0
3
0
0
0
0
1
0
1
2
1
0
1
1
1
0
2
2
1
0
2
0
1
2
0
0
2
0
0
2
0
2
2
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
2
0
3
2
0
0
0
0
0
0
2
0
0
1
0
0
2
2
0
0
0
0
0
2
0
0
2
2
0
1
1
0
0
0
0
0
0
4
1
1
0
0
1
0
0
0
2
1
0
3
0
1
0
3
0
0
1
1
0
0
0
0
0
0
2
1
0
2
2
0
0
1
1
0
1
1
0
1
0
0
2
0
0
1
0
0
0
0
1
0
2
2
1
2
0
0
0
0
1
3
0
0
1
1
6
3
0
0
2
1
2
0
0
1
0
0
0
2
1
2
2
2
1
1
2
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
2
1
1
2
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
1
2
2
0
0
0
1
2
0
0
1
2
1
0
1
0
1
2
0
0
0
2
1
0
3
1
0
2
1
1
1
2
0
2
0
0
0
2
1
1
1
1
0
1
0
0
0
0
1
0
0
1
1
1
1
1
1
0
1
0
2
0
2
1
0
0
0
2
2
0
2
0
3
0
0
0
1
2
2
1
0
0
0
2
0
0
2
0
0
0
1
0
2
0
2
0
2
0
0
0
2
1
0
0
0
1
1
1
2
1
1
0
0
0
1
0
0
0
1
0
1
1
2
1
0
0
0
0
2
1
0
1
0
0
0
0
0
0
1
0
2
1
0
0
0
2
1
0
0
1
0
0
1
0
0
0
2
2
1
1
1
1
0
0
1
2
0
1
0
1
1
1
0
0
0
2
0
0
0
2
1
1
1
0
2
2
0
1
2
2
0
2
0
0
1
2
0
2
0
0
1
0
2
2
2
1
1
0
0
0
0
0
0
0
0
0
4
2
1
1
0
0
0
0
0
1
2
1
0
0
0
0
0
1
0
0
0
1
2
2
2
1
0
0
0
2
0
0
2
0
2
2
1
1
1
0
0
2
2
2
2
0
0
2
0
2
0
0
0
1
2
0
0
2
0
1
1
1
1
1
0
1
1
0
1
0
3
0
0
1
1
1
1
0
1
0
0
0
1
3
2
2
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
1
2
2
1
1
1
0
3
2
1
0
1
0
0
0
0
1
1
0
1
2
2
1
0
0
2
1
0
0
0
0
2
0
0
1
0
0
2
0
0
1
1
0
0
2
2
1
1
0
0
0
0
0
1
5
0
0
0
1
0
0
0
0
0
1
2
2
1
0
0
0
0
0
2
2
0
3
2
2
2
3
0
0
2
1
0
1
2
0
0
1
0
1
0
2
1
0
1
0
2
0
2
0
3
2
1
1
0
0
0
1
1
0
1
0
0
1
1
1
1
0
2
2
1
0
0
1
2
1
1
1
2
0
2
1
0
1
0
1
2
0
0
0
0
0
2
1
0
1
0
2
0
0
1
1
1
0
0
0
1
2
0
0
0
2
1
0
1
2
2
2
1
1
1
1
0
1
0
1
0
0
5
0
1
0
0
1
0
0
0
2
1
0
0
2
1
1
2
0
1
0
0
1
1
0
1
0
0
1
0
0
2
1
0
0
2
0
0
1
1
0
0
0
3
0
2
0
1
1
0
2
0
0
0
0
0
1
1
1
1
2
0
2
0
0
0
0
1
2
2
0
2
1
0
0
0
1
0
1
0
0
1
0
0
1
2
1
1
2
0
0
0
1
3
2
1
0
0
0
2
2
0
1
0
5
0
0
0
0
1
0
2
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
1
0
0
2
1
2
0
2
0
0
0
4
0
2
1
1
1
0
0
0
1
0
1
2
3
0
0
3
0
0
1
0
2
0
0
2
2
0
0
1
1
1
0
1
1
0
0
2
0
0
1
1
0
0
1
2
1
2
2
1
0
7
1
0
0
0
1
0
0
0
0
0
1
0
0
1
2
0
2
0
1
0
1
0
0
0
2
2
0
0
0
1
1
2
0
1
1
3
0
1
1
1
4
1
0
1
1
1
0
2
1
0
1
0
0
0
1
2
2
0
0
1
1
1
0
0
0
0
0
0
1
0
0
2
0
0
1
1
1
0
1
0
2
0
1
0
0
1
1
2
0
2
1
0
1
0
0
1
1
2
0
1
0
0
0
1
0
1
1
2
0
0
0
0
1
1
1
0
2
1
3
2
4
1
0
0
2
1
0
0
0
0
2
2
0
0
1
1
1
0
1
2
0
5
0
0
0
0
1
2
0
0
0
0
2
0
0
0
2
0
0
1
1
1
0
2
0
1
0
1
0
0
0
1
2
2
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
2
0
2
0
1
0
0
0
0
0
1
4
2
0
0
0
5
1
0
0
2
2
0
2
0
2
0
0
1
1
0
2
0
0
2
1
0
2
0
1
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
2
1
0
1
0
0
1
2
0
0
0
1
0
0
2
1
1
0
0
2
0
1
2
1
0
2
0
0
1
0
1
0
1
2
1
0
0
2
1
0
0
0
0
1
0
0
0
1
1
0
0
2
1
2
0
1
1
1
0
0
2
0
4
0
2
5
2
2
0
1
0
2
2
0
1
1
1
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
2
0
0
0
4
2
0
2
0
0
1
1
0
1
0
1
0
0
0
1
0
1
0
2
0
2
0
0
0
1
0
1
0
0
0
2
2
1
2
0
0
2
0
0
0
0
1
1
0
0
2
0
0
0
1
1
0
0
1
0
1
0
0
0
2
2
0
1
0
0
1
1
0
2
2
0
1
1
2
0
0
0
1
0
0
1
2
2
1
0
0
2
0
0
0
0
1
0
0
0
0
2
0
1
0
1
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
2
2
1
1
0
1
0
1
2
1
1
0
2
0
0
1
1
1
2
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
1
1
0
1
1
0
0
0
0
2
0
0
1
2
1
0
0
0
0
1
1
0
0
1
0
1
0
0
0
2
0
1
0
0
1
2
0
0
0
1
0
0
2
2
0
2
2
0
0
0
0
2
1
1
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
2
1
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
2
0
0
0
0
1
2
0
2
3
0
0
0
2
0
1
0
0
0
0
1
1
0
0
1
1
0
2
0
0
0
0
1
1
1
0
1
2
1
0
0
0
2
0
0
0
2
0
0
2
1
1
1
0
0
0
1
0
2
2
1
0
0
0
0
0
2
1
0
1
2
1
0
2
1
0
1
0
0
2
1
2
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
1
1
0
0
1
2
0
0
3
1
6
1
0
0
1
2
1
0
2
0
1
0
3
0
0
0
0
0
1
0
1
1
0
0
2
2
2
1
2
0
1
0
2
2
0
0
0
1
1
0
0
0
0
0
0
2
0
1
2
0
1
2
1
0
0
0
0
1
1
0
0
0
2
1
0
1
1
1
0
0
1
1
1
1
0
1
0
0
0
0
2
2
0
0
1
0
0
0
0
1
1
0
0
1
1
2
0
0
2
1
2
2
0
0
0
2
2
2
2
0
0
1
1
2
0
1
1
0
2
0
0
1
2
0
0
1
1
0
1
1
0
0
0
2
0
0
2
1
1
0
1
2
0
0
3
2
2
0
1
0
1
1
0
2
0
0
0
1
2
2
2
1
1
0
2
0
0
0
0
2
0
2
1
1
0
1
2
2
0
0
1
0
2
1
2
0
1
1
1
1
0
0
0
0
1
0
1
0
1
0
0
1
0
2
0
0
0
1
2
1
0
1
0
0
1
1
1
0
2
0
0
0
1
0
2
0
0
2
1
0
1
4
1
1
0
2
1
1
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
3
0
2
0
3
0
1
1
0
0
0
3
1
0
0
2
1
0
1
0
2
1
0
1
0
2
0
2
1
0
0
2
0
1
0
2
1
0
0
1
0
0
1
1
0
0
2
1
0
0
0
0
0
1
0
1
3
0
0
0
1
2
1
0
1
1
1
0
2
2
1
2
0
1
2
0
1
0
1
2
0
3
1
2
2
0
1
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
3
1
0
1
0
2
0
0
0
0
0
0
1
1
0
1
2
0
0
1
0
1
0
1
2
0
0
1
0
0
1
0
2
0
0
0
0
0
2
2
0
0
1
0
1
0
0
1
2
1
1
0
1
0
0
2
1
0
0
0
0
0
0
3
1
0
0
1
0
2
0
1
1
0
1
0
1
2
0
2
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
1
2
0
1
0
1
1
0
0
0
1
0
0
0
0
0
1
1
2
1
0
0
0
2
1
0
3
1
1
0
0
0
0
0
3
0
0
0
1
0
2
2
2
0
0
2
3
1
1
1
1
0
0
0
1
1
0
0
2
1
0
1
0
4
1
0
0
0
0
0
0
0
2
0
2
0
1
1
1
0
1
1
0
1
1
0
2
2
1
1
2
0
0
2
4
1
0
2
0
0
1
0
1
2
0
0
4
0
0
0
2
0
0
1
0
0
1
0
0
1
1
0
1
2
0
2
1
0
1
0
1
1
2
1
2
1
0
1
0
0
0
0
2
1
0
0
0
2
2
0
0
0
1
0
1
0
1
0
0
1
0
0
0
2
0
0
0
1
0
1
0
0
0
1
0
1
2
2
2
1
1
3
1
1
1
2
2
2
2
1
0
0
1
0
1
1
0
0
1
0
0
0
2
1
1
1
0
2
0
1
1
0
1
2
1
0
1
1
2
1
0
0
0
1
0
0
2
0
2
0
0
0
0
0
2
3
0
1
0
1
2
1
1
0
1
2
2
1
1
0
1
1
0
1
1
0
0
2
0
1
0
1
1
2
0
2
0
1
1
1
1
0
2
1
2
4
0
1
2
2
0
1
0
4
0
2
2
2
1
0
2
0
0
0
1
0
1
0
0
0
3
1
1
3
2
0
3
0
7
1
1
1
2
0
2
1
0
1
1
0
2
0
1
0
2
1
2
5
0
0
0
0
0
2
1
0
2
0
1
2
0
2
0
1
0
0
0
1
1
1
1
0
1
2
1
0
0
1
0
0
1
0
0
1
2
0
3
1
2
0
0
0
0
0
0
2
0
0
1
0
0
1
1
0
2
1
0
1
2
0
2
1
1
0
2
1
0
0
0
0
2
1
2
0
0
0
2
0
0
1
0
0
0
1
1
0
1
1
0
0
1
1
2
0
2
2
0
2
0
0
0
2
1
0
0
0
2
2
1
0
1
4
2
1
1
0
1
0
0
0
1
1
2
0
1
2
1
0
3
1
1
1
0
0
2
0
0
0
1
0
0
0
0
1
0
1
2
0
2
2
0
1
0
0
1
0
1
0
0
0
0
1
0
0
1
2
0
2
1
0
0
0
1
0
2
1
2
2
1
0
0
0
0
0
0
0
2
2
1
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
1
1
0
0
1
1
0
0
2
0
1
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
2
2
1
0
1
0
1
2
2
0
1
1
1
1
0
1
2
0
1
0
1
1
1
1
0
0
0
2
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
2
1
0
1
0
1
0
0
2
0
0
0
2
2
0
0
0
1
0
2
0
2
0
0
1
1
2
0
0
1
0
2
1
0
0
0
0
1
0
3
0
1
0
0
2
2
0
1
0
2
0
0
0
2
2
0
0
0
1
0
0
1
0
0
0
0
1
3
2
0
2
0
2
1
0
1
0
3
1
1
0
2
0
2
0
2
1
1
0
2
2
0
1
1
0
1
0
0
0
1
0
0
0
0
3
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
2
0
0
0
0
0
1
2
1
1
1
0
0
1
1
1
0
0
0
1
0
0
6
2
0
2
0
0
1
0
1
0
2
0
0
0
0
0
1
1
1
0
2
0
1
0
0
0
0
0
1
0
0
0
2
0
2
0
2
0
2
1
0
0
0
1
1
0
0
1
0
0
2
0
1
0
0
3
0
1
2
0
0
1
2
1
1
0
2
1
0
0
0
0
1
0
1
0
1
0
0
0
1
0
2
0
1
1
1
1
0
2
1
2
0
0
0
2
1
1
3
0
1
0
0
1
1
1
0
1
2
0
3
2
0
1
1
0
0
1
1
0
2
0
0
2
0
1
0
0
0
1
3
0
2
0
0
2
1
1
0
2
1
2
1
0
1
1
0
1
0
2
0
1
2
1
0
1
1
0
0
0
0
1
0
0
0
2
0
1
0
0
1
0
0
0
2
0
1
0
0
0
4
0
1
0
0
2
2
0
0
2
2
0
2
0
0
0
0
0
0
0
1
1
1
2
0
2
2
1
0
0
0
2
0
1
0
0
0
2
1
0
0
1
2
0
0
2
0
0
3
1
1
1
1
3
2
1
2
1
2
2
0
0
0
1
0
0
0
0
1
0
2
0
2
1
3
0
0
0
1
1
0
1
1
0
1
0
1
2
2
0
0
0
0
0
2
0
2
0
0
1
0
3
1
0
0
0
0
0
0
1
0
1
0
1
1
0
0
2
2
0
0
0
1
2
0
1
1
1
0
0
0
3
1
0
1
0
1
0
1
1
0
1
0
1
0
1
0
0
2
1
2
0
1
1
1
0
2
2
0
0
2
2
0
1
2
0
2
1
1
0
0
1
0
0
2
1
1
0
0
1
0
0
0
1
0
2
0
0
2
1
2
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
1
0
1
1
0
1
1
3
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
2
2
2
0
1
0
0
2
2
1
2
0
1
1
1
2
1
0
1
2
2
2
0
2
0
1
1
0
0
1
2
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
2
1
0
0
0
0
1
0
0
0
1
1
0
1
0
0
2
0
2
1
0
0
0
1
0
0
0
2
1
0
2
1
0
0
0
2
0
0
0
2
1
0
1
0
0
1
1
0
0
1
1
0
1
0
0
0
1
0
2
0
1
2
2
2
3
1
0
0
0
0
1
1
0
0
0
0
0
0
3
0
1
1
1
0
0
2
1
2
0
1
0
0
0
0
0
2
0
2
1
0
2
1
1
1
2
1
0
1
0
0
0
0
0
2
0
2
2
1
2
0
0
0
2
0
2
1
0
0
0
0
1
0
3
0
1
2
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
1
0
0
1
0
0
2
0
0
0
2
1
0
1
0
0
0
1
1
0
1
1
2
0
0
2
2
0
0
1
1
1
0
1
0
0
0
2
1
0
0
0
0
2
0
2
0
0
1
1
1
1
1
2
2
0
2
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
2
2
2
0
0
2
0
0
1
1
1
0
0
2
2
0
0
0
0
0
0
0
1
1
0
0
2
2
0
1
0
0
1
1
0
0
0
0
2
0
2
2
1
1
2
0
3
0
1
2
1
1
0
0
0
2
0
1
1
1
0
1
0
0
1
2
1
0
1
0
1
1
5
2
1
0
0
0
0
0
0
0
0
1
1
0
0
2
3
0
1
1
1
0
1
0
2
0
0
2
2
0
2
1
0
0
2
4
0
1
0
2
1
0
0
2
1
1
0
0
5
1
2
0
1
0
0
0
0
0
0
0
0
3
1
0
0
0
1
0
1
1
0
2
1
1
0
2
2
1
2
1
0
1
0
0
1
0
0
2
0
1
1
0
0
1
1
1
2
0
2
0
0
2
1
1
0
2
0
2
0
0
0
1
1
0
1
0
0
0
1
1
1
2
0
0
2
1
1
0
1
0
2
1
0
0
0
0
1
2
0
2
0
2
2
2
1
0
0
2
2
0
0
1
2
0
0
0
1
0
0
0
4
0
0
1
0
0
0
2
1
0
2
0
0
0
2
0
0
1
4
0
0
1
1
0
1
0
0
1
1
2
1
0
0
0
1
2
0
0
1
0
1
2
0
1
1
0
2
0
0
0
0
1
0
0
0
1
2
0
1
0
1
0
0
0
2
0
1
0
0
0
0
0
1
2
2
1
0
1
3
0
2
0
1
1
0
0
2
1
1
0
0
2
0
3
1
0
0
2
0
0
0
1
1
1
0
0
0
2
1
0
1
1
0
0
0
1
3
1
0
2
0
1
0
0
1
0
0
0
1
0
2
1
3
0
0
1
0
0
0
0
1
1
0
1
1
0
0
0
1
1
2
0
4
0
1
1
0
0
1
1
0
0
0
0
0
1
0
2
0
1
0
1
2
0
1
1
2
0
0
0
1
2
0
1
0
0
1
1
2
1
2
0
0
1
0
0
1
0
2
3
2
4
0
0
0
1
0
0
2
0
2
1
0
0
1
0
1
0
0
1
1
0
0
2
1
0
1
1
0
1
0
1
2
2
2
0
0
1
0
0
2
0
0
1
1
2
1
2
0
0
0
0
0
0
1
0
0
0
1
2
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
1
2
0
0
2
1
0
2
2
1
2
0
0
1
1
0
0
0
0
0
1
2
1
0
3
2
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
2
0
0
1
1
1
1
0
2
0
2
0
0
0
1
0
2
0
1
2
0
0
0
0
0
1
1
2
1
0
0
0
0
0
2
0
0
0
2
1
1
0
0
0
0
1
0
1
0
2
1
1
1
0
0
0
2
1
0
1
0
2
0
0
0
0
3
0
0
1
0
1
2
0
0
1
2
0
1
2
2
5
0
2
2
0
2
0
0
2
0
2
1
1
0
0
0
2
0
2
2
0
1
0
0
1
2
0
1
0
0
2
2
1
0
0
0
1
1
2
2
0
0
1
1
0
1
0
1
0
0
1
1
2
2
0
1
2
1
1
2
0
0
0
0
1
0
0
0
3
1
0
0
0
0
0
1
0
1
2
0
0
1
1
0
0
0
0
1
3
2
0
2
0
0
0
2
1
0
0
0
1
0
3
0
0
0
2
0
0
2
3
0
0
0
0
1
1
1
0
1
0
0
1
1
0
1
0
1
0
1
0
0
0
2
1
1
0
1
0
2
2
0
0
0
0
1
0
2
2
0
0
0
0
1
2
0
0
0
0
0
0
2
1
2
0
0
1
1
0
0
3
1
2
1
1
0
0
2
0
0
1
0
0
0
0
1
2
1
2
0
1
2
1
1
2
2
0
0
1
2
1
1
0
4
0
0
0
0
1
0
0
0
0
0
1
2
0
1
2
1
0
2
0
0
0
1
1
2
0
1
0
1
0
2
1
1
0
0
2
0
0
0
0
0
1
2
1
0
1
0
1
0
0
0
1
0
2
1
0
0
0
1
1
0
0
0
1
0
0
3
0
2
0
0
2
2
0
0
2
1
1
2
2
2
1
2
0
0
0
0
1
0
0
0
0
1
0
0
1
2
0
0
0
0
2
1
0
0
0
0
1
0
1
0
1
0
2
0
0
2
0
0
1
0
0
0
1
1
0
3
0
2
2
1
0
1
0
0
1
2
1
1
0
0
0
4
0
0
0
1
2
2
1
0
0
0
0
0
1
0
2
2
0
0
1
2
0
0
0
1
1
0
2
0
2
1
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
1
2
0
0
0
2
0
2
0
1
0
0
1
2
0
1
1
0
0
1
1
1
1
0
1
0
0
2
0
0
1
0
1
0
0
1
0
2
0
2
2
1
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
2
0
1
2
1
1
0
1
1
0
0
0
1
2
1
0
0
2
2
0
1
0
1
1
1
2
1
0
0
1
0
0
0
0
0
1
2
0
0
2
1
0
0
0
0
1
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
2
2
1
0
1
0
0
1
4
1
0
0
0
2
0
0
0
1
0
1
0
1
3
1
0
0
2
0
1
1
1
1
1
2
1
2
2
0
0
2
2
1
0
1
0
0
2
0
2
2
2
0
0
1
0
1
0
0
3
1
1
0
1
0
1
2
0
0
1
1
0
0
1
2
0
0
2
2
1
1
1
0
0
1
2
3
0
0
2
0
0
1
0
0
0
1
0
0
1
0
1
2
1
1
1
0
1
0
0
1
0
0
1
0
0
0
1
2
0
1
1
1
0
2
2
0
1
0
1
0
1
0
0
0
0
2
1
0
2
2
1
2
3
2
0
1
1
0
1
1
2
0
0
0
2
0
0
0
0
2
0
0
1
2
1
1
0
0
0
1
0
2
1
2
0
1
1
0
0
0
1
2
0
1
0
0
1
1
1
0
1
1
2
0
2
0
0
1
1
0
0
0
0
0
0
0
2
2
0
2
0
1
2
0
0
1
0
2
1
0
0
1
1
1
1
0
0
0
0
0
1
0
2
0
0
0
2
1
0
3
1
0
1
0
3
2
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
1
1
0
0
0
1
2
2
0
0
0
2
0
0
0
1
1
0
0
0
2
1
0
0
0
1
1
2
2
0
0
1
2
1
0
0
0
2
1
2
1
0
0
2
2
0
2
0
1
0
2
0
1
2
0
0
0
3
0
0
0
2
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
1
0
2
0
1
1
2
2
1
2
0
2
1
1
1
0
1
0
0
1
0
1
2
0
0
1
2
0
2
0
0
1
2
0
0
0
0
1
1
0
0
0
0
2
0
0
0
2
0
2
2
0
1
0
0
0
0
0
0
2
0
0
0
0
2
1
1
0
1
0
0
0
0
1
2
0
1
1
2
2
1
0
2
0
0
0
1
0
0
0
0
2
1
0
0
0
1
0
0
2
1
0
2
1
1
0
2
2
0
0
0
1
0
2
2
0
1
2
0
0
2
1
2
0
0
2
2
0
0
1
0
0
2
0
1
0
2
2
0
0
2
3
0
2
0
2
2
0
1
1
0
3
2
0
1
0
3
2
2
3
1
1
2
0
2
1
1
0
0
4
1
1
0
0
2
0
0
1
1
1
1
2
2
3
2
0
0
0
1
2
0
1
2
0
1
3
0
0
0
0
2
1
1
0
3
1
1
2
1
1
1
1
2
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
1
0
0
1
0
0
1
2
0
2
1
4
0
1
2
2
0
0
0
2
0
2
0
1
1
2
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
2
0
0
2
0
1
0
1
0
1
0
0
0
2
2
2
1
1
0
0
1
2
2
2
2
2
0
2
1
2
0
0
0
0
0
0
2
3
0
1
0
0
1
2
1
1
2
0
1
0
1
1
1
0
2
0
2
2
2
2
0
0
1
2
0
1
0
0
2
0
0
1
2
1
2
0
2
0
0
1
0
1
3
1
2
2
2
1
2
0
0
0
0
0
0
2
1
1
1
0
0
2
0
0
1
1
0
1
2
2
1
1
2
1
1
1
0
0
0
1
0
3
2
0
1
0
0
0
0
0
2
0
1
2
1
0
1
0
0
0
0
1
2
1
1
0
0
0
2
2
1
0
0
0
1
1
0
0
2
0
0
1
0
2
0
1
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
2
1
2
0
0
1
0
0
1
2
0
0
0
0
1
1
0
0
0
1
1
0
0
2
0
0
1
0
0
2
0
2
0
0
0
0
1
3
1
1
2
0
1
2
0
0
0
1
2
1
1
0
1
0
0
0
0
2
3
0
1
0
0
0
2
0
0
0
0
0
2
0
2
0
2
0
0
0
0
1
0
0
2
0
0
0
0
2
1
0
1
1
0
0
1
0
0
0
2
1
1
0
1
0
0
1
0
0
1
0
0
1
0
1
1
0
0
0
4
0
1
0
1
1
2
0
1
0
0
0
2
0
1
1
0
2
1
3
0
2
0
1
2
1
0
1
0
0
0
0
0
1
0
0
0
0
4
3
1
0
0
0
2
2
0
0
2
1
0
0
2
0
0
0
2
0
0
0
0
2
2
0
2
0
2
1
0
2
1
0
2
2
1
2
0
0
0
0
0
1
0
1
1
1
0
1
2
0
0
2
1
1
0
1
1
0
1
2
2
0
0
1
2
0
2
1
1
1
0
0
0
0
2
0
1
0
2
0
1
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
1
1
2
1
2
0
0
1
0
1
1
0
0
0
1
0
1
0
0
0
0
0
2
2
0
0
1
0
2
0
0
2
3
2
2
0
0
0
0
0
0
6
0
0
0
2
0
1
0
2
2
0
1
0
0
0
2
1
2
1
1
0
2
2
1
2
0
1
1
0
3
0
0
2
2
1
0
0
2
0
1
1
2
0
1
0
0
2
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
1
0
2
0
2
0
0
2
0
0
1
2
0
0
0
0
2
0
1
0
1
0
1
0
0
2
0
0
0
2
1
0
1
2
0
1
1
2
0
0
2
2
0
1
0
0
1
0
2
2
1
1
0
0
0
0
0
1
0
2
0
0
1
1
1
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
2
2
2
1
0
1
0
0
1
1
1
0
1
1
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
2
1
4
0
0
0
0
1
2
0
2
1
0
1
0
0
1
0
0
0
0
0
1
1
1
0
1
2
0
1
0
2
0
1
0
0
2
0
0
2
0
2
1
2
0
0
3
0
0
2
0
0
0
0
1
0
0
0
2
1
0
2
0
1
0
1
2
0
1
0
0
0
1
0
0
0
2
0
1
0
0
1
1
1
2
0
0
0
1
0
1
1
2
0
1
0
1
0
0
0
0
0
2
2
2
1
0
0
1
0
2
1
0
1
2
1
0
2
0
0
0
0
0
0
0
0
2
1
0
2
2
0
0
0
0
1
0
1
1
0
0
0
0
1
0
2
0
0
1
2
1
0
2
1
0
2
2
0
1
1
1
1
0
0
0
1
2
0
2
1
2
2
1
2
0
0
0
0
0
2
0
0
0
0
1
1
0
1
0
0
2
0
0
1
0
2
0
0
1
0
0
0
2
2
0
2
0
1
2
2
0
1
0
0
2
1
1
2
0
0
1
1
0
3
0
0
1
1
2
1
1
2
0
0
1
2
0
1
1
0
0
2
0
0
1
0
0
0
1
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
2
1
0
1
1
1
0
0
0
2
2
1
0
0
2
0
0
2
1
1
0
1
2
2
0
0
0
0
0
0
2
0
1
1
1
1
1
2
0
1
2
0
0
2
1
0
2
1
1
0
0
2
0
0
0
1
2
0
0
1
0
0
0
0
0
0
1
1
0
0
0
2
1
0
1
0
0
0
1
0
0
0
0
2
1
2
0
0
0
0
0
1
1
0
0
1
0
1
2
0
0
2
0
2
0
1
0
2
0
1
0
0
1
2
0
1
0
2
0
0
1
0
0
0
0
2
0
0
0
3
0
0
2
0
0
2
0
2
0
1
1
1
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
1
2
0
1
0
0
4
1
2
1
0
0
0
0
0
3
1
0
1
1
3
0
1
0
0
0
1
0
1
1
0
1
0
0
0
0
3
0
1
1
0
0
2
1
2
1
2
0
0
1
0
0
0
0
1
0
0
2
2
0
2
2
1
0
2
2
0
2
2
0
0
0
0
2
1
0
2
0
1
0
1
0
0
0
0
2
1
0
0
0
2
2
0
0
0
1
1
0
1
2
0
0
0
2
0
0
1
0
2
0
2
0
0
1
1
0
0
0
0
1
0
2
0
0
1
1
3
0
0
0
1
2
0
0
0
1
1
2
1
2
1
2
0
0
0
0
0
1
1
1
0
1
0
1
0
1
2
0
1
0
0
0
1
2
1
1
2
1
0
0
1
0
2
2
0
1
0
1
0
0
2
0
1
1
2
0
1
2
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
2
1
1
0
0
0
1
0
2
0
0
0
3
2
1
2
1
2
2
0
1
0
0
0
1
2
0
0
0
0
1
0
0
2
0
1
2
0
0
2
2
0
0
1
0
0
0
2
1
2
0
0
0
0
1
2
3
1
2
1
2
2
1
1
0
2
0
0
1
0
0
2
1
1
0
0
2
1
2
0
0
1
1
0
2
0
0
2
1
0
2
1
2
1
0
0
2
1
0
0
0
0
1
2
0
0
0
1
0
2
2
0
0
0
1
0
1
1
0
2
1
2
2
2
1
0
0
2
1
1
1
2
0
0
0
0
1
0
2
1
0
1
0
1
2
0
0
1
1
2
0
0
0
0
1
0
0
1
0
0
0
3
0
1
0
0
0
4
0
0
0
2
2
0
0
1
2
0
1
0
0
0
1
1
1
0
1
2
0
1
0
1
2
0
1
2
1
0
1
0
0
2
1
2
0
2
0
3
0
0
0
3
1
2
0
1
1
0
1
0
0
2
0
2
1
2
0
2
0
1
0
0
1
1
1
0
1
2
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
1
0
2
0
1
0
0
0
0
0
1
0
1
2
1
2
1
1
0
0
0
1
2
0
0
1
0
3
0
0
0
0
0
0
2
1
3
0
0
0
1
0
0
1
1
2
0
1
0
2
1
0
1
0
1
0
0
1
1
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
2
2
0
1
1
0
2
0
0
2
0
1
1
0
2
1
1
0
0
1
0
0
2
1
0
2
0
0
1
1
0
1
2
0
1
0
0
0
1
0
0
0
1
0
2
3
0
2
1
2
2
0
0
0
0
0
1
0
0
1
0
2
0
1
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
1
2
0
2
0
2
0
0
2
1
0
0
1
2
0
0
0
0
0
1
1
0
1
3
2
1
1
1
0
0
0
0
2
1
0
0
2
1
0
2
2
0
1
0
1
1
0
1
2
0
1
0
2
2
1
1
2
2
2
0
0
2
0
2
2
2
1
2
2
1
0
2
1
2
1
0
2
0
0
1
0
0
1
0
0
1
0
2
0
2
0
0
0
3
0
1
2
3
0
3
0
1
0
1
0
3
1
3
0
0
1
0
1
0
2
1
1
2
1
0
2
0
0
2
0
0
2
0
3
2
1
0
1
0
0
1
0
0
2
2
0
0
1
0
0
2
0
2
0
2
1
1
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
1
0
1
1
0
2
3
1
1
1
2
2
2
0
2
0
0
0
0
0
0
0
1
1
1
0
0
1
0
2
0
0
1
0
2
2
1
2
0
1
2
0
0
1
0
0
0
2
0
1
2
1
1
1
2
0
0
0
1
0
1
0
2
0
2
0
1
2
0
0
0
2
0
1
2
0
0
2
0
0
0
0
0
2
1
0
0
0
1
0
2
1
2
1
0
2
1
2
1
2
1
1
1
1
0
1
2
2
0
0
0
1
1
0
2
1
0
0
1
0
0
0
0
0
1
0
3
2
0
1
0
0
0
2
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
2
1
1
0
0
0
1
1
1
1
1
2
0
1
2
1
1
1
0
2
1
0
0
0
0
0
2
1
2
2
2
2
2
1
1
3
0
0
0
0
0
0
1
1
0
1
2
0
1
1
2
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
1
2
2
2
2
0
2
0
2
0
1
0
1
0
0
0
0
1
2
2
0
0
0
0
2
0
1
0
3
0
0
0
0
1
0
1
0
1
2
0
1
1
2
0
1
2
1
1
0
0
0
0
1
0
0
0
0
2
0
1
0
2
1
0
1
0
3
0
0
0
0
0
3
0
0
0
2
0
2
0
0
1
1
0
1
1
2
0
2
0
3
1
1
1
0
0
1
1
0
1
1
0
1
2
0
1
1
0
2
1
0
2
2
2
3
0
1
2
1
0
1
1
2
1
2
0
1
0
1
1
0
0
0
0
1
1
0
1
2
0
2
1
0
0
0
0
1
0
0
0
1
0
2
1
4
0
1
1
0
1
0
0
2
1
0
0
2
1
1
0
2
2
1
0
0
2
1
1
0
1
0
1
2
0
1
1
0
0
0
0
2
0
1
0
0
0
0
0
1
2
0
1
0
3
0
0
0
0
0
1
0
1
2
0
1
1
1
1
0
6
2
0
1
2
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
3
0
0
1
0
1
0
1
1
0
0
3
2
0
2
1
1
2
2
1
0
1
0
0
1
0
0
0
0
1
2
1
1
0
0
2
0
0
2
0
1
0
0
1
2
0
0
2
0
0
2
1
0
2
0
1
0
0
3
1
0
0
1
2
0
0
1
2
2
1
0
1
0
0
0
2
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
2
2
0
0
1
2
3
0
0
2
1
1
0
2
0
2
0
0
0
0
1
0
0
0
1
0
0
0
1
3
0
0
0
2
0
2
2
1
2
1
1
1
0
0
1
2
0
0
0
3
2
1
0
0
1
1
0
1
0
0
2
0
2
0
0
2
2
1
2
0
2
0
0
1
0
0
1
1
0
0
0
1
1
0
2
1
0
0
0
0
1
0
2
0
0
1
1
0
2
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
2
0
0
0
0
1
1
1
0
0
1
0
0
1
2
0
2
0
2
0
2
0
0
0
1
0
2
0
0
0
2
0
2
0
0
0
1
0
0
2
1
2
0
0
1
1
0
1
1
0
3
0
2
1
1
1
0
0
1
2
0
0
1
0
1
0
0
0
1
0
0
2
0
1
2
0
2
0
1
1
0
0
0
2
0
2
1
1
1
0
1
0
1
0
2
0
1
1
0
1
0
0
0
1
0
2
0
0
1
1
2
2
0
0
2
0
0
0
0
1
0
0
1
0
1
0
4
2
2
1
0
0
0
1
1
1
0
0
0
0
2
1
0
0
0
1
1
1
2
0
1
1
1
1
0
0
1
0
1
0
2
1
0
2
0
3
2
0
0
0
0
1
0
2
2
2
1
0
2
2
0
1
0
1
2
2
0
0
0
0
0
1
2
0
0
2
0
1
0
0
0
0
4
0
0
0
1
0
2
0
0
2
0
1
0
2
0
1
2
0
1
2
2
2
0
1
2
0
1
1
0
1
1
0
1
0
1
0
0
1
3
0
2
0
2
2
2
0
0
1
0
1
1
1
0
0
0
1
0
1
0
0
2
0
0
2
0
2
2
2
0
1
0
1
0
1
1
1
0
0
0
0
0
0
1
0
1
1
0
1
2
1
1
0
2
0
0
0
1
1
0
3
2
0
1
0
1
1
0
0
1
3
0
0
0
0
0
0
0
0
1
2
1
1
0
0
1
0
0
0
1
0
0
1
1
0
1
2
1
0
0
0
0
1
2
0
1
0
0
1
4
1
0
0
0
2
1
2
0
1
0
0
0
2
0
0
1
0
0
1
0
2
1
1
2
1
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
1
0
1
2
0
0
0
0
1
1
0
2
0
0
0
0
1
0
0
0
0
0
0
2
1
1
0
0
0
0
2
1
1
1
0
2
1
0
0
1
0
0
0
1
1
0
0
0
1
0
1
0
0
2
0
4
2
2
0
1
1
0
2
2
0
3
0
1
0
1
0
0
0
0
1
2
2
2
0
0
1
0
2
0
0
0
0
2
0
2
0
0
1
2
1
2
1
0
1
1
1
4
1
0
2
0
0
1
0
0
1
1
1
0
0
1
0
1
0
1
0
0
0
0
2
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
2
0
0
1
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
2
2
0
0
0
1
1
1
1
1
1
1
0
2
1
0
0
1
0
0
1
1
2
2
0
1
0
0
2
0
1
0
0
1
0
2
0
0
0
1
2
0
1
1
2
0
1
1
1
2
0
2
2
0
2
2
0
0
1
2
0
0
0
0
3
0
1
2
2
1
0
0
0
2
0
2
2
0
0
0
0
0
1
0
2
0
0
1
0
2
3
1
2
2
2
0
0
0
0
0
2
1
2
2
0
2
0
0
2
1
1
1
0
1
0
1
2
2
1
0
2
1
0
0
0
3
1
2
0
1
1
1
1
0
0
1
2
1
1
1
2
1
1
0
2
2
0
0
1
0
1
1
0
0
0
1
0
0
2
2
3
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
1
0
5
1
0
1
1
0
2
1
1
2
1
0
1
2
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
1
0
0
0
2
1
2
0
1
0
0
1
3
1
1
0
2
0
0
1
0
0
1
0
1
1
0
0
0
2
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
1
1
1
0
1
0
1
1
2
2
0
0
2
0
1
1
1
2
1
2
2
0
0
2
1
0
0
0
0
2
2
0
0
0
0
0
1
2
0
1
0
0
0
0
2
1
2
2
2
0
0
0
0
0
2
1
1
1
0
0
0
0
0
2
2
2
0
1
2
1
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
1
0
2
0
0
0
0
0
2
0
0
2
0
1
0
1
0
1
1
2
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
1
0
3
0
2
0
0
1
0
0
1
0
0
0
0
2
0
1
1
1
0
1
0
1
1
1
0
1
2
1
0
0
2
1
0
0
1
0
1
1
1
0
1
2
1
0
0
0
2
1
1
1
0
0
2
0
0
0
3
1
0
2
0
3
2
0
0
0
2
0
0
0
0
0
2
0
0
1
2
0
0
0
2
0
2
1
1
0
0
2
0
0
2
0
0
0
0
1
0
3
1
0
1
1
0
1
1
1
0
1
0
0
1
0
0
1
2
2
0
0
1
0
0
0
2
2
0
0
0
1
2
0
2
2
1
1
2
0
1
0
2
2
2
0
0
0
2
2
0
0
1
2
1
1
1
0
0
2
0
0
0
2
2
2
1
0
2
0
0
4
0
0
0
2
0
1
1
1
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
1
0
1
1
0
1
2
4
0
0
2
0
0
2
0
2
0
1
1
2
0
0
0
0
2
3
1
2
3
1
2
0
1
2
0
1
2
2
1
0
0
0
2
2
0
0
0
2
0
1
0
2
0
0
0
2
2
1
0
0
1
0
2
1
0
0
2
1
1
1
0
0
1
1
0
2
2
4
1
0
0
0
0
1
0
1
0
0
0
2
0
0
1
0
0
0
2
1
0
1
1
0
2
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
2
0
0
2
1
0
3
0
1
0
1
0
0
1
0
0
2
0
1
0
1
0
2
0
3
1
0
2
0
2
1
1
1
0
0
0
0
0
1
0
1
1
1
2
1
2
0
2
0
8
0
0
1
1
1
2
2
2
1
0
0
2
0
0
0
1
0
1
2
0
2
0
2
1
2
0
0
2
2
0
1
0
1
2
2
0
0
1
0
0
0
0
1
1
2
2
2
0
0
0
1
2
3
0
0
0
2
0
0
1
1
2
0
0
0
0
3
0
0
0
2
0
0
0
0
0
2
0
2
1
0
2
0
2
0
1
2
0
1
0
1
0
0
0
0
1
2
0
0
0
0
2
0
2
2
0
0
1
0
0
0
0
0
0
0
2
2
1
0
2
0
0
2
0
2
1
0
0
0
0
0
2
0
0
1
0
0
0
0
2
1
1
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
2
1
1
0
2
1
0
1
0
0
0
0
0
1
1
0
0
2
0
0
0
2
2
0
1
0
1
0
0
0
2
0
0
0
0
0
2
1
0
1
0
1
2
1
0
2
1
0
1
0
1
0
0
0
2
2
0
1
2
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
1
2
0
2
1
1
0
0
0
0
0
2
0
1
1
0
1
2
2
2
0
0
0
2
0
0
2
0
2
0
2
0
0
0
0
0
0
1
0
0
1
0
2
0
0
3
0
2
0
1
0
0
1
2
1
1
2
0
0
3
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
2
2
0
0
0
2
1
1
1
2
0
3
1
1
2
1
1
0
0
2
1
1
1
0
0
2
2
0
0
0
0
0
1
0
0
2
0
0
1
1
1
0
1
0
0
2
1
0
2
0
2
3
0
2
0
1
1
1
2
2
1
1
1
3
0
1
0
1
0
2
1
2
0
0
0
0
1
0
1
0
0
1
2
0
0
0
0
0
2
1
0
2
2
1
0
1
0
0
0
0
0
1
1
2
2
2
0
0
1
4
1
2
2
0
2
0
2
0
2
0
0
0
0
2
1
2
0
1
1
0
3
0
0
0
1
1
0
0
0
0
0
1
1
1
1
2
1
2
0
0
0
1
0
1
0
0
2
0
0
2
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
2
3
0
2
1
1
1
0
1
0
0
1
1
1
4
0
1
0
0
2
1
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
1
1
1
0
0
0
1
0
2
0
1
0
0
2
0
1
1
2
1
1
0
0
0
0
0
1
0
0
0
1
3
2
0
0
0
0
0
0
0
0
1
2
0
0
0
1
2
1
0
2
2
0
0
0
2
1
2
0
2
0
0
0
0
0
0
3
2
1
0
4
0
0
0
0
0
0
1
0
2
0
4
0
1
2
1
2
0
0
3
0
0
0
0
1
2
1
0
1
1
0
3
1
1
0
0
0
2
0
1
0
0
0
1
2
1
1
2
0
2
1
2
1
2
0
0
0
1
1
1
1
2
1
0
2
2
1
0
0
0
0
0
1
1
0
2
0
0
0
0
2
0
2
1
2
2
0
1
0
0
0
2
1
1
0
0
0
0
1
0
2
0
1
0
0
0
0
2
0
2
4
1
0
1
0
1
1
1
2
0
0
0
0
0
2
0
0
1
1
1
0
1
1
1
0
0
0
1
0
2
0
2
0
2
1
0
2
3
1
0
1
0
0
0
1
1
0
0
0
1
0
0
1
1
1
1
0
0
2
0
1
1
5
0
1
1
0
3
1
2
2
0
1
0
0
1
0
1
2
0
1
0
0
0
1
1
2
2
0
0
2
0
1
0
0
1
2
1
1
1
0
1
0
0
1
1
0
1
1
2
0
0
0
0
0
2
2
1
0
0
0
2
0
0
2
0
0
0
1
2
0
1
0
2
0
0
0
0
0
0
0
2
0
1
0
1
1
1
2
3
1
0
0
1
0
2
1
0
0
0
1
2
0
2
1
0
2
0
0
1
0
3
0
1
0
0
0
1
2
0
2
0
1
1
0
0
0
0
0
0
2
0
2
0
1
0
1
0
2
0
0
0
2
2
1
0
1
0
0
1
0
2
2
0
0
2
0
0
1
1
1
0
1
0
1
1
0
1
0
0
1
0
0
1
1
0
1
0
0
1
1
3
1
0
0
1
2
1
2
2
0
0
0
0
2
2
0
0
1
0
1
0
2
1
0
0
3
2
2
0
0
0
2
2
0
1
0
0
0
2
1
2
2
0
0
0
2
0
0
0
1
0
0
0
2
0
1
0
0
3
0
2
2
0
0
1
0
0
1
1
2
2
1
0
0
0
0
0
0
1
1
0
1
1
0
1
1
2
0
0
1
1
0
0
1
0
2
2
2
1
0
2
1
2
0
0
0
0
1
0
0
2
2
2
0
1
1
2
0
1
0
0
2
1
1
1
0
0
0
0
0
1
2
1
0
0
0
2
0
0
0
0
1
1
0
0
1
0
0
0
0
1
1
0
0
1
0
0
2
1
0
0
0
2
2
1
0
0
0
2
0
2
0
2
2
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
3
0
1
0
1
0
3
0
0
2
0
2
0
1
1
1
0
2
2
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
2
0
1
0
2
0
2
0
1
2
2
2
0
2
0
1
1
1
0
2
0
2
1
1
2
0
0
0
1
1
0
0
2
0
0
1
0
6
1
1
1
0
1
0
1
0
0
1
0
0
2
1
0
1
0
0
1
1
0
0
1
0
2
1
2
2
1
0
0
1
0
2
1
0
0
0
3
0
1
0
0
0
1
2
2
0
1
2
2
1
1
2
0
0
2
1
1
0
1
0
2
1
0
0
1
1
1
0
0
0
1
2
0
0
2
0
2
0
0
2
2
0
2
0
0
2
0
2
0
0
1
1
0
0
1
2
1
0
1
3
1
2
2
0
0
3
0
1
1
0
0
0
1
0
1
2
0
1
0
1
1
1
1
0
1
2
2
1
0
2
1
1
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
2
2
0
0
0
1
1
2
0
2
0
2
1
0
0
1
0
1
1
2
1
0
0
0
0
2
0
2
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
1
2
1
1
0
2
0
0
1
2
0
0
1
1
0
0
1
0
2
0
0
1
2
3
0
1
0
0
0
0
1
0
0
0
1
2
1
2
0
0
2
1
0
0
0
0
1
1
0
1
0
2
0
1
0
0
1
1
0
1
2
0
3
2
2
0
0
2
0
0
1
0
1
0
2
0
1
0
2
0
0
1
1
2
0
2
1
0
0
2
0
0
1
1
0
1
2
0
2
0
2
0
1
0
1
0
1
1
2
1
0
1
2
3
0
1
0
2
0
0
2
1
0
2
0
3
0
3
0
0
1
1
2
1
1
0
2
2
0
2
1
0
0
2
0
0
1
0
0
0
2
2
0
0
2
0
2
0
1
1
0
0
2
0
0
0
0
0
0
0
0
2
2
2
1
0
0
0
0
1
0
1
1
2
0
0
1
0
0
0
0
0
0
1
1
2
2
0
2
2
0
0
0
0
1
0
1
4
1
0
0
0
0
1
2
1
2
1
0
2
0
0
1
0
1
0
0
2
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
2
1
0
2
2
0
0
0
2
0
1
0
2
0
0
2
0
1
2
0
0
2
1
1
2
2
0
0
3
0
2
1
1
0
0
2
2
0
1
1
0
1
3
1
2
0
1
0
0
0
1
1
1
1
1
0
2
1
2
1
0
2
1
2
1
0
1
1
0
1
0
0
0
1
0
2
0
1
2
0
0
0
0
0
1
0
0
0
0
2
1
1
1
1
1
1
0
2
1
1
0
0
0
0
1
0
0
2
0
1
0
0
0
2
0
1
0
1
0
2
0
1
0
1
0
0
0
0
1
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
2
0
2
0
0
2
0
0
1
0
0
1
1
2
3
0
1
0
0
0
0
0
0
0
2
2
0
0
0
2
0
1
0
2
2
1
2
0
0
0
1
0
1
1
1
1
1
2
0
0
2
1
1
1
1
1
0
0
1
1
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
1
2
1
2
1
0
2
0
0
0
0
0
2
1
1
3
0
1
0
0
0
2
2
0
0
0
3
2
1
0
0
0
3
0
0
1
0
2
2
2
0
0
0
0
0
1
1
1
1
1
0
2
1
2
0
2
2
1
1
0
0
1
0
1
0
0
0
2
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
2
1
0
0
0
2
3
0
0
1
0
0
2
2
0
0
1
0
1
0
1
0
0
0
2
3
1
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
3
0
1
0
0
1
0
0
0
2
0
1
2
1
0
2
2
0
1
0
0
0
0
0
0
1
0
2
1
2
1
0
0
0
0
0
2
1
1
0
1
0
1
0
0
0
0
0
1
2
2
0
2
0
2
2
0
2
0
0
0
0
0
1
2
0
2
0
1
1
3
2
0
2
1
1
5
2
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
1
3
0
1
2
0
0
0
0
0
0
0
0
2
1
0
0
0
2
1
0
2
2
1
1
3
2
1
1
1
0
0
0
1
0
1
2
0
0
0
1
2
0
0
2
0
0
0
1
0
0
1
0
1
0
0
1
1
0
0
0
1
0
2
1
2
0
0
0
1
1
0
0
2
0
1
0
0
0
0
2
2
0
0
2
0
3
0
1
1
1
0
0
0
0
1
2
2
0
0
0
0
0
1
0
0
4
0
2
2
0
2
1
1
0
0
1
2
0
0
2
1
0
1
0
1
0
0
2
1
0
2
0
0
0
1
0
0
0
3
1
2
2
0
0
2
1
1
0
0
0
1
1
0
2
0
2
0
1
2
0
2
0
1
0
0
0
2
2
0
1
1
1
0
2
1
2
2
1
0
0
2
0
1
1
1
0
0
2
1
0
0
2
0
0
0
0
1
0
2
0
2
0
1
0
1
0
1
0
2
1
0
0
0
0
0
0
0
0
0
2
2
0
1
1
0
0
1
0
1
0
1
2
1
0
0
2
1
0
3
2
0
2
0
2
1
1
2
1
0
0
0
1
0
2
0
0
0
2
0
0
0
0
1
1
1
0
1
1
0
0
2
0
1
0
2
1
1
2
0
0
0
2
0
0
2
0
2
1
0
1
0
0
0
0
0
0
2
1
0
1
0
1
2
0
2
0
0
0
0
0
2
1
0
0
0
0
0
2
2
3
2
0
1
1
0
1
2
0
0
1
1
0
0
0
3
0
1
0
1
0
0
0
1
0
1
1
0
1
1
1
0
4
0
0
1
0
1
0
1
0
0
2
1
1
0
1
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
1
1
0
0
2
0
2
0
2
2
2
0
0
0
0
1
1
0
2
2
0
1
2
1
0
3
2
0
0
2
2
0
2
0
0
0
1
1
0
2
1
2
0
0
0
1
0
1
2
2
0
2
0
2
2
0
0
2
0
0
1
0
2
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
1
2
0
1
1
3
2
2
1
2
0
0
0
2
2
0
2
3
0
1
0
0
2
3
1
0
1
1
2
0
0
1
0
2
1
2
0
0
0
0
0
0
0
2
1
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
2
2
0
1
0
2
2
0
0
2
0
0
1
2
0
2
0
0
0
1
1
0
0
0
2
0
2
1
1
0
0
1
2
1
0
0
0
2
1
1
0
0
0
1
0
2
0
2
1
0
0
0
0
0
0
0
1
1
0
1
2
0
0
1
0
1
0
4
1
0
0
2
0
2
0
2
0
0
0
1
0
0
1
0
2
1
0
0
0
2
1
0
0
0
1
1
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
1
1
2
0
2
0
0
0
0
1
1
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
1
1
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
1
1
0
0
0
1
2
0
2
0
0
2
0
0
0
1
1
0
1
5
1
0
2
0
0
0
0
2
2
2
1
0
0
2
0
0
1
0
1
0
0
2
2
1
0
4
0
1
1
0
0
0
2
2
0
2
0
0
1
1
0
0
1
0
2
0
0
2
1
0
2
0
1
1
1
0
2
2
1
0
1
2
0
0
2
2
1
1
0
0
1
0
2
2
0
0
0
1
2
0
1
2
2
0
0
2
2
2
0
1
0
0
0
0
2
2
1
1
0
1
0
0
2
0
0
0
2
0
1
2
1
0
0
0
1
1
0
0
0
0
0
2
0
2
0
0
2
2
0
2
0
1
1
1
0
1
0
0
0
0
1
1
0
0
0
0
0
2
1
2
0
2
0
1
2
0
0
1
0
3
1
0
0
3
0
0
0
1
0
0
0
0
0
1
1
0
1
0
2
0
0
2
0
0
1
0
2
2
0
1
1
0
0
2
2
0
0
1
2
1
1
2
2
0
0
2
0
2
0
1
0
0
0
0
0
3
0
0
0
0
0
2
0
1
1
1
0
0
0
0
2
0
0
1
1
0
2
1
0
2
0
2
2
0
1
1
0
1
1
1
0
0
2
2
3
0
2
2
1
0
1
0
0
0
0
0
0
1
1
0
0
2
2
1
2
2
0
1
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
2
0
2
1
1
0
1
2
0
0
1
0
2
2
0
0
0
0
1
0
2
1
0
0
2
2
1
1
1
0
2
0
0
0
0
0
3
2
1
0
1
0
1
1
2
0
1
0
2
0
2
1
0
0
1
0
0
0
0
2
2
0
0
0
1
1
0
0
2
0
0
1
0
1
1
1
0
1
1
2
0
0
1
1
2
2
0
1
1
2
0
1
2
3
0
1
2
2
0
1
4
2
2
0
0
0
1
1
0
1
0
0
2
0
1
2
0
0
0
0
0
1
1
0
0
0
1
0
1
0
2
2
0
0
2
0
2
0
0
0
2
2
2
0
1
2
2
1
0
2
0
0
0
1
1
0
0
0
1
2
0
0
0
0
0
6
0
0
2
1
1
1
1
1
0
2
0
2
1
2
0
0
0
2
0
2
0
1
0
2
1
0
4
1
1
1
0
0
2
0
2
2
1
0
1
1
0
0
0
0
1
0
0
1
2
0
0
0
1
2
2
0
0
0
0
0
1
0
0
2
0
1
0
2
1
0
1
2
2
1
0
0
0
0
2
0
2
2
0
0
2
1
1
3
1
1
0
0
0
0
1
1
0
2
1
0
1
2
0
2
1
0
2
0
0
0
1
1
0
1
0
2
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
3
0
2
2
0
0
2
1
0
0
0
0
1
0
1
0
0
1
1
1
0
1
2
1
2
0
0
0
0
0
1
0
1
0
2
3
0
1
1
2
0
1
3
2
2
0
0
2
0
0
0
0
1
1
2
2
1
1
0
0
0
1
1
0
1
2
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
3
0
2
2
0
0
1
2
1
1
2
0
2
1
1
1
2
0
0
1
0
0
0
0
1
0
2
2
2
0
2
2
1
0
2
1
0
1
0
1
0
0
3
0
0
2
0
1
0
0
0
0
0
1
0
0
1
3
2
0
2
2
2
0
0
0
0
0
2
0
1
3
2
2
1
0
1
2
0
1
2
2
0
2
1
1
0
0
0
2
2
0
1
0
2
0
1
2
0
0
0
2
2
2
1
0
0
0
2
1
0
0
2
0
2
0
2
0
2
0
0
2
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
1
1
2
2
2
0
1
1
0
2
2
0
1
0
0
2
1
2
2
2
1
0
1
0
0
1
2
1
0
2
2
0
0
1
0
0
0
0
1
0
1
2
0
1
2
0
1
0
0
1
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
3
0
0
0
1
2
2
0
0
3
1
0
0
0
0
2
1
1
0
0
0
1
0
1
1
2
1
1
1
1
2
0
1
1
0
1
1
1
0
2
0
0
0
0
1
1
2
2
1
2
2
0
2
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
2
2
0
0
0
2
0
0
2
0
0
0
0
1
1
1
0
1
0
1
1
1
0
2
0
1
3
2
0
0
0
2
2
3
0
0
0
1
1
0
1
3
0
1
0
0
0
3
2
2
0
0
1
4
0
0
0
1
1
1
2
1
0
1
0
0
1
1
0
0
0
0
0
0
1
1
1
0
1
1
2
0
0
0
0
1
1
2
1
1
0
0
1
0
0
0
0
2
0
0
0
2
2
0
1
2
1
0
2
0
0
0
1
0
0
3
0
0
0
0
2
1
2
0
0
1
0
1
2
0
1
2
0
1
2
0
4
0
0
3
1
0
3
1
1
0
2
2
2
2
0
0
0
0
0
0
1
1
2
1
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
1
2
2
1
1
1
0
2
1
0
2
1
0
0
0
2
2
2
0
3
0
1
3
1
1
1
1
0
0
0
0
2
0
0
0
1
1
1
1
2
0
1
1
0
0
2
0
1
0
0
1
0
0
0
0
0
0
1
0
2
0
1
0
1
2
0
0
0
0
0
2
0
1
1
0
0
0
2
2
0
0
0
1
0
1
0
1
2
0
1
1
0
1
0
1
2
1
0
0
2
2
1
0
2
0
0
0
1
1
2
0
0
1
0
2
2
0
0
0
0
0
2
1
0
2
2
1
0
0
1
0
2
0
2
0
0
1
1
0
0
1
2
1
3
0
2
0
0
1
1
0
1
1
1
4
0
0
0
1
1
1
1
1
2
1
1
3
0
0
2
2
0
0
1
0
1
2
0
2
2
0
2
0
1
0
0
0
0
1
1
0
2
0
0
1
0
0
0
0
1
0
0
0
2
0
0
2
2
0
0
1
0
0
0
1
2
1
2
0
0
0
0
0
1
0
0
1
1
0
1
0
0
1
1
0
0
0
2
0
0
1
1
1
2
1
0
1
2
1
0
1
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
2
0
0
0
1
0
3
0
0
0
6
3
0
0
0
0
4
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
2
0
0
0
1
0
2
0
0
2
0
1
0
0
0
0
1
0
0
2
1
2
0
0
0
0
0
0
2
0
0
0
1
0
1
2
0
0
0
0
0
1
0
0
1
0
0
0
1
0
2
1
0
1
1
2
2
2
1
0
0
0
1
0
1
2
1
0
2
0
1
0
1
0
1
0
0
0
0
2
1
0
0
0
2
1
0
0
0
0
0
1
1
1
1
0
1
0
2
0
1
1
0
0
2
0
3
1
0
0
2
0
0
0
2
1
2
0
1
0
0
0
2
0
0
2
0
0
0
0
2
2
2
1
1
0
1
0
1
0
3
1
0
0
1
0
0
1
0
0
1
0
0
0
2
1
0
0
0
1
0
0
0
2
2
0
0
6
1
1
0
2
3
2
0
1
2
0
0
1
0
0
1
0
0
2
0
0
0
3
0
0
1
2
1
0
0
1
2
0
1
2
0
2
0
1
0
0
2
1
0
1
0
1
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
2
1
1
1
0
0
0
0
0
1
0
0
0
0
2
0
1
0
1
0
0
1
2
0
0
0
2
0
0
2
0
0
0
2
2
0
2
0
0
0
1
0
2
0
1
0
0
0
1
1
1
2
0
0
0
1
0
1
0
1
2
0
2
1
1
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
1
1
0
0
0
2
4
2
2
1
0
0
0
0
0
0
0
0
1
2
1
0
2
1
2
0
0
2
0
2
2
0
1
0
2
0
0
1
3
1
1
0
0
0
1
1
0
0
1
1
1
1
2
1
2
1
0
1
1
0
0
0
0
0
0
2
1
0
0
0
1
2
0
1
0
1
0
3
0
1
1
0
0
2
1
1
1
0
1
2
0
1
0
0
1
1
2
0
1
2
1
0
0
2
0
1
0
2
1
0
0
0
0
2
0
0
0
1
1
2
0
1
2
1
1
1
1
1
1
0
1
0
1
1
0
0
0
0
2
2
2
0
0
0
1
1
2
2
2
0
1
2
0
0
0
0
2
0
1
1
2
2
2
2
0
1
0
0
0
0
1
2
0
0
1
1
0
1
2
0
1
0
0
1
0
1
2
0
0
1
2
0
1
0
1
0
1
0
0
0
1
0
1
1
0
2
0
2
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
1
1
0
1
2
1
0
2
0
0
1
1
0
1
1
0
2
1
1
0
2
2
1
1
0
0
0
0
2
5
0
1
1
1
0
0
2
2
0
3
2
1
1
2
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
2
1
0
1
0
0
0
1
2
1
0
0
0
2
0
0
0
1
0
2
1
0
0
1
1
1
0
0
3
2
0
0
1
1
0
1
4
2
2
0
1
0
0
1
1
2
0
0
2
1
4
0
0
4
0
0
0
0
0
3
1
1
1
1
0
0
0
0
2
0
0
0
0
0
2
2
0
2
0
0
0
0
1
0
0
0
0
1
1
0
0
2
0
1
0
0
1
0
0
0
1
1
0
2
2
1
0
0
2
2
2
2
1
0
0
1
1
2
0
0
0
0
1
1
0
1
1
0
1
2
0
2
0
2
1
0
0
0
0
2
0
0
0
3
1
0
0
0
0
0
0
0
0
1
1
0
4
0
1
0
1
0
0
1
0
0
0
1
0
0
0
2
0
0
1
0
1
2
1
0
2
1
0
0
2
1
0
2
0
1
0
0
2
2
0
2
0
3
0
0
1
0
1
0
1
0
1
0
1
0
0
0
0
2
2
0
0
1
1
1
0
1
2
0
0
2
1
2
2
0
1
1
0
0
2
1
1
2
2
1
0
2
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
2
0
2
1
0
0
1
0
0
2
0
2
0
2
0
4
0
0
2
2
2
0
0
0
0
1
1
1
0
0
2
1
2
2
0
0
1
0
0
1
0
2
0
2
0
0
1
0
0
1
0
0
1
0
0
2
0
0
1
4
2
1
0
2
0
1
0
0
0
1
2
0
2
2
0
1
2
2
0
1
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
1
1
0
2
0
0
0
1
0
0
0
1
2
1
3
0
1
1
0
1
3
2
1
0
2
0
2
1
0
1
2
0
0
0
1
0
0
1
2
0
0
2
2
0
0
0
2
1
1
2
2
1
0
1
0
0
0
2
0
0
2
0
2
1
0
2
0
0
2
2
0
0
0
0
0
0
1
0
2
0
2
0
0
2
0
0
2
1
2
2
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
2
1
2
0
0
1
1
0
0
1
1
2
0
0
1
2
2
0
1
0
1
1
1
1
2
0
1
0
0
2
0
2
0
2
2
1
0
0
0
0
0
2
1
1
2
0
0
0
2
0
2
0
0
0
0
2
1
2
0
0
0
0
0
1
0
1
0
0
1
2
1
1
1
2
2
0
0
1
1
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
2
0
2
1
0
2
0
2
0
1
0
3
0
2
1
1
0
0
1
0
0
0
0
1
2
0
0
0
0
0
1
1
1
2
0
0
0
2
2
2
1
2
0
0
0
0
0
0
0
1
0
1
1
1
0
0
1
1
0
0
1
0
2
0
0
0
0
2
2
1
0
2
2
0
2
0
0
1
1
2
1
0
0
0
0
0
2
0
2
0
0
2
1
0
1
0
0
2
0
0
0
2
0
0
0
0
1
1
2
2
2
1
0
0
2
0
0
0
0
0
0
0
0
0
2
1
1
2
0
2
1
0
2
0
1
0
1
0
2
0
0
0
1
0
2
0
1
1
0
1
1
0
0
2
0
0
0
1
2
2
0
1
0
1
0
0
0
0
1
0
1
1
0
2
2
0
0
0
2
0
2
0
0
1
0
1
1
3
2
1
0
2
0
0
1
1
1
0
2
0
2
2
2
0
0
1
2
0
0
1
1
0
0
1
0
1
1
1
2
2
0
1
1
1
2
1
1
1
2
1
1
0
1
2
0
0
1
0
0
1
1
1
2
1
0
1
0
1
2
0
1
1
0
1
0
1
1
1
1
1
0
1
0
1
1
1
0
1
0
0
0
0
2
0
0
1
1
2
0
0
0
1
0
0
0
4
2
0
0
0
2
0
1
2
0
1
0
2
2
2
2
8
0
0
2
0
1
0
1
1
0
1
2
1
2
0
0
0
0
2
0
0
0
0
1
0
0
1
1
0
0
2
0
0
1
2
0
0
1
1
1
0
2
1
1
0
0
0
4
1
2
1
0
1
2
1
2
0
0
0
0
0
0
0
0
0
2
0
3
2
0
0
2
0
1
0
0
0
1
1
1
1
2
2
0
0
1
1
0
0
0
1
1
1
0
0
0
0
3
2
0
0
1
0
3
0
0
1
0
0
1
0
1
0
1
1
0
0
0
0
1
1
0
1
1
1
0
0
0
2
1
0
0
1
1
2
0
0
0
0
1
1
0
2
2
2
2
2
0
0
1
3
0
1
1
2
1
1
1
0
0
2
1
0
0
1
2
1
1
1
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
1
1
0
0
0
3
2
0
0
2
0
1
1
0
0
1
0
1
0
0
2
1
1
0
0
0
1
2
0
1
0
0
2
0
0
2
2
3
0
0
1
0
3
2
0
1
1
2
0
0
0
0
0
0
0
3
1
0
0
2
1
0
2
1
0
0
2
1
0
0
1
0
0
1
3
2
1
2
0
2
0
3
0
0
0
1
0
1
2
1
0
0
0
3
0
1
0
0
1
0
1
0
1
2
1
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
1
1
1
0
0
1
2
0
1
1
1
1
0
0
0
0
0
0
0
0
2
2
1
3
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
1
2
0
0
0
2
0
2
1
0
0
2
0
0
0
1
1
1
0
0
2
2
0
3
1
1
0
0
1
0
0
0
0
0
0
4
1
0
0
1
1
2
0
0
0
0
2
2
0
1
0
2
1
2
2
0
0
1
1
0
1
0
2
0
0
3
0
1
0
0
0
1
2
0
1
2
1
1
0
0
2
1
2
2
1
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
2
2
0
1
1
1
1
1
0
1
0
0
2
2
2
0
0
2
0
1
0
0
0
0
1
0
2
0
1
1
0
0
0
0
0
1
2
0
0
0
2
0
0
1
0
1
1
0
0
1
0
0
2
0
1
2
0
0
0
0
0
0
0
2
2
1
0
0
2
0
1
0
0
1
0
0
0
1
2
0
1
0
2
2
0
0
0
1
0
2
2
0
1
0
2
0
2
1
0
1
2
0
1
0
2
1
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
1
2
2
0
0
1
2
0
0
1
0
6
0
0
0
0
1
1
0
2
0
2
2
1
1
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
3
0
2
0
1
1
0
0
0
1
0
2
0
0
0
2
0
0
1
0
2
1
0
0
1
0
1
0
2
0
2
0
0
0
1
2
1
2
1
1
0
0
0
1
0
0
0
6
0
0
0
1
1
1
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
1
2
0
0
2
0
1
0
0
0
1
0
1
1
0
0
2
3
1
0
1
1
1
0
0
1
0
2
0
0
1
2
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
1
2
0
2
1
1
0
0
2
2
0
1
2
0
0
0
1
0
2
3
2
0
2
0
2
1
0
1
0
0
2
1
1
0
0
1
1
1
0
1
0
2
0
0
3
0
0
0
1
0
0
2
0
2
0
1
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
2
1
1
0
2
2
1
0
0
1
2
3
2
2
0
0
0
1
2
1
0
0
0
1
0
0
1
0
0
0
2
0
1
1
0
0
1
1
2
0
0
0
0
0
2
0
1
0
2
0
0
0
1
1
0
3
1
0
0
0
1
2
0
0
0
1
0
0
1
1
2
3
1
1
0
2
1
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
1
0
2
0
0
1
0
0
2
2
0
0
1
2
2
2
1
0
0
0
0
1
2
1
0
0
0
0
1
0
1
0
1
1
2
0
1
0
0
1
1
2
0
2
3
0
0
0
0
0
0
1
1
0
0
4
2
0
3
1
0
0
2
2
0
2
0
3
2
0
2
0
2
1
1
2
1
0
0
0
2
0
0
2
0
1
2
0
2
0
0
1
0
0
2
0
0
1
2
1
2
2
0
0
0
2
2
0
2
0
1
1
3
1
0
1
0
1
0
2
2
0
1
0
0
0
0
1
1
1
0
0
1
0
1
2
2
0
0
2
1
2
0
0
0
0
1
2
0
2
2
0
1
0
0
2
0
2
2
0
0
4
0
0
2
2
2
0
1
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
2
0
0
0
1
0
1
1
1
0
0
2
1
2
0
0
1
1
1
0
2
0
1
3
1
2
1
1
0
2
2
1
0
1
0
1
1
2
0
0
1
0
2
2
0
0
1
0
0
0
0
0
0
1
0
2
0
2
0
2
0
1
0
0
1
0
0
1
0
2
0
2
1
0
0
0
1
2
0
1
2
0
0
1
0
0
1
0
1
1
0
2
2
2
0
0
0
0
0
0
2
2
1
1
1
1
1
1
1
0
1
0
0
0
0
1
0
0
0
2
0
1
0
0
1
0
2
2
0
1
2
0
0
0
0
1
0
0
3
0
1
0
0
1
0
0
0
0
0
0
1
2
0
2
0
2
2
0
1
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
2
1
0
0
0
2
0
0
2
0
0
0
1
2
0
0
0
0
3
0
2
0
1
0
1
1
0
2
0
0
1
2
3
2
2
0
0
0
0
0
1
1
2
0
2
0
1
2
1
2
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
2
0
1
1
0
2
2
1
1
1
2
0
0
0
1
1
1
1
2
0
1
0
1
1
2
0
0
1
0
2
1
0
1
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
1
2
0
1
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
2
0
0
2
1
0
0
1
1
0
0
2
0
0
0
0
1
2
0
0
0
0
2
1
0
1
2
1
1
1
0
2
1
0
3
2
0
1
0
0
1
0
0
0
1
1
0
0
0
0
2
0
0
0
1
0
1
0
0
1
1
1
0
0
1
1
2
2
1
0
1
0
1
2
1
0
1
0
0
2
0
1
1
1
1
1
0
0
1
0
0
0
2
1
0
0
0
1
0
1
2
0
4
0
0
3
1
1
0
0
0
0
2
0
1
0
1
2
2
2
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
1
0
1
1
1
1
0
0
0
0
2
0
1
0
2
0
2
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
2
4
2
2
0
2
1
2
0
1
0
0
1
1
0
1
4
1
0
0
2
2
1
1
1
1
0
0
0
2
0
2
0
1
1
0
0
0
0
2
0
1
1
0
0
0
0
0
2
0
0
2
2
2
1
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
2
1
1
0
1
1
1
0
1
1
0
0
0
0
0
2
0
2
1
0
0
0
2
2
0
0
2
0
0
1
2
0
0
0
2
0
1
0
0
2
1
0
2
0
0
0
2
1
1
0
0
1
1
2
1
1
0
1
1
1
0
1
0
0
1
1
2
0
1
1
1
1
2
0
0
2
1
0
1
1
0
2
0
2
0
0
1
0
1
0
0
0
0
1
0
3
0
2
0
0
0
0
0
0
0
0
1
1
0
2
2
0
1
0
1
0
0
0
2
1
1
0
2
2
0
0
2
0
2
0
1
0
0
1
1
2
1
1
1
2
2
2
2
2
0
1
2
0
0
0
0
0
1
0
2
0
2
1
1
2
1
1
1
1
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
2
1
0
1
0
1
1
1
2
1
0
0
2
1
2
0
2
1
1
0
1
0
0
2
1
1
2
2
1
0
0
2
3
2
1
0
0
0
2
2
1
1
0
0
2
2
1
0
1
0
2
1
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
1
2
0
0
1
1
0
1
0
1
1
0
0
0
0
2
0
0
2
2
0
1
1
1
2
0
0
0
0
2
1
2
2
2
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
2
0
0
1
0
1
0
0
0
0
0
2
1
0
1
0
1
1
0
0
0
0
0
1
0
2
0
1
0
1
0
1
0
1
0
0
2
2
0
0
0
1
2
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
2
2
1
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
2
1
1
0
0
0
2
0
0
0
4
1
0
0
1
1
1
1
0
0
0
2
0
2
0
1
0
1
0
0
2
1
2
1
1
2
0
0
0
2
1
1
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
3
2
1
0
1
0
0
0
2
0
1
0
1
2
1
2
1
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
2
1
1
0
1
1
1
0
0
0
0
0
1
2
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
2
0
1
0
0
2
0
0
0
0
0
0
1
0
1
1
1
2
0
0
0
2
0
1
0
2
1
0
2
0
1
0
0
2
0
2
2
0
0
0
0
0
0
1
0
0
1
1
1
1
0
0
1
1
0
0
0
1
1
2
2
0
4
1
3
1
1
2
0
0
1
1
0
1
0
2
1
1
1
1
0
1
1
1
1
1
0
1
2
1
1
1
0
0
2
1
0
0
1
0
1
1
0
0
2
0
1
1
0
0
0
1
0
1
2
2
0
3
2
1
0
1
0
2
0
2
0
1
2
3
1
0
0
1
0
1
1
0
0
0
1
0
1
0
0
0
1
1
1
2
0
1
2
2
0
2
0
0
0
1
1
0
1
2
0
0
0
1
1
0
2
1
2
0
0
0
2
1
0
1
0
1
2
0
2
1
1
0
0
0
0
2
1
1
0
2
0
0
0
1
1
0
0
0
1
1
1
0
2
0
0
0
0
0
4
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
1
2
0
0
2
1
1
2
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
1
1
1
0
2
0
0
1
2
1
0
0
1
1
0
2
1
0
0
0
0
0
2
1
1
0
2
0
0
2
2
1
2
1
1
0
1
0
1
0
2
0
1
1
2
0
0
1
2
1
0
2
0
0
1
1
1
0
1
0
1
0
0
1
0
1
2
2
2
0
0
0
0
3
0
0
1
2
0
0
0
0
1
1
0
0
1
2
1
1
1
2
2
0
1
0
2
1
0
0
1
1
2
0
2
1
1
2
1
0
1
0
0
0
0
1
0
0
2
3
1
1
0
1
0
0
0
0
0
2
1
0
1
0
4
0
0
1
2
0
0
0
1
1
0
1
3
0
2
0
2
2
2
2
0
1
1
1
0
2
2
0
0
1
0
2
0
0
2
0
0
0
0
1
2
1
0
1
2
0
0
2
0
2
0
0
0
0
0
1
1
2
0
0
0
1
1
0
2
2
0
1
2
1
1
0
0
2
2
1
0
2
4
1
0
0
0
0
2
0
0
1
0
0
0
0
2
2
0
0
0
0
0
2
1
0
2
0
1
2
2
0
0
3
2
1
1
0
0
0
0
0
2
0
0
0
2
1
1
1
1
1
0
2
1
1
0
0
0
1
0
1
0
0
2
1
0
1
1
2
0
0
0
1
1
1
0
4
2
1
0
0
1
2
0
0
0
0
0
1
1
1
0
2
1
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
2
0
0
0
1
0
0
2
1
0
1
0
0
1
2
0
0
2
2
1
1
1
1
0
0
1
0
1
0
1
1
0
1
0
0
1
0
0
0
0
2
2
1
0
2
1
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
1
1
0
1
1
1
1
2
2
0
0
1
0
1
1
0
1
0
3
0
1
2
2
1
0
0
2
0
2
0
1
2
2
1
1
0
0
0
1
0
0
0
2
0
0
1
0
2
1
2
0
0
0
3
1
0
0
1
1
2
0
0
2
0
1
0
0
0
0
1
0
0
1
5
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
2
2
0
0
0
0
0
1
0
0
0
0
0
0
1
1
2
0
0
1
2
1
1
1
1
2
0
0
1
1
1
1
1
0
1
0
0
0
0
0
0
0
0
1
0
2
2
2
1
0
2
1
1
0
1
0
2
0
1
0
0
0
2
1
2
0
0
0
1
2
0
0
2
0
3
0
2
0
0
1
1
0
2
1
2
0
1
2
0
2
0
0
0
0
1
1
1
0
1
1
0
1
0
2
1
0
1
0
2
1
1
1
0
0
0
1
2
3
1
1
1
1
0
1
0
0
2
1
2
0
0
1
0
2
2
2
0
2
0
0
0
1
0
1
2
1
0
0
0
2
0
2
1
1
0
0
1
2
0
1
0
2
0
1
1
0
1
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
2
1
0
0
1
0
0
1
0
0
2
0
0
0
0
2
0
0
2
0
0
0
1
1
1
1
1
1
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
1
1
4
0
2
0
2
1
0
1
1
0
2
0
0
2
1
0
3
0
2
1
2
1
1
2
1
0
0
1
2
0
0
2
0
1
1
0
1
1
2
1
0
1
1
0
1
0
1
2
0
1
1
0
0
0
2
1
0
2
0
1
0
1
0
0
1
0
1
0
2
2
1
1
1
0
0
2
1
0
0
1
0
0
1
0
0
0
0
1
1
2
0
2
0
2
2
1
0
2
2
0
0
0
0
1
0
0
1
2
2
0
5
1
2
0
2
2
0
0
0
0
0
0
0
2
2
0
1
1
2
0
0
0
0
0
1
0
1
0
0
2
0
1
2
0
0
0
0
0
0
1
0
3
2
0
0
0
2
1
0
4
2
1
1
0
0
2
0
1
0
2
2
1
0
2
0
0
3
0
0
0
0
0
0
2
0
0
3
0
0
0
0
2
0
1
1
1
0
0
2
0
1
2
0
2
1
1
1
0
0
0
2
2
0
2
0
1
1
0
2
3
0
0
0
1
1
1
2
1
0
0
2
2
2
1
0
0
1
1
0
1
0
0
1
0
2
2
1
2
1
1
0
0
0
0
2
1
0
0
1
1
0
0
2
1
1
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
5
0
0
1
2
0
0
0
0
3
0
1
2
1
1
0
2
2
2
0
0
2
0
0
0
0
1
1
1
1
0
1
2
1
1
0
0
0
0
1
1
0
0
0
0
2
1
0
2
2
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
1
1
0
1
0
0
3
2
1
1
2
3
0
0
0
2
0
1
0
0
1
4
1
0
0
1
0
0
2
0
2
1
0
2
2
0
1
0
0
2
2
2
1
0
0
0
2
1
1
1
2
2
0
0
1
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
2
0
0
1
2
0
0
0
1
0
1
0
1
1
0
1
0
0
0
0
0
1
2
0
0
2
2
0
1
0
1
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
1
0
1
2
0
0
1
2
0
0
2
0
0
1
1
0
0
0
1
1
1
3
1
0
2
0
1
1
1
0
0
1
0
0
0
1
0
0
0
2
0
0
2
0
0
1
1
1
1
2
1
4
0
0
1
0
1
0
0
0
0
0
0
0
2
1
0
0
4
0
0
2
0
0
0
0
2
0
0
0
0
1
0
1
0
1
0
0
0
2
1
0
0
2
0
0
0
0
2
1
0
0
0
0
1
0
0
2
0
0
1
1
2
1
0
1
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
2
2
0
1
2
0
0
1
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
4
2
2
1
1
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
2
0
2
2
1
0
1
0
0
2
2
0
0
0
0
0
1
0
2
1
0
0
0
1
2
0
0
1
2
0
0
0
0
3
2
1
1
1
1
1
0
0
2
2
1
0
1
0
0
2
0
0
0
1
2
0
1
1
1
0
1
0
1
1
1
1
0
0
0
0
0
0
1
2
0
1
0
0
0
2
1
1
0
0
0
0
0
0
2
1
0
2
2
1
1
2
1
1
0
1
2
1
0
0
0
0
1
2
2
0
0
0
0
0
2
1
0
0
0
3
0
0
1
1
0
1
2
1
2
0
1
0
3
3
1
0
0
0
1
0
0
2
0
0
0
2
0
1
2
0
0
1
0
1
0
0
2
1
1
1
1
1
2
1
1
2
0
1
1
0
1
1
1
0
1
0
0
2
2
0
2
0
2
2
1
0
0
0
0
0
0
1
2
0
0
2
0
0
2
0
2
1
1
0
0
0
0
10
0
0
1
1
1
0
1
0
0
0
2
0
1
1
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
2
1
3
1
2
0
0
0
0
1
0
0
2
1
0
2
1
0
0
0
2
0
0
0
0
1
0
0
0
0
5
2
2
0
2
0
0
2
0
1
0
0
0
1
1
0
0
0
0
2
1
0
1
2
0
1
2
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
1
0
1
1
1
1
1
0
1
0
1
0
0
0
2
1
1
2
1
0
1
0
0
0
2
1
0
1
0
0
1
2
2
1
2
1
0
2
1
0
2
0
0
2
0
0
0
0
0
2
2
0
2
0
2
0
2
0
0
1
0
1
1
1
0
0
2
1
1
0
2
0
0
2
1
1
1
1
2
0
2
1
0
2
0
0
1
2
2
0
1
0
0
0
4
2
0
0
1
2
1
0
0
1
0
2
1
1
0
1
0
2
1
3
0
0
1
0
1
1
3
2
1
2
0
1
0
1
0
0
0
0
0
2
0
1
2
0
0
0
0
1
1
1
0
1
1
0
0
0
0
1
2
1
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
1
1
0
0
1
0
1
0
0
3
0
0
0
0
1
0
1
2
2
2
1
0
1
0
2
0
2
2
0
0
0
1
0
0
1
0
2
0
1
0
1
0
0
0
1
0
1
0
0
0
0
2
0
1
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
2
0
1
2
1
1
0
0
2
1
0
2
0
0
0
2
0
1
0
2
0
1
0
2
0
0
1
1
2
0
1
1
0
1
1
0
0
0
2
0
1
0
1
1
3
0
0
0
2
0
2
0
0
1
1
2
0
0
1
0
1
0
1
0
0
0
2
1
1
0
1
2
2
1
1
3
0
0
0
1
0
0
1
0
1
1
0
2
0
2
0
0
1
0
1
1
1
0
1
0
1
0
0
1
0
2
1
0
1
2
0
1
0
1
2
1
0
0
1
0
1
0
0
0
0
1
0
2
0
0
1
0
0
0
0
2
2
0
0
1
1
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
2
1
1
0
6
1
0
1
0
0
0
0
2
1
0
3
1
0
1
2
2
0
0
2
1
0
0
0
1
0
2
0
1
2
0
0
0
0
0
0
0
1
1
0
1
1
1
2
0
1
0
0
0
1
1
0
2
0
0
0
0
0
0
1
1
0
0
1
0
1
1
0
1
2
0
1
0
1
1
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
2
2
0
0
0
0
0
2
2
0
0
1
1
0
2
1
1
2
1
0
1
0
1
1
2
3
0
1
0
0
0
1
1
2
1
0
1
0
0
1
1
0
1
0
0
0
2
1
0
1
0
0
0
0
0
1
2
0
0
0
2
0
1
0
0
0
2
2
2
1
1
0
1
0
1
0
1
0
1
1
1
0
0
2
0
0
0
0
2
1
1
1
0
2
0
0
0
0
2
0
0
3
0
0
1
0
0
2
0
0
0
0
2
0
1
0
0
2
0
0
0
1
1
0
2
0
1
0
0
1
0
1
1
2
1
0
2
0
1
1
0
2
1
1
1
0
0
1
0
0
0
0
1
0
0
2
1
0
2
1
1
0
1
1
0
2
2
0
0
0
2
1
2
0
1
2
0
0
0
2
0
0
1
0
0
2
2
0
1
1
0
2
0
2
0
0
1
0
0
2
1
0
1
0
0
0
1
0
1
0
0
0
2
0
0
0
2
0
1
0
0
1
1
1
1
0
1
2
0
0
1
0
2
1
1
0
0
2
1
0
2
0
0
2
0
1
0
1
0
0
0
2
2
2
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
3
1
1
0
0
1
0
0
1
1
0
0
2
2
1
1
2
1
0
0
0
0
1
1
0
0
0
0
0
1
2
3
0
1
0
0
2
0
0
0
3
1
0
0
3
0
0
0
4
0
0
1
1
0
0
1
1
0
0
0
0
0
1
1
0
0
2
0
0
0
1
2
1
0
1
1
0
1
1
2
1
0
1
1
0
1
0
1
1
1
4
1
1
0
1
0
2
0
1
0
1
2
0
1
0
0
2
1
2
0
0
2
2
2
1
0
0
0
0
1
2
1
1
2
1
2
0
0
0
1
0
1
0
1
2
2
2
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
2
0
0
0
0
0
0
1
0
2
2
2
0
0
0
1
0
1
2
2
0
0
0
0
1
1
2
2
0
2
0
2
0
0
0
1
0
0
2
2
1
0
1
1
1
1
2
2
2
0
0
2
0
0
0
2
0
2
0
1
0
0
0
1
1
0
2
0
1
0
0
2
0
2
0
1
0
1
0
2
0
2
1
1
0
1
0
0
2
0
2
1
1
2
1
0
2
0
0
0
2
2
0
0
2
0
0
2
2
3
0
1
0
1
0
0
0
0
0
0
0
2
1
2
1
1
0
0
0
1
0
0
1
1
0
1
1
1
1
1
0
0
1
0
0
1
0
1
2
0
1
0
0
2
2
2
0
0
1
2
0
2
1
0
0
0
1
2
0
2
1
0
0
0
1
2
0
2
0
1
0
0
0
2
1
0
1
1
0
2
1
0
1
0
1
2
2
2
0
2
2
0
1
0
1
1
0
0
1
1
1
0
1
2
0
0
1
2
0
1
1
0
0
2
0
1
1
1
1
0
0
3
0
1
1
1
2
1
0
0
0
0
2
0
1
2
2
0
1
2
0
0
0
1
0
1
2
0
0
3
0
1
0
2
0
0
0
1
0
0
1
2
1
1
2
2
0
0
2
0
2
0
2
2
1
3
2
1
0
0
0
0
0
2
0
0
1
0
0
1
1
1
0
0
0
0
1
0
2
2
1
0
0
0
1
0
0
1
1
0
1
1
0
0
1
0
1
0
0
0
1
0
2
0
1
1
1
4
0
1
0
0
0
3
0
1
1
2
4
0
0
0
1
0
2
0
1
1
2
0
2
1
2
3
0
0
2
1
0
2
0
1
1
1
1
0
0
0
0
2
2
0
1
1
0
0
2
0
1
0
0
0
2
1
0
2
0
1
0
0
0
2
1
0
1
2
0
0
0
0
0
1
0
2
1
0
5
0
1
1
0
2
0
0
1
0
0
1
0
1
0
1
0
0
0
0
1
2
0
0
0
0
0
1
0
1
0
2
0
0
0
0
2
1
0
1
0
1
1
0
0
0
1
2
0
0
0
0
1
1
0
1
2
0
0
2
0
0
1
0
1
1
2
0
0
0
2
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
1
1
0
3
1
2
0
2
0
0
2
2
1
4
0
1
0
0
1
1
0
0
1
1
6
1
1
0
0
0
0
2
0
1
0
2
0
2
2
2
0
1
1
3
1
0
0
0
0
0
2
2
0
0
0
2
2
2
0
1
0
2
2
1
1
0
0
2
0
0
1
1
2
0
0
1
1
1
2
1
2
2
1
2
0
1
2
2
2
3
0
1
0
0
1
0
2
1
1
0
1
0
2
0
1
1
0
0
1
0
2
0
0
0
0
0
2
0
1
2
0
0
0
1
0
4
0
1
2
0
0
0
0
0
0
0
0
2
0
1
0
1
0
2
0
0
1
0
1
0
0
2
0
1
2
0
1
2
0
2
2
0
2
0
2
1
1
0
1
0
2
2
0
0
0
3
1
1
0
2
0
2
0
0
1
0
1
0
1
0
1
0
1
2
0
2
1
0
0
0
0
0
2
0
0
2
0
1
1
0
0
0
1
1
2
1
2
2
1
2
2
0
2
1
0
0
0
2
2
0
0
2
0
1
0
0
1
2
1
1
1
1
1
2
0
1
0
1
1
0
2
0
0
0
1
0
1
0
0
0
2
0
1
1
2
1
1
0
1
1
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
1
0
1
1
0
0
2
0
0
0
0
1
0
2
1
0
2
2
0
0
2
1
0
0
0
0
1
2
1
1
1
0
1
2
2
0
2
1
0
1
1
0
1
0
2
0
0
1
1
0
1
0
0
0
0
2
1
0
0
0
0
0
0
1
2
0
0
1
0
2
1
1
1
3
1
2
2
0
1
0
0
2
2
0
2
2
1
0
0
0
0
3
1
0
1
1
0
0
1
1
2
0
0
0
0
2
2
0
0
2
0
0
0
1
0
2
0
2
0
0
4
1
1
1
1
0
0
2
1
0
2
0
1
0
0
1
0
3
1
2
0
0
1
2
0
0
0
0
1
2
1
0
0
1
0
0
0
1
0
0
2
1
0
0
1
0
1
0
1
0
0
2
1
1
1
1
0
2
0
1
0
2
0
0
1
0
1
0
1
0
0
1
1
0
2
1
1
1
2
0
2
1
1
2
1
0
0
1
0
0
1
0
0
1
2
1
2
0
0
2
1
0
0
1
1
1
2
0
2
2
1
2
1
2
3
0
0
7
0
0
2
0
0
2
2
2
0
2
1
0
1
2
0
0
0
1
2
1
3
3
0
1
1
0
0
0
0
2
0
2
0
2
1
0
0
0
0
2
0
0
0
2
1
0
0
1
2
0
1
0
1
1
0
0
2
1
0
1
2
2
2
2
0
1
1
0
0
0
0
0
0
2
0
1
1
0
2
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
3
1
1
0
0
0
1
1
0
0
0
0
1
0
0
1
1
0
1
1
0
1
0
1
0
0
2
0
0
0
1
0
0
1
0
0
2
0
0
1
2
0
1
2
0
0
0
2
1
0
0
1
1
2
1
1
1
3
0
2
2
0
0
0
0
1
2
0
1
0
1
2
2
1
0
2
2
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
2
1
1
0
0
1
1
0
1
0
0
0
1
0
0
0
2
2
0
1
2
0
1
1
0
1
0
0
1
1
2
0
0
1
0
0
1
1
0
0
1
0
0
1
1
0
2
0
0
2
2
0
1
0
0
1
0
1
2
1
2
2
0
0
1
0
1
2
0
2
2
1
0
0
1
0
1
2
0
2
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
1
2
1
2
0
0
0
3
0
2
0
2
0
1
1
1
0
1
0
0
1
1
0
2
0
1
2
0
0
1
0
1
1
1
0
0
2
2
1
2
0
1
0
2
0
1
0
0
1
0
2
1
0
0
0
0
1
1
0
2
1
0
1
2
2
1
1
0
0
0
0
1
2
0
0
1
2
2
2
0
1
1
0
0
1
1
3
2
0
1
0
0
0
1
2
3
1
1
0
1
1
0
1
2
2
1
2
2
0
0
1
0
1
0
0
2
1
1
0
0
1
1
1
2
0
0
0
1
2
1
0
0
0
1
0
1
2
2
1
0
2
0
1
0
1
0
0
0
0
2
0
1
0
2
0
0
2
0
1
1
1
1
1
1
1
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
2
0
0
0
0
2
0
1
0
2
0
1
0
1
0
0
0
2
1
0
0
0
1
1
0
1
0
0
0
1
2
0
1
1
0
0
2
1
0
0
1
1
0
2
0
0
1
1
0
2
1
0
0
0
0
1
0
1
2
0
0
0
2
0
1
1
1
0
1
0
2
0
2
2
2
2
2
0
0
1
0
1
0
0
2
2
0
2
0
0
1
1
2
0
2
0
0
1
1
0
0
0
0
0
1
0
0
2
0
1
3
2
0
0
0
2
0
0
0
0
1
0
1
2
0
0
2
0
0
1
0
2
2
1
1
0
0
0
0
1
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
3
0
2
1
1
2
2
1
0
2
0
2
1
1
0
2
0
0
0
0
1
0
1
1
0
0
1
1
0
1
0
0
0
1
0
0
0
2
0
0
2
0
2
0
4
0
0
0
0
0
1
3
1
1
2
1
0
2
2
1
1
1
1
1
0
1
1
1
0
0
2
0
1
1
2
0
2
0
0
1
1
0
0
1
0
1
1
1
0
0
1
1
2
0
0
1
1
0
0
0
0
0
2
0
2
0
1
1
2
1
0
2
1
1
0
0
0
2
2
1
0
1
0
0
2
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
2
2
0
2
2
0
3
2
0
1
2
0
1
0
1
0
1
1
2
0
0
0
2
1
0
0
0
2
0
0
1
0
0
1
1
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
1
1
2
1
2
2
0
0
1
2
1
0
2
0
1
1
1
1
1
0
2
1
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
3
2
0
2
0
1
2
1
0
1
0
2
2
2
2
0
2
1
0
1
0
2
0
0
1
0
0
1
0
1
1
1
1
0
0
2
1
0
0
3
1
0
1
0
0
0
0
1
1
0
1
1
0
1
0
0
0
0
0
0
1
0
0
1
1
2
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
2
0
1
1
2
1
0
0
1
0
0
1
1
1
0
1
1
2
1
0
1
1
2
0
0
0
0
1
0
0
2
0
0
1
0
0
3
1
0
2
0
0
2
0
0
1
0
1
0
0
0
0
0
2
0
2
1
0
0
2
1
0
0
0
1
0
2
2
2
1
0
2
1
0
1
0
0
2
0
0
0
2
1
0
0
2
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
2
0
1
0
2
0
1
1
1
0
0
0
0
1
0
0
2
1
2
0
0
0
2
0
0
2
1
1
0
1
0
1
0
0
0
0
0
2
2
0
2
2
0
2
0
1
1
2
0
2
2
0
0
0
2
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
2
2
1
0
0
1
2
1
1
2
1
0
0
2
1
2
1
0
0
1
0
0
2
2
0
0
0
0
0
2
0
2
1
1
1
1
2
0
1
0
2
0
0
0
2
2
0
1
0
2
1
1
2
0
2
1
0
2
0
0
0
0
2
1
1
0
1
0
0
0
1
0
0
2
1
1
2
1
2
0
0
0
0
0
0
2
0
1
1
1
2
0
1
1
0
0
0
0
1
0
0
2
1
3
0
0
1
0
3
2
0
0
1
0
0
2
0
1
1
0
0
1
0
1
0
4
2
2
0
1
1
0
1
0
2
3
3
0
1
2
0
1
0
1
1
2
0
2
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
1
1
1
2
0
1
1
0
1
0
2
2
0
2
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
1
0
2
4
1
2
0
1
0
0
0
0
3
1
1
1
0
1
0
0
0
0
0
0
0
1
0
0
2
0
2
1
0
0
2
2
1
0
1
0
0
1
0
1
0
0
2
0
0
2
0
1
0
0
1
0
1
1
2
0
0
1
2
2
0
0
0
1
1
0
1
0
0
2
0
0
0
2
2
2
2
0
2
0
0
0
0
2
0
0
0
3
0
2
1
0
0
0
0
2
2
0
0
0
0
2
0
1
0
1
0
0
1
1
2
1
1
1
1
0
2
0
0
1
1
0
0
0
0
0
2
1
1
0
2
0
0
0
1
0
2
0
3
0
0
1
1
0
0
0
2
1
1
1
1
0
1
1
2
0
0
1
1
2
1
0
0
0
1
1
0
0
0
2
0
2
1
1
1
1
0
0
0
1
0
0
0
0
1
0
0
2
1
0
0
1
2
0
0
1
1
1
0
1
1
1
2
0
2
1
1
0
0
0
0
0
0
1
0
0
1
2
0
1
0
0
0
4
2
0
1
0
1
3
2
1
1
1
1
1
0
0
0
0
1
0
2
0
2
2
2
0
2
0
0
0
1
0
0
0
2
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
2
1
1
1
0
0
0
2
0
1
1
5
0
0
0
1
1
1
0
0
2
2
0
0
0
1
0
2
1
0
2
0
2
1
1
1
0
0
0
1
1
1
0
0
2
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
2
1
0
2
2
1
0
0
0
0
1
0
0
2
0
0
2
0
0
0
2
0
1
0
2
2
0
0
0
1
0
0
0
1
0
1
1
3
3
0
1
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
1
2
0
0
0
1
0
1
1
0
0
0
0
0
0
2
1
2
1
2
0
0
1
2
0
0
0
1
0
0
1
0
1
1
1
0
2
1
0
0
0
1
2
0
1
0
1
0
1
0
1
3
2
0
1
2
2
0
0
0
2
1
1
1
0
0
0
1
2
0
0
0
0
2
0
0
2
0
0
1
0
0
0
1
0
1
2
0
2
2
0
0
0
1
1
2
0
1
0
1
2
0
0
0
1
1
0
1
0
0
1
2
2
2
2
0
2
1
0
1
1
2
0
0
2
0
0
0
1
1
2
0
1
2
1
0
0
1
0
0
1
0
1
1
4
1
2
1
1
1
0
1
1
1
2
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
2
2
0
1
2
0
0
2
0
2
1
1
0
2
0
0
1
1
2
0
2
0
0
3
1
0
0
2
2
1
1
2
2
0
0
0
2
0
2
2
2
0
2
1
2
1
0
0
1
0
2
0
1
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
1
0
1
0
1
2
1
0
2
2
1
1
0
0
0
0
2
0
0
1
1
1
0
0
2
0
0
1
0
1
0
2
0
2
0
3
0
2
0
0
0
1
0
1
0
2
1
0
2
1
0
1
0
2
2
0
0
0
0
0
0
1
0
0
0
2
0
2
0
7
2
0
0
0
0
0
1
0
1
2
0
0
0
0
2
1
0
0
2
0
2
0
1
1
0
0
2
0
2
0
0
0
0
0
1
0
1
2
0
1
1
0
0
2
0
0
1
2
2
0
0
1
1
0
3
0
1
1
2
2
2
0
0
0
1
2
0
1
0
2
0
0
2
0
0
0
1
0
0
2
0
2
0
0
0
2
0
2
0
2
2
1
0
0
1
1
0
0
0
0
0
1
0
2
2
0
1
1
1
1
2
1
0
0
1
0
1
1
1
3
0
1
0
2
0
0
1
1
0
0
0
0
0
2
1
0
2
1
0
2
0
0
1
0
0
0
2
0
0
2
2
1
0
0
2
1
0
0
0
0
0
1
2
1
2
1
1
1
0
1
0
1
0
2
1
0
1
2
4
1
2
1
0
2
0
1
0
0
1
2
0
0
1
2
1
2
0
0
1
0
1
0
1
2
1
0
1
2
0
2
0
1
0
1
0
1
1
1
0
0
2
1
2
1
1
2
0
0
2
2
1
0
1
1
0
0
2
0
0
1
0
0
1
1
1
3
1
0
1
1
0
2
1
2
2
2
0
0
0
0
1
2
0
0
3
0
2
1
0
0
1
0
1
0
1
0
0
0
0
2
0
2
2
2
0
1
1
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
3
0
0
1
0
1
0
2
0
0
0
1
0
2
1
0
1
1
1
1
1
1
1
0
1
0
0
0
0
1
4
1
1
0
2
1
1
2
0
2
1
1
1
1
1
1
0
1
0
0
0
0
1
1
2
0
0
0
0
1
0
0
1
0
1
1
0
0
0
2
0
1
2
1
0
0
1
1
3
0
0
0
2
1
1
1
0
0
1
1
1
0
2
2
2
2
1
1
2
2
2
0
0
2
0
0
1
0
2
1
0
0
1
2
3
0
0
0
2
0
0
2
2
0
1
0
0
0
1
0
2
1
1
2
0
1
1
0
0
0
0
0
2
1
2
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
2
0
1
1
1
1
1
1
0
0
0
0
0
2
0
1
0
1
0
1
2
1
0
1
0
1
0
1
0
1
1
1
0
0
0
1
0
0
1
1
0
1
0
0
0
2
1
1
0
4
2
0
0
0
0
0
0
3
2
0
0
0
0
0
0
1
0
2
2
0
0
1
0
0
0
2
0
0
0
1
4
0
0
0
0
1
1
0
4
0
0
2
1
1
0
0
0
0
0
9
1
0
0
0
1
0
1
2
1
2
0
2
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
2
1
1
0
2
4
0
1
0
0
0
0
1
0
2
1
1
1
1
1
0
2
0
0
0
0
0
0
0
0
1
0
2
2
0
2
0
0
0
0
0
1
3
0
2
0
1
2
0
0
0
1
0
1
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
2
2
0
1
1
1
1
0
2
0
0
0
0
0
1
2
0
0
1
1
2
0
1
1
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
2
0
0
1
1
1
0
2
2
0
0
1
2
0
0
0
0
0
2
2
4
0
0
2
0
0
0
2
2
0
0
2
2
0
1
0
0
0
0
0
1
0
12
1
2
1
0
0
0
1
1
0
0
2
0
1
0
0
0
0
0
1
0
0
1
2
1
0
1
1
0
1
0
2
1
0
3
1
0
0
1
1
0
0
0
0
1
0
0
1
1
1
0
1
0
0
1
0
1
2
0
1
2
2
0
1
0
7
0
1
2
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
1
0
1
2
0
1
0
2
0
0
2
2
0
0
0
0
2
0
0
0
2
2
2
0
0
0
0
0
1
2
2
0
1
1
2
0
0
2
0
0
1
0
0
0
2
1
1
0
0
0
2
2
2
1
2
0
1
0
1
0
2
2
1
0
0
1
2
2
0
2
0
0
0
1
1
2
0
1
1
0
1
1
3
0
2
1
1
1
1
0
4
0
0
2
2
1
2
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
1
2
0
1
0
0
0
0
2
0
0
1
0
0
1
2
1
0
1
0
2
2
0
2
2
2
1
1
0
0
0
1
0
0
0
0
2
2
3
0
0
2
0
0
1
0
0
1
0
0
0
0
2
2
0
1
0
2
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
1
1
2
0
0
1
2
0
0
0
0
0
0
0
4
3
2
1
2
1
0
1
1
0
0
1
0
0
1
0
0
1
0
2
0
0
2
1
0
1
0
0
0
1
1
0
0
1
1
2
0
0
1
1
0
2
0
0
1
2
0
1
1
1
0
2
2
0
2
2
1
0
0
1
0
0
0
0
1
2
0
0
1
1
1
0
1
0
1
0
0
2
0
0
1
2
0
0
1
1
1
1
2
0
0
0
4
0
0
1
2
2
4
0
1
0
1
0
0
1
0
0
0
1
2
1
0
1
0
0
0
0
0
1
0
0
0
2
0
1
0
2
1
0
0
1
1
2
0
0
1
1
3
0
2
0
0
1
0
2
2
2
1
0
1
0
1
0
1
0
0
2
1
0
0
1
0
0
0
0
1
1
0
0
0
2
1
0
1
0
1
2
0
1
0
1
2
0
1
0
1
0
0
0
0
1
0
2
0
0
1
0
0
1
0
0
2
0
2
0
0
0
0
2
3
1
0
1
0
2
1
1
0
0
1
0
1
0
1
1
0
0
2
1
0
2
0
0
1
0
2
0
0
0
1
2
1
0
1
1
0
0
2
4
1
0
0
2
1
0
0
0
1
1
1
2
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
2
0
0
2
1
2
0
1
0
0
2
0
0
1
0
0
1
1
0
0
2
1
0
2
0
0
0
1
3
0
0
0
0
0
0
0
0
2
1
1
2
0
1
0
0
1
0
2
0
1
0
3
1
0
2
1
0
2
4
0
0
2
2
2
0
2
2
0
0
0
1
0
1
1
0
0
2
2
0
2
0
2
1
1
1
1
1
0
0
1
1
0
0
0
0
0
2
0
1
1
0
0
1
2
4
1
0
1
0
1
0
1
1
0
0
0
0
2
0
0
1
1
1
2
0
0
1
0
1
0
0
0
1
2
0
1
1
0
0
1
1
0
1
0
0
0
0
0
0
1
1
2
0
0
2
0
0
1
1
0
0
2
2
0
0
1
0
2
2
0
0
0
1
2
0
0
1
0
1
1
1
1
2
3
0
5
1
0
1
0
0
2
0
0
0
1
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
1
2
2
1
1
0
2
0
1
2
2
0
0
1
0
0
3
1
0
1
2
0
0
0
1
0
2
1
0
0
0
3
1
0
0
0
0
2
2
1
2
0
1
7
2
1
0
2
1
2
0
0
2
2
2
0
3
0
1
1
0
0
0
0
0
0
1
1
1
2
4
2
2
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
2
3
0
1
0
2
2
1
0
0
0
2
1
1
2
0
0
0
2
0
1
1
2
2
1
0
1
0
2
2
2
0
0
0
1
2
1
0
2
0
0
1
1
2
1
0
2
1
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
1
2
0
1
1
1
1
1
0
0
1
1
0
0
2
0
2
2
0
0
0
0
1
1
0
1
2
0
2
0
0
0
1
0
0
0
1
1
1
0
2
1
1
0
2
0
1
0
1
0
0
1
1
0
2
0
0
2
1
2
0
2
0
2
0
1
1
0
1
0
3
1
1
0
0
0
0
2
0
0
0
1
1
2
1
0
0
2
1
2
2
1
0
0
0
2
0
2
1
2
0
1
4
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
1
1
0
1
0
0
1
2
1
1
1
1
2
1
2
1
2
0
1
0
1
0
1
0
0
0
0
0
0
1
0
2
2
1
0
3
0
0
1
1
0
0
0
1
0
0
1
1
0
1
2
0
0
2
1
1
2
1
0
0
0
1
0
1
1
0
0
1
1
1
0
1
0
2
0
1
0
1
2
0
1
0
7
0
0
0
3
0
0
2
0
1
3
1
0
0
2
1
2
1
2
1
3
2
0
0
2
1
0
2
0
0
0
1
1
0
1
1
0
1
0
0
0
0
2
1
0
0
0
0
1
1
0
2
1
0
0
1
2
0
0
2
0
0
0
0
0
0
2
0
1
1
1
0
1
0
1
0
0
0
0
0
2
0
0
1
1
1
2
0
2
2
0
0
0
0
0
0
1
2
0
0
2
0
1
0
0
1
1
0
1
0
0
1
0
0
0
0
1
1
0
2
2
0
1
1
1
0
2
1
2
0
1
0
0
0
0
1
0
2
1
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
2
0
2
1
0
0
1
0
0
1
0
1
0
2
2
1
1
2
1
0
1
1
2
1
0
1
0
2
0
0
1
1
2
0
0
1
0
0
0
1
0
2
1
0
0
0
0
0
0
2
2
2
1
0
1
0
2
1
0
0
0
2
0
1
0
2
0
1
0
0
0
0
0
1
0
2
0
3
2
0
2
1
0
0
1
1
1
1
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
3
0
2
1
2
1
0
0
0
0
1
2
1
0
0
0
0
0
2
0
0
0
1
0
0
0
1
1
1
2
1
0
2
1
1
1
0
0
0
0
1
2
0
0
1
2
1
2
1
2
0
0
2
1
2
0
1
3
0
1
1
0
0
1
1
2
0
1
0
1
1
0
1
1
1
2
1
1
0
0
2
1
2
2
0
2
3
0
2
2
2
0
0
0
1
2
1
1
0
0
1
0
0
0
0
2
1
0
1
2
0
0
0
2
0
1
0
0
1
2
2
1
2
0
2
1
1
0
0
0
1
0
0
0
2
0
2
2
1
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
1
1
0
1
1
0
2
1
0
2
1
0
0
0
1
0
0
1
0
1
2
1
0
4
0
0
0
0
1
0
1
0
0
2
2
0
0
0
1
0
0
0
1
0
0
2
2
1
2
1
0
1
0
0
0
1
0
0
0
1
0
0
2
0
0
1
0
1
0
1
0
1
0
2
1
0
2
1
1
0
1
0
2
0
1
2
2
2
0
0
0
0
2
1
1
1
1
0
2
0
2
1
0
1
1
2
1
2
0
1
0
0
0
2
1
1
0
0
1
2
0
1
1
0
0
2
0
0
1
2
1
2
2
0
0
0
0
0
1
0
0
2
2
1
0
0
0
1
1
2
1
1
0
2
0
0
1
1
2
2
0
0
0
2
2
0
1
1
0
1
0
1
2
1
1
0
0
0
2
1
0
1
0
1
0
0
0
1
0
0
2
0
0
2
1
0
0
0
2
2
0
2
1
1
0
0
0
0
0
1
0
1
1
1
3
1
1
1
1
0
0
1
2
0
1
0
1
2
1
2
0
2
0
1
0
0
2
2
2
0
0
1
0
2
0
1
1
0
0
0
1
1
0
0
2
2
0
1
1
0
1
2
0
0
1
2
0
0
1
1
0
2
0
1
0
2
2
1
1
0
0
2
0
1
2
0
1
0
2
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
1
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
1
0
0
1
0
1
0
1
0
0
2
0
2
0
1
1
0
1
1
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
1
2
2
0
0
0
1
2
2
1
1
0
0
0
1
0
1
0
0
7
1
0
0
2
3
0
0
2
1
0
1
0
1
0
0
0
0
0
0
3
0
0
0
1
2
0
6
1
0
1
2
1
0
2
0
0
0
0
1
0
1
0
1
2
0
0
1
2
1
0
0
1
0
1
0
0
2
0
2
1
2
0
1
1
0
1
0
2
1
1
0
0
0
0
2
2
0
1
1
1
0
1
2
0
0
1
0
3
0
0
0
6
0
0
1
1
1
0
0
0
0
0
1
1
0
2
0
1
2
0
0
0
0
2
0
0
2
1
2
1
0
2
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
2
1
2
3
0
1
0
0
0
0
0
0
0
0
2
1
0
0
2
2
2
1
1
0
0
0
1
1
0
0
1
1
0
0
0
0
0
2
0
0
0
1
2
0
2
0
2
0
1
0
1
0
0
3
0
0
2
1
0
2
1
0
0
1
0
3
0
0
1
2
1
0
0
1
0
1
2
1
0
0
1
0
1
1
2
0
0
2
0
1
0
1
0
2
1
1
0
0
0
0
1
0
1
0
0
0
2
1
1
2
0
0
1
1
1
0
1
1
0
0
0
0
0
1
1
0
2
1
2
2
0
2
0
2
0
0
1
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
2
1
2
0
1
1
2
0
0
1
2
2
1
0
0
2
0
0
0
0
0
1
2
0
1
1
0
2
2
2
1
0
0
2
1
1
2
3
2
1
1
1
2
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
2
3
1
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
2
1
0
0
1
0
1
0
2
2
0
1
2
1
0
0
0
1
0
1
0
5
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
1
0
2
0
1
0
1
1
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
1
0
2
2
1
1
2
0
1
1
1
0
0
0
1
0
2
0
1
2
1
0
0
0
0
1
2
0
0
2
0
0
0
1
2
0
0
0
0
1
0
2
2
1
0
2
2
0
1
0
1
0
2
3
1
1
2
0
2
0
0
1
0
0
1
1
0
0
0
0
0
2
0
2
2
0
1
1
1
0
0
0
0
2
2
1
0
2
0
0
1
2
0
1
1
1
7
0
1
1
0
1
0
2
1
0
0
1
1
0
1
1
0
2
0
1
0
0
1
1
2
2
2
0
0
0
1
0
0
0
0
0
0
2
2
2
0
0
0
0
2
3
2
0
2
0
2
2
1
1
1
0
0
1
2
0
1
1
0
2
3
1
0
0
1
2
0
0
0
0
1
1
1
0
2
2
0
0
2
2
2
2
1
1
0
0
0
0
1
2
2
0
1
0
0
0
2
2
1
0
1
2
1
0
2
0
0
0
0
0
0
2
2
2
0
4
2
2
1
1
2
0
1
2
1
0
2
2
1
0
1
0
2
1
0
1
0
2
0
0
0
3
0
1
0
0
0
0
0
1
0
0
1
1
2
0
1
2
0
1
1
1
0
1
0
0
0
0
1
1
3
0
2
0
0
1
0
0
0
0
2
1
1
1
1
1
0
0
2
2
1
0
2
0
2
1
0
1
0
0
1
2
1
0
0
0
0
1
2
0
2
2
2
0
0
1
1
0
3
2
0
1
0
2
0
0
1
0
2
1
1
0
1
0
0
0
0
0
0
1
0
0
0
2
2
1
1
1
0
1
3
1
0
2
0
1
1
2
1
0
0
0
0
0
0
0
0
1
1
3
2
1
0
0
0
0
2
2
0
0
2
1
0
2
0
0
0
1
0
2
1
0
1
0
0
1
1
0
1
0
2
2
8
1
1
1
0
2
0
0
1
2
0
1
1
0
0
2
1
3
0
2
1
1
1
1
1
0
0
0
0
0
0
0
1
0
2
0
0
1
1
1
0
0
0
0
1
0
1
1
0
2
2
0
1
0
1
2
2
0
1
1
0
1
0
0
0
0
1
2
0
0
0
2
0
2
0
0
1
1
3
2
0
1
0
1
0
1
2
1
0
2
0
0
0
0
2
1
0
0
1
2
1
0
5
0
0
1
2
1
0
3
2
1
0
0
1
0
0
0
0
2
0
1
4
1
2
0
0
1
1
0
0
1
0
0
2
1
0
1
1
0
0
0
1
0
2
1
0
0
2
1
0
1
0
1
0
1
1
0
0
0
1
1
1
0
2
0
3
0
0
1
0
0
1
0
0
0
2
0
0
0
0
2
0
2
1
0
0
1
1
2
0
2
2
0
0
1
0
0
1
0
0
1
0
0
0
2
0
0
0
2
3
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
3
1
0
1
0
1
3
0
1
2
0
1
0
0
0
0
0
0
1
0
1
0
0
2
1
0
0
1
1
0
0
0
1
3
0
1
0
0
1
0
1
0
0
0
2
1
1
0
0
0
0
1
0
0
2
2
0
1
0
0
1
1
0
1
2
0
0
0
0
1
0
0
2
0
0
1
1
0
1
0
1
0
1
1
1
0
0
1
0
0
0
0
2
0
2
2
2
0
0
1
0
0
1
1
0
3
1
0
0
0
0
1
2
0
2
1
0
0
2
2
0
0
0
2
0
0
0
1
0
2
0
1
1
2
2
1
0
1
1
5
0
0
1
0
0
2
0
2
5
0
1
1
0
1
1
2
0
2
1
0
0
0
2
1
0
1
0
1
0
0
1
0
0
0
0
0
3
0
0
1
1
0
1
0
2
1
0
0
0
1
0
2
1
0
0
0
0
0
1
1
0
1
0
0
0
2
1
1
0
0
0
0
1
2
0
0
1
1
0
0
1
1
1
2
2
0
0
2
0
2
2
2
2
0
1
2
1
0
0
1
1
0
0
0
0
2
0
0
0
2
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
1
4
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
1
1
1
1
2
2
0
0
0
0
0
0
2
0
0
2
0
2
2
0
2
1
2
3
2
2
3
1
2
1
0
2
1
0
2
1
1
0
0
0
1
1
2
2
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
2
2
1
2
0
0
2
0
2
1
1
2
1
0
0
0
2
2
2
0
1
5
0
0
0
2
4
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
2
0
0
3
2
0
2
1
1
1
2
0
2
0
0
0
2
0
2
0
0
1
2
1
0
1
0
0
0
0
0
1
0
0
2
1
0
2
1
1
0
4
1
2
0
1
0
0
1
0
0
0
1
0
1
0
1
0
2
0
3
0
0
2
1
3
2
0
0
0
0
1
0
0
2
1
1
0
0
2
1
0
0
2
0
1
0
0
0
0
0
1
0
1
0
0
2
0
1
1
1
2
1
0
1
1
0
1
0
0
2
0
1
0
2
0
1
1
0
2
0
0
0
0
2
0
0
2
2
4
2
2
0
0
0
2
1
0
0
0
1
1
1
0
0
0
1
1
2
1
0
1
0
1
1
2
2
0
0
1
0
2
1
1
1
0
1
1
1
1
0
1
0
1
3
0
2
1
0
0
1
0
2
5
0
0
0
2
0
0
2
1
2
1
0
0
0
1
3
1
1
0
1
0
0
0
0
0
3
0
2
0
1
0
0
2
2
0
0
0
0
0
0
0
1
2
0
0
2
0
0
2
0
0
0
0
1
0
2
0
0
0
0
1
0
1
2
2
0
2
0
1
0
1
0
2
0
0
3
1
2
0
1
4
1
0
0
0
2
2
0
0
1
0
2
2
2
0
1
0
0
1
2
0
2
0
1
1
0
0
1
1
1
1
2
1
0
0
0
0
2
0
0
2
1
1
2
0
0
0
2
0
0
0
3
1
0
0
0
0
2
0
1
1
1
0
1
0
0
2
4
2
1
2
2
0
0
0
0
1
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
2
0
1
0
1
1
2
2
0
0
0
2
0
2
0
1
2
0
0
0
2
0
0
2
0
1
2
1
0
2
2
0
0
0
0
1
1
0
0
2
3
1
1
1
0
0
2
0
1
0
2
0
2
0
1
2
1
1
0
3
0
0
0
0
2
3
0
0
0
0
3
1
0
1
0
1
0
2
1
0
0
2
2
1
1
0
0
0
0
0
2
0
1
1
1
0
0
5
0
0
0
1
0
0
0
1
1
0
0
2
1
1
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
1
2
0
0
2
0
0
1
2
2
1
2
1
2
2
0
1
2
0
0
1
0
0
1
0
1
0
0
0
1
1
2
2
2
1
0
0
0
2
2
2
0
0
1
0
0
0
0
1
1
2
0
0
0
1
2
0
0
0
0
0
3
1
2
1
0
1
0
0
2
1
0
0
0
0
2
2
2
2
2
0
1
0
1
0
0
2
2
0
0
2
0
1
0
0
1
0
1
0
0
0
2
0
0
2
0
2
1
0
2
2
0
1
0
0
0
3
0
1
2
1
0
0
0
1
0
0
1
0
1
0
1
2
2
2
1
1
1
0
0
0
1
1
2
0
6
0
1
2
1
0
2
2
0
2
0
1
1
1
2
1
1
1
0
2
0
1
1
1
0
1
2
0
1
2
0
0
2
0
0
1
0
0
0
1
2
0
2
0
1
1
2
0
2
2
0
0
0
2
0
1
0
0
1
0
0
0
1
1
0
0
0
2
2
2
0
0
1
1
0
1
0
1
2
0
0
1
0
0
1
2
0
0
1
0
0
1
0
0
1
1
1
1
0
1
2
0
0
0
1
1
2
1
1
0
0
0
0
2
2
0
0
0
0
2
0
1
0
0
1
1
0
2
1
1
0
2
0
1
0
1
0
1
1
2
0
1
0
1
2
0
1
0
0
1
1
2
1
1
2
2
0
0
0
1
0
0
1
0
1
0
0
0
1
2
2
0
0
1
0
1
1
0
0
0
2
0
0
2
1
1
2
1
0
0
0
3
0
0
0
0
1
2
0
1
2
0
2
0
1
1
1
0
0
1
1
1
0
1
2
0
0
2
0
1
0
0
0
1
1
1
0
1
1
1
0
0
0
0
0
1
0
1
0
2
1
1
2
0
2
0
2
0
0
0
1
0
0
2
2
0
0
0
1
1
2
2
0
0
0
0
1
0
1
0
1
1
1
0
2
0
0
0
0
0
0
1
0
2
0
2
0
1
4
0
3
2
0
0
1
1
1
2
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
1
0
0
1
1
0
2
0
0
1
0
2
2
1
0
0
1
0
1
1
0
1
1
0
0
1
1
1
1
0
1
0
0
0
1
0
3
0
0
0
0
0
0
1
1
0
0
2
1
0
1
2
0
1
0
0
1
0
0
2
1
0
0
1
0
2
1
1
1
1
0
2
0
0
0
0
2
1
1
1
1
1
1
0
0
2
0
0
0
0
0
1
0
1
1
0
1
1
1
1
1
3
0
0
2
1
0
1
0
0
1
2
2
0
0
0
0
0
2
2
0
0
1
1
2
0
0
0
2
1
0
2
2
0
0
0
1
1
1
0
1
0
0
2
0
1
0
0
0
0
2
1
0
0
1
0
0
0
1
0
2
0
2
1
0
0
1
2
1
1
0
0
2
2
0
1
0
2
0
2
2
1
1
1
0
2
0
1
1
0
0
0
0
2
1
1
0
2
1
0
0
2
1
0
0
1
2
0
0
1
0
0
0
0
2
0
0
0
2
0
0
1
1
2
0
0
0
0
1
2
1
1
1
0
1
1
1
0
0
2
1
2
0
1
2
2
0
1
1
2
0
2
1
0
1
0
1
1
0
0
0
2
0
0
2
0
2
0
1
1
0
0
1
1
0
2
2
2
1
2
1
0
0
0
1
0
0
0
0
2
0
2
0
0
1
0
1
2
1
0
0
2
2
2
0
2
0
1
1
1
0
0
1
1
0
1
0
0
1
2
1
2
0
2
0
1
1
0
0
2
0
1
1
1
2
2
0
0
2
2
0
0
2
1
0
1
1
0
0
2
0
0
1
2
2
0
1
1
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
1
0
0
2
1
1
0
2
0
0
0
1
0
2
0
1
1
0
2
0
0
0
0
0
2
0
0
1
0
1
1
0
0
0
1
0
1
2
1
2
2
0
1
0
0
1
1
0
0
1
0
0
0
1
1
1
0
0
0
0
0
2
2
3
0
1
2
2
1
2
2
0
0
2
0
0
0
1
0
0
2
0
0
1
1
1
1
1
2
0
2
1
0
0
0
0
0
1
0
2
0
0
2
0
2
1
0
0
0
1
3
0
0
1
2
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
1
0
3
0
2
0
2
0
0
0
0
1
1
1
1
0
0
0
0
1
0
0
1
12
1
2
2
0
0
0
2
2
0
2
1
1
0
1
0
0
1
1
1
0
0
1
2
0
1
0
2
1
0
1
0
0
2
2
0
0
0
0
1
0
0
2
0
0
2
0
0
2
2
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
2
0
0
2
1
1
0
0
1
0
0
0
2
1
0
0
1
0
0
0
1
0
1
1
1
0
0
1
1
0
0
1
0
0
2
0
1
2
2
0
0
1
0
0
1
1
1
0
0
1
1
0
0
0
0
1
0
1
1
2
0
0
1
0
1
1
0
1
0
2
0
1
2
0
0
2
1
0
0
2
2
1
0
2
0
1
0
1
0
2
0
2
0
0
2
1
1
2
2
2
2
1
2
0
4
0
0
0
2
1
1
0
2
0
0
0
0
1
0
0
2
2
2
2
0
1
0
0
0
0
0
0
1
2
2
1
0
0
1
0
0
1
0
0
0
2
2
4
2
0
0
0
0
0
0
2
0
2
0
0
1
0
1
1
0
0
0
2
1
2
1
2
2
0
2
0
0
0
0
0
2
2
2
3
2
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
2
1
0
1
2
1
1
3
0
0
0
2
1
1
0
1
1
0
0
0
1
0
0
1
0
0
0
2
1
0
0
2
0
0
0
1
0
2
2
0
4
1
1
0
0
0
0
2
1
0
1
2
2
2
0
1
0
0
2
0
2
0
0
0
0
1
1
2
0
0
1
2
0
1
0
2
0
0
0
3
2
1
2
0
0
2
0
0
1
0
2
0
1
0
0
1
0
2
1
1
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
2
2
0
2
0
1
0
1
0
1
0
0
0
0
0
0
1
2
3
1
0
2
0
2
0
0
0
1
2
0
0
0
0
0
1
2
0
0
2
0
1
1
1
0
0
1
0
0
1
2
1
1
0
1
0
0
0
0
2
2
2
2
1
1
0
0
2
0
1
1
0
1
1
2
2
2
0
1
1
0
2
2
2
0
0
2
1
0
2
0
0
0
2
0
0
0
3
0
2
2
2
0
0
0
1
0
1
0
0
0
0
1
0
1
2
1
2
0
1
1
0
0
2
0
1
1
0
2
1
1
0
1
0
0
2
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
1
0
0
1
0
0
0
1
2
0
0
0
1
1
0
0
2
0
2
0
1
0
0
0
0
1
1
1
1
0
1
0
2
1
2
1
2
0
1
0
2
1
1
0
0
0
0
2
1
2
0
0
0
0
1
0
0
0
0
1
0
1
2
0
2
0
1
2
0
0
0
2
2
1
2
0
0
0
1
1
2
1
4
1
0
2
1
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
1
0
0
0
1
4
0
1
0
1
2
1
0
0
0
0
0
0
0
2
2
1
2
2
0
0
0
1
0
0
2
0
1
2
1
0
2
1
0
0
0
1
2
0
0
0
2
2
0
0
2
1
0
1
2
0
1
0
0
1
3
0
0
0
2
3
0
2
1
0
0
1
0
0
0
0
1
2
0
0
2
0
1
2
0
0
0
1
2
2
0
2
1
0
0
2
2
0
0
2
1
0
2
2
0
3
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
1
0
0
0
1
2
1
1
1
0
0
0
0
0
0
0
2
1
0
0
0
2
0
2
1
0
0
1
0
1
1
0
0
0
2
1
1
0
0
2
0
1
3
0
1
2
0
0
4
0
1
0
0
1
2
2
0
1
1
0
0
1
0
2
1
0
1
0
0
0
0
1
1
0
0
2
0
2
0
2
0
1
2
2
1
0
1
2
0
2
1
3
1
0
1
1
1
1
2
1
2
1
2
0
0
1
0
0
0
2
0
0
1
0
0
0
0
1
1
0
1
2
0
1
1
0
0
0
0
1
3
1
2
0
1
0
0
1
0
0
0
0
1
0
0
1
2
2
2
0
1
1
0
0
1
0
2
0
3
1
1
2
2
1
0
0
1
0
0
0
0
0
0
2
1
1
1
2
0
1
0
0
1
0
0
1
1
0
0
2
0
0
0
2
2
2
1
0
0
2
1
0
0
0
0
0
0
2
3
0
1
0
0
1
2
0
0
2
2
1
0
0
1
1
3
2
2
0
1
1
0
1
0
0
0
1
1
0
0
0
1
0
1
0
1
0
2
1
0
0
2
0
0
1
2
0
1
0
0
0
0
0
0
0
2
0
3
1
2
1
2
0
1
0
0
1
0
1
1
1
2
0
0
0
2
0
1
0
1
0
1
0
0
1
0
0
1
0
0
0
2
0
1
1
0
0
1
0
0
2
1
0
0
0
2
1
1
1
3
2
0
2
0
0
2
0
2
0
0
0
0
0
0
2
1
1
0
0
0
2
1
1
0
0
1
0
1
0
1
1
2
0
2
1
0
0
1
2
0
0
0
0
1
0
0
1
1
2
1
2
0
2
2
0
2
0
1
4
0
0
0
0
0
1
2
0
2
2
2
0
2
1
1
1
1
0
0
2
2
0
0
0
0
1
1
1
0
0
0
2
0
0
1
1
0
2
0
1
0
0
0
0
0
0
0
0
1
0
1
2
1
0
1
2
2
0
0
0
0
2
0
0
1
2
4
0
0
0
0
2
0
1
0
1
1
0
0
1
1
2
1
2
0
2
0
0
1
0
2
0
2
1
2
1
2
2
2
0
0
0
0
0
2
2
0
0
2
1
0
1
0
0
0
1
0
0
0
1
2
1
0
0
2
2
0
1
0
1
0
1
3
1
0
1
1
0
1
0
1
1
2
0
1
0
0
0
1
0
0
1
0
1
2
0
0
2
2
0
2
0
0
1
1
4
2
0
1
0
1
0
1
0
0
0
1
0
0
2
1
1
1
2
0
0
0
1
0
0
2
0
1
1
2
1
0
1
1
0
0
1
2
0
1
1
2
3
0
1
0
1
0
1
0
0
1
0
2
2
0
2
0
2
0
0
0
0
1
1
0
0
0
0
1
0
1
2
0
2
1
0
0
2
1
0
2
2
1
2
0
2
1
1
0
0
1
1
1
0
2
1
3
2
1
1
2
0
0
0
0
1
2
2
0
0
0
0
0
0
1
1
0
1
1
1
1
0
0
0
0
1
2
1
0
0
1
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
2
1
1
0
0
1
0
2
2
0
1
0
0
1
1
0
2
0
2
0
0
0
1
0
1
1
2
2
0
2
1
0
1
2
3
0
1
1
0
0
3
1
1
0
0
0
1
2
1
1
0
1
0
0
1
2
0
0
1
0
1
1
2
0
2
1
0
1
0
1
0
0
1
0
0
0
0
0
2
2
1
0
0
1
2
0
0
1
0
1
2
0
0
0
0
1
2
0
0
0
2
1
2
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
1
1
0
0
1
0
0
0
2
0
0
1
0
1
1
0
2
0
0
1
0
2
0
0
0
0
0
1
2
1
0
0
1
0
0
0
0
1
1
0
1
0
0
1
1
0
1
2
1
0
1
0
1
0
1
1
0
0
1
2
0
0
0
1
0
2
0
2
0
0
1
0
2
0
0
0
0
1
1
0
0
1
0
0
1
1
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
3
0
0
2
2
0
1
0
1
1
0
1
1
1
1
2
2
0
0
1
1
0
1
2
2
1
2
0
1
2
1
2
0
1
0
1
0
0
1
0
0
2
1
0
2
0
0
0
0
0
0
0
1
0
0
2
1
0
1
0
1
0
2
0
1
0
0
2
1
0
2
1
2
1
1
0
1
0
0
0
0
0
0
3
1
0
0
0
0
1
2
1
1
0
1
0
0
0
0
2
0
0
1
2
2
0
2
0
0
1
1
1
2
2
0
0
0
1
1
2
1
0
1
1
1
1
1
0
1
0
1
0
1
0
0
1
1
0
1
0
0
1
2
0
0
0
0
2
0
2
2
0
1
1
3
0
2
0
0
0
2
0
1
0
0
2
1
0
0
1
1
0
0
1
0
1
1
0
0
1
2
0
0
2
1
2
2
1
0
0
1
0
0
1
0
0
0
1
1
0
0
0
2
1
0
1
0
0
0
1
2
0
1
1
0
0
0
0
1
1
0
0
0
1
0
0
1
2
0
0
1
0
0
0
0
3
0
2
0
0
0
0
0
0
0
1
3
0
0
1
0
0
1
1
1
0
0
0
0
2
1
0
0
0
0
1
0
1
1
1
0
0
1
0
0
0
1
0
2
0
0
1
0
2
2
0
1
0
0
0
0
1
0
0
0
1
0
2
1
0
0
1
1
0
1
0
0
1
2
0
0
3
1
1
0
0
0
1
2
0
2
0
1
1
0
0
0
1
0
1
1
1
2
0
0
1
2
2
0
0
1
0
1
2
2
0
1
2
2
0
1
2
0
0
0
0
1
2
0
0
1
0
2
1
0
1
2
0
2
0
1
0
0
0
0
0
0
1
2
0
0
1
1
2
1
1
2
1
0
0
0
2
0
2
0
1
1
0
1
1
1
1
1
1
1
0
1
0
0
1
0
2
0
1
2
0
2
3
0
0
0
0
0
2
1
2
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
1
1
0
0
2
1
0
2
1
1
1
0
0
0
0
1
2
2
0
0
2
1
0
0
0
0
0
1
2
0
2
2
1
0
0
2
1
1
0
2
0
1
1
0
2
0
2
2
0
0
1
0
0
0
2
1
1
0
2
2
0
1
3
0
0
0
0
2
1
0
2
1
1
0
0
1
0
0
0
2
2
0
0
0
1
0
1
0
0
1
1
2
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
2
2
1
0
0
1
0
2
2
2
1
0
0
1
0
1
1
1
0
0
0
0
0
0
0
1
0
2
1
0
2
0
1
0
0
0
1
2
0
2
0
3
2
0
1
0
2
2
0
1
0
2
0
0
1
0
1
0
2
1
1
0
3
1
1
0
1
0
0
1
0
0
1
0
0
0
1
1
1
1
1
0
0
1
2
0
1
2
1
0
2
1
0
0
0
1
0
0
0
1
3
2
1
0
2
0
1
2
0
2
0
0
0
1
1
1
2
1
0
0
0
1
0
0
0
1
2
1
0
0
0
1
2
0
0
1
0
0
0
1
0
2
0
1
0
1
0
0
0
0
2
0
0
2
0
0
1
1
0
1
0
0
1
0
0
0
4
1
0
1
1
0
1
2
2
0
0
0
1
1
0
0
1
0
2
2
0
2
0
0
0
0
0
2
1
2
0
1
2
0
0
0
0
1
0
2
2
1
0
2
1
0
2
1
2
0
2
2
1
0
1
0
0
3
0
0
0
0
0
0
2
0
0
0
1
1
1
0
0
0
0
0
1
0
1
0
0
1
1
1
0
0
2
0
0
1
0
0
2
0
0
2
1
2
1
1
0
2
1
0
2
1
0
0
2
0
1
2
0
1
1
2
0
1
0
0
1
2
0
2
2
1
1
0
0
0
0
1
1
2
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
1
2
2
0
14
0
2
2
2
0
1
3
0
1
0
1
2
0
1
1
1
0
1
0
0
0
1
1
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
1
1
2
0
0
0
0
0
1
2
0
1
1
0
1
0
0
0
0
2
1
1
1
0
0
0
0
0
0
0
0
1
0
2
0
1
0
1
0
1
0
1
0
0
0
1
0
1
0
2
2
0
0
0
0
1
1
1
0
1
2
2
0
0
1
0
2
0
1
1
0
0
4
1
0
0
0
1
1
2
0
0
0
0
0
1
1
0
2
1
0
0
0
2
0
2
1
0
0
2
4
1
1
0
1
1
0
2
0
1
1
0
0
1
2
1
2
0
1
0
4
2
0
1
0
1
0
0
0
0
1
1
3
1
1
0
1
0
1
0
1
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
1
0
0
0
1
2
1
0
0
1
1
2
0
1
0
2
0
1
0
1
0
0
1
2
0
3
1
0
1
0
1
1
1
0
1
0
0
0
1
1
2
1
1
1
3
0
2
0
1
2
1
7
2
0
0
0
0
1
0
0
2
0
0
2
0
0
2
1
1
0
0
0
0
0
1
0
2
1
1
2
2
0
0
1
0
0
1
0
2
0
2
0
2
0
0
1
0
0
0
0
0
0
1
2
1
2
2
0
0
1
0
0
2
0
0
1
0
0
1
1
2
2
1
1
0
0
2
0
1
3
0
2
0
1
0
1
0
0
0
2
0
0
1
1
0
2
1
0
1
1
1
0
1
0
1
0
0
0
0
0
1
0
2
2
2
2
1
0
0
0
2
0
0
0
1
3
1
1
0
0
0
0
4
1
0
0
0
0
0
1
0
0
1
0
2
0
1
1
0
0
1
0
1
0
2
1
0
0
2
0
0
1
1
0
0
2
1
0
1
0
0
2
0
0
2
0
0
1
0
0
2
1
1
1
0
0
2
0
0
0
0
1
1
1
1
2
2
2
2
2
0
1
0
2
2
2
0
1
2
3
0
0
0
0
1
2
0
2
3
0
0
0
0
1
0
0
1
0
0
0
1
2
0
2
1
1
1
1
1
0
0
0
0
0
2
0
2
1
0
1
0
0
0
1
0
1
1
1
0
0
2
0
0
0
2
1
2
0
0
0
1
1
2
0
0
1
1
0
0
3
0
1
8
1
1
0
1
2
0
0
2
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
1
1
0
2
1
1
2
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
2
0
0
0
0
0
0
1
1
1
0
0
0
1
2
0
0
0
0
1
2
0
0
0
1
1
2
4
3
1
2
1
2
2
0
0
2
1
2
0
0
1
1
1
1
1
0
2
0
0
0
0
0
1
0
1
2
0
2
0
1
1
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
1
2
0
1
0
0
1
0
1
0
0
2
1
0
0
1
1
0
0
1
0
2
2
0
1
2
0
3
0
0
1
1
0
0
0
1
0
0
0
0
1
1
0
2
2
1
0
0
0
0
2
2
0
1
2
0
1
0
2
0
0
0
2
2
0
2
1
0
1
0
2
2
1
0
0
0
0
1
2
2
0
1
0
0
1
0
0
2
1
0
0
0
0
1
1
2
1
0
0
1
0
0
1
1
1
0
0
1
1
1
2
0
2
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
1
4
0
0
0
0
0
1
2
0
0
0
1
0
1
0
0
0
0
2
0
2
1
1
1
0
2
0
0
2
0
0
2
0
0
1
1
1
0
0
0
0
2
0
0
2
0
0
0
1
2
0
2
2
6
0
2
0
2
0
0
0
0
1
2
1
0
0
0
0
1
0
1
0
0
2
4
0
0
0
2
0
2
1
1
0
1
2
1
0
1
0
1
1
1
0
1
1
1
0
0
1
0
1
0
0
0
0
1
1
1
1
0
1
0
1
0
0
0
0
0
0
0
2
0
0
1
0
1
2
1
1
2
1
5
1
2
2
1
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
4
2
2
0
0
0
1
1
0
2
0
0
0
1
0
0
2
1
0
0
1
1
0
2
3
0
2
0
0
1
0
2
0
1
0
0
0
1
0
2
1
1
2
2
0
0
0
0
1
1
1
0
0
2
0
0
1
0
2
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
1
2
1
1
0
0
0
1
1
1
0
1
0
0
0
1
1
1
0
1
2
2
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
2
0
0
0
1
2
2
0
1
2
0
0
1
0
2
2
0
2
0
2
0
0
2
0
1
0
1
1
0
2
1
1
1
0
1
0
2
0
0
0
1
2
0
0
0
2
0
1
0
0
0
2
0
1
0
0
0
2
1
0
1
0
0
0
1
0
0
1
0
0
2
0
2
3
0
1
0
1
0
0
1
1
2
0
2
0
1
0
0
0
0
1
0
1
0
0
0
2
1
1
1
0
1
0
0
0
1
2
1
0
0
1
1
2
2
1
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
2
2
2
0
1
7
1
0
1
0
0
1
0
1
1
0
1
1
0
1
0
2
2
1
0
0
0
1
2
2
0
0
1
2
2
0
0
1
1
0
1
0
0
2
0
1
0
0
0
2
2
2
0
0
1
0
1
0
0
0
0
1
0
0
1
0
1
0
0
2
0
0
0
0
0
0
1
0
1
0
0
1
0
2
2
2
1
0
3
1
0
1
0
1
0
2
2
0
0
0
2
2
2
0
1
0
0
0
1
1
1
0
1
0
0
1
1
0
0
2
2
0
2
1
0
2
0
0
0
0
0
0
3
1
2
1
0
0
0
0
0
0
1
2
2
0
2
1
0
1
0
0
0
2
0
1
2
0
0
1
0
2
2
0
2
1
2
1
2
0
0
0
0
0
0
1
0
0
0
0
1
2
2
1
0
0
0
1
2
1
1
2
0
3
0
2
2
0
2
1
0
1
0
0
0
0
1
0
0
1
2
1
0
2
0
1
2
0
0
1
0
0
2
0
1
1
0
0
1
1
1
2
1
0
1
2
1
1
2
2
2
0
1
0
1
0
0
0
0
0
2
0
2
1
0
0
0
2
0
1
1
1
2
0
2
0
1
2
1
0
0
1
1
0
0
0
1
1
0
0
2
0
1
3
1
1
2
0
1
1
0
2
0
1
0
1
0
1
0
2
0
0
1
0
0
1
0
1
2
0
1
0
0
2
2
0
0
1
1
0
0
2
0
1
1
1
0
0
1
2
1
0
0
1
0
1
0
0
0
0
0
0
0
2
2
0
0
2
2
0
0
1
1
0
1
0
2
2
1
2
1
0
0
2
1
1
2
2
1
1
1
0
1
1
1
0
0
0
4
1
1
0
1
1
2
1
1
2
1
0
1
0
0
0
0
2
1
0
1
0
2
2
2
2
2
0
0
0
2
2
2
1
0
0
0
2
0
1
0
2
1
0
0
2
0
0
0
1
1
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
2
1
1
0
1
1
2
0
1
0
0
1
0
0
1
1
0
2
0
0
0
0
0
0
0
0
10
0
1
0
1
2
2
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
1
2
0
0
0
1
0
0
1
1
0
2
2
0
0
2
1
0
1
1
0
2
1
0
2
0
0
0
0
0
0
2
2
0
0
0
0
2
0
1
0
0
0
1
0
0
2
4
0
1
1
3
1
1
0
1
1
0
1
0
0
0
2
1
2
0
6
2
2
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
1
0
2
1
2
1
0
1
0
1
2
0
0
2
1
0
1
0
0
0
2
0
3
2
1
0
1
1
1
0
0
1
0
1
1
1
0
2
0
1
2
1
2
2
0
0
2
0
0
1
0
1
1
1
0
0
0
0
2
1
1
0
1
1
2
1
0
0
0
0
2
1
0
0
2
1
0
0
2
0
1
1
1
0
0
0
1
0
1
1
1
2
0
2
0
1
2
2
1
0
2
0
0
2
0
0
1
2
1
1
2
4
1
0
1
0
0
1
2
1
2
1
0
1
0
0
3
0
2
1
1
1
0
1
0
2
1
2
0
0
1
0
0
0
1
0
0
1
0
0
0
1
1
0
0
2
0
0
0
2
2
0
0
2
0
0
2
1
1
1
0
1
0
1
1
0
2
0
0
1
4
2
0
0
0
2
0
0
2
0
0
2
1
0
2
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
2
0
0
0
1
1
0
0
0
2
0
0
3
0
0
0
0
0
0
2
0
1
0
0
1
2
0
1
1
0
0
2
1
2
0
1
3
0
0
0
0
0
0
0
2
2
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
1
0
0
2
1
1
2
0
1
1
2
0
0
2
1
1
2
0
0
1
1
0
1
0
0
0
1
0
0
1
0
1
0
1
2
1
1
0
2
0
1
2
0
0
0
1
1
1
0
0
2
1
1
0
1
0
2
0
0
1
0
0
2
2
1
0
0
0
2
0
0
0
0
1
1
1
1
1
2
0
0
2
1
0
0
2
0
0
1
3
0
2
0
0
0
1
0
1
2
0
1
2
0
2
1
1
0
0
0
0
2
0
0
1
0
8
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
1
2
1
0
0
1
2
0
0
0
0
2
0
0
2
0
2
1
0
1
1
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
3
0
1
2
2
0
0
0
2
0
0
2
1
2
0
1
1
2
1
0
1
0
0
1
1
2
2
1
0
1
1
0
1
2
0
1
3
0
1
0
2
1
1
1
0
0
0
1
2
1
1
2
0
2
0
1
2
1
1
1
2
0
1
0
1
0
0
0
0
0
0
1
2
0
2
0
2
0
0
1
0
0
2
2
0
0
0
2
2
0
2
1
0
0
1
1
0
1
2
1
0
0
0
0
0
2
0
1
4
0
1
0
2
0
1
1
0
0
0
0
2
0
0
1
3
1
0
0
0
1
2
1
1
2
2
2
2
1
0
1
0
0
2
2
1
1
0
0
1
1
1
0
0
0
0
2
0
0
1
0
0
1
0
1
0
2
0
0
1
1
0
0
2
0
0
2
2
1
1
2
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
1
1
0
0
1
1
0
2
0
0
0
1
0
1
2
0
0
1
2
0
2
1
1
0
2
2
1
1
1
4
0
2
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
1
1
2
0
0
2
2
0
0
0
1
0
0
0
1
2
0
0
2
0
2
2
0
2
0
0
2
0
2
0
1
0
2
0
1
0
1
0
1
0
1
1
1
1
0
1
0
0
0
0
0
0
0
0
2
1
2
1
2
2
2
1
0
0
1
1
2
0
0
0
0
0
0
2
0
0
2
0
1
2
1
2
2
1
1
2
2
2
0
1
0
1
0
2
1
0
0
0
0
1
0
0
0
0
1
0
0
2
3
0
2
2
0
0
1
1
0
2
0
0
0
2
0
1
1
2
2
0
0
2
2
0
0
0
0
0
1
1
1
0
1
0
0
0
2
1
0
2
1
1
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
1
2
2
1
0
0
0
0
0
1
2
2
1
1
0
1
0
1
0
0
0
0
1
0
1
2
1
0
0
2
0
0
2
1
0
1
0
0
0
2
4
1
1
0
0
1
0
0
0
1
1
0
1
0
0
0
1
1
0
1
0
0
0
1
0
2
0
0
0
1
0
1
0
0
2
0
1
1
0
2
2
1
0
1
1
0
0
0
2
0
2
1
0
2
1
1
0
0
2
0
2
0
2
0
0
0
2
1
0
0
1
1
0
0
0
0
0
2
0
2
2
2
0
1
3
1
1
1
1
1
0
2
0
0
0
1
0
0
1
1
0
0
1
0
2
1
0
0
1
0
0
0
1
2
0
1
0
0
0
2
2
1
0
0
0
2
2
0
1
0
0
2
0
2
0
0
1
0
0
1
1
0
0
2
0
1
2
0
2
0
0
0
0
2
0
1
1
0
0
0
2
2
0
1
0
2
2
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
1
0
1
1
1
1
1
0
0
1
0
2
0
0
2
0
2
0
0
1
3
1
1
0
0
1
0
3
0
0
1
0
2
3
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
2
1
1
0
1
0
0
1
1
0
2
4
1
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
2
0
2
0
1
0
0
0
0
0
2
1
0
2
1
3
1
0
0
2
0
2
1
0
0
0
2
0
2
1
2
0
0
2
2
0
2
0
2
1
0
1
1
1
0
1
6
0
0
0
2
0
0
1
0
0
3
1
1
0
1
0
0
1
0
1
0
0
0
0
0
2
2
0
0
0
1
1
0
0
0
1
0
1
0
1
1
1
0
0
0
0
2
2
1
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
2
1
2
0
2
0
2
0
1
0
1
0
2
1
1
2
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
2
0
2
0
1
0
1
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
2
1
1
2
1
0
0
1
0
0
0
1
0
0
2
0
1
0
0
0
0
1
0
0
0
0
1
0
2
0
1
2
2
2
2
0
2
2
0
1
1
1
1
0
2
0
1
0
1
0
1
0
1
2
1
1
0
2
3
0
1
0
0
2
2
0
0
1
0
2
1
0
0
0
1
1
3
0
1
2
1
0
0
1
1
1
0
2
1
0
0
0
1
0
2
0
1
0
0
2
0
2
0
0
2
0
0
0
0
2
0
0
0
1
0
1
1
1
2
1
5
0
0
0
1
0
2
1
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
2
2
0
0
0
2
1
0
0
0
1
1
0
2
0
0
2
2
3
2
1
1
0
0
0
0
0
0
1
0
3
0
0
1
2
1
3
1
0
2
0
0
2
1
3
0
1
0
2
0
3
0
0
2
2
0
0
2
0
0
1
0
1
0
2
0
1
2
2
1
0
0
0
0
2
0
0
0
2
1
2
1
0
0
0
1
0
1
0
2
0
1
0
0
0
4
1
0
1
1
1
0
2
0
1
0
1
0
1
1
0
0
3
0
0
2
1
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
1
0
0
0
0
1
0
1
0
0
2
1
0
0
0
1
1
0
2
1
1
1
0
2
0
1
2
0
2
0
0
0
0
1
4
0
0
0
0
1
2
0
0
1
2
2
0
0
2
1
1
1
0
3
1
0
0
2
0
1
1
0
2
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
2
2
0
1
0
0
1
2
0
0
0
0
1
0
2
0
1
0
3
1
1
1
1
0
0
1
0
0
3
0
0
0
0
0
0
2
1
1
1
0
2
0
0
0
1
2
1
1
0
2
1
0
1
1
0
1
1
1
1
1
0
2
2
1
2
1
0
2
0
1
0
0
0
2
0
0
2
0
3
2
2
0
1
2
0
1
2
1
1
0
1
0
0
0
0
0
0
0
2
1
1
1
0
0
2
2
2
0
3
0
1
2
1
0
1
2
1
1
1
1
0
0
0
2
0
2
2
0
0
0
0
1
2
1
3
0
0
1
0
2
0
1
1
2
0
0
2
2
0
1
1
0
0
0
1
2
1
1
2
0
1
2
0
1
1
0
1
1
2
2
0
0
0
1
2
1
0
0
0
1
1
2
1
0
0
0
1
1
1
0
0
0
2
0
0
2
0
2
1
0
3
1
1
0
0
0
3
0
1
0
1
0
1
2
1
0
0
1
0
0
2
2
0
0
1
2
1
0
0
0
0
0
2
0
2
0
2
2
2
0
0
0
0
0
0
2
1
2
2
0
0
1
0
1
0
0
3
0
0
0
1
0
0
0
0
1
1
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
2
0
0
1
0
2
1
0
0
2
1
1
0
2
0
1
1
1
2
0
2
1
0
0
2
1
0
2
0
0
1
0
1
0
0
0
1
2
2
2
0
0
0
0
0
2
2
0
1
0
2
0
0
0
1
2
3
0
0
0
0
0
1
2
2
0
0
1
2
1
0
2
1
0
1
0
0
1
0
1
0
0
1
2
2
1
0
2
0
1
1
1
1
2
0
3
1
0
2
1
0
0
0
2
0
2
2
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
2
1
0
0
3
0
1
1
5
0
0
0
2
0
2
1
0
2
1
0
0
2
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
1
0
0
1
2
1
1
2
11
2
1
0
2
2
1
0
2
0
0
0
0
1
2
0
1
0
0
1
0
0
0
0
2
3
2
0
0
0
2
1
2
3
1
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
1
0
1
0
2
1
0
1
0
1
0
1
2
1
1
2
2
2
1
1
1
0
0
1
2
0
0
1
0
3
0
0
2
2
0
0
1
1
0
0
0
0
1
0
1
2
0
2
1
1
0
1
1
2
0
0
1
1
0
0
0
0
0
2
2
1
1
1
2
1
2
1
0
0
2
3
0
0
2
0
0
0
2
0
0
0
1
0
0
1
1
0
0
0
0
0
2
1
0
1
2
0
0
0
0
0
1
1
0
0
0
0
1
0
1
2
0
1
1
2
0
1
0
1
0
2
0
0
1
0
0
0
0
1
0
2
2
0
0
0
0
2
2
0
2
2
0
0
2
1
1
0
1
2
0
1
2
0
0
0
1
0
0
0
2
2
2
0
0
1
0
0
1
2
2
0
0
0
0
1
1
2
1
1
0
1
1
0
0
0
2
2
2
1
0
0
2
0
0
1
0
1
0
0
1
0
1
0
1
0
0
0
0
0
1
6
1
1
2
1
1
0
0
2
0
2
0
2
2
1
0
0
1
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
2
1
0
1
1
0
0
2
1
0
1
0
2
0
0
2
0
0
1
1
2
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
2
2
1
1
2
2
2
1
0
0
1
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
2
0
0
1
1
0
1
0
0
1
0
0
0
0
0
2
0
1
0
2
0
1
0
1
1
0
1
1
0
0
0
0
2
1
2
1
1
0
0
1
0
1
1
2
0
1
1
2
2
0
2
1
2
1
1
0
1
1
1
0
1
0
1
0
2
1
0
0
0
0
0
0
0
1
2
2
0
1
2
0
0
0
0
2
2
0
2
0
1
2
0
2
0
0
1
0
0
2
0
0
1
0
0
0
1
1
0
0
0
0
1
1
2
2
0
0
2
0
1
1
1
2
0
2
0
0
0
0
0
0
1
1
0
2
2
0
0
0
2
2
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
2
1
0
2
1
0
0
2
0
2
0
0
2
0
0
0
1
2
0
1
0
0
1
0
0
2
0
0
1
0
0
2
1
0
0
1
1
1
0
2
1
2
0
0
1
1
0
0
0
2
1
1
1
3
0
1
2
2
1
0
0
1
1
0
0
1
0
2
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
2
0
0
0
0
1
0
0
1
0
1
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
2
1
0
1
2
1
1
0
2
1
0
0
1
2
1
0
0
0
0
1
2
0
0
0
0
0
2
0
2
0
0
0
1
0
0
2
0
0
1
0
2
1
1
0
0
1
0
2
1
1
1
1
2
1
1
0
0
1
0
0
0
0
0
1
2
2
2
0
2
0
0
1
0
1
0
1
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
1
4
0
1
1
1
0
0
0
0
0
2
0
0
0
2
1
1
0
0
0
0
0
1
2
2
1
1
1
2
3
0
4
2
1
0
1
2
1
2
2
0
1
2
1
1
2
0
0
1
3
1
0
2
2
0
0
5
0
2
2
0
0
0
0
1
0
0
0
2
1
2
2
0
0
0
1
1
1
2
2
1
1
0
1
2
0
2
1
3
0
0
0
2
0
1
0
0
0
0
1
2
0
1
2
0
0
0
0
1
1
2
3
0
0
1
0
0
0
1
2
1
1
0
1
0
1
0
0
2
1
0
1
1
0
0
1
1
0
2
0
0
1
1
1
1
1
2
0
1
0
1
1
1
1
1
1
1
1
0
0
2
1
0
1
2
0
0
2
2
0
2
0
0
2
1
0
2
0
1
1
2
0
0
0
1
2
1
0
1
1
1
1
0
1
0
0
1
1
0
2
2
2
1
0
1
0
0
1
1
1
1
0
1
1
1
1
1
0
0
1
2
2
1
0
2
0
0
0
2
0
0
2
1
0
1
0
0
2
0
1
2
1
0
0
0
0
0
0
1
1
1
0
0
1
1
0
0
2
2
1
0
0
0
0
0
0
2
0
0
1
0
0
2
0
3
1
0
0
0
0
1
0
0
0
0
0
2
0
2
2
0
0
1
0
0
2
1
0
1
0
2
1
1
1
1
0
2
2
2
1
2
1
4
0
0
0
0
0
0
2
0
1
0
1
0
1
0
0
1
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
2
0
0
2
0
0
1
1
0
0
0
2
2
1
1
0
0
0
0
1
0
2
0
0
1
2
0
1
0
0
0
1
1
0
2
1
0
0
0
1
1
1
0
3
0
1
2
3
0
2
1
0
0
1
1
0
0
0
0
2
2
0
0
1
0
1
1
2
1
0
0
1
1
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
1
1
5
0
0
0
0
2
2
0
2
2
0
0
0
1
0
0
0
0
0
0
2
0
2
1
0
0
0
1
0
2
1
0
1
0
2
0
0
1
2
0
0
2
0
2
0
0
0
0
1
0
0
0
6
1
1
2
0
3
2
1
2
0
0
1
2
1
2
0
0
0
1
1
0
1
0
1
0
2
0
0
1
3
1
1
0
0
0
1
0
0
0
1
0
0
4
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
1
1
0
4
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
2
1
0
0
1
0
1
0
2
2
1
1
0
1
1
1
2
0
0
1
0
1
1
0
1
0
1
0
1
2
1
1
0
0
0
1
0
1
1
2
2
1
1
1
0
2
0
0
2
2
2
1
1
1
2
0
1
1
1
0
1
2
2
1
0
0
0
0
0
1
0
1
0
1
1
0
2
0
0
0
0
2
1
3
0
0
0
1
1
0
1
2
2
0
2
2
1
2
0
2
0
0
0
1
2
0
0
1
0
2
2
0
0
2
1
2
0
0
0
0
2
0
0
2
0
2
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
1
1
0
0
0
1
1
0
2
0
0
0
1
0
2
1
1
2
0
1
0
2
1
1
0
0
1
0
0
0
0
1
1
2
1
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
2
0
1
1
1
1
0
0
0
0
0
0
2
1
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
2
1
2
1
1
1
0
0
3
0
0
1
0
0
2
0
1
0
2
3
1
0
1
0
0
0
1
0
0
1
1
0
1
0
0
1
1
2
2
0
2
0
1
1
0
0
0
0
2
1
1
1
0
0
3
2
2
2
0
0
1
0
1
2
0
0
2
0
2
0
0
0
0
0
1
1
1
1
0
1
1
0
0
0
1
1
2
1
0
1
0
1
2
0
0
0
1
0
0
2
1
0
0
1
2
0
1
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
2
0
1
1
0
0
0
1
2
0
0
0
0
1
0
3
0
0
0
2
1
1
0
0
2
2
0
1
0
0
0
0
1
0
1
4
2
0
0
1
2
0
0
2
1
0
2
1
0
0
1
2
0
1
1
1
2
1
0
0
0
1
0
0
1
0
2
0
0
0
2
1
1
1
0
2
2
0
0
1
0
0
0
0
1
2
0
0
0
0
5
0
2
0
0
2
0
1
0
2
0
0
0
0
0
0
0
1
0
2
0
1
1
2
1
1
1
0
0
2
2
0
0
0
0
2
1
1
0
2
2
0
1
0
0
1
2
1
1
2
0
1
2
2
1
0
0
2
0
1
0
1
0
1
0
1
0
0
0
0
0
1
0
1
0
0
3
1
1
1
0
0
0
0
1
0
0
0
0
2
1
1
0
1
0
0
0
2
2
0
2
1
0
0
0
2
0
0
0
0
2
1
0
4
0
0
0
0
2
0
0
0
0
2
2
0
2
1
0
0
2
1
0
0
1
1
1
0
2
0
2
1
0
0
0
2
0
2
0
0
0
0
1
1
0
1
2
1
2
0
2
0
1
1
0
1
1
3
1
0
0
1
0
2
0
0
1
1
0
1
0
2
1
0
1
7
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
1
1
1
0
1
0
1
0
0
2
0
1
0
0
0
0
0
0
2
0
3
1
2
0
1
0
0
0
1
1
1
0
1
1
2
2
0
1
0
2
2
0
0
0
0
1
0
2
0
2
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
1
1
2
0
0
2
0
2
1
2
0
1
0
1
2
3
2
1
0
0
0
0
1
0
0
1
0
1
0
0
2
2
0
0
1
0
0
2
0
0
0
0
2
0
1
1
1
0
2
2
0
0
0
0
1
2
2
0
0
0
0
3
0
0
0
1
0
0
2
1
0
0
0
3
1
0
1
0
0
2
1
0
1
1
0
1
0
0
2
0
0
1
0
0
1
2
0
2
0
2
1
0
0
1
0
0
0
0
0
2
2
2
1
0
1
1
0
2
1
1
1
0
2
2
2
2
0
1
0
0
6
2
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
3
1
0
1
0
0
2
0
0
0
1
0
0
2
0
0
0
0
1
1
2
0
0
0
0
0
0
1
2
0
0
2
2
1
1
0
0
3
1
1
1
1
0
1
1
1
2
0
0
0
0
2
0
0
2
0
1
0
2
2
0
1
1
1
1
1
1
2
1
2
1
1
1
1
1
0
0
1
1
2
0
0
0
0
0
0
0
1
0
2
0
2
1
0
0
2
2
0
1
2
0
2
2
1
2
0
1
0
1
2
2
2
1
1
2
1
1
0
0
0
1
2
0
0
0
0
1
0
2
1
1
1
0
1
0
1
0
2
1
1
0
2
0
0
0
2
3
1
2
0
0
1
0
1
1
1
1
1
2
2
0
3
1
1
0
0
0
0
1
1
1
0
0
1
1
0
1
1
1
0
0
1
1
0
1
1
2
0
0
2
0
2
0
0
2
3
0
2
0
2
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
1
2
1
2
0
1
0
2
1
0
0
0
0
3
2
0
0
2
0
2
0
2
1
1
0
0
1
0
0
0
2
0
1
2
0
2
0
0
1
2
2
1
0
0
2
0
0
2
2
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
2
0
1
0
1
0
0
2
0
0
0
0
0
1
0
2
0
0
1
0
0
2
0
2
0
0
0
0
1
2
0
0
2
0
2
0
2
2
0
0
0
0
1
1
1
1
1
0
1
1
0
0
0
3
2
0
0
0
0
0
0
0
1
1
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
1
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
2
2
0
2
1
1
2
2
1
0
1
2
0
1
2
2
1
0
0
0
0
0
1
0
0
0
2
0
1
1
2
2
1
0
2
0
0
0
2
1
1
0
2
1
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
2
1
1
1
0
2
0
1
3
0
1
2
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
1
0
1
0
0
0
0
2
1
1
8
0
0
0
2
2
2
0
2
1
0
2
2
0
2
1
0
0
1
0
2
1
0
0
2
2
2
0
0
2
0
3
0
1
0
1
0
2
1
1
0
0
1
2
1
1
2
0
0
1
0
0
0
0
0
2
2
0
0
0
2
2
2
0
0
0
2
1
0
3
1
0
1
2
1
1
0
3
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
2
1
1
1
1
0
0
0
0
1
2
0
0
0
0
0
1
0
1
0
1
2
1
1
3
0
1
2
1
2
2
1
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
1
2
2
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
1
0
0
1
0
0
1
1
0
0
2
0
0
2
0
0
0
1
0
2
1
1
2
0
0
0
2
1
0
4
0
0
0
2
0
0
1
1
0
1
2
1
0
2
1
0
1
0
0
1
0
1
0
0
1
2
1
2
0
0
0
2
0
0
1
0
0
2
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
1
1
0
2
0
1
1
1
0
0
0
1
0
0
1
0
1
0
0
1
2
0
2
2
0
0
1
1
0
0
0
2
0
0
0
0
1
1
0
1
1
0
0
1
1
0
1
2
3
0
0
1
3
0
2
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
1
0
0
0
0
2
2
1
0
2
0
1
2
1
1
2
1
0
0
0
0
1
2
2
1
1
1
1
1
0
0
1
0
0
0
0
2
2
0
2
2
0
1
0
0
0
2
0
0
2
0
0
1
1
1
1
0
0
0
1
0
1
1
0
0
0
1
2
0
2
2
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
1
1
0
0
1
2
0
1
2
0
1
1
0
0
2
0
1
1
0
1
0
0
0
0
1
2
0
0
1
0
1
0
0
0
1
2
2
0
1
3
1
0
3
1
1
2
1
1
1
0
0
0
0
1
1
0
6
0
1
0
1
2
0
1
2
1
1
0
2
0
1
1
2
0
0
1
2
2
0
0
1
0
2
2
1
2
2
1
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
1
2
1
0
0
0
2
0
0
2
1
0
0
0
0
0
3
0
1
0
0
0
1
1
0
0
2
0
0
0
1
1
0
1
0
2
1
1
5
0
2
0
0
1
2
0
0
0
1
0
0
0
2
1
0
0
0
2
1
2
1
0
0
0
1
2
1
2
2
0
2
2
2
0
1
0
0
0
0
1
0
3
0
0
2
1
0
0
1
1
0
2
1
1
0
2
2
1
2
0
0
4
1
1
2
0
0
0
0
1
2
0
2
0
2
0
0
1
1
2
1
1
0
0
0
1
0
2
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
2
0
2
0
1
0
0
0
0
1
1
0
0
0
1
2
2
1
0
0
2
1
1
1
0
0
0
2
1
0
0
2
0
0
1
0
1
0
0
2
0
0
2
2
2
1
2
0
0
0
0
0
0
0
0
1
1
3
0
0
2
0
0
0
0
1
0
1
0
2
0
0
0
1
2
1
2
0
1
0
1
1
0
0
2
2
2
0
1
0
2
0
0
1
2
1
0
1
1
1
0
2
1
2
0
1
2
0
0
2
2
0
0
0
0
0
0
0
1
0
1
0
1
2
1
0
1
0
0
1
0
0
0
1
0
2
0
1
1
2
2
0
2
2
0
1
0
0
0
0
1
1
0
0
0
1
0
0
2
0
0
0
1
0
0
2
0
1
1
0
0
0
0
2
2
0
0
0
1
0
1
0
2
0
1
0
1
0
1
0
0
0
2
2
0
1
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
1
2
1
2
1
1
0
3
0
0
1
1
0
0
0
1
0
2
0
0
1
1
2
1
0
1
0
1
0
0
0
0
0
2
0
1
1
2
1
1
2
0
0
0
0
1
0
1
0
0
0
1
2
2
0
1
2
1
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
1
2
1
1
0
1
0
0
1
1
2
0
1
1
0
0
0
2
1
1
0
0
2
0
1
1
1
1
0
1
0
0
0
2
2
0
0
1
0
2
0
1
0
0
0
1
0
0
2
0
1
0
1
0
0
1
0
2
0
0
0
0
0
1
2
0
0
1
2
2
0
1
0
2
1
2
0
4
0
0
1
0
2
0
1
0
0
1
2
1
1
2
2
0
0
2
2
1
0
0
3
1
0
2
0
0
0
0
0
2
0
0
1
1
0
3
0
1
0
0
0
0
0
1
0
1
1
0
1
2
3
0
0
1
1
0
1
0
2
2
1
0
0
0
1
0
2
1
1
0
1
0
0
0
3
2
2
0
0
1
2
0
0
0
2
1
0
1
0
1
1
0
1
1
0
0
1
2
0
0
0
0
0
1
0
2
0
0
2
0
2
0
1
0
0
1
0
1
0
0
2
1
0
0
0
0
2
0
0
1
1
1
2
0
0
0
0
0
0
1
2
0
2
2
0
2
0
2
2
0
0
0
0
0
0
2
2
0
0
1
1
1
2
1
1
0
0
0
2
1
1
0
2
0
1
2
1
0
1
0
0
0
2
0
0
0
0
0
1
1
1
0
0
1
2
0
0
0
1
0
0
0
0
0
0
2
1
1
0
0
3
0
0
1
1
0
0
0
1
0
0
0
1
1
0
0
3
1
0
2
0
0
1
1
1
2
0
2
0
1
0
0
0
2
2
0
0
1
1
2
0
0
0
1
1
0
0
1
2
0
1
0
1
0
1
0
2
2
0
1
0
0
1
2
1
0
0
0
2
0
2
2
0
0
0
2
0
0
0
2
2
2
1
0
0
1
0
1
0
1
0
3
0
1
1
1
0
0
0
0
0
1
0
1
2
0
1
2
2
0
0
0
0
2
2
2
0
1
2
0
0
1
2
0
2
0
1
1
1
0
0
2
0
0
2
1
1
1
0
0
0
0
1
0
0
2
0
2
1
1
1
0
0
0
0
0
0
2
0
0
0
2
0
2
0
1
2
0
0
2
1
0
2
0
0
0
1
0
0
0
2
0
0
0
1
0
0
1
0
2
0
1
0
0
0
0
2
2
0
0
3
0
0
2
0
1
1
3
2
0
0
1
1
1
0
0
0
2
0
0
0
0
1
1
2
1
0
1
1
0
1
0
1
0
0
2
2
0
0
0
0
2
2
0
0
2
1
2
0
0
1
0
0
0
0
0
1
2
0
0
0
1
0
2
0
0
0
2
1
0
0
2
0
0
1
0
2
0
0
0
1
1
0
0
1
1
1
0
1
1
0
1
1
1
0
2
0
0
0
1
0
0
0
0
1
2
0
0
2
0
1
0
1
1
0
1
2
0
1
0
0
2
2
1
1
0
0
0
1
1
0
0
0
0
0
2
1
0
1
0
1
0
0
0
0
0
1
0
2
0
2
0
2
0
2
0
1
0
1
2
0
1
0
1
0
2
0
2
2
1
1
2
0
2
2
1
0
0
0
0
1
0
0
1
0
2
1
1
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
2
0
1
1
1
0
0
1
0
0
0
1
0
0
1
1
2
0
1
2
0
3
0
0
1
0
0
1
5
0
1
0
0
0
0
1
0
0
1
2
1
0
0
1
1
2
0
1
1
1
0
0
0
1
0
1
0
2
0
3
2
2
1
0
1
0
0
1
0
0
0
0
1
2
1
1
0
1
2
0
2
0
0
2
2
1
0
2
0
0
1
0
0
3
1
0
1
2
2
0
0
1
2
2
1
0
1
2
1
1
1
0
0
0
0
0
2
2
0
1
0
0
2
0
1
0
0
0
0
1
3
1
1
3
0
2
0
1
0
2
0
1
0
0
0
0
0
0
1
2
2
0
1
0
1
1
2
1
1
0
1
0
2
1
2
0
0
1
0
0
2
1
2
0
0
1
1
0
0
0
1
2
0
2
0
0
1
0
0
0
0
2
1
0
0
1
0
1
1
3
1
0
1
1
0
0
2
1
2
0
0
0
0
2
0
0
0
0
0
1
0
0
2
3
2
0
0
0
1
1
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
1
2
2
0
2
2
0
1
0
0
2
1
0
2
2
0
0
0
2
0
0
1
1
0
0
1
0
6
2
1
2
0
2
0
1
0
0
2
0
1
0
0
0
1
2
0
2
2
2
0
0
2
2
0
0
1
1
0
3
1
0
3
0
0
0
0
0
1
0
1
0
1
2
1
0
0
0
2
1
1
0
1
1
0
1
1
0
3
2
2
1
1
0
0
0
0
0
1
0
0
2
0
1
1
2
1
1
1
1
1
1
1
2
0
2
1
2
2
0
0
0
1
0
0
1
0
0
0
0
1
2
1
1
1
0
1
2
0
0
0
2
1
1
0
0
0
2
0
0
0
1
1
1
3
0
1
0
0
1
0
0
2
0
2
2
1
1
0
1
2
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
2
0
2
0
0
0
0
0
1
2
2
0
1
0
0
1
0
0
2
1
0
0
0
2
0
3
0
0
2
0
0
0
0
0
0
2
2
2
0
2
0
2
1
1
1
0
2
0
0
1
2
1
1
2
0
0
0
0
0
0
0
0
0
0
1
2
0
1
1
0
0
0
2
0
1
1
1
1
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
2
3
0
1
0
0
1
0
1
0
0
0
2
2
2
0
0
0
1
0
2
2
1
0
1
0
2
0
5
0
2
1
0
0
1
0
0
0
1
2
1
2
0
3
2
0
1
1
0
2
0
2
1
1
0
2
1
0
1
2
2
1
0
2
0
1
1
1
0
0
0
1
2
0
1
0
2
0
0
1
0
1
1
2
1
2
0
0
2
0
0
0
1
0
0
2
2
0
2
2
1
0
0
0
0
0
3
0
1
2
0
1
1
1
0
2
0
0
0
1
0
2
1
2
6
2
0
1
2
1
0
2
0
0
0
3
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
2
0
1
0
1
1
1
0
2
0
1
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
2
2
2
0
1
0
0
0
1
1
1
0
0
1
0
2
0
0
0
0
0
1
0
2
0
0
2
1
0
1
2
1
2
0
0
0
0
1
2
2
0
0
1
0
0
0
1
1
3
2
0
0
0
0
0
1
1
0
2
0
2
1
1
1
2
1
0
1
0
1
2
0
2
2
0
2
0
2
0
0
0
1
1
0
0
0
2
1
2
0
0
0
1
0
0
2
2
2
0
1
0
2
0
0
3
0
0
1
0
3
0
0
1
0
0
1
0
1
2
2
0
1
1
1
0
1
4
1
2
1
1
0
1
1
2
0
2
0
1
0
0
0
0
0
2
1
2
0
0
0
0
0
1
0
0
2
1
2
1
1
1
0
1
2
0
1
0
0
1
1
0
0
0
0
1
1
1
1
0
0
2
1
1
0
0
1
0
0
1
0
2
0
0
1
0
2
0
0
0
0
0
1
0
0
1
2
2
0
0
0
0
2
0
3
1
1
0
1
0
1
0
0
0
0
2
0
1
2
1
0
0
1
0
2
2
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
1
1
1
0
0
0
0
0
2
1
0
1
0
0
0
0
1
2
1
0
1
0
2
1
0
0
0
2
1
1
4
0
0
0
0
0
1
0
1
0
0
0
0
1
0
2
0
2
0
0
2
0
0
2
0
0
1
1
0
0
0
5
0
2
0
0
1
1
1
2
0
2
0
2
1
0
0
2
1
0
0
3
0
0
0
0
0
1
0
0
1
0
1
0
0
1
1
2
0
0
1
0
2
0
2
2
2
0
0
0
2
2
2
0
2
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
2
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
1
1
1
0
0
0
2
1
0
0
0
1
1
1
0
2
2
0
2
1
1
2
0
0
2
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
1
0
3
2
1
0
0
0
1
1
0
1
0
2
0
2
2
0
0
0
0
0
1
0
0
0
1
2
2
1
1
0
4
1
0
1
0
2
0
1
0
0
0
1
1
0
0
1
0
0
0
1
1
0
2
0
0
1
0
0
0
3
1
1
0
1
0
0
2
2
2
0
1
0
0
0
0
1
3
2
0
2
0
2
0
2
1
0
1
0
1
1
0
1
0
0
2
0
0
1
0
0
0
1
2
0
0
1
0
0
0
2
0
2
2
0
1
2
0
1
0
2
1
0
0
1
2
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
2
0
0
1
2
0
0
0
1
1
2
0
2
1
1
1
0
0
2
0
0
0
0
2
1
0
1
0
1
0
1
1
0
1
0
0
1
0
0
0
2
2
1
0
0
0
2
1
0
1
1
1
2
0
0
0
1
2
0
1
0
0
0
0
0
2
0
0
0
1
0
0
1
1
2
0
0
2
0
2
1
1
0
0
2
2
2
1
0
1
0
0
2
0
0
0
1
0
0
1
1
1
0
1
1
1
0
1
1
0
0
0
0
2
2
0
1
1
1
0
0
0
0
3
1
0
2
2
0
1
1
0
2
0
0
0
0
0
1
0
0
1
1
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
1
1
0
1
0
1
0
0
0
1
1
0
0
0
2
1
2
0
0
0
1
1
1
2
0
2
2
0
0
1
0
0
0
2
1
1
1
1
0
0
0
1
0
2
0
0
1
0
1
0
1
0
1
0
2
2
1
2
1
0
2
0
2
0
0
2
2
0
1
0
2
0
0
0
0
0
2
2
1
0
0
1
2
1
0
1
0
0
1
0
0
1
1
0
1
0
2
1
0
0
0
2
0
0
0
0
2
0
1
1
0
1
1
0
0
0
2
2
0
1
1
0
0
2
0
0
0
0
2
1
0
1
0
1
1
1
2
0
2
0
0
1
1
1
2
0
0
1
1
0
2
0
2
1
2
0
0
0
4
2
1
2
2
2
0
1
0
2
0
1
1
0
2
1
1
0
0
1
0
1
0
0
0
0
2
2
1
1
0
1
2
0
2
0
2
0
1
0
0
0
0
0
1
0
1
2
1
0
2
2
0
0
2
1
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
1
2
1
0
4
0
0
2
0
0
2
0
1
0
0
1
0
2
0
2
1
1
1
1
0
0
0
2
0
1
0
1
2
1
0
1
1
1
0
3
1
0
1
0
0
2
1
1
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
2
2
0
1
1
0
0
0
2
1
1
0
0
1
0
2
0
1
2
2
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
2
0
1
0
1
1
1
0
0
0
0
0
1
1
1
1
0
1
0
0
0
2
0
0
2
0
1
2
1
2
2
6
0
1
0
2
0
0
0
0
1
1
1
0
1
0
1
1
0
0
0
1
2
1
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
2
2
2
1
2
0
0
1
0
1
2
0
0
1
4
0
2
2
0
2
2
2
0
2
3
0
2
0
1
0
1
0
1
0
0
3
0
2
1
0
0
1
2
0
2
0
1
2
1
0
0
0
1
2
2
1
0
0
0
1
0
0
0
1
1
2
1
1
0
1
0
0
1
1
0
2
0
0
0
0
1
0
1
1
1
0
2
2
2
0
1
0
1
0
2
0
2
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
1
1
0
1
0
0
2
1
0
0
0
0
2
0
1
0
0
1
2
0
0
0
0
0
2
0
1
1
1
0
0
2
0
1
0
0
1
1
2
0
0
0
0
1
0
0
1
1
2
2
0
1
0
0
1
2
0
1
1
0
0
0
1
0
2
1
0
2
0
0
0
0
1
0
0
1
1
0
1
2
1
2
0
0
2
0
1
0
1
1
0
0
1
2
2
1
0
1
0
0
2
0
0
0
1
0
0
2
2
2
4
2
0
1
0
0
1
1
0
0
2
0
1
0
2
1
0
0
0
2
2
1
0
0
1
1
2
1
3
0
1
0
1
0
0
2
1
0
0
0
0
0
2
0
2
2
1
1
1
0
1
0
0
2
0
0
1
1
2
0
1
0
3
0
1
0
0
1
1
2
0
1
0
2
0
1
1
0
2
0
0
1
2
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
1
0
2
0
0
0
0
2
0
0
0
1
0
1
1
0
2
2
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
2
1
1
3
2
2
0
0
0
0
1
1
1
3
1
0
0
0
0
1
0
0
1
0
0
2
1
0
1
0
1
1
2
0
3
0
0
1
1
1
0
2
0
2
0
1
1
6
1
4
0
1
0
2
0
0
2
2
0
0
2
0
0
0
2
0
1
0
0
0
0
2
0
0
0
1
1
2
0
1
0
0
0
1
2
0
0
1
0
1
0
4
0
0
0
2
2
0
2
1
3
0
0
2
2
1
0
0
0
1
0
2
0
2
2
2
1
1
2
0
0
4
1
1
2
1
0
2
0
0
2
2
0
1
0
2
0
0
0
0
1
0
0
1
2
0
2
2
1
1
0
1
2
0
1
2
2
0
0
0
1
2
0
1
0
3
0
0
0
0
0
1
2
1
0
1
3
1
0
1
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
1
1
1
0
2
1
0
1
0
1
2
0
0
0
0
1
0
4
1
2
1
0
1
0
0
0
0
2
1
1
1
1
0
0
0
1
0
0
4
1
1
1
3
0
1
1
1
2
2
0
2
0
2
0
1
1
0
0
2
0
0
1
2
2
0
1
1
0
1
0
2
1
0
2
2
1
0
0
0
0
1
0
1
0
1
0
2
2
2
0
0
0
0
1
0
0
5
0
2
0
0
1
1
1
1
0
1
1
0
1
0
0
0
0
2
1
1
1
2
0
2
1
0
0
0
1
1
0
1
2
1
0
2
1
1
2
0
2
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
1
1
0
1
2
0
0
1
1
0
1
2
0
2
2
1
0
0
2
0
0
1
1
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
2
2
1
0
1
0
1
2
2
0
2
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
2
3
0
0
0
0
1
1
0
0
1
2
0
0
0
3
0
0
1
1
2
2
2
0
1
0
0
0
1
0
1
0
0
2
1
0
2
0
1
2
1
2
0
0
0
0
2
1
1
0
2
1
1
2
1
0
1
1
0
0
0
2
1
0
0
1
2
0
1
0
0
1
0
1
2
0
1
0
0
2
0
0
1
0
1
2
0
3
4
0
2
0
1
0
1
0
0
0
1
4
0
0
0
0
2
2
0
2
1
1
1
0
0
1
0
0
1
0
0
1
0
2
1
0
0
0
0
1
0
2
2
2
1
1
0
0
0
0
2
0
0
0
0
1
1
0
1
0
0
1
1
1
0
0
2
1
0
0
2
2
1
1
0
0
2
0
0
0
1
2
2
0
0
1
2
2
0
0
2
1
0
2
2
1
2
0
0
1
2
1
0
0
2
2
2
1
0
1
2
1
1
2
1
1
0
1
0
0
0
0
2
1
1
0
0
0
0
1
0
1
1
1
0
0
0
2
0
0
0
1
1
0
0
0
0
0
1
1
2
2
0
0
0
1
0
2
1
1
0
2
1
0
2
1
0
0
0
0
1
2
1
1
1
0
0
2
2
0
0
2
3
0
1
1
1
1
0
0
0
0
0
0
1
2
1
2
1
1
0
3
1
0
0
0
0
0
2
0
1
0
1
1
1
0
0
2
3
0
0
0
2
0
0
2
0
3
0
0
2
0
1
0
0
1
1
2
1
0
0
2
2
1
0
0
0
0
0
0
0
2
0
1
0
2
0
2
2
1
2
0
1
0
1
2
0
0
1
0
2
2
0
0
0
0
0
1
0
4
0
0
1
1
1
0
0
1
1
1
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
1
0
2
0
0
1
2
2
0
2
3
0
0
0
0
0
2
0
2
1
1
1
1
2
0
0
0
2
2
0
2
0
0
0
0
0
2
0
1
0
0
0
1
0
2
0
1
1
1
1
0
2
2
2
0
0
1
1
0
0
1
0
0
2
1
2
1
1
0
1
2
0
1
1
1
1
0
0
0
2
0
1
1
1
0
1
1
0
0
0
1
0
0
1
0
2
0
0
1
1
0
1
0
0
0
2
2
0
0
1
0
2
0
0
0
0
4
2
2
0
2
0
0
1
1
1
0
0
0
0
0
0
0
0
1
1
1
3
0
0
1
1
0
2
1
0
0
0
1
0
1
0
2
1
1
0
1
1
0
1
0
4
0
0
0
1
2
0
2
1
1
1
0
1
2
0
0
0
0
1
0
1
2
0
0
0
0
1
0
1
1
0
0
0
0
2
0
2
0
0
0
2
0
0
1
0
0
0
0
0
1
1
2
0
2
0
0
0
4
2
1
0
0
0
0
0
0
1
8
0
1
0
2
0
1
0
0
1
0
0
1
1
1
2
0
0
2
0
0
0
0
2
0
0
0
0
1
0
1
0
1
0
0
0
2
2
1
0
0
0
0
0
0
1
0
1
1
0
0
2
1
0
1
2
0
2
0
0
3
0
0
0
1
1
2
1
0
0
0
2
2
0
2
0
1
2
2
2
2
0
0
1
2
2
0
1
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
3
1
1
3
0
2
2
1
2
1
0
1
8
0
0
2
0
0
1
1
0
0
1
0
1
2
1
2
0
1
0
0
0
2
1
2
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
2
0
1
1
1
1
0
0
0
0
0
0
1
0
0
1
2
1
0
2
1
0
1
0
0
0
2
0
0
0
1
2
2
1
0
0
1
1
0
1
0
0
2
2
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
1
0
1
2
0
1
2
2
0
0
1
0
0
1
0
0
1
2
0
0
2
0
0
0
1
1
0
2
0
0
2
2
0
0
2
0
2
0
0
0
0
2
1
0
2
3
2
0
1
0
1
0
0
2
2
1
1
0
0
2
0
1
1
0
0
0
0
0
0
1
0
1
0
0
1
0
2
0
1
0
0
1
0
1
2
1
1
1
1
0
0
2
0
0
0
1
0
1
0
0
1
0
0
1
1
0
2
1
0
0
0
0
0
0
1
0
2
1
0
2
0
1
0
1
2
0
0
1
2
2
0
0
0
2
1
0
0
0
1
0
0
1
1
2
1
1
1
0
1
0
1
1
2
0
0
1
2
1
1
0
2
0
0
1
1
2
1
0
0
0
1
2
0
0
0
0
0
3
0
0
0
1
0
1
1
0
1
0
2
0
3
1
1
1
2
0
1
2
1
0
0
1
0
2
0
0
1
0
0
0
1
1
0
2
2
0
1
2
0
0
0
0
1
2
0
1
1
2
0
0
0
2
0
2
1
1
1
0
0
0
0
0
2
2
2
0
0
2
1
0
0
1
1
0
2
0
2
2
6
0
1
0
2
1
0
0
0
2
2
0
0
0
0
1
0
0
1
2
1
2
3
0
1
0
0
1
2
0
0
1
0
0
0
0
0
1
2
0
1
0
0
1
0
0
0
1
0
1
1
2
0
2
1
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
2
1
0
1
0
0
2
0
2
0
1
0
1
0
2
1
2
0
0
0
2
0
0
2
0
2
0
0
1
2
0
2
0
2
0
0
0
2
0
1
2
0
1
2
0
0
0
2
1
0
1
0
0
0
1
1
0
0
0
2
2
2
1
0
2
1
0
0
2
0
0
2
1
0
2
1
1
2
0
2
1
0
0
0
0
4
1
2
2
0
0
1
0
0
0
2
2
0
2
1
1
1
1
1
0
2
0
0
0
2
1
0
1
0
1
1
0
0
0
0
0
2
0
0
0
0
1
0
1
2
0
1
2
0
2
2
1
1
3
0
0
1
1
0
2
1
0
1
2
0
0
1
3
1
0
0
0
1
3
0
0
0
0
1
0
0
0
0
1
1
0
1
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
2
1
0
0
0
1
0
0
1
2
0
2
0
2
0
0
0
0
1
0
1
1
1
1
1
0
2
1
0
2
0
1
0
0
0
0
2
0
0
1
1
0
2
2
2
0
0
2
1
2
1
2
3
1
2
0
0
2
2
1
1
0
1
0
0
1
0
3
1
0
4
0
0
0
0
1
0
0
2
2
0
1
2
1
0
3
0
1
0
2
2
1
0
0
0
2
1
0
0
1
2
2
1
0
0
0
0
0
1
0
0
2
1
0
1
1
0
0
1
0
0
0
1
1
0
0
0
1
0
1
0
2
0
0
1
0
1
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
2
2
2
0
0
0
2
1
2
0
1
2
0
0
1
0
2
2
1
0
2
0
0
2
0
2
2
0
2
1
0
0
1
2
3
0
2
0
2
0
0
0
0
0
2
0
1
0
1
1
1
0
0
0
2
0
0
0
0
0
0
2
0
0
1
1
2
1
0
0
0
0
0
0
0
1
2
0
1
2
0
0
0
0
1
1
0
2
0
1
0
1
0
2
1
0
0
1
0
1
0
0
1
1
1
0
1
1
0
0
0
2
2
2
0
1
0
2
0
2
0
0
2
0
2
2
0
0
2
2
3
0
0
0
0
0
2
0
0
0
2
0
0
2
0
1
1
1
0
0
0
1
1
0
3
0
0
0
1
1
1
2
0
1
1
2
0
2
2
0
0
3
0
0
1
2
0
1
1
0
0
2
0
0
3
0
2
1
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
1
0
0
0
0
0
1
1
2
2
1
2
1
0
2
0
1
1
0
0
2
2
1
0
0
1
2
0
0
1
2
1
0
0
0
1
0
2
3
0
1
1
0
1
3
0
0
0
2
0
1
0
0
2
1
0
0
1
1
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
2
2
1
1
0
1
2
2
1
0
2
1
1
0
0
0
1
1
1
0
0
0
1
1
2
0
0
0
0
2
2
0
1
0
1
1
0
2
1
0
0
0
0
0
1
1
0
1
2
1
0
0
1
0
0
0
1
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
1
0
1
2
0
0
1
3
1
1
0
2
1
0
2
1
2
0
2
0
1
1
0
0
3
1
0
1
3
0
0
0
0
2
0
0
0
0
0
1
0
1
1
2
0
0
1
1
0
0
0
0
0
1
0
0
0
0
2
0
2
0
1
0
0
0
2
0
0
2
1
2
0
0
2
0
2
0
0
2
0
0
0
0
3
1
1
1
0
1
0
0
3
1
2
1
1
0
1
0
2
0
0
0
0
0
2
3
1
0
0
0
2
2
2
0
0
1
2
1
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
6
0
0
2
2
0
1
0
0
0
0
0
2
1
1
1
0
0
1
0
1
0
1
2
1
0
0
1
1
0
1
0
0
0
3
0
1
0
2
0
0
0
0
2
1
2
2
2
1
0
2
1
2
1
1
1
1
0
2
0
0
2
2
2
1
2
2
1
0
1
0
2
1
2
2
2
0
1
2
0
2
2
2
1
0
2
1
1
2
1
1
0
1
2
1
2
0
2
2
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
1
2
1
0
1
2
2
0
2
1
1
2
2
0
2
3
0
1
2
0
0
0
0
0
2
0
1
1
1
1
0
0
0
2
1
1
1
1
1
0
1
0
1
1
1
0
1
0
0
2
2
0
0
0
0
1
1
0
1
2
0
0
1
1
1
1
2
2
0
0
0
0
1
0
0
1
0
0
1
0
2
2
0
1
0
1
1
0
0
0
1
0
0
1
0
0
0
1
0
2
0
1
0
1
0
0
0
1
2
1
1
0
0
1
0
0
0
2
1
0
2
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
1
1
1
0
0
2
2
0
1
0
0
0
3
0
0
0
2
1
0
1
0
2
3
0
0
2
0
1
1
0
0
0
0
0
2
0
2
1
0
1
1
0
1
1
2
0
0
1
2
0
0
1
0
2
0
1
0
0
1
1
0
0
0
1
0
1
0
1
0
1
2
1
0
1
1
2
0
1
2
5
0
0
0
1
0
0
3
1
0
2
1
0
2
2
0
1
0
2
0
2
0
1
1
1
1
0
2
0
0
2
1
1
3
1
0
3
0
1
0
0
2
0
0
0
2
1
1
0
0
1
1
1
1
1
0
1
1
1
2
2
1
0
0
0
1
0
0
1
2
1
0
1
1
0
0
1
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
2
1
1
6
0
0
3
1
0
2
1
0
0
0
0
1
0
0
0
1
2
1
0
2
2
2
0
2
0
1
1
0
0
1
2
0
1
2
2
0
0
2
2
1
1
0
0
2
1
0
0
2
0
0
0
1
0
2
2
1
1
0
0
8
1
1
0
0
2
2
0
0
0
0
2
1
0
2
0
1
1
0
4
0
0
0
1
0
2
1
0
1
2
0
1
1
2
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
3
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
2
0
0
0
0
1
0
2
0
2
0
0
2
2
0
1
2
0
0
0
0
1
1
2
1
2
1
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
2
2
0
2
0
0
2
0
3
2
0
2
0
0
0
1
2
0
0
0
0
2
2
0
0
0
1
0
2
1
0
3
0
2
0
2
2
0
0
1
0
0
1
0
0
0
0
4
0
0
0
1
2
3
0
2
1
0
0
2
2
1
1
2
1
2
2
0
1
0
1
1
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
2
0
1
2
0
0
2
2
2
0
0
0
0
0
0
1
2
1
0
2
2
2
0
2
0
0
0
0
2
0
1
0
0
1
0
0
1
3
2
1
2
0
1
3
0
0
0
0
1
0
1
0
0
1
2
2
2
1
0
1
2
0
0
2
1
1
2
0
0
0
1
0
1
0
0
0
1
1
0
0
1
0
1
0
1
0
1
1
0
0
0
0
0
2
1
0
0
0
1
1
1
0
2
1
0
0
2
1
1
1
1
2
0
2
1
2
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
1
2
0
3
1
2
0
0
1
1
0
0
2
2
1
2
0
1
2
3
2
2
0
1
2
0
0
1
0
1
2
0
0
0
0
3
0
2
1
2
0
0
0
2
0
0
2
1
2
1
0
1
0
0
2
0
0
2
0
0
2
0
2
2
0
0
1
0
1
1
2
0
0
2
2
2
0
3
2
2
3
0
0
0
1
1
0
2
0
0
0
0
0
1
2
2
0
0
2
1
1
0
0
0
0
1
2
2
1
2
0
2
1
1
0
0
0
0
0
1
6
0
0
0
0
1
2
0
0
0
0
0
1
1
0
1
2
1
1
1
0
2
0
1
0
0
0
1
0
1
0
2
0
1
0
1
1
2
0
0
0
0
1
0
2
0
0
1
0
0
2
2
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
2
0
0
1
1
1
2
2
1
0
0
2
0
0
0
0
1
2
0
0
2
0
0
0
0
0
1
2
1
1
0
1
0
0
1
0
2
0
0
1
0
0
0
0
2
0
2
1
0
0
1
1
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
1
1
0
0
1
0
2
0
0
3
1
0
0
0
1
0
0
2
1
1
1
0
1
2
1
1
0
1
0
0
1
2
0
0
0
2
1
0
2
2
0
2
1
2
0
1
1
0
3
1
1
0
1
1
1
2
1
2
0
0
0
1
0
0
0
1
1
1
0
0
2
0
0
0
2
0
0
2
0
1
2
1
0
0
2
1
0
0
1
3
0
0
1
1
2
1
0
1
1
3
1
0
0
0
0
0
0
0
0
2
0
3
2
0
0
1
1
0
1
2
0
0
0
1
1
0
1
1
0
1
1
1
2
1
0
0
0
1
1
1
0
1
0
0
0
2
1
0
0
0
0
5
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
2
0
0
1
0
0
0
1
0
2
0
2
1
0
0
2
2
0
7
1
0
0
0
0
0
0
0
0
1
2
0
1
0
0
1
2
0
0
1
1
1
1
2
1
0
0
0
0
1
1
0
2
2
1
1
0
2
1
1
1
1
0
2
1
2
2
0
1
2
0
0
1
0
1
2
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
2
0
0
0
0
0
2
0
1
1
0
1
1
1
1
0
0
0
2
0
0
0
0
0
0
1
2
1
0
0
1
0
1
0
2
2
2
0
1
2
0
2
2
1
1
1
0
2
0
2
0
0
0
0
1
0
4
2
2
0
1
0
0
1
0
0
1
1
0
1
3
0
2
0
0
0
0
1
0
0
0
0
0
1
2
1
2
1
0
0
1
2
0
0
3
0
0
0
1
1
1
1
0
0
1
0
1
2
2
1
0
1
0
1
1
0
0
0
0
0
1
2
0
2
1
0
2
0
0
1
0
1
0
2
1
2
1
1
2
0
0
0
0
0
1
2
1
0
1
0
0
0
0
1
1
0
0
1
1
0
0
1
1
0
1
0
0
0
0
0
1
0
2
0
0
0
2
1
2
0
0
1
1
0
2
0
0
1
0
0
2
3
0
1
1
1
0
2
1
1
0
1
2
2
0
0
2
0
1
0
1
2
0
0
0
2
0
0
0
0
0
0
1
1
1
2
1
0
0
1
2
0
1
1
1
0
2
1
2
1
1
1
0
2
0
1
0
1
1
1
1
1
0
1
0
0
1
2
0
0
0
2
1
2
2
1
0
1
0
0
1
1
1
3
0
2
1
2
2
0
1
0
0
1
1
0
0
1
0
1
0
0
0
2
0
0
0
1
0
0
0
2
2
0
0
1
2
0
0
0
1
0
1
1
0
1
0
0
2
1
1
1
0
0
4
0
1
0
2
1
1
2
0
1
1
0
0
2
2
1
0
0
2
1
0
1
0
0
0
2
0
1
0
1
2
2
0
1
0
1
0
2
0
0
1
1
1
0
0
1
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
1
0
2
1
0
0
2
2
0
1
2
0
1
3
0
0
0
0
1
1
0
0
0
1
0
1
1
2
0
0
0
0
0
0
0
1
0
0
2
2
1
1
0
0
2
0
0
1
0
1
2
0
0
2
0
1
2
0
1
1
1
1
2
0
0
1
1
0
2
2
0
4
0
2
1
1
0
2
0
1
2
1
0
2
2
0
2
1
1
2
1
0
1
2
0
0
1
0
0
0
0
0
0
1
1
0
1
1
1
0
1
0
1
1
1
0
0
0
2
0
1
0
0
0
0
0
1
0
2
2
1
0
0
1
1
0
0
0
1
0
2
1
0
3
0
1
0
0
0
0
1
1
1
2
2
0
1
0
0
2
0
0
0
0
0
0
0
1
1
0
0
1
1
2
0
1
0
1
1
0
0
2
0
0
0
0
0
1
0
0
1
2
2
0
2
0
1
2
0
0
1
0
0
1
1
0
2
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
2
2
0
0
1
1
1
0
1
2
0
0
2
1
1
1
0
1
1
0
2
0
1
2
1
0
0
1
0
0
0
1
0
1
2
0
0
0
0
0
0
2
0
0
0
0
3
1
0
1
0
0
0
1
1
0
1
0
0
1
0
1
0
1
0
0
0
0
1
3
0
2
1
0
0
1
2
1
0
2
1
2
2
1
0
0
0
0
2
0
0
1
0
1
2
1
0
2
0
0
2
2
2
4
0
0
0
0
5
0
0
1
2
0
1
2
2
2
1
0
0
1
2
0
1
1
0
1
0
0
0
0
1
0
0
2
0
2
1
0
2
0
2
0
1
0
1
0
1
0
1
1
1
1
1
0
0
0
2
0
0
0
1
0
1
1
2
0
1
0
2
0
2
2
1
2
2
0
1
0
1
0
0
0
0
2
0
0
2
0
0
1
1
3
2
2
0
0
0
2
0
3
0
0
0
1
3
1
1
1
0
0
1
0
1
1
0
0
1
0
0
1
4
0
2
0
0
0
0
0
0
0
0
0
2
1
1
0
2
0
2
0
0
1
0
2
0
1
1
2
1
0
1
2
1
0
0
2
0
1
0
2
0
1
2
2
0
2
4
0
1
0
1
0
0
0
1
2
1
0
0
2
2
0
0
0
0
2
2
1
0
0
0
0
2
1
2
1
0
0
1
1
2
1
0
0
0
1
2
0
2
0
0
1
0
2
1
0
1
1
1
1
1
0
0
0
0
2
0
1
2
0
0
2
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
2
0
1
0
0
2
0
1
0
1
2
1
0
0
1
1
1
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
2
2
2
0
3
0
1
2
0
0
2
2
0
0
0
0
2
0
0
1
2
2
0
0
1
1
2
0
1
2
1
0
0
0
0
1
0
2
2
0
1
0
2
2
1
0
2
0
1
0
1
0
2
1
3
0
0
1
0
0
0
1
0
2
0
0
1
0
2
0
2
0
1
2
0
0
1
1
0
1
2
2
1
0
0
1
2
0
1
0
1
2
2
0
0
2
1
0
0
1
0
0
2
0
0
1
0
0
0
2
0
1
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
2
0
0
0
1
0
0
2
0
2
0
1
1
0
0
2
1
0
0
1
2
2
0
0
2
2
0
1
0
1
0
1
0
0
0
4
0
2
1
0
1
1
0
0
1
0
0
0
0
0
0
1
1
2
0
1
0
1
0
0
2
2
0
1
0
0
0
0
2
2
2
2
0
0
0
1
0
0
1
0
2
1
2
1
0
1
0
0
1
1
0
0
2
1
1
3
2
0
1
2
1
2
0
1
2
1
0
2
1
0
2
0
2
1
0
0
0
1
2
2
0
2
3
0
1
0
0
1
0
0
1
1
1
0
0
1
1
3
1
0
0
2
0
0
1
0
0
0
1
0
1
0
0
2
1
0
2
1
3
2
0
0
0
0
0
1
1
0
1
1
2
0
0
0
0
2
2
1
2
0
1
0
2
1
0
2
0
2
0
0
1
2
2
0
0
0
0
1
0
0
1
1
0
0
2
0
2
2
2
1
0
0
0
0
0
0
0
0
1
0
2
2
0
0
3
0
1
0
0
2
2
1
1
0
0
0
1
0
2
1
0
0
1
0
1
0
0
2
0
0
0
2
0
1
0
0
1
2
2
0
0
0
0
1
1
1
2
0
0
1
0
0
0
2
2
0
2
2
0
1
1
2
2
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
2
1
2
2
0
2
1
1
2
1
1
0
0
1
0
2
0
0
1
0
2
0
0
1
2
0
1
0
0
0
1
2
0
1
1
0
0
0
0
0
1
2
0
0
2
0
1
0
0
1
0
0
0
1
1
1
0
1
0
2
1
2
2
0
2
0
1
2
1
2
2
1
2
0
0
2
0
2
0
0
0
1
1
2
2
0
0
1
1
0
0
2
0
0
0
2
1
1
0
1
2
2
0
0
2
0
1
1
0
1
0
0
1
0
1
1
0
2
0
1
1
0
0
0
0
1
1
0
0
0
1
1
2
0
0
2
0
0
0
1
0
1
0
1
1
2
0
0
1
2
1
2
1
0
0
1
0
0
2
1
0
1
0
0
1
0
1
0
1
0
1
1
2
0
1
1
0
2
1
0
1
1
2
2
0
0
2
0
1
1
0
1
3
1
0
2
1
1
1
1
2
2
1
2
0
0
0
3
1
1
1
0
0
2
0
2
1
2
3
0
1
0
0
0
0
0
2
1
0
1
2
1
0
0
1
1
2
1
0
1
0
0
0
0
1
3
0
1
1
1
1
0
0
1
0
0
3
0
0
0
1
3
2
2
1
0
0
2
0
2
1
0
0
2
2
0
1
2
0
2
0
2
0
0
0
0
0
1
0
1
2
0
0
1
0
1
1
2
0
0
0
0
2
2
0
0
1
1
1
2
2
0
0
1
0
0
2
0
1
1
1
0
0
1
0
0
0
2
0
2
0
1
3
0
0
1
0
1
0
1
1
0
0
1
0
1
0
0
1
0
0
0
0
2
1
1
0
0
0
0
0
1
1
2
0
0
1
0
0
2
1
1
0
0
0
3
0
0
0
2
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
1
2
0
2
0
1
0
1
0
1
1
1
0
1
0
0
0
3
2
1
2
1
1
0
1
2
1
0
0
0
1
1
0
2
0
0
0
1
0
3
2
0
0
2
0
0
1
0
0
1
2
1
0
1
1
0
0
0
2
1
1
1
1
0
0
2
0
1
0
2
1
0
0
0
0
0
0
0
1
2
0
1
0
1
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
1
1
0
1
1
2
0
0
0
3
2
2
0
2
0
1
0
0
1
0
0
1
0
0
1
2
0
1
1
1
0
1
2
1
0
1
0
0
1
1
0
0
0
0
0
2
0
2
0
2
0
2
2
2
0
1
2
0
0
2
1
0
2
1
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
1
1
1
0
2
2
0
2
0
0
2
0
2
0
2
0
1
1
1
1
2
2
2
2
2
0
2
0
2
2
0
0
1
1
1
0
0
0
2
2
0
2
2
0
0
0
0
0
2
0
0
1
1
2
2
2
0
1
1
1
0
0
2
2
1
0
0
1
0
0
2
0
1
0
1
0
1
0
0
0
4
1
1
0
1
1
0
0
0
0
0
2
1
0
0
0
0
1
2
2
1
0
0
2
1
1
2
0
0
0
0
0
0
1
0
1
2
0
1
0
1
0
0
1
0
2
1
2
1
1
0
0
0
0
2
2
0
1
1
2
1
1
0
2
1
0
2
0
1
1
1
0
0
0
1
0
0
0
0
0
2
1
2
0
2
1
0
0
2
0
1
0
0
0
0
0
2
0
1
1
0
1
0
1
0
0
0
0
2
0
2
0
2
1
1
2
1
2
0
1
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
1
0
0
2
0
1
0
1
0
0
1
0
0
0
0
0
0
1
2
0
0
2
0
0
1
3
1
0
2
0
0
2
1
0
1
0
2
0
0
0
1
0
0
0
1
0
0
2
1
1
0
2
1
1
1
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
1
1
0
2
0
2
0
0
0
1
2
1
0
1
2
0
1
0
0
0
0
1
1
0
1
0
0
0
0
1
2
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
2
1
2
0
0
1
0
2
1
1
0
2
1
1
2
0
0
2
0
1
0
1
2
0
1
0
0
1
0
0
0
0
1
0
1
0
1
0
2
0
1
0
0
0
0
1
2
2
0
2
0
0
0
2
0
4
2
0
2
0
0
2
0
0
1
0
0
0
3
0
0
0
0
1
1
2
0
0
1
0
2
0
0
0
1
2
0
2
2
2
2
0
0
1
0
0
0
0
0
1
1
0
0
1
2
0
0
0
0
4
2
0
1
0
1
1
0
1
1
0
1
0
0
3
1
0
0
1
1
1
0
0
1
0
2
2
0
0
1
1
0
0
0
0
1
0
0
0
1
2
1
0
0
2
2
1
0
0
2
2
2
0
1
1
1
0
0
0
0
1
0
1
3
0
0
2
0
0
0
2
0
2
0
0
2
2
1
0
2
1
0
0
0
0
0
0
2
2
0
1
1
0
0
0
1
0
2
0
2
1
1
0
0
0
0
1
3
4
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
1
2
2
0
2
2
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
1
0
0
2
0
1
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
1
0
1
0
2
0
0
1
0
0
1
0
2
0
2
2
0
1
1
2
1
1
2
0
1
0
0
0
1
2
0
2
1
2
0
0
0
0
2
0
1
0
0
1
1
1
0
1
1
1
1
0
1
0
0
0
0
0
0
1
0
1
0
0
2
0
0
1
1
0
1
0
1
0
2
1
0
1
1
2
2
0
2
0
2
1
1
2
2
1
0
2
2
1
1
0
3
0
1
0
0
1
0
1
0
0
2
2
0
1
2
0
2
2
0
1
1
2
1
1
0
0
0
1
0
2
1
0
0
0
2
1
0
0
1
0
2
2
0
1
3
2
0
0
1
0
1
1
2
2
1
2
2
0
2
0
2
1
0
0
0
1
0
0
0
1
1
1
2
2
0
1
0
0
0
2
0
3
1
4
1
1
2
1
0
0
0
1
0
0
1
0
1
0
0
1
0
1
0
2
1
2
0
0
0
0
1
0
1
1
1
0
0
2
0
1
1
1
1
3
0
0
1
2
0
0
2
0
0
0
0
0
1
0
0
0
2
0
1
0
2
0
0
0
1
1
1
2
1
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
1
1
0
2
1
1
1
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
1
1
1
0
0
1
2
0
0
1
2
2
0
1
0
2
0
0
2
0
3
0
0
0
0
1
2
1
0
1
1
1
0
0
1
0
2
2
0
0
0
0
1
0
1
2
0
0
2
1
0
1
1
1
0
2
1
0
3
2
1
1
0
0
2
0
0
0
0
1
0
0
0
1
0
0
2
2
0
2
2
0
0
1
4
2
1
0
1
0
0
0
0
0
0
0
3
2
1
1
0
0
0
2
0
0
0
1
2
0
1
0
0
0
0
0
1
1
1
0
1
1
2
0
2
0
0
0
2
0
0
0
0
1
2
1
1
1
0
0
0
0
1
0
2
0
1
1
1
0
2
2
0
0
1
1
0
2
0
0
0
0
2
0
0
1
0
0
1
2
1
0
1
2
1
0
1
2
0
0
0
1
2
2
0
0
0
1
0
1
0
0
2
0
0
0
1
1
0
0
0
1
2
1
0
1
1
0
0
2
1
0
2
0
0
1
0
0
0
2
3
2
0
2
0
0
1
1
0
1
1
1
2
2
0
0
0
1
1
1
1
0
2
1
0
0
0
1
0
1
2
0
0
4
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
2
2
1
0
0
2
0
0
1
0
0
1
0
1
2
0
1
3
0
1
1
0
0
2
0
0
1
1
0
1
4
1
0
0
0
1
0
0
1
0
0
2
1
0
0
0
0
1
0
2
1
1
2
0
1
1
1
2
1
2
0
1
0
1
2
0
2
0
0
2
0
1
1
1
0
0
1
8
0
0
2
2
0
2
1
1
2
0
0
2
0
2
0
1
1
0
0
0
0
0
0
0
1
1
1
1
0
1
2
1
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
2
1
0
1
2
2
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
1
1
0
0
2
0
1
1
1
0
1
0
1
0
0
0
0
0
1
1
0
0
0
1
2
1
1
0
1
0
0
1
2
0
1
0
0
1
0
0
0
1
1
0
0
1
2
0
0
0
3
1
0
0
1
1
1
1
1
3
0
1
0
1
1
2
0
2
0
0
1
0
0
0
0
2
1
0
0
3
0
0
1
1
2
0
0
0
0
2
0
0
2
0
0
3
1
0
1
0
1
1
0
0
0
1
1
3
1
1
1
0
2
1
0
0
4
2
0
0
2
2
2
0
0
0
0
0
2
0
0
1
2
0
0
2
2
0
1
2
0
0
0
0
0
1
1
1
1
0
2
1
2
0
1
2
2
0
0
2
0
1
0
0
4
0
2
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
2
2
0
1
1
2
0
2
2
2
2
0
0
1
0
2
0
0
0
0
2
2
0
1
0
2
0
2
0
0
1
0
0
1
1
0
0
0
0
0
1
0
1
0
1
1
1
0
0
0
3
1
0
0
0
1
0
1
1
0
1
0
0
0
1
0
1
0
0
1
0
2
1
0
1
1
2
0
1
0
0
1
1
0
1
1
0
2
1
1
0
0
2
1
0
2
0
0
0
2
1
2
0
2
1
1
0
0
1
2
0
2
0
0
2
0
1
1
0
1
0
0
2
0
2
1
1
1
0
1
1
1
2
1
2
2
0
0
1
1
2
0
0
1
1
2
0
0
1
0
0
0
0
0
0
0
2
0
2
0
2
0
0
1
1
1
1
0
0
0
1
1
2
0
0
0
1
0
0
0
2
1
0
2
0
0
2
0
0
1
2
0
0
1
2
2
0
1
0
1
2
0
2
1
1
0
1
0
1
0
0
1
0
0
0
0
1
0
2
0
1
2
2
0
1
0
0
0
3
0
0
0
2
0
0
0
2
2
2
0
2
0
1
0
0
0
1
1
0
1
1
2
2
1
0
1
2
0
1
0
1
0
3
0
0
0
0
0
0
0
1
0
2
0
1
2
0
1
1
0
0
2
2
0
0
1
1
0
2
3
2
2
0
0
0
1
0
1
0
1
0
2
2
0
0
1
1
0
0
0
0
2
0
0
1
0
0
1
0
0
0
2
0
0
1
1
0
0
1
1
0
2
1
0
2
0
1
0
1
1
1
2
1
1
1
0
0
0
0
2
0
0
2
2
0
2
0
1
0
0
1
0
2
0
1
0
0
0
1
1
1
0
0
1
1
0
1
0
0
1
0
1
0
2
0
0
1
3
0
1
0
0
2
0
0
1
0
0
0
2
0
1
2
0
1
0
1
0
1
2
2
1
0
0
0
0
1
1
0
0
1
0
1
0
0
1
1
0
2
2
1
2
1
0
1
0
1
2
2
0
1
1
0
2
2
0
0
0
0
2
0
2
0
0
1
0
0
2
0
2
0
1
0
0
0
1
0
1
1
2
0
0
0
0
1
1
2
2
0
0
1
0
0
2
2
0
0
2
1
0
0
0
2
0
0
1
2
0
2
0
1
2
0
1
0
1
2
1
0
0
0
0
0
1
0
0
1
0
0
0
2
0
2
0
1
2
0
2
1
0
0
0
0
0
0
2
2
0
1
1
1
1
2
1
0
0
1
0
2
0
1
0
0
1
0
2
0
2
2
3
0
1
2
1
0
0
4
1
0
2
0
0
0
1
0
2
0
0
0
0
2
1
1
3
2
2
0
0
0
0
3
0
0
1
0
0
0
2
0
1
1
2
0
0
1
0
1
0
0
0
0
0
2
1
3
0
2
0
0
0
1
0
0
3
0
2
0
2
1
1
1
1
0
0
0
0
0
0
3
0
2
2
0
0
1
3
0
0
0
0
0
1
0
0
2
2
1
0
1
0
1
0
0
2
1
0
1
0
1
1
0
0
0
0
2
0
1
0
0
2
2
0
0
0
1
2
0
1
2
1
0
2
2
0
1
1
0
0
2
2
1
0
1
1
0
3
2
1
0
2
0
0
0
2
1
0
0
1
2
2
1
0
0
1
0
2
1
1
0
0
1
0
4
0
2
0
0
1
0
1
1
0
1
0
2
0
0
2
2
2
0
0
0
0
1
1
2
0
0
1
0
2
1
1
0
0
0
0
0
1
0
1
2
0
2
2
0
2
2
2
1
1
1
0
2
0
2
1
2
2
0
0
2
0
2
0
1
0
0
1
0
0
1
1
0
1
0
2
2
1
0
0
1
0
0
0
0
0
0
2
1
2
2
0
0
0
1
2
0
1
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
2
1
2
0
0
2
0
1
0
0
0
0
2
0
0
0
2
0
0
2
1
0
1
0
0
2
0
0
0
1
1
0
1
4
0
2
2
0
0
0
0
1
0
1
2
1
2
0
1
2
1
0
0
0
0
2
0
0
4
2
0
0
2
0
2
1
0
1
2
2
1
0
1
0
0
2
0
1
0
1
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
2
0
1
0
0
2
0
1
0
0
1
1
0
0
1
1
1
0
1
0
1
1
2
0
2
0
0
2
0
1
0
0
1
0
0
0
0
0
1
0
2
1
1
1
1
0
1
0
0
1
1
0
0
0
0
0
1
1
0
2
0
0
0
2
0
2
0
0
0
0
2
2
0
2
0
0
2
0
1
0
0
0
0
2
3
1
1
0
2
0
0
0
0
2
0
2
0
0
2
2
1
0
0
2
0
1
0
0
1
1
0
0
2
1
0
1
1
0
2
0
0
1
0
0
2
0
0
0
1
0
1
0
1
0
0
0
1
0
1
0
2
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
1
1
1
1
1
0
1
2
0
0
0
0
0
0
2
1
2
0
0
2
0
2
1
1
0
2
1
0
1
1
1
2
0
0
2
2
1
1
2
0
0
0
1
1
1
1
0
2
1
1
2
0
2
1
0
2
1
0
0
2
2
2
1
1
0
0
1
1
0
0
2
2
0
0
0
1
0
0
1
0
2
0
3
1
0
2
0
5
1
0
0
0
1
1
2
2
1
1
2
0
1
0
1
1
0
0
1
0
1
0
0
0
1
1
0
1
0
2
1
2
1
0
0
3
1
2
0
1
1
0
2
1
1
0
0
2
1
0
1
0
1
0
0
2
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
1
1
1
1
1
2
0
2
2
2
3
0
0
2
1
0
0
1
1
2
0
0
1
1
0
0
0
1
0
1
0
0
2
2
1
1
2
0
0
2
0
0
0
1
0
1
0
0
0
1
1
1
2
0
2
2
1
0
1
1
0
1
1
3
0
1
2
1
2
2
4
1
0
0
0
0
1
1
1
1
0
1
0
0
0
2
0
2
0
3
1
2
1
0
0
0
0
1
0
1
0
1
0
2
1
2
0
0
1
0
0
0
1
0
0
2
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
1
1
3
1
0
2
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
1
0
0
1
2
1
1
1
1
0
1
0
1
0
1
2
1
0
0
0
0
1
2
0
4
0
0
0
1
0
1
1
1
0
2
2
0
1
0
0
0
0
2
0
0
2
1
0
1
0
1
0
2
1
2
1
0
1
1
0
1
0
0
2
0
0
0
0
2
0
0
0
0
2
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
3
1
0
0
0
1
0
0
1
1
2
0
0
1
1
1
1
0
1
2
0
1
0
2
1
2
2
1
0
0
0
2
0
0
2
0
1
2
2
1
0
0
0
2
2
2
0
0
0
1
1
0
2
1
0
1
0
1
1
3
2
0
1
0
2
2
1
0
1
0
1
2
0
0
0
0
0
0
0
0
0
1
0
1
1
1
2
1
1
2
1
2
0
0
0
2
1
1
0
0
2
0
0
1
1
0
3
1
0
0
0
2
1
1
2
0
2
1
0
0
0
0
1
2
1
0
1
0
2
1
2
2
1
0
1
0
2
1
0
2
0
0
2
0
0
1
0
1
2
2
0
0
0
0
2
0
1
0
1
0
0
0
1
0
0
0
2
1
1
0
0
0
2
0
1
0
0
4
0
1
0
2
1
1
0
1
1
0
1
0
0
0
0
2
2
1
0
1
0
0
0
1
1
2
0
1
2
1
0
0
2
1
2
0
2
3
1
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
3
1
0
2
0
1
2
1
2
2
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
1
0
0
2
2
1
0
0
0
0
0
0
2
0
0
0
0
2
0
1
3
0
1
1
0
1
0
0
0
0
1
0
0
0
1
2
1
1
0
2
0
0
2
0
2
2
1
1
2
2
1
0
2
0
2
0
0
0
0
1
1
0
0
0
2
2
1
2
1
0
1
2
2
0
2
2
0
1
2
0
2
0
2
0
1
0
1
0
0
0
2
2
0
1
1
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
1
2
2
1
1
0
0
1
0
0
1
0
1
0
0
2
0
2
1
2
0
2
2
1
0
2
1
3
0
0
1
1
1
2
0
0
0
1
1
1
0
4
2
0
1
1
0
2
0
0
0
0
1
1
0
2
0
3
0
2
1
0
2
0
0
1
0
1
1
0
0
1
2
0
1
0
0
1
1
1
2
1
2
2
1
1
1
1
0
0
0
1
0
2
2
0
2
2
0
0
0
2
1
0
1
1
0
0
1
0
0
1
2
1
3
2
0
0
2
0
0
2
1
1
0
0
1
0
2
0
2
0
3
2
1
1
2
0
0
0
0
0
0
2
2
3
2
0
0
0
0
2
1
2
2
1
1
2
0
1
1
0
0
0
0
2
0
2
2
2
1
1
2
2
1
0
0
0
0
0
1
0
0
0
0
0
4
0
1
1
0
1
0
0
2
0
0
0
0
0
1
1
0
1
1
1
2
1
0
0
0
1
1
1
0
0
0
0
0
2
1
0
2
2
0
1
1
0
2
1
0
0
0
1
0
0
0
0
2
1
0
1
0
0
0
0
2
2
0
0
1
1
2
3
1
0
1
0
1
9
0
0
1
1
0
1
0
1
1
1
2
1
1
1
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
1
1
1
1
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
2
0
0
0
2
1
1
0
2
3
1
0
0
1
0
2
1
1
0
2
2
1
1
0
1
0
3
2
0
1
0
1
2
1
0
0
0
2
2
2
0
0
1
0
0
1
0
0
2
0
2
1
0
0
0
1
1
1
0
0
0
1
0
2
0
0
0
0
0
1
1
0
0
2
0
0
0
1
2
1
0
0
0
3
0
0
0
2
0
2
2
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
2
0
0
2
1
2
0
2
0
1
2
1
0
2
2
2
0
2
0
0
0
1
2
0
1
0
0
1
1
0
0
0
1
2
0
2
1
1
0
4
0
3
2
1
0
2
2
3
0
0
0
1
2
0
3
0
1
0
2
0
0
0
0
1
0
3
0
0
0
1
2
1
0
0
1
0
2
0
1
2
0
0
1
0
0
0
2
0
1
1
0
1
1
1
2
0
0
2
1
0
1
2
0
0
0
0
0
2
0
0
2
0
0
3
0
2
0
0
2
0
1
0
1
2
2
1
4
0
2
2
0
2
2
0
1
2
0
1
2
0
0
2
0
0
0
0
0
2
2
0
0
0
0
1
3
2
0
1
0
0
0
0
0
0
0
0
0
1
2
2
1
0
0
0
0
1
0
0
2
0
1
0
0
1
0
1
0
0
1
0
0
0
0
1
0
1
0
1
2
0
0
1
0
1
1
0
0
0
0
0
1
0
0
1
0
2
1
0
0
1
0
0
2
0
2
0
1
0
0
0
0
0
2
1
0
0
1
0
1
0
1
1
1
0
2
0
0
1
0
0
0
1
2
0
0
2
0
0
0
0
1
0
0
1
1
0
1
0
2
0
0
0
0
1
0
1
0
0
0
0
2
2
0
2
0
2
1
0
2
0
1
2
1
0
1
0
1
2
2
1
2
1
1
1
2
0
0
2
1
1
0
0
0
2
1
2
0
0
0
1
2
0
0
1
1
1
3
2
2
0
0
2
1
0
0
1
0
2
2
0
0
2
2
0
1
0
2
0
1
2
0
0
0
0
2
1
2
2
1
0
0
0
2
0
2
0
2
0
1
1
0
0
0
1
1
0
0
4
0
3
1
2
1
2
1
1
1
0
0
0
0
2
0
0
0
1
1
0
0
4
1
1
1
0
0
0
0
0
3
2
0
0
2
0
0
0
2
1
0
2
0
1
0
0
0
0
0
1
0
0
3
1
1
0
1
2
1
0
0
0
0
0
0
2
0
2
2
2
2
0
0
0
0
0
1
1
1
0
0
0
1
0
0
1
0
0
3
1
1
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
1
2
0
0
0
2
1
1
1
2
1
0
0
0
0
2
1
0
0
1
0
0
0
2
1
1
0
0
0
0
2
0
1
2
2
1
2
2
2
0
2
0
2
0
2
3
0
0
0
1
0
1
2
0
1
3
0
0
1
0
0
2
2
0
0
1
0
2
1
1
0
1
1
0
1
0
1
0
2
0
0
2
0
1
0
0
1
0
1
0
2
1
0
0
0
0
0
0
2
0
3
0
0
0
1
0
1
0
2
2
0
0
0
1
0
2
0
0
3
0
0
1
1
0
0
0
0
2
1
1
2
2
0
0
0
0
1
0
1
0
1
2
0
1
0
1
0
1
0
0
0
1
1
1
0
1
2
0
2
1
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
2
1
1
0
0
0
0
0
1
0
0
1
3
1
0
0
2
2
0
2
0
2
2
0
0
1
0
2
1
0
1
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
2
0
2
0
0
1
0
0
1
1
1
2
0
1
0
0
0
2
0
2
1
0
0
2
0
1
1
0
0
1
0
1
0
1
0
2
0
1
2
1
0
0
1
0
0
0
0
0
2
0
0
0
1
1
0
0
1
1
1
0
0
3
1
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
1
1
0
7
1
1
0
0
2
0
1
2
0
0
0
2
0
0
2
1
1
1
0
1
1
0
2
0
2
2
0
0
0
3
0
2
0
0
2
1
0
1
0
0
1
1
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
2
1
0
2
0
2
2
1
0
2
3
1
0
0
2
1
3
2
0
2
0
1
2
1
0
0
0
0
0
1
1
0
1
0
1
5
1
0
0
1
2
0
2
1
1
0
0
0
1
0
1
1
1
1
0
0
0
0
0
1
2
1
1
1
1
0
1
1
1
0
3
0
2
0
1
1
0
1
1
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
1
1
0
2
2
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
3
0
0
1
0
2
0
0
0
0
2
1
2
1
0
1
1
2
1
0
2
2
0
0
1
0
0
0
2
2
0
0
0
0
1
1
0
1
0
0
1
2
0
2
2
0
0
1
0
2
1
2
0
0
1
1
0
0
1
0
0
1
0
0
2
0
0
0
1
0
0
0
1
0
2
1
1
0
2
2
0
0
1
2
0
1
1
2
0
0
0
0
2
0
2
2
0
2
2
1
1
0
0
0
2
1
2
0
1
0
1
1
0
2
1
1
2
1
1
0
1
0
0
0
0
2
1
2
1
0
0
0
0
0
0
1
0
0
0
0
0
1
3
0
0
0
5
1
2
1
0
2
1
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
1
0
1
0
1
1
1
0
1
0
0
1
0
1
0
1
1
0
1
0
0
2
2
0
0
2
1
1
0
1
0
2
4
0
0
0
2
0
0
2
1
2
0
2
1
2
0
2
0
1
3
2
0
1
0
1
0
0
1
1
0
2
0
3
1
1
0
2
2
1
2
1
1
0
0
1
0
0
0
0
0
1
1
0
1
0
0
2
1
0
2
0
1
0
2
2
0
1
0
0
2
1
1
0
0
0
2
0
1
0
0
2
1
0
0
0
0
0
0
1
1
1
2
2
0
0
1
1
0
1
1
0
0
0
0
2
0
0
4
0
0
0
0
1
0
0
0
2
1
0
2
0
2
0
5
1
0
0
1
0
0
0
0
0
0
0
0
2
2
3
1
1
0
2
0
1
1
0
0
0
0
0
1
0
0
1
0
1
2
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
1
0
2
1
0
0
0
0
1
2
0
1
1
0
2
0
0
1
1
2
2
2
1
0
0
1
0
1
0
0
1
0
1
0
0
1
1
1
0
0
2
1
1
0
0
1
0
0
0
1
0
0
0
2
1
2
0
1
0
1
0
0
0
1
2
0
1
1
1
1
0
0
1
1
0
1
0
1
0
0
0
0
2
1
0
0
2
0
2
0
0
0
0
3
2
0
0
0
1
0
1
0
0
0
0
2
1
0
1
1
0
1
0
0
0
1
0
0
0
0
0
2
0
0
1
0
1
2
1
1
0
0
0
1
1
0
0
1
0
0
0
0
3
0
0
1
0
1
0
1
1
2
1
0
0
0
0
0
0
0
0
0
0
1
1
0
2
1
2
0
0
0
2
2
1
0
1
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
2
2
1
1
2
2
0
0
0
0
0
0
0
0
0
2
2
0
3
1
0
1
2
0
0
2
1
1
1
0
0
0
0
1
2
2
2
0
0
1
0
1
2
0
1
0
0
0
0
1
2
0
1
0
0
1
1
0
0
0
0
2
1
0
1
0
0
0
1
0
2
2
0
1
1
0
3
0
0
1
0
1
1
0
2
0
1
0
0
0
0
1
0
0
0
3
0
0
0
1
2
0
0
0
1
3
1
3
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
3
0
0
2
0
2
1
0
3
1
1
2
0
1
0
1
0
0
0
0
0
0
0
1
2
0
1
0
1
1
2
0
0
0
2
1
1
2
2
2
1
2
0
0
0
0
0
0
0
0
0
0
1
0
1
1
2
0
3
0
1
1
2
0
3
0
0
1
1
0
0
0
0
0
2
0
0
1
1
0
2
2
1
2
1
2
1
2
1
2
0
0
0
0
0
1
3
2
10
0
1
1
1
0
0
1
0
1
0
0
0
2
0
1
1
1
1
0
2
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
1
2
0
0
0
1
2
2
0
1
1
0
0
0
0
2
1
2
2
0
2
0
1
2
2
0
2
0
0
2
2
0
2
0
0
1
1
0
0
2
0
0
2
2
2
1
0
0
1
0
2
0
0
2
1
0
2
1
0
0
0
0
1
2
0
1
0
0
0
0
2
2
2
0
0
0
0
0
1
0
0
2
0
0
2
0
2
0
1
0
0
1
0
1
1
2
0
0
1
2
0
0
2
0
0
1
1
2
2
0
0
4
1
1
1
0
0
1
0
2
2
1
0
1
0
1
1
2
0
3
1
0
1
0
1
1
2
0
0
0
0
3
0
0
1
0
1
0
2
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
2
0
0
2
1
1
0
0
0
0
1
2
1
1
0
2
0
1
0
0
0
0
2
2
0
0
0
1
1
0
0
1
1
0
2
0
3
2
2
0
3
0
4
1
1
0
1
2
0
2
0
1
1
1
0
1
2
0
0
0
0
4
1
0
3
1
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
2
1
1
0
0
2
1
2
1
0
0
1
0
0
1
2
0
2
1
0
2
0
1
1
0
0
0
0
0
0
2
1
0
1
0
0
1
0
1
0
1
3
1
2
1
2
0
1
0
0
2
2
1
1
1
1
2
0
0
0
0
2
1
0
0
0
0
1
0
0
2
1
2
0
0
0
1
0
0
0
0
1
1
2
0
1
0
0
1
1
1
0
0
0
2
0
0
2
0
1
1
0
0
0
2
1
1
1
1
0
0
2
0
0
0
0
0
2
1
1
0
0
0
1
0
0
1
1
4
1
1
1
0
1
0
0
1
0
0
0
2
0
0
1
0
0
1
0
1
7
0
0
1
0
0
1
1
0
0
0
2
0
0
0
3
0
2
1
2
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
2
2
0
1
0
1
0
0
0
2
0
7
2
0
2
1
0
1
0
0
1
0
1
2
2
0
1
1
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
2
0
1
0
2
0
0
0
1
2
0
0
2
0
2
2
0
0
1
0
3
0
0
0
0
4
2
0
0
2
1
1
1
1
1
0
0
1
1
0
0
1
2
0
1
0
1
1
0
2
2
1
0
2
0
0
0
0
0
2
2
0
2
1
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
2
0
0
2
0
0
2
1
0
0
0
0
1
0
0
0
2
0
2
0
0
0
1
0
0
0
0
1
2
0
1
2
0
1
0
0
0
1
2
0
1
1
2
1
1
0
0
2
1
0
1
0
0
2
0
2
2
0
0
2
1
0
2
0
0
2
2
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
1
1
2
0
1
0
1
1
0
0
1
1
0
0
1
2
0
0
0
2
0
1
0
0
0
1
0
0
2
0
0
1
0
0
1
0
0
2
1
0
0
1
0
2
1
1
0
0
2
0
2
1
2
0
0
1
0
2
0
1
0
1
1
1
1
0
1
1
0
1
1
0
1
0
1
2
1
1
2
0
0
0
2
1
2
0
0
2
4
0
0
1
1
1
0
0
1
0
2
2
1
1
1
0
0
0
0
0
1
0
1
0
0
2
0
0
1
0
0
0
2
1
2
1
0
2
0
0
0
0
1
1
2
1
1
0
1
3
0
0
0
2
0
2
0
2
2
0
2
1
0
1
0
0
2
0
1
0
0
0
2
0
1
0
0
2
0
0
2
2
2
0
2
0
0
2
2
1
1
0
8
0
2
1
0
0
0
0
0
0
2
0
1
2
2
0
0
0
0
1
0
1
1
0
1
1
0
1
0
1
0
1
0
1
1
0
2
0
1
2
1
1
1
1
0
0
0
0
1
0
0
0
2
0
0
0
4
2
1
1
0
0
1
0
0
0
1
2
0
1
0
2
0
1
0
1
0
2
1
0
0
1
1
0
0
0
1
0
1
0
0
1
2
0
1
0
0
1
0
2
0
0
2
0
0
0
0
2
2
0
0
0
1
0
0
0
0
1
2
2
1
0
1
2
1
0
1
0
2
2
0
0
0
1
0
2
3
3
2
0
1
0
1
1
2
1
1
2
1
1
0
0
1
0
0
2
0
0
2
1
2
0
1
0
1
0
1
1
2
2
2
1
1
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
1
0
0
0
1
0
2
3
0
0
2
0
0
0
1
1
0
1
0
0
0
1
2
0
1
2
1
0
0
2
2
0
0
2
1
0
1
0
1
0
0
1
2
0
0
1
2
0
0
1
2
2
0
0
2
1
0
0
0
0
1
0
0
2
2
0
0
0
2
0
0
0
1
1
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
2
2
1
0
2
2
1
0
2
1
2
1
1
2
1
1
0
1
1
3
0
2
2
0
2
1
0
0
0
1
0
2
1
1
0
1
0
3
0
4
0
1
0
0
2
0
3
1
2
0
0
2
1
0
2
0
2
1
2
0
1
1
1
0
2
1
2
0
0
1
0
0
0
1
0
1
1
0
0
1
1
0
1
0
0
0
0
1
0
1
1
0
1
2
0
2
2
1
0
0
4
1
0
1
1
0
0
0
1
0
0
1
0
2
0
1
8
0
2
0
0
2
0
0
0
1
0
1
0
1
0
0
0
1
0
4
0
2
7
1
0
0
1
1
0
0
1
2
0
0
0
0
0
1
0
1
0
1
0
2
0
2
0
2
0
2
2
0
1
2
1
0
0
2
1
0
0
2
1
0
0
0
2
2
0
2
2
0
0
2
1
1
0
1
2
2
1
0
0
0
1
2
1
1
1
1
0
0
1
2
0
1
2
0
0
1
0
0
0
0
1
0
2
2
0
0
0
0
1
0
2
0
0
2
1
0
1
1
0
0
2
0
0
3
0
0
0
2
0
2
2
1
1
0
0
2
0
1
2
2
0
0
2
0
0
2
1
2
2
2
0
1
0
1
0
0
2
1
0
2
0
0
1
1
0
0
0
1
0
0
2
0
2
0
1
0
0
0
1
0
0
0
1
0
0
1
2
0
1
2
2
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
2
1
2
2
2
2
1
1
0
0
1
0
0
1
0
1
0
1
0
1
1
1
3
0
0
0
0
0
1
0
0
2
1
1
0
1
1
2
1
0
2
1
5
0
1
0
2
2
1
0
0
1
0
0
2
2
0
1
2
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
1
1
2
2
0
0
1
0
0
4
0
2
2
0
2
0
2
2
0
1
0
0
2
0
0
1
4
2
1
2
1
1
1
0
1
1
3
0
2
1
0
0
0
1
1
1
2
2
1
1
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
2
2
2
0
0
1
0
0
0
2
0
0
1
0
1
0
2
2
0
1
0
2
2
0
1
2
2
0
2
2
2
1
0
2
1
0
0
0
1
1
0
0
2
2
0
0
2
1
0
2
0
2
0
2
0
0
0
1
1
0
0
0
0
1
0
0
1
2
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
2
0
1
0
0
2
0
1
0
0
1
2
2
1
2
0
1
1
2
1
1
2
0
0
2
0
0
0
2
0
2
0
1
0
1
2
2
1
2
2
2
2
5
3
0
0
2
0
1
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
1
2
1
0
1
2
0
2
0
2
1
1
2
1
0
0
1
0
0
0
0
0
0
1
2
0
0
1
1
0
1
1
1
0
2
2
0
2
2
2
0
0
1
1
0
1
0
0
3
1
0
2
0
1
0
0
0
1
0
2
2
0
2
1
1
0
2
0
1
0
0
2
2
1
0
0
1
1
1
1
1
1
0
1
2
0
0
0
0
1
0
1
1
3
2
0
0
0
0
0
2
0
4
3
1
3
2
0
0
1
0
0
2
3
2
1
2
0
0
0
2
0
1
3
1
0
0
1
0
1
1
0
2
2
0
0
1
1
1
0
1
1
0
1
0
0
0
1
2
1
0
0
1
0
0
0
0
3
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
1
0
1
1
0
0
0
1
0
2
2
0
0
2
0
0
1
2
1
1
2
0
1
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
2
1
1
0
1
2
1
0
0
0
0
0
1
2
2
0
0
2
0
0
1
2
1
0
1
1
0
0
0
1
1
1
1
0
2
1
0
0
2
0
0
2
0
0
0
2
0
1
0
2
1
3
1
0
1
0
1
0
2
0
0
2
1
1
0
1
0
1
1
0
0
0
2
0
0
0
2
1
0
1
1
2
0
3
0
0
2
0
0
0
2
2
0
1
0
1
0
2
2
2
1
1
0
1
2
2
0
0
4
1
1
1
0
0
0
0
2
0
0
0
3
2
1
1
0
0
2
2
2
0
0
1
2
2
2
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
1
2
2
1
1
0
1
0
2
0
0
0
1
2
1
0
2
1
2
0
1
2
0
0
1
2
0
1
0
0
0
0
0
1
0
0
0
2
2
0
0
0
1
0
1
0
0
0
0
0
1
1
0
1
0
0
2
3
2
0
0
0
2
0
1
2
0
0
1
0
0
0
1
0
2
0
0
0
2
0
0
0
1
2
1
0
0
1
0
1
0
2
2
0
0
2
2
1
1
0
0
0
0
0
2
2
1
2
2
0
0
0
1
0
0
0
2
0
1
2
1
0
0
0
1
1
0
1
3
1
0
1
0
2
0
1
0
2
0
2
0
0
1
0
0
0
2
1
0
0
1
2
1
0
1
0
2
1
0
0
1
2
0
1
2
2
0
0
1
0
0
2
0
1
2
0
0
2
0
1
0
1
1
2
0
1
0
0
0
0
1
0
2
1
0
0
2
0
1
1
0
2
0
0
1
0
1
0
0
1
2
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
1
0
2
1
0
2
1
0
3
0
0
0
0
1
0
1
1
0
0
1
1
0
2
0
1
0
0
2
1
0
0
0
0
1
0
0
3
0
2
0
2
0
2
1
1
2
0
1
1
1
2
2
0
1
0
0
1
1
0
0
2
2
2
1
0
0
0
2
0
2
1
2
0
2
2
1
2
0
1
0
0
0
0
0
0
0
0
4
2
1
0
9
0
0
3
0
0
1
0
0
0
0
0
0
1
1
0
1
0
1
1
0
0
2
1
0
2
1
2
0
1
0
2
1
0
0
1
2
0
0
2
2
0
2
0
0
0
0
2
0
1
2
0
2
0
1
0
0
2
1
1
1
2
0
1
1
0
0
0
1
0
0
0
1
2
1
2
2
2
3
3
1
0
1
1
3
1
1
0
0
0
0
1
0
1
1
2
0
0
2
1
0
0
0
2
0
1
0
0
1
2
0
3
0
0
0
0
0
0
1
0
1
0
0
0
0
3
0
0
1
1
2
0
0
0
0
1
2
2
0
0
0
0
1
0
0
2
1
0
1
2
2
0
0
2
0
0
0
1
2
2
0
2
2
2
1
0
3
0
0
2
0
0
1
2
2
0
0
0
0
2
2
2
0
1
1
0
0
0
0
2
1
0
0
2
0
0
0
2
0
2
1
0
2
2
0
2
1
2
0
2
2
0
2
1
0
1
1
0
0
0
1
1
0
1
2
1
0
0
0
0
1
0
0
2
0
2
0
1
0
0
0
1
2
0
2
3
0
2
1
0
1
1
0
3
1
0
2
0
0
2
2
0
1
3
0
1
0
0
0
0
1
0
2
2
1
1
0
1
1
0
0
2
0
0
0
3
1
0
0
2
0
2
2
0
2
2
2
0
0
0
1
0
1
1
1
1
1
0
1
2
1
0
0
2
0
2
0
0
1
2
2
0
0
0
0
1
1
0
0
0
4
1
0
1
0
0
0
2
1
2
2
2
0
2
0
0
0
0
0
1
0
1
0
2
0
0
2
1
1
0
1
0
0
0
0
2
0
1
0
2
0
2
2
2
1
3
1
0
0
1
0
1
0
1
0
2
0
0
0
0
1
0
1
2
1
2
0
1
0
1
0
0
0
0
2
1
1
0
0
2
0
0
0
0
1
0
0
0
0
1
0
1
2
2
2
0
0
0
2
0
2
2
2
2
0
1
0
1
1
7
0
1
0
1
0
0
1
0
2
2
0
2
1
1
0
2
0
2
2
1
1
1
1
0
0
0
1
2
2
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
2
1
0
4
2
0
1
1
0
0
0
1
0
1
1
1
0
0
1
1
0
0
1
5
3
1
0
0
0
0
1
1
0
2
2
0
2
0
0
0
0
1
0
2
2
0
0
0
1
0
0
0
0
1
0
0
0
1
1
1
3
0
0
0
3
0
1
0
1
1
3
2
0
2
1
0
2
1
0
2
0
0
0
1
0
2
1
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
1
1
0
1
1
0
0
0
2
1
0
0
2
2
0
0
0
1
0
0
1
0
0
0
2
0
0
1
2
1
0
0
0
1
0
2
0
1
1
0
0
1
0
1
0
1
1
0
1
0
0
0
0
2
0
0
0
2
1
0
1
1
0
1
0
0
0
0
2
0
1
2
2
1
0
1
0
1
0
0
0
0
0
2
2
0
2
0
2
1
1
0
0
0
2
0
0
0
0
1
1
2
2
0
1
1
0
0
1
1
2
1
0
0
1
0
0
0
2
1
0
1
0
1
1
0
2
0
0
0
2
0
0
2
1
1
2
2
0
2
0
2
1
0
1
2
0
1
2
0
0
0
0
0
1
0
1
1
0
2
1
0
0
1
0
0
0
0
2
2
2
1
0
0
2
1
0
0
0
1
0
0
1
2
2
1
2
0
2
2
0
0
0
0
0
0
2
2
0
0
2
1
2
0
0
0
1
3
0
2
0
2
0
2
0
1
0
0
0
1
0
1
2
1
0
2
1
2
2
0
1
0
0
1
1
1
0
0
3
0
0
1
0
1
1
0
1
1
0
1
1
2
0
0
0
0
0
0
2
1
2
0
0
3
0
1
0
0
0
1
0
1
0
1
1
0
0
2
0
0
1
0
0
1
1
2
0
0
0
2
2
0
1
2
1
0
0
0
1
0
1
2
0
1
2
2
0
0
1
0
0
0
1
1
1
2
0
0
0
0
2
0
0
0
1
2
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
1
2
2
1
1
1
1
1
3
0
0
1
1
1
0
3
0
0
1
0
1
0
0
0
4
0
1
0
1
0
1
1
1
0
1
2
2
1
1
2
0
0
2
0
0
0
1
1
0
0
0
0
1
1
0
0
1
1
1
0
0
0
2
1
0
0
0
0
7
1
1
0
0
1
0
1
1
0
2
1
1
0
0
0
0
0
2
1
1
0
1
1
1
0
0
0
1
0
0
0
1
0
2
1
2
2
1
1
1
0
0
0
0
1
3
0
0
1
0
0
0
0
2
0
2
2
1
0
1
1
0
2
2
0
0
0
2
0
0
0
1
0
0
0
2
1
0
0
1
1
1
1
1
0
2
0
0
0
2
2
1
0
2
2
2
0
1
1
1
2
2
0
1
0
1
1
0
0
2
0
1
0
0
1
0
0
1
0
0
0
1
0
1
2
0
0
2
0
1
0
0
0
2
1
1
1
0
0
0
0
0
1
0
1
1
0
1
0
0
1
1
1
1
0
1
0
2
0
1
0
0
0
1
1
0
1
0
1
1
0
0
2
3
0
0
1
1
0
1
0
1
1
0
1
0
2
1
0
0
1
0
0
1
0
0
1
2
2
1
2
1
2
0
1
2
0
0
1
1
0
0
2
0
1
0
2
1
0
1
2
0
1
0
0
0
2
0
2
0
0
0
0
1
1
0
0
0
1
2
0
0
1
1
2
0
0
0
0
1
0
0
1
2
0
1
0
1
2
0
0
0
0
1
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
1
1
2
2
0
0
0
0
2
2
0
0
0
3
0
1
1
2
0
0
1
1
2
0
1
0
1
0
1
1
0
2
3
2
2
0
0
0
0
0
1
1
0
0
1
0
2
1
1
1
0
1
0
0
1
0
1
1
0
0
1
0
2
1
1
0
4
0
0
2
0
1
0
1
2
1
0
2
2
1
2
2
2
1
0
0
0
0
1
0
2
0
1
0
0
2
0
1
2
0
0
1
0
2
2
0
0
1
0
1
1
2
2
1
0
0
0
0
0
0
0
1
1
0
1
0
1
2
0
1
0
0
0
0
0
0
0
0
1
2
2
0
1
1
0
1
0
0
1
0
0
2
0
1
1
0
0
0
0
0
0
1
0
1
4
0
2
0
0
0
2
1
1
2
1
2
0
2
1
0
1
2
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
1
0
1
1
0
2
0
0
2
0
1
0
0
0
1
1
0
0
0
0
2
0
0
3
0
1
0
0
2
0
0
3
1
0
0
2
1
0
2
0
1
2
5
1
0
0
1
0
0
1
0
2
0
0
0
1
2
2
1
2
0
0
0
0
0
1
1
1
0
1
2
0
1
1
0
0
0
0
0
0
2
2
0
0
1
1
1
0
0
0
0
0
0
1
3
0
1
0
0
1
0
0
0
1
1
1
0
0
2
1
0
2
0
1
0
0
0
2
0
1
0
1
0
2
0
1
2
0
0
0
1
1
2
2
0
1
0
0
2
0
1
0
0
1
1
0
2
3
0
0
1
1
2
3
0
1
1
1
0
0
0
0
2
0
1
0
0
2
0
0
0
0
2
0
2
2
0
0
1
1
0
0
0
0
1
1
1
0
2
1
1
1
1
2
1
2
2
2
2
2
0
2
2
2
0
0
2
1
0
1
0
2
0
0
0
1
0
1
2
2
0
0
0
1
1
0
0
1
2
0
1
0
1
1
0
2
1
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
1
1
0
1
0
1
1
2
0
0
0
0
0
0
0
0
1
0
0
0
2
1
3
0
2
1
0
1
2
4
0
2
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
1
2
1
0
1
0
0
2
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
1
0
0
1
1
0
1
0
2
0
1
2
0
0
2
0
0
1
2
2
0
0
0
0
1
1
0
0
0
1
1
2
0
2
0
0
1
1
0
1
1
0
1
1
1
1
2
2
2
0
0
0
0
0
0
2
0
0
3
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
1
1
1
1
1
2
0
2
1
1
1
0
1
1
0
2
1
1
1
0
0
1
0
1
1
2
2
2
2
2
0
0
1
0
1
1
2
0
2
2
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
2
1
2
1
0
1
0
1
1
1
0
2
1
2
1
2
1
0
0
1
2
1
0
1
0
2
1
0
2
2
0
0
1
0
2
1
0
2
0
0
3
1
0
1
1
0
2
0
2
1
2
0
2
0
0
0
0
0
4
0
0
0
0
1
0
2
1
0
0
0
2
1
0
1
0
2
1
0
1
0
1
1
2
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
1
0
2
0
1
2
1
1
1
1
2
1
0
0
0
0
1
2
2
0
1
0
0
0
0
0
0
2
3
1
2
0
0
0
0
0
0
1
0
1
2
1
2
2
0
1
0
1
1
0
2
0
0
1
1
0
0
2
3
2
3
0
0
0
0
0
2
0
0
1
1
0
1
2
1
0
0
0
0
0
0
2
0
1
0
2
0
2
1
0
0
3
1
1
0
2
1
0
0
1
0
1
0
1
1
0
0
1
1
2
0
1
0
1
1
0
0
2
2
1
0
1
0
0
2
1
0
2
2
0
1
2
0
0
2
0
4
1
0
0
0
0
0
1
2
2
0
2
2
1
1
1
0
2
1
0
1
1
2
1
0
2
0
0
0
0
1
1
2
3
2
0
0
1
0
1
0
1
0
0
0
1
0
0
0
1
0
0
2
2
1
2
0
1
1
1
1
1
1
0
2
1
2
0
1
0
0
0
1
1
1
0
0
0
0
1
1
0
2
1
1
0
0
0
1
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
3
1
0
2
0
1
1
0
0
1
1
0
1
2
0
2
0
3
1
2
1
1
0
2
0
0
0
1
2
0
1
1
1
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
2
2
1
0
0
0
0
2
1
0
0
0
0
0
0
3
0
1
0
0
1
0
0
1
0
1
2
0
1
0
0
1
2
0
2
1
0
0
0
2
0
2
1
0
0
0
0
0
1
0
2
2
0
1
1
1
1
2
1
0
2
1
0
1
2
1
1
0
2
2
2
1
0
1
0
0
2
1
1
2
0
0
1
0
0
1
0
3
0
0
0
0
1
1
0
3
0
2
0
2
1
1
1
1
1
1
1
1
0
0
1
0
0
0
0
0
2
3
2
1
0
1
0
0
1
0
0
1
2
0
2
2
1
0
0
3
1
0
0
1
1
0
0
0
0
2
2
1
1
0
0
0
0
1
1
0
0
2
0
1
0
2
2
0
0
0
1
2
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
2
0
1
0
2
0
0
1
1
0
0
2
0
0
2
0
2
0
1
1
1
1
1
0
2
2
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
1
0
2
1
1
0
1
0
2
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
3
1
1
0
1
2
2
0
0
0
0
2
2
1
1
0
0
2
2
0
2
0
1
0
2
0
1
0
0
1
2
0
0
0
0
1
1
2
1
0
2
1
0
1
2
0
1
0
0
1
1
0
0
0
1
2
0
1
0
0
0
0
2
1
0
0
0
0
1
0
2
0
0
0
0
0
2
0
2
0
0
1
2
2
0
2
0
2
0
0
0
1
2
0
2
1
0
2
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
2
0
1
1
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
2
0
0
0
2
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
1
0
2
1
0
0
2
0
0
2
0
0
1
0
2
0
2
1
0
2
0
1
0
2
0
0
0
2
0
0
1
2
1
0
1
0
0
0
4
1
0
0
0
1
1
0
0
0
2
2
0
0
0
0
2
2
0
0
2
1
1
0
0
2
1
1
0
1
0
0
2
1
0
1
1
1
1
2
2
0
0
0
1
0
0
0
1
1
1
0
2
0
2
0
1
2
2
2
1
1
1
0
0
1
0
2
2
0
0
0
0
1
2
0
1
0
0
1
1
0
0
2
0
0
1
1
1
0
2
1
0
1
2
0
2
1
0
0
2
0
1
6
3
0
0
1
0
0
0
1
1
1
1
0
0
1
0
0
0
1
0
2
1
2
0
0
1
1
0
1
1
0
2
0
0
0
2
0
0
1
2
2
0
0
0
0
1
1
2
0
1
1
0
0
0
0
2
0
1
0
0
0
0
0
2
2
0
1
0
0
0
1
0
0
0
0
1
0
1
2
1
0
1
1
1
0
1
2
1
0
0
1
2
0
0
0
1
0
1
2
0
0
1
1
2
1
0
0
0
2
1
1
2
2
1
0
0
0
0
0
0
1
1
2
0
0
0
1
0
1
0
1
0
0
0
2
2
1
2
1
2
1
1
0
0
0
1
0
1
2
0
0
0
0
0
2
2
0
2
1
0
0
1
0
0
0
2
0
0
1
0
2
1
2
1
2
0
0
1
2
1
2
0
1
1
2
0
2
1
1
1
0
0
0
1
2
0
0
1
0
1
3
1
1
1
2
0
0
2
0
2
1
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
1
4
1
2
2
1
1
1
0
1
1
2
3
1
2
0
1
1
1
2
2
0
2
0
0
3
0
0
1
1
0
1
2
2
0
2
1
0
2
0
2
1
2
0
0
0
0
0
1
0
0
1
0
0
0
1
1
1
0
1
0
0
0
0
0
0
1
1
2
0
0
0
1
0
2
2
0
2
0
1
0
1
1
0
0
3
1
0
0
0
0
0
0
0
1
0
0
2
1
2
0
0
0
1
0
0
0
1
2
2
1
0
1
2
0
0
1
0
2
0
1
3
0
2
0
0
0
0
1
0
0
1
2
0
2
0
0
0
0
1
2
2
0
1
0
1
0
0
0
1
3
0
0
1
2
4
0
1
0
0
2
1
1
0
1
0
2
0
2
2
0
1
1
0
1
1
1
1
0
2
2
0
1
2
2
0
2
0
0
0
0
0
3
0
0
3
0
2
0
0
2
1
1
1
2
0
0
0
2
0
0
0
0
1
1
0
1
0
0
2
2
1
0
2
0
1
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
2
1
2
0
0
0
0
2
2
0
4
1
2
0
2
0
1
1
0
0
2
0
0
2
1
2
1
0
0
0
2
0
0
0
1
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
4
1
0
1
0
1
0
0
2
1
0
0
1
1
0
0
1
1
0
1
1
0
2
2
0
0
2
1
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
2
1
0
1
0
1
0
0
0
2
0
0
2
1
0
0
1
1
0
0
1
0
1
2
0
2
1
1
2
1
1
2
0
0
3
1
0
0
2
0
1
2
1
0
0
2
0
0
0
1
0
0
1
2
0
0
1
1
2
0
3
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
1
1
1
0
2
1
0
2
2
2
0
1
1
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
2
2
2
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
1
0
1
0
2
1
1
2
2
1
2
0
1
2
0
2
1
2
0
1
1
0
0
1
4
0
2
0
0
0
1
1
1
1
0
0
0
1
1
1
2
0
0
1
0
2
0
0
2
0
2
1
2
0
2
0
0
0
0
0
0
0
1
0
0
1
2
0
3
1
0
1
0
0
0
0
1
2
0
0
1
0
0
2
1
0
3
0
2
0
1
2
3
1
1
0
1
0
0
1
0
2
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
2
0
1
0
1
2
0
1
0
0
0
1
0
4
2
1
0
0
0
2
1
0
0
1
1
0
0
0
0
0
0
1
1
0
1
1
2
2
2
0
1
1
0
0
0
2
0
1
0
0
2
0
0
2
1
2
0
0
2
0
1
0
1
0
1
0
0
0
1
0
1
0
1
2
0
0
0
2
1
2
1
1
1
1
1
0
0
2
7
0
1
1
1
2
2
1
2
0
0
0
1
0
0
0
1
0
2
0
1
2
0
1
1
0
2
0
0
1
0
0
0
0
0
1
0
3
0
0
0
2
0
0
2
0
1
2
1
1
0
0
0
2
0
2
0
1
0
1
0
0
0
0
0
1
1
0
0
2
2
0
1
2
1
0
0
0
1
0
0
0
0
0
0
0
2
0
4
1
2
0
2
2
0
0
0
0
0
0
2
2
0
1
2
0
2
1
1
2
0
0
2
1
0
0
0
0
2
1
0
0
0
1
1
1
2
1
0
3
1
2
1
0
0
2
1
0
1
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
2
0
0
0
0
2
2
2
0
0
0
0
0
0
1
2
1
0
1
2
0
1
0
0
1
0
0
0
1
1
0
1
2
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
1
2
0
3
0
1
2
5
0
2
0
1
0
0
1
0
0
2
0
0
0
1
1
1
0
0
1
2
2
0
0
1
0
0
0
2
0
2
0
1
0
0
1
1
3
0
0
0
0
2
0
0
1
1
1
0
0
1
0
1
0
1
0
1
0
1
0
0
1
1
0
0
1
0
0
1
1
0
2
2
0
0
1
0
1
0
0
1
0
0
1
2
0
0
3
2
1
0
1
0
1
2
0
2
1
1
0
1
0
0
0
2
0
0
2
2
1
1
0
0
0
0
2
3
0
0
0
1
0
1
0
1
0
1
0
1
1
0
0
0
0
2
0
0
1
0
1
0
0
1
1
1
0
0
3
0
2
0
2
0
2
0
2
0
1
2
2
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
3
0
3
0
0
2
2
1
1
0
0
0
0
1
0
2
2
0
0
1
2
0
0
0
0
0
1
1
0
0
0
0
1
1
1
1
1
0
2
1
0
0
2
1
0
0
1
0
2
0
0
0
1
2
0
0
0
0
0
0
1
3
0
2
0
0
1
0
0
0
0
0
1
2
1
0
0
1
1
0
0
2
1
2
2
2
1
2
0
1
0
2
0
0
1
0
1
0
1
1
0
2
0
1
0
2
0
0
1
1
1
0
0
0
0
0
1
1
2
0
1
1
0
0
0
2
2
2
0
1
2
1
0
2
0
0
2
0
0
1
0
1
0
0
1
2
0
1
1
0
0
2
0
1
0
2
0
2
1
1
2
0
1
1
0
2
0
0
0
0
1
1
0
0
1
0
0
0
2
0
0
0
0
1
0
2
1
0
1
0
2
1
2
0
1
1
1
0
0
0
0
2
1
1
0
0
2
2
1
0
0
0
4
1
0
1
0
0
0
1
0
0
1
1
2
1
0
0
1
1
0
1
0
2
2
0
0
0
1
2
2
0
0
0
0
2
0
1
0
0
1
2
1
0
1
1
0
1
1
0
1
0
0
1
1
1
0
0
1
1
0
1
0
0
1
0
0
0
1
2
0
0
2
0
0
0
2
2
0
2
2
2
1
1
0
0
1
1
0
2
2
0
0
0
1
0
2
0
5
1
1
0
2
0
0
1
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
1
1
0
0
2
0
1
2
2
2
0
2
0
0
0
1
0
0
0
2
0
0
0
0
1
1
0
0
0
1
2
2
1
0
1
0
1
1
1
0
2
2
0
1
0
0
1
2
0
0
2
1
2
1
0
1
2
0
0
2
0
1
0
0
0
0
1
0
0
0
2
0
4
1
0
0
0
0
1
1
0
1
0
0
0
2
0
0
2
0
0
2
1
1
2
0
2
0
0
0
1
2
0
0
0
0
2
1
0
1
1
0
0
1
2
1
0
2
1
0
0
2
0
0
1
0
2
0
2
0
1
2
2
0
0
0
0
1
1
0
0
0
1
1
0
0
1
1
1
1
2
1
2
0
2
1
0
1
1
0
2
1
1
0
0
1
1
0
0
1
0
0
1
0
0
2
1
0
2
0
2
2
2
1
0
0
0
2
0
2
0
0
0
0
0
1
0
1
3
0
0
1
1
1
1
0
1
0
0
3
0
1
0
1
0
0
2
0
2
0
0
0
0
2
2
0
0
1
2
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
1
0
1
2
0
0
0
1
0
0
0
1
0
2
0
1
0
0
1
1
1
0
0
0
1
0
1
1
0
0
1
2
0
0
1
1
2
0
1
0
0
0
0
1
1
0
0
0
0
1
0
4
0
1
0
0
1
2
2
1
0
1
1
0
1
0
0
2
2
0
1
0
2
0
1
0
1
0
1
1
1
0
1
0
2
0
0
1
1
2
1
1
2
1
2
0
1
0
2
2
1
0
1
1
2
0
0
0
2
1
1
1
1
0
1
0
0
1
0
2
0
1
2
2
0
0
0
2
0
1
0
0
2
4
0
0
1
1
1
0
1
1
0
1
0
0
0
2
1
0
0
0
0
1
1
2
0
0
1
0
2
1
1
1
0
0
1
2
2
2
2
2
3
2
0
1
2
2
2
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
1
3
0
0
1
2
2
2
0
0
0
1
1
0
0
0
1
0
0
2
0
0
0
0
1
0
0
1
1
0
2
2
0
1
3
0
2
0
0
0
2
0
2
0
0
0
0
2
1
2
0
0
1
0
3
0
2
2
1
0
0
0
0
0
1
0
0
3
0
0
1
1
2
0
1
2
2
1
0
1
0
1
0
0
0
0
2
0
0
0
0
1
1
0
0
1
0
1
1
0
1
1
3
0
0
2
0
2
2
0
1
0
0
0
0
0
0
0
1
0
1
1
1
1
2
0
2
0
0
0
2
0
1
0
1
1
0
0
0
0
1
1
0
0
2
0
0
1
1
0
2
0
0
0
0
0
2
0
0
0
1
1
0
2
0
2
0
0
0
0
0
1
0
0
1
1
1
2
2
1
0
1
0
0
2
0
1
2
1
0
2
2
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
2
2
1
1
2
1
0
0
2
3
1
2
1
0
0
1
1
0
2
0
0
2
2
0
0
1
0
2
0
0
0
0
0
0
1
1
1
0
0
1
0
0
1
0
1
0
0
1
2
1
0
1
0
2
0
2
0
1
2
0
3
2
1
1
0
3
1
2
0
1
1
2
0
1
2
1
0
0
2
1
0
0
1
1
1
0
0
0
1
0
0
0
0
1
1
0
0
0
2
1
2
1
2
0
2
0
0
0
0
0
6
1
0
0
0
0
4
1
1
0
2
0
0
0
2
2
0
2
1
0
1
0
0
0
3
1
0
1
0
0
1
0
2
1
0
1
0
0
0
2
1
0
2
0
1
2
2
2
0
1
2
1
1
1
1
0
1
0
1
1
1
0
0
0
0
1
2
0
1
0
0
1
1
0
0
1
0
2
0
1
0
1
2
0
2
2
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
1
0
1
1
1
1
0
2
0
1
0
0
0
1
0
1
0
1
0
0
1
0
0
2
0
0
1
1
1
0
2
1
0
0
2
0
1
0
2
2
0
0
0
3
0
0
1
0
2
0
0
0
0
2
1
0
2
0
1
3
2
0
1
0
0
0
1
0
0
0
2
3
1
0
2
0
2
0
0
0
2
2
1
0
2
3
2
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
1
0
1
0
1
0
3
0
2
0
1
0
0
0
1
0
0
2
0
1
0
0
5
2
0
0
0
2
0
1
2
1
0
1
1
1
2
2
1
1
1
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
2
1
0
0
0
0
2
2
0
0
0
0
2
0
1
0
1
2
0
0
1
2
0
0
0
0
4
0
0
0
3
2
0
0
0
0
1
1
0
2
1
1
0
1
0
2
2
3
0
1
1
0
0
0
2
2
4
0
2
0
0
0
0
2
1
0
0
0
0
0
0
2
0
1
0
0
1
0
1
1
1
0
1
1
1
0
1
2
0
1
1
2
0
1
0
0
2
0
0
1
0
1
0
0
1
2
1
1
0
2
1
2
0
0
0
1
0
2
0
0
2
2
2
2
0
2
2
1
1
0
0
0
2
2
2
2
0
1
3
0
1
0
0
0
1
0
0
2
1
1
0
1
1
0
1
2
1
1
1
0
1
1
0
3
0
0
0
1
1
0
1
0
1
2
0
0
0
0
0
0
2
0
1
2
2
1
0
1
2
0
1
0
1
2
0
0
0
2
1
1
0
0
0
1
0
0
0
0
1
1
2
0
0
1
2
1
0
3
1
0
1
1
1
0
2
1
0
1
0
1
1
0
0
0
1
0
2
0
1
0
0
1
0
0
2
2
1
0
2
2
1
0
1
1
0
1
1
0
0
0
2
1
1
1
0
0
0
0
2
2
1
2
2
1
0
0
0
0
0
0
0
3
1
1
1
0
2
0
2
0
2
0
0
0
0
1
2
1
0
0
0
0
0
0
0
1
0
0
0
1
1
2
0
2
0
0
0
1
0
1
1
1
3
0
1
0
1
0
2
2
2
2
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
4
0
2
0
3
0
2
0
2
1
2
0
0
0
2
1
1
0
0
1
2
0
1
0
1
2
0
0
0
2
0
0
0
1
1
2
1
0
0
2
0
0
1
0
1
0
1
1
2
2
1
1
0
0
0
0
0
1
1
0
2
2
0
1
0
1
2
1
0
1
3
1
0
0
0
1
0
0
0
2
2
2
0
0
2
2
1
1
1
1
1
1
1
2
0
1
0
1
0
0
0
0
0
2
0
2
0
0
0
2
0
1
2
2
0
0
0
0
2
2
1
0
1
2
1
2
0
0
0
0
0
2
0
0
2
0
0
0
1
1
2
1
1
2
0
0
1
0
0
2
0
2
0
2
0
1
2
2
1
0
1
0
0
2
1
0
0
2
1
1
1
1
1
0
0
1
1
0
1
0
1
1
1
0
2
2
1
0
0
0
1
0
2
2
0
1
0
0
0
0
0
2
0
2
1
1
0
0
0
1
2
0
0
1
0
0
0
1
0
1
0
1
0
0
2
1
0
0
0
1
1
0
0
1
2
1
1
0
0
2
2
2
3
0
0
1
0
0
0
0
2
0
2
1
2
0
0
0
0
0
2
2
2
1
2
0
0
0
0
2
1
1
2
5
0
0
1
0
0
1
1
2
2
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
1
0
1
0
2
0
1
0
0
0
0
2
0
2
0
0
2
2
1
0
1
0
0
1
0
0
2
2
0
2
0
2
0
2
0
0
1
1
0
0
0
0
0
2
0
2
1
0
0
2
2
0
3
0
1
0
0
0
2
1
2
1
0
2
2
1
0
1
1
2
1
0
0
1
5
1
0
3
0
2
1
1
0
1
1
1
0
2
1
0
1
0
0
0
0
0
0
1
0
2
0
2
0
2
1
2
1
1
0
0
0
2
0
0
2
0
0
0
0
1
0
2
0
0
1
0
0
0
1
1
0
0
0
1
0
0
1
1
0
0
1
1
0
1
0
0
0
2
0
0
0
1
1
0
0
0
2
3
0
0
0
0
0
1
2
1
2
2
2
0
0
1
0
0
0
2
0
1
2
2
2
1
1
2
0
2
0
0
4
0
1
0
0
1
0
2
0
2
2
1
1
1
1
2
1
0
1
0
0
0
2
1
1
1
2
1
3
1
0
2
1
1
0
0
0
0
0
1
0
2
0
1
0
0
1
0
2
0
0
2
2
0
2
1
0
1
2
1
0
0
0
0
1
2
1
0
0
0
0
2
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
1
2
0
0
0
0
1
0
0
2
0
1
1
2
1
1
1
1
1
0
0
2
0
2
0
0
1
2
1
0
2
0
1
3
0
2
0
2
0
0
0
2
0
0
1
0
0
0
0
1
4
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
2
0
2
0
2
2
0
2
0
0
0
1
0
0
1
1
2
2
0
1
0
0
0
1
1
2
0
2
0
1
1
0
3
0
0
0
0
2
2
0
2
0
0
0
2
1
0
0
1
0
0
1
0
1
0
0
1
1
1
3
2
0
0
1
1
0
0
2
0
1
1
1
1
0
0
0
0
1
0
0
0
2
1
2
1
0
1
0
1
1
1
0
1
0
1
1
0
1
0
0
2
3
0
0
2
1
2
2
0
0
2
0
0
0
1
0
1
0
1
0
1
1
0
1
1
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
1
0
1
0
0
2
3
2
0
0
1
1
1
2
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
2
1
1
0
0
0
0
0
1
0
0
1
0
0
1
0
1
1
1
1
2
2
1
4
0
0
0
1
0
1
0
2
2
0
2
0
2
0
1
0
2
1
0
0
1
0
1
2
0
2
0
0
2
2
1
0
1
0
0
2
2
1
2
0
0
1
0
1
0
5
2
0
0
3
0
1
1
2
1
0
0
0
0
1
2
2
0
2
1
0
0
2
0
0
1
0
2
0
0
0
0
0
0
1
0
0
2
2
0
1
0
0
0
0
0
0
0
1
2
1
0
0
1
2
0
5
1
1
0
3
0
0
0
1
0
2
0
1
0
2
0
0
0
0
2
0
1
0
0
2
0
0
2
1
0
0
1
0
1
0
2
0
1
0
1
3
0
1
2
1
2
0
0
0
0
0
0
0
0
1
0
1
1
2
0
0
1
0
0
0
3
0
1
0
0
1
1
0
0
0
1
1
0
1
0
0
2
0
0
0
1
2
1
2
1
0
0
0
0
1
1
0
0
5
1
1
0
0
0
1
1
0
1
0
0
1
1
1
2
1
0
1
0
0
2
5
1
0
2
0
0
1
1
0
1
0
0
1
1
2
0
1
2
0
1
1
0
2
1
0
0
1
1
0
1
1
0
0
0
0
3
0
0
1
2
0
0
1
0
0
0
2
2
1
1
0
0
0
2
1
2
0
2
0
0
1
1
0
2
1
0
1
0
0
1
0
0
0
1
1
1
0
0
2
2
0
0
0
2
2
1
0
3
0
2
2
2
0
0
0
0
2
1
2
1
0
0
1
1
1
0
0
1
1
0
2
0
1
2
2
2
0
0
3
0
2
2
2
0
1
1
0
1
2
0
2
0
1
1
0
0
2
0
3
0
0
0
0
0
3
0
2
3
2
2
1
0
0
0
1
0
1
0
0
0
0
0
1
2
0
2
1
0
0
1
1
0
0
1
1
3
0
0
1
1
0
1
0
2
0
1
1
1
0
2
1
1
1
0
0
0
2
2
0
1
1
2
1
2
1
2
0
0
3
0
2
1
2
1
0
1
1
2
0
0
1
0
0
2
0
0
1
0
1
0
0
0
2
1
2
0
1
0
0
0
1
0
1
0
0
2
1
0
2
0
2
0
3
1
0
0
1
1
0
1
1
2
0
0
0
1
0
0
0
0
1
2
2
0
0
1
0
2
0
0
1
3
2
0
1
0
0
0
0
0
0
0
0
2
2
1
2
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
2
0
1
0
1
2
1
1
0
0
2
2
2
0
2
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
2
0
1
2
1
0
2
2
2
1
1
0
0
0
2
0
1
1
0
0
0
2
2
0
1
0
2
1
2
0
0
0
2
2
0
2
0
0
2
0
2
1
0
0
2
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
1
0
2
1
0
2
0
0
1
2
0
0
2
1
0
1
1
2
1
1
1
1
1
0
1
3
0
2
1
2
0
2
1
0
1
2
0
1
1
1
0
1
0
0
1
1
1
0
2
0
2
0
2
1
2
0
2
1
0
0
2
2
6
2
0
1
0
0
1
0
0
0
1
0
0
0
0
1
1
1
1
0
2
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
2
0
2
0
0
0
1
0
0
2
0
2
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
1
1
0
2
0
0
2
0
1
0
0
2
0
0
1
2
0
2
0
0
0
1
1
1
2
1
0
1
0
1
0
0
0
0
0
0
0
1
1
1
1
0
1
0
0
0
0
0
2
1
3
0
0
2
1
0
2
0
3
0
0
0
0
0
2
0
0
0
1
1
1
0
0
0
1
2
1
0
2
1
2
0
0
0
0
0
2
0
1
2
0
0
0
3
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
2
1
2
0
2
2
2
0
0
1
0
1
1
0
0
0
1
2
0
0
0
1
0
0
0
1
0
1
1
2
1
1
2
1
0
2
1
0
2
0
2
0
0
2
1
2
0
1
1
1
2
0
0
0
1
0
0
1
1
1
1
0
0
0
1
2
2
0
0
0
0
1
0
2
0
0
0
0
0
1
2
0
2
1
0
1
1
1
0
0
0
2
0
0
1
1
0
1
0
1
1
1
2
1
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
1
2
0
0
2
0
0
0
0
0
2
2
1
1
2
0
0
2
0
0
1
0
0
1
1
0
0
2
0
2
2
1
0
2
0
0
0
0
2
0
2
0
2
2
0
1
0
0
0
1
2
0
1
0
0
1
2
1
2
0
1
0
0
1
1
1
0
0
0
2
1
2
2
0
3
1
2
2
2
0
0
0
1
1
2
0
1
1
0
0
2
2
1
1
1
0
0
0
1
1
2
0
0
1
0
5
0
2
0
2
0
1
2
0
0
1
2
0
0
1
1
1
1
0
0
2
0
1
0
0
0
0
1
2
0
1
0
2
0
2
0
2
0
2
0
1
0
0
0
2
0
1
0
0
0
1
0
0
1
0
2
1
2
1
1
0
0
0
0
2
2
1
0
2
1
0
0
0
0
2
0
0
0
0
1
2
0
0
2
3
0
2
0
2
0
1
0
2
0
2
0
2
0
2
1
2
1
0
1
2
1
0
0
0
2
0
0
2
0
0
1
1
1
0
0
0
0
0
1
2
1
0
2
2
0
1
1
0
2
0
1
1
0
1
0
0
0
0
0
1
0
2
2
1
0
1
0
2
2
1
1
0
2
0
1
1
1
1
1
0
0
0
0
1
0
2
0
0
0
0
2
0
3
0
2
0
1
0
1
0
0
0
2
1
1
1
2
1
0
0
0
0
2
1
0
0
1
0
0
0
0
1
0
0
2
2
1
2
1
0
0
1
0
1
0
1
0
0
1
2
1
0
1
0
0
0
4
0
1
0
0
0
2
1
0
1
0
0
1
1
0
2
0
0
0
0
1
0
1
2
0
0
2
0
2
2
1
1
0
0
4
0
2
0
1
2
2
1
0
0
1
2
1
2
1
0
1
1
0
0
0
1
2
0
0
0
1
0
1
1
2
1
0
0
0
0
2
1
0
1
1
1
0
1
0
1
1
2
0
1
2
1
0
0
1
0
1
1
1
0
0
0
1
1
0
1
1
0
2
0
0
2
3
2
1
1
1
2
2
2
0
0
5
1
0
1
1
2
2
2
2
2
2
0
2
1
2
1
0
1
0
0
1
0
0
3
0
2
0
1
1
0
0
0
3
2
0
2
2
0
0
1
2
0
1
2
1
1
0
2
0
0
0
0
2
0
0
0
0
0
1
1
0
1
1
1
0
2
0
2
2
0
0
0
1
0
2
0
0
0
0
0
2
1
2
4
0
0
2
0
2
0
1
1
2
2
2
3
2
0
0
2
2
0
0
0
0
0
0
0
1
2
0
1
1
1
0
0
0
0
0
0
2
0
1
0
1
0
0
1
0
1
0
1
1
0
1
0
1
1
0
2
0
0
0
1
2
2
3
2
1
0
1
0
1
1
1
1
2
0
0
1
2
1
0
0
0
2
0
1
0
0
1
0
0
0
1
0
1
0
1
0
0
0
2
0
0
0
2
1
3
2
2
2
2
0
0
0
2
0
0
0
0
0
0
2
0
0
1
2
2
0
0
2
1
1
0
0
0
1
0
0
0
2
0
0
2
1
2
2
0
0
0
2
0
0
2
0
0
0
0
0
0
2
1
2
0
1
0
1
0
2
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
2
1
1
1
0
0
1
1
1
0
2
2
0
1
0
1
0
0
3
1
0
2
0
0
1
0
0
2
1
1
2
1
2
0
2
0
1
0
0
0
2
2
0
0
1
1
0
1
0
2
0
0
0
0
1
0
0
0
2
0
1
0
1
0
1
0
0
2
2
0
0
0
0
0
1
2
0
1
2
0
0
3
0
2
5
2
0
0
0
2
2
0
0
1
0
0
1
0
0
2
2
1
0
1
1
2
2
0
0
0
0
0
2
0
0
0
0
1
1
1
0
1
0
2
1
0
0
1
0
1
2
0
0
1
0
2
2
0
2
0
1
2
1
1
0
1
1
0
0
0
1
0
2
2
2
1
2
0
0
0
0
0
1
0
1
0
1
2
2
3
1
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
1
1
1
1
2
0
0
1
0
2
1
1
0
1
1
1
1
1
2
2
0
0
0
0
1
1
0
0
2
0
0
0
1
1
1
0
2
2
1
2
0
2
0
2
0
1
1
5
2
1
0
0
1
0
0
0
4
2
0
2
0
1
0
0
0
1
1
0
0
0
0
0
2
1
3
2
0
0
0
2
1
0
0
0
0
2
0
1
0
1
1
1
2
1
2
0
1
0
0
1
0
0
0
0
0
4
2
0
0
0
0
0
1
0
0
0
2
0
1
2
0
0
1
1
0
0
0
2
0
0
2
0
1
1
0
1
0
2
2
1
0
0
1
2
0
0
2
1
0
2
0
0
0
0
1
0
0
0
2
0
0
2
1
0
0
2
0
1
1
0
0
1
0
2
0
1
1
0
1
4
0
1
0
2
0
0
1
1
0
1
1
0
1
0
2
0
3
2
1
0
0
0
2
1
0
0
0
1
0
0
1
0
0
0
0
2
0
1
1
2
4
2
1
0
1
2
0
1
0
1
2
0
2
2
1
4
0
0
0
1
0
2
0
0
2
1
1
2
0
1
2
2
0
0
3
0
2
0
1
2
3
0
2
0
0
0
0
1
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
1
1
0
1
2
0
0
0
1
0
1
0
1
1
0
1
1
0
2
1
2
1
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
1
2
0
2
0
2
0
1
0
0
0
1
0
0
0
0
0
2
0
2
0
1
1
0
0
0
2
2
0
1
1
2
0
2
2
0
1
0
1
0
0
1
1
0
2
0
1
1
1
0
0
0
1
2
1
0
0
0
1
0
2
0
0
1
0
0
0
0
0
1
1
2
1
1
2
2
2
1
1
0
1
2
0
1
0
2
0
0
2
0
0
0
0
0
1
0
2
0
2
0
2
0
2
0
2
2
0
1
0
0
0
1
0
1
0
1
0
1
1
0
1
1
0
0
0
2
1
2
2
1
0
1
2
2
2
1
0
0
2
0
0
0
1
0
0
3
0
2
0
0
1
2
0
0
1
1
2
0
2
1
1
1
1
1
2
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
2
0
2
1
0
0
0
2
0
1
0
0
1
0
1
1
1
0
1
1
1
0
0
1
2
2
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
2
2
2
3
2
0
2
2
0
1
1
2
0
0
0
1
0
0
2
0
1
1
1
0
1
0
0
0
0
1
2
0
0
0
0
0
1
1
3
0
1
0
2
2
2
0
2
0
0
0
0
0
0
2
0
0
2
0
0
2
2
0
2
1
0
0
0
0
2
0
0
0
0
2
0
2
0
0
1
2
1
1
2
0
0
1
0
1
0
0
1
0
1
1
0
0
0
1
2
1
1
0
5
2
0
1
2
1
0
0
2
1
0
1
0
1
1
1
0
0
0
2
0
0
0
1
0
2
1
1
2
0
2
1
1
0
0
0
0
2
1
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
1
0
1
0
0
1
3
0
0
0
1
1
1
1
1
0
0
0
0
2
2
1
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
2
2
0
1
1
0
2
0
0
1
0
1
0
0
1
2
1
0
0
0
1
0
0
2
0
1
2
2
0
0
2
2
0
1
0
0
0
2
1
0
0
2
2
1
0
2
0
0
0
0
2
2
0
1
0
2
0
2
0
1
1
0
1
1
0
1
2
2
0
0
3
0
0
2
0
1
0
1
0
1
2
1
0
2
1
3
0
1
0
0
2
1
0
0
0
1
0
0
0
2
2
0
0
0
0
1
0
1
0
0
1
0
1
0
2
1
0
1
0
0
0
0
2
1
0
1
2
0
2
0
1
1
2
0
0
1
1
1
2
0
1
1
0
1
3
1
0
0
2
2
1
1
1
1
1
1
0
0
0
1
1
0
0
1
0
0
2
2
0
1
0
0
0
2
0
1
0
2
2
1
2
0
2
0
1
2
0
0
0
0
0
0
1
0
0
1
1
0
0
2
1
0
1
0
0
0
2
2
0
1
0
2
1
1
1
1
0
0
2
0
1
1
3
0
1
3
0
0
0
1
0
1
2
0
0
0
2
4
1
2
0
3
2
1
0
1
2
1
0
0
0
1
2
0
1
0
0
0
2
2
1
1
0
1
0
0
0
1
2
0
1
0
0
0
2
1
1
1
0
1
0
0
0
0
1
0
1
0
2
2
0
0
0
1
2
0
0
0
1
0
1
2
0
0
0
0
1
2
1
2
1
0
1
1
1
0
1
2
0
0
0
0
0
0
1
0
2
0
2
2
2
0
2
0
1
2
0
2
0
1
0
2
0
0
0
4
1
2
1
0
0
0
1
0
1
0
0
0
1
0
0
1
1
0
2
0
1
1
0
0
1
0
0
1
1
1
0
0
2
0
0
3
0
1
1
0
1
0
0
0
1
0
0
0
1
2
2
0
1
0
0
0
0
2
0
1
0
0
2
0
0
1
1
0
1
1
0
0
2
1
0
0
1
0
2
0
0
0
0
2
3
0
0
2
1
0
0
0
2
0
0
2
2
1
0
0
0
2
0
0
2
0
0
2
0
1
2
1
0
2
2
2
2
0
2
1
2
2
0
1
2
1
0
2
0
2
0
0
1
1
0
5
0
2
1
1
1
0
2
2
1
0
0
2
0
0
1
0
1
0
2
2
0
2
1
0
2
0
1
0
2
0
1
0
2
0
0
1
1
0
2
0
0
1
0
0
1
0
0
2
0
0
1
0
2
2
1
0
0
2
0
0
0
0
1
1
0
3
3
0
0
0
1
1
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
4
1
1
0
2
2
0
0
1
1
0
0
0
2
1
1
1
0
0
2
0
0
0
0
1
2
1
2
1
2
0
0
0
0
0
1
1
2
1
0
2
0
1
1
0
1
0
0
1
0
1
1
1
0
0
2
0
1
2
1
0
0
0
0
1
1
1
1
0
0
1
0
2
0
2
0
0
2
0
1
1
0
2
2
2
1
2
0
1
0
0
2
1
1
0
1
2
1
0
0
0
1
3
1
0
0
0
2
0
0
2
0
0
0
2
1
0
0
0
1
2
1
2
0
0
2
1
1
0
0
1
0
2
1
0
1
0
0
2
1
0
2
0
2
1
0
0
0
2
1
2
1
1
2
2
1
2
0
0
2
0
0
3
0
0
1
0
0
1
0
1
2
1
1
2
1
2
0
0
1
0
2
2
0
0
2
1
2
0
1
0
0
2
1
1
2
0
2
0
0
2
1
1
0
0
0
2
1
0
0
1
9
1
1
1
0
1
0
2
1
1
0
0
0
0
2
1
0
0
0
1
0
0
3
0
0
0
0
2
1
0
0
1
2
1
1
0
1
1
0
2
0
0
0
0
1
0
0
0
2
2
3
0
2
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
1
2
0
0
1
2
0
3
0
1
2
2
0
1
2
1
1
0
0
0
1
1
1
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
4
0
0
1
0
0
0
0
0
2
0
1
0
2
0
2
0
0
3
1
0
2
1
0
0
1
0
0
0
4
2
2
0
0
0
1
0
0
0
2
0
0
0
0
2
1
1
0
0
0
2
1
1
0
0
0
0
0
0
1
2
0
0
1
1
0
0
0
0
1
1
2
2
0
0
1
2
5
0
0
1
1
1
2
0
1
1
0
2
2
1
2
1
0
0
1
0
2
0
1
0
1
0
0
0
2
1
0
2
1
1
1
1
1
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
1
1
0
1
0
1
0
0
0
1
1
0
1
0
1
0
0
0
0
0
1
0
2
0
0
0
2
2
1
1
0
0
1
0
1
1
1
2
0
0
1
5
0
0
0
2
2
0
2
0
0
0
2
0
0
0
0
0
1
2
2
0
0
0
0
1
0
1
1
0
1
0
1
1
1
0
2
0
1
2
0
1
0
1
1
0
0
1
0
0
1
0
0
0
2
2
1
0
0
2
1
1
1
2
0
2
0
1
0
1
0
2
0
0
0
1
0
2
0
0
0
2
0
0
0
0
2
2
2
2
5
1
0
0
2
0
1
2
0
0
0
0
0
1
1
0
1
0
0
2
0
1
1
0
2
0
0
0
2
0
0
1
0
1
0
3
1
1
0
0
1
0
1
0
0
2
1
1
1
0
2
2
0
0
0
1
0
2
0
2
1
1
0
1
0
1
0
1
1
0
1
2
0
1
0
0
0
0
0
0
2
1
0
0
2
1
0
0
2
0
0
0
2
0
1
0
0
1
0
0
1
0
0
1
0
0
2
0
0
1
0
1
1
1
0
1
1
1
1
6
0
1
0
4
0
0
0
0
0
0
0
2
2
0
0
0
1
0
3
0
1
1
1
0
0
0
2
0
2
1
1
1
1
1
0
1
2
0
0
0
1
0
0
0
0
0
3
0
0
0
2
0
2
0
0
2
0
2
2
1
0
2
0
1
0
0
0
0
0
2
2
0
1
0
3
0
2
0
1
0
1
0
0
0
1
0
0
0
0
1
0
2
0
0
1
0
0
2
0
2
0
1
1
2
2
1
1
1
0
1
0
2
1
0
1
1
1
2
1
1
2
1
1
0
0
1
0
0
0
2
2
2
0
0
0
2
1
1
2
0
1
1
0
0
2
0
1
0
0
0
0
1
0
6
2
1
0
1
0
2
0
1
2
0
0
0
0
2
1
0
1
0
2
0
1
0
0
1
0
0
1
1
0
0
0
1
3
2
1
0
0
1
0
2
0
0
0
2
0
0
1
1
0
2
0
1
1
1
1
3
1
0
1
0
0
2
0
1
0
0
2
2
0
1
1
0
0
0
0
1
2
0
0
0
1
1
1
2
3
0
2
0
6
0
0
1
0
0
2
2
0
0
3
1
0
0
0
0
1
0
1
2
0
1
1
1
0
0
3
0
2
2
0
1
0
2
3
1
2
0
2
2
0
0
1
2
1
0
1
2
2
0
0
2
1
0
1
0
0
2
0
1
0
1
1
0
0
0
1
0
0
0
1
1
0
0
1
2
1
2
0
0
1
0
0
0
1
1
1
1
0
3
1
0
0
0
0
0
2
1
2
0
0
2
1
0
0
0
0
2
0
1
0
1
0
1
1
0
0
2
2
1
0
1
1
2
0
0
2
1
1
2
2
2
1
0
2
2
0
1
0
0
0
0
0
1
0
0
0
1
2
1
1
2
0
2
0
1
0
1
1
2
1
0
2
2
0
1
1
1
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
2
2
0
2
0
0
0
2
1
4
2
3
2
2
0
2
0
0
1
2
1
0
0
2
2
1
0
0
0
0
0
0
1
1
0
0
2
1
1
1
2
0
0
2
0
2
1
1
0
2
0
0
3
2
2
1
0
0
2
0
1
0
1
2
0
1
0
1
0
2
0
1
0
0
2
0
2
2
1
2
0
1
0
1
0
2
1
0
0
0
0
0
0
0
0
1
1
0
0
0
2
1
2
1
1
0
0
0
2
0
0
2
1
0
1
1
0
2
0
0
2
0
0
1
0
0
0
1
2
0
2
1
0
1
1
2
2
1
1
1
0
2
1
2
1
1
1
0
1
1
1
2
0
0
1
2
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
1
1
1
0
2
0
2
1
2
0
0
1
0
1
0
0
0
2
1
1
4
1
1
1
2
2
1
0
1
0
1
2
0
1
0
1
0
2
1
0
2
1
2
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
2
1
0
0
2
0
0
0
1
1
0
2
3
0
2
2
1
0
0
0
0
0
0
2
0
0
1
0
1
1
2
0
0
0
0
2
1
1
0
1
2
2
2
0
1
1
0
1
0
1
0
0
1
2
0
0
0
0
2
0
0
0
1
0
0
0
0
2
2
0
2
0
1
1
2
2
0
0
1
0
0
0
0
0
0
2
0
0
1
2
0
0
0
2
1
0
0
0
2
1
0
0
0
1
0
1
0
1
0
0
0
0
0
2
0
1
1
1
1
0
0
2
1
0
1
0
1
1
0
1
0
1
0
0
0
0
1
0
0
2
0
2
0
0
1
0
1
2
0
0
2
0
0
1
2
0
1
2
0
0
2
0
0
0
1
0
0
1
5
1
0
1
0
0
0
2
3
1
0
2
0
0
1
0
1
0
0
0
0
2
4
1
1
1
2
1
0
6
0
0
1
1
2
1
0
1
1
0
1
1
0
2
2
0
0
0
0
0
0
0
0
2
0
0
2
2
0
2
2
2
2
2
0
0
0
0
1
0
1
0
0
2
0
2
0
2
0
0
0
1
0
1
1
0
0
0
1
1
0
0
0
0
1
2
1
2
0
1
0
0
0
0
3
0
0
0
0
1
0
0
0
1
0
0
2
0
0
2
0
2
0
0
2
0
1
1
0
2
2
2
0
1
0
0
1
2
0
1
1
0
0
0
1
1
1
0
1
1
1
1
0
1
0
1
0
0
2
0
0
0
0
1
1
0
1
2
0
2
0
1
0
2
1
0
0
0
1
0
0
1
1
0
0
0
0
0
1
2
1
0
1
0
2
1
0
1
1
1
1
0
0
2
1
0
0
2
2
1
1
2
0
0
0
2
0
1
0
1
3
0
1
2
2
1
0
0
1
1
0
0
0
0
2
1
0
0
0
0
1
0
0
2
1
2
0
1
0
1
1
0
0
2
2
0
0
0
0
0
2
1
0
0
1
0
2
0
2
1
1
0
2
2
1
1
0
0
0
0
3
0
0
0
0
0
1
0
0
1
1
0
0
1
1
0
2
0
0
2
0
1
2
1
0
1
1
0
2
1
0
0
0
1
2
1
1
2
2
0
0
1
1
1
1
1
2
1
0
0
1
1
0
0
0
0
1
1
1
1
2
1
2
2
0
0
2
1
0
1
0
0
2
0
0
1
2
0
0
0
2
0
2
0
1
0
0
1
0
0
1
5
0
1
0
0
0
0
0
0
1
1
1
2
1
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
1
0
1
0
1
0
0
2
2
2
1
0
0
0
2
1
1
0
1
2
0
1
0
2
1
0
2
0
1
1
0
1
0
2
0
0
0
0
2
1
3
0
1
0
1
2
1
0
0
0
0
1
2
1
1
0
3
0
0
2
1
1
2
0
1
2
2
1
0
2
0
2
0
0
2
0
0
1
0
0
2
0
2
1
2
0
0
0
1
1
0
2
1
2
0
0
0
0
0
2
0
0
2
0
0
0
0
1
1
2
1
0
1
2
2
1
1
0
0
0
1
2
1
0
2
1
0
0
0
1
1
0
0
1
2
0
0
1
2
1
1
0
0
0
0
0
0
2
1
0
1
2
1
1
1
2
0
3
0
0
0
0
0
1
0
2
0
0
0
2
1
1
0
0
0
1
2
2
0
2
1
0
0
2
0
0
0
2
1
0
0
2
0
0
0
0
2
0
0
1
2
2
1
1
0
0
1
0
0
0
1
2
1
0
0
0
2
0
2
0
0
0
1
0
1
0
2
0
0
2
0
2
1
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
1
0
0
1
0
0
2
2
0
2
2
0
2
0
2
1
0
0
1
0
0
0
0
0
0
2
0
0
1
2
1
1
0
1
1
2
2
0
0
2
1
0
0
2
5
2
0
0
0
1
2
0
2
1
2
0
0
3
0
1
1
2
1
0
1
1
0
1
2
0
2
0
0
0
1
1
0
0
1
2
1
2
0
1
0
0
2
1
1
1
0
2
1
0
2
0
0
2
2
2
1
2
1
0
0
1
0
2
2
1
1
0
0
1
0
0
0
2
2
1
1
0
0
0
0
0
0
0
2
1
3
0
0
0
0
1
0
2
0
0
0
2
2
0
0
1
2
0
0
1
0
0
0
2
1
1
1
2
1
2
1
1
2
0
1
0
2
1
1
3
1
2
2
0
0
0
2
0
1
1
0
0
1
0
1
0
0
0
1
0
0
0
1
1
2
0
1
0
1
0
0
1
0
0
1
2
1
2
1
0
0
0
0
0
0
2
2
0
0
0
1
1
2
0
0
2
1
0
0
1
2
0
0
1
0
0
1
2
0
0
0
5
0
0
0
1
1
3
0
2
3
1
0
1
0
1
2
1
0
1
1
0
0
1
0
1
0
1
0
3
0
1
0
1
0
1
0
0
2
1
0
0
0
2
0
2
0
0
0
0
1
2
2
1
0
1
0
1
0
0
2
1
1
2
2
2
0
0
1
2
2
0
0
0
0
0
0
0
1
1
0
0
13
2
0
0
2
0
1
0
2
1
0
2
0
0
0
0
0
3
2
1
1
0
1
0
0
2
0
2
2
0
1
0
0
0
0
1
1
0
0
0
1
0
2
1
1
2
0
1
2
2
2
3
1
1
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
2
2
1
0
2
1
0
1
1
2
0
0
0
0
0
1
1
0
0
2
0
0
0
2
1
2
2
0
1
1
1
1
0
0
0
1
0
1
2
1
1
0
3
0
0
0
2
1
0
1
0
2
2
1
5
0
0
0
0
1
2
1
1
0
0
0
1
1
0
1
0
0
1
2
1
3
2
1
0
0
0
1
1
3
2
2
2
2
0
0
0
0
0
0
1
0
1
2
1
0
0
0
0
0
1
1
1
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
1
2
0
0
0
0
2
0
1
0
1
0
0
1
2
1
0
0
2
1
0
0
0
0
1
0
1
1
0
0
2
1
2
2
1
1
0
1
0
1
1
2
0
1
1
1
1
1
0
2
0
0
2
0
0
1
2
1
0
1
1
0
1
2
0
2
2
0
2
1
1
0
2
2
1
1
0
2
2
0
1
0
0
1
0
0
0
0
0
1
1
0
1
2
2
0
2
0
0
1
1
1
0
2
0
1
2
1
2
0
0
0
0
0
4
1
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
2
2
0
1
1
0
0
0
2
2
0
0
0
1
0
1
0
0
0
1
1
0
2
0
2
0
1
0
0
0
3
1
2
2
2
0
0
2
1
0
0
0
0
2
1
0
1
5
0
0
0
0
1
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
1
0
0
0
0
1
3
0
1
1
2
0
1
0
1
0
2
0
1
1
1
0
1
0
2
0
0
1
0
1
0
0
0
2
1
1
0
2
2
0
0
0
2
0
0
1
2
0
0
0
7
2
1
1
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
2
0
0
1
0
1
1
1
0
0
0
0
2
2
0
1
1
0
0
1
0
3
0
1
0
0
0
0
1
1
0
1
2
0
2
0
2
0
1
1
2
0
0
0
0
1
1
0
0
0
0
1
1
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
1
1
0
1
2
1
2
1
1
0
0
1
0
0
0
2
1
2
0
0
1
0
0
3
1
2
0
2
2
0
1
0
2
0
0
1
1
1
0
1
0
1
1
1
1
0
1
2
0
0
0
2
0
1
0
0
0
2
1
0
0
1
2
1
2
2
2
2
0
1
1
1
0
0
0
0
0
2
0
0
1
0
0
1
3
0
1
0
0
2
0
0
0
0
2
0
0
1
0
2
0
2
0
0
1
0
0
2
0
0
2
0
0
1
0
1
0
0
2
1
1
1
0
2
0
0
1
1
0
2
0
0
1
0
0
1
2
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
2
2
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
1
2
0
0
1
2
1
0
1
1
2
1
1
1
0
0
1
0
0
0
4
0
0
0
0
1
2
0
2
2
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
2
2
0
1
2
1
0
0
1
1
2
2
0
0
2
2
0
2
2
1
2
2
2
1
0
1
0
1
1
0
1
1
1
2
0
0
1
0
1
0
5
0
0
0
0
2
1
2
1
0
1
1
3
0
0
1
1
0
0
2
2
1
0
2
0
2
0
0
0
2
2
0
1
0
0
2
0
0
0
0
1
1
2
0
1
0
1
3
0
0
1
1
2
0
0
1
2
1
1
2
1
1
0
0
1
1
2
1
1
1
2
1
1
0
2
1
2
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
1
2
0
0
0
0
1
1
0
2
0
2
0
2
1
1
2
0
0
0
0
2
0
0
1
1
0
0
1
0
1
0
1
1
0
1
0
0
0
0
2
1
0
0
0
0
0
1
0
2
1
1
1
0
0
0
1
0
0
0
2
0
0
0
0
1
1
2
0
2
0
1
0
3
0
1
4
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
3
0
0
0
2
0
0
2
1
1
0
0
2
0
0
2
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
3
3
1
1
1
0
0
2
2
1
0
1
0
0
1
1
1
1
0
1
1
0
0
0
3
0
0
0
0
1
0
0
0
0
1
1
2
1
1
0
0
0
2
0
0
1
2
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
3
2
0
0
2
2
1
0
0
1
2
0
0
0
1
1
0
1
1
0
1
0
0
2
0
0
0
0
0
0
0
3
0
2
1
1
0
0
0
0
2
0
0
1
0
0
1
2
2
2
0
2
0
0
2
1
0
0
0
0
0
0
1
0
2
0
2
2
1
1
1
1
1
1
0
0
1
1
0
1
0
1
1
0
0
0
1
2
0
1
2
2
0
0
1
2
0
0
2
0
0
0
0
0
0
1
0
5
2
0
0
2
2
2
2
1
1
2
1
0
2
1
1
0
0
1
1
1
0
2
0
2
0
0
1
2
0
2
2
0
0
1
1
2
0
2
0
1
0
2
1
2
0
0
2
0
0
0
1
0
0
0
0
2
1
2
1
0
1
2
2
0
1
1
1
0
2
0
0
0
0
0
0
1
0
0
1
1
0
1
0
2
1
1
0
0
0
0
0
0
0
1
0
1
2
2
2
0
0
0
2
5
0
0
0
0
2
0
0
1
2
0
1
0
3
2
1
2
0
2
0
2
0
1
1
1
1
0
1
0
0
1
0
0
0
0
2
2
0
1
0
2
0
2
0
0
1
1
0
0
0
0
0
2
1
1
2
1
1
0
2
2
0
0
0
2
0
2
0
1
0
1
0
0
0
2
0
2
1
1
0
2
2
1
1
0
2
0
0
1
0
2
1
2
0
1
0
0
0
2
0
2
2
0
1
0
0
0
0
0
1
2
0
1
0
1
0
2
1
0
0
2
0
2
2
2
1
1
1
1
0
2
1
3
0
1
0
1
0
0
1
0
0
0
1
0
0
1
0
2
0
0
3
1
1
1
2
1
0
0
1
1
1
1
1
0
1
0
0
0
0
3
1
0
0
2
0
1
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
2
0
1
1
2
1
1
0
2
1
1
0
1
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
1
0
0
1
0
2
0
0
1
0
1
1
0
1
2
4
1
1
1
3
2
0
0
0
2
2
1
0
0
0
1
0
1
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
2
2
0
0
1
0
0
0
2
1
0
0
0
0
0
1
1
1
2
0
0
0
0
0
2
1
0
0
0
1
0
2
1
0
1
0
0
2
1
0
2
0
1
0
0
0
0
0
2
0
0
2
1
1
0
0
1
4
1
0
1
0
1
1
2
0
2
0
0
0
0
0
1
0
1
2
0
0
1
0
1
0
1
0
0
0
0
0
1
0
3
2
1
0
1
0
0
1
2
3
2
2
0
0
0
0
0
2
2
0
0
2
2
0
1
0
1
2
2
1
0
0
2
0
1
0
2
1
0
0
2
1
1
0
0
2
1
2
1
0
1
1
1
2
2
2
0
0
1
0
1
2
1
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
1
2
0
0
0
2
1
0
1
0
0
1
0
2
1
0
8
2
0
0
1
2
2
0
0
1
2
0
1
1
0
0
2
0
0
0
1
0
0
2
2
1
2
0
1
2
1
0
1
2
0
0
0
0
1
0
1
0
0
0
0
1
0
0
2
0
0
0
1
1
0
0
0
2
0
0
0
0
0
4
1
1
0
0
0
0
1
2
0
0
1
0
5
2
0
0
1
0
0
1
0
0
1
0
0
0
0
2
2
0
0
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
1
0
0
0
0
1
1
2
0
1
0
0
1
0
0
0
0
1
2
1
2
0
0
1
0
0
0
0
0
1
0
0
1
1
1
0
0
2
0
0
1
0
2
1
0
0
0
0
1
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
1
2
0
1
1
0
1
1
0
0
2
0
0
1
0
0
1
1
1
2
2
0
0
0
0
0
0
1
0
1
2
1
0
5
2
0
0
1
0
1
1
1
0
1
3
0
0
0
0
0
1
0
2
2
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
2
0
0
1
1
1
2
1
1
3
0
0
1
0
1
2
2
2
2
0
2
1
1
0
1
2
2
0
2
0
2
0
0
2
2
2
0
0
0
1
1
0
1
2
0
0
0
1
0
0
1
1
0
0
0
0
2
0
1
1
0
3
0
1
0
1
0
1
0
2
0
2
1
1
0
0
0
0
0
0
1
2
0
1
1
0
2
0
1
0
2
0
0
0
0
1
1
1
0
2
1
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
2
1
0
0
0
0
0
1
2
2
3
0
0
0
0
2
1
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
1
1
0
0
1
0
2
1
0
1
0
0
1
0
2
0
2
1
1
2
0
1
2
2
1
0
0
3
0
2
0
1
0
0
2
0
2
1
0
0
0
1
1
1
0
2
0
0
0
1
0
0
0
2
2
0
2
2
0
3
1
0
0
1
1
0
0
2
2
2
0
1
1
1
0
0
1
0
0
1
2
1
1
1
2
0
2
2
2
0
3
0
0
0
0
0
1
0
2
2
0
0
1
1
0
1
0
0
0
1
1
0
1
0
0
0
1
1
1
2
0
1
0
0
0
0
2
1
1
1
2
0
2
1
1
1
1
0
0
0
0
1
0
0
0
1
0
2
1
3
1
0
2
0
2
1
0
2
0
0
2
0
1
0
1
0
0
0
0
1
0
1
0
1
1
1
1
0
0
0
2
1
0
1
0
1
1
0
4
0
0
0
2
0
0
1
1
0
1
1
1
1
0
0
0
2
2
0
0
0
1
2
0
0
1
1
2
2
0
0
1
0
0
1
0
0
1
1
0
0
0
0
2
2
2
0
2
2
0
1
0
1
2
0
1
0
1
0
2
1
1
0
0
0
3
0
0
0
1
2
3
2
0
0
0
0
0
0
0
0
0
1
3
0
0
0
1
0
1
0
0
0
0
1
1
1
2
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
2
0
1
1
1
1
0
2
2
2
0
0
0
2
0
0
0
0
2
0
2
2
0
1
1
0
1
2
0
1
0
1
0
1
1
1
0
0
1
1
1
1
0
0
1
1
4
1
1
2
1
1
0
0
1
0
0
2
1
1
1
0
0
0
0
0
1
0
1
0
0
1
2
1
1
1
1
2
0
0
0
0
2
0
0
2
1
1
1
2
1
0
0
1
0
2
0
0
0
1
0
1
1
0
0
0
0
0
2
0
1
0
0
0
1
0
2
0
0
2
0
1
1
1
0
0
0
0
2
1
2
0
0
1
1
0
0
0
1
0
0
0
1
0
1
1
1
1
0
1
2
0
0
1
1
1
0
1
2
0
0
0
1
0
0
2
1
0
0
0
1
0
0
2
2
0
0
0
1
0
0
0
1
1
0
0
1
1
0
1
1
2
2
0
0
0
2
2
1
0
1
1
0
0
0
0
1
1
1
1
0
0
2
1
0
0
0
2
0
0
1
2
0
1
0
0
2
2
0
3
1
2
0
0
0
0
1
2
0
1
1
0
0
0
0
1
0
1
0
0
2
1
1
0
1
0
1
2
2
0
0
0
0
0
0
0
0
2
1
2
0
0
0
1
1
2
2
3
1
0
2
2
1
2
0
3
0
0
0
2
1
0
1
0
2
0
0
0
0
0
2
1
2
1
1
0
0
2
1
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
4
2
2
0
0
1
1
0
0
1
0
2
2
1
0
0
1
0
0
0
2
0
0
0
0
1
0
2
2
1
1
0
1
0
2
1
1
1
1
2
1
0
0
0
0
0
0
0
1
0
1
0
2
0
0
2
1
0
1
3
0
3
0
0
0
1
2
2
0
2
2
0
1
1
0
0
1
1
1
0
2
1
0
0
0
0
0
0
2
0
0
0
1
1
0
0
2
0
1
2
1
1
1
1
2
1
1
0
0
0
0
2
0
0
0
0
1
0
1
1
2
2
1
0
0
1
0
1
0
0
0
0
1
0
1
2
3
1
0
2
0
2
1
2
2
1
0
1
0
1
2
0
1
1
2
1
2
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
1
2
0
0
1
1
0
0
2
1
2
0
0
0
0
1
1
0
2
0
0
2
1
2
2
0
0
2
1
0
2
1
3
1
2
0
3
0
2
2
0
0
1
0
1
0
2
2
1
0
0
0
0
0
1
1
0
0
2
0
1
0
0
0
1
2
0
0
2
1
0
0
2
0
0
0
1
1
0
0
2
1
0
2
0
0
0
2
2
2
2
0
2
0
0
0
1
1
1
1
0
0
0
2
0
0
0
0
1
1
2
0
2
1
0
1
2
2
2
2
2
2
0
0
0
1
2
0
0
2
1
0
1
0
1
0
2
0
0
0
1
1
0
1
1
1
1
0
0
1
0
2
0
0
0
2
1
0
2
2
0
0
2
1
0
2
0
0
0
1
0
1
1
1
1
0
0
2
2
2
0
0
0
0
0
0
1
2
2
0
2
0
3
0
0
1
0
1
0
2
0
2
0
0
0
2
0
0
0
0
1
2
1
0
1
0
0
1
1
1
0
2
0
0
2
0
2
0
0
1
1
0
1
0
0
0
0
2
0
0
0
1
0
1
0
0
0
2
0
0
2
1
0
0
0
0
2
1
1
0
2
1
2
0
0
0
2
1
2
0
1
0
0
0
0
1
0
1
2
0
1
0
2
0
1
2
0
1
0
2
0
1
0
1
0
2
1
1
0
0
0
2
2
0
0
1
0
1
1
0
0
2
0
0
2
0
0
0
0
0
1
2
1
1
1
0
1
0
0
2
2
0
0
2
1
0
0
0
0
0
2
0
0
1
0
0
0
1
0
1
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
3
0
2
0
0
2
0
2
0
2
0
0
1
0
1
1
0
1
1
0
2
1
0
1
0
0
1
0
0
3
0
0
0
1
1
0
1
0
1
1
0
1
2
1
1
0
0
2
0
2
0
0
0
1
0
2
1
0
1
0
0
2
2
1
0
3
1
1
2
0
2
2
0
0
3
1
0
0
0
1
1
2
1
1
2
0
3
0
2
2
1
1
0
1
0
0
1
2
1
0
0
0
0
0
1
0
1
2
0
0
1
0
0
1
0
0
0
0
0
0
0
3
0
0
1
0
1
0
0
1
1
0
1
0
0
0
0
1
5
0
2
4
0
0
1
0
1
2
1
1
1
2
2
1
2
0
1
1
2
1
0
2
0
0
0
2
2
0
1
2
2
2
0
0
2
0
3
0
2
1
1
0
0
1
0
1
2
2
1
0
1
2
0
1
0
2
0
0
0
0
2
1
0
1
1
0
0
2
0
0
0
0
2
0
2
2
0
0
2
2
0
2
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
1
0
0
0
0
3
2
2
0
0
0
0
1
0
0
2
2
0
0
0
0
1
0
0
1
0
1
1
0
1
0
2
1
0
0
1
1
2
0
1
0
0
0
0
2
0
0
3
1
1
2
1
2
0
1
0
3
0
0
0
2
1
1
1
1
0
0
0
1
0
0
1
0
2
0
0
2
0
0
0
0
1
0
2
3
0
0
1
0
1
0
2
2
2
0
1
2
1
2
2
0
1
1
0
2
2
2
3
0
1
1
1
1
0
0
1
0
0
2
1
0
1
0
0
2
0
0
0
0
2
0
1
0
0
2
1
2
0
2
2
0
0
6
3
1
2
1
1
0
0
0
2
0
1
1
0
0
0
0
0
0
0
1
2
1
0
1
0
1
0
1
1
4
2
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
2
0
2
0
1
0
0
0
1
0
0
0
1
0
0
0
0
2
1
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
2
1
0
2
0
4
1
1
1
2
1
2
0
2
1
1
0
0
0
1
1
0
0
0
0
2
0
2
2
2
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
1
1
0
0
0
0
2
2
1
1
2
1
0
0
1
0
0
0
0
2
0
0
1
1
0
0
2
0
1
1
0
0
0
3
0
0
0
1
2
1
0
0
0
0
0
1
1
0
0
0
1
0
1
0
2
1
0
1
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
2
0
0
2
2
0
0
1
0
0
0
0
2
2
0
1
0
1
2
0
0
2
2
0
3
0
1
0
2
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
1
1
2
1
0
0
1
1
2
1
0
1
0
1
2
2
0
0
1
1
1
2
0
0
2
1
2
1
0
0
2
0
1
0
1
0
0
0
1
0
1
2
0
0
1
2
0
0
0
0
1
0
2
1
2
1
0
1
1
0
2
1
2
0
0
0
1
0
1
0
0
0
0
0
1
1
2
1
0
2
0
0
0
0
0
1
0
0
1
2
1
0
1
1
0
1
0
1
0
3
2
1
1
0
0
0
2
2
1
1
2
0
0
1
0
3
0
1
2
2
0
0
0
2
1
0
1
2
0
0
0
0
2
1
0
2
0
1
2
1
2
0
0
0
0
0
2
0
0
2
0
1
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
3
0
0
1
2
0
0
1
1
1
0
0
2
0
0
0
2
0
1
2
2
2
0
0
1
0
3
2
0
0
0
0
2
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
2
1
2
0
2
1
5
0
0
2
0
0
0
1
0
0
0
2
0
0
1
0
2
0
2
3
3
0
0
2
0
2
2
1
0
2
0
0
1
1
1
1
2
0
1
0
0
1
2
1
1
0
1
0
1
0
1
0
1
2
0
1
0
1
1
1
1
2
0
0
0
0
0
0
1
2
1
1
2
0
2
1
0
0
0
0
2
0
0
0
0
1
0
0
1
1
2
0
0
2
1
0
2
1
0
0
0
0
0
0
3
1
0
0
1
2
1
0
0
1
5
0
0
1
2
1
4
3
0
0
2
2
0
0
2
0
1
0
0
1
0
0
0
0
4
0
1
0
0
1
1
1
2
0
0
1
1
0
1
0
0
0
1
1
0
0
0
0
0
2
2
0
0
0
2
0
2
0
0
1
1
0
0
1
0
0
1
2
2
0
2
0
0
1
2
0
1
1
0
0
0
1
0
0
0
0
1
0
1
1
0
2
0
0
1
1
2
0
0
0
0
0
2
2
1
2
2
1
2
0
2
1
0
0
0
0
0
2
0
2
0
1
1
0
0
1
0
0
0
0
2
2
0
1
1
0
0
0
2
1
2
0
0
1
5
1
0
0
0
2
2
1
2
0
0
1
0
0
0
2
2
2
1
2
1
1
1
1
1
2
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
1
2
2
0
2
1
0
0
1
1
0
1
1
1
1
0
2
1
2
0
2
0
3
1
1
0
1
0
0
0
2
1
1
2
0
1
0
1
0
3
0
4
3
0
0
0
0
4
1
2
0
0
3
0
0
1
0
2
0
0
0
2
0
1
0
0
0
0
2
0
0
0
2
2
1
2
1
0
0
0
2
1
1
1
0
0
0
0
1
0
0
0
2
1
0
0
1
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
2
1
0
0
0
2
2
0
1
2
2
1
1
0
1
0
0
1
1
0
0
2
1
0
2
1
2
0
0
1
1
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
2
2
1
0
2
0
2
0
1
1
0
0
3
0
1
1
0
0
0
1
2
2
0
0
2
2
1
1
0
0
2
4
2
0
1
0
1
2
1
0
0
0
1
0
4
3
0
1
0
0
0
2
0
1
0
0
1
2
3
0
3
0
0
0
1
1
1
0
2
0
0
1
0
2
0
1
0
0
2
1
0
0
2
1
0
0
0
3
0
1
1
0
0
1
0
0
0
1
2
1
1
2
0
0
0
2
1
1
1
1
0
2
0
0
2
0
0
1
0
1
1
0
0
0
0
0
2
0
0
1
1
0
1
0
0
3
1
0
2
0
0
1
2
1
0
0
1
0
4
0
0
1
0
0
2
1
1
0
1
0
0
1
1
0
0
1
0
0
0
0
3
2
0
0
0
0
4
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
1
0
0
2
0
1
0
2
0
0
2
1
0
0
0
1
2
3
0
2
0
1
0
2
0
1
0
4
2
0
2
0
1
2
2
2
0
0
1
0
0
1
2
2
1
1
0
1
0
0
2
1
0
0
2
1
0
0
0
2
0
0
0
1
0
1
0
0
1
1
0
2
2
1
1
2
0
1
1
0
1
0
2
2
2
2
0
1
0
0
1
2
1
0
2
0
2
0
0
1
0
0
1
2
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
1
1
0
0
0
0
0
1
0
1
1
0
2
0
0
2
1
0
2
2
2
0
0
2
2
2
0
0
2
0
1
1
1
2
1
1
0
0
2
0
2
1
0
0
0
0
1
0
2
2
2
1
0
2
0
0
1
0
0
3
1
1
0
0
0
0
1
0
1
2
1
1
0
0
2
0
0
0
1
0
0
2
2
2
2
0
2
1
0
2
2
0
0
0
2
2
2
0
0
1
0
0
1
0
0
0
2
0
0
0
1
0
2
2
0
1
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
1
3
1
0
2
0
1
0
0
2
0
0
0
3
1
1
0
0
0
0
0
0
2
0
1
0
3
0
0
0
1
0
2
0
0
1
0
1
0
0
1
1
2
1
0
1
0
0
0
0
1
1
1
1
1
0
2
1
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
1
2
0
0
2
0
1
0
0
0
1
0
0
1
0
0
1
2
2
2
0
0
0
1
3
0
2
0
1
0
0
0
1
2
0
1
1
0
0
0
0
1
0
0
1
0
1
0
0
1
1
1
3
0
0
0
1
0
1
0
0
0
0
2
1
1
2
0
1
1
0
0
1
2
2
1
0
1
0
0
2
0
0
1
0
1
1
0
1
2
1
0
0
2
0
1
5
0
0
0
0
0
0
1
1
2
0
0
2
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
1
2
1
1
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
2
1
0
0
1
1
2
0
2
0
0
0
1
0
2
2
0
0
3
0
0
0
2
0
0
0
1
1
2
0
0
0
0
1
0
1
1
0
3
0
0
3
0
0
0
0
0
1
0
2
2
0
0
0
1
0
3
0
2
0
0
1
0
0
0
1
0
1
1
1
0
2
2
1
0
0
1
0
0
0
0
0
0
1
2
0
1
1
1
1
0
0
2
1
1
0
2
0
0
0
0
1
1
0
0
0
0
2
2
0
0
0
0
1
2
1
2
0
0
0
0
1
0
1
2
1
0
0
1
0
0
0
1
0
0
1
2
1
1
0
0
2
2
0
0
1
0
1
0
0
0
2
4
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
1
1
0
2
1
1
1
0
2
2
0
0
0
1
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
1
0
0
1
0
0
0
2
1
0
2
0
2
1
2
2
0
0
0
0
2
2
1
1
1
0
0
2
3
0
2
2
0
1
1
0
0
2
0
0
2
0
0
1
1
1
1
0
0
0
1
2
0
0
0
0
1
1
2
4
0
1
1
1
0
0
0
0
0
0
0
4
2
2
0
2
1
2
2
1
0
2
0
1
0
2
0
2
0
1
2
0
0
1
0
0
0
2
0
0
2
2
2
2
0
2
0
1
0
1
0
0
2
0
2
1
2
1
0
1
0
0
2
0
1
2
1
0
0
0
1
0
0
1
1
1
0
2
0
2
0
0
0
1
1
0
0
0
0
0
2
0
0
0
1
0
2
2
0
5
1
2
0
0
0
0
0
1
1
0
1
0
2
0
1
0
0
0
2
2
0
0
3
1
1
1
0
0
0
2
0
1
1
0
0
0
0
1
2
0
0
2
1
0
0
0
0
2
1
2
1
0
0
2
1
2
0
1
0
0
0
1
1
2
0
0
2
2
0
2
2
0
1
2
0
0
0
0
0
0
1
1
3
1
0
1
1
0
1
0
1
0
0
2
0
0
1
1
0
0
1
1
1
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
2
1
0
2
0
1
2
0
0
1
1
2
2
0
1
0
2
0
1
1
0
0
1
1
1
0
0
0
0
0
0
0
1
1
2
1
0
1
2
0
0
2
1
0
1
1
0
1
1
2
1
0
0
2
1
1
2
1
0
0
2
2
2
1
2
0
1
0
1
0
0
2
0
1
0
1
0
1
1
1
0
0
1
3
0
1
0
2
0
1
0
1
2
0
0
0
0
1
2
1
0
0
1
0
1
2
0
1
2
0
3
0
1
2
2
2
0
0
2
1
1
1
0
1
0
1
1
0
1
0
1
2
8
1
0
0
0
2
0
2
1
0
0
0
1
2
0
0
1
1
0
2
0
0
0
2
0
1
0
0
0
1
0
2
2
2
0
1
2
0
2
1
0
2
0
1
1
0
3
1
0
1
1
0
1
2
1
0
1
1
0
0
0
0
1
1
0
1
0
1
2
0
0
1
2
1
1
0
1
1
2
0
0
3
1
0
1
0
0
1
0
1
0
0
2
1
1
0
1
1
1
1
7
2
2
2
0
0
0
0
0
0
1
0
0
0
1
1
1
0
2
1
0
2
0
0
0
2
1
0
2
0
0
2
1
2
0
0
0
0
2
2
0
1
1
0
0
0
2
1
2
2
0
0
2
0
1
0
1
2
0
1
0
0
1
1
2
0
0
0
1
0
1
3
0
3
0
0
1
1
0
1
0
2
0
1
1
2
0
2
2
0
2
2
2
2
0
0
2
0
0
2
0
0
1
0
1
0
0
1
1
0
0
0
0
1
2
1
0
0
2
0
2
2
2
3
0
0
0
0
0
2
0
0
3
0
2
1
0
3
4
2
2
0
0
1
0
3
0
0
0
0
0
1
2
0
0
0
0
2
1
1
0
0
0
1
1
0
1
0
1
0
1
0
2
2
0
0
2
0
0
2
1
0
2
0
2
2
2
0
2
0
0
1
0
0
0
1
1
1
1
0
1
0
1
0
0
0
0
0
0
1
2
0
0
0
1
2
0
0
0
1
1
0
1
0
0
0
2
0
0
0
0
1
0
1
1
1
1
2
1
1
1
0
4
1
0
0
0
0
0
0
1
1
2
2
1
0
1
0
0
0
0
0
2
0
0
1
1
0
0
2
1
2
2
0
1
0
0
2
0
0
0
0
0
1
0
0
0
2
2
1
2
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
2
0
1
0
0
0
1
0
2
1
2
0
1
0
0
0
1
2
1
0
1
0
0
2
0
1
1
0
2
0
0
0
0
0
0
2
0
0
1
0
2
2
0
1
0
0
2
2
2
1
0
0
3
0
0
1
0
0
0
1
0
1
0
1
0
0
1
0
1
2
0
0
0
0
0
2
0
0
1
1
0
2
0
0
0
0
1
2
0
1
1
0
0
0
1
0
0
1
1
0
0
1
0
0
1
1
1
2
1
0
2
1
0
0
0
1
0
1
0
2
2
0
2
2
0
1
0
0
0
0
2
0
0
0
1
0
0
0
1
2
0
1
0
0
0
1
2
0
0
0
2
1
0
2
0
1
3
1
1
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
2
1
1
0
1
2
1
0
0
0
0
2
0
0
2
0
2
0
0
0
2
1
0
1
0
1
0
0
0
1
0
0
1
2
0
1
0
0
0
1
0
1
0
1
3
1
2
2
2
0
0
2
2
1
1
0
2
0
1
3
2
0
2
1
0
0
0
1
2
1
0
0
1
0
0
0
1
1
2
0
2
1
1
0
0
0
0
1
0
0
1
0
1
0
0
0
2
1
0
0
2
0
1
0
1
0
2
0
0
1
0
0
1
1
0
0
0
0
0
1
1
0
2
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
3
0
1
0
0
0
0
1
0
0
2
0
0
0
1
2
0
0
0
0
0
2
2
0
1
1
1
0
0
1
0
2
1
2
1
0
0
2
0
0
0
0
0
0
2
2
1
1
0
0
0
0
2
1
1
0
0
0
2
0
4
2
2
0
0
0
2
0
2
0
0
0
0
0
1
0
1
2
0
2
0
0
0
2
0
0
0
0
1
0
0
1
2
1
0
0
0
0
2
1
0
0
1
1
1
1
0
1
1
0
0
0
1
0
0
2
1
0
1
0
1
1
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
1
2
0
2
2
0
2
2
0
0
1
0
0
2
2
0
2
0
0
0
2
1
0
1
0
0
2
0
0
0
0
2
0
2
2
0
0
0
2
0
0
2
2
4
2
0
2
2
2
0
0
1
0
1
0
2
2
0
0
0
0
0
0
1
0
2
1
0
2
1
0
0
2
2
0
0
1
1
1
0
0
0
2
0
0
0
1
1
0
1
2
0
3
1
2
1
1
1
1
2
0
1
0
2
0
1
1
1
2
0
0
1
0
0
0
0
0
0
0
1
0
2
1
0
0
1
0
1
0
0
0
1
0
2
1
0
2
0
2
3
2
1
2
2
3
1
0
0
0
0
3
0
0
0
2
1
1
1
2
0
2
0
0
4
0
0
2
1
2
1
1
1
0
1
1
1
2
2
2
1
0
0
0
0
3
2
1
0
2
0
2
1
0
0
1
0
0
0
1
1
0
0
1
2
0
0
3
1
2
0
1
2
1
0
0
0
1
0
1
2
0
2
3
2
0
2
1
1
1
0
1
0
2
2
0
0
0
0
0
2
2
1
1
2
1
2
0
2
1
2
1
1
0
0
1
1
0
2
0
0
2
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
4
2
0
1
0
0
0
2
0
2
0
2
0
0
0
1
2
1
1
0
2
1
1
2
1
0
0
0
0
0
1
0
2
0
0
1
0
0
1
1
0
3
2
0
0
0
0
2
1
0
0
0
0
1
0
0
2
0
2
2
0
2
0
0
2
0
1
0
1
1
0
0
0
1
1
1
0
0
0
1
1
0
0
1
0
0
0
0
2
1
2
2
1
0
0
3
2
1
0
0
0
2
0
2
0
0
0
0
2
1
1
0
2
1
0
0
0
1
0
2
2
0
0
2
1
0
0
0
1
0
0
0
1
2
2
1
1
1
0
1
1
0
0
1
0
2
1
2
0
0
0
0
1
0
0
0
0
1
2
0
1
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
2
1
0
0
1
1
2
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
3
2
2
0
0
0
2
0
0
0
2
1
1
1
2
2
1
1
0
0
2
1
2
1
0
1
0
0
0
1
0
1
0
2
0
1
1
0
0
0
0
0
0
2
2
1
2
0
0
0
2
1
0
0
1
0
0
2
1
0
0
2
0
0
1
0
2
2
1
0
1
2
0
0
0
1
0
1
1
0
0
0
0
0
0
2
0
1
0
0
1
2
1
0
0
1
0
0
2
2
6
2
2
0
0
1
0
1
0
1
0
0
2
0
1
6
0
1
1
0
0
1
0
0
0
0
0
0
2
0
3
2
0
0
1
0
0
1
1
2
1
0
2
0
1
2
1
0
0
0
0
0
2
2
0
0
2
0
1
0
0
0
0
0
1
1
1
2
0
0
1
2
0
1
2
2
2
0
0
1
0
1
2
0
2
1
0
1
0
0
0
0
2
1
0
0
1
2
1
1
0
0
2
2
1
0
0
0
2
0
1
1
1
1
2
3
0
0
0
0
1
1
0
0
0
2
0
0
1
0
0
0
2
0
0
2
1
1
0
2
0
1
1
1
1
1
3
1
0
2
2
0
2
0
0
0
0
0
0
2
0
2
0
2
1
1
1
0
1
0
1
3
0
0
1
0
2
0
0
2
0
0
0
0
2
1
1
0
4
0
2
0
3
0
0
3
0
0
0
2
1
0
2
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
2
1
1
0
1
1
2
0
0
1
0
0
1
0
1
0
0
0
1
1
2
2
2
1
1
1
2
2
0
2
0
1
0
0
2
3
0
0
0
0
3
2
1
1
2
0
0
0
2
2
0
0
2
2
0
0
0
1
2
0
2
0
0
1
0
0
0
0
0
0
1
0
2
2
0
0
1
2
0
0
0
1
2
2
0
2
0
2
1
0
1
2
0
0
2
1
0
2
0
1
0
0
2
0
0
1
0
0
2
1
2
0
0
0
2
0
1
2
0
0
1
0
0
0
2
1
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
1
1
0
2
1
0
2
1
2
0
2
0
2
0
0
1
2
1
1
0
0
1
1
2
2
0
2
0
0
0
0
0
2
0
0
2
1
1
0
0
2
1
1
1
1
1
0
0
2
1
0
0
0
2
0
0
1
1
2
0
0
1
10
1
0
3
2
1
0
0
0
0
0
0
2
0
0
1
2
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
3
2
0
0
0
0
1
2
0
0
0
0
1
0
2
0
1
0
2
0
0
0
1
2
0
0
1
2
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
1
1
2
0
0
0
0
3
1
1
1
0
0
0
0
1
0
0
1
1
2
1
2
1
0
0
0
1
0
0
0
1
1
0
0
1
1
2
0
0
2
1
2
2
2
0
0
2
2
0
0
2
1
0
1
0
1
0
1
0
1
1
0
0
0
2
1
1
2
0
0
1
2
1
0
2
2
0
2
1
0
0
1
1
0
0
0
1
0
2
0
2
0
2
0
1
0
2
1
0
0
0
0
1
0
0
2
0
0
0
0
2
2
0
2
0
1
1
0
0
2
0
2
0
0
1
0
0
0
2
1
2
1
1
0
2
0
0
1
1
0
0
1
0
0
1
1
1
0
1
1
2
2
0
0
2
0
1
0
0
0
1
0
0
0
1
1
0
0
1
0
0
2
0
1
0
3
0
1
0
2
1
0
0
1
0
3
0
0
0
0
1
1
0
1
0
0
2
2
0
0
0
1
0
1
0
0
1
2
0
0
2
0
2
1
1
0
2
2
2
2
1
2
0
0
1
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
2
0
2
0
2
1
0
0
1
1
3
1
1
0
0
0
0
1
2
0
0
0
3
0
2
2
1
1
0
8
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
1
0
0
1
0
1
0
0
2
1
0
2
0
3
0
0
0
1
0
0
2
2
3
2
0
2
0
0
0
1
0
1
2
0
1
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
2
1
1
0
0
2
0
0
1
0
0
2
0
1
2
1
0
0
2
1
1
1
1
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
1
2
1
6
1
3
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
2
1
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
1
0
1
2
0
2
0
0
0
1
0
0
0
1
1
1
2
0
0
0
0
0
0
0
0
0
0
2
2
2
0
1
1
1
0
0
2
1
0
0
2
2
0
1
1
0
1
1
3
1
0
0
0
1
0
1
0
0
1
0
0
2
3
1
0
0
1
0
1
0
0
2
2
0
0
1
0
1
0
2
1
0
0
1
2
0
0
0
1
0
0
0
2
0
2
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
2
0
0
1
0
0
1
0
1
2
0
0
0
0
1
1
0
0
0
1
2
1
0
0
1
0
0
2
0
0
2
0
0
0
0
1
1
2
0
0
0
0
0
0
0
2
1
1
0
2
0
1
2
1
2
0
2
0
0
2
1
0
0
0
1
1
2
0
0
0
0
0
1
1
1
1
1
0
2
0
0
1
0
1
0
0
0
1
0
1
1
0
2
2
0
0
1
2
1
0
0
0
0
1
0
2
0
1
0
2
0
1
0
1
0
2
2
0
0
0
2
2
0
1
0
1
0
0
0
2
1
2
1
1
0
0
2
2
1
1
2
1
0
2
1
2
0
0
0
0
2
1
0
0
0
0
2
2
0
0
1
2
0
0
0
0
0
1
2
0
1
2
0
1
1
0
2
2
1
1
0
1
1
0
1
0
2
1
0
1
0
0
0
2
1
1
0
2
0
0
2
0
0
2
0
2
2
2
1
2
0
0
2
1
0
2
1
1
0
1
0
2
0
2
0
0
1
0
0
0
1
0
0
2
1
1
0
2
2
0
3
1
1
1
3
1
2
0
0
0
0
0
2
1
0
1
0
0
1
2
1
1
0
0
1
1
0
2
1
0
0
1
0
0
1
0
1
2
2
2
0
2
1
0
1
0
0
1
0
1
1
1
0
1
0
1
0
2
1
2
0
3
2
0
0
2
1
0
0
1
1
0
0
2
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
4
0
2
0
2
1
0
0
0
0
0
2
1
2
1
0
0
2
0
2
1
1
1
0
0
0
1
1
1
0
0
0
0
0
1
2
3
1
1
1
1
0
4
1
0
2
1
0
1
0
0
0
1
2
1
1
0
2
0
2
1
0
1
0
2
0
1
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
1
2
2
0
1
0
2
1
0
8
1
2
2
0
0
2
2
2
1
0
0
2
1
2
1
1
1
0
1
0
1
1
1
1
0
2
0
1
1
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
1
2
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
1
1
0
2
0
0
1
0
1
0
0
3
0
1
2
1
0
1
0
0
0
0
1
0
1
1
0
1
0
0
0
0
2
2
1
0
0
1
1
0
0
2
0
1
2
1
2
0
2
0
0
1
0
2
1
0
0
0
0
1
2
0
1
1
0
3
0
0
0
1
1
1
0
0
1
0
1
2
0
0
2
2
3
0
2
2
0
1
2
0
0
2
0
1
4
0
1
0
0
2
1
2
1
0
1
0
0
2
2
0
1
1
1
0
1
0
1
0
2
0
1
2
0
0
0
2
0
0
0
0
1
1
0
0
0
0
4
0
0
1
0
1
0
0
2
2
0
1
1
2
0
0
0
0
1
1
1
0
0
0
2
0
0
1
1
1
0
1
0
1
0
2
1
1
0
0
1
0
2
2
0
0
0
2
0
0
0
1
0
0
2
1
2
0
0
0
1
0
1
1
2
0
2
0
1
2
0
0
0
0
2
1
0
0
0
1
0
1
0
1
1
1
0
0
0
0
0
0
2
2
0
2
1
0
1
0
0
0
1
1
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
1
1
2
0
0
2
0
1
1
1
2
0
1
0
1
0
1
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
2
2
0
2
2
1
2
0
2
0
1
0
1
1
2
1
2
0
3
0
0
1
2
0
1
0
0
2
0
1
1
3
0
0
0
1
2
2
2
0
2
0
0
1
1
0
1
0
0
0
2
0
0
2
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
1
2
1
0
2
1
1
1
0
0
0
1
1
0
0
1
1
0
2
0
2
0
1
2
0
1
2
0
0
0
0
0
3
1
1
1
0
1
3
1
0
0
0
1
0
0
1
1
0
0
0
2
0
1
0
0
1
0
0
1
1
2
0
2
2
0
1
0
0
0
1
0
1
0
2
2
0
2
1
1
0
1
1
3
0
0
1
1
1
0
0
1
0
1
0
0
0
1
1
0
0
1
0
4
0
0
0
1
0
1
2
0
2
0
2
2
4
1
0
0
1
0
1
0
0
2
2
0
0
0
1
0
1
1
0
0
1
2
0
1
1
0
0
2
0
1
1
0
3
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
1
1
1
2
2
2
3
0
0
1
0
2
0
2
0
2
2
0
1
0
1
1
5
0
1
1
1
0
1
1
1
0
2
0
2
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
1
1
2
0
0
2
2
1
1
0
1
0
0
0
2
0
0
0
0
0
0
2
2
2
0
2
1
1
2
0
0
1
0
0
1
0
2
0
1
2
3
2
1
1
0
1
1
0
2
2
0
0
0
0
0
0
1
1
2
1
2
1
0
0
0
1
0
1
1
1
2
1
0
2
0
0
0
2
0
0
0
1
0
0
1
1
1
0
0
0
0
0
2
1
1
2
2
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
2
2
1
0
0
1
0
2
1
0
2
2
0
2
0
1
0
2
0
4
0
2
1
2
2
1
1
0
1
0
0
3
0
0
0
2
0
1
0
2
2
0
1
0
2
2
0
0
0
1
0
2
0
1
1
0
1
0
2
0
0
3
1
1
0
1
1
1
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
1
2
0
0
0
2
1
0
0
0
1
2
0
1
1
1
0
2
0
0
1
1
3
0
1
0
2
0
0
0
7
2
2
0
0
2
2
1
0
0
2
0
2
0
3
0
0
0
0
1
0
0
0
2
2
0
0
0
0
2
1
0
0
2
0
0
0
1
1
2
0
1
1
0
0
1
2
1
2
1
2
2
1
0
0
0
1
0
1
3
2
1
2
6
0
0
1
0
0
2
2
1
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
1
0
0
1
1
0
1
0
1
0
1
0
1
0
1
1
1
1
1
1
0
3
0
0
2
1
2
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
1
1
2
0
0
0
0
2
0
3
0
1
2
0
1
0
0
2
0
0
3
1
0
0
0
0
0
0
0
2
0
2
5
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
2
0
2
0
1
0
0
2
2
1
0
0
1
1
2
2
0
2
0
1
0
2
0
2
0
0
0
3
1
2
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
1
1
0
1
0
1
1
1
1
1
0
0
0
1
1
0
1
2
0
1
1
1
0
0
0
0
2
0
1
0
0
2
1
1
2
1
0
0
0
2
2
2
0
0
0
0
0
2
0
2
1
1
0
1
2
0
0
0
2
0
1
0
1
2
2
0
0
0
0
2
1
1
0
2
0
0
2
0
0
1
0
2
0
2
0
2
1
1
0
2
1
2
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
2
1
0
0
0
2
5
0
4
0
2
1
2
1
0
0
0
1
0
3
1
2
1
0
1
0
0
1
1
1
0
0
1
0
1
0
1
0
0
0
0
0
1
0
2
0
1
0
0
1
0
0
0
2
1
0
1
1
1
3
1
2
0
0
0
1
0
0
0
2
0
0
0
0
2
2
2
0
0
1
2
0
0
0
0
1
1
0
2
1
2
0
0
1
0
0
2
3
2
0
0
0
2
1
0
0
0
2
0
1
0
3
0
0
0
2
1
2
0
2
0
2
0
0
1
1
1
1
0
0
0
0
0
0
0
1
2
2
0
1
2
1
0
2
0
1
0
2
0
0
0
0
0
0
1
3
2
1
1
1
0
2
0
1
1
0
1
2
0
1
1
0
1
0
0
1
1
0
0
2
2
4
1
0
0
0
2
2
0
1
2
1
0
2
0
0
2
0
2
0
1
2
1
0
1
0
2
2
0
0
0
2
1
0
1
2
2
0
1
0
1
1
0
1
0
0
1
2
0
0
1
1
2
0
1
0
2
0
1
1
0
1
1
0
0
2
0
1
1
0
0
2
1
1
2
0
0
1
0
1
0
0
2
0
2
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
1
0
2
1
0
1
0
0
0
0
0
1
0
0
1
1
1
2
0
1
2
1
1
0
0
1
2
2
2
1
0
1
2
1
0
0
3
2
0
0
0
3
1
1
1
0
1
0
0
0
2
0
1
0
2
2
1
1
1
0
0
0
1
0
1
0
0
2
1
0
2
0
0
2
0
0
1
2
1
2
0
1
0
2
0
2
0
0
1
0
1
1
2
0
1
1
0
1
0
2
2
0
0
2
1
0
0
1
0
0
1
0
1
2
0
0
0
0
2
0
0
0
0
2
1
0
2
0
0
1
0
0
0
0
0
0
1
2
0
0
2
2
0
1
1
1
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
1
0
0
2
2
2
1
0
2
2
1
0
0
0
0
1
0
2
2
0
2
1
2
0
0
0
0
3
0
0
2
0
1
2
0
1
0
1
0
0
1
0
1
0
2
2
0
1
0
0
0
1
0
0
0
0
1
0
0
2
1
0
0
2
0
1
1
0
1
2
0
0
0
1
2
0
0
0
1
1
0
1
0
1
1
0
2
0
0
0
0
0
0
1
0
1
0
0
0
1
2
0
0
2
1
1
1
0
3
2
0
0
1
1
0
1
0
0
1
2
1
1
0
0
1
0
2
1
0
1
0
1
0
0
0
2
1
3
0
0
1
0
0
2
1
2
1
1
2
0
1
4
1
0
1
0
0
0
0
2
0
0
1
0
1
0
0
0
0
3
0
1
0
0
0
0
0
2
0
2
2
0
0
2
0
0
1
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
2
2
0
2
0
0
2
1
1
0
0
1
0
0
2
1
0
0
2
2
0
0
0
0
0
1
0
0
2
1
0
0
1
0
1
2
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
1
1
2
0
0
1
0
0
2
0
0
0
0
2
2
1
2
2
0
0
1
2
0
0
1
0
0
1
1
1
2
0
1
1
2
0
0
0
0
0
0
0
2
2
2
2
3
1
2
0
0
2
1
0
2
2
1
2
0
0
1
1
1
1
2
0
0
0
0
2
0
0
2
1
1
0
0
1
1
0
0
0
0
1
1
0
0
0
0
1
2
0
2
1
0
0
0
1
2
1
0
0
1
0
2
1
2
2
0
2
1
1
0
2
1
1
1
0
1
0
2
0
0
0
2
0
0
0
1
0
0
1
0
1
1
0
0
2
0
1
1
1
1
2
2
1
0
1
1
0
2
1
2
0
2
0
0
2
0
0
0
1
1
0
0
1
2
0
1
2
0
2
0
1
0
0
1
1
4
2
1
0
1
2
1
0
1
1
2
0
2
2
2
1
2
1
1
0
1
2
0
3
2
0
0
0
2
2
0
0
3
2
0
2
1
0
0
0
0
0
2
2
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
1
0
2
1
1
1
2
2
2
1
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
3
0
1
0
0
1
0
0
0
2
3
0
1
2
0
0
0
2
1
0
1
1
0
0
0
2
1
2
0
0
0
0
0
1
1
0
1
1
2
1
1
0
0
1
2
0
0
1
0
1
0
0
0
1
3
0
0
0
0
0
0
1
2
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
2
0
0
1
0
2
1
0
0
0
0
0
1
1
2
1
2
0
0
1
0
1
2
1
0
2
0
2
1
0
0
0
2
0
0
2
0
0
0
1
2
1
0
2
0
2
0
0
1
1
0
1
1
5
2
2
1
1
1
1
0
0
2
1
3
0
0
0
1
1
0
2
0
0
1
0
0
1
0
1
0
2
0
0
1
0
2
0
0
3
0
1
0
1
1
1
0
1
0
0
0
0
0
0
0
1
1
2
1
2
0
1
0
0
3
0
1
0
0
0
0
1
2
0
0
0
2
0
2
0
0
0
0
2
2
0
1
1
0
0
1
2
2
1
0
1
0
2
1
1
0
1
0
0
0
1
2
2
2
0
1
0
0
1
0
0
0
1
0
0
2
2
1
0
2
0
2
0
0
0
0
0
1
0
1
1
1
0
0
2
0
0
2
0
1
0
2
2
1
0
1
2
1
0
3
1
2
2
2
1
0
1
0
1
1
0
0
1
0
0
0
6
1
2
1
2
0
1
2
2
0
0
0
2
2
1
0
0
1
0
0
1
2
0
0
0
1
0
0
0
1
0
2
0
1
1
1
2
0
1
1
0
1
2
0
2
2
1
1
0
0
2
0
2
1
2
2
1
1
0
0
1
0
0
0
0
0
2
1
2
2
0
2
2
0
2
0
1
0
2
0
0
1
0
0
2
0
2
0
0
1
1
0
4
0
0
2
0
2
2
2
0
1
0
1
0
0
3
2
2
0
0
0
2
1
2
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
1
0
2
0
2
0
0
1
1
1
0
0
1
4
2
0
0
3
2
0
2
0
2
1
3
0
0
1
0
0
0
0
0
0
2
1
1
4
0
2
2
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
2
0
1
0
0
0
0
1
0
0
0
2
2
0
0
1
2
0
1
1
0
1
2
0
0
0
2
1
1
0
1
0
0
2
0
1
0
0
0
0
0
1
0
0
2
0
2
0
0
2
2
1
1
0
0
2
0
0
0
0
2
0
1
1
1
2
1
2
0
2
1
0
1
1
1
2
2
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
1
2
0
2
0
2
2
1
0
0
1
0
0
2
1
0
2
1
0
1
1
0
1
15
0
1
2
0
2
0
1
1
2
0
0
0
0
0
0
1
1
0
1
0
2
0
2
0
0
0
1
0
1
2
1
2
1
1
1
2
0
1
1
1
0
0
0
2
3
0
1
1
2
0
1
0
0
1
0
0
1
3
2
0
1
0
1
2
1
1
0
1
1
2
2
0
2
1
0
0
0
0
1
0
0
0
0
2
0
2
0
3
2
0
0
1
0
0
0
0
0
0
3
1
1
1
1
0
1
2
0
1
1
0
0
2
1
2
0
0
2
0
1
0
1
9
0
0
0
2
0
1
2
1
2
0
2
1
0
2
1
0
0
1
2
0
1
0
2
0
0
0
0
2
2
1
0
2
0
0
2
0
0
2
1
0
0
2
1
0
1
2
2
0
0
0
1
1
0
0
1
0
3
0
0
3
0
0
0
0
1
0
0
0
0
1
2
1
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
1
2
2
2
1
0
0
3
2
4
2
0
0
0
0
3
1
2
1
2
1
1
2
0
0
1
0
2
0
1
0
1
1
0
2
0
0
2
0
1
0
2
0
1
0
0
0
1
0
1
0
1
2
0
1
0
0
0
2
0
1
2
0
0
1
1
1
0
1
1
0
2
0
1
0
0
2
0
1
1
0
1
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
1
0
0
2
0
0
0
2
1
2
2
0
1
2
1
0
1
2
0
3
1
0
0
0
2
0
0
0
0
2
0
0
2
1
0
0
0
1
1
0
0
0
0
2
3
2
0
1
0
2
1
1
0
1
0
0
1
0
0
1
2
2
1
0
0
1
2
2
1
0
0
2
0
2
0
1
1
0
0
0
0
0
0
2
1
0
0
1
2
1
0
2
0
0
0
0
2
0
1
0
0
1
0
1
1
0
1
0
2
1
0
0
1
0
1
0
0
0
0
2
1
0
2
1
1
0
2
0
0
0
0
1
0
0
1
0
0
0
0
2
3
0
0
0
1
2
1
0
2
1
1
0
0
0
1
0
2
0
0
0
1
1
0
1
0
0
0
0
2
0
3
1
0
2
1
2
1
1
0
2
0
0
1
1
0
0
1
0
2
0
0
1
2
0
0
2
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
2
1
0
1
0
1
1
0
0
0
0
0
0
1
0
0
2
0
0
1
0
2
1
2
1
2
0
0
0
1
0
1
2
0
2
1
0
1
0
0
0
1
1
1
0
1
1
0
0
0
2
2
0
2
0
1
0
0
1
2
0
0
2
2
1
0
0
0
1
0
2
1
0
2
0
1
0
1
0
0
0
0
3
1
1
0
0
0
1
0
1
0
2
0
1
2
2
1
1
0
1
0
0
0
1
2
2
0
0
2
2
0
0
0
0
2
2
0
1
1
2
3
2
1
0
0
0
0
0
2
2
0
2
0
0
2
2
1
0
0
0
1
2
1
0
1
1
0
0
2
1
0
0
0
1
2
0
0
1
2
2
0
1
2
0
0
0
0
0
0
0
0
3
0
1
0
0
1
1
0
2
0
2
0
1
1
1
0
0
0
1
0
0
1
1
0
0
0
2
0
0
2
0
1
2
0
2
1
1
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
2
0
2
2
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
1
0
1
0
1
2
2
0
0
0
1
1
0
2
0
0
0
0
2
0
0
0
1
2
2
1
0
1
0
0
0
2
0
2
0
0
1
0
2
2
0
0
2
1
2
0
1
0
1
2
2
1
1
0
1
0
1
0
2
2
1
1
0
2
0
0
0
0
0
1
1
2
0
0
0
0
2
0
2
1
2
0
0
1
0
0
2
0
1
0
2
1
0
0
0
0
2
2
2
0
0
0
0
1
0
2
2
1
1
0
2
0
0
0
1
1
2
1
0
0
1
0
0
1
0
0
0
1
0
0
1
1
0
0
1
0
1
1
0
0
2
2
0
0
1
1
1
1
2
2
0
2
0
0
2
0
1
0
2
2
1
1
0
0
2
3
0
1
0
1
1
2
0
3
0
2
1
1
3
0
1
0
0
0
1
0
0
0
0
2
1
0
2
0
0
0
0
1
1
0
2
0
1
0
3
0
1
0
1
1
0
0
0
0
0
2
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
1
0
2
2
0
0
0
2
0
0
0
2
0
1
0
1
1
2
0
1
0
0
2
0
2
1
0
1
2
1
1
1
1
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
3
0
0
1
1
1
1
0
1
1
2
1
2
1
1
2
1
0
0
0
3
0
2
0
2
0
0
1
0
1
0
2
0
0
2
2
1
2
0
0
1
2
0
0
0
0
0
1
1
0
1
1
1
0
0
1
0
0
1
1
0
1
0
2
1
0
0
0
1
1
1
2
1
2
0
1
1
0
1
0
1
1
1
2
0
1
0
1
0
0
2
0
1
5
0
0
2
2
2
1
1
2
0
0
1
1
1
0
1
0
2
2
1
0
0
0
2
2
0
2
0
2
1
0
1
2
2
0
0
2
2
1
1
1
2
0
2
0
0
0
0
0
2
0
0
0
2
0
3
2
2
0
3
0
0
0
0
0
0
1
0
1
2
1
1
1
0
0
0
0
0
1
0
1
2
2
2
2
1
1
0
2
2
0
0
1
0
1
0
0
0
0
1
2
1
2
0
0
0
1
1
2
0
2
1
0
0
1
0
0
0
0
0
2
2
0
0
0
1
0
2
0
1
0
0
0
1
0
1
1
1
1
1
0
0
0
1
0
0
0
0
0
1
2
1
2
0
1
0
0
1
0
0
0
0
0
1
0
2
2
1
1
1
0
0
3
2
2
1
0
0
2
0
1
1
2
0
0
1
1
0
0
1
1
0
2
0
1
1
1
0
1
0
1
1
1
2
0
0
1
0
3
1
1
2
1
0
0
0
1
0
0
0
1
0
0
2
0
0
2
0
0
1
0
2
0
1
0
0
0
0
2
1
0
0
0
2
0
3
3
0
2
0
2
0
1
2
0
1
0
1
0
1
2
1
2
0
1
2
1
1
3
0
0
1
1
0
0
0
0
1
2
0
1
1
1
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
1
0
0
0
2
0
1
1
0
0
0
2
0
0
1
1
2
0
0
0
0
0
0
0
1
1
1
2
2
2
0
2
0
2
2
2
0
0
0
10
0
0
0
0
0
0
2
1
0
0
1
2
0
1
0
0
1
1
0
2
2
0
1
0
1
2
0
3
0
0
1
0
1
0
1
2
0
0
2
2
0
0
0
2
0
0
0
1
2
2
0
0
0
0
0
4
1
0
0
0
2
0
0
1
0
1
2
0
0
2
2
0
2
0
0
0
0
0
0
1
0
2
0
2
2
2
2
2
0
1
2
2
2
0
0
0
0
2
0
0
0
1
0
0
1
1
0
0
0
1
0
2
0
1
1
2
0
2
1
0
0
0
1
0
2
0
1
1
2
0
0
1
0
0
0
0
0
0
1
1
1
2
2
3
0
2
2
1
2
1
2
0
2
2
0
1
3
0
1
0
2
1
2
0
4
2
2
0
0
0
0
0
0
2
1
0
0
1
1
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
2
2
0
2
0
1
2
0
0
0
1
0
0
0
0
0
1
2
2
1
1
1
0
2
0
1
1
2
0
0
1
0
1
0
1
0
1
0
0
1
1
1
0
3
0
0
2
0
2
2
0
2
1
2
0
0
2
2
3
1
1
0
0
1
1
1
0
1
0
0
2
1
0
3
0
0
0
1
0
0
0
2
1
1
0
2
1
0
0
2
2
1
1
0
2
2
0
2
0
0
1
1
1
0
0
2
0
0
0
0
1
0
0
0
3
0
1
0
0
2
1
1
2
1
0
1
2
1
0
2
0
0
0
0
3
1
0
2
1
0
0
2
0
0
0
2
1
0
2
0
0
0
1
0
0
0
0
0
0
0
2
1
0
2
0
1
0
0
1
0
0
2
0
0
2
0
0
1
1
0
2
0
1
0
0
2
0
0
2
2
0
2
1
2
1
1
1
0
0
1
1
3
1
0
0
0
2
0
2
0
0
0
0
0
2
2
0
0
0
2
1
0
0
0
1
2
0
2
1
0
0
2
0
0
0
1
1
0
1
0
0
0
0
2
3
0
0
2
0
0
1
0
0
0
0
0
0
2
1
2
5
0
1
0
0
1
0
1
2
2
0
0
1
0
0
0
0
0
0
2
2
0
1
0
1
0
1
1
1
0
0
1
0
0
0
0
3
0
2
0
2
2
1
1
2
1
1
0
0
0
0
2
0
0
0
0
1
1
2
0
0
0
0
0
0
1
1
0
0
2
0
0
2
0
0
1
2
0
0
2
1
1
2
6
0
0
2
2
0
0
2
1
2
2
0
0
0
0
2
3
0
2
2
0
2
0
0
0
0
0
0
2
2
2
0
2
0
0
0
7
2
0
1
2
0
1
1
2
0
2
0
0
0
0
2
0
1
1
5
0
0
0
0
1
2
1
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
2
0
2
0
0
0
4
0
2
0
1
1
0
1
0
1
0
0
0
2
2
0
1
2
1
1
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
1
0
0
1
0
2
1
0
0
0
1
0
1
2
0
2
1
0
0
0
0
1
1
1
1
0
2
0
2
2
1
0
1
1
1
0
1
0
2
0
1
0
1
2
0
0
0
0
0
0
1
0
0
0
1
0
0
2
2
0
1
0
1
1
2
0
2
0
0
1
0
2
1
0
0
0
0
0
0
1
0
2
2
2
2
1
0
0
1
1
0
0
2
1
0
1
0
0
2
1
0
0
0
0
1
1
1
2
0
0
2
0
0
0
0
1
0
0
0
1
2
0
0
1
0
1
0
0
2
1
0
0
0
1
1
0
0
0
0
2
0
1
2
2
0
1
1
1
1
0
0
2
1
0
1
0
0
1
1
2
0
1
1
0
0
1
1
1
0
2
2
1
1
0
2
0
0
0
0
2
1
1
1
1
2
0
4
0
0
0
0
0
1
0
2
0
0
2
0
0
1
0
2
0
0
1
0
0
2
0
1
1
0
0
0
1
0
1
0
0
0
1
1
2
0
1
0
0
1
0
1
1
2
0
1
0
0
0
0
0
0
1
0
0
0
0
1
2
0
2
1
0
0
0
0
0
0
2
0
0
2
1
0
1
0
0
1
2
0
2
0
1
0
2
2
0
2
0
1
2
0
0
0
2
0
2
0
2
0
1
1
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
2
2
2
2
2
0
0
0
0
0
1
0
1
0
1
1
0
0
2
2
1
0
1
0
0
0
0
0
0
0
0
1
2
0
0
1
2
0
0
1
0
0
0
0
0
1
2
1
1
2
1
2
2
0
0
1
1
1
0
1
1
1
2
2
3
0
2
0
2
0
0
1
0
1
0
1
1
0
0
0
1
1
0
0
1
1
0
2
0
0
0
0
0
2
0
2
0
0
1
0
1
1
0
0
2
2
2
0
0
0
2
2
0
0
0
0
1
0
0
2
1
2
0
2
0
0
0
1
2
1
0
2
0
0
0
1
0
0
0
3
2
2
0
0
1
0
0
2
2
8
0
2
1
0
0
1
1
0
0
1
0
1
0
2
0
0
0
2
1
2
1
1
2
2
0
0
0
0
0
1
2
0
0
1
1
0
1
2
1
1
0
0
0
1
3
0
2
1
2
0
0
0
0
0
0
2
0
2
0
2
0
3
2
1
0
2
0
2
2
0
0
0
3
1
0
2
1
0
2
0
1
0
0
2
0
1
0
0
0
0
1
0
2
1
0
2
0
1
1
1
0
0
0
0
1
1
1
2
1
1
1
0
0
0
0
0
2
1
2
0
2
0
0
2
1
0
2
0
1
0
0
0
0
0
1
2
1
1
0
1
0
0
1
0
2
0
2
0
2
1
0
0
2
3
0
0
0
1
0
2
0
0
2
3
2
1
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
1
0
0
1
2
1
1
1
0
0
0
2
0
0
1
1
2
2
3
0
3
1
0
2
1
0
0
0
0
0
2
4
2
0
1
0
0
1
2
0
2
0
0
0
0
2
0
0
1
2
0
0
0
2
2
0
0
1
2
0
1
0
1
0
0
2
0
1
0
0
2
1
0
0
0
0
2
1
2
0
0
1
0
2
1
0
1
0
0
1
0
1
1
0
2
1
2
0
1
2
2
0
0
1
0
0
0
0
0
2
0
0
0
2
1
2
1
0
1
0
1
1
0
2
2
0
2
1
0
0
0
0
2
1
3
0
1
0
0
2
0
0
0
2
0
1
0
2
0
0
0
0
0
0
2
3
0
1
0
0
1
0
1
0
1
0
1
1
2
0
0
2
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
2
2
0
1
2
2
1
1
1
1
0
0
2
1
0
0
0
0
0
0
0
1
0
1
1
1
1
1
1
1
3
1
1
1
0
0
0
0
1
1
2
0
1
1
2
2
0
0
2
0
0
0
0
2
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
2
2
1
0
2
1
1
0
1
2
0
2
2
2
1
1
2
0
0
2
0
0
1
1
0
0
0
1
2
0
0
1
0
0
1
3
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
2
2
1
1
1
2
0
1
2
0
1
0
1
0
2
0
1
0
1
2
0
1
0
1
0
1
0
0
1
0
1
0
0
0
2
0
1
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
1
2
4
1
0
0
1
3
3
0
1
2
3
0
0
4
0
0
1
0
2
2
1
1
0
0
0
0
0
2
1
0
0
1
1
0
2
0
0
2
0
2
1
1
0
0
1
1
0
0
3
0
0
1
0
0
0
0
1
0
0
1
0
1
1
1
2
0
2
2
0
2
0
0
1
1
1
0
1
1
0
1
2
1
0
0
0
1
0
2
1
2
2
1
0
1
0
0
0
6
2
0
0
0
0
0
3
0
2
2
2
0
0
0
1
2
0
0
0
0
2
0
1
0
1
2
1
3
0
2
4
0
0
0
0
0
1
0
2
1
1
0
1
1
1
2
1
1
1
2
1
1
0
1
0
0
0
0
0
2
1
2
0
0
1
0
0
0
1
2
1
0
3
1
1
0
0
2
0
0
0
0
1
0
1
0
3
1
0
0
0
1
2
0
0
1
1
1
0
0
0
0
3
0
0
2
0
1
0
1
2
1
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
1
0
0
0
0
0
2
2
1
0
1
0
0
2
0
0
1
0
2
0
1
2
2
1
1
0
3
1
0
0
2
1
1
2
0
0
2
1
2
0
0
1
0
1
0
0
0
0
1
1
1
2
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
1
2
2
0
1
0
1
2
0
0
2
1
1
0
1
0
2
0
0
0
2
0
0
1
0
1
0
1
2
2
2
1
1
0
0
1
1
1
1
0
0
1
0
1
0
2
1
0
2
0
2
1
0
2
2
2
1
2
2
1
0
1
0
1
2
0
0
0
3
1
0
0
1
0
0
0
0
0
2
2
0
0
0
0
1
0
0
1
1
0
0
0
1
1
0
1
0
1
1
1
0
0
1
2
2
0
0
0
0
0
1
0
0
0
1
0
2
1
1
0
1
1
1
2
0
0
0
1
0
0
1
1
1
1
1
0
0
0
0
1
0
0
2
1
2
0
1
1
0
1
1
1
2
1
0
0
2
2
0
0
0
2
0
1
2
0
2
1
1
0
2
0
0
2
0
0
0
0
2
1
0
2
1
1
1
0
0
0
1
0
0
0
1
0
2
0
1
1
1
0
0
1
1
1
0
0
0
0
0
0
1
0
0
3
0
1
0
1
0
0
0
1
0
2
0
0
3
0
2
0
0
0
0
1
2
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
2
0
2
1
2
0
0
0
1
1
1
0
2
0
1
2
0
2
0
1
1
2
0
2
0
2
2
1
0
0
0
0
6
1
0
1
0
0
0
0
0
1
0
1
0
0
0
1
2
1
0
0
1
0
0
0
1
0
0
0
0
2
1
2
2
2
0
0
0
0
0
0
0
1
0
2
3
0
2
0
2
0
0
2
0
0
0
0
0
2
2
5
2
0
0
2
0
0
0
0
2
2
2
0
0
0
0
1
2
2
0
1
0
2
1
0
1
1
0
1
1
2
2
1
1
2
0
2
0
0
2
2
0
0
1
0
1
0
0
2
0
2
1
1
0
3
0
1
0
0
0
1
2
0
0
0
1
0
1
0
0
2
0
0
0
2
1
1
0
0
0
1
0
1
0
0
0
0
0
2
0
1
0
1
1
1
0
1
2
0
0
0
2
0
0
0
1
0
0
1
1
0
2
0
0
0
2
2
0
2
0
1
0
0
0
0
0
0
0
0
2
0
1
1
0
1
0
2
0
1
1
1
1
0
0
2
2
1
1
0
1
1
1
0
0
0
2
1
0
0
2
2
1
0
0
0
0
0
2
2
1
1
0
0
1
1
2
0
2
0
0
2
1
0
1
0
0
0
0
2
0
2
1
2
1
2
0
1
0
2
1
3
0
0
0
0
1
0
1
0
0
0
1
0
1
1
1
0
1
0
0
1
1
0
2
0
0
2
5
0
1
2
2
2
0
0
1
0
2
2
0
0
0
2
0
0
0
0
2
2
0
7
1
1
2
0
1
0
1
0
5
2
1
0
0
0
2
0
2
3
1
2
0
1
0
1
1
0
0
1
2
0
1
0
0
0
1
2
2
0
1
0
1
0
0
0
0
0
0
1
1
0
0
1
2
2
1
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
1
2
2
1
1
0
1
1
0
0
1
1
1
0
1
0
1
0
1
1
1
2
0
0
0
1
2
0
0
0
1
0
2
0
2
0
1
0
2
2
0
0
0
1
0
0
1
1
1
0
1
1
0
0
0
0
0
0
0
1
0
1
0
2
0
0
1
0
1
0
0
2
2
0
2
0
1
1
0
8
1
2
1
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
2
0
1
1
0
0
0
0
0
0
0
1
1
0
2
1
0
1
1
2
0
1
1
2
0
0
2
0
0
0
0
0
0
1
1
0
1
0
0
2
1
0
0
1
0
0
2
0
1
3
0
1
0
2
0
1
1
2
2
1
0
1
1
0
0
0
1
2
2
0
0
1
0
0
1
0
1
0
1
1
2
0
1
1
3
1
0
1
0
1
1
1
0
0
1
0
3
1
1
2
1
0
1
0
0
1
2
3
0
0
0
1
1
2
0
1
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
1
2
0
2
1
0
0
1
1
2
0
1
0
2
0
2
0
0
1
1
0
1
2
0
0
1
2
2
2
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
2
0
0
0
1
1
0
0
1
0
0
0
0
2
0
0
0
2
0
3
0
2
2
0
0
0
2
2
1
0
0
0
2
0
1
0
0
2
1
0
1
0
0
0
2
0
0
0
0
0
2
1
1
1
1
1
0
0
0
2
0
0
1
1
2
0
0
0
0
0
1
1
0
1
2
0
0
2
0
2
1
1
2
0
2
0
0
1
1
0
2
0
2
1
0
0
0
0
0
0
1
1
2
0
0
0
0
1
2
0
0
1
0
0
1
0
1
1
1
2
0
0
2
0
0
0
0
0
2
1
0
0
0
1
0
0
0
2
0
1
1
0
2
2
1
1
1
0
0
0
0
2
0
1
0
0
2
0
0
0
2
2
0
2
0
1
1
0
0
2
0
0
0
1
1
2
1
0
1
0
1
0
0
0
0
0
0
2
0
0
1
0
5
0
1
0
0
0
0
1
1
0
0
2
2
1
1
0
1
0
0
1
0
1
0
4
0
0
1
1
1
1
1
0
0
2
1
0
0
2
1
1
1
1
0
2
2
0
1
1
0
1
0
0
0
0
1
1
2
0
1
0
0
1
2
0
1
1
2
0
0
2
0
0
0
1
1
0
0
0
1
1
0
0
1
0
0
2
0
0
0
0
2
0
2
0
0
1
1
0
0
0
0
0
1
0
0
1
1
1
2
1
0
1
1
1
0
1
1
0
2
0
0
0
2
1
0
2
0
1
2
0
0
0
0
1
0
2
0
0
1
0
1
0
0
0
2
0
0
0
1
0
2
2
0
2
0
1
2
0
2
2
0
1
0
1
0
1
1
1
2
0
0
1
2
0
0
1
0
0
1
1
1
0
2
1
0
2
0
2
1
0
2
1
0
2
0
0
0
1
0
1
0
1
2
0
0
7
1
2
1
0
0
0
1
0
0
1
0
2
2
0
2
1
0
1
0
0
0
2
0
2
0
0
0
1
0
0
1
0
1
0
0
1
2
2
2
2
0
0
0
1
1
0
0
1
2
2
1
2
1
1
1
2
0
1
1
2
0
0
1
2
1
0
0
0
0
0
2
1
0
1
0
1
2
1
0
1
0
2
0
0
0
2
1
0
0
1
1
0
2
0
0
1
0
2
0
3
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
2
0
2
2
1
1
0
0
0
1
0
2
0
1
1
0
1
1
0
0
1
2
0
1
0
1
1
0
1
0
0
0
0
1
0
2
1
0
0
0
1
0
0
0
1
2
2
1
2
0
1
0
1
1
0
2
0
0
1
1
0
0
0
0
1
0
2
1
2
0
2
1
1
0
1
0
0
1
1
0
1
0
1
0
0
1
1
1
0
1
0
0
0
0
2
2
0
1
2
0
1
1
3
2
5
1
2
0
2
1
0
0
2
0
2
0
1
1
1
1
0
2
1
0
0
0
1
0
0
0
1
0
2
1
2
1
0
0
2
1
0
0
0
0
0
2
1
2
1
0
0
0
0
1
1
0
2
0
0
1
2
2
0
0
0
0
1
0
2
1
0
2
0
0
1
0
2
1
0
1
2
0
0
1
4
1
2
1
2
0
0
1
1
0
2
1
1
1
1
0
0
1
0
1
4
5
2
1
2
0
0
1
0
1
0
0
0
0
1
1
0
0
2
1
3
1
2
0
2
0
0
1
0
1
0
0
1
2
0
2
0
0
0
0
0
0
2
0
1
0
1
2
0
2
1
0
0
0
0
1
2
1
2
0
0
0
1
0
1
0
1
1
1
0
0
0
0
0
1
3
1
0
0
2
0
0
0
0
2
2
2
0
0
0
1
0
0
0
0
0
1
2
0
0
2
0
0
0
0
1
0
0
2
0
1
1
2
2
2
0
0
2
0
0
0
1
0
1
0
0
2
2
0
0
1
0
0
1
0
1
2
0
0
2
3
0
0
0
0
0
2
1
1
2
2
0
0
0
2
0
0
0
0
2
2
0
2
0
2
0
0
0
1
1
2
2
1
0
2
0
0
1
1
0
1
1
0
0
0
1
1
0
0
0
0
0
0
1
0
2
2
0
1
1
1
0
0
1
1
0
2
0
1
2
0
0
0
1
1
2
2
1
2
0
0
0
0
3
2
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
1
0
1
1
0
0
1
2
2
1
0
0
0
0
1
0
2
1
0
0
1
1
0
3
0
0
2
0
1
2
2
0
0
1
1
0
0
0
1
0
1
2
0
1
2
0
0
1
1
2
1
1
0
0
0
1
2
2
0
0
0
1
1
0
0
2
0
0
0
0
2
2
2
1
0
1
3
1
0
1
0
0
1
2
1
1
2
1
0
1
0
1
0
0
1
2
0
0
4
2
0
0
0
0
0
0
1
0
0
2
1
3
2
1
2
0
0
1
2
1
3
1
2
0
1
2
3
0
0
2
1
1
0
0
0
0
1
1
0
0
0
1
0
1
1
2
0
0
0
0
1
0
0
3
0
1
1
1
0
2
0
1
2
3
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
2
0
1
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
2
2
2
1
1
1
2
0
1
2
0
1
1
1
0
2
0
2
0
0
0
1
0
2
0
3
0
1
1
0
0
0
1
1
1
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
1
1
0
0
0
0
1
1
2
0
0
0
0
0
1
0
0
1
0
2
2
1
0
0
1
0
0
0
0
0
1
1
0
0
2
0
1
0
0
2
1
0
0
1
0
1
1
1
0
0
1
1
0
1
1
1
0
1
1
0
0
0
0
2
0
2
0
1
1
1
0
1
2
2
0
0
2
1
1
0
0
0
0
0
1
0
0
0
1
2
1
0
1
0
0
1
0
2
0
0
0
0
0
2
0
0
1
0
1
0
1
2
0
1
2
1
0
1
1
2
4
2
0
0
0
1
2
1
1
0
0
0
0
0
0
1
1
0
1
0
2
0
1
2
0
1
0
1
1
0
0
0
1
1
2
2
0
1
3
0
1
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
2
0
2
1
0
0
0
2
2
0
0
0
0
2
0
1
0
2
1
2
1
2
0
0
0
1
0
0
1
2
0
0
0
2
1
1
0
1
0
0
0
0
2
2
0
0
0
2
0
1
0
0
2
0
2
0
0
1
2
1
0
1
1
0
1
1
0
2
1
2
2
2
1
1
0
1
0
1
1
0
2
0
0
0
0
1
1
2
1
1
0
2
1
3
0
0
0
1
0
1
1
0
2
0
0
0
0
0
1
0
2
0
2
1
0
1
1
0
1
0
0
1
0
1
0
1
3
0
0
1
0
0
1
1
2
1
0
1
0
0
0
1
0
0
0
0
0
0
2
1
1
0
0
0
0
2
1
2
0
0
2
0
1
0
2
0
0
1
2
0
0
2
1
2
0
2
0
0
2
0
0
0
0
2
2
0
0
1
0
2
0
1
0
0
1
0
1
2
0
0
2
0
1
0
0
0
2
0
2
0
0
0
0
1
1
0
0
0
1
0
0
1
0
2
3
0
0
0
1
1
1
1
0
0
0
1
0
0
1
2
1
0
0
0
0
2
0
2
0
1
1
0
0
1
1
1
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
1
4
0
1
3
0
1
0
0
1
0
1
1
0
0
0
0
1
0
1
2
0
0
1
1
1
1
2
1
0
0
3
1
0
2
0
2
1
2
2
0
0
1
1
0
1
1
0
2
1
0
1
2
0
1
1
1
0
0
0
2
1
0
0
0
1
2
0
0
0
0
0
3
0
2
0
2
2
1
0
2
1
0
0
1
0
1
0
2
0
1
2
0
0
0
1
1
2
0
0
0
0
2
1
0
0
0
2
4
0
1
1
2
0
2
1
1
2
1
0
2
0
1
0
0
1
0
0
0
1
0
2
0
1
0
1
0
1
2
0
0
0
1
0
1
0
1
0
0
2
1
2
0
0
1
0
1
2
1
0
3
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
2
1
0
0
2
0
2
1
3
0
1
2
0
0
2
0
2
0
1
0
1
0
0
0
0
1
0
0
0
0
1
1
1
0
1
2
0
0
0
0
2
0
2
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
1
0
3
1
0
2
1
1
0
2
0
0
0
1
0
0
0
0
1
1
0
2
1
0
1
0
0
1
1
1
0
0
0
0
0
0
0
1
1
0
0
1
0
2
1
0
0
2
2
0
1
2
2
0
2
0
0
1
1
1
0
1
1
0
1
0
0
0
0
1
0
0
0
1
2
1
0
2
1
1
0
2
0
0
0
0
1
2
2
0
0
1
1
0
2
2
1
1
0
1
2
0
2
0
0
1
2
0
2
0
1
0
0
0
3
0
1
1
1
0
0
0
1
2
2
0
0
0
0
1
0
1
2
0
0
0
2
0
1
1
0
0
1
1
0
0
0
2
1
1
1
2
0
0
0
1
1
5
2
0
0
0
0
0
0
0
0
1
2
0
2
1
0
0
0
0
2
2
3
2
1
2
1
0
1
2
0
0
0
2
1
0
0
1
0
3
0
0
0
2
2
1
0
0
0
0
2
1
1
1
0
1
0
1
0
0
0
0
1
0
0
6
0
1
1
1
1
0
0
1
2
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
2
0
0
0
1
1
1
0
3
0
0
0
0
2
1
0
0
2
0
0
1
0
0
0
2
0
1
1
0
1
0
2
0
2
0
1
0
0
0
1
0
0
0
0
0
0
2
0
3
1
0
0
2
0
2
1
0
1
0
2
0
0
0
1
2
0
1
0
2
0
1
1
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
2
1
0
0
11
1
0
1
0
0
0
0
1
0
1
2
0
1
1
2
0
2
1
0
2
1
1
2
3
2
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
2
2
2
0
0
0
0
0
1
2
0
0
2
1
1
0
1
2
1
0
0
0
0
0
0
1
0
1
0
0
2
1
0
0
0
0
0
0
1
0
0
0
1
2
2
0
0
0
1
0
1
2
0
2
1
1
0
1
0
0
1
1
1
0
0
2
2
0
1
2
2
1
0
1
0
1
0
2
2
0
5
0
0
1
1
1
1
0
0
0
2
0
0
0
3
0
1
1
0
0
0
1
2
1
1
1
2
0
0
0
1
2
2
1
1
0
0
0
1
0
0
0
1
1
0
4
0
2
0
0
0
1
2
2
0
2
0
1
3
0
0
1
0
0
0
1
0
0
0
0
2
0
0
1
1
1
0
0
2
2
0
2
1
0
0
1
0
0
0
0
0
1
0
0
2
1
0
0
0
2
2
0
0
0
1
1
1
0
0
2
2
0
1
0
1
0
1
1
0
1
2
0
1
1
0
0
1
0
1
1
1
0
1
1
0
2
2
0
2
2
2
2
1
2
2
1
0
2
1
0
0
2
0
2
1
0
2
1
0
2
0
0
0
0
2
1
0
1
0
0
2
1
2
0
2
0
2
0
1
0
1
1
0
2
1
1
0
0
2
0
2
1
0
0
2
3
0
0
0
0
1
0
0
2
1
1
1
2
2
2
1
0
1
0
1
1
0
2
0
1
2
2
1
0
1
2
0
1
0
1
2
0
2
1
0
1
0
2
2
0
1
0
1
0
0
0
1
0
0
1
0
1
1
0
1
0
1
0
1
0
2
0
0
0
1
0
1
1
0
0
1
2
1
2
2
0
1
0
1
1
1
0
1
0
1
0
0
1
0
2
0
0
0
0
0
2
0
0
1
0
2
1
0
0
0
0
1
0
4
1
1
1
0
1
0
0
1
0
0
1
1
1
0
0
0
1
3
0
0
0
0
1
0
2
1
1
0
0
0
1
2
0
0
2
0
1
2
1
2
2
0
0
0
2
1
0
0
2
0
1
0
2
0
0
1
0
0
0
1
1
1
0
0
1
0
2
0
2
0
0
0
3
0
0
1
0
2
1
0
0
0
0
0
2
2
2
2
1
2
0
2
0
2
0
1
0
1
0
1
2
2
0
0
1
3
0
1
1
0
0
0
1
1
0
0
2
2
0
2
0
2
1
2
0
0
0
2
0
0
2
1
1
1
0
1
0
3
1
2
0
2
0
2
0
2
0
0
0
1
0
3
1
2
1
0
1
2
0
0
0
1
3
0
0
1
1
0
0
0
0
2
1
0
2
2
1
2
0
0
0
1
0
0
0
0
2
1
0
0
2
2
0
0
1
0
2
2
0
1
1
1
0
1
0
0
1
0
0
2
2
1
0
2
2
2
2
0
1
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
1
1
2
0
1
2
0
0
0
0
0
1
0
2
1
2
0
0
2
1
0
0
1
0
0
2
0
0
2
0
2
2
2
0
2
0
0
1
0
1
0
2
0
0
0
0
1
2
1
0
1
0
1
1
1
0
0
2
0
1
1
1
1
2
0
1
2
0
1
1
1
1
1
0
0
0
1
0
0
0
1
1
1
1
1
0
0
0
0
2
1
0
0
1
1
1
1
1
2
2
2
2
1
0
1
1
0
2
0
0
0
0
1
0
0
0
2
1
0
0
0
2
2
0
0
0
1
0
0
1
0
0
1
2
1
0
1
2
0
2
0
10
2
0
0
2
0
0
2
0
1
2
2
2
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
1
0
0
1
1
2
0
0
2
0
0
1
0
0
0
2
0
1
1
2
2
3
2
0
0
0
0
0
0
0
2
1
1
0
1
2
0
0
0
1
2
2
0
0
0
2
4
0
0
0
0
0
2
2
0
1
1
0
0
0
0
1
1
0
0
0
1
0
1
1
0
2
0
0
0
0
0
1
0
2
0
0
1
1
1
1
0
0
0
0
2
0
0
1
0
0
1
1
0
0
0
2
2
2
1
0
0
4
0
2
1
1
2
0
0
0
0
0
1
0
1
1
0
2
0
2
1
0
2
0
3
1
2
0
0
0
1
0
1
2
0
2
0
0
0
3
4
1
2
0
1
2
0
0
1
0
1
0
0
2
2
1
0
1
2
1
0
1
0
0
0
1
0
0
1
2
2
0
1
1
2
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
1
0
0
0
0
1
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
1
0
1
1
0
0
0
0
0
0
0
2
2
1
1
0
1
1
0
2
0
2
1
0
0
2
0
2
2
1
2
1
2
0
2
0
2
0
1
0
1
0
1
0
2
0
2
0
0
0
0
2
2
0
0
1
0
2
1
1
0
1
0
0
2
1
0
1
2
0
2
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
1
1
0
2
0
0
2
0
0
1
1
0
1
1
1
1
1
0
2
1
1
1
2
0
1
1
2
2
0
1
1
1
0
0
1
1
0
0
0
0
0
0
3
2
0
1
0
0
0
0
0
0
1
0
2
2
0
0
0
2
2
0
1
2
0
1
1
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
2
1
0
0
0
1
1
1
0
1
2
0
2
1
0
0
0
0
2
1
0
2
3
0
4
0
0
0
2
1
0
0
0
1
1
0
2
0
1
1
0
0
0
0
0
2
2
1
0
1
1
0
1
2
0
0
2
1
0
0
2
0
0
0
0
2
0
1
1
2
0
0
2
1
0
0
1
0
1
0
1
0
0
1
0
0
1
1
0
2
2
0
1
1
0
0
2
0
1
2
0
0
1
1
2
0
0
0
0
0
2
0
2
1
1
2
0
2
0
0
0
0
1
2
0
0
0
1
2
0
0
2
2
2
0
0
0
2
1
0
0
2
1
0
1
1
2
2
2
2
0
0
0
0
2
1
1
2
2
0
0
4
1
0
2
0
2
1
0
0
2
0
1
2
1
0
0
1
1
0
2
0
0
0
3
0
2
1
2
1
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
2
0
0
1
0
1
0
1
0
0
0
0
1
1
0
0
0
2
0
0
0
2
0
1
0
1
0
0
0
2
1
1
0
0
2
1
1
0
2
1
0
1
1
0
2
1
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
2
0
1
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
3
0
0
0
1
2
2
0
1
1
1
0
1
1
1
1
1
0
1
0
0
0
1
0
2
2
0
2
1
1
0
0
1
0
1
2
1
0
0
0
0
2
1
1
0
1
2
0
0
0
3
2
0
2
1
0
2
0
1
1
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
3
0
2
0
2
2
0
1
0
1
0
1
0
0
0
0
1
4
0
2
0
0
0
2
2
0
1
0
0
1
0
0
0
1
0
2
1
1
0
1
1
0
0
1
1
0
1
0
0
0
1
2
1
2
0
1
0
1
0
1
0
2
0
0
0
2
1
0
1
0
2
1
0
2
0
0
0
2
0
1
2
1
0
0
0
0
1
0
0
2
0
1
1
1
0
1
0
0
0
1
1
0
0
4
0
1
0
1
0
0
0
2
0
0
1
1
1
0
2
0
0
0
1
0
0
0
1
1
2
1
2
0
2
1
0
0
0
2
1
0
0
1
1
1
1
0
0
1
0
0
0
1
0
0
0
0
1
1
2
2
2
2
0
0
1
3
0
0
0
1
2
1
1
0
0
0
2
2
0
0
1
0
0
0
0
1
1
2
0
1
0
1
0
0
2
1
0
0
1
1
0
1
0
1
1
1
0
1
0
0
1
1
0
1
1
1
1
0
0
0
0
0
1
0
0
0
0
1
2
0
2
0
3
0
1
0
1
0
0
0
1
0
1
2
1
1
0
1
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
1
0
1
2
2
0
0
0
0
0
0
2
1
2
3
0
0
1
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
2
1
0
2
0
0
2
1
0
0
1
0
1
0
0
2
2
2
2
2
1
0
0
0
1
2
0
2
0
1
0
1
0
2
0
1
0
0
1
1
1
1
2
0
2
0
0
0
2
0
3
2
0
0
0
2
0
2
2
0
0
1
0
0
0
0
1
2
0
1
2
0
2
2
0
1
0
1
0
1
1
0
0
0
0
0
2
2
0
1
0
1
1
0
2
0
0
0
2
0
2
1
1
0
0
2
0
1
1
1
1
2
1
0
2
0
1
2
0
1
2
0
2
1
1
2
1
2
2
0
0
0
2
0
2
4
0
1
2
1
0
0
0
1
1
0
0
1
0
0
0
0
0
2
2
0
4
0
0
1
0
2
1
0
0
1
0
1
2
0
1
0
0
0
0
0
2
1
1
1
0
0
1
0
1
0
1
0
1
0
1
1
0
2
0
0
1
0
0
0
0
1
0
1
0
0
2
0
0
0
3
0
3
0
3
0
2
1
0
0
1
0
1
0
0
2
0
1
0
0
2
2
0
1
1
2
2
0
1
0
0
1
0
0
2
1
2
0
2
1
0
0
0
0
1
1
0
1
1
2
1
1
0
2
0
0
1
1
1
2
1
0
0
1
1
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
1
0
0
0
2
0
0
1
2
0
1
2
2
2
2
1
0
0
0
0
0
0
1
0
1
2
0
1
0
1
0
1
0
2
0
0
0
2
1
1
2
1
2
0
0
0
1
2
0
1
2
2
2
0
0
0
0
1
2
1
2
1
0
2
2
0
2
0
2
2
0
0
2
2
1
0
2
0
1
1
0
1
2
0
0
1
0
1
1
1
0
1
3
1
1
2
1
1
2
0
0
0
0
2
1
1
0
1
0
2
0
2
2
2
0
0
0
1
0
2
0
2
1
1
0
1
0
1
0
0
0
1
2
0
0
1
0
0
0
1
1
0
2
0
0
0
0
0
0
2
0
1
0
2
1
0
0
3
1
0
0
2
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
2
1
2
0
0
0
2
1
0
3
3
1
1
2
1
2
0
0
2
2
0
2
0
0
1
0
0
0
2
0
0
2
0
1
0
1
0
2
1
1
0
2
2
1
0
1
2
0
0
2
1
3
1
0
2
1
1
0
2
2
2
2
0
1
1
0
1
0
0
0
1
0
0
0
3
0
0
0
0
0
1
0
0
2
3
2
1
0
1
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
1
2
1
0
1
0
2
2
1
1
1
1
2
1
1
1
2
0
1
1
0
1
0
0
1
0
0
1
2
0
2
1
0
0
0
0
1
1
1
0
1
0
1
1
0
1
0
0
0
2
2
0
1
0
0
0
2
0
1
1
1
1
1
0
2
0
0
2
2
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
2
2
0
1
0
0
1
0
0
0
2
0
1
1
0
0
0
1
2
1
0
0
3
0
1
0
0
1
2
1
2
0
0
1
0
1
0
0
2
0
1
0
0
0
4
0
1
0
0
0
2
1
0
1
2
0
3
1
1
1
0
2
1
3
2
0
1
0
1
0
0
2
0
0
0
1
2
0
1
0
0
2
2
1
0
0
1
0
0
2
0
2
1
1
0
2
0
0
0
0
4
0
0
2
0
1
0
0
0
0
2
0
1
1
0
2
0
1
2
2
0
2
1
0
0
2
0
1
0
0
0
1
0
1
0
0
2
0
0
1
0
1
0
0
3
0
2
0
1
0
0
2
2
0
1
0
2
1
2
0
1
1
0
1
2
0
2
1
0
0
0
0
1
2
2
0
0
1
0
1
2
0
0
0
0
1
0
0
0
0
2
2
0
0
1
0
3
1
0
0
2
1
0
0
0
0
2
0
2
0
1
0
2
1
2
0
1
0
0
0
0
1
0
0
0
1
0
0
0
2
1
1
1
0
1
2
0
1
1
0
2
0
3
2
0
0
0
2
0
0
0
0
0
1
2
1
0
0
2
0
0
2
1
1
1
1
1
0
1
0
0
0
2
0
0
2
0
0
0
3
0
0
0
2
2
0
1
0
1
2
1
1
0
2
1
1
0
0
0
2
0
1
2
0
1
1
2
2
0
1
0
0
1
1
2
3
1
1
0
2
0
0
0
2
1
0
2
2
0
0
0
0
0
0
0
1
1
1
0
1
1
2
3
0
1
0
1
1
0
0
2
1
1
0
1
0
1
0
0
0
1
0
1
1
0
0
1
0
0
1
2
0
1
1
0
1
0
1
0
2
1
1
0
2
3
0
2
2
1
0
0
1
1
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
4
0
0
2
0
1
1
0
0
1
0
0
1
2
0
1
2
0
1
1
0
0
2
0
2
1
1
0
1
1
0
0
1
2
0
2
0
0
0
2
0
2
0
0
1
0
0
1
0
0
0
0
1
2
2
1
1
2
0
0
0
0
0
1
0
0
1
2
1
1
1
1
0
0
0
1
0
2
2
0
2
2
0
0
2
1
0
0
2
0
2
2
1
1
0
2
1
0
2
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
2
2
1
0
1
0
1
0
2
2
0
0
2
2
1
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
1
2
0
1
0
0
3
0
0
0
1
0
1
2
0
0
1
0
2
0
0
1
2
0
1
0
0
1
1
1
1
2
0
0
0
0
0
0
0
2
0
0
0
2
1
1
2
2
0
1
1
2
2
1
0
0
1
2
2
1
0
1
0
0
0
1
1
1
1
2
0
2
2
0
2
0
2
1
0
2
1
1
2
1
0
0
1
1
0
2
1
2
1
0
0
2
1
0
0
1
1
3
0
0
2
2
2
2
0
1
0
2
2
1
0
0
0
0
0
2
0
2
0
1
2
2
0
2
2
0
1
2
0
0
0
1
0
0
2
0
0
1
0
0
0
0
1
2
0
1
0
0
0
2
1
0
2
0
2
0
2
2
0
1
0
0
2
1
2
0
1
0
2
1
0
0
0
2
0
0
0
0
2
0
0
1
0
0
1
3
1
2
0
0
2
1
1
0
0
1
2
0
1
2
2
0
0
1
0
0
0
0
2
1
0
0
2
1
1
2
1
0
0
0
2
1
0
0
2
1
1
0
1
2
0
2
1
1
1
2
2
0
0
3
0
0
0
1
2
0
1
2
0
0
0
1
2
1
0
5
0
1
2
1
1
1
0
1
1
1
1
0
4
1
0
0
0
1
2
2
1
0
0
2
2
1
2
1
1
0
1
0
1
0
0
0
2
1
0
0
1
1
0
0
1
1
0
0
1
1
0
0
1
0
0
3
1
0
0
1
1
2
0
0
0
1
0
2
0
0
2
2
1
0
0
0
0
1
1
2
2
1
0
0
1
1
0
0
0
2
1
1
2
2
0
2
0
0
0
0
2
2
1
0
0
1
1
0
0
0
2
0
2
0
2
0
1
0
2
1
0
0
1
0
2
0
0
1
1
0
1
1
1
0
1
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
1
1
1
0
1
0
1
0
0
0
1
2
2
1
1
0
0
0
0
1
1
1
0
1
2
1
0
1
0
0
0
0
2
1
0
0
0
0
0
1
2
0
0
0
2
0
2
1
1
1
1
0
1
1
2
0
0
0
2
0
0
0
1
2
2
1
1
0
2
0
0
0
0
0
1
0
0
0
1
1
1
1
2
1
3
0
0
0
0
1
0
1
0
0
1
0
2
1
0
0
0
0
1
0
0
2
1
0
1
0
0
0
0
0
2
1
1
1
0
0
1
2
0
0
0
1
2
2
1
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
1
1
2
0
0
2
2
0
1
0
0
0
1
1
0
0
2
1
2
0
1
0
0
0
0
0
0
1
0
0
1
0
2
0
0
1
1
0
1
2
0
2
0
4
0
2
0
0
1
1
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
2
0
1
0
1
0
0
0
0
0
1
1
2
1
1
1
1
1
1
0
0
2
2
0
0
1
0
2
1
0
1
0
2
0
0
0
2
0
0
0
1
0
0
3
2
0
1
2
0
2
2
0
2
1
0
0
0
2
0
1
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
1
1
1
0
0
1
2
0
0
1
2
2
1
0
0
3
1
0
1
0
0
1
1
1
0
0
0
2
0
2
0
0
0
2
1
1
1
0
1
1
1
1
1
0
1
2
0
1
1
1
1
0
1
1
2
0
2
0
0
1
0
2
0
0
2
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
1
1
0
2
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
1
0
0
0
0
1
0
1
0
1
0
3
0
0
0
0
0
0
2
0
1
1
1
2
1
0
0
0
0
3
1
0
2
0
1
2
0
2
0
1
1
1
0
2
1
1
0
0
1
1
0
0
0
1
1
0
0
0
1
1
0
0
0
2
0
0
2
0
0
0
0
0
0
1
1
0
0
1
0
1
0
2
0
0
2
0
0
0
0
1
1
0
0
0
0
2
1
0
2
0
1
0
1
0
0
2
0
1
1
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
1
0
0
1
0
2
0
0
1
1
2
0
2
0
0
1
0
1
1
0
0
2
2
0
0
2
1
2
2
0
0
0
2
0
0
0
1
1
0
1
0
1
0
1
2
1
0
2
1
0
1
0
2
0
2
0
2
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
1
0
0
0
0
1
1
3
1
0
0
1
2
0
2
0
0
1
1
1
0
3
0
2
0
0
0
0
2
0
0
0
0
0
1
2
2
0
2
2
0
1
1
0
1
2
1
3
0
2
1
0
0
1
0
0
0
0
0
1
2
0
0
0
1
1
0
0
0
0
3
1
2
2
1
0
0
2
0
0
0
0
0
1
2
0
1
0
0
0
1
0
0
0
0
1
2
0
0
1
0
0
0
0
2
2
0
1
0
0
0
2
1
1
0
0
1
2
0
0
2
1
2
1
0
2
0
2
0
0
0
0
0
1
2
0
2
1
2
1
0
1
0
0
2
0
2
1
2
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
2
1
1
2
0
1
0
1
1
1
0
1
0
0
2
0
2
2
2
1
0
0
0
0
1
0
0
0
2
0
1
0
2
0
0
0
1
1
0
2
1
2
2
0
2
2
0
1
1
1
2
0
0
0
2
0
1
0
0
0
1
2
1
0
0
0
1
0
1
1
0
2
0
0
2
2
0
1
0
2
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
1
2
0
1
1
0
2
0
2
0
0
0
2
0
0
0
0
0
2
1
0
0
1
0
0
2
2
0
0
0
0
0
1
1
2
1
1
0
2
0
0
3
0
0
0
1
1
2
2
1
2
0
0
1
1
1
1
0
1
0
0
0
0
1
1
0
1
0
0
0
1
1
0
2
0
0
0
2
0
0
0
1
0
2
2
0
1
0
0
1
1
2
0
2
0
0
0
1
2
1
0
2
1
0
2
2
2
0
2
0
0
0
0
0
0
0
0
1
0
0
1
3
3
0
0
2
0
0
2
1
0
1
2
1
2
0
1
0
2
0
0
0
1
0
1
0
0
1
0
2
0
1
2
1
1
0
1
0
0
0
1
1
1
0
1
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
1
0
2
2
0
0
1
0
2
0
0
0
0
2
1
0
0
1
2
0
2
0
1
0
0
0
0
0
1
0
0
1
1
1
1
2
2
0
5
2
1
0
2
1
2
0
0
2
1
1
0
0
2
1
0
1
1
0
1
1
0
1
0
1
2
1
0
1
0
0
0
0
2
0
2
0
2
2
0
0
0
0
1
0
0
0
1
0
0
0
1
2
0
0
1
0
1
2
1
3
1
0
1
0
1
3
0
1
2
0
0
0
2
0
0
2
1
1
1
1
0
0
3
2
2
1
0
0
2
1
2
0
0
1
1
1
0
1
1
1
0
0
2
2
1
0
1
0
0
2
0
1
0
1
2
0
1
2
2
2
0
1
1
1
1
2
0
0
0
0
0
0
2
0
2
0
2
0
2
1
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
2
0
0
1
0
2
2
1
0
1
1
0
0
0
0
1
0
0
0
1
1
1
1
1
0
2
1
0
1
1
0
2
1
0
0
0
1
1
1
0
0
1
0
0
0
1
2
2
1
0
1
2
0
0
0
0
0
0
2
2
0
2
2
0
0
1
0
0
0
1
2
1
0
0
0
0
2
0
0
1
0
1
2
1
0
0
0
1
0
0
0
0
0
2
4
0
2
1
0
0
2
0
2
0
1
2
0
0
1
0
2
1
2
0
1
0
1
0
1
0
1
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
1
1
0
2
1
0
2
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
1
2
0
0
1
2
1
2
1
2
0
0
2
1
2
1
0
1
1
0
1
2
0
1
2
0
2
1
1
0
2
2
1
1
0
0
0
1
2
0
0
0
1
0
0
1
0
2
1
0
0
0
2
0
2
0
3
2
2
0
0
0
2
2
0
0
0
0
1
1
1
0
1
2
2
0
0
0
1
0
2
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
2
1
2
0
0
2
2
2
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
1
0
0
0
4
2
0
0
1
2
1
1
0
0
0
0
2
0
2
0
0
3
3
1
0
1
1
0
1
0
0
1
0
2
1
0
0
2
0
2
2
0
0
0
0
1
0
1
1
0
0
0
1
1
1
0
0
0
0
2
0
1
0
1
2
2
0
2
2
0
2
0
1
0
0
2
1
0
2
1
0
0
2
1
1
0
2
1
1
1
0
0
1
0
0
1
0
0
2
0
0
2
1
0
1
0
2
0
0
2
2
2
0
0
2
2
0
1
0
0
1
1
1
1
0
1
2
1
1
0
2
0
0
2
0
0
1
0
0
0
0
2
0
1
2
0
1
1
1
0
0
2
2
1
0
1
0
2
0
0
2
1
0
1
0
0
0
0
2
0
2
0
0
2
1
0
1
0
2
1
0
2
0
0
0
2
1
0
1
1
0
3
0
0
0
2
2
0
3
0
0
1
2
0
0
0
0
0
0
2
0
1
2
0
0
1
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
1
1
0
0
0
0
0
2
0
0
1
1
2
2
0
2
0
0
1
0
1
1
1
0
0
2
0
0
2
0
1
0
0
0
1
0
0
1
0
0
0
2
1
1
0
1
0
0
1
1
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
1
0
1
0
1
3
0
0
0
2
1
0
1
1
2
1
0
0
0
0
1
0
2
0
1
2
3
1
1
2
0
1
1
0
1
0
0
2
0
2
2
0
1
3
2
0
0
6
0
1
0
1
1
0
1
0
0
0
1
2
0
1
1
0
0
2
2
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
1
1
1
0
0
0
0
2
0
0
1
2
1
0
0
0
0
2
0
3
0
2
1
0
0
1
1
0
0
0
1
0
1
1
2
0
0
1
0
4
0
0
1
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
2
0
1
2
4
1
1
0
0
2
0
1
0
0
1
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
1
0
1
2
0
2
0
0
1
1
1
2
0
1
1
1
0
0
0
0
0
0
0
0
2
2
1
1
1
0
0
2
0
2
0
0
0
1
2
0
1
1
1
1
2
1
0
0
1
2
0
1
0
0
0
0
0
1
0
1
1
0
0
2
0
1
0
0
1
1
1
2
0
0
0
0
3
1
0
0
0
0
2
1
1
2
0
0
0
0
0
1
0
0
0
2
0
2
1
0
0
0
0
0
1
0
2
0
1
0
0
1
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
1
0
2
1
0
2
2
0
2
0
2
0
1
2
1
0
0
1
0
0
0
1
2
1
0
1
0
2
1
0
1
3
1
0
0
1
1
1
0
0
0
1
2
1
2
0
0
0
0
0
2
0
0
2
0
0
1
0
1
0
0
2
0
0
2
2
0
1
0
1
0
1
2
0
0
2
1
1
0
1
0
2
0
2
1
1
1
0
3
2
2
1
0
1
1
0
0
1
0
2
1
2
0
1
1
0
0
0
2
0
0
0
2
2
1
2
2
1
0
0
0
3
2
1
0
0
0
0
2
2
0
0
1
0
2
0
2
1
0
0
0
0
0
1
2
2
0
2
0
1
1
0
0
2
1
1
0
3
2
0
0
1
0
0
3
0
0
1
0
2
0
0
1
0
1
0
1
1
0
0
0
0
1
2
2
2
2
1
1
4
0
1
2
0
3
1
1
2
0
0
0
0
0
1
0
0
2
0
0
0
2
1
0
1
1
0
1
0
0
1
0
1
1
0
0
1
2
0
1
0
0
1
0
1
0
1
1
0
0
0
1
0
2
0
2
1
0
1
1
1
1
0
1
1
1
0
0
0
0
1
1
0
2
0
0
1
0
0
0
5
0
3
0
0
0
2
1
0
2
0
1
0
2
0
1
0
0
1
2
2
1
0
2
0
0
2
1
0
1
0
0
0
1
0
0
0
0
1
0
1
2
0
0
1
1
0
1
2
0
1
0
2
1
1
3
2
1
0
1
0
0
0
3
2
0
0
0
2
0
1
2
0
0
0
1
1
0
0
2
0
1
0
0
2
1
0
0
2
2
2
0
0
0
0
2
0
1
2
2
0
0
1
1
1
1
1
0
0
0
0
0
2
0
0
1
2
0
1
2
2
4
3
1
0
0
1
0
0
1
3
0
0
1
0
0
1
2
1
1
1
0
2
0
0
1
0
0
0
3
1
0
0
1
0
2
0
2
0
0
0
0
1
0
0
2
0
0
0
1
0
0
2
1
1
2
0
0
1
2
0
0
0
0
0
0
1
0
1
0
2
1
0
1
0
0
1
0
1
0
0
2
1
1
0
1
1
0
0
1
2
1
0
2
1
0
0
0
2
1
1
0
0
1
0
0
2
1
1
0
0
0
1
1
1
2
3
0
0
0
1
0
0
0
2
1
0
2
1
4
3
0
0
1
1
0
0
0
0
3
0
1
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
2
1
1
1
0
1
0
0
2
0
0
2
0
1
0
0
0
1
0
1
0
0
0
0
1
2
0
0
1
0
2
0
2
0
1
2
0
1
1
0
2
0
0
2
0
0
0
0
1
0
2
1
1
0
0
0
0
0
1
0
0
1
0
0
0
2
1
0
0
0
0
2
0
1
0
0
1
1
0
0
1
0
0
0
1
0
0
1
3
0
1
1
0
2
0
0
0
0
1
1
0
1
0
1
1
1
0
2
1
2
0
1
0
2
2
1
0
0
0
3
0
1
1
0
1
0
0
0
2
0
0
0
2
0
1
1
0
0
0
1
1
0
0
0
0
0
2
2
0
0
0
2
1
0
2
0
1
1
2
2
0
0
2
2
0
1
0
0
0
1
2
0
1
0
0
1
0
2
0
2
0
0
0
0
0
2
1
0
0
1
1
0
0
1
0
1
0
0
0
1
0
1
0
2
0
0
2
2
0
0
1
0
1
0
0
2
0
3
1
1
1
2
2
1
0
2
0
1
1
2
0
0
0
2
0
1
1
0
2
1
1
1
0
0
2
0
1
1
1
2
1
0
1
0
0
2
0
1
1
2
0
2
1
2
1
0
0
0
2
0
1
2
2
0
0
2
0
2
0
2
0
2
0
1
1
2
0
3
0
0
0
1
0
1
0
2
1
0
0
0
0
0
2
1
1
0
1
0
0
1
1
0
0
0
0
0
0
0
5
0
0
2
5
2
0
0
1
0
0
0
1
0
2
1
1
0
2
0
0
2
0
0
0
0
2
0
0
1
2
3
0
0
1
0
0
0
1
1
0
0
0
1
1
0
2
1
1
2
0
2
0
1
1
0
1
2
0
1
0
1
0
0
0
1
0
0
2
0
0
1
2
2
0
1
0
1
0
0
0
0
0
0
5
2
0
0
0
1
1
0
0
2
1
1
1
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
1
0
1
1
0
1
2
1
0
1
0
0
0
1
4
2
0
0
1
0
0
0
0
0
1
0
0
2
2
2
0
0
0
0
0
1
1
0
1
0
1
1
1
1
0
0
1
1
0
0
0
0
2
1
0
0
0
0
1
0
0
0
1
0
1
0
0
3
0
0
1
0
0
1
1
2
0
0
2
0
1
2
2
2
1
1
0
2
2
2
1
0
0
0
0
2
2
0
0
2
0
0
0
2
2
1
0
0
0
1
0
1
1
1
1
1
1
1
0
2
1
0
2
1
0
1
2
0
2
1
0
1
1
2
0
2
1
0
0
0
0
1
1
0
1
2
0
0
0
0
0
2
1
1
1
0
0
2
1
0
2
2
0
0
0
2
2
0
1
0
0
1
2
0
1
0
2
1
0
2
0
1
0
0
0
1
0
1
1
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
1
1
6
1
2
0
1
0
1
0
1
0
0
0
1
0
1
0
2
0
0
1
1
1
0
0
0
1
0
2
2
0
2
0
0
0
2
1
2
0
0
1
0
1
0
2
1
0
3
2
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
1
2
1
0
2
1
0
0
2
2
1
1
0
0
0
0
1
0
2
1
0
0
0
2
0
0
1
1
0
0
0
0
1
1
0
0
1
1
1
0
0
0
1
2
0
0
0
1
0
0
1
0
1
2
1
0
0
0
0
2
0
0
0
0
0
2
1
0
0
1
0
0
0
3
2
0
0
0
0
1
2
2
0
0
0
2
0
3
0
0
0
1
0
0
0
1
1
0
0
2
1
0
0
0
0
2
2
0
0
2
1
1
0
1
0
2
0
0
1
2
1
0
0
2
1
1
2
2
1
1
0
0
1
1
1
1
0
1
1
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
1
0
2
0
2
0
2
1
0
1
1
0
0
2
2
2
0
2
2
2
1
1
2
0
2
2
0
0
2
2
2
0
1
2
0
1
2
0
1
0
0
1
2
0
0
0
0
0
1
0
3
0
0
2
0
1
2
1
3
2
2
1
0
1
0
1
1
0
0
0
0
1
3
1
1
0
2
0
0
0
1
0
1
0
1
2
0
2
2
2
0
1
0
0
0
0
0
0
0
4
1
1
0
1
1
1
2
0
1
0
2
1
0
0
0
1
0
1
0
1
2
3
1
1
1
0
1
0
0
0
0
1
2
0
1
0
0
0
0
1
1
1
0
0
0
0
1
0
1
0
1
0
0
0
1
1
0
2
1
0
2
0
1
2
0
2
2
0
0
1
0
0
0
1
0
0
6
0
0
0
1
2
0
2
0
1
2
0
3
0
0
1
1
0
2
0
0
0
1
1
2
0
0
1
2
2
1
0
1
1
0
1
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
1
1
1
0
0
2
1
1
1
0
0
0
0
0
1
1
0
1
2
0
0
4
2
0
0
0
2
0
0
2
0
0
0
1
0
0
2
0
2
0
0
0
0
1
0
0
1
1
1
0
0
2
0
2
0
0
0
3
0
1
1
0
2
1
2
1
0
0
2
0
2
0
0
2
2
3
0
1
0
2
2
0
0
0
2
1
0
1
1
0
0
2
1
0
1
0
0
1
1
0
0
0
0
1
2
1
0
0
0
2
0
0
0
2
2
1
0
2
0
1
1
2
1
0
1
1
1
2
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
2
0
0
2
2
1
0
1
1
0
0
0
1
0
0
0
0
1
0
1
0
1
2
2
1
0
2
0
0
0
0
2
0
0
1
0
2
0
0
2
1
2
0
0
1
0
0
0
0
1
0
2
0
1
0
2
0
1
0
0
0
0
0
0
0
1
2
0
1
0
0
0
3
1
1
2
1
1
1
1
0
0
1
0
1
1
2
0
0
1
0
1
1
0
2
0
0
1
0
1
3
0
0
0
2
0
1
0
1
0
1
0
0
1
1
0
1
1
0
1
0
0
2
0
0
0
1
1
1
1
1
0
1
1
0
0
0
0
2
1
0
1
2
0
1
1
2
0
1
2
2
1
1
0
0
0
0
2
1
0
2
0
0
0
0
0
1
2
1
0
0
0
0
1
2
0
1
1
1
2
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
2
2
1
0
2
1
1
1
1
0
0
0
1
2
1
0
1
1
1
2
1
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
1
0
0
0
2
0
0
2
0
0
0
1
1
0
0
0
0
3
2
1
0
0
2
2
0
1
0
1
0
2
0
1
1
2
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
1
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
2
1
0
0
2
0
2
2
0
0
1
0
2
2
1
0
0
1
1
1
1
0
2
1
0
1
0
0
0
1
1
2
0
2
0
2
0
4
4
0
1
0
0
0
3
0
0
0
1
0
0
0
0
0
2
0
0
4
0
0
0
0
2
0
2
0
0
0
2
0
0
0
2
1
2
1
0
0
0
2
0
0
1
0
2
2
0
0
1
0
0
0
1
0
0
0
2
1
2
0
1
0
0
0
0
0
0
5
0
2
1
3
2
2
0
1
2
2
2
0
0
0
1
0
1
0
0
2
0
1
0
0
1
0
0
0
2
1
1
1
1
0
1
1
0
1
2
2
0
0
2
0
2
0
0
2
0
1
0
6
2
0
0
1
0
2
1
0
0
1
1
2
0
1
2
0
1
1
2
1
0
1
0
0
1
0
0
1
0
1
1
0
0
1
0
0
1
3
1
2
1
0
1
0
2
1
0
2
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
2
2
0
0
0
2
1
0
1
1
0
1
0
0
1
1
0
0
1
2
1
0
2
1
1
1
0
2
1
0
0
1
0
2
1
1
2
2
0
2
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
1
2
1
1
1
0
0
2
0
2
3
2
1
1
1
0
0
0
1
0
0
0
0
2
0
1
0
2
0
2
0
0
0
2
1
0
0
2
0
0
0
2
1
0
1
1
0
1
0
0
0
1
0
1
1
0
2
0
0
1
0
0
1
1
1
0
0
1
1
1
0
1
1
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
4
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
2
0
2
2
0
0
1
2
1
2
0
1
0
0
1
0
0
1
0
0
1
1
0
0
1
0
0
0
1
1
0
1
2
1
2
1
0
1
1
1
0
0
0
0
2
2
0
0
0
0
0
2
1
0
0
1
1
0
1
0
0
2
1
0
0
1
0
1
0
1
0
2
1
2
1
0
0
1
0
1
2
1
0
0
2
3
0
0
0
0
0
2
1
1
1
0
1
0
2
1
0
0
2
0
1
2
0
0
0
0
0
2
0
2
0
1
1
0
2
2
2
0
0
2
1
0
1
2
2
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
1
0
1
2
1
2
0
1
0
0
2
0
1
0
2
2
0
0
0
2
0
0
2
1
0
1
1
0
2
1
1
1
2
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
2
1
0
0
0
0
0
1
1
0
1
1
2
0
0
1
0
2
1
0
1
0
0
0
3
1
0
1
0
2
0
1
0
0
0
2
1
2
2
0
2
1
0
0
2
0
1
0
0
0
0
0
0
0
0
2
3
1
2
0
0
2
0
0
1
0
1
0
2
0
1
0
1
1
0
0
0
0
0
0
0
2
0
0
1
1
2
0
0
2
0
0
1
0
1
1
1
0
2
1
0
2
2
0
0
1
1
0
0
1
2
0
2
0
1
2
0
0
0
0
0
1
1
0
1
1
0
1
0
2
1
2
0
1
1
0
8
1
0
0
2
2
0
6
0
0
1
0
1
0
0
0
1
1
1
0
1
2
0
2
0
1
1
2
0
0
2
1
0
0
0
2
0
1
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
1
1
0
2
0
1
2
15
0
2
0
0
2
1
0
0
0
1
0
0
1
2
2
0
0
1
0
1
0
0
0
1
0
0
1
0
1
1
2
0
0
0
0
2
0
0
1
0
1
0
0
0
1
0
0
1
2
0
0
1
1
0
0
2
1
1
0
2
0
0
2
1
1
0
0
1
1
0
2
0
2
0
2
0
1
0
0
1
0
3
0
0
2
1
1
1
0
1
1
1
1
1
2
0
1
1
1
1
2
1
0
0
2
0
0
0
5
1
0
0
0
0
1
0
2
1
0
1
2
0
2
0
0
0
0
2
0
2
1
0
0
0
0
1
0
0
0
0
1
0
0
1
1
2
0
0
2
2
1
0
1
2
2
2
2
0
0
0
0
0
1
1
0
2
1
1
1
0
0
0
0
2
2
1
1
2
2
1
2
1
0
2
2
0
0
1
0
1
0
2
0
0
1
1
2
0
2
0
0
0
1
2
1
2
0
1
0
0
2
0
0
2
1
2
1
2
0
0
1
1
0
1
2
0
2
1
1
1
1
1
1
0
0
0
0
0
2
0
2
1
2
2
0
0
1
1
2
0
0
1
1
0
1
1
0
2
2
0
1
0
1
1
3
0
1
0
1
0
2
2
2
0
1
2
3
2
1
1
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
1
0
1
1
2
0
0
0
1
1
1
2
1
1
1
2
0
0
0
2
0
0
1
1
1
0
1
0
1
2
0
1
1
2
0
2
1
1
0
0
1
1
2
0
2
0
1
0
0
1
1
0
0
0
0
0
1
2
2
0
0
0
2
0
0
1
0
0
1
0
2
1
0
0
0
0
0
1
1
0
0
1
3
0
0
1
0
0
0
0
0
1
0
2
0
0
1
1
2
1
0
0
1
2
0
0
0
0
0
0
0
0
2
1
2
1
0
1
0
0
2
0
0
1
0
2
0
0
1
2
0
0
2
1
0
0
0
0
0
1
1
0
0
0
2
0
2
0
1
0
0
0
1
0
0
0
0
0
1
1
0
1
3
3
1
1
1
2
2
0
1
0
0
0
1
1
0
1
0
0
2
0
0
0
0
0
3
2
1
2
0
1
2
0
2
1
0
1
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
2
0
2
2
0
0
2
2
0
0
0
1
2
0
1
0
2
1
0
0
1
0
0
1
0
0
2
1
2
2
2
0
1
0
0
1
1
2
2
0
1
0
1
0
0
1
0
1
0
0
0
0
2
0
0
1
0
1
1
1
2
0
0
0
2
1
0
0
1
1
0
0
0
3
1
2
2
0
0
0
0
0
0
0
0
0
2
5
0
0
1
0
0
0
0
1
0
2
1
2
0
1
1
0
2
0
0
1
0
0
1
2
0
2
0
1
0
0
1
0
0
1
0
1
2
1
2
2
0
0
0
0
1
0
0
4
1
0
0
0
1
0
0
1
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
2
2
0
3
0
1
0
2
1
1
2
0
0
0
0
0
1
1
0
2
0
0
0
0
2
0
1
0
0
0
2
3
0
1
0
0
0
1
3
1
2
0
0
0
0
0
0
0
1
0
0
1
2
1
1
0
0
0
0
0
0
0
0
1
1
0
1
1
1
0
0
2
1
5
2
0
0
0
0
1
1
0
1
3
0
0
1
0
2
0
4
0
1
1
1
0
0
3
0
0
0
0
0
1
0
2
1
0
0
2
2
1
0
1
0
0
1
2
0
0
0
0
1
1
0
0
1
1
1
0
0
2
1
1
2
0
0
0
0
2
0
0
0
2
0
1
1
0
0
0
1
0
0
2
0
0
1
0
2
1
0
0
2
1
1
1
1
0
1
1
2
0
0
0
1
0
2
2
0
0
1
0
0
1
3
1
1
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
2
0
1
0
0
1
1
0
1
0
0
0
2
2
1
0
0
1
0
1
3
0
1
0
2
0
0
0
0
2
2
0
2
3
2
0
0
1
0
0
0
0
2
0
0
2
0
0
2
1
1
0
1
2
1
2
0
1
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
2
0
0
0
0
2
1
2
1
0
0
1
2
1
0
1
0
3
1
0
2
1
0
2
1
2
2
0
1
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
2
0
0
0
2
1
2
0
0
1
0
0
1
1
0
1
0
1
1
0
1
1
1
4
0
2
2
2
1
2
2
2
1
2
1
0
0
0
2
0
0
0
0
0
0
2
1
0
1
2
0
0
1
1
0
0
1
1
2
0
0
0
1
0
2
0
2
1
0
2
2
0
0
1
0
1
1
0
2
1
0
2
1
2
1
2
2
0
1
1
2
1
0
0
1
1
0
0
0
1
0
1
1
1
1
1
3
0
1
0
0
1
1
0
0
2
1
0
1
0
1
0
2
0
1
0
1
1
0
1
0
2
2
1
0
1
0
0
1
0
0
1
1
1
1
1
0
0
2
0
0
0
2
0
2
0
0
0
2
2
4
0
1
1
0
0
0
2
0
2
0
1
1
0
1
0
0
3
2
1
0
0
1
0
0
0
1
0
0
1
2
3
0
0
2
1
0
0
0
0
2
0
2
0
0
1
0
0
1
1
1
0
0
0
0
1
0
0
2
2
2
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
1
0
2
2
1
2
1
0
1
1
2
0
1
0
0
3
1
2
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
2
1
0
0
1
0
0
2
1
0
0
0
2
0
2
0
0
0
0
0
1
0
1
0
0
0
2
2
0
1
1
0
1
2
1
0
2
1
1
1
0
0
0
0
0
2
1
0
0
1
1
0
0
1
2
0
1
1
2
0
2
1
0
1
0
1
0
0
2
2
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
1
1
2
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
1
1
2
0
0
0
1
2
0
0
0
0
0
1
1
0
2
0
1
1
0
2
0
2
2
1
1
1
0
2
0
0
0
0
0
0
1
1
1
0
0
3
1
1
0
0
0
0
0
2
0
2
0
1
0
0
1
1
1
1
2
0
0
2
0
2
2
0
0
0
0
0
0
0
0
2
3
0
0
0
2
1
1
1
1
1
1
0
1
1
0
1
0
2
2
0
1
2
0
2
1
1
0
1
0
0
1
0
0
2
0
2
0
1
2
2
2
2
2
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
2
1
2
1
2
0
0
1
1
0
2
1
2
0
1
1
2
0
3
2
0
0
0
2
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
2
1
1
0
0
0
2
2
1
0
0
0
0
1
1
1
1
1
0
0
1
1
2
1
2
0
1
0
0
2
3
0
0
1
1
1
1
2
0
0
0
2
0
1
0
0
1
4
1
0
1
1
1
0
2
0
0
1
1
0
2
2
1
1
1
2
0
2
0
1
0
1
1
0
0
2
0
0
2
2
0
1
1
0
0
2
1
0
0
0
0
2
0
0
2
3
1
2
1
0
0
0
0
1
0
0
1
2
1
0
1
1
2
0
0
2
1
2
1
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
2
0
1
0
1
0
0
0
1
0
0
0
1
0
2
0
0
0
0
1
1
3
0
2
0
0
1
0
0
0
1
0
0
1
1
0
0
2
2
1
3
0
1
1
1
2
0
0
2
0
0
0
1
1
0
1
0
0
2
0
0
0
1
0
1
0
1
0
2
0
0
2
0
0
0
1
0
0
0
0
1
1
0
1
0
2
0
0
1
1
0
0
2
2
0
3
0
0
1
0
2
1
0
0
0
0
2
2
0
1
0
2
0
2
2
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
2
1
0
1
1
1
0
0
2
0
0
0
2
0
1
2
1
0
2
0
0
1
2
1
1
0
1
1
0
0
0
0
1
1
1
0
0
0
0
0
1
2
1
0
0
0
0
0
3
0
0
0
0
1
0
1
1
0
1
1
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
1
1
0
0
1
1
0
2
0
1
1
0
2
0
1
1
1
2
0
1
0
1
0
2
2
0
0
0
1
0
1
0
0
0
2
0
2
1
0
0
0
1
0
1
0
0
0
1
0
2
0
1
2
0
1
1
2
2
0
0
1
0
0
0
0
1
3
2
2
0
3
0
0
0
1
1
2
0
2
1
0
3
0
0
0
2
2
0
0
0
0
2
0
0
1
0
0
0
0
1
1
1
0
2
1
1
0
2
0
2
1
1
0
0
0
1
2
0
0
1
0
1
2
1
1
0
0
0
2
0
0
0
1
0
2
1
0
1
0
0
2
1
0
2
0
0
0
2
0
1
0
0
1
1
0
1
1
0
0
0
0
0
1
1
0
0
1
1
2
0
0
1
1
0
0
1
1
2
0
0
2
0
0
2
0
1
1
0
0
1
0
2
2
0
0
1
0
1
1
1
0
0
0
0
2
0
0
0
0
2
2
2
1
0
0
1
2
0
0
1
0
0
1
1
1
1
1
0
1
0
2
1
0
2
2
0
0
0
0
0
1
2
1
0
0
0
0
0
0
2
0
0
1
0
0
2
1
1
1
0
1
2
0
1
2
0
0
1
1
2
1
2
0
2
2
2
0
1
0
2
2
2
1
0
0
1
0
1
1
1
1
0
1
0
1
3
2
1
1
0
2
0
1
2
0
0
1
1
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
1
1
0
1
1
1
0
0
0
0
1
2
2
0
0
0
0
0
1
0
0
2
0
1
0
0
0
2
2
1
1
1
1
0
0
1
0
0
2
2
0
0
1
2
2
0
0
0
0
0
0
0
1
2
0
0
2
1
0
0
0
1
1
0
0
1
0
3
0
1
0
2
1
0
0
2
0
1
0
0
0
1
0
2
0
0
1
1
2
0
1
0
2
0
0
0
1
2
0
1
0
0
0
1
0
2
0
0
1
2
2
1
1
1
1
0
0
2
2
0
0
2
0
2
0
0
0
1
0
0
0
1
0
0
2
2
0
1
0
0
0
2
0
2
2
0
0
0
0
0
0
1
0
3
1
1
0
3
0
2
2
1
2
0
2
0
1
1
0
2
0
1
0
2
2
0
0
0
0
1
1
0
0
1
1
0
1
0
0
0
2
1
0
0
0
1
0
1
0
1
0
1
0
2
0
0
1
1
0
2
0
2
4
0
0
2
0
2
0
0
0
0
1
1
1
2
1
0
0
0
1
2
1
0
0
0
2
1
0
2
0
2
1
0
0
0
0
1
0
1
0
0
1
0
2
0
0
2
0
0
0
0
0
1
0
1
0
1
0
0
2
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
3
2
2
1
1
0
3
0
0
0
1
2
0
2
2
2
1
2
1
0
0
1
0
0
0
0
1
1
0
0
0
2
1
0
1
0
1
0
1
1
0
0
0
1
0
0
0
1
1
1
2
0
2
2
2
0
0
0
0
2
1
2
0
1
0
1
2
0
0
1
1
0
1
0
2
0
1
0
2
2
2
0
0
2
0
2
0
1
1
0
0
1
1
1
1
1
1
1
2
9
0
0
1
0
0
0
0
2
1
1
3
3
2
1
1
0
0
0
2
0
1
0
1
2
0
0
0
1
0
0
1
2
2
0
2
0
2
0
1
2
0
1
0
0
0
0
1
0
1
0
0
1
2
1
0
1
2
0
2
1
2
0
1
0
2
0
0
0
1
2
0
0
0
2
1
1
0
0
0
0
0
2
2
1
1
1
2
1
2
2
2
0
0
1
1
0
2
0
3
1
0
2
1
0
0
0
0
0
2
2
2
1
0
2
2
1
1
0
0
2
0
0
0
0
1
2
1
0
3
0
0
2
0
0
0
0
0
0
0
0
1
1
0
1
0
0
2
0
2
1
1
0
1
2
0
0
0
0
0
1
0
0
0
0
1
1
1
1
0
2
0
1
0
1
1
0
1
2
0
0
0
0
2
1
3
1
1
1
2
1
2
1
0
0
1
0
2
2
0
1
1
0
0
2
1
0
0
0
0
1
0
2
2
0
0
0
0
0
1
1
0
0
2
0
0
0
0
2
0
0
1
0
0
1
1
0
0
0
1
0
1
0
0
2
0
0
0
2
0
0
2
0
0
1
0
0
1
0
2
0
0
0
1
0
0
0
0
2
2
2
0
0
0
0
0
1
0
1
0
0
1
1
1
4
1
0
0
1
0
0
2
0
1
2
0
2
0
1
1
0
0
2
0
0
2
2
1
0
0
2
0
0
0
3
0
0
0
0
0
2
1
2
0
1
0
0
0
0
2
2
2
2
1
0
0
1
0
1
0
2
0
2
2
0
2
0
2
0
1
2
2
2
0
0
0
0
0
0
0
1
0
1
0
1
1
1
2
1
2
1
1
0
1
5
2
1
0
1
3
0
2
0
1
1
0
1
0
2
0
0
1
0
0
1
1
1
2
1
0
0
2
1
0
2
0
0
0
0
0
0
2
0
0
3
0
2
1
0
0
0
0
0
2
0
3
2
0
0
1
1
0
1
0
0
0
0
2
0
0
0
1
0
1
2
2
0
0
1
3
3
2
1
0
1
0
2
0
0
0
0
0
2
0
2
0
2
2
0
0
0
1
0
0
2
1
0
0
1
1
1
0
0
1
0
2
1
2
2
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
1
2
3
0
0
3
2
2
0
0
2
0
2
0
0
1
2
0
2
1
0
0
0
0
1
1
0
1
0
1
1
1
0
0
2
2
0
2
1
0
1
1
0
2
0
0
0
1
0
1
1
2
0
0
0
0
0
1
1
0
0
1
1
1
1
1
1
2
0
1
1
0
0
2
0
0
0
2
0
0
0
2
0
1
0
0
1
2
0
0
1
1
0
1
1
1
1
1
2
0
0
1
1
1
0
0
0
1
0
3
0
2
3
0
2
0
1
1
2
2
0
1
0
0
1
0
2
0
0
2
0
0
1
0
1
1
1
0
0
1
2
1
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
1
0
1
0
1
0
1
2
1
1
0
2
0
0
0
2
2
0
1
0
1
1
0
1
0
0
0
1
2
0
0
0
1
1
1
0
0
1
3
0
0
2
0
1
0
1
2
0
0
0
0
0
1
0
2
2
0
1
1
0
1
2
1
0
1
0
1
1
0
1
0
2
2
1
0
0
2
0
6
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
2
2
0
1
2
0
1
1
0
1
0
0
0
2
0
2
1
2
0
2
1
2
0
0
0
2
0
2
0
0
1
0
2
0
0
0
0
0
0
1
2
0
0
0
3
0
2
1
0
1
1
1
0
1
1
0
1
0
2
0
0
0
0
0
0
0
1
0
3
2
0
2
1
0
0
2
2
0
0
1
2
2
1
0
0
2
0
0
3
0
0
0
0
0
2
0
1
1
0
2
0
0
2
1
2
1
1
1
0
0
2
0
0
0
0
1
1
0
1
0
2
2
1
0
1
1
2
0
0
1
3
0
1
0
0
2
2
0
0
1
1
2
0
2
1
0
0
1
1
1
2
0
0
0
0
2
0
0
0
2
0
2
0
1
2
2
1
0
2
0
2
1
0
2
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
1
0
1
1
0
0
1
1
0
0
0
1
1
0
0
0
1
0
1
1
0
3
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
2
1
0
2
0
0
0
1
1
0
2
0
0
1
3
0
0
2
0
1
0
0
2
2
0
0
0
2
2
0
1
2
2
1
3
1
0
2
2
0
0
2
1
0
0
2
1
0
0
0
2
2
0
0
1
2
0
0
0
1
0
0
0
0
0
1
0
0
1
2
0
0
0
1
2
0
0
0
0
1
1
0
2
0
2
2
0
0
1
2
0
0
0
2
2
0
0
1
1
0
1
0
1
2
0
1
2
0
0
0
3
2
2
1
0
0
1
1
2
2
0
1
2
0
0
2
0
0
0
2
1
0
0
2
2
0
1
0
2
0
2
0
0
1
0
0
1
2
0
0
1
0
0
0
0
2
0
1
0
2
2
1
1
0
2
0
1
1
0
2
2
0
0
1
1
0
1
0
0
1
2
0
0
1
0
1
2
1
1
0
0
1
0
1
4
0
0
0
0
0
1
0
0
0
1
0
1
0
0
2
0
0
0
0
1
0
0
0
1
2
1
0
2
3
0
0
0
1
0
0
0
1
2
4
0
2
0
2
2
2
1
0
3
0
1
0
0
1
0
2
0
0
2
0
3
2
2
2
0
0
0
2
1
1
0
0
1
0
1
0
1
0
0
2
1
0
2
0
0
2
0
1
2
0
0
0
1
1
0
0
0
1
0
0
0
0
2
1
1
0
0
2
1
0
1
0
0
3
0
2
2
0
0
0
0
2
6
0
0
1
0
1
0
2
0
1
0
0
0
0
2
0
1
0
2
1
1
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
2
2
1
0
2
6
0
0
0
1
1
0
0
0
1
0
0
0
2
1
1
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
1
1
0
1
0
0
0
2
0
0
0
2
0
0
0
0
1
1
2
0
1
0
0
1
4
0
1
2
0
0
2
0
0
0
2
0
1
0
1
0
1
0
2
0
2
1
2
1
2
2
1
1
1
1
0
0
1
0
0
1
1
1
0
2
0
0
1
1
2
0
2
1
0
1
2
0
0
0
1
2
0
0
1
0
0
2
1
0
0
0
2
0
0
1
0
0
0
2
0
0
1
2
2
2
0
0
1
0
2
0
0
1
1
0
1
0
1
1
0
0
0
2
0
1
1
1
2
0
0
0
1
0
1
0
1
2
1
1
0
1
1
0
0
0
1
0
2
2
1
2
1
1
0
1
2
0
0
0
0
0
2
2
1
1
0
0
0
2
1
0
2
0
1
1
0
0
0
2
2
2
0
1
1
2
1
0
2
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
2
1
2
0
0
2
0
1
2
1
0
0
0
1
0
1
2
0
0
0
1
2
1
2
1
2
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
2
1
0
0
2
2
2
0
0
0
3
1
1
0
0
1
0
1
0
2
1
0
0
0
0
0
2
0
1
3
0
2
0
2
2
0
1
1
0
3
4
0
0
1
1
4
2
1
0
1
1
0
1
0
0
1
0
0
0
0
4
0
2
2
0
0
1
2
0
2
0
2
0
0
0
2
2
1
0
3
2
1
0
0
1
0
2
2
1
1
3
7
1
0
1
0
1
0
0
1
2
1
2
0
0
2
0
0
2
0
0
1
1
2
0
1
2
0
0
1
2
2
0
2
0
0
0
1
0
2
0
2
2
1
2
0
1
0
0
2
0
1
0
0
1
2
0
1
0
0
2
0
2
1
0
2
2
0
1
1
1
0
0
1
1
0
1
0
0
2
0
0
1
0
1
0
1
2
0
0
1
2
4
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
1
1
1
2
2
1
0
0
2
0
0
2
0
1
0
2
0
0
0
1
1
0
0
2
0
1
0
1
3
1
0
2
2
0
2
2
0
0
1
1
0
1
0
0
2
1
3
1
0
1
0
2
0
0
1
0
2
0
0
0
1
1
1
0
1
2
0
0
1
0
0
0
0
0
1
0
0
2
0
2
0
2
2
1
2
1
1
2
0
2
2
0
0
2
0
1
1
1
0
2
0
2
1
1
2
1
0
1
2
0
0
0
2
0
1
1
0
0
2
0
0
2
1
2
0
1
0
0
0
0
2
1
0
2
2
1
2
0
0
1
2
0
0
1
5
0
0
0
0
0
2
0
0
1
0
3
0
1
1
2
0
2
0
0
2
0
1
2
1
0
0
0
2
1
1
1
2
0
0
0
0
2
1
2
0
1
0
1
1
2
1
2
0
2
0
0
1
0
0
0
0
0
1
0
1
0
2
1
2
1
0
0
1
0
2
0
2
0
0
0
0
3
0
0
1
0
1
0
3
0
1
0
1
2
2
0
1
1
3
0
0
0
1
1
0
0
1
1
2
0
0
0
2
0
2
0
2
1
0
0
1
0
1
0
1
0
2
0
1
0
2
0
2
0
1
0
1
1
0
0
0
0
3
1
1
1
0
0
0
0
1
1
1
1
1
0
0
1
2
1
0
0
1
1
1
0
0
3
0
2
2
1
1
2
1
1
1
1
0
0
2
2
1
0
0
0
0
3
0
0
0
2
2
0
0
0
1
0
1
0
1
0
1
1
2
0
2
2
0
0
2
2
0
1
0
1
0
0
1
2
2
1
1
0
0
0
0
2
0
0
0
0
0
1
1
0
2
2
0
0
1
0
2
0
0
1
0
0
2
0
1
0
0
0
2
1
0
1
0
1
1
0
0
1
1
0
0
1
2
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
2
1
0
0
1
0
1
2
0
2
1
2
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
4
0
0
0
2
0
1
2
0
2
2
0
1
0
1
0
0
0
0
0
1
2
0
0
2
0
0
1
0
0
1
0
2
2
0
0
1
1
0
0
0
0
2
1
0
2
1
1
0
1
1
0
2
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
1
0
0
1
0
4
1
0
1
1
1
1
1
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
3
0
1
2
0
2
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
1
1
1
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
1
2
1
1
0
1
1
2
0
1
0
0
1
1
1
0
2
1
0
1
0
0
1
0
0
2
0
1
1
2
0
1
0
0
0
0
1
0
0
0
0
0
0
1
2
0
1
1
0
0
1
1
0
0
2
1
0
2
0
2
1
1
0
0
0
1
0
0
0
0
0
2
2
1
0
0
0
0
1
1
1
1
0
0
2
0
2
2
0
4
0
0
3
2
0
0
1
0
2
0
0
1
2
2
0
1
3
0
1
2
0
1
0
2
1
2
4
0
0
0
0
0
2
2
1
0
0
0
0
0
0
1
1
0
2
0
3
0
0
0
0
0
1
1
2
1
0
1
0
0
0
2
1
1
1
0
1
7
1
0
0
1
2
3
1
1
1
0
1
1
0
0
0
0
1
0
2
0
0
0
0
0
1
2
2
0
0
1
1
0
0
0
1
0
0
0
1
0
0
1
0
1
1
2
0
1
2
0
0
0
1
2
1
0
0
0
3
0
1
0
0
0
0
1
2
1
0
2
1
2
1
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
2
0
2
1
1
0
2
1
1
0
1
2
1
2
0
1
1
0
0
2
0
0
0
0
2
1
0
1
2
0
0
1
0
0
0
1
0
0
1
2
0
0
2
2
0
2
1
1
0
0
0
2
0
1
2
0
0
0
1
0
2
2
1
2
1
0
0
2
0
1
0
0
1
0
1
1
2
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
2
7
1
0
2
1
0
2
0
2
1
2
1
2
0
1
2
1
1
3
0
0
0
0
1
0
0
0
0
1
1
1
0
1
0
1
1
0
2
2
1
1
0
2
1
0
0
1
2
1
0
0
1
0
0
0
0
0
2
0
0
0
0
1
1
1
0
0
2
2
2
0
1
2
0
1
2
1
1
0
4
1
0
0
2
2
0
2
0
0
0
0
3
1
0
1
0
0
1
0
0
0
0
2
0
2
0
0
0
0
3
0
2
2
0
2
1
0
0
0
0
0
0
0
0
1
2
1
2
0
1
4
2
0
0
0
0
0
0
0
0
2
0
1
0
1
2
0
0
0
0
1
0
1
0
1
2
0
2
0
0
2
0
2
0
1
1
1
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
2
2
2
0
1
0
0
0
0
0
2
0
1
2
0
1
3
0
0
1
1
2
0
0
0
2
1
0
1
0
0
1
2
0
0
2
0
1
0
1
1
0
2
0
0
2
1
2
2
0
0
1
0
0
1
0
2
0
0
1
1
0
0
0
0
0
0
0
1
0
1
2
0
0
0
1
2
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
1
0
0
0
1
1
0
2
0
0
0
0
1
0
0
2
2
0
0
1
1
2
0
2
0
1
0
0
1
1
0
0
0
0
2
2
1
0
1
1
0
1
1
0
0
0
0
2
2
2
0
0
0
2
0
1
0
0
0
0
1
1
0
1
1
2
1
0
2
1
2
2
0
0
1
2
2
0
2
1
0
1
0
0
0
2
1
2
1
1
1
0
0
1
0
1
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
2
0
1
1
0
2
0
0
1
0
0
2
2
2
0
0
0
1
0
0
0
2
0
2
1
0
0
3
0
0
0
1
0
0
2
0
0
0
1
1
1
1
1
0
0
0
2
2
1
0
2
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
1
1
0
0
0
2
0
2
0
0
2
0
1
0
0
1
2
0
0
2
1
0
1
2
0
1
2
0
2
0
1
2
1
2
0
1
2
1
1
0
0
0
1
0
1
4
1
0
1
1
1
1
0
2
1
1
0
0
0
0
1
0
0
2
2
0
2
0
1
0
1
2
0
1
0
2
2
1
2
0
0
0
1
0
1
0
1
2
1
2
0
0
1
1
0
0
0
1
0
2
2
1
0
0
0
0
0
2
0
0
0
0
0
1
2
1
0
0
0
1
0
1
2
1
0
0
1
0
1
0
1
1
0
2
2
2
0
2
1
1
0
0
0
1
2
0
0
1
1
1
0
0
0
0
0
0
1
2
1
0
0
1
1
1
1
2
0
0
1
1
0
0
1
0
0
2
2
0
1
0
2
1
2
1
0
0
2
0
0
1
1
3
0
2
0
0
1
1
2
2
2
1
1
0
1
1
0
1
2
1
0
0
0
0
1
0
1
0
2
0
1
0
0
0
2
2
2
0
2
1
2
6
1
0
0
2
1
0
1
2
2
2
0
1
0
1
2
3
0
2
2
1
0
0
0
0
1
0
0
1
2
2
0
2
2
0
0
1
1
0
2
1
1
0
2
0
0
1
0
1
0
1
1
0
0
0
0
0
0
1
0
1
1
2
2
3
0
0
1
0
2
1
2
1
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
2
1
0
1
1
1
1
1
0
0
2
2
0
0
2
0
0
1
0
3
0
1
0
0
1
1
4
2
0
0
2
0
0
0
2
2
1
1
0
0
1
2
2
1
0
2
0
0
1
0
0
0
0
0
0
2
0
1
1
0
2
3
0
1
0
3
0
0
0
0
2
0
1
0
0
0
0
0
1
0
1
2
1
0
0
0
0
0
2
0
0
1
0
2
2
1
1
1
0
1
1
1
0
0
0
2
0
1
0
1
0
1
1
0
2
1
0
1
0
0
2
1
1
1
1
0
2
2
2
1
2
0
2
0
1
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
2
0
1
2
0
0
2
0
0
2
2
0
0
1
0
1
1
1
0
2
0
0
1
0
0
2
1
1
1
2
0
0
0
0
0
0
1
2
1
2
2
1
1
0
1
1
0
0
1
3
2
0
0
0
2
2
0
2
0
1
1
1
1
2
0
2
0
1
0
0
0
2
2
0
1
1
2
1
0
0
1
2
0
0
3
0
3
0
0
0
0
0
1
2
2
0
1
1
0
2
2
1
1
2
0
0
0
1
1
0
0
1
1
1
1
1
0
0
1
0
1
0
0
1
2
0
0
0
1
0
0
1
0
0
0
0
2
2
1
0
2
1
0
1
1
1
2
2
0
0
0
0
0
0
2
1
2
0
1
2
1
1
0
0
2
0
0
0
2
0
1
0
1
1
2
0
0
1
2
0
1
0
1
0
2
2
0
0
1
1
0
2
0
0
2
1
0
1
1
2
0
0
0
1
2
1
2
1
4
1
0
2
1
0
0
2
0
1
1
0
0
1
0
2
2
2
0
2
0
0
1
0
0
0
1
2
0
0
1
2
0
1
2
2
1
2
2
0
0
0
0
0
0
1
0
1
0
0
2
0
1
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
1
1
1
0
0
1
1
1
1
1
1
0
0
1
1
0
2
0
2
2
2
0
0
2
0
0
1
1
0
2
2
2
0
1
0
0
0
0
0
0
0
2
1
1
1
0
2
1
1
2
1
1
0
1
0
0
0
0
0
0
1
2
0
0
0
0
5
0
1
0
2
0
2
1
0
0
2
0
1
0
1
1
2
0
0
0
1
0
0
1
1
0
0
1
1
1
2
0
1
2
2
0
1
0
0
1
0
0
2
0
0
0
2
0
0
1
0
0
1
0
1
1
0
2
0
2
2
1
0
0
2
1
0
1
0
1
1
0
2
2
0
1
1
0
0
1
1
0
0
1
0
2
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
2
0
0
0
1
2
1
0
0
1
0
0
1
0
2
0
1
1
2
2
0
0
1
2
2
2
1
0
0
1
0
2
0
0
1
0
1
0
1
2
2
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
1
2
2
0
0
0
0
3
3
2
2
2
1
1
2
1
1
2
0
0
1
0
0
4
2
0
1
0
0
0
1
1
0
0
1
1
2
0
0
0
2
0
0
2
1
0
0
2
1
0
1
0
0
0
0
2
0
0
1
2
1
0
0
3
0
1
0
0
1
1
0
0
0
0
2
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
2
2
0
0
0
0
1
2
0
0
1
0
0
0
0
5
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
3
1
1
3
2
2
1
1
0
3
0
1
2
0
1
0
0
0
1
1
0
1
1
0
1
0
0
0
0
0
2
3
0
0
0
0
2
0
0
0
0
1
2
2
0
2
0
2
1
1
0
2
1
0
1
0
3
1
0
0
0
0
0
0
1
0
1
0
2
1
0
2
0
1
2
2
2
0
0
1
0
0
0
1
0
2
0
0
0
1
0
1
0
0
2
1
0
0
1
4
3
1
0
0
0
0
3
0
1
0
2
0
2
4
0
0
1
0
1
2
0
0
0
1
2
0
0
0
1
0
1
0
1
0
2
1
0
2
0
1
0
0
2
0
2
2
0
0
2
5
2
0
1
1
2
0
0
2
2
0
1
3
0
1
0
0
0
0
0
0
0
0
2
1
0
1
1
1
0
0
2
0
0
0
2
0
1
1
2
0
2
0
0
1
0
2
0
1
1
0
0
0
2
1
1
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
1
1
0
2
0
0
0
0
0
0
1
0
0
2
0
2
0
1
0
3
3
2
0
0
2
0
1
1
0
2
2
0
1
0
2
1
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
2
2
1
0
0
1
0
2
0
2
0
0
0
0
1
0
0
0
0
1
0
1
1
1
1
1
1
0
2
0
0
0
0
0
0
1
0
3
0
0
2
3
0
2
0
3
0
0
0
2
0
1
0
1
2
1
1
1
0
1
0
0
0
2
0
2
2
0
1
0
2
0
0
1
0
1
0
0
3
0
1
2
2
0
2
0
0
0
0
3
1
0
2
2
2
0
0
1
1
0
0
0
0
1
0
2
2
0
0
2
1
0
0
1
0
1
1
0
0
1
0
0
0
0
0
1
1
1
2
3
1
0
2
0
2
2
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
2
0
1
0
0
2
0
1
2
1
0
0
0
2
1
2
0
2
1
0
1
2
1
2
0
0
1
0
0
2
1
2
1
0
0
1
0
0
2
0
2
0
2
2
0
1
2
0
0
0
2
2
1
0
2
0
0
3
2
1
1
1
0
0
0
0
0
1
1
2
1
2
3
1
0
1
0
3
0
0
1
3
1
0
0
0
2
1
0
1
1
1
2
0
0
0
0
2
2
2
0
1
0
2
2
2
1
0
1
0
0
0
1
2
0
0
0
2
0
0
1
2
2
0
1
0
1
0
1
1
1
0
1
0
2
1
2
1
0
0
2
0
0
1
2
0
0
2
1
0
0
0
1
0
0
0
0
0
0
1
2
1
0
0
0
0
1
0
1
1
2
0
1
1
3
0
2
1
1
0
0
1
1
1
1
0
1
0
0
0
1
0
2
0
0
0
2
1
0
0
2
2
1
1
2
1
1
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
1
1
2
0
1
0
2
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
1
1
1
1
2
1
0
0
0
0
0
0
0
2
2
0
1
0
0
1
1
0
0
0
2
0
0
4
1
2
0
1
1
1
0
0
2
1
0
2
2
0
0
2
1
1
1
0
0
0
0
2
0
2
2
0
2
2
0
2
1
2
1
2
0
1
0
0
0
0
1
0
0
0
1
2
0
0
1
1
0
1
1
0
1
0
0
1
2
1
1
2
2
1
0
0
1
2
0
0
2
0
0
0
0
0
1
0
1
2
0
1
2
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
4
1
1
0
0
0
1
1
0
1
0
1
2
0
2
1
0
1
1
1
0
1
2
2
1
1
0
0
0
0
2
1
1
2
0
1
0
0
0
2
0
0
0
1
0
1
1
1
1
1
1
1
0
1
0
0
0
0
2
0
2
1
2
0
0
0
0
0
0
0
0
1
2
0
0
0
3
2
0
1
0
2
0
0
1
1
0
2
1
2
0
1
0
0
2
1
2
2
0
2
0
0
0
0
0
2
1
1
1
1
0
2
0
2
0
1
2
3
0
1
0
2
1
0
2
0
1
0
2
0
1
2
0
1
0
0
2
0
0
0
4
2
2
0
0
0
1
0
0
0
0
1
1
1
1
1
2
0
2
0
1
4
2
0
0
0
5
2
0
1
1
0
0
0
1
0
0
2
1
1
1
0
2
0
0
0
2
1
2
2
0
2
0
0
0
0
1
2
2
0
2
0
1
1
0
0
1
2
0
0
0
1
2
0
1
0
0
1
0
1
0
0
1
0
1
3
2
1
2
1
1
0
2
0
1
2
3
2
0
0
0
0
2
2
0
0
1
1
0
0
0
1
0
1
0
0
0
1
1
0
1
1
0
0
0
2
3
0
0
1
2
2
0
0
2
1
2
2
0
0
1
1
0
1
0
0
2
0
0
1
1
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
1
2
1
0
0
2
4
2
0
0
0
0
1
0
1
2
0
3
1
0
1
0
0
0
0
1
1
0
1
0
2
0
0
1
0
1
0
0
2
0
1
0
0
0
1
0
2
1
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
1
1
1
1
0
0
2
0
2
0
1
1
0
0
0
0
2
0
0
0
0
2
1
0
1
1
0
2
1
1
1
2
0
1
1
0
0
0
0
0
0
1
1
1
0
2
2
0
0
0
0
2
2
0
4
0
1
0
0
2
0
1
1
0
2
0
2
0
1
0
0
2
1
3
1
0
0
0
1
2
2
1
0
2
0
0
2
0
0
0
0
1
2
0
1
1
0
0
1
1
0
0
4
0
1
0
0
0
0
1
1
0
1
2
0
0
2
0
0
2
0
1
1
1
0
1
1
0
2
1
0
1
1
0
0
1
2
0
1
2
0
0
0
2
1
0
0
2
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
1
0
2
0
2
0
0
1
0
0
0
0
1
0
1
1
0
0
0
1
0
2
2
0
2
2
2
0
0
2
1
0
2
2
2
2
2
1
2
1
1
2
0
0
0
0
1
0
0
1
2
0
0
0
0
1
2
0
0
0
1
2
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
3
0
0
2
2
0
0
2
0
0
0
0
1
0
2
0
0
0
1
0
0
0
2
2
0
2
1
0
0
0
0
0
0
0
1
0
3
2
2
1
0
0
1
0
0
0
0
2
0
0
2
1
1
2
0
2
0
0
1
1
0
3
2
0
0
2
0
2
0
2
1
0
0
2
0
0
1
1
1
0
1
0
0
0
0
0
0
0
1
1
2
0
1
1
0
0
2
2
2
0
2
0
2
0
2
0
1
0
1
0
0
1
0
1
1
2
0
0
0
0
0
0
2
1
2
0
1
2
0
0
1
1
1
2
0
0
1
1
1
0
1
2
0
0
2
1
1
1
1
2
1
0
2
0
0
0
2
2
2
0
0
2
0
0
2
0
0
0
0
1
0
0
1
0
2
0
2
0
0
2
2
1
0
0
3
0
0
1
0
1
0
1
2
1
1
0
2
0
1
1
2
0
1
0
2
2
1
0
0
0
2
1
0
1
1
0
2
1
0
0
0
1
0
1
2
1
1
2
0
1
2
0
2
0
0
0
2
1
0
0
3
2
0
0
0
2
0
2
0
0
1
0
1
0
1
0
2
0
0
0
2
2
0
0
0
0
2
1
2
1
0
1
0
0
1
0
0
2
0
2
1
2
2
0
2
2
0
1
1
1
0
0
2
0
0
0
1
2
1
0
0
0
0
0
1
0
2
0
0
1
1
0
2
0
0
2
2
1
0
0
1
1
0
1
0
0
1
0
0
2
0
1
1
0
0
1
2
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
1
1
1
0
0
0
3
0
0
0
0
0
0
1
0
1
2
1
0
1
2
1
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
2
1
1
2
2
0
2
3
1
0
1
0
2
4
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
1
1
0
1
2
1
0
2
2
1
0
1
2
3
2
3
1
0
1
0
0
0
1
0
3
0
2
2
1
0
0
0
1
1
0
0
1
0
1
2
1
0
1
0
0
1
0
0
0
2
0
2
0
0
2
1
0
0
1
0
1
1
1
0
2
0
1
0
0
0
0
0
1
1
2
0
0
1
0
2
0
0
0
1
0
0
1
0
0
0
0
1
0
0
2
0
0
2
0
0
3
0
1
0
0
4
0
0
2
0
1
1
0
0
0
2
0
2
0
1
0
0
0
1
0
0
2
0
2
0
0
0
0
0
2
1
0
2
1
1
0
1
0
0
0
0
2
1
0
0
0
1
1
0
0
2
0
1
2
1
0
0
0
0
0
1
1
2
2
3
2
1
2
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
3
5
0
2
1
0
0
2
1
0
0
1
2
0
2
0
0
0
2
0
1
0
0
1
1
0
0
0
1
0
0
0
1
0
2
2
0
1
0
1
1
0
1
0
1
1
0
1
0
1
1
1
3
1
0
2
0
0
0
1
2
0
2
1
0
0
1
0
0
1
0
0
2
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
1
0
0
0
2
0
0
0
0
2
0
0
2
0
2
2
0
0
0
0
2
0
0
0
0
1
2
2
0
0
0
0
0
2
0
1
1
0
1
3
0
1
1
2
0
1
0
0
2
0
0
1
1
2
1
2
2
0
0
0
1
0
1
0
0
2
0
1
0
1
0
2
1
0
1
0
0
0
1
0
2
1
2
0
0
0
0
1
2
0
1
0
1
2
0
0
1
0
1
2
1
2
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
4
1
0
0
0
0
2
1
1
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
2
1
2
0
2
0
0
0
0
1
0
1
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
2
0
1
0
2
0
1
1
0
0
0
5
0
1
1
0
1
0
1
1
1
1
0
2
2
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
1
2
0
0
0
0
0
1
2
1
0
1
1
0
0
0
3
0
2
0
0
0
2
1
1
0
0
1
1
2
0
0
1
2
0
1
0
2
1
0
0
1
2
0
1
0
1
2
2
1
1
1
0
2
0
0
2
2
1
0
0
1
3
0
0
1
0
0
1
0
1
0
2
0
2
0
1
0
0
1
1
2
1
0
2
1
0
0
2
2
2
0
1
0
1
0
1
2
2
1
0
2
0
2
1
2
1
1
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
2
2
1
1
0
1
1
6
0
1
0
0
0
2
0
2
0
1
1
1
2
2
0
1
0
0
0
1
0
0
2
1
0
0
2
0
1
4
0
0
0
5
0
1
1
1
0
1
1
0
0
0
2
0
1
1
0
0
0
2
0
0
0
0
0
1
0
0
1
1
0
2
0
0
0
2
0
1
0
1
0
0
1
0
1
2
2
0
1
0
1
0
2
2
0
0
0
0
3
1
0
0
0
1
0
0
2
3
2
2
1
1
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
1
0
2
1
1
0
2
3
1
2
0
1
0
7
0
1
1
0
1
0
0
0
1
0
0
0
0
2
0
2
0
0
2
0
2
1
2
0
0
0
0
1
0
0
0
1
0
1
1
2
1
0
0
0
1
0
1
2
1
0
0
0
0
1
1
0
3
2
0
2
2
2
1
0
0
0
1
2
0
0
2
2
2
1
1
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
2
2
0
4
1
0
0
0
0
0
0
1
1
1
2
0
1
0
1
1
0
0
0
0
0
0
1
2
1
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
2
0
1
0
1
2
1
2
2
1
0
2
0
1
1
0
1
6
0
0
0
0
1
1
0
1
0
0
0
0
1
0
1
2
0
0
0
2
0
2
1
0
1
0
0
0
0
0
1
0
2
0
0
2
1
2
0
1
2
1
0
1
0
0
0
0
0
2
0
0
0
1
0
2
1
0
0
0
0
1
0
0
0
0
0
1
1
2
1
1
1
0
1
1
0
0
2
2
2
0
2
0
0
0
2
1
0
1
0
1
0
2
1
1
0
0
0
2
1
0
1
0
0
0
0
0
2
1
2
1
0
1
0
2
0
0
0
1
3
0
2
0
1
0
1
2
2
2
1
0
1
0
1
0
0
0
0
0
0
0
0
0
2
1
2
1
0
0
1
1
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
2
1
1
1
2
0
2
0
1
1
1
0
0
0
0
0
2
2
3
1
1
1
0
2
0
0
0
0
2
2
0
2
1
1
0
0
0
0
0
0
2
2
0
1
1
0
0
2
1
2
0
0
0
0
1
0
2
1
1
2
0
1
1
0
0
0
0
0
1
0
0
0
0
2
0
1
2
0
0
1
0
0
0
0
0
0
0
2
0
2
0
1
1
0
0
1
0
1
2
2
2
0
0
1
0
0
2
1
0
1
1
0
0
0
2
1
0
1
0
1
0
0
1
0
0
1
1
1
0
0
0
0
2
0
1
0
0
1
1
0
0
0
0
2
2
1
2
0
2
0
0
2
0
0
1
0
0
0
0
1
2
0
0
0
0
2
0
1
0
2
1
1
0
1
0
0
1
1
1
0
0
0
1
0
0
1
1
0
1
0
0
1
1
2
0
1
0
1
1
2
0
1
2
0
1
0
2
0
1
0
1
0
0
0
0
1
1
1
1
2
0
0
0
2
0
0
1
0
0
0
0
1
0
2
0
0
1
1
1
1
1
0
0
1
1
2
2
1
2
0
0
1
0
0
2
1
1
0
1
0
0
0
0
0
0
0
1
1
2
1
1
2
2
0
0
0
1
0
2
2
0
2
0
2
0
1
0
1
1
0
1
0
1
1
0
0
0
0
1
1
0
0
0
0
0
2
1
0
1
0
3
1
2
2
1
0
2
2
1
3
0
1
2
2
0
2
0
1
0
1
2
1
0
0
2
1
0
0
0
1
0
0
2
1
1
0
1
0
1
1
0
2
1
2
1
3
2
0
1
0
0
0
0
1
2
0
0
1
0
0
1
0
0
1
0
0
2
2
1
1
1
1
2
1
1
0
2
1
0
0
0
1
0
0
1
2
0
1
0
2
1
4
0
0
1
0
2
0
0
0
2
1
1
0
0
0
0
1
0
2
1
0
1
2
1
2
4
2
2
0
0
1
2
0
1
0
1
0
1
0
0
2
1
0
2
1
1
2
0
0
1
1
1
0
1
2
0
2
0
2
3
0
0
1
0
0
1
1
0
0
0
2
2
0
0
1
1
0
0
0
0
1
1
2
0
1
0
0
1
1
0
1
0
0
0
0
0
1
2
0
0
1
0
2
0
3
2
0
0
2
0
0
0
3
0
0
1
2
2
2
0
1
2
0
0
3
0
1
0
0
1
2
2
0
0
0
2
0
1
1
0
1
1
1
1
0
0
0
0
0
0
0
2
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
2
0
1
1
0
1
1
0
2
0
2
1
0
2
1
0
1
1
0
0
2
1
1
2
0
1
1
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
1
1
1
0
0
1
1
0
2
0
0
2
0
0
1
0
2
0
0
2
0
0
1
0
0
2
1
1
0
0
1
0
0
0
0
0
1
0
0
1
2
1
1
0
0
0
0
1
0
2
0
0
0
1
1
1
1
1
2
0
1
1
0
2
0
0
1
2
0
0
0
0
2
0
0
3
0
1
1
2
2
1
0
1
0
1
0
0
0
0
2
0
1
2
1
0
0
0
1
0
1
2
0
2
1
0
0
1
0
1
0
0
2
1
0
2
0
1
0
2
0
0
0
1
1
1
0
2
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
2
0
1
0
1
0
0
1
0
0
0
0
1
1
0
1
0
1
1
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
3
0
0
0
0
0
0
2
1
0
1
1
2
0
1
0
1
2
3
0
1
3
0
2
1
0
0
1
1
0
0
0
2
0
0
0
0
0
2
1
2
2
2
1
2
1
1
0
2
3
3
2
1
1
0
2
0
0
0
2
0
0
0
0
1
1
1
0
1
0
2
0
0
1
0
0
0
0
1
0
0
2
1
1
0
0
0
3
2
2
0
2
0
0
1
0
2
2
1
2
1
1
0
2
0
0
0
0
0
1
1
0
2
0
1
0
2
1
0
0
0
2
1
1
2
1
2
3
0
0
1
0
1
2
0
2
1
0
0
1
0
2
2
2
0
0
1
0
2
0
3
2
1
0
0
1
1
2
1
1
1
0
0
1
1
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
2
0
2
1
0
0
2
4
0
1
0
2
2
3
0
1
2
0
1
1
0
1
1
2
6
3
1
1
1
0
2
0
2
1
0
0
2
0
1
4
1
0
1
0
1
0
1
1
0
1
1
1
1
2
0
1
0
0
1
1
2
0
0
1
1
1
2
0
2
1
1
0
1
0
0
1
2
2
0
1
2
2
0
0
0
0
0
0
0
0
2
1
1
0
0
0
1
0
1
0
0
2
2
0
0
2
0
1
1
1
1
0
0
2
0
0
0
1
2
1
0
0
1
2
0
0
0
1
0
0
0
0
1
1
1
1
3
0
0
1
2
0
1
0
0
0
0
0
2
0
0
2
1
1
0
2
2
1
0
2
1
1
0
1
2
0
1
0
0
0
0
0
1
1
0
0
1
0
2
0
2
1
1
0
0
0
1
0
1
0
1
0
0
1
0
1
1
3
2
1
0
2
0
0
0
2
0
2
2
0
0
2
1
0
1
0
2
0
2
0
0
2
0
1
0
0
0
0
1
1
0
0
1
0
0
0
2
1
0
1
1
0
4
0
0
0
1
1
0
0
0
0
0
0
1
3
1
2
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
1
2
0
1
2
2
0
2
0
2
0
0
2
0
0
0
0
1
2
0
0
1
1
1
0
1
0
0
1
2
1
0
0
1
0
0
2
2
0
1
2
0
0
0
0
0
0
2
4
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
1
1
0
1
0
0
0
1
2
1
0
0
3
1
2
1
0
0
2
0
0
0
0
0
0
2
0
2
1
0
0
2
2
2
2
0
1
2
0
0
2
2
0
2
0
0
2
0
1
1
1
1
1
2
2
1
0
0
0
1
1
0
0
0
1
2
0
0
1
0
0
0
0
0
2
2
0
1
1
0
0
2
0
1
1
1
0
0
1
1
0
0
1
2
2
0
1
2
0
2
0
1
0
0
1
2
1
1
0
0
1
2
1
0
0
0
0
1
1
1
0
0
0
1
1
0
0
1
1
0
1
0
2
1
2
1
2
0
0
1
0
0
1
1
2
2
0
1
0
1
0
1
1
0
0
1
0
2
0
0
0
2
0
2
1
1
0
2
0
0
0
0
1
0
1
1
0
1
1
0
1
1
0
2
0
0
0
0
2
1
1
2
1
0
2
0
0
0
2
2
0
1
1
0
0
0
0
0
2
2
0
0
2
1
1
2
1
0
1
1
1
1
2
0
2
0
0
2
2
0
2
1
2
1
0
2
0
0
2
1
2
1
2
0
2
1
1
2
1
2
1
1
1
0
1
1
0
2
0
2
1
1
0
0
1
1
1
0
2
1
0
1
2
3
0
0
1
0
1
0
1
1
0
0
0
1
0
1
1
0
0
1
0
2
1
0
2
3
0
1
1
0
0
2
1
1
0
0
1
0
1
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
1
2
2
1
0
2
2
1
0
1
0
0
0
0
0
2
0
2
1
3
2
0
0
0
0
1
1
1
1
0
1
1
0
2
0
0
0
2
2
0
2
1
0
0
0
1
0
1
0
0
2
0
0
2
2
0
0
0
2
0
2
2
1
0
2
0
0
1
0
0
0
2
0
0
0
2
0
1
1
0
2
1
0
0
3
1
2
3
0
0
1
1
0
2
0
0
2
1
1
1
2
0
0
0
1
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
1
1
2
1
0
0
0
1
1
0
0
2
0
1
2
1
0
0
0
2
2
0
2
1
2
0
1
1
0
1
1
1
0
1
0
0
0
1
2
0
1
1
0
1
1
0
1
0
0
0
2
0
2
1
1
2
0
1
0
2
2
0
0
0
1
1
2
2
1
0
2
2
0
0
0
0
2
2
0
0
1
0
2
2
0
1
0
0
1
1
0
2
0
0
1
0
1
0
1
0
1
0
1
2
2
0
0
1
0
1
1
1
2
1
2
0
2
1
0
0
1
0
0
0
0
2
0
2
0
0
3
2
0
0
0
0
2
1
0
2
0
0
0
2
0
2
0
0
1
1
1
0
2
1
1
0
0
0
0
2
0
0
0
2
2
2
0
0
0
0
0
0
2
0
0
0
0
2
2
3
0
1
0
0
0
0
2
2
0
0
0
1
2
0
1
1
0
0
0
1
1
2
0
0
1
2
1
0
0
1
2
1
1
0
0
1
2
1
0
0
0
1
1
0
2
0
0
1
1
0
0
2
1
2
1
0
0
0
2
0
0
1
0
2
0
0
1
1
1
0
0
1
1
1
0
1
1
0
0
0
0
0
2
0
0
1
3
1
0
0
1
0
1
0
0
1
0
1
0
2
2
0
2
2
0
0
0
2
0
0
0
0
1
0
1
2
1
1
1
1
0
1
1
0
0
3
2
2
1
0
0
0
1
1
0
1
1
0
0
2
1
0
0
1
0
0
3
0
0
0
0
0
2
0
1
0
0
1
1
1
0
1
1
0
1
0
0
2
0
4
0
2
1
1
0
2
0
1
3
0
0
0
1
0
0
1
0
2
1
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
2
0
0
0
2
2
2
0
0
0
0
1
0
0
1
0
2
0
1
0
2
2
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
3
2
5
1
2
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
1
2
1
0
2
1
1
1
0
0
2
2
0
1
2
0
2
0
1
1
0
1
0
1
0
1
0
0
1
1
1
0
2
2
0
0
2
0
2
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
2
0
1
2
1
2
0
0
2
1
2
1
0
0
0
1
1
0
0
0
2
0
1
0
1
0
0
2
0
0
3
0
0
1
1
0
0
2
0
2
0
0
0
1
0
0
0
0
0
1
2
2
2
2
0
1
1
0
0
0
0
0
1
0
0
2
2
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
1
2
0
0
1
0
0
1
1
0
0
1
0
0
0
2
1
0
1
1
1
0
2
0
0
0
0
2
0
0
1
0
0
0
0
1
0
2
0
0
0
1
0
0
0
1
1
2
0
5
0
2
1
2
0
2
2
2
0
0
0
2
2
0
0
1
1
0
0
0
1
2
1
2
2
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
1
2
0
3
0
0
2
1
1
0
0
0
0
0
2
1
2
1
1
4
0
1
1
1
0
0
2
1
0
0
1
0
0
0
2
2
1
0
3
0
2
0
0
2
0
0
2
2
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
3
0
1
1
1
0
1
0
1
1
0
2
2
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
1
0
2
2
0
1
0
0
0
0
1
2
0
1
1
0
2
1
2
2
1
2
0
1
1
1
0
1
0
0
2
0
0
1
0
1
3
2
0
1
0
0
0
0
0
0
1
1
1
2
0
0
2
0
2
3
1
2
0
0
0
1
2
0
0
1
1
1
0
0
0
2
0
0
1
0
2
0
1
0
1
1
1
0
0
2
1
0
0
0
1
2
0
0
1
0
2
1
1
0
2
0
0
0
1
0
1
0
0
1
0
0
3
2
2
1
0
0
0
1
0
0
1
2
0
2
0
1
2
0
0
2
3
0
2
1
0
1
1
1
1
2
0
0
2
0
0
0
0
1
0
0
2
0
1
1
0
0
0
0
0
1
0
1
0
0
2
2
1
2
0
0
0
1
0
2
0
0
0
0
2
1
0
0
0
2
1
1
1
2
0
1
0
1
0
0
1
1
2
0
1
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
1
2
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
1
1
1
1
0
1
2
0
1
1
0
0
1
1
2
1
1
1
2
3
1
3
0
0
1
2
0
2
1
0
1
1
0
2
0
0
0
0
0
1
1
0
2
0
0
1
0
0
1
0
0
2
0
1
0
1
0
0
1
2
1
0
1
2
0
0
1
0
2
2
2
0
2
0
2
1
0
0
0
0
0
2
1
2
1
2
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
2
1
2
0
1
0
0
2
1
4
0
0
0
0
2
0
2
0
0
1
2
2
2
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
1
0
2
0
0
0
0
0
2
0
3
2
1
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
4
0
1
2
0
2
0
1
3
3
0
1
2
0
1
0
1
0
1
2
0
0
3
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
2
0
5
1
2
1
2
0
1
0
0
1
0
0
0
0
0
0
2
1
0
0
2
2
0
0
0
2
0
0
0
1
0
1
2
0
0
1
1
0
0
1
1
1
0
1
2
3
0
1
0
1
0
1
0
0
1
0
1
2
2
0
1
2
1
1
2
0
0
0
0
2
0
0
1
0
0
2
1
1
0
0
0
1
1
0
2
2
0
0
1
1
0
2
1
1
0
1
2
1
2
0
0
0
0
0
0
0
1
0
2
1
1
0
0
0
2
0
1
0
0
0
2
0
1
1
1
0
0
0
0
0
0
0
0
2
1
1
3
0
2
0
1
0
0
0
0
2
0
0
0
0
1
1
0
1
1
1
0
0
0
0
1
0
1
0
0
0
0
2
2
2
1
0
0
0
0
0
1
0
0
1
2
2
0
1
1
1
2
1
1
0
0
0
0
0
0
2
1
0
0
1
0
0
2
1
3
1
0
1
0
0
1
0
0
2
2
1
0
0
1
2
0
1
1
0
1
0
0
0
0
0
2
0
0
0
1
1
6
0
1
0
2
0
0
0
0
0
2
2
2
2
2
1
0
0
2
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
2
0
2
0
1
2
0
0
0
0
2
0
0
0
2
2
0
1
2
2
1
0
0
1
1
2
1
0
1
0
0
0
0
2
2
0
0
2
0
1
3
2
1
0
2
0
0
1
0
0
0
1
0
2
1
1
2
5
1
1
0
3
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
3
1
2
0
0
0
2
0
1
0
0
1
1
0
0
1
0
1
3
2
0
1
0
3
1
1
0
1
2
2
0
1
0
0
0
0
0
1
2
0
1
0
1
0
1
2
0
1
2
0
2
0
0
0
0
0
2
1
2
1
1
1
2
1
0
0
1
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
4
2
0
2
2
0
1
0
0
0
2
0
0
1
1
2
0
0
0
1
1
0
0
2
0
0
0
0
4
0
1
0
1
1
1
0
2
2
0
2
0
0
1
0
0
0
2
0
1
0
2
1
1
2
0
0
2
0
0
2
0
0
0
1
0
1
1
1
0
0
0
2
1
0
0
0
0
0
1
2
0
2
0
1
1
0
3
2
0
1
0
2
0
0
0
0
1
0
1
0
0
0
0
1
0
1
2
0
0
1
0
1
1
1
0
0
1
0
1
0
1
1
0
0
0
2
0
0
0
2
2
3
0
0
2
0
0
1
0
1
2
1
0
2
0
0
2
0
2
0
1
2
2
0
1
2
0
1
2
2
1
1
1
0
0
0
0
0
0
1
2
1
0
0
1
0
1
0
0
0
1
1
0
0
1
2
0
0
0
0
2
0
1
0
2
2
0
0
0
0
0
1
2
0
0
1
0
1
0
0
0
1
2
0
0
1
0
5
1
0
1
0
0
0
0
1
1
1
2
0
2
2
0
0
0
1
2
0
1
0
0
0
1
0
1
1
1
0
1
0
0
0
1
1
0
2
0
0
0
1
0
1
0
0
0
1
0
1
0
0
1
1
4
2
0
0
1
1
0
0
1
3
1
1
2
1
0
0
2
1
0
1
0
1
1
2
0
2
1
2
0
0
0
0
2
2
0
1
1
3
1
0
1
1
1
0
0
0
0
0
0
2
2
1
1
0
1
0
1
2
1
0
1
1
0
0
0
2
2
1
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
2
0
0
0
1
0
0
0
1
2
1
2
0
2
0
0
1
0
2
1
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
2
1
1
0
1
0
2
2
1
0
2
0
1
0
2
3
0
1
0
2
1
0
0
1
1
2
2
0
0
2
3
0
0
0
0
1
0
1
0
2
0
1
1
1
0
0
0
2
2
0
2
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
2
2
2
1
1
1
0
0
0
1
0
1
0
0
0
2
2
2
0
1
0
0
0
1
2
0
0
2
0
2
2
2
0
2
2
0
1
1
0
0
2
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
1
0
1
1
1
0
1
0
0
1
0
0
1
1
2
0
0
0
2
2
1
1
1
1
0
1
0
2
2
0
0
0
0
1
0
1
0
0
0
2
2
1
2
2
0
0
0
1
0
1
2
1
2
1
0
0
0
0
1
2
0
1
2
2
0
0
1
0
2
0
0
1
0
1
0
0
1
0
0
0
1
0
1
0
1
1
2
2
0
0
0
2
0
2
1
2
1
0
0
0
0
0
2
2
0
1
0
1
2
1
2
0
1
1
0
0
4
0
1
1
1
2
0
2
0
0
1
0
3
0
2
1
0
1
0
0
1
1
2
0
2
3
1
0
2
1
2
1
2
0
0
0
1
1
1
1
1
0
0
2
0
1
0
0
1
0
0
0
1
0
0
2
0
0
0
0
1
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
1
0
1
2
0
1
2
1
1
0
0
0
1
0
1
1
2
0
0
0
1
0
0
1
1
1
1
2
0
1
1
1
1
0
2
0
2
2
0
1
1
1
0
0
1
2
0
0
2
2
0
2
0
0
2
0
2
2
1
1
0
0
3
0
0
2
1
1
0
0
0
2
0
1
0
0
1
0
1
0
0
1
0
2
1
0
0
0
0
0
1
0
0
2
0
2
2
1
0
0
1
0
1
1
1
4
1
0
0
0
2
0
0
1
1
0
2
0
2
0
1
0
0
0
0
1
2
1
2
2
2
1
0
2
0
0
0
0
2
2
0
0
0
0
1
1
2
0
3
2
0
2
1
1
0
0
1
1
0
1
1
2
1
1
0
1
0
0
0
0
0
0
0
0
2
1
0
0
1
0
1
2
1
0
1
1
2
1
1
1
0
0
0
2
0
1
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
1
2
0
0
0
0
2
2
2
0
0
0
1
0
0
1
0
0
2
0
0
0
1
0
0
2
1
0
0
0
0
1
0
0
2
3
2
0
2
2
0
1
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
1
2
0
0
1
0
0
2
1
1
1
0
0
0
0
1
0
1
0
0
0
1
1
1
1
0
1
0
2
0
0
1
0
2
2
4
0
0
0
0
4
2
0
0
0
0
1
0
1
0
1
2
1
0
0
1
0
2
0
1
0
0
1
2
0
0
0
0
0
0
2
1
1
0
1
1
0
1
0
2
0
1
2
2
0
1
0
1
0
2
0
0
2
1
0
0
1
0
0
0
1
2
0
2
2
1
1
0
0
2
1
2
1
2
3
1
2
0
0
0
2
1
0
2
0
2
1
1
0
3
1
0
1
0
0
1
2
2
2
2
1
1
2
0
0
1
2
0
0
0
1
1
1
1
1
1
0
0
0
0
2
0
1
2
1
0
1
2
1
0
0
1
1
0
2
1
2
2
4
1
1
0
0
0
2
2
0
1
0
1
0
0
0
2
0
0
1
1
2
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
3
0
0
2
2
0
2
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
1
0
0
2
1
0
0
1
1
0
1
0
4
1
1
0
0
0
0
1
1
0
0
0
1
0
2
2
1
0
1
0
0
2
0
1
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
2
0
0
1
2
2
0
1
2
0
0
0
1
1
2
0
0
1
0
0
0
4
2
1
2
0
1
0
1
1
0
1
3
1
1
2
0
0
0
0
0
0
0
1
1
0
1
2
7
1
0
1
0
2
1
2
4
0
0
1
0
0
0
1
1
0
2
2
0
0
1
0
0
2
1
0
1
1
0
0
2
0
0
0
1
0
1
0
0
2
1
1
2
0
1
0
1
0
0
1
1
0
1
0
0
2
1
2
0
0
0
0
0
1
0
1
0
0
2
1
0
1
1
0
2
0
2
1
3
2
2
0
2
1
0
1
2
1
1
2
2
1
1
0
0
0
0
1
2
0
1
0
2
2
0
1
3
0
0
1
0
0
1
0
1
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
1
1
2
0
0
1
0
0
0
0
2
1
2
0
0
1
0
1
2
3
1
0
0
1
0
0
2
1
1
1
0
0
2
1
0
1
0
2
1
0
2
0
0
2
1
1
1
1
1
1
0
0
1
0
0
0
2
0
0
0
1
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
1
0
2
2
0
2
0
1
2
1
0
0
0
2
2
0
2
0
0
0
1
0
2
1
0
1
2
0
1
2
0
0
1
0
0
2
1
0
0
0
1
3
1
0
0
0
2
0
1
0
0
0
0
1
2
1
1
0
0
1
2
1
0
0
1
0
0
1
0
0
1
0
2
1
0
0
1
0
2
2
1
1
2
1
0
0
0
0
1
0
1
2
0
1
1
0
0
2
0
0
1
0
0
2
0
5
0
1
0
1
2
2
0
0
1
0
1
0
1
2
2
1
0
1
0
1
1
0
0
0
3
2
0
0
1
0
2
2
1
0
1
3
1
0
2
1
0
0
0
1
1
1
1
0
2
0
1
0
0
0
1
0
0
0
0
1
1
2
2
0
1
1
0
2
0
1
1
1
2
1
0
2
0
1
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
2
1
0
0
0
0
0
0
1
0
1
0
1
0
1
2
0
1
4
0
0
0
2
1
0
1
2
1
0
0
0
0
1
1
3
2
1
0
0
0
0
0
2
1
1
0
1
0
2
2
2
1
1
0
0
2
0
0
0
2
0
0
2
0
2
0
0
2
0
0
1
0
0
0
2
2
1
2
3
2
1
0
1
0
1
1
0
0
0
1
1
0
2
1
0
0
0
0
0
0
0
2
0
0
0
1
1
0
2
0
0
0
0
2
0
0
2
0
2
1
0
0
2
0
1
0
0
0
2
0
0
0
2
2
0
0
0
0
0
1
0
0
2
1
1
0
2
2
0
2
2
0
0
0
1
1
2
0
0
0
0
1
2
0
34
0
1
0
2
1
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
1
3
0
0
0
1
0
0
2
2
0
2
2
0
0
0
1
2
2
0
1
1
1
2
0
0
0
1
0
1
0
2
0
1
2
2
0
0
1
0
0
2
0
0
0
2
0
0
0
0
2
0
1
1
0
0
0
0
0
0
1
2
0
0
0
3
0
2
0
0
2
2
1
2
2
0
0
3
0
0
0
2
0
0
0
1
0
0
1
0
0
2
0
0
0
4
2
1
0
1
2
2
0
1
2
2
0
0
1
0
1
1
0
0
5
2
1
3
1
0
0
0
0
1
0
1
1
0
2
1
1
2
0
2
1
2
0
0
0
2
1
0
0
1
0
1
2
1
0
2
0
2
0
1
1
0
0
1
1
0
0
0
0
2
0
0
0
0
2
2
0
2
2
1
0
0
1
0
14
2
3
2
1
0
2
0
0
1
0
3
2
1
1
0
0
1
1
0
0
2
1
1
0
0
0
0
0
0
0
1
2
1
1
0
0
0
0
2
1
1
0
0
0
0
0
1
1
0
2
1
1
0
0
2
0
0
0
0
1
0
0
4
0
0
2
2
0
0
1
0
1
0
0
2
0
1
1
0
0
0
0
1
1
2
0
0
0
0
0
0
0
2
1
2
1
0
0
1
3
0
0
0
1
0
2
2
1
1
0
0
0
2
2
1
2
0
1
2
1
12
2
0
0
1
0
0
3
0
1
1
3
1
0
0
2
1
1
0
0
2
0
2
0
0
1
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
2
0
1
0
1
1
1
1
0
2
0
1
0
2
0
0
0
0
0
0
1
0
0
0
1
0
1
1
1
1
1
1
2
1
0
1
0
1
1
2
0
0
0
2
0
0
2
2
0
2
0
1
0
0
0
1
2
0
0
1
0
1
1
1
0
2
1
0
0
0
0
1
0
0
2
0
1
1
0
0
0
1
0
0
1
2
2
2
2
2
0
2
1
1
1
1
0
0
2
0
0
2
0
0
2
2
0
0
0
0
4
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
2
2
0
2
2
0
0
0
0
0
2
0
0
0
0
2
2
0
0
1
0
2
0
2
0
1
0
3
0
2
0
0
0
0
0
1
0
1
0
0
0
4
3
1
0
1
0
0
0
2
1
1
0
0
1
0
2
1
0
1
0
0
0
0
2
2
0
0
2
2
0
1
0
0
0
0
0
0
1
2
0
1
1
0
2
1
0
2
1
2
0
0
0
1
0
2
0
1
0
1
0
0
1
0
0
1
2
0
1
1
0
1
0
1
0
0
1
1
0
0
2
2
2
0
0
2
3
0
0
0
2
1
0
3
0
0
0
1
0
2
0
0
1
2
2
0
2
0
1
0
2
0
1
1
0
1
0
0
1
0
0
4
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
2
1
1
1
0
1
1
1
0
2
0
0
1
1
0
0
1
0
1
0
2
0
2
0
0
0
0
0
0
1
0
1
2
0
0
0
0
2
1
0
0
0
0
2
2
2
2
1
0
0
1
0
0
1
2
2
3
0
0
0
0
0
0
0
0
0
1
1
1
1
1
0
3
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
1
1
2
0
2
0
0
0
0
0
0
2
0
2
0
0
1
0
2
0
0
0
0
1
0
2
0
2
0
2
1
0
0
1
1
0
0
2
0
1
0
2
1
0
1
1
0
0
2
2
1
0
0
0
0
0
0
3
0
1
2
2
1
0
0
1
0
1
3
1
2
0
1
2
2
0
0
1
2
1
1
0
1
0
0
1
0
1
0
0
2
0
1
0
0
1
0
0
0
0
1
1
1
1
0
0
0
0
0
2
0
2
0
0
0
2
0
1
1
2
0
1
0
0
0
0
0
1
2
2
0
2
3
0
0
1
2
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
2
1
2
1
0
0
0
2
1
0
2
0
1
1
0
0
1
2
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
1
0
1
2
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
2
0
1
1
1
1
0
0
0
2
0
0
2
1
1
2
1
0
1
0
0
1
0
0
1
0
0
0
2
0
1
2
0
0
1
1
0
0
0
2
1
0
1
1
0
0
0
0
1
1
1
0
0
2
1
0
3
1
0
2
1
1
0
0
1
0
1
1
1
0
1
0
1
0
0
0
2
0
1
0
0
2
0
2
0
1
0
1
0
0
1
0
1
1
0
0
1
1
0
1
0
0
1
2
1
1
0
0
0
0
1
1
1
1
0
1
1
0
0
1
1
1
0
0
0
0
2
2
0
1
0
2
2
1
0
0
0
0
1
1
0
2
1
1
0
0
1
1
1
1
0
1
2
0
1
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
1
0
1
1
0
2
1
2
0
2
1
2
0
1
0
0
0
1
1
0
0
2
3
1
0
0
0
0
1
0
1
0
1
0
2
0
0
1
0
0
2
0
0
2
2
0
0
1
1
0
2
2
1
0
0
0
0
0
0
1
1
0
0
0
1
1
2
1
2
2
0
0
0
1
1
0
1
0
0
2
0
0
0
1
1
0
0
0
2
0
2
1
1
2
0
2
0
0
1
0
2
2
0
0
1
1
0
0
0
0
0
0
0
2
2
1
0
0
1
2
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
2
0
0
0
0
2
1
3
1
0
1
0
2
0
2
0
1
0
1
0
1
1
0
1
2
0
0
0
0
0
0
0
1
0
1
0
0
2
3
1
0
0
1
0
0
1
1
0
1
0
1
0
0
2
1
0
2
1
0
1
2
0
0
0
0
1
0
0
0
1
0
2
0
0
0
1
2
2
0
0
1
0
0
0
0
0
0
2
0
0
2
0
2
1
1
1
0
2
0
0
1
1
0
3
2
0
0
2
0
2
1
1
0
1
1
1
1
2
0
2
1
0
0
0
1
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
2
1
2
0
1
1
2
0
1
0
0
0
2
2
0
2
1
1
1
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
1
1
0
0
3
0
0
1
1
1
3
0
2
1
0
2
0
0
0
0
0
0
2
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
3
2
1
0
0
0
1
2
0
2
0
2
0
0
0
0
0
1
1
1
0
1
0
2
2
0
1
0
0
2
0
2
1
1
0
1
0
0
1
0
0
3
0
1
3
0
2
0
0
1
1
0
1
1
1
2
0
1
0
1
0
0
1
0
0
0
1
1
0
0
0
1
0
2
0
0
0
0
2
0
2
2
2
2
0
0
2
0
1
3
1
0
1
0
0
0
1
0
1
1
2
0
1
2
1
0
1
1
0
2
0
0
3
0
0
2
2
0
0
0
1
0
2
2
2
0
0
1
0
0
0
2
2
4
0
0
2
0
1
2
1
0
2
3
1
1
2
2
1
1
1
2
0
2
0
0
0
0
0
1
2
0
0
2
0
1
0
1
1
0
0
2
0
1
0
0
0
0
1
0
1
0
4
3
0
0
0
1
1
0
2
0
1
1
3
2
1
0
0
2
1
1
1
0
0
0
1
0
0
0
1
1
2
1
0
1
0
0
2
0
0
0
2
2
0
0
0
1
1
0
0
1
0
0
1
4
1
1
1
0
1
0
0
0
1
0
2
0
2
1
1
0
0
1
0
1
12
0
1
2
1
1
1
0
0
1
0
2
1
0
0
0
2
0
0
0
2
1
0
1
1
0
0
1
1
0
2
1
2
1
2
0
0
0
1
0
1
1
0
1
0
0
0
0
1
1
0
1
1
1
0
0
5
0
1
0
0
0
0
1
0
0
2
0
1
2
0
1
2
0
1
1
0
1
0
1
0
1
1
0
0
0
0
0
2
0
2
0
0
2
2
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
2
2
0
0
0
2
2
0
3
0
1
0
1
0
1
2
2
0
0
2
1
2
2
2
1
1
1
0
1
0
1
1
1
2
0
0
1
0
2
0
1
0
0
1
1
0
0
2
0
1
1
0
2
0
2
0
0
0
1
0
0
2
1
0
0
0
0
0
7
1
2
2
0
0
0
1
0
0
0
0
0
1
0
2
1
0
2
0
2
0
0
2
0
1
0
1
2
0
2
0
0
2
2
0
0
2
0
1
1
3
0
1
0
1
0
0
0
0
0
0
1
2
0
0
3
0
1
1
0
0
0
2
1
0
0
1
0
1
1
0
4
1
1
0
1
2
1
0
1
0
0
0
1
1
2
0
1
0
2
1
0
0
0
1
0
1
1
1
2
0
0
2
0
1
0
0
0
2
0
0
0
1
1
0
0
0
2
0
2
0
1
1
2
2
0
0
0
0
0
1
0
0
0
0
0
1
3
0
0
0
1
0
1
2
1
1
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
2
0
0
1
2
1
2
2
0
0
0
0
2
1
1
1
0
1
1
0
2
1
1
0
2
1
1
0
0
1
1
0
0
1
0
1
1
1
0
1
0
0
0
1
2
0
0
2
0
0
2
2
2
2
0
2
0
2
2
0
0
0
0
0
1
2
0
0
2
0
0
1
0
1
1
2
0
1
1
0
0
2
2
2
2
0
0
0
1
2
0
0
0
0
1
2
1
0
2
0
1
0
0
2
0
0
2
1
0
2
0
2
3
1
0
2
1
2
0
0
0
1
1
0
0
0
1
2
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
2
0
0
1
1
0
1
0
0
2
0
0
0
0
2
0
1
0
1
0
0
1
2
0
0
1
2
0
2
0
1
0
1
2
0
1
1
0
0
2
2
0
0
0
0
1
1
0
2
0
2
2
2
0
1
1
0
0
0
1
2
0
2
0
2
2
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
2
1
0
0
2
0
0
1
2
0
2
2
2
1
1
0
2
0
1
2
1
1
2
0
0
1
1
1
0
0
0
0
1
1
0
0
2
1
0
1
1
0
1
1
0
0
0
2
0
1
1
1
1
2
0
1
2
1
1
0
2
0
1
1
0
0
0
0
2
0
1
0
0
2
2
0
0
0
2
1
0
2
1
2
2
0
0
0
0
1
1
2
1
0
1
2
1
0
1
0
2
2
0
1
0
0
1
1
1
0
1
0
0
2
0
1
0
0
0
1
1
2
0
2
0
0
0
0
1
0
1
3
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
1
1
1
0
0
1
5
0
1
0
0
0
2
0
3
0
2
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
2
1
0
0
1
0
2
1
0
0
2
1
0
2
2
0
1
2
2
2
0
2
1
5
0
0
1
2
2
0
2
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
1
2
0
2
1
0
1
1
0
0
0
0
0
0
1
2
1
0
0
2
2
0
0
1
2
0
1
0
1
0
1
1
2
0
2
3
0
0
0
1
1
0
0
1
2
1
0
0
1
2
0
0
0
0
2
0
1
2
1
1
1
2
1
2
1
2
0
1
1
1
0
0
1
0
0
0
2
1
0
2
1
1
1
1
0
1
3
0
1
1
0
2
1
0
0
2
2
0
2
1
0
0
0
1
1
0
0
0
0
0
2
1
0
0
0
0
2
1
2
0
0
1
1
2
2
2
0
1
1
0
0
0
0
1
0
0
0
0
0
2
1
0
2
0
0
0
0
1
0
2
1
1
2
1
0
0
2
0
1
0
2
1
2
2
2
4
0
1
0
2
0
2
0
2
0
2
0
0
0
1
2
0
1
0
3
1
0
2
1
0
0
1
0
1
1
0
0
0
0
1
0
1
1
0
0
0
3
0
2
1
0
0
1
0
0
1
1
0
0
0
1
1
0
2
0
0
1
0
0
1
0
0
0
2
0
0
2
0
2
1
2
0
0
0
0
1
2
0
0
0
2
0
0
3
0
1
1
0
0
1
1
0
1
2
1
0
1
0
0
2
2
1
1
0
0
1
2
0
1
1
0
2
2
1
0
1
2
1
0
2
1
2
0
2
0
0
1
2
1
0
0
0
1
1
1
4
1
2
0
1
1
0
1
1
0
0
0
2
1
0
1
1
2
0
1
0
0
0
0
0
0
0
0
1
1
2
0
0
2
0
1
0
0
0
1
1
1
1
0
0
2
2
0
0
0
0
1
0
0
2
0
1
0
0
1
0
2
0
0
0
0
2
0
0
2
0
0
0
1
4
0
0
2
1
1
1
0
2
0
0
0
0
1
0
2
0
2
0
2
0
0
2
0
0
1
0
2
0
0
1
2
1
2
0
1
2
0
0
1
4
1
0
0
0
1
0
0
0
1
2
0
1
0
1
0
0
1
1
0
0
0
0
2
1
0
1
2
1
2
2
1
0
0
3
1
1
0
0
0
2
2
0
1
1
0
0
0
0
0
0
0
1
0
2
2
1
0
2
0
2
0
0
1
1
2
1
0
1
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
2
0
0
0
0
2
0
0
1
1
0
1
0
1
0
0
1
0
0
0
0
2
2
0
0
1
0
0
1
0
0
0
1
2
0
0
1
0
2
2
0
0
0
0
2
0
0
0
0
0
0
1
1
1
0
2
0
0
1
1
2
2
1
0
0
0
2
1
2
1
1
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
1
2
2
1
0
0
0
2
2
0
0
0
2
2
0
1
3
0
1
1
0
0
0
2
0
2
0
3
0
1
1
0
1
0
2
2
0
0
2
0
0
0
2
2
0
0
0
2
1
0
0
0
0
1
3
1
2
0
1
0
0
0
1
1
1
0
0
1
0
0
1
2
1
0
2
1
2
0
1
1
2
0
0
2
0
0
0
2
0
2
0
2
2
1
0
0
2
0
3
0
0
0
0
1
0
2
0
0
0
0
1
0
1
0
1
0
1
0
0
1
1
2
0
1
1
0
4
1
0
0
0
1
1
0
0
1
2
0
1
2
1
0
2
0
1
2
2
1
2
1
0
1
1
2
1
0
1
0
1
0
0
1
1
1
0
2
1
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
1
1
0
1
1
0
1
1
1
1
0
0
1
0
0
1
1
1
0
0
0
0
1
0
0
0
1
2
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
2
3
0
0
0
2
0
1
0
1
2
1
1
0
0
2
1
0
0
0
0
1
0
0
1
1
0
1
1
1
0
0
0
0
6
2
0
0
2
0
1
0
0
2
0
1
1
0
2
1
0
0
2
1
2
0
1
0
1
0
1
0
1
1
2
0
1
0
2
0
0
1
0
0
2
1
0
1
0
1
0
2
2
1
0
2
1
1
1
1
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
2
1
0
1
2
0
0
2
0
2
1
2
0
2
1
1
0
1
2
1
1
0
0
2
1
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
1
0
2
0
0
1
0
0
0
2
2
1
1
0
0
0
0
1
0
2
2
0
1
0
0
2
0
0
1
0
0
2
2
1
0
1
0
0
0
0
1
0
1
0
1
2
1
0
0
2
0
0
2
0
2
1
0
1
2
0
0
2
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
3
0
0
2
1
2
0
0
2
0
0
0
0
0
0
0
1
0
3
0
1
0
2
1
0
0
0
0
1
0
0
1
2
1
2
3
1
1
0
0
1
0
0
0
0
0
0
0
2
1
2
0
1
0
1
1
2
0
2
0
1
2
1
1
1
0
1
0
2
1
1
0
0
2
0
2
0
0
1
1
3
0
0
0
2
0
1
2
0
2
0
0
2
2
1
0
0
1
2
1
0
0
0
1
2
0
2
0
0
1
2
0
1
2
0
0
0
0
1
0
0
2
2
2
0
0
0
0
1
0
1
1
2
1
0
2
0
0
2
0
1
0
2
0
0
0
2
2
0
0
1
0
0
1
2
0
0
2
0
0
1
2
1
1
0
0
2
2
0
0
1
0
0
0
1
0
1
2
0
0
1
0
0
0
2
1
1
0
1
1
4
1
2
2
1
1
0
0
1
0
0
0
1
0
0
1
2
2
1
1
0
0
1
2
2
0
0
1
0
2
1
2
3
1
2
0
0
1
2
0
0
0
1
0
0
0
2
0
0
1
1
2
0
1
0
0
6
1
2
0
0
1
0
1
2
0
0
1
1
1
0
1
0
0
0
2
0
0
0
1
2
0
1
1
1
1
1
1
2
0
0
0
1
1
0
0
2
1
0
2
0
1
0
2
1
0
0
0
2
1
0
0
2
0
1
1
1
0
1
0
1
0
2
1
0
0
0
0
0
2
2
0
0
0
0
1
0
1
3
0
1
1
1
0
1
0
0
0
1
0
1
3
0
0
0
0
2
0
2
1
0
1
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
1
1
0
2
0
0
2
2
0
1
1
0
2
0
0
1
1
1
0
0
0
0
1
2
1
2
0
0
3
0
0
0
1
0
2
1
0
0
0
2
1
0
0
2
2
2
1
0
2
0
1
0
0
0
1
1
0
4
0
0
0
1
3
0
1
2
1
0
0
2
2
0
0
0
1
0
1
0
1
2
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
2
0
2
2
1
0
0
0
2
2
1
2
0
0
0
0
0
0
0
1
5
0
0
1
0
0
2
2
0
2
1
0
2
2
0
1
2
2
0
0
1
2
0
0
2
2
0
0
0
2
0
0
1
1
0
0
2
1
1
0
0
0
6
0
3
1
2
0
0
0
0
0
3
1
0
1
0
2
0
0
2
0
2
0
2
2
1
0
0
0
0
0
1
1
0
1
3
0
2
1
1
0
1
0
1
0
2
1
0
1
1
1
0
2
0
0
1
1
0
0
0
0
2
0
4
2
0
1
0
0
0
2
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
1
2
0
0
0
0
0
0
1
0
0
1
0
0
1
2
3
0
1
3
0
0
2
0
6
1
0
0
0
0
0
0
1
0
2
0
1
2
3
0
1
1
0
0
1
0
1
0
1
2
2
3
0
1
0
0
0
1
0
0
0
0
1
1
2
0
0
1
0
0
1
1
0
0
0
2
0
2
0
0
1
2
2
1
0
0
1
2
1
0
1
1
2
0
1
0
2
2
1
1
1
0
1
2
2
2
2
1
0
2
2
1
1
1
2
0
0
0
1
1
1
0
0
1
2
0
1
0
1
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
2
0
2
1
0
1
3
0
0
0
2
0
0
2
0
0
2
0
1
1
0
2
0
0
2
0
2
2
0
2
1
0
1
0
0
1
2
0
0
0
0
1
0
0
0
1
0
1
2
0
0
0
1
0
2
0
1
1
2
1
0
2
0
2
2
0
1
2
0
1
1
1
2
0
0
1
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
1
0
2
2
0
0
0
1
0
0
2
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
2
1
2
0
0
0
1
2
0
2
2
0
2
0
1
0
0
2
0
4
0
2
2
2
0
0
1
1
1
2
0
1
0
0
0
1
0
2
1
1
0
0
1
2
2
2
1
0
0
0
0
1
0
0
0
2
1
1
0
2
1
1
0
0
1
0
0
0
0
1
3
1
1
0
0
1
0
0
2
0
1
1
1
0
1
0
1
1
1
1
1
0
0
1
0
1
1
1
0
0
1
0
3
0
2
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
2
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
4
0
2
0
1
1
2
3
0
1
1
0
0
0
1
0
2
0
1
1
0
2
0
2
0
0
1
0
0
0
0
0
0
2
1
0
2
0
1
2
0
2
2
1
0
0
0
1
0
2
0
0
1
0
2
1
2
0
0
0
0
0
1
2
0
1
0
0
0
2
0
0
2
0
0
2
0
1
2
0
0
0
2
0
0
1
0
2
0
0
1
0
1
2
2
2
0
0
0
1
2
1
0
1
0
1
0
1
2
0
2
2
0
2
0
0
1
0
1
1
0
1
2
2
0
1
0
0
0
2
0
0
0
0
0
1
0
2
0
0
1
0
2
0
2
1
1
0
0
2
2
1
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
1
0
1
1
0
1
0
0
0
0
0
0
1
2
2
1
0
1
0
3
0
2
0
2
0
2
0
0
2
3
0
1
1
1
0
2
0
0
1
1
0
2
0
2
2
1
2
2
1
1
0
0
0
0
0
2
0
3
0
0
1
0
2
0
0
0
0
1
0
0
1
0
0
1
0
1
0
1
2
1
2
2
0
0
0
0
1
1
2
0
2
2
0
1
1
0
2
0
2
0
0
0
0
2
0
0
1
2
0
0
0
1
0
2
0
2
1
1
1
1
2
0
1
1
2
1
0
2
0
0
1
1
2
1
0
0
0
0
0
2
1
0
0
1
2
0
0
1
0
0
0
1
2
0
0
2
0
0
0
0
1
2
0
0
0
0
0
1
1
0
6
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
1
0
0
2
0
0
1
2
0
2
0
1
0
0
0
0
0
0
0
0
2
2
1
0
2
0
2
1
0
0
0
0
1
0
1
2
2
1
0
0
0
2
0
0
0
1
0
0
1
1
0
0
1
0
0
1
0
0
2
0
2
0
0
1
0
0
1
0
0
0
0
2
0
1
0
1
0
1
1
0
0
1
2
0
0
2
1
1
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
2
0
2
0
1
0
3
0
0
0
0
1
2
0
0
0
0
0
1
1
0
1
0
1
1
0
0
0
0
1
3
1
0
0
0
0
2
0
0
1
0
0
0
2
0
1
0
1
1
2
1
0
1
2
1
1
0
0
1
0
0
1
0
0
2
0
2
2
0
1
1
2
1
1
2
0
1
0
0
1
2
0
1
0
0
2
2
1
1
0
1
0
0
3
0
0
1
0
2
0
2
1
2
1
0
2
2
1
1
0
1
0
1
0
0
0
0
1
1
1
0
0
1
2
0
0
1
0
0
1
2
0
0
0
2
0
1
0
0
2
0
0
0
0
0
1
2
1
0
2
0
0
2
0
0
0
0
2
2
0
0
1
0
2
0
0
1
0
1
1
0
0
0
1
1
0
0
0
2
2
2
2
2
1
0
1
1
2
0
2
1
0
0
0
2
2
1
0
0
1
0
1
2
2
1
1
0
2
0
1
0
0
2
0
0
2
1
0
0
1
2
1
2
0
1
2
1
0
1
0
0
1
0
0
2
0
0
1
0
1
0
1
0
1
0
2
2
2
0
0
1
2
0
1
0
1
1
0
1
0
3
1
0
0
2
2
0
1
0
0
0
0
2
0
1
0
1
1
0
3
1
1
0
1
0
0
1
1
0
0
2
1
0
0
0
0
0
1
0
2
1
0
0
0
0
3
1
0
0
1
2
0
2
0
0
4
1
0
1
0
2
0
1
0
0
0
1
0
2
1
1
0
0
0
0
0
0
3
0
2
0
0
1
1
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
2
1
1
1
1
1
0
0
0
0
1
1
1
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
3
2
1
2
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
1
1
0
0
2
0
1
2
0
0
0
2
4
1
0
0
0
0
1
0
0
0
0
1
0
0
0
2
2
1
1
2
0
0
0
1
0
0
0
2
0
1
0
2
0
0
0
2
3
2
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
2
2
2
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
5
0
0
2
0
0
0
2
2
0
0
0
1
0
1
0
1
1
1
0
0
2
1
1
0
0
0
0
3
0
1
0
0
0
0
0
0
1
2
0
0
2
1
1
0
1
1
0
0
1
2
0
2
0
0
0
1
2
2
3
1
1
0
2
0
1
0
0
0
2
2
1
0
0
0
0
0
2
2
0
0
2
2
0
0
0
0
2
1
3
2
1
1
1
2
0
1
2
0
1
2
0
2
2
0
1
3
2
1
1
2
1
0
0
2
0
2
0
0
0
1
0
2
1
4
0
4
0
1
0
1
0
0
0
1
0
0
2
0
2
0
1
1
1
1
0
0
2
0
0
2
2
0
0
1
0
2
2
0
0
2
0
0
0
1
3
2
2
0
2
0
1
1
0
1
2
1
2
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
1
1
1
0
0
1
1
7
0
2
0
1
1
2
0
0
1
2
1
1
0
0
1
0
2
0
2
1
1
1
0
0
1
0
1
1
0
1
0
0
0
1
1
1
2
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
2
3
4
0
0
8
0
0
3
0
1
1
0
0
1
0
2
0
0
2
2
0
0
1
0
2
0
1
0
1
1
0
2
0
0
1
1
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
2
2
0
0
2
0
2
0
2
1
0
0
0
3
1
3
2
1
0
2
0
2
0
3
2
0
0
0
1
0
0
0
1
2
1
1
0
0
2
1
2
4
1
2
1
0
0
9
0
2
0
0
1
0
1
1
1
2
0
2
1
0
2
0
0
0
1
0
0
2
0
0
0
2
1
0
1
0
0
1
2
0
0
0
1
0
1
2
1
1
1
3
0
0
0
0
1
0
0
1
1
0
2
0
0
1
2
2
1
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
1
1
0
0
0
2
2
0
0
2
0
2
1
2
0
1
0
1
0
1
1
1
2
0
1
0
0
0
1
0
0
0
2
1
0
0
0
2
0
2
1
0
0
0
0
0
0
1
2
1
0
1
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
1
0
2
0
2
1
0
0
0
2
2
0
3
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
2
1
1
0
2
1
0
0
1
1
1
1
0
1
1
0
1
0
1
0
0
1
0
2
1
2
0
0
0
0
0
0
1
1
0
0
0
1
2
0
2
2
1
0
1
2
1
0
1
0
1
0
1
0
0
0
0
0
0
3
2
1
0
0
1
0
0
0
0
0
0
0
2
1
2
1
0
1
0
0
2
2
2
0
1
1
1
0
0
0
0
1
1
0
1
0
0
2
1
1
2
2
0
2
0
1
2
0
0
0
1
0
0
1
0
1
1
1
3
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
1
1
0
1
0
0
0
2
2
2
0
1
0
2
0
0
2
2
1
1
2
2
1
0
0
1
0
0
1
0
1
2
0
0
2
0
0
0
1
0
0
0
0
1
2
2
1
1
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
3
2
2
1
0
0
1
0
1
1
0
1
2
1
0
0
1
0
0
2
1
1
0
1
0
0
1
2
1
2
1
0
1
0
1
1
0
2
1
1
0
0
0
0
1
1
2
1
0
0
0
0
1
0
0
1
0
0
1
0
0
2
1
1
2
0
0
1
1
0
0
1
0
2
2
2
0
1
0
0
1
4
3
0
2
0
0
0
0
0
1
0
0
2
0
2
2
1
1
0
0
0
0
3
1
1
0
1
1
1
0
2
0
2
1
0
0
1
2
2
1
0
0
2
1
0
1
0
0
0
0
2
1
4
1
0
0
0
0
1
0
1
0
1
0
0
2
1
0
1
1
1
2
1
0
0
2
2
0
0
1
0
2
1
0
0
2
1
0
0
0
2
0
1
2
1
0
0
0
1
1
1
0
2
2
1
1
0
0
0
1
0
0
0
0
0
0
2
2
0
1
0
2
0
0
0
0
0
1
1
0
0
0
0
1
2
0
0
1
0
1
5
1
0
4
0
1
1
0
1
1
1
0
1
5
1
0
0
0
0
3
0
0
2
2
1
0
0
3
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
2
0
0
1
0
0
2
0
1
1
0
0
2
0
2
1
0
1
0
0
2
0
0
1
0
2
2
0
0
1
1
1
2
1
1
2
0
0
0
0
0
2
2
2
0
0
1
0
0
0
0
0
0
1
0
2
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
2
1
0
1
0
2
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
1
0
0
1
0
2
1
0
0
1
0
2
1
0
0
0
2
0
2
0
0
0
2
2
2
0
2
0
2
2
2
1
0
0
0
0
0
2
0
0
0
2
0
1
0
0
2
0
0
2
2
2
0
0
0
0
2
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
2
2
1
2
0
2
1
2
0
0
1
0
1
0
0
0
1
1
1
0
0
1
0
0
0
0
2
0
0
2
0
0
2
1
0
0
0
0
0
1
1
0
1
0
0
0
2
0
0
1
0
0
2
2
1
3
0
2
0
0
0
0
2
1
0
0
2
1
0
0
0
4
2
0
0
0
0
0
2
2
2
0
0
2
1
0
1
0
0
1
1
3
2
1
1
1
2
0
0
1
0
0
1
0
2
0
0
1
0
0
2
2
0
1
0
3
1
0
1
2
5
0
0
0
1
0
1
2
1
0
1
3
3
1
2
0
3
1
0
0
0
0
2
0
0
0
0
0
1
2
2
1
1
0
0
2
0
1
0
1
0
2
2
2
1
0
0
1
0
0
0
0
2
4
0
0
0
0
2
0
0
0
0
2
0
2
0
1
0
0
2
0
1
1
0
1
1
0
0
0
0
1
0
0
2
0
0
1
2
0
2
2
1
2
0
0
0
0
1
0
0
2
1
1
1
2
0
2
1
1
2
1
0
1
0
0
0
2
0
0
1
0
1
0
0
2
0
1
0
0
1
0
1
0
1
0
1
0
2
1
0
0
2
0
1
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
1
0
0
1
0
0
0
0
0
1
2
2
0
0
1
1
2
2
2
1
0
1
0
0
1
0
1
1
0
1
0
0
4
2
0
1
2
0
0
2
0
0
2
1
0
2
2
2
0
0
0
0
1
2
2
2
0
3
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
1
2
2
3
0
1
1
2
0
2
1
0
0
1
1
0
2
1
0
0
0
2
1
0
0
0
1
0
0
1
2
0
0
0
1
1
1
0
1
1
1
0
0
1
1
1
1
1
0
1
0
0
2
0
1
0
1
0
1
0
0
2
1
0
2
0
0
0
1
0
0
2
1
0
2
0
2
0
0
0
0
0
2
0
0
2
1
0
2
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
1
1
0
3
1
0
0
1
2
2
0
0
1
0
1
0
0
0
2
1
0
0
0
1
2
1
1
0
0
2
2
1
0
0
0
0
2
1
2
2
1
1
1
0
2
2
2
2
0
0
0
2
1
0
0
3
0
2
0
0
0
0
0
0
0
0
1
1
0
2
0
0
1
1
1
0
0
2
0
2
1
1
2
0
1
2
0
1
1
1
1
2
1
0
2
0
0
0
2
0
2
1
0
2
0
0
0
1
3
2
2
1
0
1
0
2
1
0
0
2
0
0
1
1
1
2
0
2
0
2
1
3
0
0
1
0
3
2
0
1
0
1
1
1
2
1
0
2
1
0
0
0
1
1
1
1
0
2
2
0
0
1
2
1
1
0
1
1
1
1
2
1
1
0
1
0
1
1
1
2
0
1
2
0
0
0
1
1
2
0
2
0
0
1
2
2
0
0
0
1
1
0
0
0
1
2
0
1
0
0
1
2
0
1
0
4
0
0
1
1
0
0
0
2
0
0
1
0
0
2
0
0
1
0
0
1
1
0
1
0
1
0
0
0
1
0
2
0
2
1
1
1
0
0
1
1
1
0
0
2
1
1
0
1
0
0
1
2
0
2
0
0
0
0
2
1
2
0
0
4
0
1
1
0
0
1
0
1
0
1
2
0
0
1
0
0
1
0
1
1
1
1
0
1
0
1
0
0
2
2
1
0
0
0
0
0
1
2
1
0
1
2
2
1
0
0
1
2
0
0
0
2
1
0
0
0
0
0
7
0
2
0
0
0
2
1
1
3
2
1
2
1
0
3
2
1
1
0
2
0
0
0
2
1
0
2
2
1
2
0
2
0
1
0
1
1
1
1
0
0
0
0
0
1
0
1
0
1
2
1
1
3
0
2
0
3
3
0
2
1
0
0
1
1
0
0
0
0
0
1
0
2
1
0
1
0
2
0
0
0
2
2
0
0
1
0
2
1
0
0
0
0
1
0
1
2
0
0
0
2
0
2
2
1
1
1
2
1
1
2
0
1
2
0
0
0
2
0
0
0
2
2
0
0
2
0
0
0
0
1
0
2
0
1
1
2
0
1
1
2
2
1
0
0
0
2
1
1
1
0
1
0
0
2
0
1
0
1
0
0
2
2
0
1
2
1
0
0
1
0
2
1
0
0
1
0
2
1
1
1
0
0
2
1
3
1
2
0
1
2
1
3
0
0
1
0
0
1
1
0
0
1
1
1
0
2
0
0
0
2
1
0
0
1
1
0
0
1
1
1
0
1
2
3
1
1
1
0
1
2
0
0
0
1
1
0
0
0
0
0
1
1
0
1
1
0
2
0
2
0
1
0
1
2
0
0
2
0
0
2
0
0
1
0
0
2
0
0
0
0
2
1
2
1
0
1
1
0
0
3
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
2
1
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
2
2
1
0
2
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
2
0
3
1
0
2
1
0
0
1
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
2
2
1
1
2
2
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
3
1
0
0
0
0
3
2
2
2
1
0
0
2
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
3
1
1
1
3
1
0
1
2
1
1
1
0
0
2
3
1
1
2
0
0
1
0
0
1
0
0
0
0
1
2
2
0
0
0
1
2
0
7
0
0
2
0
0
1
0
2
0
0
1
1
2
2
3
1
2
0
0
1
1
1
0
0
0
0
0
1
1
1
0
1
0
1
0
0
2
2
1
0
0
2
0
0
0
1
0
2
2
0
2
2
2
0
0
0
2
0
0
3
0
1
1
2
0
0
0
0
1
1
0
1
0
1
0
2
0
2
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
3
0
0
2
0
2
1
0
2
1
2
0
2
0
2
2
3
0
0
1
2
0
1
6
0
0
1
0
1
0
0
0
2
0
2
0
1
0
0
0
0
0
1
0
2
0
1
1
0
0
0
2
2
0
2
0
4
0
3
1
3
1
0
1
2
2
0
0
0
0
0
1
0
0
2
1
0
2
1
2
2
0
0
1
2
1
0
0
2
0
1
0
1
0
0
0
0
1
0
1
1
0
2
1
2
1
0
1
0
0
0
2
1
2
0
2
1
0
0
0
0
2
2
0
0
0
0
1
3
0
0
0
0
0
0
0
1
1
1
1
2
2
2
0
1
0
1
0
0
0
1
0
2
1
3
1
2
1
1
0
0
1
2
0
1
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
2
0
1
0
0
0
1
0
0
1
2
1
0
2
0
6
1
0
1
0
1
0
0
1
0
0
1
2
0
2
1
1
1
2
1
2
2
0
0
3
2
0
0
1
0
0
1
0
1
0
1
0
0
3
2
0
2
3
0
1
0
2
0
0
2
1
0
0
2
1
1
0
2
0
0
2
0
1
0
0
1
2
0
0
0
0
0
1
1
0
0
0
1
0
0
2
0
1
0
0
0
0
2
0
0
0
1
0
0
0
1
2
1
1
0
1
2
0
2
0
2
3
1
0
0
0
2
0
1
0
0
1
0
1
3
0
2
0
0
2
1
2
2
0
0
0
0
2
0
1
1
1
1
0
1
1
1
0
1
2
1
0
0
0
0
0
2
1
2
0
1
0
0
0
0
0
0
0
0
0
0
2
1
1
1
2
0
0
0
1
2
1
1
2
0
1
0
1
2
1
0
1
0
0
1
0
0
2
0
2
0
0
2
2
2
0
1
0
1
1
0
2
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
1
0
1
1
1
1
0
2
2
0
0
0
2
0
1
1
1
1
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
1
2
0
0
4
0
1
1
0
0
0
1
2
2
1
0
2
1
0
1
1
0
2
0
0
2
1
0
0
0
1
0
0
0
0
3
2
0
1
1
1
1
0
0
0
2
1
0
0
2
0
2
0
0
2
0
0
2
1
2
0
0
1
2
0
4
1
0
0
1
1
1
0
0
1
2
0
0
0
1
1
0
1
2
2
1
0
0
0
0
1
2
0
1
2
2
0
1
0
0
0
0
0
0
1
0
0
2
2
1
2
0
0
0
1
0
0
0
1
1
0
0
2
0
1
2
1
0
0
1
1
0
0
0
2
1
1
2
2
1
2
0
0
1
0
2
2
0
2
0
0
0
3
2
2
2
1
2
1
1
1
1
0
1
0
1
1
1
2
1
1
2
0
1
1
0
1
0
3
0
0
2
1
0
2
0
1
0
2
0
0
0
0
0
0
2
1
2
0
0
0
1
0
0
2
0
0
0
1
2
0
2
0
1
2
2
0
0
1
0
1
0
1
1
0
1
2
3
0
0
0
1
0
0
1
0
0
0
0
2
2
1
0
0
0
2
0
2
2
1
0
1
1
1
1
0
1
0
2
1
0
0
4
0
0
1
1
2
1
0
0
1
2
1
1
2
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
2
0
0
2
0
0
0
1
1
1
0
0
1
1
2
0
1
0
1
0
0
0
1
0
2
0
0
1
0
1
0
0
0
0
0
0
1
0
1
1
2
2
0
1
0
2
1
0
3
0
0
1
2
1
2
0
1
1
0
2
0
0
0
1
1
2
1
3
2
0
1
0
2
1
0
3
1
0
0
1
2
2
1
3
0
0
0
1
0
1
1
0
2
0
1
0
1
1
0
0
2
0
0
1
2
1
1
0
0
2
1
2
0
1
2
1
0
1
0
0
0
0
0
0
2
0
0
1
0
2
0
0
1
2
0
0
1
0
0
1
1
0
0
0
0
1
0
0
1
1
0
3
1
1
0
1
1
1
0
1
1
2
2
0
1
2
0
2
2
1
0
1
1
3
1
1
0
0
2
1
1
0
2
2
2
0
0
0
0
1
0
3
3
0
1
0
0
0
1
0
2
3
2
0
0
1
0
0
0
2
0
0
3
1
0
0
1
2
0
0
0
1
0
1
2
1
1
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
2
2
0
0
0
2
0
1
1
0
1
0
1
2
0
1
2
0
2
0
2
1
0
1
1
1
2
1
0
0
0
0
2
0
0
1
2
1
0
0
2
2
2
1
2
1
1
0
0
2
2
1
2
2
0
0
2
2
0
1
0
1
0
0
2
0
0
1
0
0
0
2
0
1
0
1
1
0
1
1
0
1
0
0
0
0
1
0
1
0
0
1
0
1
0
2
0
1
0
1
0
1
0
1
1
0
2
0
0
2
1
0
1
0
1
0
0
1
3
2
2
1
0
1
0
0
0
1
0
2
0
1
0
0
0
0
0
0
1
0
0
1
1
1
2
0
1
0
1
0
1
2
1
1
0
0
1
0
2
0
0
0
0
0
1
2
1
0
0
0
2
2
2
0
1
0
1
1
1
0
0
1
1
2
0
2
2
1
0
0
1
0
1
2
3
1
0
0
3
0
0
1
0
1
0
0
2
0
0
2
0
1
0
1
1
1
1
2
1
2
0
0
0
0
2
1
1
2
0
0
0
0
0
2
0
2
0
0
1
2
0
0
0
1
0
2
0
1
1
0
0
0
0
2
0
2
2
0
0
2
1
0
1
0
0
0
1
2
0
0
1
0
0
0
3
1
2
0
1
2
0
1
0
0
0
1
2
2
0
1
0
1
1
2
0
0
2
0
1
0
0
0
0
2
0
0
1
3
0
0
0
2
0
1
1
1
0
0
1
0
1
1
1
0
1
0
2
0
0
1
0
0
10
0
1
0
1
2
0
0
0
1
0
1
2
2
2
2
0
0
0
1
0
0
1
0
2
1
0
1
2
0
2
0
2
1
0
0
0
1
0
0
0
1
1
1
0
0
1
0
1
0
1
0
0
2
0
0
0
2
0
0
2
0
0
2
0
1
1
0
0
1
1
1
0
2
1
0
2
0
2
1
1
0
0
2
0
0
0
0
1
0
0
0
1
0
0
1
1
0
2
3
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
1
1
0
1
0
0
2
0
0
0
3
0
0
0
0
4
3
0
0
1
0
0
2
1
0
0
0
0
0
0
0
1
0
5
0
0
0
1
0
2
1
0
2
0
0
0
0
0
1
0
1
1
1
0
3
0
2
1
1
0
2
0
0
0
9
0
1
1
0
3
1
1
2
0
0
0
0
2
0
3
0
1
1
0
1
0
0
0
0
0
2
1
1
0
0
2
0
0
0
2
2
0
1
0
1
0
2
1
0
0
0
1
0
1
0
2
0
1
0
0
0
0
1
2
0
0
0
0
3
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
1
0
0
2
0
0
1
2
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
2
1
0
0
2
2
1
1
1
1
0
2
0
1
2
0
0
0
0
2
0
2
2
0
0
3
2
0
1
1
1
2
0
0
2
0
1
1
0
1
0
0
0
0
1
0
3
1
1
0
1
2
4
2
0
0
0
0
0
0
0
0
0
2
0
1
1
1
1
0
0
2
1
2
6
0
3
0
1
0
1
0
1
1
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
2
1
2
0
0
0
0
0
2
2
0
2
1
0
0
1
0
1
0
1
0
2
1
2
0
0
2
2
0
0
1
0
2
0
0
2
0
0
1
1
0
2
0
2
0
0
1
0
0
1
0
0
2
0
0
2
1
0
0
1
0
0
1
0
0
1
0
0
1
0
1
3
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
1
2
0
0
0
2
0
0
1
1
0
0
2
0
1
1
2
2
0
0
0
0
0
0
2
2
1
1
0
3
0
0
0
3
4
3
1
0
0
1
0
1
0
2
2
1
0
1
0
0
1
0
0
1
0
0
1
1
0
0
1
0
1
2
2
0
1
0
0
0
1
1
2
1
1
1
1
0
0
3
0
0
0
1
0
2
2
1
0
0
0
2
0
0
0
0
1
0
0
0
0
1
2
0
1
0
0
1
1
0
0
0
0
1
3
1
0
0
0
1
1
0
0
1
1
0
2
0
1
2
1
0
0
0
0
4
0
0
2
0
0
1
1
0
1
0
0
0
2
0
3
1
3
0
3
2
2
1
0
0
1
0
2
1
1
0
0
0
0
2
0
1
2
0
0
1
1
3
0
0
0
0
1
0
1
1
2
1
1
0
1
3
1
0
0
1
1
2
2
0
0
3
0
1
0
3
1
0
2
0
0
0
0
1
0
1
1
0
2
0
2
0
2
1
2
0
1
0
2
0
0
2
0
1
0
0
1
1
0
2
2
0
0
1
2
0
0
2
0
0
0
1
1
1
0
0
1
2
0
0
0
2
0
2
1
1
0
0
1
1
0
1
2
0
2
0
1
0
1
1
2
2
0
1
0
0
0
0
1
0
2
0
0
1
0
0
1
0
0
1
2
2
0
1
0
0
0
0
0
1
1
2
1
0
1
0
0
0
0
2
0
1
0
1
1
2
0
0
0
1
0
0
0
0
1
0
2
2
0
0
1
0
2
0
1
1
0
0
0
1
0
0
0
0
2
1
0
0
0
3
0
1
1
1
0
1
1
2
0
1
0
0
2
1
1
1
0
1
1
2
2
2
0
0
0
0
0
2
2
2
1
1
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
1
1
0
0
1
0
0
1
1
0
0
0
0
2
1
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
1
0
2
1
0
0
0
1
0
0
2
0
2
1
0
1
2
1
1
1
0
0
2
2
0
1
0
1
0
1
0
0
0
2
0
0
0
1
1
0
0
1
0
0
2
2
0
0
1
0
0
0
0
0
2
0
0
0
1
3
1
2
1
1
0
0
1
0
1
0
1
1
0
1
1
0
1
1
1
3
0
1
0
0
0
0
0
0
1
1
0
0
2
1
0
0
2
2
0
2
0
1
1
0
1
1
1
1
1
0
2
0
1
1
0
0
1
0
0
2
0
1
1
0
0
1
0
0
0
0
1
2
2
1
4
2
1
0
0
3
0
0
0
2
0
0
2
1
1
0
1
2
0
1
1
0
0
1
1
0
2
0
0
0
1
1
0
0
1
1
2
0
0
0
2
2
1
2
1
2
0
0
3
0
0
2
2
0
0
2
0
1
1
0
0
2
1
2
0
2
1
1
2
1
2
1
1
2
0
2
0
0
0
1
3
0
1
2
1
0
1
0
0
0
1
0
2
0
1
2
0
1
0
0
1
0
3
0
0
0
2
4
1
0
2
0
1
2
1
2
0
1
0
1
1
2
2
1
0
0
0
0
0
0
1
2
0
2
2
1
0
0
2
0
0
0
0
0
5
0
0
1
2
1
0
1
0
0
0
1
0
3
4
1
0
0
0
1
0
0
2
0
0
2
0
1
0
1
0
0
0
2
1
0
0
0
0
1
0
0
1
0
0
0
2
0
0
1
1
1
1
0
1
1
0
0
3
1
0
0
1
1
0
0
4
0
0
0
2
0
0
1
0
1
2
0
0
0
2
2
0
0
0
2
2
2
0
0
0
2
0
2
1
0
0
0
2
2
0
2
1
0
0
2
0
1
2
2
2
1
0
1
1
1
0
0
0
4
0
1
0
1
0
0
2
0
0
0
0
1
4
2
1
0
1
0
0
0
2
0
1
1
0
1
3
2
0
1
0
0
1
2
1
2
4
1
1
0
2
0
0
0
1
1
0
0
0
0
2
2
2
0
0
0
0
0
2
0
1
1
1
2
0
0
2
0
2
0
0
0
0
0
1
2
0
2
0
0
0
0
1
1
0
0
2
0
1
1
0
0
1
0
0
0
1
2
0
0
1
0
0
2
2
0
2
1
0
0
0
3
0
1
1
2
0
2
1
0
1
0
0
1
0
0
0
2
1
0
0
1
0
2
1
0
1
0
0
1
1
0
1
0
0
0
1
2
6
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
2
0
0
1
1
1
1
1
0
1
1
0
0
1
0
2
0
1
1
1
1
2
0
3
2
2
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
1
1
1
2
0
0
0
1
0
2
0
0
0
0
2
1
0
1
0
2
0
1
0
1
1
2
0
1
1
2
0
2
1
1
0
0
1
0
2
0
0
3
0
0
0
1
2
2
2
0
0
1
0
2
2
1
0
0
1
1
0
0
1
1
2
4
0
2
2
0
0
0
0
0
1
1
0
0
2
0
0
1
0
0
1
2
1
0
3
0
1
1
0
0
2
2
0
0
0
0
0
0
0
0
1
2
1
2
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
2
2
0
0
1
1
0
1
0
0
1
2
0
0
1
2
0
2
0
1
0
0
0
2
1
0
0
1
0
1
0
1
0
0
0
2
0
0
0
2
0
0
0
2
1
0
1
1
0
0
0
0
0
2
1
1
0
0
0
1
2
2
1
1
0
3
0
1
0
0
0
0
1
0
0
1
0
0
2
0
1
1
1
1
0
0
0
2
0
2
0
2
0
2
2
2
1
0
1
0
2
1
1
2
1
1
1
1
0
1
0
0
2
0
1
2
1
2
2
2
0
1
0
0
1
0
0
1
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
2
0
1
1
0
0
1
0
1
0
0
0
0
1
1
0
1
0
0
2
0
1
0
2
1
0
0
1
0
0
1
2
1
0
0
0
1
0
0
1
1
0
0
2
1
0
0
0
0
0
0
2
1
1
0
2
2
2
1
2
0
0
1
0
0
1
2
0
0
1
0
0
0
1
1
0
2
1
0
0
1
0
1
1
1
2
0
2
0
2
0
2
0
0
0
2
1
1
1
0
2
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
2
1
2
1
1
1
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
1
3
0
2
1
1
2
1
2
0
1
1
1
0
1
1
0
2
2
2
0
0
2
2
1
0
0
1
1
0
1
1
0
1
1
1
0
0
0
1
1
0
1
1
0
0
1
0
1
1
0
1
2
0
2
0
1
0
0
2
1
1
0
0
1
0
1
0
1
1
2
1
0
0
0
0
1
2
1
0
1
1
0
2
2
2
1
2
0
2
2
1
1
1
1
1
1
1
1
2
1
2
2
1
2
0
0
0
0
0
2
1
0
0
1
2
1
1
2
1
2
2
0
0
2
1
0
1
2
1
0
2
0
1
0
1
0
1
2
0
0
1
0
0
0
0
1
1
2
0
0
0
0
0
2
1
0
0
0
1
1
1
1
0
2
0
2
0
0
0
0
0
1
0
2
0
0
1
0
0
0
1
2
0
0
1
1
2
0
1
2
2
2
2
1
2
0
0
1
2
0
0
0
1
0
1
0
1
0
0
0
2
1
0
0
1
1
0
2
1
0
0
0
1
0
1
1
1
0
0
2
0
0
1
0
0
0
0
0
2
1
2
0
0
1
3
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
1
0
0
1
0
2
0
1
0
1
0
0
1
0
1
0
1
2
1
1
0
0
0
0
1
0
0
2
0
1
0
1
0
1
2
0
2
0
1
2
0
3
0
0
0
3
2
1
2
2
0
1
3
0
1
2
0
0
0
0
0
0
1
1
2
0
1
1
0
2
0
2
1
0
0
0
1
1
0
0
1
0
0
0
0
2
1
0
0
0
0
1
0
1
0
2
0
1
1
1
1
0
0
1
2
0
2
1
0
2
1
0
0
1
0
1
1
0
0
0
0
0
2
1
0
0
0
0
0
2
2
1
0
2
2
2
2
2
1
2
2
3
1
0
0
0
2
0
0
0
0
0
1
1
0
1
1
0
0
2
2
2
0
0
0
2
1
1
1
2
0
2
2
1
1
2
0
0
1
0
3
2
0
2
0
9
1
2
0
1
0
0
2
1
0
0
0
1
1
0
1
0
1
0
2
0
3
2
1
1
1
0
1
2
2
2
2
1
0
0
2
1
1
1
0
2
0
0
1
2
0
1
0
2
1
0
0
0
2
0
1
2
2
1
1
1
2
0
0
2
1
4
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
3
2
0
0
0
0
1
0
1
2
0
2
0
0
2
0
0
0
0
1
0
1
0
0
2
1
0
1
0
2
0
2
1
2
2
2
0
0
0
2
1
0
0
2
1
2
0
0
0
1
1
0
0
2
2
1
0
1
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
1
0
1
0
0
0
1
0
3
0
0
0
1
0
2
1
1
0
2
0
2
1
1
1
3
0
0
0
0
0
1
1
2
0
0
1
1
0
0
0
0
1
0
2
0
2
1
0
2
1
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
2
0
0
2
2
0
1
0
0
0
1
1
1
0
0
1
1
0
0
2
0
1
0
2
0
2
2
2
0
0
0
0
1
0
0
1
1
1
0
0
0
1
0
3
1
2
1
0
2
2
1
0
0
0
2
2
1
0
0
0
0
0
0
0
1
0
1
2
0
1
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
1
1
1
2
2
0
0
2
0
2
1
1
0
1
0
0
0
0
0
2
0
0
1
0
0
0
1
0
2
2
1
2
1
2
0
0
0
0
2
1
0
1
2
2
0
0
0
0
0
0
0
0
2
1
0
2
0
2
0
0
2
0
1
2
2
1
2
0
0
2
0
0
2
0
2
0
0
0
0
1
0
0
1
1
2
0
1
0
1
0
1
0
0
0
1
1
2
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
3
0
0
2
1
0
0
1
0
3
0
0
0
1
1
0
0
0
0
2
0
2
0
3
0
1
0
2
0
3
2
2
2
0
1
2
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
2
0
0
1
1
1
0
1
0
0
0
0
0
1
0
0
3
0
0
0
2
0
0
1
0
0
0
1
0
0
0
2
2
0
3
0
0
1
0
1
0
2
1
1
1
0
0
0
0
0
0
0
1
0
1
2
0
0
1
1
0
0
2
1
0
1
2
0
0
0
2
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
2
0
2
3
0
2
1
1
1
2
1
0
2
0
1
0
3
0
0
1
0
5
0
1
2
0
0
0
2
0
0
0
0
0
0
0
2
0
1
1
0
2
0
0
1
1
0
2
1
2
1
0
1
1
1
1
0
1
2
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
4
2
2
2
1
0
1
0
2
0
2
1
0
0
0
0
0
1
1
0
0
1
0
0
2
0
0
1
1
0
0
1
1
0
1
7
0
0
0
1
2
2
0
2
0
2
2
0
0
0
2
2
0
0
1
0
0
3
0
2
0
1
1
0
1
3
0
0
0
2
0
0
0
0
2
1
0
2
0
0
0
0
0
1
2
2
0
0
1
2
1
0
0
1
1
1
0
1
2
0
1
1
1
0
0
2
2
0
1
0
0
0
1
0
1
0
0
1
0
0
2
2
2
1
2
0
0
0
0
2
0
0
0
0
0
0
0
1
1
1
1
3
2
1
1
2
0
0
0
0
0
0
2
1
0
0
1
0
0
0
2
1
1
0
4
2
0
0
1
2
0
0
1
0
0
0
0
0
1
0
1
4
0
1
1
1
3
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
2
1
0
0
0
3
1
1
1
2
3
2
0
0
0
0
0
1
1
0
1
1
0
2
0
0
0
2
2
0
0
1
0
2
1
0
2
2
0
0
0
2
2
1
1
2
0
0
1
1
1
1
0
0
0
1
0
0
0
2
0
0
1
0
1
1
0
1
0
1
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
1
0
0
0
2
0
1
1
0
0
1
1
0
1
0
0
1
0
0
0
0
0
1
0
1
1
0
2
0
1
0
1
0
2
1
2
1
0
0
0
2
1
1
1
2
0
1
1
2
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
1
1
2
2
0
0
1
1
1
0
1
1
2
2
0
0
0
0
0
1
1
2
2
1
0
0
1
0
0
0
0
0
1
1
1
0
1
1
2
1
2
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
1
2
0
0
1
2
1
0
0
0
1
0
0
1
0
1
1
1
1
0
0
2
0
1
2
0
2
1
1
0
1
1
1
3
0
2
0
0
1
2
1
0
3
0
0
0
1
0
1
1
0
1
0
2
0
1
2
1
1
0
0
1
0
3
0
2
1
0
0
1
2
1
0
0
1
0
0
0
1
0
2
1
2
0
0
0
3
2
0
0
2
1
0
1
0
2
2
0
1
1
1
0
0
3
0
1
1
0
0
1
0
2
0
0
0
1
3
2
0
0
1
2
0
0
2
0
1
1
2
2
0
2
0
0
0
1
0
2
1
1
3
0
0
2
0
0
1
0
0
0
0
0
0
0
2
1
4
1
2
1
1
1
0
0
0
2
1
1
1
1
0
0
2
2
1
1
1
0
0
0
2
1
1
0
0
1
2
2
0
0
0
0
1
0
0
1
2
0
0
0
0
0
2
1
0
0
1
1
1
1
0
0
1
0
0
0
1
0
0
0
0
0
1
1
1
2
1
2
1
0
1
0
0
2
0
0
0
0
2
2
1
0
2
2
2
0
0
3
1
1
0
1
1
0
1
0
0
2
2
0
0
1
0
0
1
0
0
0
0
1
0
2
0
0
1
1
0
0
1
1
2
1
0
0
1
0
1
1
0
0
1
0
0
0
0
1
0
2
0
0
1
0
2
1
0
1
1
1
0
0
0
0
0
0
0
2
1
3
2
0
2
0
2
0
0
1
1
0
0
0
0
2
0
3
0
2
1
0
0
0
0
0
0
1
1
2
2
0
0
0
4
2
0
0
0
1
0
1
2
0
0
0
0
1
0
1
0
0
3
2
0
1
1
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
1
2
0
2
0
0
1
0
0
2
2
1
0
2
2
0
1
2
1
1
2
0
0
1
1
0
0
0
2
2
2
2
0
0
0
0
1
1
0
1
0
0
0
0
0
1
1
1
0
0
2
0
0
1
2
1
2
1
2
1
0
1
0
0
2
1
0
1
0
0
3
0
0
2
1
0
0
2
0
2
2
1
0
0
1
0
2
0
0
2
7
2
1
0
2
0
0
0
0
0
0
1
0
0
2
0
0
1
2
0
0
0
2
0
2
4
1
0
2
2
0
0
0
2
1
0
0
2
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
1
0
0
1
2
0
0
0
1
1
0
0
1
1
2
1
1
2
1
1
0
2
2
0
0
1
3
0
2
0
1
0
1
2
0
1
0
1
1
2
1
2
1
1
0
1
0
0
0
0
1
2
0
0
1
1
0
1
2
0
0
2
0
1
2
1
1
0
0
2
2
1
1
1
0
2
1
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
2
1
0
1
1
2
1
0
2
0
0
1
1
0
2
1
1
0
0
0
0
0
2
7
0
2
1
0
0
1
0
2
2
4
0
0
4
0
0
1
0
0
0
1
2
1
2
2
2
1
0
1
0
0
2
1
1
1
0
1
0
1
0
2
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
1
2
2
1
0
0
1
1
1
3
0
3
1
2
0
1
0
0
0
1
2
1
3
1
1
1
0
1
0
5
0
1
0
0
0
5
0
0
2
1
0
2
0
0
0
2
2
1
2
1
2
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
2
1
1
0
0
0
2
1
1
1
0
1
1
0
1
1
0
1
0
2
1
0
0
0
2
2
0
0
0
1
2
1
0
3
0
0
0
0
1
0
0
1
0
3
1
1
2
2
0
0
0
0
2
0
0
1
3
0
1
2
0
2
0
2
1
0
0
0
1
0
1
1
0
1
0
1
2
0
2
0
1
0
0
0
0
2
0
2
0
1
0
1
2
0
2
2
0
0
0
2
1
1
1
0
2
1
1
0
0
0
1
0
0
2
0
0
1
0
2
2
1
0
1
1
2
0
0
0
2
1
0
2
2
1
0
0
0
0
0
0
0
3
0
0
0
1
0
1
3
0
1
1
1
2
0
2
2
0
0
2
2
1
0
0
0
1
0
1
0
2
0
0
0
1
1
2
2
0
2
0
3
0
0
0
2
0
0
0
2
0
1
1
0
1
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
2
0
0
1
2
0
0
1
1
1
3
0
0
0
2
0
0
1
0
0
0
2
0
2
1
0
2
2
0
0
0
1
1
1
0
0
0
1
0
0
1
1
0
2
0
2
2
2
0
2
1
1
1
0
0
2
0
1
1
0
3
0
1
0
0
0
0
1
0
2
0
0
1
0
0
0
2
0
0
2
1
1
0
0
0
0
2
1
0
0
1
1
0
2
1
1
2
0
0
1
0
0
0
1
0
1
0
1
2
0
0
1
2
0
0
0
2
0
0
0
0
2
0
2
2
1
0
0
1
3
0
1
1
2
1
0
0
1
0
0
1
2
1
1
1
1
0
0
0
2
1
0
1
1
1
0
1
2
0
1
0
0
0
0
0
0
0
2
1
0
0
0
1
2
0
0
2
0
2
1
2
1
0
0
1
0
2
0
1
2
2
1
2
0
0
0
1
0
0
1
0
0
1
1
2
2
0
0
2
0
1
0
0
0
2
1
0
2
0
2
1
2
0
1
1
2
1
2
2
0
1
7
0
2
1
0
1
2
2
0
3
0
0
0
2
1
0
0
0
0
1
0
2
1
1
2
0
0
1
1
0
0
0
0
2
2
0
1
2
0
0
2
2
1
0
0
0
0
1
1
0
2
1
1
3
0
2
0
0
0
0
2
0
1
0
1
1
2
1
1
0
0
1
2
0
1
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
2
2
2
0
1
2
1
0
0
2
0
0
0
0
2
0
2
1
2
2
0
0
2
1
0
0
2
1
0
3
1
0
1
0
0
2
0
0
1
0
2
0
1
0
2
0
0
0
2
1
0
0
1
2
0
0
1
0
0
1
2
1
0
1
2
0
0
1
1
1
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
2
1
1
0
2
5
0
0
1
2
0
1
0
0
1
2
1
0
0
0
0
2
2
0
0
0
3
2
0
2
2
0
0
1
1
0
0
0
1
0
0
2
2
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
1
2
2
1
0
2
0
1
0
0
2
2
1
0
1
0
0
2
0
0
1
0
0
1
0
2
0
1
0
3
0
0
0
2
2
0
1
2
0
1
2
1
0
0
0
1
0
2
0
0
1
1
2
0
1
0
0
2
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
2
1
1
0
1
1
2
0
0
0
0
1
0
0
1
1
2
1
0
1
9
0
1
0
0
0
0
0
1
0
1
2
0
1
5
0
1
0
0
1
1
0
0
1
1
0
0
3
0
0
0
2
1
1
1
0
0
0
0
0
1
0
0
2
1
0
1
0
0
0
0
0
0
0
2
3
0
1
0
0
1
0
1
1
1
2
0
2
0
1
0
1
0
1
1
4
0
0
0
1
0
2
0
0
0
0
1
0
2
2
1
0
0
0
1
0
2
2
2
0
2
2
0
0
1
0
0
2
0
0
2
0
0
2
1
1
0
0
0
2
1
1
0
1
1
1
1
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
3
2
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
4
1
1
0
0
0
3
0
1
0
1
1
0
0
1
0
2
0
2
1
1
2
1
0
1
0
1
0
0
0
1
0
0
1
1
0
1
0
0
2
0
0
2
1
0
0
0
0
0
0
1
1
1
0
2
0
0
2
1
0
0
0
0
2
2
0
0
2
1
0
1
0
0
2
1
0
1
3
0
0
1
0
1
1
2
2
0
0
2
0
1
0
2
0
1
0
0
0
0
9
1
1
0
0
0
0
2
0
1
0
2
0
0
2
0
2
0
2
2
1
0
0
0
0
1
0
0
2
1
1
0
1
0
2
0
2
1
0
2
1
0
5
2
0
3
1
0
0
2
1
1
1
0
0
2
2
1
1
2
0
1
1
1
0
0
0
2
3
1
0
0
0
1
0
0
2
2
2
0
0
0
1
1
0
0
0
1
0
0
1
2
2
0
1
0
2
0
1
1
0
0
0
1
0
1
0
0
0
0
2
0
1
0
1
2
2
1
1
2
1
1
1
6
0
0
2
2
0
1
0
0
0
0
0
1
2
2
1
2
1
0
1
1
0
0
2
1
0
2
0
0
0
1
2
0
0
2
0
0
0
2
0
2
1
0
1
2
0
0
0
2
0
2
2
0
0
0
0
1
2
1
0
0
2
0
0
0
2
1
0
1
0
2
0
0
2
2
0
1
2
0
1
0
0
2
0
3
0
0
0
0
0
2
0
2
0
1
0
2
0
0
0
1
2
1
1
1
0
0
0
2
0
0
1
0
1
2
1
0
1
1
1
1
2
0
2
1
0
0
0
2
1
2
1
1
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
2
1
2
0
2
0
0
0
2
1
1
0
0
1
2
0
0
2
1
1
0
7
0
0
0
0
0
1
0
0
0
2
0
2
0
0
1
0
0
0
0
0
1
1
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
1
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
1
2
0
2
0
0
0
2
0
2
1
1
0
0
0
1
0
0
2
0
0
0
2
0
1
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
2
0
1
1
2
1
2
0
2
1
0
2
1
0
1
1
0
1
0
0
0
0
2
1
1
0
2
2
2
0
1
1
0
0
0
0
0
2
0
2
0
0
1
2
0
2
0
0
0
2
1
2
0
1
0
2
1
1
0
1
1
1
1
0
0
2
0
0
1
0
0
0
2
2
1
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
1
1
0
0
0
1
0
2
0
1
1
0
0
8
0
1
1
2
2
0
0
1
0
1
0
0
0
2
1
2
2
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
1
0
1
1
0
1
2
1
1
0
0
1
0
2
1
2
0
2
0
2
1
1
0
2
1
0
1
0
1
0
0
0
0
0
0
2
0
3
1
0
0
0
2
2
0
2
2
0
0
0
1
3
0
2
1
1
2
1
0
0
0
2
0
2
0
0
0
2
2
0
2
1
1
1
0
2
1
0
2
0
0
0
0
1
1
0
1
0
2
0
0
1
0
0
0
2
0
1
0
0
0
1
1
0
0
2
0
2
0
0
2
0
1
0
1
0
2
0
0
1
0
0
0
0
1
2
1
1
2
0
2
1
0
1
0
0
0
0
0
0
0
0
1
2
0
1
0
1
0
0
1
0
0
1
0
0
1
1
0
0
2
0
2
2
1
3
0
0
0
0
0
0
2
0
1
2
0
1
1
0
2
1
0
0
0
0
1
2
0
0
2
2
0
1
2
2
0
2
0
4
0
0
1
0
1
2
0
0
0
0
1
1
0
0
0
0
0
0
0
4
0
1
0
1
1
1
0
1
1
0
10
1
2
1
1
0
2
0
0
0
0
0
0
1
2
1
0
1
0
0
2
2
0
0
0
0
0
1
1
1
2
0
0
2
0
0
1
3
0
1
0
1
1
2
0
0
0
1
2
0
2
2
0
0
1
2
2
0
0
2
4
0
1
0
0
0
0
0
2
2
0
1
0
2
1
3
0
0
0
0
1
0
0
2
0
0
0
1
0
0
2
0
1
0
0
6
0
1
2
0
2
2
0
1
0
2
0
0
1
0
1
1
0
1
0
0
0
2
0
0
2
0
0
2
0
0
0
2
1
0
2
0
2
0
0
0
0
0
0
3
0
2
1
0
0
0
2
2
1
1
0
0
0
2
0
0
0
0
1
3
3
0
1
1
2
0
2
0
1
1
2
3
0
0
0
0
2
2
1
0
1
0
2
0
0
0
0
1
1
0
0
0
0
0
2
1
1
0
0
0
0
1
0
0
0
1
0
1
2
0
2
0
1
0
0
0
2
2
1
0
0
3
1
0
1
0
0
0
0
1
0
2
0
2
1
0
1
1
2
1
0
0
0
1
2
0
2
2
0
1
0
1
0
1
0
1
1
0
0
2
0
3
1
2
3
1
2
0
0
1
0
1
0
0
2
0
0
2
1
0
2
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
1
0
0
2
1
2
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
2
0
0
1
0
0
2
0
0
0
0
1
1
0
1
1
1
1
0
0
0
1
2
2
3
0
0
2
0
1
0
2
1
0
2
1
0
1
0
0
0
0
2
1
0
4
0
0
2
2
1
0
1
0
0
2
0
1
0
0
0
0
2
0
1
0
2
0
0
0
1
2
0
0
2
0
1
2
0
0
1
0
0
0
0
2
1
0
0
0
1
1
1
0
1
0
2
1
1
1
0
2
0
0
0
0
1
1
1
0
1
2
1
0
1
1
2
0
0
0
2
0
2
0
0
1
0
1
2
0
0
1
0
0
0
2
0
1
0
1
3
0
0
2
2
0
0
1
0
1
0
0
1
0
0
0
1
2
1
3
0
2
0
0
1
0
0
0
1
2
0
0
0
1
2
2
1
0
2
0
0
2
0
0
2
1
0
1
2
1
2
1
0
0
0
0
0
0
0
0
2
0
0
2
1
2
0
0
1
1
2
0
2
1
0
1
2
0
2
1
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
2
0
1
0
3
0
2
0
0
1
0
0
1
1
1
1
1
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
2
1
2
0
1
2
2
1
1
0
1
0
0
2
2
1
1
1
1
2
0
1
1
2
1
1
1
0
0
0
0
1
2
0
2
0
4
4
0
1
1
0
3
1
1
0
1
1
0
0
1
0
1
0
0
0
1
0
0
0
1
0
1
1
0
1
0
0
1
0
0
3
2
0
0
0
0
2
0
1
2
1
2
0
2
0
1
0
0
1
4
0
0
2
0
2
0
1
2
0
0
2
1
1
1
0
2
0
0
4
0
2
1
0
0
1
0
1
1
1
0
1
0
0
0
1
1
0
1
2
1
1
1
0
0
1
0
0
0
1
0
0
3
0
0
2
1
0
0
1
1
3
0
2
1
1
2
0
1
1
0
2
0
0
0
1
1
0
2
1
0
0
0
0
0
0
1
1
2
1
3
0
2
0
1
2
0
0
1
2
1
0
1
1
2
1
1
0
0
0
1
0
2
0
0
2
2
0
0
0
0
3
1
0
2
0
0
0
1
0
1
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
2
0
2
0
2
1
1
2
1
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
3
2
0
2
0
0
2
2
2
0
0
1
1
0
4
0
0
2
2
0
1
1
2
2
1
1
1
1
0
2
0
0
0
2
0
6
0
1
2
1
0
0
0
0
0
2
0
1
0
0
2
1
1
0
0
1
1
2
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
2
2
2
1
0
0
1
0
0
2
1
1
0
0
1
0
1
2
2
0
0
0
0
0
1
1
0
1
0
0
0
2
2
0
0
1
1
0
0
0
1
0
0
0
2
0
0
0
0
2
0
2
2
0
0
2
0
0
1
1
1
0
0
2
0
1
0
1
0
0
0
1
0
2
0
0
1
0
0
1
0
0
2
2
1
0
0
1
1
0
1
0
1
1
0
2
1
0
0
1
1
1
0
0
0
0
2
1
2
1
1
1
1
0
0
0
3
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
1
1
2
0
0
0
1
1
2
1
1
1
1
0
0
0
1
0
1
0
1
0
2
0
0
0
2
2
0
2
1
2
0
1
0
0
2
0
0
2
0
0
0
0
1
1
0
2
1
0
0
1
1
1
0
0
2
0
1
0
0
0
0
0
0
2
1
1
2
0
0
0
0
2
2
2
0
0
0
0
0
2
0
2
2
1
1
0
0
0
1
0
1
1
0
0
2
0
1
0
2
0
0
0
0
0
1
2
2
0
1
0
1
1
0
2
1
0
1
1
2
0
0
2
1
2
1
0
0
2
0
2
2
1
1
1
0
0
0
2
1
0
0
0
0
1
2
1
0
0
0
1
0
2
2
0
2
0
0
2
0
1
1
1
1
2
2
1
0
2
2
0
0
1
0
0
1
0
0
0
0
3
0
2
2
0
0
0
3
1
0
2
0
0
1
2
2
0
0
2
0
2
1
2
0
0
2
0
1
3
0
0
1
0
0
1
0
0
1
1
2
0
0
0
2
0
1
0
0
0
0
0
0
0
3
0
0
2
0
0
0
3
2
0
0
2
2
0
1
0
2
1
0
0
1
2
0
1
0
1
0
0
2
0
1
0
0
0
1
2
0
2
4
2
0
1
0
2
2
1
0
0
1
1
0
0
0
0
1
2
0
2
0
0
1
0
2
0
0
2
0
0
2
0
0
1
0
0
0
0
2
1
1
0
2
0
0
0
0
3
0
0
0
2
1
2
0
0
0
0
0
0
1
2
0
0
0
1
1
5
0
0
1
0
0
1
1
0
1
1
0
1
0
0
0
1
0
0
2
1
0
0
0
0
2
0
0
1
2
2
0
0
0
0
2
0
2
1
0
1
2
1
0
0
0
0
2
0
2
1
1
1
1
0
0
0
1
0
0
0
1
0
1
1
0
2
0
1
1
0
1
2
2
2
0
0
0
0
1
0
1
0
0
2
0
0
1
0
1
0
2
1
0
0
0
1
0
0
0
2
1
1
0
0
1
0
0
1
1
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
2
0
2
0
0
0
0
1
2
0
0
1
4
1
1
0
0
1
0
2
0
2
2
0
1
0
0
1
1
1
0
0
0
0
2
0
1
0
0
0
2
1
2
2
2
0
2
1
0
2
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
2
1
1
0
1
1
1
1
1
1
1
0
1
0
1
0
1
0
1
1
0
1
0
1
0
0
0
1
0
0
1
2
2
2
1
0
0
0
2
0
1
0
0
2
1
0
0
0
2
2
0
0
2
0
0
1
0
2
0
2
1
0
0
0
1
1
0
1
0
0
0
1
0
1
0
0
1
2
0
0
2
0
1
0
1
1
0
2
0
1
0
0
2
0
0
2
0
1
5
2
0
1
0
1
0
1
1
0
0
0
1
1
2
1
0
0
0
1
1
0
0
0
0
0
0
2
2
2
0
0
1
0
0
0
0
0
1
2
2
2
0
0
0
0
0
0
0
0
1
0
2
2
1
2
1
1
0
0
0
0
0
1
0
1
0
1
2
0
2
1
1
0
1
0
0
0
1
1
0
0
1
0
2
0
0
0
2
1
2
2
0
0
3
0
0
0
0
0
0
0
2
0
3
2
2
0
1
0
2
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
2
2
0
1
1
0
1
0
0
0
0
2
2
2
1
1
2
0
0
0
0
1
0
0
1
1
0
1
1
0
0
0
0
1
0
2
1
1
0
2
1
0
0
0
0
0
0
0
0
2
0
0
2
0
1
2
0
0
2
0
2
1
0
0
1
0
0
1
1
0
0
2
0
0
2
0
0
0
0
0
0
1
0
1
0
2
0
0
1
1
0
0
1
1
1
1
0
1
1
0
0
1
0
3
0
0
2
2
1
2
1
1
1
1
2
0
1
0
2
1
1
0
0
2
0
0
0
0
2
1
0
1
0
0
1
0
2
1
1
0
0
1
0
1
1
1
0
0
1
2
0
1
1
1
1
2
2
2
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
1
1
1
2
0
0
0
0
0
1
1
0
2
2
0
1
0
2
1
2
2
0
0
1
0
0
1
1
2
2
0
0
0
0
0
0
0
0
0
0
1
1
2
1
1
2
1
2
2
0
0
0
0
0
2
1
0
0
1
0
1
1
0
0
0
0
2
2
0
3
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
2
0
2
2
0
2
0
2
0
1
1
0
1
3
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
2
2
1
0
0
0
0
2
0
1
1
1
0
0
2
1
0
1
0
0
0
1
0
1
1
0
1
0
0
0
3
2
2
0
0
1
0
0
0
0
0
2
0
0
1
1
1
0
0
0
0
1
0
2
2
1
0
0
0
1
2
0
0
0
1
2
1
0
3
1
0
3
0
0
0
0
1
0
0
2
0
1
0
1
0
1
1
2
0
2
1
1
0
0
1
0
0
1
3
0
0
4
1
0
1
1
0
0
1
0
0
0
1
0
3
0
0
2
2
2
2
1
0
1
1
2
0
2
1
0
1
1
0
1
0
1
2
3
1
2
0
2
1
0
0
0
2
0
0
0
0
0
2
0
0
2
2
2
0
1
0
0
0
0
0
2
0
0
0
1
1
2
0
2
1
2
4
2
2
0
2
0
0
1
0
0
2
0
1
2
2
0
2
0
1
0
1
1
0
0
1
0
1
2
0
0
0
2
0
0
0
0
0
0
0
1
2
0
1
0
2
1
0
0
0
1
0
0
0
1
3
0
0
1
2
0
0
0
2
1
0
0
0
1
0
0
0
2
2
0
1
1
1
2
0
0
0
1
1
3
0
0
0
2
0
0
2
0
0
0
2
1
2
3
2
2
0
0
1
1
2
0
0
2
0
0
0
1
0
0
0
0
0
1
0
2
1
1
1
0
2
0
0
1
0
2
2
2
1
2
2
0
0
0
1
2
2
2
0
2
0
1
0
1
0
2
0
2
0
0
0
2
0
0
2
1
0
0
1
1
1
1
2
0
0
0
4
2
0
0
0
0
2
4
1
2
0
0
2
1
0
0
0
4
0
2
0
1
0
0
1
0
1
0
0
0
0
2
2
0
1
2
2
0
0
0
3
0
2
0
0
1
0
2
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
2
0
1
0
1
1
1
0
1
0
1
1
0
0
0
1
2
0
0
1
0
2
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
2
2
0
0
3
0
2
1
1
2
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
2
2
2
1
2
0
0
0
0
0
1
0
1
2
1
0
1
0
0
0
2
0
0
0
0
2
1
0
0
3
0
0
0
1
2
0
0
1
1
0
0
0
0
0
1
0
0
2
0
3
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
2
2
2
3
2
0
2
1
0
0
2
0
0
0
1
0
0
2
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
2
0
0
0
2
0
2
0
0
2
1
1
2
0
1
0
5
0
0
2
0
0
2
1
1
2
0
2
0
1
1
2
0
0
2
0
1
2
0
0
2
0
1
2
2
0
0
2
0
0
1
1
2
0
0
2
1
0
3
1
0
0
0
0
0
0
0
0
1
0
0
2
0
1
2
0
0
1
0
0
1
0
0
0
1
1
0
2
2
0
0
2
2
0
0
0
0
2
1
2
0
1
0
0
0
1
1
1
0
0
0
0
1
1
0
0
2
1
0
2
0
3
0
1
0
2
0
1
0
0
0
1
0
0
1
1
0
0
1
0
0
1
0
1
1
0
0
0
2
2
1
0
2
0
2
2
1
1
0
0
1
0
1
2
1
0
2
0
1
0
0
1
0
0
0
0
2
2
1
1
0
0
0
0
0
2
0
1
2
0
1
0
0
1
0
1
0
0
2
0
0
0
0
1
0
0
2
1
1
2
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
1
1
1
2
1
0
1
0
0
0
1
0
0
0
2
2
2
1
1
2
1
0
0
0
1
0
0
4
0
0
2
0
2
1
2
2
0
0
2
0
1
2
1
0
2
0
0
1
0
0
1
2
2
2
2
2
0
1
0
0
2
2
0
2
1
2
0
0
1
0
1
2
0
0
2
2
1
0
1
0
0
1
1
2
2
0
1
1
1
1
2
0
0
2
2
0
1
1
2
1
0
1
0
2
0
2
0
0
0
0
3
2
0
0
1
1
1
2
1
2
0
1
2
2
0
0
1
1
1
0
0
0
1
0
2
0
1
0
0
1
1
1
1
0
0
0
2
2
0
1
0
1
0
2
2
1
0
1
0
0
2
1
0
0
0
1
1
1
1
1
0
0
1
0
2
0
0
1
0
0
0
0
1
0
0
2
1
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
2
0
1
0
2
1
0
1
1
1
0
0
0
0
0
0
1
0
0
3
0
1
5
0
2
0
1
1
0
1
2
0
2
0
0
2
1
3
1
0
3
1
0
2
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
1
0
1
2
1
0
2
0
1
1
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
1
2
2
0
1
1
0
1
0
1
1
1
0
2
2
2
1
0
0
0
2
0
0
1
0
1
2
0
1
1
0
0
2
1
1
0
0
0
2
1
0
2
1
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
2
1
1
0
1
1
0
1
3
2
0
2
1
0
0
0
0
0
2
1
1
0
0
1
0
0
1
0
0
2
2
2
0
0
0
0
0
0
0
0
1
2
0
2
2
2
1
2
0
1
1
2
1
0
1
0
0
2
2
0
2
0
0
2
1
1
0
0
1
2
2
2
0
0
4
0
0
1
0
1
1
1
1
0
1
2
0
0
0
1
0
1
0
2
0
0
1
0
2
2
1
2
1
1
2
0
2
3
1
0
0
2
1
1
1
6
1
0
1
0
1
0
0
0
0
1
3
0
2
0
0
0
0
2
0
2
1
0
0
1
0
2
0
0
0
3
0
1
1
1
2
0
1
1
0
0
0
0
0
1
1
2
2
2
1
0
0
2
0
1
1
2
0
0
1
2
1
0
0
2
0
1
0
0
0
1
2
0
0
2
1
1
1
1
0
0
0
0
2
2
1
1
2
1
0
0
0
0
0
0
0
0
1
1
2
2
1
0
1
2
0
0
1
1
1
2
2
1
4
0
4
0
0
1
0
2
1
1
0
0
0
2
1
2
0
1
0
0
2
0
2
2
2
2
1
2
0
0
2
0
0
0
0
0
1
0
2
0
2
2
0
1
0
0
0
1
0
2
2
2
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
1
0
0
1
1
3
1
1
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
2
2
0
0
1
0
2
0
1
1
0
0
0
0
1
0
0
2
2
0
2
0
0
0
0
1
2
0
0
2
0
1
0
2
0
0
1
2
0
0
1
2
0
2
2
1
0
0
0
1
0
0
1
1
0
2
1
1
0
2
0
0
0
2
1
1
0
0
1
2
0
2
2
0
1
0
2
1
2
0
2
0
0
0
0
2
0
0
1
0
0
0
0
1
1
1
2
1
1
2
0
0
1
0
0
1
1
0
0
1
1
1
0
0
0
2
1
2
0
0
2
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
2
0
2
0
0
0
0
0
0
2
0
1
1
2
0
2
0
0
0
1
1
0
2
0
2
1
0
2
2
2
0
1
1
1
1
0
2
1
1
1
0
1
0
2
0
2
1
1
2
1
0
0
0
2
0
1
1
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
2
0
1
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
1
2
2
1
0
0
1
0
0
0
0
2
0
0
0
1
0
0
1
0
0
2
0
0
0
1
1
1
2
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
2
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
2
1
2
1
2
2
0
0
0
0
2
0
1
2
0
1
1
0
2
0
1
0
1
0
3
2
0
1
0
2
0
0
0
0
1
0
1
0
2
2
2
0
0
2
0
2
0
1
2
1
0
1
0
0
1
0
0
2
0
0
0
0
1
1
0
0
0
2
1
2
0
0
1
2
0
0
1
0
1
0
2
0
1
2
0
0
1
0
1
0
0
2
0
1
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
4
0
1
0
0
0
0
0
1
0
1
0
0
1
1
0
0
1
0
0
0
1
1
2
0
1
0
0
0
0
0
2
1
1
1
0
0
0
2
0
0
1
0
2
1
1
0
2
2
2
0
1
0
0
0
2
0
1
2
0
0
2
1
1
0
0
1
0
0
1
2
0
0
1
0
2
2
2
0
2
1
0
1
3
0
4
0
1
0
1
2
0
0
1
1
0
1
1
0
0
0
0
0
2
0
1
2
0
0
1
1
0
2
0
2
0
0
0
2
0
2
1
0
0
0
1
1
0
2
1
0
0
1
0
1
1
0
0
2
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
1
0
1
0
1
2
2
0
0
1
0
0
0
2
0
2
1
0
0
3
2
0
0
1
1
1
0
1
0
0
0
1
1
0
2
0
0
1
0
0
3
1
0
2
2
2
0
0
1
0
0
1
2
0
1
1
1
0
0
0
0
0
0
0
3
2
2
1
1
1
0
1
0
0
0
1
0
1
0
2
0
1
0
0
0
0
0
0
1
2
0
0
2
0
0
0
3
1
2
1
0
0
0
1
1
2
0
1
2
1
0
1
0
0
0
1
0
0
2
1
0
1
0
0
1
0
0
0
0
0
1
2
0
1
1
1
0
0
0
1
1
1
2
3
1
0
1
1
0
0
0
1
0
1
1
2
0
1
0
1
2
1
2
0
0
0
1
1
0
1
1
2
1
0
0
0
0
0
1
0
1
0
2
0
0
2
1
1
0
0
0
0
0
0
1
1
0
0
0
1
2
2
2
2
0
1
1
0
0
1
1
0
0
2
0
0
2
0
0
1
0
0
0
2
0
0
3
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
2
2
0
2
1
1
1
0
2
1
0
3
1
3
1
2
1
0
1
0
2
2
0
0
2
0
1
0
0
0
1
1
1
1
1
0
2
1
0
1
2
0
0
0
0
2
0
2
1
2
0
1
2
2
1
0
0
2
0
0
0
0
2
1
0
2
0
0
0
0
2
0
2
0
3
0
2
1
0
0
0
0
0
1
1
2
0
0
0
0
0
0
1
0
3
1
0
1
0
0
0
1
2
0
3
0
1
0
0
0
0
0
0
0
0
1
1
1
2
2
1
0
2
1
2
0
0
2
2
1
1
1
2
2
0
1
1
1
0
0
0
2
1
0
1
1
0
2
1
2
1
1
0
1
2
0
0
0
0
2
0
0
2
1
1
1
1
3
2
2
2
1
1
0
0
1
0
3
1
2
2
0
0
0
0
1
0
0
0
2
1
0
0
0
3
0
3
1
0
1
1
0
0
0
1
0
2
2
1
0
0
0
2
0
1
1
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
2
0
1
1
2
0
0
0
1
2
3
0
1
1
0
0
1
2
2
2
0
0
0
0
2
2
1
2
0
0
1
0
0
1
0
0
0
1
0
2
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
1
1
1
1
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
1
2
2
1
1
0
2
0
0
1
2
0
1
0
2
2
2
1
1
2
1
1
0
0
0
0
0
1
1
1
1
0
0
2
0
0
1
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
7
0
0
0
0
2
1
0
1
1
0
0
0
0
0
0
2
1
3
0
0
1
2
2
1
1
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
2
2
1
1
0
0
0
1
0
1
0
1
0
2
0
0
2
1
2
0
0
0
0
0
2
1
0
1
1
1
0
0
0
1
2
0
0
0
1
0
0
1
1
1
0
0
0
2
0
0
0
0
0
2
2
1
0
0
2
0
0
1
0
0
1
0
0
2
0
0
1
1
1
0
0
0
0
0
0
0
1
1
1
1
2
0
0
2
0
0
0
0
0
0
0
2
2
0
1
1
1
3
1
0
0
0
0
1
1
0
0
0
2
0
0
2
1
0
0
1
0
0
0
0
0
3
1
0
2
0
0
2
2
2
1
0
0
1
1
0
0
0
1
0
2
0
0
2
0
0
0
0
2
0
0
0
1
0
2
1
0
0
1
1
1
0
1
2
1
0
2
0
1
0
0
0
2
2
0
1
0
0
0
0
1
0
1
0
0
0
2
2
1
2
0
0
2
2
1
0
2
0
0
0
0
0
4
1
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
1
0
0
0
2
0
2
0
1
2
0
1
1
2
0
1
1
2
1
0
2
0
0
1
0
2
1
0
0
1
2
0
0
0
1
2
0
2
0
2
0
0
1
0
0
1
0
0
1
0
2
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
1
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
2
0
0
1
0
0
1
1
0
0
1
2
2
1
0
0
0
1
1
0
1
0
0
0
2
1
1
0
1
0
0
1
0
0
1
0
0
0
0
1
0
7
0
1
1
1
0
1
1
2
0
1
1
0
1
2
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
2
1
0
1
2
0
0
0
0
0
0
0
1
0
0
1
0
0
2
2
1
2
1
2
0
1
1
1
0
1
0
0
1
2
0
2
0
1
0
1
1
0
0
0
1
2
1
0
1
0
1
0
2
2
1
0
1
1
1
1
2
2
1
0
0
0
3
0
0
2
0
2
1
0
1
0
1
1
1
2
0
2
1
0
0
0
0
3
0
0
2
0
0
0
0
2
3
2
0
1
1
0
0
0
0
2
0
1
0
0
0
1
2
1
0
1
0
0
0
1
0
0
1
0
0
1
1
2
0
2
1
2
1
2
1
1
0
0
0
0
2
0
1
2
0
0
2
0
0
1
2
1
0
0
0
2
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
1
2
1
0
2
2
0
0
0
0
0
0
0
2
1
0
2
1
2
0
0
1
0
0
0
1
1
3
0
0
2
0
1
2
0
0
2
2
0
0
2
1
2
0
2
0
2
1
0
0
1
0
0
1
0
0
1
0
0
0
1
2
0
0
0
0
2
0
0
2
2
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
2
1
1
0
0
1
0
0
0
1
0
0
1
0
0
1
3
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
1
0
2
2
0
0
2
0
2
0
0
0
2
0
0
0
1
0
1
2
1
0
0
0
0
2
0
2
0
2
1
2
1
2
0
0
2
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
2
0
2
1
2
1
0
0
1
0
0
2
1
2
1
1
2
0
1
1
2
0
1
0
0
1
1
3
2
0
1
0
1
1
0
0
0
1
1
1
1
1
0
2
0
0
1
0
0
2
0
1
2
0
0
0
2
0
0
0
0
1
0
0
3
0
0
1
2
2
0
1
1
0
0
0
1
1
0
0
0
2
0
0
1
1
2
0
0
0
0
0
3
1
0
1
2
0
1
1
0
0
0
0
0
1
1
0
2
0
2
0
0
1
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
1
2
0
2
0
0
1
0
1
0
0
1
0
2
0
1
2
2
2
0
2
1
0
2
2
0
0
2
0
4
1
0
0
0
3
0
1
2
1
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
1
1
0
1
0
0
2
0
0
1
1
1
1
3
0
0
0
1
0
0
0
2
1
1
1
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
3
0
0
0
0
0
3
0
0
0
1
0
2
0
0
0
0
0
0
0
1
1
1
1
2
1
1
2
0
1
3
2
2
0
1
0
0
1
0
1
1
2
0
2
2
1
0
3
3
1
0
1
2
1
1
0
1
0
2
2
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
1
2
2
1
1
0
1
1
0
3
1
0
0
1
1
0
2
2
2
0
1
0
1
0
1
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
1
0
2
1
1
2
1
0
2
0
0
3
0
1
0
1
1
0
0
0
0
0
1
0
0
2
0
1
0
0
0
1
2
0
1
0
1
0
0
0
0
1
1
1
2
0
1
0
1
0
0
0
0
2
0
0
0
1
2
0
0
0
0
2
2
0
2
2
0
2
1
2
0
1
0
1
0
0
0
1
0
2
0
1
3
0
1
2
0
0
0
0
0
2
0
2
1
1
1
4
2
0
0
0
1
0
2
1
1
1
1
1
0
1
0
0
0
1
1
1
0
0
0
0
1
1
0
1
2
1
1
1
0
0
1
0
0
0
0
2
0
1
1
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
1
0
1
0
0
1
0
1
0
0
1
0
0
0
2
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
2
1
1
0
2
2
0
0
2
2
1
2
0
2
0
2
0
0
0
0
1
0
0
0
0
0
2
2
2
0
0
0
1
2
1
0
1
1
2
2
0
0
0
2
1
2
0
0
2
0
0
0
2
0
1
0
2
1
0
1
2
0
0
2
2
0
2
1
1
0
1
0
0
0
0
0
0
0
0
0
2
1
2
2
2
0
0
2
0
0
0
0
1
1
2
1
0
0
2
0
0
1
0
2
0
0
0
0
1
2
2
0
0
2
0
0
0
0
0
1
1
0
1
1
0
1
2
1
2
0
1
1
0
1
0
1
1
2
1
1
2
0
1
1
0
1
0
0
0
1
1
0
0
0
2
2
0
1
0
0
0
0
1
1
1
1
0
2
0
0
0
1
0
0
0
1
2
0
2
2
0
1
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
3
1
0
0
0
0
0
1
0
4
1
2
0
1
0
0
2
0
0
2
0
1
0
1
2
0
0
0
0
0
0
2
1
2
0
1
0
0
0
0
1
2
1
1
0
0
1
0
0
0
2
1
2
0
2
0
0
0
0
0
1
0
3
0
0
0
0
0
2
1
1
0
0
3
0
0
0
3
0
2
2
0
2
0
2
1
0
1
1
1
2
1
0
0
1
0
2
0
2
0
0
0
0
1
2
0
1
2
4
0
0
2
1
0
0
0
2
1
0
2
0
0
2
0
0
0
2
0
0
0
1
2
0
0
0
2
1
0
0
0
0
0
1
2
2
0
2
2
3
0
2
0
0
2
1
0
1
0
2
1
1
0
2
2
0
1
1
1
0
1
2
1
0
0
2
0
0
1
0
0
0
2
1
0
1
0
2
0
3
0
0
3
0
0
0
3
0
1
0
1
0
0
2
0
2
0
0
2
0
1
1
1
1
3
0
4
0
0
2
2
2
0
2
0
1
0
1
2
1
2
2
1
2
2
2
0
0
2
3
0
0
2
4
0
2
0
0
0
0
0
1
2
1
0
0
0
0
1
1
1
2
3
2
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
2
2
0
2
0
2
2
0
2
0
0
0
1
0
0
0
2
0
0
0
1
0
1
0
0
1
0
2
1
2
0
0
0
1
3
1
1
0
1
1
7
2
0
2
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
1
1
0
1
2
1
1
0
1
0
0
0
1
0
0
2
0
1
0
0
0
0
1
2
2
2
0
0
0
0
0
0
0
0
2
0
1
0
0
1
1
3
0
0
1
0
1
0
0
0
2
2
1
0
1
1
2
2
0
1
2
1
1
0
0
2
1
0
0
1
0
1
2
1
2
1
2
0
2
1
1
2
1
1
2
2
0
0
0
2
0
0
1
6
0
0
2
0
2
0
1
0
0
2
0
0
0
0
0
1
0
0
1
1
1
0
1
0
2
2
1
0
0
1
1
6
0
0
1
2
0
0
0
1
0
0
0
2
2
0
0
0
1
2
0
2
2
0
0
0
0
2
2
2
0
2
2
0
0
1
2
2
0
2
0
1
1
0
2
0
1
1
1
5
0
0
1
1
1
2
0
0
0
2
2
0
0
1
3
0
0
0
2
2
2
0
0
0
2
1
0
0
2
1
2
1
0
1
1
0
1
3
0
0
2
0
0
2
0
0
2
1
2
1
0
0
0
0
0
2
0
1
0
0
1
1
0
0
1
0
2
1
0
2
0
1
0
0
2
0
0
0
1
0
0
0
1
0
0
2
0
1
2
0
1
0
1
0
0
0
1
2
0
0
0
1
0
0
1
0
2
1
0
0
1
3
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
1
1
1
0
2
0
0
0
2
2
0
1
0
1
0
0
2
2
0
0
2
1
2
1
2
0
0
1
2
1
0
0
0
0
0
0
0
0
1
1
1
1
2
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
1
0
2
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
4
1
0
0
2
2
4
1
0
1
0
0
2
0
1
2
0
2
0
0
1
2
0
2
0
1
0
1
1
0
2
0
0
0
2
0
2
0
0
2
1
0
0
0
1
0
1
2
0
1
0
0
2
2
1
0
2
2
0
0
2
0
0
3
1
0
0
0
0
0
1
1
0
2
0
1
0
1
3
0
1
0
1
2
0
0
0
2
1
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
3
0
0
0
1
0
0
1
0
2
1
0
0
0
0
0
1
2
0
1
0
2
1
0
0
1
0
1
0
1
0
2
0
1
0
0
2
2
3
0
1
0
0
0
0
0
3
0
1
1
1
0
0
1
0
1
0
0
1
0
0
1
0
1
0
0
0
1
0
2
1
0
1
2
0
1
1
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
2
1
2
0
2
0
1
1
1
0
2
1
0
0
0
1
0
0
0
0
0
1
1
1
0
1
1
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
4
1
0
0
1
2
0
0
0
0
0
1
0
1
0
0
1
3
1
0
0
0
0
0
1
0
2
0
0
2
0
0
1
1
1
0
0
2
0
1
0
0
0
1
0
1
0
0
0
0
0
2
0
2
0
0
1
0
0
1
1
1
2
0
2
1
1
2
1
0
0
0
0
2
0
0
0
2
1
2
0
0
2
1
0
0
0
0
2
1
2
0
1
1
0
0
0
2
2
2
0
0
0
0
1
1
0
2
0
1
2
0
2
0
0
1
1
0
1
0
0
2
0
1
4
0
2
1
0
0
1
1
1
0
1
0
0
0
0
0
2
2
0
0
2
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
1
0
1
0
0
0
2
0
0
2
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
2
0
0
2
0
0
0
2
1
0
0
2
1
2
1
1
2
0
0
0
0
0
2
0
0
2
1
1
2
1
0
0
0
0
0
2
0
0
4
0
2
2
0
0
1
0
1
2
0
0
2
0
0
0
0
0
0
2
0
0
2
0
1
1
0
1
2
0
1
0
1
0
1
0
0
1
0
0
0
1
2
1
0
2
1
2
2
0
0
1
1
2
1
0
2
0
1
2
0
1
0
0
1
0
1
0
2
0
2
2
0
1
0
1
2
1
0
0
1
0
0
1
1
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
2
1
1
1
0
2
0
0
1
1
0
0
0
0
2
4
0
2
2
0
0
0
1
0
0
0
0
2
4
1
0
1
1
0
1
0
0
1
0
0
0
1
0
0
2
1
2
2
0
1
1
0
2
1
1
2
0
2
1
0
2
0
1
0
0
2
0
2
2
0
0
0
0
0
1
2
0
2
0
2
1
1
0
1
1
0
2
0
1
2
2
1
0
1
0
0
2
0
1
1
1
1
3
0
0
2
1
0
1
1
0
0
1
1
1
0
2
2
0
1
1
0
0
2
0
1
0
0
1
0
1
2
6
2
2
2
0
0
0
0
3
1
3
1
0
2
2
0
1
0
1
0
1
0
0
0
0
2
2
1
2
0
0
2
1
0
1
0
1
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
2
1
2
2
2
0
1
1
0
0
0
1
0
0
2
0
0
2
0
1
0
2
1
0
1
0
0
0
1
0
1
1
0
1
0
0
2
0
1
1
2
2
0
2
0
2
0
0
3
0
2
2
0
1
2
1
1
0
0
0
0
0
2
0
2
1
0
0
1
0
2
0
2
0
0
1
0
2
1
0
1
1
2
0
3
1
1
0
0
0
1
0
2
0
0
0
1
2
0
0
0
2
0
0
0
0
2
2
1
0
1
5
0
1
1
1
0
0
0
0
0
3
0
1
1
1
2
0
0
0
1
0
0
1
0
1
2
1
1
0
1
0
0
1
0
0
0
1
2
0
0
0
2
2
0
1
0
1
0
0
0
4
2
2
2
1
0
2
0
0
0
1
2
1
1
0
0
2
0
0
2
0
1
0
0
1
1
1
0
1
2
1
0
1
0
0
0
0
1
0
2
1
3
0
2
1
1
0
0
0
0
0
0
0
0
0
2
1
2
1
1
1
0
1
0
0
2
0
1
0
2
2
0
1
1
0
2
2
0
0
1
0
0
2
0
1
0
2
1
2
0
2
0
0
0
0
0
2
0
0
0
1
1
2
0
0
1
1
1
1
1
0
2
1
1
0
1
0
0
0
1
0
1
0
1
2
2
0
0
0
0
1
1
0
2
0
0
2
2
0
1
0
0
4
0
2
1
0
0
0
0
0
0
0
2
1
0
3
1
2
0
0
0
0
0
1
1
1
2
0
0
1
1
0
0
1
0
2
1
0
2
1
0
0
2
0
0
0
0
0
1
1
1
2
0
1
1
1
0
0
2
2
0
2
2
1
1
4
0
0
2
2
0
0
1
0
2
1
2
0
2
0
0
2
0
0
1
1
1
0
0
2
0
2
0
0
1
0
2
1
0
0
0
0
0
0
0
0
2
1
0
1
1
0
0
0
0
0
0
2
0
0
0
2
2
1
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
2
1
0
0
0
2
1
2
1
0
2
0
0
2
2
1
1
0
2
2
0
2
2
0
0
0
0
0
2
6
0
1
2
0
1
0
0
0
0
0
0
1
1
2
0
0
1
0
2
0
1
0
0
2
0
0
0
0
0
2
0
1
0
1
0
0
0
2
2
0
2
1
1
0
0
0
0
1
0
0
0
1
0
0
1
2
1
3
2
0
1
1
2
0
0
1
1
0
0
0
2
0
0
0
0
2
3
0
0
0
0
1
0
0
0
2
1
2
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
1
0
0
0
0
2
0
0
1
0
0
1
1
0
1
0
0
0
0
2
2
0
1
2
0
0
2
0
1
0
1
1
1
0
0
0
0
2
1
1
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
1
0
1
1
1
2
1
0
2
0
0
2
1
0
2
0
0
0
0
0
2
2
3
0
1
0
1
0
0
2
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
1
1
0
0
0
2
0
0
1
1
5
0
0
1
0
2
0
0
2
0
0
1
0
1
0
0
2
0
0
1
2
1
0
1
3
0
2
1
1
0
0
1
1
0
1
1
3
0
1
1
0
0
0
1
1
0
1
2
0
0
0
2
0
1
0
0
1
1
0
1
0
1
0
0
0
1
0
0
1
0
2
1
0
0
2
0
0
1
2
2
0
0
2
0
1
0
1
1
0
1
0
0
2
2
0
0
1
1
2
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
2
2
0
2
0
0
2
0
1
2
0
0
0
0
0
2
0
0
1
2
1
0
0
2
0
0
0
2
0
1
1
0
0
1
1
2
0
0
1
2
0
0
0
2
0
2
1
1
0
1
0
1
1
0
0
1
2
1
1
0
1
1
0
1
2
0
0
1
0
1
0
1
1
3
0
2
0
0
0
0
0
1
1
0
2
0
3
2
0
1
0
0
0
1
0
2
2
1
2
0
1
0
0
2
0
1
1
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
2
2
0
1
2
1
1
0
2
0
0
2
0
0
1
0
1
0
2
2
1
0
0
0
1
2
1
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
1
0
0
1
2
1
0
1
0
1
1
2
2
0
1
0
1
1
1
0
0
0
1
0
1
0
0
1
1
0
1
2
1
1
1
3
1
0
2
1
1
0
2
0
0
2
0
2
1
0
1
0
0
0
2
1
1
0
0
2
2
1
0
2
0
0
1
1
1
2
2
0
3
0
0
1
2
2
2
0
0
0
0
0
0
2
0
2
0
0
2
0
0
1
0
0
0
0
0
2
2
0
0
0
1
0
1
0
2
2
0
2
1
0
0
1
1
0
1
1
0
0
0
0
0
1
1
2
2
1
2
0
1
0
0
1
1
1
2
0
0
0
0
2
1
0
0
2
0
0
1
0
0
1
0
0
1
1
1
1
0
0
0
1
0
0
2
1
2
1
0
0
0
0
0
0
1
0
0
0
0
2
1
0
2
2
0
1
0
0
0
0
1
0
0
0
0
0
1
1
1
1
0
2
0
1
0
1
0
0
0
2
1
1
2
1
0
1
0
2
0
0
2
0
1
0
0
2
2
5
0
0
0
0
0
0
0
1
0
2
1
1
3
2
0
0
0
0
2
1
2
0
2
2
0
0
0
2
0
1
0
0
0
1
0
0
2
0
0
2
1
0
0
0
1
0
1
1
0
0
0
2
0
0
0
1
0
0
1
2
1
1
1
0
0
0
2
2
0
1
0
2
0
0
1
0
0
0
1
0
0
2
0
0
1
1
0
0
0
3
2
1
0
1
1
0
2
0
0
0
0
1
1
0
0
0
1
2
0
0
2
0
1
1
0
0
2
0
2
2
2
1
2
4
1
0
1
1
0
0
0
1
0
0
0
1
0
0
0
2
0
0
1
1
0
1
0
1
1
0
0
0
2
2
1
1
2
5
0
0
0
2
1
0
2
0
0
1
0
1
2
0
0
2
4
0
0
1
0
2
1
1
1
0
0
0
1
0
2
2
1
0
1
1
0
2
2
0
3
0
2
0
0
2
1
3
1
0
0
0
0
1
2
0
0
1
0
1
0
1
1
2
2
1
0
0
0
0
0
2
0
2
1
1
1
0
2
2
2
2
2
0
1
0
3
0
0
3
0
2
0
0
0
1
0
0
0
2
0
0
2
2
0
0
0
1
1
0
0
0
0
2
0
3
2
0
0
2
1
2
2
2
1
0
3
0
1
0
1
0
0
0
0
2
2
0
2
0
1
0
2
0
0
0
2
0
1
1
1
2
2
2
0
2
0
7
0
0
0
1
1
2
1
0
0
2
0
1
0
2
0
2
1
2
0
0
1
0
0
4
0
1
0
1
0
1
1
0
0
0
0
1
2
0
2
0
1
1
0
2
0
0
2
1
1
0
2
2
0
1
1
0
3
0
2
0
2
0
0
1
0
1
1
2
2
1
0
0
0
0
1
1
2
0
0
0
2
2
0
2
2
2
1
0
2
1
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
1
1
2
0
0
0
0
0
1
0
2
0
0
0
0
1
1
0
0
2
0
0
0
2
2
0
0
0
1
0
1
1
2
1
0
0
0
1
0
0
2
0
2
0
0
0
1
2
1
0
3
1
0
0
0
1
0
0
0
3
2
0
0
0
0
2
1
2
0
1
1
2
0
3
0
0
1
0
0
1
0
0
0
0
2
2
2
0
2
0
0
1
0
0
1
1
1
2
0
1
1
0
0
2
0
0
1
0
0
0
0
0
0
1
1
1
0
4
0
0
2
0
1
0
2
0
0
1
0
0
1
2
1
0
0
1
4
0
1
0
0
2
2
0
1
0
0
1
0
0
0
0
0
0
0
2
1
2
1
0
0
1
0
1
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
1
1
0
1
0
1
0
0
1
1
1
1
0
0
2
0
1
0
0
0
0
1
0
1
4
0
0
0
0
1
0
1
0
2
0
1
2
2
0
2
1
0
2
0
0
2
1
0
0
1
2
1
0
0
1
0
0
0
0
0
2
2
0
1
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
6
1
1
0
3
0
0
2
3
0
2
0
0
0
0
1
0
1
3
1
0
2
0
1
2
0
2
0
1
0
0
0
2
0
1
1
1
1
0
0
1
1
1
1
0
0
0
4
2
0
0
2
1
2
2
0
0
0
1
0
0
0
3
0
0
1
1
0
0
1
2
2
2
0
0
0
0
1
0
2
0
0
0
0
1
0
0
1
1
0
2
1
0
1
0
0
0
0
1
2
1
0
0
1
1
1
1
0
1
0
2
2
1
2
4
1
0
2
0
0
1
1
0
1
1
1
2
0
0
1
2
2
0
1
1
2
2
0
0
1
0
0
0
1
1
2
0
2
1
2
1
0
0
2
0
0
2
0
2
1
0
0
3
1
2
2
0
0
0
1
1
2
0
0
2
0
0
3
0
1
0
1
1
0
1
2
1
1
0
1
2
0
0
2
2
2
0
1
1
0
1
0
1
0
1
1
2
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
1
0
1
0
2
2
1
1
0
0
0
0
1
0
0
1
2
0
0
1
2
2
1
0
2
1
0
0
0
0
1
2
1
0
0
0
2
1
1
0
1
0
0
0
3
1
0
1
2
0
1
1
0
0
0
2
0
0
0
0
1
1
0
0
0
0
1
0
0
0
2
0
2
0
1
1
2
0
0
1
2
0
1
0
0
0
0
1
0
0
0
2
2
0
2
0
1
2
2
2
0
1
0
2
0
0
0
2
1
1
0
0
0
0
1
0
2
2
0
2
0
1
0
0
0
0
1
0
2
0
2
0
0
0
3
2
2
1
2
1
0
0
0
1
1
2
0
0
2
2
0
1
0
1
4
2
0
1
1
1
1
1
0
1
0
1
0
0
0
0
0
0
2
2
0
2
0
0
1
1
0
2
1
0
1
0
0
0
2
1
1
0
0
4
0
0
2
0
0
0
3
1
1
2
2
0
0
0
2
2
0
0
0
1
2
2
1
1
1
0
2
2
0
0
0
2
1
1
1
1
1
5
1
0
1
0
2
0
0
2
1
0
2
1
2
0
2
1
0
0
0
0
1
0
0
0
1
2
0
0
0
0
3
1
0
0
1
1
0
0
5
1
0
0
1
1
1
1
0
0
0
1
0
2
1
2
1
0
0
0
1
0
1
0
0
0
2
1
0
2
0
0
0
0
0
1
2
2
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
2
2
1
0
2
0
0
2
0
0
0
1
1
0
0
2
0
1
0
0
0
2
1
0
0
0
0
1
1
2
0
0
0
0
1
0
0
0
0
2
1
0
2
2
4
0
2
2
0
1
2
0
0
0
2
0
1
1
0
2
0
2
1
1
0
0
2
1
0
2
0
0
0
2
2
0
2
1
0
1
2
2
0
0
0
0
0
2
0
2
0
0
1
1
1
0
0
0
0
0
1
0
2
0
2
0
1
0
2
2
0
1
0
2
1
2
0
2
0
1
0
0
0
0
0
0
2
2
2
0
1
0
0
0
0
2
0
1
3
2
1
0
1
0
1
0
0
0
0
0
2
0
1
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
1
0
7
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
3
2
0
2
0
2
1
0
0
1
0
0
1
2
0
0
0
2
0
1
2
0
0
0
0
0
2
3
1
0
0
0
0
2
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
1
1
1
0
1
1
2
2
2
0
0
2
0
0
0
0
0
1
3
0
0
0
0
1
0
2
0
1
1
0
2
2
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
2
2
1
1
0
0
0
0
0
0
0
0
0
2
1
0
0
1
1
3
0
1
0
1
1
0
0
2
2
1
1
1
0
0
0
0
0
2
1
0
2
2
2
1
2
2
1
1
0
1
0
0
2
0
1
2
0
2
1
0
2
0
0
2
1
0
0
2
1
0
3
1
0
1
2
0
3
0
0
2
0
1
2
0
1
0
0
0
0
1
1
0
0
1
1
0
0
0
0
2
0
1
0
1
0
0
1
1
0
0
1
1
2
2
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
1
1
2
0
0
2
0
1
0
1
1
0
1
0
1
0
0
2
1
0
0
2
0
1
0
0
0
0
1
1
2
1
0
1
0
0
0
2
2
0
0
0
0
1
0
0
2
1
0
1
2
1
0
1
1
0
2
1
2
1
0
2
0
0
1
0
0
1
1
0
1
2
0
2
0
1
0
0
0
1
2
1
0
1
0
0
0
1
2
0
1
0
1
1
0
1
1
0
0
1
0
2
2
0
0
0
1
0
0
1
1
1
1
0
0
1
0
5
2
0
1
0
0
0
1
2
1
1
0
2
0
2
2
2
0
1
0
1
0
1
1
1
0
1
0
0
0
0
0
0
0
2
1
1
0
0
0
0
2
1
1
0
2
0
2
2
0
1
0
1
2
1
0
1
1
0
0
2
0
3
2
2
1
0
0
3
0
0
0
2
0
0
1
0
0
2
2
0
0
1
0
1
0
0
2
1
3
2
0
0
0
1
1
1
2
2
0
1
0
0
0
2
1
0
2
2
1
1
1
2
0
0
2
0
1
0
0
1
0
2
0
2
1
0
0
0
1
0
2
1
0
1
0
1
0
0
0
0
1
1
1
0
0
0
1
1
1
1
0
1
0
2
1
1
2
1
1
1
2
1
1
1
2
2
1
1
0
1
2
1
0
1
0
2
0
2
1
3
0
0
0
1
0
1
2
0
0
1
1
0
0
0
2
1
0
1
0
0
1
0
0
0
2
1
1
0
1
1
3
1
1
0
2
0
0
0
0
0
1
0
1
1
2
0
1
0
0
0
3
0
0
1
2
1
0
2
1
0
1
1
1
0
0
3
4
2
0
2
2
2
0
0
0
1
2
0
0
2
2
2
1
1
0
0
1
2
0
0
1
0
0
0
0
1
0
1
1
0
1
2
1
1
2
1
0
3
0
0
2
0
1
0
0
0
1
4
0
0
0
1
1
1
1
1
0
2
1
1
0
1
1
0
0
1
1
0
0
0
2
1
0
1
2
1
1
1
0
2
1
2
0
0
0
0
0
2
1
0
1
0
0
0
1
0
0
1
0
0
0
0
1
1
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
1
0
2
1
2
2
1
2
0
1
2
0
1
0
0
0
0
0
3
1
3
0
0
0
0
1
0
1
1
1
0
0
2
0
0
0
0
1
4
2
2
0
0
0
2
0
1
0
0
3
0
1
3
2
1
0
0
0
2
0
1
0
2
1
0
2
0
1
0
2
1
2
2
0
0
1
1
0
2
0
1
1
1
0
2
1
0
1
0
1
0
0
0
1
1
0
0
1
2
2
0
2
1
0
2
0
1
2
2
1
0
2
0
0
0
0
1
0
0
0
0
1
0
2
1
0
0
1
0
0
1
1
0
0
2
1
2
1
1
0
0
0
0
0
0
0
0
0
1
0
2
1
0
2
0
0
2
1
1
0
1
0
0
2
1
0
0
2
0
1
0
1
1
3
0
0
0
0
3
0
1
0
1
0
1
1
1
0
1
1
2
1
1
1
0
2
0
0
0
0
1
0
1
2
0
0
2
0
0
0
0
1
1
1
0
0
0
1
0
0
0
1
0
0
2
0
2
1
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
1
1
0
0
0
0
0
1
2
0
0
0
0
1
1
0
1
0
0
2
1
1
1
2
0
1
2
1
2
0
0
0
0
0
0
0
0
1
2
2
1
1
0
0
0
2
1
0
0
0
0
0
0
2
2
1
2
0
1
2
0
1
1
2
1
0
1
0
0
1
3
0
2
0
1
0
2
3
0
0
1
2
0
2
2
2
0
0
0
1
0
1
0
1
1
0
2
3
0
2
0
0
2
2
0
2
2
0
0
0
1
0
0
0
0
0
1
0
1
0
1
2
2
0
3
0
1
2
0
0
0
0
0
3
0
0
0
0
2
0
1
2
0
0
2
2
0
0
0
1
0
0
0
1
1
1
2
2
0
1
0
1
0
0
1
0
2
1
2
1
0
0
0
0
0
2
2
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
2
2
1
1
2
2
1
1
0
1
2
0
2
2
1
2
1
2
0
1
0
2
0
0
1
1
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
2
0
2
1
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
2
2
1
0
3
2
0
0
0
0
1
2
1
0
2
2
0
2
2
2
0
0
1
0
0
0
0
0
0
2
0
1
1
1
1
0
0
0
1
1
1
0
0
2
0
0
1
0
0
0
0
2
2
1
0
0
2
0
1
1
0
1
0
0
2
2
0
2
0
1
2
0
1
2
0
0
0
1
1
0
1
0
3
0
0
2
1
0
0
1
0
1
0
0
1
0
1
0
2
2
0
2
2
0
1
2
1
1
0
2
0
0
2
0
1
0
1
0
2
0
0
0
1
1
1
0
0
0
2
0
2
0
1
0
1
0
1
0
0
1
2
2
0
1
0
2
0
1
2
0
1
0
2
1
2
2
0
2
1
0
1
2
0
0
1
1
0
0
2
0
0
2
0
1
1
0
1
0
2
2
0
0
0
0
0
0
0
1
2
0
1
1
2
2
0
0
0
1
0
1
2
0
0
1
2
2
1
0
0
0
1
0
2
0
0
2
0
2
3
2
2
0
0
0
0
0
1
1
0
0
0
0
2
0
2
1
2
2
2
1
2
0
0
1
2
1
1
1
0
1
2
0
1
2
0
1
0
2
2
0
1
1
1
2
0
0
7
0
2
0
0
0
1
0
1
0
2
0
3
0
2
0
7
0
1
1
0
1
0
0
7
1
2
0
0
0
0
0
1
0
1
1
2
0
1
0
3
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
1
0
1
0
1
0
0
0
1
1
2
0
1
0
1
0
0
2
1
2
1
0
2
2
0
0
1
0
0
1
0
0
0
3
0
0
0
0
0
1
1
0
0
2
1
1
0
3
5
1
0
0
0
0
3
1
0
3
2
0
0
0
0
0
1
0
2
0
0
0
0
1
0
2
0
0
1
2
1
0
1
2
1
0
1
0
2
0
2
1
0
1
1
0
1
1
0
2
1
3
0
2
1
0
0
0
0
1
0
1
0
0
0
0
3
2
1
0
0
0
0
0
0
2
2
1
1
0
0
0
0
0
0
2
0
3
0
0
2
1
0
0
0
0
0
1
1
0
1
0
0
2
1
0
1
1
0
0
0
1
2
0
0
1
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
2
0
0
2
0
1
0
0
0
2
0
2
0
0
1
0
1
1
0
1
1
2
1
0
0
3
0
0
1
0
0
0
0
2
0
0
1
1
0
1
0
0
2
0
2
0
2
2
0
2
2
1
0
2
1
0
1
1
3
1
1
1
0
0
1
2
0
2
1
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
2
1
1
0
0
0
0
0
2
0
1
0
0
2
1
2
0
1
0
1
1
2
2
0
0
0
1
2
0
4
2
2
0
2
0
1
1
2
2
1
2
2
0
0
0
0
2
0
0
1
1
2
0
0
0
0
0
0
0
0
2
2
0
1
0
0
2
1
0
0
1
1
1
0
0
0
0
2
1
0
0
1
2
1
0
0
0
0
0
0
1
2
1
0
0
2
0
1
0
1
0
0
1
1
0
2
0
0
0
1
0
0
1
0
0
2
1
2
2
0
0
2
0
2
0
2
1
0
0
3
1
1
0
14
0
0
2
0
1
0
2
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
2
0
2
1
0
0
1
1
0
0
2
1
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
3
0
0
0
0
0
0
1
2
0
1
2
1
1
0
0
0
0
1
1
0
1
2
2
0
0
2
0
0
0
0
0
0
2
0
1
0
2
1
3
0
1
1
1
2
0
3
2
2
0
0
0
0
0
1
0
2
1
0
3
0
0
1
0
0
1
1
2
2
0
0
1
0
0
0
0
1
0
0
2
0
0
2
0
2
2
0
1
0
1
0
0
0
0
2
0
0
1
0
1
1
0
0
2
1
0
0
0
0
1
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
2
1
1
0
2
0
0
1
1
0
0
2
2
0
0
0
0
2
0
1
2
0
0
1
1
2
0
1
0
0
0
1
2
0
0
0
2
2
0
0
2
0
1
0
1
0
1
2
1
1
0
2
0
0
0
0
0
0
2
2
3
0
0
1
1
1
0
0
2
2
0
0
0
1
0
1
0
2
2
0
1
1
1
2
0
0
1
1
0
0
1
0
0
2
0
1
2
0
1
5
2
1
2
2
0
0
1
0
0
0
0
1
0
2
2
0
0
1
0
0
2
0
1
0
1
1
0
0
2
0
2
0
0
1
0
0
1
1
2
1
0
0
1
3
0
1
6
0
0
0
0
1
0
0
1
1
2
1
0
2
0
1
1
2
0
0
2
0
0
0
1
2
0
0
3
0
1
0
0
2
0
2
1
0
2
1
1
0
0
1
2
2
0
2
0
0
0
0
0
1
0
0
0
3
2
0
0
2
1
0
0
0
1
0
0
1
0
1
1
2
0
0
0
0
2
1
1
0
0
1
0
0
0
1
1
0
1
0
1
2
1
0
1
1
0
0
1
2
0
1
0
0
0
0
1
0
0
1
0
2
1
3
0
1
1
2
2
0
0
2
2
2
0
0
0
2
0
0
0
0
2
1
0
3
1
1
0
2
0
1
0
0
0
0
1
0
1
1
0
2
1
2
0
0
0
1
1
1
2
0
0
0
1
2
2
0
0
2
1
0
2
1
1
0
1
0
1
2
0
0
1
2
0
0
2
2
2
0
2
0
1
0
1
2
0
0
0
1
0
1
1
0
0
1
0
5
1
2
2
0
1
2
2
0
1
0
0
1
0
2
0
0
3
1
0
0
1
1
0
0
0
0
0
0
0
2
0
1
2
1
0
1
2
2
2
0
2
1
0
2
2
0
2
0
1
2
0
1
2
0
0
1
0
3
2
0
0
0
0
0
2
1
0
0
1
4
0
0
1
1
0
0
0
1
0
1
2
0
2
1
0
0
1
0
0
0
2
0
0
1
1
1
0
0
0
1
2
0
0
1
0
0
2
2
1
0
2
2
0
0
0
0
1
0
0
0
3
1
1
1
1
0
1
0
2
0
1
1
1
0
1
0
2
0
1
0
0
0
0
2
0
0
1
1
2
0
1
1
1
1
0
2
2
1
0
0
1
0
1
2
0
0
2
0
2
1
1
1
1
0
2
1
0
0
0
0
0
1
2
0
0
2
0
1
1
0
0
0
1
0
1
0
3
0
0
1
1
0
1
0
0
1
1
0
1
0
0
0
1
0
1
2
2
0
1
0
1
0
0
0
0
1
2
0
0
1
1
0
1
2
0
2
0
2
0
1
0
1
1
1
1
0
0
0
0
0
0
0
1
0
0
2
2
2
1
0
0
0
0
0
0
1
1
3
1
0
0
2
0
0
0
0
3
0
2
0
0
1
2
0
2
0
0
0
0
0
0
1
0
1
1
0
2
0
0
1
2
0
0
0
3
2
0
0
0
0
0
1
0
2
1
0
0
0
0
2
0
2
0
0
1
0
2
1
2
0
0
1
2
2
0
0
1
0
0
1
0
1
1
0
0
0
2
1
2
1
0
0
0
1
0
2
1
0
1
0
0
0
2
0
1
0
0
2
0
0
0
2
0
3
0
1
0
1
0
2
2
1
1
1
0
0
0
0
0
1
0
2
2
0
1
0
0
0
1
2
0
1
0
1
0
0
0
1
2
0
0
0
0
0
0
1
1
1
1
1
0
2
2
0
0
0
0
0
0
0
0
2
1
1
0
2
0
1
1
2
0
2
2
0
2
1
0
0
1
0
1
1
0
1
0
0
2
2
1
0
0
1
0
1
2
2
2
1
1
1
3
2
0
0
1
2
0
1
0
1
1
1
0
1
0
0
0
4
3
0
2
0
1
1
2
0
0
0
0
0
2
2
2
1
2
0
1
0
0
0
1
1
2
0
2
0
1
0
0
0
0
1
0
2
2
0
3
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
2
0
1
1
2
1
1
1
1
1
0
1
0
0
1
0
0
0
2
2
1
0
0
1
2
1
0
0
1
0
1
0
0
1
2
2
0
2
1
3
2
1
1
0
1
0
0
0
0
0
1
0
0
2
0
0
2
1
0
3
0
1
2
0
1
1
2
1
0
1
1
1
0
0
0
0
1
2
0
2
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
1
6
1
2
2
1
1
0
2
2
0
0
1
1
0
0
0
0
2
0
2
2
2
1
0
0
0
1
2
0
0
0
0
2
1
0
0
0
0
2
2
1
2
2
0
0
0
0
2
1
1
0
0
2
1
0
1
0
0
0
0
2
0
0
0
0
0
2
1
3
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
2
0
2
0
0
0
1
0
2
1
0
0
1
1
0
1
0
0
1
2
1
0
1
0
2
2
2
2
1
0
2
0
0
1
2
2
0
0
0
0
1
0
1
1
0
0
1
5
0
0
0
0
0
2
0
0
0
0
2
1
1
1
1
3
0
0
0
1
0
0
0
0
0
2
2
1
1
0
2
0
2
0
0
2
2
2
1
0
2
0
0
0
2
2
0
2
0
1
0
0
1
1
2
0
0
0
2
3
1
0
1
2
0
0
1
2
2
0
0
0
1
0
1
1
2
0
0
1
1
1
2
0
1
0
1
2
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
1
2
0
0
0
0
1
1
2
1
0
2
2
1
0
1
2
1
1
0
0
2
0
0
0
0
1
2
1
1
2
1
0
0
0
0
0
1
2
0
0
1
1
0
0
0
2
1
1
0
1
1
2
2
1
2
0
1
2
0
3
1
2
1
0
0
0
0
0
1
0
0
2
0
1
2
1
1
0
0
2
2
1
2
1
2
2
2
1
1
2
1
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
1
2
0
1
0
1
0
0
1
0
1
0
1
2
0
0
0
1
1
0
0
0
1
2
1
0
0
1
1
0
1
2
0
6
0
1
1
2
1
0
1
1
1
1
1
1
1
0
2
1
1
0
1
0
2
0
0
0
0
0
2
1
1
1
3
1
0
0
0
0
0
2
0
2
0
1
1
0
0
0
0
0
0
1
0
2
0
1
2
1
1
0
0
1
0
2
1
0
1
0
0
0
4
0
0
6
0
2
0
3
1
3
0
2
0
2
0
1
3
1
0
1
0
0
1
1
0
0
1
2
0
0
1
0
0
1
0
1
2
0
2
1
3
0
0
0
1
2
2
3
2
0
4
0
3
0
2
2
0
0
1
0
1
1
0
0
0
0
1
2
1
2
1
2
2
1
0
1
0
0
0
2
1
0
0
0
0
2
2
2
1
1
0
0
0
0
1
2
0
2
1
1
1
2
0
1
0
0
0
0
1
1
0
2
0
1
2
2
2
1
1
2
0
1
1
1
0
0
1
1
2
0
0
0
0
1
0
1
1
1
2
0
1
0
0
0
0
0
0
0
0
0
1
3
0
1
0
0
2
0
0
0
2
1
0
2
0
2
0
1
2
2
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
2
2
0
0
2
0
0
0
0
2
1
1
2
1
0
0
0
0
2
0
2
1
0
2
0
1
2
1
1
1
2
0
0
0
0
1
0
2
0
1
0
2
1
0
0
2
0
0
0
2
0
2
1
2
0
1
0
0
1
2
0
1
0
0
2
0
0
0
0
2
1
0
0
3
1
0
0
1
0
0
0
0
2
0
3
3
0
0
0
1
0
0
1
0
1
1
1
0
0
0
1
1
1
0
0
2
0
1
1
1
3
2
1
2
0
0
0
1
0
0
2
1
0
0
1
1
1
3
0
0
0
1
0
3
2
0
0
0
1
1
0
0
0
0
0
0
0
0
2
1
0
3
0
0
2
0
1
2
0
0
4
0
1
0
2
1
1
0
0
1
1
0
2
0
2
2
0
0
2
0
2
1
0
0
2
0
1
0
0
2
0
2
0
1
0
1
1
0
0
1
0
2
1
0
2
2
0
1
2
2
0
2
0
0
0
0
1
1
0
0
0
0
0
2
2
0
1
1
2
1
2
0
2
0
0
0
0
1
1
0
2
2
0
2
1
1
0
0
0
1
0
1
0
2
2
2
1
2
0
0
0
1
0
1
0
0
1
0
1
1
0
0
0
2
1
1
0
0
0
2
0
2
0
2
0
1
0
0
0
0
1
0
1
1
2
1
2
0
2
1
2
0
2
0
0
0
0
2
2
1
0
0
1
0
0
1
0
0
0
0
0
1
2
1
0
1
0
2
0
0
1
1
0
0
1
0
2
1
2
2
1
0
2
1
1
0
0
0
2
0
1
1
1
0
2
1
0
2
1
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
1
2
1
0
0
0
0
1
0
4
0
0
0
0
1
0
0
3
0
0
0
1
0
1
0
1
1
0
2
0
1
1
1
0
0
1
2
2
0
0
2
1
0
1
1
0
0
0
0
0
1
2
2
1
0
2
0
0
1
0
1
1
1
2
0
0
3
1
0
1
2
4
1
1
1
1
0
1
0
0
3
0
0
1
1
0
1
1
0
2
2
0
2
2
1
0
2
0
1
2
1
1
0
0
2
2
1
0
0
2
0
0
1
0
2
0
0
0
2
4
0
2
0
2
1
1
2
0
2
0
0
1
0
0
2
0
2
0
0
0
1
1
1
1
0
0
1
0
0
1
0
0
2
2
0
0
0
0
2
1
0
2
1
1
2
0
0
2
2
0
0
0
2
2
2
2
2
1
1
0
1
0
1
0
1
0
0
1
1
2
1
0
2
4
0
2
0
3
0
1
2
0
0
0
2
0
0
2
0
0
0
2
1
0
2
0
1
1
0
2
0
1
0
1
2
0
2
1
0
2
1
0
3
0
0
1
0
0
1
2
0
2
1
1
0
1
0
0
0
0
0
0
0
0
1
3
0
0
1
2
1
0
2
2
0
0
0
1
0
0
2
0
0
0
0
1
2
2
1
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
3
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
2
0
0
1
2
2
1
0
1
1
0
1
0
0
0
1
1
1
0
0
0
2
0
0
0
2
0
3
2
1
2
0
0
0
0
3
0
1
0
2
1
0
2
0
2
0
0
1
0
1
1
0
1
0
2
1
1
0
0
0
3
1
0
0
0
1
1
1
0
0
1
0
0
2
1
2
0
1
2
0
1
0
1
2
0
0
1
0
2
2
2
0
1
0
1
0
0
0
0
1
2
1
0
2
1
1
1
2
0
0
0
1
1
1
0
0
2
0
0
0
1
0
0
0
1
0
1
1
2
1
1
3
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
2
1
2
2
1
0
0
2
2
2
1
0
1
1
1
0
2
0
2
0
0
0
1
2
1
2
0
0
2
2
0
0
0
2
1
1
0
0
0
0
0
2
1
0
1
0
2
0
0
0
0
0
0
0
1
2
1
0
2
0
2
0
1
0
0
0
0
2
1
0
1
0
1
0
2
0
0
0
0
0
2
0
1
0
0
3
0
0
0
1
0
1
1
0
2
2
0
0
0
1
0
2
0
2
2
1
1
0
0
0
1
0
2
2
0
0
0
0
1
0
0
0
0
6
1
2
2
0
0
0
2
0
0
0
0
0
1
2
0
2
1
1
1
0
0
0
2
1
1
0
1
0
0
0
0
0
0
2
0
0
1
1
2
2
0
0
1
0
0
1
1
0
2
0
2
0
2
0
2
0
0
0
2
1
0
2
0
0
0
0
0
2
0
0
1
1
1
1
0
0
1
1
1
0
0
0
1
1
0
0
0
1
0
2
0
0
0
1
2
0
0
0
0
0
1
4
2
0
1
0
1
2
1
1
2
0
0
1
0
0
0
1
0
2
0
0
0
0
0
1
0
0
1
0
0
0
2
1
1
2
0
0
0
0
1
1
0
1
0
1
2
2
1
0
2
0
0
1
0
1
0
1
1
0
1
0
1
1
0
0
5
0
1
1
1
0
1
1
0
1
0
1
1
0
1
0
0
2
0
0
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
1
1
2
0
2
0
0
0
1
1
0
0
1
0
0
1
2
0
1
2
0
1
1
1
0
0
0
0
1
3
0
0
1
1
1
2
0
1
1
0
0
0
0
0
0
0
0
1
4
1
1
0
0
1
0
1
0
1
0
0
2
0
0
0
0
1
1
1
1
0
1
0
0
0
1
0
0
0
1
0
2
2
1
0
0
0
0
4
0
0
2
2
2
0
0
1
1
0
1
0
0
2
0
1
0
2
0
1
1
1
0
2
2
2
0
0
0
0
2
2
0
1
0
0
1
0
1
0
2
0
0
0
0
1
1
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
2
1
0
1
0
1
2
2
1
2
0
1
0
2
2
0
0
0
2
1
1
0
2
1
0
0
0
0
1
0
1
2
1
0
1
1
1
2
0
1
0
2
0
0
0
1
0
0
1
1
0
1
0
0
2
0
1
0
0
2
2
2
0
1
0
0
0
0
0
0
2
3
1
0
2
1
0
1
2
0
0
1
0
0
2
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
1
0
2
3
0
0
0
0
0
0
1
0
1
1
0
1
1
1
1
0
2
1
1
2
1
2
2
0
0
0
1
0
0
1
2
1
0
0
0
1
3
2
0
0
0
0
1
1
2
0
0
1
0
0
0
5
0
1
0
0
2
2
0
1
2
0
0
0
0
3
0
2
2
0
2
1
2
0
2
2
0
0
0
0
0
0
2
0
0
1
0
2
2
2
0
0
0
0
1
0
0
1
0
1
0
2
0
0
0
0
1
0
0
1
0
1
0
0
3
0
0
0
2
0
0
1
2
1
0
1
1
2
0
1
3
3
1
0
2
0
0
2
0
1
0
1
0
0
0
0
0
0
2
2
1
0
0
3
1
0
1
0
1
2
0
2
2
0
1
0
2
0
2
1
1
0
0
0
1
1
0
0
2
0
0
2
0
0
0
1
0
3
1
0
1
1
0
1
0
0
0
0
1
0
0
1
1
1
2
0
0
1
3
1
1
1
2
0
2
0
1
1
0
0
1
0
1
1
1
2
0
0
0
0
0
1
0
2
2
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
1
0
2
0
1
0
1
0
0
0
2
0
1
1
1
1
0
0
0
2
1
0
1
2
2
1
0
0
0
1
2
0
0
0
1
2
2
2
0
0
0
0
2
0
1
2
2
0
1
0
2
0
0
2
0
0
0
2
1
1
1
1
1
2
0
1
1
2
1
0
2
0
0
0
0
2
2
2
1
2
0
0
0
1
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
2
0
0
0
0
1
0
0
0
0
1
0
3
2
0
1
0
0
1
1
0
2
1
0
0
2
2
0
1
5
0
1
2
1
0
1
1
2
0
0
0
0
2
1
0
1
1
0
0
0
3
2
1
0
1
1
1
1
1
0
0
1
0
0
0
1
0
0
0
1
0
1
2
1
1
0
0
1
1
1
0
1
0
1
0
5
1
1
2
0
2
0
0
1
1
0
2
0
1
0
0
0
0
2
3
1
0
0
2
0
0
1
1
2
1
2
2
5
0
1
1
1
2
0
1
2
1
0
0
0
0
1
4
2
0
1
0
2
0
0
1
2
0
2
0
0
1
1
0
0
0
0
1
0
1
1
0
1
0
0
0
1
2
0
0
1
1
0
1
1
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
2
2
0
1
0
0
0
0
0
0
2
2
0
1
1
0
0
1
0
0
1
1
0
1
0
0
0
1
0
0
0
0
1
0
0
2
1
1
3
1
1
2
0
0
0
0
1
3
0
2
2
0
0
2
0
0
1
2
0
0
0
0
0
1
0
0
0
2
2
2
1
2
0
0
0
0
0
0
0
1
1
0
0
0
3
1
2
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
1
0
2
2
1
2
0
0
0
0
0
0
0
1
1
0
0
2
0
0
2
0
2
1
0
0
0
0
1
0
0
2
0
0
1
1
2
1
0
1
0
0
2
1
0
0
2
0
1
0
0
2
0
1
0
0
0
1
1
0
2
1
0
1
0
0
0
1
0
0
0
0
2
0
1
2
0
1
3
1
1
0
0
0
2
2
2
0
0
1
1
2
1
0
0
2
0
0
1
2
2
1
0
0
0
1
1
1
2
0
1
0
0
2
0
1
2
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
2
0
2
0
2
0
0
0
1
0
0
0
1
1
0
2
1
1
0
0
0
1
0
0
1
1
0
6
1
2
1
0
2
2
0
1
0
1
1
1
0
0
1
0
0
0
0
1
2
0
1
0
1
0
0
0
0
0
1
0
2
2
1
0
0
0
0
2
1
2
1
0
0
2
0
0
1
0
0
0
1
0
1
2
1
1
1
1
2
0
1
0
1
2
0
0
0
0
1
3
0
0
1
2
0
0
1
0
0
0
1
2
0
0
2
0
0
0
0
0
0
1
1
2
0
0
0
1
0
2
2
1
1
2
2
2
1
1
2
0
3
0
0
0
0
0
0
2
0
0
1
0
0
1
1
2
0
0
0
2
0
0
0
1
2
0
0
0
0
2
0
1
0
2
1
0
0
0
0
2
1
2
2
0
2
0
1
0
0
0
1
1
0
1
8
0
1
2
1
0
2
1
2
1
1
0
0
1
0
0
1
3
0
0
1
2
0
0
2
0
0
2
1
0
0
0
2
0
0
1
1
0
0
0
0
2
1
1
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
1
0
3
1
0
1
0
2
1
0
1
1
0
0
0
2
3
2
0
2
2
1
1
0
2
1
2
2
0
0
1
0
1
2
2
1
2
2
0
2
1
1
2
0
0
0
0
0
1
0
1
0
1
1
0
0
1
0
0
0
0
0
1
0
2
0
1
1
2
0
2
0
0
1
1
0
0
1
0
0
1
0
0
1
0
2
1
0
1
0
2
0
1
0
2
0
1
0
0
0
1
0
1
1
2
2
1
0
2
0
0
0
0
0
0
0
0
2
4
0
3
0
1
1
1
0
0
2
1
0
1
2
0
0
0
0
2
0
0
2
0
0
0
1
3
1
0
0
0
0
0
0
0
2
1
1
0
2
1
1
0
2
0
0
1
0
0
2
0
0
2
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
1
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
2
0
1
0
1
0
2
2
0
0
2
0
1
0
0
0
1
1
0
1
4
1
0
0
1
0
0
0
1
0
0
1
1
0
1
2
0
0
1
0
2
0
0
0
1
0
1
3
1
0
1
0
3
0
0
2
0
1
1
0
2
1
0
1
0
0
1
1
0
0
0
2
0
2
2
0
0
2
1
1
2
0
2
0
0
0
0
0
0
0
0
0
8
2
1
1
1
2
2
0
2
0
1
1
0
0
0
0
1
0
1
0
1
2
1
1
0
0
3
1
0
0
1
0
0
2
0
1
1
2
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
2
2
1
2
0
0
0
2
0
0
0
0
1
0
0
0
1
0
1
0
2
0
0
1
0
1
2
0
2
2
1
2
1
0
0
0
0
1
0
0
0
0
2
0
0
1
2
1
2
1
2
2
0
3
3
2
0
0
0
0
0
1
0
0
2
0
1
3
1
1
0
1
1
2
0
1
0
0
1
1
0
1
1
1
2
2
0
2
4
0
1
1
0
0
0
2
0
1
3
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
1
1
2
2
1
1
1
0
1
0
2
1
0
2
0
1
0
0
1
0
2
2
0
1
0
0
0
0
2
0
0
1
2
1
1
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
2
2
0
0
2
0
2
1
1
0
1
0
0
0
0
0
1
1
2
1
0
0
0
1
0
0
0
2
1
0
0
1
0
3
0
1
0
0
1
0
0
0
0
2
1
0
1
1
0
2
0
1
2
1
1
1
2
1
2
1
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
2
0
2
0
1
0
0
0
1
0
0
1
0
1
1
2
0
0
0
3
0
0
2
0
2
1
1
0
0
1
0
0
0
2
1
0
0
1
0
2
0
1
2
0
1
2
3
0
1
2
0
0
2
0
0
0
0
0
1
3
0
1
0
0
1
3
0
0
0
0
0
1
0
0
2
1
0
2
1
2
0
0
0
1
0
1
0
0
1
1
1
2
0
0
1
0
0
0
1
1
1
0
0
2
2
0
1
0
0
2
0
2
1
0
1
4
1
2
0
1
0
1
0
0
2
2
2
1
0
0
6
0
2
3
0
0
0
1
1
1
1
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
2
0
0
1
0
0
3
0
0
0
1
0
0
0
2
2
1
2
2
1
0
2
2
1
2
1
2
0
1
1
1
1
1
1
2
0
1
0
2
0
0
0
0
1
0
0
1
2
0
1
0
0
0
1
0
0
1
0
0
0
0
3
1
1
2
1
0
2
0
1
2
0
4
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
2
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
1
2
2
0
0
0
0
0
0
0
1
0
2
2
0
1
0
1
2
0
1
2
1
2
0
3
4
1
0
0
0
0
2
0
1
0
1
0
1
0
1
0
1
1
0
0
2
0
1
0
0
0
0
2
1
0
3
0
2
2
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
2
1
0
0
2
0
0
1
1
0
2
0
1
0
2
2
2
0
1
1
0
2
0
1
2
1
0
0
2
2
0
0
0
3
1
0
1
1
0
0
0
0
2
1
0
2
1
1
0
0
2
1
1
0
1
0
1
1
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
2
0
2
1
1
1
2
2
0
1
2
0
0
0
2
0
0
2
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
2
1
1
0
1
0
0
1
0
2
0
0
0
1
2
2
0
0
0
0
1
0
0
0
2
0
1
2
0
0
1
2
1
0
2
0
2
1
2
2
1
1
0
2
1
1
0
0
1
0
2
0
2
1
1
2
0
0
3
1
1
2
0
2
1
0
2
0
0
0
0
0
1
2
0
0
2
0
0
0
0
1
0
2
0
1
0
1
0
0
0
1
2
0
0
0
0
1
0
0
2
1
0
0
0
1
0
1
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
2
2
2
0
1
0
0
0
1
0
0
0
1
2
0
1
4
1
0
0
0
3
2
1
3
0
0
2
1
0
0
0
1
0
2
0
0
0
0
1
0
1
1
0
0
0
1
0
0
6
0
1
1
0
1
1
2
0
2
2
1
0
2
1
0
1
1
0
0
1
0
1
0
1
1
0
0
0
1
0
1
0
0
2
0
0
0
2
0
0
1
0
2
0
1
2
0
1
0
0
1
3
0
3
1
1
0
1
1
0
2
0
1
0
1
0
2
0
0
0
1
0
1
0
0
0
1
0
0
0
1
1
1
1
0
0
1
0
0
0
0
2
2
0
0
1
0
0
0
1
2
0
3
1
1
2
1
0
2
1
0
1
2
2
1
1
0
0
0
0
1
1
1
0
1
0
1
0
2
2
0
1
3
1
1
0
1
0
0
1
1
0
0
1
1
1
0
0
0
0
2
0
2
0
0
1
1
2
1
0
2
0
1
0
0
0
0
1
1
1
2
0
0
1
1
0
1
0
1
2
0
0
0
2
0
0
1
0
1
0
0
0
4
0
0
0
2
1
0
1
0
1
0
0
1
2
2
0
0
0
0
0
2
0
0
2
1
0
4
0
2
1
0
0
1
0
2
0
0
0
0
2
0
0
2
1
1
2
1
0
2
1
1
1
0
0
1
0
1
1
2
0
0
2
0
0
1
1
1
2
0
1
0
0
1
0
0
0
0
0
1
2
0
1
1
0
0
0
1
2
1
0
0
1
3
1
0
0
0
0
0
0
1
0
0
2
0
1
3
0
1
1
0
0
1
0
1
0
1
2
0
0
2
1
1
0
0
1
0
2
2
0
2
0
0
0
0
0
1
1
1
1
2
0
2
0
0
0
1
0
0
2
2
1
0
2
1
2
1
1
0
2
1
0
1
0
0
0
1
1
1
0
2
0
2
1
1
1
0
0
2
0
1
0
0
2
0
0
0
0
1
0
0
2
0
1
0
2
1
0
1
2
1
1
1
1
1
1
0
0
2
0
2
1
2
0
2
0
1
0
0
0
0
3
0
5
1
0
1
1
1
1
1
0
0
1
1
0
0
2
1
2
0
0
0
1
0
0
8
0
0
2
0
1
0
0
0
1
0
0
2
0
1
2
0
0
1
0
0
0
2
0
1
2
0
0
2
0
2
0
1
0
3
0
1
0
1
2
0
1
1
0
0
0
2
0
2
0
1
2
1
3
3
2
2
0
0
2
1
0
2
1
2
0
1
1
0
0
2
0
0
2
0
2
2
0
1
1
2
2
2
2
2
1
1
1
2
0
0
0
2
1
2
1
0
0
0
2
0
0
0
0
2
2
1
0
1
0
3
1
0
4
2
2
1
0
0
0
0
1
1
0
0
2
1
0
0
1
0
0
0
0
0
0
1
0
2
1
0
1
1
1
0
5
1
1
0
0
0
1
0
0
0
0
2
0
0
2
1
0
1
2
0
1
0
0
1
0
0
2
0
0
1
0
0
2
0
2
0
0
0
0
0
2
0
0
1
3
0
1
1
1
1
0
0
1
2
0
0
0
0
0
1
2
2
2
1
1
0
0
1
1
2
2
1
0
1
0
1
0
1
2
2
1
1
2
0
0
2
0
0
0
0
0
1
2
0
2
0
2
1
1
0
1
0
0
0
2
0
0
2
1
1
0
1
2
0
2
2
0
0
1
2
0
0
1
1
0
3
0
2
0
0
0
2
0
0
0
0
1
0
2
0
0
2
0
0
1
0
0
0
0
2
1
1
1
0
1
2
2
0
0
0
1
0
2
0
1
2
1
0
2
0
0
0
0
1
2
0
0
1
0
0
1
0
2
0
0
0
2
3
3
0
0
1
0
0
0
1
1
0
0
1
0
0
0
2
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
3
1
1
0
1
0
0
0
0
1
2
0
1
1
2
0
2
0
2
0
0
0
1
0
1
2
0
0
0
2
0
0
0
0
0
1
1
1
1
0
1
2
2
2
0
0
0
0
2
0
0
0
0
0
3
1
2
0
1
1
4
2
2
1
0
0
0
0
2
1
0
1
1
1
2
2
2
0
0
0
2
0
0
2
1
1
0
1
0
1
1
1
0
1
0
2
1
0
0
0
0
0
0
0
0
1
2
0
1
0
0
1
1
0
0
1
0
0
2
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
2
3
0
1
0
0
1
0
2
2
0
0
0
0
1
2
2
0
0
0
0
0
2
2
1
0
0
1
2
2
0
0
1
0
0
2
2
0
0
1
1
1
1
2
2
2
2
0
2
0
0
1
3
0
0
0
2
2
1
0
1
0
2
1
2
0
0
1
3
0
0
0
0
1
1
0
0
2
2
0
0
0
2
0
2
0
0
0
0
2
0
1
0
0
0
2
2
2
2
1
1
1
0
2
1
2
0
1
1
0
2
0
0
0
0
0
1
0
1
1
2
2
1
2
0
0
0
1
0
1
1
0
2
0
0
1
0
0
1
2
1
1
0
2
1
1
0
1
1
0
0
0
1
0
1
2
1
0
0
0
0
1
0
0
1
0
0
2
2
1
0
1
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
1
2
0
1
0
0
0
0
0
0
1
0
1
1
0
2
0
1
0
0
1
0
2
1
1
0
1
0
0
0
1
1
0
1
1
2
0
1
1
0
1
0
1
0
2
1
2
1
0
0
2
0
0
1
0
2
0
1
1
2
1
0
0
0
0
2
2
0
2
0
1
0
1
1
0
1
1
0
1
1
0
1
2
0
0
1
2
3
1
1
2
0
2
0
0
0
1
1
0
1
2
0
1
0
0
0
1
0
0
4
0
2
1
0
1
1
0
1
1
0
1
0
0
2
0
2
1
0
1
2
0
0
0
1
1
1
1
1
1
1
2
2
0
0
0
0
0
2
2
2
1
2
1
0
0
0
0
2
0
1
3
1
2
0
0
1
0
0
0
0
0
0
0
0
1
1
0
6
0
0
1
1
0
1
0
1
1
0
1
0
0
0
1
0
2
2
2
0
0
0
0
0
1
2
1
1
0
2
0
0
0
1
1
1
0
1
0
0
2
0
8
1
1
0
2
1
0
2
4
0
0
1
0
1
2
0
2
1
2
2
0
0
0
1
1
0
1
0
1
0
0
2
0
0
2
1
0
0
2
1
0
0
0
2
1
1
0
0
1
0
0
2
0
2
0
0
4
0
5
0
0
1
2
0
0
1
1
1
2
2
0
0
2
1
0
0
1
1
0
1
0
2
1
0
0
0
1
0
2
1
0
2
2
1
1
1
0
0
0
1
1
0
0
0
1
0
0
1
0
1
1
1
1
1
0
1
0
2
0
2
1
0
0
1
1
2
0
1
1
1
0
1
0
1
1
0
2
1
1
0
0
0
0
2
2
0
2
0
2
3
2
0
2
0
2
0
2
0
0
0
1
1
0
1
0
0
2
0
3
0
0
0
1
2
1
0
0
1
0
0
1
2
2
2
2
1
2
0
0
1
2
0
0
1
2
1
0
0
0
2
0
1
3
0
0
2
1
1
1
2
1
1
0
0
0
1
3
1
0
3
0
0
2
0
0
0
0
2
0
1
0
1
0
1
0
0
0
1
2
0
2
1
0
0
0
1
1
1
0
1
1
2
2
0
2
1
0
1
1
1
0
0
0
3
0
1
4
1
2
0
1
0
2
0
1
1
0
1
0
0
0
0
1
1
2
1
1
0
2
1
2
0
2
2
2
1
0
0
0
2
0
0
0
0
0
3
0
0
0
2
2
2
1
0
0
0
0
2
0
0
0
0
1
2
1
0
0
2
0
0
0
2
0
0
2
0
2
0
0
0
1
0
0
1
4
1
1
1
2
2
5
1
1
0
1
0
1
2
1
0
0
2
7
1
0
0
2
2
0
2
0
2
1
0
1
0
1
2
1
0
1
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
1
1
1
0
0
1
2
2
1
3
0
0
0
3
0
0
1
1
1
1
2
0
0
1
0
2
3
2
0
0
0
0
2
2
0
0
0
1
2
0
2
1
1
1
0
0
0
1
2
2
2
0
2
0
1
2
1
4
2
2
1
0
2
0
0
0
1
0
0
2
0
1
0
2
0
0
1
1
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
2
2
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
2
0
0
1
2
0
0
0
1
0
1
0
1
0
0
1
1
2
0
1
0
0
2
0
2
0
0
2
0
2
0
0
3
2
2
0
0
0
0
0
1
0
2
0
0
0
1
0
0
1
0
1
0
1
2
0
0
1
0
0
1
2
0
1
0
0
1
0
0
1
0
1
2
2
1
0
0
0
0
1
2
0
0
0
0
1
3
2
1
0
0
1
0
2
0
0
0
2
0
1
1
0
3
0
1
2
2
0
1
1
0
1
0
0
0
0
0
1
2
1
2
0
0
0
0
3
0
2
0
0
2
0
1
0
0
0
0
2
0
0
0
1
2
2
0
0
1
0
1
0
0
2
0
2
1
0
0
5
0
0
2
0
0
0
0
0
0
1
1
1
1
1
0
1
1
1
1
0
1
2
1
1
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
2
2
0
2
1
0
0
2
0
0
0
0
2
0
2
0
0
0
1
1
1
1
2
0
2
0
0
1
0
0
2
0
1
1
1
0
0
1
2
0
0
1
0
0
0
1
0
0
2
0
0
0
0
1
0
0
6
0
0
0
0
1
2
0
1
2
2
0
1
0
0
0
1
2
0
0
1
1
0
2
1
0
0
0
0
0
2
0
0
0
0
1
0
0
1
1
1
0
0
0
0
2
0
0
1
0
2
0
1
3
2
0
1
0
1
0
1
0
0
1
0
0
3
1
1
1
0
1
0
2
1
1
2
2
0
1
0
1
2
0
0
2
0
1
0
0
0
0
1
2
1
2
1
0
0
1
1
0
0
1
5
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
2
0
1
2
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
1
1
2
1
2
1
0
2
1
0
1
0
0
2
1
0
1
0
0
0
0
1
0
3
2
2
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
1
0
2
0
1
0
0
2
1
0
2
0
1
0
0
1
1
0
0
0
1
0
0
0
2
2
1
2
0
0
0
2
2
0
0
0
0
3
1
2
0
2
0
0
0
1
1
3
0
0
0
1
1
1
0
0
0
2
0
2
2
0
0
2
1
1
0
0
2
0
0
2
2
1
1
0
0
0
0
0
0
0
1
3
0
0
0
0
0
1
0
0
1
0
1
1
1
1
1
2
1
1
2
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
1
2
1
0
1
0
1
1
3
0
0
0
1
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
1
2
1
1
0
1
0
0
0
1
0
1
3
2
1
0
0
0
0
0
2
1
1
0
0
1
1
0
0
1
0
2
2
1
2
0
2
2
0
1
5
0
0
2
0
1
1
1
2
1
1
0
0
2
0
1
0
1
2
1
0
1
2
2
0
0
0
0
2
3
1
0
2
2
0
0
0
0
0
1
1
0
0
0
2
2
0
2
0
0
0
2
0
0
0
0
2
1
0
0
1
1
2
0
0
1
0
2
0
0
0
0
1
2
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
3
2
2
2
1
1
1
0
2
1
1
0
0
1
1
0
0
0
1
0
1
1
0
0
0
0
1
0
2
1
0
0
2
0
0
1
2
0
0
0
1
2
1
3
0
2
0
0
2
2
0
1
0
0
0
1
0
1
0
0
0
1
3
2
1
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
2
0
1
2
0
1
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
2
2
1
0
1
2
0
0
0
0
0
0
0
2
2
1
2
1
2
0
2
0
2
0
0
1
0
0
0
1
0
1
1
0
0
0
2
1
1
0
0
2
1
2
0
1
0
0
1
0
7
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
1
0
0
1
1
2
1
2
1
0
0
0
2
1
2
1
2
2
0
2
0
2
1
0
0
0
0
2
1
0
0
0
0
1
0
2
2
0
1
1
1
0
0
1
0
1
0
0
2
3
1
0
1
1
0
1
1
3
1
0
0
0
0
0
2
2
1
2
2
0
0
0
1
0
1
1
1
0
1
2
2
0
2
0
2
0
2
1
0
1
0
1
2
0
0
1
1
2
1
0
0
0
0
0
2
1
0
0
0
0
1
2
0
1
0
0
1
0
0
0
2
1
0
1
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
1
0
1
2
1
2
1
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
2
1
0
2
0
0
2
0
2
0
0
1
0
2
0
2
0
0
0
1
2
0
0
0
0
0
3
2
0
0
0
1
1
1
0
0
0
0
2
0
1
0
1
0
0
0
2
1
1
2
0
0
0
1
0
1
0
2
0
0
0
0
1
0
3
2
2
2
0
1
1
0
0
0
3
0
1
0
1
0
0
0
0
1
0
0
1
0
2
0
1
1
1
1
0
0
2
0
1
1
0
0
0
1
0
0
2
0
0
3
0
0
0
0
0
1
1
1
1
0
1
0
1
0
2
0
0
0
2
2
0
1
1
1
0
1
0
0
2
2
0
0
0
1
0
2
0
1
2
1
2
0
0
0
0
0
0
0
2
0
1
4
2
0
2
2
0
2
1
2
0
2
1
1
0
0
1
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
2
1
2
1
0
2
0
0
2
1
1
0
0
0
1
0
0
1
4
0
0
0
0
0
0
0
0
1
0
1
1
1
1
2
0
0
0
0
0
0
2
3
0
1
0
0
0
1
2
0
0
1
1
0
0
0
1
0
0
2
2
1
0
0
0
0
0
2
1
0
1
0
1
0
0
0
0
1
0
2
2
0
0
0
0
0
1
0
0
0
2
1
1
0
0
2
1
0
3
2
0
0
1
2
0
0
0
1
0
2
0
0
0
0
1
1
2
0
0
2
0
0
1
2
0
1
2
1
0
2
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
1
0
4
1
1
0
1
1
2
2
3
2
0
0
2
0
1
1
0
0
1
2
1
0
1
0
1
2
1
2
0
2
2
0
2
0
0
1
0
1
2
0
0
0
1
0
0
0
0
1
1
0
0
0
2
1
2
0
1
0
0
0
1
1
0
4
1
0
0
2
0
2
0
2
1
0
2
1
2
0
1
0
0
2
0
1
2
2
0
1
0
2
0
0
1
0
2
0
2
0
1
1
0
0
0
2
1
0
0
2
2
1
0
0
1
0
1
1
2
1
0
0
0
1
1
0
2
1
0
1
2
0
2
2
0
0
1
1
4
0
1
1
2
0
0
1
0
0
0
1
2
1
0
0
1
1
1
0
1
2
1
1
0
0
0
2
2
0
0
0
2
0
1
5
0
1
0
0
1
0
0
0
1
0
2
1
0
2
0
2
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
1
3
0
1
1
0
3
2
0
5
0
2
1
0
0
0
0
0
1
0
0
1
0
1
0
0
2
1
0
1
1
0
0
0
0
0
2
2
2
0
2
0
2
0
0
1
1
0
0
1
0
1
2
0
0
1
1
2
2
2
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
2
2
0
1
0
0
0
2
0
2
1
1
1
0
0
1
0
0
0
2
0
1
1
0
2
0
2
0
0
0
2
2
1
1
1
0
0
0
0
0
1
0
0
2
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
2
1
1
0
0
2
0
1
2
1
1
2
0
0
0
0
0
0
1
0
0
2
2
1
0
0
0
0
0
2
2
1
0
0
0
2
2
1
2
0
1
0
1
2
2
1
2
0
0
1
0
0
0
0
1
3
0
1
2
1
1
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
1
2
0
2
1
0
1
0
1
0
0
0
2
0
0
0
0
2
1
0
2
2
0
2
0
2
1
0
0
2
1
0
1
1
1
0
1
0
2
0
0
0
0
0
2
2
0
0
3
2
0
0
2
1
1
0
0
0
1
2
1
2
1
1
0
1
0
0
2
1
3
0
0
0
0
2
0
0
0
2
0
0
1
0
0
2
0
0
1
2
0
0
1
2
0
0
0
1
0
0
1
0
0
0
2
0
0
0
1
2
1
0
1
0
2
1
2
2
1
0
2
1
0
0
1
2
0
1
0
0
0
0
1
2
1
0
0
0
0
0
2
2
0
0
0
0
0
0
2
2
1
0
2
0
1
0
0
0
1
2
0
2
0
2
0
0
0
1
0
0
0
2
0
2
0
2
0
2
0
0
6
0
2
4
1
1
0
0
0
0
1
0
1
3
2
0
0
1
1
2
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
3
0
2
2
0
0
1
2
0
0
2
1
1
2
1
1
2
0
0
1
1
2
0
3
0
0
0
0
2
0
0
0
0
2
0
0
2
2
0
0
2
1
0
2
0
0
2
0
1
0
0
3
0
0
2
0
1
2
0
1
0
0
1
0
0
0
0
3
1
0
0
1
0
1
2
0
0
1
0
0
0
0
0
0
2
2
1
0
0
2
0
0
0
2
0
2
1
2
0
0
0
1
0
2
2
0
0
1
0
1
0
1
0
0
1
2
2
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
2
0
2
2
1
0
2
1
2
0
2
1
1
2
2
1
1
0
0
0
0
1
0
1
0
2
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
1
2
1
0
2
0
0
2
0
2
0
2
0
0
0
1
0
0
0
1
1
2
0
0
2
0
0
0
1
1
3
1
1
0
1
0
0
1
0
1
1
1
2
0
0
0
0
0
0
1
2
1
0
2
0
0
0
0
0
0
2
2
2
2
1
0
0
1
0
0
1
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
1
1
1
2
2
0
2
0
0
2
1
0
2
0
0
1
0
0
0
2
0
2
0
0
1
0
0
1
0
0
1
0
1
1
0
1
0
0
0
1
0
0
4
0
1
1
4
1
0
0
0
1
1
0
0
3
1
0
1
0
1
1
0
1
0
0
2
1
2
4
1
0
0
0
1
2
1
0
0
0
0
0
2
0
2
1
1
0
0
0
1
4
3
1
0
0
1
0
0
1
1
0
1
1
1
2
0
0
0
2
0
2
0
0
2
0
1
1
3
1
0
1
0
0
0
1
1
0
1
0
1
0
2
0
0
1
2
0
0
2
0
2
1
0
0
0
0
1
1
0
0
0
1
1
1
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
1
4
0
2
0
0
2
0
2
1
0
1
2
0
2
0
1
0
2
0
0
2
1
0
2
3
1
2
2
1
1
2
2
0
1
2
0
0
0
0
0
1
1
0
2
1
0
0
0
2
0
2
0
1
1
0
4
0
1
0
3
2
0
1
1
0
1
0
0
0
0
0
0
0
0
2
1
2
0
0
1
1
1
0
1
0
2
0
1
1
0
1
0
1
2
2
2
0
0
1
0
0
0
1
0
0
1
0
0
1
0
1
1
1
2
0
0
1
1
1
0
2
0
0
2
2
2
0
0
0
2
4
1
1
1
0
0
1
0
2
1
0
1
0
0
1
0
1
1
0
3
1
2
0
1
0
0
0
1
0
3
0
0
0
0
1
0
1
1
2
2
0
1
2
0
0
2
1
0
0
0
0
1
2
1
0
1
0
2
0
1
0
1
0
1
1
0
0
1
0
0
0
2
2
0
0
0
0
2
1
1
0
1
0
1
2
1
1
0
1
0
0
1
0
0
0
0
1
2
0
0
0
1
2
2
0
0
0
1
3
0
3
0
0
1
0
0
0
1
0
0
1
0
1
2
0
0
1
1
2
0
1
2
0
1
2
1
0
0
1
0
2
2
0
1
1
0
2
0
2
0
0
0
0
1
0
0
1
0
1
2
0
2
1
0
0
1
0
2
1
0
0
0
0
2
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
1
2
1
1
0
1
0
0
0
1
0
1
0
1
0
2
2
0
1
0
1
2
3
0
2
0
1
1
0
1
0
2
1
2
2
0
2
3
0
0
2
2
2
1
1
0
2
2
0
0
1
0
1
3
0
0
0
0
1
0
0
1
0
1
1
1
0
0
0
0
0
1
0
0
2
4
0
1
1
0
0
1
0
0
4
0
0
2
0
0
0
0
2
2
1
0
0
0
2
3
2
0
2
2
0
2
0
3
0
0
1
2
0
1
2
0
0
1
1
0
0
2
0
1
2
2
0
0
0
1
0
2
0
0
2
0
1
0
1
0
1
0
2
1
1
0
2
2
1
0
1
0
0
0
0
0
1
1
2
2
0
2
0
1
0
0
0
1
0
1
1
2
0
1
0
2
0
1
0
1
2
2
3
2
0
2
1
0
0
0
1
0
1
1
1
0
0
0
0
0
2
1
2
1
0
0
0
0
1
0
0
0
2
0
0
1
2
2
0
0
1
0
0
1
0
1
2
1
0
0
0
0
1
1
0
0
0
0
2
1
2
0
2
0
0
0
1
2
1
0
0
0
1
0
1
1
2
2
2
2
2
0
3
1
0
0
0
2
0
0
1
2
2
1
0
2
0
0
0
0
2
0
0
1
0
1
0
0
1
2
1
0
1
0
1
0
0
0
0
2
0
2
0
1
1
0
2
1
0
0
0
0
0
0
1
0
3
0
1
1
0
0
0
0
0
0
2
2
0
1
0
0
2
1
1
1
2
0
0
0
0
0
0
1
1
2
0
0
0
2
1
0
0
0
0
0
0
1
0
2
0
0
0
2
0
2
0
0
2
1
2
0
2
2
1
0
0
0
2
0
0
2
3
1
0
1
1
0
0
2
0
1
0
0
0
2
1
0
0
1
1
0
3
1
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
1
1
0
1
1
1
3
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
1
1
1
0
1
0
1
0
2
0
1
0
0
0
0
0
2
8
0
0
1
2
0
2
2
2
2
0
1
0
0
1
0
0
2
0
0
0
0
0
1
0
0
2
2
2
2
0
0
0
0
0
2
0
0
0
1
0
2
1
1
2
0
0
0
0
0
2
0
2
1
0
1
1
0
0
0
0
2
2
1
0
2
1
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
2
0
0
2
1
1
0
3
0
2
0
1
0
0
0
1
2
1
2
0
0
3
0
0
1
0
2
2
0
0
0
1
0
0
2
0
1
0
2
2
2
0
0
1
2
2
2
2
0
1
0
1
1
0
1
1
1
0
0
2
0
1
0
1
0
1
2
0
1
0
2
1
1
1
2
1
0
1
1
0
2
0
1
0
2
0
1
0
0
2
0
1
0
1
0
0
1
2
0
0
2
2
0
0
1
1
1
0
2
0
0
2
2
0
0
1
2
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
2
1
1
2
2
0
1
0
0
1
3
1
1
0
0
0
0
0
0
1
0
0
1
2
2
0
1
1
1
0
1
0
0
2
0
0
2
0
2
1
2
0
2
1
0
2
2
0
0
2
1
2
0
1
1
0
0
0
0
0
1
2
0
0
0
0
0
1
1
0
1
0
0
0
2
0
0
1
2
0
0
1
0
0
0
2
0
0
0
1
1
2
0
0
1
0
0
1
0
2
1
0
1
0
2
1
0
0
3
0
1
2
1
8
1
0
0
2
1
0
1
1
0
2
0
0
1
1
1
2
1
1
1
0
0
1
1
1
0
0
0
0
0
2
0
0
0
0
1
1
0
2
0
1
0
1
2
0
4
2
0
0
0
1
1
0
0
0
0
2
1
1
2
0
0
1
1
2
2
0
0
2
2
1
0
2
0
0
0
0
0
1
0
0
2
2
2
3
2
0
1
2
0
1
0
0
3
1
0
2
0
1
0
0
2
0
1
1
1
2
0
2
0
0
1
0
0
2
0
1
1
1
0
1
0
0
1
1
2
1
0
0
0
0
0
2
1
0
0
2
1
2
2
0
0
2
2
1
0
0
1
0
1
0
0
0
1
0
1
2
0
0
0
1
3
0
1
0
0
2
1
0
2
0
2
2
0
2
1
0
0
1
0
2
2
0
1
2
2
2
1
2
2
0
0
3
2
0
1
1
0
2
1
3
0
0
1
1
1
0
0
0
1
1
0
0
0
0
3
2
1
1
0
2
2
0
0
0
2
2
1
0
0
0
1
0
1
1
0
0
1
2
0
0
2
2
0
0
2
0
0
0
0
0
0
0
1
1
1
1
0
0
2
0
1
2
1
0
2
0
3
1
0
0
0
1
1
1
0
0
2
0
1
0
1
0
1
1
1
0
2
1
2
2
7
2
2
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
1
1
0
0
3
1
0
0
1
0
2
0
0
0
1
1
0
0
0
0
0
2
0
2
0
2
0
0
2
1
1
2
1
2
0
1
2
2
0
0
0
0
1
2
2
0
0
1
0
2
1
1
1
1
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
2
1
0
0
1
1
0
0
0
0
0
0
0
4
2
0
0
0
0
0
2
1
1
2
0
1
0
1
1
0
1
1
0
0
1
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
3
0
2
1
1
0
0
0
2
2
1
2
0
2
0
1
0
2
1
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
2
2
0
2
3
0
0
0
0
0
2
0
2
0
1
0
2
1
2
1
2
0
0
0
0
0
1
1
0
0
1
0
3
2
1
1
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
2
0
0
0
1
2
0
0
1
1
0
0
2
0
0
0
3
1
1
0
2
0
0
0
0
0
0
1
1
0
0
1
2
0
2
0
0
0
0
0
0
2
1
0
2
0
0
0
0
1
1
2
0
0
0
1
0
0
0
0
1
0
2
0
0
0
1
2
2
2
2
1
0
1
2
1
0
3
0
1
2
1
0
1
0
1
1
0
1
0
1
0
2
0
2
1
3
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
2
2
2
2
2
0
0
1
2
0
0
0
1
1
0
1
1
2
0
0
0
0
1
0
2
0
1
0
0
1
1
1
2
2
2
0
1
0
1
0
0
1
1
1
0
0
0
1
0
1
1
2
1
2
0
0
1
0
1
0
0
0
2
1
0
0
1
0
1
0
0
0
1
0
2
2
0
2
0
2
1
2
0
0
0
0
3
2
0
2
0
0
0
2
2
0
1
0
1
0
1
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
2
2
0
0
1
0
0
1
1
0
0
0
0
1
1
2
6
0
1
1
2
0
0
0
2
2
1
0
0
0
1
1
0
1
2
0
0
0
0
0
2
1
2
1
1
0
2
0
0
0
0
0
0
0
4
1
2
0
1
0
1
0
2
1
0
2
0
0
3
0
0
1
0
1
0
0
2
0
0
0
0
1
1
2
0
1
0
1
2
0
2
0
1
0
0
1
0
1
0
1
0
1
0
2
2
2
0
1
0
1
0
0
0
0
2
1
0
0
2
1
1
1
2
1
2
0
0
0
0
0
2
2
0
0
0
0
2
2
0
0
1
1
0
1
0
3
2
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
1
0
2
2
1
0
0
1
0
0
3
0
0
1
0
3
0
1
1
2
2
1
0
1
0
2
0
0
0
0
1
2
0
1
0
0
0
0
1
1
0
0
1
1
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
1
1
1
0
0
1
0
1
0
2
1
0
0
0
1
0
2
1
0
2
1
1
0
1
2
0
2
0
1
0
1
2
0
0
0
1
2
0
1
2
0
2
0
0
3
1
3
0
0
0
1
2
2
0
1
0
0
1
2
1
8
1
1
1
0
0
1
1
0
1
1
0
1
1
0
1
0
1
0
0
0
0
1
1
1
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
2
3
0
2
3
0
1
2
1
1
1
1
1
0
1
2
0
0
0
0
1
0
1
0
0
1
1
0
1
0
2
1
1
0
0
2
0
3
1
6
0
0
0
0
0
0
1
2
0
0
1
0
0
1
1
2
0
0
0
1
0
0
2
2
1
2
0
0
0
1
2
1
0
0
1
0
2
0
1
1
1
2
1
2
0
0
1
1
0
1
0
0
1
1
1
1
4
0
0
1
0
0
2
1
0
0
1
1
2
0
0
0
0
1
0
1
0
2
1
2
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
1
0
1
0
2
0
1
1
0
0
0
1
0
2
1
0
0
1
0
1
0
1
0
0
1
1
1
2
1
0
0
2
1
0
1
2
0
1
1
0
3
1
0
0
0
0
0
0
2
0
0
0
3
1
0
0
1
0
0
0
1
0
0
1
0
2
2
0
3
2
0
0
0
0
4
1
0
0
1
2
0
1
2
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
1
2
1
0
0
1
2
0
0
0
1
2
1
2
0
2
0
3
1
1
1
2
0
1
0
2
2
1
1
1
1
0
2
1
1
0
1
1
2
2
0
0
0
0
0
1
2
1
1
1
1
0
0
3
0
0
0
0
1
0
2
0
2
0
1
0
0
0
2
1
2
0
1
0
1
1
0
1
0
1
2
0
0
0
2
3
0
0
0
0
2
1
1
0
0
0
0
1
2
1
0
0
0
1
1
2
1
0
0
0
2
0
0
0
0
1
0
2
2
1
2
0
0
0
0
1
2
1
1
2
0
1
2
0
0
0
2
1
2
0
0
1
0
5
0
1
0
2
2
1
0
1
1
0
2
1
0
1
0
0
0
0
1
0
2
0
1
0
0
0
1
2
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
3
1
0
1
0
3
0
1
0
0
0
1
2
0
3
1
0
0
5
0
2
0
0
0
2
0
2
0
0
2
0
1
2
1
1
2
1
0
0
0
1
1
0
1
0
2
1
0
0
0
0
2
0
1
1
1
2
1
0
1
0
1
0
1
0
0
0
1
0
2
0
2
3
0
2
0
0
1
0
2
0
0
0
0
1
0
1
1
1
0
0
0
0
0
1
2
2
1
2
0
1
0
2
0
0
0
1
0
0
0
1
1
1
0
1
2
0
0
0
2
0
2
1
1
0
0
0
1
1
0
1
2
0
0
0
2
2
0
0
0
0
0
9
0
2
0
0
2
2
0
0
4
0
1
0
0
0
0
0
2
0
1
1
0
1
1
0
2
0
0
0
0
2
1
0
0
0
2
0
0
0
0
1
0
0
0
0
1
1
2
3
0
2
2
0
1
0
3
0
2
0
1
0
0
2
0
0
3
0
0
1
0
0
1
2
0
0
0
2
2
1
0
0
2
0
0
0
2
0
2
2
2
1
2
9
1
1
0
0
2
2
1
0
1
0
0
1
0
1
0
2
1
2
0
3
0
0
0
3
1
1
0
2
0
0
0
0
2
1
0
1
1
0
1
1
0
0
0
0
0
1
2
2
2
0
0
0
1
1
2
0
0
1
2
0
2
1
0
1
0
0
0
0
0
2
1
1
0
2
0
0
1
0
0
2
0
0
0
1
1
0
0
0
2
1
2
0
1
0
0
0
2
0
2
0
0
2
2
1
0
2
2
0
0
1
2
0
1
1
2
0
3
2
5
1
0
1
0
1
0
2
2
0
1
1
1
2
1
1
0
0
2
6
0
1
0
0
1
0
2
1
0
2
0
1
0
1
0
1
3
2
1
0
2
0
1
0
1
2
1
0
2
0
0
0
0
0
0
1
1
1
0
1
1
1
1
0
0
1
0
0
0
0
1
0
0
0
2
2
0
1
1
0
0
0
3
1
0
0
0
0
2
2
0
0
0
0
1
1
1
3
0
1
1
0
0
2
0
0
1
0
1
2
3
0
0
0
0
1
0
2
5
1
0
2
0
1
0
1
1
1
2
1
1
3
0
1
0
0
2
1
1
0
3
1
1
1
1
1
2
0
1
0
2
1
0
0
1
0
2
1
1
1
0
2
0
2
0
2
1
2
0
0
0
1
1
0
0
1
0
2
1
1
2
1
0
0
0
0
0
0
0
2
1
0
1
1
0
0
2
1
0
1
0
2
0
0
0
0
2
1
1
0
0
0
2
0
2
0
2
2
1
0
0
1
1
0
2
2
0
2
0
1
0
0
2
0
0
0
1
0
1
1
0
0
2
1
0
2
2
1
2
2
2
0
1
0
1
0
1
0
0
1
0
0
2
2
0
0
1
1
0
1
0
1
1
2
0
0
0
2
2
0
1
0
1
0
2
1
0
0
0
0
0
1
2
2
0
0
0
1
1
0
0
0
0
1
0
0
4
0
1
0
1
0
1
0
0
0
0
0
1
1
1
1
2
1
2
1
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
2
0
2
1
0
0
1
1
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
2
0
1
0
1
2
1
0
1
0
0
0
0
0
1
0
0
1
1
1
0
0
1
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
2
3
1
0
0
0
0
4
1
1
0
2
1
1
0
0
0
3
0
1
0
1
2
0
1
0
0
0
0
2
0
2
0
2
0
1
0
0
0
0
0
0
0
0
3
2
0
1
0
0
1
0
0
0
1
0
2
1
0
2
0
1
0
4
0
1
1
0
0
0
0
0
1
2
0
0
0
0
0
5
2
0
0
0
2
0
0
0
0
1
2
2
1
0
1
0
0
2
0
1
0
0
0
0
0
2
0
0
0
2
1
3
0
1
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
2
2
1
1
0
0
0
2
1
0
1
0
0
2
2
0
2
0
0
0
0
0
2
0
2
2
0
1
1
1
0
0
2
0
0
1
0
0
0
0
0
1
2
1
2
2
0
1
0
0
0
2
0
2
0
3
0
1
1
2
0
0
1
2
0
2
2
1
0
0
2
1
0
0
1
0
0
1
2
1
0
0
2
2
2
1
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
3
2
1
0
1
4
1
0
1
0
1
0
0
0
2
4
2
0
1
0
0
0
2
2
0
1
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
1
2
0
2
0
0
2
0
0
0
0
0
0
0
0
2
1
2
0
0
2
2
2
2
0
0
0
0
1
0
0
0
0
2
1
0
0
0
2
1
0
0
0
0
1
2
0
1
2
0
0
2
0
1
1
0
2
0
1
0
0
1
0
0
0
3
1
2
0
0
0
0
2
0
0
1
2
0
0
2
0
0
1
2
2
0
1
0
0
2
1
0
1
1
0
3
0
0
0
0
0
2
0
0
1
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
1
0
0
1
2
3
0
0
2
0
2
2
2
1
0
0
0
2
0
0
1
0
2
2
1
2
1
1
0
0
0
0
0
2
0
1
0
0
0
1
2
1
0
2
3
1
0
0
0
0
1
2
0
0
0
1
1
1
0
0
0
0
2
0
2
2
0
1
1
2
1
1
1
2
1
2
1
0
0
0
2
0
1
1
1
2
0
1
2
1
1
0
0
1
0
2
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
2
1
0
1
3
3
0
1
0
2
0
0
2
0
2
1
2
2
0
0
0
0
1
0
0
0
0
0
2
2
2
0
0
2
0
1
1
0
0
2
2
1
0
1
2
0
0
1
0
0
0
1
0
2
0
0
1
1
2
0
0
0
0
0
0
1
2
1
1
2
3
1
1
2
0
0
2
0
1
2
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
1
0
1
2
2
0
1
0
2
1
0
0
1
2
2
1
2
2
3
0
0
1
1
0
2
0
2
1
0
0
1
0
0
1
1
2
1
0
2
0
0
0
0
0
2
0
3
0
1
0
1
0
1
1
2
0
1
0
1
2
0
2
2
0
1
0
1
2
0
0
0
1
2
0
0
0
0
0
1
0
1
2
0
1
0
0
2
0
2
1
1
1
0
0
1
0
1
2
0
0
0
2
1
1
0
2
1
0
2
1
0
0
0
1
1
1
0
1
0
1
0
0
0
2
0
0
2
0
2
0
2
1
1
2
0
0
0
2
1
2
2
0
0
0
0
0
0
0
2
1
2
1
5
2
0
0
1
2
0
0
0
1
2
1
1
1
0
2
1
2
0
0
0
1
0
0
2
0
0
0
1
0
0
1
1
0
2
0
2
0
2
1
1
0
2
0
0
1
0
1
2
0
1
0
0
0
0
1
1
0
1
1
0
0
1
0
1
3
0
2
1
2
0
1
0
0
0
0
0
1
0
1
2
0
0
1
1
0
0
1
0
0
1
2
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
1
0
2
1
0
2
1
0
1
2
2
1
0
0
0
0
0
0
2
0
0
2
0
2
0
1
3
0
0
2
0
1
0
0
0
1
2
0
2
1
0
0
0
2
0
0
1
1
0
0
1
2
0
0
0
1
2
1
0
0
1
0
0
0
0
1
2
0
0
0
0
1
2
1
0
3
2
0
0
0
0
2
2
0
1
1
1
0
0
0
0
1
2
2
0
1
1
0
1
0
0
0
0
2
2
2
0
0
0
2
2
0
0
0
2
1
0
0
0
1
0
2
0
0
0
1
1
0
0
0
2
0
0
2
0
0
2
0
1
1
1
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
1
1
0
2
1
0
0
0
0
1
2
0
1
1
0
0
0
2
0
2
0
2
0
1
4
1
0
0
0
2
0
2
1
1
2
0
0
1
2
0
2
0
0
1
0
0
2
0
1
0
1
1
1
1
1
0
1
1
1
1
1
1
0
0
2
0
1
1
0
1
0
1
0
1
0
1
0
0
2
1
2
0
0
1
1
1
1
0
1
1
0
0
2
1
0
2
2
1
0
1
0
0
2
0
1
1
0
2
1
0
2
2
2
2
0
0
1
2
1
1
0
0
0
1
1
2
2
1
0
2
0
1
0
2
0
3
1
0
1
0
0
2
1
1
1
2
2
0
0
1
0
1
1
0
0
1
0
1
1
2
2
0
0
1
0
1
0
4
1
0
1
0
1
1
0
0
0
1
0
0
0
0
0
2
1
0
1
2
4
0
1
0
2
1
1
0
0
0
1
2
0
2
2
2
1
0
0
0
0
1
0
2
1
1
1
0
0
0
2
0
0
0
1
0
2
0
0
2
2
1
0
1
1
2
2
0
2
0
0
0
0
0
0
1
0
2
1
0
0
2
0
1
1
2
0
1
0
2
0
0
0
1
0
0
1
1
0
0
0
1
1
2
2
0
1
0
0
1
0
2
0
1
0
0
2
2
0
1
3
3
0
0
0
1
1
0
0
1
1
0
1
0
0
2
0
1
1
1
0
0
2
0
2
0
2
1
0
0
0
0
1
0
1
2
0
1
0
0
1
0
0
0
1
1
1
1
0
1
0
0
1
1
0
0
2
3
2
1
1
2
0
0
0
0
0
0
0
0
0
1
0
2
0
1
2
2
0
2
2
0
7
0
0
2
1
2
1
1
1
1
0
0
0
0
0
2
1
3
1
0
0
1
0
2
2
1
1
0
0
1
0
0
2
0
0
0
1
1
1
0
0
2
1
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
1
1
0
2
0
0
2
0
1
0
2
0
1
0
1
0
1
0
1
0
1
0
1
2
1
1
2
0
0
0
0
1
2
0
2
0
1
0
0
1
0
0
1
0
0
2
1
0
0
2
1
1
0
2
1
0
2
0
1
0
0
0
0
0
0
2
2
0
0
0
1
2
0
0
0
2
1
4
0
2
1
2
2
1
0
2
0
1
0
3
1
0
1
0
0
0
1
0
1
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
2
1
1
0
0
1
1
0
0
0
2
0
0
0
1
0
1
0
0
0
1
0
0
1
0
1
0
2
0
1
0
1
1
2
2
3
1
0
1
0
1
0
0
0
0
0
3
0
1
1
0
0
0
1
1
1
1
0
0
2
2
1
0
3
2
2
2
0
2
2
0
0
0
2
0
1
1
2
0
0
0
1
0
2
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
2
1
1
0
0
1
2
0
2
1
2
1
0
0
0
1
0
0
0
2
0
0
0
0
3
1
2
0
0
1
0
0
1
2
0
2
0
2
2
0
1
1
0
0
2
2
2
0
0
1
1
0
2
0
0
2
0
0
0
2
1
1
2
0
0
1
3
2
0
2
0
1
0
2
0
3
2
1
0
1
0
0
0
3
0
2
0
2
0
1
2
2
2
0
2
0
0
2
0
0
1
0
1
1
1
0
0
0
1
1
1
1
0
0
2
2
0
2
1
0
1
0
0
1
1
0
0
2
2
0
0
0
0
1
2
1
0
0
1
2
1
2
0
2
1
1
1
0
1
1
2
0
1
0
0
1
0
0
0
5
2
1
0
0
0
0
0
1
2
0
0
0
1
1
0
0
1
0
0
0
1
0
1
0
0
2
2
1
0
2
0
2
3
1
0
2
1
2
0
0
0
0
2
0
0
2
0
2
0
0
1
0
3
0
0
1
0
0
1
0
1
1
2
1
0
0
0
0
1
1
2
0
2
1
0
0
1
0
0
0
0
1
0
0
2
2
2
1
1
2
0
0
2
0
0
3
0
2
0
0
2
1
1
0
1
2
1
0
0
1
2
1
1
2
1
0
0
0
1
1
1
0
1
2
0
0
0
1
0
0
1
2
0
0
1
0
0
0
0
0
0
0
2
0
1
0
1
1
0
0
2
1
1
1
0
1
0
3
0
0
2
0
1
0
0
0
1
1
2
0
0
0
1
2
1
0
1
1
2
1
1
0
3
0
0
0
0
0
1
0
2
3
2
1
1
0
0
0
0
2
1
0
0
1
0
1
1
1
1
1
2
0
2
0
1
0
0
0
0
2
1
1
0
1
0
1
0
0
0
2
0
1
0
2
0
2
0
2
2
2
0
1
0
1
1
0
2
0
0
0
0
1
0
1
0
1
2
11
1
0
0
0
2
0
2
0
0
0
0
0
0
0
2
1
2
0
2
0
0
2
1
0
0
1
0
1
1
0
0
1
0
0
1
0
1
0
0
0
0
1
1
0
0
2
0
2
0
0
1
0
0
0
1
0
0
2
1
2
0
1
0
0
2
1
1
2
0
2
0
2
1
1
0
0
2
0
1
2
1
1
0
2
2
0
0
0
0
3
0
2
2
0
0
0
0
2
0
2
0
1
0
2
0
0
0
1
2
1
1
1
1
0
2
1
1
2
1
0
0
2
1
2
1
0
0
0
2
1
0
1
1
0
0
0
1
2
2
0
0
1
0
0
1
2
1
0
1
0
1
0
2
2
1
1
1
1
0
1
2
0
2
0
3
0
0
0
1
1
0
1
1
0
1
1
1
0
0
2
2
0
0
2
0
0
0
1
2
2
0
0
1
1
1
2
0
0
1
0
0
1
2
0
1
0
1
1
1
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
2
0
2
1
0
1
0
0
1
0
0
0
1
0
1
2
1
2
2
1
0
0
0
0
1
1
2
0
4
1
0
0
1
0
1
0
2
1
0
1
0
0
0
1
2
0
0
1
2
1
0
1
0
2
1
1
1
0
1
1
3
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
3
1
1
0
0
1
0
0
2
1
1
1
1
2
1
2
0
2
2
0
2
2
0
2
1
1
2
2
1
1
0
1
0
2
0
0
0
0
0
0
0
0
0
2
4
0
0
0
1
1
2
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
2
2
0
0
2
0
1
0
0
1
0
5
0
0
0
2
0
0
1
2
0
1
0
0
0
5
0
0
0
2
0
1
2
0
0
0
1
0
2
0
2
0
1
0
0
1
0
1
0
0
1
1
1
2
1
0
1
2
0
0
0
0
2
1
0
2
0
1
1
2
0
0
1
2
0
2
0
2
0
0
1
0
0
2
1
0
0
1
0
1
2
0
0
0
1
0
0
0
2
1
2
1
0
1
0
2
2
1
2
1
0
0
0
0
0
1
1
0
0
2
0
1
0
2
0
0
0
1
1
2
3
2
1
0
1
2
0
1
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
2
1
1
0
0
0
0
0
2
0
0
2
1
2
1
0
0
0
2
2
1
1
1
0
0
0
0
2
1
2
2
1
0
1
1
0
1
0
2
0
0
2
0
0
1
0
1
0
2
1
0
1
1
0
2
1
1
1
0
2
1
1
0
1
0
0
0
0
2
0
2
0
0
1
1
0
2
0
0
0
3
2
0
0
2
1
0
0
1
0
0
3
1
2
1
0
2
2
1
2
0
2
0
1
0
0
1
0
2
1
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
1
2
0
1
0
1
1
0
0
0
2
0
1
1
0
2
1
0
1
1
0
2
2
0
1
0
2
2
0
0
1
0
0
2
0
2
0
1
0
1
1
1
0
1
0
0
0
0
1
0
2
0
0
1
0
1
2
0
2
2
2
0
0
2
2
0
1
0
0
1
0
0
0
2
2
0
0
1
1
0
0
0
0
2
0
2
0
0
2
2
0
0
4
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
1
1
2
0
0
0
0
2
2
0
0
0
2
0
0
2
1
0
0
0
2
2
1
0
0
0
2
1
1
0
2
2
0
2
0
1
0
1
0
0
1
2
0
2
0
1
1
0
2
2
0
0
0
2
1
0
2
2
0
2
2
3
0
1
0
0
2
0
1
0
0
2
1
1
0
1
1
0
0
2
2
0
2
4
1
0
0
1
2
0
1
0
1
1
0
0
0
0
2
1
0
0
1
0
1
0
0
1
1
2
0
2
0
1
1
1
1
0
1
2
1
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
2
1
0
0
0
1
0
2
1
0
1
1
0
0
0
0
2
0
0
2
0
0
0
2
1
0
1
1
0
1
1
2
0
2
0
2
0
3
0
0
0
0
1
1
1
0
0
1
2
0
3
0
1
2
1
1
0
0
2
2
0
1
0
0
0
0
0
2
0
2
2
2
2
0
0
1
2
0
0
0
0
0
0
2
0
1
0
0
0
1
0
2
0
1
0
1
1
1
1
0
0
0
1
0
0
1
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
2
0
1
1
1
0
2
1
1
0
0
0
0
1
1
2
2
1
0
0
0
1
2
2
1
0
1
2
0
2
1
0
0
2
2
2
0
0
1
1
1
2
0
1
0
0
0
0
1
0
0
1
1
2
1
1
0
0
1
1
1
0
2
1
0
0
1
0
2
0
0
0
1
1
1
0
2
2
0
1
1
1
0
0
0
0
1
1
0
0
0
1
0
2
0
0
1
0
0
2
0
0
0
1
1
0
1
0
0
2
0
0
1
1
1
0
0
0
1
1
2
2
0
0
0
0
1
1
0
0
0
0
0
1
1
0
2
1
2
0
2
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
3
1
1
2
2
0
0
0
1
0
2
1
0
1
2
0
0
3
0
0
2
0
1
2
1
2
2
0
1
2
1
0
1
2
2
2
2
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
1
0
0
0
1
0
1
0
1
2
0
0
0
1
1
1
2
2
1
0
2
1
2
0
2
0
2
1
1
0
0
1
1
0
0
0
0
2
2
0
0
0
2
0
1
2
1
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
2
0
0
0
1
2
1
0
0
0
0
0
0
2
0
0
0
2
1
0
1
1
1
3
0
0
0
2
2
4
0
0
0
0
0
0
1
2
0
0
0
3
0
0
2
2
0
1
0
2
0
2
0
0
0
0
0
0
1
1
0
1
0
1
1
0
0
1
1
1
0
0
0
0
2
0
0
1
1
1
3
0
0
1
2
0
1
0
0
2
1
2
2
2
0
1
2
0
0
0
0
1
1
1
1
0
1
0
1
1
0
1
0
1
0
2
0
2
1
2
2
1
0
0
0
0
0
0
2
0
0
1
0
0
1
1
1
0
0
0
1
1
1
0
1
0
0
0
0
0
0
2
2
1
0
0
0
1
0
0
0
1
0
2
0
2
0
1
3
1
0
0
0
2
1
0
0
0
2
1
2
0
1
0
1
0
1
3
0
1
1
0
0
2
0
0
0
2
0
2
2
0
0
1
1
0
2
0
1
0
0
2
2
1
0
0
1
1
1
0
0
1
2
2
0
2
1
1
0
0
0
0
0
0
1
1
1
0
0
1
0
1
0
1
1
4
2
1
0
0
0
2
0
0
0
0
0
2
2
2
0
0
2
2
0
2
1
0
2
2
0
1
2
1
0
0
1
0
0
2
0
1
0
1
2
0
0
0
0
0
1
1
1
1
0
0
0
1
1
1
0
0
2
0
1
2
2
2
1
1
1
1
2
2
0
2
1
2
2
1
2
0
1
2
0
2
0
0
0
0
2
2
1
3
0
0
1
0
1
1
0
1
1
0
2
2
2
3
1
0
0
1
0
1
2
1
0
0
1
1
2
2
0
1
0
1
0
0
0
1
0
1
1
0
2
1
0
0
2
0
2
2
1
0
1
2
0
1
0
2
1
0
2
0
1
0
0
1
0
0
0
0
1
0
2
0
0
1
0
0
0
1
0
2
0
0
1
0
2
1
0
1
1
2
0
0
2
0
0
1
0
0
1
0
1
2
0
0
1
1
0
0
3
0
0
2
1
0
1
1
0
0
1
1
2
1
0
2
1
1
2
1
3
1
0
0
1
2
0
2
0
0
0
1
1
0
1
1
2
1
1
1
2
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
1
0
1
0
0
0
1
2
1
2
0
0
3
0
0
1
0
3
1
2
0
0
2
1
1
0
0
1
1
0
1
0
3
0
0
1
0
2
1
1
1
2
0
1
2
2
0
0
1
0
0
1
2
1
0
0
0
0
1
1
0
0
2
0
1
0
0
1
0
1
0
2
2
2
0
0
0
0
1
0
0
2
2
2
2
3
0
0
0
0
0
1
1
0
2
0
0
0
0
0
2
0
1
3
1
1
0
0
0
2
3
2
0
1
1
0
0
0
0
0
0
0
3
1
0
0
0
2
0
0
1
3
2
0
1
0
2
0
0
2
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
1
1
3
0
0
3
0
0
1
0
1
0
0
2
1
3
2
1
0
2
0
6
0
0
0
1
0
0
1
0
1
1
0
0
2
1
0
1
0
0
1
0
0
1
0
0
0
2
3
0
0
1
0
1
0
0
0
1
1
0
0
2
2
1
0
0
1
0
0
0
0
0
1
3
1
1
0
3
1
2
1
2
0
0
2
2
0
0
0
0
0
0
0
1
0
2
3
0
1
0
0
1
0
1
2
1
1
0
0
2
1
0
2
2
1
0
2
1
0
2
0
1
0
2
0
2
0
0
0
1
0
2
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
1
1
0
1
0
0
0
0
0
3
2
1
0
0
1
0
0
0
0
0
1
0
0
2
0
2
1
3
0
2
0
0
1
1
0
1
2
0
0
2
0
2
0
1
0
0
2
2
1
0
2
0
2
2
0
0
0
2
1
0
2
1
1
0
0
0
0
1
0
2
0
0
0
0
0
0
1
2
0
0
0
2
1
0
0
0
2
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
1
0
2
0
2
0
0
0
2
0
0
1
1
1
1
0
0
0
1
2
1
0
1
0
0
2
0
0
1
0
1
0
0
2
2
0
0
2
0
0
0
1
1
0
2
2
0
1
1
0
0
0
0
1
0
1
0
0
1
0
2
0
1
0
0
0
0
0
0
1
1
0
0
0
0
2
2
0
0
0
2
0
1
0
0
2
0
0
0
0
1
0
0
1
1
0
0
0
2
1
0
0
0
0
2
1
0
1
0
1
1
0
1
0
0
0
1
0
1
0
1
0
1
1
0
0
1
0
1
1
1
1
2
0
0
1
2
0
1
2
0
0
0
1
0
1
2
1
0
0
1
0
1
0
2
0
0
0
0
2
1
1
1
1
1
1
0
0
0
2
0
1
1
1
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
2
1
2
1
2
1
0
0
0
0
0
1
1
0
0
0
0
1
1
1
0
0
0
0
2
0
1
2
2
2
1
0
2
0
1
0
1
0
0
0
0
1
0
0
0
1
2
1
1
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
2
1
0
2
0
2
1
1
2
2
0
0
2
1
1
0
0
0
1
1
1
1
0
1
1
1
1
0
0
1
1
4
0
2
0
0
0
1
1
2
0
0
0
1
0
2
0
1
1
2
1
2
0
0
0
0
0
1
1
1
0
0
0
4
1
2
1
0
0
0
2
0
0
2
2
0
1
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
2
2
1
0
1
0
2
2
2
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
1
2
0
1
0
0
0
0
1
1
2
1
2
1
0
0
2
0
2
0
1
1
1
2
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
1
3
2
2
0
1
0
2
0
0
0
0
1
0
2
0
0
1
0
0
1
0
0
0
0
0
2
0
1
2
0
0
2
0
1
2
0
0
0
2
1
0
0
0
0
0
1
2
1
0
3
0
1
0
0
0
0
0
0
1
0
2
2
0
2
1
1
1
0
2
0
1
1
1
0
1
1
2
0
0
0
0
0
0
1
0
1
0
2
0
0
0
1
1
0
0
0
0
2
0
0
0
1
0
2
0
1
1
4
0
2
2
0
2
2
1
0
0
1
1
2
0
0
1
0
0
0
1
2
2
0
1
0
0
0
2
1
0
2
1
1
1
0
0
1
0
0
0
0
0
1
0
0
3
1
1
0
2
2
0
2
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
1
1
0
1
2
0
2
0
0
2
0
1
1
0
0
0
1
1
0
0
0
2
2
2
1
0
0
0
2
2
0
2
0
1
0
0
1
1
1
0
2
2
0
1
1
0
0
2
2
0
2
0
1
2
1
2
0
1
0
0
0
0
2
2
2
1
0
2
2
1
2
0
0
1
0
0
1
2
0
0
1
1
0
0
1
2
0
3
0
2
0
2
0
0
0
0
1
2
2
1
0
0
0
0
0
0
1
0
1
2
1
0
0
0
2
0
1
0
1
1
0
0
0
1
2
0
2
1
1
1
5
1
1
2
2
3
1
0
1
0
1
1
1
0
1
2
0
0
2
0
0
2
0
2
0
0
0
0
0
3
1
2
2
0
2
1
2
0
0
0
1
2
0
0
1
1
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
2
2
1
0
0
0
1
2
0
0
0
1
1
0
0
0
0
1
2
1
1
0
0
1
1
1
0
1
1
1
1
0
0
2
1
1
0
1
0
0
0
2
0
0
0
1
2
0
0
1
2
0
1
0
2
0
1
0
0
0
0
2
1
0
0
0
2
0
0
0
2
0
2
1
0
1
0
2
0
0
1
0
1
2
1
0
2
0
1
0
0
0
1
0
1
0
1
0
2
2
2
0
0
2
2
0
2
0
2
2
0
1
1
2
1
0
2
0
1
2
0
0
1
0
0
0
2
0
0
0
0
2
2
2
0
0
0
0
0
0
2
1
0
0
2
0
0
0
2
1
1
1
0
0
0
0
0
0
0
0
0
2
0
2
0
2
2
3
1
0
0
0
0
2
0
0
1
1
0
0
0
1
2
0
0
1
1
1
1
0
1
0
0
0
0
1
0
0
0
2
2
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
1
0
1
1
1
2
1
0
1
1
2
0
2
2
0
2
0
1
0
1
3
1
0
2
0
1
1
1
0
0
1
1
2
2
1
2
0
1
2
0
0
0
2
0
0
7
2
0
0
1
0
1
1
0
0
0
0
0
0
2
4
1
1
2
2
0
0
0
1
1
2
0
1
1
1
2
0
0
0
2
0
1
0
2
0
0
2
1
1
0
0
1
1
4
1
0
1
0
0
1
1
0
2
0
1
0
0
2
4
2
0
1
0
2
2
0
1
0
0
0
2
2
0
0
0
2
0
0
2
1
1
0
1
0
0
0
1
0
0
2
0
1
1
2
0
0
2
0
0
1
1
0
2
1
0
1
0
1
0
0
0
0
1
2
1
2
1
0
2
0
1
2
2
2
1
0
1
0
0
0
0
1
2
0
1
1
1
0
0
0
1
0
0
1
0
0
0
0
0
4
0
0
0
0
4
1
1
0
2
0
1
0
0
0
1
2
2
0
0
1
1
0
0
0
0
2
1
0
2
1
0
0
0
0
1
0
1
0
2
0
1
4
0
2
2
0
3
0
0
0
0
2
1
0
0
0
0
2
0
2
0
0
0
3
0
0
1
0
2
1
0
2
1
1
0
1
0
2
0
0
1
0
2
1
0
0
0
0
1
1
2
0
1
1
5
1
0
1
2
0
1
0
2
2
5
1
2
0
1
0
0
0
2
0
1
0
0
1
1
0
0
0
2
1
0
1
6
1
2
0
2
0
0
3
0
0
3
0
0
0
2
1
1
0
0
0
0
1
1
1
0
1
2
1
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
1
2
0
1
0
0
2
0
3
0
1
1
2
0
0
2
0
2
0
0
1
1
2
1
0
1
0
3
0
2
2
0
1
0
2
0
0
1
1
1
1
0
0
1
0
2
1
0
0
0
1
1
0
2
0
0
0
0
0
2
0
0
0
0
0
2
1
1
0
0
0
2
0
4
1
1
1
1
1
1
0
0
0
2
1
0
0
1
0
0
0
0
0
0
2
2
0
3
0
1
1
1
1
0
0
2
0
1
1
1
0
2
1
1
0
2
8
1
1
2
0
0
0
2
0
0
0
1
0
0
0
4
0
0
2
1
0
2
0
2
0
1
1
1
0
0
0
0
0
0
1
1
1
1
1
0
1
0
1
2
1
0
0
0
1
5
1
2
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
2
1
1
0
2
1
0
1
3
2
1
2
1
0
0
0
1
6
0
0
0
0
2
2
0
0
1
0
2
0
2
0
0
0
0
0
2
1
0
1
0
0
0
2
1
0
0
1
2
3
1
1
0
0
0
1
2
1
0
0
1
0
2
0
2
0
0
0
0
1
0
1
1
2
0
0
0
0
1
0
0
1
0
1
2
0
0
1
0
0
0
2
1
2
0
3
1
0
0
1
0
3
0
1
0
1
0
0
0
2
2
2
1
0
0
1
1
2
1
1
0
0
0
1
2
2
1
0
0
2
4
4
1
1
1
0
1
1
1
0
1
0
0
0
0
2
0
0
0
0
2
2
0
1
1
1
2
2
0
0
2
0
1
0
0
0
0
0
0
1
7
2
1
2
2
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
2
0
1
1
0
0
1
0
0
1
2
0
1
1
1
2
2
0
0
0
0
0
2
2
0
0
0
0
0
2
0
2
1
0
0
0
0
0
1
1
2
0
1
0
0
2
1
0
0
0
2
0
1
0
2
0
0
0
2
2
0
0
0
1
0
0
1
1
0
0
2
1
0
0
2
1
2
3
1
0
0
0
4
0
0
1
1
1
1
1
0
1
1
1
1
1
0
0
1
2
0
2
0
1
0
0
0
0
1
1
0
1
0
0
0
2
0
0
1
0
1
0
0
0
1
0
1
0
0
2
0
1
1
0
0
1
0
0
1
0
2
1
1
2
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
2
0
1
0
2
1
0
0
0
0
1
2
0
1
0
2
0
2
1
1
1
1
2
1
0
1
0
0
0
2
0
2
1
1
1
0
0
1
2
1
1
2
0
1
0
1
2
2
0
0
0
0
0
2
0
0
2
2
0
2
0
0
2
0
0
1
0
1
0
0
0
2
0
0
0
1
1
1
0
0
1
0
1
1
0
0
0
1
2
2
1
1
1
2
1
0
1
0
1
0
1
0
0
2
0
1
2
1
1
1
1
1
1
2
0
0
0
2
0
1
0
1
1
0
0
0
1
3
0
2
2
0
3
2
1
1
0
1
0
0
0
1
0
0
0
0
1
2
0
2
0
0
1
0
1
0
0
0
0
2
0
2
0
1
2
0
0
0
0
0
2
0
2
1
2
0
1
0
0
2
0
2
1
1
1
1
2
0
1
1
2
1
2
0
0
1
0
0
2
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
13
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
1
1
1
0
1
0
0
1
0
0
0
1
2
2
2
2
0
1
0
0
1
0
0
1
0
0
2
0
1
2
0
0
1
0
2
2
0
2
0
2
2
1
0
0
4
1
0
0
1
0
1
1
0
0
0
1
2
1
0
0
2
1
0
0
1
0
0
2
0
0
0
0
2
1
2
1
0
0
0
2
0
1
0
1
2
2
0
0
2
1
0
0
0
1
2
0
0
0
0
0
0
1
1
1
1
0
1
0
1
0
0
0
1
0
0
0
1
0
1
1
2
0
0
0
0
2
0
1
2
0
2
1
0
0
2
2
2
6
0
2
1
1
0
0
0
2
0
2
1
3
0
1
0
0
2
0
2
1
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
1
2
1
0
1
2
0
1
2
0
1
0
0
0
0
0
1
0
0
2
1
0
1
0
1
0
0
1
0
0
0
0
2
0
1
1
2
0
0
1
0
1
0
2
2
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
2
2
0
0
0
0
2
0
1
0
2
0
0
0
2
2
1
0
0
1
1
1
1
0
0
0
2
0
1
1
1
0
0
1
2
2
0
0
0
2
0
0
2
0
1
0
2
3
0
0
0
1
2
1
0
2
2
0
1
0
1
0
0
0
1
1
0
1
0
2
2
0
1
0
1
2
0
1
0
2
0
0
0
0
2
0
0
2
0
1
2
0
2
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
1
0
0
2
2
0
2
2
0
0
0
0
0
1
1
1
2
2
1
0
0
0
1
0
1
0
2
1
0
0
0
2
2
0
2
1
1
1
1
3
2
1
0
1
1
0
0
0
0
0
0
0
0
0
1
1
2
0
1
0
0
1
2
0
2
2
0
0
1
0
1
1
2
1
0
0
2
0
1
3
1
0
1
1
2
1
0
1
1
1
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
1
0
0
1
0
0
2
1
0
3
0
0
0
0
0
0
1
1
0
0
2
1
0
0
1
2
2
2
1
0
1
0
2
1
0
2
0
2
2
0
1
0
0
1
1
1
1
0
2
2
1
2
0
1
2
0
0
0
0
1
3
0
0
2
0
1
2
1
1
1
0
2
1
0
1
1
0
0
1
1
2
0
2
0
0
1
1
0
1
2
0
0
2
0
1
0
0
0
0
0
1
1
0
0
1
0
1
0
1
1
0
0
0
0
0
2
2
1
1
2
2
1
0
2
2
0
4
1
0
0
0
2
2
1
0
1
0
1
0
1
2
1
1
0
1
2
0
3
2
0
0
0
0
0
0
1
2
2
2
0
1
0
2
0
1
2
0
0
2
1
0
2
3
0
0
0
0
0
1
2
0
0
1
0
3
0
0
0
0
0
0
0
0
0
2
2
2
3
1
1
0
0
2
2
0
0
0
0
2
0
0
1
2
2
2
2
2
1
0
1
0
0
0
0
1
0
2
0
0
0
4
0
0
0
0
0
2
0
0
1
1
0
1
0
0
2
1
0
0
0
0
0
1
0
2
2
1
0
1
2
2
0
2
0
2
0
3
1
0
0
3
1
0
1
1
0
4
1
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
1
0
2
0
0
0
1
0
1
1
0
0
0
2
0
1
0
2
0
1
0
0
0
2
1
1
1
0
0
2
2
1
1
2
0
1
0
4
1
0
3
2
2
1
0
1
1
2
1
1
0
1
2
1
0
1
0
0
0
0
2
0
1
0
1
1
2
0
2
0
0
0
1
0
2
0
3
0
2
2
1
0
2
0
1
0
0
0
2
1
2
2
1
1
0
2
1
0
1
2
2
0
1
2
1
1
1
0
2
1
1
1
0
2
1
0
0
1
0
1
0
8
0
1
0
0
2
0
0
1
2
0
1
3
1
1
0
0
1
0
0
0
0
0
0
2
1
0
1
0
0
0
1
0
2
0
1
1
1
0
0
0
1
3
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
1
0
1
0
2
0
2
0
0
1
0
0
0
0
0
1
0
1
1
0
1
0
0
1
1
0
2
1
0
1
1
1
1
1
1
0
2
0
1
0
0
1
0
0
0
0
0
1
2
2
2
0
0
1
0
0
0
0
1
0
2
1
3
0
0
1
0
2
0
0
0
0
1
0
1
1
0
2
0
1
1
0
0
0
1
2
0
0
0
2
0
1
2
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
2
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
2
1
1
2
1
2
0
1
0
0
1
2
0
0
2
2
2
0
1
0
2
1
2
0
1
2
0
0
0
0
1
2
0
0
0
2
1
0
0
0
0
1
2
0
2
1
0
0
0
1
0
2
1
0
0
2
3
1
0
0
1
0
0
2
4
0
2
1
2
0
0
2
0
0
1
1
1
0
0
0
1
0
2
2
0
1
0
0
2
0
1
1
0
0
2
1
1
1
0
2
1
1
0
0
0
1
2
2
2
2
1
1
0
0
0
0
0
0
0
2
1
0
1
0
0
3
0
0
2
1
0
0
2
1
1
0
1
1
0
1
0
1
2
0
0
1
0
0
1
1
0
0
0
2
0
2
2
0
0
0
1
1
2
0
0
0
0
2
1
2
0
1
2
1
2
1
0
1
0
0
1
1
2
0
1
0
2
1
1
2
0
3
0
0
1
0
2
0
1
2
1
0
1
1
2
1
2
0
2
0
0
0
1
0
1
0
1
2
1
0
2
2
0
1
0
0
0
0
0
0
0
0
2
1
1
2
0
2
1
2
0
0
0
0
1
2
0
0
0
0
1
2
0
0
1
0
0
2
0
1
0
0
0
2
0
0
0
0
2
0
2
2
0
0
2
0
2
0
0
1
1
0
2
2
1
0
0
2
0
0
1
2
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
3
0
0
2
2
2
2
0
1
4
0
2
0
0
2
2
0
5
1
2
2
0
0
0
0
0
2
0
2
2
0
2
0
0
0
2
2
2
0
1
2
0
1
0
2
2
1
2
0
0
0
1
1
0
2
0
0
0
0
0
0
2
0
0
2
1
0
2
1
0
2
0
2
0
1
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
1
0
2
1
1
0
0
0
0
0
1
0
2
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
2
0
0
1
2
0
2
0
1
1
1
1
2
2
2
0
1
0
2
2
0
0
1
1
3
1
0
0
1
0
1
0
2
1
0
0
2
0
0
0
0
1
0
0
1
1
0
0
0
1
1
2
0
0
2
0
2
1
2
0
0
0
1
2
1
0
1
0
2
1
0
0
0
2
0
0
0
1
1
1
1
0
0
0
2
1
0
2
0
0
1
2
2
0
1
0
2
1
0
0
0
0
1
1
2
0
0
0
0
1
0
0
3
0
0
1
0
1
1
1
0
1
0
0
0
2
0
0
1
0
1
1
0
1
0
0
1
0
0
2
1
0
0
0
0
2
0
0
0
1
1
1
1
0
0
1
1
0
2
1
0
1
2
1
0
1
1
0
1
0
0
1
0
1
1
0
0
0
0
0
3
1
0
0
0
1
1
1
0
0
0
1
0
0
0
1
3
1
1
1
0
0
0
0
2
0
1
0
0
1
0
1
0
2
1
2
0
0
1
1
1
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
2
1
2
1
2
1
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
1
2
2
0
1
0
1
0
0
0
2
0
0
0
0
0
2
1
0
2
1
0
0
1
0
1
1
1
0
1
2
1
1
0
2
3
2
2
0
1
0
1
2
5
2
0
0
1
0
1
1
2
1
1
0
0
1
1
1
0
1
0
0
0
2
3
1
2
2
1
0
0
2
1
2
1
2
2
0
1
1
0
0
1
0
2
0
0
0
2
1
0
0
1
0
2
1
3
0
1
0
0
1
0
1
1
1
0
1
2
0
1
1
2
2
1
1
2
0
1
1
0
0
0
2
2
2
3
1
0
3
1
1
0
0
0
1
0
0
1
0
0
0
1
2
2
2
0
2
1
0
2
0
0
0
0
1
1
2
0
0
0
0
1
2
1
1
0
2
2
0
2
0
0
1
0
0
1
0
1
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
2
0
0
0
0
2
0
2
1
0
1
0
2
0
0
0
1
0
2
0
3
1
0
2
0
0
0
0
0
2
1
2
1
2
0
2
1
0
1
1
0
0
0
0
1
1
2
1
2
0
1
0
1
2
1
2
0
2
3
1
2
2
0
1
2
0
1
1
1
0
0
0
1
0
0
2
1
0
0
2
2
0
0
2
1
1
2
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
2
0
2
0
2
0
0
0
0
2
0
2
1
2
1
0
0
0
2
0
0
1
0
2
0
0
1
0
0
2
1
0
0
0
0
0
0
1
0
0
0
2
1
1
0
0
2
1
1
2
2
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
1
1
3
0
1
1
2
1
0
0
0
1
0
2
0
2
0
2
0
0
1
2
0
2
1
0
0
1
1
0
1
1
0
1
1
0
0
1
0
0
2
0
0
1
1
1
1
2
1
1
1
1
2
0
0
1
0
1
0
0
0
1
0
0
0
0
2
2
0
0
0
1
1
1
2
0
0
0
0
0
0
2
1
1
1
0
1
0
0
0
1
2
0
0
0
1
1
0
0
0
0
0
0
2
0
1
3
2
0
1
1
0
2
0
0
1
0
1
0
0
1
1
0
0
1
1
0
0
1
0
1
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
2
2
0
1
0
1
2
2
2
0
0
1
0
1
0
1
0
0
0
0
2
0
1
0
2
1
0
0
0
2
2
1
1
0
1
1
1
0
2
2
2
0
2
1
1
1
2
0
0
1
0
0
1
2
0
1
2
0
2
1
0
1
0
1
0
1
0
2
0
0
0
1
1
0
3
1
0
0
2
1
0
1
0
2
0
1
0
1
0
1
0
1
0
0
1
1
0
1
0
3
1
0
0
1
0
0
2
2
1
1
0
1
0
0
0
4
2
1
1
0
0
0
2
2
0
2
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
2
0
0
0
1
2
1
0
0
1
1
0
1
0
0
0
1
0
0
0
0
1
1
0
1
0
2
0
1
1
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
2
2
0
0
2
1
0
0
0
0
2
1
0
0
0
2
1
2
0
2
2
0
1
1
1
0
1
1
1
0
0
2
1
2
1
0
1
0
2
0
1
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
1
2
0
2
0
1
0
1
0
0
1
1
1
0
0
0
2
2
1
0
1
0
2
0
0
0
0
0
0
0
0
1
1
0
2
1
0
0
0
0
0
2
2
1
1
0
0
1
2
1
2
1
0
3
1
0
0
0
3
2
0
1
0
0
1
0
1
0
0
2
0
1
1
0
0
1
0
1
0
0
1
1
1
0
5
1
1
1
1
6
0
2
3
2
0
1
2
0
0
0
1
0
0
0
2
1
0
1
0
1
2
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
1
2
1
0
1
2
0
0
1
1
2
0
1
0
1
1
0
2
0
1
0
2
0
0
0
0
0
0
0
1
0
1
0
1
1
2
2
1
0
2
1
0
1
0
1
1
0
0
1
1
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
1
0
2
2
2
0
0
1
0
0
0
1
1
2
0
0
0
2
1
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
2
0
0
2
2
2
0
0
0
1
1
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
1
1
1
1
1
2
2
0
1
0
1
0
1
0
0
1
2
1
1
2
1
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
2
0
1
3
1
0
2
0
1
0
0
0
1
1
2
2
0
0
1
1
0
0
1
1
0
0
0
0
0
2
0
0
2
0
3
0
0
1
1
0
0
1
0
0
0
1
2
0
0
0
0
0
1
0
1
0
1
1
0
0
1
2
0
0
1
0
1
0
0
0
0
2
1
0
2
2
0
0
0
0
2
0
1
1
0
0
0
2
0
0
1
0
0
4
0
0
0
1
0
1
1
0
1
2
3
2
1
0
0
0
2
0
2
0
0
1
0
0
2
0
0
0
0
0
1
1
0
0
0
1
1
0
2
1
0
0
0
1
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
2
0
1
2
0
0
2
0
1
2
1
0
1
0
0
0
0
2
0
3
0
0
2
0
0
1
2
2
0
0
1
2
0
2
2
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
2
1
2
2
0
1
0
1
0
1
0
2
2
0
1
0
0
2
0
0
0
0
2
2
2
0
0
1
2
1
1
0
0
2
0
0
0
3
0
0
1
0
1
0
1
2
0
0
0
1
0
2
2
2
0
0
0
1
0
1
1
1
1
2
0
0
1
6
2
0
0
0
0
0
1
1
1
3
1
2
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
2
1
1
0
0
1
0
0
1
0
0
1
0
2
2
2
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
1
0
3
2
0
1
0
0
0
0
1
1
0
2
1
1
2
0
1
0
1
2
0
1
0
0
1
0
1
1
0
0
2
0
0
0
0
0
0
0
2
2
0
1
0
1
0
2
3
1
0
0
0
0
0
0
0
1
0
0
1
2
1
0
2
2
0
0
1
0
1
0
0
0
1
0
2
1
0
0
0
2
1
2
0
0
1
1
1
0
1
0
0
2
0
0
2
0
2
0
0
0
1
1
1
0
1
1
2
2
2
1
0
3
1
0
0
1
0
0
2
2
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
1
0
2
0
2
0
1
0
1
1
0
2
1
2
0
0
1
0
1
2
2
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
2
1
2
0
1
0
0
1
1
1
0
0
0
0
0
1
0
1
1
2
0
0
2
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
1
1
0
1
0
1
2
5
0
0
2
0
0
1
0
0
0
0
1
0
1
0
0
2
0
1
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
2
0
1
1
2
0
1
2
0
1
0
0
0
0
2
0
1
1
0
0
1
0
1
1
2
0
0
0
1
2
1
1
0
0
1
2
0
0
1
0
1
0
2
0
0
0
0
1
0
2
0
2
0
1
0
1
1
0
0
1
0
1
1
0
0
1
0
0
2
1
0
2
0
1
2
1
1
1
1
0
1
0
0
2
0
2
2
2
3
2
0
2
1
0
0
2
0
0
2
0
0
3
2
2
2
0
0
0
1
0
0
2
0
0
2
1
0
2
0
2
0
1
1
1
0
0
1
0
1
2
0
0
0
2
1
2
2
0
0
1
3
1
1
0
0
2
0
2
1
1
2
0
0
0
0
0
2
2
2
0
1
1
0
0
0
0
1
0
1
1
2
0
0
4
0
0
1
2
0
0
2
0
0
2
1
1
2
0
2
0
0
2
1
1
1
1
0
2
0
1
0
1
0
1
0
0
0
2
1
2
0
2
0
0
2
1
0
0
1
0
0
1
1
1
2
0
0
2
0
0
5
0
0
0
0
1
0
3
3
2
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
2
0
2
0
0
2
1
0
0
0
0
0
5
2
0
1
0
0
2
0
1
1
0
0
1
0
1
1
1
0
0
1
2
0
1
0
0
2
0
1
2
0
1
0
0
3
0
2
0
2
2
0
0
1
0
2
0
1
1
1
2
0
2
2
0
0
0
0
0
0
1
3
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
1
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
2
1
0
2
0
0
0
0
0
0
1
2
0
1
0
3
0
0
0
2
1
1
0
1
2
1
1
0
0
0
0
0
1
0
1
2
2
0
0
1
1
0
0
1
0
0
2
1
0
1
0
0
0
0
1
0
2
2
0
2
1
0
2
0
0
0
0
0
2
2
0
2
0
2
2
0
0
0
0
1
2
0
0
0
0
1
0
0
0
2
0
0
1
2
2
0
0
2
0
2
0
2
0
1
2
1
0
2
2
0
1
0
0
1
2
0
2
0
1
0
2
0
0
2
1
0
0
0
2
2
1
1
1
0
2
2
0
0
0
0
0
1
0
2
0
1
2
0
0
1
2
0
0
0
0
0
1
2
2
2
2
2
3
0
1
0
2
2
0
0
2
0
0
1
1
0
0
1
1
0
2
1
0
0
0
0
2
2
2
0
0
0
1
0
0
0
0
0
0
0
1
2
0
2
0
1
2
0
2
0
1
0
1
0
1
0
0
1
0
0
0
1
0
1
2
2
1
1
2
0
0
0
1
1
1
0
0
2
1
1
0
0
0
1
0
0
1
0
0
0
1
0
2
0
1
0
2
5
2
0
0
0
0
1
1
2
0
1
1
1
2
2
1
2
0
0
0
0
0
0
0
0
0
15
0
1
0
2
2
1
1
0
2
1
0
2
2
1
0
2
0
0
2
2
1
0
0
0
1
0
1
0
0
2
0
0
0
1
0
1
2
2
0
2
0
0
2
1
0
0
0
1
0
0
2
0
1
2
2
1
1
0
0
1
0
1
1
1
0
1
0
0
0
0
0
2
0
2
1
1
1
0
0
1
0
0
0
1
2
1
1
1
0
1
0
2
2
0
1
1
1
0
0
0
0
0
2
0
2
0
0
1
2
0
0
0
2
0
0
2
0
1
0
1
2
1
0
1
0
0
2
0
1
2
2
1
2
0
2
3
2
0
2
0
2
0
1
0
0
0
0
0
0
2
0
2
1
0
2
0
1
3
0
0
1
0
0
1
0
1
1
0
0
0
2
1
0
0
0
0
0
1
0
2
0
0
2
2
0
2
2
0
1
0
0
0
2
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
1
0
0
1
3
0
2
0
2
1
1
0
2
0
0
0
0
0
0
0
0
2
2
0
1
1
2
0
3
0
0
2
1
0
1
2
0
1
0
1
0
2
1
0
0
0
2
1
0
1
1
1
1
2
0
0
0
0
0
1
2
0
0
0
2
0
0
1
0
0
0
2
1
1
0
0
0
2
0
1
2
1
1
2
3
0
0
0
1
0
0
0
2
1
2
2
2
0
0
2
1
1
0
3
0
0
0
1
2
0
0
2
0
0
0
1
3
0
2
0
0
2
2
0
1
0
0
0
1
0
0
0
1
0
2
1
1
0
2
0
1
0
0
2
0
1
2
1
0
0
2
1
0
2
0
0
1
0
0
2
1
1
1
0
1
0
2
0
1
1
0
2
1
2
0
2
1
0
2
1
0
3
0
0
1
1
2
0
0
0
0
0
0
1
2
1
0
0
0
0
1
2
0
0
1
2
1
2
0
1
1
2
1
1
4
8
0
1
0
2
2
0
1
0
0
0
4
2
2
0
0
2
0
4
1
0
4
0
1
1
2
0
0
3
1
0
1
1
0
0
2
1
0
0
1
2
0
0
1
1
1
1
0
0
2
0
0
1
3
1
2
0
1
0
1
1
2
0
0
0
1
1
0
0
0
1
0
1
0
2
0
2
1
1
2
0
1
1
1
2
0
2
0
0
0
2
1
1
0
1
0
1
1
0
2
1
0
2
0
1
1
1
1
2
2
1
1
0
0
1
0
1
0
2
0
1
1
1
0
1
0
1
1
0
0
2
2
1
0
1
1
2
0
1
0
2
0
1
0
2
1
0
0
2
0
1
0
0
3
2
0
2
1
0
2
1
0
1
0
0
2
1
0
1
2
7
2
1
2
0
2
2
1
0
2
0
0
2
0
2
3
2
0
0
0
0
2
2
1
0
1
0
1
2
1
3
0
1
0
2
0
2
2
2
0
0
0
0
0
0
1
0
0
2
0
1
0
0
1
0
2
0
3
0
0
0
0
1
2
2
1
0
0
2
1
2
1
2
1
0
0
0
0
1
1
0
0
0
1
1
0
0
0
1
2
0
2
2
0
2
1
0
1
1
0
0
0
0
1
0
1
0
0
0
1
0
0
2
0
0
0
0
1
0
0
1
0
1
1
1
0
1
1
0
0
0
0
0
1
2
2
0
2
2
0
0
1
2
0
1
1
0
2
1
0
2
1
0
1
1
2
0
0
1
2
0
0
1
0
2
0
1
0
0
0
0
0
1
0
1
0
2
0
1
0
1
1
0
0
0
1
2
2
1
0
2
1
0
2
0
1
0
2
1
0
4
1
0
0
0
1
1
1
2
2
0
1
1
1
1
0
2
0
2
0
2
0
2
0
2
0
0
0
0
0
1
1
0
3
0
2
0
2
1
2
1
1
1
3
2
0
4
0
1
2
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
2
2
2
0
0
2
0
1
1
0
2
0
0
0
0
1
1
1
0
1
0
0
0
2
2
0
0
2
0
0
0
2
1
0
0
1
0
1
0
0
1
0
1
0
0
1
1
0
2
0
2
0
1
1
0
2
0
0
2
0
0
0
0
0
0
1
0
0
2
1
0
1
1
0
0
0
0
0
3
0
1
2
1
0
0
0
0
0
2
2
1
1
0
1
0
0
1
0
2
2
0
0
2
0
0
2
0
1
0
2
1
1
3
0
2
1
0
0
0
2
0
0
0
0
0
0
0
1
1
1
1
0
0
0
2
0
1
0
2
2
2
0
0
2
0
0
0
3
1
1
0
0
1
1
0
0
2
2
1
1
0
0
2
0
0
2
0
1
0
1
0
0
0
0
0
1
0
0
0
1
1
2
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
2
0
2
0
0
0
1
1
1
0
1
0
2
0
0
1
0
0
3
1
2
0
2
2
0
0
1
0
1
0
0
0
1
2
1
2
0
1
0
1
0
0
0
0
1
0
1
1
2
1
0
1
1
1
0
0
0
1
0
2
1
0
0
0
0
1
1
2
0
0
2
0
3
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
2
0
1
1
0
0
1
0
0
1
0
1
1
1
0
2
1
0
2
0
2
1
0
2
2
0
0
0
1
0
3
1
1
1
1
0
0
0
2
2
0
1
0
2
0
0
1
2
1
0
2
1
0
1
2
0
1
1
0
2
2
1
0
0
0
0
2
1
2
0
0
0
2
0
2
2
0
0
0
1
0
1
0
1
1
1
0
0
0
1
0
0
1
1
0
1
2
2
0
1
1
2
0
1
2
1
1
1
0
0
0
1
0
0
0
1
3
0
2
2
1
0
0
2
1
1
0
0
1
1
3
0
0
1
0
1
0
2
0
0
1
0
0
0
1
0
1
0
0
1
0
0
2
2
1
1
0
0
1
0
0
0
1
2
0
1
0
0
1
1
2
0
1
2
2
1
0
1
2
1
1
1
1
1
0
1
0
0
2
0
0
1
1
2
0
2
0
0
2
1
1
0
0
0
0
2
0
2
1
1
0
0
0
1
0
0
0
0
1
1
2
1
0
0
2
0
0
0
0
0
1
0
0
0
1
0
2
2
0
0
1
2
0
1
2
1
1
0
0
3
2
1
0
1
1
0
0
0
2
1
2
1
0
0
1
0
2
0
0
0
0
0
0
1
2
0
3
1
1
0
1
2
0
2
0
0
1
0
0
0
1
2
0
2
0
2
1
2
0
0
1
0
2
0
2
0
0
0
0
3
1
0
0
2
0
2
2
0
1
0
0
2
2
0
0
1
0
0
0
0
0
1
0
2
0
3
0
1
2
0
0
1
0
0
2
0
3
0
0
0
0
1
0
1
0
1
2
2
1
1
0
0
2
2
0
2
1
0
2
2
1
2
1
0
0
1
0
0
0
6
0
0
0
0
0
0
2
1
0
0
1
2
1
2
2
1
0
0
0
0
1
0
0
0
1
1
0
1
2
1
2
0
1
2
0
1
0
5
0
2
1
0
0
2
0
0
0
0
0
0
0
1
0
1
1
0
0
3
2
0
0
2
1
0
3
0
0
1
0
0
1
2
1
1
1
1
0
1
0
0
1
0
1
0
1
0
2
3
0
4
2
1
1
0
1
2
2
0
0
1
2
0
1
1
1
0
0
0
0
1
0
0
1
0
2
0
1
2
0
0
0
0
0
1
1
0
0
1
2
0
0
1
0
0
0
0
1
0
0
2
0
0
2
1
2
0
0
0
1
2
1
0
0
2
2
0
0
2
0
1
0
1
0
0
2
1
1
0
0
3
0
2
0
1
0
0
0
0
0
0
2
3
2
0
1
2
1
0
0
0
0
0
1
2
0
2
2
0
0
1
0
2
0
0
2
0
1
3
0
0
0
2
1
1
0
0
4
0
0
0
0
0
0
0
0
0
0
4
2
1
1
1
1
1
1
0
1
0
1
0
0
2
0
1
0
1
0
0
1
2
1
0
0
0
0
2
1
1
0
0
1
1
0
0
0
0
0
0
1
0
0
2
1
2
0
2
0
2
2
0
2
2
2
2
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
1
0
1
0
0
0
2
0
1
0
1
0
0
1
0
0
1
0
1
0
0
0
2
0
0
1
2
0
0
0
0
1
2
2
2
0
2
0
0
1
0
1
2
0
0
0
0
1
0
1
0
1
0
0
3
0
0
2
2
0
0
0
2
1
1
0
1
0
3
0
1
0
1
2
0
0
1
0
0
1
1
1
0
0
0
1
0
0
0
0
0
2
1
0
0
2
1
1
0
1
0
3
2
0
0
0
0
0
1
2
0
0
0
0
2
0
0
2
0
1
1
2
2
0
1
2
0
0
0
2
1
0
0
0
2
0
2
0
1
0
0
0
0
1
1
1
0
2
1
1
2
0
0
0
4
0
2
2
1
0
0
2
2
1
0
0
1
0
2
0
0
1
0
0
2
0
1
2
0
1
1
0
1
1
2
0
2
1
1
0
2
3
1
1
0
1
0
0
2
2
0
0
0
0
0
0
0
0
1
2
4
2
2
1
0
2
0
2
2
1
0
0
1
1
2
0
0
2
1
0
2
0
1
0
3
0
0
0
0
2
1
1
2
2
0
1
2
0
0
2
1
2
2
0
0
0
2
1
1
2
1
0
2
1
0
2
2
0
2
0
0
0
0
2
1
0
0
0
1
0
3
2
0
2
0
1
1
0
0
2
2
0
1
2
0
0
1
0
0
0
0
1
2
0
1
1
0
2
0
0
2
0
1
1
1
0
1
2
1
0
2
2
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
2
0
1
1
0
0
0
0
1
0
0
1
2
2
0
0
0
0
4
0
0
0
1
1
2
0
1
0
0
1
0
2
1
1
0
0
2
1
0
0
0
0
3
1
0
1
0
1
0
1
0
0
0
0
1
0
1
3
1
1
1
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
3
0
2
3
1
0
1
0
2
0
2
0
0
0
1
2
2
0
0
0
0
0
1
0
0
2
1
0
2
1
0
0
0
0
2
1
1
0
1
0
0
0
1
1
0
0
0
1
0
0
2
0
0
0
3
0
1
1
0
0
2
0
0
0
1
0
1
1
1
2
3
0
0
0
1
0
0
1
2
0
0
0
0
0
0
2
0
3
0
1
0
0
2
0
2
1
0
1
0
0
1
0
1
0
2
0
2
1
2
1
2
1
0
1
0
0
0
0
2
0
1
2
0
0
0
0
0
0
1
0
1
0
2
0
3
1
1
1
1
2
0
1
0
0
0
0
2
1
0
2
2
0
1
0
0
2
1
2
1
1
1
2
0
0
1
0
0
1
1
0
0
0
1
1
1
1
2
0
0
0
1
2
0
0
0
1
1
2
0
0
0
0
1
2
0
2
2
0
1
0
0
0
0
0
2
0
0
1
1
0
2
0
0
0
0
0
2
0
0
2
0
0
0
2
1
0
0
2
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
2
0
3
0
1
0
0
0
2
1
0
0
1
0
0
1
0
1
0
2
2
1
1
1
1
3
1
0
1
0
0
0
2
0
0
2
0
0
3
1
0
0
0
1
2
2
0
0
1
2
0
0
2
0
2
1
2
0
0
1
1
0
2
0
0
0
1
3
2
0
1
0
0
0
0
2
2
0
2
0
1
0
2
0
0
2
0
0
2
1
1
0
1
2
0
2
1
1
2
0
0
0
0
1
0
0
2
1
0
0
0
1
0
1
2
0
0
0
1
1
2
2
0
1
1
0
0
2
1
1
0
1
2
1
2
2
2
1
0
0
0
1
2
0
2
0
0
2
0
0
2
1
0
2
0
1
0
0
1
1
0
1
0
2
0
1
0
2
2
0
2
1
0
2
2
0
2
2
0
0
1
0
1
0
1
0
0
2
0
0
1
2
2
0
1
0
1
1
0
0
0
2
0
0
4
0
0
0
1
0
0
0
0
0
0
3
0
2
1
0
0
0
0
0
1
2
0
0
1
1
0
0
0
0
0
2
0
0
1
1
0
1
1
1
0
2
0
1
1
1
0
0
0
0
1
0
0
0
2
0
0
1
2
2
2
0
0
2
2
0
1
0
1
1
0
0
0
1
0
2
0
0
0
0
1
0
0
1
1
0
0
1
0
0
1
1
1
2
2
0
2
0
0
3
2
1
1
0
1
1
0
1
2
0
0
0
2
0
1
0
2
0
2
1
0
0
0
1
2
1
2
1
2
0
0
0
0
1
0
2
0
0
0
0
3
0
0
2
2
1
0
0
2
2
0
0
1
0
0
0
0
1
0
0
1
0
1
2
0
1
1
0
0
1
0
1
0
0
0
1
2
1
0
0
0
2
0
0
0
0
0
0
1
0
1
0
2
2
8
0
1
0
4
0
3
2
0
0
0
0
2
1
1
1
1
0
0
2
0
0
1
0
1
0
2
0
0
0
0
1
0
2
0
0
0
2
1
1
0
0
0
0
0
0
0
1
0
2
1
1
2
2
0
2
0
0
3
1
0
0
0
0
1
2
1
2
0
0
3
0
2
0
0
0
2
0
2
1
0
1
1
0
0
1
0
2
0
0
0
0
0
2
0
0
0
1
0
2
2
0
0
0
0
0
0
2
0
1
2
0
2
0
0
2
0
0
1
1
2
0
1
0
2
2
2
0
0
0
0
0
1
0
0
0
2
0
1
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
1
1
0
0
0
2
1
1
0
1
1
3
3
0
0
1
0
0
0
2
1
0
0
0
0
2
0
2
1
1
0
0
1
1
2
0
0
0
1
0
0
0
1
0
1
0
1
2
2
0
1
1
2
1
0
0
3
0
1
0
0
2
1
2
0
2
1
0
0
1
0
0
2
0
0
0
2
2
0
0
2
2
0
2
0
1
0
1
0
0
0
0
0
1
0
1
1
2
0
1
1
0
4
1
0
0
2
2
0
0
0
1
0
1
0
2
0
2
0
1
0
2
1
0
0
0
0
1
0
0
0
2
1
1
2
1
2
1
2
1
1
0
1
2
0
0
1
0
1
2
0
0
1
2
1
1
7
0
1
1
2
0
1
1
0
1
0
2
0
0
1
1
1
2
0
0
0
0
2
0
0
1
0
0
1
0
0
1
3
1
0
0
2
0
1
0
0
0
0
3
0
1
3
0
0
0
1
1
0
2
0
0
0
2
2
2
0
1
0
0
1
0
0
1
0
0
1
1
2
0
0
1
0
0
0
1
0
0
1
0
0
2
1
1
1
2
1
0
0
0
0
0
2
0
2
0
0
0
0
1
1
1
0
0
2
2
1
0
0
1
1
0
1
0
0
0
2
0
1
0
1
1
0
0
0
0
2
3
1
0
1
0
2
1
0
1
1
2
0
1
1
2
0
2
0
1
1
1
1
2
1
2
3
1
0
1
0
2
1
0
1
2
0
0
1
1
1
2
0
1
1
0
1
1
1
1
0
2
1
0
0
0
0
0
2
0
0
0
1
0
2
1
1
1
2
0
0
0
2
0
1
0
0
0
0
1
1
0
2
0
1
1
2
0
0
1
0
0
2
2
1
1
1
0
1
1
1
0
0
0
0
0
1
0
1
2
1
4
2
0
0
1
0
0
2
0
1
0
1
2
1
1
2
2
0
1
1
0
1
0
0
0
1
0
0
1
1
2
0
2
1
2
1
0
0
0
0
2
0
1
0
0
2
0
0
1
0
0
2
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
2
2
0
0
2
0
3
1
3
2
0
2
2
0
0
1
0
0
1
0
1
3
3
0
0
0
0
2
1
1
0
0
0
0
1
0
2
2
0
1
1
1
0
0
1
0
1
2
2
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
2
1
2
0
0
1
2
1
0
0
1
2
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
2
2
0
0
0
0
0
1
0
2
0
2
0
0
2
1
2
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
3
5
0
0
1
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
3
0
1
0
2
1
0
0
1
0
1
0
1
2
1
0
0
0
1
1
0
0
2
2
1
0
1
2
1
2
2
0
1
0
0
0
1
2
1
0
2
0
0
5
1
1
0
0
0
1
0
2
0
2
0
0
2
1
1
3
2
0
1
1
1
2
0
0
0
0
0
0
1
2
2
2
0
0
1
0
2
0
0
0
0
1
2
1
0
1
0
0
0
0
2
0
1
1
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
3
0
0
2
0
0
0
0
0
2
1
1
0
1
1
2
0
2
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
2
1
2
1
0
0
0
3
0
0
0
1
0
0
2
3
1
0
2
0
1
2
0
0
0
0
0
1
0
1
0
0
0
1
0
2
0
0
0
2
2
0
0
1
1
0
2
0
0
2
1
0
0
0
1
0
0
0
0
1
1
2
0
1
0
0
2
2
0
0
0
2
2
0
0
0
2
1
0
2
0
0
0
1
0
0
0
1
2
2
0
1
0
2
5
0
0
1
0
1
1
0
0
0
0
0
0
0
0
2
2
2
2
0
2
2
1
2
1
0
0
1
2
0
1
1
0
1
3
1
0
2
1
2
0
0
1
0
1
1
2
0
2
0
1
2
0
0
1
0
1
0
0
1
0
0
0
0
0
2
2
1
2
0
2
0
0
1
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
2
2
0
0
2
0
2
1
2
0
0
1
1
0
0
0
1
1
0
1
1
1
1
0
1
0
0
2
0
0
0
1
0
1
0
0
0
0
1
0
0
1
2
3
0
0
0
1
0
1
0
1
3
1
3
1
3
1
0
0
2
0
0
1
0
1
0
0
0
1
0
2
0
1
0
1
0
0
1
0
0
2
0
1
0
1
0
0
2
0
1
0
1
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
1
1
1
0
0
1
0
2
1
5
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
1
1
2
1
2
2
2
0
1
0
1
1
0
0
2
0
0
1
0
0
0
0
0
0
0
2
1
2
0
0
0
0
1
1
0
2
0
1
2
2
1
2
0
2
2
0
1
1
1
0
0
0
0
2
0
0
1
0
2
2
0
2
0
0
3
2
0
0
0
0
1
1
3
2
0
0
1
0
0
0
2
2
0
1
1
1
0
0
0
0
0
0
0
0
0
2
1
2
0
1
0
1
1
1
1
0
2
2
1
0
0
0
1
2
2
0
1
1
2
2
0
2
0
1
0
0
1
2
0
1
1
1
0
2
0
0
2
2
1
2
2
1
0
0
0
0
4
2
2
0
0
0
1
0
0
0
1
1
1
0
0
0
1
2
0
1
0
0
2
0
0
2
0
0
1
0
0
1
1
2
0
1
0
2
2
0
1
0
0
1
1
1
3
0
1
0
1
0
2
1
2
2
0
0
1
1
2
2
2
1
0
0
2
2
0
0
0
1
0
1
1
2
1
1
0
0
0
0
2
2
1
0
0
1
1
0
0
1
2
1
0
2
0
2
0
2
0
0
2
1
1
1
5
0
0
0
1
1
0
1
0
1
0
1
2
0
1
0
2
0
0
1
0
1
0
0
0
2
0
0
0
0
1
0
1
0
2
0
0
0
1
0
1
0
0
1
1
0
1
1
1
1
0
0
1
0
0
1
0
1
1
1
1
0
1
1
3
0
1
0
1
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
1
1
0
2
1
0
2
1
1
0
1
0
3
0
0
0
1
0
1
0
2
2
1
2
1
0
1
0
0
0
0
1
0
1
1
2
0
1
0
0
2
0
0
2
0
0
0
0
2
2
0
0
2
0
2
0
0
0
0
1
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
2
0
2
1
2
0
3
0
0
1
2
0
0
3
0
0
1
0
2
2
0
1
0
1
0
0
0
2
2
1
1
0
1
0
0
0
0
2
4
0
0
0
1
0
1
2
1
0
0
0
0
0
0
2
1
0
0
2
2
0
0
1
0
0
2
0
1
0
2
0
0
2
1
1
2
0
0
0
2
1
2
1
1
0
2
1
1
1
1
1
0
0
0
1
0
0
0
0
0
1
2
1
0
0
0
0
1
0
0
2
1
0
1
0
0
2
2
0
2
3
1
0
0
1
1
2
0
2
1
0
0
2
0
1
0
0
1
2
1
0
0
2
0
0
0
1
2
1
0
0
0
1
2
0
1
2
2
1
0
0
1
1
1
2
0
0
1
0
0
0
2
0
1
1
1
1
0
1
0
0
1
0
0
2
0
1
0
3
3
1
0
0
2
0
1
0
2
0
0
0
1
0
1
1
0
0
0
0
1
2
0
1
0
0
0
0
2
0
1
0
0
0
0
2
1
0
3
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
1
2
0
1
2
2
0
2
0
1
1
2
0
1
0
1
0
0
0
0
2
2
0
2
1
1
2
4
1
0
2
2
0
0
0
0
0
2
1
0
1
0
1
0
1
0
2
0
1
2
0
0
1
0
2
0
0
1
1
0
0
1
0
0
0
2
0
0
1
1
2
0
1
1
0
0
0
0
1
0
0
2
1
0
1
2
0
1
0
1
2
0
2
0
2
0
0
1
0
1
0
0
0
1
0
1
3
4
1
0
0
0
0
1
2
0
2
2
0
0
0
0
0
2
1
2
0
0
0
0
1
2
0
1
2
0
0
0
0
2
2
0
0
2
1
2
2
0
0
0
0
0
1
0
0
1
1
0
0
2
0
1
0
0
0
0
0
1
2
0
0
2
0
0
0
0
2
2
1
1
0
1
1
0
0
1
1
0
1
1
0
0
1
2
0
0
2
2
2
1
0
1
0
1
0
2
2
1
0
2
2
0
1
1
0
1
0
0
0
0
1
0
2
1
0
0
2
0
0
1
0
0
0
1
0
3
0
1
0
0
0
1
0
2
1
1
0
0
0
1
2
2
2
0
0
1
0
0
0
2
1
0
0
0
1
0
0
2
0
1
1
0
3
0
2
0
2
1
0
2
0
1
1
0
1
1
0
0
0
1
0
1
0
1
1
2
0
2
1
0
1
2
1
0
1
1
1
1
0
2
0
0
0
0
1
0
0
0
0
0
1
1
0
2
0
3
3
0
1
0
0
0
0
2
2
1
0
0
3
0
0
0
0
1
2
0
1
1
1
0
0
0
0
0
2
0
2
2
1
1
1
1
4
0
0
1
0
2
1
1
1
0
3
2
2
0
0
1
2
2
0
1
0
0
0
0
0
1
2
1
1
1
0
0
2
0
1
1
0
2
1
1
1
2
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
1
1
2
1
2
0
1
0
1
2
0
1
2
0
2
0
0
0
1
2
0
0
0
1
0
1
2
1
0
0
0
0
2
1
1
2
0
0
1
0
0
0
2
0
0
0
2
0
1
2
2
0
0
1
0
1
1
3
0
1
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
2
1
0
0
0
0
0
1
2
0
1
0
0
0
1
0
0
1
0
1
0
0
1
2
1
0
1
1
1
0
0
0
2
1
0
0
0
1
1
1
0
2
1
1
0
1
0
0
1
0
1
1
0
0
1
0
0
0
1
0
0
0
0
2
1
0
2
2
1
2
1
0
1
0
0
0
1
1
1
0
2
1
0
2
0
0
0
0
2
1
0
0
2
2
0
0
2
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
1
2
0
0
0
1
0
0
2
1
2
0
0
2
1
1
0
0
1
4
0
0
0
0
0
0
0
2
1
1
2
2
0
1
1
0
0
0
0
2
0
2
0
0
1
0
1
0
1
2
0
0
0
1
2
1
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
1
0
1
1
1
0
0
1
0
0
0
0
1
0
0
2
2
0
1
1
0
0
2
0
0
2
0
2
0
1
0
2
0
0
1
1
0
2
2
0
1
0
0
0
1
1
2
0
2
0
2
0
0
2
0
0
1
1
1
1
1
1
1
0
0
0
0
2
0
2
0
0
1
0
2
0
0
2
1
0
0
0
0
2
0
0
0
1
0
1
1
3
0
1
0
0
2
0
1
1
1
2
0
2
1
0
0
0
0
0
0
0
1
0
1
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
1
0
3
0
1
0
1
0
1
1
1
0
1
2
0
0
0
0
2
0
2
0
0
0
0
2
1
2
0
0
1
0
1
0
0
0
0
1
0
0
1
1
1
2
1
1
0
2
1
0
0
1
2
0
3
1
0
0
2
0
2
1
1
2
1
1
0
0
2
2
0
0
0
0
0
1
2
0
0
0
0
1
0
1
0
1
0
1
0
1
0
1
1
0
2
0
1
2
2
2
2
0
0
1
2
0
2
2
1
2
0
0
1
2
0
0
0
2
0
2
2
0
2
1
1
0
0
0
1
1
0
3
1
0
2
1
0
1
0
2
0
0
2
1
2
0
5
0
1
0
0
2
1
2
0
0
0
0
1
0
0
1
1
0
2
0
0
1
0
1
1
0
0
1
0
5
1
0
0
0
1
0
0
0
0
0
2
1
0
0
2
2
0
1
1
0
1
0
1
0
0
0
2
0
0
0
0
1
0
2
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
2
2
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
1
0
2
0
1
0
0
1
1
0
0
4
0
2
2
0
0
1
0
0
0
1
1
0
0
0
2
0
3
2
0
2
0
1
2
0
1
0
3
0
1
1
4
1
0
1
2
1
0
2
0
2
1
2
0
0
0
2
0
0
2
1
0
2
0
1
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
1
0
1
1
2
2
1
1
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
2
0
1
0
1
0
1
1
0
1
3
1
0
0
1
1
0
4
0
0
2
0
1
2
0
0
2
1
0
2
0
2
1
0
1
0
0
2
2
0
0
1
1
1
0
0
0
1
0
1
0
2
1
1
0
2
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
4
0
0
1
0
0
2
1
0
0
0
2
0
0
3
0
1
0
1
1
1
2
1
0
0
1
0
0
1
1
2
0
1
1
0
0
0
2
0
0
1
4
0
0
1
2
0
0
0
1
0
0
2
2
2
0
0
0
2
0
1
1
0
0
0
0
1
2
1
2
2
0
0
0
0
0
0
0
0
0
1
0
3
2
0
0
0
1
2
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
1
2
2
1
1
0
2
0
0
0
1
0
2
0
2
2
1
1
0
0
0
2
2
0
0
1
1
0
1
2
1
0
0
0
2
0
1
2
2
1
2
0
1
1
1
0
0
1
1
0
1
0
0
0
0
0
2
2
2
0
1
0
0
2
0
0
0
1
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
2
2
0
0
0
0
0
0
1
1
1
0
0
1
1
0
1
0
2
0
2
0
0
1
0
1
1
0
1
0
0
0
0
1
1
2
0
0
0
2
0
0
2
1
0
2
0
0
3
2
2
0
2
2
1
2
2
0
0
0
0
1
0
1
2
0
2
1
0
0
0
1
0
4
0
0
0
1
2
2
0
0
0
2
1
1
1
1
2
0
0
2
1
1
0
0
0
1
2
1
1
0
1
0
1
1
1
0
0
2
0
1
0
0
2
0
0
1
0
1
0
2
0
0
2
0
0
0
2
0
2
1
0
0
1
0
0
1
0
0
1
1
1
2
1
0
1
0
1
2
1
1
2
0
1
0
4
0
0
0
0
2
1
0
1
1
0
0
0
0
1
3
0
1
0
0
0
3
0
0
1
0
1
0
2
1
1
0
0
2
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
1
1
0
2
1
0
0
1
1
1
1
1
0
1
1
0
1
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
3
1
1
2
1
1
1
2
0
3
1
0
1
1
2
2
0
0
0
1
2
0
0
1
2
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
1
2
0
2
0
0
2
1
0
0
1
0
1
1
0
2
0
0
3
0
0
0
1
0
1
1
0
0
0
1
2
1
0
0
0
1
1
2
2
0
2
0
0
0
0
0
1
2
2
0
0
0
1
0
2
1
0
0
0
0
2
2
2
0
2
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
2
1
0
2
0
2
0
0
0
4
0
2
2
1
0
2
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
3
0
0
0
2
1
0
0
0
2
2
1
1
0
0
0
0
0
0
2
2
0
1
0
1
4
0
1
2
1
2
1
1
1
0
1
0
1
0
0
1
0
0
0
1
1
0
1
2
0
0
0
0
0
0
2
0
2
0
1
1
1
0
0
0
0
2
2
0
1
0
1
0
1
2
0
0
0
2
2
2
1
2
0
1
1
2
0
3
6
0
3
0
2
1
0
1
0
2
0
2
1
2
0
2
0
2
0
0
0
0
3
1
2
1
1
1
2
0
2
2
0
6
0
1
1
0
0
0
0
0
0
2
2
0
2
3
0
0
0
0
1
0
0
0
2
0
0
7
1
2
0
0
0
0
0
2
0
1
0
0
0
0
1
1
0
0
2
2
0
0
0
1
0
2
1
1
0
1
0
2
2
0
2
0
0
1
0
0
3
0
1
0
1
0
2
2
1
1
1
0
2
0
2
0
1
0
0
1
1
0
0
1
0
0
2
1
0
2
1
0
1
1
0
0
0
0
0
1
3
0
2
0
1
2
0
2
1
0
1
0
0
0
3
0
0
0
2
0
1
0
1
1
0
0
1
0
1
1
1
0
2
0
0
0
8
0
1
0
0
0
0
1
1
1
0
0
1
0
1
1
2
0
0
0
1
2
1
0
1
1
0
2
1
4
2
0
2
0
1
0
0
0
0
1
0
0
0
0
2
0
2
0
1
1
0
0
1
0
1
0
2
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
2
0
0
1
0
2
0
0
0
2
0
1
0
0
1
0
0
2
0
5
0
0
1
1
2
2
1
0
2
1
0
0
0
0
2
1
0
0
0
0
0
1
2
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
1
5
0
2
0
0
0
0
2
0
1
3
0
1
1
2
0
1
0
0
2
0
2
2
0
0
0
2
0
1
1
1
0
0
0
2
1
0
1
2
0
0
0
1
2
3
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
2
2
1
2
1
0
2
0
1
2
0
2
0
2
0
1
1
0
0
0
1
1
0
0
1
0
0
1
1
0
2
2
2
1
2
0
1
1
1
0
1
2
1
0
0
0
0
1
2
0
3
1
1
2
2
0
1
0
1
2
0
1
0
0
0
2
1
2
2
1
0
2
0
0
2
2
2
0
1
0
2
0
0
1
0
2
0
2
1
2
0
1
2
0
0
0
0
1
0
1
1
0
1
0
0
1
0
0
0
0
2
1
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
1
2
0
2
1
0
0
1
0
2
0
2
1
1
0
0
1
1
0
2
0
0
0
1
0
3
1
1
0
0
0
0
0
1
0
0
0
4
0
2
0
3
1
2
1
0
0
1
0
3
0
0
3
1
0
1
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
2
1
0
0
2
0
1
1
0
0
0
0
2
2
1
0
1
1
2
2
1
2
2
1
1
0
0
2
3
2
1
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
2
1
2
1
0
1
2
1
0
0
0
0
2
1
0
0
1
0
0
1
2
0
0
3
0
1
0
1
1
0
0
1
0
1
1
0
1
0
2
0
1
0
1
1
0
0
0
1
1
1
0
1
0
2
0
2
0
0
2
0
1
0
2
1
0
0
0
2
0
1
2
1
2
0
1
1
1
0
2
0
3
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
1
2
2
2
1
0
0
1
0
2
1
1
0
0
2
1
2
0
1
2
1
0
2
1
2
1
0
0
0
0
3
0
0
0
0
2
1
1
1
0
2
2
0
1
2
2
1
0
2
0
2
0
0
0
2
1
0
2
2
0
0
0
0
3
0
2
0
1
2
0
1
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
1
1
0
0
0
0
2
0
0
1
2
0
2
0
0
0
2
0
0
0
0
1
0
0
0
2
2
0
2
0
2
2
0
0
0
2
0
0
2
2
1
1
0
1
0
1
2
1
0
1
2
0
0
2
0
2
0
0
0
1
0
0
2
0
0
0
0
2
0
1
1
1
0
0
1
2
0
1
1
0
0
0
0
0
0
0
7
1
0
1
2
0
0
1
0
1
1
2
1
1
0
0
1
0
2
0
0
0
0
0
0
2
1
0
2
2
1
0
0
1
1
1
1
1
0
1
2
0
1
1
1
0
0
1
0
0
1
0
1
2
0
0
0
2
0
0
2
0
1
0
2
1
0
0
2
0
2
0
1
1
1
1
2
0
1
0
0
2
1
2
2
0
2
1
0
0
0
0
0
0
1
0
0
2
1
0
1
0
0
0
0
0
1
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
1
0
0
6
1
0
1
0
2
1
0
1
0
1
1
0
0
1
1
0
1
0
1
0
0
0
2
0
1
2
0
1
1
1
0
0
1
0
1
1
1
0
2
0
0
0
0
2
0
1
1
1
0
1
1
0
0
0
0
0
0
0
0
4
0
1
0
0
1
0
1
1
1
0
0
0
0
1
0
1
0
1
1
2
1
1
2
2
0
1
1
0
1
2
1
0
2
0
0
1
1
2
0
1
1
2
0
5
0
0
2
1
1
0
2
0
2
0
0
0
1
0
0
1
1
1
1
1
0
1
0
0
1
2
2
0
0
0
1
0
0
2
1
1
1
0
0
0
0
0
0
0
1
0
1
2
1
0
1
0
0
0
0
2
1
0
6
1
0
2
2
0
1
1
1
2
0
2
0
1
0
1
1
0
1
0
0
1
1
1
2
1
2
2
1
2
1
0
0
1
4
1
2
0
0
2
2
0
2
0
1
0
0
0
0
1
1
0
0
2
1
1
0
2
0
1
0
1
1
0
3
0
0
3
1
0
0
2
1
2
0
0
1
2
1
3
0
0
1
0
3
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
1
0
1
1
0
0
1
0
2
1
1
0
0
1
0
0
0
0
0
1
1
0
0
1
2
0
1
0
1
1
2
0
0
2
0
0
0
0
1
0
0
2
0
2
0
1
2
2
1
2
0
3
2
2
1
1
1
1
0
0
1
0
2
2
0
0
0
1
1
1
0
1
0
3
0
0
2
0
0
0
0
0
1
1
1
2
1
0
2
0
0
0
0
0
1
1
0
2
0
3
0
0
0
1
0
1
2
2
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
1
0
1
0
1
2
1
2
2
0
1
0
1
0
3
0
0
0
1
0
0
0
1
0
0
2
1
0
0
0
0
0
0
1
0
1
0
0
4
2
1
0
0
0
0
2
1
0
1
0
1
1
0
1
0
1
2
1
0
1
0
0
0
0
3
2
1
1
0
2
0
0
2
2
1
0
0
2
1
1
0
2
0
1
2
0
0
0
0
0
3
0
2
1
0
2
1
0
0
1
0
0
0
2
0
2
1
2
0
2
1
0
1
1
0
1
0
0
2
2
0
0
0
0
0
1
1
0
2
0
0
0
4
0
1
0
1
0
0
1
0
0
0
3
2
0
1
0
2
1
2
2
0
2
1
0
0
0
0
0
0
1
2
2
2
2
0
0
2
1
0
0
0
0
0
1
1
1
0
0
0
1
0
0
1
1
0
0
2
0
2
0
1
0
2
0
1
2
1
2
0
2
0
2
1
1
0
0
1
0
1
2
1
0
0
0
1
0
1
0
1
0
1
2
1
0
0
0
0
0
0
0
0
2
0
4
1
0
0
0
2
2
0
0
1
0
1
1
1
1
1
2
1
0
1
2
1
0
0
1
0
0
2
1
0
2
0
2
0
3
0
2
0
0
1
1
0
2
2
2
0
0
0
1
0
0
0
1
0
0
0
0
0
2
1
2
1
2
0
1
2
0
1
0
2
2
0
1
1
1
0
1
0
1
0
0
1
1
1
0
0
1
0
0
2
1
0
0
0
0
0
1
2
0
0
0
1
1
0
0
1
1
2
0
0
0
0
0
0
1
1
1
1
2
0
0
0
0
0
1
0
0
0
0
1
1
1
0
1
1
2
2
0
0
0
0
2
1
0
0
1
1
0
1
0
0
1
2
2
0
1
2
0
0
0
1
1
0
2
0
0
1
1
0
1
1
2
1
2
0
0
1
0
0
0
0
0
0
1
2
2
0
0
0
0
2
0
0
3
1
0
1
0
1
0
0
1
1
0
2
0
0
1
0
1
1
1
0
1
0
1
2
0
0
0
1
0
2
1
0
1
2
0
0
0
0
1
0
0
0
1
0
0
0
0
1
2
1
0
0
0
0
1
0
0
0
0
10
0
2
1
2
0
0
1
0
2
2
0
0
5
0
0
2
2
0
1
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
2
1
0
0
0
0
2
1
1
0
2
0
2
0
3
1
2
2
0
2
0
1
2
0
0
0
1
0
2
1
0
6
2
1
0
1
0
2
2
1
0
1
0
1
2
0
2
0
1
2
2
2
0
0
0
1
0
2
2
0
3
2
0
2
0
1
0
1
0
2
1
1
0
0
0
1
0
0
0
1
0
1
0
0
1
0
1
1
1
1
0
0
0
0
2
1
0
6
1
0
0
0
0
1
0
3
0
1
0
2
0
1
0
0
0
0
0
0
2
0
2
1
2
1
1
0
0
0
1
0
1
0
1
0
1
0
0
1
0
1
0
1
0
0
2
0
2
1
0
0
1
1
0
0
2
1
0
0
1
0
0
0
0
1
0
0
2
0
2
1
1
0
0
2
2
1
0
0
0
0
2
3
0
1
2
1
0
0
1
1
0
1
1
2
2
0
1
2
2
0
0
0
0
0
2
2
1
0
1
1
0
0
1
0
2
2
0
2
0
0
0
2
1
0
1
0
0
1
0
0
2
1
0
0
2
0
1
2
0
0
0
0
0
0
2
2
0
1
2
1
0
0
1
1
0
0
1
0
2
1
1
2
1
0
2
0
0
2
0
0
0
0
1
1
0
0
0
1
0
2
0
1
0
1
0
0
2
0
0
0
2
2
0
1
0
0
1
0
1
0
4
0
0
1
2
0
3
0
2
0
0
1
0
2
1
3
3
1
0
1
2
1
0
0
0
0
0
1
1
0
2
1
2
0
1
1
0
2
0
1
0
0
3
0
2
0
2
2
0
0
0
1
1
0
0
0
0
0
1
2
0
0
0
1
2
0
2
0
0
0
0
1
0
0
2
1
2
1
0
0
0
1
0
0
1
1
0
0
0
1
1
0
0
2
0
0
2
2
0
0
1
0
0
0
0
0
0
0
4
2
0
0
2
1
0
0
0
10
0
2
2
2
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
2
2
2
0
1
0
0
0
3
1
0
2
1
0
2
0
0
2
0
0
1
0
0
2
1
0
2
0
2
1
2
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
2
1
1
0
5
0
1
0
0
0
2
0
0
2
2
2
1
0
2
0
0
0
0
0
1
1
1
0
2
0
2
0
0
2
0
1
0
0
0
1
1
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
1
2
1
2
2
0
0
0
2
2
0
1
0
2
2
3
0
0
1
1
1
1
0
0
0
1
0
0
0
2
1
0
0
1
1
1
0
0
2
0
0
0
0
1
0
0
1
2
0
0
0
0
1
0
2
0
0
1
1
0
1
0
1
0
2
1
2
0
0
0
0
1
2
1
0
0
0
1
2
1
2
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
1
2
2
0
1
0
0
0
3
1
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
4
0
0
0
0
1
0
0
1
0
0
1
2
2
0
2
1
0
2
1
0
1
2
2
0
0
1
0
0
1
0
2
0
1
1
0
0
0
0
0
0
1
0
0
1
0
3
0
0
0
1
1
1
0
1
0
1
0
0
0
2
0
0
0
1
0
0
0
1
1
0
2
2
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
1
1
0
2
1
1
0
0
2
1
0
1
0
1
0
2
1
0
0
0
2
0
0
4
2
0
0
2
0
1
0
1
1
0
0
2
0
1
1
0
1
2
1
2
0
1
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
2
0
0
2
2
2
2
0
2
0
0
1
2
1
2
2
3
0
0
2
0
1
0
0
1
0
3
0
0
1
1
0
1
1
0
0
0
0
1
1
0
0
0
7
1
0
0
0
1
0
1
6
0
0
3
0
2
0
1
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
1
1
2
2
0
2
1
0
0
0
0
2
0
3
0
1
0
0
0
0
2
0
0
0
2
0
0
2
1
2
0
0
0
0
0
1
2
2
0
0
2
0
0
0
0
1
2
0
1
0
0
0
1
2
1
0
0
0
2
0
0
1
0
2
0
1
0
0
0
1
0
1
0
2
0
0
0
0
1
3
2
0
2
1
0
0
0
1
1
1
0
0
2
1
0
0
2
2
2
0
0
2
0
0
1
0
0
3
0
1
0
2
1
1
0
0
1
0
0
0
2
2
0
1
0
0
0
1
0
2
0
1
0
0
2
0
2
1
1
0
0
1
0
3
0
1
0
0
0
0
2
0
0
2
1
0
1
0
2
0
0
3
0
0
2
0
2
0
1
0
0
0
0
0
0
0
3
2
0
1
1
0
1
1
1
1
0
1
0
2
2
1
0
0
0
0
2
2
1
0
0
1
0
0
1
1
1
1
1
2
0
1
1
3
1
1
0
0
0
0
0
0
0
0
1
2
2
1
1
0
0
0
2
0
1
0
0
1
1
1
0
2
0
1
0
2
0
0
1
2
2
1
1
1
0
2
0
0
0
0
0
2
0
0
1
0
1
0
0
1
1
0
0
0
1
0
0
1
1
0
2
1
0
0
3
0
0
3
0
0
1
1
0
3
3
2
1
0
0
1
1
1
3
1
0
1
1
1
1
0
0
0
1
1
1
0
1
1
0
0
1
0
2
0
0
0
0
2
1
2
2
0
0
0
0
0
1
0
0
2
0
1
0
0
1
0
0
0
0
1
1
0
0
3
1
0
0
1
0
0
1
1
0
1
2
2
0
0
0
0
2
2
2
0
2
0
1
0
0
0
0
0
2
0
1
1
0
0
1
0
2
0
0
1
2
2
2
0
0
1
0
0
0
1
0
1
0
1
2
0
0
0
0
0
0
0
1
0
2
2
2
0
2
0
1
0
0
1
2
1
0
1
0
0
2
1
1
0
2
0
0
0
0
1
0
2
2
0
0
0
1
0
1
2
0
1
1
0
1
0
0
2
0
2
1
1
2
0
1
2
0
0
0
0
1
2
2
0
2
0
3
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
2
0
2
3
0
0
0
1
1
0
0
0
2
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
2
2
1
2
1
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
1
0
0
2
0
1
2
1
2
2
0
0
0
2
1
2
0
1
1
1
0
1
1
2
1
0
0
1
1
1
0
0
1
0
1
0
0
2
0
1
0
2
1
0
0
0
1
2
1
1
0
1
1
2
0
0
0
1
0
1
2
0
0
0
0
2
1
1
0
0
0
0
2
1
2
1
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
2
0
0
0
0
3
2
1
0
2
1
0
0
0
0
1
1
1
2
1
0
1
2
0
1
0
0
0
0
1
1
0
1
2
0
0
1
1
0
0
2
1
0
0
0
0
0
0
2
1
1
1
0
1
2
0
1
0
2
0
1
0
1
2
1
2
0
2
0
1
1
0
0
1
0
0
1
0
2
0
2
0
2
2
0
0
0
1
2
0
0
0
0
0
0
2
0
1
0
0
2
1
1
0
2
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
1
1
1
2
2
0
0
0
0
2
2
2
1
2
1
1
1
2
0
0
2
0
1
2
1
0
0
0
0
2
2
0
1
0
0
1
1
1
2
0
0
0
0
2
0
0
1
2
1
2
0
2
0
2
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
1
2
1
2
1
0
0
1
2
0
0
1
1
0
0
1
2
0
3
0
1
1
0
0
0
0
0
2
2
2
0
1
1
1
1
0
1
0
1
0
1
1
2
1
3
0
0
0
1
2
1
0
1
1
1
1
0
0
0
2
0
1
1
0
0
0
0
1
1
2
3
3
1
0
0
1
2
1
1
1
1
2
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
1
0
0
2
2
0
0
0
1
1
0
2
0
2
0
2
0
0
0
1
1
0
2
2
2
0
1
0
0
3
1
2
0
0
0
0
0
0
1
1
1
0
2
0
0
1
0
2
0
1
0
2
1
0
0
0
0
1
1
0
0
1
2
0
1
0
2
1
0
0
0
1
1
1
2
0
0
1
0
0
1
1
0
0
0
0
0
2
0
2
0
1
0
0
1
1
0
0
1
0
0
0
1
1
2
0
2
0
0
1
0
0
0
0
1
0
2
0
2
2
0
0
1
1
0
1
1
0
0
0
0
0
1
0
2
1
0
1
0
2
0
0
2
1
0
1
2
1
1
0
0
1
0
2
0
1
2
1
2
2
0
1
1
0
2
0
1
0
0
1
0
1
2
0
0
1
0
1
2
0
0
0
0
0
2
2
0
0
0
1
1
1
0
0
1
1
0
0
2
1
2
1
0
2
0
2
1
2
0
0
2
0
0
1
0
2
0
0
1
0
0
1
2
0
1
0
1
2
1
0
2
0
0
1
1
0
2
0
0
2
0
0
1
3
2
0
2
0
1
2
2
1
1
0
1
1
0
0
0
2
1
2
0
0
0
2
0
0
0
1
1
0
0
0
1
0
2
0
2
2
0
0
0
0
0
0
0
1
1
2
0
2
1
0
1
0
1
0
2
1
0
0
0
2
0
2
2
0
0
0
0
1
0
0
0
0
2
1
1
2
0
0
0
0
2
0
1
0
1
2
0
1
2
2
0
1
0
0
0
0
0
1
0
1
1
0
0
2
2
1
0
0
1
0
3
0
0
0
0
0
0
0
2
0
0
2
1
1
2
1
1
0
0
2
0
0
1
2
0
1
0
2
2
1
0
0
1
2
2
1
0
0
1
0
1
0
2
2
2
0
0
0
0
0
1
1
2
3
0
1
1
1
0
3
1
0
0
2
0
1
0
0
0
2
2
1
0
0
2
0
0
1
0
0
1
1
0
0
2
0
1
0
0
1
2
1
2
0
0
0
0
0
1
0
0
1
0
0
1
0
1
2
0
0
0
1
2
2
1
0
0
0
0
0
2
0
0
0
1
0
1
0
1
3
2
1
1
2
0
1
0
0
0
0
0
1
0
1
0
2
0
1
2
2
1
1
2
2
1
1
0
0
0
2
0
0
0
2
0
0
2
1
0
1
2
2
0
2
1
0
1
2
1
2
0
1
0
1
1
0
0
2
1
0
2
1
0
0
1
1
1
0
0
0
2
0
1
0
0
1
0
0
1
2
0
0
2
0
2
1
1
0
0
1
1
0
6
0
1
0
0
0
2
1
0
1
1
1
0
0
1
0
0
1
0
0
0
2
1
0
0
0
1
0
0
1
1
0
0
2
0
1
1
0
0
0
0
0
0
0
2
2
2
0
0
1
2
1
1
0
0
0
1
1
0
1
2
0
2
0
0
2
0
1
2
1
1
0
1
1
2
1
0
2
0
1
1
1
2
1
0
0
0
1
0
0
1
1
2
0
2
1
0
1
0
0
0
0
1
0
1
0
2
0
1
2
2
0
1
4
2
2
0
1
1
0
0
1
1
1
0
0
0
1
2
0
1
0
1
2
2
0
0
1
2
1
1
0
0
2
1
1
1
0
3
0
4
0
0
2
1
1
1
1
2
0
2
0
0
1
0
0
0
2
2
0
1
0
2
1
0
2
0
1
0
0
0
2
0
0
0
2
2
2
0
1
1
1
0
1
2
1
0
2
1
0
0
0
0
0
2
2
1
0
0
2
0
0
0
0
1
0
2
2
2
0
1
1
1
1
0
1
0
0
0
0
1
5
2
0
0
1
0
0
0
2
0
0
1
0
2
0
2
2
2
0
2
2
1
2
0
0
0
0
0
0
0
2
1
0
1
0
1
1
2
2
1
0
2
1
1
2
1
0
0
0
1
2
0
2
0
4
0
1
0
0
1
2
0
0
0
0
2
1
0
1
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
1
0
1
0
0
1
2
0
1
2
0
2
0
2
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
1
1
2
0
0
0
2
2
0
1
0
0
2
1
1
2
1
0
2
0
0
2
0
2
1
2
1
0
1
2
2
2
2
2
0
0
0
0
0
1
1
1
2
1
0
0
0
0
2
0
2
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
1
2
1
2
0
0
2
0
1
2
0
2
0
1
0
0
1
0
0
0
0
0
0
2
2
0
2
1
0
1
1
1
1
1
1
0
1
0
0
0
0
2
1
0
1
2
0
2
0
0
0
2
0
0
2
0
0
0
0
2
1
2
0
0
1
0
0
2
2
1
1
2
1
0
1
0
1
2
0
0
0
0
0
2
1
1
0
1
0
1
3
5
0
0
0
0
2
1
1
0
0
0
2
2
1
0
1
0
0
0
0
2
0
2
2
1
0
1
2
0
1
0
2
0
1
1
1
0
0
0
2
0
0
2
2
0
0
1
0
0
1
2
0
0
0
0
1
1
0
2
2
2
0
2
2
0
0
1
0
0
0
0
2
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
1
0
1
0
0
1
2
1
0
1
0
0
1
1
1
1
0
1
0
1
0
0
1
0
1
0
2
0
0
0
0
1
0
1
0
1
0
0
2
0
0
1
0
2
1
0
0
0
1
1
0
2
2
0
2
1
0
1
0
0
0
1
2
0
0
0
3
0
2
2
2
2
0
2
1
0
0
0
0
2
2
0
0
0
2
1
0
1
0
0
0
1
0
0
0
0
1
1
1
2
0
0
1
1
1
1
2
0
2
1
0
0
0
2
2
2
0
2
0
0
2
0
0
1
0
1
2
0
2
3
0
0
1
0
0
1
1
0
0
0
1
0
0
0
2
1
1
1
1
1
0
0
0
1
0
0
0
0
0
1
2
0
1
1
1
0
0
0
0
0
0
1
1
0
1
2
1
2
2
1
1
2
0
1
2
0
1
1
2
0
1
0
2
1
0
0
0
2
0
0
0
0
2
0
1
0
1
0
0
1
1
2
0
0
1
0
0
1
2
0
1
1
1
0
0
0
0
0
1
1
0
0
2
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
1
1
1
0
0
2
0
1
0
0
0
0
2
3
2
1
1
1
0
3
3
2
0
0
1
2
0
0
0
0
1
0
0
2
1
1
1
1
0
1
1
0
0
2
0
2
1
0
0
0
2
0
1
2
0
1
1
0
2
0
1
1
2
2
2
1
2
3
1
2
1
0
1
0
0
2
0
1
2
0
0
0
0
2
0
1
1
0
1
1
1
1
1
0
1
2
1
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
2
2
0
0
0
1
0
0
0
0
2
0
2
0
1
2
1
7
2
0
2
0
0
1
1
2
1
1
0
0
2
1
0
0
2
2
0
1
1
1
0
0
2
2
0
0
2
3
1
0
2
1
0
2
0
0
0
0
1
0
0
1
2
0
0
0
2
0
1
1
0
0
1
0
1
1
0
2
0
0
0
1
1
1
0
1
1
2
0
0
3
2
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
2
0
2
0
0
0
0
1
0
0
0
0
5
0
0
0
0
0
2
2
0
2
0
0
0
1
2
1
0
2
0
1
0
1
0
2
2
0
2
0
0
0
0
0
2
0
1
3
0
1
0
1
2
0
0
1
0
0
0
1
0
2
0
2
0
1
0
1
1
1
1
0
0
0
1
1
3
1
0
0
2
0
0
0
1
2
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
1
0
2
0
0
1
2
3
1
0
0
0
1
1
2
0
0
1
0
2
0
5
0
2
1
0
0
0
1
0
2
0
0
0
2
1
0
1
0
2
1
0
0
1
0
2
0
0
0
1
1
1
0
1
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
1
1
1
2
0
0
0
1
0
0
2
1
0
0
1
0
2
0
0
3
0
1
0
0
0
0
1
0
0
0
1
2
0
2
0
1
2
2
0
0
0
1
2
2
0
1
1
0
0
0
0
1
2
1
1
2
0
0
2
1
2
0
0
0
1
0
2
1
1
0
0
0
1
2
1
1
1
2
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
1
2
1
0
2
0
2
0
1
2
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
1
1
1
0
2
2
1
2
0
0
1
2
2
1
0
2
0
0
0
0
2
1
1
0
0
1
0
1
0
0
0
0
0
0
1
0
2
3
1
0
1
0
2
0
0
1
0
0
0
0
0
0
0
1
2
0
1
0
1
0
0
0
2
1
0
0
2
0
0
2
1
0
0
1
2
2
0
1
1
2
0
0
0
1
0
2
2
0
1
2
2
0
0
1
0
1
1
2
0
1
0
1
1
1
0
0
0
1
0
2
0
2
0
0
2
0
2
1
1
0
1
2
0
0
0
2
0
0
1
0
0
0
0
1
1
1
0
1
0
0
0
0
2
0
0
1
0
0
2
2
2
0
0
0
0
0
0
0
1
0
1
0
2
0
2
1
1
1
0
0
0
0
2
1
0
0
1
0
3
0
0
1
1
2
1
1
0
0
1
0
0
2
1
0
0
0
3
0
1
1
0
1
0
1
1
1
2
0
2
0
1
0
0
0
2
3
2
1
1
0
1
0
0
0
1
0
0
0
0
1
2
1
1
1
0
2
2
1
2
1
0
1
2
3
1
0
1
0
0
2
2
2
1
0
0
1
0
1
1
1
0
1
0
1
0
1
1
1
0
2
0
0
0
0
0
0
1
2
0
2
2
1
0
2
2
0
0
1
1
0
1
1
0
0
2
1
0
2
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
2
2
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
1
2
0
0
0
0
1
0
0
2
1
2
1
0
2
0
1
0
0
2
1
2
0
2
1
2
0
1
0
0
1
0
0
0
2
0
1
0
1
0
0
1
1
2
0
2
0
2
0
0
1
0
0
0
2
0
1
0
1
0
1
2
0
0
0
1
0
1
1
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
1
1
0
1
0
0
0
0
0
1
0
0
1
0
1
0
2
0
1
1
3
0
0
0
1
1
1
0
3
1
0
0
0
0
2
0
0
0
2
0
1
3
0
0
0
1
1
2
0
0
1
0
1
1
5
0
0
0
1
2
0
2
0
1
0
0
0
0
0
1
0
0
3
1
0
0
2
0
1
0
0
0
1
0
1
1
0
2
1
0
1
0
0
2
3
0
2
0
1
0
2
0
0
2
0
1
1
1
0
0
0
0
0
1
1
0
1
0
0
1
0
2
4
0
0
0
1
0
0
1
1
3
0
0
2
1
0
2
2
2
2
0
0
1
0
0
1
0
2
1
2
0
1
0
0
0
0
0
1
0
2
2
0
2
2
0
0
0
2
0
2
0
1
2
2
2
0
4
1
1
3
0
1
0
0
1
1
0
0
1
0
0
2
0
2
2
0
0
2
2
1
2
0
0
1
2
2
0
0
0
0
0
0
0
1
1
0
0
0
0
1
2
0
1
0
2
0
0
3
0
1
0
0
0
1
1
0
1
0
3
1
0
0
2
0
0
1
0
2
0
0
0
2
0
0
0
3
0
1
2
1
0
0
0
2
1
0
0
1
2
0
0
1
0
0
0
1
0
3
0
0
2
0
1
0
2
1
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
2
0
0
1
0
0
0
0
1
1
0
1
2
0
1
1
0
1
1
0
0
0
0
0
0
2
0
1
0
1
0
1
5
1
0
1
1
1
0
1
0
0
1
2
2
2
0
2
0
1
0
0
0
1
2
0
0
1
1
5
1
1
0
1
1
0
2
2
0
0
0
0
0
0
0
0
1
3
1
0
3
1
0
0
2
0
0
1
0
1
0
0
0
1
2
0
2
0
1
1
0
0
1
0
0
1
1
0
1
2
0
0
0
0
0
0
2
0
2
0
0
0
1
1
1
2
0
0
0
2
1
0
0
0
2
0
2
0
0
2
0
1
1
0
0
0
0
1
0
2
0
0
0
0
2
0
2
0
3
2
0
4
2
1
2
1
1
0
1
0
1
1
0
0
1
1
2
0
0
0
1
0
0
2
1
1
0
3
0
0
2
2
1
2
2
0
0
0
1
0
2
0
4
1
0
1
1
0
1
1
2
1
2
0
0
2
1
0
1
0
0
0
2
1
0
2
0
2
0
1
2
2
0
0
1
0
2
1
2
0
1
1
1
0
0
1
0
1
0
0
0
0
0
0
2
2
1
2
0
1
2
0
1
0
0
0
1
0
0
1
0
0
0
2
0
0
0
2
0
0
1
1
0
0
0
2
1
0
0
0
0
0
2
0
4
0
7
3
0
1
1
0
1
0
3
0
0
1
0
6
0
1
0
2
1
0
1
1
1
1
2
0
2
0
0
2
0
0
1
2
0
0
0
1
1
0
0
0
0
0
1
0
0
3
0
0
0
2
1
2
0
0
0
2
2
1
0
0
1
0
1
0
3
0
2
1
1
0
0
1
0
1
0
1
1
0
1
1
1
1
0
1
0
1
2
0
0
0
0
0
2
2
0
1
2
1
2
1
2
1
1
3
0
1
0
1
0
2
1
0
1
0
1
1
2
0
1
1
0
0
0
0
2
0
0
0
0
0
0
1
1
0
2
0
2
2
0
1
0
0
0
0
0
0
1
0
2
1
1
0
0
1
1
1
1
0
0
0
0
0
0
2
0
4
0
1
0
2
2
0
0
2
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
1
0
1
1
2
0
1
0
1
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
2
2
2
1
1
0
0
1
0
1
0
0
0
0
0
3
1
1
2
2
0
0
0
2
1
0
1
1
2
0
0
0
0
1
1
1
0
1
1
0
2
2
0
0
0
0
1
0
2
1
1
0
0
0
0
0
2
0
0
0
2
0
2
2
0
0
2
2
1
1
0
2
0
0
0
1
2
1
0
1
0
3
0
2
0
2
0
0
0
2
2
0
0
1
2
0
2
2
3
0
1
3
3
1
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
1
0
1
2
3
1
0
1
2
0
2
0
0
0
1
0
4
2
2
1
2
0
3
1
1
0
0
1
1
0
2
1
0
0
2
0
2
0
1
0
1
0
1
2
2
0
0
0
0
2
0
1
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
2
2
0
2
0
0
0
1
0
0
0
1
0
2
0
1
0
0
0
3
0
0
0
0
3
0
0
0
0
0
1
2
0
0
0
0
0
1
1
0
0
1
0
1
0
2
1
0
2
0
2
0
2
0
1
1
0
0
1
1
0
3
0
2
2
1
1
0
0
0
1
0
2
0
2
0
0
2
1
3
0
0
0
0
0
2
1
2
2
0
1
2
0
0
1
1
0
0
1
0
0
2
0
0
0
1
1
0
1
0
0
2
2
2
0
2
0
2
2
0
1
0
0
1
1
2
1
1
2
0
2
0
0
2
0
2
2
0
0
1
2
0
2
2
0
0
2
0
1
0
2
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
2
0
0
1
0
1
1
0
1
0
0
0
2
0
1
0
0
1
0
0
0
0
2
0
1
0
0
0
1
1
2
1
2
0
1
1
0
0
2
1
1
1
0
0
0
0
2
1
0
0
1
0
0
4
1
1
0
1
3
0
1
0
1
1
0
0
1
0
2
0
1
1
2
0
3
0
0
2
0
1
1
2
0
0
3
0
0
0
0
2
2
1
2
0
0
2
0
2
0
3
0
0
0
1
0
0
2
1
0
3
0
1
0
0
1
1
1
0
1
1
0
0
2
3
2
0
1
0
0
2
1
0
0
0
0
0
1
2
1
0
0
1
1
0
2
0
0
3
2
2
0
0
0
2
0
2
0
0
1
2
0
1
0
1
0
1
1
0
2
0
1
0
0
1
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
2
0
0
2
1
1
2
1
1
0
0
1
3
0
0
3
0
2
0
0
0
2
0
3
0
0
2
0
0
0
0
0
2
1
0
3
0
0
0
1
0
1
0
0
0
2
0
0
0
1
1
2
0
2
0
0
1
1
0
2
0
0
2
0
1
0
0
1
2
0
2
1
0
1
0
0
0
1
0
1
0
1
2
0
0
2
0
0
1
3
0
1
0
0
1
2
0
1
2
0
1
0
1
1
1
0
1
2
2
0
4
1
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
2
2
1
1
2
0
0
0
1
0
0
0
0
2
0
1
0
0
2
0
0
2
0
2
2
0
2
2
0
2
0
0
0
2
0
1
1
0
2
2
0
1
2
0
0
1
0
0
1
1
2
1
0
2
0
1
2
2
1
1
0
0
0
0
0
0
1
0
1
0
1
2
0
0
1
2
0
1
2
0
2
0
1
0
0
0
1
1
1
0
0
0
0
0
2
0
1
0
2
0
0
2
0
0
1
2
1
3
0
2
0
2
0
0
0
0
0
0
0
0
1
1
0
1
0
2
0
0
0
1
1
0
0
0
1
2
1
0
0
0
2
0
1
2
0
2
0
2
0
0
0
1
0
1
2
1
0
0
0
2
1
3
0
1
3
0
1
0
0
0
0
1
0
2
0
1
1
2
0
0
1
1
0
2
4
0
2
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
1
0
1
1
0
1
1
1
0
0
1
2
0
0
0
0
0
0
1
1
1
2
1
0
3
2
0
0
2
0
1
0
1
0
0
1
0
2
0
0
0
0
2
0
0
1
1
0
0
0
1
2
1
2
1
0
5
1
1
2
0
0
2
2
3
2
0
1
0
1
1
0
1
1
0
0
0
2
0
2
2
2
2
1
2
0
1
0
1
0
1
0
1
1
2
0
0
0
0
1
2
1
0
2
2
2
0
0
1
1
10
2
0
0
1
0
0
0
1
0
5
1
1
0
1
0
1
0
0
0
1
1
0
0
1
0
1
2
0
0
2
1
2
1
2
0
2
0
1
0
0
0
1
1
3
0
0
1
0
1
0
0
0
0
0
0
5
1
2
1
0
1
4
3
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
1
2
1
0
2
2
2
1
0
2
1
0
2
1
0
0
0
1
2
0
1
0
2
1
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
1
1
0
2
0
1
0
0
2
1
0
2
0
0
2
0
0
2
0
1
1
2
0
4
0
2
0
2
0
2
1
0
0
1
0
0
1
2
0
1
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
2
0
0
1
2
2
0
0
1
0
0
0
0
2
3
0
1
0
0
0
2
0
1
1
0
2
1
0
0
0
0
0
2
0
0
0
0
0
1
2
0
1
2
0
0
1
0
0
2
1
0
2
0
2
2
0
0
0
0
0
0
1
1
0
0
0
3
3
0
0
1
0
2
0
0
0
0
0
0
1
0
1
1
0
1
0
0
1
0
0
1
0
0
1
0
1
0
0
0
1
1
0
2
0
0
1
2
0
0
2
1
0
1
0
2
0
0
0
0
1
1
0
1
0
0
0
2
0
0
1
1
0
0
1
1
0
0
1
1
2
0
0
0
0
2
1
0
2
1
1
0
0
0
0
2
2
2
0
0
0
0
0
2
0
2
0
1
2
0
0
2
0
0
0
1
0
1
0
0
1
0
0
2
2
1
2
0
2
0
0
2
0
1
1
1
0
0
1
1
2
3
1
0
0
1
0
0
2
0
0
1
0
0
2
1
0
0
4
0
1
0
1
2
2
0
1
0
0
0
0
0
1
0
0
1
0
1
1
1
2
0
0
0
0
2
0
1
0
1
1
0
1
1
1
0
1
2
1
1
2
2
1
1
2
2
0
0
0
1
1
2
0
2
2
2
0
0
0
0
2
1
0
0
0
2
0
1
0
2
0
0
2
2
0
0
0
1
1
0
0
1
0
1
2
0
1
8
1
0
1
1
0
1
1
0
1
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
1
0
2
0
1
2
2
0
0
0
1
2
2
1
1
0
0
1
0
0
0
1
0
1
1
0
0
1
1
1
0
1
0
0
1
0
2
0
0
0
2
0
0
2
3
0
2
0
0
1
0
1
0
2
1
0
0
0
0
1
1
1
1
0
2
1
0
0
0
0
2
1
0
0
1
1
2
0
2
0
0
0
0
0
1
0
2
0
0
0
0
1
2
0
1
2
0
0
2
0
0
0
0
1
1
1
1
0
0
0
1
0
0
2
0
1
0
0
0
2
0
2
1
1
0
0
0
0
0
0
2
0
0
0
0
2
1
1
1
0
2
0
0
0
0
1
0
2
0
0
1
2
0
0
2
0
0
1
0
0
0
0
2
0
2
0
2
2
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
1
0
1
0
0
2
0
1
0
2
0
1
0
0
1
0
2
2
1
0
0
1
0
2
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
2
2
0
0
1
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
2
1
0
2
1
2
1
2
0
3
0
0
0
1
1
0
2
1
0
1
0
0
0
0
2
0
1
1
2
0
0
2
0
0
0
0
1
0
3
0
1
0
0
0
0
1
1
1
1
0
0
2
0
1
0
2
0
2
2
0
1
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
2
1
2
0
0
2
1
0
0
1
0
1
0
1
0
1
1
0
0
0
2
0
2
0
0
0
0
1
0
1
0
0
0
2
2
1
0
0
0
0
0
0
0
1
0
1
0
1
2
0
0
1
0
0
0
2
0
2
0
2
0
0
2
1
1
0
0
1
3
1
0
0
0
0
1
2
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
1
0
0
0
2
0
0
1
0
1
0
0
1
1
1
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
1
0
0
2
0
2
0
2
2
1
0
1
0
1
2
1
2
0
0
1
0
2
0
2
2
2
0
0
2
0
0
2
1
1
1
0
1
2
0
0
0
0
1
0
0
1
0
1
0
0
2
0
0
2
1
1
2
2
1
0
2
2
5
0
0
1
0
2
1
0
0
1
2
1
2
0
1
1
0
0
0
1
1
0
0
0
1
1
0
0
1
3
0
0
1
1
2
2
0
1
1
0
0
0
2
2
0
1
1
0
0
0
0
2
0
0
0
0
1
0
0
2
1
0
2
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
1
0
0
3
2
0
0
2
2
2
0
0
0
1
1
1
0
0
2
0
3
2
0
0
1
0
2
0
0
0
0
2
2
1
1
2
1
0
0
1
1
2
0
0
2
0
0
0
0
2
5
1
2
0
1
0
0
1
1
0
1
0
0
1
0
2
1
0
1
0
2
0
0
1
2
0
0
1
0
0
1
1
0
0
0
0
2
1
1
0
0
1
0
1
1
2
0
2
1
0
2
0
0
0
0
2
1
0
1
0
1
1
0
1
0
1
1
2
0
2
0
0
0
0
1
0
2
1
0
0
0
0
2
2
1
2
0
1
2
0
1
2
2
0
0
1
1
0
0
2
0
0
0
1
0
1
0
2
1
2
1
0
0
0
1
0
0
0
2
1
7
2
0
0
0
1
0
1
0
1
1
1
2
0
2
1
1
0
0
2
0
2
0
0
2
0
1
0
0
0
1
1
2
1
1
0
2
0
0
2
0
1
0
2
0
1
2
0
0
1
1
1
0
2
1
4
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
2
2
0
2
2
1
1
0
0
0
0
1
0
0
2
1
0
2
1
2
1
0
0
3
1
0
2
2
1
0
1
2
1
1
1
1
0
0
0
0
0
0
0
2
2
0
1
1
0
0
1
0
0
2
2
0
1
0
0
0
0
0
0
2
1
0
0
0
0
2
1
0
1
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
2
0
0
0
6
3
0
0
0
0
0
4
3
1
0
0
0
0
0
0
0
2
1
1
0
1
0
1
0
0
0
0
0
1
0
0
0
1
2
3
1
2
0
0
0
1
0
0
0
0
1
0
0
1
0
2
1
2
0
0
2
1
0
1
0
0
0
0
1
2
0
2
1
2
1
1
0
0
1
2
0
0
0
2
1
0
2
3
0
1
0
0
1
1
1
1
0
0
1
4
2
0
2
0
1
2
1
0
0
0
0
1
0
0
1
1
0
0
2
2
2
2
0
0
2
0
0
0
0
1
0
0
0
0
1
2
0
2
0
0
1
0
0
0
0
2
0
2
0
0
0
2
2
0
0
0
2
0
1
0
0
2
0
1
2
2
1
0
0
0
0
1
0
0
1
0
0
0
0
2
0
1
0
0
1
0
0
0
0
1
1
0
0
2
0
1
0
0
0
2
0
1
2
1
1
0
0
0
2
1
1
0
0
1
3
0
2
2
0
2
0
1
0
1
1
0
1
0
0
0
0
2
0
0
2
0
0
1
0
0
1
0
0
0
1
0
1
0
3
2
5
2
0
2
0
0
0
1
0
1
0
0
0
5
0
2
5
0
0
0
2
2
2
1
0
1
0
0
1
0
1
3
1
0
2
0
1
0
1
0
0
0
1
0
1
0
0
1
0
1
0
1
0
0
0
2
0
2
2
1
2
0
0
0
1
2
1
2
0
0
0
1
0
0
2
0
2
0
3
1
0
2
1
0
1
2
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
2
1
2
0
0
0
0
1
2
1
0
0
1
1
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
2
1
1
0
0
0
0
2
1
0
1
3
0
0
1
0
1
0
0
0
2
0
1
0
0
0
0
2
0
1
0
1
2
0
0
0
2
0
1
2
2
0
1
2
2
0
0
1
0
0
1
0
1
0
1
1
0
0
1
1
0
0
1
0
2
2
2
2
0
0
1
0
1
0
1
1
1
0
2
1
2
0
0
0
3
0
1
1
1
1
2
2
0
1
0
1
1
0
1
0
0
0
0
0
2
0
0
2
0
0
0
3
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
2
0
1
0
2
2
0
2
3
0
0
2
0
0
0
3
0
2
2
1
1
1
0
0
2
0
0
1
1
0
1
0
0
2
0
1
2
1
0
0
2
0
1
0
0
0
2
2
0
0
0
0
1
0
1
2
0
0
0
2
0
0
0
1
0
2
1
0
2
2
2
0
0
0
0
0
0
0
0
2
1
0
0
0
1
1
2
0
1
1
1
2
1
0
0
0
0
0
2
0
0
0
3
0
1
0
1
2
1
2
3
1
1
0
1
0
1
0
2
0
0
3
1
0
0
0
2
0
1
0
0
1
1
0
1
0
1
0
1
1
2
0
0
1
4
2
0
0
0
1
0
0
1
0
0
0
0
1
2
0
2
0
0
0
0
1
2
2
2
0
2
1
0
0
0
1
1
0
1
2
0
0
0
1
2
0
0
0
1
0
0
1
0
0
2
1
1
0
0
0
1
1
2
2
1
1
0
0
0
0
2
0
0
2
0
1
0
0
1
2
1
0
0
2
0
0
0
0
1
3
0
1
1
0
0
0
1
1
2
2
0
0
1
1
1
0
0
1
0
0
1
2
1
0
0
0
0
1
0
0
2
0
0
2
0
0
1
2
1
0
0
0
0
0
0
2
0
1
0
2
0
1
0
2
0
0
1
0
2
0
0
0
0
1
0
1
2
1
0
2
1
3
0
0
1
0
1
0
1
0
1
2
0
0
0
1
3
2
0
0
2
0
0
0
0
1
1
0
2
1
0
0
0
1
1
2
1
0
1
1
0
0
1
0
1
2
0
1
1
2
1
2
1
0
1
2
2
0
1
1
0
0
2
0
1
0
1
0
0
2
0
0
0
0
1
1
3
0
2
0
0
1
2
2
0
1
1
2
0
0
0
0
3
0
0
1
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
1
0
0
1
2
0
2
0
2
3
0
1
1
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
1
0
0
1
1
2
1
3
0
5
0
1
1
0
0
0
0
2
0
1
1
1
0
2
0
0
0
1
1
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
1
0
5
0
0
0
0
0
0
1
2
0
1
1
1
1
0
0
0
2
0
2
0
0
1
1
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
1
2
0
1
2
1
1
1
0
0
1
0
0
0
0
3
0
1
1
1
1
0
0
1
0
1
2
2
0
1
2
0
1
0
0
2
0
1
0
2
1
0
0
2
0
0
1
2
0
1
1
0
0
1
0
2
2
0
0
0
2
2
0
2
0
0
2
1
3
2
0
0
1
0
0
0
0
0
1
0
1
1
0
2
0
0
0
1
1
1
0
0
2
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
2
1
2
0
2
1
0
3
0
2
0
0
0
2
2
0
1
1
0
1
0
0
1
0
1
0
1
1
1
0
1
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
1
0
1
0
0
1
0
0
1
1
2
1
0
2
1
1
2
1
0
0
0
1
1
0
0
0
1
0
0
1
2
0
0
1
0
2
0
1
0
2
0
0
2
2
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
2
1
2
1
2
1
1
0
0
1
0
0
0
0
3
0
1
1
1
0
0
2
0
1
1
2
4
0
1
0
0
2
2
2
0
1
3
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
2
0
1
2
1
2
0
2
1
0
1
2
1
2
2
0
1
0
0
2
1
5
0
0
0
0
0
2
0
0
2
1
0
0
2
0
1
2
0
0
0
0
0
0
3
0
0
0
0
0
0
2
2
1
2
0
1
0
0
2
0
0
2
1
0
1
0
2
0
0
2
0
0
2
1
0
2
2
2
1
1
0
1
2
0
2
0
0
2
0
0
1
0
0
1
2
1
1
1
0
0
0
0
2
5
0
2
1
4
0
0
1
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
1
0
1
1
1
1
2
1
1
0
1
2
1
1
0
2
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
3
2
0
0
2
0
0
1
1
0
0
2
0
0
1
0
2
1
1
1
0
0
2
0
1
1
0
1
1
1
2
0
2
1
2
0
0
0
0
0
0
0
0
2
1
1
2
1
0
0
1
0
0
0
2
0
1
1
0
0
0
1
1
2
1
0
0
0
2
0
1
0
0
2
0
0
1
0
0
0
2
0
1
0
2
1
0
0
2
0
0
0
0
1
1
1
1
0
1
0
0
2
0
1
0
1
0
0
0
1
0
0
2
0
0
0
1
1
0
0
0
2
0
1
2
1
1
2
2
2
0
1
1
1
0
0
1
0
0
2
0
6
0
0
0
0
0
0
3
0
1
0
1
1
0
0
2
2
1
0
0
0
0
1
1
2
0
0
1
1
2
1
0
2
2
0
2
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
2
0
2
1
1
1
0
0
2
0
0
0
0
0
1
1
0
1
0
0
0
0
2
0
0
0
1
0
0
1
2
0
0
0
0
1
0
1
0
0
0
2
3
2
0
0
0
0
1
0
0
2
2
0
1
2
0
1
2
1
0
0
0
0
0
0
0
2
1
2
1
0
1
0
0
2
0
1
1
0
3
2
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
1
0
0
1
1
0
1
0
0
0
2
1
1
1
2
0
0
0
1
0
0
1
0
0
0
1
1
0
0
1
0
1
2
1
2
1
2
2
1
0
2
1
2
1
2
0
0
1
2
1
2
0
0
1
0
0
1
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
2
0
0
1
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
2
1
0
1
0
0
1
0
1
2
1
0
0
1
1
0
0
0
0
0
0
1
0
2
2
1
2
1
0
0
1
1
2
1
2
0
2
2
0
0
0
0
1
2
1
1
1
2
0
0
0
0
0
2
0
0
0
2
0
1
0
1
1
0
0
1
1
0
1
1
1
1
2
1
0
0
2
0
0
0
0
0
1
0
0
1
2
1
0
0
0
2
1
0
3
2
0
0
0
0
0
2
1
1
0
0
0
1
1
2
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
1
0
2
2
0
0
1
1
2
2
1
1
0
0
1
0
1
1
0
2
1
2
0
2
0
0
0
2
2
0
0
0
0
0
2
0
1
0
2
0
0
0
0
2
0
2
0
0
3
0
0
2
2
0
0
0
0
1
0
0
0
0
1
2
2
1
0
2
0
2
0
2
0
2
0
1
0
0
0
2
0
0
3
1
2
2
1
0
0
2
0
2
1
2
0
0
1
2
0
0
2
1
1
0
0
0
2
0
0
0
0
2
0
0
2
2
0
1
2
2
0
0
0
2
0
1
0
0
2
0
0
1
1
1
0
1
2
1
1
1
3
0
0
0
1
0
0
0
0
1
0
0
2
1
1
1
0
1
1
2
0
2
1
1
2
0
2
0
1
1
0
1
2
0
0
0
0
1
0
0
0
0
0
1
1
1
2
2
0
0
1
1
0
0
0
0
0
1
3
0
0
0
2
0
3
0
1
0
1
1
1
0
0
1
0
1
1
0
1
0
0
2
0
1
1
1
0
0
2
0
0
0
2
0
1
3
0
1
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
1
2
2
2
0
0
0
0
0
2
0
2
2
2
0
0
0
0
2
0
2
2
1
0
1
2
1
0
1
2
0
4
0
0
0
1
2
0
0
0
1
0
1
1
1
3
0
0
0
0
0
1
0
2
1
0
0
2
0
1
2
1
1
0
1
0
0
1
0
2
2
0
0
1
3
1
0
1
0
0
1
1
0
1
0
1
7
0
2
1
0
0
0
0
0
2
2
1
1
0
0
0
0
4
0
0
1
1
0
2
0
2
1
1
1
0
0
1
1
0
0
1
0
0
0
1
0
2
0
0
1
0
1
0
0
1
2
1
0
0
0
2
0
1
1
0
1
0
0
0
2
2
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
2
2
2
0
1
2
0
0
0
0
1
0
2
1
1
0
0
2
1
0
0
0
2
1
0
0
0
0
1
1
0
0
0
2
0
0
1
2
0
0
0
1
2
0
1
0
2
1
4
0
0
0
0
0
0
0
0
1
0
0
0
2
1
1
1
2
2
0
3
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
1
1
2
1
1
0
0
1
2
0
0
0
0
2
0
1
1
0
1
0
0
0
0
0
3
1
0
1
0
1
2
2
0
2
0
0
0
1
1
0
2
0
1
0
1
1
1
0
1
0
2
0
0
0
1
1
0
0
0
1
2
2
1
0
2
2
1
2
1
1
1
2
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
1
0
1
1
0
1
0
1
0
0
2
2
0
0
2
0
1
0
2
2
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
2
2
0
1
0
1
2
2
0
2
0
0
1
1
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
2
1
2
0
0
0
0
1
1
1
1
2
0
0
0
3
0
0
0
0
0
1
0
0
1
1
1
2
2
2
0
0
1
0
1
1
0
0
1
0
1
0
0
0
2
1
0
0
1
1
0
1
2
1
1
1
0
0
1
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
1
1
2
2
0
0
1
0
2
0
0
2
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
2
0
1
1
0
0
2
1
0
0
0
0
2
2
1
0
2
1
2
0
1
0
0
1
1
2
0
2
0
0
1
1
1
1
1
0
0
0
1
1
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
1
0
0
1
1
1
1
3
2
2
0
4
1
0
2
2
0
0
0
0
2
0
0
0
2
1
0
1
1
2
0
1
1
1
0
0
2
0
0
0
2
0
2
0
2
2
2
1
2
2
2
1
1
0
0
2
0
0
0
3
0
1
1
1
1
1
0
0
0
0
2
1
0
0
0
2
0
0
1
0
0
2
1
0
2
0
1
2
0
1
0
1
0
2
0
0
1
1
5
0
0
2
0
1
0
0
0
2
1
0
0
0
2
2
1
1
1
2
2
0
0
0
1
0
2
0
0
2
0
0
1
2
1
0
2
3
0
1
1
0
0
2
0
1
0
1
0
2
0
1
2
2
0
0
0
1
2
0
0
0
0
2
0
0
0
1
3
0
1
0
0
0
1
0
2
0
2
2
0
0
0
1
0
5
2
0
0
1
1
2
1
0
0
2
0
2
0
0
1
1
0
0
0
1
0
0
1
2
2
0
0
3
1
1
0
0
0
0
2
0
1
0
3
0
0
0
0
2
3
0
0
2
0
1
0
0
0
0
0
1
1
1
2
0
1
0
0
0
1
2
0
2
1
0
0
0
1
1
0
2
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
5
1
0
1
0
0
0
1
2
3
0
1
1
1
0
1
0
3
1
0
0
0
0
0
1
0
0
1
0
1
0
1
2
0
1
0
1
0
0
0
1
2
0
0
1
0
1
0
0
0
0
1
0
0
2
0
1
0
0
1
1
0
0
2
0
0
0
1
0
0
1
0
0
3
1
1
1
0
1
0
0
0
0
1
2
0
1
0
0
0
1
1
0
0
1
1
1
0
1
0
1
2
2
1
1
1
1
2
0
1
1
0
1
0
0
2
1
0
1
1
0
0
1
2
0
0
0
2
2
0
0
1
0
0
0
0
1
1
0
0
1
1
0
0
2
0
4
0
0
1
0
1
0
2
2
1
1
0
1
0
0
1
1
2
0
0
2
0
1
2
0
0
0
1
2
0
0
1
1
0
3
2
0
1
0
2
1
0
0
0
0
2
1
0
0
1
0
0
1
1
0
1
2
0
0
0
2
2
0
0
1
3
0
1
1
2
0
0
0
1
0
2
0
0
0
2
0
1
0
0
2
1
0
1
1
0
0
0
2
0
0
1
0
0
0
1
0
1
0
0
1
2
2
1
2
1
0
0
0
1
0
0
0
1
2
1
2
0
0
0
1
2
0
0
0
0
0
0
0
2
2
1
0
1
0
0
2
0
3
1
2
2
0
1
2
0
0
1
0
1
0
0
1
0
1
5
2
0
1
1
0
0
1
0
0
0
2
1
1
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
2
0
0
0
0
1
1
1
1
0
0
0
0
2
1
5
1
2
3
0
2
0
2
2
1
0
2
0
2
0
0
1
0
0
0
2
1
0
1
1
1
0
0
0
1
0
0
0
0
2
2
1
0
2
0
0
1
0
1
0
2
0
2
1
2
0
0
0
0
2
0
1
0
0
1
0
2
0
1
2
0
0
0
2
2
0
0
0
2
2
0
1
2
0
2
1
1
2
0
0
1
2
0
2
0
0
3
1
0
0
2
0
1
0
0
0
0
0
0
0
1
1
0
0
5
0
2
0
0
2
2
0
2
0
1
2
0
1
2
0
0
3
0
1
2
0
0
2
1
0
2
1
0
1
1
0
0
2
1
1
0
0
2
0
1
0
0
1
2
1
0
2
0
1
0
1
1
0
0
2
0
1
1
2
1
1
0
1
0
1
3
0
0
0
0
1
2
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
5
0
2
0
1
0
1
0
1
2
1
1
2
3
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
1
5
0
1
0
1
1
2
0
0
0
0
1
1
0
2
0
2
1
0
1
1
0
1
1
0
0
3
0
1
1
2
1
0
1
0
0
1
0
0
0
2
1
1
0
0
1
0
1
0
2
2
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
2
0
0
0
2
1
1
0
0
0
1
0
1
2
2
0
2
0
0
0
0
0
1
0
1
2
1
1
0
0
0
0
0
1
1
1
0
1
0
0
2
2
0
0
1
0
2
1
1
1
0
0
0
0
0
0
0
0
0
2
2
1
2
0
0
0
1
0
0
0
0
0
1
2
0
0
0
1
1
1
0
1
2
0
0
0
0
1
1
0
2
0
2
1
0
2
1
0
1
1
2
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
2
0
0
1
0
0
0
0
3
1
0
1
2
1
0
1
0
0
0
0
1
1
0
2
2
1
0
0
1
1
2
2
0
2
1
0
0
2
0
0
0
0
0
0
1
1
0
2
1
0
1
0
2
0
0
0
2
1
1
0
2
2
0
1
2
0
0
0
1
1
0
1
0
0
0
0
0
1
1
1
1
2
1
1
2
0
2
1
1
2
1
1
1
2
1
1
0
2
2
1
1
2
1
2
0
0
4
0
2
1
5
0
0
2
1
0
2
1
0
1
2
0
0
1
2
2
0
0
0
2
2
2
0
2
1
0
2
1
1
1
2
0
0
0
0
2
0
0
1
2
1
2
0
0
1
0
2
1
1
2
0
2
0
2
1
0
1
0
2
0
2
0
0
1
1
2
0
2
2
2
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
2
1
0
0
2
2
0
0
0
0
0
0
0
1
1
0
2
1
1
4
2
0
0
1
0
1
0
2
1
1
2
0
1
0
2
0
0
1
0
0
0
0
0
2
0
1
1
0
1
0
2
0
0
0
2
0
1
2
0
0
0
1
0
1
0
0
0
0
1
0
2
0
0
1
0
0
1
2
0
1
2
1
2
1
0
1
1
0
0
1
0
0
0
1
0
0
2
1
2
0
0
1
2
1
2
0
0
3
2
1
1
2
0
0
0
1
0
0
0
1
3
0
0
1
0
0
0
0
0
0
0
1
1
2
0
1
0
0
1
1
0
0
1
0
1
1
0
0
1
0
0
1
1
0
0
1
0
1
0
1
0
0
2
2
0
2
1
0
1
1
0
0
0
0
0
1
1
2
0
2
0
0
1
0
0
0
1
0
1
1
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
1
1
0
1
0
1
2
0
3
2
0
1
1
0
4
1
1
0
0
1
1
0
0
1
3
2
1
0
2
2
0
2
0
0
2
2
2
0
1
0
1
0
0
2
0
1
1
0
0
0
0
1
2
2
1
0
0
1
2
0
1
1
1
1
1
1
1
2
2
1
2
1
0
1
0
0
1
0
0
0
0
1
3
0
1
0
1
0
0
0
2
2
0
0
2
1
2
2
2
2
0
0
3
0
2
0
0
0
0
0
1
0
0
2
0
0
0
1
2
4
1
1
2
0
0
0
1
1
1
1
3
1
0
0
0
2
0
0
0
2
1
0
2
1
1
1
0
0
0
0
1
0
1
0
0
2
0
1
1
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
2
2
0
2
1
2
1
0
1
1
2
0
2
1
0
1
0
2
1
1
1
4
0
2
0
1
0
0
2
2
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
2
2
2
1
2
1
1
1
0
2
1
0
0
1
1
1
1
0
0
2
1
0
1
0
0
2
0
2
2
0
0
0
1
0
0
0
0
1
0
2
2
0
0
1
0
1
0
2
1
2
0
0
2
0
0
0
0
0
1
2
2
0
1
0
0
0
0
4
1
0
1
1
2
1
0
0
0
0
0
1
2
0
2
1
0
1
1
0
2
0
1
1
0
0
1
2
1
0
1
1
1
0
1
0
0
2
0
5
0
1
0
2
1
0
1
2
2
3
0
0
0
0
0
2
0
1
2
1
0
0
2
1
0
0
1
1
1
2
0
1
2
0
0
0
1
1
0
0
2
2
0
0
2
2
2
1
4
2
0
2
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
2
0
1
1
0
2
0
1
0
1
2
1
0
1
3
1
0
0
0
0
0
0
1
0
0
2
1
4
2
0
3
1
0
2
0
1
0
1
0
1
0
0
0
1
0
1
1
0
2
0
0
1
0
2
0
0
1
0
2
0
5
0
0
1
0
0
0
2
0
0
2
0
0
0
1
2
1
0
1
0
4
1
2
1
0
0
0
2
2
0
1
0
2
1
0
1
1
2
4
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
2
2
0
0
2
2
0
2
0
1
1
1
1
0
0
0
1
1
1
0
1
0
0
1
0
2
2
2
1
0
1
0
3
0
1
0
0
0
1
1
0
1
1
1
0
1
0
0
0
0
2
0
1
0
0
0
1
0
2
2
0
0
1
1
2
2
1
0
1
0
1
1
0
0
1
2
1
1
0
1
2
2
1
4
0
1
1
0
2
2
0
2
0
0
1
0
0
1
2
2
0
2
1
0
1
0
0
2
2
1
1
0
0
0
1
0
1
0
1
0
0
1
0
0
2
0
0
0
2
2
0
1
0
2
0
0
0
2
2
0
0
0
1
0
0
0
1
0
1
0
1
1
0
1
0
0
0
1
0
0
0
1
0
0
2
0
2
0
0
0
0
0
2
1
2
0
0
2
0
0
0
2
1
1
0
0
2
0
1
2
0
2
0
1
1
2
0
1
2
0
0
1
1
0
0
2
0
2
2
0
0
4
1
1
1
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
2
2
2
0
0
0
0
1
1
0
1
0
0
0
1
1
0
0
0
2
0
0
2
1
0
0
0
0
0
1
0
0
0
1
2
1
1
0
2
1
0
0
1
1
0
1
1
0
1
0
0
0
0
1
0
0
1
0
0
1
0
2
0
0
1
0
1
1
0
0
2
1
2
3
0
0
0
2
0
0
0
1
0
2
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
2
0
1
1
2
0
0
0
2
0
0
0
0
0
0
1
1
1
0
1
0
3
2
1
0
0
0
1
0
1
0
0
1
0
0
0
1
0
1
0
2
1
0
1
1
2
1
2
0
0
0
0
0
0
0
2
2
0
0
2
0
2
1
0
1
0
1
0
2
0
0
1
0
1
2
0
0
2
0
0
2
1
2
1
1
2
0
1
0
2
0
1
2
1
1
1
0
2
2
0
1
2
2
0
1
7
2
0
0
0
0
0
1
1
1
0
0
1
2
1
0
0
1
0
1
3
2
0
0
0
1
2
0
0
1
0
1
0
0
0
2
1
0
2
0
0
0
0
0
1
1
0
0
1
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
2
0
0
0
0
1
0
0
1
1
0
0
2
1
0
1
0
3
0
1
0
0
1
0
1
0
2
1
0
2
0
0
0
1
1
0
0
0
0
1
0
1
2
0
0
1
0
1
0
0
2
0
0
2
1
0
2
1
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
1
1
0
1
1
0
1
0
0
0
0
0
1
1
0
1
2
1
0
1
1
0
0
0
1
0
1
0
1
0
2
0
1
0
0
1
1
0
0
0
1
0
1
0
1
1
0
2
1
0
2
0
1
0
1
2
0
2
1
0
0
0
0
0
2
1
0
0
0
4
3
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
2
2
1
0
2
1
0
0
1
2
0
2
0
1
2
0
0
0
1
0
0
0
0
0
2
0
0
0
1
1
0
0
0
2
0
0
0
0
1
2
0
0
1
0
0
1
1
0
2
0
0
1
1
0
2
0
0
1
1
1
1
0
2
1
0
1
0
1
0
1
1
0
0
0
2
0
0
1
2
0
2
2
1
0
2
0
0
1
0
1
1
2
2
0
1
2
0
2
1
0
0
1
1
1
2
0
2
0
2
0
1
0
1
0
0
1
2
0
0
1
0
2
0
1
1
0
0
2
0
0
1
0
1
3
2
2
2
2
1
0
0
1
1
2
0
0
2
1
1
1
3
2
0
0
2
0
1
1
0
1
0
0
2
1
0
1
0
0
0
0
1
0
0
0
0
1
0
1
2
2
2
0
0
1
0
0
0
1
1
2
0
2
0
2
0
3
2
1
0
1
0
0
0
2
1
0
1
2
1
1
0
2
1
2
1
0
0
0
1
0
3
0
0
1
0
0
0
0
0
0
0
0
2
2
0
2
0
1
0
0
2
0
0
0
1
1
0
0
2
2
1
1
2
1
1
7
2
0
1
0
0
1
0
2
1
1
0
0
0
0
0
1
2
1
0
0
1
0
0
0
0
0
0
1
0
2
0
2
2
1
2
0
1
0
0
1
1
0
0
2
0
0
2
1
0
0
1
1
1
2
0
0
0
0
1
1
0
0
2
0
0
1
0
1
1
2
0
1
0
1
0
0
0
2
0
0
0
0
1
2
1
0
1
2
0
0
0
0
0
1
0
1
1
3
0
0
0
2
0
1
0
1
0
2
1
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
1
1
0
0
0
1
1
3
1
1
0
2
1
0
0
1
2
2
0
0
0
0
0
0
0
1
1
1
0
0
1
1
2
0
0
0
2
0
1
1
0
0
0
1
0
0
2
1
1
2
0
1
0
1
0
2
0
1
0
0
1
2
0
1
0
0
0
0
2
1
2
1
0
0
1
2
0
0
0
0
1
0
3
0
1
0
0
0
0
1
2
0
1
1
1
0
0
0
0
0
0
1
0
2
0
1
2
1
0
1
0
0
1
0
0
0
0
2
0
0
1
0
0
1
0
1
0
1
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
2
0
1
0
1
0
0
0
0
0
2
2
1
0
1
0
0
0
0
1
2
0
0
1
0
1
0
2
0
1
1
1
0
0
0
0
2
2
0
2
2
1
2
0
2
2
2
3
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
1
1
0
2
2
0
1
2
0
2
0
2
2
0
1
1
0
1
1
0
0
2
0
1
0
2
1
0
0
0
0
0
1
0
1
1
0
1
2
0
0
1
0
2
0
1
0
0
0
0
0
0
1
1
1
2
0
2
0
2
0
0
2
0
0
0
0
0
1
0
2
0
0
1
0
0
2
2
2
0
0
2
2
0
0
0
0
0
0
2
0
1
1
0
2
1
0
1
0
0
0
0
1
1
1
0
2
2
0
0
2
0
0
0
0
2
2
0
0
2
1
1
1
0
0
1
2
0
0
1
1
0
0
1
1
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
2
0
1
2
1
0
0
0
2
0
2
0
1
1
1
0
0
2
2
0
0
1
0
2
0
1
1
0
0
1
2
0
1
1
0
0
0
0
0
0
0
0
1
1
2
0
0
3
0
2
2
1
1
1
1
0
1
0
2
1
1
1
0
1
0
0
1
0
1
0
0
0
1
1
0
0
0
2
1
1
0
2
0
0
0
0
0
0
0
2
0
0
1
1
1
0
1
1
2
0
1
2
2
1
2
0
0
0
3
0
1
1
0
0
0
1
0
1
0
2
2
0
1
0
0
1
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
2
2
0
1
0
0
1
2
2
1
0
0
0
1
0
1
0
1
1
0
0
0
1
1
0
0
1
0
0
0
2
1
0
2
1
3
0
1
0
2
0
1
2
1
1
0
0
1
2
2
1
0
2
0
0
1
1
1
1
0
2
1
2
0
0
1
0
0
0
1
0
0
0
2
0
1
0
0
4
1
1
1
0
0
2
0
0
0
2
5
0
0
0
4
2
0
1
1
0
0
0
1
1
0
1
0
2
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
1
1
0
0
0
2
4
1
1
1
2
0
1
0
3
2
0
0
0
1
0
0
0
0
0
0
2
0
1
2
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
1
1
0
1
0
0
0
2
1
0
0
0
1
3
1
0
0
1
2
0
0
1
2
0
1
0
0
1
2
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
2
1
0
2
0
1
1
0
1
0
1
1
0
0
0
0
0
1
0
0
1
0
1
2
0
0
0
0
0
2
2
2
1
1
3
0
0
2
0
1
0
1
0
2
0
1
0
0
0
1
0
0
0
2
0
0
0
1
0
0
2
0
1
0
2
2
0
0
1
0
0
0
2
0
1
2
0
0
1
2
0
1
2
2
2
1
0
0
1
2
1
0
2
2
0
1
0
0
0
0
2
2
1
2
2
0
0
0
0
0
2
0
0
2
0
2
0
0
0
2
2
0
1
0
2
0
0
2
0
0
0
2
0
0
1
0
0
0
1
2
2
0
2
0
0
1
0
1
2
2
0
1
1
2
0
1
0
1
0
2
1
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
1
0
0
2
1
0
1
1
1
1
1
2
0
0
0
0
0
0
1
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
3
2
0
1
1
1
0
2
1
0
0
2
1
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
2
0
1
0
1
0
1
2
0
2
0
0
1
2
2
0
0
0
0
0
1
1
0
2
0
0
0
1
0
0
0
0
0
2
1
0
0
0
1
1
3
2
0
2
1
2
1
1
1
0
0
0
1
1
2
2
0
1
0
0
0
2
0
0
1
0
0
0
1
1
1
0
1
1
0
0
0
2
0
1
2
0
0
0
0
2
2
0
0
2
0
2
1
1
2
0
1
0
0
0
1
0
2
1
0
0
0
1
0
1
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
2
0
1
2
0
0
0
1
0
2
0
2
0
1
0
1
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
2
1
1
0
0
1
1
0
0
2
1
1
0
2
0
1
2
0
0
2
0
0
2
1
0
1
0
1
0
2
1
2
1
0
1
0
0
0
0
1
0
2
0
2
0
1
0
2
0
2
1
0
1
0
0
0
1
2
2
0
2
0
1
0
2
1
2
2
1
0
1
0
0
0
1
0
2
0
2
2
2
1
1
0
1
2
1
3
1
1
0
2
1
1
1
0
0
0
0
2
1
1
3
0
1
2
0
0
0
0
1
1
1
0
2
1
0
0
1
0
1
2
1
0
0
0
2
0
1
0
1
1
0
1
2
1
0
0
2
0
0
0
1
0
0
0
0
0
1
2
0
0
1
1
2
1
0
0
1
0
2
1
1
2
0
1
1
1
0
0
0
0
0
0
0
6
0
0
1
1
0
2
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
1
0
0
1
2
1
0
2
2
1
0
0
1
0
1
0
1
0
0
0
1
2
0
2
1
1
3
1
2
0
0
0
2
0
0
0
0
0
1
1
0
1
1
0
1
0
0
0
0
0
0
1
0
1
2
0
1
0
2
0
0
0
0
0
2
1
1
2
2
3
0
1
0
1
0
0
0
0
2
1
2
0
0
0
0
0
0
0
1
0
1
0
2
2
0
0
1
1
0
0
0
2
0
1
2
1
0
0
2
1
1
0
1
0
2
0
2
0
0
0
0
1
0
0
1
0
2
1
2
0
0
0
2
1
1
0
1
0
2
0
0
0
2
0
0
0
0
0
1
1
0
0
1
2
1
0
2
0
0
0
1
0
0
0
0
1
0
2
1
0
0
1
2
0
0
2
0
2
0
0
0
0
2
0
1
2
0
0
2
0
0
1
0
0
2
2
1
1
0
1
0
0
0
0
2
0
2
0
1
2
0
2
0
1
1
0
1
0
0
1
0
0
0
0
2
1
0
1
3
2
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
1
2
0
0
1
0
2
2
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
1
0
2
1
1
2
2
1
1
0
0
1
3
0
0
2
0
1
2
1
0
0
0
2
1
2
1
1
2
1
1
0
2
1
0
0
1
0
2
0
0
0
1
2
0
1
0
0
0
0
2
2
0
2
2
0
0
1
3
2
0
1
1
1
1
0
0
2
0
0
2
0
3
0
2
0
0
0
1
0
2
1
0
0
0
2
0
1
0
3
1
0
0
1
0
0
1
2
2
0
1
2
0
0
1
2
0
1
0
0
2
0
2
0
0
3
2
0
0
1
0
1
1
0
1
0
3
0
0
1
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
1
1
0
0
3
0
0
0
2
1
1
0
2
0
2
1
0
1
0
1
0
2
0
0
2
2
0
0
0
0
1
1
0
2
2
0
0
2
0
0
1
0
0
0
1
1
0
0
0
0
0
2
1
0
0
1
0
0
1
2
0
0
0
1
0
0
2
2
0
0
0
1
0
1
0
0
2
1
1
1
1
0
2
0
0
0
0
1
0
1
0
1
1
2
1
0
0
0
2
2
0
0
0
1
1
2
1
2
2
1
0
0
0
1
2
0
0
0
0
0
2
0
3
0
2
2
2
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
2
1
2
0
1
2
0
1
2
2
3
0
0
0
1
0
3
1
0
0
1
2
1
0
0
0
1
2
1
2
0
0
0
1
0
0
0
0
3
0
0
0
1
0
4
0
0
0
2
0
0
0
0
0
0
1
2
0
1
0
0
0
2
2
1
1
1
1
0
1
0
0
4
0
0
1
0
0
0
0
1
1
0
0
0
1
2
1
0
1
0
1
1
0
0
0
2
1
0
0
0
0
1
0
1
0
1
0
0
2
0
0
2
1
0
2
1
0
1
0
1
2
1
0
0
0
3
3
0
0
0
0
2
0
2
0
1
2
0
0
1
0
0
0
1
0
1
2
1
0
1
0
0
1
2
1
0
0
2
4
1
2
0
0
0
1
1
1
1
0
2
2
0
1
0
0
1
0
1
0
2
2
0
0
2
1
0
1
2
0
1
0
1
0
0
2
0
2
0
0
0
0
1
2
0
2
0
0
0
2
1
2
2
0
0
0
0
0
0
2
2
0
2
0
0
0
0
1
1
2
0
0
1
0
0
0
2
0
1
0
2
0
1
1
1
0
2
3
2
0
2
2
0
2
1
0
1
0
3
2
2
0
2
0
2
0
2
0
1
2
0
0
0
0
1
0
2
3
0
0
0
2
1
1
0
0
0
1
0
1
1
1
1
1
1
0
2
0
0
0
0
1
2
1
1
1
0
2
0
1
2
1
2
2
1
2
2
0
2
1
0
1
1
1
0
0
0
0
2
0
1
2
1
1
2
0
1
1
0
1
2
1
0
1
1
0
0
1
0
0
1
0
0
2
0
0
2
0
0
1
0
0
2
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
1
2
2
0
2
1
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
1
0
1
2
2
0
0
0
1
0
1
2
2
1
1
0
0
0
0
1
1
2
0
0
0
1
1
0
0
1
2
3
2
0
1
0
1
0
0
1
0
1
1
0
1
0
1
0
2
1
0
1
0
2
0
2
0
1
0
0
0
2
0
0
1
0
2
0
2
0
2
0
1
0
1
0
1
0
0
0
2
2
0
0
1
0
1
0
0
1
0
0
0
1
2
0
0
2
2
0
2
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
2
1
1
0
1
1
2
1
2
0
2
0
0
1
1
0
0
2
0
2
0
0
2
0
3
0
0
1
0
2
0
0
1
2
0
1
2
2
0
0
1
1
0
0
0
3
1
0
0
0
0
0
0
0
2
2
1
2
2
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
1
0
0
2
1
0
0
0
0
2
0
1
0
1
1
0
3
2
0
0
0
1
1
0
0
0
0
1
0
1
0
1
2
1
1
0
1
2
2
2
0
2
1
1
0
0
1
0
2
0
2
1
0
0
4
0
1
2
2
0
2
0
0
1
0
1
0
3
2
1
2
0
2
1
0
1
2
0
0
0
5
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
2
0
1
0
0
2
2
2
1
0
0
2
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
1
0
0
0
1
2
0
0
1
1
0
0
0
0
1
1
2
2
0
1
0
0
1
0
1
0
2
0
0
0
2
2
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
1
1
1
0
1
0
1
1
0
0
0
0
2
0
0
0
0
2
1
2
0
0
0
0
0
1
0
0
3
1
0
2
1
2
0
0
0
0
3
0
1
1
3
1
2
1
2
0
1
0
2
0
0
0
0
1
0
0
2
0
2
5
2
1
2
0
2
0
2
0
2
0
3
0
0
0
2
0
0
1
2
1
1
1
1
0
2
7
1
1
1
0
0
0
0
0
1
0
1
1
2
2
2
0
1
1
0
1
0
2
1
0
1
0
0
0
1
0
0
0
1
2
2
2
0
0
0
0
2
0
0
2
0
3
1
1
0
2
0
2
3
0
1
0
0
1
1
0
0
0
0
2
2
2
1
0
1
0
2
2
0
0
1
2
2
0
0
2
0
2
1
0
2
0
1
1
1
2
1
1
0
2
0
1
1
2
0
0
1
1
0
1
0
2
2
0
2
2
0
0
0
1
0
1
1
1
0
2
1
0
0
2
1
1
2
0
1
0
2
0
0
1
0
0
2
0
0
0
0
1
0
2
1
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
2
2
1
2
2
1
1
0
1
0
0
1
0
0
1
1
0
1
1
0
0
0
1
0
0
0
1
2
0
2
2
0
1
1
3
0
0
0
1
2
0
0
0
1
0
2
0
0
1
1
1
1
1
0
0
0
0
0
0
0
2
0
2
0
2
0
0
1
0
1
1
0
0
0
2
0
1
2
1
0
1
1
1
2
0
0
0
1
2
0
2
0
2
0
2
0
0
0
0
0
2
1
0
1
1
0
1
0
2
2
2
0
0
0
0
0
1
0
0
0
1
0
1
2
0
1
1
1
0
0
1
1
1
0
2
1
1
0
1
1
1
1
2
1
2
1
1
2
0
0
2
1
2
0
0
0
1
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
1
0
1
1
1
0
2
0
0
2
0
1
0
0
0
0
0
1
1
1
0
0
0
1
2
0
2
2
0
0
2
1
2
1
1
1
1
1
1
1
2
0
2
2
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
2
1
0
1
2
1
0
2
0
2
1
0
0
0
1
2
0
2
2
0
0
2
2
2
0
2
0
0
0
3
1
1
3
0
0
0
0
0
0
0
0
0
0
0
2
1
1
2
1
0
0
0
0
0
1
1
2
1
1
1
0
1
0
2
0
0
0
1
1
0
1
3
1
0
2
0
0
0
0
0
2
1
0
1
0
0
0
1
0
2
0
0
1
0
2
1
0
1
0
0
0
1
4
0
0
2
2
0
0
0
2
2
2
0
1
0
2
0
2
1
0
0
2
2
0
2
1
0
0
2
1
1
0
0
1
0
0
0
1
0
2
0
1
2
1
0
0
1
0
0
1
0
5
0
0
0
0
0
2
1
2
0
2
0
0
0
1
0
2
0
0
0
0
2
1
0
2
2
0
0
2
1
2
0
0
1
1
2
1
0
0
0
0
2
2
0
0
1
3
2
0
1
0
0
0
1
1
1
0
1
2
0
0
0
0
1
1
1
1
0
1
0
0
0
1
2
1
0
2
0
1
1
3
2
0
1
2
1
0
2
1
1
0
2
0
2
0
0
1
0
0
0
2
0
2
0
0
0
0
1
0
0
0
1
2
2
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
2
0
0
0
2
0
2
0
1
2
2
0
1
0
1
1
0
1
0
1
1
1
2
0
0
0
1
0
1
0
0
0
0
1
0
0
0
2
0
0
0
1
1
3
1
4
1
0
0
1
0
2
2
2
1
2
0
0
0
2
0
0
0
1
1
1
1
1
0
1
0
1
1
0
0
0
0
0
1
0
0
3
0
0
1
0
0
1
1
1
0
0
0
2
0
2
2
1
2
0
1
0
1
0
0
0
0
2
2
0
2
1
1
1
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
1
0
3
0
0
1
1
0
0
1
0
0
0
0
0
0
2
2
0
1
0
0
1
1
0
3
1
2
1
1
0
0
0
1
0
0
0
1
0
1
2
0
1
1
0
1
1
0
2
0
0
3
2
1
0
0
0
0
3
0
1
0
0
0
1
0
0
2
0
2
0
2
1
0
3
0
2
0
0
0
2
4
0
2
0
0
0
0
1
0
1
1
1
2
2
1
1
1
0
2
0
2
2
1
0
2
2
0
1
0
0
0
3
1
0
2
0
0
2
1
0
0
0
0
0
0
2
1
0
1
0
2
0
0
0
1
0
0
1
2
1
0
2
1
1
1
0
2
0
1
0
0
0
0
1
2
0
6
2
0
3
0
1
1
2
2
1
1
0
0
0
0
1
2
0
0
1
0
2
1
0
0
0
0
1
0
0
0
0
1
0
2
0
0
2
2
0
0
0
1
0
0
1
1
0
1
2
1
0
1
2
0
3
2
0
0
2
0
2
0
2
0
2
0
0
0
0
0
0
0
0
1
2
1
2
0
1
2
1
2
0
0
0
0
0
0
1
0
2
1
1
0
1
2
0
2
0
0
0
0
0
2
0
1
1
0
1
1
2
1
3
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
2
1
0
2
0
1
0
0
3
1
1
0
0
2
0
0
0
0
1
0
2
1
2
1
1
1
0
0
1
2
0
2
1
0
2
0
0
0
0
2
0
0
2
0
0
1
2
0
1
0
0
0
0
0
2
1
1
0
2
1
0
1
1
3
0
0
1
0
2
1
0
0
1
2
0
0
1
1
2
1
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
2
1
1
2
0
1
2
0
0
0
1
3
0
0
0
0
0
1
0
1
2
2
2
0
2
0
2
2
1
0
1
0
1
1
1
0
1
0
1
0
2
1
2
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
2
2
0
0
1
2
0
0
0
1
0
1
1
0
1
0
2
2
0
2
1
1
1
1
2
0
1
0
0
1
1
0
0
0
0
2
1
0
1
0
0
1
0
1
2
0
0
0
0
2
1
1
0
0
1
2
1
0
0
0
2
0
1
0
0
0
0
1
0
1
1
0
1
0
2
0
0
2
2
0
0
1
0
2
0
0
0
1
1
2
2
0
0
1
1
0
2
0
1
0
0
2
0
0
2
2
2
1
0
1
0
0
2
2
0
2
0
0
0
1
0
2
1
0
2
0
2
1
0
0
2
1
0
2
3
0
2
0
2
1
1
1
0
2
0
2
0
1
0
1
0
1
2
0
0
1
1
1
0
0
1
0
0
0
2
0
0
1
0
1
1
1
0
1
1
1
2
1
2
0
2
7
2
0
2
2
0
1
2
0
2
0
1
2
0
1
0
1
2
1
0
1
0
1
2
1
2
0
0
2
1
0
2
0
1
1
0
1
1
1
2
0
1
0
0
3
1
0
0
0
0
1
2
0
2
1
0
1
2
1
0
2
0
0
0
1
2
2
0
1
0
0
0
0
0
1
1
1
0
1
1
1
2
0
2
1
1
0
1
1
1
0
0
0
1
1
0
0
0
2
2
0
0
1
0
0
2
0
2
1
2
0
0
0
0
0
1
0
0
0
3
0
1
0
1
1
3
0
0
2
0
2
1
1
1
1
1
1
2
1
0
2
0
0
0
1
0
1
3
0
1
2
1
0
0
0
0
1
1
0
0
0
0
2
1
0
0
0
2
0
0
1
0
0
0
1
0
1
1
0
2
0
0
0
2
0
0
2
0
1
1
0
0
1
0
1
1
0
1
1
1
0
0
1
1
0
2
0
0
0
0
0
0
2
1
1
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
2
1
1
1
1
1
1
1
1
1
2
2
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
1
0
1
1
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
1
0
2
0
1
0
0
0
2
1
0
0
0
2
0
0
1
1
2
0
0
1
1
0
1
0
0
0
0
1
1
0
0
0
0
0
1
3
1
2
1
0
1
2
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
4
2
0
0
1
0
0
1
0
0
0
1
0
0
1
1
0
0
2
0
2
1
0
0
0
0
2
2
0
1
0
0
4
2
2
0
0
0
0
0
1
0
2
0
0
1
2
1
0
3
0
0
1
0
0
1
0
1
1
0
1
3
0
1
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
1
0
0
2
2
0
0
0
0
1
1
0
1
2
0
0
0
1
1
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
2
2
0
1
0
1
0
0
0
0
0
0
0
1
1
1
0
1
0
0
1
0
2
1
2
0
0
1
0
0
1
0
0
0
1
2
0
1
1
2
0
2
0
1
1
1
0
0
2
1
4
1
0
2
1
1
0
0
2
0
0
1
2
2
1
2
1
0
0
0
2
1
1
0
1
0
1
0
1
1
1
0
2
2
2
0
2
0
0
0
2
1
0
0
2
1
0
1
0
0
1
0
2
1
0
2
1
1
0
0
0
3
1
0
0
0
2
2
0
0
2
1
2
1
0
2
0
1
3
0
0
0
0
0
1
0
0
0
0
0
2
1
0
2
0
1
1
0
2
0
0
0
0
0
2
1
0
1
0
0
1
0
1
0
0
2
1
1
1
0
0
1
0
1
2
2
0
1
1
0
2
1
1
1
2
1
0
0
0
1
1
2
4
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
2
2
0
3
2
0
0
1
0
1
1
2
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
1
0
0
2
0
0
1
1
0
1
0
2
2
0
0
0
0
2
1
0
0
1
1
0
1
2
0
0
0
0
1
0
1
0
0
1
1
0
1
1
1
0
0
0
1
0
0
1
0
0
1
0
2
0
2
2
5
0
0
1
0
0
2
0
0
4
0
0
0
0
2
1
0
0
2
1
1
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
2
2
10
0
0
1
1
2
0
0
0
0
0
0
0
0
0
1
0
1
2
2
2
0
2
0
1
1
2
2
0
2
0
0
0
0
1
0
0
2
0
0
0
1
0
2
2
1
1
2
2
0
2
0
0
0
0
0
0
5
0
0
3
0
1
2
1
0
0
1
0
0
0
2
1
0
0
0
0
1
1
0
2
1
2
1
1
0
2
0
0
2
2
2
3
1
1
0
2
2
1
0
0
2
0
2
2
0
2
0
1
1
0
2
0
0
2
2
0
0
1
2
0
0
0
0
0
1
2
0
1
2
1
1
0
0
0
0
0
0
1
2
0
0
0
1
1
1
2
0
0
0
0
1
1
0
1
2
0
0
0
0
0
1
1
0
1
2
1
1
0
0
0
0
2
0
1
2
0
1
1
0
1
2
0
0
0
0
0
1
2
0
2
2
2
2
0
1
2
1
0
0
0
1
0
1
0
0
1
0
1
0
2
2
2
1
0
0
1
0
0
2
0
1
2
0
1
0
1
2
0
0
0
2
0
1
2
0
1
2
0
2
1
1
0
0
0
0
1
0
0
1
0
0
0
0
2
1
2
0
1
2
1
0
3
1
2
1
1
0
0
0
0
0
1
0
1
0
0
1
0
1
1
5
2
0
0
2
0
1
0
0
0
1
0
2
1
2
0
1
1
1
0
2
1
1
0
0
2
3
0
2
0
1
0
1
0
0
1
0
1
1
2
1
0
1
0
0
0
2
0
2
3
0
0
1
1
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
2
0
2
2
2
1
2
0
1
2
2
1
2
1
0
1
2
0
0
1
0
0
0
1
0
1
5
0
0
1
0
0
0
0
2
2
0
0
2
0
0
2
0
0
0
0
1
1
0
0
0
2
2
1
0
4
0
1
1
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
2
0
0
1
0
0
0
0
0
2
2
0
0
1
0
1
0
0
2
0
2
0
2
2
0
0
1
0
0
2
1
0
2
2
1
0
0
0
1
2
0
2
2
0
0
1
2
0
0
2
2
0
2
0
1
3
2
1
0
2
1
0
0
0
0
2
0
0
0
1
1
0
1
1
0
0
0
1
1
0
0
0
1
3
1
1
1
1
0
2
0
0
1
0
0
0
2
0
1
0
0
2
0
1
0
0
1
0
2
1
1
0
1
0
2
0
0
1
2
1
0
0
0
2
2
1
1
0
1
0
0
2
1
0
2
0
2
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
1
0
0
2
2
0
3
1
1
2
0
2
0
0
2
0
2
0
1
0
0
0
1
1
0
2
0
0
0
2
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
2
2
2
0
0
0
0
2
0
2
2
1
0
0
0
2
7
0
1
1
2
2
0
1
0
4
0
2
0
0
1
0
0
0
2
2
1
0
1
1
1
2
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
1
0
0
1
0
1
1
0
0
1
1
0
0
1
0
1
1
0
0
0
0
0
1
1
1
1
2
0
1
0
0
0
0
2
3
0
0
0
0
0
1
0
2
1
0
1
1
0
0
1
0
1
0
0
2
1
2
0
0
0
2
1
1
0
2
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
1
2
2
0
2
2
1
0
0
0
1
0
1
0
0
0
0
1
0
1
1
1
0
2
0
2
0
0
1
1
2
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
1
2
0
2
0
1
2
2
1
1
2
0
1
0
0
0
3
0
2
0
1
3
0
0
0
1
1
2
2
0
2
0
1
0
0
2
0
1
1
0
2
2
2
0
0
0
1
1
1
0
0
1
2
0
0
0
2
0
0
1
0
1
0
0
0
1
2
1
2
2
0
0
1
0
0
0
0
1
1
2
2
2
0
0
2
0
0
0
1
0
0
1
0
0
1
0
0
1
0
1
1
1
0
0
2
0
1
2
0
2
1
2
0
0
1
0
1
1
0
2
1
2
0
0
2
0
2
0
0
2
0
0
1
0
1
0
1
0
2
1
0
0
0
0
0
0
0
2
0
1
1
0
1
0
1
1
0
0
0
2
2
2
0
2
2
0
1
0
0
1
0
0
1
2
0
0
2
0
0
0
0
0
1
2
1
0
0
0
0
0
0
2
0
1
1
0
2
2
0
2
2
0
2
2
3
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
3
1
0
2
1
0
1
0
0
1
2
0
2
0
0
1
2
0
0
0
1
0
0
2
6
0
0
0
4
1
0
2
0
0
1
2
0
0
2
2
0
2
0
0
0
0
0
1
2
3
1
0
2
1
0
1
0
1
0
1
1
2
1
0
0
0
1
2
0
1
2
0
1
0
2
0
1
0
2
0
2
0
1
0
0
3
2
0
0
2
2
0
0
0
0
0
2
1
0
1
1
1
0
1
1
0
0
2
1
1
1
0
3
0
1
0
1
0
0
2
2
2
0
0
1
3
2
1
1
1
2
1
1
0
1
1
2
0
1
0
0
0
2
1
0
0
1
0
2
0
1
0
1
2
0
1
0
0
1
0
1
2
1
0
1
2
0
2
2
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
1
0
0
1
1
2
2
0
1
0
0
2
0
2
1
0
2
0
3
2
0
0
0
0
2
1
0
1
0
0
1
0
1
0
1
0
0
2
2
2
0
0
1
1
0
1
0
1
1
0
1
0
1
0
0
2
0
1
0
1
0
2
1
2
1
1
1
1
0
2
0
0
1
0
2
1
2
2
2
1
1
0
0
1
0
0
0
3
2
0
2
1
0
0
0
1
2
0
0
0
4
1
1
1
0
1
0
1
1
0
0
0
0
0
1
2
1
2
0
0
0
2
2
0
2
2
0
0
0
1
2
0
0
0
0
2
1
2
0
0
1
1
1
2
2
0
0
0
0
0
0
0
2
0
2
2
0
2
0
0
0
0
2
0
0
0
1
0
2
1
1
1
1
1
1
1
2
0
1
2
2
0
0
2
0
0
1
1
0
1
2
0
0
0
1
1
1
0
1
2
0
2
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
2
1
0
2
0
1
2
0
2
0
0
0
0
1
1
2
1
0
0
2
1
0
0
1
1
2
0
0
1
0
0
0
0
2
2
0
0
1
1
1
0
2
1
2
0
2
0
1
0
0
1
2
2
1
1
2
2
2
1
1
0
0
1
1
2
0
0
2
0
1
0
0
1
0
1
0
1
1
0
1
3
1
1
2
0
0
1
0
0
3
0
2
0
0
0
2
0
0
1
0
2
0
1
1
0
0
0
2
0
0
1
0
1
2
1
1
2
0
0
3
0
1
1
0
2
0
2
2
0
2
0
4
1
2
0
1
1
0
2
1
2
1
1
0
1
2
0
0
0
0
0
1
1
0
2
1
1
0
1
1
0
0
1
0
0
1
0
0
0
2
0
0
0
2
2
1
0
0
0
1
0
2
0
2
0
1
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
1
3
2
0
0
0
0
1
1
2
0
1
3
0
0
0
1
0
2
1
0
2
1
0
1
2
0
0
0
2
2
0
3
0
0
0
0
0
1
0
0
1
1
3
2
1
1
1
1
2
1
1
0
0
0
3
0
0
3
2
0
2
0
2
0
3
0
2
2
0
1
0
1
0
1
2
2
1
2
1
1
1
0
1
0
0
1
2
0
0
1
2
0
2
0
0
0
0
0
0
2
2
2
0
0
2
0
1
1
2
0
0
1
0
1
0
2
1
0
2
0
2
0
0
1
0
2
2
0
0
1
0
1
1
0
2
0
0
2
1
1
0
0
2
1
1
0
0
1
1
1
1
0
0
0
1
0
2
0
0
0
0
0
1
0
1
1
1
0
1
1
0
2
0
0
0
0
0
1
0
0
0
1
0
1
0
1
1
0
1
0
0
2
2
0
0
1
3
0
2
1
2
1
1
1
1
1
1
1
1
3
1
1
2
0
2
0
0
1
0
2
0
0
2
2
3
0
0
1
0
0
0
1
2
0
0
1
1
0
1
0
2
1
0
1
1
0
0
0
0
0
1
1
1
0
1
1
0
2
0
1
1
0
0
1
1
1
4
2
0
1
2
2
0
0
2
2
0
1
1
0
1
0
4
0
0
0
2
2
0
1
2
0
0
2
1
0
2
2
0
2
1
2
1
0
0
2
0
0
0
1
0
0
0
1
1
2
1
0
2
1
2
3
0
1
0
0
0
1
0
0
1
1
0
2
0
0
0
0
1
1
0
0
0
1
0
1
0
1
0
0
0
2
2
1
2
0
0
2
0
0
2
1
0
1
0
0
2
2
0
1
2
2
2
2
0
0
0
3
0
3
0
2
0
2
2
1
0
1
0
0
2
0
1
0
0
0
0
1
0
0
1
2
2
1
1
0
2
1
0
0
0
2
0
0
1
1
2
1
1
1
1
0
2
0
0
1
0
1
0
0
1
0
0
1
2
1
0
1
0
3
0
2
0
0
0
0
2
0
2
0
1
0
1
0
0
0
3
0
0
2
1
0
0
2
0
0
0
1
1
0
0
0
2
1
1
0
0
0
1
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
2
1
1
0
0
2
1
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
1
0
0
0
2
0
0
0
0
1
0
0
0
1
3
0
0
0
0
0
0
1
0
0
1
1
2
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
2
1
1
1
2
0
2
0
0
0
1
2
0
1
0
1
4
0
0
0
0
1
0
2
0
1
0
0
2
0
2
0
0
2
0
1
2
0
1
0
0
2
0
1
2
1
2
0
1
0
2
0
2
0
2
1
1
0
0
2
0
2
0
0
2
1
3
1
0
1
2
1
0
2
0
0
0
0
2
0
0
0
0
0
0
2
2
0
2
2
0
2
1
0
0
0
1
1
1
1
2
1
0
2
0
0
0
2
1
0
0
0
1
0
0
0
0
0
2
0
2
1
0
0
0
1
0
1
2
3
2
0
1
2
0
0
0
0
1
0
1
0
0
2
0
1
0
0
1
0
0
0
1
0
0
0
2
1
1
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
1
1
1
2
2
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
1
1
0
0
0
1
2
0
1
2
1
3
2
0
0
0
0
0
2
0
0
1
1
1
0
1
0
0
1
0
0
1
0
1
2
0
1
0
1
1
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
1
1
1
2
0
1
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
2
0
1
0
4
2
1
0
1
2
3
2
0
1
0
0
1
2
1
0
0
2
2
1
3
1
1
1
1
1
1
0
0
0
2
0
0
1
0
1
0
2
2
0
1
2
0
1
0
1
1
2
2
0
0
0
0
2
1
0
0
0
0
2
1
2
1
1
1
1
2
0
2
0
0
2
1
0
0
0
2
0
2
0
0
1
0
0
1
1
0
1
1
0
0
1
0
2
1
0
2
0
2
0
0
0
1
0
0
0
0
2
0
0
2
1
0
0
0
1
2
0
1
2
1
2
1
1
0
0
2
1
0
2
1
1
0
2
2
0
0
2
2
2
0
1
0
2
2
2
1
0
1
0
0
2
2
0
0
0
0
1
0
0
1
0
0
0
2
0
2
1
2
2
1
2
0
0
0
1
1
1
1
0
2
0
0
1
0
1
0
2
0
2
0
1
2
0
0
3
0
1
2
2
0
2
0
1
0
0
0
0
0
2
1
6
0
0
1
1
2
0
1
0
1
0
1
1
0
0
1
1
0
1
0
0
1
1
1
1
0
1
0
2
1
1
0
2
0
0
1
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
2
1
0
0
1
1
2
1
1
0
0
0
2
0
0
1
1
0
2
0
0
2
0
0
0
1
0
0
2
0
0
1
0
2
1
2
1
0
0
0
0
2
0
0
0
0
0
1
1
0
0
1
2
0
1
0
0
0
0
2
1
0
3
3
0
0
0
0
0
0
0
2
1
1
1
0
0
2
0
1
0
1
2
2
1
2
1
0
1
2
2
0
0
2
1
0
2
0
0
1
2
0
0
1
1
1
1
0
0
0
2
0
1
0
1
0
0
1
0
0
3
0
2
2
0
1
0
0
2
2
0
1
1
1
2
0
0
2
0
0
0
2
1
0
1
2
0
0
1
1
0
0
0
5
1
1
1
0
0
0
0
1
1
0
1
0
0
2
0
0
2
0
0
0
0
2
0
1
0
1
1
3
2
2
0
0
1
1
2
2
0
0
1
0
0
0
0
0
3
1
0
0
1
0
1
1
0
1
1
0
1
0
0
2
1
0
0
0
2
1
0
2
0
1
0
0
1
0
0
1
1
1
0
1
1
0
1
2
2
1
1
0
0
0
0
1
1
0
1
0
5
1
1
1
1
1
0
0
0
0
2
0
0
0
1
0
1
1
1
0
0
0
0
2
2
1
0
0
0
0
0
1
0
0
2
1
0
0
2
0
2
0
0
2
1
2
0
1
1
0
0
2
1
0
0
0
1
0
1
0
0
1
2
0
0
0
1
2
0
2
1
1
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
2
2
2
0
0
2
1
0
0
0
2
1
0
0
2
0
1
0
2
0
1
0
2
1
2
0
0
0
2
1
0
0
1
0
0
2
0
1
0
3
0
2
0
2
1
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
2
0
0
0
2
0
0
0
2
0
0
1
1
0
0
2
2
1
0
0
2
0
0
2
1
0
1
1
0
0
0
2
2
0
2
0
0
1
0
2
2
1
0
0
2
0
0
0
1
3
1
2
0
0
2
0
0
1
2
0
0
0
0
2
2
0
0
0
2
0
2
2
0
1
1
0
3
2
1
0
0
0
0
1
1
0
2
0
0
1
2
2
1
0
2
2
2
0
0
0
1
2
4
0
0
1
2
0
2
0
1
0
1
2
1
1
0
0
0
0
0
0
2
1
2
0
0
0
0
0
2
1
0
1
1
0
0
0
1
0
0
0
1
1
1
1
3
0
2
0
1
0
1
0
1
0
2
0
0
1
0
2
4
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
1
2
0
1
0
1
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
2
1
1
0
0
0
1
2
2
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
2
1
1
0
0
0
1
2
0
1
0
1
1
1
0
0
0
1
0
2
0
2
2
2
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
1
0
0
0
0
1
2
1
0
0
1
0
0
0
4
2
0
1
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
1
0
2
1
1
0
1
2
1
0
1
1
0
2
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
2
0
3
0
2
1
0
0
0
1
0
1
2
1
0
2
1
0
0
0
1
0
0
0
2
0
0
0
2
0
1
2
0
0
2
0
2
0
3
0
0
0
0
0
0
0
1
0
0
0
2
2
0
1
1
0
1
0
0
1
1
3
1
2
0
0
1
1
0
1
0
0
2
2
1
1
0
0
1
0
0
0
1
2
1
1
0
0
0
2
0
0
2
1
2
2
0
1
1
1
1
0
1
1
1
2
1
0
0
0
1
0
1
2
0
0
2
1
3
1
1
0
2
1
0
0
2
0
0
1
1
1
0
0
0
1
0
0
0
2
1
0
0
2
1
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
2
1
2
1
1
0
0
0
1
0
1
0
2
0
0
5
0
0
0
1
0
0
1
1
1
0
1
0
3
2
2
2
1
0
2
0
2
1
0
0
2
0
1
3
0
0
0
1
1
1
1
1
0
1
0
2
0
0
1
0
0
0
1
2
0
1
1
1
1
1
0
0
0
2
2
0
1
2
1
1
0
3
0
2
0
0
1
0
1
0
0
1
1
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
1
1
1
1
0
0
1
0
0
1
0
2
1
2
1
0
0
0
1
0
0
0
0
0
2
1
2
1
1
0
0
0
0
1
0
0
1
0
0
2
2
0
0
0
1
2
0
2
0
0
0
0
1
1
0
0
1
1
0
2
0
0
2
0
2
0
1
0
1
1
1
0
1
1
1
2
2
1
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
1
0
0
2
2
0
2
1
0
1
0
1
1
0
0
0
0
1
1
0
1
1
0
1
0
0
0
1
0
3
0
0
0
0
1
1
0
0
1
2
0
2
1
0
2
0
2
1
2
0
2
1
0
0
0
6
1
0
0
0
4
0
2
0
1
1
1
0
2
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
1
0
2
4
1
1
0
1
2
0
0
0
0
0
0
1
2
0
1
2
0
0
0
2
1
1
2
0
2
0
1
0
2
0
0
0
2
1
0
0
1
1
1
2
2
0
0
2
1
0
2
0
0
2
0
2
0
0
2
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
3
0
2
1
1
0
2
0
2
1
0
0
2
2
0
3
1
2
0
0
2
0
0
1
1
0
0
0
1
1
0
0
0
2
1
0
1
0
2
0
2
0
1
2
1
0
0
0
0
0
0
0
3
1
0
0
0
1
0
0
1
0
0
0
0
0
0
2
3
0
1
0
4
0
2
0
0
1
1
0
0
0
0
1
1
1
0
2
0
1
1
1
1
0
1
0
1
1
1
0
1
2
2
0
0
0
1
0
2
2
1
0
2
0
3
0
2
2
0
0
2
0
0
0
0
0
0
2
0
2
0
0
2
0
0
2
0
0
0
0
0
1
1
0
3
0
1
1
0
1
3
1
1
1
1
0
2
1
1
2
0
2
0
0
0
0
1
2
0
1
1
0
0
0
1
0
1
1
0
0
3
0
2
0
0
1
0
0
1
0
1
2
0
0
2
1
0
0
0
0
1
1
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
1
1
1
2
0
0
1
1
1
0
3
0
0
0
2
0
0
0
0
2
0
0
0
0
0
3
1
1
0
2
0
1
1
1
0
2
1
2
1
0
1
0
3
0
0
0
0
1
0
1
1
1
0
0
0
2
0
1
0
1
2
0
1
1
1
2
0
1
0
0
2
0
0
0
2
2
2
0
0
1
2
1
0
0
0
2
0
1
0
1
0
0
2
0
0
4
3
2
0
0
0
2
2
2
1
0
0
0
1
0
1
0
0
3
1
0
1
0
1
0
2
0
0
2
0
1
0
0
1
0
1
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
1
0
2
2
1
1
0
2
1
2
0
0
0
0
2
0
0
0
0
1
0
0
2
1
2
0
2
2
1
1
0
0
0
1
0
1
1
0
0
1
0
0
0
1
0
0
2
0
0
2
1
1
2
1
2
0
1
3
0
1
0
0
1
2
1
1
0
2
0
2
0
1
0
1
0
0
0
0
1
2
0
1
2
0
0
1
0
2
1
0
1
2
1
2
0
1
0
0
0
0
0
0
1
1
0
0
2
1
0
1
0
1
0
1
1
2
2
2
1
2
2
1
0
0
1
1
0
2
1
2
1
0
0
0
0
0
0
0
2
2
0
2
0
2
0
2
1
2
0
0
1
0
1
0
0
0
0
0
0
4
0
2
1
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
2
1
1
0
0
2
0
2
2
0
2
0
0
0
2
0
1
0
1
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
1
3
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
2
2
2
0
0
0
1
1
2
0
0
1
1
0
0
2
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
1
1
0
1
1
0
0
0
0
2
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
1
0
1
0
1
0
1
0
2
1
2
2
1
1
2
0
1
1
0
2
0
0
0
1
1
2
0
2
1
0
0
0
0
0
0
0
1
0
1
2
4
0
0
0
0
1
0
0
1
2
3
2
0
1
0
0
0
0
0
2
0
2
0
1
0
0
0
3
0
0
1
0
1
0
1
1
0
1
0
3
0
1
0
0
0
2
0
1
0
2
0
2
1
1
0
0
0
2
0
0
1
1
0
0
2
0
2
2
3
2
0
0
0
2
0
0
0
0
0
0
1
2
2
0
2
1
1
0
0
0
1
1
0
2
0
2
0
0
0
1
2
2
0
0
1
1
3
0
0
0
1
0
2
0
2
0
0
1
1
0
0
1
1
2
0
1
0
0
0
1
0
1
0
2
1
1
2
1
1
0
0
2
2
2
0
0
1
2
0
0
0
1
2
0
0
0
0
0
0
2
1
0
0
0
0
1
0
1
0
0
2
1
1
0
0
2
1
0
0
1
0
0
0
1
1
0
0
0
1
1
0
0
0
0
1
1
0
0
1
2
0
2
0
3
2
1
1
0
0
1
3
1
0
1
0
1
0
1
2
1
2
1
1
2
0
0
1
0
1
0
0
0
2
1
0
0
0
0
1
2
0
1
0
1
0
1
1
1
2
2
2
0
2
0
1
0
0
0
1
1
2
0
1
0
2
0
1
0
2
0
0
0
1
2
0
0
2
0
0
1
1
0
1
2
0
0
0
1
0
0
1
0
0
2
0
1
1
2
1
0
0
1
0
0
0
1
2
0
1
1
1
2
3
1
1
1
2
1
0
1
0
0
2
0
0
2
0
2
0
0
1
0
0
2
1
1
1
0
2
1
2
0
1
1
2
1
0
2
0
2
1
0
5
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
1
3
0
1
1
2
2
1
1
2
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
2
0
0
2
1
2
2
0
0
2
0
2
0
1
0
1
0
1
0
0
2
1
0
1
2
0
1
1
2
0
2
4
0
1
0
1
0
0
0
0
2
1
2
0
2
0
1
0
2
1
1
0
2
0
0
1
0
0
1
1
1
1
1
0
2
0
0
2
1
0
0
0
2
2
1
2
0
0
1
0
1
2
0
1
0
3
0
2
2
1
1
1
0
1
1
1
0
2
0
1
0
0
0
0
0
1
0
0
3
0
1
2
1
0
0
2
0
2
1
0
0
0
1
1
2
0
0
2
1
0
1
0
0
0
0
1
2
0
1
1
0
0
1
1
0
2
0
0
2
0
0
1
1
3
1
1
0
0
0
2
0
1
2
2
1
1
0
2
0
0
1
1
1
1
0
0
3
0
0
0
2
1
0
0
0
1
2
0
2
2
2
0
0
0
1
1
0
1
0
1
0
1
0
2
0
1
0
0
0
0
0
1
1
0
1
2
1
1
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
1
0
0
0
0
2
1
0
1
0
0
2
2
1
2
2
2
1
1
0
0
1
0
1
0
1
0
2
1
0
1
0
0
2
1
2
0
0
0
2
0
0
2
0
2
0
0
2
1
2
0
0
1
1
1
2
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
1
0
2
1
0
0
0
1
1
0
0
0
0
0
0
1
0
1
1
1
1
0
0
2
0
0
2
4
0
2
1
0
0
0
3
3
1
2
1
0
0
0
1
2
0
1
0
2
0
0
0
0
2
1
0
2
0
0
2
0
0
2
0
0
2
0
1
3
2
0
0
1
0
0
0
2
1
1
0
0
1
0
1
1
1
3
0
1
0
2
0
0
1
0
2
0
1
0
0
0
1
2
1
0
1
1
1
2
0
2
1
1
1
0
0
1
0
1
0
2
0
2
0
0
0
1
1
0
1
1
1
0
2
1
0
2
0
2
1
1
1
0
1
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
1
2
1
0
0
0
0
2
0
0
1
1
0
1
0
1
0
0
0
0
1
1
0
2
1
1
0
0
0
0
1
0
0
2
0
1
0
0
0
2
0
0
0
0
1
0
0
1
2
2
2
0
0
0
0
1
0
2
0
1
0
2
0
0
1
2
1
0
0
2
0
0
0
1
0
0
2
1
0
0
0
2
0
0
2
0
2
2
1
1
1
2
1
1
3
0
1
0
0
2
1
0
0
2
2
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
1
0
0
0
2
2
0
1
0
3
0
1
0
1
1
0
1
1
0
2
0
0
1
0
0
0
0
0
1
0
0
3
1
0
0
0
0
0
1
1
1
0
0
0
0
1
1
0
1
3
0
2
1
0
0
1
0
1
1
0
0
0
2
0
1
2
0
0
0
0
2
1
0
0
2
0
0
0
1
2
0
0
0
0
0
0
1
0
2
1
0
0
0
0
1
0
0
1
0
2
2
0
0
0
0
0
0
2
0
1
0
2
0
0
2
0
0
0
2
0
2
1
0
2
0
1
0
0
1
2
0
1
1
1
0
0
1
2
0
1
2
0
0
2
0
0
2
1
1
0
1
0
0
2
1
0
0
2
0
2
0
0
0
0
0
1
1
2
0
0
0
1
0
0
1
0
1
1
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
1
0
1
2
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
1
2
1
2
0
0
0
1
1
0
1
1
1
0
3
0
0
1
1
2
0
1
0
0
0
1
2
1
1
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
2
0
0
2
2
1
2
0
0
0
2
2
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
2
1
1
0
1
1
0
0
0
1
0
1
0
2
0
1
0
0
0
1
0
1
0
0
0
1
0
0
1
0
2
1
0
0
1
0
0
1
0
1
2
0
0
0
2
1
0
1
1
0
1
1
2
0
0
2
1
0
0
1
1
2
3
0
0
0
0
0
1
2
1
0
2
0
2
1
2
2
0
0
1
0
1
0
0
0
0
3
0
0
0
1
1
0
1
2
10
2
1
0
0
0
2
0
0
1
1
2
0
0
0
0
1
1
0
0
1
2
3
0
0
0
1
0
1
0
2
1
0
4
0
2
0
0
0
0
1
1
0
1
0
2
1
0
1
0
0
0
1
0
1
0
1
0
0
2
1
1
1
0
0
1
1
1
2
0
0
1
2
0
0
0
2
1
1
0
3
0
0
0
0
0
3
1
1
0
2
2
2
2
1
2
1
0
0
2
0
2
0
1
1
0
0
0
2
0
2
0
0
0
0
2
0
2
0
1
1
1
1
1
0
2
1
0
0
1
0
0
1
1
0
1
0
2
2
0
1
0
1
0
1
1
1
0
1
0
2
1
0
2
0
0
2
0
1
1
2
0
1
0
0
1
0
0
0
2
3
0
1
0
1
1
0
1
1
2
2
0
0
3
2
1
0
0
0
0
0
0
1
0
0
1
1
0
1
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
1
1
0
0
0
1
0
0
0
0
1
0
0
2
0
0
2
0
2
0
0
1
1
2
0
5
1
1
0
2
1
0
0
1
1
0
0
0
0
1
0
3
0
0
1
0
0
2
2
2
1
0
0
1
0
2
0
0
0
1
1
0
0
0
0
0
2
0
2
2
0
0
0
0
0
1
0
2
2
0
0
1
0
0
0
2
0
4
0
1
0
1
0
0
1
0
6
3
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
1
0
1
0
0
1
0
0
1
0
2
1
0
1
0
1
0
1
0
0
1
2
2
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
2
1
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
1
1
2
2
2
1
0
2
1
0
0
0
0
0
1
2
1
1
1
2
0
0
0
0
0
1
0
2
1
0
0
0
2
0
0
0
1
1
2
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
2
0
2
0
2
1
1
0
1
2
2
2
2
0
2
0
0
0
0
2
0
0
0
1
7
2
0
0
0
2
1
0
1
0
0
2
1
0
4
2
0
2
2
0
0
1
2
1
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
2
1
1
2
0
1
0
1
1
0
2
0
0
0
0
2
1
0
0
0
1
1
2
1
1
0
1
2
0
0
1
0
0
1
3
0
1
2
1
0
0
0
0
0
2
1
0
1
0
0
1
1
2
0
0
2
0
2
1
0
1
1
0
0
0
0
1
0
1
0
1
0
1
0
0
1
2
1
0
3
0
1
2
0
3
0
1
2
0
0
2
2
0
1
0
0
1
0
2
0
2
1
0
0
1
0
1
0
1
0
0
0
1
0
2
0
0
2
1
2
0
1
1
2
0
0
2
0
1
0
2
0
0
1
2
0
1
0
1
0
0
0
0
2
2
0
0
0
1
0
2
1
1
0
1
1
0
2
0
0
0
0
0
0
1
2
2
2
0
1
0
1
0
0
1
2
3
1
1
1
2
0
2
1
2
0
1
1
0
0
2
0
2
0
2
1
1
0
0
0
0
2
0
0
0
1
1
0
0
0
2
0
0
0
0
1
2
0
0
0
1
2
1
0
2
0
1
0
0
1
0
0
1
0
0
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
1
0
2
1
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
2
0
2
1
0
0
0
0
2
2
2
1
0
1
0
1
1
0
0
1
1
1
2
2
0
1
0
0
0
2
1
2
0
1
1
1
0
0
0
1
0
2
0
0
1
1
2
0
0
0
0
0
0
0
0
0
2
0
1
1
1
1
2
1
0
1
0
0
1
2
2
0
1
0
0
0
0
4
5
1
0
0
0
0
0
1
0
1
0
2
2
0
2
2
1
0
0
0
0
1
0
2
0
0
0
2
2
1
0
2
0
0
1
0
0
0
1
0
0
2
0
2
1
1
1
0
0
0
0
3
1
0
0
0
0
1
1
0
0
2
2
0
1
0
2
0
0
1
0
1
0
1
0
2
0
1
0
0
0
2
0
0
2
1
1
0
0
0
0
1
1
1
1
0
0
1
0
1
0
0
1
0
0
2
1
1
0
2
1
1
2
0
1
2
2
2
0
0
0
1
1
0
1
0
3
0
1
2
2
1
1
0
0
2
2
2
2
0
2
1
0
2
1
0
0
0
0
2
0
1
0
0
0
2
0
2
4
1
0
0
2
0
1
2
0
0
0
0
0
1
1
0
0
1
2
0
2
2
0
2
0
0
0
1
0
1
0
0
1
1
0
2
1
1
0
1
0
0
0
2
1
0
0
1
2
1
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
2
1
0
1
0
2
0
2
0
3
2
0
0
1
1
0
1
0
2
3
1
1
0
0
0
0
1
2
0
1
2
0
2
1
2
0
0
1
0
0
0
1
0
0
0
0
1
1
0
1
0
0
2
1
2
0
0
1
0
1
0
0
0
0
1
2
2
0
2
0
2
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
1
0
0
5
0
1
0
0
2
0
0
2
1
2
0
0
1
0
1
1
0
1
0
1
2
2
2
0
0
0
2
0
0
0
0
1
0
0
2
1
0
1
0
0
2
0
1
0
0
1
0
0
1
0
0
2
0
0
1
0
0
0
0
1
2
0
0
0
1
2
0
0
1
2
2
0
1
0
0
1
1
0
2
0
0
0
0
0
2
2
5
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
2
0
1
0
1
0
0
0
0
0
2
0
0
2
1
0
0
2
0
0
1
1
0
0
1
0
0
2
4
0
2
0
0
2
0
0
1
1
2
0
0
1
1
0
0
1
0
0
2
1
0
0
1
0
0
2
0
1
1
0
1
1
1
1
0
2
0
1
2
0
2
0
0
0
1
0
0
1
0
0
1
1
1
1
3
1
1
1
0
2
0
1
0
0
0
0
1
1
1
0
0
1
0
0
1
2
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
2
0
2
1
0
1
0
0
0
0
1
1
2
0
1
1
2
0
4
1
0
0
2
1
0
2
0
2
0
0
0
0
0
2
2
2
0
2
0
0
0
2
0
0
0
0
3
0
0
0
0
0
1
0
0
6
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
3
2
1
0
1
0
1
0
1
1
1
1
1
0
0
1
0
0
0
1
2
0
0
1
3
0
1
0
0
0
0
1
2
1
1
2
1
2
0
0
1
0
0
0
2
0
0
1
2
0
1
2
1
2
0
0
2
1
0
2
0
2
0
0
0
0
0
0
2
2
0
1
0
0
1
2
0
0
1
1
2
0
2
0
0
3
0
1
1
0
0
1
1
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
1
0
1
2
0
0
1
1
0
0
1
0
2
0
0
2
2
1
0
0
0
2
0
1
1
0
0
1
1
1
2
0
0
2
0
1
0
0
0
0
0
2
0
2
0
1
0
2
1
0
0
1
1
2
0
1
0
0
1
0
2
0
0
1
2
2
4
0
0
0
1
0
2
0
1
1
1
1
1
2
1
0
1
2
0
1
2
1
0
1
0
2
2
0
1
1
0
1
0
0
0
2
2
1
2
2
0
1
0
0
0
2
0
1
2
0
0
0
1
1
2
0
1
0
2
2
3
2
2
1
2
0
2
1
0
0
0
0
0
1
1
0
1
1
0
0
1
1
0
1
0
0
0
0
0
2
0
2
2
2
0
3
0
0
2
0
2
0
0
0
0
0
0
0
2
0
2
1
7
0
0
0
2
1
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
2
2
0
2
0
0
0
2
0
0
3
2
0
2
0
0
2
0
0
0
0
0
1
1
1
1
0
0
0
0
2
0
0
2
2
2
1
2
1
2
2
2
2
1
0
1
0
2
1
3
0
1
0
2
0
2
0
1
1
2
0
1
1
0
0
0
0
0
0
1
1
3
1
1
0
2
2
1
2
2
0
0
2
0
0
0
0
0
0
1
1
0
1
1
2
2
1
1
1
0
0
1
0
0
0
2
0
2
0
0
4
0
0
0
0
0
2
0
2
1
0
1
1
1
2
0
0
0
1
2
0
2
0
2
0
1
1
0
0
3
1
0
0
1
1
0
2
0
2
1
0
1
1
1
0
2
0
0
0
0
1
0
0
0
1
0
0
4
0
1
0
1
0
2
0
2
1
0
1
1
4
2
0
0
0
0
2
2
0
1
0
1
0
1
1
0
0
0
1
0
1
0
2
1
1
1
2
1
1
0
0
1
0
2
0
1
0
0
0
0
0
2
0
0
1
0
0
1
0
2
0
0
0
1
0
2
2
0
2
0
0
2
1
2
1
1
0
2
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
1
1
2
0
0
0
0
1
1
0
0
2
1
1
1
1
1
1
1
0
2
1
0
2
4
0
0
0
0
2
0
2
0
0
1
2
0
1
0
1
1
0
0
1
1
1
0
1
2
2
2
0
2
0
0
0
0
2
1
1
2
0
1
0
0
2
1
0
1
1
0
0
0
0
1
0
2
1
0
1
0
2
3
1
0
1
2
2
0
2
0
0
2
0
0
3
0
2
1
0
1
0
0
2
1
2
0
0
0
0
2
2
0
2
4
0
1
1
0
0
0
0
0
0
1
1
1
2
2
0
1
1
2
1
1
1
0
0
1
0
1
2
0
0
3
1
2
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
1
2
1
0
1
2
0
0
0
0
1
1
0
0
0
0
0
5
1
1
0
0
0
0
0
0
2
2
2
1
0
0
0
1
1
2
2
0
1
2
0
0
1
0
2
0
1
0
2
0
1
2
1
2
0
0
2
0
0
2
0
1
1
1
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
1
1
0
0
0
2
1
1
2
1
3
1
0
0
0
1
1
1
1
0
0
0
0
1
1
0
1
0
1
0
0
0
2
0
1
0
1
0
1
0
0
2
2
2
0
0
0
2
1
0
2
1
2
2
1
0
3
0
0
0
0
0
1
0
1
1
1
1
0
1
0
0
0
0
0
0
2
0
0
2
0
1
0
0
2
1
0
0
2
1
1
1
1
2
1
0
0
2
0
3
0
2
2
0
0
1
0
0
0
0
2
2
0
0
1
2
0
0
0
1
1
0
0
1
2
0
1
0
0
0
1
1
0
2
0
0
1
0
0
0
1
0
2
2
2
0
0
1
1
0
2
1
0
0
2
1
2
0
0
0
0
1
1
2
0
0
0
2
0
2
1
2
1
0
2
2
0
1
1
2
0
1
1
0
0
0
1
0
1
0
0
1
0
2
1
0
0
1
0
1
0
1
2
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
1
2
2
1
1
0
2
1
1
1
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
2
0
1
1
0
0
0
0
1
1
1
3
2
0
0
0
0
1
0
2
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
2
1
0
0
2
0
0
0
0
2
0
1
0
1
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
2
0
2
1
0
1
0
0
1
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
1
2
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
2
0
0
1
0
0
0
2
2
1
0
1
0
2
0
2
2
0
0
1
0
0
0
0
0
2
2
2
1
0
0
2
0
0
0
0
0
1
0
0
0
1
0
1
0
2
0
0
1
1
1
0
0
0
2
2
0
1
1
0
1
2
1
0
1
2
0
1
1
0
3
2
2
0
2
0
0
2
2
0
2
1
0
2
1
1
1
1
0
1
0
0
1
0
0
0
1
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
1
2
0
2
2
0
0
1
0
0
2
0
2
0
0
1
0
0
2
2
0
1
0
0
1
0
1
1
0
0
0
0
0
2
0
2
2
2
2
1
1
0
0
1
0
2
0
0
0
2
1
0
2
0
2
0
1
1
0
2
1
0
0
0
0
3
1
1
2
0
1
0
0
0
1
0
0
0
2
1
1
2
2
1
0
2
2
0
0
0
0
0
1
1
1
2
1
0
0
0
2
1
0
0
3
1
0
0
0
1
0
2
0
2
0
0
1
1
0
0
1
0
1
0
1
0
0
0
1
2
2
0
0
1
0
0
2
1
0
1
0
0
0
1
0
0
1
0
1
0
2
0
2
2
0
0
0
2
0
0
1
0
0
0
2
1
0
0
1
1
1
0
0
0
1
2
0
0
1
1
0
2
0
0
0
1
0
1
1
2
1
1
1
0
0
0
1
0
2
1
1
1
0
3
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
2
1
2
0
1
0
0
2
0
1
0
0
0
1
0
0
1
0
0
2
0
0
2
2
0
0
1
1
2
2
2
0
1
1
1
2
1
0
2
0
0
0
1
2
0
1
1
0
0
0
0
3
0
0
2
2
0
0
0
2
0
0
3
0
1
1
1
0
1
0
0
0
0
1
1
0
2
0
1
0
1
2
2
0
0
0
0
0
0
0
1
0
0
1
1
0
1
1
1
2
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
1
1
3
0
0
0
2
0
0
0
1
0
0
2
2
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
2
0
2
1
0
2
1
0
0
0
0
1
1
1
0
0
1
0
0
1
1
0
2
0
0
0
0
0
2
0
1
3
1
0
2
4
0
1
0
0
1
1
2
0
0
0
1
3
0
0
0
1
1
0
0
0
0
1
1
0
0
1
2
0
0
0
0
1
0
1
1
0
0
0
1
1
0
1
0
0
0
1
1
0
2
1
0
1
0
0
0
0
2
0
0
2
0
0
0
2
2
0
1
0
0
0
0
1
0
0
0
0
0
1
2
1
0
1
1
0
0
0
0
1
2
1
0
1
0
0
0
0
0
0
1
2
0
2
1
0
1
1
2
1
0
1
0
0
0
0
0
2
0
2
0
1
0
2
0
1
0
2
1
1
1
0
1
2
3
0
0
0
1
0
0
0
1
0
0
1
0
2
0
1
1
0
2
2
2
0
0
1
2
1
0
0
0
1
1
0
2
1
0
2
0
2
0
0
2
0
2
0
0
0
1
2
0
2
1
2
0
0
0
0
1
2
0
0
2
1
0
0
0
0
0
0
0
0
1
1
0
2
0
2
0
0
0
2
0
1
2
0
1
0
2
1
0
0
1
0
0
1
2
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
1
2
0
0
0
2
2
1
2
0
0
1
2
0
0
3
1
0
0
1
0
1
2
1
0
0
0
1
1
2
1
0
0
0
1
0
1
1
1
0
1
0
1
0
2
0
1
2
0
0
0
0
0
0
2
2
1
0
1
0
1
0
1
0
2
2
2
1
1
1
1
0
2
0
1
0
1
1
0
0
0
0
0
2
0
0
1
2
2
0
1
1
1
2
0
2
0
2
1
2
0
0
2
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
1
0
0
1
0
0
1
0
0
0
1
1
0
0
2
0
2
2
2
1
0
0
0
3
1
0
1
0
1
1
1
1
2
2
0
0
0
2
0
1
0
1
2
1
3
0
0
2
0
2
0
2
0
0
0
1
1
2
0
1
1
0
0
0
1
2
0
1
1
0
0
1
2
2
0
0
1
0
0
1
1
0
1
0
0
0
0
1
1
1
2
0
2
1
0
0
0
0
1
1
1
0
0
1
0
2
1
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
1
1
1
3
0
3
2
0
0
0
0
0
0
0
0
0
1
2
0
1
2
0
0
0
1
0
0
0
3
2
0
0
0
2
2
0
1
0
0
1
0
2
0
0
1
1
1
1
0
0
1
0
1
1
0
2
1
0
0
1
2
0
1
0
1
0
0
0
3
0
0
0
0
1
1
3
0
0
1
1
0
0
0
0
0
2
0
1
2
0
1
0
0
0
2
2
1
2
0
1
0
0
0
0
1
0
2
0
1
0
0
1
1
0
0
2
3
2
0
0
0
1
0
0
0
1
0
0
2
0
2
1
2
2
0
0
0
2
1
1
2
1
0
1
0
0
1
1
0
0
1
2
0
0
0
1
3
0
0
1
0
1
0
0
0
1
0
1
1
0
0
0
2
1
0
0
1
0
1
1
1
1
1
1
0
2
0
0
2
1
1
1
0
1
1
1
0
0
4
0
0
0
0
1
1
1
2
2
0
1
0
1
0
2
1
0
0
0
0
2
2
1
1
1
1
2
1
2
0
1
0
2
0
0
0
0
2
1
0
0
0
1
0
0
1
0
3
0
0
2
1
0
5
1
2
1
0
0
2
2
1
0
2
0
1
0
0
0
2
2
0
0
2
0
0
1
1
0
1
0
0
0
1
0
0
1
1
0
0
0
0
2
1
0
2
1
1
1
2
1
0
1
1
2
1
1
1
0
0
1
0
1
2
1
2
1
0
0
1
1
0
0
0
2
0
1
0
1
2
1
0
2
1
2
1
0
0
0
0
3
0
1
0
0
0
0
0
0
1
0
1
1
0
1
2
0
0
1
0
1
0
1
0
1
0
1
0
0
2
1
0
0
0
1
0
2
0
1
0
0
1
0
0
1
0
2
2
1
2
0
1
0
2
0
1
0
1
0
0
2
0
0
0
0
1
0
0
0
2
3
0
0
1
0
0
0
0
1
1
0
3
1
0
1
1
2
3
1
2
0
3
1
0
2
0
3
0
0
2
0
1
2
1
2
1
0
1
0
2
2
0
2
0
2
0
0
2
0
2
0
1
0
0
2
0
2
0
0
0
2
1
0
1
1
1
1
0
0
1
0
0
0
1
0
2
1
0
1
1
0
0
1
1
1
2
0
0
2
2
1
0
0
0
1
0
1
0
2
0
0
0
2
1
0
2
1
1
1
0
1
1
0
2
0
2
0
0
0
0
0
0
2
0
2
1
0
2
0
0
5
0
0
0
0
0
0
0
0
1
0
1
1
0
0
2
0
2
0
1
0
1
0
0
1
1
0
1
1
0
2
1
0
0
0
1
0
2
1
0
1
1
0
0
0
0
2
0
0
1
1
0
0
1
0
1
2
0
1
1
0
0
0
0
0
0
0
2
0
0
0
2
2
1
2
1
1
0
2
1
1
0
0
0
2
0
0
0
0
0
1
1
0
0
2
0
0
2
0
0
2
1
2
0
1
0
0
0
1
0
2
2
1
0
2
1
1
2
1
0
0
1
0
2
0
1
4
0
0
1
0
0
2
1
0
0
1
0
0
0
1
0
1
0
1
0
1
1
2
2
1
0
1
2
1
1
2
0
0
0
0
1
0
0
0
2
0
2
1
2
1
1
0
0
2
1
0
1
3
0
2
3
0
0
0
2
1
0
0
0
1
0
0
0
0
0
2
0
0
2
0
1
0
5
0
0
0
1
0
0
0
0
2
2
0
1
0
0
0
2
0
0
0
1
0
2
1
1
0
0
1
0
1
0
0
0
0
0
3
2
0
1
4
0
2
0
0
0
0
0
0
2
1
1
2
2
2
0
0
1
1
0
0
0
1
4
1
0
0
2
0
0
0
0
1
0
2
1
0
2
3
1
1
0
0
1
0
1
0
2
0
1
0
3
0
0
1
1
0
3
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
3
0
0
1
0
0
0
0
0
2
0
2
1
0
0
1
2
1
0
0
0
0
1
0
1
0
3
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
1
0
0
2
0
2
1
1
0
0
0
1
0
1
0
0
1
0
0
1
2
1
0
2
0
0
0
1
0
2
0
1
0
0
2
0
0
2
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
2
1
0
2
1
0
1
0
1
1
0
2
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
1
0
0
1
0
0
0
2
0
0
3
2
1
0
0
0
1
0
0
2
0
0
1
0
1
1
0
0
1
1
1
2
0
1
0
0
0
1
0
2
0
3
0
1
2
1
0
0
1
2
2
0
2
0
2
1
0
1
1
1
2
0
1
0
0
1
0
1
0
0
0
0
2
3
1
0
1
1
1
0
0
0
1
0
0
0
2
1
1
0
0
0
3
0
0
0
0
1
0
2
0
0
3
1
0
1
0
2
2
0
0
0
0
1
0
0
1
1
0
0
1
0
2
0
0
1
0
0
2
1
1
0
2
1
0
0
0
1
0
0
0
0
0
2
4
1
0
0
0
0
0
1
0
1
1
0
0
0
1
1
0
0
1
0
1
2
1
1
1
1
0
0
2
1
0
0
1
1
0
0
0
0
2
2
0
0
1
0
1
0
2
2
0
0
2
0
1
0
1
1
0
2
1
0
2
1
1
2
0
0
2
1
0
0
0
1
2
0
0
1
0
0
2
0
1
0
0
2
1
0
1
1
0
1
0
0
0
0
1
2
0
0
0
2
0
3
2
1
0
1
0
0
0
0
2
0
0
2
0
0
0
1
2
0
0
1
1
1
1
0
0
1
0
0
1
0
2
0
0
1
1
0
1
1
2
0
1
1
0
0
0
0
0
1
0
1
2
1
1
1
2
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
2
0
0
0
5
1
2
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
1
1
1
2
0
0
0
0
2
0
1
2
2
0
2
1
0
0
0
0
2
1
0
0
1
0
2
0
3
2
2
0
2
0
0
0
1
0
0
1
1
0
0
0
0
0
2
0
1
1
0
3
2
0
2
0
0
0
2
3
0
1
1
0
0
0
1
2
0
0
1
0
2
2
1
2
0
0
0
0
0
0
0
2
1
0
0
0
0
1
2
2
1
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
1
0
1
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
2
0
0
2
2
0
0
0
2
1
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
1
5
0
0
2
2
3
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
2
1
1
0
1
0
0
0
1
0
2
0
1
1
1
0
1
1
0
2
0
1
1
2
0
2
0
0
2
0
1
0
0
0
0
0
2
0
0
0
3
0
0
1
0
0
2
0
0
1
0
0
1
2
0
0
0
2
2
0
1
1
2
0
2
0
0
0
1
0
1
2
1
1
0
1
3
2
1
0
2
1
0
1
0
0
1
0
1
2
1
0
2
3
1
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
1
0
0
0
1
1
2
0
1
2
1
0
2
0
1
0
2
4
0
0
1
0
0
2
1
1
0
0
1
0
0
2
1
1
1
0
2
0
0
0
2
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
2
0
1
1
0
0
1
0
2
2
2
0
0
0
2
0
2
0
1
2
2
1
0
1
0
0
2
0
1
0
2
0
0
0
1
0
0
1
0
2
0
0
0
0
1
0
0
0
0
2
1
0
2
0
1
0
2
0
0
0
2
2
0
0
0
1
1
0
0
2
0
0
1
0
0
0
0
0
1
2
0
0
1
2
0
1
0
0
1
0
0
1
0
0
0
2
0
0
0
2
0
2
1
0
0
0
4
0
1
1
1
2
2
2
0
1
1
2
2
1
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
1
0
1
2
1
1
0
0
0
1
2
0
0
0
1
0
1
0
0
0
0
1
1
2
1
2
1
3
0
1
2
0
1
0
1
1
0
0
0
2
1
0
1
2
0
0
0
1
1
2
2
0
0
0
1
1
0
0
2
0
0
0
0
2
0
0
0
3
1
2
0
1
0
0
0
0
1
0
2
2
2
0
0
0
1
0
1
0
0
0
0
2
0
2
0
0
0
3
0
0
0
0
0
0
0
1
2
3
0
1
0
0
0
1
2
1
2
0
2
0
1
4
2
0
0
0
0
1
0
0
2
0
1
1
2
0
0
0
0
1
0
0
0
2
1
0
0
0
1
2
0
0
2
0
1
0
0
0
2
0
0
0
2
0
2
1
1
1
0
0
0
0
2
1
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
2
0
1
1
4
0
0
2
0
0
0
0
1
0
0
0
0
1
0
1
0
0
3
1
0
0
0
0
0
0
1
2
2
1
1
1
2
0
0
0
0
0
3
2
0
0
1
1
1
0
0
1
1
0
2
0
0
2
0
0
1
0
0
1
0
0
1
1
1
2
0
0
0
0
0
0
1
0
0
0
1
0
1
0
2
1
0
2
0
0
1
1
3
1
2
0
4
2
0
2
0
0
1
0
1
4
1
2
1
1
1
0
1
0
1
0
2
1
2
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
2
0
0
0
0
0
2
0
0
2
0
0
1
0
1
1
2
0
2
0
1
0
0
0
0
0
0
0
2
1
1
3
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
2
2
2
0
0
0
2
0
1
0
2
0
0
0
1
3
1
0
0
1
0
0
1
2
0
0
0
1
0
0
0
0
0
0
1
0
0
1
2
2
0
2
0
1
1
0
0
0
0
2
0
2
0
0
2
0
2
1
0
1
0
1
1
0
0
0
2
1
0
1
2
0
1
0
2
0
0
0
1
0
0
1
2
2
1
2
0
0
2
0
2
1
0
0
0
2
2
2
0
1
2
0
2
1
2
0
2
1
0
0
1
0
1
2
0
2
0
0
0
1
0
0
2
2
0
0
0
0
2
0
1
1
0
0
0
0
1
0
0
1
2
1
1
2
1
2
0
0
1
0
0
1
0
1
0
0
1
0
1
0
1
2
0
0
0
2
0
0
2
2
0
1
0
0
0
2
2
1
0
0
1
0
2
2
0
0
1
0
1
1
0
3
0
0
1
2
0
1
0
0
2
0
2
0
0
1
0
0
1
0
1
2
0
0
0
0
1
1
0
0
1
2
1
1
1
1
2
0
2
2
0
1
0
0
1
1
1
0
0
0
0
1
1
2
2
0
1
1
2
0
0
1
0
1
1
0
0
0
2
0
2
0
1
1
0
0
2
2
0
0
1
1
0
2
1
2
0
0
0
2
0
2
2
2
0
1
4
2
2
0
0
0
1
0
1
2
1
1
0
1
2
1
0
2
0
0
2
0
2
0
0
1
0
1
0
0
0
1
0
1
1
0
0
1
1
1
2
0
1
0
4
0
2
0
0
0
0
1
1
0
2
0
1
0
0
1
0
0
0
0
1
0
1
2
2
0
3
0
2
0
1
0
2
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
1
2
0
2
2
2
0
0
0
0
0
1
0
0
0
2
2
0
1
2
0
1
2
0
0
0
0
0
0
0
1
0
0
1
2
0
1
0
1
1
0
0
0
1
2
0
2
0
0
1
0
1
0
0
2
3
0
1
0
0
0
0
1
1
1
2
0
2
0
0
1
2
1
0
2
0
2
2
0
0
3
2
0
0
1
1
0
1
0
0
1
1
0
0
0
1
1
0
2
2
0
0
0
2
1
0
2
2
0
1
2
2
0
2
0
0
2
2
1
1
2
1
2
0
1
0
1
0
1
2
1
0
0
1
0
2
0
0
0
0
0
1
1
2
0
1
0
0
1
0
0
0
1
0
0
2
0
1
1
2
1
1
0
0
1
2
2
0
0
1
1
0
1
2
0
0
0
2
0
2
0
0
0
0
2
0
2
0
0
0
0
2
1
0
2
0
1
1
0
0
1
0
2
0
0
1
0
2
1
0
2
0
1
1
3
2
0
0
2
1
1
2
0
1
0
1
1
0
0
1
0
2
0
1
0
2
0
0
0
2
0
2
0
1
0
1
0
0
1
0
1
0
0
1
0
2
0
1
2
0
0
0
1
2
0
0
1
2
0
2
0
0
2
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
2
0
0
2
2
2
0
0
0
5
1
1
1
0
2
1
0
1
0
1
0
1
0
1
2
2
2
1
0
0
0
0
2
2
0
0
0
2
0
0
0
2
1
0
0
0
0
0
2
0
2
0
2
1
1
2
0
0
3
0
0
0
0
0
0
0
0
3
0
0
0
0
2
2
0
0
0
2
0
0
0
1
0
0
0
0
3
2
1
0
1
0
2
0
0
0
0
1
1
0
0
1
0
2
0
1
0
0
0
0
0
1
0
0
2
0
1
0
0
2
0
0
2
0
0
1
0
0
2
2
0
0
0
1
0
1
0
2
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
1
0
2
0
1
2
0
1
0
1
0
0
0
1
2
0
0
2
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
2
2
2
0
2
0
0
0
1
0
2
0
1
1
0
1
2
2
1
0
2
0
0
0
1
0
0
1
1
2
0
2
0
0
1
0
0
0
0
2
0
1
0
0
1
2
1
2
2
1
2
0
0
2
1
2
0
0
0
1
0
0
2
2
0
0
0
2
0
0
0
1
1
0
1
2
0
0
0
0
0
2
0
0
1
0
1
1
1
0
0
1
0
0
0
1
1
0
1
0
0
0
1
0
0
1
0
0
2
1
0
0
0
0
2
2
0
2
0
1
1
1
0
2
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
2
3
3
1
0
1
0
2
1
1
1
1
1
0
2
2
0
1
0
1
1
0
0
0
0
2
0
0
1
1
1
1
0
1
0
2
0
1
1
2
2
0
1
0
0
0
1
0
0
1
0
0
1
1
1
1
1
0
0
2
1
0
0
0
0
0
1
1
2
0
0
2
0
0
1
0
1
4
2
2
0
1
0
1
1
0
2
0
1
0
0
0
1
0
1
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
2
2
1
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
2
1
0
1
1
2
0
0
2
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
1
1
2
1
0
0
1
2
3
1
0
1
0
2
0
0
0
2
0
0
0
0
1
1
2
1
0
0
2
2
1
0
0
2
2
2
0
0
0
1
2
0
2
0
0
1
0
0
0
1
1
0
1
0
0
1
0
2
1
1
0
0
1
2
1
1
0
0
2
0
0
0
2
2
0
1
2
0
0
2
0
0
2
0
0
0
1
0
2
0
1
0
0
1
0
0
0
0
0
2
0
0
2
1
0
0
1
1
0
2
2
0
2
0
2
0
0
1
0
1
0
1
0
1
0
2
3
0
0
0
0
1
0
1
1
1
0
0
0
0
0
1
0
0
2
1
2
0
1
0
1
0
1
0
1
1
0
1
1
0
0
0
0
1
0
1
0
0
0
0
2
1
0
2
0
0
2
1
0
2
0
1
1
0
1
1
1
0
2
0
0
0
2
0
2
1
3
1
1
0
0
1
1
1
1
0
1
0
3
2
0
0
0
1
2
1
0
3
0
2
1
2
0
0
2
0
0
2
0
0
1
2
0
1
2
0
0
0
2
2
2
1
1
0
0
2
0
0
0
0
0
0
2
0
1
0
0
1
0
0
2
1
1
0
1
1
0
0
2
2
1
0
1
1
1
0
0
0
1
2
1
2
0
2
0
0
1
1
0
1
1
1
1
1
1
0
0
2
2
2
2
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
1
2
1
1
0
1
2
1
0
2
2
0
0
1
0
0
0
0
1
0
2
0
0
1
2
2
2
2
1
1
2
2
0
0
0
1
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
1
0
1
0
0
0
1
1
2
0
0
0
0
2
2
0
0
2
1
0
1
0
1
0
1
2
0
1
2
0
0
1
0
0
1
1
0
2
1
0
0
1
2
2
1
1
2
0
1
1
0
2
0
1
1
0
1
0
0
1
1
3
0
1
1
0
0
1
0
0
0
0
0
0
2
0
0
1
0
1
0
3
2
0
0
0
2
1
1
0
0
0
1
0
2
1
1
1
0
0
0
0
1
2
2
3
0
0
2
0
2
1
1
1
0
0
0
0
2
0
0
0
0
2
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
2
1
0
0
0
1
0
0
3
1
2
1
1
2
0
1
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
2
1
1
0
0
0
0
2
1
1
2
1
0
2
2
0
1
0
0
0
1
1
0
0
2
0
1
0
0
2
0
0
2
2
1
2
1
2
1
3
1
2
2
0
2
0
1
0
2
1
0
0
1
0
2
1
2
1
0
0
1
1
1
1
0
0
0
0
0
1
1
0
0
0
2
0
0
1
0
0
2
1
1
2
0
0
0
0
0
1
0
2
1
0
2
0
2
1
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
3
0
1
0
0
1
0
1
0
1
0
1
2
0
0
1
2
2
2
2
0
0
0
1
0
0
1
0
0
0
2
0
0
1
1
0
0
0
1
1
0
0
0
0
0
2
0
1
0
1
0
0
0
0
2
0
0
0
0
0
1
1
2
2
0
0
0
0
0
0
0
0
0
3
0
2
0
0
1
2
0
0
0
1
1
0
0
0
1
1
0
1
0
1
0
1
2
1
1
0
2
2
1
0
1
0
1
1
0
0
3
1
0
1
1
1
0
1
2
1
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
2
3
1
0
0
0
1
0
2
1
1
0
1
1
1
0
0
0
0
0
0
0
0
0
2
1
1
1
0
2
1
0
2
0
0
0
2
1
0
0
2
0
1
1
2
0
0
3
0
0
0
0
2
2
0
0
0
0
1
1
2
0
0
1
2
0
2
1
2
1
0
0
2
0
0
1
1
0
2
1
0
0
0
2
1
1
2
2
0
1
0
0
2
0
2
1
2
0
1
1
1
0
1
0
1
0
1
0
5
2
0
2
0
0
4
0
0
0
1
0
0
0
2
1
0
0
1
0
0
0
0
0
0
1
0
1
2
0
0
2
0
2
2
0
2
1
0
1
0
1
0
0
0
0
1
0
2
2
0
0
1
2
2
1
1
1
0
2
0
0
1
1
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
3
1
0
1
1
2
0
0
2
1
0
0
0
1
0
2
1
1
0
0
0
1
0
1
1
1
1
0
0
2
0
1
0
0
0
7
2
1
1
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
1
2
0
0
2
0
1
0
0
1
1
0
2
0
2
0
1
0
0
0
1
0
1
2
1
0
0
2
0
0
0
0
2
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
2
1
2
0
0
1
0
1
2
1
1
2
1
2
0
0
1
0
1
0
0
1
2
0
0
1
1
2
2
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
1
2
0
2
1
0
0
0
0
0
2
0
0
0
2
1
2
2
0
0
0
0
1
3
0
1
1
3
0
0
0
1
0
0
0
0
0
1
0
2
1
0
0
0
0
3
0
3
1
1
0
0
0
0
0
0
0
0
1
0
2
1
1
0
0
1
1
0
0
0
0
0
1
1
0
2
0
2
2
0
1
2
1
1
1
1
0
0
1
0
0
0
1
0
0
0
0
1
0
2
1
1
1
2
1
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
1
1
1
1
0
0
0
1
2
0
1
2
0
0
2
0
1
1
1
0
0
2
1
0
1
0
0
1
0
0
1
1
0
2
2
1
0
0
1
2
2
0
0
0
0
0
2
0
2
1
0
1
0
1
2
0
0
2
1
0
0
1
0
0
0
0
0
1
0
0
1
0
1
2
2
2
0
0
0
0
2
1
2
0
0
0
2
1
0
0
2
2
2
2
0
0
1
0
4
0
0
0
2
1
0
0
0
2
1
0
0
0
1
0
0
2
0
1
1
1
0
1
2
1
0
0
0
1
1
0
1
0
0
2
1
0
2
0
2
0
0
1
0
0
0
0
0
0
2
0
1
2
2
0
0
1
0
0
1
1
0
2
0
0
0
1
2
0
0
0
2
0
0
0
0
1
0
0
0
0
1
1
0
2
2
0
2
0
0
0
1
0
0
2
0
1
1
1
1
2
1
0
0
3
0
2
2
1
2
0
2
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
3
1
1
2
0
0
0
0
2
0
0
2
2
0
0
1
1
0
1
2
0
0
2
0
0
0
0
1
2
0
2
0
1
1
1
1
0
1
0
2
0
0
0
0
2
0
1
0
1
0
0
0
1
0
0
2
2
0
2
2
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
1
1
0
1
0
0
1
0
2
2
2
1
1
0
1
2
0
0
0
1
1
1
2
0
0
0
0
1
2
1
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
2
1
0
2
0
1
0
1
1
0
0
0
0
0
1
0
1
2
0
0
0
1
0
0
0
0
0
0
0
1
0
2
1
2
1
0
0
2
1
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
1
3
1
0
0
0
2
2
0
0
1
3
1
0
3
0
0
0
0
0
1
1
0
1
0
0
0
3
0
2
2
1
0
1
0
2
1
0
1
0
1
0
1
1
0
0
1
1
0
0
1
0
0
0
2
1
0
1
1
1
1
0
2
1
1
0
2
0
0
1
2
2
0
0
1
2
0
0
0
2
2
1
1
1
1
0
2
0
0
0
1
1
1
0
0
0
1
0
0
0
2
1
2
0
0
0
1
0
1
0
0
0
0
0
3
2
0
2
0
0
2
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
2
2
0
0
2
6
2
2
0
0
1
1
0
1
1
1
0
1
2
0
1
0
0
0
2
1
0
0
0
3
2
0
1
1
3
2
2
0
1
2
0
0
0
0
0
0
1
0
0
3
0
2
0
0
1
2
0
1
1
0
0
1
0
0
0
2
0
0
1
1
1
5
0
0
1
2
0
0
0
2
1
1
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
2
0
1
0
1
0
1
0
0
0
1
2
0
1
0
1
1
0
0
1
1
0
0
0
0
0
0
1
2
1
2
3
2
0
0
2
0
0
0
0
1
0
0
0
1
0
1
1
0
0
2
1
1
1
0
1
0
0
1
1
0
0
0
0
2
0
0
0
0
0
2
1
2
1
1
0
0
0
2
1
2
0
0
0
0
0
2
0
1
0
0
0
1
0
1
2
1
1
0
0
0
0
1
2
0
0
2
0
1
2
1
1
0
2
0
1
0
3
0
1
2
0
1
2
0
1
0
2
0
1
0
0
0
0
1
0
0
0
2
1
0
0
1
0
0
2
0
0
2
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
2
1
3
0
0
1
2
2
0
0
2
0
0
2
1
1
0
0
0
1
2
2
0
0
0
0
0
0
1
1
1
2
2
1
0
1
0
2
1
0
0
2
0
1
1
3
0
0
1
0
0
1
0
0
2
2
0
1
0
2
2
0
1
1
0
1
0
0
0
0
0
1
0
1
2
2
2
1
0
0
2
0
0
0
3
2
0
1
0
2
0
0
0
1
0
1
1
0
0
1
1
1
2
0
0
0
0
1
0
2
1
2
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
2
1
0
1
0
1
0
1
3
0
0
0
1
0
0
0
0
2
0
0
0
0
2
2
3
0
0
1
1
0
1
0
2
0
0
1
1
0
0
0
2
1
0
0
1
0
0
0
2
0
0
0
0
0
1
0
1
0
1
2
1
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
1
1
1
2
1
0
1
1
1
1
1
1
1
0
1
0
1
2
0
2
1
4
1
2
0
0
1
2
0
1
1
1
0
0
2
0
1
0
0
1
2
0
0
1
0
0
0
0
2
0
1
0
3
1
2
1
0
0
1
0
1
1
2
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
2
0
1
1
0
2
0
0
0
4
0
1
2
0
1
0
0
0
1
1
1
2
0
1
1
2
4
1
1
0
1
0
0
1
0
0
2
0
2
1
0
1
1
0
2
1
0
6
5
1
10
1
0
0
2
0
0
0
1
0
0
2
2
0
0
1
0
0
2
1
2
0
1
0
1
0
0
3
1
0
0
0
0
0
0
2
0
2
1
0
0
0
0
1
1
2
0
0
0
1
0
1
1
0
2
1
0
0
0
0
0
0
0
0
0
2
0
2
1
1
0
0
0
0
1
0
0
2
0
3
2
0
2
0
0
0
0
1
0
2
0
1
2
2
0
2
2
0
0
1
2
2
0
1
2
0
0
4
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
2
1
0
0
1
1
0
0
0
0
0
2
2
0
0
1
1
0
2
0
1
0
2
0
0
2
0
0
1
2
2
1
2
0
1
0
0
1
0
1
0
0
2
0
2
0
1
0
2
0
1
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
1
3
0
2
1
0
0
1
0
0
2
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
2
2
1
2
0
2
1
1
0
1
2
0
0
0
0
2
0
0
0
1
1
2
0
0
1
0
1
0
0
0
0
0
0
1
2
1
1
1
0
1
1
2
1
0
0
0
0
2
0
0
0
0
0
1
5
0
2
0
2
2
0
0
1
1
3
0
1
0
0
2
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
2
1
0
0
0
1
1
0
0
1
0
1
2
1
2
0
1
0
0
0
1
0
0
0
0
0
1
2
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
1
1
2
1
0
1
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
1
1
1
0
0
1
2
2
2
0
0
2
0
0
2
0
2
2
0
0
0
1
0
0
0
2
0
0
1
1
0
0
1
0
1
0
0
1
1
0
1
1
1
1
0
2
2
2
0
2
0
2
1
0
1
1
0
0
0
2
1
0
0
1
0
1
1
1
0
0
0
0
1
2
0
2
0
2
1
0
0
0
0
0
1
0
1
0
2
2
1
2
2
1
1
1
0
2
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
1
0
2
0
0
1
0
0
1
2
0
0
0
2
0
3
2
1
1
1
0
0
1
2
0
2
0
2
1
0
2
1
0
1
0
0
0
0
0
2
0
0
0
2
0
2
2
0
2
1
0
2
0
0
0
0
0
1
2
3
0
2
1
0
0
2
2
0
1
1
2
0
1
2
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
2
1
0
0
1
0
2
0
1
1
0
0
1
1
2
0
1
1
0
0
1
0
1
2
0
0
0
1
2
0
0
0
0
0
2
1
0
1
1
2
1
2
1
1
1
0
0
0
1
0
1
2
0
0
0
2
0
2
0
2
1
0
0
0
1
0
0
0
0
1
2
0
0
1
4
0
2
1
0
0
0
1
0
1
0
0
2
2
2
1
1
0
0
0
0
0
0
0
1
1
1
0
1
1
1
0
1
0
0
3
2
1
0
0
2
2
1
1
3
0
0
3
0
0
0
2
0
1
0
0
1
1
0
2
1
0
1
0
0
0
0
2
2
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
2
0
0
2
2
1
0
0
0
3
1
1
0
0
0
2
0
0
0
2
0
0
2
0
2
1
0
1
3
0
0
1
2
0
1
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
1
0
2
1
0
0
1
2
0
0
1
1
0
1
0
0
0
0
1
1
0
0
0
1
0
0
1
1
1
0
2
0
2
0
1
1
0
1
0
0
1
0
1
2
1
0
0
1
1
2
0
0
2
1
1
2
0
2
1
0
1
0
0
1
3
2
0
1
3
0
0
0
2
0
0
2
0
1
0
0
1
0
1
0
0
4
2
0
0
1
0
1
2
0
1
0
0
2
1
2
0
0
2
1
0
0
0
2
0
2
0
1
0
1
2
0
0
2
0
0
0
0
0
0
0
0
1
0
2
2
1
0
2
1
1
0
2
0
0
1
0
3
1
0
0
0
1
0
2
0
0
1
0
1
2
2
0
1
7
2
2
1
1
0
0
2
0
2
1
0
1
0
2
1
1
0
1
0
0
0
0
0
2
1
1
1
0
0
0
2
2
2
2
1
1
1
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
2
0
0
0
1
1
0
1
0
0
2
1
0
0
0
2
1
0
0
0
0
2
0
0
4
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
1
1
2
0
0
0
1
1
2
1
2
0
0
1
0
0
0
0
1
0
1
0
0
1
0
1
1
1
1
0
0
0
2
1
1
0
2
0
0
2
0
0
0
0
0
1
0
0
6
2
0
0
0
1
2
1
0
1
0
2
1
0
1
0
2
1
0
0
0
0
0
1
0
2
1
0
1
2
2
0
1
0
2
0
0
1
2
2
2
0
2
1
2
1
2
2
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
1
0
1
6
0
1
0
0
0
0
1
0
1
2
0
1
0
1
2
2
2
0
0
0
2
0
1
2
0
0
0
2
0
2
1
0
0
0
1
1
0
0
0
1
0
2
0
3
0
0
1
1
0
1
2
1
1
1
0
0
0
1
1
0
1
0
2
0
4
0
1
1
0
0
2
2
1
2
1
2
0
0
4
2
0
0
0
0
0
0
1
2
3
0
2
0
0
0
0
0
2
1
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
1
2
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
1
1
0
1
1
2
0
0
2
3
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
2
1
2
0
0
0
1
0
2
1
0
1
0
1
0
0
2
2
0
1
1
1
2
0
0
2
0
3
1
1
1
4
1
0
0
2
1
0
0
1
0
3
0
1
0
1
0
0
1
1
2
0
1
2
0
1
1
1
0
2
1
0
0
3
0
1
0
1
1
0
0
2
0
0
2
0
0
0
1
1
0
0
2
1
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
1
0
1
0
0
1
1
1
0
1
2
0
2
0
0
0
0
1
1
0
0
1
1
1
1
2
1
0
1
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
5
0
0
1
0
0
2
2
0
1
1
0
0
2
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
2
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
1
1
0
2
2
2
0
2
1
0
0
0
0
1
1
0
0
0
1
0
2
0
0
2
0
1
0
0
1
0
0
3
2
0
0
1
0
1
1
0
0
0
2
2
0
0
1
2
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
2
1
0
0
2
2
1
0
1
2
4
1
1
4
1
0
0
2
2
0
2
0
0
0
0
2
0
1
1
1
0
2
0
0
2
0
1
0
0
0
0
1
0
1
0
2
2
0
1
0
0
0
2
1
1
0
0
0
2
2
1
1
0
0
1
1
0
0
2
0
1
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
2
0
0
0
1
0
0
4
0
2
0
0
2
1
1
2
2
1
2
0
0
0
0
1
1
0
0
0
3
1
2
2
0
0
3
1
2
0
0
0
1
0
0
0
1
0
2
1
0
1
1
0
0
0
0
0
1
2
1
1
1
1
2
1
0
0
0
0
2
0
2
0
0
0
0
1
1
2
1
0
0
1
2
1
1
0
0
0
0
0
0
1
0
1
0
1
1
1
0
0
0
1
0
1
0
0
1
1
3
0
1
0
0
0
1
0
0
0
1
0
2
0
0
1
1
0
0
0
2
0
0
1
0
1
0
2
0
0
0
0
2
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
2
0
0
0
0
1
2
2
0
0
0
2
0
0
0
1
1
1
0
0
0
0
2
1
0
0
0
2
2
2
1
0
1
0
2
0
2
4
2
0
0
0
2
1
0
0
5
2
0
1
1
1
0
2
0
1
1
0
1
1
1
0
0
1
0
0
3
2
0
1
0
1
0
2
0
0
2
0
0
2
1
1
1
1
2
0
2
0
1
0
0
0
0
2
0
2
0
0
1
1
0
1
0
2
0
0
0
0
1
0
0
2
0
0
0
0
2
2
0
0
0
2
1
1
0
0
0
2
0
0
0
2
0
0
0
1
0
0
1
1
0
0
1
2
0
0
0
0
0
0
4
2
0
0
1
2
0
1
1
0
2
1
0
5
0
3
0
0
1
0
1
2
1
1
1
0
0
3
0
0
2
1
2
0
2
2
1
0
1
0
0
1
0
2
1
1
2
0
2
0
0
0
4
2
0
0
1
0
16
2
0
0
0
0
0
1
2
3
0
0
0
2
0
2
0
1
0
0
1
0
2
1
0
0
1
2
0
0
0
0
1
0
0
0
0
1
1
1
1
0
0
0
1
0
2
1
1
0
2
0
1
1
1
1
2
0
1
2
0
0
0
0
2
0
1
1
2
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
1
1
0
0
2
2
1
0
1
3
2
0
3
0
1
2
2
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
2
4
0
0
1
0
0
2
2
2
0
2
0
0
0
0
0
1
0
2
1
0
2
1
1
0
1
2
0
0
2
2
0
1
0
2
2
1
0
0
2
0
1
0
0
2
2
0
1
1
1
0
0
1
2
1
0
0
0
1
1
0
1
0
0
0
0
0
1
1
1
1
0
1
1
0
0
0
1
0
0
2
0
0
0
3
1
0
1
0
0
2
1
0
0
0
1
0
0
2
0
1
0
0
2
0
1
1
1
0
1
0
0
0
2
2
0
0
2
0
1
1
2
0
0
2
1
1
0
0
0
0
1
0
1
3
0
0
0
0
1
1
1
1
1
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
3
0
0
1
0
1
2
0
0
0
0
0
0
1
2
0
0
0
0
1
0
2
1
0
2
0
0
1
0
0
0
1
2
0
0
0
2
0
2
0
1
2
0
0
0
1
2
0
2
2
2
0
1
2
2
1
0
2
0
0
0
0
2
0
0
1
0
1
0
0
2
0
0
0
0
2
0
2
0
1
0
0
2
0
0
0
1
0
2
0
1
1
0
0
1
0
0
0
1
1
0
0
1
1
0
1
0
2
2
1
0
0
0
3
0
0
0
1
1
0
0
1
0
2
0
2
0
1
2
0
0
2
1
2
1
0
1
0
0
2
0
1
0
1
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
1
0
1
1
0
1
0
1
0
1
0
1
1
0
0
0
0
2
0
0
1
0
0
2
0
0
0
1
0
2
0
0
0
0
1
0
0
1
1
0
0
0
2
1
0
0
0
2
1
2
3
2
0
0
0
1
0
0
3
0
2
1
0
0
0
2
0
2
2
1
0
1
0
0
2
0
0
0
1
1
2
0
1
1
2
2
0
2
3
2
1
2
0
0
1
0
0
2
1
1
1
0
0
0
0
4
2
1
2
2
0
1
1
0
2
1
0
1
0
0
2
1
0
0
0
0
1
0
4
1
1
0
0
1
0
2
1
0
1
1
0
0
0
1
2
0
0
2
0
2
0
1
2
0
0
2
1
1
0
0
2
0
1
1
0
0
1
1
0
1
0
1
0
0
0
2
0
0
2
2
2
1
0
1
2
0
2
0
0
0
0
0
0
0
2
0
1
0
0
1
0
1
1
0
1
0
0
0
0
1
2
0
0
0
0
1
2
0
0
0
0
0
1
1
2
2
2
0
0
0
1
0
0
2
0
2
1
0
2
2
0
1
0
2
0
0
1
2
2
2
0
1
0
2
2
0
1
2
0
0
0
2
0
0
0
0
0
2
1
0
2
1
0
2
1
1
0
0
0
2
0
1
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
2
0
0
1
0
2
0
0
0
0
0
0
2
2
0
2
0
2
2
0
0
1
0
1
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
2
1
2
0
2
2
0
1
0
0
0
0
0
2
0
1
0
1
0
0
2
0
0
2
0
1
0
2
2
0
0
0
0
0
2
0
1
0
0
1
1
0
0
0
1
0
0
0
0
2
1
2
2
0
2
1
2
1
0
0
1
1
0
0
1
2
1
1
0
1
0
0
2
0
0
0
1
0
3
1
2
2
2
2
1
1
0
0
0
1
0
0
2
2
0
1
1
0
1
0
2
0
2
1
2
1
0
2
2
1
0
2
1
0
2
0
0
0
0
2
1
0
0
0
1
1
2
2
1
0
1
0
3
0
0
1
1
0
1
0
1
1
0
0
0
1
0
0
0
0
1
0
1
2
0
0
0
1
1
0
2
0
0
0
0
2
2
1
0
0
0
0
1
0
0
0
1
0
0
1
0
2
3
2
0
1
1
2
1
2
0
1
0
0
0
0
2
0
2
1
1
0
1
0
0
1
2
1
2
1
0
2
0
2
1
1
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
9
0
0
0
4
2
1
1
0
1
0
0
0
0
0
0
0
2
0
0
0
2
2
1
0
0
1
1
0
0
2
1
1
0
0
0
1
0
0
1
2
1
1
0
1
0
2
0
0
0
2
2
1
0
2
0
2
0
1
1
1
0
0
0
0
0
0
1
2
2
1
0
1
2
0
1
0
0
0
0
0
3
0
2
0
0
1
2
1
0
2
0
0
2
1
1
0
0
1
0
0
1
2
0
0
2
2
0
0
1
2
1
0
1
0
2
0
0
0
1
1
2
0
2
1
0
1
0
1
0
2
0
0
0
1
0
0
2
1
1
2
0
1
1
0
2
0
1
0
2
4
0
0
1
3
1
2
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
1
2
0
2
0
0
0
0
1
0
0
0
1
1
2
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
1
1
0
1
1
0
1
1
0
0
0
2
2
2
0
0
2
0
2
0
2
1
0
0
1
0
0
1
2
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
1
2
0
0
1
2
0
1
2
0
4
2
1
1
0
0
3
1
1
0
1
3
0
0
0
0
0
1
0
0
2
2
0
0
1
2
1
2
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
1
1
1
0
1
0
0
3
0
0
0
1
2
1
2
0
1
1
1
0
0
0
1
1
0
2
1
2
2
0
1
1
0
0
0
0
2
0
0
2
0
2
1
2
1
2
1
2
0
1
0
2
0
1
0
2
1
0
2
1
0
0
1
2
0
2
1
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
2
0
0
0
0
0
1
2
2
1
2
0
0
3
0
2
0
0
1
2
1
2
0
2
0
0
0
1
0
1
1
0
0
0
1
0
1
1
0
2
0
1
3
0
2
1
0
3
0
0
0
0
0
1
1
1
0
1
0
1
1
2
2
1
0
0
0
0
0
0
0
2
2
0
0
3
1
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
1
0
0
2
0
1
0
0
0
2
0
0
1
0
1
0
2
2
0
0
2
1
0
1
0
0
0
0
1
1
0
2
0
0
1
2
0
1
3
1
1
1
1
0
0
2
0
0
0
0
2
0
0
0
2
1
1
1
1
1
0
1
0
1
2
1
0
1
1
2
0
0
0
2
2
0
1
2
1
0
1
0
2
4
1
2
0
1
0
3
1
1
1
0
1
0
1
0
0
1
2
0
2
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
2
1
0
1
0
2
1
2
0
0
0
0
2
0
0
0
0
1
0
2
0
1
0
0
1
2
0
0
3
0
0
0
1
0
0
0
2
1
1
2
2
0
2
0
2
2
1
1
1
1
1
0
0
1
0
2
0
0
1
0
0
2
2
1
0
0
0
0
0
0
2
0
0
1
1
0
0
1
2
0
1
1
1
0
1
2
0
1
1
0
1
0
0
0
0
1
2
1
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
1
0
1
1
2
1
2
1
0
0
0
0
0
1
1
2
0
0
1
1
0
0
0
0
0
0
0
1
1
0
3
0
0
0
1
5
0
2
0
0
1
0
2
2
1
1
2
0
0
1
2
1
0
1
1
0
1
2
0
1
0
0
1
2
0
1
0
0
0
0
2
0
2
1
2
0
0
0
1
1
2
0
2
0
0
2
0
2
1
1
0
0
0
0
1
0
2
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
4
2
1
2
0
0
0
0
0
0
0
0
2
0
0
2
1
1
1
2
0
0
0
0
1
0
0
0
0
0
1
2
0
2
1
0
0
0
0
0
0
1
2
2
1
3
2
1
1
2
0
0
0
2
0
1
0
1
0
1
0
0
1
2
0
2
2
0
1
0
2
1
1
3
0
1
1
0
1
0
0
2
2
0
0
0
2
1
1
1
1
0
0
1
0
1
1
1
2
0
2
0
0
0
1
1
0
1
2
0
0
0
0
0
0
0
1
2
0
1
1
0
1
2
0
0
0
0
0
1
0
1
2
1
2
2
0
0
0
2
0
1
0
1
1
2
0
0
0
0
0
0
0
1
1
1
2
0
0
2
0
1
0
1
3
1
0
1
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
1
0
2
0
2
2
0
1
1
0
0
2
2
0
0
1
0
0
2
1
1
0
1
1
0
2
0
2
1
2
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
3
0
1
1
0
0
0
2
2
2
0
2
0
2
2
0
0
1
1
0
0
1
0
3
2
2
0
1
1
1
3
0
0
0
0
0
1
0
1
1
0
2
0
2
1
0
0
1
1
1
1
0
0
0
1
1
3
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
1
3
0
3
0
0
1
0
1
1
0
0
1
2
1
0
0
1
0
1
2
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
1
0
0
1
1
2
2
0
2
0
0
3
0
1
1
0
0
1
2
0
0
1
2
0
1
1
0
2
0
1
0
1
0
0
0
3
0
0
0
0
0
2
2
1
0
0
2
1
1
0
0
0
2
1
0
2
0
2
0
0
2
0
0
0
1
2
1
0
0
2
1
2
0
1
0
0
0
1
1
0
0
0
4
1
0
0
2
2
0
0
3
0
2
1
0
1
0
1
1
0
1
0
2
1
1
0
1
3
0
0
0
1
1
2
1
1
0
0
1
0
0
0
1
1
1
0
0
0
1
0
2
1
0
0
1
1
2
0
0
0
0
0
0
1
2
0
2
1
0
1
1
1
2
0
5
1
0
0
1
0
1
0
2
1
0
2
0
1
1
0
0
2
1
0
0
5
0
0
0
0
0
1
0
0
0
0
0
0
2
1
2
2
0
2
0
0
0
1
3
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
2
1
0
2
2
0
0
1
1
0
0
1
0
2
1
2
0
0
1
0
1
0
0
0
0
1
0
0
2
0
0
0
1
0
1
0
0
0
1
2
0
0
1
2
0
0
2
0
0
2
0
2
0
1
0
2
0
0
2
2
0
0
0
0
2
0
2
0
0
1
0
1
2
0
0
0
2
1
0
2
0
0
0
0
1
2
1
1
2
0
2
1
2
0
1
2
0
2
0
1
2
1
0
1
2
0
0
0
0
1
0
2
0
0
0
1
0
0
2
2
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
1
2
0
1
1
1
0
2
1
0
0
0
0
1
0
1
1
0
1
2
1
1
1
0
1
0
0
0
1
2
2
0
1
1
0
0
1
0
3
2
0
0
1
0
0
0
0
0
0
2
1
0
1
0
1
1
0
0
2
2
2
1
0
0
0
0
1
0
2
1
1
1
2
0
0
0
1
0
0
0
1
0
0
0
1
2
1
0
0
0
1
2
0
1
2
1
0
0
2
2
2
1
1
2
0
1
1
0
2
0
1
2
0
0
0
0
0
1
0
0
2
2
0
0
0
2
1
0
1
1
1
0
1
0
1
1
0
0
0
2
1
0
1
2
1
0
0
1
0
1
1
1
0
0
0
0
0
0
2
0
0
1
2
0
0
1
0
3
0
1
0
2
2
0
1
0
0
1
0
2
1
1
0
1
1
0
2
0
1
1
1
2
1
0
0
2
0
0
1
0
2
2
0
2
1
2
1
1
0
0
1
0
0
0
0
1
0
1
1
0
0
0
1
1
1
0
0
1
2
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
1
2
0
1
0
2
0
1
0
0
1
1
0
0
0
1
2
0
0
0
2
1
0
1
2
0
0
0
2
0
2
0
0
2
1
0
0
0
1
0
0
1
1
0
1
2
0
0
1
0
2
1
0
0
0
2
0
0
0
1
0
1
1
1
0
0
1
2
0
0
1
0
0
2
2
0
1
0
1
0
1
0
0
2
1
1
0
1
0
0
1
0
1
0
0
0
0
2
0
5
0
0
1
0
2
1
0
1
2
0
0
1
0
1
3
0
0
0
1
0
2
1
1
2
0
0
1
2
0
0
0
4
0
0
0
0
2
0
1
0
0
1
0
1
2
0
4
0
1
1
0
1
0
1
0
1
0
1
0
2
0
0
0
2
0
2
0
0
0
2
1
0
1
0
0
0
0
0
1
2
0
2
0
2
0
1
0
0
0
0
2
2
0
1
0
2
0
2
2
0
1
1
2
0
1
0
0
0
0
2
0
0
2
1
0
1
0
2
2
2
2
2
0
0
1
2
1
1
2
0
0
0
0
0
1
0
0
0
1
0
1
0
0
2
3
0
4
2
2
0
0
1
0
1
1
2
0
0
0
0
1
0
0
0
1
2
1
3
0
0
0
1
0
2
1
1
1
0
2
0
0
0
1
0
0
2
0
1
0
1
1
2
2
2
2
0
0
2
2
0
2
0
1
1
0
2
0
0
2
2
1
0
0
1
0
1
2
0
0
0
2
0
0
0
2
1
0
2
0
1
1
0
0
0
1
1
1
3
2
0
0
1
0
2
0
0
0
0
0
0
0
0
1
2
2
5
1
1
1
1
1
1
2
1
1
0
0
0
1
1
1
2
1
2
0
0
1
0
1
2
1
2
0
2
0
0
0
0
1
1
0
0
1
1
1
0
0
0
2
0
1
0
0
1
0
1
1
1
1
0
2
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
2
0
2
0
0
1
1
0
0
1
1
0
1
0
1
1
2
0
2
0
0
0
1
0
0
0
2
3
0
1
2
2
1
2
0
0
2
0
0
1
0
1
2
0
1
0
1
0
0
0
0
1
2
0
1
0
0
0
2
1
1
0
1
0
0
0
1
1
1
0
2
2
2
2
0
0
0
0
1
1
2
0
0
6
0
1
0
1
1
0
0
1
0
0
0
1
0
0
1
0
2
0
2
0
3
0
1
0
0
1
0
2
1
1
0
0
1
2
2
2
0
1
1
0
1
0
1
2
2
2
2
0
1
1
0
0
0
2
0
2
2
1
0
2
0
0
1
0
1
0
0
0
0
0
1
1
0
2
2
1
1
0
1
2
0
0
3
0
0
0
2
3
0
2
2
0
0
0
2
2
0
1
1
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
2
2
2
1
0
0
0
2
1
0
0
2
1
2
2
1
1
0
0
0
1
2
0
2
2
0
2
1
0
0
0
0
1
0
1
0
2
1
0
0
1
3
0
0
1
1
1
2
0
1
0
0
0
0
2
0
2
2
0
2
0
0
2
2
0
2
2
1
0
0
2
0
0
0
1
1
0
1
0
2
1
1
1
2
0
1
1
0
1
0
0
0
1
1
0
1
1
2
1
0
0
1
0
2
1
1
0
1
2
1
2
2
0
0
0
1
2
0
0
0
1
0
0
1
0
0
2
2
1
0
0
2
0
0
1
0
0
1
0
0
2
1
0
0
1
1
1
0
1
1
0
2
0
0
0
0
0
0
2
2
1
0
1
0
0
2
1
0
0
0
2
1
2
1
0
0
2
2
0
1
2
0
1
0
0
2
2
1
0
1
0
2
2
1
0
2
2
0
0
5
2
0
0
1
0
0
2
1
2
0
1
1
0
0
2
0
1
0
0
1
0
2
0
0
0
0
0
0
2
1
2
2
1
0
0
1
0
0
0
0
1
2
2
0
1
0
2
1
1
2
0
0
0
3
0
0
0
2
2
0
1
0
2
1
1
1
0
1
0
0
2
1
2
0
1
0
2
0
2
1
0
1
0
2
1
1
0
2
0
2
0
2
1
2
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
2
3
0
0
0
0
0
2
0
0
3
2
2
1
1
0
1
1
2
0
1
0
1
0
2
1
3
1
0
2
1
0
2
0
0
1
2
0
0
1
0
1
0
0
0
0
0
2
1
1
4
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
2
0
2
0
0
2
1
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
1
1
0
1
0
1
0
0
0
1
0
0
0
1
0
2
0
0
2
1
3
0
0
0
0
2
0
2
1
0
1
1
2
0
2
2
2
2
0
1
2
0
2
0
0
1
0
0
0
0
0
0
1
1
1
0
1
1
0
1
0
1
0
0
1
3
1
1
0
2
2
2
0
1
1
2
0
0
0
0
1
3
0
0
2
0
0
0
0
0
0
0
1
2
1
0
0
0
2
0
2
1
0
0
0
0
0
0
1
0
0
0
1
0
1
2
0
0
0
0
0
2
1
0
2
0
0
1
1
0
2
0
1
2
0
0
1
0
1
0
0
1
2
1
0
0
1
2
0
2
1
1
1
1
0
1
2
0
0
2
2
0
2
0
1
0
0
1
0
2
0
0
2
0
0
1
1
1
2
0
1
1
2
0
0
2
0
1
2
1
0
0
1
0
2
2
0
0
0
2
0
1
0
0
0
0
1
0
0
1
1
2
0
0
1
0
2
1
0
0
0
2
0
1
0
0
0
1
2
0
2
0
0
0
0
0
0
0
4
1
0
1
2
1
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
2
2
3
1
0
1
0
0
2
1
0
2
1
0
0
2
0
2
0
1
0
0
0
2
0
1
0
2
2
0
1
0
0
0
0
0
2
1
2
1
1
1
2
0
2
0
2
1
4
0
0
0
1
0
1
0
0
0
0
0
1
1
2
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
4
0
0
2
0
2
1
1
1
0
2
1
1
2
2
1
4
1
1
2
2
1
1
2
1
0
0
1
0
0
0
1
1
1
0
0
1
0
1
0
0
2
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
2
2
0
0
1
2
0
0
1
0
0
1
0
0
1
1
0
0
2
1
0
0
1
1
1
1
0
2
1
2
2
2
2
0
0
0
2
0
0
0
0
2
0
0
0
3
1
0
2
0
0
0
0
9
2
0
0
0
0
0
2
2
0
1
4
1
0
1
0
2
0
2
2
0
2
1
0
0
1
2
0
0
0
1
1
0
2
2
2
0
0
0
3
1
2
0
0
0
0
2
3
0
1
2
0
1
1
0
0
3
2
3
0
1
2
0
0
1
2
0
2
2
0
0
0
1
0
0
0
0
0
2
0
0
2
2
0
0
2
1
0
1
0
2
2
0
1
1
0
2
0
0
2
0
0
0
0
0
4
2
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
1
2
0
1
0
2
2
0
1
1
1
0
2
0
2
0
1
1
1
1
1
0
0
0
0
2
2
1
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
2
0
0
0
0
0
0
0
2
2
1
1
0
1
0
0
1
0
2
1
0
0
1
1
0
0
1
2
0
1
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
2
0
0
1
2
2
0
1
2
2
2
0
1
0
1
0
1
2
0
1
1
0
1
0
0
0
1
0
0
3
1
0
0
1
1
2
1
1
0
0
1
1
1
1
0
0
2
0
1
2
2
0
0
1
1
1
0
1
1
1
1
1
0
0
0
2
1
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
3
1
0
0
2
0
2
0
0
2
0
4
1
0
0
2
0
0
0
1
0
2
0
0
0
1
1
0
1
0
2
1
1
2
1
2
2
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
1
0
0
1
1
0
1
0
1
0
0
0
0
2
1
1
0
0
0
1
1
0
0
0
0
0
0
3
1
0
0
1
1
0
1
0
0
0
2
0
0
1
2
0
1
0
0
2
2
0
1
1
0
1
2
0
1
0
0
2
0
1
0
0
0
0
0
0
1
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
2
1
0
1
0
1
1
0
0
1
0
2
0
0
1
0
1
0
1
0
0
2
0
2
0
0
2
0
1
0
3
1
0
2
1
2
1
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
1
1
0
1
0
0
0
0
1
0
0
2
1
0
2
0
1
1
0
0
1
0
0
0
0
0
0
2
0
0
1
1
2
1
3
2
1
1
1
0
0
0
0
1
0
0
1
0
1
0
2
0
1
1
0
1
1
0
2
0
0
1
1
2
2
1
1
1
0
0
2
0
0
1
0
0
0
0
0
1
0
1
0
0
0
2
2
0
2
10
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
2
1
0
1
0
2
2
0
2
2
1
0
0
1
0
1
0
0
2
1
1
0
0
0
2
1
0
0
0
1
0
5
0
0
2
1
0
0
0
0
2
0
0
0
1
1
0
0
2
1
2
1
1
2
0
0
1
0
0
3
2
0
0
0
2
2
1
3
0
2
1
0
0
0
1
0
2
0
1
0
0
0
1
1
0
4
1
1
0
1
1
1
2
0
0
2
0
0
1
1
0
0
0
0
0
0
2
1
0
1
0
0
1
0
1
0
2
0
0
0
1
0
1
0
1
0
0
2
2
0
2
0
0
0
2
2
0
1
0
0
2
0
0
2
0
0
1
1
2
2
0
1
0
2
1
0
1
0
1
1
0
1
0
0
1
0
0
0
0
0
1
1
0
1
0
2
1
2
1
0
0
2
1
2
0
0
0
2
0
0
0
2
1
0
1
0
1
0
0
0
0
1
2
2
1
1
2
0
0
2
2
0
0
0
0
0
0
0
1
0
1
0
0
1
4
0
1
1
0
0
1
0
0
2
1
1
0
1
1
0
1
3
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
3
1
0
0
1
4
0
1
0
0
2
1
0
1
0
0
1
0
1
1
2
0
1
0
0
0
0
0
0
1
0
0
0
2
1
2
0
0
1
0
0
1
0
0
1
0
2
0
1
1
3
0
1
0
0
0
0
2
1
0
2
0
1
0
2
0
0
0
0
0
2
0
0
1
2
2
1
1
1
0
0
1
1
0
0
1
1
1
0
0
0
0
0
0
0
2
0
0
1
2
0
1
1
2
0
1
0
0
1
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
1
0
2
0
0
0
0
1
0
0
0
1
2
0
0
1
1
0
0
0
0
0
0
1
1
1
2
0
1
0
2
1
2
0
0
3
1
0
0
1
2
1
0
0
0
1
2
0
0
0
1
1
0
0
2
1
0
0
0
0
0
0
1
0
0
1
0
4
0
0
0
3
1
0
1
0
2
0
1
0
2
2
0
0
1
2
1
1
0
1
1
2
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
1
2
2
0
2
0
1
0
0
1
1
1
2
1
1
0
0
0
0
1
0
1
0
2
2
1
0
2
0
0
1
0
0
0
2
1
0
2
1
1
2
0
0
0
0
0
2
1
1
2
0
0
0
4
2
0
2
2
0
0
1
0
1
2
2
0
0
0
0
0
0
0
0
0
0
2
3
2
1
0
0
1
2
0
0
1
0
0
0
0
0
1
2
1
1
0
2
0
2
0
0
1
2
2
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
3
0
2
0
1
1
2
0
0
0
0
0
0
0
0
2
0
3
0
0
1
0
2
1
0
0
0
1
3
3
0
1
0
0
0
2
0
0
2
0
0
1
0
2
4
0
0
1
1
0
0
0
0
1
3
1
1
2
0
0
0
1
1
2
1
0
0
2
0
0
0
1
0
0
2
2
0
0
2
1
2
0
1
0
2
0
1
0
1
3
0
1
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
2
0
0
1
0
1
0
0
2
0
2
0
2
2
2
0
0
0
0
0
2
0
0
0
2
2
2
0
2
0
0
1
1
0
1
1
0
2
0
0
2
0
2
0
0
0
0
2
0
0
0
0
2
0
2
0
2
1
2
2
0
1
0
2
2
2
0
0
1
2
0
1
1
0
1
0
1
0
0
0
2
2
0
0
1
0
0
1
0
2
1
1
2
0
1
1
0
0
0
1
2
1
1
0
1
0
1
1
2
0
0
2
1
0
2
1
1
0
1
0
1
1
0
1
0
0
0
2
0
2
0
0
0
1
0
0
1
2
0
0
0
1
0
1
2
1
2
2
0
1
2
0
3
0
0
2
0
0
0
1
0
2
2
1
0
2
0
2
0
0
0
1
1
0
0
0
1
2
1
0
0
0
2
0
1
1
3
1
1
0
1
1
0
0
2
0
0
2
2
2
1
0
2
1
1
0
0
1
2
0
1
1
1
0
1
0
1
2
2
0
1
0
0
0
0
1
0
3
1
0
1
0
1
0
0
0
2
1
2
0
0
0
2
0
2
0
0
1
0
1
0
2
0
0
0
0
1
0
1
0
0
2
1
0
0
1
0
1
0
1
2
2
2
0
0
1
0
1
2
2
1
1
0
1
0
0
0
0
2
0
1
0
0
1
0
1
0
1
0
1
0
2
0
2
0
1
0
1
2
0
2
0
1
2
0
0
0
2
1
0
2
2
1
0
0
2
1
0
1
1
0
1
0
0
1
0
1
0
0
1
0
1
0
0
2
0
0
2
1
0
0
0
0
0
1
2
1
0
2
0
0
0
0
0
0
1
1
0
0
1
2
0
3
1
2
1
0
0
2
1
0
0
2
0
1
0
2
0
2
1
1
0
1
1
0
1
0
0
0
2
0
1
2
0
2
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
2
0
1
0
1
1
1
1
1
3
0
2
2
2
0
0
0
2
2
1
0
2
2
1
2
1
2
1
1
0
0
0
0
1
0
1
2
0
1
1
1
0
0
2
0
1
0
1
2
1
2
0
0
0
1
0
2
0
0
0
1
2
1
1
0
1
0
0
0
0
0
2
3
0
0
2
0
2
2
0
0
1
0
0
1
0
1
0
0
0
2
1
0
1
1
2
2
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
2
0
1
3
2
0
0
0
3
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
2
2
1
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
2
1
2
1
1
0
2
1
1
1
0
2
0
2
1
0
0
1
0
0
3
0
1
2
4
2
0
0
4
0
0
0
0
1
2
2
2
0
1
0
2
0
2
1
0
2
0
0
1
0
1
0
0
0
0
0
2
0
0
1
0
2
0
0
0
1
0
0
0
0
1
2
0
0
3
2
1
1
1
1
1
1
0
0
0
1
0
2
1
1
2
0
0
2
0
1
0
1
0
0
0
0
1
0
1
0
1
0
0
0
2
2
2
0
0
1
1
0
1
0
1
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
1
0
2
1
1
0
1
0
0
2
0
0
0
0
0
0
1
0
0
2
0
2
1
0
0
1
1
0
0
3
2
0
0
0
2
0
1
2
0
1
0
0
2
1
1
0
1
0
1
0
0
0
0
0
0
1
1
1
1
0
1
0
0
0
1
0
0
1
1
0
1
4
2
0
0
0
0
1
0
1
2
1
0
1
0
1
0
2
1
1
0
0
2
0
1
1
1
2
1
2
0
0
1
1
0
1
1
0
0
0
1
0
0
0
2
0
1
2
0
1
1
2
0
1
1
1
1
1
1
0
1
2
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
2
0
1
0
0
2
2
1
3
0
0
2
2
0
0
1
1
1
2
0
1
0
2
1
0
0
0
0
1
0
2
0
2
1
0
0
0
1
1
0
2
0
0
1
0
1
1
1
1
2
0
1
0
1
1
1
2
1
1
0
2
2
0
0
1
0
0
0
0
1
1
0
2
0
1
3
2
0
1
2
2
2
2
1
1
1
0
1
2
1
2
0
1
0
0
0
2
0
1
0
0
1
1
2
0
1
0
1
0
2
0
2
0
0
0
1
1
0
1
0
2
2
0
1
0
2
0
2
0
2
0
0
0
0
1
0
1
0
0
0
1
1
0
0
1
2
0
1
0
1
1
1
0
0
1
0
0
0
1
2
1
0
0
0
0
1
2
1
0
2
0
3
0
2
1
0
0
1
0
1
2
0
1
0
1
0
0
2
2
0
0
0
2
0
1
0
0
2
1
0
0
2
0
0
0
0
2
0
0
0
0
0
1
1
1
0
2
1
0
0
0
0
2
0
0
1
1
0
0
2
0
0
1
0
2
1
1
1
1
2
0
0
0
2
2
2
0
0
0
1
1
0
3
0
1
0
0
0
1
2
0
1
0
1
0
0
0
0
0
2
1
2
0
2
0
2
1
0
0
2
0
2
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
1
0
0
0
1
2
2
0
0
0
0
0
0
1
0
2
1
0
1
0
1
1
0
0
2
2
0
0
0
2
1
0
2
1
0
2
2
3
2
2
2
2
2
0
2
1
0
0
1
0
1
1
0
0
1
0
0
2
2
0
1
0
0
1
1
0
2
1
0
1
0
1
0
0
1
2
0
1
0
1
0
0
0
1
0
0
0
0
0
1
1
1
2
1
0
0
0
2
0
2
0
0
0
1
0
1
0
0
0
1
2
0
0
1
2
2
0
0
0
0
2
0
1
2
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
2
0
1
2
0
2
1
2
1
0
1
1
2
0
1
1
0
0
0
1
0
1
0
0
0
2
0
0
0
1
0
1
0
1
0
0
2
0
0
0
1
0
0
0
1
0
0
2
0
1
0
0
0
2
2
0
1
1
0
2
0
0
1
1
0
1
1
2
1
3
0
2
0
2
1
1
1
1
1
1
0
0
0
2
1
0
0
0
1
1
2
0
1
2
0
0
1
1
0
0
1
1
1
1
0
0
0
2
0
1
2
1
2
1
0
0
0
1
0
0
1
1
0
1
0
1
0
0
3
0
0
1
1
2
1
1
1
1
1
0
1
2
2
0
2
1
0
0
0
0
0
0
2
1
0
0
0
2
1
0
1
0
1
1
1
0
2
1
0
1
0
0
0
2
1
2
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
2
1
0
1
1
0
2
1
1
2
0
1
0
0
1
0
0
0
2
4
1
2
0
0
0
1
0
0
2
0
0
0
1
0
0
2
0
0
2
1
1
1
2
1
0
4
1
2
1
0
0
1
0
0
1
0
2
0
0
1
1
1
2
0
2
1
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
2
2
2
1
0
0
0
1
0
1
1
0
1
0
0
1
0
0
1
0
1
2
2
0
0
2
2
1
1
0
0
1
0
1
3
0
0
2
2
2
0
0
2
0
0
0
1
0
2
0
1
0
0
0
0
2
2
0
0
1
0
1
0
1
0
1
0
2
0
0
0
2
0
2
0
2
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
3
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
2
2
2
1
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
2
0
0
1
0
0
2
0
0
2
0
1
2
0
1
0
0
2
0
0
0
2
1
0
0
2
0
0
6
1
0
2
2
2
0
1
1
0
2
2
0
0
0
2
1
0
0
2
1
0
2
0
0
2
0
0
2
2
0
2
0
1
0
0
1
0
2
0
0
1
0
1
0
1
1
1
0
2
1
1
1
1
0
1
0
2
0
1
3
0
0
2
0
1
2
0
2
2
1
1
1
2
0
0
0
0
3
2
0
2
0
0
1
2
1
2
2
1
0
0
0
0
2
0
0
2
2
0
0
0
2
1
2
0
1
2
1
2
0
2
0
0
1
2
0
1
1
0
0
1
0
1
1
2
0
2
0
2
0
1
0
0
2
2
2
0
0
0
0
0
1
1
0
0
1
2
2
0
2
1
0
0
0
0
2
0
2
0
0
0
1
2
0
2
1
0
3
0
1
2
1
1
0
0
1
0
0
0
0
0
0
2
2
0
2
0
0
2
0
0
1
0
1
0
2
0
2
1
0
1
0
2
2
0
3
1
0
0
0
1
2
1
0
0
1
2
0
2
0
1
2
1
0
1
0
0
3
1
0
0
0
1
1
0
0
0
0
2
0
1
0
2
1
1
1
1
2
0
0
0
0
1
0
0
0
0
0
1
1
0
0
2
1
0
0
1
0
0
1
1
1
1
0
0
1
2
1
1
1
0
2
1
1
0
0
0
2
2
1
0
0
2
2
2
2
0
0
2
2
0
0
2
0
2
0
0
1
4
0
2
0
6
1
2
0
0
0
1
1
2
0
0
1
0
0
0
0
1
2
0
2
1
0
1
2
0
0
1
1
3
0
0
0
0
2
0
1
0
1
0
0
2
1
0
0
0
0
2
0
0
2
1
2
1
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
2
0
0
0
2
1
2
0
0
0
0
1
1
1
2
0
1
0
1
0
0
1
2
1
1
2
0
0
0
0
2
0
1
0
0
1
1
3
1
0
0
1
0
0
0
2
1
1
0
0
1
2
0
1
2
0
2
1
0
0
0
1
0
0
1
0
1
1
0
0
0
0
1
0
0
0
1
0
0
1
1
2
2
0
0
0
1
1
2
1
2
0
1
0
1
2
0
0
1
0
2
2
1
0
1
1
0
2
1
1
0
0
1
1
4
1
1
0
1
2
1
0
0
1
0
0
2
0
0
0
1
0
2
1
0
0
1
0
0
0
1
1
0
0
0
1
1
1
2
4
0
2
0
1
3
1
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
1
2
2
0
2
0
1
0
0
1
2
2
0
2
2
0
0
1
0
2
1
0
0
0
1
1
0
0
2
2
1
0
0
1
1
0
0
0
0
1
1
1
1
0
0
1
1
0
2
2
0
0
2
0
2
0
2
0
2
1
0
1
1
3
2
2
0
3
0
0
1
1
1
2
0
2
1
0
0
2
0
0
0
0
1
2
0
0
1
0
0
1
1
2
1
1
1
0
0
2
0
1
0
2
1
0
1
0
2
0
0
0
1
0
0
0
1
1
0
2
0
0
0
1
0
2
2
1
1
0
1
0
0
2
1
1
2
2
1
0
4
0
0
0
0
1
0
1
0
0
0
2
0
0
2
0
0
0
0
2
1
0
0
2
1
0
0
1
2
2
1
2
0
1
0
0
2
0
1
0
0
0
1
0
1
0
2
1
2
2
0
0
0
2
0
1
0
0
0
2
2
0
0
1
1
0
1
0
2
1
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
2
0
1
0
0
0
2
2
1
2
0
0
0
1
2
3
2
0
0
1
1
3
0
3
2
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
2
1
0
2
0
1
0
0
0
2
2
0
3
0
0
2
2
0
1
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
1
1
0
2
0
1
2
1
0
3
1
2
2
1
1
1
2
0
1
0
2
3
1
2
0
3
0
1
0
0
2
0
0
0
2
2
0
0
2
0
1
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
2
0
1
1
0
2
2
1
1
1
0
1
1
0
0
2
0
0
1
0
2
1
2
1
2
0
2
3
0
0
0
1
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
3
0
1
2
3
0
1
1
2
0
1
1
0
0
0
0
2
2
1
0
2
1
2
0
0
2
1
0
0
0
0
0
0
2
1
0
0
4
0
2
0
2
0
2
2
0
1
0
2
1
3
0
1
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
2
0
1
0
0
1
0
0
1
1
2
1
0
1
0
2
2
1
3
0
0
0
0
1
0
2
0
2
1
1
0
1
1
1
0
2
0
1
3
0
0
0
1
0
0
0
0
0
0
2
1
0
0
1
1
0
1
1
0
0
0
0
1
0
1
2
2
2
1
2
1
1
1
0
1
2
0
0
1
1
4
2
0
2
0
0
1
0
2
2
2
0
1
0
2
0
1
1
1
0
0
0
0
1
0
1
0
2
1
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
3
2
2
0
0
1
0
2
0
1
0
0
0
0
0
1
0
1
1
0
2
0
0
0
0
0
0
1
2
0
0
0
2
0
2
2
0
0
0
0
2
0
2
1
0
0
0
2
0
0
2
0
1
1
2
0
0
2
2
0
2
2
0
0
0
0
2
0
0
2
0
2
0
0
2
1
2
1
1
1
1
0
0
1
0
0
1
1
0
1
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
1
0
2
2
2
0
1
2
1
2
0
0
2
2
0
1
2
2
3
2
0
2
0
2
0
1
1
0
1
1
1
1
2
0
1
1
0
2
1
0
0
2
0
1
0
0
0
1
0
0
3
1
2
0
0
1
1
0
1
0
0
1
1
1
1
2
1
1
0
0
1
1
0
0
0
2
0
1
1
0
2
1
1
0
0
0
1
1
1
2
1
0
1
0
2
0
0
2
1
0
0
0
0
0
0
2
1
0
1
2
0
0
1
0
1
2
2
2
0
2
0
1
0
0
1
0
0
2
2
0
0
0
1
0
0
0
0
2
3
0
0
1
2
1
2
2
2
0
2
0
0
1
0
0
2
2
2
2
1
1
3
1
1
1
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
1
1
1
2
1
2
1
2
0
0
0
1
2
1
1
1
0
1
1
1
1
1
0
0
0
0
1
1
0
0
1
1
1
0
0
2
0
0
0
0
1
0
1
1
0
0
2
1
0
2
0
0
0
0
0
2
0
1
1
1
3
2
1
0
1
1
2
0
0
0
0
0
0
2
0
1
1
0
1
0
0
2
1
2
0
1
0
1
0
1
0
1
1
0
1
0
1
0
1
0
0
3
1
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
1
0
1
0
2
0
2
0
0
0
1
2
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
2
0
0
2
2
0
1
1
0
2
2
1
0
1
0
0
2
0
2
0
2
1
0
0
0
2
0
0
2
2
1
0
0
0
0
0
1
1
2
2
2
0
0
2
0
1
2
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
1
2
0
0
0
2
3
1
0
1
0
0
0
0
0
1
0
2
0
0
0
2
2
0
0
1
1
2
1
0
0
0
1
1
0
2
0
0
2
2
0
0
2
0
0
1
0
2
1
1
1
2
0
1
2
0
1
0
0
0
2
0
0
0
0
1
0
1
1
0
1
1
1
3
0
0
3
1
1
0
1
0
0
0
1
2
1
0
0
0
1
2
0
1
1
0
0
2
0
0
0
0
0
0
0
2
2
0
0
1
0
0
1
2
0
0
1
2
0
0
0
0
0
0
2
2
0
2
0
2
2
0
1
0
0
0
2
2
1
0
0
1
1
0
0
0
1
1
1
2
0
0
0
1
1
2
0
0
0
2
2
1
0
0
0
1
0
0
3
2
2
0
0
0
0
1
1
2
1
2
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
1
1
0
1
2
0
0
2
0
0
1
0
0
1
0
1
1
0
0
1
0
0
2
2
0
2
0
0
0
0
2
1
1
1
0
0
2
0
2
2
1
0
0
0
0
1
0
0
2
0
0
1
1
1
1
1
0
0
1
0
0
0
0
2
1
2
0
2
0
0
1
2
0
1
0
1
1
2
1
2
0
2
1
0
0
1
0
2
2
0
0
0
0
1
2
1
0
1
1
1
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
2
0
0
1
0
0
0
2
0
2
0
2
1
0
0
0
0
0
0
2
0
0
1
0
1
1
0
1
1
1
0
0
0
3
5
2
0
0
2
1
0
1
0
0
1
1
1
1
0
2
0
0
0
0
2
2
1
0
1
0
2
0
2
1
0
0
2
0
1
0
3
2
0
0
2
1
0
3
1
0
0
2
0
1
1
0
0
3
0
2
0
1
1
0
0
0
0
0
1
2
0
1
0
0
1
2
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
2
2
0
0
0
0
0
1
2
1
0
0
2
1
0
0
3
2
0
0
0
0
2
0
2
3
0
0
1
0
0
1
0
1
1
0
1
0
1
0
0
0
0
0
0
1
0
2
1
0
1
0
0
1
1
1
2
0
0
1
0
0
2
1
0
0
0
1
2
0
1
1
4
1
1
0
2
0
0
0
2
2
0
2
0
1
0
1
1
2
0
0
2
0
1
0
1
0
1
0
0
0
2
1
1
2
0
2
2
2
2
0
0
1
0
1
1
2
0
1
0
1
2
0
0
0
1
0
1
3
2
0
0
0
0
1
0
0
3
0
1
0
0
1
2
2
2
1
1
2
1
0
1
0
0
1
1
1
0
1
2
2
2
1
1
3
2
2
0
3
2
1
0
0
1
0
2
0
0
0
0
1
3
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
3
2
2
0
0
1
0
2
2
2
1
0
1
0
2
2
0
0
0
0
0
0
0
1
0
0
1
2
1
1
2
1
0
1
0
0
3
2
0
1
1
0
0
1
0
1
2
0
1
0
1
0
1
0
1
2
0
1
1
1
0
0
1
2
1
1
0
0
1
2
0
1
1
0
1
0
0
2
0
2
0
0
1
1
2
2
1
0
2
0
1
0
1
0
1
2
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
2
1
0
0
0
1
0
0
2
0
2
0
0
0
1
1
0
0
1
0
3
0
0
0
0
0
1
0
0
0
0
1
2
0
2
0
1
1
1
0
0
0
1
0
3
0
0
1
0
2
0
1
1
0
0
0
0
1
1
1
1
2
0
0
1
0
0
0
0
0
0
0
1
1
2
1
0
0
0
2
0
2
0
3
0
0
0
2
0
0
0
0
1
0
0
0
0
4
1
2
0
1
0
2
0
0
1
1
0
0
0
0
1
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
2
1
2
1
0
0
0
1
0
1
1
0
0
0
0
0
0
2
0
2
1
7
0
1
0
0
1
0
0
3
0
0
1
0
0
0
0
0
0
0
1
2
0
1
0
0
4
1
0
0
0
0
1
0
1
3
2
0
2
0
0
2
0
1
2
1
1
1
2
1
2
0
0
0
0
0
2
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
2
0
0
0
0
0
0
1
0
2
2
3
1
1
3
0
0
2
0
0
1
0
1
2
0
0
0
0
0
2
0
2
2
0
0
2
0
0
1
0
0
1
2
0
0
2
0
0
0
1
0
0
2
0
1
2
0
2
0
0
0
2
5
0
0
2
1
0
1
0
2
0
2
0
0
0
1
1
2
0
2
1
0
1
0
0
1
0
2
2
1
3
0
1
0
2
1
0
2
0
0
1
0
2
0
2
0
0
0
0
2
1
1
0
1
0
2
0
0
2
0
1
1
0
1
2
1
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
1
1
0
1
1
0
1
2
0
0
0
0
1
0
1
0
0
0
0
1
2
0
2
1
2
0
1
1
1
0
2
1
1
1
0
2
1
0
0
0
0
0
0
0
0
1
2
1
1
0
1
1
1
0
1
0
1
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
1
2
0
0
2
1
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
2
0
1
0
0
2
2
1
1
0
0
0
0
0
0
1
0
2
2
2
0
0
1
1
0
0
2
1
1
0
0
0
0
1
0
3
0
0
0
0
2
1
0
0
2
1
2
0
1
1
0
0
2
0
1
0
2
0
2
1
0
1
1
1
0
0
1
0
0
1
0
1
0
2
0
1
0
1
0
1
1
0
0
2
1
1
0
0
2
1
0
1
1
2
2
0
1
0
0
0
0
0
1
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
2
0
0
0
1
1
0
0
0
1
0
0
1
0
0
1
0
0
1
1
1
0
1
0
0
2
2
0
1
0
1
2
0
1
2
1
1
0
2
1
1
0
0
0
0
4
0
1
1
0
2
0
1
0
0
1
1
1
0
2
1
0
1
2
0
0
0
0
1
2
2
0
0
1
0
1
0
0
0
2
0
1
0
2
0
0
2
0
1
1
0
0
0
0
1
1
1
1
1
0
0
0
0
0
0
2
0
0
2
0
2
0
2
1
0
1
4
2
1
0
3
2
0
1
3
2
1
2
2
2
0
0
2
1
0
1
1
0
2
2
0
0
0
0
3
1
0
0
1
2
8
2
1
2
0
0
0
1
0
4
1
0
2
0
0
0
1
1
2
1
1
1
0
3
1
1
1
0
1
0
1
0
0
2
1
3
1
1
0
0
2
0
0
2
2
0
0
1
0
2
0
2
2
0
0
0
1
2
1
0
0
1
0
0
1
0
1
2
0
1
0
0
1
2
0
0
2
1
0
0
2
0
0
0
0
2
0
0
2
0
2
2
2
0
2
0
2
0
1
1
2
0
0
0
2
1
0
0
0
1
0
1
1
1
2
0
0
0
2
1
0
0
2
0
1
1
1
0
0
1
0
1
0
1
1
1
0
2
0
0
1
1
0
1
1
2
0
1
0
0
1
0
1
0
1
0
0
0
0
2
1
0
1
0
2
2
2
2
1
0
0
0
2
0
0
0
2
0
2
1
0
0
0
1
2
0
1
2
1
0
0
0
0
0
0
1
0
0
2
0
1
0
1
2
0
0
0
1
1
2
0
0
1
0
2
0
0
0
1
0
2
2
0
2
0
1
2
0
0
2
1
0
0
0
1
3
0
1
0
1
0
2
0
2
0
0
0
2
1
0
1
1
0
0
0
1
2
0
0
1
1
0
0
0
0
0
2
1
1
0
0
2
2
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
1
0
2
1
0
0
0
2
0
0
2
1
0
2
2
2
2
0
0
2
0
0
1
1
1
0
0
0
0
4
2
1
1
2
1
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
2
2
0
2
1
0
0
0
0
0
0
2
1
0
0
1
1
0
0
0
0
2
2
0
1
0
2
0
2
2
0
2
2
0
1
1
1
2
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
1
1
1
1
1
1
2
2
1
0
0
0
4
1
1
1
0
0
1
0
0
1
0
1
0
4
1
0
1
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
2
1
2
0
0
1
0
1
2
3
2
0
0
2
0
2
0
0
1
1
0
1
2
0
0
0
1
0
0
0
1
0
1
2
1
2
0
0
0
0
1
0
1
4
0
1
0
0
0
2
0
2
1
1
2
1
0
0
1
0
0
0
0
1
1
1
0
0
0
0
4
0
1
0
0
2
0
0
0
0
0
2
1
0
0
0
0
1
2
1
0
2
0
0
0
0
0
2
0
0
0
0
1
1
1
0
0
1
1
0
0
0
1
0
1
0
2
0
0
0
1
0
0
2
0
0
1
1
0
0
2
2
0
1
1
2
0
0
2
0
0
0
0
1
1
2
0
2
1
0
1
2
0
2
1
0
0
0
0
0
0
2
0
2
1
1
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
3
1
0
3
0
2
2
0
1
2
2
0
0
1
0
0
1
1
0
2
0
0
0
0
2
0
0
0
0
2
1
1
0
0
0
1
2
3
0
1
0
0
2
1
0
1
2
0
2
0
1
0
1
0
1
0
0
0
0
2
2
0
2
0
1
0
0
0
1
1
1
1
0
1
0
0
0
0
1
2
2
1
0
1
1
1
0
1
2
1
2
2
2
1
1
0
1
0
0
1
2
0
2
0
0
2
2
0
0
1
0
0
2
2
0
0
0
0
0
2
2
0
1
0
2
2
0
0
0
0
2
0
0
0
0
2
0
0
2
0
1
0
1
1
2
0
0
0
2
1
1
1
0
0
0
0
0
0
0
1
0
0
1
2
1
0
2
0
0
1
1
2
0
0
0
0
1
0
2
0
2
0
0
2
1
2
1
1
2
2
1
1
0
3
1
0
0
1
1
0
0
2
1
0
1
0
2
2
0
1
0
0
2
1
1
0
0
0
0
1
2
2
0
0
2
0
0
2
0
0
2
0
0
2
2
0
0
1
0
1
0
0
1
0
1
1
1
0
0
1
1
0
0
2
1
0
2
0
0
0
0
0
0
1
0
1
0
1
0
0
2
2
2
0
0
2
0
1
1
1
1
2
0
0
1
0
1
1
0
2
1
2
0
1
2
1
0
0
0
0
1
0
2
0
0
1
0
1
0
2
0
0
0
0
2
0
2
0
0
0
2
0
0
0
2
1
0
1
0
3
1
0
2
0
0
0
0
0
2
0
2
0
2
0
2
1
2
0
0
2
0
0
1
1
1
0
1
0
2
0
1
0
0
1
0
0
1
2
1
0
0
1
2
0
2
0
0
1
0
0
1
1
0
2
0
1
2
2
1
0
1
1
0
1
0
0
1
1
0
1
0
0
2
0
0
1
0
0
0
0
1
0
1
0
0
1
2
0
2
2
0
0
0
2
0
0
3
0
0
2
0
1
2
1
0
0
1
0
2
2
0
2
0
2
1
0
2
0
2
0
0
0
1
0
2
0
0
1
0
2
0
1
0
1
1
0
0
0
0
0
1
0
0
0
2
0
1
0
0
1
0
2
0
0
0
1
1
0
1
0
0
0
0
0
0
1
3
1
0
1
1
0
1
0
1
0
1
3
2
1
0
1
0
0
1
0
0
2
0
0
0
1
0
1
1
0
1
1
1
0
0
3
0
1
0
0
2
0
2
0
0
1
0
3
0
1
0
1
1
1
0
0
1
0
0
1
2
2
2
0
0
2
0
0
1
0
2
0
0
0
2
0
0
2
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
2
0
2
1
0
1
1
3
1
0
0
0
1
2
2
1
0
0
0
0
0
0
1
0
2
1
0
2
1
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
1
2
0
0
0
1
1
0
0
0
2
2
0
1
2
2
2
1
1
0
1
0
2
0
0
0
2
2
1
0
0
0
1
0
0
2
0
0
0
0
1
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
2
0
0
1
0
0
1
3
0
0
0
0
0
1
1
0
0
1
0
2
1
0
1
1
1
0
2
0
1
0
0
2
3
0
1
2
0
0
1
2
0
0
0
2
1
2
0
1
0
1
2
2
3
2
0
1
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
1
1
1
0
2
2
0
1
0
0
1
1
2
2
2
2
0
2
0
4
0
1
0
0
3
1
1
1
2
0
2
0
0
2
1
1
1
1
2
1
0
1
0
0
0
0
0
2
0
0
2
2
0
2
2
1
2
0
0
1
2
0
3
0
0
0
0
0
0
0
1
3
2
2
2
1
2
0
1
1
1
0
1
0
0
2
1
0
1
0
0
0
2
0
1
1
1
2
2
2
1
0
1
3
0
0
1
0
0
0
2
0
2
0
0
0
1
0
1
0
0
1
0
1
0
2
0
1
0
0
0
0
1
1
2
2
0
0
1
1
2
0
0
2
0
2
2
1
0
0
1
1
0
0
1
0
2
1
0
1
0
0
1
0
2
0
1
0
2
2
0
2
0
0
2
0
0
0
2
2
0
0
2
0
0
1
0
2
0
0
1
1
0
0
1
1
2
0
0
0
0
0
0
2
0
1
0
0
1
2
2
0
0
0
0
0
1
0
0
2
0
0
2
1
1
1
0
0
2
1
0
0
1
1
0
2
0
1
1
0
0
2
0
0
0
1
1
1
0
0
0
2
0
0
0
2
0
0
2
0
0
1
3
1
0
0
0
0
2
1
0
0
0
2
1
0
1
2
0
0
2
1
0
1
0
1
1
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
1
0
1
3
0
0
0
0
0
0
2
0
1
1
0
0
2
1
0
0
0
0
1
2
1
0
1
1
0
6
2
1
0
1
0
0
1
1
0
1
0
0
0
1
1
0
0
2
0
0
0
1
2
1
0
0
1
0
0
1
0
0
0
1
2
1
1
0
2
0
2
2
0
0
0
1
1
1
2
2
2
1
1
0
1
2
2
1
0
0
0
2
1
2
0
1
1
0
2
2
0
0
2
0
0
0
0
2
0
0
1
1
0
2
0
0
2
0
0
0
0
0
1
0
0
1
0
1
0
0
2
1
1
1
0
1
2
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
1
0
0
0
0
1
1
1
1
0
0
0
5
0
0
0
0
1
1
0
0
0
1
2
1
2
0
0
2
1
1
2
1
1
0
1
0
0
2
3
1
0
1
1
0
1
0
2
0
0
2
2
0
1
0
2
0
0
2
2
1
2
0
2
1
1
0
0
2
0
0
0
2
1
1
0
0
0
0
0
2
1
1
2
0
2
1
2
1
0
1
1
0
2
1
1
0
2
2
1
1
2
0
1
1
1
1
2
0
1
2
0
0
0
0
2
2
0
0
0
1
0
0
0
1
0
2
1
0
2
1
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
3
1
0
1
0
0
0
1
0
1
0
1
3
2
1
2
1
0
0
3
2
0
0
1
1
0
2
0
1
0
1
1
0
0
0
2
1
0
2
1
1
0
1
1
0
0
2
1
1
0
1
0
0
0
1
0
0
0
2
0
0
2
3
1
2
0
0
1
0
0
2
0
0
0
0
0
0
2
0
1
1
2
0
1
0
1
2
0
0
0
1
1
0
1
1
1
0
0
1
0
1
0
1
0
0
0
0
0
0
2
2
0
0
0
1
0
0
1
0
0
2
1
0
0
2
1
0
0
1
0
0
0
0
1
2
0
0
1
0
0
1
0
1
0
1
13
0
1
1
1
0
1
1
4
0
0
0
0
0
0
2
2
0
0
2
1
0
0
2
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
5
0
0
1
1
2
1
0
1
0
0
1
2
1
0
0
0
0
0
3
0
0
2
0
1
0
0
2
0
1
0
0
0
2
0
0
0
2
0
1
2
0
1
2
0
1
0
0
0
1
0
3
0
0
0
0
1
1
2
0
2
0
1
3
0
0
0
0
0
0
2
2
2
0
2
0
0
1
0
1
0
2
1
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
3
2
1
0
3
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
2
1
1
0
1
2
2
0
1
1
0
1
0
1
2
1
0
0
1
0
0
1
0
0
2
2
0
2
0
1
1
2
2
0
0
3
0
0
0
1
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
2
1
0
0
0
0
1
1
2
0
2
0
0
0
2
0
0
2
0
0
0
0
2
2
1
1
0
0
1
0
2
0
2
2
2
0
1
1
0
0
1
0
2
0
3
2
0
2
1
0
1
0
1
0
1
1
0
0
1
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
2
0
2
0
2
1
2
0
1
0
1
1
0
0
0
2
1
2
0
0
0
1
0
1
2
0
2
1
1
1
0
0
1
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
1
2
1
2
0
0
0
2
0
0
1
0
0
1
0
2
0
0
2
0
2
0
1
0
0
1
0
0
2
0
2
1
2
2
0
2
2
2
2
0
0
2
1
0
2
0
0
1
0
0
0
0
0
2
0
1
2
2
0
0
3
1
0
0
0
0
2
2
0
0
0
0
0
1
0
1
0
0
1
0
1
0
2
1
1
1
0
0
1
1
3
1
3
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
1
1
2
0
1
1
0
0
0
2
1
0
0
2
2
0
0
2
0
1
0
0
0
0
2
0
1
2
0
0
2
1
1
2
1
1
1
2
0
2
1
1
1
0
2
0
1
0
1
0
1
0
2
0
0
2
2
0
0
0
2
0
0
2
0
2
1
0
0
0
2
0
0
0
1
1
2
1
0
1
0
1
0
0
0
0
2
0
1
1
0
2
0
1
1
2
0
1
1
1
2
3
2
1
2
0
0
0
2
0
0
0
0
1
0
1
0
1
0
0
0
0
2
1
0
1
0
0
2
2
2
0
0
3
0
0
0
1
0
0
2
0
0
1
0
1
0
1
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
3
1
1
1
0
0
1
0
0
0
0
0
3
0
1
1
1
0
0
2
0
2
1
0
2
0
1
2
0
1
0
0
2
1
0
0
0
0
0
0
0
0
2
0
1
0
1
0
1
0
2
2
2
1
1
0
1
0
2
2
2
1
0
2
0
0
1
1
1
0
0
0
1
0
0
1
0
0
1
0
0
2
3
2
2
0
0
0
2
2
0
0
1
0
0
0
2
1
0
2
1
0
0
0
1
0
1
1
0
1
2
1
0
1
0
0
0
0
1
1
1
0
2
1
0
2
0
0
0
3
0
0
1
0
1
1
1
3
0
1
0
0
0
1
3
0
1
1
1
0
0
0
0
2
1
0
0
1
0
0
1
0
0
3
0
0
1
0
2
0
0
0
0
0
2
0
1
2
0
1
0
0
0
0
0
1
1
1
0
0
0
0
2
0
1
1
1
0
0
3
0
2
0
2
0
0
0
1
1
0
1
0
1
0
0
0
1
0
0
1
0
0
2
1
0
1
1
2
1
1
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
1
1
2
0
2
0
1
2
1
1
1
0
0
0
2
0
0
0
2
1
1
0
0
1
1
0
1
2
0
0
1
1
0
1
1
2
2
0
2
0
0
0
0
0
0
0
1
0
2
0
1
0
1
0
1
0
0
1
0
0
2
1
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
1
2
1
0
0
0
1
3
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
10
2
0
1
1
0
0
0
1
2
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
2
2
1
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
2
0
1
0
1
0
0
1
0
0
1
2
0
1
2
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
3
0
1
0
2
0
1
0
1
1
1
0
0
1
1
0
2
0
1
6
1
0
1
0
0
2
1
2
0
0
0
0
0
1
1
2
0
1
1
0
0
1
1
0
1
0
0
1
0
0
0
1
0
0
1
3
0
1
1
2
2
2
0
1
0
2
0
0
0
0
1
1
0
1
0
0
0
0
0
0
2
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
1
1
0
1
0
1
0
1
1
1
1
1
1
1
1
0
0
0
0
1
0
2
2
0
0
2
2
0
3
0
1
0
1
2
0
1
0
0
2
1
0
0
0
1
1
0
1
0
0
0
0
4
1
0
1
1
1
0
2
0
2
0
1
0
1
0
1
1
1
0
0
0
1
0
0
0
0
2
0
2
0
0
0
1
2
0
0
2
0
0
0
0
1
0
0
1
0
1
1
2
0
0
0
0
1
0
1
2
0
0
1
3
0
1
2
0
0
0
1
4
2
0
0
0
2
1
1
0
1
0
0
1
0
1
0
2
1
1
0
0
0
1
0
0
0
1
2
1
0
1
0
4
2
1
0
1
0
1
1
0
1
1
1
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
2
1
1
1
0
0
1
0
3
2
0
1
0
0
0
1
0
0
0
2
1
3
0
2
1
1
1
0
2
0
0
0
0
1
0
3
0
0
0
0
1
0
0
0
0
1
1
1
1
0
0
0
0
0
0
1
1
1
2
0
0
0
3
1
0
2
2
0
0
0
0
0
6
1
0
1
0
1
0
0
0
1
2
2
0
1
1
0
0
2
0
2
1
0
3
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
2
0
1
0
1
1
1
0
0
0
0
1
0
0
2
2
0
0
0
1
2
0
0
1
0
2
1
0
0
0
0
2
2
0
0
1
2
1
0
1
0
1
0
0
0
2
2
1
0
2
1
3
2
0
0
1
0
2
2
2
0
0
0
1
0
0
2
0
1
0
0
0
2
0
1
0
0
1
0
0
2
1
0
1
2
0
1
0
0
0
0
0
2
1
2
0
0
1
1
0
0
1
2
0
1
0
2
1
1
0
1
1
0
0
0
0
1
0
1
0
0
0
0
2
0
2
0
2
0
0
0
1
0
1
2
3
0
0
2
1
1
0
0
1
1
0
1
0
0
0
1
1
2
0
0
0
2
1
0
0
1
1
1
0
2
1
2
0
1
0
1
1
2
2
0
0
1
2
0
0
1
2
0
0
2
0
2
0
0
0
2
0
0
0
0
1
1
0
0
1
2
0
2
0
2
0
4
0
2
2
1
1
1
1
1
1
1
1
0
0
0
1
0
0
1
0
0
2
1
1
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
2
0
0
2
0
0
0
1
1
0
0
0
2
1
0
0
2
1
1
2
0
0
0
0
1
2
0
0
0
2
1
0
0
0
0
0
1
2
0
1
1
0
0
0
3
1
1
0
0
2
1
0
2
0
0
0
0
2
2
1
2
0
2
3
1
0
0
1
0
1
0
0
2
1
0
0
1
0
2
1
0
0
2
0
1
0
0
0
1
0
1
1
0
0
0
2
2
1
2
2
0
0
0
0
1
1
0
0
1
1
1
0
0
2
2
0
1
2
0
2
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
2
2
0
0
0
0
0
0
2
1
2
0
0
1
1
1
2
0
2
2
0
1
0
0
2
0
1
2
0
1
0
0
2
0
0
1
1
2
0
1
0
0
0
0
0
1
1
2
0
0
0
0
0
2
0
1
2
0
0
2
0
0
0
2
0
2
0
0
2
0
0
0
0
1
0
1
1
2
3
1
2
2
1
0
1
1
1
0
0
0
2
0
2
1
0
2
0
0
0
0
1
2
0
0
2
1
1
1
0
5
0
0
0
1
0
0
1
2
0
1
1
1
0
0
0
0
0
2
1
0
0
1
2
1
2
4
0
2
0
2
2
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
2
0
0
2
1
1
1
0
2
0
1
0
0
0
2
0
2
2
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
2
1
2
1
0
0
0
1
0
2
0
2
2
0
1
1
0
0
0
2
1
0
2
0
0
2
1
1
2
1
3
2
2
0
1
1
0
2
0
2
2
0
1
1
2
1
0
4
0
2
1
1
4
0
2
1
0
1
0
1
1
1
0
0
0
0
0
0
2
2
1
0
0
1
1
0
1
0
1
0
0
0
1
1
0
0
1
2
0
0
0
3
1
0
0
0
1
1
0
0
2
0
1
2
2
0
1
1
1
2
0
2
0
2
0
0
1
0
0
2
1
0
1
0
1
0
1
0
1
0
1
1
1
1
1
1
1
0
0
0
2
0
0
1
0
0
2
1
2
2
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
1
0
2
1
2
0
0
1
1
0
1
3
0
0
0
1
1
0
1
0
1
1
0
2
1
2
0
0
0
0
2
0
0
0
0
2
2
2
1
0
2
1
0
0
0
0
0
0
0
0
0
2
0
2
1
1
0
1
0
0
1
1
0
0
2
2
0
0
0
0
2
0
1
1
2
0
2
0
0
2
0
0
0
0
1
1
2
1
0
0
0
2
2
1
2
0
0
0
0
1
0
0
1
0
0
1
2
0
0
1
0
0
0
1
1
0
0
2
0
0
1
0
0
2
0
2
0
0
0
2
0
1
2
3
0
1
0
0
1
1
4
2
1
1
0
0
0
0
0
0
2
1
0
0
1
1
1
2
0
1
2
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
2
2
0
0
1
0
1
1
0
1
0
1
0
0
1
2
1
0
2
0
0
0
2
0
0
2
1
0
2
0
0
1
0
0
2
3
0
1
1
1
0
2
0
1
3
3
1
2
0
2
1
0
2
3
2
2
1
0
1
0
0
0
0
2
1
1
0
1
2
1
0
0
3
2
0
0
1
0
3
1
0
0
0
0
0
0
1
2
0
1
1
1
1
1
0
2
1
0
2
0
0
1
2
1
2
0
0
1
0
2
2
2
0
0
1
0
1
1
0
0
1
1
0
3
2
3
1
1
1
0
1
0
0
0
0
0
0
1
0
2
0
0
0
2
1
2
0
2
2
0
0
1
0
0
1
0
0
0
0
0
1
1
1
3
2
1
0
2
0
2
2
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
2
6
0
3
2
1
2
3
1
0
0
0
1
0
0
1
2
0
2
0
1
2
1
0
0
1
0
0
1
0
2
2
0
0
0
2
0
1
0
0
3
0
0
1
2
2
1
0
0
1
0
0
2
0
0
0
1
2
0
1
2
0
2
4
0
2
2
1
1
1
0
1
1
1
1
0
2
0
0
2
0
0
0
0
2
0
1
2
1
0
0
2
1
0
2
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
2
0
1
0
0
1
0
0
1
2
1
2
0
1
0
0
0
0
2
0
0
2
1
2
0
2
0
0
1
2
2
2
1
0
0
1
1
0
2
2
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
1
1
0
2
1
0
0
0
2
1
0
2
2
0
0
2
1
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
3
1
0
0
2
0
0
0
2
1
0
1
0
0
1
0
0
0
1
0
1
2
0
1
0
1
0
0
1
1
0
0
1
0
1
1
0
1
0
0
2
0
2
0
1
1
0
0
1
2
2
0
0
2
1
0
2
2
0
0
0
1
1
0
0
0
1
0
1
0
2
2
0
2
0
1
0
0
1
3
2
0
0
2
1
0
0
0
0
0
0
1
0
3
2
2
0
0
1
0
0
0
0
0
0
8
0
1
1
0
0
0
0
0
0
2
1
0
0
0
2
0
0
2
0
2
0
1
0
0
2
0
0
1
0
2
2
0
1
0
1
2
2
2
0
2
1
0
0
0
1
0
5
1
1
0
0
0
2
1
1
1
1
2
1
0
0
1
0
0
2
0
2
0
0
0
1
0
1
1
0
0
0
2
0
0
0
1
2
2
0
1
2
0
2
2
0
1
0
1
0
2
0
1
0
0
2
1
0
1
0
2
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
1
0
2
2
0
1
1
0
0
1
2
0
2
0
0
0
0
1
0
2
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
1
2
0
0
0
0
2
2
0
1
1
2
1
0
0
2
2
0
1
0
1
0
2
2
1
2
2
2
0
1
0
0
1
0
2
0
0
0
1
6
1
2
1
0
0
2
0
0
0
0
0
0
0
0
1
2
0
2
0
3
2
0
0
1
0
0
3
0
0
1
1
1
0
0
0
0
2
0
1
0
1
1
0
1
0
0
1
0
0
2
1
1
2
1
2
0
0
0
1
0
2
0
2
0
0
0
0
0
2
0
4
1
2
1
0
2
0
1
5
0
0
1
2
0
0
0
0
2
0
0
3
1
3
0
0
2
1
0
0
0
1
0
1
0
0
0
0
1
0
0
2
0
0
0
0
1
2
1
2
0
0
1
0
2
0
2
0
1
0
0
0
0
1
0
1
0
1
1
1
1
2
1
2
3
0
2
2
1
4
0
1
0
2
1
2
1
0
0
0
0
1
0
0
1
1
2
2
4
0
0
0
0
1
0
1
1
0
1
1
0
1
0
0
1
0
1
0
0
0
0
0
1
0
1
0
1
2
1
1
0
0
0
0
0
0
0
0
0
0
1
3
0
1
2
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
2
0
1
0
1
2
0
1
1
1
2
3
0
0
1
2
1
1
2
2
0
0
1
1
0
1
0
2
0
0
1
0
0
1
0
1
2
0
0
2
0
0
0
0
2
0
0
2
1
1
0
0
1
1
1
0
0
1
0
0
1
1
0
0
1
0
0
0
2
0
0
0
0
0
1
1
0
0
1
0
1
0
0
1
1
3
2
0
0
0
2
1
2
2
2
0
1
0
0
1
0
0
0
2
0
1
0
1
2
2
2
1
0
1
0
2
1
2
0
1
1
0
1
0
0
1
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
1
2
0
0
0
0
1
0
1
1
0
1
0
0
1
2
2
6
0
1
0
2
0
1
0
0
0
0
0
0
0
2
1
0
0
1
2
1
0
0
2
0
1
0
0
0
2
0
0
0
0
1
0
0
2
1
0
0
0
1
0
0
0
0
0
1
2
2
2
2
1
0
0
0
1
1
1
0
1
1
1
0
1
1
0
0
2
0
1
0
1
2
2
2
1
1
0
1
0
1
0
0
2
0
2
0
0
2
2
1
2
0
0
0
0
0
1
0
0
0
2
1
1
0
0
2
0
0
0
0
1
0
2
1
2
1
0
0
0
2
2
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
1
1
0
2
0
0
2
2
2
2
0
1
1
0
2
0
1
1
0
0
0
0
2
1
1
0
0
0
1
0
0
1
2
1
1
1
0
1
0
1
0
1
2
1
0
2
0
1
0
3
0
1
0
0
0
2
4
1
0
1
1
0
0
0
0
2
2
0
1
0
0
1
1
3
1
0
0
1
0
0
0
0
1
2
2
0
0
0
0
0
0
5
0
2
0
0
1
2
1
0
0
2
1
0
0
0
1
1
0
0
1
0
2
1
0
1
2
0
0
2
1
0
2
0
0
1
1
1
2
2
2
1
0
1
2
1
2
0
2
0
2
1
2
0
0
2
2
2
0
0
0
0
0
1
2
1
1
0
5
0
0
1
0
2
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
2
0
1
2
0
0
1
1
0
1
0
0
0
0
0
2
0
1
0
0
0
2
1
1
2
0
0
0
2
1
0
2
1
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
1
0
0
2
1
1
1
1
1
0
2
2
1
0
1
1
1
0
2
2
0
0
0
1
2
1
1
1
1
0
0
1
2
0
0
1
0
1
0
0
0
0
0
2
1
2
2
2
2
0
2
0
0
1
1
1
0
1
6
0
0
1
0
0
2
0
0
0
2
1
1
1
0
0
2
0
0
0
1
0
0
0
0
1
2
2
1
1
0
3
2
2
0
1
1
0
2
2
0
0
1
0
1
0
0
1
0
2
3
0
2
0
0
0
0
0
2
0
1
0
2
1
1
0
1
1
0
0
2
3
0
1
2
0
1
1
2
0
0
0
0
1
2
0
0
0
0
4
3
2
2
1
2
2
0
0
1
2
1
0
1
2
2
1
1
2
0
0
0
3
1
0
1
1
0
1
2
0
1
0
0
1
0
2
2
0
3
2
1
0
0
0
1
2
1
2
1
0
0
0
2
1
0
1
3
0
1
0
0
0
0
2
0
0
2
1
1
0
2
2
1
0
1
2
0
0
2
0
1
0
1
1
2
0
1
0
3
2
0
0
0
0
0
2
0
1
3
1
0
0
0
0
0
2
0
1
2
1
2
2
0
0
0
2
1
1
1
2
0
2
0
1
0
0
0
0
0
1
4
0
0
1
1
0
0
2
0
0
2
2
0
0
0
0
1
0
0
1
0
0
1
0
0
2
2
0
0
2
1
2
2
0
0
0
2
0
1
1
1
2
1
1
0
0
0
0
3
2
0
2
1
0
1
2
1
2
0
2
1
1
1
1
0
1
1
1
0
0
0
0
2
0
0
1
4
0
1
0
2
1
2
0
1
1
2
2
0
0
0
2
0
0
1
1
0
1
0
0
0
1
0
2
1
0
0
0
1
1
0
0
0
0
2
2
0
0
0
0
1
1
3
0
0
0
0
0
3
0
0
0
2
2
2
3
0
2
0
2
0
2
1
1
1
0
0
1
0
1
2
1
0
1
0
1
0
1
0
1
0
0
2
2
0
0
0
0
2
0
0
2
0
1
1
3
0
0
0
0
1
0
2
2
0
1
0
2
0
1
0
0
2
1
0
1
1
0
1
1
0
0
1
0
2
0
2
2
0
0
2
0
0
0
2
0
1
0
1
0
2
0
0
1
1
0
1
1
0
0
0
2
1
0
0
2
0
2
1
2
0
1
1
0
0
0
0
2
0
0
0
2
0
0
0
0
3
0
2
0
2
1
4
1
0
2
1
2
0
2
0
0
1
2
1
1
0
2
1
0
0
1
2
0
1
1
0
2
0
0
1
3
2
0
1
0
1
2
0
0
1
2
1
0
0
2
0
2
0
1
0
0
2
1
0
0
1
0
1
2
0
0
1
0
1
1
1
0
0
2
0
1
1
1
2
2
1
2
0
2
0
1
1
0
1
2
1
1
0
1
0
3
0
0
0
0
2
2
1
2
0
1
0
0
0
1
0
0
0
1
2
2
0
0
0
0
2
2
0
0
0
0
0
1
1
1
0
1
0
0
3
0
1
0
3
1
0
2
0
0
0
0
1
0
2
2
0
2
0
2
1
0
1
1
0
1
1
0
16
0
3
0
0
0
0
2
0
1
0
2
2
1
1
1
1
0
0
2
1
0
2
2
1
2
0
0
0
0
0
2
0
2
0
0
0
1
0
1
0
1
0
0
0
2
0
2
2
0
2
1
0
1
0
1
2
0
0
1
2
2
0
0
2
1
0
2
0
0
0
2
0
0
0
2
2
2
0
0
0
0
1
0
2
2
2
2
1
1
0
0
0
0
1
1
0
0
1
0
1
0
0
1
0
1
2
2
0
0
0
1
0
0
0
1
0
2
3
0
0
2
2
0
0
2
0
2
0
1
2
0
2
2
0
0
0
1
0
2
3
1
0
1
1
2
0
1
0
2
0
1
0
0
0
0
2
1
0
0
0
1
2
0
1
2
2
0
2
1
1
0
2
2
1
1
1
3
0
0
2
0
1
0
2
1
2
1
0
1
0
1
1
2
0
1
0
1
0
0
0
1
2
1
0
2
0
0
0
2
1
1
2
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
2
0
1
0
0
0
0
1
2
1
2
0
3
2
0
1
0
2
0
0
0
0
0
2
2
0
0
2
0
1
0
1
0
0
0
1
1
0
0
0
1
1
0
0
1
0
0
0
0
1
1
0
2
1
2
1
2
0
0
0
1
0
0
0
1
0
1
1
2
1
0
0
1
0
1
3
1
1
2
2
0
1
0
0
2
0
0
0
0
1
1
2
0
1
1
3
0
1
2
1
1
1
2
2
0
1
0
0
0
0
1
0
2
2
1
0
0
0
0
0
2
0
2
1
0
3
1
0
1
1
1
0
0
2
3
0
1
1
1
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
2
0
0
1
2
0
1
0
1
1
2
1
2
0
2
2
0
1
0
1
0
0
1
0
0
0
0
2
0
0
1
2
0
0
0
0
2
4
0
1
0
1
1
2
1
0
0
1
0
0
0
0
1
2
1
1
0
2
0
1
2
2
0
1
0
0
0
1
0
2
1
0
1
2
0
0
0
0
0
0
0
1
0
0
1
0
1
0
2
2
0
0
0
1
1
0
0
0
1
0
1
1
1
0
0
0
2
0
1
0
2
1
1
1
1
0
2
0
0
0
2
2
0
0
2
0
0
0
1
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
2
0
0
0
2
1
2
0
0
0
2
3
0
0
0
2
0
1
2
1
2
2
0
2
2
2
1
6
0
0
0
0
0
2
2
2
2
1
1
1
0
1
0
2
0
1
1
2
2
0
1
2
1
0
1
0
1
0
0
2
0
0
0
1
2
2
1
0
2
2
1
2
0
2
0
1
2
1
1
0
1
0
1
0
2
2
2
1
0
0
0
4
0
0
1
2
2
0
0
0
0
2
0
0
1
1
0
2
0
3
1
2
0
1
2
0
0
2
0
0
5
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
1
2
1
0
0
1
0
0
2
0
0
0
2
0
0
0
1
0
0
2
0
1
1
2
0
1
1
0
10
1
2
2
0
0
0
0
0
0
2
0
2
1
1
2
0
1
0
0
2
0
2
1
2
0
1
1
1
0
0
0
1
2
0
2
2
2
1
2
2
2
1
0
1
0
0
0
0
0
1
2
2
2
0
1
1
0
0
0
1
0
0
1
1
0
1
0
0
2
0
2
0
1
1
1
0
1
0
0
0
2
0
0
0
1
0
0
0
1
2
2
1
0
1
1
0
0
0
2
1
1
0
0
0
1
2
0
1
0
0
2
0
1
1
2
0
1
1
2
0
0
2
2
0
0
0
2
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
2
2
0
2
2
0
0
0
0
0
2
3
2
0
0
0
0
3
0
1
0
0
0
1
0
2
0
0
1
0
1
1
0
2
0
0
0
1
2
1
0
2
1
0
1
0
0
0
2
1
1
0
0
2
1
0
0
0
0
0
3
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
2
0
1
0
0
2
1
0
0
0
1
0
1
3
1
1
2
0
0
0
0
1
1
0
2
0
0
0
1
0
2
0
0
0
0
2
0
2
0
0
0
2
1
1
0
0
0
0
2
1
2
2
1
1
0
0
0
2
0
0
0
0
0
1
2
2
2
2
1
0
2
1
1
1
0
1
1
1
0
2
1
0
0
2
1
0
3
0
2
0
2
1
2
0
0
1
0
0
1
1
3
2
0
1
2
0
2
2
2
0
2
0
0
0
1
0
1
0
1
4
2
0
2
0
0
1
0
0
0
1
1
0
1
0
0
0
0
2
0
0
0
1
0
3
0
1
1
0
1
1
1
0
1
2
0
0
0
0
1
1
2
0
1
1
0
0
1
0
0
2
0
1
1
2
0
2
0
1
0
0
0
0
1
2
0
4
0
1
1
1
0
0
1
0
1
2
3
1
0
2
0
0
2
2
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
1
1
1
1
0
0
1
0
0
2
0
0
1
1
2
0
1
0
1
0
2
1
0
1
0
0
2
2
0
1
1
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
2
0
0
1
0
1
0
0
0
2
0
1
0
0
2
0
1
1
1
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
1
1
2
0
0
1
0
0
3
0
0
2
0
2
0
1
2
1
0
0
0
2
1
1
2
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
3
0
1
4
0
0
0
2
0
0
2
0
0
1
2
1
0
0
1
0
0
0
2
0
1
1
1
0
2
2
0
2
0
0
2
0
0
2
0
2
0
1
0
2
1
2
0
0
0
0
0
1
0
1
1
0
0
0
2
0
2
0
0
1
4
2
0
1
0
0
1
0
0
0
0
1
1
2
0
1
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
2
2
1
0
0
0
0
1
0
0
0
1
0
0
0
0
2
1
0
1
0
1
0
0
0
0
0
2
1
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
2
1
0
0
2
1
0
0
0
0
0
0
6
0
0
1
2
2
2
2
1
1
3
1
1
2
0
0
0
1
2
1
0
1
1
2
2
1
0
0
2
0
1
0
1
0
2
0
0
2
0
0
2
1
1
0
0
0
3
0
1
0
1
1
1
0
0
0
2
0
2
0
0
0
2
2
0
0
1
1
2
0
0
0
2
1
0
0
1
0
7
1
0
0
0
0
0
0
0
0
0
0
1
0
0
3
2
2
1
1
0
0
0
1
0
1
2
0
1
0
1
0
0
0
0
1
2
0
0
0
0
1
2
1
2
2
1
0
1
1
0
0
2
1
2
0
2
0
1
2
1
0
0
1
0
0
0
0
0
0
0
1
2
2
0
0
2
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
1
1
1
1
2
1
0
0
0
0
0
0
1
0
1
1
0
0
0
2
0
0
1
0
1
0
0
2
0
1
3
0
2
0
0
0
2
1
2
1
1
0
1
0
2
1
0
2
2
0
1
0
0
1
2
2
0
0
1
0
0
1
0
1
0
1
1
1
1
0
2
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
2
0
0
0
2
2
0
0
0
1
1
1
1
1
0
1
7
2
2
0
0
1
0
1
0
1
1
0
0
0
2
0
0
0
1
0
0
0
2
0
2
2
0
1
0
0
1
1
0
1
2
2
2
0
2
0
1
0
0
0
0
0
0
0
2
1
0
0
1
0
0
2
0
0
1
1
2
2
2
0
0
2
0
0
0
1
1
2
0
0
1
0
0
0
0
0
2
2
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
2
1
0
1
0
0
1
1
0
0
0
1
0
2
0
0
0
2
1
0
2
0
0
1
3
0
2
0
0
0
0
0
1
0
1
0
1
1
0
0
0
2
1
0
2
1
0
0
2
0
0
2
2
0
4
0
0
0
0
1
3
0
0
1
1
1
0
1
0
2
2
0
1
1
2
2
0
1
0
0
0
1
0
0
1
0
0
0
2
1
0
2
0
1
0
0
1
0
2
0
0
0
1
0
0
0
1
0
0
1
1
2
1
1
1
0
1
0
2
2
0
0
0
2
0
0
1
2
1
0
3
0
2
0
0
1
1
0
0
2
0
0
1
1
0
1
1
0
2
0
0
0
1
0
0
3
0
0
1
1
1
2
0
0
1
2
0
0
0
0
0
1
2
1
1
0
2
0
1
0
0
0
0
2
0
0
0
1
0
1
1
0
2
1
2
2
0
0
1
1
1
2
2
2
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
1
0
1
0
1
0
1
1
1
0
0
0
0
1
1
1
1
2
3
0
0
2
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
2
0
1
0
1
0
8
1
2
1
0
0
3
0
0
1
2
0
1
1
1
2
1
0
2
0
2
0
0
2
2
0
0
2
0
1
2
0
0
1
1
2
0
0
0
0
1
1
0
0
0
1
0
0
1
2
0
1
2
1
1
1
1
2
2
1
2
0
1
2
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
2
2
2
1
0
2
0
0
1
0
0
0
1
1
0
2
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
3
1
0
1
1
2
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
1
0
0
0
1
1
1
0
1
3
3
1
1
0
0
0
0
0
1
0
0
1
0
2
0
1
0
0
1
1
0
1
0
1
1
1
1
1
2
0
0
0
1
0
0
2
0
0
1
2
0
1
3
2
1
0
0
1
0
1
2
0
0
0
2
1
1
0
1
0
0
2
0
0
1
1
1
2
1
1
2
0
2
1
0
0
1
0
1
0
1
3
2
0
2
0
0
0
0
4
0
0
1
2
0
2
0
0
1
2
0
1
3
0
1
1
0
2
0
0
0
0
0
0
1
0
2
0
0
2
0
2
0
0
0
1
1
0
1
1
2
1
0
0
0
1
1
0
0
1
0
0
2
1
0
0
1
1
2
1
1
1
1
1
0
0
0
0
1
0
2
3
1
1
0
0
0
0
0
1
0
0
1
0
2
1
2
0
1
0
0
0
0
0
0
2
0
1
0
1
2
2
2
1
2
2
2
1
0
0
2
1
0
2
1
1
2
1
2
2
0
1
0
1
0
1
2
0
0
0
2
0
0
2
1
0
0
0
1
0
0
1
0
5
2
0
0
0
0
1
0
1
1
0
1
2
0
1
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
2
2
2
0
0
0
1
0
1
2
0
0
0
0
2
0
0
1
0
0
0
2
0
0
2
0
0
0
1
0
1
0
1
2
1
0
0
0
0
1
0
1
2
0
0
0
1
0
1
2
0
0
0
2
1
1
2
1
1
0
1
1
4
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
2
0
0
2
1
2
0
1
0
0
0
0
2
0
0
0
1
0
1
2
0
1
1
2
0
0
1
0
0
0
0
2
1
2
0
0
0
0
0
0
0
3
0
0
0
1
1
1
2
2
1
2
2
0
2
1
0
0
1
0
2
2
1
0
2
0
0
0
0
1
0
1
0
0
2
0
1
0
0
0
2
0
1
0
1
1
2
0
0
0
0
1
0
1
0
0
1
2
1
0
0
0
2
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
2
1
2
2
1
0
4
1
1
0
1
0
0
0
0
1
0
2
0
1
2
1
1
1
0
1
1
2
2
1
1
0
2
0
2
0
0
2
1
0
2
0
0
4
0
1
2
0
2
1
1
0
3
0
1
1
0
0
1
1
1
1
0
0
0
1
2
2
0
2
0
0
0
1
1
1
2
2
0
0
0
2
1
0
2
2
0
2
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
1
0
2
1
2
0
0
2
2
0
1
1
0
0
1
0
1
0
2
2
0
0
0
1
0
1
0
0
1
0
0
1
0
2
2
0
2
1
2
0
2
1
2
1
0
2
0
2
1
1
0
1
0
0
0
0
0
0
1
2
0
0
0
1
0
2
0
1
1
0
2
0
1
2
2
0
1
0
1
2
0
2
0
0
0
0
1
0
0
1
1
0
2
0
0
1
2
1
0
0
1
0
2
0
1
2
1
3
0
0
2
0
0
1
0
0
1
4
1
0
1
2
1
0
1
0
2
1
1
2
2
1
2
0
0
1
1
2
0
0
2
2
1
0
0
2
3
1
0
3
0
1
1
0
0
0
0
0
0
2
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
1
0
0
2
0
1
1
1
0
1
0
0
0
0
1
2
0
1
2
1
0
2
1
0
0
0
0
0
1
2
2
0
3
0
1
0
1
0
1
0
0
0
1
0
0
0
2
0
1
2
0
2
1
1
0
0
2
0
1
0
0
0
1
1
1
2
2
1
0
2
1
0
0
0
1
2
0
0
2
1
1
2
2
2
0
2
1
1
1
3
0
1
0
1
0
0
0
1
0
2
0
2
0
0
1
0
0
1
0
2
2
0
0
0
1
0
0
0
1
1
0
0
1
0
1
0
0
1
1
0
0
2
0
1
0
3
1
1
0
2
2
1
0
0
0
0
0
0
0
1
0
1
0
0
1
1
2
0
2
1
0
0
0
1
0
0
1
0
2
0
0
0
1
2
0
0
2
0
1
0
0
0
0
1
1
0
0
0
0
2
0
1
1
1
0
1
0
0
0
1
0
1
1
1
0
1
0
1
1
1
0
2
0
1
2
0
0
0
2
1
0
0
2
0
1
0
2
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
2
0
1
1
0
0
0
0
0
1
0
2
0
1
0
0
0
1
1
1
2
2
2
1
0
0
2
1
0
1
0
0
0
2
0
1
1
1
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
1
0
0
2
0
1
0
2
2
0
2
0
1
1
1
1
0
0
0
1
1
1
0
0
0
0
1
2
0
0
0
2
2
0
2
2
0
1
0
0
0
1
0
1
0
2
1
0
0
0
2
2
0
0
0
0
0
2
0
2
1
1
0
0
0
0
0
0
0
2
1
1
2
1
1
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
5
2
0
0
2
1
0
1
1
2
0
2
2
1
1
0
1
0
3
0
1
0
0
0
2
0
2
3
0
0
0
2
0
0
0
2
0
4
1
1
0
1
1
2
1
0
0
1
1
0
0
1
1
1
2
1
1
2
0
0
0
2
1
0
1
2
2
1
0
0
0
0
0
0
0
1
0
2
1
0
0
1
0
0
2
0
0
0
0
0
0
1
1
3
0
0
1
2
3
0
1
0
1
2
1
0
0
2
1
1
0
0
1
0
1
1
2
1
0
0
1
2
0
1
0
1
0
0
0
1
0
1
0
2
2
0
2
2
0
0
0
2
4
0
1
0
0
2
0
0
1
4
1
0
0
2
1
0
1
0
0
1
0
4
0
0
1
1
0
0
0
0
2
2
0
1
1
0
1
0
0
1
0
2
2
1
0
1
1
2
0
1
5
1
1
0
2
0
1
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
2
0
0
3
0
0
1
0
3
1
0
2
0
1
2
0
1
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
1
1
1
1
2
0
2
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
1
1
2
2
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
3
0
1
0
0
0
0
0
1
2
0
2
1
2
2
1
0
1
1
0
0
0
0
1
0
0
0
2
1
1
0
0
1
0
1
2
0
0
2
0
1
0
0
1
0
2
0
2
0
0
0
0
1
0
0
4
2
0
0
0
0
0
1
0
0
0
1
1
0
0
0
4
0
1
1
0
0
2
1
0
0
0
0
1
2
0
2
2
1
0
1
0
0
0
0
0
0
2
0
0
1
0
2
0
1
1
0
0
2
0
2
1
0
1
0
2
0
1
1
2
2
2
1
0
1
0
0
0
0
2
1
0
1
0
1
0
2
1
2
2
0
1
1
0
0
1
0
0
0
2
0
1
1
0
1
0
2
0
0
0
0
2
0
2
0
0
0
1
2
2
3
0
0
0
1
0
1
0
2
0
0
2
1
0
1
1
0
0
1
0
1
1
2
0
1
0
0
1
0
2
1
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
1
0
2
1
0
2
2
1
0
1
1
1
3
0
2
2
1
1
1
0
0
1
0
0
0
1
1
0
2
0
0
2
0
2
1
1
0
0
1
0
2
0
0
1
1
0
0
0
0
1
1
0
2
1
0
0
0
1
1
2
3
1
0
0
3
1
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
1
1
1
1
1
1
1
0
0
0
1
2
0
0
0
1
0
1
0
1
3
0
2
0
1
0
0
1
1
0
0
2
0
0
1
1
0
2
1
0
1
0
2
2
2
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
1
1
0
1
0
0
2
3
3
1
1
1
0
1
0
1
0
0
0
2
0
0
1
1
1
2
0
0
0
0
1
2
2
1
2
2
2
0
0
0
1
0
0
2
1
0
0
0
0
2
0
1
1
0
2
2
0
1
2
2
0
0
0
1
0
1
0
0
0
2
0
1
1
2
1
0
2
0
2
1
0
2
1
2
2
1
0
1
0
0
1
1
2
0
1
0
0
0
1
0
0
1
1
1
0
2
1
2
0
1
1
0
0
1
0
0
2
1
0
0
0
1
1
0
1
0
1
0
1
0
0
0
2
0
0
1
0
2
1
1
2
0
0
1
0
1
1
0
0
2
0
0
2
0
4
0
0
2
2
0
1
0
0
1
0
1
1
0
0
0
1
2
2
0
1
0
2
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
1
0
0
1
0
3
2
1
2
0
1
2
2
0
0
3
0
0
0
1
1
0
0
1
0
1
2
1
0
1
1
1
1
0
0
0
1
2
0
0
0
0
0
1
2
2
0
2
0
1
0
1
1
1
0
0
0
2
0
1
0
1
0
0
0
2
1
0
0
0
0
2
2
2
1
2
0
0
0
0
0
1
1
2
0
1
0
0
2
2
4
2
0
0
0
1
0
0
2
0
0
0
1
2
0
1
1
2
0
0
0
1
2
0
3
2
1
0
2
2
0
0
1
2
1
0
1
0
0
0
0
0
0
0
2
2
0
2
1
2
0
0
0
1
0
0
0
0
0
0
2
2
0
0
3
0
2
0
2
0
0
0
2
1
1
2
0
0
0
1
0
1
1
0
1
0
2
2
2
1
3
1
1
1
2
1
0
1
1
2
0
0
1
1
0
0
1
1
0
1
2
1
1
0
0
0
2
1
1
0
0
1
0
1
2
1
2
0
0
1
0
2
2
2
2
2
1
1
0
0
1
1
2
0
1
2
0
0
2
2
0
0
0
0
1
1
0
1
0
1
1
2
1
1
1
2
0
1
3
0
0
0
2
0
1
2
2
2
0
1
1
0
0
1
5
0
2
0
1
0
1
2
0
0
0
1
0
1
0
1
0
2
0
2
2
0
2
0
0
0
1
0
0
1
2
2
1
0
0
2
3
1
2
0
3
0
3
0
1
1
0
1
1
1
2
0
1
0
2
1
2
1
1
2
1
2
0
2
1
3
0
0
0
2
1
1
0
1
0
0
2
4
0
1
0
0
1
1
0
1
0
1
0
0
0
1
1
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
1
2
2
0
0
1
0
1
0
0
0
1
0
0
0
2
0
1
0
1
0
0
1
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
1
0
1
0
0
2
0
2
0
1
2
0
2
0
3
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
1
0
0
2
1
1
0
1
0
0
1
0
0
0
0
1
2
2
1
2
1
1
2
1
0
0
3
2
1
2
0
2
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
3
0
1
0
1
0
2
0
1
0
0
3
0
1
0
2
1
0
0
0
0
2
0
0
2
1
0
0
0
1
0
2
0
0
1
1
2
2
0
0
1
0
0
0
0
0
0
1
0
1
2
0
0
0
0
2
2
1
1
0
0
0
0
0
2
0
2
0
3
0
0
1
0
1
0
1
1
2
0
0
0
1
0
0
0
0
2
0
2
0
2
0
0
0
2
2
2
3
1
1
2
1
0
0
0
2
0
0
0
0
0
1
0
0
0
2
2
0
2
0
1
0
2
0
1
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
3
2
2
2
2
0
2
2
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
1
2
1
0
2
2
1
2
0
2
2
0
0
2
5
1
0
0
2
1
0
0
4
1
1
2
2
1
0
1
0
1
0
1
0
0
2
0
0
0
3
1
0
1
2
0
3
0
0
1
0
0
0
0
0
0
1
0
1
0
0
5
0
2
2
2
0
0
0
0
1
0
0
0
0
0
0
0
2
1
1
0
0
0
0
1
0
1
1
0
0
1
1
0
2
2
0
0
0
1
0
7
1
0
0
1
1
0
2
2
0
1
1
2
0
1
1
2
1
1
1
1
0
2
0
1
1
2
1
1
0
2
2
1
0
0
1
0
2
2
0
1
0
1
0
0
2
2
0
2
0
1
2
0
0
0
0
2
1
0
0
0
1
1
0
0
1
2
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
2
0
0
0
1
0
0
1
1
0
0
1
1
0
1
0
1
2
0
0
0
1
1
0
0
0
1
0
0
3
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
1
2
1
0
0
1
1
1
0
1
1
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
1
1
2
0
2
1
0
2
0
0
0
1
2
2
0
0
0
2
0
0
1
0
1
0
0
1
0
0
2
0
0
1
1
0
0
0
0
1
3
0
1
0
1
2
0
0
0
2
1
0
1
0
0
0
3
1
0
0
0
0
0
1
1
1
1
0
0
1
0
1
2
1
2
1
0
0
0
2
0
0
0
1
1
0
1
1
1
0
1
0
0
2
0
2
2
0
0
1
0
0
1
2
0
2
0
2
0
0
0
2
1
1
0
1
1
0
0
0
1
1
0
0
0
0
1
0
2
2
1
0
0
0
2
0
1
0
1
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
1
0
2
0
0
0
2
0
0
1
0
0
2
0
0
0
1
0
0
2
1
0
2
1
0
2
0
2
0
0
0
0
1
0
1
1
2
0
0
0
2
3
0
2
0
0
2
0
0
0
0
0
2
0
1
1
1
0
1
0
1
0
1
0
0
2
0
1
0
1
0
1
0
0
0
1
2
0
0
0
0
0
1
0
1
0
1
0
0
0
1
2
2
0
3
0
2
2
0
2
1
0
0
0
0
0
0
0
2
1
0
0
0
2
1
0
0
0
0
1
2
0
1
0
1
2
1
2
0
0
1
1
0
1
4
1
3
0
0
2
2
0
0
0
1
0
1
3
0
1
2
0
1
0
0
0
0
2
2
0
1
0
1
2
0
0
0
0
0
0
2
0
0
0
1
3
0
1
2
3
1
2
2
0
2
0
2
1
0
1
0
1
0
2
1
0
1
2
0
0
0
0
0
0
0
1
0
1
2
2
1
0
2
0
2
1
0
0
0
0
1
0
1
0
1
0
1
1
0
4
1
2
0
2
0
2
0
0
3
0
2
0
0
0
2
0
0
0
0
0
1
2
0
2
1
1
2
1
1
1
1
2
0
1
1
0
2
2
2
1
2
0
1
1
0
0
0
0
3
0
0
0
0
1
2
2
2
0
0
5
0
1
1
0
0
2
1
0
0
1
0
0
0
1
0
2
2
1
2
1
0
0
1
0
0
1
0
0
1
1
1
2
0
2
0
1
0
2
1
0
1
1
1
2
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
1
2
1
0
0
0
2
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
1
0
0
1
1
0
2
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
1
0
2
1
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
2
1
0
1
2
0
0
2
2
0
1
0
8
2
2
0
0
0
1
4
0
0
2
0
1
1
2
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
1
1
1
2
1
2
1
2
0
1
1
1
1
1
2
0
1
2
0
0
0
0
0
2
0
0
0
1
2
2
2
2
1
1
0
2
1
0
2
0
2
0
0
1
1
0
4
1
0
0
1
2
0
0
0
2
2
0
0
2
0
0
2
0
2
1
3
0
1
2
2
0
0
0
4
1
0
0
0
0
1
1
0
1
1
2
1
0
0
0
1
2
0
2
0
1
0
0
1
0
0
0
1
0
1
1
0
0
0
1
0
1
0
2
2
0
1
1
0
0
2
1
1
3
1
0
0
1
0
0
1
0
0
1
1
2
0
0
0
0
0
1
1
2
1
1
0
0
1
1
1
0
0
2
1
0
1
0
0
0
4
1
2
0
1
0
0
2
2
1
2
1
0
1
0
0
0
1
1
1
2
0
1
0
1
0
0
0
1
2
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
1
0
1
2
0
0
0
2
2
0
0
1
0
1
0
0
0
1
1
0
2
2
0
0
1
1
1
0
1
0
2
2
0
0
0
2
0
0
0
1
1
0
1
1
1
1
1
0
0
1
0
0
1
0
0
1
3
0
0
1
1
1
0
0
0
0
1
1
5
1
0
0
0
3
1
0
0
1
0
0
0
2
0
1
2
0
1
1
2
0
1
0
0
0
0
0
3
0
2
2
0
0
0
0
1
2
3
1
1
2
0
1
0
0
0
0
2
2
0
1
2
1
0
0
2
1
0
0
1
0
1
0
1
1
1
0
0
1
0
1
0
0
0
0
0
0
2
1
1
0
1
2
0
2
1
0
0
2
0
3
2
2
1
0
1
1
0
0
1
0
0
0
1
0
0
1
2
0
0
2
0
5
0
1
2
2
1
0
0
0
0
0
1
2
0
0
3
0
2
1
0
2
0
1
0
0
0
1
0
1
0
2
0
0
1
0
0
0
3
0
0
0
0
2
1
1
0
1
1
2
3
1
1
3
1
0
0
2
2
1
0
1
2
0
0
2
0
4
1
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
2
1
0
2
0
1
0
0
0
2
2
2
2
0
2
0
0
2
0
0
1
2
0
0
1
0
1
4
0
1
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
1
3
0
2
0
1
0
1
1
2
2
0
0
2
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
1
0
2
1
0
0
0
2
0
0
0
0
1
2
1
0
2
1
2
1
1
0
0
0
0
1
0
0
0
1
0
0
2
0
0
2
0
0
2
0
0
0
0
1
1
2
2
2
0
1
2
1
0
2
0
2
2
1
0
0
0
0
0
1
1
0
2
0
1
2
0
1
0
2
1
0
1
2
1
1
0
0
0
0
1
1
1
0
2
0
0
1
0
2
0
0
0
0
0
0
1
2
0
2
0
1
0
0
0
0
0
0
0
0
2
2
2
2
2
0
1
0
2
0
1
0
0
1
0
1
2
0
1
0
0
1
0
2
2
1
0
0
1
1
0
2
0
0
0
0
1
0
2
1
0
1
2
1
1
2
0
0
0
0
0
0
0
0
2
1
0
1
0
0
1
0
1
2
2
2
1
0
0
2
0
0
0
1
1
1
1
0
0
0
1
1
2
0
0
0
0
0
0
0
1
1
1
3
4
3
2
2
1
1
0
2
2
2
0
1
0
0
1
0
2
0
1
1
0
0
0
1
0
0
0
0
1
0
2
0
1
0
2
0
0
0
1
2
0
0
0
1
0
0
0
0
1
1
3
2
1
0
2
2
1
1
0
0
0
1
2
1
0
0
2
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
2
0
0
1
1
0
0
1
0
1
1
1
0
0
0
2
0
0
0
0
0
1
0
0
2
3
0
0
1
1
0
1
0
0
1
0
0
0
0
2
0
1
0
0
0
1
2
0
0
1
1
2
0
0
0
0
0
0
2
0
1
1
1
0
0
2
1
0
1
0
2
2
1
0
1
2
0
0
2
0
1
1
1
0
1
1
0
0
2
0
1
1
1
0
0
0
0
0
1
1
0
1
0
1
1
3
0
1
0
0
0
1
0
0
0
2
1
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
1
0
2
2
0
0
0
1
0
0
0
0
0
2
0
0
2
3
1
0
0
1
0
1
0
1
0
0
1
0
0
1
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
1
0
0
2
0
2
0
1
0
0
1
0
2
1
1
1
0
0
0
2
0
2
1
0
1
1
0
0
2
0
2
1
2
4
1
0
2
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
1
1
0
2
1
1
1
0
3
1
1
0
2
2
1
0
0
1
0
1
0
0
2
2
0
0
1
1
1
2
0
0
2
1
2
0
1
0
0
2
2
1
2
0
0
1
0
0
1
1
1
1
1
0
2
3
0
1
0
2
0
0
0
0
0
0
0
2
1
0
0
1
0
2
2
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
3
2
0
1
0
1
1
0
0
3
0
1
0
0
2
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
3
0
0
0
1
2
0
1
0
0
1
0
2
0
0
1
2
0
0
0
0
0
1
1
2
0
0
1
2
0
0
1
0
1
1
2
1
0
0
2
2
0
0
0
1
0
2
0
0
0
0
2
0
2
0
0
0
2
1
2
0
2
1
2
0
1
0
2
0
1
0
0
1
2
0
0
0
0
2
0
1
2
1
0
0
0
0
1
0
2
0
1
0
0
0
2
0
2
2
0
0
0
0
1
0
1
0
0
2
0
1
1
0
2
0
0
0
0
0
1
0
0
2
0
0
1
1
0
0
0
0
0
0
2
2
1
0
0
0
1
0
3
0
0
1
0
0
0
0
1
0
2
2
1
0
0
0
1
0
1
0
3
0
7
2
1
2
0
0
0
2
2
0
0
3
2
1
2
2
2
0
0
1
0
2
0
0
1
0
2
0
0
1
0
2
1
0
0
1
0
2
0
0
2
0
0
0
2
4
0
0
0
1
0
1
2
0
0
1
0
2
0
0
0
1
2
0
1
0
2
2
0
0
0
0
2
2
0
0
0
2
0
1
2
0
0
4
0
2
1
0
0
2
0
0
0
0
0
0
1
2
1
0
0
1
0
0
0
1
0
1
0
2
0
2
0
1
0
0
2
0
0
1
2
1
0
1
1
1
2
0
0
0
1
0
1
0
1
0
2
0
1
2
0
0
1
3
0
0
1
1
1
1
1
1
2
1
0
2
2
2
2
0
2
0
0
0
1
0
1
1
1
1
0
2
0
0
1
0
0
0
2
1
3
2
1
0
0
1
2
1
0
2
2
1
0
1
2
0
0
0
0
1
0
0
1
2
0
1
1
2
2
1
0
0
0
0
0
1
0
1
2
0
1
2
0
0
2
0
0
3
0
0
0
2
0
0
0
1
0
1
0
0
2
1
0
0
0
0
3
0
0
2
1
2
3
2
3
0
0
2
0
2
0
0
1
1
0
1
0
1
0
1
1
0
0
0
2
1
0
1
0
1
1
2
0
0
0
0
1
0
1
2
1
1
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
1
0
1
1
2
0
0
1
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
1
0
0
1
0
1
0
2
1
2
0
1
1
0
0
0
1
0
1
2
0
1
0
0
0
1
2
0
1
2
1
0
2
1
0
3
1
1
0
1
2
1
2
2
0
0
0
0
1
2
1
1
0
0
0
2
0
1
0
2
0
0
0
2
2
0
1
1
1
0
1
1
1
1
0
0
0
0
0
0
0
1
1
2
0
0
1
0
0
1
0
0
1
3
1
0
2
1
0
2
0
1
0
0
1
2
1
0
1
1
2
0
0
0
2
0
0
3
0
0
0
1
2
0
0
0
0
0
1
0
0
2
2
1
1
1
2
0
0
1
0
0
1
2
0
0
0
0
0
2
0
0
0
0
2
1
1
1
0
1
5
2
1
0
2
0
0
2
0
0
2
2
0
1
1
0
0
1
0
1
0
2
1
2
0
0
0
2
1
0
1
2
1
2
0
0
0
1
1
0
0
0
0
0
0
2
2
1
2
0
0
2
0
1
2
0
0
1
0
0
1
0
0
0
2
1
1
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
3
0
2
1
1
0
1
0
0
0
3
0
1
0
0
2
0
1
0
1
1
1
2
2
0
2
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
2
0
1
0
1
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
2
2
2
0
0
1
0
0
2
0
0
0
0
2
0
0
0
1
0
2
0
0
2
2
0
0
2
1
0
0
2
2
1
0
2
5
0
0
1
0
1
0
2
1
0
4
0
1
2
0
0
0
2
1
0
0
1
1
2
0
0
2
1
0
0
0
1
0
0
0
4
0
2
2
1
0
2
1
0
0
2
0
0
2
1
1
0
0
2
0
1
2
0
0
4
1
1
0
1
0
1
0
1
0
1
2
1
0
1
1
2
1
1
1
2
2
1
1
1
1
0
1
0
1
2
2
0
1
2
0
0
1
0
1
0
0
0
0
1
0
2
2
1
1
2
0
2
0
0
1
2
1
1
2
0
0
0
1
0
0
0
2
2
0
0
0
1
0
1
1
2
1
2
1
0
1
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
1
0
1
0
0
1
0
1
1
0
0
0
1
2
0
0
0
2
0
2
1
0
0
0
1
2
1
0
2
1
0
0
0
0
2
0
1
0
2
0
1
1
0
1
0
0
1
1
2
0
2
1
0
0
1
1
2
2
1
1
2
2
0
0
0
1
1
1
0
2
0
0
1
2
0
1
0
0
2
2
0
2
0
2
1
0
0
0
0
0
0
1
0
0
0
0
1
2
1
2
2
1
2
0
0
2
1
2
1
3
0
2
2
0
2
2
0
0
1
1
0
0
0
2
1
0
0
1
1
1
0
0
0
1
1
2
0
0
0
0
0
1
0
0
0
0
1
0
1
0
2
0
1
2
2
0
2
0
1
2
0
0
0
2
2
0
1
3
2
0
0
2
3
2
0
0
0
2
0
2
0
0
1
3
3
0
1
2
1
0
0
0
1
2
1
0
0
1
2
2
0
2
0
2
1
0
1
1
0
0
1
0
0
0
0
3
0
1
0
2
2
1
2
0
1
2
2
3
2
2
2
0
0
1
0
1
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
1
0
0
2
0
2
1
2
2
2
0
2
0
2
0
0
2
1
0
0
0
1
0
0
1
2
1
1
0
2
0
1
0
1
0
0
0
1
1
1
1
1
0
1
2
0
0
0
0
2
1
1
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
2
2
0
1
2
0
0
0
0
1
0
0
0
0
1
0
2
1
1
0
1
0
0
2
0
0
0
0
0
1
0
2
0
2
1
0
0
2
0
1
0
1
0
2
0
0
0
0
2
0
0
1
2
2
0
1
2
2
0
1
0
2
0
2
2
1
0
2
2
0
1
0
0
0
0
1
1
1
2
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
1
0
0
0
2
1
1
0
1
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
2
3
1
1
2
0
2
0
0
3
0
2
1
0
2
0
2
0
0
1
0
0
2
1
2
2
2
0
1
0
0
0
1
0
0
1
0
0
1
2
2
2
0
0
0
0
0
2
1
1
0
1
1
1
0
2
0
0
1
0
0
0
1
1
0
0
1
0
1
0
1
0
1
0
0
1
1
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
1
2
0
0
1
1
0
0
2
0
0
0
0
0
0
1
2
0
1
0
2
0
0
0
0
0
2
0
2
0
3
2
0
2
2
1
1
0
0
2
1
0
0
1
0
0
0
1
2
0
1
1
1
0
0
0
0
0
1
0
1
1
1
1
2
2
2
0
1
0
2
1
0
0
1
1
1
0
1
0
0
0
1
2
0
2
1
1
0
0
1
1
0
0
0
0
0
2
0
2
2
2
1
2
1
0
1
0
0
2
0
0
1
0
0
0
0
0
0
1
1
1
0
2
0
1
0
0
0
2
2
3
1
1
0
1
2
6
0
0
3
1
0
0
0
1
2
0
2
0
2
0
0
0
0
2
1
1
0
2
0
0
0
0
0
2
1
1
2
0
0
0
0
0
1
1
1
1
0
0
0
2
1
2
0
2
1
1
5
3
0
1
0
2
0
0
0
2
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
1
2
0
1
1
2
0
2
2
2
0
2
0
1
1
1
0
2
2
1
2
4
2
0
1
1
2
0
0
0
0
1
1
0
2
2
1
1
0
5
1
0
1
0
0
1
0
0
2
0
0
1
1
3
0
0
1
0
1
2
0
0
0
0
1
2
2
1
2
2
1
0
1
0
0
0
0
1
0
1
2
0
0
2
2
1
0
0
1
1
1
1
1
0
2
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
1
1
0
1
1
2
1
1
1
2
0
0
0
1
1
0
2
0
0
0
8
0
1
2
2
1
0
1
1
0
5
1
0
0
0
2
0
0
1
4
2
1
0
2
1
0
2
2
1
1
0
2
0
1
2
0
2
1
0
0
1
0
0
0
1
1
0
2
0
0
2
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
2
1
0
1
1
2
2
0
2
0
1
0
2
0
3
1
1
1
1
1
0
1
0
2
0
0
0
0
1
0
2
1
0
0
0
1
0
1
0
1
0
2
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
3
2
1
0
0
2
0
2
0
0
0
0
0
1
0
1
1
0
2
1
0
0
0
0
1
0
1
1
2
2
0
0
2
2
0
0
0
1
1
0
0
0
0
0
1
1
0
0
2
0
0
0
2
0
1
0
0
0
1
1
1
0
0
0
0
2
2
2
0
2
1
1
1
0
1
2
1
0
0
1
0
1
2
2
1
2
0
1
2
1
1
0
1
2
2
1
2
1
0
1
1
0
0
0
1
0
0
0
1
2
1
1
0
0
0
1
2
0
0
0
0
1
1
2
0
1
1
2
1
0
0
1
0
1
0
0
0
0
2
0
0
0
0
2
1
3
0
0
0
1
2
0
0
2
0
2
2
0
2
1
1
0
0
0
1
1
0
1
1
1
1
1
1
1
0
0
1
0
2
0
2
1
0
2
0
0
2
1
1
0
0
1
0
2
0
2
0
2
1
1
0
2
2
0
1
0
0
0
0
0
2
0
0
1
0
0
2
2
1
0
0
0
1
0
1
1
2
0
0
1
0
1
1
1
0
0
0
4
0
0
0
0
2
2
2
2
0
0
0
0
2
1
1
1
0
0
1
3
1
0
2
0
0
0
0
1
2
1
2
0
2
1
0
1
0
0
2
1
0
1
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
2
0
1
1
1
2
2
2
1
0
0
1
0
0
1
0
1
1
0
1
2
1
0
2
0
2
0
0
0
2
1
3
1
0
0
0
1
0
1
0
1
0
0
1
3
0
0
0
3
0
0
2
0
2
0
0
0
2
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
2
0
1
0
0
1
2
0
0
0
2
1
2
0
0
1
1
1
1
0
1
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
2
0
0
0
1
0
2
1
0
0
0
0
2
0
0
1
0
1
0
0
2
1
1
0
0
1
1
0
1
2
0
1
1
2
0
0
0
0
1
2
1
0
0
2
0
0
2
2
0
1
0
1
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
2
1
1
2
0
0
0
0
0
2
0
0
0
2
1
0
0
0
2
0
1
2
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
1
2
0
2
1
0
0
2
0
0
1
2
0
0
1
0
1
0
2
0
2
4
0
2
0
0
0
0
0
1
1
0
0
0
2
0
2
0
1
1
0
1
1
0
1
0
1
1
2
1
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
1
1
3
0
0
1
1
1
2
0
1
0
2
1
1
0
2
2
0
1
1
2
0
0
0
0
0
1
0
0
1
0
2
1
2
0
1
1
0
2
0
0
0
2
0
0
1
1
1
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
2
2
1
1
0
0
0
2
1
0
0
2
1
1
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
2
0
0
0
2
2
0
1
0
1
0
2
0
1
1
0
1
0
1
0
0
0
2
0
1
2
0
0
0
0
0
0
2
0
2
0
1
1
2
0
2
0
0
1
0
0
0
0
0
0
1
0
2
0
1
1
0
1
0
0
0
0
0
0
0
2
0
1
2
2
1
0
1
2
1
0
4
1
1
0
0
1
0
1
2
1
0
2
0
0
0
0
1
0
2
0
0
0
0
1
3
0
2
1
1
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
1
0
1
0
0
2
0
3
0
0
1
2
2
1
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
2
0
0
0
0
0
1
0
0
0
2
1
0
1
0
1
0
0
2
0
1
1
0
1
1
0
1
1
0
2
0
1
0
0
0
2
0
0
0
3
1
0
1
0
0
0
1
2
0
0
0
1
0
1
1
1
0
2
1
0
0
0
1
0
0
0
2
1
0
0
3
0
1
0
0
0
3
1
0
0
0
0
1
0
2
0
1
1
1
2
2
0
0
1
0
0
1
1
3
2
1
0
2
2
1
2
1
1
0
1
1
0
2
3
2
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
1
1
2
0
1
0
1
0
0
1
0
0
0
1
2
1
0
0
0
2
2
1
0
0
2
0
1
0
2
2
2
2
0
1
0
0
1
0
0
2
2
0
1
1
2
0
0
1
2
1
0
0
0
1
1
2
2
0
0
0
0
0
0
2
2
1
0
2
0
2
0
0
0
0
0
0
0
2
1
1
1
0
1
0
0
2
0
0
2
0
3
0
0
2
1
1
1
0
2
0
0
1
0
1
0
0
0
0
2
2
1
2
0
2
1
2
0
0
1
0
1
1
0
0
0
0
1
0
0
0
1
0
0
2
1
2
0
0
0
2
0
2
0
0
0
2
0
0
2
1
1
2
0
0
1
1
0
0
2
0
1
1
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
2
0
0
2
0
1
1
0
0
0
1
2
0
0
0
1
2
0
0
0
0
0
2
0
0
0
2
2
0
0
2
0
1
1
0
1
1
1
3
0
2
1
1
1
2
0
0
0
0
2
0
1
2
1
1
0
0
4
1
2
1
2
0
1
0
0
0
0
1
1
0
0
1
1
1
1
0
0
0
3
2
1
2
0
1
0
0
0
4
0
0
0
0
1
2
2
1
1
1
1
0
1
1
1
0
0
1
0
2
1
1
1
0
0
2
1
2
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
2
2
0
0
0
1
0
0
0
1
1
2
0
0
2
1
0
0
0
0
2
1
1
2
0
1
0
1
0
0
0
2
0
0
0
1
2
0
0
1
2
1
0
1
1
1
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
1
0
4
1
0
0
0
2
1
2
1
1
0
0
1
2
2
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
1
2
4
1
2
0
0
0
2
1
0
0
2
2
1
0
2
2
1
2
1
0
1
0
0
0
2
2
1
2
0
0
1
0
2
1
0
1
2
0
0
0
0
1
0
0
0
0
1
0
2
1
1
1
2
0
2
0
1
1
0
0
0
0
1
0
2
0
0
1
0
0
2
2
1
1
1
0
1
0
2
2
2
0
0
2
1
0
2
0
0
0
1
4
1
0
2
1
0
1
1
2
1
0
2
1
2
1
0
0
0
1
1
1
0
1
0
0
0
0
1
0
1
0
1
0
2
1
1
1
2
2
1
0
0
0
2
0
0
0
2
0
2
0
1
0
1
2
1
2
0
0
0
0
2
1
0
1
1
1
2
0
0
0
1
2
2
0
1
0
2
1
1
2
6
1
0
2
1
1
0
2
0
1
0
0
1
2
0
1
0
0
0
0
1
1
2
0
0
1
1
0
1
0
2
1
0
3
1
1
2
2
0
0
0
0
0
1
0
1
1
2
0
1
1
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
2
2
0
1
2
0
0
3
2
0
2
1
0
0
0
1
2
0
2
0
0
1
0
2
2
0
3
0
2
1
2
0
0
1
1
0
0
1
0
4
0
1
0
1
0
0
0
0
0
0
0
1
0
2
1
2
4
1
2
2
0
2
1
0
1
0
0
1
0
1
2
0
0
0
0
2
0
1
0
0
1
1
0
0
0
1
1
1
2
1
1
1
1
0
1
0
0
0
0
0
0
2
1
1
2
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
2
2
2
2
2
2
0
0
2
0
0
1
2
0
1
0
1
0
0
0
0
1
1
0
1
3
0
2
2
1
1
0
0
2
0
2
2
2
0
0
1
0
0
1
0
2
0
0
1
1
0
0
0
1
2
0
2
0
1
2
0
0
3
0
0
2
2
1
2
2
1
0
2
1
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
1
2
0
1
1
1
1
0
0
1
1
2
2
2
0
0
0
1
0
2
1
1
0
0
1
2
2
0
1
0
0
0
2
1
2
2
0
1
0
0
1
0
1
1
1
0
0
2
2
0
0
1
1
1
1
1
2
0
1
0
2
2
2
2
1
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
1
0
0
0
0
2
1
0
0
1
0
0
2
1
0
2
0
2
0
1
1
0
1
0
0
2
0
0
0
2
2
2
0
2
0
0
2
1
0
2
2
0
1
0
2
0
0
2
1
0
0
1
0
1
0
0
0
1
1
1
1
0
0
1
0
0
0
2
0
2
1
2
1
1
2
0
0
1
0
1
0
6
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
2
2
0
1
0
0
1
0
0
2
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
1
0
2
0
2
1
0
0
0
0
1
1
2
0
0
2
0
1
0
2
0
0
0
0
1
2
0
1
1
2
2
2
0
1
0
0
1
0
1
2
0
0
1
1
0
1
1
1
0
1
0
2
0
1
0
2
0
2
0
0
1
1
2
0
0
3
1
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
1
2
0
0
1
1
0
2
0
2
0
1
0
2
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
2
0
2
1
1
1
3
1
1
0
0
0
2
1
1
0
1
2
0
2
2
2
2
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
1
1
0
0
0
0
0
0
2
0
0
2
0
0
1
1
0
0
0
1
1
3
0
1
1
0
0
1
3
2
0
0
2
0
1
0
0
1
0
2
0
2
0
2
0
0
1
2
0
0
2
2
0
0
0
2
1
1
0
2
1
1
0
0
0
1
0
1
1
1
0
3
1
0
0
0
1
1
1
1
0
0
0
0
1
1
0
0
0
2
1
2
0
0
0
1
2
1
0
0
0
1
0
0
2
0
2
1
2
1
0
1
1
2
0
0
0
3
1
1
2
0
2
1
0
1
2
0
1
0
4
0
0
0
0
0
2
0
0
0
1
2
1
2
1
2
0
0
1
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
1
1
2
1
1
2
0
2
1
0
0
2
1
2
0
1
0
0
1
0
0
1
0
0
4
0
0
0
2
2
1
1
0
0
0
0
0
2
0
0
1
1
1
2
0
2
1
1
0
2
1
3
2
0
0
0
1
1
0
1
1
0
3
0
0
12
0
0
0
2
1
0
1
0
1
2
1
2
2
0
0
2
1
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
2
1
0
1
0
0
0
2
0
4
1
0
2
2
0
0
1
1
0
0
0
1
0
0
2
2
0
2
1
0
2
0
0
0
0
1
0
2
0
0
2
1
2
1
0
0
0
0
2
1
1
2
0
2
0
0
2
0
0
1
2
1
0
0
0
1
0
1
1
2
0
2
0
1
0
1
1
0
0
0
1
1
0
2
0
0
0
2
0
2
2
0
0
0
0
2
0
1
0
0
2
2
0
2
1
0
2
0
0
0
0
1
1
2
0
2
2
0
0
2
2
0
1
0
0
1
0
0
0
1
1
0
0
1
2
1
2
0
0
4
0
0
1
0
3
1
1
0
0
0
0
2
0
0
1
1
0
5
1
0
2
0
0
2
0
0
0
1
2
0
2
1
1
0
1
2
2
1
1
0
0
0
1
0
0
1
0
0
0
0
1
1
2
0
0
0
3
3
0
0
2
0
2
0
0
0
1
0
0
2
2
1
2
0
2
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
5
1
0
1
0
1
1
1
0
0
0
0
1
2
0
2
0
0
0
1
1
0
1
1
0
2
1
0
0
0
1
0
0
1
1
1
2
1
1
0
0
0
0
1
2
0
1
0
2
0
0
0
2
1
0
1
0
0
1
0
1
0
2
1
1
1
1
0
2
3
4
0
0
1
0
1
0
0
0
2
0
0
1
2
0
2
1
0
0
2
1
1
2
2
1
1
0
0
1
0
3
0
0
1
1
1
0
2
1
1
1
1
0
1
0
3
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
1
0
0
0
2
1
1
1
1
0
0
1
0
0
0
2
3
1
0
2
0
0
0
0
2
0
2
1
0
1
0
0
0
0
2
0
0
0
1
1
0
0
0
2
1
0
0
0
2
1
1
0
0
1
0
0
0
0
1
1
0
0
1
0
1
0
0
2
2
1
2
0
1
0
0
2
1
0
1
1
0
1
1
0
0
1
0
0
0
0
0
0
1
2
2
2
2
2
0
2
2
2
0
0
2
1
0
0
1
0
0
0
0
0
1
0
0
2
0
0
1
0
2
2
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
1
2
1
0
2
0
0
0
5
1
0
2
2
0
0
2
1
0
1
1
0
2
0
0
2
2
0
0
0
2
0
2
1
2
2
1
0
0
2
1
1
0
0
1
0
0
0
1
0
2
0
1
1
2
0
0
0
1
0
0
2
2
1
2
0
0
0
0
3
2
0
0
0
1
0
0
1
1
3
0
1
0
0
1
0
2
1
0
0
0
1
0
2
2
0
0
0
0
0
2
1
0
0
1
0
0
0
0
2
0
0
1
0
0
1
1
1
0
0
0
1
1
0
0
0
1
1
2
1
0
0
0
0
0
1
3
0
0
0
0
2
0
2
1
2
1
1
2
0
0
0
0
1
0
0
0
1
0
1
1
2
0
0
0
0
0
1
2
0
1
0
1
0
2
1
2
2
0
2
1
0
2
2
2
0
1
1
0
2
0
3
0
0
0
2
0
0
1
1
2
2
2
1
1
0
1
0
2
0
0
0
0
2
1
2
2
0
0
0
0
1
1
1
2
1
0
0
1
0
0
0
2
0
1
1
0
1
0
1
0
0
0
0
2
0
2
0
1
0
0
0
1
0
1
1
1
0
0
2
1
0
0
0
1
2
2
0
0
0
0
2
1
1
0
0
1
0
0
0
0
2
0
0
2
1
0
0
0
1
0
1
1
1
0
1
1
1
0
0
0
2
1
1
0
2
0
0
0
0
2
3
1
1
1
0
0
1
0
0
0
1
1
1
2
0
0
2
0
2
0
2
0
3
2
0
0
0
1
2
1
2
0
0
0
0
0
0
3
1
0
0
0
0
1
0
0
4
0
1
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
1
0
0
0
2
0
2
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
2
1
0
0
1
0
0
2
1
0
0
0
3
0
1
2
2
1
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
2
2
0
0
2
0
0
0
1
1
0
0
0
1
1
2
0
2
0
0
0
0
1
0
2
1
3
1
0
0
1
0
0
1
0
1
0
1
3
1
0
0
0
0
1
0
0
0
0
0
2
1
0
1
0
0
0
0
0
1
2
1
1
0
0
2
0
2
1
2
1
1
1
1
0
1
1
1
0
1
1
1
0
0
1
1
2
1
0
1
0
0
1
1
1
2
0
0
1
1
2
0
1
1
0
0
1
1
1
2
0
2
0
2
2
0
0
0
0
1
0
1
0
0
0
0
0
2
3
1
0
0
2
0
0
2
1
0
0
1
1
0
2
0
1
0
1
0
2
1
2
0
0
1
0
0
1
0
0
0
2
0
0
2
0
0
0
1
1
1
0
2
2
0
0
1
0
0
1
0
0
2
1
0
0
1
2
0
0
1
2
0
1
0
15
0
1
0
0
0
1
0
4
0
0
2
0
1
1
2
1
0
0
0
1
1
0
1
1
0
1
1
1
0
1
2
1
0
2
0
2
2
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
2
0
1
0
1
2
1
1
2
0
0
1
0
0
0
1
0
2
1
0
0
0
0
1
0
0
0
0
0
1
1
2
0
2
0
0
1
0
1
0
0
1
1
0
1
1
1
1
2
0
0
1
2
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
2
0
2
0
1
0
1
0
3
0
1
0
2
1
1
0
0
0
0
0
2
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
1
2
0
1
1
0
1
1
0
2
1
2
1
0
0
0
0
1
1
0
0
0
1
0
0
1
1
1
0
0
3
1
0
0
0
6
1
1
0
1
2
0
2
0
0
0
1
2
2
1
0
1
1
1
0
2
1
0
0
0
1
0
0
1
1
1
2
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
2
1
1
2
0
0
0
1
0
1
0
1
1
0
0
2
0
0
2
6
1
0
0
1
1
1
1
2
2
1
1
2
0
0
1
0
0
0
0
2
2
0
0
2
1
2
1
0
1
0
1
1
1
1
0
0
2
1
0
1
2
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
2
1
0
2
0
0
1
0
0
2
0
0
0
1
2
0
0
1
0
2
2
1
2
0
1
1
1
0
1
0
2
0
0
0
1
1
1
0
1
0
2
0
1
1
1
1
2
0
1
1
3
1
0
0
0
0
0
2
0
2
0
2
1
0
2
0
1
0
0
0
2
1
0
2
0
0
1
0
2
1
0
3
2
1
2
0
0
1
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
2
1
0
1
1
0
0
1
2
0
0
0
1
1
0
0
0
1
0
2
2
2
2
2
2
0
1
0
0
2
2
0
0
0
1
0
0
1
0
0
0
0
1
2
1
0
1
1
1
1
0
2
2
1
1
2
1
0
0
0
0
1
0
0
1
2
1
1
0
0
0
3
0
0
2
2
0
2
0
2
0
1
0
0
0
0
0
1
0
0
1
0
0
2
0
3
1
2
2
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
1
0
0
2
1
2
2
0
1
2
1
0
2
2
1
2
2
1
0
3
0
0
0
2
0
0
2
2
2
2
2
0
0
2
0
0
0
0
1
0
1
2
0
0
1
2
1
0
0
0
1
2
0
0
0
1
0
0
4
1
2
0
0
2
0
2
2
0
1
2
1
1
0
0
1
0
1
0
1
0
2
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
1
3
1
0
0
1
1
1
0
1
1
0
2
0
0
0
1
0
0
0
1
1
0
0
0
0
1
1
2
0
0
0
0
0
1
1
0
2
3
1
0
0
0
0
0
1
0
1
0
0
2
1
3
1
2
1
0
0
0
0
0
0
0
0
1
0
1
3
1
0
0
1
1
0
0
2
1
2
0
2
8
1
0
0
1
0
0
2
2
0
2
0
1
0
0
1
0
1
0
0
2
1
0
1
2
2
0
0
1
0
0
1
2
2
0
0
0
0
0
1
2
0
2
2
0
0
1
2
0
1
0
2
0
0
0
0
0
1
1
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
6
1
2
0
0
0
0
2
0
0
1
0
0
3
0
2
1
1
0
0
0
0
1
1
0
2
2
1
2
1
2
0
0
0
1
3
0
2
2
0
1
1
0
0
2
0
1
0
2
0
2
1
0
1
0
0
2
3
1
2
1
0
0
0
2
2
1
0
1
0
1
1
2
0
1
1
0
0
1
0
0
0
2
0
0
2
0
0
0
0
1
0
1
2
2
0
0
0
1
1
2
1
0
0
1
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
2
0
0
1
1
1
0
1
0
1
0
0
0
0
2
0
0
1
1
0
1
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
1
0
0
0
1
1
0
0
4
0
1
1
0
2
1
1
0
1
1
2
1
0
1
2
0
0
1
0
0
2
1
0
0
0
2
1
1
0
0
1
2
2
0
1
1
0
1
0
0
1
0
0
1
0
1
1
0
2
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
2
0
1
0
2
0
1
1
2
0
2
0
0
1
2
0
1
2
0
1
2
0
0
2
0
1
0
2
0
0
0
0
1
1
0
0
2
2
1
0
1
2
1
0
2
0
2
1
0
1
1
2
2
0
0
0
1
0
0
1
0
1
1
0
2
0
0
0
2
1
1
0
1
0
1
1
0
2
1
0
0
0
2
2
0
2
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
2
0
2
0
0
2
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
1
0
0
2
1
0
0
0
0
0
1
1
0
1
0
1
1
2
0
1
4
1
2
0
0
1
1
0
0
0
2
0
0
0
1
2
1
1
0
0
0
0
0
2
1
1
0
1
0
0
1
2
2
2
0
1
0
0
2
0
0
0
1
3
1
0
1
0
0
1
1
1
0
2
0
0
2
0
2
1
1
0
2
1
1
1
0
0
2
1
0
1
1
2
2
0
0
0
1
0
2
0
2
1
0
2
0
0
2
1
0
0
0
2
0
0
2
3
2
2
0
0
0
1
1
0
0
0
0
0
2
0
0
1
2
0
2
0
1
2
0
0
0
0
2
2
0
0
2
1
1
0
2
0
0
0
0
0
0
2
2
0
1
1
0
2
2
1
2
2
0
0
2
0
0
0
0
2
1
0
2
0
2
1
1
2
1
0
1
0
2
2
0
2
0
0
0
0
2
1
0
0
1
2
0
1
2
2
0
1
0
0
0
0
2
0
1
0
3
1
0
0
0
2
0
2
2
1
1
0
2
0
0
2
0
1
2
1
2
2
0
0
1
2
1
0
0
0
0
1
1
1
2
0
1
0
1
0
2
1
1
1
0
0
2
0
0
1
1
1
0
1
0
1
0
5
2
2
2
0
1
2
0
0
1
1
2
0
0
0
1
0
0
3
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
1
0
0
1
0
2
0
0
2
0
0
2
0
1
0
0
0
0
0
1
2
0
2
1
0
0
2
1
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
2
1
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
1
2
0
1
1
1
3
0
0
1
0
2
1
1
0
0
2
0
2
2
1
1
0
0
0
2
2
1
1
2
1
0
1
0
0
0
0
0
0
0
0
1
0
2
1
2
1
1
0
2
2
0
0
0
0
1
0
0
0
0
2
1
0
0
1
1
3
2
0
1
1
0
2
1
1
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
1
1
1
1
1
0
0
1
1
1
1
1
1
0
2
0
0
0
2
2
0
2
1
0
0
0
0
2
2
1
0
0
0
1
0
1
2
0
0
1
0
0
0
1
0
1
2
1
0
3
0
0
0
0
1
0
0
1
1
0
2
0
0
1
0
0
0
1
2
0
0
0
0
0
0
2
1
2
0
0
0
1
0
2
1
1
2
0
2
3
2
0
1
2
0
0
0
1
1
0
1
0
2
0
1
0
3
0
1
2
1
1
1
0
0
1
1
0
0
1
0
0
0
0
0
0
5
1
0
0
0
0
0
1
0
1
0
2
1
2
0
0
1
0
1
0
0
0
6
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
1
0
0
1
0
0
1
2
0
1
0
3
2
2
2
0
0
1
2
1
0
0
0
1
0
2
0
0
1
0
1
0
0
0
0
0
1
0
1
1
2
2
0
1
1
0
0
2
0
0
0
2
2
2
2
0
2
0
2
0
2
0
1
0
0
0
1
1
0
2
1
0
0
0
1
0
0
0
0
2
0
2
0
0
1
0
0
2
0
2
2
1
1
0
0
0
1
0
2
0
0
0
0
2
2
2
0
3
0
2
0
0
1
1
0
0
0
1
1
2
2
1
0
1
0
1
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
1
0
1
0
0
1
1
1
0
0
2
0
0
2
2
0
1
1
1
2
2
0
0
0
1
0
0
0
2
0
1
2
2
4
2
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
1
1
2
2
0
4
1
0
0
1
1
2
0
1
0
1
0
2
1
1
1
2
1
0
0
0
1
5
2
1
0
0
0
0
0
1
0
0
1
1
0
0
2
0
0
0
2
1
2
2
1
1
1
2
1
2
1
0
0
2
0
0
0
0
0
0
0
1
1
2
1
1
0
2
0
1
0
1
0
2
0
0
1
1
0
3
0
1
1
2
0
0
2
0
1
0
0
1
1
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
2
1
0
2
2
0
0
2
0
1
2
4
0
0
0
0
2
2
0
2
0
0
1
1
1
0
2
0
1
0
1
0
0
1
0
0
0
1
1
0
1
0
1
1
0
2
2
0
1
1
0
0
2
0
0
1
0
2
1
0
0
1
1
1
2
2
2
1
1
0
2
0
0
1
1
0
0
0
2
0
1
0
0
0
0
1
0
0
1
2
2
0
0
0
1
0
1
3
0
0
0
2
0
1
0
0
1
2
2
0
0
1
0
2
3
0
2
0
2
2
0
0
1
0
1
0
0
2
0
0
6
0
1
2
2
0
3
1
1
1
0
0
1
0
0
2
1
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
1
0
1
0
1
0
3
0
1
0
0
1
0
0
0
2
0
0
0
1
5
1
1
1
1
1
1
1
2
0
0
2
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
2
0
1
1
1
0
0
0
2
2
2
0
1
0
1
1
2
2
0
0
1
0
0
1
1
0
3
0
4
2
3
0
2
0
0
0
0
2
0
0
0
0
3
2
1
1
1
1
3
2
1
2
0
0
0
1
1
2
1
0
1
2
0
2
0
0
2
0
2
0
0
0
0
2
0
2
0
0
0
1
0
0
1
1
1
2
1
0
1
1
0
2
1
2
0
1
0
2
0
0
0
0
2
0
0
0
2
2
0
0
0
0
2
1
0
0
2
0
0
1
0
1
1
0
0
0
0
0
2
2
1
1
1
0
0
2
0
0
2
0
2
2
3
0
0
0
0
1
1
0
1
2
1
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
4
0
0
1
0
1
0
2
0
0
2
2
1
1
2
0
0
2
3
0
1
2
0
1
1
0
0
2
5
2
1
0
1
0
0
1
1
0
0
1
2
0
1
1
0
1
0
0
1
1
0
1
1
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
1
0
0
0
1
0
0
0
1
1
1
2
1
1
0
2
0
2
1
1
0
2
0
2
0
1
2
0
0
0
1
0
0
0
0
0
0
2
0
2
0
1
0
2
1
0
2
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
1
0
1
0
2
2
0
0
2
0
0
1
0
0
3
0
0
4
0
0
0
2
2
2
0
0
1
0
1
0
0
0
1
1
1
2
1
0
0
0
0
0
3
1
0
0
1
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
2
2
2
0
0
0
1
0
1
0
1
1
0
0
0
1
0
0
0
1
2
0
2
0
1
0
2
1
1
2
2
0
0
0
0
1
2
0
2
2
0
0
2
1
0
2
1
1
1
1
0
2
0
0
2
1
0
1
1
1
0
0
0
1
0
2
0
0
0
2
0
0
1
0
1
2
0
0
0
0
0
2
0
2
2
0
1
0
2
2
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
2
1
1
1
0
0
1
0
0
0
1
1
1
2
2
2
2
2
0
0
2
3
0
0
0
0
0
1
0
2
1
2
2
1
0
2
0
0
2
0
0
0
0
1
1
1
0
2
0
0
2
2
0
0
0
1
0
2
0
1
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
4
0
0
0
1
1
0
0
2
0
1
0
0
2
0
0
2
2
0
0
0
0
2
0
1
0
2
5
2
0
0
2
1
0
1
0
1
1
0
0
0
0
0
2
0
0
0
1
0
1
0
2
1
4
2
2
0
0
0
0
0
0
1
2
1
0
0
0
0
2
2
0
1
1
1
1
1
0
0
1
0
1
0
1
0
2
0
1
1
1
1
1
1
0
1
1
1
0
0
3
0
1
0
1
0
0
0
2
0
1
0
1
0
0
1
0
0
2
1
0
0
0
0
2
2
1
0
2
0
2
1
0
1
0
1
2
0
0
0
1
1
1
0
0
0
1
0
0
2
2
0
0
1
0
2
2
2
0
0
1
2
2
0
0
0
0
2
1
0
0
0
2
1
1
1
1
1
0
0
0
1
1
0
0
1
1
0
2
3
0
0
2
1
0
0
0
2
0
0
2
0
2
2
0
1
1
0
2
0
1
2
2
1
0
1
0
1
2
0
0
2
0
3
0
0
2
1
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
2
1
0
2
1
0
2
2
0
0
0
0
0
1
3
0
2
0
0
0
1
0
1
1
0
1
0
0
0
2
1
1
0
0
0
1
0
0
1
0
2
2
0
1
1
1
2
0
0
0
1
3
2
2
1
3
1
0
1
0
0
1
2
0
1
0
0
2
0
0
0
1
1
0
0
2
0
2
1
0
4
0
1
1
0
0
0
2
2
0
1
2
2
1
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
1
0
1
0
2
2
1
0
0
0
0
2
0
0
1
0
1
2
0
0
0
2
1
1
0
0
2
2
2
0
0
0
0
1
2
0
1
0
1
0
0
0
0
0
2
2
0
2
0
2
0
0
2
0
0
1
1
0
0
0
0
0
0
1
2
1
1
0
2
0
0
0
1
2
1
2
0
3
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
2
1
0
1
0
0
0
2
0
0
0
2
0
2
1
1
0
0
0
1
1
0
2
0
2
0
1
0
1
0
0
1
0
0
2
0
2
2
2
0
0
0
0
2
2
0
2
4
1
6
1
0
2
0
0
0
0
0
0
1
0
1
0
0
0
3
0
0
1
0
1
1
0
1
0
0
1
0
1
0
1
2
1
2
0
2
1
1
2
2
0
0
0
0
1
0
2
1
0
0
0
0
0
0
1
0
2
2
1
0
0
0
2
0
1
0
0
1
0
0
0
1
2
2
0
2
0
1
0
2
1
1
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
2
1
2
1
1
0
0
0
0
0
0
0
2
1
2
0
2
3
1
2
0
0
2
1
0
2
2
0
3
0
0
0
0
1
0
1
1
2
0
1
0
0
0
0
1
1
1
1
0
2
2
1
0
2
0
1
0
0
0
0
0
1
0
1
2
0
1
0
0
0
0
2
0
1
0
1
1
0
0
0
0
0
1
0
2
0
2
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
0
0
0
0
2
2
0
1
1
0
1
2
0
2
0
0
0
3
0
1
1
1
0
1
1
0
0
0
0
0
2
2
3
0
0
0
0
0
1
0
1
0
3
1
0
0
1
2
2
1
1
1
0
2
2
0
1
1
0
0
0
0
0
0
1
2
1
1
0
0
1
0
0
0
2
0
0
1
0
1
0
0
0
1
0
0
1
0
2
0
2
1
1
0
1
0
0
1
0
0
0
0
0
4
0
1
0
0
1
1
0
0
2
2
0
0
1
1
2
0
0
0
0
0
2
0
0
0
5
0
3
0
0
1
1
0
0
3
2
0
2
1
0
0
1
2
1
0
2
0
2
0
1
0
2
2
2
0
0
2
1
4
0
1
1
1
0
1
0
0
2
0
1
0
1
2
0
0
0
0
2
0
2
0
1
0
2
0
1
0
0
1
2
1
0
1
0
1
0
0
0
0
3
1
0
1
0
2
2
0
1
0
0
0
0
1
0
1
0
2
1
0
2
0
0
2
3
0
0
0
2
2
0
2
0
0
0
0
2
0
0
2
2
0
0
0
1
1
2
1
2
0
0
0
0
0
0
2
0
0
0
1
2
0
2
2
0
0
1
0
0
1
0
0
2
1
1
1
2
0
0
1
1
4
0
1
0
0
0
2
2
0
0
2
0
0
0
0
2
1
0
0
0
2
0
0
0
1
0
2
1
0
1
0
0
1
3
0
1
1
0
2
0
0
2
2
1
0
0
0
1
0
1
1
1
1
2
2
2
1
1
1
0
1
1
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
2
1
0
0
0
0
2
2
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
2
2
1
1
1
0
3
1
0
0
1
0
0
0
1
1
0
0
0
1
0
0
1
2
2
0
2
0
2
1
1
1
1
0
0
1
0
1
0
0
3
2
0
0
0
0
0
3
1
0
1
0
0
0
0
1
0
1
0
0
2
2
0
0
1
0
0
1
1
1
2
0
0
2
0
0
2
0
0
0
0
0
2
0
1
0
0
1
0
2
0
1
2
0
0
0
0
2
1
0
1
0
0
0
0
2
2
0
0
1
0
1
1
0
1
0
0
2
2
2
1
0
0
1
1
1
1
0
1
2
0
1
2
2
1
2
1
0
1
1
2
3
0
0
2
1
2
0
1
0
2
2
0
0
1
1
0
0
0
0
1
0
0
1
1
2
0
0
0
0
1
0
0
0
1
0
1
2
2
0
0
2
0
0
0
2
2
1
2
2
0
1
1
0
1
1
2
1
2
1
0
2
0
0
2
1
0
1
0
1
1
0
1
2
2
0
1
0
0
2
0
0
0
0
0
2
1
1
3
0
0
2
0
2
0
0
0
0
0
0
0
1
1
0
0
0
2
0
2
2
0
0
0
0
1
0
1
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
2
2
0
1
0
2
0
0
2
0
1
2
1
1
0
0
2
0
1
0
0
2
0
0
2
0
2
2
1
0
0
0
0
0
2
0
0
1
0
1
3
1
0
0
2
2
0
1
0
0
0
1
1
2
0
2
0
1
0
0
0
2
1
0
0
0
3
0
0
1
1
1
0
1
0
0
1
1
2
1
2
1
1
0
1
2
1
2
1
2
2
2
2
0
2
2
0
0
0
1
1
0
2
1
1
1
0
2
2
0
2
0
1
2
3
2
1
1
1
0
0
2
0
1
0
2
1
0
1
1
0
0
1
0
0
0
1
0
2
1
1
0
1
0
0
2
1
2
1
1
2
2
2
0
0
0
3
0
0
0
0
0
0
0
3
2
0
1
2
0
0
0
0
0
1
1
4
0
1
2
0
2
0
0
1
0
0
3
0
1
0
0
1
0
0
0
0
0
0
0
1
0
2
1
1
1
0
0
2
2
1
0
0
1
2
0
0
1
1
0
0
1
0
0
0
0
1
2
1
1
0
1
2
0
0
2
0
0
0
1
0
2
0
2
0
2
0
1
2
0
0
1
0
1
2
1
0
0
0
0
1
2
0
0
1
2
2
0
1
1
2
0
1
1
2
2
1
1
0
1
1
0
2
2
0
0
0
0
1
1
1
1
1
0
1
0
0
1
0
0
2
1
0
2
2
0
0
1
0
1
2
1
0
0
1
0
1
2
1
0
0
0
0
2
3
0
2
0
1
0
0
1
0
2
0
2
0
1
0
2
0
0
0
0
0
0
2
1
0
1
3
0
0
0
0
1
0
0
1
1
0
1
1
1
0
0
2
0
2
0
1
0
0
2
1
1
0
2
1
3
1
0
0
1
2
4
0
2
0
2
0
0
1
2
0
1
0
1
2
2
0
1
0
1
2
2
1
0
0
2
2
1
0
0
2
0
0
1
0
2
0
0
0
0
2
2
0
0
2
0
0
1
0
0
2
0
1
0
0
2
1
1
1
1
2
2
1
0
0
0
0
0
0
1
2
2
0
1
0
0
3
2
1
0
1
0
0
2
2
2
1
1
2
2
2
0
1
2
0
0
1
0
2
0
4
1
0
0
0
0
0
2
1
0
0
2
2
0
2
2
2
1
1
2
0
1
0
0
0
3
0
0
2
0
0
1
1
1
3
0
0
2
1
1
0
0
2
0
1
0
2
0
0
0
1
3
1
0
0
0
0
1
0
1
1
0
0
1
0
2
0
0
0
1
1
1
0
0
0
1
2
2
0
0
0
1
1
0
0
2
0
2
1
0
2
1
0
0
1
0
0
2
0
1
0
1
0
1
0
2
0
0
1
0
0
2
0
0
0
0
0
0
3
0
0
0
0
1
0
1
2
0
0
2
1
1
0
0
0
1
1
2
2
0
2
0
2
2
0
1
0
1
0
1
0
0
1
0
1
2
0
0
1
0
0
3
2
2
0
0
2
2
1
3
0
0
2
0
2
0
0
2
2
0
1
0
0
1
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
2
0
1
0
0
0
0
0
2
1
0
1
1
1
1
1
0
0
0
1
0
0
0
0
0
1
3
1
1
2
2
0
1
1
1
1
1
0
1
0
1
0
2
0
0
1
1
0
1
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
1
0
0
0
0
1
2
0
1
0
2
2
1
0
2
0
0
0
1
2
0
0
0
1
0
0
1
0
0
0
0
2
0
0
1
0
1
0
1
0
0
1
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
2
2
0
0
1
0
0
2
2
0
1
1
0
0
0
2
1
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
3
2
0
0
0
0
1
1
1
0
1
0
0
0
0
2
2
1
0
0
0
0
0
4
0
0
0
3
0
1
0
1
1
2
0
2
2
1
0
0
0
1
1
2
2
0
2
0
0
0
0
2
1
1
0
0
0
1
8
0
2
0
2
0
1
1
0
0
0
0
1
0
2
0
2
1
2
0
1
2
0
0
2
0
0
2
0
0
0
1
1
2
2
0
2
1
0
0
1
0
0
0
1
0
1
0
0
1
0
0
2
0
1
2
2
1
1
0
2
1
0
2
2
2
0
1
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
1
0
1
2
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
2
0
1
1
0
0
1
1
2
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
2
0
1
0
1
1
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
2
3
0
2
1
0
1
1
1
0
0
2
2
2
0
0
0
0
0
0
1
1
2
1
0
1
3
1
0
1
0
0
2
0
0
0
0
0
0
1
2
0
0
0
2
0
1
1
1
0
2
0
2
0
0
1
0
0
2
2
0
0
1
1
0
1
0
0
0
1
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
1
0
0
0
0
2
0
2
0
0
0
0
1
0
1
0
1
2
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
1
0
0
1
0
0
0
2
1
1
0
0
1
1
1
0
0
0
0
0
0
1
1
0
0
1
1
1
2
0
0
0
0
0
0
2
0
0
1
0
1
0
0
1
2
0
0
0
2
0
1
1
1
1
0
0
1
1
0
0
2
1
2
1
0
1
1
0
0
0
0
0
1
1
5
0
0
0
0
0
1
0
0
1
2
0
1
0
0
3
0
1
1
2
1
1
0
3
0
1
0
1
0
0
0
0
2
0
0
1
1
1
0
2
0
1
2
0
0
1
0
1
0
0
1
0
2
0
0
1
2
0
0
1
0
1
1
0
0
2
0
0
1
2
0
1
2
2
1
0
2
2
0
0
0
0
2
1
2
2
0
0
2
2
1
1
0
0
0
0
0
1
0
0
0
1
1
1
1
0
2
0
2
1
1
2
0
1
1
1
1
0
0
1
0
2
2
2
0
0
0
2
2
0
0
0
2
0
0
2
4
0
0
0
1
1
1
2
1
1
0
1
0
0
3
0
1
1
1
2
0
0
0
0
2
0
0
2
0
1
2
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
2
0
0
1
1
1
1
0
1
1
1
0
1
0
0
1
0
1
0
1
1
2
0
0
1
0
0
0
2
1
1
0
2
0
0
1
2
0
1
0
0
1
0
0
1
1
0
0
1
0
2
0
0
1
0
0
6
2
0
0
0
1
1
1
2
0
1
0
0
0
0
0
4
2
2
0
0
3
1
0
0
1
2
1
1
1
0
0
2
1
1
0
1
0
2
3
0
2
1
0
0
1
0
0
1
0
0
2
0
1
1
2
2
0
0
0
1
3
0
2
0
1
2
2
0
0
0
1
0
0
0
2
0
2
0
0
1
0
0
1
2
1
1
2
2
0
0
0
0
0
0
1
1
0
0
0
2
0
0
1
1
0
0
0
0
1
1
0
1
1
1
0
0
1
1
1
0
0
0
0
0
0
0
0
2
1
2
0
0
1
0
0
2
1
0
2
1
1
1
0
0
0
1
0
0
2
0
1
1
2
1
0
1
0
0
1
1
1
7
2
0
1
1
0
0
0
1
1
1
0
0
1
0
1
0
0
4
2
0
1
1
2
3
0
2
1
3
1
0
1
0
0
0
1
1
0
0
0
1
1
0
1
0
0
1
0
0
0
0
3
0
0
0
0
0
1
0
1
0
2
1
0
0
1
2
0
0
3
3
1
0
0
2
0
1
0
1
0
1
0
0
1
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
2
2
1
2
0
1
1
1
0
1
0
1
0
0
2
0
1
2
0
2
1
0
1
0
2
1
1
2
2
0
4
0
2
0
0
0
2
0
0
2
2
1
1
0
0
2
2
0
3
0
0
1
0
1
2
0
2
1
0
0
0
1
2
1
0
1
1
0
5
0
0
0
0
0
1
2
3
2
3
0
0
0
0
0
0
0
2
1
1
1
1
0
0
1
0
1
1
2
2
2
0
0
0
1
1
0
1
2
0
0
1
5
2
0
0
0
0
1
0
1
2
1
0
0
1
0
0
2
0
1
1
1
1
2
0
0
0
1
2
1
0
1
2
0
0
1
1
0
2
0
2
0
0
1
0
0
2
2
0
2
1
2
0
1
2
2
1
0
0
1
0
0
7
1
0
2
0
0
2
1
0
0
0
1
0
1
0
1
0
2
1
1
0
0
0
0
0
0
2
0
0
2
1
2
1
0
0
3
0
0
0
0
0
0
1
1
0
0
0
2
0
1
0
1
1
1
0
0
0
1
0
0
1
0
1
0
0
1
1
0
0
2
1
2
1
0
1
0
0
2
2
0
0
2
2
0
1
1
0
0
0
2
1
1
0
0
0
0
2
0
1
0
0
0
1
2
1
1
0
3
0
1
1
0
0
2
0
1
0
1
0
0
2
2
0
2
1
1
0
0
0
0
0
0
0
2
0
0
0
1
2
1
1
0
1
0
1
0
1
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
2
1
0
0
0
1
2
2
0
1
0
0
0
3
4
0
0
0
0
2
2
0
0
0
0
1
1
0
0
0
0
1
1
2
0
0
0
1
0
1
0
0
1
1
2
1
0
0
0
1
0
0
0
2
1
0
1
1
2
2
1
0
2
0
2
1
0
0
0
0
1
0
0
0
0
0
2
1
0
1
0
1
1
0
2
1
2
4
0
0
2
0
0
1
2
1
0
0
0
0
0
0
0
1
0
1
0
2
2
0
1
0
0
0
0
1
0
0
2
0
0
2
0
2
2
1
1
0
3
0
1
0
0
0
0
1
0
1
2
0
0
1
2
1
2
1
1
0
1
0
2
2
2
1
0
2
0
1
1
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
4
3
2
4
2
0
0
0
0
2
0
2
2
0
0
1
2
2
0
0
0
1
0
0
1
1
0
2
0
1
2
0
0
3
1
0
1
0
2
0
1
0
0
1
0
1
0
1
0
1
0
4
1
0
1
0
1
2
0
2
0
0
1
2
2
2
0
0
0
0
0
2
1
0
2
1
0
0
1
2
2
1
0
2
0
2
2
0
0
1
0
1
2
2
2
2
0
2
0
0
0
0
1
0
2
1
1
0
2
0
0
1
1
1
0
0
1
0
1
0
1
0
2
0
0
1
1
1
2
2
2
2
0
1
0
1
0
0
1
0
1
1
0
0
1
1
0
0
1
2
4
0
0
1
0
0
0
1
0
1
0
2
0
0
3
0
0
1
0
2
0
2
0
0
2
0
2
0
0
0
2
2
0
0
0
0
2
2
0
2
1
1
0
2
0
1
1
0
0
2
0
2
0
2
0
0
0
2
2
0
1
2
1
0
2
1
1
0
0
0
0
0
0
0
0
2
1
3
1
0
1
1
1
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
3
0
0
0
1
0
0
1
0
2
2
2
0
1
0
0
0
0
3
0
0
1
0
0
0
0
1
0
2
2
0
3
1
2
0
1
1
2
2
1
0
2
2
0
1
0
1
0
0
3
1
2
0
1
1
2
0
0
2
1
1
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
1
2
2
4
2
2
0
2
0
0
1
1
0
0
2
3
1
0
2
2
0
1
0
2
0
0
2
0
2
1
0
1
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
3
1
0
2
0
0
1
1
1
0
0
0
0
0
1
2
1
1
2
2
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
2
1
0
0
0
2
0
0
0
2
2
2
1
0
1
1
0
0
0
2
0
2
2
2
0
1
1
3
1
0
0
0
0
1
0
1
0
0
2
0
1
0
0
0
0
0
2
0
0
1
1
0
0
1
0
1
0
1
2
2
0
0
1
0
0
0
0
1
2
1
3
2
0
2
0
1
1
2
1
2
2
1
1
2
1
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
2
3
0
0
0
2
0
2
1
2
0
0
0
2
0
0
0
2
1
1
0
0
0
0
0
2
1
0
2
0
0
0
3
2
0
2
2
0
1
0
0
0
1
0
2
0
1
0
0
0
0
1
0
2
0
2
1
2
1
0
0
0
1
0
0
1
0
0
1
1
0
0
2
0
1
2
1
0
0
0
2
2
2
0
0
0
0
0
0
0
2
2
0
0
0
1
0
1
1
0
2
1
1
0
2
2
0
2
1
2
1
0
0
0
2
2
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
1
2
1
0
2
1
2
0
0
2
0
1
3
1
2
0
1
2
2
1
0
1
1
1
0
1
2
1
0
0
0
1
0
0
1
0
0
1
2
1
0
0
0
2
1
0
2
1
0
0
1
0
2
2
1
0
0
2
2
0
2
0
0
3
1
0
2
0
1
0
2
1
1
2
1
0
1
0
2
2
0
0
2
0
0
1
0
0
0
1
1
0
0
0
1
0
1
0
1
2
0
1
0
1
0
0
0
0
2
1
0
0
0
0
1
1
0
0
2
0
2
0
1
0
0
2
2
2
2
0
2
1
0
1
0
0
0
0
2
0
0
0
2
0
0
1
0
0
1
0
0
0
1
0
1
0
2
0
0
1
1
0
0
0
0
2
1
0
3
0
1
1
3
1
0
2
1
0
0
1
0
0
0
0
0
2
1
1
0
1
0
0
0
1
0
0
2
0
4
1
1
2
2
2
0
0
0
2
0
1
0
2
0
2
0
2
0
0
1
0
0
1
1
1
0
2
2
0
2
0
0
0
1
0
1
0
1
1
2
2
0
0
0
1
1
0
0
0
0
2
0
3
0
0
1
1
2
0
0
0
0
0
1
0
0
1
0
1
0
2
2
2
0
0
0
0
0
1
1
0
0
2
1
1
1
0
0
0
0
0
1
0
2
0
0
1
1
0
0
2
0
0
0
3
2
0
1
1
0
1
1
2
2
1
0
0
0
0
1
0
1
0
0
0
1
1
0
1
1
0
1
0
1
2
1
0
0
3
1
1
0
5
0
1
2
0
0
1
0
0
0
2
0
0
2
0
3
2
1
0
0
1
0
0
0
1
2
0
1
2
3
0
0
0
1
0
1
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
2
2
1
1
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
2
2
0
0
2
1
0
1
0
0
0
1
1
0
3
0
1
0
0
1
0
1
0
0
0
1
2
2
0
0
2
2
0
1
1
1
0
0
1
0
2
0
2
0
1
1
1
1
1
2
0
0
1
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
2
0
0
2
0
0
1
1
0
1
1
0
1
1
0
0
0
1
0
0
1
0
0
1
0
0
1
1
2
1
1
2
1
2
2
0
1
0
1
1
2
0
1
0
1
0
1
0
0
0
0
0
0
0
2
0
1
0
1
1
0
1
3
0
2
0
0
2
2
1
2
0
0
2
0
1
0
2
0
2
1
2
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
2
2
0
1
0
1
1
0
2
0
0
1
2
1
1
0
1
0
0
0
0
0
1
0
2
2
1
0
0
0
0
2
0
1
2
0
0
0
0
0
2
0
1
0
2
1
0
0
2
0
0
0
0
0
1
2
1
0
1
1
0
2
0
1
1
2
1
1
0
2
0
2
0
1
0
0
0
0
1
1
1
1
0
0
0
0
1
2
0
0
0
0
2
0
1
1
2
0
2
0
0
0
1
0
0
2
1
1
0
1
0
0
0
1
3
1
0
2
1
0
2
0
2
2
1
1
0
0
2
1
0
0
0
1
3
2
0
0
1
0
2
0
0
1
1
0
1
2
1
0
4
1
1
0
0
2
0
1
1
0
1
0
0
3
2
1
2
2
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
2
0
2
0
0
1
0
0
0
1
1
0
0
0
0
2
1
2
0
0
2
1
0
0
0
0
0
3
0
0
1
1
2
2
1
0
0
1
0
0
0
0
1
1
0
1
1
0
1
0
1
1
1
0
0
1
3
3
0
0
2
0
3
1
0
0
0
1
0
0
2
0
1
1
2
1
0
1
1
1
3
0
0
0
0
0
0
0
1
1
1
0
2
0
0
1
0
2
1
0
1
1
1
1
1
0
2
0
0
0
1
0
2
1
0
0
2
2
2
0
0
0
2
0
1
2
0
0
0
0
4
0
0
0
0
0
0
1
0
0
2
0
1
1
2
0
5
1
1
0
0
0
0
2
0
2
0
2
0
2
1
0
1
0
0
2
1
1
2
2
2
2
0
0
0
0
2
0
0
0
0
0
1
2
1
0
1
1
0
0
2
0
2
0
1
2
3
1
0
0
0
1
2
0
0
2
0
0
0
1
0
0
1
0
4
1
0
0
2
0
0
0
2
0
0
1
0
1
0
0
1
0
0
0
0
0
2
0
1
1
1
1
2
0
0
1
0
1
1
0
1
4
1
0
0
0
1
1
0
0
2
1
1
1
0
0
1
0
0
1
2
2
0
1
0
0
0
0
1
2
0
2
1
0
0
0
2
0
0
0
0
0
0
1
1
1
2
0
0
0
2
1
0
0
1
2
1
1
0
0
0
0
2
0
1
0
0
1
1
0
1
0
0
1
2
0
0
3
1
2
1
0
1
0
2
1
2
1
0
2
2
0
1
0
0
0
1
0
1
0
1
1
1
3
0
0
2
2
0
2
2
0
2
1
0
0
0
1
0
0
0
1
0
0
2
0
2
0
2
2
1
2
2
0
0
0
0
1
0
1
0
0
1
2
2
1
1
0
0
1
0
0
2
0
0
0
0
1
1
0
1
3
0
0
2
2
0
5
0
3
0
2
1
0
2
0
2
1
4
2
1
0
0
0
1
1
0
0
2
1
0
0
0
1
2
0
1
2
1
1
1
0
0
2
1
0
0
2
1
0
2
2
0
1
2
2
2
2
2
0
2
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
2
1
2
2
2
0
0
1
0
0
0
1
0
1
0
1
0
0
2
0
0
1
1
0
1
2
1
2
1
0
2
2
0
0
0
3
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
1
2
1
1
2
0
1
0
0
0
2
1
1
1
0
1
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
1
0
0
2
1
1
0
1
0
0
2
1
2
0
2
0
0
0
0
2
2
1
0
0
1
2
2
1
0
2
0
0
0
2
0
1
0
2
0
2
0
2
1
0
0
2
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
2
1
4
0
2
0
0
1
0
0
2
1
0
0
0
0
0
1
2
0
2
2
2
0
1
0
2
0
1
1
2
0
0
2
2
0
0
1
0
0
1
1
1
2
2
1
0
0
2
0
1
2
0
0
2
0
1
1
0
1
1
0
0
2
1
0
2
3
0
2
2
1
1
1
1
1
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
1
0
1
0
0
0
2
0
2
2
0
0
2
2
2
2
2
1
1
0
1
0
1
1
1
0
1
0
0
1
0
0
0
2
0
1
1
2
2
0
2
0
0
1
2
2
1
0
0
1
0
0
0
0
1
0
0
0
3
0
0
0
2
0
0
0
1
0
0
2
0
0
1
1
0
0
2
2
0
2
1
0
2
0
0
0
0
0
1
1
1
0
0
4
0
0
2
0
1
1
0
1
0
0
0
0
1
2
2
0
1
0
2
0
1
2
0
0
1
0
1
1
1
0
1
0
1
0
2
0
2
0
1
0
0
0
0
1
2
0
1
0
0
0
1
0
1
2
0
2
0
0
0
0
0
0
0
1
1
0
0
0
1
1
5
2
2
0
0
1
1
0
2
1
2
2
0
0
0
2
2
0
2
0
0
0
2
0
1
0
1
0
0
0
0
1
1
2
0
0
2
2
2
1
2
2
0
1
0
1
1
0
0
2
2
0
1
1
1
2
0
0
1
2
2
1
2
2
3
0
0
3
0
1
0
2
0
1
0
1
2
1
0
2
0
1
0
1
1
0
0
1
1
1
1
0
1
0
1
0
1
0
1
1
1
0
0
0
0
0
2
1
2
2
0
0
1
0
0
0
0
2
0
0
0
0
0
4
2
0
0
4
1
1
2
0
1
0
0
1
0
1
2
2
1
0
1
1
1
0
0
1
0
2
1
0
2
2
2
2
2
0
0
2
2
0
1
1
1
0
0
0
5
2
4
0
1
1
1
0
3
2
0
2
1
5
0
1
1
0
2
1
1
0
0
0
2
2
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
1
1
1
0
1
1
1
0
0
2
0
1
1
4
0
0
0
2
0
2
0
1
1
1
0
1
0
0
2
0
1
0
0
2
1
0
0
2
0
2
1
0
1
1
3
1
0
2
1
2
0
1
1
1
2
1
0
2
0
0
2
0
0
2
0
0
0
2
0
0
2
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
1
2
0
0
2
1
2
0
1
1
0
1
0
0
0
2
2
0
2
1
0
0
0
0
1
0
2
0
1
2
0
0
1
2
0
2
2
0
0
0
0
1
0
0
0
0
0
1
0
2
2
0
0
0
1
1
1
0
0
1
1
1
1
2
2
0
1
0
1
2
0
2
2
0
0
0
1
1
0
0
0
1
0
1
2
0
3
0
0
0
1
1
2
1
1
0
1
1
0
2
2
0
1
2
2
0
0
1
2
1
0
2
0
0
0
0
0
0
0
0
1
0
2
0
1
2
0
6
3
2
1
0
1
0
0
0
1
3
1
0
0
0
0
1
2
0
2
0
2
0
1
0
0
0
1
0
0
0
0
2
2
1
1
2
1
0
1
0
2
0
0
0
0
2
0
2
0
1
0
2
2
2
0
0
1
0
0
0
1
0
0
0
1
2
0
0
1
0
1
0
8
0
2
1
2
0
0
2
0
0
2
0
0
1
2
0
0
3
1
2
1
0
0
2
3
0
1
1
0
2
0
0
0
0
0
1
1
2
2
1
0
1
0
0
0
2
0
0
0
2
1
2
1
1
0
0
2
2
0
0
0
0
0
2
2
0
0
0
0
1
1
0
0
0
2
1
1
0
2
2
4
0
2
0
0
2
1
0
0
0
2
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
6
0
1
0
1
0
0
0
0
1
1
0
0
0
0
1
1
0
2
1
1
1
0
0
0
1
0
0
2
0
1
2
0
2
0
2
2
1
0
1
0
1
1
1
0
0
1
2
0
0
0
1
0
0
0
0
1
0
3
0
0
2
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
2
2
2
0
2
0
0
0
2
1
0
0
3
0
2
0
2
1
0
0
1
0
0
2
0
1
2
1
0
0
1
0
0
1
0
1
0
0
2
0
0
1
1
1
2
1
0
0
2
0
2
0
0
1
1
0
2
0
0
0
0
2
1
0
0
0
1
0
2
0
2
4
0
1
1
1
0
1
0
0
0
0
0
0
0
0
2
1
0
0
1
0
2
1
1
1
0
2
0
1
0
0
0
2
0
0
1
0
0
0
0
5
0
1
0
0
2
0
0
0
1
3
1
2
1
0
0
1
0
0
0
1
0
0
1
0
1
2
0
0
0
1
5
0
0
1
1
0
0
1
0
1
3
0
1
1
2
0
0
0
0
0
0
1
2
1
0
2
0
1
1
0
1
2
0
3
0
0
0
2
1
0
1
0
2
0
1
1
0
0
0
0
1
2
2
0
0
0
2
0
1
1
2
2
2
2
0
1
0
1
2
1
1
0
1
0
0
0
2
0
1
0
1
0
0
1
1
0
1
0
2
1
0
1
0
0
2
1
3
0
1
0
0
2
0
2
2
1
0
0
0
0
0
1
0
1
1
0
0
0
0
1
2
1
0
2
0
1
0
1
1
2
1
1
0
2
0
0
2
1
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
1
1
0
1
2
1
2
0
1
0
0
2
0
0
4
0
0
1
0
0
1
1
0
1
1
1
1
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
1
0
0
2
1
1
1
1
0
0
0
0
0
1
2
0
0
2
0
1
2
1
1
1
0
2
1
2
0
1
2
2
0
2
0
0
0
2
1
1
1
0
0
1
2
0
0
0
1
0
1
0
2
0
2
2
0
1
2
0
0
0
2
0
1
0
0
0
1
0
5
0
0
1
1
0
0
1
0
0
0
1
0
3
1
2
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
1
3
2
1
1
0
0
0
1
0
1
0
0
1
0
0
2
0
0
1
2
0
2
2
1
0
1
0
2
1
3
2
2
0
1
0
2
0
1
0
2
0
1
0
0
0
2
0
0
0
0
0
0
3
2
0
2
2
0
2
0
1
1
0
0
2
1
2
0
0
0
2
1
0
0
0
1
1
0
2
0
0
0
2
2
1
0
1
0
0
0
0
0
1
1
0
0
0
2
0
0
2
2
0
0
0
0
2
2
0
0
0
1
0
1
2
0
0
2
0
2
0
0
2
1
0
2
1
2
1
0
1
0
0
2
2
0
3
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
1
1
1
0
1
1
0
2
1
0
2
1
1
0
0
0
1
4
1
1
1
1
1
0
0
2
1
0
0
0
2
3
0
0
0
1
0
0
2
0
0
0
1
0
0
0
2
1
0
0
0
0
1
1
0
2
1
0
0
0
0
1
0
2
1
0
0
1
1
1
1
1
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
1
1
2
0
0
0
0
1
1
1
0
0
0
1
0
1
1
5
0
0
0
1
2
0
0
0
1
0
1
3
0
0
0
0
0
1
0
2
0
0
0
1
2
0
1
1
0
0
1
2
1
0
1
0
0
0
2
1
1
1
0
1
0
0
1
0
2
1
0
1
0
0
0
0
1
0
2
1
0
0
0
0
1
3
2
2
1
0
0
0
0
2
2
2
0
0
2
0
1
2
4
0
0
1
0
2
1
0
0
1
0
2
1
0
2
0
0
1
0
0
0
2
1
0
1
0
1
0
1
0
2
2
0
2
1
0
2
0
0
0
0
2
0
1
1
0
1
2
1
0
0
0
0
1
0
2
0
0
1
0
1
0
0
2
2
2
0
0
0
1
1
0
1
0
2
2
2
2
0
1
1
1
0
0
1
2
1
2
2
1
0
0
1
0
2
1
1
1
1
2
0
3
0
0
2
0
0
1
0
2
0
0
1
0
0
0
2
0
0
2
0
0
2
0
2
1
1
2
1
0
0
0
0
1
1
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
1
2
1
0
2
2
0
1
2
4
2
1
0
2
1
1
2
0
0
0
1
1
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
1
3
2
0
4
0
0
1
0
1
0
1
0
0
2
1
0
2
2
0
0
2
1
0
2
0
0
2
0
1
1
0
1
1
2
0
0
0
0
1
0
0
2
0
0
2
0
1
2
1
1
2
0
0
0
2
1
1
0
0
0
2
1
0
2
1
2
2
0
0
2
0
0
3
0
0
0
0
0
2
1
0
0
1
0
2
0
0
0
2
0
1
1
2
1
1
1
0
0
2
0
1
2
0
0
0
2
0
2
1
1
1
0
0
0
0
1
2
0
0
3
0
1
3
1
0
2
0
0
1
0
1
0
0
0
0
0
1
0
0
0
2
0
3
0
0
1
2
0
0
0
0
1
1
1
0
0
0
0
2
0
2
2
0
0
1
0
0
0
0
1
2
1
1
0
1
0
2
1
0
1
1
0
1
0
2
2
0
0
0
0
1
1
1
0
2
0
2
0
0
2
1
2
1
0
0
2
0
0
2
1
0
1
1
1
1
1
1
1
0
0
0
0
0
0
2
1
3
1
0
2
0
0
0
2
0
0
1
2
0
0
1
0
2
1
1
2
0
0
1
0
1
1
0
0
2
0
0
0
0
0
1
1
0
0
1
2
1
0
0
0
0
2
0
0
1
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
2
1
0
1
0
0
2
0
2
0
1
0
2
2
1
0
1
0
2
2
0
0
2
1
2
0
2
0
2
0
0
0
0
0
1
1
1
1
0
0
0
0
0
3
2
1
0
1
0
0
0
3
1
2
1
2
2
0
0
1
2
0
0
1
2
0
2
0
2
4
0
0
1
1
0
1
0
0
1
0
2
1
1
0
0
1
1
1
0
2
2
0
0
0
0
1
2
2
1
2
1
0
1
0
2
0
2
0
2
0
1
1
1
1
2
0
1
1
0
0
0
1
0
1
0
0
0
2
0
0
0
2
0
0
1
1
0
0
0
1
0
0
3
0
0
1
2
1
2
0
1
0
1
0
2
1
0
0
1
0
0
0
0
2
0
2
0
2
2
0
0
1
1
0
0
2
0
0
1
1
0
2
0
0
0
0
1
3
1
0
0
0
2
1
0
0
2
1
0
0
0
0
1
2
0
0
1
0
1
0
1
1
0
0
0
0
1
0
3
0
6
1
2
0
0
2
0
1
0
1
1
1
0
2
1
1
0
1
2
1
0
0
0
0
0
2
2
0
1
0
0
2
0
1
2
0
0
1
1
0
0
0
0
1
4
0
0
0
1
0
0
1
0
0
2
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
2
0
2
1
1
1
0
0
1
0
2
0
2
0
0
0
0
0
0
3
0
1
0
0
1
0
1
0
0
1
1
1
2
0
0
2
1
1
0
2
1
0
0
0
0
2
0
0
2
0
0
0
2
1
0
2
0
0
0
2
0
0
0
4
0
0
0
1
0
2
0
0
1
1
0
1
0
0
0
1
0
2
2
2
0
0
0
0
2
0
2
1
1
0
0
2
0
1
0
0
0
2
1
0
0
1
2
0
0
0
1
1
1
0
1
1
1
0
0
1
0
0
1
0
2
2
0
0
1
1
1
3
1
1
0
1
0
1
0
0
1
2
2
0
3
2
1
1
0
0
0
0
1
0
0
1
2
1
1
1
0
2
2
0
1
0
1
1
0
0
0
2
0
0
2
0
0
0
2
0
0
0
3
1
0
1
0
0
1
0
0
0
1
0
1
1
2
0
0
0
0
0
2
0
1
2
0
1
1
1
0
0
1
1
0
0
1
0
1
0
0
2
0
0
2
3
0
0
2
1
2
1
0
1
1
0
0
1
0
0
0
1
2
2
0
1
1
0
0
0
0
0
0
1
0
0
2
1
1
2
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
1
1
1
0
0
2
1
2
1
0
2
0
0
1
0
0
1
1
1
0
1
0
2
0
1
0
0
1
1
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
2
1
2
1
1
1
2
0
0
0
0
1
2
0
2
0
0
1
2
0
0
1
0
0
1
0
0
0
0
0
1
0
1
1
2
0
0
0
2
0
1
0
0
1
0
0
2
2
0
1
2
0
1
1
2
0
1
0
1
2
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
3
2
1
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
1
1
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
2
1
2
1
1
2
1
1
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
1
0
2
0
2
1
0
1
0
0
1
0
0
1
0
0
1
0
1
0
0
1
1
1
0
0
0
1
0
1
0
1
1
0
0
1
0
0
0
0
1
1
0
0
1
0
1
1
0
0
1
0
1
0
1
1
1
0
1
0
0
3
2
2
0
0
1
2
1
1
3
0
0
1
0
0
1
0
0
1
2
0
0
0
0
1
2
2
0
2
0
0
1
1
0
0
1
3
0
0
1
1
0
0
2
2
0
2
2
0
1
2
0
1
0
1
0
0
0
0
0
1
2
2
0
1
0
0
0
1
2
0
1
1
2
1
2
2
0
0
2
0
0
2
0
0
1
0
2
1
8
0
0
0
0
1
0
2
1
1
0
1
1
1
0
2
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
3
0
0
0
1
2
0
1
0
0
1
0
0
0
0
0
2
0
2
0
1
0
1
3
0
0
0
1
0
0
2
2
1
0
1
0
1
0
0
0
0
0
1
2
0
0
0
1
0
1
1
0
2
0
0
1
1
1
2
2
1
2
0
1
0
0
1
2
0
1
0
0
0
1
1
0
2
0
0
1
0
0
0
0
0
2
0
0
2
0
2
1
3
2
2
0
0
0
0
2
0
0
1
2
0
1
0
0
1
2
1
0
0
1
2
0
0
0
0
0
1
2
2
1
1
0
1
1
0
0
0
2
1
2
0
0
1
0
0
0
0
2
0
2
0
0
1
2
1
0
0
0
2
0
0
2
1
2
0
1
0
1
2
0
0
0
0
0
1
0
2
1
1
0
0
2
0
0
0
2
0
1
2
0
2
0
1
0
2
1
1
2
0
3
1
0
0
0
1
1
0
1
0
1
1
1
1
2
0
2
0
1
0
0
1
2
0
0
0
0
0
2
1
1
1
0
2
0
0
0
1
2
1
2
8
0
1
0
0
0
0
1
2
1
0
0
2
0
2
0
0
0
0
1
0
1
2
1
0
1
4
1
0
0
0
0
0
2
0
0
1
1
0
0
2
1
1
0
2
2
0
1
0
0
2
1
2
1
0
1
0
0
1
0
0
0
0
2
0
0
1
0
2
1
1
0
0
2
2
0
0
2
1
0
0
1
0
0
0
1
1
0
1
0
0
2
2
0
0
0
1
2
1
1
2
0
2
0
1
2
0
0
0
0
0
1
0
0
1
0
2
0
2
0
0
0
1
0
2
1
1
1
0
0
1
1
2
0
0
0
0
0
0
0
2
2
0
2
0
2
0
0
1
1
0
2
2
1
1
1
0
0
2
3
1
1
2
2
2
1
0
0
0
2
2
1
0
1
1
0
1
0
1
1
1
0
1
2
0
2
1
0
3
1
0
0
0
2
1
1
2
0
0
1
2
0
1
1
0
2
1
1
0
2
1
1
0
0
2
0
0
0
0
2
0
0
1
0
1
0
0
2
0
2
0
1
0
0
2
2
2
0
0
1
0
0
0
0
0
0
0
1
1
1
1
0
3
2
0
1
0
0
0
2
0
0
1
2
1
0
1
1
2
1
0
1
0
1
2
1
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
2
0
2
0
2
1
0
0
0
1
0
0
0
1
0
1
0
2
2
0
1
2
1
0
2
0
0
2
1
1
1
0
2
1
1
0
2
1
1
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
1
0
4
2
1
2
2
2
2
0
2
0
0
0
0
2
0
0
0
0
0
1
2
0
1
1
1
2
0
0
0
0
1
0
2
0
0
1
3
1
1
0
0
1
0
0
2
0
1
1
0
0
1
0
0
1
0
0
1
4
1
0
1
1
0
1
1
0
0
2
0
1
0
0
3
0
0
0
1
1
0
1
2
0
0
2
1
0
1
2
1
1
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
1
2
0
2
1
0
0
2
3
1
0
2
2
1
1
1
2
1
1
0
2
1
0
0
2
0
0
0
0
1
1
0
0
2
0
0
4
1
1
0
2
2
2
1
0
0
1
2
2
0
1
0
1
0
1
0
1
0
1
0
0
2
0
0
1
0
2
0
1
2
0
1
1
0
0
0
0
1
0
0
1
2
2
0
2
1
0
0
1
0
0
0
0
2
0
0
2
0
0
0
1
1
1
0
1
0
0
1
1
0
1
0
0
0
2
0
0
1
1
0
1
0
2
0
2
0
0
1
1
0
0
0
1
0
1
0
0
0
2
2
0
0
1
1
1
2
0
0
0
1
0
1
2
1
1
2
0
0
2
2
0
1
1
1
1
0
2
2
0
0
0
0
0
3
1
2
0
2
2
1
2
1
0
0
2
0
0
1
1
0
2
0
2
1
2
2
0
0
0
2
0
2
1
1
1
2
0
0
1
0
1
2
2
0
0
1
0
0
2
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
3
0
1
2
2
0
3
1
1
0
2
2
0
1
2
1
1
0
0
1
0
1
0
0
0
2
1
1
4
2
0
0
0
0
0
2
1
0
0
2
0
1
0
0
0
0
0
0
1
0
1
1
1
1
0
1
1
1
2
1
2
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
1
1
1
1
0
0
2
0
1
2
1
1
1
2
1
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
2
2
2
0
2
1
2
0
0
1
0
0
0
2
0
1
0
3
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
2
2
0
1
2
1
0
0
2
2
0
0
0
0
2
2
0
1
0
0
1
0
0
0
2
0
0
0
1
0
0
0
2
2
1
0
1
1
0
2
0
2
0
0
1
1
0
0
0
0
0
0
0
2
1
2
0
0
1
1
0
0
1
1
0
1
2
0
0
1
0
0
2
0
1
0
0
0
1
1
1
1
1
0
0
0
0
2
1
0
0
2
1
1
0
0
0
0
0
2
1
2
1
0
1
0
0
2
2
0
1
1
1
0
0
2
0
0
1
0
1
0
2
2
2
0
0
1
0
0
0
2
0
2
1
0
0
2
0
0
2
1
2
0
2
1
1
2
0
2
1
1
0
0
2
1
0
0
0
1
2
2
1
2
2
0
0
0
0
0
0
0
1
1
0
1
1
0
0
1
2
3
2
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
2
0
0
0
1
0
1
1
8
0
1
1
0
0
0
2
0
0
1
2
0
2
2
2
0
1
1
0
1
3
0
0
0
2
2
1
0
1
0
1
2
0
0
0
1
0
1
0
0
0
2
0
3
0
0
0
0
1
1
1
1
0
0
0
0
2
0
1
2
0
1
0
0
2
0
1
0
2
0
1
0
0
2
0
0
2
0
2
0
2
1
1
0
1
1
2
2
2
0
0
0
2
2
0
2
0
0
0
0
1
0
0
0
2
2
0
0
0
1
0
0
1
0
0
0
2
2
0
1
0
0
1
0
0
1
1
3
0
0
0
0
2
2
2
0
2
1
3
1
0
2
2
2
0
1
0
0
0
2
0
1
0
2
0
0
1
2
2
0
2
0
1
2
2
2
0
0
0
0
1
2
0
2
1
0
0
2
0
2
0
1
0
2
0
0
1
1
1
1
1
1
1
1
2
1
2
0
0
0
1
0
0
2
1
1
4
1
2
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
1
4
1
0
0
1
0
2
1
1
0
2
2
2
2
0
1
0
1
1
0
0
2
2
1
0
2
1
1
0
2
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
1
2
2
0
2
2
2
0
2
0
2
2
0
0
0
2
0
1
0
0
1
2
0
1
2
1
1
0
0
1
0
0
2
0
0
1
0
2
0
0
2
0
2
1
2
0
0
2
0
0
0
0
2
0
0
0
2
3
0
3
0
1
0
2
0
2
0
0
0
0
0
1
0
1
0
1
0
0
1
3
0
2
0
1
0
1
0
1
1
0
0
0
2
2
1
1
2
1
0
0
2
0
0
1
1
1
0
0
1
2
0
1
0
0
0
2
1
1
0
1
0
0
6
0
0
0
1
0
1
0
0
1
2
0
0
1
2
2
1
0
0
2
0
1
0
0
2
0
0
1
1
0
0
0
1
1
2
4
0
0
2
0
0
1
2
1
0
2
1
1
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
2
2
0
1
0
1
0
2
0
0
0
1
0
0
2
0
1
0
1
0
0
1
2
0
0
0
0
1
1
1
2
1
2
0
0
2
0
0
3
1
1
1
1
1
0
2
0
1
0
1
0
0
0
0
2
2
1
0
0
0
1
1
0
0
1
0
1
0
0
0
1
0
0
1
0
0
2
0
0
0
2
0
0
0
0
2
1
0
4
1
1
0
0
0
1
0
1
2
0
2
1
1
0
0
0
2
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
2
0
2
0
2
2
1
1
0
0
0
2
1
0
0
2
2
1
5
0
1
2
2
0
0
0
0
0
0
1
0
0
0
0
1
1
2
0
1
1
0
1
2
0
0
2
1
0
1
0
0
0
1
0
0
0
0
2
1
0
0
0
2
0
1
0
1
1
0
0
0
1
0
2
0
0
0
0
0
0
2
0
1
1
1
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
3
0
2
2
0
1
0
0
0
1
1
1
2
0
1
0
0
2
1
1
1
1
0
0
1
1
0
1
1
1
0
2
0
0
1
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
1
0
2
1
0
1
0
0
2
0
0
0
1
0
1
0
1
0
1
1
0
2
0
1
0
0
2
2
1
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
1
1
0
0
1
0
0
3
0
0
0
1
0
1
2
0
0
0
0
1
0
0
1
1
1
0
1
0
0
1
2
0
0
0
1
0
0
0
0
2
1
1
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
2
1
1
1
0
0
1
0
0
0
2
0
0
1
2
2
0
0
2
3
1
0
0
0
3
1
0
0
3
1
2
0
0
1
2
1
2
0
2
0
1
0
0
0
0
0
2
0
0
2
2
0
2
0
3
0
1
2
0
0
0
0
0
2
1
0
0
0
1
2
0
0
0
0
1
1
1
0
0
1
1
0
0
0
2
0
1
1
2
2
0
0
1
0
2
0
1
1
1
1
0
0
1
1
0
0
0
0
0
0
0
0
1
2
1
1
1
0
1
0
2
0
2
1
0
0
1
0
0
0
0
0
0
2
0
0
0
2
1
1
1
0
0
1
3
0
0
0
0
2
0
0
2
1
2
0
2
1
0
0
0
0
0
0
0
0
0
2
1
2
0
1
2
2
1
1
0
0
0
0
0
0
1
0
2
1
0
1
0
2
0
0
2
0
0
0
0
1
0
1
2
0
2
1
1
0
0
0
0
1
2
0
1
1
0
1
3
0
0
0
0
0
0
0
2
0
0
2
2
0
1
1
0
0
0
0
0
0
1
1
1
0
2
2
0
2
0
1
1
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
2
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
1
0
1
0
0
1
0
0
0
2
0
0
0
1
1
1
0
0
0
0
0
0
0
2
2
1
1
0
0
0
0
1
0
2
0
2
1
0
2
0
0
0
0
1
3
1
0
2
0
2
1
1
1
0
0
0
0
1
0
0
0
2
0
1
0
0
0
2
2
2
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
1
0
0
1
1
2
0
2
0
0
0
2
0
1
0
0
0
2
0
2
0
0
0
2
1
2
2
0
2
0
0
0
0
0
0
1
0
1
1
2
0
0
0
0
0
0
2
2
1
2
0
0
2
0
1
0
1
2
0
1
0
1
1
0
2
1
0
2
1
2
0
1
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
1
2
0
2
0
0
0
0
2
2
2
1
0
1
1
2
0
1
1
0
1
0
0
1
0
2
0
2
1
2
1
0
0
0
2
2
1
0
0
0
2
0
2
2
0
2
1
0
3
0
0
2
2
2
1
0
0
1
0
1
0
0
0
0
0
1
0
2
2
0
2
0
1
0
0
2
1
0
1
2
0
0
0
2
1
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
2
2
1
1
1
2
2
2
2
1
2
0
2
0
2
0
0
0
0
0
1
0
1
2
0
0
1
0
1
0
1
0
1
1
0
2
0
0
0
0
1
1
0
0
0
0
2
0
0
1
0
1
0
2
0
0
2
0
0
2
2
1
2
0
0
0
0
2
2
0
1
0
0
0
0
2
0
0
2
0
2
1
0
0
0
1
0
0
2
1
1
2
0
1
0
0
0
0
1
0
1
2
0
1
2
1
0
1
1
2
1
2
0
1
1
0
1
0
1
0
1
0
0
2
1
1
1
0
0
0
0
1
1
0
0
0
2
2
0
0
1
1
2
0
0
1
0
1
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
2
1
2
2
0
0
1
0
1
0
0
0
0
1
0
2
2
0
0
0
0
1
0
1
1
1
0
3
1
0
0
0
2
0
0
1
2
1
2
0
2
0
2
0
0
0
0
1
2
1
0
1
0
1
0
1
1
2
1
0
0
1
2
1
1
2
0
2
0
0
2
1
1
0
1
1
0
1
0
0
1
2
0
0
0
1
0
0
1
0
1
1
1
2
2
1
0
1
2
1
2
1
0
0
2
0
0
2
2
0
0
0
0
2
0
1
2
1
1
0
1
0
2
0
1
0
2
0
1
1
1
0
2
2
1
0
0
0
2
1
0
0
1
1
1
0
2
0
0
4
0
0
0
0
1
0
0
1
0
0
2
1
0
1
0
2
0
2
1
0
2
5
1
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
1
0
1
1
1
1
1
0
1
0
2
1
0
2
3
1
2
1
0
0
1
0
2
0
2
0
0
2
0
2
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
2
1
1
1
0
0
1
0
1
1
1
1
0
2
0
1
1
0
0
0
0
1
0
0
0
2
1
0
1
2
0
0
0
1
2
1
0
1
0
0
0
2
0
0
2
1
2
0
1
0
3
1
2
0
2
1
2
1
0
0
0
0
0
2
2
1
0
0
1
0
0
0
2
0
1
1
2
0
0
0
1
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
1
2
0
0
0
1
2
2
0
1
2
0
0
1
0
1
0
0
0
2
0
0
0
2
1
0
0
0
1
2
0
1
1
1
0
0
1
0
0
2
1
2
0
2
0
2
0
1
0
1
2
0
2
0
2
0
1
1
0
1
2
1
1
1
1
0
2
1
2
2
0
0
0
0
0
1
1
0
1
0
1
0
1
0
0
0
1
0
0
0
0
1
5
4
0
0
1
1
0
1
1
0
0
2
2
2
0
3
0
1
0
0
1
2
0
0
0
1
0
1
1
1
2
0
0
2
0
0
0
1
1
1
1
2
0
1
1
0
0
0
0
2
1
0
1
2
0
0
1
1
0
1
0
4
0
0
0
2
1
0
1
3
0
1
1
4
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
1
2
2
0
0
3
0
0
1
0
0
1
2
1
0
2
2
0
0
0
0
0
0
0
0
1
2
1
2
1
2
1
0
0
0
1
1
1
1
0
0
0
3
1
1
2
0
0
2
0
3
0
1
1
0
2
0
2
1
2
2
0
1
0
0
0
0
2
0
1
0
1
0
0
0
1
1
0
1
0
2
1
1
2
1
0
0
1
0
0
0
1
2
0
0
0
2
0
0
2
0
1
0
1
0
2
0
0
1
0
1
2
0
2
1
0
0
0
0
2
3
1
1
1
1
0
1
0
0
1
0
0
2
1
1
0
2
0
0
0
0
0
1
0
1
0
1
0
2
0
2
0
2
0
2
1
1
2
0
0
1
0
0
1
2
0
0
0
2
1
0
0
0
2
1
0
2
0
1
0
1
0
0
2
1
1
0
0
0
2
0
0
0
0
2
0
3
2
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
1
1
1
1
0
1
0
0
0
2
2
0
2
0
3
2
0
1
2
1
0
0
0
1
2
0
1
2
2
2
2
0
0
2
1
2
0
1
1
1
0
0
1
0
0
1
2
0
0
1
1
1
1
0
0
0
0
2
0
1
1
1
0
2
0
3
0
2
0
0
1
1
0
0
1
2
0
1
0
1
0
0
1
1
2
1
1
1
2
0
2
2
0
0
3
1
0
2
0
0
0
0
0
1
0
1
1
0
2
0
0
1
2
2
2
0
0
0
0
0
2
1
0
0
2
1
1
1
1
1
0
2
2
1
1
1
0
1
0
2
1
0
3
2
0
2
2
0
0
2
2
0
1
1
2
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
2
0
1
0
0
1
0
0
0
2
2
0
0
0
1
0
0
0
0
0
1
0
0
2
2
0
1
0
1
1
0
0
0
0
0
0
1
1
1
1
1
0
1
1
0
2
0
1
0
0
0
0
0
0
1
1
1
0
0
2
1
0
2
2
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
1
1
2
4
1
0
0
0
0
0
0
2
2
1
1
2
0
0
2
0
1
2
2
0
0
0
0
0
0
0
2
2
2
0
0
0
0
1
0
2
0
0
0
0
2
1
0
0
0
1
1
1
2
0
0
2
1
0
0
1
0
0
0
0
0
0
1
3
1
0
1
0
2
0
2
0
0
2
1
2
1
0
1
1
1
2
1
0
1
1
0
1
1
2
2
2
0
2
1
0
0
0
0
1
2
1
2
2
0
0
0
0
1
0
0
0
1
0
2
1
0
0
2
0
0
0
1
0
1
0
2
2
0
1
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
1
2
2
0
0
1
1
0
0
0
0
0
2
1
0
2
2
1
3
0
0
1
1
0
0
1
1
0
1
0
1
0
2
0
0
0
2
0
0
0
1
0
0
1
2
2
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
1
0
1
0
1
1
0
2
0
1
0
1
0
1
0
0
2
0
0
1
3
1
2
0
0
0
0
1
2
0
1
3
0
0
0
0
2
0
1
2
0
2
0
1
0
0
0
0
0
0
1
0
0
2
2
0
1
2
0
0
0
0
2
2
2
3
0
1
0
0
2
0
0
1
2
1
1
0
1
1
0
1
0
2
0
1
1
1
1
1
0
1
1
0
0
0
2
0
0
0
1
2
0
0
0
1
0
0
0
2
0
0
0
0
1
5
0
0
0
0
0
2
1
0
1
1
1
1
2
0
0
2
0
0
1
0
0
1
0
2
0
1
0
0
2
0
1
0
2
0
0
0
0
1
0
0
0
0
2
2
0
2
1
0
0
0
0
0
1
0
1
2
0
1
1
0
1
1
0
0
0
1
1
0
1
1
0
0
0
0
0
1
1
2
1
0
1
0
1
0
0
2
2
0
0
0
2
1
2
1
0
2
1
0
1
1
0
0
0
1
0
0
0
0
1
2
1
1
0
2
0
1
1
0
0
2
0
0
0
0
0
1
1
0
0
2
0
1
1
1
2
2
0
0
0
0
0
0
0
0
0
2
2
2
2
0
0
0
2
2
0
2
1
0
0
1
0
0
0
2
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
2
0
1
2
2
0
2
1
0
0
0
2
1
2
0
0
0
1
2
0
0
0
0
0
0
2
1
1
2
0
2
1
2
0
1
1
0
0
0
0
1
0
0
0
0
1
1
0
2
0
0
2
2
2
0
2
0
0
0
0
0
2
1
0
0
2
0
1
2
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
2
2
0
0
1
0
0
2
1
1
0
1
0
0
2
1
0
0
2
0
0
0
0
0
1
1
0
0
0
1
0
0
2
2
0
2
2
0
0
0
1
0
1
2
1
2
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
1
2
0
2
1
0
1
2
1
1
0
2
0
1
2
0
1
0
0
0
2
2
2
1
1
0
0
0
1
2
0
1
1
1
0
1
1
2
0
0
0
0
1
0
0
0
0
2
1
0
1
1
2
0
0
0
0
2
1
1
0
0
0
0
0
1
1
1
0
0
1
2
0
0
4
1
1
1
0
1
1
2
0
0
2
1
2
0
0
3
0
1
0
0
0
0
0
1
0
2
2
0
1
0
0
1
1
1
1
0
1
0
1
3
2
2
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
1
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
2
1
0
1
1
1
2
1
2
2
0
0
2
2
0
1
1
0
0
1
1
0
2
3
2
0
0
0
0
1
3
1
0
0
0
0
1
2
0
2
2
1
0
1
0
0
0
2
0
0
0
0
0
1
1
0
1
0
0
2
1
0
1
0
1
0
0
1
1
1
1
2
0
0
0
0
1
0
0
2
2
2
2
1
0
2
1
0
0
0
3
0
1
0
0
2
0
0
0
1
0
0
1
2
3
0
0
0
2
2
2
1
0
0
3
2
1
0
1
0
1
0
0
2
1
0
1
2
0
1
8
0
1
0
1
0
1
1
1
0
0
0
0
2
0
0
2
0
0
2
2
2
2
2
0
1
0
2
0
0
0
0
0
0
0
0
1
0
2
0
1
2
0
0
0
2
3
1
3
0
0
0
0
0
2
0
2
0
1
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
2
1
1
0
1
0
0
0
1
0
2
0
0
2
0
1
1
1
2
0
0
2
0
1
1
0
0
0
0
0
2
0
0
2
0
2
0
0
1
0
2
1
2
1
3
2
4
2
0
1
0
0
0
0
0
0
1
1
0
4
0
0
0
0
0
0
1
0
0
1
0
3
0
0
0
1
2
0
1
1
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
1
2
2
0
1
0
1
0
1
1
0
0
2
0
0
0
3
1
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
1
0
0
1
0
0
0
2
0
1
0
0
0
0
2
1
2
0
1
0
5
0
2
0
0
0
2
1
1
2
0
2
0
1
0
0
2
0
0
1
0
2
0
0
1
1
0
0
1
2
1
0
1
1
2
2
1
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
2
0
2
1
1
1
1
1
0
1
0
0
1
0
2
0
1
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
1
1
1
0
2
3
0
2
0
0
0
0
1
0
0
1
0
2
1
1
0
0
1
1
0
2
2
0
0
1
0
1
0
0
1
0
0
1
0
2
0
2
2
1
0
0
0
1
2
0
1
1
0
1
0
2
1
0
2
1
0
2
0
0
2
0
0
2
0
0
1
1
2
0
1
2
1
0
1
2
0
1
0
1
0
0
3
0
0
0
2
0
0
0
1
0
1
0
0
1
2
2
0
0
0
1
2
0
1
1
0
2
3
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
1
0
0
1
1
0
0
0
1
0
2
2
0
1
1
0
2
1
0
0
0
0
2
2
2
1
2
1
1
0
0
0
1
2
0
0
0
0
0
1
1
0
0
1
0
1
0
1
1
0
1
0
1
0
0
2
1
1
0
1
0
0
0
0
2
0
2
1
2
0
2
0
0
0
1
2
0
0
0
0
1
0
2
1
0
2
0
0
0
0
0
0
1
0
0
0
1
3
0
0
1
0
0
1
0
0
0
1
1
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
2
0
1
0
1
1
0
0
1
0
2
0
1
0
0
2
1
0
0
1
1
1
1
1
2
0
1
1
0
1
0
0
0
1
0
0
0
1
1
2
0
0
1
0
1
0
1
2
0
1
1
0
0
0
0
0
1
0
0
0
1
0
2
1
0
1
0
1
1
0
0
1
2
0
1
0
0
2
1
2
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
2
1
2
2
2
0
0
1
1
0
1
3
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
1
0
2
2
0
1
0
0
2
1
0
2
1
1
0
2
2
0
2
0
0
0
2
1
0
0
0
2
2
0
0
1
0
0
2
2
0
2
0
2
1
2
1
0
1
2
0
1
2
0
0
0
1
0
1
0
1
0
1
2
2
0
2
1
0
0
2
1
2
0
0
0
1
0
0
1
0
0
2
2
1
0
0
0
1
0
0
0
0
0
1
1
2
2
0
1
1
2
1
1
0
2
1
1
0
0
0
0
1
2
1
1
1
0
2
2
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
1
1
1
2
1
1
0
0
1
0
1
2
0
1
0
0
0
0
2
0
2
2
2
0
1
0
2
1
0
0
3
2
0
0
0
0
0
2
0
2
0
0
1
0
2
0
0
0
1
1
2
2
3
1
2
0
2
2
3
2
2
0
0
0
2
1
1
0
0
1
2
1
1
0
1
1
0
1
0
1
0
0
1
1
1
0
0
2
0
0
4
1
0
0
0
0
2
0
1
1
1
1
1
2
0
1
2
1
1
1
1
2
0
2
1
0
0
0
1
0
0
0
0
1
2
0
0
2
1
0
0
2
0
0
1
1
0
0
0
0
0
0
1
0
2
0
2
2
1
1
1
2
0
1
1
0
2
0
1
2
2
0
1
2
0
0
1
1
1
1
0
1
0
1
1
0
1
1
0
0
0
1
0
1
1
0
0
2
0
2
1
0
2
1
0
0
0
0
0
0
1
2
1
1
2
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
2
0
1
0
1
0
0
0
2
0
0
0
1
0
0
1
1
0
0
0
0
2
7
0
0
0
2
1
1
2
0
1
2
2
0
0
1
0
0
0
0
0
0
0
0
2
2
1
0
0
1
1
1
0
2
1
2
2
1
0
0
1
0
1
0
1
1
1
2
0
0
0
0
0
0
1
0
1
2
1
0
1
1
2
2
0
1
0
0
0
2
1
1
0
0
2
2
2
0
2
0
0
0
0
2
1
1
2
2
1
2
1
1
2
0
1
0
1
2
0
0
0
0
0
0
1
1
0
1
1
0
1
0
1
0
2
2
2
2
0
0
7
1
2
2
1
1
2
0
0
1
0
2
0
1
0
0
1
0
1
1
0
0
1
2
1
0
1
0
1
0
0
0
0
2
0
1
2
1
1
0
0
0
0
2
2
0
2
1
0
0
1
0
0
1
0
2
0
2
0
0
0
2
1
0
0
0
1
2
0
0
1
1
1
1
0
0
1
0
1
0
0
0
0
1
0
0
2
1
2
0
2
2
0
1
2
0
1
0
0
0
1
2
8
0
1
2
0
0
0
0
0
0
2
1
0
1
0
2
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
2
0
1
2
2
0
0
1
1
1
3
1
2
0
3
0
2
0
2
1
0
0
1
1
0
0
0
0
0
2
0
0
2
2
0
1
3
1
0
0
0
0
2
0
0
2
0
1
0
0
2
1
1
0
0
0
1
2
1
1
0
1
2
0
1
0
0
0
1
0
0
1
0
1
0
1
0
2
0
0
2
1
0
1
2
1
2
2
0
0
0
0
1
0
2
0
1
0
1
0
0
0
2
0
2
1
0
0
1
0
1
1
0
1
1
2
0
0
2
0
0
1
0
1
2
2
0
1
0
0
1
4
1
0
2
2
0
2
0
0
2
0
2
0
2
1
0
0
0
2
1
1
0
1
0
2
0
0
1
0
0
1
2
2
0
0
0
0
1
2
0
1
1
0
0
2
0
0
1
1
0
0
1
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
2
0
0
1
0
2
0
0
0
1
2
1
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
1
1
1
1
2
0
0
2
0
2
1
1
0
0
0
0
0
0
0
2
0
2
2
0
0
0
1
2
1
0
2
0
1
1
2
2
0
2
1
0
2
0
1
2
1
1
0
0
0
1
0
1
0
1
2
0
2
1
2
2
1
0
1
0
0
0
0
0
1
6
1
2
2
2
0
2
0
1
2
1
2
1
0
0
3
3
1
2
2
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
2
1
0
1
2
0
0
0
0
3
0
0
0
0
1
1
0
0
2
0
1
1
0
1
0
0
1
0
0
0
0
0
1
2
1
2
1
0
0
0
1
2
1
0
1
0
1
1
1
0
0
0
2
0
1
1
0
2
0
0
0
0
1
0
0
0
1
1
1
0
0
3
0
0
1
0
0
0
0
1
0
0
0
0
0
2
1
0
0
1
0
0
1
0
0
0
0
2
1
0
1
0
0
0
0
1
1
1
1
0
1
2
0
1
0
0
0
0
1
0
2
1
1
0
1
1
3
0
2
2
0
0
1
1
0
2
0
0
0
1
0
1
0
1
0
1
1
1
0
1
2
1
0
2
2
0
2
0
0
0
0
0
1
1
2
1
1
0
2
0
0
1
1
1
1
0
1
0
0
1
0
0
0
1
0
1
1
0
0
0
1
0
0
0
1
0
0
1
0
1
1
1
1
0
0
1
1
2
2
0
1
1
0
0
0
0
0
0
2
2
0
0
2
1
1
0
0
2
0
1
4
1
0
1
0
1
2
2
0
0
3
0
0
0
0
0
1
1
0
0
3
0
1
0
0
1
1
0
0
1
1
0
0
0
1
0
0
2
0
2
1
0
1
0
0
1
1
0
0
0
0
0
1
0
2
0
1
0
0
0
0
1
0
0
0
1
0
0
1
1
2
1
0
0
0
1
0
2
2
0
2
0
0
2
2
0
1
0
0
0
0
1
0
1
2
2
0
0
0
0
0
2
1
0
0
2
0
3
0
0
0
0
2
0
0
0
2
0
1
1
1
0
0
0
0
1
0
0
0
0
2
2
1
2
0
2
0
2
0
0
1
0
0
1
2
0
0
0
0
0
0
1
1
2
0
1
2
0
0
0
2
0
1
1
0
1
0
1
0
0
4
0
0
2
1
2
0
2
1
1
1
1
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
2
1
1
0
2
0
0
0
0
0
1
0
1
2
0
0
0
2
2
0
0
2
1
0
0
2
0
2
0
0
1
0
2
0
0
1
1
1
3
0
3
2
1
1
0
1
1
1
1
0
2
0
1
0
1
1
1
0
0
1
0
0
2
0
0
1
0
0
1
0
2
0
1
0
4
0
0
1
2
0
0
2
4
0
0
1
1
1
1
0
0
2
0
0
0
2
1
0
0
0
0
0
1
1
2
0
1
2
0
0
0
0
2
2
0
1
2
1
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
1
0
0
2
2
1
0
2
0
1
0
0
0
1
1
0
0
0
1
0
2
5
2
0
0
1
1
2
0
2
0
0
1
0
2
1
0
0
1
0
0
0
1
0
0
1
1
2
2
0
2
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
2
1
0
0
0
0
2
1
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
1
0
2
0
0
0
1
0
0
0
1
0
2
0
0
3
0
1
0
0
0
2
0
0
0
0
0
2
1
0
3
0
2
2
2
2
2
2
1
2
2
0
0
0
2
0
0
2
1
1
0
0
2
0
1
1
0
0
2
1
1
0
2
2
2
0
1
1
0
0
0
2
1
1
2
0
1
1
0
1
1
1
1
1
1
1
2
2
1
0
0
0
0
1
0
0
0
1
1
2
1
1
0
0
0
1
0
0
0
2
0
0
1
0
0
1
0
2
1
0
1
0
1
1
1
0
1
0
0
0
0
0
0
1
1
1
1
0
0
1
0
2
0
0
0
1
1
2
0
0
2
2
1
0
2
1
0
0
0
0
1
3
2
2
2
0
0
1
1
2
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
2
0
1
0
0
2
1
0
0
1
0
0
1
2
2
2
2
0
0
1
1
0
1
0
0
0
1
0
3
0
1
0
0
1
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
3
0
1
0
2
0
2
2
1
1
0
2
0
1
2
0
1
0
0
0
0
1
1
2
0
1
2
1
0
1
0
0
1
0
1
1
0
2
1
0
0
0
0
1
1
1
0
0
2
0
0
1
0
0
1
3
2
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
1
2
0
0
1
0
0
0
1
0
0
0
2
1
0
0
1
0
0
0
2
0
0
1
0
1
1
0
1
1
0
0
2
1
0
0
2
2
3
1
1
3
2
1
1
2
1
1
2
2
0
0
1
1
3
0
0
1
0
1
1
1
0
0
2
0
2
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
1
0
2
1
2
1
0
0
0
1
0
0
0
1
0
1
0
0
2
2
1
2
0
0
1
0
0
0
0
0
2
0
2
0
0
1
2
0
0
2
1
1
0
0
0
0
0
0
2
1
0
1
2
0
0
1
0
2
2
0
0
0
3
0
0
0
0
0
2
0
1
0
0
0
1
0
1
0
0
0
0
1
1
1
0
0
0
0
4
2
2
2
0
0
1
2
0
2
0
1
2
4
0
1
1
0
0
0
0
2
0
0
0
2
1
0
1
2
1
1
2
0
0
0
0
1
1
0
2
0
0
2
0
0
2
1
2
1
1
0
0
0
1
0
3
0
0
0
0
0
1
1
0
0
1
1
2
0
1
0
0
2
0
1
0
0
0
1
2
0
2
0
2
0
0
1
0
0
1
1
2
0
1
1
1
2
2
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
2
0
0
2
0
0
1
2
1
0
0
1
0
0
0
0
2
0
1
2
0
0
1
0
1
0
0
0
1
0
0
1
2
2
1
0
0
0
2
0
1
0
0
0
1
0
1
0
0
1
2
0
1
1
2
0
0
0
2
0
1
0
1
0
1
0
2
2
2
0
2
0
0
0
0
0
1
1
0
0
2
2
0
0
2
0
0
2
0
1
0
2
0
0
1
2
0
2
0
2
0
1
0
2
0
2
0
0
0
2
2
6
0
0
1
1
0
0
0
1
2
2
0
2
2
0
1
0
0
0
0
0
0
1
0
3
2
0
0
2
0
0
0
2
2
2
0
0
0
1
0
0
0
0
1
0
0
2
2
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
2
2
0
2
1
0
0
2
0
1
0
1
0
1
0
2
3
1
1
2
1
0
0
1
2
1
0
2
1
1
0
1
2
0
0
1
2
0
1
0
0
1
2
0
1
0
0
1
1
0
4
0
1
1
2
2
2
1
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
1
0
2
1
1
1
0
0
0
1
0
2
0
0
0
0
1
0
0
0
2
1
1
1
0
2
0
0
0
0
2
2
1
0
0
0
0
0
1
0
0
1
0
0
1
0
1
2
0
0
1
0
1
2
0
0
0
1
0
2
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
1
1
1
0
2
1
0
1
0
0
0
2
2
1
1
2
0
0
11
0
0
0
2
1
2
2
1
2
1
0
0
1
1
0
1
1
0
1
0
1
1
2
2
0
2
1
1
0
0
0
2
2
0
1
2
0
1
0
0
2
1
0
0
0
0
2
1
0
2
0
0
0
1
1
0
2
0
1
2
0
1
1
1
1
0
0
1
0
1
0
2
1
0
0
0
0
0
0
2
0
1
0
0
0
0
3
2
0
0
1
0
0
0
1
3
1
1
2
2
0
0
2
0
1
1
1
0
1
0
0
0
0
0
2
0
1
0
0
1
2
0
0
0
2
1
0
0
0
2
2
2
0
2
2
5
1
2
1
0
0
1
1
0
0
1
0
0
2
1
0
0
1
0
0
1
0
2
0
0
2
0
1
0
1
0
0
0
0
1
0
2
1
0
0
0
1
1
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
2
0
0
0
1
2
0
0
0
1
2
2
0
0
1
2
1
1
0
1
1
0
0
0
2
1
0
2
0
0
0
0
1
0
0
2
0
2
0
2
0
1
0
1
0
1
0
1
3
0
0
1
1
0
0
0
0
2
0
0
2
0
0
1
0
0
1
1
2
0
5
3
0
2
0
0
0
0
0
0
1
1
1
0
1
0
1
0
1
0
0
0
1
0
2
2
1
2
1
0
1
0
1
2
0
2
2
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
1
0
2
0
1
1
1
3
0
0
1
0
1
0
0
0
0
1
0
0
0
2
1
1
0
1
0
0
0
1
1
0
1
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
2
1
0
0
0
0
1
0
1
1
2
0
0
0
2
0
0
0
1
1
2
0
0
0
1
0
0
0
2
0
0
3
1
0
0
2
0
0
2
1
0
1
0
2
0
0
2
1
0
1
0
0
1
0
1
2
0
0
0
0
0
0
2
2
0
0
1
2
0
0
2
0
0
0
0
0
2
0
1
1
1
1
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
2
2
0
0
0
1
0
0
0
2
0
2
0
0
0
0
1
1
0
1
1
2
0
0
0
0
1
0
0
1
2
0
0
2
2
1
0
1
0
1
0
0
0
1
0
0
1
0
1
0
0
2
0
1
0
1
1
1
2
2
0
0
2
1
0
1
0
2
0
0
1
0
0
1
0
0
1
1
0
0
1
0
0
2
0
1
3
1
2
2
0
1
1
1
2
0
0
0
2
0
1
1
2
1
1
0
1
1
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
1
3
0
0
0
1
0
0
1
1
2
0
0
0
2
2
0
0
0
1
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
1
2
1
0
0
0
0
0
0
0
3
1
1
0
1
2
1
2
0
2
1
2
0
1
1
0
2
1
0
0
2
0
2
2
0
0
2
1
2
0
1
1
0
2
0
0
0
0
0
0
0
2
0
0
1
1
0
1
1
1
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
1
2
2
0
1
0
0
2
0
1
1
0
2
1
0
5
1
0
0
1
1
0
1
1
2
0
0
1
1
1
1
0
0
0
0
1
0
3
0
1
1
0
0
0
0
0
1
2
0
0
2
0
1
2
2
2
0
1
0
2
1
2
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
2
0
1
2
2
0
0
0
1
1
0
1
1
1
0
3
1
1
1
0
0
0
0
2
1
0
2
1
0
2
1
2
2
0
2
0
1
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
1
1
2
0
0
1
2
0
2
0
2
0
0
2
0
0
2
1
2
1
1
0
1
0
1
0
1
2
2
3
0
1
1
1
2
0
1
0
2
0
0
2
0
1
0
3
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
1
2
1
0
0
0
0
0
0
2
1
0
0
1
0
0
0
2
1
0
0
0
1
2
0
0
2
2
0
1
1
0
0
1
2
0
1
0
0
0
0
0
2
0
1
0
0
1
1
0
2
2
1
1
1
0
1
0
0
2
1
0
0
1
0
0
1
0
0
2
0
1
0
1
2
1
0
0
1
0
0
2
1
1
0
0
2
0
0
0
1
0
0
0
2
1
0
1
0
2
0
1
2
0
0
2
1
0
2
0
1
0
3
2
0
1
0
0
2
2
0
0
2
0
0
0
1
0
1
0
1
2
0
2
1
0
0
0
2
0
1
0
0
1
2
0
0
0
1
1
2
0
0
0
2
1
0
0
1
3
0
0
0
0
1
0
1
0
1
1
0
0
2
0
0
2
1
0
0
0
1
1
0
0
0
0
0
0
1
1
1
0
0
2
0
1
1
0
0
1
0
2
0
0
0
0
1
2
0
0
0
0
0
0
1
1
0
0
0
1
0
2
0
1
0
0
0
0
2
1
0
0
2
2
1
3
0
0
1
1
0
1
0
0
0
1
1
1
0
1
0
3
2
2
0
1
2
0
0
0
0
0
0
0
1
2
2
0
2
2
1
2
4
1
0
2
1
0
1
1
0
0
1
0
0
2
0
0
2
0
2
0
1
2
0
0
1
0
2
0
0
0
1
0
0
1
0
0
1
1
0
2
1
0
2
0
0
0
0
0
1
1
1
0
0
2
1
0
1
1
1
0
0
2
0
0
1
1
0
1
0
0
0
2
2
2
0
2
1
0
1
3
0
1
2
0
0
1
0
0
2
0
2
0
0
0
1
1
2
2
0
0
1
1
1
0
0
2
0
1
2
0
1
0
2
1
0
2
0
3
1
0
0
0
1
0
1
1
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
1
0
0
0
1
0
1
1
1
2
2
0
2
1
0
2
0
2
0
0
0
0
0
1
1
2
0
0
3
0
0
2
0
0
0
1
1
0
0
0
2
0
0
0
1
0
1
1
0
2
0
1
1
2
0
0
0
2
3
0
0
1
0
0
0
2
1
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
1
1
2
0
0
0
0
2
1
1
1
0
0
1
1
1
1
0
2
0
0
0
0
2
0
2
2
0
0
0
0
1
2
2
0
3
0
0
0
0
1
1
0
0
0
0
1
0
0
1
2
0
0
1
0
0
1
0
0
0
2
2
0
0
0
2
1
1
0
0
1
4
0
2
1
1
0
0
0
0
0
0
1
1
2
2
2
0
2
0
3
1
0
0
0
1
0
2
1
0
2
1
3
0
0
0
1
0
0
2
0
0
0
0
2
0
1
2
0
0
0
0
0
2
0
0
1
2
0
0
0
0
1
0
1
0
0
0
0
0
1
1
2
1
0
1
0
2
0
1
2
2
0
2
0
0
0
0
1
3
2
0
1
0
0
0
3
0
2
0
0
1
0
1
0
0
2
0
2
1
1
0
0
1
2
1
0
0
0
3
0
1
3
0
0
1
0
1
2
0
0
0
0
3
0
0
0
0
0
0
0
2
1
0
1
0
2
0
0
0
0
2
0
0
1
1
0
0
1
0
2
0
1
0
0
0
0
2
0
0
0
1
0
2
0
0
2
0
0
1
2
3
1
1
0
1
1
0
0
0
1
1
0
0
0
0
1
1
2
2
1
2
3
0
0
2
0
2
1
1
2
0
2
0
0
1
1
0
1
0
1
0
0
0
0
1
0
2
0
2
0
0
0
0
0
1
3
0
0
3
2
0
0
2
0
0
1
0
3
0
0
1
1
0
1
0
0
1
0
0
0
2
0
0
0
2
0
0
2
2
0
1
0
1
1
0
1
1
1
3
3
0
0
0
0
0
1
1
0
2
0
0
0
0
0
1
1
2
2
0
2
3
0
2
0
0
0
0
2
1
1
2
1
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
1
1
0
2
2
0
0
1
0
0
1
2
2
0
0
2
2
0
2
1
0
2
2
0
0
2
2
0
1
0
0
0
0
0
2
1
1
0
0
0
0
1
0
1
0
2
0
1
1
1
1
1
0
2
1
1
0
0
1
0
1
2
2
0
0
0
2
0
1
0
0
0
3
0
1
1
2
0
0
1
4
1
0
0
2
0
2
1
0
1
0
0
0
0
0
1
0
1
1
1
2
0
0
1
1
1
0
1
0
0
0
0
2
0
0
1
1
2
0
2
3
0
0
0
0
0
1
0
0
1
1
0
2
0
1
2
0
2
1
2
0
0
2
1
0
0
0
0
2
0
0
2
0
1
0
0
0
0
1
0
2
0
0
1
1
1
0
1
0
0
0
0
0
0
1
1
1
1
1
0
0
1
1
0
1
2
2
0
0
0
0
0
0
2
2
0
1
1
3
1
0
2
1
0
0
2
1
1
1
1
1
0
2
0
1
1
0
0
2
0
0
1
2
0
2
2
1
1
0
0
0
0
2
0
0
0
2
1
0
0
1
2
0
0
0
0
0
1
2
0
0
2
2
2
2
0
0
1
0
2
0
0
0
2
2
0
1
0
0
0
0
2
2
0
0
0
1
1
3
2
0
0
1
0
1
1
2
0
2
1
0
0
0
1
0
0
0
0
0
1
0
0
1
2
0
2
0
0
0
0
2
2
0
2
0
0
2
0
0
0
0
0
1
1
0
1
1
2
1
2
0
0
0
1
0
0
3
1
0
0
2
3
0
0
0
0
0
0
2
0
1
2
0
2
0
0
1
0
1
0
2
0
0
0
1
3
2
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
2
0
0
0
1
1
0
0
1
2
2
1
0
0
0
0
0
0
1
2
0
1
0
0
0
1
2
0
3
0
0
0
1
1
2
1
0
0
0
0
0
1
1
1
0
0
1
0
0
2
0
0
0
0
2
1
2
1
0
3
0
0
1
1
2
0
0
0
0
0
1
3
0
1
0
0
2
0
0
0
0
1
2
1
2
0
1
2
0
1
0
1
1
0
0
2
0
0
0
1
0
1
0
0
0
1
0
2
1
0
2
0
0
0
0
2
0
2
0
1
0
1
2
0
0
0
0
1
0
0
0
1
1
0
2
0
0
0
2
3
0
0
0
1
1
0
0
0
0
0
1
0
2
0
0
0
1
0
2
0
1
0
0
2
0
0
1
2
0
0
2
1
0
2
2
0
0
2
1
0
2
1
0
1
1
0
2
1
1
0
2
0
2
3
1
0
2
0
1
0
1
2
0
2
0
2
1
0
2
1
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
2
2
0
0
2
2
2
0
1
1
1
2
2
1
1
0
0
0
2
0
0
0
0
2
1
1
1
2
1
1
0
1
2
0
2
1
0
0
0
0
0
1
1
1
0
0
1
0
2
1
1
0
0
1
1
0
1
3
0
0
2
0
0
2
1
0
1
1
0
1
2
1
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
2
1
0
0
1
0
1
2
0
0
1
0
0
0
2
0
2
1
0
0
0
0
0
1
0
0
2
0
1
1
0
1
0
1
0
0
1
0
1
1
1
2
0
0
12
1
2
0
0
0
2
2
0
0
0
0
1
1
2
2
0
0
2
2
2
0
0
0
0
2
0
0
1
0
0
1
0
0
1
0
1
0
1
0
0
1
2
0
0
2
0
1
1
2
0
0
0
0
0
1
0
2
2
2
2
0
0
1
0
0
0
1
1
1
1
0
0
2
1
1
2
0
2
0
0
0
0
2
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
1
0
0
3
0
0
0
1
1
0
0
1
2
0
1
2
2
1
0
0
0
2
2
0
1
0
0
0
1
0
1
0
0
0
1
1
1
1
0
0
0
0
0
0
1
0
2
0
0
1
1
0
0
0
1
2
2
0
0
0
2
2
0
1
1
2
1
0
1
1
2
0
0
0
1
0
0
0
1
2
0
0
2
1
2
0
2
0
0
0
0
1
0
1
2
0
0
2
1
1
0
0
1
0
0
2
0
0
0
2
0
1
0
0
0
1
1
0
0
0
0
2
1
3
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
2
0
1
0
1
3
1
0
0
0
0
1
1
1
1
0
2
2
1
0
1
0
2
0
0
0
2
1
1
2
0
2
0
1
0
0
0
2
0
0
0
1
2
1
2
4
2
0
0
2
2
1
2
1
2
2
1
2
2
1
0
0
1
2
1
1
0
0
2
0
2
0
0
0
1
0
2
2
0
0
1
1
0
2
1
0
4
2
1
1
0
2
0
1
2
0
1
1
2
1
1
0
0
0
0
0
0
3
0
0
1
0
0
0
0
2
1
0
1
0
1
0
3
2
0
1
1
0
1
2
1
0
0
0
0
0
1
0
2
0
3
0
2
0
0
2
1
1
2
1
1
0
1
0
0
0
1
0
1
0
1
0
0
2
0
1
1
0
1
2
0
2
2
1
2
1
0
0
2
0
1
2
0
2
0
0
0
1
0
0
0
1
0
0
0
1
1
0
2
2
2
0
1
2
1
0
4
1
2
0
0
0
1
1
0
0
1
0
0
0
1
0
2
1
0
0
2
0
2
1
2
0
1
1
0
0
0
1
0
0
0
1
0
0
0
2
2
0
0
0
0
2
0
2
0
2
0
1
1
1
2
1
0
2
0
3
1
2
0
1
2
0
0
1
0
0
0
2
1
2
1
0
1
2
0
1
1
0
1
0
1
0
2
1
2
1
0
1
0
0
1
1
2
1
1
0
1
1
0
0
0
0
0
1
2
1
1
0
1
0
2
0
1
1
0
0
1
0
1
2
0
0
2
2
2
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
2
1
0
1
2
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
1
0
0
2
0
0
0
0
1
0
0
2
1
2
0
2
2
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
1
2
0
0
0
0
1
0
2
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
3
1
0
0
0
0
1
2
0
0
2
0
1
0
0
1
0
0
0
1
1
0
0
1
1
0
0
0
1
1
1
1
1
0
0
0
2
0
0
2
0
3
0
1
0
0
0
2
4
1
1
1
1
0
0
0
1
0
2
2
2
0
2
0
0
1
1
2
1
0
1
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
2
0
2
0
0
2
2
0
2
0
1
1
1
2
0
1
1
0
2
1
1
0
1
1
0
2
0
0
0
2
0
0
0
0
0
2
1
0
1
0
0
3
0
1
3
0
0
1
2
0
2
2
1
1
1
1
0
0
2
0
1
2
0
0
2
0
1
2
0
0
0
0
2
2
0
2
0
0
1
0
2
1
0
0
0
0
0
0
0
1
0
2
0
0
1
2
2
0
1
0
0
0
3
0
2
2
1
0
0
1
1
2
2
2
1
0
0
0
1
0
1
1
1
2
0
0
0
1
0
1
2
1
3
2
2
0
2
0
0
1
0
0
1
1
0
0
0
1
0
1
2
0
1
2
0
0
2
0
2
2
1
1
2
1
0
0
2
0
0
2
0
2
1
1
2
0
1
0
2
1
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
2
1
2
1
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
2
2
0
0
0
1
0
0
1
1
0
1
1
0
2
0
0
1
0
0
0
2
1
1
0
0
0
1
0
2
0
1
0
0
0
0
0
1
0
0
1
1
0
2
0
2
1
0
2
0
0
0
0
1
0
0
1
3
0
4
0
2
1
1
1
0
0
2
0
1
1
0
1
1
0
0
2
2
0
2
0
0
0
2
2
0
0
0
2
1
1
2
0
0
0
2
0
0
0
3
1
0
0
0
2
2
0
2
0
0
0
1
2
0
1
1
1
0
2
1
1
0
0
0
1
0
2
1
2
0
2
0
1
0
2
0
2
1
1
1
0
1
2
0
2
0
1
1
0
0
0
1
0
1
2
2
0
0
2
1
1
0
3
0
1
0
0
1
0
0
0
1
0
1
0
0
2
0
1
1
2
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
1
1
1
1
1
0
1
2
1
1
1
0
1
1
1
0
0
2
3
2
0
2
0
1
2
0
1
0
0
0
2
2
0
1
1
1
0
0
1
1
0
1
1
0
4
2
0
0
0
0
1
2
0
0
0
1
0
1
0
0
2
1
1
0
0
0
1
0
2
1
0
1
2
2
3
0
1
3
1
2
0
0
0
1
2
0
1
0
0
0
1
2
1
1
2
1
1
0
0
2
0
0
0
1
2
0
1
0
1
0
0
1
1
2
0
0
1
0
1
0
0
1
1
2
0
0
1
2
1
2
0
0
0
0
0
2
0
0
0
0
3
0
2
1
0
0
1
1
0
0
1
0
0
2
0
0
1
0
0
2
2
3
0
0
2
2
0
2
1
0
0
1
1
0
1
2
0
1
0
1
0
0
1
2
2
2
0
2
1
1
0
0
4
2
0
0
0
2
1
1
0
2
1
2
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
3
0
0
0
1
0
0
0
0
2
0
0
2
1
0
0
0
1
0
0
0
1
2
0
2
1
0
0
0
0
1
0
0
0
0
1
4
1
0
0
0
1
0
0
1
0
0
1
1
0
2
2
0
0
1
0
0
1
2
1
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
1
2
1
0
0
1
0
0
0
1
1
0
1
0
0
1
0
1
1
0
1
0
0
0
1
0
1
2
1
1
2
1
0
3
0
1
0
3
0
1
0
0
0
0
2
1
1
0
3
0
0
0
0
0
0
0
2
3
1
0
1
1
0
1
0
0
1
0
0
2
1
0
0
2
1
0
0
0
1
0
0
0
1
2
0
0
2
0
0
1
2
1
0
0
1
1
2
0
0
0
0
1
0
1
1
1
1
1
1
0
1
0
0
1
0
0
0
1
1
1
0
0
0
0
0
3
2
2
0
2
0
0
0
0
0
0
2
1
1
0
1
1
0
1
0
2
1
1
1
0
0
1
2
0
1
0
2
0
1
0
0
2
0
0
0
2
0
1
0
0
0
1
0
0
2
0
0
0
0
2
0
2
1
1
0
2
0
0
2
1
1
1
0
1
1
0
0
0
2
0
0
0
0
1
1
1
1
1
0
2
0
1
0
2
1
0
3
1
2
1
0
0
0
1
3
2
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
1
0
1
0
2
0
1
2
0
0
1
0
0
0
1
1
2
0
2
0
1
0
1
0
1
1
0
1
1
0
0
0
1
2
2
2
0
0
2
1
0
0
0
0
2
2
1
1
0
0
2
0
0
0
0
1
2
0
3
0
0
1
2
0
0
1
2
0
1
0
1
4
0
1
0
1
2
0
1
1
1
4
1
2
0
0
2
0
0
2
1
0
0
1
1
0
0
1
0
0
0
1
2
3
2
1
0
1
0
1
0
0
0
2
0
1
0
1
1
0
2
0
0
0
0
1
0
3
1
0
0
0
0
3
2
0
2
2
2
0
1
2
2
0
2
0
0
0
0
0
3
0
1
2
2
0
0
0
1
0
0
0
1
0
0
2
0
0
0
2
1
1
0
0
1
0
2
0
1
2
0
2
0
0
0
2
2
0
2
2
1
0
0
2
1
0
2
1
2
0
0
0
0
1
2
1
2
0
1
1
0
2
0
0
1
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
4
1
2
0
0
1
1
0
2
0
0
0
1
0
2
0
2
0
0
1
1
0
0
0
1
0
0
1
0
0
1
2
0
2
4
0
4
0
0
0
1
1
0
1
1
0
1
2
1
0
0
2
0
1
0
0
1
1
1
0
3
1
0
0
0
2
2
0
0
0
1
0
1
1
1
0
2
1
0
0
1
1
1
1
2
0
2
0
0
3
1
0
1
1
0
0
0
2
0
0
0
0
1
0
0
0
2
1
0
0
2
0
1
0
0
2
2
1
0
1
1
2
2
0
1
1
0
0
0
1
0
0
0
0
1
0
2
0
2
0
0
1
2
0
2
0
2
1
0
0
0
1
0
0
0
0
2
0
0
0
0
1
2
2
0
1
0
1
0
0
0
0
1
0
1
2
0
0
0
0
0
1
0
1
0
0
2
1
2
3
0
0
0
1
1
2
4
0
2
1
0
2
0
1
0
3
0
1
0
1
0
2
0
2
2
2
1
0
1
1
3
0
0
2
2
0
2
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
2
0
2
0
2
2
2
1
0
0
0
0
1
0
2
2
0
1
2
0
2
1
0
2
0
2
0
0
0
0
2
2
1
0
1
1
0
2
2
1
0
1
1
3
0
1
2
0
0
0
0
0
1
1
2
0
2
0
2
1
1
1
0
1
1
0
3
1
1
0
0
0
2
4
0
1
1
1
0
0
1
1
0
0
2
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
1
0
1
0
0
0
3
0
0
0
2
1
2
0
0
1
0
2
2
2
0
1
1
2
0
1
0
1
0
3
3
0
0
2
0
0
0
0
2
2
2
0
0
1
0
0
0
1
0
0
2
0
0
1
0
2
0
0
0
0
1
2
1
3
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
2
2
0
1
1
1
2
1
1
0
0
1
1
1
2
0
1
0
0
0
2
0
2
0
0
1
1
0
1
0
0
1
1
0
0
1
0
3
0
1
2
1
1
0
1
0
1
0
0
0
0
2
0
2
1
2
1
0
0
0
0
0
8
1
0
0
1
0
0
1
1
0
1
1
1
2
2
0
0
2
2
0
1
0
0
0
0
3
2
4
2
0
1
1
2
0
2
0
0
0
0
0
2
1
0
2
2
0
2
0
2
0
0
2
0
1
0
2
2
0
0
0
0
1
0
0
0
1
1
0
1
0
0
2
0
0
0
0
1
1
1
2
2
0
0
0
0
1
0
1
0
0
1
1
1
0
0
2
3
2
0
0
1
0
0
1
2
0
0
0
1
0
2
0
0
1
2
0
2
1
0
2
0
0
0
0
0
1
0
2
2
0
1
0
0
1
0
2
2
0
0
0
2
0
1
0
3
0
0
0
3
0
1
1
2
1
2
0
0
0
1
0
0
1
0
1
0
0
0
0
1
2
2
1
1
0
1
0
1
2
2
0
2
2
0
1
0
1
0
1
0
1
0
1
2
1
1
0
2
2
0
0
0
1
0
0
2
0
1
0
0
0
0
1
2
1
0
0
1
1
0
2
0
0
1
0
1
2
2
0
0
0
1
0
1
1
0
0
1
0
1
0
0
2
1
0
1
0
1
2
0
1
2
0
2
1
2
2
0
0
0
1
0
2
0
1
1
0
0
1
0
0
0
0
0
0
0
2
0
0
2
1
0
0
2
2
0
1
0
1
2
1
2
0
0
1
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
1
2
0
1
1
1
1
0
0
1
0
0
1
0
2
1
2
1
0
0
0
0
1
2
2
0
0
2
1
0
0
0
1
0
0
0
0
2
0
1
1
0
0
1
2
4
0
0
1
1
0
0
1
0
0
0
3
2
2
1
1
2
1
0
0
0
0
0
0
0
0
0
1
2
1
2
2
1
0
0
0
0
1
2
2
0
0
1
0
0
0
2
1
0
2
1
2
0
1
2
0
1
1
2
0
1
2
1
0
1
1
2
1
0
1
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
2
0
0
2
1
0
2
0
0
0
0
0
0
0
1
1
0
0
4
0
1
1
0
0
0
0
1
2
0
2
3
0
1
0
0
1
1
1
0
0
1
0
1
1
0
1
0
0
0
0
0
0
2
1
0
0
1
2
2
0
1
0
1
2
0
1
1
0
0
0
0
0
2
2
7
1
1
1
1
0
0
2
1
0
2
0
1
1
1
2
1
0
1
0
1
0
2
0
2
0
0
2
2
0
1
0
0
0
0
2
0
1
0
2
2
2
2
2
0
1
0
0
1
1
1
0
1
0
0
1
2
0
0
0
1
0
0
0
2
1
1
1
0
1
0
2
0
0
0
2
2
0
1
1
1
0
0
2
1
0
1
1
0
0
0
1
0
0
1
1
0
0
2
0
1
1
2
0
0
0
0
2
0
0
0
0
2
0
2
1
0
2
0
1
2
0
1
1
0
1
2
0
1
0
1
2
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
2
2
1
1
0
0
0
0
0
0
1
0
2
0
0
1
1
0
0
0
2
0
0
0
0
2
2
1
1
0
0
0
2
0
0
1
2
0
0
0
1
1
0
0
1
0
1
0
1
2
0
1
2
1
1
1
0
1
1
2
0
1
0
1
2
0
1
0
2
2
0
1
1
0
0
7
0
0
0
2
0
0
0
0
2
0
0
0
1
2
2
1
1
0
2
0
2
0
2
2
2
1
1
2
2
0
2
0
0
0
0
1
1
0
0
1
0
0
0
2
1
0
2
0
0
1
0
0
0
1
0
2
0
1
0
0
2
1
0
0
0
2
2
0
0
1
0
0
2
0
1
1
0
3
0
0
2
0
0
1
2
0
0
2
0
0
0
0
2
1
1
0
1
0
1
1
2
3
0
1
0
1
0
0
1
2
0
0
0
3
1
2
0
0
0
3
2
0
0
0
1
2
1
1
1
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
1
2
0
0
1
2
1
0
0
0
0
3
0
0
0
1
0
2
0
0
1
2
2
1
0
0
0
0
0
0
0
1
2
0
0
2
1
0
2
0
0
0
0
0
0
1
2
2
1
1
1
1
0
2
2
1
0
0
0
0
0
0
2
1
1
0
2
0
1
0
1
0
0
0
0
3
0
1
0
0
1
0
2
3
2
0
0
0
0
1
1
0
1
2
0
0
0
1
0
0
0
1
1
0
1
0
1
0
1
2
0
0
2
0
0
1
0
2
1
0
0
1
0
0
1
0
1
2
1
0
2
0
1
2
1
0
2
0
1
0
1
0
0
0
0
1
2
0
0
1
0
0
0
0
1
1
1
0
0
1
2
0
0
2
2
2
2
0
0
0
0
1
2
0
1
0
1
3
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
1
1
1
2
1
1
2
0
2
0
0
0
2
0
0
1
0
2
1
0
1
0
2
4
0
0
0
2
2
2
0
1
0
0
0
0
0
0
0
2
1
0
0
1
1
0
0
0
0
0
2
0
0
1
1
0
0
0
1
0
1
2
0
0
0
0
0
2
0
0
0
0
2
1
3
2
1
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
2
1
0
0
0
0
2
1
2
0
0
1
0
1
2
2
1
1
1
0
1
2
0
1
1
1
0
1
0
1
2
0
4
1
0
2
1
0
1
0
3
0
0
3
0
1
1
0
0
0
0
0
0
2
1
1
1
2
0
1
0
0
0
0
0
1
0
2
0
0
1
0
0
1
0
1
0
1
0
0
2
1
2
0
0
1
2
1
0
7
1
1
0
1
3
0
1
0
0
2
0
0
0
0
0
0
0
2
0
2
0
2
0
2
1
0
0
4
2
1
1
0
0
0
0
2
2
3
2
1
0
1
2
0
2
0
2
2
0
0
0
1
1
0
1
0
2
1
0
1
1
0
1
0
2
0
1
2
0
1
2
0
0
0
0
1
0
0
2
0
1
2
2
2
1
2
1
0
0
2
1
1
0
0
2
1
0
0
0
1
0
0
0
1
0
0
1
1
1
2
0
0
0
0
1
0
1
0
0
1
0
1
0
0
2
1
2
0
0
2
2
1
0
1
2
2
1
0
0
1
0
0
1
0
1
0
1
3
0
0
1
0
0
1
0
1
2
0
0
1
0
0
2
0
0
0
2
2
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
1
1
2
0
1
0
0
1
0
1
0
0
2
1
0
2
0
0
0
1
4
1
1
0
2
1
2
1
1
0
0
0
2
0
2
0
4
0
0
0
1
2
2
0
1
3
2
1
2
0
0
2
0
0
0
1
4
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
2
2
0
1
1
0
0
0
0
0
2
1
1
0
0
1
0
0
0
2
0
1
1
2
2
0
0
0
2
0
0
0
0
0
0
0
1
0
1
1
1
1
1
0
0
2
0
0
1
0
1
0
1
0
2
2
0
1
2
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
2
0
0
0
0
2
0
2
0
1
2
1
1
0
2
2
0
0
3
0
1
0
1
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
1
0
0
2
0
0
2
0
5
1
2
0
0
1
1
3
0
1
1
2
0
0
1
0
0
4
0
1
0
2
0
2
1
1
0
2
0
0
1
0
0
1
0
2
0
2
1
0
0
1
1
0
0
0
3
0
3
1
1
1
2
0
1
0
1
1
0
1
0
0
1
0
2
1
0
0
0
2
0
1
1
0
1
2
2
0
1
0
1
0
0
2
0
2
2
3
0
2
2
1
1
0
0
0
0
2
0
1
0
0
0
1
0
2
0
0
1
0
2
1
1
0
0
0
2
0
0
1
0
2
0
1
2
0
0
0
1
0
2
3
0
0
2
0
0
1
2
2
2
1
1
1
1
0
1
2
1
2
3
0
1
0
0
2
1
0
2
2
1
0
0
0
0
1
0
1
0
1
0
2
1
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
2
0
0
0
3
0
0
0
0
2
1
0
0
1
0
0
1
0
0
1
0
0
0
2
0
2
2
0
0
2
0
1
0
1
2
0
2
1
3
2
0
2
2
0
0
0
0
0
0
2
0
0
2
1
0
0
2
0
0
2
1
0
1
0
0
1
2
1
0
1
0
0
0
1
2
2
1
1
2
1
0
0
2
1
0
2
0
0
0
0
0
3
2
1
0
2
0
0
0
0
1
0
1
0
0
0
0
2
0
1
2
3
1
3
0
2
0
0
0
0
0
2
0
0
0
0
1
1
0
1
1
1
1
1
0
2
3
1
1
2
2
0
0
1
0
2
1
0
1
2
0
0
0
0
1
0
1
1
2
0
0
1
1
0
1
0
0
1
0
1
0
2
0
3
1
0
1
0
0
0
1
0
0
2
0
0
1
2
1
2
1
1
1
1
1
1
0
1
1
2
0
1
0
0
0
2
1
0
2
2
0
0
1
0
0
0
0
1
0
1
1
2
1
0
1
0
0
0
2
1
2
3
0
2
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
1
1
1
2
0
2
0
2
1
3
2
0
1
1
0
0
1
4
1
1
0
0
2
0
1
2
0
1
0
0
3
0
0
1
2
0
0
3
0
0
3
0
2
0
0
0
0
0
0
5
0
2
0
0
0
2
2
0
0
0
0
2
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
2
1
2
2
1
0
1
2
1
0
2
0
1
0
0
2
1
0
1
0
1
1
0
0
2
2
2
2
0
0
2
1
0
2
1
0
0
2
0
0
2
1
0
0
0
0
2
1
0
2
1
0
2
1
2
1
1
0
0
1
2
2
0
0
1
0
0
0
1
0
0
2
0
0
1
0
4
0
1
0
1
0
0
2
2
1
1
2
0
0
1
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
1
0
1
0
1
1
1
2
6
2
0
0
1
1
0
1
3
2
0
0
0
2
1
0
0
2
1
0
1
1
0
0
2
1
0
0
2
0
8
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
2
0
1
1
0
0
0
0
0
0
0
0
2
2
2
0
1
0
0
2
5
0
1
0
2
2
1
3
1
0
1
2
1
2
1
0
0
0
0
1
0
1
2
0
0
2
0
0
0
0
1
1
2
0
0
2
1
2
2
2
0
2
0
0
1
0
0
0
0
1
1
1
0
2
0
0
0
1
1
1
0
0
0
0
0
3
0
0
1
0
2
1
2
1
1
1
2
0
0
1
0
2
1
1
0
2
0
1
0
1
0
0
2
0
2
0
2
2
0
1
1
0
1
0
0
0
0
0
0
1
0
2
0
2
0
0
1
0
2
0
0
2
2
0
0
1
0
2
2
1
0
1
1
0
0
0
0
0
0
1
0
2
2
1
0
0
2
0
1
0
0
0
0
0
0
0
2
2
1
1
0
0
0
2
0
2
0
1
0
0
1
0
0
0
0
1
1
0
1
2
1
2
1
1
0
0
0
1
0
0
2
1
0
1
1
1
0
1
1
0
1
0
1
0
0
1
1
0
1
2
2
0
0
1
2
1
1
0
0
1
0
0
0
1
1
0
1
0
1
0
0
0
0
2
1
1
0
2
0
0
0
0
0
0
0
0
0
0
2
4
1
0
1
2
0
0
1
0
2
4
0
0
0
1
0
3
2
0
1
0
0
2
0
2
0
2
1
1
0
0
2
1
1
2
1
1
2
1
0
0
0
0
0
0
2
0
2
1
1
0
2
0
0
0
0
0
0
0
2
0
1
0
2
0
2
0
0
1
1
1
0
1
0
1
1
2
0
1
0
0
2
0
0
1
0
0
0
0
1
0
2
0
1
1
1
0
0
0
1
0
0
1
1
0
1
0
3
2
2
0
2
0
0
0
2
1
0
2
1
1
1
0
0
2
4
1
1
2
0
1
1
2
0
0
1
1
0
2
0
1
0
1
0
1
0
0
0
0
1
0
0
1
0
4
0
1
0
0
0
0
1
1
1
1
0
0
0
0
2
1
0
0
0
0
0
0
2
0
1
1
0
1
2
1
1
0
0
1
1
1
0
3
2
0
1
0
0
0
1
1
0
2
1
0
1
1
1
0
1
0
0
1
2
0
0
2
0
1
1
0
1
0
0
0
2
1
2
2
0
0
0
0
1
1
1
0
0
1
0
1
0
0
0
2
2
0
1
1
1
0
1
1
0
1
0
0
1
0
0
1
3
2
0
2
3
0
0
1
0
0
0
0
0
1
2
1
1
1
0
0
1
1
1
2
1
2
2
1
2
0
0
1
0
5
1
0
1
0
0
0
0
1
0
0
0
0
0
2
1
0
2
3
0
1
2
0
2
0
1
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
1
1
2
2
2
1
2
0
1
0
1
0
0
0
0
0
0
0
0
0
1
2
2
2
0
0
3
0
1
0
0
1
1
2
0
0
0
0
1
0
1
0
0
0
0
3
1
0
0
1
0
0
0
0
0
1
1
1
1
1
0
2
1
2
0
1
0
1
0
3
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
2
1
1
2
1
2
0
0
1
0
0
2
0
3
0
0
1
0
1
1
1
1
2
1
0
1
0
1
2
0
1
0
0
0
2
0
1
2
0
0
1
0
1
0
0
2
1
1
1
0
2
0
1
3
0
0
1
0
2
0
2
2
0
2
2
0
0
0
0
0
0
0
1
2
2
1
1
1
1
1
0
3
0
1
0
0
0
1
0
2
0
1
0
0
1
0
0
0
0
0
2
1
2
2
0
1
1
0
0
1
1
2
2
0
1
1
1
0
0
0
2
0
0
2
1
0
2
2
6
1
0
2
0
0
0
0
0
0
2
1
0
1
0
0
0
3
1
2
1
0
2
1
2
1
0
2
1
0
0
0
1
0
1
0
1
1
2
1
1
0
0
0
2
3
1
0
1
0
2
1
0
1
1
0
1
0
1
0
0
0
0
2
2
0
0
1
0
0
0
0
2
0
0
0
1
1
2
1
0
2
0
0
0
2
0
2
0
2
2
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
1
0
2
1
0
0
2
2
0
2
1
1
0
0
2
1
0
2
2
0
0
2
1
0
0
2
0
0
0
0
0
3
0
1
0
0
1
0
0
1
2
0
0
1
0
1
1
0
0
0
0
1
0
2
0
0
7
1
2
0
0
0
0
1
1
2
2
2
0
1
2
0
2
1
1
2
0
2
0
0
1
2
0
0
0
2
2
0
2
0
0
2
2
1
3
0
4
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
1
1
0
0
1
0
2
0
0
0
2
1
1
1
2
0
2
1
0
0
2
3
0
0
1
1
1
1
2
2
0
0
0
0
1
0
0
0
0
1
0
2
0
0
1
2
1
0
0
0
0
0
0
0
1
0
1
1
0
0
2
0
0
0
2
1
0
3
1
0
1
1
2
0
0
1
0
0
2
0
1
0
0
1
0
0
0
2
0
2
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
2
2
1
1
2
1
0
2
0
1
0
1
1
0
0
1
0
0
1
0
2
2
0
0
2
2
2
2
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
2
2
1
0
0
2
0
2
0
1
0
1
2
0
0
0
1
0
0
0
2
1
1
2
0
0
1
0
1
0
1
0
0
0
1
0
3
0
1
2
2
0
0
1
0
0
0
0
1
0
0
0
1
0
0
2
2
0
1
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
1
1
0
2
0
0
0
1
0
1
0
2
0
1
0
4
1
0
0
0
0
1
2
0
0
0
1
0
2
1
0
0
0
2
1
1
0
2
1
0
0
0
1
0
0
1
1
0
3
1
2
0
0
0
2
0
0
1
0
1
0
0
1
0
0
2
1
0
0
1
1
0
0
2
0
0
2
0
0
1
4
0
1
0
7
0
0
0
0
2
2
1
0
0
0
0
0
0
1
0
2
0
0
1
0
0
1
0
0
0
1
4
2
0
1
1
1
1
0
0
9
0
1
0
1
1
0
2
0
0
0
0
0
1
0
1
1
0
2
1
0
2
2
2
0
1
0
0
2
1
1
2
0
0
2
2
0
2
1
1
1
0
1
0
0
2
5
0
2
1
0
0
0
1
0
1
0
0
0
0
1
2
0
0
2
0
2
0
0
2
0
1
0
0
0
2
1
2
1
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
3
1
0
0
1
2
0
0
0
0
2
1
1
1
1
1
0
0
0
2
1
2
1
1
1
2
0
0
2
0
0
1
1
2
1
1
2
2
1
2
0
0
1
0
2
0
0
0
1
1
0
0
2
0
0
1
0
1
2
0
0
1
0
2
0
0
0
0
2
0
2
0
1
0
2
2
1
1
0
1
2
1
0
2
0
0
2
1
0
2
1
1
1
0
0
0
1
0
2
0
0
2
1
0
0
2
2
0
1
0
0
0
0
2
0
2
0
0
0
0
2
2
2
0
0
0
2
1
1
4
1
0
0
1
0
0
2
0
1
0
0
1
0
1
0
0
2
0
2
1
0
0
2
0
0
0
3
0
2
0
3
1
0
1
1
0
2
2
0
0
0
2
2
0
0
0
0
0
0
0
0
4
2
2
0
0
1
2
0
2
0
0
0
0
2
2
1
0
2
0
1
2
0
0
0
1
0
1
1
2
1
0
0
0
0
2
1
0
0
2
0
0
0
2
0
0
2
1
0
0
0
0
1
1
0
0
0
2
1
2
0
1
1
1
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
2
0
0
2
1
2
0
2
1
0
0
5
0
1
1
1
1
0
0
3
0
1
3
1
0
2
0
0
0
0
0
1
0
0
1
2
1
0
1
1
1
0
1
0
0
1
2
1
2
0
1
0
1
2
1
0
2
0
0
2
2
0
0
4
2
0
3
0
2
0
0
0
0
2
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
2
1
2
0
0
2
0
0
1
1
4
2
0
1
0
0
0
0
0
0
0
2
1
0
1
2
1
1
1
1
2
0
0
0
0
0
0
0
0
1
2
1
1
2
1
0
1
0
2
2
0
0
0
1
0
0
0
0
1
1
1
1
2
0
1
2
1
1
0
1
0
0
4
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
1
0
0
0
1
0
3
1
1
0
0
2
0
0
0
1
1
1
0
0
0
0
2
1
1
1
0
0
0
0
1
1
1
1
0
0
0
1
0
0
0
0
2
2
1
0
2
0
0
1
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
1
2
2
0
0
1
0
1
1
0
2
2
2
2
0
2
1
1
1
0
0
0
0
1
2
3
1
1
0
0
1
0
2
2
1
0
1
0
1
1
0
0
0
0
0
1
2
0
1
0
0
0
0
1
2
1
0
0
1
0
0
0
0
0
2
2
0
1
0
2
0
0
0
0
1
1
1
1
0
1
0
1
0
1
1
0
0
0
2
0
1
0
0
0
0
0
0
0
1
1
1
0
2
1
0
2
1
1
1
0
1
1
1
0
0
0
2
2
1
2
1
0
2
1
2
0
0
0
0
0
0
0
1
0
0
3
2
2
1
0
2
0
0
0
0
1
1
0
1
2
2
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
2
0
0
1
0
0
0
0
2
1
0
0
0
1
0
0
0
1
2
0
1
0
0
0
0
0
0
1
2
2
0
1
0
1
0
0
1
1
0
0
0
0
2
1
0
2
0
1
0
1
2
1
0
1
0
1
2
0
2
1
2
0
0
2
2
0
0
0
2
0
2
0
1
1
2
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
1
1
2
1
0
0
2
0
0
0
2
0
2
2
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
1
0
0
0
1
1
1
0
2
0
1
0
1
0
0
2
0
0
2
0
1
0
0
0
2
1
0
0
0
1
0
1
0
1
0
0
0
2
1
0
0
1
1
0
4
1
0
0
0
0
2
1
0
0
1
0
0
0
0
1
1
0
1
1
0
2
0
1
0
1
2
1
2
1
1
0
0
0
0
0
1
1
2
0
0
1
1
1
0
0
0
0
0
1
0
0
0
2
0
1
1
0
2
0
0
0
0
0
1
0
0
1
0
2
1
0
0
2
0
2
2
2
2
1
0
0
1
0
0
0
0
1
0
0
0
2
0
0
1
1
0
1
2
0
2
1
0
1
0
1
1
2
0
1
1
0
0
1
2
0
0
2
5
2
2
0
1
0
1
2
0
0
2
0
1
0
1
0
0
0
2
0
1
0
0
0
1
0
1
1
0
1
0
0
0
0
2
0
1
0
1
0
2
1
0
2
2
0
0
6
1
0
0
2
0
1
2
1
0
2
0
0
0
2
0
2
0
0
1
1
0
2
0
2
0
1
1
2
2
1
2
0
1
0
1
2
2
0
0
1
0
1
0
1
1
0
0
0
0
2
1
3
2
1
0
0
0
2
4
0
0
0
2
0
2
0
1
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
2
0
1
0
1
0
0
0
2
0
0
2
1
0
1
0
2
0
1
0
1
0
0
0
1
2
1
0
2
0
2
0
2
0
1
0
0
0
1
0
0
2
3
0
1
0
0
0
1
2
0
1
0
0
1
1
0
2
0
0
0
0
3
0
0
1
0
0
0
1
0
0
3
0
1
0
1
0
0
0
0
2
0
1
0
1
0
0
0
0
2
0
0
0
2
0
1
2
1
1
1
2
2
1
2
0
0
2
0
1
0
0
1
0
2
0
1
2
1
1
1
0
0
2
1
0
0
0
1
0
2
0
2
1
2
1
1
0
2
0
0
0
0
0
2
0
0
2
0
2
0
0
0
2
1
2
2
1
0
0
2
1
1
0
1
2
0
1
0
1
0
0
1
0
0
2
0
2
0
0
0
0
0
1
1
2
0
0
2
0
0
0
0
1
1
2
1
2
0
0
0
1
1
1
2
0
0
2
1
2
2
2
0
2
0
2
1
1
1
1
1
1
0
0
0
1
1
2
1
2
1
1
0
0
0
0
0
0
1
0
2
0
2
2
2
0
0
0
0
2
0
0
1
1
1
1
2
1
0
1
2
0
0
0
0
1
0
1
0
1
0
0
0
1
5
0
1
1
1
2
0
0
1
2
1
0
0
1
1
3
0
1
3
1
0
1
1
0
0
0
1
2
2
2
0
1
0
0
1
0
1
0
0
1
0
2
0
3
1
1
0
0
1
0
0
1
0
0
1
0
2
1
0
0
0
0
1
1
1
1
0
1
0
0
0
0
2
0
0
2
0
0
0
2
0
2
0
2
2
0
3
0
0
0
1
0
2
0
1
1
0
0
0
1
0
0
0
0
0
3
0
0
1
1
0
2
0
0
0
2
2
0
0
1
1
1
2
1
0
0
0
0
1
0
0
1
0
2
0
0
1
0
0
0
2
0
0
3
0
0
2
2
0
0
1
1
0
0
0
2
0
2
2
1
2
1
1
0
0
0
0
0
8
0
1
2
2
0
0
2
0
0
0
0
0
0
0
1
1
1
0
1
1
2
0
3
1
0
1
1
0
1
0
2
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
1
0
0
2
0
1
1
0
2
1
1
0
1
1
1
1
2
0
1
2
2
0
1
0
0
0
2
1
2
0
0
2
0
0
1
2
0
0
0
0
1
2
0
1
0
2
0
0
1
1
1
0
0
1
2
0
2
0
2
0
0
0
2
0
0
1
1
0
1
0
3
0
2
1
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
1
1
1
0
0
1
0
1
0
2
2
1
3
0
0
2
1
0
0
1
2
0
2
0
0
2
2
2
2
2
1
1
1
0
0
0
0
1
2
0
0
1
0
0
2
2
2
2
0
2
1
0
1
0
1
0
0
2
0
1
2
2
2
0
0
0
2
2
1
1
1
0
1
0
0
1
2
0
2
1
0
0
0
2
0
0
0
2
1
2
2
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
1
1
0
0
0
2
1
0
0
0
0
0
1
2
1
1
1
0
0
0
2
1
0
0
1
0
0
0
0
3
0
0
1
2
1
1
1
0
0
2
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
3
1
2
0
0
2
1
0
0
0
2
1
0
0
2
1
1
1
3
0
0
1
1
1
0
0
1
0
6
0
0
2
2
2
1
1
0
0
2
0
2
1
0
1
1
1
1
0
2
1
0
1
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
2
1
2
0
2
2
0
0
1
0
0
0
1
1
2
0
1
0
0
1
2
2
2
0
0
0
1
0
2
0
1
0
0
1
0
3
1
1
2
0
2
1
1
0
2
0
0
0
1
0
2
1
0
0
4
1
2
0
0
1
0
2
0
2
2
0
0
1
1
2
0
0
1
0
0
2
4
1
0
2
0
0
0
1
0
2
1
2
0
0
1
2
0
2
0
0
1
0
2
1
0
1
1
2
0
3
2
2
0
0
1
0
2
2
0
2
1
0
0
0
2
1
2
0
0
1
1
0
1
2
1
0
0
1
0
2
0
0
2
0
2
1
0
0
2
2
2
1
1
0
0
1
0
2
1
1
0
0
0
0
0
0
0
0
0
1
2
1
1
0
0
2
0
2
0
2
2
1
1
0
0
0
1
2
0
2
1
0
1
0
1
0
0
0
1
0
0
0
0
0
2
1
0
0
1
0
1
1
0
2
0
0
0
0
0
0
2
1
0
1
1
0
0
0
0
0
2
0
1
0
1
2
0
1
1
0
0
1
0
0
2
1
1
0
1
0
1
2
0
0
1
0
0
2
0
0
1
0
0
2
0
0
1
1
1
1
0
0
0
0
0
0
1
0
2
1
1
2
2
2
3
2
2
2
0
1
0
0
2
1
1
1
0
0
2
1
1
1
0
2
1
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
1
0
3
1
0
0
0
0
1
1
0
0
0
2
2
0
1
1
0
0
1
0
1
1
0
2
0
1
2
0
1
2
1
0
1
0
0
2
0
2
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
2
1
0
2
1
1
2
2
0
1
0
1
1
0
2
0
1
2
0
0
2
0
1
1
2
0
1
0
0
1
2
1
1
1
1
0
1
0
0
1
2
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
3
1
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
1
0
0
0
2
0
2
0
2
2
1
0
0
2
2
1
0
1
0
1
1
1
0
2
0
0
2
1
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
1
0
1
1
0
0
0
0
1
0
2
2
0
2
3
0
0
0
0
0
3
0
0
2
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
1
2
0
2
0
2
1
0
0
0
2
0
2
1
2
0
0
1
0
9
2
0
0
0
0
0
2
1
0
0
2
0
0
2
1
0
1
1
1
0
2
2
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
2
2
1
0
0
0
2
0
1
1
1
2
0
0
3
2
0
0
0
2
0
1
0
0
2
0
0
1
0
1
0
2
0
0
0
0
0
2
0
1
2
0
2
1
0
0
0
0
0
2
1
0
0
0
2
0
2
0
0
0
0
0
0
1
1
0
2
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
2
2
1
0
0
0
2
1
0
0
1
0
0
0
0
0
0
2
0
0
0
2
1
0
1
0
0
0
0
1
0
0
2
0
1
2
1
1
1
1
1
0
0
1
1
1
0
0
1
0
0
2
0
1
1
0
0
1
0
0
0
2
0
1
0
0
2
2
2
0
1
2
1
1
1
0
1
0
0
2
0
1
1
2
1
1
0
1
0
2
0
1
2
2
0
0
0
1
0
0
0
1
0
1
2
0
3
0
2
0
0
2
1
4
0
2
1
0
0
1
0
0
1
2
2
1
1
0
3
2
1
0
1
0
0
1
3
0
1
0
2
2
0
2
0
2
0
0
2
2
0
2
0
0
0
2
0
1
0
1
0
1
0
2
0
1
0
1
0
1
2
0
1
1
2
1
1
0
2
2
0
0
1
1
2
2
1
1
2
2
1
3
0
1
1
0
0
2
1
1
0
2
0
0
1
1
1
0
0
1
2
1
2
0
5
0
1
2
3
0
0
1
0
1
0
2
0
2
0
1
1
0
0
0
1
0
2
0
1
1
0
0
0
0
0
3
0
0
0
2
2
2
1
1
0
1
0
2
1
0
1
2
1
1
0
3
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
1
3
1
3
0
0
0
0
1
0
1
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
1
1
1
0
2
1
1
0
2
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
2
1
1
2
0
2
1
1
0
2
0
0
2
0
1
1
0
0
7
0
0
0
1
0
2
0
0
0
0
0
0
1
2
1
0
2
0
0
2
2
0
3
1
1
0
0
1
0
1
0
0
2
1
0
1
0
0
0
0
1
2
0
0
2
1
1
0
1
0
0
0
0
2
0
1
0
0
2
0
1
0
0
2
1
0
0
0
2
0
2
0
0
1
0
2
0
2
0
0
0
1
0
0
1
1
1
0
2
0
1
2
1
1
0
0
1
1
1
0
1
0
2
0
1
0
1
1
3
2
2
2
2
0
0
0
0
0
2
0
0
1
2
3
0
0
4
0
0
0
0
0
0
0
0
1
1
1
2
1
0
0
1
0
0
0
0
1
0
0
1
2
1
1
1
2
0
1
1
0
0
0
0
0
0
0
2
0
2
1
1
0
0
0
2
0
0
1
1
0
0
0
0
0
0
2
2
1
2
1
2
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
1
1
1
1
2
0
1
1
1
0
0
2
1
1
1
0
2
1
0
0
1
1
1
0
0
1
0
2
0
0
2
1
0
0
0
0
0
0
2
0
1
1
2
0
0
0
1
0
2
2
0
1
0
1
0
0
1
0
0
1
0
0
1
1
2
0
0
0
0
1
1
1
1
0
2
0
0
1
0
1
1
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
2
2
0
1
1
0
0
0
1
1
2
0
2
0
0
0
1
0
0
1
0
0
0
0
1
0
1
1
1
0
2
0
0
2
1
1
0
1
0
2
0
1
1
0
0
0
0
1
1
0
0
2
1
1
2
0
2
0
2
0
1
0
0
0
0
0
2
0
0
1
1
1
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
1
1
0
0
2
0
0
0
1
1
0
0
2
0
0
0
0
1
1
0
2
0
2
0
0
0
0
2
1
1
2
1
0
0
1
0
0
0
2
1
0
2
0
1
0
0
0
3
0
1
1
0
0
1
0
0
2
2
1
0
0
1
2
1
0
1
0
0
1
0
2
0
1
1
0
0
0
0
2
1
2
1
1
0
1
0
0
1
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
2
0
0
1
2
0
0
0
1
0
1
0
0
10
2
0
0
2
0
1
0
0
3
0
0
1
2
2
0
0
1
0
0
0
0
1
2
1
0
0
0
2
0
1
0
2
5
0
0
0
0
2
0
0
1
3
0
0
1
1
0
0
1
2
0
0
1
0
2
0
1
2
0
1
1
1
1
0
0
0
0
1
2
0
0
0
1
1
0
0
1
1
1
0
3
0
1
2
0
0
0
1
1
1
1
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
2
1
2
0
1
2
1
1
0
2
2
2
3
1
1
1
0
0
0
0
0
0
2
2
0
1
0
2
0
2
1
1
1
0
1
1
2
1
1
0
0
1
1
2
0
0
1
0
0
0
2
1
0
2
2
1
2
1
0
0
1
0
0
0
0
2
2
0
1
0
0
1
0
1
0
0
1
0
2
1
0
0
0
0
1
1
1
2
0
1
0
0
1
0
0
0
0
4
1
1
0
1
1
2
1
0
0
1
0
2
2
1
0
1
0
0
2
1
0
1
0
0
0
0
0
0
0
2
0
0
0
1
1
1
2
1
0
0
0
0
2
0
0
3
0
0
0
0
1
0
0
1
0
1
0
1
0
0
1
1
0
0
3
0
0
0
2
0
0
2
1
0
0
1
3
1
0
0
1
1
0
0
0
0
0
1
0
0
1
0
1
2
2
1
0
0
1
2
0
2
0
2
1
2
1
1
0
2
1
2
0
1
2
0
0
3
0
1
0
0
0
2
1
1
1
0
0
2
0
1
0
0
1
1
1
0
1
1
2
0
1
0
0
0
0
0
2
0
0
1
3
0
2
1
0
1
0
2
0
0
0
2
0
1
0
0
0
0
2
3
0
0
0
1
0
1
0
1
0
0
2
0
0
0
1
1
0
1
0
2
1
0
2
3
0
2
3
0
0
0
0
2
1
0
0
0
0
0
1
2
1
1
1
2
0
0
1
0
1
0
0
0
2
1
1
2
0
0
0
2
0
0
1
1
0
0
2
0
0
2
0
0
0
0
0
2
1
2
2
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
1
0
0
2
0
0
0
0
0
1
0
0
2
0
0
1
0
0
1
1
1
2
1
0
0
0
0
0
1
1
1
1
0
1
1
2
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
2
0
0
1
1
1
2
1
0
0
0
0
1
2
0
0
1
1
1
0
1
0
0
0
2
0
1
1
1
0
0
2
0
1
0
2
1
0
0
0
1
1
0
1
2
0
0
1
0
0
0
2
0
2
0
0
1
0
2
1
0
0
1
0
0
2
0
1
1
1
1
0
1
1
0
1
0
0
2
0
2
1
3
0
0
1
0
2
0
1
2
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
1
1
2
2
2
0
1
0
0
0
2
1
1
2
0
0
0
0
0
0
0
2
0
0
1
1
0
1
4
1
0
0
1
1
0
1
2
1
0
0
1
1
0
1
0
0
2
2
0
2
0
0
0
1
3
2
1
2
1
1
0
0
2
2
0
1
1
2
0
1
3
0
1
1
0
2
0
0
0
2
1
1
2
0
0
0
1
0
1
2
0
1
1
0
1
1
0
0
0
0
1
0
2
2
0
0
0
2
1
3
0
3
0
0
0
0
0
0
1
2
0
2
0
0
2
0
1
0
3
1
0
2
0
1
1
0
1
2
0
2
0
2
0
0
0
0
1
2
1
0
0
1
0
2
2
1
2
2
2
4
0
0
1
2
1
0
0
0
0
0
0
0
1
0
2
2
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
3
0
0
0
1
2
1
0
0
1
0
0
2
0
0
0
1
0
3
2
0
0
2
1
1
1
2
0
1
0
0
1
1
0
1
1
2
1
0
1
1
0
0
1
1
1
3
2
2
0
0
0
0
2
2
3
0
0
3
3
0
2
1
0
1
0
0
0
1
1
0
1
3
1
0
2
1
0
2
1
4
2
2
0
1
0
2
1
2
1
1
1
0
0
1
0
0
0
0
2
0
0
0
1
2
0
1
2
0
2
1
0
2
2
1
1
0
1
2
0
0
1
1
1
0
0
0
0
1
0
0
0
0
1
0
2
0
0
1
2
0
0
0
2
1
1
2
3
0
1
0
2
0
0
0
1
0
1
2
0
0
1
2
1
2
1
1
1
0
0
2
0
1
1
0
0
0
2
1
3
0
1
0
1
0
1
0
0
2
0
0
0
0
1
2
0
1
0
2
2
4
0
2
0
0
1
0
0
0
2
1
0
0
0
1
2
0
0
0
1
0
0
0
1
2
1
2
2
2
2
0
0
0
0
0
1
0
0
2
0
0
2
0
3
0
0
4
0
1
2
2
1
2
0
0
0
0
3
0
1
2
1
0
0
0
0
1
0
1
2
0
1
0
0
2
2
0
0
0
0
0
0
0
1
2
1
0
0
0
0
1
1
2
0
3
2
2
0
0
0
1
0
1
1
1
1
1
2
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
1
2
2
1
0
0
1
0
1
2
0
0
1
0
1
0
3
0
0
1
0
0
0
0
0
0
1
1
0
0
2
0
2
0
1
0
1
1
0
0
0
0
1
2
0
0
1
2
0
0
0
2
0
0
1
1
0
0
2
0
1
0
1
0
2
1
0
1
1
1
0
1
0
0
2
1
0
0
0
0
1
1
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
1
0
1
3
1
0
0
1
0
2
0
0
0
2
0
1
4
0
0
0
1
0
0
0
2
0
0
0
2
0
2
1
0
0
0
0
0
1
0
1
0
0
2
0
2
1
0
1
1
0
0
0
0
1
0
0
0
0
1
1
2
0
1
0
1
2
0
1
0
0
0
3
3
1
0
0
0
0
0
0
0
0
4
0
1
0
0
0
1
2
0
2
1
0
0
0
0
2
0
0
0
0
1
0
1
1
0
2
1
0
1
1
0
0
1
0
2
3
1
2
2
2
0
0
0
0
0
2
0
0
0
1
0
1
0
0
1
2
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
2
0
1
2
0
1
0
0
0
0
1
0
2
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
3
3
0
0
0
1
2
0
0
1
0
0
1
2
0
1
0
0
3
0
2
0
2
1
0
0
1
1
0
1
2
2
2
1
2
0
0
0
1
1
0
2
0
2
1
1
3
0
0
2
0
2
0
1
0
1
1
2
0
2
0
1
0
1
0
0
0
2
1
0
2
0
2
4
3
0
0
0
0
1
0
2
0
2
1
2
0
0
0
1
0
0
1
2
0
0
1
1
0
1
1
2
0
1
1
1
0
0
1
0
1
1
1
2
2
3
0
0
0
2
0
0
0
0
2
1
0
1
2
1
0
0
0
0
2
0
1
1
0
0
2
2
2
1
0
1
0
0
2
0
2
0
2
0
0
1
1
0
2
0
3
0
0
1
1
2
1
1
1
0
1
1
0
1
1
0
1
0
1
0
0
0
3
0
2
1
0
1
0
0
0
0
1
1
2
0
2
0
0
5
0
3
0
1
0
2
1
1
0
2
0
0
2
2
1
0
0
0
1
2
2
0
1
2
0
0
2
2
2
0
3
1
1
1
0
1
0
1
0
0
0
1
1
0
0
1
2
0
0
0
0
0
0
1
1
0
0
1
2
1
0
1
0
1
1
1
0
2
0
2
0
0
0
1
0
2
0
1
0
1
1
0
0
2
0
0
0
0
2
1
0
2
0
1
0
0
0
0
2
0
1
0
2
1
2
0
1
2
0
1
2
0
0
0
0
1
0
1
0
0
1
0
1
0
1
2
0
0
1
0
0
1
3
0
2
2
0
1
1
0
0
2
0
0
0
0
0
0
1
0
2
2
0
1
0
0
2
0
2
0
0
0
1
0
0
0
0
3
1
3
2
0
0
0
2
0
0
1
0
0
0
2
0
2
2
1
2
2
0
3
0
1
0
1
0
0
2
2
0
1
0
0
2
0
0
0
0
0
1
2
0
4
1
0
0
3
0
1
1
1
0
1
1
1
1
2
0
0
0
3
0
0
2
1
0
2
1
0
1
0
1
0
2
0
0
0
1
0
1
0
2
0
0
1
1
2
1
0
1
0
0
0
3
0
0
0
0
2
1
0
2
1
1
1
1
2
1
1
0
0
2
0
0
0
1
2
1
0
1
1
0
2
1
1
1
0
2
0
0
2
1
0
0
1
1
0
0
0
0
0
0
2
1
2
1
1
0
0
2
2
0
1
0
1
1
2
1
2
0
1
0
0
1
2
0
2
0
1
1
3
0
4
5
0
1
2
0
1
1
1
2
1
0
1
1
0
2
2
1
0
1
0
2
0
0
1
0
0
1
0
2
2
0
2
0
1
0
0
0
0
0
0
1
0
2
1
0
0
1
2
2
2
1
0
2
3
0
0
1
0
2
0
0
2
1
0
1
0
1
2
1
2
0
4
0
0
0
2
0
0
2
2
1
1
0
0
0
0
1
0
2
0
0
0
1
2
0
0
1
1
1
0
0
0
0
0
4
1
1
3
0
1
0
0
1
0
2
0
0
3
1
0
0
0
1
1
0
1
0
0
0
2
2
2
2
0
0
0
0
0
0
2
0
0
2
0
2
3
1
1
1
0
1
0
2
2
0
0
0
1
0
2
1
0
1
1
0
2
0
0
0
2
2
1
0
0
2
0
2
1
1
0
0
0
1
0
0
0
0
2
1
1
0
0
1
0
1
2
0
2
2
2
0
2
1
0
1
0
0
2
0
1
0
0
0
0
1
0
2
2
1
2
1
0
0
2
0
0
1
2
1
1
1
1
2
0
1
2
0
1
1
0
0
1
0
1
1
0
0
0
1
1
1
3
2
1
1
2
1
2
0
0
0
1
0
0
0
0
1
0
2
1
0
0
0
0
2
0
1
0
0
1
0
2
0
0
0
0
0
1
2
1
0
1
2
0
0
0
1
1
0
0
0
1
4
2
1
2
0
0
2
2
2
0
0
2
2
1
1
1
0
0
0
1
2
0
2
0
0
0
0
0
1
2
1
0
0
1
0
1
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
2
0
2
0
0
3
0
2
0
2
1
1
1
0
0
0
2
0
1
0
0
0
0
0
2
0
0
1
4
0
1
0
0
1
2
0
1
1
0
0
0
2
0
0
1
0
0
2
0
1
3
3
0
3
0
2
0
0
0
1
2
0
0
1
1
0
2
0
0
1
0
0
2
0
1
1
0
1
0
2
0
1
1
1
2
2
0
0
0
0
1
0
0
0
0
0
0
1
2
2
0
0
1
2
0
2
1
1
0
0
0
2
1
0
0
1
1
0
0
0
0
0
1
2
1
2
0
2
0
0
0
0
0
0
0
0
2
1
2
2
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
1
2
0
1
1
0
3
2
0
0
1
0
0
1
1
0
0
0
0
0
0
2
2
1
0
1
0
0
0
0
0
2
2
0
0
1
0
1
0
2
1
2
0
2
2
1
0
0
0
0
2
0
2
0
0
0
1
1
0
2
0
4
2
2
0
0
1
2
2
0
1
1
1
0
0
2
1
0
0
0
2
1
0
0
0
1
0
2
0
0
0
1
0
0
0
0
2
1
0
1
2
2
0
0
0
1
1
0
0
1
2
0
2
1
0
0
0
0
0
3
0
0
0
2
0
1
1
2
0
1
1
0
1
0
0
0
0
1
1
0
1
2
0
3
0
0
1
1
0
0
0
1
0
0
2
0
0
0
0
0
1
2
0
0
1
0
0
0
0
3
0
0
0
0
1
1
1
0
2
2
0
0
1
0
1
2
2
1
0
0
0
0
0
0
1
0
1
1
1
2
0
1
0
0
0
0
0
0
1
1
3
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
4
1
0
1
0
2
0
1
0
0
1
3
0
0
0
0
7
0
0
2
0
2
0
0
2
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
1
2
1
1
1
1
1
2
1
0
0
0
4
1
0
1
1
2
3
0
1
0
2
1
1
0
0
1
0
0
0
3
0
0
2
1
0
0
0
1
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
2
2
0
2
0
0
0
0
1
0
4
1
2
0
0
0
1
0
1
0
0
0
0
1
0
1
0
1
1
0
0
2
1
0
0
0
0
2
1
0
0
0
1
0
0
2
1
10
0
2
0
0
2
1
2
0
1
1
0
2
1
0
0
0
1
1
0
0
1
3
1
2
0
0
1
2
2
0
0
2
2
1
0
1
0
0
2
1
0
2
0
2
0
0
2
0
1
0
2
0
0
0
1
0
0
0
2
2
0
1
1
1
2
0
0
1
0
1
0
2
1
0
0
0
0
3
2
2
0
0
0
2
0
0
0
2
2
0
1
0
2
0
1
0
3
0
2
0
0
0
0
0
1
0
0
1
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
1
2
0
0
2
0
1
2
0
1
0
1
0
2
0
0
0
0
0
2
1
0
1
0
0
0
1
0
2
1
0
1
3
0
0
0
0
2
1
0
0
1
1
2
2
0
6
0
1
0
2
1
1
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
2
1
0
1
1
0
0
1
0
2
2
1
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
2
2
1
0
0
0
0
1
0
1
0
0
0
0
2
2
2
0
1
0
0
2
0
0
0
0
0
0
2
0
0
1
1
2
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
2
2
0
1
1
1
0
0
2
1
1
1
1
1
1
2
0
1
0
0
2
3
0
1
1
2
0
3
0
0
0
0
1
0
2
0
0
0
0
1
0
1
0
1
1
0
2
1
0
0
0
2
1
2
2
0
0
0
0
0
0
0
2
1
1
1
0
0
0
0
0
1
0
2
1
0
0
0
0
1
0
0
0
0
1
2
2
2
0
1
2
1
0
0
2
1
0
0
0
2
0
0
1
1
0
0
1
0
0
1
1
3
3
0
0
0
0
0
0
0
0
0
1
0
1
0
2
1
1
0
2
0
1
0
0
0
1
0
0
0
1
2
0
1
0
0
0
1
2
1
0
0
0
0
2
1
0
1
0
0
1
0
0
1
0
2
0
0
2
2
2
0
1
1
0
1
2
2
1
1
0
0
2
1
1
1
0
0
1
0
0
0
0
0
1
0
2
1
1
1
1
3
1
0
1
0
0
2
1
0
2
0
0
2
0
0
2
0
0
0
2
1
0
0
2
1
0
1
1
1
2
0
1
3
0
1
1
1
0
2
0
1
2
1
0
0
0
2
0
2
0
2
0
2
0
1
3
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
1
1
0
0
2
1
0
0
2
1
1
0
2
1
0
2
0
1
1
1
0
1
0
0
0
0
0
2
0
1
0
1
1
0
0
0
0
2
0
0
0
0
0
2
1
2
0
1
0
2
2
0
0
2
1
1
1
1
1
0
1
0
1
0
1
1
1
2
1
0
0
0
2
1
1
0
0
0
0
1
0
1
1
1
0
1
1
2
1
1
2
0
1
1
0
2
1
0
0
0
1
1
1
0
2
1
0
0
1
1
0
0
0
1
1
1
2
2
1
2
0
0
0
1
0
0
1
0
0
1
1
0
1
0
0
0
0
2
0
2
0
0
2
1
1
0
0
2
2
1
0
2
0
1
0
1
0
0
1
1
0
0
2
1
0
0
0
1
1
0
2
2
0
0
0
1
0
1
0
1
2
1
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
2
0
2
0
0
0
0
0
0
0
0
2
0
2
1
1
0
2
3
0
0
2
0
1
3
1
2
0
0
0
2
2
0
2
0
2
0
0
2
2
0
0
1
1
0
0
0
0
1
0
0
0
2
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
1
1
1
1
0
0
1
2
4
0
0
0
1
0
0
2
2
0
0
2
0
1
0
0
0
0
1
2
2
2
2
1
0
0
0
0
0
1
0
2
0
2
2
2
0
0
0
0
0
0
0
1
0
0
0
0
1
1
2
3
0
2
0
0
0
2
1
0
2
0
1
1
2
2
0
1
1
0
1
0
2
2
0
0
1
0
0
0
0
1
1
0
2
1
0
0
1
2
0
1
0
0
1
0
1
0
0
2
0
0
0
2
0
2
0
0
1
2
2
1
0
0
0
0
2
0
1
0
1
0
0
1
0
3
0
1
1
0
0
0
1
0
0
0
0
0
0
1
2
2
0
0
0
1
2
0
0
1
1
0
2
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
2
0
0
1
2
2
1
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
2
2
2
2
1
0
0
0
0
1
0
0
0
0
0
0
2
0
1
2
0
0
1
2
0
0
0
0
1
1
1
1
0
0
2
2
0
1
2
2
0
0
0
2
0
1
0
0
0
2
1
2
2
2
0
2
0
0
1
1
1
0
2
2
1
0
0
0
0
2
2
0
1
0
0
0
0
1
2
1
2
0
0
1
0
0
2
2
0
2
0
0
0
2
0
2
0
1
0
0
2
2
0
0
0
1
1
0
1
1
1
2
2
1
0
0
1
2
0
0
0
1
0
0
0
0
0
2
0
0
2
1
2
1
0
1
1
0
1
2
1
1
0
0
0
2
1
1
2
1
0
0
1
0
3
2
0
0
2
1
3
1
1
2
0
0
0
0
2
0
0
1
1
1
0
0
0
0
0
1
0
1
0
1
3
2
2
1
1
0
0
0
0
0
1
0
0
2
2
2
1
1
0
0
1
0
1
1
1
0
1
0
0
1
0
0
1
2
1
1
0
2
2
1
2
0
1
0
2
1
1
0
0
0
0
2
2
0
0
1
1
2
0
6
0
1
1
1
0
1
1
2
0
0
2
1
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
2
0
1
1
2
0
0
1
0
0
2
2
0
0
2
1
1
1
0
0
0
0
0
0
0
0
1
0
0
3
2
0
0
1
2
1
1
2
0
2
1
0
0
1
0
1
0
4
0
0
0
0
0
2
2
1
1
0
0
0
2
2
0
0
2
2
0
1
0
0
0
1
2
0
0
2
0
0
0
2
0
0
1
0
1
2
2
0
0
0
0
2
2
0
0
0
0
1
0
2
0
0
2
0
3
2
1
2
0
0
2
1
0
1
2
0
1
0
2
0
6
1
0
0
2
0
0
0
3
2
0
1
0
1
2
1
0
0
0
1
0
0
0
1
0
0
0
0
1
2
3
1
2
0
2
2
0
0
0
0
3
0
0
1
1
2
0
2
0
1
1
1
0
0
1
2
0
2
0
2
1
0
0
2
1
0
1
3
0
1
0
0
1
0
1
1
2
1
1
0
1
1
0
2
2
0
0
3
0
0
0
1
0
1
0
2
0
1
1
0
1
1
0
2
1
1
0
1
0
0
1
0
2
1
2
1
0
0
2
0
1
2
1
2
0
0
2
0
0
0
0
0
0
1
2
2
0
3
6
2
0
1
0
0
0
3
1
0
0
0
0
1
2
0
0
0
1
0
0
1
0
0
1
1
2
0
0
0
1
0
0
0
1
2
2
1
0
2
1
0
0
0
2
0
2
0
1
0
0
1
0
0
0
2
0
2
2
0
0
0
0
0
0
3
2
1
1
0
0
1
0
1
2
0
3
2
0
0
0
0
0
2
1
1
0
2
0
1
0
1
2
1
1
0
0
3
1
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
1
2
1
0
0
0
1
1
0
0
0
1
1
2
1
1
1
1
2
2
0
0
0
1
0
0
0
1
0
0
0
2
1
1
0
1
0
0
1
0
0
3
0
1
0
0
1
0
1
0
2
0
2
0
2
0
0
2
2
2
2
0
0
1
2
0
1
2
0
0
0
0
0
0
0
0
1
2
1
0
1
0
0
0
0
0
2
0
0
2
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
1
0
2
2
0
0
1
0
3
1
2
1
0
2
0
0
2
2
1
2
1
1
1
3
2
0
1
1
1
1
0
0
0
2
0
0
0
1
2
0
0
0
2
2
0
1
1
3
2
0
2
0
0
0
2
0
2
2
1
0
0
0
1
0
2
2
0
0
0
0
1
2
2
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
1
1
0
0
2
2
0
0
0
2
1
1
1
0
2
1
0
0
1
2
2
0
0
1
0
2
1
0
0
0
0
0
0
1
1
2
0
2
0
0
1
1
0
0
2
2
1
2
0
2
1
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
1
1
1
0
1
2
1
2
0
1
2
1
1
1
1
1
0
1
0
0
2
0
1
0
2
1
2
2
0
0
0
2
0
0
0
0
2
0
0
0
2
0
2
1
0
0
3
1
1
0
0
0
0
1
1
1
1
1
2
0
2
0
0
0
0
0
1
2
0
2
0
2
0
0
0
2
0
1
1
1
4
0
1
3
0
1
0
0
1
1
2
0
2
2
1
0
0
1
0
0
0
1
1
2
0
2
1
1
2
0
0
1
0
1
1
2
0
0
0
3
0
0
0
1
2
2
1
0
2
0
0
1
0
0
0
1
0
0
1
0
0
0
2
2
0
0
2
1
2
2
1
2
1
1
1
2
0
1
2
1
1
0
1
0
2
0
0
1
1
0
1
1
0
0
0
2
0
0
2
0
0
2
1
1
1
0
0
2
1
0
2
1
1
2
0
0
0
0
1
0
0
2
2
2
0
0
0
1
0
0
0
1
2
1
0
0
0
0
0
1
1
3
2
1
0
0
0
0
0
0
1
0
1
0
0
0
2
0
2
0
0
1
0
0
1
3
1
0
0
0
0
0
2
1
3
1
0
1
0
0
1
1
0
0
2
0
0
1
1
0
1
3
0
0
1
0
1
1
0
0
1
0
1
2
1
1
0
0
1
1
1
2
1
0
1
1
1
3
0
1
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
3
2
0
1
0
0
1
0
0
0
1
1
0
2
0
2
0
2
0
1
1
1
0
1
2
2
1
2
2
0
0
1
1
0
1
0
2
1
1
0
1
2
0
0
2
1
0
1
2
2
0
1
0
1
2
2
0
0
0
2
2
1
1
1
1
0
1
1
1
0
0
0
1
0
0
0
1
0
2
1
1
0
0
1
1
0
2
1
1
0
2
0
2
0
2
2
1
0
2
2
0
0
1
0
2
0
0
1
0
2
2
0
1
0
0
0
0
1
0
2
1
0
0
1
2
0
0
0
2
0
0
0
0
1
0
1
0
0
1
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
1
3
0
1
2
0
0
1
0
2
2
0
0
1
2
2
0
0
1
1
0
1
1
3
0
0
1
0
0
1
2
1
2
0
1
0
0
2
1
0
1
0
2
0
0
0
0
0
1
0
2
2
1
0
0
2
1
0
1
4
0
0
0
2
0
2
0
0
0
3
1
1
1
1
2
1
0
0
0
1
0
0
1
0
0
2
1
0
1
2
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
3
1
2
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
2
0
1
1
0
0
0
2
0
0
1
0
0
0
2
2
2
0
0
0
0
2
0
2
1
0
2
1
0
2
0
2
0
0
2
0
1
0
0
0
2
1
1
0
0
0
0
2
0
0
2
0
1
1
0
2
0
0
2
1
2
0
0
1
0
0
1
1
0
2
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
1
0
2
1
0
1
0
2
0
1
1
0
0
0
0
1
5
0
2
0
0
2
1
1
1
3
0
0
0
2
0
1
0
0
2
0
1
2
1
2
0
0
0
0
0
2
1
0
0
1
0
0
2
1
0
0
0
1
2
0
2
0
0
2
0
0
0
1
0
0
2
0
0
1
2
2
1
1
1
2
0
0
0
2
1
0
0
1
0
2
0
0
2
2
0
0
0
1
0
2
3
0
1
0
0
1
1
0
2
2
1
2
0
4
0
1
0
1
2
0
1
0
2
1
1
2
0
1
1
2
1
1
0
3
0
2
2
2
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
2
2
1
0
0
0
0
0
1
1
1
0
0
0
0
0
2
0
3
1
0
0
0
2
2
0
1
0
2
1
0
0
2
0
0
1
0
0
2
1
0
0
2
1
0
0
0
1
0
1
0
1
0
0
1
0
2
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
2
0
2
2
0
1
0
0
0
1
0
1
0
1
1
0
0
1
0
2
0
1
0
0
1
0
2
1
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
2
2
1
1
0
1
2
0
0
1
0
0
1
0
3
0
1
0
2
1
0
0
0
1
2
0
1
0
0
0
0
0
2
0
1
2
2
0
2
0
0
0
2
2
0
0
0
0
0
1
1
1
1
0
0
0
0
1
2
0
1
0
0
1
0
0
0
1
0
1
0
1
1
2
1
0
2
0
3
1
1
0
0
1
0
2
1
0
2
2
2
1
0
1
0
0
0
2
2
0
1
2
0
0
0
2
0
1
0
0
2
0
1
0
1
0
1
0
0
0
0
0
0
0
2
0
1
1
0
0
1
0
0
1
0
1
0
0
0
2
2
0
2
2
1
1
1
3
0
0
1
1
0
0
0
1
1
3
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
1
2
0
0
0
0
2
0
2
2
0
0
1
0
1
2
1
0
0
0
0
2
1
1
0
2
1
1
0
0
0
1
1
0
0
1
1
0
0
1
0
1
1
2
1
0
0
1
0
2
0
1
0
0
1
2
0
3
1
2
0
0
0
0
0
1
0
0
0
0
1
0
1
0
2
1
0
2
1
0
0
2
0
0
0
0
2
0
0
2
0
0
2
2
0
2
0
0
0
0
2
2
0
1
2
2
1
0
1
2
1
1
0
0
1
0
2
2
2
1
0
0
1
1
0
2
1
0
2
0
0
0
5
0
0
1
0
0
1
2
1
0
1
1
0
2
1
1
0
1
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
1
0
1
1
0
1
1
0
0
0
2
0
1
1
2
0
0
2
1
1
0
0
0
2
0
2
2
2
0
0
2
2
1
0
0
0
1
1
0
0
1
0
0
2
1
0
1
2
1
0
2
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
2
0
2
1
0
2
2
0
1
0
2
2
0
0
1
0
1
1
0
1
2
1
2
2
1
1
0
0
1
0
2
1
0
0
0
0
2
4
0
0
2
0
0
1
1
2
0
2
0
1
0
0
1
1
0
2
2
0
0
0
1
0
0
1
0
0
0
0
2
0
2
0
0
0
2
1
2
1
0
0
1
1
0
2
0
0
0
0
2
2
1
2
1
0
0
0
0
0
0
2
2
0
1
1
2
0
0
0
1
2
0
2
0
2
3
1
0
1
0
1
2
0
1
1
0
0
0
1
0
0
3
0
0
1
0
0
0
1
2
1
0
0
0
0
1
0
1
1
0
2
1
0
0
2
0
2
0
1
0
0
2
0
2
2
0
2
1
0
0
0
1
0
1
1
0
2
2
2
2
0
2
1
0
0
0
0
0
0
0
1
0
1
1
0
0
1
1
2
2
0
0
1
0
1
1
3
3
2
1
0
1
0
0
0
3
0
1
0
1
1
1
1
0
0
0
2
0
0
0
0
0
1
0
2
0
0
1
2
0
0
1
1
1
0
2
1
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
1
1
0
0
2
2
1
0
1
0
0
0
0
3
0
1
2
1
0
1
2
2
1
0
0
0
0
2
0
2
0
2
0
1
2
1
1
1
0
1
2
0
1
1
0
2
0
0
0
0
0
0
3
1
0
2
1
0
0
2
0
0
0
2
0
1
0
0
0
2
1
0
1
0
0
1
1
0
0
1
0
2
1
0
1
2
1
2
0
0
1
0
1
3
0
2
0
0
0
0
1
1
0
1
0
0
1
1
0
0
0
2
0
1
0
0
0
0
1
0
1
1
0
2
0
0
0
0
0
0
1
1
0
0
0
1
2
2
0
0
0
1
0
0
1
2
3
1
1
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
2
3
3
0
1
0
0
0
0
1
1
1
2
0
0
1
2
0
2
0
1
2
1
0
2
2
0
0
1
0
0
2
2
1
0
0
0
0
0
1
0
1
1
0
1
0
0
2
0
1
1
0
0
1
0
1
1
2
0
1
1
0
0
2
1
0
1
0
0
0
0
1
2
0
2
1
2
0
0
3
0
2
0
0
0
0
0
2
0
0
0
0
2
0
1
1
2
3
0
2
2
0
1
2
1
0
0
1
1
0
0
1
0
0
0
0
2
0
0
1
0
2
0
1
1
0
6
0
1
1
2
1
0
2
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
3
0
0
0
0
0
1
3
0
1
0
0
0
0
0
1
0
2
0
0
2
0
2
1
0
1
1
0
1
0
1
1
1
0
0
0
0
1
2
1
3
2
1
2
3
2
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
2
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
1
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
5
0
0
1
0
1
2
2
1
1
0
2
0
0
0
0
2
0
0
3
0
1
1
0
0
2
0
2
0
0
1
2
0
1
1
0
2
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
2
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
2
0
1
0
0
0
0
2
1
1
1
0
1
0
3
0
0
0
0
1
0
2
0
3
1
2
0
1
0
1
1
0
0
0
0
0
1
0
2
3
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
2
0
0
0
1
2
0
2
1
0
0
1
0
1
1
1
1
1
0
1
0
0
2
0
0
2
0
0
0
1
2
2
0
1
0
0
1
1
0
1
0
0
0
1
1
2
2
2
0
0
2
0
1
0
2
2
2
2
2
2
1
0
0
0
1
2
0
1
0
1
0
0
0
1
2
0
1
0
0
1
2
0
0
1
0
0
0
2
0
0
1
2
0
1
0
1
0
0
0
2
0
1
1
0
0
1
2
1
2
0
0
2
2
0
0
1
0
0
2
0
1
1
0
0
0
1
0
1
0
1
0
0
1
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
2
2
1
0
0
2
2
2
0
0
1
1
2
0
1
0
0
0
5
0
0
3
2
0
0
1
0
0
0
1
1
2
0
0
0
0
0
0
0
2
1
1
1
0
1
2
0
0
0
1
0
1
2
2
1
0
1
1
0
2
1
0
0
0
1
0
2
1
2
0
1
0
0
2
2
0
0
1
0
0
2
0
0
1
2
0
0
2
0
2
2
0
0
1
2
0
0
2
2
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
1
0
2
1
1
1
0
0
0
0
2
0
0
1
3
0
2
0
1
2
0
0
0
0
0
2
1
0
0
0
1
0
1
0
1
0
1
2
0
1
2
0
0
0
0
0
0
0
0
1
1
0
1
1
2
0
0
0
2
1
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
1
2
0
0
3
0
1
0
0
1
0
1
1
2
0
0
0
1
0
1
1
0
0
2
0
1
1
0
0
0
0
0
1
3
2
0
0
2
1
2
2
0
0
1
0
0
0
2
1
0
2
1
2
1
1
2
0
1
1
0
1
0
0
0
2
1
1
2
2
0
0
0
0
0
2
1
0
0
1
0
1
2
1
1
1
1
0
0
2
0
2
0
0
1
2
1
0
1
0
1
0
0
0
0
1
0
2
0
1
1
0
1
2
0
0
2
0
0
0
0
2
2
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
2
2
2
2
0
0
0
1
0
0
0
2
2
0
0
0
1
0
0
0
1
1
2
0
1
0
1
2
1
0
0
0
2
2
2
0
0
0
0
2
0
1
1
1
0
0
1
0
2
2
2
0
0
2
1
0
0
2
1
2
1
2
0
1
0
0
1
1
0
1
1
0
0
0
2
0
0
1
1
0
0
0
0
1
0
0
1
1
1
0
0
1
2
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
3
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
2
0
0
2
1
2
0
0
0
2
1
0
0
1
0
0
0
0
0
0
1
0
0
3
2
1
0
2
2
1
2
0
0
0
1
1
1
1
0
1
2
0
0
0
2
1
0
1
0
0
1
0
0
1
0
1
0
1
1
0
1
2
0
2
0
1
2
0
1
0
1
2
2
0
0
1
1
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
1
1
0
0
0
3
2
0
0
1
2
2
1
1
0
1
0
0
0
2
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
2
1
0
0
0
1
0
1
2
0
3
2
0
2
0
0
0
2
0
1
2
0
2
1
0
2
0
2
0
0
2
2
3
1
2
1
1
1
0
2
2
0
0
2
2
1
1
0
1
1
2
0
1
0
0
1
1
0
0
0
0
0
0
1
0
1
2
0
0
0
1
1
0
2
2
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
2
1
0
0
1
1
1
0
0
2
1
0
0
0
0
3
0
0
2
1
2
0
0
0
1
1
0
2
0
0
0
1
1
0
0
1
1
1
0
2
2
0
2
0
2
0
1
0
1
0
2
0
1
0
0
1
0
0
1
1
0
0
0
2
1
0
0
0
1
0
1
0
2
0
1
1
0
0
1
1
2
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
2
0
1
1
0
2
1
2
1
1
1
0
2
2
1
1
1
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
2
0
0
0
1
1
0
1
0
2
0
0
0
1
1
0
0
1
0
2
0
1
0
2
0
2
0
1
1
0
2
2
2
1
2
0
3
2
0
1
0
1
0
0
0
0
1
1
1
0
0
0
1
2
1
1
0
0
0
0
0
2
0
2
0
2
1
1
1
0
1
2
2
2
0
0
0
0
0
0
1
1
1
0
2
1
2
0
1
2
0
0
0
0
0
0
1
0
1
0
0
1
2
0
0
2
2
0
0
0
2
1
0
0
1
0
0
0
0
0
0
4
0
0
2
1
0
0
0
0
0
1
2
0
2
0
0
2
2
1
0
1
0
0
2
0
1
0
0
1
2
0
2
2
2
2
2
2
1
0
1
2
0
2
0
0
2
1
0
0
0
0
2
0
1
0
0
0
1
0
2
0
1
2
1
0
1
1
0
1
0
0
0
1
0
0
0
2
1
2
0
1
0
2
0
2
0
0
0
2
0
0
0
1
0
2
2
1
1
3
1
3
1
2
1
0
1
1
0
1
1
1
0
0
0
1
0
1
0
0
0
1
2
0
0
0
1
0
0
1
3
2
2
0
0
0
0
0
0
1
1
0
0
1
1
0
1
0
0
0
1
0
2
0
0
2
2
1
1
0
2
0
0
1
0
0
0
2
1
0
0
1
2
1
1
2
0
2
0
2
0
0
0
0
0
0
0
0
0
1
1
3
6
1
0
1
0
1
1
0
0
2
0
1
1
1
1
0
3
1
1
1
0
0
1
2
0
1
0
2
0
1
0
3
2
2
0
0
0
1
0
2
0
0
1
1
2
0
0
0
0
0
0
1
1
1
0
0
1
2
1
1
0
1
0
0
0
0
1
1
1
1
2
1
2
0
1
1
2
0
1
0
1
0
2
0
1
2
2
1
2
1
0
2
0
0
0
0
2
0
0
0
1
1
0
0
1
0
1
1
0
2
0
2
0
0
2
3
2
0
1
0
0
0
0
2
0
0
0
0
3
0
0
0
1
0
0
2
0
0
0
2
0
1
2
0
0
3
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
3
0
4
2
2
0
1
0
0
0
3
0
2
2
0
1
0
2
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
1
0
0
1
0
0
0
2
0
0
0
1
0
1
0
2
2
0
1
0
0
1
2
1
1
1
1
1
0
0
1
0
0
2
2
0
2
0
0
0
0
0
0
0
2
1
3
1
1
0
1
0
1
0
0
2
0
2
0
0
0
1
0
1
0
2
2
0
2
2
1
0
1
1
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
2
0
0
2
0
1
1
3
0
2
0
1
0
3
1
0
1
1
0
2
0
0
0
0
2
0
0
2
0
0
0
3
0
0
4
2
0
2
0
2
1
0
2
2
0
2
1
2
5
2
0
0
0
1
2
1
1
0
1
0
1
1
0
0
0
2
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
2
0
0
0
0
1
2
3
0
0
2
1
1
1
1
1
0
0
2
2
3
1
1
0
2
1
0
2
2
0
0
1
2
1
0
1
1
0
0
0
2
1
1
1
0
1
0
0
0
0
2
0
0
0
1
1
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
1
3
0
2
0
2
1
0
1
0
1
2
3
1
0
0
2
1
0
0
0
2
2
0
0
0
0
0
0
0
1
1
0
0
1
1
0
1
2
0
0
0
0
0
0
0
2
0
0
2
1
2
1
0
0
1
1
0
1
0
0
1
2
1
1
1
2
0
0
0
1
0
1
0
0
2
0
2
0
2
2
1
2
2
0
1
1
0
1
2
0
0
2
2
2
2
0
1
1
1
0
1
2
0
2
0
0
0
1
1
3
1
1
0
3
0
1
0
1
0
0
1
1
2
1
0
1
0
1
1
0
0
1
0
0
0
0
0
0
1
3
0
2
2
0
0
1
0
0
0
2
1
2
0
0
1
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
1
1
0
2
2
0
0
2
1
1
0
2
0
0
0
5
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
1
1
0
1
2
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
2
0
2
0
1
1
5
1
2
1
1
0
0
2
1
0
0
0
0
1
0
0
2
1
0
0
1
1
0
0
1
0
2
1
1
0
2
1
2
1
1
0
2
1
3
2
1
0
2
1
2
0
0
1
2
0
1
0
0
0
2
0
0
1
0
2
1
1
0
1
0
1
2
2
0
1
0
0
0
1
1
0
1
1
0
1
0
0
2
2
1
1
0
0
1
0
0
1
2
2
1
0
1
0
0
1
0
0
1
0
0
0
1
0
0
1
1
0
0
2
2
1
0
0
0
2
1
1
1
3
1
1
0
0
0
0
1
0
0
2
1
1
0
1
0
0
0
0
0
1
1
1
3
0
0
0
1
1
1
0
1
1
1
0
0
0
0
1
1
0
0
2
0
1
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
1
1
1
0
2
0
0
1
0
0
0
1
1
1
0
1
1
0
2
1
2
2
0
0
0
1
1
2
0
1
0
2
0
0
2
2
0
1
2
1
1
0
2
1
0
2
2
0
0
1
1
0
0
2
0
0
1
1
0
0
6
0
2
0
0
1
0
0
0
0
1
0
1
1
3
0
0
0
1
0
3
1
0
3
1
0
3
0
0
2
2
1
2
1
1
0
1
0
0
1
2
0
2
1
2
1
2
0
1
0
0
0
0
1
0
0
0
2
0
3
0
1
0
0
0
2
1
1
1
1
1
0
0
0
0
0
1
1
0
0
1
1
1
0
1
0
1
0
0
0
0
3
1
1
0
0
0
2
0
1
2
0
1
0
0
1
1
0
2
2
1
2
0
1
0
1
0
0
1
1
1
0
2
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
2
2
2
0
0
0
0
0
2
1
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
2
2
0
2
1
0
2
2
1
2
1
0
0
0
0
2
2
1
0
0
0
0
1
0
0
0
0
0
2
1
0
2
0
1
1
0
0
1
0
0
0
0
0
1
0
0
2
1
2
0
4
0
3
0
1
2
1
0
0
1
0
0
1
0
1
2
0
0
1
1
1
2
2
0
1
1
0
2
0
0
1
0
0
0
0
1
1
1
0
2
2
0
0
0
1
2
2
0
1
2
0
0
2
0
2
1
2
0
1
0
0
1
4
1
0
1
1
1
0
3
0
0
0
0
0
0
0
1
0
1
2
1
2
0
0
2
0
2
2
1
1
2
0
1
0
0
0
1
0
1
1
2
0
1
2
0
2
0
0
0
2
0
2
0
0
0
0
0
2
0
2
0
1
0
0
1
2
0
4
0
0
0
1
2
0
2
1
1
0
1
2
0
2
1
1
1
0
2
0
1
2
0
2
2
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
3
0
0
2
2
0
2
0
0
2
1
2
1
1
2
0
0
0
2
1
2
0
1
0
1
1
0
0
1
2
0
0
2
2
0
1
2
1
1
2
1
0
0
1
0
0
2
4
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
2
0
1
2
0
0
2
2
0
2
1
0
2
2
1
0
1
0
2
0
1
1
0
2
0
2
0
1
1
0
2
0
0
0
4
0
0
1
1
0
0
0
1
2
0
0
2
0
0
0
0
0
1
1
1
1
2
2
1
0
1
0
0
0
3
2
1
0
0
0
0
1
0
2
1
1
1
0
1
2
2
0
2
0
1
0
0
0
0
1
5
1
0
1
0
1
0
0
1
0
2
0
0
0
3
1
0
0
0
1
0
0
1
0
1
0
2
2
0
2
3
0
2
0
0
0
0
1
0
0
0
0
0
2
0
1
1
0
0
1
2
2
2
0
1
2
0
1
2
3
2
2
1
3
0
0
0
1
2
0
0
0
2
0
3
0
0
1
2
2
2
0
1
0
0
0
2
0
1
2
1
0
2
2
0
0
2
0
1
0
0
0
0
1
2
0
0
1
0
1
0
1
2
2
0
0
2
1
3
0
0
1
0
0
1
0
2
0
0
0
0
1
2
0
3
0
0
0
0
0
2
1
1
2
0
1
0
2
3
0
2
0
0
0
0
2
0
0
0
1
0
1
0
0
1
2
0
2
2
0
0
0
0
1
1
0
1
0
0
1
0
1
2
0
1
0
0
0
2
1
0
0
1
0
2
0
0
1
0
0
1
0
0
0
2
2
1
0
0
0
0
2
2
2
0
2
2
0
3
0
0
0
2
0
1
0
2
0
1
2
0
0
0
0
3
2
0
0
0
1
0
0
2
1
0
2
1
0
0
1
0
2
1
0
1
0
1
2
2
1
1
0
0
0
1
0
0
0
0
0
0
0
1
1
2
0
2
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
1
0
1
1
1
0
0
2
2
0
2
0
2
2
0
0
1
2
1
0
0
0
0
0
4
0
2
1
0
1
0
2
0
0
0
0
2
0
0
2
0
1
1
3
0
1
2
1
3
0
0
0
2
0
1
0
0
0
0
3
2
0
0
1
0
2
1
0
0
1
1
0
0
2
0
0
0
2
2
1
1
2
2
1
0
2
2
1
1
2
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
3
0
1
0
0
0
2
0
2
0
0
0
1
2
1
0
0
0
1
2
2
0
0
1
0
1
3
0
0
1
0
1
1
1
2
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
1
2
0
1
0
0
3
2
1
1
0
0
0
1
3
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
2
0
1
1
2
1
1
0
0
1
0
0
1
1
1
0
2
0
0
1
0
2
0
1
0
0
2
1
1
0
1
1
0
0
0
0
0
3
2
0
2
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
2
0
2
2
0
1
2
0
3
0
3
0
0
0
1
1
0
0
1
1
2
2
1
0
0
0
0
2
0
0
0
0
3
0
0
1
0
1
2
0
1
0
1
1
0
0
0
1
0
1
2
0
0
0
1
1
0
0
2
1
0
1
1
0
1
1
1
1
0
0
2
1
1
0
1
0
1
0
1
0
2
2
0
2
0
2
1
0
0
1
1
1
2
0
0
1
2
0
1
1
1
0
0
2
0
0
2
2
1
0
0
0
0
0
0
2
0
2
1
2
1
0
1
0
0
0
2
2
2
0
0
0
0
1
2
0
0
2
1
0
2
0
0
1
0
0
3
1
0
0
0
0
0
0
1
0
0
3
0
0
1
0
1
2
2
0
0
1
1
2
1
0
0
0
0
2
0
0
1
0
0
0
0
2
2
1
3
0
0
0
2
0
1
0
0
1
0
1
0
2
0
0
2
0
0
1
1
0
0
0
0
2
2
1
2
1
0
2
1
0
0
0
2
1
0
2
2
4
3
0
0
0
4
2
1
0
0
1
0
0
0
0
0
0
1
0
0
1
2
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
1
2
0
2
0
0
0
0
0
2
1
1
0
0
1
1
1
0
0
1
0
2
1
1
2
0
0
0
1
0
0
0
0
0
3
1
0
1
2
2
0
0
0
2
2
0
1
0
1
0
1
0
1
2
0
0
0
0
1
2
2
0
0
1
1
0
1
0
2
2
2
0
0
0
2
2
0
0
0
1
0
1
2
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
2
2
1
0
0
0
0
1
1
1
0
0
0
0
1
1
3
0
1
2
1
2
1
1
2
2
1
3
0
0
1
2
0
0
2
2
0
1
0
0
2
1
0
2
0
2
0
0
0
1
1
2
2
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
1
2
1
0
1
2
0
0
0
0
0
0
1
0
1
0
2
0
1
0
0
1
1
0
2
0
0
1
2
0
1
0
0
0
0
1
0
0
2
2
0
1
0
1
1
0
0
2
0
0
0
1
1
1
2
0
1
1
0
0
0
2
0
1
1
1
1
0
0
0
0
0
1
2
0
0
1
2
2
2
0
0
0
0
2
1
0
2
0
0
0
1
0
0
2
0
1
2
0
0
0
1
0
0
0
2
0
0
0
2
2
2
0
1
0
2
1
0
0
0
2
1
0
2
2
1
1
0
1
0
0
0
1
0
2
1
1
2
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
3
0
2
0
0
2
2
1
1
1
2
0
1
2
1
0
0
3
0
0
0
0
1
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
2
0
1
1
1
0
0
2
0
0
2
0
1
1
1
0
1
0
1
0
1
2
0
0
0
0
1
3
0
1
0
2
2
2
0
2
0
0
2
2
0
2
0
0
1
0
0
0
1
0
2
2
2
0
0
0
0
1
0
0
0
0
2
0
1
0
0
1
2
0
1
3
0
0
1
0
1
2
0
1
0
0
0
0
0
1
0
0
1
0
2
1
1
0
1
0
0
0
2
0
0
0
1
0
0
2
0
1
0
0
2
0
0
0
0
1
2
0
0
1
0
0
2
3
1
1
0
2
0
1
1
1
0
0
1
0
0
0
1
0
1
2
0
1
0
0
2
1
0
0
0
0
1
0
0
0
2
0
0
3
0
1
1
0
4
0
0
2
0
0
0
0
1
1
0
0
5
1
0
1
0
2
1
1
0
0
1
0
0
0
0
0
0
1
0
0
2
0
2
0
1
1
0
2
0
0
0
0
0
0
0
0
0
2
0
2
1
1
0
1
0
1
0
0
2
0
1
0
2
1
1
2
0
1
0
0
0
0
1
0
0
0
2
1
4
0
2
2
2
1
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
2
2
1
0
2
2
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
1
1
0
2
1
2
1
1
2
2
1
0
0
1
0
0
0
2
0
1
0
0
1
0
2
1
0
0
0
1
0
0
2
1
2
0
0
2
0
1
0
1
0
2
0
2
0
0
0
3
0
1
0
0
2
0
2
0
0
0
0
0
0
2
2
0
2
0
0
2
0
0
0
0
0
0
0
0
1
2
1
0
0
0
1
1
0
1
1
0
0
2
1
2
0
1
1
0
1
1
3
0
1
1
1
0
0
0
1
0
1
1
0
1
1
1
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
1
0
1
2
0
1
0
1
2
2
0
0
0
0
0
0
1
0
1
0
1
1
1
0
0
2
0
0
0
0
3
0
0
0
0
0
0
2
1
0
0
0
0
0
1
1
1
0
0
0
0
2
0
0
0
0
1
0
0
2
0
1
0
0
2
0
0
0
1
0
4
0
0
0
0
0
3
2
2
1
1
0
1
0
1
1
0
1
2
1
2
2
0
0
0
0
0
2
0
0
1
0
2
0
0
1
1
0
0
2
0
0
1
0
2
2
0
0
0
2
0
0
0
0
0
0
2
0
2
2
1
0
0
0
0
0
2
0
0
1
0
0
0
1
1
1
1
1
1
0
2
1
0
0
1
2
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
2
0
1
0
0
2
1
1
0
2
0
3
0
0
0
0
1
0
1
1
0
1
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
2
1
0
1
1
1
1
0
0
0
1
1
0
1
1
2
1
2
0
1
1
1
2
2
2
0
0
0
0
2
0
1
2
0
0
0
1
0
1
2
0
0
0
0
1
0
2
0
0
0
2
1
1
1
0
2
2
0
1
0
0
1
0
1
2
0
0
0
0
0
1
0
0
0
0
2
1
0
1
2
1
0
1
0
0
0
2
1
2
1
0
0
0
0
0
2
0
2
1
1
2
0
2
0
2
1
0
1
1
2
0
1
1
0
0
0
0
5
1
1
2
0
1
0
1
0
0
0
0
0
1
1
5
0
2
0
0
1
1
1
1
1
0
0
1
0
0
1
0
2
0
0
0
1
1
1
0
0
1
0
1
0
0
0
1
1
2
2
0
0
0
0
0
0
0
0
2
0
1
0
1
1
0
0
0
1
2
2
1
0
0
0
0
0
1
0
0
2
3
0
0
0
0
0
1
0
0
1
2
0
2
2
1
0
0
0
1
0
0
2
2
1
1
1
0
1
0
0
1
1
0
2
1
1
0
0
1
1
1
0
0
0
0
0
3
2
0
1
3
1
0
0
0
2
1
2
0
2
1
1
0
0
2
3
1
1
1
0
2
1
2
0
0
2
0
2
1
2
2
0
1
0
0
0
1
1
1
0
2
0
2
0
0
2
1
2
0
1
0
1
1
1
0
1
1
2
0
2
0
0
0
0
0
2
1
3
0
0
0
2
2
1
2
0
1
0
1
0
0
2
0
2
0
0
2
0
0
1
1
0
0
2
2
0
1
1
0
1
2
0
2
0
0
0
0
1
0
0
0
1
0
2
0
2
2
0
0
0
0
0
2
0
2
1
2
0
0
2
1
0
2
0
2
0
0
0
0
2
0
0
1
0
1
0
1
0
0
1
0
2
2
2
1
1
0
0
0
1
1
0
0
1
0
0
0
1
2
3
1
2
0
0
0
0
0
1
0
0
2
0
0
0
1
1
0
1
0
1
2
0
1
0
0
0
0
0
0
0
2
0
2
1
2
0
3
1
2
0
2
2
0
1
1
0
7
0
0
0
0
0
2
1
0
2
0
0
2
1
0
0
1
1
0
0
0
0
1
0
1
1
3
1
0
0
0
0
1
1
1
0
0
1
0
1
0
0
0
2
0
2
0
0
2
2
2
2
0
2
1
0
2
2
1
1
0
0
2
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
2
2
0
2
0
0
1
0
2
0
0
0
0
0
1
0
0
2
1
0
1
2
0
0
1
2
1
0
0
0
0
1
2
0
0
1
0
0
1
0
0
0
0
0
2
2
1
0
0
0
1
0
0
0
2
0
3
0
0
0
1
0
0
1
2
0
0
1
0
0
1
1
2
2
0
2
0
2
0
0
2
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
2
2
1
1
1
0
1
1
0
0
0
0
2
0
0
0
0
2
0
2
0
1
0
2
0
0
0
1
0
1
2
0
1
0
0
1
2
1
1
1
0
2
0
1
0
2
0
0
0
2
0
0
0
2
1
1
0
0
2
1
1
1
1
1
1
0
0
0
1
0
0
1
0
0
1
3
1
0
1
2
0
1
0
0
1
1
0
2
0
0
1
0
1
0
0
0
0
2
0
0
1
2
0
1
0
0
0
0
0
3
0
0
2
2
2
2
0
1
0
2
1
0
0
1
0
0
0
0
0
1
0
1
2
2
1
1
0
0
1
0
1
0
0
2
0
0
1
2
0
0
0
0
0
0
2
0
2
0
0
0
3
0
0
1
1
0
0
0
0
2
0
0
0
1
0
0
0
1
1
2
0
0
1
0
1
0
0
0
0
0
0
0
1
1
1
2
0
3
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
3
0
0
1
2
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
1
4
2
0
0
1
0
0
1
0
2
2
0
0
0
1
1
2
2
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
2
1
0
0
1
0
0
0
0
2
0
0
1
0
0
0
1
0
2
2
0
0
2
0
1
0
0
1
0
2
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
1
2
0
0
0
0
4
0
1
1
2
2
0
1
0
0
2
0
2
1
1
0
1
0
2
2
1
0
1
0
1
0
3
0
0
1
1
1
1
0
3
0
4
3
1
0
1
0
1
2
0
0
3
0
1
0
2
2
1
1
2
0
0
0
2
2
0
1
2
0
1
0
0
2
0
0
0
2
0
1
4
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
1
0
1
1
1
3
0
0
1
2
1
0
0
0
3
0
1
0
0
1
2
2
1
2
1
1
1
0
0
0
0
0
1
1
1
0
0
0
2
0
0
1
1
0
0
2
0
2
1
0
0
0
1
0
0
1
2
0
1
0
2
0
0
0
0
0
2
0
0
0
2
0
1
2
1
0
0
0
2
0
2
2
1
1
0
0
1
2
0
2
0
0
0
0
0
1
1
0
2
1
2
0
0
0
1
1
1
0
1
0
0
0
0
0
2
0
2
1
1
0
2
1
0
1
2
1
0
1
0
0
0
1
1
0
0
2
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
2
0
1
1
0
0
0
2
0
2
0
1
2
1
0
0
1
0
0
0
2
0
2
2
1
2
1
0
1
3
0
0
4
1
0
1
1
1
0
1
1
0
1
0
0
0
1
2
1
2
0
0
0
0
0
1
2
2
1
1
2
0
2
1
0
2
0
1
0
0
2
0
1
0
0
2
2
0
0
0
1
0
2
0
2
0
0
0
1
0
0
0
2
0
1
0
0
2
1
0
0
2
1
0
0
1
0
1
3
2
0
1
0
1
2
0
0
0
0
1
1
0
1
2
1
4
0
0
0
0
2
1
0
2
1
2
3
0
0
0
1
2
0
2
0
2
1
0
0
0
0
2
1
0
0
1
1
0
1
0
0
2
0
0
1
2
0
0
0
0
0
1
1
2
0
1
2
1
0
1
0
2
1
1
0
0
0
2
2
1
0
1
0
0
2
2
2
0
0
0
0
3
0
2
0
1
0
0
1
1
0
1
0
1
0
0
0
0
1
0
0
2
2
0
1
2
2
0
0
0
0
1
1
2
1
0
0
0
1
1
1
0
1
0
0
0
0
1
1
2
0
2
2
1
0
1
2
1
0
0
0
0
0
2
2
0
0
0
0
0
0
3
1
1
2
0
2
1
2
2
1
4
1
1
0
1
0
0
2
1
0
2
0
0
1
0
2
0
1
0
0
0
1
2
0
0
0
0
1
0
1
0
1
0
0
0
1
2
1
1
1
2
1
0
1
0
1
1
1
0
2
1
0
1
0
1
0
0
0
1
1
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
1
0
0
1
1
1
1
0
1
0
0
1
0
0
0
0
2
0
2
2
0
0
0
0
1
0
2
0
0
1
1
0
0
0
0
0
0
0
6
1
1
0
2
0
2
0
1
1
1
0
2
1
1
1
1
0
0
2
2
0
1
1
1
0
0
0
1
0
1
0
0
0
1
1
0
0
1
0
1
1
0
1
1
0
2
1
0
2
0
1
2
0
2
2
3
0
0
3
2
0
0
0
1
0
2
0
0
1
0
1
0
0
0
0
0
2
1
1
1
0
2
0
1
2
0
0
2
2
1
2
2
0
0
0
1
0
0
0
0
2
0
1
0
1
0
2
0
0
0
1
0
0
2
1
0
3
1
0
0
0
0
2
2
1
1
2
0
0
0
0
1
0
1
2
4
0
0
1
0
2
2
1
0
3
0
2
2
0
2
2
0
1
3
1
0
1
1
0
0
0
0
0
0
2
2
0
0
2
0
1
0
0
1
0
1
0
0
0
1
2
0
1
0
0
0
2
1
0
0
0
0
0
1
2
0
1
0
0
0
0
0
1
0
2
0
1
1
0
0
0
3
2
1
2
1
1
2
0
2
1
0
0
0
0
0
2
1
0
0
0
2
0
1
1
0
1
1
1
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
1
1
0
0
0
1
0
0
0
2
0
1
0
0
0
0
1
1
2
3
2
0
1
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
1
0
1
0
0
2
0
0
1
0
0
0
2
0
1
1
0
0
2
2
0
2
0
0
0
0
2
0
2
0
1
1
0
2
1
0
0
0
0
1
0
0
1
1
1
0
0
0
1
1
0
2
0
0
0
1
0
1
2
2
1
1
0
2
2
0
2
1
1
1
0
0
0
1
0
1
0
4
0
1
0
0
0
2
2
2
1
2
2
0
0
2
2
0
1
0
0
2
2
0
1
1
1
1
0
1
0
1
1
2
1
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
1
0
1
2
2
0
1
0
1
1
0
0
0
0
2
0
3
0
1
0
1
1
0
2
0
0
2
0
2
0
0
2
0
0
0
0
0
0
1
1
0
0
0
2
0
0
1
0
0
0
0
0
0
3
2
0
0
2
1
0
1
1
2
1
2
0
0
0
1
2
0
0
0
2
6
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
1
0
0
2
1
3
0
1
1
0
0
0
0
0
0
1
3
0
0
0
1
3
1
2
0
0
0
2
2
2
1
0
1
0
0
0
0
0
1
0
2
0
2
0
1
1
1
1
2
0
0
0
0
0
1
0
0
0
1
1
1
2
0
1
0
1
0
2
1
3
2
0
0
0
2
0
0
2
0
0
0
1
0
2
2
0
0
0
2
1
0
0
1
2
1
1
1
1
2
0
0
1
0
4
0
0
1
1
0
0
0
0
0
2
1
0
0
0
0
1
0
0
1
1
2
0
0
0
0
1
1
1
0
0
0
1
0
1
2
0
1
0
0
0
2
1
1
1
2
1
0
0
0
0
0
0
1
0
1
0
1
2
1
2
2
1
3
1
0
0
0
1
0
0
1
1
1
0
0
2
1
1
2
0
0
0
0
1
2
0
0
3
1
0
0
0
2
0
0
1
1
0
4
1
0
2
2
0
0
0
1
1
2
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
1
1
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
1
0
0
0
0
1
2
1
1
0
1
0
1
0
1
2
2
0
1
1
2
1
0
0
2
0
1
1
0
0
0
0
0
0
2
2
1
0
1
0
1
1
1
1
1
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
1
1
0
2
0
1
0
0
2
0
1
2
0
1
1
0
0
1
3
0
1
1
0
2
1
2
0
0
2
1
0
1
0
0
2
2
1
0
0
0
0
2
1
1
1
1
0
0
0
0
1
0
0
0
0
1
2
2
0
0
0
3
0
0
0
0
1
1
1
0
0
0
0
0
1
2
1
0
0
1
0
3
0
0
1
1
1
1
2
0
0
0
1
0
3
0
1
2
0
0
1
2
2
1
0
0
0
2
0
1
1
0
0
0
1
0
0
2
0
0
0
1
0
2
1
1
0
0
0
0
1
1
0
1
0
0
0
0
0
2
3
1
2
0
0
2
0
0
1
1
1
1
0
0
1
1
1
2
0
2
0
0
0
0
1
0
0
1
0
0
1
3
2
0
0
0
1
1
0
0
1
1
3
0
0
0
0
1
0
0
0
1
0
2
1
0
2
0
0
2
1
0
0
0
0
1
1
1
0
0
0
2
2
2
0
0
1
0
0
0
1
0
0
0
1
0
0
0
2
2
0
1
1
2
2
1
1
0
1
0
1
2
0
2
2
2
0
1
0
0
3
1
1
1
0
1
0
1
0
0
0
0
0
1
1
2
0
1
2
0
1
2
1
1
0
0
1
0
0
1
0
0
2
1
0
1
0
0
2
2
0
2
0
1
1
0
0
0
0
1
0
0
1
0
2
1
0
0
0
1
0
0
0
0
0
1
2
0
0
2
0
1
2
1
0
2
1
2
0
0
1
0
1
0
1
2
0
2
0
0
0
2
0
1
1
0
0
1
2
0
2
0
1
0
0
1
2
2
0
0
0
1
1
0
0
2
2
0
0
0
1
1
1
1
0
3
1
0
0
2
0
0
0
1
2
0
0
2
0
0
0
2
0
1
0
1
0
0
1
0
1
0
2
0
5
1
1
0
1
1
0
0
0
0
0
0
1
2
2
0
2
2
1
0
0
0
0
2
1
0
0
2
1
0
0
1
2
0
2
0
0
1
0
1
7
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
1
0
1
1
1
0
0
0
0
0
2
0
1
1
1
0
1
1
0
0
2
0
1
2
0
0
1
1
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
1
1
0
0
2
2
1
0
3
1
0
1
2
2
0
0
0
0
0
2
2
2
2
1
0
0
2
1
0
1
0
1
1
0
0
0
0
0
0
2
0
3
0
0
0
1
0
1
0
1
2
1
2
2
0
0
0
1
1
1
0
0
1
0
2
2
0
0
1
0
1
0
1
1
0
0
0
1
0
0
0
2
1
1
2
1
0
0
0
0
1
2
1
1
2
0
1
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
1
3
5
0
1
2
0
1
0
0
0
0
2
2
2
0
0
2
0
0
2
0
0
1
0
1
2
2
2
2
0
0
0
0
1
2
0
0
2
1
1
1
1
1
1
1
0
2
0
1
0
0
2
0
0
1
0
2
1
1
1
1
0
3
2
0
0
2
2
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
1
1
0
0
0
2
0
0
1
2
1
0
3
8
1
0
0
0
2
0
0
2
0
1
0
0
1
1
0
2
0
1
2
1
1
0
0
1
1
0
0
0
1
0
0
1
1
1
0
0
1
0
0
0
2
0
2
2
0
1
1
0
1
1
0
2
1
2
0
0
1
0
0
1
1
0
0
2
2
1
2
0
0
0
1
1
2
2
0
0
0
2
0
0
3
1
0
0
1
0
1
0
0
2
0
0
1
0
0
0
2
3
1
0
0
0
0
2
0
1
2
0
0
0
0
1
0
2
0
0
0
0
0
1
1
1
1
0
0
0
0
1
2
0
1
2
0
0
0
1
1
1
2
0
1
0
1
0
0
0
1
0
1
1
2
2
0
0
2
1
2
1
0
1
1
1
0
0
1
0
0
0
0
0
0
4
0
0
0
1
0
0
0
1
0
0
0
0
2
0
1
2
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
3
0
0
1
2
1
0
1
0
1
1
3
1
0
1
0
2
1
0
2
2
0
1
0
2
2
1
0
0
0
0
1
0
0
0
2
1
0
0
1
1
0
0
0
2
2
0
0
0
2
0
2
0
1
1
2
0
2
0
1
0
0
2
2
0
0
1
0
1
1
0
0
0
0
0
0
0
1
1
1
0
2
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
2
2
0
1
0
2
1
2
0
0
0
2
0
1
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
1
2
1
0
1
1
0
1
0
2
0
0
0
0
1
1
10
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
2
1
0
1
2
0
0
0
0
2
0
2
1
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
2
2
0
0
1
0
0
2
2
2
2
0
0
0
1
4
1
1
0
2
0
2
0
0
0
1
0
1
0
0
0
0
2
0
0
2
0
0
0
3
3
1
0
0
0
1
1
0
1
1
0
2
2
1
0
0
0
1
2
0
0
1
0
1
0
1
1
1
2
0
0
1
1
2
2
2
0
1
0
0
0
2
1
0
2
3
2
0
1
1
0
2
2
2
0
2
2
2
0
7
2
2
2
2
0
0
0
1
1
0
0
0
1
2
1
2
0
2
1
2
0
1
0
1
1
1
0
2
3
0
0
0
0
0
2
2
2
0
0
2
0
1
0
0
0
1
2
1
0
0
0
0
1
0
2
0
0
1
0
2
0
1
1
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
2
2
1
0
0
2
3
0
0
1
1
1
0
2
0
1
1
0
0
1
0
0
1
1
2
0
0
0
2
0
0
0
0
0
1
2
0
0
1
0
1
0
0
1
0
0
0
0
2
0
0
0
0
2
0
1
2
0
0
0
2
0
1
0
0
1
0
0
0
0
1
0
0
2
1
1
0
2
0
2
1
1
0
2
0
3
0
0
0
1
2
0
1
1
0
0
0
0
0
0
2
0
1
2
0
0
1
0
0
1
2
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
2
1
2
1
2
0
0
0
0
1
2
2
0
2
0
0
0
1
0
0
0
0
2
2
2
0
1
1
1
0
2
0
1
2
0
0
0
0
0
0
2
2
0
0
0
0
1
1
2
1
1
2
0
1
1
0
1
0
1
2
0
1
1
1
2
2
0
1
0
1
0
2
0
2
0
1
2
2
0
0
0
2
1
0
0
0
0
2
1
0
0
2
0
0
2
0
1
0
0
1
0
0
0
0
2
0
1
1
0
0
0
0
1
0
1
2
1
0
0
0
1
2
0
1
0
0
0
1
0
2
2
1
0
0
0
0
0
0
1
0
0
0
0
2
1
2
0
0
1
4
0
1
2
0
1
0
0
0
0
0
1
0
1
0
0
0
2
1
0
1
0
0
0
0
1
0
0
0
1
0
1
2
0
1
2
2
2
1
0
2
1
0
2
0
2
2
1
1
0
0
1
2
1
1
0
0
0
0
1
2
1
2
2
2
4
0
0
0
0
0
0
1
1
0
2
0
1
0
2
0
0
1
1
2
0
0
0
2
0
0
0
0
2
1
1
0
0
2
2
0
0
1
0
2
1
0
0
2
2
1
0
0
2
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
2
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
3
0
2
2
0
1
1
2
0
2
0
1
0
2
2
2
0
2
0
0
3
0
1
0
1
0
0
2
0
0
2
1
0
1
0
0
1
1
0
1
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
6
1
2
0
0
1
0
0
2
2
0
0
0
0
0
2
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
4
0
0
1
0
0
0
0
0
3
1
2
1
0
1
2
0
2
0
0
2
1
2
1
2
0
2
0
0
1
2
0
2
0
0
0
0
1
0
0
0
0
1
0
1
1
0
1
0
2
0
1
0
0
0
1
2
0
0
0
2
1
0
0
1
2
0
0
1
2
1
1
2
0
2
1
1
3
0
4
0
0
1
2
0
0
2
0
0
0
0
2
0
1
0
1
1
2
0
0
2
0
0
0
0
0
0
0
1
2
1
0
0
2
0
0
1
2
0
0
0
1
2
1
1
1
0
0
1
2
0
1
0
2
0
2
2
0
2
2
2
0
0
1
1
0
1
0
2
2
0
0
0
2
0
0
2
0
0
0
1
0
1
0
0
2
0
2
0
1
4
1
3
2
0
1
0
2
0
2
2
2
1
0
1
0
2
2
0
1
0
0
2
3
0
0
2
0
0
0
0
1
2
0
0
0
0
1
0
1
1
0
1
0
0
0
0
1
0
2
1
0
0
2
1
2
0
0
1
0
1
1
0
1
1
0
0
1
1
1
1
2
1
2
2
1
1
2
0
2
0
0
2
1
1
0
1
0
0
1
0
2
1
0
0
2
0
0
0
0
1
0
0
0
0
0
2
1
0
1
0
1
0
1
2
0
0
1
1
0
1
1
2
1
1
0
1
0
2
0
0
2
1
0
1
0
0
1
0
3
0
1
2
1
0
2
0
0
2
1
0
2
2
0
0
0
1
0
1
0
1
2
2
0
1
0
0
0
1
0
0
1
0
0
2
0
0
0
1
0
1
3
1
0
1
1
0
2
1
0
0
0
0
3
2
1
2
1
1
0
0
2
3
2
1
0
0
1
0
0
2
2
0
2
0
1
1
0
1
0
0
0
0
0
2
1
0
0
0
1
0
1
0
0
1
1
2
1
0
1
2
0
0
2
0
1
1
1
1
1
1
2
0
0
1
2
1
0
2
0
1
3
1
3
1
0
0
2
1
1
0
1
0
1
1
0
2
2
0
2
1
1
0
0
0
0
2
0
1
0
0
1
1
0
0
4
1
3
0
0
0
1
0
0
0
0
2
1
0
0
1
0
0
2
1
0
2
0
0
1
1
0
2
2
2
1
1
0
2
0
2
0
0
0
0
0
1
1
1
1
2
0
3
1
1
0
0
1
0
2
1
0
0
1
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
1
1
1
0
0
0
1
1
5
0
0
0
3
0
2
2
2
0
2
2
0
0
1
1
1
2
1
0
0
2
3
1
2
0
1
0
2
1
2
1
1
0
0
1
1
1
0
0
2
0
0
0
2
0
0
1
0
0
1
0
1
2
0
0
1
0
1
1
3
2
0
1
1
2
0
0
1
1
1
0
1
2
0
1
0
1
0
2
0
0
1
2
0
1
1
2
0
0
0
4
2
0
1
0
0
1
0
0
2
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
1
1
2
1
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
1
1
2
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
2
1
2
2
1
0
2
0
1
1
0
0
0
2
0
0
0
1
1
0
0
0
1
1
1
2
2
0
0
0
2
2
1
1
1
0
1
0
0
2
1
1
2
1
0
0
0
0
0
0
0
0
0
1
0
1
1
1
2
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
2
0
0
1
0
1
2
0
0
3
0
0
0
0
0
1
1
0
1
0
1
1
0
0
0
0
0
1
1
0
2
0
0
0
1
0
0
0
0
0
2
0
1
1
2
1
2
0
0
2
1
1
0
2
0
0
4
1
1
0
0
1
0
2
0
1
2
0
0
0
2
1
0
0
0
1
0
0
0
2
0
0
0
0
1
2
0
1
0
2
1
0
0
0
2
0
1
0
2
2
0
0
2
0
2
2
1
0
0
0
2
2
1
0
0
0
1
0
0
2
1
1
1
0
0
0
0
2
1
2
2
0
0
0
1
1
1
2
0
1
0
1
0
1
0
0
2
1
0
0
3
0
1
0
1
1
0
0
1
1
1
1
0
1
1
0
0
2
0
0
2
0
2
0
0
1
0
2
1
0
1
0
0
0
0
0
1
2
0
0
1
2
2
0
1
0
0
1
2
2
2
1
2
0
1
0
0
0
0
1
1
0
2
0
0
2
1
0
0
2
0
0
2
1
1
0
0
0
0
2
0
0
0
0
2
2
1
1
1
1
0
0
1
2
0
0
0
2
1
0
3
1
2
0
2
0
0
0
0
0
1
0
2
1
0
0
0
0
1
2
2
0
1
0
0
0
1
1
0
0
0
1
0
4
1
1
2
1
0
0
0
2
0
1
6
3
1
0
2
1
0
1
0
0
0
1
2
2
0
0
1
0
0
2
0
0
2
0
1
2
0
2
1
0
1
1
0
0
0
0
2
2
2
0
1
2
0
1
2
0
1
0
0
2
1
2
1
0
1
0
1
2
0
1
1
0
0
1
1
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
2
1
0
2
2
1
0
0
0
2
3
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
1
1
0
1
0
2
3
1
1
1
1
1
0
0
2
1
0
1
1
1
0
0
0
0
2
1
0
2
2
0
2
2
3
0
0
0
0
0
2
0
0
2
1
1
2
0
1
4
1
1
0
0
1
1
0
0
0
0
1
1
2
1
2
0
2
0
1
1
0
0
0
2
1
0
3
0
0
2
0
1
0
2
0
2
0
2
0
0
0
1
0
1
0
1
3
0
0
2
2
1
0
1
2
1
0
2
2
0
1
3
0
1
2
2
1
0
1
1
1
1
0
1
2
0
2
3
1
0
2
0
2
2
1
0
2
0
1
2
2
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
2
1
0
1
0
1
2
1
0
0
2
1
0
0
0
0
0
3
0
2
2
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
1
0
1
0
2
0
1
0
0
0
3
1
0
0
1
0
1
0
2
1
1
2
0
1
0
0
0
2
0
1
1
3
0
0
0
0
1
1
2
0
0
1
2
1
0
1
0
0
0
1
1
1
1
0
0
2
1
2
2
0
2
1
0
0
1
0
0
0
0
2
0
2
0
1
1
1
0
1
1
0
1
1
0
0
2
0
0
2
0
1
0
1
0
0
0
3
1
2
0
2
0
1
3
10
0
0
2
2
0
0
0
0
0
0
0
1
0
1
2
1
0
0
2
2
0
0
0
1
0
2
2
0
0
0
0
2
0
0
2
0
2
1
1
1
0
1
0
0
0
1
0
2
2
1
0
0
0
0
0
0
2
0
1
0
1
1
1
1
0
0
1
1
2
0
2
0
1
0
0
0
1
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
3
2
1
1
0
0
1
0
0
2
2
0
1
0
0
0
0
1
2
0
0
0
0
0
1
2
1
1
0
1
1
2
3
2
0
1
2
0
0
1
0
0
2
0
1
0
0
2
1
0
1
0
0
0
0
0
1
0
2
0
0
2
1
0
0
1
0
1
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
1
1
0
0
1
0
1
0
2
2
0
0
0
0
0
1
1
0
2
1
0
0
0
1
2
0
0
1
2
0
1
0
0
3
1
0
1
0
1
1
2
0
0
2
1
1
2
0
0
0
0
1
0
2
0
1
0
0
0
5
0
2
0
2
0
1
1
2
0
1
0
0
0
0
1
0
0
1
2
0
0
0
0
2
1
0
1
0
0
0
0
2
0
0
2
0
1
2
0
3
0
0
0
1
0
0
0
1
1
0
1
0
0
2
0
0
0
0
1
1
1
2
0
1
1
2
0
1
0
1
1
2
1
1
0
1
1
0
2
0
0
2
0
2
0
1
0
1
0
2
0
3
0
0
1
0
1
1
0
2
0
1
0
2
2
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
2
1
0
0
0
0
1
0
2
0
0
0
0
2
3
0
1
0
1
0
0
0
0
0
1
1
1
2
2
0
1
1
0
0
1
0
0
1
0
2
0
0
2
0
0
2
1
0
1
0
0
1
0
2
1
0
0
0
2
0
0
1
0
1
2
1
1
0
0
0
2
0
0
0
1
1
0
0
0
1
0
1
0
1
2
2
2
0
1
0
1
1
2
1
1
0
1
0
2
1
1
0
0
0
1
0
0
2
2
1
0
1
0
0
1
0
1
2
1
0
0
2
2
1
2
0
4
1
2
1
0
0
2
0
0
0
0
1
2
0
1
0
0
0
2
1
1
1
1
1
0
2
0
1
0
0
0
0
4
2
0
2
0
0
1
0
0
0
1
0
0
2
0
0
1
0
1
0
1
2
2
0
1
0
0
0
1
1
0
0
0
0
2
1
0
2
0
2
1
1
0
0
3
0
0
2
0
1
0
0
1
0
1
0
0
2
0
0
0
0
0
1
0
0
5
0
0
2
2
0
0
1
2
2
2
0
1
0
0
0
0
1
0
1
0
1
0
2
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
3
0
2
2
1
1
1
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
1
0
2
0
0
2
0
0
0
0
0
4
1
0
1
1
0
0
0
0
2
0
0
1
0
1
1
0
1
1
2
1
0
0
0
1
1
0
2
1
0
1
0
1
0
0
1
0
0
0
0
2
0
0
2
0
1
2
0
0
1
0
2
0
1
0
2
0
0
0
0
1
3
1
0
2
0
2
0
1
0
1
0
2
0
0
0
0
0
0
0
1
1
0
2
0
1
1
0
0
1
0
0
0
1
0
1
1
0
0
0
2
1
2
0
0
0
0
0
1
0
0
1
4
1
0
3
1
0
0
0
0
0
2
0
0
1
0
0
2
1
1
1
0
0
0
2
0
0
0
2
2
0
0
2
0
0
0
0
1
0
1
2
0
0
2
2
4
0
1
1
0
2
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
1
3
0
1
2
2
0
1
1
2
1
0
0
2
0
0
0
0
2
0
0
0
1
0
1
0
2
0
0
2
2
0
0
0
0
0
2
0
1
1
0
2
2
0
1
2
1
2
2
3
0
2
1
0
0
2
2
2
2
0
1
0
0
1
0
0
0
0
1
2
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
2
3
2
0
0
2
1
0
0
2
2
2
1
1
1
2
2
3
0
0
2
0
2
0
1
2
1
0
0
0
1
0
0
0
0
2
0
0
1
2
0
2
5
1
0
1
0
1
0
0
2
1
0
1
1
2
0
0
2
2
1
0
0
1
1
0
1
1
2
0
13
2
2
0
0
0
0
2
0
2
0
2
1
0
1
1
0
0
0
2
1
0
1
1
2
2
0
0
2
0
1
0
0
1
0
1
1
1
1
0
0
2
0
2
2
1
1
0
1
1
2
0
0
1
1
2
1
0
1
0
0
2
0
0
1
0
0
2
0
0
0
0
0
2
2
1
1
0
1
0
0
0
0
2
0
0
2
1
0
1
2
0
2
1
0
0
0
2
0
0
1
1
5
1
1
1
0
1
2
0
0
0
0
1
0
0
2
1
1
1
0
1
0
4
2
1
2
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
1
2
4
2
2
0
0
0
1
0
2
1
0
1
0
2
1
0
2
0
1
0
0
2
0
0
0
2
0
2
0
1
1
1
2
2
0
0
0
0
1
0
2
0
0
0
1
0
0
1
1
1
1
1
3
0
1
0
1
0
0
0
0
0
0
2
0
0
0
2
2
0
1
0
2
0
1
1
0
0
0
0
0
0
0
0
2
2
1
0
1
0
0
1
1
0
2
2
0
0
0
0
0
2
1
2
0
0
0
0
1
1
0
1
0
1
0
1
1
0
0
0
0
0
0
1
0
0
3
0
4
2
0
0
0
1
1
0
1
1
0
0
1
1
1
2
0
1
1
1
2
2
0
0
0
0
2
0
2
1
0
0
0
1
2
1
0
1
0
1
2
0
0
1
1
1
0
1
0
0
2
0
0
0
0
1
1
1
0
0
1
1
2
0
0
1
0
0
2
0
0
0
0
0
0
1
0
1
2
1
1
2
1
0
0
0
0
0
1
1
0
2
0
0
2
0
1
2
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
2
3
0
0
1
0
0
0
2
0
2
0
2
2
1
0
1
1
1
0
2
11
1
1
0
0
0
0
0
0
1
1
0
1
0
1
0
0
2
1
0
1
0
0
0
0
1
1
0
2
0
1
0
0
0
0
0
2
0
0
1
2
0
1
1
2
2
1
2
0
0
0
0
0
0
2
0
0
0
1
1
1
0
0
0
0
1
3
2
2
1
2
0
0
1
2
0
1
1
0
1
0
0
0
0
0
3
0
0
1
2
0
1
3
1
2
0
0
1
1
0
1
1
0
0
0
4
2
3
0
0
0
3
0
0
1
0
2
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
1
0
1
1
2
0
0
2
0
1
0
1
0
0
2
0
2
2
0
1
0
0
0
1
0
0
0
2
1
2
1
1
0
0
0
2
1
1
0
1
0
1
0
1
0
0
2
2
0
0
0
0
2
2
2
2
1
2
1
0
0
1
1
0
1
0
0
0
0
1
2
1
0
2
0
2
0
2
0
2
0
1
2
0
2
0
1
0
0
0
0
0
1
1
2
2
0
1
2
0
0
0
1
2
2
1
1
0
0
0
0
0
2
1
0
2
2
2
0
1
1
0
0
1
0
1
0
2
2
0
1
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
1
0
1
0
0
0
1
0
0
2
2
0
0
2
1
0
1
0
3
1
1
2
0
0
1
0
1
0
0
4
1
1
0
0
0
0
1
1
0
1
2
0
1
1
0
0
2
0
0
1
0
1
0
0
1
0
3
0
0
0
1
2
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
1
1
2
0
0
0
0
0
2
0
1
1
0
1
1
0
0
0
1
1
0
2
1
1
2
1
2
0
0
2
0
0
0
2
2
0
0
0
0
0
0
1
1
2
0
0
0
0
1
0
0
0
2
0
1
0
1
1
1
1
1
2
1
0
2
1
0
2
0
0
2
2
1
1
2
0
0
2
0
2
2
2
0
1
0
1
0
1
2
2
0
2
0
0
2
0
2
1
2
1
1
0
1
0
1
1
0
1
1
0
0
2
1
0
2
0
2
0
0
1
0
1
0
0
1
1
1
0
0
1
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
1
0
1
0
0
1
1
0
0
1
2
0
1
0
0
1
0
2
1
0
0
1
4
1
0
0
0
2
1
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
2
1
0
0
0
3
0
1
0
0
1
2
1
0
1
1
0
0
0
1
1
0
1
0
0
0
0
1
0
1
2
0
0
2
1
1
0
0
2
2
2
2
1
0
1
0
2
2
0
0
0
2
0
0
1
0
2
0
0
0
1
0
0
0
0
2
1
2
0
2
0
0
0
0
2
0
0
0
2
0
2
0
0
0
1
0
1
2
0
1
0
0
0
0
0
1
2
0
1
0
1
1
0
0
0
0
2
1
0
0
0
1
1
0
1
2
0
1
1
0
2
0
2
0
2
5
0
0
0
0
1
1
0
2
2
2
0
0
1
0
0
1
1
0
0
4
0
0
1
0
0
2
1
1
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
2
0
1
0
1
0
1
1
0
0
1
0
2
0
0
3
0
0
0
0
2
1
0
0
2
1
2
1
1
0
2
0
1
0
2
1
0
0
0
2
1
0
2
1
1
1
0
0
0
0
0
1
2
1
2
0
0
0
0
2
0
0
1
1
0
2
2
1
1
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
1
2
2
1
0
0
3
0
0
0
2
1
0
1
1
0
0
2
0
1
0
0
0
1
0
0
0
1
0
1
1
1
0
1
0
1
2
1
2
2
1
0
0
2
0
1
3
0
1
0
1
0
1
1
0
0
0
0
1
1
0
0
2
0
0
1
0
0
2
1
1
1
1
0
2
1
0
2
0
0
3
1
0
0
2
0
1
0
0
2
0
0
2
0
0
0
0
0
0
2
1
0
0
5
1
2
0
1
1
0
1
0
0
1
1
1
1
0
0
0
0
0
1
0
0
2
1
0
1
1
1
0
0
1
0
0
0
1
0
0
0
0
0
4
2
3
0
1
0
1
0
1
2
1
0
1
1
0
0
1
1
5
1
0
0
0
1
3
0
1
1
0
1
0
1
2
1
0
2
1
0
0
1
0
2
1
2
1
0
3
0
0
0
0
1
0
0
0
2
0
2
2
0
0
0
2
1
1
0
0
0
0
0
0
1
1
0
2
1
2
2
1
1
2
2
0
1
0
0
0
2
0
2
0
2
0
1
2
1
2
2
2
2
2
0
1
1
0
0
0
2
1
2
1
1
2
0
1
2
0
2
0
0
0
0
0
0
0
1
1
1
0
1
0
1
0
0
1
0
2
0
0
0
2
0
0
0
0
2
0
0
2
2
0
0
0
2
2
1
0
2
0
1
0
0
0
2
0
0
2
0
1
1
0
1
0
1
1
1
1
0
2
1
2
0
8
0
0
0
0
0
1
1
0
2
1
0
0
0
0
0
1
0
0
0
1
0
1
1
1
1
1
1
2
1
2
2
2
1
1
1
2
1
1
1
0
0
1
1
1
1
0
0
0
1
2
1
0
0
0
1
2
1
0
1
0
0
0
2
1
1
2
1
2
2
1
1
1
0
1
0
1
0
1
0
0
1
2
0
2
1
1
1
1
0
0
0
1
1
0
0
2
0
0
2
0
1
0
0
1
0
1
0
0
0
0
2
0
1
1
2
0
0
0
0
0
1
0
0
1
2
1
1
2
2
1
0
0
0
0
1
2
0
0
0
1
0
1
0
0
1
2
0
0
2
1
0
1
1
1
1
0
0
1
0
0
2
1
0
0
0
0
2
0
1
0
0
2
0
1
1
0
1
0
0
1
0
1
2
2
1
2
2
2
2
0
0
1
0
0
1
2
2
0
1
0
0
1
0
0
0
1
0
3
3
1
0
0
2
0
0
0
1
1
1
1
1
1
1
3
1
0
2
2
0
0
1
1
0
0
1
1
0
0
0
2
0
1
0
0
0
1
0
2
0
2
0
0
0
1
0
1
0
0
2
0
1
2
0
0
2
0
2
1
1
5
0
2
0
3
0
0
0
2
0
0
2
1
1
1
1
0
1
1
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
2
0
0
2
1
0
0
1
2
2
1
0
0
1
0
0
0
1
2
0
0
2
2
0
3
0
0
1
0
1
0
2
1
0
0
0
0
0
2
0
1
0
0
0
1
0
0
1
0
2
0
0
1
1
1
1
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
1
1
0
0
0
2
0
0
0
1
0
0
0
3
1
2
6
1
2
2
1
1
0
0
1
0
0
2
0
0
1
1
0
2
0
1
2
0
0
2
2
0
1
2
0
0
1
2
0
1
0
0
2
1
0
1
0
0
0
2
1
0
1
1
0
0
0
0
0
2
1
1
2
0
0
1
1
2
0
0
0
1
0
2
1
0
0
0
1
0
1
2
1
0
1
2
0
2
2
1
0
0
2
0
0
0
0
0
1
1
2
1
0
3
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
2
0
0
0
0
0
1
2
1
2
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
1
1
0
1
2
1
2
0
0
0
2
0
2
0
1
2
1
0
2
0
1
2
0
0
0
1
2
1
0
0
0
1
0
0
0
2
2
1
2
2
2
0
1
0
3
1
0
0
0
0
1
0
2
2
2
0
0
0
0
0
2
1
1
3
0
0
2
2
4
2
0
0
1
2
1
1
1
0
0
2
1
2
0
0
3
2
1
1
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
1
1
0
2
0
1
1
0
1
0
1
0
0
3
0
1
0
0
1
0
1
2
0
1
2
0
0
0
0
0
0
2
2
1
0
0
0
0
0
1
0
0
1
2
0
2
0
1
0
0
1
2
0
1
0
0
1
1
0
1
0
0
0
0
2
0
0
0
3
0
0
0
0
1
0
0
0
1
1
1
0
0
1
2
0
0
1
0
0
1
0
0
0
0
0
3
1
1
0
0
0
0
1
0
2
0
1
0
1
1
2
2
0
0
0
2
2
1
0
1
0
2
1
0
1
0
0
1
0
1
0
0
1
0
0
0
2
2
1
1
0
0
2
2
0
0
0
1
1
0
0
0
0
2
2
0
2
0
0
0
0
1
0
0
3
1
0
0
2
1
0
0
0
0
2
2
1
1
2
1
0
2
0
0
0
0
2
1
0
7
0
0
0
0
2
3
1
0
1
0
0
1
2
2
1
0
2
1
2
1
2
0
0
2
0
2
0
0
1
0
2
0
0
2
0
0
1
2
0
1
0
2
0
0
0
0
1
0
0
2
2
3
1
2
2
1
0
0
0
1
0
1
0
2
0
2
1
0
1
2
0
2
3
1
0
1
0
1
1
0
2
0
1
1
1
2
0
0
2
0
1
1
2
0
2
1
1
1
0
1
0
2
0
0
0
1
2
2
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
4
0
2
0
1
2
2
0
0
1
2
0
0
0
0
0
1
0
1
0
1
2
0
2
2
0
0
2
2
2
0
0
1
0
0
2
1
0
2
0
0
2
1
0
1
0
0
0
0
3
1
0
0
1
0
1
1
0
0
0
0
0
0
1
0
2
2
0
0
2
1
1
1
0
0
0
2
0
1
1
1
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
1
2
1
2
1
1
2
0
2
3
0
0
2
0
1
0
0
0
2
0
1
1
1
2
0
0
0
0
2
1
1
0
2
0
0
1
2
0
1
1
0
3
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
1
0
2
0
1
0
2
2
0
2
0
0
0
0
1
0
0
1
0
0
0
3
0
0
0
1
0
0
0
0
1
3
0
1
2
2
2
2
2
0
2
0
0
0
2
1
0
0
2
0
1
2
0
0
1
1
1
0
0
0
0
1
0
2
1
0
0
1
0
1
0
0
2
2
0
0
2
2
1
0
0
3
3
0
2
0
2
0
2
1
2
1
0
1
0
1
1
0
2
0
2
0
0
0
1
0
0
1
0
1
0
1
0
1
1
2
1
1
0
2
1
0
0
2
0
1
0
1
0
3
0
2
0
0
1
1
0
1
0
0
0
1
0
2
1
0
0
1
0
1
0
1
1
1
2
0
0
0
0
0
0
0
2
0
1
1
2
0
0
0
0
0
0
0
2
1
0
1
0
1
1
0
0
1
0
1
2
2
0
0
2
1
3
1
1
0
0
0
0
1
1
2
0
0
0
1
2
0
2
2
0
0
0
0
0
1
2
0
0
0
2
0
1
1
0
0
0
1
0
1
2
1
2
1
0
0
2
2
0
0
0
0
2
5
0
0
1
0
1
1
0
0
2
3
1
0
2
0
2
0
1
0
2
0
6
0
0
1
0
1
0
1
0
2
0
0
2
0
2
0
0
0
0
0
2
2
0
0
0
1
0
1
1
1
0
2
0
1
1
0
0
0
0
0
3
0
0
0
2
1
0
0
0
0
0
0
1
3
0
0
2
2
0
0
0
0
1
2
0
0
0
1
0
1
1
0
0
1
1
0
2
1
0
0
1
2
0
1
0
0
0
1
0
0
0
0
2
0
2
0
2
2
1
0
0
0
0
0
0
2
2
2
0
2
2
0
0
0
0
0
1
2
1
1
2
0
0
2
0
0
2
0
2
1
1
0
2
1
0
0
2
0
1
0
1
1
0
0
0
0
0
2
0
3
1
2
2
0
0
0
0
1
1
1
2
0
1
0
1
2
1
0
3
0
1
1
0
0
0
2
0
0
0
2
2
1
2
0
0
0
0
2
2
0
0
0
1
1
1
0
2
0
1
1
0
2
2
0
0
1
0
1
0
1
0
0
2
3
0
0
0
0
2
0
0
0
3
1
0
0
0
0
0
0
1
0
0
3
0
0
1
0
0
0
0
1
1
0
2
1
1
0
0
2
1
0
0
0
1
2
2
0
1
0
2
1
0
0
0
0
1
0
0
0
0
2
2
1
1
1
2
0
3
0
1
2
0
0
0
0
2
1
1
1
1
1
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
1
0
1
0
0
1
2
0
1
1
0
0
1
1
0
0
0
2
0
0
2
0
0
0
0
1
0
1
0
0
2
1
0
2
0
2
1
2
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
2
1
2
0
2
4
0
0
1
2
0
0
1
0
1
2
2
0
0
0
2
0
2
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
2
0
0
1
0
2
2
2
0
1
0
1
1
2
1
2
1
1
0
1
0
0
0
1
0
2
2
0
1
0
2
0
0
0
2
1
0
0
2
1
0
0
2
1
0
4
0
1
0
2
1
0
0
1
2
0
0
0
0
2
0
0
0
2
2
0
0
2
1
0
0
1
1
0
0
2
0
1
1
0
2
0
0
0
1
2
1
0
1
0
0
1
2
1
0
0
0
0
2
1
0
0
0
1
0
1
0
0
0
2
1
0
0
2
3
0
1
0
1
2
0
0
0
0
2
1
0
0
0
0
0
1
1
2
1
1
2
1
0
1
0
0
1
1
0
1
9
0
2
0
0
1
0
0
0
2
0
0
1
0
0
2
2
0
0
1
0
0
4
1
0
0
0
0
0
1
1
2
0
0
1
0
0
0
2
2
0
0
2
0
0
0
0
0
2
0
0
2
0
0
3
1
0
2
0
1
1
1
1
2
1
0
0
2
0
0
2
1
1
2
1
2
0
0
1
0
0
1
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
1
2
0
1
1
0
0
2
2
1
2
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
1
0
2
3
1
2
1
1
0
0
0
0
0
0
1
1
2
3
1
1
2
0
0
3
0
0
1
1
1
2
0
0
0
0
0
1
0
1
1
0
0
0
0
1
1
1
0
0
2
1
1
1
1
0
0
0
0
2
0
1
0
0
0
2
1
0
0
0
0
1
2
0
0
0
0
0
1
1
1
1
0
0
0
0
0
2
1
0
0
0
0
2
0
1
0
0
0
0
0
0
1
1
0
0
0
2
1
1
1
3
1
2
0
1
0
2
0
1
0
1
0
0
2
0
0
1
0
0
0
1
2
1
0
3
2
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
1
0
1
2
0
0
2
2
0
2
0
0
1
1
0
0
0
0
1
1
2
0
0
0
1
2
2
1
1
1
1
0
2
0
2
1
2
0
0
0
0
0
0
0
2
1
1
1
2
2
2
0
1
0
0
0
0
0
2
0
2
0
2
1
0
1
0
1
2
0
1
0
0
1
2
0
0
2
0
0
0
3
1
2
0
1
1
1
1
0
0
0
0
0
0
1
1
0
0
0
3
0
0
1
0
0
1
1
1
1
1
0
0
1
0
2
1
2
1
0
1
2
0
0
0
0
0
0
1
2
1
1
0
0
1
2
1
0
2
2
0
2
0
0
0
0
0
2
1
2
1
1
1
0
0
1
0
1
0
0
2
0
0
0
0
2
1
0
1
1
2
0
2
1
0
1
2
0
0
0
2
0
0
2
2
0
0
2
0
0
3
1
0
0
0
1
0
2
0
0
0
0
1
0
1
1
0
2
0
0
0
1
0
2
0
0
0
0
1
1
1
3
0
0
2
0
0
0
1
0
1
1
2
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
1
2
0
0
2
0
0
0
0
0
2
2
1
2
0
0
1
0
0
0
0
1
3
1
0
0
1
0
2
0
0
0
1
1
1
0
2
0
1
1
0
1
2
0
0
0
0
0
0
0
2
2
0
2
2
0
2
0
2
1
2
1
0
1
1
0
1
0
0
0
0
0
0
2
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
3
0
2
0
0
0
0
3
1
0
0
1
0
2
0
2
0
0
0
0
1
0
1
1
0
0
1
1
1
1
0
0
3
0
0
2
1
0
1
0
0
0
1
0
2
2
0
0
2
0
3
2
1
0
0
0
2
0
0
2
1
2
3
0
0
0
2
0
0
0
0
1
0
1
0
0
2
0
0
2
0
1
0
0
1
1
2
1
1
0
0
0
1
1
0
2
1
1
0
0
2
0
0
0
0
0
0
1
1
0
1
0
0
0
2
1
0
2
1
2
0
1
2
1
0
0
0
0
0
0
0
0
1
0
1
2
0
0
1
0
2
0
0
0
0
0
1
1
0
1
0
2
0
0
0
0
2
0
0
1
0
0
2
0
1
0
2
0
3
1
2
0
1
2
1
1
0
0
0
1
0
0
1
0
0
1
2
0
2
1
0
0
2
1
1
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
4
2
2
0
2
0
0
0
0
2
3
1
0
1
0
2
0
0
1
0
0
2
2
0
0
1
0
1
1
1
2
0
2
0
0
0
1
1
2
2
0
2
0
2
0
1
1
1
0
0
2
0
0
0
0
2
0
0
0
1
1
1
1
1
1
1
0
0
1
0
1
0
1
1
2
2
3
0
0
0
1
1
0
2
2
1
2
0
0
1
0
2
0
2
2
2
0
0
0
1
2
1
1
0
0
0
2
0
2
0
2
1
1
0
1
0
0
0
1
1
4
0
0
1
0
1
2
3
1
2
2
2
2
0
0
1
0
0
1
0
1
0
0
0
0
2
0
0
0
2
1
0
1
1
0
1
0
1
0
0
0
2
0
0
2
1
0
0
0
0
4
0
0
2
0
0
1
1
0
0
0
2
0
0
2
0
4
2
0
0
1
1
3
0
0
0
1
2
0
0
1
1
3
2
0
0
2
1
0
1
1
0
0
2
0
2
0
0
0
2
2
0
1
2
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
2
2
1
2
0
0
1
0
0
0
2
1
0
0
3
1
4
1
2
0
0
0
0
2
1
0
1
0
0
1
0
1
1
2
1
0
0
2
0
3
1
2
1
1
0
1
2
0
0
0
1
1
1
0
1
1
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
1
1
0
1
0
1
0
0
2
1
1
0
1
2
2
1
0
2
1
0
0
0
0
1
1
2
1
0
0
0
1
0
2
1
0
1
0
0
4
0
0
4
0
2
1
2
0
0
0
2
1
0
0
0
1
2
1
1
0
0
0
2
1
0
0
0
0
1
0
0
0
1
0
0
1
0
2
2
0
2
0
0
0
2
0
0
0
2
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
1
2
1
0
0
0
0
0
1
2
0
2
0
1
2
4
0
1
2
2
0
0
0
1
0
1
2
0
0
0
0
1
0
1
1
2
2
2
1
0
0
2
1
0
2
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
2
2
0
0
2
0
1
0
2
0
0
0
0
0
0
6
1
1
0
1
0
0
0
0
0
0
2
2
0
0
2
0
2
2
0
0
0
0
4
1
1
2
0
0
1
0
1
2
0
2
2
3
5
0
2
1
1
2
0
0
0
1
0
2
0
0
0
2
0
0
0
2
0
1
1
0
1
0
0
0
2
2
0
0
0
1
1
1
0
2
0
0
1
0
0
0
1
0
0
2
2
2
2
2
1
2
0
0
2
1
0
0
0
0
1
0
2
0
1
2
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
1
1
0
0
1
1
0
0
1
2
0
0
1
1
1
0
0
0
1
1
1
0
1
2
0
2
0
0
0
0
0
2
0
0
0
1
0
1
1
0
1
1
1
0
2
0
0
0
0
0
0
0
2
0
1
1
2
1
2
1
0
0
2
0
0
2
0
0
0
1
0
1
1
1
0
2
0
0
0
0
0
3
1
0
1
1
2
1
0
2
0
1
0
4
2
0
0
0
0
0
2
0
0
0
1
2
0
2
0
0
2
2
0
1
0
1
0
2
1
0
2
0
1
1
2
2
2
0
0
0
0
1
0
0
1
2
0
1
2
1
2
0
0
0
0
1
0
4
0
2
0
2
2
0
0
0
2
0
0
2
0
3
1
0
1
1
1
0
0
0
0
2
1
1
2
0
0
0
1
0
0
0
0
2
2
0
2
0
2
0
0
0
1
1
1
0
0
0
0
2
2
2
0
2
0
0
0
0
0
1
1
2
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
2
1
0
0
2
0
1
2
2
0
0
0
2
1
2
0
0
0
2
1
0
0
0
3
0
0
0
0
1
0
2
2
0
0
0
0
2
2
0
2
2
0
1
1
1
0
0
2
0
1
3
2
0
1
1
3
0
0
1
0
0
0
0
2
1
0
1
0
0
0
1
0
1
0
0
8
0
0
1
2
2
0
2
0
0
0
2
2
0
0
0
0
1
0
1
0
2
2
0
0
0
1
1
1
2
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
1
0
0
2
0
0
0
1
1
2
1
1
1
0
0
2
0
0
0
0
2
2
1
0
0
0
1
0
0
0
2
2
0
2
1
0
0
2
2
1
1
0
2
2
0
2
0
3
0
0
0
1
2
2
1
0
2
1
7
1
0
0
0
1
1
0
0
0
2
1
0
0
0
0
1
0
0
0
1
0
1
0
0
2
1
0
0
0
3
0
0
1
0
0
1
2
0
0
0
1
1
1
0
1
2
1
1
0
3
0
0
0
2
0
0
0
1
0
0
1
0
2
2
0
0
2
0
1
1
0
2
0
1
2
0
2
0
0
0
0
0
1
0
0
0
2
1
2
0
0
1
2
1
0
2
0
0
2
0
0
0
1
2
0
0
1
0
0
0
0
2
0
0
1
1
2
1
0
1
0
2
2
1
0
0
2
1
1
1
0
0
3
2
2
0
2
1
0
2
1
1
0
2
2
3
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
3
0
1
0
1
0
0
2
0
0
1
0
2
0
0
0
0
0
0
1
1
1
0
1
2
2
2
0
1
0
1
0
1
0
0
0
0
0
1
2
0
0
0
0
0
1
2
1
0
2
2
1
0
1
0
0
1
2
0
0
0
2
2
2
0
0
2
0
1
0
1
0
0
2
2
0
1
1
2
0
2
0
1
0
0
0
0
1
0
2
0
0
2
0
1
2
2
0
1
2
0
1
1
0
2
0
0
1
0
2
0
0
0
1
0
0
1
0
0
0
1
2
1
1
0
0
1
0
2
0
1
1
2
1
0
0
0
2
2
0
0
0
0
0
4
2
0
0
2
1
0
2
1
1
0
3
1
2
2
0
0
0
0
0
1
0
1
1
0
0
0
1
1
0
2
2
1
0
0
0
2
2
0
1
2
0
1
0
0
7
1
2
1
1
0
0
1
2
0
0
0
1
2
0
0
0
0
2
1
0
2
0
0
0
1
1
0
2
1
0
1
0
0
1
0
0
0
0
0
2
0
1
1
0
0
1
2
0
0
2
1
0
0
0
0
1
1
1
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
2
0
0
2
1
0
0
1
0
0
1
1
1
2
0
0
1
1
0
1
1
0
2
0
1
0
2
0
0
2
1
1
1
0
1
1
1
0
0
1
0
0
0
1
0
1
1
0
2
3
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
2
0
0
1
0
0
1
0
0
1
2
0
1
0
1
1
1
0
0
0
1
2
0
2
0
1
0
0
0
1
1
1
2
1
0
1
1
0
0
1
2
2
0
0
1
0
2
0
0
1
0
0
2
0
0
2
0
0
0
3
2
1
2
2
0
0
0
1
1
0
1
1
2
0
2
0
1
1
1
2
0
0
2
3
0
2
0
2
1
2
1
2
1
0
0
0
1
0
2
0
0
0
1
0
1
0
0
1
2
1
0
0
1
0
0
0
2
0
1
0
2
0
0
1
3
1
0
0
1
0
1
2
0
0
0
2
2
0
1
1
1
0
1
1
0
0
1
0
0
0
0
2
0
2
0
1
2
0
0
1
0
0
2
0
0
2
1
2
1
2
0
1
0
0
2
1
2
1
0
0
0
3
0
1
0
2
1
0
0
0
0
1
1
2
0
0
1
2
0
0
0
0
0
1
1
0
1
1
3
0
3
0
0
0
1
2
2
1
0
2
1
0
1
0
2
2
0
1
0
0
0
0
0
0
0
1
0
0
0
2
2
0
1
0
2
0
2
3
1
2
0
0
0
0
1
0
3
0
5
0
0
2
1
0
0
0
0
1
2
2
0
0
2
2
0
2
0
0
1
0
0
0
0
1
0
2
0
0
0
1
0
1
1
0
0
1
1
2
0
2
0
2
0
0
1
0
1
2
1
1
2
1
1
0
1
0
0
0
2
2
0
2
0
3
1
2
0
0
0
1
2
2
0
0
0
2
0
0
1
1
0
2
3
0
1
2
0
1
1
3
0
2
0
2
0
0
0
1
1
1
1
1
0
0
1
0
1
0
2
0
0
2
0
0
1
1
0
2
1
0
3
0
1
0
0
1
0
2
0
0
0
2
1
3
0
1
0
2
0
0
1
2
0
0
0
2
1
1
0
1
2
0
0
0
2
0
0
0
0
6
0
0
0
0
0
0
0
1
0
0
1
1
2
0
2
2
0
1
1
0
1
1
0
0
0
0
2
2
0
0
1
0
0
2
1
0
0
0
2
0
1
0
0
0
3
1
0
1
1
0
1
0
0
0
0
0
2
3
0
0
0
1
0
0
0
2
0
0
2
1
2
0
1
0
0
2
0
0
1
0
1
2
1
0
1
1
2
1
0
0
0
0
0
0
0
1
0
1
0
2
0
2
1
4
2
1
0
1
0
0
0
0
0
1
1
2
0
1
2
0
0
2
0
0
0
0
1
1
0
1
1
1
0
3
1
2
0
1
2
0
2
0
2
0
0
2
2
0
0
0
1
1
2
2
2
2
1
2
0
0
0
2
2
1
2
1
0
0
0
0
2
2
0
1
3
0
0
2
1
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
2
1
1
0
2
0
0
1
1
0
0
0
2
1
1
0
2
4
0
2
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
2
0
0
1
0
0
0
0
1
0
1
1
0
0
1
2
1
1
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
2
0
1
0
1
0
2
1
1
1
2
0
0
0
0
2
1
2
0
1
0
0
2
1
0
1
0
0
0
1
0
0
0
0
2
1
0
1
2
0
0
0
0
1
0
0
0
0
1
0
2
0
2
0
2
0
0
2
1
0
0
0
2
0
1
0
0
0
1
1
2
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
2
0
0
1
1
2
0
0
2
0
1
2
1
0
2
0
0
0
1
2
0
0
0
0
0
2
0
0
2
0
0
2
1
0
1
1
0
0
1
1
1
0
1
0
0
0
0
0
2
0
1
2
0
0
0
3
0
0
4
0
2
1
0
0
2
0
2
0
1
0
0
2
0
1
2
1
2
0
0
0
0
0
2
0
1
1
1
2
0
0
2
0
0
1
0
0
1
0
0
1
2
4
2
0
0
2
0
2
0
0
1
0
1
2
1
0
0
0
0
0
0
0
1
0
2
2
0
1
0
2
0
1
0
2
0
0
2
0
0
2
1
2
0
0
2
0
0
0
0
2
1
0
1
0
2
1
2
0
0
1
0
1
1
0
0
0
0
1
0
2
2
2
0
0
0
0
0
1
2
1
0
0
2
2
1
0
1
1
0
0
0
1
1
0
0
0
1
2
2
1
1
0
2
1
0
2
1
2
0
1
2
0
0
1
1
1
0
0
0
0
2
1
0
0
0
2
3
2
0
0
0
1
1
1
2
2
0
0
0
1
2
0
2
0
0
0
2
2
2
3
2
1
2
2
0
0
1
0
0
0
0
2
0
0
2
2
0
0
0
0
2
2
1
0
1
2
1
2
2
1
0
1
0
0
0
0
0
7
1
2
0
1
1
1
0
2
0
1
0
1
0
4
1
2
0
0
0
1
0
2
2
0
0
0
1
1
0
2
0
1
1
0
0
0
0
1
1
2
0
0
2
0
0
0
0
2
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
1
1
0
1
0
2
0
1
0
3
0
0
0
0
1
2
2
1
1
0
2
0
0
1
0
0
1
1
0
1
1
0
1
0
0
2
0
1
0
0
0
0
2
2
1
1
2
1
1
1
3
1
1
2
0
2
1
1
2
0
0
0
2
2
0
1
1
0
0
0
2
0
0
1
0
1
0
0
0
0
0
1
2
2
1
0
2
0
2
0
0
1
2
1
1
1
0
0
2
0
1
0
1
0
0
1
0
1
0
0
0
0
2
2
1
0
2
0
0
2
0
0
0
1
0
0
0
1
0
1
0
1
0
0
2
2
2
0
2
2
0
1
0
1
2
1
0
2
0
1
1
2
0
0
0
0
0
2
0
1
0
1
2
2
0
1
1
1
0
2
2
1
0
1
2
0
0
0
1
0
0
1
0
2
0
1
1
0
2
0
0
2
1
0
0
1
1
0
0
0
0
0
0
0
0
0
3
1
0
3
2
1
0
2
0
1
2
0
2
0
2
0
2
0
1
2
1
0
0
2
2
0
1
0
0
0
1
0
2
1
0
0
0
1
1
2
0
0
1
2
0
1
0
0
0
2
0
1
1
0
1
0
2
1
0
0
0
0
0
0
1
3
0
0
1
0
1
0
0
0
0
0
1
0
0
0
2
2
0
1
2
2
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
2
0
0
2
0
0
1
0
0
0
2
1
2
2
1
2
1
0
1
0
1
4
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
1
0
2
0
0
0
1
0
0
0
2
0
2
0
0
1
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
2
0
0
2
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
2
1
0
0
0
1
0
2
0
2
0
0
2
2
2
2
1
0
0
10
0
2
0
0
2
0
1
1
0
0
0
0
2
2
0
0
1
2
3
1
0
0
0
2
0
0
0
0
1
2
3
0
2
0
1
2
0
1
2
1
5
2
1
1
0
2
2
1
3
0
1
0
2
0
0
0
1
0
0
0
2
0
2
0
0
0
0
1
0
0
1
0
1
0
2
0
0
0
1
0
0
1
1
1
0
0
0
1
0
1
0
1
2
0
0
0
1
0
0
2
0
1
0
1
1
1
2
0
0
0
0
1
1
1
0
1
1
0
0
0
2
0
1
2
0
5
2
0
0
0
0
0
0
2
0
1
1
1
0
0
0
2
0
0
0
0
0
2
0
1
0
2
0
1
2
1
0
0
1
0
0
1
1
0
0
1
2
1
0
0
0
0
2
0
0
0
0
0
0
0
2
1
2
0
1
2
0
0
2
0
0
0
0
1
0
0
0
1
1
0
0
2
2
0
0
2
0
1
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
1
1
0
2
2
1
0
1
0
0
0
2
1
0
1
2
0
0
0
1
1
2
1
0
0
0
0
0
1
0
1
0
0
1
2
2
0
0
2
0
1
1
0
2
0
1
2
1
0
2
1
0
0
2
1
2
2
0
1
0
1
0
0
1
3
2
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
3
1
0
0
1
0
0
0
2
0
0
2
0
0
0
1
2
2
0
0
0
0
0
1
0
0
0
2
0
1
0
1
1
1
2
0
0
2
0
0
0
0
1
1
0
0
2
0
0
1
0
0
0
0
1
0
1
0
1
1
2
1
0
0
1
0
0
1
2
1
0
0
0
1
0
2
0
0
2
1
1
2
0
1
0
1
0
0
2
0
1
1
0
0
0
1
0
0
0
2
0
1
1
0
1
0
0
0
0
0
1
0
0
0
2
0
1
1
1
2
0
0
0
0
0
0
1
1
0
0
1
2
2
3
2
0
2
0
0
2
2
0
1
0
2
0
1
0
2
0
1
0
0
0
1
2
1
2
0
2
0
1
0
1
0
0
1
0
0
1
1
2
0
0
2
2
1
0
1
1
1
1
2
2
0
2
0
0
2
0
1
0
1
0
2
0
0
0
0
1
1
1
0
1
0
0
0
1
1
0
1
2
0
0
0
1
0
0
0
2
0
1
0
2
0
0
2
0
2
1
2
2
0
0
1
1
1
0
0
0
1
0
2
1
0
1
0
2
1
0
0
2
0
2
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
1
1
0
0
0
1
0
0
3
1
0
1
0
1
0
2
0
1
0
0
2
2
2
0
0
2
1
1
0
0
0
0
1
1
1
0
1
0
0
1
1
0
2
0
1
1
0
0
0
1
1
0
1
2
1
3
0
2
0
0
0
1
0
0
0
0
1
0
0
1
6
1
1
0
0
1
0
1
1
2
1
1
0
1
0
1
0
1
1
0
2
0
1
0
1
1
1
0
0
2
2
0
3
1
1
0
1
2
1
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
2
0
3
0
0
2
2
0
2
2
0
0
0
0
0
4
0
1
1
0
2
2
1
0
1
0
0
0
1
1
2
0
2
1
1
0
0
0
0
0
0
0
1
1
0
1
0
1
2
1
2
1
0
2
1
1
0
3
2
0
1
1
0
0
1
0
3
2
0
2
1
0
0
1
1
0
0
1
0
0
0
0
2
0
0
0
0
0
1
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
2
1
1
3
1
1
0
0
2
2
2
0
2
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
2
1
2
0
0
2
1
0
0
1
0
1
0
2
0
0
2
0
1
2
1
0
0
1
0
1
0
1
2
0
2
0
0
2
0
2
0
2
0
0
2
0
0
0
2
0
0
0
2
2
3
0
0
2
0
3
3
0
0
1
0
2
2
0
3
1
1
1
0
0
0
0
2
0
2
0
2
0
2
1
2
0
0
1
1
0
2
4
0
1
0
0
0
0
0
1
0
2
0
0
2
0
0
0
2
0
2
1
1
1
0
0
0
0
0
0
1
1
0
2
0
0
0
1
2
1
0
0
0
2
1
0
0
1
0
0
0
0
0
1
2
1
0
0
1
1
0
2
0
1
0
0
1
0
1
0
2
0
1
2
2
1
0
0
2
0
0
1
0
1
0
2
0
0
1
1
0
1
2
0
1
0
2
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
1
0
2
0
1
1
2
0
0
0
0
1
1
0
0
1
2
2
0
0
0
2
2
0
0
0
2
1
1
0
1
0
1
1
2
0
1
0
2
0
0
1
1
0
0
0
0
0
2
1
1
0
0
0
0
2
1
1
1
0
0
1
1
3
0
0
1
0
0
0
2
0
2
0
2
0
0
1
1
2
0
0
1
0
0
1
1
0
1
0
1
1
0
2
1
0
0
1
0
2
0
1
3
0
2
2
1
0
0
0
1
0
0
2
2
0
0
0
2
4
0
1
0
1
1
0
0
2
1
1
1
2
1
0
0
0
1
0
0
0
1
0
2
2
0
2
1
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
2
1
0
2
0
0
1
2
0
7
2
0
1
2
1
0
1
1
0
0
0
1
0
0
2
1
0
1
0
1
0
0
3
2
0
4
1
2
0
0
1
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
1
2
0
0
1
1
2
1
1
2
2
1
0
0
1
0
0
0
0
2
1
0
1
0
0
0
2
0
0
0
1
2
2
0
0
1
1
0
2
0
0
1
1
2
0
0
0
2
1
2
1
1
2
0
0
2
1
0
0
0
1
1
2
0
0
2
1
0
1
0
0
0
0
0
2
1
0
2
0
0
0
1
2
0
0
2
1
2
1
0
0
2
0
0
1
1
0
0
0
0
0
1
2
0
1
0
0
0
2
1
0
3
2
1
1
1
0
1
1
1
2
2
0
0
4
1
1
0
0
0
2
0
0
2
2
2
1
2
0
0
0
1
2
0
0
2
0
0
0
2
1
2
1
1
1
2
1
0
2
0
0
2
0
1
0
0
0
0
0
2
2
0
1
0
2
0
2
1
1
1
1
0
0
0
0
0
0
3
0
2
2
1
1
1
0
1
1
2
0
3
1
1
2
1
2
0
0
1
0
0
2
1
1
1
0
1
2
0
0
2
1
0
0
0
0
1
0
1
0
0
1
0
0
1
1
1
0
2
4
0
0
1
2
0
0
2
2
0
1
0
0
0
0
0
1
1
1
2
2
0
1
0
1
0
1
2
1
2
1
0
1
1
1
0
0
2
2
0
0
0
0
2
1
2
0
2
0
0
0
0
0
2
0
1
3
2
1
0
0
0
1
1
1
1
0
0
2
0
0
1
0
3
0
0
2
0
0
1
3
1
0
1
0
0
0
1
1
0
2
0
0
2
0
0
0
0
1
1
0
2
0
3
1
1
1
0
0
0
0
3
1
0
0
2
0
0
0
2
2
0
2
0
2
0
0
0
0
0
2
0
2
2
0
2
0
0
0
1
0
0
1
1
4
0
0
0
1
2
0
0
0
0
1
0
1
0
3
2
0
0
0
0
2
1
1
1
0
0
2
0
1
0
0
0
2
1
2
0
0
0
2
0
2
1
1
1
2
0
0
0
1
0
2
1
0
2
1
1
0
2
1
0
1
0
0
0
0
0
1
2
0
2
1
0
0
0
1
0
0
0
0
1
2
0
1
0
1
2
0
1
2
1
0
0
0
2
0
0
0
2
1
2
1
0
2
2
1
0
2
0
0
0
0
1
2
1
2
2
0
2
0
1
0
1
0
0
1
2
1
0
1
0
1
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
2
1
2
2
0
2
0
0
1
2
0
2
0
2
0
1
0
2
0
2
1
2
2
0
3
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
1
0
2
0
0
0
2
0
0
0
2
2
1
2
1
0
0
0
2
0
2
1
0
0
0
2
0
0
1
0
0
2
0
2
2
2
0
2
0
1
1
0
0
0
1
2
0
1
0
1
1
0
2
1
2
0
0
1
0
0
0
0
1
0
0
1
0
0
2
1
4
1
0
0
3
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
1
0
0
1
1
2
1
0
0
0
0
1
0
0
1
1
1
0
1
2
0
0
2
2
0
1
0
0
1
1
0
1
2
0
1
2
0
1
1
0
1
1
0
1
2
0
2
0
1
0
1
1
1
0
1
0
1
3
2
0
2
1
0
0
1
1
1
2
0
0
1
0
0
0
0
0
0
1
1
0
2
0
1
0
0
0
3
0
0
1
1
0
0
0
0
0
0
2
0
2
1
0
0
0
2
2
2
0
0
0
0
2
0
2
1
0
0
0
3
0
1
0
2
2
3
0
1
1
1
0
2
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
2
0
2
2
0
1
0
0
2
0
0
0
3
0
1
2
0
0
2
0
0
0
1
0
1
1
0
1
0
0
2
0
1
0
0
0
0
2
0
1
0
2
1
0
0
0
2
0
2
2
2
1
1
0
0
2
0
1
0
0
0
0
0
3
0
0
4
1
0
0
2
0
0
0
0
0
0
1
0
2
1
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
1
0
0
1
1
0
2
1
0
0
0
1
1
0
0
2
1
1
0
1
1
2
0
1
0
0
2
2
0
2
0
2
0
1
0
1
1
1
0
0
0
2
0
1
0
0
1
0
0
1
0
0
0
0
2
2
2
1
0
1
1
2
0
0
1
2
0
2
0
2
2
2
0
1
0
1
0
2
0
1
0
0
0
1
1
1
2
2
0
0
2
0
0
2
2
0
0
2
0
3
0
0
0
0
0
1
0
0
0
2
1
0
0
0
1
0
1
1
1
0
0
2
0
1
2
0
2
0
0
1
2
1
0
0
0
1
2
0
2
2
2
0
0
0
0
0
0
1
0
2
0
2
0
0
1
0
0
1
0
2
2
0
1
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
1
1
0
0
3
0
1
1
0
1
0
0
1
0
1
0
0
0
2
3
1
0
0
1
1
2
0
0
0
0
0
0
2
1
1
2
0
1
1
2
1
0
0
2
0
2
0
2
0
0
0
0
0
0
0
1
2
1
2
1
1
2
0
1
2
0
1
0
0
0
0
0
1
2
0
1
0
1
0
0
1
1
2
2
0
1
2
0
1
1
0
0
0
2
1
1
0
2
0
2
0
0
0
2
0
1
0
0
0
0
2
1
0
0
2
0
0
0
2
2
2
1
1
1
0
0
0
1
1
0
0
2
0
0
2
1
1
0
0
1
0
1
0
0
0
0
0
0
1
1
2
1
0
0
1
2
1
0
0
2
0
1
2
1
2
2
0
2
3
0
1
2
0
0
1
0
0
3
1
1
2
0
0
0
0
0
0
0
2
1
1
2
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
1
2
0
2
1
2
0
0
0
0
1
1
1
1
1
0
0
0
1
0
3
0
2
0
1
0
1
0
2
0
1
1
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
2
1
0
0
2
0
2
1
1
1
0
2
0
0
0
0
0
5
0
0
2
2
0
0
0
1
1
0
0
0
0
3
0
0
0
1
2
1
1
0
0
1
2
0
0
0
2
0
0
0
0
2
0
1
0
0
1
0
0
0
0
1
2
2
1
0
0
0
2
0
2
0
0
0
0
2
0
5
1
1
2
0
0
1
2
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
3
2
0
2
2
1
0
1
1
0
2
2
0
0
0
1
0
0
0
1
0
1
0
3
2
0
0
2
1
0
2
0
1
1
2
0
2
0
0
0
2
0
0
1
1
1
0
0
2
0
1
0
2
1
1
0
0
3
2
1
2
0
2
1
2
0
1
2
2
0
2
1
0
1
2
0
1
2
2
2
1
0
2
2
0
0
0
0
0
0
0
0
1
2
1
2
1
0
0
2
2
0
1
0
0
0
0
1
0
0
0
2
1
2
0
1
1
0
1
2
0
1
0
0
0
2
0
1
1
0
2
1
1
0
0
1
0
0
2
0
2
2
2
0
1
0
2
0
0
2
0
0
0
1
0
0
0
0
1
0
1
1
1
0
1
1
1
1
3
0
0
1
0
1
0
0
2
1
0
0
0
2
2
1
0
0
0
1
0
0
0
1
0
1
0
1
0
0
1
1
2
0
0
0
0
0
0
1
1
0
1
0
0
0
2
1
0
0
0
0
2
0
0
1
2
1
0
1
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
1
2
0
2
2
0
2
0
0
0
0
0
1
0
0
2
2
0
1
0
0
1
2
0
2
0
0
1
0
1
0
0
0
1
0
1
1
1
2
0
1
0
0
0
1
0
0
1
1
0
1
0
1
0
0
0
0
6
0
2
2
2
1
0
2
1
1
0
0
0
1
2
2
0
1
0
0
3
2
0
1
0
1
0
0
0
1
1
1
2
0
0
0
1
0
3
1
1
3
0
1
2
2
1
1
0
2
1
1
2
0
0
0
2
0
0
2
0
2
2
1
1
2
2
1
0
1
1
0
1
2
0
3
0
2
1
2
0
2
0
1
0
1
2
0
2
0
0
0
1
0
0
1
1
2
0
0
2
0
0
0
2
0
2
0
2
0
1
2
0
0
2
1
0
0
2
1
0
1
0
0
0
0
0
2
1
0
0
1
0
0
0
2
0
1
2
0
2
1
1
0
0
0
0
0
0
2
0
1
1
2
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
1
5
0
1
0
2
2
2
1
0
0
0
0
0
0
0
0
1
0
1
2
1
0
1
2
1
1
0
1
0
0
2
0
1
1
0
0
0
0
2
0
2
2
0
0
1
0
0
1
2
0
2
2
2
1
0
0
1
0
0
0
0
1
2
0
0
1
0
2
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
1
0
1
2
1
2
0
2
0
1
2
2
0
0
0
0
0
2
0
2
0
1
1
0
0
1
0
1
3
0
0
1
1
2
2
1
0
0
0
0
0
1
2
1
2
0
2
1
0
0
3
2
0
0
0
0
1
0
2
2
1
0
3
0
1
0
0
0
1
0
0
1
2
1
1
1
0
0
0
1
1
0
0
0
0
1
1
0
1
1
0
1
0
0
1
0
1
0
0
3
1
1
0
0
3
1
1
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
2
2
1
2
2
0
0
0
1
1
0
2
0
2
1
1
0
1
0
1
1
0
0
0
0
0
0
1
0
1
2
2
2
0
2
0
0
0
0
0
2
2
1
1
1
1
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
1
1
0
0
0
1
0
1
1
2
1
1
0
1
0
2
0
1
2
0
0
1
0
0
0
0
1
0
1
0
0
2
1
0
2
0
0
1
0
1
2
1
1
1
0
2
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
2
0
2
0
3
1
1
2
0
1
2
0
1
0
2
0
0
0
2
0
2
0
2
0
0
0
0
2
0
1
1
0
0
1
1
1
0
0
1
0
2
1
1
0
1
0
0
0
0
0
2
0
2
0
0
2
2
0
0
2
0
1
0
0
1
0
0
0
0
1
2
0
0
0
2
1
2
1
0
0
1
0
0
2
0
0
1
0
1
0
3
0
2
0
0
0
0
0
2
2
0
2
0
1
2
1
0
1
1
0
1
0
0
0
0
2
0
0
0
1
1
2
1
0
1
0
1
0
0
0
0
0
1
1
1
0
0
0
1
2
1
0
0
0
2
0
3
0
1
2
1
0
0
1
0
0
2
0
2
0
0
0
0
0
2
0
1
1
2
0
1
0
0
1
1
1
1
0
0
1
0
1
0
0
0
1
0
1
1
2
0
2
1
1
0
1
1
2
0
1
2
0
2
2
0
1
1
0
1
0
0
2
2
0
0
2
0
0
0
2
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
1
2
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
2
0
2
0
0
1
0
0
1
0
2
0
0
2
0
2
0
0
0
1
0
1
0
1
2
2
1
0
0
0
1
0
0
1
0
1
0
0
2
0
0
0
2
0
3
0
0
0
0
2
0
5
2
1
0
0
0
0
1
0
0
0
1
0
2
0
2
2
0
1
0
1
0
0
0
0
0
1
2
2
2
0
1
2
0
1
0
2
2
0
0
0
2
1
0
1
0
0
2
0
0
0
1
2
0
0
1
0
1
0
0
1
2
1
1
0
0
0
1
0
0
0
0
0
1
0
1
2
0
2
1
0
0
0
0
0
1
0
0
1
0
0
1
1
0
2
1
0
1
2
2
0
2
2
1
0
1
0
0
0
3
0
0
2
0
0
2
0
2
1
1
0
1
1
0
0
0
1
0
1
0
0
2
1
0
0
0
0
0
2
1
1
3
2
1
0
0
1
0
1
0
0
2
0
0
2
1
0
1
0
0
0
1
1
1
0
1
1
0
0
0
0
3
2
0
1
0
0
0
0
1
2
2
2
2
1
1
2
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
2
0
0
0
0
2
0
1
1
2
0
1
0
1
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
1
1
0
0
1
2
0
2
1
0
0
1
2
1
1
1
2
0
1
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
2
0
0
0
2
2
1
2
0
0
2
0
2
2
0
0
0
1
0
0
2
2
2
0
1
0
2
0
0
0
0
0
2
0
2
0
0
0
1
2
1
0
0
1
2
2
2
0
0
2
2
0
0
2
1
0
0
1
0
2
0
0
0
2
0
0
2
0
0
0
2
0
1
0
1
0
2
1
0
1
0
0
0
2
1
0
1
3
0
0
0
0
1
0
0
0
3
0
1
2
1
1
1
2
1
0
2
2
2
1
1
0
0
2
0
0
1
0
1
1
0
1
0
0
0
0
2
0
2
1
2
0
1
2
1
1
1
0
1
0
0
1
2
0
0
1
0
0
2
1
1
2
1
0
2
0
1
0
0
0
1
0
0
1
0
0
1
1
2
0
2
1
0
1
1
0
2
1
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
2
2
0
1
2
1
1
1
2
0
1
0
0
0
1
1
1
0
0
0
1
1
2
0
0
0
2
3
2
0
1
0
0
0
0
2
0
1
0
0
0
3
0
0
0
1
1
4
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
1
1
0
1
0
1
2
2
0
1
0
0
0
0
1
0
1
1
0
0
1
2
1
0
0
2
0
0
1
0
2
2
0
2
0
0
2
1
0
0
0
2
1
2
0
0
1
2
0
1
1
2
0
1
0
0
0
3
0
0
0
2
0
0
1
0
0
1
0
1
0
1
3
1
0
2
1
0
0
2
1
2
1
2
0
0
1
2
1
0
1
2
1
2
0
1
1
1
2
0
0
0
2
0
1
2
2
0
0
1
1
0
1
0
2
1
2
0
0
0
0
1
0
2
0
0
1
0
2
0
1
1
1
0
1
2
1
3
1
0
0
0
0
1
0
1
0
3
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
2
1
0
1
1
0
0
1
0
0
0
2
1
0
5
0
0
0
0
0
0
1
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
4
0
0
0
0
2
2
0
1
0
2
0
1
1
0
2
1
0
0
2
2
1
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
1
0
2
2
2
1
2
1
1
3
2
1
1
2
0
0
2
0
0
0
1
0
1
0
2
2
0
0
1
0
1
2
0
2
0
0
0
1
1
0
0
2
0
2
2
0
1
2
0
2
0
0
2
2
1
3
0
1
0
1
0
0
2
0
2
0
0
1
1
0
1
2
0
1
0
1
1
1
0
0
1
0
0
1
0
2
0
2
2
0
2
0
0
2
1
1
1
0
0
2
0
2
0
0
0
1
2
0
2
0
2
1
2
1
2
1
2
1
1
1
0
2
0
0
2
2
8
0
2
1
13
0
1
0
1
1
1
0
0
0
0
0
2
1
1
1
0
0
0
1
0
0
2
0
0
2
0
1
2
0
1
2
0
2
0
2
1
1
2
0
0
0
1
0
0
0
2
2
0
0
0
2
1
0
0
1
2
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
1
0
0
2
0
0
2
0
1
0
2
0
0
0
2
1
0
1
1
2
0
0
2
0
0
1
2
1
1
1
1
0
1
1
1
0
2
0
0
2
0
2
1
0
1
0
1
1
1
0
3
0
0
0
0
0
0
0
0
1
0
2
1
2
0
0
0
0
3
1
1
2
0
1
0
0
0
0
0
2
0
0
0
0
1
2
1
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
2
0
0
0
1
0
2
1
2
2
0
0
0
1
1
0
0
0
0
3
1
0
1
1
1
0
2
2
1
0
1
1
0
1
0
0
0
2
0
0
1
0
0
0
0
0
2
0
1
1
0
0
0
2
0
0
1
0
1
1
1
0
0
2
0
2
2
0
0
0
0
0
0
0
0
1
0
2
0
1
0
2
0
1
1
0
0
1
0
1
0
0
1
0
1
0
0
1
1
0
0
2
1
0
2
1
1
1
1
0
0
0
1
1
1
2
0
0
0
1
1
0
1
0
0
0
0
2
1
0
0
2
1
0
0
2
0
1
1
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
2
0
1
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
1
1
3
1
2
1
0
0
1
0
1
0
1
1
0
1
0
2
1
1
1
0
0
0
1
0
3
0
0
0
1
0
1
0
0
1
1
3
1
2
2
0
0
0
0
1
0
2
2
2
0
2
1
0
0
0
0
2
2
0
0
1
1
0
0
0
3
0
1
0
2
2
2
2
0
1
2
1
1
3
1
1
2
1
1
0
0
0
1
0
0
0
0
1
2
0
0
0
1
0
0
1
0
0
1
2
1
2
0
2
1
0
0
3
1
2
0
2
1
1
1
0
0
0
2
1
2
1
2
1
0
1
2
1
1
0
1
0
3
2
0
2
0
2
2
0
2
0
0
0
0
0
0
0
1
0
0
1
0
2
2
2
2
1
0
0
2
0
1
1
2
1
0
2
1
0
0
1
0
1
1
0
2
0
1
0
0
2
2
0
1
0
0
2
0
0
0
0
0
0
2
2
1
2
3
0
2
2
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
1
1
1
2
2
0
0
2
2
1
0
0
1
0
0
1
0
0
0
2
0
1
1
0
1
0
1
1
0
1
1
0
0
0
0
2
2
1
1
0
0
0
2
2
0
0
1
0
1
0
0
2
2
0
0
0
1
0
0
1
1
0
0
2
2
1
1
0
1
0
0
0
0
1
0
0
2
0
0
1
1
0
1
0
1
0
1
1
0
1
2
0
1
1
1
0
0
0
0
0
2
1
3
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
1
1
0
2
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
1
2
0
0
1
1
0
0
1
1
2
0
2
0
1
0
1
2
0
0
1
0
0
2
3
1
0
0
1
2
1
3
0
1
0
0
2
2
1
0
2
0
0
1
1
2
0
3
0
0
0
0
0
2
2
1
2
1
0
1
1
0
0
1
0
0
1
0
1
1
1
2
0
0
2
0
0
2
0
0
1
2
0
2
0
1
0
1
2
2
3
0
1
2
1
0
1
1
1
0
2
2
0
0
0
0
2
1
0
1
0
1
0
0
0
0
2
2
2
1
0
0
1
1
1
2
0
1
0
0
0
0
0
1
2
0
0
2
1
0
0
0
2
0
2
1
0
0
0
2
0
0
0
0
0
0
0
2
1
2
0
0
2
2
0
3
2
0
0
2
2
0
1
0
1
0
0
2
0
2
1
0
1
1
1
0
1
0
1
2
2
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
1
1
0
2
0
0
1
0
0
0
0
1
2
2
0
0
0
0
1
0
0
2
1
1
2
1
0
1
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
6
0
0
2
1
0
0
2
3
1
2
0
1
0
2
1
0
0
0
3
0
1
0
1
3
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
2
0
0
0
0
2
1
0
2
0
1
2
0
1
0
2
1
0
1
1
0
0
0
0
2
0
0
0
2
0
2
2
2
0
0
0
0
0
1
0
2
0
0
0
0
0
2
1
0
2
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
1
1
0
3
1
0
0
1
0
2
0
1
0
0
1
1
0
0
1
2
0
0
0
1
1
1
2
0
0
2
1
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
1
0
0
0
0
2
0
0
2
1
0
0
1
0
1
2
5
2
0
0
0
2
0
2
2
1
1
0
0
0
1
1
0
0
1
1
0
0
2
2
0
0
1
1
0
0
0
0
1
1
1
0
1
0
0
0
2
0
2
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
2
0
0
1
0
1
1
0
0
0
1
0
0
1
0
1
0
0
0
1
2
1
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
1
0
0
0
0
1
0
0
2
2
1
1
0
0
2
0
0
0
0
0
0
1
2
1
3
0
0
0
0
1
1
2
0
0
0
0
1
0
1
0
0
2
1
2
0
0
1
2
0
0
2
0
0
2
2
0
1
0
2
0
0
1
0
0
2
2
0
2
1
0
0
1
0
1
2
0
1
0
0
2
0
2
1
0
0
0
0
0
1
0
0
2
2
2
1
1
0
0
0
0
1
1
2
0
2
0
0
0
1
2
1
0
0
1
1
0
0
0
2
0
0
0
1
0
2
0
1
0
0
2
2
2
0
0
0
2
1
0
2
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
1
1
1
1
3
0
1
4
2
1
2
0
0
0
2
0
1
2
0
1
1
2
0
1
0
0
0
0
0
1
1
2
3
0
0
0
1
0
0
3
0
0
0
0
0
2
3
0
2
1
2
0
1
0
0
0
0
0
0
1
1
0
0
1
2
0
0
0
0
1
0
1
0
0
1
0
2
0
1
1
1
0
0
1
0
0
0
0
0
2
2
1
1
0
2
0
2
2
0
0
2
2
2
0
2
1
0
0
0
1
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
2
2
2
0
2
1
0
1
1
0
0
0
1
0
4
1
0
0
0
2
0
1
1
0
2
4
1
0
1
1
2
1
0
0
0
0
2
0
0
0
1
2
0
0
0
0
1
2
2
0
0
1
0
0
0
2
0
1
0
0
0
1
1
0
0
0
1
2
0
0
0
0
3
0
0
1
2
0
2
0
1
0
0
0
0
0
0
0
1
0
2
2
1
0
0
0
0
1
1
4
2
0
0
2
0
0
0
0
0
2
0
0
3
0
1
0
0
0
0
2
1
1
0
2
0
0
0
1
2
0
0
0
2
0
2
0
1
2
3
0
1
0
0
0
0
0
2
2
2
1
0
2
0
0
0
0
2
1
1
0
0
1
0
0
0
0
2
1
0
1
1
2
2
0
1
2
2
1
1
0
0
0
0
0
1
1
0
1
0
0
0
2
0
0
0
1
0
0
0
3
2
1
0
2
1
1
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
1
1
2
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
1
2
2
0
0
1
0
0
0
0
2
1
0
1
0
1
0
0
1
1
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
3
0
0
1
1
0
4
0
0
0
0
0
0
1
0
0
0
1
2
0
0
1
0
0
1
2
1
0
0
0
1
0
2
2
2
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
4
0
1
1
0
0
0
0
0
0
2
1
2
0
1
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
2
1
1
1
2
0
1
1
2
0
0
2
0
0
0
2
0
2
0
0
1
1
0
1
1
0
1
1
2
2
1
2
1
2
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
1
0
1
2
2
0
1
1
0
1
0
0
1
0
0
0
1
1
0
2
1
1
1
0
2
1
0
2
1
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
1
3
0
0
2
2
2
2
1
0
0
0
0
0
1
0
0
1
0
0
1
2
0
0
0
0
0
0
2
1
0
2
0
0
1
0
0
0
2
0
0
2
0
2
1
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
2
0
0
1
1
0
1
2
0
0
0
0
0
1
1
0
1
0
1
0
1
1
0
0
1
1
0
4
0
0
0
0
0
0
1
0
0
2
0
0
0
2
2
0
0
0
1
0
2
0
1
0
2
2
1
2
0
2
1
0
0
1
1
2
0
0
0
0
1
1
0
0
0
2
1
0
1
1
1
1
3
1
0
2
0
0
1
1
0
2
0
0
2
0
2
3
2
1
2
1
1
0
0
0
0
0
0
2
1
2
0
1
0
0
0
1
1
2
1
0
0
1
0
1
0
1
0
0
0
0
2
0
0
1
0
1
0
1
2
0
2
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
1
0
0
0
2
1
2
0
0
2
0
0
4
1
1
1
0
2
1
0
2
2
2
1
2
3
1
2
0
0
0
0
2
1
0
0
2
0
1
0
0
0
0
0
1
0
0
1
1
0
1
1
1
3
0
2
0
0
1
0
1
0
1
1
1
3
0
0
1
0
0
0
1
2
0
1
0
1
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
1
0
1
0
2
0
1
0
0
2
0
1
2
1
2
1
2
1
2
1
0
2
1
0
1
0
2
2
1
2
2
2
0
0
0
2
1
0
0
2
2
2
1
0
0
0
0
0
1
1
1
2
2
2
0
0
0
2
0
0
1
1
1
0
1
2
0
2
0
1
0
0
0
2
0
0
2
0
0
2
1
0
2
1
1
0
0
1
2
2
0
0
0
1
0
0
2
0
0
0
2
0
1
0
2
2
2
0
0
0
1
2
2
0
0
4
1
1
0
1
2
0
2
2
0
0
0
1
0
1
0
2
2
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
2
0
4
0
0
0
1
1
1
0
1
0
0
1
0
2
2
0
1
0
2
0
1
0
1
0
0
0
2
0
1
0
1
2
2
1
2
2
2
0
2
6
2
1
1
2
0
0
0
0
2
0
0
0
0
0
2
1
2
0
0
1
0
0
2
1
2
0
1
1
0
0
0
2
1
0
1
2
1
1
1
1
1
3
0
0
1
0
0
1
2
0
0
1
0
1
0
1
1
1
3
0
0
6
0
2
1
2
0
1
1
1
0
1
0
0
2
2
0
0
2
0
0
0
2
0
2
1
1
2
2
0
0
2
1
1
1
0
0
0
1
0
0
0
0
0
0
1
2
2
0
0
0
1
0
0
0
2
1
1
2
1
2
5
0
0
2
0
1
0
1
2
0
0
0
2
2
0
1
0
0
2
0
0
0
0
0
1
1
1
1
1
0
0
0
1
0
0
0
1
1
1
2
0
2
0
1
0
2
1
3
1
0
1
1
0
2
0
1
0
0
0
0
1
0
0
0
1
0
1
1
0
0
1
2
2
1
1
0
2
2
0
1
0
3
0
0
3
1
0
2
2
0
0
2
2
1
1
0
0
0
1
0
1
2
0
0
1
1
0
1
0
1
1
0
0
0
2
0
0
0
0
0
0
2
2
1
0
0
1
2
0
0
2
2
1
2
2
0
1
0
0
2
0
3
0
0
2
1
0
1
0
2
2
0
2
0
0
0
0
2
0
0
2
0
2
1
2
1
2
1
1
2
0
1
1
1
0
4
0
0
3
2
0
0
0
1
0
0
0
1
0
0
1
2
1
0
1
1
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
1
0
2
0
0
1
1
0
1
5
1
1
0
0
0
1
1
1
1
0
2
2
2
0
1
1
1
0
0
2
0
0
1
1
0
1
0
1
0
0
1
0
2
1
0
0
2
0
0
0
0
2
0
1
0
0
1
2
2
2
0
2
0
0
1
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
2
1
0
0
0
0
0
1
0
2
2
2
2
0
0
2
0
0
0
0
1
0
1
2
0
0
2
0
0
0
1
2
2
0
0
1
1
1
0
2
0
1
1
2
0
0
0
0
0
1
0
1
0
1
1
1
1
0
0
0
1
2
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
2
1
2
0
0
0
1
2
0
0
0
1
1
0
0
2
0
2
2
2
1
1
0
0
0
1
2
1
2
1
2
1
0
2
0
2
0
0
0
0
2
2
1
1
1
0
2
2
0
0
0
1
0
0
1
1
1
0
0
0
1
0
0
1
0
1
0
0
0
1
0
1
2
0
0
0
0
0
3
0
0
0
2
1
1
0
0
1
1
0
2
1
2
0
2
2
0
0
1
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
1
2
0
2
0
0
0
1
0
0
2
0
0
1
1
0
0
0
2
0
0
0
2
3
0
0
0
0
0
1
0
2
2
1
1
2
0
1
0
2
1
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
7
0
1
1
1
0
0
1
0
2
0
1
2
0
0
1
2
0
2
0
2
2
1
0
2
0
1
1
1
2
1
1
0
1
0
0
0
1
2
0
0
0
1
0
0
2
1
1
2
1
0
1
1
0
0
0
2
0
1
2
2
0
2
1
2
1
0
2
0
1
1
0
0
0
0
0
0
0
2
0
2
1
0
1
2
0
0
1
0
1
3
0
1
0
0
0
1
0
0
1
0
4
0
0
0
0
0
2
0
2
0
2
0
0
2
2
0
1
2
1
0
0
2
0
0
0
2
0
0
1
2
2
0
1
0
1
0
1
2
0
0
1
3
0
2
1
0
0
2
0
0
1
0
0
1
1
2
1
2
1
0
0
2
1
0
1
0
3
1
0
0
0
2
1
0
0
1
2
0
1
1
1
0
1
0
2
1
0
0
0
2
1
0
0
0
2
0
0
0
2
1
0
2
0
0
1
0
0
1
1
0
0
2
0
0
1
1
2
0
1
1
2
2
1
1
1
1
0
2
0
0
0
2
0
0
1
0
2
0
2
1
0
0
0
0
2
0
2
0
1
0
0
0
1
1
1
2
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
2
1
0
1
1
0
2
1
2
2
0
0
1
0
2
2
0
1
0
0
0
0
0
0
0
1
0
0
3
2
0
0
0
1
0
1
0
0
0
0
2
2
0
0
2
2
2
2
1
0
1
0
0
1
0
2
0
0
1
0
1
1
0
0
2
0
2
2
1
1
2
1
0
0
0
0
0
0
0
2
1
0
1
0
2
1
1
2
0
1
0
0
1
1
2
0
0
1
2
0
2
1
0
0
0
1
3
2
0
0
0
2
0
1
0
1
2
0
0
0
2
0
1
0
1
1
0
1
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
3
0
1
1
1
0
1
0
0
0
0
0
0
2
1
0
1
0
2
2
0
0
2
0
3
1
1
1
2
2
5
2
1
2
0
0
0
2
0
2
0
0
0
2
0
0
0
2
2
2
1
0
0
2
0
0
0
0
1
2
0
0
2
0
1
0
0
2
1
2
0
2
0
0
2
0
1
1
2
0
0
0
0
0
2
1
2
1
0
1
0
0
1
0
0
0
1
0
1
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
2
2
1
0
2
0
1
0
2
1
0
0
0
1
0
0
1
0
0
0
1
1
0
2
1
0
0
0
1
0
0
0
2
1
2
0
2
1
0
0
0
1
0
0
0
0
1
1
0
2
1
2
0
0
0
2
1
2
0
0
1
0
2
0
1
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
1
0
0
1
0
0
1
0
1
0
1
1
1
1
2
2
0
0
0
0
0
2
2
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
1
0
2
1
0
0
0
1
0
1
1
0
1
0
2
0
2
0
3
0
0
1
0
0
0
0
2
2
0
0
1
0
1
1
0
0
2
0
0
0
2
0
0
2
1
1
0
0
2
0
1
0
0
1
0
1
0
0
0
1
0
1
1
0
2
1
1
1
0
0
0
0
1
3
1
2
0
0
0
0
0
1
2
2
0
0
0
0
1
0
0
1
0
0
0
2
1
0
0
0
1
0
0
2
0
0
0
2
0
2
0
2
0
1
1
2
2
0
2
2
1
1
1
0
0
0
2
0
1
0
0
1
1
1
2
2
0
0
0
2
0
1
1
1
0
0
1
2
0
0
1
0
0
0
0
0
1
0
0
1
0
3
1
2
0
0
1
0
2
1
1
2
0
0
1
0
0
2
1
2
1
1
1
2
2
1
2
0
0
1
2
0
0
0
1
1
0
1
0
2
0
0
1
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
3
1
1
0
1
2
0
1
1
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
1
0
0
0
0
0
1
0
2
0
1
0
1
2
3
0
2
2
0
0
2
2
0
3
1
2
1
0
2
0
2
1
1
1
0
0
0
0
1
0
0
2
0
1
2
0
0
0
2
0
0
0
2
0
0
1
0
0
0
1
1
0
1
0
0
0
1
0
0
1
2
0
2
1
0
0
0
0
0
1
2
0
0
0
0
0
3
2
1
2
0
0
1
0
0
0
0
0
1
1
0
1
1
0
1
0
1
2
1
1
0
0
1
0
0
0
2
0
1
2
0
0
2
2
1
1
1
2
1
0
0
2
3
0
0
0
2
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
1
1
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
1
2
0
1
0
0
0
2
2
0
1
1
1
1
0
0
0
0
0
0
2
0
1
0
0
2
1
2
0
1
0
0
0
0
0
1
1
0
1
1
0
0
0
1
1
1
0
1
1
1
0
4
6
1
2
1
1
1
2
0
0
2
0
0
1
1
2
2
0
0
0
1
2
1
0
1
0
0
2
2
3
1
0
0
1
0
1
2
0
0
1
2
2
2
2
0
0
0
1
0
2
0
0
0
1
0
1
2
1
0
2
4
0
0
0
1
1
0
4
1
2
0
0
0
1
0
0
1
0
1
1
2
0
2
1
0
0
1
0
2
2
0
0
0
2
1
0
0
0
0
0
1
0
1
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
2
0
2
0
0
1
2
1
1
2
2
1
0
1
0
0
2
0
0
0
1
0
1
0
0
0
0
2
1
1
0
0
2
1
0
0
2
0
0
0
0
3
0
1
1
0
2
2
0
0
1
0
0
1
0
1
1
0
2
1
1
2
0
0
1
1
2
0
0
2
0
0
1
0
1
0
0
2
1
0
0
1
2
2
1
1
0
0
2
1
1
2
0
0
2
0
2
2
1
0
1
0
0
0
2
0
0
1
0
2
0
2
0
2
0
0
1
2
0
2
0
2
2
2
1
2
1
0
2
1
0
0
0
2
1
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
2
0
1
1
0
2
2
0
0
0
0
0
1
2
0
0
2
1
1
0
2
0
1
2
2
0
0
0
2
1
0
2
2
2
0
3
1
2
1
1
0
2
1
2
0
0
0
0
1
0
1
2
1
2
0
0
0
0
1
0
2
3
1
0
0
2
0
0
2
0
2
0
0
1
2
1
1
0
0
0
0
0
2
4
0
1
2
2
0
2
2
0
2
2
0
0
0
0
0
2
0
2
2
1
0
2
0
0
0
0
0
0
1
0
0
0
0
1
1
2
2
1
0
0
1
0
1
0
0
0
0
0
2
0
0
2
1
0
0
0
1
1
0
1
0
1
0
1
0
0
0
1
0
0
0
1
2
2
1
0
1
0
2
1
1
1
2
2
1
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
1
2
2
2
0
2
1
1
1
0
0
0
0
0
0
0
2
0
1
0
0
0
1
1
1
0
2
0
0
0
1
2
0
0
1
0
0
0
0
2
1
0
1
0
0
1
0
2
0
0
2
1
0
2
0
1
0
1
0
1
0
0
0
0
2
2
2
0
0
1
2
0
1
2
2
1
2
0
0
0
1
0
0
0
0
1
1
2
2
1
0
0
1
0
0
0
1
2
2
0
1
0
1
0
1
2
0
1
0
0
0
2
0
2
0
1
1
1
1
2
0
0
0
0
1
0
1
0
2
0
0
1
0
2
1
2
0
0
2
1
2
1
20
0
2
0
1
0
1
0
2
1
0
0
0
2
1
1
2
0
0
2
0
1
1
0
2
2
0
2
2
1
0
1
1
2
0
0
0
0
0
0
3
0
2
1
2
1
0
0
0
0
2
1
2
0
0
0
0
0
2
0
0
1
2
0
0
2
2
3
1
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
1
2
2
1
2
0
0
0
1
0
2
0
1
0
1
0
0
1
2
0
0
0
0
2
4
1
0
2
2
0
1
1
0
0
0
0
0
1
0
0
2
2
0
1
4
2
0
0
1
2
2
0
0
0
1
0
0
1
4
1
0
0
1
2
0
0
0
2
2
2
0
0
1
0
0
0
0
0
2
2
0
1
0
0
2
0
1
1
1
0
2
1
1
0
2
3
1
1
0
1
2
0
1
1
1
0
0
0
0
0
1
1
0
1
0
2
0
0
0
0
0
0
0
2
1
1
2
1
0
1
0
0
0
0
0
3
0
2
2
2
2
0
1
0
2
3
0
0
0
1
0
2
0
0
0
1
0
0
0
0
2
1
0
1
1
1
0
3
0
2
0
1
2
1
0
1
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
2
2
0
2
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
2
0
1
0
1
0
0
1
3
0
2
0
1
2
2
0
0
0
0
0
1
0
0
1
1
2
4
0
0
0
1
1
1
0
1
0
2
0
1
2
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
2
2
1
0
0
3
0
0
0
2
2
1
0
3
2
0
1
0
0
0
1
1
2
2
1
2
1
0
2
0
0
12
0
2
0
0
1
0
1
0
0
1
0
0
1
1
0
0
1
1
1
1
1
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
4
0
1
1
0
1
1
2
1
2
0
0
4
0
0
0
0
0
0
0
2
0
0
0
3
0
2
5
2
0
1
0
0
1
2
2
0
0
0
2
1
0
0
0
0
2
1
0
1
0
0
0
2
0
1
2
0
1
0
0
0
0
0
0
0
1
4
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
2
2
1
0
0
2
0
3
1
2
0
1
0
0
2
1
2
2
2
1
0
0
2
0
0
2
2
0
3
0
2
1
0
0
2
0
0
0
0
0
0
0
1
1
2
1
0
0
1
2
1
0
0
2
0
2
0
0
2
0
0
2
0
1
0
4
2
2
1
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
1
1
0
0
2
1
2
0
1
0
0
0
2
0
0
0
0
2
1
1
1
1
2
2
0
1
0
2
1
1
2
2
1
0
0
0
0
1
1
1
0
0
0
0
2
2
0
0
1
0
0
1
1
1
1
0
1
0
0
2
2
2
0
0
0
1
0
0
1
0
1
1
2
2
1
2
0
3
1
0
0
2
1
1
0
0
1
1
1
0
0
0
0
2
0
0
2
2
2
0
1
1
0
0
1
1
0
0
5
0
2
0
0
0
1
0
0
0
0
1
0
0
1
0
0
2
0
0
2
0
0
0
0
1
0
0
1
2
1
0
0
0
1
0
1
2
1
2
2
0
1
0
0
0
1
0
1
1
0
1
1
1
0
0
0
1
2
5
2
2
0
0
2
3
0
0
1
2
0
0
1
0
1
0
2
1
0
2
0
0
1
1
0
0
2
0
0
0
0
0
0
1
1
0
0
0
2
0
2
0
0
0
0
2
1
1
2
0
0
0
2
2
1
0
0
1
1
0
0
0
1
5
1
0
0
0
0
2
1
0
1
2
1
1
2
2
0
0
0
2
1
0
1
0
0
1
0
0
0
0
0
0
2
0
1
0
0
2
0
0
1
2
1
1
1
1
0
0
0
2
1
0
1
1
0
1
0
2
2
0
0
1
1
0
0
2
2
2
0
0
2
3
0
0
1
1
1
0
1
0
1
0
0
0
0
1
0
0
1
2
0
3
0
0
0
1
0
0
2
2
0
2
0
0
1
2
0
0
2
0
2
0
0
2
0
0
2
0
0
0
0
1
3
0
0
2
1
0
2
1
0
0
1
0
2
1
0
0
0
1
0
3
0
0
1
0
0
1
1
0
1
1
1
0
2
2
1
1
1
1
0
2
0
1
0
0
1
0
0
1
2
2
2
2
2
1
0
1
0
2
0
2
0
0
0
0
0
2
0
0
2
0
1
0
0
0
1
0
2
0
1
0
0
0
1
1
0
1
2
0
2
2
1
0
0
1
0
0
0
0
0
2
0
2
1
1
0
1
0
0
1
1
1
1
0
0
0
0
0
2
1
1
0
0
0
2
1
1
0
0
0
0
1
0
0
0
0
2
0
0
1
1
1
0
1
0
0
1
1
0
1
0
0
2
2
2
2
0
0
0
1
0
0
0
3
0
0
2
0
2
2
0
0
0
1
0
1
1
0
1
0
0
1
1
0
1
1
1
0
0
1
1
0
1
0
0
0
0
1
0
4
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
1
0
1
2
0
2
0
0
1
0
0
2
0
0
1
0
1
1
0
0
1
0
0
2
2
2
1
1
0
0
1
0
0
0
1
1
0
0
2
1
0
0
0
1
1
2
0
1
2
0
0
1
0
0
2
0
1
0
1
0
2
1
0
1
1
0
1
1
0
1
1
2
0
1
0
2
1
0
3
0
0
0
0
0
0
2
0
2
2
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
1
0
1
1
0
0
0
1
0
1
0
1
2
0
2
1
2
0
0
0
3
1
0
5
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
1
0
1
0
2
1
0
2
2
2
0
0
2
1
0
0
1
2
0
1
0
0
2
1
0
1
1
2
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
1
0
0
0
1
4
2
0
1
3
0
0
0
2
0
1
2
2
0
1
1
0
1
2
0
0
2
0
0
0
0
1
0
2
0
0
2
0
0
0
1
0
1
0
0
0
0
0
1
1
3
1
0
0
2
1
3
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
2
1
0
1
0
0
0
0
0
1
0
0
0
2
0
2
1
0
0
0
0
1
2
1
1
0
1
0
1
2
0
0
1
1
0
2
0
0
2
1
1
2
0
0
0
2
0
0
1
2
2
0
0
2
0
0
0
0
1
2
8
0
0
0
2
0
0
1
0
0
2
0
2
0
0
0
1
1
0
0
2
1
1
0
2
0
0
0
0
2
1
0
1
1
1
1
2
0
0
1
1
0
1
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
1
2
0
1
2
2
2
2
2
1
2
0
2
0
0
0
0
2
1
0
1
0
0
0
0
1
0
1
0
0
0
0
2
0
1
1
2
1
0
3
1
1
1
0
0
0
2
0
0
1
2
0
0
0
2
1
1
0
0
2
2
0
1
0
1
0
0
2
2
0
2
2
0
2
2
0
0
0
0
2
0
0
2
2
0
0
0
0
2
1
1
1
1
0
0
1
2
0
0
2
2
0
0
0
1
0
0
0
2
2
2
2
0
0
1
1
3
0
0
0
0
0
0
2
2
1
2
0
0
0
0
1
1
2
0
2
0
0
0
0
1
0
1
0
0
2
2
2
1
0
0
1
1
0
2
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
2
1
0
1
0
1
0
0
2
0
1
3
0
0
1
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
1
0
1
3
1
0
1
1
1
1
0
2
1
1
0
1
1
2
1
1
0
0
2
1
0
0
1
0
1
3
1
0
0
5
0
2
2
3
0
0
0
0
2
2
0
0
0
2
2
0
0
4
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
1
0
0
2
1
0
0
1
1
2
1
0
0
2
0
1
0
1
2
0
1
0
3
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
1
0
2
0
2
0
2
1
1
2
0
2
0
0
1
1
2
1
2
0
0
2
1
1
2
1
0
1
2
2
1
2
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
2
2
1
0
0
0
2
1
3
0
1
3
1
2
1
0
0
0
0
1
1
0
2
1
0
2
1
0
0
0
1
1
2
3
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
2
0
3
0
0
1
2
0
2
1
0
2
0
2
1
1
1
0
1
0
0
2
0
1
0
0
1
1
2
1
0
0
1
1
0
1
1
0
0
0
0
0
2
1
2
1
0
0
2
0
0
1
0
2
0
1
0
0
1
1
7
1
4
1
0
0
1
0
2
1
0
1
0
0
2
1
0
0
2
0
1
0
1
0
1
0
2
1
0
0
2
1
0
0
1
0
1
3
2
2
0
0
4
1
1
2
1
0
1
0
0
1
0
0
2
0
2
0
0
0
1
2
1
0
2
0
2
1
0
0
2
0
0
1
1
0
0
0
1
0
0
0
2
0
1
2
1
0
0
0
0
0
2
0
0
0
1
2
0
0
2
2
2
2
0
2
1
0
0
0
0
1
5
3
0
1
0
1
1
0
2
0
0
1
0
0
0
0
0
0
1
0
0
1
1
2
0
1
0
0
0
1
0
2
1
0
0
1
0
0
1
0
0
2
1
0
2
0
0
1
2
0
2
0
0
0
2
0
0
2
0
1
1
0
0
2
0
1
1
0
0
2
0
0
2
1
1
0
5
1
1
2
0
0
1
1
0
0
2
2
2
2
0
0
0
2
1
0
1
1
2
1
1
0
3
0
0
0
0
2
0
0
2
1
0
0
0
0
0
1
2
2
2
2
1
0
2
0
2
0
1
0
1
0
0
0
1
1
0
0
2
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
1
2
3
1
0
2
1
0
0
1
0
2
2
1
0
2
2
0
1
1
2
0
0
1
0
1
0
0
0
1
1
2
0
0
1
2
0
0
0
1
0
0
0
0
1
2
0
1
1
0
0
0
0
2
1
0
0
1
0
1
0
1
1
0
2
2
2
0
1
2
1
2
2
0
3
1
1
0
2
0
0
0
3
0
1
1
0
2
0
0
0
1
0
2
1
0
0
2
0
1
0
0
2
0
0
0
0
5
1
2
0
1
0
0
2
1
0
0
0
0
0
0
0
2
0
0
2
1
1
0
0
1
3
1
0
1
0
2
0
2
0
2
0
0
2
0
2
1
0
0
0
2
0
1
0
0
1
1
1
0
0
0
0
1
0
0
0
1
3
0
6
0
2
0
0
0
0
0
0
0
1
2
0
1
0
0
2
0
1
0
1
1
1
0
1
1
1
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
3
1
2
0
1
0
1
1
1
2
0
2
1
0
1
2
0
1
0
1
0
0
2
1
0
0
2
0
1
1
2
0
0
1
0
1
1
0
0
1
1
0
0
2
0
0
0
0
2
0
2
2
1
0
2
0
1
0
0
2
0
0
0
0
0
2
2
2
2
0
2
2
0
0
2
0
0
1
0
2
0
0
1
2
0
1
2
2
2
0
1
0
1
1
0
2
0
1
0
2
0
2
1
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
2
2
1
0
0
0
2
0
0
0
2
0
1
0
0
1
2
0
0
1
2
0
2
0
1
3
0
0
0
0
2
1
0
0
0
1
1
0
1
2
0
2
2
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
1
1
2
1
1
0
2
2
1
1
2
1
0
0
2
0
2
1
0
1
1
0
0
0
1
0
2
0
0
0
1
3
4
0
2
0
0
0
0
0
2
2
1
4
2
0
1
0
1
0
1
0
0
0
2
0
0
0
3
1
0
0
0
2
0
2
1
1
1
0
1
0
0
1
0
2
1
0
0
2
1
0
0
2
0
0
1
2
0
0
0
2
0
2
0
0
0
0
0
0
1
1
1
1
1
0
1
0
0
0
0
0
2
0
1
0
0
2
0
0
1
0
3
1
0
2
1
0
1
2
0
0
2
0
1
0
0
0
1
1
0
2
0
3
0
0
1
0
0
1
0
2
0
0
1
1
0
2
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
2
0
1
0
1
0
2
0
0
0
0
1
2
0
1
0
0
1
0
0
2
0
2
1
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
1
1
0
2
0
1
0
0
0
1
0
0
2
0
0
2
1
2
0
0
2
0
0
0
0
1
4
0
1
2
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
1
1
0
1
1
0
2
0
1
0
0
1
0
2
0
1
1
0
0
0
0
2
2
1
2
1
0
0
0
1
0
2
1
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
4
0
2
0
0
0
2
0
1
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
3
0
0
1
1
1
2
0
0
1
0
1
2
1
0
1
1
1
1
0
3
3
0
1
2
1
1
2
0
0
2
0
0
0
0
2
0
1
3
0
0
0
1
0
0
0
0
0
1
1
1
0
1
0
1
1
0
1
1
1
0
0
0
0
0
0
2
1
1
0
1
3
2
0
0
1
0
2
2
2
1
2
0
0
2
3
0
1
1
0
2
0
0
0
1
2
0
0
3
0
1
0
0
0
1
1
0
0
0
0
2
0
0
2
1
0
1
0
0
0
0
0
2
0
2
2
1
0
1
0
2
1
0
0
1
1
0
0
0
0
2
0
0
0
1
2
0
3
0
0
0
0
0
1
1
2
2
1
1
0
0
1
1
1
1
0
1
0
1
0
0
2
1
0
0
1
0
0
1
0
0
1
2
1
0
0
2
0
1
1
1
0
0
0
0
2
2
1
0
0
0
0
2
0
1
0
2
2
1
0
0
1
2
0
1
1
0
0
2
0
1
0
1
0
0
2
0
1
1
0
0
0
0
0
0
2
1
1
0
0
0
0
1
1
1
0
1
0
0
2
0
1
0
0
1
0
0
0
0
2
0
0
2
0
1
1
0
0
1
2
1
0
1
0
2
2
2
0
0
1
0
0
0
0
2
2
0
0
0
0
2
2
0
2
2
0
0
0
0
0
0
1
2
2
0
0
1
2
1
1
0
2
0
0
2
2
0
0
0
0
1
0
0
0
1
0
0
2
0
1
0
1
0
0
1
0
1
0
1
1
2
1
0
0
0
0
2
2
0
0
0
2
0
1
3
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
1
1
1
0
0
0
0
3
1
0
1
0
0
1
1
1
0
0
2
2
0
0
1
0
0
0
1
0
0
0
0
0
1
2
1
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
3
0
1
1
2
1
0
0
1
0
1
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
2
0
1
1
0
0
0
0
0
1
0
0
0
2
2
0
0
0
2
1
2
0
0
0
0
0
2
0
0
0
1
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
2
0
0
0
0
0
1
2
0
1
0
2
0
0
1
0
1
1
0
0
2
0
2
0
2
0
0
1
2
1
2
0
0
0
0
1
0
2
2
4
0
1
0
2
2
1
2
1
1
0
2
0
0
0
1
0
4
0
0
0
0
0
0
0
1
1
0
0
1
0
1
1
0
0
1
2
3
0
2
1
2
0
2
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
1
2
0
1
0
0
0
0
0
3
2
2
1
0
2
5
0
0
2
0
1
0
0
0
1
0
0
0
0
0
2
2
0
0
0
1
1
1
1
0
0
0
1
0
1
0
2
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
2
2
0
2
0
0
2
2
0
0
0
1
0
0
2
1
0
0
2
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
1
2
0
1
0
1
0
1
0
0
0
0
0
3
1
0
2
0
1
1
0
0
0
0
1
0
0
2
0
0
1
0
0
2
0
2
1
0
0
1
1
2
0
0
1
0
0
0
1
1
0
2
0
0
0
0
2
2
2
2
0
1
1
0
2
2
1
0
0
0
2
1
1
0
1
2
2
2
1
3
2
0
1
2
0
1
0
0
0
1
0
0
4
1
0
1
1
0
0
0
0
0
0
1
0
2
0
0
2
0
3
0
3
0
1
2
0
2
2
2
1
1
4
0
0
0
2
2
0
0
0
2
1
1
2
0
2
1
0
2
0
0
0
1
0
0
2
2
0
1
0
0
2
3
1
2
1
0
2
2
0
0
1
0
0
2
2
1
0
1
0
0
2
0
2
0
2
0
2
1
0
2
0
0
0
0
1
0
1
0
0
1
2
1
0
1
0
0
0
0
1
0
0
2
0
0
1
1
1
2
0
0
0
2
1
2
0
0
0
1
0
2
0
1
1
1
1
1
0
1
1
1
0
1
0
1
1
0
0
2
0
0
1
1
1
0
0
0
2
2
0
0
0
1
2
0
1
1
2
2
0
4
2
0
1
0
2
1
2
0
0
2
1
0
1
1
0
0
0
2
0
1
1
2
0
0
1
0
2
0
0
0
0
2
1
0
0
2
4
0
0
0
2
0
0
2
0
1
1
1
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
2
1
0
0
0
1
0
2
0
2
0
0
2
1
0
0
0
1
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
2
1
1
2
0
1
0
0
1
2
2
1
0
1
2
1
0
0
0
2
2
2
0
0
2
2
0
0
0
1
0
0
2
2
0
1
2
1
1
1
1
0
1
0
2
0
3
0
0
1
0
1
0
1
1
2
0
2
2
0
0
0
2
2
0
1
1
0
0
1
2
0
1
2
0
0
0
1
1
1
1
2
2
1
1
2
0
1
0
1
2
0
1
1
2
0
3
0
2
1
1
0
0
0
0
0
0
0
0
1
1
1
1
1
0
0
0
1
2
2
0
1
0
0
2
2
1
0
0
0
0
0
1
2
1
2
1
1
1
2
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
2
1
0
1
2
0
1
1
1
1
2
0
0
0
1
0
0
1
0
0
2
2
1
0
1
0
1
0
2
0
0
0
0
0
1
0
1
1
0
1
1
1
0
1
2
2
1
0
2
0
0
2
0
0
0
2
1
0
0
0
0
1
0
0
1
0
1
0
0
2
1
0
2
0
1
0
0
2
0
0
0
3
2
1
0
1
2
0
2
0
1
1
0
1
1
0
1
1
0
1
0
0
0
0
2
1
0
1
2
0
0
0
1
1
0
1
1
1
0
0
0
0
1
0
2
0
1
1
1
0
1
0
0
0
1
0
2
1
0
0
0
1
0
0
1
2
0
1
0
0
0
1
0
1
0
1
1
0
2
2
0
0
0
0
1
0
0
0
1
2
0
0
1
0
0
0
0
1
0
0
1
0
1
1
0
1
2
0
2
2
1
0
2
0
1
0
0
0
0
0
2
1
2
2
0
0
0
0
0
1
0
0
0
1
1
1
2
0
0
0
1
0
0
1
1
0
1
0
1
0
1
0
0
1
2
0
2
0
0
1
0
2
4
0
1
0
2
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
2
2
2
1
2
0
1
1
1
0
0
1
1
0
1
2
0
0
0
0
0
2
1
0
0
0
1
0
1
0
0
1
0
0
2
0
0
1
1
1
0
0
0
1
0
2
0
2
1
0
0
0
1
0
0
0
0
0
0
1
1
1
1
0
0
2
2
1
0
0
1
0
0
2
0
0
0
0
0
1
1
1
1
1
0
0
0
0
0
0
0
1
1
0
0
7
0
2
1
2
0
1
0
1
1
0
0
2
0
1
0
0
2
1
0
2
2
1
1
2
0
2
2
0
1
0
1
0
1
2
0
0
0
2
0
1
1
0
1
0
0
2
2
2
2
0
1
0
0
0
0
0
0
2
1
0
1
2
1
0
3
0
2
0
0
0
0
0
2
1
2
1
2
0
0
0
2
2
1
0
0
0
0
1
2
1
0
0
1
0
2
1
0
0
1
0
0
1
1
1
0
2
0
0
0
2
0
0
0
0
1
1
0
2
1
0
1
0
0
2
0
2
1
0
0
0
2
0
1
0
0
1
2
0
1
2
0
0
1
2
1
1
0
0
0
0
0
2
0
0
1
2
0
2
1
1
0
0
1
0
0
2
2
1
0
2
0
2
2
0
0
1
0
0
0
0
1
1
0
0
0
2
3
0
0
2
2
2
0
2
1
1
1
0
0
1
0
0
2
1
1
1
1
0
1
0
1
2
1
1
0
2
1
2
0
0
1
0
1
0
0
0
1
1
0
2
0
2
0
0
0
0
0
0
0
2
0
1
0
2
2
0
1
1
0
1
1
2
0
0
2
2
1
0
0
2
2
0
0
0
0
0
0
2
1
0
0
1
0
0
1
0
0
2
1
0
1
0
0
0
0
2
2
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
1
4
1
1
0
3
2
1
2
0
0
1
1
0
2
2
1
2
1
1
1
2
0
1
0
1
1
0
2
2
1
0
0
2
0
3
0
1
0
0
2
0
0
1
0
2
2
0
1
0
0
1
1
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
2
0
1
0
0
0
0
1
1
0
2
0
2
1
0
1
0
2
1
1
0
0
0
0
0
0
1
0
0
2
2
1
1
2
0
0
1
2
2
0
0
2
0
0
0
2
0
1
2
1
0
1
0
2
0
0
1
0
0
0
0
0
0
1
1
1
1
0
2
0
3
0
0
0
2
3
0
0
0
0
0
1
0
0
0
2
0
2
0
0
1
0
2
2
0
0
1
1
0
0
0
0
0
0
3
0
1
2
0
1
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
1
1
1
1
1
2
0
1
2
1
1
0
0
0
1
0
0
0
2
4
0
1
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
1
1
0
2
0
0
1
2
0
1
2
0
0
1
0
0
1
1
1
0
0
0
2
0
1
0
0
0
0
1
2
1
1
0
0
0
2
1
0
2
0
0
1
0
3
0
0
0
0
1
0
0
0
0
4
2
0
1
0
0
1
0
0
0
2
2
2
1
1
0
0
1
0
0
0
0
1
3
2
0
0
0
3
2
3
0
0
0
0
1
0
1
0
1
2
0
0
0
0
1
0
2
1
1
2
2
1
2
1
1
0
0
1
0
0
1
0
0
0
1
0
1
2
1
4
0
0
0
0
2
0
0
0
0
2
0
0
2
1
0
1
1
2
0
2
0
2
2
0
0
0
2
0
0
2
0
0
0
0
0
2
2
1
0
1
1
2
2
2
2
1
0
1
0
1
0
2
0
0
2
0
0
1
0
5
0
0
1
0
0
0
1
2
2
2
0
0
2
1
0
0
1
2
0
2
1
1
0
1
1
0
0
2
1
0
0
1
2
0
2
1
1
0
0
0
2
1
2
0
2
1
1
0
1
1
0
1
0
0
0
0
1
2
1
2
0
1
0
2
0
0
2
0
0
0
1
0
0
1
0
0
1
1
0
2
3
0
0
2
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
2
0
1
1
0
0
3
2
0
0
0
0
0
1
0
0
1
2
2
0
0
1
0
2
1
0
2
1
2
0
1
1
1
1
2
0
2
2
1
1
0
0
0
4
0
0
1
0
1
0
0
2
0
0
2
1
0
0
1
2
1
0
0
0
2
0
0
0
2
4
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
3
1
2
2
0
0
2
2
1
2
0
1
2
3
0
1
3
1
0
0
0
1
1
0
0
1
1
0
0
0
1
0
0
0
2
0
1
0
0
0
2
1
2
0
0
1
2
2
0
0
0
0
2
0
0
0
0
0
1
0
0
2
1
2
2
0
2
0
1
1
0
0
0
0
1
1
1
0
0
0
2
0
1
1
0
1
0
2
2
0
1
0
1
2
2
1
1
0
0
0
1
0
0
2
0
0
1
0
0
2
0
2
0
0
2
2
2
2
1
0
0
2
3
0
1
2
0
1
0
0
0
0
2
0
2
0
1
0
2
0
2
2
0
2
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
1
0
2
0
0
0
1
0
0
1
0
0
0
0
0
1
1
2
3
0
0
0
0
0
0
1
2
0
1
0
1
0
0
0
1
0
0
0
0
1
1
2
2
0
1
2
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
2
1
0
0
2
0
0
2
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
3
0
2
0
0
2
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
2
2
1
0
2
0
2
2
0
0
0
2
0
2
0
0
2
1
1
0
2
2
0
0
0
2
2
2
1
0
0
1
1
1
0
0
0
0
2
2
0
1
2
0
2
0
0
0
1
2
0
0
0
1
1
0
0
0
0
0
0
2
0
1
1
1
2
0
2
5
1
0
3
1
0
0
0
1
0
1
0
0
0
0
1
0
2
0
0
2
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
2
0
1
1
1
0
2
0
0
0
0
1
0
0
1
4
0
1
0
0
9
0
1
0
1
2
1
0
1
0
2
2
0
1
0
2
0
1
0
2
0
0
0
2
1
0
2
0
0
1
0
2
0
0
0
1
0
1
1
2
0
0
0
1
1
2
1
0
0
0
0
1
2
1
1
2
2
1
0
0
0
5
1
0
0
0
0
1
3
2
0
0
0
0
0
2
0
0
2
0
0
0
1
1
1
1
0
0
0
1
0
2
0
0
1
0
0
2
0
1
2
0
0
2
1
1
0
1
1
2
1
0
1
0
0
1
0
1
0
2
2
2
0
0
1
2
0
0
2
0
0
2
0
0
3
2
0
2
1
0
0
0
0
0
2
0
1
2
0
0
0
1
0
1
1
1
0
0
2
4
0
0
0
5
1
3
0
0
0
0
0
0
1
0
2
0
0
1
0
0
2
0
0
1
0
0
2
2
0
1
0
0
0
1
0
1
0
0
1
1
0
0
1
0
2
0
0
1
2
2
0
2
1
2
1
0
1
1
1
2
0
0
0
2
0
1
1
0
2
0
0
1
0
0
0
0
0
0
2
0
1
1
0
1
2
1
0
1
0
0
2
0
1
2
0
1
0
1
1
0
0
1
0
2
0
0
2
1
1
0
0
0
0
2
1
0
2
0
1
1
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
2
1
2
0
2
0
1
0
2
2
1
2
0
1
0
0
0
0
3
0
1
0
0
0
0
2
2
3
2
0
0
0
1
0
1
2
0
0
1
1
0
1
0
0
2
0
1
0
1
0
1
0
0
1
0
0
0
1
0
0
1
2
2
1
0
0
0
1
0
0
2
2
2
0
0
1
2
1
0
0
0
0
2
1
0
1
0
0
1
0
0
1
1
0
2
0
0
1
1
0
0
2
1
0
0
0
2
0
1
0
1
0
1
0
1
2
1
0
1
0
1
1
2
0
0
2
0
2
0
1
0
1
1
1
0
0
2
1
0
2
0
0
3
0
0
1
2
1
2
1
0
0
0
0
2
1
0
2
1
3
2
2
2
0
2
2
1
1
0
0
1
2
0
0
1
0
0
1
0
2
2
0
2
1
0
0
0
0
2
0
1
0
2
0
0
0
2
2
0
0
0
0
1
1
0
2
0
0
3
2
2
2
0
2
2
0
2
1
0
1
0
1
0
2
2
1
0
2
0
1
0
0
1
0
1
2
2
0
2
1
0
0
1
1
0
0
0
0
0
1
0
1
1
1
0
1
2
2
1
2
0
1
0
0
1
2
2
0
0
0
2
0
0
1
0
1
2
0
1
1
2
2
0
1
2
0
1
0
1
0
1
1
0
2
2
2
0
2
1
0
0
0
2
0
1
0
1
2
1
1
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
1
2
2
6
2
1
0
0
0
0
0
0
1
0
1
0
0
0
2
2
1
1
1
2
1
1
0
1
0
0
0
0
0
1
2
0
0
0
1
0
3
0
0
0
0
2
2
2
2
0
0
1
2
1
1
0
0
0
0
0
2
2
0
0
0
0
1
1
2
3
0
1
2
0
0
1
0
2
1
2
2
0
2
2
2
1
0
0
0
1
0
0
0
0
2
1
0
0
2
0
0
1
0
0
0
0
1
0
1
2
2
1
0
1
1
0
2
2
0
0
1
1
0
0
0
0
2
1
0
0
1
0
0
1
0
2
3
0
0
0
1
0
2
0
2
2
0
2
0
0
1
0
1
0
3
1
2
0
0
0
3
2
1
3
1
0
1
1
2
2
0
1
0
2
1
0
1
0
1
1
0
2
1
0
0
0
0
2
2
0
2
0
2
0
0
0
0
0
1
1
0
2
2
0
1
1
0
2
1
2
1
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
1
1
1
3
0
2
1
0
2
1
1
1
0
1
1
0
3
2
0
0
0
1
0
0
2
0
1
1
0
2
0
1
0
0
2
1
1
0
1
0
0
0
0
1
1
1
0
2
0
0
1
2
1
2
2
2
1
0
0
2
2
1
0
0
0
0
1
0
11
0
1
0
0
0
0
0
2
0
2
0
3
0
0
0
1
0
0
1
0
2
0
0
0
1
3
0
0
0
1
0
0
0
0
1
1
0
0
0
2
0
1
1
2
0
1
1
2
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
2
0
0
1
0
1
2
0
2
1
2
0
0
0
1
0
0
1
2
1
0
0
1
1
0
2
1
0
0
0
0
1
0
1
2
0
0
1
1
0
0
2
2
0
1
0
1
0
1
1
0
1
0
0
0
1
0
0
0
1
1
1
0
0
2
0
1
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
1
0
0
1
1
0
1
0
0
2
1
2
0
0
0
1
0
0
0
1
0
2
0
2
2
1
1
1
0
2
0
0
0
2
1
1
2
1
0
0
0
0
1
0
2
2
1
0
0
0
0
2
0
0
1
0
0
1
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
1
2
1
1
1
0
1
0
1
2
0
2
1
2
0
0
0
2
3
0
0
0
2
1
0
2
0
1
0
3
1
2
0
0
0
2
1
0
0
0
0
1
0
1
1
4
0
1
0
0
0
1
2
0
2
2
0
0
1
0
0
0
0
1
0
1
0
1
2
0
2
0
0
1
0
0
3
0
0
1
1
2
0
0
0
2
0
2
0
0
0
0
2
0
2
0
0
1
0
1
0
1
2
0
0
0
2
1
0
0
0
0
0
0
1
1
0
0
0
1
2
1
1
2
1
0
2
0
1
1
2
1
0
0
2
0
1
0
1
1
0
0
0
1
0
0
1
1
0
1
1
1
0
2
0
1
0
0
2
2
0
0
2
2
0
1
0
0
1
0
0
0
1
2
1
2
1
2
2
0
0
1
2
0
0
2
1
0
0
0
0
1
2
0
0
1
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
1
1
0
0
1
2
0
1
3
1
0
1
1
2
0
0
0
1
1
1
0
1
1
0
1
3
0
0
1
1
2
1
1
0
1
0
0
1
0
1
0
0
1
2
0
2
1
0
0
0
0
0
1
2
1
0
0
0
0
1
0
0
1
1
2
2
1
0
0
0
0
2
0
0
1
2
0
0
0
2
1
2
2
0
2
1
1
1
0
0
1
0
0
0
0
1
0
0
2
3
2
0
0
0
0
2
0
0
1
0
0
0
2
1
0
2
0
2
0
2
2
0
2
0
0
2
0
1
1
1
0
0
0
0
0
1
2
0
1
0
0
1
1
2
0
0
1
2
0
0
1
0
1
0
0
2
1
0
3
0
0
0
1
2
0
0
1
0
2
1
0
1
0
0
0
1
0
0
1
0
0
1
0
2
0
2
0
0
0
0
0
1
0
2
1
0
0
0
0
1
1
3
0
0
0
0
0
0
1
0
0
0
2
1
3
0
3
0
1
1
2
1
1
0
0
0
0
0
0
0
0
2
0
1
0
3
0
0
1
0
0
1
0
1
1
1
1
0
0
2
2
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
2
2
1
2
2
0
2
1
0
2
1
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
2
0
0
1
0
0
2
1
2
0
0
0
2
2
0
1
2
1
1
0
1
1
0
0
2
1
1
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
2
2
3
0
1
0
1
0
1
1
5
0
1
1
1
0
0
2
1
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
2
2
2
0
0
1
1
1
2
2
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
1
2
1
0
0
2
1
1
0
0
0
0
1
2
2
2
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
1
0
3
0
0
0
0
0
0
2
2
0
0
0
6
1
0
0
2
2
0
1
1
0
4
0
1
0
2
1
0
1
1
0
0
2
0
1
2
1
1
0
1
0
0
2
1
0
2
0
1
1
3
0
0
0
3
1
0
0
2
2
0
0
0
1
1
3
2
1
0
2
1
0
0
2
1
0
0
1
1
2
0
0
1
0
0
2
1
0
0
0
1
0
0
1
2
1
1
1
0
0
2
0
1
1
1
0
3
0
1
3
1
0
3
0
0
0
0
1
0
0
1
0
1
1
2
0
2
0
0
1
1
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
1
0
0
2
0
0
0
0
2
1
0
0
1
1
2
2
1
0
0
1
2
0
1
2
0
0
0
2
1
0
2
0
1
3
2
2
0
2
0
2
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
2
0
1
2
0
0
0
2
0
1
1
0
0
0
1
0
0
2
3
1
2
0
2
1
0
2
2
3
0
1
2
0
0
0
1
2
0
1
1
1
0
1
1
0
2
1
0
0
0
0
1
1
1
0
0
3
0
1
0
1
1
0
1
0
2
1
2
0
3
2
0
0
2
0
2
2
0
3
2
0
1
0
1
0
2
0
2
2
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
2
2
1
1
2
2
1
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
2
1
1
1
1
2
4
2
1
1
0
2
0
0
9
1
0
2
1
0
1
2
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
2
0
0
0
2
1
1
1
0
2
1
2
2
0
0
5
0
0
2
1
1
1
1
2
2
0
1
2
1
1
0
0
0
0
1
2
1
0
0
1
0
2
2
0
1
2
1
1
1
0
1
1
0
0
0
0
0
0
0
0
0
3
1
0
0
1
0
0
0
1
0
1
0
1
1
0
1
1
0
0
2
0
3
0
0
0
0
2
0
2
0
1
1
2
1
1
0
0
1
0
2
0
0
0
0
0
2
2
2
1
0
1
0
1
0
1
2
0
1
0
0
2
2
0
0
0
2
2
1
0
0
2
2
2
2
2
0
0
2
0
1
1
2
2
0
0
0
0
2
1
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
2
0
0
2
0
2
2
1
2
0
1
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
1
0
1
0
1
1
0
0
0
1
1
0
1
1
0
0
3
2
0
2
0
1
0
0
1
0
1
0
1
0
2
0
0
2
1
2
1
0
0
0
1
0
2
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
1
0
1
1
0
2
1
0
0
0
2
0
2
0
1
0
1
0
0
1
1
0
0
0
3
1
2
0
2
2
1
1
0
0
0
1
1
1
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
1
0
0
1
1
0
5
0
0
1
0
0
0
1
0
0
2
2
0
0
1
0
2
0
2
1
0
0
1
1
1
0
1
0
0
2
0
0
0
1
0
2
0
0
2
1
0
1
0
2
2
0
1
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
1
0
0
0
0
1
0
0
2
0
1
0
0
1
1
1
3
2
0
0
2
0
2
0
0
0
0
0
0
1
1
0
0
1
0
0
1
1
1
2
0
0
0
1
1
0
0
0
0
1
1
1
0
2
2
2
1
1
0
2
0
2
1
2
1
0
0
0
1
2
1
0
1
1
1
1
0
0
1
2
0
1
2
0
0
1
1
2
1
1
0
0
1
0
0
1
0
2
1
3
0
0
1
1
1
0
1
1
0
2
0
0
0
1
0
2
0
1
0
1
0
2
0
1
1
0
1
0
0
2
2
0
0
2
1
0
0
0
0
1
2
0
2
0
0
2
0
1
0
0
2
0
0
0
0
2
0
0
0
1
0
2
2
0
0
2
0
2
1
2
1
0
0
0
0
1
2
1
1
1
2
1
1
1
0
0
0
1
1
2
1
0
0
2
1
1
0
0
0
0
0
1
2
0
0
0
1
0
0
0
2
2
2
0
2
2
0
1
0
0
0
2
0
0
2
0
3
1
0
1
0
1
0
1
1
1
2
2
2
2
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
1
1
1
1
0
0
1
2
1
2
0
0
0
1
0
2
0
0
1
0
1
0
4
1
1
2
1
1
0
0
0
0
0
0
0
0
2
1
1
0
1
2
0
0
0
0
0
0
1
1
0
1
0
2
2
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
2
1
0
2
0
0
1
3
1
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
2
1
1
1
1
0
2
0
2
0
0
0
1
0
1
0
1
0
2
0
2
0
0
1
0
1
0
2
2
1
1
0
2
0
0
2
1
1
0
2
0
0
0
0
1
2
2
1
2
0
0
0
1
1
0
0
0
2
0
0
5
0
1
0
2
1
0
1
2
2
0
1
0
0
1
1
2
0
0
0
1
0
1
1
1
1
1
2
0
1
0
0
0
0
1
0
2
0
0
0
0
1
0
2
0
1
0
0
2
0
1
1
0
2
0
2
0
2
0
0
0
1
0
0
0
1
0
1
0
2
1
1
2
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
1
2
0
1
0
0
0
1
0
0
0
1
1
2
0
0
0
0
0
0
2
2
1
0
0
2
0
2
1
0
0
2
1
0
1
0
1
2
1
1
0
0
0
0
2
0
0
3
5
0
0
0
0
2
0
1
0
0
0
0
1
2
0
2
0
1
0
2
1
0
0
0
0
0
0
0
0
2
0
2
1
0
2
1
2
1
0
0
0
0
1
1
2
1
0
1
2
2
0
1
0
1
0
1
0
0
0
3
2
2
0
2
0
0
0
2
0
0
2
2
0
0
0
1
0
0
0
0
2
1
2
0
0
0
1
0
1
1
0
2
0
2
0
1
0
0
2
1
1
0
0
1
0
2
0
1
3
0
2
1
0
0
1
1
0
1
1
0
2
1
1
2
1
1
2
1
1
0
1
0
2
0
0
2
1
2
2
3
0
0
0
2
0
1
0
0
0
0
0
3
2
1
2
0
0
2
0
3
0
0
1
2
1
2
1
0
0
0
0
0
0
0
2
1
2
0
1
1
0
3
0
1
2
2
0
0
0
2
1
1
0
0
0
0
1
0
1
0
1
2
0
0
2
0
1
0
2
1
3
2
2
0
2
1
0
1
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
1
1
0
1
0
2
0
2
0
1
0
0
1
0
0
1
1
0
1
2
1
1
0
1
0
0
0
2
0
0
0
2
0
2
1
0
1
2
2
0
0
1
0
1
2
0
0
0
1
0
0
1
2
0
3
2
0
0
0
2
0
0
0
1
1
0
0
0
1
2
0
1
1
1
1
0
4
2
0
0
0
0
0
1
1
1
0
1
0
1
0
4
1
2
1
1
0
0
0
1
2
0
0
0
0
0
0
1
2
0
0
0
0
1
2
0
0
0
0
0
1
0
0
1
1
0
0
2
2
0
0
0
2
0
2
2
1
0
0
0
1
0
0
1
1
0
0
1
0
1
0
0
1
0
0
2
0
0
0
0
1
0
1
0
0
2
1
0
1
0
0
2
1
8
0
1
0
1
0
1
2
1
0
0
0
0
2
0
0
2
1
1
0
1
0
1
0
0
2
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
3
1
1
1
1
1
0
0
0
0
0
1
2
0
2
1
1
0
0
0
0
0
0
1
2
2
1
1
0
0
0
0
0
0
0
1
0
1
2
1
0
0
1
0
2
1
0
1
2
1
2
0
0
0
2
1
2
0
1
0
0
1
0
0
1
1
1
1
1
0
1
1
1
1
0
2
1
0
1
1
0
2
0
0
0
0
1
0
0
1
0
0
1
2
0
1
1
1
0
1
0
2
1
0
0
0
2
0
0
0
0
0
0
1
2
1
0
2
1
0
0
0
1
0
0
1
8
0
2
0
0
0
1
1
2
1
2
0
0
0
1
1
1
0
0
6
0
0
1
0
0
2
0
1
0
0
0
2
3
2
1
1
2
0
1
0
0
0
1
0
2
0
1
2
0
2
1
0
2
1
2
2
0
0
2
3
1
0
0
0
0
0
1
0
0
0
1
1
0
2
0
0
0
0
2
1
0
0
0
2
0
0
1
0
1
1
0
0
0
1
0
1
0
1
1
2
2
1
0
0
0
2
0
0
1
0
2
0
1
0
2
3
1
0
0
2
0
2
0
0
1
0
0
3
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
1
1
1
0
1
0
1
2
0
0
0
2
1
0
0
0
2
2
0
0
2
0
0
0
1
2
1
1
2
0
2
2
1
2
0
2
0
1
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
2
0
1
0
1
2
0
0
0
0
2
0
1
2
0
2
0
0
0
0
2
1
0
0
0
0
0
1
1
2
0
1
0
2
0
0
1
0
0
1
0
0
0
1
1
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
1
0
2
0
1
0
2
0
1
1
0
1
0
0
1
1
0
0
1
0
2
1
0
0
1
3
1
0
1
0
0
0
0
1
0
2
0
2
2
2
1
0
0
1
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
2
1
0
1
2
0
0
0
2
0
0
0
0
0
1
0
2
2
0
2
1
3
0
0
2
2
1
0
1
1
2
1
0
4
1
2
0
0
0
0
0
1
2
1
2
0
1
0
0
0
0
1
0
1
2
2
1
0
0
1
0
0
2
0
1
1
0
0
0
2
0
1
0
3
0
2
0
0
0
0
0
0
5
1
1
0
2
1
0
0
0
0
0
0
1
0
0
1
2
0
1
0
2
1
0
1
0
0
0
1
0
2
2
0
0
0
1
0
0
2
1
1
0
0
2
2
0
1
0
0
2
1
0
0
2
0
1
1
0
0
2
0
0
0
2
2
0
0
0
0
2
0
1
2
0
1
0
0
0
0
0
0
0
1
0
2
0
2
1
0
3
1
1
0
0
0
2
0
0
0
0
0
0
1
2
1
0
1
0
1
1
1
0
2
0
1
0
2
1
0
2
2
1
1
0
0
0
1
0
0
2
1
0
0
0
0
0
2
0
0
1
2
1
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
2
2
0
1
0
0
0
0
1
0
0
0
0
0
2
1
2
1
0
2
0
0
2
2
2
0
1
2
0
0
0
1
0
0
0
1
0
0
1
2
0
0
1
0
0
0
0
0
1
2
0
1
0
3
0
1
2
2
2
0
0
2
1
0
1
0
0
0
0
1
0
0
0
2
0
1
1
1
0
1
1
0
0
0
1
1
0
0
0
2
1
2
0
3
1
3
0
0
0
1
2
2
2
1
0
0
2
0
2
0
1
1
1
1
1
0
2
2
0
0
2
0
1
2
1
1
1
0
1
1
0
1
2
1
0
0
1
1
1
0
4
1
0
0
1
0
1
0
1
0
0
0
1
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
1
1
0
0
0
3
0
1
2
1
0
0
2
0
1
0
0
0
0
2
0
0
0
1
1
0
0
1
2
0
0
2
1
0
1
1
0
0
0
0
0
2
0
1
1
0
0
0
2
1
0
3
1
0
1
0
0
1
2
2
2
0
0
0
1
1
0
0
0
2
0
0
1
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
2
0
3
0
0
2
2
2
0
1
0
1
1
0
2
0
0
2
2
1
0
1
0
2
0
1
2
1
0
0
0
2
1
0
1
0
2
0
0
2
2
0
0
0
0
0
0
2
2
1
0
2
0
0
0
3
1
0
2
0
0
0
1
2
0
2
1
1
0
1
0
0
0
2
1
2
0
0
0
1
0
0
1
1
0
0
0
0
1
2
0
1
1
0
0
0
0
0
2
1
0
0
1
0
1
2
2
1
2
2
0
1
0
1
2
0
0
0
0
0
2
1
0
3
0
0
3
4
0
2
0
0
0
0
0
0
0
3
1
2
0
2
0
1
2
0
1
2
2
2
1
2
1
0
0
1
2
2
0
0
0
1
1
1
0
0
2
0
0
0
0
2
1
1
2
0
2
0
1
0
1
0
0
0
1
0
2
0
0
2
1
1
1
2
0
1
0
2
0
1
1
0
0
0
0
2
0
0
0
2
0
0
0
0
1
2
0
0
1
0
0
0
1
0
0
1
2
1
1
2
1
0
0
0
0
0
2
0
1
1
0
0
2
1
0
2
0
0
0
1
0
0
0
0
1
1
0
1
0
0
2
0
0
1
1
0
2
0
0
0
2
1
2
2
0
1
1
1
0
1
0
2
0
0
1
0
0
2
1
0
1
1
2
2
1
1
0
2
0
1
0
0
1
0
0
0
1
0
0
1
0
2
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
3
4
1
0
0
0
2
0
2
1
2
2
0
0
1
1
0
0
0
0
0
1
0
0
1
0
1
0
2
1
0
0
0
1
0
1
0
1
0
0
0
0
2
1
0
1
0
0
0
0
2
2
1
0
0
0
0
2
0
0
0
0
1
0
0
2
0
1
1
0
2
0
0
1
1
1
0
2
0
0
1
2
0
2
2
2
1
0
2
1
0
2
0
0
2
1
1
1
1
1
2
0
0
1
1
0
0
2
1
1
0
1
3
1
0
0
1
0
0
0
0
0
0
1
3
1
0
1
2
0
0
0
0
0
2
0
0
0
1
1
0
0
1
1
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
2
1
1
0
1
0
2
0
0
0
1
0
0
2
0
2
0
0
2
0
0
2
2
0
1
0
0
0
1
2
0
1
0
1
0
1
2
2
0
2
2
1
0
2
0
0
0
0
0
2
2
0
1
1
0
2
1
0
2
0
0
1
0
0
0
2
0
0
1
1
0
0
1
0
0
2
2
2
0
2
0
1
1
0
0
0
0
0
0
1
2
2
0
0
0
0
0
1
1
3
0
1
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
3
3
3
0
1
1
0
1
2
1
2
0
0
1
0
0
2
2
0
1
2
0
0
0
2
0
0
0
0
2
0
1
0
1
2
0
0
0
0
0
1
1
0
0
2
2
0
2
0
0
2
0
0
0
1
0
0
2
2
2
0
1
2
0
2
0
3
1
0
1
1
1
1
0
1
0
1
0
0
2
2
2
1
0
0
0
0
0
1
2
0
0
1
0
1
0
1
0
2
1
1
1
0
0
0
2
2
0
1
0
1
0
0
2
0
0
0
0
1
0
1
0
0
0
3
1
1
0
0
0
1
0
0
0
0
2
1
1
0
2
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
2
1
2
0
1
0
0
0
2
1
0
1
2
1
0
1
0
0
2
0
0
2
0
1
0
2
0
2
0
0
0
0
1
1
0
1
0
1
0
0
0
1
1
0
2
0
0
0
2
1
0
1
1
3
1
1
2
0
2
1
0
0
2
2
1
0
0
3
1
1
1
0
0
0
0
0
0
2
0
0
2
1
0
2
0
2
1
0
1
2
0
0
0
0
0
0
1
0
0
1
0
1
0
2
1
0
2
0
0
1
0
0
2
2
2
0
0
0
0
0
0
2
0
0
1
0
0
0
1
2
0
0
0
0
2
0
0
1
1
1
2
0
0
0
0
0
1
0
2
0
0
2
2
0
0
1
1
1
2
1
0
0
2
0
0
0
0
0
1
0
1
1
0
0
2
2
2
1
0
0
1
2
0
2
2
0
0
1
1
0
0
4
1
1
1
1
0
1
1
1
0
0
0
2
0
2
0
1
0
2
0
0
1
0
0
2
2
1
2
1
1
1
2
1
1
0
0
0
0
1
0
1
2
2
5
0
1
0
1
1
0
0
2
1
1
1
0
2
2
1
0
1
1
1
0
0
1
0
0
1
1
0
1
2
0
0
1
2
0
0
0
0
1
2
0
1
1
3
0
0
2
1
0
0
0
2
0
1
1
2
2
0
2
0
0
3
1
0
2
0
0
1
0
1
0
0
1
2
1
0
0
0
0
0
0
1
1
2
0
2
0
0
0
0
1
0
0
0
0
1
2
0
0
1
0
2
2
1
1
0
0
0
0
2
0
2
2
2
0
0
0
2
0
0
3
2
2
0
0
0
0
2
1
0
1
0
0
0
1
0
0
1
0
1
0
2
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
1
1
1
2
0
2
1
0
0
0
0
2
0
0
0
2
0
2
1
0
1
2
0
0
1
0
2
1
1
2
1
1
0
0
0
2
0
1
0
1
1
0
2
1
2
1
3
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
1
0
3
0
1
0
0
0
0
1
0
0
1
0
1
0
0
2
1
2
1
0
3
1
0
0
1
2
0
0
0
1
1
4
0
0
0
2
2
0
0
0
1
1
0
0
0
2
1
2
1
2
0
2
0
0
1
1
1
0
2
0
1
1
0
0
0
1
3
0
0
1
1
0
0
1
0
2
1
0
1
0
0
1
1
1
0
2
0
0
2
2
1
0
0
0
1
0
0
2
0
0
1
2
1
0
0
0
4
0
1
1
0
0
1
1
0
2
0
0
0
2
0
2
0
1
1
0
0
2
0
0
1
2
0
0
1
1
1
1
1
0
0
2
2
0
1
0
0
1
0
0
0
0
2
1
1
0
0
0
1
0
0
1
1
2
1
0
1
1
0
2
2
0
0
0
2
0
0
0
3
0
1
1
2
0
1
0
0
0
0
0
0
0
0
0
0
2
1
2
2
0
0
1
2
0
1
0
1
0
0
0
0
2
0
2
0
1
0
1
2
0
2
1
0
2
0
1
0
0
2
0
0
1
0
1
1
0
0
2
2
2
1
0
1
0
0
0
0
0
1
1
1
0
2
1
1
1
0
0
2
2
0
1
1
0
1
1
0
1
1
0
1
2
1
1
1
0
0
2
0
0
2
1
2
0
2
0
0
3
1
1
0
0
1
0
3
0
0
2
0
1
0
0
0
1
0
1
0
1
0
1
0
0
0
0
1
0
0
1
1
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
1
1
2
1
2
1
0
1
2
0
7
0
0
0
0
1
0
1
0
2
2
3
0
0
0
1
2
1
1
0
0
2
1
0
1
1
0
0
2
0
0
1
0
1
0
2
2
0
1
1
1
0
1
1
0
0
0
1
0
0
2
0
4
0
0
2
0
1
0
0
1
0
2
2
0
2
0
0
0
2
1
2
0
0
0
0
2
2
0
1
0
2
1
2
0
0
1
1
0
0
2
0
0
1
0
0
1
0
2
0
0
1
2
0
0
2
1
0
0
1
1
0
2
2
1
1
0
0
1
0
0
2
0
2
1
1
0
0
1
1
0
0
1
1
0
0
0
5
0
1
1
1
0
0
1
2
0
0
1
0
0
2
0
2
0
1
1
0
1
0
0
2
2
1
2
2
0
0
1
1
2
2
0
2
1
0
2
2
0
1
2
0
0
1
0
1
2
0
0
1
1
1
2
0
1
2
0
0
0
0
0
1
1
0
1
1
0
0
0
1
0
0
0
2
0
0
1
1
0
1
0
1
0
0
0
2
0
0
7
2
2
1
1
0
0
2
1
0
0
1
0
2
0
2
0
2
2
0
0
0
0
0
1
1
0
2
0
2
0
1
0
0
1
0
2
0
0
0
1
1
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
2
0
0
2
0
0
1
0
0
1
0
0
2
1
1
0
2
0
0
0
0
0
1
0
0
1
1
0
2
0
0
3
1
1
2
3
1
2
2
6
0
3
0
0
1
0
2
0
1
1
0
1
0
0
0
0
0
0
0
1
4
2
0
1
0
0
1
2
1
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
2
1
3
1
0
0
2
0
0
1
2
1
0
0
1
0
0
1
2
0
1
2
2
2
6
0
0
0
0
2
1
1
1
0
0
0
2
2
0
1
0
2
1
1
0
1
0
0
2
0
1
0
2
0
0
0
1
0
0
1
2
1
2
1
2
1
2
2
0
0
2
0
0
0
1
2
1
1
2
0
1
2
0
1
1
0
1
1
0
0
1
2
0
0
0
2
0
0
1
0
0
0
0
1
1
0
2
0
2
1
1
1
2
0
0
1
1
1
1
0
0
0
0
1
1
2
2
0
0
0
0
0
2
0
2
0
1
2
0
0
0
0
2
2
0
0
1
1
0
0
2
1
1
0
1
0
3
0
0
1
0
0
0
1
0
0
0
2
1
1
0
2
2
1
0
1
1
0
2
0
0
1
1
1
2
2
2
2
0
0
0
0
1
0
1
1
0
2
2
2
0
0
2
0
1
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
1
1
0
1
2
0
2
0
1
0
0
1
0
1
2
2
1
0
0
0
0
3
1
0
3
0
2
1
0
0
0
0
0
1
2
2
1
0
0
3
0
1
0
0
1
0
1
0
0
0
2
1
2
2
2
0
0
0
0
1
1
1
1
0
1
0
2
0
1
1
1
0
1
0
1
0
1
0
0
1
0
0
0
0
1
0
1
0
0
2
1
1
0
0
1
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
1
2
2
0
2
1
1
2
0
0
0
1
1
0
0
2
0
2
0
1
0
1
0
1
1
0
0
0
2
1
1
1
0
1
1
0
1
2
1
1
0
1
1
2
0
0
0
2
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
3
1
2
2
3
0
0
2
0
2
2
0
0
0
2
0
0
1
0
0
0
0
1
0
0
1
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
1
0
1
2
1
0
0
0
1
1
0
0
0
0
0
3
0
1
0
1
1
2
0
0
2
0
2
0
0
2
2
0
1
0
2
1
2
1
0
1
0
2
1
1
0
2
0
1
1
1
0
2
1
1
2
0
0
2
2
2
1
0
2
2
0
2
0
0
0
1
2
0
0
0
2
1
2
1
2
1
0
0
0
0
1
0
1
2
1
0
1
1
2
0
0
6
1
1
2
0
0
0
0
0
1
2
0
1
0
2
0
0
1
1
1
1
0
1
1
2
1
0
0
0
2
1
0
0
2
0
0
0
0
0
0
2
2
0
1
1
1
1
0
0
1
0
2
0
0
2
0
2
2
0
1
0
1
0
2
1
2
0
0
0
0
1
1
2
0
0
0
0
0
0
0
2
0
0
0
1
2
1
0
0
2
2
0
0
0
0
0
0
2
1
0
2
0
2
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
1
0
1
0
1
1
2
1
0
0
0
0
2
3
2
1
0
0
0
1
0
1
1
0
1
0
0
0
0
1
0
2
0
1
0
1
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
1
1
0
0
1
1
2
1
2
0
1
1
0
0
0
0
1
1
0
0
1
1
2
0
0
1
0
2
1
0
0
2
0
2
0
2
0
0
2
2
2
2
2
0
4
0
0
3
0
1
0
1
2
0
0
1
1
1
0
1
0
2
2
0
0
0
1
0
0
2
0
1
0
0
2
0
0
0
1
2
0
1
0
0
0
1
2
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
2
0
2
0
0
0
0
2
2
0
0
2
0
1
0
0
1
0
0
0
0
1
2
1
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
1
0
0
0
0
1
1
0
1
0
0
1
0
1
2
0
1
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
2
0
0
0
2
0
0
1
1
0
0
1
1
1
1
0
1
0
0
2
0
0
0
1
1
0
2
1
0
0
1
0
0
0
1
0
0
0
0
2
0
0
1
0
1
1
2
0
1
2
1
0
0
0
1
2
2
0
0
0
2
2
0
0
0
1
2
1
2
0
0
0
1
1
0
0
0
1
1
2
1
2
0
0
0
1
0
0
0
0
0
1
1
2
2
1
0
2
1
0
1
0
1
0
0
2
0
1
0
2
0
0
1
2
0
1
2
7
0
2
0
0
2
2
2
1
0
1
2
0
1
0
2
0
2
2
1
0
1
0
0
1
0
1
1
0
1
1
2
0
0
0
1
1
1
1
0
0
0
0
0
0
0
2
1
0
0
0
2
1
0
0
1
0
0
0
1
2
0
2
0
0
0
1
0
0
0
3
0
0
2
2
2
0
1
0
2
0
0
1
0
0
1
0
1
0
2
1
1
0
0
1
1
2
0
0
2
2
0
1
0
0
0
0
2
0
0
0
0
0
2
1
1
0
0
2
0
2
0
0
0
0
2
0
0
2
0
0
0
1
0
2
2
0
1
4
0
0
0
0
0
0
0
0
4
2
0
1
0
2
2
0
2
0
0
1
0
1
1
2
0
1
2
0
1
0
1
0
0
1
1
0
2
1
2
0
2
0
1
0
0
1
1
0
2
1
0
0
2
1
0
1
2
1
1
2
0
0
2
0
2
0
0
1
2
1
0
1
2
0
0
0
1
0
0
2
2
0
1
2
0
0
2
1
0
0
0
1
0
1
0
1
1
0
0
2
2
0
1
0
1
1
0
1
1
2
0
0
0
0
0
2
0
5
1
0
0
1
0
0
0
0
2
1
1
0
0
0
0
0
2
1
0
0
0
0
0
3
0
0
0
1
0
2
1
0
0
0
0
1
3
0
2
0
0
0
0
1
0
0
0
1
0
1
2
2
1
1
1
1
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
1
2
1
0
2
1
0
1
0
0
2
1
0
0
0
1
0
1
0
1
0
1
0
2
1
0
1
2
0
1
0
0
0
0
0
0
2
0
1
0
0
0
1
0
1
2
1
1
1
0
2
0
0
1
1
1
1
1
1
1
0
2
1
0
0
0
0
0
1
1
0
2
2
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
1
0
0
2
0
2
0
0
1
0
1
0
0
0
0
2
0
2
0
2
1
0
0
2
0
1
0
0
0
1
1
2
0
1
0
1
0
0
1
2
0
0
0
1
0
1
0
1
3
0
2
2
0
0
0
2
2
0
0
0
1
1
0
0
0
1
0
1
0
2
0
0
2
0
0
2
0
0
0
1
2
2
1
2
0
0
1
1
0
1
0
0
0
2
2
0
2
2
0
1
2
0
0
1
0
2
2
0
2
0
1
2
2
1
0
0
2
0
1
1
1
0
0
2
0
0
0
1
0
0
2
2
1
0
1
0
1
0
0
2
3
1
0
2
0
3
0
0
0
0
2
1
0
0
0
1
0
2
2
1
1
0
0
0
0
2
0
0
1
0
2
2
1
1
2
1
2
3
1
0
1
0
2
0
2
0
0
0
0
0
1
0
0
2
2
0
0
0
1
0
0
2
2
1
2
0
0
1
1
0
1
0
1
1
0
2
0
1
2
2
0
0
0
0
0
0
2
0
0
2
0
0
3
1
0
1
1
1
0
0
1
0
0
1
1
1
0
0
1
2
1
1
2
1
1
1
0
0
0
0
1
1
1
2
0
2
0
0
1
0
0
0
1
1
1
2
0
2
0
0
1
0
2
1
0
0
0
0
2
0
0
0
0
0
0
2
2
2
0
0
2
2
0
0
2
1
0
0
0
0
0
0
0
1
2
1
2
2
2
0
0
0
0
2
0
3
2
0
0
1
1
2
2
0
2
2
0
1
1
0
0
2
0
0
2
0
0
0
0
0
1
2
0
0
2
1
0
1
2
1
1
0
0
2
2
0
0
1
0
0
0
1
0
2
1
2
0
2
0
0
0
0
0
1
2
0
0
2
2
0
3
1
0
0
1
0
2
0
0
0
1
1
0
0
0
0
1
1
1
0
0
0
0
0
2
0
1
0
0
0
1
1
0
3
0
1
4
0
2
1
0
1
0
1
0
1
0
0
2
0
1
2
1
0
0
2
0
0
0
0
1
2
2
2
0
0
0
1
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
1
2
0
0
1
0
0
0
0
2
0
1
0
0
0
0
1
1
0
1
2
1
0
0
0
1
0
2
0
0
1
1
0
0
2
1
0
2
0
0
0
0
0
0
0
1
1
1
2
2
2
2
2
1
0
1
0
0
0
2
3
0
0
0
1
2
0
0
0
1
0
0
1
0
0
2
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
2
0
2
0
2
0
2
1
2
0
0
2
2
0
0
0
1
0
5
2
0
0
2
0
0
1
2
0
1
2
0
2
1
2
2
1
2
0
2
0
2
0
1
0
2
2
0
0
2
0
1
0
2
0
2
0
0
2
0
2
1
1
0
0
2
0
1
2
1
0
1
0
2
0
2
0
0
0
0
1
1
1
1
2
1
0
0
0
2
2
1
0
0
0
1
0
1
1
0
1
0
1
1
0
2
1
1
1
0
1
0
0
1
0
0
0
0
2
0
0
1
2
2
1
2
1
1
1
2
2
0
1
3
0
1
0
1
0
0
3
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
1
2
0
1
0
6
2
0
0
2
0
2
2
2
1
1
2
1
0
0
5
0
0
0
6
0
0
1
0
1
2
0
1
0
0
0
0
0
1
0
1
0
0
0
0
2
1
2
0
3
1
1
0
1
2
1
0
1
0
2
0
0
2
1
2
0
2
0
0
0
1
0
0
1
2
0
2
0
0
0
1
2
2
1
1
2
0
0
2
0
0
0
0
0
1
2
2
2
0
0
2
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
2
3
2
2
0
0
2
0
0
0
1
2
0
1
0
2
0
2
2
1
2
0
0
1
1
2
4
2
0
2
2
0
0
0
0
0
0
2
1
2
0
0
0
0
1
0
1
0
2
0
0
1
3
0
0
1
0
1
1
0
1
0
0
0
0
2
2
0
0
0
1
0
0
1
2
0
0
0
1
1
0
0
2
0
5
2
0
1
1
1
1
0
0
0
1
0
1
0
0
0
0
1
0
0
2
1
1
0
0
0
0
1
0
0
0
1
2
1
0
3
1
1
1
0
0
0
3
0
1
1
1
0
0
0
0
2
1
0
1
1
2
0
1
1
2
2
2
0
0
0
0
0
0
0
0
2
1
0
0
2
1
0
0
3
0
0
3
0
0
0
2
1
2
1
1
0
1
2
0
0
0
0
0
0
0
1
0
0
0
1
1
2
0
2
3
0
1
2
0
0
0
0
0
2
0
1
2
0
0
1
1
0
1
1
0
0
0
0
0
2
2
0
0
0
1
2
0
1
0
0
0
1
2
1
0
0
3
1
0
0
2
0
2
1
2
1
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
1
0
0
2
0
2
0
0
0
0
0
0
1
0
2
0
2
0
2
1
0
3
1
0
1
2
0
0
1
0
0
2
0
0
1
1
0
0
0
0
1
1
0
0
1
1
1
0
0
1
2
1
0
0
2
1
1
0
0
0
2
1
1
1
0
1
0
2
1
1
2
2
0
0
0
1
0
0
0
2
0
2
0
0
1
0
0
0
1
0
1
2
0
0
0
2
1
0
0
1
1
0
0
0
0
0
0
2
0
2
0
4
0
1
0
0
0
1
0
0
0
1
0
2
1
1
1
0
0
0
0
0
0
1
0
1
1
2
2
0
0
1
0
0
0
1
0
0
2
0
0
1
0
0
0
1
1
1
2
1
2
0
0
2
1
0
2
0
1
0
1
0
0
0
2
1
0
1
0
0
1
0
0
2
1
0
2
2
1
3
1
0
1
1
0
0
0
0
2
2
2
0
0
0
2
1
1
1
0
2
1
1
0
0
1
0
2
0
2
2
1
2
1
0
1
0
1
1
0
2
0
1
0
0
1
2
2
0
2
0
0
0
1
0
1
1
0
0
0
0
2
0
1
0
0
1
0
0
1
0
0
0
0
2
0
1
2
1
0
0
0
1
0
0
1
0
0
1
1
0
0
2
1
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
3
1
1
0
0
1
2
2
0
1
0
2
0
2
0
0
2
0
0
0
1
2
0
1
2
2
2
1
0
2
0
2
0
2
0
0
0
0
0
2
0
0
1
0
0
1
1
2
2
1
0
0
0
0
2
0
1
0
2
0
0
0
2
0
2
1
0
0
7
0
0
1
1
1
2
0
1
1
0
0
1
0
0
0
1
0
1
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
2
0
0
2
0
2
0
1
0
0
1
1
0
0
0
0
1
2
1
0
1
0
0
0
2
1
0
0
0
2
0
0
1
2
1
0
0
1
0
0
1
0
1
0
1
1
2
0
1
0
0
1
1
2
1
2
0
1
1
1
2
0
2
4
0
0
3
1
0
0
0
0
0
0
1
0
1
0
1
2
0
0
0
1
2
0
0
2
0
2
0
0
2
0
1
2
0
0
0
1
0
2
0
0
1
0
0
1
0
1
0
2
1
0
0
0
0
1
0
0
0
2
0
1
0
0
1
0
1
0
1
1
2
0
0
0
1
2
0
1
0
1
1
2
0
1
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
1
2
1
1
0
0
1
0
2
1
1
0
2
2
1
0
0
0
0
0
0
1
2
1
0
0
0
0
1
0
0
0
2
2
0
0
3
1
0
1
0
1
1
0
0
0
0
1
0
0
2
1
1
0
1
0
0
1
1
0
2
2
2
0
1
1
0
0
1
1
0
0
0
0
0
1
1
1
0
1
1
0
1
1
0
0
0
0
0
2
0
0
1
0
1
0
0
1
1
1
2
0
0
0
1
2
0
0
0
0
2
1
0
1
0
0
2
4
3
2
1
0
0
0
0
1
0
0
1
2
0
0
0
0
2
0
0
0
0
0
2
1
0
1
3
1
2
0
1
0
1
2
1
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
2
0
2
1
0
1
0
0
0
0
0
1
2
1
1
0
0
1
0
0
1
1
0
0
0
1
1
0
0
1
1
0
0
0
0
0
1
0
0
2
0
3
0
2
1
0
2
0
0
0
0
0
0
1
0
1
0
1
0
2
3
0
0
0
0
1
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
2
1
1
0
2
0
0
0
0
2
2
0
1
0
0
1
0
0
0
1
0
2
1
2
0
7
0
0
0
1
0
2
0
0
2
0
0
0
1
2
0
1
0
1
0
0
0
1
0
2
0
3
2
1
0
0
1
2
0
0
1
0
2
0
0
2
2
2
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
1
1
0
0
1
0
0
0
0
0
4
0
4
0
0
3
2
0
1
2
1
1
1
0
2
2
0
2
2
2
0
0
1
0
1
1
0
1
2
0
1
1
3
3
1
0
0
1
0
2
0
1
1
0
1
0
0
1
0
0
1
1
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
2
2
0
1
0
0
2
0
1
0
1
0
2
2
0
1
0
0
0
0
0
0
0
2
0
0
1
1
0
0
1
0
0
1
0
3
0
0
0
0
0
2
0
1
0
2
2
0
0
0
0
2
0
0
1
0
0
2
0
0
1
0
2
2
1
0
0
2
1
0
1
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
1
2
2
2
1
0
0
0
0
0
1
1
0
0
2
1
0
2
2
0
1
1
0
0
0
1
0
1
2
1
0
2
0
1
2
1
0
0
0
0
0
2
1
1
2
0
0
1
0
0
1
0
0
1
0
0
0
2
1
1
0
1
0
2
2
0
1
2
2
1
1
0
2
0
0
0
0
2
2
0
0
2
1
0
1
0
1
0
0
0
2
0
2
1
1
0
0
2
0
2
0
0
1
1
2
0
0
0
1
2
1
1
0
2
1
1
1
0
1
0
2
0
0
0
1
1
2
1
1
1
0
1
0
1
1
2
0
0
1
1
0
1
0
0
1
1
2
0
1
0
1
0
1
2
0
2
1
0
1
0
1
2
1
2
0
1
2
2
0
2
0
0
0
0
1
0
2
0
1
1
0
0
1
1
1
1
0
0
0
1
2
1
0
0
1
1
0
2
1
0
2
0
0
0
1
0
0
0
2
0
1
0
3
0
0
1
2
2
1
0
1
0
2
0
0
0
0
2
2
1
0
2
0
0
0
0
1
0
0
2
0
2
1
0
0
1
0
1
1
1
0
0
0
1
0
1
0
0
2
0
0
0
1
0
0
0
0
0
1
0
1
0
0
2
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
3
1
0
0
2
0
0
2
0
0
0
1
2
1
2
1
1
0
2
0
1
0
1
0
2
1
2
1
1
0
0
0
0
0
1
1
0
0
1
1
2
0
0
2
0
1
0
2
0
0
0
2
0
1
0
2
0
1
1
1
1
1
2
0
0
0
2
0
2
0
0
0
1
1
0
0
0
2
2
0
2
0
1
2
0
0
1
1
2
3
1
0
4
0
0
0
0
0
0
1
0
0
2
2
0
3
3
1
2
0
1
1
1
3
1
2
0
0
0
0
2
2
1
0
0
0
0
0
1
0
2
1
2
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
2
1
0
0
0
0
1
0
1
1
1
1
2
0
0
0
0
1
2
0
0
2
0
0
0
0
2
0
0
0
1
2
0
2
1
0
0
1
2
0
1
1
2
2
1
2
2
0
1
1
0
1
0
1
1
0
1
2
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
1
1
0
0
2
3
0
2
0
0
0
0
0
1
0
1
1
2
2
0
0
0
1
0
1
0
1
2
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
1
1
0
0
2
1
0
2
0
0
2
2
1
0
2
0
1
1
0
0
0
2
2
0
1
1
0
0
0
2
0
1
0
1
2
2
1
1
0
2
0
2
2
0
1
0
0
1
0
0
0
2
0
2
0
1
1
0
2
0
1
0
0
0
0
0
0
1
0
0
1
2
3
0
1
0
1
0
2
0
1
2
0
0
1
4
1
0
0
0
2
0
0
1
2
1
2
1
0
1
0
0
1
1
1
2
1
0
0
0
0
1
0
0
2
0
0
1
0
0
1
1
2
1
0
1
0
0
0
1
2
2
0
1
1
1
0
0
2
6
0
1
2
1
0
1
1
1
2
0
2
0
0
0
0
0
1
0
2
1
1
0
0
0
0
1
2
0
0
0
0
0
2
2
1
0
1
0
0
0
2
0
0
0
1
1
1
1
0
0
1
0
0
0
2
1
1
0
1
0
1
0
0
0
0
0
0
0
2
2
0
2
0
2
0
0
0
1
1
0
1
0
2
0
1
1
2
0
1
2
0
0
0
1
2
3
0
0
2
0
0
0
1
0
2
1
4
0
1
2
2
0
0
0
0
3
0
0
2
2
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
3
1
7
0
0
0
1
0
1
0
0
0
0
1
1
2
1
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
3
1
0
0
3
1
1
2
0
1
0
0
0
0
0
0
0
0
0
2
1
0
2
2
1
1
2
1
0
1
0
1
2
0
2
0
0
1
0
1
0
0
2
0
0
0
1
0
0
2
0
2
2
2
1
2
1
0
0
0
1
2
0
0
0
1
1
1
0
0
0
0
1
0
0
0
1
0
0
0
2
2
0
1
0
0
0
0
1
2
0
0
2
0
2
1
1
1
0
2
1
0
0
3
2
1
2
0
1
1
0
1
2
1
0
0
0
1
1
0
0
1
0
0
1
1
1
3
0
0
0
2
2
1
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
4
6
2
0
0
0
2
0
0
0
0
2
1
2
2
0
1
0
0
0
2
0
0
1
1
1
2
0
0
2
2
0
0
0
2
0
0
0
1
0
0
2
0
1
1
0
0
0
2
0
0
0
2
2
0
2
4
0
1
1
1
1
0
2
0
0
1
2
1
1
1
2
0
1
0
0
2
0
1
1
0
2
0
1
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
1
0
2
1
1
0
0
0
0
1
0
0
0
0
1
0
0
2
0
1
1
1
0
0
0
0
0
0
0
0
2
0
0
1
1
1
2
2
1
0
0
0
2
1
2
1
3
0
2
1
0
1
3
0
0
0
0
0
0
0
0
1
2
1
0
1
1
2
1
1
0
0
0
1
2
1
0
2
0
0
0
1
0
0
1
1
1
1
0
0
0
1
1
0
1
0
0
1
1
0
0
0
1
1
0
0
0
0
1
0
0
1
1
0
2
0
0
0
2
0
1
1
0
0
1
1
0
0
1
0
1
2
2
2
1
2
1
0
3
0
0
1
0
1
0
0
0
0
0
1
0
1
1
0
1
0
2
0
1
0
3
0
1
0
1
1
1
1
2
0
0
3
0
0
2
0
0
0
2
0
0
0
1
2
0
2
0
0
0
0
1
0
0
0
1
0
0
2
0
0
2
0
1
1
0
0
0
0
0
1
2
1
1
0
2
1
0
0
2
0
1
0
0
1
1
1
0
1
1
1
1
0
0
1
1
1
1
0
0
2
0
0
1
0
0
2
1
0
0
1
2
0
0
0
3
1
0
1
4
0
1
2
0
2
0
1
0
0
0
0
0
0
0
3
0
2
2
0
0
2
1
0
0
1
1
0
0
0
0
0
0
2
0
2
3
0
0
1
2
1
0
0
0
0
0
0
0
2
1
1
0
0
0
2
2
2
0
0
1
0
2
0
1
0
0
4
0
2
0
0
0
0
1
1
1
0
0
0
0
1
0
1
0
1
2
2
0
0
0
2
0
0
0
1
0
0
1
1
0
0
1
1
0
0
2
0
0
1
1
0
2
0
0
0
0
2
1
2
1
1
1
2
1
0
1
1
1
1
0
2
1
1
2
0
0
1
1
0
0
2
0
0
1
0
0
0
0
1
0
2
2
3
0
0
1
0
3
0
1
0
2
0
0
1
0
0
1
0
1
2
0
1
1
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
2
0
1
1
0
0
0
0
1
0
1
0
0
2
0
0
0
4
0
0
0
2
2
0
2
1
1
2
2
1
1
0
1
0
0
0
1
2
0
3
2
2
0
2
1
0
0
0
2
0
1
0
0
0
2
1
0
1
0
2
0
0
1
0
1
2
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
2
3
0
0
1
2
0
0
0
1
0
2
0
1
0
1
0
1
0
2
0
1
2
0
0
2
0
0
1
2
0
2
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
1
1
1
1
0
0
0
0
0
0
1
0
2
1
0
1
0
1
1
0
2
0
0
0
0
2
0
0
1
0
2
2
0
0
1
2
1
0
1
0
1
0
1
1
0
0
0
3
1
0
0
1
0
2
0
3
1
2
2
0
0
1
1
0
1
0
2
0
0
1
0
0
1
0
0
1
0
0
0
2
0
1
0
0
0
0
1
1
1
0
1
1
0
0
2
0
0
1
1
2
2
2
0
1
0
0
0
0
1
2
1
0
2
0
0
0
0
0
1
0
0
1
2
1
0
1
0
0
2
0
1
0
1
1
0
0
0
0
0
0
1
0
1
1
1
0
1
1
0
0
0
0
1
0
0
1
0
2
1
0
0
1
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
4
0
1
1
1
0
1
2
0
2
1
1
0
2
1
1
1
0
2
2
0
0
1
0
1
1
0
2
1
1
0
0
0
0
0
1
0
0
2
0
2
0
1
3
1
0
1
2
0
2
0
0
0
0
0
2
0
0
1
1
0
1
0
0
1
1
1
0
0
0
1
1
0
2
1
0
0
2
1
0
0
0
2
0
1
1
0
3
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
2
0
0
2
1
0
2
0
0
1
0
1
0
0
1
0
1
0
0
0
0
2
2
0
1
0
0
2
0
1
0
0
1
0
0
2
1
0
0
0
1
0
0
0
1
0
1
1
0
2
0
2
0
3
1
0
1
0
2
2
1
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
2
1
2
1
0
1
0
0
0
2
1
0
2
0
2
2
0
1
1
0
0
0
1
0
2
0
1
0
0
1
1
2
1
0
0
0
2
0
0
2
1
2
3
1
2
0
2
1
0
0
0
0
3
2
0
0
0
2
2
0
2
0
1
0
1
0
0
1
0
0
0
2
1
2
1
1
1
1
0
0
0
2
2
0
0
2
0
1
0
0
2
0
0
1
1
0
0
0
0
0
1
1
0
0
2
1
0
0
0
3
1
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
2
1
0
1
0
1
2
0
0
2
1
1
1
2
0
0
1
1
3
0
0
0
3
1
1
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
1
2
1
2
0
0
0
0
0
2
0
0
0
0
1
0
2
2
0
2
2
1
0
0
1
0
0
0
0
0
2
2
0
2
2
0
0
0
0
0
2
0
1
2
2
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
2
2
0
0
2
0
0
0
0
0
1
1
1
0
1
0
2
1
0
2
1
0
0
0
2
0
1
2
2
1
1
2
0
1
1
1
2
2
0
0
0
0
0
2
1
1
3
1
0
0
0
1
0
0
0
2
0
1
2
2
2
1
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
3
1
0
0
1
2
2
0
2
1
2
0
0
0
1
0
1
0
0
1
0
0
2
0
1
1
2
0
1
0
0
0
1
1
0
1
2
0
1
2
2
1
0
0
1
0
0
0
1
0
1
0
0
1
0
1
0
1
0
0
0
2
1
1
3
2
0
0
0
1
0
0
1
0
0
2
0
1
0
1
3
0
0
2
0
0
0
0
1
1
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
1
0
1
0
1
0
1
0
0
0
0
2
1
0
0
1
0
0
1
1
2
0
0
0
3
1
1
1
0
0
1
0
0
2
1
0
2
0
0
0
0
2
0
2
0
0
1
0
1
0
0
0
1
1
2
2
0
2
0
0
1
0
2
4
1
0
0
0
2
0
2
1
0
0
1
1
2
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
1
0
1
0
1
0
1
1
2
4
2
1
1
1
0
0
0
0
0
0
3
2
1
0
0
0
0
1
0
0
0
2
0
0
0
0
1
1
0
0
2
2
1
0
1
1
1
0
0
1
0
1
0
1
1
0
1
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
1
0
0
2
0
0
1
1
0
2
0
0
1
0
2
1
0
1
0
0
1
2
0
2
0
3
0
2
2
0
1
1
2
2
0
1
1
0
2
0
2
0
0
2
0
0
1
1
0
1
1
0
3
0
1
0
0
1
1
0
1
2
1
0
0
0
2
0
0
1
2
0
2
2
0
1
0
1
2
0
0
0
2
2
0
0
1
0
0
0
0
0
1
2
1
0
0
0
0
0
1
0
1
0
1
0
2
1
0
0
0
0
2
0
2
0
3
0
1
2
0
0
0
0
0
0
0
2
2
1
2
0
1
0
2
0
1
1
0
0
0
0
1
0
0
0
0
2
0
2
0
2
2
1
0
1
1
0
0
0
0
0
2
1
0
0
0
0
1
2
0
0
1
0
1
1
0
0
0
1
1
1
0
0
0
1
1
1
0
0
1
2
1
0
0
1
0
0
1
1
0
2
0
1
0
0
0
1
0
0
0
2
2
2
1
0
0
0
1
0
1
1
0
1
1
1
0
0
0
2
1
2
0
1
0
0
2
2
0
1
1
1
3
2
0
0
2
1
0
0
0
1
0
1
0
0
0
1
1
0
0
1
3
0
1
0
1
0
1
1
1
0
0
1
3
0
5
0
0
0
1
1
0
0
2
2
2
2
2
0
2
2
2
2
0
0
0
2
0
2
2
0
0
1
0
0
0
2
0
3
0
1
0
1
0
1
0
1
0
0
2
0
0
2
0
0
0
2
1
1
0
0
2
0
1
0
1
0
0
2
1
3
0
0
1
0
2
0
1
1
1
1
0
2
0
2
2
0
0
2
0
0
2
0
0
0
0
2
1
0
0
0
0
1
0
0
0
1
2
0
0
1
0
1
0
0
0
0
1
0
0
2
0
1
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
1
0
1
0
1
0
0
1
0
2
0
2
0
0
2
2
0
0
0
0
0
2
1
2
0
1
0
1
0
2
0
0
0
0
0
2
0
0
2
2
0
0
1
1
2
3
1
0
0
0
1
0
0
1
0
1
1
1
0
1
2
1
0
1
0
1
2
0
2
0
1
1
1
0
1
1
0
0
1
1
0
0
0
1
2
0
0
0
2
2
0
0
2
1
1
0
0
3
2
1
1
0
1
1
2
0
0
2
0
1
0
1
0
2
0
0
2
0
2
1
1
0
1
0
1
0
0
0
1
1
2
1
3
0
1
2
2
0
0
2
0
1
1
0
1
1
2
1
0
2
0
0
1
1
2
0
0
0
1
1
0
2
0
0
0
1
0
2
2
0
2
0
0
0
0
0
0
1
1
1
0
1
0
2
1
0
0
0
1
0
0
0
2
0
0
0
0
4
0
0
0
2
0
0
2
2
0
2
2
2
0
1
0
1
1
2
1
0
2
1
0
1
0
1
1
0
2
0
1
1
0
2
1
1
2
0
0
0
1
0
0
0
1
2
0
2
1
0
0
3
2
1
0
0
4
0
2
1
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
1
0
0
3
0
2
0
2
0
1
0
1
0
1
1
1
2
0
2
0
2
0
0
1
1
0
2
0
2
0
0
0
1
0
1
1
0
2
0
0
1
2
0
1
2
2
0
0
2
0
1
0
1
1
0
0
0
1
0
1
0
0
2
0
0
2
1
0
0
2
0
2
0
0
1
2
2
0
1
1
10
0
0
0
0
2
1
0
0
2
0
1
0
2
0
0
0
1
1
0
0
0
0
0
1
1
2
1
2
0
1
0
1
0
2
0
1
0
2
2
1
0
0
3
1
0
1
1
2
2
0
0
0
0
1
0
0
0
1
0
0
0
0
2
1
1
0
0
0
0
1
0
1
1
2
1
0
0
1
0
1
2
2
0
0
0
1
1
1
0
1
2
0
2
2
0
1
0
0
0
0
2
3
0
0
2
0
1
2
2
0
2
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
1
2
2
2
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
2
0
2
0
0
1
0
0
2
2
0
2
1
1
1
0
1
1
0
0
0
1
0
0
0
2
1
0
0
0
1
2
2
0
0
1
1
0
0
1
2
0
2
0
0
0
1
0
0
1
1
0
1
0
1
1
2
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
1
2
2
0
0
0
1
0
0
0
1
0
0
1
0
0
2
2
0
0
0
0
1
0
0
0
2
0
0
0
2
2
1
0
0
1
0
1
0
1
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
1
2
0
0
0
0
1
1
0
1
0
2
0
1
1
0
2
0
1
0
0
2
1
1
3
2
2
1
0
0
1
0
0
1
1
0
0
0
1
0
0
2
0
2
0
0
2
1
0
0
0
0
1
1
2
0
2
1
1
1
0
2
1
0
0
0
0
1
0
1
0
2
1
1
2
0
1
0
0
0
0
0
0
0
2
1
0
3
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
3
0
0
2
0
0
0
1
0
0
0
1
0
0
3
2
0
0
0
2
0
1
2
2
1
1
1
0
0
0
2
2
2
1
1
0
2
0
0
0
3
0
0
0
0
0
2
0
1
2
2
0
0
1
0
1
1
1
0
0
0
0
0
0
1
0
2
0
0
2
1
2
2
0
0
0
1
2
1
1
0
0
2
0
0
1
0
0
2
2
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
1
1
1
2
0
2
0
0
2
1
2
0
0
2
1
0
1
2
0
0
2
2
0
0
0
0
0
1
0
0
1
2
2
1
0
2
1
1
0
0
0
1
1
2
0
0
0
0
0
0
0
2
0
0
1
2
0
1
0
0
1
0
0
0
0
2
1
0
0
1
0
2
0
0
1
1
1
0
1
2
0
0
2
1
1
2
0
0
0
1
2
2
0
1
3
1
1
0
1
2
0
2
1
1
2
2
2
0
3
1
1
0
2
1
2
1
1
0
0
0
0
0
2
1
0
0
0
1
0
3
2
0
1
0
0
2
0
2
0
2
0
1
1
0
1
0
0
1
1
1
1
0
0
1
0
0
0
1
0
2
5
0
0
0
0
0
2
3
0
0
0
0
0
0
1
0
0
0
1
0
0
1
2
0
2
0
0
2
1
0
0
2
0
0
1
1
0
0
2
2
0
0
1
1
0
0
1
3
2
0
0
1
2
0
0
0
0
0
0
3
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
2
7
1
0
2
0
2
0
2
1
2
1
1
2
2
0
0
2
1
0
0
2
0
2
0
0
1
0
2
1
1
0
0
1
0
0
0
3
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
1
0
0
1
0
1
1
2
0
0
3
2
2
1
1
0
2
0
0
0
1
0
1
2
2
0
0
0
2
1
0
0
1
1
1
0
0
0
0
0
0
1
1
0
1
1
0
1
1
2
0
0
0
0
2
1
0
2
1
1
0
0
0
1
0
1
0
1
1
3
1
1
0
2
0
0
0
0
3
0
0
1
0
0
0
1
0
2
0
2
0
3
0
0
1
0
2
2
0
2
2
2
0
1
0
2
0
1
2
0
0
0
1
0
2
2
0
0
0
0
1
2
2
0
2
0
1
0
2
2
1
0
2
2
0
1
1
1
0
0
0
0
2
0
0
1
2
0
0
0
0
0
1
0
2
0
0
1
0
3
2
1
0
2
0
0
2
2
1
1
2
2
1
1
0
0
1
1
1
0
0
1
1
0
1
2
1
2
0
0
1
1
0
0
0
1
0
1
1
0
0
0
0
1
1
0
1
0
0
0
0
0
1
2
2
0
1
1
3
0
1
2
0
0
2
0
0
1
0
0
1
1
1
0
0
0
0
0
1
1
0
2
0
0
2
0
1
0
1
0
1
1
0
1
1
0
0
1
2
0
1
0
1
1
1
0
0
0
1
0
0
1
2
1
0
2
2
2
0
1
0
0
2
1
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
3
0
2
0
1
0
0
0
1
1
0
0
0
1
1
0
1
2
2
0
0
2
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
2
2
2
1
0
0
0
0
1
0
0
0
1
1
0
1
2
0
2
2
1
2
2
2
0
0
1
0
1
0
0
0
1
0
1
1
2
0
1
2
1
3
0
1
0
2
2
0
1
2
4
1
0
0
5
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
3
1
0
0
1
1
0
0
1
0
0
0
2
2
4
2
1
1
0
0
1
0
0
0
1
2
0
0
2
1
1
1
1
0
0
0
1
2
0
0
0
0
0
1
0
2
0
0
0
0
0
2
2
1
1
1
2
0
0
0
1
0
0
1
2
2
2
3
0
2
0
1
2
0
0
1
0
1
6
3
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
2
2
0
0
1
0
0
0
2
2
1
1
0
1
2
0
0
0
0
2
0
1
1
2
0
2
0
1
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
1
2
1
1
0
0
0
0
1
1
2
0
2
3
0
0
3
1
0
2
0
1
0
1
1
0
0
0
0
0
1
0
0
0
1
2
0
0
1
0
1
0
0
2
2
2
2
0
0
0
1
0
0
0
0
0
2
3
3
2
2
2
1
0
0
1
1
0
1
1
0
2
0
2
2
3
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
1
1
0
0
2
2
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
1
0
3
0
1
0
0
0
2
0
1
5
0
1
0
1
0
1
0
0
0
0
0
0
1
2
0
2
0
0
0
1
2
0
0
0
3
1
0
0
1
0
2
2
1
0
1
0
1
1
0
1
0
3
1
1
2
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
1
1
0
1
4
1
1
0
0
1
0
0
0
2
2
1
0
1
0
0
0
1
0
2
0
0
0
0
2
0
1
1
2
0
1
2
2
5
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
2
0
1
1
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
1
2
0
2
0
0
2
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
1
0
0
1
2
0
0
0
0
2
0
2
1
2
2
2
0
0
0
0
1
0
1
0
0
2
0
0
2
0
2
2
0
2
0
0
0
1
0
1
1
0
0
0
0
0
1
3
0
1
0
0
0
0
0
1
0
0
1
2
2
1
1
3
1
1
2
0
0
1
0
0
2
1
2
0
1
1
0
0
0
1
0
2
0
2
0
0
1
1
2
0
0
0
4
0
2
1
0
2
0
1
1
2
0
2
1
1
1
0
2
0
0
0
0
1
1
2
0
0
1
0
2
2
1
1
1
2
0
0
0
1
0
1
0
1
0
1
1
2
0
0
0
0
1
2
0
2
1
0
0
0
0
1
0
0
1
1
0
0
0
0
3
0
2
0
0
2
2
1
0
0
0
0
1
1
1
0
1
1
2
2
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
1
0
1
1
0
2
1
0
2
0
1
0
1
1
3
0
1
0
0
0
0
2
0
2
0
2
1
1
2
0
3
0
0
0
1
0
0
0
1
0
0
3
1
3
0
1
0
2
2
2
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
2
3
2
0
2
0
1
0
0
0
0
0
1
1
2
0
0
0
1
0
1
0
0
0
1
3
0
0
2
0
0
1
2
1
1
1
1
0
2
2
1
0
1
2
0
2
0
0
1
2
3
0
0
0
1
1
2
1
2
2
1
1
1
0
0
0
2
1
0
2
1
0
1
0
0
2
2
1
2
0
0
0
0
0
0
1
0
2
0
0
2
0
0
1
0
0
0
0
1
1
1
3
1
0
0
2
0
0
1
1
0
1
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
4
0
2
1
0
0
0
0
0
0
0
1
0
2
1
2
1
0
0
2
0
2
0
1
0
1
1
0
0
2
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
2
0
1
0
2
0
1
1
0
1
1
1
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
3
1
1
0
1
0
0
1
1
1
2
1
0
1
1
1
2
0
2
1
0
0
2
0
1
2
0
0
2
0
2
0
1
0
1
1
0
0
1
1
0
1
0
0
1
0
1
0
0
1
2
0
0
1
1
1
2
0
0
0
2
0
1
1
0
0
1
1
0
1
0
0
0
2
0
0
2
0
1
0
2
1
0
0
2
2
0
1
0
0
0
2
0
0
0
2
0
0
0
0
2
0
2
0
0
1
0
1
1
0
0
1
1
0
2
0
1
0
0
0
2
0
2
1
1
0
0
0
2
0
0
1
2
0
1
2
0
0
0
0
0
0
1
0
0
2
2
1
0
2
0
2
0
0
0
0
0
1
0
2
1
3
2
0
2
1
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
2
1
1
0
0
1
2
1
2
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
2
0
0
2
0
3
2
0
2
0
1
0
2
0
1
0
0
1
0
0
2
0
0
0
1
0
0
0
1
0
1
0
2
1
1
0
1
2
0
0
0
1
1
0
1
1
1
0
0
0
0
1
0
1
2
2
0
0
0
2
0
1
0
0
0
1
0
2
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
1
1
2
1
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
1
0
1
0
0
0
1
0
0
1
1
1
2
0
2
0
2
2
1
2
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
1
1
1
1
1
0
0
1
0
2
1
1
1
0
0
1
2
0
1
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
1
2
0
1
0
1
0
1
0
1
0
1
0
0
0
2
0
2
0
2
0
2
0
0
2
0
0
1
0
2
0
0
0
0
1
1
0
0
1
0
2
0
2
0
0
0
0
2
0
1
1
1
0
0
0
0
0
1
0
0
0
2
0
0
1
2
0
0
0
0
1
0
0
1
0
1
1
1
3
1
0
1
0
1
1
0
0
1
1
1
2
0
0
1
0
1
0
0
1
2
0
0
0
0
2
2
0
2
0
2
0
2
0
0
1
0
0
1
1
0
0
0
0
1
0
1
0
2
2
0
1
1
0
0
0
1
2
0
0
1
4
0
2
0
0
0
0
0
0
2
1
0
2
0
0
0
0
1
2
0
2
0
2
0
1
2
1
2
1
2
0
0
3
1
2
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
2
0
1
0
0
2
0
0
1
0
0
2
2
2
0
0
0
2
2
1
2
0
1
0
1
1
0
2
1
0
0
1
0
1
0
4
1
1
1
1
2
2
0
1
0
1
0
2
0
2
0
0
1
0
0
0
1
2
0
2
0
2
2
0
0
1
0
0
2
1
3
1
0
1
0
2
1
1
0
0
1
1
0
0
1
0
0
0
0
0
0
1
2
0
2
1
1
0
0
0
1
1
1
1
0
0
1
1
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
2
2
0
0
2
1
0
0
1
1
0
2
2
0
0
0
2
0
0
0
0
0
2
0
2
0
2
0
0
1
0
0
1
0
2
0
1
0
0
0
0
2
1
2
2
2
1
0
2
0
2
0
0
0
0
0
2
1
0
1
2
1
0
0
0
1
2
2
0
0
2
0
0
0
2
2
0
0
0
2
1
2
0
1
0
0
0
1
2
0
2
0
0
0
0
0
3
0
1
0
1
1
1
3
2
0
0
0
1
0
2
4
0
0
0
1
0
0
2
1
2
2
1
0
1
1
1
2
0
0
1
0
0
1
0
1
1
1
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
1
0
2
1
0
0
2
2
0
0
1
0
0
0
1
0
0
0
1
0
0
2
1
1
0
0
0
0
0
3
2
0
1
2
2
2
0
0
0
3
0
1
1
0
0
0
0
0
0
1
0
0
2
0
0
0
2
1
0
0
1
0
0
1
0
1
1
2
0
1
1
0
1
2
1
0
1
0
2
0
1
0
2
2
0
2
1
2
0
0
0
0
0
0
5
0
1
2
0
1
1
3
1
0
0
2
1
2
1
0
2
0
1
0
2
2
2
0
0
1
1
1
0
0
2
0
0
1
2
0
0
0
0
1
1
0
1
1
1
1
2
2
0
1
0
2
0
2
0
3
0
2
3
1
0
0
2
0
0
0
0
1
0
1
2
0
4
2
2
0
1
0
1
2
2
2
1
2
0
0
0
0
0
1
0
1
0
0
0
0
1
1
2
1
0
0
0
0
2
0
0
0
1
2
0
1
1
0
2
1
1
0
2
0
2
1
0
0
0
4
0
2
0
1
0
0
0
0
0
0
0
1
2
2
1
0
0
0
1
2
0
0
2
0
0
0
4
0
0
0
0
2
4
2
0
3
1
1
0
0
3
0
1
0
0
0
1
3
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
3
0
0
0
0
1
0
0
0
0
0
6
1
0
0
0
1
0
2
1
0
0
0
1
0
0
0
2
2
1
2
0
0
0
0
0
0
1
0
1
1
2
0
1
0
0
1
2
1
2
2
0
2
0
1
0
2
1
0
0
1
0
1
0
0
0
0
0
1
2
3
0
0
1
1
0
0
2
0
0
0
2
0
1
0
1
0
0
1
0
0
1
0
0
2
0
1
0
0
1
2
1
1
0
0
1
0
0
0
1
0
1
0
1
1
0
0
0
0
2
0
1
1
0
2
0
0
0
2
0
1
0
0
0
1
0
0
1
0
1
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
2
0
2
2
1
0
2
0
0
2
0
2
2
0
0
0
1
0
0
0
2
1
1
1
0
1
0
2
0
1
0
0
0
2
0
1
2
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
2
1
0
3
3
2
0
2
0
2
0
1
0
1
0
0
0
1
0
0
0
0
0
2
0
2
1
0
0
2
1
0
0
0
0
2
1
2
0
0
0
1
2
0
0
0
0
1
0
1
1
0
2
0
1
1
0
0
0
1
2
0
0
0
2
1
2
2
0
1
0
0
2
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
7
0
2
0
0
0
0
0
1
0
1
1
0
1
1
0
0
0
1
0
0
1
4
1
0
0
0
0
1
1
0
0
2
0
0
1
0
0
0
0
3
0
0
2
1
2
1
1
2
0
0
0
2
2
2
0
1
0
0
0
0
1
1
2
0
0
0
3
1
1
1
0
0
1
0
0
1
1
0
0
0
1
0
0
3
0
1
0
0
1
2
1
0
0
0
0
0
0
3
2
3
2
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
1
0
0
2
2
0
2
0
0
0
0
2
0
0
0
4
0
2
0
1
0
2
2
1
2
1
0
2
0
0
0
0
2
1
1
1
1
0
0
0
2
1
2
2
1
0
0
1
0
0
2
1
1
1
0
0
0
1
0
0
0
2
1
1
0
1
0
0
1
0
1
0
2
0
1
0
3
1
2
1
2
2
1
2
0
3
1
0
0
0
0
1
0
0
1
1
0
0
1
2
0
0
0
0
0
1
1
0
2
0
0
0
3
3
0
0
1
0
0
0
2
2
1
0
0
1
0
2
0
0
0
0
0
2
0
1
0
0
0
2
2
0
2
0
0
1
1
0
2
0
0
0
1
0
2
0
0
1
0
0
2
0
2
0
1
1
0
1
2
1
0
2
3
0
0
0
3
2
0
0
2
2
2
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
1
1
0
1
2
0
0
0
1
0
1
0
0
0
1
1
1
0
1
1
0
2
1
0
0
0
0
0
2
1
1
0
2
1
1
1
0
0
1
2
0
2
0
0
2
0
1
1
2
0
2
2
1
2
6
1
0
1
1
0
0
0
0
0
1
0
0
1
1
1
0
0
0
2
0
0
0
1
2
0
0
0
4
2
1
0
1
1
1
2
0
2
1
1
2
0
1
0
0
0
1
0
1
1
1
2
1
0
1
0
0
1
1
2
0
0
3
0
0
1
0
0
1
1
0
0
0
0
6
0
0
0
0
0
3
1
0
1
0
0
4
2
2
0
1
2
2
1
0
1
0
2
0
1
0
2
0
0
2
1
1
2
0
2
0
1
0
2
0
0
0
1
1
0
2
0
1
0
1
2
1
0
2
1
0
0
0
1
1
1
0
0
1
0
0
1
0
2
2
0
0
1
0
2
5
0
0
0
0
0
0
1
0
0
0
2
2
1
2
0
0
0
0
0
2
2
0
1
1
2
1
0
1
0
0
0
0
2
1
2
2
1
0
0
2
0
3
0
0
0
0
0
0
0
0
0
1
0
1
1
1
1
3
0
0
0
0
0
2
1
4
2
1
0
0
1
0
1
2
0
0
0
2
0
0
2
2
1
0
0
2
0
3
1
0
0
1
2
0
2
1
0
0
0
0
0
2
2
0
0
1
2
1
2
2
1
3
0
0
0
2
1
0
2
0
2
1
2
0
2
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
2
1
1
0
1
0
2
0
0
0
0
2
0
0
0
0
0
1
1
2
1
0
2
2
0
0
2
1
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
1
0
1
0
0
1
2
0
0
1
0
0
1
1
0
0
2
0
0
0
0
2
0
1
1
0
0
1
1
1
1
0
0
0
0
2
0
0
0
1
0
0
0
0
1
2
0
1
0
1
1
0
1
2
1
0
2
0
0
0
0
1
0
0
0
0
1
1
0
2
0
2
0
0
3
1
0
0
2
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
2
1
1
1
1
1
1
0
0
0
1
0
1
0
0
1
2
1
0
3
0
0
3
2
1
0
1
0
1
0
2
1
1
0
2
0
0
0
0
0
0
0
1
1
1
0
1
0
0
1
5
1
0
3
0
0
1
0
1
0
0
0
0
0
0
2
2
0
0
1
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
1
2
0
2
0
0
0
1
1
0
0
0
1
1
0
0
1
0
0
0
0
1
3
2
1
1
0
0
0
0
0
0
0
2
0
0
1
1
0
0
2
0
0
2
0
0
1
2
0
0
2
0
2
1
0
2
0
2
0
0
0
2
2
0
0
0
2
1
0
0
0
1
0
0
1
2
0
0
2
0
0
0
1
2
0
1
0
2
0
1
1
0
1
1
2
0
0
0
5
2
0
0
0
1
1
1
0
0
0
2
2
0
2
2
1
0
0
1
2
0
1
0
1
0
0
0
0
1
0
1
0
2
0
2
1
0
0
0
0
0
3
0
2
1
1
3
0
0
0
0
1
2
1
2
1
1
0
1
0
3
1
1
0
0
1
0
0
0
0
2
0
2
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
2
0
0
0
1
0
0
0
2
0
1
1
1
0
0
0
0
0
1
0
2
0
2
0
2
0
0
0
0
0
0
2
1
2
0
1
0
0
0
1
2
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
1
0
0
2
1
2
1
1
0
1
0
2
0
0
0
2
0
0
2
0
2
1
1
1
0
0
1
0
0
2
1
4
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
1
2
0
1
2
2
2
1
0
0
1
0
0
0
2
0
1
1
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
2
1
2
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
2
0
0
2
1
1
0
3
2
0
1
1
0
1
0
2
0
1
0
1
0
2
0
0
1
0
0
1
2
0
0
0
1
0
2
0
1
1
1
1
0
0
0
0
1
0
0
0
1
1
1
0
0
0
2
0
0
2
2
0
1
0
0
0
1
1
2
1
0
0
0
2
1
2
2
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
1
0
0
0
1
1
1
0
0
0
2
0
0
0
0
1
0
0
1
0
1
2
2
1
0
0
0
0
0
0
1
1
0
1
0
3
1
0
1
1
2
0
2
2
1
0
0
2
3
1
0
0
0
2
2
2
0
0
1
0
2
0
2
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
2
0
2
2
2
0
3
0
0
2
2
1
0
0
2
0
2
2
0
2
1
0
2
1
0
1
1
2
0
2
1
0
0
3
1
0
2
2
1
0
1
0
0
0
3
0
0
2
0
0
2
0
0
0
1
0
0
0
0
1
0
1
0
1
1
1
2
0
0
2
0
2
1
0
0
0
2
0
0
0
0
0
1
0
1
1
2
0
1
0
1
2
2
0
3
0
0
2
1
0
0
0
0
1
1
1
0
0
0
1
1
0
1
0
1
0
0
3
2
0
1
1
0
0
1
2
2
0
1
2
0
2
2
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
2
1
2
2
2
1
0
1
1
0
2
2
2
1
0
1
0
1
0
1
2
0
2
0
0
1
0
2
2
0
2
0
2
1
1
3
0
2
2
0
0
2
0
0
0
0
2
1
0
2
0
0
0
1
2
0
2
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
1
1
1
0
0
0
1
1
0
1
2
0
2
0
0
0
0
0
0
1
2
0
0
0
2
1
1
0
0
1
2
2
0
0
2
0
1
0
1
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
1
2
0
2
0
1
0
0
0
0
0
2
0
2
0
2
0
0
1
0
0
1
0
1
0
0
1
2
0
2
2
0
0
1
1
0
0
2
0
1
0
3
0
0
1
1
0
2
1
1
0
0
2
2
0
1
0
2
0
3
0
7
0
0
0
0
0
1
0
2
0
1
2
0
3
1
1
2
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
1
0
1
0
0
1
1
0
1
0
1
0
1
1
1
2
0
0
0
1
0
0
1
0
0
0
2
1
0
1
0
0
0
0
2
1
2
1
2
1
1
0
0
1
0
2
1
1
0
1
0
0
2
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
2
2
3
0
0
1
2
0
0
2
0
1
2
2
0
0
0
0
0
0
1
2
0
0
2
2
2
1
2
2
1
0
2
0
0
0
2
1
2
0
0
2
0
0
0
2
1
0
2
0
2
0
0
2
1
2
0
2
0
0
3
2
2
0
0
0
5
1
0
1
1
2
2
2
2
2
2
1
0
1
1
0
1
1
2
0
0
0
2
0
0
2
0
1
0
1
2
0
2
2
0
1
1
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
2
2
1
1
2
0
1
1
0
0
0
0
0
1
1
0
0
0
1
0
2
2
2
1
0
0
0
0
1
0
0
1
2
0
2
1
1
0
0
0
1
0
0
0
1
0
0
1
0
1
0
1
3
0
1
1
0
5
0
0
3
0
0
0
2
0
1
2
2
1
0
3
3
0
1
0
1
0
0
0
1
1
3
0
0
2
2
0
0
0
1
0
0
0
2
1
0
2
0
2
0
0
2
0
0
0
0
0
2
2
1
1
2
0
2
0
1
1
0
0
1
2
0
2
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
2
1
1
1
0
0
1
1
2
1
0
0
1
0
0
2
0
2
0
1
2
0
1
1
1
1
2
0
1
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
2
0
1
0
1
0
1
1
0
0
2
1
0
0
1
0
1
1
1
0
0
0
2
1
1
1
2
1
0
0
0
0
0
1
1
1
0
1
2
0
2
0
0
2
0
0
2
1
2
1
2
2
0
0
2
0
1
0
0
0
1
0
2
0
0
2
0
1
0
0
2
2
2
1
1
1
0
2
0
0
2
0
0
1
1
0
1
2
1
1
1
0
1
2
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
1
0
1
1
0
1
1
2
0
2
2
1
0
0
1
0
0
0
0
0
0
0
1
2
0
0
1
1
0
2
0
0
2
0
0
0
0
0
2
0
2
1
0
0
0
0
3
0
0
1
2
0
0
1
0
0
2
0
1
0
1
1
1
0
0
2
1
0
0
0
0
1
2
1
2
1
1
0
1
1
0
1
2
0
0
0
0
1
1
0
0
2
0
0
0
2
0
0
0
0
0
2
0
1
1
2
1
0
1
0
2
0
2
2
0
1
1
0
0
2
1
1
0
1
0
1
0
0
0
0
2
1
0
0
1
0
0
0
2
1
1
0
0
0
0
1
2
1
3
0
1
1
0
0
0
0
0
1
0
0
0
0
0
2
2
0
1
0
0
2
0
2
1
0
0
0
1
4
0
3
2
0
2
0
1
2
0
0
1
0
0
2
0
0
0
0
1
2
0
0
1
1
1
2
0
0
2
1
1
1
0
0
1
1
0
1
0
1
1
0
1
2
0
0
0
0
0
1
1
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
1
0
3
0
0
0
0
1
0
0
1
0
0
1
2
2
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
2
2
2
2
2
0
0
2
0
0
0
0
1
2
2
1
2
1
1
0
0
1
0
2
0
2
0
0
2
0
2
0
1
0
0
0
0
0
3
1
0
1
0
2
0
0
0
1
0
0
1
0
1
0
0
1
1
0
0
1
1
0
0
1
0
0
1
1
0
0
1
0
1
0
0
1
2
1
0
0
0
2
1
0
0
1
2
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
1
2
2
1
0
0
0
2
0
0
0
0
0
0
3
2
1
0
0
0
2
1
0
0
0
1
0
0
1
0
0
0
0
2
2
2
1
1
1
1
1
0
0
0
0
2
0
1
0
2
1
0
0
2
2
0
0
0
0
1
0
1
0
2
0
1
0
0
0
2
1
1
2
1
0
2
0
0
0
1
0
0
1
1
0
1
2
1
0
1
1
1
0
0
0
1
2
1
0
0
0
2
0
0
0
2
0
1
0
0
0
1
0
1
0
2
0
0
1
0
0
0
2
1
0
0
1
1
1
0
0
0
1
2
0
3
0
0
1
0
1
1
1
2
1
0
0
2
1
0
2
2
1
0
1
0
0
1
0
0
0
1
1
1
2
1
0
0
2
0
1
0
0
0
0
1
0
0
1
1
3
0
0
0
3
0
2
0
2
0
2
0
0
1
2
1
0
0
1
3
1
0
2
0
1
1
0
2
1
0
0
1
1
3
0
1
2
2
0
0
0
1
1
0
0
2
2
0
2
0
0
0
0
0
2
0
1
0
1
0
1
1
0
1
0
1
0
0
0
3
3
1
1
1
2
0
0
0
1
0
0
0
1
2
0
2
0
1
2
0
1
0
0
0
0
2
4
2
2
0
1
0
3
0
1
2
0
0
1
1
2
2
0
2
0
0
1
1
0
1
0
0
1
0
0
1
1
2
2
0
0
1
1
2
2
0
0
2
0
0
1
0
2
1
2
2
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
3
1
1
0
0
0
1
0
2
0
0
1
1
0
1
0
0
2
0
0
1
1
0
0
1
0
1
2
0
1
2
1
0
0
0
0
1
0
0
2
0
0
2
2
0
0
0
0
3
0
2
1
0
0
2
0
1
0
1
0
2
0
0
1
0
1
1
1
0
2
1
1
0
1
0
0
0
0
1
0
1
0
0
0
2
0
1
1
2
0
2
0
0
1
2
2
0
0
0
0
2
1
2
0
3
2
1
1
0
1
1
0
0
0
1
0
0
0
0
1
2
2
0
0
0
2
0
1
1
0
0
0
1
0
0
1
0
1
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
2
0
0
1
0
2
1
0
2
0
1
1
2
0
1
0
0
2
1
0
0
0
0
0
0
0
1
1
1
0
0
1
0
2
0
0
0
0
0
2
1
1
1
0
0
0
0
3
0
6
0
2
1
0
1
0
0
1
0
2
2
1
0
0
1
2
0
0
2
0
0
1
0
1
1
1
1
0
0
1
2
0
2
2
1
2
0
1
0
1
0
1
3
0
2
0
0
0
0
0
0
2
1
2
1
0
0
0
0
0
0
2
1
1
0
2
1
2
1
0
2
0
0
2
2
1
2
0
0
0
2
1
2
0
2
0
0
2
1
0
0
1
0
0
0
0
0
1
1
0
2
0
0
1
1
0
1
2
1
0
0
0
1
2
0
0
4
1
0
0
1
2
0
3
0
0
0
0
2
0
1
0
1
0
0
2
2
0
0
1
0
0
0
1
0
0
2
1
0
0
0
1
0
0
1
0
1
1
1
1
1
0
1
0
0
0
2
2
2
0
1
0
1
1
1
1
0
0
0
0
1
0
0
0
1
2
2
1
0
1
0
2
0
0
1
2
1
0
0
0
0
0
2
1
0
2
2
0
0
4
2
2
0
0
0
0
0
1
0
0
2
2
2
2
1
2
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
2
0
0
1
0
1
0
0
1
0
2
1
0
0
2
2
2
0
0
2
0
0
1
0
2
0
0
0
0
8
0
0
0
1
1
0
1
0
2
2
2
2
0
0
2
0
1
0
0
5
2
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
1
0
2
2
0
0
1
1
0
2
1
2
1
1
4
1
0
1
2
2
0
1
1
0
0
0
1
0
0
0
1
1
0
1
0
0
1
0
1
1
0
0
2
3
1
1
2
0
0
2
1
0
1
2
0
1
0
0
0
1
1
0
2
0
1
1
0
0
2
0
0
2
0
2
0
1
0
1
1
0
1
1
0
2
0
0
0
0
0
1
2
0
0
2
2
0
0
1
2
0
0
0
0
1
1
0
0
0
0
1
0
3
0
0
2
0
2
0
1
1
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
3
0
2
0
1
1
0
0
2
1
0
0
0
0
0
3
3
1
1
2
0
0
0
1
1
0
0
1
0
0
1
0
1
4
2
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
5
1
0
0
0
0
0
1
2
0
0
0
0
1
2
1
1
1
0
2
2
2
1
1
1
0
3
0
1
2
1
2
0
2
2
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
2
1
3
2
0
2
0
2
1
1
1
1
0
0
1
0
1
2
0
0
1
0
3
1
0
1
1
1
1
0
0
2
1
0
1
0
0
1
0
0
1
1
0
0
1
0
1
2
0
0
1
0
1
1
0
2
0
0
3
2
0
1
1
1
1
0
0
0
2
1
1
0
0
0
0
0
1
1
1
0
0
2
0
1
1
2
1
0
1
1
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
1
0
0
0
1
0
2
0
0
0
0
0
3
2
2
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
2
1
0
1
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
2
0
1
1
0
2
0
0
0
0
1
0
0
1
1
1
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
2
1
1
0
3
0
0
2
0
1
0
0
1
1
0
0
3
0
2
0
1
0
0
2
1
0
1
0
0
2
2
0
1
1
0
2
2
1
1
0
1
0
0
2
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
2
0
1
0
1
0
2
2
1
1
0
0
0
4
0
0
2
3
0
0
1
0
2
0
0
1
0
0
1
0
0
0
1
0
0
1
2
1
2
1
0
1
0
0
0
2
0
0
1
1
0
0
0
1
2
0
0
0
1
1
0
2
0
2
0
0
2
1
0
1
0
0
1
2
1
0
2
4
0
0
1
0
0
2
1
1
1
2
0
2
1
5
2
0
1
1
2
2
1
0
0
0
1
1
0
0
1
1
0
1
0
1
0
0
1
0
1
0
1
1
0
1
0
0
1
2
0
0
0
1
0
0
1
0
0
2
4
2
0
2
0
0
0
0
1
0
0
0
0
1
1
1
1
0
1
3
0
0
0
0
2
2
0
0
0
1
1
0
0
0
1
1
1
0
0
1
0
2
0
2
0
0
0
1
0
1
2
2
1
1
2
0
0
0
0
0
0
0
1
1
1
1
2
3
2
2
0
0
0
1
0
2
2
1
0
2
0
0
1
2
1
1
0
0
0
1
0
2
0
2
0
2
0
2
2
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
1
1
2
1
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
1
2
0
0
1
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
1
1
0
2
1
1
1
0
2
2
1
0
0
0
0
0
1
1
0
0
2
0
1
0
0
1
0
0
1
1
2
0
0
0
1
0
0
0
1
0
0
0
1
0
0
2
2
1
0
1
2
0
0
0
0
1
0
0
1
1
2
2
4
0
2
2
1
0
0
1
0
0
1
1
3
0
0
2
1
0
0
0
1
2
2
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
1
1
0
1
1
1
1
1
0
1
1
0
0
0
1
2
1
0
2
0
0
1
2
2
1
0
1
1
2
0
0
0
1
2
2
1
2
0
2
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
1
4
0
2
0
0
0
1
1
2
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
1
0
2
0
0
1
0
0
2
2
2
0
0
1
0
0
0
0
1
1
2
1
0
2
2
0
1
1
1
0
0
0
1
0
0
2
2
0
0
1
1
1
0
0
1
0
0
0
0
2
0
0
1
0
1
0
0
0
1
0
0
0
2
1
0
2
0
2
0
1
0
1
0
0
2
0
0
0
0
0
1
2
1
2
0
2
1
0
1
0
1
1
2
0
0
1
1
0
2
2
1
2
1
1
1
1
1
0
0
0
0
0
0
2
0
2
2
1
0
0
2
0
0
0
2
0
1
0
0
2
0
2
1
1
2
2
0
1
0
3
2
0
0
0
0
3
1
1
1
2
0
0
1
0
0
2
0
4
0
1
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
2
1
0
1
0
0
0
1
0
2
0
1
1
1
1
2
1
0
1
0
2
0
0
0
1
1
1
1
2
1
0
0
0
0
1
0
0
2
0
0
0
0
2
2
1
3
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
1
0
0
0
0
1
0
2
0
2
0
1
0
1
0
2
0
0
2
2
1
0
0
0
1
0
0
1
1
0
0
1
0
0
0
2
1
2
0
0
1
1
2
0
2
0
0
2
1
0
0
0
0
2
2
0
0
0
1
1
2
0
1
0
0
2
0
0
0
2
0
0
2
2
0
1
0
2
0
0
0
0
0
2
0
1
2
2
0
1
0
1
2
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
2
0
2
2
1
0
0
0
0
1
1
0
2
0
0
0
1
1
1
0
0
0
0
0
0
2
0
0
1
0
1
1
2
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
3
0
2
2
1
0
2
0
1
0
1
1
0
2
0
0
2
0
2
1
0
2
0
1
2
0
0
0
1
0
0
0
1
2
0
1
0
2
2
0
2
0
1
1
1
0
1
2
2
2
2
1
0
0
1
1
5
1
1
1
0
0
1
0
0
0
3
0
0
0
0
1
0
0
1
1
0
0
1
2
1
2
0
1
0
1
0
2
0
0
0
0
2
1
0
0
2
2
1
0
1
0
1
0
0
0
1
1
0
1
1
1
1
0
0
0
0
0
0
1
1
0
1
0
0
0
1
1
2
2
0
1
2
2
0
0
1
0
0
2
2
2
0
0
2
1
2
0
2
0
1
0
2
2
0
0
1
2
0
2
0
1
1
0
1
0
0
0
1
2
0
2
0
2
1
0
0
2
1
0
1
2
0
1
0
2
3
1
0
0
2
0
2
2
1
0
2
0
2
2
0
0
0
2
0
0
0
1
2
1
1
2
0
2
0
3
1
0
0
2
1
0
2
0
0
0
0
1
0
1
1
0
0
0
1
0
0
1
0
1
0
0
0
2
0
0
0
1
2
0
0
1
0
2
0
0
0
0
1
1
2
1
2
0
1
1
1
1
2
0
1
0
2
0
0
0
1
0
2
0
1
3
0
0
1
0
2
2
0
2
0
1
0
0
0
1
2
2
0
1
4
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
2
2
1
1
2
4
0
0
0
1
2
0
1
1
0
1
2
0
2
0
0
0
2
4
1
0
2
0
0
0
0
2
0
0
1
0
1
2
2
0
0
0
0
0
1
2
0
0
0
0
2
2
0
0
0
0
0
1
2
1
2
0
1
2
0
0
2
2
0
1
1
3
0
0
0
1
2
1
1
2
1
0
2
1
0
0
2
0
0
2
0
1
1
0
1
0
0
0
0
1
0
1
1
1
0
1
0
0
2
0
0
0
0
1
1
0
4
1
1
2
1
0
0
2
0
0
2
0
1
0
1
0
0
2
0
0
2
0
0
0
0
0
7
1
0
1
0
0
2
0
0
2
1
0
1
2
0
0
3
1
0
2
0
0
2
0
1
2
0
1
0
0
0
1
1
0
1
1
0
0
0
1
1
0
2
0
0
1
0
1
2
0
0
1
1
0
0
2
1
2
0
1
0
1
0
0
2
0
1
1
0
0
1
1
2
2
0
0
0
0
1
2
0
1
0
0
2
0
0
0
0
1
1
0
0
1
0
2
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
1
0
1
0
1
0
2
1
2
0
0
2
3
1
1
0
1
0
0
0
0
2
1
2
2
0
1
0
1
0
0
0
0
1
1
0
1
1
0
2
0
0
1
0
0
0
1
0
2
2
0
0
0
2
0
0
1
0
0
0
0
1
0
0
1
0
1
0
2
0
0
0
2
0
1
1
0
2
0
2
0
2
2
0
2
0
0
2
1
2
1
1
0
2
1
0
0
2
0
2
1
1
0
2
3
2
1
0
0
2
1
1
0
1
0
0
0
1
0
2
0
2
0
7
2
0
2
1
2
1
1
0
0
0
2
1
0
1
2
2
1
0
0
1
0
0
0
0
0
0
0
1
0
1
2
2
2
0
0
1
1
0
1
0
0
0
1
1
2
0
1
0
0
1
0
0
2
0
2
2
1
0
0
0
1
1
0
1
2
1
0
1
1
2
2
1
0
1
0
0
2
1
0
1
0
0
1
2
1
0
1
0
1
1
0
1
0
2
1
0
0
2
1
2
1
2
0
0
0
0
2
2
2
1
0
1
0
1
1
2
0
0
0
0
0
1
1
1
0
1
1
1
0
1
2
1
2
2
0
0
1
1
2
1
5
2
2
1
0
2
0
0
0
1
1
1
0
0
0
2
2
1
0
0
0
0
0
1
0
1
1
0
0
0
1
0
1
2
2
2
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
2
2
1
1
1
1
1
0
1
0
0
1
0
1
0
1
2
0
1
2
0
0
2
0
0
0
1
0
0
0
0
1
2
0
0
0
0
1
1
0
0
1
0
2
1
2
0
1
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
2
1
2
2
1
0
1
1
2
0
1
0
0
0
0
3
0
0
1
1
0
0
1
1
2
0
0
0
1
1
0
1
0
1
4
0
0
0
2
0
0
0
1
0
0
0
1
0
2
1
0
0
0
1
0
2
0
1
2
0
0
0
1
1
0
0
2
0
2
1
1
0
1
0
1
1
3
0
0
1
1
1
0
0
1
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
2
2
0
1
1
1
1
0
1
0
1
0
2
0
0
1
0
1
0
2
2
0
1
0
2
0
0
1
1
2
2
2
2
0
0
1
0
0
2
1
1
0
0
0
1
0
0
1
4
0
0
1
0
0
0
0
1
2
0
0
2
0
2
0
0
1
1
2
2
0
0
2
2
2
0
0
0
0
0
2
0
0
0
0
2
2
0
0
2
2
1
1
2
1
2
2
0
2
0
0
0
0
2
0
0
1
1
0
2
0
0
2
0
1
0
2
2
0
0
0
0
2
1
0
1
1
0
3
1
1
1
1
1
1
1
1
0
0
0
2
1
0
1
1
0
0
0
0
1
0
2
0
0
2
1
0
0
0
2
1
1
0
0
1
2
2
0
2
0
0
1
2
2
1
0
0
0
0
0
0
0
1
2
0
1
2
2
1
2
0
0
1
2
1
0
1
0
1
1
2
2
1
0
0
2
0
0
0
1
2
0
0
2
0
2
2
1
0
0
0
2
1
0
2
1
1
2
0
1
0
1
0
0
0
0
1
0
0
0
0
0
2
1
0
0
1
3
0
0
0
3
0
0
1
0
0
0
0
2
2
1
0
0
0
0
0
2
0
0
1
2
2
2
0
2
1
0
0
1
0
0
2
1
1
0
0
2
1
0
1
1
0
0
1
2
0
2
0
1
0
1
1
1
0
0
0
0
1
0
2
0
0
1
0
0
2
0
1
0
0
0
0
0
2
2
2
2
1
0
2
2
1
0
0
0
1
1
0
1
0
1
0
0
2
2
1
1
1
0
5
0
0
1
0
2
1
2
1
1
0
0
2
1
0
0
2
0
2
0
1
0
0
1
1
1
1
0
1
2
1
1
1
0
1
1
1
2
1
0
0
1
0
1
0
0
0
2
0
1
0
0
1
0
0
1
0
1
1
1
3
0
3
0
2
2
1
1
0
0
0
1
0
0
1
0
0
0
0
1
0
2
1
0
1
1
3
0
2
2
2
0
2
2
1
0
0
1
2
1
2
1
2
0
1
0
1
2
0
0
0
2
0
0
0
2
2
1
1
2
0
1
1
0
0
1
0
0
1
0
2
1
0
0
0
0
0
0
1
2
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
3
1
2
3
1
1
0
0
0
1
2
1
1
0
0
1
2
0
0
1
0
2
1
1
2
0
0
0
1
0
1
0
1
0
1
1
0
0
2
0
0
0
1
1
0
2
0
0
0
2
0
2
1
0
1
1
0
0
1
2
1
0
1
0
0
1
1
0
1
2
0
0
2
0
0
2
1
0
0
0
2
2
0
1
0
2
0
1
0
0
2
2
0
1
1
0
0
1
2
0
1
1
0
0
0
0
1
1
2
1
2
0
2
0
2
1
0
1
1
0
1
0
1
0
1
0
0
2
0
2
0
0
1
0
1
2
1
1
1
2
2
0
2
2
1
2
0
2
0
1
1
0
2
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
3
0
3
1
0
1
1
0
2
0
0
0
2
0
0
1
0
0
0
2
3
0
0
0
2
2
2
1
0
1
1
0
0
1
0
0
1
2
1
0
1
2
1
0
2
1
0
1
0
1
5
0
0
0
0
0
1
2
0
0
1
0
1
3
0
1
0
0
0
0
1
1
0
2
0
0
0
0
1
1
0
0
2
1
1
1
0
1
2
0
2
1
1
0
2
4
0
0
1
1
0
2
0
0
0
0
1
2
0
2
0
0
0
2
1
0
0
2
0
0
0
0
1
0
1
0
1
0
1
0
0
0
1
1
2
1
0
0
0
1
1
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
2
1
1
1
1
2
1
0
1
1
1
6
0
4
0
2
0
3
2
1
0
0
0
0
1
0
0
0
1
0
1
1
0
1
2
2
0
0
2
1
2
2
3
0
1
2
1
0
2
2
2
0
0
3
0
2
1
1
1
0
0
0
2
0
0
0
0
1
0
1
0
0
2
1
2
1
2
2
2
1
1
0
0
2
1
0
3
0
0
1
2
0
0
2
2
0
2
0
0
0
0
0
1
0
1
0
1
2
3
0
2
2
2
2
0
0
1
0
1
2
0
0
1
2
0
0
0
2
0
1
0
1
0
2
1
1
1
1
2
1
0
0
1
2
2
0
2
2
1
0
0
1
0
2
2
0
1
0
2
1
0
2
3
1
0
0
2
0
2
0
0
0
0
0
1
2
1
2
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
2
0
0
1
0
0
1
0
1
1
1
0
1
5
0
0
2
1
0
0
0
0
0
0
0
2
0
2
0
2
0
0
1
1
1
0
1
0
1
0
0
0
2
0
1
1
0
1
0
0
1
0
0
0
1
2
2
0
2
0
2
1
0
0
1
2
2
4
0
0
2
0
0
0
1
1
0
1
1
2
0
1
2
0
0
0
1
0
0
0
3
2
1
1
0
0
0
1
1
0
0
0
2
1
2
2
0
0
1
1
0
1
2
0
0
1
0
1
0
0
0
2
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
1
0
0
0
2
1
2
0
1
2
2
2
0
0
1
0
0
1
2
0
0
1
0
2
0
0
0
2
1
1
0
2
0
1
0
0
0
2
0
0
0
2
0
0
2
0
1
0
2
0
1
0
2
1
0
2
2
0
2
1
5
0
1
1
0
0
1
0
0
1
0
0
0
1
2
2
0
1
0
0
1
1
1
0
1
1
0
0
2
1
2
2
0
0
0
1
0
0
0
2
0
2
0
0
0
2
0
0
2
1
1
0
0
2
2
1
1
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
1
1
0
0
2
1
0
0
1
2
1
0
0
0
2
1
0
1
0
2
0
1
2
0
1
0
1
3
2
0
2
4
0
0
0
0
0
0
1
3
0
1
1
1
2
0
0
0
0
0
0
2
0
3
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
2
0
1
1
2
1
0
2
0
2
1
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
1
2
1
0
0
0
0
0
1
0
1
1
0
0
0
0
2
1
0
1
1
1
2
0
2
0
1
0
1
0
0
1
0
0
0
1
0
2
0
2
0
1
2
0
2
0
1
0
0
1
2
2
0
0
0
0
0
3
0
0
1
0
1
2
0
1
0
0
2
0
0
0
0
1
0
1
1
2
0
0
1
0
1
3
2
2
0
0
0
2
1
0
2
1
2
1
0
1
0
0
0
0
0
0
1
0
2
3
0
0
1
1
0
1
0
0
0
1
1
1
0
1
2
1
0
2
0
1
0
2
2
0
1
1
0
0
1
0
0
0
2
1
1
0
0
3
0
0
1
0
0
1
1
0
0
0
1
0
0
0
2
1
0
0
0
2
2
1
0
1
1
0
0
2
1
0
2
0
2
1
1
0
0
0
1
0
1
0
0
0
0
2
0
2
1
0
2
1
2
0
0
2
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
2
0
1
0
1
0
2
1
0
0
1
0
2
0
0
0
0
1
0
0
1
1
0
0
0
0
2
0
0
0
0
2
2
1
0
0
1
1
2
1
2
0
2
2
2
0
0
0
1
0
1
0
0
0
1
1
2
0
4
1
0
1
2
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
1
0
0
1
1
0
1
0
1
0
0
1
0
0
0
2
0
0
0
0
1
1
2
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
10
0
0
2
1
0
0
0
0
2
1
0
1
0
1
1
0
1
1
0
1
0
2
2
2
0
0
3
0
0
1
2
2
2
1
1
0
0
0
1
1
0
1
1
1
0
2
1
0
0
0
0
0
2
0
2
0
0
1
1
0
0
0
0
0
2
2
0
1
0
0
2
1
1
2
0
0
0
2
0
0
2
0
0
0
0
1
1
0
2
0
0
0
2
2
0
1
0
2
1
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
1
1
1
1
2
0
2
1
0
2
0
0
2
1
1
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
2
0
0
0
1
0
2
0
0
0
1
0
0
2
0
1
0
0
2
0
1
0
0
0
0
1
0
0
2
1
0
1
2
0
0
1
0
2
0
1
0
1
0
0
2
0
0
0
1
1
0
0
0
0
1
0
0
2
0
0
1
0
0
2
0
0
2
2
0
2
2
1
0
0
1
1
2
1
1
0
0
1
0
0
1
1
1
1
0
0
2
2
0
0
0
2
0
3
0
2
0
1
0
0
0
0
0
2
1
1
1
0
0
0
0
0
2
0
0
0
2
0
0
2
1
1
1
0
2
0
0
0
1
1
0
0
0
0
0
0
1
0
2
0
0
0
3
0
1
0
2
0
0
1
1
2
0
2
2
0
0
0
0
1
0
2
0
2
1
0
0
0
1
2
2
0
1
0
0
2
0
0
0
0
0
2
1
0
2
2
0
1
1
1
0
0
0
0
2
2
1
1
2
2
1
1
1
1
1
1
2
0
1
0
2
0
2
1
0
0
0
0
0
2
2
0
0
0
2
0
1
3
0
1
0
2
0
0
2
1
4
0
1
2
1
0
1
1
2
0
2
0
0
2
0
0
0
3
0
0
0
0
0
2
2
1
2
0
0
0
0
1
1
0
0
1
2
0
2
0
0
0
1
0
1
0
0
1
3
0
1
0
2
0
0
1
1
0
0
0
1
1
1
0
0
3
1
0
1
0
0
2
1
1
3
3
0
0
1
1
2
0
0
0
2
2
0
0
0
0
2
2
0
0
2
1
2
2
0
0
2
0
1
0
2
2
0
2
0
0
3
1
0
2
1
2
0
1
0
0
1
0
0
0
2
0
2
0
2
0
0
0
0
0
0
2
1
1
3
1
2
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
1
0
2
0
0
1
1
0
0
0
2
2
0
0
2
0
1
0
4
1
0
2
0
0
2
3
5
1
2
0
0
1
2
0
0
0
1
0
1
2
2
1
1
2
0
0
0
1
1
1
1
0
0
2
2
0
0
0
0
0
1
1
2
1
0
0
0
0
2
0
1
0
0
0
3
0
1
1
2
1
2
1
0
0
0
0
0
0
0
1
0
1
1
0
0
2
1
0
0
2
1
2
0
0
1
2
1
0
1
0
2
1
0
2
0
0
0
0
1
1
1
0
0
1
1
2
0
0
1
0
0
1
2
1
1
0
1
0
0
0
1
1
1
2
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
2
0
2
1
0
0
1
1
1
1
0
0
2
2
2
1
1
0
0
1
2
0
0
2
1
2
1
0
1
6
3
0
2
0
0
1
2
1
1
1
2
1
0
0
0
0
0
0
1
2
1
0
1
0
2
0
0
2
2
0
2
2
1
1
1
2
0
0
1
0
2
2
0
0
1
2
0
1
1
1
0
0
1
0
0
1
0
0
1
0
1
0
0
1
2
0
0
2
0
0
2
0
4
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
1
2
0
1
0
0
0
0
1
2
1
1
0
0
1
1
2
0
2
0
0
2
2
0
5
0
1
0
0
0
0
0
0
2
2
1
0
0
0
1
0
1
0
1
0
1
1
1
0
1
0
2
3
0
0
2
0
0
2
0
0
2
2
0
1
2
1
1
1
0
1
0
1
1
1
0
0
1
0
0
0
0
2
1
1
0
1
0
0
0
0
1
0
0
1
1
0
0
2
1
0
4
2
0
0
1
0
2
0
1
0
1
1
1
0
2
0
1
2
0
0
0
0
0
1
0
0
1
2
0
1
2
0
0
0
1
2
0
1
0
2
0
2
1
0
1
0
0
0
0
1
1
2
0
0
1
1
0
1
2
1
1
2
0
0
1
0
1
1
5
1
0
0
2
0
1
1
0
0
0
1
0
0
3
2
2
1
1
0
0
0
0
1
4
0
0
1
0
0
1
0
0
1
0
1
0
2
2
0
0
0
0
2
2
0
0
0
0
1
0
0
2
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
1
0
2
0
2
2
3
2
0
2
1
0
0
2
2
0
0
0
1
0
1
1
1
1
0
0
2
2
2
0
0
2
2
0
1
2
0
1
0
2
0
0
1
1
0
0
1
1
4
0
0
0
0
0
0
1
0
2
2
2
0
1
0
0
1
0
1
0
1
1
0
1
0
1
0
0
2
0
1
4
1
0
2
1
0
1
3
0
0
1
0
2
1
3
0
2
0
2
0
0
2
0
1
1
0
1
0
0
2
0
0
0
1
1
2
0
1
0
2
4
0
0
2
0
0
0
1
0
0
1
1
0
0
0
0
1
0
1
0
0
2
0
0
0
1
0
0
1
0
1
1
2
0
0
1
2
0
1
0
0
0
2
0
2
3
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
1
0
2
0
0
1
0
1
0
3
0
0
0
1
0
2
0
2
1
1
2
0
0
0
0
0
0
1
0
2
0
0
0
2
0
1
1
2
1
2
0
2
0
1
0
0
0
0
0
2
0
2
1
0
1
0
2
0
1
0
0
0
0
1
0
2
0
1
0
2
0
2
0
0
1
0
2
1
1
2
0
0
2
0
0
0
0
0
0
0
1
1
0
0
1
1
1
0
3
0
2
2
0
1
0
0
1
0
1
1
0
2
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
2
0
2
3
2
2
0
1
0
1
0
1
1
2
1
0
0
2
0
1
1
0
1
2
2
0
0
1
0
1
0
0
0
0
3
2
0
0
1
0
2
1
0
1
2
1
0
1
0
0
0
0
0
1
1
2
0
0
0
0
1
1
0
0
1
0
2
0
1
0
0
0
0
2
1
0
0
1
2
2
0
2
0
1
0
0
0
1
2
1
0
0
1
0
1
1
1
0
0
0
1
0
3
0
0
0
1
0
2
2
2
1
1
0
0
0
1
3
0
0
0
1
0
2
0
0
0
1
5
1
2
1
0
2
1
2
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
2
1
1
0
0
1
1
2
0
0
1
0
0
3
0
0
1
0
2
0
0
0
0
0
2
2
1
2
1
0
0
0
0
2
2
1
1
0
1
0
1
2
1
2
0
0
2
1
0
1
2
0
2
0
2
0
0
0
0
1
1
0
0
1
1
0
0
0
0
2
2
0
0
0
1
0
2
0
1
1
2
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
2
2
2
0
1
0
1
0
2
0
0
0
2
0
1
0
2
2
2
1
0
0
1
1
2
1
0
0
1
0
2
3
1
0
1
0
1
0
1
2
0
1
0
1
1
1
1
0
1
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
1
0
0
2
2
0
1
0
0
0
0
1
2
2
2
1
0
1
0
0
0
2
2
1
0
2
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
2
2
1
1
2
0
0
3
1
0
2
1
0
0
0
2
0
0
2
1
1
4
1
0
0
1
0
2
1
0
1
0
0
1
0
0
0
1
0
2
1
1
0
2
2
1
1
0
0
0
2
0
0
1
0
0
0
0
2
0
2
0
0
2
0
0
1
0
0
4
0
0
0
0
2
1
3
0
0
2
3
1
1
0
0
0
1
1
2
1
0
0
1
1
2
2
1
0
1
2
0
1
1
2
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
2
1
0
1
1
0
0
0
1
2
0
0
2
0
0
1
1
0
0
2
2
2
2
2
0
0
2
0
0
0
2
0
0
0
1
1
0
0
1
0
2
0
0
0
0
0
0
0
0
1
2
1
0
0
1
4
0
0
0
0
0
2
2
1
0
0
1
0
1
1
0
0
0
1
1
2
1
0
1
0
0
0
1
0
2
0
1
3
0
0
1
0
0
1
1
1
2
0
1
0
2
0
0
2
2
2
0
0
3
1
0
0
0
1
0
0
0
1
0
1
0
0
0
2
0
0
1
1
2
2
1
0
1
0
0
0
1
0
0
0
0
0
0
1
1
2
0
0
0
2
0
1
0
0
0
0
1
1
0
0
0
1
0
0
1
1
0
2
0
1
2
1
2
0
0
1
0
1
0
2
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
2
0
1
1
0
0
0
1
0
0
0
0
0
2
0
2
0
1
1
1
0
1
0
0
2
0
0
0
1
1
1
2
0
0
1
0
1
0
1
0
1
1
1
2
0
0
1
0
0
2
0
0
0
0
1
1
2
1
1
2
4
0
1
2
0
0
0
1
2
1
0
0
2
0
0
0
0
1
0
0
0
2
1
2
0
0
0
0
1
0
2
1
1
1
1
0
0
0
0
0
2
0
0
0
0
0
0
1
1
1
1
1
2
2
0
0
0
2
0
0
0
2
2
1
1
0
2
0
0
0
1
0
1
2
2
3
2
0
0
1
0
2
1
3
0
0
2
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
3
2
0
1
2
1
1
1
0
0
1
2
1
2
0
2
0
1
1
0
0
0
0
0
0
3
2
0
0
0
1
0
0
2
1
1
2
0
0
2
2
0
0
0
1
1
0
0
1
0
0
1
0
2
0
0
1
1
0
0
0
1
1
0
0
2
0
0
0
0
1
2
1
2
0
0
1
0
1
1
1
2
1
1
0
2
0
0
2
2
0
0
1
2
1
2
0
0
2
1
1
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
1
0
1
2
2
2
2
1
0
1
0
0
0
0
1
1
2
0
2
2
0
2
1
2
2
0
2
0
1
0
0
0
0
0
1
7
0
0
3
0
1
0
0
0
2
0
2
0
0
1
0
0
0
1
1
0
0
0
1
1
0
1
0
2
2
0
1
3
0
2
0
2
1
0
0
0
1
0
0
0
0
0
2
1
1
1
2
0
1
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
2
2
2
4
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
1
2
0
1
2
0
0
0
0
2
0
2
2
1
1
0
2
1
0
0
0
0
1
1
1
1
1
1
0
3
0
0
2
2
0
0
2
2
0
0
0
0
0
2
2
1
0
2
0
2
2
0
1
0
0
0
0
2
1
1
0
0
2
2
1
0
1
2
0
1
1
0
2
0
1
1
0
0
1
0
0
0
0
1
1
1
4
2
2
1
0
1
3
2
0
0
2
0
0
2
1
1
0
0
1
2
0
0
0
2
2
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
2
2
0
2
1
0
0
0
0
0
0
0
2
0
3
1
0
1
0
2
3
0
1
0
2
0
0
1
1
0
0
1
1
2
1
2
1
0
0
0
0
0
2
0
0
2
2
2
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
2
1
0
0
1
0
0
0
2
0
0
0
0
0
1
1
1
0
2
0
1
0
0
0
0
1
2
1
0
3
0
0
0
1
1
1
2
2
0
0
0
1
0
2
0
1
0
1
0
0
0
0
2
1
1
0
1
1
2
1
0
0
1
0
2
0
2
2
0
0
0
4
0
2
0
0
1
1
1
1
0
0
3
0
0
1
0
0
1
0
0
0
0
1
1
1
0
1
0
2
1
1
1
0
0
0
3
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
2
0
1
0
0
0
0
0
2
0
0
0
0
1
3
0
0
0
0
0
0
1
0
0
2
2
0
2
0
2
0
1
2
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
2
2
1
1
2
0
0
3
1
0
1
1
0
2
0
4
0
2
2
0
0
0
1
2
1
0
1
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
1
0
3
1
1
0
0
0
0
2
0
2
1
2
0
1
1
1
0
2
0
0
0
1
1
1
6
1
0
0
1
0
0
0
2
1
1
0
0
1
2
0
1
0
2
0
0
0
1
0
0
0
0
1
2
0
0
0
0
1
1
2
0
2
0
1
0
0
1
0
2
0
1
2
1
1
0
0
1
1
1
0
0
1
2
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
1
1
3
0
2
0
1
1
0
0
2
0
0
1
0
0
0
2
0
1
0
2
0
2
4
0
0
1
0
1
1
0
0
0
2
1
2
1
0
2
0
2
1
1
2
0
0
0
2
0
0
0
0
0
2
1
0
1
0
1
3
0
1
2
1
0
1
2
2
1
0
2
2
0
3
0
0
0
1
2
3
1
1
1
1
2
1
1
2
1
2
1
0
0
0
1
0
3
0
0
2
2
0
1
1
2
1
0
0
2
2
0
2
0
0
0
0
2
0
0
0
1
1
2
0
1
0
0
1
0
1
0
0
4
1
2
0
1
2
3
0
0
0
1
0
2
0
0
1
3
0
1
0
2
2
1
2
2
0
0
0
1
0
2
0
2
1
0
1
1
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
2
0
0
2
0
2
2
0
0
0
0
0
0
0
0
2
1
1
2
1
0
1
1
1
0
0
1
0
0
2
2
0
0
0
1
0
0
2
0
0
1
1
0
1
0
2
0
0
2
2
1
2
0
0
0
2
0
4
0
0
0
0
1
0
0
0
0
2
0
0
1
2
2
1
0
0
0
0
0
0
0
0
2
1
0
0
2
1
0
2
0
0
1
0
1
0
1
0
2
0
0
1
0
2
1
0
0
1
1
0
0
1
1
0
1
1
1
0
1
0
0
1
0
0
0
2
0
0
1
0
0
2
1
1
0
0
0
0
2
0
0
0
1
0
1
1
1
0
0
0
1
0
0
0
1
0
0
0
0
1
1
1
1
1
1
0
0
1
0
5
0
0
1
2
0
0
2
2
0
0
2
1
1
1
0
0
2
1
1
0
0
0
0
0
1
0
0
1
2
0
1
0
0
1
0
0
0
1
2
1
0
2
2
1
4
0
0
0
2
1
3
0
0
0
2
1
0
2
1
0
0
0
0
0
2
1
0
0
1
0
0
0
0
1
1
0
0
1
0
1
0
0
0
2
0
0
0
0
0
1
2
2
2
1
1
0
0
0
0
1
1
0
0
0
2
1
0
0
3
0
0
0
1
2
1
2
0
0
0
1
0
0
1
0
2
1
0
0
1
1
2
2
1
0
0
0
1
0
2
0
0
1
0
0
0
0
0
1
3
0
0
1
0
1
2
0
2
0
2
1
0
0
2
1
2
0
0
0
2
0
1
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
3
0
2
0
1
1
0
0
0
1
0
0
1
1
0
2
0
0
1
2
1
0
1
1
0
1
0
0
0
0
2
0
0
0
2
3
0
0
0
2
0
2
1
0
2
2
1
0
1
1
0
0
2
0
0
1
0
0
0
0
2
1
1
1
3
1
0
1
1
1
0
0
0
1
1
0
0
3
2
0
1
2
0
0
1
2
0
0
2
0
1
0
1
0
0
1
0
0
0
0
1
0
1
0
1
1
0
0
0
2
0
0
0
2
1
0
0
1
4
0
2
1
0
0
0
0
2
1
1
1
1
2
2
1
0
1
3
1
2
1
2
0
1
0
1
1
0
0
2
0
0
0
0
0
1
1
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
1
3
1
2
1
2
1
1
2
0
1
0
2
0
1
0
0
0
0
0
2
1
0
2
2
0
0
1
0
0
1
4
1
0
1
2
0
2
0
0
0
0
2
0
1
0
0
2
1
1
0
0
0
2
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
1
2
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
2
0
0
2
0
1
1
0
1
1
2
1
0
2
1
0
0
0
0
0
1
2
0
0
2
0
0
0
1
0
1
0
1
0
0
0
2
0
0
2
0
0
0
2
0
0
0
2
2
1
0
0
0
0
1
0
0
1
1
0
0
1
0
2
2
3
2
0
0
0
2
0
1
0
1
1
2
1
0
2
0
2
2
0
0
0
1
0
0
1
1
0
0
1
2
1
0
0
1
0
0
0
0
2
0
0
2
1
0
0
3
2
2
0
0
0
2
0
2
1
0
0
0
1
0
1
0
0
0
2
0
2
1
2
0
1
2
2
0
0
0
0
0
1
2
0
1
0
1
0
0
0
0
0
1
2
2
2
2
0
2
0
2
1
2
0
0
1
2
0
0
1
0
1
0
2
0
2
0
0
0
0
2
0
0
2
1
1
2
0
0
0
1
0
2
0
0
0
1
2
0
0
2
0
1
1
1
2
0
0
1
2
2
1
0
0
0
0
1
0
2
0
0
0
2
0
0
0
2
0
0
2
2
0
0
2
0
0
2
0
0
2
1
0
1
0
2
0
1
1
0
0
0
1
0
0
0
1
1
2
0
0
2
2
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
2
1
0
0
0
2
0
1
0
2
0
1
0
0
1
0
0
0
0
1
0
0
1
0
1
0
2
0
0
1
2
2
1
0
1
2
0
1
0
1
2
2
0
0
0
1
2
0
2
0
0
2
0
1
0
1
0
0
0
0
0
0
1
6
2
0
0
0
0
0
1
0
0
1
0
1
0
2
1
0
2
1
1
1
1
0
0
0
1
0
1
0
1
1
0
1
1
0
1
2
0
1
1
0
2
0
2
0
1
0
1
1
0
0
0
1
0
2
0
0
0
0
1
0
1
0
1
0
4
1
0
1
3
0
2
0
1
2
1
0
1
0
1
2
1
0
0
0
1
3
0
1
0
0
1
0
0
1
0
0
0
1
2
1
0
0
2
0
0
2
0
2
1
0
0
0
2
1
1
1
1
1
0
1
0
0
3
0
1
2
0
0
2
1
0
0
2
1
1
0
0
2
3
1
0
0
0
1
0
0
1
1
2
2
0
0
0
0
2
2
2
0
0
1
1
0
0
1
2
2
2
0
2
1
2
2
0
0
0
0
1
0
0
2
1
0
0
1
0
1
2
0
0
0
2
2
0
1
0
1
2
2
2
1
0
0
2
0
0
0
0
1
0
1
1
0
3
0
2
0
0
0
2
1
2
1
0
2
0
0
0
0
0
0
0
2
2
0
1
3
1
3
1
1
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
1
0
2
1
0
1
0
2
1
0
2
1
0
0
2
1
0
1
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
1
1
0
1
1
0
2
1
0
1
0
1
1
0
0
0
1
2
1
1
1
0
1
1
0
2
1
2
0
2
3
0
1
0
0
0
0
1
0
1
0
1
0
1
1
1
1
2
0
2
1
2
1
2
0
0
0
2
1
0
1
1
0
0
0
2
1
2
0
4
2
0
0
0
1
0
1
0
0
2
1
1
1
2
0
2
0
1
1
0
0
0
2
0
0
0
1
2
0
1
0
0
0
0
0
1
0
0
2
0
2
1
0
0
0
2
0
1
2
1
1
0
0
2
1
0
0
2
1
0
0
0
0
0
3
1
0
1
0
2
1
0
0
1
0
0
0
1
2
0
1
0
0
0
1
0
0
0
0
0
1
0
2
2
0
0
4
3
0
0
0
0
2
0
0
0
2
0
1
2
0
1
1
1
2
0
0
4
0
1
0
2
4
2
0
0
1
1
1
1
0
3
1
2
2
0
0
1
2
0
0
1
0
1
1
0
1
0
1
2
0
0
0
0
1
2
1
0
0
1
2
1
0
1
2
0
1
2
0
0
1
1
0
1
1
0
0
0
2
0
1
1
1
2
0
0
2
2
0
0
2
0
0
0
0
0
1
1
2
0
0
1
1
0
0
1
0
2
0
0
0
2
1
0
0
0
0
1
0
0
0
1
1
0
0
1
1
2
0
1
0
1
0
2
2
0
0
1
1
2
0
0
1
2
0
0
2
0
1
1
0
2
0
0
0
1
1
1
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
2
0
1
1
0
0
2
0
0
0
0
1
1
1
2
0
2
0
4
1
0
1
0
1
0
0
0
0
1
1
1
2
2
0
0
1
2
0
3
0
1
0
0
0
0
1
1
1
2
0
2
2
0
1
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
2
0
2
1
0
2
1
0
2
0
0
1
0
0
0
2
0
0
2
1
1
1
2
0
0
0
1
1
1
0
0
0
1
1
2
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
2
1
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
1
2
3
1
0
0
1
0
0
1
0
2
1
1
0
0
1
0
2
2
2
0
0
0
1
0
1
0
0
2
2
0
0
0
1
0
0
0
0
2
2
0
0
1
1
0
2
0
2
4
1
1
1
2
1
0
2
0
0
0
2
1
2
2
0
2
0
1
1
0
0
0
0
5
0
0
1
1
0
0
1
0
0
5
0
0
1
0
2
2
2
0
2
0
1
2
0
0
2
2
0
0
1
1
0
0
0
0
1
0
0
1
1
1
0
1
1
1
0
0
1
1
1
0
1
0
1
0
1
1
0
0
1
2
2
1
1
3
0
2
2
0
0
0
0
1
1
0
0
0
2
0
1
2
0
0
2
2
1
2
0
0
1
0
1
1
0
1
0
5
0
0
0
2
2
0
0
0
0
0
1
0
0
0
2
0
0
0
3
1
1
0
1
0
0
1
0
0
0
0
1
2
0
0
0
1
0
0
0
2
0
2
1
0
0
0
1
0
0
0
0
0
0
1
1
1
0
1
2
0
0
1
1
1
0
2
6
2
0
3
2
0
2
0
2
1
0
0
1
1
0
1
0
0
0
0
1
0
1
2
0
0
1
1
2
0
1
0
0
0
1
1
0
1
0
1
2
0
1
2
2
0
2
0
2
0
0
0
0
0
0
2
1
1
0
0
0
0
1
0
0
0
2
1
2
0
1
0
0
0
1
2
0
2
1
0
0
0
1
1
0
1
1
2
0
0
0
2
1
1
2
1
0
2
0
0
0
0
0
1
2
0
0
0
0
0
2
0
3
1
2
0
0
0
0
1
0
2
2
1
1
2
1
2
0
0
0
0
2
0
0
2
0
0
0
2
1
1
0
0
8
3
1
1
0
1
0
0
1
0
1
0
0
0
1
0
0
0
1
2
1
0
1
2
1
0
3
0
2
0
1
0
0
0
3
0
0
0
2
2
2
1
1
0
0
2
0
0
0
0
1
4
0
2
1
2
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
1
1
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
2
0
0
0
1
1
0
0
0
1
0
0
0
1
1
1
2
0
0
1
0
0
1
1
0
1
1
1
0
0
0
2
0
0
1
0
2
1
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
2
1
0
1
0
2
2
2
0
2
0
1
2
1
0
2
0
2
2
2
0
1
0
1
1
0
1
0
0
1
0
0
0
2
0
1
0
0
4
0
1
0
1
0
1
1
3
2
0
0
0
0
1
0
2
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
1
1
0
1
0
2
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
2
2
0
0
0
1
0
2
0
2
0
2
1
0
0
1
0
0
1
1
0
2
2
1
1
1
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
1
0
2
0
0
0
1
1
0
2
0
1
1
1
1
0
0
0
0
0
0
1
0
1
2
0
1
0
1
2
0
1
0
2
0
0
1
0
1
0
1
1
2
2
2
0
1
0
1
0
2
0
1
0
0
0
0
0
1
0
2
0
1
1
0
0
1
2
0
0
1
0
0
0
1
2
0
0
1
1
0
0
2
0
1
1
1
1
1
0
0
2
0
2
1
2
0
1
0
0
0
0
2
1
0
0
0
0
3
1
2
0
0
0
0
1
0
0
0
1
2
0
0
1
0
2
0
0
1
1
0
1
0
2
0
0
1
0
0
1
0
0
1
1
0
0
0
0
1
0
0
2
0
2
0
0
1
2
1
1
0
0
2
0
0
0
0
2
2
1
0
2
0
1
1
2
0
1
0
0
1
0
1
1
2
0
0
0
0
2
1
0
0
3
1
0
0
0
1
2
1
2
0
0
1
1
0
1
1
0
0
0
1
1
1
0
2
1
0
1
0
0
1
2
0
1
1
1
0
0
0
1
0
1
1
0
0
1
1
2
0
0
0
0
0
0
0
1
2
0
2
1
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
2
0
0
1
0
0
2
2
2
0
0
2
0
0
0
0
0
0
2
0
1
1
1
0
2
0
2
0
1
0
2
1
1
0
1
0
0
0
2
1
0
1
1
0
0
1
2
0
0
1
0
0
0
0
2
0
0
1
1
1
1
1
0
1
1
1
0
0
0
0
0
0
2
0
1
2
1
0
0
2
0
0
0
2
2
1
0
2
2
1
0
0
3
1
0
1
0
1
2
0
0
0
0
0
1
0
0
0
2
2
0
1
1
2
0
0
0
2
0
1
0
1
0
0
1
2
0
0
0
2
1
1
0
0
1
0
0
0
0
0
1
2
0
1
2
0
0
0
2
0
0
2
1
3
0
0
1
3
2
2
0
0
2
0
0
0
1
0
2
2
1
0
2
1
0
0
0
0
0
1
1
0
0
0
1
2
1
2
0
0
0
0
1
1
2
0
1
0
1
0
2
0
0
0
3
1
0
0
0
1
2
0
0
0
0
0
0
0
1
0
1
1
0
0
2
0
0
2
1
2
0
0
2
0
0
1
0
0
0
0
1
1
0
2
0
1
0
3
1
0
2
1
0
1
0
0
0
0
0
2
0
0
1
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
2
2
0
0
1
0
2
2
0
0
2
0
1
1
0
2
2
1
0
2
0
0
2
3
2
1
1
0
0
2
0
2
0
1
0
1
1
0
0
2
0
2
0
2
1
0
0
1
1
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
2
0
2
1
0
1
1
1
0
0
0
2
0
0
0
0
0
1
1
1
1
0
0
0
1
0
0
1
0
2
0
1
2
1
2
0
0
0
0
0
1
0
1
1
0
0
1
1
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
5
0
1
0
0
0
2
2
1
3
0
2
1
0
1
2
1
1
1
0
2
1
0
1
0
0
0
3
0
0
0
1
4
1
0
1
1
0
0
0
2
2
0
0
2
1
0
0
0
2
2
1
2
0
0
0
1
0
2
0
2
0
0
0
0
1
0
0
1
8
2
0
1
1
1
1
0
0
0
0
0
0
2
2
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
3
2
0
1
0
1
1
2
0
3
1
2
0
1
0
0
1
1
0
0
0
1
0
0
1
1
0
0
1
0
0
1
0
2
0
1
0
1
0
2
0
0
1
0
0
2
0
1
3
1
0
0
1
1
3
1
1
1
0
2
0
2
2
2
1
1
1
1
2
0
0
1
2
1
0
2
0
2
1
2
1
0
0
0
1
0
0
3
0
1
0
2
0
0
0
1
0
0
0
2
0
2
0
0
2
1
0
1
0
0
1
1
0
1
0
2
2
2
0
0
1
0
0
2
2
0
1
0
0
0
0
0
1
0
1
1
0
0
2
0
1
0
1
2
2
0
2
1
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
3
0
2
0
2
1
0
0
2
0
0
2
0
2
2
0
0
0
1
0
2
1
0
0
2
2
0
2
0
1
2
1
1
2
1
0
0
2
0
0
0
0
1
0
0
0
2
1
2
1
0
2
1
0
1
1
0
2
0
0
0
0
1
0
2
0
0
0
1
0
0
1
0
0
2
2
1
2
2
0
2
1
1
0
0
0
0
0
1
1
0
0
1
0
1
0
1
1
0
1
0
0
1
1
0
0
0
1
1
1
1
0
2
0
1
0
0
2
0
2
0
2
0
0
0
2
0
0
2
1
0
0
0
2
0
0
1
2
1
2
1
0
0
0
2
2
2
2
1
0
1
0
1
0
0
1
0
0
2
0
0
2
0
0
2
0
0
0
0
1
0
2
0
1
0
0
2
2
2
2
2
3
3
0
1
1
0
0
0
0
2
2
0
0
1
0
0
0
0
0
2
0
2
0
0
1
1
1
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
1
0
2
1
0
0
1
1
0
1
2
0
1
0
0
0
2
0
2
2
0
2
0
1
0
1
1
0
0
0
0
0
1
0
0
2
0
1
2
0
2
0
2
1
0
0
0
1
2
2
2
3
0
0
0
2
0
0
0
0
1
1
0
0
3
1
0
0
0
1
0
1
0
0
1
0
0
2
1
1
0
0
1
0
0
0
1
2
0
0
0
0
1
0
0
1
1
0
0
2
2
2
0
2
0
1
1
1
0
0
1
0
2
0
0
3
0
0
0
1
0
1
1
2
0
0
1
3
2
2
1
1
0
1
2
1
0
0
0
0
0
0
2
2
0
1
0
1
1
0
0
0
0
0
0
2
1
0
2
1
0
1
0
0
1
2
0
0
2
1
1
1
2
0
1
1
2
1
1
0
0
2
0
0
0
1
0
0
0
2
0
2
1
0
0
1
2
0
1
1
2
0
2
0
1
0
1
2
1
1
2
0
0
0
0
0
2
0
0
0
3
0
0
0
1
1
1
1
1
0
0
0
0
1
0
0
0
1
2
0
0
0
1
1
1
0
0
2
0
0
2
0
0
2
0
0
1
0
1
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
1
2
0
3
0
2
0
1
1
2
0
1
2
0
0
0
1
0
2
0
0
0
0
2
1
0
1
2
0
0
2
0
1
0
2
2
0
2
0
1
1
0
2
1
0
2
2
1
0
0
2
0
0
0
1
0
0
1
2
0
2
1
0
2
1
1
2
0
0
0
0
0
0
1
2
0
0
0
2
2
1
1
0
1
0
0
4
0
1
1
2
0
1
1
0
0
0
2
0
1
1
0
0
2
1
2
0
0
0
0
4
0
0
1
2
1
0
1
2
0
2
1
0
2
0
0
2
2
2
0
2
0
0
0
0
0
1
0
0
2
0
0
2
1
0
0
2
0
1
0
1
2
0
0
0
2
2
0
2
5
0
0
2
0
0
2
0
1
0
0
1
0
0
0
2
0
1
1
0
1
2
1
1
1
0
1
1
2
2
2
2
0
0
1
0
2
1
0
2
3
1
2
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
2
0
1
1
0
2
0
2
0
1
0
0
0
0
1
0
0
0
0
2
0
1
0
0
1
2
1
0
0
0
0
1
0
0
2
1
0
0
1
0
2
0
1
0
0
1
0
2
1
1
1
0
0
0
0
0
1
1
0
0
1
1
2
1
2
0
0
0
0
0
0
0
0
2
0
0
1
1
0
1
3
0
1
0
0
0
0
2
2
0
0
2
1
0
0
0
0
1
0
1
1
0
0
0
0
1
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
2
2
2
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
2
2
2
1
2
2
0
0
1
0
0
0
0
0
2
0
0
2
1
1
2
1
2
0
2
0
1
0
0
0
0
1
0
1
2
0
0
1
2
0
0
1
2
2
0
0
1
2
1
2
0
0
2
1
2
0
1
1
0
2
2
1
0
0
0
1
2
3
0
2
1
0
1
1
0
1
2
0
0
1
0
0
2
1
1
1
0
2
0
2
1
1
2
0
0
0
2
0
4
0
0
0
0
1
0
0
0
0
1
1
2
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
2
1
0
0
0
0
1
0
2
2
2
0
1
0
1
1
0
2
2
1
1
2
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
1
2
1
1
2
2
1
2
1
0
0
0
0
0
2
0
0
0
1
3
1
2
0
0
1
0
1
3
0
2
0
0
0
0
2
0
0
1
0
1
3
0
2
1
1
1
0
1
0
0
0
0
1
0
0
1
3
1
0
0
2
0
2
0
2
0
2
0
0
0
0
2
0
0
0
0
1
0
0
2
1
0
0
0
0
2
2
0
1
0
1
1
2
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
2
0
2
2
0
0
0
1
0
0
1
2
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
3
0
2
0
0
2
1
0
1
0
0
0
0
2
0
0
0
0
0
2
2
0
0
1
1
0
0
2
0
0
1
0
0
0
2
0
2
1
1
0
0
0
2
0
2
2
0
0
0
0
0
0
0
1
0
2
2
2
0
0
0
1
0
1
0
0
0
0
3
2
0
0
0
1
2
0
1
0
0
0
0
0
2
0
1
0
0
1
1
2
2
3
0
0
3
0
1
0
0
2
0
1
2
1
1
2
0
0
1
0
0
2
2
1
0
1
1
0
0
0
2
1
0
0
1
0
0
0
0
1
0
0
2
1
1
0
0
1
0
0
2
0
0
2
1
0
0
0
1
0
1
0
2
2
0
0
0
0
1
0
2
2
0
1
0
0
0
1
2
0
0
2
1
0
1
1
2
2
0
2
0
0
2
0
1
1
2
1
1
1
1
2
1
1
0
0
1
0
3
0
1
1
2
1
1
0
1
0
0
1
0
2
2
1
1
0
1
0
1
0
2
3
1
2
0
0
2
2
1
1
1
0
0
0
2
1
2
1
0
0
0
2
1
0
0
0
0
3
0
0
1
0
1
1
2
0
0
0
1
1
1
2
2
2
1
0
0
1
0
0
2
0
0
1
0
1
3
0
1
1
0
1
0
0
3
0
0
2
0
0
0
0
1
0
0
0
7
0
1
3
0
0
2
1
0
0
1
2
0
1
1
0
0
2
0
1
0
0
0
0
1
1
0
0
2
0
1
0
2
0
0
0
2
0
1
0
0
0
2
0
1
0
0
1
1
2
0
2
0
0
0
2
2
2
1
1
0
2
0
0
0
0
2
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
2
0
0
0
1
1
0
0
0
1
0
0
0
0
1
1
2
0
0
0
1
0
0
1
1
0
0
0
2
1
0
0
0
1
1
2
1
0
2
1
2
0
2
0
0
1
0
0
0
0
3
0
2
1
0
0
0
0
0
2
2
1
0
0
2
2
0
1
0
1
0
2
1
0
0
1
0
2
0
1
0
0
1
1
0
1
0
0
0
0
0
0
1
1
0
1
2
0
2
1
0
0
2
2
2
0
3
0
0
0
2
2
0
0
1
2
1
0
2
2
1
0
2
0
1
1
1
0
0
0
1
0
1
0
1
1
1
3
0
0
0
0
0
0
1
0
1
2
0
2
0
1
1
1
0
1
1
2
0
0
0
1
1
0
1
2
0
0
1
0
0
0
1
0
0
2
0
2
0
1
2
2
0
1
1
1
0
0
0
0
2
2
0
1
1
0
3
0
1
0
2
1
1
2
2
1
0
0
1
0
2
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
2
2
2
0
0
0
3
0
1
4
0
1
2
2
1
0
2
2
1
0
2
2
0
0
1
0
2
0
0
1
2
0
1
2
0
1
1
0
1
0
0
1
1
1
0
0
1
0
0
2
0
0
1
0
0
4
3
1
1
1
2
0
1
1
2
0
0
0
1
2
0
2
1
0
0
1
0
0
0
3
0
2
0
2
2
0
0
1
0
0
1
0
2
2
0
1
2
0
0
0
0
1
2
2
0
2
2
2
0
0
0
0
0
0
0
0
0
2
0
1
1
2
1
0
0
1
1
2
0
0
0
0
4
1
0
2
0
0
0
0
2
0
4
1
2
1
0
1
0
0
2
1
0
0
0
1
1
0
1
2
2
2
2
1
2
0
0
0
0
0
0
2
1
0
0
0
0
2
0
1
2
0
0
0
0
1
3
3
1
2
0
2
0
0
0
1
0
1
1
0
0
2
0
2
1
2
0
0
0
2
2
2
0
1
0
2
0
1
0
2
2
0
0
0
2
2
2
1
2
1
0
0
0
0
0
1
0
0
1
0
1
1
0
0
1
8
0
1
0
0
0
1
0
0
0
0
0
2
1
2
1
1
0
0
2
2
1
2
0
1
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
2
1
1
0
0
0
1
1
0
0
0
0
0
1
4
0
2
0
1
0
1
1
1
0
0
0
0
1
1
0
0
3
0
1
1
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
2
2
1
2
0
0
0
1
1
1
1
2
0
1
1
1
0
0
0
1
1
1
0
2
0
0
1
1
1
0
0
0
0
1
2
2
2
0
0
1
1
2
1
0
6
2
2
1
2
0
1
0
0
2
0
2
0
4
0
1
1
1
1
0
0
9
0
0
1
2
1
0
0
0
0
2
2
1
1
0
0
1
1
1
0
0
1
1
0
1
1
0
2
0
0
2
1
0
1
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
1
0
2
0
3
0
1
0
1
0
0
1
0
0
0
1
0
0
2
1
0
0
1
1
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
1
1
0
1
0
0
1
0
0
1
0
1
4
1
0
0
0
1
2
2
1
0
1
1
0
0
0
2
2
0
0
0
2
2
0
1
3
0
2
0
1
0
0
1
5
1
0
2
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
1
1
2
3
0
1
0
0
0
0
2
0
0
2
0
0
1
0
1
0
0
0
1
0
0
2
0
1
1
2
1
1
2
2
0
2
0
1
0
2
2
1
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
2
0
0
2
1
1
1
0
2
0
0
0
1
2
1
2
2
0
1
0
1
0
1
0
0
0
0
3
2
0
0
0
2
0
1
1
1
0
0
0
2
0
0
2
0
0
0
1
0
1
2
2
0
0
2
0
0
1
1
1
1
2
2
1
0
0
0
0
0
1
0
0
1
0
1
2
0
0
2
0
0
1
0
1
0
2
0
3
3
2
0
0
1
2
1
1
1
0
0
2
0
1
1
0
3
0
0
0
0
2
0
1
2
2
1
1
0
0
2
1
0
1
3
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
1
0
2
1
0
0
0
0
1
2
1
1
0
0
1
2
0
0
2
2
0
0
1
2
1
0
0
0
0
2
1
0
2
0
0
0
1
2
2
1
0
2
0
0
1
2
0
1
0
0
2
0
0
0
0
1
2
1
0
1
0
2
1
1
1
2
0
0
1
1
1
0
0
0
0
2
1
0
0
0
1
0
1
1
2
0
1
0
0
2
1
2
0
1
2
1
0
2
0
0
0
1
3
2
2
0
2
1
0
0
0
1
0
1
2
0
0
2
2
0
0
2
0
2
2
3
2
0
0
0
0
2
1
2
1
0
0
2
0
1
0
0
1
0
1
1
0
1
0
0
2
0
0
2
0
1
0
1
0
0
2
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
4
0
2
1
1
0
0
0
0
2
1
0
0
1
0
0
1
1
0
1
1
0
0
1
0
2
0
1
0
0
1
0
0
0
0
2
1
3
0
0
1
1
1
1
0
0
2
0
3
0
0
2
1
0
0
1
2
0
0
0
0
1
1
0
1
2
0
0
0
1
0
0
1
2
2
0
2
0
0
0
0
0
2
1
0
1
2
1
0
2
1
0
1
0
0
0
1
1
0
1
0
0
0
0
0
1
1
1
1
1
0
0
1
0
2
1
1
1
2
0
0
0
1
0
0
0
0
14
0
0
0
0
0
2
1
0
1
0
1
1
1
0
2
2
0
0
1
0
0
0
0
1
2
0
0
0
2
0
0
1
1
1
0
0
2
1
0
2
1
0
1
3
0
1
2
2
0
1
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
2
2
1
0
1
1
2
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
1
2
1
1
0
0
0
2
2
1
0
0
1
0
1
1
2
0
0
0
1
0
1
1
1
2
1
0
0
0
0
0
1
1
0
1
1
2
0
0
1
0
0
1
0
2
2
1
0
3
0
0
1
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
1
0
0
2
0
0
1
0
1
1
0
1
0
1
2
1
0
0
1
1
1
0
0
0
0
2
0
0
1
1
2
0
0
1
2
0
0
0
1
2
1
0
0
0
0
2
1
1
2
0
2
0
0
0
0
0
1
0
0
0
2
1
0
0
0
2
2
0
0
2
1
2
0
0
0
1
1
0
2
1
0
1
0
2
0
0
0
0
0
2
1
1
2
2
1
2
1
2
1
2
0
2
0
3
0
2
0
0
0
0
1
2
2
2
0
2
0
1
0
0
0
2
1
1
0
2
0
2
1
2
0
2
2
0
0
0
1
2
0
1
2
0
0
1
1
0
0
2
1
0
1
0
2
0
0
2
2
2
0
1
0
0
0
1
0
2
0
1
0
0
0
1
2
1
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
1
0
1
1
2
0
0
0
0
1
1
2
0
1
1
1
1
2
0
0
1
0
2
0
0
2
0
1
2
2
0
1
1
1
0
0
2
0
1
2
0
0
0
2
0
0
0
1
0
2
2
0
1
2
0
0
0
0
1
1
0
2
2
0
0
0
0
1
0
0
1
2
1
1
0
0
0
0
0
1
0
2
2
0
0
0
1
1
1
0
0
0
1
1
0
2
0
0
0
2
0
0
1
0
1
0
1
2
0
0
0
2
2
2
0
1
0
2
0
0
1
0
0
2
0
1
0
1
2
0
0
2
0
2
0
1
0
0
2
0
0
4
0
2
0
1
2
1
1
0
0
0
2
0
0
2
1
2
1
1
1
2
2
1
0
1
0
0
1
2
0
1
0
3
1
0
0
0
0
0
0
2
0
0
0
0
0
2
1
2
1
4
2
0
1
1
1
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
2
2
0
2
0
0
1
0
1
1
0
1
0
0
0
2
0
2
1
3
2
0
2
0
1
2
1
0
0
1
0
1
0
0
0
0
2
0
0
0
0
2
1
0
0
2
1
0
0
0
0
0
0
2
2
1
2
2
0
0
0
2
1
1
2
0
1
0
3
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
1
2
2
1
1
1
1
0
0
2
0
0
0
0
1
0
3
0
0
0
1
4
2
0
2
0
0
0
0
1
0
2
0
0
1
0
1
0
0
2
0
0
0
0
1
1
0
0
0
0
2
1
0
1
0
2
0
1
1
1
0
0
0
2
0
2
2
0
2
1
1
0
1
0
1
0
0
0
2
0
0
1
0
1
0
0
2
0
0
0
4
2
0
1
0
1
2
2
0
0
0
0
0
0
0
0
0
1
0
0
1
3
2
1
2
2
0
1
0
1
1
1
0
2
0
0
1
0
2
0
0
0
1
2
1
1
0
0
2
0
0
1
0
1
1
1
0
0
2
2
0
0
0
4
1
2
1
1
1
0
1
0
0
1
0
1
2
2
1
1
0
1
0
2
2
1
0
0
0
1
2
0
1
0
0
2
0
0
1
1
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
1
0
2
0
1
1
1
0
0
0
3
1
0
0
0
0
0
0
0
4
1
0
2
0
2
0
0
0
2
2
2
1
1
0
0
1
1
1
0
0
3
1
1
0
1
1
2
0
0
1
0
2
0
0
0
2
0
1
0
1
0
1
0
2
2
0
0
2
0
0
1
1
1
2
0
2
0
1
0
1
0
0
0
0
0
2
0
3
0
0
0
1
0
0
1
1
0
1
2
0
0
0
0
0
1
0
2
1
0
0
0
1
0
0
1
0
0
0
3
0
1
0
0
2
1
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
3
1
0
2
0
1
0
0
0
1
0
0
0
1
0
1
0
0
1
2
0
0
0
0
0
0
0
2
0
2
1
2
1
1
1
2
1
0
1
1
0
2
0
2
2
0
0
0
1
0
0
0
0
1
0
1
0
2
0
0
0
0
0
1
0
0
1
1
1
3
0
2
0
2
1
0
1
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
2
1
0
0
3
1
0
0
1
1
1
2
0
2
0
0
2
0
1
1
0
0
2
0
0
0
1
1
0
1
2
0
0
0
0
1
1
0
0
1
3
1
2
0
0
1
1
1
0
1
1
0
0
1
0
0
0
0
1
2
2
0
0
1
0
0
1
1
0
1
0
0
0
0
0
1
0
0
1
0
1
4
1
0
0
1
1
1
3
2
0
0
1
2
0
2
1
1
1
2
0
0
0
0
2
2
0
0
0
1
0
2
1
2
0
1
0
0
0
2
3
4
0
0
0
1
0
0
0
1
0
0
0
0
1
2
1
0
0
0
1
3
0
2
0
2
1
0
0
3
2
0
0
0
3
1
0
2
1
0
0
1
0
1
0
2
0
0
0
1
0
0
0
2
1
0
1
0
0
1
2
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
1
1
1
2
2
1
0
1
1
0
1
1
2
1
1
0
2
0
0
0
2
0
2
1
0
0
2
0
0
1
0
2
2
0
1
0
0
2
1
0
1
0
0
2
0
4
0
0
0
1
1
0
0
2
0
0
1
0
1
0
0
3
2
0
0
2
2
0
0
3
0
1
1
0
1
0
0
2
2
1
2
0
0
0
2
1
0
0
2
0
2
1
0
0
1
1
0
0
0
1
0
0
1
0
1
2
0
2
1
0
0
0
0
0
0
1
0
0
0
2
2
1
1
0
0
2
0
0
2
1
0
2
3
1
1
0
0
0
1
0
0
1
1
1
1
0
0
0
0
0
0
2
1
2
3
0
0
0
1
0
0
0
0
1
0
2
1
0
0
0
2
2
2
1
1
0
0
0
0
0
0
1
0
0
1
1
0
1
1
1
0
2
0
0
0
1
0
0
0
0
1
2
0
1
2
0
1
0
0
2
0
2
1
0
1
1
0
0
0
0
0
0
1
0
0
0
1
1
1
1
0
1
2
2
0
1
0
1
0
0
1
0
2
0
1
2
1
0
1
1
1
0
0
1
0
1
1
2
0
0
1
0
0
0
0
0
2
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
1
1
1
0
1
1
0
1
2
0
0
0
1
1
0
2
1
2
1
0
0
2
0
1
2
2
1
0
2
0
1
0
1
1
2
0
2
0
1
0
1
0
0
2
0
0
0
1
0
1
2
0
0
2
1
0
2
0
1
0
0
0
1
0
1
2
0
0
0
1
0
0
1
0
3
2
1
1
0
0
0
0
2
0
0
1
0
1
2
1
0
1
0
0
0
0
0
1
2
2
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
2
0
1
1
0
2
1
0
3
0
1
0
1
1
1
2
0
2
2
0
2
0
0
0
0
0
3
2
0
2
2
0
2
1
0
2
2
2
0
1
0
1
0
0
0
2
1
2
1
0
0
0
0
0
1
2
0
2
0
1
1
0
0
0
0
0
1
0
0
1
1
0
0
2
0
0
2
1
0
0
2
0
1
0
2
0
0
0
1
2
1
0
1
2
2
0
0
2
0
0
0
1
0
0
0
0
0
1
2
1
0
0
0
1
1
1
1
0
2
1
1
2
0
1
2
2
2
1
1
0
2
1
1
1
0
0
0
2
0
2
2
1
0
0
2
0
0
1
0
1
0
0
0
3
1
1
2
0
0
0
0
1
1
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
3
0
1
1
0
1
1
1
1
0
0
3
1
1
0
0
2
0
1
2
0
2
0
0
2
2
1
1
0
2
2
2
3
0
1
1
0
1
0
0
2
0
0
0
0
2
0
0
1
1
1
1
0
0
0
2
0
0
1
2
0
1
1
2
0
0
0
0
0
1
0
1
1
0
1
1
3
0
1
1
1
5
0
0
2
1
1
1
0
1
0
3
0
3
1
0
0
0
1
0
0
1
0
1
2
2
1
0
0
0
2
0
0
0
0
0
0
1
1
0
0
2
0
2
0
0
2
0
0
4
0
0
2
2
0
0
0
2
1
2
1
2
2
3
1
0
0
2
1
0
2
0
0
0
1
0
0
1
1
2
0
1
0
1
0
2
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
2
0
1
1
2
1
0
0
0
0
2
0
0
0
0
3
1
0
1
1
1
0
1
1
2
0
2
0
0
1
1
2
0
0
1
0
0
1
0
2
2
0
0
0
2
2
0
0
0
1
1
1
2
0
0
2
0
5
2
1
0
0
0
1
1
0
0
1
1
1
1
0
0
0
0
0
1
2
1
1
0
0
3
0
1
0
2
2
1
0
0
0
0
1
0
1
2
0
0
1
0
0
1
0
0
2
1
0
1
0
1
5
1
0
2
0
0
1
1
1
0
0
1
0
0
0
0
1
2
1
0
0
3
1
2
1
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
1
2
2
0
0
0
0
0
0
3
1
1
1
0
0
0
0
0
0
0
0
1
2
0
1
2
0
0
1
0
0
0
0
1
0
0
1
0
2
2
2
0
0
0
0
0
2
1
2
0
0
0
0
0
2
0
0
1
1
0
2
1
0
0
2
2
0
2
0
0
2
0
3
1
0
0
1
0
2
0
2
0
0
0
2
0
0
0
1
0
0
2
2
0
1
4
0
2
1
1
2
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
4
0
1
2
0
0
0
2
0
0
0
2
0
0
1
2
1
0
2
2
0
0
0
0
0
2
0
3
2
1
0
0
4
1
0
0
1
0
2
0
0
2
0
1
1
1
0
0
0
1
0
0
1
1
1
0
0
0
1
2
4
2
1
1
0
1
0
1
0
1
0
2
0
0
1
1
4
0
0
1
1
2
0
2
2
0
1
0
0
0
0
0
0
0
2
2
2
0
0
1
1
0
0
0
0
1
1
0
0
0
1
0
1
2
0
1
1
0
2
0
0
0
0
1
2
1
0
1
0
0
0
0
0
0
2
0
0
2
2
3
1
0
1
1
2
0
1
0
2
0
0
2
0
2
0
1
2
1
2
1
2
3
2
0
0
0
0
1
0
0
2
0
2
2
2
1
1
0
0
0
1
0
0
1
2
1
2
1
2
0
1
2
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
1
1
0
0
0
1
1
1
0
1
0
4
0
1
2
0
1
0
0
1
2
0
2
0
0
2
0
0
1
2
0
1
0
0
1
1
0
2
1
1
0
0
2
1
0
0
1
1
2
2
1
0
1
1
0
0
0
1
0
1
0
2
0
0
2
1
0
2
0
1
1
1
1
0
1
2
0
0
1
3
0
2
1
2
0
1
0
1
1
0
0
0
2
3
0
0
2
0
1
0
0
2
0
1
0
2
2
0
2
0
1
0
0
2
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
1
0
2
0
1
0
7
1
0
1
0
1
2
1
0
1
1
1
1
2
0
1
2
2
0
0
2
1
1
2
0
1
2
0
0
0
0
0
3
0
0
0
0
1
1
0
1
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
2
2
2
0
1
2
0
1
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
1
0
2
0
2
0
1
0
2
0
0
1
0
1
1
2
0
0
2
0
1
1
0
1
1
0
0
0
2
1
2
1
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
1
0
3
0
0
0
2
2
0
2
1
2
0
1
0
4
0
1
0
0
0
0
2
0
2
1
0
0
0
1
0
0
2
0
1
0
1
1
0
2
1
2
0
2
1
2
0
1
2
0
0
0
1
2
0
1
0
0
0
0
0
1
1
0
2
0
1
2
0
0
0
0
0
0
2
0
1
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
2
0
2
0
0
2
2
2
1
0
2
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
1
0
0
0
1
0
1
2
1
0
0
1
2
0
1
0
0
2
0
0
0
1
2
0
1
0
0
2
0
0
0
0
1
0
0
0
2
0
1
0
0
0
1
0
2
1
2
1
0
0
1
0
0
1
0
0
2
0
2
0
2
0
0
0
0
1
1
0
0
0
0
2
0
1
2
1
0
1
0
1
0
0
0
0
2
1
1
0
0
1
2
0
1
0
1
0
0
1
0
0
0
0
0
2
1
0
2
2
0
0
1
0
0
0
1
0
2
2
0
1
0
0
0
0
0
1
1
0
0
0
1
1
1
0
2
1
0
2
0
1
1
1
0
0
0
2
1
1
0
0
0
1
2
2
1
1
0
1
2
0
0
0
2
1
0
0
2
1
0
3
1
0
1
0
0
0
2
1
0
0
1
1
1
2
1
1
0
0
1
0
0
0
0
0
1
2
0
2
0
1
0
0
2
0
1
2
2
1
2
0
0
1
2
4
0
1
2
1
1
2
0
1
1
0
1
0
1
2
1
1
0
1
0
1
0
2
0
2
0
0
0
4
0
1
0
0
2
2
1
0
0
0
1
2
0
0
2
0
1
0
2
2
2
1
0
0
0
1
2
2
2
1
0
0
0
1
0
0
0
1
0
1
1
0
1
0
0
2
2
0
0
2
1
1
0
1
0
1
2
0
0
0
1
2
0
0
0
0
1
0
0
0
0
1
0
1
2
2
0
1
0
0
0
0
0
0
0
1
3
0
1
0
0
0
2
3
0
0
2
0
0
1
0
2
0
1
1
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
2
0
2
4
1
1
0
1
2
0
1
2
0
3
0
1
0
0
1
4
1
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
1
0
0
1
0
0
2
0
1
0
1
0
0
0
0
1
0
1
0
2
0
1
0
1
1
0
0
0
0
1
0
0
0
0
2
1
0
1
2
0
1
1
1
2
2
0
1
0
0
0
0
0
0
1
0
0
0
1
3
1
0
1
1
0
1
1
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
1
0
1
0
1
1
1
0
0
0
1
0
0
0
0
0
7
0
1
2
3
1
0
1
2
1
2
0
1
0
1
1
2
1
2
0
1
0
0
0
1
2
0
0
1
1
1
0
0
0
1
0
0
0
0
0
2
0
0
1
2
1
1
0
1
0
0
2
0
2
0
0
0
0
1
1
0
0
2
2
2
1
2
0
2
1
2
0
0
0
1
0
0
0
0
1
2
0
2
0
0
0
2
0
2
1
2
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
3
0
2
0
0
0
0
0
2
2
1
0
2
0
0
2
0
2
2
0
1
0
1
0
2
0
2
0
0
0
2
2
0
1
1
0
0
0
2
0
0
1
1
1
2
1
0
1
0
0
1
2
0
1
0
1
0
0
2
0
1
1
0
1
0
2
1
1
0
0
0
0
0
0
1
1
0
1
0
0
1
3
0
0
2
0
0
0
0
0
1
0
2
0
1
1
0
1
0
2
2
0
1
1
1
2
0
3
1
0
2
0
3
1
2
1
0
0
0
0
2
1
2
0
0
2
1
1
1
2
2
0
0
2
0
0
0
1
2
0
1
1
0
0
1
2
2
2
2
0
1
1
2
2
0
1
0
0
0
0
2
2
1
0
0
0
0
0
3
1
2
0
0
1
0
1
0
0
1
0
3
0
2
2
1
1
2
0
0
0
0
0
1
1
0
0
2
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
2
0
1
2
2
0
2
0
1
1
0
1
0
1
0
2
1
2
1
0
0
1
0
1
2
1
3
2
0
1
0
0
2
0
2
0
0
0
2
0
2
0
1
0
0
2
1
0
5
0
1
0
0
0
2
0
1
0
2
0
0
0
1
0
0
0
1
1
2
0
1
0
0
1
0
1
1
1
1
1
0
0
1
0
0
1
3
0
2
1
0
0
0
1
2
2
0
1
2
2
0
3
1
2
1
0
0
0
2
0
0
0
1
2
0
1
1
0
0
0
2
0
0
0
1
1
1
2
2
0
2
0
0
3
2
0
0
0
0
1
1
0
2
2
0
2
2
0
0
2
0
0
0
0
2
1
2
2
0
0
0
0
1
0
2
1
2
0
1
0
2
1
0
1
0
1
0
1
1
2
2
0
0
0
0
1
2
0
1
2
2
0
2
1
1
2
0
0
0
0
0
0
2
2
0
2
0
1
1
0
1
0
0
2
1
0
1
0
1
2
0
0
2
2
0
2
0
1
0
2
0
0
0
1
0
0
2
0
0
3
1
0
1
0
0
2
0
0
0
1
1
2
0
0
0
1
0
1
0
0
2
1
0
0
1
1
0
1
0
1
1
0
0
0
2
0
0
0
1
0
0
1
1
2
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
1
1
1
1
0
1
0
0
2
0
0
1
0
0
1
1
1
1
0
0
1
0
0
0
1
0
1
0
0
1
1
0
0
0
1
2
3
1
0
1
1
2
4
1
1
0
2
1
0
0
1
0
1
0
2
1
0
0
0
2
0
2
2
2
0
0
0
0
2
1
2
0
1
0
1
1
0
1
2
0
1
1
0
2
1
0
0
0
0
0
1
0
0
2
2
0
1
0
1
0
0
0
0
0
0
1
0
2
1
0
0
1
0
2
0
2
2
0
1
0
1
0
0
0
2
1
2
0
0
0
1
0
2
0
1
1
1
1
0
0
0
1
1
2
0
1
2
0
0
1
0
2
2
0
2
1
0
1
3
2
1
0
1
0
0
0
1
2
2
0
1
0
0
0
0
0
0
2
0
0
0
3
0
2
3
3
1
1
1
0
0
2
1
2
0
0
1
0
2
0
1
0
1
0
0
2
0
0
1
0
0
1
0
0
3
0
0
0
0
1
1
1
1
3
0
0
2
1
1
0
0
2
2
0
1
0
0
2
0
0
3
1
0
0
1
1
0
1
1
0
3
0
0
0
2
0
0
1
0
2
0
0
2
2
1
0
0
0
0
0
2
0
0
0
1
3
0
1
0
1
2
0
0
1
0
0
0
3
2
2
2
0
3
1
0
1
0
0
0
1
0
0
0
1
1
0
0
2
0
2
0
0
2
0
1
0
0
1
1
0
0
0
0
0
0
2
0
1
0
0
2
2
0
1
2
0
2
0
0
2
1
0
1
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
1
1
2
0
0
3
0
0
0
2
0
1
0
0
0
2
0
3
0
2
0
1
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
2
1
0
1
1
2
0
1
1
0
1
1
1
1
0
2
1
0
1
1
2
1
1
0
2
1
1
0
1
0
1
1
0
0
1
1
2
0
1
2
0
2
1
2
2
0
0
3
2
2
1
0
1
0
1
1
0
0
0
2
0
2
0
0
2
0
2
0
0
0
3
1
2
2
0
0
0
0
1
0
1
1
1
0
1
0
0
2
0
1
2
0
0
0
0
1
1
0
2
0
1
0
2
2
1
1
0
0
2
0
0
0
1
2
0
2
1
0
2
0
2
0
2
2
2
1
0
0
0
2
1
1
1
0
0
0
0
3
1
0
0
0
0
2
0
1
0
2
0
0
0
0
1
0
0
2
0
1
0
2
0
0
0
0
0
1
1
2
0
1
1
1
2
1
5
0
0
0
2
1
0
0
0
2
1
1
1
0
1
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
2
0
0
1
1
1
0
1
0
2
0
1
0
0
0
1
0
0
1
0
1
1
1
0
2
0
0
0
2
0
0
0
1
2
0
0
1
2
2
2
2
0
0
2
3
0
0
0
0
2
0
0
0
0
0
0
2
1
1
1
2
0
0
1
2
0
0
0
2
0
2
2
0
2
0
1
0
0
2
0
0
0
1
1
0
0
2
1
0
1
2
1
2
0
1
2
0
0
2
0
0
1
0
1
2
0
0
2
1
1
0
1
1
1
0
3
0
0
3
0
1
1
0
1
0
0
1
1
0
2
0
1
2
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
2
0
3
0
0
1
0
0
0
1
1
0
0
0
0
1
2
0
0
0
0
0
2
1
0
0
0
1
0
0
1
1
0
2
0
2
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
1
1
2
2
1
1
1
1
2
0
1
1
0
1
0
0
0
0
1
0
1
1
0
1
2
0
0
0
0
2
1
1
2
0
0
0
0
2
2
2
2
1
0
2
1
0
0
0
1
0
0
0
2
0
1
1
1
1
0
1
2
2
0
1
0
1
0
0
1
0
2
0
2
0
1
1
1
0
0
0
0
1
0
0
0
1
1
0
1
0
0
1
2
0
0
1
0
2
2
0
1
0
1
2
2
0
3
2
0
0
0
1
0
0
2
1
1
1
2
0
3
1
0
0
0
0
0
0
0
3
0
2
1
0
0
1
0
1
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
4
0
0
0
0
2
0
0
1
1
0
2
0
2
2
0
2
0
0
0
0
0
2
0
1
0
3
2
0
1
1
0
0
1
0
2
0
1
0
1
1
0
0
1
1
2
0
1
0
1
0
0
1
2
2
0
0
1
0
10
1
1
0
0
6
1
1
0
2
1
1
0
1
0
0
1
1
0
1
0
1
2
0
1
1
0
0
0
2
0
2
0
2
0
0
2
1
1
0
0
2
0
4
2
2
0
0
0
2
0
2
0
0
2
0
0
0
0
2
0
0
0
1
0
0
1
0
0
4
0
2
0
0
1
0
0
0
0
1
0
0
0
1
1
2
2
1
1
0
1
1
1
0
1
0
0
1
1
0
2
1
3
2
1
1
0
0
1
0
0
0
1
1
0
0
2
0
1
1
3
0
1
2
0
0
0
0
0
2
0
1
0
0
2
0
0
0
2
2
5
0
1
0
0
1
2
2
0
0
0
2
1
0
1
2
0
0
0
1
2
1
0
0
1
1
1
0
1
0
1
2
0
1
0
1
1
2
1
0
3
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
2
2
0
0
1
0
1
0
0
4
0
2
0
1
0
2
0
0
1
1
0
0
1
1
0
1
2
1
1
0
1
3
0
0
0
1
0
0
1
0
2
1
0
0
1
0
0
2
1
0
1
1
0
0
0
2
1
0
0
0
1
1
0
0
1
0
2
2
1
0
2
1
0
2
1
2
3
1
2
0
0
1
0
0
0
2
0
1
2
0
0
2
1
0
0
2
1
1
1
0
0
1
1
5
2
1
2
0
1
0
1
0
0
0
0
0
0
3
1
0
2
0
1
0
2
0
1
0
0
0
0
1
2
4
2
0
1
2
0
1
0
1
1
0
0
0
0
2
0
0
0
1
0
1
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
2
1
1
0
3
3
0
1
1
0
2
0
1
0
2
0
0
0
2
1
1
2
0
0
2
1
1
2
1
0
1
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
2
2
1
0
2
2
0
1
3
0
0
2
0
0
0
3
0
1
0
0
2
0
0
1
2
3
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
2
0
0
1
0
0
0
0
1
0
2
0
1
0
1
0
2
1
0
0
0
0
0
0
2
2
1
0
0
0
2
1
3
1
0
2
1
0
2
1
0
1
0
0
1
0
2
4
0
0
0
1
0
0
4
2
0
1
1
1
0
2
1
2
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
2
2
2
0
0
2
1
1
0
2
1
2
0
1
0
1
2
1
2
0
1
2
1
0
0
1
1
2
0
1
0
0
0
0
0
1
2
1
0
2
0
2
0
2
0
0
0
2
0
3
1
0
0
2
2
0
0
2
0
0
1
0
0
0
0
3
1
1
0
1
0
1
0
2
2
0
1
2
1
1
2
0
0
0
2
1
0
0
0
0
0
0
1
1
0
1
0
1
0
0
2
1
1
1
0
0
0
0
2
0
1
0
0
0
0
1
0
0
2
2
0
0
2
0
0
2
0
0
0
0
2
0
0
1
2
0
1
0
1
2
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
1
0
1
0
1
0
1
2
0
0
0
0
1
2
0
1
2
2
0
1
0
0
1
0
2
0
0
0
2
0
0
2
0
1
2
0
0
0
2
1
0
0
1
0
1
0
0
0
0
1
1
3
1
0
2
0
0
0
1
0
0
0
0
1
1
2
0
0
1
2
1
1
0
0
0
2
2
2
2
2
3
1
1
0
2
0
0
2
1
1
0
2
0
1
1
0
1
2
1
0
0
1
0
0
0
2
2
2
0
1
0
0
0
0
1
0
1
0
0
2
3
1
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
2
0
2
1
0
0
1
1
1
0
1
0
1
2
0
0
1
1
0
1
1
0
2
0
0
4
1
1
1
2
2
0
1
2
1
1
2
0
1
1
2
3
0
0
0
2
2
0
0
0
1
1
1
0
0
0
0
0
1
1
2
0
0
0
0
2
1
0
1
0
2
3
0
1
2
0
0
0
0
0
2
0
0
0
1
0
1
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
2
2
0
0
0
0
0
2
0
1
2
2
0
1
3
0
0
0
0
0
1
0
0
0
2
0
0
1
0
6
1
2
0
0
1
3
1
0
2
0
2
0
0
0
1
2
0
0
0
0
2
1
0
0
0
1
2
1
1
0
0
1
0
2
2
1
0
2
0
2
1
1
0
0
0
2
0
0
2
0
2
1
1
0
2
0
0
1
0
0
1
1
2
0
2
0
0
0
0
2
1
2
0
2
1
2
2
0
0
2
1
0
0
0
0
1
2
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
1
0
1
1
0
0
1
1
1
0
1
0
1
0
0
0
0
0
0
1
1
1
0
1
1
1
0
0
0
0
2
0
0
1
1
0
1
0
2
0
1
1
1
0
2
1
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
3
2
0
0
0
0
0
0
2
2
0
1
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
1
0
2
1
0
2
0
1
1
0
2
0
0
1
1
0
4
0
0
3
1
0
1
1
0
0
2
0
2
0
1
0
1
0
0
0
1
0
0
0
1
2
2
1
0
0
1
0
1
0
0
2
1
1
2
0
2
3
2
0
1
0
0
0
0
2
1
2
0
0
0
0
0
0
2
1
1
2
1
1
2
1
1
0
2
3
0
0
0
1
0
0
1
0
2
0
0
0
1
0
0
1
1
1
1
1
0
2
0
1
0
1
1
0
0
1
0
0
1
1
1
0
0
2
0
0
0
1
2
2
0
0
1
2
0
0
1
1
2
1
0
1
0
0
0
0
1
1
0
2
1
0
1
0
2
0
2
1
1
1
0
1
2
0
1
0
0
0
0
0
2
3
0
0
1
4
2
2
5
0
0
1
0
0
1
1
1
1
2
2
0
0
0
0
0
1
2
0
0
0
1
1
4
0
1
1
1
2
1
0
0
0
1
0
0
1
0
0
1
2
0
1
2
1
0
0
0
0
0
1
0
2
1
2
0
0
0
0
2
1
0
0
2
0
2
0
0
0
2
2
2
0
0
0
1
1
0
0
2
0
2
1
2
2
1
0
1
0
0
2
0
1
2
2
2
0
0
0
2
1
0
0
0
0
0
0
1
0
1
0
1
0
1
1
1
0
0
0
0
2
2
0
0
0
1
0
0
2
0
0
0
1
2
2
0
1
0
2
0
1
2
0
0
0
2
2
0
2
0
1
1
0
2
0
0
2
2
2
0
0
1
1
0
0
2
0
1
0
1
0
1
0
3
1
2
2
0
1
3
1
1
1
0
2
0
1
1
0
0
1
0
1
0
1
2
2
2
0
2
1
0
0
1
1
2
1
0
0
0
0
1
0
3
1
0
1
0
0
0
0
3
1
0
0
2
0
0
5
2
0
0
0
1
0
2
2
0
0
0
2
0
1
1
0
0
0
1
2
2
2
0
2
2
0
1
0
1
0
1
1
1
0
0
0
0
1
0
1
1
0
0
2
0
2
2
0
0
0
0
2
1
0
0
0
2
0
0
0
1
1
3
1
0
0
1
1
1
1
2
0
2
0
0
1
0
0
2
0
0
0
1
2
1
1
0
0
0
0
2
1
0
1
0
2
0
1
0
0
2
0
0
0
0
0
0
2
2
0
0
1
0
2
0
1
2
0
0
1
0
0
0
0
0
1
0
0
2
0
0
2
0
2
0
1
0
1
0
0
0
1
0
2
0
0
0
0
0
2
2
0
1
1
0
3
0
2
1
1
0
1
1
2
0
2
0
2
1
2
0
0
0
1
2
0
2
0
0
0
2
0
0
1
0
0
1
2
1
0
1
2
0
0
1
1
2
1
0
0
0
0
1
2
1
0
2
0
1
0
0
2
0
3
3
0
1
0
0
1
0
1
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
2
0
0
2
0
0
0
0
1
0
1
0
1
0
0
1
2
0
0
0
1
1
0
0
1
0
0
2
0
0
2
1
0
0
1
0
0
1
1
1
1
0
2
0
1
2
2
0
1
0
1
1
0
2
0
2
0
1
0
1
0
1
0
1
1
0
1
2
1
0
1
2
2
1
2
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
2
1
0
2
0
2
2
0
0
0
1
0
0
0
1
0
0
2
1
0
2
1
1
1
0
0
0
0
2
1
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
1
0
0
1
0
2
2
0
2
2
0
0
1
0
0
1
1
0
1
0
0
1
0
1
0
0
0
2
0
0
1
1
1
0
1
0
0
1
2
1
0
0
0
0
0
1
1
1
0
0
0
0
2
0
1
0
0
0
0
0
3
0
1
2
1
0
0
1
3
0
2
0
0
2
2
0
1
0
1
2
1
2
0
1
0
1
2
2
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
2
1
1
1
0
1
1
0
0
0
0
2
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
2
1
2
0
1
1
1
1
0
1
0
0
0
2
1
0
2
0
2
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
3
1
0
1
0
1
2
1
0
0
0
2
0
1
0
1
1
0
0
0
0
0
2
1
1
0
2
2
2
2
0
0
1
2
0
0
2
0
1
0
0
0
0
0
1
0
1
2
2
0
0
0
1
0
1
0
1
2
1
2
1
0
0
0
1
2
0
0
0
1
2
1
0
1
0
0
3
1
0
0
0
1
1
0
0
0
1
0
0
2
1
0
0
0
1
1
0
1
1
1
2
0
0
2
3
0
2
1
1
1
0
2
0
1
2
0
0
1
0
1
0
2
2
2
1
0
2
1
2
1
0
1
1
0
0
0
0
0
10
1
0
1
0
1
0
0
0
0
1
1
0
1
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
1
1
0
0
0
1
0
2
0
0
2
2
1
0
2
1
1
0
1
2
0
0
0
1
0
2
0
0
1
0
0
3
0
1
1
3
0
1
0
0
1
0
2
1
1
2
2
1
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
2
2
0
0
0
0
1
2
2
0
1
3
1
1
2
0
2
0
0
2
1
3
0
2
0
0
0
2
0
0
0
0
2
2
0
0
2
1
1
1
0
1
1
0
1
1
0
2
0
0
0
0
0
1
0
1
0
1
1
0
1
0
0
2
0
1
0
2
0
3
1
0
1
0
2
0
2
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
2
1
0
2
2
0
1
2
0
2
1
0
0
0
1
0
1
1
2
0
0
1
1
0
0
1
0
1
1
0
3
1
1
0
1
0
2
5
3
0
0
0
0
0
1
2
1
0
0
1
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
1
0
2
1
2
2
0
2
0
0
2
2
2
1
2
0
0
0
0
1
0
0
1
0
0
2
2
2
0
0
1
2
0
2
0
2
0
0
0
0
0
1
1
1
2
2
0
0
2
0
1
2
0
0
0
0
1
0
0
1
1
2
0
0
2
0
1
0
0
2
3
0
2
0
0
0
2
0
1
2
2
1
1
0
0
2
0
0
0
2
1
0
2
0
2
1
1
1
0
0
1
0
1
0
2
0
0
2
0
2
2
1
3
0
0
0
1
0
2
0
0
1
1
2
0
0
0
0
0
0
0
2
0
1
1
2
0
0
2
0
0
0
1
0
2
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
1
0
0
2
1
1
2
1
2
2
0
2
1
1
1
0
2
2
0
0
0
2
0
0
1
2
2
0
0
0
0
0
1
0
0
1
0
0
1
0
0
2
0
0
0
2
0
0
0
0
1
0
2
1
0
2
1
0
0
1
0
1
1
0
0
0
0
0
0
2
0
0
0
0
2
0
1
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
2
0
2
2
0
2
1
1
0
2
0
1
0
0
0
1
1
0
2
5
1
0
0
1
0
2
1
0
0
2
0
0
2
1
1
0
1
1
0
0
1
0
1
0
0
2
1
1
0
0
1
2
0
1
3
0
0
0
0
0
2
1
1
0
0
1
0
0
1
0
1
0
0
0
0
0
1
2
2
0
1
0
0
0
1
0
1
1
0
1
2
1
1
2
2
1
1
0
2
0
2
0
0
1
1
0
1
0
0
2
0
1
0
1
0
0
0
0
0
2
1
0
0
0
2
0
0
2
0
0
0
3
0
3
2
1
0
0
1
1
1
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
1
1
1
2
0
1
1
1
1
0
1
0
0
0
0
0
2
2
0
0
1
0
0
0
1
2
0
2
2
0
0
0
1
1
0
2
0
0
0
0
1
0
1
0
0
0
2
0
1
0
0
0
3
1
2
0
0
1
0
2
0
0
1
1
0
1
2
0
1
0
0
0
0
0
2
0
2
0
2
0
0
0
2
1
1
0
1
2
0
0
0
0
1
2
0
0
0
1
0
0
0
2
0
0
0
0
1
1
2
1
1
1
2
0
1
1
0
0
0
1
0
0
0
0
2
1
0
3
1
2
0
2
1
1
0
0
2
2
0
0
0
2
0
1
1
2
0
0
1
0
2
2
1
0
1
1
0
0
0
0
1
2
0
1
0
1
3
2
0
1
0
0
0
1
0
0
1
0
0
0
1
2
0
0
1
2
2
1
0
2
1
2
0
0
0
1
3
0
1
0
0
0
0
0
0
0
2
0
1
0
0
1
1
1
1
0
4
2
0
2
0
0
0
0
0
2
0
1
2
1
0
4
0
1
1
0
0
1
1
0
0
0
2
1
1
1
2
1
0
1
2
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
2
1
0
0
1
0
0
0
0
2
0
1
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
1
2
2
2
3
1
1
0
0
0
0
0
1
2
1
2
2
0
2
0
0
0
2
0
2
0
0
0
0
1
0
0
1
0
1
1
0
0
2
0
0
0
1
0
0
0
0
2
0
0
1
2
2
2
0
0
0
0
0
2
0
0
2
2
0
0
1
1
2
1
0
2
2
0
1
2
1
0
2
2
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
1
0
2
0
2
0
0
1
1
0
1
0
0
1
0
0
0
1
0
0
3
2
3
0
1
0
0
1
2
0
0
0
0
1
0
1
1
2
1
1
2
0
3
0
3
0
1
2
0
0
2
0
1
2
0
2
0
0
2
0
2
0
1
2
0
1
0
0
2
0
2
1
1
1
0
1
2
0
0
0
1
3
2
0
1
0
2
2
1
2
1
0
0
0
1
1
2
2
2
1
2
1
0
0
2
0
1
0
1
0
0
0
1
0
0
1
0
2
1
0
1
0
0
1
1
1
0
2
1
0
1
0
0
0
0
1
0
3
1
0
0
0
0
1
2
0
1
2
1
3
1
2
0
1
0
0
0
2
1
2
0
0
0
2
1
1
0
1
0
1
1
1
2
1
2
1
1
0
1
0
1
1
1
2
0
1
1
1
0
2
0
1
0
0
0
2
0
0
1
2
0
0
1
0
0
0
0
0
0
0
2
0
0
1
1
3
2
1
1
0
4
0
0
0
0
0
0
1
2
1
0
0
3
0
2
0
0
3
0
0
1
1
0
0
0
1
0
0
2
0
1
0
0
0
0
0
1
0
1
2
0
2
0
0
2
1
0
1
1
0
0
0
0
1
1
0
2
1
0
0
2
0
1
0
0
0
2
1
0
1
0
1
1
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
1
2
2
2
2
0
0
3
0
1
2
1
1
2
0
0
2
1
3
0
4
0
0
0
1
0
2
0
1
1
0
2
0
0
0
1
0
0
2
2
0
2
2
0
1
0
1
0
1
0
0
0
2
1
1
0
2
0
1
0
0
1
1
0
1
1
0
0
1
0
1
0
1
0
0
1
0
0
3
0
1
0
1
0
1
1
0
0
0
0
1
0
0
1
0
0
2
4
1
1
3
2
2
1
1
1
1
1
0
0
1
2
0
2
1
1
1
1
0
0
0
2
0
0
0
1
2
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
2
2
0
1
0
3
0
1
1
1
0
1
1
1
0
0
2
2
1
0
1
1
0
0
2
0
0
0
2
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
1
0
0
2
3
0
0
0
0
0
1
2
0
0
0
1
1
0
0
0
1
2
0
0
0
0
1
2
0
0
3
2
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
2
3
2
1
1
1
0
1
0
0
1
0
2
0
1
2
0
0
1
0
2
0
0
0
1
1
0
1
2
0
0
2
1
0
8
2
1
0
0
1
0
2
1
1
0
2
0
1
2
1
2
1
1
0
0
1
1
0
1
2
0
3
0
0
0
1
0
0
1
0
0
0
2
0
2
0
1
1
2
1
1
0
2
0
1
0
1
0
3
1
0
0
2
1
2
0
0
0
0
0
1
0
0
0
2
0
1
2
0
2
2
2
1
0
0
0
0
2
0
1
0
0
0
0
0
0
2
1
0
0
2
2
0
0
0
2
1
1
0
2
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
1
0
1
0
1
0
3
1
0
0
0
0
0
2
2
0
0
2
1
0
3
0
1
1
0
0
0
1
0
0
2
0
1
1
1
2
0
1
0
0
1
2
3
0
1
2
0
0
0
1
3
1
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
2
0
0
0
1
1
2
4
0
0
0
0
0
0
2
0
0
0
1
0
2
2
4
0
1
0
2
1
0
2
0
0
0
2
1
2
1
2
0
0
1
1
0
0
0
1
0
1
0
1
1
0
0
0
1
0
1
2
0
0
0
0
2
2
0
1
1
0
0
1
0
2
0
0
0
1
0
0
2
0
0
0
0
2
0
1
1
2
0
0
1
0
1
0
1
0
0
2
2
2
2
2
0
0
0
0
1
0
1
0
0
0
3
0
2
0
0
1
1
2
0
1
0
2
2
0
1
1
0
0
0
2
2
0
0
2
0
2
0
0
1
0
0
1
0
0
1
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
1
0
0
1
2
2
0
0
0
0
0
2
0
0
2
1
0
0
1
0
0
2
0
2
0
2
2
0
0
1
0
0
0
1
0
1
1
0
1
1
0
1
2
1
0
0
0
0
0
1
1
1
0
1
0
2
1
0
2
5
0
0
0
2
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
1
0
0
0
1
1
0
1
1
1
0
0
0
0
0
0
2
1
2
0
1
0
0
0
0
2
0
2
0
2
0
0
0
2
1
0
0
3
0
0
2
2
0
0
0
0
0
1
2
0
0
0
1
0
0
2
0
0
1
0
1
0
3
1
0
2
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
2
1
1
0
0
1
2
1
0
1
0
0
2
0
0
0
1
1
1
1
1
0
0
1
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
1
0
1
0
0
1
0
0
2
0
2
0
0
1
2
0
1
1
0
0
1
0
2
0
2
1
2
1
0
0
1
1
0
0
1
0
0
1
2
0
1
2
2
1
0
1
0
2
0
1
0
0
2
1
0
0
1
0
1
1
0
0
0
0
2
2
0
0
1
1
1
0
3
1
2
1
1
2
0
0
0
0
0
0
2
0
4
1
1
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
2
1
0
0
0
1
1
3
2
2
0
0
1
0
0
1
0
0
2
0
0
0
2
1
0
1
3
0
0
2
2
2
1
0
2
2
0
1
0
0
0
0
0
0
0
1
0
0
1
2
2
0
1
2
0
2
2
0
1
2
0
1
1
3
0
1
3
1
0
1
1
1
2
2
0
2
1
0
0
0
0
1
1
0
1
0
0
0
2
0
1
0
0
2
0
0
2
4
2
0
0
0
0
2
0
1
2
1
0
0
0
0
1
1
2
0
0
2
4
1
0
0
0
2
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
1
1
1
1
0
0
0
0
2
1
0
1
0
0
1
0
0
1
2
2
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
1
2
0
0
1
2
0
2
0
2
0
0
1
0
0
0
1
0
0
0
0
0
1
2
0
0
0
1
3
0
2
0
2
2
1
0
1
1
0
0
2
0
2
0
0
1
2
0
2
1
1
0
0
0
0
0
2
0
0
2
2
3
3
1
0
0
1
1
0
0
0
0
1
0
1
0
1
0
1
1
0
0
2
0
2
0
1
0
0
0
0
0
0
2
2
1
1
1
2
1
1
1
0
2
0
2
0
0
0
1
0
2
2
2
0
0
0
2
0
0
0
1
2
0
0
1
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
2
2
0
0
0
1
0
0
0
2
0
1
1
0
0
0
0
2
1
0
1
1
0
0
0
2
1
0
1
0
1
1
0
3
0
0
2
1
0
0
1
1
0
0
1
0
1
2
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
1
0
1
0
0
1
1
2
0
0
0
0
0
0
2
0
1
0
1
0
0
0
1
1
0
9
0
0
0
2
0
1
0
0
0
1
0
0
0
0
2
1
1
0
0
1
0
1
0
0
2
0
0
0
2
0
0
2
1
0
0
1
0
0
3
1
2
0
0
0
0
0
2
1
0
0
0
0
2
1
1
0
1
0
0
1
0
0
0
0
0
2
0
2
0
1
1
2
1
0
3
2
0
1
2
2
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
2
1
2
1
1
2
2
0
2
0
0
1
0
2
0
0
2
1
0
0
0
0
0
0
2
0
1
1
1
0
2
0
1
0
1
0
1
1
1
3
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
1
1
2
0
1
0
0
5
3
0
0
0
2
0
1
0
2
0
1
2
0
0
0
2
0
0
1
1
1
0
1
0
0
0
0
1
0
0
0
1
1
0
1
2
1
1
1
2
1
2
1
2
0
1
2
1
2
0
2
2
0
0
2
0
0
2
0
0
0
0
0
0
1
1
2
1
0
1
0
0
2
2
0
1
0
2
0
1
0
0
0
0
1
0
2
0
0
1
1
1
0
0
2
3
0
0
0
0
0
1
1
1
0
0
0
0
1
0
2
1
2
1
1
0
0
2
0
2
0
1
0
0
0
1
0
3
0
0
0
0
1
0
0
1
2
0
3
1
0
3
2
0
0
1
1
1
1
0
0
1
1
0
0
0
2
0
0
0
1
0
1
0
2
2
0
1
0
0
2
3
1
2
1
0
1
0
0
0
1
0
0
1
2
0
0
1
0
1
1
0
2
1
4
0
0
0
2
2
1
1
1
1
1
2
2
1
1
1
0
1
0
4
0
0
1
2
1
2
3
0
0
2
1
3
0
0
2
2
1
1
0
0
0
2
0
2
0
0
1
0
2
2
1
0
0
1
1
0
2
0
1
0
0
0
0
0
0
2
1
1
0
1
1
0
0
0
5
2
0
0
2
0
0
0
2
0
0
1
0
3
0
0
2
0
0
2
2
2
0
0
0
0
2
0
2
1
0
0
1
2
2
1
0
0
2
4
0
0
0
0
2
0
2
1
0
0
0
0
1
0
0
0
0
1
2
2
0
1
0
2
0
0
0
1
0
0
2
0
0
0
1
2
2
0
0
0
0
0
0
0
0
2
1
1
1
1
3
1
0
0
3
0
0
1
0
0
0
1
0
1
0
1
3
2
0
2
2
1
1
1
0
1
1
1
0
0
2
0
0
0
0
1
1
0
0
0
1
0
2
3
0
1
2
0
0
0
1
1
0
0
2
0
0
0
1
0
2
1
0
1
1
0
2
0
0
0
1
0
2
0
0
0
2
0
0
0
1
0
2
1
0
0
1
1
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
3
0
0
1
0
0
1
0
0
1
2
0
1
1
0
1
1
2
0
0
0
4
0
2
0
0
2
0
0
1
1
0
2
0
1
1
0
1
0
2
0
0
2
0
1
0
2
0
0
1
0
0
0
0
1
1
1
0
0
0
0
1
1
1
1
0
1
1
0
0
1
1
0
0
2
2
0
0
0
1
0
2
0
0
2
0
1
0
1
2
0
0
0
0
1
0
4
0
0
0
1
0
2
0
0
0
1
0
2
1
2
0
0
0
1
0
2
2
1
0
0
2
0
2
0
1
1
2
0
0
0
0
0
0
0
2
1
1
1
2
2
2
1
1
0
1
2
1
2
0
2
0
0
0
0
1
2
0
0
2
0
1
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
2
2
0
2
0
0
0
1
0
1
0
0
1
2
1
1
1
3
1
0
1
0
0
2
0
0
1
2
1
2
0
0
0
0
1
2
0
0
0
1
2
0
1
0
0
1
1
0
2
0
1
0
0
0
0
0
0
0
2
0
2
2
0
1
0
0
0
0
1
1
3
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
1
1
1
1
0
0
1
0
0
0
1
2
1
0
2
0
1
0
1
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
3
2
1
2
0
1
0
0
0
0
2
1
2
2
0
1
0
0
4
0
1
1
0
1
0
0
0
0
1
2
0
1
3
0
0
1
0
0
2
0
0
2
1
0
0
2
0
2
0
0
0
1
0
0
0
0
1
1
2
1
0
1
1
1
1
0
2
0
1
0
1
0
0
2
0
1
0
0
1
1
0
2
1
0
1
0
0
0
0
0
0
2
1
0
2
2
0
2
2
3
0
2
1
3
1
1
0
1
0
0
1
0
0
0
0
1
0
0
1
1
0
2
2
1
1
0
0
1
0
0
0
2
0
0
2
0
2
1
0
1
0
1
0
0
0
0
0
0
2
0
1
1
0
0
0
2
2
0
0
0
1
1
1
0
0
2
0
0
0
0
0
0
0
0
1
2
2
1
0
1
1
2
2
3
1
0
2
2
0
2
1
0
1
0
0
0
0
0
2
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
1
2
0
3
1
2
2
2
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
1
2
2
0
0
0
0
0
2
0
2
2
0
0
0
0
1
1
2
0
0
0
1
0
0
1
1
0
0
1
1
1
0
1
2
1
0
2
2
1
0
1
1
0
1
0
1
2
2
0
1
0
2
0
1
0
0
1
0
4
0
1
1
0
0
3
0
1
1
8
2
0
1
0
1
2
0
0
2
1
2
5
0
1
1
0
0
0
1
0
3
0
2
0
0
3
1
0
2
1
0
1
1
0
0
1
0
0
0
0
0
3
0
1
1
0
1
3
1
0
1
2
0
1
0
0
0
1
0
2
0
0
0
0
1
0
1
0
0
0
2
0
1
0
2
0
10
0
3
2
0
1
1
0
1
2
1
0
0
2
0
2
0
1
2
2
1
2
0
0
0
2
0
2
2
1
0
2
2
0
2
0
0
1
0
3
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
2
1
2
0
1
1
0
1
0
0
0
1
0
0
1
0
0
2
2
0
1
1
0
1
1
0
2
0
1
1
1
2
0
1
0
0
0
0
3
2
2
0
0
1
2
0
1
0
2
0
1
0
0
2
1
1
0
1
1
0
3
2
0
0
2
2
0
0
0
1
0
0
1
0
0
2
1
0
2
0
0
0
2
1
0
1
0
0
2
0
0
0
1
0
0
0
1
0
1
2
1
0
1
1
0
2
2
1
0
2
0
0
0
0
0
0
2
2
0
1
0
0
0
2
2
1
0
2
2
0
1
0
1
0
0
1
0
1
1
0
2
0
0
1
2
0
1
3
1
0
1
2
0
0
3
0
1
0
0
0
0
2
1
2
0
1
0
0
0
0
0
1
1
2
0
0
2
0
1
0
0
0
2
0
2
0
1
0
1
0
1
2
2
0
0
0
0
0
0
0
1
3
1
0
0
2
1
0
1
1
1
0
0
0
0
0
2
0
2
0
0
0
1
0
2
2
2
0
2
0
0
1
2
0
2
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
1
1
1
0
1
0
0
1
0
1
0
0
2
0
2
1
0
2
0
1
0
0
0
0
0
1
0
2
0
2
1
0
1
0
0
0
0
0
0
1
2
0
0
0
1
2
0
2
2
1
2
0
0
0
1
0
0
1
0
2
0
2
2
0
4
0
2
1
0
0
0
0
0
0
0
1
3
2
1
0
2
0
3
0
2
1
0
2
1
2
1
1
0
0
0
0
1
1
1
0
0
2
2
0
0
0
1
1
1
0
0
1
2
0
1
2
3
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
1
2
1
2
0
0
3
0
1
2
0
1
2
0
0
0
1
0
1
0
0
0
4
1
0
0
2
1
1
0
2
0
2
0
0
1
0
2
0
1
1
2
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
1
0
1
0
2
0
0
0
1
0
0
0
0
0
1
1
0
0
1
1
1
0
2
0
0
0
2
0
1
2
0
2
0
1
0
0
0
0
2
0
3
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
2
1
2
0
0
0
1
0
1
2
1
2
0
2
1
1
0
0
2
0
2
0
0
0
1
2
2
0
1
2
1
2
1
3
2
1
0
0
0
1
1
3
1
3
2
0
2
0
0
0
2
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
2
2
2
1
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
1
0
2
0
1
1
0
0
0
0
0
0
0
1
2
2
1
2
0
1
0
0
0
1
0
0
0
2
1
2
2
0
1
1
1
2
0
0
0
0
0
2
0
0
0
0
0
1
1
0
1
0
0
2
0
0
0
0
2
2
0
0
1
1
1
1
1
3
0
1
0
0
0
2
0
1
1
0
0
2
2
1
0
0
2
2
0
2
0
0
2
0
0
0
0
2
0
0
1
1
2
0
2
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
1
2
2
0
0
0
0
2
2
0
0
0
2
1
1
0
2
0
0
2
2
0
0
0
3
1
1
0
0
0
0
0
1
0
2
1
0
0
1
0
2
2
2
1
1
1
1
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
2
2
1
0
2
0
2
0
1
1
0
0
1
1
0
2
0
2
0
2
0
0
1
2
1
0
2
3
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
1
2
0
0
0
0
0
0
1
0
1
0
0
1
2
0
1
1
0
2
3
1
1
0
2
0
0
0
2
0
0
2
1
1
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
1
0
0
2
2
2
1
0
0
1
1
0
0
2
1
0
1
0
0
1
0
0
0
1
1
0
0
2
0
1
0
2
0
0
1
1
1
1
3
0
0
3
0
0
0
0
1
2
0
1
0
1
1
0
0
1
2
2
0
2
1
3
0
0
0
1
1
2
0
1
0
0
0
1
3
1
2
2
0
4
0
1
0
2
0
0
1
1
2
1
0
0
0
2
1
1
0
1
2
1
2
2
0
2
3
1
0
2
0
2
0
2
0
0
2
0
0
0
2
2
0
1
1
1
0
0
0
2
0
1
0
1
0
1
0
0
0
2
0
1
2
1
0
0
1
1
0
0
0
1
2
2
0
1
1
0
0
0
1
0
0
0
1
2
0
0
0
2
0
1
1
0
1
2
0
1
0
0
2
0
1
2
1
1
0
1
0
0
0
1
2
1
0
1
1
0
1
0
2
0
0
1
1
0
0
0
2
0
2
0
0
0
0
2
1
2
1
0
1
0
2
0
0
3
0
2
0
0
0
0
2
2
0
0
0
2
0
0
1
0
2
0
1
1
0
1
1
0
2
1
0
2
0
0
2
2
1
0
0
0
1
1
2
0
0
2
0
2
2
0
1
0
0
3
0
0
0
0
0
0
1
0
1
1
0
0
3
0
0
0
2
1
0
1
0
0
0
1
1
1
0
0
2
0
2
2
0
2
2
1
0
2
0
1
1
0
0
2
0
2
1
0
1
2
2
0
0
0
0
2
1
1
1
0
1
1
0
1
2
1
0
2
0
1
1
1
0
0
0
1
1
0
0
1
0
0
1
0
1
0
0
2
0
0
0
1
0
0
0
2
0
1
1
0
1
2
5
0
2
0
3
1
2
2
0
1
0
1
0
2
1
1
0
0
0
0
0
1
0
0
0
1
1
1
0
0
2
2
0
2
0
0
1
0
0
0
1
0
0
0
2
1
1
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
1
1
0
0
3
0
2
2
1
2
0
1
0
0
0
0
0
2
1
0
0
0
0
2
1
1
1
0
0
2
1
2
0
0
0
1
0
0
2
0
2
0
0
2
2
0
0
0
0
0
2
0
0
0
0
1
0
0
2
2
0
0
1
0
0
2
0
0
1
1
1
0
0
0
0
1
0
2
0
1
0
0
2
0
1
0
0
1
0
2
0
3
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
1
2
0
1
2
0
0
0
2
0
0
2
1
2
1
4
2
0
1
0
0
1
0
2
3
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
1
1
0
1
6
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
1
0
2
1
3
2
1
0
2
2
2
3
2
2
0
1
1
2
0
0
0
0
0
2
0
2
0
0
1
2
1
1
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
4
0
0
0
1
0
1
0
1
0
0
2
0
0
0
0
0
1
0
0
0
2
1
1
1
0
0
1
0
1
2
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
2
0
1
1
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
2
2
0
0
1
1
0
4
2
0
0
0
0
0
1
0
0
0
0
0
2
1
1
0
0
0
0
1
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
3
0
0
0
0
1
0
1
0
0
0
0
2
2
1
2
1
0
0
1
0
0
0
3
0
1
0
1
0
0
1
0
3
1
1
0
0
1
0
0
6
0
0
0
0
0
0
0
0
0
0
4
0
2
2
0
0
2
0
0
1
1
0
0
0
2
1
0
2
0
1
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
3
1
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
1
0
1
0
1
1
0
3
0
0
0
0
2
1
2
0
0
0
0
1
0
0
0
0
4
0
0
1
0
0
0
1
0
2
0
0
2
0
0
0
1
0
1
1
2
0
1
0
2
1
2
0
1
0
0
0
0
2
1
1
0
0
0
1
1
1
0
1
0
1
0
1
1
0
0
0
0
0
0
0
1
0
2
0
2
2
1
0
1
2
1
2
0
0
0
0
0
2
1
1
2
0
1
0
1
0
2
3
0
0
0
1
1
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
1
1
0
2
1
0
0
0
1
2
0
1
0
0
0
0
1
2
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
2
0
1
0
2
1
1
0
2
0
0
2
0
1
1
2
2
2
0
2
0
2
6
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
2
3
4
1
0
0
0
0
0
0
0
0
2
2
0
0
1
1
0
2
0
2
0
3
0
1
0
0
2
1
0
1
1
2
0
1
1
2
0
17
0
1
0
1
1
0
0
1
0
1
2
1
1
1
0
0
0
1
0
0
2
0
1
2
0
0
2
0
0
1
0
2
0
1
0
0
1
1
2
2
2
0
0
1
1
0
0
0
1
0
0
0
0
2
1
1
1
2
0
2
0
0
0
0
0
1
0
0
0
0
1
2
1
0
1
0
1
0
0
2
0
2
1
0
2
0
1
0
0
1
1
0
1
0
0
0
2
2
0
1
1
0
2
1
0
0
0
0
2
0
0
2
2
1
2
0
0
0
2
1
1
2
2
1
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
1
2
3
0
1
1
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
1
0
1
1
0
2
0
1
1
0
0
1
1
0
2
0
0
0
1
3
0
2
0
2
3
0
1
1
2
0
0
1
0
2
0
2
2
0
1
0
0
2
1
0
1
0
1
1
0
0
1
0
0
1
1
1
2
3
0
0
0
0
2
2
0
2
0
1
2
0
0
1
1
0
0
0
2
1
1
0
2
1
1
0
0
0
0
1
2
0
0
1
0
0
0
1
0
1
0
0
2
0
0
1
0
0
0
2
0
1
0
0
0
2
0
0
0
2
0
2
1
0
1
0
0
1
1
0
0
0
1
0
3
1
1
2
2
0
3
1
0
0
0
3
1
2
0
1
0
0
0
1
1
2
1
0
0
0
1
2
2
0
2
1
0
0
2
1
2
0
1
1
2
2
0
1
2
1
2
1
0
0
0
2
1
1
0
0
0
1
1
0
0
0
1
1
0
0
2
0
0
0
1
0
2
1
1
1
2
0
2
0
0
2
0
0
0
0
2
0
2
1
0
2
0
1
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
2
2
1
0
0
0
1
1
2
0
2
1
0
1
0
2
0
1
2
2
0
1
0
0
0
1
0
0
1
0
2
0
0
0
1
0
0
2
0
1
0
0
2
0
1
0
0
0
0
0
0
0
2
0
1
0
1
0
1
1
0
1
1
0
0
0
0
1
0
0
0
2
0
0
0
0
1
1
1
0
0
0
1
0
0
1
2
0
0
1
1
0
0
1
0
0
1
2
0
0
0
3
2
2
1
0
1
1
1
0
0
0
0
1
1
2
2
1
1
2
1
0
0
1
0
0
1
1
1
0
0
1
0
2
0
2
1
1
1
0
0
1
3
1
1
2
0
0
2
0
1
1
1
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
2
2
1
2
0
0
0
0
0
1
1
0
2
1
2
0
1
0
1
0
0
1
2
0
0
1
2
0
1
0
1
3
1
0
0
0
0
2
0
1
1
0
0
2
2
0
1
1
0
0
2
0
0
3
0
2
0
1
1
0
0
1
0
0
1
2
3
0
2
2
1
0
1
0
2
0
0
0
0
1
1
1
0
0
0
0
1
1
0
0
2
0
1
1
3
0
0
0
2
0
0
1
0
0
0
0
1
2
0
0
2
1
0
0
1
0
2
1
0
0
1
1
0
1
0
2
2
3
0
1
0
1
0
1
0
0
0
3
0
1
1
0
0
1
2
0
0
1
2
2
0
3
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
1
1
1
0
0
0
0
0
2
0
1
0
0
0
0
2
2
0
0
1
0
0
1
3
0
2
0
0
2
0
1
1
0
2
1
0
0
0
2
0
0
0
1
1
0
1
0
1
1
1
0
0
1
0
1
1
1
1
0
0
0
0
0
0
1
0
2
1
0
2
0
0
0
1
0
1
1
0
0
0
2
0
0
0
0
2
1
0
0
0
0
2
2
3
0
0
0
0
0
3
2
2
0
1
0
0
1
1
0
2
0
1
0
0
0
0
1
2
0
2
0
1
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
2
1
1
1
0
2
0
2
0
0
2
0
1
0
2
0
2
2
2
0
1
2
0
2
0
0
0
0
3
0
0
0
3
2
2
2
2
1
0
0
0
0
1
0
1
1
2
0
1
1
0
3
0
2
2
0
0
4
0
1
1
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
1
2
1
0
1
1
0
1
2
0
1
2
1
0
1
0
1
0
1
1
0
0
0
0
2
0
0
0
0
0
1
2
2
1
2
0
0
0
1
1
0
2
4
1
2
1
1
0
2
1
1
0
0
0
2
0
0
0
0
0
0
1
2
0
2
0
2
2
1
0
0
1
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
1
2
0
1
0
0
1
0
0
2
0
0
0
0
0
0
1
1
1
1
0
2
0
0
1
2
1
1
2
1
0
0
0
0
0
0
0
0
8
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
3
2
3
0
2
0
1
0
0
1
0
2
3
2
0
2
1
1
0
1
3
0
0
0
2
0
1
2
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
1
2
1
0
0
3
0
2
2
1
0
1
1
1
0
0
0
0
2
1
1
2
2
0
1
1
1
0
0
0
0
1
3
1
0
0
1
0
1
1
0
1
0
1
2
0
0
1
3
0
0
0
0
2
1
1
0
0
1
0
0
0
2
1
0
1
2
0
0
0
2
2
1
1
0
1
2
0
0
2
2
0
1
1
0
0
2
0
1
1
0
0
0
1
1
0
1
2
1
0
0
1
1
0
0
2
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
1
2
0
0
1
0
2
1
2
0
0
0
0
2
0
0
1
1
2
2
0
0
0
1
1
1
4
1
0
1
1
1
0
1
0
5
0
0
1
1
2
2
1
2
0
1
0
2
2
0
0
2
2
2
0
2
2
0
0
2
0
0
2
0
0
2
0
1
0
2
2
0
1
0
0
0
3
2
0
0
1
0
0
0
0
1
2
0
0
0
0
1
2
1
0
0
1
1
2
0
0
1
1
0
0
1
2
0
0
2
0
1
0
2
2
2
1
2
1
0
0
0
1
1
2
1
0
1
1
0
0
0
1
0
2
0
2
1
0
2
0
2
0
0
0
2
0
0
1
0
1
0
1
1
1
1
0
0
0
2
0
1
2
2
1
0
0
0
1
1
3
1
4
1
0
0
0
0
1
1
1
1
1
0
1
0
2
1
1
0
2
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
2
1
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
3
2
0
0
0
0
1
0
0
0
2
1
1
0
0
2
0
1
1
2
0
1
1
1
2
2
0
0
1
1
2
0
2
0
0
1
0
0
3
0
1
2
0
1
1
1
0
0
0
1
0
0
0
0
1
2
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
2
2
1
1
1
0
2
0
0
0
0
0
0
2
0
2
2
0
0
1
1
0
0
3
0
3
1
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
1
1
0
1
1
0
0
2
0
1
2
1
0
2
2
0
0
0
0
0
1
0
1
1
0
0
2
1
1
0
0
0
1
0
1
1
0
1
0
2
2
1
0
0
0
0
2
0
0
1
0
0
0
0
1
2
1
0
1
0
0
0
2
0
1
0
3
0
2
0
1
1
1
0
0
0
0
0
1
0
0
2
1
0
1
2
1
0
2
2
0
2
2
0
2
0
0
2
0
1
0
0
0
0
0
1
0
0
1
0
2
0
1
0
1
0
0
2
0
1
1
1
1
2
1
0
1
0
0
0
0
1
1
1
1
0
1
3
0
1
0
1
0
1
1
2
0
1
0
0
1
1
1
0
0
0
1
0
1
0
1
1
0
2
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
2
0
1
1
0
0
0
1
0
1
1
0
2
1
0
0
0
1
0
0
1
1
0
0
2
1
0
0
0
0
0
1
1
0
1
1
0
0
0
1
1
0
0
0
2
0
0
1
1
2
1
1
3
0
0
2
1
0
2
1
0
1
2
2
0
0
4
2
0
1
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
2
1
0
0
2
0
1
1
2
0
0
2
1
1
0
0
0
1
0
0
2
2
0
1
0
0
0
2
0
0
2
1
2
1
1
1
0
1
1
0
0
3
0
3
0
0
0
2
2
1
2
0
2
0
2
1
1
0
0
0
0
3
2
0
0
0
0
2
1
2
0
0
0
1
0
0
1
0
0
1
1
2
1
0
2
0
1
0
0
1
0
1
1
0
0
1
0
0
0
2
0
0
0
1
1
0
1
0
0
2
1
1
2
1
0
0
0
0
0
1
2
2
0
0
0
0
1
2
1
0
0
1
1
0
1
0
1
1
0
2
0
0
1
1
1
1
1
0
2
0
0
1
1
0
2
0
1
0
0
2
2
1
1
0
2
0
1
0
0
0
0
2
0
0
0
2
0
1
0
0
0
2
0
0
0
3
2
2
0
0
1
5
1
0
1
1
0
1
1
0
0
0
2
2
0
1
1
1
1
1
1
2
0
1
1
0
0
2
0
0
2
0
0
1
2
2
1
0
2
0
1
0
0
2
0
1
1
0
0
1
0
1
0
1
0
0
3
1
2
0
2
1
1
0
0
0
0
0
1
1
1
0
2
1
1
0
0
1
1
2
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
2
3
0
1
0
1
1
0
1
2
0
0
1
0
3
2
2
0
2
1
1
0
0
0
2
1
2
1
1
0
1
2
2
2
2
0
0
0
1
0
0
0
1
0
0
0
2
0
1
1
0
2
1
0
0
0
1
0
0
0
0
2
0
2
0
0
2
1
0
1
1
0
0
0
0
2
0
0
2
0
0
1
1
0
0
1
0
0
0
0
0
0
2
0
2
2
3
0
0
0
2
0
0
2
2
0
1
0
0
0
0
0
1
2
0
1
0
0
1
0
0
1
1
2
1
0
1
3
1
0
2
0
1
1
0
2
0
1
0
5
2
1
0
0
0
1
2
0
0
0
2
1
2
0
0
1
1
0
2
0
0
1
0
0
1
2
1
0
1
2
0
0
1
0
0
2
0
0
0
1
0
1
0
0
1
0
1
0
0
2
1
1
1
1
0
1
0
0
1
1
0
1
0
2
1
2
0
2
2
0
0
0
0
1
2
1
1
0
1
2
3
0
1
0
1
0
0
2
0
0
1
1
2
1
2
2
2
0
0
1
0
0
1
2
0
1
0
1
0
1
2
1
0
1
2
0
0
0
2
2
0
2
2
0
1
1
1
1
0
0
2
2
2
1
1
0
0
2
0
0
0
1
2
0
4
2
0
0
1
0
1
0
0
2
0
0
0
0
1
0
0
0
1
0
2
2
0
1
1
0
1
2
1
1
1
1
2
1
0
1
1
0
1
0
0
0
1
0
0
2
2
0
0
2
0
0
0
0
3
0
0
1
1
0
2
2
0
2
0
1
0
0
0
1
0
2
0
1
0
1
2
0
1
0
1
0
0
1
0
1
1
2
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
7
0
0
2
0
2
0
0
3
0
1
0
0
1
0
1
2
0
2
0
1
2
0
0
1
0
1
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
3
1
0
2
1
1
0
1
1
0
0
0
2
0
1
2
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
1
0
1
2
1
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
1
2
0
0
0
0
1
1
1
0
2
1
1
1
1
0
1
1
0
0
0
0
0
2
0
0
0
0
0
3
1
1
1
2
1
4
0
1
2
0
2
0
0
0
0
0
0
1
1
2
0
0
0
1
1
2
0
0
0
0
2
0
0
1
0
1
1
0
1
0
1
0
0
2
0
1
0
0
2
1
1
0
2
1
0
1
0
0
0
1
0
0
1
1
0
0
0
1
0
1
0
0
0
1
0
2
0
0
0
3
0
0
2
1
2
0
1
0
1
0
0
0
1
0
0
2
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
2
0
0
0
2
0
0
0
1
0
0
1
1
0
0
0
0
2
1
1
0
0
0
2
1
1
0
0
2
2
0
0
0
2
0
0
3
2
0
2
0
2
2
1
1
0
0
2
1
1
0
1
0
1
0
1
0
1
0
3
0
1
2
0
0
0
0
0
2
0
2
0
2
0
2
0
0
0
0
0
0
0
1
2
0
2
1
2
0
0
1
0
0
0
2
2
1
0
2
0
1
0
0
1
0
2
0
1
2
0
1
0
0
0
2
0
0
1
3
0
0
2
0
2
1
2
1
2
0
1
0
3
0
2
1
2
1
3
0
0
2
0
2
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
2
0
0
0
0
2
0
0
1
1
1
0
0
0
2
1
0
0
0
0
1
1
0
0
0
2
2
0
2
1
0
1
1
1
1
0
0
0
0
1
0
0
0
0
2
0
0
0
1
1
0
1
0
0
3
0
1
0
0
0
0
0
0
0
2
0
2
2
2
0
1
0
1
0
1
0
1
1
0
0
1
2
2
3
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
3
0
1
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
2
3
2
2
0
1
1
0
1
2
1
0
0
0
2
1
1
2
1
0
0
1
0
0
2
0
0
2
0
4
1
0
0
1
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
3
3
0
0
1
1
1
0
1
1
0
0
0
0
2
2
0
0
0
2
1
1
2
2
2
1
0
1
0
1
0
0
0
0
1
1
0
0
2
0
0
0
2
1
0
1
0
0
0
2
0
0
1
1
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
2
2
1
2
1
1
1
0
1
2
2
0
1
0
2
1
0
0
0
4
1
0
0
0
2
0
1
2
0
0
0
0
1
0
0
0
1
0
1
0
0
0
2
0
2
1
1
1
0
2
1
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
2
0
2
2
1
0
0
2
1
1
0
1
0
2
2
1
0
1
3
1
2
2
1
2
1
0
1
0
1
0
0
0
1
0
1
0
0
2
0
0
0
0
3
1
0
0
0
0
0
0
0
2
0
1
2
0
1
1
0
1
1
0
0
0
1
0
0
0
0
0
2
0
1
2
0
0
0
0
0
1
0
2
0
1
0
0
7
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
1
1
0
2
0
1
2
2
1
0
2
0
2
0
1
1
2
2
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
1
1
0
0
0
1
1
0
0
2
2
0
0
2
0
2
2
0
1
0
2
0
0
0
0
0
0
0
0
0
2
3
2
0
0
3
0
0
0
0
1
0
1
0
2
0
0
6
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
1
2
1
0
0
0
0
0
1
0
2
0
0
0
1
0
2
1
0
0
1
0
0
1
0
1
2
2
2
2
0
0
1
0
0
0
2
0
2
0
1
1
0
0
1
0
0
0
0
0
2
2
2
0
2
2
0
1
1
0
0
1
2
1
1
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
2
1
0
2
0
1
0
0
0
0
0
0
0
1
0
2
2
0
0
2
1
0
1
1
0
0
1
1
0
0
0
0
2
2
0
0
0
0
2
0
0
0
1
0
0
3
0
1
0
0
2
0
0
0
2
0
0
1
0
0
0
1
1
0
1
2
0
0
2
0
1
0
1
1
1
2
0
0
0
1
1
0
0
1
0
2
0
0
1
0
1
0
0
2
0
0
0
0
0
0
1
2
0
0
0
1
0
2
1
1
0
1
1
0
0
2
0
0
0
1
2
0
2
0
0
2
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
1
1
0
0
0
1
1
2
0
1
0
1
0
1
1
2
0
1
0
0
2
1
0
0
2
1
0
2
0
2
0
0
0
0
0
0
2
2
2
0
0
1
0
2
1
0
2
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
2
0
0
1
0
1
0
2
1
0
0
0
3
0
2
0
0
1
1
0
0
0
0
0
2
1
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
1
2
1
0
2
1
0
0
0
1
0
1
1
0
0
2
2
0
0
0
1
2
1
0
2
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
1
0
0
0
1
0
1
1
1
0
1
0
0
0
0
2
0
2
1
0
0
2
1
0
0
0
0
0
0
0
1
2
0
0
1
0
1
0
2
0
1
2
1
2
0
1
1
0
0
0
0
1
3
0
0
2
0
0
1
0
2
1
1
1
0
0
0
2
2
2
1
0
0
0
2
0
0
1
1
0
0
2
0
0
0
0
2
0
1
1
1
0
1
0
1
0
0
0
2
3
1
0
0
0
1
4
0
1
2
3
0
1
0
2
0
0
0
0
1
2
2
0
1
2
0
1
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
2
0
0
2
1
0
1
1
0
0
0
1
0
0
1
1
0
0
2
1
0
0
0
0
0
0
1
0
2
0
0
1
1
2
0
2
0
1
1
1
0
1
0
0
0
0
1
0
0
2
0
2
2
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
4
1
0
0
0
0
1
0
1
0
0
1
1
0
0
2
1
2
1
0
0
0
2
1
2
0
2
1
1
1
1
0
0
2
0
0
0
0
0
0
1
3
2
1
0
0
0
0
1
1
0
0
0
0
0
1
1
0
1
1
1
0
1
2
1
1
0
2
0
0
1
0
2
1
0
1
0
0
2
0
0
1
1
1
2
0
1
0
2
0
1
0
3
2
1
0
0
2
0
0
0
2
0
0
2
2
1
0
1
0
0
0
0
0
0
2
2
0
1
0
0
0
2
0
3
1
2
0
0
0
0
0
0
1
1
1
2
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
1
2
0
0
2
0
3
0
0
0
0
0
0
1
2
0
0
1
0
2
0
0
0
0
1
1
0
0
0
0
0
0
1
2
0
2
1
1
0
1
0
0
0
1
0
2
0
2
0
0
0
2
0
1
2
0
2
1
1
1
0
0
1
0
1
1
0
2
0
0
0
2
2
1
0
0
0
0
1
0
0
0
2
3
1
0
0
0
0
0
2
1
0
1
1
0
1
0
1
0
0
0
0
4
0
1
1
1
1
1
0
0
1
2
0
1
0
0
1
1
0
1
0
2
0
1
2
1
0
2
0
2
0
1
0
0
0
0
0
0
2
0
3
1
0
0
0
0
0
2
2
1
0
1
0
0
2
0
0
0
0
2
1
0
1
1
0
0
0
0
1
0
0
0
0
0
3
2
2
0
2
0
2
0
2
0
0
2
1
1
2
1
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
1
0
0
2
0
0
1
0
0
2
0
1
0
1
0
2
0
0
0
0
2
1
0
0
2
0
0
0
0
0
2
0
3
1
0
0
0
1
1
0
0
0
1
1
1
1
2
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
1
0
1
0
0
0
1
2
0
2
0
1
1
0
0
3
1
0
2
2
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
1
0
2
0
0
1
0
0
2
1
2
0
0
0
1
0
0
1
2
0
1
0
0
0
0
0
0
2
0
1
1
0
0
2
2
2
0
0
0
2
0
0
0
1
1
2
1
1
1
0
0
0
1
0
1
1
0
3
1
1
0
0
3
1
3
0
1
1
0
2
1
0
0
0
0
1
0
2
1
0
0
0
2
2
0
2
0
0
1
0
1
1
2
0
2
1
0
2
0
0
0
0
0
0
0
0
0
1
1
0
2
1
1
1
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
2
1
0
3
1
0
1
0
0
1
1
1
1
1
2
0
0
2
0
0
0
4
1
0
2
2
0
0
0
1
0
0
0
2
0
0
0
0
1
0
1
0
0
0
2
0
0
1
0
0
0
2
1
1
1
0
0
0
2
2
2
2
2
0
1
0
2
0
2
1
0
0
0
0
0
0
0
0
2
0
2
0
1
2
0
0
0
0
2
1
0
1
1
0
1
0
2
0
0
0
0
2
0
0
0
0
0
2
2
1
0
1
0
0
0
1
1
1
0
1
0
1
0
1
0
0
0
0
2
0
0
0
1
0
0
3
0
0
0
1
0
1
1
0
2
1
2
1
2
0
0
0
1
0
0
0
0
0
0
0
1
0
2
2
0
0
1
2
1
1
0
0
0
0
0
0
0
0
1
3
1
0
0
0
2
2
0
0
0
0
2
0
2
2
0
0
0
0
2
2
2
0
0
0
4
0
0
0
0
0
1
0
1
2
0
0
1
1
1
0
0
2
0
0
0
2
0
1
0
1
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
2
1
0
2
0
2
0
1
1
0
0
0
2
1
0
0
0
0
0
3
1
0
1
2
2
0
0
3
0
1
1
1
0
0
0
3
1
0
0
1
2
0
0
1
0
0
0
1
2
1
2
1
1
0
0
0
1
1
0
0
0
2
1
1
0
1
2
1
1
0
2
2
0
0
2
0
1
0
0
2
1
0
1
1
0
1
0
0
2
1
0
1
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
2
1
0
0
1
0
1
0
1
0
2
1
0
0
0
1
0
1
0
2
0
1
0
0
0
0
0
0
2
0
1
0
0
1
1
0
0
0
1
1
0
2
2
0
2
2
1
0
0
2
1
1
0
2
0
0
1
0
1
1
0
0
0
0
0
1
1
0
2
0
0
1
0
2
0
0
1
2
1
1
2
1
3
0
1
0
0
1
0
0
0
0
0
4
2
1
2
0
0
0
1
0
0
2
0
1
0
2
0
1
2
2
1
1
7
0
1
0
1
1
1
2
2
0
1
2
1
2
0
0
0
1
1
1
0
1
2
0
1
0
1
1
0
2
2
0
1
2
1
1
0
2
2
0
2
2
6
0
0
0
1
2
0
0
0
2
1
4
2
2
1
1
0
1
2
1
2
1
1
1
0
0
0
0
0
0
2
2
0
1
1
1
0
0
1
1
0
1
0
0
0
0
0
0
2
0
1
0
0
1
2
1
1
0
0
0
0
1
1
2
1
1
0
0
2
1
1
0
0
2
0
0
0
1
0
2
2
1
1
2
0
0
0
0
1
1
1
0
0
2
2
0
0
1
0
1
0
1
0
0
0
0
1
0
0
1
2
2
0
0
2
0
2
2
0
0
1
1
1
0
0
1
0
2
0
0
1
1
1
0
0
1
0
2
0
2
0
0
0
1
0
0
0
0
1
0
0
0
1
2
1
1
0
2
0
0
1
0
0
0
1
1
0
0
2
0
0
0
0
5
0
0
0
0
0
0
0
3
0
0
1
1
0
0
0
0
1
0
1
1
0
0
0
0
2
0
2
2
0
0
1
1
2
1
1
0
0
0
0
0
0
1
0
0
2
1
0
4
2
0
1
1
1
0
0
1
1
0
0
1
2
1
0
2
1
2
0
1
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
1
0
3
1
2
1
0
0
0
1
0
2
0
0
1
0
1
0
1
1
0
0
0
1
0
2
0
0
0
0
0
1
0
0
1
1
0
0
1
0
1
1
1
1
0
0
1
1
0
2
0
0
2
1
0
0
1
1
1
0
2
0
0
0
0
0
2
1
2
0
1
1
1
0
1
1
1
0
0
1
1
0
0
0
0
0
0
1
1
0
1
0
0
0
1
1
1
0
0
0
0
0
1
0
0
1
1
1
0
0
2
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
2
1
2
1
0
0
0
0
1
0
0
2
0
0
1
2
0
0
0
1
2
0
1
0
2
0
2
2
2
0
1
0
1
0
1
0
0
0
1
4
0
1
0
0
0
0
1
0
0
0
1
0
0
3
2
1
0
0
2
3
0
2
2
1
0
0
0
0
2
2
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
1
0
0
1
2
0
0
1
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
3
1
0
1
0
1
1
0
0
0
10
0
0
0
0
2
0
0
0
0
2
0
3
0
1
0
0
0
0
1
0
0
0
1
1
0
1
0
2
0
1
2
1
2
0
3
0
1
1
2
1
1
1
0
2
1
2
2
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
3
2
0
0
0
1
0
0
1
2
1
2
0
0
2
1
0
0
0
1
1
1
0
2
3
0
1
0
0
3
1
0
0
2
2
1
0
3
0
0
0
1
1
1
2
0
1
2
1
0
2
2
1
1
1
0
0
1
1
0
0
0
1
1
3
1
0
2
0
0
2
0
0
0
2
0
0
1
2
0
0
0
0
2
2
2
2
2
0
0
1
2
0
0
1
1
0
2
1
0
1
1
0
1
0
0
0
2
1
1
2
0
0
0
1
0
1
1
0
2
2
0
0
0
1
1
0
0
0
1
0
1
0
1
1
0
0
1
0
2
0
1
0
2
2
2
0
1
0
0
1
0
0
0
1
0
0
1
6
0
2
0
2
0
1
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
1
0
1
0
2
1
2
0
0
1
0
1
1
0
2
0
0
0
1
0
2
0
1
2
0
1
1
0
2
1
2
2
1
0
0
0
2
2
2
0
2
2
1
0
0
2
1
2
2
0
0
0
1
0
0
2
0
1
1
1
2
1
0
2
0
1
0
0
0
0
2
0
1
0
1
1
1
1
0
2
3
1
2
1
0
0
1
0
0
1
2
0
0
0
0
2
2
1
0
0
1
1
0
0
2
0
0
0
2
1
2
2
2
0
0
1
0
1
0
2
1
0
1
1
0
1
1
2
5
0
0
1
0
0
0
0
2
0
0
0
1
1
0
1
1
1
0
1
0
2
2
0
0
1
0
1
0
0
0
2
2
2
2
0
0
0
1
0
0
2
1
0
0
0
0
0
0
1
0
2
0
0
1
1
0
0
0
0
1
0
1
0
0
0
1
0
2
0
0
0
1
0
2
0
0
1
1
2
2
2
0
2
2
2
0
2
0
1
1
0
1
0
2
0
5
0
1
0
1
3
0
2
0
1
0
0
3
2
0
2
1
0
1
1
2
2
2
1
0
0
0
1
1
0
0
0
2
0
0
1
2
0
0
0
0
0
2
0
0
3
1
0
1
0
0
0
0
0
1
0
2
3
0
2
2
0
0
2
0
0
0
0
2
0
0
1
0
0
2
1
0
2
0
4
0
2
1
2
1
2
0
1
2
0
2
0
0
0
1
1
3
0
0
1
1
1
1
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
2
1
1
1
0
3
1
0
2
2
0
0
0
0
0
0
0
1
3
1
0
0
1
1
1
0
0
1
0
1
0
0
1
0
0
2
1
0
0
0
1
0
0
1
0
0
2
0
0
0
0
2
0
1
0
0
0
1
0
0
1
0
0
2
1
1
2
0
0
0
3
0
0
1
0
1
1
0
0
0
0
1
2
2
1
1
1
0
0
0
0
2
0
1
1
0
0
0
0
0
1
0
6
0
1
1
2
1
2
0
4
0
0
1
1
1
2
1
0
1
0
2
0
1
1
0
1
1
0
2
1
2
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
2
1
1
0
3
5
0
0
0
0
0
2
2
0
1
0
2
0
0
1
0
0
1
2
1
0
2
0
0
0
0
0
0
2
0
2
0
1
1
0
0
1
0
0
1
2
0
1
0
0
0
0
0
1
1
1
0
2
1
0
1
1
0
0
2
0
1
0
2
0
1
0
0
0
0
2
2
0
1
1
1
0
2
1
0
0
0
2
2
0
0
0
1
0
0
1
0
0
1
1
1
1
0
0
0
1
1
2
1
0
0
0
0
0
2
0
0
1
1
1
2
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
2
0
0
1
0
0
0
1
0
1
0
0
0
2
1
0
1
1
0
0
3
0
2
1
2
0
0
0
0
0
0
0
0
0
2
2
2
0
1
1
0
0
0
0
1
0
2
0
0
2
1
2
0
1
0
0
0
1
1
0
0
0
2
2
0
0
1
1
1
0
2
2
1
0
1
2
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
2
0
1
0
2
0
0
0
0
0
0
1
0
7
2
0
2
2
1
0
0
0
1
1
2
0
1
1
0
0
2
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
1
2
2
2
2
0
0
0
1
2
0
2
0
0
0
1
0
2
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
3
1
0
0
1
0
0
1
2
2
0
0
2
0
1
1
1
1
1
2
1
0
0
0
0
1
1
2
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
1
2
0
2
0
2
0
0
1
0
0
2
1
0
0
1
1
0
0
2
0
0
1
0
0
0
1
1
1
1
1
0
2
0
2
1
0
2
0
0
2
0
1
2
1
0
0
1
1
1
1
1
0
0
1
1
0
0
1
0
0
2
0
0
1
0
1
1
2
0
0
1
0
2
1
0
0
0
1
0
0
1
0
0
2
1
1
1
0
2
1
0
0
1
0
0
1
2
2
1
2
0
2
0
1
1
3
2
1
3
1
0
1
0
1
1
1
0
0
1
0
2
2
1
0
2
0
1
0
0
0
7
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
4
0
0
2
0
2
1
0
0
1
0
0
0
2
0
0
2
0
0
2
0
0
0
0
2
2
0
1
3
2
4
2
0
0
2
0
2
0
1
0
1
2
0
1
2
2
1
0
0
3
1
1
0
0
0
1
0
4
0
0
2
0
1
0
0
2
1
0
1
2
1
0
2
0
0
0
0
1
0
2
0
1
0
1
0
1
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
2
1
0
0
1
1
0
2
0
2
0
2
0
0
1
1
0
1
0
1
0
1
2
0
0
0
0
1
0
0
0
2
0
1
0
3
0
0
0
0
0
1
2
1
0
2
1
0
0
1
1
0
2
0
0
2
3
1
1
0
1
1
1
1
2
2
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
3
0
0
1
0
0
1
1
9
1
0
0
2
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
4
2
1
1
0
1
0
2
2
1
0
0
2
2
0
0
0
1
0
2
0
2
0
1
0
1
2
0
1
1
0
2
2
0
2
0
3
0
0
2
0
1
0
2
0
0
0
1
1
1
0
1
1
0
0
0
0
0
1
2
1
0
2
1
0
1
0
0
1
1
0
0
0
2
0
0
0
2
2
2
0
1
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
2
0
1
0
2
0
2
2
1
4
0
1
0
0
0
0
0
1
2
0
0
2
0
0
0
0
1
0
2
1
0
1
0
2
0
1
0
1
1
0
0
0
1
0
4
1
1
0
1
1
0
1
1
2
0
0
1
1
0
0
1
1
1
1
0
0
0
1
2
0
1
0
1
1
1
0
1
1
0
0
0
2
0
0
2
1
0
0
0
1
0
0
0
0
4
0
0
1
0
0
0
0
1
0
1
0
0
1
0
2
3
0
1
1
2
2
0
1
0
2
1
0
0
1
1
0
2
1
0
2
1
0
0
2
0
0
2
0
2
2
1
0
0
0
1
0
2
0
0
0
0
0
2
1
0
1
0
0
0
0
1
0
1
1
0
0
0
0
2
2
2
0
0
1
0
2
0
0
2
0
1
2
0
0
1
0
1
1
2
0
0
0
0
0
0
0
0
1
0
1
2
1
1
1
0
0
2
0
0
0
0
0
0
2
0
0
0
1
2
1
0
0
1
2
1
1
0
0
0
0
0
2
0
0
1
1
3
0
0
0
0
1
0
2
2
2
0
1
2
0
0
0
0
0
0
1
0
0
0
2
0
2
0
2
0
2
0
0
0
1
16
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
2
1
0
0
0
2
0
0
3
1
0
2
0
0
1
0
2
0
0
1
1
0
0
1
0
2
1
0
2
0
0
1
2
2
0
2
1
0
1
1
0
2
0
0
0
1
2
0
2
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
2
1
0
1
0
0
0
0
1
1
1
0
0
1
0
1
0
1
1
0
1
1
0
2
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
2
2
1
1
0
1
2
0
0
2
1
2
0
0
0
0
0
1
1
0
0
1
1
1
0
0
0
0
2
0
0
0
1
0
0
0
0
2
1
0
0
0
0
1
0
1
0
0
0
0
2
0
0
1
1
1
2
1
1
1
0
0
0
2
2
1
0
0
0
1
0
0
0
1
0
1
0
0
0
2
0
1
1
0
0
0
0
4
1
0
0
1
2
0
2
2
0
1
1
2
0
0
0
2
0
1
0
0
0
1
1
1
2
0
0
2
0
0
3
0
2
0
0
0
1
1
0
2
0
2
2
2
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
1
0
2
0
2
0
2
0
0
1
2
0
0
1
0
1
0
0
0
2
1
1
0
1
0
0
0
4
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
1
2
1
2
1
1
1
2
2
1
1
1
1
2
0
2
1
2
0
0
0
0
0
0
0
0
2
0
0
1
9
3
2
0
2
0
0
1
1
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
1
1
0
0
0
1
2
0
1
1
0
1
2
2
1
0
3
1
0
0
0
1
2
0
4
2
0
0
0
2
2
0
0
0
0
2
0
0
1
0
0
2
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
2
2
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
1
0
0
0
2
0
0
1
1
0
0
0
1
0
0
1
2
0
1
1
1
1
0
1
1
0
0
1
1
1
2
2
0
0
2
2
2
2
0
3
1
2
0
0
0
0
1
0
0
0
0
1
1
1
1
1
0
2
0
0
0
0
1
2
2
0
0
0
0
1
1
1
1
1
1
1
0
0
0
0
0
1
0
1
2
0
2
0
2
0
0
0
1
1
0
2
1
1
0
2
0
0
0
0
0
0
1
0
0
1
0
2
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
1
0
2
0
0
2
0
0
0
0
2
0
2
0
4
1
0
1
1
0
1
0
1
1
0
1
2
0
1
2
0
2
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
1
0
1
1
0
1
1
2
0
1
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
1
2
0
0
0
0
1
0
1
2
0
0
1
0
1
0
0
1
0
0
0
2
1
0
0
0
0
1
0
0
2
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
2
1
2
2
0
1
0
0
0
1
0
1
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
2
0
1
2
2
2
0
0
0
0
2
0
1
2
2
1
1
1
2
0
0
2
0
0
0
0
2
0
0
0
1
1
1
0
0
1
1
0
0
0
2
1
0
2
1
1
0
0
2
5
0
0
1
0
1
0
1
0
0
2
0
0
1
0
1
0
0
0
0
0
1
2
1
2
2
2
0
0
0
1
0
0
0
0
1
1
1
0
1
0
0
2
2
1
0
0
1
2
1
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
1
0
0
0
3
2
3
0
3
0
2
2
0
1
0
1
2
3
0
0
1
2
1
0
2
2
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
1
2
3
0
0
0
2
0
0
0
0
1
0
0
0
0
2
1
0
0
0
2
0
0
0
1
2
0
0
0
2
1
2
1
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
1
0
1
1
0
2
2
2
0
0
0
2
1
1
0
0
0
1
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
1
2
2
1
0
0
0
0
1
2
0
0
0
0
2
0
0
1
0
0
2
2
1
0
0
1
1
0
0
0
0
1
1
0
1
0
0
0
2
0
1
0
0
1
0
2
2
2
2
0
0
0
2
0
2
0
0
0
0
0
2
0
2
1
2
3
0
1
0
0
0
0
2
3
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
1
1
2
1
1
0
3
4
0
2
2
2
0
1
1
0
0
1
1
1
2
0
0
2
1
2
0
0
0
0
0
1
1
0
0
0
0
2
0
2
1
0
0
0
1
2
0
1
2
0
1
0
0
1
0
0
0
1
0
2
0
1
1
0
0
0
0
0
0
0
2
2
0
1
1
2
2
1
0
2
2
0
2
0
1
2
1
1
2
1
1
2
3
0
1
1
1
3
0
0
0
0
2
1
0
1
0
0
1
0
1
0
0
3
0
0
2
2
1
0
0
0
0
0
0
0
2
0
2
0
0
1
1
0
0
2
2
0
1
0
1
0
0
0
2
2
1
0
2
0
0
0
0
0
2
1
0
0
0
0
0
1
1
1
0
0
2
0
0
0
0
2
1
2
1
3
1
1
0
0
0
0
2
1
0
0
0
2
0
0
1
0
0
0
1
0
2
0
0
0
0
1
1
0
0
1
2
0
2
1
0
0
2
0
2
1
2
0
0
0
1
1
1
1
2
0
0
2
0
1
0
0
0
0
0
2
2
0
1
2
0
0
1
1
0
1
2
0
2
0
1
0
0
11
0
0
0
0
0
0
0
2
0
0
0
2
1
0
2
1
1
1
1
2
1
1
0
1
0
0
2
0
0
0
2
0
0
0
1
1
0
1
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
2
0
0
0
0
0
2
3
1
0
2
1
1
2
0
1
4
0
0
0
2
0
0
0
1
2
0
0
0
2
20
0
2
2
1
0
0
3
0
0
2
1
0
1
0
0
1
1
0
0
0
1
0
1
1
0
0
0
0
0
3
0
2
0
2
0
1
0
0
1
0
0
1
0
0
1
0
2
2
0
1
1
0
2
2
0
1
2
0
0
1
0
0
0
2
0
1
1
0
0
2
2
3
0
1
1
2
1
1
0
0
1
0
0
1
1
2
0
0
0
0
1
1
1
0
0
1
0
1
1
2
0
0
0
2
0
2
0
3
0
0
2
0
0
1
1
1
1
1
3
0
0
0
0
0
2
1
0
1
1
1
0
0
0
1
3
0
0
2
1
2
0
0
0
1
2
2
1
0
0
0
0
0
0
0
2
0
2
0
0
0
2
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
1
1
0
0
0
0
1
0
2
0
1
0
1
0
2
0
0
1
2
0
1
2
2
1
2
2
0
1
1
0
0
0
2
0
0
0
1
0
0
0
1
2
0
0
0
3
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
2
0
0
0
1
0
0
1
0
0
1
0
1
1
0
0
0
2
0
0
1
2
0
3
1
0
0
0
2
0
0
0
0
0
2
2
0
0
0
1
1
0
0
0
0
1
0
2
0
0
1
1
0
0
0
0
0
0
1
2
0
3
0
1
1
1
0
2
0
1
0
1
0
0
0
1
0
0
2
2
0
0
2
1
1
0
1
2
0
0
0
1
0
0
1
0
1
0
0
1
0
2
1
0
0
0
1
2
0
2
1
1
0
1
1
1
2
0
4
1
0
0
0
0
1
3
0
0
1
2
1
2
0
2
0
1
1
1
0
3
0
1
1
0
0
0
1
2
2
0
1
0
4
0
0
0
0
2
0
0
0
0
1
1
1
0
0
0
2
2
0
2
2
1
1
0
0
0
0
2
0
2
0
0
0
1
2
0
1
1
0
1
0
1
0
0
0
1
2
1
0
1
2
0
0
2
0
0
1
2
2
1
1
0
1
0
1
1
0
0
2
1
0
1
2
0
0
1
1
0
1
1
0
0
0
1
0
1
0
0
1
0
0
2
2
2
3
0
0
1
2
0
1
2
1
1
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
2
1
0
0
2
1
1
0
1
0
0
0
0
0
2
0
1
1
0
1
1
0
0
1
0
2
0
0
1
2
0
0
0
0
0
0
0
2
1
0
1
2
1
0
1
0
0
2
1
0
1
0
0
1
2
0
2
2
2
5
1
1
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
1
2
1
1
0
0
1
2
0
0
0
0
0
2
0
1
2
0
1
0
0
0
1
1
2
2
1
0
1
1
1
0
0
0
0
0
1
1
0
0
0
0
1
2
2
0
0
0
1
0
2
0
0
0
1
2
0
1
2
1
0
3
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
2
1
0
1
0
0
0
1
0
1
2
0
1
0
1
1
1
1
1
2
1
0
1
0
0
0
0
0
0
2
0
1
1
2
2
1
0
0
0
0
0
0
0
2
0
1
1
0
1
0
2
0
2
2
0
2
1
0
0
1
1
0
2
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
2
3
2
0
2
1
1
1
0
1
4
0
3
0
0
1
0
1
0
0
0
3
2
2
0
1
0
0
0
2
2
0
0
0
1
0
2
0
2
3
0
2
0
1
1
0
0
2
3
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
1
0
0
1
0
0
0
0
0
0
1
1
1
0
2
0
1
0
2
1
0
2
1
1
0
1
3
1
0
2
1
0
0
2
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
2
0
1
1
0
4
0
0
1
1
1
2
0
0
0
0
2
0
2
1
0
1
1
0
2
0
0
0
0
2
1
0
1
0
1
1
0
0
1
2
0
6
0
1
0
2
2
0
1
0
3
0
2
1
2
2
1
0
0
0
2
0
0
0
0
1
1
1
0
0
0
0
1
0
1
0
1
0
2
0
2
0
1
1
2
1
0
0
2
0
1
0
0
1
0
0
1
1
0
2
1
0
0
0
2
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
1
2
2
3
0
2
0
2
2
1
0
2
2
0
1
0
0
0
0
0
0
2
0
0
3
0
0
2
0
0
0
2
1
2
2
0
2
0
2
1
0
0
0
0
1
1
2
1
0
1
0
0
0
1
1
1
0
0
0
2
0
2
0
0
0
0
2
1
0
0
0
0
1
0
1
0
3
0
0
0
0
0
0
0
1
1
2
0
0
0
1
0
1
2
0
0
0
1
0
3
0
2
3
1
1
0
0
0
0
0
2
0
2
0
4
0
0
0
1
2
0
0
2
0
1
0
1
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
2
2
2
0
0
1
1
0
1
2
0
0
1
0
2
2
0
0
2
0
1
1
1
0
0
1
0
0
0
2
0
1
1
1
0
1
0
1
2
1
0
0
0
0
2
2
0
1
0
1
0
1
0
2
0
1
0
1
0
0
0
2
0
1
2
0
2
0
0
1
0
0
2
1
0
1
2
0
2
1
0
2
1
0
0
0
2
1
0
0
1
2
0
2
0
2
2
0
0
2
2
1
1
2
0
1
2
0
2
0
0
1
1
0
0
2
0
3
1
2
2
0
0
0
0
0
0
0
0
3
0
0
1
1
0
1
2
1
1
2
0
1
2
0
0
0
2
0
1
1
0
1
0
1
0
0
1
3
0
2
0
1
0
3
0
0
0
2
2
2
0
1
0
0
0
0
2
0
0
2
2
1
1
1
1
0
0
2
0
0
2
1
0
0
1
0
0
0
2
2
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
1
0
1
1
0
1
2
0
1
1
0
1
0
0
2
0
2
1
0
1
2
2
2
1
2
0
4
0
0
2
1
2
2
0
0
0
0
0
2
0
5
2
1
0
1
0
0
1
2
3
2
0
0
2
2
2
1
2
1
1
0
2
0
1
0
0
0
1
0
1
1
2
0
0
2
2
0
1
0
0
0
0
1
2
2
2
1
0
2
0
1
0
1
0
0
2
0
0
1
0
1
2
0
3
1
1
2
0
0
1
1
0
0
0
0
0
0
2
0
1
1
0
2
2
0
1
0
0
2
1
1
1
0
0
1
0
0
0
0
1
1
1
2
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
1
1
0
1
2
1
1
1
0
0
2
2
0
1
0
2
2
1
0
2
1
2
0
0
0
1
2
2
4
0
0
2
2
0
2
2
1
1
1
2
0
0
1
1
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
1
2
1
1
0
4
1
0
0
1
1
2
0
0
2
1
0
0
0
1
0
0
2
0
1
3
0
0
0
2
0
2
0
3
1
3
0
2
4
2
0
0
1
0
1
0
0
1
0
1
1
2
0
1
1
3
0
1
0
1
0
0
1
0
2
0
3
0
1
0
0
2
2
0
1
0
2
0
0
2
0
1
4
0
2
0
0
2
2
1
1
0
0
2
0
3
1
2
2
2
0
1
0
1
1
1
0
1
1
0
0
0
1
0
2
1
0
1
2
0
1
1
0
2
2
2
2
1
0
0
2
1
0
0
0
0
0
0
0
0
1
2
0
1
2
0
0
1
1
0
0
2
0
0
1
1
0
2
0
0
2
0
0
0
0
2
2
0
1
0
1
2
2
0
1
0
1
0
0
0
2
1
2
1
0
2
0
0
0
1
4
0
1
1
0
0
1
1
0
0
0
1
0
1
0
1
0
1
1
2
1
1
0
2
0
0
0
0
1
2
3
2
0
0
0
0
0
2
2
0
1
1
1
0
2
0
1
0
2
0
2
0
2
2
1
0
2
0
1
0
0
2
1
2
1
2
0
2
2
0
0
0
2
2
2
2
2
0
1
4
2
1
0
0
0
0
2
2
0
0
0
0
0
2
0
0
1
0
0
0
1
2
0
0
1
2
0
0
0
1
0
2
0
1
0
0
0
0
2
2
5
2
0
2
0
0
0
1
0
0
2
1
0
0
1
0
0
2
2
0
2
0
2
0
0
2
2
0
0
2
0
1
2
1
1
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
5
0
1
0
0
0
0
2
0
0
0
0
1
0
1
1
2
0
1
1
2
0
1
0
0
2
0
0
0
0
0
0
0
0
3
0
2
2
3
0
0
1
2
2
0
0
1
3
2
1
0
2
0
0
0
0
0
1
1
1
1
2
0
1
2
2
0
0
2
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
2
1
2
2
1
0
0
1
1
1
2
0
2
2
0
0
0
0
0
4
0
2
1
1
0
1
0
0
0
1
0
1
1
2
0
1
1
2
0
1
0
1
0
2
1
2
0
0
1
1
3
1
0
1
0
2
2
1
0
0
0
0
0
0
2
0
1
0
1
1
0
0
1
2
4
2
0
0
1
1
1
0
0
0
1
1
2
0
0
1
2
0
2
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
1
0
1
1
2
0
0
0
2
2
0
2
1
1
1
1
0
1
0
0
0
0
2
0
0
2
0
0
0
2
0
1
0
0
0
1
0
1
0
2
2
3
0
2
1
1
2
2
2
2
0
1
1
0
2
0
2
0
0
2
1
0
0
0
0
1
0
1
0
0
0
0
1
2
2
0
1
1
0
0
2
0
0
2
0
0
0
2
0
0
1
2
0
0
0
2
1
0
0
0
0
1
0
4
0
2
1
1
0
0
3
1
2
2
1
1
0
0
1
0
0
0
0
2
0
1
1
0
1
1
0
2
2
5
1
2
1
0
0
4
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
1
1
1
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
2
2
2
0
0
1
1
0
2
1
1
0
1
0
0
0
1
0
0
2
2
1
0
1
2
1
0
0
0
0
0
0
0
1
0
0
3
1
1
0
0
2
2
0
0
0
0
0
1
0
2
1
2
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
1
1
0
0
0
0
2
0
0
1
0
1
1
0
1
0
1
0
0
1
0
0
1
1
1
1
2
0
0
1
0
0
1
1
2
3
0
0
2
0
0
2
1
0
1
1
0
0
0
0
0
2
0
0
0
1
1
0
3
0
1
2
0
2
0
1
2
0
0
2
1
0
0
0
1
0
0
2
0
1
1
0
1
2
0
1
2
0
2
2
2
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
2
0
0
0
2
0
0
0
1
0
0
1
0
0
1
4
0
0
2
0
0
0
0
1
1
0
0
1
1
1
0
1
0
0
2
1
1
0
0
2
0
0
1
2
0
2
0
2
2
0
1
0
0
0
0
0
1
0
2
1
0
4
0
1
0
0
0
1
2
2
0
0
0
1
0
1
0
2
0
2
0
0
0
0
2
0
0
0
0
2
3
1
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
1
1
2
2
1
0
1
2
0
0
0
2
2
0
1
0
0
1
0
0
1
1
2
2
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
2
0
0
0
3
1
1
0
0
1
1
0
0
0
2
0
1
1
1
0
1
1
0
2
0
0
1
1
0
1
0
2
3
1
0
1
0
0
1
0
0
3
1
0
2
0
1
2
0
1
1
2
0
2
0
0
2
0
0
0
0
1
0
0
0
0
1
1
2
0
2
0
1
2
0
2
1
0
2
3
0
0
0
0
1
0
0
1
1
0
2
1
2
2
2
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
1
0
1
2
0
0
0
2
1
3
2
0
0
0
1
0
0
1
0
2
1
1
1
0
0
0
0
0
0
1
2
1
0
0
1
0
0
2
2
0
0
0
0
2
0
0
1
1
0
2
0
1
0
1
0
0
1
2
0
1
2
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
2
0
1
0
0
1
0
0
2
0
0
0
0
3
2
1
1
0
0
0
2
0
1
0
2
1
0
1
1
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
1
0
0
2
1
0
1
2
1
0
0
1
0
2
1
0
1
0
2
2
0
0
0
0
2
1
1
1
0
0
0
2
0
1
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
2
0
0
2
1
0
0
2
0
0
2
1
0
1
5
0
0
1
1
1
2
1
0
0
1
1
2
0
0
0
2
2
1
0
0
1
0
1
1
1
0
0
1
0
1
0
1
0
1
1
2
0
0
1
0
2
1
0
2
0
0
0
1
0
1
0
2
0
0
0
1
3
1
0
0
0
0
0
0
1
2
2
0
0
1
0
0
0
0
1
0
0
2
0
0
2
2
1
2
2
0
0
0
0
0
0
2
1
2
0
1
0
1
5
1
0
0
1
0
0
0
0
0
2
1
0
2
0
2
0
1
0
0
2
0
0
0
3
0
0
0
0
0
0
2
0
2
2
0
5
0
0
2
2
1
2
2
1
2
0
0
2
0
0
0
1
1
2
1
0
0
1
3
0
0
0
1
3
1
2
0
0
0
1
0
0
0
0
2
0
0
0
1
0
1
0
1
1
2
1
0
0
0
1
0
0
1
0
1
0
1
0
1
2
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
1
0
0
1
2
1
1
0
0
1
0
2
0
0
1
0
0
0
0
0
0
2
1
0
0
1
1
2
1
1
0
0
2
0
1
1
4
0
1
0
0
1
1
2
0
0
0
0
1
0
0
2
1
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
2
2
1
0
1
1
1
2
2
2
1
1
0
1
2
0
0
0
0
1
0
0
1
0
1
0
0
0
2
0
0
0
1
2
1
2
0
2
3
0
1
1
0
1
0
1
1
0
0
1
1
2
0
2
2
0
0
0
2
0
1
0
0
0
0
0
1
1
1
0
1
1
1
1
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
1
1
2
0
2
0
0
0
0
1
0
1
1
2
0
0
1
0
2
0
1
0
1
0
1
0
0
0
2
2
0
2
0
0
0
0
2
0
1
1
1
0
5
0
0
0
0
1
0
0
0
2
2
1
0
1
2
0
1
0
2
1
1
0
2
0
0
1
0
1
0
0
1
1
0
1
1
0
0
2
0
1
2
1
2
2
1
1
1
0
0
1
1
0
0
0
1
3
2
0
1
1
2
2
2
0
1
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
1
2
0
0
2
2
1
2
2
0
2
1
1
0
0
2
0
0
1
0
0
0
0
0
2
0
1
0
3
0
0
2
0
1
0
1
2
0
0
1
0
0
0
1
2
0
2
2
0
0
1
2
0
1
1
3
0
1
2
2
0
2
0
0
0
1
0
0
1
2
1
0
1
0
1
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
1
1
1
0
1
0
0
0
0
1
1
1
1
2
0
0
4
0
1
2
1
1
2
1
0
0
0
0
2
0
1
1
0
1
1
0
0
2
0
1
1
0
1
0
0
1
1
1
0
0
2
1
2
0
1
2
2
0
0
1
1
1
2
0
0
1
0
0
2
1
0
1
0
0
1
0
0
2
1
1
0
1
0
2
2
1
1
1
1
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
1
1
1
0
0
2
1
0
1
0
2
0
0
0
1
2
0
1
0
0
0
3
0
1
0
0
2
2
1
0
2
1
1
0
0
2
0
0
0
4
2
1
0
1
0
0
1
0
0
2
2
2
0
2
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
1
1
0
1
2
1
1
1
0
0
0
1
0
1
0
0
1
1
0
0
2
0
0
0
2
0
0
2
0
2
0
0
2
3
0
0
0
2
1
3
0
0
1
0
2
0
0
0
0
0
1
2
2
0
0
1
0
0
0
2
0
0
2
2
0
0
1
0
2
0
1
1
1
0
1
2
1
0
0
1
1
0
1
2
0
1
0
0
3
1
0
1
1
0
0
1
0
0
1
2
0
2
0
1
0
0
0
3
0
0
0
0
0
0
2
0
1
0
0
0
1
2
0
0
1
0
1
0
0
1
1
1
1
0
0
1
2
2
0
0
0
1
1
0
0
0
0
1
0
1
0
2
0
0
2
0
1
1
1
1
4
1
2
0
0
1
0
0
2
1
2
0
0
0
0
1
0
1
2
0
0
1
2
1
0
1
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
2
2
0
0
1
0
1
0
1
0
0
1
1
1
0
2
0
2
1
0
1
1
2
0
1
0
2
1
1
1
0
0
0
1
1
1
1
2
0
2
0
2
0
0
0
0
0
1
1
1
0
1
0
0
0
1
1
1
2
0
1
1
2
3
1
1
1
0
1
2
1
0
1
2
1
0
0
0
1
1
4
0
0
1
3
0
0
0
2
0
1
2
0
0
0
0
0
0
2
1
1
9
2
0
0
1
0
0
2
0
0
2
0
2
0
0
0
0
1
2
0
2
0
1
2
2
1
1
2
0
1
0
1
0
0
0
1
1
0
2
2
2
0
0
0
0
2
0
0
1
0
0
0
2
1
0
1
0
0
2
0
0
2
1
1
2
2
0
2
1
0
0
1
0
1
1
1
2
0
0
0
0
0
0
0
2
2
0
0
0
2
0
1
1
0
0
2
1
2
2
0
1
0
2
0
3
0
1
0
1
1
2
0
0
1
0
0
0
0
2
0
1
5
2
0
2
0
2
2
2
0
0
0
2
0
2
0
1
0
0
0
0
1
2
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
2
1
0
0
2
0
0
0
1
2
0
1
0
0
1
0
2
0
0
2
1
0
0
1
0
2
0
0
2
2
2
0
0
0
2
1
0
1
0
0
1
0
1
1
2
1
1
2
1
1
2
0
0
2
0
0
0
0
0
0
1
0
0
0
1
2
2
1
0
1
0
1
1
0
6
1
1
0
1
0
0
3
1
0
2
1
0
1
1
0
0
0
0
0
0
2
3
9
0
0
2
0
0
0
0
2
0
0
0
0
0
1
1
0
1
0
0
1
2
0
0
1
0
1
0
2
2
0
1
0
1
1
1
0
0
0
2
1
0
0
2
0
0
0
0
1
0
0
1
2
0
0
1
0
0
0
0
0
0
1
2
0
1
0
2
0
0
0
0
0
1
1
1
1
0
0
1
0
2
0
1
1
0
3
1
1
2
0
0
2
0
1
2
2
0
0
0
2
0
2
0
1
0
1
0
2
0
0
0
2
0
2
0
0
0
2
0
1
2
0
1
0
0
0
0
1
3
0
0
0
0
1
0
2
1
2
0
0
0
0
0
1
0
2
0
1
0
0
0
0
1
2
1
1
0
0
0
0
1
0
0
1
0
1
0
0
2
0
1
2
0
0
0
1
2
0
2
1
2
1
1
0
0
1
1
2
1
0
2
0
2
1
1
0
0
0
1
0
0
3
0
0
0
2
0
2
0
1
0
0
0
2
2
0
0
2
0
0
0
0
1
0
0
2
1
0
2
0
0
0
0
0
0
1
1
1
1
1
0
0
1
1
1
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
1
0
2
2
1
1
0
1
0
2
1
1
0
0
2
0
0
1
0
0
0
1
0
2
2
2
0
0
1
0
0
1
2
0
0
1
1
0
1
0
0
1
1
2
2
0
0
0
0
0
2
0
0
0
1
1
0
2
1
1
0
0
0
1
2
1
2
1
0
0
0
0
2
2
0
1
2
0
0
0
2
0
1
0
1
0
0
2
2
2
0
2
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
2
0
0
1
0
0
0
2
0
0
1
1
2
0
1
2
2
0
2
0
2
2
1
1
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
1
0
2
0
0
2
2
0
4
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
1
2
1
0
2
1
2
0
0
1
0
1
1
0
1
0
0
1
2
2
0
0
1
0
0
1
0
0
3
2
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
2
0
2
0
1
0
0
1
1
0
0
1
2
2
1
2
2
0
0
1
1
0
0
1
1
1
1
1
2
1
0
0
0
2
2
0
2
1
0
2
2
0
2
0
0
0
1
4
0
2
2
0
1
0
0
2
1
1
0
2
0
0
0
2
0
1
0
0
2
2
0
0
0
1
0
1
0
2
0
0
0
2
2
2
1
0
2
0
0
1
0
1
0
0
1
0
0
1
3
0
3
3
1
0
1
2
2
0
1
2
1
1
0
1
0
0
0
0
0
4
0
0
0
1
1
1
0
0
2
1
1
0
1
2
0
0
0
2
1
0
0
1
0
2
1
0
2
0
0
0
2
2
0
1
1
0
2
0
1
2
0
2
0
0
0
0
3
0
0
2
0
0
2
0
2
0
0
0
0
1
0
1
1
0
0
1
0
0
0
2
0
2
0
2
1
0
0
2
1
0
0
1
0
0
0
1
1
0
0
2
0
2
0
0
0
0
0
1
1
0
0
2
1
2
0
2
2
1
2
0
2
1
0
1
2
0
0
2
0
0
1
1
0
0
0
1
0
1
3
0
2
1
1
1
1
0
0
0
1
1
1
0
1
0
2
1
1
2
1
0
1
0
0
0
1
0
0
1
2
1
2
2
0
1
0
0
1
0
0
0
0
0
1
2
0
0
1
0
2
0
0
1
3
1
0
0
3
0
0
2
0
2
0
0
0
2
2
0
2
1
1
0
2
1
0
0
0
1
0
2
1
2
3
2
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
2
1
2
2
0
0
2
4
1
1
2
2
2
0
0
2
0
1
0
0
0
0
0
1
2
0
1
0
0
0
2
0
2
0
0
0
0
0
1
2
1
0
2
0
0
1
1
2
2
1
0
0
2
0
2
2
1
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
4
0
1
0
1
2
2
0
1
0
1
2
1
0
0
2
2
2
0
0
0
2
2
0
0
2
0
2
2
2
0
0
0
1
0
0
2
3
2
0
1
2
0
1
2
0
2
0
1
1
0
2
0
2
1
0
0
0
2
0
0
1
0
0
1
0
0
0
1
1
2
0
0
0
0
0
2
1
1
0
0
2
0
2
0
0
6
0
2
2
1
0
2
2
1
1
0
2
0
0
0
1
2
0
0
0
0
4
2
0
0
1
0
0
0
0
2
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
1
1
1
0
2
1
2
1
0
1
2
0
0
0
0
2
1
0
0
1
1
0
0
1
1
0
2
2
0
0
0
0
1
0
0
0
2
2
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
1
0
2
0
0
2
1
0
0
0
0
0
1
1
0
1
2
0
2
1
0
0
0
0
2
1
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
1
1
0
2
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
2
1
2
1
0
0
2
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
3
0
0
1
2
1
2
1
1
1
1
1
0
0
0
2
1
2
0
0
0
0
0
0
1
2
1
1
1
0
1
1
1
0
0
1
0
0
1
0
0
1
0
0
1
0
0
2
0
1
1
2
0
1
2
1
2
0
1
0
1
2
0
0
1
1
1
0
1
1
1
0
0
0
0
1
0
1
2
1
2
1
2
0
1
1
0
1
0
0
0
1
0
2
2
0
1
0
1
0
1
0
1
0
0
0
0
2
1
0
0
2
0
2
0
0
2
0
1
0
0
0
1
0
0
0
1
0
1
0
0
1
0
2
2
1
0
0
2
2
1
0
2
0
0
2
0
0
1
0
1
1
2
2
1
1
2
0
1
0
2
0
2
2
1
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
1
2
0
0
0
0
0
1
2
0
3
5
0
0
0
0
0
1
0
0
0
2
1
1
1
2
2
1
1
1
2
1
1
0
0
0
0
0
0
0
0
1
4
0
0
1
2
1
0
2
0
8
1
0
2
2
4
0
0
2
2
2
2
1
1
1
0
0
0
1
0
1
0
1
1
2
1
1
1
0
2
1
1
2
2
0
0
1
0
2
1
1
0
1
0
0
2
0
0
0
1
0
2
0
0
2
2
0
1
2
0
1
0
0
1
2
0
0
1
2
0
0
0
1
2
0
1
0
0
1
1
0
0
0
0
0
1
1
1
0
0
2
0
2
1
0
2
0
2
0
2
0
1
2
0
1
1
1
0
0
1
2
2
0
0
0
0
1
1
1
0
0
1
0
1
0
2
2
0
3
0
1
0
0
0
2
0
1
0
0
0
1
3
0
0
1
0
1
0
0
1
0
0
1
0
0
2
1
0
2
1
0
0
1
1
2
0
1
0
0
1
0
0
3
1
0
0
0
0
0
0
1
0
2
1
0
1
0
0
1
0
1
0
0
0
1
0
1
0
4
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
2
0
0
0
2
0
0
0
1
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
1
3
0
0
2
0
0
1
0
0
2
0
2
2
2
0
1
2
0
0
1
0
0
2
2
2
0
0
1
1
1
0
1
0
0
0
2
0
0
0
1
0
1
0
0
1
0
0
0
1
0
1
2
0
1
1
0
0
0
1
0
0
0
2
0
0
1
2
0
1
0
0
0
0
2
0
1
1
1
1
0
1
0
1
2
1
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
1
1
1
2
0
0
2
0
0
0
0
1
2
1
1
1
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
1
1
1
2
0
1
1
0
2
1
1
0
1
1
2
1
1
0
1
1
3
1
2
0
0
0
2
0
0
1
0
0
1
0
0
2
0
0
1
0
2
0
0
1
1
1
1
0
0
0
2
0
0
1
0
2
1
1
2
1
0
0
1
2
0
0
2
0
0
0
0
1
0
1
2
2
0
0
0
0
0
1
2
1
0
1
1
0
0
0
1
1
0
0
0
2
1
2
1
0
0
0
0
0
0
0
2
0
0
1
1
2
2
0
0
3
0
0
0
2
2
0
0
2
1
1
1
0
0
1
2
2
0
1
1
2
1
0
0
0
0
2
0
0
2
0
0
0
2
1
0
1
0
2
1
2
2
2
2
0
2
1
0
0
0
0
0
0
5
2
0
1
0
2
0
2
0
1
2
2
0
2
1
0
1
0
2
0
1
1
0
0
1
1
2
0
7
0
1
0
0
0
1
2
2
0
0
2
0
0
0
1
0
0
1
1
1
1
0
1
2
0
2
0
0
0
1
2
1
1
2
1
1
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
1
1
1
0
0
0
1
0
2
0
1
0
0
2
0
2
2
0
0
0
0
0
1
1
1
1
0
0
0
2
1
0
0
1
0
1
0
1
2
1
2
0
0
0
1
0
1
0
2
0
0
0
0
0
1
2
0
1
0
0
2
0
0
1
0
0
2
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
1
2
1
1
2
1
0
0
0
0
1
2
0
2
2
0
2
0
0
1
0
3
2
2
0
2
2
2
0
2
2
2
2
0
1
1
0
0
1
0
0
2
0
0
1
1
2
0
0
2
0
0
0
0
4
1
0
2
1
0
2
0
1
0
0
0
1
0
0
2
0
1
1
0
0
0
1
0
1
0
1
0
0
2
0
0
0
0
0
2
2
3
2
0
0
0
0
0
1
2
1
1
1
1
0
2
0
0
1
0
0
1
0
1
2
0
0
1
2
1
0
0
0
1
0
1
2
2
0
0
0
0
0
2
1
0
2
2
1
2
0
0
1
1
0
1
0
1
0
0
2
2
0
0
0
0
1
0
0
0
1
0
1
0
0
2
1
1
1
0
0
0
0
1
0
0
0
1
0
1
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
1
0
0
2
0
1
1
2
0
1
2
0
0
0
0
1
0
1
1
0
0
0
2
1
0
0
0
0
1
0
1
1
1
1
0
0
0
0
0
0
2
0
2
1
1
0
2
0
0
0
0
2
0
0
0
0
2
0
1
1
1
0
0
2
1
1
0
2
2
0
1
0
2
1
0
0
2
2
0
0
0
1
0
2
0
0
3
0
1
2
2
0
2
0
0
2
0
0
0
1
2
0
2
0
0
0
0
0
0
1
2
0
0
1
0
2
0
2
0
1
0
4
1
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
1
0
2
0
0
0
2
0
0
3
1
0
0
0
2
3
0
0
0
2
1
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
1
0
0
1
0
1
1
0
2
1
0
0
2
1
0
0
2
1
1
2
0
1
0
0
1
0
1
0
0
4
0
1
0
0
0
0
0
1
1
0
2
2
0
2
1
0
0
0
0
1
0
1
1
1
0
1
0
1
0
1
2
2
0
1
1
0
0
2
1
0
0
0
1
0
1
1
0
0
2
2
2
2
0
0
0
1
0
1
0
0
1
0
2
0
0
0
1
2
0
0
1
2
0
0
1
0
1
0
2
0
0
0
3
3
1
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
2
1
2
0
1
0
1
1
0
1
1
0
1
0
2
0
2
0
0
2
0
0
1
0
0
1
0
0
0
0
1
2
0
1
2
2
0
1
2
1
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
1
0
0
2
1
1
0
1
1
0
0
0
0
0
2
0
0
2
2
0
1
0
0
0
2
1
2
0
2
1
2
1
1
0
1
0
0
2
0
0
2
0
1
1
0
0
0
2
0
2
0
2
1
0
0
0
1
0
1
2
0
2
0
0
0
1
0
0
0
1
0
3
0
2
2
0
3
1
1
0
2
0
0
0
0
1
1
1
2
0
0
0
1
0
1
2
0
2
1
1
2
1
2
0
3
0
0
0
2
1
0
0
0
1
2
0
0
1
0
0
0
0
1
0
1
1
0
1
2
0
0
0
0
0
1
0
0
2
0
1
2
0
0
0
0
0
0
0
3
0
0
1
0
1
2
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
1
2
1
1
0
0
0
2
1
1
0
3
0
1
0
1
1
2
0
0
0
1
0
2
1
0
2
2
2
0
0
0
2
1
0
1
2
0
2
1
2
0
0
0
0
0
0
1
0
0
1
2
2
0
1
0
2
1
0
0
0
1
0
1
2
0
2
0
2
1
1
2
0
2
0
2
0
0
0
0
0
1
2
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
1
1
1
0
2
0
2
3
1
2
1
1
0
2
1
1
0
1
1
2
0
0
0
0
0
1
0
0
2
0
0
1
4
0
1
2
0
0
2
0
1
3
1
0
0
0
2
1
0
0
1
0
0
0
1
0
0
0
0
1
2
1
0
0
0
0
1
0
0
0
2
1
0
0
1
1
2
1
1
1
0
2
1
0
3
1
0
0
1
2
0
0
0
2
0
2
2
0
1
0
0
0
2
2
0
0
0
2
1
0
0
1
0
1
2
0
0
0
0
1
1
0
0
1
0
1
0
0
1
0
1
2
2
2
0
1
1
0
0
0
0
1
0
2
1
0
0
0
1
2
2
0
1
0
1
1
0
0
2
1
0
1
0
0
1
0
2
0
0
1
0
0
1
0
0
1
2
2
0
0
2
2
1
2
2
0
0
2
0
1
2
0
0
0
0
1
0
2
1
1
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
1
2
2
2
1
0
1
0
2
0
4
2
1
1
0
2
2
2
2
0
2
1
1
1
0
0
2
0
2
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
3
0
1
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
3
1
0
0
0
0
0
2
1
0
0
0
0
0
2
2
0
0
2
0
1
1
0
0
0
0
1
2
2
1
2
0
1
0
0
0
0
1
2
1
1
0
1
0
0
1
2
1
1
1
0
0
0
0
2
0
2
1
1
1
2
0
1
0
1
1
1
2
0
0
1
1
1
2
0
0
2
0
0
1
0
1
0
1
0
0
0
2
0
0
0
0
0
1
1
2
0
1
1
0
1
0
1
0
1
0
0
2
0
2
1
1
0
2
1
1
0
0
2
1
1
2
0
1
2
0
1
0
1
0
1
1
0
0
0
0
1
0
2
0
10
0
0
0
0
2
1
2
0
1
1
2
1
0
1
2
2
1
2
0
1
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
1
0
0
0
0
0
1
1
2
0
1
2
2
0
2
0
2
0
0
1
1
0
1
0
0
2
2
2
2
1
0
1
0
1
0
1
0
2
0
1
0
0
0
1
0
0
2
0
0
1
2
1
0
0
2
0
1
2
2
1
0
0
2
0
1
1
1
0
3
0
0
0
0
2
0
0
2
0
0
1
0
3
2
0
0
2
1
0
0
1
0
0
1
0
0
0
1
2
0
2
0
2
0
0
1
2
0
0
0
0
0
1
1
0
0
3
0
0
0
0
1
1
2
1
2
2
1
0
0
0
2
0
0
1
0
0
0
1
0
3
0
1
1
2
1
0
0
1
0
1
2
0
2
1
1
1
1
0
1
0
0
1
0
2
2
0
0
1
2
0
0
2
0
1
0
1
0
2
2
0
0
2
0
3
2
1
0
0
2
0
0
0
1
2
0
0
0
0
0
0
1
2
2
1
4
0
1
0
1
0
0
1
0
0
0
1
1
2
2
0
0
1
1
0
2
4
1
0
2
2
0
1
0
1
0
0
0
1
0
0
1
2
0
0
0
0
1
0
2
0
0
1
0
0
0
1
2
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
1
2
1
1
1
1
0
0
0
0
1
2
2
0
0
0
0
0
0
1
1
0
0
1
2
0
2
1
0
1
1
0
0
0
0
1
0
0
2
1
0
2
0
1
0
2
1
1
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
2
1
0
0
1
1
0
0
1
0
0
1
0
2
1
1
0
1
1
1
3
0
0
3
0
0
2
1
2
0
0
1
1
1
0
1
1
1
1
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
1
1
2
2
2
0
0
2
0
0
0
0
0
2
0
0
1
0
2
0
2
1
2
1
0
1
0
1
0
0
1
3
0
0
1
0
0
1
1
2
1
0
0
1
0
0
0
5
0
0
2
0
2
0
2
0
0
1
0
0
1
0
2
0
0
1
0
0
0
0
0
0
1
2
1
1
0
2
1
0
0
0
0
1
0
0
1
1
0
2
1
1
1
0
0
1
2
2
0
1
1
0
1
1
0
0
0
0
1
0
1
0
0
1
1
0
0
2
0
0
0
0
1
1
0
0
0
1
1
1
1
3
0
0
0
2
0
0
0
2
0
2
1
0
1
1
2
0
0
0
0
2
0
2
0
0
1
1
1
0
0
0
2
2
2
0
0
0
2
0
7
0
0
1
1
1
2
0
0
2
1
1
0
1
2
0
2
1
0
0
1
0
0
0
1
0
0
0
2
2
1
0
0
1
0
1
2
0
3
2
0
1
0
3
2
1
1
1
1
2
0
0
2
0
1
2
1
2
1
0
0
0
1
0
1
0
2
1
0
0
1
1
0
0
1
3
0
0
1
2
2
1
0
1
0
0
4
2
2
0
0
0
2
0
0
0
1
2
1
0
1
1
0
2
1
0
2
1
2
0
1
1
1
2
2
0
1
2
2
1
1
0
0
0
1
0
1
0
0
0
1
2
0
2
0
1
1
0
1
0
0
2
0
1
2
0
2
1
0
1
0
0
2
1
0
0
0
0
1
1
2
0
0
1
1
2
0
0
0
0
0
1
0
3
1
0
0
2
0
0
0
0
0
1
0
2
0
2
1
0
0
0
2
0
1
2
1
0
0
0
1
0
0
1
0
2
0
1
1
1
0
2
1
1
1
0
0
0
0
1
1
2
1
0
0
2
2
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
2
0
1
2
0
2
2
0
2
0
0
2
0
0
0
0
0
1
2
0
0
1
1
1
2
2
0
0
0
3
1
1
2
0
2
1
0
0
2
0
0
0
1
0
0
2
1
0
0
1
0
0
1
1
2
1
0
1
2
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
2
0
0
0
1
1
1
2
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
1
0
3
0
2
2
0
0
0
0
1
0
0
1
0
0
0
0
2
2
2
0
2
1
0
2
0
0
0
1
0
0
2
0
0
0
0
2
1
0
1
1
0
2
0
0
5
0
1
0
0
1
1
0
0
2
1
1
0
0
2
0
0
1
2
0
0
2
2
0
1
2
2
2
0
2
0
1
0
0
0
4
2
0
2
0
2
1
2
2
1
1
3
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
2
1
0
1
1
0
0
0
2
0
0
0
0
0
1
1
0
0
2
1
0
2
0
0
0
1
0
1
0
1
1
3
1
0
0
1
1
0
0
0
1
0
0
1
1
0
0
1
0
0
2
0
0
1
2
0
0
0
2
2
1
0
1
2
3
0
0
2
1
0
0
0
2
1
0
0
1
0
0
0
1
0
3
1
1
1
1
0
2
1
0
0
1
1
0
0
0
2
0
1
2
1
1
0
2
2
0
0
0
2
2
1
0
0
0
0
0
1
1
0
0
0
0
2
0
3
2
1
3
3
0
2
0
1
1
2
0
0
0
1
1
1
2
1
1
0
0
0
0
0
0
2
1
0
1
0
0
0
2
1
0
0
0
0
1
1
0
0
1
0
0
0
2
0
2
0
0
3
1
0
2
2
0
2
1
2
0
0
0
2
3
0
0
0
0
0
2
1
2
0
0
1
2
0
0
3
0
1
0
0
0
2
0
0
1
0
0
1
2
1
0
0
0
0
1
1
0
0
0
0
2
0
2
3
0
2
2
1
2
2
0
2
2
0
1
2
1
0
2
0
1
2
0
0
0
0
1
0
0
1
0
0
1
0
0
2
1
0
3
0
1
0
0
0
0
1
0
1
2
0
2
0
2
0
0
0
0
1
0
0
1
0
0
0
0
2
1
0
2
0
3
1
0
0
0
1
0
2
1
0
2
1
0
1
1
0
0
0
2
0
2
2
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
2
1
2
1
0
0
0
0
2
0
1
1
0
1
1
0
0
0
0
1
0
1
0
2
0
0
0
0
0
1
0
0
2
0
0
1
1
1
2
0
1
2
0
0
0
1
0
1
1
0
2
2
1
1
0
1
1
0
1
1
0
1
1
0
0
1
0
1
0
1
0
0
1
0
1
0
0
3
1
0
1
0
1
2
0
2
2
1
0
1
0
1
0
0
0
1
2
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
2
0
1
2
0
0
1
2
0
0
0
1
0
0
0
1
1
0
0
0
2
2
2
2
2
0
0
1
0
1
0
0
0
0
0
2
1
2
0
0
0
1
2
2
0
1
2
0
0
1
2
1
0
0
1
1
0
0
2
0
1
1
2
0
0
2
0
1
0
0
0
2
0
0
2
1
2
0
1
1
0
1
1
0
2
0
1
1
2
0
0
0
0
0
0
2
2
0
1
1
2
0
1
0
2
1
0
2
0
1
2
0
0
0
0
1
1
0
0
2
0
0
1
2
1
1
1
1
0
1
0
0
2
0
1
0
2
2
0
1
1
1
1
0
1
0
0
1
0
2
2
1
1
0
0
2
0
0
1
0
0
1
2
0
2
0
1
1
2
0
1
2
0
0
2
0
0
0
0
0
2
0
0
0
0
1
2
0
2
0
1
2
1
0
2
0
0
0
0
0
1
2
0
0
2
1
1
2
1
0
0
0
2
0
0
0
1
1
1
0
0
1
0
0
2
0
0
1
0
0
2
0
1
1
1
2
2
1
0
1
0
2
0
0
0
0
1
1
0
0
1
1
0
0
0
0
2
2
0
1
0
2
2
1
0
0
2
2
2
0
1
0
0
0
0
2
1
0
2
0
2
0
1
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
1
0
2
1
0
2
0
0
2
0
1
1
1
0
1
2
0
0
0
2
2
1
0
2
3
1
0
0
2
1
0
1
2
2
0
0
1
0
1
1
2
0
1
2
0
0
0
0
0
0
2
0
1
0
0
0
2
1
2
0
0
3
0
1
0
0
0
2
0
0
0
1
2
2
0
1
0
2
2
0
1
0
2
0
1
1
0
1
2
0
0
0
1
0
0
2
2
0
0
0
0
0
1
2
0
2
0
0
0
0
0
2
0
0
1
0
0
0
2
0
2
0
0
2
0
1
0
1
0
1
0
0
2
1
0
1
1
0
1
3
2
0
1
1
0
2
2
1
0
0
0
0
1
2
1
0
0
2
0
1
0
0
1
1
2
1
1
1
0
0
3
0
0
2
0
3
0
2
0
0
1
0
0
1
0
0
3
1
2
0
0
1
1
0
0
0
0
0
0
2
0
0
1
0
1
1
0
1
0
1
0
1
1
0
0
1
2
2
1
2
3
0
1
0
1
0
0
0
1
1
0
0
1
0
1
2
0
0
0
1
1
1
1
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
1
1
1
0
1
2
0
1
0
1
0
2
1
1
1
0
0
0
2
0
0
2
0
0
1
0
1
0
0
2
0
0
0
0
1
0
0
1
2
2
0
1
0
0
0
2
1
0
0
1
0
2
0
0
1
0
0
0
1
1
0
0
2
0
1
1
0
2
0
0
2
0
0
1
0
0
2
0
0
0
1
0
1
0
2
0
1
0
1
0
0
0
1
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
1
0
2
0
0
2
0
1
0
1
2
1
0
2
0
0
0
0
1
2
0
0
2
0
2
1
1
0
2
0
0
1
0
0
0
0
0
2
0
0
1
2
0
0
0
1
0
0
1
2
0
0
0
0
1
1
2
1
0
1
0
1
1
2
2
0
0
0
2
1
0
1
0
0
0
1
0
0
1
1
1
0
0
0
0
1
1
0
2
2
1
0
2
0
2
2
1
0
0
2
2
0
0
0
2
1
2
2
0
1
0
0
0
2
1
2
0
0
1
1
0
1
0
0
1
1
0
1
1
2
0
0
1
0
0
0
0
0
0
1
2
0
2
2
0
0
1
0
0
2
0
2
2
0
0
2
0
2
0
0
0
0
1
1
1
0
0
1
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
2
0
0
0
2
0
2
0
1
0
1
0
0
0
2
0
0
2
0
0
0
1
1
0
1
0
0
0
1
0
1
1
0
0
1
0
1
2
0
0
0
0
0
0
0
1
1
0
0
2
0
3
0
0
1
1
1
0
2
0
2
0
0
1
0
0
0
2
0
2
0
0
1
1
0
0
1
2
2
0
0
0
1
2
0
0
1
2
2
0
0
1
0
2
0
0
0
0
0
2
2
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
1
0
2
0
0
2
0
0
0
0
1
1
0
0
0
1
0
1
1
2
5
0
1
0
1
0
0
0
2
0
0
0
2
2
0
0
0
0
1
0
0
6
0
3
2
1
0
0
0
3
2
0
0
1
0
0
0
0
2
2
1
0
1
2
0
0
0
1
0
0
2
1
2
2
2
1
0
0
0
0
0
2
1
2
0
1
1
1
1
0
2
2
2
0
0
0
1
0
0
2
2
1
0
1
2
0
0
2
0
2
0
1
2
1
0
1
1
1
0
0
0
1
2
2
1
0
2
0
0
0
1
0
2
2
1
0
0
1
0
0
0
0
1
1
2
0
2
1
0
1
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
2
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
1
1
2
0
0
1
0
0
0
0
0
0
1
0
1
1
2
0
3
0
0
2
0
0
2
0
0
0
1
1
0
2
1
2
0
0
0
2
0
0
3
2
4
0
0
1
2
0
2
0
2
0
2
0
0
1
0
0
0
0
2
1
2
1
0
3
0
1
1
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
2
0
1
0
0
0
1
1
0
2
0
2
0
2
1
0
2
0
0
0
1
1
0
3
0
2
0
0
1
0
1
0
2
0
2
0
1
0
0
1
0
0
2
0
1
2
1
1
1
1
1
0
0
0
1
0
1
0
1
0
0
2
8
0
0
0
0
1
0
6
0
1
0
3
0
0
1
2
0
2
0
0
1
0
2
0
0
0
1
0
2
0
0
0
0
0
2
1
1
1
2
0
0
0
1
2
0
1
1
0
2
1
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
1
0
0
1
0
0
2
2
2
2
1
0
0
0
1
0
0
2
1
0
1
0
0
0
1
1
0
1
0
0
0
0
1
1
2
3
0
1
0
0
2
1
0
4
2
0
2
2
2
3
2
2
1
2
1
1
1
0
0
0
2
0
0
1
2
2
1
1
2
1
1
0
0
0
0
0
0
0
1
0
0
1
1
1
2
0
2
0
2
2
1
1
1
0
2
2
2
0
0
0
1
0
0
0
2
1
0
0
0
2
0
0
0
2
1
2
0
0
0
0
0
1
0
2
1
1
1
0
0
1
0
1
0
1
0
0
0
1
2
0
0
0
0
1
0
0
0
0
2
1
2
0
0
0
1
1
0
0
0
2
0
0
1
0
2
1
2
0
0
1
1
1
1
3
0
0
0
1
0
0
0
2
0
3
0
2
0
1
2
1
2
1
1
0
1
2
2
3
1
0
2
1
0
2
2
2
1
0
1
2
0
0
0
1
2
0
0
1
0
0
1
0
2
1
3
0
0
1
0
0
1
1
0
0
2
0
0
1
0
0
0
1
1
1
0
0
0
0
2
0
0
1
0
0
0
1
1
0
1
1
0
0
2
0
0
1
0
0
0
1
2
0
0
0
0
2
0
1
1
0
0
0
0
0
2
3
0
0
0
0
0
14
2
0
0
0
1
0
1
0
2
6
0
0
0
2
0
0
1
1
0
1
0
0
1
0
0
0
0
1
0
1
0
1
2
1
1
1
1
1
1
0
0
0
2
0
1
2
0
1
1
1
2
2
0
1
0
1
0
0
0
0
0
2
0
1
1
1
0
0
1
1
0
2
0
0
0
0
1
1
0
0
1
0
1
0
0
1
0
2
1
0
2
0
2
1
3
1
1
1
0
1
0
1
0
0
0
0
0
2
3
0
0
4
0
0
0
1
4
2
0
0
0
1
0
2
0
0
1
0
1
1
0
0
0
3
0
0
1
0
0
0
0
2
0
0
0
1
0
1
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
2
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
2
0
2
0
2
1
2
0
1
0
0
0
0
1
1
0
0
0
1
2
0
0
2
0
2
2
1
0
3
1
0
0
2
1
0
0
2
1
1
0
0
2
1
2
1
1
2
0
0
0
1
1
1
1
1
0
2
1
2
1
0
0
2
0
2
0
0
1
1
0
1
0
0
1
0
4
0
0
0
2
0
1
0
0
2
2
0
1
0
1
0
2
0
1
2
1
1
0
1
2
0
2
0
1
0
2
0
0
5
0
0
1
0
1
0
1
2
0
0
0
1
0
2
0
0
2
0
0
1
1
2
0
2
1
2
1
0
0
0
0
0
0
0
0
0
1
2
1
0
1
0
1
0
0
0
2
0
3
0
0
1
0
1
1
1
1
1
2
1
2
0
1
0
3
2
1
0
2
1
0
1
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
2
0
0
2
2
4
4
2
1
2
1
1
1
1
0
0
0
1
2
3
0
0
5
2
1
2
0
1
0
0
0
1
0
1
1
0
0
1
1
1
0
0
0
2
0
1
1
0
2
2
1
1
0
0
1
1
0
0
2
2
0
1
0
0
1
0
0
0
1
1
0
2
0
1
0
2
1
0
0
1
0
1
2
1
0
0
0
0
0
0
1
0
0
3
0
0
1
0
0
2
1
1
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
1
1
1
1
1
0
0
2
2
0
0
1
2
0
0
2
2
1
0
0
1
2
0
1
0
1
0
1
2
0
1
2
1
0
0
1
2
0
0
1
0
0
0
1
1
1
2
0
2
1
1
0
0
0
0
0
0
1
2
0
1
0
0
0
5
0
0
0
0
2
1
2
0
0
0
2
0
1
0
0
1
1
0
2
0
0
0
2
1
1
0
0
0
1
0
0
1
1
0
1
0
0
2
2
0
2
1
0
0
2
0
2
0
1
2
0
0
1
0
0
1
2
1
0
0
0
1
0
2
0
0
0
0
1
3
0
0
0
1
2
0
1
0
0
0
0
3
0
2
0
0
0
2
0
1
2
0
2
0
2
2
1
2
0
0
1
6
1
0
1
1
1
0
0
0
0
0
0
1
2
0
0
2
0
0
2
2
0
0
2
0
1
0
0
1
0
0
0
0
0
2
1
0
0
1
0
1
1
2
2
0
0
0
1
0
0
1
1
1
1
1
0
2
1
2
1
0
0
0
1
1
2
0
0
1
1
0
0
2
0
0
0
0
0
0
1
1
2
1
2
0
0
1
0
0
0
0
0
0
0
0
2
0
2
1
1
0
2
1
0
1
1
0
0
1
2
0
1
0
2
1
0
0
2
0
0
2
0
6
1
0
0
0
0
1
2
0
0
2
0
2
1
2
0
0
1
1
0
0
3
0
1
0
0
0
0
0
3
2
1
0
1
2
2
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
2
0
1
0
0
1
0
0
0
3
0
0
1
1
0
1
0
1
0
0
0
0
0
0
2
0
2
1
1
2
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
2
1
1
2
2
1
0
1
1
0
4
1
0
1
1
0
2
1
0
0
2
2
1
1
1
1
0
0
1
0
2
1
1
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
2
2
1
2
0
4
0
1
1
1
0
2
0
0
1
0
0
1
0
1
0
1
1
1
2
0
1
1
0
1
1
1
0
0
0
1
2
0
1
0
0
1
2
2
1
0
1
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
1
1
0
1
0
3
0
0
1
0
2
2
0
3
0
1
0
1
0
2
0
0
2
1
1
0
0
0
0
2
2
0
0
2
1
0
1
0
2
0
1
0
0
1
2
1
0
0
0
1
2
0
0
0
1
2
2
1
0
0
0
2
0
1
0
2
1
0
1
0
0
1
2
0
2
0
0
1
1
1
3
0
1
0
2
0
2
0
0
1
0
0
2
1
2
2
0
0
0
1
2
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
2
0
2
0
0
3
0
1
2
0
0
1
0
0
0
0
1
1
4
0
1
1
0
2
1
0
1
1
2
2
0
0
0
1
0
1
1
1
0
1
0
0
1
0
0
2
0
0
1
0
0
2
2
1
1
0
0
1
1
0
0
0
2
0
0
1
0
0
1
2
0
1
1
0
0
0
0
0
1
1
0
2
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
2
0
0
1
1
0
0
0
0
1
0
2
0
1
2
2
1
1
0
0
2
0
1
1
0
1
0
0
0
0
0
1
0
2
0
0
2
0
0
1
0
0
2
2
1
0
0
0
1
1
0
0
0
0
0
1
0
1
2
0
0
2
2
0
0
0
0
0
0
2
1
1
2
0
0
0
0
2
0
0
1
1
2
1
0
2
0
9
1
0
0
0
0
0
1
0
0
0
0
2
2
0
0
2
0
1
1
2
0
0
1
1
2
0
0
2
1
1
0
0
0
0
0
1
2
2
1
0
2
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
2
0
0
0
0
1
0
2
1
0
2
0
2
0
0
0
0
1
1
2
0
1
0
0
0
0
0
1
0
0
2
1
0
2
2
1
2
0
2
0
0
1
0
1
0
1
1
0
0
0
1
1
0
1
0
0
0
1
0
0
2
1
2
2
0
0
1
1
0
0
2
4
2
0
0
2
0
0
0
1
2
0
0
0
2
0
0
0
1
2
1
1
0
0
0
0
2
1
0
0
3
1
0
2
1
0
2
1
1
2
0
2
0
1
0
1
0
0
0
0
2
2
1
2
0
0
2
2
2
2
0
2
0
0
0
1
0
0
0
0
1
0
2
2
0
0
0
0
1
1
0
0
1
2
0
0
0
0
0
0
2
0
0
1
0
1
2
0
2
0
0
1
0
0
2
2
0
2
0
0
0
0
1
1
1
0
1
0
1
3
2
0
0
0
2
0
2
0
2
1
0
2
1
0
0
1
1
0
0
0
2
0
0
1
0
1
1
0
0
3
0
0
2
0
1
1
0
0
0
0
0
2
2
2
0
0
0
1
2
0
2
0
1
2
0
1
0
0
2
1
2
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
2
0
2
0
0
2
0
0
0
0
2
1
1
1
1
1
1
1
0
1
1
1
0
0
2
0
0
0
1
0
1
0
0
4
0
1
1
0
1
0
2
0
0
0
0
0
0
0
1
0
0
1
2
0
1
2
2
0
0
1
2
0
1
0
2
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
2
0
0
2
0
0
1
0
0
2
0
1
2
2
2
2
0
1
2
1
2
2
0
1
1
0
0
0
0
0
3
0
0
0
2
2
0
2
4
1
0
1
0
0
2
0
1
1
0
2
1
2
2
0
2
0
1
1
0
2
2
0
0
1
2
0
1
1
2
1
2
2
0
0
1
1
0
0
0
1
2
0
1
0
0
2
0
1
0
1
1
2
2
0
0
1
0
1
0
1
0
1
0
2
1
0
2
1
1
2
0
0
0
2
0
0
0
1
0
0
0
1
0
1
2
0
0
0
2
0
0
2
0
1
2
0
2
1
0
0
1
2
1
0
0
0
1
0
0
1
2
1
0
2
2
0
2
1
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
1
0
1
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
2
2
0
2
0
0
0
2
0
0
0
1
1
1
0
0
0
1
0
1
2
2
0
2
1
2
0
1
0
2
0
0
1
0
2
0
2
0
0
0
0
3
0
0
0
0
0
2
0
2
0
0
2
1
1
2
0
0
0
0
0
1
1
1
0
1
0
0
0
2
0
1
0
0
2
0
0
1
2
0
2
0
0
0
0
1
0
0
2
0
1
0
0
2
2
0
2
1
1
1
0
0
2
2
0
2
0
0
1
1
0
1
0
0
1
0
0
0
0
1
1
0
2
1
1
0
1
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
2
0
0
2
0
1
1
0
1
0
3
3
2
2
1
2
0
3
1
1
0
0
0
1
2
0
1
1
0
0
1
0
2
2
0
1
3
0
1
0
0
1
2
0
1
0
0
0
0
2
0
0
0
2
1
0
0
1
0
1
0
2
0
1
1
2
0
0
0
3
0
0
0
0
0
0
0
1
0
3
0
1
1
1
0
0
1
2
0
1
1
2
0
0
0
2
0
0
0
3
2
0
0
0
0
1
2
1
2
0
0
0
1
0
1
1
0
4
2
1
0
1
0
0
2
1
1
0
0
1
1
0
1
2
0
2
0
1
0
1
0
0
1
2
1
0
0
0
0
0
0
1
0
3
0
1
2
0
0
0
0
1
2
2
0
0
0
0
1
0
2
0
1
2
4
2
3
2
1
0
0
0
0
0
0
0
1
1
2
0
0
0
0
1
0
2
3
0
2
1
2
0
0
0
0
2
0
0
1
0
2
1
0
2
1
1
0
1
0
0
1
1
0
2
0
0
0
0
0
0
1
0
0
1
0
1
0
0
2
2
1
2
0
2
3
1
2
0
1
0
1
0
1
1
0
0
0
1
3
1
0
1
3
0
1
0
0
0
0
2
1
0
1
0
2
0
0
0
0
0
0
1
2
0
1
0
2
1
0
1
0
0
1
0
0
2
1
0
2
0
0
0
0
0
0
3
1
1
0
1
1
0
1
0
1
0
1
0
2
2
1
1
2
0
0
1
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
2
0
0
3
1
0
1
0
0
0
1
0
1
0
1
0
1
3
0
0
0
0
10
2
1
0
1
0
0
0
2
0
2
2
0
1
2
0
1
1
0
1
2
1
0
0
0
1
0
0
0
0
1
0
0
1
0
2
1
1
0
1
0
4
1
0
0
0
1
0
0
0
0
0
0
1
2
0
0
1
2
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
1
2
0
0
1
0
2
0
2
1
0
2
0
0
1
0
1
0
1
1
1
0
1
1
0
0
2
1
0
0
0
1
0
0
1
0
1
1
1
1
0
1
0
0
4
1
1
3
1
1
1
0
1
0
0
1
2
2
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
2
0
3
1
2
0
1
0
0
0
0
0
0
2
0
3
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
2
2
0
2
1
1
1
1
2
1
2
0
1
0
0
0
0
1
2
0
2
1
2
0
2
0
1
0
1
1
1
2
0
3
0
2
0
1
0
1
0
0
0
1
0
0
0
2
0
0
0
1
0
1
0
0
1
1
0
0
1
0
1
1
1
1
0
1
1
0
1
3
0
1
2
0
0
2
0
3
0
1
2
0
0
0
2
0
4
0
2
0
0
1
1
0
0
2
0
0
0
1
2
0
0
2
2
0
0
0
0
0
3
1
0
1
1
0
3
0
1
1
3
1
2
1
2
1
0
0
0
0
1
0
0
2
2
2
0
1
0
0
2
1
2
1
2
2
2
1
0
1
2
1
0
1
1
1
1
1
1
0
1
0
0
0
0
0
0
1
1
0
0
1
1
0
0
2
0
0
1
2
0
0
0
2
0
0
1
2
0
2
3
2
1
1
1
2
2
0
0
0
0
1
1
1
2
2
0
0
1
0
0
1
0
0
2
0
0
1
0
0
1
2
1
1
1
2
0
0
0
1
1
0
4
2
2
1
3
1
1
3
1
0
1
2
1
0
2
0
0
0
0
2
0
1
0
1
0
0
1
2
2
1
1
0
0
0
0
1
1
0
1
1
1
0
2
0
0
0
1
1
0
0
1
0
1
0
0
1
0
0
1
0
2
0
0
0
2
0
1
0
1
0
0
2
1
2
0
1
1
1
0
1
0
0
0
0
5
5
2
2
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
1
0
1
1
0
0
1
0
1
0
1
0
1
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
2
0
1
0
1
0
2
2
0
0
2
0
1
1
0
1
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
1
1
2
0
0
0
0
0
2
0
0
2
0
1
0
0
2
0
0
0
0
2
2
0
2
0
0
1
0
1
0
0
0
0
0
0
2
2
1
2
0
2
1
1
2
2
0
0
2
1
0
0
1
2
0
2
1
1
0
0
0
0
0
0
1
0
2
0
1
1
0
2
0
2
0
1
0
0
4
1
0
0
0
2
0
1
1
0
2
0
1
2
0
2
1
1
0
0
0
0
0
0
1
0
0
0
0
2
2
1
2
1
0
2
2
0
1
0
0
0
0
2
0
0
0
3
0
0
0
1
2
0
2
1
1
0
1
0
0
0
0
5
1
0
1
2
0
2
1
1
0
1
2
0
1
0
2
1
0
0
0
0
0
1
0
1
0
2
0
0
1
2
2
1
0
1
2
0
2
0
0
1
0
0
2
2
0
1
0
0
1
0
1
1
0
0
0
0
1
1
1
0
1
0
0
0
1
0
0
1
1
0
2
1
1
0
0
2
0
1
0
0
0
2
0
0
1
2
0
1
0
2
1
0
2
1
1
1
0
0
2
2
0
0
0
0
0
1
0
2
0
0
1
0
2
1
0
0
2
1
0
0
1
0
2
1
1
0
0
1
2
1
1
1
1
0
3
0
1
1
0
1
0
0
2
2
1
0
0
0
2
0
0
1
2
0
0
2
0
0
1
0
0
1
0
2
0
1
0
0
1
0
0
0
0
0
2
0
0
1
0
1
0
0
2
4
0
0
0
2
1
1
2
3
0
0
2
2
0
1
2
1
0
1
0
1
0
1
0
0
0
2
2
0
0
4
2
2
0
0
2
1
2
2
1
0
1
1
0
2
2
0
2
0
0
1
0
0
1
3
2
1
0
2
0
0
2
2
0
1
0
1
2
2
1
0
0
0
1
0
0
0
2
2
0
1
0
1
0
3
1
1
0
1
1
0
1
0
2
0
1
2
0
0
0
2
0
2
1
2
0
2
0
0
1
0
0
0
2
0
0
0
1
1
0
1
0
0
0
2
0
1
0
2
0
2
1
0
2
0
0
1
1
1
2
2
1
1
1
1
0
0
0
0
2
0
0
2
0
2
1
2
2
2
0
1
0
0
1
0
0
2
2
0
1
0
2
0
0
0
0
2
0
0
0
2
1
0
0
0
1
1
1
1
1
2
2
0
1
2
0
0
0
0
1
0
2
2
0
1
2
0
0
2
0
0
0
0
1
2
0
1
0
0
1
1
1
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
2
2
2
0
1
0
0
0
0
2
0
2
0
0
0
2
0
0
2
1
3
0
0
0
0
0
1
2
0
0
0
0
0
1
1
0
0
2
0
2
2
2
0
0
1
1
2
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
3
0
2
2
1
0
1
0
0
1
0
2
1
1
0
0
0
3
1
1
1
0
0
0
3
1
0
1
0
0
1
2
1
0
0
2
0
0
1
0
2
0
1
0
0
1
1
0
0
2
1
0
0
0
0
0
2
0
0
1
0
2
1
1
0
0
1
0
1
0
0
1
0
0
1
2
1
0
0
2
0
0
0
0
2
1
0
1
11
1
1
0
2
0
1
0
1
0
0
0
2
0
0
2
0
0
0
1
2
1
0
2
0
1
0
0
1
0
2
0
0
0
6
1
1
2
0
2
0
0
0
0
0
0
1
1
1
3
3
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
2
2
0
0
1
1
0
1
0
2
1
0
0
2
0
0
0
0
0
0
1
2
2
0
0
0
0
1
1
1
1
1
0
1
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
1
0
0
0
1
1
1
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
1
1
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
2
1
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
1
2
0
1
0
0
1
0
3
0
1
2
2
0
2
1
0
1
0
0
0
1
0
0
1
1
2
0
0
2
2
1
1
2
0
1
1
1
1
0
2
0
0
1
0
1
2
2
3
1
2
0
0
1
0
0
0
0
0
0
1
1
1
1
0
2
0
0
1
0
0
0
0
1
3
0
1
0
0
2
2
0
1
0
1
1
0
0
0
3
0
0
1
3
3
2
1
1
0
1
0
2
1
1
1
1
1
0
0
1
1
4
0
1
1
0
1
1
1
1
1
0
0
1
2
0
0
2
1
0
0
2
1
2
1
0
1
1
0
1
2
0
2
0
1
0
0
0
1
1
0
0
2
2
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
2
1
0
0
0
2
0
0
0
0
1
3
0
0
1
0
2
0
1
0
0
1
0
2
0
2
0
1
0
0
2
2
1
2
0
0
2
2
2
1
2
0
1
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
2
1
1
1
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
3
0
0
2
0
0
0
2
1
1
0
1
0
0
0
0
2
0
2
1
0
0
0
2
0
0
0
0
0
1
2
0
1
0
0
0
0
2
0
4
1
1
1
0
0
0
2
0
3
1
2
0
0
1
1
0
2
0
1
1
1
0
0
0
0
0
2
0
0
0
0
0
1
1
0
2
1
1
0
0
0
0
2
2
0
2
0
0
1
0
0
0
0
1
2
0
0
1
2
0
0
0
2
1
2
2
2
0
0
0
0
0
0
0
0
3
1
1
1
0
0
1
1
1
0
1
0
0
0
0
0
1
0
1
0
0
1
1
1
2
2
1
1
1
2
2
2
0
1
1
0
2
1
0
2
1
0
0
2
2
2
1
0
0
0
0
2
0
0
2
2
4
1
0
0
1
2
1
1
0
0
0
0
0
3
1
0
3
1
0
0
0
2
0
2
1
0
0
1
0
0
1
1
2
0
0
0
2
0
2
1
0
0
0
1
1
0
0
0
2
1
1
0
1
0
2
2
0
2
2
1
0
0
0
2
1
1
2
0
2
0
1
0
0
0
2
0
0
1
0
0
0
0
0
1
1
2
0
0
0
0
1
0
2
1
1
2
0
2
1
1
1
1
2
1
2
0
0
2
3
1
0
0
0
0
2
0
0
2
1
3
2
2
0
1
2
1
2
2
1
2
0
2
0
0
0
2
0
0
1
1
1
2
0
4
0
0
0
0
0
2
0
1
0
0
1
2
2
0
2
0
2
2
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
1
1
1
1
0
1
1
0
0
0
1
0
0
0
0
1
2
0
1
0
0
2
2
2
2
1
0
1
0
2
0
2
0
2
0
0
2
0
0
0
2
2
2
0
7
2
2
0
0
0
0
1
1
0
2
0
0
0
1
1
0
1
4
2
1
1
2
1
3
0
0
2
1
0
3
1
0
1
1
1
1
1
0
1
0
0
0
0
2
1
0
2
0
0
0
1
2
0
0
0
1
1
1
2
1
0
0
2
0
1
2
1
2
3
2
0
1
1
2
0
0
1
0
1
1
1
0
0
1
1
0
1
1
0
0
2
1
2
1
2
0
0
0
0
0
0
0
2
0
2
2
2
0
0
1
2
2
2
1
0
0
1
1
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
1
0
1
2
2
0
0
0
0
0
0
0
0
1
0
1
0
1
2
2
0
2
1
0
1
0
0
0
0
0
1
0
0
0
1
2
1
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
1
0
1
0
1
0
1
2
1
2
1
0
0
0
0
2
0
1
0
1
1
1
2
0
0
2
2
2
0
0
0
1
3
0
2
0
2
0
0
1
0
1
0
2
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
2
1
1
0
0
0
1
2
0
0
0
0
4
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
2
1
2
0
1
2
0
0
1
0
0
0
0
0
1
2
2
2
2
1
2
2
1
1
0
2
0
0
0
2
1
1
1
0
2
2
1
0
1
1
1
1
0
2
0
0
2
2
0
2
1
0
0
0
1
0
0
0
0
0
0
1
2
1
1
1
3
0
0
0
0
1
0
0
0
2
1
1
2
2
2
1
0
0
0
2
0
0
0
0
0
1
1
2
0
0
0
1
0
0
1
1
0
1
0
0
2
0
0
0
3
2
0
0
1
0
0
0
0
1
1
0
0
2
0
0
0
1
0
1
0
2
2
1
0
0
2
0
2
0
1
3
0
0
0
2
1
0
0
0
1
0
0
1
1
2
1
0
0
3
2
2
0
2
0
0
0
0
0
0
0
0
3
0
3
1
2
0
3
0
1
0
1
0
0
2
1
0
2
2
0
0
2
1
1
1
0
0
1
2
0
0
1
0
0
1
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
2
0
2
0
2
1
2
2
1
2
1
1
0
2
3
0
0
2
0
0
0
1
1
1
1
0
0
0
2
1
1
1
0
0
0
1
2
0
0
0
0
2
0
1
1
0
2
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
2
0
0
0
0
0
1
0
2
1
0
1
1
1
2
0
0
0
0
1
1
1
0
0
2
3
0
2
0
1
0
2
2
2
1
0
0
0
2
0
0
2
0
0
0
0
0
1
0
2
0
2
0
2
0
0
1
1
0
0
0
0
1
1
0
0
0
0
2
0
0
0
2
2
1
2
0
2
2
0
1
0
0
3
2
1
1
0
0
0
0
0
0
0
0
2
0
1
0
3
2
2
2
1
0
2
1
1
1
0
0
0
0
2
0
0
1
2
0
0
1
0
0
0
2
2
2
0
0
0
1
1
0
1
0
0
0
0
0
2
0
1
0
0
1
2
0
2
2
1
0
0
2
1
0
0
0
1
2
2
1
1
0
3
2
0
2
1
0
2
0
0
2
0
0
0
2
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
2
0
2
0
2
1
0
0
2
1
2
0
0
0
0
0
2
1
0
1
2
2
1
0
1
1
1
0
1
2
0
0
2
2
2
1
1
0
1
0
1
0
1
2
1
0
0
2
0
2
1
2
0
1
0
0
0
1
0
2
0
0
0
3
0
1
1
0
2
2
1
0
2
3
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
2
0
1
2
1
0
0
0
0
1
2
1
0
2
1
0
0
2
2
0
2
0
0
1
2
0
0
1
0
2
2
1
0
0
1
1
2
0
0
0
1
0
0
1
0
0
0
2
1
2
1
1
0
1
2
2
0
0
1
0
0
2
0
2
1
2
0
0
0
0
1
0
1
0
0
0
0
1
0
0
2
0
0
0
0
2
1
0
0
2
1
2
1
0
0
0
0
2
0
0
2
0
1
1
1
0
2
1
0
0
0
1
2
0
0
1
0
0
1
2
1
1
0
0
2
0
0
0
1
0
1
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
1
1
0
2
2
2
0
0
0
1
0
2
0
0
1
2
1
1
1
1
0
1
0
0
0
0
0
2
0
0
0
0
1
3
0
1
2
0
2
0
1
1
2
0
1
1
1
0
2
0
1
0
0
1
2
2
2
0
1
2
1
0
0
0
0
0
0
1
2
2
1
0
1
0
1
0
0
0
0
2
0
0
1
2
1
0
2
0
1
0
2
0
0
2
0
0
0
0
1
0
0
1
0
0
1
1
2
0
0
0
0
0
0
1
0
1
0
0
0
0
2
1
2
0
1
1
0
1
0
0
0
1
0
1
0
0
2
0
1
1
1
0
2
1
0
0
2
0
2
0
0
0
0
0
0
0
1
2
0
2
0
2
0
0
2
1
0
2
0
1
2
1
1
0
6
0
1
0
2
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
1
0
1
0
1
0
2
0
0
2
0
0
1
2
0
2
2
2
2
1
2
1
0
1
2
1
1
0
0
0
2
0
0
0
2
1
0
0
2
2
0
0
0
1
2
1
1
1
0
0
0
0
0
0
1
2
1
0
2
2
1
0
2
2
0
2
1
0
1
0
2
0
2
0
0
1
1
0
0
0
0
4
0
2
0
0
0
0
0
0
1
0
1
2
0
0
0
2
1
1
0
1
0
2
0
2
0
0
2
0
1
3
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
2
0
1
2
0
0
0
0
0
1
1
1
0
0
2
1
1
3
2
1
0
0
0
0
0
0
2
0
1
0
1
3
2
2
1
1
2
2
0
0
0
0
2
3
2
0
2
3
1
0
0
2
2
0
0
0
0
2
1
1
0
0
1
0
2
0
1
1
2
2
3
2
0
0
0
1
1
0
0
1
0
2
1
0
4
1
0
0
0
0
1
1
2
1
1
0
0
1
0
0
0
0
1
0
0
2
0
0
2
2
1
1
0
2
0
0
1
0
2
1
0
0
0
0
0
0
0
2
0
1
0
0
1
1
0
0
0
1
1
1
0
1
2
0
0
2
0
2
0
1
0
1
5
0
1
2
2
0
1
2
0
0
0
0
2
1
0
0
0
1
2
1
0
1
0
0
1
0
0
0
0
0
2
1
0
0
2
0
0
2
0
1
2
0
0
0
0
1
1
2
0
2
0
0
1
1
0
0
1
1
1
2
1
1
1
0
0
3
0
0
2
0
0
0
0
1
1
2
0
2
1
2
0
3
1
0
0
0
2
0
0
0
1
1
0
0
1
0
0
1
1
0
0
0
0
0
2
1
1
0
4
2
2
0
1
1
2
1
0
0
5
0
0
0
1
1
0
2
0
2
0
0
1
1
2
3
0
2
2
2
1
0
2
0
0
0
0
0
1
1
0
1
0
0
0
1
2
0
0
0
0
1
0
1
1
2
1
2
1
2
1
2
1
0
0
0
0
0
1
1
2
2
1
0
1
0
2
0
0
0
2
3
3
0
1
0
1
0
2
2
1
2
0
1
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
2
1
0
1
2
1
0
0
1
2
2
1
2
0
0
0
2
0
2
0
0
1
0
0
0
2
2
2
0
0
0
0
0
0
2
1
0
0
1
0
1
4
0
1
0
0
0
0
0
1
1
2
0
2
0
1
0
1
0
0
1
0
1
0
1
3
2
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
2
0
0
0
2
1
1
2
0
2
1
0
3
0
2
1
1
0
1
2
0
0
0
0
0
0
0
0
1
2
0
0
2
2
0
0
2
0
2
1
2
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
2
1
0
2
2
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
1
1
1
0
0
0
1
1
2
0
2
1
0
0
1
0
0
0
0
2
2
0
0
0
0
1
0
2
2
0
0
1
0
0
0
0
0
1
2
0
2
1
1
0
0
1
1
3
0
0
1
0
2
1
1
2
2
2
0
0
2
1
1
0
0
0
1
0
0
1
0
0
2
1
1
0
0
0
0
2
1
2
0
1
1
1
0
0
0
0
0
1
1
0
0
2
0
1
0
0
3
0
1
0
2
0
1
2
0
1
2
1
2
2
0
1
0
1
0
1
0
0
2
0
0
1
0
2
2
1
0
2
1
1
0
0
0
0
2
4
0
0
1
1
0
0
1
0
0
0
0
1
0
0
1
0
1
2
0
0
0
2
2
0
0
1
2
0
1
0
1
0
1
1
1
1
0
1
0
1
0
0
1
0
2
0
2
0
2
2
1
1
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
1
0
2
2
1
1
0
0
1
0
0
0
0
0
1
3
0
0
2
0
0
0
2
0
2
0
0
0
2
0
0
2
0
2
1
2
1
1
1
2
0
0
2
0
0
1
0
0
1
0
2
2
0
0
2
1
2
2
0
1
0
0
3
2
0
0
0
2
0
2
0
1
1
0
0
0
0
2
1
0
4
1
1
2
0
0
4
1
0
2
1
1
0
0
0
1
0
1
1
0
1
0
0
2
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
2
2
2
0
0
2
2
2
1
2
1
2
0
0
0
15
2
1
1
1
1
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
2
0
0
0
0
0
2
0
2
1
1
1
0
2
0
0
0
0
0
0
1
2
0
1
0
0
1
0
0
1
0
0
0
0
0
2
2
0
0
1
0
2
1
2
0
1
0
2
0
2
1
0
0
3
2
1
2
0
0
1
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
2
0
1
2
1
1
0
0
0
1
2
2
0
1
0
0
2
2
1
2
2
1
1
0
3
2
0
0
0
0
2
1
0
0
0
2
1
0
0
0
0
1
1
2
2
0
0
2
2
1
0
0
0
1
0
2
1
0
0
1
1
0
0
0
1
0
0
1
0
1
0
2
1
0
1
0
1
0
0
0
1
0
1
2
2
2
2
0
1
1
0
0
0
2
1
0
0
0
0
0
0
0
1
1
2
2
0
0
0
0
0
2
1
0
0
2
0
0
0
0
2
1
0
0
2
0
0
0
0
1
0
0
2
1
0
0
1
3
2
1
0
0
1
3
1
1
0
2
0
0
0
0
0
1
0
1
0
1
0
2
2
0
0
0
2
1
1
0
1
1
1
1
4
1
0
2
2
0
0
0
0
0
4
0
0
1
1
1
0
2
2
2
3
0
0
1
0
0
2
0
0
1
3
2
0
0
0
0
0
1
1
0
0
0
2
1
1
1
0
1
0
1
0
1
0
1
2
0
0
0
0
1
1
0
1
0
2
1
0
0
0
0
0
2
2
1
0
1
1
1
2
0
0
1
1
0
1
0
0
1
0
0
1
0
2
2
2
1
3
1
2
2
2
1
1
1
0
0
2
0
2
1
0
0
0
0
0
0
0
2
0
1
2
0
0
0
2
1
2
1
0
0
1
0
1
1
1
0
0
0
1
1
0
2
1
2
2
2
0
2
2
1
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
1
0
2
1
1
0
2
0
0
0
2
0
2
0
1
0
1
0
0
2
1
1
0
1
1
1
0
1
2
1
0
1
0
0
2
0
1
0
0
0
0
1
0
1
0
1
0
2
1
1
0
2
0
1
2
0
1
2
0
0
0
0
2
0
0
0
0
1
1
3
0
0
0
0
0
2
0
2
0
2
2
2
0
1
0
0
2
0
2
2
1
1
1
2
0
1
0
0
2
0
0
0
1
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
1
0
2
0
1
0
0
2
0
0
0
8
0
1
2
0
0
0
0
0
1
0
2
0
2
0
0
1
0
0
0
0
1
1
1
1
1
1
1
0
1
0
0
2
2
0
0
0
0
1
2
0
1
2
0
0
0
0
2
0
0
0
1
1
0
1
2
0
0
0
1
0
2
0
0
1
0
0
1
0
1
1
0
0
2
2
2
1
0
8
0
0
0
2
2
0
1
0
1
0
2
0
0
2
3
1
0
2
0
1
0
1
0
0
0
0
2
1
1
0
1
1
1
0
0
3
0
0
2
0
2
1
1
1
2
0
1
0
0
2
0
2
0
0
1
1
0
2
1
0
0
0
1
0
0
0
1
0
0
0
0
1
2
0
0
2
1
0
1
0
0
2
2
1
0
2
0
2
0
2
0
3
1
0
0
0
0
1
0
0
0
0
2
1
2
0
0
2
1
1
1
0
0
0
1
1
0
0
1
0
0
0
1
0
2
2
0
0
1
2
0
0
0
1
0
1
0
1
1
0
1
0
1
2
0
6
0
0
0
0
2
0
0
1
0
0
2
0
0
2
1
0
0
3
0
0
1
0
2
0
0
2
0
0
0
1
1
3
0
0
1
1
0
1
0
0
0
0
0
0
1
0
1
2
0
0
0
0
1
1
0
0
0
2
2
2
0
2
1
0
0
0
1
0
1
1
0
1
0
1
3
0
1
2
0
0
0
1
0
0
2
0
1
2
0
1
2
0
1
0
0
0
2
1
0
2
0
2
0
0
0
2
0
1
1
2
1
0
1
1
0
1
0
2
0
1
0
2
0
0
0
0
0
0
2
0
1
3
0
1
0
2
1
0
0
1
2
2
0
3
2
0
0
0
1
0
0
0
0
2
0
0
1
1
1
0
0
0
0
0
0
2
1
2
1
0
0
2
1
2
1
0
1
1
0
1
0
0
2
0
0
0
1
0
0
1
2
0
0
1
2
1
0
0
0
0
0
1
0
1
1
0
0
1
0
0
2
0
0
1
1
0
2
0
1
1
1
0
1
1
1
0
0
0
1
0
0
2
1
0
0
2
0
0
1
0
0
0
0
1
2
0
0
1
1
2
2
0
0
0
0
0
2
1
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
2
0
1
1
1
1
0
2
0
0
0
0
0
1
0
2
3
0
0
0
1
0
0
0
1
1
0
0
0
1
0
1
3
0
1
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
2
0
0
0
0
0
0
2
0
0
2
0
0
2
1
1
0
0
2
0
0
0
0
1
0
0
2
1
1
1
1
1
0
0
0
0
0
2
0
2
0
2
2
1
2
0
2
1
0
0
0
0
0
0
0
0
2
1
3
1
2
0
2
0
0
3
2
1
2
1
0
0
0
0
1
2
0
1
0
0
0
1
0
0
0
0
2
2
2
2
0
2
1
0
2
1
1
1
1
0
0
0
1
0
0
2
2
2
2
0
0
1
1
0
2
2
0
1
2
0
1
2
0
1
0
3
1
0
1
1
2
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
1
2
1
2
2
0
0
0
0
0
2
1
2
0
0
1
0
1
2
2
0
0
0
1
0
2
0
0
0
0
0
2
2
0
0
0
0
1
0
0
2
3
1
2
2
1
0
2
0
1
1
0
1
0
0
1
1
1
1
0
1
2
2
0
1
0
2
1
0
1
1
2
2
0
0
2
0
1
1
0
2
0
0
1
2
0
0
2
0
0
0
1
1
3
0
1
2
1
0
1
0
2
1
0
0
2
1
0
4
0
0
0
2
1
1
0
1
1
1
0
0
0
1
0
1
1
1
0
2
0
0
0
2
1
0
2
0
0
0
1
0
0
0
2
0
0
0
1
1
0
0
0
0
0
1
2
0
2
0
1
0
2
0
0
1
0
2
1
2
2
0
0
2
0
0
1
0
1
2
1
1
0
2
1
2
0
0
2
0
2
2
1
0
2
0
0
1
1
2
0
0
1
0
1
1
1
0
0
0
0
1
0
0
1
1
2
2
0
1
2
1
0
2
0
1
0
1
0
0
0
2
0
1
0
3
0
0
1
1
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
1
4
1
1
2
0
3
2
0
1
0
1
0
1
1
0
0
0
0
1
0
0
2
0
0
0
1
1
0
1
3
0
0
0
2
1
2
2
0
1
2
0
0
0
2
1
2
2
0
2
0
1
1
0
0
1
0
1
0
0
0
1
1
1
0
2
2
0
0
1
0
0
1
1
0
0
1
2
2
1
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
2
2
2
0
1
1
2
3
1
0
2
0
2
0
2
0
0
0
0
0
0
2
0
2
0
0
0
3
1
1
1
2
1
0
0
0
1
2
0
0
1
1
0
0
1
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
2
0
0
1
2
2
0
0
0
0
1
0
2
0
0
0
2
0
2
0
0
0
2
0
2
0
1
0
2
0
0
0
0
0
0
0
1
0
0
1
2
0
2
3
0
1
0
0
1
1
0
0
1
2
0
2
1
1
0
0
0
0
1
0
0
0
0
0
0
2
1
1
0
2
1
2
1
0
0
0
0
1
0
2
0
0
2
0
0
0
1
0
2
2
2
1
1
2
0
1
2
2
0
0
2
0
2
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
1
2
0
0
0
1
1
1
0
0
2
0
0
1
0
0
2
0
2
2
1
2
0
3
1
0
2
0
0
1
0
0
0
2
0
1
2
1
1
0
2
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
2
0
0
2
0
2
0
2
0
0
0
1
0
0
1
1
1
1
0
1
0
0
2
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
1
0
2
2
1
0
1
3
2
1
2
1
1
0
1
1
2
2
0
2
1
0
0
1
0
3
0
0
0
1
5
0
0
0
0
2
0
0
1
1
2
0
0
1
2
0
1
2
0
2
1
1
0
1
0
1
1
0
1
1
2
0
1
2
0
0
0
0
0
0
2
0
0
2
0
1
0
1
2
2
0
0
1
0
1
3
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
2
0
0
1
2
0
2
0
0
0
2
1
1
1
0
1
1
0
1
0
2
2
1
0
2
0
2
1
0
2
0
0
2
0
3
1
0
1
1
0
0
2
0
2
0
1
1
1
1
0
0
2
0
2
0
1
0
1
1
2
1
2
2
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
1
1
2
1
2
1
1
2
2
0
2
2
0
2
1
0
1
2
1
0
1
1
0
0
1
1
0
1
0
0
0
0
0
0
2
0
0
0
2
1
0
2
0
0
3
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
1
1
0
0
0
3
3
0
0
0
2
2
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
2
1
0
1
1
1
1
0
0
0
0
2
0
0
1
0
0
2
0
0
1
0
0
0
2
2
1
0
1
2
2
0
0
0
0
2
0
2
0
2
2
0
0
1
0
1
0
0
1
2
0
0
1
2
0
2
1
2
1
0
1
2
0
1
3
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
2
1
2
0
0
0
0
0
1
0
2
3
0
1
2
2
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
2
0
1
0
0
2
2
1
1
0
1
2
1
1
1
0
2
1
0
2
0
1
1
0
1
1
1
2
0
0
0
2
0
1
1
1
0
0
2
0
0
0
0
1
2
0
1
0
2
1
0
2
0
2
0
0
0
1
0
0
1
1
0
0
2
0
0
2
0
0
1
0
2
0
0
0
2
1
0
0
0
0
0
2
0
1
2
0
1
0
2
2
1
0
2
0
0
2
0
1
0
0
0
2
0
0
1
1
1
1
0
4
2
1
1
0
0
1
0
0
0
0
0
1
2
0
0
2
0
1
2
1
0
2
0
1
2
0
1
0
2
0
2
0
1
2
0
0
2
0
1
0
0
3
0
0
0
0
0
0
1
1
2
1
0
0
1
0
1
2
0
0
0
1
1
0
1
0
1
2
2
0
2
0
0
2
2
1
0
1
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
1
1
2
0
0
1
1
0
0
2
0
0
2
0
2
1
0
2
1
0
2
0
2
1
1
0
1
0
1
2
0
2
0
2
1
0
2
2
2
0
0
0
0
2
2
0
0
3
0
1
0
0
0
2
0
2
2
2
0
1
0
1
0
1
0
2
0
2
3
0
2
0
4
0
1
1
4
0
0
0
0
0
0
2
0
0
2
1
1
0
1
2
0
0
2
1
0
1
0
1
1
2
0
0
4
2
1
0
0
2
2
0
0
2
1
1
0
2
0
0
0
0
0
2
0
0
3
1
2
1
0
0
1
2
2
1
1
0
0
0
1
0
1
1
0
0
0
4
0
0
1
1
0
0
0
1
2
0
1
2
1
0
3
1
1
0
1
1
0
0
0
0
0
1
0
2
0
1
0
1
1
0
0
0
2
1
1
0
1
0
1
1
0
1
0
1
0
0
2
1
0
1
1
2
0
1
1
1
1
0
1
0
2
1
0
0
0
3
2
1
0
1
2
0
1
0
1
1
0
0
2
0
1
1
0
0
1
2
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
2
0
1
0
1
1
0
0
2
0
0
2
0
1
2
1
1
0
0
1
0
0
1
0
1
1
1
0
1
1
0
0
1
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
2
0
1
1
2
1
0
0
1
0
0
2
0
0
1
0
0
0
0
1
1
2
2
0
0
1
2
0
0
0
1
0
0
1
0
0
2
0
0
0
8
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
1
0
0
2
0
0
0
1
0
2
0
2
1
0
0
1
2
2
1
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
2
0
0
0
0
1
2
2
1
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
2
0
3
1
0
2
1
0
2
0
0
0
0
0
0
2
0
0
1
1
0
1
1
0
1
2
0
0
0
0
2
1
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
1
2
1
2
2
2
0
0
0
0
0
1
0
2
1
0
0
0
0
1
1
0
2
0
1
0
1
0
2
0
0
0
1
0
1
0
0
2
0
1
0
0
0
1
0
0
0
0
2
1
0
0
2
1
1
1
1
0
0
2
2
1
0
0
2
1
0
0
0
2
2
0
3
0
1
0
0
0
0
1
0
2
4
0
0
3
2
0
0
0
0
0
0
1
1
1
0
2
2
0
0
2
0
1
0
0
0
1
2
0
1
1
0
0
0
4
1
1
1
1
0
0
2
2
0
0
0
0
0
1
1
3
1
2
0
2
0
0
3
0
1
1
0
0
0
0
0
1
1
0
2
1
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
2
2
1
3
1
0
1
0
1
0
0
0
0
1
0
0
0
0
1
2
1
0
2
2
0
2
0
1
2
1
0
1
0
0
0
1
1
0
0
0
2
0
0
0
1
1
0
0
0
1
0
0
1
2
0
2
1
0
1
2
0
0
0
2
2
2
2
0
0
0
0
2
0
2
0
1
0
1
0
0
1
2
0
0
0
1
2
1
1
0
2
0
0
1
1
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
3
0
0
0
0
1
1
2
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
2
2
0
0
0
1
0
2
0
1
0
1
2
0
1
1
0
0
1
0
2
0
0
0
0
0
1
1
1
0
1
2
3
0
2
2
0
1
2
0
2
0
0
0
0
1
0
0
1
0
1
1
1
1
0
0
2
2
0
1
2
0
2
3
0
0
1
1
2
0
1
0
1
1
1
2
0
0
0
2
2
2
2
0
0
2
0
2
0
0
1
0
2
0
2
3
0
2
2
0
0
1
1
1
0
3
2
2
0
0
0
0
2
2
1
2
1
1
1
1
0
0
1
1
0
0
1
0
0
2
2
1
1
0
2
1
0
0
0
2
1
1
0
0
1
0
0
2
2
0
0
2
0
2
0
0
1
1
0
0
0
1
2
0
0
1
2
0
0
0
2
0
0
1
0
0
2
0
2
0
0
0
0
1
0
0
2
1
0
0
2
1
0
0
2
0
0
0
1
0
0
0
1
1
1
1
0
0
0
2
1
0
3
0
0
0
0
1
0
2
1
0
2
1
0
2
1
1
0
2
0
0
2
2
2
0
0
1
1
0
0
1
2
1
1
1
0
0
0
2
0
0
2
0
1
0
0
1
2
0
0
1
1
0
0
2
3
2
0
1
0
0
0
1
2
0
1
0
2
1
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
2
0
0
1
0
2
1
1
1
2
2
0
1
0
2
0
2
1
2
0
0
1
2
0
1
0
2
1
0
0
2
0
1
0
0
1
0
2
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
2
0
3
1
1
0
0
2
1
0
0
0
0
0
2
0
2
1
0
0
0
0
1
0
2
2
2
1
2
0
1
2
2
0
0
2
0
0
0
0
2
2
2
0
2
0
0
0
1
0
2
0
0
0
1
0
0
2
0
0
0
2
0
1
0
1
0
0
0
7
1
0
0
1
0
0
2
2
1
0
1
0
4
2
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
2
2
0
1
0
1
0
1
0
1
1
1
0
2
0
1
0
0
2
1
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
2
1
0
1
0
0
0
0
1
0
0
0
2
0
0
1
1
1
0
1
0
0
2
2
1
0
0
2
0
1
0
0
0
1
2
1
1
2
0
0
1
0
1
2
0
0
0
1
2
2
2
2
0
0
3
1
2
0
0
0
0
1
1
1
0
0
0
2
0
2
1
0
2
0
1
1
1
2
0
0
0
2
2
0
0
2
0
1
2
0
1
2
0
0
0
2
0
0
1
0
0
3
0
1
1
0
0
0
2
2
0
1
0
0
0
1
0
0
1
1
2
0
0
0
2
2
0
1
1
0
0
0
1
0
0
2
1
0
0
1
0
0
2
0
1
0
1
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
1
0
2
2
1
0
0
0
0
1
0
0
1
1
1
0
0
0
2
7
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
1
2
2
0
2
0
0
0
1
1
1
0
1
0
2
1
1
1
3
0
0
0
1
0
0
0
0
2
1
0
1
1
1
0
1
0
0
2
0
0
0
0
0
1
2
1
2
0
0
0
2
0
2
0
1
1
0
0
1
0
1
0
0
2
1
2
0
0
0
2
2
2
2
2
0
0
1
0
2
1
0
2
2
0
2
1
0
1
0
2
0
2
2
0
1
0
2
0
1
1
1
0
0
0
0
2
0
2
1
0
1
2
1
2
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
2
2
0
0
2
0
3
0
0
1
2
0
1
0
2
1
0
1
0
0
0
1
1
1
0
1
0
0
0
0
1
0
0
1
0
1
2
0
0
2
1
1
0
0
1
0
2
2
0
2
2
0
0
1
0
1
2
2
0
1
0
2
0
2
0
2
1
2
0
2
0
0
1
0
2
1
2
0
0
0
0
2
0
0
2
2
2
0
2
0
2
0
0
1
3
3
1
1
0
1
0
1
0
0
1
2
0
0
1
3
2
2
1
2
0
2
3
2
1
0
0
0
0
3
1
0
0
1
0
0
2
0
0
0
0
2
0
1
1
0
0
1
0
0
0
1
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
2
2
2
1
0
2
2
0
3
0
1
0
1
1
0
0
0
0
0
0
0
1
1
1
0
0
1
1
0
1
0
0
1
2
0
0
2
0
2
2
1
0
1
1
1
0
1
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
2
0
1
1
1
0
1
3
0
2
0
1
0
0
0
0
2
0
2
0
1
0
0
1
0
1
0
2
0
1
0
2
0
1
2
0
6
0
1
1
0
1
1
2
0
1
1
0
0
0
0
0
1
2
0
1
1
0
0
1
4
0
1
13
1
0
1
1
0
0
1
0
0
1
2
0
8
2
0
0
1
1
0
1
1
1
1
1
0
2
0
2
0
1
1
1
0
0
1
1
0
0
2
0
1
0
3
1
0
0
2
2
1
2
2
0
2
1
8
2
0
0
2
0
1
0
0
0
1
2
0
2
0
0
1
0
1
1
1
1
2
1
0
0
0
0
0
0
0
1
1
0
2
1
1
1
0
1
0
0
1
2
1
0
0
1
2
0
0
0
2
2
0
0
0
0
1
0
1
0
0
1
0
2
1
2
0
2
0
1
0
0
3
0
3
2
0
0
2
1
0
1
0
0
0
2
0
1
1
0
2
0
1
0
2
0
0
0
1
0
0
0
2
0
2
0
2
2
1
0
1
1
0
0
0
1
1
0
2
0
2
0
0
3
2
0
1
2
0
0
1
0
0
0
1
1
0
0
1
0
3
1
1
0
0
0
2
1
2
0
2
0
1
1
1
0
0
1
1
0
0
0
0
1
0
0
4
1
1
0
1
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
2
2
0
1
1
1
0
1
1
0
0
2
1
0
2
0
0
0
1
1
2
0
0
2
0
0
2
1
0
0
0
1
0
2
0
1
1
0
2
1
0
0
1
0
0
0
0
0
0
0
2
2
2
1
3
0
1
1
0
0
0
1
1
2
2
2
0
2
0
0
0
1
2
2
0
0
0
1
0
0
0
0
0
1
2
0
0
1
0
1
1
0
0
1
2
0
0
0
0
1
2
2
0
0
1
0
0
1
0
0
2
3
0
0
1
0
2
0
0
0
0
2
1
3
0
0
2
2
0
0
0
0
3
0
1
0
1
0
2
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
1
1
2
0
1
2
0
1
0
1
0
0
0
1
2
2
1
2
0
1
0
1
0
2
3
0
2
1
0
2
0
0
2
2
2
0
1
2
1
0
1
0
1
0
0
2
0
0
0
0
2
0
1
1
2
0
2
1
0
0
0
0
0
0
0
1
2
2
2
1
0
1
0
1
0
0
0
2
0
1
0
0
1
2
1
2
0
0
0
0
2
0
0
2
0
2
1
1
0
1
0
0
5
2
0
1
0
2
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
2
0
3
0
2
0
1
1
1
0
0
0
1
0
1
0
0
0
2
0
0
0
1
1
2
0
0
0
0
0
0
2
2
1
0
1
0
0
2
1
0
1
0
0
0
1
2
2
1
0
0
0
2
0
0
0
0
4
0
0
2
0
2
2
0
2
0
0
2
0
0
1
0
2
5
2
0
0
1
1
0
0
1
2
0
2
0
1
0
1
0
0
2
0
0
2
1
1
0
1
0
0
0
1
0
1
1
1
0
0
1
1
0
0
3
2
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
2
0
0
1
3
0
0
0
0
0
0
2
1
0
1
0
0
4
1
0
0
0
1
1
0
2
3
0
0
1
0
1
1
1
0
1
0
0
0
0
1
1
0
0
0
1
1
0
0
0
2
0
0
0
0
0
1
0
1
0
3
2
1
0
0
1
1
1
1
0
0
0
2
4
0
0
0
0
0
0
1
0
2
0
1
0
0
0
1
1
0
2
1
2
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
2
3
0
1
0
1
1
0
0
0
1
0
0
2
1
2
0
1
0
0
1
2
0
0
0
0
0
0
2
1
0
0
2
2
2
2
0
0
1
0
1
0
1
0
0
1
1
0
1
0
0
1
0
0
1
0
0
1
0
0
1
2
0
2
1
1
0
0
1
0
1
0
0
1
2
0
0
1
2
2
2
0
2
0
0
1
0
0
0
1
1
0
2
0
0
3
0
0
2
0
0
1
0
0
2
0
1
0
2
1
0
0
1
0
0
0
1
0
0
1
0
0
0
2
2
1
2
0
0
2
0
0
1
0
2
1
0
0
0
0
0
1
1
0
2
1
0
2
0
0
0
2
1
0
2
2
1
2
1
4
2
0
0
1
2
2
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
2
0
2
2
1
0
2
0
0
0
0
0
2
0
1
0
2
2
0
0
2
1
1
0
0
1
0
0
1
0
1
3
2
0
0
2
0
0
0
0
0
1
1
0
0
2
0
1
0
2
0
2
2
1
0
1
1
1
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
1
2
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
2
1
1
0
0
2
0
2
0
2
2
0
2
1
2
1
0
2
0
1
0
0
3
3
0
1
0
1
2
2
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
1
1
3
0
1
0
2
0
0
0
1
1
1
0
0
0
2
0
2
0
1
0
0
1
1
2
4
2
2
0
0
0
0
1
0
1
2
2
0
1
0
1
4
3
1
0
0
0
0
0
1
1
1
0
0
0
2
0
0
2
1
2
2
0
2
2
0
2
0
0
0
0
1
0
0
1
1
0
3
0
0
0
1
0
0
1
0
2
2
1
3
0
2
0
0
1
0
0
0
2
0
2
0
1
0
0
1
1
2
1
0
0
0
1
2
0
0
0
1
0
1
0
1
1
2
2
0
0
0
0
1
0
1
1
0
1
1
0
0
1
0
0
2
1
1
0
0
0
1
0
1
0
0
0
2
2
1
0
1
0
1
2
0
1
2
1
2
0
1
0
1
0
0
0
2
2
0
2
0
1
2
1
0
0
0
0
1
1
1
0
0
0
1
0
0
1
2
2
0
0
1
0
0
1
1
0
1
0
0
1
2
1
0
2
0
0
0
1
1
1
3
2
0
0
0
1
0
1
0
2
0
2
1
0
0
1
2
1
1
0
0
0
0
0
2
0
0
0
2
1
1
0
0
0
0
1
2
0
1
0
0
2
0
1
0
0
0
1
3
1
1
2
0
1
1
1
0
0
2
2
1
0
1
3
1
0
0
2
0
1
1
0
0
1
0
0
1
0
0
2
0
2
2
0
0
1
0
2
1
0
0
1
0
3
0
2
0
0
2
0
1
1
0
2
1
0
0
1
0
2
2
0
0
1
0
2
4
2
0
1
1
0
2
0
1
1
1
2
2
0
0
1
2
0
2
1
0
2
0
0
2
2
2
0
0
2
2
0
1
2
2
0
2
2
0
1
0
4
2
0
1
0
0
0
0
0
0
0
0
1
2
1
2
1
0
1
2
0
0
0
0
1
1
1
2
0
2
1
1
0
1
1
2
0
0
2
1
0
0
1
0
2
1
0
0
1
0
6
0
0
0
0
2
0
0
0
0
1
2
1
0
0
0
0
0
1
0
2
1
1
0
0
1
3
2
1
0
2
0
1
1
1
4
0
0
0
2
0
0
3
0
3
2
0
0
0
2
0
2
2
0
0
1
0
1
0
1
0
2
0
2
0
1
2
2
0
0
0
1
1
0
2
0
2
2
0
0
2
0
0
0
0
1
3
2
0
0
0
2
1
0
0
0
1
1
1
0
0
0
1
0
1
0
2
0
0
1
0
1
1
2
1
2
0
0
0
2
0
1
1
1
0
0
0
1
3
0
0
0
0
0
0
0
1
0
1
0
1
1
1
0
1
0
2
0
0
0
1
0
0
0
1
1
1
9
1
1
2
1
0
1
0
1
1
2
2
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
2
2
0
0
0
0
0
1
1
0
0
0
1
0
0
1
1
0
2
1
2
3
0
1
0
2
2
1
0
2
1
1
2
0
3
0
0
1
1
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
2
2
0
2
1
0
2
0
0
0
0
0
2
2
0
1
0
1
1
3
1
0
2
0
1
1
0
0
0
2
2
0
1
1
1
0
2
0
2
1
2
1
1
0
0
2
0
1
2
0
1
0
2
0
2
0
2
0
0
1
1
0
0
0
1
1
1
0
1
0
2
1
0
0
0
2
0
1
2
1
2
1
0
1
1
1
0
0
1
0
1
0
2
0
2
0
0
0
2
2
3
0
1
1
1
0
1
3
0
1
0
0
0
1
1
0
0
0
2
0
1
0
2
1
1
1
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
1
1
0
1
0
2
1
0
2
0
2
1
0
0
2
6
0
0
0
0
2
0
1
0
0
0
0
0
0
2
1
0
2
0
0
1
0
0
1
0
2
0
0
1
1
0
0
0
0
1
0
0
0
1
1
0
3
0
0
0
0
1
0
0
2
0
1
1
1
1
0
0
2
0
0
0
0
0
2
1
1
1
0
1
2
1
1
1
1
1
0
1
2
1
0
0
0
1
2
0
1
2
0
2
1
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
2
1
2
2
0
0
1
1
1
0
2
0
0
0
2
1
2
1
0
1
1
0
1
0
0
0
1
1
0
1
0
2
2
1
0
0
1
0
0
1
0
2
0
0
0
0
1
0
1
1
1
0
0
2
1
2
0
0
0
1
2
1
1
1
0
0
0
2
0
2
0
0
0
3
0
1
2
0
0
0
2
0
0
1
0
1
0
2
2
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
1
2
0
0
2
0
0
1
0
0
1
1
0
0
0
2
0
0
2
0
0
2
0
0
2
2
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
1
0
0
1
1
0
2
0
0
0
0
1
1
2
1
1
1
1
0
0
1
0
1
0
0
0
0
0
2
1
1
0
0
0
0
0
1
0
0
0
1
0
0
1
2
1
2
0
0
2
2
1
1
0
2
2
0
2
0
1
0
0
1
1
0
1
0
1
0
0
0
0
2
0
4
0
4
0
0
0
0
2
0
2
1
2
0
2
0
0
1
0
1
0
1
0
0
0
1
1
1
1
2
0
0
2
0
1
0
0
0
1
1
0
0
0
0
0
3
1
0
2
0
2
0
0
0
0
0
1
0
0
3
1
2
0
0
0
0
0
1
1
0
2
0
0
0
0
1
1
0
1
0
1
2
0
0
1
0
1
1
2
2
1
0
2
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
1
1
0
2
2
0
0
1
0
1
1
2
0
0
1
1
1
2
1
0
0
1
2
1
1
1
0
1
0
1
0
0
1
0
0
0
1
0
4
1
0
0
0
0
0
0
1
0
0
2
0
0
1
0
1
2
1
0
0
0
0
0
1
0
3
1
2
0
2
0
1
1
2
0
0
0
0
1
0
0
1
1
1
0
2
1
0
1
0
0
0
2
2
0
0
0
0
0
1
3
3
1
0
3
1
0
0
1
0
0
2
2
1
1
1
2
0
0
0
1
1
2
1
1
0
0
0
0
2
0
1
2
1
1
2
0
1
2
0
1
0
0
0
1
0
1
2
1
0
0
0
0
0
0
1
1
0
1
0
0
1
0
1
0
0
0
0
1
0
0
2
2
0
1
3
0
0
0
2
1
0
1
1
4
2
0
2
0
0
0
2
0
0
1
0
0
2
0
1
1
0
1
0
0
2
1
1
0
0
4
2
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
2
1
1
0
1
2
0
2
2
1
2
2
0
0
0
0
0
1
0
0
0
2
1
0
0
0
2
0
2
1
0
1
1
0
2
0
2
0
2
0
1
0
2
2
0
0
0
0
0
2
2
0
0
1
0
2
0
0
0
0
2
2
0
0
0
2
0
0
0
1
2
0
0
0
1
0
1
1
2
1
0
1
0
0
0
0
1
2
0
4
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
5
0
1
0
0
0
0
2
0
0
1
2
0
0
0
0
2
0
0
2
1
1
1
1
2
0
1
2
1
1
0
0
0
1
0
1
1
0
2
0
0
0
0
0
1
1
0
0
0
2
3
2
0
0
0
2
0
0
0
0
4
1
2
1
0
1
0
0
1
0
1
2
0
2
1
3
0
1
0
0
1
0
0
1
0
1
2
1
1
0
2
0
0
1
2
1
2
2
1
0
0
2
2
0
0
0
1
2
0
1
2
0
0
2
0
0
1
0
1
1
0
0
1
1
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
1
0
1
2
2
2
0
1
0
0
1
2
0
2
0
0
1
1
0
0
2
0
1
0
2
0
0
0
1
2
1
0
2
1
2
0
0
0
0
1
0
1
0
2
1
2
2
0
0
0
0
1
2
2
1
0
0
1
1
1
0
2
1
0
0
1
0
0
0
2
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
2
2
1
0
2
1
1
0
0
2
0
2
0
1
0
0
2
2
1
0
0
3
2
1
0
2
1
0
0
0
0
0
1
0
2
0
1
2
0
1
0
2
0
1
0
0
2
0
0
0
1
1
0
1
2
0
2
1
0
1
0
1
4
1
0
0
0
0
1
0
0
0
1
0
3
0
1
1
0
2
0
2
0
0
0
0
0
1
2
0
0
0
2
1
3
0
1
0
1
0
1
3
1
2
0
0
0
0
0
2
0
2
2
2
0
1
0
0
1
1
2
0
0
0
0
2
2
0
1
0
2
2
2
0
0
1
0
2
0
0
1
0
1
0
1
2
1
2
0
0
0
2
1
1
0
0
2
0
1
0
0
0
2
0
0
0
0
2
1
0
2
0
0
1
2
1
1
2
0
0
0
0
2
0
0
0
2
2
1
2
0
0
2
0
1
2
1
2
0
2
2
1
2
2
0
0
0
0
2
1
0
1
0
0
2
0
3
0
2
0
0
0
1
2
0
2
0
1
2
2
0
0
1
0
1
2
0
1
0
2
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
1
4
2
2
0
0
1
0
0
0
2
2
0
0
0
0
0
1
1
0
0
1
0
0
0
0
2
0
1
5
0
1
3
0
1
0
0
0
1
2
1
2
0
1
3
2
0
2
2
0
0
1
0
2
0
2
0
0
0
0
2
1
0
0
1
0
1
1
0
1
0
0
1
1
0
0
2
1
0
0
0
0
2
1
0
0
1
0
0
2
2
0
2
4
0
0
0
1
0
2
2
1
1
0
1
0
0
0
0
1
1
0
1
1
0
1
0
0
2
0
2
0
0
0
0
0
0
2
0
1
0
1
2
3
2
0
0
1
0
2
0
0
4
0
2
0
2
3
0
0
0
2
1
0
1
0
0
0
0
1
0
0
0
2
0
1
1
1
0
0
1
0
2
0
0
0
0
0
0
1
3
0
1
0
1
2
1
2
2
1
0
0
0
0
0
2
2
1
0
0
0
1
0
0
0
1
1
2
2
1
0
2
2
0
0
2
0
0
2
0
1
0
1
0
2
0
0
0
0
0
0
0
2
2
2
2
0
2
2
1
0
2
1
1
1
0
1
0
0
0
4
2
1
0
0
1
2
0
2
1
1
1
0
0
2
1
0
1
1
0
0
1
0
2
1
2
1
2
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
16
0
0
0
0
0
0
0
2
3
1
1
2
2
1
1
2
0
0
2
1
0
0
2
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
2
2
1
1
0
0
2
1
1
0
0
0
1
0
0
1
4
3
0
2
0
2
1
3
0
0
0
1
2
2
2
0
2
1
2
2
0
1
0
0
2
0
0
1
0
0
4
0
2
0
0
0
2
2
0
0
0
0
0
0
2
0
1
0
0
2
0
1
0
1
1
1
1
0
0
2
0
1
2
1
1
0
0
1
1
1
2
0
2
0
0
0
1
0
2
1
0
0
0
1
0
1
0
1
0
0
0
2
0
0
0
0
1
2
0
2
1
1
1
2
0
0
0
2
1
0
0
0
1
2
0
0
0
1
0
1
1
1
0
2
0
2
0
1
2
0
1
0
0
0
1
2
2
1
0
0
0
0
2
0
2
1
1
0
0
0
1
0
0
0
6
0
0
2
2
0
2
0
0
0
2
0
0
0
2
2
1
2
1
0
0
0
1
0
1
0
0
2
0
1
0
1
0
2
0
2
0
1
1
0
0
2
0
1
0
1
2
2
0
2
1
1
1
0
0
0
0
1
0
2
0
1
2
0
0
2
0
2
0
2
0
0
1
1
0
2
2
0
0
0
0
2
1
0
0
1
2
2
1
1
0
0
0
0
1
0
2
2
0
0
0
0
2
0
0
2
1
0
2
3
1
1
1
0
3
1
0
0
0
0
1
0
2
1
1
0
0
0
0
0
1
0
0
1
0
1
1
1
2
0
2
0
0
0
1
1
0
1
2
0
0
0
1
1
0
0
0
0
2
2
2
1
1
0
0
1
1
2
1
0
2
0
0
1
2
1
0
0
1
0
0
2
0
0
0
2
2
0
0
1
2
2
1
0
0
2
1
0
2
0
1
2
1
0
1
1
0
2
0
2
0
1
0
0
0
0
1
0
1
1
1
0
0
0
0
0
1
1
0
2
1
1
1
1
2
3
0
0
1
0
1
1
0
2
1
2
1
0
1
0
1
1
2
1
2
0
0
1
1
0
0
0
2
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
2
1
1
0
1
2
2
0
0
1
1
0
1
0
1
0
2
1
1
0
1
0
2
0
2
0
3
3
0
1
1
1
1
2
0
0
0
0
1
0
0
0
2
0
2
1
0
1
0
0
0
1
0
0
2
1
1
1
0
1
0
0
1
0
2
0
1
1
0
2
1
2
1
3
1
0
0
0
1
0
1
0
2
0
1
2
0
0
0
2
1
2
0
1
2
1
0
1
1
0
2
2
0
1
0
0
0
0
2
0
1
1
0
2
1
1
1
1
1
2
0
0
1
1
1
2
2
0
4
0
0
1
0
0
0
0
0
1
0
2
2
0
1
0
2
1
2
2
1
1
1
0
0
1
1
0
2
2
0
0
2
3
2
0
1
2
0
0
1
1
1
0
0
0
2
0
2
0
2
0
0
0
0
0
2
1
2
2
0
2
0
0
0
0
0
2
1
0
0
2
1
2
0
0
0
0
1
1
2
1
3
0
1
0
2
1
0
2
0
0
2
1
1
1
1
0
0
1
1
0
1
0
1
0
3
2
1
0
0
2
1
1
1
2
2
0
0
0
2
2
1
2
2
0
1
2
1
2
0
1
2
0
0
0
0
2
2
0
5
0
0
0
1
0
2
1
2
1
0
2
0
1
0
1
1
0
2
1
0
0
1
0
2
0
2
2
0
0
0
0
0
0
1
2
2
0
0
2
0
2
0
0
2
0
2
1
0
1
1
0
0
0
0
0
1
3
0
0
2
1
0
0
0
2
1
2
2
1
0
2
0
0
0
0
0
0
2
0
0
0
0
2
1
0
2
2
0
1
0
0
0
0
1
1
0
2
0
0
1
0
0
0
0
1
0
0
0
1
2
3
1
0
1
0
1
1
2
0
0
0
0
2
1
2
1
3
1
1
0
2
0
1
2
0
0
0
1
1
2
0
0
0
0
2
0
0
1
0
0
1
1
1
0
1
0
0
1
2
1
0
1
0
1
0
1
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
2
2
0
0
1
0
0
0
1
1
0
1
1
2
0
0
0
1
0
2
0
0
1
1
0
4
1
1
2
1
1
2
0
3
0
0
0
2
0
2
0
0
2
0
0
1
1
1
0
0
1
0
1
2
1
0
0
0
2
0
0
2
0
0
1
0
1
0
0
0
1
3
2
2
2
0
2
0
8
0
0
0
2
2
0
1
0
2
0
0
1
2
1
0
1
0
2
0
0
0
0
1
0
1
1
0
0
1
2
2
1
0
1
0
1
1
1
2
0
0
0
2
0
0
4
0
0
0
0
3
1
0
1
2
2
1
0
0
0
2
0
0
5
2
3
0
1
0
1
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
1
0
1
0
1
2
0
0
1
0
2
1
1
2
0
1
0
0
1
0
0
2
2
2
0
1
0
0
0
1
3
0
0
2
0
1
0
0
0
0
0
0
2
0
2
0
2
2
1
0
1
0
1
0
1
1
2
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
1
0
0
0
1
0
1
1
1
0
1
0
2
0
2
2
0
0
1
2
1
1
0
2
0
3
1
0
2
2
4
0
0
0
1
1
1
1
0
2
2
0
1
0
2
0
1
2
2
0
1
0
0
0
2
1
0
1
0
2
1
1
0
0
1
1
1
1
1
1
2
1
0
0
0
1
0
1
0
1
0
1
1
1
0
0
2
0
0
1
0
0
0
1
1
0
0
0
0
0
0
2
0
2
0
0
0
2
1
0
0
0
0
0
0
2
0
0
1
0
1
0
1
0
0
0
0
1
2
2
0
1
2
0
2
0
0
2
1
0
1
2
1
0
1
1
1
0
2
0
0
0
0
2
0
2
0
0
1
1
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
1
0
1
1
1
0
2
1
0
2
1
2
0
0
0
0
1
0
0
1
1
3
0
2
2
1
1
0
2
0
2
0
0
2
2
0
0
1
2
1
0
0
0
1
1
0
0
2
2
0
1
0
0
0
0
0
2
2
0
0
0
0
0
2
1
1
1
0
1
0
2
1
0
1
0
0
0
1
0
0
1
0
1
2
2
0
0
1
2
0
0
1
1
0
2
1
0
2
1
2
1
0
2
1
0
0
1
1
0
2
0
0
0
0
0
1
1
1
1
0
0
0
2
2
0
0
0
0
1
0
2
1
1
0
1
0
1
1
2
0
0
0
1
1
0
1
1
0
0
0
0
1
3
1
0
2
1
0
0
2
0
2
0
0
1
2
0
3
2
0
0
1
0
1
0
0
2
0
1
0
1
0
2
0
0
1
1
1
3
0
1
0
0
3
0
0
0
1
0
0
0
1
0
0
1
2
0
1
0
0
0
2
1
1
0
1
0
0
1
1
0
0
0
1
1
0
0
2
1
2
0
0
0
1
0
0
0
2
2
0
0
2
0
0
0
2
0
0
0
0
4
0
1
1
0
5
0
0
0
0
2
0
1
1
1
1
0
1
0
0
2
0
0
0
0
1
0
0
5
0
0
0
2
0
2
1
0
0
1
1
0
1
2
0
2
0
1
1
0
0
2
1
1
1
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
2
1
2
0
1
0
0
0
0
2
0
0
2
2
0
0
2
0
2
1
0
2
0
0
1
0
0
1
1
2
0
0
0
2
1
0
2
0
0
0
1
0
1
3
2
1
0
1
1
2
2
0
0
1
0
0
0
2
2
0
0
1
0
1
0
0
0
0
2
1
0
2
0
2
1
1
2
1
0
2
0
0
0
1
0
0
0
2
2
1
2
0
2
0
1
2
0
1
0
0
2
1
2
3
2
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
2
0
0
2
0
1
0
2
1
0
0
2
0
0
0
1
3
1
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
1
1
2
2
1
2
0
2
1
0
0
0
2
2
0
0
0
0
1
0
0
1
1
2
1
2
1
1
2
0
0
2
1
0
3
0
2
0
0
0
0
0
0
1
2
1
2
0
0
0
0
1
1
0
2
1
0
1
0
2
0
0
1
2
0
1
0
2
0
1
2
0
2
2
1
1
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
2
1
0
1
0
1
0
2
2
2
2
1
2
0
0
0
0
0
1
0
0
0
0
1
1
2
1
1
1
1
2
2
0
0
1
2
0
0
0
0
0
0
2
1
1
1
2
2
0
0
0
0
0
0
0
0
2
0
1
0
0
1
2
0
0
1
0
1
2
0
1
0
1
0
0
0
1
1
0
1
1
0
1
1
2
1
0
0
1
0
0
0
2
0
1
1
0
0
0
1
1
0
2
1
4
1
0
0
1
0
1
0
1
1
0
0
1
0
2
1
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
2
0
0
0
0
1
3
0
0
1
1
2
3
0
0
0
1
2
0
2
0
1
1
0
0
1
0
1
1
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
1
1
2
2
1
0
0
0
1
0
1
0
0
2
0
0
1
0
1
1
2
0
0
0
1
1
0
0
0
2
0
1
1
1
0
0
0
1
0
2
2
0
0
1
3
2
2
1
2
0
1
0
2
0
0
0
2
1
2
0
0
1
1
0
0
0
0
0
0
0
0
2
0
1
2
0
2
1
0
0
0
0
1
0
0
0
0
4
2
2
1
1
1
1
0
0
0
0
1
3
0
0
0
0
0
0
1
1
3
0
0
0
0
0
0
2
0
0
1
0
1
2
0
0
1
0
0
0
3
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
2
0
1
0
1
0
1
0
1
0
1
1
2
0
0
0
2
0
1
2
2
1
0
1
1
2
1
3
0
0
0
0
0
1
1
0
2
1
0
2
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
1
0
0
0
3
1
0
4
1
0
0
0
0
0
1
1
0
0
1
2
0
0
2
1
0
0
0
1
0
2
0
2
0
0
1
0
0
0
2
0
0
1
0
0
1
1
2
1
0
0
2
1
0
0
0
0
0
1
1
1
0
0
0
0
2
0
2
0
0
2
1
0
1
1
2
0
2
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
3
0
1
0
2
0
1
0
0
2
2
0
1
1
0
1
1
0
0
0
0
1
2
0
0
1
2
2
1
1
0
2
0
2
1
0
0
2
2
0
0
1
1
2
0
0
0
2
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
1
1
0
1
0
0
1
2
0
2
0
0
0
1
0
1
1
2
0
0
0
3
1
2
0
0
0
0
0
0
0
0
0
2
0
3
0
2
0
2
2
0
0
1
3
1
0
1
2
1
0
1
0
0
1
0
0
1
2
0
4
1
0
1
0
2
1
0
0
0
2
0
0
0
1
0
0
0
0
2
1
3
0
1
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
2
0
2
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
2
2
1
0
0
0
2
0
0
0
1
0
1
1
1
2
1
0
1
0
0
0
0
1
2
0
0
0
1
1
0
1
1
0
1
2
0
0
2
1
1
0
0
0
1
0
1
2
0
1
1
1
1
2
0
0
2
0
2
2
1
0
1
1
0
0
1
2
0
2
1
2
0
0
0
2
0
1
0
1
1
0
0
0
1
1
0
1
0
1
0
0
0
1
2
0
0
1
2
2
1
1
0
2
0
1
1
1
0
1
1
2
0
1
1
2
0
1
1
2
2
2
1
0
0
2
0
0
0
0
2
2
0
1
0
0
0
1
0
0
1
1
0
0
4
1
0
2
1
1
0
2
0
0
0
0
0
0
2
0
0
2
3
0
0
2
1
2
0
2
0
1
0
1
1
0
1
0
1
2
0
1
0
1
1
1
2
2
1
4
0
2
0
1
0
0
2
1
1
1
1
0
0
1
0
0
1
0
0
1
2
0
1
2
1
2
0
2
1
0
0
0
0
3
0
1
1
0
0
0
4
0
0
0
1
0
0
0
0
2
0
0
2
1
0
0
0
1
1
0
1
1
1
2
0
0
1
0
0
0
0
1
2
0
0
0
1
0
2
0
0
0
2
0
0
2
0
0
1
2
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
1
2
0
0
2
1
1
0
1
2
1
1
2
1
1
1
1
0
1
0
0
0
0
2
2
1
2
0
0
2
2
0
1
2
0
0
0
2
0
1
2
0
0
1
1
0
1
1
2
2
1
1
2
1
0
0
1
0
0
0
0
1
0
2
1
2
1
0
0
0
1
2
1
2
1
0
0
0
0
0
2
1
0
0
2
3
2
1
0
0
3
1
0
1
0
0
0
1
1
1
0
0
2
0
0
0
0
3
1
2
1
1
0
0
0
1
0
0
2
1
0
1
1
0
0
0
1
0
0
2
1
2
0
1
0
1
0
2
1
0
3
0
1
1
0
1
1
0
0
0
1
2
1
0
1
1
1
0
0
2
0
0
1
0
0
2
0
0
0
1
1
1
0
1
0
2
0
0
0
0
0
0
0
2
0
0
2
1
1
2
0
0
0
0
2
2
0
1
1
0
1
0
0
2
1
0
0
1
2
0
2
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
1
0
2
1
0
3
0
0
1
0
0
2
1
0
0
1
2
1
2
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
2
0
2
2
1
0
0
0
0
1
1
0
0
2
0
1
1
0
1
0
0
0
2
1
0
0
2
1
1
0
1
0
0
1
0
1
1
0
1
1
1
0
2
0
2
0
1
2
1
2
0
1
0
0
1
1
1
2
2
0
0
1
1
0
1
0
1
2
0
0
3
1
0
0
2
2
0
0
0
2
2
0
0
0
1
1
0
0
0
1
0
1
1
0
0
1
0
0
0
1
0
1
0
0
0
0
1
1
2
0
0
0
0
0
0
2
0
1
0
2
2
0
1
2
0
0
0
1
2
1
2
2
0
0
0
1
0
2
0
0
0
1
2
0
0
0
0
2
2
1
0
0
0
0
1
0
0
0
0
1
0
0
0
2
1
2
0
1
0
2
2
2
1
1
0
0
2
0
0
2
0
2
0
0
1
0
2
0
0
0
1
2
1
0
2
0
1
1
0
0
0
0
1
0
1
0
0
1
0
1
0
0
2
1
0
0
0
2
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
2
2
0
0
1
2
5
0
0
0
2
2
0
0
2
1
1
1
1
1
1
0
0
0
2
0
1
1
1
0
1
1
0
0
2
0
0
2
1
1
0
2
0
0
0
3
2
0
0
1
0
0
0
1
1
0
1
0
1
0
2
0
1
1
0
0
2
2
0
0
0
0
0
1
0
0
0
3
1
0
0
2
2
1
2
1
0
0
0
1
0
0
0
0
1
0
0
0
2
1
0
2
0
2
1
0
0
1
2
2
1
0
1
1
0
0
2
0
1
0
0
0
1
0
0
1
2
0
0
1
0
0
2
2
0
0
0
0
1
1
2
1
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
1
2
1
0
0
1
0
0
0
0
2
0
0
0
0
2
0
2
2
1
1
0
0
0
0
2
0
2
0
0
1
0
0
1
0
3
0
0
2
2
1
2
0
1
1
1
1
0
0
0
0
1
0
2
2
0
1
2
2
0
0
1
2
0
0
1
1
0
1
0
0
1
2
1
0
0
3
0
2
1
2
2
0
1
0
1
0
0
2
1
2
1
1
0
1
0
0
0
2
0
2
2
1
0
0
0
0
1
0
0
2
1
1
1
1
2
2
0
0
1
0
1
2
1
0
0
0
2
0
2
0
2
2
0
1
2
1
2
0
0
2
0
1
0
2
2
3
0
0
2
0
0
0
0
1
0
0
1
1
1
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
2
2
0
0
0
2
1
0
2
1
0
0
0
2
2
2
2
1
1
1
0
2
0
0
2
0
0
0
0
4
1
4
2
1
0
2
0
0
0
2
1
0
0
2
1
0
2
0
1
0
1
1
1
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
2
1
1
2
0
0
2
0
1
0
0
0
1
2
2
1
0
0
0
2
1
2
0
1
2
3
0
2
1
0
2
1
1
0
2
1
0
0
1
2
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
2
1
0
2
4
2
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
1
0
3
0
1
2
0
1
1
0
0
1
1
0
0
2
1
0
0
1
0
1
1
2
0
3
0
2
2
0
2
0
1
2
1
0
2
0
2
2
0
1
0
0
1
0
0
2
2
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
3
0
2
0
0
1
0
1
0
0
2
0
0
2
0
2
1
2
0
1
1
2
0
0
0
0
3
0
0
2
0
0
1
0
4
1
0
1
0
2
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
2
0
1
0
2
0
0
1
2
1
0
0
1
2
0
0
0
1
1
1
1
1
1
0
0
2
1
0
0
1
1
0
1
2
0
0
0
1
1
1
0
2
0
0
1
0
0
4
1
0
0
0
2
2
0
0
1
0
0
2
0
2
0
0
0
2
0
2
1
0
2
0
0
3
0
0
2
2
1
0
0
0
2
0
2
2
1
0
2
1
2
0
0
0
1
1
7
1
1
0
2
0
0
2
1
0
2
1
0
0
0
0
2
0
0
2
0
0
1
0
2
0
0
0
2
1
2
0
1
0
0
0
0
1
1
0
2
2
1
1
2
1
1
0
0
2
1
1
0
0
2
0
0
0
1
1
0
0
0
2
1
0
2
0
1
1
0
2
1
0
0
3
0
3
0
0
1
2
1
0
1
0
2
1
0
1
0
0
1
0
0
2
1
0
1
0
0
0
1
0
1
2
2
0
0
0
0
0
0
0
1
0
1
0
1
0
2
2
0
1
2
2
0
2
0
1
2
0
0
1
3
2
2
0
0
0
2
1
0
0
0
0
0
2
4
0
1
1
0
0
2
0
2
1
0
0
2
0
1
1
0
0
1
2
1
0
0
0
1
3
0
0
0
0
1
0
1
0
0
0
2
0
1
2
1
1
2
0
0
0
2
0
0
1
2
1
2
0
1
2
1
0
0
0
1
2
0
0
0
2
2
0
0
1
0
0
1
1
0
2
0
0
1
0
2
1
2
0
0
0
2
1
0
1
1
1
0
1
1
0
0
0
0
1
0
1
1
2
2
1
0
1
0
1
0
2
1
0
0
2
1
1
0
0
0
0
0
0
1
0
1
0
0
0
2
1
0
0
1
0
1
1
0
0
0
2
0
2
0
0
0
0
1
2
0
1
0
1
0
0
0
0
0
2
2
0
0
0
1
2
0
0
0
2
1
0
0
0
0
0
1
0
0
0
2
0
0
1
1
2
0
2
2
0
0
0
1
0
0
0
2
0
0
2
0
0
0
2
1
1
2
0
0
0
1
2
2
2
0
2
1
0
2
1
0
0
0
2
2
0
0
0
2
0
0
0
1
1
0
0
1
0
2
0
0
0
0
1
0
0
0
1
2
1
0
2
2
0
2
2
1
1
0
1
1
5
0
1
1
0
0
2
0
0
2
1
3
1
0
3
1
1
2
0
1
2
0
1
1
2
1
0
3
1
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
1
1
1
0
0
1
1
0
2
2
0
0
1
2
2
3
2
1
0
0
0
0
1
1
2
0
0
1
0
1
1
0
0
0
1
0
0
1
1
1
0
1
2
0
1
1
2
2
0
0
3
2
0
1
0
0
2
0
1
2
2
0
2
2
0
0
0
0
0
0
2
0
0
2
0
1
1
0
0
2
1
1
0
1
0
2
0
0
3
2
0
1
0
0
0
2
0
2
0
0
2
0
1
0
1
0
0
0
2
0
0
0
0
0
1
1
0
2
0
0
0
0
5
1
1
0
0
0
1
1
0
0
0
0
0
0
1
1
1
1
0
1
2
2
3
0
2
1
0
2
0
2
3
0
0
2
2
1
1
0
2
0
2
2
1
1
0
1
2
0
1
2
1
0
1
1
1
1
2
0
1
1
2
1
0
0
1
0
0
2
1
2
1
0
0
2
1
0
0
2
0
0
1
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
5
0
3
0
0
1
2
1
2
1
1
2
0
2
0
0
0
0
0
0
1
2
0
0
0
1
0
0
2
0
0
0
1
0
1
1
0
0
0
2
1
0
0
0
0
3
2
1
0
0
1
2
0
2
0
1
0
1
0
0
1
1
0
2
1
0
0
0
1
0
0
0
1
1
0
2
0
0
0
2
0
0
0
0
2
0
2
0
0
2
0
0
0
1
1
0
0
0
2
1
3
1
1
0
0
0
1
1
1
1
1
0
0
0
0
2
1
0
2
0
1
1
1
2
2
0
0
0
1
3
2
0
1
1
0
0
2
1
2
2
2
0
1
0
2
0
0
1
1
1
0
2
1
0
1
0
0
0
0
2
1
0
1
0
2
0
0
0
2
0
2
2
0
0
0
0
0
0
1
0
2
1
0
1
2
0
2
2
0
0
1
0
2
1
0
0
0
0
2
1
0
0
0
2
1
0
2
0
0
0
1
0
0
2
0
0
2
2
0
2
1
0
3
0
1
0
1
0
0
0
0
0
1
0
1
1
0
2
0
0
0
2
1
1
0
1
2
2
3
2
0
2
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
1
1
1
0
1
0
2
0
1
2
1
0
0
2
1
1
0
0
0
0
1
0
0
0
0
2
0
2
2
1
2
0
2
0
0
0
0
0
2
2
0
1
1
0
0
1
1
1
0
0
0
0
2
2
0
0
2
1
0
0
0
0
1
0
1
0
0
0
0
2
2
0
2
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
1
1
0
1
1
1
2
0
0
3
2
2
0
1
0
0
1
2
0
0
0
2
0
1
2
0
2
2
0
0
1
1
1
1
2
1
0
1
6
0
0
0
0
1
2
1
0
0
0
0
2
2
2
2
1
1
2
0
2
2
2
0
1
0
1
1
1
0
1
0
2
0
2
2
0
2
0
0
1
1
0
1
2
0
1
2
0
0
1
0
0
0
1
2
2
2
2
1
1
0
2
1
1
0
0
1
1
0
0
1
3
2
2
0
2
1
0
0
0
1
0
2
1
2
2
0
0
1
1
1
0
0
2
0
2
0
0
0
2
1
1
0
0
0
0
2
3
1
0
0
0
1
1
0
2
1
2
0
1
1
0
0
2
0
0
0
1
0
0
2
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
3
1
0
0
0
0
1
1
0
0
2
0
1
2
0
0
0
0
1
1
2
2
1
2
0
1
2
0
0
1
1
0
0
2
0
2
2
1
3
0
0
3
0
0
2
0
1
2
0
0
1
0
0
2
2
1
0
2
0
0
0
1
0
1
3
0
0
1
0
0
0
1
1
1
0
0
0
2
1
2
0
2
0
0
1
0
2
0
1
1
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
2
2
0
0
2
2
0
1
1
0
1
0
2
0
0
2
0
0
1
0
2
2
0
0
1
0
1
2
1
0
2
0
0
0
2
0
2
1
0
0
2
2
0
0
1
0
0
0
0
2
1
0
2
0
0
0
1
0
1
1
0
0
0
1
0
1
2
0
0
2
0
0
1
1
2
0
1
2
3
0
2
2
0
2
2
0
4
0
0
2
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
2
1
0
1
1
0
0
1
1
0
2
2
1
2
0
2
1
0
1
0
1
0
0
0
0
5
1
1
1
0
0
0
1
2
1
0
1
1
0
2
0
2
1
1
0
0
0
1
1
2
0
2
0
0
0
2
2
1
4
0
0
2
0
0
0
0
0
2
1
1
2
1
0
2
1
0
2
1
1
2
1
1
0
0
2
0
0
0
0
2
1
0
2
0
0
2
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
1
2
0
1
1
2
0
0
0
1
0
0
1
2
2
1
0
3
2
0
2
0
0
2
0
0
3
0
0
0
0
2
0
1
2
1
2
2
3
0
0
0
0
1
1
0
0
2
0
1
0
0
0
1
0
1
0
0
1
0
2
0
2
0
0
0
1
1
0
0
1
3
0
1
0
0
0
2
1
0
2
1
1
0
0
1
0
2
0
2
0
2
1
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
1
1
0
1
0
1
1
2
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
2
1
1
0
2
0
0
0
0
0
0
0
1
1
1
2
1
0
0
0
0
0
0
0
1
0
0
5
2
0
0
1
1
2
0
1
0
0
0
2
2
1
1
1
1
0
2
1
0
0
0
1
0
0
0
1
0
1
1
1
2
0
1
0
0
1
0
1
0
2
0
1
1
0
1
9
0
0
1
0
0
1
0
0
0
1
0
0
0
1
2
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
1
2
0
1
3
1
0
0
1
0
0
0
0
2
1
0
2
2
1
2
2
0
1
1
1
0
1
2
0
0
0
0
0
0
1
0
0
1
2
0
1
0
2
0
0
1
2
0
2
0
0
0
1
0
2
1
0
2
0
1
0
0
0
0
2
0
0
2
0
0
1
0
2
0
2
1
0
0
1
1
0
0
1
1
0
1
1
0
2
0
0
1
0
0
0
1
2
0
1
0
1
0
0
0
1
0
1
0
0
1
0
1
0
0
0
2
2
0
1
0
0
0
0
0
1
2
0
1
1
1
2
0
2
1
1
0
2
0
1
1
0
1
1
1
2
2
0
2
0
0
1
2
0
0
0
5
2
1
0
0
2
2
2
3
0
0
2
1
2
0
0
1
2
0
1
2
0
0
3
1
0
0
0
1
2
0
0
0
2
0
2
1
2
0
1
2
0
3
0
1
2
1
2
1
0
0
0
1
0
0
0
1
2
0
0
0
1
0
0
0
2
0
0
2
0
0
1
1
0
1
2
1
0
1
0
0
0
1
2
0
0
4
1
2
0
1
0
0
2
1
2
0
0
2
0
0
1
0
2
1
0
0
0
0
2
0
0
2
0
0
0
2
2
0
0
1
1
0
0
0
0
2
0
0
3
0
3
1
0
0
0
0
0
1
2
2
0
0
1
2
0
2
1
1
2
0
0
1
1
0
0
0
0
0
4
1
2
1
2
0
1
1
0
2
0
2
1
1
1
0
1
0
0
0
1
0
0
1
0
0
1
0
1
2
1
0
2
0
2
2
1
1
0
0
0
0
0
1
1
0
0
0
4
2
1
1
0
0
1
1
1
0
1
1
0
0
1
1
0
0
1
0
1
0
0
0
0
2
0
0
0
2
1
0
0
1
0
0
2
2
1
2
0
2
1
1
2
2
2
2
0
0
1
0
1
0
0
0
2
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
1
2
2
0
1
2
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
2
0
1
1
0
2
2
0
0
1
1
1
0
1
1
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
5
0
1
2
2
2
0
0
0
2
2
1
1
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
1
2
0
2
2
0
1
1
1
3
1
0
1
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
2
1
0
2
0
1
0
1
1
0
1
1
0
2
0
1
1
2
0
2
0
0
0
2
0
1
0
0
0
0
1
1
0
0
3
1
1
0
0
0
0
0
0
0
1
2
1
2
0
0
0
2
0
2
0
0
0
0
1
1
2
0
3
0
0
0
0
0
1
1
0
0
0
0
2
2
1
2
1
0
2
0
0
0
1
1
0
0
1
0
0
2
1
0
0
0
1
0
0
2
1
0
0
0
0
1
1
0
2
1
1
2
0
1
0
0
1
1
0
0
0
0
0
0
0
3
0
1
1
1
0
0
0
0
1
0
2
0
1
0
0
1
1
0
1
0
0
1
2
1
0
0
1
1
0
0
0
0
2
1
2
1
0
0
1
2
0
0
1
0
0
2
2
1
0
2
0
2
1
0
2
2
1
1
0
0
1
1
1
0
0
0
0
0
2
2
0
2
0
0
0
0
2
2
0
1
2
0
2
0
2
0
2
1
0
0
0
0
1
0
0
0
0
2
1
0
3
1
0
0
1
1
0
1
0
2
1
1
0
0
2
0
1
2
0
0
0
0
1
0
0
0
0
1
0
0
0
1
3
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
2
2
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
1
2
0
1
0
2
0
0
2
2
0
0
0
1
0
0
4
1
2
0
1
2
0
1
2
0
0
1
0
0
0
1
0
2
1
0
1
0
1
1
0
0
1
0
0
1
0
1
0
2
0
0
1
1
0
1
0
0
0
0
3
0
2
0
2
0
0
0
2
0
1
0
0
1
0
0
2
1
0
1
1
0
1
2
0
1
1
1
0
0
2
1
0
1
1
0
0
2
2
0
0
0
2
1
0
0
0
0
1
0
0
0
0
1
0
1
1
0
4
0
0
0
0
0
0
2
1
2
0
1
2
0
0
1
1
0
0
0
0
1
0
2
0
1
0
0
2
0
2
0
2
0
2
2
2
2
1
1
0
3
2
1
1
0
0
0
0
2
0
0
1
0
0
0
0
0
1
1
0
1
0
2
0
0
1
2
0
1
3
2
0
0
0
0
1
3
0
0
2
1
3
0
1
2
1
0
1
0
2
0
7
0
2
2
0
0
0
4
3
0
0
0
1
0
1
0
0
0
1
0
0
2
0
1
0
0
0
0
1
1
1
0
0
0
1
0
0
2
0
2
1
1
0
0
1
0
2
0
0
1
1
1
2
0
2
1
3
1
0
0
0
2
1
0
0
2
2
2
0
0
0
0
0
1
1
0
0
0
1
0
2
0
0
2
2
0
1
0
0
0
1
0
0
0
0
1
1
3
0
1
2
0
0
0
1
2
0
0
1
0
1
0
0
1
0
0
1
2
0
0
2
1
1
1
1
0
0
0
4
0
2
0
1
1
1
0
0
0
0
2
0
0
0
1
2
0
2
1
0
0
2
2
0
0
0
2
1
0
3
2
0
1
1
0
1
0
0
1
0
0
0
0
0
2
0
0
0
1
1
1
2
0
2
1
2
0
0
3
0
1
0
2
0
1
0
2
2
0
1
0
1
2
0
1
2
2
1
2
0
0
1
2
2
0
2
0
0
2
0
0
2
2
2
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
1
1
1
2
0
2
0
0
1
1
0
0
2
0
0
0
1
0
0
0
1
1
2
0
1
0
0
2
0
0
0
0
0
0
2
0
1
1
2
0
0
1
0
2
1
0
0
2
2
0
2
0
0
0
1
0
0
2
0
2
0
2
0
2
1
3
1
2
0
0
1
0
0
0
0
0
0
1
1
3
1
2
0
2
1
0
0
1
2
1
2
2
0
1
0
0
0
1
0
0
2
0
0
0
2
0
0
0
1
0
2
2
0
0
0
1
1
2
0
1
0
2
0
0
2
0
0
0
0
0
2
2
0
0
0
0
2
0
2
2
1
1
2
0
0
1
0
1
1
0
2
0
0
0
2
2
1
0
0
1
2
1
0
0
0
0
1
2
1
2
0
2
0
0
0
1
0
2
0
0
1
1
2
1
2
2
0
1
0
0
0
2
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
2
0
2
1
2
0
0
1
0
2
0
2
3
1
1
0
1
2
1
0
0
2
1
0
1
0
2
2
1
1
0
1
0
2
1
2
0
0
0
1
1
0
1
1
1
2
2
0
1
2
0
1
1
1
1
0
1
1
2
2
0
0
0
1
0
1
1
1
1
0
0
0
0
1
1
4
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
1
0
0
1
0
0
0
0
0
2
0
1
0
1
0
0
0
1
0
0
0
1
0
2
1
2
0
2
1
1
0
0
2
0
2
2
3
0
2
0
1
2
1
0
2
0
1
0
0
1
1
0
1
0
2
0
2
2
0
0
0
2
1
0
2
0
0
1
2
0
1
0
1
0
0
0
2
0
1
0
1
0
2
1
0
2
1
0
0
0
2
1
2
1
0
0
1
2
2
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
1
0
2
0
0
0
0
1
0
0
0
0
2
0
1
3
1
0
0
1
0
2
6
1
1
1
0
1
2
0
0
1
1
0
1
0
0
1
0
2
1
1
0
2
0
0
2
0
0
0
1
0
0
0
2
0
1
0
0
2
1
3
2
0
1
0
0
1
0
1
2
0
0
0
2
0
0
1
1
0
1
0
1
2
4
1
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
2
2
0
1
0
2
0
2
2
0
1
0
1
1
3
0
0
2
0
0
1
2
0
0
2
0
0
2
0
1
0
1
1
2
0
2
0
2
1
0
1
2
1
1
0
2
0
2
0
0
1
0
0
3
2
1
1
1
2
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
2
2
0
1
0
0
0
1
2
0
1
0
0
2
0
0
0
1
0
0
2
1
1
0
0
1
4
2
1
0
1
1
0
1
1
0
1
0
0
1
0
0
0
0
1
2
0
0
0
1
2
1
0
1
1
1
1
0
0
0
0
1
1
2
1
2
1
0
0
0
0
0
0
4
0
0
1
0
0
2
1
2
2
0
1
0
0
1
0
0
1
0
2
0
0
0
0
0
1
1
0
0
1
0
0
2
0
1
1
0
0
1
0
0
4
1
0
0
0
1
2
0
1
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
2
1
1
1
2
2
1
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
2
1
0
0
1
0
0
1
0
1
1
2
2
0
0
0
2
1
0
0
0
3
0
0
1
0
0
1
0
0
0
1
2
0
0
2
2
0
2
1
0
0
1
2
0
2
1
1
2
2
2
3
0
0
0
1
0
0
0
0
2
2
1
0
0
2
0
0
1
0
0
0
0
1
1
1
0
2
0
1
2
0
1
0
1
1
2
1
1
0
1
2
0
2
0
2
1
0
0
1
0
0
0
0
0
1
0
0
1
2
2
2
0
0
1
0
2
2
0
1
2
0
1
2
1
0
0
0
0
2
0
0
0
0
2
0
0
1
2
0
0
0
0
1
2
0
0
0
1
1
1
1
0
1
2
0
0
0
0
1
2
0
1
2
0
1
0
2
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
1
0
1
0
2
0
0
0
0
0
1
0
0
1
0
2
0
0
0
1
2
0
1
1
0
0
3
0
0
1
0
1
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
1
0
0
0
0
1
3
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
2
2
0
2
0
0
0
1
1
0
1
1
1
1
2
1
1
1
0
0
0
1
0
0
0
0
1
0
1
2
0
1
1
2
1
0
0
0
0
2
0
2
1
0
1
2
0
0
1
1
1
2
1
2
2
0
1
0
0
1
0
2
0
0
1
0
1
0
1
2
0
1
1
1
2
0
0
0
1
0
0
0
2
0
1
0
2
0
3
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
1
0
2
0
0
0
0
2
5
2
0
0
2
0
1
5
0
0
0
1
2
0
0
0
0
0
0
2
1
2
0
0
2
1
0
0
2
0
1
1
1
1
1
0
1
1
1
0
2
1
2
0
0
0
0
0
1
2
0
1
0
2
2
1
0
0
0
0
0
1
0
0
0
2
1
2
1
0
1
0
1
1
0
0
0
0
1
1
0
0
0
0
2
2
1
0
1
0
2
2
5
2
0
1
0
0
1
0
1
1
0
0
1
0
0
1
0
2
2
1
0
0
2
0
0
0
2
1
2
0
2
0
0
0
0
2
0
0
0
0
0
0
1
1
0
2
1
0
0
0
0
0
0
0
2
0
2
0
2
2
0
1
0
2
0
1
0
0
0
0
0
0
0
2
0
0
2
2
1
0
0
0
2
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
2
0
1
0
0
1
1
1
0
0
0
1
0
0
0
1
0
2
0
2
0
1
0
1
0
0
0
0
0
0
1
1
1
0
2
0
0
1
0
2
1
0
2
1
2
1
1
2
2
1
0
0
1
1
0
0
2
0
0
0
0
0
2
1
0
0
1
0
0
2
1
1
0
1
0
2
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
2
1
0
2
0
6
1
0
2
0
0
0
0
0
0
1
0
1
0
0
0
3
0
1
1
1
1
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
2
0
0
0
0
1
0
1
1
0
0
1
0
1
0
2
1
2
0
0
2
0
2
3
2
0
2
0
0
0
2
2
2
2
1
1
0
1
2
0
1
1
3
1
0
0
1
2
1
0
2
0
1
1
1
0
1
0
0
0
1
0
0
0
1
0
1
0
0
2
0
0
0
0
3
0
1
1
0
1
0
1
0
0
1
0
1
0
0
0
0
1
2
0
0
1
0
0
2
1
1
2
0
2
0
0
1
1
0
0
0
0
0
0
1
1
1
0
1
0
4
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
1
0
1
1
2
1
0
0
2
2
0
0
0
0
0
1
2
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
3
2
1
1
0
0
1
0
1
1
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
2
0
0
0
1
0
2
0
2
0
2
0
0
1
2
0
2
1
1
1
0
1
0
1
2
2
0
1
1
1
0
1
1
1
0
1
0
0
0
0
2
1
3
1
1
2
1
2
2
0
2
1
6
1
1
0
1
0
0
2
0
2
0
1
0
7
0
0
0
0
0
0
2
0
0
0
5
1
2
0
0
0
0
0
0
1
2
1
0
1
0
3
0
2
1
2
0
0
1
2
1
0
1
1
2
2
2
0
1
2
2
0
1
1
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
1
0
1
0
0
1
0
1
1
0
0
1
1
2
0
3
0
0
0
0
0
0
4
1
0
0
2
0
2
0
0
1
2
3
0
2
0
2
1
0
0
0
0
0
2
0
2
0
0
2
0
0
0
2
2
0
1
0
2
2
0
1
0
0
2
2
2
0
2
1
1
0
1
0
0
2
0
0
2
0
0
0
0
1
0
3
1
2
0
0
0
1
0
1
2
1
0
1
2
0
0
0
0
0
0
0
1
1
0
0
0
2
0
2
1
0
0
0
1
0
0
2
1
0
2
0
1
2
0
1
2
0
0
0
0
0
2
0
1
0
0
2
1
0
0
2
0
0
2
0
0
1
2
1
0
2
0
2
1
1
0
1
0
1
0
0
0
0
0
1
3
0
1
1
0
1
0
2
0
1
2
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
2
1
0
3
0
2
0
0
0
1
0
0
2
2
1
0
0
1
1
1
0
0
1
3
1
1
3
0
0
0
0
2
1
0
0
0
0
0
0
1
2
1
0
0
0
1
0
2
0
2
0
2
0
1
0
0
0
1
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
2
1
0
1
3
0
0
0
0
0
0
1
2
1
2
0
1
2
2
0
1
0
1
0
1
1
2
1
2
2
0
2
0
2
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
2
2
1
1
1
2
0
0
0
0
1
1
1
0
1
0
0
1
2
0
1
2
1
1
1
0
1
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
2
1
1
0
1
1
0
0
1
2
0
2
0
0
1
0
2
2
0
2
1
2
0
2
1
2
0
0
0
1
1
0
0
0
1
1
0
0
2
2
2
0
0
0
1
0
0
1
2
0
1
0
1
1
1
0
0
2
1
0
0
1
0
1
0
1
0
1
2
0
0
0
2
0
0
2
1
0
0
2
1
0
1
0
0
0
0
0
1
0
1
1
1
0
4
0
1
2
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
1
1
1
0
0
2
1
0
0
2
0
0
0
1
2
2
1
0
1
1
1
0
1
1
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
1
0
2
0
0
0
0
0
2
1
0
0
1
0
2
0
1
0
0
2
2
2
1
0
0
0
1
0
1
0
1
2
0
0
0
1
0
0
0
0
0
2
0
0
1
0
2
0
2
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
1
2
1
2
0
0
2
2
2
2
0
1
0
0
2
0
0
1
1
0
1
0
2
0
2
0
0
1
2
0
3
1
0
0
0
0
1
0
1
0
2
0
1
0
2
1
2
0
0
1
2
0
1
2
1
0
1
1
0
0
0
2
0
2
1
0
2
2
1
1
0
2
0
0
0
0
0
2
0
0
2
0
1
2
1
1
1
0
0
0
0
0
0
0
0
1
0
2
0
1
0
1
0
0
0
0
2
0
0
1
2
0
0
2
1
0
0
1
1
0
0
1
1
0
2
0
1
0
0
0
0
0
1
0
1
0
1
0
1
1
1
1
0
2
0
0
0
0
0
1
0
1
1
3
2
0
1
0
1
2
0
1
0
2
2
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
2
1
0
0
0
0
2
0
3
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
4
0
0
1
2
0
2
2
2
1
0
0
0
1
0
2
0
2
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
1
0
0
1
1
2
2
1
0
0
2
1
1
0
0
1
1
2
0
1
2
2
2
0
0
1
1
0
1
0
0
1
0
0
0
1
2
1
1
1
1
0
1
0
0
2
2
1
0
1
0
2
2
0
1
1
2
0
1
1
2
0
0
1
0
0
0
0
1
1
0
0
1
2
0
0
0
1
2
1
1
2
2
0
1
1
1
2
1
2
1
0
0
0
2
0
1
2
0
1
1
0
3
0
0
2
2
1
0
1
0
0
1
0
0
0
2
1
0
0
0
0
0
1
0
2
0
0
1
0
0
1
0
0
0
0
3
1
2
2
2
0
0
2
0
0
2
2
0
0
0
0
1
0
2
3
0
0
2
1
0
0
1
0
0
2
0
0
2
0
1
1
0
0
1
0
3
1
2
0
2
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
2
2
1
0
2
0
2
2
0
1
1
1
0
1
2
1
0
0
0
0
1
0
0
1
1
0
0
1
2
0
0
0
1
0
1
1
1
0
0
1
2
1
0
1
2
0
0
1
1
0
0
2
3
0
0
0
3
0
1
0
1
0
0
0
0
1
0
0
0
2
0
2
1
2
0
2
0
0
0
0
6
0
1
1
0
0
0
0
2
0
1
1
1
0
3
1
0
1
0
1
0
0
4
2
0
0
2
1
0
0
1
2
1
0
0
0
0
0
0
0
0
1
1
1
1
0
0
2
1
1
3
0
0
1
1
1
1
2
1
0
1
2
2
0
0
2
1
0
2
2
1
0
0
0
0
2
0
1
0
1
0
0
0
2
0
0
0
1
0
2
0
2
0
1
1
0
2
2
1
3
1
0
1
0
0
0
0
1
0
0
1
1
0
0
0
2
0
0
1
1
1
0
1
0
1
0
0
0
2
0
2
0
0
2
6
1
0
1
2
0
2
0
0
0
0
1
1
1
1
0
0
2
2
1
0
1
4
1
2
1
2
0
1
0
1
0
1
0
0
0
1
0
0
1
2
1
2
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
2
2
2
0
1
0
0
1
0
2
1
1
0
2
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
2
2
1
0
0
0
0
2
2
0
0
0
1
1
0
1
0
1
2
0
0
0
0
1
4
0
3
1
0
0
2
0
0
0
0
2
2
1
2
1
0
2
0
1
0
1
0
0
0
0
0
0
3
0
0
1
0
1
0
2
2
0
0
2
0
0
0
0
0
1
0
1
0
0
0
1
1
2
0
0
1
0
1
2
2
0
2
1
2
0
0
2
0
2
2
1
1
0
1
2
0
1
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
5
0
0
1
1
1
2
2
0
0
0
6
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
1
1
2
1
0
1
0
0
0
0
2
0
0
0
2
0
0
0
1
1
0
1
0
1
1
0
0
1
0
2
2
1
1
2
0
1
1
6
3
1
1
0
0
2
0
1
1
2
0
2
0
1
0
2
0
1
1
2
1
1
0
0
0
0
0
3
2
0
2
0
2
1
0
2
1
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
3
2
1
0
2
0
1
1
0
3
0
2
2
0
1
0
0
1
0
1
0
1
0
2
0
1
0
0
0
2
1
0
1
0
2
1
1
2
0
0
1
0
0
2
0
0
0
0
0
2
0
0
1
1
0
3
1
2
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
1
0
2
2
0
0
0
0
1
0
2
0
2
0
0
0
1
0
2
2
1
2
0
0
1
2
1
1
0
0
0
1
0
0
0
0
0
0
2
1
1
1
0
2
1
1
1
0
0
0
0
0
0
2
2
0
4
3
0
1
1
0
0
0
0
2
0
0
2
0
0
0
0
1
3
0
0
0
0
0
1
1
0
0
1
1
0
1
1
0
1
2
1
1
1
0
0
0
0
1
0
1
1
0
1
0
0
0
0
2
1
0
0
1
1
3
0
1
1
0
2
0
2
0
1
0
2
1
1
0
0
1
2
0
3
1
0
0
1
0
1
1
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
1
0
0
0
1
0
1
0
2
0
0
1
2
3
0
1
0
0
0
1
2
2
0
2
1
0
0
1
1
0
0
2
0
2
0
1
2
1
1
1
0
0
1
2
2
0
2
1
0
2
1
1
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
1
0
2
2
1
2
1
0
1
2
2
2
1
0
0
0
2
1
0
0
1
1
0
0
0
0
3
2
2
2
2
1
1
2
0
0
0
2
1
0
1
1
0
2
0
0
0
2
1
1
2
0
0
0
0
0
2
0
1
0
0
0
2
1
0
1
0
0
1
0
1
2
0
0
1
2
2
1
1
0
1
0
1
1
1
0
0
1
2
2
0
0
0
2
0
1
1
0
2
2
1
0
1
0
1
0
1
1
0
1
1
0
0
1
0
1
0
2
0
2
1
2
0
2
0
2
1
0
2
2
2
0
2
2
0
1
0
0
1
0
2
0
2
2
2
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
2
0
1
0
2
0
1
0
0
0
2
0
2
1
0
0
0
2
0
2
1
1
0
1
2
0
0
0
0
0
2
2
0
0
1
2
0
3
1
2
2
0
0
4
1
2
2
0
2
0
0
0
0
4
1
1
0
0
1
0
0
0
1
0
0
0
1
0
4
2
0
0
0
0
0
0
2
2
0
2
2
0
2
0
0
1
0
2
0
3
2
2
0
0
2
0
2
0
0
0
0
0
0
0
2
2
0
0
2
1
2
0
0
2
0
1
1
5
0
2
1
1
1
0
1
1
2
0
0
0
2
0
0
0
0
1
2
0
0
1
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
1
0
1
1
0
0
2
0
0
0
1
0
1
0
0
2
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
2
0
1
0
1
1
0
1
0
0
0
0
0
1
1
0
0
1
1
0
1
2
2
0
0
1
2
0
0
0
3
1
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
2
0
0
4
0
0
0
2
0
0
0
1
1
0
0
0
0
2
0
0
0
0
1
0
0
1
0
1
1
1
1
0
1
1
1
0
0
0
0
1
0
2
0
1
0
2
0
2
0
0
0
0
4
0
1
0
0
2
2
0
1
2
2
1
1
2
1
2
0
0
0
6
1
1
0
1
1
0
2
1
0
0
1
2
1
1
0
2
0
3
0
0
1
0
2
1
0
0
0
1
1
1
1
0
1
1
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
1
2
0
1
1
1
1
2
1
0
0
0
0
0
1
1
1
1
1
2
0
1
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
2
0
1
0
0
2
0
2
1
1
0
0
0
4
0
0
2
0
0
2
0
2
0
0
0
1
0
2
2
0
0
0
0
0
1
0
0
2
0
1
2
0
2
2
1
2
1
0
0
0
1
0
0
2
1
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
1
2
0
2
2
1
0
1
0
2
0
1
0
0
2
1
1
0
2
1
1
0
2
0
2
0
0
2
2
0
0
0
1
1
1
1
0
1
0
1
0
1
3
0
0
0
0
0
1
0
0
0
0
0
1
1
2
0
0
1
0
2
0
0
1
1
0
0
0
1
0
2
2
2
0
0
0
0
1
0
0
2
4
0
1
0
0
0
1
1
0
0
0
0
1
0
2
0
0
1
2
2
1
2
0
0
1
2
0
0
1
3
0
2
0
1
0
1
2
0
1
2
0
2
1
0
0
1
1
0
2
1
1
0
0
2
1
2
2
2
0
2
1
0
1
0
2
0
0
2
0
1
2
0
0
0
1
5
1
0
2
1
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
3
0
1
2
1
1
1
0
0
1
0
0
1
1
0
0
2
0
0
0
2
0
0
0
2
0
1
0
0
1
0
0
2
0
0
0
0
0
0
1
1
1
0
3
0
1
0
0
1
0
0
0
1
1
0
0
1
0
2
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
1
0
2
0
0
1
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
1
3
0
1
0
1
0
2
1
0
2
1
0
0
0
1
0
0
0
1
0
0
2
1
0
1
0
2
0
1
1
0
0
1
0
2
2
1
0
2
0
0
0
0
0
0
0
2
0
1
2
2
0
0
2
0
0
0
0
1
2
0
2
0
0
2
0
2
0
1
1
0
2
0
1
0
0
0
0
0
0
2
2
2
1
2
0
0
1
1
2
3
0
1
1
2
1
0
0
0
1
1
1
0
0
0
1
2
0
1
0
0
0
1
0
0
2
3
0
2
0
2
1
1
2
0
0
0
1
0
0
2
0
0
1
2
0
1
2
0
2
0
0
1
1
2
0
0
3
1
0
0
1
0
1
2
1
0
2
1
2
0
1
2
2
0
0
0
2
0
0
2
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
2
0
0
0
1
1
2
2
2
0
0
2
1
1
0
0
0
0
0
4
0
1
0
2
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
3
1
0
1
0
2
2
2
0
1
2
0
0
0
1
0
0
2
1
0
0
2
0
0
1
1
0
1
0
0
0
1
1
0
0
0
0
2
0
0
0
2
1
0
0
1
0
0
2
2
0
1
0
0
1
0
0
2
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
2
1
0
0
1
0
0
0
1
0
4
1
0
1
0
0
0
0
2
0
0
1
0
0
0
1
2
2
0
0
1
1
1
0
1
0
0
1
2
0
1
1
1
2
1
1
0
2
0
0
0
0
0
0
0
2
2
0
2
0
0
0
1
2
1
2
0
0
0
1
0
1
1
1
2
1
1
0
2
1
0
2
1
2
0
0
0
0
0
1
0
0
2
2
1
1
0
0
0
0
2
1
2
1
4
1
2
0
1
0
2
0
4
0
0
0
1
2
1
1
0
0
0
1
1
0
0
2
0
1
0
1
3
1
2
0
1
1
1
1
1
2
0
0
0
0
1
1
1
2
0
1
2
0
2
0
0
0
2
2
2
0
1
0
1
0
1
0
0
1
1
0
2
2
0
1
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
2
2
2
2
1
0
0
1
0
0
3
1
0
2
1
2
1
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
4
1
2
0
0
0
1
0
0
0
0
0
0
2
0
0
1
2
0
0
2
1
0
0
0
0
0
1
1
1
0
2
2
0
0
0
5
0
2
0
1
0
0
2
0
0
1
0
0
0
0
0
2
1
2
2
0
0
0
0
0
2
0
1
0
2
1
0
0
0
0
4
1
0
2
2
0
1
0
0
0
3
2
0
0
3
1
0
0
0
2
0
0
1
0
0
1
0
0
2
1
3
1
0
1
0
1
2
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
1
0
2
1
2
0
0
0
0
1
1
2
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
1
1
0
0
1
0
1
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
2
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
2
1
2
2
0
1
1
0
1
2
0
1
0
2
0
0
1
0
0
1
2
1
0
3
0
1
2
2
0
1
0
2
0
2
2
2
0
2
0
2
0
0
2
0
1
2
2
0
0
0
0
2
2
2
0
1
0
0
1
0
0
1
0
1
2
1
1
0
1
0
0
1
0
0
0
2
0
0
0
1
1
0
0
2
0
1
0
0
2
0
1
0
1
0
0
0
1
2
0
1
0
0
0
0
2
1
0
1
1
0
0
2
1
0
0
1
0
1
1
1
1
0
2
0
2
0
2
1
2
2
2
0
3
0
0
0
0
0
0
1
0
0
0
5
0
0
0
0
1
1
0
0
2
2
2
0
1
0
2
0
1
3
1
0
0
0
0
2
0
0
0
1
0
0
0
3
1
2
0
2
1
1
0
0
0
1
0
0
0
0
2
1
1
1
1
0
0
0
0
0
0
2
1
1
1
1
1
0
0
1
0
1
0
4
2
0
0
1
0
1
0
0
0
1
1
1
3
0
1
2
0
2
1
1
0
1
1
2
0
0
0
1
0
0
0
1
0
1
3
0
0
0
0
1
1
0
0
0
0
0
2
0
1
1
2
2
1
0
0
0
2
0
1
3
1
0
0
1
0
2
2
0
1
0
0
2
0
2
0
0
0
1
2
0
1
0
0
3
1
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
1
0
2
2
1
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
1
0
0
0
1
0
2
2
1
2
1
0
2
0
0
0
0
0
2
0
0
1
2
0
0
0
3
0
0
0
1
2
2
2
0
0
0
0
0
1
1
2
0
0
0
1
0
1
2
1
1
0
2
0
0
1
1
2
1
0
0
0
0
2
2
0
0
0
1
0
1
0
2
1
0
0
1
0
1
1
0
0
0
2
2
1
1
0
2
2
0
1
0
0
2
0
2
0
0
1
0
2
0
2
1
0
1
1
0
0
1
0
0
2
0
2
1
2
1
0
0
2
0
0
2
0
0
2
1
2
2
1
0
0
0
0
1
1
1
0
0
1
1
0
0
1
0
0
2
1
0
0
1
0
0
0
4
1
0
0
1
0
0
1
0
1
0
1
0
0
0
3
1
0
3
0
0
1
0
0
0
1
0
2
0
0
0
1
0
0
1
1
0
0
0
0
2
0
0
1
0
0
0
3
2
2
0
0
0
2
0
1
0
0
1
0
0
0
0
1
2
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
1
0
0
0
2
0
0
0
2
1
0
2
0
0
1
0
1
0
0
0
2
0
0
0
1
0
0
1
0
0
1
1
0
1
2
3
1
2
1
0
1
0
1
0
0
0
0
0
0
2
2
2
2
0
0
2
1
0
1
0
0
0
0
0
0
1
1
0
0
2
1
2
0
2
0
0
1
0
0
0
1
2
2
1
1
0
1
0
2
0
0
2
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
1
2
0
0
0
2
0
0
0
0
0
1
0
0
1
1
2
2
0
2
0
0
1
0
0
1
1
1
1
0
0
2
1
0
0
2
0
0
0
0
1
1
1
0
0
0
0
2
0
0
0
0
1
0
1
1
0
1
0
0
2
0
0
0
1
2
2
0
0
2
0
0
1
2
1
1
1
0
0
0
1
0
0
1
0
0
0
1
2
0
2
0
4
0
0
2
1
2
0
1
1
2
0
1
2
3
0
0
0
0
0
0
0
0
1
0
0
2
1
1
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
1
0
2
0
0
1
0
1
1
0
1
1
3
0
1
2
0
0
2
0
1
0
1
0
0
0
1
0
2
0
0
0
1
0
2
0
0
1
0
0
1
0
1
1
1
0
2
1
0
0
0
2
3
0
0
0
0
2
0
0
1
1
0
0
2
0
0
2
3
0
0
1
0
1
0
0
1
1
0
2
0
0
0
0
0
1
1
1
1
0
0
0
0
1
0
1
0
0
2
2
0
1
1
0
0
0
1
0
2
0
0
2
0
0
0
0
1
0
0
0
0
1
0
1
1
1
0
0
1
0
0
2
2
1
1
2
0
0
0
0
0
0
1
1
0
0
4
1
1
2
1
0
0
2
0
1
0
1
0
1
3
1
2
0
0
0
2
0
0
2
2
0
2
0
1
0
1
0
2
0
1
1
1
0
1
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
1
1
0
3
0
0
1
0
0
2
1
0
1
1
0
0
0
2
0
0
1
0
0
0
2
1
1
0
0
0
1
1
0
1
0
0
0
2
0
0
0
3
1
0
0
1
0
0
1
1
0
1
2
0
1
1
0
1
1
0
2
0
0
1
0
0
0
0
2
0
0
1
0
2
0
0
0
0
2
2
0
2
1
1
2
2
2
0
0
1
0
0
0
2
0
2
0
0
1
2
1
1
0
0
0
2
2
0
0
2
0
2
1
0
0
0
2
0
0
0
2
1
0
0
1
0
1
0
0
1
2
2
2
1
1
1
1
0
1
2
0
1
0
1
0
0
0
0
0
1
2
1
0
0
1
0
7
0
2
1
0
0
0
0
1
0
3
0
0
2
1
1
1
1
1
0
2
0
1
1
1
0
0
1
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
2
0
0
2
0
0
0
0
1
0
0
2
1
0
0
2
0
0
1
1
1
0
0
0
0
1
3
0
0
0
0
0
2
0
0
2
0
1
0
2
2
2
0
0
0
0
0
1
1
1
0
1
0
0
1
0
1
2
1
2
0
1
0
1
0
0
1
0
2
1
0
0
0
0
0
0
2
1
1
0
0
3
1
0
3
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
2
1
1
1
1
2
1
2
0
1
1
1
2
0
0
0
1
0
1
0
0
0
0
2
2
0
0
0
2
1
0
2
5
0
0
0
0
0
2
2
0
1
1
2
0
3
1
0
0
0
0
1
0
0
0
0
4
0
1
3
1
0
0
0
0
0
0
0
2
0
1
0
2
2
2
0
0
2
0
2
2
1
1
0
0
1
0
0
1
1
0
0
0
0
2
1
1
0
2
0
0
2
0
2
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
1
0
1
1
0
1
0
0
0
0
2
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
2
2
1
0
0
2
0
0
1
1
1
1
0
0
2
2
1
1
0
0
1
0
0
0
2
1
0
1
0
1
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
2
0
0
0
0
1
2
0
0
0
0
0
1
2
0
1
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
1
0
0
1
1
1
0
3
0
0
0
1
2
1
0
0
0
1
0
0
0
0
0
0
2
0
0
2
1
0
1
0
0
0
0
0
0
0
0
1
1
2
2
2
1
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
2
0
0
0
2
0
1
0
2
0
1
0
1
2
1
0
0
2
0
1
0
0
1
0
0
1
2
0
2
1
0
0
0
1
0
1
1
1
1
0
2
0
0
1
0
0
0
0
0
2
2
2
0
2
0
0
0
2
3
1
1
0
0
1
3
1
0
0
2
0
0
0
0
1
1
3
1
0
1
0
1
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
2
0
1
0
0
0
1
0
1
0
1
0
0
4
0
0
1
2
0
0
0
1
0
0
2
0
2
1
2
2
0
0
0
3
1
2
0
1
0
0
0
0
2
2
0
0
0
1
2
2
0
0
0
1
0
2
0
1
0
1
0
1
1
2
1
0
1
0
0
1
0
0
3
0
1
1
0
2
0
2
1
0
1
0
1
2
0
0
0
0
1
1
1
2
0
0
1
0
1
1
0
0
1
0
2
0
0
1
2
0
2
0
0
0
0
0
0
0
0
2
1
2
0
0
1
0
1
2
2
2
2
0
0
0
3
0
0
1
0
1
2
0
0
1
0
1
0
0
1
2
2
0
0
1
0
0
0
2
2
2
0
2
1
2
1
1
0
1
0
0
2
1
0
0
2
2
0
1
0
1
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
1
1
0
1
1
1
0
0
2
0
0
0
0
1
2
1
0
1
0
0
1
1
0
2
0
0
1
1
0
0
1
1
0
0
0
0
0
0
1
2
0
1
0
0
0
1
1
1
0
0
0
1
0
0
2
2
2
0
0
1
1
1
1
0
0
2
1
1
1
1
2
0
1
1
3
2
1
0
1
0
1
2
0
2
0
0
0
0
0
1
2
0
2
2
2
0
1
0
1
2
1
2
0
1
0
2
0
0
0
0
2
2
1
0
1
0
0
0
0
0
1
1
2
0
2
0
0
1
2
1
0
3
0
1
2
1
1
0
2
0
0
1
2
0
2
2
0
0
2
0
2
2
2
1
0
1
2
1
0
1
0
0
0
1
1
0
0
2
0
0
0
5
0
1
2
0
2
4
1
0
0
0
1
0
1
0
0
2
1
0
0
0
1
1
0
0
0
1
2
0
3
0
1
0
0
0
1
2
0
0
1
0
1
0
2
0
2
1
0
1
2
0
2
0
1
2
0
2
1
0
0
0
2
1
0
0
1
1
1
1
0
1
1
0
0
1
0
1
1
0
2
1
0
1
0
0
0
2
0
1
1
0
1
0
0
2
4
2
2
1
2
1
2
0
1
1
1
1
1
0
0
2
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
2
7
2
1
0
1
2
0
0
2
0
0
0
0
0
0
2
1
2
2
0
0
0
0
0
2
1
0
0
0
1
0
0
1
3
0
1
0
1
0
2
1
2
0
0
0
1
0
0
0
2
0
0
2
0
1
0
0
0
0
0
3
0
0
1
0
0
3
0
5
1
0
0
0
0
0
0
1
3
0
0
1
0
1
1
0
1
0
1
1
1
0
2
0
0
0
1
0
1
0
2
0
0
0
2
0
1
2
0
1
0
0
0
0
1
0
1
2
0
2
2
0
0
1
0
1
0
2
0
0
1
1
0
0
2
1
1
1
0
0
0
0
1
0
0
2
0
2
0
0
1
2
0
2
3
0
1
1
2
0
0
0
3
0
0
0
2
0
0
0
2
0
0
1
2
1
0
1
0
2
1
9
0
0
0
2
2
0
1
0
0
2
0
1
0
0
0
0
0
2
0
0
0
1
3
0
0
1
0
0
1
0
1
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
1
2
1
0
2
0
1
1
2
0
0
0
1
0
0
2
0
2
0
0
0
0
1
0
2
0
0
0
1
0
2
0
0
2
1
1
0
1
0
1
0
2
1
0
0
0
0
2
1
1
0
1
0
2
1
1
0
2
2
1
0
0
0
0
1
0
0
0
0
1
0
1
0
2
0
1
2
1
0
0
2
0
2
1
1
0
0
0
0
2
1
0
2
0
2
1
0
0
2
0
1
0
1
0
1
0
1
0
1
0
0
3
2
0
0
2
0
0
2
0
0
0
1
0
1
0
0
0
2
1
1
0
0
0
0
0
0
1
2
0
1
0
0
0
2
0
0
0
0
0
1
2
2
1
1
0
0
1
1
0
4
1
1
0
1
0
0
1
0
0
1
0
2
3
2
0
1
1
0
1
0
3
0
1
0
0
0
0
2
1
0
0
0
0
2
0
0
1
0
0
1
1
0
1
2
0
0
2
1
1
0
0
1
2
0
2
2
2
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
1
0
2
0
1
1
2
0
1
2
1
0
1
2
1
2
0
0
0
0
0
0
0
2
0
0
2
2
1
1
1
2
1
2
0
0
2
0
0
0
0
0
0
0
0
1
1
2
0
1
0
2
0
1
0
1
2
1
0
0
2
0
1
1
0
0
1
2
2
2
0
0
0
2
2
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
5
1
0
2
2
0
1
2
2
0
1
0
0
1
0
1
2
0
1
0
1
0
0
0
0
1
2
0
1
0
0
1
2
0
1
0
0
2
0
0
2
0
0
0
1
1
0
0
0
0
1
2
0
0
1
0
1
2
0
0
0
1
0
2
2
0
0
0
2
2
0
2
2
2
0
1
1
1
1
0
1
0
0
0
0
0
0
2
2
0
0
0
0
1
0
2
0
1
1
1
1
3
2
0
1
1
1
1
1
0
0
0
0
1
2
0
0
2
3
0
0
0
1
1
2
0
2
0
0
0
0
0
1
2
1
0
0
2
0
0
0
0
2
2
1
0
0
1
1
0
0
0
0
2
0
1
1
1
2
0
0
0
2
0
2
1
0
0
0
2
0
2
1
1
0
0
0
3
0
1
0
0
0
2
2
1
0
3
2
0
1
0
0
0
2
0
0
2
0
1
0
2
0
1
0
0
0
0
2
1
0
1
1
1
0
2
0
0
0
1
1
0
0
1
0
0
2
0
0
1
1
2
0
1
2
1
3
0
2
0
1
2
0
1
0
1
0
0
0
0
1
0
2
2
1
0
0
0
2
1
0
0
0
0
0
1
1
0
2
0
0
1
0
0
0
1
2
1
0
1
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
2
0
2
1
1
0
1
1
1
0
1
2
1
0
0
0
0
0
1
0
2
0
0
0
2
2
0
0
2
0
0
1
0
1
0
1
2
0
2
0
0
1
2
0
1
0
0
1
1
1
0
0
2
0
3
1
1
1
0
0
3
1
2
0
1
0
1
0
0
0
0
1
1
2
0
1
0
1
0
0
0
0
2
2
0
0
2
0
1
0
0
2
2
0
2
0
0
1
0
2
0
0
0
2
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
2
0
1
1
1
0
1
2
2
0
0
1
0
3
1
0
0
0
1
1
0
1
1
0
0
2
0
0
0
0
2
0
0
1
1
1
0
0
0
2
1
0
0
2
0
0
2
3
0
0
1
2
3
0
0
1
0
0
0
1
1
1
2
0
2
1
0
0
0
0
2
2
1
1
1
1
1
0
0
0
2
2
0
0
1
3
0
1
1
1
0
0
0
0
0
1
1
1
2
0
0
0
1
1
0
0
2
1
2
0
1
1
1
2
0
0
1
0
1
1
0
1
4
0
1
1
0
1
0
0
0
0
1
0
0
0
0
2
1
0
0
1
1
0
0
1
0
0
0
0
2
0
0
2
1
0
0
0
2
2
2
1
0
0
2
0
1
1
0
1
1
0
0
0
0
3
1
0
0
1
0
2
0
0
0
2
0
0
1
1
2
1
0
2
1
1
0
1
3
0
1
1
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
2
1
0
0
0
1
1
1
0
1
0
0
0
0
2
0
0
0
2
0
1
1
0
0
0
0
0
1
0
0
1
1
0
0
2
0
0
1
1
1
1
0
0
0
1
0
1
0
1
1
1
1
0
2
0
1
0
0
0
1
1
2
0
0
2
0
2
0
0
1
2
2
0
0
2
0
0
0
1
2
0
2
0
1
2
1
0
2
1
0
0
0
0
0
1
1
1
1
2
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
1
0
1
1
1
1
0
2
1
0
1
0
0
0
0
0
0
0
2
0
2
1
2
0
1
0
0
0
0
3
0
0
0
0
1
5
0
1
0
1
0
0
1
0
0
2
0
1
3
0
0
0
2
2
1
0
0
0
0
0
1
0
1
0
0
0
1
2
1
1
0
2
0
3
0
0
0
0
0
0
2
1
0
0
0
0
1
2
0
0
1
0
0
1
0
2
1
0
0
0
2
0
0
1
1
0
0
1
1
2
1
2
2
0
1
0
1
0
0
0
2
0
1
1
2
1
2
0
1
0
0
0
0
1
1
0
0
1
1
1
0
1
2
0
1
2
0
1
1
0
2
0
1
1
0
1
1
0
2
0
2
0
0
0
2
1
0
0
0
0
1
1
1
0
1
2
2
1
0
1
1
0
0
1
0
2
2
2
0
0
1
1
1
0
0
0
1
1
1
1
2
1
1
3
1
0
1
0
0
0
0
0
0
0
1
0
0
3
1
0
2
0
2
1
0
2
0
1
1
0
0
1
0
0
2
0
0
0
1
0
0
2
1
1
0
0
2
0
0
1
0
0
1
1
0
2
0
1
1
1
2
2
2
0
2
2
3
0
0
1
1
0
0
2
2
4
1
0
1
2
1
0
0
0
0
0
1
0
0
0
0
2
1
1
0
0
2
2
0
1
0
1
2
0
1
0
2
1
1
0
0
0
2
0
0
1
1
0
0
0
0
1
1
1
2
0
1
2
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
1
0
1
0
0
1
1
1
1
0
2
0
2
0
0
1
0
0
0
0
1
1
2
2
0
0
0
1
2
0
0
1
1
1
1
1
0
0
0
0
0
0
1
2
0
0
0
2
0
1
1
0
0
0
1
1
0
1
0
1
1
2
0
0
0
1
2
1
1
1
0
0
1
1
0
0
1
0
1
2
0
1
2
3
0
1
1
0
0
0
0
0
0
1
0
2
1
2
0
2
1
0
0
0
0
2
1
2
1
1
0
0
0
2
0
2
0
4
0
1
0
0
0
1
2
0
0
2
0
1
0
0
3
0
1
0
2
1
1
1
2
2
0
2
1
1
2
2
0
2
0
1
0
0
0
0
1
3
2
1
3
0
1
0
0
0
0
1
2
1
0
2
2
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
2
2
1
2
0
0
3
0
0
2
1
1
1
1
0
0
0
0
0
2
1
0
2
1
2
1
2
0
1
0
0
2
1
2
2
0
0
0
1
1
0
0
0
0
0
2
0
1
2
0
0
2
0
0
0
2
0
2
0
0
4
1
1
1
2
0
0
1
0
2
2
1
2
4
0
0
1
2
2
0
1
0
2
0
2
2
0
0
1
0
0
1
0
1
0
1
2
2
0
0
0
0
0
1
1
0
0
0
1
0
2
0
0
0
2
0
0
0
2
0
2
1
1
0
2
0
0
1
0
0
1
0
0
0
2
2
0
2
0
0
2
1
2
0
0
1
2
0
2
0
2
0
0
0
1
0
0
2
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
2
1
0
1
0
0
0
0
1
2
1
1
1
1
0
0
0
0
0
0
3
0
1
0
0
0
0
0
1
0
3
0
0
2
2
0
0
0
2
0
1
1
0
1
0
2
2
0
1
2
0
2
1
0
0
3
0
0
0
0
0
1
2
0
0
1
1
0
0
0
0
1
1
0
2
0
2
3
0
0
0
0
2
1
1
2
0
0
2
1
0
0
2
1
2
0
2
1
2
0
1
2
1
2
0
2
0
0
2
0
0
3
0
0
0
1
0
0
0
1
1
1
1
2
0
1
1
1
2
0
2
1
0
1
0
1
1
0
0
6
0
0
1
0
1
3
0
0
0
0
2
1
0
0
0
1
0
1
1
0
0
0
2
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
1
0
2
2
0
0
0
0
1
0
1
0
0
2
1
1
2
0
2
2
0
1
1
0
0
2
1
0
2
1
0
2
1
1
0
0
1
0
0
0
1
1
2
0
0
0
0
0
0
2
0
2
1
2
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
2
2
1
0
0
1
2
2
0
1
0
2
2
2
0
0
2
0
0
0
2
2
2
1
2
1
8
0
1
0
0
1
0
2
1
1
1
0
1
0
0
0
0
1
0
0
1
0
2
2
0
0
0
0
0
2
0
2
1
0
0
0
0
2
0
0
2
0
2
1
1
2
1
0
2
1
0
1
1
0
0
2
1
2
1
3
0
1
1
2
2
2
0
2
0
2
0
2
0
1
0
0
0
2
1
0
0
2
2
0
2
0
0
2
1
0
0
1
2
1
0
0
1
0
0
1
0
0
3
0
5
3
1
0
0
0
1
1
1
0
2
2
0
2
1
0
1
0
0
0
0
1
0
0
1
2
1
0
0
0
0
2
0
0
1
0
0
0
1
0
1
0
0
1
1
0
3
1
0
2
0
0
2
0
0
0
0
1
0
0
2
1
0
1
1
0
0
0
0
1
0
0
2
2
2
1
0
2
0
0
0
0
0
2
0
0
1
0
1
2
0
0
0
0
1
0
4
0
0
3
0
3
0
0
1
0
0
0
0
2
0
0
1
2
1
1
0
0
0
2
1
0
1
0
2
2
1
0
1
0
0
0
0
1
0
0
0
0
0
2
1
0
1
0
0
0
0
2
0
0
0
0
0
1
2
0
0
1
2
1
0
1
1
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
3
1
0
0
0
0
1
2
0
2
0
2
1
0
0
2
0
2
1
0
0
0
0
0
0
1
0
0
2
0
0
1
1
0
2
2
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
2
0
2
1
1
1
0
0
0
0
0
0
1
0
2
0
0
2
0
1
0
1
1
2
0
0
0
0
0
0
1
0
1
0
1
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
2
0
0
0
2
0
1
0
1
2
0
0
0
1
0
1
1
1
0
2
0
0
1
0
1
2
2
0
1
0
0
0
0
0
0
0
2
0
0
2
2
0
0
1
2
1
2
0
2
4
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
2
0
0
0
1
2
0
0
0
0
2
1
0
0
2
0
0
2
1
0
1
0
2
2
1
5
1
1
2
0
0
0
2
0
1
0
2
1
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
2
0
1
0
1
0
0
2
0
1
0
2
1
1
1
0
1
2
1
2
2
0
2
0
0
2
0
0
0
2
2
2
0
0
2
1
0
1
2
2
2
0
0
0
1
0
2
3
0
1
0
1
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
3
1
0
0
0
0
1
1
1
0
0
0
2
0
2
0
0
2
0
2
0
0
0
0
1
0
0
1
1
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
2
1
0
2
0
2
2
0
1
2
0
1
1
3
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
1
1
0
0
2
0
1
0
0
1
2
3
0
0
0
2
1
1
1
0
0
0
0
2
0
2
0
1
0
2
0
0
0
2
0
1
0
1
2
0
1
2
0
0
1
0
0
0
2
1
0
2
2
1
0
0
0
2
0
0
2
2
0
2
0
0
0
0
0
0
2
2
0
0
1
0
1
2
1
2
1
0
0
1
2
3
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
2
0
0
1
0
2
0
0
1
0
0
1
2
1
2
0
1
0
1
0
0
0
0
1
0
0
1
1
2
0
1
0
1
1
0
0
0
0
1
1
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
1
3
1
1
0
0
1
0
0
0
0
1
1
2
0
2
1
0
1
2
2
1
0
0
1
0
1
0
0
1
1
1
0
1
2
2
0
0
0
2
1
1
2
1
3
0
2
0
1
2
0
0
0
2
0
0
2
1
1
1
1
0
1
0
0
3
0
1
1
0
0
0
2
1
1
1
0
1
1
0
0
2
1
2
0
0
0
0
2
0
0
2
1
0
0
0
0
2
2
1
1
1
0
0
0
0
0
0
0
2
1
0
0
2
0
1
1
0
0
0
0
0
0
1
0
1
0
2
0
0
2
0
1
0
0
0
2
1
1
0
0
0
1
1
0
0
0
0
2
0
0
4
0
0
0
1
1
1
2
2
1
1
0
0
2
0
1
0
0
2
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
3
1
0
0
0
2
1
1
0
0
0
2
0
1
0
2
0
0
0
2
0
0
2
0
2
2
2
0
1
1
0
0
0
2
0
0
1
3
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
2
1
1
0
1
1
0
2
1
0
0
1
0
2
0
1
1
2
0
2
2
1
2
0
0
0
0
0
1
0
2
0
0
2
2
0
0
1
2
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
2
0
0
3
0
0
1
0
0
2
0
0
2
1
0
0
3
0
0
1
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
2
1
0
0
2
2
0
1
2
1
1
2
0
1
0
0
0
1
3
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
1
1
0
0
0
1
1
0
2
0
0
0
0
1
2
2
0
1
1
1
0
0
1
0
0
0
2
2
0
2
2
2
0
1
1
0
1
0
0
0
0
0
2
0
2
3
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
2
2
2
0
1
0
1
1
0
0
2
2
0
1
2
0
1
1
0
0
0
1
0
1
1
0
2
0
2
1
0
1
0
0
0
2
1
0
0
1
2
0
0
0
0
0
1
2
2
0
2
0
1
1
1
2
2
0
0
0
0
0
0
1
2
2
0
2
1
0
0
1
0
2
0
1
0
0
0
1
0
0
0
0
2
2
0
2
1
2
1
2
0
2
0
2
0
1
0
0
0
0
0
2
1
0
2
0
2
2
0
0
0
2
0
0
2
0
2
0
0
1
1
0
1
1
0
1
1
2
1
0
1
0
2
0
1
0
0
0
2
1
0
0
1
0
0
2
1
1
0
1
1
2
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
2
1
2
0
1
0
0
1
2
0
0
0
0
1
0
1
1
0
0
0
1
0
2
0
0
2
2
1
0
2
2
0
0
0
0
0
1
0
1
2
0
0
2
0
2
1
2
0
1
2
1
0
0
2
2
1
0
1
0
1
2
1
0
1
3
2
0
1
2
1
2
0
0
2
2
1
0
1
0
1
0
0
1
2
1
0
2
1
1
1
0
0
0
1
0
2
0
0
0
0
0
0
1
0
2
0
2
0
0
3
0
0
3
2
0
0
0
0
0
2
1
0
0
0
0
0
2
2
2
0
0
2
1
0
1
0
0
0
0
2
1
2
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
1
2
2
1
2
1
0
2
0
0
0
2
0
7
0
1
2
0
1
1
0
0
1
0
0
0
2
1
2
0
2
0
0
0
1
2
2
1
1
0
0
1
1
1
0
0
0
1
2
0
2
1
0
4
0
0
0
0
1
0
0
2
2
0
1
2
2
0
0
2
0
1
0
0
1
0
0
1
0
0
2
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
2
1
2
2
0
2
0
0
2
1
0
0
0
0
2
2
1
1
0
1
1
0
1
0
0
2
2
0
1
1
0
0
0
2
0
2
0
1
2
1
0
1
0
0
1
0
0
1
0
0
2
0
2
0
0
0
1
0
1
0
0
2
1
2
0
0
1
1
0
0
1
0
0
1
1
1
1
1
0
0
2
0
3
0
0
1
0
0
0
0
1
2
0
0
2
1
0
0
0
5
1
2
0
0
0
0
0
1
0
2
2
4
3
0
2
0
0
0
2
0
0
2
0
0
2
0
1
2
2
0
2
0
2
1
1
1
1
1
0
2
1
0
0
0
0
1
0
1
0
1
0
0
1
2
1
0
1
0
0
1
0
0
0
0
2
1
2
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
2
3
0
0
2
1
0
0
0
1
0
0
1
2
0
0
0
0
3
2
0
2
0
0
1
0
1
0
2
1
0
0
0
1
0
2
0
1
1
1
2
0
0
0
1
0
1
0
2
0
0
0
0
2
1
0
1
0
1
2
0
1
1
2
3
1
0
0
0
2
0
1
2
0
0
0
1
2
0
0
1
2
0
0
0
0
1
0
1
0
0
0
2
2
0
0
1
1
1
0
1
0
2
0
0
1
0
2
2
1
0
0
0
1
0
0
0
0
0
0
1
0
1
2
0
0
0
2
0
1
0
0
0
1
1
0
0
2
0
0
1
2
2
2
1
0
0
1
2
0
0
1
0
0
1
0
0
1
1
0
0
0
2
0
0
1
0
1
1
1
2
0
0
1
0
2
1
0
1
2
0
3
1
0
1
0
0
2
0
0
2
2
0
0
0
1
0
2
0
1
1
0
0
0
0
0
0
0
0
1
1
1
2
0
2
0
0
0
0
0
3
2
2
0
0
0
1
0
0
0
2
2
0
2
0
0
0
1
2
1
0
2
1
0
1
2
0
0
0
1
0
0
0
0
0
0
1
0
0
2
1
0
1
0
0
2
2
1
2
0
0
2
0
0
0
0
0
1
0
1
1
1
0
0
0
2
0
1
0
0
2
0
0
0
0
2
1
0
0
1
1
2
0
0
0
1
1
0
0
2
1
2
0
1
0
2
2
2
0
0
0
0
0
3
1
0
0
1
1
0
1
0
1
0
0
0
1
0
2
0
0
0
1
1
1
0
0
0
1
2
0
1
2
2
0
0
1
2
1
0
0
0
0
2
0
0
2
0
1
3
0
0
2
2
1
1
1
1
0
2
2
0
2
0
2
1
1
0
2
0
0
0
2
1
0
0
0
0
3
2
0
2
0
0
0
2
2
2
3
2
0
0
1
0
0
1
2
1
0
1
0
2
0
0
0
2
2
1
0
0
0
1
0
2
0
0
2
1
2
1
1
0
0
1
0
2
0
1
0
1
1
0
2
0
2
1
2
2
0
1
1
1
2
1
0
0
0
2
0
0
2
1
0
1
0
0
1
2
2
2
2
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
3
1
0
0
1
0
0
0
1
2
1
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
4
1
0
0
2
0
0
2
0
1
0
2
1
0
1
2
0
0
2
0
0
0
1
2
0
1
1
0
1
1
1
1
0
2
1
0
1
2
1
1
2
0
0
1
0
2
2
0
1
0
1
1
0
0
1
0
1
1
1
0
0
1
0
2
0
1
0
2
1
0
1
2
1
1
2
0
0
2
0
0
1
1
2
0
0
1
1
2
2
1
2
0
2
2
0
1
0
2
0
1
3
0
2
0
0
1
2
1
0
2
0
1
0
0
1
2
1
2
2
0
0
0
1
1
0
0
0
0
0
2
1
0
2
3
0
0
0
2
1
0
2
0
0
0
2
1
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
1
0
0
1
1
1
0
2
0
0
3
2
0
0
0
1
2
0
1
0
0
0
2
0
0
2
0
0
5
0
0
2
0
3
2
0
1
0
0
1
0
0
0
0
0
1
0
0
1
3
0
0
0
1
1
1
2
2
2
2
0
0
0
1
1
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
2
0
0
1
0
2
0
0
0
2
0
1
2
1
0
0
1
0
0
2
0
0
1
0
0
0
2
1
0
0
0
0
2
0
2
1
2
0
0
0
2
0
0
2
1
0
1
1
0
1
0
0
0
0
2
0
0
0
1
2
2
0
0
1
1
1
0
0
0
0
1
0
0
2
2
1
0
0
0
0
1
0
0
0
2
2
1
0
0
0
2
1
0
2
1
0
2
1
0
2
0
2
0
1
0
2
1
0
0
1
0
1
0
1
0
0
2
1
0
0
0
0
2
1
0
0
0
0
1
1
0
0
0
0
2
0
0
0
1
1
0
0
0
2
2
2
2
1
0
0
0
0
0
1
0
1
0
2
1
1
0
1
0
1
2
1
1
0
0
0
2
0
1
3
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
1
0
0
1
2
0
0
1
1
2
1
1
1
2
0
0
2
0
2
0
0
0
2
1
1
0
0
0
0
0
1
2
0
2
0
0
0
1
2
0
1
1
2
0
0
0
0
0
0
1
2
1
1
0
1
1
0
0
0
0
0
1
0
2
0
0
1
1
0
0
1
0
0
1
0
1
2
0
2
0
2
0
1
1
1
0
0
1
1
2
0
1
0
1
0
2
0
1
2
0
0
0
0
1
1
0
2
0
0
0
0
0
0
2
0
1
2
1
2
0
1
1
2
0
0
0
2
0
1
1
2
0
0
0
0
1
0
0
0
2
1
1
0
2
0
0
0
1
0
0
0
1
0
0
2
1
1
1
0
4
3
0
1
1
0
0
0
2
2
1
0
1
0
0
1
2
2
0
2
0
1
2
0
2
0
1
1
2
2
1
1
0
0
0
3
1
1
0
0
1
0
0
0
1
0
0
2
0
0
1
0
0
3
0
2
1
2
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
1
1
0
2
1
1
2
0
0
0
1
0
0
1
1
2
1
1
0
1
1
0
1
1
1
0
1
0
1
0
0
0
0
2
0
1
2
1
0
0
0
2
0
0
0
0
1
3
0
0
1
1
0
0
2
1
0
0
1
1
1
1
1
1
1
2
0
1
4
0
0
2
1
0
0
1
1
0
2
2
0
0
3
0
0
0
0
1
1
0
2
0
0
0
2
0
0
3
0
0
1
0
2
1
2
0
2
0
1
2
0
2
0
0
1
2
0
0
1
1
0
0
2
1
1
0
1
1
3
0
2
2
0
2
2
2
2
0
0
0
1
0
0
2
0
0
0
1
1
0
0
2
0
2
2
1
0
1
2
3
0
0
0
1
0
0
0
2
0
1
0
0
0
2
0
1
3
1
0
0
2
0
1
0
2
0
1
0
0
0
1
0
0
0
0
1
2
1
0
1
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
2
2
1
0
2
1
0
0
1
0
1
1
2
0
2
1
0
2
0
2
0
0
0
0
0
0
0
0
0
2
1
1
0
1
2
1
2
1
4
2
0
1
1
0
1
0
1
2
0
2
0
1
0
1
0
1
0
0
0
0
1
2
0
0
1
0
0
2
0
0
1
0
1
2
0
1
0
0
0
0
0
0
0
0
0
1
0
2
2
2
0
2
0
0
0
1
1
1
1
1
1
2
0
1
0
1
1
0
0
1
1
0
2
0
0
0
2
0
2
1
0
0
0
1
1
0
1
1
2
1
0
0
0
0
0
1
2
2
0
0
0
1
1
0
0
0
0
1
1
1
0
1
3
1
0
0
0
0
0
1
1
0
0
2
0
0
0
0
1
0
1
0
0
0
0
1
0
2
0
2
0
1
0
0
0
0
2
0
0
6
0
0
2
0
1
1
2
0
0
0
1
3
0
0
0
1
1
0
2
1
0
2
0
0
1
0
2
0
1
0
0
1
1
2
1
0
2
0
0
0
0
0
1
1
0
0
1
0
0
0
0
2
0
1
0
2
0
0
0
1
1
0
1
2
0
2
0
3
0
0
0
0
2
1
0
0
0
0
1
1
0
0
1
1
2
2
2
1
1
0
0
0
1
2
0
0
0
3
1
0
0
0
0
0
0
0
1
0
3
0
0
0
2
1
0
1
0
2
0
1
0
0
2
0
2
0
1
0
2
0
1
2
0
0
0
0
2
2
2
0
1
0
0
0
0
0
0
2
2
1
0
2
0
0
0
0
2
2
0
1
0
1
1
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
1
1
0
1
0
0
0
0
1
1
0
1
0
0
2
2
0
1
0
1
2
2
0
0
0
1
1
2
2
1
0
1
0
1
2
0
1
2
1
1
1
2
1
1
2
0
0
2
0
2
0
1
0
2
3
1
0
0
1
2
1
0
0
0
0
0
1
0
0
1
2
0
1
0
0
0
2
1
0
1
0
0
1
0
0
0
0
2
0
2
0
0
1
0
1
0
2
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
2
4
0
2
0
0
0
0
2
3
1
1
0
0
2
2
0
0
0
0
3
1
0
0
0
0
1
1
0
0
1
1
0
0
0
0
2
0
0
0
2
0
0
2
0
0
1
2
0
0
1
0
0
0
0
1
2
0
1
1
0
0
3
0
2
2
0
0
1
0
0
0
1
0
0
2
0
1
1
0
1
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
1
1
0
0
1
1
1
1
0
1
2
2
2
1
2
1
0
1
0
2
0
1
0
1
1
1
2
0
1
0
0
0
1
0
0
2
0
1
0
1
2
0
0
0
0
0
1
1
0
2
1
0
1
1
1
0
1
1
2
0
0
2
0
0
4
1
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
2
1
2
2
2
0
1
1
0
0
1
0
0
0
0
2
1
0
2
1
0
1
2
1
1
0
0
1
1
0
2
2
2
2
1
2
1
0
0
0
1
2
0
2
2
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
2
2
0
0
2
0
0
0
1
0
0
0
3
2
0
1
0
0
0
2
0
2
0
1
2
0
2
2
0
0
0
1
0
0
2
2
0
0
1
1
2
1
0
1
0
0
2
1
1
0
1
0
2
2
1
1
1
2
1
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
2
1
0
2
0
2
1
0
0
0
0
3
0
1
1
1
0
0
0
3
2
0
0
2
0
0
0
0
0
0
2
1
1
2
0
0
0
0
1
2
2
0
3
0
0
0
0
1
0
0
1
0
2
1
1
1
0
0
2
0
2
1
2
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
1
1
2
2
0
2
2
1
1
0
2
0
0
0
0
0
1
0
1
0
1
2
0
0
0
2
0
0
1
0
0
1
2
0
0
2
0
1
0
1
0
1
3
0
1
1
0
0
0
1
0
0
2
0
0
1
1
0
1
2
2
0
1
0
1
1
1
0
2
2
0
1
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
2
0
2
1
0
0
1
0
2
0
3
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
1
0
0
0
1
0
0
1
0
0
2
1
2
0
1
0
1
0
0
1
1
0
0
2
1
1
0
1
2
0
2
0
0
0
2
0
1
2
0
1
1
0
0
0
0
1
0
0
1
2
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
1
2
1
0
1
0
1
1
0
0
0
0
0
0
1
1
0
2
0
2
0
1
1
0
1
0
1
0
1
0
2
0
0
1
0
2
2
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
1
2
0
1
0
1
0
0
1
2
1
0
2
0
0
0
0
2
1
0
0
0
2
0
0
1
2
1
0
3
0
0
0
1
0
0
0
1
1
1
0
1
1
0
1
1
0
1
0
0
0
2
2
2
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
2
2
2
2
0
2
1
2
1
0
1
0
1
2
1
1
0
0
1
1
2
0
2
2
0
0
1
2
1
1
0
0
1
0
0
1
1
0
0
2
1
2
2
0
0
0
0
0
2
0
0
1
0
1
0
4
0
2
1
1
1
1
1
2
2
0
0
3
2
1
0
0
0
0
1
2
0
2
1
0
3
1
0
0
0
1
0
0
0
2
0
1
2
0
0
0
2
0
0
1
1
0
0
0
1
1
2
3
2
1
1
0
1
1
2
1
0
0
0
0
0
0
2
0
3
4
3
0
0
3
1
1
1
0
0
0
0
2
1
0
1
2
0
1
0
0
1
2
0
2
1
1
0
1
0
0
3
0
1
0
1
3
1
0
2
0
2
0
0
0
2
0
0
2
1
1
1
1
3
0
0
0
0
1
2
1
1
2
2
5
2
0
0
2
0
2
1
1
2
0
1
0
0
1
0
0
2
0
0
1
1
0
1
2
0
0
2
3
0
0
1
0
0
0
2
3
0
1
0
0
1
0
0
2
1
1
2
1
1
3
0
1
1
0
0
0
0
0
0
1
0
2
0
0
0
0
1
1
3
1
0
0
2
2
0
1
2
0
0
2
0
0
2
1
0
0
2
2
1
0
0
0
1
1
2
0
2
2
0
1
2
0
0
2
2
0
2
1
2
0
0
0
0
2
0
0
3
0
1
2
0
0
0
2
0
1
1
0
1
0
0
3
1
1
0
2
0
2
0
0
1
0
1
1
0
2
2
2
2
0
0
0
1
2
1
1
2
0
2
0
2
5
1
1
0
0
0
0
0
0
2
0
1
0
3
0
2
0
0
2
1
0
1
0
2
1
1
0
0
2
0
0
1
0
1
1
0
0
1
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
1
1
2
1
1
0
1
2
1
0
0
2
0
1
0
2
0
0
0
0
0
2
1
0
1
1
1
1
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
1
2
2
0
0
1
0
3
0
2
0
1
0
2
0
2
0
0
2
0
2
0
0
1
0
0
0
1
0
2
0
0
0
0
1
1
0
0
0
0
2
1
0
0
0
0
2
0
1
1
0
0
1
1
0
3
0
1
0
0
1
0
2
0
0
1
0
0
0
1
0
1
2
0
0
2
0
0
0
1
0
0
0
1
0
1
0
0
2
0
0
0
0
1
0
0
0
2
1
0
0
1
0
1
0
2
1
0
0
0
0
1
0
0
2
1
0
0
1
1
2
2
1
0
1
1
2
0
2
0
2
0
0
1
1
1
2
0
1
0
0
1
2
2
0
0
2
1
1
0
1
2
0
0
1
0
1
0
0
3
0
3
0
1
1
0
1
2
0
0
0
2
0
0
0
1
1
0
2
1
1
0
1
1
0
0
1
0
2
0
0
0
0
2
0
2
0
2
0
0
0
0
0
1
0
2
0
0
0
2
1
0
0
2
2
1
0
1
1
1
1
0
0
1
1
0
1
0
2
2
0
0
2
1
1
0
1
0
0
0
2
0
0
2
1
0
1
1
0
1
0
1
2
0
1
0
1
0
1
0
2
1
2
3
0
0
2
0
2
0
2
0
0
1
0
2
0
0
0
1
1
2
0
1
0
0
0
2
0
2
2
1
0
0
1
2
0
0
0
1
1
1
1
0
1
0
0
0
0
0
1
2
0
2
1
1
1
0
2
2
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
1
0
0
1
0
0
0
2
0
0
1
2
0
1
0
2
0
0
0
2
0
0
0
1
0
0
1
0
0
1
1
1
1
1
0
2
1
0
0
1
0
0
2
1
0
2
0
2
1
0
1
2
0
0
2
2
0
0
1
0
1
1
0
0
0
1
1
0
0
0
0
2
0
1
1
0
0
1
1
2
1
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
2
2
0
0
1
1
0
0
0
0
0
1
3
2
0
1
1
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
1
1
2
1
0
2
2
1
1
0
0
0
0
0
0
0
0
1
1
0
2
1
1
1
0
2
0
0
1
2
0
0
0
0
2
0
2
0
1
2
0
1
0
0
1
0
1
1
1
0
1
0
2
0
1
0
0
2
0
2
4
2
2
0
0
0
2
2
2
0
3
0
0
0
1
0
1
2
0
0
2
0
0
0
0
0
1
1
0
0
0
2
1
0
0
0
0
2
1
0
0
1
0
1
0
2
0
3
1
0
0
0
1
0
0
0
1
2
1
0
0
2
1
0
0
0
1
2
0
1
0
2
0
1
1
2
2
0
0
0
0
0
2
0
0
1
2
0
1
0
0
0
0
0
2
0
0
1
2
0
0
1
1
0
0
0
2
0
1
0
0
1
1
2
2
0
0
0
0
1
1
1
0
1
0
1
1
2
2
0
3
2
0
0
0
2
0
2
0
0
0
2
1
0
1
1
0
2
0
0
0
2
1
1
0
1
0
1
0
0
0
2
1
1
1
1
0
0
1
1
0
0
0
0
4
0
0
1
0
0
0
0
0
0
1
2
0
0
1
0
1
0
2
1
1
0
0
0
6
2
1
0
1
0
1
0
1
0
0
0
0
0
1
0
1
2
0
0
0
1
0
0
2
1
0
1
0
2
1
0
2
2
1
0
2
0
1
1
0
2
1
0
0
0
1
0
2
2
0
0
2
1
0
1
3
0
2
0
2
2
0
2
0
2
2
0
1
2
2
0
0
2
2
0
0
1
2
2
2
0
0
0
0
1
0
2
1
0
0
1
0
1
0
0
1
0
1
0
1
1
1
1
0
2
1
2
0
2
0
1
0
2
2
0
1
2
1
1
2
2
2
1
0
0
0
1
0
2
0
0
3
0
0
0
0
0
0
1
0
2
1
1
0
0
0
0
0
2
1
2
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
2
3
0
2
2
1
0
0
1
4
2
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
2
1
2
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
1
2
1
2
0
0
0
0
1
1
0
1
2
0
2
2
0
0
1
0
0
0
1
2
2
1
0
0
0
0
1
2
0
1
0
0
0
1
1
0
0
0
0
1
0
2
2
0
1
0
0
0
0
8
0
1
2
2
1
0
0
1
0
1
1
0
0
2
0
0
0
0
1
1
2
1
1
0
0
2
0
2
0
0
2
4
0
0
0
2
2
0
2
1
0
0
1
0
1
0
1
0
0
0
1
0
0
1
1
1
0
1
1
0
1
0
0
0
2
0
0
0
2
0
0
1
1
0
1
0
3
0
0
2
0
0
2
2
0
1
2
0
0
4
1
1
2
0
0
0
2
2
0
2
0
2
0
0
0
0
0
2
0
2
0
0
1
0
0
1
1
1
0
0
0
2
0
0
0
1
1
0
0
0
2
1
2
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
1
0
1
1
2
2
2
2
0
2
1
0
0
0
1
1
2
0
0
0
1
1
0
1
0
1
2
1
0
2
2
0
0
1
0
1
0
0
1
2
1
1
0
0
0
1
2
0
1
0
0
0
0
1
0
0
0
1
1
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
1
2
1
0
1
0
2
1
2
0
1
0
0
0
1
1
0
1
0
2
2
0
0
1
2
0
0
2
0
1
0
1
0
0
2
1
1
1
3
0
0
0
0
0
0
0
2
4
1
2
2
2
2
0
0
2
1
1
1
0
0
0
0
0
2
2
1
0
0
0
0
0
0
2
0
2
0
0
0
2
0
1
0
2
1
0
0
2
2
1
0
0
0
1
2
0
0
0
2
0
0
2
1
0
0
1
0
1
0
2
2
1
0
0
0
0
0
0
2
0
1
2
2
2
0
0
0
0
0
2
1
1
2
1
1
0
0
0
1
0
0
0
2
0
0
1
0
2
0
0
0
3
2
1
0
2
0
0
0
2
0
1
0
2
0
0
1
0
1
2
0
0
4
0
1
1
0
0
0
2
1
0
0
0
1
0
2
1
2
0
1
0
0
0
0
1
0
2
1
1
0
0
0
0
7
0
0
0
0
2
2
0
0
0
0
0
2
1
0
2
2
2
0
1
0
0
0
0
1
1
2
1
1
2
1
2
0
0
1
0
0
0
2
0
1
0
0
0
2
2
0
0
0
1
2
2
1
1
0
1
0
0
1
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
2
0
2
4
0
0
0
2
0
2
2
1
1
0
0
0
0
0
0
2
1
1
0
0
2
1
0
0
1
0
0
0
0
4
0
0
1
1
2
0
0
0
1
0
0
5
0
0
0
0
1
2
2
0
1
0
2
2
0
0
0
1
0
0
0
0
0
2
2
1
0
0
0
0
1
1
0
1
0
1
1
0
0
0
1
0
1
0
0
0
2
0
2
0
0
0
1
1
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
1
2
1
0
0
0
2
0
0
1
0
0
1
1
2
0
1
0
2
0
0
1
0
0
0
2
2
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
2
0
1
0
1
1
0
2
1
0
1
2
0
0
0
0
0
0
2
0
1
2
0
1
1
2
2
0
1
1
0
0
4
0
0
0
1
0
1
2
0
1
2
0
0
2
0
1
0
3
0
0
0
3
2
1
0
2
0
0
2
1
1
2
0
0
0
0
1
0
1
0
2
0
0
2
0
0
1
1
0
0
0
0
2
0
2
0
3
0
0
2
0
0
0
1
2
2
2
2
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
1
2
1
0
1
0
1
2
2
0
0
1
0
0
3
0
1
0
3
2
0
0
2
1
0
2
1
0
0
0
0
2
2
1
0
0
1
2
1
0
0
2
0
0
0
0
0
1
0
0
1
2
1
0
1
1
1
0
0
0
0
0
1
0
0
1
2
0
0
1
2
1
1
0
1
0
1
0
0
0
2
1
0
0
0
0
0
1
0
0
0
1
1
0
0
2
0
2
0
1
2
0
0
1
0
2
0
1
1
1
1
0
0
1
0
1
0
1
0
0
1
0
1
1
0
2
1
2
0
2
1
0
0
0
1
0
2
0
0
0
1
0
0
1
0
1
0
0
0
2
2
1
1
0
0
2
0
0
1
0
1
1
0
0
2
0
0
0
0
0
0
1
2
3
2
0
0
2
0
0
2
0
0
0
0
2
2
0
1
2
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
2
0
1
1
1
0
1
0
0
2
1
2
0
1
1
2
0
0
0
0
2
0
6
0
2
1
0
0
2
0
1
2
3
0
1
0
1
1
0
0
1
2
0
0
2
0
2
1
1
0
2
0
1
0
0
1
2
1
0
0
1
0
0
2
2
0
0
0
0
0
0
0
1
2
0
0
1
1
1
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
1
2
0
1
0
2
0
0
0
0
0
0
2
1
0
1
0
1
1
0
1
1
1
1
0
1
0
0
0
1
2
2
0
0
1
0
1
0
0
1
0
1
0
1
0
0
3
0
0
0
2
2
0
0
0
2
1
0
1
2
0
0
0
2
0
2
1
2
0
1
2
0
1
1
0
0
0
3
2
1
2
0
0
0
0
3
1
2
1
1
0
1
1
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
1
2
1
1
0
2
2
2
1
0
2
1
3
0
0
1
2
2
3
0
0
2
1
0
1
1
0
0
0
2
2
1
2
0
3
2
0
1
0
0
0
1
0
0
2
0
0
1
1
1
0
1
2
2
2
2
0
4
0
1
0
0
0
0
1
1
0
0
0
1
0
2
0
0
0
1
2
0
0
0
2
0
0
1
1
0
1
1
1
1
2
0
1
0
3
2
2
0
0
1
2
0
0
1
0
0
0
0
0
1
0
0
0
3
0
1
2
2
2
1
0
1
2
0
1
1
0
0
0
0
0
1
2
0
2
0
2
0
0
1
0
3
0
0
2
0
1
1
1
2
1
0
0
0
1
2
0
0
0
2
0
0
0
2
0
2
0
3
1
2
0
1
0
1
0
2
0
0
0
0
0
0
0
2
0
0
2
1
1
0
2
0
0
0
0
0
1
0
2
3
1
0
2
1
0
3
0
2
0
2
0
0
1
2
2
0
0
0
0
2
0
0
1
0
0
1
0
2
2
0
0
2
1
2
2
0
0
0
0
0
1
2
0
1
1
1
3
0
3
0
1
0
0
0
0
2
0
0
2
2
0
0
1
2
0
0
1
1
1
0
1
1
1
2
0
1
1
2
1
0
1
1
0
0
1
0
2
1
0
1
2
2
1
0
0
2
1
0
0
0
2
0
1
0
2
1
1
0
2
0
0
0
1
2
1
3
0
1
1
0
0
0
1
0
1
1
1
2
1
1
2
0
1
0
1
1
0
2
0
0
2
1
1
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
3
2
2
0
2
0
1
0
0
0
0
0
0
2
0
1
1
0
1
1
0
1
0
2
2
0
0
2
1
1
2
2
0
2
1
5
0
0
0
2
1
0
0
0
0
1
0
0
0
3
1
2
0
1
0
0
0
0
2
1
1
2
0
0
0
1
0
0
0
1
1
0
2
0
1
0
2
0
1
0
1
0
1
2
1
1
1
2
1
1
1
2
0
2
0
0
0
2
2
2
2
0
0
0
0
1
0
2
0
2
2
0
0
2
1
2
0
2
0
1
0
2
0
1
0
1
0
0
0
0
3
2
1
1
0
0
2
2
0
1
1
1
0
0
0
1
0
0
3
0
0
2
2
1
0
0
0
1
0
1
1
0
0
2
0
1
1
0
1
0
0
1
4
1
0
0
0
0
0
0
0
2
2
2
1
0
2
0
2
2
1
1
1
1
2
0
1
1
0
0
1
0
1
1
5
1
2
0
1
2
1
0
0
1
0
1
1
1
0
0
1
0
0
1
0
1
0
2
2
0
0
1
0
2
0
3
0
2
0
0
1
3
1
1
0
0
0
0
0
2
0
0
0
1
2
0
1
0
2
2
2
0
2
0
1
0
2
1
0
0
0
0
0
1
1
0
0
2
1
0
1
0
0
1
0
0
1
6
2
0
0
2
2
0
2
0
0
1
0
2
0
1
0
2
0
2
1
0
0
0
1
0
2
0
2
0
1
2
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
2
0
1
2
1
1
1
2
1
0
1
0
3
0
0
1
0
1
0
0
0
1
1
1
0
0
2
0
1
0
2
0
2
2
0
0
0
2
2
4
0
1
2
0
0
0
2
0
2
1
0
2
1
2
0
0
2
0
0
0
1
0
0
2
0
0
2
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
1
2
2
0
0
0
1
2
0
1
1
0
0
1
0
0
2
1
1
1
0
2
3
0
0
1
0
2
0
0
1
0
1
1
1
0
1
0
0
0
1
0
0
0
1
1
0
0
1
2
1
2
2
1
1
2
0
0
0
1
1
1
1
1
2
0
0
0
1
0
2
0
1
0
0
0
0
1
2
0
0
0
0
0
2
1
1
0
2
0
0
0
1
0
0
3
1
1
2
0
0
1
1
1
2
0
0
0
2
2
1
1
0
2
0
0
3
2
2
1
2
0
0
0
0
1
2
0
0
1
3
1
1
1
0
1
1
1
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
1
0
2
2
0
2
1
0
1
1
0
2
0
1
0
0
0
0
0
0
2
0
0
1
2
0
2
2
0
0
0
0
0
2
2
0
0
0
2
0
2
0
2
1
0
2
1
2
0
0
1
0
0
1
0
1
2
0
2
0
0
0
2
2
0
0
0
0
1
2
2
0
2
0
0
0
1
0
0
1
1
0
2
0
0
0
0
0
1
3
0
0
0
2
0
1
2
2
2
0
0
0
1
1
1
0
0
0
0
0
0
1
1
2
0
0
0
0
2
4
0
1
0
1
7
0
2
1
0
0
1
0
1
1
0
0
0
2
1
0
0
1
0
2
0
0
0
2
0
1
0
1
0
3
2
0
1
0
2
0
1
0
3
1
0
0
2
0
0
0
1
1
0
0
2
1
0
0
0
2
2
0
0
0
2
0
1
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
2
1
3
0
0
2
0
2
0
0
0
1
0
0
1
0
0
1
1
0
1
0
1
1
0
0
1
1
2
0
0
0
2
0
0
1
0
1
0
0
2
1
1
0
0
0
2
1
0
0
2
2
0
2
0
2
1
1
2
0
2
0
0
2
0
1
0
3
0
1
0
1
2
0
1
0
0
0
0
1
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
2
0
1
0
0
0
0
0
0
2
0
0
1
0
0
2
0
1
2
0
0
1
0
0
1
0
0
0
1
1
1
2
2
0
1
3
0
0
2
0
2
0
0
0
1
2
0
2
1
0
0
2
2
0
0
1
0
1
0
1
1
1
0
1
1
2
1
2
2
5
1
1
0
0
1
0
0
1
1
3
1
1
1
0
1
1
1
0
1
0
1
0
1
1
0
2
0
0
1
0
0
2
0
2
0
2
1
1
1
2
1
1
1
1
2
1
2
0
0
1
0
0
0
1
2
0
0
0
0
0
3
1
0
0
1
0
0
0
2
0
2
0
2
1
2
2
0
0
0
0
2
0
2
1
0
0
1
0
1
0
0
1
0
0
2
0
0
1
1
0
2
0
0
1
0
0
0
1
1
0
0
1
2
0
2
1
1
1
0
1
0
0
1
0
0
0
3
0
2
0
0
2
0
0
0
1
0
2
2
1
0
2
1
3
1
0
1
1
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
2
2
0
1
2
1
1
1
2
2
0
0
2
1
1
1
2
0
0
0
0
1
2
0
0
2
1
2
1
1
0
0
6
0
0
0
0
0
0
2
2
0
0
2
0
1
0
1
0
0
2
1
0
1
2
2
0
0
0
0
0
0
0
0
1
2
0
2
0
0
1
0
0
0
0
3
1
0
2
1
0
0
1
1
1
1
1
3
0
1
0
0
0
0
0
2
0
2
0
2
2
0
1
2
0
1
1
0
1
0
1
1
1
1
2
1
0
1
1
1
2
0
0
0
0
1
1
0
0
1
0
1
0
0
1
2
1
1
0
0
1
0
1
1
0
2
2
1
0
2
1
2
0
0
1
2
0
0
2
0
1
1
1
1
1
2
0
1
2
2
0
1
1
1
1
3
0
1
0
0
1
1
0
2
0
0
0
0
1
1
0
2
2
0
0
0
0
1
1
1
2
2
0
1
2
0
1
0
0
1
1
0
1
1
2
2
0
1
1
0
1
1
0
3
1
0
1
0
0
0
1
0
0
2
0
0
0
2
0
1
1
0
1
2
0
0
2
2
1
2
0
0
1
0
0
1
2
1
0
0
1
1
1
0
2
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
1
1
0
1
2
1
2
0
0
0
1
0
2
0
0
0
0
0
0
2
0
2
1
1
0
16
0
0
0
1
0
0
1
2
0
2
1
3
1
2
1
0
0
1
0
1
1
2
0
0
0
0
2
0
0
2
0
0
0
1
0
0
1
4
1
2
1
0
0
2
0
2
0
0
1
2
0
0
1
2
1
1
0
1
2
0
2
0
0
3
2
1
1
0
1
2
1
1
2
1
0
0
0
3
2
0
0
1
0
0
1
0
0
2
1
0
0
0
1
0
0
0
0
0
1
1
1
0
1
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
2
1
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
1
0
0
1
2
2
0
0
0
1
0
0
2
1
0
3
0
2
0
0
0
2
2
0
1
1
1
0
0
0
0
7
2
0
1
2
3
0
1
0
1
1
0
1
3
0
1
0
1
2
1
3
0
0
1
1
0
0
2
0
3
0
0
0
0
0
1
2
0
0
1
0
1
2
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
2
2
1
0
0
3
0
0
1
2
0
1
0
0
2
0
1
0
2
2
0
0
2
1
0
0
1
1
2
0
0
0
0
0
0
0
1
2
1
0
0
0
1
0
0
1
0
0
1
1
0
0
0
2
0
0
0
0
7
0
2
0
0
2
0
0
0
0
1
1
0
2
0
0
0
2
1
0
1
1
1
0
2
0
4
1
2
0
1
0
3
1
0
1
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
1
5
2
0
0
1
2
1
0
1
0
0
2
1
3
1
1
0
0
0
0
0
2
2
1
1
1
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
1
1
2
0
0
1
0
1
0
2
0
3
1
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
3
1
0
1
0
2
0
1
1
2
1
2
0
1
0
1
1
0
1
1
1
0
0
3
0
0
0
0
1
1
1
0
1
1
2
0
0
0
1
0
1
0
1
0
2
1
0
0
0
2
0
0
0
2
2
2
0
2
1
2
2
0
1
0
0
2
1
0
1
0
0
0
1
0
0
1
1
2
1
1
0
0
0
0
2
0
0
2
0
1
1
0
0
0
1
2
0
1
0
1
0
0
0
2
0
0
1
0
1
1
0
4
2
0
0
0
1
1
1
0
0
0
1
2
0
0
3
0
0
0
1
2
0
1
0
0
0
0
1
1
3
0
2
0
0
1
2
0
0
1
0
1
2
1
2
1
2
0
2
2
0
0
0
1
0
3
0
0
1
0
2
0
0
0
1
0
2
1
1
0
2
0
1
0
1
0
0
2
1
2
2
2
0
0
0
2
0
0
0
1
0
2
1
0
0
0
0
1
2
0
0
2
0
0
1
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
1
1
0
0
2
0
0
1
0
2
0
0
0
0
1
1
0
0
0
0
0
0
1
0
2
2
0
2
0
1
0
0
1
3
0
1
0
0
0
0
1
0
3
2
1
2
0
1
0
1
0
1
2
1
2
2
0
0
0
0
2
0
0
0
1
1
2
0
1
0
0
1
0
0
1
0
2
2
2
0
0
0
1
0
1
0
2
1
0
2
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
2
0
1
0
1
2
0
0
0
1
0
1
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
1
0
3
2
1
2
0
0
1
0
2
0
0
0
2
0
1
0
0
0
0
0
2
0
0
1
0
1
2
0
1
0
0
2
1
0
0
2
0
0
1
1
0
2
1
0
0
0
2
0
0
2
0
0
1
0
0
2
0
2
1
0
0
0
1
0
0
2
0
0
0
0
0
3
0
0
2
0
0
0
2
1
0
1
0
0
1
0
1
0
0
2
2
2
0
0
1
0
0
1
0
1
0
1
0
0
0
1
2
0
1
0
2
0
0
1
2
0
1
0
0
1
4
2
1
1
12
2
0
1
0
0
0
0
1
1
0
1
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
1
0
0
2
0
0
0
0
0
0
1
2
2
1
1
2
2
1
0
0
2
1
1
0
0
0
2
0
2
0
1
0
1
1
2
0
1
0
2
0
0
0
4
0
1
1
2
1
2
0
0
0
0
0
2
0
1
1
2
0
1
0
0
0
0
1
0
0
2
0
0
0
1
2
1
0
0
1
0
2
2
2
2
1
0
0
1
2
1
0
0
0
0
1
0
0
0
1
0
2
2
0
1
1
0
0
0
1
0
0
0
1
0
0
0
1
2
1
1
0
0
0
0
2
0
1
0
0
0
0
0
0
1
2
0
0
0
3
0
0
1
2
3
0
0
2
1
0
1
3
3
2
0
0
0
0
2
0
0
1
1
1
1
3
2
1
1
0
2
0
0
1
0
0
2
1
2
1
0
0
0
2
1
0
2
0
0
1
3
0
1
2
2
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
2
0
0
1
2
0
0
1
0
1
0
0
1
1
2
0
0
0
2
2
0
2
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
2
0
1
0
3
2
0
1
0
2
0
0
1
0
0
0
0
0
2
2
0
1
2
2
0
2
0
0
1
0
0
0
1
2
0
0
2
0
2
0
2
0
0
1
2
2
0
0
2
3
1
0
2
1
0
1
1
2
1
0
1
0
1
1
0
0
1
1
2
0
2
1
0
0
0
2
0
0
0
0
0
3
0
0
2
1
0
1
2
2
0
0
2
0
0
0
0
2
2
1
1
2
0
0
0
0
0
0
0
2
1
0
2
0
1
1
2
0
1
0
2
1
0
1
2
1
0
0
0
1
2
2
1
1
0
0
0
0
2
2
1
0
0
3
0
0
1
2
0
1
1
0
0
3
1
0
0
1
0
1
1
2
0
0
1
1
0
0
0
1
0
2
1
0
2
2
1
1
0
0
0
1
1
0
2
2
0
1
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
1
1
2
1
2
0
1
2
0
0
0
0
1
1
1
1
2
1
1
2
1
0
0
1
1
0
0
0
0
1
2
2
2
1
2
1
2
2
3
1
1
0
2
0
0
1
2
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
2
2
1
2
0
0
2
2
1
2
0
0
2
0
0
0
0
1
2
2
2
0
2
0
1
2
0
0
0
1
2
0
0
1
0
1
0
0
1
0
1
1
0
0
0
2
1
2
0
0
1
1
0
2
0
1
0
0
0
2
6
2
0
0
1
0
1
0
0
3
0
0
0
0
0
0
0
1
1
2
1
3
0
1
1
0
1
1
0
3
0
2
0
0
0
2
0
0
0
1
0
0
2
0
1
0
0
0
1
0
3
1
0
1
0
1
1
0
0
0
0
1
2
0
0
0
1
0
0
2
0
2
2
0
5
1
3
0
1
0
0
1
0
0
1
1
0
3
0
0
0
0
0
1
2
0
0
0
0
0
2
2
1
2
0
0
1
1
0
1
2
0
1
0
0
2
0
2
0
0
2
0
0
0
0
1
0
0
0
1
0
1
1
2
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
1
2
2
2
0
2
0
1
1
1
1
1
0
0
2
0
0
0
0
1
1
2
2
0
0
1
1
0
0
0
0
0
1
1
0
0
2
1
2
1
1
2
0
0
0
0
4
1
0
0
1
2
1
0
1
2
0
1
0
0
0
0
2
2
0
0
2
1
1
1
2
2
2
2
0
0
1
0
2
0
0
2
0
0
1
1
1
0
0
0
0
0
1
0
3
1
2
0
0
2
1
0
0
0
0
1
0
2
0
1
1
0
0
0
1
0
0
2
0
3
1
1
0
0
0
1
1
0
2
0
1
0
2
0
0
2
2
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
1
2
2
1
0
2
0
2
0
1
0
0
0
0
0
0
0
0
1
0
1
2
3
0
2
4
0
2
0
2
2
0
2
1
2
0
1
1
0
0
1
1
1
0
1
0
0
0
0
1
0
3
0
1
0
0
1
0
0
1
1
0
0
0
2
1
1
0
0
2
0
0
0
2
0
0
0
1
2
1
0
0
0
1
1
0
0
1
0
1
1
0
0
0
0
0
1
0
1
0
0
1
1
3
0
0
1
3
3
0
0
2
1
0
0
0
1
0
0
2
0
1
0
1
2
2
1
0
1
0
0
0
0
0
1
2
0
1
1
1
0
1
0
2
1
0
2
0
0
0
1
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
1
2
0
2
0
0
1
1
0
1
1
1
0
0
0
0
0
0
1
0
0
0
1
2
0
1
0
1
2
1
2
1
0
0
0
0
1
5
0
0
1
1
0
0
2
1
1
0
2
0
1
1
0
2
0
2
0
1
0
1
0
0
1
1
2
0
0
3
1
2
2
1
1
1
2
2
0
2
2
0
0
1
2
0
0
2
0
2
2
2
0
0
2
2
2
0
0
0
1
1
1
0
2
1
0
0
2
0
1
0
0
0
0
0
0
1
1
1
1
0
1
0
0
0
0
0
1
0
1
1
0
2
0
0
1
2
1
0
0
2
2
1
2
0
0
0
1
0
1
1
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
1
4
0
0
0
2
2
2
1
2
0
0
0
0
2
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
1
1
2
0
0
0
2
0
1
2
1
0
0
0
0
1
2
1
0
1
0
2
1
0
1
2
0
0
1
1
2
0
1
1
0
1
2
2
0
2
0
1
0
1
0
0
0
1
1
1
0
0
0
0
1
0
1
0
0
2
0
1
0
2
0
1
0
0
1
0
1
1
0
0
2
0
0
0
0
1
0
2
1
2
2
2
0
1
0
0
0
0
0
0
1
1
1
7
0
0
1
0
1
1
0
0
3
0
0
0
0
0
0
0
0
0
1
0
3
0
1
2
2
0
2
1
2
0
1
0
2
0
2
0
1
1
0
1
2
1
0
0
0
0
2
0
0
1
1
0
0
2
1
0
1
1
0
0
1
0
2
1
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
2
3
0
0
0
0
2
1
1
1
0
1
0
1
1
1
2
0
0
2
0
1
0
0
2
0
0
0
2
0
1
0
1
2
1
0
2
0
0
2
0
0
1
2
0
2
1
0
0
0
2
1
0
0
1
0
0
3
0
1
0
0
1
0
0
1
0
2
1
1
1
0
0
1
1
0
1
0
0
0
0
4
1
0
3
0
0
1
1
1
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
2
2
1
1
0
0
1
2
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
2
0
2
0
0
0
0
2
0
1
2
0
0
2
0
2
1
0
2
0
2
0
1
2
0
0
0
0
1
0
2
2
0
1
0
0
1
1
0
0
0
1
2
0
0
1
0
0
2
0
0
1
0
2
1
1
0
0
0
0
2
1
0
0
1
2
2
0
0
1
0
1
1
1
0
2
0
0
0
2
0
1
0
0
0
1
2
2
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
2
0
1
1
0
0
0
1
1
0
2
0
0
0
1
0
2
0
0
1
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
1
1
0
2
2
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
2
1
2
1
1
2
0
2
1
2
2
0
0
1
2
0
0
1
0
0
0
1
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
2
0
1
2
0
0
1
1
1
0
0
0
4
1
0
2
2
0
0
3
2
0
0
1
0
2
0
0
0
0
0
1
2
1
0
0
0
2
1
0
0
2
0
1
0
0
0
1
0
1
1
1
0
0
2
2
1
0
1
0
0
0
1
2
2
0
2
0
0
1
0
2
0
0
0
0
2
0
4
0
2
0
2
1
1
1
1
0
1
2
1
0
0
1
0
0
0
2
2
0
0
2
0
1
0
2
1
1
0
0
0
0
0
3
0
0
0
0
1
1
1
1
0
0
2
0
2
1
3
0
0
0
0
1
0
0
1
0
0
1
0
2
3
2
0
2
2
3
3
2
2
1
1
1
2
1
0
0
0
2
0
1
2
0
0
0
1
0
0
0
0
0
1
1
0
0
1
1
1
2
1
0
0
0
1
0
0
0
0
0
0
2
0
6
1
1
1
0
1
1
2
2
0
0
1
1
0
2
2
1
0
1
0
2
0
3
0
0
1
0
0
2
0
1
0
0
2
0
0
0
6
0
0
1
1
0
0
0
0
0
0
1
1
0
1
0
2
1
0
1
2
0
0
3
1
1
0
0
0
0
2
0
0
0
1
2
2
0
0
0
0
0
0
0
0
1
0
0
2
1
1
0
0
0
1
0
2
1
0
0
2
0
2
2
0
2
2
1
2
1
0
1
0
1
2
0
2
0
0
0
0
0
0
1
0
2
2
0
0
0
1
1
2
0
0
0
2
0
0
1
0
1
0
0
1
0
1
2
1
0
0
1
0
1
1
0
2
0
1
1
0
0
1
0
0
2
1
2
0
1
2
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
2
1
0
1
0
1
0
0
0
0
0
0
1
0
0
2
0
1
0
0
2
2
0
1
0
0
1
2
0
0
2
1
2
2
1
0
0
2
1
1
0
1
1
0
0
0
0
1
0
0
0
1
0
0
2
0
2
0
1
0
2
0
1
0
0
0
3
0
0
2
2
0
0
2
2
0
0
2
1
1
1
0
0
2
2
0
0
1
0
1
1
1
2
0
0
0
1
0
0
2
2
0
0
1
0
1
1
2
0
1
1
0
3
0
0
1
0
0
1
0
0
0
1
0
2
1
2
0
1
0
0
1
1
0
0
0
0
0
2
1
0
2
1
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
1
2
0
0
0
2
2
0
0
0
2
2
1
0
3
0
0
0
1
2
0
1
0
0
1
2
0
1
0
0
0
1
0
1
0
1
0
2
0
0
0
0
2
0
0
0
1
7
1
0
1
0
0
0
0
0
1
0
1
1
2
0
0
2
0
0
0
2
2
0
1
1
0
0
0
2
1
2
0
2
0
0
2
0
2
3
0
0
0
2
0
2
0
2
0
1
1
0
0
1
2
0
1
1
0
2
1
0
0
0
0
5
0
1
0
0
1
0
1
0
2
0
2
0
0
1
1
1
0
2
1
1
0
2
1
0
0
2
0
0
1
2
0
2
0
0
0
1
0
0
1
0
2
0
2
0
2
2
0
0
0
0
2
1
0
2
3
1
2
2
0
1
0
1
0
1
0
1
0
0
2
2
1
0
0
0
0
1
1
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
3
1
0
0
0
1
0
0
0
0
0
0
2
2
2
0
1
1
0
1
1
0
4
1
2
1
0
0
2
0
0
0
2
3
0
1
0
0
2
1
1
2
0
0
0
2
1
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
1
1
1
1
1
1
0
0
0
1
1
2
1
0
0
0
0
2
2
2
1
0
0
0
0
1
2
2
0
0
1
1
0
0
2
0
0
1
2
2
1
1
0
0
0
1
0
0
0
0
1
2
0
2
1
0
2
0
0
0
2
1
0
0
2
0
0
1
1
0
3
0
0
0
0
1
2
0
0
2
0
0
0
1
2
0
1
1
0
0
2
1
0
0
0
2
0
0
0
1
3
4
0
0
0
0
1
1
1
0
1
0
1
0
2
1
2
0
0
0
0
2
2
0
1
0
0
1
1
0
1
0
2
0
1
0
0
1
0
1
0
2
0
2
2
0
0
0
2
1
0
1
0
2
0
0
1
0
0
1
0
0
3
2
3
0
2
0
1
0
1
0
0
2
0
0
1
0
2
0
0
0
0
1
0
2
1
1
1
1
0
0
1
2
3
1
1
0
1
0
0
0
1
1
0
1
2
2
1
0
0
1
1
0
0
0
1
2
1
0
2
0
2
0
0
0
0
0
0
0
0
0
3
1
1
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
1
0
0
0
1
0
1
2
3
0
0
0
0
0
0
2
0
0
1
3
0
0
1
0
0
0
2
2
0
1
0
0
2
1
0
1
2
1
0
1
1
0
6
2
0
1
1
0
0
2
2
2
0
0
0
1
0
0
1
2
0
0
2
1
1
0
2
0
2
0
2
1
2
1
0
1
0
1
0
0
1
0
0
0
0
2
0
0
2
0
0
0
1
0
2
1
0
0
2
1
0
0
2
1
0
0
1
1
0
0
0
2
0
1
0
0
1
1
0
0
2
0
0
2
2
1
0
1
1
0
2
0
0
0
0
0
2
1
1
0
0
0
0
1
2
0
2
0
2
0
0
2
0
0
2
1
1
0
2
0
2
2
0
2
0
1
1
0
1
0
2
1
1
0
1
1
2
0
0
0
1
0
2
0
0
1
0
0
2
2
0
1
3
0
1
0
2
2
0
0
1
1
0
0
0
2
2
0
2
0
1
1
1
1
0
0
1
0
1
1
1
0
0
0
0
0
2
2
1
0
0
0
1
1
0
0
0
1
2
0
1
2
0
0
0
2
1
0
0
0
2
0
1
0
1
0
1
1
0
0
0
0
0
2
2
1
0
0
2
1
1
2
1
0
0
0
0
1
0
0
2
1
2
1
2
1
1
0
0
1
2
0
2
2
1
2
1
1
2
0
1
0
2
1
1
0
0
1
1
2
1
2
0
1
0
1
1
0
1
0
0
1
0
0
1
0
1
0
1
1
0
0
0
1
0
0
0
0
1
0
1
2
0
0
1
1
1
0
1
2
2
0
1
0
2
0
0
0
0
0
2
2
0
2
2
0
0
0
0
0
0
0
2
2
2
1
0
0
4
1
0
0
0
0
2
0
0
0
1
2
2
1
1
1
1
0
1
0
0
1
0
2
0
3
2
0
0
0
0
1
1
2
0
0
0
1
0
0
0
1
2
1
1
0
1
0
2
0
2
1
0
0
0
1
1
1
1
0
1
0
2
0
1
2
1
0
0
0
2
1
2
0
1
0
0
1
1
0
0
2
2
1
2
1
1
0
0
0
2
2
1
1
1
0
0
0
0
0
1
0
1
0
2
0
1
2
2
0
0
0
0
0
0
0
2
1
0
0
2
0
2
1
1
0
0
1
1
0
2
0
1
0
0
0
0
0
1
5
1
0
0
0
0
1
0
0
2
0
1
1
2
0
1
1
0
0
0
0
2
1
0
0
0
1
0
0
2
1
4
0
1
0
1
0
0
0
0
0
0
0
1
3
0
0
0
0
1
0
0
0
0
2
2
1
0
0
1
0
1
0
0
2
0
1
1
0
1
1
1
0
2
0
1
0
1
0
1
0
2
2
2
0
1
1
1
0
0
1
0
0
1
0
1
1
1
1
0
1
1
1
1
0
1
1
2
1
1
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
2
2
1
0
1
0
2
1
0
6
0
0
0
0
1
2
1
2
0
2
0
1
0
0
2
1
0
1
0
0
1
0
0
1
2
0
0
0
2
0
0
1
1
0
1
1
0
1
2
0
2
1
0
0
0
0
0
0
0
2
1
0
0
0
1
1
2
0
0
0
0
0
0
2
1
1
1
0
0
0
0
2
0
2
2
3
0
0
1
0
1
0
0
1
0
2
2
1
1
0
1
1
2
0
0
1
0
0
0
1
1
2
1
2
0
2
1
2
1
0
0
1
2
0
0
2
0
0
0
3
1
2
0
0
2
0
0
2
0
1
1
0
1
1
0
1
3
0
0
2
0
2
1
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
2
1
1
1
0
1
0
0
0
1
0
2
0
0
2
1
0
1
0
0
1
0
0
0
1
2
0
0
1
1
0
0
0
0
2
1
1
0
1
0
1
0
1
1
0
0
2
1
13
0
1
1
0
1
0
1
0
2
0
0
0
1
2
1
0
1
0
0
0
0
2
0
2
0
2
0
2
0
0
0
0
2
0
1
1
1
2
0
1
0
0
0
0
0
0
1
1
0
1
0
0
2
2
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
2
0
2
2
0
0
1
0
2
0
1
1
0
0
1
0
0
2
0
1
0
1
1
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
3
2
0
0
2
0
1
2
2
0
0
0
1
0
0
3
1
0
1
0
0
2
0
0
0
0
1
0
0
1
0
0
0
1
2
1
0
0
1
1
2
0
0
1
1
0
0
0
2
2
0
0
0
0
0
1
1
0
0
0
2
2
0
1
2
0
1
2
1
1
7
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
2
0
2
2
0
1
2
0
1
1
1
0
1
0
0
1
0
2
0
2
1
1
2
0
0
2
0
0
0
1
0
0
1
2
3
2
1
1
0
0
0
0
1
0
2
1
0
1
1
0
0
2
0
0
1
2
1
0
0
0
0
1
0
0
1
2
2
1
0
0
2
0
6
0
0
0
0
1
0
0
2
0
0
0
0
2
1
0
2
0
0
0
1
1
0
1
2
0
2
0
0
1
2
1
1
0
1
2
1
1
2
3
3
0
0
0
0
2
2
2
1
0
0
0
0
0
0
2
4
2
2
2
0
0
1
0
1
2
0
0
0
0
0
0
2
1
0
0
4
2
0
0
0
0
0
0
0
1
2
0
2
0
0
0
1
0
2
0
1
1
1
0
0
0
1
2
0
0
2
0
0
0
1
0
0
0
1
0
2
1
1
0
0
0
0
0
0
0
1
1
2
2
1
2
0
0
0
0
0
2
0
0
1
0
1
1
2
1
2
2
0
1
0
0
1
0
1
0
0
2
0
0
0
0
2
0
2
1
0
1
0
0
0
2
1
2
1
0
0
1
0
3
0
1
1
0
0
0
2
0
2
2
0
0
0
0
0
0
2
4
2
0
2
0
0
1
0
0
2
2
0
1
2
0
1
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
2
0
1
0
0
0
0
1
0
1
0
3
0
2
2
1
1
1
0
1
0
2
0
2
1
2
0
1
2
2
0
1
1
0
0
1
0
0
2
0
0
0
1
0
0
1
1
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
2
1
1
0
0
0
0
0
0
0
1
1
0
0
1
2
0
0
1
2
1
1
0
1
3
0
0
0
0
1
0
0
0
2
1
2
0
0
0
0
2
0
0
0
0
2
0
1
0
2
0
2
2
0
0
0
0
0
1
0
2
1
0
0
2
0
0
1
1
2
1
1
0
0
2
0
0
1
1
1
2
1
2
1
3
0
0
0
1
0
0
0
1
0
2
0
0
1
0
0
1
1
0
0
2
1
0
1
1
1
0
1
1
1
1
0
0
1
1
2
2
0
0
0
1
1
0
0
0
0
0
0
2
2
1
2
0
0
0
1
0
0
1
0
0
0
2
1
0
0
0
1
2
2
0
1
0
0
2
0
0
0
1
0
0
2
0
1
1
0
0
2
1
0
1
0
1
0
2
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
2
1
0
1
2
0
1
0
2
1
0
0
3
2
1
1
0
1
0
1
0
2
1
2
0
1
2
2
2
0
2
0
0
0
1
1
0
2
0
2
0
0
2
2
0
0
0
0
0
3
2
1
2
0
1
1
2
1
1
0
1
2
0
0
0
1
0
0
1
0
0
0
2
2
2
1
0
0
2
0
1
1
0
0
0
1
2
2
1
0
0
0
1
2
0
0
1
1
2
2
2
2
2
0
1
1
0
0
0
0
0
0
0
1
0
1
0
2
1
0
0
1
1
2
0
1
0
2
1
2
2
10
0
0
1
0
0
2
0
0
0
0
0
2
1
3
2
0
2
2
0
1
1
0
2
0
2
0
0
2
2
1
2
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
1
0
1
0
1
1
0
0
1
2
0
0
0
2
1
2
1
1
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
2
1
1
1
0
0
0
0
0
0
1
1
2
0
1
0
0
0
1
1
1
0
2
1
0
2
2
3
1
2
0
0
0
0
0
1
2
1
0
0
1
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
3
0
0
0
1
0
0
1
2
0
1
0
0
0
2
0
0
0
0
1
3
2
1
2
0
1
1
2
0
1
0
3
0
2
2
2
0
0
0
0
2
0
0
1
0
2
2
0
0
1
0
0
0
1
0
0
0
2
3
1
0
0
0
2
2
0
0
0
0
0
2
0
0
2
1
1
0
0
1
0
2
0
1
3
0
0
1
0
1
0
1
1
1
0
2
0
0
0
1
2
2
0
0
0
3
0
1
0
0
1
0
0
0
2
1
0
0
0
0
1
0
0
1
0
0
0
0
1
2
1
2
0
0
1
0
0
5
0
0
0
0
0
0
1
0
0
2
0
0
0
2
2
0
1
0
0
2
0
1
1
0
1
4
0
2
0
1
0
0
0
1
2
1
2
0
0
0
1
2
2
1
1
0
0
2
1
0
0
0
0
0
0
2
2
1
0
0
0
1
0
0
1
1
2
2
1
1
1
0
2
2
0
0
1
0
0
2
1
2
2
0
1
0
2
0
0
0
1
2
0
0
0
0
0
1
2
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
1
2
0
0
0
1
0
0
0
2
1
1
1
1
0
2
0
0
1
0
0
0
2
0
0
0
1
0
0
1
0
1
2
1
2
0
1
1
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
1
2
2
2
0
0
0
0
0
1
1
0
0
2
1
1
0
0
0
0
0
1
1
0
0
0
1
1
0
0
1
1
0
1
0
0
1
0
1
1
0
0
0
1
1
2
0
0
2
2
0
1
0
1
0
0
0
2
1
0
0
0
1
0
0
0
0
4
0
0
0
1
0
2
0
1
2
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
2
2
0
2
0
0
1
2
1
0
1
0
0
1
1
2
0
1
2
0
0
2
3
0
2
3
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
2
0
4
1
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
1
2
1
0
0
2
1
0
0
2
0
0
2
1
0
0
0
2
0
0
0
0
0
0
3
0
1
0
0
0
0
1
0
2
0
0
0
2
1
1
0
2
0
0
0
2
0
1
0
0
0
0
1
1
2
2
7
0
0
0
1
0
0
2
1
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
2
2
1
2
0
0
0
1
0
2
1
0
2
0
0
0
2
0
2
0
0
0
2
0
1
0
1
0
0
1
0
0
0
0
1
0
1
1
0
2
2
1
2
1
1
0
0
3
2
1
0
1
0
1
0
0
1
0
0
2
1
0
0
1
0
0
2
0
1
0
0
0
0
0
2
1
1
1
0
0
2
0
0
2
0
1
0
1
0
0
0
0
2
0
0
0
1
1
1
1
0
0
0
2
1
0
2
2
0
2
1
1
0
2
4
0
0
0
0
1
0
1
1
0
0
0
1
1
1
0
1
1
1
0
0
0
3
0
2
2
0
0
0
1
3
2
1
0
0
0
0
0
0
0
2
1
1
1
0
0
2
0
1
1
1
0
0
3
1
1
0
0
3
0
0
2
0
3
0
0
4
0
0
1
1
1
0
0
1
0
0
0
0
2
3
1
0
0
0
1
0
2
1
1
1
0
0
1
2
0
0
0
0
0
2
1
2
0
0
2
3
0
2
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
2
2
0
0
0
2
1
0
2
0
0
1
1
0
0
1
1
1
0
1
0
0
0
0
1
0
0
2
0
0
1
0
1
0
2
2
1
0
0
1
0
1
1
0
1
1
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
2
0
1
1
0
0
1
0
0
0
1
0
0
0
0
1
1
1
2
1
0
0
0
1
1
0
3
2
0
2
1
2
1
2
0
0
1
0
0
1
1
1
0
0
2
3
1
1
0
1
1
0
0
1
1
0
0
2
1
0
0
0
2
0
1
0
0
0
0
0
1
1
0
0
2
1
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
1
2
3
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
1
1
0
0
0
0
1
1
0
2
1
0
1
2
0
1
0
0
0
0
1
0
0
2
0
2
1
0
1
2
0
1
1
1
2
1
0
0
0
0
2
0
0
2
0
1
0
2
0
1
1
0
0
1
2
1
0
0
1
2
1
3
2
2
2
0
0
1
0
0
2
0
0
2
0
0
0
0
2
2
1
1
0
1
0
0
2
0
0
2
2
2
0
1
0
0
1
0
0
2
2
0
0
0
5
0
2
0
2
3
0
0
0
0
0
2
2
0
2
1
0
1
0
0
1
0
2
0
1
0
0
0
2
2
0
2
2
0
0
0
1
1
0
2
1
0
0
1
2
1
0
1
0
0
0
2
1
0
0
0
2
2
0
1
1
2
1
0
1
2
0
0
1
0
0
0
0
1
0
1
2
2
1
0
1
1
0
2
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
2
1
0
0
0
0
1
1
2
2
0
1
1
0
2
0
2
0
2
0
3
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
2
1
0
2
0
2
1
1
2
1
1
0
1
0
0
1
1
0
0
1
0
1
1
0
0
0
3
0
2
1
0
2
0
1
0
0
0
3
1
0
1
0
0
0
1
0
1
0
1
0
1
1
1
1
0
1
0
1
1
0
2
0
1
0
0
2
0
2
1
0
2
0
0
0
1
0
2
1
1
0
2
0
2
0
2
2
2
1
2
1
4
0
0
0
1
0
0
0
0
0
0
2
0
1
0
2
1
0
0
0
0
2
0
1
2
1
1
0
0
0
0
0
0
0
2
2
0
1
0
2
2
2
0
0
0
1
0
0
0
0
1
0
0
1
2
0
1
0
0
0
2
0
0
0
1
1
1
0
0
1
0
2
1
1
0
0
2
1
1
2
0
0
0
0
0
0
1
0
2
2
0
2
1
2
1
0
0
0
1
0
0
2
0
1
0
1
0
1
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
1
2
2
0
1
0
2
1
0
0
0
2
0
3
0
1
0
0
0
0
0
2
1
0
0
0
2
0
0
0
2
0
0
0
1
0
2
0
2
1
0
0
2
0
0
1
0
0
1
0
0
0
1
0
1
2
0
0
2
2
2
0
0
1
0
2
1
0
0
2
0
1
0
0
0
0
1
1
1
0
0
2
2
0
0
0
0
1
0
0
1
1
0
0
2
0
2
0
2
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
5
1
0
0
0
0
0
2
0
0
1
1
0
0
0
0
1
0
1
5
0
1
1
0
2
0
0
0
2
1
1
1
2
0
0
0
0
2
0
0
0
1
2
0
1
0
0
0
1
0
1
0
2
0
2
0
0
0
0
0
0
0
0
2
1
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
2
2
0
2
0
2
0
1
0
3
1
0
1
0
2
0
1
0
0
2
1
0
0
0
1
0
0
1
0
1
0
1
0
0
1
0
0
0
2
1
0
2
2
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
1
1
1
1
0
0
2
0
0
0
1
0
2
0
1
0
0
2
0
2
0
0
0
0
1
1
0
1
0
2
2
0
0
0
0
0
0
0
2
0
1
0
1
1
0
0
1
2
1
0
0
0
2
0
2
1
0
1
1
1
0
2
0
0
1
1
0
0
1
1
1
0
1
0
0
2
0
0
0
0
0
1
1
2
1
0
0
1
0
0
0
2
2
1
0
0
0
0
1
2
0
0
0
1
0
1
1
0
0
0
1
1
0
2
0
3
0
1
0
1
1
0
2
1
1
0
0
0
0
0
0
0
3
0
0
1
0
0
2
0
1
0
0
0
2
0
0
0
3
0
0
0
2
0
0
0
2
1
2
0
1
1
1
2
0
2
0
0
2
0
0
1
0
0
0
0
0
1
2
0
0
0
2
0
1
0
0
0
0
2
0
2
0
2
0
0
0
0
0
1
0
0
2
0
2
1
0
1
0
0
0
2
1
2
0
0
0
2
0
0
0
0
1
0
1
1
0
2
1
0
1
0
1
0
1
1
0
0
0
2
1
0
0
0
0
0
1
1
1
0
1
0
0
1
0
1
0
2
0
0
0
0
0
2
1
0
2
1
0
0
0
2
2
0
0
0
0
0
1
0
0
1
0
0
0
2
2
0
2
1
1
0
3
0
0
2
1
1
1
1
2
1
2
0
0
0
2
0
1
0
2
2
0
0
1
1
2
1
1
0
1
3
1
2
2
1
3
1
0
0
2
2
0
2
3
0
1
2
1
0
0
1
0
2
0
2
0
2
1
1
1
0
2
1
0
0
1
0
2
4
0
1
0
0
0
2
0
0
0
0
2
0
0
1
0
0
2
0
2
0
1
2
0
2
0
0
0
2
2
0
0
0
0
0
1
0
0
1
0
1
1
2
0
0
0
2
4
4
1
2
0
2
0
1
1
0
1
2
1
2
0
0
2
1
0
1
1
1
0
0
0
2
1
2
0
1
0
0
1
0
0
0
2
2
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
3
1
0
0
1
0
2
0
1
0
0
2
2
0
0
0
2
0
1
2
0
1
2
0
0
0
0
1
1
0
1
1
0
2
0
0
0
0
2
2
0
0
2
2
2
0
0
0
0
0
1
0
0
2
0
1
2
0
0
0
1
1
2
2
0
5
2
1
0
0
0
1
1
0
1
0
0
0
0
0
2
2
2
1
0
2
1
1
0
0
0
1
0
0
0
0
1
2
0
2
0
2
0
1
1
1
0
1
0
0
0
1
1
0
1
2
2
1
1
2
0
1
0
1
0
1
0
2
2
2
0
0
0
2
2
1
1
0
1
0
0
2
1
2
3
2
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
2
2
1
1
0
1
0
1
0
1
0
2
0
0
0
1
0
2
0
0
0
0
2
2
0
2
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
2
2
1
1
0
0
0
2
0
1
1
0
2
0
0
1
0
1
0
0
0
0
5
0
0
1
0
2
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
1
2
0
0
2
0
1
0
0
1
2
0
0
0
2
1
0
1
0
0
0
0
2
2
1
0
1
0
0
3
0
0
1
1
3
0
0
2
1
2
0
2
0
0
0
0
2
1
3
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
2
2
0
2
1
1
1
0
0
2
0
1
0
2
1
0
1
0
0
1
5
2
1
0
1
1
0
1
0
2
0
0
0
0
1
0
2
1
0
1
1
0
1
0
2
1
0
0
0
0
0
1
1
2
1
1
0
0
1
1
1
1
0
0
0
1
1
0
2
0
2
0
3
2
0
1
1
2
0
0
1
0
1
1
2
0
0
0
0
1
1
1
1
0
2
0
2
1
1
2
2
1
2
1
0
0
0
0
0
2
0
2
0
2
0
2
0
0
1
0
0
1
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
1
1
0
0
2
0
0
0
2
1
3
0
2
2
0
0
0
0
1
0
1
0
0
2
2
1
1
0
0
2
1
2
0
1
0
2
1
0
0
0
0
0
0
1
1
2
1
2
2
0
2
2
0
1
0
2
2
0
0
1
0
1
1
0
0
1
2
1
1
0
0
0
0
0
2
2
2
0
2
0
0
2
0
0
0
1
0
0
1
2
0
0
0
1
0
1
1
0
1
0
2
0
0
1
0
0
0
2
2
2
0
0
0
0
2
0
1
0
0
0
0
0
0
3
0
2
0
0
1
1
0
3
0
0
0
2
0
2
1
1
2
1
1
2
2
1
0
1
2
1
3
1
0
1
0
1
1
0
0
2
0
0
0
2
0
2
2
1
1
0
2
2
0
1
0
3
1
0
0
0
0
2
1
0
0
1
0
1
1
0
0
1
2
0
3
0
0
0
0
1
2
0
1
0
0
1
1
1
0
0
2
0
1
0
1
0
0
1
0
0
10
2
1
0
0
0
1
0
3
0
0
1
0
0
0
1
0
0
1
0
0
3
1
3
0
2
0
0
1
1
2
0
2
0
0
0
1
2
3
0
0
0
1
1
2
1
2
2
0
2
2
1
0
2
1
2
1
2
1
1
0
0
0
0
0
0
0
1
1
1
2
1
0
1
2
0
2
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
2
0
2
0
2
2
0
0
2
0
2
0
2
0
0
1
0
1
1
2
2
0
2
0
0
0
0
1
2
0
1
1
1
2
0
1
0
2
2
1
1
1
0
0
2
0
0
0
0
0
0
2
0
2
1
1
1
0
0
1
2
0
2
2
0
0
0
2
2
0
1
4
1
0
1
0
0
2
1
0
1
0
0
1
0
1
0
0
0
2
1
2
0
2
0
0
0
0
0
1
0
0
0
0
1
2
2
1
1
0
1
0
0
1
0
1
2
2
0
1
0
1
1
0
0
0
0
0
0
0
2
1
0
0
1
0
6
0
0
0
0
1
1
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
1
2
1
2
0
0
0
1
1
0
0
0
1
1
0
2
0
1
1
1
1
0
0
2
0
0
0
0
2
0
2
1
0
1
2
2
0
0
2
2
2
0
0
0
0
0
0
2
0
3
0
1
1
2
1
2
0
1
0
0
0
1
2
0
2
0
0
0
0
2
1
0
0
0
0
1
0
2
2
0
2
0
0
0
1
1
0
2
1
0
0
3
0
0
2
1
0
2
0
2
1
2
0
1
0
0
1
0
1
1
0
1
2
2
2
1
0
0
1
0
0
3
0
2
1
0
0
0
0
2
0
2
1
1
0
2
1
0
1
1
1
1
1
0
0
0
0
2
0
1
1
1
1
0
2
0
0
0
0
2
2
0
1
0
0
2
0
3
1
0
1
0
0
0
0
1
0
0
0
1
0
2
3
1
0
2
1
0
1
0
0
2
0
0
2
0
2
1
0
0
2
0
0
0
1
0
0
0
0
0
1
1
0
1
1
0
0
0
1
0
0
1
0
2
0
0
1
2
2
0
2
1
2
5
0
0
0
1
1
1
2
1
0
0
0
2
0
1
1
0
0
1
2
0
2
0
0
1
1
2
2
0
2
0
0
2
0
2
1
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
3
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
2
0
0
0
3
1
0
0
0
0
1
0
0
2
2
0
0
3
0
0
2
1
0
0
0
1
0
2
0
1
1
0
1
0
0
2
1
0
1
2
0
0
2
2
1
1
0
0
2
1
0
2
2
0
0
1
2
1
0
1
0
0
1
1
2
1
0
1
0
0
0
0
1
0
1
0
2
2
0
0
1
0
0
0
1
2
0
0
2
1
1
0
1
4
0
0
0
0
0
0
0
1
0
1
2
0
2
0
0
1
0
2
0
2
2
0
0
1
1
0
0
2
0
2
1
1
0
2
0
2
0
0
0
2
0
0
0
1
1
2
1
1
0
0
2
1
3
0
0
1
3
1
2
2
0
2
0
1
3
2
2
0
1
0
1
1
2
0
1
1
0
0
0
0
1
1
2
1
0
1
1
0
1
0
2
0
1
0
0
1
0
1
0
0
1
0
2
2
1
0
0
1
0
1
2
1
2
0
0
1
0
1
1
0
1
0
2
1
1
3
0
0
0
0
1
0
1
2
0
0
1
0
0
0
1
3
2
0
0
0
0
1
0
0
1
2
1
0
0
1
2
1
1
0
2
2
1
1
0
0
2
0
0
1
2
0
0
1
0
0
0
1
0
0
0
1
0
2
0
0
1
1
1
0
0
0
0
0
1
2
1
0
1
0
2
0
1
1
0
2
0
2
0
2
2
1
0
1
1
1
1
1
0
2
1
1
0
0
0
0
1
2
0
2
0
0
2
0
1
0
1
0
0
0
1
0
0
1
0
2
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
3
0
0
1
2
0
1
0
1
0
0
1
0
0
0
2
0
3
1
0
1
0
3
1
2
0
2
1
1
0
1
2
2
3
3
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
3
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
1
0
1
0
3
0
2
0
0
0
0
2
2
0
1
0
1
1
1
0
0
1
2
3
2
0
2
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
2
0
0
2
2
0
0
0
0
0
0
0
2
0
0
1
2
1
2
1
0
0
0
2
0
0
2
1
0
0
0
0
1
0
0
1
3
1
0
2
0
1
0
0
2
1
0
0
0
2
0
0
1
0
0
1
1
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
2
0
1
2
2
2
0
0
1
1
0
1
0
0
2
2
1
0
1
1
0
0
1
0
0
0
0
0
2
2
2
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
2
1
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
4
1
0
1
0
0
1
0
0
1
2
0
2
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
4
0
0
1
1
0
0
0
0
2
0
1
1
0
0
0
0
0
2
1
0
0
0
1
2
0
0
1
1
1
2
0
2
0
2
0
1
0
0
3
2
1
1
1
0
2
1
2
0
2
0
1
2
1
0
1
0
0
1
1
2
0
0
1
2
1
0
1
0
0
2
0
2
0
0
2
0
0
4
0
0
0
0
0
1
0
2
2
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
4
0
0
0
1
0
1
2
0
1
0
0
2
1
0
1
0
2
0
0
0
0
0
1
1
0
0
1
0
1
1
0
0
0
0
3
0
2
2
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
1
1
2
0
2
2
2
1
2
2
1
3
0
1
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
3
0
1
0
0
0
1
0
0
1
0
0
1
0
2
0
1
0
0
1
0
1
1
2
1
2
0
2
1
2
0
0
2
1
0
2
0
2
2
0
0
0
1
0
1
0
0
1
1
1
0
0
2
0
2
0
1
2
1
0
0
0
2
1
0
1
1
1
1
2
0
1
1
1
0
2
1
1
1
0
0
0
0
1
0
0
2
0
2
0
0
0
1
0
0
0
0
0
1
1
0
0
2
0
1
0
2
0
2
1
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
2
4
0
0
0
0
0
0
1
4
0
2
2
2
0
0
2
1
2
0
2
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
1
0
1
1
0
0
0
0
2
0
0
1
1
1
0
1
2
0
2
0
1
0
2
0
1
0
1
0
0
0
0
2
2
2
1
1
2
1
1
0
2
1
0
2
0
0
0
1
0
1
0
0
2
2
0
0
0
1
1
0
2
0
0
0
0
2
1
0
1
1
0
0
1
2
0
1
0
0
0
2
0
2
0
0
2
2
0
0
0
3
2
0
1
0
2
0
1
0
1
0
1
1
1
0
0
1
0
0
1
0
3
1
0
1
0
0
0
1
0
2
1
1
1
2
0
0
0
1
2
0
0
1
0
2
1
0
0
0
1
1
0
0
0
0
2
1
0
1
1
1
2
0
0
2
0
1
2
2
0
0
0
2
0
0
2
2
0
1
1
1
0
0
0
0
1
2
2
0
0
1
1
1
1
1
1
0
2
3
1
0
0
0
1
1
1
3
1
0
1
2
0
0
2
0
1
0
0
0
2
2
0
1
0
0
2
0
1
0
0
0
1
1
0
0
2
2
0
2
1
0
0
0
0
2
2
0
0
0
2
2
0
0
0
2
0
1
1
0
1
0
1
1
2
2
0
0
0
0
0
2
1
0
0
1
1
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
2
0
1
0
1
1
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
1
2
1
0
1
0
2
0
0
1
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
2
1
0
0
1
1
0
2
2
0
0
2
2
0
1
0
0
0
2
2
0
1
1
0
1
0
1
2
3
1
1
0
0
1
1
0
0
1
0
0
1
2
0
2
2
0
1
0
2
1
1
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
1
2
0
2
1
0
0
0
0
0
0
2
0
0
1
2
0
1
0
0
0
0
1
0
0
1
0
0
1
1
0
1
2
0
0
0
0
2
0
2
0
2
2
2
1
1
0
0
2
0
0
0
0
0
0
1
2
0
0
0
1
1
1
0
1
2
2
2
0
1
0
0
2
0
1
1
0
1
3
0
1
0
0
3
2
1
1
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
7
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
2
0
0
0
5
1
2
0
0
1
0
1
0
2
0
0
0
2
0
0
0
1
0
2
2
0
0
0
0
2
0
2
0
0
0
1
1
1
2
2
1
2
0
0
2
2
0
0
0
0
1
0
1
0
0
0
2
0
0
2
0
1
2
1
0
1
0
2
0
0
0
0
0
2
2
0
1
0
2
1
1
0
1
2
2
0
0
2
2
1
2
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
3
2
0
1
0
0
2
2
0
1
0
0
0
2
0
0
2
2
0
0
0
2
0
1
0
1
2
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
1
2
1
0
0
1
2
1
1
0
0
0
0
1
2
0
1
1
0
0
0
0
1
0
1
2
0
0
0
0
0
0
1
0
3
0
0
0
2
1
0
0
1
1
2
2
1
0
1
0
1
1
3
2
2
0
0
2
0
2
0
2
1
0
1
1
0
0
1
1
2
0
0
2
0
2
1
0
2
0
1
0
1
0
0
2
0
1
1
2
0
0
0
0
0
0
0
2
2
2
0
0
1
1
1
0
2
0
1
0
1
1
0
1
0
0
0
0
2
0
0
1
1
0
0
0
1
6
0
1
2
2
1
1
2
1
1
0
0
2
0
2
0
0
0
0
0
1
0
2
1
0
0
0
0
1
0
0
3
0
1
2
0
0
0
1
0
0
1
1
0
0
0
3
0
0
0
1
0
1
1
0
0
1
2
0
0
1
0
0
2
1
0
0
1
2
0
2
1
0
0
0
0
1
2
0
0
2
2
0
0
0
0
0
2
0
1
1
0
1
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
1
1
0
1
1
2
1
0
0
2
0
0
0
0
0
1
0
2
0
1
0
1
1
0
2
2
0
1
0
2
0
0
0
1
0
0
1
0
3
2
1
0
2
0
3
1
0
0
0
1
0
2
2
0
2
2
1
0
1
2
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
2
0
0
0
2
2
0
0
0
0
0
2
0
0
2
2
2
0
0
1
2
0
0
0
1
0
1
2
1
0
1
0
0
0
0
0
2
2
2
0
0
0
2
1
0
2
0
0
0
2
0
0
1
1
1
2
1
2
1
0
1
0
0
1
0
0
1
0
0
1
1
2
0
1
0
2
1
0
0
1
0
1
0
0
1
0
0
0
2
2
1
2
1
0
0
0
1
0
1
3
2
0
0
0
0
0
0
2
1
2
0
0
2
0
1
1
1
0
2
0
0
1
0
1
1
2
1
0
2
1
1
2
0
2
0
0
1
0
0
0
0
1
2
0
2
0
2
0
2
1
0
3
0
0
1
2
1
1
0
0
0
2
1
1
0
2
0
0
1
1
2
1
2
1
2
1
0
2
0
2
2
1
1
1
2
0
0
0
0
0
1
0
0
0
3
1
0
0
0
2
0
2
1
2
2
0
0
0
2
2
0
2
1
0
1
3
0
0
2
0
0
0
1
1
0
0
0
0
1
1
0
0
0
1
0
0
3
0
0
2
0
0
2
1
2
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
2
3
0
0
0
0
2
1
2
0
0
1
0
0
1
2
1
1
0
0
0
1
0
0
1
1
0
1
1
2
3
2
0
0
1
2
2
1
0
2
0
1
0
2
1
0
0
2
0
1
0
1
0
1
1
2
1
0
0
0
0
0
1
0
0
2
0
2
1
2
1
0
0
0
2
3
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
4
0
1
0
2
0
0
1
2
2
0
0
0
1
1
0
2
1
0
1
0
3
0
0
0
0
0
0
1
1
1
1
0
1
2
2
0
2
0
0
0
2
0
0
0
1
2
0
0
0
0
1
0
1
2
0
1
2
0
2
1
2
1
1
0
2
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
3
2
2
0
0
1
0
1
0
2
2
1
2
0
0
0
0
1
1
1
2
1
0
0
1
0
0
0
0
0
1
0
1
1
0
2
0
1
0
0
1
0
0
0
0
0
1
1
2
0
0
0
2
0
1
0
1
0
1
2
0
0
1
0
2
1
1
0
1
0
2
2
0
0
0
2
1
1
0
2
2
4
2
0
0
0
0
1
1
1
0
1
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
2
1
0
1
0
0
0
1
0
1
1
0
1
1
2
0
2
0
2
0
0
1
0
1
1
2
2
2
1
2
3
0
1
0
2
1
0
0
0
1
0
1
0
2
1
2
0
2
1
0
0
2
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
2
1
0
0
0
1
0
0
0
2
2
0
2
0
0
0
1
0
0
0
0
1
2
1
3
0
0
0
0
2
1
1
1
0
0
0
1
1
0
0
2
3
2
0
0
1
2
0
0
0
0
0
2
1
2
0
0
0
0
2
1
0
1
2
0
0
2
0
0
0
0
1
1
2
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
1
1
0
2
0
0
0
0
1
1
0
0
0
1
0
0
1
2
0
0
2
0
2
0
2
1
0
1
0
1
0
2
0
1
0
0
0
3
1
0
2
3
0
0
2
4
1
0
1
0
0
2
0
0
0
0
0
2
2
1
0
0
0
1
4
0
0
2
1
1
1
1
0
0
0
0
0
0
2
1
1
2
1
1
0
0
2
1
0
1
0
1
2
1
0
2
0
2
0
0
0
0
1
1
1
1
2
2
0
2
2
2
1
2
2
2
1
1
0
1
2
0
2
1
2
1
1
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
2
0
1
0
0
1
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
2
1
1
1
0
2
0
1
0
0
2
0
2
0
0
2
0
1
0
0
0
0
0
0
1
1
2
1
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
3
2
2
0
0
0
0
0
1
2
0
1
0
0
0
1
1
1
0
0
1
0
0
0
0
2
0
0
1
0
1
0
0
2
0
1
0
1
2
0
0
0
0
0
0
1
2
2
3
0
2
2
0
0
2
0
2
1
0
1
0
0
0
1
2
1
0
0
0
1
1
2
0
0
1
2
0
0
0
1
0
1
0
0
1
1
0
0
0
1
0
1
3
0
0
0
0
0
0
1
2
5
2
0
1
2
0
0
1
0
1
0
1
2
2
0
1
0
0
2
1
2
2
1
1
0
1
2
0
0
0
0
2
2
1
1
0
0
0
1
0
0
2
0
2
0
1
0
2
1
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
3
1
0
0
2
2
0
0
0
0
0
0
2
1
0
0
0
0
1
1
2
0
0
1
1
3
0
0
0
0
2
0
1
1
0
0
2
2
0
3
4
1
1
0
0
0
1
0
0
0
0
0
2
1
0
0
1
0
0
2
1
0
0
0
2
2
1
1
0
0
2
0
0
0
1
2
0
0
0
2
0
2
2
1
0
0
2
0
0
0
0
1
0
2
0
0
1
2
1
0
2
0
0
0
3
1
0
0
0
1
0
0
0
1
1
2
1
2
3
2
1
0
2
0
0
1
0
2
0
2
0
1
0
2
0
0
2
0
1
1
1
0
2
0
1
2
0
0
1
0
1
0
1
1
1
0
2
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
2
2
1
3
1
3
2
0
0
0
2
1
0
1
0
0
2
2
2
1
2
1
0
2
2
0
0
2
0
1
0
0
2
0
1
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
2
1
0
0
2
0
2
1
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
1
2
2
2
0
0
2
0
0
2
0
1
2
1
0
2
0
0
0
0
0
0
1
1
0
0
1
0
0
2
0
0
0
1
0
2
0
0
2
0
0
0
0
0
2
1
0
1
2
2
0
2
2
1
1
0
1
1
0
1
0
2
0
1
0
1
0
0
1
2
0
0
0
1
0
2
0
0
0
0
1
2
0
2
0
0
2
1
2
0
3
0
0
1
2
0
2
2
2
2
2
0
0
2
0
0
1
0
0
0
0
0
0
1
0
1
2
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
3
0
0
1
0
1
2
1
0
1
0
0
0
0
0
2
0
0
0
0
1
0
2
0
1
1
2
0
0
0
2
1
0
1
0
0
1
2
1
0
1
2
1
1
1
0
1
0
0
0
0
0
1
1
0
0
1
0
2
0
2
2
1
0
0
0
1
1
1
1
0
2
0
2
0
2
2
0
0
2
0
0
0
0
1
1
2
1
0
1
1
1
0
2
0
0
0
1
2
1
2
0
2
0
1
0
2
0
1
0
2
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
2
2
1
2
0
2
1
2
0
0
0
1
0
0
0
0
0
1
1
0
1
0
1
0
0
0
1
1
0
1
2
0
2
0
4
0
0
2
0
0
0
0
0
2
0
0
1
0
1
0
0
0
1
3
0
2
0
1
1
0
2
0
0
0
1
1
0
0
1
0
0
1
2
2
0
1
0
0
0
0
1
0
1
0
2
2
0
0
1
1
2
2
0
0
0
1
2
0
1
2
0
1
2
2
1
2
0
0
1
0
0
2
1
0
1
0
0
2
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
1
0
0
3
0
0
0
1
1
0
2
0
0
0
1
0
2
0
0
0
0
1
1
2
2
0
0
2
1
1
0
0
1
1
2
0
0
0
0
1
1
0
1
2
2
2
1
0
0
2
1
1
0
0
1
0
1
1
0
0
0
1
2
0
0
0
0
1
0
1
0
2
0
0
2
0
0
0
1
0
0
0
2
0
0
0
1
2
2
1
1
0
0
0
1
0
0
2
1
0
0
0
2
0
0
0
0
0
1
0
0
1
2
1
1
0
0
0
0
0
1
0
2
2
1
2
1
0
2
2
2
0
1
0
0
0
1
2
0
0
0
0
2
1
2
0
0
0
0
1
2
1
1
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
3
2
1
0
0
1
2
0
0
0
2
0
2
0
2
0
0
0
0
0
0
1
0
0
2
0
1
1
0
2
2
2
1
0
0
1
0
0
0
0
0
2
0
1
0
2
2
2
1
1
2
0
2
0
1
2
0
0
0
0
2
1
2
0
2
0
0
0
2
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
1
2
0
1
0
0
0
1
0
1
0
0
0
2
0
0
1
2
0
0
2
2
1
0
2
0
1
0
0
0
0
0
2
0
0
2
1
0
0
1
1
0
0
0
2
0
2
0
0
0
0
1
0
0
3
2
2
1
1
0
0
0
0
0
2
2
1
0
0
0
0
1
1
2
1
0
0
2
1
2
1
2
0
0
1
0
0
1
0
1
0
0
1
4
2
0
2
2
0
1
2
1
0
2
0
2
4
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
2
1
0
1
0
2
0
0
0
1
1
0
0
2
0
2
0
0
2
2
2
2
0
2
0
1
0
0
0
0
0
0
3
1
0
0
1
0
0
0
0
2
0
0
2
2
1
0
0
1
0
0
0
1
0
1
0
2
1
2
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
1
1
0
1
0
0
0
0
1
3
0
2
2
2
0
0
1
1
1
0
1
1
1
2
1
0
0
3
1
0
0
0
0
1
2
1
0
2
1
0
0
0
0
1
0
0
1
0
1
1
2
2
0
0
1
0
1
2
2
0
2
0
1
0
0
1
2
0
0
0
0
0
2
2
1
1
1
2
1
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
1
0
1
0
2
1
0
1
2
2
0
0
0
1
1
2
0
0
0
1
0
0
0
2
1
0
0
0
1
1
1
0
2
0
0
0
0
0
0
2
1
0
0
1
0
0
1
0
1
0
1
0
0
0
1
0
1
0
0
0
1
0
2
2
1
2
2
1
1
0
0
2
0
1
1
0
2
2
0
0
0
1
0
0
0
1
0
1
0
2
2
0
2
0
0
1
0
0
0
2
2
1
0
0
0
0
0
0
0
2
1
1
0
1
1
0
2
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
2
2
0
0
1
0
0
0
0
3
0
0
0
0
1
0
0
2
0
1
1
0
0
0
0
0
0
0
0
1
0
1
2
2
0
1
0
1
0
1
2
1
0
1
0
0
2
0
2
0
2
0
0
2
0
0
1
2
2
0
0
0
2
1
2
1
1
0
2
1
2
1
0
1
2
0
2
2
0
1
0
0
2
0
0
1
1
1
1
1
2
1
0
1
2
0
1
0
0
0
0
1
1
1
2
0
0
0
0
2
2
0
1
1
1
0
0
0
0
0
1
1
1
0
1
2
0
0
1
0
0
0
1
0
1
0
0
0
1
0
1
0
2
0
0
1
0
1
0
1
1
2
1
1
0
0
1
1
0
0
0
2
2
0
0
0
2
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
1
1
2
0
1
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
2
0
0
1
0
0
0
0
2
4
0
3
1
2
0
0
1
0
2
1
2
1
0
0
1
1
0
2
2
0
0
0
0
0
2
2
0
1
2
0
0
0
0
0
0
2
2
0
0
2
1
0
2
0
2
0
2
0
2
0
1
1
0
0
2
0
2
2
1
4
1
0
0
0
1
1
1
0
0
0
0
0
0
1
1
1
0
1
0
1
1
1
2
2
1
2
0
0
0
0
2
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
1
3
1
0
0
0
0
0
1
0
0
1
1
0
0
0
2
0
1
0
0
1
0
0
0
1
0
0
0
1
2
2
1
1
0
0
2
1
1
2
0
0
0
1
1
1
3
3
0
0
2
0
0
0
0
1
0
2
1
2
0
1
1
0
2
2
0
1
0
0
0
1
2
0
1
2
0
1
2
2
0
2
1
0
0
1
1
0
0
1
2
1
2
2
0
1
1
0
2
1
0
1
0
0
0
0
0
1
0
1
1
1
2
0
2
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
3
2
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
2
0
3
2
2
0
2
0
0
1
1
0
2
0
0
0
1
0
2
0
0
2
1
0
0
1
0
3
1
0
2
2
0
0
0
1
2
0
0
0
1
0
2
0
0
0
0
0
0
2
0
2
1
1
0
1
2
0
0
1
0
0
2
1
2
1
1
0
2
0
0
0
0
0
0
0
1
1
0
2
0
0
2
1
1
1
0
1
2
1
1
0
0
0
0
2
0
1
0
0
0
0
1
1
2
2
0
0
1
2
2
0
1
1
2
0
2
0
1
0
2
0
1
0
1
2
2
1
0
0
1
1
0
0
0
0
0
2
2
1
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
1
0
2
1
0
1
0
2
3
2
0
0
1
1
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
2
1
0
0
0
0
1
0
1
0
0
2
2
2
0
4
0
0
0
0
0
0
1
0
1
2
2
2
0
0
1
2
0
0
1
0
2
1
2
1
0
0
0
1
1
0
0
0
0
0
2
2
0
0
0
0
0
1
0
2
2
1
2
1
1
0
2
0
0
0
0
0
0
0
2
1
1
0
1
1
0
0
2
2
0
1
1
0
0
2
0
0
1
0
0
0
0
1
0
2
1
1
2
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
3
1
0
2
2
0
0
2
0
1
2
0
0
0
0
0
1
0
0
0
1
0
1
3
1
1
0
0
3
1
1
4
1
0
2
0
1
1
0
0
0
0
0
2
1
0
2
0
0
0
2
1
0
1
1
0
1
0
0
0
1
1
3
1
2
0
0
1
0
0
2
1
1
2
0
2
1
0
0
0
0
1
1
0
1
0
0
1
0
1
2
0
0
0
0
0
1
2
0
2
2
0
1
1
1
0
1
0
0
0
2
0
0
1
1
1
1
0
2
2
0
0
2
1
0
0
0
0
1
0
0
0
2
2
0
0
2
0
1
0
2
0
0
2
0
0
0
1
2
0
1
0
0
0
1
2
0
2
1
0
0
3
2
0
2
0
0
0
0
1
4
1
0
2
0
1
0
0
2
2
0
1
1
0
0
1
0
2
1
0
0
1
0
2
0
1
1
1
0
0
1
2
1
2
0
0
2
2
0
2
2
0
0
0
1
0
2
1
0
2
0
0
0
1
2
0
0
1
1
1
1
0
0
1
0
1
0
1
0
1
3
1
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
1
1
3
0
0
0
0
0
2
1
1
0
1
0
1
0
0
1
2
0
2
0
1
0
1
2
2
2
0
2
1
0
1
2
1
1
0
1
0
0
2
2
1
2
1
0
0
0
2
2
0
2
2
1
0
0
1
0
1
2
0
0
0
0
1
0
1
1
1
2
0
0
0
0
1
1
2
0
0
1
2
0
0
2
1
0
0
0
3
0
0
0
0
2
1
1
2
0
0
2
0
0
1
0
0
2
2
0
0
0
0
1
1
1
0
1
0
0
1
0
1
0
0
0
0
2
0
1
1
0
2
0
2
2
0
0
1
2
0
1
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
1
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
2
1
0
2
4
1
2
0
1
2
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
1
2
2
0
0
0
0
2
2
1
1
1
1
2
1
2
0
2
0
2
2
0
0
0
0
0
0
2
0
1
0
3
1
0
0
0
1
0
2
0
2
0
0
1
1
0
0
2
1
0
2
0
0
1
0
0
0
1
2
0
0
0
0
0
2
2
0
1
0
1
1
2
1
0
1
0
1
2
0
0
1
0
2
1
0
0
0
0
1
2
1
0
1
1
0
2
0
1
0
1
1
0
0
0
1
0
2
0
0
1
0
3
1
0
1
1
0
0
0
0
1
0
0
1
0
0
2
0
0
2
0
0
0
0
1
1
4
0
0
0
0
0
0
2
1
0
0
0
0
1
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
2
0
2
2
0
0
0
2
1
0
0
0
0
1
0
0
0
1
1
2
0
0
0
0
0
1
1
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
2
0
0
0
1
0
2
2
2
2
0
1
0
0
0
2
1
1
0
2
0
2
0
1
0
0
0
1
0
0
0
0
1
0
2
0
2
0
0
2
1
2
0
2
1
0
0
0
0
0
0
2
2
0
0
2
0
0
2
1
1
2
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
2
2
0
0
2
0
0
1
0
1
0
2
0
1
0
5
0
0
0
2
2
1
0
0
0
0
0
1
0
0
1
0
2
1
1
0
0
1
1
1
2
1
1
0
1
0
0
0
0
2
1
0
0
0
0
2
2
0
1
0
1
1
0
0
1
1
3
1
1
1
0
0
0
0
0
1
0
0
1
1
1
0
2
1
2
0
0
0
1
0
0
2
0
1
1
1
0
0
2
2
1
0
1
0
1
1
1
2
0
1
1
2
0
0
3
4
2
0
1
2
0
1
0
0
0
2
2
2
0
2
1
2
1
0
0
0
1
0
0
1
1
0
1
0
0
0
1
1
0
0
2
1
1
3
1
2
2
2
0
0
1
0
0
0
1
0
0
0
1
1
0
1
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
2
0
0
2
0
0
2
2
0
2
1
2
0
0
0
0
0
0
1
6
0
0
2
0
0
1
0
0
0
1
0
0
2
0
1
0
0
0
0
0
1
2
2
2
2
0
0
1
1
0
1
0
0
0
0
0
0
4
3
1
0
1
0
1
0
1
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
2
1
2
0
0
2
0
1
0
0
0
0
1
1
0
0
0
0
0
1
1
0
1
3
2
2
0
0
0
1
0
2
0
1
1
1
0
0
2
0
0
2
2
1
1
1
0
1
1
0
0
2
0
1
0
1
0
0
0
1
0
1
0
2
0
2
0
0
1
0
1
0
0
0
1
0
1
2
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
2
2
2
1
0
0
1
1
0
0
1
1
2
2
0
0
1
0
1
0
0
0
2
0
2
0
0
2
1
0
0
2
0
0
0
2
2
1
2
2
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
2
2
2
0
2
0
1
1
1
1
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
3
0
0
2
0
0
0
1
1
1
0
0
0
2
1
1
0
0
11
0
2
1
2
0
2
2
1
0
0
1
0
0
0
0
1
1
1
0
2
2
0
2
1
0
0
0
0
0
0
1
0
0
0
0
1
1
1
2
0
1
0
2
0
0
0
2
7
0
0
0
0
0
0
0
2
0
2
1
0
3
2
2
0
0
0
1
0
0
2
0
1
0
0
0
1
0
2
0
2
1
0
0
1
0
0
0
2
0
0
1
0
0
0
2
1
1
2
0
0
0
2
2
0
0
1
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
1
1
0
1
0
0
1
2
0
1
1
0
2
2
0
2
0
2
0
1
2
0
0
0
0
1
1
2
0
2
1
11
1
0
1
2
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
2
2
0
2
1
1
1
0
0
2
1
0
2
2
0
0
2
0
1
0
1
0
1
1
2
0
0
0
1
0
0
0
0
6
0
3
1
0
0
1
0
0
1
0
1
0
0
0
2
1
1
0
0
1
2
1
2
0
0
2
0
0
1
0
1
0
0
1
0
0
2
0
0
0
0
1
0
0
2
2
0
4
1
0
2
0
0
2
2
1
1
0
0
0
0
1
0
1
0
0
0
2
2
1
0
2
2
0
0
2
1
1
1
0
1
1
0
0
1
0
2
0
0
0
0
1
0
0
0
1
3
0
2
1
0
0
0
0
0
1
1
0
2
1
1
1
0
0
2
0
1
0
1
0
2
1
0
0
0
2
1
2
1
2
1
1
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
2
1
1
2
1
2
1
0
1
0
0
1
1
1
0
1
4
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
3
0
1
1
4
0
0
2
1
0
2
0
0
0
1
0
1
0
2
0
0
1
0
2
0
2
0
2
2
2
1
0
2
1
0
0
0
0
2
1
0
0
0
1
2
1
1
1
0
0
2
0
2
0
0
1
1
0
2
0
0
0
0
1
0
0
0
1
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
1
2
0
2
0
0
0
2
0
0
3
2
0
3
0
0
1
0
0
1
0
0
0
2
0
2
0
0
0
0
1
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
2
0
3
0
0
0
0
1
0
1
0
0
2
1
1
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
2
2
2
1
1
1
1
0
2
2
0
0
4
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
2
0
1
0
2
2
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
1
1
1
0
0
0
2
0
0
2
2
1
0
0
0
0
1
1
1
1
1
1
0
0
1
2
2
0
2
0
0
0
0
0
0
0
3
1
2
0
2
2
0
0
2
0
0
2
0
2
0
0
1
2
0
0
2
0
0
0
1
0
2
0
0
2
0
1
2
1
0
1
0
1
2
0
0
0
2
0
1
2
1
0
0
0
1
0
1
2
0
2
0
1
1
1
1
1
1
0
0
1
0
0
1
0
2
0
3
0
2
2
0
0
0
0
1
2
1
0
0
0
0
0
0
0
2
0
2
1
1
4
1
0
0
2
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
1
1
0
2
1
0
0
0
0
3
0
0
1
0
0
0
1
1
0
1
2
0
2
1
0
1
0
4
1
1
2
0
1
0
0
0
0
1
1
1
0
2
2
2
0
0
0
0
2
0
0
0
2
2
0
0
2
1
3
1
0
2
0
0
2
0
1
0
1
0
1
2
0
0
0
1
1
0
2
0
2
2
1
0
0
2
3
2
1
0
3
1
2
0
1
2
0
0
2
0
0
2
1
1
1
0
2
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
1
0
0
0
0
1
0
1
0
2
1
0
1
0
0
0
1
0
0
0
4
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
1
1
1
1
0
1
0
0
0
0
2
1
0
0
0
0
1
0
0
1
1
0
0
1
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
1
1
2
1
1
1
0
1
0
1
0
0
0
2
2
2
0
1
0
1
2
1
0
1
3
0
2
0
0
2
2
0
1
3
1
2
1
2
0
0
0
1
0
2
0
0
0
1
1
2
0
1
0
0
1
0
0
0
2
0
0
0
0
0
1
1
2
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
2
0
1
1
0
1
1
1
0
2
0
0
0
0
1
0
1
2
0
0
2
0
0
0
2
0
1
2
0
1
1
1
2
2
1
2
0
0
0
2
0
1
1
0
1
0
0
1
1
1
1
0
2
0
0
0
1
0
0
0
2
2
0
0
0
2
0
0
1
0
1
0
2
0
0
0
0
1
0
0
0
1
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
1
0
2
2
1
3
2
0
0
0
0
0
0
2
0
0
1
1
0
1
0
0
0
0
0
1
0
2
2
1
0
0
0
0
0
0
2
1
0
4
0
0
0
1
2
0
0
0
0
1
2
2
1
0
1
0
2
0
1
0
1
0
1
1
0
3
0
1
0
2
0
0
2
1
0
1
2
1
3
0
1
0
1
1
2
1
0
0
1
0
0
0
1
0
2
0
2
2
0
0
1
1
0
1
0
1
1
1
1
1
2
2
0
1
1
1
0
1
0
2
0
2
0
3
0
0
3
0
2
0
0
1
0
2
1
1
1
2
0
0
1
2
0
1
0
2
0
1
2
1
2
2
2
2
1
0
2
0
0
2
0
1
2
0
1
0
0
0
1
0
1
2
0
0
0
0
1
2
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
1
1
1
0
2
2
0
1
2
0
0
0
2
0
1
0
0
1
0
0
1
2
0
1
0
0
0
0
3
0
1
2
2
2
0
1
2
1
1
0
0
0
1
1
0
0
2
2
2
0
1
1
0
1
0
0
1
2
0
2
0
2
0
0
1
0
2
2
2
2
1
1
0
1
1
0
1
2
0
1
2
0
0
0
3
0
1
1
0
2
2
0
1
0
3
0
0
0
0
0
1
0
0
0
1
0
2
1
0
1
0
0
1
0
1
2
1
1
0
2
0
0
2
0
0
0
0
5
1
1
2
0
0
0
0
0
2
0
0
0
0
2
0
3
0
1
0
0
0
1
2
1
2
2
1
2
0
1
0
0
0
0
0
1
2
1
2
0
1
0
0
3
2
1
0
0
1
7
2
2
0
2
0
1
1
0
0
1
1
0
1
0
0
0
0
0
2
1
1
0
1
0
0
0
0
0
1
0
0
0
0
2
1
0
1
0
2
0
1
1
1
0
2
0
1
1
0
1
1
1
0
0
0
0
0
2
0
0
2
2
2
1
1
0
0
2
0
0
0
1
1
0
1
1
0
1
0
2
1
2
1
2
1
3
0
0
2
2
3
0
0
2
1
0
2
1
1
0
0
0
2
0
0
2
1
3
1
0
0
1
0
0
1
2
2
0
0
0
2
0
0
2
1
1
1
0
1
1
3
1
0
0
0
1
0
0
0
1
0
1
1
1
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
1
0
2
0
0
2
0
2
2
2
2
1
0
6
1
1
0
3
1
0
0
0
1
2
0
0
0
2
0
0
2
0
2
0
2
1
1
0
0
0
0
0
2
1
0
4
0
0
1
0
0
0
1
2
0
2
2
0
0
0
1
0
0
0
0
1
0
2
0
1
0
2
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
1
0
0
1
2
0
0
2
1
0
0
1
0
0
0
0
0
1
1
1
0
1
2
0
2
0
3
0
0
0
2
0
0
0
1
0
0
0
0
0
1
3
0
0
0
1
0
2
1
1
0
1
0
0
1
1
0
0
0
0
0
1
2
0
1
2
2
0
0
0
0
0
2
1
3
1
1
0
2
1
0
0
0
0
0
2
0
0
0
1
0
1
0
0
1
0
2
1
0
2
0
0
0
0
1
1
0
0
0
0
0
2
1
2
2
0
0
0
0
0
0
2
0
1
2
1
1
0
1
2
2
0
2
0
1
2
2
0
1
2
0
0
0
0
2
0
0
0
2
1
1
0
0
0
1
0
0
0
2
2
0
1
0
0
2
0
2
0
0
0
2
0
2
1
1
0
2
0
2
0
1
0
0
1
0
0
0
0
1
3
0
0
1
0
3
2
2
0
0
0
1
0
0
0
0
1
1
1
0
0
0
1
2
1
0
0
1
0
1
2
2
1
0
0
1
1
1
0
0
0
0
0
1
2
0
0
2
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
2
0
2
0
1
1
0
1
2
1
0
0
0
0
1
0
1
0
0
1
3
0
1
0
1
0
1
0
0
1
0
2
0
0
2
2
0
0
0
0
1
2
1
2
1
0
1
0
0
2
0
0
0
1
2
0
1
0
1
1
2
2
0
1
1
1
3
1
0
0
0
0
0
0
2
0
0
1
2
1
0
0
0
0
1
0
1
0
0
1
1
0
0
0
2
2
2
6
1
1
2
1
1
1
1
1
0
0
1
0
6
0
1
2
0
0
0
1
2
0
0
0
0
0
0
0
1
0
1
0
0
1
2
0
0
0
1
0
2
0
0
2
0
0
2
1
1
0
0
1
0
0
0
2
1
0
1
0
1
2
1
1
2
3
0
0
1
0
3
0
1
0
0
0
1
2
0
0
0
0
0
1
1
2
1
1
0
1
0
0
0
1
0
0
0
2
1
0
0
0
0
2
1
0
1
0
0
1
0
1
0
0
0
1
1
1
0
0
1
3
0
0
0
0
0
1
2
3
1
1
2
0
3
0
0
2
1
0
0
0
0
2
1
0
0
0
1
0
0
0
0
1
0
0
0
2
2
0
2
0
2
1
2
0
1
0
0
1
1
2
1
0
2
1
0
0
0
2
1
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
1
0
4
1
0
2
0
0
0
3
1
0
1
2
1
0
0
0
0
2
0
2
3
0
0
1
0
2
0
1
0
0
1
0
0
1
1
1
2
0
1
0
0
0
1
0
2
0
1
1
0
0
0
1
0
1
0
1
0
0
1
0
1
2
3
0
1
2
1
0
0
0
1
1
1
0
0
1
1
2
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
1
0
0
1
0
0
0
1
3
0
0
0
0
0
2
2
2
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
2
0
0
1
2
0
0
1
0
1
1
2
1
1
2
0
0
1
1
1
1
1
1
1
1
0
1
0
1
0
0
0
2
0
0
1
1
1
2
2
0
0
2
1
1
0
2
0
2
2
2
0
0
0
0
0
1
0
0
1
1
0
1
0
2
0
0
0
3
1
0
2
0
2
1
0
0
2
0
1
0
1
0
0
0
0
0
0
0
2
1
1
0
1
2
0
0
0
0
0
1
1
0
0
1
2
0
1
0
0
2
0
0
0
0
1
0
1
0
0
2
4
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
2
1
0
0
0
2
2
2
2
1
1
2
0
1
0
1
0
0
2
0
0
0
0
0
1
0
0
2
2
0
0
1
0
0
0
1
2
0
0
0
0
0
1
0
0
3
0
1
1
0
0
0
2
0
1
2
2
0
0
3
2
0
0
2
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
2
2
0
1
0
2
0
0
1
0
1
0
0
0
2
1
0
2
0
2
0
2
0
0
0
1
1
2
0
2
0
2
3
0
0
2
1
0
1
0
0
0
2
1
0
1
0
2
1
0
0
1
0
0
0
0
0
0
0
0
1
1
2
2
2
1
2
0
0
2
0
0
0
0
1
1
1
1
1
2
2
2
1
1
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
2
0
2
0
2
1
0
0
0
1
0
0
0
2
2
0
1
0
1
1
1
0
0
0
1
0
2
2
1
1
1
0
0
0
0
0
0
1
0
1
2
0
1
0
1
3
0
0
0
0
0
1
1
1
2
2
1
0
0
0
0
0
1
0
0
2
0
0
1
0
0
2
0
0
2
2
1
0
0
1
0
0
0
0
0
1
0
0
1
0
2
1
0
2
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
1
2
1
2
2
1
0
0
1
2
1
0
0
0
1
0
1
0
1
1
0
2
0
0
0
0
0
2
1
2
0
0
0
0
0
2
0
1
0
0
1
0
0
2
1
0
1
2
1
1
0
0
1
0
2
1
0
1
0
2
2
2
0
0
3
1
0
1
2
0
0
2
0
0
1
1
0
2
0
2
1
2
2
0
1
0
2
1
2
0
0
1
0
2
1
0
1
0
2
2
0
1
0
0
2
1
2
2
0
0
0
1
0
0
0
0
0
1
1
0
1
1
0
0
1
1
0
0
2
0
2
1
0
1
1
0
1
0
0
0
0
0
2
1
1
0
0
2
0
0
2
0
0
0
1
1
0
0
4
0
2
0
0
0
0
2
2
1
2
2
1
0
0
1
0
1
1
2
0
1
2
2
2
0
0
2
0
0
2
0
0
0
0
2
0
1
0
1
0
0
0
2
2
1
2
2
1
0
0
1
1
4
2
0
0
0
1
2
2
0
0
1
1
0
2
0
1
0
0
0
0
1
2
0
0
1
0
0
0
0
0
1
1
2
1
3
1
0
0
3
0
0
2
1
1
0
1
1
2
0
2
2
1
2
2
2
0
0
1
0
0
1
2
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
1
0
2
2
0
0
2
3
0
1
0
0
0
1
4
0
0
1
0
0
1
0
2
1
0
0
2
0
0
0
1
2
1
0
0
0
0
0
0
0
1
0
1
1
0
2
0
1
0
1
0
1
2
0
1
0
1
0
1
0
3
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
1
2
0
2
0
0
1
0
1
0
0
2
2
0
0
0
2
0
0
0
3
0
0
1
0
0
1
2
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
1
0
0
0
0
1
2
1
0
0
2
0
0
0
1
0
1
1
0
0
0
0
0
1
2
2
1
3
0
0
0
1
0
0
1
1
2
0
0
0
1
1
2
1
0
1
0
1
1
1
0
0
0
0
3
0
1
0
0
1
0
0
0
0
1
2
0
1
0
0
0
0
0
2
1
0
2
1
1
0
0
1
0
2
0
0
0
0
0
1
1
1
2
1
0
0
0
1
0
2
0
0
0
1
0
1
0
1
0
0
2
0
0
1
0
2
0
1
0
0
3
0
0
0
2
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
1
1
1
0
2
0
2
0
0
0
0
1
0
1
1
0
1
0
0
2
0
2
0
1
1
0
0
1
1
0
0
4
2
1
0
2
1
1
2
1
4
0
1
1
1
2
1
0
1
0
0
0
2
2
0
0
2
2
2
0
2
1
0
0
0
0
2
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
3
1
1
0
0
2
1
0
2
2
0
1
0
0
1
0
2
0
0
0
0
0
0
1
3
0
0
1
0
2
0
0
0
0
0
2
0
0
0
1
0
1
0
1
2
0
0
0
0
2
0
2
2
0
0
0
1
0
0
0
0
1
1
0
2
2
1
0
0
1
2
0
0
0
0
7
1
0
0
0
1
2
0
2
2
0
1
1
0
1
0
0
0
0
0
0
1
0
2
2
0
0
1
0
0
0
0
1
0
0
0
1
0
1
6
1
0
1
1
0
0
1
4
0
0
1
1
1
0
1
2
0
2
0
2
1
1
2
1
4
0
0
0
0
1
0
0
0
1
0
0
2
4
2
0
0
4
1
0
0
0
2
1
0
2
0
0
2
2
0
2
3
0
0
2
0
2
0
0
0
0
0
1
0
1
0
0
1
0
1
1
1
0
1
0
2
0
2
2
2
0
2
0
0
0
0
0
0
0
1
0
2
0
1
0
2
0
2
2
0
0
0
2
2
1
0
0
2
0
1
1
1
0
0
2
2
0
2
3
0
1
2
0
1
1
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
2
0
2
1
1
1
0
1
2
0
0
0
0
0
0
0
0
2
1
0
0
2
0
2
2
0
1
3
0
2
1
0
1
0
2
2
2
0
0
2
0
0
2
1
1
1
2
0
2
0
0
0
2
0
2
1
0
0
0
0
0
1
0
1
2
2
1
1
1
1
0
1
1
1
0
0
0
9
4
2
0
0
1
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
1
0
0
0
0
2
0
1
1
0
0
0
1
0
1
2
0
0
2
0
0
0
2
0
0
2
1
0
0
0
1
1
2
0
0
1
1
0
0
1
0
0
2
0
1
0
1
0
1
1
2
1
0
0
0
0
3
0
2
0
0
0
0
1
0
1
0
1
0
1
1
0
0
0
2
0
1
1
0
1
3
0
2
0
3
1
1
0
0
0
2
2
0
0
2
3
0
2
1
0
2
0
1
1
0
1
1
0
0
2
2
2
0
1
1
0
0
0
0
2
1
2
0
1
1
1
1
2
0
1
2
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
1
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
1
0
1
1
1
0
2
1
2
0
1
2
0
1
1
1
2
0
0
0
2
0
1
0
1
1
0
0
0
2
2
1
2
1
0
2
1
0
1
0
0
0
2
1
0
0
0
0
0
0
1
0
0
2
0
1
1
2
0
3
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
2
1
1
0
1
0
0
1
0
0
1
0
0
0
0
2
0
1
1
1
0
0
2
1
1
0
1
1
0
0
1
0
0
1
2
1
2
1
1
1
0
1
1
0
0
1
1
2
3
0
2
0
2
2
0
1
0
1
1
3
0
0
0
0
0
0
0
0
0
1
1
2
0
1
0
1
0
0
0
3
2
0
0
2
0
0
2
0
2
0
2
2
0
0
0
0
0
0
1
0
0
2
2
0
0
0
1
1
1
0
0
0
2
1
0
0
0
0
0
2
1
0
2
1
0
0
1
0
0
2
2
3
1
0
0
0
1
0
0
1
0
1
0
4
1
0
2
0
0
2
1
0
0
0
0
2
0
0
0
3
0
2
4
0
0
1
0
1
0
0
0
0
2
0
0
1
2
0
2
0
0
1
2
1
0
0
0
0
0
0
1
1
1
0
2
2
0
0
0
0
0
0
0
0
1
1
0
0
3
1
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
2
0
1
2
0
1
0
0
2
0
0
0
0
0
0
0
1
1
0
0
1
1
1
0
0
0
0
2
1
0
0
0
0
0
0
1
2
1
0
0
0
0
1
0
0
0
1
2
0
2
0
0
0
2
2
1
0
0
0
0
0
1
0
1
0
0
2
0
3
1
0
0
0
0
0
1
0
1
1
0
2
1
2
0
0
0
1
0
2
1
0
0
1
0
0
0
0
0
0
1
2
0
2
0
0
1
1
0
0
0
1
0
1
0
0
0
1
2
2
0
1
0
0
1
0
0
1
2
0
1
2
0
1
0
0
1
2
0
0
0
1
0
0
0
1
2
1
0
0
0
1
0
0
1
0
0
1
0
0
3
0
2
0
0
1
0
0
0
2
0
0
1
2
1
0
0
0
1
0
2
2
0
2
1
2
1
2
0
0
1
2
0
1
0
0
0
0
1
2
0
0
1
2
0
1
0
0
4
1
0
0
2
0
0
1
0
1
0
0
0
1
0
0
2
0
1
0
2
2
0
1
0
0
1
0
2
2
1
2
0
0
0
0
2
0
0
2
0
0
1
1
1
2
1
0
0
0
0
1
0
0
2
0
1
1
2
2
1
1
0
2
1
0
2
0
2
0
0
0
2
0
0
2
0
0
0
2
0
0
1
0
2
0
2
1
1
1
0
0
1
2
3
0
1
1
1
0
1
0
0
0
1
2
3
0
0
0
0
1
1
1
0
1
1
0
0
2
0
0
2
0
4
2
0
2
0
0
0
0
0
0
2
0
0
1
0
1
0
2
0
0
0
1
0
1
0
0
1
0
1
2
1
0
1
1
1
0
0
0
0
0
1
1
0
2
0
1
0
0
1
0
1
0
2
0
2
2
0
2
2
2
0
1
1
0
0
1
1
1
2
1
0
0
2
0
0
0
0
0
1
1
0
2
2
0
1
0
0
1
2
0
0
1
1
2
4
1
0
0
1
1
2
0
0
0
1
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
2
1
2
2
1
2
0
1
1
2
0
1
0
0
0
0
0
0
0
1
3
0
0
0
0
0
1
1
1
1
0
0
1
1
0
0
1
0
1
3
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
9
2
0
1
0
0
1
0
0
0
3
0
0
0
0
1
0
1
0
1
1
0
0
0
0
2
2
1
2
0
0
0
1
0
0
2
0
1
0
1
0
1
2
1
0
1
0
0
2
2
0
0
0
0
1
2
2
0
0
0
0
2
2
0
1
2
0
0
2
2
1
0
2
2
0
1
0
2
1
0
0
2
0
0
1
0
0
1
0
2
0
0
2
0
0
0
0
2
0
0
0
0
2
1
1
1
0
0
1
0
0
2
0
2
1
1
1
2
2
0
1
0
0
0
0
2
0
1
0
2
0
3
0
0
0
0
2
1
0
0
0
0
0
1
0
0
2
0
0
0
1
0
2
0
1
1
1
1
2
1
4
0
1
3
0
1
0
0
2
2
2
0
2
0
0
1
1
0
0
0
1
1
0
1
2
1
0
0
8
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
1
1
0
2
0
2
1
0
0
2
0
0
1
0
1
0
2
0
0
0
0
2
0
0
0
2
0
2
0
1
2
0
0
2
3
0
0
0
1
1
0
0
0
0
1
0
0
0
0
2
2
0
2
0
0
1
0
0
1
0
2
0
0
0
2
0
0
1
0
0
1
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
1
2
2
0
0
0
0
3
1
2
0
1
1
2
0
0
1
1
0
2
0
1
0
1
0
1
1
0
0
1
1
2
1
0
0
0
2
0
0
3
2
2
0
0
0
0
2
0
0
1
2
0
1
0
2
2
0
2
0
0
1
1
0
0
3
0
1
0
0
0
1
0
3
2
0
2
0
0
0
1
1
1
1
2
0
2
1
2
0
0
0
0
1
0
0
2
2
2
1
1
0
0
1
0
1
0
0
0
2
1
0
0
0
0
1
2
2
1
1
2
1
4
0
0
0
0
0
0
1
0
0
0
1
2
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
3
0
0
2
0
0
2
0
1
3
3
2
0
0
0
2
0
1
0
0
0
1
0
0
0
0
3
0
1
0
0
0
1
2
2
0
1
1
0
2
0
1
1
1
0
2
1
1
0
0
2
0
0
0
0
2
0
0
1
0
0
1
0
3
0
1
0
0
1
2
0
2
1
1
2
1
0
0
0
2
0
2
0
0
1
0
0
1
4
0
2
0
0
0
2
1
0
0
0
1
2
2
3
1
0
1
0
0
0
2
0
1
1
1
1
3
1
2
0
2
0
0
0
0
0
2
1
0
1
0
2
1
3
1
0
0
0
1
0
0
1
2
2
1
2
1
1
1
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
1
1
1
0
2
1
1
2
0
2
2
2
2
0
2
1
2
1
1
2
0
2
2
0
2
0
2
1
2
0
0
1
0
3
0
2
2
1
0
2
0
0
0
0
0
2
1
2
1
1
1
0
1
1
0
0
3
1
0
1
2
2
0
2
0
1
1
2
0
1
2
1
0
0
0
0
0
1
2
2
1
1
0
0
0
1
1
0
1
1
0
4
2
1
1
0
0
0
2
0
0
0
0
1
1
0
0
0
0
2
2
0
0
0
2
2
0
1
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
2
1
0
0
0
4
1
1
2
0
0
0
1
2
0
1
0
2
0
1
0
1
1
2
0
0
1
1
0
0
0
1
0
1
2
0
0
2
0
0
1
1
2
2
0
1
0
1
1
2
1
1
0
0
0
1
0
2
0
2
0
0
0
2
2
2
0
0
1
1
0
1
2
0
0
1
2
0
0
0
0
0
1
2
1
0
1
0
0
1
0
0
2
1
2
2
0
0
1
1
1
0
1
0
0
0
1
1
2
0
1
0
0
0
0
0
0
0
2
0
2
3
0
2
0
0
0
2
0
0
0
1
1
1
5
1
0
0
2
0
1
0
2
0
1
2
1
1
0
0
0
1
2
0
0
0
3
2
0
0
1
2
0
2
1
0
0
1
1
1
0
1
0
0
1
0
1
1
0
0
0
1
0
2
2
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
1
4
0
2
1
2
0
5
0
1
0
0
0
2
1
0
1
0
0
2
1
1
1
0
0
1
0
0
0
2
2
0
2
0
1
0
1
0
0
0
1
1
2
0
0
0
0
0
1
0
1
1
2
1
0
0
2
0
0
4
0
0
1
1
0
0
2
1
1
2
0
2
0
0
0
1
0
3
2
0
0
0
0
1
1
2
2
2
0
2
0
1
0
2
1
1
2
2
0
0
0
2
3
2
1
1
0
0
1
1
0
0
0
1
1
2
1
1
1
0
1
0
3
0
1
2
1
1
2
1
0
0
1
0
1
2
2
1
0
2
0
2
2
2
3
0
0
0
1
1
0
0
1
0
0
1
0
1
1
2
1
1
0
1
1
0
0
2
1
0
1
1
1
2
0
0
2
0
1
1
0
0
2
1
0
0
1
0
2
1
0
3
0
0
0
0
0
2
1
0
0
0
2
2
0
0
1
0
0
0
0
0
2
0
2
3
0
0
0
0
0
1
0
0
0
0
1
2
1
0
0
0
0
0
0
2
0
0
0
0
4
0
1
0
2
0
0
0
0
1
1
0
4
0
0
1
3
0
0
0
0
4
1
0
0
1
0
1
0
0
2
0
1
1
0
1
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
3
1
0
2
2
0
2
0
1
1
1
0
2
2
0
0
0
0
1
2
0
0
0
0
0
1
0
0
1
2
0
2
1
1
0
0
0
0
3
0
1
0
0
0
0
0
1
2
0
0
1
2
2
0
2
0
2
0
0
2
2
1
0
1
1
2
1
0
0
2
0
1
1
0
1
1
2
2
2
2
0
0
1
0
0
0
0
0
0
0
1
0
3
0
0
0
3
0
0
1
1
0
1
0
2
0
0
0
0
0
2
0
1
2
1
2
1
0
0
1
0
1
0
0
1
0
0
0
1
0
1
2
0
1
0
0
2
1
0
1
1
0
2
0
2
0
0
0
1
0
1
2
0
2
2
1
0
0
1
0
1
0
3
6
0
0
1
0
0
2
1
0
0
1
0
0
2
0
2
2
2
0
0
0
1
1
0
0
0
1
3
2
2
2
0
0
0
0
0
1
0
0
0
0
1
2
0
2
0
0
0
2
0
0
3
0
0
0
2
0
0
2
2
0
0
2
0
2
0
2
0
0
0
1
1
2
1
3
2
2
0
0
1
0
0
2
0
0
0
1
0
4
2
1
2
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
2
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
2
2
0
1
0
0
1
2
1
0
0
1
0
0
0
0
2
2
0
1
1
1
0
0
0
2
1
2
3
0
1
1
1
2
0
1
0
0
0
2
1
2
0
0
0
0
0
0
1
0
1
2
2
2
0
0
0
1
0
0
0
2
2
1
0
2
1
2
4
1
0
1
2
4
0
0
0
2
1
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
2
1
0
0
2
0
0
0
1
0
2
0
1
1
1
0
0
0
2
2
0
0
2
0
3
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
2
0
2
0
0
2
2
1
0
0
2
0
0
0
0
0
0
1
1
2
0
0
1
1
1
0
0
1
0
0
0
1
0
0
0
1
1
0
1
0
0
1
1
0
0
0
1
0
1
0
0
0
2
0
0
2
0
0
0
1
1
2
0
1
0
1
0
0
1
0
1
0
2
2
1
1
1
1
0
2
0
1
0
2
1
0
1
3
0
2
0
0
0
0
2
2
0
0
1
0
0
1
2
2
2
2
1
1
0
0
0
0
2
0
2
0
3
0
2
1
0
0
0
0
0
0
1
2
0
2
0
0
1
0
0
0
0
0
0
2
0
1
2
0
0
0
0
1
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
2
1
0
0
0
2
0
1
1
1
2
0
0
0
0
0
1
1
0
0
1
1
2
0
0
0
2
0
1
0
0
1
1
0
0
0
1
0
1
2
0
1
0
0
0
1
1
1
0
1
1
1
2
0
1
0
1
0
1
0
0
2
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
2
2
0
0
2
0
1
0
2
0
2
0
0
1
0
0
0
2
1
0
1
1
0
0
0
0
0
0
1
2
0
1
1
0
0
0
2
1
0
1
2
1
1
1
1
0
0
0
1
2
0
2
0
1
2
0
1
0
2
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
1
2
1
0
0
2
0
2
1
1
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
2
0
1
2
0
0
0
1
0
1
1
2
1
0
0
1
0
0
0
1
2
0
1
1
0
2
3
0
0
1
1
2
0
2
0
0
0
1
0
0
1
0
0
0
0
2
1
0
2
0
0
1
0
0
1
0
1
2
0
2
0
2
0
0
1
0
0
0
0
2
0
0
1
0
1
0
0
0
1
1
2
0
0
0
2
0
0
2
0
1
2
0
1
2
0
1
1
0
0
1
0
0
1
0
0
0
2
2
0
0
0
0
0
0
2
1
1
0
2
1
1
1
1
1
0
1
0
0
0
1
2
2
0
0
0
0
2
0
2
0
0
0
0
2
0
1
2
0
0
1
2
0
0
1
1
1
1
0
0
0
0
2
0
2
2
1
2
0
1
2
1
1
2
2
2
1
7
0
0
0
0
0
1
1
0
0
1
0
1
1
0
0
0
1
0
3
2
2
0
0
0
1
2
0
5
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
1
1
0
1
1
1
2
1
1
0
2
0
2
1
0
0
0
2
0
0
2
0
2
0
0
0
0
1
0
2
1
0
0
1
1
1
0
0
1
2
1
0
0
0
0
0
2
1
1
0
0
1
0
0
0
0
0
3
1
1
1
0
0
0
1
1
2
0
2
1
0
0
2
1
2
0
1
0
0
0
0
0
0
0
2
0
0
2
2
1
0
0
2
1
1
1
0
0
0
0
4
0
0
1
1
0
1
0
0
0
1
2
0
0
0
2
0
2
0
1
0
2
2
0
1
1
3
0
1
0
1
2
0
0
1
0
2
0
1
0
0
2
2
0
0
2
0
0
0
1
0
1
1
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
1
1
2
0
0
1
0
0
0
1
0
0
0
0
1
3
0
0
0
0
2
2
1
1
0
0
0
1
1
0
0
1
1
1
1
1
1
2
0
0
0
1
2
0
0
1
1
1
1
0
0
1
2
2
0
0
1
0
1
0
0
0
2
0
2
0
0
1
1
2
0
0
0
0
2
1
0
2
0
0
1
0
2
2
0
2
1
0
0
0
3
0
1
2
0
1
2
0
1
0
0
1
0
0
2
2
2
3
2
0
0
2
1
1
0
2
2
1
0
1
0
0
0
0
0
0
0
1
2
0
2
0
0
2
3
0
0
0
1
0
0
2
0
2
0
2
0
2
2
1
1
0
2
0
0
0
2
0
2
1
1
1
1
2
0
0
1
1
0
1
0
2
0
0
0
2
0
0
0
1
0
1
2
0
1
0
0
0
0
0
0
0
0
1
2
2
0
0
2
0
0
0
0
0
2
0
1
2
0
2
1
1
0
0
0
0
1
0
1
0
2
0
2
1
1
1
0
1
1
0
1
2
0
0
2
2
1
0
1
0
0
1
0
1
2
2
0
0
0
2
0
0
0
1
0
2
2
0
1
2
0
0
1
1
2
2
1
1
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
1
1
2
0
0
2
0
1
1
0
0
0
0
0
1
0
3
3
3
0
0
2
0
3
0
1
0
0
0
2
1
0
0
0
0
0
1
0
2
2
1
1
0
0
0
0
1
0
1
0
1
0
1
0
0
2
2
2
1
0
0
0
2
1
1
0
2
4
1
2
1
1
0
1
0
2
2
0
0
0
0
1
0
0
0
1
0
0
0
2
1
0
2
0
0
0
0
0
0
1
0
2
2
0
0
2
0
1
0
1
1
0
0
0
2
0
0
0
1
0
2
0
2
1
0
0
2
0
0
2
0
0
0
1
2
0
1
0
1
0
0
0
2
0
0
1
0
0
2
0
2
1
0
1
2
0
1
1
0
0
2
0
0
1
0
0
0
0
1
0
1
2
0
2
2
0
1
0
0
1
1
0
1
2
2
2
0
1
2
1
0
0
0
0
1
1
1
0
0
1
0
1
0
0
1
2
2
0
2
0
0
0
2
0
0
0
0
1
0
2
1
1
1
1
1
0
0
1
0
0
2
1
0
0
1
1
0
1
0
0
0
1
0
0
1
2
0
0
1
2
2
1
0
2
1
0
2
1
1
2
2
0
0
3
0
0
0
0
1
0
2
0
0
2
1
2
2
0
1
2
0
0
2
2
0
0
2
1
0
2
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
1
1
1
0
0
1
3
2
0
1
0
0
0
1
2
0
1
0
2
1
2
2
2
2
0
0
1
1
0
1
2
1
0
1
0
1
1
1
0
0
1
3
1
0
2
1
0
0
0
0
1
1
0
0
0
1
0
1
2
1
1
3
2
0
0
2
0
1
1
1
0
0
2
0
2
1
2
0
2
0
0
0
2
0
0
1
1
0
0
1
2
1
3
1
1
0
2
0
2
0
0
2
0
0
0
2
0
0
1
0
1
1
1
1
0
0
0
2
1
0
0
1
1
1
2
2
1
0
2
2
2
0
1
1
2
0
1
1
0
1
0
0
0
0
1
3
0
0
2
0
0
1
0
0
0
0
1
2
2
0
0
0
1
2
0
2
1
1
0
2
1
0
0
0
0
3
1
0
0
0
1
0
0
1
1
0
2
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
1
2
1
2
0
0
0
0
2
0
2
2
0
2
0
0
1
1
1
0
1
2
0
0
0
1
0
1
0
0
0
0
1
3
0
1
2
1
0
1
0
2
1
0
2
0
1
0
2
1
0
1
0
1
0
2
2
0
1
3
0
0
1
2
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
2
0
1
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
2
2
5
0
0
0
0
1
0
1
0
0
2
1
2
0
0
0
1
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
2
1
1
0
0
1
0
1
0
0
0
0
1
0
0
0
1
2
0
1
0
0
1
1
0
0
1
3
1
0
2
0
0
1
2
0
1
1
0
2
1
0
2
1
2
3
0
0
0
1
2
1
0
0
1
0
1
0
0
1
0
2
2
0
0
1
0
1
0
0
0
0
1
1
0
0
2
0
0
0
3
1
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
2
0
2
0
0
1
0
1
0
0
0
2
0
0
1
0
2
2
2
2
0
1
1
1
0
2
1
1
0
0
0
1
3
0
1
0
0
2
0
2
0
0
0
1
0
1
2
0
2
1
2
0
0
0
2
1
0
0
0
1
2
0
1
0
1
0
0
2
0
0
2
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
1
2
1
0
0
0
0
0
1
2
0
0
0
1
1
0
0
2
1
0
1
1
2
0
0
1
2
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
2
0
1
0
0
0
0
1
2
1
0
0
2
1
0
1
0
1
2
1
3
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
2
0
0
1
0
2
2
1
0
0
1
1
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
3
0
1
2
2
1
0
1
1
2
0
0
1
1
0
2
1
2
2
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
2
2
0
1
0
0
0
0
1
2
1
0
0
0
0
1
3
0
0
0
0
1
0
0
0
0
1
1
1
1
1
2
0
1
2
2
1
0
0
1
0
2
0
0
1
0
0
1
0
0
0
0
2
2
0
0
2
1
1
0
2
0
2
0
0
1
0
0
1
0
0
0
0
2
2
0
2
1
1
0
2
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
1
0
0
1
1
0
0
1
1
0
2
2
0
1
0
0
0
0
0
0
1
0
0
0
0
1
2
2
0
0
0
1
3
1
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
1
0
0
2
1
0
0
0
2
0
0
1
3
0
1
2
0
0
0
0
2
0
1
0
0
1
0
0
2
0
2
0
2
1
0
2
0
0
0
0
1
1
1
2
0
0
1
0
0
0
3
0
3
1
0
0
2
1
0
0
0
0
1
0
0
2
1
2
1
0
0
0
2
1
1
1
1
0
2
2
1
1
1
1
1
0
1
2
0
0
0
0
2
2
2
1
0
2
1
1
0
0
0
1
0
1
1
0
0
0
0
0
1
2
0
1
1
0
2
0
1
2
0
1
0
0
0
1
0
2
1
0
1
0
1
0
0
1
2
0
2
0
1
0
0
0
0
0
1
1
2
0
0
3
0
1
0
0
1
0
2
0
1
2
0
3
2
0
1
1
2
1
0
1
0
0
0
3
0
1
0
0
0
1
0
1
1
0
1
3
1
0
1
1
0
2
1
1
0
1
0
2
0
0
0
1
2
2
0
2
0
2
1
0
2
0
1
0
0
0
0
0
0
2
0
0
0
1
0
1
0
1
0
2
2
1
0
2
2
0
1
0
1
0
2
0
0
0
0
0
2
1
0
0
0
2
0
0
2
1
1
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
1
2
2
0
1
0
0
1
0
0
0
0
1
1
1
4
0
0
2
1
0
2
0
0
2
0
1
0
0
1
0
1
1
0
0
0
0
2
1
0
1
0
0
1
0
1
1
2
2
1
1
0
1
0
2
1
2
0
1
2
0
1
2
0
2
0
1
3
0
1
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
1
1
2
1
0
2
2
0
1
1
0
0
1
0
0
2
2
0
0
2
0
2
0
0
0
0
0
1
2
1
0
0
2
1
2
0
0
1
0
1
0
0
1
0
0
0
0
1
1
0
2
0
2
1
2
1
1
1
0
1
0
2
0
0
2
2
0
0
0
1
0
2
2
2
0
1
0
3
0
0
0
2
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
1
0
0
1
0
1
3
1
0
0
1
0
2
0
1
0
0
2
0
1
0
1
0
0
0
0
2
2
1
0
0
1
0
0
1
0
0
0
0
0
0
2
3
0
1
0
1
2
0
0
3
0
1
1
0
1
2
0
0
0
2
0
1
1
1
2
1
1
0
1
1
0
0
1
0
2
0
0
0
1
0
0
0
0
1
0
0
0
2
1
1
1
1
0
0
0
2
0
0
0
1
2
0
0
0
2
0
0
1
3
2
0
0
0
1
1
0
1
0
1
1
1
0
2
0
0
2
0
1
0
2
1
2
2
0
1
2
1
0
0
0
0
2
0
0
2
0
2
0
2
2
0
0
0
0
0
0
1
2
0
1
2
2
2
2
0
2
1
0
0
1
0
2
0
0
1
2
2
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
1
0
0
0
0
1
0
0
1
0
0
2
0
0
4
0
2
0
0
0
0
0
1
1
1
0
3
0
0
1
0
2
0
1
1
0
0
0
0
0
0
0
2
1
1
0
2
3
2
0
0
1
0
0
0
1
0
0
1
0
0
2
0
2
0
1
0
2
0
2
0
2
0
0
0
2
0
0
1
1
1
2
0
0
0
0
1
1
1
1
1
1
0
2
1
0
0
1
0
0
1
1
2
0
0
1
1
2
0
2
1
0
1
2
0
1
1
0
2
2
0
1
0
1
2
2
0
2
1
0
1
0
1
1
1
2
1
2
1
1
0
1
0
0
0
1
0
0
2
0
1
0
1
2
1
1
1
1
1
1
0
1
2
0
2
2
0
0
0
1
0
2
1
0
1
2
1
0
0
0
2
2
0
0
1
0
1
2
2
0
0
0
0
1
0
0
1
1
0
1
2
0
0
0
1
2
1
0
0
0
0
0
0
1
2
1
2
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
2
0
0
1
1
0
0
0
2
2
0
0
0
0
0
1
0
2
0
0
2
1
0
0
0
0
0
0
2
0
0
2
2
2
0
2
2
0
0
0
1
1
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
1
1
0
0
2
3
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
1
0
1
0
0
0
1
0
0
1
0
2
1
0
2
0
2
0
1
0
2
1
0
1
1
1
0
2
0
0
1
2
0
0
1
2
1
0
0
1
2
0
0
2
2
0
2
0
2
2
2
1
0
0
0
0
1
0
1
0
0
1
1
0
1
0
2
1
1
2
2
2
2
7
1
1
2
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
1
1
0
0
1
0
1
0
2
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
2
0
1
0
0
1
0
0
2
1
0
3
2
1
0
0
0
0
0
2
2
1
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
2
1
2
1
2
0
2
0
1
2
0
1
0
2
2
2
0
1
4
0
0
0
0
0
0
2
0
0
0
1
1
0
2
1
0
0
1
1
2
1
1
0
1
0
1
1
1
1
0
0
3
0
1
1
1
0
2
0
1
1
0
0
1
1
1
0
1
1
0
0
2
1
1
0
2
0
2
2
1
2
0
1
0
0
0
0
1
0
2
1
1
0
0
0
0
2
0
2
0
0
1
0
1
1
1
0
0
0
0
0
3
0
3
0
0
0
0
0
0
2
1
0
0
1
0
0
1
3
2
0
0
2
0
1
2
0
0
2
1
0
0
0
1
0
0
0
1
6
1
2
0
0
0
0
0
0
0
1
3
1
1
1
2
1
1
1
3
2
2
0
1
0
0
0
2
0
2
1
2
0
0
2
1
0
0
0
2
2
0
1
0
2
1
1
1
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
3
1
0
0
1
0
2
1
2
1
1
0
0
1
0
0
0
1
0
2
1
1
0
0
3
1
0
3
0
0
0
1
2
0
0
0
0
2
1
1
0
1
3
0
0
1
1
2
2
0
1
0
0
1
2
1
0
1
1
2
4
0
2
1
0
0
0
2
0
0
0
1
0
0
0
0
2
0
1
1
0
0
0
1
1
1
1
0
2
1
0
0
0
1
0
0
1
0
1
2
2
0
1
0
0
0
3
2
4
2
2
0
1
1
1
0
2
0
0
0
2
0
1
0
0
0
0
0
1
0
0
2
0
1
2
0
0
2
0
0
1
2
0
0
1
0
0
2
0
0
0
1
0
2
2
0
0
0
0
1
0
1
0
2
2
0
0
0
2
2
2
1
1
1
2
0
1
0
0
1
0
2
0
1
0
0
1
1
0
1
1
0
2
0
0
0
1
1
2
0
0
2
1
0
1
0
1
1
0
0
0
0
2
0
1
2
1
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
2
1
2
0
0
2
0
1
2
0
2
4
0
0
0
0
1
3
2
0
2
0
0
1
1
0
1
0
2
1
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
1
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
1
1
0
0
0
1
2
2
2
0
1
1
1
0
1
0
0
1
0
2
0
2
0
0
1
1
0
1
1
0
0
0
0
0
0
1
1
0
0
2
2
0
2
1
1
1
1
0
0
1
2
0
3
0
1
0
2
1
0
0
1
0
1
1
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
1
0
1
1
1
0
0
2
2
1
0
2
1
1
1
0
1
1
1
2
0
3
1
2
0
0
0
2
0
2
0
0
4
1
1
0
0
1
0
0
2
1
0
0
1
1
0
1
0
2
0
2
0
1
2
1
0
0
1
0
2
0
1
0
0
2
2
0
0
1
0
0
0
2
0
0
0
0
1
0
0
2
1
0
0
0
0
1
0
2
0
0
2
2
2
0
0
1
0
0
0
1
2
0
0
2
0
0
0
0
2
0
1
0
2
1
1
0
2
2
1
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
2
0
0
0
0
1
1
0
1
1
0
1
1
2
2
2
0
0
0
4
1
0
0
0
2
2
0
1
0
0
0
1
1
0
0
1
1
0
1
2
0
0
0
0
0
2
3
2
0
0
1
3
0
2
2
0
0
1
0
0
0
1
0
1
2
1
1
1
0
0
0
0
2
0
0
1
0
0
3
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
2
0
2
1
1
0
1
1
0
0
0
1
0
0
0
0
0
1
0
2
0
0
1
2
0
0
2
0
2
1
4
0
0
2
1
0
0
8
2
2
1
1
1
0
1
2
1
0
0
0
2
0
1
2
0
0
2
0
0
0
2
0
1
0
0
0
0
0
1
1
0
1
1
0
0
0
0
1
2
1
2
0
1
0
2
3
0
2
0
2
0
0
0
0
2
0
0
1
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
2
0
0
0
3
0
0
0
1
1
0
1
0
1
1
0
2
0
1
0
0
0
1
3
0
2
0
2
2
0
0
0
1
1
1
1
0
1
0
0
0
2
1
3
2
0
0
1
1
0
0
0
1
2
0
2
0
0
1
1
0
0
1
0
0
0
0
2
1
2
0
0
2
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
1
1
0
2
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
2
1
1
0
1
1
0
0
1
0
0
0
0
2
2
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
2
1
1
0
2
0
2
4
1
0
0
0
0
1
0
1
1
0
0
1
0
1
2
1
0
1
2
0
0
0
0
1
0
0
0
0
0
0
1
1
2
2
0
0
2
0
0
0
1
2
0
1
0
0
1
1
0
0
0
0
0
1
1
0
0
1
0
0
0
2
0
0
1
0
0
1
1
0
3
1
0
0
0
0
0
0
1
1
0
0
0
2
1
0
0
0
0
2
2
0
0
1
0
0
0
1
0
0
0
0
2
0
2
2
0
1
0
0
1
1
1
2
0
1
0
2
1
0
0
0
1
1
1
0
1
0
2
0
0
0
2
0
1
1
0
0
0
0
0
1
1
0
0
0
1
0
2
0
2
0
1
1
0
2
1
2
2
1
1
1
0
0
0
0
1
2
0
2
0
1
1
0
1
0
0
1
0
1
0
1
1
1
0
3
2
2
1
0
2
0
2
0
0
1
0
0
1
0
1
2
0
0
0
2
0
4
1
1
0
2
1
1
1
0
0
1
1
2
0
0
1
0
0
1
1
0
0
1
4
0
0
2
1
2
2
0
1
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
2
1
0
0
1
2
0
0
0
0
0
2
1
0
1
2
0
2
1
1
2
1
0
0
1
2
0
0
1
0
0
1
0
0
0
0
0
3
0
1
0
2
1
0
2
1
0
4
0
0
1
0
0
0
0
2
1
0
0
0
0
6
0
2
1
1
0
0
0
2
0
1
1
0
1
0
2
1
1
2
2
0
2
0
1
0
1
0
1
2
2
0
2
0
0
3
0
0
3
0
2
1
1
5
2
0
0
2
2
2
1
1
1
0
0
3
1
2
0
1
0
2
1
1
2
1
0
1
2
1
0
2
0
0
0
1
2
1
0
0
0
2
0
0
0
2
0
0
0
1
1
0
2
2
1
0
0
1
1
0
0
0
0
3
0
2
0
0
0
2
0
0
0
0
0
3
0
2
0
2
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
2
0
1
0
1
1
0
1
0
0
0
0
0
0
8
0
0
1
0
0
1
0
2
0
0
0
0
1
3
2
1
0
2
0
0
1
1
0
0
0
0
1
0
0
2
2
0
0
0
1
0
0
2
0
0
2
0
0
0
1
0
1
0
2
1
1
1
1
2
1
0
0
1
0
0
0
0
0
1
0
1
0
2
0
0
0
1
1
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
1
1
2
1
0
0
1
1
0
0
2
0
2
2
0
2
2
0
1
0
0
0
1
0
0
0
0
6
1
0
0
0
2
2
0
0
1
1
0
2
2
0
1
0
1
0
1
0
0
0
0
1
2
2
0
1
0
2
0
1
0
0
0
2
0
0
0
2
1
0
1
1
0
0
0
1
0
0
2
1
2
0
0
0
0
2
3
1
2
0
0
2
0
0
0
0
1
1
0
0
2
0
2
0
0
1
0
0
1
1
2
0
0
1
1
0
0
0
2
0
2
0
0
0
1
1
0
0
0
2
0
1
0
0
1
1
1
0
0
0
1
0
2
0
0
1
0
1
0
2
4
0
0
0
0
2
1
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
1
0
0
1
0
1
1
1
1
0
1
0
1
0
0
0
0
2
0
0
1
0
1
0
2
2
2
0
2
1
0
2
1
0
0
0
1
0
1
1
2
1
0
0
1
0
1
0
0
2
0
0
0
0
1
0
1
2
1
0
1
1
0
2
1
2
2
0
2
0
0
0
0
0
0
2
2
2
0
0
0
0
1
0
1
0
0
0
0
0
2
1
0
0
2
0
1
1
0
0
0
2
0
0
2
0
0
1
1
1
1
0
1
1
0
1
0
1
0
0
1
1
2
0
0
2
0
2
0
2
0
0
2
0
0
0
1
0
2
0
0
1
2
2
1
2
2
1
0
2
1
2
0
1
2
0
1
2
1
1
2
0
0
2
1
1
0
2
0
0
1
0
1
0
2
1
0
1
0
1
0
0
0
1
0
1
0
0
0
1
0
2
0
2
2
0
2
1
2
0
0
0
2
0
0
2
0
2
1
0
1
2
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
2
0
4
0
1
2
1
2
0
0
2
0
0
0
0
0
2
1
0
1
2
2
1
0
2
4
1
0
2
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
2
0
0
0
0
1
0
1
1
1
0
1
0
0
0
2
0
0
0
7
1
1
0
0
0
0
2
0
0
2
3
0
1
1
2
0
0
0
2
0
0
2
0
0
0
0
0
2
1
0
0
1
2
3
0
0
0
0
0
0
1
0
0
2
0
1
0
1
0
2
1
1
1
0
1
0
1
1
0
2
0
1
2
0
2
0
1
0
0
0
1
2
1
1
1
1
2
1
1
1
0
1
1
0
0
0
0
2
0
2
0
1
0
0
0
0
1
2
1
1
1
1
1
0
0
1
0
1
0
1
1
0
2
0
0
0
0
0
2
2
2
2
1
1
0
0
2
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
1
2
0
1
4
0
0
0
0
2
2
0
0
2
2
2
0
0
0
1
0
1
0
1
1
1
0
0
2
1
0
0
0
0
1
0
2
0
0
0
0
1
1
2
2
1
0
1
1
0
3
2
0
2
1
0
0
0
0
0
1
0
2
0
1
2
0
1
0
0
0
0
0
1
1
2
1
0
0
4
1
1
0
0
0
1
0
0
0
2
0
0
1
0
0
1
0
1
0
0
2
1
0
0
0
1
0
0
0
0
0
1
1
1
0
1
0
1
1
0
2
2
0
0
2
0
2
0
1
2
0
2
0
2
0
0
0
0
1
0
0
2
2
1
2
1
2
0
0
1
0
0
0
0
0
1
0
0
2
1
2
1
2
1
0
2
0
1
0
0
1
0
0
1
2
1
0
0
2
1
0
0
0
2
0
1
0
1
1
3
0
2
0
0
2
1
1
0
0
0
0
0
2
2
1
0
2
0
2
1
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
1
1
2
0
0
2
0
1
1
0
2
0
3
0
1
0
2
1
1
0
2
0
2
0
0
2
1
1
2
0
1
1
0
1
1
3
0
0
1
0
0
1
0
0
1
0
2
1
0
1
1
0
0
0
0
0
0
0
2
0
0
0
1
0
2
2
1
1
0
1
1
1
0
2
1
0
1
2
0
0
1
0
2
1
0
0
0
3
0
2
0
1
1
0
0
0
2
0
0
0
0
1
1
1
1
0
1
0
1
0
1
0
0
1
0
2
0
0
0
0
0
2
0
0
1
2
0
1
0
0
2
2
2
0
1
0
2
0
1
1
0
0
2
0
0
0
1
1
1
1
0
2
0
1
2
1
1
1
0
1
0
0
1
2
1
0
1
1
0
1
0
0
0
0
2
2
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
1
1
0
1
0
3
1
0
0
0
1
2
0
2
2
0
2
2
0
1
0
0
1
1
0
2
0
0
0
0
1
1
0
1
3
0
2
0
0
1
0
2
1
2
2
2
0
1
0
0
0
0
1
1
1
0
0
0
0
3
0
2
0
2
0
1
2
1
0
0
0
1
2
2
1
0
0
0
0
2
0
1
0
0
2
1
0
0
2
1
1
0
0
1
1
0
1
14
1
0
1
0
1
1
0
2
0
0
1
0
0
1
1
0
0
0
2
0
2
2
0
0
1
0
0
1
0
0
0
2
0
1
0
2
0
2
1
0
2
0
0
2
1
1
1
1
2
1
1
0
2
1
0
1
0
0
2
0
1
0
1
1
2
0
2
0
2
1
0
0
0
0
0
0
1
2
2
2
1
0
1
2
0
1
1
0
1
0
0
0
0
1
2
2
0
1
0
0
0
0
2
2
1
1
2
0
0
2
2
0
0
1
1
2
1
1
1
0
0
0
1
1
1
1
2
0
1
0
2
1
1
2
0
0
1
1
2
1
0
0
0
0
2
0
1
0
0
1
0
2
0
0
0
1
0
1
0
2
2
0
0
1
0
0
1
1
0
0
0
0
1
2
0
1
0
1
0
0
0
2
0
0
0
0
2
0
2
1
0
0
2
0
0
2
0
2
1
2
1
0
0
0
0
1
0
0
0
2
0
1
0
0
1
0
0
2
1
0
2
0
1
2
0
0
0
1
4
1
0
2
0
0
0
0
2
1
0
2
0
0
0
1
0
2
1
0
1
0
1
0
0
0
1
0
0
0
1
1
1
0
0
0
0
1
0
2
0
0
1
0
0
1
0
2
1
0
1
3
2
0
1
0
0
0
1
1
0
0
2
2
1
2
0
0
0
2
0
0
1
0
1
0
0
2
1
0
0
1
1
0
0
1
1
1
1
1
1
1
1
0
0
3
0
0
2
1
2
1
0
2
1
2
1
0
4
2
0
0
0
0
1
2
2
1
0
2
0
2
0
1
0
1
0
0
2
1
0
0
1
0
0
0
4
2
0
2
1
1
1
0
2
2
0
2
2
0
1
0
0
0
2
0
1
0
0
1
1
0
0
0
0
0
0
2
0
0
1
1
0
0
0
1
0
1
0
2
0
1
2
1
0
0
3
2
0
1
0
0
0
0
0
0
1
1
0
2
0
0
0
0
1
0
12
1
2
0
0
2
0
2
1
0
0
0
2
2
0
0
1
1
1
0
1
0
0
0
0
1
0
2
0
1
0
0
0
1
0
2
0
2
0
0
0
1
0
2
0
1
2
1
1
2
2
0
0
1
0
3
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
2
1
0
0
0
0
0
1
2
0
2
2
2
0
2
1
1
2
2
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
2
0
0
1
2
3
0
2
1
1
1
2
2
1
0
0
2
1
0
1
0
3
2
3
1
0
2
0
0
2
2
0
0
2
0
0
2
0
2
2
2
0
0
1
0
0
1
0
3
0
2
1
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
1
1
1
0
1
0
1
1
0
0
1
1
1
1
0
0
2
2
1
0
1
1
3
1
0
0
2
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
1
0
0
0
0
2
1
0
0
0
1
0
0
2
2
1
2
0
3
1
2
0
0
0
1
1
0
0
2
3
1
2
0
1
1
1
0
0
0
0
3
1
0
0
0
0
2
0
2
0
1
3
2
0
1
1
0
0
1
1
0
0
2
0
0
2
0
1
2
0
0
1
0
1
1
0
0
1
0
3
0
0
1
1
1
1
1
1
0
1
0
2
1
1
2
0
0
0
0
1
2
2
0
1
0
1
0
0
0
0
0
2
0
0
1
2
1
0
0
0
0
0
1
1
0
0
0
1
2
0
0
0
1
0
1
1
0
0
0
0
0
2
1
2
1
1
1
0
0
3
0
0
2
0
0
0
1
0
0
1
2
2
0
0
2
1
0
2
1
0
2
0
1
1
0
0
0
1
1
1
0
0
3
0
0
0
0
2
0
2
2
2
0
0
0
5
0
0
0
0
1
1
0
0
0
0
1
2
0
1
0
2
1
0
0
0
0
0
0
1
0
0
2
0
0
2
1
1
2
1
0
2
1
0
0
1
1
2
1
0
1
1
1
3
2
0
2
0
0
0
1
1
1
0
0
0
2
1
1
1
0
0
0
1
0
1
1
2
0
0
0
0
2
0
2
2
1
1
2
1
3
0
1
0
0
1
1
2
1
2
2
0
1
1
2
0
1
0
0
0
1
1
0
0
0
2
0
0
1
3
0
1
0
2
2
1
2
2
1
1
0
1
2
1
2
0
1
0
2
1
0
0
0
0
2
2
0
1
1
3
0
1
1
0
2
0
1
0
1
1
0
0
2
2
0
0
0
0
1
3
0
0
0
0
4
2
1
0
1
1
0
0
2
0
2
1
0
0
0
0
2
4
0
0
1
2
2
0
2
0
3
0
0
0
1
2
1
2
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
1
1
0
0
1
0
2
0
0
2
1
0
0
0
0
2
0
2
1
2
0
2
2
0
12
1
1
0
2
1
0
1
0
0
2
2
0
1
0
0
0
2
1
0
2
1
1
1
0
2
1
1
0
0
0
2
2
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
1
0
0
2
3
2
0
1
0
0
1
0
0
2
0
1
1
1
1
0
0
1
2
0
2
1
2
1
0
0
1
0
0
3
2
0
1
2
1
0
1
0
1
2
1
0
1
0
2
0
2
0
0
1
0
0
1
0
0
1
0
2
1
1
0
0
1
0
2
1
1
0
2
0
0
2
0
2
2
0
2
1
1
0
2
0
0
1
0
1
2
1
0
0
3
0
2
2
1
0
0
2
0
0
2
1
0
2
0
1
2
0
0
0
1
1
0
1
0
0
0
0
1
0
3
1
0
0
0
0
2
2
0
1
0
2
0
0
1
0
0
0
0
2
1
0
0
1
0
0
2
0
2
1
0
0
2
0
2
2
2
1
1
1
0
2
1
0
0
0
0
1
0
2
0
0
0
2
2
0
2
0
0
0
2
0
0
0
1
0
0
1
2
0
1
1
0
2
1
0
1
2
0
2
0
1
1
2
3
0
1
2
1
2
0
0
0
1
0
0
0
1
2
2
0
0
0
1
0
1
0
2
2
1
1
2
1
0
2
2
0
1
0
0
0
0
2
1
1
0
0
2
1
1
0
0
1
0
0
0
0
0
0
2
1
1
2
2
0
1
0
0
2
2
0
2
0
1
2
0
1
1
2
1
0
0
3
0
0
2
1
0
0
1
0
2
0
2
0
0
0
1
0
0
1
1
0
1
0
1
2
2
0
0
0
1
1
0
1
1
0
0
2
0
0
1
0
0
2
1
0
0
1
0
1
0
1
0
2
2
0
0
0
2
0
0
0
0
1
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
8
2
1
0
0
1
0
0
0
2
1
0
0
0
1
0
0
1
1
0
2
0
0
1
1
0
0
0
1
0
2
0
0
0
0
2
1
2
0
1
0
1
0
0
2
0
2
2
1
0
0
0
0
0
0
0
2
0
0
1
0
2
3
2
1
1
0
2
0
2
1
0
0
0
2
0
0
0
3
0
1
0
0
0
0
0
1
1
2
1
0
0
0
0
0
0
1
1
2
2
0
3
0
0
0
3
1
2
2
2
2
0
2
1
1
0
0
0
2
0
0
0
0
2
0
1
0
2
0
0
0
1
1
0
1
2
0
0
1
1
0
0
0
2
2
1
2
2
0
0
0
0
0
3
0
0
0
0
0
0
2
0
2
1
0
1
0
0
0
1
1
0
0
2
0
2
0
0
0
1
1
1
2
0
1
0
2
1
1
2
2
0
1
0
0
0
2
0
1
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
1
5
1
2
0
0
2
2
1
1
3
0
0
1
0
0
1
1
0
0
2
0
0
1
0
9
1
0
0
2
1
2
0
1
0
0
0
0
0
2
1
0
0
2
0
0
0
0
1
1
2
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
2
2
2
0
2
0
2
1
0
1
1
2
0
0
2
0
2
0
1
0
1
1
0
0
1
2
0
0
0
2
0
2
0
0
2
2
2
2
0
0
0
2
0
1
0
0
0
2
2
0
0
0
0
0
1
0
0
0
3
0
1
0
0
0
1
1
0
1
0
0
0
3
0
1
1
1
2
0
1
0
0
0
0
1
0
0
1
1
2
0
0
0
1
0
0
2
2
2
1
0
0
0
1
0
1
0
2
2
1
2
1
0
2
0
2
0
0
0
1
0
0
1
2
0
1
0
1
0
0
2
0
2
0
2
2
1
0
1
0
0
1
1
0
0
0
1
2
1
0
0
0
1
0
0
0
2
2
2
0
0
1
2
0
2
0
0
0
0
1
1
2
2
1
0
0
1
0
2
0
1
1
0
0
2
0
0
3
0
2
0
1
0
0
0
1
2
1
0
0
1
0
0
3
1
1
1
1
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
1
2
1
1
0
0
0
2
2
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
2
1
0
0
1
0
0
0
0
0
0
1
2
2
0
0
0
2
0
0
1
0
0
0
1
0
0
0
1
0
1
1
3
1
2
2
2
1
1
0
2
2
1
1
2
0
2
3
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
3
0
2
0
1
2
1
0
0
0
0
0
4
0
0
0
1
0
1
4
1
0
1
2
0
0
2
1
0
1
0
2
0
1
0
2
0
1
2
1
1
1
2
2
0
2
0
0
0
1
1
1
2
1
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
1
1
1
1
0
1
0
0
1
2
2
0
0
1
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
2
2
2
0
0
0
1
2
1
0
0
0
2
0
1
2
1
0
0
0
0
0
2
0
0
0
0
0
2
6
2
0
2
1
1
2
0
0
0
0
1
1
0
0
0
2
0
0
0
2
1
0
0
0
0
1
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
2
1
1
1
0
0
0
1
0
0
1
0
1
2
2
0
1
1
1
0
1
2
2
2
0
0
0
1
1
2
1
2
1
0
2
2
2
0
1
0
1
0
1
1
0
1
1
1
0
0
0
0
7
1
0
0
2
0
2
0
1
2
1
0
1
2
1
0
0
2
1
2
2
6
0
0
2
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
1
1
2
0
2
0
0
1
0
2
2
0
1
2
0
2
0
2
0
0
2
1
0
0
0
0
0
3
0
0
2
0
0
2
0
0
2
1
1
0
1
1
1
0
0
1
0
0
0
0
1
2
0
0
0
1
0
2
1
2
1
1
1
2
0
0
0
1
2
0
0
1
1
2
0
0
0
0
3
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
2
1
0
0
1
1
0
0
2
0
1
1
0
2
0
1
2
0
0
0
0
1
0
1
1
0
1
2
0
2
0
1
0
3
1
2
2
0
0
1
1
0
1
0
1
1
2
0
0
2
1
0
1
0
0
0
2
1
0
0
0
1
1
1
0
0
1
0
0
0
0
1
1
0
0
0
0
1
2
0
1
0
0
1
0
0
1
2
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
2
2
0
1
0
2
1
1
1
1
0
0
0
1
0
0
1
2
0
1
0
0
0
1
1
2
1
1
0
2
0
1
1
0
0
2
2
0
0
0
1
0
1
0
2
2
1
1
1
2
0
2
1
1
1
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
1
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
8
0
0
1
0
1
0
0
2
1
2
0
0
2
2
0
0
0
0
1
1
1
1
0
2
0
0
0
1
0
0
0
0
0
0
0
1
1
0
2
1
0
1
0
0
0
2
2
1
0
1
0
0
1
0
0
1
3
0
1
2
0
0
5
0
1
1
2
0
0
1
0
0
2
3
0
0
0
3
0
0
1
0
2
1
0
2
0
1
0
0
3
2
0
0
1
0
1
2
1
0
1
0
1
0
3
1
0
0
3
1
1
0
0
0
2
0
3
0
0
1
2
0
1
0
2
0
0
0
2
1
2
2
0
2
0
1
0
0
2
1
1
0
2
2
0
1
1
0
1
2
1
2
0
0
1
0
1
0
0
0
2
0
1
1
1
0
0
0
0
2
0
0
0
0
0
1
1
0
2
2
1
2
0
1
1
2
0
0
1
0
4
2
0
0
0
0
0
0
1
2
0
2
0
1
1
1
0
0
0
1
0
0
0
1
1
1
0
0
0
0
1
0
2
2
1
1
0
2
0
0
0
0
0
1
2
0
0
1
0
2
0
2
2
1
0
0
0
0
2
0
0
0
0
1
1
0
0
1
1
2
0
0
1
1
0
1
0
0
1
0
0
0
2
0
2
0
0
2
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
1
0
0
0
2
3
2
0
1
0
1
0
2
0
0
0
1
0
0
2
0
2
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
1
2
2
1
2
0
4
2
0
1
0
0
1
0
0
0
0
1
0
0
1
2
0
1
2
0
0
1
2
1
1
1
0
0
1
2
0
0
2
0
0
0
0
0
1
2
0
0
1
0
0
0
0
1
0
1
0
0
1
1
1
0
1
0
0
0
1
0
0
2
0
0
2
0
0
0
2
0
2
0
0
1
0
0
1
1
2
0
0
0
1
1
1
0
0
2
0
0
0
0
0
0
1
0
0
2
1
0
0
2
0
0
1
0
1
2
0
0
0
0
0
1
0
2
0
1
0
0
1
1
2
0
0
0
4
1
0
1
3
1
0
1
2
0
1
0
1
2
0
3
0
2
0
1
0
2
2
1
2
0
0
0
1
0
0
0
3
1
0
1
0
0
2
0
0
2
1
0
0
2
2
1
0
1
2
0
0
3
0
1
0
0
1
0
0
2
2
0
0
3
0
1
2
0
0
1
1
0
2
0
0
1
0
1
0
1
1
0
2
0
2
0
2
1
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
2
2
1
0
0
2
0
0
0
2
0
3
1
0
1
0
0
2
0
2
2
1
0
2
0
0
1
0
1
0
1
2
0
1
0
0
0
1
2
2
4
1
0
0
0
3
2
0
0
1
0
0
0
2
1
1
2
0
0
0
0
2
2
0
0
0
2
2
0
0
2
0
1
0
2
0
4
1
0
2
0
2
0
1
1
1
2
0
0
0
1
1
1
0
2
2
2
1
2
1
0
0
1
1
0
1
1
0
1
3
0
0
0
0
0
0
1
2
1
0
2
1
0
0
0
0
0
2
1
1
0
0
0
1
1
1
0
1
0
2
1
0
0
0
0
1
0
2
1
0
0
0
2
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
2
2
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
3
2
2
2
0
0
0
2
0
2
2
1
2
0
1
2
0
1
0
1
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
1
0
0
0
1
0
0
2
2
1
1
0
0
0
1
2
0
0
1
0
1
0
2
0
0
1
1
1
0
1
1
2
0
2
0
1
1
1
0
0
0
1
0
1
1
1
0
0
2
2
2
1
1
2
0
2
1
0
1
2
2
1
0
3
1
0
0
1
0
0
0
1
2
1
2
1
0
1
0
0
0
1
0
4
1
0
2
0
0
2
0
0
1
2
0
1
0
0
2
1
0
1
0
2
1
0
1
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
1
1
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
2
0
2
0
1
0
2
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
1
1
2
2
0
2
0
0
1
1
0
3
0
2
0
1
2
1
0
2
0
0
0
0
2
2
0
0
0
0
2
0
1
1
4
0
0
0
2
1
1
0
1
1
0
0
1
0
0
0
1
0
0
0
1
0
5
0
1
2
0
2
0
0
0
0
0
1
2
0
2
0
0
0
1
1
0
1
0
0
0
6
1
1
2
2
0
1
1
2
1
0
0
2
2
1
0
0
2
0
2
2
0
1
1
0
2
0
0
0
0
2
2
0
1
0
1
0
0
2
1
1
1
0
1
2
1
1
0
0
0
0
0
1
2
0
2
0
3
2
2
0
0
3
1
1
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
6
0
0
0
1
2
1
1
0
0
1
1
1
0
0
0
2
0
1
1
0
1
1
0
0
0
0
2
0
0
0
1
2
0
0
0
2
0
0
3
0
0
0
0
1
1
0
2
0
0
1
0
1
1
2
0
2
1
2
3
0
1
0
1
0
0
2
1
0
0
1
2
0
0
1
2
0
0
1
0
0
0
0
0
0
0
1
2
0
0
1
0
1
2
0
2
0
1
1
3
2
2
0
2
2
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
2
2
2
0
0
4
2
2
0
1
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
1
1
1
1
0
1
1
1
1
1
2
0
1
2
1
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
4
2
0
1
2
1
0
1
2
1
0
1
2
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
2
2
0
3
0
0
1
3
0
2
1
0
0
0
0
2
3
1
0
1
0
0
0
2
4
0
1
1
0
0
0
0
1
2
2
3
1
0
2
2
1
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
1
2
2
1
1
2
1
0
0
0
1
0
0
1
0
0
1
2
1
0
0
0
3
0
1
1
2
0
0
0
0
2
0
0
0
2
0
0
3
0
0
2
0
0
0
0
0
2
0
1
0
0
2
2
0
1
2
0
0
1
2
5
1
2
0
0
2
1
1
0
1
2
0
1
0
0
2
0
0
0
0
1
0
0
0
1
1
0
0
1
0
2
2
2
2
0
0
1
1
2
0
2
0
2
0
0
1
0
0
0
0
2
2
2
0
0
1
0
0
2
0
0
2
1
1
2
1
0
0
2
0
2
0
0
0
0
1
2
0
1
0
0
0
0
2
1
2
0
0
0
0
1
0
2
0
0
0
1
1
0
1
0
1
0
0
0
0
0
1
1
0
0
2
0
1
1
0
1
0
1
1
0
1
0
0
1
1
0
2
0
0
0
0
0
0
1
1
0
0
1
0
2
1
1
0
0
0
2
2
1
0
0
0
0
0
3
0
2
2
0
2
2
0
0
0
0
1
0
1
1
0
0
1
0
2
0
0
2
0
1
0
1
0
1
1
0
0
0
0
0
0
3
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
2
1
1
0
0
0
0
0
2
0
1
0
2
2
2
0
1
1
2
1
0
3
2
2
1
2
1
1
0
1
0
0
0
0
0
1
1
0
1
0
1
0
0
2
1
0
0
0
0
1
0
0
0
0
1
0
0
1
2
0
0
2
0
2
0
2
0
1
0
2
0
1
0
0
2
0
0
2
0
2
2
1
1
2
1
2
0
0
0
0
2
1
2
0
1
0
0
0
0
2
2
1
2
1
1
0
1
0
2
1
1
1
0
0
2
1
0
0
0
1
0
0
0
0
0
2
0
1
0
0
1
2
0
0
0
2
2
2
0
1
2
0
0
2
0
0
2
0
2
1
1
0
0
2
1
1
1
0
0
1
0
9
0
2
1
0
1
0
0
1
2
0
3
0
1
1
0
1
0
0
0
0
2
0
0
1
1
0
2
2
1
0
0
0
2
2
2
1
0
1
1
0
1
0
2
0
1
1
1
5
2
0
0
1
0
0
1
0
0
0
1
0
1
1
2
2
1
1
1
1
0
0
2
0
1
0
1
0
1
0
0
0
0
1
0
1
1
0
2
2
0
0
2
0
0
2
2
1
0
0
0
0
0
2
0
2
0
0
0
1
0
1
0
0
0
1
0
1
0
2
2
2
1
0
0
2
1
0
1
1
0
0
0
0
2
2
0
2
0
0
1
0
1
0
1
1
0
1
2
3
2
0
0
0
1
0
2
0
1
0
1
1
0
0
0
0
1
0
0
0
0
1
2
0
1
0
0
0
0
0
0
2
0
0
1
1
1
0
1
3
0
1
0
0
0
0
1
0
0
1
0
1
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
1
2
1
1
2
3
0
0
0
1
1
1
2
0
0
2
0
1
1
0
0
0
0
2
0
2
0
0
0
1
2
0
0
0
0
1
1
1
0
2
0
0
1
2
2
1
0
0
0
1
1
0
2
0
0
1
1
0
0
2
0
1
0
0
2
0
0
1
0
2
0
1
2
9
1
0
0
0
1
2
0
0
2
0
1
2
1
1
0
2
0
0
0
1
0
0
2
2
2
1
2
0
0
0
0
2
0
1
0
0
0
0
0
1
0
2
1
0
1
2
0
0
0
0
0
1
0
1
1
0
0
0
2
0
2
0
1
0
0
1
0
2
0
0
0
2
0
2
2
0
2
0
0
1
0
1
2
1
3
0
0
0
0
1
0
1
0
1
1
1
0
3
0
0
1
2
0
0
1
2
0
0
2
0
2
0
1
1
0
0
1
0
1
0
0
1
2
0
0
0
0
0
1
0
1
2
0
1
0
1
0
1
2
2
0
1
1
0
0
0
1
0
0
0
0
0
0
2
1
1
0
1
1
0
0
0
0
0
0
1
2
0
1
0
1
2
2
3
2
1
1
2
0
0
0
0
0
2
1
1
0
2
1
0
3
0
0
1
1
1
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
2
1
2
2
0
1
2
2
0
2
1
2
0
1
0
0
0
0
2
1
2
0
1
0
0
0
2
0
2
0
1
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
1
2
1
0
1
2
2
0
0
0
1
1
2
0
2
1
0
0
0
0
0
3
1
0
2
0
0
0
2
1
2
0
0
0
2
0
2
0
0
0
2
0
0
1
0
1
0
1
2
0
2
1
0
0
0
1
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
1
0
1
0
2
1
0
0
0
0
0
1
2
0
0
0
0
0
1
1
0
0
0
2
2
0
0
0
0
0
2
0
2
0
0
2
0
0
2
0
0
1
0
0
0
1
0
2
0
0
0
1
1
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
1
0
3
2
2
2
0
1
0
1
2
0
2
2
2
0
1
2
0
0
0
0
1
2
0
1
1
1
0
0
0
2
1
0
0
1
1
0
0
1
0
1
0
1
2
0
0
0
0
1
2
0
1
0
1
0
0
2
0
1
0
2
0
0
2
1
2
1
1
0
2
0
1
1
2
0
2
0
0
0
3
0
0
1
2
0
0
2
2
0
1
0
1
0
0
1
1
0
0
1
0
2
0
0
0
0
2
2
2
0
1
1
6
1
7
0
2
0
1
0
2
0
0
0
0
0
1
3
0
2
0
0
1
1
2
1
0
0
1
0
2
2
2
2
0
2
1
1
0
0
1
1
0
1
0
0
1
0
1
3
2
1
1
0
0
2
0
1
1
1
1
2
0
0
2
0
2
0
0
0
3
2
2
0
0
0
2
0
0
0
2
3
0
0
0
2
0
1
3
2
0
2
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
1
2
0
0
0
4
0
0
1
1
1
2
0
1
1
1
2
0
1
1
1
2
0
0
0
0
1
2
0
1
2
0
0
1
0
0
2
0
1
0
0
2
2
0
1
0
1
1
2
0
1
0
1
2
0
1
1
0
1
1
0
0
0
0
1
1
1
1
0
2
0
0
2
1
1
0
0
2
0
0
1
0
0
0
0
2
0
1
1
2
0
0
1
2
2
1
1
0
1
1
0
0
0
0
1
1
0
0
0
0
0
2
0
0
3
1
0
0
0
1
2
0
0
2
1
2
1
2
2
0
0
2
1
1
0
2
0
0
1
1
2
0
1
1
0
1
1
1
0
1
2
1
1
0
2
0
2
0
0
1
0
1
0
0
0
2
0
0
1
2
1
0
2
0
1
0
0
0
0
2
1
1
0
2
0
1
0
2
0
0
1
0
0
2
0
0
0
0
0
2
1
1
1
0
2
2
0
2
0
0
0
2
1
2
2
0
0
0
1
1
2
0
1
0
1
0
0
1
1
0
3
0
1
0
0
0
0
3
0
1
1
0
2
3
0
0
0
2
2
0
0
1
0
0
0
2
0
1
2
1
1
2
2
2
0
1
0
0
2
2
0
5
2
1
1
0
0
0
2
0
1
0
1
0
0
0
0
1
2
1
0
2
0
0
0
2
0
1
2
0
2
1
0
0
2
0
0
0
0
0
0
1
2
1
1
1
0
1
1
0
2
0
2
2
0
3
0
0
0
1
1
1
2
0
0
1
0
0
0
0
1
0
0
2
0
0
2
0
0
1
0
0
0
0
3
2
1
0
2
0
1
0
3
0
0
1
0
0
0
2
0
0
1
0
0
1
1
0
0
0
2
0
0
0
1
2
0
1
1
1
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
2
2
0
1
0
2
0
0
0
0
1
2
0
0
1
0
0
1
1
0
1
0
0
0
0
1
0
1
1
0
0
2
0
2
1
3
0
0
0
0
0
0
0
3
0
1
0
2
2
0
0
0
0
2
2
0
0
2
0
2
1
0
0
1
0
0
1
2
1
1
2
0
2
3
2
0
0
0
0
2
0
0
0
2
1
1
0
0
1
1
0
0
0
2
0
0
0
0
0
2
2
0
2
0
0
1
2
2
1
0
0
2
1
0
0
1
1
0
0
0
1
1
1
1
2
0
0
0
1
0
2
0
0
0
2
2
0
1
0
1
0
4
0
0
0
1
0
3
2
2
2
0
2
0
1
0
0
0
1
0
2
0
1
3
0
1
0
0
0
1
0
0
0
0
2
0
1
0
0
1
2
0
1
0
0
1
2
0
2
0
2
1
0
1
1
0
1
0
1
0
0
1
1
0
0
0
0
2
1
2
0
2
1
0
2
0
2
0
0
1
0
0
0
2
0
0
1
2
1
1
0
2
1
0
2
3
0
1
0
0
0
0
0
1
3
0
0
1
0
1
2
2
1
0
1
0
0
1
0
2
3
2
1
2
0
5
1
0
0
1
2
2
0
1
1
0
1
2
0
0
0
0
0
0
0
0
0
5
2
0
2
2
0
2
2
0
1
0
1
0
1
1
0
0
0
3
2
1
1
0
1
2
0
0
1
1
0
0
2
0
0
0
1
0
0
1
2
1
1
1
0
0
2
2
1
0
1
0
0
0
2
2
1
0
2
2
0
0
0
2
0
0
0
2
0
0
0
0
2
3
0
0
0
1
0
0
0
2
0
1
0
3
0
0
1
0
0
1
0
0
1
0
3
0
0
0
0
0
0
2
2
2
0
1
1
2
2
0
0
2
1
1
0
0
0
2
1
1
0
2
2
0
1
0
0
0
1
0
1
2
2
2
0
0
2
2
0
1
0
0
1
0
1
2
2
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
2
1
0
2
0
2
2
0
0
2
1
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
1
1
1
1
0
1
1
2
0
0
0
1
1
0
2
1
0
0
0
0
1
3
0
1
2
0
1
0
1
0
0
1
0
0
1
0
0
0
1
1
1
0
2
0
5
0
0
0
2
1
0
2
0
3
1
2
1
0
1
0
1
1
2
0
0
2
1
0
0
1
0
2
2
2
0
1
1
1
1
4
1
1
1
2
0
0
2
0
0
1
1
1
2
1
0
0
0
0
0
2
0
1
4
2
0
0
1
0
0
0
1
0
2
0
0
0
2
2
1
0
0
1
1
1
2
2
1
0
0
0
3
0
2
0
0
2
0
1
1
0
0
0
2
0
2
0
2
1
0
0
2
0
1
2
0
2
1
0
0
0
0
0
0
2
0
0
1
0
2
2
2
0
2
2
0
0
2
1
1
0
0
1
1
0
0
1
0
0
0
0
0
1
0
1
2
0
2
0
0
2
0
0
1
0
2
0
1
1
0
1
1
0
0
0
0
0
0
0
1
0
2
0
2
0
1
0
0
0
2
0
2
2
1
1
1
0
0
1
2
2
0
2
1
0
1
1
0
0
0
0
1
1
0
1
0
0
0
0
2
0
1
0
1
0
1
0
0
1
0
2
2
1
0
0
0
1
0
2
0
2
0
0
0
0
1
0
0
1
0
0
0
1
0
2
2
0
0
0
2
2
0
0
0
1
0
0
0
1
2
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
3
0
3
0
0
0
2
1
0
0
0
2
2
0
1
0
0
0
1
2
3
0
2
0
1
0
0
0
1
0
0
1
0
0
1
0
0
2
1
0
0
2
0
0
0
2
0
0
2
0
3
0
1
2
0
2
0
1
0
0
2
2
1
0
3
0
0
0
0
0
0
0
1
0
1
2
0
0
1
2
0
1
1
0
0
0
0
2
0
2
1
1
1
0
0
0
2
0
0
0
1
2
1
2
0
0
2
0
3
0
0
0
0
0
1
0
0
4
2
2
0
0
0
2
0
0
0
2
0
0
2
9
1
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
2
0
2
0
0
1
0
2
0
1
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
1
2
1
2
0
1
0
1
2
0
2
0
0
2
1
1
0
1
2
0
0
1
0
0
0
0
0
2
0
2
1
0
1
0
0
1
0
1
0
0
2
0
0
2
1
1
0
0
3
2
0
3
1
2
2
0
0
3
0
2
1
0
0
0
0
1
1
1
2
0
0
0
0
2
0
0
1
2
0
0
0
1
0
1
0
1
0
0
2
0
2
1
2
0
0
2
1
0
0
0
1
0
0
0
2
2
1
1
1
2
2
1
2
0
0
2
1
1
0
0
1
1
0
1
2
2
1
0
0
1
2
0
0
0
2
0
0
2
0
0
0
1
0
1
0
1
1
1
0
1
1
0
0
0
2
2
0
0
2
0
0
3
0
1
1
0
2
0
1
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
1
0
2
2
2
2
1
0
0
0
0
3
1
3
2
0
0
0
0
0
1
1
2
0
2
0
0
0
0
1
1
2
0
1
2
2
0
0
0
1
0
0
1
0
1
0
1
0
2
0
0
0
0
0
0
2
0
1
2
0
2
2
1
0
2
2
0
1
0
1
0
0
1
0
2
0
1
1
0
0
1
2
1
1
0
3
1
0
1
1
0
0
1
0
0
0
0
1
1
0
2
0
0
0
2
2
0
0
2
1
1
1
0
0
1
0
2
0
2
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
2
2
1
2
2
1
0
1
1
0
1
2
0
0
0
0
0
2
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
1
0
3
0
2
0
2
0
0
0
0
1
1
1
1
0
1
0
1
0
1
1
1
2
0
0
0
2
2
0
0
1
2
2
0
1
0
2
1
1
0
1
2
0
1
0
0
2
0
0
1
1
2
0
1
1
0
0
0
0
1
2
0
2
1
1
0
0
1
1
2
0
1
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
2
0
1
0
0
1
0
2
2
0
2
1
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
1
0
0
1
0
1
1
0
0
2
2
0
1
1
0
0
2
1
0
0
1
1
1
1
0
0
0
0
1
0
2
1
0
2
2
1
0
1
0
0
3
1
0
0
0
0
1
1
2
2
1
2
1
1
1
0
0
1
2
0
1
1
1
0
1
1
0
0
0
2
1
0
0
0
0
0
0
2
0
2
6
1
1
1
1
0
2
1
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
1
0
0
1
0
1
0
1
0
0
0
2
1
0
1
1
1
0
0
0
0
2
0
2
0
0
2
2
1
2
0
0
1
0
0
2
2
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
1
0
2
0
0
2
1
2
2
0
1
0
0
0
0
1
1
0
0
0
0
3
1
0
0
0
0
0
0
2
2
1
0
0
0
0
0
2
0
0
0
2
2
1
2
0
0
1
0
0
0
1
1
0
1
0
1
1
1
0
0
0
0
0
0
1
0
0
1
2
1
1
2
0
1
2
2
0
0
2
1
1
0
0
0
0
2
0
0
1
1
1
2
2
1
0
0
2
0
0
0
0
0
0
0
1
0
1
1
2
2
0
0
1
2
0
0
0
1
0
0
0
0
0
0
1
1
0
2
0
1
0
1
0
1
0
0
0
2
2
0
1
0
2
0
1
0
2
0
1
0
1
0
0
1
0
1
1
0
1
3
1
1
0
1
0
0
0
1
1
1
0
1
0
0
1
0
1
1
2
0
0
1
3
0
3
0
2
0
1
2
0
1
0
1
2
0
0
0
0
0
1
1
1
0
0
2
0
1
0
1
1
2
2
2
0
0
1
0
0
1
2
1
0
0
0
0
0
1
1
1
0
2
3
2
0
2
0
0
0
0
0
0
2
1
0
1
1
2
0
0
0
1
7
1
0
1
1
0
0
2
2
1
2
2
1
0
0
0
2
2
2
1
2
0
0
0
2
0
2
1
0
0
1
0
0
0
1
0
2
1
1
0
0
0
0
0
1
1
1
2
1
0
1
0
0
0
0
1
3
2
0
2
0
0
0
0
1
0
0
1
2
0
1
0
1
2
1
2
1
1
0
1
1
2
0
0
2
1
0
0
1
1
0
1
1
3
2
1
2
0
2
1
2
0
0
0
0
0
0
1
0
1
2
0
0
1
0
0
0
2
0
0
0
0
1
0
0
2
1
1
2
0
0
0
0
2
1
2
2
1
0
4
0
0
0
1
0
0
1
1
0
0
2
1
2
0
2
0
0
2
0
0
2
0
2
1
0
1
1
1
0
1
0
0
2
0
2
0
0
0
0
0
0
0
1
0
8
0
2
1
2
0
2
1
0
0
2
0
0
2
0
0
1
0
0
2
0
1
4
1
0
0
0
1
2
0
2
0
0
1
0
1
0
0
0
2
1
1
1
0
0
0
2
2
1
0
0
0
0
0
0
0
0
2
1
0
0
1
1
0
0
3
1
1
1
0
2
2
1
1
0
3
1
0
0
0
0
0
1
0
1
1
1
1
0
2
0
0
0
1
0
2
0
0
0
0
0
0
1
1
0
0
0
0
1
2
0
1
2
2
0
0
2
2
1
0
1
0
2
0
0
1
0
1
0
0
0
1
1
2
0
1
1
1
1
2
2
2
2
1
2
1
0
0
4
1
2
0
1
1
0
1
2
0
0
0
2
0
2
0
0
2
2
2
2
3
2
0
1
1
0
1
0
0
1
0
0
2
2
2
0
0
0
2
2
2
0
1
1
1
0
0
0
0
0
0
2
0
1
2
0
2
3
0
0
1
1
0
1
0
0
0
0
1
2
2
0
2
0
0
0
0
2
2
0
1
0
0
0
0
1
0
2
0
2
1
2
9
2
2
1
1
0
0
0
0
1
0
0
2
1
0
0
1
1
0
1
2
0
0
2
0
2
0
0
2
0
0
1
0
1
2
1
0
2
6
0
1
1
2
1
1
3
0
1
2
0
1
2
2
0
0
3
0
0
0
2
0
0
2
2
0
0
1
0
2
1
0
1
2
0
2
2
2
2
2
2
1
0
0
2
3
0
0
0
2
2
1
0
2
0
0
1
1
0
2
2
0
0
1
0
0
0
3
0
0
0
0
0
1
0
0
0
1
1
0
0
2
0
1
1
1
0
0
4
0
2
0
2
0
2
2
0
1
0
0
0
0
0
2
0
0
2
2
0
0
1
0
2
2
2
1
2
0
0
1
2
0
0
1
0
0
1
1
1
0
2
0
1
0
0
1
2
0
2
0
0
1
0
0
0
2
2
1
0
3
0
2
0
0
0
0
2
0
2
0
0
2
2
1
1
2
1
0
3
0
1
0
2
1
2
0
0
0
1
0
2
1
0
0
1
0
0
0
2
0
1
1
0
2
1
0
0
2
2
3
2
0
1
0
0
1
1
1
1
1
2
0
0
1
0
2
0
1
1
2
0
0
0
1
0
0
0
1
3
0
2
0
2
0
0
1
2
2
0
2
0
1
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
3
2
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
1
0
1
0
0
1
0
0
1
2
1
2
0
0
0
0
1
3
0
0
0
1
2
0
0
0
1
0
0
0
1
0
2
1
1
2
1
0
2
0
2
0
1
0
3
0
0
0
2
0
1
0
2
0
1
2
0
1
0
1
0
2
0
0
0
1
0
0
2
2
0
1
0
2
2
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
1
0
0
2
2
0
0
0
1
2
1
0
0
1
1
0
0
1
2
0
0
1
2
2
2
0
1
2
2
0
0
1
2
0
2
0
2
0
1
0
4
0
1
0
0
1
0
0
1
2
0
2
0
2
0
1
2
0
0
0
2
0
2
1
0
1
1
1
2
0
1
1
2
0
2
2
2
0
1
0
0
1
1
2
2
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
2
0
1
1
2
1
0
0
1
1
1
1
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
1
2
0
2
3
2
0
1
0
2
1
2
4
0
0
2
2
0
0
2
1
0
0
2
2
2
2
0
0
1
0
1
0
0
2
2
2
2
0
1
0
1
3
0
0
2
5
1
1
0
1
0
2
0
2
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
3
2
1
1
0
0
0
0
1
0
0
0
0
2
2
0
0
2
2
1
1
0
0
0
2
1
1
0
1
0
1
2
0
0
0
0
2
2
2
2
1
1
1
0
0
0
0
0
0
0
0
0
2
0
0
3
0
2
0
0
1
0
0
0
0
1
2
1
2
0
1
0
0
1
0
2
0
0
2
1
1
1
4
0
1
1
1
1
2
2
0
0
0
0
0
0
0
0
2
2
2
0
0
0
2
1
0
0
2
0
0
0
0
0
1
0
0
1
0
2
0
0
1
2
0
2
2
0
1
0
0
1
1
0
0
3
2
0
0
3
0
0
1
0
0
0
1
0
0
0
2
2
3
0
1
1
0
1
0
1
1
0
1
1
1
0
2
2
1
0
0
2
1
0
2
0
2
0
0
2
1
0
2
1
0
1
2
0
0
0
2
1
2
0
2
1
1
0
1
0
0
2
0
0
1
0
0
1
0
0
2
0
2
1
0
1
0
0
2
1
1
0
1
0
0
1
2
0
0
0
1
2
2
0
1
1
0
0
0
1
1
2
0
0
1
0
0
2
0
1
0
1
0
0
0
0
2
0
0
0
1
2
0
0
1
0
1
0
0
0
1
0
1
0
1
2
0
1
0
0
1
1
0
0
2
1
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
2
1
1
0
0
2
0
1
0
2
1
1
1
1
1
1
0
1
1
0
1
2
2
1
3
0
0
3
1
2
0
0
0
2
0
1
0
1
1
1
1
0
0
2
0
1
0
1
0
1
0
2
1
2
1
0
0
0
7
1
0
2
0
1
0
1
1
0
1
0
0
0
2
1
2
1
1
0
1
0
1
0
2
1
0
0
0
0
0
1
2
4
0
1
0
1
2
0
2
3
1
0
1
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
1
1
0
0
1
0
0
2
1
0
0
0
0
0
3
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
1
2
2
1
2
0
1
1
0
1
0
0
0
2
0
0
1
0
0
1
2
0
2
1
0
1
0
1
0
1
0
1
0
0
3
0
0
0
0
0
0
0
0
1
0
1
0
1
2
0
2
0
0
0
1
0
1
0
2
2
1
2
2
0
0
0
2
0
0
1
0
0
2
4
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
2
1
1
0
0
2
1
0
2
0
0
0
0
0
0
2
1
0
0
1
1
0
1
2
1
0
0
2
0
1
0
0
1
2
2
1
0
2
0
1
2
0
0
2
2
0
0
0
1
0
0
0
1
2
0
0
2
0
0
0
2
0
0
2
1
0
0
0
1
0
0
0
1
2
0
0
1
0
3
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
1
0
1
0
0
0
1
2
1
1
0
1
1
1
2
0
0
0
0
2
0
2
2
2
1
0
1
0
2
0
0
0
0
1
2
0
0
0
1
0
0
0
2
2
0
1
1
0
0
1
0
1
0
2
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
2
1
0
2
1
0
4
1
1
2
2
0
0
4
1
0
0
2
0
0
1
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
1
0
1
2
1
0
2
0
2
2
2
0
1
1
2
0
0
3
0
0
0
1
2
1
2
2
1
0
2
0
0
1
2
0
1
0
0
0
0
2
0
1
1
1
0
0
1
1
0
1
1
0
1
3
0
0
0
0
0
0
2
1
0
1
0
2
2
1
0
0
1
0
0
1
1
1
1
2
1
2
0
0
1
1
0
1
2
2
0
1
1
0
1
2
1
3
0
3
0
0
0
1
0
0
1
1
1
1
0
0
2
0
1
1
1
0
1
2
0
0
0
1
2
0
0
1
2
1
1
1
2
2
0
4
2
2
0
1
2
0
0
1
1
0
1
2
0
0
2
0
2
0
1
2
1
0
2
0
0
0
0
1
2
2
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
1
2
2
2
1
0
0
0
0
1
1
0
0
1
0
1
1
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
1
2
0
1
0
0
2
0
0
0
0
0
1
0
2
0
0
0
2
1
0
0
1
4
2
0
0
2
0
2
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
1
2
3
1
1
0
0
2
0
0
0
1
0
0
2
1
2
2
1
0
0
0
0
0
1
2
1
1
2
1
1
1
0
1
0
0
1
2
6
2
0
1
0
2
2
0
0
1
1
0
0
0
2
1
1
0
0
2
1
1
0
0
1
0
2
2
1
0
1
0
0
0
1
0
0
2
0
0
0
0
1
0
0
1
0
2
0
0
1
2
0
2
1
1
1
1
0
2
0
0
0
0
0
1
2
2
0
0
0
1
3
2
0
2
0
1
0
0
1
0
1
1
1
0
1
0
1
1
0
2
2
1
1
0
1
2
1
0
0
0
0
0
0
2
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
1
1
1
2
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
1
1
0
2
1
0
2
0
2
0
0
0
0
2
1
0
0
0
1
0
0
0
1
0
0
0
0
1
2
0
0
0
0
2
0
0
0
1
0
0
0
1
0
1
1
0
2
0
0
0
1
1
1
0
0
0
3
1
2
1
2
1
0
1
0
2
0
0
0
2
1
0
0
0
1
2
0
0
0
1
1
0
0
1
0
0
2
1
1
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
2
2
1
0
0
1
1
2
0
0
0
2
0
2
0
1
2
2
0
0
1
1
0
1
0
1
0
2
1
1
1
0
2
0
0
1
1
0
0
2
0
0
0
0
0
0
1
1
0
2
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
1
2
0
1
1
1
0
0
2
0
0
0
0
0
1
0
0
2
1
2
0
0
0
0
3
1
0
0
2
0
0
1
2
0
0
1
2
4
1
0
2
0
1
0
0
2
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
2
0
0
0
2
2
0
1
0
2
0
2
2
0
1
0
0
0
2
1
1
1
2
0
0
0
0
1
1
0
0
1
0
0
1
1
1
0
0
0
2
1
0
1
0
2
2
1
0
0
0
1
2
1
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
2
0
0
0
2
0
2
0
0
2
1
1
2
0
0
0
0
1
0
2
1
0
1
0
0
0
2
0
0
1
2
0
2
0
0
1
0
2
1
0
1
0
1
0
0
0
1
1
1
1
0
2
2
0
0
0
2
0
3
0
0
1
2
1
0
0
0
1
0
0
0
2
0
0
0
1
0
1
2
1
0
1
0
1
0
0
0
0
0
0
1
1
1
0
2
0
0
0
0
0
2
0
2
3
2
2
1
0
0
1
1
4
0
2
2
2
2
0
0
2
0
1
1
1
1
0
0
0
1
0
0
0
0
0
1
0
2
2
2
1
1
1
2
2
2
0
0
1
0
1
2
3
2
2
1
2
1
0
0
2
1
1
2
2
0
0
2
0
2
0
0
0
1
0
2
2
1
2
0
0
2
0
1
1
0
0
2
1
2
1
0
0
0
0
2
0
1
2
1
0
2
0
1
0
0
0
2
1
0
1
1
0
2
1
0
1
0
0
0
0
2
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
1
0
2
0
0
1
1
0
1
0
2
0
2
1
1
1
1
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
1
1
2
0
1
2
0
0
0
0
0
3
1
0
6
0
0
1
2
0
2
0
1
0
1
0
1
0
0
2
0
0
1
2
0
2
0
0
2
2
3
0
0
1
0
0
2
2
3
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
2
0
1
0
1
1
0
0
0
2
2
1
2
0
0
0
1
1
1
0
0
0
2
1
0
1
0
0
2
0
1
6
1
0
0
0
0
1
1
1
0
0
0
1
0
0
1
1
0
0
3
0
1
0
0
0
1
0
2
1
0
2
2
0
2
0
0
2
0
0
0
1
1
1
1
2
1
0
1
0
0
0
2
0
1
0
0
0
0
1
1
3
0
0
0
0
0
0
2
0
1
0
1
2
1
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
2
0
2
1
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
3
0
1
0
2
0
2
2
2
0
0
0
2
1
0
0
2
2
2
0
1
0
1
2
0
0
2
1
1
0
0
2
0
1
0
2
1
0
0
0
2
0
0
1
0
0
0
2
2
0
0
1
0
0
0
0
2
0
1
2
0
1
0
0
0
0
2
1
0
2
0
0
0
0
1
1
0
1
0
0
0
2
0
0
0
0
0
2
0
1
2
0
0
1
0
0
2
1
2
0
0
0
1
1
1
1
0
0
2
3
0
0
1
0
1
1
0
1
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
2
0
0
1
2
1
1
0
0
2
2
0
1
1
2
1
0
1
1
0
0
0
2
0
0
0
0
0
2
0
0
0
2
1
1
1
0
2
1
0
1
1
0
0
1
1
0
0
0
0
0
0
0
1
1
0
5
0
0
2
0
1
0
2
0
0
1
0
1
0
0
0
1
2
2
0
1
1
1
1
0
0
1
0
1
2
2
0
0
1
0
0
2
0
2
1
0
1
0
1
2
1
2
0
1
0
0
0
4
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
2
1
0
0
0
0
0
1
1
1
0
2
2
2
1
0
3
0
0
1
0
0
0
0
0
1
0
1
0
0
2
0
0
0
1
2
1
1
2
1
0
0
0
0
0
0
0
1
0
1
0
2
3
0
0
2
0
1
0
1
0
0
0
0
1
1
0
0
1
1
1
2
0
0
1
0
0
0
0
1
2
0
1
0
0
0
0
0
2
0
0
1
2
1
1
2
0
2
1
0
0
0
0
0
0
0
0
1
0
1
1
0
2
1
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
1
2
2
0
1
2
1
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
2
2
2
0
0
0
0
0
3
4
1
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
1
1
1
0
1
0
1
1
2
1
1
0
0
1
1
0
0
2
1
2
1
0
0
0
0
0
2
0
1
2
0
1
0
1
0
0
0
0
2
0
1
3
1
1
0
0
1
0
2
0
0
2
0
0
2
1
0
0
0
2
0
0
0
1
2
2
0
1
2
3
0
2
0
2
1
0
0
2
0
0
1
1
0
0
2
2
0
1
1
0
0
2
0
0
0
2
0
0
0
0
2
0
2
0
0
2
3
0
0
0
0
5
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
1
1
0
2
0
0
2
2
4
1
0
1
1
2
0
0
0
0
1
2
2
0
0
1
0
2
0
1
2
0
1
2
1
0
0
0
0
0
2
1
0
0
2
1
1
2
1
2
0
0
0
2
0
0
0
1
0
0
2
1
1
1
1
2
2
2
1
2
0
0
0
2
1
1
0
1
1
0
2
0
0
1
0
0
2
1
1
2
0
1
2
0
0
0
1
0
0
0
1
2
0
0
3
1
0
1
2
1
2
0
0
0
0
1
1
0
0
0
1
0
0
1
1
2
1
2
4
0
0
0
0
1
2
0
2
0
0
0
0
2
0
0
0
0
0
2
0
1
2
0
1
0
2
1
0
2
3
0
0
0
0
0
0
1
1
0
0
2
0
1
0
1
2
1
0
0
0
0
0
2
0
0
1
0
0
2
0
0
1
0
2
0
1
2
2
5
1
1
1
1
0
0
0
1
0
2
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
2
2
1
2
1
0
1
1
0
0
1
2
2
1
1
0
2
1
1
0
0
1
2
0
2
0
1
3
0
0
1
0
2
1
0
0
0
0
0
2
0
1
1
0
2
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
1
1
2
0
0
0
0
0
0
0
2
2
1
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
1
0
0
2
2
1
1
0
0
0
0
0
1
0
1
2
0
0
0
0
1
0
3
0
0
0
0
1
0
0
0
0
1
0
2
0
1
2
3
0
0
0
0
0
0
0
1
0
0
0
2
2
0
2
1
1
2
2
1
0
0
0
0
1
0
0
0
1
2
2
2
1
0
0
1
0
0
0
0
1
0
1
2
1
1
1
1
0
0
0
5
2
1
2
1
0
0
0
0
1
1
1
1
0
2
0
2
0
0
1
1
0
1
0
0
1
0
0
0
1
0
2
1
1
2
0
0
2
1
0
0
0
2
0
2
0
0
0
0
1
5
1
2
0
1
0
1
1
0
1
2
1
3
0
1
0
1
1
2
0
0
1
1
0
1
1
0
1
0
0
1
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
1
3
2
0
0
1
2
1
0
0
0
2
0
0
2
0
2
0
0
0
0
2
1
0
0
2
1
0
1
0
2
1
0
0
1
0
0
1
0
2
1
0
0
0
0
1
2
0
0
0
1
10
0
1
2
2
1
1
0
0
2
1
2
2
0
0
0
2
2
1
1
0
0
0
2
0
0
0
0
2
1
2
4
0
2
3
0
1
2
0
2
1
2
1
0
0
1
0
1
2
0
0
1
0
1
0
2
2
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
1
1
2
0
0
2
2
2
2
1
0
0
2
1
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
2
0
0
0
0
0
2
0
0
0
1
2
0
2
0
0
0
0
1
1
0
0
0
1
0
0
0
0
2
0
0
1
0
0
1
2
0
3
0
2
0
0
2
1
0
0
1
0
1
0
0
0
0
4
1
0
1
0
0
1
0
2
1
2
0
2
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
2
2
2
0
1
1
0
2
0
0
1
1
0
1
1
0
2
0
1
0
0
1
1
1
1
2
0
7
1
2
0
1
0
1
0
1
1
1
1
1
0
1
1
1
2
0
2
0
0
1
0
2
0
0
1
0
0
0
0
2
0
0
1
1
2
0
0
2
1
0
0
2
0
0
1
0
0
0
0
2
0
1
0
1
0
0
0
2
0
1
0
1
0
0
1
2
3
0
1
3
0
1
0
0
0
0
2
0
1
1
2
0
2
0
0
3
0
0
0
0
0
2
3
1
1
0
1
0
0
0
0
1
1
1
1
0
1
1
0
0
0
0
1
0
0
1
0
0
2
2
0
1
4
1
1
3
0
0
0
0
1
1
0
0
0
2
2
0
1
1
2
2
1
0
1
2
0
0
0
2
2
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
1
1
0
0
2
1
0
0
0
0
0
2
2
0
1
0
4
0
2
0
0
0
2
1
0
0
0
0
0
0
0
2
1
2
0
2
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
2
1
1
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
3
0
1
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
1
2
2
3
1
0
0
0
0
0
0
0
2
0
1
0
0
1
1
1
0
0
0
0
0
0
2
0
1
0
2
2
0
0
1
1
1
1
2
0
2
1
0
2
1
0
1
2
0
2
2
0
0
0
2
0
0
0
0
1
2
1
1
0
1
0
1
0
2
2
0
2
1
1
1
2
0
2
1
0
0
3
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
1
1
0
1
1
2
1
1
0
2
0
0
3
0
0
0
0
1
0
1
0
0
0
1
3
1
0
1
0
1
0
2
2
1
2
1
0
0
1
1
0
1
0
0
1
2
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
2
1
1
1
1
0
0
1
2
0
0
0
0
2
2
0
1
0
0
1
1
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
1
2
0
2
2
1
0
0
2
0
3
2
0
2
0
1
2
0
0
0
0
0
2
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
2
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
2
0
0
0
1
1
2
0
0
1
1
0
1
0
0
0
1
1
0
2
2
1
3
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
1
1
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
1
0
1
3
0
2
1
2
2
2
1
0
0
0
2
0
2
2
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
2
1
0
1
1
0
1
0
0
0
0
0
0
0
1
2
1
0
1
2
2
0
0
0
0
1
0
1
0
1
5
0
0
0
0
1
0
1
2
0
0
2
0
2
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
2
0
0
1
0
0
0
0
1
1
2
0
0
4
1
0
0
0
1
2
0
0
1
0
1
2
2
1
0
2
2
0
0
2
0
0
0
0
2
2
2
1
0
1
0
0
0
0
0
2
2
0
2
0
0
0
0
2
0
5
0
2
1
0
2
1
1
0
1
0
0
0
2
0
1
0
1
0
2
1
2
1
1
0
2
0
0
0
0
0
0
2
2
0
1
1
0
0
0
1
0
0
2
0
2
1
0
2
2
2
0
2
0
0
1
0
0
2
0
2
0
0
0
0
2
2
0
0
0
2
2
1
2
0
2
0
0
1
0
1
1
1
0
3
0
2
0
0
1
1
0
0
0
12
2
2
1
0
0
1
0
1
0
1
0
0
0
1
0
0
2
2
2
0
2
0
0
0
1
2
0
1
0
2
0
0
1
1
0
0
1
0
0
0
1
0
1
0
2
2
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
1
1
2
1
1
1
0
0
0
1
0
1
1
0
2
1
2
1
1
2
0
3
1
1
1
0
0
2
0
1
2
0
1
2
0
1
3
0
1
0
3
0
1
0
0
1
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
3
0
0
0
0
0
2
0
0
0
0
2
1
0
0
1
1
0
1
0
0
0
0
2
1
0
3
2
0
1
1
3
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
1
1
1
1
1
2
0
2
0
0
1
0
1
0
1
1
1
0
0
0
0
0
1
1
0
0
1
2
0
2
0
1
1
0
0
2
2
1
0
0
4
1
0
1
0
2
0
0
0
0
0
2
1
1
1
1
2
0
1
0
0
2
2
0
2
2
2
1
0
0
0
1
3
0
0
0
0
0
0
1
1
1
2
1
2
2
0
0
0
0
2
2
2
0
2
1
0
0
1
1
0
0
1
0
0
0
0
1
0
2
6
0
0
2
1
3
1
0
2
2
0
0
0
0
0
0
2
1
1
2
0
0
2
0
0
1
1
0
1
0
0
1
1
1
1
0
2
0
1
0
0
1
0
2
1
2
0
1
2
0
1
0
0
0
0
1
0
1
0
0
0
0
3
0
2
2
1
2
0
2
2
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
2
2
0
2
0
0
0
2
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
3
2
0
0
1
0
0
1
1
0
1
1
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
2
2
0
2
0
0
0
2
0
3
2
1
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
1
0
1
2
1
0
1
0
1
0
0
2
0
0
0
0
0
1
0
1
2
1
0
0
0
0
0
0
0
3
2
1
2
0
0
0
2
0
2
0
2
2
3
0
2
1
2
1
1
0
1
0
1
0
1
1
0
1
1
2
3
0
0
1
1
0
2
1
0
1
0
0
1
0
1
2
1
0
1
1
1
2
0
2
1
0
0
1
0
0
1
0
1
0
0
1
0
0
1
1
0
0
0
2
1
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
1
2
0
0
0
1
0
1
1
0
2
0
0
2
2
2
0
0
2
2
1
1
0
0
0
2
0
1
2
0
1
1
0
2
1
0
3
1
1
1
0
0
1
0
0
0
1
1
1
1
0
1
0
0
1
1
1
0
1
0
0
0
0
2
0
1
0
2
0
1
1
0
1
1
0
1
0
2
2
0
0
0
2
0
1
1
1
0
0
0
1
0
0
2
0
0
1
0
0
0
1
2
0
1
1
1
2
3
0
0
0
0
2
1
0
1
0
0
2
0
0
0
0
1
2
2
0
0
0
1
3
0
0
0
0
1
1
2
2
1
1
0
2
0
1
0
1
0
2
0
1
1
2
0
0
1
1
4
1
2
0
0
1
0
1
0
1
0
1
0
0
0
0
0
6
0
0
0
1
0
0
2
1
0
1
1
1
2
0
2
1
0
1
0
0
1
2
0
0
1
1
0
0
0
0
2
0
0
2
2
0
0
1
0
0
0
0
2
0
0
0
0
0
3
0
0
0
2
2
0
0
1
2
1
1
2
0
0
0
0
2
0
0
1
0
2
0
0
0
1
0
2
0
2
0
1
0
2
0
0
0
1
1
0
0
4
1
0
0
1
0
1
0
0
0
1
0
3
0
0
0
1
0
0
2
1
0
2
0
0
0
0
2
1
1
0
2
0
0
1
2
1
1
2
2
2
0
1
2
0
2
1
2
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
3
1
1
0
0
2
1
1
1
1
2
1
1
1
0
0
0
0
1
2
2
0
0
0
1
0
0
2
0
2
0
0
0
0
2
0
0
0
1
0
1
0
0
0
2
0
0
1
1
1
1
1
0
2
3
3
2
1
1
1
0
1
0
0
0
0
0
0
1
0
2
0
1
1
1
1
0
0
1
0
0
0
2
0
2
1
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
1
0
2
0
0
0
0
1
2
2
1
0
0
0
1
0
1
2
0
2
0
1
2
0
1
2
0
2
0
0
0
2
1
0
1
0
0
0
1
2
0
1
0
0
0
1
0
0
0
1
2
2
0
1
0
1
1
2
1
0
0
1
0
0
1
2
0
1
1
2
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
2
0
1
1
0
0
1
0
0
0
2
1
1
2
2
1
0
3
2
1
0
0
2
1
1
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
2
1
0
0
2
0
0
0
0
0
0
0
0
2
2
0
1
0
0
2
1
0
1
2
0
1
1
1
0
1
0
0
0
0
0
2
0
2
1
0
0
1
2
2
1
2
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
2
0
2
2
0
2
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
3
2
2
2
0
0
1
0
1
0
0
2
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
1
1
0
1
1
0
0
0
0
2
1
0
2
0
0
0
0
1
0
2
2
0
1
0
0
1
1
0
1
2
2
0
0
2
0
2
0
0
2
2
1
1
0
1
1
1
1
0
2
0
1
1
0
1
0
0
1
2
0
1
0
0
1
0
0
0
0
0
2
2
0
0
0
1
0
1
1
1
1
0
2
2
2
1
0
0
0
2
0
0
1
1
0
0
0
1
2
0
2
0
0
0
1
0
0
2
0
0
1
2
2
1
1
0
0
2
1
1
0
0
0
0
0
1
0
0
0
2
1
0
1
0
0
1
0
1
0
0
1
2
0
1
2
2
0
0
2
0
2
1
1
0
3
3
0
0
1
0
0
0
0
2
1
1
2
1
1
1
0
2
2
0
1
0
0
1
2
0
0
2
0
1
3
1
1
0
1
1
1
0
2
0
2
0
0
0
2
0
0
0
1
1
0
0
2
0
1
1
2
1
0
0
1
2
0
1
3
1
1
0
0
0
1
2
1
0
0
0
0
0
0
1
1
2
2
1
0
0
1
1
0
2
2
2
0
1
0
1
0
0
1
0
0
0
0
1
2
2
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
2
0
1
0
0
0
0
1
1
2
0
0
1
1
0
2
0
2
0
0
4
1
1
0
0
0
2
0
2
0
1
0
0
1
0
0
2
0
1
2
2
1
1
2
2
0
0
0
0
0
1
2
1
0
2
1
0
2
0
0
0
0
0
1
0
1
1
2
0
1
1
0
1
0
2
0
1
0
0
0
1
2
0
0
0
0
0
1
0
0
2
0
2
3
0
0
0
0
2
0
2
0
2
5
0
0
0
0
2
1
0
2
0
1
1
2
0
1
0
0
1
2
0
0
0
1
2
0
0
1
0
0
0
0
0
1
2
1
2
0
0
0
4
1
2
1
2
1
2
0
0
2
1
2
2
0
1
1
1
1
0
2
0
0
0
0
1
1
0
2
2
2
2
0
0
0
0
1
1
0
1
0
0
1
1
2
0
2
1
1
0
2
1
0
0
0
0
0
2
0
0
1
1
2
4
0
1
0
1
0
0
1
1
0
0
0
1
1
0
1
0
2
2
1
1
0
0
2
2
2
1
0
1
0
0
0
1
1
0
0
0
2
0
0
2
2
2
1
2
2
0
0
0
0
0
0
1
1
0
2
0
1
0
1
1
1
2
0
0
2
0
0
1
1
1
0
0
0
0
1
0
0
1
0
0
3
1
1
2
0
0
1
0
0
0
2
1
0
0
1
0
0
1
0
0
0
2
1
0
1
2
1
0
2
0
0
0
1
2
1
1
0
0
2
1
0
1
2
0
0
0
0
2
1
0
2
0
0
2
0
3
0
1
2
0
0
0
2
2
2
2
0
0
0
0
2
2
0
2
2
2
1
0
0
1
0
1
1
0
0
2
1
1
2
1
2
2
0
2
0
0
1
1
2
2
2
1
0
0
0
1
1
0
1
0
0
1
2
1
0
0
2
0
0
0
2
0
0
0
0
0
1
2
2
1
0
2
0
2
1
2
0
1
0
0
0
0
1
1
0
0
1
0
2
0
0
0
0
0
1
1
2
2
2
0
0
2
0
0
2
1
0
1
0
2
0
0
1
0
2
2
0
3
0
0
0
0
0
0
0
0
0
0
1
5
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
1
2
0
0
1
1
0
3
2
0
2
0
0
3
1
0
0
1
0
1
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
1
3
2
1
2
0
0
1
0
2
0
0
5
2
2
2
0
0
1
0
0
0
0
0
0
3
1
0
3
1
2
1
0
0
0
1
0
2
1
0
0
1
0
0
2
0
1
0
1
1
0
0
0
2
1
1
2
0
1
0
0
0
2
0
1
1
0
1
0
1
1
0
1
2
0
0
0
0
1
1
1
2
1
0
0
0
1
0
1
0
0
3
0
0
0
0
0
0
0
1
1
1
0
0
0
2
0
0
2
1
2
0
0
2
2
1
0
0
1
0
0
1
0
2
1
1
2
2
0
0
1
0
0
0
0
1
1
1
2
0
0
2
0
0
0
1
1
1
2
0
0
2
0
1
0
0
2
2
0
1
0
0
0
0
1
1
0
2
0
2
2
0
2
2
0
1
0
0
0
0
2
2
2
1
0
4
0
1
2
0
2
0
0
1
1
1
1
0
0
0
2
2
0
0
0
1
0
1
0
2
0
1
0
1
2
0
0
2
0
0
1
0
0
1
0
2
0
0
0
1
1
2
0
2
0
1
0
1
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
1
1
1
0
0
0
2
0
1
0
0
0
1
2
0
1
1
2
1
0
1
1
0
0
1
1
1
0
1
0
0
1
0
0
0
0
0
3
0
0
0
2
0
1
1
2
0
3
0
1
0
0
1
1
0
0
1
0
1
0
1
4
0
0
1
0
1
0
2
2
0
0
1
1
3
0
0
2
0
1
0
0
2
0
1
0
2
0
0
0
1
2
0
0
0
2
0
1
1
1
1
1
0
1
0
0
1
2
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
1
0
0
2
3
1
0
0
0
0
2
1
2
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
1
0
0
0
1
0
2
1
0
0
0
2
0
0
1
1
0
0
2
0
0
1
1
0
1
0
2
0
0
4
2
0
2
0
0
0
2
1
1
0
0
0
0
2
0
0
0
1
2
0
1
1
2
0
0
0
2
0
0
1
0
0
3
0
1
0
2
0
0
0
1
0
0
1
1
1
0
0
0
1
0
0
0
2
2
1
0
0
2
2
1
0
0
2
1
2
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
3
0
0
0
0
2
1
0
0
0
0
2
1
0
0
0
2
1
0
1
1
0
0
0
0
0
1
0
0
1
1
0
1
0
1
2
0
0
0
0
3
0
1
2
1
2
0
1
1
1
0
0
0
2
0
1
0
1
0
3
0
1
1
0
2
0
0
0
0
0
1
0
1
1
2
2
0
0
0
0
0
0
1
0
0
1
0
0
2
1
0
0
1
1
0
2
0
0
1
2
0
0
1
0
0
0
0
0
1
2
1
1
0
0
0
2
0
0
0
0
0
1
2
0
1
1
2
0
2
1
2
0
0
2
1
2
2
2
0
0
0
0
1
2
0
0
0
0
0
2
1
0
1
0
2
1
0
2
1
0
0
0
0
0
2
0
0
1
0
1
2
2
0
0
1
1
0
0
0
0
0
0
1
2
0
0
0
0
1
2
1
2
3
0
1
0
1
0
2
0
1
2
0
0
1
0
0
0
0
0
2
0
0
0
0
2
1
0
0
1
2
2
0
0
0
0
1
0
0
0
0
2
0
0
2
0
1
0
1
1
2
0
1
0
0
1
1
2
2
2
0
3
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
1
1
1
1
0
1
2
0
1
1
0
0
0
2
1
0
0
2
2
1
2
2
3
0
2
1
1
1
2
2
2
0
0
0
0
1
0
1
0
2
0
0
1
0
0
0
0
2
2
0
0
1
2
0
2
1
2
2
0
0
0
0
0
0
1
0
1
1
0
2
0
0
0
0
0
2
0
0
0
0
0
3
2
1
0
0
0
0
1
0
2
2
2
1
2
0
0
0
0
1
0
1
0
0
3
0
1
1
1
0
0
0
0
1
0
1
0
1
1
2
1
0
0
1
2
0
0
0
0
0
2
2
0
1
0
1
3
1
1
2
0
2
2
1
0
0
0
1
0
2
0
1
0
1
0
1
0
0
2
0
0
0
0
2
1
2
1
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
1
0
1
0
0
0
3
1
0
0
0
0
0
0
1
1
1
1
0
1
0
1
1
0
0
1
0
2
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
1
0
1
0
0
0
0
0
2
2
1
1
2
0
0
0
0
0
0
1
0
0
0
0
1
2
2
0
1
0
0
0
0
0
1
2
1
1
1
1
0
1
2
0
0
0
0
2
0
2
0
0
1
1
0
0
3
2
0
1
0
1
0
1
2
2
2
0
1
0
1
0
1
1
0
0
1
0
1
1
0
2
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
1
1
3
0
1
0
2
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
1
1
1
1
0
1
1
2
0
1
1
0
1
0
1
0
2
1
0
0
1
0
0
0
2
2
0
0
0
1
0
0
0
1
1
1
0
1
0
0
1
1
1
0
1
1
1
0
0
2
0
1
1
0
1
1
0
0
2
2
0
0
3
0
2
0
2
0
0
2
1
1
0
2
0
1
0
0
0
0
1
2
0
1
0
2
2
0
2
0
1
2
0
0
0
1
1
1
1
0
1
0
0
2
0
0
1
1
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
2
1
2
2
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
1
0
1
0
1
1
0
2
1
1
1
2
1
2
1
0
1
0
0
0
1
2
0
2
0
0
1
2
0
1
0
0
1
0
0
2
0
0
1
0
0
0
1
0
0
1
2
0
1
0
0
0
1
2
0
2
2
2
2
0
0
0
0
4
2
3
0
1
1
1
0
2
0
1
2
2
1
2
0
0
2
0
0
2
2
2
0
0
0
0
1
2
1
0
0
1
3
0
1
2
0
0
0
0
1
0
0
0
6
1
0
0
1
2
0
0
1
0
0
0
1
2
1
0
2
0
2
1
0
0
0
2
1
2
0
0
1
1
2
1
2
1
0
0
1
0
1
1
0
0
0
1
0
0
0
0
1
3
2
0
2
1
2
0
0
0
2
2
0
1
0
0
0
0
1
0
1
0
0
0
1
1
0
1
0
0
1
2
0
1
0
0
1
0
0
0
0
2
1
0
0
1
0
0
2
2
0
3
1
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
3
3
1
0
1
0
0
0
2
0
2
0
2
0
1
1
1
2
1
1
2
0
0
1
2
2
0
0
0
1
0
0
1
0
3
1
1
0
2
1
1
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
4
1
2
0
0
0
2
0
0
1
2
0
0
1
2
2
0
0
0
0
0
1
0
2
0
1
1
0
1
1
2
1
1
0
0
1
3
0
2
1
0
0
0
2
2
0
2
1
0
1
3
1
0
0
0
0
0
0
0
1
1
0
1
1
0
1
0
0
2
0
0
0
0
1
1
2
1
0
0
1
1
2
1
1
0
1
1
0
0
0
2
0
0
3
0
0
2
0
1
2
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
1
2
0
1
0
0
0
0
0
0
0
2
2
0
0
0
1
3
0
2
0
0
0
2
0
1
0
0
0
1
0
0
2
2
1
1
1
0
0
1
1
1
0
0
0
1
0
0
1
0
0
0
2
1
2
0
2
0
0
0
2
1
2
0
0
1
0
1
0
2
2
2
0
0
2
0
1
0
2
0
0
0
1
2
2
2
2
2
0
2
2
0
0
0
0
1
1
1
1
0
0
0
1
1
0
1
1
0
0
2
1
0
1
0
2
0
1
0
0
1
0
1
0
2
0
0
0
2
1
0
1
0
1
2
1
2
2
2
1
0
1
0
0
2
2
0
0
0
3
0
0
1
0
0
2
2
0
0
1
0
1
1
0
1
1
0
0
0
0
0
0
1
1
0
2
1
0
2
1
0
0
0
2
1
0
2
1
1
0
0
0
0
0
0
1
2
2
0
0
2
0
0
1
2
0
0
3
1
0
1
0
2
0
0
0
1
0
1
1
2
2
1
0
2
0
2
0
0
0
0
1
1
1
2
0
0
2
2
1
1
1
0
0
0
0
1
0
1
1
1
4
1
0
1
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
1
0
0
1
0
0
1
1
0
0
0
2
0
1
2
0
0
0
0
0
1
1
0
0
5
1
0
0
0
0
1
0
1
1
1
1
1
2
2
1
1
0
1
2
5
0
0
1
2
0
1
1
0
2
0
0
0
0
0
0
0
0
1
2
1
1
1
1
1
0
0
0
0
3
0
2
0
1
2
1
0
0
2
0
0
0
1
1
2
1
0
0
0
2
2
0
1
2
1
1
0
3
4
0
0
0
0
1
0
2
1
0
0
0
0
1
1
1
0
1
1
0
0
0
1
2
1
2
1
4
0
0
1
0
1
1
0
1
0
1
0
0
1
0
0
1
2
1
2
4
0
2
2
1
1
1
0
0
1
2
0
0
2
1
2
0
1
0
2
0
0
0
0
1
0
0
3
2
1
0
0
0
2
1
0
0
1
1
0
0
1
0
0
0
1
0
2
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
2
0
1
0
0
0
0
0
0
2
0
1
2
1
1
0
0
1
1
0
0
0
0
1
0
0
0
1
0
2
0
1
1
0
1
2
0
1
0
0
0
3
1
0
2
0
1
2
2
1
1
0
0
0
0
0
1
0
1
1
2
1
0
0
2
1
1
1
0
0
0
0
2
2
2
0
2
0
1
0
2
1
0
0
1
0
1
0
0
2
0
3
0
2
0
2
0
2
2
0
1
1
2
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
2
0
1
1
0
0
1
0
1
0
0
2
0
2
0
1
0
2
0
0
1
1
4
2
2
0
0
1
0
1
2
1
0
2
0
2
1
0
2
0
0
2
0
0
2
0
0
1
2
1
0
0
0
0
1
0
0
2
0
0
2
0
0
3
1
0
0
1
0
0
2
0
0
0
2
0
1
1
0
2
1
0
1
2
1
0
2
0
1
0
2
1
0
2
1
0
1
1
0
2
0
0
0
1
0
0
0
0
0
0
2
2
2
0
2
1
2
0
0
2
0
1
0
2
1
1
0
1
0
1
1
0
2
0
0
1
0
2
2
1
2
1
0
2
3
2
0
0
0
2
2
1
0
0
0
0
2
0
0
2
0
1
0
2
1
0
0
0
0
0
1
0
1
0
1
2
0
0
0
1
0
1
0
1
2
0
2
0
0
2
0
0
0
1
2
0
0
2
2
0
0
0
2
0
0
0
0
2
0
1
1
0
0
0
2
2
0
0
1
0
0
1
0
0
2
0
0
0
0
1
0
1
0
2
0
1
2
0
0
0
1
0
0
0
0
1
0
2
0
0
2
1
3
0
0
0
0
1
0
1
1
2
0
0
2
2
1
1
0
0
1
1
0
0
0
2
0
0
1
0
0
2
0
0
1
0
2
2
2
1
2
2
1
0
1
0
1
0
0
1
1
1
0
0
0
0
0
2
1
0
2
0
0
0
2
0
0
0
0
1
0
1
2
0
2
2
1
0
1
2
0
1
0
1
0
0
0
0
0
3
0
1
0
3
1
0
1
0
0
2
0
0
2
2
0
1
2
1
2
1
0
0
0
2
0
0
0
0
0
1
1
0
0
2
2
0
2
2
0
0
2
1
1
0
0
0
0
0
0
0
0
0
2
2
0
1
0
1
0
1
0
0
0
0
0
1
2
0
0
1
0
1
0
0
2
1
0
0
0
1
1
0
2
2
0
0
0
0
1
1
0
0
0
1
0
0
0
1
1
1
0
5
0
2
0
2
0
0
0
0
0
0
2
2
0
0
3
0
1
1
0
1
0
0
1
0
0
1
0
0
0
0
0
2
1
0
1
1
0
2
1
0
1
0
2
2
0
1
0
1
0
0
0
1
0
2
1
0
0
2
0
0
1
0
0
0
0
0
1
1
1
1
0
2
1
2
4
0
0
1
0
2
0
1
1
0
2
2
1
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
1
2
0
0
0
0
0
0
2
0
0
2
1
0
1
0
2
0
1
0
0
2
0
2
1
1
2
0
0
1
0
0
0
0
0
1
2
2
0
0
2
0
1
0
0
0
1
2
0
2
0
2
0
0
0
0
0
1
1
1
2
0
0
1
0
2
0
2
1
0
0
0
2
1
0
0
0
2
0
0
1
0
0
0
0
0
0
2
1
2
0
0
2
1
0
0
0
0
0
0
1
0
0
1
0
1
0
2
0
0
0
1
0
0
0
3
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
6
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
2
1
1
0
3
1
2
0
0
0
1
0
1
0
1
0
3
1
1
0
0
1
0
0
1
0
0
0
1
0
1
1
0
0
0
2
2
0
0
1
0
0
1
0
2
0
4
0
2
0
1
2
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
2
1
0
0
2
0
0
0
1
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
1
0
2
0
1
1
2
0
0
0
1
0
3
0
1
2
0
3
0
1
2
2
1
0
1
1
1
0
0
0
0
0
1
2
0
1
0
2
0
2
0
4
0
0
0
1
0
0
3
0
0
2
0
0
1
0
0
0
0
1
0
1
0
0
0
1
2
0
0
1
0
2
0
0
1
1
2
0
2
1
1
0
1
0
2
2
0
0
0
0
0
0
1
0
1
1
0
0
0
2
0
0
0
1
0
2
0
2
0
0
0
3
0
0
1
0
2
2
1
1
0
0
0
0
0
2
0
2
0
0
2
0
1
0
0
1
1
0
1
2
2
2
0
0
0
2
0
1
0
1
5
2
0
0
2
0
2
1
1
2
0
1
0
0
1
1
1
0
0
0
1
0
1
0
2
0
1
2
0
0
0
1
2
0
0
0
1
1
0
2
0
0
0
2
0
0
0
1
0
1
4
0
2
1
2
0
1
0
2
0
0
0
1
0
2
0
0
0
0
1
1
1
2
0
2
0
0
2
0
0
1
1
1
1
0
1
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
2
2
0
1
3
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
1
0
0
0
0
1
0
1
0
1
1
1
0
0
0
0
0
0
0
1
1
0
0
0
1
2
0
0
1
2
1
1
1
0
0
2
0
1
0
1
1
2
1
0
0
2
0
0
0
2
1
1
1
1
1
2
0
0
2
1
1
1
0
0
2
2
2
1
0
1
2
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
2
3
2
0
1
2
1
0
0
2
0
2
2
1
1
2
0
0
1
1
1
0
0
0
2
0
1
2
0
0
1
0
0
1
0
3
0
0
0
2
2
0
0
0
1
2
1
0
2
1
2
0
0
2
0
0
0
0
2
1
0
1
0
0
1
0
2
0
1
2
1
0
2
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
1
1
1
1
2
1
2
2
0
0
0
1
1
0
0
0
0
0
3
0
2
0
0
0
1
0
2
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
3
0
2
1
2
1
2
0
2
1
1
0
0
0
1
0
0
0
0
1
2
0
1
0
2
2
0
0
0
2
2
0
1
0
2
0
0
1
2
0
0
0
1
0
0
2
0
2
0
0
2
1
0
0
0
0
1
1
1
1
2
3
0
1
1
1
1
2
0
1
1
0
2
0
0
0
1
1
1
1
0
2
0
1
0
2
1
1
1
0
2
0
0
2
2
2
0
0
0
1
0
1
0
1
2
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
2
0
2
0
1
1
1
1
0
0
0
1
3
0
0
2
1
0
0
0
1
1
1
0
0
1
2
0
2
0
0
0
3
0
0
1
0
1
0
0
1
1
0
0
0
0
1
2
1
2
1
2
0
0
0
1
0
0
1
0
0
2
1
0
0
2
0
0
0
2
0
0
0
1
0
2
1
0
0
0
1
2
0
1
1
1
1
0
1
1
0
0
1
1
0
0
1
2
0
1
0
0
1
1
0
0
0
1
0
1
2
0
2
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
2
1
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
2
2
1
2
2
0
2
0
0
2
1
0
1
2
0
0
2
0
3
1
1
0
0
0
2
0
1
1
2
1
0
2
0
2
0
3
0
0
0
1
1
1
0
0
1
0
2
1
1
0
1
0
2
1
0
2
1
0
1
0
1
2
0
0
1
2
0
2
2
2
1
3
0
1
1
1
1
1
2
0
1
0
1
0
0
0
0
0
0
1
1
1
2
2
0
1
0
2
0
0
0
2
0
2
0
0
2
2
0
1
1
1
0
0
1
2
0
2
0
0
2
0
0
1
0
0
0
0
0
1
2
1
0
0
0
0
0
0
1
2
2
2
1
0
1
1
0
0
1
1
0
1
1
1
0
0
0
1
0
1
0
1
3
0
0
2
1
1
0
0
1
0
1
0
0
1
1
0
5
0
1
2
0
0
2
2
0
0
1
2
1
2
0
0
2
1
2
0
1
0
0
1
1
2
2
0
0
1
2
0
2
0
2
2
0
0
0
0
0
1
1
0
0
1
0
2
0
0
1
3
1
0
0
1
2
0
1
1
0
0
0
0
2
2
0
0
2
1
2
0
1
0
0
0
0
1
0
0
0
2
1
0
0
0
4
0
2
0
1
1
0
2
1
0
2
0
0
0
0
0
1
0
3
0
1
0
2
0
0
1
0
1
1
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
2
2
0
0
1
0
5
0
2
0
0
1
2
0
2
0
2
2
0
0
1
0
1
2
2
2
3
1
0
0
0
0
0
0
2
1
0
2
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
1
0
1
1
0
0
0
2
2
2
0
0
0
1
1
0
0
0
2
0
1
0
1
0
1
1
1
1
0
0
6
1
1
0
0
2
1
0
0
0
4
1
0
0
1
2
1
0
0
0
1
0
0
0
0
1
1
2
1
0
0
0
1
3
2
1
1
0
2
2
0
0
0
0
0
1
0
1
2
1
2
0
2
2
0
0
1
0
1
0
1
2
2
1
0
0
0
0
0
2
0
0
0
1
1
0
1
0
0
1
0
3
2
1
0
0
1
1
1
0
0
1
1
0
5
2
0
2
0
0
0
4
1
0
1
2
0
1
0
1
0
0
0
1
0
0
2
0
0
1
1
0
1
0
2
2
1
0
0
0
0
0
1
0
1
0
0
0
1
0
1
2
2
0
2
1
2
0
0
1
1
0
0
0
0
3
0
2
0
0
0
1
0
2
1
0
0
0
1
1
0
0
1
2
0
0
0
1
2
2
0
1
0
1
1
1
1
1
0
1
2
0
1
0
1
1
1
1
0
0
0
0
0
2
0
1
1
2
1
0
1
1
2
2
2
0
2
2
1
0
0
1
2
2
2
2
2
0
0
0
0
0
3
1
2
1
0
1
0
1
2
2
2
3
1
0
1
1
1
0
2
0
0
1
0
1
2
1
1
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
1
1
1
0
1
0
2
0
0
1
0
0
1
1
2
0
0
0
1
2
1
1
0
0
0
0
0
0
0
0
1
2
0
2
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
2
1
0
2
1
0
1
0
2
2
0
1
0
2
1
1
0
0
1
2
1
0
1
2
0
0
1
1
1
0
0
0
0
1
2
2
0
0
1
0
0
2
2
1
0
0
0
0
1
0
2
0
0
2
0
1
0
0
1
0
0
1
2
2
0
0
0
0
2
4
0
0
1
0
2
0
0
1
0
0
2
0
2
1
0
0
0
0
0
0
0
1
3
1
0
0
2
0
0
4
2
1
0
0
2
0
0
1
1
0
2
0
1
1
0
0
0
0
0
0
0
0
2
1
0
0
0
2
1
0
1
0
1
2
2
1
1
0
2
0
1
0
0
4
0
2
1
0
2
2
0
1
1
0
0
2
2
1
2
2
4
0
2
2
2
1
0
1
0
2
0
1
2
3
0
0
0
2
2
0
0
2
2
0
2
1
0
0
1
0
2
2
0
1
0
1
0
1
0
0
1
0
0
0
3
1
0
0
0
1
0
0
1
0
0
5
0
1
0
0
1
0
1
2
1
0
0
1
0
2
4
1
0
1
1
0
0
1
2
0
1
1
0
0
0
0
0
2
2
1
0
0
0
2
1
3
1
1
2
2
0
0
0
0
1
2
0
0
2
0
0
1
1
0
0
1
1
0
1
0
0
1
3
0
0
2
1
0
1
0
0
0
2
2
1
2
2
1
0
0
0
0
0
0
0
2
0
3
2
1
0
2
2
0
0
2
0
2
2
0
2
0
0
1
0
0
1
0
0
0
0
1
0
2
0
2
0
2
0
1
0
0
2
1
1
2
0
2
2
1
2
2
0
1
2
1
1
1
0
1
2
0
1
2
0
2
0
0
1
0
1
1
1
2
2
0
1
0
2
1
1
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
4
0
1
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
2
2
0
1
0
1
0
1
2
2
0
1
1
0
0
0
0
1
0
0
2
2
1
1
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
2
0
0
0
1
1
0
2
0
2
0
1
0
0
0
0
0
1
2
1
1
0
2
1
0
1
0
1
0
1
0
0
0
1
1
0
0
0
0
1
0
1
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
2
1
0
0
1
0
0
1
2
0
1
1
1
1
0
2
1
0
0
1
0
0
0
2
1
0
1
0
0
0
0
0
1
1
2
1
2
0
0
1
3
2
0
2
2
0
2
0
2
2
1
1
0
0
1
0
0
1
0
0
0
2
2
1
0
1
0
0
0
0
0
2
1
2
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
3
1
1
0
0
1
0
1
1
0
0
0
0
1
0
1
1
2
0
2
0
1
0
0
1
0
1
1
2
1
0
0
2
1
0
1
1
2
0
1
0
1
2
0
0
1
3
1
0
1
5
0
0
2
0
1
1
0
0
2
2
0
1
0
1
0
2
0
1
0
1
0
0
1
1
0
1
2
3
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
3
1
0
0
2
0
1
0
1
0
3
1
1
2
1
0
0
0
0
0
3
0
0
0
0
0
2
0
2
0
0
1
0
1
0
1
1
1
0
1
2
0
0
1
1
0
1
0
0
2
0
1
0
0
0
2
0
1
2
1
0
1
0
0
0
1
0
0
2
0
1
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
1
2
0
0
1
2
0
0
4
1
1
0
0
4
0
1
0
2
1
2
0
2
1
2
0
0
0
1
0
2
1
1
1
0
1
2
1
0
2
1
2
0
3
2
1
2
4
0
2
1
0
0
1
1
0
1
1
1
2
3
2
1
1
1
1
1
2
1
1
1
0
2
0
1
1
0
0
0
1
0
0
0
0
0
2
2
0
2
1
0
0
1
0
3
2
0
1
0
2
0
0
2
1
0
2
1
0
0
1
1
2
0
1
1
0
0
0
0
1
0
1
0
2
1
2
2
0
1
1
0
0
0
0
1
1
0
1
0
0
0
2
1
0
2
0
0
1
0
1
2
2
1
2
0
0
2
0
0
0
1
2
2
0
1
1
1
2
1
0
0
0
0
1
2
1
1
0
0
0
0
1
0
0
0
0
0
1
1
0
1
2
2
2
2
0
0
1
0
0
1
0
0
0
0
0
2
1
0
0
0
2
1
0
0
0
0
0
0
2
0
1
0
0
2
4
0
2
2
2
3
2
0
0
2
1
1
1
0
1
2
0
0
1
0
0
0
0
0
0
1
1
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
2
2
2
2
2
1
2
2
1
0
1
1
2
0
1
2
1
0
0
0
0
0
1
1
0
1
0
0
2
0
0
2
0
0
0
1
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
2
0
1
0
2
0
1
0
0
0
1
1
2
0
0
0
1
0
2
1
0
0
2
1
1
2
1
2
4
2
1
2
1
0
0
0
0
0
2
0
2
0
0
0
0
0
1
1
0
0
0
5
2
0
1
1
0
2
1
1
0
0
1
0
1
0
2
1
0
2
2
0
1
0
2
1
2
0
1
2
0
0
0
0
0
0
1
2
0
2
1
0
1
0
1
0
0
0
2
1
1
2
0
0
1
0
0
0
1
0
0
0
0
2
0
0
1
2
0
2
0
1
0
0
1
0
2
0
0
2
1
1
0
0
0
1
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
1
2
0
1
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
2
0
0
0
2
0
1
0
1
0
1
4
1
0
0
1
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
1
1
1
1
2
0
2
1
1
2
2
2
1
0
0
0
0
0
0
1
1
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
1
1
0
1
1
0
0
0
0
2
0
2
1
2
1
0
0
0
1
0
3
0
0
2
1
0
0
0
1
1
0
1
2
0
2
1
0
1
1
1
0
2
0
0
1
1
1
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
1
0
0
2
1
0
2
0
0
3
0
1
0
1
1
0
0
0
2
0
0
0
1
0
0
0
1
3
0
0
1
0
1
0
0
0
1
0
1
0
1
1
4
0
0
1
0
0
0
0
1
0
2
0
0
0
2
1
0
0
2
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
2
0
0
1
0
1
0
0
2
0
1
1
2
0
0
0
1
0
0
0
0
1
0
1
1
2
0
1
1
1
1
0
1
1
0
2
0
0
0
0
0
0
0
2
0
1
1
1
1
0
0
1
0
0
2
1
0
0
2
0
1
2
1
0
1
1
0
0
0
1
0
0
2
1
0
0
1
1
1
2
0
1
2
0
0
1
1
2
2
2
2
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
1
1
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
2
1
1
2
0
1
2
0
0
2
1
2
1
0
0
0
1
0
0
0
0
0
0
0
4
0
0
1
0
0
0
1
0
0
0
0
0
1
2
1
0
1
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
1
0
4
0
0
1
0
1
2
0
0
0
1
2
2
0
1
0
0
2
1
1
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
4
1
0
0
1
2
0
0
0
0
2
0
1
0
2
1
0
0
0
1
1
0
0
0
1
1
0
1
0
1
1
1
2
1
0
1
2
0
0
1
0
0
0
0
1
1
2
0
1
0
0
1
0
1
0
0
2
0
0
2
0
2
1
0
0
2
1
0
1
1
0
0
0
0
2
0
0
0
0
0
2
2
0
1
1
2
2
0
1
0
0
0
0
1
0
1
2
0
2
2
0
1
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
1
2
2
2
1
0
0
0
1
0
0
2
1
0
1
1
0
0
1
0
2
0
0
1
1
1
2
0
0
0
0
1
0
0
1
0
2
2
0
0
0
0
0
1
2
2
1
1
1
2
0
2
0
2
0
0
2
0
0
2
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
2
1
0
0
2
1
2
2
1
0
0
2
2
0
0
0
2
0
2
0
2
1
2
2
0
2
0
0
3
0
2
0
0
2
0
0
0
0
0
2
0
1
0
2
1
0
2
2
2
4
0
0
0
1
1
0
1
5
1
0
0
0
1
0
0
2
2
0
1
0
1
2
0
0
1
0
1
1
0
1
1
1
0
2
2
1
2
0
1
0
1
0
0
0
0
0
1
0
0
2
1
0
3
0
2
0
0
0
2
2
0
0
1
1
2
1
0
2
0
2
2
0
0
0
0
1
0
0
1
1
2
0
1
0
0
1
1
0
0
0
1
0
1
1
1
1
1
0
0
0
0
2
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
1
1
0
0
0
1
0
2
1
0
0
1
0
1
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
2
3
0
1
2
0
0
0
2
0
2
0
0
1
2
0
1
0
1
0
2
1
2
2
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
2
2
1
2
0
1
0
0
2
0
0
1
1
1
1
0
0
2
0
0
2
1
1
0
0
2
0
0
0
1
0
0
0
1
1
2
0
2
1
0
1
0
0
2
1
1
0
0
3
0
1
0
0
0
0
0
0
2
2
0
0
0
1
0
1
1
1
0
1
0
2
0
0
0
0
0
1
0
1
0
0
2
0
4
1
0
0
1
2
7
0
0
2
0
0
1
2
0
1
3
2
0
1
0
0
0
2
2
0
0
2
0
0
0
2
0
2
3
1
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
1
0
2
0
0
2
0
1
1
2
0
0
0
0
1
0
0
2
1
0
0
2
0
1
1
0
2
0
0
3
2
0
1
0
0
0
1
1
0
0
1
2
1
1
2
1
2
0
1
0
1
2
0
1
0
0
0
1
0
0
1
0
2
0
0
1
1
2
1
2
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
1
0
1
0
1
0
1
2
0
0
2
1
1
0
1
2
1
1
0
2
3
0
0
0
0
0
1
1
0
0
0
0
1
2
0
2
0
1
2
1
0
0
2
2
2
0
1
0
0
0
0
1
1
0
0
0
0
0
1
1
0
2
5
1
3
0
2
0
1
1
0
0
1
0
1
2
0
0
0
1
4
2
0
0
1
1
0
2
2
0
0
0
0
5
2
0
0
0
2
0
0
0
1
0
1
0
1
0
0
0
2
1
2
1
1
0
2
1
2
0
0
0
0
1
0
2
6
1
2
0
0
2
0
1
0
0
0
0
0
1
0
1
0
0
0
2
2
1
0
1
0
0
0
0
0
0
2
0
2
0
0
1
1
0
2
1
0
0
1
0
0
1
1
2
0
2
0
1
2
0
0
1
0
0
1
2
0
0
1
0
1
0
1
0
2
0
0
1
2
2
0
0
0
1
2
0
0
2
1
1
2
0
1
2
0
1
1
1
1
2
0
1
1
2
0
0
0
0
1
2
0
1
0
1
2
1
2
2
0
1
0
2
0
2
0
0
0
0
0
1
0
0
0
0
1
2
2
0
1
1
0
0
0
0
1
3
0
2
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
2
0
1
1
0
0
0
0
2
0
0
2
0
1
1
0
2
0
0
2
0
0
0
0
0
2
0
0
2
1
1
0
0
0
0
2
0
1
1
2
0
0
2
1
0
2
0
0
2
0
0
0
0
2
2
0
0
0
1
2
0
2
1
2
0
0
0
0
2
0
2
0
0
2
1
0
1
0
1
0
0
0
1
1
2
0
1
0
0
1
1
0
1
2
0
0
0
0
1
1
0
2
2
0
0
0
0
0
0
0
3
2
0
1
0
3
0
4
2
0
0
0
0
0
0
1
2
0
0
0
1
0
0
1
0
0
1
0
1
1
0
0
0
1
1
1
1
1
0
0
0
1
0
2
0
0
0
1
0
0
0
0
1
2
2
2
1
1
0
0
0
0
0
0
0
0
1
0
2
1
0
1
0
0
3
1
1
0
1
1
1
2
0
0
2
2
0
4
0
0
0
2
0
0
0
1
1
1
2
0
0
1
1
1
0
0
0
2
0
0
0
0
1
0
1
1
1
0
0
1
2
0
0
0
2
1
1
2
0
0
0
2
1
1
0
0
0
0
1
0
2
0
0
1
0
0
0
2
1
0
2
0
0
0
2
0
1
4
0
0
0
2
0
1
0
0
0
0
0
1
0
2
1
0
0
1
2
0
2
0
0
1
2
0
2
2
0
1
0
0
1
0
0
2
0
1
0
1
0
1
2
1
0
2
0
0
0
0
2
2
1
1
1
0
0
0
0
2
0
0
1
0
0
0
0
1
1
1
0
1
2
2
1
2
1
0
0
0
1
1
1
0
2
2
1
2
2
0
1
2
2
1
1
0
1
2
0
0
1
0
1
0
0
0
1
0
1
0
2
0
1
0
0
0
0
0
0
1
3
0
0
1
0
0
2
0
0
0
0
2
1
0
1
2
0
1
0
0
1
2
0
1
1
0
1
2
0
3
1
1
0
0
0
2
0
0
0
0
3
0
2
2
1
2
0
2
0
2
0
1
0
0
2
0
0
0
1
5
1
2
1
0
2
0
0
0
1
2
0
0
1
1
0
0
0
1
2
0
1
1
2
0
0
0
0
3
1
0
0
2
0
0
1
1
1
0
2
0
0
1
1
0
2
1
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
1
0
1
0
2
2
0
0
1
1
0
0
1
2
0
1
2
2
0
0
0
0
0
0
0
0
0
2
1
0
1
0
1
0
0
1
0
0
1
2
1
2
0
0
1
4
2
1
0
0
3
0
0
3
0
1
1
0
1
1
1
0
1
0
0
0
2
0
0
1
0
0
4
0
1
0
1
2
1
1
1
0
2
0
0
2
1
4
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
3
1
0
0
0
0
2
0
1
0
0
1
2
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
1
2
0
1
0
1
1
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
2
0
0
1
0
1
2
0
2
6
0
0
1
0
0
0
2
1
2
0
0
1
0
0
0
1
2
2
0
5
2
0
0
1
0
1
2
2
0
0
0
0
0
0
1
1
1
0
2
2
0
0
2
0
2
0
0
0
1
0
0
2
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
1
1
0
2
0
1
1
0
0
0
0
0
0
1
0
1
1
2
2
0
2
0
0
1
1
2
4
0
0
2
1
0
0
2
3
1
0
0
0
0
2
0
1
0
1
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
2
0
1
1
2
0
0
0
1
0
1
0
1
2
0
0
1
0
2
0
1
2
0
1
0
0
1
1
0
1
1
1
0
2
2
3
0
0
0
0
0
1
0
1
0
0
0
2
1
0
0
0
2
1
0
1
0
1
3
0
0
0
3
2
0
0
0
1
0
1
1
0
0
0
0
1
1
0
0
0
3
0
1
2
1
1
0
1
1
1
0
2
2
2
2
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
3
0
2
0
1
1
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
1
0
1
0
0
1
2
1
1
1
1
0
2
1
1
0
0
2
2
0
2
2
0
1
0
0
0
2
1
1
0
0
0
0
1
2
2
0
0
0
1
1
0
0
0
1
1
0
0
0
2
2
0
0
3
1
1
0
2
0
1
1
1
1
2
1
0
0
0
2
1
0
0
0
0
0
1
0
0
2
0
0
2
0
2
0
1
0
0
2
2
2
0
2
0
0
2
0
0
2
0
0
2
2
0
0
2
1
0
2
1
1
1
0
1
0
0
1
1
0
0
0
0
0
1
0
1
0
1
2
0
0
2
2
0
1
0
2
0
0
0
0
0
1
0
0
1
1
0
0
0
2
0
0
0
1
1
0
0
0
0
0
2
2
0
2
0
0
1
2
2
0
0
0
0
1
2
1
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
3
2
2
2
0
0
1
0
0
3
0
1
0
1
0
2
1
1
0
1
1
0
1
0
0
0
0
2
1
0
0
1
2
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
2
0
1
1
0
0
1
2
0
2
0
0
0
1
2
1
0
1
1
0
1
0
0
0
0
0
2
0
0
0
2
0
0
1
1
0
1
1
2
2
2
2
1
1
0
2
2
0
2
0
2
0
0
0
0
2
0
1
1
1
2
0
0
0
0
1
0
0
1
2
0
1
2
1
0
0
1
1
0
0
0
1
0
0
0
1
0
0
2
0
0
1
0
0
2
1
0
0
0
2
1
2
2
1
0
2
2
2
0
3
0
0
2
0
0
1
0
2
1
1
2
0
0
1
3
0
2
1
0
1
0
0
2
1
0
2
0
0
1
1
2
0
1
0
0
2
2
6
2
2
0
0
0
1
1
0
0
3
1
0
0
0
0
1
0
1
0
0
0
1
0
1
2
1
2
0
2
0
0
0
1
2
2
0
0
1
0
0
1
0
1
0
2
2
0
2
0
0
1
1
2
1
0
0
0
1
0
1
1
5
0
2
0
2
2
0
0
0
0
0
1
0
0
0
2
0
1
1
0
0
0
0
2
0
0
0
1
0
1
0
0
2
1
0
1
0
0
0
0
1
2
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
3
0
0
1
0
1
1
1
0
0
1
0
0
0
1
1
1
2
1
0
0
2
0
1
0
1
0
1
2
1
2
0
2
2
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
2
1
0
1
1
0
1
1
1
2
0
0
2
0
2
0
1
0
2
0
1
0
0
0
2
1
3
0
2
2
1
0
1
2
0
0
2
2
0
1
1
2
0
2
0
0
0
0
2
0
0
1
1
1
1
2
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
3
0
3
1
0
0
0
2
0
0
1
1
1
1
1
0
2
1
2
1
1
0
0
0
0
2
0
0
2
1
1
1
0
0
0
1
2
0
0
2
0
3
0
1
0
0
2
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
1
1
0
1
1
0
2
0
0
0
0
2
0
1
2
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
1
0
0
1
0
2
0
0
1
1
2
2
0
2
1
1
0
0
0
2
2
1
2
2
0
0
1
0
1
0
0
0
1
2
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
2
2
0
1
2
0
1
0
0
0
0
0
2
1
0
0
0
1
0
1
1
0
2
0
0
0
0
1
0
0
0
4
2
2
0
0
1
0
2
2
2
0
0
1
0
1
0
2
0
0
0
0
2
1
0
0
1
2
2
0
0
2
1
0
0
0
1
2
1
0
2
2
0
1
0
1
1
1
2
1
0
0
0
2
2
1
0
1
1
0
0
0
0
0
0
2
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
2
1
0
1
0
0
0
2
2
0
1
1
0
0
0
2
2
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
1
0
0
3
0
1
0
1
2
0
2
0
1
0
0
1
0
2
0
1
2
1
0
0
1
0
0
2
1
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
1
0
0
1
2
2
1
0
0
0
0
0
0
0
0
1
1
2
1
0
2
2
1
0
2
1
1
2
0
2
2
1
0
1
1
0
0
0
0
0
1
0
2
1
0
0
0
0
1
0
0
2
0
0
1
0
1
2
1
0
1
0
0
0
0
2
2
0
1
0
0
2
0
0
0
2
0
0
2
1
2
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
2
1
1
0
0
1
0
0
2
2
0
2
1
1
0
1
2
2
0
0
0
0
0
0
1
1
2
1
1
0
2
0
2
2
0
0
0
1
2
1
0
0
0
1
2
0
0
2
0
2
2
1
0
2
1
1
1
2
0
1
0
0
1
2
1
0
1
0
0
0
1
2
0
1
2
3
1
0
2
0
1
2
0
0
0
1
1
0
0
1
1
3
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
2
1
1
2
0
0
1
0
0
1
1
1
0
2
2
1
0
1
0
0
0
2
0
0
0
1
0
1
0
2
0
0
2
0
1
2
0
0
0
1
1
0
0
0
0
3
0
2
0
0
0
1
0
0
0
1
1
0
0
1
0
2
1
0
2
2
0
2
0
0
0
0
1
0
0
1
2
2
2
0
1
1
1
2
0
3
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
1
1
2
0
1
0
0
0
1
0
0
0
1
0
2
0
0
1
1
1
3
0
0
0
0
0
2
1
2
0
1
1
0
0
0
0
0
1
0
2
0
0
2
0
1
0
0
2
0
1
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
1
1
0
0
1
2
0
0
0
0
1
2
0
0
2
0
0
2
0
0
0
0
2
0
2
0
0
0
1
1
1
0
2
2
0
1
0
2
1
0
2
0
0
0
2
0
2
0
0
1
2
0
1
0
0
0
2
1
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
1
0
1
1
0
1
0
1
0
0
0
0
2
1
0
4
0
1
0
0
0
1
0
0
4
2
0
1
1
1
2
0
0
0
0
2
1
2
2
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
1
0
1
0
1
0
0
0
2
3
1
0
2
1
0
2
0
1
1
0
1
2
0
1
0
2
1
5
0
0
2
1
2
0
0
0
0
0
0
3
2
2
1
0
0
1
2
3
2
0
0
0
0
0
1
0
1
1
1
0
0
2
2
0
5
1
0
1
0
0
2
0
0
0
2
0
0
0
2
0
0
1
0
0
1
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
1
0
2
1
2
2
1
1
0
1
0
0
0
0
1
0
0
2
1
3
2
0
0
0
0
0
0
1
0
1
2
0
1
0
2
0
0
2
0
1
2
1
2
0
1
0
0
0
0
0
1
2
0
1
1
3
0
0
2
0
0
0
0
1
0
0
2
2
0
1
0
1
1
1
1
0
1
1
0
0
0
2
0
0
0
2
2
1
2
1
0
2
0
0
0
2
0
2
2
0
0
0
0
2
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
2
0
0
1
1
0
0
2
1
0
0
0
0
0
0
1
1
1
1
0
0
1
1
4
2
2
0
2
0
0
0
0
0
1
1
0
1
0
0
2
0
0
1
0
0
0
1
0
3
1
1
0
0
2
1
1
0
1
1
0
0
1
0
0
0
0
2
0
0
0
1
1
2
0
0
1
1
0
0
2
1
1
1
2
0
1
2
0
0
0
0
0
2
0
0
0
1
0
1
2
0
2
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
2
2
0
1
0
0
7
1
0
0
0
0
1
0
0
0
0
0
0
1
2
2
0
0
0
2
1
1
0
0
0
2
1
1
0
0
1
4
0
1
0
0
2
0
0
0
1
2
0
2
0
1
2
0
0
0
1
2
0
0
0
0
1
1
0
1
2
0
2
0
1
0
1
0
0
0
0
2
0
1
0
1
1
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
1
0
0
1
0
1
0
0
1
1
0
0
2
0
0
1
1
0
0
0
1
1
0
0
1
0
0
2
1
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
1
0
0
0
1
1
2
0
3
2
1
1
0
0
0
1
2
1
0
0
2
0
2
1
1
0
2
0
1
1
0
2
0
0
0
1
0
0
2
1
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
3
0
0
0
0
2
1
0
0
2
1
0
0
0
0
2
0
2
0
0
0
0
2
1
0
0
1
0
1
0
1
1
2
0
1
0
1
0
0
0
1
1
0
0
1
0
0
4
2
1
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
4
1
0
1
0
0
0
2
2
0
0
0
1
3
2
1
0
0
2
0
0
0
2
0
0
1
0
0
0
0
2
2
1
2
0
1
2
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
1
0
2
1
0
0
1
2
1
0
0
0
0
1
0
0
0
2
0
1
2
0
0
0
1
0
0
0
0
1
2
1
0
2
1
1
0
2
0
2
0
2
0
2
0
1
0
0
1
0
1
0
2
0
0
1
2
1
3
0
0
1
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
1
0
0
2
0
1
2
1
0
0
0
1
0
1
0
0
3
0
0
1
0
0
0
0
3
0
0
0
1
0
0
0
0
2
0
0
1
1
0
2
2
0
2
0
0
1
2
0
0
0
1
1
2
0
0
0
0
2
0
0
0
0
2
0
0
1
3
0
0
2
1
0
1
0
2
0
1
2
0
1
0
0
1
0
0
2
0
2
2
1
0
0
0
1
1
0
2
1
0
0
2
0
1
0
0
0
0
0
0
0
0
2
1
1
1
0
0
0
0
2
0
1
0
0
2
0
2
0
1
2
1
0
2
2
1
1
0
0
0
1
2
0
1
2
0
0
0
0
2
0
0
0
2
0
1
2
1
0
0
0
0
0
1
2
1
1
0
0
0
1
2
2
0
2
0
0
0
0
1
0
0
1
0
0
2
0
0
1
3
0
0
0
0
1
0
0
0
2
0
0
1
0
0
2
0
2
0
0
1
1
0
0
0
2
1
0
1
0
0
0
1
0
0
1
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
2
0
0
0
0
2
2
0
0
0
0
0
0
2
2
1
0
0
2
1
0
1
0
0
0
1
0
1
2
0
1
0
2
0
1
1
2
0
0
0
0
0
0
0
2
2
2
0
0
0
0
2
1
0
1
1
0
1
0
0
0
6
0
1
0
2
1
0
2
3
1
0
0
0
1
2
0
1
1
0
0
0
0
0
1
0
3
0
1
1
0
0
2
1
3
0
0
2
0
1
1
2
0
2
0
0
2
2
4
2
1
1
1
0
0
1
1
3
0
1
1
1
0
1
0
1
0
2
0
1
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
1
2
1
0
1
0
0
1
0
2
2
0
0
2
2
1
0
0
2
1
0
0
2
0
0
0
1
2
1
1
0
0
0
0
2
1
0
1
0
2
2
2
0
0
0
1
1
1
1
0
0
0
2
0
1
1
1
1
2
0
2
1
0
0
9
1
1
0
0
0
1
1
1
0
0
2
0
1
1
0
0
0
0
0
0
0
1
0
1
6
1
2
2
0
0
1
1
0
2
0
0
1
1
0
1
0
0
2
1
0
2
2
2
2
2
0
1
1
2
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
1
0
0
0
2
1
2
1
1
0
0
0
0
1
0
1
0
2
0
1
0
1
2
0
0
2
0
2
0
0
3
0
0
2
0
0
0
1
0
1
0
1
1
1
1
1
0
4
0
0
0
0
0
1
1
2
1
1
0
2
1
0
2
1
0
1
2
2
2
2
0
0
2
0
1
0
0
2
0
0
2
0
0
0
2
1
0
0
2
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
1
0
0
0
0
1
0
0
1
1
0
2
1
2
1
1
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
2
0
0
1
0
1
2
0
0
1
1
0
2
0
0
0
0
0
0
2
2
1
2
0
0
0
0
2
1
2
0
1
0
2
0
0
0
0
0
1
1
0
0
0
2
0
2
1
1
2
0
3
0
0
1
0
0
2
0
0
2
1
0
0
1
1
0
4
1
0
0
1
0
0
0
0
0
1
0
2
0
0
1
2
1
1
0
0
2
0
1
0
0
2
2
0
2
1
1
2
0
0
0
4
2
2
0
0
1
1
0
0
1
1
1
1
0
2
1
1
0
1
0
1
0
0
0
1
1
0
0
1
0
1
1
0
0
0
2
0
0
1
1
0
2
1
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
2
0
2
0
0
0
0
1
2
1
2
2
1
1
1
0
1
0
2
0
1
1
0
0
2
0
2
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
2
0
0
3
1
0
0
0
2
2
0
1
3
0
1
0
0
0
0
2
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
1
7
2
0
0
1
0
2
1
0
0
1
0
0
0
2
1
2
0
0
1
0
1
2
0
0
1
3
0
2
2
2
0
0
1
0
0
0
2
2
2
1
0
0
0
1
1
0
0
2
0
0
0
0
2
2
0
0
2
1
0
1
0
0
0
3
0
2
2
1
0
0
0
2
1
0
2
0
0
0
0
0
2
0
2
2
1
1
0
2
1
0
0
2
2
2
0
0
2
0
1
1
0
0
2
0
1
0
0
0
0
0
2
1
0
2
1
0
0
0
0
1
0
0
1
0
1
1
0
3
1
0
2
1
1
2
0
0
0
0
0
1
0
0
2
1
0
2
2
0
1
0
2
1
1
0
1
0
3
0
0
0
3
0
1
0
1
2
0
1
1
0
1
2
0
2
1
0
0
0
0
0
2
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
2
1
1
0
1
2
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
1
1
1
0
1
0
0
1
1
1
2
1
0
2
2
0
0
2
2
1
0
0
0
2
0
0
0
0
0
1
0
1
2
1
0
1
0
0
0
2
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
3
0
1
0
5
3
0
1
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
2
0
0
2
0
1
0
1
0
2
0
0
2
2
0
0
1
0
0
0
0
0
1
0
0
2
1
1
0
1
1
0
0
1
0
1
0
2
0
0
2
1
0
1
1
1
0
3
1
0
0
0
0
2
0
0
1
2
2
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
1
0
2
1
0
2
1
0
0
0
0
0
0
0
0
0
1
1
1
0
2
0
1
0
0
1
1
0
1
0
0
1
2
1
1
0
0
0
1
1
0
0
1
0
1
0
0
1
0
0
1
1
2
2
0
2
1
1
0
0
0
0
0
2
0
1
0
1
1
2
1
0
2
0
0
0
2
0
5
0
0
0
0
0
1
0
1
1
0
0
0
1
1
0
0
3
1
0
0
0
0
1
0
2
0
1
1
1
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
1
2
2
3
1
2
0
0
1
3
2
1
0
0
1
1
2
1
1
0
0
1
0
1
0
0
2
2
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
1
0
0
0
2
2
1
1
2
1
0
0
0
0
1
0
2
1
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
2
1
1
1
0
1
0
0
0
0
1
0
2
1
2
2
2
0
1
0
2
2
0
0
2
0
0
0
2
2
1
4
1
0
0
0
3
2
0
1
0
0
2
1
2
1
0
0
0
1
0
3
2
1
0
0
0
0
0
0
0
2
2
0
0
1
0
2
2
0
2
1
0
1
2
1
1
1
1
2
2
0
0
1
0
1
0
0
2
1
1
0
2
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
2
0
2
0
0
1
0
1
1
0
1
1
2
0
1
0
0
1
1
2
0
1
0
1
2
1
0
0
1
1
4
1
1
0
1
0
0
1
3
0
0
2
1
1
0
0
0
0
2
1
1
0
1
0
1
1
0
1
1
0
1
0
0
2
0
1
0
1
0
0
1
0
2
0
0
0
0
2
0
0
0
1
0
2
0
0
0
1
0
2
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
2
0
0
0
1
0
2
2
0
0
1
3
1
0
1
0
1
3
1
1
0
0
1
0
1
0
0
1
3
1
2
0
0
0
2
0
1
0
2
1
0
0
0
0
0
1
4
1
0
2
2
1
0
1
1
2
1
0
0
2
0
2
0
1
1
2
0
1
1
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
1
0
0
2
0
0
2
0
1
1
0
0
0
0
1
1
0
0
0
1
1
0
0
0
2
2
2
0
0
1
0
0
0
0
0
1
2
1
0
0
0
0
1
2
0
2
2
2
1
2
0
2
1
0
1
0
1
0
0
0
0
2
2
0
2
0
0
0
0
2
0
1
2
0
0
0
0
0
2
3
0
0
1
1
2
1
0
2
0
0
0
1
0
1
0
0
0
0
1
1
0
2
2
2
0
0
0
2
1
0
0
0
0
0
0
2
0
1
1
0
0
0
1
1
0
2
0
0
0
0
0
1
0
0
0
0
1
1
1
0
1
2
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
2
1
1
0
1
0
2
3
1
1
0
0
2
0
1
0
0
1
0
1
1
0
1
0
0
0
0
2
1
0
0
0
0
1
1
1
0
2
0
2
1
1
0
0
4
2
0
0
1
1
1
0
0
1
2
1
1
0
2
2
1
1
1
0
2
1
0
2
0
2
0
2
2
2
1
0
0
0
1
1
0
1
0
0
0
0
1
1
2
1
0
0
0
2
2
1
0
1
0
2
0
1
0
0
1
0
0
0
4
0
0
0
0
2
0
1
2
1
0
1
0
0
1
2
0
0
2
2
3
1
0
0
1
1
0
0
2
0
0
1
0
0
0
1
1
1
0
1
1
0
0
1
0
0
0
0
0
1
2
1
1
0
3
0
0
1
2
1
0
1
1
1
2
1
0
2
1
0
1
2
0
1
0
0
0
1
0
1
1
1
2
1
2
0
1
0
0
0
2
0
1
0
0
0
0
0
1
0
1
2
0
2
0
0
0
0
0
1
1
1
1
2
1
0
0
0
0
1
0
2
0
0
0
0
2
1
1
0
0
0
1
3
1
1
0
2
1
1
0
0
0
0
1
1
0
0
0
1
1
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
1
0
0
2
0
0
0
1
0
2
0
0
0
0
0
1
0
1
3
1
0
0
2
0
1
0
0
0
0
0
0
1
2
0
0
2
2
1
1
0
2
2
2
0
1
0
0
0
1
0
1
1
2
0
2
3
0
1
0
3
0
0
2
1
0
0
1
2
0
0
1
1
2
0
0
0
2
1
1
0
0
0
2
1
3
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
2
4
2
0
1
1
0
0
0
1
3
1
2
2
5
1
0
1
0
1
0
0
0
0
0
1
0
2
0
2
2
0
0
0
0
0
0
0
0
2
2
0
1
1
0
0
3
0
0
1
0
2
1
1
0
1
2
0
0
1
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
2
1
0
1
2
2
0
0
0
2
0
0
1
0
0
2
2
2
2
1
0
1
0
2
0
0
0
1
3
0
1
0
0
1
2
1
1
1
2
1
0
1
0
1
0
0
1
1
2
0
2
0
1
0
1
1
0
3
1
0
1
2
2
1
0
0
2
0
0
0
0
1
0
0
2
0
1
0
0
1
0
1
0
0
1
0
0
1
0
2
0
0
0
3
0
1
1
0
2
0
1
1
2
0
0
0
1
0
0
0
2
0
1
0
2
1
0
1
0
1
0
0
3
0
0
1
2
1
1
0
0
2
0
1
0
1
0
0
0
0
1
0
0
0
1
0
2
1
0
2
1
1
1
1
1
1
1
0
2
0
0
0
1
0
0
1
0
0
0
1
1
1
1
1
0
1
0
1
0
0
0
2
0
0
0
0
1
1
0
1
0
0
1
2
0
1
0
0
1
2
0
0
0
0
0
1
2
0
2
0
0
1
0
2
3
3
2
0
2
1
2
0
2
1
3
2
0
1
0
2
2
1
0
0
1
1
0
0
0
0
1
2
1
1
1
0
0
1
0
0
0
0
2
1
0
1
0
0
0
0
4
0
2
0
2
0
0
0
2
0
0
1
2
2
0
1
0
1
1
1
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
2
1
1
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
3
0
0
2
0
0
0
1
0
2
1
1
2
1
0
0
0
2
0
1
0
1
0
1
1
0
0
1
0
0
1
0
2
0
0
1
1
1
0
0
3
0
1
0
1
0
1
1
2
1
0
0
2
2
0
0
1
0
0
1
2
0
2
0
1
0
0
0
3
0
1
0
0
2
0
0
2
0
1
0
1
1
0
0
1
0
1
0
1
2
1
2
0
0
2
1
0
0
0
2
1
0
0
0
0
0
0
3
0
1
1
0
0
1
0
1
4
1
0
2
0
0
1
0
0
1
1
0
2
0
1
0
0
2
0
0
1
2
2
0
0
1
2
2
0
0
0
0
0
1
2
0
2
0
0
0
1
2
0
0
0
0
0
1
2
0
0
0
1
1
4
1
2
0
2
0
1
0
0
0
0
2
0
1
0
2
0
0
8
0
0
0
0
2
1
0
0
2
1
0
0
0
0
2
2
0
0
0
0
0
0
0
1
2
1
1
0
0
0
2
1
0
0
1
1
2
1
1
0
0
0
1
0
1
0
1
0
1
0
0
2
2
3
0
2
1
3
2
2
0
2
1
2
1
1
1
0
2
0
1
0
2
0
2
0
0
2
0
1
0
0
1
0
0
0
0
2
0
0
2
0
0
2
1
2
1
0
1
0
0
0
0
2
0
2
0
0
1
0
2
1
1
0
1
2
0
0
1
1
0
3
0
0
0
2
0
1
1
0
1
2
0
0
2
0
1
1
0
0
2
5
0
2
2
0
0
2
0
1
1
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
2
1
0
1
1
0
0
1
0
0
0
1
2
2
1
1
0
2
1
0
1
1
0
1
0
0
0
2
0
0
0
0
1
1
0
2
0
0
0
2
0
0
2
0
0
1
2
1
3
0
0
1
0
1
0
2
1
2
2
1
0
2
0
2
1
2
1
2
0
0
0
0
1
1
1
2
0
0
0
1
0
0
1
0
0
0
1
2
0
1
1
0
0
0
0
1
1
1
1
1
0
1
0
1
0
0
1
0
0
0
1
1
1
2
0
0
0
0
0
1
2
0
0
0
1
0
0
1
0
0
0
0
0
3
0
0
0
0
0
1
1
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
2
2
0
0
0
0
0
0
1
0
1
0
2
0
1
0
1
0
0
1
0
3
0
0
2
0
0
0
2
1
3
0
0
0
1
0
0
1
1
0
0
1
0
0
2
1
2
1
1
0
2
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
2
0
1
1
1
0
0
0
0
1
0
0
2
1
2
2
0
4
1
0
0
0
0
0
1
0
1
1
0
2
0
0
1
0
1
0
1
1
0
0
2
1
0
2
0
2
2
1
2
0
0
0
1
0
2
0
1
1
0
2
1
2
0
1
0
2
0
1
0
3
0
0
0
0
2
1
2
1
0
0
1
1
1
1
0
0
2
0
0
1
1
0
0
0
1
2
0
0
0
2
0
2
2
1
0
1
2
7
0
0
0
1
0
0
2
2
2
0
1
0
2
1
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
3
1
0
0
2
0
1
0
0
0
0
1
0
0
2
1
0
0
1
0
1
2
2
0
2
0
2
0
0
0
1
0
2
0
0
1
1
0
1
0
0
2
2
0
0
0
0
0
1
2
3
0
0
2
0
1
0
0
2
2
0
0
2
0
1
1
0
0
1
1
1
1
0
0
0
0
1
0
0
1
0
0
2
1
0
3
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
8
1
2
2
0
2
0
0
2
1
0
0
1
1
0
2
2
4
1
0
0
1
1
2
1
0
0
2
1
1
0
0
1
0
0
1
0
1
0
1
1
0
4
1
0
0
2
0
2
0
1
2
2
1
1
1
0
2
0
2
1
0
0
1
1
0
0
2
0
0
1
1
0
0
0
0
0
1
1
1
0
0
0
2
2
3
2
0
0
2
0
1
0
1
0
0
0
0
3
0
1
1
1
0
0
2
0
0
1
1
0
0
1
0
1
0
0
0
1
0
2
0
0
2
2
0
1
0
1
0
0
1
0
1
0
0
1
0
3
1
1
1
1
0
2
0
0
0
1
0
0
0
2
0
2
0
0
0
0
1
1
0
0
0
1
1
1
0
0
2
0
1
2
0
2
0
0
1
1
1
0
0
0
0
1
0
1
0
0
2
0
1
0
0
0
0
0
2
2
1
2
0
0
0
1
1
0
0
0
0
0
0
0
1
2
3
1
1
0
1
1
1
0
0
2
1
1
0
2
0
2
0
1
2
0
1
0
2
1
1
0
1
0
0
0
0
0
1
0
2
1
1
2
0
1
1
0
2
1
2
2
0
1
0
0
0
0
1
2
1
0
1
1
1
1
2
0
1
0
0
2
0
0
0
1
1
2
0
0
0
0
0
1
2
0
1
0
0
0
0
2
2
1
0
0
1
0
1
0
0
2
2
2
0
0
0
1
3
2
0
0
1
0
1
0
0
0
1
2
0
2
2
1
1
0
1
2
0
0
0
0
0
0
1
1
2
2
1
1
0
1
2
0
2
2
1
1
1
2
0
2
1
0
0
2
0
1
0
1
0
1
1
0
1
2
2
2
0
2
0
2
1
1
1
0
1
3
0
2
0
1
2
2
0
1
2
0
0
1
0
2
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
2
7
1
0
0
0
1
0
0
2
1
1
2
1
1
0
0
1
0
1
0
0
1
0
0
0
2
0
0
2
1
0
2
0
1
2
0
1
0
2
0
0
1
1
1
1
1
0
0
0
0
0
0
2
2
0
0
0
0
1
0
2
2
0
0
1
0
0
3
0
0
1
0
1
0
2
0
0
0
0
0
0
2
0
1
1
0
0
2
0
0
0
1
1
0
0
0
0
1
0
1
0
0
3
0
1
4
1
5
0
0
2
1
0
0
1
0
2
2
1
0
2
0
1
1
0
2
1
0
2
0
0
2
0
1
0
0
0
0
1
1
0
0
2
0
0
0
2
3
0
0
0
1
0
0
1
1
0
0
2
2
0
0
2
2
0
1
1
0
0
1
0
2
0
2
0
0
2
1
0
2
0
2
1
1
0
0
1
2
0
0
1
0
0
2
2
0
0
1
1
1
0
0
0
0
0
1
0
2
0
0
0
3
0
0
1
0
1
0
0
0
2
0
2
3
0
1
0
3
1
1
1
0
0
0
0
2
0
2
0
1
2
0
1
1
0
2
4
1
0
2
1
2
2
0
0
0
0
0
0
0
0
2
1
0
0
2
1
0
0
0
0
2
0
0
1
0
1
1
2
0
1
0
1
2
2
0
2
1
1
1
0
0
1
2
1
1
0
0
0
0
1
1
0
0
2
0
0
0
2
2
1
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
2
0
3
2
0
0
1
0
0
0
0
0
2
0
0
1
2
1
1
0
1
2
1
1
0
0
0
0
0
1
0
1
0
0
1
1
0
0
2
0
0
0
1
1
2
1
0
0
0
0
2
0
2
2
1
0
0
0
0
2
0
0
0
1
0
0
0
1
0
1
1
2
1
1
2
1
0
0
1
1
0
0
1
0
2
0
1
1
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
3
2
0
2
0
0
0
0
0
0
0
2
1
2
0
2
1
0
0
0
0
1
0
2
0
0
1
0
0
0
2
0
0
1
0
1
1
1
1
0
0
0
0
2
2
0
2
0
2
0
0
0
0
0
1
1
0
2
2
0
0
0
0
1
0
1
1
2
0
1
2
0
1
0
0
0
0
2
0
1
0
0
0
1
1
2
0
1
0
0
0
1
1
0
2
0
0
0
0
3
2
0
0
2
2
1
0
0
0
2
1
3
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
1
2
2
1
2
2
0
0
2
0
0
0
0
0
0
1
1
0
2
0
0
2
0
0
1
0
0
3
0
0
0
1
0
0
1
1
2
0
0
1
1
0
2
1
0
0
0
3
0
0
0
0
2
0
0
1
1
1
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
2
0
2
0
1
2
1
1
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
1
1
2
2
0
2
2
1
0
1
1
0
4
0
1
0
0
1
2
0
1
0
0
0
2
1
1
0
2
2
0
2
0
0
2
1
0
2
0
2
1
1
0
0
1
0
0
1
1
0
0
0
0
0
8
1
3
0
1
0
0
3
0
0
0
2
0
0
3
0
0
1
0
2
0
1
0
3
1
1
1
1
0
0
2
0
1
1
2
1
0
0
0
0
1
1
1
0
0
1
2
0
0
0
2
0
0
1
0
2
3
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
1
0
0
1
2
2
1
2
0
0
0
2
1
0
1
0
0
0
1
1
0
1
1
0
1
0
2
1
1
0
0
3
1
0
0
1
1
0
0
0
1
0
2
1
0
1
0
2
0
2
1
0
2
2
0
0
2
0
0
1
2
0
0
0
1
2
0
0
0
1
0
0
2
0
0
1
0
0
0
0
1
1
0
1
0
2
1
0
0
0
1
0
0
1
0
0
0
2
0
1
0
2
1
1
2
1
0
1
1
1
0
1
2
1
0
0
0
0
0
0
0
1
2
0
1
1
0
0
2
0
0
1
0
0
2
2
2
0
1
0
5
0
1
2
2
1
1
0
2
1
0
1
0
1
1
2
0
0
0
1
1
0
2
0
0
0
1
0
0
5
0
2
1
0
1
2
0
2
1
1
0
1
0
0
2
0
1
0
0
1
1
0
2
0
1
2
1
0
2
1
0
2
2
0
0
2
1
1
0
0
1
0
0
2
0
2
0
3
2
0
0
0
2
2
1
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
1
1
0
2
0
0
2
1
0
0
1
0
1
1
0
2
1
1
2
1
0
0
2
0
1
2
0
0
2
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
1
0
2
0
0
0
1
1
0
0
0
2
0
1
0
2
0
1
2
0
2
1
0
0
1
0
0
1
0
0
0
0
0
0
2
3
2
2
1
0
1
0
0
0
0
2
0
0
0
1
2
3
2
2
0
0
0
2
2
0
0
3
2
0
0
0
1
1
2
2
0
0
0
1
1
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
1
0
0
2
2
1
0
2
0
1
0
0
1
2
0
0
3
2
0
1
0
1
0
0
0
2
1
0
1
1
2
0
1
1
3
0
2
2
1
2
1
0
0
0
0
0
0
2
1
1
0
0
1
0
0
2
3
1
1
1
2
0
1
0
1
1
0
0
1
0
1
0
0
0
0
2
0
1
0
1
1
0
0
2
1
1
1
0
1
1
0
2
0
0
1
0
0
0
2
0
0
1
1
1
2
3
2
2
0
1
1
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
1
0
1
0
0
0
2
1
2
0
0
0
1
0
0
2
0
0
2
1
0
1
0
0
1
0
0
0
0
2
2
2
0
2
2
0
0
3
0
0
0
1
0
0
2
1
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
1
1
1
0
2
0
0
0
2
1
2
1
0
0
0
0
1
1
0
2
0
1
0
2
1
0
0
1
2
0
2
1
1
2
1
0
0
1
0
1
1
0
1
1
1
0
0
0
2
2
0
2
1
0
0
0
0
1
1
0
0
1
2
0
0
1
9
1
0
0
2
0
4
3
0
2
0
1
1
0
2
2
0
1
0
1
2
0
0
3
2
0
2
2
0
0
1
1
0
0
0
0
0
1
0
2
2
0
1
0
1
1
2
0
0
1
2
2
0
0
0
2
0
0
1
0
0
0
0
1
2
3
0
2
0
0
0
0
2
0
0
0
0
1
0
1
0
0
2
0
1
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
1
0
2
2
0
0
0
0
1
0
0
1
2
0
0
0
2
0
1
0
2
2
0
0
0
2
0
0
1
0
0
0
0
0
0
1
2
1
0
2
0
0
0
0
1
0
3
0
1
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
3
3
1
0
0
2
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
2
2
0
0
2
0
0
2
0
0
0
0
0
1
2
1
1
2
0
1
0
0
1
0
2
1
1
0
0
0
0
2
1
0
2
0
1
0
1
0
0
2
0
0
1
0
0
1
0
1
0
2
0
1
2
0
0
0
0
0
2
2
0
0
1
0
1
2
1
2
0
2
1
0
0
1
1
2
2
2
1
0
1
1
0
1
2
2
0
1
0
0
1
0
0
0
1
0
0
2
2
0
3
0
1
1
1
1
0
1
1
2
0
1
1
0
0
0
0
6
0
1
1
0
2
0
2
2
1
0
0
1
0
0
0
2
0
0
1
1
1
2
1
0
0
1
1
0
0
0
0
0
0
0
4
2
2
0
0
1
0
1
0
2
1
1
0
0
0
2
2
2
0
0
0
2
1
0
0
1
0
0
0
1
2
0
0
0
1
1
0
0
1
2
1
2
0
1
0
0
2
1
2
1
2
1
1
2
2
0
0
1
0
0
0
2
1
0
0
0
1
2
0
2
1
2
0
0
0
0
0
0
0
2
2
0
2
1
0
2
1
1
4
1
0
0
1
2
1
0
0
1
2
1
1
0
0
0
0
1
1
1
0
0
0
2
0
2
0
2
0
0
2
1
2
1
0
0
0
1
2
0
2
2
0
0
1
2
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
2
2
1
3
0
0
0
1
2
1
2
0
2
0
0
0
0
0
1
0
2
0
2
0
0
1
0
0
2
0
2
0
0
2
0
0
1
1
1
1
0
0
1
1
0
2
0
0
0
0
1
2
0
2
1
0
0
2
0
0
2
0
0
0
2
0
0
0
0
2
2
0
0
1
2
0
2
0
0
2
1
0
1
0
2
0
0
0
0
2
2
2
0
2
0
0
0
1
2
0
2
2
2
2
0
0
1
2
1
0
0
2
2
0
0
1
2
0
0
0
0
0
0
0
0
3
0
0
2
0
1
0
1
0
0
0
1
1
0
2
2
0
0
1
1
2
2
0
0
1
0
2
1
1
1
2
2
0
1
0
2
1
0
2
1
1
0
0
2
0
0
2
1
1
0
0
0
0
1
0
1
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
1
0
1
0
0
3
0
0
2
1
2
0
2
0
1
0
0
2
1
0
0
0
1
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
1
1
2
0
0
0
2
2
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
2
0
0
0
1
0
1
1
2
0
0
0
1
1
0
0
0
2
1
1
0
1
0
0
0
0
2
1
0
0
2
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
1
1
0
0
0
0
0
1
0
12
0
0
0
0
0
2
1
0
0
2
0
2
0
4
1
0
0
2
0
1
0
0
2
0
1
0
0
1
0
2
2
0
1
0
0
0
0
0
0
0
0
0
4
1
1
0
0
2
0
2
0
0
0
2
1
0
4
2
1
1
2
0
0
0
0
0
0
0
2
1
2
0
0
1
0
1
0
0
1
1
0
2
2
1
0
0
2
2
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
2
1
2
0
1
1
0
1
1
0
0
1
0
0
0
0
2
0
0
1
1
0
0
1
2
5
1
2
1
0
0
0
1
1
2
1
1
0
1
1
1
0
1
1
0
0
1
2
1
0
1
1
1
0
0
0
0
0
0
0
2
1
0
1
1
0
2
1
0
0
0
2
0
2
0
2
0
0
0
2
1
0
2
2
0
0
2
1
0
1
0
2
0
0
2
3
0
0
3
0
0
0
0
1
0
0
1
2
1
0
0
0
0
0
2
1
0
2
0
0
0
2
1
2
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
1
0
1
1
0
0
1
0
2
0
0
1
0
1
0
0
0
1
2
2
0
0
2
1
0
0
0
0
0
2
2
0
0
0
1
0
0
1
0
1
1
0
1
1
0
0
0
1
0
0
0
0
0
0
1
1
0
2
0
1
1
0
0
1
0
0
2
0
0
0
0
0
2
1
0
1
0
0
0
1
1
2
0
1
0
0
0
0
2
0
0
3
0
1
1
0
1
1
1
0
0
1
0
0
1
1
0
2
0
0
2
1
1
2
0
1
0
1
0
2
0
1
2
1
0
0
1
0
0
2
0
0
2
1
0
0
1
2
0
0
2
1
1
0
2
1
0
1
0
0
0
0
3
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
1
2
2
1
2
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
1
2
0
2
0
0
1
0
0
2
0
0
0
2
3
0
0
1
1
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
1
0
2
0
0
0
2
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
2
0
0
1
2
0
0
0
0
0
3
0
1
0
2
0
1
2
1
0
2
0
0
2
1
2
3
2
0
0
0
2
0
1
0
0
0
2
2
0
0
3
1
1
0
2
2
1
1
1
1
1
1
0
2
0
0
3
1
0
2
1
1
2
2
0
0
2
0
1
1
1
0
0
0
1
0
2
2
1
0
2
0
0
2
2
2
0
0
1
0
0
0
0
1
2
0
0
2
0
0
2
0
0
0
1
0
0
2
1
1
0
2
0
2
1
0
2
2
0
1
0
2
0
0
1
2
0
1
0
0
0
0
1
0
0
0
1
1
0
1
0
1
1
0
0
0
11
2
0
0
0
0
1
0
1
2
0
0
1
2
0
0
2
0
0
2
0
0
0
0
2
3
1
0
0
2
1
0
2
0
0
0
3
3
0
0
0
0
0
1
1
1
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
2
0
0
1
3
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
1
2
2
1
2
2
0
0
1
1
0
2
0
2
3
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
1
2
1
1
0
0
0
3
2
0
1
2
1
1
1
1
1
0
1
0
1
1
2
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
1
0
2
0
2
1
0
2
7
1
0
0
1
0
2
2
1
1
1
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
2
1
0
0
1
0
0
2
1
2
1
1
0
0
0
0
0
0
0
1
1
0
1
2
0
1
0
0
1
0
1
1
0
0
1
1
1
1
0
1
3
0
0
0
0
0
1
0
1
2
0
0
1
2
0
1
1
2
0
0
0
1
1
0
0
2
0
0
0
0
0
0
2
1
2
0
2
1
1
1
2
0
0
3
0
5
1
0
2
0
1
1
2
0
1
1
0
0
0
0
1
0
0
0
1
0
3
0
0
1
2
0
1
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
1
2
2
1
2
3
2
0
1
2
2
0
1
0
0
0
0
1
1
0
2
1
0
2
0
2
2
0
0
0
0
0
0
0
0
1
0
0
1
2
1
0
0
0
0
0
1
2
0
0
0
2
0
1
0
1
1
0
2
0
1
1
1
0
0
0
0
0
0
0
1
0
0
2
1
2
0
3
0
1
0
2
1
0
0
0
0
0
2
0
0
2
2
0
1
0
1
1
0
0
1
0
1
2
2
0
0
3
1
0
1
0
0
2
0
0
0
0
1
1
2
2
0
0
1
2
0
1
0
1
0
0
2
1
2
0
0
0
0
0
0
0
1
1
0
0
0
0
2
2
0
1
0
0
2
0
0
2
0
0
0
1
1
0
2
0
2
0
0
2
0
0
0
0
1
0
0
0
0
2
0
2
0
0
1
2
0
1
0
0
2
0
1
1
1
1
1
0
1
0
0
0
0
0
0
0
1
0
1
2
2
0
0
1
0
2
3
0
0
1
0
1
3
2
1
1
0
0
1
2
0
1
1
1
0
1
0
1
0
0
2
0
0
0
0
2
0
1
0
1
2
1
2
0
2
1
2
0
1
1
1
0
2
1
1
1
1
0
0
0
1
0
2
0
1
2
2
0
0
1
0
0
4
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
3
1
2
0
1
0
0
0
0
0
0
2
0
1
0
2
2
0
2
0
0
4
1
2
0
0
1
2
1
2
1
0
0
1
0
0
0
1
1
1
0
0
0
0
0
1
2
0
2
1
0
0
1
0
2
0
0
0
0
0
1
0
0
2
0
0
1
0
1
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
1
0
0
0
0
1
0
3
1
1
0
1
0
1
1
0
1
2
0
1
0
1
1
0
0
1
0
0
2
0
1
4
0
0
1
1
2
0
1
1
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
1
2
2
1
1
3
1
0
0
2
0
0
3
0
1
1
2
0
1
0
0
0
0
0
1
3
0
1
1
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
1
1
0
0
1
0
0
0
0
2
0
2
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
1
1
0
0
0
3
0
1
0
3
0
0
0
0
0
3
2
1
2
0
0
1
0
0
0
0
2
0
0
0
2
1
1
3
0
0
2
1
0
0
1
1
0
1
0
1
0
2
0
2
1
0
0
1
0
0
1
1
1
1
1
2
0
1
2
0
1
2
1
1
0
0
1
0
2
1
0
1
1
0
2
1
1
1
0
0
1
0
1
2
1
1
2
0
2
0
1
1
0
0
2
2
0
1
1
0
2
0
1
0
0
1
0
0
0
1
1
0
1
0
2
2
0
2
0
0
0
0
0
1
0
0
2
2
2
0
0
0
1
2
1
1
0
1
3
1
0
1
1
1
1
0
0
0
0
1
0
2
2
0
0
0
0
0
0
1
1
1
2
0
0
1
0
0
2
0
0
1
3
1
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
2
2
1
2
0
2
0
0
1
1
0
0
1
0
0
0
0
2
0
2
0
1
0
2
0
2
1
1
0
0
2
0
0
1
1
1
0
2
0
2
1
2
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
1
1
1
1
1
0
0
0
1
0
1
2
2
1
1
3
1
0
1
1
1
2
0
2
2
1
0
2
1
2
0
0
0
2
0
0
1
2
2
0
1
0
1
2
1
0
1
2
2
0
1
0
0
0
0
2
1
1
0
2
0
2
0
3
3
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
1
0
2
0
0
1
2
2
2
0
1
0
0
0
1
2
0
0
1
1
0
0
0
2
0
0
2
0
0
0
0
0
1
0
1
2
1
1
1
0
0
1
1
2
1
0
2
1
0
0
2
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
1
2
1
0
0
1
0
1
3
2
2
0
0
0
0
0
1
2
2
0
1
1
0
0
0
0
2
0
2
0
1
3
2
1
0
2
1
0
0
0
0
0
1
0
0
1
2
0
0
0
0
2
0
0
2
1
2
1
0
0
0
2
2
1
0
0
0
1
0
0
1
1
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
2
0
2
0
2
1
2
0
0
0
1
0
0
1
0
1
0
0
2
1
0
2
2
2
0
1
0
0
1
0
0
1
1
0
0
1
0
1
0
0
1
2
0
1
0
0
1
0
1
0
0
1
2
2
0
2
2
1
0
1
0
0
0
0
2
1
0
0
1
2
0
1
1
2
1
2
0
0
2
0
1
1
0
2
2
0
1
0
0
1
0
1
0
0
0
0
1
0
1
0
0
1
1
0
1
0
0
0
1
0
0
0
1
1
2
0
1
0
1
2
0
0
2
1
0
2
2
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
2
1
0
0
2
1
2
1
1
0
1
0
0
0
0
1
0
0
0
0
2
2
2
2
0
1
2
2
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
2
0
0
2
0
2
0
1
1
2
0
0
0
2
0
1
1
1
1
0
0
0
2
0
2
0
0
0
0
0
3
0
0
0
0
0
1
2
0
2
1
2
0
0
0
2
0
0
0
0
0
1
1
0
0
1
1
2
1
0
2
0
1
1
1
1
2
0
1
0
1
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
1
0
2
1
0
2
1
0
0
1
0
1
0
0
1
0
0
0
1
2
1
0
2
1
0
0
0
0
2
0
2
0
1
0
0
0
2
0
0
0
1
0
0
0
1
0
1
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
1
0
0
0
1
1
2
1
1
1
1
0
0
1
1
2
0
0
0
1
1
0
0
0
3
2
1
2
0
2
1
0
0
1
0
0
1
2
1
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
1
2
1
3
0
0
0
1
1
0
0
0
1
0
0
2
1
2
0
0
0
0
0
1
0
2
0
1
1
0
2
2
2
2
1
0
0
1
0
0
0
0
1
0
2
0
1
0
1
2
5
0
1
1
1
0
0
1
2
0
0
0
1
0
0
0
2
0
0
1
0
1
0
0
2
2
1
0
0
0
0
2
1
0
1
0
2
0
0
0
1
0
0
0
0
0
1
0
3
0
0
0
0
1
0
0
0
0
0
1
1
1
3
1
0
2
0
0
0
1
0
2
0
0
1
0
4
0
1
2
2
0
1
0
1
1
4
2
0
1
1
1
0
0
1
2
2
0
0
1
0
1
0
1
1
1
0
0
1
0
2
4
0
2
0
0
0
1
1
2
2
0
1
0
0
0
0
0
0
2
3
0
0
2
1
0
1
0
3
0
2
0
0
2
1
0
0
2
0
0
3
1
0
0
0
0
2
0
3
0
0
4
1
0
0
0
2
0
0
1
1
1
1
2
0
1
1
2
1
0
1
0
0
0
0
0
4
1
0
1
0
0
0
0
1
0
0
1
0
2
1
0
0
0
0
1
0
0
0
1
1
0
1
1
0
1
1
1
0
1
1
1
0
1
0
0
0
0
2
0
0
0
1
1
2
2
2
2
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
2
0
2
0
0
1
1
1
1
2
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
1
1
0
0
1
0
1
0
2
1
3
0
0
0
0
2
0
2
1
0
1
2
2
0
2
1
1
0
2
0
1
0
0
2
0
0
1
0
0
0
1
0
2
0
0
3
0
0
2
0
0
0
1
0
1
0
2
0
0
0
2
0
1
1
1
2
2
0
2
2
1
2
0
1
2
2
2
1
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
2
0
2
0
0
2
2
2
0
1
1
0
2
0
1
2
0
0
0
1
1
0
0
1
2
0
0
1
1
1
0
1
0
2
0
1
0
0
1
0
1
1
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
1
0
0
2
1
1
0
2
1
1
0
1
0
0
0
0
0
2
1
2
2
1
0
1
1
1
0
1
2
2
0
0
2
0
0
0
2
2
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
1
0
0
1
0
0
2
1
0
0
1
0
0
0
1
2
1
1
0
2
0
0
2
0
1
2
3
0
0
0
4
0
0
1
1
0
2
0
1
0
0
1
1
1
0
1
0
0
0
0
2
0
1
1
2
1
0
0
0
2
0
0
0
0
1
0
0
0
1
2
0
0
2
0
2
1
2
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
1
0
1
2
4
1
2
0
2
0
0
0
1
1
0
0
1
2
2
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
2
2
4
1
2
2
0
0
1
0
0
1
0
1
2
0
0
0
0
1
1
0
0
2
0
0
0
0
2
0
0
2
0
1
0
1
1
0
1
2
2
0
1
1
1
1
1
1
1
1
0
0
0
0
0
2
1
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
1
1
1
2
0
1
2
0
0
0
2
0
0
0
0
0
2
0
2
0
0
1
2
0
1
2
2
1
3
2
0
0
0
1
0
2
0
2
1
0
1
1
0
0
1
1
2
0
2
1
0
1
0
0
0
2
0
0
3
1
0
0
0
2
2
3
0
2
1
0
1
0
0
0
1
2
0
0
0
1
0
0
0
2
2
0
0
0
2
0
0
0
1
0
2
0
1
1
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
2
0
0
0
1
1
2
2
0
3
2
2
4
0
0
0
2
0
2
2
0
0
0
0
0
1
3
0
2
0
0
1
2
0
1
1
0
2
0
0
0
0
0
0
1
2
0
0
2
0
1
0
0
2
1
0
0
2
3
0
2
0
2
1
0
0
0
0
1
0
0
2
1
0
0
2
0
0
1
0
1
0
4
2
1
0
2
0
1
2
0
0
0
0
2
2
2
2
0
0
0
0
0
1
0
0
2
2
0
0
0
0
2
0
2
1
1
1
1
0
0
1
1
2
3
0
1
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
3
0
1
0
1
0
1
0
2
1
0
0
0
1
0
0
0
0
0
1
1
0
0
2
1
2
0
1
1
2
2
0
0
0
1
0
0
2
1
0
1
0
0
2
1
1
0
0
2
2
2
1
1
0
1
0
2
0
2
0
1
2
1
1
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
1
1
0
1
1
0
0
1
0
3
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
1
1
0
0
0
0
2
1
1
2
1
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
0
1
2
0
2
0
1
0
0
2
2
1
1
0
0
0
3
0
0
1
0
0
0
0
0
2
1
0
0
0
1
1
0
2
1
0
2
2
1
0
2
2
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
1
0
2
1
0
0
0
1
0
0
0
1
1
2
0
0
1
0
2
2
1
0
0
0
0
0
1
1
1
2
1
0
1
1
0
0
0
0
1
2
1
0
0
2
0
0
2
1
0
2
1
2
0
0
1
0
0
0
0
0
0
0
2
1
0
2
1
1
0
0
0
2
0
2
0
0
0
0
1
0
1
1
1
0
0
1
0
1
0
1
0
1
0
2
0
0
0
1
1
1
0
0
1
1
0
2
0
1
1
0
1
2
2
0
0
1
0
0
0
0
2
2
0
2
2
0
3
0
0
2
0
0
0
0
1
0
1
0
0
0
1
2
1
0
2
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
3
0
0
0
0
0
2
1
0
1
1
0
0
1
1
1
2
0
2
1
1
1
2
0
1
0
0
2
0
2
0
2
0
2
0
1
0
0
2
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
2
0
0
1
1
0
0
2
4
0
0
0
0
1
0
0
1
0
1
0
2
1
1
1
0
0
1
1
0
2
0
0
0
1
0
2
1
2
2
2
3
0
0
0
0
0
1
1
0
0
0
0
0
2
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
1
0
6
0
0
1
0
0
0
0
2
2
0
0
1
0
7
0
0
3
3
1
2
0
0
2
0
1
0
0
0
0
0
0
0
0
2
2
1
1
0
2
2
1
1
0
1
0
0
0
1
0
2
2
2
1
0
1
0
0
0
1
0
0
2
0
0
0
0
3
0
0
1
1
0
2
4
0
0
0
1
1
0
2
0
2
1
1
1
1
1
1
1
0
0
0
1
0
2
2
0
1
1
1
0
0
2
2
1
1
1
2
0
0
0
0
1
0
2
1
0
0
1
1
0
1
0
0
0
2
1
0
0
0
2
1
0
0
3
1
0
2
0
0
0
1
0
1
0
0
0
0
1
0
1
1
2
1
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
1
0
1
2
0
2
0
2
0
1
0
0
1
3
2
2
2
1
2
0
1
0
0
0
0
2
2
0
0
0
1
2
0
2
1
1
0
0
1
2
0
0
1
0
0
2
1
4
1
0
1
0
5
0
1
2
0
2
0
1
0
0
2
1
0
2
0
1
0
1
0
0
0
0
0
0
0
1
1
0
1
1
1
2
2
1
2
2
0
0
0
0
2
2
0
2
0
0
1
1
0
0
0
0
2
0
0
1
0
1
0
0
0
1
0
0
0
0
2
0
1
0
1
0
2
2
1
1
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
2
1
1
0
0
1
2
2
0
0
0
0
0
2
0
0
1
1
0
0
0
0
1
3
1
0
2
1
1
0
1
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
1
3
2
1
0
0
2
2
0
2
0
0
3
0
0
3
0
1
1
0
1
1
0
2
0
0
1
0
1
0
0
0
1
1
1
2
1
2
0
2
1
0
0
1
0
1
2
2
2
2
1
2
0
0
4
1
1
0
0
0
0
1
0
0
0
2
0
0
3
1
1
1
2
0
0
0
2
2
2
1
0
0
0
0
0
2
1
1
1
1
0
0
2
0
1
2
0
2
0
1
0
0
3
0
0
2
0
0
0
1
0
0
2
0
0
1
0
0
0
0
1
1
1
1
0
0
0
0
1
0
2
0
2
2
2
0
0
0
0
2
1
0
2
1
0
1
2
1
2
0
1
2
2
0
1
0
1
0
0
1
0
0
0
2
1
0
0
1
0
2
2
1
2
0
0
1
0
1
2
0
0
2
0
1
1
2
0
2
2
0
0
1
1
0
1
1
0
0
0
2
0
3
2
2
2
3
2
1
0
0
1
0
1
1
0
0
0
0
2
0
0
0
0
1
1
1
0
2
0
0
0
1
0
0
1
0
0
0
1
0
0
3
0
0
2
1
2
0
2
2
0
2
2
0
1
0
1
1
0
4
1
1
0
2
1
0
0
0
0
0
0
0
0
1
1
0
2
1
0
2
0
0
0
0
0
0
2
2
1
0
1
0
1
1
0
0
0
0
1
1
0
1
1
0
0
2
1
0
0
0
1
0
0
0
1
0
1
0
2
0
0
0
1
2
2
0
0
0
0
1
2
0
0
0
1
0
1
3
0
2
0
1
2
2
0
2
0
1
0
0
0
0
0
2
0
0
1
0
2
2
0
3
1
1
2
1
2
0
0
0
2
2
0
0
1
0
0
0
2
0
1
1
0
0
1
0
3
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
3
1
0
0
0
0
0
1
2
1
1
0
1
0
1
1
0
2
0
0
1
0
1
0
0
0
0
1
2
0
0
1
0
0
1
1
1
0
0
0
1
2
0
1
0
2
1
0
3
0
0
1
0
2
0
0
0
2
0
0
3
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
1
2
0
2
3
0
0
2
0
0
1
2
0
1
2
0
0
2
0
0
2
2
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
1
1
1
1
2
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
2
1
0
6
2
2
2
0
0
1
1
0
1
1
4
0
2
0
1
1
0
2
0
0
0
1
2
1
1
0
2
0
0
0
2
0
0
0
1
0
2
0
0
0
1
2
0
0
0
0
0
1
1
1
0
0
0
2
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
1
0
2
1
0
3
2
0
1
0
1
0
1
2
0
0
0
0
2
1
1
2
0
0
2
0
0
1
0
0
1
0
1
1
0
1
1
0
1
0
1
0
0
2
0
2
1
0
2
2
0
0
0
1
1
0
1
1
3
2
0
0
1
0
0
2
1
0
1
0
1
0
0
2
2
2
0
0
0
0
3
1
1
0
1
0
0
2
2
0
0
2
1
0
1
0
1
0
0
2
2
2
2
0
0
0
0
1
0
0
0
1
4
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
1
1
0
0
0
0
0
3
2
0
0
0
2
1
1
1
0
2
1
0
0
0
2
0
0
0
0
0
0
2
0
2
0
1
2
1
0
1
2
1
2
1
2
3
0
0
1
0
0
0
0
2
0
1
2
0
0
0
0
0
2
1
2
2
2
0
1
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
3
0
0
0
0
0
1
0
0
1
0
0
0
2
1
2
2
0
0
0
0
0
2
0
0
0
1
1
1
1
2
1
1
0
0
2
1
0
0
2
1
9
0
0
0
1
0
0
1
0
2
0
0
1
1
2
2
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
2
2
1
0
0
2
0
0
0
0
2
2
3
0
0
0
1
2
1
6
5
2
1
0
0
2
0
1
2
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
2
1
2
1
2
0
0
0
1
1
0
0
0
2
2
1
2
1
1
2
1
0
0
0
2
0
0
0
0
1
1
0
1
0
0
0
4
0
0
2
2
0
0
1
1
1
0
0
1
0
2
1
0
2
1
3
1
2
2
3
0
1
2
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
1
1
3
2
0
0
2
0
1
1
0
0
0
1
1
0
0
1
1
0
0
0
0
2
1
0
0
2
0
1
0
1
0
2
1
0
0
2
1
0
0
2
2
0
0
0
0
2
1
0
1
2
0
1
1
1
0
0
0
2
0
1
1
0
0
2
2
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
1
0
2
0
0
0
1
1
0
0
2
1
5
1
0
2
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
1
2
0
0
0
0
2
0
0
1
0
0
0
1
0
0
2
2
2
3
2
0
1
2
1
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
1
1
0
1
2
1
0
1
2
1
0
2
1
0
1
0
0
1
1
0
1
0
2
0
0
2
1
0
2
0
0
1
1
1
1
1
1
0
1
0
0
0
1
0
0
1
0
2
0
2
2
2
1
0
0
0
1
1
0
1
0
0
0
1
0
2
1
0
1
1
0
0
2
1
1
0
0
1
2
0
0
1
2
1
0
0
0
0
1
2
0
0
0
1
1
2
2
1
2
0
0
3
0
1
1
0
2
1
1
2
0
0
1
2
0
2
0
0
1
0
1
2
2
1
0
1
2
0
0
1
1
2
2
0
1
0
2
0
0
0
0
2
2
0
0
2
1
1
0
1
1
1
1
1
0
0
1
0
2
0
0
3
1
1
1
1
0
0
0
0
1
1
0
0
2
2
0
0
0
0
1
2
0
0
0
0
0
1
0
2
0
2
0
1
2
4
0
0
1
1
0
1
0
1
1
0
0
1
2
0
2
2
0
1
0
3
0
0
1
0
0
1
2
1
1
1
0
0
1
0
0
2
0
1
2
1
0
1
1
1
1
0
0
1
2
2
0
0
0
2
2
0
0
0
0
1
2
0
0
1
1
1
0
1
0
0
0
2
0
0
0
0
0
2
2
2
0
0
0
0
1
1
0
2
2
1
1
1
0
2
0
0
1
0
0
1
1
0
0
0
1
0
0
2
1
1
0
1
3
0
2
1
1
1
3
1
1
0
0
1
1
2
0
2
1
0
2
3
1
0
0
0
0
1
0
2
0
0
1
0
0
0
2
1
0
1
0
0
0
0
2
0
0
1
0
1
0
2
0
0
0
1
1
2
2
2
2
2
3
0
2
0
0
1
0
2
0
0
1
2
2
0
1
0
1
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
2
1
1
0
0
2
1
0
1
0
1
0
2
1
2
1
0
1
1
0
0
2
0
0
1
0
0
2
1
1
0
1
0
2
0
2
0
2
0
0
0
2
1
0
0
2
0
0
1
0
1
0
0
0
2
0
1
2
1
0
0
0
0
0
0
2
0
1
1
1
2
1
0
2
0
2
2
0
2
0
0
0
2
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
6
0
2
0
1
0
0
0
0
3
0
0
0
2
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
1
0
0
1
1
0
0
1
1
0
1
2
0
2
0
0
2
0
0
0
1
0
2
0
0
0
0
2
1
0
0
0
0
1
2
0
0
0
0
1
1
2
1
0
1
0
0
0
0
1
0
1
1
0
0
1
0
2
0
0
2
0
2
0
0
0
1
0
0
1
0
3
0
0
0
0
1
1
0
0
0
0
0
1
1
2
0
0
1
0
1
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
1
2
1
1
0
0
2
0
1
0
0
0
2
0
0
1
0
0
2
0
0
2
1
0
0
1
2
1
0
0
0
1
0
2
0
1
0
0
0
1
2
2
1
0
0
2
0
1
0
0
1
1
2
0
1
0
0
0
2
0
0
2
1
0
0
2
1
2
2
0
0
1
0
0
2
1
0
1
0
0
1
0
1
1
1
0
0
0
0
1
1
1
0
1
2
1
1
0
0
0
2
1
1
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
2
0
3
2
0
0
1
0
1
0
2
0
0
0
0
2
1
0
1
2
2
1
0
0
2
1
2
0
0
0
0
1
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
6
2
0
0
1
1
1
0
0
1
1
1
0
0
1
0
1
0
0
2
1
0
2
1
1
1
0
0
0
0
1
0
0
0
1
1
0
2
0
0
0
0
1
2
1
0
2
0
1
0
0
0
0
0
0
0
0
0
2
1
1
2
1
3
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
1
0
0
1
1
1
1
0
3
1
0
0
2
0
2
0
0
0
1
2
2
0
2
0
0
1
1
3
1
0
1
2
2
0
1
1
1
0
1
2
1
1
0
0
0
2
1
1
1
3
0
2
1
0
2
0
1
0
0
1
2
0
2
0
0
1
2
0
0
1
2
0
0
2
2
0
2
0
0
0
1
1
0
2
2
1
0
0
0
0
1
0
0
0
0
1
0
2
1
0
0
0
1
2
0
0
2
0
0
0
0
1
0
0
0
1
0
0
1
1
1
2
0
0
0
0
0
1
2
1
0
0
0
0
0
1
2
0
2
0
0
1
0
0
1
1
0
2
0
2
1
0
1
1
0
0
0
1
0
5
1
1
0
0
0
3
0
1
1
0
0
1
1
0
2
0
2
0
0
2
4
1
1
0
2
0
1
2
1
2
2
2
1
1
1
0
0
0
0
6
1
2
1
2
0
1
0
1
2
0
0
0
2
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
2
0
2
0
1
1
0
1
1
0
2
0
1
2
1
0
1
1
0
2
0
0
0
2
0
1
2
0
0
0
0
2
2
0
0
0
2
0
0
1
0
1
0
0
0
1
0
0
1
0
2
1
2
3
2
0
0
0
1
1
0
0
2
0
1
2
2
1
2
2
0
1
2
0
2
0
0
0
0
1
1
1
0
2
0
0
3
0
2
0
2
1
0
0
0
0
0
0
1
0
2
2
0
2
0
0
1
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
1
0
2
2
0
0
0
0
0
0
0
0
0
1
2
0
1
0
5
0
1
0
0
2
0
1
0
0
2
1
2
1
1
0
2
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
3
0
0
1
2
0
1
3
0
2
0
0
0
1
0
2
2
2
0
1
0
1
1
1
0
0
0
0
0
1
0
0
2
0
1
1
1
0
1
1
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
1
1
1
1
1
1
1
1
1
1
0
0
2
0
0
1
1
0
0
0
1
0
0
0
1
2
0
1
0
0
2
1
2
2
0
2
2
2
0
0
1
0
0
1
0
3
0
2
0
0
0
0
0
0
0
1
2
0
1
1
0
0
0
0
1
1
1
1
0
0
2
1
1
1
0
0
0
0
1
0
0
0
0
0
2
0
2
2
0
2
0
0
1
0
2
1
1
2
0
0
2
1
0
2
3
0
0
0
1
1
0
0
1
0
2
0
0
0
0
1
0
1
1
2
0
2
0
1
2
0
0
0
2
1
0
1
1
0
1
1
0
0
2
0
1
2
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
1
1
2
0
2
0
0
1
0
0
1
1
0
0
0
0
2
1
1
0
0
0
0
0
0
2
0
0
1
0
1
0
0
1
0
1
3
0
1
0
0
1
0
1
2
1
0
1
1
1
1
0
1
0
2
2
0
1
0
2
0
1
3
0
0
0
1
0
2
0
1
0
0
2
2
1
1
1
1
1
2
0
0
0
1
1
0
0
2
0
0
1
0
1
0
2
2
0
0
1
0
0
1
0
2
1
0
5
0
2
2
1
1
0
0
1
0
0
0
1
1
0
4
1
0
1
2
0
0
0
0
2
2
0
1
1
2
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
1
1
2
2
2
1
1
0
0
0
0
0
1
2
0
2
0
0
1
0
0
0
2
0
1
0
0
2
1
0
1
0
1
1
2
1
0
2
0
1
0
0
0
1
2
0
1
0
0
0
2
0
1
1
2
0
2
0
2
2
2
0
0
0
0
0
1
1
0
0
0
0
2
2
0
2
1
0
1
0
2
0
2
0
2
0
2
1
1
0
2
1
0
0
0
2
1
2
0
0
0
0
2
0
0
2
0
0
0
1
2
0
3
1
0
1
2
0
1
0
1
0
0
0
1
0
0
1
0
0
2
0
0
0
1
0
0
1
0
1
2
0
0
0
2
2
0
3
0
0
3
0
1
0
2
0
0
0
0
0
0
2
0
0
0
1
2
1
2
0
1
0
0
0
0
0
0
1
2
0
0
0
2
1
0
2
0
1
1
0
4
0
2
1
1
2
0
0
0
0
1
1
1
1
0
2
2
0
2
1
2
2
0
5
0
1
0
0
0
0
0
2
1
0
0
0
1
0
0
1
0
1
1
0
0
2
0
1
0
0
1
1
0
1
0
0
0
1
1
0
1
1
1
3
0
0
0
0
0
1
1
2
1
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
2
2
0
0
1
0
0
1
0
1
1
1
2
0
2
0
0
0
0
3
1
2
2
0
2
0
0
1
2
1
0
1
2
1
1
2
0
2
0
2
0
0
2
0
0
2
0
0
0
1
1
0
0
0
0
1
2
2
0
6
0
0
8
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
2
1
1
0
0
2
1
0
2
0
1
0
0
0
0
0
0
2
0
1
1
0
0
0
2
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
2
2
1
4
1
1
1
2
0
2
1
2
0
0
1
2
2
3
2
0
0
2
0
0
2
2
2
1
0
0
0
1
0
0
1
2
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
2
0
1
1
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
2
0
2
3
2
0
0
0
1
1
0
1
1
1
2
0
2
0
1
2
1
0
0
2
1
2
0
0
0
0
1
2
1
0
0
0
0
0
2
1
0
2
0
0
1
0
2
2
2
1
1
0
0
2
2
0
1
0
1
1
0
0
0
1
0
2
0
0
1
1
2
2
0
0
0
0
1
0
1
0
1
0
2
0
0
1
1
0
1
0
0
0
0
0
1
1
0
2
0
0
0
0
2
2
0
0
2
0
1
0
1
1
0
0
1
0
1
0
2
0
0
2
0
0
0
0
2
0
0
2
0
0
0
2
1
0
2
0
0
1
5
3
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
2
2
1
0
0
2
1
2
0
0
2
0
0
1
1
1
0
3
1
2
0
1
0
0
0
1
1
1
0
1
2
1
0
0
0
0
0
0
0
1
0
2
2
1
0
1
2
0
0
0
1
1
0
0
2
0
0
1
3
0
0
2
0
1
1
0
2
0
0
0
1
1
0
0
1
0
2
0
0
1
0
1
2
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
2
0
0
0
0
1
2
0
2
2
3
2
0
0
0
0
0
2
2
1
2
0
3
0
0
1
2
1
0
2
2
1
0
0
0
1
2
2
1
1
0
0
2
1
0
0
0
2
0
2
0
0
0
0
0
2
1
1
0
1
0
3
1
0
1
1
1
1
3
0
0
0
2
0
0
1
1
0
0
2
0
1
1
1
1
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
1
2
0
0
2
0
0
0
1
1
0
2
0
2
2
0
2
1
7
1
1
1
2
0
0
0
0
1
1
1
0
2
1
0
1
1
1
2
0
0
0
2
0
0
1
0
0
1
0
2
0
1
0
2
0
1
2
0
0
0
2
0
0
0
2
0
2
0
0
0
1
0
0
0
2
0
1
0
0
2
0
2
2
0
0
0
2
2
0
2
0
1
0
0
0
1
0
0
1
1
0
0
2
0
3
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
1
1
1
0
3
0
1
3
0
1
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
1
0
0
2
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
1
0
0
1
2
1
0
1
2
0
0
0
0
2
0
1
0
0
1
0
2
1
2
0
1
0
0
0
0
0
1
2
1
2
1
2
1
1
1
1
0
0
2
0
1
1
0
1
1
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
1
2
3
0
0
1
1
0
0
0
0
2
0
0
2
0
1
0
1
1
0
2
0
0
2
1
0
1
1
0
1
0
2
2
1
0
3
1
2
2
2
1
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
1
0
1
0
2
0
2
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
2
3
0
2
0
0
1
1
0
0
1
0
4
1
2
1
0
1
0
0
0
0
0
0
0
0
2
2
2
1
1
1
2
1
2
1
0
2
0
2
1
2
0
0
0
2
1
2
2
1
1
0
0
0
2
0
0
1
1
0
0
1
0
0
0
0
0
2
1
1
2
0
0
0
3
0
2
0
1
0
1
0
2
2
1
1
3
0
3
0
0
2
0
0
0
3
2
3
0
0
0
0
1
1
0
1
2
0
0
0
0
0
1
1
2
0
0
0
0
1
1
0
0
1
0
0
2
1
0
2
0
0
1
0
1
0
1
1
0
1
0
0
2
0
0
0
0
1
0
0
0
1
0
1
0
1
1
1
2
1
2
2
2
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
2
0
0
2
0
1
1
0
1
1
1
1
1
1
1
3
0
1
1
0
2
0
2
1
0
3
3
0
0
0
0
0
0
2
0
0
1
2
0
0
0
2
1
2
0
1
1
0
0
0
0
0
0
2
2
0
1
1
1
0
2
1
2
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
2
0
2
0
0
0
1
0
0
2
0
0
2
2
0
2
0
2
0
1
1
0
1
0
0
2
1
0
0
1
1
1
0
1
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
1
2
0
0
1
0
0
2
1
2
0
1
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
2
0
1
2
1
1
1
0
0
10
1
0
2
2
0
0
0
0
0
1
0
1
0
2
1
0
0
0
0
0
1
0
2
1
0
0
0
1
0
0
2
0
0
0
0
3
2
2
0
0
0
1
1
0
1
1
0
2
1
0
0
0
1
0
5
1
0
1
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
1
0
0
2
0
0
1
0
2
1
0
0
0
2
0
0
1
1
0
1
0
2
1
2
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
1
0
2
1
0
1
2
2
0
2
0
3
0
3
0
1
2
0
0
0
1
0
0
0
1
1
0
0
0
1
1
2
1
0
0
0
1
0
0
1
2
1
0
0
1
0
0
1
2
1
0
2
0
1
1
0
1
0
2
0
0
2
1
1
0
0
1
0
1
2
1
0
1
0
0
0
2
2
0
2
0
1
2
1
0
2
0
2
0
2
0
2
2
0
2
1
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
2
0
1
1
1
0
1
3
2
0
2
0
0
0
0
0
1
0
2
0
0
1
2
0
1
0
1
0
2
1
2
1
0
2
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
1
0
2
0
2
1
2
0
1
1
2
1
0
0
0
1
3
0
1
0
1
1
0
0
1
0
0
0
1
1
0
0
0
1
0
1
0
1
0
0
2
0
0
0
0
0
0
0
1
2
0
1
1
1
0
0
0
0
1
1
2
0
1
0
1
2
0
1
2
0
0
2
2
0
0
2
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
1
1
0
1
0
1
2
2
0
1
0
1
0
0
0
1
0
0
2
2
0
1
0
1
2
0
3
0
3
0
0
1
0
2
0
2
2
1
0
0
0
0
1
0
1
0
3
3
0
0
0
2
2
0
0
0
0
0
0
2
0
1
0
2
1
0
0
2
0
0
2
1
1
2
1
1
0
0
1
2
0
0
0
2
0
0
0
0
0
2
0
0
2
2
2
0
0
0
0
1
2
0
0
1
0
0
1
0
1
0
2
2
1
0
2
0
1
0
1
1
0
0
1
1
0
0
0
0
1
2
2
2
0
1
0
0
0
1
1
0
0
0
2
1
0
2
1
0
0
1
0
0
1
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
2
2
2
0
1
0
1
0
2
0
2
0
2
0
0
2
0
0
2
1
0
2
1
1
0
0
0
0
1
1
2
1
0
1
0
2
0
0
1
0
0
0
1
0
4
1
1
1
1
2
1
0
0
0
0
5
0
1
1
1
0
0
0
2
0
0
2
1
1
0
0
2
0
0
0
1
1
1
0
1
2
2
1
2
0
0
0
2
0
0
1
1
0
0
1
1
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
1
0
0
2
1
1
0
0
0
1
0
2
0
0
0
0
1
1
0
0
0
0
0
2
2
0
0
0
2
0
0
2
1
0
2
2
1
2
1
0
0
0
1
0
0
3
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
1
1
0
2
1
2
0
1
3
0
0
2
1
1
0
2
0
0
0
0
0
2
0
1
2
0
0
4
0
0
1
2
0
0
2
0
2
0
2
2
0
1
2
1
0
2
1
1
0
0
0
0
0
0
0
1
1
1
0
0
2
0
0
1
0
0
0
2
1
0
0
0
0
1
0
2
0
0
2
0
1
0
0
1
1
1
1
0
1
1
0
1
1
0
2
0
2
0
2
0
2
0
0
0
0
0
0
0
1
0
2
2
2
1
2
4
0
0
1
2
0
0
1
0
1
2
2
0
0
1
2
0
0
2
0
0
0
0
0
0
1
0
0
2
1
2
0
0
2
0
0
0
1
2
0
2
2
1
2
0
1
0
0
1
0
3
0
0
0
2
0
2
0
0
0
0
3
1
0
2
2
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
3
1
1
0
0
0
0
1
2
1
0
2
0
0
1
1
2
0
1
0
1
1
1
2
2
2
0
0
1
0
1
0
1
2
2
0
0
0
0
0
1
0
1
0
0
1
2
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
1
2
0
2
0
2
2
1
1
1
1
0
0
1
0
0
1
1
2
1
0
0
0
1
1
0
0
1
1
1
1
0
1
0
1
1
1
1
1
0
1
2
2
1
0
0
0
2
1
0
0
0
1
0
2
0
2
0
4
0
1
4
0
0
2
1
0
0
0
0
1
1
0
1
0
2
0
0
2
2
1
0
2
0
0
1
0
2
0
0
1
0
1
1
0
0
1
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
2
0
2
1
1
0
1
1
1
3
1
0
0
0
0
0
1
1
0
0
0
1
0
0
1
2
1
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
2
2
1
0
0
0
0
0
1
0
2
0
0
0
1
1
2
0
2
0
1
2
1
0
2
2
0
1
0
0
0
0
2
0
1
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
2
1
0
1
2
3
1
1
0
0
3
2
0
0
0
2
2
2
0
0
0
0
0
1
0
2
0
0
1
0
2
1
0
0
0
1
1
0
0
2
1
0
0
1
0
3
1
0
1
0
0
0
1
0
2
0
2
0
0
5
2
0
1
0
1
2
0
0
0
0
1
2
0
0
1
0
0
1
2
0
0
1
2
0
0
2
1
2
2
0
0
0
0
1
0
1
0
0
0
1
0
2
1
0
0
0
1
0
0
1
0
1
1
1
0
0
0
0
1
0
2
1
0
0
0
0
0
2
0
1
1
2
1
2
1
1
0
1
0
0
2
0
0
2
2
0
0
1
2
1
1
0
2
0
1
0
1
2
2
0
0
2
1
0
0
2
0
1
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
2
0
2
0
0
2
4
0
1
0
1
1
0
2
0
0
1
0
0
0
1
0
0
5
0
1
0
1
1
0
0
1
1
2
2
1
1
0
0
2
2
0
2
0
2
1
0
1
2
1
0
1
4
0
0
2
0
1
0
1
1
2
0
0
0
0
5
0
1
0
3
0
0
0
0
0
0
1
1
0
2
0
2
0
2
0
2
0
0
0
0
2
1
0
2
0
2
1
0
1
2
0
0
0
1
0
2
1
1
0
2
0
0
0
0
1
0
1
2
0
2
1
1
1
0
1
0
0
2
1
1
0
0
0
2
0
0
0
2
2
0
0
2
0
1
1
0
2
0
0
0
0
0
2
1
0
1
1
0
0
0
1
1
0
0
0
2
0
0
0
2
0
0
0
2
2
1
1
0
0
0
1
0
2
0
0
0
2
1
2
0
0
0
1
2
0
0
1
0
1
0
1
1
1
1
0
2
0
1
0
1
0
1
0
0
2
2
1
0
2
1
1
2
0
1
0
0
1
1
0
2
0
0
0
1
0
0
1
1
1
1
0
0
0
0
0
2
0
2
1
1
1
2
0
1
2
0
1
0
1
0
0
0
0
2
2
1
0
1
1
0
0
0
0
2
2
1
0
0
1
0
1
1
0
1
0
2
1
1
0
1
2
1
0
0
2
0
0
0
1
0
0
1
0
1
2
2
3
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
1
1
1
2
0
2
2
2
1
1
0
0
1
2
2
2
0
1
0
1
0
2
0
0
0
0
2
1
3
2
0
0
0
1
2
0
1
0
2
0
0
0
2
0
0
1
2
0
1
0
1
1
0
1
2
1
0
1
2
0
0
0
1
0
0
2
1
0
0
2
1
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
2
0
1
2
1
0
1
1
2
0
1
2
0
2
2
1
2
1
0
0
1
0
0
2
0
1
2
0
0
0
1
1
1
2
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
2
2
0
0
0
0
1
1
0
1
0
0
1
1
0
1
1
1
0
0
0
2
0
0
1
1
0
1
0
0
1
1
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
2
3
1
0
0
0
1
0
2
5
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
2
2
0
0
0
2
0
2
0
1
1
0
1
0
0
0
0
0
0
0
2
0
1
2
1
2
0
0
1
0
2
1
2
0
0
1
0
0
0
0
0
0
0
2
2
0
1
1
2
4
1
0
2
0
0
0
2
2
0
0
0
2
1
1
1
2
1
1
0
0
2
0
2
1
1
0
2
0
0
0
0
0
0
0
1
0
1
2
1
3
0
1
2
1
0
0
0
0
2
1
2
1
0
0
2
0
0
0
2
2
1
0
1
0
0
2
0
1
0
0
0
1
0
0
1
0
0
0
2
2
0
1
0
1
0
0
2
0
1
0
0
0
0
0
0
0
3
0
0
2
3
2
1
0
0
0
0
0
1
1
0
0
2
1
0
1
1
0
2
0
0
2
0
1
0
2
1
0
0
2
0
0
0
0
1
0
1
3
0
0
0
1
0
0
2
1
1
1
0
2
0
2
0
0
0
1
0
0
0
1
2
1
1
1
1
2
0
0
0
0
0
2
0
0
0
0
0
0
1
1
1
0
2
0
0
1
1
1
0
0
2
2
1
0
0
0
1
1
0
1
0
0
0
3
0
1
0
0
1
1
2
2
1
2
1
0
0
0
0
1
0
1
0
2
2
0
0
0
0
0
0
1
0
2
1
0
0
0
2
0
0
0
1
1
2
1
2
1
0
0
0
1
1
2
2
0
2
0
1
0
0
0
0
0
0
0
0
2
1
0
1
1
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
3
2
1
1
0
2
0
1
1
1
2
2
1
0
0
0
0
0
0
2
0
0
0
0
5
0
2
0
1
3
2
4
2
0
1
2
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
2
0
0
1
0
2
1
0
0
1
0
1
0
2
2
0
0
3
1
1
0
1
0
1
0
0
1
0
0
1
1
0
1
1
1
0
0
0
0
0
0
1
0
1
1
0
1
2
2
3
2
0
1
0
0
1
2
0
0
1
0
1
2
2
2
1
0
0
0
1
3
2
2
1
2
1
0
1
0
2
0
2
0
0
0
0
0
4
0
1
0
1
0
2
1
0
1
2
0
0
0
0
2
1
3
0
0
0
0
1
3
0
0
2
0
3
1
0
0
0
2
0
0
0
2
2
0
1
0
1
0
0
0
1
1
1
1
0
0
1
0
1
2
0
1
1
2
0
2
2
0
0
2
1
1
2
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
1
1
1
1
0
0
0
0
1
0
2
0
1
0
1
2
1
0
0
1
1
1
0
3
0
2
0
0
2
0
1
0
2
1
0
0
2
2
2
1
0
0
1
0
0
1
0
2
0
0
1
0
1
1
1
2
1
1
1
2
0
0
0
1
1
1
0
2
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
1
1
1
0
0
1
0
0
0
1
1
0
0
0
2
0
2
3
0
5
2
1
0
0
0
1
1
0
0
1
0
2
1
1
0
2
2
1
0
0
0
2
0
1
1
1
1
0
0
2
2
0
1
2
0
2
0
1
0
1
0
2
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
3
2
0
2
0
0
0
2
1
1
1
1
2
1
0
1
1
2
1
0
1
0
0
2
0
1
0
0
0
1
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
2
1
1
1
2
2
1
2
1
0
2
0
0
0
0
0
1
1
0
0
1
0
0
2
0
0
0
0
1
0
0
1
2
0
0
0
0
1
0
2
2
1
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
1
1
1
0
0
1
1
1
0
0
0
0
1
0
1
0
1
0
1
2
1
0
0
0
0
1
2
2
0
0
0
0
2
0
0
2
3
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
2
1
0
1
0
0
0
1
0
0
2
2
2
0
0
2
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
1
0
0
0
3
2
1
0
0
0
0
2
0
2
1
0
0
1
0
2
0
0
0
1
2
2
0
0
0
0
0
1
1
2
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
1
0
0
0
3
0
2
1
2
1
0
2
1
2
1
0
0
0
2
1
3
2
0
0
0
2
0
1
1
0
2
0
0
0
2
0
0
2
0
1
0
0
0
0
1
2
0
0
1
0
0
2
1
3
2
0
0
2
1
0
2
0
1
1
0
1
1
0
0
2
0
0
1
1
1
0
1
2
0
1
1
0
2
0
2
0
2
0
1
0
0
2
0
0
0
0
0
2
0
0
1
0
2
2
2
0
0
0
1
1
2
0
0
1
1
1
2
1
1
1
1
0
5
0
0
0
1
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
1
0
1
1
1
5
0
0
0
0
3
0
1
0
0
2
0
0
0
2
0
1
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
2
2
0
2
2
1
0
1
1
0
0
1
0
0
0
2
0
0
0
1
0
1
0
0
0
0
2
0
1
2
2
0
0
0
0
2
0
1
0
0
2
2
1
0
0
2
0
0
1
1
0
1
2
1
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
3
0
0
1
0
2
2
0
0
1
1
0
0
1
0
0
0
1
0
1
0
0
0
2
2
1
2
0
0
1
1
0
1
1
0
1
0
2
0
1
2
1
0
2
2
0
2
0
0
0
1
1
0
2
1
2
0
0
2
0
0
0
0
2
1
0
0
0
1
0
1
0
1
0
2
1
0
4
2
0
0
1
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
1
1
0
2
1
2
0
0
0
1
0
3
1
0
0
1
1
0
0
0
2
5
1
0
1
1
0
1
1
0
1
0
2
0
1
1
0
0
0
0
0
0
1
1
1
2
2
0
1
1
2
2
0
1
3
0
2
0
0
0
2
0
2
0
0
1
0
2
0
0
1
0
2
1
0
0
1
1
2
0
1
0
2
0
1
2
1
0
2
0
1
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
2
0
0
2
2
0
0
1
0
1
2
1
2
2
0
0
1
0
0
0
1
1
0
1
2
0
0
2
0
0
2
1
0
0
2
2
2
0
1
0
2
1
2
0
0
4
0
2
1
1
2
0
1
1
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
2
1
0
0
0
0
2
2
1
1
2
0
0
0
0
0
1
1
0
0
0
1
0
0
2
1
1
0
1
1
0
1
0
0
0
0
3
2
0
3
0
2
0
0
2
1
2
2
0
0
0
0
0
0
1
0
1
0
0
0
0
1
2
0
0
0
1
2
0
2
0
2
0
2
2
1
0
0
0
0
0
1
1
3
2
1
2
1
1
0
1
0
1
0
0
1
0
2
0
1
0
0
1
1
1
1
0
1
1
0
0
2
0
1
2
0
5
2
1
0
1
0
0
0
0
2
1
0
0
0
2
0
0
1
1
2
2
0
2
0
2
0
3
2
0
0
0
1
1
2
0
2
0
2
1
0
0
2
1
2
2
0
0
0
0
1
0
1
1
0
1
1
0
0
0
0
0
2
1
1
2
2
0
0
0
0
0
0
2
0
0
1
1
0
2
2
0
0
0
2
2
1
0
0
0
1
2
2
0
2
0
0
0
0
1
1
0
0
2
0
0
1
0
1
3
3
0
2
0
0
1
1
0
2
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
3
0
1
0
1
1
0
1
0
0
2
1
0
2
0
1
2
0
0
2
0
1
0
0
0
1
0
1
0
0
0
0
1
0
2
0
2
0
0
1
2
0
2
2
0
2
0
0
0
2
1
0
1
2
0
0
1
0
0
0
2
2
1
0
0
0
0
0
1
2
0
0
0
1
0
0
0
1
0
2
0
0
2
0
2
1
0
0
2
0
2
1
0
1
1
1
0
1
0
1
2
1
1
0
0
2
0
2
2
1
0
0
2
1
2
0
0
2
0
2
0
0
2
1
1
2
0
0
1
0
2
1
2
0
0
2
0
2
2
2
1
0
4
1
2
1
0
0
0
2
1
0
1
1
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
2
0
1
1
1
0
1
2
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
2
2
2
0
0
1
1
1
1
0
1
1
0
1
2
2
0
0
2
2
1
0
3
1
0
2
1
2
1
2
1
0
0
0
0
1
1
1
1
0
0
2
0
0
0
2
2
2
2
0
2
1
1
0
0
0
1
0
1
2
0
2
1
0
2
2
0
0
1
0
0
0
1
2
0
0
0
1
0
0
1
2
1
2
0
1
0
2
2
0
0
1
0
2
0
0
1
1
2
2
1
3
0
0
0
0
1
0
2
0
0
2
0
4
1
4
0
0
0
0
2
1
0
0
1
1
1
2
1
0
0
0
0
2
0
0
0
1
0
2
2
0
0
1
0
0
0
0
0
0
2
0
0
2
2
0
2
0
0
1
2
0
1
1
1
0
0
0
2
2
1
0
2
1
1
0
0
1
0
0
1
1
0
0
2
2
1
1
0
2
2
0
0
1
0
0
0
2
2
1
2
0
2
2
0
2
0
1
0
2
0
0
0
0
1
2
2
0
1
1
0
2
1
0
0
2
1
2
0
0
3
0
2
1
0
1
0
2
0
0
0
2
0
0
1
0
2
1
0
0
1
1
0
1
1
0
1
0
2
2
0
1
0
2
0
2
0
0
3
0
0
2
0
2
1
1
0
1
2
1
3
0
0
0
2
1
0
0
0
0
0
1
1
0
2
2
1
0
0
0
1
0
1
2
2
0
0
1
0
0
0
0
0
0
0
2
2
1
0
0
0
1
0
1
2
1
0
0
1
2
0
1
1
2
2
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
1
0
0
2
1
1
1
2
1
0
1
1
0
0
0
3
1
0
3
0
2
2
1
0
2
1
0
0
2
0
1
1
2
1
1
0
1
0
1
0
0
1
0
2
1
2
0
2
0
1
2
4
2
2
2
1
1
0
1
1
1
1
4
1
0
1
1
1
6
1
0
0
1
0
1
1
0
0
0
1
1
0
0
1
1
0
0
3
0
2
0
0
1
0
0
0
0
2
1
0
2
0
1
0
0
0
0
0
0
0
1
0
2
2
0
1
0
0
2
0
0
0
0
1
1
0
1
0
0
0
1
2
0
0
0
0
0
2
2
0
0
0
1
0
0
0
1
1
0
1
1
2
0
1
2
0
0
0
0
2
1
0
0
2
0
0
0
2
0
0
0
1
0
3
1
0
1
0
2
1
1
0
2
0
0
0
2
1
0
1
0
0
0
1
2
0
1
1
1
1
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
3
0
0
2
0
0
2
0
0
0
0
2
1
0
1
1
1
2
1
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
2
0
1
2
1
0
1
1
1
0
1
0
0
2
2
1
1
3
2
1
1
0
0
1
0
0
4
1
0
1
0
1
0
0
0
0
0
2
1
0
0
0
0
2
1
1
2
0
0
0
2
0
1
0
2
0
0
0
0
1
1
0
1
0
2
0
0
2
1
0
0
0
0
2
0
0
1
0
2
2
0
2
0
1
0
0
2
0
1
3
1
0
1
0
0
1
2
1
1
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
1
0
3
2
0
2
0
0
2
0
0
0
0
0
1
1
0
1
2
0
1
1
1
0
0
2
1
2
0
0
1
0
0
0
0
2
0
1
1
1
0
0
2
0
1
2
0
0
1
0
0
0
0
0
2
1
0
1
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
1
1
2
0
1
2
0
0
0
0
0
0
1
1
0
2
0
0
1
1
0
2
2
2
2
1
1
2
1
2
0
1
0
0
0
2
2
1
1
2
0
1
2
2
2
1
0
0
2
0
2
1
2
0
0
1
0
0
0
2
0
0
1
1
0
2
0
0
2
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
1
1
1
1
2
1
2
2
0
0
2
0
0
0
2
2
2
0
2
1
0
2
1
2
2
1
2
2
2
0
0
2
1
1
3
0
1
0
1
0
0
1
0
0
0
2
0
2
2
0
2
0
0
0
1
0
0
0
0
0
0
0
4
2
1
0
0
0
0
1
0
0
2
0
2
2
0
1
0
2
1
2
0
1
3
1
0
1
0
2
1
0
0
0
0
1
0
0
1
0
0
1
0
1
2
1
2
2
0
0
0
0
0
0
0
2
0
1
1
1
0
1
0
2
0
0
2
0
2
0
0
2
0
2
2
0
1
0
1
1
1
0
2
2
0
1
0
0
1
0
1
0
1
1
0
0
0
0
2
1
1
0
0
1
0
0
2
0
0
0
0
0
0
1
2
0
0
1
2
0
2
0
1
1
0
0
1
3
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
2
1
0
0
0
2
2
1
0
0
1
1
2
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
1
0
2
0
3
2
2
2
0
1
2
0
0
0
2
3
1
2
0
1
2
2
3
0
0
2
1
0
1
0
0
0
1
1
1
1
0
2
1
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
2
1
1
2
0
2
0
1
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
2
2
1
1
0
0
2
1
0
0
0
2
0
1
1
0
0
0
1
1
2
0
0
0
2
0
0
0
0
0
2
0
0
1
1
2
1
2
0
1
0
0
1
1
1
3
2
0
3
0
0
1
0
0
2
1
0
1
2
2
0
0
0
2
0
0
0
2
1
2
2
0
1
0
1
1
0
1
1
0
0
0
2
1
0
1
0
1
0
1
1
2
0
1
1
1
0
0
0
2
0
1
0
0
2
0
0
0
1
0
2
0
0
0
0
1
3
1
0
0
0
1
0
0
1
2
2
1
1
1
1
0
0
1
0
1
0
0
0
0
0
2
0
2
2
0
0
0
0
1
2
1
0
2
1
0
0
1
0
1
2
0
1
0
0
0
2
0
2
0
0
0
2
0
1
1
0
2
0
3
0
1
2
0
2
0
1
0
0
1
0
2
2
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
2
2
2
0
0
2
0
0
3
0
0
0
2
1
1
0
1
1
0
0
2
2
0
3
0
0
1
1
1
0
0
0
0
2
0
0
0
2
1
1
2
2
0
1
1
1
0
2
1
0
1
0
0
0
2
1
0
2
3
0
0
0
0
0
0
1
1
0
1
2
1
0
2
1
0
1
0
0
0
2
0
1
2
0
1
0
0
2
0
0
0
1
1
1
0
0
0
1
1
1
0
1
0
0
2
0
0
0
0
1
0
0
1
1
1
0
0
1
0
0
0
0
0
1
0
2
0
1
0
0
0
0
1
2
2
0
1
1
0
0
0
2
0
1
0
1
2
2
2
2
2
0
2
2
0
0
1
0
1
1
1
0
1
1
0
0
0
1
0
2
0
0
1
0
0
2
0
1
0
0
0
0
0
2
2
1
1
0
0
1
1
2
2
1
1
0
3
0
1
0
0
0
1
0
0
2
1
2
0
0
2
0
0
0
0
1
2
0
1
0
0
0
0
0
2
0
0
0
0
1
1
0
0
2
0
0
1
1
1
0
3
0
0
0
0
1
0
0
2
2
0
1
0
2
1
0
1
2
1
0
1
2
0
0
0
2
2
1
0
0
3
2
0
1
1
0
0
0
0
0
2
1
0
0
0
0
1
2
0
0
0
0
0
1
0
0
1
0
0
1
1
0
1
0
2
0
0
1
0
2
2
0
0
1
0
0
1
1
0
0
1
1
0
0
0
1
2
0
2
0
1
0
0
0
2
2
3
0
0
1
0
0
2
2
1
0
0
0
2
2
1
1
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
2
2
1
1
0
0
1
2
1
2
1
0
1
2
0
2
1
1
0
1
1
0
0
1
0
2
2
0
2
0
0
1
0
0
0
0
1
0
2
0
1
1
0
0
1
3
2
1
0
1
0
0
0
1
0
2
1
0
0
0
0
0
0
1
0
2
3
1
1
2
1
1
0
1
2
2
0
1
1
0
0
0
0
0
2
0
0
0
1
0
1
0
0
2
0
0
1
0
0
2
1
0
1
0
1
0
0
0
1
0
2
0
1
2
0
2
2
2
0
0
0
1
1
0
0
0
0
1
2
0
0
1
0
2
1
2
0
0
0
1
0
2
1
0
0
0
1
0
2
1
2
2
0
2
0
0
1
2
2
0
1
1
0
0
2
2
0
1
0
2
1
0
1
2
2
1
1
1
1
0
0
2
2
0
0
0
0
1
1
1
1
1
2
2
0
0
0
2
0
2
0
0
2
1
0
1
1
0
0
0
2
0
0
0
0
2
1
0
3
0
0
1
0
1
2
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
1
1
2
0
1
1
0
0
1
2
0
1
0
0
2
0
0
0
0
3
0
1
1
0
0
0
2
1
0
0
1
0
0
0
0
2
1
2
0
3
0
0
2
1
0
0
2
2
0
0
1
1
2
0
2
5
0
2
2
1
0
0
2
0
0
2
1
2
0
1
1
1
0
0
0
2
2
0
2
0
0
0
0
0
0
0
2
1
1
2
1
2
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
2
0
0
6
1
0
1
1
1
0
1
0
0
0
0
2
0
2
2
0
1
0
0
2
1
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
1
1
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
2
2
0
0
0
1
1
1
0
1
0
0
2
2
2
1
2
1
0
1
2
3
0
2
1
0
3
1
2
0
1
2
0
1
0
2
0
1
0
0
2
0
2
0
1
2
0
1
0
0
1
0
0
0
0
0
0
2
2
1
0
1
1
0
0
2
1
0
0
0
2
0
0
2
2
2
3
1
2
0
0
2
0
0
0
2
2
0
2
0
0
0
1
1
0
0
1
0
0
3
0
0
0
2
0
0
1
0
1
2
0
0
0
0
2
0
2
0
2
0
0
1
0
0
0
1
1
0
1
0
0
2
0
0
0
0
0
2
0
0
1
1
0
2
1
1
2
2
2
0
1
1
0
2
0
0
0
0
0
0
0
0
1
0
1
0
1
2
0
0
0
1
1
0
1
1
0
1
2
0
1
2
0
0
2
2
0
2
1
2
0
0
0
4
0
2
1
1
2
1
0
0
1
3
2
0
1
0
0
0
0
2
0
0
0
2
1
0
2
0
0
1
0
1
2
0
1
0
1
1
2
0
0
0
1
0
2
1
2
0
0
0
1
0
0
0
0
1
2
0
3
0
0
0
0
0
0
2
1
1
0
0
1
0
2
0
0
0
0
0
1
1
3
0
2
0
0
4
0
0
0
2
0
1
0
2
2
2
0
0
0
0
2
0
0
0
1
2
0
0
1
0
2
1
0
0
0
0
0
0
0
0
2
1
2
2
0
1
0
2
1
0
0
2
1
0
0
2
1
0
0
0
0
0
0
0
1
0
2
0
1
0
0
1
0
1
2
2
1
1
0
1
1
1
3
0
1
2
1
0
2
0
0
0
4
0
0
2
0
2
0
0
1
0
0
2
0
0
1
2
0
0
2
0
0
2
0
2
0
2
2
1
0
0
0
1
1
1
0
2
0
0
0
0
2
0
0
2
2
0
0
1
0
1
0
2
1
0
0
0
2
0
0
2
1
2
0
0
0
1
2
0
1
0
1
0
0
0
0
1
2
3
0
0
0
0
0
1
1
0
2
0
0
0
1
0
1
0
0
1
2
0
0
1
1
0
1
0
3
0
1
0
2
1
0
1
0
2
0
0
2
1
1
1
2
0
0
0
0
1
1
0
0
0
0
0
0
2
2
1
1
0
0
0
0
1
0
0
1
1
0
0
0
2
0
0
2
0
0
0
1
2
0
0
0
2
2
1
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
1
0
2
0
0
0
1
1
0
0
2
0
0
2
0
1
1
1
1
1
0
0
1
0
2
0
1
2
1
2
2
1
1
0
0
0
0
1
0
0
5
1
2
1
0
0
1
1
0
2
1
0
0
1
0
0
2
0
1
2
0
0
0
1
2
0
1
2
0
0
1
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
1
0
2
0
2
1
4
1
2
2
0
2
2
0
1
1
0
0
2
0
0
0
1
0
0
1
2
0
0
3
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
1
0
2
1
0
2
2
2
2
2
1
2
0
1
0
0
0
2
0
0
2
1
1
1
0
1
1
0
0
0
2
0
0
1
0
2
1
0
2
2
0
2
0
2
2
0
1
0
0
2
0
0
1
0
2
0
1
0
1
0
2
2
0
5
0
0
1
1
0
0
0
1
2
2
5
0
0
0
0
0
0
0
0
0
1
0
2
1
0
2
1
2
0
0
0
0
0
0
0
0
0
0
3
0
1
2
0
2
0
1
0
0
1
0
0
1
0
0
2
0
1
0
1
1
0
1
1
0
1
0
0
0
0
0
2
0
0
2
0
2
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
1
1
1
0
0
0
0
1
2
0
1
2
0
0
1
0
0
3
0
0
0
0
2
1
0
0
0
2
2
0
2
1
0
2
2
2
1
0
0
0
0
0
2
1
1
2
1
1
2
1
0
2
0
0
1
0
0
2
0
0
1
1
1
1
0
2
0
2
2
0
2
0
2
2
1
2
1
0
0
0
2
2
1
0
0
0
1
1
0
0
1
0
1
2
1
0
0
2
2
3
1
0
0
2
1
0
1
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
1
2
0
1
0
0
2
1
0
0
0
0
1
0
2
0
0
0
0
0
0
1
2
0
1
0
2
0
0
0
0
0
0
0
1
0
2
1
0
0
0
2
0
2
0
0
0
0
1
0
1
2
0
1
0
0
1
1
0
0
0
0
0
1
1
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
2
0
1
2
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
1
2
0
1
0
1
0
0
1
0
0
1
0
0
0
2
1
0
0
0
0
0
2
2
1
0
3
0
0
1
4
0
0
1
0
0
0
0
2
1
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
2
0
0
2
0
0
1
3
1
0
2
1
1
2
1
0
0
1
1
1
0
0
0
0
0
1
1
1
0
0
1
1
0
2
0
2
2
1
0
2
0
0
1
3
1
1
0
0
1
2
0
0
2
0
0
1
0
2
0
0
1
0
1
2
1
2
2
0
0
0
0
0
0
1
2
2
1
0
0
1
2
2
0
0
1
1
2
0
0
0
1
0
2
0
0
0
0
1
0
1
2
0
0
0
1
0
1
0
1
0
0
2
2
3
0
0
2
0
0
0
0
1
0
0
2
2
1
0
2
0
2
0
1
2
2
0
4
1
0
0
1
2
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
2
1
0
1
0
1
0
2
0
2
1
0
0
1
0
1
0
0
1
1
0
1
0
2
1
0
1
1
0
2
0
2
0
1
0
0
1
0
0
0
0
2
1
2
0
0
0
0
0
2
0
0
0
0
2
1
2
2
2
0
0
0
2
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
2
0
2
0
0
1
1
0
0
1
1
0
1
1
0
2
0
0
2
0
0
0
0
0
2
2
0
0
2
0
0
0
0
1
4
0
2
0
2
0
1
1
0
1
0
0
0
1
1
0
0
0
0
2
2
1
2
0
0
1
0
2
1
0
0
2
1
2
2
0
0
0
1
2
3
1
0
1
1
0
0
1
0
1
0
1
0
0
0
1
1
1
0
0
1
2
2
1
1
0
0
0
2
0
2
1
2
0
2
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
2
0
2
0
0
2
0
1
0
1
1
0
2
0
0
2
1
5
0
2
1
0
0
1
0
2
3
2
0
0
0
0
2
0
0
1
0
0
2
0
0
1
2
0
0
0
0
0
0
1
0
0
0
1
0
1
1
3
1
2
0
1
0
1
0
1
3
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
2
1
1
2
1
0
1
0
0
0
1
1
1
2
0
0
0
3
2
0
0
1
2
0
1
1
1
2
1
0
1
0
1
2
1
1
0
2
2
0
0
3
0
1
0
0
0
0
2
0
0
2
2
0
0
0
0
0
1
2
1
2
0
0
2
0
0
1
0
0
1
2
1
0
1
1
0
0
1
0
0
1
0
1
1
1
0
2
1
0
2
2
0
2
2
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
1
0
1
0
0
0
0
2
1
2
0
0
0
0
1
1
1
1
2
0
3
1
1
0
0
1
0
1
0
1
0
0
2
0
2
2
0
0
1
0
1
0
0
0
2
1
0
0
0
0
0
1
0
1
1
0
1
0
3
2
0
0
2
0
2
0
0
1
1
2
1
1
0
2
0
1
0
0
1
0
1
2
0
0
1
0
0
0
1
2
1
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
2
2
1
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
1
2
1
1
1
1
1
3
2
1
0
0
2
2
1
0
1
2
0
0
1
0
0
0
1
0
0
1
1
0
0
2
3
2
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
3
1
0
2
0
1
1
3
2
0
0
0
1
0
0
2
2
0
0
2
2
1
0
0
0
2
1
1
0
0
0
2
1
0
0
0
2
0
2
1
0
0
0
3
1
2
1
0
0
2
0
0
0
1
0
0
0
0
1
3
2
0
0
0
1
0
0
0
0
2
0
1
1
0
1
1
0
0
0
0
2
0
2
1
2
2
0
0
0
1
0
0
1
1
1
0
2
1
1
0
1
0
0
0
0
2
2
1
2
1
0
2
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
1
2
0
1
0
1
1
0
1
0
1
2
1
2
2
0
2
0
2
0
1
0
2
1
0
0
0
0
2
0
0
2
1
0
2
0
2
0
0
2
0
0
1
2
0
1
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
1
2
0
0
0
2
1
0
2
2
0
2
0
0
6
3
0
0
2
0
0
2
2
2
0
2
0
1
2
0
1
0
0
2
2
1
1
1
2
2
1
1
0
1
0
1
0
0
0
2
1
2
1
0
0
2
0
0
1
1
1
0
0
0
0
0
0
0
3
2
0
1
0
2
0
0
0
2
0
0
1
0
0
2
1
0
0
1
0
0
2
1
0
0
1
0
0
0
3
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
1
0
0
2
0
2
0
2
0
1
0
0
0
1
4
0
0
0
0
2
0
1
1
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
2
2
2
0
0
0
1
0
1
0
0
2
0
0
1
1
1
0
0
3
2
1
1
0
0
0
0
1
2
0
1
0
2
0
0
0
1
0
2
0
0
1
1
0
0
1
0
1
0
0
1
0
3
1
1
4
1
0
0
2
1
2
0
0
1
0
0
1
2
2
2
2
2
0
2
0
0
1
0
0
0
0
0
1
0
1
1
0
1
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
1
0
2
0
1
0
2
0
1
1
2
0
0
0
0
0
2
0
0
3
0
5
1
0
0
0
1
0
0
1
0
1
1
0
0
2
2
0
2
0
0
1
2
1
1
0
2
1
0
5
1
2
0
2
1
0
2
0
0
0
2
2
0
0
0
0
3
0
0
1
0
1
0
1
1
0
1
0
0
0
0
1
2
1
0
1
0
0
2
1
0
1
2
0
0
0
0
0
2
1
1
0
0
0
0
1
0
2
0
0
0
2
2
1
0
0
0
2
1
2
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
2
1
0
2
2
0
0
1
2
1
2
0
1
2
2
1
1
3
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
2
0
2
0
1
2
2
1
0
1
0
1
0
0
2
0
1
0
0
1
1
0
2
0
0
0
1
0
1
0
1
1
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
2
0
2
1
1
0
1
0
2
1
1
0
0
0
1
0
0
0
0
1
2
0
0
2
2
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
2
0
0
0
1
2
0
0
0
0
1
0
2
0
0
0
0
1
0
0
1
0
2
0
1
2
1
1
1
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
2
2
0
2
0
0
0
0
1
0
4
1
0
1
0
0
1
0
0
0
1
1
2
0
0
2
1
0
0
1
2
0
0
2
1
4
0
0
2
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
3
2
3
2
0
0
0
0
0
1
0
1
0
0
1
0
2
0
0
0
0
1
0
1
1
0
0
1
0
0
1
0
0
0
1
1
1
0
0
2
7
1
0
0
0
0
2
0
0
0
0
0
2
1
1
1
0
1
1
2
2
1
1
2
1
1
0
0
1
2
3
0
0
0
1
0
3
0
0
1
0
2
0
0
0
0
1
0
1
3
2
0
1
0
0
0
1
1
0
0
0
0
0
0
0
2
0
2
0
0
2
2
0
0
0
0
2
1
1
1
1
2
0
0
0
0
1
0
2
0
1
1
0
0
1
0
0
0
0
2
0
2
0
0
1
0
0
1
0
0
0
0
1
1
0
0
1
0
2
1
0
1
1
0
0
0
0
0
0
2
0
0
1
1
5
0
1
0
0
0
0
0
3
1
2
0
0
0
2
0
0
0
0
0
0
2
0
0
1
1
0
2
0
2
0
0
2
2
0
1
1
1
1
1
0
1
0
0
2
0
0
0
1
1
0
1
0
1
0
2
0
0
1
0
0
0
0
1
0
0
0
1
2
2
0
0
0
1
0
0
1
1
2
0
0
0
1
1
2
2
0
0
0
1
2
0
2
1
0
0
2
1
1
0
0
1
0
2
0
0
0
1
2
0
2
1
1
0
0
0
2
2
1
1
1
0
0
0
0
2
0
1
0
2
0
0
1
0
2
0
0
1
1
1
0
0
0
1
0
0
1
1
0
2
2
2
0
1
1
2
1
0
0
0
0
0
2
1
2
3
0
0
2
0
0
0
0
0
2
1
1
1
0
1
0
0
2
0
2
0
0
2
0
0
2
0
0
0
2
0
0
2
0
2
0
0
0
3
2
0
2
0
0
1
0
0
1
2
0
1
2
2
0
2
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
1
0
1
0
2
2
0
0
2
0
0
1
0
2
1
4
0
0
0
0
0
0
0
1
2
0
0
0
2
1
0
0
2
1
0
0
0
1
1
1
0
0
0
1
2
0
0
0
0
1
0
0
1
0
1
0
0
2
2
0
2
2
0
0
1
1
1
0
0
0
1
0
0
1
1
2
0
0
1
1
0
1
0
2
0
2
2
1
3
0
0
0
0
1
0
0
1
0
0
0
1
1
0
1
0
1
2
0
0
0
0
1
0
0
1
0
0
4
0
1
1
0
0
0
0
1
1
0
1
0
1
2
0
0
1
0
2
2
0
1
3
0
1
2
2
0
0
2
0
0
2
0
0
0
1
0
1
2
0
0
0
2
3
0
0
0
0
0
2
1
2
0
0
0
0
1
0
0
0
0
2
0
0
2
2
0
1
2
0
0
1
2
2
2
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
1
1
2
2
0
3
0
0
0
0
0
2
3
0
0
0
0
2
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
2
0
0
0
2
1
2
2
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
10
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
1
0
1
1
0
0
0
0
1
0
1
2
0
0
0
0
0
2
0
0
2
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
1
2
0
1
2
1
1
1
0
2
0
2
1
1
2
2
0
2
0
2
0
0
0
1
0
2
0
0
1
8
0
0
1
0
0
0
2
0
0
2
1
0
1
0
2
1
1
2
0
0
0
0
0
2
0
1
3
0
2
2
0
0
1
0
0
1
1
0
1
2
1
0
0
0
1
0
1
1
0
1
0
0
0
1
1
0
2
2
0
0
1
0
0
2
2
1
0
0
3
0
0
1
2
0
0
0
0
0
2
0
0
0
1
2
1
1
2
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
2
2
0
0
0
1
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
2
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
1
1
1
1
3
0
0
1
0
0
0
1
0
1
0
0
1
0
3
0
0
2
0
1
1
1
0
0
0
2
2
1
0
2
2
1
0
0
0
1
0
0
2
1
0
2
1
2
1
2
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
1
2
2
0
0
0
0
0
0
2
0
0
2
0
0
1
1
1
0
0
0
0
0
0
2
0
0
1
1
1
2
2
1
0
0
0
1
0
0
0
1
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
2
0
1
0
0
0
1
0
2
0
1
0
2
1
0
0
1
1
0
2
2
0
1
2
2
2
0
1
0
2
1
1
1
11
1
0
0
0
0
3
0
0
1
0
0
2
0
0
0
0
1
1
0
0
0
0
0
2
0
1
2
0
0
0
0
1
2
0
2
0
0
2
3
2
0
1
1
1
0
0
1
0
1
0
0
2
1
0
1
0
0
0
2
0
0
0
0
1
0
1
0
1
1
2
0
0
0
2
0
3
2
0
0
0
2
0
0
2
1
0
1
2
1
0
1
1
0
1
0
1
1
0
2
0
0
0
1
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
2
0
1
0
1
1
2
0
2
2
1
0
1
0
2
0
0
0
0
2
0
1
0
2
0
0
0
1
0
0
2
0
0
0
0
1
1
0
1
2
0
2
2
2
0
1
2
0
0
0
2
1
1
0
0
0
0
2
3
0
1
2
0
0
2
0
1
0
1
0
0
2
0
0
0
0
1
1
1
1
0
0
1
0
1
2
2
2
1
1
1
1
2
0
0
1
0
0
1
1
0
0
3
1
10
0
1
0
0
0
2
0
1
0
1
1
0
1
0
0
0
2
0
2
1
1
1
0
0
2
0
1
2
1
0
2
1
0
1
0
1
0
2
0
1
0
1
2
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
1
0
2
0
1
2
1
1
0
0
0
0
1
0
0
0
2
1
3
0
1
0
0
0
2
2
0
0
1
0
0
0
0
0
2
0
0
0
1
1
0
2
0
0
0
1
0
0
1
0
0
2
0
1
1
0
0
0
0
0
0
1
2
0
2
0
2
1
1
0
2
1
0
2
0
0
1
0
1
1
0
1
1
0
0
0
2
0
2
2
2
2
1
1
0
1
2
0
0
0
0
2
0
1
0
1
1
0
0
0
0
0
1
0
1
0
2
0
0
2
1
0
2
0
2
0
0
0
2
2
0
0
2
2
1
0
1
2
0
1
1
0
2
0
2
0
0
0
1
2
0
1
0
0
0
2
0
0
0
1
1
0
2
1
0
2
2
0
0
2
0
2
5
2
0
5
1
0
0
1
0
0
1
0
0
0
1
0
2
1
1
0
0
1
1
2
0
2
1
1
2
0
1
1
1
0
0
1
2
0
1
0
2
0
2
0
0
1
0
0
1
0
1
2
0
0
1
0
2
0
0
0
1
0
0
0
0
2
1
2
2
0
0
2
1
2
3
1
0
0
1
1
0
1
0
0
0
1
1
0
1
1
2
1
1
0
1
1
0
1
0
2
0
1
1
0
4
1
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
1
2
0
1
0
0
1
2
1
0
0
1
0
1
0
2
1
3
2
0
1
2
0
1
2
0
1
2
0
2
1
0
6
0
0
1
0
1
1
0
2
2
1
1
1
0
2
0
2
1
0
2
0
1
2
2
1
1
1
0
0
1
0
2
0
2
2
0
0
0
2
0
0
0
0
0
2
0
0
2
1
10
0
0
0
0
2
0
0
2
0
1
2
0
1
1
0
0
0
2
2
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
2
1
0
0
1
1
0
1
0
2
0
0
0
0
0
0
2
0
2
0
1
2
0
1
2
1
0
0
2
0
0
0
2
1
0
2
1
2
0
1
1
2
0
1
0
0
0
0
0
1
1
1
0
2
2
0
0
2
0
0
1
0
0
0
1
1
1
2
0
0
0
0
1
0
2
0
7
1
1
0
0
0
0
0
2
0
1
2
0
0
0
0
1
0
2
1
4
0
2
0
0
0
0
1
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
2
0
1
0
0
2
2
2
1
1
1
0
0
2
2
0
0
0
0
2
2
1
1
0
0
1
0
0
2
1
2
1
0
0
0
1
2
1
2
0
2
1
1
1
2
1
2
0
0
1
0
0
1
2
0
1
1
0
1
0
1
2
0
1
1
1
0
0
0
0
1
1
0
1
0
0
0
2
0
0
0
1
0
2
1
1
1
2
0
2
1
0
1
0
0
0
0
0
0
0
2
1
1
0
0
1
1
0
0
1
0
1
1
0
2
2
1
0
0
0
1
0
2
1
1
0
0
0
0
2
0
0
0
0
2
0
2
2
1
0
0
0
1
1
1
0
1
2
0
2
4
0
0
0
0
1
2
1
1
0
0
2
0
1
2
0
0
0
2
1
0
1
0
1
0
1
1
2
0
0
1
2
1
0
0
0
2
0
1
0
0
2
2
0
0
2
0
1
1
2
0
0
2
1
0
0
1
0
1
2
2
1
0
1
0
0
2
2
0
0
0
2
1
0
0
2
0
0
0
2
0
1
0
0
2
0
0
1
1
0
2
1
0
2
1
1
0
1
0
2
0
0
2
1
1
1
3
0
1
0
0
1
3
0
2
2
0
0
0
0
0
1
0
1
4
1
1
0
0
2
0
1
0
0
2
0
2
2
1
1
0
1
0
1
2
2
0
1
2
0
1
1
0
1
1
3
0
0
0
0
2
1
0
1
2
0
0
0
1
0
1
2
1
0
1
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
1
0
2
0
2
1
2
1
2
1
1
2
2
0
0
0
2
1
1
0
2
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
1
0
3
0
1
2
0
0
0
0
0
0
0
0
1
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
2
2
1
0
1
1
0
2
2
0
0
0
2
0
0
0
2
0
2
1
2
0
0
0
2
2
0
2
1
0
1
0
2
1
0
0
1
0
0
1
2
0
1
0
2
0
0
0
2
0
0
0
1
2
0
0
1
0
0
0
2
0
1
0
0
2
1
1
3
0
0
0
0
1
2
0
0
0
1
0
2
0
1
0
3
0
0
2
0
1
0
2
0
2
0
1
0
1
1
1
0
1
0
1
1
0
0
1
3
2
2
0
0
1
1
0
2
1
1
0
0
0
1
0
0
0
2
0
0
2
1
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
2
2
1
0
0
0
0
0
0
1
2
0
0
0
0
0
2
1
0
1
1
0
0
2
2
0
0
2
1
0
1
2
2
0
2
0
1
0
2
1
2
1
1
1
0
0
1
1
0
0
0
0
3
1
0
1
2
1
0
2
0
0
2
0
1
0
2
1
1
0
0
0
0
2
0
1
0
2
0
0
2
3
0
0
2
2
0
0
1
0
0
0
1
1
0
1
2
1
1
0
0
1
2
1
0
2
1
0
1
2
2
2
0
1
3
1
1
0
0
1
2
2
0
0
0
0
0
1
1
0
1
0
0
0
0
2
0
1
2
2
0
2
0
0
0
1
0
0
2
2
2
0
2
1
0
1
0
1
0
0
0
2
0
0
2
2
2
0
2
2
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
1
1
2
1
2
0
0
0
1
3
1
0
0
0
0
0
1
0
0
1
3
0
0
0
0
0
2
0
1
0
0
0
2
1
0
2
1
0
2
2
0
0
0
2
0
0
0
0
0
2
1
1
2
0
0
3
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
1
1
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
1
1
1
1
7
0
0
1
0
0
3
1
0
0
2
0
0
0
3
0
1
1
1
2
0
0
2
1
0
0
2
0
0
2
0
0
0
1
0
1
1
0
1
0
0
0
0
0
2
1
5
2
2
1
0
0
0
0
1
0
1
1
0
0
1
0
0
1
0
0
1
0
0
0
2
2
2
2
1
0
1
2
0
1
2
2
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
2
0
0
2
0
0
0
1
0
0
0
0
2
2
0
0
1
0
2
2
0
1
0
0
2
2
1
0
1
0
1
2
0
0
2
0
1
1
1
0
2
0
1
0
0
1
1
1
2
2
0
1
0
1
1
0
0
0
1
1
0
2
0
2
0
0
1
0
0
1
2
1
1
0
2
2
0
0
1
2
0
2
2
0
0
1
1
0
2
1
1
2
1
0
0
1
1
0
0
2
1
0
0
0
0
0
0
2
0
2
0
1
0
2
0
2
2
0
0
3
0
2
1
1
1
1
1
0
3
0
0
1
1
0
0
1
2
1
1
0
0
1
0
1
2
3
0
1
2
2
2
1
0
0
1
2
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
1
0
1
0
0
1
0
3
0
0
0
0
1
0
0
2
0
2
2
2
1
1
1
0
1
0
0
0
0
0
0
0
0
0
2
1
1
0
1
0
1
0
0
0
1
3
0
0
2
0
0
0
1
1
1
1
0
1
1
0
1
0
0
0
1
2
1
0
0
0
0
1
0
0
0
2
0
2
1
0
1
0
0
0
1
0
0
0
1
1
0
2
2
0
1
0
1
1
0
0
0
2
0
0
0
0
0
1
0
1
1
0
0
2
4
1
0
2
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
1
0
1
1
0
1
3
2
0
0
0
0
0
1
0
0
1
0
0
0
3
0
0
1
1
0
2
0
2
1
0
0
1
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
1
1
1
1
0
1
1
0
0
0
0
0
0
0
1
0
0
2
1
2
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
2
2
0
0
1
1
1
2
0
1
1
0
0
0
1
1
0
0
0
0
1
0
2
0
1
4
0
0
0
0
0
1
1
0
0
0
0
1
2
0
1
0
2
2
0
1
2
0
1
2
0
0
1
2
2
4
0
1
1
0
0
1
0
0
1
2
0
0
2
0
2
1
0
1
0
2
0
2
2
1
0
0
0
0
2
0
1
1
0
3
3
0
0
0
0
1
0
2
2
0
2
0
0
0
1
2
0
0
0
1
3
0
0
1
2
0
1
1
0
1
0
0
1
1
0
1
0
0
0
0
1
0
0
2
4
2
2
0
1
0
0
1
2
1
2
2
2
1
2
1
2
1
1
2
0
2
2
2
0
0
0
0
1
1
0
1
2
0
0
3
0
0
1
2
0
1
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
2
2
1
1
1
0
1
0
0
0
0
0
0
2
2
1
0
0
0
0
0
2
0
2
0
0
2
0
2
2
1
0
1
1
0
0
2
1
0
0
0
1
0
3
1
1
0
2
0
2
0
2
2
1
1
0
0
0
1
0
1
0
0
0
1
0
2
0
0
1
2
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
2
0
0
1
0
2
0
0
2
2
2
0
3
1
2
0
2
0
0
2
0
2
1
0
0
0
1
1
2
2
1
1
3
2
1
2
1
2
0
2
0
1
0
1
2
1
2
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
1
2
2
2
2
0
2
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
1
1
0
1
0
0
0
0
1
1
2
1
0
0
0
1
0
1
0
1
0
2
1
0
2
1
0
1
1
2
0
1
0
1
0
0
0
0
3
0
0
0
1
2
1
0
0
2
0
0
2
1
0
1
0
0
2
1
1
1
0
1
1
1
1
1
2
0
0
0
3
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
1
1
0
0
1
2
0
0
1
0
1
0
3
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
1
1
1
1
1
1
1
0
0
1
3
1
0
0
0
1
1
0
0
0
0
1
1
0
2
0
0
1
1
1
0
0
1
0
0
0
2
0
0
0
2
0
0
1
0
2
1
1
0
0
0
1
0
1
2
0
3
1
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
1
0
2
0
0
1
0
2
0
0
0
2
0
0
0
1
1
0
4
1
0
1
1
0
1
2
1
1
1
0
0
2
3
0
0
1
2
0
1
2
0
0
0
0
1
0
1
0
0
2
1
2
0
0
0
1
0
0
2
0
2
0
0
0
0
0
1
0
3
0
2
0
0
0
0
1
0
2
0
0
0
0
0
1
1
2
1
1
0
1
0
0
1
2
0
0
0
2
0
0
1
2
1
2
0
0
0
1
1
0
1
0
2
1
0
0
1
0
0
1
0
1
0
1
1
2
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
2
0
0
2
0
0
0
1
0
1
1
4
0
0
0
2
1
0
1
2
0
1
1
0
0
0
1
0
1
1
0
0
0
0
1
1
0
0
0
4
2
0
0
0
2
1
0
0
1
0
0
2
0
1
2
0
0
0
1
0
0
0
1
2
2
0
1
0
0
1
3
0
0
2
0
0
1
1
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
1
0
1
1
0
0
3
0
0
2
3
0
0
2
2
0
0
1
0
0
0
0
0
0
0
2
0
1
0
2
2
0
0
0
0
0
2
1
0
2
0
0
2
0
0
2
1
2
1
0
0
0
2
2
0
2
1
0
1
0
0
1
5
1
0
0
0
1
0
0
0
0
0
0
0
2
0
2
1
2
0
0
0
2
1
0
0
0
2
2
2
0
2
1
0
0
1
2
0
2
2
0
0
1
1
1
2
1
1
0
0
0
2
0
2
0
3
0
0
1
0
0
3
1
0
0
0
0
2
0
0
2
0
2
2
0
1
2
2
0
1
0
2
1
0
0
0
2
2
1
2
1
0
0
3
1
3
0
0
0
0
0
1
1
0
0
2
2
0
1
1
1
0
0
1
2
0
0
0
2
0
0
0
0
0
1
0
1
2
1
0
0
0
1
0
0
0
1
1
0
1
1
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
2
1
0
0
0
1
1
0
0
0
0
1
0
0
2
0
2
1
2
1
0
2
0
2
0
2
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
1
0
0
2
0
2
1
0
0
1
1
2
0
0
0
1
0
2
0
0
0
0
0
0
0
3
0
0
0
1
1
0
1
2
0
2
0
0
1
1
0
1
2
2
1
2
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
1
1
0
1
2
0
0
1
1
0
0
1
0
0
0
1
0
1
0
0
2
2
2
1
2
0
1
0
0
0
2
0
2
2
1
0
0
0
0
2
1
0
1
9
1
0
2
1
2
2
1
0
0
2
0
0
0
2
2
0
0
1
2
1
1
1
2
0
1
2
0
0
0
0
0
0
0
2
0
0
1
0
0
1
2
2
0
0
0
1
2
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
4
0
0
1
0
0
0
0
1
2
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
2
1
0
2
1
1
0
0
1
0
0
2
0
0
0
1
1
0
0
0
2
0
0
1
2
0
0
0
0
1
0
1
0
0
0
2
0
1
0
1
3
1
2
0
1
0
0
0
0
0
2
1
1
0
2
1
2
0
1
0
0
1
0
0
2
2
1
0
2
1
2
2
0
0
0
0
1
2
0
2
0
1
1
0
1
0
0
1
2
0
2
1
1
1
0
2
0
0
0
0
1
2
0
0
2
0
0
1
0
1
2
0
0
0
1
1
2
0
0
0
0
2
0
0
3
0
0
3
0
0
1
0
0
2
2
0
1
0
0
0
2
0
0
0
2
0
0
1
0
1
2
2
0
0
0
1
0
0
1
0
0
0
2
3
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
1
1
2
1
0
1
1
0
0
0
0
1
0
0
1
0
0
2
0
0
0
2
1
0
1
0
2
2
0
0
0
0
0
1
0
0
0
0
0
1
1
0
2
0
0
0
1
0
3
1
0
2
3
3
2
0
2
1
2
0
1
1
1
0
0
0
0
2
1
2
0
0
1
0
0
1
0
2
2
2
2
0
0
0
0
2
2
2
0
0
2
1
3
0
2
0
0
1
0
0
2
2
1
0
2
1
0
1
2
1
0
0
0
2
0
0
0
2
0
0
2
2
0
1
1
1
2
0
0
0
0
0
0
1
0
1
0
1
1
0
2
0
0
0
1
0
0
0
1
0
0
1
0
0
1
1
1
2
0
0
0
0
1
0
1
0
1
0
0
0
1
0
2
0
2
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
1
0
0
0
0
0
0
2
1
0
1
2
2
0
0
0
2
1
0
1
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
1
2
0
2
0
0
1
0
1
0
0
0
3
0
0
2
2
2
1
4
2
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
2
2
0
0
0
1
2
0
0
2
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
2
0
0
2
1
1
0
0
0
3
2
0
0
1
4
0
1
2
2
1
0
0
5
0
0
1
2
0
2
1
1
2
1
0
1
2
0
1
2
1
0
0
0
0
1
0
1
0
0
2
0
0
1
2
2
2
1
1
2
0
0
1
1
0
0
0
0
3
0
0
1
1
0
1
0
0
0
0
0
1
2
1
0
0
0
1
0
2
0
0
0
0
0
2
0
0
1
0
0
1
0
2
0
0
0
0
0
1
2
0
0
2
1
0
1
0
0
0
1
0
1
0
1
2
1
0
0
0
0
0
0
2
1
0
2
0
0
1
2
0
1
2
0
1
1
1
1
2
1
1
0
1
1
0
0
0
0
0
1
1
0
0
1
0
0
2
0
0
2
0
0
0
1
0
2
0
0
0
0
2
1
0
2
0
1
1
0
2
0
2
2
0
0
0
0
1
1
0
0
2
0
2
0
0
0
0
0
0
0
1
2
0
0
1
0
0
1
1
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
1
1
0
1
0
2
0
0
1
2
0
1
0
0
0
0
1
0
0
2
2
2
0
1
1
2
0
0
1
0
0
0
0
0
1
0
0
2
0
0
2
0
1
1
0
0
2
0
0
0
0
0
0
1
2
2
0
2
0
0
0
0
0
0
0
1
0
2
2
0
2
1
1
1
0
0
0
1
2
1
0
2
0
0
0
0
0
1
1
0
1
1
2
1
0
0
5
2
0
0
1
0
0
2
1
1
1
0
0
0
0
0
2
0
0
0
1
0
1
1
2
0
0
2
2
2
0
2
0
0
3
0
0
0
0
1
2
1
3
1
0
0
2
0
4
0
1
1
2
0
1
0
0
1
0
0
2
1
0
0
3
0
2
0
0
0
0
0
0
2
0
2
0
0
1
2
2
0
0
2
1
1
0
0
1
0
0
2
0
1
2
0
0
2
0
0
0
0
1
2
1
0
2
2
1
0
0
4
0
1
0
0
2
2
0
2
0
0
1
2
0
0
1
1
0
0
2
2
0
0
2
1
1
0
1
0
3
0
1
0
2
2
0
0
0
1
0
2
3
0
0
1
0
1
2
2
0
0
2
0
0
1
0
0
0
0
1
2
0
0
0
0
2
0
0
2
2
0
0
2
1
0
2
0
0
1
0
2
2
2
2
0
0
0
0
1
0
0
0
0
0
1
1
1
1
0
1
1
2
0
0
0
0
2
2
0
0
0
0
2
0
0
3
0
0
0
0
0
0
1
0
2
0
1
2
1
0
2
2
0
0
0
1
0
3
2
0
0
1
1
0
0
2
0
1
2
0
1
2
0
0
0
0
0
0
1
0
1
0
1
1
1
0
0
0
2
0
0
0
1
0
0
2
1
0
0
0
0
1
0
2
1
0
0
1
1
0
3
0
2
2
2
1
2
1
0
0
1
0
1
1
0
1
1
0
0
0
2
0
2
0
0
1
2
1
0
0
0
0
0
0
1
0
0
1
0
0
0
2
2
0
1
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
2
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
1
1
1
0
0
0
1
0
0
1
1
2
2
0
1
2
0
1
4
5
2
0
2
2
0
1
0
0
1
0
0
1
0
1
0
1
0
2
0
0
2
0
1
0
1
0
0
2
0
1
1
0
1
2
0
2
2
2
1
0
2
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
2
1
0
0
0
2
2
0
0
0
1
1
1
1
0
0
2
1
0
0
0
0
0
1
1
2
0
1
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
2
2
0
0
0
0
1
1
1
3
1
2
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
8
0
0
0
2
0
0
0
0
0
1
2
1
0
1
0
2
0
0
2
0
1
1
1
1
0
0
0
2
2
0
0
2
1
2
2
0
2
0
2
0
0
1
1
0
1
0
1
0
0
0
0
0
2
2
0
1
1
2
2
0
0
0
1
0
0
0
0
1
0
0
0
1
0
2
0
2
1
0
0
1
1
1
0
0
0
0
0
0
3
0
0
0
0
1
1
1
1
2
1
0
0
1
0
2
1
2
3
0
1
1
2
0
2
0
1
0
0
0
0
0
2
1
0
1
0
0
0
1
1
3
0
0
0
1
1
2
2
4
0
0
0
0
1
0
2
2
0
0
1
1
1
2
0
0
0
1
0
0
3
3
0
0
1
1
0
1
0
3
0
1
2
0
2
1
0
1
0
1
1
0
0
2
1
1
1
0
1
0
1
0
2
1
2
0
0
0
0
0
0
0
1
2
2
2
0
1
0
1
0
0
0
1
0
1
1
0
0
0
1
2
1
2
2
0
2
0
0
1
1
0
0
1
1
0
0
0
2
0
2
0
0
1
1
2
3
0
1
0
2
0
0
2
1
0
2
0
0
0
1
2
0
2
0
0
0
2
1
0
0
0
0
1
0
0
0
0
3
2
0
0
1
0
2
1
0
2
1
0
2
0
1
0
1
1
0
0
2
2
1
0
2
2
0
0
2
2
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
2
0
0
1
0
0
2
2
0
0
1
1
0
1
0
0
2
0
2
1
2
0
1
1
2
0
0
0
1
2
0
0
0
0
2
2
1
0
0
1
1
0
0
1
0
1
0
0
0
2
2
0
0
0
2
1
0
1
0
1
0
0
2
1
0
0
1
4
0
0
0
2
1
0
0
2
3
0
1
0
1
0
0
3
0
0
0
0
0
0
0
2
2
0
0
0
0
2
1
2
2
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
1
2
0
0
1
1
2
1
1
1
0
0
0
0
1
1
0
1
1
1
1
0
1
0
2
2
0
3
1
0
0
2
1
1
1
1
1
0
1
0
0
0
0
2
0
0
0
2
0
0
0
2
1
3
1
0
0
0
2
0
2
0
0
2
0
2
0
2
2
2
0
0
0
1
1
2
0
0
2
0
0
1
0
0
1
0
0
0
0
2
0
2
1
1
0
0
1
0
1
1
0
0
0
0
2
0
1
0
2
2
2
0
3
2
1
0
0
0
2
1
2
2
1
0
0
2
1
0
0
1
1
2
0
1
2
0
1
0
2
0
3
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
1
1
0
2
0
0
0
1
0
2
0
2
2
1
0
1
0
1
2
1
0
1
2
0
1
2
1
1
2
0
1
0
2
1
0
0
0
1
0
0
1
3
1
2
1
2
2
0
1
2
1
0
0
1
0
1
1
3
0
0
0
1
0
1
0
0
0
2
0
0
2
1
0
2
1
0
0
1
2
0
0
0
0
1
0
1
0
0
0
2
0
0
0
1
2
0
1
0
2
0
0
2
0
0
2
0
1
1
0
0
0
0
2
2
0
2
1
0
2
2
0
0
0
0
0
0
1
0
1
1
1
0
0
0
1
1
1
1
0
0
0
0
0
1
1
0
1
0
1
0
1
1
0
0
0
1
0
0
2
1
2
0
0
0
2
1
0
3
1
0
0
0
1
0
0
2
2
0
0
0
0
0
0
2
2
2
2
2
2
1
1
1
2
0
2
1
0
1
1
2
0
2
0
0
2
0
0
0
2
2
2
0
1
0
0
0
0
0
2
1
0
0
0
0
1
0
2
0
2
1
1
0
0
1
0
0
0
1
1
2
0
1
2
0
0
0
0
1
2
1
0
0
2
2
1
0
3
0
0
1
0
0
2
0
0
0
1
2
0
3
0
6
1
0
1
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
1
0
1
2
0
2
0
2
2
1
0
0
1
2
0
2
1
0
2
0
1
1
1
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
2
2
2
0
2
0
0
2
1
0
0
1
0
0
1
0
0
1
2
0
1
0
2
0
0
1
0
0
0
0
1
2
0
1
2
1
1
0
0
1
1
0
1
1
1
2
2
1
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
2
2
1
0
2
0
2
0
2
0
0
0
1
0
0
1
0
1
1
0
2
2
0
0
2
0
1
1
1
1
1
0
0
2
0
1
2
2
2
1
1
0
0
0
1
2
2
0
2
2
1
1
0
1
2
1
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
1
0
0
0
0
1
0
1
0
1
1
0
1
0
0
1
1
0
1
2
0
0
1
1
1
0
1
0
0
0
2
0
0
0
2
0
2
1
2
1
2
0
0
2
0
1
2
2
2
1
0
2
0
0
1
0
0
2
2
0
0
1
0
0
2
0
0
2
0
0
0
0
1
1
2
0
1
0
2
2
1
0
2
2
1
0
0
0
0
2
1
0
0
1
0
0
0
0
2
0
0
1
2
1
2
2
1
0
0
0
0
0
2
1
1
0
1
0
0
1
2
0
0
0
0
0
2
0
0
1
0
0
1
1
0
0
1
0
2
2
0
1
2
0
1
1
1
0
2
2
2
2
0
2
0
0
2
0
0
0
0
1
0
0
2
2
4
0
2
1
0
2
1
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
1
1
0
0
0
2
1
1
0
2
1
1
0
1
1
0
0
1
2
1
0
2
1
0
0
0
2
1
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
3
0
1
0
2
2
1
1
2
0
2
2
1
2
0
2
0
0
0
2
0
1
0
1
0
0
1
1
2
0
1
0
0
0
3
0
2
0
1
1
0
0
0
0
1
2
0
0
0
1
1
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
2
0
1
0
2
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
1
0
0
1
2
1
0
2
1
0
1
0
0
1
3
0
0
0
1
1
1
1
0
2
0
0
1
0
2
2
0
0
0
0
0
0
2
0
0
0
0
2
2
2
0
0
1
0
1
0
0
2
0
0
0
1
0
0
0
2
1
1
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
3
2
0
0
1
0
2
1
2
1
2
1
0
1
0
1
0
0
0
0
0
0
1
0
3
0
0
0
1
2
2
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
3
1
0
0
0
2
0
0
1
1
0
1
0
0
0
2
0
1
1
0
1
2
0
1
1
1
1
2
0
3
2
1
2
0
2
0
0
0
2
0
0
0
1
0
0
1
1
0
0
1
3
1
2
2
1
0
0
1
0
0
1
1
2
0
1
1
1
0
0
1
0
2
0
0
1
2
0
2
0
0
1
0
1
2
1
1
0
2
1
1
0
0
0
0
1
0
3
2
0
0
0
0
0
0
2
2
0
2
2
1
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
1
2
0
2
0
2
1
0
2
2
0
1
2
0
0
1
1
2
0
1
0
0
0
2
0
2
0
1
0
1
3
4
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
2
1
0
2
1
0
0
0
2
0
1
0
1
0
1
1
2
0
1
1
0
1
1
0
2
2
0
0
1
0
0
1
2
0
0
2
0
1
0
0
1
2
1
0
2
0
0
0
2
0
2
2
1
2
0
1
0
0
1
1
1
5
0
0
0
0
1
0
0
0
2
0
4
0
2
0
0
2
2
0
2
1
2
1
0
0
1
0
2
0
0
2
1
1
0
0
1
0
0
1
2
0
1
2
0
0
0
0
2
0
0
0
0
0
2
1
1
0
1
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
1
1
0
0
0
1
1
1
1
0
0
0
2
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
8
1
1
2
0
0
0
1
0
1
0
2
2
0
0
0
2
1
1
1
0
0
2
1
2
1
0
1
1
1
2
1
1
0
0
0
0
0
0
1
0
1
0
0
0
2
1
1
0
0
0
0
0
2
1
2
1
1
0
1
0
2
0
0
0
0
2
1
1
0
0
3
0
0
2
0
0
0
2
1
1
0
0
0
1
0
0
1
0
1
1
0
2
1
1
0
0
0
0
0
1
0
0
2
2
0
2
0
2
0
0
1
0
0
0
0
1
2
2
1
0
0
1
1
1
2
0
1
1
0
0
0
0
0
1
0
1
0
2
1
2
1
0
0
0
0
2
1
1
0
0
0
0
0
0
2
2
1
0
1
1
0
0
1
0
2
0
0
0
1
0
0
2
0
0
0
0
5
3
0
0
2
1
0
0
1
0
2
0
3
2
1
2
0
0
1
0
0
2
3
0
2
0
0
0
0
0
1
0
0
0
2
2
0
0
2
0
0
0
0
0
1
0
2
1
0
0
2
0
0
2
2
0
1
0
1
2
0
1
1
3
0
0
2
0
1
0
1
0
0
1
0
1
2
0
0
2
0
1
1
1
0
0
0
0
1
1
0
2
1
1
1
2
0
0
1
0
0
2
0
1
0
2
0
2
0
0
0
0
0
0
1
1
0
2
0
1
0
0
0
0
1
2
0
0
0
2
1
0
1
2
0
2
2
1
0
0
0
0
1
1
2
3
3
2
0
0
0
1
1
1
2
1
0
0
0
1
0
3
0
0
0
0
0
2
0
1
2
1
0
0
0
0
2
0
1
0
1
2
0
0
0
0
0
1
1
0
1
1
2
1
3
2
1
0
0
0
2
0
0
0
0
0
0
2
1
1
1
0
0
0
2
0
2
0
0
1
0
2
1
0
1
0
0
2
2
0
0
1
2
0
1
2
0
0
1
0
0
0
1
0
2
2
1
0
2
1
1
1
0
0
0
0
1
0
2
0
1
1
0
0
2
0
3
1
0
0
0
3
2
1
0
2
0
0
0
1
0
1
0
2
1
0
0
1
0
2
1
0
1
2
0
0
1
1
0
2
2
2
0
0
2
2
0
2
0
0
2
0
1
0
0
1
1
2
0
2
2
0
0
1
2
0
2
1
1
0
2
1
0
0
2
0
0
0
0
2
2
0
2
2
0
1
0
0
1
0
2
2
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
2
0
0
0
1
1
1
0
0
0
2
0
0
0
2
0
1
0
2
0
0
2
2
0
2
1
2
0
1
1
2
1
1
0
2
0
2
0
2
0
2
0
1
0
0
0
2
0
1
0
0
2
0
0
2
0
0
0
1
0
0
1
1
0
1
0
1
0
2
0
1
0
1
0
0
0
1
0
0
2
2
0
0
2
1
0
2
0
1
1
1
0
2
0
1
1
2
2
0
2
2
0
0
0
0
1
1
0
1
0
0
0
2
0
1
2
0
0
0
3
2
1
2
2
0
1
0
1
2
0
1
2
0
0
2
2
2
0
1
1
0
1
2
0
0
0
0
0
0
0
2
0
0
1
2
0
0
1
0
2
0
1
0
0
0
1
0
1
2
2
0
5
0
2
1
2
0
0
0
0
1
0
0
2
0
0
0
2
0
2
1
1
0
1
1
0
1
0
1
2
0
1
1
0
2
1
0
1
2
0
0
0
1
1
1
0
0
2
1
0
0
0
0
1
0
0
0
0
0
2
1
2
0
1
0
1
2
0
0
1
1
0
0
1
2
0
1
1
4
1
2
0
1
0
1
0
0
0
0
0
2
0
1
2
1
2
1
0
1
2
2
0
0
0
0
1
0
2
1
0
1
0
2
0
0
0
2
0
2
0
0
0
0
2
0
0
1
0
0
0
0
2
0
2
1
2
0
0
0
2
1
0
1
1
0
0
0
3
1
0
1
0
2
0
1
1
2
0
2
0
1
0
1
0
0
0
0
1
1
0
2
2
1
1
0
0
0
1
0
1
0
0
0
1
0
0
11
0
0
1
0
0
1
0
0
0
0
1
1
0
2
0
0
0
0
1
0
1
1
0
2
0
2
2
0
0
2
0
0
0
0
2
0
2
1
2
1
2
0
2
1
2
1
0
0
0
0
0
1
0
0
0
1
0
2
0
3
1
1
0
1
0
0
2
1
1
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
2
1
0
4
1
0
0
0
1
0
1
1
2
0
2
1
1
0
2
0
0
1
0
1
1
1
0
1
0
0
0
2
1
0
1
1
0
0
2
0
1
0
0
0
2
0
1
1
2
0
0
1
2
0
0
1
0
2
2
1
1
1
0
2
0
0
2
1
1
1
0
1
0
0
1
1
0
0
1
1
0
2
0
1
0
1
1
0
0
0
0
1
0
0
0
4
0
0
0
0
1
0
1
1
0
0
1
1
0
0
2
1
0
0
2
0
1
1
2
0
0
1
1
2
1
0
0
2
0
0
1
0
0
0
0
2
0
2
2
0
0
1
2
0
2
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
1
1
0
0
1
0
1
2
0
1
1
0
1
1
1
0
1
0
0
0
2
0
0
1
2
0
2
0
2
0
0
3
0
0
0
0
1
1
0
0
1
1
1
0
1
0
2
0
1
0
0
0
0
1
0
2
2
2
1
0
0
0
0
1
0
1
0
2
1
0
0
0
3
2
1
0
0
0
2
2
1
0
1
0
0
1
0
1
0
1
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
1
2
0
0
2
1
1
0
0
1
1
0
2
2
0
0
1
0
1
2
1
1
0
0
0
0
1
1
2
0
1
1
0
0
0
0
0
1
1
3
0
0
1
0
0
1
2
0
2
1
0
1
1
0
2
0
2
0
0
0
2
1
0
0
0
1
0
2
0
0
0
1
1
1
1
0
0
1
2
0
0
1
3
2
3
0
0
0
1
0
0
0
1
0
0
1
1
0
0
2
0
0
0
1
0
2
0
2
1
2
0
1
1
1
0
0
1
2
1
2
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
2
0
2
0
7
1
0
1
0
0
1
3
1
2
2
1
0
0
0
1
0
2
2
0
0
2
1
0
0
0
2
0
0
0
0
0
1
0
0
0
2
2
2
2
2
1
1
0
2
0
0
0
1
2
0
0
1
0
1
2
0
1
0
2
2
0
2
0
1
1
1
0
0
1
1
0
0
1
1
2
0
2
0
1
0
0
0
1
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
1
1
1
2
2
1
0
0
0
2
2
0
2
0
0
1
0
2
1
0
0
2
1
1
0
1
0
1
1
0
1
0
1
0
1
0
1
0
0
2
1
0
4
0
0
2
0
1
0
0
1
1
0
1
0
0
0
0
2
2
0
2
0
0
2
1
0
1
2
0
0
0
2
0
1
1
0
1
0
0
2
1
1
3
0
0
1
2
0
0
0
0
2
2
0
2
0
0
0
2
0
1
0
0
2
0
1
1
0
0
2
0
0
0
0
0
1
1
1
0
1
0
2
0
0
0
1
0
2
0
1
0
1
2
0
0
0
1
0
1
1
1
0
0
1
1
1
0
0
1
1
0
2
2
1
0
0
2
1
0
0
0
1
0
1
0
0
0
0
0
2
0
1
2
0
0
2
1
2
0
2
1
0
2
0
1
0
0
1
1
1
0
1
0
0
0
1
1
0
0
0
2
0
1
0
0
0
0
0
0
1
2
0
1
0
0
0
0
1
0
0
0
2
2
1
0
0
2
0
0
0
0
0
1
0
0
2
1
1
0
0
1
1
2
0
2
0
1
2
1
0
3
0
0
1
0
1
1
1
1
1
2
1
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
2
1
2
0
1
1
0
1
4
1
0
3
0
1
0
0
0
0
2
1
1
0
1
0
2
0
1
1
0
0
1
1
0
0
0
3
0
2
0
0
1
0
0
2
0
2
0
1
0
4
2
0
2
0
0
2
2
1
1
1
0
1
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
2
0
0
0
3
0
0
0
2
1
0
0
0
1
1
0
0
2
0
0
0
0
2
0
0
1
1
0
0
1
0
1
0
0
1
0
0
0
1
2
0
0
1
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
2
0
0
0
0
3
0
0
0
2
0
0
0
0
0
2
1
0
1
0
0
1
0
0
0
0
2
2
2
0
0
2
2
2
1
1
2
0
0
2
0
0
1
2
1
0
2
0
0
0
2
0
2
0
1
1
0
0
0
0
0
5
1
0
1
1
2
0
0
1
1
0
0
1
1
0
0
1
2
2
1
0
0
0
0
0
1
0
0
1
1
0
2
0
1
0
0
2
0
0
0
0
1
0
1
2
2
0
0
0
1
0
1
0
2
1
0
0
0
0
0
0
0
2
0
2
0
1
0
1
0
0
1
0
0
0
0
0
1
0
1
0
2
0
1
0
2
2
2
0
0
0
1
0
1
0
0
0
1
1
2
0
0
2
1
0
0
0
0
1
2
1
0
1
0
1
1
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
1
0
0
0
0
2
0
0
0
2
1
0
0
2
2
0
3
0
0
0
0
0
2
0
0
1
2
1
0
0
0
1
0
0
1
0
2
1
2
2
0
0
1
2
1
2
2
0
2
0
0
0
0
2
2
1
0
0
0
0
0
1
1
1
0
1
0
1
2
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
1
1
1
1
0
1
0
0
0
2
0
2
0
0
0
0
0
1
0
0
1
1
0
1
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
2
1
1
1
0
1
0
2
2
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
1
1
1
2
0
1
2
1
0
2
0
0
2
0
0
0
1
1
1
0
2
0
0
1
2
0
1
0
0
2
1
2
0
2
0
0
1
1
1
0
1
2
0
2
2
0
1
1
0
0
2
1
2
0
2
0
1
0
0
0
0
0
1
1
0
0
2
0
1
2
2
1
2
0
0
0
2
2
0
2
1
0
1
0
2
2
0
1
2
0
0
1
0
0
2
0
2
1
1
2
0
2
2
0
0
0
0
1
1
2
1
0
1
1
1
0
2
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
2
1
3
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
1
1
1
0
2
0
0
0
0
1
2
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
1
0
0
1
0
0
0
1
0
1
1
0
2
2
1
2
1
3
2
3
2
1
0
1
0
0
2
1
1
0
2
0
1
0
1
0
0
2
0
0
1
1
0
2
0
0
0
0
1
1
2
0
0
0
0
1
2
0
0
1
1
1
2
0
1
0
1
1
0
0
1
2
0
2
2
0
0
2
0
0
1
0
1
0
0
0
1
2
0
0
1
0
1
0
1
0
1
0
2
0
2
1
0
0
0
2
0
0
0
0
1
1
0
1
0
0
1
0
2
1
0
2
0
1
0
1
2
2
0
0
1
0
4
0
0
0
0
2
1
0
1
0
0
1
0
0
0
1
0
2
2
0
0
0
0
0
1
0
2
1
2
2
1
1
0
0
0
2
0
0
0
2
0
0
2
2
1
0
0
1
0
0
1
1
1
1
4
1
2
1
0
0
0
0
0
0
0
1
2
1
0
0
1
0
0
0
0
0
1
1
0
1
1
2
0
0
0
0
0
2
2
0
0
0
0
0
1
1
1
2
0
0
1
1
1
0
1
0
1
0
0
1
2
0
0
2
1
2
1
0
1
1
2
0
2
2
0
2
1
0
1
1
0
0
1
0
0
0
2
0
2
2
0
0
0
2
0
0
2
0
0
2
1
2
0
2
0
3
1
0
2
0
1
0
0
0
2
0
2
0
2
1
1
0
2
0
2
0
1
0
1
0
0
2
0
0
0
1
0
2
0
1
1
0
0
0
2
0
0
2
1
2
0
0
0
0
0
2
0
0
0
1
2
1
0
0
0
0
0
1
0
1
1
1
0
1
1
0
1
1
0
1
0
0
1
1
0
1
1
0
2
0
0
2
0
0
0
2
0
1
1
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
1
1
1
2
0
0
1
0
0
3
1
0
1
0
0
1
2
3
1
0
0
2
2
2
2
0
0
0
0
1
0
1
0
0
0
3
0
2
1
2
0
0
3
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
1
5
2
2
0
2
1
2
0
0
0
2
0
0
2
0
2
0
1
0
0
2
0
0
2
1
0
1
0
0
0
2
0
0
0
1
0
1
2
0
0
1
0
2
2
0
0
0
1
1
0
2
0
0
0
0
0
2
0
0
2
1
0
0
1
0
0
0
2
2
1
0
2
1
2
0
1
1
0
1
1
0
1
1
1
0
1
0
2
0
0
0
0
1
2
2
1
2
1
1
1
1
2
1
2
0
1
0
1
1
3
2
1
0
0
0
1
0
0
0
2
0
0
2
0
0
0
2
1
0
1
1
2
0
2
0
1
2
0
1
0
0
0
1
1
1
0
2
0
1
0
0
0
1
3
2
0
0
1
0
1
1
1
2
0
2
1
0
0
1
0
0
2
0
0
1
0
0
2
2
0
0
0
0
1
2
1
1
0
0
0
0
1
0
1
2
0
0
1
0
1
2
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
1
0
1
2
2
2
1
1
0
0
0
1
0
0
2
0
2
2
0
2
2
0
2
2
1
0
1
0
1
0
1
0
2
1
2
1
2
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
2
2
0
0
0
2
2
0
2
0
1
0
0
2
0
2
1
0
0
2
3
0
1
0
1
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
1
1
1
0
1
0
2
1
2
2
0
1
0
0
0
0
2
0
2
0
0
2
0
0
2
2
0
0
2
0
1
0
1
0
2
0
1
2
0
0
0
2
1
0
1
2
0
0
1
1
2
1
0
0
0
2
0
0
2
2
1
2
0
0
2
0
1
1
0
0
1
0
0
2
0
0
0
0
0
0
2
0
1
2
1
2
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
1
1
2
0
1
1
0
1
0
2
1
0
2
0
0
0
0
1
0
1
1
0
1
0
0
1
1
0
0
0
1
1
2
1
0
0
0
1
0
2
1
1
1
0
1
2
0
0
0
1
0
0
0
0
1
0
0
0
1
0
2
0
1
3
0
0
0
2
0
0
2
1
0
1
1
1
2
0
0
0
0
0
2
2
0
0
1
1
1
1
1
0
2
0
3
0
0
1
2
0
1
0
0
0
1
1
0
1
0
0
2
0
0
3
0
0
0
0
0
2
0
0
1
2
0
1
1
0
0
0
0
0
0
3
1
2
2
1
0
0
4
0
0
2
1
0
0
2
1
2
4
2
0
0
1
0
0
2
0
1
7
0
3
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
1
0
1
2
3
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
2
1
0
2
2
1
1
1
1
3
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
1
0
0
1
0
1
1
1
0
1
2
2
0
0
2
2
0
0
2
0
1
2
0
0
0
1
0
0
2
1
0
2
1
0
1
2
2
2
2
0
0
2
2
1
0
3
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
2
2
0
0
2
0
0
0
0
2
2
2
1
0
1
0
2
0
1
1
1
0
0
0
0
0
0
1
2
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
3
0
0
2
2
2
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
1
2
0
1
0
0
0
0
0
1
2
0
0
1
0
5
2
2
1
1
0
0
0
0
1
2
1
0
0
1
0
0
0
1
0
1
0
0
0
0
1
2
0
1
1
0
0
0
0
2
1
2
0
2
2
3
2
0
0
2
0
2
0
0
0
0
2
0
0
4
0
1
0
0
0
1
1
1
0
0
0
2
1
0
2
2
0
0
1
0
0
1
2
0
2
0
2
1
0
1
1
0
1
2
2
0
0
2
0
1
0
0
0
2
0
2
1
0
0
0
1
0
1
0
1
2
1
1
3
1
1
2
1
0
0
0
2
0
0
0
2
1
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
1
2
0
1
3
0
0
1
3
1
0
0
3
1
0
1
0
0
1
0
1
0
0
0
2
2
2
1
0
2
0
0
0
2
1
0
1
2
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
1
1
1
2
1
0
0
0
0
2
3
2
2
0
0
1
0
2
1
2
2
1
2
0
0
0
3
2
2
0
0
2
2
0
0
1
0
1
2
0
1
1
2
0
1
1
1
2
1
0
2
0
0
1
0
0
1
1
0
0
0
2
2
1
2
1
0
0
0
0
2
1
0
1
0
0
1
0
0
2
1
2
2
1
0
0
0
2
0
0
2
2
2
0
3
0
4
0
1
0
0
0
2
0
0
0
0
1
0
1
1
1
2
1
1
0
3
2
1
2
0
0
0
2
2
0
0
0
1
0
2
0
0
0
0
0
0
2
2
0
1
2
0
0
0
1
0
1
0
0
1
0
0
0
1
3
1
2
2
2
2
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
2
0
0
2
0
0
0
1
1
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
1
1
1
1
1
0
0
1
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
2
0
1
2
1
0
0
1
1
0
0
0
2
1
0
0
0
0
0
0
0
0
2
1
1
1
1
0
1
2
0
0
0
0
1
1
0
2
1
0
2
0
0
0
2
0
0
0
1
0
1
1
1
0
1
0
0
2
0
0
0
1
1
0
1
0
2
0
0
0
2
0
2
0
3
2
0
0
0
2
0
2
0
0
0
0
2
0
0
2
1
0
0
1
0
0
0
2
1
1
0
1
1
2
0
2
0
0
0
2
2
3
1
0
2
1
0
0
1
0
0
0
0
0
0
2
0
0
0
2
1
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
1
2
0
0
1
2
1
0
2
1
1
1
0
2
2
0
0
0
2
1
0
0
2
0
1
0
1
1
2
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
1
1
2
2
0
1
2
0
1
0
0
2
0
2
0
1
0
1
2
0
0
0
1
0
0
2
1
0
0
0
0
0
1
1
0
0
5
0
0
0
0
0
1
0
2
0
0
0
1
1
0
0
2
2
0
1
0
4
0
0
2
0
0
2
0
4
0
0
0
2
1
2
0
0
0
1
0
0
0
0
4
2
0
1
1
1
2
0
0
2
0
0
1
2
4
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
1
1
0
0
0
0
1
0
1
0
2
2
2
0
2
2
0
1
2
0
0
0
2
2
0
0
1
1
0
0
0
0
0
2
0
1
1
0
1
0
0
1
0
1
0
2
0
0
1
3
0
0
0
1
0
2
1
0
1
0
0
2
1
0
0
1
1
0
2
0
2
0
1
2
0
0
0
1
2
0
0
1
0
1
0
2
0
2
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
2
0
0
2
2
4
0
0
2
1
1
1
0
1
1
2
0
0
3
0
2
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
2
1
2
0
0
0
0
2
2
0
0
2
0
0
0
0
0
2
2
1
1
3
2
2
0
0
1
2
0
0
1
0
2
0
1
2
1
0
1
0
0
1
0
0
2
1
0
0
0
0
0
2
1
0
0
1
0
0
0
0
1
2
0
1
2
0
2
2
0
2
0
0
0
0
1
0
1
2
2
0
0
2
0
0
1
2
1
0
0
1
0
1
0
0
0
0
0
2
1
1
1
2
0
0
0
2
0
0
0
0
0
1
0
1
0
0
2
1
0
0
0
0
0
0
2
1
0
1
2
0
0
1
0
0
0
1
2
2
1
0
0
0
1
1
2
0
0
0
2
0
0
2
0
2
2
1
0
0
0
0
1
1
0
1
0
1
1
2
2
1
2
0
2
0
1
1
1
0
1
1
2
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
1
0
0
1
1
0
2
0
3
2
0
1
0
0
2
2
1
0
3
0
1
2
0
3
0
2
0
1
1
0
0
1
2
0
0
0
0
0
0
1
0
1
1
1
2
0
0
0
1
2
0
0
2
0
0
0
1
1
1
2
0
2
1
4
0
1
1
0
0
0
1
0
0
0
0
0
0
0
2
1
2
0
1
0
1
1
0
0
0
0
2
1
0
0
0
0
0
1
2
2
2
0
1
2
0
1
0
0
0
0
1
0
2
0
1
0
0
1
3
2
0
1
0
2
0
1
0
0
1
2
0
0
0
1
2
0
0
1
0
2
1
0
0
1
1
0
0
0
1
1
0
1
1
1
1
0
0
0
1
0
0
0
3
0
1
1
0
0
0
1
1
2
1
0
0
0
1
0
2
1
0
1
1
1
0
0
1
2
0
2
0
2
0
0
2
0
0
0
0
0
0
0
4
3
0
0
0
1
1
0
1
0
0
1
0
0
2
0
2
0
2
0
0
2
0
1
1
1
0
0
2
2
7
2
0
0
2
2
0
0
0
0
1
0
0
1
0
0
2
2
1
2
2
2
2
0
0
0
1
2
0
0
0
2
0
0
1
3
0
0
0
1
0
2
1
1
0
0
1
0
0
1
1
0
0
1
1
1
0
1
0
0
0
0
1
1
0
2
0
2
0
2
0
0
0
1
0
0
0
1
0
0
1
0
2
2
0
0
1
1
0
0
1
0
0
1
2
0
0
0
2
0
2
0
1
2
0
0
0
0
1
1
2
0
0
1
0
1
0
0
0
0
0
2
0
0
1
0
2
1
0
0
0
0
2
0
0
2
1
4
1
1
1
2
0
1
0
1
3
0
0
0
1
0
2
0
1
2
1
0
0
0
2
1
1
1
0
2
0
0
2
1
1
2
1
2
0
2
0
3
0
2
0
2
0
1
0
0
0
0
1
1
0
0
1
2
1
1
1
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
1
0
0
0
0
1
0
0
2
0
0
0
2
0
1
0
0
2
0
0
0
1
2
1
0
0
0
2
2
0
1
0
1
1
0
2
0
0
0
0
0
0
1
1
1
2
1
1
1
0
0
0
2
0
3
0
0
0
2
0
0
2
0
0
2
0
1
2
0
0
0
0
1
0
1
0
3
0
2
0
3
0
0
0
2
0
2
0
0
1
0
2
2
0
0
0
1
0
1
2
0
1
0
1
0
0
2
0
0
2
0
0
2
0
1
0
0
2
1
0
0
1
0
0
0
0
0
2
0
1
3
1
1
2
1
0
0
0
0
0
1
0
1
0
1
0
0
0
1
2
2
1
3
0
0
1
0
0
0
1
0
0
2
0
2
0
2
1
4
0
0
2
0
1
0
1
2
0
1
2
0
1
1
0
0
2
0
0
0
2
1
0
2
1
0
0
0
1
1
1
2
0
0
0
1
0
0
1
1
2
0
0
2
0
0
0
3
0
0
0
0
0
1
1
2
2
0
0
2
0
2
0
0
2
0
4
4
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
2
5
0
1
2
0
2
0
0
0
2
1
0
0
0
0
0
1
0
2
0
0
1
0
2
1
0
0
1
1
0
1
2
0
0
1
0
1
0
0
2
1
0
0
0
2
1
1
0
0
1
0
0
1
1
0
1
0
2
0
2
0
2
0
0
0
1
2
1
0
2
0
0
1
0
0
1
2
1
1
0
0
1
0
0
0
0
1
0
2
2
0
0
0
1
0
1
0
0
0
1
1
2
0
3
1
0
0
0
0
0
0
0
0
0
2
0
0
0
4
0
1
0
2
0
1
2
0
0
2
0
1
0
0
0
1
0
2
2
1
0
0
0
1
0
4
0
2
0
0
2
2
2
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
2
1
0
1
2
1
0
0
0
0
1
0
0
2
2
1
0
2
1
0
1
0
1
0
2
0
0
0
2
0
1
2
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
2
1
0
1
2
0
0
1
0
2
0
0
0
1
1
0
0
0
0
1
0
1
1
0
0
1
1
2
0
1
1
1
1
0
2
0
1
1
0
0
1
1
0
2
0
1
0
1
0
0
1
2
1
0
1
1
0
0
0
0
1
0
0
0
2
0
3
3
0
0
2
0
0
0
2
1
0
2
0
2
0
0
0
1
2
0
2
2
1
0
0
1
1
0
0
0
2
1
1
0
0
0
2
0
2
2
0
0
2
0
1
1
1
0
2
2
0
2
0
1
2
2
0
0
0
0
2
0
0
2
0
1
0
1
0
0
0
1
0
0
0
1
1
0
1
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
2
0
1
1
1
0
8
1
2
2
0
2
2
0
0
2
0
0
0
1
1
0
1
2
0
2
1
0
1
0
0
1
0
3
0
0
0
0
0
2
0
0
1
0
1
0
2
0
0
2
0
2
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
2
2
2
2
0
3
2
2
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
1
0
3
2
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
2
1
3
0
2
2
1
1
0
1
0
0
2
1
0
0
0
0
0
0
0
2
2
1
1
1
0
0
2
2
1
3
0
1
1
0
1
1
1
0
0
0
0
0
1
1
1
1
1
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
2
2
2
1
2
2
1
0
0
2
1
2
0
1
1
0
0
1
0
1
0
0
0
1
1
0
1
2
2
0
0
0
2
0
2
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
3
1
1
3
0
1
0
2
2
0
0
0
2
0
1
0
0
1
0
1
2
2
1
2
0
0
0
2
0
1
1
0
0
1
1
0
2
3
1
0
0
2
2
1
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
2
2
1
1
1
0
1
0
1
0
2
1
0
2
0
1
3
0
1
0
1
0
2
2
0
0
0
0
0
1
0
0
1
1
0
1
1
0
2
2
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
2
2
0
2
1
1
2
0
0
1
0
0
2
0
0
0
3
0
2
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
2
1
0
0
1
2
1
1
1
0
2
2
0
0
0
0
0
0
0
2
3
0
2
0
0
0
1
2
1
1
2
1
0
1
0
0
0
0
1
1
0
1
0
1
1
0
2
1
1
0
2
0
0
2
0
1
0
0
2
1
0
3
0
1
1
0
0
1
0
2
1
0
0
0
2
0
1
1
1
2
0
0
2
0
0
0
1
0
0
2
0
0
2
0
2
2
0
1
2
2
0
2
0
0
0
0
0
0
2
1
0
1
0
0
1
1
1
0
2
1
1
0
0
2
0
0
0
1
0
0
0
2
0
1
1
0
0
1
0
0
0
0
1
1
0
0
1
0
0
1
1
1
0
0
2
0
1
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
1
0
2
1
2
0
2
2
0
0
0
0
1
0
0
1
2
1
0
0
0
0
0
1
0
1
2
0
0
1
1
2
1
0
1
1
1
0
0
0
2
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
2
1
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
2
2
0
2
1
0
0
2
1
1
0
3
0
2
0
2
0
0
0
2
1
2
0
2
0
0
0
2
0
1
2
0
0
1
2
0
2
0
0
0
0
1
1
0
1
0
2
0
2
0
1
1
0
2
2
0
2
2
1
2
0
1
2
0
1
0
1
1
0
0
1
0
1
0
0
0
1
0
3
2
2
2
1
1
1
2
2
2
0
2
0
0
0
2
0
1
2
0
0
0
2
3
0
0
0
0
2
0
0
0
0
4
1
1
0
0
0
1
1
1
1
2
1
2
2
0
0
0
0
0
0
0
1
1
0
1
1
0
1
2
1
0
0
2
0
0
0
2
1
0
1
1
1
0
0
0
1
2
2
0
0
1
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
2
1
2
0
0
2
1
0
3
0
0
1
0
1
1
1
0
0
0
0
2
0
1
0
0
0
3
2
0
0
0
0
3
1
0
0
2
1
2
1
1
0
0
0
0
0
1
0
2
0
0
2
1
0
0
2
1
1
0
0
0
0
0
1
0
2
1
0
0
0
0
1
0
0
1
2
0
2
0
1
2
2
1
1
2
2
0
0
1
0
0
1
1
0
0
0
1
0
0
2
2
0
1
1
0
2
0
1
0
0
5
0
0
0
1
0
0
0
0
1
1
0
2
0
1
0
0
2
1
1
0
1
1
0
0
0
0
0
2
0
0
0
2
0
0
0
1
1
0
2
0
0
0
1
0
0
0
1
0
2
2
0
1
0
2
2
0
0
2
0
9
2
0
2
0
1
1
0
1
1
2
1
0
0
2
0
1
1
2
0
1
1
1
0
0
0
0
0
1
2
1
1
0
0
1
1
0
0
0
0
2
0
0
0
0
0
2
2
0
4
0
1
0
2
1
0
1
2
2
1
1
0
1
2
1
2
0
0
1
0
1
1
1
2
1
2
1
0
2
0
0
0
0
0
2
0
0
2
1
2
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
1
2
1
2
0
1
0
0
1
0
0
1
1
0
2
0
1
1
1
0
0
0
1
0
1
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
2
0
0
0
0
2
1
0
1
0
1
2
0
0
1
0
0
0
1
0
3
2
0
0
1
0
0
1
1
1
2
2
0
2
1
0
0
1
0
2
0
4
0
0
2
1
0
2
1
2
0
0
2
2
1
1
1
0
2
2
2
2
1
0
0
0
0
0
2
0
1
0
0
0
0
1
0
2
2
0
0
1
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
2
2
1
1
2
0
0
2
0
0
2
0
1
1
0
2
2
0
1
1
0
1
0
1
2
1
0
1
0
1
0
0
0
0
0
2
1
2
2
0
1
1
0
0
0
0
1
0
0
0
0
2
2
2
0
0
0
2
2
0
1
0
2
0
2
0
2
0
0
1
2
2
1
1
0
0
0
0
1
1
0
3
0
0
2
2
1
0
1
0
2
2
0
0
0
1
0
0
2
0
0
0
0
2
2
0
2
0
1
1
0
2
0
1
0
0
0
2
0
0
2
1
0
1
1
0
1
0
0
0
2
0
0
1
1
1
2
1
0
0
0
0
0
0
1
0
0
0
1
1
2
0
2
0
1
1
0
0
0
0
1
0
0
0
1
0
8
0
0
1
0
0
0
2
2
0
0
1
2
1
0
2
3
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
1
0
1
1
0
1
1
0
1
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
2
2
0
0
2
0
1
0
0
0
1
0
1
2
0
0
1
0
0
0
1
2
0
2
0
1
1
1
0
0
2
0
0
1
0
0
0
1
1
0
1
1
2
0
0
0
0
1
1
2
2
2
1
0
0
0
0
0
0
0
2
0
0
0
2
1
1
1
2
2
0
2
0
1
2
2
2
2
1
1
0
1
0
1
0
2
0
2
0
1
2
0
1
1
1
0
1
2
2
0
2
0
0
1
3
1
0
0
1
0
1
1
0
2
0
0
2
1
0
2
1
0
1
0
1
0
0
1
0
0
0
2
0
2
0
0
0
2
2
2
0
1
2
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
2
3
0
1
1
0
2
0
2
2
0
0
0
1
0
0
2
0
0
0
0
1
0
2
1
0
1
0
0
1
1
0
0
0
0
0
0
2
1
0
1
0
2
0
0
1
0
1
2
0
2
1
0
2
1
0
0
0
2
1
1
0
1
1
0
0
2
0
0
0
1
1
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
2
0
2
1
1
0
1
1
1
0
0
0
0
0
1
3
1
1
1
0
0
1
0
0
0
0
1
4
1
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
2
3
1
0
1
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
2
5
0
2
2
2
0
0
1
1
1
0
0
0
1
0
2
2
0
2
0
2
0
0
1
0
0
1
0
1
0
0
0
0
1
0
2
0
0
0
0
0
3
0
0
1
1
0
1
0
0
0
1
0
0
0
1
0
0
2
0
0
0
2
0
0
1
1
2
0
0
0
1
0
2
0
0
0
2
1
0
0
2
0
2
0
0
2
1
1
1
1
1
1
0
0
0
1
0
0
1
0
0
1
0
0
2
0
1
0
0
2
3
0
1
1
9
0
0
2
0
0
1
0
1
1
1
1
2
1
2
0
0
1
1
1
0
0
0
0
2
4
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
2
1
1
0
2
1
0
1
0
1
0
0
1
0
0
1
0
2
2
1
1
0
0
2
2
2
1
1
2
2
0
0
0
1
0
0
2
2
0
1
2
1
1
0
0
0
0
1
2
0
1
0
2
2
0
0
0
0
0
1
2
1
1
0
0
2
0
2
0
0
0
1
2
0
0
1
0
0
0
1
2
0
0
1
1
0
0
0
2
0
0
2
1
1
1
0
2
1
1
1
0
1
2
1
0
0
0
1
0
0
0
2
1
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
2
0
0
3
0
0
1
0
2
2
1
0
0
2
2
0
0
1
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
2
1
0
0
0
1
0
1
0
0
0
0
1
0
2
2
1
0
2
1
2
2
0
0
2
0
3
0
1
0
0
0
0
1
1
3
0
0
0
2
0
0
3
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
2
4
2
1
0
0
2
0
2
0
1
2
0
0
0
0
0
0
0
0
1
2
2
0
0
2
1
0
0
2
0
0
0
1
2
2
2
0
0
0
0
0
0
2
0
1
0
0
0
0
1
3
0
0
2
1
1
1
1
1
1
0
1
0
0
0
1
0
0
0
1
0
0
0
1
2
2
1
2
0
2
0
1
1
3
0
0
2
1
2
2
2
1
4
2
0
1
1
0
1
1
2
0
1
0
0
3
0
2
0
0
2
0
1
1
1
1
0
2
0
0
0
0
1
2
0
3
0
3
1
0
0
1
0
0
0
1
0
0
2
0
2
0
2
0
0
2
0
0
1
0
1
0
2
0
1
2
2
1
0
0
0
2
1
0
0
0
0
1
0
0
1
0
2
2
0
2
0
1
1
0
2
2
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
2
0
0
1
0
0
0
1
2
1
1
1
0
1
0
0
0
2
1
0
1
0
2
2
1
1
0
0
0
1
0
1
0
0
0
1
0
2
1
1
2
0
2
0
1
1
1
2
0
2
0
1
0
1
1
2
1
0
1
0
1
2
0
1
2
1
0
0
1
0
1
0
0
0
0
1
2
1
0
1
0
0
0
1
0
0
0
2
0
2
1
1
0
1
0
1
2
0
2
0
0
0
0
1
0
2
2
1
0
0
0
1
2
1
1
2
0
1
1
2
0
1
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
1
1
1
1
3
0
1
0
0
0
1
0
0
2
1
0
0
0
1
2
0
1
2
0
0
0
2
0
1
1
0
2
1
0
2
2
0
1
3
0
0
0
0
0
0
2
0
1
1
1
0
0
0
0
0
0
1
1
2
1
2
0
1
0
0
1
2
1
0
1
0
2
0
0
0
1
0
0
0
10
2
0
0
1
1
1
0
0
0
0
0
1
0
0
0
2
1
1
1
2
1
1
0
2
1
1
0
0
1
0
1
2
3
1
0
1
0
2
0
0
1
2
2
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
1
0
1
0
1
0
1
1
2
0
0
0
0
0
2
0
2
0
0
0
1
0
0
1
0
2
0
0
0
0
1
1
2
0
0
0
1
1
0
0
0
1
0
1
0
0
1
0
0
2
0
0
0
3
0
0
0
1
0
1
2
1
0
0
2
1
2
0
0
2
0
0
2
2
0
1
0
0
2
0
1
0
1
2
0
0
0
1
3
0
1
0
1
1
1
2
1
0
0
1
1
0
0
0
1
1
3
1
2
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
2
1
0
1
0
1
2
0
1
0
1
0
0
2
1
0
1
2
1
0
1
0
0
0
0
1
2
2
1
2
0
0
1
0
1
0
0
0
0
2
0
1
1
0
1
1
1
0
1
1
0
0
2
0
0
0
2
2
0
2
2
1
1
2
0
1
2
0
0
1
0
2
1
0
0
2
0
0
0
0
0
0
1
2
1
1
2
1
0
1
1
2
0
0
0
0
0
0
1
1
0
2
0
0
0
0
2
1
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
4
0
0
2
1
0
2
2
0
1
0
0
2
2
1
1
2
0
2
0
0
1
0
0
0
2
0
0
1
0
1
2
1
0
0
0
0
1
0
0
0
0
0
0
0
2
1
1
0
1
1
0
0
1
1
1
2
2
0
0
0
1
1
0
0
1
0
0
0
0
0
0
2
0
2
0
2
0
1
1
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
2
2
0
0
2
0
0
2
2
1
1
0
0
2
2
0
0
0
0
1
1
0
2
1
0
2
1
0
0
2
0
0
0
0
1
0
1
1
3
2
1
1
1
0
0
2
2
2
2
2
0
0
2
0
0
0
2
2
0
0
0
1
1
0
0
2
0
1
0
0
0
2
0
1
1
1
0
0
1
0
1
1
0
0
1
1
1
1
0
2
0
0
1
1
0
1
0
2
1
0
0
0
0
0
1
3
1
3
1
1
0
0
1
1
0
2
2
0
1
1
1
0
1
0
0
2
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
1
0
0
1
0
0
0
3
0
0
0
2
1
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
2
1
0
0
0
2
0
0
1
0
1
0
0
0
0
1
0
0
1
2
2
0
1
0
2
1
0
1
1
4
1
0
0
1
0
0
2
2
1
0
0
0
0
0
2
1
0
0
1
2
1
1
2
1
1
0
2
0
2
0
2
2
0
0
1
1
0
0
0
0
6
0
0
0
2
0
0
2
1
0
3
0
2
2
0
2
1
0
1
1
1
0
1
1
1
0
0
2
0
2
1
0
0
0
1
0
1
2
2
0
0
0
0
1
0
0
0
0
1
1
0
2
0
1
1
0
1
1
2
0
2
1
0
1
1
1
0
0
2
0
2
0
1
0
0
0
2
1
0
0
0
0
2
1
3
0
1
3
1
0
1
1
0
0
2
0
2
0
0
1
2
1
2
1
0
0
1
2
0
0
1
0
0
2
0
2
2
0
0
2
0
2
0
2
0
1
2
0
1
0
2
2
0
1
2
0
0
0
3
0
0
2
0
0
0
2
2
0
1
0
0
2
0
0
0
1
0
0
0
2
0
2
2
1
0
0
0
2
2
3
2
1
1
0
1
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
1
3
0
0
2
0
0
1
1
0
0
1
0
0
0
1
0
2
2
1
0
0
1
0
1
0
0
2
3
1
2
0
0
0
0
1
0
1
1
2
0
0
0
3
0
1
1
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
1
1
1
2
0
0
2
1
1
0
0
2
2
0
0
0
0
1
0
1
0
1
2
0
1
3
0
0
0
1
0
0
0
0
0
1
1
1
1
0
0
0
1
0
0
0
0
0
1
2
0
0
1
1
2
0
1
0
0
0
0
0
1
0
2
0
0
0
1
1
0
2
0
2
1
0
0
0
1
0
0
1
0
0
3
0
0
0
2
0
1
2
1
0
0
0
0
1
1
0
0
0
3
0
1
1
1
0
1
4
2
2
0
0
0
2
0
2
1
0
2
0
0
1
1
0
0
0
0
0
2
5
1
0
0
2
0
2
1
2
0
1
0
0
0
2
0
2
0
2
0
0
0
0
0
2
2
1
0
3
2
0
1
1
1
0
0
2
0
2
0
0
0
1
1
0
1
0
2
1
2
1
0
0
2
0
0
2
0
0
2
0
0
0
0
2
2
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
1
2
0
0
0
0
1
1
2
1
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
1
1
1
2
2
0
1
1
2
0
1
0
2
0
2
1
2
1
0
0
2
0
0
0
0
0
0
2
0
2
1
0
1
0
2
0
2
0
1
1
0
0
1
2
0
2
2
1
0
1
0
1
1
0
1
1
2
0
0
0
1
2
2
1
0
0
0
0
0
0
0
1
2
1
0
2
0
2
2
1
1
0
1
1
3
1
2
2
3
0
0
1
0
0
1
0
1
0
0
2
0
1
0
1
0
0
1
2
1
0
0
2
0
0
0
0
0
2
0
2
1
1
1
0
1
0
0
0
2
1
0
0
0
1
0
2
1
0
0
1
1
0
0
1
1
0
2
0
1
2
0
1
0
2
1
2
2
2
0
0
0
1
2
0
0
1
1
1
0
0
0
0
3
0
0
1
0
1
0
2
0
0
1
1
2
0
1
0
0
0
0
1
0
2
0
3
1
2
1
2
0
1
0
1
2
0
1
0
1
0
0
1
0
1
0
1
0
0
0
0
1
0
0
1
0
0
2
1
0
2
1
0
0
0
1
1
0
1
0
1
0
0
1
1
0
0
0
0
0
1
1
1
0
0
0
0
2
1
1
0
1
0
2
0
1
2
1
2
2
0
0
0
0
0
0
0
1
0
2
0
1
1
3
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
1
2
1
0
0
3
0
0
1
2
0
0
0
1
0
0
2
0
0
2
0
0
2
1
0
2
2
0
2
0
2
2
1
1
0
2
0
0
0
0
1
0
2
2
1
2
0
0
0
2
2
0
2
0
0
0
0
2
2
0
0
1
1
0
1
0
0
3
0
0
0
0
0
0
1
0
5
0
0
1
0
1
0
1
1
0
0
0
0
2
0
1
2
2
0
2
0
0
1
0
0
1
2
0
2
1
2
1
0
1
3
2
1
0
0
0
0
0
1
1
0
0
0
0
0
2
1
0
0
2
0
1
1
1
1
2
2
0
0
2
2
1
0
0
0
1
1
0
1
0
1
1
2
2
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
2
0
1
2
1
1
1
0
1
1
1
0
2
0
0
1
2
1
2
2
1
1
0
0
1
0
0
2
2
0
1
0
2
1
0
0
1
1
1
0
0
0
3
0
0
2
2
1
1
1
0
1
0
1
0
0
1
2
0
1
0
2
0
0
2
0
0
0
1
0
2
3
1
0
0
0
1
0
1
0
0
3
0
3
1
0
2
1
0
0
2
0
1
2
2
0
0
0
2
1
2
2
0
0
1
0
0
1
1
0
0
2
3
2
1
0
0
1
0
0
1
2
0
2
0
0
0
2
1
2
1
1
2
0
1
0
0
0
2
1
0
0
1
0
1
0
0
0
2
0
0
2
2
1
1
0
1
0
1
1
0
0
0
0
2
0
2
1
1
1
0
1
0
0
0
2
1
1
2
0
0
0
3
2
0
2
1
0
1
0
0
1
1
0
0
2
3
0
1
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
2
0
2
2
0
1
0
0
0
0
2
1
2
1
0
1
0
0
0
1
1
0
1
1
1
0
0
0
0
0
6
0
2
0
0
0
3
1
3
0
1
0
2
1
0
1
2
0
0
2
2
1
1
0
0
2
0
3
2
1
1
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
2
0
0
3
1
1
0
2
2
0
2
0
2
0
0
0
1
2
3
1
1
0
1
2
1
2
0
0
1
0
1
1
2
1
0
1
0
0
1
2
0
0
0
0
1
3
1
2
0
0
0
2
0
0
0
0
2
0
0
1
0
1
1
1
1
0
0
0
2
0
2
0
1
0
0
0
0
1
0
1
1
2
1
1
0
2
0
0
0
0
0
1
0
0
0
1
2
0
0
0
2
0
0
2
0
0
0
0
1
0
1
1
1
1
0
0
1
0
1
2
1
0
0
0
0
0
1
0
1
3
2
1
1
0
0
0
0
0
2
2
1
0
0
4
1
1
0
0
0
2
0
1
2
1
1
0
1
0
0
0
0
0
1
0
0
1
1
1
1
0
0
0
0
0
1
0
1
1
1
2
1
1
0
1
0
2
0
0
0
0
2
1
1
0
0
0
0
0
2
2
2
0
0
1
0
2
0
1
0
0
1
2
2
2
0
1
1
1
0
2
0
0
0
2
1
1
0
1
0
1
0
0
0
1
2
1
0
1
1
2
2
1
2
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
2
1
0
1
0
0
0
0
0
3
1
3
2
2
0
0
2
2
0
0
0
0
0
0
1
0
0
0
3
2
0
2
2
0
1
1
0
0
0
0
2
1
0
0
0
1
4
2
8
2
1
1
0
2
0
0
2
0
1
0
0
1
1
0
0
2
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
2
1
2
0
1
0
0
2
0
1
1
0
1
0
1
1
1
0
2
0
0
2
0
0
0
0
0
0
5
1
0
0
2
0
1
1
2
0
0
0
0
1
2
2
1
0
0
1
0
2
0
2
0
1
0
0
2
0
2
0
0
2
0
1
0
2
0
0
0
2
2
0
0
1
0
0
1
1
0
0
0
1
1
2
1
0
0
0
1
1
1
0
0
2
1
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
5
0
0
0
0
0
0
1
0
1
1
0
4
1
0
1
1
1
0
0
0
1
1
2
0
0
0
0
0
0
0
0
1
1
1
0
2
0
0
1
1
1
1
0
2
2
2
0
1
0
0
1
2
0
0
0
3
1
2
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
1
0
2
2
0
0
0
2
0
1
0
2
2
0
1
2
1
0
2
1
1
2
1
0
0
2
0
0
2
0
1
3
1
1
2
0
0
2
0
1
0
0
1
2
0
0
2
0
0
0
1
0
2
0
0
0
1
0
0
0
2
0
0
0
2
2
0
1
0
1
1
1
0
2
0
0
0
0
2
2
0
0
0
1
1
0
0
1
2
0
0
0
1
1
0
0
2
2
0
0
0
1
2
0
2
1
0
2
3
0
0
2
0
0
0
0
1
1
0
2
3
0
2
0
0
1
0
0
0
2
0
0
0
0
2
0
1
2
0
2
0
0
1
0
1
0
0
1
2
1
0
1
0
0
0
0
0
0
0
2
1
1
0
2
1
1
0
0
0
2
0
2
0
0
0
1
0
2
2
0
0
0
0
1
0
1
0
1
0
0
0
2
2
0
1
0
2
0
0
0
1
1
0
1
1
0
0
0
1
2
0
2
0
2
0
0
1
1
2
0
2
0
1
0
0
1
0
2
0
1
1
0
1
0
1
3
2
1
0
0
1
5
2
0
3
0
0
2
0
1
2
0
1
1
0
1
0
0
0
0
2
1
2
1
1
1
0
1
2
0
0
1
2
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
2
1
1
0
0
0
1
0
0
0
1
1
1
0
0
0
2
2
1
2
2
2
0
0
2
0
1
0
0
0
2
1
2
0
0
1
0
0
0
0
2
1
1
1
0
2
3
0
0
4
0
1
0
0
2
0
0
2
1
0
0
1
1
0
0
2
0
2
1
0
2
1
1
1
2
0
1
0
1
1
0
0
0
0
0
0
2
1
0
2
1
0
1
1
0
0
0
2
1
0
0
1
1
0
1
0
2
0
1
0
1
0
0
0
2
0
0
1
1
1
2
0
1
0
0
1
1
2
0
1
1
1
2
3
2
0
1
3
0
0
0
2
0
1
0
0
0
1
1
2
0
0
1
0
1
0
0
0
2
0
1
2
0
0
0
0
1
0
2
0
1
0
1
0
2
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
1
1
2
0
1
4
0
1
2
0
2
0
0
0
0
0
1
0
2
2
0
0
1
2
0
0
0
2
0
1
1
1
0
1
2
0
0
1
0
1
4
0
0
1
0
0
0
2
0
1
0
2
1
0
2
2
2
0
0
0
1
4
0
2
0
0
1
0
2
0
0
2
1
1
0
0
0
2
0
0
1
0
1
2
0
0
2
0
1
0
2
1
2
0
0
2
0
2
1
1
2
0
0
0
0
2
2
1
0
1
0
2
0
0
0
0
1
0
1
1
1
0
1
0
1
0
0
0
0
2
0
1
0
0
1
2
0
2
0
0
1
0
2
0
0
0
0
1
0
0
0
1
0
3
0
0
1
0
1
0
1
0
1
1
0
0
2
0
0
0
3
0
0
1
0
2
0
0
2
2
0
1
0
1
0
1
0
6
0
4
0
0
3
1
1
0
0
2
1
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
1
3
0
1
2
0
0
0
0
0
1
1
1
0
0
0
0
1
0
2
0
1
2
2
0
0
0
2
1
2
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
1
0
1
0
0
1
0
0
1
0
0
0
0
3
1
1
1
1
0
2
1
0
1
0
0
0
2
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
1
1
0
2
0
0
2
1
2
0
1
1
0
0
2
2
2
0
0
2
0
3
0
0
2
0
0
0
1
1
1
0
1
0
1
0
0
2
1
1
2
0
0
1
1
1
0
0
0
1
0
0
0
1
0
1
2
0
0
1
0
0
1
2
0
1
0
2
2
0
2
1
0
0
0
0
0
2
0
0
0
2
1
1
0
2
0
0
3
0
1
0
0
1
2
0
1
1
2
1
0
1
0
2
2
0
2
1
2
1
2
4
0
0
0
1
0
2
0
1
0
2
0
3
1
0
1
0
0
1
2
0
0
1
1
2
0
0
1
0
1
0
0
2
1
1
0
2
4
2
0
0
2
1
1
0
0
1
1
0
0
0
1
1
0
1
0
0
0
0
0
0
1
1
0
2
0
0
2
0
1
2
0
1
1
0
3
1
0
0
2
1
2
2
1
1
2
0
2
1
0
2
1
1
1
2
2
0
0
2
0
2
2
0
2
1
1
0
0
0
1
0
0
0
2
1
0
1
1
1
0
1
2
0
0
1
0
1
2
1
1
0
0
0
0
1
0
0
3
1
0
0
0
1
2
0
2
0
0
0
0
2
0
0
1
0
1
3
0
0
0
1
0
0
0
0
0
1
0
1
1
1
1
1
2
0
4
0
3
0
2
1
2
0
1
0
0
0
0
0
0
1
1
0
2
0
1
0
3
1
2
0
0
0
0
1
0
0
1
2
0
1
0
0
0
0
1
1
0
0
1
0
1
3
0
1
0
0
0
1
0
0
1
2
0
2
0
2
0
2
0
2
0
2
2
2
0
1
0
2
0
1
0
2
0
2
3
0
2
3
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
2
1
0
0
1
1
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
1
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
2
0
0
2
0
0
2
0
2
0
0
0
1
0
2
0
2
1
2
1
1
2
0
2
0
1
2
0
0
0
0
2
0
0
1
1
1
1
0
2
0
0
0
0
1
0
2
0
1
0
0
1
0
1
1
0
0
1
0
1
0
2
0
2
2
0
2
1
0
2
1
0
0
0
1
2
0
1
1
1
0
0
0
0
2
1
0
2
2
1
0
4
1
0
1
0
0
2
0
1
0
0
0
0
1
2
2
0
0
1
2
1
2
0
0
0
2
2
0
1
0
0
1
2
2
1
0
0
4
1
1
1
2
0
1
2
2
2
0
0
0
0
0
1
0
0
2
1
1
0
0
0
0
1
1
0
0
1
1
0
0
2
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
1
1
1
0
2
0
0
0
0
1
1
0
0
0
1
0
0
1
2
1
1
0
0
2
2
2
0
0
0
2
2
0
0
2
1
0
0
1
0
0
2
0
1
2
1
0
1
0
3
2
2
2
0
0
0
1
1
0
1
0
2
2
2
2
0
0
0
1
1
1
0
2
3
2
0
1
0
14
0
0
0
2
2
2
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
2
0
1
2
1
1
0
1
2
1
1
1
0
0
1
1
0
0
1
0
0
0
1
0
1
2
0
3
1
1
0
0
2
0
0
0
0
2
0
0
1
2
1
2
0
1
0
0
0
0
1
0
0
0
2
0
0
1
0
0
1
0
0
0
1
0
0
0
2
0
2
0
3
1
0
0
1
0
0
0
0
2
2
1
2
2
0
1
1
1
0
2
1
0
2
0
0
2
2
0
0
1
2
0
0
0
1
0
1
1
2
0
1
1
1
0
2
0
0
2
2
0
1
0
1
2
0
1
0
0
0
0
1
1
0
0
0
2
2
0
1
0
0
0
4
1
1
2
0
1
6
1
0
3
1
0
2
0
2
2
0
2
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
2
2
0
2
0
0
0
0
0
0
1
2
1
1
1
0
0
0
0
0
2
0
1
0
1
0
0
1
0
0
2
0
1
0
2
1
2
2
1
0
6
0
2
2
0
1
5
0
0
0
1
0
2
0
0
1
0
1
2
0
1
1
2
1
1
1
1
2
0
1
0
0
1
2
0
0
2
2
0
3
0
4
0
2
1
2
0
1
1
0
2
1
0
0
0
0
0
0
2
0
0
0
0
2
2
0
2
0
2
0
0
0
0
2
0
0
0
0
2
2
1
2
0
0
2
0
0
0
0
1
1
1
0
1
0
1
4
2
2
0
0
1
0
2
0
0
0
2
1
1
0
0
1
0
0
2
1
0
0
0
0
0
0
0
2
0
1
2
1
2
2
0
1
0
0
0
1
2
0
2
1
0
0
0
0
0
0
0
3
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
1
2
2
0
0
0
0
0
1
0
2
1
2
0
0
0
2
2
1
0
0
0
0
1
1
0
2
0
1
2
1
0
2
1
0
2
1
1
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
2
0
2
2
0
0
2
0
1
2
0
0
2
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
2
1
0
0
2
1
2
0
0
1
0
1
0
1
0
1
0
1
0
2
0
0
2
0
0
0
0
0
0
0
1
1
0
3
2
0
0
1
0
0
1
0
3
0
2
1
0
1
1
1
2
0
0
2
2
0
0
1
1
1
0
0
2
2
1
0
0
0
1
2
2
1
3
2
0
1
0
0
1
0
0
0
1
0
0
2
1
0
0
1
0
1
1
0
0
0
1
1
2
0
1
1
0
1
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
2
2
0
0
0
0
0
0
1
2
0
2
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
1
1
1
1
2
1
3
0
0
0
2
0
1
0
2
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
2
2
1
2
1
0
1
0
0
1
1
0
0
0
0
0
2
1
0
2
1
0
0
0
0
2
1
1
0
2
1
1
1
1
1
0
0
0
0
1
0
0
3
0
0
1
0
2
2
0
1
0
1
0
0
0
1
1
0
0
0
0
1
1
2
0
1
0
1
1
0
0
0
0
1
0
5
0
0
0
0
1
0
0
1
1
2
0
0
0
1
1
1
2
2
2
1
1
2
0
3
0
2
0
1
2
0
0
0
2
2
1
0
1
0
2
0
0
0
0
0
0
1
1
0
0
1
0
2
1
0
0
0
0
1
1
0
1
0
2
1
0
0
0
1
2
1
0
0
0
1
0
1
1
0
3
2
1
0
0
0
0
0
1
1
0
1
1
1
0
1
0
2
1
1
0
0
0
2
1
0
0
2
0
1
1
0
0
1
0
2
0
0
2
3
1
2
2
0
1
0
2
0
0
1
0
0
1
2
2
1
0
0
2
0
2
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
2
2
1
0
1
0
1
0
2
1
0
0
1
4
0
2
0
0
1
1
1
0
1
0
1
0
1
1
0
0
1
0
0
0
2
0
1
1
2
0
0
1
0
0
1
0
1
1
1
0
0
1
2
0
1
0
1
0
0
0
2
0
2
2
1
1
0
0
0
0
0
0
5
2
2
1
1
0
4
0
2
0
0
1
2
2
0
0
0
0
0
0
2
0
1
1
0
1
2
2
2
0
0
0
0
1
2
1
0
0
1
0
0
1
1
1
1
1
0
2
1
0
1
0
0
2
2
0
0
2
1
0
1
0
2
1
0
0
0
0
0
2
0
0
2
1
0
1
0
0
0
0
0
0
2
2
1
0
0
0
0
2
0
0
1
0
0
1
2
2
1
0
1
1
1
0
1
1
1
0
0
0
2
1
1
1
0
2
0
0
0
1
0
0
1
0
2
0
1
6
1
0
0
2
1
0
1
0
1
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
1
2
2
2
0
0
0
1
2
2
0
1
2
2
0
2
0
2
0
0
0
0
2
2
1
0
1
1
0
4
0
0
1
0
0
1
0
2
0
2
1
1
0
0
0
2
0
2
0
2
0
2
0
2
2
2
2
0
0
2
2
0
0
0
1
4
0
0
2
0
1
2
2
1
0
1
0
0
0
0
0
2
0
10
1
0
0
2
0
1
0
0
0
0
2
1
1
2
0
0
0
1
2
2
1
1
2
0
0
1
2
0
0
1
0
0
0
2
2
2
0
0
1
0
2
0
0
1
0
0
1
0
0
2
0
1
2
0
0
0
1
0
0
2
1
1
2
2
0
2
2
0
1
2
2
0
2
0
0
1
0
0
2
0
2
0
0
0
2
0
0
0
1
0
2
2
1
0
0
0
1
1
1
1
0
0
1
2
2
0
2
1
0
1
2
0
0
1
1
1
2
2
1
1
0
0
0
3
0
1
0
0
0
2
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
1
2
1
2
0
2
0
1
0
1
1
1
0
0
0
0
0
1
0
2
2
0
2
0
1
2
1
1
0
0
0
1
1
1
0
2
0
0
2
0
1
2
0
0
0
2
1
4
2
0
0
2
0
0
0
0
0
0
2
2
0
0
2
2
2
0
1
1
0
1
2
0
0
0
2
3
0
4
2
1
2
2
0
2
0
0
1
0
0
1
0
1
2
0
0
0
1
1
1
0
3
0
2
0
0
1
0
0
0
0
0
2
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
1
3
2
3
0
2
0
1
1
1
0
0
0
0
1
1
1
1
0
0
1
1
0
0
1
0
2
0
0
1
1
2
0
1
1
0
0
0
0
0
0
0
1
0
2
0
1
0
2
0
0
0
0
1
2
1
1
0
0
0
0
0
0
2
1
0
0
0
1
2
1
0
2
0
2
3
0
0
1
1
1
0
1
3
2
0
0
0
0
0
1
0
0
0
1
0
0
2
2
2
3
1
0
2
1
0
2
1
3
1
0
2
1
2
0
1
0
0
0
1
0
0
1
2
2
0
0
0
0
0
1
0
1
0
0
1
1
1
0
1
1
2
1
1
0
1
1
1
2
1
2
0
0
1
0
0
0
1
0
0
0
1
0
0
2
3
0
2
3
0
0
0
1
1
0
0
0
2
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
2
0
1
0
0
0
2
0
1
2
0
1
0
0
1
0
2
2
1
1
4
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
1
2
1
0
1
0
5
1
1
0
1
0
0
1
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
2
2
0
1
1
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
2
0
1
2
0
4
0
1
2
0
0
0
0
0
1
0
0
0
1
2
0
0
2
1
1
0
1
0
4
0
0
1
0
0
0
0
1
0
0
1
0
2
1
0
1
0
2
1
0
0
1
0
0
0
0
2
2
1
0
0
1
1
0
2
0
0
1
0
2
0
3
1
2
0
0
0
0
0
1
0
0
1
0
0
1
0
1
2
2
0
0
1
1
0
1
0
0
1
2
0
1
0
0
0
1
0
0
1
0
1
1
0
0
0
1
0
1
2
2
2
0
0
0
0
1
0
1
0
1
1
0
0
1
0
0
1
0
1
2
0
0
2
0
2
0
2
1
2
0
0
1
0
1
1
0
0
1
1
1
1
0
0
0
2
0
2
0
0
1
0
2
2
0
2
3
1
0
1
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
2
0
1
1
0
1
1
0
1
1
1
1
4
0
0
0
0
0
1
0
0
3
3
0
0
2
0
0
2
2
1
0
1
0
1
2
1
1
0
1
2
0
1
0
2
1
0
1
4
0
0
2
0
1
1
0
1
2
2
0
1
0
0
0
0
0
2
0
0
0
0
4
0
2
0
0
0
0
0
0
1
0
1
1
0
1
0
2
2
0
0
2
0
1
3
0
0
1
0
2
0
0
0
1
1
0
1
1
0
9
1
0
0
0
0
1
1
2
0
0
2
0
2
0
2
1
0
0
1
0
2
0
0
0
0
0
0
0
2
1
0
0
3
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
1
2
0
1
2
0
0
0
0
1
0
0
0
2
1
0
5
0
0
1
1
0
2
1
0
0
1
0
2
1
0
0
0
0
3
1
0
0
0
2
1
0
0
0
0
0
1
1
0
1
2
0
0
0
2
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
2
0
2
1
0
0
0
1
1
2
0
0
0
1
0
5
0
0
1
0
1
1
2
0
0
0
2
0
2
0
1
0
0
1
0
0
1
1
1
0
0
0
1
1
2
0
1
0
1
1
0
3
0
0
0
0
1
1
0
0
1
0
0
0
0
2
0
1
1
0
0
0
1
2
1
0
2
0
0
2
1
1
1
0
1
0
1
0
1
0
0
3
0
1
1
2
1
1
0
0
0
0
1
1
2
1
0
2
0
2
0
1
2
0
2
0
0
0
1
0
0
0
0
0
0
3
0
0
1
2
1
1
0
0
0
1
0
1
2
0
0
0
1
0
0
4
2
0
2
5
1
2
2
1
1
1
1
0
2
1
0
0
0
0
0
1
1
2
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
2
2
2
0
1
1
0
1
0
1
1
1
3
1
0
0
2
0
0
2
0
0
0
0
1
0
0
2
2
0
0
1
2
0
0
2
0
0
0
1
1
0
1
1
0
1
0
0
0
0
1
2
0
1
1
0
0
2
1
2
1
0
1
1
0
0
1
1
0
0
0
0
1
0
0
0
1
1
0
0
1
1
3
0
0
0
2
0
0
1
0
0
1
0
2
0
1
0
2
2
2
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
2
2
0
0
1
0
0
0
0
0
0
1
1
2
0
0
0
2
0
0
2
1
0
0
1
3
1
1
1
0
2
0
0
0
0
0
0
0
1
0
0
0
2
1
0
2
0
1
2
0
1
1
0
2
0
0
1
0
2
0
0
0
0
1
2
0
0
1
1
0
1
1
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
2
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
2
1
2
2
2
1
2
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
1
1
0
0
1
1
2
1
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
2
1
2
1
1
2
0
2
1
2
0
1
0
1
2
0
1
1
2
2
1
0
0
0
1
0
1
1
0
2
1
0
0
2
1
2
1
2
3
1
0
0
2
1
2
0
0
0
1
0
0
0
0
1
0
2
0
0
1
1
2
0
2
1
0
0
0
0
0
0
2
0
0
0
1
1
0
1
1
1
2
2
2
1
1
1
0
0
0
0
2
0
0
0
0
1
0
2
2
1
0
0
0
0
1
2
1
0
1
0
0
1
0
0
3
0
0
0
0
2
1
1
2
3
0
0
2
1
2
0
2
0
0
1
0
2
1
1
0
2
0
0
1
2
0
0
2
1
0
1
0
1
0
1
1
2
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
2
0
2
0
1
0
1
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
2
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
2
2
4
0
0
4
1
2
0
2
2
1
2
2
0
0
0
3
2
0
0
0
0
2
0
2
2
2
0
1
0
0
0
2
1
1
2
1
1
0
1
0
1
2
1
0
0
0
2
2
0
0
0
0
2
0
2
1
1
0
2
0
2
0
0
1
1
1
1
0
0
0
3
0
0
0
0
1
0
0
0
0
2
2
1
0
1
2
1
0
1
0
2
0
2
0
0
0
0
0
1
0
1
0
0
1
3
0
0
1
2
0
2
1
0
2
0
2
1
0
0
0
0
0
0
1
2
1
0
1
0
2
0
2
1
2
2
1
0
1
0
2
0
0
0
0
0
3
0
1
1
0
1
5
1
0
1
0
0
2
0
2
1
1
1
1
0
0
1
0
0
0
1
0
1
0
1
0
2
0
0
0
0
2
0
2
2
1
0
1
1
2
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
3
1
0
2
1
0
0
1
1
0
2
1
0
2
0
2
2
0
0
0
1
1
1
2
2
4
0
2
0
0
2
1
1
1
1
0
1
0
0
1
1
0
1
1
0
0
0
0
0
1
2
3
1
0
0
0
0
2
1
1
1
1
0
2
0
1
1
0
0
0
0
1
2
2
2
1
0
2
0
0
0
0
2
0
0
0
0
1
0
2
0
1
0
0
0
4
2
2
0
2
1
0
0
1
1
0
2
0
0
0
0
0
2
0
3
2
0
1
2
0
1
1
1
1
2
2
0
0
0
0
1
0
0
0
0
1
2
2
2
0
2
0
2
1
0
2
2
0
0
0
0
0
0
2
1
0
0
1
2
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
1
0
1
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
5
1
1
0
0
0
4
0
0
0
0
0
0
0
0
1
1
2
0
0
2
1
0
1
0
0
0
1
1
2
0
1
1
1
0
1
0
0
0
0
0
1
1
0
2
0
0
0
0
0
2
0
0
1
1
0
2
1
0
0
2
1
0
0
1
0
1
2
0
0
0
0
0
2
2
0
0
0
0
2
0
0
2
1
1
2
2
0
1
1
0
0
0
1
1
0
1
0
1
2
0
1
0
1
2
2
3
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
2
0
1
0
0
0
0
2
1
2
0
2
0
2
0
0
2
0
0
0
0
0
1
0
2
1
2
0
1
0
1
0
2
1
2
0
1
0
1
0
1
0
0
2
1
0
2
2
2
1
1
0
2
0
0
1
1
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
1
0
0
2
1
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
2
1
0
0
0
1
0
2
0
2
1
0
0
0
2
0
1
2
0
0
2
0
1
0
2
1
0
0
0
1
2
1
0
0
0
1
0
0
2
1
1
0
0
1
0
0
0
7
2
0
0
0
0
1
1
0
0
2
1
1
0
0
0
2
0
2
0
0
1
0
0
0
2
1
2
2
2
1
0
1
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
2
0
0
1
0
0
0
2
0
0
2
1
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
2
1
0
1
0
0
0
0
0
2
3
0
2
0
1
0
1
1
2
0
1
1
0
1
2
2
2
1
1
1
3
0
0
0
0
1
0
0
1
5
0
0
0
0
2
1
0
1
0
0
0
0
2
0
0
1
2
0
0
1
0
1
2
0
0
0
1
0
2
2
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
1
2
0
1
0
0
1
1
0
0
0
1
1
0
1
0
2
2
3
0
2
1
0
2
0
0
0
0
1
0
1
0
2
0
1
1
2
0
2
0
0
0
0
0
1
0
0
0
2
0
2
1
0
1
0
0
1
0
2
0
2
1
1
1
0
0
1
0
2
1
0
0
2
0
2
0
2
0
2
1
0
0
0
1
2
0
0
0
2
0
0
0
1
0
0
2
0
0
1
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
2
2
1
0
1
1
1
0
3
1
2
1
0
2
0
2
1
2
1
0
0
2
0
0
2
0
2
0
0
5
0
2
0
2
0
0
0
0
2
0
0
0
1
2
1
0
0
0
1
1
1
0
0
0
1
0
0
3
1
0
0
0
1
1
0
1
0
0
0
0
1
1
1
4
0
0
0
1
0
0
2
0
0
0
4
1
0
1
2
2
1
0
0
0
2
0
1
4
0
2
0
0
1
1
2
0
0
0
4
4
0
2
2
2
0
0
1
1
1
1
0
2
1
0
0
1
0
0
1
2
0
0
0
2
0
2
0
0
1
0
0
2
2
1
0
0
1
1
2
2
1
0
4
0
2
2
0
0
1
0
0
0
1
2
1
0
0
0
0
2
0
0
1
1
0
0
0
0
1
0
2
0
2
1
0
1
2
0
0
1
1
1
0
2
0
0
3
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
2
1
0
1
0
1
0
0
2
2
0
0
0
0
2
0
0
0
2
0
0
0
1
2
2
0
3
0
2
0
2
0
0
0
1
0
2
0
1
1
0
0
0
0
2
2
2
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
1
1
1
3
0
0
1
1
1
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
2
0
0
1
4
0
2
0
1
2
0
1
0
0
2
2
0
0
0
0
2
1
0
0
2
0
0
0
2
1
0
0
4
2
3
0
0
0
0
2
1
0
0
1
0
0
0
2
2
0
1
0
1
0
1
0
2
2
0
0
0
0
1
1
1
0
0
0
2
0
1
2
1
1
1
0
0
5
2
0
1
1
0
1
2
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
1
2
0
0
0
1
2
0
0
0
2
1
1
1
0
0
0
1
2
0
0
0
0
0
1
0
0
1
2
2
0
0
0
0
1
0
4
0
0
1
0
2
0
0
0
0
0
1
0
1
0
1
2
2
0
0
0
2
1
0
0
0
0
1
0
0
1
1
0
1
0
0
0
2
2
0
0
0
2
1
0
2
0
0
0
0
1
2
1
1
1
0
0
0
0
1
0
0
2
1
1
1
2
0
1
1
1
1
0
0
0
0
1
0
1
1
2
2
0
0
2
0
0
0
1
1
0
0
0
1
0
0
0
3
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
4
0
2
0
2
0
2
1
2
0
1
0
0
0
0
0
2
2
1
2
2
1
0
0
2
0
0
1
0
0
0
2
0
0
1
2
0
0
2
2
0
1
2
0
1
0
1
0
1
0
1
1
0
0
0
1
0
0
1
0
0
2
2
1
3
1
0
2
0
0
2
1
1
2
0
0
0
0
1
2
0
0
2
1
0
2
3
0
0
1
4
0
1
0
2
0
0
0
0
0
0
0
1
1
2
1
2
0
0
1
0
0
0
1
0
0
0
0
0
1
1
1
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
2
2
0
0
0
0
1
0
0
1
1
0
0
1
1
0
1
1
0
2
0
0
0
1
0
0
1
0
2
2
0
0
0
2
0
2
0
0
0
1
2
0
0
0
1
0
1
1
0
2
1
0
1
1
2
0
0
1
0
2
2
0
0
0
0
0
1
1
1
0
0
1
0
0
0
1
1
0
1
1
0
1
0
1
0
0
0
0
0
2
2
1
0
2
3
0
0
0
0
1
0
1
1
1
0
2
0
1
0
1
2
0
0
2
0
0
2
0
0
0
0
1
1
1
2
0
0
0
0
0
0
0
0
1
0
4
0
1
0
2
3
1
1
0
2
2
0
2
1
0
2
1
1
1
0
0
0
1
0
0
1
1
3
1
0
0
2
0
1
2
2
0
2
2
2
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
1
0
2
1
0
0
2
2
0
0
1
1
0
2
0
1
1
0
2
2
1
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
1
3
0
1
0
0
0
0
0
1
1
0
0
1
0
0
2
0
1
0
2
0
1
1
0
1
0
0
0
1
0
0
0
2
0
0
0
0
2
1
0
1
0
0
0
1
0
1
0
1
1
0
0
0
0
0
2
0
0
2
1
0
2
2
0
1
1
2
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
1
0
0
0
0
1
2
0
1
0
2
1
3
1
1
2
0
0
0
1
1
3
0
1
0
0
0
0
0
2
0
1
0
0
0
1
1
2
2
2
0
0
5
0
0
0
2
0
0
1
0
1
0
1
0
2
2
0
0
0
1
1
2
0
2
0
1
3
0
0
2
0
1
2
1
0
1
1
0
0
1
0
0
0
1
0
1
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
1
0
1
2
0
1
0
2
1
0
0
0
4
2
0
0
0
2
1
0
1
0
1
0
1
0
0
0
1
0
1
2
0
1
2
0
0
0
1
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
2
1
1
1
2
0
1
2
0
0
0
0
0
0
1
0
3
2
0
0
2
3
0
0
2
0
0
0
1
0
0
0
0
1
2
0
2
0
1
0
1
2
1
0
0
1
0
0
0
2
0
2
0
1
2
0
1
2
2
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
1
2
1
2
0
0
0
2
0
0
0
3
1
2
0
0
2
0
2
0
0
0
0
0
0
2
2
0
1
0
0
2
1
0
0
0
2
1
0
0
0
1
0
1
0
0
0
1
3
2
2
0
1
2
1
1
2
1
2
0
0
0
1
0
3
0
0
1
1
1
2
0
1
1
2
0
0
1
0
0
1
1
2
0
2
0
1
1
0
3
1
1
0
1
2
2
0
1
1
0
2
0
1
0
2
0
1
0
1
1
2
0
1
2
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
2
1
0
0
0
1
1
2
0
3
2
0
0
0
0
1
0
0
0
1
2
1
0
2
0
0
0
2
0
2
0
0
0
1
1
2
1
0
1
2
0
1
0
0
1
0
2
0
0
1
0
0
0
1
2
2
0
1
1
1
0
0
0
0
0
0
1
2
0
4
0
1
0
0
1
0
0
2
2
0
0
0
0
0
0
0
2
0
0
1
2
1
2
1
1
0
0
0
0
1
1
0
0
0
1
0
2
0
0
1
0
2
0
0
1
2
0
1
0
0
2
0
0
0
0
2
0
0
0
2
1
0
1
1
2
2
1
0
0
1
1
1
0
2
0
2
1
0
2
0
0
1
0
0
0
0
1
2
2
0
1
1
2
0
0
0
0
0
0
0
0
1
0
1
0
2
3
1
0
2
0
1
0
0
0
0
0
1
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
1
0
2
1
0
0
1
0
2
0
1
0
1
0
1
4
0
2
1
0
2
2
2
0
0
2
0
2
0
0
1
2
0
0
0
2
0
0
0
0
1
1
1
0
1
0
0
2
2
2
0
0
1
1
0
1
0
0
0
1
2
2
1
0
1
1
1
1
0
0
2
0
1
1
0
2
0
0
0
5
0
1
0
0
0
1
0
1
1
1
1
0
1
1
0
0
0
0
1
2
2
1
0
1
1
0
2
0
0
1
0
1
0
1
0
0
0
1
1
1
0
0
0
0
0
2
2
2
0
1
2
0
2
0
1
0
0
0
1
0
0
0
2
2
0
3
0
0
1
1
0
1
0
2
0
2
0
1
0
0
0
0
0
0
3
0
1
0
0
0
0
2
2
0
1
0
1
0
0
0
1
2
2
0
0
2
0
1
1
1
0
0
1
0
0
1
0
1
0
0
1
0
0
1
1
0
0
1
2
0
2
0
2
2
0
0
1
0
0
1
2
0
1
0
0
0
1
0
0
0
1
0
2
1
2
0
1
0
1
0
2
0
2
0
0
2
0
0
0
2
3
0
0
1
2
0
2
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
1
0
2
1
0
2
1
0
2
1
1
2
1
0
2
0
0
1
1
0
2
0
2
0
1
3
2
2
2
1
0
0
4
0
0
0
0
0
2
1
0
2
0
1
1
0
2
2
0
1
0
2
1
1
1
0
0
2
1
0
1
2
1
1
0
1
2
1
0
0
0
0
0
6
1
0
0
0
4
0
0
0
2
1
1
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
2
0
2
2
2
2
1
1
0
2
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
2
2
0
0
2
0
0
1
0
1
2
1
0
1
2
0
0
0
0
0
0
2
0
0
0
2
1
0
2
2
0
1
1
0
0
0
0
1
1
0
0
2
1
0
1
2
0
0
0
0
0
0
0
1
2
0
2
0
2
0
0
1
2
0
0
0
0
2
0
0
0
0
0
1
2
0
2
0
0
0
0
1
0
3
0
0
0
1
0
2
0
0
0
0
0
2
0
2
0
0
0
2
0
1
1
1
2
0
1
0
0
0
2
0
3
2
1
2
0
1
1
0
0
0
1
2
1
2
0
0
1
2
0
1
0
1
2
1
1
1
1
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
1
1
0
1
0
0
0
1
2
2
0
1
1
0
1
2
3
2
0
0
0
0
0
1
0
0
0
0
2
2
0
0
1
1
1
0
2
0
0
0
2
2
0
0
0
0
0
2
0
2
1
0
0
2
1
1
0
2
2
0
2
0
2
2
1
0
0
2
0
8
2
2
2
0
1
0
0
0
0
1
1
0
1
1
0
0
0
2
1
0
0
0
0
2
2
2
0
1
2
0
0
0
0
2
2
0
2
0
0
0
2
1
0
0
0
2
1
2
0
1
0
1
0
1
0
0
2
0
1
1
1
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
2
0
0
1
0
0
0
2
0
1
0
1
2
0
1
0
0
1
2
0
1
0
0
0
2
0
0
0
1
0
0
0
1
1
0
2
0
0
0
1
1
1
1
0
1
1
0
0
2
2
0
1
0
1
0
2
2
1
0
1
0
0
2
2
2
0
0
1
0
2
2
0
1
0
0
0
1
1
1
1
1
2
2
2
0
1
0
0
2
0
0
0
0
0
0
0
1
1
1
1
1
2
2
2
0
1
1
0
0
0
0
0
2
1
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
2
0
0
0
0
2
0
0
2
0
2
0
0
2
1
1
2
1
2
1
0
2
0
1
1
0
1
2
0
0
2
0
0
0
2
2
1
0
0
2
2
1
2
3
0
1
1
0
0
1
0
2
0
1
0
0
0
1
0
2
1
0
0
0
2
0
2
0
1
0
1
2
0
1
2
0
1
0
2
0
0
0
1
2
0
2
0
2
0
5
0
1
2
1
0
0
2
1
1
1
0
2
0
0
1
0
1
1
0
2
0
1
0
2
1
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
1
2
0
1
0
1
0
0
0
0
0
0
0
2
1
2
0
1
0
0
3
1
2
0
2
2
0
2
0
0
0
1
0
0
1
0
2
0
1
0
0
1
0
1
2
0
0
2
0
2
0
0
2
2
0
0
0
1
0
1
1
1
1
0
1
0
1
0
0
0
2
2
0
2
0
0
1
1
0
2
1
0
0
2
0
0
2
0
2
0
2
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
1
3
2
0
2
0
0
1
2
2
0
0
0
0
0
1
2
1
0
1
1
2
0
2
1
0
1
2
1
0
1
1
0
0
0
0
2
1
1
1
0
0
2
0
1
0
0
2
0
0
0
1
2
1
0
0
0
0
1
0
2
1
4
0
1
0
1
0
2
1
1
0
0
0
1
0
0
0
0
1
2
2
0
0
0
0
0
0
1
2
1
2
0
0
1
2
1
0
0
2
0
0
0
2
1
1
0
1
0
0
0
2
1
2
2
1
2
0
0
0
1
3
0
1
2
0
2
1
0
1
0
0
2
0
0
2
0
0
2
1
2
0
0
0
0
0
1
0
1
0
1
0
2
0
0
0
0
0
0
0
0
1
2
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
2
1
0
1
0
0
2
2
0
0
2
0
2
0
0
0
0
0
2
0
2
2
0
1
0
0
1
1
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
1
2
2
0
2
2
2
0
2
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
1
2
1
0
1
1
0
1
0
0
0
0
1
0
0
1
1
2
0
0
0
0
2
1
1
0
4
0
0
2
3
1
0
0
0
0
0
0
1
0
1
0
2
0
0
2
0
2
0
1
0
1
1
2
0
0
2
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
2
1
2
0
2
0
1
0
1
0
2
0
0
0
0
0
1
2
0
1
0
2
0
0
1
0
0
0
0
2
2
0
0
0
0
0
1
1
1
2
0
2
1
0
1
5
0
2
0
1
0
0
0
1
1
0
0
0
0
3
1
0
0
1
0
0
1
2
2
1
0
0
0
0
3
2
0
2
2
0
0
2
1
0
0
1
2
3
1
2
0
3
0
0
1
0
1
2
0
1
0
0
0
0
0
2
1
1
1
0
2
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
2
0
0
0
1
1
0
2
2
0
0
2
1
2
0
0
1
1
2
0
0
0
0
0
2
0
3
0
1
0
1
0
0
2
0
1
0
0
0
0
2
1
1
0
1
2
2
0
0
1
2
2
0
0
0
0
2
0
0
0
0
0
2
0
1
2
0
0
1
1
2
0
0
0
0
2
0
3
2
0
0
0
0
1
0
0
0
2
2
1
0
0
1
0
0
1
2
0
1
2
0
2
0
0
0
0
2
0
2
0
2
2
0
2
0
0
0
2
0
0
0
0
2
0
3
0
2
1
0
1
0
0
1
0
2
2
0
1
0
0
0
1
0
2
0
0
0
1
1
0
0
0
1
2
0
1
2
0
1
1
0
0
2
1
0
1
0
0
0
0
1
0
1
1
1
0
1
2
0
0
0
2
0
3
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
2
2
3
1
0
2
1
0
1
1
0
1
0
0
0
1
0
1
0
2
0
0
1
0
1
0
1
0
1
1
0
0
0
2
0
0
0
2
0
0
2
1
0
2
0
0
1
0
0
2
1
0
0
1
2
0
0
1
1
0
2
3
0
0
0
1
0
1
2
1
0
0
0
1
2
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
2
2
0
2
0
0
0
1
2
3
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
2
3
0
1
0
2
2
0
0
2
0
1
0
3
1
0
2
0
0
0
2
0
2
0
2
0
0
1
1
2
0
0
0
1
1
1
2
2
2
2
0
2
2
2
1
0
0
0
0
0
2
2
0
1
2
1
0
2
0
1
2
0
1
2
0
0
2
2
0
0
2
2
0
2
2
1
0
1
0
3
2
0
0
2
0
0
1
0
0
0
0
0
0
0
4
0
1
0
1
0
0
1
0
3
0
2
2
1
0
2
1
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
2
0
1
0
1
2
1
1
4
1
0
0
2
0
2
1
1
2
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
2
0
3
0
1
0
0
0
0
1
0
0
0
2
0
1
0
0
0
1
0
0
1
0
2
0
2
0
1
2
0
1
2
1
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
1
1
1
2
1
0
1
0
1
0
1
1
0
0
1
0
2
0
0
2
2
0
0
2
0
0
2
0
2
0
0
0
2
0
0
0
0
0
2
0
2
0
2
1
0
0
1
0
0
2
0
1
1
0
1
0
0
0
0
3
1
0
0
1
1
0
0
0
0
0
2
1
0
1
1
0
0
1
2
3
0
1
2
2
1
0
0
1
0
0
0
0
2
1
0
1
2
1
0
0
0
0
0
1
0
0
0
2
0
2
0
1
0
2
2
1
0
0
0
0
0
2
2
1
2
0
1
1
2
0
2
2
0
1
2
0
1
0
0
2
3
0
0
0
0
0
0
1
0
1
0
1
0
1
2
1
2
0
2
2
1
0
1
0
1
0
0
0
0
0
1
2
0
0
2
0
2
2
2
0
0
2
0
1
2
1
2
0
3
2
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
1
1
1
0
0
0
1
1
0
1
0
1
1
0
0
0
0
1
0
1
0
0
0
1
1
0
2
0
0
0
0
0
0
0
2
2
1
0
2
0
1
1
3
0
0
1
2
0
0
1
2
1
0
3
0
2
1
2
2
2
0
1
3
1
0
1
0
2
0
0
0
0
0
0
0
1
1
0
2
2
1
0
1
2
2
0
0
0
3
2
0
1
1
0
1
0
0
0
0
2
1
0
0
0
1
1
1
0
1
0
0
0
0
0
2
0
3
1
0
1
3
0
0
0
0
0
2
3
0
0
1
2
0
1
1
1
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
2
0
0
2
0
2
0
0
0
0
0
1
0
2
0
0
1
0
0
0
3
1
0
1
1
0
0
1
0
0
1
0
1
1
0
1
0
0
2
1
0
1
1
0
0
2
1
0
2
0
2
0
0
0
0
2
1
0
0
2
0
2
1
0
0
0
2
2
2
1
2
2
0
0
2
1
1
0
0
0
1
1
1
0
1
1
1
2
0
0
0
0
2
1
0
2
1
1
0
0
0
2
0
0
1
0
0
0
0
0
0
3
3
1
0
0
2
0
0
1
0
0
0
0
0
0
0
3
1
1
0
0
0
2
1
0
0
0
1
0
1
4
0
1
2
0
1
0
0
0
2
1
2
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
1
0
2
1
1
0
0
1
0
1
1
1
2
1
2
0
0
2
0
2
1
0
0
0
0
1
1
0
0
1
1
0
1
1
0
2
2
0
0
0
2
0
0
5
0
1
0
2
0
0
0
0
0
1
1
4
1
0
0
0
0
1
1
3
2
1
1
1
0
3
2
0
0
2
0
0
0
0
1
1
0
0
0
1
0
0
0
1
2
2
3
0
1
0
0
1
0
2
3
0
0
1
0
0
0
2
0
0
1
2
0
0
0
2
1
0
2
1
0
0
0
0
0
0
1
0
0
4
0
2
0
0
0
1
1
1
1
0
1
1
0
1
0
2
0
2
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
2
0
0
2
2
1
1
1
0
0
0
2
0
1
1
2
0
0
0
0
0
0
2
0
1
0
2
1
1
2
0
1
1
0
0
0
1
2
1
1
0
0
0
0
0
0
0
0
1
3
1
2
0
0
1
1
0
0
1
1
0
1
0
1
0
0
2
3
0
1
0
1
0
0
0
1
2
0
2
0
1
2
0
1
1
0
3
2
2
0
0
0
0
2
1
1
1
0
2
0
1
0
2
0
1
0
0
0
0
1
2
0
0
1
0
1
0
0
0
1
2
0
1
1
0
1
1
0
1
0
0
3
0
1
0
0
0
1
1
2
1
2
0
2
0
2
0
0
0
2
0
1
3
1
0
0
1
2
1
0
0
2
0
0
2
0
0
0
1
1
0
1
0
0
0
1
1
3
1
1
1
0
0
1
2
2
2
2
0
0
1
2
1
0
2
0
1
2
0
1
2
0
2
0
1
0
0
0
1
2
1
2
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
1
1
0
2
0
2
1
2
1
0
0
0
1
2
0
1
0
2
1
1
1
1
1
1
0
1
0
0
0
2
0
0
0
0
0
0
1
1
2
2
2
0
2
0
0
2
0
0
0
2
0
2
2
1
0
1
2
0
0
0
1
0
0
0
1
0
0
0
2
0
0
1
0
0
2
0
2
0
0
0
0
0
0
2
1
0
1
2
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
2
2
0
2
0
2
1
0
0
0
0
0
1
0
0
0
0
1
1
1
1
1
2
1
2
1
0
0
1
0
1
0
1
0
0
0
1
0
1
0
1
1
0
2
4
1
0
0
1
2
2
1
0
0
0
2
0
0
0
1
0
1
0
1
0
2
0
1
0
0
2
2
1
0
0
0
0
0
1
0
0
1
2
0
0
0
1
0
0
0
1
1
0
3
1
1
2
0
0
1
0
1
2
0
0
2
1
0
0
2
0
0
0
0
0
0
2
0
2
0
1
0
0
1
0
2
2
0
0
0
0
2
1
0
0
0
0
1
0
1
1
3
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
3
2
0
1
0
0
1
2
0
1
2
0
0
0
1
1
0
1
1
1
0
1
2
0
0
0
2
0
1
1
0
0
1
1
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
1
1
0
2
1
2
0
2
1
0
4
1
0
0
2
0
0
2
0
0
1
0
0
2
2
0
0
2
0
0
0
1
0
0
4
0
0
1
1
2
1
0
0
0
0
0
0
0
0
2
4
4
1
0
0
0
1
1
1
0
0
1
1
1
0
0
0
0
1
0
4
1
0
1
0
1
0
0
1
0
0
0
0
0
3
2
2
0
2
0
0
2
1
0
1
0
0
1
1
0
0
2
0
0
1
0
0
1
2
1
1
1
1
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
1
0
0
2
2
0
2
0
1
0
2
0
1
1
0
0
0
0
0
1
1
0
2
0
0
0
1
0
0
0
1
0
1
0
2
2
0
0
0
2
0
1
0
0
1
0
0
0
1
1
1
0
0
2
1
0
2
2
1
0
0
0
0
0
2
2
1
1
1
0
1
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
2
0
2
1
0
0
0
0
1
2
1
0
0
0
0
1
0
0
0
2
1
0
1
0
2
0
1
1
0
0
0
0
0
0
2
1
0
0
1
0
0
1
2
0
2
0
1
1
0
0
1
2
0
2
1
0
4
0
1
0
2
1
1
2
0
0
0
0
2
0
2
1
0
2
0
1
1
0
0
1
0
1
1
2
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
2
0
5
2
0
1
2
1
0
1
0
1
2
0
0
1
0
0
1
1
0
0
0
2
3
0
0
1
1
1
0
0
2
2
0
0
2
2
2
1
0
1
2
1
0
0
0
2
2
2
2
1
0
1
0
1
1
2
0
0
2
1
0
1
2
1
1
0
1
1
0
0
2
0
1
2
1
1
0
2
1
2
1
1
2
0
0
0
2
0
0
0
1
2
1
1
1
0
0
1
0
0
0
1
2
0
0
0
0
0
1
2
1
0
0
1
0
0
0
0
0
0
2
0
2
0
0
1
0
0
1
0
0
0
1
0
0
0
0
2
2
2
1
0
1
2
0
0
1
1
0
2
1
2
0
0
0
0
0
2
2
3
0
0
4
0
0
0
0
0
1
2
1
0
0
0
1
0
0
0
0
0
1
0
2
0
0
2
0
1
0
1
0
0
2
2
0
1
1
1
0
1
1
1
2
2
2
1
0
0
0
0
2
1
2
0
2
0
0
2
1
1
0
1
0
0
0
0
2
2
0
0
2
0
1
0
0
0
1
0
0
0
0
1
1
1
1
1
2
1
2
1
0
0
2
3
0
0
0
0
0
0
0
1
1
2
0
1
1
2
0
1
0
1
0
1
0
0
1
1
2
0
2
0
0
0
2
2
1
2
0
0
2
0
1
0
0
2
0
2
1
2
2
1
3
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
3
1
1
0
2
0
0
0
0
2
0
1
1
0
0
2
1
1
2
0
0
2
0
3
0
2
0
0
2
0
1
1
1
1
0
4
0
2
0
2
0
1
2
1
1
0
0
0
1
0
1
0
1
0
0
0
0
2
1
1
0
0
0
1
2
0
0
2
0
1
1
0
0
0
1
0
0
0
1
0
0
0
2
2
2
0
1
0
1
0
1
0
2
2
0
0
2
0
0
0
1
0
0
2
1
0
2
0
0
0
0
0
2
0
1
0
1
0
2
2
0
0
3
0
2
0
0
1
0
2
0
1
2
0
3
2
0
1
0
0
0
0
1
0
0
1
0
2
0
2
2
1
0
0
2
2
0
0
0
0
2
1
2
0
2
0
2
0
1
0
0
0
0
0
2
0
2
0
0
0
0
1
2
0
1
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
2
2
1
1
0
0
0
1
0
0
0
0
2
2
1
1
0
2
0
0
2
2
0
1
2
0
0
2
0
0
0
0
0
0
0
1
1
2
1
0
2
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
1
2
0
0
0
1
1
0
1
0
0
0
0
1
2
1
1
0
1
2
0
2
0
2
0
2
0
0
2
1
0
1
0
0
2
2
1
2
0
2
1
2
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
1
2
0
0
1
1
2
1
2
0
0
0
0
0
1
0
1
0
0
1
2
1
0
0
0
1
0
0
0
0
1
1
1
2
1
2
2
3
2
0
0
0
2
2
0
2
0
3
0
2
2
0
1
1
2
2
0
2
0
0
3
0
1
0
0
0
1
2
1
1
0
2
0
0
11
2
0
0
0
0
1
1
0
1
0
1
2
1
0
1
0
1
0
1
0
3
0
1
0
1
0
1
0
0
0
1
2
2
0
2
1
1
1
2
0
0
0
2
0
0
0
2
0
1
1
0
2
0
0
1
1
0
1
0
2
0
0
0
2
0
2
0
1
1
0
0
0
1
1
7
1
0
2
2
2
0
1
1
1
0
2
2
1
2
2
0
0
1
0
0
0
1
2
2
0
2
0
0
0
2
0
1
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
2
2
0
2
1
0
0
0
0
0
0
0
1
2
2
0
2
0
2
1
3
0
1
1
0
0
1
0
0
0
2
2
1
0
0
0
1
2
1
2
0
0
0
3
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
1
2
2
1
2
0
0
1
2
0
1
2
0
2
2
0
0
0
1
1
0
2
0
0
0
1
0
0
0
1
2
0
0
1
0
0
2
0
0
0
2
2
0
1
0
0
0
1
1
0
2
1
1
1
1
0
2
0
1
0
1
0
2
0
1
0
0
0
0
0
1
4
2
1
1
1
1
0
1
3
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
2
0
1
0
0
0
1
0
1
0
0
2
1
0
1
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
2
2
2
0
0
0
0
1
0
2
0
0
0
0
0
1
1
0
3
0
0
0
0
2
0
0
0
0
2
0
2
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
2
3
0
2
2
0
0
0
3
0
0
0
2
0
0
1
1
0
0
1
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
2
2
0
2
0
1
0
0
0
0
0
3
2
1
2
0
2
0
2
0
1
0
0
2
2
0
0
0
0
2
0
1
0
1
1
2
2
0
2
0
0
0
2
2
1
0
2
1
0
0
0
0
0
1
0
1
0
0
1
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
1
0
1
1
0
2
1
1
0
5
1
1
0
2
2
0
1
2
0
1
1
0
0
0
0
0
1
0
0
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
2
1
2
0
0
1
1
0
2
0
0
2
0
0
2
2
0
0
0
0
2
0
0
0
0
1
1
0
1
2
0
1
0
1
0
0
4
0
0
0
4
2
1
0
0
2
0
1
0
2
2
2
1
0
0
0
0
0
1
2
0
2
0
0
0
1
0
2
0
1
0
1
2
0
0
0
0
1
5
0
0
1
0
0
1
2
0
0
0
1
0
2
1
1
0
0
0
0
1
6
0
2
1
3
1
0
1
1
0
1
0
1
1
0
0
0
0
2
0
1
1
0
1
0
2
0
0
0
0
1
0
1
1
2
1
1
1
0
0
1
1
0
2
1
1
0
0
0
1
0
0
1
0
1
2
0
0
1
0
0
0
0
0
1
0
2
2
0
1
0
2
1
2
2
1
2
0
0
2
2
0
0
1
1
1
0
0
0
1
1
0
2
2
0
1
2
1
0
3
2
0
2
1
0
2
0
0
1
0
2
0
0
1
2
0
0
1
1
1
2
0
0
1
1
2
0
1
0
0
2
0
1
2
0
1
0
0
0
0
0
2
0
0
0
1
0
0
3
0
2
2
0
2
0
2
3
1
1
0
0
2
0
0
1
1
1
0
0
2
0
0
0
2
0
0
2
1
0
0
2
1
0
1
1
2
1
1
2
0
2
1
2
0
0
2
2
1
2
1
0
3
0
0
0
0
1
1
1
1
0
0
0
6
0
2
0
0
0
0
2
0
0
2
2
1
1
1
0
1
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
2
0
1
1
0
0
0
1
2
0
0
0
0
0
0
2
0
2
2
0
0
2
0
0
0
0
2
0
0
2
1
0
0
1
0
1
0
1
2
0
1
0
2
0
0
0
0
2
2
0
0
2
0
0
1
1
0
2
0
0
1
2
3
0
1
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
1
1
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
2
0
0
2
1
2
0
2
0
1
0
1
0
0
0
2
1
0
1
2
1
1
0
0
0
1
1
1
0
0
2
0
0
0
1
0
1
0
0
0
2
0
1
1
1
2
0
1
0
0
2
2
1
0
1
0
0
0
2
0
2
0
0
0
2
1
2
0
1
1
0
2
2
2
1
0
2
2
0
2
2
1
2
1
1
1
0
0
0
0
2
0
2
1
0
0
1
2
1
0
0
5
1
0
1
1
0
0
0
2
0
1
0
0
2
0
1
2
0
0
1
0
0
1
1
0
1
1
2
1
18
2
0
0
0
2
2
1
1
0
0
0
0
1
0
2
1
1
0
0
1
0
0
2
0
0
0
2
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
1
1
0
1
0
0
1
0
2
2
1
1
2
0
0
0
0
0
3
0
0
3
1
0
3
0
0
0
1
0
1
0
0
0
0
2
0
1
1
0
0
0
1
0
2
2
2
0
1
1
2
0
1
1
0
2
1
2
0
1
0
2
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
1
2
2
2
0
2
1
0
0
1
0
0
1
0
0
0
2
0
0
1
0
1
2
1
1
0
0
2
2
0
2
4
0
0
0
0
0
0
0
1
1
0
0
0
3
0
0
1
0
0
0
1
0
1
0
1
1
0
0
0
0
1
0
2
0
0
1
0
0
0
2
2
0
2
0
0
1
1
1
0
0
2
0
0
2
0
0
2
0
1
0
1
0
1
0
1
2
0
1
1
1
0
0
0
1
0
0
1
2
2
0
0
2
1
0
0
1
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
2
0
1
0
2
0
0
0
1
0
0
2
1
1
0
0
0
0
0
2
2
1
0
0
0
0
2
1
2
0
0
1
0
1
0
0
1
2
0
0
0
2
0
2
1
1
0
0
0
0
2
1
0
0
0
1
0
0
3
0
2
0
0
0
0
2
0
1
2
0
0
1
0
1
0
0
0
0
1
2
1
0
1
1
1
0
1
0
1
2
1
0
1
0
0
1
1
0
0
0
0
2
0
0
0
1
0
2
0
1
1
1
2
0
0
0
0
0
0
0
0
0
2
1
2
0
1
0
0
1
1
0
0
1
0
0
1
1
0
0
0
4
4
0
0
2
2
0
2
0
0
2
1
1
1
2
1
2
0
0
1
2
0
1
0
1
1
0
1
0
3
0
0
0
2
2
0
0
2
0
0
0
1
0
2
0
0
0
1
0
0
0
0
2
0
1
0
0
1
1
1
2
0
1
0
0
0
2
0
1
0
1
1
2
0
2
0
1
2
0
1
2
2
0
0
1
0
0
2
0
1
0
1
3
0
0
1
0
0
1
1
2
2
1
1
0
0
2
0
0
0
1
0
0
0
0
1
5
0
0
2
0
1
1
0
2
2
0
0
0
1
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
1
0
2
1
1
0
0
0
0
1
2
0
1
2
0
2
0
0
0
0
1
0
1
1
1
0
1
2
1
1
0
0
1
1
0
2
1
0
0
0
1
2
2
1
1
1
0
1
1
0
2
0
0
1
0
1
0
0
1
0
0
2
1
1
0
0
2
1
0
2
2
0
0
3
1
0
0
1
0
0
1
1
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
2
0
0
1
0
2
1
2
0
0
0
0
0
1
0
2
0
2
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
3
1
1
0
1
0
0
0
2
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
2
2
1
0
0
0
1
0
0
2
0
2
5
1
0
0
1
0
1
1
0
2
0
0
0
1
1
1
1
1
0
0
1
0
1
0
0
1
1
0
0
2
0
2
0
0
0
2
2
4
2
0
0
0
4
0
1
1
0
0
0
1
0
0
2
0
0
2
1
1
1
0
2
1
0
0
0
2
0
0
0
2
2
0
1
0
0
0
0
1
0
0
0
2
2
1
0
2
0
0
1
1
1
1
2
0
0
1
0
1
0
0
1
1
1
1
1
0
0
0
0
2
0
2
0
0
0
2
0
1
2
0
2
0
1
0
0
0
0
0
1
1
2
1
0
2
0
1
2
0
1
4
0
0
1
2
0
0
1
0
2
0
0
0
1
0
2
0
2
2
0
1
0
2
0
1
0
1
0
0
2
3
1
0
2
2
2
2
0
1
3
0
0
1
0
1
2
2
0
2
0
0
1
2
1
0
0
0
2
0
2
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
1
0
0
0
1
0
2
1
2
0
0
0
0
0
2
0
1
2
0
0
2
0
0
3
1
1
0
2
1
0
0
1
0
2
0
1
1
2
0
2
0
1
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
1
0
0
2
0
1
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
2
2
0
1
1
0
0
0
0
0
0
1
2
0
1
2
0
1
2
2
2
0
2
0
1
0
0
0
0
0
1
1
1
0
0
0
2
1
2
2
1
2
1
0
1
1
0
2
1
1
0
0
1
0
0
2
0
2
1
1
2
0
2
0
0
1
0
2
0
0
2
2
0
0
0
0
0
0
0
0
1
2
0
2
0
2
1
0
0
0
0
0
0
1
0
3
1
2
0
1
0
1
0
0
1
0
2
1
1
2
0
0
1
2
0
1
0
0
2
0
0
0
0
0
0
2
1
1
2
0
0
0
0
2
2
0
0
0
0
2
2
1
0
1
2
1
2
2
2
0
2
1
2
0
0
1
0
0
1
1
3
3
1
1
0
3
1
1
0
2
1
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
1
1
1
0
2
1
0
1
0
0
1
1
1
0
1
2
0
2
1
2
0
0
0
0
2
2
0
0
1
1
1
0
2
1
0
0
3
0
0
1
0
0
0
0
1
0
1
2
1
2
1
0
1
0
1
0
0
1
2
1
0
0
2
1
0
0
0
1
1
0
0
2
0
0
1
0
0
1
2
2
0
2
0
1
0
0
0
1
0
0
1
0
2
1
0
0
2
0
1
0
0
0
2
0
0
0
0
0
2
0
1
2
0
1
1
0
0
1
0
1
0
0
0
2
1
0
2
0
2
1
0
0
2
0
1
0
1
1
2
0
1
1
1
0
1
0
2
1
1
0
0
0
0
0
3
0
2
0
1
3
0
2
0
0
1
1
0
1
0
0
0
0
1
2
0
0
0
0
0
2
0
1
0
2
0
0
0
0
1
0
3
0
1
1
0
1
3
1
0
1
1
4
0
1
0
0
2
1
0
1
0
0
1
2
0
2
1
0
1
0
1
2
0
1
0
0
0
0
2
2
1
0
2
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
2
0
1
1
0
1
0
0
0
2
2
2
1
0
1
1
0
0
2
1
0
0
0
0
0
0
2
2
1
0
2
0
0
0
2
0
0
1
1
1
0
1
1
0
0
1
2
0
2
1
2
1
1
1
0
0
0
2
0
0
1
0
0
0
0
2
0
2
0
0
1
0
0
2
1
0
1
0
0
1
0
2
2
2
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
1
0
2
1
2
2
1
3
0
0
0
1
1
1
1
2
2
0
2
0
2
0
0
1
0
0
1
0
2
0
1
0
0
2
1
0
1
0
0
1
0
0
0
1
0
1
0
1
1
2
0
0
0
2
2
0
0
1
0
0
0
0
1
2
1
0
0
0
1
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
3
0
0
0
1
2
1
0
0
1
1
1
0
1
1
0
1
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
2
2
0
1
0
0
2
1
0
0
2
0
1
0
1
1
0
1
2
0
0
1
0
0
2
2
1
1
2
2
2
1
0
2
1
1
1
0
0
0
0
1
2
0
2
0
0
0
0
0
6
0
0
0
0
2
2
0
2
0
0
0
0
0
1
0
0
1
1
2
2
0
0
0
0
3
0
1
1
2
1
0
1
0
0
0
0
0
1
2
2
0
0
0
5
1
1
0
0
1
0
1
0
2
2
2
0
2
2
1
0
1
2
1
0
0
0
0
1
1
1
0
0
1
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
2
1
1
2
0
0
0
0
1
0
0
0
0
1
3
0
0
3
1
0
0
4
0
0
0
3
0
1
1
0
1
1
0
1
2
0
0
0
2
1
2
1
1
0
0
0
1
1
2
1
0
1
0
0
0
2
2
0
0
0
1
1
0
1
0
0
0
1
2
0
1
0
0
1
2
2
0
0
0
0
0
2
0
2
0
0
1
2
0
0
0
1
0
2
2
1
0
0
0
0
0
0
1
0
1
0
0
2
1
1
1
1
0
1
3
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
2
0
1
0
1
0
0
0
0
1
1
2
0
2
0
1
0
1
1
0
0
2
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
2
0
1
0
1
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
1
0
0
1
0
1
2
1
0
0
0
1
1
0
0
1
2
0
2
2
0
0
1
0
2
1
0
2
0
1
0
0
0
0
0
1
1
2
1
4
0
0
2
0
0
1
1
1
0
0
0
1
0
0
1
1
1
1
0
0
2
1
3
1
0
0
2
0
1
3
1
0
0
5
0
2
1
0
0
0
1
0
0
0
0
0
0
0
2
0
1
1
0
0
1
2
0
0
2
2
0
0
2
0
0
0
2
0
0
2
1
1
0
2
0
0
0
0
1
0
2
0
0
2
2
1
2
1
0
0
2
0
0
0
3
1
1
0
0
1
1
2
0
1
0
2
1
0
0
0
0
0
1
0
1
0
0
0
2
2
1
0
0
0
0
3
2
1
1
2
0
0
1
0
1
0
1
0
0
1
1
1
0
0
1
0
2
1
0
0
1
0
2
0
1
0
0
0
1
0
1
1
0
0
0
1
0
1
1
0
2
2
1
0
1
0
0
1
1
0
2
1
0
1
2
0
1
0
0
1
0
2
2
1
2
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
1
2
3
1
1
0
0
1
1
2
1
1
2
0
0
0
2
0
1
1
2
2
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
2
0
2
2
1
0
0
1
1
0
1
2
0
2
1
0
0
2
1
1
1
0
0
2
1
2
0
1
0
0
1
1
3
0
0
0
0
0
0
0
1
2
0
0
0
2
2
0
2
1
1
1
3
2
2
0
0
0
0
0
0
0
0
0
2
2
0
2
1
2
0
0
2
1
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
1
1
2
0
2
2
1
0
0
2
0
0
0
1
1
1
3
0
2
0
1
2
1
0
2
0
2
1
1
2
0
0
0
0
1
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
1
2
2
1
2
2
0
2
1
1
0
0
2
0
0
2
0
2
0
1
0
0
2
0
0
0
2
0
1
0
1
0
0
2
0
0
3
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
1
1
1
0
1
0
2
0
1
2
2
1
3
0
0
1
0
0
1
0
0
3
0
1
0
0
1
1
0
0
2
1
0
0
0
0
0
0
0
3
0
1
0
0
0
2
2
0
0
0
1
3
0
1
0
0
2
0
0
0
2
1
2
0
1
0
2
0
0
0
0
1
0
0
2
0
2
0
2
0
0
2
0
1
0
0
0
0
0
2
0
0
0
2
2
0
0
1
0
2
0
0
0
0
1
1
1
0
0
0
2
1
0
1
0
2
0
1
0
1
0
1
0
0
2
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
5
1
2
0
1
1
0
12
2
3
1
2
3
1
1
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
1
2
2
1
1
0
0
0
0
0
0
0
0
1
2
0
2
2
0
0
0
1
2
0
1
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
1
2
1
0
0
0
1
0
2
0
0
2
0
1
0
1
3
0
0
0
0
1
2
0
1
0
0
2
1
1
0
0
0
0
0
0
2
1
1
0
1
2
0
0
1
0
0
1
1
0
0
2
1
0
1
1
0
0
1
1
2
0
2
0
1
2
0
0
2
0
0
2
0
2
1
0
1
1
1
0
0
0
0
2
0
0
1
2
1
0
2
0
1
0
2
0
0
3
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
2
0
2
1
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
2
0
2
0
1
3
1
0
2
0
2
2
0
1
0
0
2
0
0
0
2
0
0
1
1
1
1
0
2
2
0
1
1
0
2
0
0
2
1
0
0
1
2
0
0
1
0
0
1
1
0
2
1
0
0
0
0
2
0
0
1
0
2
2
0
0
0
0
2
2
1
0
1
0
0
0
2
2
0
0
1
1
1
0
0
2
0
1
0
0
0
0
2
1
0
0
2
2
0
1
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
2
1
3
1
1
0
0
1
0
0
0
2
2
1
0
1
0
0
1
1
2
1
0
2
0
0
1
0
1
2
1
1
1
2
2
2
0
4
0
0
0
0
1
4
0
0
1
1
1
0
2
0
0
0
2
0
2
1
0
1
1
2
2
2
2
0
0
0
0
0
0
2
0
0
0
1
0
1
0
2
0
2
0
0
0
0
2
0
1
1
0
0
1
0
1
0
0
0
0
2
0
0
0
1
1
0
0
2
0
0
1
0
3
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
2
2
2
1
0
0
2
2
1
0
2
0
0
0
2
4
1
0
2
0
2
0
0
0
0
1
1
0
0
2
1
0
2
0
1
0
0
2
4
0
2
2
0
0
2
0
0
0
2
0
1
2
2
3
0
0
0
0
1
2
0
0
1
2
1
1
1
2
1
0
1
0
2
1
0
0
1
0
3
6
0
0
0
0
1
0
0
0
0
2
0
1
1
1
0
0
0
0
0
0
1
2
2
3
0
0
0
0
2
2
0
0
0
0
1
1
2
2
0
0
0
2
0
0
0
2
0
0
2
0
0
1
3
0
1
1
1
1
2
1
0
0
1
0
1
2
0
1
2
2
0
0
0
0
0
0
0
0
1
0
2
2
0
2
1
0
0
0
0
0
0
2
2
0
0
2
0
0
0
2
0
1
0
1
0
2
1
2
0
2
0
5
1
0
0
1
1
0
1
3
0
0
0
1
2
0
0
0
0
0
2
1
0
0
2
1
0
0
1
0
1
1
2
1
1
1
1
1
2
0
2
0
0
0
0
0
0
0
1
0
0
2
3
2
0
0
0
0
0
1
2
0
0
0
1
2
2
2
1
2
2
2
1
0
0
1
0
1
1
1
1
0
2
0
0
2
0
0
0
1
2
2
1
0
0
1
2
1
2
0
0
2
1
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
1
0
0
1
1
0
2
1
0
0
0
0
1
1
0
1
0
2
2
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
1
3
0
3
0
1
0
1
2
1
0
0
2
0
0
0
1
3
1
0
0
1
2
0
0
1
0
0
1
0
0
0
2
0
0
0
2
0
1
1
0
0
0
2
0
0
0
0
2
0
2
0
0
1
0
0
0
2
0
0
1
1
2
0
0
0
0
1
0
2
1
0
1
2
3
2
0
0
0
1
2
0
1
1
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
2
0
0
1
0
2
0
0
2
1
0
0
0
1
1
0
0
1
0
0
1
3
0
0
1
0
2
0
0
1
1
1
4
0
2
0
0
2
2
0
1
0
1
1
1
1
1
0
0
0
2
0
0
0
0
0
0
2
1
2
0
0
0
1
0
2
0
1
0
1
0
0
2
2
2
2
0
0
2
1
2
1
2
0
0
0
0
0
1
1
0
0
2
0
1
0
0
1
3
0
1
1
2
2
0
0
0
2
0
0
2
2
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
1
0
2
0
2
0
2
0
0
2
2
0
0
1
0
3
0
1
1
1
1
1
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
1
2
2
0
0
0
1
1
1
0
0
2
1
0
1
1
0
0
1
0
3
0
0
1
1
0
2
0
0
0
0
2
1
1
1
2
2
2
1
0
1
1
0
0
1
0
0
1
0
0
0
0
2
0
0
1
0
1
1
0
1
0
1
0
1
0
5
0
2
1
2
0
0
1
1
1
0
0
0
1
2
0
0
0
0
0
0
1
0
1
1
1
2
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
2
0
0
3
2
2
0
0
0
2
2
2
0
0
1
0
1
1
0
0
2
1
1
0
1
0
0
0
1
2
1
1
1
0
2
2
0
2
2
1
0
0
0
4
0
1
1
1
5
0
0
1
1
2
0
0
4
2
0
0
1
2
2
0
1
0
0
0
0
1
0
2
2
0
0
0
0
2
0
2
0
1
0
0
0
2
0
0
0
1
1
0
1
0
2
0
1
1
0
1
0
0
0
1
0
0
2
2
0
1
1
0
1
0
0
2
1
0
0
0
2
2
2
4
0
2
2
2
4
0
0
0
1
1
2
0
0
1
2
0
2
1
1
1
0
1
1
1
0
0
2
1
0
0
1
2
1
0
2
0
0
0
0
0
2
1
1
0
3
0
3
0
0
0
0
2
1
2
3
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
1
2
0
2
2
0
0
0
1
1
0
0
2
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
1
1
1
1
1
0
3
0
0
3
0
0
2
0
2
1
2
2
0
2
0
0
2
1
1
0
0
1
2
1
0
1
0
2
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
2
1
0
0
1
0
0
2
2
1
0
2
0
2
0
0
0
1
0
0
1
0
0
1
2
1
1
0
0
2
2
0
1
0
0
2
0
0
0
0
0
0
2
2
1
0
2
0
0
1
2
2
1
0
0
2
1
0
1
2
0
2
0
1
1
1
0
0
2
0
0
0
0
0
2
0
2
2
2
2
2
0
0
2
0
0
0
2
1
1
0
0
0
4
0
1
1
2
2
1
0
2
2
0
2
0
1
0
0
1
0
0
1
2
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
1
1
0
1
1
0
0
1
0
1
0
1
0
0
1
0
2
0
2
2
0
0
1
1
0
1
1
0
1
2
2
0
2
0
2
0
1
0
2
0
2
1
1
0
1
0
0
2
0
3
2
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
2
1
0
0
1
1
0
2
0
0
1
2
2
2
1
1
0
1
1
0
1
1
1
0
0
1
0
0
0
0
1
0
0
0
2
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
2
2
1
0
0
0
1
0
0
0
1
0
0
1
2
0
0
0
0
0
2
2
0
0
0
1
1
0
4
0
0
0
2
0
1
0
0
4
0
0
0
0
1
0
2
0
0
1
2
0
2
0
2
0
1
0
1
2
0
1
1
1
2
0
1
1
1
0
2
1
0
0
0
1
1
0
0
0
2
2
0
2
1
0
0
1
1
0
2
2
0
2
1
2
2
0
1
0
0
1
0
0
1
0
0
1
2
0
0
2
0
0
4
0
1
0
2
0
0
0
0
0
1
0
2
0
0
1
0
0
2
2
1
2
4
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
1
0
2
0
0
0
0
0
0
1
1
0
0
0
1
2
0
1
1
0
0
0
0
1
1
1
0
2
0
1
0
1
1
2
0
1
3
1
0
0
3
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
1
1
1
0
1
0
0
1
0
1
2
1
1
0
2
0
1
2
0
2
0
1
0
0
0
0
2
1
0
1
1
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
2
2
0
0
0
2
1
1
2
2
0
1
0
2
2
0
2
0
0
1
0
0
0
1
0
2
1
0
0
0
0
0
2
1
1
0
2
0
0
0
1
0
2
0
1
2
0
2
0
0
0
0
0
0
1
0
1
0
0
2
0
0
1
0
0
0
2
2
0
0
1
0
2
1
0
0
2
0
0
1
1
0
0
1
0
1
0
0
1
1
0
0
0
0
1
3
0
2
2
0
0
3
0
3
0
2
3
1
0
1
1
0
0
2
1
1
1
0
1
0
2
0
1
1
0
0
2
0
0
0
1
0
0
0
2
2
2
0
2
2
0
0
2
0
0
2
0
1
0
2
0
1
2
1
1
1
0
1
2
0
0
0
2
1
0
2
1
2
0
0
0
1
1
0
1
0
0
2
4
0
0
0
0
0
0
0
0
1
2
1
0
2
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
1
2
1
1
1
1
1
1
0
0
1
1
1
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
1
1
0
0
1
1
2
0
1
0
0
0
2
2
2
1
2
0
1
0
0
1
0
0
2
0
0
1
1
0
2
0
0
2
1
0
3
0
1
2
0
0
1
0
3
0
0
0
1
1
2
0
0
2
0
2
0
1
2
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
1
2
1
0
1
0
0
0
0
1
2
1
0
0
0
0
1
2
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
2
0
2
1
0
0
0
2
0
1
0
0
1
0
1
2
0
0
2
2
0
1
1
1
0
1
1
2
0
1
2
0
0
0
0
0
0
1
0
1
1
2
0
1
1
0
0
1
3
2
1
2
0
2
1
0
1
0
0
1
1
0
0
1
2
2
0
0
0
1
2
0
1
2
2
1
0
0
2
0
1
1
0
0
2
0
2
2
2
1
4
1
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
2
0
2
1
1
2
0
0
1
1
3
0
2
0
1
1
1
0
0
2
2
0
2
0
0
0
0
1
0
2
0
1
0
1
0
1
0
0
0
1
1
1
2
1
1
2
0
0
0
0
1
1
0
2
0
0
0
1
0
2
0
1
0
0
0
1
0
0
1
1
1
0
0
2
2
0
4
0
1
2
2
0
0
2
0
0
0
1
0
0
2
0
1
0
0
1
0
1
0
1
0
0
1
2
1
0
0
1
1
2
0
0
2
0
0
0
0
2
1
2
0
0
0
0
2
2
0
0
0
0
1
2
0
1
1
0
1
0
2
1
1
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
2
0
0
0
2
2
1
1
1
0
0
2
0
0
4
0
0
0
0
0
0
0
1
1
1
1
0
2
1
0
0
0
0
2
0
2
0
0
1
2
2
1
1
1
1
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
2
2
0
1
2
0
2
2
0
0
2
1
0
1
1
2
0
2
2
2
2
0
0
2
1
0
2
1
2
3
0
1
0
0
0
0
2
0
0
2
1
1
0
0
3
1
3
0
1
3
0
1
2
0
1
0
0
0
1
1
1
0
0
0
0
1
2
1
0
0
0
1
0
0
0
0
0
0
1
1
2
0
0
2
0
2
1
1
2
1
0
0
0
2
0
1
2
1
1
1
1
2
0
1
0
0
1
0
1
2
0
0
0
0
1
0
1
0
2
0
0
0
0
2
0
1
0
1
2
2
1
0
0
1
0
1
0
1
0
1
0
3
0
1
3
0
0
0
0
2
0
0
2
1
0
1
0
1
2
2
1
0
0
4
2
0
0
1
2
0
0
1
0
3
0
2
2
0
1
1
1
0
0
3
1
0
0
0
2
0
0
0
1
1
2
0
0
0
1
1
0
1
0
1
1
0
0
1
1
1
2
0
0
0
2
1
0
0
2
0
1
0
0
0
2
1
1
2
0
0
2
0
1
0
2
0
1
2
0
0
0
1
0
0
1
2
0
0
1
1
0
1
2
1
0
0
0
0
0
0
0
0
2
0
0
1
2
2
2
0
0
2
1
0
1
0
2
0
2
0
1
1
2
2
0
1
0
2
0
0
0
2
2
2
1
1
0
2
0
1
0
2
2
0
2
0
1
0
2
1
0
0
0
1
2
0
0
2
0
0
4
0
0
0
1
0
1
1
1
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
2
0
2
1
2
0
0
1
1
1
0
0
1
0
0
1
0
0
1
1
1
0
4
0
2
1
0
1
0
0
0
2
1
2
1
2
1
1
1
1
0
1
2
0
2
2
2
0
1
0
0
0
1
1
6
0
1
0
0
1
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
1
1
1
0
0
1
0
0
0
0
0
2
1
2
1
0
2
1
1
1
0
1
0
1
1
0
0
2
2
0
0
0
0
1
0
1
1
2
0
0
1
2
0
0
1
0
0
0
0
0
1
0
1
0
1
1
0
2
2
0
0
0
0
1
2
0
1
0
1
1
1
0
0
2
0
0
2
0
2
0
0
0
0
1
0
0
3
0
2
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
1
2
0
2
0
0
1
0
0
0
0
0
4
1
0
3
0
0
0
1
1
1
0
1
2
1
0
2
0
0
1
1
0
0
2
1
0
1
1
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
2
0
1
0
1
0
1
1
0
0
2
1
0
0
2
1
0
0
2
2
2
3
0
2
1
0
0
0
2
1
1
2
2
0
0
1
2
1
1
1
0
2
1
0
0
2
2
0
1
0
0
0
0
0
2
0
0
0
0
1
3
0
0
0
2
0
1
3
3
1
1
0
1
0
1
2
0
1
0
0
0
1
0
0
0
0
0
1
0
2
2
0
0
1
1
1
2
2
0
0
1
2
3
0
0
0
0
0
2
1
0
1
0
0
1
0
2
2
0
1
0
0
0
0
3
0
0
0
0
1
0
0
0
3
0
0
2
2
0
0
0
1
0
2
0
1
1
0
2
2
0
0
1
0
1
1
2
0
0
0
1
0
1
1
0
2
2
2
1
0
1
0
2
0
2
0
1
2
0
1
0
2
0
2
0
0
0
1
0
1
2
1
0
2
1
1
1
0
0
0
2
0
0
0
0
0
3
0
0
1
2
0
0
0
0
3
0
0
0
0
1
0
0
0
2
0
0
1
0
0
1
2
2
0
1
1
0
0
0
0
1
1
1
2
2
0
0
0
0
1
1
1
0
0
1
1
2
1
2
0
0
1
2
1
0
0
0
0
0
2
1
1
1
3
1
0
2
1
1
0
1
0
0
2
0
4
0
2
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
2
1
1
0
0
0
1
1
0
2
0
1
1
0
2
2
2
1
0
0
0
2
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
2
0
1
1
0
1
0
2
0
0
4
0
0
0
0
0
1
1
0
0
1
2
1
1
2
2
2
1
0
2
0
0
2
0
0
0
1
0
1
0
1
0
1
2
1
1
0
0
1
1
0
2
0
0
0
0
0
3
1
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
1
0
1
1
0
1
1
0
0
0
1
2
0
1
3
0
0
0
4
1
2
2
0
2
0
1
2
1
2
0
0
2
1
0
0
0
2
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
2
1
0
1
0
2
0
2
1
1
0
0
0
3
0
1
0
1
1
0
2
0
2
0
1
0
1
1
2
1
0
1
2
0
0
0
2
0
0
0
0
0
0
1
2
2
1
0
0
2
2
0
0
4
2
0
1
2
0
0
0
1
2
0
1
2
2
0
1
2
1
1
0
0
0
2
0
0
0
2
2
0
0
1
2
0
1
1
0
2
0
1
1
0
2
0
1
2
0
1
2
1
0
0
0
1
1
0
0
0
0
0
1
0
2
1
2
2
1
1
1
0
1
1
0
6
2
0
2
1
0
0
1
0
1
1
1
0
1
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
2
0
0
3
0
0
0
0
1
2
2
0
0
2
0
0
1
0
0
1
2
3
2
0
0
2
0
0
2
0
1
0
0
1
1
0
0
2
0
0
0
4
0
0
0
2
0
0
2
0
2
0
1
0
0
0
0
0
2
2
1
0
1
0
0
0
0
2
0
0
1
1
0
1
1
2
0
0
2
0
0
0
0
0
3
1
0
1
0
0
0
1
1
0
2
1
1
1
1
0
2
1
1
0
0
1
1
0
0
2
0
2
1
2
2
1
3
1
1
0
0
1
0
0
0
3
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
1
0
2
4
0
0
0
5
0
1
0
2
0
1
1
0
0
1
1
1
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
1
0
0
0
1
3
1
1
0
0
0
2
0
0
0
0
2
0
1
0
0
2
0
1
1
0
2
4
2
0
1
0
0
0
1
2
2
0
0
1
0
1
3
1
2
2
0
0
3
0
1
0
0
0
0
0
1
0
0
9
2
0
1
0
0
3
0
1
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
2
0
1
2
1
0
1
0
0
2
2
0
0
0
2
0
1
2
2
0
2
0
1
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
2
1
2
1
2
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
2
0
1
2
2
0
0
0
1
1
0
1
2
0
1
1
2
0
0
4
1
0
2
2
1
2
0
1
2
0
0
1
0
0
6
0
2
2
1
1
2
1
0
1
0
0
1
1
0
0
0
1
1
2
0
1
2
0
2
2
4
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
3
2
0
1
1
2
2
0
0
0
1
0
1
1
0
1
1
1
1
0
0
1
1
0
1
2
0
0
0
1
0
0
0
1
1
0
0
1
1
0
0
0
1
2
1
1
2
0
0
2
0
0
1
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
1
0
1
0
0
1
2
1
0
0
0
1
1
0
2
0
2
0
2
1
1
0
0
0
0
2
1
0
1
0
2
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
2
0
2
1
1
0
2
1
1
2
1
2
0
1
1
0
0
0
2
2
2
0
1
1
0
0
0
0
0
1
1
23
0
1
0
0
1
2
1
0
0
1
2
2
0
0
0
0
1
2
0
2
0
0
0
1
1
0
0
0
0
0
2
0
0
1
0
2
0
1
2
0
0
0
2
0
0
0
0
0
1
0
0
1
0
1
0
2
0
0
3
1
1
1
0
1
0
0
0
1
0
1
0
0
2
0
0
2
1
0
1
0
1
0
4
0
1
1
0
2
0
2
1
0
1
0
0
0
0
0
1
0
0
0
0
1
1
1
2
0
0
1
0
0
0
0
0
2
0
0
1
0
0
2
0
1
1
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
3
0
1
0
0
0
0
0
0
0
3
0
1
0
0
1
0
2
0
1
0
0
1
0
1
0
2
0
0
0
0
0
2
2
2
1
0
0
0
1
0
0
2
2
0
2
1
0
1
1
0
0
1
1
0
0
0
0
1
2
2
1
2
0
1
1
0
0
1
2
1
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
2
0
1
1
1
1
0
0
1
1
0
0
1
0
0
0
2
2
0
0
1
5
1
2
0
1
1
0
0
0
0
3
2
2
2
0
0
0
0
0
1
1
1
0
0
2
0
0
0
0
0
0
2
0
0
2
1
0
0
1
2
0
0
1
0
0
2
2
2
0
1
1
0
1
3
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
2
0
0
2
2
0
2
2
0
0
0
3
1
2
2
2
1
1
2
0
1
1
0
0
0
0
0
2
0
2
2
0
1
0
1
1
0
1
0
0
0
2
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
2
2
1
2
0
1
0
0
0
1
1
0
1
0
0
1
2
0
0
0
0
1
0
0
1
0
2
1
2
2
0
0
3
1
0
0
2
0
0
0
2
1
2
0
0
1
2
3
1
0
2
1
0
2
2
0
0
1
2
1
0
0
0
0
0
1
2
0
2
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
1
4
0
1
1
0
1
2
0
2
0
0
0
0
1
0
1
1
1
1
2
0
0
0
0
0
1
2
3
0
0
0
2
1
1
2
1
0
2
0
0
0
1
0
1
0
1
2
1
2
1
2
1
0
1
0
0
1
0
2
2
2
0
0
0
0
1
0
2
0
0
1
0
1
0
2
0
1
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
1
0
2
2
1
1
0
1
0
0
0
1
1
1
2
1
0
3
0
0
0
0
0
1
0
0
1
1
0
0
1
0
1
0
0
1
1
1
1
1
2
0
2
0
0
0
0
0
0
0
3
0
1
0
0
0
1
2
2
1
1
1
0
0
0
0
0
1
2
0
0
0
1
1
0
3
0
0
0
0
1
1
0
2
1
0
1
2
0
1
0
0
1
0
3
0
2
0
0
0
0
0
0
3
1
0
1
0
0
0
2
1
3
0
2
0
1
0
0
1
2
0
1
0
1
1
0
0
2
2
1
3
0
0
0
0
0
1
1
1
0
1
1
0
0
0
1
0
0
0
1
0
1
1
0
0
2
2
1
0
1
1
1
1
0
0
0
2
0
2
0
3
3
2
0
2
0
2
1
2
0
2
2
1
1
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
1
1
0
0
2
0
0
0
1
2
1
0
0
0
1
1
0
0
1
0
2
0
0
0
1
0
0
0
0
1
0
0
2
1
1
0
0
0
1
2
0
0
2
0
1
2
0
0
0
3
0
1
0
1
1
1
0
0
0
1
2
0
0
0
0
0
1
2
0
1
6
1
0
0
0
0
2
0
0
0
1
2
1
0
1
0
0
1
1
0
0
0
0
0
1
0
2
1
1
2
0
1
0
0
0
0
1
2
0
0
2
2
0
1
1
2
3
0
0
0
0
1
1
0
1
0
0
2
0
0
0
0
2
0
0
0
1
0
2
0
1
0
0
0
1
0
0
1
0
2
0
0
0
2
2
0
0
0
0
2
0
0
2
1
1
0
0
2
1
0
2
2
2
0
2
1
2
1
0
2
0
1
0
0
2
2
0
1
1
2
2
1
0
0
0
0
0
1
0
1
0
0
1
0
2
1
3
1
0
0
0
0
2
0
1
0
0
1
0
0
1
1
0
1
2
0
2
1
0
0
0
0
2
2
0
1
0
0
0
1
1
3
0
0
1
2
2
0
0
0
2
1
0
0
4
2
1
1
0
0
0
1
0
0
1
0
0
0
1
4
1
0
2
1
2
1
1
1
0
0
0
0
2
0
0
7
0
3
0
0
1
2
1
1
0
0
2
0
0
0
1
2
0
2
1
0
1
2
1
0
0
0
1
0
0
1
0
0
0
2
0
1
1
2
0
0
0
1
0
0
1
1
0
0
2
0
1
1
0
1
0
0
0
0
0
0
0
0
2
0
2
0
3
1
2
2
2
1
1
2
0
0
1
1
1
1
0
1
2
1
1
2
2
0
2
0
0
0
0
2
0
1
1
1
0
2
2
1
1
2
0
2
2
1
0
0
0
0
2
0
2
1
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
2
0
1
2
2
0
2
0
2
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
2
1
1
1
0
0
0
2
2
0
0
0
0
0
0
0
1
1
0
0
1
0
2
0
2
2
1
1
0
2
1
0
0
0
5
0
2
0
1
2
1
0
0
2
0
1
0
2
0
1
0
1
0
0
0
2
0
2
2
0
1
0
0
0
2
0
0
3
2
0
1
0
0
2
0
0
1
0
0
0
1
1
0
2
1
1
0
0
1
0
0
0
0
0
0
2
1
2
1
0
0
2
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
1
0
0
1
0
2
0
0
1
0
0
2
2
0
0
0
0
1
0
3
1
2
0
0
0
0
0
2
1
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
3
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
2
0
2
1
0
2
0
1
0
0
0
1
1
0
0
3
0
1
0
1
0
1
0
0
0
0
2
0
2
0
0
1
0
0
0
1
0
0
0
1
0
1
0
1
1
1
0
0
0
1
1
2
2
0
0
2
1
0
0
2
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
2
2
1
2
2
0
1
1
0
1
0
1
3
0
0
1
0
3
1
0
1
1
1
0
2
1
1
0
1
2
0
0
1
1
0
1
0
0
0
0
0
1
3
0
0
2
0
2
0
0
0
1
2
0
0
0
1
1
0
1
0
1
1
0
0
0
2
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
1
0
2
2
2
0
1
0
2
2
0
1
1
0
2
0
0
2
2
0
0
0
0
1
2
2
0
0
1
0
2
0
0
3
0
0
0
0
0
1
1
4
0
0
0
0
2
0
2
1
0
0
2
1
0
0
1
0
0
0
1
0
2
1
0
0
1
2
0
1
2
0
1
0
0
1
0
0
0
0
1
1
1
2
0
0
0
0
0
2
2
1
1
0
1
0
1
0
2
2
0
0
2
0
0
1
1
2
1
0
2
2
0
0
0
1
1
0
2
3
1
1
0
0
2
0
0
0
1
3
2
0
0
1
1
1
0
1
1
3
2
0
2
0
2
1
1
0
0
1
0
0
0
2
1
2
3
0
2
0
0
0
0
0
1
2
0
0
0
1
2
0
0
1
2
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
1
0
2
0
2
1
0
0
0
2
0
1
0
0
0
1
0
1
0
0
0
1
0
0
1
3
0
1
0
0
0
0
1
0
2
1
0
0
0
2
1
0
0
0
2
0
0
2
0
1
1
0
0
0
2
1
0
1
2
0
2
2
1
2
0
0
4
0
2
2
0
1
0
2
1
0
0
2
0
2
1
2
2
0
2
0
1
0
0
0
0
2
0
0
1
0
0
1
1
0
1
0
0
5
1
1
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
3
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
2
2
0
2
0
0
0
0
0
1
1
2
0
0
0
1
1
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
1
1
2
1
0
0
1
2
0
1
0
1
0
2
0
0
2
0
0
0
2
2
0
0
0
2
0
2
0
1
2
1
0
1
0
0
0
1
1
2
1
1
0
2
0
1
2
2
0
1
1
1
0
0
0
0
2
2
1
0
0
0
1
0
2
0
0
2
0
0
1
0
2
0
0
1
2
0
0
1
1
0
0
0
0
0
1
0
0
0
0
2
2
1
2
0
0
1
0
2
1
0
0
0
1
1
1
0
0
0
2
0
1
2
0
0
1
0
0
0
2
1
1
0
1
0
0
1
0
2
0
1
0
0
2
1
0
0
0
0
1
2
2
1
2
0
0
2
2
2
0
1
0
1
0
0
0
1
0
0
0
1
0
1
0
1
2
0
0
1
2
1
0
0
0
1
0
2
1
2
0
1
0
1
0
0
1
1
1
1
0
0
1
1
0
0
2
0
0
1
0
1
1
3
2
2
2
0
0
0
0
1
0
1
2
2
0
2
2
0
0
0
2
1
1
0
0
1
0
0
0
0
1
3
1
0
0
3
1
0
0
1
3
0
2
0
2
0
1
1
0
1
1
0
1
0
2
0
0
1
2
0
1
0
0
1
1
0
0
0
1
1
1
0
2
0
0
0
0
0
1
2
1
0
0
1
0
0
2
0
0
2
1
0
0
1
0
0
1
2
1
0
0
0
0
0
2
0
0
1
0
0
0
1
1
1
2
0
0
0
0
2
0
0
0
0
2
1
0
0
0
1
1
2
1
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
1
0
2
0
2
2
2
2
0
1
2
3
1
1
0
2
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
2
0
0
1
0
0
1
1
1
2
0
1
2
0
1
0
0
2
0
0
0
0
0
1
0
0
2
1
0
1
0
2
1
2
2
0
0
0
1
0
2
0
1
0
0
2
0
0
1
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
1
0
2
2
0
2
1
0
0
2
0
0
1
2
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
1
0
0
2
1
1
1
0
0
0
1
2
2
0
1
0
2
0
0
2
0
3
0
1
0
1
1
0
0
1
0
1
0
0
1
0
0
0
0
0
1
1
0
1
0
1
1
1
0
2
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
2
2
0
0
2
3
2
1
0
2
1
1
0
1
0
0
2
0
0
0
0
0
0
2
0
1
2
0
2
2
0
0
0
1
0
0
1
2
0
0
1
0
0
0
1
0
0
1
0
0
3
0
1
2
0
0
1
0
1
2
0
0
1
2
0
2
2
2
0
0
2
1
1
1
0
2
0
0
3
2
2
0
1
0
0
1
0
0
0
0
2
0
2
3
0
0
0
0
0
0
0
0
0
1
0
1
2
2
0
1
1
0
1
0
3
0
2
1
0
0
2
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
2
0
1
0
2
2
2
2
2
1
0
1
2
2
1
1
0
0
0
2
0
2
2
0
0
2
0
2
2
1
1
0
2
0
1
2
0
1
0
0
0
2
0
0
2
0
2
1
0
1
1
0
1
1
1
0
0
1
1
1
0
0
1
1
0
1
0
0
3
0
0
1
0
2
0
0
0
1
1
1
0
0
1
0
1
1
2
0
0
3
0
1
3
0
1
1
2
1
0
0
1
1
1
0
2
1
1
0
0
1
2
1
0
0
0
0
1
2
2
0
3
1
1
2
1
2
0
0
0
0
2
2
1
3
1
3
0
2
0
2
0
0
0
0
1
0
0
0
2
0
1
0
0
2
0
2
2
1
0
2
0
0
1
0
1
0
0
0
2
3
0
0
0
0
1
2
1
3
1
0
1
0
3
1
2
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
1
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
1
0
0
1
1
0
2
1
0
2
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
2
3
1
1
1
0
1
2
0
2
1
0
0
2
0
0
0
1
2
2
0
0
0
0
2
0
0
2
1
0
0
2
2
0
0
0
2
0
1
2
3
0
0
0
0
0
0
1
0
2
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
2
1
1
1
0
0
2
0
0
0
2
1
1
0
0
1
0
1
0
0
0
0
1
0
0
0
2
2
1
0
0
0
1
1
0
1
0
1
0
3
0
1
1
0
0
0
0
2
0
2
2
0
0
0
0
2
1
0
0
0
1
1
2
0
1
0
1
2
0
0
0
1
1
0
1
0
2
0
0
0
0
0
2
0
0
0
1
0
1
0
2
0
0
1
1
0
1
2
2
0
2
0
2
0
2
0
0
1
1
0
0
0
1
0
1
1
1
0
0
0
2
2
1
0
1
1
1
0
1
2
2
1
2
1
2
0
2
2
0
0
0
2
2
0
2
0
1
1
1
1
1
1
0
0
0
0
2
0
0
2
1
1
0
1
0
1
0
0
1
0
2
0
2
0
0
0
2
1
0
1
1
1
0
1
2
2
0
2
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
1
0
0
1
0
1
0
1
0
0
1
0
1
2
5
0
1
0
0
2
1
0
1
1
1
0
4
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
1
0
1
0
0
2
2
1
0
0
1
2
1
0
0
0
2
0
0
0
0
2
1
1
0
0
0
0
1
0
1
0
0
0
2
1
0
0
1
0
0
2
0
2
0
2
0
0
1
0
1
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
4
1
0
1
0
3
2
0
1
0
0
2
0
0
0
0
0
2
0
1
1
0
0
0
0
0
2
1
0
1
1
0
0
2
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
1
1
1
0
1
0
0
0
0
0
0
2
1
0
0
2
1
0
1
1
2
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
1
0
2
0
1
2
0
0
0
2
0
0
1
0
0
2
2
0
0
1
0
0
0
1
2
2
1
0
0
1
0
0
1
0
1
0
0
0
2
0
1
0
2
0
0
1
2
0
0
0
0
2
0
0
0
0
1
1
1
0
1
1
0
0
2
2
0
1
0
0
1
0
2
0
2
2
3
2
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
3
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
2
1
0
0
2
0
0
0
0
1
0
0
1
0
0
1
1
2
0
1
2
0
0
0
1
1
0
1
2
0
0
2
1
0
0
1
2
0
0
1
0
1
0
1
2
0
2
0
0
0
0
0
2
0
0
1
0
0
0
2
4
1
1
0
1
1
1
0
0
1
0
0
1
0
3
0
1
0
1
1
1
2
1
1
0
0
0
0
0
1
1
1
1
1
0
0
1
2
0
0
1
0
1
0
1
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
1
2
0
0
0
2
0
0
0
0
0
1
0
2
1
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
3
1
2
0
0
0
2
1
2
0
2
1
1
0
0
1
0
2
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
1
1
0
0
2
0
1
2
1
0
1
0
0
1
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
2
1
0
1
0
0
1
0
1
0
2
1
0
0
0
2
0
0
1
2
0
0
0
0
2
2
1
0
0
0
1
1
0
1
0
0
0
0
1
2
1
0
2
1
0
1
0
0
0
0
2
0
1
0
0
1
0
0
1
0
0
1
0
0
2
1
2
1
0
0
0
1
0
1
2
1
0
2
0
2
1
0
1
0
0
2
2
1
0
0
0
0
0
0
0
0
2
2
2
1
1
2
1
0
2
0
0
1
0
0
1
0
0
0
1
2
1
0
2
2
2
0
0
2
0
1
1
0
0
2
2
2
0
0
0
0
0
1
0
0
2
0
0
1
1
1
0
0
0
1
2
0
0
2
2
0
1
2
1
2
2
0
0
2
2
0
0
0
1
0
0
2
1
0
0
0
0
0
1
1
0
1
0
2
1
1
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
1
2
1
0
0
1
2
0
0
0
1
0
2
2
2
0
0
0
0
0
0
2
0
1
1
0
0
1
1
1
2
0
0
2
1
2
2
0
1
2
0
0
1
2
0
0
1
0
0
3
0
2
1
0
0
0
0
0
0
0
0
2
1
0
16
1
0
1
1
0
0
0
0
0
2
1
1
2
2
0
0
2
0
0
0
0
1
1
3
1
2
0
0
1
0
0
0
0
0
1
2
1
4
1
0
4
0
0
2
0
1
1
1
0
1
0
0
0
1
0
1
2
2
0
0
1
0
0
2
0
0
1
1
0
1
0
0
0
1
3
0
2
2
0
2
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
2
0
0
0
0
0
4
0
0
0
0
2
1
3
1
1
2
0
0
2
0
0
0
0
0
1
2
2
0
2
1
1
0
0
2
0
0
0
0
1
0
2
0
2
1
2
0
0
0
2
0
0
2
0
1
0
2
0
0
1
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
2
0
2
1
0
1
0
0
1
3
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
2
3
2
0
1
2
0
0
2
1
1
2
1
0
0
2
1
0
0
1
3
1
2
0
1
0
0
0
3
1
0
3
1
2
1
2
2
0
0
0
1
0
0
1
1
1
0
2
0
2
0
0
2
0
0
2
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
1
0
1
2
0
0
2
0
0
0
0
2
0
1
0
2
2
2
1
2
1
2
2
0
0
0
0
0
0
0
1
0
0
1
1
2
0
1
2
0
1
1
0
0
1
0
2
2
0
0
0
1
0
0
1
0
0
0
0
0
0
4
0
1
0
2
0
1
1
0
0
1
0
2
0
2
0
0
1
1
0
0
0
0
0
6
0
0
5
0
0
2
2
0
0
0
1
0
2
1
1
2
0
3
1
0
1
0
0
0
2
1
1
1
1
0
0
0
1
2
0
0
1
0
2
1
0
1
3
2
0
1
0
0
0
2
1
0
0
0
0
0
2
0
0
0
2
1
0
0
2
1
0
2
0
1
0
2
2
0
0
0
0
1
0
0
2
0
1
1
0
1
0
0
0
0
2
1
2
0
0
1
0
1
0
0
1
0
1
0
1
0
2
0
0
0
0
0
0
1
1
1
1
2
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
1
4
0
0
0
0
0
0
2
1
2
0
2
0
0
2
0
1
1
3
0
0
1
2
2
1
1
1
2
2
0
0
1
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
1
1
0
0
0
1
1
0
1
2
2
1
1
0
0
0
0
1
0
2
0
1
0
0
1
3
2
2
0
1
1
1
0
2
1
0
0
0
0
2
2
1
1
1
0
0
3
0
1
0
0
0
0
2
1
0
2
0
0
0
1
1
0
0
0
0
2
0
1
0
0
3
1
1
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
2
2
0
0
1
2
1
1
0
0
0
0
2
1
2
1
3
2
2
1
0
3
0
0
0
0
0
0
0
0
3
0
2
2
2
0
0
0
0
0
2
2
0
0
0
2
0
0
0
1
1
1
0
1
1
0
0
0
1
0
2
0
0
2
0
0
0
1
0
0
0
2
0
0
1
3
0
0
1
1
2
1
1
0
1
0
0
2
0
0
0
2
0
1
0
1
0
4
0
2
0
0
0
3
2
2
2
1
0
0
1
1
0
1
0
1
3
0
2
0
1
0
0
0
2
2
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
1
2
0
1
0
0
1
2
2
1
2
2
0
1
0
2
0
1
0
0
0
0
2
1
0
0
13
0
0
3
0
1
0
0
0
0
0
0
2
0
0
1
1
1
0
1
0
0
0
0
1
1
2
0
0
2
0
1
1
1
0
2
0
1
0
2
0
0
2
0
0
0
1
1
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
1
0
0
0
0
2
0
0
0
0
1
1
0
1
2
0
0
0
1
2
0
0
0
0
2
1
0
2
1
0
2
2
1
1
0
2
1
0
2
2
0
2
0
0
1
0
2
1
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
1
0
0
1
2
0
1
1
0
1
1
1
2
0
0
0
0
0
6
0
0
0
0
0
0
2
0
2
1
2
0
1
0
0
0
0
0
3
1
0
1
0
0
0
0
0
0
3
0
2
0
1
0
0
0
0
1
2
3
1
0
1
1
3
0
0
2
1
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
2
2
0
2
0
0
1
2
0
0
2
1
1
1
0
1
2
0
1
0
0
1
1
0
1
0
2
0
1
2
1
2
0
0
2
1
2
0
1
1
2
2
2
0
2
0
1
0
0
2
0
2
0
0
0
2
0
1
1
1
0
0
0
0
2
0
0
1
2
2
1
0
2
1
0
2
2
0
0
0
1
2
0
0
0
1
2
1
2
0
0
0
0
0
0
0
0
1
0
0
3
0
1
0
4
2
1
3
0
1
0
0
2
0
0
1
0
0
0
1
1
2
0
0
1
0
1
1
0
1
2
0
2
1
1
0
0
0
0
1
3
1
1
0
2
0
0
2
0
1
1
0
2
0
0
0
0
2
0
0
1
1
0
1
0
0
0
0
1
1
0
2
2
2
1
2
0
1
0
1
0
0
0
0
1
0
1
0
2
2
2
0
1
0
0
0
2
0
0
1
1
0
0
0
1
2
2
2
0
2
1
2
0
2
1
1
1
0
0
0
1
0
1
1
1
1
0
2
0
0
0
1
2
0
0
1
0
2
1
1
1
0
1
0
1
0
2
0
0
0
1
1
0
0
0
1
0
1
0
2
1
2
0
1
2
0
3
2
0
1
0
0
0
0
2
0
2
0
0
1
2
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
1
2
1
1
1
0
0
1
0
0
1
1
2
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
1
1
0
1
1
1
0
3
0
2
0
0
0
0
1
3
0
1
1
0
0
0
2
0
0
1
2
0
1
3
0
0
0
0
1
1
2
0
0
0
0
1
0
2
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
3
0
0
2
2
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
2
0
3
1
0
1
0
2
0
1
0
1
0
0
1
1
0
1
1
0
0
4
3
0
1
0
1
0
0
0
1
2
2
0
2
0
1
0
1
0
1
1
0
0
1
0
0
2
1
0
2
0
1
0
1
0
0
2
1
2
0
1
0
1
0
1
0
0
2
2
2
0
0
0
1
0
2
0
2
0
1
2
0
0
1
3
0
1
0
2
0
0
1
0
2
0
1
2
1
0
1
1
2
0
0
1
0
0
0
0
0
2
1
1
0
0
1
1
0
1
2
0
2
0
0
1
1
0
1
0
0
2
0
2
0
1
0
2
1
0
0
0
0
0
0
0
1
0
1
0
0
2
0
1
0
2
0
2
1
0
1
0
2
1
0
0
2
0
1
1
1
0
0
0
1
3
3
0
0
1
0
0
0
1
0
2
0
1
0
1
0
0
0
0
0
2
1
0
2
0
0
2
1
1
0
1
0
0
0
1
1
0
1
1
0
0
1
2
2
2
1
1
0
1
2
1
2
0
0
1
0
1
0
1
0
0
0
0
1
2
1
2
0
0
1
2
0
0
0
1
0
1
0
2
1
0
0
1
0
1
2
0
0
1
0
2
0
2
1
1
0
0
1
1
0
2
3
2
0
0
0
0
0
0
1
0
0
0
1
0
0
2
4
2
1
1
0
2
0
0
1
1
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
1
2
2
1
1
0
1
0
1
2
3
0
3
0
0
2
1
1
1
2
0
0
2
0
0
0
0
3
0
1
3
1
0
0
2
0
0
1
2
0
2
1
0
0
0
0
2
0
0
1
3
0
1
1
0
1
2
1
1
0
0
0
1
2
2
0
0
0
2
2
0
1
2
1
0
0
0
0
0
1
1
1
0
0
2
0
1
0
2
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
2
1
3
1
1
1
2
2
2
0
1
0
1
0
1
0
0
1
2
1
0
1
2
1
0
0
0
3
0
0
0
2
1
2
0
0
0
2
2
0
0
1
1
1
0
1
1
1
0
2
0
0
0
2
2
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
2
1
1
0
0
2
2
2
0
0
0
0
0
0
2
0
0
1
0
2
1
0
0
2
0
0
0
0
2
1
2
0
0
0
1
0
0
0
1
0
1
0
0
1
1
3
0
2
2
0
1
0
3
1
0
0
0
2
3
0
2
0
1
1
0
0
1
1
0
1
2
0
0
0
2
1
0
3
1
7
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
2
2
0
1
1
0
0
0
0
2
2
1
1
0
2
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
2
0
1
1
0
1
2
1
0
0
0
1
0
1
0
1
0
2
1
0
2
2
0
2
0
2
1
2
0
0
1
1
0
1
1
2
2
0
0
1
1
0
2
1
0
1
0
0
0
0
0
0
1
2
0
2
0
0
0
1
0
1
1
1
2
1
0
2
1
2
1
1
1
0
0
0
2
0
1
0
2
1
0
0
0
0
2
1
0
0
1
0
1
0
0
1
0
0
0
1
0
1
0
0
2
1
2
1
1
0
1
0
0
0
0
1
1
2
0
0
1
3
2
0
0
0
1
0
0
0
1
0
1
1
2
1
1
0
0
1
1
2
3
0
0
0
0
1
0
0
0
2
0
3
1
0
0
0
0
0
2
2
1
0
2
0
0
0
5
0
0
0
0
1
0
2
0
1
1
0
0
2
0
0
1
0
0
2
1
2
1
0
1
1
0
0
2
0
1
1
2
2
2
2
2
0
1
0
2
0
0
0
1
0
1
2
2
2
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
3
0
1
0
1
0
1
0
0
1
1
2
0
2
0
0
0
1
0
0
0
1
2
0
2
0
1
1
0
1
0
1
0
0
1
1
1
1
0
2
1
0
0
2
0
1
1
0
1
0
1
3
2
0
3
2
2
0
0
0
0
0
1
1
2
0
0
0
1
0
2
0
0
0
0
1
3
2
0
0
0
1
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
2
0
0
2
2
0
0
1
0
1
0
2
0
0
2
2
0
2
0
0
0
0
4
1
0
1
0
2
1
0
1
0
0
0
3
0
1
2
0
0
1
1
0
2
0
1
1
2
0
2
0
2
2
0
0
0
0
0
0
1
0
2
1
0
0
1
1
0
0
0
1
2
1
0
1
1
1
1
2
0
1
1
0
0
0
0
1
0
0
0
2
1
0
0
1
3
0
0
0
1
0
2
2
0
0
1
2
1
0
1
2
2
0
0
0
2
0
0
0
0
0
0
3
2
0
2
0
0
0
0
1
0
1
1
0
0
0
1
2
2
0
1
0
1
0
0
0
1
2
1
2
0
2
0
0
2
0
1
0
2
2
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
2
1
0
1
0
0
0
2
0
2
1
0
1
2
1
0
1
1
1
0
0
1
2
0
0
2
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
2
0
1
0
1
0
2
0
1
1
0
0
0
0
0
1
2
1
0
0
1
1
0
0
0
0
0
2
0
2
1
0
0
2
0
0
1
1
0
2
3
0
0
0
2
3
0
1
2
0
0
0
0
0
0
0
1
2
0
1
0
1
4
2
1
1
2
0
0
0
0
0
0
0
2
2
2
2
0
0
1
0
1
0
1
0
2
0
1
1
1
3
3
2
0
1
0
2
0
0
0
0
0
0
2
4
2
0
0
0
0
0
1
2
1
0
0
2
1
3
0
0
1
0
0
0
2
0
1
1
0
0
0
1
0
2
1
0
2
2
2
0
2
1
0
0
0
2
0
2
2
0
0
0
1
0
2
3
2
1
0
0
0
0
1
1
0
2
0
1
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
4
0
1
2
1
0
2
1
1
1
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
2
1
1
2
0
2
0
0
2
0
1
0
1
0
1
1
1
0
0
0
0
2
1
0
1
0
0
1
0
0
1
0
2
0
2
1
1
0
0
0
2
0
0
2
0
1
0
2
3
1
2
2
0
0
0
1
0
2
0
0
0
1
0
2
0
1
0
0
1
0
0
0
0
2
0
3
0
0
0
2
2
0
1
1
2
0
0
0
0
3
0
0
0
0
0
2
2
1
0
1
1
1
2
0
1
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
2
0
2
1
2
0
0
1
1
0
2
2
1
0
2
1
0
2
2
0
2
1
1
0
2
1
1
1
0
0
1
0
0
1
2
1
0
0
0
0
2
0
0
1
2
1
1
0
0
2
0
0
0
1
0
0
0
0
0
1
0
2
1
0
0
1
2
2
2
2
0
1
0
0
1
0
1
1
1
0
0
0
0
2
1
0
0
2
1
0
0
1
0
2
0
0
1
1
2
0
2
0
2
2
1
2
2
1
2
2
0
0
0
0
1
0
0
0
0
0
0
0
1
5
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
2
0
1
0
0
0
1
1
0
1
1
1
2
2
0
0
1
3
0
0
0
1
1
0
1
0
0
1
1
2
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
2
1
2
1
1
1
2
0
3
2
1
0
0
0
0
0
0
0
1
2
1
2
0
1
0
0
2
0
4
1
0
0
0
0
1
0
2
1
3
3
0
2
0
0
0
0
2
2
1
0
0
1
1
0
0
2
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
2
0
1
1
2
1
2
2
0
2
1
0
0
3
2
2
0
2
0
2
2
0
1
2
0
2
0
0
0
2
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
1
2
0
2
1
1
4
3
0
0
0
1
0
1
0
0
0
1
1
0
0
0
1
0
2
1
0
0
0
1
0
2
0
2
0
0
2
2
0
0
0
0
0
0
2
1
1
2
2
0
2
1
0
0
1
1
0
1
0
2
1
0
0
2
0
2
3
0
1
1
1
0
1
1
1
1
0
0
1
0
1
1
0
2
0
0
1
0
2
0
0
0
0
3
1
1
1
0
3
0
1
0
1
0
0
0
0
1
1
0
0
0
0
2
1
1
0
0
1
0
0
2
1
1
0
2
0
1
0
1
0
1
2
0
1
0
0
0
0
0
1
0
2
0
2
2
1
0
0
1
0
1
2
0
0
2
0
0
2
1
1
0
0
1
1
0
0
2
0
1
1
1
0
0
1
0
0
0
0
0
0
0
2
0
1
3
1
0
1
1
0
2
0
0
1
0
0
0
0
0
0
2
1
1
1
1
0
0
2
1
0
2
1
0
0
1
2
1
2
0
1
0
0
1
0
0
1
1
0
0
0
0
0
2
0
1
2
1
0
1
0
0
0
0
2
0
0
0
0
1
2
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
2
0
1
1
0
1
0
0
0
0
2
0
0
2
1
1
2
1
0
1
2
1
0
0
2
0
0
0
2
0
1
1
2
1
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
2
0
0
1
2
0
1
0
2
0
1
0
0
0
0
0
2
1
0
1
2
1
1
2
0
2
0
0
1
1
2
0
0
2
2
1
0
0
1
1
1
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
1
2
1
0
0
0
0
0
0
0
2
2
1
0
1
0
0
0
1
0
5
0
0
2
0
2
1
1
1
1
0
1
2
0
0
0
0
1
1
0
1
1
1
1
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
1
2
0
2
0
2
2
0
0
2
0
2
0
0
0
1
0
3
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
1
2
0
1
2
0
0
1
1
1
0
0
0
1
0
0
1
0
1
1
0
2
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
3
1
0
1
0
2
1
0
1
0
2
0
1
1
0
0
0
2
1
2
0
0
1
0
2
0
1
0
1
0
2
1
1
2
2
2
1
1
0
0
1
0
0
2
0
0
2
0
2
2
0
0
0
2
0
0
2
0
0
0
1
0
2
0
2
0
3
0
2
0
0
2
0
0
0
0
0
0
2
1
2
0
0
1
0
0
1
0
0
2
0
1
0
3
2
0
0
0
0
1
0
0
0
1
2
0
2
0
2
0
1
0
0
0
0
2
0
2
0
0
0
1
3
2
1
1
0
0
0
0
0
0
0
1
0
0
2
1
1
2
0
0
1
1
2
0
4
1
1
0
0
0
2
2
0
0
2
0
0
0
0
0
2
0
2
1
1
0
1
1
1
0
0
0
0
2
1
0
0
0
1
2
1
0
2
0
1
0
2
2
0
0
1
5
0
0
2
3
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
3
0
2
0
2
3
2
0
1
1
1
0
1
2
0
1
1
0
1
2
1
0
2
2
1
1
0
1
1
1
0
0
0
0
0
0
0
1
0
2
2
0
1
2
0
0
2
0
2
0
0
2
0
1
2
0
0
1
0
0
0
0
0
0
0
3
1
0
3
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
1
0
2
1
0
0
0
0
0
1
0
0
1
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
2
0
1
0
1
1
0
0
1
0
0
0
0
1
1
0
1
1
2
2
0
1
1
1
3
0
0
2
0
0
4
0
2
1
2
0
0
0
0
0
1
1
1
3
0
0
2
2
1
2
0
2
2
2
0
0
0
2
0
0
0
0
0
1
0
0
3
0
1
3
0
0
0
0
0
0
2
1
0
2
2
0
2
2
0
0
0
2
1
0
0
0
2
0
0
0
1
0
1
0
1
0
1
0
1
2
1
1
1
0
1
2
2
0
0
1
2
1
0
1
0
2
0
2
1
0
0
2
2
0
0
0
0
2
0
0
2
0
2
1
0
0
0
3
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
2
2
0
0
0
1
1
2
0
1
0
0
2
0
1
1
0
1
0
0
2
1
0
0
1
0
2
0
0
1
1
1
0
1
1
0
0
1
1
1
0
0
0
0
1
0
2
1
0
1
0
0
2
0
1
0
0
0
1
1
0
0
0
0
2
2
1
0
2
0
1
2
1
2
1
0
0
2
1
0
0
1
0
0
1
0
0
0
0
0
1
2
0
1
1
2
1
0
1
2
0
1
1
0
2
2
0
1
0
1
0
0
1
0
0
1
0
1
0
1
0
1
1
0
0
2
2
0
1
0
2
2
0
1
0
0
1
1
0
0
2
1
1
0
0
1
2
1
0
0
1
0
1
0
0
0
2
0
1
0
2
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
2
1
0
1
0
1
1
2
0
0
0
1
0
1
0
0
0
0
2
0
0
0
2
0
2
1
0
3
1
2
2
1
2
1
2
0
0
2
0
0
0
0
2
1
1
0
1
0
0
2
1
0
0
0
4
1
0
0
0
0
1
0
1
1
1
1
1
0
0
0
7
0
2
0
1
0
1
0
1
1
0
1
0
1
1
0
0
1
2
0
0
0
0
2
2
0
0
2
0
0
1
0
1
0
0
2
0
0
2
0
0
0
2
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
1
2
2
1
2
0
0
0
2
0
0
3
2
0
0
0
1
0
2
2
0
2
0
0
0
0
0
2
0
0
2
4
2
3
0
0
0
0
2
2
1
0
0
0
0
0
2
2
1
1
0
0
2
0
0
0
0
1
0
0
2
0
1
0
0
1
1
1
0
0
0
0
3
1
0
1
1
2
0
3
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
1
2
0
1
0
0
2
0
2
0
2
1
2
1
0
0
0
1
1
1
2
1
1
0
0
1
0
0
1
1
0
2
1
2
0
2
0
1
0
0
1
1
0
0
1
1
0
2
2
1
1
1
0
1
1
0
0
0
2
0
2
0
0
2
1
1
2
0
0
1
0
1
1
1
3
0
0
1
0
0
0
1
2
0
0
0
2
0
2
1
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
2
0
0
1
1
0
0
0
0
0
2
1
1
1
7
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
2
1
1
0
0
0
1
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
1
2
0
0
0
1
0
2
1
0
0
0
2
1
0
1
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
2
0
0
1
0
0
1
1
0
0
0
0
0
2
0
2
1
1
0
0
2
0
0
0
1
0
0
0
0
0
1
1
1
0
2
2
2
0
0
1
0
1
1
0
1
0
1
0
2
2
0
0
0
0
2
0
1
0
0
0
1
1
0
0
0
2
0
1
2
0
1
0
0
0
0
1
0
1
2
0
0
2
1
0
0
0
1
1
2
0
0
0
1
1
0
2
2
1
0
0
0
1
0
0
0
1
0
4
0
0
0
0
2
0
0
1
0
1
2
0
0
0
1
2
1
1
3
0
2
1
1
2
0
0
0
0
0
4
2
0
0
2
0
2
2
0
0
0
0
2
2
0
0
0
1
0
0
0
2
1
0
0
1
0
0
2
0
0
0
0
1
0
0
2
0
0
1
0
2
0
0
0
0
2
0
0
2
0
3
0
1
1
2
1
0
0
1
0
1
0
0
0
3
1
2
1
0
0
1
0
0
0
1
0
2
0
0
0
2
2
2
2
1
0
2
0
2
0
1
1
1
1
0
1
1
2
0
1
2
1
0
2
0
1
0
0
0
0
0
0
4
0
0
2
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
1
2
1
2
1
0
0
0
0
2
2
2
0
0
1
1
0
0
1
1
0
2
2
0
2
0
2
2
0
0
1
0
1
0
1
0
0
0
1
0
1
2
0
0
2
1
2
0
0
1
2
2
0
2
0
0
0
0
0
0
0
0
0
2
0
7
3
1
1
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
2
2
1
2
0
1
1
0
1
0
1
2
2
0
0
1
2
2
2
0
1
0
0
0
0
2
1
0
0
1
0
0
0
0
0
1
1
1
1
1
0
0
0
2
0
0
1
2
0
0
0
0
1
2
0
2
0
1
0
0
0
1
0
1
2
0
0
1
0
2
1
0
2
0
0
2
2
0
0
2
0
0
0
0
0
2
0
1
0
0
0
3
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
3
0
1
0
1
2
0
0
1
0
1
0
0
1
2
0
0
0
0
0
1
1
0
1
0
0
0
2
1
0
2
0
2
3
1
2
0
2
0
4
2
1
0
1
1
1
2
0
0
0
0
2
1
0
0
0
2
0
0
2
1
1
1
1
1
1
1
1
0
2
1
0
1
0
0
1
2
2
0
1
1
0
1
2
1
2
0
0
0
2
2
1
0
2
1
0
0
0
1
2
2
0
0
0
0
1
0
1
0
1
1
1
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
2
0
1
0
2
1
0
1
0
1
1
0
0
1
0
0
1
0
0
0
2
1
0
2
0
0
0
0
0
3
1
0
2
2
1
0
0
2
1
2
1
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
2
0
0
0
1
1
1
0
0
0
0
0
0
1
0
1
2
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
2
0
4
2
0
4
2
2
2
0
2
1
0
0
2
0
0
0
1
0
0
0
0
1
0
0
2
0
0
2
0
0
0
1
0
2
1
1
2
0
0
1
0
0
0
1
2
2
0
2
1
0
0
2
0
1
0
0
1
0
0
2
1
0
2
0
2
0
0
0
0
0
0
2
1
0
0
0
2
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
1
0
1
0
2
0
1
0
0
0
0
2
0
0
0
2
0
0
1
2
2
2
0
2
0
0
0
0
1
0
2
0
0
1
0
0
0
1
0
0
1
0
2
0
0
1
0
2
0
1
1
0
2
0
1
1
0
1
3
0
0
1
2
2
0
0
2
0
1
0
2
0
2
0
0
3
0
0
1
1
0
0
0
0
1
0
0
1
0
1
1
2
0
0
2
1
0
2
0
0
0
0
1
0
2
3
0
0
0
1
1
1
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
2
2
2
1
2
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
2
1
0
1
3
0
0
5
0
0
1
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
1
0
0
1
0
0
2
0
1
0
2
1
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
2
0
2
2
0
2
0
0
1
0
1
0
0
1
1
0
1
2
2
3
1
0
0
1
0
7
0
0
2
0
0
1
2
0
1
1
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
1
0
0
0
1
2
1
2
3
0
0
1
0
0
1
0
0
0
0
1
2
0
0
1
2
1
0
1
2
0
0
2
0
1
0
2
1
1
0
2
0
1
0
0
2
1
0
0
1
0
0
0
3
2
0
1
0
0
0
0
1
1
1
2
0
2
0
2
0
1
0
0
1
0
0
0
1
1
1
2
1
1
2
0
0
0
0
2
2
2
2
2
0
0
0
0
0
0
3
0
1
1
1
0
0
2
0
2
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
1
0
0
0
1
0
1
1
0
1
1
2
1
0
0
0
2
1
1
1
0
2
0
1
0
2
0
1
0
2
0
0
0
3
1
1
0
1
1
0
0
0
1
2
2
1
0
0
0
0
2
2
1
3
0
1
2
0
0
2
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
2
0
0
2
0
2
1
0
2
0
1
2
2
1
2
3
2
1
0
0
1
0
1
1
0
2
0
3
0
2
1
0
0
2
2
3
1
0
1
0
3
0
1
0
1
0
0
0
1
1
0
2
0
1
1
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
1
2
0
2
0
0
1
1
2
6
1
0
0
0
0
0
0
3
0
2
1
0
1
1
0
0
0
0
0
0
1
0
2
1
2
0
0
3
0
2
1
0
1
2
0
0
0
0
0
0
1
2
0
1
0
1
1
0
0
1
1
0
0
0
0
0
3
2
0
1
1
2
0
2
1
0
0
0
0
0
0
0
0
1
0
0
2
0
1
2
0
0
2
0
0
1
0
1
0
0
1
2
0
0
2
0
0
2
1
2
0
0
1
0
2
0
2
2
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
2
2
0
3
1
0
1
0
0
1
0
2
0
2
1
0
0
2
0
1
0
0
0
2
0
0
0
0
1
2
0
0
1
2
0
0
0
0
1
2
1
0
2
1
0
0
0
1
0
2
0
0
1
0
0
1
0
0
0
2
0
2
1
0
0
1
0
2
0
2
0
2
1
0
0
1
0
2
0
3
0
2
1
1
1
0
3
1
2
0
1
1
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
2
1
1
0
4
0
0
1
1
0
0
0
0
1
0
0
2
0
0
2
1
0
2
0
0
2
1
1
0
0
2
2
0
0
0
1
0
0
1
0
0
2
0
2
0
0
1
1
0
0
0
2
2
1
5
1
0
2
0
0
1
2
2
2
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
2
0
0
0
1
1
0
5
2
1
2
0
0
0
0
1
1
0
0
9
0
2
0
2
0
1
0
2
0
0
0
0
0
2
1
2
1
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
2
0
2
0
0
0
0
2
2
2
0
0
0
2
2
2
1
0
0
1
0
1
1
0
1
0
2
3
0
0
0
0
0
2
0
0
0
2
0
2
2
1
0
0
0
2
2
2
0
0
2
0
0
0
0
1
0
1
1
0
2
1
0
0
0
0
1
0
0
0
0
1
3
1
0
0
0
0
0
1
1
1
0
1
0
1
0
0
0
0
0
0
0
1
2
1
0
0
2
2
0
0
0
0
2
0
0
1
0
0
2
1
0
1
1
1
0
0
0
2
0
1
1
1
0
2
0
1
1
0
0
1
0
0
0
2
2
2
4
2
0
1
0
1
0
2
1
0
1
0
0
0
1
0
1
1
1
2
0
0
1
1
2
2
2
0
2
1
2
0
0
0
1
0
2
0
1
0
0
1
0
2
1
2
1
0
1
0
0
1
0
1
0
0
0
0
2
0
2
2
0
2
0
0
1
1
2
0
0
2
3
0
0
2
0
0
2
0
0
0
2
1
0
2
0
2
1
2
0
0
0
0
0
0
3
2
1
1
0
1
2
0
2
1
1
1
0
1
1
0
0
0
0
0
1
2
0
0
0
1
0
3
0
1
1
2
1
1
1
0
1
1
1
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
1
1
1
0
0
1
0
2
0
2
0
0
1
0
0
0
1
2
0
1
0
1
0
0
1
0
0
2
0
0
0
0
0
0
2
3
1
2
0
0
1
3
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
4
0
0
2
2
0
0
1
0
1
2
0
0
1
0
0
1
1
2
0
0
0
1
1
2
0
1
1
0
0
2
0
0
0
1
0
1
0
1
0
0
1
0
2
0
0
2
1
1
0
0
0
0
1
0
0
1
0
1
0
0
2
0
0
2
0
2
2
0
0
2
2
0
1
2
0
0
0
0
1
0
0
0
0
1
0
2
0
1
0
2
1
0
0
2
0
0
1
2
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
2
0
0
2
0
1
1
5
0
0
0
2
0
2
1
0
0
0
2
2
0
0
2
2
0
1
0
0
2
2
0
0
1
0
1
1
0
1
2
1
0
0
0
2
1
1
0
0
0
1
2
2
1
1
0
0
1
0
0
1
3
0
0
0
1
0
0
2
2
2
1
0
1
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
1
3
0
2
0
2
1
0
2
1
0
0
0
0
2
0
0
1
0
0
0
2
1
0
3
0
0
0
0
0
1
1
0
0
2
1
0
1
1
0
2
0
0
0
2
2
0
2
2
1
0
0
0
0
0
0
0
3
0
0
2
1
0
0
1
1
0
2
0
1
1
0
0
0
1
0
0
0
1
1
0
0
0
1
0
1
2
1
0
0
0
0
0
0
2
0
0
2
0
1
0
0
1
1
0
1
0
0
2
0
1
0
0
1
1
0
1
0
1
0
1
1
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
1
2
0
0
0
2
0
0
0
2
0
0
1
2
0
1
2
0
2
0
0
1
0
1
2
1
2
0
2
1
1
0
1
0
0
2
0
0
0
0
1
1
0
2
5
0
2
0
2
1
2
1
2
0
1
2
1
0
0
0
1
1
0
1
0
2
2
0
0
2
1
2
0
1
0
2
0
2
1
2
1
0
1
0
0
1
2
0
2
1
1
1
1
0
2
0
2
0
0
1
0
0
0
1
1
1
2
0
0
0
2
0
1
0
4
0
0
2
2
0
3
0
2
0
0
1
0
1
1
3
0
2
0
0
0
0
0
2
0
2
1
2
1
2
0
0
0
0
0
0
0
1
1
1
1
1
1
0
3
0
2
2
2
1
0
2
2
1
2
0
0
0
0
0
0
0
4
0
1
0
1
0
1
1
0
3
0
2
2
0
0
0
2
0
0
2
0
1
0
0
0
1
0
0
0
0
0
2
2
1
0
3
2
2
2
0
0
0
1
2
2
0
0
0
0
1
0
1
0
2
3
0
0
1
0
2
1
0
0
0
0
2
1
0
1
0
1
2
0
2
0
2
2
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
1
0
0
0
2
0
3
3
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
1
0
2
2
0
0
0
1
4
1
0
0
0
0
0
1
2
3
1
0
0
0
2
1
2
1
0
2
1
0
2
0
0
2
0
1
1
2
0
1
0
0
0
1
0
2
0
2
1
1
1
1
1
0
0
0
2
2
0
2
0
0
2
2
0
0
1
0
0
0
1
0
2
1
2
0
2
0
1
1
0
0
1
0
1
0
0
0
2
1
0
0
1
0
0
0
2
2
0
0
2
0
1
2
1
2
0
2
0
2
1
1
0
0
1
1
1
0
0
0
0
1
1
4
0
3
2
2
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
1
0
1
0
0
0
2
0
2
0
0
1
1
0
2
0
0
1
0
1
1
0
0
0
0
0
0
1
0
1
0
2
0
0
1
0
1
0
0
2
0
0
0
2
2
0
1
0
0
0
0
0
0
2
0
0
2
1
1
2
1
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
2
1
1
0
0
0
0
1
0
0
0
2
1
0
0
1
1
0
2
0
0
1
0
1
1
0
1
0
0
2
2
0
1
0
0
2
0
1
1
0
1
1
1
1
1
0
2
3
2
0
1
1
0
2
1
0
2
0
0
2
1
2
1
0
0
1
0
2
0
0
0
0
1
0
0
0
0
1
1
2
1
2
1
0
0
2
2
1
0
2
1
0
1
0
0
2
0
1
2
3
0
0
2
0
0
0
1
0
2
0
0
1
1
0
2
2
0
0
2
1
1
0
1
0
2
1
2
1
0
0
0
1
0
1
2
0
1
1
0
0
0
0
1
0
0
1
2
3
1
0
2
0
0
1
0
0
0
1
1
1
0
1
0
2
0
1
0
0
1
0
0
2
2
2
3
1
0
0
0
0
2
1
0
2
0
2
1
1
0
0
0
2
1
1
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
2
2
1
0
1
0
1
0
2
2
1
2
0
0
0
0
2
3
0
1
0
2
1
1
1
0
0
0
2
1
0
0
1
0
1
2
2
0
1
0
0
0
1
1
1
2
0
0
1
0
1
0
0
0
0
2
2
2
0
0
0
0
2
2
0
0
2
1
1
0
1
0
0
2
1
0
2
2
1
0
1
2
0
0
1
2
0
2
0
0
1
0
1
0
1
0
0
3
1
0
0
0
0
1
0
0
1
0
0
1
3
2
2
1
0
2
0
0
0
2
0
0
2
0
1
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
3
1
0
4
0
1
0
1
0
1
2
0
0
0
2
2
0
3
0
0
0
0
1
0
0
0
0
0
0
1
0
2
1
0
0
0
2
2
0
2
0
2
0
1
0
2
0
0
0
4
0
1
0
2
0
0
0
2
1
0
1
0
2
0
0
0
3
2
2
0
2
0
0
0
0
2
0
0
1
1
3
1
0
1
2
0
1
1
1
0
2
0
1
0
0
0
0
0
1
2
2
2
0
0
0
1
1
1
0
1
1
1
0
1
1
2
0
1
1
0
1
1
1
0
1
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
2
1
2
2
1
1
2
0
0
3
0
2
2
3
0
0
0
0
1
0
1
1
3
1
0
0
0
2
0
0
1
0
0
2
1
0
2
1
1
0
2
0
0
1
1
0
0
2
0
0
1
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
1
0
0
1
1
0
1
1
0
2
2
0
0
2
0
1
1
0
1
2
1
1
2
0
0
1
2
0
0
1
2
1
0
1
2
0
0
1
2
0
1
1
0
2
0
0
2
0
0
0
0
0
1
2
1
2
1
2
0
0
2
0
3
1
0
0
1
0
0
0
0
2
0
2
0
1
2
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
2
2
0
1
2
0
0
1
0
2
0
1
1
0
2
0
2
0
2
1
0
0
0
1
1
0
2
2
1
0
4
0
0
0
0
1
1
0
0
3
0
0
0
0
2
0
0
2
1
0
0
2
0
0
0
0
0
0
2
1
0
0
0
1
1
2
1
0
0
1
0
0
0
2
0
0
0
0
0
1
1
2
0
0
2
0
0
0
0
0
2
0
0
0
0
3
2
0
1
1
0
0
1
0
1
0
0
0
2
0
0
0
2
0
2
2
0
1
2
0
1
2
1
1
0
0
1
2
2
0
2
2
1
0
0
2
0
0
0
1
1
0
1
0
2
0
2
0
0
1
6
2
0
0
2
0
0
0
0
0
2
1
0
1
1
0
2
2
2
0
0
0
1
1
0
1
0
0
1
0
0
2
0
1
0
0
0
2
0
1
2
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
2
0
1
1
0
0
0
0
2
0
2
2
0
0
0
2
0
1
1
1
1
2
2
0
0
0
0
0
0
0
2
0
2
0
0
1
1
1
2
0
1
0
0
2
0
1
1
0
0
2
0
1
0
2
0
2
0
2
2
0
2
2
0
0
1
1
3
1
1
1
0
0
0
0
3
0
1
2
2
1
1
0
1
0
0
2
0
0
2
2
1
2
0
0
0
0
0
2
2
2
2
0
0
1
0
0
2
0
0
0
0
2
0
1
0
0
0
0
1
0
2
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
1
1
0
0
1
2
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
1
3
1
0
1
0
0
2
0
0
0
2
0
0
1
1
1
2
0
1
0
2
0
0
0
0
0
2
3
0
0
0
0
0
1
2
0
2
2
1
0
0
2
2
2
0
0
0
0
0
1
2
0
0
0
1
0
1
2
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
2
0
0
0
1
1
0
2
0
1
0
0
0
1
0
1
0
1
1
0
2
1
0
0
1
0
0
0
1
2
1
0
0
0
0
0
0
2
0
1
2
1
1
4
1
0
0
0
0
1
1
1
3
0
1
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
5
0
0
0
2
2
1
0
1
2
1
0
0
1
0
0
1
1
1
0
5
0
1
0
2
0
0
2
1
0
0
2
0
0
0
1
2
0
0
2
0
1
0
2
0
0
1
0
2
0
1
2
1
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
2
2
1
2
1
0
2
2
0
0
0
1
1
1
0
0
1
1
0
0
0
2
1
2
2
1
0
0
0
0
1
0
2
0
0
1
0
0
1
0
0
1
0
1
2
0
2
5
2
1
0
1
1
0
2
0
0
2
0
0
0
1
2
0
3
1
2
2
1
0
2
0
1
2
0
0
0
1
0
1
0
0
0
1
0
1
0
2
1
0
0
0
1
1
1
1
1
3
0
1
4
2
0
2
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
2
1
2
2
2
2
1
0
1
0
0
2
2
2
2
0
0
2
0
0
2
0
0
0
0
1
2
1
0
3
1
0
0
2
0
1
0
0
0
2
2
2
2
1
1
2
0
0
0
0
2
1
2
2
0
0
0
1
0
0
0
2
1
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
1
0
0
0
2
2
1
0
0
1
2
1
0
0
1
1
0
1
0
0
0
2
0
1
0
0
1
1
0
0
1
0
1
2
0
1
1
0
0
2
0
0
0
0
0
2
0
0
2
0
0
1
0
0
1
1
1
2
0
0
2
1
1
1
2
2
2
1
1
1
1
2
0
1
0
0
0
0
1
0
0
1
2
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
2
1
0
0
3
1
0
0
0
2
1
0
1
2
1
0
1
1
0
1
1
0
0
0
0
0
0
2
1
1
1
0
0
0
2
0
0
2
0
1
1
1
1
1
1
0
2
1
0
1
0
0
3
0
0
1
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
3
0
2
1
0
0
4
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
2
0
1
2
0
0
0
0
2
0
0
0
3
2
0
0
0
1
2
1
2
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
1
1
1
1
1
0
0
2
0
0
0
0
2
0
0
1
1
1
0
0
2
1
0
2
2
2
1
3
0
0
0
2
0
2
2
1
2
0
0
2
0
1
0
0
1
0
2
0
2
1
2
1
0
0
0
0
1
0
1
2
1
0
1
1
0
0
1
0
0
0
1
0
0
1
2
2
0
0
0
6
0
0
0
0
0
1
1
2
0
1
1
1
2
1
0
1
0
2
0
1
2
0
2
4
0
0
1
3
0
1
0
1
0
0
0
1
2
0
6
0
2
0
1
1
0
0
0
0
0
0
1
0
0
0
0
2
2
2
1
0
1
0
0
0
2
2
1
2
0
0
0
2
0
0
0
1
0
1
0
1
0
2
0
2
1
0
2
1
1
0
2
0
0
0
2
0
2
1
2
0
0
0
0
0
1
1
2
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
2
0
0
1
0
1
0
0
2
1
0
1
1
0
0
1
0
1
1
1
1
1
0
0
1
2
2
1
2
2
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
2
1
0
0
0
0
3
2
3
1
0
1
0
2
1
1
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
2
2
0
0
0
0
1
0
2
0
0
6
0
1
0
1
1
2
0
0
2
0
1
0
1
1
1
0
0
0
0
2
2
0
0
1
0
0
0
0
0
2
0
1
0
0
0
1
0
2
0
0
0
2
2
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
1
1
0
2
2
0
1
2
0
2
0
0
1
1
2
1
1
0
1
0
0
0
1
0
0
0
2
0
2
0
0
0
0
2
1
0
1
0
0
0
0
1
2
1
2
0
0
4
0
1
0
0
1
0
0
2
0
2
0
0
0
2
0
0
2
0
0
1
0
0
1
2
0
0
1
0
1
0
0
0
0
1
1
0
1
2
0
1
2
0
2
0
0
0
0
0
0
0
0
2
0
0
2
3
2
2
0
0
2
0
2
2
2
1
0
2
2
1
0
1
0
1
1
2
0
2
1
1
2
0
1
0
0
2
0
1
0
2
2
0
2
0
0
0
0
1
1
0
0
1
2
0
1
0
0
2
2
1
0
0
2
1
1
0
1
0
1
0
0
2
1
0
1
2
0
0
1
2
1
2
0
2
2
2
0
1
0
1
0
0
3
0
0
0
2
0
2
1
0
0
2
0
0
0
2
1
0
0
0
2
2
0
1
0
0
0
0
0
0
2
0
2
0
2
0
2
0
0
0
2
0
2
0
1
0
0
2
0
0
0
2
2
0
0
0
1
0
0
1
1
1
1
0
0
1
0
0
0
0
2
2
0
0
0
0
1
2
0
2
0
0
0
0
2
0
1
0
1
0
2
1
1
0
0
2
0
0
2
2
2
0
1
2
1
0
2
2
0
1
0
0
1
2
0
2
1
0
2
0
1
0
0
1
1
1
2
0
2
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
2
1
1
0
0
0
1
0
0
0
9
0
2
0
2
2
1
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
2
1
0
1
1
0
0
0
2
1
3
1
0
3
0
0
2
2
1
1
1
1
0
0
0
2
1
0
2
1
1
0
0
0
2
0
2
1
0
0
1
2
0
0
0
0
0
2
2
0
0
2
0
0
1
0
2
0
0
0
0
0
0
2
1
2
0
2
0
0
1
0
0
1
1
1
0
2
1
0
0
2
0
0
0
1
0
1
1
2
0
0
2
1
0
1
0
0
2
0
2
0
0
0
1
2
0
0
2
0
3
1
2
2
1
0
0
1
0
1
1
0
0
0
1
3
0
1
5
0
0
0
0
1
0
1
1
2
0
0
0
0
2
0
1
0
2
0
1
0
0
1
0
0
0
0
2
0
0
0
2
0
1
1
2
0
1
0
2
0
0
0
0
0
1
0
1
1
2
0
0
0
0
0
0
1
2
1
0
0
2
1
0
1
0
2
0
0
0
0
1
0
1
0
0
2
0
2
1
0
1
1
0
2
2
1
2
0
0
0
0
2
1
0
1
0
2
0
1
2
1
1
0
0
0
0
0
0
2
3
0
0
0
0
1
1
1
2
2
0
0
0
2
0
2
2
1
1
0
1
0
1
0
2
0
4
0
2
0
0
0
1
0
2
0
1
1
1
1
1
1
0
0
0
2
0
1
0
0
1
1
0
0
1
0
0
3
0
0
0
0
2
1
1
0
1
1
2
0
1
0
0
2
0
2
0
0
2
0
2
0
2
1
1
1
0
0
0
1
2
0
0
0
0
0
1
2
0
2
0
0
0
2
2
0
1
0
1
0
2
0
1
0
0
2
2
4
0
2
2
0
0
0
0
0
0
1
2
0
1
0
0
2
0
1
1
0
2
2
0
0
0
3
5
0
1
2
0
2
0
0
2
0
0
0
0
2
1
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
2
2
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
1
0
2
0
1
1
0
0
0
2
0
1
0
1
0
0
2
1
2
2
0
0
1
1
1
1
0
0
2
0
0
1
0
0
0
1
3
1
0
0
1
1
0
0
2
2
0
0
0
0
2
0
0
0
0
0
1
0
0
1
2
1
2
2
0
0
2
0
0
2
0
0
0
0
0
0
3
1
0
0
0
0
1
2
0
0
2
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
2
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
1
0
0
1
4
0
0
0
1
0
1
2
1
0
2
1
0
0
0
4
2
0
1
0
0
0
0
1
1
0
1
1
0
0
2
1
1
1
0
0
0
0
4
2
0
0
0
0
0
0
2
1
0
1
2
0
0
0
0
1
0
1
0
0
0
3
2
3
0
1
1
3
0
1
0
0
2
2
0
0
1
1
0
0
0
0
0
0
2
0
2
1
2
1
2
1
1
1
0
1
2
0
1
0
0
0
0
1
0
0
0
0
0
0
1
3
0
0
2
0
0
0
1
0
2
2
1
0
0
0
0
0
0
2
1
0
0
2
2
0
2
0
0
1
3
0
0
2
0
2
0
0
1
1
1
0
0
2
1
0
0
2
2
0
0
0
1
3
3
1
1
2
1
1
0
2
0
1
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
2
0
1
1
0
2
1
0
1
0
0
3
2
1
1
2
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
1
2
0
1
0
2
0
1
0
1
0
2
2
0
0
0
2
0
0
0
1
0
0
0
2
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
1
1
3
0
0
0
2
0
1
0
1
0
1
2
4
0
0
0
0
2
0
0
1
2
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
2
0
1
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
2
0
2
0
0
1
0
2
0
0
0
2
0
2
0
0
1
2
0
0
0
1
0
0
0
2
2
2
1
2
2
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
1
0
3
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
1
0
2
0
0
0
0
2
2
2
0
2
0
0
0
1
0
1
0
2
0
1
1
1
0
0
1
2
0
0
0
0
0
2
0
2
2
0
0
0
1
0
0
0
0
1
1
2
0
0
0
2
1
1
3
0
0
2
0
0
1
0
2
0
0
2
2
1
1
1
0
1
1
0
0
1
0
1
0
2
2
0
0
0
0
1
0
2
0
0
1
0
2
0
1
2
2
2
1
0
1
0
0
0
0
0
2
0
1
1
2
0
2
0
0
0
1
0
2
0
1
1
0
2
3
0
2
2
2
0
1
0
0
0
1
1
0
0
0
2
1
0
1
0
1
2
2
1
1
1
1
0
0
2
1
0
2
1
1
0
1
1
1
0
2
0
1
0
0
2
1
2
0
2
0
0
1
2
0
0
0
1
0
0
0
0
1
0
0
0
1
2
1
0
0
1
2
0
0
0
0
0
0
0
2
1
2
0
0
1
0
0
2
0
0
1
1
2
2
2
0
1
1
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
1
2
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
2
3
0
1
3
0
0
1
1
1
0
1
0
0
0
3
0
0
1
0
0
1
2
1
0
0
0
2
0
1
0
1
2
0
0
1
3
0
2
1
1
2
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
1
0
0
0
2
2
1
0
2
0
1
1
1
1
0
0
2
0
3
1
0
0
1
1
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
1
2
0
0
0
0
0
1
0
0
2
0
2
1
1
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
1
2
0
0
0
1
0
1
2
2
0
0
1
0
0
0
0
0
0
0
1
0
2
1
3
0
0
2
0
2
0
1
0
1
0
2
0
0
0
1
1
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
2
0
0
0
0
1
1
1
0
1
2
0
2
2
1
0
2
0
2
0
0
0
2
2
0
1
1
1
2
2
0
0
1
1
2
0
0
1
1
3
0
0
2
1
2
1
1
0
2
2
0
0
0
1
0
0
1
2
2
0
3
0
0
1
1
0
1
3
0
0
1
2
1
1
1
1
0
2
0
1
0
2
0
0
2
2
2
1
0
0
0
1
0
0
1
0
2
1
0
0
0
0
2
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
3
0
1
3
1
2
2
0
2
0
2
0
0
0
0
1
0
0
0
0
2
0
2
0
1
1
0
0
0
2
1
0
0
0
0
0
0
0
2
0
1
4
1
0
0
0
0
0
1
0
0
4
0
0
1
0
1
2
0
1
2
1
2
0
0
0
1
0
0
2
0
2
1
0
0
0
0
0
2
1
2
1
0
1
0
1
1
0
0
1
0
0
0
0
2
0
0
0
2
2
1
1
0
2
1
1
0
0
2
1
0
0
0
2
2
1
0
1
3
3
2
0
1
0
1
0
2
0
0
0
0
2
2
0
0
2
0
3
1
1
0
0
0
0
1
0
2
0
0
4
0
2
0
1
2
2
2
0
0
0
0
0
0
1
0
1
1
1
0
0
2
0
1
0
0
0
1
0
0
2
2
0
0
0
0
2
1
1
0
0
0
2
0
1
0
1
1
0
0
0
0
1
1
0
0
0
0
2
0
3
2
0
1
0
0
1
3
0
0
0
2
0
1
1
0
2
2
2
0
1
0
2
1
0
2
0
0
0
0
1
0
0
1
2
0
0
1
0
0
0
0
0
2
1
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
1
0
2
1
0
0
0
0
1
0
0
2
1
2
2
2
1
2
2
0
0
2
3
0
2
0
0
1
1
1
0
1
2
0
0
0
0
2
1
0
2
0
3
1
2
1
1
1
0
1
0
2
0
2
0
0
0
0
0
2
2
1
0
0
1
1
2
1
5
1
2
1
0
0
0
0
1
0
0
2
1
0
1
0
3
0
1
1
0
0
2
0
0
0
0
1
0
1
0
2
1
1
1
0
0
2
0
4
0
1
0
2
0
1
0
0
0
0
0
0
0
2
0
1
0
0
2
1
0
2
0
2
1
1
0
0
2
2
0
0
1
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
1
0
1
2
2
2
0
0
0
0
0
2
2
1
1
1
0
2
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
2
1
1
0
2
2
0
1
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
2
1
0
1
0
0
0
1
0
0
0
1
0
2
0
0
0
3
0
2
1
8
0
2
0
1
0
0
2
1
0
2
1
0
0
1
0
2
2
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
2
1
2
0
2
2
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
1
1
5
0
0
0
2
2
2
2
0
0
2
0
0
1
0
2
2
1
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
1
0
3
1
1
1
0
0
1
0
0
2
0
0
2
0
0
0
1
0
1
0
0
2
2
0
0
1
0
2
1
2
0
1
2
2
0
2
0
0
0
0
0
0
0
0
3
0
0
0
1
2
0
1
2
0
1
1
1
2
0
2
2
0
1
2
1
1
0
2
0
1
0
0
2
0
1
1
2
0
2
2
2
0
2
0
0
1
1
1
1
1
2
1
0
0
1
3
0
0
2
0
2
0
1
0
1
0
0
0
1
0
1
1
0
1
2
1
2
1
0
0
0
1
2
0
2
0
2
0
0
1
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
2
1
2
1
0
1
0
0
3
0
0
0
0
0
1
1
0
1
0
1
0
1
0
0
0
2
0
0
0
0
2
0
0
0
2
2
0
0
2
0
0
0
0
1
0
0
1
1
0
1
0
0
0
1
0
0
2
1
2
0
1
0
1
2
1
0
0
0
2
2
0
1
1
0
0
0
0
0
0
0
2
0
0
2
1
0
1
2
0
1
0
1
0
0
1
2
2
0
0
0
0
2
0
0
2
1
1
0
1
0
1
1
0
0
1
0
3
0
1
1
0
0
0
0
1
2
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
2
0
0
0
1
0
2
0
0
2
1
2
0
0
0
2
1
0
2
1
1
0
0
0
0
0
0
0
1
0
0
1
2
2
0
0
2
0
2
1
0
0
0
0
0
0
2
0
0
0
1
1
0
1
0
0
1
2
0
0
0
1
0
2
0
1
0
1
0
2
1
1
2
0
2
0
0
1
0
1
0
0
0
2
0
0
0
0
1
1
3
2
0
0
0
2
2
0
0
1
1
0
1
0
1
0
2
2
1
2
0
0
2
0
1
2
2
0
2
1
1
2
0
0
0
1
2
2
1
2
0
1
2
0
1
0
2
0
1
1
1
0
1
0
1
0
2
0
3
0
2
0
0
0
0
0
0
0
2
1
2
0
1
0
1
2
3
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
2
2
1
2
0
0
0
2
0
1
2
0
0
2
2
0
1
0
0
0
1
2
2
0
3
2
2
1
0
0
0
0
1
0
0
0
0
1
1
2
1
0
0
0
2
0
2
1
2
0
0
0
2
0
0
0
1
1
2
0
2
2
2
0
1
0
1
2
2
1
1
1
0
0
1
2
2
1
0
0
1
2
0
0
2
1
2
1
0
0
0
1
1
0
0
0
0
0
1
1
1
0
0
0
1
0
0
1
3
0
2
0
0
0
0
1
0
0
0
0
2
2
3
1
1
5
0
0
1
0
0
1
0
1
2
1
1
0
2
0
0
0
0
2
1
1
0
0
1
0
0
0
2
0
1
0
0
0
0
2
0
0
3
0
0
1
1
0
0
0
2
0
2
3
1
2
1
0
3
1
1
0
2
0
0
0
0
0
2
1
0
0
0
1
0
1
2
0
0
0
1
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
1
1
2
2
0
0
1
2
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
1
2
2
1
1
0
2
0
0
1
0
0
0
0
1
0
0
2
1
0
0
1
1
0
0
1
2
0
1
1
1
0
0
0
1
2
2
0
1
0
0
1
0
0
0
1
0
0
0
1
3
0
2
0
0
1
0
0
0
0
0
1
1
1
0
1
1
0
0
0
0
0
2
0
2
1
2
0
0
2
0
0
0
1
0
0
0
2
0
2
0
1
0
1
0
0
0
0
0
2
1
0
0
1
0
2
1
1
2
3
2
2
1
0
0
0
0
2
0
1
0
0
0
0
2
1
0
1
0
2
0
0
1
1
0
0
2
1
4
0
2
0
2
2
0
0
2
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
1
0
2
0
0
0
1
0
2
0
1
0
0
0
2
2
0
0
3
0
1
0
1
2
2
3
0
0
0
1
0
1
2
0
2
0
0
0
0
0
2
1
2
1
0
0
1
2
0
0
1
0
0
0
0
0
2
1
1
1
1
1
1
0
1
2
0
0
0
2
1
0
0
0
0
1
0
1
1
1
2
0
2
0
2
0
2
1
0
1
0
0
0
1
1
1
1
2
1
0
0
2
0
2
0
2
2
0
1
4
1
2
0
0
1
1
1
2
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
2
2
2
0
0
0
0
1
0
2
2
1
1
0
0
0
2
2
0
0
2
0
1
0
2
0
2
0
1
1
2
2
1
2
0
1
0
1
1
0
0
0
0
2
0
0
2
0
1
3
1
0
0
2
0
0
0
0
2
0
1
0
0
0
3
2
0
0
0
1
1
0
0
2
1
2
0
1
1
0
2
1
0
1
0
1
0
0
2
0
1
1
3
1
0
0
0
1
0
2
1
0
0
1
1
0
2
0
0
2
0
1
1
2
2
3
1
0
0
1
1
0
1
1
0
0
2
0
0
0
1
1
3
1
0
0
1
0
2
1
0
0
1
1
0
0
0
1
2
2
1
1
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
2
0
1
0
0
0
1
0
0
0
2
1
1
3
0
1
2
0
0
1
0
0
1
0
1
0
1
1
0
0
1
0
1
1
0
2
0
1
0
1
0
0
0
0
2
0
0
0
2
0
2
0
0
0
2
0
0
1
2
0
1
0
1
0
1
1
0
0
0
2
1
1
3
0
1
1
0
0
0
3
0
0
3
0
0
0
2
0
1
1
0
2
0
0
1
2
1
0
0
1
0
0
2
1
1
2
1
1
0
0
0
0
1
1
2
0
0
0
1
1
2
0
0
1
0
1
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
1
1
0
0
0
1
1
0
0
2
0
0
0
1
0
1
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
1
0
1
1
1
1
1
0
0
1
1
2
0
0
0
0
0
0
0
0
3
1
1
0
1
0
0
0
0
1
1
0
1
0
2
2
0
2
0
2
0
1
0
0
2
0
2
0
1
0
0
0
2
1
2
0
1
1
0
0
1
2
0
1
0
2
1
0
0
1
1
3
0
0
1
0
0
2
0
1
2
0
0
1
0
1
0
0
1
0
0
2
0
1
2
1
0
0
0
0
2
0
0
2
1
2
1
0
0
1
2
1
0
0
1
0
1
0
1
0
3
0
0
1
1
2
2
3
2
1
1
1
0
1
2
2
0
1
0
1
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
1
2
1
0
2
0
1
0
0
0
1
4
0
0
2
0
1
1
0
1
2
0
1
0
0
1
1
0
0
3
2
1
0
2
3
0
2
0
1
1
1
4
0
1
1
1
1
0
0
0
2
0
0
2
0
0
0
0
1
0
1
0
0
0
2
0
0
0
1
1
2
0
0
1
0
0
0
0
2
0
3
2
2
2
0
0
0
1
0
0
2
0
0
0
0
0
0
2
2
2
2
1
2
1
0
1
0
0
0
0
2
0
4
0
0
0
1
0
0
0
0
2
2
0
0
0
2
1
0
0
0
0
1
1
0
2
0
0
1
3
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
1
0
0
0
2
0
0
0
0
0
1
1
0
1
0
0
0
0
0
2
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
1
2
0
2
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
1
1
2
0
0
2
0
1
0
2
1
1
2
1
2
0
2
2
1
0
0
2
0
0
0
2
0
1
0
0
1
0
1
1
0
0
0
0
2
2
1
2
1
0
0
0
1
1
0
0
0
1
0
1
2
1
0
0
1
0
1
2
0
1
1
0
2
0
0
2
0
2
0
1
1
1
0
2
2
0
0
2
0
1
3
0
0
1
0
0
0
0
1
0
1
0
0
1
0
2
0
0
1
1
0
0
0
1
2
2
2
2
0
1
1
1
1
0
0
2
1
1
2
0
2
0
0
0
0
0
0
2
2
1
1
2
0
2
2
1
0
0
1
2
0
0
0
1
0
1
0
0
2
0
0
1
2
2
1
1
0
1
0
0
1
0
0
2
0
0
1
1
2
2
0
0
1
0
0
0
1
0
0
0
0
0
1
1
1
1
0
1
0
2
2
1
0
2
0
0
0
0
0
0
2
2
1
0
0
0
0
0
8
0
2
2
1
1
1
0
2
1
1
0
2
0
2
0
0
1
0
0
2
1
1
0
2
0
0
1
2
2
0
0
1
1
0
0
0
0
0
1
2
1
0
0
2
0
0
0
0
0
2
1
1
0
2
1
1
0
0
0
2
0
0
0
0
0
1
0
0
2
2
0
1
1
1
0
0
1
1
1
2
1
0
1
1
0
1
0
0
0
0
0
1
0
1
1
0
0
2
1
1
0
0
1
1
0
0
0
2
0
2
0
2
0
0
2
1
2
0
0
0
0
1
0
1
0
1
0
0
1
1
0
0
0
1
1
0
2
3
2
0
1
0
0
2
2
2
0
1
1
2
0
1
1
0
1
0
0
1
1
0
0
0
0
1
2
1
7
0
0
1
0
0
1
0
0
2
1
1
1
1
0
3
0
0
0
0
0
0
0
0
2
1
2
1
0
0
1
1
0
1
0
0
1
1
0
2
0
0
1
0
0
0
0
0
0
0
0
2
1
1
0
2
0
1
0
1
0
2
2
0
0
0
0
0
0
1
1
2
0
0
2
1
0
0
1
1
0
0
0
1
0
0
0
1
2
0
2
0
2
0
0
0
1
0
1
1
0
2
1
1
0
3
1
2
1
0
2
3
0
0
0
2
1
2
0
0
2
2
2
1
0
1
0
2
0
1
0
0
1
0
1
2
2
0
2
1
2
0
2
0
0
1
1
3
2
0
0
0
2
2
0
3
0
1
0
2
0
0
1
0
1
2
1
0
0
1
1
2
1
0
0
0
0
0
1
1
2
1
0
1
1
5
0
2
0
1
0
2
0
0
3
3
2
2
0
0
0
1
0
0
0
0
0
0
1
2
1
0
2
1
0
0
0
0
0
0
1
1
1
1
2
2
0
2
0
0
0
1
0
0
1
0
1
0
0
1
1
0
1
2
2
0
1
2
1
1
0
1
0
0
0
0
2
2
2
1
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
1
2
1
0
2
2
0
1
0
0
2
3
1
1
0
0
0
0
0
2
2
1
0
0
0
0
1
1
2
2
0
0
1
2
1
0
2
1
0
0
2
2
1
0
0
1
1
0
1
1
0
0
0
0
2
1
0
0
0
1
0
0
2
0
1
2
0
2
0
2
0
2
2
1
0
1
0
1
0
1
1
0
0
1
1
0
4
1
1
0
1
0
1
2
1
0
0
2
0
0
0
1
0
0
0
2
1
0
1
0
1
0
1
2
0
0
0
1
0
0
0
0
0
0
2
0
2
2
2
1
1
0
0
0
2
0
0
0
0
1
0
2
1
1
0
0
2
2
1
0
2
0
2
1
2
0
1
0
0
0
0
1
2
0
0
0
0
2
0
1
1
0
0
1
0
2
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
2
2
0
0
2
0
2
2
1
0
2
0
0
1
2
0
0
0
0
0
1
0
1
0
0
2
1
1
0
0
2
3
2
2
1
1
1
0
0
0
1
6
0
1
1
0
1
0
0
0
0
1
2
2
0
2
1
1
0
0
0
0
2
1
2
2
0
0
2
2
1
0
2
0
1
1
0
0
1
1
0
0
2
2
0
0
1
0
1
1
0
1
0
2
0
1
1
1
1
2
0
1
0
0
0
0
0
1
0
2
1
0
0
2
0
0
0
2
1
0
2
1
0
0
2
0
1
3
2
0
2
1
2
0
0
0
3
0
0
0
0
0
0
1
2
0
2
0
0
0
1
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
1
0
2
2
0
0
1
0
3
2
0
2
0
2
1
1
0
0
0
2
0
1
1
1
0
0
2
1
2
2
1
1
2
2
1
0
0
2
1
0
0
0
1
2
0
2
0
1
0
0
0
0
0
0
0
1
1
2
0
0
3
1
0
0
0
0
1
0
0
3
1
0
0
1
1
0
1
0
1
0
2
2
0
2
2
0
3
0
0
0
0
2
0
0
0
0
0
1
1
0
2
0
0
1
0
1
0
0
1
0
0
2
1
0
2
0
4
1
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
1
0
1
0
3
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
2
2
0
2
2
1
0
0
0
0
2
1
2
0
2
0
1
0
2
2
3
1
1
2
1
1
0
1
0
1
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
2
0
0
1
1
0
0
0
0
0
1
2
0
0
0
2
2
0
1
0
0
2
0
2
1
0
0
2
2
2
0
0
0
2
0
1
2
1
0
0
1
0
0
1
2
0
0
1
1
2
0
0
0
0
0
0
4
0
0
2
1
0
0
2
0
0
0
1
2
0
0
0
0
1
0
0
0
2
2
0
0
1
2
1
2
0
2
1
1
2
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
1
0
2
1
1
1
2
0
0
1
0
1
2
1
1
0
0
0
1
2
0
0
1
2
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
2
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
1
2
0
1
1
0
0
0
1
0
0
1
0
0
3
1
1
1
1
0
1
0
1
2
1
1
2
2
0
1
0
2
0
0
0
0
0
2
1
0
0
3
0
0
1
0
0
0
3
1
0
0
2
0
2
1
0
0
0
0
1
0
0
0
1
0
1
2
1
1
1
0
1
2
0
0
0
0
0
1
1
0
2
0
1
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
1
0
2
1
2
1
2
1
1
2
1
0
0
1
0
0
1
0
2
4
0
0
0
1
0
1
0
1
0
0
1
1
0
0
1
0
1
1
2
2
0
0
2
0
2
1
1
0
1
0
2
2
1
0
0
0
0
1
0
0
3
0
0
0
1
1
2
0
0
1
0
0
0
2
0
1
1
1
1
0
1
1
0
0
1
0
2
0
1
0
2
0
0
1
0
0
0
0
1
0
1
1
1
0
0
1
1
0
1
1
0
2
0
0
0
0
1
0
0
0
2
0
0
0
1
1
0
0
2
2
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
1
3
0
0
1
0
0
0
1
0
0
2
0
1
1
1
0
0
0
2
1
3
0
0
0
0
1
0
0
0
2
0
0
1
0
0
1
2
0
0
0
0
1
1
2
2
0
8
0
0
0
0
1
1
1
0
0
0
0
2
0
1
2
1
0
1
0
0
2
0
0
2
0
1
1
2
2
1
0
1
0
2
0
2
0
2
0
0
0
0
1
0
2
0
0
2
0
0
2
1
3
3
1
0
0
0
1
0
0
2
0
0
1
7
2
2
2
0
2
0
3
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
2
0
1
0
0
0
2
2
1
2
2
0
0
1
0
1
1
0
0
0
0
0
2
2
2
0
0
1
1
0
1
2
0
0
1
1
0
0
0
0
0
1
1
0
2
1
0
0
1
2
0
2
0
2
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
1
0
0
1
0
0
0
0
2
1
0
2
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
2
1
0
2
0
0
0
0
1
0
1
1
0
0
1
0
0
0
1
1
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
1
0
2
0
0
0
0
1
1
0
0
0
1
0
1
0
0
2
1
1
0
0
1
0
0
0
0
0
2
0
2
0
3
0
0
0
1
0
1
0
0
1
0
1
0
2
2
0
0
2
0
2
1
1
0
1
0
0
2
0
0
2
2
0
0
1
0
0
1
0
0
0
2
2
0
0
1
1
0
0
0
1
1
0
2
0
0
0
0
0
0
1
1
0
0
1
0
1
0
1
1
2
1
0
0
0
1
0
2
0
1
0
1
2
1
0
0
0
1
0
0
0
0
0
0
1
0
2
0
1
2
0
1
0
0
1
1
0
2
1
1
0
1
1
2
1
2
2
0
2
2
1
1
1
1
1
0
0
0
2
0
0
0
2
0
2
1
1
1
2
2
0
1
2
2
1
0
1
0
0
0
1
1
0
2
0
0
1
2
0
0
0
0
0
0
0
1
0
0
2
1
2
0
1
0
0
1
0
1
0
1
0
1
0
0
0
0
2
2
0
0
0
0
1
0
2
0
1
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
1
0
1
1
0
1
0
0
0
1
1
4
0
0
1
2
2
1
1
0
0
0
0
0
1
2
0
0
0
0
0
1
0
2
1
1
2
0
1
0
1
0
1
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
3
1
0
0
2
0
0
1
0
0
1
0
0
1
2
0
0
0
0
2
1
1
0
2
1
0
0
0
0
1
2
0
0
0
1
0
2
0
1
2
2
0
0
0
0
0
0
0
0
1
0
0
2
2
3
0
2
0
2
1
0
0
2
0
0
0
1
0
1
0
0
0
2
2
1
0
0
0
0
0
4
0
2
0
0
1
1
7
2
0
1
0
1
0
1
1
0
0
1
0
0
0
0
0
0
1
1
0
2
0
0
2
1
0
1
0
0
1
0
1
2
0
2
0
2
1
0
0
0
0
0
0
0
1
2
0
1
2
0
0
0
1
2
1
0
0
1
1
2
0
0
2
0
0
0
2
0
1
0
2
1
0
1
1
0
0
1
0
0
1
2
1
0
0
0
0
0
1
0
2
0
0
1
1
2
2
1
0
2
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
1
1
1
1
0
2
0
0
0
0
2
4
2
2
0
2
2
3
1
1
0
0
2
1
0
1
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
4
0
0
1
2
0
1
0
0
0
0
1
0
1
0
1
1
0
0
0
1
1
2
1
0
1
0
2
0
0
0
0
1
0
0
1
0
2
1
0
0
0
0
1
2
2
1
1
0
1
0
1
0
0
2
0
1
0
2
0
0
1
0
0
1
1
0
0
0
0
1
2
2
0
1
0
1
0
1
1
0
0
0
1
2
0
0
0
0
1
0
3
0
1
2
0
0
0
2
2
0
1
0
0
0
0
0
1
1
0
2
0
1
0
1
2
2
1
2
0
0
1
1
1
2
0
2
0
3
0
1
1
0
0
1
2
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
1
0
2
0
1
0
2
0
2
0
2
2
1
0
0
1
0
1
0
0
1
0
5
1
0
0
0
0
1
0
0
0
0
1
2
1
1
0
1
1
0
1
1
1
1
1
0
0
0
0
2
0
1
0
2
0
1
1
2
1
0
0
1
2
0
0
1
2
1
0
1
1
1
2
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
2
1
0
0
0
1
0
3
0
0
4
2
0
0
2
2
4
0
0
1
0
2
2
0
0
2
0
1
1
2
0
0
1
0
1
0
1
1
1
2
0
2
0
1
2
2
0
1
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
1
0
0
2
1
1
0
1
0
2
2
1
1
0
1
0
1
1
1
2
4
0
0
2
3
0
0
2
2
1
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
2
2
0
1
1
0
0
0
0
0
0
0
1
0
0
2
0
0
1
1
0
0
0
0
2
1
0
1
2
0
1
0
1
0
0
0
2
0
0
0
0
1
0
1
1
2
2
1
2
0
1
1
2
2
0
1
1
0
1
0
0
0
2
0
3
1
0
0
2
1
2
1
1
1
0
1
1
0
0
0
2
0
0
0
1
1
0
2
1
1
0
3
1
1
0
1
0
0
0
2
0
0
2
2
0
2
0
1
1
0
1
1
0
0
0
2
2
0
0
1
1
2
0
0
2
1
0
0
0
0
2
2
0
0
0
1
0
1
1
3
1
0
2
0
1
1
2
1
0
1
1
1
2
2
0
0
2
1
0
0
2
0
0
0
4
1
2
1
2
0
0
0
0
0
0
1
0
0
0
0
1
3
0
0
0
0
1
1
0
0
0
1
1
0
2
2
0
2
1
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
1
1
1
2
0
0
0
0
1
2
2
0
1
1
0
0
0
2
0
2
0
0
0
0
0
2
0
2
0
0
2
0
1
0
1
0
0
0
1
1
0
0
2
1
1
2
0
1
1
0
0
0
2
0
0
0
2
1
0
0
0
2
1
1
0
0
0
2
1
0
0
1
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
1
0
2
0
1
1
2
0
2
0
2
2
1
1
0
1
0
0
0
1
1
1
0
2
2
2
2
0
0
0
0
2
2
1
0
0
2
0
3
0
0
1
1
0
0
1
0
2
1
1
1
2
1
2
2
1
1
0
1
1
2
0
0
2
1
0
1
1
2
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
4
0
1
0
0
2
0
1
0
0
0
2
2
0
0
2
0
1
0
0
2
0
0
0
2
0
1
0
2
0
0
2
1
0
0
0
2
1
1
2
2
2
1
1
0
1
0
2
0
0
0
2
0
0
0
1
0
1
2
1
3
0
0
1
1
0
0
0
3
0
2
0
2
2
0
1
1
2
0
1
1
0
0
0
1
0
1
2
0
2
0
0
0
0
0
0
0
1
0
0
0
3
1
1
0
0
0
0
2
2
0
0
1
2
1
2
0
1
0
1
3
2
3
1
1
2
0
0
1
1
2
0
0
0
2
0
0
0
0
1
0
0
2
0
0
2
2
0
0
1
2
0
0
0
1
1
0
0
1
1
2
1
0
1
2
2
0
0
0
1
2
0
0
0
0
0
1
1
1
0
2
1
0
1
2
0
0
2
0
1
0
0
0
0
2
2
1
0
1
3
0
2
2
0
2
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
1
2
1
0
1
1
0
0
0
1
0
1
2
1
1
0
0
1
0
0
2
1
1
0
0
0
1
0
0
2
1
0
1
2
1
1
1
0
1
0
0
2
0
0
0
3
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
1
0
2
0
2
1
0
2
0
0
3
0
3
2
0
0
0
0
3
1
2
1
0
0
0
0
0
1
1
1
1
2
0
1
0
1
0
1
0
1
22
0
0
1
1
1
0
2
0
0
0
0
0
0
0
1
2
0
0
2
0
1
2
0
0
2
2
1
0
1
0
0
0
0
0
1
0
1
3
1
2
0
1
0
0
2
2
1
0
0
1
0
0
0
0
1
0
1
0
2
0
0
1
0
0
1
0
0
1
0
2
0
0
1
0
1
2
2
0
2
1
3
0
2
0
0
0
0
0
1
1
0
0
0
0
0
1
1
2
2
1
1
0
0
0
2
2
2
1
1
1
0
0
0
0
2
0
0
1
0
1
2
0
0
0
1
0
0
1
2
0
0
1
0
1
0
0
1
0
0
1
2
1
0
0
1
0
0
2
0
0
0
1
1
2
1
0
0
0
2
2
0
0
0
0
0
2
2
0
1
0
1
2
0
0
0
0
1
0
2
2
1
2
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
2
0
0
0
0
2
2
1
2
0
0
2
0
0
0
2
0
2
0
2
2
0
2
1
0
2
1
0
0
0
0
0
0
3
0
0
2
0
0
1
1
2
0
0
1
0
0
0
0
0
1
2
0
0
1
2
2
2
1
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
2
0
1
1
1
0
0
1
1
1
2
0
1
1
0
0
1
1
0
0
2
1
0
3
0
1
0
2
0
1
0
0
0
0
1
0
4
1
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
1
2
2
0
0
2
2
0
1
2
1
0
2
0
2
1
2
1
0
0
2
0
0
1
1
1
0
1
0
0
2
0
0
0
1
0
1
0
0
1
1
0
0
2
1
0
2
0
0
2
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
2
0
0
1
1
2
1
0
0
1
1
1
2
1
1
0
0
2
1
0
1
0
0
1
0
2
0
0
0
2
0
1
1
1
0
1
2
1
1
2
3
1
1
1
1
1
1
0
0
0
2
0
1
0
0
1
2
0
1
0
0
2
2
2
0
0
0
2
0
2
2
0
0
1
2
2
5
2
0
0
0
2
0
0
4
0
2
1
0
0
0
1
0
0
2
0
0
0
0
2
0
2
1
2
2
0
3
1
1
2
0
1
1
1
0
0
0
1
0
1
0
0
0
2
0
1
1
0
0
0
0
0
2
0
0
1
0
0
0
2
2
0
1
1
2
1
1
2
0
0
0
3
3
2
0
2
1
2
2
0
2
0
1
2
0
2
0
0
0
0
4
3
0
0
0
1
2
0
2
0
2
0
1
2
0
2
1
1
0
0
1
1
0
2
0
2
1
0
2
2
1
0
0
1
1
1
0
1
1
0
0
2
6
0
1
2
0
1
1
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
2
2
2
0
0
2
0
1
2
3
2
0
0
1
0
0
1
0
0
1
0
1
0
2
2
0
0
2
0
1
1
1
1
0
0
0
0
0
1
0
0
0
0
2
0
2
2
1
0
2
0
0
1
0
0
1
1
0
1
1
1
0
0
2
0
0
0
1
0
0
0
1
5
1
1
1
1
0
1
0
2
1
2
0
0
1
2
2
1
2
0
1
0
0
2
2
0
0
1
1
0
1
0
1
0
1
0
0
1
0
2
0
0
6
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
1
2
0
2
0
0
0
2
1
0
1
0
1
0
0
2
0
2
0
0
1
2
1
1
3
0
1
0
1
2
2
1
0
0
8
1
4
2
0
0
2
0
0
0
2
0
1
0
0
1
2
0
0
1
2
0
0
2
1
0
0
0
1
1
4
0
0
0
1
2
0
0
1
0
2
0
1
0
1
0
0
0
1
0
0
1
0
3
0
0
0
0
1
0
0
1
0
1
2
1
1
1
0
0
0
0
0
2
2
1
2
0
0
2
2
0
0
2
2
0
0
2
0
1
0
1
2
1
0
0
0
0
1
0
1
0
2
0
2
0
2
0
2
1
0
1
0
0
0
2
1
0
2
2
0
2
0
1
0
2
1
1
0
1
1
0
0
1
0
1
0
0
0
0
1
0
1
1
2
0
1
2
2
0
3
0
1
0
2
2
1
2
1
0
0
0
2
2
1
1
1
3
0
0
0
0
0
1
1
0
2
1
0
0
0
0
1
1
0
1
0
1
0
0
1
1
0
0
0
2
0
1
0
4
1
0
1
0
0
0
2
0
0
0
1
2
0
0
0
1
4
0
0
1
0
2
0
2
1
1
0
0
0
1
0
0
1
0
1
1
2
1
1
0
0
1
0
0
2
0
1
0
2
0
1
0
0
2
2
0
0
1
0
2
0
1
0
1
1
2
0
2
0
0
1
0
0
0
1
1
2
0
1
1
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
2
0
0
1
0
0
0
0
3
0
0
0
1
1
0
0
0
0
0
0
2
1
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
2
1
0
2
3
0
1
1
1
2
0
1
0
0
1
2
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
1
1
1
2
0
0
0
0
2
2
0
2
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
1
0
0
0
1
2
0
0
1
0
1
0
1
0
0
2
0
0
3
2
1
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
1
1
0
2
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
2
2
0
1
1
0
1
2
0
0
1
2
2
0
0
0
2
2
2
0
0
2
0
0
1
0
0
0
1
0
0
2
0
0
2
1
1
0
2
0
0
0
0
2
2
0
0
0
2
2
1
2
1
0
0
0
0
0
0
0
1
1
5
2
1
1
0
2
1
0
1
1
2
1
1
0
1
0
1
0
2
0
2
2
0
0
2
1
2
0
0
0
1
0
0
0
2
1
0
1
0
2
1
0
0
0
2
1
0
0
1
0
0
2
1
1
0
1
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
2
0
1
3
2
1
2
2
1
0
0
0
2
1
2
0
0
1
1
1
1
0
2
0
1
1
0
1
0
0
1
2
0
0
2
1
0
1
0
1
2
0
0
0
0
1
0
0
0
2
2
0
0
2
2
0
0
2
2
1
0
2
0
3
0
0
1
4
2
2
0
2
0
2
0
1
0
0
0
0
0
2
2
1
0
0
1
1
1
0
3
0
0
2
2
0
0
0
1
2
0
0
1
2
2
2
2
0
1
0
2
1
0
0
0
2
0
1
3
2
0
2
1
0
0
2
0
1
0
1
0
0
0
0
2
2
2
0
2
0
0
1
0
0
0
1
0
0
2
2
1
2
0
0
0
2
2
2
1
0
1
0
0
1
2
0
2
1
1
1
0
0
0
1
1
2
0
2
0
1
2
1
0
2
1
2
0
0
1
1
0
0
0
0
0
1
1
2
1
1
0
0
1
0
0
1
0
1
0
0
0
2
0
0
1
1
2
0
0
1
0
0
0
0
1
0
1
0
2
2
1
2
2
0
3
0
0
0
3
2
0
0
0
1
1
0
1
2
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
1
0
0
2
0
0
1
0
0
2
0
0
0
0
1
1
0
2
1
1
0
0
0
0
1
1
0
0
2
0
3
2
0
0
0
1
0
0
1
0
2
1
1
0
2
2
0
1
2
2
1
1
0
2
2
1
2
2
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
2
0
0
1
0
2
1
2
0
0
0
1
2
0
1
0
0
0
2
0
2
1
3
0
0
2
1
0
0
0
0
1
1
0
0
1
1
1
2
2
0
1
2
0
0
0
0
0
1
0
1
0
0
2
1
2
0
0
2
0
3
0
2
0
0
2
0
1
1
0
1
1
0
0
0
1
0
2
0
2
2
0
2
0
1
0
1
0
0
0
0
2
0
0
2
0
2
0
0
2
0
0
1
1
1
1
0
1
2
0
1
2
0
0
0
2
1
0
3
0
0
1
0
1
1
0
3
0
0
2
2
2
0
0
0
0
0
1
2
0
0
0
0
2
0
2
2
1
2
2
0
2
2
0
3
1
1
0
1
0
0
1
1
2
1
0
3
1
0
0
1
0
1
1
0
0
3
0
2
2
0
0
1
4
0
2
2
1
2
0
2
2
1
0
1
0
1
1
0
0
2
0
2
1
0
4
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
2
2
2
0
0
1
0
0
0
0
0
1
0
0
2
1
1
0
1
0
0
0
1
0
0
2
0
0
2
0
0
1
2
2
0
2
0
3
0
0
2
2
0
0
2
2
0
0
0
2
2
3
1
2
0
1
0
1
3
0
0
1
0
0
0
1
1
0
2
1
0
0
1
0
1
0
0
2
1
2
1
3
0
0
2
0
2
0
0
0
2
0
0
1
0
1
0
0
0
0
2
1
1
0
1
0
1
1
2
0
2
0
2
0
1
0
0
0
1
0
2
0
0
1
0
0
2
1
0
0
0
1
1
0
0
2
0
2
3
2
2
0
0
0
2
2
2
2
0
0
1
2
0
1
0
0
1
0
1
0
0
1
1
0
1
1
1
2
2
1
0
1
1
1
0
1
0
1
1
0
1
2
0
0
0
0
1
0
0
2
0
0
2
0
1
2
0
0
0
0
0
1
0
0
1
2
2
2
0
1
1
2
2
0
1
0
2
0
0
2
2
0
2
0
1
0
0
2
0
0
1
0
2
0
1
2
1
0
0
2
1
0
2
0
2
0
2
0
2
0
0
2
2
0
0
0
0
0
0
2
0
2
2
1
0
0
0
1
1
3
0
1
1
1
1
0
0
1
2
0
0
0
1
1
0
0
0
0
1
0
0
1
0
5
0
1
2
0
0
0
1
0
1
3
1
2
0
1
2
0
3
2
0
1
1
0
1
0
1
0
0
1
0
0
2
0
0
2
1
1
1
0
2
4
0
1
0
1
2
2
0
0
0
0
0
3
0
0
2
0
1
0
2
1
0
0
0
1
1
0
0
3
2
2
1
1
0
2
0
1
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
1
2
2
2
2
1
0
2
0
0
0
0
0
0
1
1
0
2
1
0
0
0
0
1
1
1
2
0
0
0
0
1
2
2
1
1
0
0
0
0
0
2
4
1
2
2
1
2
0
0
1
2
0
0
0
0
0
1
1
1
0
2
1
0
0
2
0
2
0
0
0
2
0
0
1
0
0
0
2
0
1
2
0
2
0
0
3
1
0
1
2
1
0
0
0
2
0
3
0
1
2
1
2
3
2
0
0
0
0
0
1
0
2
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
2
3
0
1
1
2
0
1
0
0
0
1
2
2
1
1
2
0
0
0
2
0
2
1
1
0
0
1
2
1
0
2
0
0
0
0
1
0
1
1
2
0
0
0
0
2
0
0
1
1
0
0
2
2
0
0
0
2
0
1
0
0
0
2
1
1
0
1
0
0
1
0
0
0
1
2
0
1
0
0
0
1
0
0
1
0
2
0
1
0
0
2
2
0
0
1
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
2
1
0
2
2
0
0
0
2
1
1
2
0
1
3
1
3
0
0
1
0
1
0
2
1
1
0
2
1
1
2
0
2
2
2
0
1
1
0
0
0
0
1
0
0
2
1
0
2
1
0
0
0
1
0
1
0
3
1
0
2
0
1
0
0
1
0
2
0
1
1
5
0
1
1
0
0
1
1
0
0
2
1
2
2
2
0
1
0
1
1
1
0
0
2
1
2
0
0
2
0
0
1
0
0
1
0
0
0
0
2
1
3
2
0
1
0
1
2
2
0
1
1
0
0
0
1
2
0
0
0
0
0
0
1
5
2
1
0
2
2
2
3
2
0
1
0
2
0
1
1
0
1
0
1
2
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
1
2
0
2
0
1
0
0
0
3
0
3
2
0
0
0
0
1
2
2
0
0
0
1
0
2
1
1
2
1
0
0
0
0
2
2
1
1
0
0
0
1
0
3
0
0
0
4
0
0
0
0
0
3
1
3
2
2
0
1
0
1
0
0
0
2
0
0
2
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
2
1
0
0
0
1
0
0
0
2
2
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
1
1
0
0
0
0
2
0
0
0
2
1
2
1
0
0
0
2
2
2
0
0
2
1
0
1
0
2
1
2
0
0
1
0
0
0
1
0
1
0
1
1
0
0
1
2
0
0
3
0
0
3
0
0
0
1
1
2
2
1
0
0
2
0
0
0
0
1
0
1
0
0
0
0
2
1
2
0
0
1
1
0
0
2
1
0
0
0
0
1
0
0
2
0
2
0
1
1
0
2
1
0
0
0
0
1
3
2
1
0
2
0
0
0
1
0
0
0
0
1
0
1
1
0
1
1
1
2
2
0
0
0
1
0
0
0
2
2
0
0
0
2
1
0
1
1
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
1
2
0
1
2
2
0
2
0
2
0
1
2
0
1
0
0
2
1
0
2
1
1
0
2
0
0
1
0
0
2
0
0
2
1
0
0
1
1
0
0
0
3
2
1
1
1
2
0
0
0
2
0
1
0
0
3
1
1
0
1
0
0
1
0
2
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
2
1
1
0
1
0
0
0
1
0
2
1
0
2
0
0
1
0
0
1
2
0
2
2
0
1
1
0
2
0
0
2
0
1
0
0
1
3
0
0
0
0
0
1
0
1
2
0
1
0
2
0
2
0
0
0
2
2
0
0
2
0
0
1
2
1
0
1
0
1
1
1
0
1
1
0
1
0
1
0
0
2
1
2
1
2
0
0
0
0
2
0
0
1
0
1
0
2
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
1
0
0
1
1
1
0
1
0
2
0
2
1
1
0
1
0
2
1
0
2
1
0
0
2
0
2
2
0
1
0
0
2
1
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
1
2
0
0
0
0
1
0
0
1
0
0
0
1
2
0
2
0
2
1
0
2
0
0
0
0
1
1
0
1
0
1
2
2
1
2
0
2
0
2
0
0
0
0
2
0
2
1
0
1
0
0
0
0
2
0
0
2
0
0
0
2
2
2
0
0
1
0
1
2
0
0
0
0
1
2
1
0
0
1
0
0
2
1
2
0
2
1
0
1
2
0
0
0
0
1
0
0
2
1
1
3
1
1
0
0
1
1
1
0
0
0
3
0
0
0
0
3
0
0
1
0
1
0
0
2
1
1
1
1
2
0
0
1
0
0
2
3
0
0
0
0
2
0
2
0
1
1
1
0
0
0
0
0
0
2
0
0
0
0
0
2
2
3
2
0
0
0
3
2
1
2
0
0
1
1
0
0
0
0
0
2
0
1
0
0
2
2
0
2
1
1
0
2
2
0
0
0
0
0
2
1
0
1
0
4
0
1
0
2
1
0
0
1
0
2
1
0
0
2
1
0
1
0
2
0
0
2
1
1
1
1
2
1
6
0
1
1
2
1
0
0
0
2
1
0
0
1
0
2
2
0
0
0
2
1
0
0
2
0
0
2
0
0
2
0
3
0
3
1
0
0
0
1
1
0
0
0
0
0
1
0
0
3
0
2
1
0
2
0
1
0
2
0
2
0
1
0
2
2
4
0
0
1
1
2
2
0
1
1
2
0
0
0
1
2
0
0
0
0
1
0
1
0
0
1
0
0
0
2
0
2
1
0
0
0
0
2
2
0
0
1
1
1
0
0
2
2
1
0
2
0
2
0
1
1
0
1
2
0
0
0
0
0
2
2
0
0
0
2
0
2
0
0
2
0
2
0
1
0
1
1
0
0
0
1
2
1
1
0
2
1
0
0
1
0
0
1
0
2
3
0
0
1
0
1
0
0
0
0
0
0
1
1
1
2
1
2
2
1
2
1
2
0
0
1
0
1
1
0
2
2
1
0
0
0
0
2
0
2
0
0
0
1
0
1
0
1
0
0
0
2
0
1
1
0
1
0
0
0
2
0
1
0
0
2
2
0
0
0
1
0
1
0
1
0
1
0
1
1
0
1
0
2
0
0
0
1
0
2
0
0
0
0
0
0
3
1
0
0
0
0
4
0
1
0
0
1
1
0
0
1
1
0
1
2
0
2
1
1
2
0
2
0
2
1
3
0
0
1
0
2
0
0
2
0
2
0
0
0
2
0
0
0
0
2
1
2
0
0
2
0
0
1
2
0
1
0
0
0
1
0
2
2
2
0
1
1
0
0
2
1
2
0
2
0
2
1
0
1
0
1
2
0
1
1
1
0
0
1
0
3
1
1
1
0
0
1
2
0
0
0
0
0
2
0
2
2
0
0
0
0
1
0
1
1
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
1
1
1
0
2
1
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
1
1
1
1
0
0
2
0
0
1
0
0
1
1
1
0
0
0
3
0
0
1
2
1
0
0
0
2
1
1
0
0
0
2
0
0
1
0
0
0
0
0
0
1
1
2
2
0
0
1
1
0
1
2
2
1
0
2
0
0
0
1
2
0
1
2
1
2
2
1
0
2
0
0
0
0
1
2
0
0
2
0
1
0
0
0
2
1
0
1
0
0
1
0
0
0
2
2
1
0
2
1
0
0
0
2
0
0
2
0
1
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
2
1
1
0
0
0
2
0
0
0
0
1
1
0
0
0
1
2
1
1
0
0
0
0
0
2
0
2
0
2
2
1
2
3
1
0
0
0
1
1
1
0
2
0
2
3
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
1
2
0
0
0
1
2
0
0
0
2
0
0
2
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
1
1
2
2
2
0
0
1
2
0
0
0
0
1
2
1
0
1
0
5
1
0
0
0
0
1
0
1
0
3
1
1
1
0
0
0
0
0
3
0
1
0
2
1
1
1
1
1
0
1
1
1
1
0
0
2
0
0
0
0
1
0
2
2
0
0
2
0
1
1
0
1
1
0
2
1
2
0
1
0
2
1
0
1
0
0
1
1
1
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
1
2
1
0
1
0
0
2
1
0
1
2
0
0
2
1
1
1
2
0
0
0
0
1
0
2
1
2
0
0
0
0
0
0
0
2
0
1
1
0
1
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
2
2
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
2
1
2
0
0
0
1
2
2
0
0
0
2
1
0
0
2
0
1
0
0
0
0
0
2
0
0
0
1
1
2
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
1
1
0
0
0
1
2
0
1
0
0
0
0
1
2
1
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
1
0
2
0
0
1
2
0
3
1
1
0
2
1
0
1
0
0
1
2
1
1
1
0
0
0
1
0
1
2
0
1
2
0
0
2
0
0
2
0
0
2
1
0
2
1
1
1
2
1
0
0
1
1
0
0
0
1
1
2
2
0
0
1
0
0
0
1
0
0
0
1
0
1
0
2
0
0
1
0
0
0
0
0
1
1
2
0
0
0
0
0
1
0
2
1
0
0
0
0
1
0
4
2
0
0
1
2
0
0
2
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
1
0
1
1
2
2
1
2
0
0
2
2
0
1
0
2
1
0
0
0
1
0
0
2
1
0
1
1
0
1
2
0
2
2
1
0
0
1
0
0
2
0
0
0
0
0
2
1
0
1
1
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
2
0
1
0
1
3
1
0
0
1
0
0
0
0
0
0
1
1
0
0
2
3
0
1
0
2
0
1
0
0
0
0
1
0
0
2
1
0
0
0
0
0
2
0
2
0
0
0
0
0
2
2
2
0
1
0
1
1
1
0
1
0
1
0
0
0
0
1
1
0
0
1
2
0
2
0
0
2
0
2
0
2
0
0
0
2
2
1
1
0
2
1
0
1
0
0
1
2
0
1
0
0
0
1
0
0
0
0
1
2
1
1
1
0
2
1
0
2
0
0
0
2
2
2
0
1
1
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
2
1
0
0
0
1
1
0
0
0
0
2
1
0
1
1
0
2
1
0
0
2
1
1
0
0
1
0
2
0
0
1
1
0
0
0
2
0
0
1
1
1
3
0
0
0
0
3
0
0
1
0
2
1
0
1
1
2
0
1
2
1
1
0
0
1
1
1
1
2
2
0
0
1
0
0
0
0
1
0
0
1
0
2
0
2
0
2
0
0
0
0
0
3
1
0
0
1
0
0
0
2
0
0
1
1
0
0
0
1
1
1
1
1
1
2
2
0
1
2
0
0
1
0
0
2
0
0
1
0
2
0
0
1
2
0
1
0
2
0
2
0
0
0
1
0
0
0
0
1
0
0
2
0
1
0
0
2
1
1
1
2
2
0
0
0
0
2
2
0
0
0
1
2
0
0
0
0
4
1
0
2
0
0
0
3
1
2
0
0
0
2
1
0
0
0
0
0
0
2
0
1
0
2
0
2
0
1
1
0
0
0
2
2
0
1
2
2
1
0
0
1
0
0
0
0
1
1
1
1
0
0
0
0
0
0
2
0
0
0
2
0
0
1
1
0
2
0
0
2
0
2
2
1
0
1
1
0
2
1
0
1
2
2
0
0
0
0
2
1
2
2
2
0
1
2
0
1
2
0
0
1
0
0
1
0
0
0
1
0
2
0
2
0
0
0
0
3
0
0
1
1
2
2
2
1
0
1
0
1
1
1
2
0
0
3
0
0
0
2
0
0
2
0
0
1
1
1
0
0
2
0
1
0
2
2
1
0
2
0
0
1
1
3
0
0
0
1
0
0
0
2
1
0
1
0
1
1
1
4
0
2
2
2
1
2
1
2
0
1
0
0
2
0
2
2
1
0
0
4
0
0
0
2
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
3
0
1
0
2
0
0
0
1
0
0
0
0
0
1
3
1
1
0
0
0
1
0
0
0
2
1
2
2
1
2
0
0
0
0
0
0
0
2
2
1
1
1
0
2
2
1
0
1
0
0
1
0
1
0
1
0
0
0
0
0
2
0
2
1
1
2
0
0
0
0
0
0
0
0
0
1
1
2
1
1
1
1
2
1
0
1
2
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
2
0
0
1
2
1
0
0
0
0
2
0
0
1
1
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
6
1
2
0
2
2
1
0
0
0
1
1
0
1
0
0
1
1
0
0
0
0
0
0
0
2
2
0
0
0
5
0
0
2
0
0
0
0
1
0
2
2
0
2
0
0
1
2
1
2
0
1
0
0
2
0
0
1
2
1
0
0
0
3
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
2
0
2
0
0
1
2
2
2
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
1
4
1
0
1
0
0
0
0
0
1
0
2
0
1
1
0
0
0
0
0
0
0
0
2
1
2
1
1
0
1
0
0
1
0
2
0
0
1
2
2
0
0
1
0
0
3
0
0
1
0
1
0
0
0
0
1
0
1
2
1
0
0
1
1
0
0
0
1
1
2
1
1
1
0
0
2
1
2
0
1
0
0
0
0
2
2
1
0
0
1
0
0
2
0
2
0
1
1
2
1
3
0
0
2
0
2
0
0
0
0
0
0
1
0
1
2
1
0
0
1
1
0
0
0
0
0
1
0
0
2
1
3
0
2
1
0
2
2
2
0
0
0
0
1
0
0
0
1
0
3
0
2
0
0
0
1
0
0
1
1
1
0
0
2
0
1
0
0
2
2
0
1
0
0
0
0
0
1
3
0
0
0
1
0
2
0
0
0
0
1
0
1
1
1
3
1
0
0
1
0
0
1
2
2
0
0
0
0
2
0
0
0
2
0
2
0
2
0
0
0
0
2
0
0
0
2
2
0
0
1
0
1
1
0
0
2
0
0
1
0
1
0
0
0
0
0
2
1
0
0
2
1
1
0
0
2
0
2
0
0
0
1
1
1
0
0
0
2
0
0
0
2
0
1
1
0
2
1
0
2
0
2
2
2
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
2
0
2
2
2
0
0
0
1
1
0
2
2
1
0
0
1
0
0
0
0
2
1
2
2
2
0
2
1
0
0
1
2
0
2
0
0
0
1
0
1
1
0
1
0
2
1
1
0
2
0
0
0
1
1
1
1
0
0
0
0
0
2
0
2
1
0
0
0
1
0
0
1
0
0
1
2
2
0
0
0
2
5
0
2
1
0
1
0
2
1
0
0
2
3
1
0
1
0
1
1
1
2
1
1
1
0
0
0
0
2
1
2
0
1
0
1
0
1
0
1
0
0
1
2
0
2
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
1
1
0
2
0
1
2
0
0
1
1
0
0
0
0
0
0
1
1
0
1
0
1
0
0
2
1
1
2
0
0
0
0
4
0
2
2
0
2
0
2
2
0
1
0
2
2
0
1
0
0
0
0
1
2
1
1
1
0
0
0
2
1
2
0
0
0
0
0
2
1
0
2
0
0
1
0
0
1
2
1
0
0
1
1
0
1
0
1
0
0
0
1
0
0
0
0
1
0
2
1
0
2
0
0
0
0
1
0
0
0
1
3
0
1
0
0
2
0
0
2
0
2
0
2
1
0
0
0
2
3
0
0
2
0
0
0
0
0
2
0
1
0
0
0
2
1
2
0
0
0
1
0
1
2
0
2
1
0
0
2
0
0
0
0
0
0
2
1
0
0
1
1
0
0
1
0
1
0
0
0
2
1
2
2
2
2
0
2
2
0
0
1
0
0
0
0
2
1
1
0
0
2
1
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
2
0
0
0
0
2
0
0
1
1
1
1
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
1
0
2
1
1
0
1
0
0
1
1
0
0
0
1
0
0
2
0
1
0
1
2
0
1
0
0
0
2
1
1
1
0
1
1
1
2
2
0
0
0
0
0
1
2
0
0
0
0
0
2
0
2
0
1
0
0
0
1
1
1
1
0
1
3
0
0
0
0
0
2
0
0
0
2
1
0
0
1
0
0
0
0
2
0
0
1
1
1
1
1
2
0
0
0
0
0
2
0
0
0
0
2
1
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
1
1
2
0
2
0
2
0
0
1
1
0
2
2
0
0
0
0
3
2
2
2
1
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
2
0
3
1
0
0
0
1
0
2
0
0
1
0
1
0
1
0
1
0
0
1
1
2
0
2
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
1
1
0
1
0
0
0
2
0
0
0
0
0
0
1
1
2
0
3
1
0
1
1
1
0
0
0
1
1
0
1
2
0
0
2
2
0
0
0
1
1
0
1
0
0
0
2
2
1
3
0
1
2
1
0
1
2
0
2
1
2
1
0
2
0
1
1
1
2
1
0
1
2
0
0
1
2
2
2
0
0
0
2
0
2
2
0
1
0
2
0
0
0
0
0
3
2
1
2
0
0
2
0
0
2
1
0
0
2
2
3
2
0
2
1
1
0
0
2
3
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
2
2
0
0
1
0
0
0
0
0
2
0
1
1
1
0
0
2
1
0
1
1
1
0
1
1
0
0
1
0
1
1
0
1
0
0
1
1
0
0
2
0
0
3
0
4
1
2
0
0
2
1
2
0
2
2
0
0
0
0
0
2
2
0
4
1
2
0
0
1
0
0
2
0
0
0
2
0
1
0
2
2
0
1
0
0
1
0
1
0
0
0
2
1
2
0
0
1
0
2
0
1
0
1
1
0
0
0
1
2
1
0
2
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
2
1
0
0
1
0
0
1
0
0
2
0
0
0
1
2
1
1
2
0
1
0
0
0
1
0
0
0
1
0
1
0
2
0
2
2
1
0
0
0
1
0
0
1
1
1
2
0
0
1
0
1
0
0
2
1
1
4
0
1
0
1
2
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
1
2
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
1
0
1
0
1
4
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
1
1
0
2
0
1
0
0
0
1
1
0
1
1
2
2
0
0
0
0
0
0
1
0
0
0
1
2
1
0
0
0
1
0
0
1
1
1
0
0
2
0
1
0
2
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
2
0
2
0
0
0
0
0
2
0
0
1
1
3
1
0
1
0
1
1
0
0
0
1
0
2
1
2
0
0
0
2
0
0
0
0
1
1
2
0
0
0
1
0
0
0
1
0
1
1
1
0
0
0
0
0
0
4
0
0
0
2
1
0
2
2
1
0
1
2
1
1
2
2
0
2
0
0
2
1
0
3
0
1
0
0
0
0
0
0
0
1
0
0
0
2
1
0
1
0
1
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
2
0
0
0
2
2
0
2
1
0
1
0
0
1
0
1
1
2
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
1
0
0
0
1
0
1
0
0
2
2
0
0
1
1
0
1
0
1
0
0
1
0
3
0
0
2
0
0
1
0
2
2
1
1
1
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
1
0
0
1
0
0
0
1
2
2
1
1
0
0
2
0
0
0
0
1
0
1
0
2
0
2
0
0
2
1
0
1
0
0
0
0
2
1
0
1
0
0
0
0
1
2
1
0
0
2
0
2
1
0
0
0
0
1
0
2
1
1
1
2
0
2
2
0
0
0
1
0
1
1
2
0
1
1
0
0
0
0
0
1
2
1
0
0
0
0
2
0
1
2
0
2
0
1
1
2
1
2
1
1
1
0
2
2
0
2
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
2
1
3
2
0
0
2
1
0
0
2
0
0
0
0
0
0
1
2
0
0
1
0
1
0
2
0
1
0
5
0
2
1
6
1
0
0
0
0
1
2
0
0
0
0
0
2
1
4
0
0
0
0
0
2
3
1
1
1
1
1
1
0
1
2
0
2
0
0
1
1
0
1
0
0
0
1
1
2
2
0
1
0
0
1
1
0
1
1
1
0
0
1
2
1
2
0
1
1
1
1
0
1
0
0
0
0
2
0
1
1
3
1
0
0
1
0
2
0
1
0
1
0
0
1
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
2
0
0
0
1
0
2
0
0
2
0
1
0
0
3
1
0
1
1
1
0
2
0
0
0
3
0
0
0
2
2
0
0
0
1
0
0
0
1
0
0
1
2
2
1
0
1
1
0
1
1
0
2
2
0
2
2
2
0
2
1
1
2
2
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
1
3
1
2
1
0
0
1
0
0
0
1
0
3
1
0
0
1
2
0
1
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
1
0
2
1
0
0
2
0
2
0
1
0
0
1
0
1
1
0
0
0
0
0
0
2
0
0
2
1
0
13
1
0
0
0
0
0
2
0
1
2
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
2
2
1
0
0
2
1
0
2
2
0
1
2
0
0
2
0
0
0
2
0
1
0
0
1
0
1
1
2
0
1
0
0
0
2
0
0
0
2
0
0
1
0
1
1
2
0
0
0
1
2
2
1
0
0
0
1
2
0
0
1
3
0
0
2
2
2
0
0
2
0
2
2
1
1
0
0
0
0
0
0
1
2
0
0
2
0
0
0
2
0
0
0
0
0
5
0
2
2
2
1
1
2
0
2
2
0
0
1
1
1
0
0
2
0
0
0
1
0
2
2
0
2
2
0
1
0
0
0
0
0
2
0
2
1
1
0
0
1
1
2
0
0
1
0
2
1
1
1
1
0
1
0
0
1
0
1
0
4
0
1
2
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
1
2
1
0
0
1
2
0
1
0
0
0
2
2
0
0
0
0
0
2
1
2
0
0
0
2
0
0
1
2
0
0
1
2
0
0
1
3
0
1
0
2
0
2
2
0
2
0
1
1
1
2
1
0
0
0
2
1
0
0
0
2
1
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
1
1
0
0
0
2
1
1
1
0
0
0
0
0
0
2
0
2
0
0
0
0
1
1
0
1
2
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
2
1
1
0
2
0
1
0
1
0
1
0
1
2
2
2
1
1
1
0
0
0
1
2
0
0
0
1
1
0
0
0
2
1
2
1
0
2
0
1
0
0
0
2
1
1
0
0
0
0
2
2
2
0
0
1
0
2
1
1
1
0
0
2
0
0
0
1
0
1
1
0
2
3
0
1
0
0
0
1
0
1
2
0
0
0
1
1
0
0
0
1
2
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
2
2
0
1
0
0
2
1
2
0
0
2
2
2
2
0
0
0
0
0
2
2
1
2
0
1
0
0
1
0
0
2
0
2
0
2
1
2
0
0
2
1
0
0
5
0
1
2
1
0
0
0
0
0
2
1
0
0
1
0
4
1
2
1
2
1
0
1
0
2
1
0
0
1
1
0
0
1
0
1
0
0
1
2
2
1
0
0
0
0
0
3
0
1
0
2
0
0
1
1
1
0
1
0
0
0
0
0
0
0
2
2
0
0
0
1
1
0
1
1
1
0
1
0
1
0
2
1
1
0
2
3
2
0
0
0
2
0
0
0
0
2
2
0
0
0
2
2
0
0
2
1
0
0
0
2
1
0
0
1
0
0
0
0
2
0
0
1
0
2
0
1
0
2
0
0
0
0
0
0
0
0
1
1
0
0
1
0
2
0
0
0
0
0
2
0
0
1
1
1
1
2
1
0
0
0
3
0
1
3
0
1
1
0
0
0
5
0
0
0
1
0
0
1
0
0
1
1
0
2
0
1
0
2
0
1
1
2
2
2
0
0
1
0
0
1
2
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
2
0
0
2
2
1
3
0
0
0
0
0
1
2
0
2
2
0
0
2
0
0
0
0
1
0
2
0
0
1
0
0
0
1
1
2
1
0
1
2
0
0
1
0
1
0
0
0
1
0
2
0
0
1
0
2
0
0
2
1
1
2
0
0
0
2
2
1
0
0
2
1
1
1
2
1
2
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
1
1
1
1
0
2
1
2
0
0
0
0
0
0
1
0
0
0
0
1
0
2
2
2
2
0
1
2
0
0
0
1
1
1
1
0
0
0
0
1
2
0
0
2
0
1
0
2
1
1
0
1
2
1
0
0
0
0
0
0
0
0
1
0
0
1
3
1
2
0
1
1
0
0
0
0
4
0
1
1
0
0
0
1
0
0
0
2
0
2
2
0
0
0
0
2
1
0
0
0
0
0
1
1
0
0
0
2
2
0
2
1
0
2
1
0
2
2
4
0
2
2
0
1
0
0
1
0
0
0
0
2
0
1
0
2
1
0
1
0
1
1
2
0
1
2
1
1
0
0
2
0
1
1
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
1
2
1
0
0
1
2
1
3
0
0
0
0
1
0
0
0
0
1
2
0
2
0
0
0
0
0
0
2
0
2
0
0
2
0
1
0
1
0
2
0
2
3
1
1
2
2
1
1
2
0
2
0
1
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
2
0
0
0
0
0
0
0
0
2
1
2
1
0
2
0
2
0
0
0
1
1
0
0
0
0
0
0
1
2
2
1
2
0
1
0
0
2
0
0
1
2
2
0
0
1
2
0
1
0
0
2
3
2
0
0
0
1
2
2
0
0
0
0
0
0
0
1
2
1
0
0
0
0
1
4
2
0
2
1
0
0
1
0
0
0
0
4
0
1
0
1
1
0
0
2
2
2
0
2
0
0
0
0
0
0
2
2
1
2
0
0
0
1
2
1
0
1
0
0
0
2
0
0
3
1
1
1
0
0
0
0
1
2
0
0
1
0
2
1
2
0
1
0
0
1
2
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
1
2
0
0
0
0
2
2
1
2
1
1
1
0
0
1
0
0
1
1
0
0
2
0
0
0
0
3
2
2
0
1
2
3
0
0
0
0
0
2
0
2
2
2
0
0
0
0
0
0
0
0
2
0
2
2
0
1
0
0
0
1
0
0
1
0
2
1
2
0
0
1
1
2
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
2
0
2
0
1
0
1
1
2
1
1
0
1
2
2
2
0
0
0
1
0
0
2
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
2
0
1
1
0
1
0
2
1
1
2
0
0
2
0
1
0
0
0
2
1
0
1
0
0
2
0
0
0
1
0
1
0
0
2
1
1
3
0
2
0
2
2
0
2
0
0
0
1
0
0
0
0
0
1
1
0
2
2
2
0
2
2
0
2
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
1
0
2
2
0
2
2
2
2
0
0
1
0
2
2
2
2
0
0
0
0
1
0
0
0
1
1
0
2
1
1
0
2
1
0
1
0
1
1
1
0
2
1
1
0
0
1
4
2
1
0
2
1
0
0
1
0
0
1
1
1
1
1
2
0
1
0
0
0
4
2
1
2
0
0
0
0
1
1
0
2
0
2
0
2
0
2
0
1
1
2
1
0
0
2
1
0
1
0
0
0
1
2
0
0
1
1
0
0
0
0
2
1
2
1
2
1
2
0
1
0
0
0
0
0
2
1
2
0
1
1
0
0
0
1
1
0
2
2
0
0
2
0
0
1
1
0
0
0
2
1
2
0
2
2
0
1
0
0
2
2
2
0
2
1
1
1
1
1
1
2
0
0
0
1
0
2
0
0
0
2
2
0
0
0
1
0
0
0
4
0
0
0
2
1
1
0
1
0
2
1
1
0
0
2
1
1
0
0
1
1
2
2
2
0
1
2
0
1
0
0
0
1
1
1
0
3
1
0
0
3
0
1
1
0
0
0
0
1
0
0
0
2
0
0
1
2
3
0
0
0
0
1
0
0
0
0
0
5
0
1
0
2
2
0
0
1
0
0
0
0
2
0
0
2
1
1
2
2
2
0
0
0
0
0
0
1
0
4
0
2
2
0
0
0
0
1
0
2
0
0
0
0
1
3
1
2
0
2
0
0
1
2
0
0
0
1
1
1
0
2
0
0
1
1
0
1
1
1
0
1
2
0
0
2
0
0
0
1
0
0
0
2
0
2
0
0
0
0
1
0
0
2
2
0
0
0
0
0
1
1
1
0
2
1
0
1
2
1
0
1
0
0
0
0
1
1
2
0
1
0
1
0
1
1
0
0
1
0
0
0
0
1
0
1
0
0
0
1
1
0
0
1
1
2
2
1
3
0
0
0
0
1
0
0
1
0
3
0
0
1
0
0
2
0
2
0
1
2
2
0
0
0
1
1
1
0
2
1
0
2
2
0
0
0
1
2
1
0
0
0
0
0
0
0
0
1
0
1
1
2
2
0
1
2
2
1
3
1
0
0
2
0
1
0
2
0
1
8
5
0
0
0
0
2
1
2
2
1
3
0
1
0
2
0
2
0
0
4
1
0
0
0
1
2
0
2
1
2
1
0
2
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
2
2
0
0
1
1
2
1
1
0
2
2
1
0
0
0
1
0
0
0
2
1
0
0
1
0
0
1
2
2
3
0
1
0
0
0
0
1
1
1
0
2
0
2
0
0
0
1
0
1
2
0
0
2
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
1
2
1
0
1
2
2
1
0
1
1
0
5
2
0
1
2
0
0
0
1
0
1
2
2
0
0
0
0
2
1
0
3
2
0
2
0
2
0
1
0
0
1
0
2
1
1
1
2
0
0
2
1
1
2
2
0
1
0
0
2
0
0
1
0
1
2
2
0
0
2
1
0
2
0
0
0
4
0
1
1
0
0
2
1
0
0
0
0
1
0
0
0
0
2
0
0
2
0
2
1
0
1
1
0
1
1
0
0
0
0
1
1
3
1
2
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
2
2
0
3
0
0
1
1
0
0
0
0
0
0
0
0
0
3
2
0
1
0
0
1
3
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
2
0
2
0
2
1
1
1
0
1
0
0
0
0
0
0
0
3
0
0
2
0
0
1
2
1
0
1
2
2
0
1
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
1
1
1
1
1
0
1
1
2
0
0
0
0
0
0
1
0
1
1
2
1
0
0
2
0
2
0
1
0
4
2
0
1
0
1
0
1
0
0
0
0
1
0
2
1
0
0
1
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
2
0
1
2
1
1
0
0
2
0
2
0
2
2
2
0
2
0
0
2
0
1
3
1
1
3
1
0
2
0
1
0
0
0
0
0
0
0
0
2
0
1
1
1
0
0
0
0
1
0
0
0
2
0
0
2
0
2
2
0
1
0
2
0
0
3
2
2
1
0
1
0
0
0
1
1
1
1
0
0
0
2
0
1
2
2
1
0
0
0
0
0
0
0
0
1
3
1
2
0
1
0
0
0
0
1
2
2
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
1
2
1
0
0
0
2
0
0
1
0
0
0
0
1
1
1
0
0
1
0
1
0
1
1
1
2
0
0
0
0
1
0
3
0
1
1
0
2
0
2
0
0
1
0
0
0
1
2
0
0
0
1
3
1
0
0
2
0
0
2
1
0
0
1
4
1
0
0
2
1
0
1
5
2
1
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
1
0
2
0
3
1
0
2
1
1
1
1
1
0
0
2
1
2
1
1
1
0
2
2
2
0
0
2
0
2
0
1
0
0
0
0
0
0
1
0
0
1
0
0
2
0
2
2
0
2
0
1
1
1
0
1
0
2
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
1
3
1
0
2
0
2
0
0
0
0
1
2
0
3
1
0
1
0
0
1
2
0
0
1
1
0
0
2
2
2
2
0
1
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
1
2
0
0
2
1
0
1
0
0
0
1
0
1
0
1
1
0
0
2
1
1
0
2
0
0
2
0
0
0
0
0
0
2
1
0
1
0
1
2
2
0
0
0
0
0
1
0
2
1
0
0
0
0
1
2
1
2
0
0
0
0
2
0
0
2
0
0
0
1
2
2
1
1
0
0
3
0
0
0
0
1
1
0
0
2
0
2
2
3
1
1
0
0
1
1
0
0
0
1
1
1
1
0
1
0
0
0
1
1
0
0
2
0
0
1
0
2
1
0
1
2
2
0
0
0
0
1
1
0
0
0
0
2
5
0
0
0
2
0
0
0
1
0
0
0
0
1
1
0
0
2
0
2
1
0
0
0
2
0
0
1
1
0
0
0
1
0
1
0
1
0
1
0
0
0
0
2
2
0
0
0
1
0
0
2
0
0
0
1
0
2
0
0
0
1
1
0
2
2
1
0
6
2
0
0
0
1
0
0
0
0
1
1
0
0
1
1
1
0
2
0
1
1
1
0
0
1
1
0
1
2
0
0
1
1
1
3
1
0
0
4
0
1
0
3
0
0
0
0
2
2
0
0
1
0
0
0
2
0
0
1
0
0
0
0
1
2
0
1
0
0
0
0
1
0
1
0
1
1
1
0
0
0
0
1
3
0
0
0
0
1
0
1
2
2
0
0
0
0
0
0
1
0
0
0
0
1
0
3
2
0
0
0
0
0
0
2
1
0
0
0
0
0
3
0
2
1
3
0
0
1
0
0
0
0
2
0
1
2
2
0
1
0
0
2
1
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
2
0
2
0
1
0
2
0
2
2
0
2
2
1
0
0
1
0
2
0
0
1
2
0
3
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
5
2
0
0
2
1
1
1
0
2
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
1
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
1
4
4
0
2
0
2
0
1
0
0
1
2
1
3
2
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
1
2
4
1
7
2
2
1
2
3
1
0
0
0
0
0
0
0
1
0
1
2
2
0
0
2
2
0
1
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
2
1
0
2
0
0
0
2
1
0
0
0
2
2
0
2
2
3
0
2
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
1
0
0
2
1
0
0
2
1
0
0
1
0
1
1
0
1
0
0
0
1
1
0
0
0
1
2
1
0
3
0
1
1
1
1
0
3
0
1
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
1
2
1
0
0
0
2
1
0
0
2
0
0
0
1
1
0
0
0
2
1
2
2
1
2
0
0
0
0
0
1
1
2
1
2
0
0
0
0
0
0
0
1
0
2
0
2
2
0
1
2
1
2
0
0
0
0
0
0
0
1
1
0
2
0
0
2
1
1
0
0
1
0
0
0
2
1
2
2
0
0
2
2
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
1
0
0
0
0
2
1
0
0
0
0
1
0
0
0
1
2
1
0
0
1
1
0
0
1
0
2
2
2
0
2
1
0
0
0
1
1
0
1
1
0
2
3
0
1
0
1
1
2
0
0
0
0
0
1
2
2
0
2
0
1
0
2
0
0
1
1
0
0
1
1
1
0
1
2
0
1
2
0
0
1
0
0
0
0
1
0
0
0
0
0
4
0
0
0
2
0
0
1
1
0
0
1
0
2
0
0
2
1
0
1
0
0
0
2
0
2
0
2
0
0
0
0
0
2
0
2
0
0
2
1
1
0
0
2
0
4
1
0
0
1
0
0
0
0
1
2
0
0
2
0
1
2
0
1
1
0
1
2
0
0
0
3
0
1
0
2
0
1
0
0
0
1
2
0
0
0
0
0
2
0
0
0
2
2
1
0
1
0
0
2
1
0
0
0
0
1
0
2
1
2
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
2
0
1
0
0
0
1
2
2
4
0
0
0
1
2
0
0
1
1
0
0
0
1
1
2
0
1
0
1
0
2
1
0
0
1
2
1
2
2
0
0
0
0
0
1
0
2
0
0
2
0
2
2
1
0
1
1
1
2
1
1
2
0
0
2
1
0
0
1
2
0
0
0
1
0
0
2
1
0
1
0
2
1
0
0
2
1
1
0
1
0
1
1
0
0
0
1
1
0
0
1
2
2
1
1
2
0
0
0
1
2
2
0
0
1
1
1
0
1
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
1
1
2
1
2
0
0
0
0
2
1
1
0
0
2
0
0
0
3
0
1
0
0
1
0
2
0
1
2
1
1
0
1
1
0
1
1
0
0
2
0
2
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
1
2
1
0
2
1
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
1
0
1
2
0
1
0
0
1
2
0
0
0
3
0
0
0
1
0
2
2
0
2
0
0
0
0
1
2
0
0
2
2
0
1
2
5
1
1
0
0
0
0
1
1
0
1
4
0
0
0
0
2
0
0
0
0
2
1
0
3
1
0
2
1
0
1
2
1
0
1
0
0
0
0
0
2
1
2
0
0
1
0
0
0
2
0
0
0
0
2
2
0
1
1
0
1
0
0
0
0
2
1
0
1
1
0
2
1
1
1
0
0
1
0
0
1
1
0
1
2
3
0
0
0
0
0
0
0
2
0
1
2
2
0
0
1
0
1
0
0
0
1
0
0
0
1
1
0
1
1
1
1
0
1
0
0
0
1
0
2
1
0
1
0
0
0
1
3
2
0
0
0
0
0
0
0
1
2
0
2
2
0
2
1
0
2
2
0
0
0
1
1
1
0
2
2
0
4
2
1
0
1
0
1
1
0
1
1
2
0
0
1
2
0
0
2
1
1
1
1
1
1
2
0
1
0
1
0
2
0
2
0
0
0
1
0
1
0
1
0
0
2
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
2
0
1
2
0
0
0
2
1
0
0
0
0
0
0
1
3
1
1
0
1
0
1
2
0
0
0
0
1
1
0
0
2
1
2
2
0
0
0
0
2
1
1
2
2
0
0
2
0
1
1
0
1
0
0
1
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
3
1
0
0
0
1
2
1
1
1
2
0
2
0
0
2
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
1
0
4
2
0
1
2
0
2
2
0
0
2
0
1
0
0
2
0
2
0
1
0
1
1
0
0
0
0
0
2
0
0
1
0
4
0
1
2
1
1
0
0
1
0
0
0
3
0
0
0
2
0
1
0
1
0
0
2
0
2
0
0
2
1
0
0
0
0
1
2
1
0
1
0
0
0
0
1
0
0
0
1
0
0
1
2
2
1
0
0
0
2
0
2
0
0
2
0
1
0
0
1
0
0
1
1
0
1
0
0
0
0
2
0
1
0
0
2
2
0
0
3
0
0
0
1
1
0
0
0
0
0
0
0
2
1
0
0
1
0
0
2
1
1
0
2
0
0
0
0
0
0
0
0
1
0
2
0
1
2
2
1
2
1
0
1
0
0
0
0
0
1
0
2
2
1
1
0
0
0
2
1
0
0
2
0
0
0
0
1
2
2
2
0
1
0
0
2
0
0
1
10
1
0
0
2
2
0
0
0
0
0
0
1
1
0
0
1
0
1
2
1
0
1
0
1
1
0
0
0
0
0
1
2
2
0
1
0
2
1
0
1
0
1
0
2
0
0
0
0
0
1
1
0
0
1
1
1
2
0
0
1
0
1
2
0
1
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
2
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
1
0
0
2
2
0
1
2
0
2
0
1
0
2
0
0
2
2
0
0
0
0
0
2
1
2
0
0
0
2
0
0
1
2
0
1
2
0
1
0
2
0
0
1
0
2
0
6
0
0
1
0
1
2
0
0
0
2
1
0
0
1
2
0
2
0
2
1
1
2
0
2
3
2
0
0
1
2
2
1
0
0
0
0
0
1
0
1
0
0
0
3
0
1
0
0
0
0
2
2
1
0
0
1
1
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
2
1
0
0
1
2
0
2
1
1
0
0
0
0
1
2
0
2
2
0
3
1
1
1
1
0
0
0
0
1
0
1
1
2
0
1
0
1
1
2
2
1
0
2
2
0
0
1
0
0
0
0
0
1
0
0
2
0
1
0
1
0
0
1
0
1
0
0
0
0
0
2
0
1
1
3
0
1
0
0
0
0
0
0
0
1
0
2
0
3
0
0
0
1
2
0
0
1
2
3
2
1
0
2
0
2
0
2
0
0
1
0
2
1
0
0
0
1
0
0
1
0
2
2
0
0
1
2
0
2
0
0
0
0
2
1
1
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
2
2
2
1
2
1
0
0
2
2
3
0
0
0
0
0
0
0
0
2
2
0
1
2
1
1
0
1
0
0
0
1
1
0
0
0
1
1
2
1
0
0
0
0
0
0
1
5
2
0
1
0
2
0
0
3
0
0
0
0
1
0
0
1
1
0
1
1
0
0
2
2
1
0
1
0
0
2
0
0
0
2
0
0
2
1
0
0
2
2
0
1
0
0
2
1
1
0
3
0
1
0
2
0
0
2
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
1
0
2
1
0
0
0
0
0
0
2
0
0
2
0
0
2
1
0
2
2
0
2
1
3
0
2
2
2
1
0
0
2
0
0
0
1
0
0
0
1
0
0
1
1
2
2
0
0
0
0
1
0
2
2
0
1
0
1
0
0
1
0
2
0
1
2
2
1
2
0
1
0
0
0
2
0
0
0
0
0
2
2
0
2
1
0
0
1
0
1
3
0
1
2
2
0
2
1
0
0
1
2
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
1
0
1
1
1
0
1
1
0
1
2
0
0
2
2
2
0
0
1
1
0
0
3
0
0
2
0
0
0
0
2
0
0
0
0
3
0
0
1
0
0
2
2
0
0
0
1
1
2
0
0
0
2
0
0
2
0
1
0
1
0
0
0
1
0
3
0
0
0
0
1
1
1
2
0
2
0
2
0
1
0
1
0
2
0
0
0
0
0
0
2
0
0
1
1
0
2
0
0
0
0
0
2
1
0
1
0
1
0
0
0
0
2
0
0
2
1
0
0
0
0
1
1
0
3
0
2
1
2
0
1
0
2
1
0
1
1
0
0
2
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
1
2
1
2
0
1
2
0
0
1
1
0
0
0
1
0
1
0
1
3
0
2
0
0
0
1
0
1
1
2
0
1
2
2
2
0
0
1
0
0
1
0
0
2
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
2
0
1
0
0
0
0
2
2
2
0
1
1
0
1
2
0
1
0
1
0
2
0
1
2
0
2
1
0
2
0
0
0
2
0
0
0
2
0
1
0
0
1
0
0
4
0
2
1
2
0
2
0
2
0
0
0
0
1
0
0
2
0
0
2
1
0
0
2
0
0
0
2
0
0
0
0
1
0
1
0
0
3
2
0
0
1
0
1
0
0
2
2
3
1
0
2
2
2
1
1
2
0
1
0
0
2
0
1
1
0
1
0
0
0
1
0
0
1
1
0
1
0
1
1
0
3
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
1
2
0
0
0
0
2
0
0
1
0
2
2
2
0
3
0
1
0
0
0
0
1
0
0
0
0
1
2
1
2
2
0
0
4
2
5
0
1
0
0
0
1
0
1
1
0
0
1
1
2
1
2
0
0
1
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
2
0
1
1
0
0
1
0
2
0
1
0
1
0
2
0
1
1
0
3
2
0
0
0
2
2
0
0
2
0
1
0
3
0
2
1
0
0
1
0
0
0
0
2
2
0
0
2
1
2
1
2
2
0
1
0
0
0
1
0
2
1
0
2
0
4
0
0
1
0
0
1
0
1
1
0
1
2
2
1
1
0
1
0
0
1
0
1
0
1
0
3
2
0
0
1
0
0
1
2
0
0
2
0
2
0
0
2
0
0
0
0
0
1
1
0
1
2
2
0
1
1
1
1
2
2
1
1
1
0
1
2
0
1
2
2
2
2
3
0
2
1
1
1
0
0
0
1
1
1
0
0
2
2
0
2
0
0
2
0
0
1
2
1
0
0
2
0
2
0
1
1
0
4
2
1
0
1
0
2
2
0
0
0
2
1
2
1
0
1
3
1
1
0
0
0
0
0
0
2
0
2
0
0
1
2
3
1
0
0
0
0
1
1
0
0
2
0
0
0
1
2
1
0
0
0
1
1
0
2
2
0
0
1
1
1
0
0
1
2
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
2
1
0
1
0
0
0
0
0
1
0
1
0
0
2
0
2
0
0
3
2
0
0
0
0
0
0
0
1
2
0
0
1
0
0
2
1
1
0
1
0
0
1
0
3
1
0
1
2
0
1
0
0
0
0
0
1
1
1
0
0
2
1
1
1
0
5
0
1
0
0
2
1
1
0
2
2
0
0
2
0
0
1
0
2
0
0
0
1
0
0
1
0
0
0
0
3
0
1
0
1
1
0
0
0
1
1
0
0
0
0
1
0
2
0
0
1
2
1
0
0
0
1
1
1
0
0
1
0
0
1
0
2
0
1
0
0
1
0
0
0
1
0
0
0
2
4
0
0
0
1
2
1
0
0
1
1
1
0
0
0
0
1
1
2
6
0
0
0
0
4
2
0
1
1
0
1
0
1
0
1
0
0
2
1
0
0
0
2
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
1
0
2
2
2
1
1
0
0
0
0
2
1
0
2
0
0
0
0
1
0
0
2
1
0
2
1
0
1
2
0
2
0
0
0
0
2
2
0
0
1
0
2
0
2
0
2
1
0
0
0
0
2
1
0
0
2
1
0
0
1
0
0
2
0
2
0
3
0
1
2
1
2
3
1
0
1
0
0
0
0
0
1
2
0
1
0
0
1
2
0
0
0
1
1
1
1
1
3
2
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
1
2
0
1
0
1
1
2
0
0
1
1
1
2
0
1
0
2
0
2
0
0
0
0
2
2
0
0
1
0
1
0
1
0
1
0
2
0
2
0
2
0
2
0
0
0
3
0
5
1
0
1
2
2
0
0
0
0
2
0
0
2
0
2
1
1
1
2
1
0
0
3
1
0
0
0
0
0
1
0
2
0
1
0
0
0
1
1
1
0
0
0
0
3
2
0
0
1
0
0
0
1
0
1
0
1
0
0
1
0
0
0
2
0
0
0
1
0
1
1
0
1
1
2
0
0
1
0
1
0
2
0
1
1
0
0
1
0
1
0
1
0
0
0
0
1
1
0
2
0
3
1
2
1
1
2
1
1
0
0
1
1
0
0
1
1
2
0
2
0
0
2
0
0
3
2
0
2
0
0
1
0
1
2
1
0
2
1
4
1
0
1
2
1
0
0
0
1
2
0
2
1
0
1
1
1
0
0
0
1
1
0
1
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
2
1
1
0
0
1
2
1
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
1
0
2
0
0
0
1
1
0
2
0
1
1
0
2
2
2
0
0
0
0
0
2
0
0
0
0
0
1
1
1
0
0
2
0
1
0
1
0
1
0
0
2
0
3
1
1
1
2
0
1
1
1
0
2
1
0
0
2
0
0
1
0
0
1
2
0
0
0
2
0
0
2
0
2
1
0
0
0
0
0
0
0
0
1
0
1
1
2
2
0
0
0
2
1
1
0
0
0
2
2
2
0
2
2
1
1
1
0
0
0
0
1
0
2
3
1
0
1
2
3
2
0
1
0
0
5
0
1
0
0
4
0
0
0
0
0
1
1
2
0
2
1
2
1
0
0
1
0
0
1
0
1
0
1
1
0
0
0
0
0
1
2
0
2
2
2
2
1
1
0
0
1
0
0
1
3
2
0
0
1
2
2
0
0
1
1
0
2
1
0
1
1
2
2
0
0
0
0
0
1
0
0
1
2
0
0
0
0
2
1
2
0
3
3
0
4
0
0
0
2
0
0
1
1
0
2
0
1
1
0
2
2
2
0
1
2
2
0
1
0
0
0
2
1
1
0
0
1
0
1
1
2
0
3
0
0
0
0
0
1
2
1
1
2
1
0
0
2
0
0
1
1
3
0
1
3
5
0
1
2
0
0
0
0
0
0
1
1
0
0
0
1
0
1
1
0
0
0
1
0
0
1
1
0
0
2
1
1
0
0
0
0
0
0
2
1
1
0
1
2
0
1
2
2
0
0
0
2
0
2
1
1
0
2
1
1
3
3
0
0
0
2
1
1
1
0
1
2
0
1
0
0
0
1
1
0
0
2
0
2
2
0
0
2
1
0
2
0
1
0
0
3
1
0
0
0
2
1
1
1
2
1
0
0
1
1
1
2
0
2
1
2
0
1
0
0
0
1
0
2
1
0
2
1
0
0
2
0
0
3
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
1
0
0
0
1
0
0
1
0
1
2
1
0
3
0
2
2
0
2
0
2
2
1
0
0
0
1
0
2
0
2
0
1
0
0
1
1
1
1
1
1
0
1
1
2
0
2
1
0
1
1
0
1
2
1
2
1
2
2
0
0
2
2
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
8
0
1
0
0
0
3
0
0
0
0
2
0
0
2
0
0
1
2
2
2
0
1
1
2
0
2
0
0
2
0
0
2
1
2
2
0
0
0
0
0
2
0
0
1
0
2
1
0
0
2
0
0
0
0
0
2
0
0
0
2
1
0
0
2
2
1
1
0
0
0
0
0
1
0
0
0
0
3
5
1
0
0
2
2
2
1
0
0
1
0
0
4
1
0
2
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
2
1
1
2
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
2
1
2
0
0
0
0
0
1
0
2
0
0
0
0
0
2
2
0
0
2
1
0
0
2
0
1
1
2
1
2
2
0
1
0
1
0
1
0
0
0
1
1
0
1
2
1
2
1
1
0
2
0
1
2
2
2
0
1
2
0
1
1
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
2
2
0
1
0
2
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
1
0
0
1
0
0
1
2
1
0
2
0
2
1
0
0
1
0
0
1
0
1
1
1
0
0
2
0
0
2
0
0
0
0
3
2
2
0
0
2
0
2
0
1
1
1
2
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
1
0
0
2
0
0
0
1
0
0
0
0
3
2
0
1
2
2
2
1
0
1
2
2
0
0
0
2
2
0
0
0
2
3
0
1
0
2
0
1
1
0
0
1
0
0
1
0
0
2
2
0
0
0
0
2
2
0
0
0
1
0
1
0
1
1
2
0
1
2
2
0
1
1
0
0
0
2
1
2
1
1
1
1
1
0
0
0
1
0
1
0
2
0
1
0
0
0
0
0
0
0
1
0
2
1
0
1
2
0
0
2
0
0
1
1
2
1
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
1
0
0
0
0
2
1
0
2
1
2
0
0
0
0
0
0
0
1
2
0
0
1
2
2
0
1
0
0
0
0
0
0
0
0
0
2
2
2
2
1
1
5
0
0
0
2
0
0
1
1
2
0
2
1
0
1
2
0
1
0
0
0
0
0
2
1
2
1
1
0
0
0
2
2
0
0
0
2
1
0
0
2
1
0
1
1
1
0
0
2
0
0
0
0
0
1
0
1
0
0
0
2
0
1
2
1
1
0
2
0
0
0
1
0
0
1
0
0
0
2
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
2
0
2
1
1
0
0
0
0
1
1
0
1
1
0
2
0
0
2
0
0
2
0
0
0
1
0
1
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
2
0
0
2
2
0
0
1
2
2
0
2
0
0
0
2
0
0
2
0
1
2
0
1
0
3
0
0
0
0
0
0
2
0
1
2
0
0
0
0
1
2
2
0
1
1
3
0
1
1
1
0
2
0
0
0
2
1
0
0
1
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
1
0
2
2
1
2
0
2
0
2
0
0
0
1
3
0
2
0
0
2
1
0
1
1
1
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
1
2
1
0
1
0
0
2
1
1
1
0
1
1
0
2
0
0
1
2
0
0
0
0
0
1
1
1
2
1
2
0
2
2
2
1
0
0
2
0
0
2
0
0
2
2
1
2
0
0
1
0
0
0
0
2
2
3
0
0
2
0
3
0
1
0
2
3
1
0
2
0
2
2
0
0
2
1
0
0
1
0
0
0
1
1
0
0
0
1
0
1
0
2
2
2
0
1
0
0
2
0
0
0
1
0
0
0
2
1
2
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
2
0
0
1
3
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
2
1
1
3
0
1
0
2
2
0
3
0
1
0
0
0
0
2
0
0
0
0
1
2
0
0
0
2
1
0
0
0
2
0
0
1
0
2
0
0
2
0
0
3
0
0
1
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
2
0
0
0
0
2
2
0
0
1
1
0
0
2
2
0
0
0
0
1
0
2
1
0
2
1
0
0
0
1
2
0
1
0
2
0
0
0
2
2
2
0
2
1
1
1
0
0
1
2
1
1
2
0
2
1
0
0
0
0
1
1
1
1
0
1
1
1
0
0
0
1
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
2
0
1
2
2
0
2
1
2
0
0
0
2
2
1
0
0
0
0
1
1
0
2
0
1
0
0
0
0
0
0
0
2
1
1
1
2
2
0
0
2
0
0
0
2
1
2
0
0
1
0
0
0
0
0
2
3
0
1
0
0
0
2
1
0
0
0
1
0
5
1
0
0
2
0
1
2
0
0
5
0
2
0
0
1
0
3
1
0
0
0
0
0
0
1
0
2
4
0
1
0
0
1
0
0
2
0
2
1
2
0
0
0
2
0
1
0
0
0
0
0
0
1
2
0
0
0
2
0
0
1
0
1
0
2
0
2
0
1
2
2
1
0
0
1
2
1
0
2
0
0
2
4
0
1
1
2
0
1
0
0
1
0
0
0
0
0
0
1
2
1
2
2
0
1
1
2
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
1
2
0
1
1
0
1
0
1
0
1
0
0
1
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
3
0
0
1
2
0
0
2
0
1
0
0
0
0
1
0
0
0
0
2
0
2
2
0
0
2
0
0
1
1
0
2
0
1
0
2
0
0
0
0
1
1
2
1
2
0
0
1
1
0
0
0
2
0
1
0
0
1
0
0
1
2
0
0
1
1
0
1
0
0
0
1
1
2
0
0
1
2
1
0
1
0
0
1
0
0
0
0
2
2
1
2
0
1
2
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
1
4
0
1
0
1
0
1
2
0
0
2
0
0
0
0
1
0
0
0
1
1
2
3
1
0
0
0
1
0
2
1
1
0
1
0
1
0
0
0
0
2
0
0
2
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
2
2
2
1
0
0
0
1
0
1
2
1
1
3
3
2
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
2
3
0
0
0
0
2
0
0
0
0
0
0
2
1
0
1
0
1
0
0
0
0
0
2
0
2
0
1
2
0
2
1
0
0
1
1
1
2
1
1
2
1
0
0
0
0
0
0
1
2
0
0
0
0
2
1
0
2
0
0
1
0
0
0
0
0
0
1
1
1
0
0
1
1
0
2
2
2
0
1
0
1
0
0
0
1
1
1
2
0
0
1
2
0
0
0
0
0
2
3
2
0
0
0
0
0
1
2
0
0
0
2
2
1
0
2
1
0
0
0
1
0
1
1
2
3
1
0
0
2
1
0
1
0
1
0
1
1
0
2
0
1
0
1
1
0
0
1
0
0
0
4
0
1
0
0
1
1
0
1
1
3
3
3
2
0
0
1
1
1
2
0
2
1
2
0
0
1
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
3
2
0
0
2
0
0
0
2
1
1
0
2
1
0
1
0
0
0
0
0
1
0
0
0
0
1
2
0
0
1
2
2
0
0
0
0
1
0
0
0
2
0
0
0
1
0
1
0
0
0
1
2
4
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
1
2
0
0
0
0
1
0
0
0
2
0
0
1
1
1
0
1
0
0
0
0
1
1
1
0
0
0
1
2
0
1
2
2
0
1
0
0
0
0
1
0
0
5
0
1
0
1
1
0
0
0
0
0
0
2
0
1
1
2
0
0
0
1
0
0
0
0
2
0
0
0
0
1
1
2
0
0
1
2
2
0
0
0
0
0
0
2
0
0
0
2
1
0
0
2
1
0
1
2
0
2
2
0
1
0
0
0
0
1
1
1
1
0
1
0
2
1
1
0
0
2
1
1
1
0
0
1
2
2
1
1
0
1
0
2
2
1
1
0
0
0
1
0
0
1
2
2
2
0
1
2
1
1
0
0
0
0
2
1
1
1
0
1
3
2
2
2
0
2
2
0
2
1
2
0
4
0
0
0
0
2
0
2
1
2
1
2
0
0
0
0
3
2
0
0
0
0
1
1
2
0
2
0
2
2
2
1
0
1
1
2
0
2
1
1
2
1
0
0
0
1
2
0
1
0
2
0
1
0
0
1
1
0
1
0
2
0
0
0
0
0
2
2
1
0
0
1
2
1
1
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
2
0
2
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
2
1
0
1
0
1
1
1
0
1
0
0
1
0
0
1
1
0
2
2
2
0
0
0
2
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
1
4
0
0
1
2
2
2
0
1
2
1
0
1
1
2
1
1
1
0
1
0
0
0
0
1
0
1
2
0
0
0
1
1
0
0
1
2
1
1
2
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
2
4
1
0
0
1
0
1
0
1
2
2
1
1
2
1
0
2
0
0
0
0
0
2
2
1
2
2
2
2
2
0
0
0
2
1
0
2
0
0
2
2
1
1
0
0
0
0
0
2
0
2
2
0
2
1
2
2
2
1
0
1
0
0
0
2
1
0
1
0
0
0
0
1
1
1
2
2
0
0
0
2
0
2
1
0
0
1
1
0
0
0
0
2
1
1
1
0
0
1
0
0
2
0
0
1
2
0
1
0
2
0
2
0
1
0
0
1
0
0
1
2
0
0
0
3
2
0
0
2
0
1
0
1
0
2
0
1
0
1
0
0
1
1
1
0
2
2
1
1
0
2
1
2
1
1
0
0
2
1
0
4
2
2
0
1
0
1
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
1
1
1
0
1
0
0
2
2
0
0
1
2
0
2
0
1
0
1
0
1
2
1
2
0
0
0
0
0
0
2
1
1
1
0
0
0
2
0
1
2
0
2
0
0
4
1
2
0
0
1
0
0
1
0
1
2
0
0
2
0
1
1
0
0
1
1
1
0
2
2
0
0
1
1
0
1
0
2
2
0
0
0
1
0
0
0
0
0
0
2
2
2
0
0
0
2
2
0
0
0
2
0
0
0
2
1
1
0
0
0
1
0
1
2
0
2
2
1
1
4
0
1
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
1
3
0
6
0
1
0
0
1
2
1
1
0
1
2
1
1
0
0
0
0
0
0
0
0
2
1
0
1
0
0
1
0
1
0
0
1
1
0
2
0
0
0
1
0
0
0
0
0
1
0
2
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
1
2
0
1
1
2
0
0
0
1
2
0
1
1
1
1
0
1
0
0
1
0
1
1
1
0
0
2
1
0
1
0
1
1
0
0
2
2
0
0
1
0
0
0
0
0
0
2
0
2
0
1
2
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
3
1
2
1
0
0
1
0
1
0
1
2
1
1
0
0
2
0
1
0
3
2
0
1
1
0
1
0
0
2
1
0
0
0
1
0
0
1
0
2
0
2
1
2
2
1
2
1
0
1
1
0
0
0
0
0
0
2
1
1
1
1
1
2
0
0
0
0
1
1
0
2
0
0
0
1
2
0
1
0
1
0
2
1
1
1
1
1
2
0
0
0
2
2
2
1
2
1
0
0
0
2
1
2
0
2
1
0
0
2
0
0
0
1
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
1
0
0
0
0
0
1
1
1
1
0
0
0
2
0
0
1
2
0
1
0
0
1
0
1
1
0
0
0
2
0
0
3
0
0
0
1
0
1
0
1
1
0
0
2
0
2
2
0
0
0
0
0
2
1
1
0
0
0
1
1
0
0
1
0
2
0
0
0
0
1
1
0
1
1
2
3
0
1
0
0
1
2
2
0
0
0
1
0
2
0
1
1
0
0
2
1
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
1
0
1
0
2
0
2
0
1
0
2
2
0
1
1
2
0
0
1
2
0
0
2
0
2
0
0
0
1
2
0
0
1
0
2
1
2
1
1
1
0
0
0
1
0
0
2
1
0
2
5
0
0
0
0
0
0
2
0
2
2
1
1
2
0
0
0
0
0
0
1
2
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
2
0
0
1
0
1
1
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
1
0
1
2
1
0
2
1
2
2
0
0
2
0
0
2
0
0
0
0
0
1
1
0
1
0
0
1
0
1
1
0
2
1
0
0
0
1
1
1
0
0
2
1
1
0
0
0
0
1
0
2
0
2
0
1
2
0
1
0
0
0
0
0
2
0
1
2
0
2
0
0
1
1
1
2
0
1
2
0
2
0
0
1
1
0
0
1
1
0
0
0
0
1
2
0
0
1
0
1
1
2
1
0
0
1
1
1
0
1
1
2
1
5
0
0
0
0
0
1
0
1
2
0
2
1
1
3
0
0
2
2
1
0
0
1
0
1
1
0
2
2
0
0
0
2
0
2
1
1
2
1
2
0
0
1
2
0
1
0
0
0
2
0
0
0
1
4
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
2
2
0
0
0
0
0
1
0
0
0
0
1
0
1
2
0
1
0
0
0
0
0
0
2
1
0
1
0
0
1
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
1
2
0
2
0
0
0
0
0
1
2
0
1
1
2
0
2
0
1
0
1
0
0
1
1
1
0
0
0
0
2
1
2
0
0
1
0
3
0
0
0
0
0
0
2
0
0
0
0
2
1
0
1
0
0
2
1
2
0
0
0
1
0
1
1
2
0
2
1
1
0
0
4
1
1
0
0
0
2
0
0
0
2
1
0
0
0
0
1
0
2
1
0
0
0
1
2
1
0
0
2
0
1
0
1
0
2
0
1
0
0
0
1
2
1
2
0
0
1
0
1
0
0
0
0
0
0
2
0
0
1
2
0
0
0
2
2
0
0
1
1
2
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
2
2
0
2
2
0
0
0
1
1
0
0
2
0
2
0
0
0
0
0
0
0
2
2
1
0
2
0
0
1
0
1
0
0
0
1
2
1
0
2
0
1
0
0
0
0
2
0
2
0
0
0
0
0
2
1
2
4
1
2
0
0
2
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
2
2
1
0
2
0
1
0
2
0
0
0
0
1
2
0
4
1
1
0
1
0
1
0
0
0
0
0
1
2
0
0
0
0
4
1
1
0
1
0
0
0
1
0
1
0
1
0
1
0
1
0
1
0
0
0
2
1
3
1
1
0
2
0
0
2
0
2
0
0
2
2
0
2
0
0
1
1
1
1
2
2
0
2
1
0
0
0
0
1
1
1
0
0
0
2
0
1
0
1
4
1
3
0
0
1
1
0
2
0
0
0
2
0
2
2
0
1
0
1
1
1
0
0
0
0
1
1
0
1
1
0
2
2
0
0
1
0
0
0
0
1
1
1
0
0
2
1
1
0
0
2
0
0
2
0
2
1
1
0
0
0
2
1
1
0
1
2
0
0
1
0
0
0
2
3
0
0
2
0
0
1
0
0
0
0
0
0
2
0
1
1
1
0
2
2
2
2
0
0
0
0
3
0
0
0
0
0
2
0
0
3
0
0
0
0
0
2
1
0
1
0
0
0
1
0
0
0
0
0
3
1
1
0
0
2
2
0
1
0
0
1
2
0
0
0
3
0
1
3
0
0
0
1
0
1
2
0
0
0
0
0
3
2
1
2
2
1
0
2
2
0
0
1
5
2
0
1
0
0
1
0
2
1
1
0
1
0
2
0
1
1
0
2
0
3
1
0
0
0
1
0
1
0
1
0
0
2
0
0
2
0
1
2
1
0
2
1
0
2
1
0
2
0
0
0
0
2
0
1
0
2
1
1
1
1
0
0
0
2
1
1
0
0
0
3
2
0
0
0
0
1
0
0
4
0
0
0
0
0
0
1
2
1
0
2
1
0
0
0
0
0
2
2
0
0
0
3
2
2
0
0
1
0
0
1
1
0
1
0
0
0
2
2
0
0
0
0
1
4
1
0
0
0
0
1
0
0
0
1
0
0
1
1
2
0
1
0
2
0
1
1
2
0
1
0
1
0
1
1
0
0
1
0
0
0
1
0
0
2
0
0
0
0
2
1
2
0
0
0
0
1
1
0
2
2
1
0
1
3
0
2
0
0
0
2
1
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
3
0
0
0
2
2
2
0
0
0
0
0
1
1
0
0
2
0
5
1
0
2
0
1
0
2
0
1
2
1
2
2
0
0
0
1
0
1
2
0
0
0
0
1
0
1
1
2
0
2
0
0
0
0
1
0
0
3
0
1
2
1
2
0
0
2
0
0
1
2
1
0
0
2
0
1
2
0
0
2
2
0
1
0
0
2
0
0
0
2
2
2
1
2
2
0
0
1
2
2
0
0
0
1
2
0
0
1
2
0
1
2
0
1
2
1
0
0
0
0
1
0
2
2
1
0
0
3
1
0
2
1
2
1
1
0
0
1
0
0
0
1
1
2
0
1
1
0
0
0
0
1
0
0
0
0
1
0
2
1
2
1
0
1
1
1
0
1
2
2
1
1
2
0
2
0
0
1
0
0
0
3
1
0
0
1
0
0
0
0
1
0
0
1
0
2
0
5
3
2
2
0
0
2
0
1
2
0
0
0
0
1
2
0
0
1
0
2
1
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
3
2
0
2
0
1
0
1
0
0
2
0
0
0
0
0
0
0
1
2
0
2
0
0
0
2
0
1
0
2
1
1
1
2
1
0
0
2
0
0
0
3
0
2
2
0
0
1
1
1
2
0
0
0
0
2
0
4
0
0
0
0
2
0
0
1
1
2
1
2
2
1
0
1
0
0
0
0
0
0
1
0
0
0
1
1
1
0
2
0
0
0
0
0
1
0
0
1
0
1
0
0
2
0
1
2
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
1
1
1
1
0
2
1
0
0
4
1
0
1
0
2
1
2
0
1
1
1
0
1
0
0
0
1
0
2
0
0
2
1
0
3
1
1
2
0
0
0
0
0
1
0
1
1
2
0
1
0
0
0
1
1
0
0
0
2
1
0
2
2
0
0
0
2
1
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
1
1
0
0
2
0
0
0
1
0
1
1
0
0
1
0
0
0
1
1
2
0
2
0
0
2
3
1
1
0
0
2
0
2
0
0
0
0
0
1
1
2
1
0
0
0
2
0
0
1
0
0
0
2
0
0
1
0
2
1
1
0
2
0
0
0
0
0
1
0
1
2
2
0
1
3
1
0
0
0
1
0
2
1
0
1
1
2
1
0
0
1
0
2
0
0
0
0
3
2
0
0
1
0
2
2
0
0
1
1
0
0
1
2
0
0
0
1
1
1
0
0
0
0
0
1
0
1
1
0
0
1
0
1
0
1
0
1
1
1
2
1
0
0
0
1
0
1
0
2
3
0
1
0
2
0
0
2
2
0
0
3
2
2
1
2
0
1
2
2
3
0
1
0
0
0
1
0
1
0
1
2
0
0
0
0
2
0
0
0
2
0
0
2
0
1
1
0
0
0
0
2
1
0
1
2
0
1
0
0
0
1
2
0
1
1
0
0
1
0
2
0
0
1
1
0
3
0
0
0
1
0
0
1
0
2
0
1
1
2
2
1
1
2
2
3
0
0
2
1
1
0
1
0
0
0
1
1
0
0
0
0
0
1
0
1
1
1
0
0
2
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
2
0
2
1
1
0
0
0
0
0
0
0
1
2
1
0
0
3
2
0
1
0
0
1
0
1
1
0
0
2
2
0
2
0
0
2
0
0
2
2
1
0
0
0
1
1
0
1
0
0
1
0
1
2
1
2
0
1
0
0
2
1
0
0
1
0
0
0
1
1
0
0
1
0
0
1
1
0
0
1
0
1
0
2
1
0
0
0
2
1
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
2
1
1
0
0
0
1
0
0
0
1
2
0
2
1
0
2
2
0
2
1
0
1
1
2
2
0
2
1
1
1
1
0
2
1
0
0
1
2
2
2
0
0
0
2
0
0
0
2
1
2
1
0
1
1
1
2
0
2
0
3
1
0
2
0
2
2
1
0
1
0
1
1
1
0
0
1
1
0
1
0
0
1
1
1
0
0
0
1
0
0
1
0
0
0
1
1
0
0
1
0
0
0
1
1
0
0
1
1
0
1
1
0
2
1
2
0
0
0
1
2
1
0
0
1
0
0
0
0
1
1
1
0
0
0
1
0
0
5
0
0
0
1
0
2
1
2
0
1
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
1
0
1
1
0
0
1
1
2
0
0
0
0
1
0
0
1
0
0
2
1
0
1
2
0
0
0
2
0
0
1
1
0
2
2
0
1
1
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
1
0
2
0
0
2
2
0
0
0
2
0
0
0
1
2
0
1
0
2
0
0
0
4
0
4
0
0
0
0
1
2
1
0
0
0
1
2
1
0
0
0
1
0
0
0
0
4
0
0
0
0
1
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
1
1
0
2
3
0
1
0
2
1
0
0
4
2
1
2
0
0
4
0
0
0
2
0
2
0
2
0
0
0
2
2
0
0
1
1
2
1
1
0
0
2
0
0
0
0
0
1
1
0
1
0
1
1
2
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
3
1
1
1
1
0
1
0
0
1
1
0
0
1
2
0
0
2
2
1
1
1
0
1
0
0
2
0
0
0
0
3
0
0
1
0
1
0
0
1
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
2
2
0
2
0
1
0
1
0
0
0
0
1
1
2
2
0
0
2
1
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
1
0
0
2
2
0
0
0
2
1
1
0
0
0
0
0
0
1
3
1
0
0
0
0
1
2
0
0
2
1
0
0
0
0
1
2
1
0
2
0
1
1
3
1
2
0
0
2
0
1
0
0
1
0
0
2
2
0
0
0
1
0
2
0
1
0
1
0
0
2
1
1
1
0
2
2
2
2
1
0
0
0
1
0
1
1
0
2
2
0
1
1
0
0
0
1
2
0
0
0
2
4
0
2
0
0
1
0
1
2
1
2
1
0
0
0
1
2
2
0
1
0
0
2
2
2
0
0
2
2
1
2
0
1
1
2
0
1
1
0
2
1
0
0
0
0
0
0
1
2
1
0
0
2
0
0
0
0
0
2
4
2
2
0
0
0
0
2
0
1
0
0
2
2
1
2
1
0
1
2
0
1
0
1
1
1
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
3
0
0
2
1
0
0
0
2
0
3
0
0
0
1
0
0
1
0
1
1
0
0
2
0
1
0
2
0
0
0
3
0
0
0
0
1
0
1
0
1
1
2
1
0
0
1
0
2
1
0
0
0
0
0
1
1
2
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
2
1
2
0
1
1
0
0
0
1
2
1
2
0
1
0
1
0
0
0
0
0
1
1
1
0
0
3
2
0
1
0
0
0
0
0
0
1
0
2
1
2
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
2
1
1
0
2
1
1
1
0
2
1
0
1
0
1
0
2
0
0
0
1
2
0
0
1
0
0
2
2
2
0
1
3
0
3
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
2
0
0
1
0
2
0
2
1
0
0
1
2
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
1
1
1
0
0
0
0
1
2
2
0
1
0
0
0
0
2
0
0
2
0
0
2
1
0
1
2
0
0
1
2
1
1
2
0
0
0
1
2
1
0
0
1
0
0
0
1
0
1
0
1
2
2
0
0
2
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
1
0
2
0
0
2
1
0
0
0
2
0
1
0
1
0
3
0
2
0
1
1
1
2
1
3
2
2
0
1
0
1
1
1
1
2
0
0
4
1
1
0
0
0
2
1
2
0
0
2
0
0
0
0
0
0
0
1
2
1
0
0
0
0
3
1
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
2
1
0
1
1
1
1
2
0
1
1
0
0
0
8
0
0
2
0
1
2
2
0
0
2
0
1
0
1
2
2
1
0
0
2
2
0
0
2
1
1
0
0
0
2
1
1
2
0
1
1
2
0
0
0
1
0
0
1
1
1
1
1
0
1
0
0
0
1
0
0
1
0
0
0
2
0
2
0
2
1
2
1
0
0
2
0
2
1
0
0
0
0
1
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
1
1
2
0
0
0
0
0
1
2
2
0
1
0
0
1
1
0
0
1
1
1
0
0
2
2
0
2
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
2
0
0
1
0
0
1
0
0
0
2
0
0
0
0
2
0
2
2
0
2
1
0
0
2
0
1
2
0
2
1
0
0
2
2
2
1
0
2
2
1
0
0
0
0
2
0
0
0
2
2
0
1
0
0
0
1
2
0
2
2
2
1
0
2
2
0
0
0
1
2
0
0
0
1
0
0
2
1
0
2
1
0
2
2
1
2
0
0
0
2
1
0
1
0
0
0
1
0
3
0
1
0
1
4
0
1
0
0
0
1
0
0
2
0
0
1
0
0
0
0
1
0
1
1
1
0
0
2
2
2
0
2
0
1
0
2
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
3
2
2
0
2
2
2
0
1
2
0
0
1
1
0
0
1
1
1
0
1
2
2
2
1
1
0
2
0
1
2
0
0
0
1
0
0
1
2
0
0
2
0
0
1
1
0
0
4
1
1
2
1
0
0
0
0
1
2
0
0
1
1
0
1
1
2
0
0
3
0
1
1
1
0
0
0
1
1
0
0
2
0
2
0
1
2
0
1
2
0
1
2
0
0
0
0
2
7
2
1
2
2
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
3
2
0
0
0
1
1
0
0
0
0
0
0
2
1
0
0
0
0
2
1
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
1
1
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
2
0
2
4
0
0
0
0
1
2
1
0
2
2
2
0
0
0
1
1
2
0
1
2
0
0
2
0
2
0
0
2
1
2
1
2
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
1
0
0
0
1
3
1
1
1
1
2
0
2
0
0
3
2
0
0
2
2
0
0
2
0
0
1
1
0
1
0
0
0
1
1
0
0
0
0
1
1
2
0
2
1
1
0
0
0
0
1
0
0
0
0
1
1
2
0
0
0
1
2
0
2
2
0
2
0
1
0
0
0
0
2
0
0
2
0
0
1
0
1
0
2
0
0
0
2
1
0
2
0
0
1
0
0
1
2
0
0
0
1
1
1
2
0
2
2
0
2
1
0
0
1
0
2
1
0
0
0
0
2
1
0
1
1
2
2
2
1
1
1
2
2
0
1
1
1
1
0
0
2
0
0
0
0
2
1
2
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
2
1
2
0
2
1
1
0
0
2
0
0
1
1
2
1
1
1
1
2
0
1
2
2
2
1
5
2
0
0
2
0
0
0
0
1
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
3
1
2
2
0
1
1
0
1
0
2
1
0
2
1
0
2
0
0
2
0
1
0
0
1
0
2
0
0
0
1
2
0
1
2
0
0
0
0
0
1
1
2
1
3
3
0
0
1
1
0
0
0
1
2
0
1
0
1
0
2
0
0
2
0
0
1
0
0
2
0
0
0
1
0
2
0
2
1
0
0
0
1
0
0
2
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
2
0
2
0
0
2
0
0
0
0
1
2
0
1
0
0
0
0
0
1
0
2
1
1
0
0
0
1
0
1
2
1
0
1
1
1
1
0
0
1
2
5
0
1
0
2
1
0
2
2
0
0
2
0
1
0
1
0
0
2
0
2
2
0
0
0
0
0
0
2
1
0
2
2
2
0
2
2
1
0
2
0
0
0
1
1
2
0
0
0
0
0
0
0
1
0
2
0
0
1
1
0
0
0
0
2
1
0
0
2
0
1
2
1
2
0
1
0
0
0
1
0
2
0
0
1
0
1
0
1
1
0
1
0
0
1
0
0
1
0
2
4
1
2
0
2
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
1
0
0
1
1
0
0
0
0
0
0
3
1
0
2
0
2
1
1
0
1
1
0
0
0
2
0
2
0
0
1
1
2
1
1
1
0
1
1
2
2
2
1
2
2
0
0
1
0
0
1
2
2
0
0
0
0
1
2
0
0
1
0
2
0
0
2
0
0
1
1
0
0
0
2
0
0
3
0
2
0
0
0
2
3
1
0
0
1
2
2
0
1
0
0
1
1
2
2
0
2
0
0
0
1
1
2
0
0
1
0
0
2
1
0
0
0
2
2
0
0
0
0
1
2
0
2
0
2
1
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
1
1
0
0
1
0
1
0
1
0
1
1
2
0
0
1
1
3
0
0
1
0
0
1
2
0
0
1
1
0
0
3
1
0
1
0
0
1
0
2
0
1
0
1
0
1
1
0
2
2
1
2
0
1
0
0
1
0
2
1
0
1
1
0
0
1
0
0
0
0
0
1
0
2
0
2
2
1
2
0
0
0
2
0
0
0
2
2
1
0
0
0
0
0
2
0
2
0
2
1
0
1
0
0
2
1
0
0
0
0
2
1
0
1
0
0
0
0
1
1
1
1
0
0
3
0
1
2
1
0
0
1
0
0
0
2
0
0
1
0
1
0
1
1
2
0
2
0
0
0
2
2
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
1
0
0
2
0
0
0
1
1
0
2
1
1
2
2
0
0
0
0
0
0
0
0
1
1
0
2
0
1
2
0
0
0
2
1
0
0
1
0
2
0
1
0
3
0
0
1
0
1
1
2
2
1
1
0
1
0
0
0
0
0
1
0
1
1
0
0
0
1
1
1
2
0
0
0
0
0
0
2
0
0
0
0
1
2
2
2
2
2
0
2
1
0
1
0
0
0
0
0
0
0
0
2
1
1
1
0
1
0
1
2
0
2
0
0
0
0
0
2
0
0
0
0
2
0
2
1
1
2
1
0
0
1
0
0
0
2
1
0
1
0
2
0
0
1
1
1
0
2
2
1
0
0
0
2
2
0
0
1
0
0
0
3
2
0
1
1
0
1
0
1
2
0
0
0
0
1
0
0
0
0
0
2
0
1
1
0
0
1
1
1
0
2
0
0
0
0
1
0
0
1
3
0
0
1
1
0
1
1
2
0
1
2
0
1
0
0
1
0
0
0
0
2
0
1
0
0
0
1
0
2
0
0
0
1
0
4
2
2
0
0
1
0
2
0
1
2
2
0
0
2
0
0
0
1
0
1
0
1
0
1
0
0
0
2
2
1
0
0
1
1
1
1
0
1
0
2
0
0
1
0
3
2
1
0
2
0
3
0
0
0
0
0
0
1
0
1
0
0
1
1
0
1
0
0
1
2
1
0
2
1
0
0
1
0
0
1
0
2
2
1
0
1
0
0
0
0
3
2
0
0
0
2
0
1
0
2
0
0
1
2
2
0
0
0
2
0
1
1
2
2
0
0
0
2
1
0
0
1
2
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
1
0
1
2
2
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
2
0
0
1
0
0
0
0
2
1
0
0
0
1
2
0
2
0
0
0
0
2
2
0
1
1
0
1
2
0
1
0
0
0
1
2
0
0
1
0
0
2
0
0
1
1
0
0
1
0
0
0
2
2
1
0
2
11
2
3
1
0
0
0
1
0
0
1
0
2
0
0
0
3
0
2
0
0
0
0
0
0
2
2
1
2
1
0
1
0
0
2
1
0
0
0
0
0
1
2
2
2
0
0
0
0
0
1
0
0
0
0
0
2
1
2
1
0
4
0
0
2
2
1
1
1
0
0
1
0
0
1
2
2
2
1
0
0
2
0
0
0
0
0
1
1
2
1
0
1
2
1
1
2
0
0
2
0
0
0
0
0
1
0
1
1
1
1
2
0
2
1
2
2
0
0
0
0
0
0
0
1
1
0
2
1
0
1
0
0
1
0
1
2
0
1
1
2
1
2
0
1
1
1
0
0
2
0
0
0
0
1
0
0
3
2
0
0
3
1
0
0
2
0
2
1
0
2
1
0
2
0
1
0
1
0
0
0
1
1
1
2
0
0
1
2
0
1
0
2
0
2
0
0
1
2
0
1
0
2
0
0
1
0
0
0
2
0
2
0
0
0
1
0
1
0
1
0
1
0
0
2
0
0
0
1
2
1
1
0
2
0
0
0
2
2
0
0
1
2
0
2
0
0
1
0
2
0
1
0
0
0
0
0
1
2
2
1
0
0
0
0
0
0
1
0
1
0
1
2
1
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
2
0
1
0
0
1
0
0
0
1
2
0
2
0
3
1
0
1
0
0
1
1
0
2
1
0
1
0
0
0
0
1
1
2
0
1
1
1
0
1
1
1
1
0
0
2
1
1
2
2
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
1
2
0
0
0
1
1
2
1
0
1
1
0
0
0
1
0
2
1
0
0
1
0
0
2
4
2
2
1
0
1
2
1
2
2
1
0
1
0
2
0
2
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
2
0
1
0
0
1
1
2
1
3
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
1
1
1
0
0
1
0
0
0
0
0
1
0
2
0
2
1
2
2
0
0
1
6
0
0
1
0
2
0
0
0
1
0
1
0
1
0
2
2
1
0
0
0
0
1
0
0
1
1
2
0
2
2
1
1
0
2
0
1
0
3
0
1
1
0
2
0
2
0
1
2
2
0
0
2
0
1
1
0
1
0
0
3
2
2
0
0
0
3
0
0
0
0
1
0
2
2
0
2
0
1
2
0
0
2
0
1
1
0
1
0
0
0
2
0
0
1
0
2
2
1
2
0
0
0
0
1
0
1
0
0
0
0
0
3
1
0
0
0
0
0
1
0
0
2
1
0
0
1
1
0
1
2
2
2
1
0
0
2
1
0
1
0
0
2
0
0
1
0
0
1
1
1
0
1
0
3
1
2
0
2
0
0
0
2
1
0
0
1
2
0
1
0
1
1
2
3
0
1
0
2
2
0
0
1
1
0
0
1
0
0
0
1
0
1
2
0
0
2
0
1
1
0
0
2
1
2
0
1
0
0
1
1
0
0
2
2
2
0
3
3
0
0
2
0
0
0
0
0
0
0
2
1
0
0
1
0
0
2
0
0
1
2
2
0
0
0
0
1
0
1
1
1
0
0
0
2
0
0
3
0
0
0
0
0
1
0
1
3
1
1
1
0
0
0
0
2
1
0
0
0
0
1
1
0
0
0
1
2
0
0
0
2
0
1
2
1
0
0
0
0
0
0
2
1
2
0
1
1
1
0
2
0
2
0
0
0
2
1
1
1
0
1
0
1
1
0
0
1
0
0
2
2
0
0
0
0
2
0
0
1
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
5
0
0
2
1
0
1
0
1
1
0
0
0
2
0
0
0
1
2
2
0
1
1
2
1
0
1
1
0
1
1
2
2
0
0
0
0
1
1
0
1
0
1
1
0
2
1
0
2
2
0
1
0
2
1
0
0
0
2
0
2
0
0
0
0
0
2
1
0
0
1
1
2
0
0
0
0
0
0
0
2
1
2
0
1
0
0
2
1
2
2
0
0
0
2
0
1
0
0
0
1
1
2
3
0
0
0
1
0
0
0
2
0
0
2
3
1
2
2
1
2
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
1
2
0
2
1
0
1
0
0
1
0
0
0
1
1
2
1
1
0
1
0
0
1
1
0
1
1
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
2
0
1
1
0
0
0
0
0
2
5
0
0
1
0
0
0
0
0
2
2
0
2
0
0
2
2
0
0
0
1
2
2
2
0
0
2
0
0
0
2
2
0
1
0
0
0
0
2
0
1
0
2
1
1
0
0
0
2
2
0
1
0
0
0
1
1
2
1
0
2
7
0
2
2
0
0
2
0
3
0
2
1
0
2
3
0
2
0
0
0
2
0
0
0
2
0
0
2
2
0
1
0
0
1
0
0
2
0
1
0
0
0
0
0
0
4
1
0
0
1
0
0
0
1
0
1
0
0
0
4
1
1
0
0
2
0
0
2
0
0
0
0
1
0
1
2
2
0
2
0
0
0
0
0
1
1
0
1
1
2
0
2
0
1
0
2
1
0
1
0
0
2
1
1
0
2
1
0
0
0
0
1
1
0
0
0
0
0
2
1
2
2
1
0
0
1
1
1
1
1
1
0
2
0
0
1
0
0
0
0
0
1
0
2
0
0
2
0
2
0
0
1
2
0
2
2
0
0
1
2
0
1
1
2
2
0
0
1
1
1
0
0
1
0
1
1
2
1
0
0
0
0
2
0
0
0
1
1
0
0
1
0
0
1
1
0
0
2
1
0
0
0
0
0
3
0
0
0
1
1
1
2
0
0
2
0
0
2
0
2
0
1
0
0
0
1
0
0
0
1
1
0
0
0
2
1
0
0
2
0
0
0
2
0
0
1
2
0
1
0
0
2
0
1
1
1
0
0
0
2
1
0
0
0
2
0
0
0
1
0
1
2
0
0
2
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
1
2
2
0
1
0
2
2
3
0
8
0
0
1
0
0
0
0
1
0
0
1
1
2
0
0
1
1
2
0
1
0
0
0
1
2
1
0
1
1
0
0
2
1
1
0
0
1
1
1
2
0
0
2
1
0
0
0
4
0
2
2
1
0
0
0
1
2
0
1
0
0
1
0
1
1
1
0
0
0
2
0
1
1
2
2
0
1
2
0
0
1
0
1
2
0
2
0
0
0
0
0
2
0
0
0
2
0
0
1
1
0
0
1
0
0
0
1
1
1
0
0
0
0
1
0
1
2
2
0
0
1
0
3
0
0
0
0
2
1
0
0
0
1
1
0
1
1
0
0
1
0
0
1
1
0
0
2
0
1
0
2
0
3
0
1
1
1
0
0
2
1
0
1
2
2
2
1
0
0
1
0
0
0
3
0
0
0
0
0
2
1
1
1
0
0
0
2
1
2
1
0
1
1
1
2
1
0
2
0
2
1
0
2
0
0
1
1
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
2
0
0
1
0
0
0
3
0
0
1
0
0
0
0
1
0
1
0
2
0
0
0
2
1
0
0
2
0
1
0
2
2
1
2
1
0
0
0
2
0
0
2
2
2
0
1
0
2
0
0
0
2
2
0
0
3
3
1
1
2
0
0
0
3
2
0
2
0
1
3
0
1
3
0
2
2
2
2
0
0
2
1
0
1
0
2
1
0
1
0
2
0
0
2
0
0
2
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
1
0
0
0
1
2
2
2
0
0
0
2
1
0
0
1
0
2
0
2
0
1
2
0
1
0
0
2
2
0
1
2
0
1
0
0
2
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
2
0
1
2
1
1
2
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
3
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
1
2
1
0
0
2
1
1
1
0
2
1
2
0
1
0
0
0
0
2
0
2
0
0
0
1
0
0
0
2
0
0
1
0
1
1
1
0
0
0
3
0
1
0
0
1
1
2
0
0
1
0
0
0
2
0
0
1
2
2
1
0
1
2
1
0
1
1
1
2
0
0
0
1
0
2
0
0
0
0
0
2
1
0
1
1
1
2
1
0
1
0
0
0
0
1
2
0
1
0
0
2
1
1
0
0
0
1
1
1
1
0
0
0
0
0
2
0
0
2
0
1
1
2
2
1
2
0
1
0
0
0
0
0
0
0
1
1
0
2
1
1
0
0
0
2
0
0
2
1
0
0
0
0
0
0
1
0
2
1
0
0
2
0
0
1
0
0
1
0
1
0
0
0
1
2
0
2
2
1
0
0
0
1
0
0
0
0
2
2
2
1
0
1
0
0
0
0
0
2
0
1
0
0
3
4
0
2
0
3
2
0
0
0
2
0
2
0
1
1
0
1
0
0
0
3
2
2
1
1
0
0
2
0
2
0
2
0
2
2
1
0
0
0
0
0
1
0
1
0
0
1
1
2
0
1
0
3
0
0
0
0
1
0
0
1
4
1
0
1
1
1
1
0
1
2
2
0
1
1
1
2
2
0
0
1
1
1
0
0
0
0
0
0
1
0
0
2
0
1
1
0
1
0
0
1
13
0
0
2
0
2
1
1
0
1
0
2
0
0
0
2
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
1
2
0
0
0
2
0
1
1
1
1
0
0
0
0
0
0
2
0
1
1
1
1
2
1
0
1
0
0
2
0
1
1
2
0
0
0
1
0
1
3
0
0
1
0
2
0
0
0
0
2
0
0
1
3
2
0
1
2
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
1
1
1
0
2
1
2
1
0
1
1
0
1
0
2
0
0
0
2
0
1
0
0
0
0
0
2
2
0
3
0
1
0
1
0
2
1
1
1
1
0
1
0
2
1
2
3
1
1
2
0
2
0
1
2
2
0
0
0
2
2
0
1
1
0
0
2
1
0
2
0
0
2
0
0
0
0
1
0
0
0
0
2
0
1
2
0
0
0
1
2
0
0
1
0
0
0
0
0
2
0
2
1
0
1
2
1
0
1
0
1
0
0
2
2
1
0
1
1
0
0
1
1
0
1
1
2
1
1
0
1
2
2
0
0
0
0
1
2
0
0
2
0
0
1
1
1
0
2
0
0
1
1
1
1
0
0
1
0
0
1
2
2
1
1
2
1
1
0
0
0
0
0
1
1
1
0
2
0
2
2
0
1
1
2
0
1
0
1
0
1
1
1
0
0
0
1
2
0
0
2
2
1
0
0
0
2
1
1
2
2
2
1
1
0
2
1
0
1
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
2
1
2
2
1
0
0
2
2
0
1
1
1
1
0
2
1
2
1
0
0
2
0
1
1
0
0
1
1
1
1
4
0
0
0
0
0
1
0
0
0
1
2
1
2
0
0
0
0
0
0
1
1
0
0
0
0
2
4
0
0
1
0
0
0
0
0
2
1
2
0
2
3
0
0
2
1
0
0
0
0
0
0
0
0
1
1
0
3
1
0
2
0
0
0
0
2
0
0
1
1
1
1
2
1
1
0
1
0
2
0
0
0
3
0
2
1
0
0
0
0
0
1
0
1
1
0
2
1
0
0
1
1
2
0
2
1
0
2
0
2
2
2
2
0
2
0
0
0
0
0
2
1
0
2
1
2
0
1
1
0
0
1
0
0
2
2
1
0
2
0
0
1
1
1
0
0
0
0
1
1
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
1
1
0
2
0
2
1
2
2
0
0
4
0
0
1
2
2
0
2
2
0
0
0
2
1
1
0
0
0
1
2
1
1
0
1
2
2
1
1
0
0
0
2
0
2
1
1
1
0
0
1
2
0
1
1
1
1
0
1
0
3
2
2
2
0
1
2
0
0
2
3
0
0
7
2
0
0
0
0
0
0
0
1
0
1
2
0
2
1
0
0
1
0
0
0
0
2
0
0
2
0
1
2
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
2
0
1
2
2
2
0
0
2
1
0
1
0
2
0
0
2
2
0
2
0
0
0
0
0
0
0
1
2
0
0
0
2
0
1
1
1
2
0
0
0
0
0
2
1
1
0
1
0
2
2
0
0
0
2
0
1
0
0
0
0
1
0
0
1
2
2
0
2
0
1
0
0
2
0
1
0
0
1
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
1
0
2
1
2
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
1
1
2
2
0
0
1
1
0
2
0
1
1
0
1
2
2
0
1
1
0
1
2
0
1
2
0
1
0
1
1
1
2
0
0
0
2
1
0
1
0
1
1
0
1
0
1
1
0
0
0
1
1
0
2
2
0
2
0
1
0
1
1
1
1
0
1
0
0
1
2
2
2
2
2
0
1
1
1
0
0
1
3
0
2
0
2
1
2
1
0
0
0
0
0
1
2
4
2
1
1
0
0
0
0
1
0
2
0
0
0
2
2
0
0
0
2
1
0
0
0
0
0
0
1
0
3
2
1
2
0
0
0
1
0
1
4
0
0
0
2
1
3
1
2
2
1
2
2
0
1
0
0
0
2
1
0
1
1
0
1
0
1
0
1
1
0
2
1
1
1
1
1
0
1
1
2
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
3
1
1
2
0
0
0
0
0
3
2
2
0
1
2
1
0
1
0
0
0
2
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
2
2
1
1
0
0
2
7
2
2
0
1
0
0
1
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
2
1
1
1
0
0
0
0
2
0
0
0
0
1
0
1
0
3
0
0
0
2
1
1
0
1
0
1
2
0
2
0
1
2
0
0
0
0
1
1
0
1
0
5
2
0
1
1
1
0
2
0
1
0
1
0
0
0
1
1
0
0
0
2
1
0
1
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
2
1
0
0
2
2
2
0
0
0
0
0
0
0
1
1
0
2
1
0
1
0
0
2
1
0
1
2
0
1
0
0
1
1
1
0
2
2
0
0
2
1
3
0
2
2
0
2
0
2
0
1
0
2
0
0
0
0
1
2
1
1
1
0
0
2
0
0
1
0
0
2
1
1
0
2
2
2
2
1
1
2
1
2
0
1
0
0
0
2
1
0
0
0
1
0
3
0
0
0
1
1
0
0
0
3
0
0
0
0
3
0
0
3
0
0
0
1
1
0
1
2
0
2
0
2
1
1
0
0
0
0
2
0
1
0
0
0
0
2
1
0
1
0
2
0
0
0
0
2
1
2
0
0
2
0
0
0
2
0
0
0
4
1
2
0
2
2
0
0
2
1
2
1
0
2
0
0
0
0
1
0
0
1
1
1
0
2
0
0
1
1
0
0
1
2
2
0
2
1
0
1
0
0
1
0
0
0
0
0
1
1
1
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
1
1
0
0
1
0
1
1
0
2
0
0
0
0
2
0
1
1
1
0
1
1
0
1
0
1
0
0
1
0
2
0
0
0
2
0
0
2
1
0
1
0
2
1
1
1
0
2
2
0
0
0
2
1
0
0
2
1
0
2
1
0
5
0
1
2
2
2
1
0
1
0
0
1
0
2
0
2
2
1
2
2
0
2
0
3
0
0
1
0
1
0
2
0
0
0
0
2
1
0
0
2
0
2
1
0
2
0
0
0
1
0
0
0
0
0
0
2
0
1
0
2
0
0
1
2
1
0
0
1
1
1
0
0
1
1
0
0
0
0
0
1
0
2
2
0
2
2
1
0
0
0
1
1
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
1
2
0
1
1
1
2
1
0
0
2
2
1
2
0
0
2
2
1
1
2
1
1
1
1
2
2
2
0
2
0
1
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
2
0
0
1
1
0
1
1
2
0
0
2
2
1
0
2
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
1
1
2
1
0
0
0
1
0
2
0
0
0
1
0
1
0
0
0
0
0
2
1
0
2
0
1
1
0
0
0
0
1
1
1
2
0
0
0
1
2
1
0
2
0
0
0
0
0
1
0
2
1
0
0
2
2
2
0
2
2
0
2
0
0
0
1
1
0
1
1
2
0
0
1
0
1
1
0
1
0
2
1
0
0
0
0
1
1
0
0
1
1
0
1
2
1
0
1
2
0
1
0
2
0
0
1
0
1
0
0
1
1
0
1
0
2
2
0
2
1
0
0
0
0
0
0
2
1
0
0
2
0
2
2
1
0
0
0
0
0
0
2
2
0
2
0
1
0
0
1
0
0
2
1
0
1
2
2
2
1
0
0
1
1
1
2
0
1
2
1
0
1
0
1
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
1
1
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
2
0
2
1
0
0
0
0
0
0
0
0
2
0
2
2
0
0
3
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
1
1
0
0
0
1
0
1
0
1
1
0
0
0
2
0
0
2
2
0
1
2
0
1
0
0
0
0
0
0
2
1
1
1
2
0
0
1
0
0
1
0
1
1
0
2
1
2
1
0
0
0
1
1
0
0
0
2
1
0
2
0
1
2
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
2
0
0
2
1
2
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
1
0
0
1
2
0
0
1
1
1
1
1
0
0
2
0
1
1
0
0
0
1
2
0
2
0
0
1
0
2
0
1
1
1
1
1
2
0
0
1
0
1
0
0
0
2
0
1
0
0
1
0
2
2
0
2
0
0
2
0
0
0
1
1
0
0
2
2
1
1
0
2
2
0
0
0
1
1
2
0
1
1
1
1
1
1
2
1
4
0
0
0
0
0
0
1
2
1
1
1
2
0
1
0
2
0
2
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
2
0
0
1
1
0
0
1
0
2
2
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
1
1
1
0
0
1
3
2
2
0
1
1
0
2
0
0
1
1
0
1
1
0
1
2
0
0
0
0
1
2
1
3
2
2
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
1
0
1
1
1
0
2
0
1
1
0
0
1
0
1
1
0
0
0
3
0
0
2
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
1
0
2
3
2
1
1
1
3
0
0
0
0
1
1
0
0
2
2
0
2
1
1
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
1
0
0
2
1
0
2
1
3
1
0
0
0
0
2
1
0
2
0
1
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
1
0
2
0
0
0
1
0
1
0
0
0
0
0
1
2
1
1
1
0
0
0
2
0
0
1
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
1
1
0
2
0
0
1
2
2
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
2
2
1
0
2
1
0
2
2
0
0
0
1
0
1
0
1
1
1
0
0
0
2
1
0
2
0
2
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
1
1
0
1
1
2
1
0
2
0
0
0
1
0
0
1
1
2
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
1
2
1
2
3
1
2
0
0
0
2
1
2
1
0
0
0
0
0
0
0
1
0
1
6
1
2
0
0
1
2
0
0
0
1
1
1
2
2
0
1
0
1
2
0
0
1
2
2
0
1
0
0
3
0
0
0
1
0
1
1
2
1
0
1
1
0
1
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
1
0
1
0
1
0
0
2
1
2
1
0
0
0
0
0
0
0
1
2
0
0
1
1
0
0
3
0
1
2
0
2
0
0
0
0
3
1
0
1
0
1
0
1
2
0
0
0
1
2
0
2
2
3
1
1
0
2
1
0
1
0
0
0
2
0
0
2
0
1
1
0
1
0
0
2
0
0
2
0
1
2
0
0
0
0
0
2
1
0
3
0
1
0
0
3
2
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
1
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
2
2
1
0
2
0
0
0
2
0
2
2
1
1
1
0
2
2
0
1
0
2
0
1
0
0
0
1
0
2
2
1
1
0
2
0
1
0
2
1
0
1
0
0
2
2
0
2
0
0
2
1
2
1
1
0
0
0
0
0
0
1
0
2
0
1
0
0
0
1
0
0
2
0
0
0
3
1
1
0
0
1
0
2
2
0
0
1
0
0
0
1
1
0
2
0
0
1
1
1
1
0
0
0
0
1
2
0
2
0
0
2
2
0
1
0
0
1
0
0
1
0
0
1
2
1
1
1
0
0
0
1
0
1
0
0
2
0
0
0
0
1
0
0
1
0
1
0
1
1
0
0
1
2
1
2
0
1
0
2
1
0
0
2
0
0
2
0
0
1
2
0
0
0
0
0
0
0
1
2
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
2
0
2
1
0
0
2
0
0
1
0
0
1
6
1
2
1
0
0
0
0
2
0
1
1
0
0
2
0
0
0
0
1
1
0
1
4
0
0
1
0
1
0
0
0
1
0
0
0
1
0
1
0
1
1
1
0
1
0
2
2
1
3
2
0
0
0
0
0
1
2
1
1
1
0
1
0
0
0
0
1
1
1
1
0
0
1
0
0
0
0
2
2
1
1
0
0
0
0
0
0
1
2
2
1
2
2
2
0
0
2
0
0
0
0
0
0
0
2
0
2
1
0
0
2
3
0
0
2
2
0
2
0
0
0
2
0
0
0
0
0
2
0
1
2
1
0
0
0
1
3
0
0
0
2
0
2
1
2
0
2
1
0
0
1
2
1
1
2
0
0
0
1
0
0
0
1
0
2
2
1
0
1
1
0
2
1
2
2
0
0
0
1
1
1
1
1
2
0
0
1
1
0
0
0
1
0
2
0
2
0
0
0
0
1
2
1
0
1
0
0
0
0
2
1
0
1
1
2
0
0
0
2
0
0
1
1
0
0
2
0
0
0
3
0
0
1
1
2
1
1
0
3
0
0
0
1
1
2
0
0
0
0
3
1
2
1
0
1
1
0
0
0
2
0
0
0
1
0
2
1
2
0
2
0
0
1
0
2
0
0
1
1
1
0
0
0
2
2
0
0
0
1
0
0
2
1
0
1
1
0
0
0
0
2
0
0
0
0
1
0
0
0
1
2
0
0
1
0
0
1
2
0
0
2
0
1
0
0
2
1
2
2
0
0
0
1
0
0
2
2
2
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
1
2
1
1
1
0
1
1
1
0
0
1
2
0
2
2
2
1
0
2
4
2
0
0
1
0
3
1
1
1
0
2
0
0
1
1
2
1
0
0
0
1
0
2
1
2
1
2
0
0
4
0
0
1
1
1
2
2
0
1
0
0
0
1
1
1
1
0
1
0
0
0
0
2
0
0
0
2
1
2
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
2
2
0
0
0
0
1
0
0
1
0
2
0
1
0
1
1
1
0
0
3
1
1
0
2
1
1
1
0
0
0
2
0
0
2
0
2
0
0
0
0
2
0
2
1
0
0
2
2
0
0
5
1
0
1
1
2
2
0
2
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
5
1
0
0
0
0
1
0
1
0
2
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
2
1
0
1
0
4
2
0
1
0
1
1
0
0
1
0
1
0
2
2
2
1
2
0
1
1
2
2
0
1
0
0
1
3
0
1
0
2
0
1
0
0
2
0
0
1
0
0
0
0
1
1
0
0
0
0
2
1
0
2
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
1
2
1
1
1
0
0
0
4
2
1
1
1
0
0
0
0
1
2
0
0
1
0
1
0
1
1
2
1
2
0
0
3
0
1
0
0
0
2
1
1
0
1
0
1
0
2
0
0
0
1
1
0
2
0
0
0
0
0
1
1
1
2
2
2
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
2
0
0
0
1
0
0
0
0
0
1
0
0
2
1
1
0
0
3
0
2
1
1
1
2
0
0
1
0
2
2
0
0
0
1
0
2
0
1
0
0
0
0
0
9
0
0
0
2
0
0
0
1
0
5
1
0
1
1
0
2
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
1
1
0
0
2
1
2
1
2
1
1
1
0
1
1
0
1
0
0
3
1
0
0
1
2
0
2
0
2
1
1
2
1
1
1
2
1
2
0
0
1
1
0
0
2
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
1
1
0
0
2
0
0
0
0
0
2
0
1
0
3
0
0
2
0
1
2
1
1
0
0
0
2
0
2
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
1
1
0
0
0
2
1
3
0
1
0
0
2
2
0
0
0
1
0
0
0
0
1
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
2
0
0
1
1
2
1
0
1
0
1
3
0
1
2
2
1
0
0
0
4
0
3
0
0
0
2
0
2
1
0
0
1
0
2
0
2
1
4
1
1
0
3
1
0
1
2
0
1
1
0
0
2
2
0
0
0
0
0
2
1
0
1
0
2
0
0
0
0
1
1
2
0
1
0
2
0
0
0
1
0
2
2
0
0
0
0
0
1
0
2
0
1
0
1
1
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
2
2
0
1
1
2
2
2
2
1
1
1
0
0
0
3
0
1
2
1
2
0
0
1
0
2
0
0
2
0
0
0
1
3
1
0
2
0
1
1
1
2
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
3
0
2
0
0
0
1
0
0
0
0
3
0
0
1
0
0
0
1
1
0
0
1
0
0
1
1
2
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
1
0
0
0
0
2
0
2
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
8
1
1
1
0
1
2
0
0
0
1
1
2
2
2
0
1
0
0
1
0
0
1
0
1
0
0
0
2
0
2
0
0
0
0
0
2
0
1
2
0
0
0
0
1
3
1
0
1
0
0
0
0
1
0
0
2
0
0
0
1
1
2
3
0
0
1
1
0
1
2
0
0
1
0
1
1
0
0
0
2
0
1
2
0
1
2
0
0
0
0
0
0
2
0
2
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
3
0
0
1
1
0
0
0
0
1
2
0
2
0
0
0
2
0
0
2
2
0
1
0
0
2
0
1
1
0
0
0
1
0
1
2
2
2
1
2
0
0
1
0
0
0
0
2
0
1
0
0
0
2
1
2
0
2
1
2
2
0
0
2
0
1
0
2
2
1
0
0
0
0
0
2
0
2
0
0
1
2
0
1
0
0
2
1
0
1
0
0
0
1
0
1
0
2
0
1
0
0
0
0
2
0
2
2
1
0
0
2
0
0
0
0
1
2
0
3
1
0
0
2
0
1
1
2
0
2
0
2
0
2
4
0
0
1
2
1
2
2
1
2
0
0
0
2
1
0
0
2
3
0
0
1
0
2
1
1
0
2
0
2
0
1
1
0
0
1
1
0
1
0
0
0
0
1
0
2
0
0
0
0
0
1
0
2
0
1
0
0
1
1
0
0
2
2
2
0
0
1
0
2
1
2
1
2
1
2
1
2
0
2
9
0
2
0
0
0
1
1
0
1
0
1
2
1
0
1
2
0
3
0
2
0
0
2
0
0
0
2
2
0
2
1
3
2
2
1
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
2
1
1
0
1
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
3
1
1
2
0
1
2
0
0
1
1
1
1
1
2
2
0
0
1
0
2
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
1
1
1
0
0
1
0
0
1
0
2
0
1
0
2
3
0
0
0
2
2
0
1
0
0
0
0
0
0
1
0
0
0
2
0
2
1
0
1
1
0
0
0
1
0
0
0
0
0
1
0
1
1
2
0
2
0
1
0
1
1
0
1
2
0
2
1
1
1
0
1
2
0
0
0
1
1
1
0
0
0
0
0
0
3
0
0
1
1
0
0
1
1
2
0
1
1
0
1
2
0
0
0
0
1
0
2
0
0
1
0
1
0
2
1
0
0
1
0
1
1
1
0
0
2
2
0
0
2
0
1
2
0
0
1
0
2
0
2
0
0
0
2
1
0
0
0
0
2
0
1
0
0
1
1
0
2
1
0
0
0
0
0
1
2
0
0
1
0
0
0
0
1
0
2
0
2
1
1
0
0
1
0
1
1
1
2
1
2
0
2
0
2
0
0
0
1
2
0
1
0
0
2
0
2
2
3
3
2
0
0
0
0
1
2
1
1
0
0
1
0
1
0
0
2
0
2
0
2
0
0
2
2
0
0
2
0
3
2
0
0
0
1
0
2
0
1
0
0
1
1
1
1
1
0
1
1
0
1
1
0
1
1
3
0
0
0
0
0
2
4
0
0
1
2
0
0
0
0
4
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
2
1
0
0
1
0
0
1
3
3
2
0
0
1
0
2
0
1
2
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
3
2
0
0
1
0
3
0
0
2
0
0
2
0
0
2
1
1
0
0
0
2
0
1
0
0
0
1
1
0
0
2
1
0
2
0
2
2
1
0
1
1
0
2
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
2
0
1
1
1
0
0
0
1
0
0
2
0
0
2
0
2
2
1
1
0
0
0
1
2
1
0
0
0
2
1
2
0
1
2
1
0
1
1
0
0
0
2
1
2
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
3
2
0
1
0
0
1
1
1
0
1
1
1
1
0
0
2
0
0
0
2
0
4
0
1
0
1
0
0
2
2
0
2
1
2
1
2
1
0
2
0
0
2
0
0
1
1
0
2
3
0
0
0
1
0
1
0
0
1
2
1
2
0
2
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
2
0
0
1
1
2
0
1
0
0
1
0
0
2
0
2
2
0
0
2
0
0
2
0
0
0
0
1
0
0
1
0
1
2
0
0
0
2
0
1
0
2
3
2
2
0
0
0
0
1
0
0
1
1
2
2
0
0
0
1
2
0
1
0
0
0
0
3
0
0
1
1
0
0
0
0
1
0
0
2
2
0
0
1
2
2
0
0
0
1
1
0
0
1
0
2
0
2
2
0
2
0
1
2
0
1
1
1
2
0
2
0
0
1
1
0
2
0
1
0
1
0
1
2
0
1
0
1
0
0
1
1
1
0
0
2
0
0
1
1
0
0
1
0
1
0
0
0
2
2
0
0
0
0
0
0
2
0
1
0
1
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
2
0
0
2
0
1
0
0
0
1
0
1
0
1
0
1
0
1
1
2
2
0
1
2
0
3
1
0
0
0
0
0
3
1
1
1
1
0
1
0
0
0
1
0
2
1
2
0
1
1
0
1
0
2
0
1
1
0
0
0
0
1
0
1
2
0
2
0
0
0
0
1
0
0
0
1
0
0
2
1
2
0
1
0
1
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
2
0
0
0
1
2
0
1
0
0
2
1
1
0
0
2
2
0
1
0
2
1
1
0
0
0
1
0
0
2
2
0
0
1
1
0
0
1
0
2
0
0
1
0
0
2
0
0
0
1
1
0
1
0
0
2
1
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
1
1
0
5
0
0
0
0
2
1
0
2
0
2
1
1
0
0
0
2
0
0
0
0
0
0
1
0
1
1
1
2
0
0
2
2
1
1
1
0
2
3
0
2
0
2
0
0
0
2
2
0
0
0
0
1
0
0
0
1
0
0
0
1
1
2
1
0
0
2
2
1
1
1
0
1
1
0
0
1
2
0
0
1
1
0
0
0
1
2
0
1
1
2
0
0
2
1
0
0
0
1
1
0
1
0
0
2
0
2
2
1
0
0
2
2
0
2
1
2
0
1
1
1
1
0
1
2
1
2
0
2
1
1
0
0
0
0
1
0
0
0
2
1
2
0
0
2
0
1
1
0
0
0
1
1
1
1
0
0
2
0
0
1
1
0
1
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
2
0
1
5
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
2
0
0
0
2
1
1
2
0
0
0
2
0
1
3
0
0
0
1
0
0
0
0
0
2
2
1
0
1
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
1
2
2
1
1
0
0
0
1
2
1
1
0
0
0
0
2
2
1
0
0
0
0
0
0
0
1
0
2
1
0
1
1
0
0
0
1
0
0
0
0
0
2
0
1
2
1
0
2
1
0
1
0
0
2
1
0
2
0
0
0
1
0
4
0
1
0
0
1
0
2
0
2
1
0
0
2
0
0
0
0
1
1
1
2
0
2
2
0
0
0
1
0
0
0
0
1
0
2
1
0
0
0
0
0
0
1
0
2
1
1
0
0
0
0
0
1
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
2
1
1
0
1
0
0
0
1
1
0
0
3
2
0
0
0
2
0
0
3
1
0
1
0
0
0
1
1
0
1
0
1
0
1
0
4
1
0
1
0
0
0
0
2
0
2
2
1
2
0
2
1
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
1
0
2
2
1
0
0
0
1
0
0
1
2
0
0
0
0
2
2
2
0
0
1
1
2
1
0
0
0
0
2
1
0
2
0
2
2
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
2
0
2
0
0
2
1
0
0
0
0
2
8
0
0
0
0
2
1
1
0
2
0
0
2
0
1
0
0
0
0
0
0
2
2
2
0
0
0
1
2
0
0
0
0
0
3
1
2
0
2
3
1
0
1
0
0
2
1
0
0
1
1
0
0
0
1
2
0
1
1
1
2
0
1
1
0
0
2
0
1
0
0
0
2
2
1
0
1
1
0
1
2
1
1
2
2
0
0
1
0
1
2
0
1
0
0
1
0
2
0
0
3
0
2
0
2
1
1
1
0
2
1
1
2
2
0
6
2
0
0
1
0
0
0
2
1
1
0
1
1
0
1
1
0
1
0
1
1
1
1
0
0
0
2
0
0
2
0
0
2
0
0
0
0
1
2
0
0
1
0
1
0
2
0
0
0
1
1
0
1
0
0
0
0
0
0
1
1
1
1
1
0
1
0
0
0
0
2
0
2
2
0
0
0
0
1
0
2
0
2
1
0
0
0
1
0
2
0
0
0
1
0
2
0
1
2
0
0
1
5
0
0
2
0
1
0
1
0
1
0
1
2
1
2
0
0
0
0
0
1
0
0
2
1
1
0
0
0
1
2
0
1
1
1
0
0
0
2
1
2
2
0
0
0
0
1
1
0
0
0
2
0
0
2
0
0
0
2
0
0
2
0
2
1
2
0
2
3
0
1
0
3
2
0
1
0
1
0
0
1
0
0
2
0
0
0
0
1
0
2
1
1
1
0
0
1
1
0
2
2
1
0
1
0
0
0
2
2
0
2
0
1
0
2
0
1
2
1
0
1
2
2
2
2
0
0
0
1
0
2
0
0
1
0
1
2
1
1
0
2
0
2
0
0
0
0
2
0
1
0
2
2
1
0
0
1
2
1
0
0
0
0
0
1
1
3
2
0
0
0
0
2
0
2
0
1
0
2
1
0
0
0
0
1
1
1
2
0
1
0
1
1
0
1
1
0
0
2
0
0
1
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
3
0
1
0
0
2
0
0
0
1
0
0
0
0
2
1
0
0
1
1
1
0
0
0
0
2
0
2
2
0
0
1
0
2
0
0
0
0
1
0
2
3
0
0
0
0
2
0
2
0
0
1
2
0
0
1
2
2
2
0
0
0
0
0
0
2
0
0
2
0
0
1
0
2
0
1
2
0
0
0
2
0
0
1
0
1
0
1
2
0
0
0
0
2
1
0
0
0
1
2
1
0
2
1
0
0
1
1
0
0
0
1
0
4
0
1
0
0
2
1
0
1
0
0
1
2
1
0
1
1
1
1
0
0
2
0
2
1
0
0
0
0
0
0
2
2
1
0
0
2
0
0
2
0
2
2
2
0
0
1
1
0
1
2
2
1
0
2
1
1
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
1
2
0
0
0
0
1
0
0
0
2
0
0
1
1
1
0
1
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
1
0
1
1
1
0
4
0
1
0
2
0
1
1
0
0
0
0
2
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
1
0
0
0
0
3
0
0
0
2
0
2
0
1
5
0
0
0
0
0
1
0
0
0
1
0
0
2
1
0
2
2
2
0
0
0
0
2
1
0
0
0
1
0
0
1
0
0
0
0
2
0
0
1
0
0
1
0
1
0
0
0
0
0
2
1
0
1
0
2
2
1
2
0
2
0
0
0
0
0
1
1
1
0
2
0
0
0
2
2
0
0
2
0
0
1
2
2
0
2
1
1
0
0
0
0
0
0
0
0
0
0
2
1
2
0
1
0
0
2
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
2
2
1
1
1
2
2
1
0
0
1
0
1
1
0
0
2
0
2
0
0
1
0
1
0
1
0
1
0
0
0
0
0
2
2
0
1
0
2
0
0
2
1
0
0
0
0
0
0
1
0
1
2
1
0
2
0
0
0
0
1
0
2
2
1
2
0
0
2
0
2
0
1
0
0
0
1
1
1
2
1
0
0
0
2
0
0
0
2
0
0
0
1
0
1
0
0
1
2
2
0
2
1
2
1
0
0
0
1
0
1
0
0
0
0
2
1
2
1
0
2
1
0
0
1
2
0
1
0
2
2
1
0
1
1
2
0
0
2
0
0
1
2
0
0
0
1
0
0
0
1
0
0
1
0
1
1
0
2
1
0
2
2
0
1
1
1
1
1
2
0
2
0
0
0
0
1
1
1
1
0
0
0
1
0
0
3
1
2
2
1
0
2
0
2
0
1
0
1
1
0
0
3
0
2
0
0
2
0
0
1
1
1
0
1
0
2
1
2
0
1
0
0
2
0
1
0
0
1
0
1
0
2
0
0
0
2
0
0
0
0
2
0
0
1
1
0
0
2
0
1
2
0
0
1
0
1
0
1
0
2
0
1
1
0
0
0
0
1
1
1
1
1
0
0
0
1
0
0
0
0
0
1
0
0
2
1
5
2
1
0
0
3
0
1
1
0
1
0
1
0
0
2
0
0
0
0
0
1
0
3
0
0
0
0
0
1
1
0
0
3
0
1
0
0
0
0
1
2
0
1
1
2
1
0
0
0
0
2
2
2
0
2
0
0
1
0
2
2
2
0
0
0
0
4
0
0
3
0
0
1
2
0
0
0
2
0
0
2
3
0
0
0
1
0
0
2
2
1
0
0
1
0
2
0
2
0
0
0
1
2
1
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
1
0
0
1
0
1
2
0
0
0
0
2
2
0
0
0
5
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
2
0
2
0
0
1
2
2
1
0
2
2
2
0
1
0
1
0
0
2
0
1
0
0
0
1
0
0
0
2
2
1
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
2
0
0
2
2
2
2
0
2
2
0
1
0
0
1
0
0
0
0
2
1
0
2
0
1
0
0
1
1
0
0
0
1
0
1
2
0
0
3
0
0
0
2
1
0
2
0
0
1
2
0
1
0
0
1
1
2
0
1
0
0
2
2
0
2
1
1
1
1
0
0
0
0
2
0
1
2
2
0
2
0
0
1
1
1
0
0
0
0
0
1
1
1
3
2
2
1
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
1
2
0
2
0
0
0
0
2
2
2
0
1
1
1
0
0
2
1
0
2
0
0
0
2
0
0
2
1
1
0
2
1
0
0
0
1
5
0
2
0
0
0
0
0
3
2
0
1
1
0
0
0
0
4
0
1
1
1
1
1
2
1
1
0
1
1
0
1
1
2
2
2
2
1
0
2
2
1
0
1
2
0
0
0
1
0
1
1
0
1
0
1
0
2
0
2
0
0
2
0
0
0
1
0
0
1
2
0
1
1
1
2
0
1
0
0
1
2
1
0
0
0
2
2
0
0
0
0
0
2
0
0
2
2
0
1
0
0
0
2
1
2
2
0
2
2
0
0
0
0
1
2
2
1
0
0
0
2
1
2
0
1
4
2
0
0
1
0
0
1
0
1
1
0
2
0
1
1
2
2
0
0
0
2
1
0
0
2
0
1
2
0
1
0
1
0
1
1
1
0
0
0
0
0
0
2
0
0
3
0
0
0
2
1
0
1
2
0
1
0
2
0
0
1
0
0
1
0
0
1
2
1
2
1
0
0
1
0
0
0
0
2
1
3
1
1
1
0
1
0
1
2
0
2
0
0
2
0
0
0
2
1
1
0
0
2
2
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
1
0
1
0
0
2
1
0
1
1
0
3
2
0
1
1
0
0
0
1
2
1
0
0
1
0
1
1
0
0
2
0
2
1
2
1
1
3
0
1
2
2
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
2
2
0
1
0
1
0
0
0
0
2
0
0
0
0
0
1
2
0
2
2
1
0
0
0
0
0
2
2
2
0
1
1
2
0
1
0
2
2
0
1
2
0
0
1
2
0
0
0
0
1
2
1
0
0
1
0
1
0
0
2
1
0
2
0
0
0
0
0
0
0
1
0
2
0
0
1
2
0
0
1
1
2
0
0
2
2
2
0
0
0
2
0
1
2
1
1
2
0
0
0
2
0
2
0
2
2
0
0
0
0
2
2
0
1
0
1
1
1
1
2
1
2
0
2
1
0
0
2
0
0
0
0
0
0
1
0
0
0
1
1
0
2
2
2
3
0
1
0
2
0
0
0
2
1
2
2
0
3
1
1
1
1
1
0
1
2
1
0
2
0
0
2
0
1
1
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
2
0
1
0
0
0
0
0
2
0
1
1
4
2
4
0
0
0
0
0
1
1
0
0
2
1
1
0
0
0
1
3
0
0
2
1
0
0
0
0
0
2
2
1
1
0
0
2
2
0
0
0
0
0
1
0
1
2
0
2
1
0
1
0
1
1
2
0
1
0
0
1
0
1
2
2
0
2
0
2
2
2
0
0
0
0
0
0
0
0
1
1
1
1
1
0
1
1
0
0
2
0
0
4
1
0
0
1
1
0
0
0
0
1
0
2
2
0
0
0
0
0
0
1
2
1
1
0
0
1
0
1
0
0
2
0
0
2
0
0
2
1
2
0
1
1
1
1
0
1
0
0
0
0
0
1
2
0
0
1
1
0
2
2
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
1
2
2
2
2
0
1
0
1
2
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
2
2
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
1
2
0
2
0
2
0
0
0
0
1
1
1
0
1
0
1
0
0
0
2
2
2
2
0
1
0
0
0
1
2
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
1
0
0
0
1
1
0
0
1
3
0
0
2
1
1
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
4
1
0
2
1
0
0
0
1
0
2
0
0
0
0
1
1
0
1
0
1
2
2
0
1
1
0
0
2
0
0
1
0
2
0
0
1
0
0
0
2
1
0
2
0
2
0
1
1
0
0
0
2
2
1
0
0
2
0
0
1
0
2
0
2
1
1
0
1
0
0
2
2
0
0
2
2
1
2
0
0
1
1
2
1
1
1
2
2
0
1
1
1
0
0
1
1
0
2
1
0
0
2
2
0
0
0
7
0
2
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
1
2
2
2
1
0
0
0
0
0
2
0
2
2
0
1
1
2
2
3
2
0
0
0
0
2
2
0
0
2
3
2
1
0
0
0
1
2
0
2
0
2
1
2
0
0
2
2
0
0
1
1
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
2
0
2
2
2
1
0
1
0
2
1
0
1
2
0
0
0
0
2
0
1
2
2
0
2
0
2
2
0
0
1
1
1
2
0
1
1
0
2
0
2
0
1
1
3
0
2
1
0
1
0
0
0
2
0
0
1
0
2
0
0
1
0
2
0
2
0
3
1
2
0
0
2
2
0
0
2
0
1
1
0
2
0
2
0
0
0
0
0
1
0
2
1
2
0
1
0
0
0
1
0
1
2
0
1
1
1
2
1
2
0
0
1
0
0
0
1
0
0
0
0
1
0
2
1
0
0
0
1
0
0
2
1
2
2
0
1
0
0
2
2
0
0
0
2
2
0
0
1
2
0
1
2
0
2
0
1
2
0
0
0
0
1
2
0
1
2
0
1
0
0
1
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
2
0
1
0
1
0
0
0
0
2
0
2
0
2
1
1
0
1
0
1
3
1
2
1
0
2
0
0
0
2
0
0
1
1
0
0
0
2
2
0
2
2
0
0
0
3
0
0
0
1
2
0
1
0
0
0
1
1
1
0
0
1
2
0
0
1
0
1
1
1
2
0
0
1
0
0
0
0
0
1
1
2
2
2
0
1
1
2
3
2
1
0
2
0
0
3
2
0
0
4
0
0
2
0
0
1
0
0
2
2
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
1
1
0
2
1
0
1
1
0
0
2
2
1
2
1
0
0
1
0
1
1
0
0
0
1
1
0
2
2
1
0
1
2
2
2
0
1
1
1
0
0
0
1
0
1
0
1
1
0
0
0
4
1
2
0
0
2
0
0
0
2
0
2
0
0
0
1
2
0
0
2
0
0
1
0
0
1
1
1
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
1
2
1
0
0
0
0
0
0
0
0
2
2
0
1
1
0
0
0
0
2
0
1
0
1
1
6
1
0
2
1
0
0
0
0
1
0
2
2
0
1
2
0
2
0
0
0
0
2
0
3
0
1
0
0
2
0
0
1
1
1
0
1
1
0
2
0
0
0
2
0
1
0
1
0
1
2
0
1
1
0
0
2
1
2
2
1
0
0
2
2
0
1
0
1
1
2
0
0
0
0
0
0
1
1
0
0
0
2
0
0
2
2
0
1
2
0
0
0
1
1
2
2
1
1
1
2
2
1
0
2
1
0
0
2
0
1
0
0
0
0
0
1
1
1
2
0
2
0
2
2
2
0
0
0
1
0
2
0
0
1
1
0
1
0
3
0
0
0
1
2
1
1
3
0
0
2
0
2
0
0
0
2
0
0
0
0
0
1
1
1
0
0
1
1
0
0
0
1
0
1
0
1
1
1
0
1
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
2
2
0
0
1
1
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
1
0
1
1
0
0
1
0
0
2
0
0
2
1
3
0
2
0
1
0
0
1
0
2
2
0
0
1
0
1
1
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
2
1
1
0
1
0
0
0
2
0
4
0
0
0
1
2
2
2
2
0
0
0
2
0
0
0
2
0
0
0
0
1
2
0
1
0
0
0
0
2
0
0
2
1
0
0
0
1
1
1
0
1
0
2
2
1
1
0
0
0
1
0
1
1
0
0
0
2
0
0
2
0
1
1
1
2
0
0
1
0
1
0
0
0
0
2
2
0
0
0
1
0
1
0
1
3
0
0
1
1
0
1
0
0
0
0
0
1
2
0
0
0
0
0
1
0
2
0
0
2
0
0
0
1
1
3
0
1
0
0
0
0
1
2
2
0
0
0
2
0
0
1
1
0
0
1
2
0
0
0
0
2
0
0
0
0
2
0
0
0
1
2
0
1
1
1
2
1
2
0
0
0
0
1
0
1
1
0
2
0
2
0
2
0
2
0
0
2
0
0
0
0
0
0
2
1
0
0
0
2
0
0
2
1
1
2
0
2
0
0
0
2
1
1
1
2
0
1
2
4
0
0
0
0
0
0
1
0
0
0
0
0
3
0
2
1
1
0
0
0
1
1
0
0
2
0
2
0
2
2
0
1
1
0
1
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
1
2
0
0
0
0
1
2
0
0
0
1
1
2
0
0
2
1
0
2
0
0
0
0
0
2
2
2
0
0
0
0
0
0
2
0
1
0
0
1
2
0
0
1
1
0
0
0
0
0
0
1
1
2
0
2
0
2
0
0
3
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
3
2
0
1
1
1
0
2
1
1
0
0
0
1
1
2
0
0
0
0
1
0
0
0
0
2
0
0
1
0
2
2
1
1
2
1
0
4
2
1
0
0
0
1
0
0
1
0
1
0
0
0
3
1
2
1
0
2
0
2
1
1
1
0
0
0
2
2
0
0
1
2
1
0
0
0
1
2
0
0
1
1
1
1
0
0
1
0
0
0
0
2
0
1
3
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
2
1
0
2
1
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
2
0
0
1
0
0
1
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
1
3
2
2
1
0
0
0
1
0
2
0
0
0
2
0
2
0
0
1
0
0
1
0
0
0
0
2
1
0
1
0
2
3
0
2
0
2
0
1
3
0
2
0
2
0
0
0
0
2
1
0
0
0
2
1
2
0
0
0
2
0
1
0
1
1
2
0
1
0
0
0
0
0
0
1
0
2
2
0
2
0
2
0
2
0
0
0
0
2
1
0
1
0
0
0
2
2
2
0
2
0
0
1
1
0
0
1
0
0
3
2
0
0
1
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
1
1
0
1
0
2
0
0
0
0
0
0
1
1
0
1
0
2
0
0
0
2
0
3
1
0
0
2
0
1
2
3
0
1
2
2
2
0
0
1
1
0
0
0
2
0
0
0
2
0
1
1
0
0
2
1
4
1
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
1
1
2
1
0
1
0
1
1
1
0
0
0
2
0
2
0
0
1
0
0
1
2
2
1
0
1
1
0
1
1
0
1
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
1
1
3
0
1
2
2
0
0
0
2
2
0
0
2
0
2
0
0
0
0
1
0
2
2
3
2
0
1
0
2
0
0
0
1
0
2
2
2
0
0
0
0
2
1
0
1
1
1
1
0
0
0
0
1
1
0
0
0
1
2
0
2
1
0
1
1
1
0
0
0
2
2
2
0
1
0
0
2
0
2
2
0
1
1
3
1
0
0
1
0
0
2
0
1
1
1
1
0
0
0
1
0
2
0
2
0
0
0
0
2
0
1
2
1
4
1
2
0
0
0
1
1
1
1
0
1
2
0
1
1
0
2
2
0
2
0
0
0
2
2
0
0
2
0
0
0
0
0
3
0
0
0
0
1
2
2
0
1
1
0
2
0
0
2
1
0
1
1
1
0
1
1
0
1
2
1
1
0
0
0
1
2
0
1
2
2
0
2
0
2
0
2
0
0
0
3
0
1
0
0
0
0
0
0
0
0
3
2
0
0
0
2
0
2
0
0
0
0
0
0
1
0
1
0
1
0
0
0
2
0
2
0
1
1
0
2
0
0
2
2
1
1
0
1
1
0
1
1
0
0
0
0
1
0
0
2
0
0
2
0
0
2
1
0
0
1
2
2
0
2
0
1
0
2
1
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
4
2
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
1
2
0
3
0
0
2
0
1
0
1
0
2
0
0
2
0
0
2
0
1
0
0
0
0
0
1
3
0
0
1
1
0
0
0
0
0
2
0
1
3
2
0
2
0
0
0
0
2
1
0
2
1
5
0
0
1
1
0
2
1
2
0
1
0
0
0
1
0
0
0
1
2
0
0
0
2
0
2
0
1
1
0
2
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
2
2
1
1
1
0
0
0
0
0
0
1
2
0
3
2
0
0
0
1
1
1
0
0
0
1
0
0
2
2
1
0
1
1
0
2
2
2
0
0
1
0
0
2
0
1
1
0
0
0
1
1
2
0
1
0
1
2
0
1
0
1
0
0
0
3
2
2
1
3
0
1
1
2
0
1
0
1
0
1
2
1
0
0
0
2
0
1
1
0
1
1
1
1
1
2
1
2
1
1
0
0
1
2
0
0
0
1
2
2
0
1
0
0
1
1
0
0
1
0
0
0
2
0
1
1
2
0
0
0
0
0
0
2
0
0
2
0
0
0
1
1
1
1
0
0
0
1
0
0
2
0
0
1
2
1
0
0
0
0
1
2
1
0
0
2
0
2
0
1
1
0
2
0
0
1
6
0
0
0
2
0
0
0
0
0
0
0
1
2
0
2
0
0
0
1
2
2
0
0
0
2
1
0
1
3
2
1
2
1
0
1
1
2
2
1
0
2
2
1
1
2
1
0
1
2
1
0
0
1
1
2
0
1
1
0
0
2
1
2
0
0
1
0
0
0
0
0
1
2
1
2
3
2
1
0
0
0
0
0
0
0
1
0
0
2
2
0
1
1
2
1
0
0
0
6
1
1
0
1
2
0
1
4
1
1
0
1
0
0
1
0
2
1
1
1
2
0
1
2
1
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
2
3
1
0
1
1
0
0
1
2
1
2
1
3
0
0
0
0
0
2
0
2
2
0
2
0
2
2
0
0
2
0
0
2
0
0
1
1
1
0
0
0
1
2
0
0
0
0
1
2
1
1
2
2
2
0
2
1
0
0
1
1
0
0
1
0
0
0
1
1
0
3
1
0
1
1
2
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
1
1
2
2
0
2
0
0
1
1
2
0
0
1
0
6
2
0
1
0
0
0
0
1
2
2
0
1
0
0
2
1
2
1
0
0
0
2
2
0
1
2
0
0
4
0
1
0
2
0
1
0
0
0
0
1
1
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
1
1
0
2
1
2
0
0
1
0
0
1
1
1
2
2
0
0
1
0
0
0
3
1
1
2
4
0
1
0
0
0
1
2
0
0
2
0
1
0
0
0
2
0
2
1
1
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
1
2
0
0
1
1
1
2
1
0
1
1
1
0
0
0
0
0
2
0
1
0
1
2
0
2
0
1
0
0
0
0
0
0
2
0
3
2
0
0
1
0
0
4
0
0
0
1
0
0
1
0
0
2
2
2
2
2
0
0
0
0
2
0
1
1
0
0
1
1
0
1
2
0
0
0
1
0
0
1
0
1
0
0
0
0
0
2
0
1
1
0
0
1
0
1
0
0
0
1
1
2
1
0
1
2
2
1
1
1
2
1
0
2
0
1
0
0
2
4
0
2
0
4
0
3
0
1
0
0
0
1
0
1
1
0
0
1
1
0
0
2
0
0
0
0
2
2
0
0
0
1
0
2
0
0
0
0
2
2
0
2
1
1
0
0
2
0
1
0
0
1
1
1
1
2
0
1
2
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
2
0
0
1
2
0
1
2
2
0
0
1
0
2
1
0
0
0
0
1
0
1
2
0
0
0
0
2
0
0
0
2
1
3
0
1
0
1
0
0
1
1
0
0
2
0
0
0
1
0
0
2
3
0
0
1
2
1
0
0
1
2
0
1
0
0
2
0
0
0
2
0
0
1
0
0
1
1
0
0
1
2
3
4
0
1
0
0
0
0
1
0
0
0
1
1
2
0
0
1
0
0
2
3
0
1
0
0
2
1
2
0
0
2
0
3
1
1
1
0
0
0
0
1
5
2
2
1
2
0
0
0
0
0
2
0
0
0
1
1
0
1
0
0
0
0
0
2
0
0
1
1
0
1
2
0
0
3
1
1
0
0
2
2
2
0
1
1
0
0
1
2
2
0
2
0
2
1
0
1
2
0
0
1
0
2
1
1
1
0
2
0
0
0
2
0
0
2
2
2
0
0
1
2
0
2
1
0
0
0
0
0
1
1
1
0
3
1
1
0
0
2
0
0
0
0
2
1
0
1
1
2
1
0
1
0
2
0
3
5
1
0
0
0
2
0
1
2
1
0
0
0
0
0
2
2
0
0
1
1
1
2
4
2
1
1
1
0
0
2
0
0
2
0
0
0
2
0
0
0
2
0
1
1
1
1
2
1
0
4
1
0
0
2
1
2
2
0
0
1
0
4
0
2
0
2
2
0
2
0
0
1
0
1
1
2
0
2
0
0
0
0
1
1
0
2
0
0
1
2
0
0
2
2
1
0
0
1
2
0
0
1
0
2
2
0
0
0
2
0
2
1
0
1
0
2
1
1
0
0
1
0
2
1
0
0
1
2
2
2
1
5
2
0
0
0
0
1
0
0
2
0
0
1
0
2
1
0
2
0
1
2
2
1
0
1
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
2
1
0
1
0
0
1
0
1
0
0
0
2
0
0
0
0
1
0
2
0
0
2
4
2
1
1
0
0
0
0
1
0
2
0
3
0
0
1
2
0
2
0
2
0
0
1
0
0
0
0
0
0
2
1
0
0
1
2
1
1
2
1
2
0
0
0
1
0
0
0
4
1
0
0
0
0
1
2
0
0
0
2
0
0
0
2
0
0
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
1
1
0
1
1
0
0
1
0
0
0
1
0
0
2
0
0
0
2
1
0
2
0
0
0
2
2
0
2
0
0
1
0
1
2
0
0
2
1
2
0
1
1
1
0
0
2
1
0
0
0
0
1
2
2
0
0
0
0
2
0
0
0
4
0
0
1
0
1
0
0
1
0
0
0
0
1
1
1
0
1
1
2
2
1
2
0
1
1
0
0
0
1
2
0
0
1
2
2
0
0
1
5
2
1
1
0
1
2
2
2
0
2
0
1
1
3
1
0
1
1
2
0
1
0
0
2
2
0
2
2
1
0
1
2
2
1
1
0
2
1
0
2
1
0
1
0
0
1
2
1
0
1
1
1
1
2
1
2
0
1
0
1
0
0
0
2
2
1
1
0
0
0
0
0
1
1
2
0
3
0
0
0
1
0
1
0
0
0
1
2
0
0
0
1
1
0
2
2
0
1
1
1
0
0
1
0
1
0
1
2
3
1
1
1
0
0
0
0
0
0
2
0
0
1
2
0
0
1
0
1
1
0
0
0
1
2
1
0
0
2
0
1
0
0
0
1
0
0
0
1
2
0
0
1
2
2
0
2
0
0
0
0
0
0
1
2
1
1
1
0
0
0
0
1
0
0
0
1
2
0
2
0
1
1
2
1
0
0
1
2
2
0
2
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
1
2
0
1
2
0
2
0
2
0
1
1
0
0
1
0
0
1
2
1
0
0
0
0
0
1
0
0
0
1
0
0
1
2
0
0
0
0
1
1
1
1
1
0
0
2
0
0
0
2
0
2
1
0
1
1
1
0
0
0
0
0
0
0
2
0
1
0
2
1
1
0
0
1
1
1
1
1
0
0
0
0
1
0
1
1
1
1
0
1
0
0
0
2
0
1
1
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
2
1
1
0
1
0
2
0
0
1
0
1
0
0
0
1
1
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
1
0
0
0
0
0
1
3
0
0
0
1
0
2
0
0
1
0
0
0
0
1
1
0
0
1
1
1
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
12
0
2
0
1
2
3
2
0
0
2
3
0
0
1
0
0
2
1
1
1
0
0
2
1
0
0
0
0
0
2
0
2
1
0
0
0
1
0
0
1
1
0
0
0
1
0
2
1
0
2
0
2
0
0
2
0
1
0
2
1
0
2
1
0
1
0
0
0
1
0
1
1
0
0
0
0
2
2
0
0
0
0
1
1
0
1
0
1
0
0
2
1
0
2
2
0
0
1
0
0
0
2
0
0
2
0
0
0
0
2
0
0
1
2
0
2
0
1
0
0
2
1
0
2
0
2
0
0
1
0
0
0
1
1
2
0
0
2
0
0
0
1
1
3
0
0
0
0
2
0
2
0
2
0
0
0
0
0
3
0
0
0
0
0
2
0
0
1
1
0
0
0
1
1
6
1
1
0
1
2
1
2
1
1
0
1
0
1
0
0
0
2
2
0
0
2
0
0
1
0
0
2
2
2
1
0
1
0
1
0
1
1
2
0
0
0
1
2
0
0
1
0
0
0
0
0
1
3
1
0
0
1
0
0
0
1
0
2
2
0
0
0
1
0
0
0
1
0
0
2
0
0
0
1
1
0
0
0
1
1
0
2
0
1
1
2
2
0
1
0
1
0
0
1
0
0
1
1
1
0
0
0
1
0
0
1
0
0
0
1
1
0
0
2
0
1
1
0
2
1
1
1
1
4
0
2
1
1
0
1
0
0
2
0
0
2
0
0
1
1
2
2
1
0
1
0
0
2
0
0
0
0
1
0
0
0
2
0
2
1
0
1
0
1
1
0
2
1
0
1
0
1
2
0
1
0
0
0
0
2
1
1
0
0
2
0
0
0
2
0
0
0
0
2
1
1
1
7
2
1
0
0
2
0
1
1
1
0
2
0
1
0
2
1
0
0
2
0
1
0
1
0
1
0
0
0
0
1
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
1
1
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
1
1
0
0
1
0
0
1
1
2
0
1
0
0
1
1
2
2
0
2
2
0
2
0
0
2
0
0
1
0
2
0
2
0
1
1
1
0
0
0
0
1
1
2
1
1
0
1
0
0
1
1
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
1
1
1
2
0
0
0
2
0
0
2
0
4
0
2
0
0
0
1
1
1
2
0
0
0
0
0
0
1
0
0
3
0
1
0
1
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
7
1
0
0
0
0
1
0
0
1
0
0
2
1
0
0
1
0
1
0
0
1
2
1
0
0
2
0
1
1
1
0
2
0
1
1
0
1
0
0
0
0
0
2
0
0
0
2
1
0
0
0
2
2
0
0
1
1
3
0
2
0
0
0
1
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
1
1
1
0
0
2
0
0
1
1
0
0
0
0
0
3
2
1
2
0
2
0
1
1
2
2
2
0
0
0
0
0
0
1
0
2
1
1
1
0
0
2
1
1
2
0
0
0
0
0
2
0
2
1
0
2
1
1
0
0
2
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
2
0
1
0
2
0
1
1
0
0
1
1
1
2
1
0
0
0
1
0
0
2
0
2
1
0
0
0
2
0
0
0
2
2
3
2
2
1
0
1
0
0
1
0
4
0
0
1
2
1
0
1
0
2
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
2
0
2
2
1
0
0
1
0
2
0
2
0
1
1
0
1
0
0
0
1
0
2
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
2
2
2
0
0
0
1
4
0
0
0
0
1
0
1
0
2
0
0
2
1
1
0
0
0
1
2
0
0
1
1
0
0
1
2
1
0
2
0
2
0
0
1
1
2
2
0
1
1
0
0
0
0
2
1
2
2
0
0
1
0
0
1
1
1
0
1
1
2
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
2
0
2
0
2
0
2
0
1
1
2
0
0
2
0
1
0
0
1
1
0
2
0
0
2
0
1
2
0
0
0
1
0
0
0
3
0
2
2
2
0
2
0
1
0
0
3
1
0
0
0
1
0
1
0
2
2
0
0
1
2
0
1
1
2
1
2
0
2
2
1
0
0
0
1
2
2
1
2
0
2
0
1
1
0
1
0
0
0
0
0
2
0
0
1
1
2
1
1
1
0
0
0
0
2
1
0
3
0
1
0
0
1
1
1
1
0
0
3
0
2
2
0
0
0
1
0
2
1
0
1
0
0
1
0
1
0
1
1
0
1
0
0
0
0
0
1
3
1
2
1
1
0
1
0
2
1
0
2
0
0
1
0
0
1
0
2
2
0
0
0
1
1
1
0
0
0
1
2
0
0
2
0
0
1
0
0
0
3
0
1
2
0
0
0
2
2
0
1
1
0
1
0
0
0
0
1
0
0
0
0
1
1
1
2
0
1
1
2
1
0
0
1
0
0
0
0
1
2
0
0
2
3
1
0
1
0
0
2
1
0
0
2
0
0
0
1
1
1
0
1
0
1
2
1
0
0
0
1
1
1
1
1
2
1
0
0
2
1
0
1
2
0
0
1
2
0
0
1
0
0
1
0
2
0
0
0
2
0
2
3
1
0
2
0
0
0
1
2
1
0
0
2
1
0
0
0
1
0
1
0
0
0
1
0
1
0
3
2
0
0
1
1
0
0
1
1
0
0
1
0
1
0
2
9
0
1
0
0
0
2
2
0
0
2
0
0
0
2
1
0
0
1
1
0
1
0
1
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
2
0
0
1
1
1
0
2
0
2
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
1
0
2
1
2
0
1
0
0
0
1
2
0
1
1
3
0
1
0
1
0
0
0
0
2
0
0
1
1
0
2
0
0
0
2
1
0
0
0
0
1
0
2
2
0
0
0
0
1
0
0
2
2
0
0
2
1
1
0
0
0
2
0
1
0
1
0
1
0
0
0
2
1
0
1
1
0
0
2
0
1
2
1
1
0
0
0
2
0
1
0
0
0
2
1
0
0
1
2
0
0
2
0
1
2
1
0
0
2
0
2
0
0
0
0
0
1
1
0
0
2
0
1
0
0
1
0
0
0
1
0
1
2
0
1
2
2
0
0
2
1
3
0
1
0
2
0
0
2
1
0
1
0
0
3
0
0
0
2
2
0
0
1
1
0
0
0
0
0
3
0
2
1
0
0
2
1
0
0
0
0
0
0
2
2
1
0
0
0
0
0
1
2
0
0
1
1
0
0
0
0
0
1
0
0
2
0
1
1
0
1
2
1
0
2
1
0
1
1
0
0
0
1
0
0
2
1
0
2
1
0
2
1
1
0
0
1
0
1
2
2
0
2
5
1
0
1
1
0
0
1
0
0
2
1
1
1
0
1
0
1
0
0
0
1
2
0
1
2
0
2
1
0
0
0
0
0
0
1
2
0
1
0
0
0
0
2
1
0
0
0
1
2
1
1
0
2
0
1
1
0
2
2
0
2
0
1
0
1
0
0
1
1
1
0
1
1
0
0
0
1
0
0
2
0
2
0
0
1
2
0
0
1
3
0
1
4
1
1
4
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
2
1
1
0
0
0
0
0
1
0
2
0
1
0
1
1
1
3
2
0
1
0
1
1
2
0
1
0
0
2
1
0
2
0
0
2
0
1
2
0
1
0
1
1
1
1
2
1
0
0
0
2
0
1
2
0
0
2
0
0
0
2
0
0
0
2
1
1
0
1
2
0
2
2
2
2
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
1
3
1
3
0
0
1
0
1
2
1
0
0
0
0
1
2
0
2
0
1
2
0
2
2
1
2
0
1
0
0
2
2
0
0
0
0
0
0
1
2
1
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
3
1
1
2
1
3
0
0
0
0
2
1
0
0
1
1
2
0
0
1
0
1
2
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
3
0
4
1
0
0
0
2
0
1
1
0
0
1
0
0
2
2
0
2
1
0
1
1
0
0
0
0
0
2
0
2
1
0
1
0
0
0
1
1
2
0
0
0
0
0
1
2
0
0
1
2
2
1
1
0
0
0
1
0
1
1
0
0
1
2
0
3
0
1
0
0
0
0
0
0
1
2
3
2
1
1
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
1
1
0
0
0
0
0
2
1
0
0
1
0
0
0
0
2
0
2
0
0
2
1
1
2
1
2
0
1
0
0
2
0
0
1
1
0
0
0
0
1
4
0
2
0
0
0
2
2
2
2
2
2
0
2
1
0
1
2
0
0
0
0
0
0
0
1
0
1
0
0
1
1
2
1
1
2
0
1
1
1
1
0
2
0
1
0
2
0
0
0
0
3
2
0
0
0
1
1
2
0
1
2
0
1
1
1
2
0
0
1
1
0
0
1
0
1
0
1
2
0
1
0
0
1
0
0
1
0
1
0
2
2
0
2
0
2
0
0
0
1
1
1
2
5
2
1
0
0
2
0
0
0
0
1
0
0
1
0
0
0
2
1
2
0
1
0
0
0
1
1
0
2
2
0
1
4
1
2
0
0
0
1
1
0
1
1
0
1
0
1
1
0
1
0
0
0
6
1
2
0
0
1
0
0
1
1
0
2
0
1
1
1
2
0
0
1
0
0
0
2
3
1
2
0
1
0
1
0
1
1
0
1
2
2
0
0
0
1
0
0
1
2
0
2
0
0
1
0
0
0
1
2
0
2
1
0
0
0
3
0
0
0
0
0
0
1
0
0
2
2
0
1
0
0
0
0
0
1
1
2
2
0
1
1
0
1
0
0
0
0
0
1
0
0
1
0
0
2
2
2
0
0
0
1
0
1
1
1
1
1
1
2
0
2
2
0
1
1
1
0
0
0
1
1
2
0
0
0
1
1
0
2
2
0
0
0
1
2
1
0
0
0
0
0
2
0
0
1
1
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
7
2
1
2
3
0
0
0
1
1
0
1
1
1
0
0
0
2
1
1
1
1
0
0
1
0
1
0
0
0
2
2
1
0
0
1
1
1
4
1
0
0
0
1
2
0
2
3
0
0
0
2
2
0
2
0
1
0
2
1
0
0
2
0
0
0
0
0
0
1
0
2
1
1
2
1
0
0
0
1
2
2
0
1
1
0
1
0
1
1
1
0
0
3
0
2
0
1
2
1
0
3
0
0
1
2
0
0
0
0
2
1
2
1
0
0
1
1
1
0
1
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
2
0
2
1
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
2
2
0
0
0
0
0
2
0
2
0
1
2
2
0
0
0
1
0
0
0
0
2
2
0
1
1
0
0
2
0
0
1
0
0
0
1
1
0
2
2
1
0
0
0
0
2
0
2
1
0
2
2
1
2
2
0
2
2
0
1
0
0
0
2
0
1
0
0
0
14
0
0
0
1
0
1
0
0
0
0
0
2
2
1
0
2
0
0
0
1
0
0
0
1
0
1
2
2
2
0
0
1
0
0
0
0
2
0
1
0
0
0
0
1
0
1
1
2
0
1
0
1
1
0
0
1
2
2
0
0
1
0
0
0
0
1
1
2
0
2
1
0
1
2
0
0
0
0
0
0
0
0
1
0
2
1
1
2
1
2
0
0
1
1
0
2
1
2
1
1
0
0
4
1
0
0
1
1
2
1
2
0
1
0
0
0
0
0
0
1
0
0
1
0
2
1
1
0
0
0
0
0
1
0
2
2
0
2
1
2
0
0
1
1
2
0
0
2
0
0
1
0
0
0
0
0
2
1
0
0
2
0
0
2
0
2
2
2
0
0
0
1
1
0
1
0
2
0
0
2
2
0
0
0
1
1
0
1
0
2
2
1
2
0
0
1
0
4
0
0
1
1
0
0
2
1
0
0
0
0
0
1
1
2
0
1
0
0
2
0
0
1
0
2
1
2
0
1
1
0
0
0
0
1
0
1
1
2
0
1
0
0
0
1
0
2
2
0
0
1
0
2
1
0
1
1
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
1
0
2
2
0
0
0
2
1
0
0
1
2
2
0
0
0
0
0
1
1
1
0
1
0
1
0
1
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
2
7
1
1
2
0
0
1
0
3
0
0
0
0
0
1
1
2
2
1
0
2
0
1
0
1
2
0
0
1
0
2
0
1
1
1
1
1
1
2
1
0
2
0
0
0
0
3
1
2
0
1
0
2
0
2
3
0
0
1
2
1
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
2
0
1
1
2
1
0
0
1
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
1
0
1
2
0
1
0
0
1
2
0
1
2
0
0
0
1
0
0
1
1
2
1
0
1
0
0
0
2
0
2
2
0
0
1
1
0
0
0
0
2
1
0
0
0
1
1
1
0
0
0
0
0
0
0
2
0
3
0
2
2
0
0
0
0
1
2
0
0
0
1
0
2
0
3
0
1
0
1
0
0
2
0
0
1
0
0
1
0
2
0
2
0
0
0
0
0
0
0
2
1
1
2
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
1
2
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
1
1
0
0
0
0
2
1
0
2
0
1
1
0
1
1
0
0
0
2
0
0
2
0
0
0
1
1
0
0
0
2
0
0
4
3
1
0
0
0
1
2
0
0
1
0
2
0
1
1
0
0
1
0
2
0
1
2
0
0
0
0
1
1
1
1
1
0
0
1
0
0
0
2
1
0
0
0
0
0
0
1
2
2
0
0
1
1
0
0
0
0
0
0
1
1
0
2
1
1
0
2
1
0
3
2
0
2
0
0
1
0
0
1
0
0
0
1
2
0
0
2
0
0
0
0
1
0
0
1
2
0
0
3
1
0
1
2
1
0
0
1
1
0
1
0
2
0
1
0
0
0
0
2
1
0
0
0
1
1
0
0
2
0
0
1
1
0
0
0
1
1
0
1
0
2
2
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
1
1
1
1
1
0
0
2
0
2
1
0
0
2
2
2
0
0
0
0
1
0
1
0
1
0
0
0
0
1
2
0
1
1
0
0
0
1
0
2
2
0
0
0
1
1
0
1
2
0
1
0
0
2
1
1
1
0
0
1
1
0
0
0
2
1
0
0
0
1
0
0
3
0
0
1
2
0
0
0
1
0
1
0
1
0
0
0
2
1
0
0
0
0
2
1
0
2
1
1
0
0
0
0
1
1
0
0
1
0
2
2
1
2
2
2
1
0
0
0
0
0
2
0
0
0
2
2
0
2
1
0
1
0
1
0
2
0
2
0
0
2
1
0
0
2
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
1
1
1
0
2
0
0
1
0
1
0
2
0
1
0
0
1
0
2
2
0
0
0
2
1
0
1
1
1
0
1
2
0
0
0
0
0
2
0
1
0
0
0
1
0
0
1
1
0
1
0
1
1
1
0
2
1
2
2
0
1
0
0
0
0
1
1
0
2
0
1
1
0
0
0
1
1
1
1
1
1
2
2
2
0
0
3
1
0
1
0
1
1
0
0
0
1
2
1
0
2
0
0
0
0
2
0
1
1
2
2
0
4
0
0
5
1
0
1
0
1
0
0
0
0
2
1
2
1
1
0
2
1
0
0
0
0
3
0
0
1
0
0
2
0
0
1
2
0
0
0
1
1
1
3
0
0
1
0
0
1
2
0
1
0
0
0
2
1
1
2
3
1
0
1
0
0
2
0
2
1
0
0
2
0
0
2
0
0
1
1
2
0
2
1
2
0
2
2
3
0
0
0
0
2
0
2
2
2
0
1
0
2
2
0
0
1
0
1
2
0
0
0
1
1
0
1
2
0
0
0
0
2
2
1
1
0
0
0
0
0
0
0
2
0
0
0
1
1
1
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
2
6
1
1
0
0
0
1
2
0
2
0
1
0
2
2
0
2
1
1
0
0
0
1
0
1
0
0
1
1
0
0
1
0
1
1
2
0
1
2
1
0
2
1
2
0
0
1
0
1
0
1
1
2
0
0
2
2
2
0
0
3
0
0
0
0
1
0
0
1
1
2
0
0
1
0
0
1
3
1
0
2
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
1
2
0
0
0
2
1
0
0
0
0
0
0
0
0
2
2
1
0
1
2
0
1
0
0
1
0
2
0
1
1
1
0
1
0
0
0
2
2
2
2
0
0
1
0
1
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
1
0
1
0
0
0
1
1
1
1
2
0
2
2
1
0
0
0
1
0
1
1
1
2
2
0
0
0
1
1
0
0
2
0
2
0
1
0
0
1
0
1
2
2
2
0
0
0
0
0
1
2
0
0
4
0
0
1
1
2
0
0
0
1
0
0
1
0
1
4
0
0
0
1
0
4
2
2
2
2
0
2
2
1
0
1
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
2
0
2
0
0
1
0
0
0
3
1
0
0
3
1
2
0
0
0
2
1
0
0
2
0
0
1
2
0
1
1
1
0
1
0
0
0
0
1
2
0
1
0
2
2
2
1
2
1
1
1
1
0
0
2
0
0
0
2
0
1
0
1
0
1
0
1
0
0
1
2
1
0
1
1
0
0
0
1
0
0
1
1
1
0
0
1
0
1
1
0
2
0
2
2
1
0
0
0
0
0
0
0
0
2
0
2
1
0
0
3
0
1
0
0
1
1
1
1
0
1
0
2
2
0
0
1
2
2
0
0
0
0
2
1
0
1
1
0
1
0
0
0
1
1
0
1
1
1
1
0
1
1
2
1
0
2
1
1
2
1
2
2
1
2
0
0
1
0
1
0
2
0
1
4
0
0
1
0
1
1
1
2
2
0
0
0
0
2
0
2
0
0
1
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
2
2
0
1
2
2
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
2
2
1
0
0
0
1
0
1
1
0
2
0
0
1
0
0
1
0
0
2
1
0
0
1
1
0
0
1
2
3
0
0
1
0
1
2
0
0
2
0
1
3
1
0
0
2
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
2
0
0
0
0
0
3
2
2
0
0
0
2
0
2
0
1
0
2
1
1
0
1
0
0
0
2
0
3
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
1
0
1
1
1
0
0
2
1
1
2
0
0
0
0
1
0
0
0
1
2
2
0
1
2
1
0
2
1
1
0
0
1
2
1
1
0
0
3
1
2
1
3
0
0
0
1
0
0
0
1
0
0
2
0
1
0
0
0
0
1
0
0
2
0
2
0
0
0
2
0
2
0
2
0
1
0
1
0
1
2
0
2
2
2
0
2
0
0
1
0
0
2
1
2
0
0
2
0
0
0
0
0
0
0
2
1
0
2
1
0
0
2
0
1
2
2
2
1
1
1
0
1
3
0
1
0
1
0
0
0
0
1
0
0
0
1
0
3
1
0
1
3
0
0
0
3
0
0
0
2
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
2
0
2
0
1
1
1
0
0
1
0
0
2
0
0
0
0
2
0
1
0
0
1
0
0
0
0
1
1
2
4
2
0
1
0
1
0
1
0
2
2
0
1
1
0
1
0
0
0
0
1
1
3
0
0
0
0
0
1
2
1
0
1
0
0
0
2
0
1
0
0
2
0
0
2
0
0
2
1
0
1
1
2
0
0
0
1
1
2
0
0
0
0
0
0
1
2
1
0
1
0
0
2
0
2
1
0
0
0
0
2
1
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
1
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
1
0
1
1
2
1
0
2
0
1
0
0
2
0
0
1
0
1
0
1
1
0
1
0
0
2
2
1
0
2
0
0
2
0
1
0
0
2
0
2
0
1
0
1
1
0
0
1
1
0
0
2
1
1
1
3
2
0
0
0
1
1
2
1
0
1
2
2
0
2
0
1
1
0
0
0
0
4
0
1
2
2
2
0
0
0
2
1
0
2
1
2
2
0
2
2
2
1
1
1
0
2
1
3
2
0
0
0
1
1
0
0
2
0
0
1
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
1
2
0
0
3
4
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
1
0
1
1
0
1
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
2
1
2
0
0
2
0
0
2
0
0
1
2
0
0
1
0
0
1
2
0
1
2
0
0
2
0
2
0
0
3
0
0
1
0
0
0
2
0
0
0
0
1
2
0
2
0
1
0
0
0
0
2
1
1
0
1
0
2
1
0
5
1
0
2
2
0
0
1
2
1
0
1
0
0
0
0
1
0
0
1
0
0
2
0
1
2
1
0
0
0
1
1
0
1
0
1
1
2
1
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
1
2
1
0
0
0
0
1
2
2
0
0
1
1
1
0
2
2
0
0
0
0
0
1
1
1
0
0
1
1
0
1
0
1
2
0
0
2
0
1
0
0
0
0
0
1
0
1
0
1
1
1
0
0
0
2
0
1
0
2
0
0
2
2
0
0
2
1
0
0
0
1
0
2
0
0
1
0
1
9
0
0
1
0
0
1
2
2
0
1
0
2
1
0
2
0
0
2
0
0
0
0
0
0
1
1
1
0
1
0
1
1
1
0
0
1
0
0
1
2
0
0
0
0
2
1
1
0
2
0
0
0
1
0
0
0
0
2
0
2
0
2
0
0
2
0
0
0
2
0
0
1
0
0
0
2
2
0
2
1
2
2
0
1
1
1
1
0
0
0
2
0
0
0
0
0
0
14
2
0
0
0
2
1
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
1
1
1
0
1
2
0
0
0
0
2
1
1
1
1
0
2
0
0
1
0
0
1
0
1
0
0
2
0
0
2
1
0
1
3
0
2
1
0
1
1
0
0
2
1
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
1
1
2
0
2
1
0
1
1
2
0
2
0
0
0
2
0
1
0
0
2
1
0
0
2
1
0
2
0
0
0
0
3
0
0
4
1
2
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
2
1
0
0
0
2
1
0
0
0
0
0
0
1
2
0
1
3
0
1
0
0
2
1
0
0
1
1
0
0
0
0
2
0
0
0
2
1
2
0
0
1
0
2
0
0
2
1
0
1
1
0
2
0
0
0
0
0
0
0
0
1
2
0
2
1
0
1
0
0
0
0
1
0
1
2
1
1
2
0
1
0
0
0
0
0
1
1
1
2
2
0
2
0
2
0
0
1
1
1
0
0
2
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
2
0
1
2
0
0
1
2
2
0
1
0
0
2
0
0
0
1
0
0
2
0
0
0
1
1
1
0
0
2
0
0
0
2
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
2
1
1
0
1
2
1
2
0
1
2
0
0
0
1
0
0
0
1
0
1
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
2
2
1
1
0
1
0
2
2
1
0
0
0
0
2
0
0
2
1
2
0
2
2
0
1
0
1
0
1
1
0
0
0
0
1
0
2
2
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
1
0
2
2
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
1
2
2
2
1
2
0
0
3
1
0
0
2
1
1
1
0
0
1
2
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
1
0
1
0
0
1
0
0
0
0
3
0
2
2
4
0
1
1
2
0
0
0
0
0
1
1
2
0
2
0
0
2
0
1
2
1
0
2
2
0
2
1
1
0
2
2
0
2
1
0
2
2
1
2
1
0
1
0
1
0
1
2
2
0
2
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
1
1
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
3
0
1
0
0
1
0
0
1
0
2
0
0
0
0
0
0
2
0
0
2
2
0
0
2
0
0
0
0
0
0
1
0
0
0
1
1
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
2
0
1
0
1
2
1
0
1
0
2
0
0
1
0
1
1
0
1
0
0
1
2
1
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
1
0
1
0
2
1
1
0
0
2
2
2
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
2
2
5
0
0
1
1
1
1
0
1
0
0
3
0
0
0
0
2
0
1
2
1
0
0
0
0
0
0
0
2
0
0
0
2
0
2
1
0
0
1
0
0
0
0
1
1
0
0
0
0
1
2
3
2
0
0
0
1
1
0
2
0
1
0
1
1
0
2
0
0
1
0
1
1
0
0
1
1
0
0
0
0
1
0
0
1
1
0
1
0
1
2
1
2
0
0
0
1
0
1
1
5
0
0
1
0
0
0
2
1
0
1
0
0
0
0
2
0
0
0
1
2
0
1
0
1
1
1
2
2
1
1
1
2
0
0
1
0
0
0
0
1
2
0
0
0
0
1
3
2
1
0
2
0
0
1
0
0
1
2
0
2
0
0
1
1
0
0
0
0
0
0
1
0
3
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
1
0
0
1
0
0
0
1
0
0
1
1
0
2
1
2
0
0
2
2
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
2
0
0
0
0
0
2
0
2
1
0
0
0
1
3
0
0
0
1
2
1
2
1
0
0
0
0
1
0
0
0
2
2
0
2
0
0
0
2
2
1
0
0
2
0
0
2
1
1
1
0
1
2
1
0
0
0
0
0
0
0
2
2
0
1
0
1
1
1
1
2
0
1
2
2
0
0
2
2
0
0
0
2
2
1
0
1
1
1
1
1
1
0
0
0
0
0
2
0
2
0
0
2
0
1
1
2
1
1
2
0
0
0
0
0
0
2
2
1
0
0
1
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
2
0
1
2
0
1
0
2
0
1
0
1
1
0
0
1
0
1
1
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
1
0
1
2
0
0
2
0
1
1
1
0
1
0
1
0
1
1
0
2
1
1
0
2
0
1
0
2
0
0
1
1
0
0
0
2
0
1
0
2
0
0
1
0
0
2
0
1
0
2
0
0
0
1
0
0
1
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
2
0
1
1
0
1
2
0
1
1
0
2
1
0
2
1
0
1
1
0
1
2
1
1
0
5
0
0
0
1
0
0
2
1
2
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
1
0
0
1
2
0
0
0
0
2
0
0
2
2
0
0
1
0
0
1
1
0
0
0
0
1
1
0
1
1
2
1
0
0
2
0
2
0
0
2
0
0
0
1
1
2
0
1
2
1
0
0
0
1
1
0
1
1
0
1
0
0
1
2
2
1
1
0
3
0
2
2
0
0
1
1
0
2
0
1
1
0
2
1
0
0
0
0
0
0
0
2
1
1
0
1
1
0
0
2
2
1
2
1
2
0
2
0
0
0
3
1
0
1
0
0
0
1
2
1
2
0
0
1
1
0
0
2
0
0
1
1
1
0
1
1
1
6
0
2
0
0
1
0
1
2
2
1
0
1
2
2
1
0
1
0
2
1
0
2
0
1
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
2
1
2
1
0
2
0
1
0
2
2
0
2
0
0
1
1
3
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
4
2
0
0
2
1
2
1
0
1
2
0
1
0
2
0
2
0
0
0
0
2
0
0
0
2
2
0
1
2
1
0
1
1
1
0
2
0
0
1
2
0
2
1
0
8
0
1
0
1
0
2
0
1
0
0
0
2
2
1
2
2
0
0
0
2
0
0
10
2
2
1
0
0
0
0
2
0
2
0
2
0
0
1
0
1
2
0
2
1
2
0
2
0
1
0
2
2
0
3
0
0
0
0
1
0
0
1
0
0
1
0
1
2
1
0
1
1
0
0
0
2
2
1
1
1
1
4
0
2
1
0
0
0
1
0
0
1
1
1
1
1
2
1
1
3
1
0
0
0
0
1
0
1
0
2
1
0
0
0
1
0
1
0
2
0
0
1
0
0
0
0
0
1
0
1
0
1
1
0
2
0
0
1
0
0
1
1
0
2
2
1
0
0
0
2
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
2
0
0
2
2
0
0
1
1
2
0
0
2
0
0
0
2
2
0
0
0
1
0
0
2
1
0
1
0
3
0
1
0
1
1
0
2
1
0
1
0
1
2
0
1
0
1
1
0
0
0
1
1
0
2
0
0
0
0
1
2
2
0
0
2
0
2
2
0
0
1
1
0
0
0
1
2
0
0
0
0
0
4
2
1
0
0
0
2
0
1
0
0
0
2
0
1
1
2
0
0
0
1
0
0
0
1
2
0
0
0
1
1
1
1
0
0
2
0
1
0
0
1
0
0
2
2
0
0
2
1
6
0
0
0
1
2
2
0
3
1
0
0
0
0
0
1
1
2
1
1
0
1
1
0
4
0
0
2
0
0
0
1
2
1
2
0
1
2
1
1
0
1
0
0
2
1
0
0
2
2
2
0
3
0
2
0
0
2
0
1
0
1
0
1
0
2
0
0
0
0
0
2
0
2
1
0
1
1
2
0
0
0
0
2
8
1
1
1
1
1
0
1
1
0
1
0
0
2
0
1
2
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
1
1
1
0
0
0
3
0
0
0
0
0
0
0
1
1
1
0
0
1
0
2
1
2
2
0
0
1
0
2
0
0
0
0
3
0
1
1
0
0
0
1
2
2
1
0
0
1
0
4
2
2
0
2
2
0
0
1
1
1
1
0
2
0
0
1
0
1
1
2
0
0
0
1
0
2
0
1
2
0
0
0
0
2
1
0
0
2
0
0
1
0
0
2
1
0
1
0
0
0
1
1
2
0
0
0
2
2
1
1
0
1
2
1
0
0
2
1
2
1
1
0
2
0
1
2
1
0
1
2
2
0
1
0
2
3
0
0
1
0
1
0
0
0
2
0
1
1
0
0
0
1
3
0
0
0
1
0
1
0
0
2
2
0
2
2
4
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
2
0
2
1
0
0
0
2
1
2
0
1
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
2
2
1
2
0
0
0
0
0
0
0
1
0
1
1
2
2
0
0
0
1
2
1
0
0
0
2
0
0
0
0
1
0
2
0
0
2
3
0
2
2
0
1
0
0
1
0
0
2
0
0
0
1
1
0
1
0
1
2
0
4
2
0
0
1
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
2
1
0
0
0
0
0
2
1
0
0
0
0
0
0
1
2
1
0
2
1
0
1
0
1
2
0
0
0
2
1
0
1
0
1
1
0
0
0
0
0
0
1
2
1
1
0
0
1
0
2
2
0
0
0
0
0
0
1
0
0
2
0
1
2
2
0
0
0
1
0
1
0
2
1
0
2
1
0
2
1
1
0
0
2
0
1
3
2
0
0
1
0
0
0
1
0
0
2
2
1
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
1
0
2
0
2
0
1
0
0
0
2
1
0
0
0
0
0
0
2
2
1
1
1
0
0
1
0
0
0
0
0
0
1
0
2
0
0
2
0
2
0
1
0
0
2
0
0
2
2
1
2
0
1
1
2
2
0
3
2
0
2
0
1
0
0
1
0
1
1
0
0
0
0
0
1
2
0
1
1
0
2
0
0
1
1
1
1
1
1
2
0
1
0
1
0
0
0
2
0
2
1
0
2
0
1
0
0
2
2
2
2
2
0
0
1
1
1
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
1
3
0
2
0
1
2
1
0
0
0
0
0
3
1
1
0
1
0
0
2
0
1
1
1
2
0
2
0
0
0
2
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
2
2
1
2
0
2
0
2
0
0
1
0
0
1
0
0
0
2
1
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
2
2
2
2
0
2
0
2
0
0
0
0
2
0
0
2
0
0
1
1
0
0
1
1
1
1
0
1
0
0
0
0
2
1
0
0
3
0
0
0
0
3
0
1
0
0
1
1
1
0
2
2
0
2
0
0
1
0
0
2
0
1
0
0
1
1
2
1
0
1
2
2
0
2
1
0
1
0
0
1
1
0
0
0
1
0
1
2
0
0
0
0
2
1
1
0
0
0
2
2
0
0
0
1
1
0
0
1
0
0
0
2
1
2
0
1
2
0
1
0
1
1
1
1
0
1
1
2
0
1
0
1
2
0
1
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
2
2
0
0
0
0
0
3
1
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
2
1
0
0
1
1
0
2
1
0
1
0
0
1
1
0
0
1
1
1
0
0
1
2
0
0
1
0
0
0
0
0
1
2
0
0
0
1
0
4
1
0
0
0
0
1
0
0
0
0
3
0
1
1
2
0
0
1
1
1
1
0
0
2
1
2
2
0
1
0
0
0
2
1
0
2
1
0
0
2
0
0
2
1
2
2
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
2
0
2
1
2
0
3
1
0
0
0
2
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
1
0
1
3
2
2
0
0
1
0
1
1
2
1
0
0
0
0
0
0
1
1
2
1
0
2
0
0
0
1
0
0
0
0
1
0
1
2
0
1
1
0
1
1
0
0
2
1
0
1
1
0
1
0
0
0
0
1
2
2
0
0
3
2
1
1
0
0
2
2
1
1
1
0
2
1
0
0
0
1
2
2
1
1
1
0
0
1
3
2
2
0
1
0
2
0
0
1
2
0
0
1
1
1
0
0
0
0
1
2
0
1
0
0
0
0
0
1
1
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
3
1
1
0
1
1
0
0
0
0
0
2
1
1
1
0
1
0
1
0
0
0
1
2
0
0
4
0
0
0
0
2
0
1
4
0
0
0
0
1
0
0
2
0
2
1
0
0
1
0
0
1
0
1
0
0
0
2
0
0
0
1
1
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
1
2
0
1
0
0
2
1
0
2
0
1
1
0
1
0
0
2
2
2
0
0
2
1
0
0
0
0
2
1
1
0
0
3
0
2
0
0
0
0
0
0
1
2
2
0
0
3
1
1
0
1
2
0
0
1
0
0
0
2
0
2
1
0
2
0
0
1
0
2
1
2
2
0
2
2
0
0
2
0
2
0
0
2
0
1
1
0
2
0
0
0
2
0
1
2
2
2
0
0
2
0
0
1
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
2
0
0
3
2
0
0
0
1
1
1
2
0
1
1
1
0
2
0
0
0
2
0
0
0
1
1
0
3
0
0
1
1
0
0
0
0
0
0
0
0
0
2
2
0
0
1
2
2
0
0
1
0
0
3
0
0
1
1
0
0
0
1
1
0
1
0
0
0
0
0
1
1
0
1
0
0
2
1
1
2
0
0
1
0
1
0
0
2
0
1
0
2
0
1
0
1
0
0
1
0
1
0
1
0
2
1
0
1
2
0
0
0
0
0
0
2
2
1
0
0
1
1
1
1
0
2
0
0
2
1
0
1
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
3
0
1
1
0
0
0
2
0
0
0
0
0
2
0
1
0
1
1
0
0
0
1
1
0
0
1
0
0
1
1
1
1
0
1
1
1
1
1
0
1
0
0
1
1
1
1
0
2
0
1
0
0
0
0
0
0
1
2
0
1
1
0
1
1
0
0
2
0
0
0
0
0
0
2
1
1
3
0
0
0
0
0
2
0
0
0
1
1
0
0
0
1
0
0
3
2
1
1
1
0
0
0
0
0
1
2
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
6
0
1
1
0
1
0
0
0
1
1
2
1
2
2
4
1
0
3
0
0
0
0
1
1
0
0
0
0
1
1
2
0
1
0
0
2
2
2
2
0
0
0
0
0
0
0
0
0
2
2
0
2
2
1
0
1
0
0
1
0
4
0
2
1
0
1
2
0
0
0
3
1
2
1
0
0
1
2
1
1
1
3
1
0
2
0
1
0
1
1
1
0
0
1
3
0
2
0
0
2
0
1
0
0
0
0
0
1
0
0
5
2
0
2
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
1
2
0
0
0
0
1
0
1
0
0
0
0
0
1
1
1
1
1
1
1
0
0
2
0
0
1
0
2
0
1
2
0
1
0
1
0
0
0
1
2
0
1
0
1
2
0
0
0
0
0
3
2
0
0
0
1
0
2
0
2
0
0
2
0
0
0
2
0
1
0
0
2
0
2
1
0
1
0
0
2
2
0
0
1
0
0
2
0
0
0
1
1
1
1
2
2
1
0
2
0
2
0
0
1
2
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
2
1
1
1
1
0
2
0
2
0
0
0
0
2
1
0
1
0
1
0
0
0
0
0
1
0
2
0
1
0
0
4
2
1
2
1
0
2
0
0
2
2
0
0
0
0
0
1
1
0
0
2
2
9
1
0
0
1
2
0
2
1
0
0
0
1
1
1
3
0
0
0
0
0
2
0
0
0
1
2
2
2
0
0
0
1
0
1
0
0
2
0
0
0
0
1
1
2
0
0
0
2
0
2
0
1
1
1
0
1
0
0
1
2
0
0
0
0
2
0
0
0
0
1
2
0
1
1
0
2
0
1
2
1
0
2
3
0
1
2
0
0
0
0
0
0
0
0
1
2
0
1
0
0
2
1
1
0
2
0
0
1
0
2
2
0
0
0
0
2
2
0
0
0
0
0
1
2
0
1
1
1
0
0
1
1
0
1
2
0
2
0
0
0
1
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
1
1
0
2
0
0
0
1
1
0
2
0
2
2
2
0
1
2
0
1
0
1
0
2
0
1
1
0
0
1
1
0
1
2
1
1
0
0
0
2
0
2
0
0
1
0
2
0
0
1
1
1
0
1
2
3
2
2
0
0
1
0
2
1
2
0
2
0
0
1
0
0
5
3
1
0
0
1
1
0
0
0
0
0
0
0
0
2
1
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
2
2
1
1
1
3
1
1
5
0
0
1
1
0
1
1
2
0
2
2
0
2
0
1
0
2
0
0
0
1
0
2
0
1
0
1
0
1
2
0
1
1
2
0
1
1
2
1
0
0
0
0
2
2
0
0
1
0
0
0
0
2
0
1
1
0
1
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
1
0
0
0
0
2
3
1
1
0
1
2
1
1
0
1
0
0
0
2
2
0
0
0
0
2
0
1
0
1
0
0
2
1
2
0
0
0
0
2
1
2
1
1
0
0
0
0
1
0
0
1
0
1
2
0
1
0
0
1
1
0
1
0
1
0
1
0
1
2
0
2
0
0
0
1
0
0
0
1
2
0
0
2
1
2
0
1
3
0
0
4
0
1
0
0
0
0
0
0
1
1
1
0
0
0
2
2
4
0
0
1
0
0
0
1
1
2
1
2
2
1
0
2
0
1
1
0
0
1
0
0
0
0
0
1
0
1
0
2
1
2
0
1
0
2
1
0
1
2
2
2
0
2
1
0
2
0
1
0
0
2
0
1
5
0
0
2
0
0
0
1
0
0
0
0
1
2
1
0
2
2
1
1
1
0
2
1
2
0
0
2
0
1
1
0
0
0
1
0
2
2
0
0
0
0
0
1
2
0
2
1
0
0
0
0
0
2
0
1
0
0
2
0
0
0
3
1
2
1
0
1
0
1
0
2
0
0
0
2
2
0
0
0
0
2
0
0
0
1
0
0
0
1
2
0
1
0
0
0
3
0
0
0
1
2
1
0
0
0
0
2
0
0
1
0
2
0
0
0
1
0
0
1
0
2
0
0
1
0
0
2
0
1
1
0
3
2
1
0
0
4
0
0
0
2
1
0
1
0
0
0
0
0
1
2
2
0
0
0
1
0
2
0
0
1
0
0
1
0
1
0
0
1
0
1
0
2
0
2
0
2
0
1
1
1
0
2
2
0
1
1
0
0
2
0
0
0
0
0
1
2
0
1
2
0
0
2
1
1
2
1
0
0
0
0
0
2
1
2
1
1
0
1
2
2
0
1
2
2
0
0
1
2
0
0
1
0
0
1
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
1
0
0
1
2
0
1
0
1
1
1
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
2
0
0
0
2
1
1
1
0
0
0
0
0
1
1
1
0
0
2
1
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
2
0
0
1
2
0
0
0
0
2
1
2
1
2
0
1
2
1
0
0
1
0
1
1
0
1
0
0
0
2
1
0
0
0
0
2
3
0
0
1
0
2
2
1
0
0
1
0
0
0
0
3
0
0
1
1
1
3
2
0
1
0
2
4
0
0
0
0
1
0
2
0
1
0
1
0
3
0
1
1
1
0
0
0
0
1
0
2
1
1
0
1
0
0
4
0
1
1
0
0
1
0
0
0
0
0
1
2
0
0
2
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
2
0
4
0
1
0
1
0
0
2
0
1
2
0
0
1
2
0
0
1
0
0
0
0
0
2
1
1
0
2
0
2
0
0
0
0
0
2
1
0
0
2
0
2
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
2
1
1
0
0
2
0
2
0
1
0
2
0
1
2
0
0
2
1
0
1
1
0
2
1
0
1
1
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
2
1
0
2
1
0
0
1
1
1
2
2
0
2
0
2
2
2
2
0
0
0
1
0
0
1
2
2
1
2
0
1
2
0
1
1
0
1
0
0
0
1
0
1
2
2
0
0
2
0
0
2
1
0
1
1
0
0
1
1
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
3
1
0
2
2
0
2
5
3
0
0
0
0
1
1
2
0
0
0
0
0
3
0
2
0
0
1
1
2
0
1
0
0
2
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
3
2
1
0
1
2
0
2
0
1
2
2
2
0
0
0
0
2
1
0
0
2
0
2
2
0
2
1
0
0
0
0
0
0
1
4
0
0
2
0
1
0
2
1
1
0
1
2
1
0
2
0
0
0
0
1
0
1
1
1
1
0
1
1
2
1
2
1
0
1
1
0
0
1
0
1
1
0
1
0
0
1
1
0
0
1
0
1
0
1
1
0
0
0
2
2
2
0
1
1
0
1
0
1
2
0
2
0
0
0
2
0
1
1
1
2
2
2
0
0
0
1
0
1
0
1
0
2
1
0
0
0
0
1
3
2
1
0
1
1
0
0
1
2
2
2
0
1
0
0
2
2
0
1
0
1
2
0
0
0
0
2
1
1
0
1
0
0
1
2
0
0
2
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
1
0
1
0
0
1
2
2
2
0
0
0
0
2
0
0
0
0
0
7
2
1
17
0
2
0
1
0
0
1
0
0
2
0
0
0
0
0
2
1
2
0
0
1
2
0
0
1
0
0
0
0
2
0
0
1
0
2
1
0
2
0
0
0
0
2
0
18
0
0
1
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
1
0
0
1
1
2
1
0
0
0
0
0
2
0
2
2
0
0
0
0
2
0
0
0
0
1
2
1
0
1
1
0
0
3
1
2
2
2
1
0
0
2
1
0
0
1
1
1
1
0
2
0
1
0
1
0
0
0
0
0
0
2
1
1
1
0
0
0
0
2
0
3
0
0
2
1
1
0
1
0
0
0
0
1
0
0
1
1
1
0
0
2
1
1
0
2
0
0
1
1
0
5
0
0
0
1
0
0
0
0
0
3
0
1
0
0
2
0
0
1
1
1
1
1
1
1
0
1
0
0
0
0
0
2
0
0
1
0
3
2
0
0
0
2
1
1
0
0
2
1
0
1
4
0
0
0
2
0
0
2
0
0
0
2
1
0
0
0
0
0
0
1
0
1
1
0
0
1
0
1
0
1
0
0
2
0
0
2
4
0
2
2
0
0
0
2
0
1
2
0
1
2
0
0
0
0
0
0
1
1
2
4
2
2
0
3
0
0
1
0
0
0
1
2
1
1
2
2
0
1
1
1
0
1
0
2
1
0
0
2
0
3
1
1
1
0
1
1
0
0
1
0
0
0
3
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
1
0
1
2
0
1
0
2
2
1
1
0
0
0
2
1
1
1
0
2
1
0
1
1
0
0
0
0
0
1
0
2
2
2
1
2
2
1
0
0
1
1
0
0
1
0
1
3
0
1
1
0
1
1
0
1
2
0
0
1
0
1
0
0
1
1
3
1
0
0
1
0
0
0
0
0
1
2
2
2
0
0
1
0
0
2
0
0
1
2
0
2
0
2
0
0
2
1
0
2
0
0
2
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
2
1
1
0
1
0
0
1
0
1
2
0
0
1
0
1
0
2
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
1
1
3
1
2
0
0
0
0
0
1
2
1
0
0
1
1
0
0
0
2
1
0
0
0
0
2
0
1
0
0
3
0
2
1
2
0
2
1
0
1
0
1
0
2
0
1
0
2
0
0
1
0
1
0
1
0
1
1
2
0
0
1
0
1
1
1
0
2
2
0
0
2
1
2
1
0
2
0
2
2
1
2
0
0
3
0
1
0
2
0
1
1
2
3
2
0
2
0
0
1
0
0
1
0
1
0
2
0
0
0
0
2
0
0
0
2
0
0
1
1
0
2
1
1
1
1
1
0
0
2
1
2
1
0
0
2
0
2
1
4
0
0
2
0
0
0
1
0
2
1
0
2
3
0
3
1
0
0
0
1
0
0
0
0
2
0
0
1
1
2
1
1
2
0
0
2
2
0
1
2
2
1
2
0
1
0
0
0
1
2
2
0
1
0
0
0
0
0
1
1
0
0
1
0
2
1
0
0
1
0
2
0
0
0
1
2
0
1
2
2
1
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
1
0
1
0
2
0
2
2
0
3
2
0
0
0
2
0
1
1
0
2
0
2
1
2
0
0
0
0
1
0
2
0
2
0
0
1
2
0
0
3
0
0
2
1
2
0
1
1
0
1
0
0
0
3
0
0
0
0
0
2
1
0
1
0
0
0
0
2
0
0
0
2
1
0
2
0
0
1
1
0
9
2
1
0
1
0
1
0
0
0
0
1
0
1
2
0
0
0
0
0
0
1
6
2
0
0
2
1
1
0
1
1
0
1
1
2
1
2
0
1
0
0
3
0
0
1
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
2
0
2
1
0
0
0
0
0
0
1
2
2
0
0
1
2
0
0
1
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
2
2
2
0
2
0
0
1
2
1
0
0
0
3
2
0
1
1
2
1
1
0
1
2
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
2
2
0
0
0
0
1
1
0
1
2
1
0
2
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
2
1
1
1
2
0
0
0
0
0
2
1
0
2
2
0
1
1
0
0
0
0
1
0
1
2
0
0
2
0
1
0
0
1
1
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
1
1
1
3
2
0
0
0
0
2
2
1
0
1
0
2
1
0
1
2
0
2
0
2
1
1
0
0
0
0
1
0
3
2
1
1
0
1
2
1
2
0
0
0
2
2
0
0
0
1
2
2
0
1
2
0
2
0
1
1
0
0
0
2
0
1
0
1
1
1
0
2
1
2
0
0
0
0
1
0
1
2
0
0
5
0
0
2
0
2
1
0
3
1
1
0
0
1
0
0
0
1
0
0
1
1
1
0
0
0
0
2
1
0
0
0
0
1
0
0
1
1
2
2
0
0
0
2
0
0
1
0
2
0
0
0
1
1
1
0
0
0
0
1
0
0
2
1
0
2
0
1
0
2
2
1
0
0
1
0
1
0
0
2
0
0
2
0
0
0
0
0
1
0
1
0
0
0
3
0
1
0
0
2
1
1
2
0
0
1
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
4
0
0
1
0
0
1
2
0
2
2
2
1
0
0
2
1
0
1
0
3
2
0
0
2
0
0
0
1
1
2
2
1
0
1
1
2
2
2
1
0
1
0
0
0
1
0
2
1
1
2
0
0
2
0
1
0
0
2
1
0
2
0
2
2
1
2
1
2
1
0
2
1
0
0
0
0
2
0
1
1
1
0
1
2
1
1
1
2
0
1
1
2
3
0
0
0
1
0
0
1
0
1
0
0
0
2
2
0
2
0
0
0
0
0
11
2
0
2
0
0
2
0
0
1
3
2
2
0
0
0
2
0
1
0
0
0
1
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
2
1
0
2
0
0
0
2
0
2
0
1
1
1
0
1
0
0
1
2
1
0
1
0
0
2
1
1
2
1
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
1
0
2
1
1
0
0
1
0
0
0
1
0
0
1
0
0
1
1
2
0
2
0
0
0
0
0
2
0
0
1
2
0
2
0
0
0
0
0
1
2
0
0
1
1
0
2
0
0
1
1
0
1
2
1
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
2
3
2
3
0
0
1
0
0
2
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
2
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
1
1
0
2
0
0
0
0
0
2
0
0
0
2
0
1
1
1
0
1
1
0
0
0
0
1
2
3
2
1
0
1
2
0
0
0
1
1
0
2
2
0
2
1
2
2
1
1
0
2
1
1
0
0
2
0
0
0
2
0
0
0
2
1
0
0
0
0
1
0
0
0
0
1
2
0
1
2
2
1
1
0
1
1
0
2
0
0
2
2
1
2
1
2
0
0
1
1
2
2
1
2
0
0
1
2
2
2
0
1
1
2
1
2
1
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
2
1
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
2
2
1
0
0
1
0
0
1
2
1
0
2
1
1
0
1
0
1
1
0
0
0
0
1
0
1
1
1
0
0
0
1
1
0
0
0
2
0
0
0
1
0
2
2
0
0
0
0
2
2
0
1
2
2
1
0
0
1
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
2
1
0
1
1
1
0
0
0
0
2
2
1
2
0
0
1
1
0
0
0
0
0
2
2
1
0
0
0
0
0
1
2
2
1
1
0
0
2
0
0
1
2
1
1
2
2
1
0
0
0
1
1
0
1
1
0
0
1
0
2
0
0
1
0
0
0
0
0
1
0
2
0
1
2
0
0
2
2
1
2
0
1
0
2
0
1
2
0
0
0
0
0
2
1
0
0
1
0
2
0
2
0
0
1
0
0
0
1
0
0
1
0
2
0
1
0
0
1
2
2
1
1
0
4
1
0
2
0
2
0
1
0
0
0
2
0
0
0
3
0
0
1
0
1
4
1
0
0
0
2
0
1
2
0
3
0
0
0
0
0
1
1
0
0
2
2
3
1
0
1
0
0
0
0
1
0
0
1
0
0
1
1
0
0
2
0
1
1
0
0
0
1
2
0
1
1
0
1
0
0
1
0
2
1
1
0
2
2
2
0
0
1
0
0
1
1
0
0
2
0
2
0
0
0
1
0
0
0
1
2
1
0
0
2
1
0
1
1
0
0
0
1
0
0
1
1
1
1
0
3
0
1
3
2
2
0
1
0
0
0
2
0
1
1
0
0
0
1
0
2
1
0
1
0
0
0
2
0
0
1
0
2
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
1
2
2
0
1
0
2
1
0
2
1
1
0
1
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
1
1
0
1
0
1
0
0
0
1
0
2
0
0
0
1
0
0
0
1
1
0
2
2
0
1
2
1
2
0
2
2
1
2
0
0
0
1
2
0
0
0
0
1
1
0
2
0
0
2
2
1
2
0
0
0
0
2
2
1
0
0
0
2
1
2
1
2
2
1
1
0
0
2
1
0
1
4
2
0
2
4
0
2
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
1
2
1
2
0
0
0
1
1
2
0
0
0
1
2
1
1
4
0
1
0
2
0
1
1
0
1
0
1
1
0
0
0
0
0
3
2
2
0
0
2
2
0
0
0
1
0
2
1
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
2
2
1
1
0
1
0
0
0
1
1
1
1
0
0
0
0
0
1
2
0
0
1
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
2
2
0
0
0
1
0
0
0
0
1
0
2
0
1
0
1
1
1
1
1
0
0
0
1
2
0
1
0
1
0
5
1
1
0
0
0
0
0
0
2
1
2
2
1
0
0
1
1
0
2
2
0
0
0
0
0
0
0
1
0
2
0
1
0
1
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
2
2
0
1
0
2
0
1
1
2
0
0
3
0
0
2
0
2
0
0
0
0
1
0
0
0
1
2
0
1
3
0
2
0
6
0
1
2
0
1
0
0
0
2
0
0
0
2
0
0
2
1
1
0
0
4
0
3
0
0
0
0
0
2
0
0
0
0
2
1
0
0
1
0
0
1
0
2
0
2
0
1
2
2
2
2
1
0
0
0
0
0
2
0
0
0
3
0
2
0
0
0
1
1
0
1
1
0
1
3
1
0
0
2
1
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
2
1
0
0
2
0
1
0
2
1
0
0
1
0
2
2
0
0
1
2
2
0
2
2
0
2
0
2
2
0
2
2
3
0
0
0
2
1
1
0
2
2
0
1
0
2
1
0
0
1
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
1
2
1
2
2
0
1
0
2
1
1
1
0
2
1
1
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
1
0
2
1
0
0
2
0
0
2
0
0
0
2
1
2
1
0
0
1
0
1
0
1
1
2
0
0
2
0
0
0
3
0
1
2
1
0
2
0
0
0
1
1
0
0
1
2
2
0
0
1
3
0
0
0
1
0
0
0
0
0
2
1
0
0
0
2
0
1
1
1
0
2
0
2
0
0
0
2
3
0
3
0
2
2
0
1
0
0
0
1
2
0
1
1
2
3
0
0
1
1
0
1
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
1
2
0
1
2
1
2
2
0
2
0
1
0
0
0
0
2
0
1
1
0
1
0
1
0
1
1
0
0
0
1
2
0
2
1
1
2
0
1
1
2
1
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
1
3
2
0
0
0
0
0
1
0
1
2
3
0
0
2
0
0
0
1
1
6
0
0
0
0
1
3
0
1
0
2
0
1
2
2
2
2
2
1
1
0
1
0
1
0
1
0
0
1
0
2
2
0
0
0
0
0
0
0
0
1
0
0
2
0
2
2
2
1
2
2
0
0
0
2
0
0
0
0
1
0
0
0
2
0
1
1
1
0
0
0
0
1
1
0
1
0
1
2
4
0
1
0
1
1
0
0
2
0
0
1
2
0
2
0
0
0
2
0
0
1
2
1
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
1
0
2
3
2
0
0
0
1
0
0
1
0
0
1
0
0
2
1
0
1
0
0
1
0
0
2
0
2
0
1
1
2
0
0
0
0
0
0
1
1
2
2
0
0
3
1
0
2
0
0
0
0
0
1
0
0
0
1
4
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
3
1
0
0
2
0
0
2
1
1
4
0
2
0
1
0
0
0
0
0
2
0
1
2
2
0
1
0
0
1
1
2
0
0
0
0
0
2
2
0
2
0
2
1
1
0
0
1
1
2
0
0
0
0
1
0
2
1
0
0
0
0
2
0
1
0
1
0
1
2
0
1
0
2
1
0
2
0
2
0
0
0
2
0
0
3
0
2
0
0
1
0
1
0
1
2
0
2
0
2
1
0
0
2
2
1
0
0
0
0
2
2
2
0
0
0
1
1
0
0
0
0
0
1
0
1
1
2
0
0
0
3
0
0
1
0
0
0
1
0
1
0
0
2
0
1
0
0
1
0
0
2
2
0
0
0
1
0
0
0
0
2
0
1
2
0
0
0
0
1
1
1
1
1
2
2
1
0
2
0
2
0
2
0
0
2
0
2
1
0
0
0
0
0
0
1
0
0
3
0
1
0
1
1
2
0
0
1
2
0
2
2
0
2
0
0
2
4
0
0
0
2
0
1
0
2
1
0
1
2
1
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
4
1
0
0
2
0
1
0
0
2
1
0
0
0
1
0
3
0
1
0
0
1
1
0
1
1
0
0
2
0
0
0
2
2
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
1
2
1
0
0
2
0
2
1
2
0
2
1
1
1
1
1
0
0
0
2
0
0
1
0
1
1
0
0
0
0
1
2
0
1
0
0
2
2
2
1
2
0
2
0
0
1
2
2
0
2
1
1
0
0
0
1
0
1
0
1
2
1
1
0
1
2
0
1
1
1
0
0
0
0
2
0
0
0
2
1
1
2
0
1
2
1
2
3
0
0
0
0
2
0
0
2
1
0
1
0
0
1
0
2
3
0
0
3
0
2
2
1
0
2
0
0
1
1
0
0
1
0
1
0
0
1
1
0
1
0
0
0
1
1
0
0
0
0
0
3
1
0
1
0
0
0
0
2
1
1
1
0
2
0
0
0
0
2
2
1
2
2
0
0
2
0
0
0
2
2
1
0
0
0
2
0
1
1
0
0
0
2
1
2
0
0
0
0
1
1
2
0
1
1
2
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
2
0
0
1
0
0
2
2
0
2
1
2
1
1
0
0
2
0
0
2
1
1
0
0
0
0
1
0
0
1
1
0
1
0
1
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
2
2
1
0
0
0
0
0
0
1
1
2
0
1
1
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
1
2
0
0
0
0
1
1
0
2
0
1
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
1
0
1
2
0
0
1
0
0
0
0
0
2
0
2
3
2
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
2
0
0
2
0
0
0
0
1
1
0
2
1
0
0
1
0
0
1
0
0
2
1
0
2
2
1
1
0
1
1
1
2
0
1
1
0
1
0
2
0
0
1
2
0
0
0
1
2
2
0
1
0
1
1
2
0
1
1
1
2
2
2
0
2
0
0
0
0
1
0
1
2
1
2
1
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
2
1
0
1
0
0
0
2
1
1
0
0
0
1
0
0
0
2
1
2
0
0
0
0
0
1
0
0
0
1
0
0
0
1
2
0
0
0
0
1
0
2
1
0
3
0
1
0
0
0
2
1
0
0
1
2
0
0
0
2
0
0
1
0
2
0
0
0
2
0
0
2
0
0
0
1
2
1
0
0
1
0
0
0
0
1
0
0
0
1
1
2
0
0
1
1
0
1
0
1
2
1
1
0
0
0
0
1
0
0
0
0
2
1
1
1
0
1
2
0
2
1
0
1
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
1
2
1
0
0
1
0
0
0
2
0
1
1
0
0
0
0
0
1
2
0
0
1
0
0
1
2
2
1
0
2
0
0
0
2
0
1
0
1
0
0
1
0
0
0
0
2
0
1
0
0
1
0
1
1
0
0
2
0
2
0
0
1
2
2
1
0
2
1
0
0
0
1
2
0
0
1
1
0
1
1
0
0
0
1
0
0
0
2
2
1
0
0
0
1
1
0
2
0
2
0
1
2
1
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
1
1
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
2
0
1
1
0
1
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
1
0
1
5
2
1
2
0
0
0
1
0
0
1
1
2
0
1
2
1
0
0
0
0
0
0
0
0
0
1
2
1
0
1
1
0
0
4
0
0
0
0
0
1
1
2
2
1
0
0
0
1
1
1
0
0
2
0
1
0
0
1
1
0
1
0
0
0
2
2
0
0
1
2
0
0
1
0
1
2
1
0
0
1
0
0
0
0
0
2
1
0
2
0
0
0
2
2
0
2
2
1
1
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
1
3
0
0
0
0
1
1
1
0
2
0
0
0
0
2
0
1
0
0
0
3
0
0
0
1
0
0
1
1
2
1
0
0
1
0
1
0
0
0
0
0
0
0
2
4
0
1
2
2
2
1
0
2
0
2
0
0
0
0
0
1
1
1
0
1
0
2
0
0
0
1
2
2
0
1
0
0
3
1
0
0
0
0
0
0
0
1
0
2
1
1
2
0
0
1
2
3
0
0
0
0
3
2
2
0
0
1
1
1
0
2
0
0
2
1
2
1
1
0
0
0
0
0
0
2
0
1
0
0
3
0
0
0
0
1
1
2
1
2
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
2
1
1
1
0
1
1
0
2
1
0
0
0
0
1
0
0
0
0
0
3
1
0
1
0
0
1
0
0
1
0
1
0
1
0
2
1
0
1
0
2
1
2
2
0
0
2
1
2
2
0
0
2
0
2
1
0
1
1
1
1
0
2
0
1
2
1
1
0
2
1
0
0
3
1
2
0
0
1
1
1
2
0
0
4
0
1
2
0
0
1
0
0
0
1
2
0
0
2
0
0
2
0
1
0
0
0
0
0
1
2
0
0
1
0
1
1
0
0
1
2
2
1
1
2
2
1
2
1
1
1
0
0
1
0
2
1
2
1
0
1
1
0
0
2
0
2
0
1
0
0
1
0
0
1
1
2
0
2
0
1
0
0
0
2
1
0
2
1
0
1
0
0
0
0
0
0
2
1
0
2
0
2
1
1
2
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
1
3
1
0
0
1
0
0
0
0
1
0
3
2
2
1
0
1
0
2
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
1
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
1
1
2
2
0
0
1
0
0
0
1
1
1
1
0
1
0
0
0
1
0
0
0
2
0
2
0
2
2
1
0
0
0
2
0
0
0
0
1
0
0
2
0
1
1
1
2
0
0
2
0
2
0
0
2
0
0
0
0
2
0
0
2
1
2
0
0
0
2
1
0
0
0
2
1
2
0
1
0
1
0
0
1
0
0
1
1
1
2
2
0
0
1
0
0
1
2
1
1
1
0
0
1
0
0
0
0
2
0
1
0
0
0
0
2
1
1
0
0
0
2
0
2
2
0
0
0
1
0
0
0
0
3
0
0
0
0
1
1
0
2
2
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
2
1
2
1
1
2
1
1
1
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
4
1
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
1
1
4
0
0
0
0
2
1
1
0
0
0
1
0
0
1
0
0
1
0
1
2
0
2
0
0
0
2
0
1
1
0
2
1
0
0
2
3
0
0
0
0
2
0
0
2
0
1
0
1
0
2
0
0
0
0
1
1
2
0
1
0
0
1
2
0
1
0
4
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
3
1
0
0
0
0
0
1
0
2
1
1
1
0
0
0
1
2
2
0
0
1
0
0
0
0
0
1
1
0
3
2
0
2
1
1
2
0
0
2
0
2
1
2
0
0
1
0
2
0
0
1
0
1
0
2
2
0
1
1
1
0
1
2
2
1
0
1
2
0
0
1
1
2
2
1
2
1
1
2
0
2
1
4
1
0
0
0
0
0
0
2
0
0
0
1
1
0
1
2
0
0
2
1
1
1
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
1
0
0
1
1
2
0
0
1
2
1
1
0
0
2
0
0
0
1
2
0
2
0
0
1
1
0
1
2
2
0
1
0
1
1
1
0
1
0
0
2
1
2
2
1
0
0
0
1
0
1
4
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
2
0
1
0
0
0
2
2
1
0
1
2
1
0
2
1
1
0
2
0
2
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
1
1
1
0
0
0
1
0
2
2
2
0
0
0
1
0
0
0
2
0
3
0
0
0
2
2
0
1
2
0
2
1
0
1
0
1
1
2
0
1
0
0
0
1
0
0
0
2
0
1
2
1
0
2
2
1
3
2
0
0
1
0
1
0
1
0
0
0
0
1
0
0
1
2
0
1
1
2
2
2
0
0
0
1
1
0
1
1
0
0
0
0
0
0
2
0
2
1
0
0
1
0
0
1
2
2
0
1
1
2
0
0
0
0
0
0
0
1
2
1
0
0
0
1
0
1
0
2
1
0
2
2
1
0
2
0
1
1
0
0
0
2
0
2
0
0
0
0
0
0
0
1
1
0
0
2
2
1
0
0
2
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
2
0
3
2
0
0
0
0
1
2
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
1
1
0
2
0
1
3
1
1
0
0
0
1
1
2
0
0
0
0
0
2
1
0
0
1
1
2
0
0
1
0
1
1
0
1
0
1
0
4
0
0
0
1
0
2
1
1
0
0
3
2
0
0
0
0
1
0
0
1
0
0
0
0
1
0
2
2
0
1
0
2
1
0
0
0
1
2
2
3
1
1
1
1
1
0
0
1
1
0
2
1
0
0
1
0
2
1
0
1
1
0
1
2
0
1
0
1
0
0
1
0
0
0
0
0
2
2
2
1
1
2
2
0
1
0
2
0
0
3
0
1
3
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
1
0
0
1
1
0
2
0
0
2
1
0
1
0
2
2
1
0
2
2
1
0
0
1
1
1
3
0
0
2
0
1
2
1
0
0
1
0
0
2
1
1
1
1
0
0
1
2
1
0
0
1
0
0
0
1
2
0
0
0
0
0
2
2
0
0
0
0
2
2
0
0
0
0
1
2
0
1
2
0
0
1
0
1
0
1
0
1
0
1
0
0
0
0
2
2
0
1
0
1
4
0
1
1
1
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
1
0
2
1
0
0
0
1
1
0
1
2
0
0
0
2
0
3
2
0
2
2
2
1
0
1
2
0
0
0
2
0
0
1
1
0
0
0
2
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
3
1
0
2
0
1
0
0
2
0
1
0
0
0
2
0
0
0
1
0
0
1
2
1
0
0
1
1
2
2
0
0
1
0
2
1
0
2
0
1
0
1
0
0
2
0
2
0
0
1
1
1
0
0
1
0
2
2
1
1
0
1
1
1
0
1
2
2
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
2
1
2
2
2
1
1
1
1
2
0
0
0
0
0
0
0
0
2
0
1
4
0
0
0
2
2
1
2
0
0
0
3
2
0
0
0
2
1
1
0
0
0
2
0
0
0
0
2
1
0
0
0
2
0
2
1
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
1
1
1
1
1
1
0
0
2
1
1
0
0
0
0
0
0
2
1
0
0
2
0
0
2
0
0
0
0
0
1
0
1
0
2
1
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
1
1
0
2
1
0
1
0
0
1
0
1
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
1
0
0
1
0
0
2
1
0
0
0
2
1
0
1
3
0
0
1
1
1
1
0
3
0
0
0
0
1
0
2
0
1
1
1
2
0
0
0
2
0
0
0
0
1
1
2
0
0
0
0
0
0
1
0
1
0
2
2
0
1
0
0
0
2
2
0
1
2
1
0
0
2
0
2
0
0
0
0
0
2
0
2
0
6
1
2
0
0
1
0
1
0
0
0
0
1
0
1
0
1
1
1
1
1
1
1
0
1
1
1
2
0
1
1
0
0
0
2
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
2
1
2
2
2
0
0
2
0
0
0
0
2
0
0
2
0
0
1
3
0
0
2
1
0
0
0
2
0
0
1
0
1
0
0
0
0
2
0
0
2
0
0
0
1
1
2
0
2
1
0
0
0
0
1
1
1
0
1
0
0
0
0
2
0
0
2
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
1
0
1
2
0
2
0
0
1
0
1
1
0
0
2
4
1
1
0
0
1
0
0
1
0
0
0
1
0
0
1
1
0
2
0
2
0
0
0
0
0
1
0
1
0
0
2
2
0
0
2
0
2
0
0
2
0
0
0
1
3
0
0
0
0
0
1
1
1
0
0
1
0
2
0
0
0
0
0
2
0
0
3
0
0
2
0
2
1
1
1
0
1
2
2
1
1
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
1
1
1
0
0
1
1
0
2
1
2
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
2
1
2
0
0
0
0
2
0
0
0
0
0
1
1
1
0
2
2
0
0
1
0
0
1
1
1
0
0
0
0
0
2
0
1
0
0
0
2
2
2
0
2
3
1
0
0
0
0
0
0
0
2
2
2
1
0
2
0
1
0
2
0
2
0
0
0
2
0
0
1
1
0
0
0
1
0
0
0
0
2
0
0
2
0
0
2
1
0
1
2
0
2
0
0
1
0
2
2
1
0
2
1
2
1
2
0
0
2
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
1
0
1
1
0
0
2
2
0
1
0
0
1
1
0
0
0
0
0
1
1
0
0
0
3
2
1
0
0
0
2
2
2
0
1
0
2
0
3
0
2
0
0
0
0
1
1
0
2
0
0
0
0
0
0
3
0
0
0
2
1
0
4
1
0
0
0
1
0
2
0
0
0
0
2
1
0
2
2
1
2
1
1
1
1
2
1
1
1
0
2
0
0
1
0
2
1
0
1
0
1
1
0
2
0
0
0
2
2
0
0
0
6
0
1
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
1
1
0
1
1
0
2
0
1
0
1
2
2
1
2
2
0
0
0
0
2
1
2
0
0
2
0
0
0
1
1
0
0
0
0
1
0
2
0
0
1
1
1
1
0
1
2
3
0
0
1
1
2
1
2
0
2
1
1
0
1
2
1
0
0
2
0
0
0
0
1
0
2
1
1
2
2
0
1
1
2
0
2
1
2
0
3
0
0
0
0
1
0
1
4
1
0
1
0
0
1
2
2
0
1
0
1
1
0
1
1
0
1
0
0
2
0
1
1
2
0
1
1
2
0
0
1
1
0
1
2
2
0
3
1
1
2
2
0
1
0
1
1
0
1
1
1
0
2
1
1
2
0
0
0
1
0
0
0
0
0
0
0
3
0
0
1
2
0
1
2
2
0
0
1
2
0
0
2
0
0
0
0
2
0
2
0
1
1
0
2
2
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
3
1
0
0
0
0
0
0
0
0
2
2
0
0
0
2
3
0
0
1
2
0
0
0
0
0
2
0
0
1
0
1
0
0
2
1
1
0
0
1
2
2
1
0
0
2
0
2
0
2
1
0
1
1
0
0
0
1
1
0
0
1
1
0
0
0
1
0
0
0
2
1
3
3
0
1
0
0
1
1
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
1
1
0
1
0
2
0
0
2
2
0
0
1
0
0
2
1
2
0
0
0
2
0
0
0
2
0
0
1
0
2
0
1
2
0
0
1
0
0
2
0
0
0
2
0
0
2
3
0
0
0
1
1
2
0
0
0
1
0
2
1
2
1
0
1
0
1
1
0
2
0
0
0
1
2
0
0
0
1
1
1
2
0
0
0
1
1
0
0
0
0
0
3
0
0
1
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
1
0
0
1
2
0
2
2
0
0
0
1
0
0
0
1
0
0
0
2
2
1
2
2
1
0
0
1
2
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
2
1
0
1
0
0
1
0
0
2
0
2
0
2
2
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
1
0
1
1
0
0
2
2
0
0
2
0
1
0
0
2
0
2
2
2
0
0
2
0
1
1
0
2
0
0
0
0
2
0
0
2
2
1
1
0
1
0
0
0
0
0
2
0
0
2
2
2
1
0
0
0
1
0
0
1
0
1
0
0
2
1
0
0
1
2
0
2
2
0
0
0
0
0
0
2
0
0
1
0
1
1
1
0
0
1
0
2
1
2
0
1
0
2
0
0
0
1
0
0
1
2
1
0
0
0
2
2
1
0
0
2
0
4
0
2
0
3
2
0
2
0
0
0
1
1
0
0
0
0
0
1
0
1
1
3
0
2
2
0
0
1
1
1
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
2
0
0
3
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
1
1
0
1
1
0
0
3
0
0
0
0
0
0
0
1
0
0
2
1
0
1
0
0
2
2
0
0
0
2
1
0
0
0
0
2
0
0
1
1
0
1
1
0
0
0
1
0
0
2
3
1
1
0
1
1
0
2
1
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
2
2
1
1
1
2
0
3
1
0
1
1
1
0
1
0
0
2
2
0
1
2
2
1
1
1
0
2
0
1
0
0
0
0
1
1
2
0
2
0
2
0
1
0
0
1
1
0
0
3
1
1
2
2
0
3
0
0
1
0
1
1
0
0
1
0
0
1
0
1
1
0
1
0
0
2
0
0
1
2
0
0
0
2
1
0
1
1
2
2
0
0
1
1
0
1
3
1
1
0
0
0
1
0
2
1
2
1
3
2
0
0
0
1
1
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
2
0
1
0
1
2
0
1
2
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
2
0
0
1
0
2
0
1
1
2
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
2
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
1
1
1
0
0
0
0
0
0
2
1
0
1
2
0
0
0
0
0
0
0
0
0
1
1
0
1
1
1
0
0
0
1
0
2
0
2
2
0
1
0
0
3
0
0
0
0
0
2
0
2
2
2
2
2
1
3
1
0
0
1
0
0
4
0
0
0
0
2
0
0
0
0
0
1
2
0
0
1
2
1
1
0
1
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
2
2
0
0
1
0
1
1
0
1
1
1
0
2
2
0
1
0
2
0
0
2
0
0
1
0
1
2
1
1
0
1
2
2
0
2
0
0
0
1
1
0
0
1
1
0
1
0
0
0
1
0
2
0
2
0
0
1
0
0
1
2
0
1
1
1
1
0
2
1
0
0
2
0
0
2
0
0
2
1
1
1
0
0
1
2
0
0
0
2
4
1
0
1
0
0
1
0
1
0
0
0
0
0
2
0
1
2
0
1
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
3
0
0
1
1
2
0
1
0
2
0
2
0
4
2
0
1
0
2
0
0
2
0
1
0
0
1
0
1
0
1
0
0
0
1
1
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
1
2
1
0
1
0
2
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
3
1
2
3
0
1
1
0
0
1
0
0
0
0
0
1
0
2
0
0
1
1
2
4
0
1
6
1
1
0
0
0
0
1
1
0
0
0
2
0
0
0
2
0
1
0
2
1
2
0
0
1
0
0
1
0
2
1
0
1
0
4
0
0
1
0
0
1
1
1
1
0
1
0
0
1
2
2
2
1
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
2
0
1
0
0
2
1
2
2
0
0
0
0
0
1
1
0
0
2
2
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
2
0
1
0
2
1
0
0
2
2
0
0
1
1
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
2
0
2
2
0
2
0
1
2
1
0
5
1
2
2
0
2
0
2
2
0
0
2
1
0
1
2
0
1
2
0
1
0
0
2
1
0
0
2
0
1
0
0
2
0
1
0
1
0
5
1
0
0
1
0
1
0
1
2
1
2
0
2
0
0
0
0
0
0
1
0
2
0
1
0
2
1
1
1
2
0
1
0
2
0
2
2
3
0
1
0
1
2
0
1
0
0
0
0
1
2
0
0
0
2
0
1
0
0
1
1
0
1
1
0
0
0
1
0
0
0
3
1
1
0
0
0
2
0
1
0
0
2
0
0
0
6
1
2
0
0
2
1
2
0
1
2
1
2
1
1
0
0
2
0
0
2
0
0
0
0
0
2
1
1
1
1
2
0
2
0
1
1
0
0
2
0
2
0
0
2
1
0
1
1
1
0
2
0
0
0
0
1
1
0
1
0
1
0
1
2
2
2
2
2
0
0
0
0
0
0
1
2
2
0
1
0
1
2
1
1
1
3
0
2
2
0
2
0
0
0
0
0
1
2
0
0
2
2
0
1
0
0
1
1
1
0
2
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
1
2
0
0
1
0
1
0
0
1
1
1
0
0
0
2
0
0
0
2
1
1
2
0
0
0
0
2
1
0
1
1
0
2
0
1
1
1
0
0
0
0
0
0
1
0
1
2
1
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
1
2
0
2
2
0
0
1
1
2
0
0
1
0
2
2
0
0
0
0
0
0
1
0
4
0
1
0
0
0
2
0
2
0
1
1
0
2
0
2
0
1
0
0
1
1
1
0
0
0
0
1
0
1
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
3
2
1
2
1
2
2
0
1
1
1
0
0
0
0
2
0
0
0
1
2
2
0
1
0
0
2
0
0
0
0
1
0
2
0
0
1
0
1
1
0
1
0
1
1
2
1
0
1
2
2
2
1
0
0
1
0
1
1
1
0
0
1
0
2
0
0
1
0
8
0
0
0
2
1
0
0
0
0
0
1
0
1
1
0
1
2
1
0
0
3
0
0
0
0
0
1
0
2
1
0
0
2
1
2
0
1
2
2
0
0
1
0
1
1
0
1
2
0
2
2
0
0
0
0
1
1
1
0
0
0
0
0
1
0
1
2
1
1
2
0
1
0
0
1
0
2
0
1
1
0
1
0
1
1
1
0
0
0
1
1
0
0
0
0
0
2
2
0
2
1
0
0
1
0
0
1
2
0
0
0
2
0
0
1
2
0
2
0
0
0
0
2
0
0
1
0
0
2
0
0
2
0
1
1
1
0
2
1
2
0
0
0
0
0
0
2
0
1
0
1
0
2
2
1
2
2
1
0
3
0
0
1
0
1
1
2
0
1
1
0
0
0
3
2
1
1
1
0
1
1
2
0
3
0
0
1
1
1
0
1
0
1
2
0
0
0
2
1
0
0
0
0
0
0
0
2
1
0
2
2
0
1
0
2
1
1
0
0
0
1
0
0
0
1
2
3
0
2
1
2
1
2
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
1
0
1
0
0
1
0
0
0
2
1
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
2
3
0
1
1
2
1
0
1
0
1
0
0
0
2
1
1
0
0
1
0
0
1
0
1
0
0
2
1
1
0
0
1
1
1
0
2
0
2
1
3
1
0
0
0
0
1
1
0
1
2
0
1
2
1
1
1
1
2
0
0
2
0
0
1
2
1
0
0
0
1
0
0
1
0
0
1
2
0
2
2
0
0
1
1
0
0
1
2
2
0
0
2
0
0
2
2
1
1
0
1
0
2
1
1
2
2
1
0
0
1
1
0
1
0
0
2
1
2
2
1
2
0
1
0
0
0
0
1
1
0
0
0
2
0
0
1
0
2
0
0
2
0
1
2
1
0
2
2
1
0
0
0
0
2
0
1
2
0
0
0
0
1
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
2
0
1
0
0
1
1
2
1
2
1
1
0
0
0
0
0
1
2
2
0
1
0
1
0
2
2
0
0
0
1
0
0
0
1
2
0
0
0
1
0
1
0
0
0
1
1
0
0
9
1
3
1
0
1
0
1
0
1
2
0
0
0
1
2
2
1
1
1
2
2
1
0
0
2
2
0
0
0
0
2
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
2
4
0
0
2
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
2
2
1
0
0
0
1
0
1
2
2
0
0
1
2
0
0
2
2
0
1
3
0
2
0
2
1
1
1
0
1
0
1
2
0
1
2
0
0
0
2
0
1
0
0
1
2
1
0
2
0
0
0
0
0
0
2
0
1
1
0
0
0
2
1
0
0
0
1
1
2
1
0
0
2
0
0
2
0
0
0
2
0
2
2
1
2
0
2
0
0
0
0
2
2
1
2
0
1
1
2
1
0
1
0
0
0
1
1
1
0
1
1
2
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
1
1
0
2
2
1
0
2
2
0
2
1
0
1
0
2
1
1
0
0
0
1
2
1
0
0
0
2
3
0
0
2
1
0
2
1
0
0
0
2
2
0
1
1
1
0
1
1
0
0
2
1
0
0
3
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
1
2
2
1
1
0
0
2
1
2
0
0
1
0
1
0
1
2
3
0
0
1
0
0
0
2
0
2
0
2
2
2
0
1
2
0
1
0
1
0
1
2
1
0
0
1
1
0
1
0
0
2
0
0
1
0
0
0
1
2
0
0
0
4
0
1
0
0
0
0
1
0
2
2
2
1
2
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
1
1
3
0
0
0
1
0
1
0
0
0
1
1
0
2
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
2
1
0
2
0
0
1
2
1
0
2
2
1
0
0
0
0
2
0
1
0
1
0
2
1
0
2
0
0
0
0
0
1
3
0
2
0
0
2
1
0
2
1
1
2
0
0
0
0
1
3
0
1
0
1
0
0
0
1
1
2
0
2
0
1
0
1
2
2
0
0
1
0
1
1
0
1
1
2
2
1
2
1
1
2
0
0
0
0
0
0
0
1
0
2
0
1
2
0
4
0
2
0
0
0
0
0
2
0
3
0
0
0
0
0
1
2
3
0
0
0
1
0
0
0
0
1
0
1
2
2
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
1
1
0
1
1
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
1
1
2
0
0
0
2
1
0
0
0
0
2
2
0
0
1
1
2
1
0
0
0
2
1
0
0
2
1
1
0
0
2
2
0
0
3
0
1
0
1
0
0
2
0
0
0
2
1
0
0
2
0
0
1
0
2
0
0
1
1
0
2
0
0
2
2
1
0
2
1
2
0
3
0
1
0
0
2
2
0
0
1
1
2
0
1
1
0
2
1
2
2
0
0
1
2
0
1
0
2
0
2
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
2
1
0
1
0
0
1
1
0
0
3
1
0
0
0
1
1
0
0
0
2
1
0
0
0
1
1
1
1
0
1
2
0
2
0
1
0
0
0
2
0
0
0
0
1
1
1
0
0
0
1
1
0
1
2
0
1
3
0
2
0
0
0
0
0
0
0
1
1
1
0
2
0
0
1
0
1
0
1
0
1
1
0
0
0
0
2
4
2
1
0
2
0
0
0
0
0
4
1
0
0
0
1
2
1
2
2
0
2
0
0
2
1
2
0
2
0
1
0
1
0
4
0
0
1
1
0
0
2
0
0
0
2
0
0
1
1
2
0
2
1
0
2
2
0
1
1
0
2
0
1
1
0
1
1
0
2
2
1
1
0
0
2
1
2
1
0
0
0
0
0
0
0
1
0
0
2
0
1
1
2
1
1
1
0
0
1
0
2
2
2
1
1
2
0
4
0
0
0
4
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
3
0
2
0
0
0
1
0
0
0
0
1
2
3
0
0
2
1
2
0
0
0
2
2
0
0
2
1
1
2
1
0
0
0
3
1
1
0
2
3
1
0
1
0
0
2
0
2
0
0
2
2
1
0
1
0
2
0
0
2
1
2
1
4
0
0
1
0
1
2
1
0
1
1
3
0
0
0
1
0
0
0
1
1
2
1
1
1
0
2
5
1
0
0
2
1
1
0
0
2
0
0
0
0
2
0
2
0
0
0
1
1
0
1
0
0
0
0
0
0
2
1
1
9
1
0
1
0
1
0
0
0
0
0
1
2
1
2
0
0
0
1
0
2
1
0
3
1
2
2
0
1
0
0
0
2
2
0
2
0
2
0
1
1
1
2
0
2
0
0
2
0
1
2
2
1
0
0
0
0
0
0
1
0
0
0
1
0
1
1
1
0
2
2
0
0
0
0
2
0
0
0
2
1
1
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
2
0
0
0
1
2
0
0
2
0
1
1
0
0
0
0
0
2
0
0
1
1
2
0
0
0
0
1
1
2
1
0
1
0
0
0
0
2
0
2
0
1
0
1
1
1
0
1
2
2
0
1
1
0
1
2
3
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
2
0
1
0
1
0
0
0
0
1
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
1
2
0
2
0
0
1
2
2
0
1
2
1
1
0
2
2
0
1
1
1
0
0
0
0
1
1
0
1
0
2
0
0
0
0
1
2
0
0
2
2
0
1
2
3
2
0
0
1
2
2
0
0
0
0
0
0
2
1
2
2
1
1
0
1
0
0
0
0
2
2
2
0
1
2
1
0
1
1
1
0
0
1
0
0
2
0
0
0
1
1
0
1
1
2
0
0
1
0
0
0
0
1
2
2
0
2
1
0
0
2
0
0
0
2
2
0
2
1
2
0
0
0
2
1
2
2
0
0
0
0
0
0
1
1
0
0
1
0
3
1
1
0
0
0
1
2
2
2
2
0
2
1
1
1
1
0
1
2
0
1
0
0
2
2
0
0
2
0
0
1
0
0
1
0
0
0
1
1
1
3
1
2
1
0
0
1
0
2
1
2
2
2
0
0
1
3
0
1
1
0
2
0
0
0
6
2
0
0
0
2
1
2
2
0
2
2
0
1
2
0
0
1
0
0
0
0
0
1
2
2
0
3
0
1
0
0
0
2
0
2
1
0
0
2
1
2
0
3
0
1
0
1
0
0
0
1
0
1
1
1
0
0
1
1
0
2
0
0
0
1
2
0
0
1
0
0
2
2
2
2
0
1
0
2
1
0
0
1
0
1
0
0
0
1
2
0
0
2
2
1
1
1
3
0
0
0
1
0
3
0
2
0
2
2
1
2
0
0
1
0
0
0
2
0
1
0
1
1
0
0
2
0
0
2
0
0
0
1
0
0
1
2
2
0
0
2
0
0
1
1
0
2
0
2
0
0
0
2
2
2
0
4
2
0
2
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
1
0
0
1
0
1
0
0
0
1
2
1
0
0
0
0
0
1
3
0
0
0
0
0
0
1
3
1
0
0
0
0
0
2
0
2
0
0
1
0
0
2
2
1
0
2
0
0
2
0
1
0
1
0
0
2
0
0
1
0
2
0
1
2
0
0
0
0
2
0
0
0
2
1
2
1
1
2
2
0
0
0
2
2
0
1
2
0
2
0
0
0
0
2
3
1
0
1
1
0
3
0
0
0
0
1
0
1
1
3
0
1
2
0
0
1
0
0
1
0
1
5
0
0
1
1
2
0
1
1
0
2
2
0
3
1
1
1
2
0
1
1
0
1
2
1
0
1
1
2
0
0
2
0
2
0
1
1
1
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
1
2
1
1
0
1
0
0
2
0
2
0
2
0
0
0
0
2
4
2
0
0
0
1
0
2
0
1
0
0
2
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
1
2
0
2
1
2
0
0
2
0
1
0
0
0
2
0
2
0
2
0
0
0
0
0
0
2
2
0
2
0
0
0
1
0
0
0
2
1
1
2
0
2
3
1
0
0
2
1
2
1
0
1
0
0
0
0
0
0
1
0
0
2
1
1
0
1
2
1
2
2
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
1
1
0
0
2
0
0
0
0
1
2
0
3
1
0
0
1
0
0
1
0
0
0
0
0
2
2
0
0
1
0
0
2
0
2
0
0
1
2
2
1
0
0
2
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
2
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
2
2
1
0
1
0
3
0
2
2
2
2
1
1
2
1
0
1
0
2
0
1
0
0
0
1
1
0
0
1
2
0
0
0
1
0
2
0
1
2
0
0
2
0
0
2
0
0
1
0
0
0
2
0
0
1
2
0
0
1
0
0
1
0
2
1
1
2
0
1
0
0
1
1
0
1
1
0
0
0
1
0
2
2
0
2
1
0
0
0
0
0
1
0
0
0
0
2
0
2
2
2
0
0
1
0
1
1
0
1
0
0
1
0
1
0
2
0
0
1
0
3
0
0
1
1
0
1
0
0
0
2
0
0
0
2
0
0
2
0
1
0
0
0
0
1
1
1
2
0
2
0
0
0
3
0
2
0
0
2
1
2
0
0
2
2
1
0
0
0
1
0
2
2
0
0
2
0
2
2
0
2
3
0
0
2
1
1
0
1
0
0
1
1
0
0
2
0
2
0
0
2
3
0
0
0
0
1
0
0
0
2
0
0
1
1
0
2
0
1
1
0
2
1
2
0
0
0
2
1
0
0
1
1
0
0
1
1
0
2
1
0
0
2
2
0
0
1
2
1
3
0
0
2
0
0
0
2
0
0
0
0
1
2
1
0
0
1
0
0
2
0
0
0
0
0
0
0
1
1
0
4
0
0
0
0
1
1
0
2
0
0
2
2
2
1
0
0
0
1
0
0
0
1
0
0
0
0
2
1
1
0
0
1
0
1
0
0
0
0
2
0
2
0
2
0
0
1
1
2
2
2
0
1
1
2
2
0
0
1
0
1
3
2
0
2
0
1
0
2
0
0
1
1
0
0
0
2
1
2
0
1
0
2
1
0
0
1
1
0
0
1
0
0
1
1
1
0
0
2
0
1
1
0
1
0
0
1
7
2
0
2
0
0
0
1
0
0
0
2
1
1
1
1
0
2
2
0
3
1
1
2
0
1
2
2
0
0
2
2
1
2
0
0
0
0
1
1
2
2
0
0
0
0
0
2
0
2
0
1
0
0
2
0
0
0
1
0
2
1
0
0
0
2
1
0
0
0
0
0
0
1
2
0
0
2
0
3
1
0
3
0
2
1
1
0
0
1
5
0
0
2
1
0
0
0
2
1
0
0
1
1
0
2
1
1
2
3
2
1
0
0
0
1
1
0
0
0
0
1
0
2
2
0
1
0
2
2
0
0
1
0
0
0
0
2
2
0
1
0
3
0
0
0
1
2
2
0
0
0
0
0
2
0
0
2
1
0
0
0
3
0
0
1
1
0
2
1
0
3
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
2
0
0
1
1
1
2
1
0
0
2
0
1
2
0
0
0
0
0
1
2
2
1
0
0
2
2
0
1
0
2
0
2
3
0
0
0
0
2
2
2
1
1
0
1
2
1
2
0
0
2
0
2
1
2
0
0
0
0
0
0
0
0
2
6
0
0
1
0
0
0
0
1
2
1
0
0
1
2
0
1
0
0
2
0
1
1
0
1
0
0
0
0
2
0
2
1
0
0
2
0
0
1
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
1
0
0
0
2
0
1
0
2
1
0
3
2
0
2
1
0
2
0
2
0
0
0
0
1
0
2
0
0
0
3
0
2
0
0
2
0
0
0
0
2
1
1
0
1
0
1
1
0
0
0
1
1
0
0
0
0
2
2
1
0
1
2
1
2
0
0
0
0
0
0
0
1
1
0
0
1
0
0
2
0
1
1
1
0
1
0
1
1
0
0
1
0
8
0
0
0
0
0
0
2
0
0
1
1
1
2
2
0
2
0
1
0
0
1
0
0
2
1
2
1
0
1
2
2
0
2
0
1
0
0
0
0
0
0
1
0
0
1
0
1
2
0
0
1
0
2
1
0
0
0
1
1
2
0
0
1
0
2
0
2
2
0
0
0
2
2
1
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
2
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
1
1
0
2
0
2
0
0
1
1
0
2
1
2
1
0
0
2
0
1
0
1
0
1
0
1
0
1
1
1
0
1
0
3
0
0
0
0
0
1
1
0
0
1
0
0
2
0
2
1
0
0
2
0
0
0
1
2
2
0
0
2
2
0
0
1
0
1
1
2
3
1
0
0
1
1
1
1
0
0
2
0
1
3
1
1
0
2
1
0
2
2
0
0
1
0
0
2
0
0
3
0
1
0
2
0
1
1
2
0
2
2
1
3
1
2
2
1
0
0
1
0
2
1
0
0
0
2
5
0
0
0
2
0
0
1
1
1
1
0
3
1
2
0
2
0
1
0
0
0
1
0
0
1
0
0
2
1
0
0
1
1
1
0
0
0
0
0
0
2
0
0
0
1
0
2
2
0
1
1
0
0
0
0
1
2
2
0
1
1
0
2
0
2
0
0
0
0
0
2
1
0
0
2
1
0
1
2
0
0
1
1
0
1
0
1
0
1
0
2
0
0
0
2
1
0
0
0
2
2
1
0
0
2
0
2
0
0
2
1
0
0
1
1
2
0
0
1
0
1
0
2
0
0
2
2
1
1
0
0
0
0
1
0
2
0
1
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
1
1
1
0
0
2
2
2
1
1
1
1
0
0
2
1
1
0
0
2
2
2
1
0
0
0
1
0
0
1
0
0
1
0
1
0
1
1
0
0
2
0
2
2
2
0
2
1
0
0
1
0
2
0
1
3
0
0
0
1
0
0
0
2
0
2
0
2
0
1
2
0
0
1
3
1
0
0
0
2
0
1
1
1
0
0
1
0
2
2
2
0
2
2
0
0
1
0
3
0
0
1
0
1
1
0
0
3
0
0
2
0
2
0
1
1
0
0
2
0
0
1
0
0
2
1
2
0
0
0
0
1
0
0
0
0
0
1
1
2
0
0
1
0
0
0
1
2
2
1
0
0
0
1
2
1
2
0
0
1
0
0
2
0
2
0
0
0
2
2
2
1
0
0
0
1
0
2
2
0
1
1
0
1
0
2
0
0
1
0
1
0
0
0
2
0
1
0
1
0
0
2
0
0
0
0
2
0
2
1
2
3
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
2
0
0
0
2
0
2
0
1
0
1
2
0
0
1
1
1
0
0
0
2
0
0
0
1
0
0
1
1
0
2
0
0
0
2
0
2
0
0
3
0
1
0
0
0
0
4
0
0
1
3
1
1
8
1
0
1
0
2
2
1
2
0
1
1
0
1
1
0
2
0
0
0
2
1
0
0
2
0
2
0
1
1
1
2
1
1
2
0
0
0
0
0
0
0
0
0
2
1
1
2
1
0
2
0
1
2
0
2
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
2
4
2
1
0
0
0
0
0
2
0
0
0
2
0
1
0
2
0
0
0
1
1
0
2
2
1
0
0
1
0
2
1
0
0
2
1
4
1
0
1
1
2
0
0
0
0
1
0
0
0
1
0
2
1
0
1
0
0
0
0
0
1
0
0
1
0
1
0
1
1
0
1
0
1
2
0
0
1
0
0
0
1
1
2
0
1
0
1
2
1
0
4
2
0
0
3
1
1
0
0
1
0
0
0
0
1
2
0
0
0
0
0
1
0
1
0
0
2
1
0
0
0
2
0
1
0
0
3
1
0
0
1
1
2
0
0
0
0
0
0
0
0
2
1
2
2
1
0
0
0
0
1
2
0
0
2
1
1
0
0
1
0
0
1
3
2
1
0
2
0
0
1
0
0
2
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
2
2
1
0
2
2
0
0
1
2
1
0
0
0
2
0
1
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
1
2
0
0
0
2
2
2
0
1
1
0
0
1
2
2
0
1
1
0
2
0
2
1
2
2
2
2
2
2
2
0
0
1
4
1
0
0
0
0
0
2
1
0
2
0
0
0
1
2
0
2
0
0
0
0
2
0
0
1
3
0
0
0
1
2
0
2
2
2
1
0
1
0
0
0
0
0
2
0
1
0
2
0
2
2
1
1
1
0
2
1
0
2
0
0
2
2
2
2
1
2
0
1
0
0
2
0
1
0
0
0
0
2
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
1
0
0
2
3
2
0
0
0
1
1
0
2
1
0
1
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
2
2
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
1
0
0
2
1
2
1
1
1
0
0
1
2
1
2
2
0
1
1
0
0
0
1
0
1
0
2
0
0
2
0
0
1
1
3
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
3
2
0
0
0
1
1
0
0
0
1
0
2
0
0
0
1
0
1
0
0
0
2
2
0
0
4
2
0
1
0
1
1
1
1
0
0
1
0
0
0
0
1
2
1
0
0
0
0
1
1
0
2
1
2
0
0
0
2
0
0
2
2
0
0
3
4
1
0
2
0
2
1
2
0
2
1
0
0
1
1
2
0
1
2
1
0
0
1
2
0
1
0
3
0
2
0
0
2
2
2
0
0
0
3
2
1
0
1
2
1
1
0
0
0
0
0
0
0
0
1
1
2
1
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
1
1
0
2
0
0
2
0
2
1
0
0
0
0
0
1
2
0
0
1
0
1
1
1
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
1
2
1
0
0
0
1
0
0
0
1
2
0
2
2
2
2
0
1
0
2
0
0
2
0
1
0
0
0
2
1
0
1
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
1
0
1
0
2
3
1
0
0
0
1
1
1
2
1
0
0
0
1
1
0
1
1
4
0
2
0
2
0
1
1
0
0
0
3
0
2
0
1
2
2
2
0
2
1
1
1
1
0
0
1
0
2
0
0
0
1
0
2
0
2
0
0
2
1
0
1
2
1
2
0
0
2
0
1
0
1
0
0
1
0
0
2
0
1
0
2
1
0
1
0
0
0
1
1
1
2
0
0
1
1
1
2
1
2
1
1
2
1
0
2
0
2
0
0
1
1
2
0
1
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
1
2
2
1
3
0
1
0
0
1
2
0
0
0
0
2
0
1
0
0
0
2
2
0
0
1
0
2
0
0
4
0
1
0
0
0
0
2
1
0
0
2
0
0
1
3
0
0
0
1
0
0
1
0
1
1
2
0
0
3
2
1
0
0
0
1
0
0
0
2
1
2
0
1
2
4
0
1
0
0
0
3
1
1
1
0
0
0
1
2
0
1
2
1
1
0
1
0
0
0
1
0
0
0
2
2
0
0
1
0
1
0
0
0
0
1
2
2
0
0
1
0
2
0
2
1
0
1
2
3
0
1
0
0
2
1
2
2
0
2
1
2
0
0
0
2
1
1
2
2
1
1
0
0
0
1
1
0
1
2
1
1
0
2
1
0
2
0
2
1
0
0
0
2
0
0
2
2
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
2
0
0
1
1
0
2
0
2
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
1
2
0
1
0
2
0
0
4
2
1
2
1
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
1
0
2
0
0
0
0
2
1
4
0
2
0
0
0
0
1
0
0
1
1
1
0
0
2
0
2
0
2
0
1
1
1
1
0
1
0
0
0
1
2
0
1
1
0
0
1
1
1
1
0
1
0
1
0
0
2
0
0
0
1
0
0
1
4
0
2
1
2
1
1
2
0
1
2
0
1
0
1
0
1
2
1
1
0
2
0
0
2
0
2
0
1
0
4
1
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
4
1
0
2
0
0
0
0
1
0
1
1
0
0
0
0
2
0
2
0
0
1
1
1
1
2
1
0
0
1
0
0
1
0
0
1
2
1
0
0
1
0
1
0
1
1
0
1
0
0
0
0
0
1
0
2
0
1
0
0
0
1
0
0
2
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
1
0
2
3
0
1
0
2
0
0
2
0
0
0
0
1
0
2
0
1
1
1
0
3
0
0
0
0
1
1
0
1
1
1
0
0
2
1
0
3
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
2
0
1
0
0
1
0
2
0
0
0
1
1
0
0
2
2
1
0
2
0
0
2
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
1
1
0
0
0
0
2
1
0
0
1
0
1
0
0
1
0
0
1
0
0
1
1
0
0
0
0
1
0
0
2
2
0
0
0
0
0
1
0
2
0
3
1
2
2
1
1
0
2
1
2
0
0
1
1
0
0
0
0
1
0
0
0
1
1
0
0
1
0
1
3
1
1
0
0
0
0
2
0
0
2
1
1
0
0
0
2
1
0
0
1
2
1
0
2
1
0
2
1
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
1
1
1
0
2
0
0
1
1
0
1
0
1
1
0
0
0
1
2
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
4
2
1
1
1
0
0
3
2
0
0
2
0
1
0
0
0
2
2
1
0
1
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
2
1
1
0
0
0
0
0
2
1
1
0
0
2
0
1
2
0
2
1
2
0
0
1
1
0
0
0
2
0
0
0
0
2
1
1
2
0
2
1
1
1
0
0
1
1
2
0
0
2
3
0
0
0
2
1
0
0
0
1
1
1
0
0
0
2
0
0
1
0
0
1
0
1
0
2
1
0
0
0
0
1
0
1
0
0
1
2
0
2
0
0
2
0
0
0
1
1
0
1
1
0
0
0
0
0
2
2
1
1
0
0
1
1
1
2
0
0
0
1
2
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
2
1
0
1
2
1
0
2
1
2
1
0
0
2
2
1
1
0
2
0
2
0
0
0
0
1
1
0
1
0
0
0
0
3
0
0
0
1
2
0
2
0
0
0
0
1
0
0
1
0
0
0
2
0
1
0
0
2
0
0
0
0
0
2
0
2
0
1
0
2
1
1
2
2
1
0
2
0
2
0
0
2
2
4
0
0
0
2
0
0
1
0
0
0
0
1
1
0
1
1
0
0
0
0
1
0
0
3
1
0
0
2
1
1
2
0
2
0
0
0
2
0
0
0
2
0
0
0
1
1
0
0
0
0
2
2
0
2
0
0
0
0
0
1
2
2
0
1
0
0
0
0
0
1
1
1
0
1
0
0
0
1
1
0
1
0
0
0
2
0
1
0
0
2
2
2
0
0
0
1
1
0
0
0
0
1
0
2
0
0
1
2
1
2
1
1
0
1
1
0
1
1
1
0
0
2
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
2
0
1
1
1
0
1
0
0
0
2
0
0
1
0
0
0
0
2
0
0
2
0
0
4
0
2
0
1
0
0
1
0
0
1
1
0
2
1
0
3
1
0
0
0
2
1
2
0
0
0
2
0
0
1
0
1
2
0
0
1
0
1
1
0
1
1
0
0
0
0
0
0
1
1
1
0
1
0
1
0
0
1
2
2
0
1
0
0
0
0
0
0
2
1
2
1
2
1
2
1
0
0
2
2
2
3
2
2
1
1
0
2
2
0
0
2
1
1
0
0
0
2
1
2
1
0
0
3
0
0
1
2
0
0
0
2
1
3
0
0
1
0
0
0
0
0
0
1
2
0
2
0
1
0
0
0
0
0
1
0
0
1
0
0
0
2
1
2
0
0
0
0
0
2
1
0
2
0
0
1
0
0
0
1
1
1
0
0
1
0
1
1
2
1
0
1
1
0
1
0
1
0
0
0
2
2
0
0
0
1
0
0
0
2
0
1
2
0
4
0
1
1
0
0
0
0
0
2
1
0
1
2
1
1
0
1
2
2
1
1
4
0
0
0
0
2
0
0
0
0
1
0
1
0
1
0
2
2
0
0
1
0
2
2
0
0
0
0
0
2
0
0
0
0
1
2
1
0
0
1
0
1
0
6
8
0
0
0
2
1
2
2
0
1
0
1
0
1
0
0
2
0
2
0
0
0
0
1
0
2
0
0
0
0
2
0
2
1
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
1
2
0
0
1
0
1
1
2
0
0
0
1
0
1
0
0
0
0
2
0
0
0
1
0
1
2
0
1
0
0
0
1
0
0
2
0
2
1
0
2
1
0
2
3
1
2
4
1
0
0
0
0
0
0
0
1
0
0
2
2
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
1
0
2
2
1
0
0
0
0
0
1
0
1
0
0
2
0
2
2
0
1
1
0
1
0
1
2
0
1
0
0
1
2
1
1
0
0
0
1
0
0
1
3
1
1
0
0
0
3
0
0
0
0
0
1
0
0
0
2
1
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
2
0
1
2
0
0
2
0
1
0
0
2
1
1
2
0
0
1
1
2
0
1
0
0
0
1
0
1
2
0
1
0
2
2
1
0
1
0
2
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
1
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
2
0
2
1
0
0
2
0
1
0
0
0
2
0
0
0
2
0
1
1
1
2
0
0
0
1
0
1
0
1
0
2
0
2
2
0
1
0
0
1
1
1
0
0
0
0
0
0
0
2
2
2
0
0
1
0
2
1
0
0
2
2
1
0
0
0
1
0
0
1
0
1
0
1
1
2
2
0
1
1
2
2
1
0
0
1
0
2
0
2
1
1
0
0
1
0
0
1
0
0
0
2
1
0
0
0
0
1
2
3
1
1
1
0
0
1
0
2
1
0
0
0
1
0
0
2
1
0
2
2
1
0
0
0
0
1
1
1
2
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
2
1
1
0
1
2
0
0
1
0
1
0
0
0
2
1
0
2
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
2
2
1
1
0
2
0
0
0
1
0
0
1
0
2
0
0
1
2
0
1
0
2
0
0
1
0
2
1
1
1
0
1
2
0
0
0
2
0
1
4
1
0
2
1
0
0
0
0
0
0
0
2
0
2
1
0
0
2
2
0
2
0
0
0
1
1
0
2
3
0
1
0
1
0
0
0
0
1
4
0
0
0
1
2
0
0
2
2
1
2
0
2
1
0
0
1
1
2
0
3
2
0
0
0
2
0
0
0
1
0
0
1
0
0
4
0
0
2
0
1
2
1
1
3
0
0
1
0
0
1
1
0
1
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
3
0
0
1
0
0
2
0
2
1
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
1
0
1
1
0
0
0
2
0
0
0
2
0
0
2
0
0
1
0
0
2
0
1
0
0
2
2
0
1
0
0
2
0
1
1
0
2
1
0
0
0
0
1
0
1
0
0
1
0
0
2
2
1
1
0
1
1
1
0
0
0
0
2
2
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
2
2
2
0
1
0
0
0
0
1
2
0
2
0
1
0
0
0
2
0
3
0
0
0
0
0
1
2
0
5
0
0
1
2
0
1
0
0
0
0
1
2
1
1
0
0
0
0
0
0
3
0
0
1
0
0
0
0
2
0
0
2
1
2
0
1
0
0
0
1
0
1
1
0
2
3
0
0
0
0
0
0
1
1
1
0
2
1
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
1
1
0
4
0
0
0
0
0
1
0
0
0
0
2
2
0
2
0
0
0
1
0
1
0
0
0
2
2
0
0
1
1
0
1
0
0
3
3
1
0
0
1
0
0
0
1
0
0
1
0
1
2
0
0
2
1
0
0
0
0
0
1
1
0
2
0
1
1
0
2
2
0
0
0
1
0
1
2
0
1
2
0
0
0
1
2
0
1
1
1
0
2
0
0
0
0
0
1
0
0
0
0
2
1
2
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
1
1
2
1
0
2
1
0
1
0
0
0
3
0
1
2
0
2
2
0
0
2
0
0
2
0
0
2
0
1
0
0
2
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
1
1
1
1
0
2
0
1
1
0
0
1
1
1
0
1
1
0
2
0
0
0
0
2
0
0
1
2
0
0
1
0
0
0
1
0
1
1
0
0
0
2
2
0
2
0
0
0
3
0
1
2
0
1
2
0
2
0
0
0
0
0
0
2
3
0
2
0
0
0
0
0
1
2
0
0
0
2
0
1
0
0
0
0
1
1
0
0
0
2
2
0
0
4
0
1
1
0
2
0
1
0
0
1
0
1
0
0
2
0
0
0
2
2
0
0
2
0
0
0
2
0
0
2
1
0
0
2
0
0
2
0
0
0
0
0
0
1
0
6
0
2
3
0
1
2
2
0
3
0
3
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
2
5
1
1
2
0
0
0
2
0
1
1
0
2
2
2
0
1
0
0
2
2
0
0
2
0
0
0
0
0
0
1
0
0
1
0
2
0
2
0
1
3
0
2
0
0
0
0
0
0
2
1
2
1
0
2
1
1
0
2
2
0
2
1
1
0
0
2
2
1
0
1
0
0
1
0
1
2
0
0
1
1
1
2
0
1
1
0
1
2
0
0
0
0
2
0
0
1
1
0
1
1
2
0
0
0
0
2
1
1
1
0
0
1
0
1
1
1
8
1
1
0
1
0
0
0
5
0
1
0
1
0
0
0
2
0
0
1
0
4
0
2
0
0
2
2
0
1
0
2
2
1
0
2
2
1
0
0
2
0
0
1
1
2
1
2
1
1
2
2
0
0
0
1
0
2
2
1
0
0
0
0
0
0
0
0
1
0
1
1
1
2
1
0
1
0
0
0
0
1
0
2
1
0
2
0
5
6
2
1
0
1
0
0
0
0
0
1
2
0
0
1
1
0
0
1
1
0
2
1
0
0
0
2
1
2
1
0
2
0
2
1
1
1
0
1
0
0
0
0
2
1
2
0
2
1
1
1
1
0
1
0
0
1
0
1
2
0
0
0
1
2
0
0
0
1
0
0
1
2
3
0
1
1
0
2
1
1
0
0
2
2
1
0
1
0
0
1
0
0
0
0
0
1
0
2
0
0
0
1
1
0
2
1
1
2
0
0
1
2
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
1
1
1
1
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
1
2
0
2
0
1
2
0
0
2
0
0
1
0
0
2
4
0
0
2
0
1
0
3
2
0
1
0
0
3
0
1
3
0
2
0
0
3
0
0
0
0
1
0
2
0
1
1
0
1
0
0
1
0
1
0
2
0
2
1
0
0
0
1
0
0
0
0
0
0
2
0
2
1
0
0
0
3
2
2
0
2
0
1
2
1
1
2
0
0
2
2
2
0
2
1
0
0
0
2
1
0
1
0
0
0
1
1
2
1
0
0
0
0
0
2
2
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
2
2
1
1
0
0
0
0
0
0
0
0
1
0
0
1
2
0
1
0
0
1
1
1
0
2
2
0
0
1
0
1
0
0
1
2
0
0
0
0
0
3
1
0
2
0
0
0
0
1
1
1
1
2
0
1
0
0
1
0
0
0
2
0
1
0
0
0
3
1
0
0
0
0
0
0
0
0
2
0
0
2
3
1
0
0
0
0
0
2
0
0
0
0
1
2
1
2
2
0
1
1
2
2
0
0
0
0
0
2
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
1
2
1
0
0
0
1
0
0
0
1
1
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
1
2
0
0
2
1
1
1
0
1
0
0
0
0
1
2
2
0
0
2
2
0
1
0
0
1
0
0
0
1
3
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
2
0
0
1
1
2
1
2
2
0
0
0
1
2
0
0
0
1
1
1
0
0
0
0
0
1
0
2
1
0
0
2
1
1
1
0
2
0
1
0
2
1
0
0
0
2
0
0
1
0
1
0
1
0
2
0
0
0
1
0
1
1
0
0
0
1
0
2
0
0
1
0
1
1
0
1
0
0
1
1
0
0
1
0
1
0
0
1
1
2
0
0
0
1
0
0
0
2
1
2
1
2
0
0
0
2
0
1
0
1
1
1
0
2
3
0
0
0
0
1
0
2
1
0
0
0
1
2
1
0
0
0
2
0
0
1
0
0
1
1
0
0
0
0
2
0
0
2
1
1
0
1
0
0
0
1
1
2
1
1
1
0
2
0
0
0
0
2
0
1
2
0
1
0
1
0
1
2
0
0
0
1
0
0
0
1
1
0
0
0
0
1
1
0
1
2
1
0
0
0
0
1
0
0
0
1
0
0
1
1
2
0
2
0
3
0
1
0
3
2
0
1
2
0
1
0
2
1
0
1
2
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
1
0
0
1
1
1
0
0
0
1
0
0
1
1
0
0
1
0
0
0
1
0
0
2
1
0
0
2
2
0
1
1
2
2
1
2
0
0
2
0
2
1
0
2
0
2
0
1
1
0
2
0
1
0
0
0
0
1
0
1
0
1
1
0
0
0
0
1
3
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
1
1
2
0
0
1
0
2
0
0
1
0
1
0
0
1
0
0
0
0
1
0
1
4
0
1
0
0
0
3
0
0
0
0
1
1
0
0
1
2
0
1
0
1
1
0
2
0
0
0
0
0
0
1
2
1
3
1
1
0
0
1
0
0
0
2
0
1
0
0
2
0
0
0
1
1
0
0
0
0
0
2
1
0
0
0
2
0
2
1
1
1
1
1
0
0
1
3
2
0
0
0
0
1
1
0
2
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
3
0
0
2
0
0
2
2
1
1
0
1
1
0
0
0
2
0
2
2
0
0
0
2
0
1
2
0
0
0
0
1
2
2
1
2
2
1
0
0
0
1
2
1
0
2
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
1
2
0
0
0
1
0
2
0
0
0
1
2
2
1
1
1
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
1
4
0
1
0
0
0
0
0
0
2
2
1
0
2
1
1
1
2
2
0
0
1
0
1
0
0
1
0
0
1
1
1
0
0
3
1
2
0
0
1
0
0
1
1
0
2
3
2
1
2
0
0
0
0
0
2
0
1
0
1
0
0
0
2
0
2
0
0
1
1
0
1
0
2
1
2
0
1
0
1
2
1
0
2
2
1
1
1
0
2
0
3
0
1
0
0
2
0
2
1
0
0
0
0
2
2
0
2
2
1
1
1
1
0
0
1
1
0
0
0
0
0
2
0
1
2
2
1
0
1
0
1
2
0
1
1
0
0
2
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
4
0
2
1
2
0
0
1
0
0
1
1
1
1
5
0
1
0
0
0
0
0
1
0
2
2
0
0
1
1
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
1
0
0
1
1
1
1
0
1
0
0
0
0
1
2
2
2
2
1
0
2
1
0
2
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
3
0
0
0
0
0
2
1
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
2
0
0
0
1
0
4
1
1
2
0
0
2
2
0
0
0
2
0
1
1
1
0
0
0
2
0
0
1
1
1
0
2
0
0
1
1
0
1
0
3
0
0
0
1
0
1
1
0
2
0
1
0
1
0
1
0
0
2
0
2
0
2
1
0
4
1
2
0
0
0
2
0
1
0
0
1
2
0
1
1
1
2
2
0
1
2
0
0
0
1
0
0
0
0
0
0
0
2
2
1
1
0
2
0
0
0
1
2
0
0
0
1
1
1
1
0
0
0
1
0
0
1
1
1
1
0
0
2
0
0
0
1
0
2
0
2
0
1
0
0
0
2
0
0
0
1
0
0
1
0
0
1
1
2
1
0
0
0
1
1
2
0
0
1
0
0
0
0
2
0
1
0
0
0
4
0
2
1
1
0
0
1
0
0
0
0
0
1
1
2
0
0
1
1
2
0
0
1
1
0
0
0
0
0
1
3
1
1
0
1
0
0
0
0
2
0
2
1
0
0
0
2
2
1
0
0
2
0
2
0
1
0
2
0
3
0
2
1
0
1
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
1
1
0
0
2
0
0
1
1
0
2
1
0
0
0
1
0
2
1
2
1
0
0
1
1
2
0
0
0
2
1
0
0
0
1
2
1
1
1
0
0
0
1
0
2
0
1
0
0
1
2
0
1
1
1
1
1
0
0
0
0
0
0
2
2
2
0
2
0
2
1
0
2
0
0
0
1
0
1
2
0
0
0
0
0
1
2
2
2
1
0
1
0
2
0
1
0
0
0
0
0
0
1
0
1
3
0
1
0
1
4
0
1
1
4
2
1
2
1
1
0
0
2
0
1
3
1
0
1
0
1
2
2
1
0
1
1
1
0
0
0
2
0
1
0
0
0
0
0
2
0
2
0
3
0
0
0
1
2
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
1
0
1
1
1
2
1
0
0
0
0
1
1
1
0
1
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
6
0
0
0
0
0
2
0
0
0
2
2
1
1
0
0
0
1
1
1
1
0
0
2
0
0
2
3
0
0
2
0
1
1
0
2
2
0
0
0
2
0
0
0
0
2
0
1
0
1
1
0
2
1
0
0
0
0
0
0
0
1
0
2
2
0
0
2
0
1
0
1
1
2
2
0
2
0
3
0
1
1
0
3
1
0
2
2
0
0
0
0
2
2
1
2
1
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
2
0
1
0
2
0
2
2
1
1
0
0
1
2
1
2
2
0
1
1
0
0
0
0
1
0
1
0
0
1
0
0
4
0
1
1
2
0
0
0
0
0
1
0
2
1
0
1
1
0
0
4
0
2
0
1
1
0
0
1
0
1
0
2
0
0
0
0
0
0
1
1
1
2
1
0
2
2
1
1
1
2
1
2
1
1
2
0
0
0
0
1
0
0
0
1
0
1
0
1
1
0
0
0
2
0
1
0
0
3
2
2
0
0
0
2
3
1
0
2
0
0
2
2
3
0
1
0
1
0
2
0
0
0
0
1
2
0
0
1
0
1
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
2
0
0
1
1
0
1
0
0
1
3
1
2
0
2
0
2
2
0
0
1
1
2
0
0
0
1
0
2
2
1
0
0
2
0
1
0
0
1
0
0
2
1
0
0
0
0
1
2
1
2
0
1
0
0
1
1
0
1
0
0
1
0
1
2
0
1
0
2
2
1
1
0
0
1
1
1
1
3
2
0
0
1
0
0
1
0
1
2
0
1
1
1
0
0
0
2
0
2
0
2
0
2
1
0
1
1
0
0
0
0
0
0
2
2
0
1
2
0
1
0
0
0
0
0
0
2
1
0
1
0
0
6
1
0
0
1
0
0
1
1
0
0
1
1
2
2
1
2
2
1
0
0
0
0
1
0
0
0
1
0
0
0
0
3
0
2
0
1
0
2
0
0
2
0
1
2
2
2
0
3
1
0
0
2
0
0
0
2
0
0
0
2
2
0
1
0
1
1
1
0
2
1
0
2
2
1
1
2
0
5
0
0
0
0
1
0
2
3
0
0
1
0
0
0
0
0
1
1
0
2
0
1
0
2
0
0
0
2
0
0
0
0
0
1
2
0
1
0
0
0
1
0
0
2
2
2
0
0
6
0
2
0
0
0
0
0
1
0
2
0
1
1
1
3
1
2
1
0
0
0
0
2
0
0
0
0
0
0
1
1
2
0
2
0
0
1
1
0
1
0
0
1
2
2
0
0
0
0
0
1
0
0
2
1
0
0
1
0
0
0
1
0
0
0
1
1
1
0
1
2
1
0
2
1
0
2
1
2
0
2
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
2
1
0
1
1
1
0
0
0
3
2
0
1
0
0
2
0
0
0
0
0
0
0
2
2
0
3
0
2
2
0
0
2
0
0
0
0
1
1
0
0
0
1
0
2
2
1
0
2
0
0
0
0
0
1
0
2
1
0
1
0
0
0
0
0
0
1
2
0
0
2
1
0
1
0
2
0
0
0
0
0
0
0
2
2
0
1
1
0
2
1
2
0
1
3
3
2
0
1
0
1
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
5
2
0
2
1
1
0
2
2
0
0
1
0
1
1
0
0
1
0
2
2
2
0
2
1
0
0
1
0
0
0
0
0
0
1
0
1
0
3
2
0
0
1
0
0
1
1
0
2
1
0
2
2
0
0
2
2
0
0
1
0
0
2
0
0
0
1
0
0
2
0
1
1
0
0
0
0
0
2
4
2
2
0
0
0
1
0
0
2
0
0
2
0
0
0
1
0
0
2
0
1
1
1
2
0
0
0
1
0
0
0
2
1
0
0
0
2
0
1
0
2
1
1
2
0
2
1
0
1
4
1
1
2
2
0
0
2
2
0
1
1
1
2
1
0
0
2
0
1
0
2
0
0
0
0
0
0
2
0
1
2
2
0
0
2
0
1
2
0
1
2
0
1
1
0
1
0
0
0
2
0
0
2
2
1
0
0
2
0
0
0
2
1
2
2
0
1
0
0
0
0
0
2
0
1
0
0
2
2
3
2
1
0
0
1
0
0
1
1
2
0
0
1
0
2
0
0
0
1
0
2
0
0
0
1
2
1
0
1
0
1
1
2
1
0
0
2
2
1
0
1
1
0
2
2
0
2
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
2
0
0
2
2
1
1
0
2
1
0
1
2
0
3
2
0
0
0
2
0
0
0
1
2
2
0
1
0
0
1
1
0
0
2
2
2
2
0
1
1
0
0
3
0
0
1
5
0
0
0
0
1
0
0
0
1
2
2
1
2
2
0
0
0
2
2
2
0
0
2
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
1
0
1
2
1
2
0
0
0
1
1
0
2
0
2
2
0
1
2
1
0
0
0
0
0
0
0
0
0
2
0
2
2
1
0
0
0
2
1
0
0
1
1
0
2
2
0
0
2
2
1
0
0
1
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
1
0
0
2
1
0
0
0
1
0
0
2
0
0
0
1
1
2
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
1
0
0
2
0
0
1
6
0
1
1
2
2
2
3
2
2
0
0
1
3
0
0
1
0
1
1
0
1
2
0
1
1
0
0
0
0
0
2
0
0
1
1
1
0
0
0
2
2
0
0
0
1
1
0
0
1
0
2
0
0
0
0
2
0
1
2
0
2
0
1
0
0
2
0
2
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
1
0
0
2
0
0
2
0
0
0
0
2
4
2
2
0
0
0
1
0
0
1
2
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
2
1
0
0
0
0
1
0
0
0
1
2
3
0
1
2
2
1
0
2
2
1
0
0
1
0
0
0
2
2
0
2
1
1
0
0
0
1
1
0
3
0
9
1
1
0
0
1
1
0
0
0
2
1
0
0
0
1
0
0
0
0
0
1
1
0
0
2
0
1
0
1
0
0
1
0
1
0
0
1
0
2
0
1
0
0
0
0
0
1
1
0
1
1
0
0
0
0
2
0
0
0
0
1
1
0
0
1
0
0
2
2
2
1
0
1
1
0
1
2
0
2
2
0
1
0
2
0
0
0
2
2
2
2
0
0
0
0
2
0
0
2
0
0
0
0
2
2
0
2
2
0
1
0
0
1
0
1
1
2
1
0
0
0
0
0
2
0
1
0
0
0
0
2
1
3
0
1
0
2
0
0
0
1
2
1
0
1
0
0
0
0
0
1
1
0
0
2
0
0
0
1
2
3
0
0
1
2
2
2
2
0
0
2
0
0
1
1
2
3
1
1
1
1
2
0
0
2
1
0
1
3
2
0
2
1
2
0
0
1
0
0
0
2
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
1
2
2
1
1
2
1
0
0
2
1
0
1
0
0
1
2
0
0
0
0
1
1
0
0
0
0
3
1
0
0
0
0
2
2
1
1
0
0
0
0
0
0
0
0
2
1
1
1
2
1
2
0
2
0
0
0
0
5
2
0
0
0
1
0
2
1
2
0
0
0
0
1
0
1
2
2
0
0
0
2
1
0
1
0
0
0
2
1
0
0
0
0
0
1
0
2
2
0
0
0
0
0
1
0
2
1
2
0
0
0
0
0
2
0
0
0
0
0
0
1
1
1
0
0
0
0
4
0
1
1
1
2
0
0
1
0
1
0
1
2
0
1
2
0
0
0
0
1
0
2
0
2
0
2
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
1
0
0
1
2
1
0
1
0
2
1
0
0
0
0
1
0
0
0
0
1
3
0
0
0
0
1
0
2
1
0
0
1
0
1
1
2
0
1
0
1
0
1
0
0
0
0
5
1
2
0
1
2
0
0
1
0
2
1
1
0
0
2
0
0
2
1
0
1
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
1
0
0
0
1
1
0
1
1
0
2
2
1
0
1
2
1
0
0
0
1
0
2
0
2
1
1
2
0
2
0
0
1
2
0
3
0
0
0
0
0
0
0
0
1
2
2
0
1
0
0
0
0
0
2
1
0
2
1
0
1
1
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
2
0
1
2
1
2
2
2
0
0
0
0
2
0
0
0
0
0
1
1
0
2
1
0
0
0
0
1
1
1
2
0
0
2
1
0
1
1
0
0
0
0
0
0
0
2
1
1
0
0
0
0
2
0
2
2
1
1
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
1
2
2
0
1
0
1
0
1
0
0
0
0
1
2
1
1
0
2
2
0
2
2
0
0
0
0
0
1
0
0
0
2
2
0
0
2
0
2
0
1
1
0
0
0
0
0
2
5
1
1
2
1
0
0
0
0
0
1
0
0
1
1
1
0
0
0
2
0
1
1
1
0
0
1
0
2
2
0
0
0
1
2
1
0
0
0
1
1
0
0
2
0
1
2
3
0
1
2
0
2
1
2
2
1
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
2
1
1
2
2
0
1
0
1
0
0
1
0
2
2
0
1
1
0
0
1
1
0
1
2
2
0
1
0
0
0
0
1
1
2
0
0
0
1
2
2
0
2
0
2
0
0
1
0
1
0
2
2
0
0
3
0
2
0
1
0
0
2
2
0
0
1
0
0
0
0
2
1
5
1
0
0
2
1
0
1
0
0
0
0
0
1
0
0
2
2
1
0
1
0
2
0
3
0
0
0
2
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
1
2
1
0
0
0
0
2
3
0
1
0
0
0
1
0
0
0
1
1
4
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
3
2
0
2
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
1
1
2
1
0
1
3
1
1
0
0
0
1
0
1
1
2
0
0
0
2
2
0
1
2
0
0
1
0
0
1
2
2
2
1
0
0
1
0
2
0
0
0
1
2
1
0
2
0
1
1
0
0
1
0
0
1
2
2
0
1
2
2
0
1
0
2
0
0
0
0
0
0
2
2
0
1
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
1
1
0
1
0
0
0
1
0
1
0
0
1
0
1
0
0
1
0
0
1
0
0
2
0
0
1
2
1
2
0
1
2
0
0
2
2
0
1
1
0
2
0
1
1
1
0
0
3
2
2
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
1
0
2
2
0
0
1
0
0
0
2
0
2
1
0
0
0
2
1
1
1
0
0
0
0
0
0
0
0
2
0
1
2
0
2
4
2
2
2
0
0
0
1
1
2
3
1
1
1
0
1
0
1
0
2
1
0
0
2
1
1
1
0
0
2
2
0
0
1
1
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
2
2
1
0
1
3
2
1
1
0
1
0
3
1
3
2
2
1
0
0
0
2
0
0
0
0
2
0
2
4
2
1
2
1
0
4
2
0
1
0
0
0
0
0
0
0
3
0
1
1
0
1
0
0
2
2
1
0
0
2
0
2
1
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
1
1
3
0
0
0
1
0
0
0
0
3
0
1
0
0
2
0
2
2
0
1
1
1
2
0
1
0
0
1
0
6
0
0
1
2
0
0
1
0
0
1
0
0
2
0
0
1
2
1
2
0
0
0
2
0
2
1
1
0
0
0
1
2
2
1
2
1
2
1
0
0
1
2
0
0
0
2
0
0
1
1
0
0
0
2
2
1
0
0
0
2
0
0
0
0
0
1
1
0
2
0
1
0
2
0
1
1
1
0
0
0
2
0
0
0
2
0
2
2
1
0
0
0
2
0
1
0
2
0
0
0
0
0
1
0
0
0
0
2
0
2
2
2
0
2
0
0
0
1
4
3
2
1
0
0
0
0
0
2
2
0
0
0
1
1
0
1
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
2
2
0
1
2
0
0
1
0
3
1
2
0
1
0
1
1
1
2
0
0
1
1
0
1
0
1
0
2
1
0
0
2
2
3
0
1
0
0
0
1
2
1
0
1
0
1
0
0
1
1
0
3
2
1
0
1
1
1
0
0
2
1
0
2
0
0
2
1
1
2
3
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
2
2
0
1
0
0
3
1
2
2
0
0
1
0
1
1
0
2
1
0
2
1
2
0
1
2
0
0
0
0
1
2
2
0
2
0
0
1
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
1
0
0
0
1
2
0
0
2
0
1
1
0
0
1
0
0
0
0
2
0
0
2
2
0
0
0
0
1
2
1
2
2
0
1
0
4
0
1
2
1
0
0
1
1
0
1
1
0
1
0
1
0
0
0
0
0
3
1
2
0
2
0
2
0
0
1
2
1
0
1
0
0
0
1
0
0
1
2
1
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
1
0
1
0
0
1
0
0
0
2
1
1
0
1
0
0
0
1
1
0
0
0
1
0
1
0
0
2
1
1
0
0
1
2
0
0
0
3
0
0
0
1
2
0
0
0
2
1
1
1
1
0
0
1
2
0
2
1
1
3
1
0
0
0
0
0
1
2
1
0
0
0
0
2
1
0
1
2
2
0
3
1
2
0
0
0
0
2
0
3
1
0
0
1
0
1
1
0
0
1
1
0
1
2
4
2
0
2
0
0
0
0
0
1
2
3
2
0
1
2
0
1
0
0
0
0
0
2
0
0
0
2
0
1
0
0
1
0
0
0
2
0
2
0
0
0
2
1
4
1
0
0
2
1
1
1
1
1
0
0
0
0
1
2
0
1
0
0
1
1
2
1
0
0
1
0
0
0
0
1
0
0
2
2
0
0
0
1
0
2
1
1
0
2
1
0
1
0
0
0
1
2
0
2
0
0
0
0
2
2
1
2
2
2
3
0
1
0
0
2
1
2
0
0
2
0
2
0
0
1
2
3
1
3
0
0
0
0
0
0
1
1
1
0
0
0
2
2
0
0
1
2
0
0
0
1
0
1
1
0
1
0
0
1
1
0
0
2
2
0
0
2
0
0
2
0
2
0
0
0
2
2
0
3
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
3
0
0
0
1
0
2
1
0
1
0
0
1
0
1
0
0
0
0
1
0
0
2
0
2
2
2
1
2
0
0
0
0
2
1
0
2
3
1
1
0
0
0
1
1
1
1
0
0
0
1
1
2
0
1
0
2
0
0
2
0
1
2
2
1
2
3
0
1
0
1
0
1
1
0
0
0
0
0
1
1
1
2
2
0
0
0
0
0
0
0
0
0
2
0
1
3
0
0
0
0
2
0
2
2
0
0
2
2
1
1
0
1
0
1
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
2
3
1
1
0
0
1
0
1
1
1
0
0
1
0
1
1
0
0
0
1
1
2
0
0
4
1
0
1
0
1
0
0
0
0
0
0
2
1
3
1
0
1
0
0
0
2
0
0
1
0
1
0
2
0
0
0
1
2
0
1
1
1
3
1
0
2
0
0
1
0
1
0
0
0
2
2
1
0
2
0
0
0
1
4
0
1
1
0
4
0
1
2
0
0
0
0
1
0
2
1
0
0
0
0
0
0
5
0
1
1
2
2
0
1
0
0
0
1
0
0
2
1
0
0
0
0
1
0
0
0
0
2
0
2
0
1
0
2
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
1
0
1
0
0
1
1
1
0
0
0
0
1
1
2
1
1
2
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
2
0
1
1
0
0
0
2
0
1
2
0
2
1
2
1
0
1
0
0
0
0
1
1
2
0
3
1
0
0
0
1
1
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
2
1
0
1
0
1
0
1
0
0
0
1
0
2
0
0
3
0
1
1
0
1
0
0
0
0
2
2
0
0
1
2
0
0
0
2
0
0
1
0
1
0
0
2
4
0
1
1
2
0
0
1
2
2
1
1
0
1
1
1
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
2
0
1
0
1
2
0
0
1
1
0
0
1
0
2
0
0
1
2
1
2
0
2
0
1
0
0
0
0
1
1
2
1
0
0
0
0
1
1
1
0
2
0
1
1
0
2
1
1
0
2
0
1
0
1
1
0
2
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
3
2
2
0
0
0
2
0
0
0
1
1
0
2
2
0
2
0
2
2
0
2
0
0
0
0
2
0
0
0
0
2
0
1
2
1
1
2
0
0
1
0
0
0
1
0
2
0
0
0
0
0
1
0
0
1
1
2
0
1
0
3
0
1
0
2
0
1
0
0
2
0
1
0
0
2
0
0
0
0
1
0
1
2
2
1
1
2
0
2
0
0
2
0
0
2
1
2
0
2
3
0
1
2
1
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
1
1
0
0
0
0
0
2
1
0
0
1
0
0
3
2
0
0
2
1
0
0
2
2
0
0
2
0
0
0
0
0
2
1
1
0
0
1
0
1
0
2
1
1
0
0
0
3
0
1
1
0
0
0
1
1
0
1
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
2
0
2
2
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
1
2
0
0
0
1
0
0
1
1
1
0
0
2
0
0
1
1
2
1
0
1
1
0
0
1
0
0
0
0
1
1
2
2
0
1
1
0
0
0
0
2
2
0
0
0
0
1
0
0
0
2
0
2
1
2
1
0
2
0
2
0
0
0
0
1
0
2
1
3
2
2
0
0
0
0
2
2
2
1
0
2
2
2
0
1
2
0
1
0
0
2
0
0
2
0
2
0
0
1
1
2
0
1
2
2
2
0
0
0
0
0
0
0
0
0
1
2
0
0
2
3
2
2
2
2
0
0
0
0
1
0
0
0
0
2
0
1
2
0
0
0
1
0
2
2
1
0
0
0
0
1
0
1
0
1
1
1
0
0
3
2
0
0
0
1
1
0
2
0
0
2
0
0
2
0
0
2
2
1
0
1
0
2
0
2
0
1
0
2
1
0
0
2
2
0
0
0
0
2
2
2
2
0
0
0
2
2
0
1
0
2
2
0
1
1
1
0
0
0
0
1
0
0
1
0
1
1
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
2
0
0
2
1
2
0
0
2
0
0
0
1
2
0
1
2
0
1
1
1
0
0
2
1
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
3
0
2
1
0
0
1
2
2
0
1
0
1
0
2
1
0
2
2
2
0
1
1
0
2
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
1
0
1
0
1
2
0
0
0
0
0
0
2
2
0
1
1
0
0
1
2
0
2
1
2
1
0
0
1
0
1
0
1
1
1
1
2
0
0
0
0
2
2
0
0
0
1
0
0
1
0
0
0
1
1
1
0
0
0
1
0
0
1
1
0
1
2
0
0
1
1
0
0
0
2
0
0
1
0
0
0
1
1
2
0
2
2
0
0
1
1
1
0
0
1
0
1
1
0
0
3
0
0
0
0
2
1
1
3
0
0
1
2
0
0
2
1
0
1
1
1
2
0
0
0
0
4
0
1
0
1
0
0
0
0
2
0
1
2
1
0
2
0
2
0
1
0
0
1
1
2
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
2
1
2
0
0
0
1
1
0
0
0
0
2
0
0
1
0
0
3
0
2
2
2
2
0
2
1
3
0
2
1
1
2
0
0
0
0
1
1
1
2
3
2
0
1
1
1
2
0
0
1
0
0
2
2
0
0
0
1
1
0
1
0
1
0
0
2
2
1
0
0
1
1
1
0
2
0
2
0
0
0
1
1
0
2
0
2
0
0
0
0
0
2
0
1
0
0
1
1
2
2
0
0
2
0
0
0
0
2
0
0
2
0
1
0
2
2
2
1
2
0
1
0
1
1
0
2
2
1
1
2
0
0
1
0
0
0
0
0
1
3
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
3
0
0
0
1
0
2
0
0
2
0
2
2
2
0
1
2
0
1
1
1
2
1
0
0
2
0
0
1
0
1
1
0
1
0
2
0
0
1
0
1
1
0
2
0
0
1
1
2
1
0
1
1
0
0
2
1
0
1
0
1
0
0
1
0
2
0
0
1
1
0
0
0
1
0
1
0
0
1
2
0
0
0
2
0
2
0
1
0
0
0
1
0
0
1
0
0
1
0
2
1
0
0
0
0
1
0
2
0
0
0
1
1
0
0
0
2
0
0
0
2
1
1
0
1
0
1
0
0
0
2
1
0
1
3
0
1
2
0
1
0
0
1
2
0
1
1
2
0
2
0
0
2
1
0
0
1
0
2
1
1
0
1
0
0
1
2
2
1
0
0
0
2
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
2
0
1
1
2
0
0
0
1
0
1
1
2
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
2
0
1
2
1
0
0
1
0
0
0
0
0
0
4
2
0
3
0
1
2
0
0
0
0
2
0
0
2
0
0
1
0
2
2
0
1
0
2
1
0
0
0
0
2
2
2
0
1
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
2
2
0
1
2
2
2
0
1
0
0
0
2
0
1
0
0
1
1
0
1
0
0
0
1
2
1
1
0
0
0
0
0
3
0
2
2
0
0
0
1
2
1
2
0
2
0
2
2
1
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
3
0
0
2
3
2
0
1
0
2
2
0
1
0
1
1
0
0
2
0
0
2
2
0
1
0
0
1
0
0
2
1
2
1
1
0
1
0
1
0
2
0
1
2
0
2
2
2
1
1
0
2
1
0
1
1
0
0
1
0
0
0
1
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
2
0
2
2
0
0
0
0
0
1
0
0
1
1
0
0
2
0
1
0
0
2
0
0
0
2
0
0
0
0
0
2
1
1
0
3
0
3
0
1
2
0
1
0
0
1
0
0
1
0
1
2
0
1
0
1
0
0
1
0
0
0
0
0
1
0
1
1
0
2
0
0
0
0
0
0
2
0
2
0
1
0
2
2
1
0
1
2
2
2
1
0
1
0
1
2
2
1
1
1
2
0
1
0
0
0
1
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
2
1
1
2
2
1
2
2
0
2
2
2
0
2
1
0
1
0
2
0
0
0
0
0
0
0
1
0
1
0
0
2
1
1
1
0
0
2
0
0
0
0
2
0
1
0
0
0
2
0
0
0
2
1
2
0
1
0
1
0
0
1
0
3
0
0
2
1
0
0
0
1
2
0
2
0
1
0
1
0
0
2
0
2
0
1
0
2
0
1
0
2
2
2
11
1
0
1
1
4
1
0
2
1
0
0
0
0
0
2
0
0
2
1
3
1
2
0
0
1
1
1
1
0
2
0
0
1
0
2
0
2
4
2
0
0
2
2
0
0
1
2
2
0
0
1
2
1
2
0
2
0
0
0
0
0
0
2
0
1
0
1
0
1
0
0
0
0
0
1
2
1
1
4
0
4
0
1
0
1
1
0
2
0
0
0
0
1
2
0
0
0
0
2
1
1
1
0
0
0
1
2
0
0
0
0
0
0
1
0
0
1
0
1
0
1
3
0
1
0
1
2
2
2
0
0
3
0
1
0
1
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
2
0
0
2
2
0
1
3
0
0
2
0
0
0
1
0
0
0
1
0
1
0
2
0
2
1
0
1
1
0
1
0
0
1
1
1
1
1
0
0
0
0
0
1
0
0
2
2
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
2
2
2
0
0
0
2
0
2
0
2
1
0
1
6
0
0
2
1
2
0
0
0
1
1
0
0
3
0
1
0
0
2
0
0
1
1
1
0
0
2
2
0
3
0
0
0
0
0
1
1
0
0
1
2
2
3
1
0
0
1
2
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
2
0
2
0
2
2
3
0
0
0
1
1
2
0
1
0
0
1
0
1
0
0
0
1
0
1
2
1
0
1
1
0
1
0
1
1
0
1
1
0
0
0
3
2
2
2
1
0
3
1
2
0
0
0
0
0
0
1
0
0
2
2
0
2
2
0
0
1
2
1
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
7
1
0
2
2
1
1
0
0
2
1
2
0
0
0
1
0
1
1
0
2
1
0
1
2
0
0
0
0
2
0
0
2
1
0
2
1
0
0
0
0
0
2
0
2
0
1
0
2
0
2
0
0
1
0
0
3
2
2
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
2
0
0
0
1
1
2
2
2
0
1
2
0
0
1
1
0
1
3
1
0
1
3
0
0
2
1
1
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
3
0
3
1
0
1
0
0
0
1
1
0
0
2
0
1
3
2
0
1
2
0
0
1
1
0
0
0
0
0
0
0
1
1
2
1
0
1
0
0
1
0
0
0
0
1
0
0
0
1
1
0
1
0
0
1
0
2
0
0
2
1
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
2
2
0
2
2
0
0
0
0
1
0
0
1
0
2
0
3
1
0
2
0
1
0
1
1
0
2
0
1
2
1
1
0
1
1
0
2
1
0
2
0
0
1
1
0
1
2
2
2
0
0
0
0
0
3
1
2
0
0
1
1
0
0
0
0
1
0
2
1
0
2
1
0
1
0
0
1
1
3
0
0
0
0
2
0
0
0
1
0
0
1
1
0
1
0
0
4
0
0
0
0
0
2
1
0
0
2
2
0
2
1
3
2
0
1
0
0
2
2
1
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
2
0
2
0
2
0
1
1
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
2
1
0
0
2
1
0
2
2
2
0
0
2
3
0
0
0
2
1
1
1
2
0
1
2
0
4
0
2
0
1
2
2
1
1
0
0
2
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
1
0
2
0
0
1
2
2
2
1
1
2
0
0
0
0
1
0
2
0
1
1
1
0
0
1
1
0
2
0
1
0
0
1
2
0
0
2
0
0
1
1
0
0
1
0
0
2
2
0
2
2
0
2
1
0
1
1
1
0
1
0
1
0
2
1
1
2
1
0
0
2
2
1
1
0
0
0
2
0
0
1
0
0
0
2
0
0
0
2
1
0
1
1
0
0
1
0
0
1
0
0
0
0
2
0
2
0
1
0
0
0
0
2
0
0
0
0
1
0
1
1
0
0
0
2
2
0
1
0
0
0
2
2
1
0
1
2
1
0
0
0
0
1
2
1
0
2
2
0
0
0
0
0
1
2
0
0
1
1
1
1
0
0
0
1
0
0
2
2
0
0
0
1
1
4
2
3
0
2
1
0
1
0
2
2
0
0
1
2
0
1
1
0
0
1
0
1
0
0
2
0
0
0
2
2
0
0
1
1
2
0
0
2
0
0
1
0
0
1
0
2
0
0
0
0
0
0
1
1
2
1
0
0
2
1
0
0
2
1
0
0
1
0
0
0
0
0
0
0
2
1
1
0
0
0
0
2
1
1
1
0
1
0
0
1
1
2
1
1
0
1
1
2
0
2
1
1
0
2
2
2
2
2
2
2
0
2
0
0
1
1
2
0
0
0
0
2
1
0
0
2
1
0
1
0
1
0
0
2
2
0
2
0
0
0
0
1
0
2
2
2
0
0
0
2
2
1
0
0
0
2
3
0
1
1
0
0
1
0
0
0
1
0
0
0
1
2
0
2
1
0
2
1
1
0
0
0
0
0
0
0
0
0
2
1
0
2
2
2
1
0
3
0
0
0
0
1
0
2
0
0
0
1
1
1
0
2
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
1
3
0
0
1
1
0
0
0
0
0
1
0
0
0
0
2
1
6
0
3
1
0
0
0
2
0
0
0
3
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
1
1
4
1
0
0
1
1
2
2
0
0
2
1
0
2
0
0
1
0
0
1
2
0
2
1
2
2
0
1
0
1
0
0
2
0
0
0
0
1
1
0
0
0
1
0
1
0
2
1
0
0
0
1
0
0
0
1
0
0
0
0
1
2
0
0
0
1
1
0
0
0
0
2
1
2
0
2
1
2
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
2
2
0
2
0
0
1
0
0
0
1
0
0
0
0
2
1
0
2
0
0
0
0
0
1
1
0
1
1
1
0
0
1
1
0
0
1
2
1
2
2
0
0
2
0
0
0
0
1
2
0
0
0
0
0
1
2
0
0
0
0
0
2
1
0
0
0
0
3
0
5
2
0
0
0
0
1
0
1
0
0
1
0
2
0
0
0
0
1
0
2
1
0
0
0
1
0
1
0
0
0
2
0
1
1
0
2
0
0
1
0
0
0
0
1
1
1
1
1
0
0
2
2
2
2
0
0
0
0
2
1
0
2
2
0
0
0
0
1
1
0
0
1
0
1
1
1
2
1
0
0
3
0
0
0
2
0
2
0
2
0
0
0
0
1
0
0
1
2
0
0
1
0
1
0
0
2
0
2
2
0
0
1
1
1
2
0
2
0
0
1
0
0
0
0
0
2
0
0
1
2
1
2
0
0
0
0
1
0
1
0
0
0
1
2
0
4
1
0
0
1
1
0
0
1
2
0
1
2
0
1
0
0
0
2
1
1
0
0
0
0
2
0
0
0
2
0
2
4
0
1
2
0
0
0
0
1
0
1
1
1
0
2
0
2
0
2
2
2
0
1
2
0
0
1
0
2
0
0
0
1
1
1
0
1
1
1
0
2
0
2
0
3
0
1
0
0
1
2
2
0
1
0
2
1
0
1
1
2
0
2
0
0
0
1
1
0
0
2
1
0
0
0
1
2
2
1
0
0
0
2
0
0
1
0
0
0
0
0
2
0
1
0
2
2
2
0
0
0
0
0
3
1
0
2
1
1
0
2
0
2
0
0
0
1
0
0
1
1
0
2
1
1
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
1
1
0
2
1
1
0
0
0
2
1
1
0
1
2
0
1
0
0
0
0
1
2
0
2
0
0
1
0
1
0
2
0
1
1
0
0
0
0
1
0
0
1
1
1
2
0
0
0
3
1
0
0
2
2
0
2
0
0
1
1
0
0
1
2
0
1
0
1
0
0
0
0
0
2
1
0
2
2
0
2
2
1
0
2
0
0
0
0
1
0
2
1
0
0
1
0
0
2
3
1
1
0
1
2
0
0
0
0
0
1
0
0
2
1
2
0
0
4
2
0
0
0
0
0
1
0
1
3
0
0
1
2
0
2
2
1
2
2
1
0
2
1
0
0
0
0
0
0
0
0
0
1
0
2
1
1
0
0
0
0
1
1
0
0
0
2
0
2
1
0
0
0
1
2
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
2
0
2
2
1
0
0
0
2
1
1
0
0
0
0
1
0
2
1
0
0
0
0
0
0
2
0
0
0
1
0
3
1
1
0
1
0
1
0
1
1
0
0
0
1
1
1
0
0
0
1
0
0
0
1
0
0
1
2
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
1
2
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
2
0
0
0
2
1
1
0
0
2
1
1
2
0
2
1
1
0
0
2
0
0
0
0
5
0
0
0
0
1
0
1
0
2
0
2
2
1
1
1
1
0
0
0
1
0
1
2
2
1
2
0
2
2
0
1
1
2
0
0
0
0
1
0
2
0
2
0
2
1
2
0
2
2
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
1
0
1
0
1
0
1
0
1
0
0
0
0
0
1
0
0
2
0
2
3
0
0
1
0
2
0
0
1
0
2
0
0
3
2
1
1
0
0
0
0
0
1
2
0
1
0
1
1
1
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
2
1
0
0
1
2
0
1
1
0
0
2
0
0
2
0
0
3
1
0
1
2
0
0
0
1
0
2
0
1
1
2
1
0
2
0
1
0
0
0
1
0
1
0
2
0
0
0
2
0
1
0
0
1
0
0
1
2
0
0
1
0
1
2
0
0
3
1
0
1
0
0
0
2
0
0
2
0
1
0
0
0
0
1
2
0
0
0
1
2
1
0
4
0
1
0
0
0
0
2
1
2
2
0
1
0
0
2
0
0
0
1
2
2
0
0
1
0
1
1
0
1
1
0
1
2
4
0
1
0
5
0
2
2
0
0
1
1
2
0
1
2
2
1
0
0
0
0
0
0
0
0
0
3
0
0
1
1
0
2
0
0
0
0
0
1
0
2
0
1
0
0
3
1
0
1
2
0
0
1
1
1
1
0
1
0
1
2
0
1
1
0
1
0
0
1
2
1
2
0
0
0
0
0
1
2
0
0
1
0
2
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
1
0
1
0
0
0
0
0
1
1
2
1
0
2
0
4
0
1
2
0
2
0
2
0
0
1
2
0
2
2
1
2
1
0
2
0
1
0
2
0
3
2
1
0
1
0
0
3
0
1
1
0
2
0
2
2
0
0
0
1
0
1
1
0
0
0
1
3
0
1
1
0
2
1
0
0
0
1
0
0
2
1
0
2
2
0
0
1
0
3
1
0
1
0
0
1
4
0
1
1
2
1
1
0
0
0
1
1
0
1
1
1
0
1
1
0
0
0
0
3
0
0
0
0
0
3
0
2
1
0
0
2
0
1
0
2
0
0
0
1
1
2
0
0
0
1
0
0
0
0
2
1
1
0
1
0
1
1
0
2
1
2
1
1
0
0
0
0
4
1
0
0
3
0
1
0
0
0
0
0
0
4
0
0
2
0
0
2
0
2
2
0
1
1
1
0
0
0
1
0
0
0
0
0
2
0
0
1
0
2
0
0
1
0
1
0
0
0
2
1
2
1
0
2
0
1
0
0
0
0
0
0
0
1
1
0
0
0
2
1
0
2
0
0
1
1
2
1
0
0
0
6
1
1
0
0
0
0
0
2
1
0
0
0
0
0
2
1
0
0
0
0
0
0
1
1
1
1
2
2
0
1
0
1
0
2
1
2
2
0
2
0
1
2
0
1
2
1
1
1
2
0
2
0
0
0
2
1
0
0
0
0
0
1
0
2
0
1
1
2
0
0
0
1
0
0
0
1
2
2
2
2
0
0
1
0
2
3
1
0
0
2
0
1
0
0
2
0
1
1
0
0
2
2
0
0
0
1
1
1
0
0
3
0
2
0
2
0
0
0
2
0
2
2
0
2
2
0
0
2
0
1
0
3
1
0
4
0
0
0
1
2
0
1
0
0
1
0
10
0
2
0
0
3
6
0
1
1
2
0
0
0
0
0
1
1
1
0
0
0
1
0
1
0
0
0
0
1
1
0
0
1
1
1
1
0
1
2
1
0
0
2
0
2
0
0
3
1
2
1
0
1
0
0
1
0
2
0
1
1
0
0
1
0
1
1
1
2
0
0
1
2
2
0
0
0
2
0
2
0
0
0
0
0
2
0
2
0
0
5
0
5
0
0
0
1
0
0
0
1
2
0
1
1
0
0
1
0
0
1
0
1
0
1
2
1
2
0
0
0
2
0
1
1
2
0
2
2
0
0
0
0
2
0
0
2
0
1
1
1
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
1
2
1
2
1
1
0
0
0
3
0
1
0
1
2
0
1
0
0
2
0
0
1
0
1
1
0
0
0
0
2
0
0
0
1
2
1
0
2
0
1
0
0
0
0
1
1
0
1
0
0
1
0
1
0
0
2
0
1
0
0
1
2
0
1
0
1
1
0
2
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
1
0
1
2
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
2
0
1
0
1
1
0
1
0
0
0
0
0
1
2
2
1
2
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
2
0
0
2
0
2
2
0
0
0
0
0
2
0
0
0
1
0
2
3
0
0
2
2
0
0
1
0
2
0
0
2
1
0
1
0
1
0
2
2
1
1
1
1
0
0
2
0
0
2
0
0
0
0
1
1
0
1
0
1
0
2
2
0
0
2
2
1
0
0
0
2
2
2
0
0
0
0
1
0
5
2
2
1
2
1
1
1
0
1
0
1
0
0
2
0
1
0
0
1
0
2
0
2
1
1
2
0
0
0
0
1
0
2
0
2
0
1
2
1
0
2
0
0
1
2
2
1
0
2
0
2
2
0
2
1
0
0
1
0
1
1
1
0
1
0
1
2
0
0
1
1
0
2
1
1
1
0
0
2
1
1
1
0
1
0
2
0
0
0
2
2
0
0
0
1
0
0
1
2
0
1
0
1
1
0
0
0
2
1
1
1
0
0
2
0
0
2
0
2
1
1
2
0
1
0
0
1
1
0
0
0
1
0
0
0
2
2
2
0
0
0
1
2
1
0
1
1
2
0
0
1
1
0
2
2
2
0
0
2
2
0
1
0
1
0
0
0
0
2
0
3
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
2
2
0
0
2
0
2
1
1
1
3
2
0
1
0
0
0
1
0
1
1
0
0
1
1
2
0
1
1
0
0
0
14
0
1
0
0
1
0
0
1
1
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
3
2
0
0
0
2
2
0
1
0
0
2
1
0
0
1
0
0
1
0
1
1
1
2
1
4
0
2
2
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
1
0
2
2
1
1
2
2
0
1
0
1
0
1
2
0
2
0
1
2
0
1
1
0
2
1
0
2
0
0
0
1
2
0
0
0
1
2
1
1
2
0
0
0
2
0
0
0
0
0
0
2
0
1
0
2
0
0
2
0
0
2
1
2
0
0
2
1
0
0
0
1
1
2
0
2
1
2
1
0
0
0
0
2
0
0
0
0
0
1
0
1
2
0
0
0
0
1
1
1
2
0
0
0
0
0
0
1
0
2
2
0
2
1
1
1
2
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
3
0
0
0
0
0
0
0
0
3
1
0
1
0
2
1
0
0
0
0
0
0
2
0
1
0
1
0
1
0
0
2
1
0
2
1
1
0
0
1
0
0
0
0
3
1
4
1
1
0
0
2
0
1
0
0
2
0
2
0
1
0
1
0
1
0
1
0
0
1
2
0
2
0
0
1
0
3
1
1
0
0
1
2
1
0
1
1
0
0
2
0
0
0
1
0
0
2
2
0
0
0
0
1
0
0
0
1
1
2
0
1
0
0
0
0
1
1
2
1
0
0
0
2
2
1
0
1
0
2
2
0
0
1
2
0
0
0
0
0
1
0
1
0
0
2
2
1
1
0
2
1
0
0
2
1
0
0
3
0
0
1
2
1
1
1
0
2
0
2
1
0
0
2
0
0
0
2
1
0
2
0
0
2
2
0
0
0
0
0
1
0
2
0
1
0
2
0
1
1
0
0
1
2
2
0
0
0
0
1
1
0
0
1
1
0
1
0
1
1
0
0
0
0
1
0
2
2
1
0
0
1
0
1
0
0
3
0
2
2
2
0
1
2
0
2
1
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
2
0
0
0
0
0
2
1
0
0
1
0
1
2
0
0
1
2
0
0
0
2
1
0
1
1
0
1
1
0
1
0
0
1
0
2
0
0
1
0
1
2
2
3
1
0
2
2
0
0
0
1
1
0
0
0
0
3
0
2
0
0
0
1
0
2
0
1
0
2
0
2
0
0
2
3
0
0
0
2
0
0
1
2
0
1
2
2
0
0
1
2
0
0
2
1
1
0
2
2
2
0
0
2
1
1
4
2
0
0
0
2
1
2
0
1
0
1
0
0
2
1
0
1
0
2
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
1
0
1
0
1
1
0
2
2
1
1
0
0
1
2
1
1
1
0
0
1
0
0
0
2
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
1
1
2
1
0
0
2
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
2
2
1
2
0
1
1
1
0
2
0
0
0
2
2
3
0
0
2
0
1
2
0
2
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
2
0
1
0
2
1
0
2
1
1
0
0
1
0
0
0
2
0
2
1
0
0
1
1
1
2
2
0
1
0
0
1
2
0
0
0
0
0
0
1
0
1
0
1
0
2
2
0
2
0
0
0
1
1
0
0
2
0
0
1
0
2
0
2
2
0
0
0
1
1
2
0
0
0
1
1
1
0
1
0
0
0
1
2
0
2
0
1
1
0
1
0
2
1
0
0
0
0
1
2
1
0
1
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
1
0
2
2
2
1
2
0
1
0
1
2
0
1
0
1
0
0
0
0
0
0
2
2
2
1
0
1
0
2
0
0
3
0
2
1
1
0
2
2
0
2
0
0
0
1
0
0
0
0
1
2
1
0
1
1
0
0
0
0
1
0
0
2
1
0
0
3
0
0
0
1
0
1
2
0
2
1
1
0
1
2
0
0
2
1
0
3
0
2
0
2
0
2
2
0
1
2
0
1
0
1
1
0
0
1
0
2
3
0
0
0
1
1
2
1
1
1
2
0
0
0
0
1
3
1
0
0
0
0
0
1
0
0
2
1
1
0
0
0
1
0
0
2
2
1
1
1
0
0
0
0
0
0
2
0
0
2
1
0
0
2
0
0
0
0
0
0
1
0
1
0
2
0
0
0
1
4
1
0
2
0
1
3
0
0
0
1
2
1
0
0
0
2
0
0
0
2
1
3
0
0
1
0
2
1
2
1
2
0
0
0
0
3
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
2
2
1
2
2
2
1
2
0
0
0
1
0
2
1
0
1
0
3
1
1
1
1
0
0
2
0
0
0
1
1
2
2
1
1
0
0
2
1
1
0
0
2
0
0
0
2
0
2
0
1
3
0
1
2
1
0
1
1
0
0
0
2
0
0
1
1
0
1
2
1
0
0
2
0
1
0
0
0
0
2
2
0
1
0
1
0
0
1
0
0
1
0
0
1
2
2
1
0
1
0
0
2
0
0
1
0
1
0
0
1
0
0
0
0
1
1
1
1
0
0
0
0
1
0
0
0
1
2
1
0
0
0
0
4
1
1
0
0
1
0
2
2
0
2
3
0
0
2
0
3
2
2
0
2
0
0
0
1
1
0
0
2
2
0
0
1
0
2
1
1
1
2
0
0
1
2
2
3
1
1
2
0
1
1
2
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
2
0
2
1
0
1
1
2
0
2
0
0
1
0
2
1
1
1
1
0
0
0
0
0
0
2
2
1
1
0
0
0
0
1
0
0
1
2
1
2
1
1
1
0
2
1
0
2
2
0
0
0
0
2
0
2
0
0
0
0
2
2
0
2
1
0
0
0
1
0
2
0
2
0
2
0
1
0
0
1
0
1
0
1
1
0
0
2
1
1
1
1
0
0
1
0
2
0
4
1
0
1
2
0
0
0
0
0
1
1
1
1
0
0
1
0
2
0
2
2
0
1
2
0
2
1
0
0
2
2
1
0
1
0
0
3
0
2
0
0
0
0
0
2
1
0
0
1
1
0
0
0
2
0
1
1
2
0
1
1
1
0
0
2
1
0
1
2
0
1
0
0
3
0
0
0
0
0
1
1
1
2
2
0
1
0
1
1
0
3
0
0
1
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
2
2
0
0
2
2
0
1
0
0
2
1
2
2
0
2
0
1
0
0
1
1
0
1
1
0
0
0
0
0
0
1
1
0
2
0
2
0
0
0
2
2
0
0
1
0
1
0
0
0
1
1
2
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
1
2
2
0
0
2
1
0
0
0
2
1
0
0
1
0
0
0
0
0
1
1
2
0
0
1
0
0
1
0
1
0
2
0
0
1
0
0
0
1
2
1
0
0
0
0
2
0
0
0
0
0
2
3
0
1
0
2
0
0
0
2
2
1
0
3
2
1
0
0
1
0
0
0
0
2
0
0
0
4
0
1
2
1
0
3
1
0
0
0
0
0
0
0
1
0
0
1
1
2
0
0
0
2
1
0
1
0
0
0
2
2
0
0
2
2
0
2
0
0
0
0
1
2
0
0
0
0
1
1
0
2
1
0
2
0
2
0
0
0
0
1
2
2
0
1
0
2
0
0
2
2
0
2
0
1
0
0
0
0
0
0
0
2
0
2
0
2
0
0
2
0
1
0
0
0
0
1
0
0
0
2
0
2
2
2
2
0
2
1
0
1
0
1
2
2
2
8
2
0
2
2
1
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
1
1
0
0
0
0
0
1
1
0
1
0
2
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
2
0
0
0
2
1
1
0
0
0
1
1
1
0
2
1
2
0
0
0
2
2
0
0
1
0
1
0
2
2
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
1
0
2
2
1
0
0
2
0
3
0
0
0
0
0
2
2
3
0
2
0
0
0
0
0
0
0
5
0
0
0
2
0
0
1
0
0
2
1
1
0
0
0
1
0
0
1
2
0
0
2
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
2
0
1
1
2
1
1
0
2
1
0
1
1
0
0
1
2
0
0
1
1
2
1
0
0
1
0
2
0
2
1
1
0
2
0
0
0
2
0
0
0
2
3
1
0
0
0
0
2
0
2
0
0
0
1
0
0
0
1
0
0
0
1
2
2
0
0
0
1
2
0
2
2
2
0
0
2
1
2
0
2
0
0
0
0
0
0
0
1
0
0
0
1
1
1
3
1
0
1
0
0
4
2
2
0
0
1
2
0
1
2
0
2
0
0
1
0
0
0
0
0
1
0
2
0
0
0
1
0
0
1
0
1
1
0
1
0
1
2
4
0
1
1
1
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
2
1
0
1
0
1
1
0
1
0
0
0
0
0
3
0
2
2
0
2
2
0
2
0
0
0
1
1
3
1
2
0
1
0
1
1
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
1
1
0
1
0
0
2
3
1
4
1
2
0
0
1
0
1
2
0
2
0
0
0
1
0
1
0
0
1
0
1
2
0
0
0
0
0
1
0
2
0
0
0
0
2
1
0
2
0
0
1
0
1
0
0
0
0
0
1
2
0
0
2
2
0
1
0
0
0
0
1
2
2
0
0
0
2
0
2
2
0
2
1
1
1
0
2
0
2
0
1
0
2
2
1
0
0
0
3
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
1
0
1
1
0
2
0
0
1
1
0
0
0
0
2
1
0
0
1
1
1
0
0
0
0
0
2
0
1
1
0
1
2
2
0
2
0
0
2
0
0
1
0
0
2
0
2
0
0
1
2
0
0
1
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
1
0
2
0
0
0
0
1
0
1
1
2
0
2
0
2
0
0
0
0
0
1
1
0
0
0
0
2
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
2
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
1
1
1
0
2
0
2
0
0
1
1
0
1
1
0
0
2
0
0
0
0
0
1
0
2
1
0
1
0
2
0
2
1
0
1
1
0
0
0
0
0
2
0
0
0
0
0
1
3
0
2
0
0
0
1
0
1
0
0
2
1
2
2
0
3
0
0
0
2
0
2
2
0
0
2
0
0
0
1
1
0
1
1
0
0
1
1
0
2
1
1
0
0
2
0
0
2
0
2
3
1
0
0
0
2
0
0
0
2
2
1
0
0
0
2
0
1
3
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
1
2
0
2
0
0
2
1
0
0
0
2
0
0
3
0
0
1
0
2
0
0
1
1
0
1
1
1
1
2
1
2
1
1
1
0
0
1
0
1
0
0
0
1
2
0
0
0
1
0
1
2
2
0
0
0
2
2
0
2
0
1
2
3
1
1
0
2
2
1
1
1
0
0
0
0
0
0
0
1
0
1
0
1
1
2
1
0
1
0
1
0
2
0
1
0
0
0
1
0
0
0
0
0
0
2
0
2
2
0
1
1
0
0
0
1
1
2
0
0
5
0
0
0
0
0
2
1
1
0
0
0
2
0
2
6
1
1
2
0
0
1
0
0
1
0
1
0
2
0
2
2
1
0
1
0
1
0
1
0
2
1
1
0
1
1
1
0
0
2
0
2
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
2
0
0
2
0
2
0
2
1
0
1
0
2
3
1
0
0
2
0
1
0
0
0
2
0
1
1
0
1
1
2
2
1
0
0
1
2
0
1
0
0
1
0
0
0
0
2
1
0
0
1
0
0
2
0
0
0
0
0
2
0
0
1
1
0
0
2
0
0
1
1
1
0
1
4
1
0
3
0
0
0
2
0
0
0
1
0
1
0
2
2
1
0
0
0
1
0
0
0
1
0
2
0
1
1
0
2
2
1
0
0
1
0
0
0
3
0
2
0
1
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
1
1
0
0
0
2
0
1
2
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
2
2
1
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
1
0
2
0
0
2
0
2
0
2
1
2
0
1
2
2
0
0
0
0
0
0
1
2
0
0
0
1
1
0
2
0
0
1
2
0
1
0
0
0
0
0
0
0
0
3
0
2
0
1
1
0
0
1
1
1
2
2
1
1
0
0
0
3
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
1
0
0
1
1
2
0
0
1
2
0
0
2
0
0
1
2
1
1
1
0
0
1
0
0
2
2
2
0
1
0
0
1
0
0
2
2
0
0
0
1
0
0
0
2
0
1
0
2
1
0
0
1
2
1
0
0
0
1
0
1
4
0
2
2
1
0
2
2
0
1
0
0
0
1
0
0
0
0
0
0
0
2
2
0
2
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
1
3
1
2
0
0
2
2
0
2
1
1
0
0
2
0
0
0
0
0
0
0
1
2
0
1
0
0
1
0
0
0
2
0
1
1
2
0
1
2
1
0
1
1
0
1
0
0
0
2
0
0
0
0
1
1
1
4
3
1
0
1
0
0
0
1
1
0
1
0
0
0
0
0
2
1
0
2
2
0
0
0
0
2
0
2
1
0
0
1
0
2
2
1
0
0
2
3
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
1
2
2
1
1
1
1
1
1
0
0
0
0
0
0
0
2
1
0
0
1
1
1
0
0
0
1
1
0
0
0
0
0
1
2
0
0
2
0
2
1
0
0
0
1
2
2
0
0
1
2
1
2
1
2
1
0
7
0
0
1
0
1
0
0
2
0
2
0
1
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
2
0
0
2
1
1
2
2
1
0
2
0
0
1
0
0
1
1
1
0
0
1
0
0
1
0
0
0
0
0
2
2
0
3
0
2
1
0
0
0
2
1
0
0
1
2
0
0
0
0
0
1
1
2
1
1
0
1
0
2
0
0
0
2
1
0
1
2
0
0
3
0
1
0
0
2
0
0
2
0
0
0
0
0
2
0
1
0
2
1
1
1
2
0
1
1
0
3
0
1
0
1
2
2
2
0
0
0
2
0
0
0
2
2
2
0
2
1
2
2
0
1
0
0
0
2
1
0
2
1
0
2
0
0
0
0
0
1
1
0
0
0
2
2
0
2
0
1
0
0
0
0
1
1
0
2
0
0
0
0
2
0
0
2
1
0
2
0
0
0
1
2
2
2
0
0
2
0
0
0
1
0
1
2
0
1
0
0
2
2
1
0
1
1
3
0
0
2
0
1
0
0
1
1
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
1
0
0
0
0
0
2
0
0
1
0
1
0
0
0
2
0
1
0
1
0
3
0
0
0
2
0
1
0
0
2
0
0
1
0
0
0
0
1
2
1
0
0
0
0
2
2
0
0
2
0
1
2
1
0
0
0
1
0
0
0
2
1
0
1
0
0
0
1
1
0
1
1
0
0
0
0
0
0
1
2
0
0
0
1
0
1
0
0
1
0
0
5
0
0
2
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
4
0
0
1
0
2
0
1
0
0
0
2
0
1
2
1
1
0
2
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
5
2
0
0
2
0
1
0
2
0
0
0
1
1
3
0
0
0
2
1
1
0
3
0
1
1
1
1
2
2
0
1
0
0
1
0
2
1
0
0
0
0
0
1
2
0
1
0
2
2
0
1
0
0
0
2
0
0
0
1
1
1
0
0
0
1
0
2
0
2
0
0
1
0
2
0
0
0
2
1
2
2
2
2
0
1
2
0
0
2
2
2
1
1
0
1
2
2
1
0
2
0
0
1
2
0
2
0
0
0
3
0
0
0
2
0
1
2
0
1
2
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
1
2
2
1
2
0
0
0
0
0
2
1
0
0
1
0
0
2
0
2
1
0
0
0
1
0
0
0
2
2
2
0
0
0
1
0
0
2
1
2
0
2
0
1
0
0
1
2
0
2
1
0
1
0
2
0
0
0
2
0
1
3
1
0
0
0
0
0
0
1
0
1
4
1
0
2
1
1
0
0
0
0
0
0
0
1
1
2
0
0
1
0
0
2
1
2
0
0
1
3
0
1
0
1
0
0
1
0
1
0
2
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
2
0
1
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
1
0
2
2
0
0
2
0
3
0
4
0
1
2
1
1
2
0
0
0
2
1
1
0
1
0
2
0
2
1
1
0
0
0
2
1
0
0
1
2
1
0
0
1
0
1
0
1
0
0
1
2
1
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
2
0
0
2
2
0
0
0
0
3
1
0
0
0
2
0
0
0
0
1
3
2
2
1
2
2
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
2
0
0
1
0
2
0
1
0
0
0
0
1
1
2
2
0
0
0
1
0
1
0
2
0
1
0
0
0
0
2
2
2
0
2
0
0
3
0
1
0
1
1
0
0
1
1
0
2
0
0
0
2
2
1
0
2
1
2
2
2
0
0
0
0
0
0
1
0
1
0
1
2
2
4
1
1
2
1
0
0
2
0
1
2
1
0
1
0
0
2
0
2
0
0
2
1
0
0
0
1
2
0
1
0
0
0
1
1
0
2
1
2
1
0
2
0
1
2
2
6
1
2
2
0
1
0
0
2
1
1
1
1
0
0
0
0
0
0
0
0
0
1
0
3
2
0
0
0
0
1
0
1
0
0
0
1
0
2
1
2
1
0
2
1
1
0
0
1
2
1
0
2
2
2
1
0
0
1
0
1
0
1
0
1
0
0
0
0
1
0
0
1
1
0
0
2
1
0
1
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
2
0
1
1
0
1
0
1
0
0
0
1
0
2
0
0
0
0
1
1
1
1
1
1
0
1
0
0
0
2
1
1
0
1
1
1
0
0
2
1
1
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
1
1
2
1
0
2
2
0
0
0
2
2
0
0
2
1
2
0
1
0
1
1
1
2
1
0
0
2
1
0
2
1
2
2
0
0
1
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
2
1
1
0
2
0
4
0
0
1
0
2
1
0
0
0
0
0
0
0
0
2
0
1
1
0
0
1
0
0
0
0
1
0
0
1
2
0
0
0
2
0
1
1
3
1
2
1
0
1
0
0
1
1
0
0
2
1
0
0
0
1
0
1
0
0
2
0
3
0
2
2
2
0
2
0
0
0
2
2
1
0
0
0
1
0
0
1
0
0
0
0
2
2
1
0
2
0
0
0
1
0
0
2
3
1
0
0
0
1
0
1
1
1
0
0
1
0
0
0
2
1
0
0
2
2
1
0
0
0
2
2
0
0
0
0
1
1
0
0
1
2
3
0
1
0
0
0
2
3
0
0
2
2
0
3
1
0
2
1
1
0
0
1
0
3
0
2
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
7
1
2
0
1
2
0
0
2
0
1
2
0
1
0
0
0
2
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
2
1
0
1
1
0
0
2
0
0
0
0
1
1
0
2
0
1
1
0
0
0
1
2
2
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
2
0
1
0
0
0
0
2
0
1
0
0
0
0
1
2
1
2
1
0
0
0
0
0
0
2
1
0
2
1
0
0
1
0
0
1
2
0
2
0
0
0
0
2
0
2
2
1
0
0
0
3
1
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
2
1
2
2
0
1
0
4
0
0
0
1
0
0
0
1
1
2
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
2
1
2
0
0
0
0
0
0
0
0
2
0
0
0
3
3
0
0
2
2
0
1
0
0
1
0
1
2
0
0
0
0
0
0
1
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
2
1
0
0
1
0
1
0
0
1
0
0
2
0
0
0
0
2
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
2
0
1
1
0
0
1
2
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
4
0
1
2
0
0
1
0
0
0
1
0
1
0
2
2
0
0
0
0
2
0
0
4
0
0
1
2
0
2
1
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
1
2
0
0
1
0
0
0
2
0
1
0
0
1
2
0
2
0
0
0
0
0
0
0
2
0
2
0
0
2
2
1
2
0
0
0
2
1
2
1
1
1
0
1
1
2
1
2
0
2
1
2
0
2
1
0
0
2
0
0
0
1
0
0
0
2
1
0
0
2
0
0
0
2
0
0
1
3
1
0
1
0
0
0
0
1
0
1
0
2
0
0
0
2
1
1
0
0
3
1
0
0
1
0
3
1
1
0
1
0
0
1
0
1
1
1
0
1
1
0
0
1
0
0
0
0
2
0
1
0
0
1
1
0
2
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
2
2
0
0
1
2
2
1
2
1
0
0
0
0
1
0
0
0
1
0
1
2
0
0
0
0
0
1
0
0
2
0
1
2
0
1
0
0
1
1
2
2
2
0
0
2
0
0
2
0
2
0
0
0
1
0
0
1
1
0
0
2
0
0
0
2
2
0
0
2
1
0
1
1
0
0
1
1
0
2
0
0
2
0
2
0
2
2
0
0
1
2
2
1
1
2
0
2
0
1
0
0
1
1
1
0
0
0
1
2
1
1
1
0
0
2
0
1
0
2
1
1
2
0
1
0
0
1
0
1
2
0
0
5
2
0
0
1
1
0
2
0
2
0
1
0
1
2
2
1
1
2
1
3
1
1
0
0
2
1
2
2
0
0
0
0
0
0
1
2
0
2
0
0
0
2
0
2
0
0
0
2
0
0
2
0
0
2
0
1
1
1
0
0
2
0
0
0
0
1
0
0
2
0
1
1
0
0
1
0
4
2
0
0
2
3
1
0
0
0
0
0
0
0
0
1
2
0
0
0
1
2
1
1
0
2
2
4
2
1
0
0
1
0
1
2
0
0
0
0
1
0
1
0
1
0
2
1
1
0
0
2
1
0
0
1
2
0
0
2
2
0
0
2
2
1
0
0
2
1
2
0
1
0
3
1
1
0
0
0
0
0
0
1
0
2
0
1
0
0
0
2
0
0
0
2
0
0
0
2
1
0
0
0
0
0
2
2
0
0
0
1
2
0
0
1
2
0
2
1
0
2
0
2
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
1
1
3
1
0
0
1
2
1
0
0
1
2
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
2
0
0
2
0
1
0
0
0
1
0
0
3
1
2
1
0
0
0
0
1
0
0
0
0
1
1
0
0
2
0
1
2
0
0
0
2
0
1
0
1
4
0
2
0
0
0
0
0
1
0
1
4
1
2
2
0
0
1
1
0
3
4
1
2
0
0
0
0
2
0
2
2
0
0
0
0
0
0
1
0
0
1
0
1
0
0
2
0
2
0
1
0
2
0
0
2
0
4
1
2
0
0
0
0
0
0
0
0
0
1
0
1
2
0
1
0
2
0
2
0
0
1
1
0
0
2
1
0
1
1
0
1
2
0
2
1
0
2
0
2
1
1
0
0
0
1
0
2
1
0
2
2
0
1
2
1
1
0
2
0
2
0
2
0
0
0
2
2
0
0
0
1
2
0
0
0
0
0
1
0
2
2
2
0
0
1
1
0
1
2
1
2
0
0
0
0
2
2
0
0
2
0
3
0
1
1
0
0
1
0
0
0
3
0
0
0
1
3
0
2
2
1
2
0
1
0
2
0
0
2
0
2
1
1
0
0
0
0
0
2
1
0
0
0
0
1
0
2
1
2
0
0
0
1
0
1
1
2
0
1
2
0
2
0
0
0
0
1
0
0
0
2
1
0
1
2
0
0
0
0
2
0
2
0
2
0
2
2
1
0
0
0
1
1
0
0
0
0
3
0
1
0
1
1
1
2
0
0
1
1
1
1
0
1
0
0
2
2
1
0
1
0
1
0
0
2
1
0
0
1
0
1
1
0
0
1
2
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
1
1
0
3
2
1
1
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
1
1
0
2
1
1
0
0
2
1
1
0
2
2
0
1
0
0
2
0
2
0
0
0
1
1
0
1
1
0
0
2
0
1
2
1
0
0
2
0
0
0
2
0
2
0
2
1
1
0
0
0
1
2
0
2
0
0
0
0
0
0
1
2
1
1
0
0
0
0
0
2
0
2
1
0
0
2
0
2
0
1
0
0
0
0
1
0
2
1
1
1
0
0
1
2
0
2
2
0
0
0
2
0
2
1
0
1
0
0
2
0
0
0
0
2
0
0
0
2
1
2
0
0
0
0
0
0
2
2
0
0
2
1
1
1
0
0
0
2
0
2
0
0
0
0
2
0
0
0
1
1
1
0
1
1
0
0
2
1
0
2
0
0
0
2
1
0
0
1
0
2
0
0
0
0
1
0
0
0
2
0
1
1
0
0
2
0
0
0
1
1
2
0
0
1
0
2
2
0
2
0
1
0
0
0
2
1
2
0
1
0
1
2
1
1
0
0
0
0
0
0
2
0
2
2
1
0
0
2
0
0
0
1
0
0
1
1
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
1
1
0
1
0
0
0
2
3
1
0
1
0
1
0
1
0
2
1
1
1
1
1
2
1
0
2
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
1
2
2
0
1
2
0
0
0
2
1
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
1
2
0
0
1
0
4
0
1
0
0
2
0
0
2
0
0
1
0
0
1
1
2
2
2
3
2
0
0
0
0
0
1
0
1
0
1
1
1
0
1
0
2
0
0
0
0
0
1
0
4
0
0
0
0
0
0
2
2
2
0
2
0
0
0
1
0
2
0
3
0
1
3
2
2
0
0
1
1
0
1
0
0
1
0
0
0
1
0
1
2
0
1
0
1
0
0
0
1
0
2
2
0
0
0
1
0
2
0
1
0
1
0
1
2
0
0
0
2
0
0
0
1
2
0
0
0
0
1
0
0
0
1
0
2
1
0
1
0
1
1
1
0
2
0
2
2
2
0
1
1
0
0
0
0
2
1
1
0
0
0
0
0
1
3
0
1
2
0
2
1
0
2
0
2
0
1
0
0
2
1
1
2
0
0
0
0
1
0
0
1
2
0
2
0
0
2
0
1
0
2
0
0
0
1
0
1
0
3
0
1
0
0
2
0
2
0
0
0
2
1
0
2
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
1
1
0
0
0
0
0
1
1
2
1
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
1
0
0
0
1
0
0
0
1
0
2
3
0
0
1
0
0
2
2
0
0
3
2
1
1
0
0
1
0
1
1
0
0
3
0
1
1
14
2
0
2
0
1
2
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
1
2
2
3
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
1
1
1
2
0
1
0
1
2
1
1
1
2
0
0
0
1
0
0
0
0
2
0
1
0
0
3
1
0
1
1
1
2
0
1
1
2
0
0
1
0
1
2
2
2
0
2
0
2
0
1
0
0
1
2
1
2
0
1
2
0
0
2
0
0
2
1
0
0
0
0
1
1
2
1
1
2
0
0
1
0
2
0
0
1
2
0
2
0
0
1
0
0
1
1
1
0
0
0
1
1
1
0
2
0
0
0
0
2
1
0
2
3
1
2
0
0
1
2
1
2
0
2
1
0
0
0
0
2
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
1
1
0
0
0
2
0
0
2
1
1
0
0
2
0
0
1
0
2
2
0
0
0
0
0
1
0
2
2
0
1
0
0
0
1
1
0
0
0
0
0
0
0
3
1
1
0
2
0
0
0
0
1
0
0
3
2
1
2
2
2
0
0
0
0
0
0
1
0
2
2
1
0
2
0
4
0
1
0
1
0
0
0
2
0
2
1
0
1
2
0
2
0
0
0
0
2
0
0
2
1
0
2
3
2
0
1
1
3
0
3
1
2
0
1
0
0
0
0
0
0
1
0
1
2
1
0
0
0
0
1
0
3
0
1
0
1
3
0
2
3
0
0
2
0
1
1
0
0
0
0
2
0
2
1
1
1
0
0
0
0
1
1
0
0
2
0
0
2
0
0
1
0
2
0
0
0
0
1
0
0
1
2
0
1
1
0
0
2
0
2
0
2
0
1
0
0
2
1
0
0
0
2
0
3
0
0
0
2
0
2
0
0
2
1
0
1
2
0
2
1
2
0
0
2
0
0
0
0
0
0
0
1
2
0
0
1
2
0
1
2
0
1
2
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
2
1
1
0
0
0
0
1
0
0
0
2
0
0
2
0
1
0
0
1
1
1
0
0
1
1
2
1
0
1
0
1
0
0
2
0
2
0
0
0
0
2
2
0
0
0
2
0
0
1
1
1
0
0
1
0
1
1
1
1
2
1
1
2
0
0
1
0
0
0
2
0
0
0
2
0
2
1
0
0
0
0
3
0
1
0
0
2
2
1
0
0
2
0
2
1
2
0
2
0
0
0
0
2
0
0
2
0
0
0
2
2
2
0
1
0
1
0
0
1
3
0
0
0
3
4
0
1
0
0
0
0
1
1
0
0
1
0
3
2
0
0
0
0
0
1
1
0
2
2
0
0
0
0
0
1
2
0
2
0
0
2
1
0
0
2
0
2
2
0
0
1
2
0
1
0
1
0
0
0
0
1
0
1
0
0
0
1
1
0
0
1
2
2
0
2
0
1
0
1
1
2
0
0
0
0
0
0
2
0
2
1
2
0
2
0
0
2
1
0
0
2
0
1
0
1
1
1
1
1
0
0
1
0
2
0
0
0
1
0
0
2
0
0
1
2
0
2
1
1
0
2
0
2
1
0
0
0
2
0
1
1
2
2
0
0
2
1
2
0
0
1
1
0
0
0
0
0
1
2
0
2
1
1
1
2
2
0
0
1
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
2
2
0
0
1
0
0
0
0
2
1
0
1
2
1
1
2
0
0
0
0
0
1
2
3
0
0
2
0
0
2
0
1
1
0
0
0
1
2
0
0
3
0
0
0
0
1
2
0
0
1
0
0
1
0
1
0
0
0
0
0
2
0
1
0
1
1
1
0
0
1
2
2
0
1
0
1
0
0
0
0
0
0
2
0
1
3
2
2
1
0
0
0
1
0
0
0
0
2
2
0
0
0
0
1
0
0
1
0
0
1
2
2
0
1
0
0
2
0
0
0
0
2
1
0
2
3
2
2
0
1
0
3
2
0
0
1
2
2
1
0
0
2
0
1
1
0
0
0
1
1
1
0
2
2
1
1
1
2
0
0
4
2
1
1
1
2
1
0
2
0
1
1
0
0
0
0
0
2
0
1
0
2
0
0
0
0
2
0
1
1
0
1
0
2
1
1
0
2
0
1
0
0
2
0
8
0
0
1
0
1
0
2
0
0
2
1
0
1
0
1
0
1
1
2
1
0
0
2
1
1
0
0
0
1
1
1
1
0
1
0
0
0
0
0
0
0
0
0
2
1
0
2
2
0
0
1
0
1
1
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
2
1
2
0
0
0
0
2
0
0
1
0
1
0
1
0
0
0
0
2
0
1
0
0
0
1
0
2
0
0
2
2
2
0
1
0
0
0
1
1
0
0
0
1
1
1
2
2
1
2
0
0
1
0
2
0
2
2
1
0
1
0
0
0
0
0
2
1
1
0
1
2
1
0
2
0
1
1
1
1
2
2
0
0
1
2
1
0
0
1
0
0
0
2
2
1
1
1
0
0
2
0
2
0
0
0
2
2
1
0
0
0
0
2
2
0
1
0
0
0
0
1
1
1
2
0
2
0
0
0
0
1
0
0
2
5
0
0
1
0
0
1
0
0
1
2
2
0
2
2
2
0
0
0
1
0
2
0
2
1
0
1
0
2
0
1
0
0
2
0
2
0
0
2
2
0
1
2
0
0
2
2
1
1
1
0
0
0
0
0
2
2
1
0
1
1
2
0
2
1
0
2
1
0
1
0
1
0
1
0
0
0
3
0
0
0
0
0
0
2
1
3
0
1
0
0
2
0
2
0
2
1
0
0
0
1
0
1
2
0
0
0
1
2
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
2
0
0
0
0
0
1
2
0
0
0
0
0
1
0
1
0
0
0
1
0
1
1
0
1
0
2
0
0
0
0
1
0
0
0
2
1
1
0
0
2
1
0
1
1
0
1
0
0
2
1
0
1
2
1
0
0
0
0
2
2
0
1
2
2
5
2
2
0
1
1
1
3
0
0
2
0
0
2
0
1
0
1
2
0
0
0
0
0
1
2
0
1
0
0
0
2
1
0
0
0
0
4
1
1
1
2
0
0
2
1
0
1
0
3
0
0
1
1
0
0
0
1
0
1
1
1
3
0
0
1
2
2
0
1
2
1
0
3
0
2
1
0
0
0
2
2
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
2
0
1
2
0
0
2
0
1
1
0
0
0
1
1
0
2
2
0
2
1
0
0
0
0
0
0
0
2
2
0
1
1
0
0
1
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
2
2
0
0
0
2
0
0
0
1
1
1
1
1
0
0
0
1
0
0
1
0
1
0
2
2
0
0
0
2
0
2
0
0
1
0
1
2
0
1
0
2
1
0
1
0
1
1
0
2
1
0
0
0
0
0
0
1
0
0
1
0
2
2
0
0
0
0
1
0
2
0
0
2
1
1
0
1
1
1
0
2
0
1
0
0
0
0
0
0
0
1
4
1
0
0
1
2
0
1
2
1
0
0
1
0
4
0
2
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
2
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
2
0
3
1
1
0
2
4
0
0
0
1
0
1
0
2
2
0
0
0
0
1
1
1
2
0
0
1
1
0
2
0
1
0
0
1
0
1
2
0
2
0
2
2
1
1
1
0
1
2
1
2
0
2
2
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
2
1
0
0
0
1
0
2
1
3
0
0
0
0
1
2
0
1
0
2
0
3
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
2
0
0
1
1
1
2
1
0
2
0
0
2
0
0
0
1
2
0
0
1
3
2
0
3
0
1
0
0
1
0
2
1
0
0
0
1
0
2
1
0
2
1
0
2
0
0
1
3
2
0
2
2
0
0
1
0
1
1
0
1
0
3
2
0
0
2
0
2
0
2
0
0
3
1
2
1
0
2
0
0
0
2
0
0
0
1
2
1
0
2
1
1
0
0
0
2
1
1
0
1
0
2
0
0
0
1
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
2
1
1
0
1
1
1
0
1
1
0
1
2
2
0
0
0
2
1
0
1
0
0
0
2
0
0
2
0
2
0
2
2
1
0
1
0
0
2
1
0
0
1
0
1
0
0
0
0
1
1
0
2
2
0
0
0
1
0
1
0
1
1
1
0
0
0
0
1
1
1
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
2
0
0
2
1
1
2
0
2
1
0
0
2
1
0
0
0
0
0
2
1
0
0
0
0
1
1
2
1
2
0
1
3
0
1
2
0
0
0
2
0
0
0
1
2
0
0
0
2
0
1
0
3
1
0
0
0
0
1
0
0
2
0
0
0
0
2
2
2
0
2
0
0
0
1
0
0
1
0
2
1
0
1
1
0
0
0
2
0
1
1
0
2
1
0
1
1
1
0
2
0
1
1
0
1
0
0
0
0
1
0
1
0
0
1
1
2
2
0
2
0
1
0
2
0
2
0
0
2
2
0
2
1
0
1
0
1
1
1
0
2
1
2
0
1
0
0
0
0
0
0
1
2
2
1
0
1
1
0
0
6
1
0
0
0
1
0
2
1
2
0
0
0
0
0
0
0
1
0
2
1
0
0
1
2
0
0
0
3
2
0
2
0
0
0
1
0
1
1
0
2
1
0
0
1
0
1
0
0
1
1
1
2
0
0
0
0
0
1
0
1
0
0
0
0
0
2
1
1
0
0
0
2
0
0
2
0
0
0
0
0
2
1
1
1
1
0
0
2
2
0
2
0
2
1
2
1
2
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
3
0
1
2
0
0
0
0
0
1
0
2
0
1
0
2
2
0
1
0
0
1
0
0
0
0
0
2
1
2
0
1
0
1
0
0
0
0
1
0
1
0
0
1
1
0
2
1
0
2
0
3
0
0
1
2
1
0
2
0
1
0
0
0
1
0
0
0
2
1
3
1
2
2
2
0
0
1
0
0
0
0
1
0
0
2
0
2
2
0
2
1
0
1
0
1
0
1
0
5
0
0
0
1
0
0
2
1
2
2
2
0
0
1
0
1
2
0
2
1
1
2
2
2
0
2
0
0
0
0
0
0
1
0
3
0
0
0
1
2
2
1
0
0
1
2
0
1
0
0
0
2
1
0
0
0
1
0
1
0
1
0
0
3
0
0
0
0
2
0
2
2
0
0
0
0
1
1
0
1
0
0
0
1
2
0
1
1
1
5
1
0
0
0
0
0
2
0
0
2
3
0
0
0
0
0
2
1
1
1
0
2
1
2
1
2
8
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
4
3
0
0
2
3
0
1
2
0
1
1
0
0
0
0
1
0
1
1
1
0
0
0
1
0
0
1
0
0
2
0
0
1
0
1
0
0
1
0
2
1
2
0
1
2
5
0
0
2
0
1
1
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
2
0
0
1
0
0
0
1
0
0
2
1
0
1
0
0
0
0
1
2
2
2
1
0
0
1
2
1
1
2
0
0
2
0
2
3
0
0
0
0
0
3
0
0
0
0
0
2
0
1
1
0
0
0
1
1
1
0
0
0
2
0
1
1
0
0
0
2
2
0
1
2
0
1
0
0
0
0
0
1
2
2
0
0
0
1
0
1
0
0
2
1
2
0
2
1
0
0
0
0
2
1
0
0
0
1
1
0
0
0
0
0
1
0
1
0
2
2
0
0
0
0
1
1
7
0
0
0
0
2
1
0
0
0
0
0
0
7
0
2
0
0
0
1
1
2
0
0
0
0
2
2
0
2
0
0
0
0
2
1
2
0
0
0
2
0
2
1
1
0
0
0
2
1
1
0
2
0
0
1
2
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
1
2
0
0
0
1
2
1
1
0
1
1
1
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
2
2
2
1
0
1
2
4
0
2
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
2
1
0
0
1
0
0
0
2
0
1
0
0
0
0
1
0
1
0
2
0
0
1
2
0
0
1
1
1
0
2
0
0
0
2
0
2
0
0
1
4
0
0
2
0
2
0
0
0
2
0
0
2
0
3
0
1
0
1
2
1
1
0
0
0
0
2
1
0
0
0
1
2
1
0
2
0
1
0
0
2
0
0
1
0
2
1
0
0
0
1
0
1
1
0
1
1
1
0
1
2
0
0
1
0
1
0
2
1
1
2
0
1
1
0
0
0
2
1
2
0
0
1
1
0
2
1
0
0
2
1
0
3
0
0
1
0
1
0
1
0
0
0
2
0
1
0
0
1
1
1
0
0
0
0
0
1
1
1
3
2
0
1
0
0
2
2
2
0
0
1
0
0
1
0
0
2
2
0
1
0
0
0
0
0
0
0
1
1
1
1
0
0
1
0
0
2
1
0
2
2
1
0
0
0
1
0
2
0
0
0
2
1
2
0
0
2
0
0
1
0
0
1
0
3
0
0
0
1
1
0
0
0
0
0
0
0
2
2
0
0
0
1
1
1
0
1
0
1
2
0
0
1
0
1
0
1
1
2
0
2
0
0
0
0
0
1
0
1
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
2
0
0
1
1
0
2
1
1
1
0
0
0
2
0
1
0
1
1
1
0
0
1
2
1
0
2
0
0
1
3
2
0
0
1
0
0
1
0
0
0
0
0
1
2
0
1
1
1
1
2
1
0
0
0
1
2
2
1
0
0
0
1
0
0
0
0
1
1
0
2
0
1
0
0
2
1
2
0
0
3
0
0
0
0
2
2
0
1
2
2
0
0
2
0
0
0
1
0
0
1
1
0
1
0
1
2
0
0
0
1
0
1
1
0
0
1
2
0
1
1
0
0
0
0
0
0
0
1
2
0
0
2
0
0
1
1
1
1
0
0
1
1
0
0
0
1
0
0
2
1
1
1
0
1
0
0
3
0
0
0
1
0
2
2
1
0
1
0
1
1
1
0
0
1
0
0
0
1
1
2
0
1
0
0
0
1
0
0
1
2
2
2
0
1
1
2
0
0
1
0
1
0
1
1
2
1
0
2
0
0
0
0
0
2
2
0
0
0
0
1
2
0
1
1
3
1
2
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
1
1
1
1
0
0
0
2
0
1
0
0
0
2
0
2
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
1
2
2
0
2
1
0
3
1
0
1
7
2
2
1
0
0
1
1
0
1
0
0
0
2
1
1
1
0
1
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
5
2
0
0
0
1
0
0
1
2
0
2
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
2
2
0
2
0
0
1
1
0
1
2
0
0
0
2
0
1
0
0
2
0
1
0
1
3
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
1
0
2
2
0
2
0
0
0
5
1
2
1
1
1
2
0
2
0
1
2
0
2
2
0
2
0
1
0
0
1
2
0
2
0
1
0
0
2
0
1
2
0
0
2
0
0
0
0
0
0
1
0
1
0
0
2
1
0
2
2
2
0
0
2
2
1
0
0
2
0
0
0
0
2
1
0
0
0
0
2
0
1
1
2
1
2
0
1
0
1
0
2
1
2
2
1
0
0
2
0
0
2
0
0
0
2
0
0
1
1
0
0
0
0
1
0
0
1
2
0
0
0
0
0
4
2
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
2
1
0
1
1
0
2
2
1
0
1
0
2
0
1
1
1
0
1
0
0
1
0
1
2
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
3
0
0
0
1
1
0
1
2
0
2
2
0
0
2
0
0
1
0
0
2
0
0
0
2
0
2
2
0
1
2
0
0
0
2
1
0
0
2
1
3
1
3
1
1
0
0
0
1
0
1
0
1
2
2
1
1
0
2
1
0
2
1
0
2
2
0
0
0
0
2
0
2
1
1
2
0
1
0
0
0
0
2
0
0
0
2
1
2
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
1
0
2
2
0
0
0
0
0
2
1
1
4
2
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
1
0
1
0
0
1
0
0
0
0
0
0
1
2
0
1
0
2
0
0
0
0
0
1
0
1
1
0
3
0
0
1
1
0
0
0
1
1
0
0
0
2
0
0
0
2
0
2
1
0
0
0
0
2
1
1
0
0
1
0
2
0
2
0
1
2
2
0
0
0
0
0
0
0
0
0
1
2
0
1
2
0
0
1
2
1
0
0
0
0
2
1
0
0
0
0
2
0
0
0
1
2
2
0
0
2
0
0
2
1
1
1
0
1
1
2
0
1
1
2
0
0
0
1
1
0
0
1
1
2
0
0
0
1
2
0
1
0
0
0
2
0
1
2
1
2
1
2
2
2
0
0
0
1
2
0
0
0
0
5
0
0
1
0
1
0
2
0
0
1
0
0
2
0
0
1
0
0
0
0
0
2
5
0
0
0
2
2
4
0
1
0
2
1
2
0
1
1
0
0
0
2
2
0
2
1
0
0
0
0
2
0
0
0
0
1
0
2
1
0
1
0
1
1
0
2
0
0
3
1
0
1
0
0
0
2
0
2
0
0
2
2
0
0
0
0
2
2
2
1
0
2
1
2
2
0
0
0
1
2
1
1
0
5
2
0
0
0
2
0
1
0
2
0
0
0
0
1
1
0
2
0
0
0
1
0
1
0
0
0
2
0
0
1
1
0
0
2
0
0
0
0
2
0
1
0
0
1
0
0
2
0
2
0
1
0
0
1
1
1
0
1
1
1
2
0
2
0
2
2
0
1
0
2
0
1
0
1
0
1
3
3
1
1
0
1
0
0
0
2
0
0
0
0
0
1
1
1
0
0
0
0
2
0
0
0
0
2
1
1
1
0
0
0
0
1
1
0
4
0
0
3
0
1
0
1
0
0
2
0
0
2
1
0
0
1
0
0
1
0
0
0
0
1
1
0
2
0
2
0
1
0
0
2
1
2
2
0
0
2
1
0
1
1
0
0
3
1
1
0
1
1
0
1
1
0
0
1
0
0
0
0
2
0
2
2
0
2
0
1
1
0
1
1
0
0
0
1
0
0
0
2
0
0
0
1
2
1
0
0
0
1
0
1
1
0
2
0
0
0
0
0
0
1
0
0
0
2
0
1
1
2
1
1
0
0
2
0
0
0
1
2
1
0
0
0
1
0
0
1
1
0
0
3
0
0
0
0
0
0
0
1
0
0
1
0
2
1
0
0
0
1
0
0
2
0
0
2
0
0
1
0
0
0
0
2
1
2
0
4
0
2
1
1
1
0
2
0
1
2
0
2
0
0
2
0
1
0
1
1
1
0
0
1
0
0
0
2
1
0
0
0
0
0
1
0
5
1
0
0
1
1
2
2
1
0
2
1
0
0
1
0
0
1
1
3
0
2
0
0
1
0
2
0
2
1
0
0
0
2
1
1
0
2
1
2
0
1
0
2
1
0
0
1
0
2
0
0
1
2
0
0
0
1
1
0
0
1
3
0
0
1
1
2
0
2
0
0
0
0
1
1
0
2
3
0
0
2
0
0
0
0
1
1
0
1
0
0
2
0
0
2
1
0
1
2
1
2
2
0
2
0
0
2
0
0
0
1
2
0
0
0
3
0
1
3
0
0
0
0
2
2
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
2
0
2
0
2
0
2
1
0
0
0
0
0
1
0
1
3
3
1
0
0
1
1
0
0
2
0
0
2
2
1
0
0
0
0
0
0
0
0
0
2
3
1
0
0
1
2
0
0
1
2
1
0
2
0
0
0
1
0
1
0
0
0
2
2
0
0
0
1
0
0
0
0
0
2
2
0
0
0
7
0
0
2
0
0
0
0
2
0
0
1
0
0
1
0
1
1
0
2
0
0
1
0
0
0
0
3
0
0
2
2
0
0
0
2
0
0
0
0
2
0
2
2
0
2
2
1
0
2
0
1
0
0
0
2
2
0
1
2
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
1
2
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
1
1
1
0
1
1
0
2
1
2
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
1
1
1
0
1
2
0
0
2
0
0
0
0
0
0
0
1
0
0
2
2
1
2
2
0
0
0
0
0
0
0
2
1
0
1
0
0
1
0
1
2
0
0
0
1
0
0
0
1
0
2
0
2
1
1
1
0
0
0
0
1
2
1
0
0
2
0
0
1
1
0
0
2
0
0
0
0
2
0
0
1
0
0
2
0
1
3
5
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
2
1
2
0
0
0
1
0
1
1
0
1
1
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
1
0
0
0
2
0
1
1
1
0
2
0
1
1
0
1
0
1
2
1
1
2
0
0
0
1
0
0
2
2
0
2
1
0
0
0
0
1
2
0
1
0
0
0
0
3
0
0
2
2
1
0
2
1
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
1
0
1
0
0
0
2
2
1
0
0
3
0
1
0
0
1
0
0
0
0
0
1
0
0
0
2
3
1
1
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
1
0
1
2
3
0
2
0
2
1
1
2
0
0
0
1
2
0
2
0
0
1
0
0
1
0
2
2
1
1
0
2
0
1
1
0
0
0
2
1
0
1
0
1
0
2
1
0
1
1
1
0
0
0
2
1
0
0
0
1
0
1
1
2
0
3
0
0
0
1
1
2
0
1
0
1
1
1
0
0
1
0
1
0
2
1
5
0
0
2
1
0
0
1
0
0
2
2
2
0
2
2
0
2
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
2
2
0
0
2
1
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
1
2
0
0
1
2
1
1
1
0
1
2
1
0
1
0
0
0
0
2
0
2
0
0
0
1
1
0
0
2
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
2
0
0
0
0
1
0
0
2
0
0
2
2
0
0
0
2
0
0
1
0
2
0
0
0
2
0
1
0
0
1
3
1
3
1
1
0
1
0
0
0
1
1
1
1
1
0
0
0
0
2
2
1
0
2
0
1
1
2
1
0
1
0
0
2
2
2
0
2
0
0
0
0
0
0
0
0
1
0
2
1
1
2
0
0
0
0
0
0
1
0
1
0
0
2
0
0
1
2
1
0
2
1
0
2
4
0
0
0
0
0
0
0
0
0
2
1
2
0
0
1
2
1
1
0
1
0
2
1
0
0
1
0
1
1
0
0
0
1
2
3
0
0
0
2
1
0
1
1
3
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
2
0
0
1
0
0
1
1
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
1
0
2
1
0
1
2
0
0
2
1
1
0
0
0
1
1
2
2
2
1
1
2
1
1
0
0
0
1
0
2
0
1
0
2
2
1
0
0
0
0
0
0
1
1
2
2
0
2
0
0
2
0
0
0
1
2
0
1
1
1
1
0
0
2
1
0
0
0
2
0
2
2
1
2
1
0
0
0
0
2
0
0
0
1
2
9
0
1
0
0
1
2
1
0
0
4
1
0
0
2
0
4
0
0
0
0
0
0
1
0
0
0
1
0
1
2
1
0
0
0
0
2
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
3
0
2
1
1
3
1
2
1
2
4
0
1
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
1
0
2
0
0
0
2
0
1
0
0
1
0
1
1
0
0
1
0
1
2
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
2
1
0
3
0
1
0
1
1
0
1
1
0
0
0
1
2
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
1
1
0
1
0
0
2
1
1
0
1
0
0
2
2
0
0
0
0
2
0
0
1
0
1
0
0
0
2
1
0
1
1
1
0
2
0
1
0
0
1
1
1
1
0
1
1
0
2
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
2
0
0
0
2
2
0
0
2
0
0
1
0
2
1
1
0
0
1
0
0
2
0
2
1
0
1
1
0
1
0
0
1
0
2
0
0
1
0
0
1
0
0
0
0
2
1
1
1
2
0
0
0
0
0
0
1
1
1
0
0
0
0
1
2
0
0
0
0
2
0
2
1
0
0
1
4
0
1
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
1
0
2
1
2
2
1
0
0
0
0
0
2
0
0
0
2
1
2
0
0
0
0
2
0
0
2
1
0
0
1
0
3
2
2
1
0
0
1
1
0
1
0
4
0
1
0
0
0
0
1
0
0
2
1
2
2
0
0
2
0
2
0
0
0
0
1
1
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
1
2
2
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
1
0
0
0
0
1
1
0
0
2
0
0
0
0
0
2
1
1
1
0
2
0
0
2
2
0
1
0
0
2
2
0
1
0
0
0
3
0
0
0
0
1
0
2
0
1
0
0
1
2
1
1
0
1
2
1
2
0
0
2
0
0
0
0
0
0
1
1
0
0
2
2
0
2
0
2
1
0
2
0
0
0
1
1
0
0
1
4
3
0
1
2
1
0
1
2
0
0
1
0
2
0
1
0
0
2
0
0
0
2
0
0
0
0
1
0
2
2
0
0
0
0
0
0
1
2
0
2
1
1
1
2
1
0
0
0
0
0
0
0
2
0
1
1
0
2
0
0
0
0
0
0
2
2
0
1
0
2
3
0
0
1
0
3
1
1
2
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
2
0
2
0
1
1
2
2
1
1
0
1
1
0
0
0
2
2
1
0
0
0
2
0
1
1
0
1
0
0
1
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
1
2
0
1
0
0
0
2
2
0
0
1
0
1
2
2
1
1
0
0
2
1
0
0
0
0
0
0
1
2
1
2
0
2
2
1
2
2
2
1
2
1
0
0
1
1
1
1
0
1
0
2
1
2
0
2
0
0
1
1
0
2
0
1
0
0
0
0
0
1
2
0
1
0
0
0
0
1
1
0
0
0
0
2
0
2
1
2
0
2
0
0
0
0
2
0
0
0
0
0
2
1
2
1
0
0
0
1
0
1
1
1
1
2
0
0
0
2
1
0
2
0
1
1
0
0
0
0
0
0
0
2
0
1
2
2
1
2
0
0
1
0
0
3
0
0
0
0
2
2
1
1
0
0
0
0
2
1
0
0
0
0
0
1
2
0
0
0
2
0
0
0
2
2
1
0
0
0
2
2
1
0
1
0
0
0
0
0
3
0
1
0
0
1
2
0
0
2
0
0
1
2
0
1
0
0
0
0
2
1
0
0
0
0
0
2
2
0
1
2
0
0
0
1
1
0
1
1
0
2
1
2
1
0
2
0
0
0
0
0
0
2
1
1
0
0
0
2
2
0
1
1
1
0
0
0
1
1
1
6
0
1
2
0
0
1
0
0
0
0
2
1
1
3
1
1
2
1
0
1
0
1
1
0
0
0
0
0
0
2
0
2
0
0
0
1
0
2
1
0
0
2
0
1
0
1
0
0
0
1
0
1
1
0
1
1
1
0
0
1
1
0
2
1
1
0
1
2
1
0
0
0
2
2
1
0
0
2
1
1
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
2
1
0
0
1
0
2
1
0
1
1
4
2
1
1
0
1
1
2
1
0
0
1
1
1
1
4
0
0
0
1
0
2
0
2
0
0
0
2
2
0
0
2
1
0
0
0
0
0
0
1
0
0
3
1
0
0
2
1
2
1
2
0
2
2
1
1
0
0
1
1
0
0
2
1
0
1
0
1
0
0
0
2
1
2
0
0
2
0
1
0
0
1
1
0
0
2
1
3
1
1
1
0
2
0
1
1
1
0
0
2
1
2
0
3
0
0
2
1
0
0
3
0
1
2
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
1
1
0
0
0
2
0
2
0
0
1
2
0
0
0
0
2
0
1
0
0
0
1
2
0
0
0
0
1
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
3
1
0
0
0
1
2
0
0
1
0
0
1
2
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
2
1
0
0
1
2
1
0
0
0
0
0
2
0
4
1
0
2
2
0
0
0
0
1
2
1
0
0
0
0
2
2
0
0
2
2
0
0
2
0
1
0
2
2
0
1
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
1
0
0
2
4
1
0
0
0
1
1
0
1
0
1
0
0
0
1
1
0
1
0
2
1
3
2
1
2
0
2
1
0
0
0
2
0
1
1
0
0
1
0
3
1
1
0
0
0
0
2
2
1
2
1
0
1
0
1
2
0
0
1
1
0
0
1
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
2
0
3
0
0
2
3
0
0
0
1
1
1
1
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
3
0
0
1
0
1
0
0
0
2
0
1
0
3
0
1
2
0
1
0
0
1
0
0
1
1
0
0
0
2
0
0
0
0
2
2
1
1
0
0
2
2
1
2
0
0
0
0
0
1
0
0
2
1
0
0
2
0
1
0
1
1
0
0
1
0
0
1
2
0
0
2
0
1
1
1
0
2
2
1
2
2
2
2
0
0
1
2
1
0
1
2
1
0
2
3
1
0
0
0
0
0
2
0
2
1
0
0
2
0
2
1
0
2
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
2
1
1
2
1
2
0
0
3
0
2
1
0
0
0
2
2
0
3
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
2
1
0
0
1
0
0
0
0
0
1
0
2
2
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
1
0
0
2
2
1
0
0
0
2
0
1
0
2
2
0
1
0
1
0
1
0
0
0
1
0
0
2
2
0
1
2
1
1
0
2
0
0
0
1
0
0
0
0
1
0
2
0
2
0
0
0
2
1
0
1
2
2
1
0
1
2
0
0
0
0
1
1
2
1
0
0
0
3
0
0
2
0
0
2
2
1
2
0
1
3
0
1
0
0
0
1
0
2
0
0
0
0
0
1
0
2
0
3
0
1
1
1
0
2
0
0
0
0
2
0
1
0
0
2
1
0
0
1
2
0
1
1
0
0
2
2
0
0
3
0
2
0
0
0
0
1
3
1
2
2
2
0
0
1
0
1
1
0
2
2
1
1
0
0
2
0
1
1
0
0
2
0
2
0
0
0
0
2
0
0
1
0
1
0
2
2
2
0
2
0
0
2
1
0
1
1
0
0
0
0
0
2
2
2
0
0
5
0
1
0
0
2
0
3
0
2
0
0
1
0
1
1
0
1
1
3
0
0
1
0
0
0
1
2
0
0
0
0
1
2
2
0
1
0
0
0
2
0
0
2
2
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
1
0
1
1
1
0
2
0
1
2
0
0
0
0
0
0
0
0
2
2
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
2
1
1
0
2
1
0
0
0
1
1
0
0
0
2
0
0
0
2
0
0
1
1
2
0
1
1
3
0
2
0
1
2
1
1
0
0
0
1
0
1
0
0
0
1
3
0
0
2
0
5
1
2
1
0
0
0
1
0
1
1
2
2
1
2
1
0
0
0
0
1
0
0
0
4
1
1
0
0
0
0
0
1
0
0
2
2
0
1
2
0
2
1
0
1
1
0
0
0
2
0
0
0
2
0
0
1
0
2
0
0
0
0
0
1
1
0
1
2
2
0
2
3
1
0
1
1
1
1
0
0
3
0
0
0
1
2
1
0
0
1
0
0
0
2
0
0
0
0
0
1
1
0
1
1
0
1
1
1
1
1
2
0
2
1
1
1
9
1
0
0
0
0
1
2
1
2
2
1
0
1
0
1
1
1
0
0
2
1
1
0
1
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
2
0
1
0
0
1
0
2
0
0
2
0
0
3
2
1
0
0
0
0
2
0
0
2
0
1
0
2
0
1
0
1
0
0
0
1
2
0
1
1
1
0
1
2
2
0
0
0
0
0
0
0
0
1
0
0
2
1
1
0
0
1
0
0
0
2
2
0
1
0
0
0
0
2
2
1
2
0
0
0
0
0
0
0
1
1
0
1
1
1
1
1
1
1
0
0
1
1
0
0
0
0
0
0
0
0
2
2
2
0
0
2
0
0
0
0
0
0
0
0
2
1
0
1
2
1
0
0
0
1
2
1
2
2
1
2
2
0
1
0
0
1
0
0
1
1
0
2
0
0
2
0
1
0
1
2
1
1
0
2
0
2
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
1
2
2
0
0
2
0
1
1
2
0
2
1
1
2
0
0
0
0
0
0
0
1
0
2
2
0
1
0
2
1
0
0
0
0
1
0
2
0
0
2
0
2
0
0
1
1
0
2
2
1
3
1
0
1
1
1
1
0
0
1
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
2
0
1
0
1
1
2
0
1
0
0
6
0
2
1
0
1
0
0
2
2
1
0
0
0
0
1
2
1
1
1
2
0
0
0
2
0
1
0
0
1
0
0
0
1
0
2
0
0
0
1
0
0
2
0
1
0
0
2
0
0
1
0
0
0
0
1
0
0
0
3
0
0
1
0
2
2
2
1
0
1
0
0
1
0
2
1
0
1
1
1
0
0
2
1
0
2
3
0
1
0
0
0
1
0
1
0
0
1
1
2
0
0
2
0
2
0
2
0
0
2
0
1
1
3
0
1
0
0
1
1
1
2
0
0
2
0
0
0
2
0
0
0
1
2
1
2
3
0
0
1
0
0
2
0
0
1
0
0
0
2
2
0
1
3
1
2
1
2
0
1
0
1
4
0
0
2
3
0
2
0
1
2
3
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
2
0
1
1
0
0
0
2
0
1
1
1
2
0
1
2
2
0
2
1
0
0
0
1
4
2
1
3
0
2
0
2
0
1
1
1
0
1
1
0
1
0
0
1
0
0
2
0
2
0
2
0
1
0
1
2
0
1
2
1
3
1
2
2
0
1
0
0
1
1
0
0
2
1
0
0
3
1
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
2
0
0
1
0
1
1
2
3
2
2
2
1
1
1
0
2
1
0
1
2
2
1
0
0
0
0
1
1
1
1
0
0
2
0
0
0
0
1
0
2
1
1
0
0
1
2
0
1
0
1
0
1
0
0
0
1
0
1
2
1
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
2
0
2
1
1
2
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
2
0
0
1
0
0
2
1
1
0
0
0
1
0
0
0
2
9
0
1
0
0
0
0
2
1
1
2
0
0
0
0
0
1
0
1
0
0
0
2
0
0
1
0
0
1
2
1
2
0
0
0
0
0
2
1
1
0
2
1
0
2
1
0
1
0
2
1
0
0
1
0
0
2
2
0
2
0
0
1
1
1
0
2
1
1
0
0
1
1
0
0
2
0
1
0
0
0
1
0
0
0
2
1
1
1
0
0
0
0
1
2
0
2
0
0
1
2
0
0
0
0
1
0
0
1
1
1
2
0
1
1
1
0
2
2
0
0
1
0
0
0
0
2
0
0
0
2
0
2
1
0
0
1
2
2
0
1
1
0
0
1
0
0
1
1
1
0
2
2
1
0
4
2
0
0
1
0
1
0
1
1
0
0
0
0
0
1
1
0
0
1
2
1
0
0
1
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
1
0
1
0
0
1
0
0
0
6
0
0
0
0
0
1
0
2
2
0
0
0
1
0
2
1
0
0
1
1
0
1
0
1
0
0
1
0
1
1
0
2
2
1
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
6
1
1
1
1
0
1
6
0
0
2
1
2
0
0
1
2
2
0
0
0
0
1
1
2
1
1
0
1
2
1
2
2
0
0
0
1
0
0
1
2
0
1
0
0
1
2
2
0
0
0
2
1
2
2
1
1
0
0
0
1
1
0
1
0
1
0
2
2
2
1
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
3
1
0
0
0
0
2
2
0
2
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
1
0
0
4
1
0
0
1
2
1
0
0
1
0
0
0
0
1
0
0
2
0
0
2
0
0
2
1
0
1
0
1
0
0
1
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
1
1
2
0
0
0
0
0
0
2
0
2
0
0
0
2
0
1
0
0
0
0
1
0
0
1
0
2
0
0
3
0
0
2
0
2
0
2
1
1
0
0
1
0
0
0
0
1
0
1
1
0
1
0
0
0
2
2
0
0
2
2
0
0
1
0
1
0
0
1
1
1
2
0
0
0
0
0
2
0
1
0
0
1
1
0
0
0
0
0
1
1
0
0
2
2
0
0
1
1
0
2
0
0
1
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
1
0
0
0
0
0
2
1
1
0
0
2
0
0
0
0
0
1
2
0
0
0
1
2
0
0
2
1
0
1
1
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
3
0
1
1
0
0
0
2
0
1
0
2
2
0
1
0
1
0
2
1
0
2
1
2
0
2
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
1
1
0
0
1
0
0
0
1
2
2
0
0
1
1
2
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
2
0
2
2
1
2
2
0
0
0
0
1
1
2
0
0
0
2
1
0
1
0
1
0
0
1
1
0
1
2
1
1
0
1
2
1
0
2
0
1
1
0
0
0
1
0
6
0
0
1
1
2
2
0
0
0
2
1
0
7
1
2
0
1
0
0
0
0
2
0
0
0
0
0
2
1
1
0
0
0
1
1
1
0
0
1
0
2
0
3
0
1
2
0
0
0
2
0
0
0
0
0
1
2
0
2
0
2
0
2
0
0
0
0
2
0
0
1
0
0
0
1
2
0
0
2
0
1
0
0
2
1
0
1
0
1
2
0
1
0
1
0
1
2
2
2
1
0
2
2
0
0
0
0
1
0
0
2
1
0
1
2
0
0
2
0
0
1
0
0
0
1
0
0
1
2
2
0
1
0
1
0
0
1
0
0
0
0
2
0
2
0
1
0
0
1
1
2
1
0
1
1
1
0
0
1
0
0
0
1
2
0
0
0
1
0
1
2
0
1
2
0
0
0
0
0
2
0
0
2
2
1
0
1
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
3
1
1
2
1
0
2
2
0
0
0
1
1
1
2
1
0
0
1
0
0
0
0
2
2
1
1
0
1
0
0
2
0
1
0
0
1
1
2
0
0
0
0
1
0
1
1
1
0
2
2
0
0
0
2
0
0
0
2
0
0
2
1
0
1
1
1
0
0
0
0
1
0
2
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
1
0
1
1
1
1
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
2
2
0
1
1
0
0
0
1
2
0
0
0
2
0
0
1
0
0
1
1
2
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
1
1
0
2
2
0
2
1
2
0
0
0
2
0
2
2
0
0
1
0
0
0
0
2
0
0
1
0
1
1
0
0
1
0
1
0
2
0
0
2
0
0
5
0
0
0
0
0
2
2
0
1
0
0
1
0
0
0
0
0
1
0
2
1
0
1
2
1
0
0
0
0
2
0
0
0
0
2
0
1
0
2
0
0
3
0
0
0
1
2
1
0
1
1
0
0
2
1
0
2
0
0
2
2
2
0
0
0
0
1
1
3
0
0
2
0
1
2
1
2
3
1
1
0
0
2
0
0
0
0
2
2
0
0
0
10
1
0
1
1
0
0
0
0
0
0
2
0
2
1
0
2
0
0
1
0
0
1
1
0
0
0
1
1
0
2
1
1
0
0
1
0
0
0
1
1
1
0
1
0
0
0
0
1
0
3
0
0
2
0
2
0
1
0
1
0
0
1
0
1
2
0
1
1
0
0
1
1
3
1
0
1
1
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
1
0
0
4
0
0
1
2
0
0
2
2
2
0
0
1
2
0
0
0
3
0
0
2
2
0
0
1
2
1
2
1
0
0
1
0
0
2
1
1
0
0
0
1
0
0
0
0
1
1
0
0
0
2
0
1
2
0
0
2
1
3
0
0
0
1
2
1
1
1
2
0
0
0
2
2
0
0
1
0
2
0
0
0
20
2
0
3
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
1
2
0
0
1
0
2
1
0
0
0
0
0
0
0
0
1
0
3
2
0
0
2
0
0
0
1
0
2
1
1
0
1
1
2
0
2
0
2
0
0
0
0
0
0
0
2
1
0
1
1
2
0
0
1
0
2
0
0
2
1
2
2
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
1
1
1
0
0
1
0
0
1
2
2
4
2
0
1
0
1
1
2
0
1
0
0
1
1
1
0
0
2
1
2
1
1
1
1
0
0
0
0
0
2
0
1
2
1
1
0
1
1
0
2
0
2
0
0
0
0
0
2
0
2
2
2
0
0
1
2
0
0
2
1
1
2
1
0
0
1
0
2
1
0
0
2
0
0
0
0
1
0
0
1
1
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
2
3
1
2
2
0
0
0
0
2
0
2
0
1
0
0
2
0
2
0
1
2
0
0
1
1
2
2
1
0
1
2
2
2
0
2
1
2
1
0
2
0
1
2
0
0
2
2
1
1
1
0
0
1
1
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
1
1
0
0
0
0
0
2
0
0
2
0
1
1
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
2
2
2
0
0
2
2
2
0
1
2
1
0
0
0
0
0
2
1
1
1
1
1
0
0
0
0
1
0
1
0
0
0
2
0
0
2
0
2
0
0
0
2
1
0
0
1
0
0
2
0
0
0
1
1
1
0
0
0
1
0
1
0
0
0
0
4
0
0
0
0
2
0
1
0
2
2
2
0
2
1
0
1
2
0
0
2
0
1
1
0
2
0
0
3
0
0
0
2
1
0
1
1
2
0
0
2
0
2
2
0
1
1
0
1
2
0
0
0
1
1
2
0
0
0
0
0
2
3
2
2
1
0
1
2
1
0
2
0
0
2
0
0
0
1
0
0
1
0
2
0
1
1
0
1
0
1
1
1
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
2
0
1
1
1
0
2
1
0
2
1
0
0
0
2
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
2
2
3
0
1
0
0
1
2
0
0
1
0
0
0
0
0
2
0
0
2
0
0
1
0
2
2
2
2
1
1
1
0
2
0
1
0
0
0
2
0
1
1
0
0
0
0
2
2
3
0
0
2
0
1
0
0
0
0
4
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
1
1
2
2
0
1
2
1
2
2
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
2
1
0
0
0
1
0
0
2
0
2
2
0
2
1
0
2
0
0
3
0
2
0
1
2
0
0
0
1
1
2
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
2
0
2
1
1
1
0
0
0
1
0
1
0
0
0
0
2
1
1
1
2
0
0
0
1
0
1
0
0
2
1
2
0
2
0
1
2
2
1
0
0
2
0
0
0
0
1
0
1
1
1
3
0
0
0
0
0
0
0
1
1
0
1
0
1
0
2
0
1
2
0
0
0
0
0
0
1
2
0
0
0
1
0
0
1
0
3
1
1
0
0
2
0
0
0
1
0
0
1
2
0
0
0
2
0
0
1
0
2
0
0
0
0
0
1
2
0
1
0
0
1
2
3
1
2
0
2
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
1
0
0
0
2
0
1
0
0
2
1
0
2
2
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
2
0
0
0
1
0
3
0
1
1
2
2
2
0
1
0
0
1
2
2
0
1
1
1
2
0
0
3
0
1
1
0
0
0
0
0
0
1
0
2
0
0
0
0
2
1
0
1
0
0
1
0
1
0
1
0
0
0
1
0
2
0
3
0
0
1
0
0
0
1
1
0
0
2
0
0
0
0
1
2
0
1
0
0
0
0
1
0
2
1
0
1
0
1
1
0
0
1
1
2
1
0
0
1
1
1
1
0
0
3
0
1
2
0
2
0
2
2
1
1
0
0
1
2
0
0
0
1
0
1
0
0
0
0
1
0
0
0
2
1
2
0
0
2
1
2
2
1
0
0
0
0
2
0
7
2
0
1
2
0
0
1
2
1
3
2
1
2
1
2
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
1
0
1
2
0
0
1
2
2
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
2
0
1
2
1
0
0
1
2
2
3
1
0
0
0
0
1
1
0
2
1
0
1
0
1
1
0
0
2
1
0
2
0
1
0
2
0
1
0
0
2
0
1
0
2
2
0
1
2
0
0
4
0
1
0
1
0
0
3
0
0
0
3
0
1
0
2
0
1
1
1
0
0
0
0
0
0
0
0
2
2
0
1
3
1
1
0
2
1
0
0
0
0
0
1
0
1
0
0
0
0
2
2
2
0
0
0
0
0
0
1
0
0
1
0
1
1
1
3
0
2
0
2
2
0
0
1
0
1
0
2
1
2
3
0
0
0
0
0
1
0
2
0
1
0
2
2
2
0
2
1
1
0
0
0
1
2
2
0
1
1
0
0
1
1
0
0
0
3
0
0
1
1
0
1
1
1
2
1
0
0
0
0
0
4
0
1
1
2
2
0
1
0
1
2
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
2
0
1
1
1
1
1
0
0
2
2
0
0
0
0
1
2
0
0
0
0
0
0
1
0
2
1
2
0
0
0
0
1
1
1
0
0
2
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
3
1
0
0
0
1
0
2
0
0
2
0
0
1
0
2
1
1
0
1
0
0
0
2
2
3
2
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
1
2
2
0
1
0
0
0
0
0
1
1
1
2
0
2
0
1
0
0
0
0
2
0
0
0
1
2
0
1
0
0
1
0
0
0
0
3
0
0
2
0
0
1
0
1
1
1
1
0
1
2
0
0
0
0
0
0
0
1
1
6
1
0
1
0
1
0
1
0
0
0
1
2
0
0
2
0
0
1
1
3
2
0
0
0
2
1
0
2
0
0
0
2
0
0
2
0
2
0
0
1
0
0
2
0
1
0
0
0
1
0
1
2
1
2
1
2
1
0
0
2
3
0
0
2
1
1
0
0
0
3
0
0
0
3
0
0
0
0
0
0
1
0
1
2
3
2
1
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
2
1
2
0
1
2
1
0
0
0
0
0
2
0
0
2
3
1
0
1
0
1
1
0
0
2
0
1
0
0
0
2
2
1
0
1
1
0
0
2
0
0
2
2
0
1
0
2
1
2
2
0
0
0
1
0
2
0
0
2
1
0
2
0
1
0
1
1
0
1
0
2
2
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
2
0
1
3
0
1
1
2
0
0
2
2
0
0
0
0
0
2
1
0
0
2
1
0
1
1
1
1
0
1
1
1
0
0
1
0
1
1
0
0
0
0
0
0
1
0
2
1
0
0
0
2
0
3
2
0
0
0
2
2
0
1
1
0
0
0
1
0
2
0
1
0
1
0
1
0
2
0
1
0
2
1
0
2
2
2
2
2
0
0
1
0
0
0
1
0
0
1
2
0
0
0
0
0
1
0
0
1
2
0
2
1
0
1
0
1
1
0
0
0
1
1
0
0
0
0
1
3
0
2
0
0
0
0
0
1
1
2
0
1
0
0
0
0
4
0
0
1
0
0
0
0
0
2
0
1
2
0
0
0
2
0
0
0
1
0
2
2
0
2
1
0
0
0
0
1
1
1
0
2
0
1
0
2
0
0
1
2
1
0
2
3
2
1
1
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
2
2
4
0
0
0
1
1
0
0
1
2
0
1
2
0
2
0
0
0
0
0
2
2
0
0
1
1
0
2
1
1
1
0
0
1
0
0
0
0
2
0
2
4
1
0
0
1
1
0
2
0
0
0
1
1
0
1
2
0
0
1
0
0
0
1
1
0
2
0
0
0
0
2
0
0
1
1
0
0
0
0
0
1
1
0
1
0
1
0
2
0
2
1
2
2
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
2
0
1
0
0
1
2
0
0
1
1
1
0
1
2
0
1
0
0
0
0
0
3
2
0
1
2
0
0
0
0
1
1
1
0
1
3
1
0
0
0
2
2
1
1
0
1
0
0
1
1
1
0
1
0
1
0
2
0
1
0
0
1
0
1
0
0
0
0
0
0
0
3
1
2
3
0
0
0
0
0
0
1
1
3
1
0
2
3
0
1
1
0
2
1
0
2
0
0
0
0
0
2
1
2
1
1
0
1
3
1
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
2
0
1
1
1
1
0
0
0
0
0
0
0
1
0
1
1
0
1
3
0
0
0
0
0
3
0
0
0
1
0
0
2
2
0
0
0
1
0
0
0
0
1
2
0
0
0
2
0
0
2
0
1
1
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
2
0
2
0
2
0
0
0
0
1
1
0
0
3
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
2
2
0
0
2
1
0
2
1
1
0
0
1
1
1
2
0
1
0
1
0
0
0
0
0
0
1
0
2
4
0
1
0
0
2
0
0
0
0
2
2
1
0
0
1
2
1
1
1
1
0
0
0
2
2
2
1
1
0
0
0
2
3
1
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
2
0
0
2
0
1
0
0
1
0
0
1
0
1
3
0
2
1
0
0
0
1
0
0
2
0
2
2
1
0
1
0
0
1
0
0
1
0
0
0
0
2
0
0
0
1
1
2
0
0
2
1
0
2
2
0
1
1
2
0
1
1
0
0
1
0
0
1
0
2
0
3
0
1
0
1
0
0
1
1
1
0
0
1
2
0
1
0
0
0
0
2
0
0
0
3
0
1
0
1
2
0
2
0
2
0
0
2
1
1
2
0
0
1
1
3
0
0
0
1
2
1
2
2
2
0
2
2
0
0
0
0
2
2
1
3
0
2
0
2
1
2
0
1
0
1
0
0
2
0
0
2
0
1
0
0
0
0
1
1
0
0
0
1
2
0
1
0
1
0
0
2
0
2
0
1
1
0
2
0
1
0
2
0
1
0
2
0
0
1
2
0
2
2
0
2
1
0
1
0
0
0
0
0
2
0
0
1
0
0
1
1
0
0
0
2
1
2
2
0
0
3
1
2
0
1
0
0
0
0
1
2
0
0
0
2
1
1
1
2
0
0
0
2
1
0
1
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
1
1
1
0
1
2
0
0
0
1
3
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
1
2
2
0
0
1
1
0
2
0
0
1
1
0
1
1
2
0
0
1
0
1
0
0
2
0
1
0
2
0
0
2
2
1
0
0
0
0
1
2
0
0
2
1
1
0
1
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
1
1
2
0
1
0
0
0
0
0
0
1
2
2
2
2
1
1
0
1
5
0
1
2
0
2
1
2
2
2
1
2
1
0
0
0
0
0
0
2
1
0
2
0
2
0
0
0
0
0
0
2
0
2
1
1
1
0
0
0
1
1
1
0
0
3
0
0
0
1
0
2
2
0
0
0
1
0
2
0
2
1
2
1
0
1
1
2
0
2
0
0
2
0
0
1
0
0
0
0
0
1
0
0
2
3
1
0
2
2
1
0
0
0
0
0
0
1
0
1
1
1
1
1
2
1
1
0
1
1
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
2
2
0
2
0
1
1
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
1
2
0
2
0
0
0
1
0
1
0
2
1
0
0
0
1
2
1
2
1
0
0
0
0
0
0
2
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
1
1
0
2
0
0
0
0
0
2
0
0
1
1
0
1
3
0
2
0
2
0
0
0
0
0
0
0
1
2
0
0
1
0
0
1
3
2
0
1
0
0
1
1
1
1
2
1
0
1
2
0
0
0
0
0
0
2
2
0
1
2
0
1
1
0
0
1
0
2
0
0
0
2
0
0
0
1
4
2
0
0
0
1
1
0
0
0
1
1
0
2
0
0
0
2
0
1
2
0
0
1
0
0
0
0
0
0
0
2
0
2
1
2
0
0
1
0
0
0
0
0
0
0
1
1
2
2
0
0
1
2
1
3
2
1
1
2
0
0
1
0
2
0
2
0
1
0
0
1
1
0
0
0
1
0
0
1
1
0
0
0
2
1
1
1
1
0
1
0
1
2
0
2
1
1
0
0
0
2
1
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
1
0
5
0
2
1
0
0
1
1
1
1
0
0
1
1
0
1
0
0
0
0
2
0
4
0
0
0
1
0
1
1
0
1
0
0
0
0
2
0
0
0
0
1
0
2
1
2
0
0
1
0
0
2
0
0
0
0
0
1
1
1
0
0
1
0
0
1
1
0
2
2
0
0
2
0
1
3
1
4
0
1
1
0
0
2
0
0
1
2
4
0
1
2
0
0
0
1
2
0
2
0
0
0
0
0
2
0
1
2
1
1
0
0
0
2
0
2
0
0
0
0
2
0
1
0
4
0
1
2
2
0
2
1
1
0
3
0
0
0
2
0
0
0
0
0
1
2
2
1
1
1
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
2
0
0
0
1
2
0
0
0
2
1
1
0
0
0
0
0
3
0
0
1
0
0
0
0
0
2
1
0
2
0
4
1
2
1
2
0
0
0
0
0
1
0
1
2
2
0
1
0
0
0
1
0
2
2
0
2
1
0
0
2
1
0
1
0
2
0
0
0
0
2
1
1
7
0
1
1
3
0
0
2
0
0
2
1
0
1
0
0
2
1
2
0
0
1
2
0
0
2
1
0
0
0
0
2
0
0
0
0
2
1
0
0
0
1
2
0
2
2
0
0
0
1
2
0
2
1
0
0
2
0
1
1
2
0
0
0
2
0
1
0
0
0
0
0
1
0
1
0
2
2
0
2
4
1
0
0
2
0
1
0
0
2
1
1
1
1
1
0
0
1
2
2
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
1
0
1
0
2
1
1
2
1
0
1
1
0
1
0
0
1
1
2
1
1
0
1
1
2
1
2
0
2
2
0
2
2
1
0
1
1
0
2
0
1
0
0
1
1
0
0
1
0
0
2
0
0
1
2
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
2
1
0
1
1
1
1
1
0
0
0
0
0
2
0
0
0
2
0
2
2
3
1
0
0
4
0
0
0
0
0
2
0
1
1
2
1
1
1
0
1
0
0
0
2
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
1
0
0
0
8
1
0
0
0
0
0
2
0
0
0
0
0
1
1
2
2
1
0
0
0
0
1
0
2
2
0
0
1
0
1
2
1
2
0
0
0
0
0
0
1
0
2
1
0
0
2
0
0
2
2
2
0
3
0
0
2
2
0
0
1
0
2
1
2
0
0
0
0
0
0
2
2
0
0
0
1
1
0
0
0
0
0
2
2
0
0
2
0
2
1
1
3
0
0
0
0
0
2
1
1
2
0
0
0
2
0
1
1
0
0
0
0
0
2
0
1
0
0
0
0
0
1
2
2
0
0
1
1
0
0
2
0
0
1
2
0
1
0
0
1
1
1
0
0
2
0
0
0
2
0
1
0
0
2
0
2
1
0
0
1
0
0
0
2
0
0
0
2
2
0
0
0
2
4
1
0
0
0
0
1
0
0
1
1
2
1
0
1
1
2
2
1
2
0
1
0
0
0
2
0
0
0
1
0
0
0
1
2
1
0
0
1
1
1
0
0
0
1
1
0
2
0
0
0
0
0
1
1
0
1
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
1
1
0
0
0
2
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
4
0
0
1
2
0
0
2
2
0
1
0
1
0
0
1
0
0
2
2
4
1
0
0
2
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
2
2
0
0
0
0
0
2
1
1
1
0
1
1
1
1
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
1
0
0
0
0
1
2
2
0
2
1
1
0
0
0
0
4
0
1
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
3
0
2
1
2
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
2
1
1
0
2
1
1
0
0
0
2
0
0
0
2
0
0
1
3
1
0
0
1
0
0
3
2
0
0
0
0
1
1
0
2
0
1
2
2
2
0
0
1
0
2
0
0
0
0
2
1
2
0
0
1
0
0
3
1
0
1
1
2
2
1
2
1
0
1
2
3
1
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
1
3
1
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
2
2
0
0
0
1
2
2
0
0
0
1
1
1
1
0
0
0
0
1
0
0
2
1
0
0
0
0
2
1
0
0
0
2
1
0
0
0
0
0
0
2
0
2
1
2
0
0
0
0
2
2
3
0
1
1
3
0
1
1
1
2
0
0
1
0
0
1
0
0
0
0
2
1
1
0
0
0
2
1
1
0
0
1
2
0
5
0
0
1
2
1
0
2
2
2
1
0
0
0
1
0
0
2
1
0
0
0
1
2
0
0
2
0
2
2
0
2
0
0
0
0
1
0
0
1
1
0
2
0
1
0
0
0
1
0
1
1
0
2
0
1
0
0
4
2
0
0
1
1
1
2
0
1
0
2
2
2
0
0
0
1
1
1
0
1
3
0
2
0
1
0
1
0
2
0
2
0
2
0
2
0
1
1
0
1
0
1
1
1
0
2
3
2
0
3
1
0
0
0
1
1
0
2
0
0
0
0
2
0
0
0
2
1
0
0
2
0
2
0
0
1
0
1
2
2
1
14
0
1
0
0
2
0
0
2
0
1
0
0
0
2
2
0
0
1
2
1
1
3
0
0
2
0
2
0
2
1
2
2
0
2
1
3
2
2
0
0
2
0
2
0
0
2
2
0
2
2
0
0
0
0
2
1
2
3
0
1
2
0
0
1
0
0
0
1
1
0
2
1
1
0
0
2
1
0
0
0
1
0
0
1
0
0
2
2
0
1
1
2
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
2
1
0
1
0
1
0
0
2
2
0
2
0
0
2
0
0
1
0
1
0
0
1
1
1
2
0
1
0
0
3
0
0
0
2
0
0
1
1
2
0
1
0
0
0
0
0
0
0
2
0
2
0
1
1
0
0
1
0
2
2
1
2
0
1
1
0
0
2
3
1
0
2
0
2
0
1
1
0
0
6
0
0
1
2
1
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
2
0
0
0
0
0
0
1
1
0
5
0
0
0
0
1
1
0
2
0
0
1
0
2
1
0
0
0
0
0
2
1
1
1
1
0
0
0
0
1
0
0
0
1
1
0
0
2
0
3
1
0
0
8
1
0
0
1
0
1
0
0
0
2
0
0
1
0
2
6
0
0
0
0
2
0
0
0
0
1
1
0
1
0
0
0
0
0
1
1
0
1
0
2
0
0
0
2
0
1
2
0
0
0
1
0
1
0
1
1
0
1
2
0
0
2
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
2
1
1
1
0
0
2
0
2
0
0
0
0
0
2
0
1
2
2
1
0
0
1
1
2
0
2
0
0
0
0
2
2
0
0
0
1
0
0
2
2
1
1
0
0
0
2
0
2
2
1
4
2
2
0
0
2
1
0
2
0
0
1
0
0
0
1
0
0
0
2
2
1
0
1
0
0
0
0
2
0
1
1
1
2
0
0
1
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
1
0
0
2
1
1
0
0
1
3
0
0
1
0
2
0
0
0
2
0
2
1
0
0
0
0
1
0
0
0
2
2
2
0
0
2
0
2
2
0
1
2
0
0
1
2
1
0
0
0
0
0
2
0
0
2
0
2
1
2
2
0
0
0
0
1
0
1
1
1
2
1
1
1
0
1
0
0
0
0
2
1
0
0
0
1
1
0
1
1
1
1
0
1
0
2
1
1
2
2
0
0
0
2
0
0
0
1
0
0
0
0
2
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
1
1
0
0
1
1
1
2
0
0
2
1
2
0
2
1
0
0
1
1
1
1
0
0
1
1
0
2
0
1
1
0
0
2
0
0
0
0
2
0
0
0
1
1
1
0
2
0
0
0
1
1
0
0
0
1
1
0
0
1
0
0
0
2
2
0
2
2
1
0
1
0
1
0
0
2
0
1
1
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
2
1
0
2
1
0
0
0
4
1
1
1
0
1
2
0
1
0
1
0
0
0
1
0
1
1
0
0
0
1
0
0
2
0
1
1
1
0
0
2
2
0
1
1
0
0
0
0
0
2
0
0
1
0
4
0
1
1
0
1
1
1
0
0
1
0
1
1
0
0
0
2
0
0
2
0
0
0
2
0
0
0
1
0
0
2
0
2
0
1
2
0
2
0
2
0
1
1
1
0
2
1
1
0
0
1
2
0
4
1
0
0
1
1
2
0
0
1
1
2
0
0
1
0
0
0
0
1
1
1
2
5
0
0
1
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
1
2
1
0
1
0
0
1
0
0
1
1
2
2
1
2
2
0
0
0
0
0
0
2
2
3
0
0
2
0
2
2
0
0
1
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
1
1
0
0
0
0
2
0
0
0
2
1
0
2
1
2
3
3
2
0
0
2
1
1
1
0
1
0
2
0
2
1
0
3
0
2
0
0
0
0
2
0
1
2
1
2
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
3
0
1
0
1
0
0
0
0
0
2
2
0
2
1
0
0
0
0
1
0
0
3
0
0
0
1
1
0
2
1
3
1
0
2
0
0
0
0
0
1
0
0
0
2
1
0
2
0
2
2
0
1
1
0
2
1
0
0
0
3
0
0
0
0
0
2
0
1
1
0
1
1
1
0
3
0
0
0
2
0
0
2
2
0
1
0
0
0
1
0
0
0
0
0
1
0
0
2
2
0
2
0
1
0
1
1
0
0
0
1
0
2
0
0
2
0
1
0
0
0
0
2
0
2
0
0
2
0
0
0
1
2
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
1
2
0
2
1
0
0
1
2
1
0
0
1
1
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
2
0
0
0
0
2
7
0
0
0
0
0
0
0
2
1
0
1
1
0
0
2
0
2
0
0
0
2
2
0
2
4
0
1
0
1
0
0
2
2
0
0
0
0
0
1
3
2
2
0
0
0
0
2
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
1
2
0
0
0
0
1
1
0
0
1
0
0
1
2
0
2
1
0
0
0
2
0
1
1
2
2
0
0
0
0
0
0
0
2
2
2
0
0
0
0
1
1
0
0
2
1
0
0
1
0
0
0
1
0
1
0
0
0
0
2
1
1
1
3
0
0
0
2
2
0
0
1
0
0
0
0
2
0
0
0
0
1
1
1
0
0
0
1
0
0
0
3
0
0
0
0
2
0
0
1
1
0
0
1
2
2
0
0
0
1
1
0
2
0
0
0
2
0
0
0
1
0
0
1
0
0
1
0
0
1
1
0
2
0
0
1
0
1
0
0
2
0
1
0
0
0
0
0
2
1
0
0
2
0
0
0
1
0
1
0
0
0
0
0
3
0
0
2
0
2
2
2
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
2
0
0
1
1
0
0
1
0
0
2
0
1
2
1
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
2
1
0
0
0
1
0
1
0
0
3
0
0
1
2
0
0
0
2
2
0
2
2
0
1
0
1
0
0
0
0
0
1
0
0
1
0
2
0
1
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
2
2
2
0
2
0
1
0
0
0
1
0
0
0
4
2
1
0
2
0
2
2
1
1
0
1
0
0
1
0
0
1
1
0
0
1
2
0
0
1
0
2
0
1
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
2
1
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
2
2
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
2
0
2
0
0
0
0
0
0
0
0
1
2
0
0
2
0
2
1
0
1
0
0
2
2
0
1
0
1
1
0
0
0
0
2
0
0
0
0
0
1
0
2
2
1
1
1
0
1
2
1
0
0
2
1
2
1
2
2
1
0
0
2
0
0
2
0
2
1
0
2
2
2
1
2
1
1
1
0
1
1
0
2
1
0
0
0
2
0
1
0
1
3
0
0
2
0
2
0
0
0
1
2
0
0
2
2
5
0
0
1
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
1
1
2
2
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
2
2
1
1
0
0
0
1
1
3
2
0
1
0
0
1
0
0
0
1
0
0
0
1
2
0
2
0
0
0
1
0
2
1
0
2
0
0
0
0
1
0
0
5
2
1
1
2
1
0
0
1
1
1
2
1
0
0
0
0
2
2
0
0
3
1
2
0
1
0
0
0
1
0
2
3
2
0
0
0
0
2
1
0
2
2
0
1
0
1
2
1
0
0
0
0
2
0
0
0
0
0
1
0
1
1
0
0
0
1
2
2
2
2
0
0
2
0
0
1
0
0
0
0
0
1
1
1
2
0
0
0
0
1
1
0
0
1
0
0
1
0
0
1
0
1
0
0
0
1
2
1
1
0
0
0
0
0
1
0
1
1
2
0
0
2
2
0
2
0
0
0
0
2
1
2
0
0
0
0
2
2
1
2
0
0
0
1
2
0
0
0
2
0
1
0
1
0
0
2
3
1
2
0
0
2
0
0
2
0
0
0
2
1
2
2
1
0
1
1
1
0
2
2
0
1
2
0
2
0
1
0
0
1
2
0
0
0
1
2
1
2
1
0
0
1
0
0
0
3
0
1
0
0
1
0
0
0
0
2
2
1
1
2
0
0
0
0
0
0
0
0
0
2
0
0
2
4
0
1
0
2
1
1
2
0
0
2
0
1
1
4
1
0
1
0
0
0
0
0
2
0
1
1
1
2
0
0
2
0
0
1
1
0
0
0
0
0
1
2
1
0
2
0
0
0
0
0
0
2
0
0
2
0
1
2
2
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
1
0
0
0
1
1
0
0
0
1
0
0
3
1
1
0
2
2
0
1
1
0
1
0
0
0
1
0
2
0
1
0
1
1
0
0
1
0
1
0
0
2
3
0
0
1
0
2
0
2
0
1
0
0
1
4
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
1
1
2
0
2
0
0
0
0
1
2
1
0
0
0
1
2
1
2
0
1
1
0
0
2
0
0
0
0
2
2
0
0
2
2
0
1
1
1
1
2
3
2
0
0
0
0
1
1
0
0
0
1
2
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
2
0
1
0
0
0
0
2
0
1
1
1
0
2
2
1
0
2
0
0
0
0
0
1
1
1
0
0
0
1
0
1
1
0
2
0
0
1
0
3
2
1
1
1
0
0
0
2
0
0
2
1
0
0
0
1
0
2
1
1
0
0
0
1
1
2
0
0
1
0
0
2
1
2
2
0
0
1
1
1
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
2
1
0
1
0
1
2
2
0
0
1
0
1
1
1
0
1
0
2
0
0
1
0
2
2
0
0
1
2
2
2
0
0
0
0
2
0
0
0
1
2
0
0
2
0
0
2
0
0
2
1
0
2
0
2
1
0
0
0
1
0
0
0
1
0
1
2
0
1
2
0
0
1
2
2
1
1
1
3
1
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
1
0
1
0
1
2
0
0
0
2
0
0
0
0
2
3
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
3
0
0
1
1
2
0
2
1
1
2
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
2
0
0
0
2
0
2
0
2
1
0
1
0
3
0
0
0
0
1
0
1
0
0
0
2
0
1
1
1
2
0
2
1
0
1
1
2
1
9
0
0
2
1
1
0
1
0
0
1
2
1
2
0
0
2
1
0
2
0
1
2
2
0
1
0
0
2
2
0
0
0
0
0
0
0
1
0
1
0
1
1
0
1
0
0
0
0
0
0
0
1
0
1
1
2
1
0
0
1
0
1
0
0
2
0
0
0
0
0
0
1
0
1
0
0
1
1
0
1
0
0
1
1
0
0
0
0
0
2
0
0
2
3
2
2
0
0
0
0
1
0
2
0
0
2
2
1
0
2
1
0
2
0
0
0
1
2
2
0
0
0
0
0
0
0
1
2
0
0
1
0
2
0
1
0
0
0
1
1
3
1
0
1
2
2
0
0
1
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
2
0
0
0
2
2
0
0
0
0
1
0
0
1
2
1
0
1
0
0
3
1
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
1
2
1
1
0
0
0
0
0
3
1
0
2
0
1
2
0
0
2
2
1
1
0
1
0
2
1
1
0
1
0
0
0
1
2
1
0
0
0
0
1
2
1
2
0
0
0
1
0
0
0
2
0
2
0
1
2
0
0
0
0
1
1
2
1
2
1
0
0
0
3
0
0
1
2
2
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
2
1
0
0
1
0
2
0
0
0
0
1
0
0
1
0
1
1
0
2
1
0
0
0
1
1
0
1
2
1
0
0
2
1
2
1
1
0
0
0
0
1
0
0
1
0
0
2
0
1
1
0
2
0
0
1
0
0
0
1
2
0
0
2
0
1
0
0
0
0
0
1
1
0
0
1
2
0
2
0
0
2
0
0
0
0
0
2
2
1
3
1
0
2
0
0
1
2
1
2
1
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
1
2
2
2
1
1
1
1
0
0
1
0
1
2
2
0
0
0
0
0
0
0
1
0
0
1
2
1
2
0
0
0
1
0
1
1
1
0
1
2
1
0
0
1
0
1
1
0
0
0
2
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
2
0
2
1
0
2
0
1
0
0
1
0
1
0
1
0
0
1
0
0
1
2
1
0
0
1
0
0
1
2
2
0
1
1
1
1
1
2
0
0
0
0
2
0
0
1
0
1
0
0
1
0
2
0
0
2
1
2
0
1
0
1
0
2
1
1
0
0
0
0
1
0
1
0
1
0
1
0
1
0
1
0
0
0
0
0
1
1
0
2
1
1
1
0
0
0
0
0
1
2
0
0
0
0
0
2
0
1
2
1
2
0
0
2
1
2
0
0
2
2
0
2
0
0
0
1
1
0
1
1
0
0
0
2
1
0
1
2
2
2
1
2
2
2
0
0
0
0
1
1
0
2
1
0
0
0
0
0
0
0
0
1
1
0
2
1
1
1
0
0
2
0
1
0
0
3
1
0
0
1
2
0
0
1
1
0
0
0
1
2
1
0
2
2
1
1
1
0
0
2
0
1
2
1
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
2
1
0
6
1
0
0
0
0
0
1
1
0
1
3
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
1
1
1
2
0
1
2
0
1
0
2
3
2
0
0
0
0
1
0
0
0
3
0
0
0
0
1
1
2
0
0
2
0
0
1
1
1
0
2
0
1
2
2
0
3
1
0
0
1
1
0
0
0
0
0
2
0
1
3
0
0
0
0
0
2
0
2
0
0
0
0
2
0
2
0
1
0
1
0
2
1
0
0
0
0
11
0
0
0
0
4
2
2
2
1
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
2
0
2
2
0
1
0
0
0
0
0
1
3
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
2
0
0
2
0
0
1
0
0
1
4
0
2
1
0
4
2
0
3
0
0
1
2
0
0
0
0
0
0
0
0
2
0
2
1
0
0
1
0
0
0
1
0
0
0
0
0
1
1
2
0
0
0
0
0
1
1
0
1
2
0
2
0
0
0
1
0
1
2
2
0
0
2
2
0
0
2
1
0
2
3
0
0
3
0
0
0
2
1
1
0
0
1
0
0
1
0
0
1
2
0
1
0
2
0
1
0
2
0
0
0
0
1
2
0
0
2
0
1
0
0
0
1
1
0
0
1
0
2
0
1
1
2
0
0
0
0
2
2
0
0
0
2
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
3
1
1
1
1
0
2
1
1
0
0
0
2
0
1
0
2
0
0
1
0
0
2
1
0
1
0
1
0
0
0
0
0
0
2
1
1
2
1
2
2
1
0
1
3
1
1
0
0
0
2
2
2
0
1
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
1
1
0
1
0
1
1
2
0
0
0
0
2
0
2
0
2
1
0
0
0
1
1
0
0
2
0
0
1
2
0
0
1
0
0
0
0
1
1
0
1
0
3
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
2
0
0
2
1
0
0
1
0
1
0
0
1
0
1
1
1
0
0
2
1
1
1
1
0
0
0
0
0
0
1
0
1
2
0
0
0
2
1
0
0
0
0
2
2
0
0
0
0
2
0
0
2
1
3
1
0
0
1
1
2
0
0
2
0
0
0
2
2
0
0
0
0
0
2
0
1
1
1
2
2
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
2
0
2
0
0
2
0
1
0
0
0
0
0
1
0
0
0
1
0
0
2
1
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
1
1
0
2
0
0
0
0
0
2
1
1
0
0
0
1
0
0
2
2
1
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
1
0
2
0
0
2
0
0
0
0
3
0
2
1
0
2
0
2
0
1
0
0
0
2
1
0
1
1
0
2
1
0
0
0
1
1
0
0
1
2
1
0
2
0
0
0
2
1
0
1
0
1
1
0
1
0
0
2
1
0
0
1
1
2
2
0
0
0
0
1
0
0
3
0
1
0
2
0
0
0
2
1
2
0
1
0
0
2
2
0
0
2
1
0
1
1
1
0
0
0
0
0
2
2
0
1
2
0
2
0
0
2
0
0
2
2
2
2
2
0
1
2
1
0
2
2
1
1
0
1
1
0
0
0
0
0
0
0
2
1
2
2
1
0
3
2
0
2
0
0
1
0
2
0
0
0
0
2
0
0
0
0
2
2
3
2
0
0
1
2
0
1
0
0
1
0
0
2
0
1
4
2
0
1
1
0
0
0
1
1
2
1
1
1
1
0
1
1
2
1
1
1
0
2
0
1
0
0
2
2
0
0
0
1
1
0
0
1
1
2
0
0
0
2
1
1
2
0
0
0
1
0
2
2
0
0
0
0
1
0
1
0
0
0
1
2
0
2
1
0
0
1
2
1
0
0
1
0
0
0
0
2
2
0
1
0
1
0
0
1
1
1
1
2
0
0
1
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
2
1
0
2
0
0
0
0
1
1
1
0
1
1
1
0
0
0
0
3
0
1
1
0
1
0
0
0
0
1
0
2
1
2
1
0
1
1
2
1
1
0
1
0
2
2
3
2
0
0
2
0
1
0
1
1
0
1
1
0
1
0
0
0
1
0
1
0
1
0
2
0
0
2
1
0
2
1
1
1
0
0
0
0
1
1
0
1
0
1
0
1
0
0
2
2
0
2
0
0
1
2
0
2
1
2
2
0
3
2
1
2
0
0
0
1
1
0
0
1
1
0
1
2
1
1
1
2
0
0
0
1
0
0
0
2
1
1
2
0
0
1
1
0
2
0
0
1
0
1
1
0
0
0
1
0
0
0
0
2
0
0
0
3
0
0
0
0
0
2
2
1
1
1
0
2
0
0
0
0
0
0
1
1
2
2
0
1
0
0
1
0
2
0
2
3
0
1
0
2
1
2
2
2
0
0
1
1
0
0
1
0
0
0
2
0
1
0
0
0
0
0
2
0
2
1
0
2
0
1
0
1
2
0
1
0
0
1
0
2
1
0
0
3
1
0
0
2
0
3
0
0
0
0
0
2
2
2
0
0
2
0
1
1
2
0
1
0
1
0
0
0
0
1
0
2
1
0
0
1
1
2
0
2
0
0
1
2
2
1
2
2
1
2
0
1
0
0
0
1
1
0
0
0
1
2
0
2
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
2
0
0
2
1
0
0
2
0
2
0
0
1
1
0
0
0
2
1
1
2
1
0
0
0
1
1
1
2
0
0
0
1
0
0
1
0
2
2
2
0
0
0
2
0
2
2
0
1
0
0
1
0
0
2
0
2
2
2
0
0
1
0
2
0
0
2
0
1
0
0
0
0
2
2
0
1
2
2
0
1
2
2
0
0
0
2
2
0
2
4
1
1
1
1
0
0
0
0
2
2
2
0
0
0
0
0
2
1
5
2
0
0
1
1
1
2
0
2
0
2
0
0
0
0
0
0
0
1
2
0
0
1
1
0
1
2
0
0
0
0
0
1
0
0
2
0
0
2
0
0
1
0
1
2
0
0
0
2
0
1
0
2
0
0
0
0
2
1
0
0
0
0
0
1
2
2
0
2
0
1
2
0
3
0
1
2
1
0
3
1
1
1
2
0
0
2
1
1
1
0
2
0
0
1
0
2
2
1
0
0
1
0
1
1
1
0
2
2
1
1
1
0
0
0
4
1
2
0
0
2
0
1
1
0
0
1
2
0
0
0
35
1
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
1
2
1
1
0
0
1
1
1
0
0
0
0
1
0
1
0
0
0
1
0
0
2
2
0
0
2
1
1
1
2
2
0
0
1
2
2
0
1
2
1
0
0
2
1
0
0
1
1
2
0
0
1
1
0
0
0
2
2
0
0
0
1
0
2
0
2
0
1
0
3
0
0
2
0
0
0
0
0
0
1
1
1
0
0
0
0
2
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
2
0
0
1
0
0
1
1
0
1
1
1
0
0
0
0
0
1
0
0
2
2
0
0
1
0
1
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
2
1
0
2
2
0
1
0
0
1
0
0
0
1
0
1
2
0
2
1
0
1
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
2
0
2
2
1
0
0
0
1
0
0
0
1
1
0
2
0
1
1
0
0
1
0
0
0
1
1
1
0
1
0
1
0
0
2
2
2
0
3
0
1
2
0
2
1
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
3
0
1
1
2
0
0
2
0
0
0
0
2
1
2
0
0
1
0
2
2
2
1
0
0
0
2
0
0
1
0
0
0
0
0
2
0
1
0
0
0
3
0
0
0
0
0
0
2
1
0
0
0
0
1
1
0
0
0
1
0
1
1
0
0
2
2
0
1
0
1
2
2
0
0
2
1
2
1
1
0
2
0
1
0
2
2
2
0
1
1
0
0
1
2
0
2
2
0
1
1
1
1
2
0
0
0
0
0
0
0
0
2
2
0
2
1
0
0
0
0
2
0
2
1
0
0
1
2
0
0
0
1
1
0
0
1
1
0
1
0
1
1
2
1
1
0
0
1
2
0
0
0
0
1
0
1
0
2
0
1
1
1
0
0
0
2
0
0
0
2
0
0
2
1
0
0
0
2
0
0
1
0
1
2
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
2
2
0
0
2
1
0
0
0
0
1
1
0
2
2
0
2
0
0
2
2
0
0
1
1
1
0
2
0
0
0
0
2
1
0
0
2
0
0
0
0
0
2
0
0
0
0
2
1
0
1
0
0
0
2
1
0
0
1
1
0
0
0
0
0
0
2
1
2
1
1
0
0
0
0
1
0
2
0
0
2
0
0
2
0
2
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
2
1
0
1
0
0
1
1
0
2
0
0
2
0
2
1
2
0
0
2
0
0
0
0
0
0
0
0
2
1
1
1
2
2
1
2
2
0
2
0
0
0
2
1
0
1
3
0
0
1
0
0
0
0
2
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
2
2
1
1
1
1
0
1
2
0
1
0
0
2
0
0
1
0
0
0
1
1
1
0
0
3
0
0
0
0
2
0
0
0
0
0
0
1
1
2
0
2
0
2
1
0
1
0
0
0
0
1
0
0
0
0
0
5
0
0
0
0
0
0
0
1
0
2
0
0
0
1
1
0
0
1
2
0
0
0
0
1
2
1
1
0
1
2
1
0
0
1
0
1
2
1
0
3
1
0
1
1
0
0
2
0
0
0
1
2
0
0
1
2
0
2
0
1
0
0
0
0
2
1
0
1
0
1
1
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
2
0
0
2
2
0
2
2
0
1
0
0
1
1
0
0
2
1
0
0
1
0
0
1
1
1
0
0
2
0
2
0
1
0
2
0
0
1
1
0
1
1
1
0
1
1
1
2
0
0
0
1
0
0
2
0
0
1
1
2
2
0
2
1
1
2
1
2
1
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
2
0
1
0
0
2
0
0
0
1
0
0
0
1
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
2
0
2
1
0
0
0
2
1
1
1
0
0
1
0
0
2
0
2
0
2
0
0
1
2
0
0
2
1
2
1
2
2
2
1
0
0
2
2
0
1
1
0
0
2
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
1
2
1
2
0
2
1
1
2
0
0
0
2
0
7
1
0
1
0
0
1
0
0
0
0
1
0
0
0
2
0
0
2
1
2
1
1
2
0
0
1
1
0
0
1
0
1
0
0
1
2
0
1
1
0
0
0
0
2
1
0
0
1
1
1
2
1
0
0
2
0
0
3
1
0
1
3
0
0
0
0
0
2
4
2
0
1
0
0
2
1
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
1
1
0
0
0
1
0
0
1
2
0
1
2
0
0
0
0
0
2
0
1
0
0
1
2
1
2
0
0
2
1
0
0
0
0
3
0
0
0
0
0
0
0
0
2
1
2
0
0
0
2
0
0
0
0
0
0
2
1
0
1
1
0
1
0
0
1
1
1
2
0
1
0
0
1
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
1
0
0
3
0
1
1
2
0
0
1
1
2
0
0
2
0
1
2
0
2
0
1
2
0
0
1
0
0
1
2
3
1
0
2
0
1
0
1
0
2
0
2
1
1
1
1
0
0
0
0
0
0
2
2
0
0
1
0
1
0
0
0
0
0
0
0
2
2
0
3
0
1
0
1
0
1
1
1
1
0
2
0
2
0
0
0
0
0
0
0
1
0
2
2
0
0
1
0
1
1
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
2
0
2
1
0
1
0
2
0
0
0
0
2
0
1
1
1
0
0
0
0
1
0
2
0
2
0
0
1
0
2
0
0
0
2
0
0
1
0
0
0
1
0
0
0
1
0
2
2
2
2
1
0
1
0
1
1
0
2
0
0
2
2
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
1
0
2
0
0
0
2
1
1
0
0
0
1
0
1
1
0
0
0
2
2
0
0
1
1
0
0
0
0
0
2
0
2
2
0
1
2
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
2
1
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
3
0
1
2
1
1
2
2
1
0
0
1
0
0
2
0
0
2
0
2
2
2
0
2
0
0
2
2
0
0
1
0
1
1
2
0
2
0
0
1
0
0
2
1
0
1
0
0
0
0
2
0
0
1
1
1
0
0
0
2
1
0
0
0
0
1
2
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
2
2
0
1
0
1
2
1
0
0
0
0
1
0
1
0
0
1
0
0
1
0
1
0
1
2
0
0
2
1
0
1
2
0
0
1
0
0
0
0
0
1
0
0
1
2
2
0
0
1
2
3
2
0
0
2
2
0
0
0
0
0
1
1
0
0
1
0
0
0
2
0
2
0
0
0
2
1
1
2
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
1
1
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
1
2
2
0
1
0
0
0
0
0
0
0
0
0
2
2
1
0
0
2
1
0
0
1
0
0
1
0
0
0
0
0
2
3
2
0
1
1
0
0
1
2
0
0
2
1
2
2
3
1
1
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
1
1
1
1
1
2
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
1
1
2
1
0
2
0
0
0
0
0
1
0
0
1
2
0
1
1
0
1
2
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
2
0
1
1
1
0
1
1
2
2
0
0
0
2
2
0
0
2
2
0
1
0
0
0
0
2
1
1
2
0
0
1
0
1
2
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
1
0
2
3
0
1
0
0
0
1
3
0
1
1
0
0
0
0
0
0
1
0
0
2
2
0
1
0
1
0
0
1
0
0
2
0
1
0
1
0
0
0
0
0
1
0
0
1
2
0
0
2
0
2
0
1
2
0
1
2
0
0
0
2
0
2
0
2
2
0
0
0
1
0
0
2
0
0
2
3
2
1
0
1
1
0
1
1
2
0
1
0
2
0
1
0
0
1
2
0
1
0
2
0
0
0
2
0
1
0
1
0
0
0
1
0
0
0
1
0
0
2
0
0
1
0
0
2
0
0
0
0
3
0
1
0
0
1
1
0
0
3
2
1
0
0
0
1
2
2
2
0
1
5
2
0
0
2
1
2
0
0
1
0
0
2
1
0
1
2
0
0
2
1
0
0
2
1
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
2
1
2
0
0
0
2
1
0
0
2
0
3
0
0
1
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
2
2
0
2
2
0
2
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
1
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
2
1
0
0
0
0
2
0
1
0
0
0
2
1
2
2
2
0
0
0
2
1
0
2
0
0
1
1
1
0
1
0
0
0
1
3
0
2
0
2
1
0
0
0
1
0
0
1
1
1
2
2
0
2
0
1
0
0
2
1
0
0
3
0
1
0
2
0
1
0
0
1
1
0
2
0
1
2
0
1
0
1
0
0
0
3
0
0
1
0
0
1
1
0
1
2
6
0
0
0
0
0
0
1
0
2
0
0
1
2
0
1
0
0
0
0
2
4
0
1
0
2
0
1
0
0
1
2
0
1
2
1
0
1
1
0
0
0
1
0
0
0
1
1
1
1
1
2
1
0
1
0
2
0
1
1
0
0
1
0
1
0
1
0
3
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
2
2
1
0
0
1
0
0
0
0
2
0
0
0
1
0
2
0
1
1
2
2
0
1
1
0
0
1
0
0
2
0
0
1
1
1
0
0
1
1
0
0
2
1
1
2
2
0
2
0
0
1
1
0
2
0
1
0
0
2
2
0
0
0
1
2
0
2
1
3
2
0
0
0
1
0
2
0
0
1
0
0
2
2
0
0
2
0
0
0
1
1
0
0
1
1
0
0
0
2
1
3
0
1
0
2
1
1
0
1
2
1
1
0
0
1
0
2
0
0
2
1
1
2
0
2
0
0
2
0
0
0
1
2
0
0
1
2
0
0
1
0
0
2
2
2
0
1
0
0
0
1
0
2
0
0
1
0
0
1
0
0
3
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
1
2
0
1
0
2
1
2
1
0
1
1
2
1
0
2
2
0
2
1
2
2
0
1
0
1
2
2
2
0
1
2
1
1
0
2
0
0
0
2
2
1
2
1
0
0
1
0
0
1
0
0
0
1
2
0
1
0
1
1
1
0
2
0
2
0
0
1
2
0
1
1
2
0
1
2
2
1
0
1
2
2
2
0
0
2
0
1
2
1
0
0
0
0
1
0
1
0
0
0
2
0
1
0
1
0
2
2
1
0
0
2
2
0
0
0
2
1
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
1
0
1
1
2
0
0
2
1
0
1
0
0
1
0
4
0
2
1
1
1
0
0
0
0
1
0
0
0
0
2
1
0
2
4
3
0
1
2
2
2
0
2
1
0
2
2
0
0
1
0
0
0
0
0
1
2
0
2
0
0
2
2
0
2
1
0
0
0
1
0
2
0
1
1
0
2
1
0
1
1
0
0
0
0
0
0
0
2
0
0
0
1
1
2
1
0
2
1
0
2
0
0
0
0
0
1
0
0
0
2
1
1
0
0
1
0
1
0
0
0
0
0
2
0
2
0
2
1
1
0
2
0
0
1
0
1
1
0
2
0
0
0
0
1
1
1
1
0
0
1
1
0
3
2
0
0
0
2
2
1
1
0
1
0
0
0
1
1
0
1
0
0
2
0
1
0
1
2
0
0
0
1
2
2
0
2
0
2
1
1
2
0
0
0
0
0
1
0
0
0
1
0
0
0
1
2
0
0
1
0
0
1
1
1
1
1
0
2
2
2
2
0
0
1
1
1
0
2
0
2
2
0
0
1
0
0
1
1
1
0
0
0
2
0
0
0
0
2
1
1
2
0
1
4
3
0
1
0
0
2
1
3
0
1
0
1
2
5
0
2
0
0
1
1
0
0
1
0
2
0
1
1
0
1
1
0
2
0
1
2
0
0
0
2
1
2
0
0
0
0
1
1
2
2
0
0
0
1
0
1
2
2
0
1
0
2
0
0
2
2
0
1
0
1
2
0
0
2
0
2
0
1
0
0
2
0
2
2
8
0
0
0
0
0
0
0
2
0
0
2
3
1
1
1
1
1
2
2
2
0
4
0
2
0
0
1
0
0
0
0
0
1
0
2
0
1
0
0
2
0
0
0
0
0
2
0
0
0
2
1
0
0
0
2
2
1
0
1
1
0
0
0
2
0
2
0
0
1
0
2
1
2
2
0
1
0
0
2
0
1
0
0
0
1
0
1
0
2
0
2
0
2
0
0
1
0
0
2
0
1
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
1
2
2
1
0
2
0
0
0
0
0
2
1
0
1
0
0
1
0
2
1
0
0
0
2
1
1
2
2
0
0
0
1
2
0
1
0
1
0
2
1
0
0
1
2
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
1
0
1
1
0
1
0
1
1
0
1
0
1
0
0
2
0
2
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
2
0
2
2
1
0
0
4
0
0
1
1
0
1
0
2
0
2
0
0
0
0
0
1
1
2
0
0
0
2
1
0
1
1
1
0
0
0
3
2
2
0
0
2
2
2
2
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
2
2
1
2
2
1
0
1
2
2
0
1
0
1
0
2
0
0
0
1
1
1
0
2
2
0
0
1
0
2
2
2
0
2
0
0
0
0
0
1
2
1
2
0
1
1
3
1
0
1
1
0
2
2
0
0
1
0
1
0
0
2
2
1
0
1
0
1
1
0
1
1
0
1
0
0
1
1
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
2
0
0
2
1
0
0
2
0
0
0
0
8
2
0
0
3
0
0
0
2
1
0
1
0
0
0
0
1
1
2
0
0
0
1
0
2
1
2
1
1
0
0
0
1
2
2
0
1
1
1
0
1
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
1
2
0
2
0
2
0
0
0
4
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
1
0
1
1
0
0
2
0
1
1
2
0
2
0
2
0
1
0
0
1
1
0
1
0
1
1
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
2
0
1
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
3
1
0
0
2
2
0
0
3
0
0
1
0
0
0
0
0
1
1
2
1
0
0
2
0
2
0
0
0
0
2
1
3
1
1
1
2
0
0
2
2
0
1
2
0
0
0
1
0
0
0
2
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
1
0
2
0
3
0
0
1
0
0
1
0
1
1
0
2
1
2
2
0
1
1
0
2
1
0
0
1
1
3
2
3
0
1
0
1
2
2
0
2
0
0
2
0
0
0
0
0
2
0
2
0
2
1
0
1
2
1
1
0
2
1
2
2
1
0
1
0
0
0
0
2
0
0
0
2
0
0
1
0
0
1
1
1
0
0
0
0
0
1
0
1
0
2
2
1
0
1
0
0
0
0
2
2
0
0
0
0
1
0
0
1
0
0
2
0
0
0
2
0
0
2
0
2
2
0
0
1
0
0
0
2
0
0
1
1
0
1
2
0
0
2
1
0
1
0
1
2
1
0
1
0
1
0
0
0
2
1
0
0
0
0
0
2
2
2
0
1
1
0
1
0
0
1
0
2
0
0
2
0
1
0
1
1
1
0
0
0
1
0
0
1
0
2
1
1
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
1
0
2
0
1
0
1
0
1
2
0
2
0
0
0
1
2
0
0
0
0
0
0
2
2
0
0
1
2
2
0
0
0
0
0
0
1
0
2
1
2
1
0
3
5
0
0
2
0
0
0
2
2
2
1
0
2
1
1
0
0
2
3
0
0
0
1
1
0
1
0
1
1
1
2
1
0
0
0
1
0
0
0
0
0
0
2
1
1
0
0
2
0
0
1
0
2
1
2
1
1
1
1
2
0
0
2
1
2
0
2
0
2
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
1
2
0
0
0
0
1
0
1
0
0
1
0
1
0
0
1
2
0
0
1
2
0
1
0
1
2
0
2
0
0
0
4
0
0
0
1
1
0
2
2
1
0
0
3
0
0
1
1
1
0
1
0
0
0
1
1
1
0
0
1
0
0
1
1
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
3
0
2
2
0
0
0
0
2
0
0
2
0
0
0
1
3
2
0
4
0
0
1
0
2
1
0
2
0
0
1
0
0
0
2
0
1
0
1
1
0
0
1
0
1
0
0
0
2
3
1
0
1
0
0
1
0
1
0
0
0
2
0
1
2
0
0
2
0
3
2
1
0
0
1
0
1
2
2
0
3
1
1
1
0
0
2
0
0
1
2
0
0
2
1
1
0
0
0
1
2
2
0
2
0
0
0
1
1
0
2
1
0
1
0
2
2
0
0
2
1
2
2
0
0
0
0
1
1
0
0
0
2
4
2
1
1
1
0
1
2
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
2
2
0
0
1
0
0
0
2
0
4
0
2
0
1
0
2
2
1
2
0
1
1
0
1
3
0
0
0
0
1
0
0
0
0
1
1
1
0
2
0
2
1
2
0
0
2
0
0
0
2
1
0
1
1
0
0
1
2
1
4
1
0
0
0
1
1
4
0
2
0
1
0
2
2
1
0
1
1
0
0
1
0
0
0
0
2
2
0
1
0
0
1
0
0
0
2
1
0
1
2
1
0
3
2
0
1
1
1
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
2
0
0
2
1
0
1
1
0
1
1
1
2
0
0
0
0
0
1
2
0
2
0
0
1
2
0
3
0
0
1
0
0
0
0
2
0
4
2
1
1
2
0
2
0
2
1
1
1
2
0
0
0
0
0
1
0
0
0
1
0
1
1
1
0
0
1
1
0
1
0
0
0
0
1
1
3
0
2
2
2
1
2
0
0
0
1
0
0
2
1
2
1
0
0
1
1
2
0
1
0
0
0
2
1
14
1
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
2
0
2
1
0
0
0
0
2
0
0
2
1
1
1
2
0
0
2
0
1
1
1
2
0
0
0
0
0
2
1
0
1
0
1
0
0
0
1
0
2
2
0
0
2
1
0
0
1
1
0
0
2
1
2
1
0
2
0
1
1
0
0
2
1
0
0
2
0
0
0
1
2
2
1
0
0
2
0
0
1
2
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
2
2
0
0
1
1
0
0
0
1
0
1
2
0
0
2
2
0
1
0
0
2
2
0
2
1
2
1
0
1
0
0
0
0
2
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
3
2
0
2
1
2
0
2
1
0
0
2
1
0
0
0
0
1
0
2
0
1
1
2
2
0
0
0
1
0
0
0
1
0
1
0
2
1
2
0
1
2
0
0
0
2
1
2
2
0
0
2
1
2
2
0
2
2
1
2
1
0
1
1
2
2
2
0
2
1
0
0
1
1
1
0
1
0
0
1
3
0
1
0
0
1
3
1
2
0
0
0
0
1
0
1
0
0
1
0
1
2
1
0
1
2
0
0
1
1
2
2
2
2
1
0
1
0
2
0
0
2
1
0
2
1
0
1
0
0
2
0
0
1
0
1
2
0
2
0
0
1
0
2
0
1
0
2
0
1
2
2
0
0
0
1
1
3
2
1
2
0
0
0
0
0
0
0
1
1
2
0
3
2
2
0
0
0
0
2
2
0
2
0
0
1
0
2
0
0
1
0
0
2
1
1
0
2
2
0
1
0
0
0
1
0
1
0
2
2
0
1
0
2
0
1
0
0
0
0
3
0
0
1
2
0
2
0
2
2
0
0
2
1
2
0
0
0
0
2
0
0
0
1
1
2
2
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
2
2
0
2
0
0
2
1
0
1
0
0
2
5
1
0
0
1
1
1
0
0
0
0
2
2
2
2
0
0
0
2
0
0
0
0
2
1
2
1
0
3
1
6
0
1
0
0
0
1
0
0
0
1
0
0
1
0
1
1
2
1
0
1
0
0
0
2
0
0
0
0
1
2
0
1
1
1
0
0
0
1
1
0
0
2
2
2
0
0
1
0
1
0
1
0
0
1
1
0
0
1
0
0
0
2
0
0
1
0
0
1
1
2
0
0
2
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
1
1
1
0
1
2
0
0
0
2
0
0
1
0
2
1
0
1
1
0
1
0
1
1
1
0
0
0
0
1
0
0
1
0
0
2
2
1
0
1
0
0
2
0
1
1
1
1
1
2
0
0
1
0
2
0
2
1
0
2
0
1
0
0
2
1
0
1
0
0
1
0
0
0
0
1
2
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
2
1
0
0
1
0
0
2
0
2
2
0
0
0
0
0
1
1
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
2
0
2
1
2
2
1
0
0
0
0
0
0
0
3
0
2
0
0
0
1
1
0
0
1
2
2
0
0
1
0
0
0
1
0
1
0
0
0
1
2
2
0
0
2
0
1
0
0
0
0
0
2
0
2
2
0
1
0
1
1
0
0
0
0
2
1
1
3
0
0
0
1
2
1
0
0
1
1
1
2
0
0
2
0
1
1
2
0
0
1
0
0
2
0
1
0
2
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
1
0
0
2
0
0
2
2
0
1
0
1
0
0
1
1
1
2
0
0
0
0
2
0
2
0
2
0
0
0
0
2
0
0
1
0
3
1
0
2
1
0
1
2
2
0
2
0
0
1
0
0
1
1
0
1
0
0
0
2
1
0
6
0
0
0
1
1
2
1
1
0
1
0
1
1
0
0
0
0
2
0
0
1
1
0
1
2
2
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
2
0
0
2
2
0
0
1
0
3
0
0
1
2
1
0
0
1
2
1
0
2
0
2
6
0
1
2
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
2
2
0
2
0
0
0
0
0
0
2
0
0
2
0
2
1
0
0
0
2
0
2
1
0
0
2
0
0
6
0
0
0
3
1
0
2
1
0
0
1
0
0
0
2
0
1
0
0
1
0
2
0
0
0
2
1
0
1
0
1
2
2
2
1
0
0
2
1
1
0
0
2
1
2
1
2
3
0
1
0
0
2
2
0
1
0
0
0
0
1
0
1
0
0
0
0
1
2
0
0
1
1
2
2
0
1
0
2
0
0
0
1
1
2
0
0
2
2
0
1
2
1
0
0
1
0
2
0
2
0
0
2
2
0
0
1
0
2
0
1
0
1
1
0
1
1
1
0
1
0
0
0
0
1
1
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
1
2
1
0
0
0
0
1
0
0
0
1
0
0
0
2
1
0
0
0
0
0
2
0
1
0
0
1
1
1
0
2
1
0
0
3
0
2
1
2
1
1
0
0
0
1
0
0
0
0
0
1
1
2
0
0
0
0
3
0
2
0
0
2
2
0
0
0
3
0
1
0
0
0
3
1
0
2
0
1
0
0
2
0
0
0
1
0
0
0
0
1
0
0
2
0
1
3
1
0
0
0
0
1
2
0
0
2
0
1
0
0
0
2
0
0
2
0
0
2
1
0
0
2
0
1
0
1
2
2
0
0
1
1
1
0
0
0
0
1
1
1
2
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
2
1
0
1
0
0
0
1
0
0
0
1
0
2
0
1
1
0
3
0
1
1
0
1
4
2
2
0
0
0
0
1
1
1
0
0
0
0
2
0
2
0
0
4
0
0
0
0
3
1
0
0
0
0
1
1
2
0
0
1
0
0
3
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
1
2
0
1
0
2
0
1
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
1
2
1
0
0
2
2
0
0
1
0
0
1
2
1
1
0
2
2
4
0
2
3
0
1
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
2
0
0
4
0
1
0
2
0
1
1
2
2
2
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
2
0
0
0
1
0
1
1
1
1
2
1
0
3
0
0
0
1
0
1
0
1
2
1
0
2
2
0
2
2
1
0
1
0
1
2
0
0
0
0
1
1
0
0
0
1
1
0
0
1
0
2
1
0
0
0
2
0
0
2
2
0
0
1
1
1
1
0
2
0
0
0
0
1
0
2
1
1
0
0
2
0
2
2
0
0
1
2
0
0
2
0
3
1
0
0
0
0
2
2
1
0
1
3
3
2
0
1
0
1
0
0
0
1
1
0
5
3
2
2
1
0
0
0
2
0
1
0
1
1
2
0
0
3
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
1
0
1
0
1
0
0
1
0
0
1
2
1
0
0
4
2
1
0
0
3
0
0
0
0
1
1
0
2
1
1
0
0
1
2
2
0
0
2
0
1
0
0
2
0
0
0
2
1
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
1
2
0
0
0
2
0
3
2
1
0
0
0
0
3
0
0
1
2
0
0
0
10
0
1
2
0
2
2
0
2
1
1
0
0
0
0
0
0
0
2
2
2
2
1
0
0
1
2
0
2
2
2
0
1
1
1
1
1
0
2
1
0
1
0
0
0
2
0
1
0
0
0
0
0
1
2
0
2
0
1
0
2
0
1
2
0
2
0
0
1
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
2
0
2
0
0
1
1
1
1
0
1
0
2
2
0
0
3
0
0
0
2
1
0
0
1
1
1
2
0
0
1
0
0
1
0
0
1
3
0
2
0
0
1
3
2
1
1
1
2
2
1
0
0
2
0
0
0
1
0
0
1
0
3
0
2
0
0
1
1
0
0
0
0
1
0
2
0
0
0
2
1
1
1
1
2
1
2
2
2
0
1
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
2
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
1
0
2
0
0
1
0
0
0
1
0
0
0
0
0
2
1
1
0
0
0
0
0
1
0
0
0
0
2
2
2
0
1
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
1
0
2
0
2
0
2
0
3
2
2
3
0
1
1
0
0
0
0
2
0
0
2
0
2
0
1
1
0
1
0
0
0
1
1
3
1
0
0
1
0
2
0
2
0
0
0
0
2
0
0
1
0
1
2
1
0
4
0
2
0
1
1
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
1
1
0
2
2
0
0
2
1
2
0
0
0
0
0
2
1
1
1
2
0
0
2
3
0
2
1
0
1
2
0
0
0
0
1
1
0
0
0
0
0
3
2
1
1
0
0
1
2
0
0
1
1
1
2
0
0
2
0
0
1
1
0
2
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
2
1
1
0
0
2
0
0
1
0
0
0
0
0
1
2
1
2
0
0
0
1
0
2
1
0
2
0
0
2
0
0
0
0
0
1
0
0
0
2
1
0
0
0
1
0
0
2
0
0
0
0
1
2
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
1
0
2
0
2
0
2
0
0
1
1
2
0
1
1
1
2
0
0
0
0
2
0
0
2
2
1
0
0
0
1
2
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
1
0
0
0
2
2
0
0
1
0
0
0
0
1
1
2
2
1
1
0
1
0
0
0
0
0
0
0
0
2
1
1
0
0
1
0
0
3
0
0
1
0
1
2
1
2
0
0
2
0
0
2
0
0
0
1
0
1
1
1
0
2
2
0
0
2
0
2
1
2
1
0
0
0
0
1
0
0
0
2
0
0
1
0
1
0
1
0
0
3
2
0
1
0
2
1
1
0
2
0
0
0
0
0
0
2
1
2
1
0
0
0
1
0
0
1
0
1
0
0
2
1
0
1
0
1
2
0
3
0
3
2
2
2
1
0
1
0
2
0
2
0
0
0
0
2
0
0
0
3
0
0
1
0
0
2
0
0
0
0
0
0
3
0
1
2
1
1
4
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
1
0
2
0
0
2
2
2
0
1
0
0
0
1
0
0
2
1
2
0
1
2
2
0
2
1
2
1
1
0
0
1
2
2
0
0
1
1
1
1
0
0
0
1
1
1
0
1
0
1
0
0
0
0
1
0
2
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
2
2
0
1
1
0
0
0
2
2
1
1
0
0
1
1
1
2
0
1
0
2
1
1
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
1
1
1
0
0
1
0
2
0
1
0
0
1
1
0
2
0
2
1
1
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
2
0
0
0
0
2
3
2
0
0
2
0
0
0
0
1
1
1
2
2
0
0
1
0
2
0
3
1
0
0
0
0
0
1
1
1
0
1
0
0
0
1
2
0
0
1
0
0
0
1
0
1
0
1
1
1
1
2
0
0
0
1
0
0
1
0
1
0
2
0
0
1
0
0
0
2
0
1
2
1
2
1
1
0
0
2
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
2
0
1
0
1
0
1
1
0
0
0
2
2
2
0
0
2
0
0
0
1
0
0
1
0
4
0
0
2
0
0
2
0
1
0
2
0
1
2
1
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
1
0
0
2
1
2
0
2
0
1
0
2
0
0
2
0
0
4
0
2
0
1
0
0
0
0
2
0
0
2
0
0
0
0
1
1
0
0
3
1
0
1
0
1
0
1
1
0
1
0
0
1
4
0
0
1
0
1
0
1
1
1
0
1
1
0
2
2
0
0
0
0
0
1
0
1
2
3
0
0
1
1
2
1
0
1
2
0
0
2
0
0
2
1
1
1
0
0
2
0
0
0
0
1
2
0
0
0
0
1
0
1
2
0
0
1
1
0
0
1
0
0
0
0
2
3
1
2
2
1
1
0
0
1
0
1
0
2
3
0
1
0
0
1
1
1
1
2
0
0
2
2
1
0
1
2
1
0
0
2
0
2
0
2
1
0
2
0
1
1
2
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
1
2
0
0
1
0
0
1
0
2
2
0
2
1
1
0
1
2
1
0
0
1
0
0
0
2
1
2
2
0
0
1
1
0
1
0
1
0
0
0
0
1
0
0
1
2
0
2
2
2
1
0
0
0
1
0
0
0
0
2
0
0
0
1
0
1
5
0
1
0
2
1
2
0
0
1
0
3
1
1
2
0
1
2
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
2
2
1
1
0
1
0
0
1
1
1
2
2
0
0
0
0
0
5
0
0
0
0
0
1
0
0
1
0
0
0
2
1
1
0
2
2
1
0
0
1
0
0
0
2
0
2
0
0
0
1
2
0
2
0
0
0
3
0
0
0
1
0
1
0
0
1
0
1
0
2
0
0
0
0
2
0
0
0
1
0
0
0
2
0
1
1
2
1
1
0
0
0
0
0
4
0
1
0
0
0
2
1
0
2
0
2
0
1
1
0
0
2
1
0
0
2
0
2
1
0
0
0
0
1
0
0
1
0
2
2
0
2
1
0
0
0
0
0
3
2
0
2
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
2
2
0
2
0
0
2
0
1
0
0
0
1
0
1
1
2
0
2
0
0
2
0
0
2
0
1
2
0
1
1
1
0
1
2
1
1
0
1
2
2
0
0
0
0
0
2
0
0
0
0
1
0
0
1
2
0
0
0
2
0
0
2
1
1
0
2
1
0
0
2
6
2
1
1
2
0
2
0
0
0
2
0
3
0
0
2
0
2
2
0
0
0
1
1
0
0
1
1
0
2
1
0
0
1
0
1
0
3
2
1
0
0
0
2
0
0
0
0
0
1
2
0
2
1
1
0
0
1
1
0
0
1
0
2
1
0
0
1
0
0
1
2
1
0
0
0
0
3
0
2
2
0
1
0
3
2
1
0
0
2
0
0
0
2
0
0
0
0
0
2
2
0
0
1
1
2
1
0
0
0
2
0
0
0
2
0
1
2
0
0
0
2
1
0
0
1
1
0
0
2
1
1
0
2
2
2
0
1
2
0
0
1
0
0
0
0
1
0
1
0
1
0
1
0
0
1
1
0
1
0
1
0
0
0
2
0
0
1
1
1
0
2
0
1
0
0
0
0
0
2
0
0
1
2
0
1
1
0
0
0
1
0
2
1
2
1
0
0
1
1
0
0
0
2
0
1
0
0
1
2
2
1
0
3
0
2
2
0
0
2
0
0
1
1
0
0
1
2
0
3
1
0
1
0
1
2
2
0
0
0
0
1
1
0
0
2
0
0
2
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
2
1
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
2
0
2
0
0
1
0
2
0
0
2
0
1
2
1
0
0
1
0
0
1
3
1
0
2
0
0
0
0
1
2
0
1
1
0
1
1
1
0
0
2
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
2
0
2
0
1
2
0
0
4
0
1
0
1
0
2
2
0
1
0
1
0
2
1
1
0
4
0
1
0
0
1
0
0
0
2
0
0
1
0
3
3
1
1
1
1
0
0
0
2
0
0
0
0
1
0
1
0
1
0
1
1
1
1
0
2
2
1
0
0
0
0
1
0
2
0
2
1
0
2
0
0
0
0
1
1
0
0
0
1
1
2
0
2
0
1
1
0
1
2
0
1
1
2
0
1
2
2
1
0
0
1
0
0
0
1
2
2
0
0
2
3
1
1
0
0
0
0
1
0
0
2
2
0
0
0
1
2
0
3
0
0
0
0
1
0
1
0
0
0
1
0
1
2
0
1
1
1
2
0
2
2
1
0
2
1
1
3
2
0
0
0
2
0
0
0
0
1
0
1
2
1
1
2
2
2
0
0
0
2
1
0
0
0
1
2
1
2
3
0
0
0
2
1
0
2
1
0
0
2
2
0
2
0
1
1
0
0
0
2
1
0
0
2
0
0
0
0
2
2
0
0
0
2
1
0
0
1
0
0
0
0
1
2
1
2
2
0
1
0
0
1
0
0
0
0
2
0
2
0
1
0
2
1
1
6
0
1
1
2
4
1
1
0
0
0
2
0
1
1
0
2
0
0
0
0
1
1
2
0
0
0
1
1
1
2
0
0
2
0
0
0
0
0
0
0
1
0
1
0
1
3
1
0
0
1
1
1
0
1
0
0
0
2
2
0
0
0
2
1
1
0
0
0
0
0
1
1
0
1
1
0
0
2
1
2
0
2
1
2
0
1
0
2
0
0
0
1
0
2
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
1
1
2
2
2
1
0
0
1
0
2
0
1
2
0
1
0
2
1
1
1
0
1
1
0
1
1
2
0
0
0
0
1
0
2
2
2
0
1
2
1
0
0
0
1
2
0
2
2
0
1
1
1
2
2
1
2
0
0
1
1
1
0
0
0
2
1
1
1
0
0
1
1
0
1
1
0
0
0
2
0
0
1
2
1
0
0
2
0
2
0
1
1
0
0
2
3
0
0
0
0
2
0
0
0
2
1
2
2
2
0
0
0
1
1
1
3
0
2
0
1
0
0
0
0
2
1
2
1
0
0
0
0
0
0
0
1
0
2
1
1
0
0
0
1
0
2
0
0
0
1
0
2
0
0
0
1
0
2
0
1
2
2
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
2
1
0
1
2
0
2
1
0
1
0
0
0
0
0
1
0
1
0
1
0
1
0
2
0
1
1
3
2
0
2
0
0
1
2
0
0
0
0
0
2
0
0
0
4
2
1
0
0
0
0
0
1
0
2
2
0
0
2
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
1
2
2
1
1
1
0
3
2
1
0
2
1
0
0
0
1
0
1
2
1
0
0
1
1
1
2
1
0
0
0
0
1
0
0
3
0
2
1
1
0
0
0
1
2
0
0
0
1
0
2
0
5
0
1
0
2
1
4
0
0
0
0
0
2
0
0
0
0
2
1
1
1
0
2
2
1
0
0
2
0
0
1
0
1
2
0
0
2
0
1
1
0
0
0
2
2
0
1
0
0
2
0
0
1
4
0
1
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
3
0
1
1
2
1
0
1
0
1
0
0
0
2
0
1
1
0
1
0
2
0
1
2
1
2
0
0
1
0
0
2
1
0
1
1
0
0
1
1
1
1
0
0
2
1
2
0
2
1
1
1
2
0
0
1
1
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
2
0
1
0
2
2
0
0
1
0
0
0
2
1
0
2
1
1
0
0
0
0
0
0
2
1
0
0
0
0
1
1
0
1
1
0
0
0
0
1
2
0
1
0
2
1
0
0
1
0
0
0
0
0
0
0
2
1
2
1
0
2
0
0
0
0
1
0
3
1
0
0
2
0
2
0
1
0
2
3
0
2
1
1
2
0
0
0
0
1
2
0
0
2
1
0
0
1
1
2
0
0
0
0
2
0
0
0
2
0
1
2
0
1
2
0
0
1
1
1
2
0
0
0
2
0
0
2
0
0
0
1
2
0
0
0
2
0
0
3
0
1
2
2
2
0
1
2
1
0
2
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
1
1
0
0
0
1
0
0
2
0
1
2
1
0
2
4
2
0
0
2
0
1
0
0
1
0
0
0
1
3
1
0
0
0
2
2
0
0
0
0
2
0
0
1
0
2
0
0
2
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
3
0
0
2
2
2
0
1
1
1
0
2
0
2
0
0
0
2
0
1
1
1
0
1
1
0
0
1
1
2
1
1
1
0
0
1
1
0
2
2
0
0
0
1
2
0
0
0
2
2
0
0
1
1
0
2
1
0
1
0
0
2
0
1
0
2
1
2
0
0
0
0
1
1
0
0
0
1
1
0
1
0
0
2
0
3
1
0
0
0
0
0
2
0
0
0
1
0
0
0
1
1
2
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
4
0
1
0
1
1
0
0
0
1
0
2
1
0
1
3
0
0
0
2
0
1
1
0
0
0
0
1
0
0
2
1
2
0
0
0
0
2
0
2
2
0
0
1
1
0
0
2
0
2
2
1
1
3
0
1
2
1
2
2
0
0
2
0
0
0
1
0
2
3
2
0
2
2
0
1
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
1
1
2
0
0
2
2
0
0
0
0
0
1
1
0
2
0
0
0
1
0
2
1
0
1
0
0
0
1
2
0
2
0
0
1
0
0
1
0
2
0
0
0
1
2
0
1
0
0
0
2
2
2
2
0
0
0
0
2
0
0
0
2
2
2
3
0
0
2
2
0
0
1
0
0
1
0
0
2
1
1
2
2
0
1
2
0
1
2
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
1
1
0
2
0
0
0
0
0
1
0
1
1
0
2
1
1
0
0
1
0
1
0
2
1
2
1
2
2
2
1
0
0
1
0
1
0
0
1
0
1
0
2
0
0
1
0
2
2
0
1
1
0
2
1
1
0
1
2
1
1
0
0
1
0
0
0
0
0
1
1
1
0
0
0
1
1
0
2
0
2
0
0
1
0
0
0
0
0
1
2
2
0
0
0
0
1
0
0
1
0
0
0
0
1
1
1
1
0
0
1
1
1
0
1
0
0
2
0
0
1
0
0
0
0
2
0
0
0
1
0
2
0
1
1
0
1
0
1
0
0
1
0
0
0
1
2
1
0
2
0
1
2
3
1
1
1
2
0
0
0
0
1
1
1
1
0
3
1
1
0
0
0
0
3
0
1
1
0
2
2
0
2
1
0
1
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
1
1
0
0
0
2
0
0
1
2
2
3
2
0
0
1
1
1
2
1
0
0
0
0
0
0
0
1
0
0
0
2
1
0
3
1
0
1
2
0
0
0
0
1
2
1
1
0
0
3
0
2
0
2
1
2
1
2
0
2
2
0
0
0
2
1
0
0
1
1
0
2
0
1
0
2
0
2
0
0
0
1
0
0
2
0
0
1
0
1
0
2
0
2
0
0
2
0
0
0
1
1
0
2
3
0
0
0
1
0
0
1
0
2
0
1
2
0
2
0
0
0
2
0
0
0
2
0
1
0
0
0
0
2
4
1
2
0
1
0
0
1
1
0
2
0
0
0
2
0
2
2
0
0
1
0
1
1
0
1
0
0
2
1
0
2
0
0
2
0
1
2
0
1
2
0
0
2
0
0
0
0
0
0
0
0
5
1
2
0
2
2
2
0
0
1
1
1
0
1
2
1
0
1
0
0
0
2
0
1
0
1
3
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
1
0
0
0
0
0
2
0
2
1
0
0
3
0
1
1
0
0
1
1
0
4
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
2
1
0
2
0
2
0
1
0
2
0
1
1
0
2
1
0
0
1
0
0
1
1
2
2
0
0
1
2
0
1
0
1
0
0
0
3
0
2
2
2
0
2
2
1
2
2
1
0
0
1
1
2
0
1
1
1
0
1
1
0
0
0
3
0
2
0
5
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
2
2
1
1
0
0
1
1
0
0
0
0
1
0
0
0
3
1
2
0
0
2
0
2
0
1
0
1
2
0
0
0
1
0
0
2
0
0
1
1
0
0
1
1
0
2
0
1
1
0
2
2
0
0
0
2
0
0
0
1
0
1
0
2
1
1
1
0
2
0
1
1
0
0
1
0
0
1
0
2
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
1
2
0
1
1
1
0
0
2
0
0
0
0
0
2
2
0
0
1
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
1
0
1
0
2
0
0
1
1
3
2
0
0
1
0
1
8
1
0
2
1
2
0
0
2
0
2
3
2
0
0
0
0
1
0
0
2
2
0
2
2
0
0
3
0
2
0
0
0
0
0
0
0
1
0
2
0
2
0
1
1
0
1
0
2
1
0
1
2
1
2
0
3
0
0
0
0
0
1
0
0
0
3
2
0
0
0
0
0
0
1
1
0
2
0
2
0
1
0
0
2
0
2
0
0
0
1
0
0
0
1
1
0
0
0
1
2
0
1
1
0
0
0
1
1
0
0
2
2
0
0
0
1
0
0
1
2
2
0
1
0
0
2
0
0
1
0
0
0
1
0
1
1
0
0
2
0
0
1
0
1
0
0
0
0
0
2
1
0
1
1
0
0
1
2
0
0
1
1
0
0
2
1
0
2
0
0
0
0
0
2
2
2
1
1
2
0
1
2
0
0
1
1
0
0
0
0
0
0
2
1
0
2
0
1
2
0
0
0
3
1
1
5
2
1
0
2
0
2
1
1
0
0
0
0
0
0
0
0
2
0
0
2
0
1
1
0
0
2
2
0
0
1
0
0
2
0
1
2
3
1
0
1
0
1
0
0
0
2
0
1
0
2
2
1
0
0
0
0
0
0
1
1
1
0
2
0
1
0
0
0
1
1
1
0
0
2
0
0
0
1
0
0
0
4
0
1
0
2
0
2
0
0
0
3
1
2
0
0
0
0
0
2
2
1
0
0
0
2
0
1
1
1
0
1
0
0
1
0
0
1
0
2
0
0
2
0
1
0
0
0
1
0
1
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
2
1
1
1
0
1
0
0
0
0
0
0
2
0
2
0
2
0
2
2
2
0
2
2
1
1
1
0
0
0
1
2
2
0
0
0
1
2
0
0
0
1
0
0
0
0
2
0
0
1
2
1
0
0
2
2
0
0
0
3
0
0
0
1
1
0
0
1
1
2
0
0
0
2
2
1
0
2
0
2
1
1
2
0
0
0
0
2
2
0
0
1
2
1
0
0
2
0
0
0
0
0
1
1
0
2
0
2
1
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
3
0
1
2
2
1
2
1
0
2
0
1
0
2
1
0
1
1
0
2
2
0
0
1
0
0
0
0
1
0
2
2
0
1
0
4
2
0
1
1
1
1
0
2
0
3
0
2
2
2
0
1
1
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
1
1
0
1
3
0
0
0
0
0
2
0
1
0
0
1
1
0
0
1
0
0
2
0
0
1
0
0
0
2
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
2
2
0
2
1
0
1
2
3
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
2
0
0
0
1
0
1
1
0
1
0
0
0
1
0
0
1
0
0
2
2
1
1
0
0
0
0
1
2
0
2
0
0
0
2
0
0
0
1
2
2
0
0
0
2
0
0
2
2
1
1
0
3
1
1
0
1
1
0
0
1
2
2
0
1
3
0
0
1
0
2
1
1
0
2
0
2
1
1
0
0
0
2
0
0
0
0
0
0
2
0
1
1
4
1
1
1
2
0
0
1
1
2
0
2
1
1
2
0
0
0
1
0
0
1
0
1
0
0
1
6
1
2
1
0
0
2
2
0
2
2
1
0
1
3
0
0
1
1
1
0
0
0
0
1
0
1
0
2
0
0
0
0
0
2
0
1
0
2
0
1
0
0
0
1
1
1
3
0
2
2
0
1
0
0
0
1
0
0
0
1
0
2
2
0
0
0
0
2
2
0
2
1
0
0
1
2
0
1
0
1
0
1
1
1
0
0
0
1
1
0
1
0
1
0
2
1
1
1
0
0
1
1
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
2
0
2
2
0
0
2
2
2
1
1
1
0
0
3
1
0
0
0
2
1
2
0
2
2
1
0
3
2
0
0
2
1
0
1
0
0
2
0
3
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
1
0
0
2
2
0
1
1
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
2
2
0
2
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
1
2
0
0
2
1
2
0
0
3
0
2
0
2
0
0
1
0
0
2
0
0
0
1
0
0
2
2
0
2
0
0
0
1
0
1
0
2
2
2
0
1
1
0
0
1
0
1
2
1
2
0
0
4
1
0
2
0
1
1
0
2
0
0
0
0
0
0
1
0
1
0
2
1
1
1
0
1
1
0
1
1
0
0
0
2
1
0
0
0
0
2
0
2
0
1
0
0
1
0
1
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
2
1
0
2
0
0
1
3
3
0
2
2
0
0
2
0
0
0
1
0
0
0
0
4
0
1
2
1
1
1
0
2
0
0
2
2
0
0
0
0
1
1
0
0
1
1
1
0
0
1
1
0
0
1
4
1
1
0
6
0
0
0
1
0
0
1
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
2
1
1
0
0
2
0
1
2
2
2
2
1
1
2
0
2
1
0
3
0
0
0
0
1
0
0
0
0
0
0
1
2
0
2
0
0
1
0
2
1
0
0
2
0
0
0
0
0
2
2
1
2
0
0
2
0
1
2
0
1
1
2
1
1
0
0
2
1
0
1
0
2
0
2
0
1
0
2
0
2
0
0
0
1
2
2
1
0
0
0
0
0
2
0
1
5
2
2
2
0
0
0
2
0
0
0
1
2
0
2
0
1
1
0
0
2
0
0
0
1
0
1
1
3
0
0
0
0
0
0
2
4
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
3
2
2
1
0
0
0
0
0
2
2
1
0
0
1
0
1
0
0
0
1
0
2
0
0
1
0
1
0
2
0
2
0
0
0
1
0
0
0
1
1
2
0
0
0
2
1
1
0
0
1
0
1
0
0
0
2
0
0
0
1
1
2
0
0
0
1
2
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
2
2
1
0
0
0
0
0
0
1
0
2
0
0
1
1
1
2
0
1
2
0
1
1
1
0
0
0
2
1
2
1
2
1
2
0
1
1
0
0
0
1
2
0
0
0
1
1
0
0
0
1
0
2
1
0
0
2
0
0
0
1
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
1
2
1
2
0
0
0
0
1
0
0
0
1
0
0
0
1
2
0
0
0
0
1
2
0
0
1
1
0
2
0
1
0
0
1
0
0
1
1
2
0
1
1
2
0
0
0
1
0
0
2
1
0
0
0
0
4
0
1
0
0
0
0
0
2
0
2
0
2
0
1
1
0
1
0
2
0
1
0
0
0
1
1
0
0
0
1
0
1
0
1
0
2
0
2
0
0
0
2
0
2
1
2
1
0
0
2
2
3
2
2
0
1
0
2
1
2
0
1
2
0
2
0
0
0
1
1
1
1
0
1
0
0
1
0
2
2
0
1
2
0
0
1
2
1
0
2
2
2
1
0
1
0
2
1
0
2
0
2
0
1
0
1
0
1
0
0
0
5
2
0
1
0
1
2
1
0
0
0
0
1
0
2
0
0
0
0
0
0
1
2
0
0
0
2
1
0
0
0
0
1
1
2
0
0
2
1
1
0
2
1
0
0
1
0
0
2
2
0
0
2
0
2
2
0
0
0
2
2
1
0
0
2
2
1
0
0
2
0
1
0
0
2
2
1
0
4
2
0
1
2
0
1
0
0
1
3
0
2
0
1
0
1
2
1
0
1
2
1
0
0
1
1
0
2
0
0
0
4
1
0
0
2
0
0
0
1
1
1
0
1
1
0
0
2
0
0
2
0
1
1
1
1
0
1
2
2
0
1
0
0
1
2
0
3
0
0
2
1
0
2
1
2
2
0
0
0
1
1
2
0
1
0
1
1
0
0
0
2
0
2
0
1
0
3
0
0
0
1
3
0
0
0
1
1
2
0
0
0
0
0
0
1
0
1
1
0
2
0
0
0
2
1
0
2
1
0
0
1
0
1
0
0
1
0
2
1
0
0
0
0
1
1
1
0
0
1
1
0
1
0
0
0
2
2
0
0
2
2
2
2
2
1
2
0
1
1
0
0
0
2
1
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
2
1
2
1
2
1
1
0
1
1
0
1
1
0
0
2
0
0
0
1
9
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
1
1
0
2
0
0
0
0
1
0
0
0
0
1
2
0
2
1
1
0
1
1
0
0
0
1
0
1
0
0
2
1
2
1
1
0
1
3
0
2
2
2
2
0
2
0
0
0
0
0
2
2
0
0
0
0
2
0
1
0
0
1
0
2
1
0
0
0
0
0
0
2
2
0
2
1
1
0
0
3
0
1
0
1
0
0
0
2
2
0
2
1
0
2
1
0
0
2
0
0
2
0
0
1
1
1
0
2
1
1
0
0
1
0
0
0
0
1
0
0
9
0
4
0
1
1
0
0
0
0
2
0
0
0
0
1
1
0
1
1
1
0
0
0
2
2
0
0
2
1
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
1
1
0
0
1
0
0
1
0
1
0
2
0
2
0
0
0
0
1
1
2
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
2
1
1
0
0
1
1
0
0
1
0
0
1
2
0
2
0
0
0
1
2
1
1
1
1
2
0
0
0
0
0
0
0
1
0
0
2
1
1
2
0
0
0
0
2
1
0
0
0
1
2
2
0
0
1
1
1
0
0
0
1
1
0
0
1
3
0
0
2
0
0
2
1
3
0
0
3
2
0
3
0
2
0
1
0
0
1
2
0
2
0
0
2
1
0
2
0
1
1
1
2
0
1
2
2
0
0
0
2
0
0
1
0
0
1
0
0
0
2
0
1
1
1
0
0
1
1
1
2
0
0
0
1
6
2
2
0
0
1
1
0
0
0
2
0
1
0
1
2
0
1
0
1
0
0
2
1
0
1
0
0
0
0
0
1
0
1
0
2
1
3
2
0
0
2
3
2
0
1
2
2
2
2
0
1
0
0
2
1
0
0
1
2
1
0
0
1
0
1
0
0
2
0
0
2
0
2
0
1
0
1
1
0
0
0
0
2
0
0
0
0
2
1
0
0
1
2
0
0
0
0
2
1
1
0
1
2
2
0
0
1
0
0
0
0
0
2
1
3
0
0
0
1
0
1
1
1
2
0
0
2
0
0
0
0
0
2
0
2
1
0
0
2
2
0
0
2
0
0
1
0
0
1
1
1
0
0
0
0
1
0
2
0
0
1
0
1
0
1
0
1
0
0
0
1
1
1
2
0
0
0
0
0
0
0
2
0
0
1
0
1
2
1
0
0
1
0
0
2
0
0
0
1
3
0
1
0
1
0
2
0
0
1
2
2
1
0
2
2
0
2
2
1
0
0
0
0
0
1
0
2
1
0
1
2
3
1
0
0
0
1
1
1
2
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
2
0
2
1
2
2
1
0
1
2
0
1
1
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
1
0
0
0
1
0
0
1
2
0
0
0
1
0
0
1
1
0
2
0
0
0
1
2
0
1
0
0
0
0
2
0
2
1
0
0
0
2
2
1
2
0
1
0
0
0
2
1
0
0
2
1
2
0
2
0
1
2
0
0
0
3
0
0
1
0
0
2
0
1
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
1
0
1
0
1
1
1
0
1
0
0
0
0
0
1
0
1
0
0
2
1
0
0
2
0
0
1
1
1
0
0
0
2
0
2
2
0
0
0
0
0
1
2
2
0
0
4
2
3
0
2
1
0
0
1
0
0
0
1
1
1
1
2
2
1
0
0
1
1
0
1
3
1
0
1
0
0
0
1
1
1
2
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
2
0
2
0
0
0
2
2
1
0
0
1
1
1
1
0
0
0
1
0
0
0
1
2
0
0
0
1
0
0
1
1
2
1
0
0
0
0
1
1
2
0
0
0
0
1
1
0
1
1
1
0
1
0
0
1
0
0
0
1
2
0
0
0
0
2
1
2
0
0
2
1
2
0
2
0
1
2
1
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
3
1
0
0
0
0
0
1
2
0
2
2
2
0
0
1
0
0
1
0
1
0
0
1
0
0
0
2
0
1
1
0
1
3
2
0
1
1
1
0
0
0
2
0
0
1
0
1
1
2
1
0
1
2
2
1
0
0
2
1
1
2
2
0
2
0
0
1
1
2
0
1
2
0
0
0
2
2
0
0
2
0
2
0
0
0
0
0
0
1
0
1
1
0
0
1
1
0
2
0
1
3
0
0
1
1
1
1
2
1
2
2
0
1
1
0
2
2
0
0
1
1
0
1
1
0
0
3
1
0
2
1
0
1
1
0
0
2
0
0
1
0
1
0
0
0
0
2
0
0
0
2
3
0
1
2
0
1
0
0
1
1
2
0
0
1
1
1
0
1
1
0
1
0
0
0
1
0
0
0
1
1
2
0
1
0
1
1
1
0
2
2
0
0
1
0
0
1
1
0
2
0
1
2
2
0
1
0
0
0
4
1
1
1
0
2
0
0
1
0
0
1
1
0
1
0
0
1
0
1
1
2
0
1
2
1
0
0
0
0
1
1
0
1
0
1
2
1
0
2
0
0
0
1
0
0
2
0
0
0
1
0
0
2
1
3
2
2
0
2
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
2
2
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
1
0
1
0
0
1
0
1
1
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
2
0
1
1
1
0
0
0
0
2
1
2
2
1
0
0
1
0
3
2
1
0
0
2
2
0
0
0
1
1
2
0
0
0
1
0
0
0
2
0
1
0
0
3
2
0
0
0
0
1
2
1
0
1
0
1
0
2
2
1
0
0
0
0
0
0
2
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
2
1
2
1
0
0
2
1
0
1
0
0
0
2
1
0
2
2
1
0
0
0
1
2
1
0
2
1
1
0
1
0
2
0
0
0
0
1
0
0
0
0
0
1
2
0
1
4
1
0
1
0
0
0
1
0
0
2
0
1
0
0
2
0
1
1
0
0
0
0
0
0
1
0
1
1
1
0
0
2
0
0
2
0
5
0
1
1
0
0
0
0
0
2
1
0
2
0
2
0
0
0
1
1
0
0
0
0
1
0
0
0
2
2
2
0
1
0
0
0
1
3
0
2
1
0
0
1
0
1
0
1
0
1
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
1
0
2
0
1
0
2
0
0
1
0
2
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
3
1
2
0
0
0
0
1
2
2
2
2
0
0
3
1
1
2
0
0
2
0
2
0
0
2
0
0
0
0
2
2
2
2
2
0
1
2
1
0
0
1
2
2
1
2
0
0
0
1
0
1
0
0
0
2
2
2
0
1
2
0
0
0
0
1
1
0
0
2
0
2
1
2
2
0
1
0
0
0
0
0
2
2
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
2
0
1
0
0
0
0
2
2
0
1
0
0
0
0
0
1
1
1
0
2
2
0
1
0
0
0
0
0
2
2
0
0
1
2
0
0
0
0
1
2
1
0
1
0
0
0
1
0
1
0
0
2
1
0
0
1
2
0
1
1
2
1
2
1
2
2
1
0
1
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
1
2
0
0
0
1
0
0
0
0
2
1
0
1
2
2
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
1
4
0
0
0
0
0
0
1
2
1
2
2
1
0
2
0
1
0
1
2
0
1
1
0
1
2
0
0
1
1
1
1
0
1
0
0
0
1
0
0
0
0
0
1
1
1
0
2
2
0
0
1
2
0
0
0
0
1
0
0
1
2
0
2
0
0
0
0
1
0
0
2
1
1
2
0
0
0
0
0
0
0
3
0
2
1
1
1
0
0
0
0
2
0
1
0
0
0
2
1
0
2
0
1
2
2
2
1
0
2
2
2
1
0
1
0
0
1
0
0
1
2
0
0
2
2
0
1
1
0
0
0
1
2
0
1
0
0
2
1
0
2
0
1
1
0
0
1
2
0
0
0
2
2
0
2
1
0
0
0
0
2
1
2
0
0
2
0
0
0
0
1
0
1
0
0
0
0
1
1
1
0
2
1
1
3
0
0
0
0
1
0
0
0
0
2
2
0
1
0
2
0
0
1
0
3
0
2
2
0
2
2
1
0
0
1
0
1
1
1
2
0
0
1
0
0
0
1
2
0
0
1
0
0
1
1
2
0
1
2
0
0
0
0
0
0
2
2
2
0
0
1
0
2
2
0
1
1
0
0
0
0
0
1
0
1
1
2
0
0
0
1
1
2
0
0
0
1
0
0
1
2
2
0
2
1
0
0
0
0
0
1
2
2
2
2
2
0
0
0
0
0
0
2
2
1
0
0
1
0
0
1
0
0
2
1
1
1
1
2
2
1
1
0
3
0
2
0
0
0
0
0
0
0
0
2
2
1
1
2
2
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
1
2
2
1
0
0
2
1
0
0
0
2
0
1
0
2
1
0
1
2
0
0
0
0
1
0
0
3
1
0
0
0
0
0
0
4
0
2
1
0
1
0
1
3
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
1
1
3
1
0
0
0
1
3
2
1
0
1
0
0
0
0
0
1
0
1
0
1
2
0
0
0
0
2
1
0
2
1
1
1
0
1
0
0
0
1
0
0
2
1
0
0
0
0
1
2
0
0
2
0
0
0
0
1
1
0
0
0
0
2
1
0
0
1
0
2
1
0
0
1
2
0
0
0
0
1
1
0
2
1
0
0
2
0
1
0
2
1
0
2
0
1
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
2
2
0
0
1
0
0
2
1
1
1
0
1
0
0
2
1
0
3
0
2
0
0
0
2
0
0
1
0
0
0
2
2
0
0
0
2
0
1
2
3
2
0
0
0
1
0
0
0
1
0
1
1
0
1
1
2
0
0
0
0
0
1
0
2
1
1
2
0
0
1
0
0
0
1
0
0
2
0
0
1
0
1
0
0
1
1
1
2
0
0
0
1
0
0
3
0
0
0
0
2
1
0
1
0
2
2
0
0
0
1
0
0
0
0
0
1
0
1
0
1
1
0
1
0
0
1
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
2
0
1
0
0
0
0
0
1
2
1
0
0
0
2
0
2
0
1
1
0
0
0
0
0
1
0
2
0
0
1
1
0
0
0
0
3
0
0
0
2
0
0
0
2
2
0
0
2
2
2
2
0
2
1
0
1
0
0
0
1
1
0
0
0
0
1
0
0
1
1
0
0
1
0
3
0
2
1
2
0
1
1
1
0
1
1
0
0
1
0
0
0
0
0
2
1
1
0
1
1
0
2
0
2
0
0
4
0
1
0
0
0
0
0
0
1
0
0
2
1
2
1
0
1
0
1
2
3
0
0
0
2
0
0
1
0
0
1
0
0
0
0
2
1
0
1
0
0
2
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
1
1
0
0
1
1
0
1
2
0
0
0
0
0
1
1
0
0
1
1
1
1
1
0
1
0
2
2
2
0
0
0
0
0
2
0
0
3
2
0
1
2
0
0
1
0
1
2
0
3
2
1
2
1
0
0
0
1
1
0
1
1
1
0
0
1
0
1
1
1
0
0
0
0
1
1
0
1
0
0
3
0
2
2
0
1
0
2
1
0
0
0
2
2
0
1
0
2
2
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
2
0
2
1
1
1
0
1
1
0
0
0
0
0
0
0
1
3
0
2
0
0
2
1
0
1
0
0
0
2
0
1
2
0
2
2
2
0
0
0
0
1
0
1
2
2
0
1
1
0
0
1
0
1
0
1
1
0
0
1
2
0
0
0
0
0
2
2
0
1
1
1
1
2
2
1
0
0
0
0
0
0
0
0
3
3
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
2
1
2
0
2
1
0
0
0
0
0
2
1
1
1
1
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
2
1
0
2
1
2
2
0
1
0
2
0
1
1
0
1
0
0
1
1
0
0
1
1
2
2
2
1
2
0
2
0
0
1
0
2
2
1
1
2
1
0
0
2
0
0
0
1
2
0
1
0
0
0
0
1
2
2
0
0
0
2
1
0
0
0
0
0
2
0
0
1
0
2
0
3
1
1
2
1
1
0
1
0
2
1
0
0
0
0
1
1
0
0
0
0
0
2
2
2
2
12
1
1
0
0
2
0
1
2
0
0
2
0
0
0
1
0
0
1
0
1
3
0
0
1
0
1
0
1
0
0
1
0
0
0
0
2
0
1
0
2
0
2
1
0
1
2
0
0
1
0
0
1
0
0
1
0
0
0
1
2
0
2
0
0
0
0
2
0
0
0
0
2
0
1
0
2
2
2
0
1
2
2
2
2
0
0
1
2
0
0
0
2
0
0
2
1
1
1
1
2
1
1
2
0
2
0
1
0
2
0
2
1
2
0
2
1
0
0
2
1
1
2
2
1
1
0
0
0
0
0
2
0
2
3
2
1
0
0
0
0
0
2
0
0
2
0
0
0
1
1
0
1
1
0
0
1
0
0
1
0
0
0
1
0
0
0
2
0
1
1
1
1
0
2
0
2
0
2
2
0
1
2
0
1
0
1
0
0
2
0
0
0
1
0
1
0
0
0
1
0
0
0
1
1
1
1
2
1
1
2
0
0
2
0
0
0
2
2
1
1
0
0
0
2
0
0
2
0
0
1
1
2
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
1
2
1
1
2
1
1
0
1
2
0
2
1
2
0
1
0
1
2
3
1
0
2
1
0
0
0
1
0
1
0
0
3
1
0
2
0
1
1
2
0
1
3
2
0
2
0
2
1
0
2
0
0
2
1
0
1
2
1
2
2
0
0
0
0
0
2
0
1
1
0
1
1
0
0
0
0
0
0
2
0
0
1
0
2
1
2
0
0
0
1
2
1
0
0
0
0
2
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
2
0
1
2
2
2
2
0
0
2
0
0
1
2
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
2
2
0
0
0
3
2
0
1
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
2
1
1
1
1
1
0
1
0
1
1
0
0
2
0
0
0
1
0
0
1
0
0
2
0
1
0
0
2
1
3
1
0
0
2
2
0
0
2
2
0
0
0
0
2
0
2
2
0
1
0
3
0
0
0
0
0
0
2
1
0
0
1
2
2
1
0
0
1
1
1
1
0
0
0
0
0
2
0
0
2
1
0
1
0
0
2
1
0
0
0
2
0
2
0
1
0
0
2
2
2
0
1
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
1
1
0
0
1
2
0
1
0
1
0
3
1
1
0
0
2
1
1
0
0
0
1
1
2
2
0
1
1
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
2
1
0
0
0
2
1
1
0
1
0
2
0
2
1
0
2
0
2
2
2
0
0
2
0
0
2
1
2
2
1
0
1
1
0
0
1
2
2
0
0
0
0
1
0
0
0
1
3
1
1
0
1
0
0
2
0
0
0
1
1
1
1
0
0
1
0
0
1
1
0
1
0
1
0
0
0
1
2
0
1
0
2
0
0
0
2
0
0
0
1
1
2
2
2
1
1
1
1
0
1
0
0
2
0
1
1
0
2
0
0
0
0
0
0
2
2
0
3
1
0
1
0
1
2
1
2
0
1
0
1
0
1
0
1
0
0
2
0
2
2
1
0
0
2
2
0
1
0
2
0
0
0
2
1
1
0
0
1
1
0
1
0
3
1
0
2
1
2
2
0
0
1
0
0
2
2
0
1
1
1
0
0
0
0
0
1
0
1
2
0
2
0
2
0
1
0
0
1
0
1
0
0
2
0
1
0
0
3
1
0
1
0
0
0
0
2
0
1
1
0
0
2
2
0
1
1
2
0
2
2
3
0
1
2
1
1
1
0
1
1
0
0
0
0
0
0
1
0
2
0
2
0
2
0
2
0
3
0
0
0
1
1
0
1
1
0
0
2
0
0
1
2
0
0
0
0
2
0
2
1
1
1
1
2
1
0
0
0
0
0
0
3
0
1
1
0
1
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
2
1
0
1
0
4
1
1
0
0
0
0
0
0
1
1
1
1
2
0
0
0
1
1
0
2
1
2
0
0
0
0
1
0
0
1
1
1
0
0
1
0
1
1
0
0
0
0
1
1
0
1
1
0
1
3
2
1
0
0
2
1
0
1
1
0
0
0
1
0
2
1
1
1
0
0
1
0
0
1
2
2
0
2
0
0
0
0
2
0
0
2
0
1
1
0
0
1
1
1
0
2
1
0
0
2
2
0
1
0
0
2
2
1
0
1
0
0
0
2
0
0
0
0
1
0
0
1
2
1
1
0
0
0
0
1
1
0
0
0
0
1
0
0
1
1
0
1
1
0
0
1
1
1
1
0
0
0
1
0
1
0
0
2
2
0
0
1
0
2
1
2
2
1
0
0
0
2
2
2
0
0
2
0
0
0
0
0
2
3
0
1
3
2
2
0
1
2
4
0
0
1
1
0
0
0
0
1
0
2
2
0
2
0
1
1
0
0
0
1
0
1
0
1
0
0
0
2
0
0
0
2
1
1
2
0
0
0
2
0
1
0
1
0
1
1
0
2
0
0
2
2
0
0
2
0
2
1
1
1
0
0
0
2
0
0
0
0
0
0
1
0
0
1
2
2
0
0
0
1
1
1
0
2
0
1
0
1
1
0
0
0
1
0
0
3
0
1
1
0
0
0
1
2
1
0
0
0
0
0
0
2
0
1
1
2
4
0
2
1
1
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
1
1
0
0
2
0
2
0
1
1
0
2
0
2
1
0
0
2
2
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
2
2
0
1
2
1
2
0
1
2
0
0
0
0
0
0
0
0
2
3
0
0
3
1
0
0
0
1
0
0
0
2
2
0
0
0
1
0
0
0
1
0
0
0
2
1
0
0
2
0
0
1
0
0
2
1
0
1
1
0
2
0
2
0
0
0
0
0
0
1
2
1
0
0
0
0
0
2
0
2
0
0
1
0
1
0
2
0
2
2
1
1
0
2
1
0
0
2
0
0
2
0
0
0
2
0
0
1
0
2
0
1
2
2
0
2
1
0
1
0
0
0
1
0
1
0
2
0
1
1
2
0
0
1
0
0
3
2
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
1
2
0
0
1
0
0
0
0
1
1
1
0
0
3
1
1
0
0
0
0
2
3
2
0
0
0
1
1
0
1
0
0
2
0
0
1
2
0
0
0
1
0
1
2
0
2
0
0
2
3
0
0
0
0
0
1
1
2
0
2
0
0
0
1
1
3
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
2
1
0
0
1
0
0
0
0
0
0
3
2
1
0
0
0
2
1
2
0
0
1
0
0
2
2
0
0
1
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
2
0
1
0
0
0
0
0
2
0
0
0
2
0
3
0
1
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
2
0
5
2
2
1
0
1
0
0
1
1
0
2
0
0
1
0
2
0
1
1
1
0
0
0
2
1
0
2
0
0
0
1
0
1
2
1
2
0
0
0
0
2
2
0
0
2
2
1
0
0
0
2
2
2
0
0
0
2
0
0
3
0
0
3
0
0
1
0
0
0
0
2
0
0
1
1
2
0
1
0
0
1
0
1
0
2
0
0
0
0
1
2
0
0
0
0
0
1
2
1
0
2
0
0
2
1
1
2
0
1
2
0
0
2
0
1
0
0
3
0
0
0
1
0
2
2
0
0
1
2
2
2
1
0
0
2
0
0
1
0
1
0
1
0
0
0
0
2
1
0
0
0
0
2
1
0
0
2
0
0
0
2
0
2
0
0
0
0
1
0
0
1
1
1
1
3
1
1
0
2
2
2
0
1
0
0
0
0
0
0
1
5
2
0
1
0
2
0
0
0
1
2
0
0
0
1
0
0
2
0
2
0
0
0
1
2
1
1
0
2
0
1
0
0
0
0
0
0
2
1
0
0
0
1
0
2
0
0
0
1
1
0
1
0
1
0
0
0
1
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
3
0
2
1
2
0
2
2
0
0
0
1
1
1
0
1
2
1
2
1
1
0
1
1
0
0
1
2
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
1
2
1
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
2
0
1
0
0
2
1
2
2
0
1
2
1
1
0
0
0
1
3
2
0
2
2
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
2
2
1
2
0
0
3
1
1
0
1
2
0
1
2
0
0
1
1
2
0
0
0
2
0
0
0
0
0
0
1
3
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
2
0
2
2
1
0
0
0
0
0
2
1
2
2
1
0
0
0
0
0
0
2
0
0
1
0
2
0
1
2
2
0
1
0
1
1
0
0
1
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
2
1
1
1
1
0
1
2
0
1
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
1
0
2
2
0
0
1
0
0
0
0
0
2
0
1
1
0
0
1
2
1
0
0
2
2
0
0
2
2
1
0
1
1
0
2
2
0
0
0
0
1
0
1
0
2
1
0
2
0
1
0
1
0
1
0
2
1
2
0
1
2
1
0
1
2
1
0
0
1
2
1
1
0
0
2
0
0
2
2
2
0
0
0
0
0
1
0
0
0
2
0
0
0
1
1
0
2
0
0
0
0
1
1
1
1
0
1
0
2
1
0
0
0
2
0
1
0
0
1
0
0
0
0
0
1
2
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
2
0
0
0
2
0
0
1
0
3
0
3
1
2
1
1
1
2
0
1
1
2
0
2
3
2
0
1
0
1
0
1
0
0
1
2
0
0
1
0
2
2
0
1
0
2
0
1
0
2
0
0
2
0
0
0
1
0
1
2
0
2
2
4
0
0
0
0
0
0
2
1
1
2
1
0
1
2
0
2
1
3
0
1
0
0
0
0
2
1
1
2
1
0
0
3
0
0
0
0
2
1
0
0
1
2
1
0
2
1
1
0
0
0
0
2
0
1
1
2
0
2
0
0
2
0
1
1
2
0
1
0
2
0
1
0
2
0
0
0
0
0
1
0
1
2
2
0
1
2
0
0
1
1
0
1
0
0
0
0
1
1
0
1
0
1
1
1
0
2
1
0
0
2
2
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
1
1
1
0
0
0
1
0
0
1
0
2
2
0
0
0
2
0
0
1
1
1
0
0
1
0
3
0
2
1
2
0
0
0
2
0
2
2
0
1
0
0
1
1
0
2
0
1
1
0
1
0
2
0
2
0
2
1
1
1
0
0
1
0
2
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
2
1
2
0
1
0
0
0
0
2
0
0
0
1
2
0
0
1
0
2
2
1
0
2
1
2
1
1
0
0
1
0
0
2
0
0
0
2
2
0
1
0
0
0
2
0
0
0
0
1
0
2
0
0
1
0
2
2
1
0
2
0
1
0
0
1
1
1
0
2
0
0
0
0
2
1
2
1
3
0
2
2
0
1
2
2
0
2
0
0
0
0
0
0
1
0
0
0
2
2
2
0
0
2
2
0
0
1
0
0
0
0
0
0
0
2
1
1
1
0
0
2
1
0
0
2
2
1
0
0
1
1
1
1
0
1
2
0
0
0
0
0
2
0
1
0
0
2
1
0
2
0
1
0
0
0
0
0
1
0
2
0
1
0
2
0
0
2
2
1
0
0
0
0
1
1
0
1
2
0
1
0
2
2
1
1
1
0
2
3
0
1
1
0
0
2
0
2
1
0
1
0
2
1
2
0
0
2
0
1
0
2
2
0
3
0
2
1
0
1
1
0
1
2
0
0
0
0
0
2
0
0
0
2
1
0
2
0
2
2
1
0
0
0
1
0
2
1
1
1
0
2
0
1
1
1
0
1
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
2
1
0
2
1
0
0
1
0
0
0
0
0
0
1
0
1
0
2
0
1
2
1
0
2
2
0
0
1
3
0
2
0
0
0
0
0
0
0
0
0
3
0
1
0
2
1
0
1
0
0
0
2
0
0
2
1
1
0
0
2
0
0
0
0
2
0
0
0
0
1
2
0
1
1
0
0
0
0
1
1
0
0
0
0
1
2
0
2
0
2
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
2
2
1
2
0
0
0
1
0
0
2
3
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
1
1
0
0
2
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
1
1
2
1
0
1
0
0
0
0
2
2
0
1
0
0
0
1
1
0
0
0
2
0
0
0
1
4
2
0
1
0
0
0
2
1
0
0
2
2
2
1
2
1
0
1
1
0
2
2
0
0
1
2
1
2
0
2
0
0
0
1
0
0
0
1
2
0
0
1
0
3
2
0
3
0
0
2
0
0
2
2
0
0
0
0
0
0
0
1
0
2
0
0
1
0
2
2
1
0
0
0
1
0
1
1
0
0
2
3
0
0
0
1
0
1
2
0
0
0
0
0
2
0
0
0
2
0
1
2
0
2
1
1
0
1
2
0
0
0
0
0
2
0
0
1
0
1
1
1
0
0
0
0
0
0
0
3
2
1
1
0
0
3
0
1
2
0
1
0
0
1
0
0
1
2
1
1
0
1
0
0
0
1
2
2
0
2
0
0
0
0
0
0
0
1
1
2
0
3
0
0
0
1
1
0
1
0
0
0
1
0
2
0
2
2
1
0
0
0
0
0
0
1
1
1
0
1
1
0
2
1
2
1
0
1
2
1
0
0
2
2
1
0
0
2
1
2
2
0
1
1
2
0
0
1
0
2
2
1
0
0
0
2
0
2
0
1
0
2
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
1
1
0
2
0
3
1
2
3
2
3
1
0
2
0
0
0
0
0
0
0
1
2
0
3
0
2
2
0
1
0
1
0
1
2
0
2
0
1
2
2
1
1
0
0
1
0
1
1
0
0
0
1
1
0
0
0
1
1
1
1
2
2
0
3
0
0
1
1
0
1
2
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
3
2
3
2
0
0
2
2
0
2
0
4
0
1
0
2
0
0
0
2
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
1
0
0
3
2
0
1
1
1
0
1
1
0
0
1
2
0
0
2
0
0
2
0
1
1
1
0
2
2
0
0
0
2
2
0
0
0
0
1
0
1
1
0
0
0
0
0
2
0
0
0
2
0
1
0
0
1
2
1
1
0
0
1
2
0
2
0
0
0
0
0
2
2
0
0
1
2
0
0
2
0
0
0
0
0
2
0
1
0
2
0
1
0
0
2
0
0
1
0
2
3
0
0
1
0
2
1
0
1
0
1
0
2
2
2
3
3
1
2
0
0
0
0
0
0
1
2
0
0
1
0
2
0
0
0
0
0
1
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
2
0
0
0
2
1
1
0
0
1
1
0
2
0
0
2
0
2
1
1
2
0
2
0
0
1
2
1
0
0
0
1
1
0
0
2
0
0
0
0
2
1
1
0
0
1
2
1
0
2
0
0
1
2
0
0
2
5
3
1
2
0
1
0
2
0
0
2
1
0
2
0
1
1
0
2
0
0
0
1
0
2
2
0
0
0
2
1
0
0
0
1
0
0
2
3
2
1
2
1
1
0
0
0
5
0
0
1
1
0
2
0
0
0
0
0
0
0
1
1
1
0
1
1
1
1
2
3
1
1
2
0
0
0
2
0
0
0
1
0
2
2
1
0
0
0
1
0
0
0
0
1
3
1
1
0
1
2
2
1
0
1
2
0
0
1
0
0
0
1
0
0
1
1
0
2
1
0
1
0
1
0
2
0
0
1
0
1
1
0
2
1
0
0
0
2
1
0
0
0
0
2
0
0
0
1
0
1
2
0
1
2
2
1
0
0
2
1
1
0
1
0
0
0
1
1
0
2
0
2
2
1
0
1
1
0
0
0
1
2
0
0
0
0
0
1
0
0
2
3
0
0
1
0
0
0
1
0
2
0
2
0
1
0
0
0
1
2
1
1
0
1
2
1
2
0
2
2
1
2
2
1
0
2
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
1
3
2
0
0
1
1
0
1
0
1
1
1
1
0
1
0
2
0
0
1
1
0
2
0
0
0
0
0
0
1
1
0
1
1
2
1
1
0
0
2
0
0
2
1
0
2
1
0
2
1
1
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
1
1
0
1
1
0
2
0
1
1
0
1
0
3
0
2
1
1
0
0
0
0
0
0
0
3
1
0
1
0
3
0
1
1
2
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
2
0
2
1
0
0
0
1
2
0
1
0
0
2
0
0
0
0
2
2
1
1
1
0
0
2
0
0
0
1
0
0
0
3
1
1
0
0
0
0
2
1
0
2
0
1
1
1
0
0
1
0
0
0
2
0
0
0
1
0
2
1
1
1
0
2
1
0
2
1
0
1
0
1
1
0
1
1
0
1
1
2
1
2
0
1
0
0
0
1
0
1
0
1
0
2
1
0
1
1
0
0
0
0
2
1
0
0
2
2
0
0
0
0
0
0
1
1
0
0
1
1
0
2
1
2
1
0
2
0
0
2
1
0
0
0
1
2
0
1
2
0
2
1
2
1
1
0
4
0
0
3
0
2
1
1
1
2
1
0
0
1
0
3
0
2
0
0
0
1
0
0
0
3
0
2
1
0
0
1
3
0
2
0
0
0
0
1
0
0
0
0
0
2
0
1
1
0
0
0
2
1
1
1
0
0
0
0
0
9
0
0
2
2
2
1
0
0
0
0
0
0
2
0
0
0
1
0
2
0
2
2
1
2
1
0
0
2
3
0
0
0
1
0
1
0
0
0
2
2
2
0
0
0
0
0
0
1
2
0
0
0
0
1
1
1
0
0
1
0
2
0
0
0
0
1
0
2
1
2
0
0
0
0
0
0
1
0
2
2
2
0
1
0
0
2
2
0
1
0
2
0
0
0
0
1
0
1
0
2
1
0
2
2
0
1
2
0
1
1
1
2
1
1
0
0
3
4
0
2
0
2
2
0
1
2
0
1
1
0
2
0
1
1
0
0
0
0
0
0
2
0
0
0
1
1
0
2
1
1
2
2
2
0
2
0
2
1
2
3
1
2
0
0
0
0
1
0
2
0
1
0
1
0
0
1
0
1
0
2
1
0
0
0
0
2
0
2
0
2
0
1
1
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
2
1
1
2
0
0
0
0
0
3
1
0
0
1
2
0
1
2
2
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
1
2
0
1
0
0
0
2
0
0
1
0
0
2
1
1
0
0
0
0
1
1
1
0
1
2
0
0
1
0
2
1
0
0
0
0
2
0
1
0
1
0
0
1
1
0
0
0
0
1
2
2
2
0
0
0
0
0
0
0
1
2
2
2
0
0
0
0
1
0
1
0
1
0
1
0
0
2
0
0
3
1
2
1
1
1
0
1
0
0
1
2
2
0
2
0
0
0
2
0
0
1
0
1
2
0
1
0
1
0
0
0
2
0
1
0
0
1
2
0
2
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
2
0
2
1
2
0
0
0
2
0
1
0
0
0
1
0
1
1
1
0
1
1
0
0
1
1
1
1
0
0
1
1
1
2
0
2
1
2
1
0
0
2
0
0
2
0
1
1
0
1
0
0
0
2
0
2
0
1
2
0
1
0
1
2
0
0
0
0
1
1
0
1
3
0
0
2
1
2
2
0
1
0
0
0
1
2
0
1
0
0
1
2
0
1
2
1
1
0
1
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
1
2
0
0
0
2
0
0
0
0
0
3
0
0
1
0
2
0
2
0
1
1
0
1
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
2
1
0
0
1
0
0
0
1
1
1
0
0
2
0
2
0
1
0
0
1
1
2
0
1
0
1
1
1
0
1
1
0
0
0
2
1
1
2
0
0
0
0
0
0
2
0
0
2
0
2
1
0
1
1
0
0
0
1
2
2
1
0
0
0
0
0
0
0
0
1
1
2
1
0
2
1
0
0
1
2
0
1
2
0
0
0
0
1
0
2
2
1
0
0
0
0
0
1
2
0
0
0
2
0
1
2
0
1
0
1
0
0
1
0
0
0
2
0
0
0
2
0
0
2
2
1
1
1
0
0
0
2
2
1
0
1
1
0
2
0
0
1
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
2
3
1
3
0
0
0
0
0
0
2
0
0
2
2
2
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
2
0
0
2
1
0
0
1
0
1
0
0
1
0
1
0
0
0
1
1
0
1
1
3
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
1
1
2
1
0
1
0
1
2
0
2
1
2
0
0
0
1
0
1
1
1
1
0
0
0
2
2
0
0
0
2
0
0
1
0
0
0
2
0
1
0
2
0
0
2
2
0
0
0
0
2
0
0
1
2
2
0
0
2
0
2
0
2
1
0
1
0
2
0
1
0
0
0
0
1
1
1
0
0
1
0
1
1
0
2
3
0
0
7
1
0
0
2
1
1
1
0
1
3
0
0
2
0
0
1
2
1
4
1
2
2
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
1
1
1
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
1
0
0
0
2
0
0
1
0
0
1
0
0
0
2
0
1
1
2
0
1
1
1
0
1
2
1
0
0
1
3
0
1
0
0
0
0
1
1
0
1
0
0
0
1
0
2
0
0
0
2
0
1
0
2
1
1
0
1
0
1
0
1
0
1
1
0
4
1
2
2
2
0
0
0
2
2
0
0
0
0
0
2
2
2
2
6
0
2
0
1
0
0
0
1
0
0
0
2
0
1
2
2
2
1
1
0
0
2
0
1
0
2
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
1
2
0
1
1
0
2
0
2
0
1
1
2
0
0
0
0
2
1
0
0
1
0
0
0
2
2
0
1
1
2
0
0
0
0
0
0
2
0
0
2
1
0
3
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
2
1
0
1
1
0
0
0
1
0
0
2
0
0
2
1
0
1
0
0
0
2
0
1
1
0
0
0
2
1
2
0
0
0
2
1
0
1
1
0
2
0
0
0
1
0
1
0
2
0
1
2
1
0
1
0
1
1
2
0
2
0
2
0
1
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
1
0
2
2
1
0
1
1
0
0
0
1
1
0
2
2
0
2
1
1
1
0
1
0
1
0
0
2
0
1
0
1
0
2
2
2
3
0
1
0
0
0
0
0
2
0
0
1
0
2
0
0
0
4
0
2
2
2
1
0
2
1
2
0
0
0
0
0
0
1
0
2
0
0
2
0
2
0
2
0
0
0
0
2
0
1
1
1
1
0
0
2
5
0
0
1
1
0
0
0
2
0
1
2
2
0
1
0
0
0
1
2
2
2
3
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
2
1
2
0
0
0
1
1
0
0
2
2
0
2
0
1
1
0
1
0
1
0
2
1
2
0
1
0
1
1
1
0
0
1
2
0
0
2
1
0
0
1
1
0
0
0
2
2
0
0
1
1
0
1
2
0
1
0
0
0
0
1
1
2
1
0
2
1
0
1
1
0
0
2
0
0
2
0
0
1
0
0
0
2
1
2
2
2
0
0
2
2
2
1
0
2
0
1
0
1
0
1
2
0
1
2
1
1
0
0
3
0
1
2
0
0
0
0
0
0
0
1
1
0
0
2
1
1
0
0
0
0
1
0
2
0
0
0
2
0
0
1
0
0
0
1
2
0
0
0
2
1
0
0
1
0
0
2
0
0
0
2
0
2
1
2
0
0
2
2
0
0
0
2
1
0
0
0
2
0
1
0
2
1
0
0
1
0
0
2
0
0
1
0
0
0
1
2
0
0
0
1
0
0
2
0
0
0
0
3
1
0
0
1
2
0
0
0
1
1
1
0
2
1
0
0
2
0
0
0
0
4
0
1
1
0
1
1
0
0
0
1
0
0
1
0
0
0
0
1
1
1
1
0
0
2
0
1
0
0
0
0
0
1
0
1
0
2
0
0
0
4
0
1
0
2
1
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
2
1
4
0
0
1
1
0
2
0
0
0
1
0
1
0
1
0
2
1
0
1
2
0
0
0
1
0
0
0
0
0
2
0
0
0
2
2
0
1
1
2
0
0
4
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
2
0
0
0
2
1
1
0
0
0
0
5
0
0
3
2
0
0
2
0
0
0
0
2
2
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
1
1
2
1
0
0
1
2
2
2
2
0
1
0
2
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
1
2
0
1
2
0
0
1
0
2
0
0
0
1
0
0
2
1
0
0
0
0
0
2
2
1
1
0
0
0
2
0
0
3
2
1
0
1
0
0
2
1
1
0
0
2
1
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
1
2
1
0
0
0
1
2
0
1
0
1
2
2
0
0
1
1
0
0
2
1
0
0
1
1
3
2
0
1
0
0
0
0
0
1
2
0
0
0
0
0
1
0
2
0
2
0
1
0
0
0
0
0
0
0
0
3
0
2
2
2
1
0
0
0
0
0
0
0
4
1
1
1
0
1
0
0
1
0
1
0
1
0
0
0
1
0
2
1
0
2
0
2
3
0
2
0
0
2
1
0
0
1
1
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
1
2
0
0
0
0
0
1
1
0
1
1
3
1
0
0
0
2
0
0
1
0
0
0
1
0
0
0
2
0
1
1
1
1
1
1
2
0
0
0
2
0
1
2
1
0
1
1
1
0
0
2
0
1
0
1
1
0
1
0
2
0
0
0
0
1
0
0
1
0
0
0
0
2
0
2
2
0
2
1
0
1
0
0
0
1
0
1
2
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
1
0
1
0
0
0
2
0
0
2
2
0
1
0
2
1
2
0
0
2
1
2
1
1
2
0
0
0
0
0
1
1
0
0
0
3
2
1
1
2
1
2
0
1
0
1
0
0
0
1
0
0
2
2
1
1
1
0
0
0
0
1
0
1
0
0
0
2
0
1
2
2
0
3
0
2
1
0
2
0
0
2
0
1
0
0
1
0
0
0
0
0
3
0
1
1
0
1
1
2
0
0
0
0
0
0
0
0
1
0
1
1
0
0
3
5
0
0
0
0
2
1
0
2
1
0
2
0
0
2
0
1
0
1
0
2
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
1
3
2
2
1
0
1
1
1
0
3
1
1
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
2
2
0
0
2
0
2
0
1
2
1
0
0
0
0
2
0
1
0
0
0
1
0
0
1
2
1
1
2
0
1
0
0
1
0
2
1
2
0
0
0
0
0
0
0
0
2
0
1
2
0
0
1
1
1
0
2
1
1
0
0
1
0
3
0
2
1
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
1
1
0
1
2
0
0
0
1
0
2
1
1
2
0
0
2
0
0
0
1
0
0
0
3
0
2
0
1
1
1
1
0
0
2
0
1
2
1
0
0
0
1
0
1
0
2
0
0
2
0
0
1
2
1
0
2
0
0
1
1
0
0
0
2
1
0
1
0
2
0
1
0
0
0
0
0
0
2
1
1
2
1
0
0
1
1
1
1
1
0
0
0
2
0
1
2
2
2
1
2
0
0
2
3
0
0
0
0
1
1
0
2
0
1
0
0
0
1
1
0
2
1
1
0
2
1
0
0
2
0
1
0
2
0
0
1
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
1
2
0
0
0
0
1
0
2
0
2
0
2
1
1
1
1
0
1
0
1
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
2
1
1
1
0
2
1
0
0
0
1
2
0
0
9
0
0
2
0
0
1
0
0
0
0
1
0
6
1
0
2
2
1
1
1
1
4
0
2
0
1
0
0
1
1
5
2
2
1
0
1
1
0
0
1
1
0
0
0
0
0
2
0
2
1
0
0
2
2
0
2
0
0
0
1
1
0
0
1
0
0
1
0
1
0
3
0
2
0
1
1
2
2
0
0
3
1
0
0
2
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
1
0
0
2
2
0
0
6
0
2
0
2
2
0
0
2
0
0
0
0
1
1
0
0
0
0
1
0
0
0
2
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
1
0
1
0
0
2
1
2
0
2
0
2
1
0
0
0
0
0
1
1
0
0
2
0
0
0
0
2
1
2
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
1
1
2
0
0
2
0
1
0
1
0
3
2
0
1
2
0
0
2
0
2
2
0
0
2
1
0
0
1
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
2
0
0
1
2
0
0
1
1
0
1
0
1
0
1
0
0
0
0
0
0
2
0
2
0
0
0
2
3
0
2
1
1
2
0
2
0
0
0
1
2
2
0
0
0
2
0
0
0
1
1
0
2
0
1
2
1
0
0
0
1
0
0
2
0
0
0
1
0
0
1
2
0
1
0
1
0
0
0
0
0
0
0
1
2
1
1
0
1
2
1
0
1
0
1
0
0
0
0
0
0
2
2
0
0
0
2
0
1
1
1
0
1
0
2
0
0
0
0
1
0
2
2
1
3
0
0
1
1
0
0
0
0
0
1
0
2
0
1
1
0
3
0
0
0
2
0
1
0
0
0
0
0
1
0
1
0
0
0
2
2
0
0
2
2
0
1
0
0
1
2
0
0
0
0
0
0
0
1
0
0
1
0
2
1
0
1
1
0
0
1
0
1
0
0
2
1
1
1
3
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
1
0
7
1
0
0
2
0
0
0
2
1
0
1
1
0
1
0
0
1
0
1
0
2
0
2
2
0
0
0
1
0
0
0
0
2
0
1
2
0
2
1
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
2
1
0
2
0
2
0
4
0
3
1
1
0
3
0
1
0
1
0
1
0
0
0
0
0
2
0
0
1
1
0
2
0
0
1
2
0
1
2
0
3
1
2
0
0
0
2
2
1
3
0
0
0
1
0
0
0
0
0
3
0
1
0
0
1
0
2
0
0
2
1
2
1
0
2
1
0
2
1
1
0
0
0
1
3
2
0
0
0
1
1
0
0
0
1
0
0
1
0
0
1
0
3
2
0
0
2
0
0
2
0
0
0
0
0
0
0
2
2
0
2
0
1
1
0
0
1
0
0
1
4
0
0
0
1
2
2
0
1
1
1
0
0
2
2
1
0
0
0
0
1
2
0
2
1
0
0
0
0
0
0
0
0
0
2
0
1
0
3
1
1
0
0
2
0
2
0
0
0
0
1
0
0
0
0
2
0
2
1
2
0
0
1
1
0
2
0
0
0
1
0
0
0
0
1
2
0
1
1
1
1
0
2
0
1
0
0
0
0
0
0
0
0
1
2
2
0
0
0
3
0
0
0
0
0
2
2
1
1
0
1
1
0
0
4
1
1
1
1
2
2
0
1
0
2
0
1
0
0
0
0
0
0
0
3
2
0
0
0
2
0
1
2
0
0
1
1
0
0
0
0
1
0
1
1
1
1
0
0
2
1
1
2
0
2
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
1
2
1
2
1
1
0
1
1
2
0
1
1
1
1
0
0
0
0
3
0
0
0
0
0
0
2
1
0
2
4
0
1
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
1
0
0
2
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
3
2
1
2
1
0
0
0
0
0
0
0
1
0
2
2
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
2
0
2
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
2
2
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
1
0
0
1
1
0
0
0
0
0
1
2
0
0
0
0
1
0
0
1
0
2
3
0
0
0
0
0
1
1
0
1
2
1
0
0
3
1
2
1
0
0
0
1
0
0
2
1
1
2
1
0
1
1
2
0
2
0
2
0
0
0
0
2
0
2
3
0
0
1
0
1
0
0
0
0
0
0
2
1
2
2
0
0
1
0
0
0
0
1
0
0
1
1
0
2
0
1
1
0
1
2
0
0
0
0
0
0
1
1
0
0
2
0
0
1
0
1
2
1
1
0
2
0
0
1
0
1
0
2
0
1
1
0
1
0
3
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
2
2
2
1
0
2
0
0
0
0
1
1
0
1
0
1
2
1
0
2
1
0
0
0
0
0
0
0
0
1
0
2
0
1
0
4
0
2
0
0
0
0
2
2
0
0
2
0
0
0
1
0
0
2
2
2
0
0
1
1
0
1
0
0
2
1
0
2
0
0
3
0
0
0
1
1
0
2
0
1
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
4
2
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
1
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
1
2
1
4
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
2
0
0
0
2
1
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
1
0
2
1
0
0
0
0
1
2
0
0
2
0
2
1
0
2
0
2
2
0
2
0
0
2
0
2
0
1
2
0
0
1
0
0
0
1
0
1
0
0
3
0
1
0
0
1
0
2
1
0
1
0
0
0
0
0
1
1
1
0
0
0
1
2
0
0
0
2
1
2
0
0
0
4
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
1
2
1
2
1
0
2
1
2
0
0
2
0
0
0
0
0
1
0
1
0
0
0
2
1
0
0
1
0
3
0
2
0
1
0
0
0
1
0
0
1
0
1
0
1
2
0
0
1
0
0
3
1
0
0
2
2
3
0
0
1
1
6
0
2
0
0
0
3
0
0
0
0
1
0
2
1
2
1
0
1
1
1
0
0
0
1
1
2
2
0
1
0
0
1
0
0
0
2
0
1
2
0
1
2
1
0
0
0
0
0
0
0
1
1
2
0
1
0
1
0
1
0
3
1
1
1
1
1
0
1
0
0
0
2
0
0
0
2
0
2
1
0
1
0
0
2
1
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
2
1
1
5
0
1
0
1
0
3
2
0
1
0
1
1
2
1
0
1
0
0
1
1
0
0
2
0
1
0
1
0
0
1
1
0
0
0
0
2
0
1
0
2
0
1
1
0
0
2
2
0
0
1
0
0
3
0
4
1
2
0
0
2
0
1
0
1
1
2
0
4
0
2
0
1
1
0
0
2
0
1
0
0
0
1
0
1
2
0
0
1
0
5
0
1
0
0
2
0
0
0
1
1
0
0
0
0
1
0
1
1
1
2
0
2
1
0
0
0
2
0
1
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
2
1
1
0
0
2
0
2
0
0
2
1
1
0
1
1
0
1
0
0
1
0
1
1
0
1
1
1
1
1
1
0
2
0
2
0
2
0
0
0
1
0
0
2
1
0
1
0
1
0
0
1
1
2
1
0
1
0
1
0
2
0
2
1
0
0
0
1
0
0
1
0
2
3
0
0
1
2
0
1
2
0
0
0
0
1
0
0
0
0
1
0
1
0
2
0
0
2
1
2
1
0
0
0
0
1
2
0
2
0
1
1
2
0
0
1
2
2
0
1
2
2
0
0
2
1
1
2
0
2
1
0
0
1
0
1
0
0
0
0
2
0
2
0
0
0
0
1
0
1
2
1
0
2
2
1
0
0
2
0
0
0
0
0
2
1
1
1
1
0
2
0
0
0
0
1
2
0
2
0
2
1
0
1
0
0
0
0
1
2
0
2
0
1
0
0
2
0
0
0
0
1
0
0
0
0
1
1
0
2
1
0
0
0
0
0
0
1
0
4
0
0
0
2
1
2
0
1
0
0
1
1
0
2
1
0
1
2
0
0
0
0
1
2
1
0
0
0
0
0
0
2
0
2
1
0
2
0
0
1
2
1
0
1
2
0
2
0
1
2
0
1
0
2
1
0
0
1
1
2
0
1
0
1
1
0
1
2
0
2
2
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
3
2
0
2
0
0
1
0
1
2
0
2
0
2
0
1
1
2
2
1
0
2
2
2
0
0
0
2
0
2
2
1
1
0
0
1
1
2
1
0
0
1
1
1
1
0
3
0
0
0
0
0
0
1
0
1
0
2
0
2
1
1
0
0
2
0
0
2
1
2
0
1
0
1
1
0
2
0
1
0
2
1
0
2
3
0
1
0
0
1
0
0
0
0
2
2
0
0
0
2
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
2
3
1
0
0
1
0
2
0
0
0
0
0
2
0
1
0
1
0
1
0
0
0
1
1
1
0
0
1
0
2
2
1
2
0
1
0
0
0
0
2
0
2
1
0
2
1
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
2
1
0
0
2
1
0
0
2
2
0
1
0
1
2
1
0
2
2
0
0
0
0
1
2
1
0
0
0
0
1
0
2
0
1
0
2
0
0
0
1
0
5
3
1
1
1
0
0
2
1
0
0
1
1
0
0
3
0
2
0
1
2
1
1
0
0
0
3
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
1
2
0
0
0
0
0
0
1
0
1
0
1
1
1
1
0
0
1
2
0
0
2
0
0
3
0
1
0
0
0
0
0
1
0
0
2
0
0
1
1
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
2
2
1
1
0
2
0
2
1
0
0
2
1
1
0
0
2
0
1
1
1
1
0
1
0
1
0
1
0
0
1
0
0
2
0
0
1
2
2
2
0
2
1
1
3
0
0
1
0
0
0
0
1
1
0
1
0
2
1
1
0
3
0
1
0
0
0
0
2
0
0
1
0
0
1
2
1
4
0
0
0
4
1
0
0
0
1
1
0
2
0
2
2
0
0
1
0
0
0
0
0
2
0
0
0
0
1
3
1
2
0
2
0
2
0
0
2
1
0
2
0
1
0
0
1
0
2
0
1
0
0
0
2
2
1
2
0
0
1
0
1
0
0
1
0
0
0
1
0
1
2
2
2
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
1
2
0
2
0
1
2
0
1
1
0
0
2
0
0
1
2
0
1
0
0
0
0
0
0
1
0
1
2
4
1
1
0
0
0
2
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
2
0
4
0
0
2
0
0
0
0
0
2
0
0
1
1
0
1
1
1
0
0
0
1
1
1
0
0
0
2
0
0
0
0
1
0
2
0
1
1
2
0
0
0
1
0
0
0
0
2
0
2
0
2
1
0
2
0
0
1
0
0
1
0
0
2
0
1
0
0
0
2
0
2
1
0
1
0
1
0
0
0
0
0
3
1
1
0
0
0
1
0
0
0
0
0
0
1
1
2
0
0
0
0
0
1
1
2
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
1
0
0
0
0
1
2
0
0
0
0
0
1
0
0
1
1
2
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
2
1
1
2
0
1
2
0
2
1
0
0
0
0
1
1
0
2
0
0
0
0
2
0
0
0
1
2
0
0
2
1
0
1
0
0
0
0
1
0
1
2
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
1
0
0
2
0
0
0
0
1
1
2
0
0
0
0
3
1
0
0
0
1
2
2
0
0
0
0
0
1
1
0
0
0
1
0
2
0
0
3
0
0
2
0
2
0
0
0
0
0
0
2
2
2
1
2
1
2
1
0
0
1
0
1
1
0
1
1
1
0
2
2
2
0
0
1
0
0
2
0
0
0
0
2
0
0
0
2
1
0
0
0
2
2
0
0
0
2
1
1
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
2
0
2
0
0
0
2
0
2
1
2
0
1
0
1
0
0
0
0
0
2
2
0
1
0
0
1
3
2
0
1
1
2
0
0
0
1
0
0
0
2
0
0
1
0
2
1
1
1
0
0
0
0
0
0
2
0
1
0
2
1
0
0
0
0
0
0
1
0
1
0
2
1
1
0
2
2
0
1
0
0
0
0
1
0
1
0
1
0
1
0
2
4
1
1
7
2
0
0
0
0
2
2
2
1
0
0
3
0
0
0
0
0
0
0
1
0
2
1
2
0
0
0
0
1
1
0
0
0
1
0
1
0
2
1
0
2
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
2
1
0
1
1
0
0
1
0
0
1
0
0
0
0
2
0
1
1
2
1
2
0
2
0
0
0
0
1
1
2
0
0
1
0
2
1
0
1
2
0
0
2
0
1
0
2
0
1
1
1
0
0
0
0
1
0
0
2
1
1
1
1
0
2
0
2
0
0
0
0
0
0
0
0
2
2
0
1
0
2
3
0
0
2
0
0
1
1
0
0
2
1
2
0
0
1
2
1
0
1
0
1
0
0
0
0
0
2
2
0
1
0
1
2
1
0
0
0
0
2
0
0
1
0
0
2
1
1
2
2
0
1
1
0
2
2
0
0
0
0
0
0
1
2
1
2
1
0
2
0
1
2
2
0
0
0
0
0
1
0
1
0
2
1
0
0
2
1
1
0
2
1
0
0
0
0
1
2
1
0
2
0
0
1
1
2
1
0
0
0
0
0
0
2
2
1
1
1
1
2
0
0
0
1
0
2
2
1
0
1
1
0
0
1
1
1
1
1
1
0
1
0
0
1
1
0
0
0
1
1
1
0
1
2
0
1
1
0
0
2
2
2
0
0
0
0
0
1
0
0
2
2
0
1
1
0
0
0
0
0
1
0
2
1
0
1
0
0
1
0
0
0
0
2
0
1
1
2
0
0
0
0
0
8
0
1
1
0
0
1
0
1
0
2
1
0
0
0
1
0
0
3
0
1
0
0
0
0
2
1
0
1
0
0
0
0
0
0
3
2
0
0
0
0
1
1
1
1
0
2
0
2
0
1
1
2
1
2
2
1
2
2
0
0
1
0
0
1
0
0
1
0
1
0
1
1
0
0
0
2
3
0
0
2
0
0
2
0
2
0
0
2
1
0
0
2
2
0
0
1
2
0
1
0
0
0
0
0
0
2
2
1
0
2
0
1
0
0
0
1
1
0
0
0
1
1
0
0
2
1
2
0
0
0
2
0
0
0
2
0
1
0
0
2
0
0
0
1
2
0
0
1
0
0
2
1
0
2
0
1
3
1
1
1
0
2
1
0
0
1
2
1
3
0
0
1
3
3
1
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
2
0
2
0
0
2
1
0
0
1
0
0
0
2
1
0
0
0
3
1
1
0
2
2
3
0
1
1
1
2
0
0
0
0
0
0
0
0
2
1
1
0
1
0
0
0
1
2
0
0
2
1
1
0
1
0
1
3
1
0
0
0
2
0
0
3
0
1
2
0
2
2
1
0
0
0
0
1
0
0
0
2
0
1
1
2
0
0
1
1
0
0
0
1
0
1
2
1
1
2
0
0
1
0
0
2
2
2
0
0
1
0
0
0
0
0
0
2
0
2
2
1
2
0
0
1
0
0
0
0
2
2
1
1
0
0
2
0
2
2
0
1
0
0
1
0
1
2
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
1
1
0
0
2
1
3
0
0
0
2
0
0
1
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
1
2
0
1
1
0
0
0
0
1
0
1
0
1
2
1
0
0
0
1
0
0
2
0
2
0
0
2
0
0
0
2
1
1
0
2
0
0
2
0
1
0
0
0
0
1
1
0
0
2
2
2
1
1
0
3
0
1
0
1
0
0
2
0
0
0
1
2
2
2
0
0
0
0
0
3
1
0
2
2
2
1
2
2
1
1
1
2
1
0
0
0
0
1
2
0
0
0
0
1
2
1
1
0
0
0
0
0
2
1
2
0
0
2
0
0
1
1
1
2
2
2
1
3
1
1
0
1
0
3
1
0
2
0
0
1
2
1
1
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
2
2
0
0
1
0
0
0
2
2
4
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
2
1
1
3
2
1
0
0
0
2
1
0
2
1
2
0
2
0
1
0
0
0
0
0
0
2
3
2
0
0
2
1
0
1
0
1
2
1
0
1
0
1
1
1
0
2
0
1
1
2
2
1
1
0
0
1
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
2
0
5
0
4
1
1
1
1
0
3
1
2
0
0
0
0
1
2
0
0
0
2
1
0
0
0
2
0
1
1
2
0
0
0
2
0
2
0
0
0
1
0
0
2
0
1
2
1
2
0
0
2
0
2
2
2
0
2
1
0
0
1
0
0
0
1
0
0
2
0
0
1
0
1
1
0
1
0
2
0
1
5
0
0
0
0
0
1
1
1
1
0
0
0
0
1
1
0
2
0
0
0
0
1
0
0
0
1
0
1
0
0
3
0
0
0
0
2
0
1
1
1
0
0
1
0
0
3
0
1
0
0
0
0
3
0
0
2
1
0
0
0
0
2
1
0
0
0
0
0
0
0
1
1
0
2
0
1
0
2
0
1
0
1
1
1
0
0
3
2
2
0
0
0
0
0
1
0
0
2
0
0
1
0
3
1
1
0
0
2
1
2
1
2
0
0
1
0
0
1
1
2
0
0
1
0
0
0
4
0
0
1
2
1
1
1
0
0
2
2
1
2
1
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
3
0
0
2
2
0
1
0
0
0
0
0
2
2
0
0
2
1
0
0
0
0
1
2
2
2
0
0
1
1
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
1
0
2
1
0
0
0
2
1
1
1
1
0
0
3
0
1
0
0
0
1
0
0
0
0
0
2
1
0
2
1
0
0
2
1
2
0
0
0
2
0
0
0
0
0
1
0
3
0
2
0
1
0
0
1
0
7
2
0
0
1
0
1
1
0
0
0
1
0
0
2
0
0
0
0
0
3
0
0
1
0
1
0
0
2
0
1
2
1
0
0
0
0
0
0
2
0
0
1
3
1
1
3
1
1
2
0
0
2
0
0
0
2
0
2
0
0
1
0
0
1
1
0
1
1
0
0
1
0
1
1
1
1
1
0
0
0
0
0
0
1
0
0
0
1
0
2
0
1
0
1
1
0
1
0
1
1
0
0
2
0
0
2
2
0
0
0
5
1
1
0
1
0
0
0
3
0
2
2
1
2
0
1
2
3
1
2
0
0
1
0
2
0
0
0
0
2
0
2
1
2
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
1
1
0
0
2
1
0
0
1
1
0
0
2
0
0
2
2
2
0
0
1
0
0
2
2
2
1
0
2
0
0
0
0
2
1
1
0
2
0
1
1
2
1
0
0
0
2
1
3
0
4
1
1
0
1
0
0
1
0
3
1
0
2
1
0
0
2
0
0
1
0
0
0
0
1
0
0
1
2
1
1
0
0
0
0
0
0
2
0
0
2
0
1
0
2
0
1
0
0
1
0
0
1
0
0
0
0
1
1
0
1
0
0
0
2
0
1
3
2
2
3
0
0
1
2
1
0
2
2
1
0
0
0
3
0
2
0
2
0
1
1
0
2
2
2
1
2
0
1
0
1
0
0
0
1
0
1
2
0
1
0
1
3
0
1
1
2
2
0
1
0
0
2
2
0
2
0
0
0
0
0
2
0
2
2
0
0
2
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
3
0
1
2
3
0
0
2
1
0
0
0
0
1
0
0
0
0
1
2
1
0
0
0
0
2
2
0
2
3
2
0
0
0
2
1
1
0
0
0
0
1
2
2
1
0
0
0
2
1
0
0
2
0
0
0
1
0
0
1
0
0
2
0
1
1
1
0
2
2
1
0
2
0
2
0
0
0
0
0
1
0
2
0
1
1
1
0
0
1
2
0
0
0
0
0
0
0
0
1
0
2
0
0
1
2
0
1
1
0
1
2
0
1
2
2
1
0
0
2
0
0
0
1
0
0
0
0
0
1
0
3
1
0
1
2
1
2
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
1
0
0
0
0
1
0
1
0
2
0
1
0
1
2
2
1
2
0
1
0
0
3
0
2
1
2
2
1
2
0
1
0
2
0
2
0
1
0
2
0
2
0
0
0
2
2
0
0
1
0
1
2
0
0
3
0
0
1
0
0
0
1
0
0
3
0
0
0
1
2
1
2
0
0
0
1
2
1
1
0
0
0
0
0
0
1
3
2
1
0
2
2
2
0
0
1
2
1
0
1
0
1
0
0
0
0
1
0
1
0
0
1
0
2
1
0
1
0
2
0
2
0
1
1
2
0
0
0
0
1
0
1
0
0
1
1
0
0
1
1
1
2
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
2
0
3
3
0
0
1
0
1
1
0
1
0
2
2
1
0
0
0
1
0
1
0
0
0
0
0
2
2
0
1
1
0
0
2
0
0
0
1
0
2
1
3
0
1
0
1
0
0
2
0
2
0
0
1
2
1
2
0
2
0
1
0
2
1
1
0
0
0
0
0
0
0
2
1
2
2
0
0
0
1
0
1
1
1
0
1
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
2
0
1
1
0
2
1
0
2
0
0
0
0
1
0
1
1
0
1
0
1
0
1
0
1
0
0
0
1
0
0
0
2
0
0
3
2
2
0
1
3
1
2
0
0
0
0
2
1
0
1
1
4
2
0
2
1
2
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
3
1
2
1
0
0
0
0
0
4
0
0
2
1
1
0
0
0
2
1
1
0
1
0
0
1
1
0
0
1
0
0
0
3
1
0
0
0
1
2
0
2
0
0
0
1
2
0
0
2
1
2
2
0
2
0
0
0
1
2
2
1
1
0
0
2
1
0
2
0
1
0
1
2
1
0
0
0
2
2
0
1
1
1
0
1
1
1
0
0
1
1
1
2
0
0
0
0
0
2
3
0
0
0
1
1
2
3
0
1
0
0
0
2
2
0
0
0
0
0
0
0
1
1
0
4
0
1
1
0
0
1
2
0
0
0
0
2
1
1
0
1
2
0
1
0
1
1
0
2
0
1
2
0
1
0
0
0
0
1
3
0
1
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
3
0
0
0
0
0
2
1
0
1
0
0
2
1
0
2
1
1
2
1
0
1
1
2
1
4
0
2
2
1
1
1
2
2
0
1
1
1
2
0
1
0
0
0
1
6
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
2
2
0
0
1
1
0
2
2
1
0
0
1
0
1
0
2
0
0
0
1
0
0
2
0
0
1
2
1
1
0
0
0
2
0
0
0
0
1
0
1
1
0
2
0
1
2
0
0
2
0
2
1
1
0
0
1
1
1
0
2
0
0
1
0
1
1
0
0
0
0
0
2
0
0
0
1
0
2
0
2
0
0
0
0
1
0
0
0
0
2
0
1
0
1
0
1
0
1
1
1
1
0
3
2
0
0
2
0
0
0
0
1
1
0
1
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
1
1
2
0
2
1
0
0
0
1
2
1
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
2
1
1
1
1
0
0
0
3
1
1
0
0
2
1
0
2
0
0
0
1
0
1
1
0
1
0
3
0
2
0
0
2
0
0
0
1
1
0
0
1
3
0
0
0
1
1
1
0
0
0
0
0
0
2
0
1
2
0
0
1
0
2
0
1
0
2
2
0
2
1
3
2
2
1
1
0
2
1
2
0
0
0
1
2
0
0
2
3
1
1
1
1
0
0
2
2
0
1
0
0
0
0
1
0
2
1
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
2
0
0
1
2
0
1
2
1
0
0
1
0
0
0
2
1
0
0
0
1
2
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
1
0
2
0
0
1
1
0
1
2
1
0
0
0
0
0
0
0
2
1
1
1
0
0
0
1
0
1
0
0
0
0
1
2
0
1
0
0
0
0
2
1
1
1
1
0
0
0
0
0
0
1
2
0
0
0
0
1
3
0
1
2
0
1
1
0
0
0
0
1
0
0
0
1
2
1
0
2
2
1
0
2
0
0
0
0
0
1
0
1
0
2
1
2
1
0
1
0
0
2
0
0
0
0
1
2
2
0
2
0
1
1
0
0
1
2
2
0
0
0
2
1
0
0
0
0
0
1
0
0
2
0
0
0
1
0
1
0
2
0
1
1
1
0
0
0
2
2
1
1
2
1
1
0
0
1
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
2
0
2
1
0
1
0
0
0
0
0
0
1
0
0
2
0
0
1
2
1
1
2
1
1
0
3
0
0
0
1
0
0
0
0
2
2
0
0
2
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
3
0
2
1
0
2
2
1
2
0
0
0
0
0
0
1
1
2
0
0
0
0
2
0
4
0
0
0
0
4
1
1
0
0
1
1
2
2
0
0
1
0
0
2
3
0
0
1
0
1
0
1
0
0
2
0
0
1
1
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
2
0
0
0
2
0
0
1
2
1
0
0
0
0
0
1
1
0
1
2
0
0
0
2
0
0
1
0
0
0
1
0
1
1
1
0
2
1
0
0
1
0
0
0
0
1
1
0
0
0
0
2
0
3
2
0
0
1
1
4
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
1
0
0
1
2
2
0
1
0
0
0
0
0
0
2
2
1
0
2
0
0
2
1
0
0
0
1
1
2
0
1
1
1
1
0
0
0
0
1
0
0
0
3
1
2
2
2
0
0
0
0
0
1
0
2
0
1
0
0
1
0
1
1
2
1
0
2
2
0
2
0
2
0
2
0
0
2
1
1
0
1
2
2
3
0
0
2
1
1
0
2
0
2
2
0
2
1
0
1
2
0
0
1
0
2
2
0
0
0
0
1
0
0
0
2
2
0
0
3
2
0
1
0
1
0
0
2
0
0
0
1
1
0
0
2
0
0
0
0
1
1
0
1
2
0
0
0
2
0
0
0
0
0
0
2
1
2
2
2
1
0
2
0
0
0
0
0
2
0
0
0
1
0
1
0
0
1
0
1
0
1
2
1
1
0
1
2
0
0
0
0
1
0
0
1
0
0
0
0
1
2
0
1
0
0
0
1
0
1
2
0
0
2
0
0
1
0
0
2
1
1
0
1
3
2
0
0
0
1
0
0
0
1
0
2
1
0
0
0
3
0
0
0
2
0
0
0
1
1
2
0
1
1
1
2
0
1
2
0
0
2
0
0
0
2
0
1
0
0
0
0
2
1
2
0
1
2
0
1
0
0
0
2
0
0
0
0
2
1
0
0
2
3
2
1
0
1
0
1
0
3
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
1
1
0
0
2
0
0
0
0
0
2
0
1
2
1
0
0
0
1
0
0
0
1
0
2
1
0
0
1
0
1
0
2
1
0
0
2
1
0
0
0
0
1
2
1
0
0
2
1
1
0
0
0
1
0
2
0
1
0
2
2
0
0
0
2
0
1
2
0
1
1
3
0
2
0
0
0
0
0
1
0
2
0
2
2
0
1
3
0
1
0
0
2
0
0
0
0
1
1
0
0
0
0
0
2
3
2
1
0
1
0
1
2
2
2
1
0
0
0
0
2
0
2
0
0
0
2
2
0
2
1
0
1
0
0
0
0
2
0
1
0
2
0
2
1
0
1
2
2
1
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
2
1
0
2
1
0
1
1
1
2
0
0
2
0
0
2
1
0
1
0
0
0
0
1
0
0
0
1
0
1
0
1
1
1
4
2
0
0
2
1
0
2
2
0
1
0
0
0
1
1
0
1
2
1
0
2
0
0
0
1
0
0
0
0
0
0
2
1
1
0
2
0
0
0
0
2
0
0
0
0
1
1
0
2
0
0
0
0
0
0
2
0
1
0
0
2
0
1
0
1
1
0
2
2
1
3
1
2
0
0
2
1
0
1
0
0
2
1
0
0
0
0
0
2
1
1
0
1
0
1
0
1
0
1
1
3
0
2
0
0
0
0
0
0
2
2
1
1
0
1
1
1
1
0
2
0
0
0
0
0
1
0
0
0
2
2
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
2
0
1
0
0
0
2
0
0
2
2
0
1
0
2
2
2
2
0
1
3
0
1
0
0
2
2
0
2
3
1
0
0
0
0
2
2
0
0
0
1
0
0
0
0
2
0
0
2
1
2
0
0
1
2
0
0
2
2
1
1
2
0
2
3
0
0
1
0
0
0
0
0
0
0
0
0
2
2
1
0
2
2
1
1
2
1
1
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
1
0
0
0
2
1
1
0
0
2
2
2
1
0
0
1
2
0
0
0
0
1
0
1
0
0
1
0
1
0
1
2
1
0
0
0
0
1
0
0
0
1
0
0
1
2
2
2
2
0
2
0
3
0
0
0
0
0
2
0
1
0
2
1
0
1
0
1
0
0
0
0
2
1
0
0
2
1
1
0
1
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
3
2
0
0
3
0
0
0
1
2
1
1
0
1
0
1
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
1
1
0
2
1
0
0
1
2
2
2
2
0
0
3
0
0
0
1
0
0
0
0
0
2
2
3
0
1
0
2
0
1
2
2
0
0
0
0
1
0
2
0
0
2
0
0
2
0
1
0
1
1
1
0
0
3
2
0
1
0
2
0
0
0
0
0
2
0
2
0
0
0
2
0
2
1
0
0
2
0
0
0
2
1
0
0
1
1
0
1
1
0
0
0
1
0
0
1
0
1
0
2
1
0
0
1
1
0
0
2
0
0
1
0
1
1
0
0
0
0
2
1
0
2
0
1
0
0
0
0
2
0
2
0
1
1
0
0
3
0
1
0
1
1
0
2
0
1
1
1
0
0
0
0
0
1
0
0
1
3
2
1
1
0
0
0
0
2
0
2
2
0
0
0
2
1
0
2
0
0
0
1
1
0
0
2
1
0
0
0
0
0
0
0
2
0
0
2
1
0
2
2
1
0
2
0
2
0
1
0
0
0
0
2
2
2
0
0
0
0
1
2
0
2
0
0
0
1
2
0
1
2
0
0
0
0
1
1
0
0
0
2
0
2
2
0
0
3
2
0
1
0
0
1
5
0
0
1
0
0
0
0
2
2
0
0
0
1
1
0
0
1
2
0
1
0
2
0
1
0
1
0
1
2
0
1
0
1
1
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
2
2
0
1
1
0
0
0
0
2
1
1
1
0
0
0
1
1
0
0
1
0
2
2
0
0
2
0
1
1
1
0
1
0
2
0
1
0
2
2
1
0
0
1
1
0
2
2
0
1
0
0
1
0
0
0
1
1
1
1
1
0
0
1
2
2
0
1
0
0
0
0
0
1
0
1
2
2
0
3
0
0
3
1
2
1
0
3
0
1
0
1
0
2
2
0
0
1
1
2
2
0
2
1
2
1
0
0
2
1
2
2
1
0
0
3
2
1
0
1
0
0
2
0
0
0
0
0
2
2
0
0
0
1
1
0
2
1
1
5
2
5
1
0
2
2
0
0
2
1
1
0
0
1
2
0
2
0
2
1
0
1
0
0
0
1
1
2
1
0
1
1
2
2
2
0
1
0
0
0
2
0
4
1
1
0
2
0
1
2
0
0
1
1
0
0
1
0
1
0
1
2
1
0
2
1
0
2
0
2
2
1
2
1
1
1
0
0
2
1
1
0
0
0
1
0
0
1
0
0
0
0
2
0
0
2
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
2
1
3
1
0
2
0
1
1
0
1
0
0
2
1
2
1
2
2
0
1
0
1
3
2
0
3
1
2
0
1
1
0
0
0
0
2
2
2
2
0
0
1
1
2
2
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
7
1
1
1
0
2
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
2
0
2
2
0
3
0
0
0
2
1
0
0
1
0
1
1
0
2
2
0
0
0
0
2
1
0
2
2
0
1
2
0
0
0
3
2
0
1
4
0
2
0
1
0
0
0
1
0
3
2
0
1
0
0
0
0
0
0
2
2
2
2
0
0
1
2
1
1
2
2
0
0
2
2
0
0
0
2
0
0
0
1
0
1
2
1
0
0
0
2
0
2
1
0
0
1
2
0
0
1
2
1
2
0
2
0
1
1
3
1
0
0
2
0
1
1
1
1
0
0
1
4
0
0
2
1
0
0
0
0
0
0
3
0
0
1
1
1
2
1
0
1
2
2
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
2
0
2
2
0
0
0
1
1
0
0
2
1
1
0
1
0
0
0
0
2
1
1
0
3
0
0
2
2
0
0
2
2
0
0
2
0
0
0
0
0
0
1
1
1
2
1
0
1
1
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
2
1
2
2
1
0
1
0
2
1
2
1
0
0
0
0
1
1
0
0
1
2
1
1
2
1
0
2
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
2
1
2
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
2
0
1
0
1
0
3
2
1
3
0
1
0
1
1
0
1
0
3
2
0
2
1
0
2
0
1
0
0
0
2
0
2
1
2
1
2
5
0
2
0
0
1
2
0
0
1
1
0
2
1
6
0
1
2
0
0
0
1
0
1
1
2
0
0
2
1
0
1
0
1
1
0
1
0
0
0
2
0
0
0
0
1
2
0
0
1
3
0
0
1
0
0
1
0
2
2
0
2
2
1
0
0
1
1
0
1
2
0
0
0
0
0
0
1
0
0
0
1
0
2
1
1
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
2
2
0
0
2
0
0
1
2
0
2
2
1
2
2
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
2
1
1
1
0
1
0
0
2
0
0
2
2
0
0
0
0
2
1
0
0
0
2
0
1
1
0
0
0
0
2
0
1
2
0
2
1
1
0
0
0
2
2
0
0
0
0
0
1
2
0
0
3
0
2
2
0
0
2
0
2
0
2
0
0
0
1
0
1
0
1
0
0
1
1
0
2
0
0
2
2
0
1
2
0
2
0
0
0
0
0
0
0
0
2
1
2
2
3
0
0
1
0
0
0
0
2
1
1
2
0
0
0
1
0
2
0
0
1
0
1
1
0
0
1
1
0
1
0
1
2
2
0
0
0
1
2
2
2
0
2
0
2
7
0
0
0
2
1
0
0
0
2
1
0
1
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
1
0
0
0
2
2
0
2
1
1
0
0
0
0
0
0
1
1
1
0
1
0
2
0
2
0
3
2
2
1
0
0
0
0
1
2
0
2
1
1
2
2
0
0
1
0
0
0
1
0
1
0
1
1
2
0
1
1
0
0
0
1
2
2
0
0
1
1
1
0
0
0
0
0
0
2
1
0
0
0
0
0
2
1
2
0
0
2
0
0
0
0
0
0
0
0
0
1
2
1
1
1
0
0
3
0
1
1
0
2
2
2
0
1
0
0
3
3
1
1
1
0
2
0
1
1
1
0
0
0
5
1
1
2
0
0
2
0
0
0
1
0
2
0
0
0
0
1
1
0
2
0
0
1
1
2
0
0
1
0
0
2
0
0
1
0
1
0
3
4
0
0
1
0
0
1
0
0
0
2
0
1
0
0
0
0
0
2
1
2
0
2
1
0
0
1
0
0
1
0
1
0
0
0
2
0
0
2
1
0
1
0
0
0
0
1
2
2
0
0
2
0
1
0
0
1
2
1
0
0
0
0
2
0
0
0
1
2
2
1
0
3
0
1
2
0
0
0
2
1
0
0
0
0
0
1
2
0
0
0
0
0
2
2
0
0
0
1
0
1
1
0
0
1
2
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
1
1
2
0
2
0
1
0
0
1
0
2
0
0
1
2
1
2
1
2
0
1
0
0
0
1
0
3
0
1
1
0
1
2
0
0
1
1
1
0
1
1
2
1
0
0
1
1
1
2
0
1
0
2
0
2
0
1
0
2
4
1
3
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
1
1
0
0
0
0
2
0
0
0
0
2
0
0
1
1
2
0
0
0
2
0
0
1
1
0
0
0
3
0
2
0
1
0
0
0
0
2
2
2
0
0
2
0
0
0
0
1
2
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
1
0
1
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
1
0
1
0
0
0
0
2
2
0
0
2
1
1
0
0
0
1
1
0
1
2
1
2
0
1
2
0
0
0
0
1
2
2
0
1
0
1
0
2
2
0
0
0
0
1
0
0
2
0
0
5
0
0
0
1
0
1
0
0
0
1
1
1
0
0
1
1
1
0
0
0
2
2
0
0
0
0
0
0
2
1
1
0
0
2
2
0
3
0
1
0
1
0
2
1
0
0
1
1
0
0
0
1
2
0
0
0
1
0
1
0
2
2
2
0
0
1
1
1
0
1
0
0
3
2
0
2
5
3
1
1
2
0
0
0
0
0
0
2
1
0
1
0
2
1
1
0
1
0
2
0
0
0
0
1
1
3
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
2
0
0
0
0
0
2
2
0
0
2
0
0
0
1
0
0
3
1
0
1
0
1
0
0
0
0
1
1
2
1
2
0
2
0
1
1
0
2
0
2
0
0
0
3
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
1
0
0
0
0
1
2
2
2
1
0
0
0
1
0
0
0
0
1
1
1
0
0
1
0
0
0
1
0
0
0
0
2
0
1
2
0
2
0
2
2
1
0
0
0
3
2
1
2
0
1
1
1
0
0
3
0
2
0
1
1
0
3
0
1
0
2
0
0
1
0
0
1
2
0
0
2
1
1
2
1
0
2
0
2
1
1
0
1
0
0
1
2
0
0
2
0
0
0
2
0
1
2
0
0
0
0
2
0
0
1
0
1
2
1
1
0
0
0
2
1
0
0
2
0
1
0
1
2
0
2
2
1
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
4
0
1
0
1
1
0
0
2
1
0
0
0
1
0
0
4
0
8
0
2
0
0
2
1
0
3
0
0
0
0
1
2
2
0
1
0
1
0
0
0
1
0
0
4
1
1
0
0
0
1
0
2
1
1
0
0
0
1
0
1
1
0
0
2
2
0
1
0
1
1
0
2
1
2
2
2
1
0
0
0
2
0
2
1
2
0
1
0
1
0
1
0
0
3
0
0
2
2
0
0
0
3
2
0
2
0
0
0
0
1
0
0
2
1
0
0
1
0
1
2
0
2
0
1
2
2
1
2
0
0
1
0
0
3
1
1
3
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
2
1
0
0
0
0
2
0
1
1
1
1
0
0
0
0
1
1
2
0
2
1
0
0
1
2
0
0
1
1
0
0
1
0
0
1
4
0
2
1
1
0
0
2
0
2
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
2
0
0
0
1
0
1
2
1
2
2
0
0
0
1
1
1
0
0
0
1
1
0
0
1
0
2
1
2
0
0
0
3
3
0
0
0
1
1
1
1
0
2
1
0
1
1
0
2
0
3
0
0
1
0
2
1
2
0
1
0
1
0
0
2
0
0
0
0
0
2
0
2
0
0
2
0
1
1
1
3
0
0
0
0
2
0
1
1
2
2
1
1
1
1
0
2
0
0
0
0
0
0
2
0
2
0
0
0
2
2
1
2
1
2
0
1
0
0
1
2
0
0
1
1
1
0
0
1
0
0
0
1
0
2
2
0
0
0
2
0
2
0
0
1
1
1
0
0
0
1
0
0
2
0
1
1
2
0
0
2
0
2
0
0
0
0
0
1
2
1
0
1
1
0
2
0
1
1
1
1
0
0
0
0
1
0
2
2
2
1
2
1
1
0
0
2
1
2
0
0
0
0
1
1
0
0
2
1
0
0
1
1
1
0
2
0
2
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
1
0
1
2
2
2
0
1
0
1
0
0
0
0
2
1
1
0
0
0
0
2
0
0
2
0
0
0
1
0
2
0
2
0
0
0
1
0
2
0
0
2
0
1
0
1
1
0
2
0
0
0
2
0
2
0
0
0
2
1
1
0
1
0
2
0
1
0
0
0
0
2
2
0
0
1
0
1
0
2
2
0
1
1
0
1
0
0
1
1
2
0
2
1
0
2
2
1
0
0
0
2
2
2
1
0
0
0
0
0
1
2
0
0
0
0
0
0
6
0
0
0
0
1
1
0
1
0
2
0
0
2
1
1
0
0
2
0
0
1
3
0
1
1
0
3
1
1
0
1
2
1
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
1
1
0
0
1
0
2
1
0
1
2
0
1
2
2
0
1
1
2
0
1
0
1
1
0
0
0
1
1
0
1
0
1
0
2
1
0
0
2
1
3
2
2
0
0
0
2
0
0
0
0
1
2
2
2
2
0
1
1
1
1
3
0
0
1
0
0
1
1
1
3
1
0
1
2
0
0
1
0
0
1
0
0
1
1
2
2
8
0
0
2
1
2
0
2
0
2
0
2
1
2
0
2
1
0
1
1
1
2
1
3
0
1
0
1
1
1
0
0
1
0
0
1
1
0
0
1
0
0
1
1
0
2
0
1
0
1
1
2
0
1
0
0
0
1
2
0
0
1
0
0
0
0
4
0
1
0
0
1
1
1
2
1
2
0
0
0
1
2
0
0
0
1
0
2
1
0
0
1
0
2
1
1
0
0
2
0
1
0
1
2
0
1
1
0
0
0
1
2
2
2
0
0
3
0
0
1
2
0
2
2
0
1
0
2
0
0
1
1
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
1
0
3
0
0
0
2
2
0
1
0
0
1
0
2
0
2
0
0
1
0
0
0
0
2
1
0
1
2
0
0
0
3
1
1
2
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
1
0
0
2
0
0
0
1
0
0
1
0
2
1
0
2
2
0
0
1
1
2
0
1
0
1
0
0
0
0
2
1
1
0
1
0
2
1
0
0
0
1
0
2
0
2
0
2
0
0
0
0
0
1
0
2
0
0
0
1
2
1
0
0
1
1
1
1
1
1
1
1
1
0
2
0
0
1
1
2
2
2
2
1
0
0
0
0
0
2
0
1
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
2
1
1
0
2
0
0
0
0
0
2
1
0
0
0
2
2
0
0
1
2
0
1
2
2
1
0
0
2
0
2
2
1
0
2
2
0
0
0
0
1
1
2
1
1
3
0
0
1
0
0
0
3
1
1
0
0
0
0
0
1
0
0
0
1
3
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
2
2
0
0
0
0
1
0
0
1
0
1
0
1
2
0
0
1
0
2
1
0
1
0
2
0
0
0
0
0
1
0
1
0
2
0
0
1
0
0
2
1
0
1
2
0
0
5
0
0
2
0
0
0
2
0
0
2
0
0
1
0
1
1
0
1
2
1
1
0
1
0
1
1
0
0
1
1
0
2
0
0
1
2
0
0
1
0
1
0
2
1
1
0
0
0
2
0
1
0
2
0
0
0
1
1
1
1
0
0
0
2
1
0
0
1
0
2
0
1
0
0
0
2
3
0
0
2
0
1
1
0
0
1
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
1
0
0
0
4
2
1
2
1
1
0
2
0
1
0
2
0
0
1
1
2
0
0
0
0
0
0
2
0
1
1
2
1
0
0
0
0
0
0
0
0
0
1
0
0
3
2
0
1
1
1
2
1
2
0
4
2
1
2
1
2
0
2
0
1
2
1
0
1
0
1
0
0
0
0
0
1
0
2
3
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
2
1
1
0
0
2
1
0
0
0
0
0
0
2
2
0
1
0
2
1
0
0
2
2
2
2
2
2
2
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
2
1
0
2
0
1
3
0
2
0
0
0
0
1
0
1
0
1
0
1
0
2
0
1
0
2
0
2
0
0
3
0
0
1
1
0
1
0
1
0
1
0
0
0
1
1
1
0
0
0
0
0
2
0
0
1
2
0
0
0
0
1
1
1
0
0
0
0
2
2
0
0
0
1
2
2
2
2
2
0
0
2
0
0
2
2
2
0
0
1
0
2
1
0
1
2
0
1
1
0
0
1
0
1
1
0
2
0
0
0
0
0
2
1
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
1
1
0
1
0
0
2
0
2
0
0
0
0
1
0
1
0
1
1
2
2
0
1
1
0
0
0
0
0
1
1
3
1
1
0
0
2
0
2
2
0
1
1
0
1
0
0
0
2
0
0
0
2
0
1
0
0
2
1
0
0
0
1
3
1
0
0
0
0
0
1
2
0
1
1
0
2
0
1
2
2
0
1
2
1
0
0
0
0
0
0
0
2
0
0
3
0
1
0
1
0
0
0
2
1
1
2
2
0
1
0
0
0
0
0
0
2
0
1
1
0
0
1
1
2
0
0
2
0
0
0
2
2
0
0
0
1
0
1
2
1
2
0
2
0
0
2
0
0
1
0
0
1
0
0
2
1
0
0
1
1
1
2
0
2
0
2
1
0
0
2
1
2
0
1
0
0
0
0
1
1
0
0
0
0
2
2
0
0
1
0
2
0
0
1
1
0
0
0
0
0
0
0
1
1
0
1
1
1
1
1
2
2
2
0
0
0
0
0
1
1
0
0
0
0
2
0
1
2
0
0
0
5
0
1
0
1
2
1
0
0
0
0
0
2
0
0
0
2
0
2
0
0
1
1
2
0
0
1
1
0
0
0
0
0
1
0
3
2
0
0
2
0
2
0
0
0
0
0
0
1
1
1
1
2
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
1
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
1
0
2
0
0
0
1
1
0
1
0
3
0
1
2
0
0
0
0
2
0
2
0
8
2
1
3
1
2
1
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
2
0
2
0
2
2
2
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
2
1
0
2
1
1
1
3
0
0
2
0
2
0
2
0
0
1
0
1
0
0
2
1
0
2
2
1
0
2
0
2
0
2
0
3
0
0
0
0
0
0
0
1
0
0
1
3
0
1
0
0
0
0
0
2
0
1
1
2
0
1
0
1
0
2
2
1
4
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
1
0
2
1
0
1
0
1
0
0
0
0
1
2
0
0
0
1
0
0
0
0
1
0
0
2
2
2
0
1
1
1
1
0
0
0
2
0
1
1
1
0
3
0
1
0
2
0
2
1
0
2
0
0
1
0
0
2
2
2
0
0
0
0
2
0
1
2
2
0
2
0
0
1
1
0
1
1
0
0
2
0
0
2
0
0
2
1
0
3
1
0
0
1
0
0
2
1
0
0
1
1
0
1
0
0
0
0
1
2
1
2
2
0
0
1
2
0
1
0
0
1
2
2
0
0
0
0
5
2
0
0
0
2
1
0
0
2
2
0
0
2
2
1
1
1
0
0
0
0
1
0
0
2
1
1
0
0
0
2
1
0
2
2
1
0
1
0
2
0
2
1
2
1
0
2
0
1
1
0
2
1
1
0
2
1
2
0
0
1
1
1
0
0
0
1
0
0
2
1
2
1
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
1
1
0
0
1
1
0
1
0
0
0
1
1
0
0
0
0
2
1
1
0
0
1
2
0
0
2
1
0
1
0
1
1
0
0
2
0
0
0
0
0
1
0
0
1
0
2
0
0
1
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
2
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
1
0
0
1
0
2
1
0
1
1
0
1
4
1
0
2
0
1
0
0
0
1
0
0
1
1
1
1
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
2
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
1
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
2
1
2
0
0
0
0
2
0
1
0
2
0
3
1
1
0
0
0
2
0
1
2
0
0
0
1
1
0
0
0
2
0
0
1
0
0
2
2
0
1
1
0
1
1
1
2
1
0
0
1
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
2
0
1
0
1
1
1
0
2
1
0
3
0
2
1
3
0
0
1
0
0
2
1
0
0
0
1
2
1
0
1
0
1
1
0
1
0
2
0
0
2
1
1
0
2
1
0
0
0
0
2
3
0
3
0
0
0
0
2
1
0
0
0
0
0
0
2
1
1
0
1
0
1
1
0
0
2
1
0
0
0
3
1
0
1
2
0
0
2
0
2
0
0
4
3
3
2
1
0
0
1
2
0
2
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
3
2
0
0
0
0
2
2
1
0
1
0
0
1
1
1
3
0
0
1
2
0
1
2
0
0
0
1
0
0
2
0
0
2
2
1
0
1
2
0
0
0
0
1
0
1
1
0
0
0
0
2
2
0
0
0
0
0
2
3
0
2
0
1
0
1
0
0
0
1
2
2
2
3
1
1
0
2
0
0
0
2
2
1
0
1
1
1
1
0
0
0
2
0
2
2
1
1
1
0
0
0
2
0
2
1
2
1
0
0
1
1
3
0
1
1
0
1
1
0
0
1
1
0
0
0
0
0
0
1
2
2
0
1
0
0
1
0
0
0
2
0
0
0
2
0
1
1
0
1
0
2
0
0
0
0
0
0
0
1
0
0
2
3
1
0
0
0
1
1
0
1
0
1
2
0
0
0
1
2
1
2
0
2
0
2
2
1
0
1
0
1
1
0
2
0
1
1
1
0
0
0
0
2
0
1
0
1
0
2
0
0
1
0
0
0
2
0
0
3
0
0
1
0
0
1
0
0
0
0
0
1
0
1
1
1
0
1
0
0
2
0
1
0
1
3
0
0
0
0
1
1
0
2
0
0
2
0
0
2
0
0
1
1
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
1
2
0
0
0
2
0
0
1
2
1
2
1
1
0
0
1
0
0
2
0
2
1
0
0
3
0
0
0
2
0
1
0
1
1
1
2
1
0
0
1
0
3
2
2
0
0
0
1
0
1
0
1
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
1
1
0
2
0
1
1
1
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
1
1
2
1
0
2
2
0
1
1
2
0
0
0
2
1
2
0
0
1
0
1
0
2
0
0
2
4
2
15
0
0
1
0
0
2
0
2
0
2
1
0
0
1
3
1
2
2
1
0
1
3
1
0
2
2
0
0
2
1
2
1
1
0
2
0
1
0
0
0
2
1
2
1
0
0
0
0
1
0
2
0
0
3
0
1
1
1
1
0
2
0
0
0
0
1
0
0
2
0
0
0
2
2
1
3
0
1
0
0
3
2
0
4
0
3
2
0
0
0
1
1
1
2
1
0
0
0
2
2
2
2
0
1
0
2
2
0
1
0
1
0
0
1
0
0
0
2
0
1
1
1
0
0
0
0
0
2
1
0
0
1
0
1
1
2
1
0
2
2
0
1
1
0
0
0
0
0
0
0
1
0
2
0
1
2
1
0
2
2
0
1
0
1
1
0
0
0
1
1
0
1
0
2
0
0
1
0
2
0
0
1
2
0
0
0
1
1
0
1
0
1
1
1
2
2
0
1
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
2
0
2
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
1
1
1
1
3
0
0
2
0
0
0
1
2
1
0
2
0
0
0
2
0
0
1
0
1
0
2
0
0
0
1
1
0
0
2
0
0
0
0
0
0
1
0
2
2
0
1
1
0
0
0
2
0
1
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
2
1
1
1
0
2
0
0
2
0
1
0
3
1
1
0
0
1
0
0
0
1
1
2
0
0
0
0
1
0
3
0
0
1
1
2
0
0
0
0
2
1
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
1
0
2
2
1
0
1
0
1
1
0
0
1
0
0
2
1
0
0
1
0
0
0
2
0
1
1
1
1
0
0
0
2
1
0
2
0
0
2
2
0
2
1
0
3
1
0
0
0
0
1
0
0
0
0
0
1
1
1
0
1
0
2
2
0
1
2
1
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
1
1
0
0
1
1
3
1
1
2
0
0
2
0
0
0
0
0
0
0
2
0
1
2
2
0
2
2
2
1
0
1
3
1
2
0
0
0
0
1
0
1
2
1
0
0
0
0
0
0
0
2
3
1
2
0
0
1
0
1
1
0
0
0
0
1
0
1
0
0
2
0
0
1
0
0
0
0
0
1
2
1
0
0
1
1
1
1
0
1
0
1
2
0
1
2
2
0
1
2
0
1
0
2
0
0
0
0
1
0
2
0
0
0
2
0
1
2
0
1
0
2
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
2
0
1
2
3
1
0
0
2
0
1
0
0
2
0
0
0
0
0
0
1
1
2
0
1
1
0
0
2
0
0
0
1
0
2
0
0
2
2
0
2
2
0
2
0
0
2
2
1
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
1
2
2
1
1
1
2
0
0
0
0
0
1
1
0
0
0
0
1
1
0
2
1
0
0
2
1
1
0
0
1
0
2
0
3
0
1
0
0
2
1
1
1
0
2
2
0
0
0
0
0
0
0
1
2
2
1
1
0
2
1
2
2
0
0
0
1
0
0
0
1
1
0
2
0
1
0
1
1
1
2
0
0
1
0
2
0
0
0
0
1
1
2
2
1
1
0
0
6
2
2
0
0
0
0
1
0
3
2
0
0
0
1
0
2
0
2
0
1
0
2
0
2
2
1
1
0
1
0
2
1
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
2
0
0
1
0
1
0
0
1
0
0
1
1
0
0
0
2
2
0
1
0
0
2
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
2
2
1
0
1
0
0
0
2
0
1
3
0
0
1
1
2
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
3
0
1
1
0
2
2
5
1
1
1
0
1
2
0
2
0
2
0
3
4
2
1
0
0
0
0
0
2
2
0
0
1
2
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
1
2
0
1
1
2
0
0
0
2
0
0
2
0
0
1
1
0
2
1
0
1
2
0
0
2
0
2
2
0
0
0
0
0
1
1
0
0
0
2
1
1
3
1
0
1
2
0
0
0
0
1
1
0
0
0
1
0
0
1
1
0
0
1
0
0
2
2
0
0
2
1
0
0
1
4
0
0
2
2
2
0
0
1
0
1
1
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
1
2
0
2
0
0
2
0
0
2
0
1
1
0
1
0
2
1
0
1
1
0
1
0
1
0
1
0
0
0
1
2
1
0
2
1
0
0
0
0
2
1
0
1
0
0
0
0
0
1
1
2
0
1
0
1
0
0
0
1
0
3
2
1
0
0
1
1
0
1
0
2
0
1
1
0
0
0
0
2
0
2
2
0
1
1
2
0
1
0
2
0
0
0
0
0
2
1
2
0
2
0
1
0
1
2
0
2
0
1
1
2
3
2
0
2
0
1
0
0
1
0
1
1
2
0
1
1
1
0
0
2
0
0
2
0
0
1
1
0
2
0
0
0
1
0
0
1
1
0
2
0
1
0
1
1
0
2
0
1
1
1
0
1
0
1
1
1
0
3
0
0
1
1
0
1
0
1
0
1
2
2
0
0
0
2
2
0
0
2
3
0
0
0
1
0
0
1
3
1
2
0
0
1
0
1
0
0
1
0
0
4
0
1
0
1
2
0
5
0
1
2
1
0
1
0
2
0
0
1
0
0
0
2
0
4
0
1
0
0
0
0
3
1
2
2
0
0
1
2
0
2
0
0
2
3
0
1
2
0
2
1
0
4
0
2
1
2
2
0
0
0
0
1
0
0
1
0
0
1
0
2
0
0
1
2
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
1
2
1
1
2
0
2
1
0
0
2
0
2
2
0
0
2
0
0
3
1
0
2
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
2
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
1
1
0
0
0
1
0
0
1
1
0
0
0
0
0
2
0
0
0
2
0
0
2
1
2
1
0
2
1
1
0
0
1
1
1
0
0
2
1
0
0
0
0
0
0
0
0
1
1
0
0
2
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
2
0
1
0
0
2
0
1
1
1
0
0
4
1
1
2
4
2
2
0
0
1
2
0
2
0
0
0
0
1
0
0
0
1
1
1
0
0
2
1
1
0
1
1
1
0
0
1
2
0
2
0
0
0
2
1
0
0
0
2
0
1
2
2
3
0
0
0
2
1
2
1
0
2
0
0
0
1
0
0
0
0
1
0
4
0
0
0
0
1
0
0
1
2
2
1
0
2
0
0
0
1
1
2
0
0
0
1
2
1
0
0
1
0
2
0
0
0
0
0
2
0
0
2
0
2
0
0
1
1
0
2
0
1
1
0
1
0
2
0
1
1
0
1
0
1
1
0
0
0
0
1
1
0
0
0
2
1
0
2
0
0
2
0
1
1
0
0
2
0
0
1
0
1
0
0
0
1
0
0
1
1
2
0
2
0
1
0
0
1
0
0
0
0
2
0
0
1
1
2
2
1
1
0
0
1
0
2
2
0
0
0
1
0
0
0
1
1
2
0
2
1
0
0
0
0
1
0
1
2
0
2
0
0
0
1
3
1
0
1
0
0
1
1
2
2
2
0
1
0
0
0
0
2
2
0
2
2
0
1
2
0
2
4
0
0
0
1
0
2
0
2
0
0
1
2
3
1
1
0
1
0
0
0
0
4
1
0
2
3
0
1
1
0
2
1
0
0
0
1
0
2
1
0
0
0
1
1
1
0
0
2
1
3
0
0
1
0
0
0
0
0
1
0
1
0
3
2
0
1
0
1
0
1
1
2
0
1
2
2
2
1
0
3
1
0
1
2
2
0
2
0
4
1
0
0
1
0
1
1
3
0
2
2
0
1
0
0
2
0
2
0
0
2
0
2
2
0
0
2
0
2
0
0
0
2
0
0
1
1
0
1
0
0
2
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
2
2
2
1
0
3
2
6
2
1
2
0
1
0
1
1
1
3
1
0
2
1
1
1
2
1
0
0
2
0
0
0
0
2
0
1
1
1
0
1
0
0
2
0
0
1
1
1
2
1
0
0
2
1
1
2
0
1
2
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
1
2
0
1
0
0
0
1
0
0
0
0
1
0
3
0
1
0
1
1
0
0
2
2
2
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
2
0
1
0
0
2
0
2
0
3
0
1
3
0
0
0
0
0
1
0
2
2
0
0
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
1
2
0
1
0
0
0
1
1
1
0
0
0
0
0
0
2
2
2
2
0
1
0
1
1
0
0
0
0
0
1
0
1
2
0
1
0
1
2
0
0
0
0
0
1
1
0
0
0
0
0
2
0
2
1
0
0
0
1
2
2
0
0
0
0
2
0
1
0
0
0
1
0
1
2
0
1
1
0
1
1
1
1
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
1
1
1
0
2
0
2
2
0
1
2
0
0
2
0
1
0
0
0
0
2
2
0
0
1
0
0
3
2
0
2
0
0
0
0
0
1
0
1
0
2
0
2
0
1
0
0
1
0
0
1
0
1
0
0
0
2
0
2
0
0
0
0
1
0
0
0
2
1
0
2
1
1
2
0
0
4
0
1
0
0
0
0
1
1
0
0
1
0
1
2
0
2
0
0
0
0
0
0
1
1
0
0
0
1
0
2
1
2
1
0
0
0
0
0
1
0
2
2
1
0
2
0
0
0
2
2
0
0
0
0
1
0
0
0
1
2
2
0
2
1
0
1
1
1
0
0
1
2
0
2
1
0
2
0
2
0
2
1
0
0
1
0
0
2
2
0
0
0
0
0
2
0
2
2
2
0
2
0
1
1
1
0
2
0
0
3
0
0
0
0
0
1
0
0
0
0
1
2
0
1
0
2
0
0
2
1
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
1
0
2
0
0
0
0
1
0
0
0
1
0
1
2
2
0
2
2
0
0
0
0
1
0
3
0
2
0
0
0
1
1
1
0
1
0
2
0
1
0
0
0
0
0
0
2
1
2
1
2
2
0
0
0
0
2
0
1
0
0
1
1
0
2
1
0
2
0
0
1
2
1
3
2
0
0
2
0
2
0
2
1
1
2
0
2
0
1
2
1
2
2
0
2
1
0
2
0
1
1
1
2
1
0
2
1
1
0
0
1
0
1
0
1
0
0
0
1
2
0
1
0
1
0
1
0
1
2
2
0
1
2
0
0
0
0
2
0
2
2
3
0
1
0
0
0
0
0
0
2
2
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
1
2
1
2
1
1
1
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
1
1
1
2
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
2
1
0
0
2
0
0
1
0
1
0
2
2
1
0
0
0
0
0
2
2
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
1
1
0
0
0
1
1
0
0
1
1
0
1
2
0
1
0
0
0
0
1
1
1
1
0
0
1
0
0
2
0
0
3
2
0
1
1
0
0
2
0
0
0
0
1
2
1
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
2
0
0
0
2
0
0
1
0
0
0
2
1
0
0
2
2
1
0
0
0
0
0
0
0
1
0
2
0
1
1
2
1
0
2
2
2
2
0
0
1
1
0
1
2
2
1
1
0
0
0
0
1
2
0
2
1
2
2
2
4
5
1
4
0
1
0
1
2
2
2
0
1
0
1
0
0
1
0
1
2
1
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
2
2
1
1
1
0
0
1
1
2
2
1
0
0
0
1
2
1
2
1
0
1
0
0
0
0
0
2
2
0
2
1
0
2
1
0
2
0
1
0
1
0
0
1
1
1
2
2
2
0
0
0
1
4
2
0
0
0
0
0
1
2
1
0
0
2
1
1
0
4
1
0
0
0
1
1
2
0
1
0
2
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
3
0
0
0
1
2
1
0
2
0
0
1
2
0
0
1
0
2
1
0
2
1
1
0
2
0
1
0
2
1
1
0
0
1
1
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
1
2
1
3
0
0
0
2
2
0
0
0
1
0
0
0
3
3
3
0
1
0
1
2
2
4
0
2
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
1
2
2
2
0
2
2
1
1
0
0
0
1
0
0
0
1
1
1
0
1
2
0
0
2
1
1
0
0
0
2
1
0
0
2
0
0
0
2
0
0
3
0
1
0
0
1
0
3
0
0
0
0
1
0
1
0
1
0
1
1
1
0
1
0
0
0
2
2
0
0
2
1
1
0
0
2
2
1
3
1
0
1
2
0
0
0
0
0
1
0
1
0
1
2
1
1
2
0
1
0
1
0
1
0
2
0
0
1
4
0
0
0
0
1
1
0
0
0
0
2
0
0
0
2
0
0
1
1
0
2
0
0
0
2
0
0
0
0
2
1
0
2
1
1
1
0
0
6
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
1
1
1
0
1
2
0
2
0
0
0
1
1
1
0
1
0
0
0
0
1
5
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
2
1
0
0
2
0
0
2
0
2
1
0
0
0
1
0
2
0
1
1
0
1
0
0
0
0
1
0
3
0
3
0
2
0
0
1
1
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
2
0
1
0
0
0
1
0
1
0
1
1
0
1
0
2
0
1
2
1
2
1
1
0
1
0
0
0
0
1
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
2
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
1
1
1
0
2
1
1
0
2
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
1
0
1
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
1
2
2
0
0
0
0
1
2
0
2
0
1
0
0
0
1
1
0
1
0
1
0
2
1
2
1
0
1
0
0
0
1
0
2
1
2
0
0
1
2
2
1
0
2
0
0
0
0
1
0
2
0
0
2
2
1
0
2
0
1
1
1
0
0
1
2
0
2
0
2
0
0
2
0
2
0
1
0
1
0
2
0
0
0
0
0
0
0
2
1
1
0
3
2
2
0
1
1
0
0
2
2
0
0
1
1
2
0
1
0
1
2
0
1
0
0
1
0
0
0
0
0
5
0
2
2
0
0
1
0
0
1
0
0
0
0
2
0
1
0
0
0
0
1
1
2
0
0
0
0
1
3
1
0
0
0
0
0
1
0
1
1
1
0
0
0
0
2
0
0
0
1
1
1
1
0
0
2
0
1
0
0
0
2
1
1
0
2
2
1
1
1
2
2
1
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
1
1
0
1
0
2
0
0
0
0
0
0
2
0
1
1
0
1
0
0
1
0
3
0
0
1
1
0
0
1
1
0
1
0
2
0
0
2
0
0
1
1
0
0
0
1
0
1
0
0
2
2
0
1
2
1
0
0
2
0
2
1
2
2
0
0
4
1
0
0
0
0
0
2
1
0
2
0
1
1
0
0
2
1
1
0
1
0
0
1
0
0
0
0
2
0
0
0
2
2
1
0
1
0
0
0
0
0
2
0
0
2
0
0
0
1
1
0
0
2
0
2
2
2
0
0
0
0
1
1
0
0
0
0
2
1
0
1
1
1
0
0
2
2
0
0
0
2
0
2
0
1
2
1
2
0
2
0
2
0
2
0
1
0
0
2
1
1
0
0
1
0
0
0
0
0
0
1
2
2
2
2
0
0
2
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
2
1
0
0
1
2
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
1
2
1
0
0
3
0
0
0
0
1
6
2
0
0
2
0
0
0
2
0
0
0
0
1
0
1
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
1
0
2
0
1
2
2
1
0
1
0
1
1
0
0
0
2
1
0
0
0
1
0
2
0
0
2
0
0
1
0
2
1
0
2
0
0
1
1
0
0
1
1
0
1
0
1
0
0
1
0
1
1
1
0
0
0
0
1
1
1
0
0
0
0
0
3
0
0
0
0
0
0
0
2
3
1
0
1
1
0
1
0
1
0
0
0
2
1
1
2
1
2
0
0
0
0
2
1
0
0
0
3
0
0
3
0
1
2
0
2
0
1
0
0
0
0
1
0
2
0
0
0
0
0
2
1
0
0
1
0
1
1
0
1
0
0
0
0
0
1
0
0
0
2
1
2
2
0
1
3
0
2
0
0
0
2
0
2
0
0
1
1
0
0
0
0
0
1
0
0
2
0
1
0
1
1
0
0
1
1
2
1
1
2
2
0
1
0
0
0
0
1
0
1
1
1
0
1
1
1
0
0
2
2
0
1
0
2
2
2
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
1
0
2
1
0
2
2
0
0
0
0
0
1
0
2
0
1
1
0
1
1
0
2
2
1
2
1
0
0
0
0
0
0
0
0
1
0
0
1
2
2
0
0
2
2
0
0
0
0
2
1
0
0
1
0
0
1
0
1
0
0
1
2
1
0
2
3
0
1
0
1
0
0
0
0
0
2
2
0
0
0
0
0
1
1
2
2
0
0
0
2
0
1
1
0
0
0
1
0
0
2
1
2
0
0
2
0
0
0
3
0
0
0
0
1
2
0
1
0
0
0
4
1
0
2
0
2
0
0
0
0
0
0
0
2
2
0
0
1
0
0
2
1
0
0
2
0
2
0
0
0
2
1
0
0
2
2
0
1
0
0
0
1
0
1
2
2
0
1
2
1
0
2
1
1
2
0
1
0
0
0
0
1
0
2
0
1
0
2
1
0
1
2
3
0
0
2
0
2
1
0
0
2
0
0
0
2
0
2
0
2
0
0
1
2
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
1
0
2
1
0
1
1
1
0
2
2
0
0
1
2
1
0
0
1
0
1
0
0
0
0
1
0
0
1
2
0
1
0
2
0
2
1
2
1
2
0
0
1
2
0
0
0
0
0
2
0
2
0
0
1
1
0
0
2
0
0
0
1
0
0
1
0
0
1
1
2
0
0
0
1
1
2
1
2
0
1
2
1
1
0
2
2
0
0
0
1
1
2
0
0
0
1
0
0
2
0
0
0
0
1
0
0
3
2
2
1
2
2
0
0
1
1
0
1
0
0
1
2
1
1
1
0
1
1
0
1
2
1
2
1
3
1
2
1
1
2
1
0
0
2
0
0
0
0
1
0
2
0
2
0
0
1
2
0
0
2
2
0
2
0
0
2
0
0
0
0
0
2
2
0
2
1
1
0
0
0
1
2
1
1
0
0
0
0
0
0
0
1
0
1
1
1
0
2
0
0
0
1
2
1
0
2
0
0
0
2
0
2
1
0
0
0
2
1
0
0
0
0
0
0
2
2
0
1
0
2
0
0
0
0
2
2
0
1
2
0
1
0
0
0
1
1
0
1
0
2
0
1
1
0
1
0
0
0
0
0
0
0
1
3
2
0
0
0
0
1
2
1
0
1
0
2
2
0
0
2
0
2
0
0
2
1
0
0
0
2
0
2
2
0
0
1
1
0
0
0
0
2
1
0
0
1
3
0
0
2
1
2
1
0
2
0
0
1
0
0
0
2
1
2
1
1
0
0
2
1
0
0
0
2
1
0
2
2
0
2
1
0
1
1
1
0
0
0
3
0
0
2
2
0
1
2
0
1
0
0
0
0
0
1
0
1
2
2
0
0
0
0
1
0
0
1
1
1
0
0
2
0
0
1
1
2
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
2
2
1
0
1
1
0
0
1
1
2
0
1
0
0
0
3
1
1
0
2
0
1
2
0
0
2
0
0
1
2
1
1
1
0
0
2
0
0
0
2
0
3
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
1
1
2
0
2
2
1
0
1
0
2
2
1
0
1
0
1
4
0
1
0
1
2
0
1
1
1
2
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
1
1
1
2
1
0
0
1
2
2
0
1
0
3
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
2
0
0
0
0
1
3
0
0
0
11
0
0
2
0
0
2
1
1
2
2
0
0
1
0
0
1
0
2
2
0
0
3
0
0
0
0
0
1
1
0
0
2
1
0
2
0
0
0
1
1
0
1
0
0
0
2
1
0
1
1
0
0
1
2
0
1
0
0
2
0
1
0
2
0
0
0
1
0
1
0
0
1
0
0
0
2
2
0
2
0
0
1
0
0
2
0
3
2
1
2
2
2
0
0
1
0
0
0
1
2
0
1
0
1
0
1
0
1
0
0
3
2
0
0
2
1
0
2
0
1
2
4
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
2
0
1
0
0
2
0
0
0
2
0
1
1
0
0
2
0
0
0
1
1
0
0
0
1
1
2
1
1
2
0
0
0
8
3
1
0
0
2
0
1
2
0
3
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
2
1
1
0
1
0
0
0
0
0
2
0
0
0
2
0
3
1
0
0
0
0
0
1
2
0
0
0
1
1
1
2
0
2
2
0
1
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
2
1
2
1
0
2
0
2
1
0
1
1
0
1
1
0
0
1
0
0
1
0
0
3
0
1
2
0
0
0
0
2
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
2
0
0
0
0
1
0
1
0
0
0
1
0
2
2
0
0
0
3
0
1
2
0
0
2
2
0
2
1
0
1
0
0
1
0
2
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
1
0
1
0
2
0
1
0
0
3
0
2
1
0
1
2
0
0
2
2
0
0
2
0
0
3
0
0
0
1
2
1
2
0
0
0
1
0
0
2
0
2
2
3
0
0
0
1
0
0
1
2
1
1
2
0
1
0
0
4
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
2
1
0
1
2
0
2
1
1
1
0
2
0
1
0
0
1
1
1
0
0
0
0
2
0
0
2
1
0
0
0
0
1
0
0
1
1
0
2
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
1
0
2
1
0
1
4
2
2
0
1
0
0
2
2
1
2
0
2
1
0
1
0
0
2
0
1
0
1
2
2
0
0
1
1
0
0
0
1
0
2
0
0
2
2
0
1
0
2
0
0
0
0
1
2
1
0
0
1
1
2
2
1
0
0
0
0
0
0
1
0
1
0
0
2
0
1
1
0
0
0
2
1
0
0
1
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
1
0
0
0
1
0
1
0
0
2
0
0
0
1
0
0
0
2
2
0
0
1
0
1
0
1
0
3
2
1
1
2
0
0
0
1
2
2
0
0
0
2
2
0
0
1
1
0
0
0
1
2
0
0
0
1
0
2
0
0
1
1
1
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
1
2
2
1
0
3
0
1
2
1
0
2
0
0
0
0
1
2
1
0
0
2
0
1
2
0
0
0
0
0
0
0
1
5
0
2
2
0
0
1
2
0
0
2
2
1
1
1
0
1
0
2
1
1
0
0
0
0
3
1
0
0
0
0
1
0
1
0
1
3
1
1
0
1
0
0
0
3
0
0
0
0
0
1
1
2
0
2
2
5
0
1
1
0
0
2
0
0
0
2
0
1
0
0
2
2
1
0
1
0
1
1
2
2
0
0
0
2
1
2
0
2
1
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
1
1
0
1
0
0
2
0
2
2
1
1
0
0
0
2
2
2
0
0
0
0
0
2
1
0
0
0
2
2
0
2
1
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
1
3
0
0
0
0
0
0
1
0
1
0
1
0
2
0
0
0
2
0
2
0
2
0
1
0
0
1
0
1
0
1
0
1
0
2
2
2
0
0
0
1
2
0
2
0
2
1
0
3
0
1
0
0
2
1
2
0
2
1
1
0
0
2
0
0
2
1
0
0
1
0
1
3
2
1
0
2
2
1
0
1
1
1
0
2
2
0
0
0
1
0
1
3
0
1
1
0
0
1
1
0
1
0
0
0
1
0
2
0
0
2
0
0
0
0
2
0
0
2
1
1
1
2
0
0
1
1
1
1
0
0
0
1
1
0
2
0
0
0
1
1
2
0
1
2
0
0
2
1
0
0
0
0
0
2
1
1
1
2
0
0
0
0
1
2
2
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
1
1
0
1
2
0
0
0
0
1
1
0
1
0
1
0
0
2
1
0
2
2
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
1
0
1
1
0
0
0
0
1
1
1
0
0
1
0
1
1
1
0
0
0
0
0
4
2
0
2
2
2
0
0
0
0
0
1
0
1
0
1
0
2
2
0
2
2
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
1
1
0
2
1
0
1
0
1
1
1
1
2
2
1
0
2
0
0
0
2
0
0
3
0
2
0
2
0
2
0
1
0
0
1
0
1
0
2
0
2
2
0
1
0
1
2
1
1
1
2
1
0
0
0
1
1
1
1
2
2
1
1
1
0
2
1
0
0
0
0
0
2
0
1
1
1
2
2
2
0
2
0
1
1
0
0
0
1
1
0
0
0
2
0
1
1
0
2
0
2
1
2
0
0
2
0
0
1
2
1
0
1
2
1
1
0
0
1
0
1
1
0
1
1
1
2
1
0
0
0
0
2
1
1
0
0
0
0
1
0
0
0
0
1
0
1
2
3
1
0
2
0
0
2
0
2
0
1
1
0
0
0
1
0
2
0
0
0
0
0
2
0
1
2
0
2
0
2
0
2
0
1
0
0
0
2
1
1
1
0
0
0
1
1
0
0
0
1
2
0
0
2
0
2
1
0
0
0
1
0
0
0
1
0
1
0
0
2
2
0
1
2
1
0
2
0
0
0
0
0
0
2
1
0
0
0
2
1
1
0
1
1
1
1
0
2
0
2
0
0
2
2
0
0
2
2
0
2
2
0
2
0
1
0
1
0
0
2
1
0
0
0
0
0
0
2
1
1
1
0
1
0
1
0
0
3
0
0
1
0
1
2
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
2
0
0
0
1
0
1
0
0
1
0
1
0
1
0
1
0
0
0
0
1
0
1
0
2
2
1
0
1
2
2
0
1
1
0
1
1
1
2
0
0
1
1
0
1
1
0
0
1
0
0
0
2
2
0
2
0
1
1
0
0
1
1
2
0
2
4
1
0
0
2
0
1
1
0
1
1
1
0
0
0
1
1
1
0
0
0
1
1
1
0
0
1
2
2
1
1
0
0
0
0
0
0
0
1
2
1
0
0
0
1
0
2
0
1
1
0
1
1
0
0
2
2
0
0
1
0
0
0
1
1
0
2
0
0
1
2
1
2
1
2
0
0
2
0
1
0
0
0
2
0
0
0
0
2
1
0
0
0
2
0
1
1
0
0
0
0
0
0
1
2
1
0
7
0
1
1
2
1
0
1
2
1
0
0
1
0
0
3
2
0
1
1
1
0
0
0
1
0
1
2
0
0
0
0
2
0
0
0
0
2
0
1
0
0
2
0
1
0
0
0
0
0
0
1
1
0
2
1
0
0
0
0
3
0
1
0
0
0
1
0
0
1
0
3
0
0
0
0
1
0
0
0
1
1
1
0
2
0
1
2
0
0
0
1
0
2
2
0
1
2
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
3
1
0
1
1
1
0
0
1
0
2
0
1
2
2
0
2
0
0
1
1
2
0
1
0
1
0
2
1
0
1
2
0
0
1
0
0
0
2
0
0
0
0
1
0
2
1
2
0
0
3
1
0
1
1
2
2
0
1
1
1
0
1
1
0
0
0
0
1
1
2
0
2
0
2
1
1
3
0
0
0
0
1
1
1
0
1
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
2
1
0
1
0
2
0
1
2
0
1
0
0
1
0
0
2
2
0
0
1
1
2
1
4
0
0
0
1
0
0
0
0
2
0
0
2
1
0
1
0
0
0
2
1
0
2
0
1
1
0
0
0
0
1
0
0
0
0
1
1
0
0
2
0
0
2
0
1
0
0
0
1
0
0
0
0
1
1
2
1
0
0
1
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
1
1
2
2
0
3
0
0
0
0
2
2
2
0
0
2
2
0
1
0
1
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
1
1
0
1
0
0
3
2
1
0
0
0
0
1
0
0
0
2
0
0
0
0
3
0
0
0
2
2
0
1
1
1
2
0
1
0
0
2
0
1
1
0
1
0
2
1
0
0
0
0
0
1
1
1
0
0
0
1
2
2
2
0
1
0
1
0
2
2
3
0
2
0
2
2
1
0
1
2
0
2
2
0
3
0
2
0
3
5
2
2
0
1
0
0
0
0
0
0
0
0
0
2
1
0
1
2
0
0
0
0
0
0
0
0
3
0
1
0
0
1
1
2
2
2
0
0
0
3
1
0
3
2
1
1
0
0
0
0
0
1
0
0
0
1
0
0
2
0
1
0
1
0
0
3
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
2
2
1
2
1
1
7
1
2
0
0
1
0
0
0
0
0
2
1
1
0
2
0
2
0
2
1
0
1
2
0
0
2
0
1
1
1
0
0
0
0
3
0
0
0
2
2
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
1
2
0
0
2
1
2
0
2
0
1
0
1
0
0
1
0
0
1
2
1
0
2
2
0
1
0
1
0
0
1
2
0
0
2
0
1
2
1
0
2
2
2
0
1
1
1
0
0
0
0
1
1
0
0
2
2
1
1
0
1
1
2
0
1
0
0
2
1
1
1
0
1
0
0
0
0
0
0
0
2
0
1
0
1
2
1
0
1
3
0
0
2
0
1
0
0
1
0
0
0
2
0
1
1
1
1
0
2
2
1
2
1
0
1
0
1
1
1
1
0
1
0
1
0
1
0
0
1
1
1
2
0
0
0
2
0
0
0
4
1
3
1
0
2
2
0
2
0
1
1
1
0
1
1
0
0
0
0
1
0
1
1
2
0
0
1
3
5
2
0
1
1
2
1
0
0
0
2
1
0
0
0
2
0
1
0
2
0
1
2
1
2
1
0
1
2
2
1
1
0
0
0
2
0
2
0
1
1
0
0
1
1
0
2
2
2
0
1
1
2
0
2
1
0
2
2
0
0
0
1
0
0
1
0
0
1
0
0
2
1
0
1
0
0
2
1
1
1
0
0
1
0
1
2
1
2
1
1
2
1
1
0
0
3
2
2
0
0
1
0
0
0
1
1
1
0
1
0
0
2
1
1
0
0
2
0
1
0
0
0
1
0
0
1
0
0
1
0
0
2
1
0
0
0
0
1
2
0
1
1
0
1
1
0
0
0
0
1
0
0
1
1
0
0
1
0
0
1
0
2
1
0
1
0
1
0
2
2
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
1
2
2
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
1
0
2
2
0
1
1
2
0
0
1
0
0
0
0
1
0
0
2
0
2
0
0
2
3
0
0
2
0
1
1
0
1
0
2
0
0
1
0
0
0
2
3
1
0
1
1
0
2
1
0
1
1
2
2
1
2
0
0
1
0
0
0
0
1
0
2
0
0
0
1
1
1
2
2
1
0
0
2
1
0
0
0
2
0
2
2
0
0
0
2
0
2
0
0
1
1
0
1
0
2
0
0
0
1
1
2
0
0
2
0
0
0
0
0
2
0
0
2
1
3
2
0
0
1
2
1
0
1
2
1
0
1
0
0
1
1
2
1
0
0
0
0
0
0
1
0
0
0
3
0
0
1
2
0
2
2
3
0
0
2
2
0
2
0
1
0
2
1
0
0
0
0
0
0
1
0
1
1
2
0
1
0
1
0
0
0
0
0
0
2
1
0
2
1
2
0
1
0
1
0
1
1
0
0
0
0
2
0
0
1
0
0
2
0
0
0
2
0
1
1
2
0
0
0
2
1
2
0
1
0
0
2
0
0
1
1
1
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
1
0
0
1
2
1
0
0
0
0
0
1
0
0
0
0
3
2
2
3
0
0
2
0
2
2
2
0
1
1
0
0
0
1
1
2
0
2
1
1
0
0
2
1
3
0
0
1
2
0
0
0
0
2
0
0
2
2
2
1
0
0
0
0
2
0
1
0
0
2
2
0
1
0
2
2
0
2
2
3
0
0
2
2
0
1
0
1
0
0
3
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
2
0
2
0
2
1
1
3
1
0
0
0
2
3
2
0
1
0
1
1
0
3
2
1
1
1
0
0
0
1
1
2
0
0
3
2
1
1
0
1
3
0
0
2
1
1
0
5
1
0
0
0
0
2
1
0
1
2
0
1
0
0
1
1
1
0
6
1
1
0
2
0
0
1
1
0
1
0
0
0
0
2
0
0
1
1
0
0
1
2
2
1
3
3
2
1
1
1
1
0
0
1
1
1
0
2
0
1
0
0
2
0
0
0
1
0
0
2
0
2
0
0
0
0
1
0
2
1
2
1
0
2
0
0
1
1
1
0
0
0
2
0
2
1
1
1
0
0
0
1
0
2
1
0
2
0
1
0
0
1
0
0
1
0
1
0
2
0
1
1
0
2
0
2
1
0
0
0
0
0
1
0
0
0
1
0
3
2
0
0
0
0
0
1
2
1
1
0
1
1
1
0
0
0
0
1
1
0
1
1
0
0
1
0
1
2
2
0
1
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
1
1
1
0
3
0
2
0
0
0
0
0
1
2
0
0
1
0
1
0
0
1
0
1
0
1
0
0
1
1
0
0
0
0
0
2
0
1
0
0
0
1
0
1
0
1
0
0
1
0
2
0
1
1
0
0
0
0
1
1
0
0
0
3
2
0
1
1
0
0
0
0
3
1
2
1
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
2
0
2
2
3
1
2
1
0
0
0
0
0
0
0
1
2
2
2
1
3
0
0
0
1
0
0
1
1
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
2
0
2
0
2
0
1
0
0
2
0
0
0
1
0
0
0
0
2
2
2
0
0
2
0
1
0
0
2
1
0
0
0
2
0
0
0
1
2
0
0
2
0
0
0
0
1
1
2
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
2
1
0
1
0
0
1
0
0
1
0
0
1
0
0
2
0
1
1
0
0
0
1
0
0
0
2
2
0
1
0
0
0
1
1
2
1
0
1
0
0
0
1
0
1
1
1
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
3
2
0
3
0
0
1
0
1
2
0
0
0
1
2
0
0
0
2
0
0
1
1
0
1
2
2
0
0
2
3
0
2
1
1
0
0
1
1
1
0
2
0
0
0
0
2
2
2
0
1
0
1
1
2
1
2
0
0
0
0
2
0
0
1
0
2
0
0
1
0
0
0
2
0
2
0
0
0
0
1
0
0
2
2
2
1
3
0
0
2
1
0
1
3
1
0
0
0
0
1
1
0
0
0
0
1
1
1
0
0
0
1
2
2
0
0
0
1
0
2
0
0
2
0
0
1
0
1
0
0
1
2
0
0
1
1
0
1
2
1
0
0
1
0
0
0
0
1
0
0
1
1
1
1
0
2
1
1
0
0
1
0
0
0
1
2
0
0
0
1
2
0
1
0
2
1
0
0
0
0
0
2
0
1
0
1
2
1
0
2
2
2
0
0
1
1
0
1
1
3
1
0
0
6
0
0
1
2
3
0
0
0
1
1
0
0
1
0
1
0
1
2
2
0
2
0
2
1
0
0
2
0
0
0
0
1
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
2
0
0
1
0
2
1
1
0
1
1
1
0
1
1
0
0
2
0
0
1
1
3
1
2
1
2
1
0
0
0
1
1
0
1
0
1
2
3
0
1
1
0
2
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
2
2
2
1
0
2
1
1
1
0
0
0
0
0
0
2
0
1
1
2
0
0
0
0
0
2
1
0
2
0
1
1
0
0
1
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
2
0
0
1
0
0
0
1
1
0
1
0
2
0
0
0
0
1
0
0
3
0
0
0
1
1
0
2
1
2
0
1
0
0
1
2
0
1
2
0
1
1
0
0
1
2
0
1
1
1
0
1
2
0
2
0
1
0
1
0
2
1
0
0
0
1
1
0
1
0
3
0
1
0
0
0
0
2
1
2
0
0
1
1
0
1
1
2
0
2
0
0
2
0
0
2
1
1
0
2
2
0
0
0
0
0
0
0
0
0
2
1
0
1
0
1
1
0
1
1
0
0
1
0
0
0
0
0
0
0
1
1
1
2
0
0
4
0
0
2
0
0
1
0
1
2
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
2
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
2
2
0
1
1
1
1
0
1
2
2
0
0
1
1
1
0
1
1
0
2
0
1
0
0
0
2
2
2
0
1
1
1
0
1
2
0
2
0
0
1
1
0
0
0
0
0
2
1
2
2
0
0
0
1
1
0
1
1
2
0
0
0
0
0
1
1
0
1
0
0
0
2
2
4
0
0
1
0
2
0
0
0
1
0
3
1
2
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
1
0
2
0
1
2
0
0
1
2
0
0
0
0
0
0
0
1
3
0
1
0
0
0
0
2
1
0
3
1
0
0
0
0
0
0
1
0
0
0
1
2
2
0
0
1
0
1
2
0
0
2
2
2
0
0
1
0
0
0
0
0
0
2
0
2
2
0
2
0
1
2
3
2
1
2
0
0
0
0
0
1
1
2
0
0
1
0
1
0
1
2
0
0
0
1
0
0
1
1
0
2
0
0
2
0
0
0
0
0
0
1
0
2
2
0
0
1
1
1
2
1
0
0
2
0
2
0
0
0
0
0
0
0
2
2
0
1
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
2
0
2
1
0
0
2
0
2
1
0
0
1
0
0
0
0
1
2
2
0
0
0
1
0
1
1
0
0
0
0
0
0
1
2
2
0
0
0
2
0
1
0
0
1
0
0
1
1
0
0
2
0
0
1
0
0
2
1
1
1
2
0
1
0
2
1
0
0
0
0
0
2
2
0
0
1
0
0
0
2
1
2
0
1
4
0
0
0
2
2
0
1
1
2
2
2
2
7
0
1
2
0
0
1
0
1
1
1
0
2
2
2
1
2
0
2
0
1
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
2
0
1
0
1
0
1
0
1
0
0
0
0
2
0
0
2
1
3
0
0
0
1
0
0
0
2
1
1
0
0
2
0
2
0
0
0
1
1
0
1
2
0
0
0
1
3
2
1
0
0
0
1
0
2
0
1
0
1
0
1
1
1
0
1
0
0
0
2
0
0
2
0
0
2
0
1
0
1
0
1
0
0
1
0
2
0
0
0
2
2
0
0
2
0
0
1
0
1
1
0
0
2
0
0
0
1
2
0
3
2
2
0
1
0
2
0
0
0
3
0
2
0
0
3
2
1
1
3
1
1
2
0
1
0
0
0
2
1
1
0
0
0
0
0
0
0
1
0
2
2
0
2
1
1
0
0
0
2
2
1
1
1
1
1
1
0
0
0
2
1
0
1
3
0
0
2
0
0
0
0
1
0
2
0
1
1
0
4
1
0
0
2
0
0
2
0
1
1
1
0
1
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
1
3
1
0
1
0
0
0
0
1
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
2
2
0
0
2
0
1
2
0
0
0
1
0
1
0
1
0
0
1
2
1
0
0
0
1
2
0
0
1
0
0
3
1
0
0
0
2
0
2
2
2
0
0
2
0
0
0
0
3
0
0
0
2
0
0
0
0
0
2
2
0
2
1
0
0
1
0
1
0
0
1
1
0
2
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
1
1
2
1
2
1
0
0
1
0
0
2
0
0
0
2
0
1
1
0
0
2
0
2
2
1
2
1
0
1
0
2
0
0
2
2
1
0
0
0
1
2
0
0
0
0
0
0
0
1
2
1
0
0
0
0
1
0
3
0
0
1
1
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
1
0
0
0
0
1
2
0
0
1
0
1
1
0
0
0
0
0
0
1
1
2
0
1
0
0
2
2
0
2
0
1
0
3
1
2
0
1
1
0
1
0
0
0
0
0
5
0
2
2
0
1
0
0
0
2
1
1
1
0
0
0
2
1
0
0
1
2
1
2
0
1
1
1
2
0
2
0
1
1
1
0
0
0
0
1
0
1
0
0
0
0
0
2
1
2
2
0
1
2
2
0
0
0
0
3
1
0
0
1
0
0
1
0
1
2
0
2
0
1
0
0
0
0
1
2
0
1
0
1
0
1
0
0
0
1
1
0
0
2
1
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
1
2
0
0
1
1
3
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
2
2
1
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
1
0
1
0
2
0
0
0
2
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
1
0
2
0
0
1
0
0
1
1
2
0
0
0
0
1
1
0
0
0
0
2
0
2
1
0
0
3
0
2
0
2
2
1
0
2
0
0
0
1
2
2
0
0
0
0
1
2
0
0
1
1
0
0
0
0
2
0
1
0
3
2
0
0
0
0
2
0
0
1
1
0
2
1
0
0
0
0
1
0
0
1
1
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
2
0
0
0
1
1
0
0
0
1
0
2
0
0
0
1
1
1
0
0
0
0
0
3
1
3
1
1
2
0
0
0
2
1
0
0
0
2
0
2
2
1
2
2
0
0
1
0
1
0
0
0
1
0
1
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
5
1
0
0
1
0
0
0
1
0
0
2
0
0
0
1
0
0
2
1
1
0
1
1
0
0
2
2
2
0
0
2
2
0
0
2
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
2
0
0
0
0
1
0
2
2
0
0
0
1
2
6
0
0
0
1
0
2
1
2
1
1
2
2
0
0
0
1
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
2
0
0
2
0
0
1
1
2
2
0
0
1
0
0
0
2
0
0
0
1
1
1
0
1
0
0
1
1
1
0
2
0
2
1
0
1
1
2
2
0
0
0
0
0
2
1
0
2
2
0
1
2
1
2
0
0
0
2
0
1
0
4
0
0
0
1
1
0
0
2
0
2
0
1
0
0
2
0
0
0
0
0
2
0
1
1
0
0
0
0
1
0
0
2
0
1
0
1
1
2
0
2
0
0
0
1
1
0
0
1
0
0
0
0
1
2
0
1
1
2
0
0
0
2
1
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
1
0
0
0
0
0
0
4
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
1
0
1
0
3
0
0
0
1
2
0
0
0
1
0
1
0
1
2
2
0
0
0
1
1
1
0
0
0
0
2
0
3
0
2
0
3
1
0
0
0
2
0
0
1
0
1
0
1
1
0
0
1
0
0
0
0
0
1
2
2
1
0
1
1
2
1
1
1
0
1
0
1
0
0
1
0
1
1
2
0
1
0
1
3
2
0
0
1
0
0
1
3
0
1
0
2
0
0
2
1
2
1
0
1
1
2
0
1
2
2
1
2
0
1
0
0
1
0
3
0
2
0
1
0
2
2
0
0
0
1
1
0
0
2
1
0
1
1
1
3
0
0
0
0
0
0
1
3
2
0
1
1
0
2
0
2
1
1
1
0
0
2
1
4
2
1
1
0
1
1
1
0
0
0
1
0
2
0
1
2
0
0
1
1
0
0
1
2
0
0
0
0
0
0
1
1
1
1
2
0
0
0
2
0
1
0
1
0
0
1
0
0
0
2
2
0
0
1
0
1
1
0
0
0
0
1
1
1
1
1
1
1
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
2
2
0
0
0
1
0
0
0
0
0
2
1
0
0
2
2
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
1
0
0
4
1
0
0
1
0
3
1
2
0
1
0
0
1
0
1
0
0
2
1
1
0
1
2
0
0
0
0
1
0
0
3
2
0
3
0
0
0
0
0
0
5
0
1
0
2
4
2
0
1
1
0
2
0
1
3
0
0
1
0
2
1
2
1
1
0
0
3
0
0
1
1
1
1
1
0
1
0
0
0
0
0
0
1
2
0
1
1
0
2
0
2
0
1
0
0
0
0
0
2
0
2
1
0
0
0
0
1
0
0
2
1
1
2
0
2
1
0
0
2
0
1
0
1
0
1
1
0
0
0
0
1
0
2
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
1
0
0
1
1
1
0
1
2
1
0
1
1
0
0
0
2
1
1
1
0
2
1
0
0
1
2
0
1
0
0
1
2
0
1
0
2
0
1
1
0
0
0
0
2
1
1
1
0
0
1
1
2
2
0
0
0
0
0
0
1
0
0
1
0
0
0
3
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
2
2
1
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
1
0
1
1
0
0
0
0
2
4
1
0
1
0
2
0
1
1
2
0
0
0
1
0
0
0
0
2
2
0
2
0
1
2
2
1
0
2
0
2
0
1
0
1
0
0
0
1
0
1
0
1
0
0
2
0
0
0
2
0
0
0
2
2
0
0
1
0
1
2
1
0
0
0
0
0
0
0
0
1
2
1
0
1
0
1
15
1
2
0
2
2
2
3
0
2
0
2
1
2
2
2
1
0
1
1
1
2
1
1
0
0
0
0
2
0
2
0
2
0
2
0
0
0
2
0
0
3
0
1
0
2
1
0
0
1
0
1
0
0
0
2
0
0
2
0
0
0
2
2
2
2
0
0
0
1
1
0
1
1
0
0
2
2
1
0
0
0
2
1
0
0
0
1
1
1
1
0
1
1
2
0
1
1
0
0
0
0
3
2
1
0
0
1
3
5
0
0
2
0
0
0
0
0
0
3
1
1
1
1
3
1
0
1
4
0
0
0
0
1
0
3
0
0
2
0
0
2
0
2
1
2
0
1
1
0
0
1
0
0
0
0
0
0
1
2
2
0
0
3
2
0
1
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
2
1
1
0
1
0
1
0
0
1
2
0
3
0
2
0
2
1
1
0
2
0
1
1
0
0
0
2
0
2
0
0
2
0
0
0
0
0
1
0
0
1
1
2
0
0
1
2
0
0
1
2
0
0
0
0
2
0
0
0
1
2
3
0
2
0
0
2
0
0
0
0
3
1
0
2
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
2
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
2
1
0
2
0
0
0
1
0
2
1
0
0
2
1
0
1
1
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
2
0
0
0
2
1
2
0
2
0
0
2
0
1
0
0
0
1
0
1
0
2
0
0
0
1
0
0
0
0
1
2
0
1
0
0
1
1
0
1
0
0
0
0
1
0
0
1
0
2
0
0
0
1
0
1
0
0
0
1
3
0
1
0
0
1
0
0
0
2
2
0
1
2
1
1
0
2
0
2
2
2
0
1
2
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
1
1
3
2
1
2
0
0
0
0
2
2
2
1
1
0
0
1
0
2
0
0
0
2
0
1
2
1
0
1
0
0
1
0
1
3
0
0
1
2
2
1
0
0
0
2
1
0
0
0
3
0
0
1
0
0
1
0
0
2
2
0
0
1
0
1
1
0
0
5
0
1
0
1
1
2
0
2
0
2
1
0
0
1
1
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
2
1
2
2
0
0
1
0
2
0
0
0
1
0
0
0
1
1
0
0
1
3
0
0
0
0
0
0
1
0
2
1
0
0
1
0
0
0
0
0
0
0
1
3
1
0
0
1
0
0
0
0
0
2
0
3
2
0
0
0
1
0
0
1
0
2
2
0
1
0
0
0
2
1
2
0
0
1
1
1
2
2
1
2
2
1
2
0
0
1
2
0
0
2
0
1
0
0
1
0
2
0
1
1
1
1
0
0
2
2
2
0
0
0
1
1
0
1
0
0
2
0
2
0
1
2
0
0
2
0
1
1
0
0
1
1
1
1
0
1
0
0
0
1
3
2
2
1
1
1
2
2
0
0
1
1
2
2
1
1
1
1
2
0
0
0
0
0
1
1
0
0
2
0
1
2
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
1
0
0
0
1
1
1
0
0
0
1
0
1
0
2
1
0
0
0
0
1
0
2
2
0
0
0
0
1
0
0
1
4
1
2
1
0
1
0
1
1
0
0
2
1
0
1
0
0
2
0
3
1
2
2
2
1
0
1
1
1
1
1
1
0
1
0
1
2
0
2
0
0
2
0
2
0
0
0
0
0
2
2
2
0
2
0
0
2
1
2
0
0
1
2
0
0
1
0
2
0
0
0
0
2
2
0
3
0
2
0
2
0
1
0
2
0
1
0
0
2
0
0
0
0
1
1
0
1
1
1
4
0
1
1
0
1
0
2
0
2
0
2
0
1
0
0
0
0
0
2
0
0
1
0
2
1
1
1
0
0
0
0
0
1
1
0
1
0
0
0
2
1
1
0
0
2
3
0
1
1
0
1
0
0
0
5
0
1
0
0
0
2
0
1
0
1
0
0
1
0
1
1
2
1
0
1
0
1
2
1
0
2
0
1
0
0
1
0
0
0
1
2
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
2
1
1
0
0
1
2
1
0
0
0
0
0
0
0
1
1
0
0
1
2
0
2
0
1
0
0
0
2
0
0
0
0
0
0
2
0
2
1
0
1
1
0
1
0
0
1
0
0
0
1
0
0
2
1
0
0
0
1
1
1
2
1
0
0
1
2
0
0
0
0
1
2
2
0
0
1
0
0
0
2
1
0
0
2
1
2
1
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
1
2
0
0
0
0
0
0
1
2
0
7
1
2
0
0
1
0
1
0
1
2
0
1
2
1
1
1
0
0
0
0
1
0
1
2
0
1
3
0
1
0
0
1
0
0
0
1
0
2
1
1
0
1
0
0
0
0
1
0
2
2
0
0
0
1
1
1
2
0
0
0
0
0
1
3
1
0
0
0
0
0
0
0
0
2
0
2
0
1
1
1
2
1
2
2
0
0
0
1
0
0
0
0
1
0
0
1
1
2
1
0
2
1
1
2
2
0
1
1
0
0
0
0
0
2
2
0
2
2
2
2
2
2
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
1
1
0
3
0
2
1
0
2
1
0
0
1
0
0
2
0
0
1
1
2
0
2
0
2
1
0
0
2
0
2
0
1
0
0
0
2
2
0
1
2
0
2
2
0
1
1
0
0
0
0
1
4
0
2
2
2
1
0
2
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
1
2
0
4
1
1
2
0
0
0
1
0
0
0
0
2
1
1
0
0
1
1
1
0
1
0
0
1
0
2
1
0
0
0
2
0
1
1
0
2
2
0
1
0
0
0
2
0
1
1
1
0
1
1
2
2
1
0
0
2
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
2
1
2
1
0
0
2
0
0
1
0
1
0
2
0
1
0
0
1
1
0
0
2
0
0
0
0
0
2
2
2
0
0
0
0
1
1
1
0
0
2
0
0
0
1
0
0
2
0
1
1
0
1
2
0
1
0
0
0
1
0
0
0
1
0
2
2
2
1
0
0
1
0
0
0
0
2
1
0
0
2
1
0
0
0
1
0
1
0
1
0
2
2
0
0
1
0
0
0
0
0
0
1
0
1
1
0
1
2
2
0
0
1
1
0
2
0
0
0
0
1
1
0
2
1
3
3
3
0
1
0
2
0
0
0
0
0
1
0
2
1
1
0
15
0
2
1
0
2
3
0
2
0
2
0
2
0
0
1
1
2
0
0
2
2
0
1
2
0
2
0
2
1
2
0
2
1
1
1
1
0
3
0
0
0
2
1
0
2
3
0
0
0
1
1
0
0
3
0
0
1
1
2
0
0
0
1
2
0
1
0
1
1
0
2
0
0
0
1
1
1
0
0
0
0
0
1
0
1
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
1
0
2
4
1
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
2
0
0
2
1
0
1
1
2
0
1
2
1
0
2
2
0
1
0
1
1
1
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
2
1
0
0
2
1
0
0
0
3
0
2
1
1
0
0
1
0
2
0
0
0
0
0
1
0
0
1
0
0
1
0
1
1
2
0
0
2
2
0
0
0
0
0
0
2
0
0
1
0
1
2
1
0
0
0
2
0
1
0
1
0
1
0
0
0
0
1
0
0
2
1
0
0
0
0
1
0
0
0
1
0
1
0
0
1
2
0
0
0
2
1
4
2
0
0
2
0
4
0
1
0
0
0
1
1
0
0
1
0
1
0
0
2
0
3
1
2
1
0
1
0
1
0
1
0
0
2
0
0
1
3
0
1
0
0
1
1
1
2
0
1
0
0
2
1
1
0
1
0
0
0
0
0
0
1
1
0
1
1
0
1
1
4
0
1
2
2
0
2
0
0
0
0
0
0
0
1
0
1
3
2
1
2
1
0
0
1
1
2
0
1
0
2
3
1
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
1
0
1
2
1
2
0
2
1
2
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
1
1
0
1
0
0
2
1
0
1
2
0
0
1
0
2
1
0
1
0
2
1
2
1
2
0
1
2
0
2
0
2
0
0
2
2
0
0
2
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
2
0
1
4
0
0
2
1
2
0
1
1
2
0
0
0
0
1
0
2
0
0
0
0
0
0
2
1
3
0
2
0
1
0
2
2
2
0
0
0
2
0
2
0
0
2
2
0
1
1
0
0
1
0
1
1
0
0
1
0
0
2
1
1
1
1
2
0
0
0
0
0
4
1
0
0
2
0
0
0
2
1
2
1
0
0
2
0
0
1
0
0
1
0
0
0
2
0
2
0
0
1
1
0
0
1
1
1
0
0
1
2
0
0
0
0
2
1
0
0
1
0
1
1
0
0
1
0
2
0
0
1
0
0
0
2
0
1
1
0
1
0
0
0
1
0
0
1
2
0
1
1
0
0
0
0
1
1
1
2
2
2
1
1
1
0
1
1
0
0
0
0
1
0
2
1
3
0
2
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
1
2
1
1
2
2
0
1
0
0
0
0
1
2
1
1
2
0
0
1
0
0
1
0
1
2
0
2
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
2
0
0
2
0
1
4
0
2
0
0
0
0
1
1
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
2
1
0
2
1
0
0
1
0
2
1
0
1
0
0
0
2
0
0
0
2
2
0
0
0
2
2
4
0
0
1
0
1
2
0
0
2
0
0
2
0
2
0
3
0
0
1
0
1
1
1
2
0
1
2
0
0
1
0
1
1
0
2
1
1
1
1
0
2
2
2
0
1
0
2
1
0
2
0
1
2
2
0
2
3
1
0
0
2
1
0
1
1
0
0
1
0
0
0
0
1
1
2
1
0
3
0
0
2
0
1
1
2
2
1
1
0
1
0
0
2
1
1
0
2
2
0
0
0
0
0
1
0
0
1
0
0
0
1
2
0
0
0
0
0
0
2
2
0
4
1
1
1
0
0
1
1
1
2
1
0
1
2
0
1
1
2
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
2
0
2
1
1
0
0
0
1
0
2
0
0
1
0
0
0
0
2
0
1
0
0
1
0
1
0
0
1
0
0
0
1
1
2
2
0
2
0
0
0
1
0
0
2
0
0
0
2
0
1
0
1
1
2
0
0
1
0
0
1
1
1
1
0
0
0
1
0
0
0
1
0
0
0
0
1
2
0
1
0
0
1
0
2
1
0
0
6
2
2
0
1
0
0
2
1
1
0
1
0
1
0
0
2
2
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
1
1
0
2
1
2
0
1
2
2
0
1
0
2
0
1
0
0
1
0
0
0
0
1
2
0
2
0
2
1
1
1
0
0
1
1
0
0
0
0
0
0
1
2
0
0
2
2
0
1
1
1
1
2
0
2
2
1
0
1
0
2
0
0
0
1
0
2
0
0
1
0
0
0
2
0
1
0
1
1
0
0
0
0
0
0
1
0
2
2
0
3
1
0
0
2
0
0
0
0
0
0
1
0
1
0
1
1
2
0
0
0
0
1
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
4
0
0
1
2
1
0
4
0
0
0
0
0
0
2
0
2
0
1
2
2
3
0
2
2
1
0
1
0
0
0
2
0
1
0
0
0
0
1
0
0
0
2
0
0
2
0
2
0
1
1
1
1
1
0
1
0
0
2
0
1
2
1
0
2
0
2
0
2
3
2
0
1
1
1
2
2
1
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
1
2
0
0
0
2
2
0
0
0
1
0
2
0
0
2
1
0
0
0
2
0
1
2
3
0
1
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
1
4
0
0
1
0
0
0
0
0
1
0
0
2
2
0
0
0
2
0
2
1
1
0
0
1
2
1
2
1
1
0
0
0
3
0
0
0
3
0
0
0
1
0
2
2
1
0
0
2
0
0
1
0
0
0
0
1
1
2
0
0
0
1
0
2
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
3
1
2
0
0
2
0
0
1
1
1
0
0
1
0
2
0
2
1
0
0
0
0
1
0
0
2
0
2
0
0
0
2
1
2
0
0
3
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
1
0
2
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
2
0
1
1
2
1
2
0
2
0
1
0
2
1
0
1
0
2
0
0
0
0
0
2
1
1
0
1
0
1
2
2
1
0
0
1
0
1
0
0
2
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
1
1
1
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
1
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
1
3
1
0
0
2
0
0
0
1
0
0
0
2
0
2
1
0
2
0
0
2
0
0
1
2
0
0
2
0
1
0
0
0
0
0
0
1
0
1
0
0
1
1
0
2
2
1
0
0
1
0
1
1
1
1
0
3
2
0
2
2
2
1
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
1
0
1
1
0
1
1
0
0
0
1
0
2
1
0
0
1
0
2
0
2
2
0
0
2
1
3
2
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
1
0
1
1
1
1
2
0
0
0
1
2
0
0
0
1
1
0
2
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
1
0
1
2
0
0
0
0
0
0
0
2
0
1
1
0
0
0
3
0
0
2
0
0
0
0
1
1
0
1
0
1
1
2
2
0
1
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
1
2
1
2
1
0
0
0
0
2
0
1
0
0
4
0
0
2
0
0
0
0
0
0
0
5
0
0
0
1
0
0
0
1
1
0
1
2
2
0
0
0
2
2
1
0
1
0
1
1
1
1
1
0
2
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
2
1
2
3
1
0
1
2
1
2
2
2
0
4
0
0
0
0
1
1
1
1
0
2
2
0
1
2
0
1
0
0
0
0
0
1
2
2
1
0
0
1
2
0
0
2
1
2
0
2
0
1
1
1
2
2
0
2
0
2
2
0
0
0
0
0
2
2
2
0
0
1
0
0
0
1
0
0
1
2
0
2
1
2
0
2
1
0
0
0
1
2
8
0
0
0
2
0
0
0
1
0
1
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
1
0
0
2
0
1
0
0
0
0
1
0
2
1
2
2
0
1
2
0
0
2
2
2
1
1
0
2
0
1
0
1
1
0
0
1
1
0
1
2
1
0
2
1
0
0
0
0
0
0
0
0
2
1
0
0
2
0
2
0
0
0
1
0
0
0
1
0
0
0
1
0
1
2
0
0
0
2
0
2
1
1
1
0
0
1
0
0
0
0
1
0
2
1
0
2
0
0
0
2
0
0
1
1
1
0
1
1
1
2
1
1
0
1
2
0
0
2
1
2
1
1
6
2
1
1
0
0
1
0
0
0
2
2
0
1
2
0
1
1
0
0
2
0
0
0
1
2
0
0
0
0
1
1
1
2
0
0
2
1
0
1
0
0
0
1
0
1
1
1
1
3
0
1
0
0
1
0
2
1
1
0
1
0
5
1
2
0
0
0
1
0
1
1
3
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
1
0
1
0
1
0
0
1
1
2
0
0
2
0
0
0
0
0
2
0
1
1
0
0
0
1
2
1
2
0
0
0
2
0
1
0
1
0
0
2
0
1
0
1
0
2
2
2
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
2
0
0
0
2
2
1
0
0
0
3
0
0
0
2
1
0
0
1
1
0
2
2
0
1
0
0
2
0
2
1
0
1
1
0
2
0
1
1
0
1
0
2
1
0
1
0
2
0
1
0
2
6
0
1
0
0
0
1
2
0
2
2
1
2
0
0
0
0
1
2
2
1
0
1
0
2
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
2
1
1
0
0
0
0
1
0
1
1
0
0
1
2
2
1
0
3
1
2
0
0
0
1
0
2
0
0
0
0
2
2
0
1
0
3
1
2
0
0
1
2
1
5
0
2
1
0
0
0
2
1
0
3
0
2
0
1
1
1
1
0
0
0
1
0
0
1
0
0
2
0
0
1
1
0
0
0
1
0
0
0
0
4
0
0
1
1
1
2
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
2
0
0
1
0
2
0
2
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
1
1
0
2
0
0
2
0
0
2
0
2
1
1
0
2
0
1
2
0
0
1
1
1
0
1
2
0
0
0
1
0
1
0
0
0
0
0
2
2
0
1
2
1
1
0
0
2
2
0
1
0
0
2
0
1
0
0
0
1
0
0
1
3
2
1
0
0
0
0
0
2
1
1
1
0
0
2
0
1
0
0
0
0
2
2
1
1
0
0
0
2
0
2
1
0
0
1
0
2
2
1
1
0
0
2
2
0
2
2
1
1
0
2
1
0
1
0
1
0
2
0
0
0
0
0
0
2
0
1
0
1
2
0
0
0
1
0
1
1
0
0
1
0
1
1
1
1
0
1
1
2
1
1
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
1
2
0
2
1
0
0
0
0
2
0
2
1
0
0
2
0
2
0
1
0
0
1
1
2
2
0
0
0
2
2
1
1
0
1
1
0
2
0
0
0
0
1
1
0
1
2
0
1
0
0
0
1
1
0
0
2
0
0
0
0
0
1
1
2
0
6
1
0
0
1
1
0
0
2
0
0
0
1
1
2
0
4
1
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
1
0
0
1
0
0
2
1
1
1
2
0
0
0
2
0
0
2
0
0
0
0
2
2
0
1
2
0
0
0
2
0
0
1
1
2
0
2
0
0
2
0
1
0
0
0
0
2
0
0
2
1
1
0
0
1
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
2
0
1
0
1
0
0
1
0
1
0
0
1
0
1
0
0
1
2
1
1
0
1
0
0
0
0
0
3
1
0
0
0
2
0
0
1
1
1
0
0
0
2
1
0
1
0
0
0
1
0
3
1
2
1
2
0
0
0
0
1
0
0
1
2
1
0
0
1
0
1
0
0
0
0
0
0
1
1
1
1
0
0
0
0
2
0
1
0
0
1
1
0
1
2
2
0
2
0
0
0
0
0
0
1
0
3
1
2
2
0
0
0
0
0
1
0
0
2
0
0
1
0
2
1
0
1
1
0
0
0
2
0
0
0
0
2
0
0
2
2
0
0
0
0
2
1
1
2
3
2
0
3
1
1
1
0
0
0
1
0
0
0
0
0
1
1
3
0
0
1
0
0
1
2
1
1
0
0
0
0
2
0
0
0
0
1
0
0
2
0
2
0
2
0
0
1
0
0
0
1
1
1
1
0
1
1
1
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
2
0
1
0
0
2
0
0
1
0
0
1
0
1
0
0
0
0
0
3
1
0
0
2
2
2
1
0
1
2
0
0
2
2
0
0
0
0
1
0
2
0
0
0
2
1
0
0
0
0
0
2
0
1
0
1
0
2
0
1
0
1
0
1
0
0
1
1
0
1
0
0
1
1
1
2
1
2
0
1
0
2
0
1
0
1
0
2
1
2
0
1
1
2
0
0
2
1
0
0
3
2
0
0
2
0
0
0
2
1
0
0
1
0
1
0
0
0
0
2
0
0
1
1
0
0
0
2
2
1
2
1
0
0
1
2
0
0
1
0
0
0
1
0
1
0
1
2
1
0
0
0
0
1
0
0
1
1
2
2
1
1
1
1
0
0
0
0
1
0
0
0
2
1
0
0
0
1
2
0
0
0
0
0
1
3
0
0
2
2
0
0
0
0
0
4
2
0
2
0
0
0
1
1
2
1
2
2
2
0
1
0
0
0
0
0
0
0
2
1
0
0
1
0
2
2
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
2
1
0
1
1
1
2
0
2
0
0
0
0
0
2
0
0
3
2
0
1
3
1
0
0
1
2
2
1
1
1
1
1
1
3
2
0
0
1
1
1
2
0
0
1
0
0
1
1
2
1
1
0
0
1
0
0
0
1
1
1
0
0
0
0
3
0
0
1
2
0
1
2
0
0
0
0
2
0
1
0
0
1
0
2
1
0
0
0
0
0
0
1
0
2
1
1
2
2
1
1
0
2
0
1
1
2
0
0
3
2
2
0
0
2
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
2
0
0
1
1
0
0
0
2
2
0
0
2
0
0
2
0
0
0
1
2
0
2
1
1
0
0
2
2
3
5
2
2
0
1
0
1
0
0
2
0
0
1
3
2
0
0
2
0
2
1
1
1
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
1
2
0
0
0
2
1
0
2
2
0
1
2
1
0
2
1
1
0
0
1
1
2
0
0
0
0
4
0
0
0
2
2
1
2
0
0
0
1
0
0
0
1
2
0
1
2
2
0
0
0
1
2
0
0
0
1
0
2
0
2
1
2
0
0
0
1
1
1
1
0
2
0
0
1
0
0
0
0
1
0
0
2
0
0
1
1
0
0
0
0
2
0
0
3
0
1
0
0
0
0
0
0
0
0
1
1
1
2
1
0
0
1
2
0
1
1
0
2
0
0
0
0
0
1
0
1
1
2
1
4
1
0
1
1
0
1
0
0
0
2
1
0
0
2
0
1
0
2
0
0
2
0
0
2
1
3
1
0
0
0
1
0
2
1
0
0
2
2
1
1
1
1
2
2
1
1
0
0
1
1
0
1
0
0
0
2
1
0
2
0
0
1
0
0
0
1
0
2
2
2
0
0
0
1
0
0
0
1
1
0
1
0
0
2
1
1
0
0
1
0
0
1
0
2
1
0
0
0
2
0
1
2
0
0
2
0
0
1
1
0
0
1
0
2
2
0
0
0
1
0
0
0
2
0
0
0
1
2
0
1
2
0
1
0
1
0
1
0
0
0
0
0
1
0
1
0
2
2
0
0
0
2
0
2
1
0
1
2
0
2
2
2
0
0
0
1
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
1
0
1
0
0
0
0
0
2
1
0
1
3
0
0
0
1
1
1
1
0
0
0
1
0
2
0
2
2
0
0
1
0
1
1
0
2
2
1
0
1
0
1
1
0
0
1
1
0
1
6
0
0
2
0
2
2
1
2
0
1
1
0
1
1
0
0
2
1
1
1
0
0
0
1
1
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
1
1
0
0
0
0
0
1
2
0
0
0
4
1
0
1
0
0
2
0
0
1
0
0
1
0
3
2
1
2
0
1
0
2
2
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
2
2
0
1
0
0
0
0
2
1
0
0
1
1
1
1
1
1
0
2
0
0
0
0
0
0
1
3
0
1
0
0
0
1
1
0
2
0
0
0
0
0
1
0
0
2
0
0
0
1
1
1
0
1
2
0
2
1
0
0
0
0
2
2
0
0
1
0
0
0
0
2
1
0
0
0
0
1
0
1
0
0
0
0
3
0
0
1
2
1
0
1
0
0
0
0
0
1
1
1
0
1
1
2
2
2
1
3
0
1
0
0
1
1
0
2
2
0
0
0
3
0
1
0
2
0
1
1
0
0
1
0
1
1
0
0
0
0
0
1
2
0
1
0
2
1
0
0
0
0
0
0
2
1
0
0
1
1
0
0
2
0
0
0
2
2
1
0
0
0
2
0
0
0
1
1
2
2
2
0
2
2
0
0
3
2
2
0
0
0
3
1
0
1
2
0
0
1
1
0
0
1
1
0
1
0
0
0
3
0
0
2
0
1
0
0
1
1
1
2
0
1
0
0
0
0
0
2
0
1
0
1
1
1
0
0
0
3
0
1
0
1
0
0
1
1
2
2
0
0
2
0
1
1
1
1
2
0
0
0
0
3
0
0
2
1
2
4
0
0
0
4
0
0
0
1
2
0
0
0
0
0
2
1
2
1
0
1
1
0
0
3
2
3
0
1
0
0
0
2
0
0
0
1
0
0
1
0
0
1
1
2
3
0
0
0
0
0
0
0
0
0
0
1
3
0
2
1
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
2
1
2
1
0
0
2
0
2
1
1
2
1
1
0
1
0
0
2
0
1
2
0
2
1
0
1
0
0
1
0
0
0
2
0
1
2
1
0
0
0
0
1
0
0
2
0
0
1
1
1
0
1
2
0
0
0
0
0
0
0
0
1
2
1
0
0
1
0
1
1
0
0
0
0
1
0
1
2
2
2
0
1
3
0
0
1
1
0
0
0
3
2
0
0
0
0
1
2
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
1
0
1
2
0
0
0
0
0
3
0
2
1
0
2
1
0
1
0
0
0
0
2
0
2
0
0
2
1
2
2
0
1
0
0
0
2
0
4
0
0
0
1
2
1
0
0
0
0
0
0
1
1
0
3
0
0
1
0
0
1
1
0
0
0
2
0
2
0
0
2
0
5
0
1
2
0
0
0
0
0
0
0
6
1
1
0
1
2
0
2
0
0
0
0
0
0
1
0
1
1
1
1
0
0
1
0
1
0
2
1
0
7
0
0
1
2
1
1
1
0
0
0
2
0
1
0
0
3
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
2
2
2
1
0
0
0
1
0
0
0
0
2
3
2
2
2
0
2
0
1
5
0
0
1
0
2
0
2
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
2
1
0
0
1
0
2
0
0
0
0
0
0
0
1
1
2
0
1
1
0
1
0
0
1
0
2
0
0
0
1
0
3
2
0
0
3
2
0
0
0
0
1
1
0
1
0
0
1
0
0
0
1
1
1
1
0
2
2
0
0
0
1
1
1
0
2
0
1
1
1
2
0
0
2
0
0
0
0
2
0
2
0
0
1
1
0
0
0
0
0
2
1
0
1
0
0
1
0
0
1
2
0
0
0
0
1
0
0
0
1
0
0
2
0
1
0
0
1
1
1
1
2
2
1
1
2
2
2
2
0
1
0
2
0
0
0
2
0
1
0
0
1
0
1
1
0
0
0
0
0
0
1
1
1
0
0
1
1
1
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
1
0
1
3
0
0
0
0
2
1
1
0
2
0
2
1
0
2
0
1
0
0
0
1
0
0
0
0
2
0
0
1
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
1
0
0
2
0
0
0
0
0
0
0
1
1
1
2
0
2
2
2
3
0
1
0
2
0
0
1
0
1
0
0
0
0
1
2
2
0
0
1
0
0
1
2
0
0
1
0
0
0
2
0
0
0
2
0
1
0
1
0
0
0
1
0
0
2
0
2
1
2
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
2
0
2
0
0
0
2
0
0
1
2
0
0
0
0
0
2
0
0
0
2
1
0
0
1
0
0
3
0
2
0
0
5
2
1
0
2
1
0
0
1
2
0
0
1
2
0
1
0
1
1
0
0
0
1
2
3
0
2
0
0
0
1
0
0
1
0
2
0
2
0
0
1
0
3
0
2
0
0
1
0
0
1
1
2
2
2
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
2
0
2
0
1
0
0
0
0
0
0
2
1
0
2
0
0
0
0
1
2
1
1
1
1
1
2
1
2
1
1
0
0
2
0
0
0
0
1
0
0
4
1
1
2
0
0
0
0
0
0
1
1
0
2
2
0
0
0
1
0
2
1
2
0
0
0
0
1
0
2
2
1
1
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
2
0
1
2
1
2
2
1
0
1
1
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
1
0
1
0
0
0
1
1
0
0
0
3
0
2
0
2
1
0
1
0
0
3
1
0
0
2
0
2
0
2
2
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
2
1
2
1
0
0
3
2
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
2
0
1
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
2
1
1
2
2
1
1
1
0
0
0
0
0
0
1
0
2
0
0
2
0
0
2
0
1
0
5
0
1
2
1
0
1
1
1
0
1
0
2
0
0
0
0
1
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
3
0
0
1
2
2
0
0
0
2
0
2
0
1
2
0
1
2
1
1
0
1
2
0
0
1
0
2
0
0
1
1
1
0
1
2
0
0
0
1
0
1
0
2
1
1
1
2
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
1
0
2
0
2
1
0
0
0
0
0
0
0
0
3
0
1
0
1
2
0
2
1
0
0
0
0
2
0
1
1
0
2
2
0
2
0
0
2
0
0
1
1
1
0
1
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
1
0
0
2
0
1
0
0
2
0
0
0
0
2
0
0
0
2
2
0
0
0
2
2
0
3
0
2
0
0
1
0
0
1
2
0
0
0
0
0
1
2
0
0
0
1
0
3
0
1
0
2
1
1
0
2
1
2
3
0
0
1
0
2
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
2
0
1
0
0
0
1
0
0
0
0
0
0
2
0
1
1
1
2
0
0
1
0
2
0
0
3
2
0
1
0
1
2
0
2
0
1
2
0
1
1
0
1
0
0
3
0
0
2
2
1
0
2
0
2
0
0
0
0
1
0
1
1
2
0
0
1
0
1
0
0
1
0
0
8
0
0
2
2
0
0
0
2
2
1
0
0
1
0
2
2
1
0
0
3
0
1
1
1
0
0
0
0
0
1
1
1
1
0
0
0
0
2
1
1
1
0
0
0
0
1
2
0
2
0
0
2
0
0
1
0
2
2
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
1
2
0
1
2
1
0
0
1
0
1
0
2
3
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
2
0
0
0
0
0
4
0
1
0
2
1
0
0
1
0
2
0
1
2
0
1
0
1
1
1
2
0
0
1
2
0
1
2
0
2
0
0
2
3
1
1
0
1
1
1
1
1
0
0
0
1
0
0
1
1
0
3
1
2
0
2
2
0
0
1
1
2
0
0
2
1
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
2
1
0
2
2
0
0
0
1
1
1
1
2
2
1
1
0
0
2
0
2
2
0
2
1
1
0
2
0
1
2
1
0
0
0
0
1
1
0
1
0
1
1
0
2
0
2
0
1
2
0
1
1
0
0
1
0
0
1
2
0
0
2
0
0
1
0
0
0
0
0
2
0
0
1
1
0
2
0
0
2
3
3
2
0
0
1
0
2
0
1
0
2
1
0
0
1
0
0
0
0
0
2
0
1
0
1
2
0
1
0
0
0
1
1
0
0
0
1
1
2
0
1
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
1
0
2
0
0
0
2
0
0
0
1
0
0
3
1
1
0
1
0
1
0
0
0
2
1
2
0
1
0
2
1
0
0
0
0
0
0
2
1
0
1
1
2
2
0
1
0
1
2
0
0
2
3
2
2
1
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
2
1
0
0
0
2
0
1
0
1
1
1
0
2
2
2
1
0
0
0
0
2
0
0
3
0
1
1
1
0
1
0
0
0
1
0
0
6
0
1
2
1
0
0
2
0
1
0
2
0
2
2
0
0
2
2
0
0
0
0
2
0
1
1
1
2
2
0
3
0
0
0
2
0
1
0
1
1
0
2
0
0
2
1
2
4
0
0
2
0
1
1
2
0
0
0
2
0
1
0
0
0
0
0
0
1
0
1
0
1
1
1
0
0
0
0
1
0
0
2
2
1
0
0
0
0
0
0
1
0
2
1
0
2
1
0
0
0
0
0
0
0
0
1
1
0
0
2
1
0
0
3
1
1
0
0
5
0
0
1
0
0
0
2
0
0
0
1
2
1
3
1
2
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
1
0
0
0
0
1
0
1
1
2
0
1
1
0
0
2
0
0
0
1
1
0
0
2
0
0
1
0
0
0
1
0
1
1
3
0
2
0
0
2
1
0
0
1
2
0
0
2
0
1
0
1
0
0
2
1
1
0
1
2
0
0
0
1
0
0
0
2
0
0
0
2
2
2
0
2
0
1
0
0
2
0
1
0
0
0
0
0
2
0
2
0
3
0
1
0
0
0
0
0
4
1
2
0
0
1
1
0
0
0
1
2
0
3
1
2
1
1
0
1
2
0
0
0
0
1
2
0
2
1
2
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
2
2
0
0
0
0
0
1
0
0
1
0
0
1
0
4
0
1
1
0
0
2
0
1
2
0
0
0
0
0
2
0
1
1
1
0
0
2
0
1
1
1
2
0
2
1
0
0
1
0
1
0
1
0
0
0
0
0
2
1
0
0
0
0
0
2
0
2
1
1
0
1
0
1
2
0
0
0
0
2
0
2
1
2
2
1
1
0
2
2
1
1
0
2
0
1
2
0
1
1
0
0
1
0
2
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
1
0
0
1
0
2
1
0
0
0
0
0
1
2
3
2
1
1
0
0
0
0
1
2
0
0
1
2
1
0
2
2
0
1
0
0
1
2
0
0
0
1
1
1
2
0
2
0
0
0
0
0
1
2
2
0
0
2
0
3
0
0
0
3
2
1
0
1
0
1
0
0
0
0
1
1
0
1
2
0
0
1
0
0
1
0
2
0
1
0
1
3
2
1
0
1
0
0
2
1
0
2
0
0
0
2
0
0
0
0
1
0
3
2
3
0
0
0
0
1
0
0
0
0
1
0
1
2
0
0
0
2
2
1
0
0
2
1
1
1
0
2
0
2
0
0
0
2
0
5
0
1
0
1
1
1
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
2
2
1
2
0
0
1
1
0
0
1
0
0
2
0
0
2
0
1
0
0
0
2
2
0
1
1
0
0
1
0
0
1
0
2
0
0
1
3
1
1
0
2
0
0
0
0
0
1
1
0
2
0
0
1
2
1
0
1
0
0
0
1
0
2
0
0
0
1
0
1
1
1
1
1
0
0
2
1
2
1
1
2
0
1
0
1
0
0
1
1
2
0
0
2
0
0
0
0
0
3
1
1
0
2
1
0
0
0
1
0
2
1
0
1
0
0
1
1
0
1
3
1
0
0
0
0
0
9
0
0
0
0
0
0
1
0
2
0
0
0
5
0
2
0
1
2
1
1
1
1
1
1
0
2
3
1
0
0
2
0
1
0
2
0
1
0
4
0
2
2
0
2
0
2
0
0
0
1
2
0
1
0
2
0
0
0
1
1
2
3
2
0
0
1
0
0
0
1
1
0
0
0
0
2
0
0
0
1
2
1
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
1
0
1
1
1
0
0
0
1
0
1
0
0
0
1
5
0
0
2
0
1
2
0
1
0
0
0
2
0
0
0
1
2
1
1
1
2
0
0
0
2
2
1
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
2
0
2
2
0
0
0
1
0
0
2
1
2
0
3
0
2
0
0
0
1
0
0
0
0
0
0
1
0
2
2
1
2
2
1
2
0
2
0
0
1
2
0
1
0
2
0
2
0
2
0
3
1
1
0
0
2
3
1
2
1
0
0
1
0
0
0
2
0
1
0
3
0
1
1
0
0
0
0
1
0
0
0
1
0
0
3
0
1
0
0
0
0
0
2
0
2
0
0
0
1
0
1
1
2
1
0
1
0
0
0
0
2
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
2
1
1
0
0
1
0
1
1
0
2
1
0
2
1
0
1
0
0
0
0
0
2
1
0
0
0
0
0
1
2
0
0
1
2
0
2
1
0
0
0
0
2
0
0
0
0
0
0
4
0
1
0
1
0
1
1
2
1
0
1
0
0
0
0
1
2
1
0
1
1
0
0
0
0
1
2
1
1
0
3
1
0
4
0
2
0
1
3
0
0
1
0
2
2
1
0
2
0
0
2
1
0
3
1
2
0
0
0
0
0
0
2
3
0
2
1
2
1
1
1
2
1
0
0
0
1
0
1
0
1
3
0
0
0
1
0
0
2
0
2
2
1
0
0
1
2
1
0
2
0
0
2
1
0
1
2
0
1
1
2
0
0
1
1
2
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
2
0
1
0
0
2
0
0
1
1
0
0
0
0
1
0
1
1
1
0
0
3
0
0
2
1
1
0
0
1
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
2
0
2
0
1
0
1
1
0
0
0
1
0
0
0
0
1
0
2
1
0
1
1
0
0
0
0
1
3
2
0
0
2
0
0
0
2
1
1
2
1
5
0
0
1
0
0
0
0
0
0
0
2
0
1
1
0
1
3
0
5
1
0
0
0
1
1
0
0
4
0
2
0
0
1
0
1
0
0
0
0
0
0
2
0
2
2
0
2
0
2
0
0
2
0
2
0
1
2
0
2
0
2
2
1
1
0
2
2
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
3
2
0
2
2
0
2
1
1
0
0
1
0
0
2
0
3
0
0
0
0
0
2
0
1
1
1
0
0
2
1
1
1
2
0
1
0
0
2
2
0
2
2
0
1
2
0
5
2
0
2
2
0
1
0
1
1
0
2
1
1
1
3
1
2
0
1
1
0
1
1
1
1
1
2
0
0
1
0
1
0
0
2
1
0
0
2
0
0
0
1
1
0
0
0
0
0
2
1
2
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
2
2
0
0
2
1
2
0
2
0
2
1
0
0
0
1
2
0
0
2
0
0
1
0
0
3
0
1
0
1
2
0
1
0
2
0
1
1
0
2
2
0
0
0
1
1
0
2
0
0
0
1
0
3
0
2
2
1
0
0
0
0
0
1
1
2
0
1
0
0
0
0
2
0
1
2
0
1
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
2
1
0
2
1
1
3
0
1
1
0
0
0
2
0
0
0
1
1
0
0
0
2
0
0
0
2
0
1
1
1
2
2
1
2
0
1
0
2
0
1
0
0
1
2
0
0
0
2
0
0
0
2
4
0
0
0
0
1
2
2
0
2
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
2
1
0
0
1
0
0
0
1
0
1
2
1
0
0
0
1
2
2
2
0
3
0
2
1
2
2
1
2
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
1
2
0
2
3
1
0
1
3
1
2
2
0
1
0
0
0
1
0
2
0
1
0
0
1
0
0
1
1
0
0
0
0
2
0
1
0
1
1
1
1
1
2
1
1
1
0
0
1
0
1
0
2
1
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
3
0
0
1
0
0
2
0
1
5
2
2
1
0
0
2
2
0
1
0
0
0
0
1
0
0
1
0
0
2
2
0
2
0
1
2
2
2
1
0
0
0
0
0
2
2
1
0
2
1
0
1
0
0
0
1
2
1
2
2
2
0
2
0
0
0
0
0
2
2
1
1
0
1
0
0
2
2
0
1
0
0
0
2
1
0
0
1
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
1
2
0
1
1
0
0
0
0
0
0
0
0
0
0
1
2
1
1
0
0
1
1
0
1
0
0
0
1
0
0
0
0
2
0
1
2
0
0
2
3
0
0
0
1
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
2
1
1
0
0
0
0
0
0
1
2
0
1
0
0
0
2
1
1
3
2
1
2
2
2
0
2
0
2
0
0
1
2
0
0
1
0
0
1
0
2
0
0
0
2
2
0
1
0
0
1
1
1
0
1
2
0
2
1
0
0
1
0
2
2
2
3
1
1
1
0
0
1
1
1
0
2
0
1
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
1
2
1
0
0
0
1
2
0
0
1
1
2
2
0
0
0
2
0
1
0
0
0
0
0
1
0
2
0
2
0
2
0
3
0
2
0
2
1
1
1
0
1
0
0
1
2
0
2
0
1
1
0
1
0
0
2
0
0
0
2
2
0
2
0
2
0
0
1
2
0
0
1
1
0
0
0
0
1
1
1
0
1
1
1
2
0
0
1
0
0
0
0
2
0
0
2
0
2
2
1
0
0
0
0
0
2
0
0
1
0
0
1
2
1
1
2
1
1
0
0
0
1
0
0
1
0
2
1
2
1
0
0
1
0
0
1
1
1
0
0
0
2
0
1
0
0
0
0
1
0
0
2
2
0
0
0
2
2
1
0
0
2
0
0
0
2
0
0
0
1
0
2
0
1
1
1
1
0
1
0
0
0
0
1
0
0
2
0
1
1
1
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
2
1
1
0
0
2
0
0
0
1
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
2
2
0
2
2
0
2
0
0
0
1
1
2
0
0
2
2
0
2
2
0
1
1
1
1
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
2
3
0
1
2
1
0
0
0
2
0
0
1
0
0
1
2
1
1
0
0
1
0
0
2
2
0
1
0
0
0
1
0
0
1
2
0
0
2
1
1
0
1
0
1
0
6
2
0
1
1
0
0
0
0
2
1
0
0
0
1
1
1
0
0
0
1
1
0
2
0
0
0
0
2
0
2
0
0
2
0
0
1
0
1
0
2
1
3
1
0
0
0
0
0
0
0
1
2
1
0
1
2
2
1
0
0
0
0
0
0
3
2
0
1
1
0
2
2
0
0
0
0
1
0
1
1
0
2
1
2
0
1
0
2
0
2
0
1
1
0
2
0
2
0
3
0
2
1
1
1
1
0
0
0
0
1
0
0
1
2
2
1
2
0
2
0
1
0
0
0
1
0
1
2
1
2
0
0
0
1
2
0
0
0
2
2
0
0
0
0
2
2
2
1
2
1
2
0
2
1
2
2
0
0
0
1
2
0
0
0
2
1
1
0
2
2
0
1
2
0
0
1
0
3
0
1
2
1
0
0
0
0
2
0
0
0
0
2
0
2
0
1
0
0
2
0
0
2
2
0
0
2
0
1
0
0
0
0
0
3
1
1
0
0
2
2
0
0
0
0
0
1
1
0
1
1
1
1
0
0
1
0
0
1
0
1
0
1
1
0
0
0
1
0
0
0
1
3
0
0
1
2
0
0
0
0
0
0
0
0
2
0
2
2
2
2
1
0
1
1
2
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
2
0
1
2
2
1
2
1
0
0
0
0
1
2
0
0
2
0
0
0
1
1
1
0
1
0
3
0
2
0
0
0
0
1
0
0
0
0
1
0
0
1
0
2
2
0
0
4
0
0
1
0
0
0
0
2
1
0
2
2
0
1
0
0
0
1
0
2
1
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
1
2
0
4
2
5
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
2
0
0
0
1
3
0
2
1
0
2
3
5
0
1
0
0
1
1
0
1
1
1
2
0
0
0
0
0
0
0
0
2
0
0
1
2
1
1
0
1
0
0
1
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
2
0
0
0
1
1
2
1
0
0
1
1
2
2
0
1
2
0
1
2
0
1
1
0
0
1
1
0
0
0
2
0
2
0
0
1
0
0
0
0
1
0
1
0
0
1
2
0
2
1
0
0
1
1
2
0
0
1
0
0
0
0
0
0
2
1
1
2
1
2
1
0
0
2
0
3
1
1
0
0
2
0
1
1
0
0
0
0
0
2
1
0
0
0
2
0
1
0
0
1
2
0
2
2
0
1
2
0
1
0
0
2
1
0
0
1
1
2
0
0
0
0
0
2
1
1
0
0
0
1
0
1
0
0
0
0
1
1
2
0
0
2
2
1
2
1
1
1
1
1
0
0
1
2
0
2
0
0
0
0
0
1
0
1
2
0
1
0
1
0
0
1
1
2
1
0
0
2
0
1
0
0
1
0
0
2
0
2
1
0
0
0
0
2
0
1
0
1
0
0
0
0
1
2
0
0
0
1
0
0
0
0
2
0
2
2
1
0
0
2
1
0
3
1
1
2
0
0
0
1
2
2
2
0
2
2
0
0
2
1
1
0
2
0
0
1
0
0
2
0
1
0
1
3
0
2
0
0
1
0
0
1
0
1
0
2
0
0
0
0
0
2
0
3
2
1
2
2
0
1
1
2
0
0
0
1
0
0
1
1
1
0
0
2
0
0
0
1
1
2
0
1
0
2
2
0
0
0
0
2
0
0
1
0
2
1
2
2
2
0
1
2
1
0
1
1
1
0
1
1
2
1
0
0
2
0
1
0
2
0
0
1
0
2
1
1
0
0
0
0
2
0
0
2
1
0
1
3
0
0
0
1
0
1
0
0
1
1
0
2
0
1
0
0
2
1
0
0
0
0
0
0
0
3
2
0
0
2
2
1
0
0
0
0
1
0
2
1
0
1
1
1
2
2
0
0
0
0
0
2
2
0
2
0
0
0
2
0
0
1
1
2
0
0
1
1
0
0
0
0
2
0
1
2
2
0
0
0
0
1
0
2
1
0
0
1
0
0
0
0
1
0
0
2
0
0
1
1
2
2
1
0
1
0
0
1
2
1
0
0
2
0
0
1
0
0
0
0
0
2
1
0
2
0
0
0
2
0
0
0
1
0
2
1
0
0
0
2
1
2
0
0
2
0
2
3
0
0
2
0
1
0
2
1
0
0
2
1
1
1
0
0
0
0
1
1
0
0
0
0
1
0
0
2
2
2
0
0
1
0
0
2
0
0
1
0
0
1
0
1
2
0
2
2
2
0
4
2
1
2
2
1
0
2
4
1
0
0
0
1
0
1
0
2
0
1
0
0
1
2
0
1
0
2
1
0
0
2
0
1
2
0
2
0
0
2
1
1
0
0
0
0
0
1
0
1
0
0
1
0
2
0
0
2
2
0
2
2
2
1
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
1
2
0
2
0
0
0
1
0
2
1
1
1
0
0
0
0
0
1
0
0
0
0
2
0
2
1
2
2
0
0
0
1
3
0
0
0
1
1
1
2
0
0
0
0
0
1
0
0
0
0
0
2
1
0
1
1
0
2
0
2
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
2
0
1
1
1
0
0
0
0
1
0
0
0
1
1
0
0
1
0
1
0
0
0
2
2
1
1
0
2
1
0
0
2
0
1
2
1
0
1
0
0
0
1
0
1
2
0
0
1
2
0
1
3
0
1
2
1
2
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
1
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
1
0
2
1
0
1
1
1
0
2
0
0
2
2
2
1
0
0
0
0
0
2
0
0
2
1
2
0
1
0
0
1
1
2
1
2
0
2
2
0
2
1
1
0
0
1
1
2
0
0
1
0
0
0
0
2
1
2
1
1
0
1
1
0
0
0
3
2
0
0
2
1
2
0
1
0
2
0
2
0
0
2
0
1
2
0
0
2
0
2
0
3
2
1
0
0
0
0
1
1
0
1
0
0
1
2
0
1
1
6
2
1
0
0
0
0
0
0
1
0
2
1
2
0
0
1
1
1
1
0
2
0
2
0
0
0
0
0
3
0
2
1
0
1
0
2
1
1
0
0
0
0
2
0
0
1
0
0
1
0
1
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
1
2
2
0
3
2
0
1
0
3
0
2
0
0
2
0
1
0
1
0
1
0
1
0
2
1
0
0
0
0
0
2
2
1
0
0
0
1
2
1
2
0
0
0
1
2
2
1
0
0
0
0
0
0
0
0
0
0
2
2
1
0
1
2
0
0
0
2
2
1
0
2
1
1
0
0
2
2
0
0
0
2
1
0
0
1
1
0
0
0
1
1
0
2
1
1
0
2
2
0
0
0
2
1
0
1
1
0
2
2
0
0
2
2
2
0
1
0
0
0
1
0
0
0
2
0
0
0
0
2
0
2
1
0
0
2
1
2
0
0
0
2
1
0
0
2
0
0
0
3
1
1
0
1
1
1
1
1
0
0
1
0
0
0
2
0
2
0
1
0
0
2
0
1
0
2
1
1
2
0
0
0
0
0
0
0
1
1
0
0
1
0
0
2
1
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
2
2
0
2
0
1
2
2
0
0
0
0
2
1
8
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
1
1
1
1
0
0
2
3
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
2
0
0
2
2
1
0
1
2
0
0
0
0
1
0
1
2
0
0
0
0
0
1
0
2
2
0
0
1
0
0
0
0
2
0
2
0
2
0
1
2
1
0
1
1
0
0
0
2
2
2
0
1
0
1
2
0
0
0
0
0
0
2
1
0
0
1
1
1
0
0
0
1
1
3
0
1
0
3
0
2
1
0
0
0
0
1
0
1
0
0
0
2
2
2
0
0
2
0
0
2
2
0
2
0
0
2
0
0
1
1
1
1
0
0
0
0
1
2
0
1
1
0
1
2
1
0
0
0
1
2
0
0
0
0
2
0
0
2
1
0
2
0
0
2
0
0
2
0
1
0
0
1
1
0
0
0
0
0
0
1
2
2
0
0
0
0
2
0
0
0
0
0
2
0
3
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
1
0
0
2
1
0
2
1
3
0
0
1
1
2
2
1
0
2
1
1
0
0
2
1
1
1
2
0
2
0
0
0
0
1
0
0
0
0
8
0
0
1
0
4
0
0
2
0
1
1
1
2
2
1
0
1
0
1
1
1
0
1
0
1
2
2
0
2
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
1
0
2
0
1
2
2
2
2
0
0
0
2
0
1
0
0
0
1
1
0
0
1
0
1
0
0
1
0
0
0
0
1
3
0
1
0
0
5
0
0
1
0
2
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
2
2
0
0
0
0
1
0
0
0
2
0
0
1
2
2
1
0
0
0
0
0
0
0
0
2
0
0
0
2
3
1
1
1
0
0
1
0
2
0
2
1
0
0
1
0
1
1
2
2
0
1
0
1
0
0
0
1
2
0
0
1
0
1
2
0
2
0
0
0
0
1
0
0
1
0
1
0
0
2
1
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
3
0
0
0
2
1
0
0
0
1
0
0
1
0
0
1
2
1
0
1
2
2
2
1
0
0
1
1
2
0
2
2
2
0
0
2
0
2
1
0
2
0
0
1
0
2
0
2
0
0
1
1
0
1
0
0
3
1
3
0
2
2
1
2
2
0
0
1
0
2
0
0
0
1
2
2
2
0
2
1
2
0
1
0
0
0
1
0
1
1
1
0
0
0
2
2
4
0
0
0
1
1
7
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
2
1
0
0
1
0
0
1
2
0
1
1
2
2
0
1
2
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
1
2
1
0
3
0
0
2
0
1
2
0
0
4
0
2
0
1
0
0
0
0
0
7
0
0
0
1
2
0
0
0
0
2
2
0
0
2
1
0
1
0
0
0
2
0
1
0
1
0
1
1
2
1
1
1
0
1
0
2
2
0
0
1
1
0
3
2
2
0
2
0
0
0
0
1
2
1
0
0
1
1
1
0
2
0
0
0
2
1
1
2
0
0
0
0
1
0
0
1
1
0
0
1
0
2
0
0
2
1
0
0
1
0
0
1
0
0
1
1
0
2
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
2
1
2
0
2
1
1
0
1
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
1
2
2
1
1
0
1
0
2
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
2
0
2
2
0
1
0
0
2
1
0
0
0
1
0
1
0
1
1
2
0
0
2
0
2
2
0
0
0
0
0
0
0
1
8
0
0
0
2
3
0
2
1
2
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
2
0
2
2
0
1
2
1
2
0
1
0
2
2
2
2
0
3
0
1
1
2
4
0
0
0
2
2
2
0
0
2
1
0
3
0
0
0
1
2
0
2
0
0
0
3
1
0
1
0
0
1
1
0
0
1
1
2
1
2
0
0
1
0
2
0
0
0
0
2
0
0
0
1
1
0
0
0
4
1
2
2
0
0
0
3
2
0
2
2
0
0
2
0
3
0
0
0
0
0
1
1
0
0
2
0
2
1
0
0
0
0
0
0
2
2
0
2
1
0
0
0
0
0
2
0
0
1
0
0
1
1
2
0
2
1
0
2
1
1
0
0
1
1
0
1
0
0
2
2
0
0
2
1
0
1
1
0
1
1
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
2
0
1
0
0
2
1
0
2
1
1
2
0
1
0
0
0
1
0
0
0
1
2
0
0
0
0
0
1
1
1
0
0
0
2
0
0
0
0
0
0
0
2
1
0
1
1
0
0
0
7
1
2
2
0
1
1
0
0
0
2
2
1
2
0
0
0
0
1
1
2
0
0
0
2
2
0
2
0
2
0
0
0
0
2
1
0
1
0
1
0
1
2
0
0
1
0
1
2
2
0
0
1
0
0
1
2
0
0
0
2
0
0
0
1
0
2
0
1
3
0
2
0
0
0
1
0
2
0
0
0
1
1
0
0
0
0
0
2
0
0
1
2
0
2
1
0
0
0
2
0
0
0
1
0
0
0
5
0
1
2
0
1
0
0
0
0
2
0
0
0
2
2
2
0
1
0
3
2
0
0
0
0
1
2
2
0
1
0
0
1
0
0
1
0
1
2
1
0
0
1
0
0
1
2
0
1
0
1
1
0
0
0
1
2
1
1
0
2
2
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
4
1
2
0
2
1
0
0
2
0
0
0
0
2
0
2
1
2
3
0
2
0
0
2
2
0
2
0
1
0
0
0
2
0
0
0
0
0
2
0
0
2
6
0
2
0
1
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
1
1
2
0
1
0
0
0
1
0
2
2
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
2
0
0
0
2
0
2
0
0
3
2
0
0
0
1
0
0
1
0
0
0
2
0
1
2
2
2
1
1
1
0
2
0
2
1
0
1
0
2
1
0
2
0
2
0
3
0
1
0
0
1
2
0
0
0
1
1
1
0
0
0
1
0
2
3
0
0
0
1
1
0
0
1
1
0
2
2
2
2
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
1
1
1
1
1
0
2
0
2
1
1
1
0
2
0
0
2
0
0
0
1
2
2
2
1
0
1
0
2
2
0
2
2
1
1
2
5
1
0
1
3
0
1
1
0
1
0
0
1
0
0
1
1
1
2
0
0
1
1
0
1
0
2
2
0
0
0
1
0
1
2
0
1
0
2
0
3
1
0
0
0
0
0
1
0
0
2
0
0
0
1
2
1
1
2
2
0
0
0
2
0
0
0
0
2
1
0
0
0
0
2
0
1
0
0
0
2
2
1
0
0
1
0
0
2
0
0
0
0
1
0
0
1
1
0
0
1
1
0
0
1
2
5
0
1
2
0
0
0
2
1
0
0
1
1
1
0
0
1
0
1
1
0
0
0
0
2
1
0
0
1
2
0
0
2
0
0
0
0
0
2
0
0
0
1
0
1
1
0
1
1
1
0
0
1
1
3
0
0
0
0
2
0
0
0
1
1
0
1
0
0
2
0
2
0
2
1
0
0
0
1
1
4
0
2
0
0
0
1
1
0
0
0
0
0
0
1
2
0
0
2
0
2
0
0
1
0
0
0
1
1
0
0
1
1
0
0
1
1
2
2
0
1
1
0
1
1
0
0
1
0
0
1
0
0
0
2
0
2
0
1
0
0
1
1
0
1
0
5
2
0
0
2
0
2
2
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
2
1
0
2
0
0
2
1
2
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
2
1
0
1
0
2
0
0
2
0
0
1
0
1
2
2
2
0
0
4
0
1
2
1
0
0
0
2
2
0
0
0
0
1
0
1
0
0
0
0
0
0
2
2
1
0
2
1
1
1
2
0
0
1
0
2
0
2
0
0
1
2
0
0
0
2
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
1
1
2
0
0
0
2
0
0
1
2
0
2
1
0
2
0
0
1
0
2
0
2
0
1
0
1
3
0
1
1
0
1
0
0
0
0
1
1
2
2
1
3
2
2
0
2
0
2
1
0
2
1
2
2
0
1
1
0
2
1
1
0
2
0
0
0
0
0
1
3
0
1
5
0
0
0
0
0
1
2
0
0
0
1
1
2
1
0
1
2
2
0
1
2
0
0
0
0
2
2
0
0
0
0
1
0
1
0
1
2
0
1
1
0
0
1
1
0
1
1
0
0
0
0
1
0
2
2
1
0
2
0
0
0
0
0
1
0
1
0
0
0
2
0
0
3
0
2
1
1
0
1
2
2
1
0
0
1
0
0
0
2
0
0
0
1
0
1
2
2
0
0
1
0
0
0
1
0
0
0
0
0
1
4
0
1
1
0
0
2
0
0
2
1
1
2
0
0
1
0
0
2
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
2
1
0
2
0
0
2
2
2
0
0
0
0
0
1
1
0
0
2
0
1
2
2
1
1
1
2
0
2
0
0
0
0
2
0
0
2
1
2
2
1
0
0
1
1
0
1
0
1
13
0
1
0
0
1
1
0
2
1
2
2
1
0
1
0
1
1
0
2
0
4
2
0
0
0
2
0
2
2
0
2
2
1
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
1
2
1
0
0
0
1
8
0
0
0
1
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
1
0
0
0
2
0
1
2
0
1
0
0
2
2
3
0
3
0
0
1
2
2
2
1
0
4
1
0
0
0
0
0
0
0
0
0
0
0
3
2
0
2
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
2
1
0
0
1
1
0
0
0
0
2
2
1
2
0
1
2
1
1
2
0
1
0
2
0
1
2
0
2
1
0
4
0
0
0
0
0
0
2
1
1
0
2
0
0
0
0
1
0
0
0
1
0
1
1
2
1
2
1
2
2
2
2
0
0
0
1
0
1
1
0
0
0
0
2
0
1
0
0
0
2
3
0
0
0
0
0
0
0
2
1
0
0
2
2
0
0
2
0
2
0
0
0
0
2
2
1
0
1
0
0
0
4
0
0
1
1
0
1
0
2
0
1
1
1
0
0
0
1
0
1
2
0
1
2
2
2
0
1
1
1
0
0
1
2
1
0
0
1
1
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
1
1
1
1
0
2
0
0
1
0
1
0
1
0
0
0
0
0
0
0
3
0
0
0
1
3
0
1
1
0
0
2
0
1
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
2
1
1
0
0
1
0
0
0
0
2
1
0
2
0
2
1
0
0
0
1
1
0
2
2
0
1
0
0
0
0
1
0
2
0
3
0
2
1
0
2
0
0
2
0
0
2
1
1
1
1
0
1
1
0
1
0
0
0
0
0
1
2
0
0
0
1
0
1
0
2
1
2
2
2
0
2
1
1
1
0
0
0
1
1
0
0
0
2
1
0
0
1
1
0
0
0
0
1
0
1
0
1
2
1
1
0
1
3
0
1
0
0
0
0
0
0
1
0
1
0
0
2
0
0
2
0
0
0
3
0
0
1
2
2
0
3
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
2
0
0
0
1
2
0
1
0
0
0
0
0
2
0
0
1
0
2
1
2
0
0
1
2
1
2
1
2
2
0
2
1
2
0
1
2
2
2
0
0
2
0
0
1
1
0
0
1
0
2
3
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
3
1
1
1
1
0
0
1
0
0
0
1
0
1
2
0
0
0
0
1
0
1
3
0
0
0
0
1
1
0
0
0
1
3
1
0
0
0
0
0
2
0
0
0
0
1
0
1
0
2
0
0
0
0
2
0
0
1
1
2
2
0
2
1
0
0
2
0
0
0
0
2
0
0
1
2
0
1
0
3
0
0
1
0
2
0
0
0
2
2
0
2
1
0
0
1
0
2
0
0
0
0
0
2
1
1
0
2
1
1
0
0
0
0
1
1
1
0
0
1
0
0
1
0
2
2
0
2
0
0
0
0
0
0
2
1
1
0
3
0
1
1
0
1
0
2
0
0
0
0
0
2
0
0
1
2
0
0
1
0
0
0
1
2
0
0
2
2
0
0
1
2
0
1
2
0
0
1
0
0
0
3
2
0
1
0
0
1
0
1
2
0
2
1
2
3
1
1
0
1
1
2
1
0
0
1
0
0
0
1
1
1
0
0
0
1
2
0
0
2
0
1
0
1
0
0
0
1
0
0
2
0
2
2
0
0
0
0
0
1
2
1
2
0
0
1
0
0
0
0
0
2
1
0
1
2
1
1
0
0
1
3
1
0
2
0
1
0
3
3
2
0
0
0
2
0
0
1
0
1
1
2
2
1
0
0
1
0
1
0
2
1
0
0
1
3
0
2
1
0
0
1
1
0
1
0
0
0
0
2
1
0
1
0
0
0
0
0
1
1
1
1
1
1
0
0
1
1
0
0
1
0
2
0
0
2
0
0
0
0
2
2
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
1
1
2
0
1
2
0
0
2
0
0
0
2
5
0
0
0
3
0
1
1
2
2
1
0
0
0
2
0
2
1
0
0
0
1
0
0
1
0
0
0
2
0
2
1
0
2
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
3
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
1
2
0
0
0
2
1
2
0
1
1
0
1
0
1
0
1
0
0
1
0
4
0
0
2
1
0
2
0
1
0
1
0
2
0
4
0
2
0
1
1
0
0
0
2
0
4
0
1
1
0
0
1
0
2
0
0
1
0
2
0
0
1
0
2
0
2
1
1
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
4
2
0
0
0
0
0
0
2
2
0
0
1
2
2
2
1
0
0
1
1
0
0
1
1
2
1
2
1
1
0
0
0
0
1
1
1
0
2
0
1
0
2
0
0
3
0
1
2
0
0
1
0
1
1
1
0
0
0
0
3
1
0
0
0
0
0
1
1
1
0
1
1
1
0
2
0
0
0
0
0
2
2
2
0
1
0
0
0
1
0
2
1
2
2
0
0
2
0
0
1
0
1
0
1
0
0
2
0
0
0
0
1
1
2
2
0
1
0
0
1
0
1
2
2
0
0
1
1
2
2
0
0
1
2
0
1
0
2
0
1
2
2
1
0
2
0
0
1
0
1
2
0
0
2
4
0
0
0
2
2
1
0
1
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
1
0
1
2
2
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
2
0
1
2
0
1
0
0
1
0
1
1
0
0
0
1
2
2
0
0
0
0
0
0
0
2
0
2
0
2
2
0
1
0
0
0
0
1
0
1
2
0
2
0
0
0
0
1
0
2
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
1
1
0
0
1
0
2
2
1
0
0
0
1
0
0
0
2
1
2
0
0
2
0
0
1
1
1
0
0
1
2
2
0
2
0
2
2
0
1
1
0
2
0
2
0
10
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
1
1
2
1
1
2
1
1
0
0
2
2
2
0
0
0
1
2
2
1
2
1
1
0
2
0
5
0
0
2
1
2
0
1
0
2
2
2
0
2
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
2
0
2
0
1
0
1
0
2
0
2
0
0
1
0
0
1
2
2
2
1
0
0
1
0
2
0
0
0
1
0
0
0
0
0
1
2
0
0
0
2
0
2
0
0
1
3
3
1
2
0
0
0
2
1
0
0
0
1
0
0
0
1
0
2
0
1
1
2
2
2
0
2
0
0
0
0
0
0
0
0
1
3
3
2
0
0
0
0
1
1
2
0
1
0
2
0
2
1
0
1
0
1
2
0
0
0
1
1
0
1
0
0
0
2
1
0
0
0
1
0
1
0
0
0
0
1
2
0
1
0
0
0
1
2
0
0
0
0
0
2
0
1
1
0
2
0
1
0
0
0
1
2
1
1
1
0
0
1
2
1
2
1
2
1
1
2
1
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
2
1
0
0
1
0
1
0
1
0
0
1
2
0
0
1
2
1
2
0
0
2
0
0
0
2
1
0
1
0
0
0
0
0
1
0
2
0
1
1
0
0
0
0
2
1
1
0
0
0
0
1
0
0
0
0
1
2
2
2
0
0
0
0
1
2
1
0
1
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
1
1
0
3
2
1
2
1
1
0
1
1
0
3
1
0
2
0
0
1
0
0
2
2
0
0
0
2
2
1
1
1
0
0
0
0
2
0
0
2
2
0
2
0
0
0
1
1
1
2
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
2
0
0
1
1
0
0
0
0
2
0
1
0
2
0
0
0
1
0
0
1
0
0
2
1
1
1
1
1
1
1
2
1
2
0
1
0
1
0
0
2
1
1
0
0
2
1
2
0
1
0
1
1
2
1
2
1
0
0
0
2
2
2
0
3
0
0
0
1
0
2
0
0
1
0
1
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
2
1
0
2
4
2
0
2
0
1
0
2
2
0
0
2
1
0
2
1
0
1
1
1
0
0
2
0
0
2
1
1
1
0
0
0
2
1
0
1
2
0
0
0
2
2
0
0
0
0
2
1
0
1
0
0
0
0
1
0
0
1
1
0
2
2
0
1
2
0
1
1
0
0
0
2
2
1
1
0
2
1
0
0
0
1
2
0
0
0
2
2
2
2
1
0
1
1
1
1
0
2
0
0
0
3
1
2
2
0
0
0
3
1
1
0
0
1
2
0
1
0
0
1
0
0
0
0
2
1
0
0
2
1
2
2
0
0
2
2
0
0
0
0
0
1
2
0
0
0
1
2
2
1
1
0
0
0
0
2
1
0
4
2
0
0
0
1
0
0
0
0
1
0
0
2
2
1
2
2
2
1
1
0
0
0
1
0
2
0
2
0
1
2
1
0
2
0
0
0
1
1
0
0
0
0
1
2
0
1
2
0
0
1
1
0
1
3
0
0
1
3
0
0
0
0
1
0
0
1
1
0
1
0
1
1
2
0
0
0
0
2
0
0
0
0
0
1
1
0
1
0
0
1
3
1
0
2
0
0
0
1
0
0
0
0
2
0
0
0
2
3
2
5
1
0
2
0
2
1
0
1
2
0
2
4
0
2
0
0
0
1
1
1
1
1
1
0
0
1
0
1
1
0
0
0
2
2
0
0
1
0
0
1
0
2
2
2
0
1
0
0
0
2
1
2
0
0
0
0
0
1
0
1
1
0
0
0
1
1
0
0
2
1
1
3
0
2
2
0
1
0
2
1
2
0
0
0
1
2
2
0
0
1
0
1
3
0
0
0
1
0
1
2
2
2
1
0
0
0
1
0
2
1
2
0
0
2
3
0
0
2
0
0
0
1
0
1
0
0
1
1
1
1
1
1
0
1
0
2
0
2
2
1
1
0
0
0
0
0
0
1
0
1
2
1
0
2
0
1
2
0
2
0
1
0
0
1
2
0
0
0
0
0
1
0
0
2
0
1
1
1
1
0
0
2
1
0
1
1
0
1
0
2
0
0
2
2
2
0
0
0
1
2
1
0
0
0
1
1
2
0
0
0
0
2
1
2
2
2
1
0
1
2
0
2
0
1
1
1
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
2
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
1
1
1
0
2
0
1
1
0
1
0
0
0
2
0
0
2
2
0
1
0
3
0
2
0
0
2
0
0
1
0
2
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
5
2
2
0
0
1
0
0
0
1
1
2
0
0
0
0
0
2
2
0
1
1
0
0
0
2
0
1
0
0
0
1
1
0
2
2
1
1
0
2
1
0
1
1
1
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
2
0
2
2
2
1
0
1
0
0
0
2
0
0
1
0
0
0
0
2
2
2
0
1
0
2
2
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
1
0
1
0
0
0
1
0
1
0
1
0
2
1
0
2
0
0
1
0
0
0
1
0
1
1
2
1
1
2
0
0
1
1
2
1
1
3
1
1
0
0
2
0
0
0
2
0
0
0
0
2
0
2
0
2
1
1
1
0
3
2
1
0
0
0
0
0
2
1
0
1
0
0
1
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
1
2
0
2
0
1
2
0
0
0
0
1
2
3
0
1
0
1
0
0
0
2
1
2
1
0
2
1
0
0
0
0
0
2
1
0
1
2
1
0
1
0
2
1
1
0
0
0
2
1
0
0
1
1
0
1
1
0
0
0
0
0
2
0
1
0
0
1
0
2
0
0
2
0
0
0
0
0
0
1
1
0
0
0
4
2
1
1
1
0
0
2
0
0
0
2
0
0
1
2
1
0
0
0
0
0
0
1
0
0
1
0
0
2
1
0
0
0
1
0
0
2
0
2
2
0
0
2
2
0
0
0
2
1
0
2
0
2
0
0
2
0
2
0
0
1
0
1
0
0
3
0
2
0
1
2
2
1
0
0
0
0
0
0
0
0
1
1
0
1
1
2
1
0
0
2
0
0
0
0
2
0
0
1
0
4
1
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
2
2
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
1
2
0
0
0
0
0
2
2
1
0
0
2
0
1
2
2
0
0
0
2
0
0
0
0
2
0
1
1
0
2
0
0
0
4
0
0
2
0
1
0
0
0
0
2
0
0
1
2
0
1
2
1
2
0
1
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
2
1
0
0
0
2
0
2
0
2
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
1
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
3
0
1
0
0
2
0
1
0
2
0
0
1
0
0
2
2
0
0
0
1
1
1
0
1
0
0
0
2
0
1
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
1
1
1
0
2
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
2
2
1
0
3
0
2
0
0
2
2
0
0
1
0
0
1
0
0
0
0
1
0
1
0
1
2
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
2
0
2
0
1
3
2
0
1
0
0
0
0
0
0
2
0
0
2
0
2
2
0
1
0
0
1
2
2
0
1
0
2
1
0
0
0
5
2
0
0
2
0
2
0
0
0
1
2
0
0
2
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
1
0
0
1
2
2
0
1
2
1
1
0
0
0
3
1
2
0
2
0
0
2
0
2
2
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
1
1
0
2
0
2
1
2
2
2
0
0
2
0
1
1
1
0
1
0
1
0
0
0
1
2
0
3
0
1
2
0
0
0
2
0
0
0
0
1
2
0
3
0
2
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
1
1
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
2
3
1
0
1
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
1
0
0
1
2
2
2
0
1
1
1
1
0
0
0
2
2
1
2
0
0
0
0
0
0
2
1
0
1
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
1
0
0
0
2
0
1
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
2
0
0
1
0
1
0
0
0
0
2
1
2
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
3
0
0
0
0
0
1
1
0
1
0
1
5
1
0
0
2
0
2
1
2
0
0
2
0
2
0
1
0
0
0
0
1
2
0
2
1
0
0
2
0
0
1
2
2
0
0
0
2
1
1
0
0
1
0
1
3
2
0
0
0
0
2
1
0
2
1
2
1
0
0
0
1
2
1
0
3
1
0
1
1
1
2
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
2
0
0
3
1
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
2
0
0
0
0
2
0
2
0
0
1
1
0
1
1
0
0
1
1
1
1
1
4
1
0
0
0
1
1
2
0
0
0
1
0
2
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
2
3
0
0
2
1
1
0
0
0
2
1
2
1
0
0
0
0
2
2
0
0
1
0
0
0
0
3
2
1
0
2
0
2
2
0
2
0
0
0
0
2
0
2
0
2
0
0
0
2
1
0
0
0
1
1
0
0
1
0
0
0
0
1
2
0
2
1
0
2
0
0
0
1
0
0
2
1
1
0
0
0
0
2
0
0
0
1
1
1
2
1
2
0
0
0
0
0
0
0
0
0
1
2
3
0
1
0
0
0
0
2
1
0
0
2
0
1
2
2
0
2
1
0
3
2
1
0
0
2
2
2
0
0
0
1
0
0
0
0
0
0
2
2
0
1
0
0
1
2
0
0
1
2
1
0
1
0
0
0
0
0
1
1
2
0
1
0
1
2
2
1
0
0
0
0
0
2
2
0
2
1
0
0
0
0
0
0
0
0
1
1
0
1
2
1
2
0
0
0
0
1
1
1
2
2
0
0
0
0
2
2
1
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
2
0
1
1
0
0
0
0
0
1
0
2
2
0
1
2
1
2
0
1
2
1
1
2
0
0
0
0
0
0
0
1
0
0
0
1
1
0
2
0
0
1
0
2
0
0
0
1
2
1
1
1
3
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
1
1
0
1
0
1
0
1
1
0
1
0
0
1
0
1
2
0
2
2
2
0
2
1
1
2
1
2
0
0
2
3
2
2
1
2
0
0
0
0
1
1
1
0
0
0
0
0
2
0
0
1
0
0
1
0
2
0
0
0
2
0
0
0
3
0
0
3
2
2
0
0
0
2
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
1
0
1
0
1
2
0
1
1
2
1
0
0
0
2
1
0
1
0
0
0
0
0
1
0
2
0
1
0
0
0
2
2
1
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
2
0
2
2
1
0
0
0
0
2
0
0
1
1
0
2
2
2
2
0
1
2
2
1
0
0
0
1
1
0
0
1
0
1
0
1
0
1
3
1
0
1
0
0
0
3
0
0
0
1
0
2
0
0
3
1
1
1
1
1
4
1
0
2
2
0
1
0
1
0
0
0
0
0
2
0
0
3
1
2
1
0
1
1
1
0
0
1
0
1
0
1
0
0
0
0
0
1
0
1
0
2
0
0
1
3
0
1
0
1
0
2
1
0
0
1
0
1
0
0
1
0
1
0
0
2
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
5
0
1
2
0
1
0
0
2
0
0
0
0
0
1
0
1
3
0
2
0
0
1
0
0
0
0
0
0
0
4
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
2
2
0
2
1
0
0
2
0
2
1
0
0
2
1
1
1
1
1
2
1
2
0
2
1
0
0
0
2
0
0
1
0
0
1
0
0
1
0
2
0
2
0
0
1
1
0
0
0
0
1
2
0
0
0
2
0
0
2
0
1
0
0
0
0
2
1
0
0
2
0
2
0
0
2
0
1
0
1
0
2
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
1
0
2
0
0
1
0
2
1
2
0
3
0
1
0
2
0
0
0
2
1
1
0
0
0
1
1
0
0
0
0
1
0
1
1
0
0
1
1
0
2
0
0
0
1
2
0
2
1
2
0
0
2
0
1
0
0
2
0
0
0
1
0
0
0
1
0
1
0
0
1
0
1
3
0
1
1
1
1
1
1
0
0
2
1
0
3
2
0
1
1
0
2
0
0
0
1
0
1
0
0
0
0
1
0
0
2
0
1
0
0
2
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
2
0
0
1
1
0
1
0
0
0
1
1
0
0
1
2
2
1
0
2
0
2
0
0
0
0
1
1
0
1
2
0
0
0
0
0
1
1
1
0
0
0
0
2
1
0
0
0
2
2
0
1
1
0
0
0
0
1
0
1
2
2
0
1
0
0
2
1
2
0
0
0
0
2
1
0
2
0
1
1
0
1
1
2
0
0
0
1
0
0
1
2
0
1
1
0
0
1
1
0
2
0
2
0
0
0
1
2
0
2
0
3
0
0
0
2
0
0
1
1
2
0
0
1
0
1
2
0
0
0
1
2
1
1
2
1
0
0
0
0
0
1
2
1
2
0
0
0
1
0
0
0
4
2
1
0
0
1
0
3
0
0
2
0
0
1
0
1
0
1
1
1
0
3
0
1
1
0
0
1
1
1
0
0
2
2
0
1
0
2
2
2
3
0
2
0
0
0
1
1
1
2
0
2
2
0
2
1
0
0
0
0
0
0
1
1
1
2
0
0
2
0
2
0
0
1
0
0
0
1
1
0
0
2
2
0
0
0
0
0
1
1
2
1
2
0
1
0
0
2
0
0
0
0
1
0
0
6
1
2
0
1
3
1
0
1
0
2
1
1
0
2
0
0
0
2
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
1
1
0
0
0
1
2
0
0
0
0
1
6
0
1
2
0
0
2
0
0
2
0
1
0
2
0
1
0
1
0
0
0
1
0
0
0
0
2
0
2
3
1
2
1
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
2
1
1
0
2
0
2
0
2
0
0
2
1
2
2
0
2
0
0
1
0
0
1
1
0
1
1
2
1
2
0
0
0
2
0
1
0
2
0
2
0
0
1
0
0
0
2
0
0
0
2
0
2
0
1
0
0
0
0
0
0
4
1
2
2
1
3
2
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
2
0
1
2
1
1
0
0
0
2
0
0
0
0
0
0
0
1
1
0
1
0
0
4
0
0
0
0
2
1
0
1
0
1
0
6
3
0
0
2
1
1
1
2
1
2
2
0
0
0
0
2
0
0
1
0
0
3
0
1
0
0
0
3
0
0
2
1
2
0
2
0
0
0
2
0
0
0
0
1
0
3
2
1
0
0
0
0
2
1
1
0
0
0
0
3
0
1
1
0
1
0
2
3
2
2
0
0
0
1
0
0
0
0
2
0
0
1
0
1
2
1
1
0
2
0
2
2
0
1
0
0
1
0
0
0
0
1
1
1
0
0
0
3
0
0
2
2
1
1
1
0
2
2
2
0
2
2
0
0
0
0
2
0
1
1
0
0
0
0
1
0
1
0
0
1
2
2
0
0
1
0
0
0
0
3
1
0
2
1
1
1
1
0
1
0
1
0
0
0
0
2
0
1
1
0
2
1
2
0
3
1
0
0
1
0
0
0
0
2
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
3
0
0
1
0
0
0
0
0
0
2
4
0
2
2
1
0
1
0
1
1
1
2
3
0
0
1
0
0
3
0
0
1
2
2
0
0
1
2
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
1
2
0
2
0
0
2
0
2
0
0
1
0
0
2
1
1
0
0
1
2
0
0
1
0
1
0
1
0
0
0
0
2
0
0
2
0
0
0
1
2
0
2
0
1
1
0
2
1
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
2
0
1
0
1
0
0
1
2
5
0
0
0
0
0
1
1
3
2
1
0
3
0
1
0
0
0
0
1
3
0
0
2
1
2
0
0
1
0
0
0
2
0
1
1
0
0
5
0
0
2
0
1
2
0
2
0
2
1
0
2
0
1
0
0
0
0
0
1
0
1
2
2
0
3
0
0
0
4
0
1
0
0
2
0
1
1
0
0
1
1
0
0
0
1
0
0
2
2
0
0
0
0
1
0
1
0
1
1
1
2
0
6
1
0
0
0
2
0
0
0
1
1
0
1
15
0
0
0
0
0
2
0
0
2
0
0
1
2
1
0
4
1
2
0
1
0
2
1
1
1
0
0
1
1
0
0
2
0
1
0
1
2
0
0
0
1
0
0
1
1
0
1
2
1
2
0
1
1
0
2
1
0
0
2
1
1
1
1
0
1
0
2
1
1
0
1
1
2
0
2
0
0
0
0
0
2
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
1
1
0
1
0
1
2
5
2
2
2
2
2
0
1
0
0
1
0
1
0
1
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
1
0
0
0
0
0
1
0
1
1
1
1
0
1
0
1
1
1
1
2
1
0
0
0
0
1
0
0
0
0
0
2
1
0
0
3
1
0
0
2
0
0
2
0
2
0
0
2
2
0
1
0
0
2
0
0
3
0
0
1
0
0
2
1
0
2
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
1
2
0
0
2
0
1
1
0
0
0
1
0
1
0
2
0
0
1
1
2
0
0
0
0
0
0
1
1
0
1
2
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
1
0
1
0
1
1
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
1
0
2
0
0
0
0
7
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
2
0
1
0
2
1
0
0
4
0
2
0
0
2
0
0
0
0
1
0
2
2
1
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
3
2
0
0
2
0
2
0
1
1
0
0
0
2
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
2
1
0
0
1
1
3
1
1
0
2
2
0
2
0
1
0
1
1
0
0
0
2
1
0
2
0
2
0
1
0
0
0
0
1
0
1
2
0
0
0
0
1
0
0
1
2
1
1
0
0
0
2
0
2
0
0
2
1
1
3
1
0
0
0
1
0
0
0
1
2
0
0
1
0
0
0
0
1
0
0
0
0
1
2
0
2
0
2
2
2
2
0
0
2
1
0
0
0
0
0
1
0
2
0
0
0
2
0
1
0
1
2
0
1
0
0
0
2
0
2
0
1
1
0
1
0
0
0
0
0
2
0
2
0
1
0
0
0
0
1
0
1
0
0
1
1
2
0
2
3
0
2
0
1
2
1
1
0
2
0
2
1
0
0
0
0
0
0
0
1
2
0
0
1
2
0
7
0
2
0
0
0
0
0
2
1
0
1
1
2
1
0
1
0
0
0
0
1
2
1
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
1
0
1
0
0
1
2
0
0
1
0
0
2
0
2
0
0
1
1
1
1
1
0
2
0
0
2
0
1
1
0
2
0
0
0
0
0
1
0
0
2
0
1
1
2
0
2
1
1
2
0
0
0
1
1
0
1
0
0
0
0
2
0
1
1
0
1
2
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
2
0
0
1
0
2
1
0
0
0
1
0
1
1
0
0
0
0
0
2
3
0
2
2
0
0
0
0
0
1
1
1
0
1
1
2
1
1
0
2
0
1
1
0
1
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
2
0
2
0
2
1
2
1
0
1
0
0
0
0
0
0
2
0
1
2
1
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
2
1
2
1
1
0
0
0
2
0
1
0
0
0
1
0
0
1
1
2
1
2
0
0
1
2
0
0
1
2
1
0
0
1
2
2
0
1
0
2
1
0
2
0
0
1
0
0
0
0
2
0
0
1
0
2
1
2
1
0
0
2
0
0
1
0
0
0
1
2
0
0
0
1
0
1
2
2
0
0
0
2
0
0
3
0
0
2
1
0
1
0
0
0
0
0
0
1
0
0
0
2
1
0
3
0
0
1
3
0
0
2
0
0
0
0
0
1
0
1
0
1
0
0
0
1
1
1
2
0
0
0
0
0
3
0
2
0
0
1
1
3
4
0
2
2
0
0
1
0
2
2
2
2
0
2
0
0
0
1
2
1
1
2
1
2
0
2
2
0
0
0
1
0
0
0
0
1
0
0
0
2
0
1
0
0
2
0
0
2
1
0
0
2
1
2
0
2
2
0
0
0
2
1
1
1
0
1
2
0
2
2
0
0
2
2
1
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
1
1
1
3
0
1
0
0
0
1
0
0
1
2
2
3
0
2
1
1
2
0
0
1
2
0
2
1
0
1
0
0
1
1
1
1
0
1
0
3
1
2
1
0
3
0
0
0
1
1
0
1
2
0
0
2
0
0
0
1
1
1
1
1
1
0
2
2
0
1
0
0
2
1
0
2
1
1
2
0
0
1
1
1
2
0
1
2
1
1
0
0
0
0
1
0
1
0
2
1
1
1
0
2
0
2
0
0
0
0
6
0
0
0
1
1
1
0
1
1
0
0
1
2
1
2
0
0
0
2
1
0
0
0
0
2
1
2
0
2
0
0
2
0
0
2
0
0
0
1
1
2
0
1
0
1
0
0
2
1
0
1
0
0
0
3
0
0
1
2
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
2
2
1
0
0
2
2
2
2
2
0
2
2
0
0
0
3
1
0
0
0
0
0
2
1
2
2
1
0
1
0
0
2
2
1
0
0
0
0
2
0
0
0
2
1
0
5
0
0
0
1
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
2
1
0
1
0
3
2
0
0
0
1
2
2
0
0
2
1
3
2
0
0
1
1
0
2
2
0
2
0
0
0
2
1
0
0
0
0
2
0
1
0
1
1
0
0
1
2
1
0
1
0
0
0
0
0
0
2
0
0
1
0
0
4
2
1
2
0
0
3
0
1
0
0
0
0
1
1
0
1
0
0
0
0
2
0
0
0
0
2
2
1
0
0
0
2
2
2
1
0
1
0
0
0
0
0
0
0
1
2
1
1
2
1
1
1
3
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
2
2
2
2
0
0
0
1
0
0
0
0
1
0
2
0
0
0
2
0
1
1
1
1
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
1
0
0
2
0
0
1
0
0
1
0
0
7
1
0
0
0
2
0
0
1
2
0
0
1
2
2
0
0
1
1
2
2
0
0
1
0
0
0
0
2
0
1
0
2
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
1
2
2
2
0
0
2
1
0
1
0
2
0
0
0
2
0
1
0
1
2
2
0
0
0
1
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
2
0
1
1
0
0
0
1
1
0
1
0
0
1
0
0
1
1
1
2
1
0
0
1
0
1
2
0
0
0
0
0
2
0
0
2
2
2
0
0
2
2
1
0
0
0
0
2
3
0
0
0
0
1
0
0
0
1
1
0
0
1
0
1
1
0
1
2
0
0
1
0
1
0
0
1
0
0
0
1
2
2
2
1
2
0
1
0
0
0
0
0
0
0
0
1
1
0
2
1
0
0
0
0
0
2
2
0
1
1
0
0
0
0
0
1
0
0
0
1
0
1
0
2
0
1
1
0
2
0
0
0
0
0
0
3
3
2
0
0
1
0
1
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
1
0
1
0
1
0
2
1
1
0
0
0
0
1
0
0
2
1
1
2
1
2
1
0
0
1
2
0
2
2
0
1
2
1
1
0
0
1
0
0
2
0
1
1
0
0
1
2
1
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
1
0
0
2
1
1
0
0
0
0
2
1
0
1
0
0
1
2
0
0
2
0
1
2
1
1
0
1
2
2
1
1
2
1
0
0
0
0
2
2
0
2
0
0
0
0
2
0
0
1
2
1
2
0
1
0
0
2
1
2
2
0
0
1
2
0
0
2
1
0
0
2
1
0
0
0
1
0
0
2
0
0
0
0
2
0
1
0
0
0
1
0
1
0
1
1
0
0
0
2
1
0
0
0
0
6
0
1
2
0
1
2
3
0
0
0
0
0
0
1
2
2
0
2
0
2
2
0
0
1
0
0
0
2
2
0
0
0
0
0
0
1
0
2
0
1
2
0
1
0
1
0
3
0
3
0
0
0
1
0
0
0
0
2
0
1
1
0
0
0
0
1
1
2
0
0
0
0
2
1
0
1
2
1
2
1
1
0
2
0
1
0
0
2
0
0
1
1
2
1
1
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
1
0
0
2
3
2
1
2
0
1
1
1
0
2
0
0
1
2
1
0
2
1
0
0
1
0
0
0
2
1
2
0
0
0
2
0
0
0
0
0
0
0
0
1
3
1
0
0
0
3
0
2
1
0
0
0
2
0
0
1
0
0
2
1
0
2
0
1
0
1
0
2
0
0
1
1
1
2
0
1
0
2
1
0
1
2
5
0
0
0
0
2
0
0
2
0
1
1
0
2
2
0
2
1
0
0
0
0
0
2
0
0
1
0
0
1
0
7
2
0
1
0
0
0
2
3
3
1
0
1
2
0
0
1
0
1
0
0
2
0
0
1
0
0
0
0
1
3
0
1
2
0
1
1
0
1
2
0
0
0
0
2
2
0
0
1
0
2
0
1
1
1
2
1
1
0
1
1
1
0
0
1
2
0
0
0
0
1
0
0
1
0
2
0
3
2
0
0
1
0
0
1
4
0
0
0
6
0
4
2
3
0
1
0
0
0
0
2
1
0
2
0
0
0
1
0
2
5
0
0
1
0
0
2
0
0
1
0
0
0
1
0
0
0
2
2
2
0
0
2
1
4
0
0
0
1
1
0
0
1
1
0
3
2
2
1
0
0
0
0
0
2
1
0
3
1
2
3
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
1
0
0
0
0
0
1
2
0
0
0
2
0
0
0
1
1
3
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
1
0
2
2
0
2
0
0
0
0
2
0
0
1
1
0
1
0
2
0
0
0
2
3
0
0
0
1
0
1
0
2
1
0
0
0
1
0
0
2
0
0
0
0
1
1
2
0
0
1
1
0
0
0
0
1
0
0
0
1
0
2
1
0
1
0
0
1
0
1
1
1
1
1
0
0
0
2
2
0
0
1
3
0
0
1
1
0
2
1
2
1
0
0
0
2
1
2
0
0
2
0
0
2
2
0
1
0
2
0
0
0
1
1
0
2
0
1
2
0
0
0
2
0
0
1
0
0
1
1
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
1
0
2
0
0
0
0
2
2
4
1
0
0
0
2
0
0
1
1
0
0
0
1
0
1
0
0
4
0
0
0
0
1
0
0
2
2
1
1
0
0
0
1
1
0
0
0
0
0
1
0
2
0
0
0
2
0
1
2
0
2
1
0
0
0
1
0
2
0
2
0
1
2
0
2
1
0
1
0
0
0
1
2
0
2
0
0
1
3
0
0
0
2
1
1
0
0
0
0
0
0
0
1
0
0
1
2
0
0
2
0
1
0
1
0
2
1
4
0
0
1
0
0
0
2
0
1
1
0
2
0
0
0
1
1
0
0
1
0
0
1
0
0
0
2
3
0
0
2
0
2
0
0
1
0
2
2
1
0
0
0
2
0
2
0
0
0
0
0
0
1
1
0
2
2
0
0
1
0
0
0
2
0
0
1
1
1
0
2
0
1
0
0
0
1
2
2
0
0
0
2
1
4
1
0
0
0
1
0
1
1
0
1
1
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
2
0
0
0
0
1
2
2
2
0
2
0
0
0
0
1
0
0
2
0
3
0
0
2
0
2
0
0
0
2
0
2
1
2
0
1
1
0
0
0
0
0
0
0
0
0
2
0
2
7
2
0
1
0
1
1
2
2
0
2
2
0
0
0
0
2
0
1
2
2
0
0
0
0
4
1
0
0
0
1
0
5
0
1
1
0
1
2
0
1
0
0
0
2
0
0
0
0
0
2
0
0
2
0
2
2
0
0
0
0
0
1
0
0
0
2
0
0
2
1
0
0
2
1
0
1
1
1
1
1
1
0
0
0
2
1
0
2
0
2
1
0
1
2
0
0
1
0
0
1
3
2
0
2
1
0
0
0
0
1
0
0
1
0
2
2
1
0
0
0
0
0
0
0
1
0
2
0
1
0
2
0
0
1
0
1
0
2
1
1
0
1
0
2
1
0
0
2
0
2
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
1
1
4
2
1
2
0
0
0
0
3
2
0
2
1
0
1
0
0
0
0
2
0
1
0
1
2
1
0
1
0
2
0
1
1
2
0
0
0
0
2
2
1
0
3
2
2
1
1
2
0
0
0
0
0
0
0
1
1
0
2
1
1
1
3
2
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
2
0
1
1
1
1
0
0
0
1
2
1
1
0
2
0
0
0
1
0
2
1
0
1
1
0
1
0
3
2
0
1
0
1
2
0
0
0
0
2
0
0
0
0
0
2
2
0
2
1
0
0
0
1
2
1
0
1
0
1
0
3
3
2
0
1
0
0
3
2
0
0
0
1
0
0
2
2
0
0
1
1
2
2
0
0
0
0
0
0
0
0
0
0
3
0
2
0
2
0
1
0
0
1
0
0
1
0
1
0
2
0
1
0
1
2
0
2
0
0
0
0
1
1
4
2
2
2
0
0
1
2
0
2
0
1
0
1
0
1
0
1
0
0
0
4
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
2
1
0
0
0
2
0
2
0
1
0
2
0
0
1
0
2
1
1
2
2
0
1
2
0
1
0
0
0
2
1
1
0
0
1
0
0
0
0
0
0
0
4
2
1
2
0
0
2
0
1
1
0
1
0
0
1
0
0
0
1
0
1
1
0
1
0
0
1
3
0
0
0
0
0
0
1
1
2
0
0
1
1
0
2
0
0
2
1
1
2
0
0
1
1
0
1
1
0
0
0
2
0
1
1
0
0
0
2
0
2
1
1
1
1
0
0
2
1
0
3
0
0
0
1
0
1
0
1
0
0
0
3
1
2
0
0
0
0
1
1
2
2
2
0
2
0
1
1
0
0
0
2
0
0
0
1
0
0
2
1
2
1
0
2
0
3
0
0
0
0
0
0
0
2
0
0
0
1
0
1
1
0
3
0
1
1
0
1
0
0
2
0
0
1
0
0
2
0
2
0
2
0
0
2
0
0
0
1
0
4
0
0
2
1
0
2
2
1
0
1
2
1
0
0
1
1
1
2
1
1
0
1
1
0
0
0
1
0
0
2
2
0
2
2
1
0
0
2
3
0
1
1
2
0
2
2
0
0
0
3
0
0
0
1
1
2
0
0
2
0
2
2
0
0
0
1
1
1
0
0
2
0
0
0
0
1
0
0
0
1
0
0
2
0
1
0
0
1
0
0
0
2
2
1
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
1
0
3
1
2
2
0
0
2
2
0
2
0
0
0
0
0
1
2
0
0
0
0
2
1
1
0
2
1
0
1
0
2
0
2
0
2
3
0
1
1
0
0
0
1
0
2
0
0
0
1
2
1
0
0
1
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
1
2
0
0
2
1
0
2
2
1
1
2
2
1
0
3
0
1
1
0
0
2
1
0
1
1
0
0
1
0
0
1
1
0
0
1
0
3
2
3
0
0
0
0
2
0
0
0
0
1
2
0
1
0
0
0
0
2
0
1
0
0
1
0
1
1
0
0
0
0
0
0
1
2
0
0
0
1
2
0
0
0
0
2
1
1
0
1
0
1
0
2
1
0
1
0
0
2
0
0
0
2
0
0
0
3
2
0
1
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
1
2
1
1
0
0
0
0
2
0
2
0
0
0
0
2
1
1
1
0
0
0
0
0
0
0
0
2
0
1
0
1
1
0
1
0
1
0
1
0
0
2
1
0
1
0
3
0
0
0
2
0
2
2
0
2
2
0
0
4
2
0
1
2
0
2
3
0
1
1
0
0
1
0
0
0
0
1
1
1
3
1
0
0
0
0
2
0
1
2
1
2
0
0
0
0
0
0
0
2
3
0
1
0
0
0
0
1
1
1
0
0
2
0
2
2
1
0
0
1
0
0
0
0
2
1
0
0
0
2
0
0
1
1
0
1
1
0
1
1
0
1
1
0
0
0
2
0
0
2
0
2
2
0
0
2
0
0
1
1
0
0
3
2
0
0
0
2
1
0
0
1
3
1
0
0
0
1
1
0
0
1
0
1
1
0
1
2
0
1
0
1
1
0
0
0
0
2
2
0
0
1
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
1
0
1
1
1
0
1
1
2
1
2
2
2
2
0
0
0
1
1
0
0
0
0
2
0
0
0
0
2
0
0
1
2
1
0
2
0
0
0
1
1
2
0
1
0
1
0
1
2
1
0
2
0
3
1
0
0
0
0
0
0
1
0
1
0
1
1
2
0
1
0
2
1
1
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
1
0
0
1
2
1
1
0
0
0
2
2
0
0
1
1
0
0
0
1
1
1
1
0
0
2
1
2
2
0
0
1
2
3
2
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
1
1
2
1
1
2
0
0
1
1
1
2
1
1
1
2
1
0
1
0
0
2
2
0
1
0
0
4
1
0
0
0
0
0
2
1
0
0
0
0
0
1
0
2
1
0
1
0
1
0
0
1
0
0
4
1
1
1
0
0
1
2
2
0
0
0
0
0
1
1
0
0
0
1
0
0
0
5
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
4
0
0
0
1
1
0
0
0
0
1
0
2
0
1
0
0
0
0
1
0
1
0
2
0
1
1
0
0
1
0
1
0
2
1
1
2
0
0
0
1
0
2
0
1
0
1
1
0
3
0
0
1
0
0
2
1
0
1
0
2
1
0
0
3
2
0
2
1
0
4
0
0
1
1
0
4
0
0
0
1
0
0
0
1
2
2
2
2
0
0
0
1
2
0
1
0
1
3
0
0
0
2
2
0
0
0
2
1
1
1
0
0
2
1
0
1
0
0
4
0
1
0
2
0
1
2
0
2
2
0
0
3
0
0
1
0
1
2
0
2
0
2
1
1
1
2
0
0
2
0
1
1
1
0
0
1
0
2
0
0
0
1
5
0
0
2
2
1
0
1
1
0
0
0
3
2
1
2
2
2
0
1
1
1
3
1
2
0
0
0
0
0
0
1
1
0
2
1
0
1
2
3
3
0
0
0
0
1
3
1
0
2
0
0
1
0
0
3
0
1
0
0
0
0
2
0
0
0
0
0
0
2
2
2
1
0
3
2
0
0
0
0
1
2
0
0
0
1
1
0
1
1
0
1
1
0
1
0
0
0
2
5
0
0
0
0
2
0
2
0
3
2
0
1
1
2
1
0
0
0
0
1
0
1
1
0
0
0
2
1
0
0
0
0
0
0
0
2
2
2
2
0
1
0
0
2
0
0
2
1
0
2
2
1
1
1
1
0
0
1
2
0
4
2
2
0
1
0
0
1
0
0
0
2
0
1
1
0
0
0
0
0
1
1
1
0
0
2
2
0
1
0
0
0
0
1
2
0
0
0
0
2
1
1
0
2
0
1
1
0
2
1
0
0
0
0
0
2
0
0
1
0
1
1
0
0
2
0
1
0
0
0
0
0
2
2
2
0
0
1
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
1
0
1
0
2
0
1
0
1
2
0
0
0
1
2
1
0
1
0
0
2
0
0
0
2
0
1
0
1
2
0
1
1
0
3
1
1
0
2
0
0
0
0
0
1
1
1
3
3
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
3
0
0
0
1
0
0
2
0
0
2
1
1
1
0
2
2
2
2
0
0
1
0
0
1
0
0
1
1
0
2
1
0
0
1
1
0
1
3
1
3
1
0
1
2
0
1
1
1
0
2
0
1
0
1
1
0
1
0
1
2
0
1
2
0
0
2
1
2
1
0
2
0
3
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
1
1
1
0
1
1
0
2
0
0
2
0
0
1
0
0
0
0
2
0
0
1
0
1
0
0
0
2
0
1
2
1
0
1
0
2
1
0
3
1
1
0
0
0
2
0
1
1
0
0
0
1
1
2
1
0
0
1
0
0
3
0
1
2
0
0
2
1
0
0
2
1
1
1
0
0
0
2
2
2
1
0
1
0
1
1
0
0
1
0
2
0
3
1
3
0
1
0
0
0
0
0
0
1
2
0
0
1
0
0
2
0
1
0
3
2
4
1
1
1
0
0
0
1
2
1
0
0
2
2
0
0
0
0
2
2
2
0
1
0
0
0
0
0
0
1
0
2
2
3
1
0
2
0
1
3
0
0
0
0
0
0
0
2
0
2
2
0
2
2
1
0
0
1
1
0
0
3
0
0
0
1
1
0
0
0
0
0
1
0
2
1
0
2
1
1
5
0
2
0
0
0
1
1
0
0
0
2
0
1
0
1
0
0
0
1
2
2
0
1
0
0
0
1
0
0
2
0
0
1
0
0
0
1
0
2
0
0
0
1
1
2
0
1
0
2
2
0
0
0
1
1
0
0
0
0
0
0
0
3
1
0
6
0
0
1
0
1
0
0
1
0
0
2
0
1
0
1
0
1
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
1
1
0
2
0
0
0
2
0
1
0
0
0
0
0
1
1
0
0
1
1
2
0
0
0
0
1
2
0
0
0
0
2
0
2
0
0
1
2
0
0
1
0
0
0
1
0
0
0
1
0
0
0
2
2
0
1
0
0
0
0
1
0
3
0
1
0
0
0
0
1
0
0
2
1
1
0
0
0
3
1
2
2
0
2
1
1
0
0
3
0
0
0
0
0
1
0
0
0
1
1
2
0
2
0
0
1
0
1
1
2
1
2
2
0
0
0
1
0
0
0
3
0
2
0
2
1
0
1
1
2
0
0
1
0
1
0
0
1
2
1
0
0
0
0
0
2
2
0
0
0
0
0
0
5
2
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
1
2
0
0
0
0
0
0
1
1
2
0
0
2
0
2
2
0
0
2
0
0
0
1
0
0
0
0
3
0
0
0
0
3
0
1
1
0
0
1
1
1
1
2
0
0
1
2
0
0
2
1
0
0
2
0
1
0
1
2
1
0
1
2
0
0
3
2
1
0
0
2
1
0
0
0
0
0
2
1
1
2
2
0
0
0
0
0
1
1
2
0
0
0
0
1
2
1
1
0
0
1
0
1
0
2
1
2
0
1
0
2
0
0
0
0
0
1
0
0
0
2
0
0
2
0
1
0
0
0
2
1
0
0
2
0
2
2
2
1
1
0
1
2
0
0
0
1
1
0
0
0
0
1
1
2
1
0
2
2
0
0
2
1
0
1
1
0
1
0
1
0
1
0
1
2
0
0
2
0
0
0
0
1
0
0
2
1
2
0
1
0
0
1
0
0
1
1
2
2
2
1
0
1
2
0
1
0
0
0
0
1
2
0
2
0
0
1
0
4
1
1
0
1
0
0
0
1
1
0
1
0
0
1
2
2
0
2
2
2
0
1
0
1
0
2
2
1
2
0
0
1
2
1
0
1
0
0
0
2
0
0
0
1
0
1
0
0
1
3
1
0
1
0
0
0
1
1
0
0
2
2
2
0
0
0
0
0
0
0
0
1
0
2
0
1
2
1
0
2
1
0
0
2
0
0
1
0
2
2
0
2
3
0
0
0
2
1
1
0
0
2
0
1
1
0
0
0
1
4
0
0
1
1
1
0
1
2
1
1
0
1
3
0
0
1
0
0
1
2
0
0
1
1
0
0
0
3
0
0
2
2
2
0
2
4
0
0
0
1
1
0
1
1
0
0
2
0
0
2
0
0
0
1
1
0
0
0
0
0
1
0
0
0
2
0
2
0
0
2
1
0
0
0
2
0
2
0
3
0
2
1
2
0
2
1
0
0
0
0
0
0
1
2
0
2
0
0
0
1
1
2
0
1
2
2
0
1
1
1
0
1
0
0
1
0
0
1
0
1
0
1
0
0
2
1
1
0
0
0
1
0
0
3
0
1
0
2
0
1
0
2
2
2
2
0
3
2
0
0
2
0
0
3
1
0
0
0
1
2
0
1
0
2
0
1
0
0
0
0
2
0
1
0
1
0
0
0
2
0
0
0
0
2
0
0
0
1
1
0
1
0
0
0
5
1
0
0
1
0
0
2
1
1
0
1
1
0
0
0
1
0
0
0
0
1
2
0
0
1
1
0
2
0
0
0
1
2
0
0
0
2
1
2
1
1
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
3
1
1
0
2
0
2
1
0
0
1
0
0
0
0
2
0
0
0
1
0
1
0
0
2
1
0
0
0
1
0
1
1
0
0
1
2
0
0
0
0
0
0
2
0
0
2
0
0
1
1
1
0
1
1
0
0
0
0
2
1
0
0
2
0
0
0
0
1
0
2
2
0
0
0
0
1
0
0
1
1
0
2
0
0
1
0
0
1
2
0
0
0
0
0
1
1
0
2
1
0
2
2
1
1
0
2
1
0
2
0
2
0
1
0
1
0
0
0
0
2
0
2
1
2
0
0
1
1
0
1
0
0
2
0
0
0
2
1
0
2
0
2
0
0
0
0
1
0
0
1
1
0
0
0
2
2
0
0
1
0
1
1
2
2
0
0
0
1
0
0
1
2
0
0
1
0
2
2
1
0
1
2
0
2
0
0
0
0
0
0
2
0
0
2
0
2
0
2
1
0
2
0
2
1
1
2
1
0
1
0
1
0
1
2
2
1
1
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
1
2
1
0
0
0
2
0
0
0
1
0
1
0
1
0
2
1
0
0
0
2
0
1
0
2
0
2
0
0
2
1
0
2
0
1
2
0
3
2
1
0
2
0
2
2
2
0
0
0
0
1
2
1
1
2
0
1
0
0
3
1
2
0
0
2
0
1
0
0
1
2
2
1
0
2
1
2
1
0
0
0
0
0
0
0
1
1
0
3
2
1
1
0
2
4
0
1
0
2
0
0
0
3
0
0
1
1
1
2
0
1
0
0
2
3
1
0
0
0
0
0
0
1
1
0
0
2
0
1
0
0
0
0
1
0
0
2
0
2
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
1
1
0
0
0
0
0
0
1
0
2
0
2
2
0
0
1
2
2
0
0
0
0
0
2
2
0
0
0
0
1
2
2
0
1
2
0
0
2
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
2
2
0
2
2
1
0
1
2
0
1
2
2
0
2
0
0
1
1
0
0
0
2
0
0
2
0
0
0
0
1
0
0
2
0
0
2
1
0
1
0
0
0
0
0
2
0
0
0
1
1
0
1
0
0
4
2
1
0
1
1
0
2
0
1
1
1
0
0
3
0
2
0
0
1
0
0
0
0
2
0
0
1
0
1
0
1
0
0
1
2
0
1
0
1
0
0
0
0
1
2
0
2
0
0
0
2
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
2
1
1
1
0
0
0
0
0
1
0
3
1
2
0
2
0
2
0
0
0
0
0
1
2
1
0
0
0
0
0
0
1
3
2
1
0
1
1
2
0
1
2
2
0
2
0
1
1
1
2
0
1
0
2
0
2
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
2
4
0
0
1
1
1
1
2
1
1
0
0
1
2
0
2
0
0
0
0
0
0
1
1
2
0
2
0
0
0
2
0
0
0
0
1
0
0
2
1
0
1
0
1
2
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
2
1
0
0
0
2
1
0
0
2
2
0
2
0
2
0
0
0
2
0
1
2
1
1
2
0
0
0
1
0
1
0
0
1
2
0
1
1
1
1
0
0
0
2
0
1
1
0
1
2
0
0
1
4
0
1
0
1
0
0
1
0
1
0
0
1
0
0
0
0
2
0
2
0
2
2
2
2
2
1
0
0
1
0
1
0
0
1
1
2
0
1
0
0
2
0
0
0
1
0
0
1
1
1
0
0
2
0
0
1
2
1
2
1
0
2
2
0
2
1
2
0
1
0
0
0
0
1
2
1
0
0
0
2
0
1
0
0
2
2
1
2
0
0
0
2
0
1
1
1
1
0
1
1
1
2
0
0
0
0
0
1
0
2
0
2
0
1
2
1
1
1
2
2
0
1
1
1
0
2
1
0
1
0
0
0
0
0
1
0
0
1
0
2
1
0
1
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
2
0
1
2
0
0
0
2
0
1
1
0
1
0
3
0
0
0
0
1
0
1
1
0
0
0
1
0
2
1
1
1
0
1
1
2
2
0
1
0
0
1
1
1
0
0
0
0
0
2
1
0
1
1
0
0
0
0
0
3
2
0
0
2
0
0
2
2
0
3
0
0
1
0
1
0
1
0
1
0
0
0
2
2
0
0
2
2
1
2
0
0
0
2
2
0
2
0
0
0
1
1
2
2
0
0
0
0
2
0
0
0
0
1
0
1
0
0
3
0
0
1
0
1
0
2
0
2
1
2
1
0
0
0
0
0
0
0
0
0
0
0
3
0
1
1
0
1
0
2
0
2
0
0
0
0
2
0
0
2
2
0
1
2
0
0
2
1
0
0
0
2
2
0
2
0
0
0
0
1
2
1
1
1
0
0
0
1
1
0
1
0
2
1
0
0
0
2
1
1
0
1
1
0
2
0
0
0
0
2
2
0
1
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
2
1
1
2
0
0
0
1
0
0
1
1
0
1
1
0
2
0
0
0
0
1
0
0
0
4
1
1
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
1
0
0
1
2
2
1
0
2
0
0
1
1
0
2
0
0
0
0
1
0
0
2
1
2
0
2
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
4
0
0
1
1
0
0
1
4
0
0
0
0
1
0
2
0
1
0
2
0
1
0
1
2
1
0
0
0
1
0
0
0
2
0
0
0
1
1
2
0
1
0
0
0
2
0
0
0
2
1
0
0
0
1
1
1
2
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
2
1
1
0
1
0
0
0
0
0
0
1
1
0
2
0
0
1
0
1
0
0
0
2
0
2
11
0
1
0
0
0
1
1
2
1
1
1
0
3
0
0
0
0
2
2
2
0
0
0
0
0
2
1
2
0
0
2
0
0
1
1
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
2
1
0
1
0
2
0
0
1
1
2
1
0
0
0
0
3
1
0
1
1
0
0
0
0
1
0
0
0
0
2
2
0
2
1
1
1
2
1
0
0
2
0
2
0
0
1
1
1
1
0
0
0
3
1
2
0
1
0
0
0
0
2
0
0
1
1
0
1
0
0
1
0
1
0
2
0
2
0
0
0
0
2
0
0
0
0
2
2
1
1
2
0
0
2
1
2
1
0
2
1
2
1
0
0
1
0
1
0
0
2
3
0
2
1
2
0
2
1
0
2
1
0
0
0
0
0
0
3
0
1
2
0
0
2
0
2
1
0
0
0
2
2
0
0
2
4
2
0
0
0
1
1
0
0
2
1
1
0
1
0
2
0
2
2
0
1
0
0
0
0
1
0
1
2
0
0
1
1
0
1
0
1
0
0
0
0
0
2
2
0
2
0
1
0
1
0
0
2
0
2
0
1
0
2
0
2
0
0
1
0
2
1
1
1
0
0
1
2
1
2
1
2
2
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
2
0
1
0
1
2
2
0
1
1
0
1
0
0
1
0
0
0
0
0
2
3
2
4
0
0
0
1
0
1
2
1
0
2
3
0
0
2
2
0
0
1
0
1
0
0
2
0
2
2
0
0
1
1
1
1
1
2
0
2
1
2
0
0
0
0
1
2
0
0
0
0
0
0
1
2
0
1
1
0
0
2
0
1
0
0
0
0
1
1
2
0
2
0
1
0
1
2
1
0
1
0
1
1
1
0
2
0
0
0
1
1
0
1
1
0
2
1
1
1
1
1
0
0
0
0
0
0
0
3
0
0
2
0
0
2
2
1
0
1
0
0
0
0
0
2
2
0
1
0
2
0
1
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
1
1
2
1
0
2
0
2
0
1
0
0
0
1
2
1
0
1
0
1
0
0
0
0
2
0
2
0
3
1
1
1
0
1
0
2
0
1
1
1
0
0
1
1
1
1
0
0
3
1
1
2
2
0
0
0
0
0
0
0
4
2
0
0
1
0
0
0
2
1
0
0
1
0
1
1
1
1
1
0
0
0
2
2
0
2
2
2
1
0
2
2
1
0
2
0
1
0
0
0
0
1
0
1
0
1
1
0
0
1
1
0
2
1
3
1
0
0
1
0
0
0
0
2
1
1
1
3
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
2
1
2
1
0
0
0
1
0
2
1
1
0
1
0
6
1
2
1
0
0
0
2
0
1
0
1
2
1
2
3
0
1
0
1
2
1
1
0
1
0
0
2
0
0
2
1
0
0
1
0
0
1
0
0
0
2
1
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
1
1
0
0
1
0
1
1
1
2
0
0
0
1
0
0
1
0
0
0
0
0
2
0
2
0
0
1
0
0
1
0
0
2
1
0
2
1
5
0
0
0
0
2
0
0
1
2
0
2
1
1
0
0
2
0
0
0
3
2
0
1
0
0
0
2
0
0
0
1
0
1
1
2
1
2
0
0
0
0
2
1
2
0
2
1
1
0
0
0
0
0
2
0
1
0
1
2
1
0
2
1
0
1
0
1
0
0
1
2
2
0
2
0
2
0
2
1
0
0
0
1
0
0
1
0
1
1
2
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
1
1
1
2
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
3
1
0
2
0
1
0
0
0
0
1
0
0
0
0
1
1
1
2
0
0
0
0
0
0
0
3
0
1
0
2
0
0
0
0
1
1
2
1
0
0
0
0
2
1
0
0
1
0
2
0
2
2
0
2
1
0
2
0
2
1
0
1
2
0
1
0
2
2
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
2
0
4
0
0
0
0
0
4
0
0
1
1
0
2
0
1
1
1
0
0
0
1
1
0
0
1
0
0
0
1
0
0
1
0
2
0
2
1
2
1
2
1
0
0
2
2
1
1
0
0
0
0
1
0
0
1
1
3
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
1
1
0
2
1
0
2
0
1
1
0
2
0
1
0
0
0
2
2
0
2
0
0
1
2
2
0
0
1
3
2
2
2
0
2
0
0
0
0
1
0
2
4
0
2
1
0
2
0
0
2
1
1
0
0
0
2
0
0
0
0
2
0
1
7
2
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
1
1
2
0
2
0
1
1
0
0
0
1
1
2
1
0
0
2
0
0
0
0
0
1
1
0
1
0
0
2
0
1
0
1
0
0
0
3
1
2
1
1
0
2
2
0
2
1
0
2
0
1
1
1
1
2
1
0
0
0
0
2
1
0
1
2
1
0
3
1
0
2
2
0
1
0
0
0
1
1
2
2
0
0
1
1
1
2
2
2
0
1
1
1
0
0
1
0
0
1
1
0
0
0
0
2
2
0
0
0
0
1
0
0
2
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
2
0
2
0
1
0
1
0
2
0
0
0
2
0
0
1
0
1
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
2
0
0
0
0
1
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
3
0
1
0
2
3
2
2
2
1
0
0
0
1
0
0
0
2
1
1
1
2
2
1
0
0
2
0
0
0
2
0
1
2
2
1
1
0
0
0
1
3
1
4
1
3
1
0
0
1
0
2
1
1
2
2
5
0
2
2
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
1
0
1
2
0
2
0
0
0
0
0
1
1
3
0
0
0
1
0
1
0
0
0
3
1
0
0
0
0
0
1
2
0
0
2
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
1
2
1
2
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
2
2
1
1
2
2
0
0
0
0
2
1
1
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
1
2
1
3
1
0
0
2
0
1
0
0
2
0
0
0
2
1
1
1
1
2
0
0
4
2
0
1
0
0
2
0
0
0
1
0
0
0
0
0
1
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
1
0
1
0
1
0
3
2
2
0
1
1
0
0
0
2
0
0
0
2
0
0
2
3
0
0
1
1
2
2
0
0
2
2
2
2
1
2
0
0
1
0
2
1
0
0
0
1
2
0
0
1
0
0
0
0
0
1
2
4
0
0
0
1
2
0
2
0
0
2
3
1
3
0
0
2
0
2
0
2
0
0
2
0
1
0
0
1
2
0
2
0
0
0
4
1
0
0
0
2
1
1
3
1
1
0
0
0
0
0
1
0
1
0
0
1
0
0
1
1
0
1
1
0
0
0
0
2
1
2
1
0
1
2
0
0
1
0
1
1
1
0
2
0
0
1
1
2
1
1
0
2
0
2
1
1
0
2
0
1
2
2
0
1
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
1
1
0
2
1
1
1
1
0
1
1
0
0
1
2
3
0
0
1
2
0
0
0
1
0
0
0
0
2
2
2
1
0
2
0
0
3
0
1
0
3
2
0
0
0
2
0
1
0
2
0
0
2
1
0
0
1
0
2
0
1
0
1
0
1
1
2
0
2
3
0
1
2
0
0
1
0
0
0
1
2
2
0
0
0
0
0
1
0
1
0
1
1
2
2
0
0
0
0
0
0
1
2
2
0
0
0
2
0
0
0
0
1
0
0
0
0
2
2
0
1
2
2
0
2
1
1
2
1
0
0
2
0
2
2
0
2
0
2
0
1
0
2
0
2
0
0
2
0
0
1
0
0
0
0
0
2
1
1
0
2
0
2
2
0
1
1
0
0
0
0
2
2
1
0
1
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
2
0
1
1
0
1
1
1
2
0
0
0
1
1
2
0
0
1
1
0
1
0
0
0
0
1
2
1
0
0
0
1
1
0
2
0
2
1
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
1
1
3
0
0
0
2
1
1
0
2
0
2
0
1
1
0
1
0
1
0
0
0
0
0
2
0
2
0
0
0
2
1
1
0
0
1
1
0
1
1
2
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
1
1
0
0
1
2
2
0
1
0
0
1
2
0
1
2
2
0
1
1
0
1
2
1
1
0
0
1
1
0
4
1
1
2
0
0
1
0
0
0
0
0
0
1
0
0
2
0
1
0
1
0
1
1
0
1
0
2
2
0
1
0
1
0
2
1
0
0
2
1
0
1
0
0
0
3
0
0
1
0
0
2
0
3
0
0
1
1
1
1
1
0
0
0
1
1
0
0
1
1
0
1
0
1
3
1
2
1
2
0
1
2
1
0
0
1
0
0
0
0
1
2
0
2
0
1
0
0
2
1
1
0
0
0
0
2
1
0
0
2
0
0
0
0
0
1
0
1
0
1
0
0
0
2
0
2
1
1
0
0
0
0
0
0
1
0
1
0
2
3
3
2
0
0
0
2
1
0
2
0
0
0
3
0
0
0
0
1
1
1
0
2
1
0
0
0
1
9
0
0
0
0
1
2
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
2
2
1
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
2
1
2
0
2
0
0
1
2
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
3
1
0
0
1
2
0
0
2
2
0
0
2
0
0
1
0
2
0
0
2
2
0
2
0
2
1
0
1
0
1
2
0
0
1
0
1
1
0
1
1
0
0
0
0
0
0
2
0
1
1
0
1
0
0
0
0
0
0
2
0
0
0
1
0
2
0
1
0
2
1
2
2
0
0
0
1
2
2
0
1
0
10
0
2
1
0
0
1
0
0
1
0
1
2
0
0
0
2
1
0
2
0
0
2
0
0
2
1
1
0
3
0
0
0
1
0
0
0
0
2
0
1
0
0
2
2
0
1
0
0
2
2
0
0
0
1
0
0
1
1
1
2
0
1
0
0
1
2
1
0
1
0
0
1
1
0
1
0
0
0
0
0
3
2
0
1
0
3
0
1
0
0
0
1
0
2
0
2
0
1
0
1
2
1
0
2
1
2
0
2
2
0
0
0
1
2
0
0
0
1
2
0
0
1
1
0
0
1
2
0
0
0
0
0
2
1
2
1
0
0
1
1
0
0
2
0
0
0
2
0
1
1
0
1
0
2
0
2
1
0
0
2
3
1
0
0
0
1
0
0
0
0
0
0
1
2
0
3
0
2
1
1
0
0
0
1
0
1
0
2
0
0
0
0
0
2
2
0
0
1
0
2
2
0
1
3
0
0
1
1
0
2
2
1
2
3
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
5
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
3
0
0
1
2
0
0
0
0
0
1
1
0
2
0
1
0
0
1
1
0
2
0
0
1
0
2
0
0
1
0
0
0
1
0
2
2
0
0
0
0
2
0
0
2
0
0
0
0
1
2
0
2
1
1
1
1
0
0
0
1
0
0
0
2
0
0
0
2
2
0
0
0
0
2
2
0
3
0
0
0
0
2
1
3
0
1
0
0
0
2
2
0
0
0
3
1
0
0
2
0
0
0
0
2
2
1
2
1
2
0
0
2
0
0
0
1
0
0
1
0
1
2
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
2
2
0
1
0
0
2
1
1
0
0
2
1
0
2
2
1
1
0
1
2
0
0
1
2
2
2
0
1
1
2
0
0
0
1
0
1
0
0
0
0
2
1
2
0
2
1
0
2
0
0
0
1
0
2
1
1
0
0
0
1
0
2
1
0
2
0
0
0
1
1
0
0
0
0
4
2
3
1
2
0
0
0
0
0
2
2
0
0
2
1
1
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
1
1
2
1
0
0
0
1
1
0
2
0
1
1
2
0
1
0
0
0
0
0
2
2
1
0
0
1
0
1
0
0
0
0
0
1
1
1
0
0
0
2
1
0
0
1
0
1
3
2
2
3
0
2
0
0
0
0
0
0
0
0
2
0
0
1
2
2
1
0
2
0
1
1
0
0
1
0
0
2
0
0
2
0
0
2
1
0
0
0
2
1
0
2
1
2
2
0
1
0
0
1
0
0
1
0
0
0
2
0
1
1
3
0
1
0
1
0
1
0
0
1
1
2
1
0
1
1
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
1
2
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
1
0
0
1
2
1
1
0
2
0
2
2
0
1
0
1
3
0
0
0
0
2
0
0
0
0
1
0
4
1
0
0
0
2
1
0
0
3
0
1
3
0
0
0
1
0
1
0
1
0
1
0
1
0
0
0
0
1
0
0
0
2
0
0
2
0
0
1
1
0
0
1
1
2
1
1
1
1
1
1
0
2
2
2
1
1
1
1
0
0
2
0
0
2
1
0
1
2
0
0
0
2
2
0
0
1
1
2
0
0
1
1
1
1
1
2
0
0
0
0
0
1
1
1
0
0
0
2
1
1
0
2
0
0
2
0
1
0
0
0
0
2
0
0
2
0
2
2
1
2
0
1
2
0
2
2
0
2
1
0
0
0
0
0
0
0
2
2
1
0
0
1
0
1
1
0
1
1
2
2
1
2
2
0
1
0
1
1
0
0
2
1
2
0
2
1
0
0
0
2
0
0
2
1
1
0
3
0
0
2
2
0
2
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
1
0
0
4
2
1
0
2
2
0
0
0
2
2
2
0
0
0
1
0
1
2
2
0
1
0
0
1
1
0
0
0
2
0
1
2
1
0
1
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
4
2
0
0
1
1
0
0
1
1
1
1
1
0
1
0
0
2
0
0
0
1
1
0
2
0
1
5
1
2
1
0
0
0
0
1
1
0
0
0
2
0
2
2
0
0
3
1
0
2
0
0
0
1
0
2
0
0
0
2
0
1
0
0
2
0
0
2
0
0
0
1
0
1
2
1
0
0
0
0
1
0
1
0
2
2
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
1
0
1
0
4
0
0
0
0
0
1
2
0
1
0
0
0
1
0
2
0
0
0
1
0
1
1
0
0
1
0
2
3
1
2
0
0
2
1
1
2
1
2
1
0
0
2
0
0
2
1
0
0
0
0
0
0
0
1
1
0
0
1
0
2
0
3
1
0
2
0
0
2
0
0
0
0
0
2
1
1
1
0
1
0
1
0
0
1
1
0
0
1
1
1
2
0
0
1
1
2
1
0
0
1
1
1
1
0
0
0
1
0
0
0
3
2
0
0
2
2
1
0
0
0
0
2
0
1
1
2
0
0
2
2
0
1
0
3
2
0
0
0
0
0
1
0
0
0
0
2
0
5
0
0
0
1
1
0
2
0
0
0
0
1
1
2
1
2
1
2
1
2
1
2
0
1
1
0
0
0
0
0
0
2
0
2
1
1
0
2
0
0
2
0
1
1
1
0
0
0
1
0
0
0
1
0
0
0
2
0
0
1
0
0
2
0
0
1
0
0
0
0
1
0
1
0
1
1
0
0
2
0
1
1
1
0
0
1
1
1
0
0
0
0
0
3
0
0
5
0
0
0
1
0
0
0
0
0
1
0
2
1
0
0
2
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
2
0
0
1
0
0
0
0
1
0
2
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
2
1
0
0
0
1
2
2
2
0
0
0
0
0
0
0
1
2
2
1
1
2
0
2
0
0
0
0
2
1
0
2
0
0
0
0
1
0
1
0
1
1
2
0
0
0
2
0
1
2
1
3
0
2
0
2
0
0
1
2
1
0
0
0
2
0
2
2
2
2
1
0
0
0
0
0
0
2
0
1
2
0
0
2
0
0
2
0
1
0
1
0
0
2
0
2
1
2
0
2
0
1
2
2
2
0
1
0
0
0
0
0
0
2
1
1
0
0
1
0
1
0
1
0
0
0
0
0
0
2
0
0
0
1
1
0
0
2
1
1
1
1
0
2
1
0
1
1
0
1
2
0
2
1
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
2
0
0
0
2
0
0
0
1
0
0
0
0
1
1
2
0
2
0
6
2
2
1
0
1
0
0
0
2
2
0
0
0
2
1
1
2
0
0
1
1
3
0
0
1
0
2
0
0
1
1
0
2
0
2
0
0
0
1
2
1
0
2
1
0
0
2
0
0
0
2
0
0
1
1
0
2
0
1
1
2
0
1
0
0
2
2
0
2
1
2
0
1
0
0
1
2
0
0
1
1
2
2
2
2
0
3
1
0
1
0
0
2
1
1
0
2
0
0
0
2
1
0
2
1
0
2
0
1
0
0
0
2
0
0
0
2
1
0
0
1
0
2
2
1
0
1
0
1
1
2
0
0
0
0
2
1
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
2
0
0
2
1
0
0
1
0
0
0
2
2
1
0
1
0
0
0
0
3
0
1
2
1
0
0
0
2
0
2
0
2
2
0
1
0
1
0
0
0
1
2
0
2
1
1
1
0
1
0
1
5
1
1
0
2
1
0
1
0
1
2
0
1
0
0
0
4
0
0
0
0
0
2
2
2
0
0
0
3
0
2
0
1
0
2
0
2
3
0
0
2
0
0
2
1
2
2
0
0
2
1
0
1
1
0
2
1
0
0
1
3
0
0
2
0
2
1
0
0
0
2
0
2
1
0
0
0
1
2
0
2
0
1
0
4
0
0
1
0
3
0
0
2
0
1
0
1
2
2
0
0
0
1
0
2
0
2
0
2
0
0
0
1
2
2
0
0
1
0
0
0
1
1
0
3
0
0
0
1
0
0
0
0
2
0
1
1
3
0
3
0
1
1
1
0
0
4
0
1
0
0
0
0
0
2
0
1
1
0
2
0
0
0
2
0
1
0
0
2
1
2
0
1
3
0
0
0
0
1
2
0
0
0
2
0
0
2
2
1
0
2
1
0
0
8
3
0
0
1
0
2
1
0
2
0
0
2
0
0
0
0
0
0
1
1
0
2
0
2
1
0
0
2
1
1
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
2
0
0
2
1
0
1
0
2
0
1
0
0
0
2
0
0
2
2
0
2
0
0
0
2
1
2
0
2
0
0
1
1
0
1
0
2
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
2
1
1
2
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
1
2
0
2
2
0
1
1
1
2
0
3
0
0
0
0
2
0
0
0
2
0
2
0
0
2
1
1
0
0
1
1
2
1
0
2
1
0
0
1
0
0
2
1
0
1
2
0
0
0
0
0
2
0
2
0
1
2
1
0
0
0
0
0
0
0
0
2
0
2
2
0
0
1
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
3
1
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
6
2
0
1
0
2
1
2
1
0
0
1
1
0
0
2
0
0
1
1
2
1
0
0
0
1
1
0
0
2
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
1
0
1
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
1
0
0
1
1
2
0
1
1
0
3
0
1
0
0
0
0
0
2
0
0
0
2
2
0
2
0
0
1
2
1
2
2
0
1
0
1
0
1
0
0
2
1
0
3
1
1
0
1
0
0
0
1
2
0
1
2
0
0
0
0
1
1
0
0
0
0
1
2
1
2
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
2
0
1
1
0
2
0
0
0
0
0
5
0
0
0
2
2
2
1
1
1
0
0
0
1
0
0
0
0
0
1
2
0
3
4
0
1
0
1
1
1
0
0
0
0
1
0
0
1
0
1
1
0
0
0
1
0
2
1
0
0
1
0
1
0
0
1
0
1
0
0
2
0
2
1
0
0
1
0
0
0
0
1
0
1
0
0
0
3
1
1
2
0
1
0
0
0
2
0
0
0
1
0
0
3
0
0
0
2
0
2
2
0
0
0
2
1
0
0
1
1
0
2
1
1
1
0
2
0
0
0
0
0
2
0
2
1
0
0
2
0
2
2
0
0
1
0
1
0
0
2
2
0
2
2
0
0
2
0
1
2
2
1
0
1
0
0
0
0
0
1
0
0
1
0
3
0
2
0
3
1
1
2
2
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
9
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
2
1
2
0
2
0
0
0
0
1
0
0
1
2
0
0
1
1
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
1
0
0
2
1
1
0
0
0
1
0
0
0
1
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
1
0
0
0
1
0
0
2
2
2
0
2
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
4
1
1
0
2
1
1
2
2
0
0
3
0
2
1
0
1
0
1
0
0
0
0
2
0
0
1
0
0
3
0
2
2
2
2
0
2
0
1
0
0
1
1
1
1
0
0
2
1
0
1
0
0
0
0
1
1
1
1
2
1
2
1
0
0
1
3
0
1
0
2
1
0
0
1
0
2
1
0
0
1
0
1
1
2
0
0
0
2
2
0
0
1
0
2
0
1
1
1
2
0
2
1
0
1
2
0
0
0
0
0
1
2
0
2
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
1
0
0
2
0
0
0
2
0
0
0
1
0
1
0
1
0
2
1
2
1
0
2
0
0
2
2
2
1
0
2
0
0
2
1
0
0
1
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
2
1
0
2
1
0
0
1
0
2
1
0
0
2
0
0
0
0
1
0
0
0
2
0
0
3
0
2
0
0
0
0
0
0
2
0
0
1
1
0
1
0
0
0
0
1
0
1
0
1
1
2
0
0
1
0
0
0
0
1
2
2
0
2
0
2
2
0
0
1
0
0
0
0
0
0
2
0
1
0
2
1
1
1
0
0
0
1
0
2
1
0
0
1
2
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
1
2
0
2
0
1
0
0
0
0
2
2
1
2
0
1
0
0
1
1
2
0
0
2
0
1
0
0
0
0
0
1
1
0
1
0
2
2
0
1
0
0
0
2
0
0
0
0
0
2
1
1
2
0
2
1
0
1
0
2
0
0
2
0
0
0
0
1
0
1
0
0
2
0
2
2
0
0
2
0
2
2
1
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
2
2
1
0
0
1
2
0
2
1
1
0
2
0
2
0
0
2
2
0
2
0
2
0
1
0
2
0
1
1
0
0
0
1
0
2
1
1
1
0
3
0
1
0
0
0
0
2
0
1
0
0
2
0
0
0
1
0
1
0
2
0
1
0
0
1
1
0
1
1
1
0
0
0
1
0
0
1
1
2
0
0
0
0
1
0
2
2
0
0
1
2
0
0
2
0
0
2
1
0
0
0
0
1
0
2
2
2
0
0
1
0
2
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
2
0
0
1
1
0
1
0
0
0
0
0
1
0
0
2
0
2
1
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
2
0
2
0
0
0
0
1
1
0
0
1
1
0
0
1
0
2
2
1
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
1
0
1
0
0
1
2
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
1
3
0
0
0
1
1
0
0
0
2
0
0
0
1
0
0
0
2
0
0
2
1
0
0
0
0
2
1
2
1
0
1
0
1
0
0
0
0
2
0
1
1
2
0
0
1
1
2
0
1
2
1
1
0
0
0
0
2
0
1
0
0
1
3
0
1
0
0
0
2
1
0
0
1
1
1
0
2
1
0
0
3
0
0
0
1
0
1
0
0
2
0
0
1
1
0
2
0
0
1
0
1
0
0
1
3
0
0
0
1
0
4
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
1
1
0
0
0
2
1
0
1
1
0
0
0
0
1
0
2
1
0
0
0
2
1
1
0
1
0
2
0
0
0
2
2
2
2
1
0
0
0
1
0
0
1
1
0
0
2
1
0
2
1
0
0
1
0
0
2
0
2
0
0
0
0
2
0
1
1
2
2
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
2
0
1
0
1
1
2
0
1
1
1
0
0
3
1
1
1
1
1
0
1
1
4
0
2
2
0
0
0
1
0
2
0
0
1
1
1
1
0
2
2
1
0
1
1
1
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
1
2
0
1
0
1
2
2
1
1
0
1
0
0
0
0
0
0
1
1
2
1
1
2
1
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
1
1
1
1
0
1
1
0
2
0
0
0
2
0
2
1
0
0
2
1
0
0
0
4
1
0
0
0
0
0
1
2
1
2
1
0
2
0
2
1
0
2
0
1
0
0
0
0
1
1
2
0
0
0
2
1
0
0
0
1
2
0
0
0
0
2
1
0
1
0
1
0
0
2
1
1
1
1
0
0
0
0
0
0
0
0
2
0
0
0
2
1
1
0
0
1
2
0
0
0
0
1
1
1
2
0
2
2
0
0
0
1
0
0
0
5
0
0
0
1
1
0
2
1
2
1
1
2
0
0
0
1
2
1
0
0
2
1
0
1
0
2
2
0
1
2
0
1
0
0
0
0
0
0
2
0
2
2
1
1
1
1
0
1
3
1
2
2
0
0
0
0
1
1
0
0
0
1
1
1
1
1
0
2
0
0
0
0
0
0
4
3
0
0
5
2
0
0
0
1
1
0
0
1
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
2
0
1
0
1
2
2
2
0
0
0
1
0
5
0
0
0
0
1
0
0
0
0
1
0
1
2
1
2
1
0
1
0
0
1
3
2
1
0
2
15
0
2
0
2
1
1
0
2
4
2
2
0
0
1
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
1
1
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
2
3
0
0
0
0
2
0
0
1
0
1
0
2
3
3
0
0
0
0
1
1
1
0
1
0
0
2
0
0
1
1
2
1
0
0
2
0
0
0
1
1
0
0
3
1
0
0
2
0
0
0
2
2
0
0
1
1
0
1
0
2
2
0
2
0
3
0
0
1
1
2
0
2
1
0
0
0
1
0
0
1
0
1
1
2
1
0
0
2
1
0
0
0
2
2
0
0
0
2
2
0
0
0
0
1
1
2
0
2
0
1
2
0
1
2
1
1
2
0
0
2
0
1
1
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
2
1
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
1
2
2
0
2
0
1
0
0
1
1
1
0
0
0
2
0
0
1
0
2
2
0
0
0
1
0
1
1
0
0
1
0
2
0
0
0
0
1
2
2
1
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
2
2
0
0
0
1
2
0
0
2
0
2
0
1
2
1
2
0
1
0
0
0
0
2
2
1
0
1
0
0
1
1
1
0
0
1
0
1
0
1
0
0
1
0
0
0
2
1
0
0
1
0
1
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
2
2
1
0
1
2
0
2
0
0
1
1
2
0
1
0
1
1
2
1
0
0
2
1
1
2
1
0
1
2
1
0
0
2
3
0
2
1
1
0
0
0
0
2
0
0
1
2
2
2
1
2
0
0
0
0
1
2
1
0
1
3
1
0
0
2
0
1
1
0
1
3
0
0
0
3
0
2
0
0
2
0
8
0
1
0
0
1
1
0
3
0
0
2
0
0
0
2
1
0
1
1
0
0
1
2
0
2
2
0
2
0
1
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
2
1
2
0
1
0
2
1
0
0
0
0
0
1
1
1
0
1
0
2
0
0
1
0
1
2
1
0
0
0
0
0
1
2
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
1
1
0
0
1
0
0
0
2
1
0
1
1
0
1
1
1
2
1
1
2
2
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
2
1
0
1
1
0
2
3
1
0
0
2
0
1
0
2
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
1
2
2
0
1
0
1
0
2
1
1
0
0
0
2
0
0
0
1
0
0
1
0
0
1
1
0
1
2
1
2
1
0
0
0
0
2
1
2
0
0
0
0
0
0
2
2
1
2
1
0
0
0
0
2
2
0
1
2
0
0
1
0
0
0
1
0
1
0
1
0
2
1
1
2
1
0
0
2
2
2
1
2
2
0
1
1
0
1
0
0
2
1
1
1
2
0
0
0
2
1
0
2
0
0
1
1
0
0
3
1
3
1
2
2
1
1
0
1
1
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
2
0
2
2
2
1
0
0
1
1
0
1
0
0
0
0
2
0
1
1
1
0
1
0
0
1
2
2
0
2
0
1
1
0
0
1
0
2
2
0
0
0
1
2
1
0
0
2
0
0
1
0
0
0
1
1
2
0
0
2
2
0
0
0
0
0
2
1
1
0
0
0
2
0
0
0
0
2
0
0
1
0
0
1
1
0
1
1
1
2
0
0
0
2
1
2
1
0
2
0
1
0
0
0
2
0
0
2
0
0
0
0
1
1
1
0
0
0
0
1
0
2
2
0
0
0
0
2
3
0
0
0
1
0
0
0
0
0
1
0
0
1
0
2
2
0
0
0
1
0
2
1
3
0
1
1
2
2
0
0
0
0
1
0
0
0
2
0
0
0
1
2
1
1
0
2
0
0
0
0
1
0
2
2
1
0
1
0
0
0
2
1
0
0
0
4
1
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
1
0
0
0
2
1
0
0
0
0
2
1
1
0
0
0
0
3
0
2
0
1
1
1
0
1
0
0
0
2
2
0
0
0
1
2
1
0
2
0
0
1
0
1
0
3
0
1
0
1
1
2
0
0
0
0
2
0
0
0
2
0
2
0
2
0
0
0
1
0
1
0
2
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
9
2
2
0
2
0
0
0
5
4
1
0
0
2
0
0
2
0
2
0
3
0
0
0
0
0
2
0
2
0
2
1
1
0
0
2
0
1
1
1
0
2
2
0
1
2
0
0
1
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
1
1
0
2
1
1
1
2
0
2
0
0
0
0
0
0
0
2
1
1
0
0
2
3
1
0
0
1
0
0
1
2
0
0
0
0
0
0
0
2
1
1
1
0
1
1
0
0
0
2
2
0
0
0
1
0
0
0
0
2
0
2
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
3
1
0
0
0
0
0
1
0
0
1
1
2
0
0
1
0
0
0
1
0
0
2
1
0
0
2
2
0
1
1
2
2
2
1
0
1
0
1
0
0
0
1
2
1
0
0
1
1
1
1
1
0
2
1
0
2
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
1
0
7
0
0
2
0
2
0
2
0
2
2
1
0
0
0
0
0
0
2
1
1
0
1
0
0
0
0
0
2
1
0
0
1
1
2
0
0
0
0
1
0
1
0
0
1
2
1
0
0
0
1
0
0
0
2
0
0
0
0
0
1
1
0
2
0
2
0
0
2
0
0
1
1
1
0
2
0
0
0
2
2
2
1
0
1
0
0
0
0
1
0
2
0
2
0
1
0
2
1
1
0
1
2
0
1
1
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
1
2
0
2
0
0
0
2
1
1
0
0
2
0
0
1
2
2
0
2
0
0
0
0
0
1
1
2
0
0
0
1
2
0
0
0
0
0
0
0
2
0
2
2
0
1
1
0
0
0
0
2
1
1
2
0
0
0
0
0
1
1
0
2
1
0
0
2
0
0
0
0
1
1
1
1
0
2
2
2
0
0
2
1
0
0
0
2
0
0
1
0
0
0
0
1
2
0
0
2
1
0
1
1
0
0
0
1
0
0
0
2
2
1
0
1
0
1
0
1
1
0
1
2
2
2
0
0
0
0
1
0
2
2
0
0
0
2
2
1
0
0
0
0
1
0
3
1
0
0
0
1
1
2
2
5
0
1
0
0
2
0
0
0
0
0
1
1
0
3
1
0
0
1
0
0
2
0
2
1
1
0
2
0
3
0
2
1
0
1
1
1
0
0
2
1
0
1
0
0
0
0
1
0
2
0
0
1
2
2
1
0
2
0
0
2
0
1
1
0
1
2
1
0
2
0
0
0
0
0
1
1
1
0
1
2
0
2
0
2
1
2
0
2
1
0
0
1
2
1
0
2
0
0
2
2
0
2
0
0
0
0
0
1
2
2
0
2
1
0
1
0
0
0
1
2
1
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
2
0
1
0
0
2
0
0
0
2
3
0
0
1
0
1
0
0
2
2
2
0
0
1
2
0
0
0
0
0
2
0
2
1
1
1
1
0
0
0
2
2
0
2
2
0
1
1
0
0
0
1
0
1
0
0
0
2
0
0
0
0
1
0
2
2
0
0
1
0
0
1
1
2
1
0
1
0
0
1
1
2
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
1
0
1
0
1
0
0
0
0
2
0
1
0
0
1
0
0
1
2
1
0
0
0
1
0
0
0
1
0
0
1
1
0
2
2
0
0
1
0
2
4
0
0
2
0
0
2
2
0
1
0
1
0
0
0
1
2
0
2
1
0
0
1
1
0
0
0
0
2
0
1
0
0
0
0
2
0
1
0
1
0
3
1
0
0
0
0
0
0
0
0
4
0
2
1
1
1
0
0
0
0
0
2
0
0
1
0
2
2
0
0
0
0
2
1
0
0
0
0
2
0
1
0
1
0
1
2
0
2
0
1
0
0
0
1
2
1
0
1
1
0
0
1
2
0
0
1
0
0
2
3
0
1
0
0
1
2
0
1
0
1
0
0
0
1
0
0
3
1
1
2
2
0
1
0
2
0
0
0
0
1
1
0
1
0
0
2
2
1
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
3
0
0
1
0
0
0
0
0
1
0
0
1
2
1
0
0
1
0
0
0
0
1
1
0
2
1
0
1
2
0
2
0
0
1
2
0
0
2
0
0
0
1
1
1
0
2
0
1
2
0
2
0
0
1
0
0
0
0
1
4
0
1
1
2
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
1
2
2
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
1
2
2
0
0
1
0
1
1
0
0
0
0
1
2
0
0
0
1
2
0
2
0
0
1
0
1
1
2
1
1
0
2
0
1
2
0
0
2
0
0
0
1
0
0
1
0
2
1
0
2
2
0
0
2
0
1
0
1
1
0
1
0
0
2
0
0
1
0
0
0
2
0
0
0
1
0
0
0
2
0
0
1
2
0
2
0
0
1
1
0
3
1
1
0
0
0
1
1
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
1
2
1
0
0
0
0
1
2
0
1
0
2
0
0
1
1
2
1
1
0
0
0
0
0
2
0
2
1
0
0
1
1
0
1
0
0
2
0
0
0
0
1
2
1
1
2
0
1
0
1
0
1
1
0
1
2
0
1
2
0
0
3
0
0
0
1
0
1
0
0
0
2
0
0
1
0
1
0
2
0
1
1
13
2
0
0
2
2
1
1
0
0
2
0
2
1
2
0
1
0
0
0
0
1
0
1
0
1
0
2
0
0
1
0
0
0
3
1
0
1
0
2
2
1
0
0
2
1
0
0
1
2
0
0
1
0
1
1
2
0
0
1
1
0
2
0
2
0
1
0
4
1
0
0
2
0
2
1
0
0
1
0
1
0
0
0
2
0
0
2
1
2
0
3
2
0
1
0
0
0
1
0
4
0
2
1
2
2
2
0
0
0
1
0
0
0
0
0
0
1
1
1
2
0
0
1
0
0
2
0
0
0
1
2
0
1
0
1
0
0
2
0
0
0
0
0
1
1
0
0
0
0
2
2
1
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
1
1
1
0
2
0
0
0
0
1
1
0
2
0
2
0
0
1
2
1
0
0
0
1
2
0
0
3
0
1
1
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
6
3
1
1
0
0
1
2
0
0
5
2
1
3
0
0
2
0
2
2
1
2
0
0
0
0
0
1
1
1
0
0
0
1
0
1
0
0
0
2
0
1
0
0
0
0
1
1
2
1
2
2
3
0
0
2
1
1
0
0
1
2
0
0
0
2
0
0
2
1
2
2
0
0
2
1
0
1
2
1
0
1
2
2
0
1
0
0
0
1
0
0
2
1
0
0
0
0
0
2
2
3
1
0
0
0
0
2
2
0
2
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
2
0
2
0
0
0
0
1
1
0
0
0
2
0
0
2
0
1
0
0
0
1
1
0
4
0
2
0
0
1
1
1
0
1
0
1
1
0
2
0
2
1
0
2
0
0
0
1
1
1
0
0
0
1
2
1
0
2
3
1
1
0
1
2
0
0
0
1
0
0
0
0
0
1
2
1
0
0
0
2
1
1
0
1
2
1
2
0
1
1
2
0
0
0
0
0
0
0
0
1
0
0
1
0
2
1
1
0
1
0
0
0
0
0
0
1
0
2
2
2
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
2
1
0
0
0
1
0
2
1
2
0
0
0
0
0
2
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
1
1
1
1
2
0
1
2
2
2
0
2
0
2
1
2
0
0
0
0
2
1
0
1
0
1
4
0
0
0
2
0
0
2
0
2
0
1
0
2
0
0
1
0
2
0
0
2
0
0
1
0
0
0
0
0
0
2
2
2
0
1
0
0
0
0
0
0
0
1
2
1
2
1
1
0
1
1
2
2
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
2
1
1
0
1
1
0
3
0
0
0
0
0
0
1
2
0
1
1
1
2
0
2
1
1
0
0
0
2
0
0
0
2
1
1
0
0
1
0
0
0
0
0
4
2
0
2
1
0
2
0
2
0
0
0
0
0
1
1
0
2
2
1
2
0
2
0
0
3
1
1
0
0
0
0
1
1
1
1
0
1
1
0
0
1
0
0
0
1
2
1
2
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
1
2
1
2
0
1
0
1
0
0
0
2
0
0
0
0
0
1
1
2
0
0
1
1
2
1
0
0
0
0
1
2
0
0
1
1
0
0
0
1
0
1
2
0
1
0
0
0
0
2
1
2
0
0
1
0
1
1
0
0
0
2
1
0
2
2
2
1
1
3
0
2
1
2
2
0
0
2
0
0
0
2
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
2
0
0
0
0
0
1
0
1
2
2
0
0
1
1
0
1
2
0
0
1
1
0
2
2
1
1
1
2
0
2
0
0
0
0
2
2
0
0
1
1
0
3
2
1
0
0
1
2
0
0
0
0
0
0
0
2
0
1
0
1
0
0
1
2
1
3
0
1
0
1
0
1
0
0
0
2
0
0
1
1
0
0
0
2
0
2
1
0
1
1
2
1
0
1
0
2
0
0
2
0
0
0
2
1
3
0
1
0
0
2
1
0
0
0
0
0
1
2
2
2
0
0
2
0
1
0
0
0
0
1
2
1
1
1
0
1
0
0
0
0
2
0
0
0
1
1
2
0
1
0
1
1
0
0
1
0
2
2
0
0
0
0
1
1
0
0
0
1
0
1
0
0
2
0
1
0
2
0
0
0
1
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
2
1
0
1
0
0
0
1
0
0
0
2
0
1
3
0
1
0
0
0
0
0
0
0
0
0
2
1
0
2
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
2
2
0
1
2
2
0
0
0
2
1
0
1
0
0
0
4
0
2
0
0
0
0
1
0
2
2
0
0
2
2
0
0
0
2
0
0
0
0
0
2
0
2
0
0
1
0
1
0
2
0
2
1
0
0
2
2
1
2
0
0
1
2
0
0
0
2
2
2
2
2
0
1
2
0
0
1
2
5
2
1
0
0
0
0
1
1
0
0
0
1
0
1
0
2
1
0
0
1
0
2
1
1
0
2
0
0
0
0
1
0
0
0
0
2
2
0
2
0
1
1
1
0
0
1
2
0
0
0
1
0
0
2
1
2
2
1
1
0
1
1
0
1
3
0
0
0
0
2
0
2
1
0
1
2
0
2
1
2
2
0
0
1
1
1
0
1
0
2
0
2
1
1
1
0
0
2
0
0
0
0
0
2
0
1
1
1
2
1
2
0
0
0
0
1
1
0
1
2
0
1
2
0
0
0
0
0
1
2
1
0
1
2
0
1
1
3
2
1
2
0
2
0
2
1
2
0
0
1
2
2
2
0
0
1
0
0
2
2
2
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
1
0
1
1
0
0
1
1
1
0
0
0
0
1
2
0
0
1
0
1
1
0
0
1
0
1
1
1
1
0
1
0
0
2
1
0
0
1
2
0
2
0
0
1
0
0
1
2
0
0
2
1
2
2
2
0
0
0
0
1
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
2
1
2
2
1
2
1
0
0
0
2
0
1
0
2
2
2
1
0
2
0
1
2
2
1
2
0
2
2
1
0
3
1
0
0
0
2
2
1
0
1
0
0
3
0
0
1
1
0
2
2
0
1
0
0
0
2
2
0
0
1
0
0
0
1
2
0
1
1
2
1
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
3
1
0
1
0
0
0
0
0
1
1
2
6
1
0
2
0
1
2
0
0
0
1
1
2
0
2
3
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
1
1
0
0
0
0
0
0
1
2
2
0
0
0
3
0
2
2
2
2
0
1
0
0
2
0
1
2
2
0
0
0
2
1
0
1
0
0
2
2
0
0
0
0
2
2
0
0
1
0
0
2
1
1
0
0
0
0
0
1
0
0
2
1
0
1
1
1
2
3
0
2
1
0
0
1
0
0
0
1
0
0
2
1
0
0
2
1
1
0
2
1
2
1
0
0
2
1
0
1
0
1
0
0
0
0
1
0
2
0
1
0
0
0
0
0
1
0
2
1
4
0
2
2
1
1
0
2
0
0
1
1
1
1
1
0
2
0
0
1
0
0
1
2
2
0
0
0
0
1
0
2
0
1
2
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
1
0
0
2
1
0
0
0
0
0
0
0
2
0
1
1
0
1
0
1
0
2
1
0
0
1
2
1
0
0
2
2
0
2
0
4
0
1
0
1
1
0
0
2
1
0
0
0
0
2
2
0
0
0
1
0
0
0
0
1
0
2
2
1
0
0
3
2
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
1
2
2
2
0
1
0
0
0
0
0
1
1
0
0
1
0
0
2
1
2
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
1
1
2
1
1
0
3
1
0
2
2
3
0
1
0
0
2
1
2
0
2
0
0
1
0
1
1
0
0
0
1
0
0
2
1
2
1
0
2
2
2
0
1
1
0
0
0
2
0
0
1
1
0
0
0
0
4
0
0
2
0
0
0
0
1
0
1
0
1
2
0
0
2
2
1
0
1
0
0
1
1
1
0
0
2
2
0
0
1
1
0
1
1
0
1
0
0
0
0
0
0
0
1
2
1
2
0
0
1
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
2
2
2
0
0
1
2
1
0
1
1
2
0
1
0
0
0
2
2
1
2
1
0
0
1
1
0
0
1
0
1
1
0
0
0
0
2
1
2
0
0
0
0
1
0
0
0
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
1
0
1
1
0
1
0
0
2
0
0
2
0
1
0
0
2
0
1
0
3
1
1
0
2
2
0
0
1
0
2
0
2
1
0
2
1
0
0
0
0
2
3
0
0
0
0
2
1
2
0
2
2
2
1
0
0
0
0
0
1
1
1
0
0
2
0
0
0
0
1
0
2
0
0
0
2
2
0
0
0
0
0
0
0
2
0
1
0
1
2
2
1
1
0
2
0
2
0
0
0
0
2
0
0
0
1
2
1
2
0
1
0
2
0
0
1
2
1
1
3
2
0
0
0
1
0
1
1
0
0
1
0
0
2
2
0
2
2
0
2
1
0
2
6
1
1
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
1
0
0
1
1
0
0
0
1
0
1
0
1
0
1
0
1
2
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
1
2
0
2
0
0
1
0
1
0
0
0
2
1
0
0
1
2
0
0
1
0
0
0
4
2
0
2
0
0
0
1
1
1
0
2
2
2
0
2
0
1
0
1
2
0
0
0
0
2
2
0
1
0
2
2
2
0
2
0
0
1
0
0
1
1
2
0
3
0
0
0
1
0
2
2
1
2
0
2
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
2
1
1
2
1
1
1
0
0
2
0
0
0
1
2
0
0
0
1
0
2
0
0
1
1
0
2
0
0
1
0
1
2
1
0
0
1
0
1
1
0
0
0
0
0
2
2
1
2
3
0
2
1
0
0
2
1
0
0
1
2
0
1
1
0
0
1
0
0
0
0
0
0
1
2
3
0
0
0
2
2
1
0
0
0
0
0
0
0
1
0
2
0
0
2
1
1
0
0
2
1
1
0
1
1
0
1
0
1
1
0
1
0
0
1
0
0
0
1
2
0
2
0
0
2
0
2
0
0
0
0
2
2
0
1
1
2
2
2
0
0
2
0
0
0
2
1
1
1
0
2
0
0
0
1
1
1
2
0
0
0
1
2
0
1
1
0
1
1
0
0
0
0
1
0
0
1
1
0
0
2
0
2
0
0
1
0
0
1
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
2
0
0
1
0
0
0
3
2
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
2
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
2
2
0
0
1
0
0
1
2
0
0
0
1
0
1
2
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
3
1
1
1
0
1
2
0
0
1
1
3
2
1
0
0
6
2
0
0
2
2
3
0
0
0
0
1
2
0
2
1
0
1
0
2
2
0
0
3
0
0
0
1
1
0
0
0
2
0
1
0
2
1
0
3
1
2
1
0
0
0
1
1
2
0
1
0
0
2
0
0
4
2
0
1
0
2
0
0
0
1
0
0
2
2
2
0
2
0
1
1
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
1
1
2
0
1
0
2
0
0
2
0
1
0
1
2
0
0
0
1
1
1
1
0
0
0
0
0
0
0
2
0
0
0
1
2
0
2
1
1
1
1
0
2
1
0
0
2
1
1
1
2
0
0
0
1
1
0
0
1
2
2
0
0
0
0
0
1
0
1
0
0
0
1
0
3
2
2
1
1
2
1
0
2
1
0
2
1
2
2
1
1
0
1
1
0
0
0
1
0
1
0
1
2
0
2
0
2
0
0
1
0
0
2
1
0
0
0
1
0
2
0
0
0
0
2
1
0
0
1
1
2
0
0
0
1
0
0
2
0
0
1
1
2
4
2
0
1
2
1
1
0
0
2
0
0
1
0
0
0
0
1
2
1
0
0
2
0
0
0
2
0
0
0
1
2
0
0
0
0
0
2
0
2
0
0
0
0
1
1
1
0
0
0
0
0
1
0
2
2
0
0
0
0
0
2
0
0
1
0
2
2
2
0
0
0
0
0
3
2
1
0
0
0
1
0
0
0
2
2
2
0
1
1
2
2
0
0
0
2
0
0
1
0
0
2
1
1
0
0
1
0
0
0
0
0
2
2
0
1
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
1
0
1
1
2
1
0
1
0
0
0
2
2
0
0
1
0
1
2
0
1
0
0
0
0
0
2
2
1
0
0
1
1
0
1
0
0
0
1
0
2
1
0
1
2
0
2
1
2
2
0
0
2
0
0
0
0
2
0
2
0
1
0
1
0
0
0
0
0
2
3
0
2
0
2
1
0
1
0
0
1
0
1
1
0
0
1
1
0
2
0
0
0
0
1
0
1
0
2
0
0
2
0
1
0
1
0
1
1
0
0
0
0
2
0
5
0
0
0
0
1
0
0
2
0
0
0
0
1
2
1
0
1
1
1
0
0
1
0
0
1
0
1
1
0
2
1
1
0
0
0
1
0
2
0
0
1
0
1
0
1
0
1
0
0
2
2
0
0
0
1
1
0
2
0
2
1
2
0
2
0
0
1
0
0
0
2
1
1
0
1
2
1
2
0
0
0
1
0
2
0
0
0
0
2
0
0
0
1
0
0
2
0
2
0
0
2
1
0
0
2
0
1
2
2
0
2
0
1
0
0
0
0
0
3
1
2
0
1
0
1
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
2
0
0
0
1
0
0
2
0
1
2
0
0
0
1
0
1
2
0
0
1
1
0
2
2
1
1
0
1
3
2
0
1
0
2
0
2
1
0
0
1
1
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
2
2
0
1
1
2
1
0
0
1
0
0
0
0
3
1
0
0
0
2
1
2
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
2
0
1
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
1
0
1
0
1
0
0
0
2
1
0
2
0
0
0
0
0
1
2
1
0
0
1
2
0
0
0
1
1
0
0
0
0
2
0
2
1
2
0
9
0
1
0
0
0
1
2
1
0
4
0
1
0
0
2
1
0
0
0
0
0
2
1
1
0
1
2
0
0
2
0
1
1
0
0
1
2
0
0
0
2
1
0
1
0
0
1
2
1
0
1
0
0
0
1
1
1
0
1
0
0
0
2
0
2
1
1
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
1
2
0
0
2
1
1
0
2
2
1
1
1
2
0
1
0
1
2
0
2
0
1
4
1
0
0
1
1
7
0
1
1
2
0
1
1
0
2
1
0
0
1
2
0
1
1
1
1
0
1
0
0
0
0
0
0
0
1
2
1
2
2
2
2
0
0
2
1
1
1
0
0
2
3
2
1
0
2
0
2
0
1
2
1
0
2
0
1
0
1
0
0
1
1
2
0
0
0
0
1
2
0
0
2
1
0
0
1
2
0
0
1
0
2
0
2
2
1
0
1
1
3
1
0
0
0
2
1
1
0
0
1
4
0
2
0
2
1
1
1
1
1
0
0
0
0
0
1
0
0
1
2
0
0
2
1
1
0
0
0
0
1
0
1
0
1
2
2
1
0
1
0
0
0
1
1
0
0
1
1
0
1
1
0
1
1
0
1
0
1
2
1
1
0
2
0
0
0
1
1
0
2
1
2
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
2
1
0
1
2
1
0
0
0
0
1
1
2
0
1
0
1
1
0
1
1
0
0
2
1
0
1
0
1
2
0
0
0
0
0
0
0
1
0
2
1
0
4
1
2
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
4
0
1
2
1
2
0
0
1
1
1
0
1
0
1
2
0
1
0
0
0
2
1
1
2
1
1
0
1
2
1
0
0
0
2
0
1
2
0
0
2
2
2
0
2
1
0
0
0
2
0
0
0
0
1
1
2
0
0
0
0
0
0
2
2
0
0
0
0
1
1
0
1
1
0
0
1
1
0
0
0
0
4
1
0
0
0
1
0
0
1
0
2
0
0
0
1
2
2
0
2
1
0
0
2
1
0
0
2
0
0
0
2
1
0
1
1
0
0
2
0
0
0
0
0
1
0
2
0
1
0
0
2
1
2
0
2
0
1
0
0
1
0
2
1
2
0
1
1
2
1
0
0
0
2
0
1
0
2
2
2
0
1
0
1
2
2
2
0
0
1
0
1
0
1
0
1
0
2
2
0
0
2
0
0
0
1
2
1
2
4
2
0
0
0
2
1
1
0
1
1
2
1
0
0
0
2
1
2
0
1
0
0
0
1
0
1
1
2
0
0
0
1
0
0
0
1
0
0
2
1
0
0
1
0
0
2
0
2
0
0
1
0
0
0
1
0
0
2
0
1
0
0
1
0
0
0
2
0
2
1
0
0
0
2
0
0
0
1
2
1
2
2
1
0
0
0
1
2
3
1
1
2
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
1
3
0
0
0
0
1
0
2
1
1
1
0
1
0
2
0
0
0
0
2
0
1
2
1
0
1
0
1
0
2
1
1
2
1
0
0
0
0
1
1
1
0
1
0
0
0
1
0
3
0
0
0
0
0
0
0
2
1
1
0
0
1
1
0
1
1
0
2
0
0
0
0
0
0
1
1
0
1
0
0
0
2
1
0
1
1
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
2
1
0
0
0
0
1
2
1
2
1
0
0
0
0
1
2
0
0
0
0
2
2
0
0
0
1
4
1
0
1
2
0
0
3
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
1
0
0
2
1
0
0
1
0
3
1
1
2
1
1
0
1
2
2
1
0
2
0
0
0
0
0
1
2
0
0
1
2
0
1
2
0
1
0
0
1
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
2
0
0
0
2
2
0
2
0
0
0
2
2
2
0
3
1
0
2
0
1
1
0
0
2
2
1
0
0
1
0
0
0
2
0
1
4
1
0
0
0
3
0
2
0
0
0
1
0
0
0
0
1
0
1
2
2
0
2
1
2
0
2
1
2
0
0
0
0
1
0
1
0
0
0
2
2
2
2
3
0
1
0
0
0
0
2
0
1
0
1
2
2
1
0
2
1
0
0
2
0
1
0
2
0
0
0
0
0
0
1
2
1
2
0
0
2
1
2
0
0
0
1
1
0
2
2
0
0
3
0
0
1
0
2
0
1
1
1
0
1
3
0
2
1
0
0
0
0
1
0
2
1
0
0
0
2
1
1
2
1
1
1
0
0
0
1
0
2
0
0
0
2
3
2
0
1
0
1
0
1
0
0
2
1
2
0
0
0
0
1
1
2
1
1
1
1
1
0
0
0
1
0
0
0
2
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
2
0
0
1
0
2
1
1
0
0
0
2
0
0
0
0
0
1
0
0
2
1
1
1
1
0
1
2
0
1
0
0
0
0
1
0
2
1
2
0
0
1
0
0
0
1
1
0
0
2
2
1
2
1
1
0
0
1
1
0
1
2
0
1
2
2
1
0
1
0
1
3
1
2
0
2
0
1
2
2
0
1
0
0
2
2
0
2
1
0
2
0
0
2
0
1
0
0
1
1
0
0
1
2
0
0
0
2
0
0
1
0
1
1
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
1
2
1
0
2
0
2
1
1
3
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
1
0
1
0
2
2
0
1
0
1
0
2
0
2
2
0
0
0
1
0
0
2
1
0
0
1
0
0
3
0
0
2
1
2
1
1
0
3
0
1
1
0
0
1
0
0
1
1
2
0
2
2
1
1
0
1
2
0
0
1
1
0
0
0
1
1
0
0
1
0
0
0
0
2
0
1
2
1
1
0
1
0
0
2
1
0
0
2
0
1
1
1
1
1
1
2
0
0
4
2
2
2
0
0
0
0
2
1
1
0
0
0
1
2
0
0
0
0
0
0
0
2
0
1
1
3
0
0
0
0
4
1
1
2
2
0
1
0
0
1
2
0
0
2
0
2
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
2
0
1
0
1
0
0
2
1
2
1
1
2
1
2
0
0
2
1
1
0
0
0
3
2
1
0
0
2
2
0
0
4
1
0
2
2
0
1
1
2
0
0
0
1
0
1
1
0
0
2
1
0
0
0
1
0
1
0
0
0
1
0
2
1
0
1
0
0
0
0
0
0
2
1
2
0
0
0
0
0
2
2
0
1
0
1
1
1
0
0
2
0
0
0
2
1
1
0
1
1
0
0
0
0
1
0
0
2
0
2
0
1
2
1
1
1
1
0
1
2
0
0
0
0
1
0
0
0
2
2
2
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
1
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
1
2
0
2
0
1
1
1
1
2
0
2
0
1
0
1
0
0
1
0
2
2
0
1
0
1
0
1
0
0
2
1
1
0
1
2
3
0
2
2
2
0
0
1
0
1
0
1
0
1
2
0
2
0
0
0
0
0
0
0
0
1
0
1
1
0
2
1
0
0
0
2
2
0
2
0
1
1
0
0
0
0
0
1
0
1
1
0
1
0
1
0
0
2
0
2
2
0
0
0
2
1
0
0
1
0
1
1
0
1
0
2
0
0
0
2
2
1
1
0
1
1
1
0
0
1
0
1
0
0
1
1
2
2
0
0
1
0
1
0
1
0
0
0
0
0
0
2
1
1
0
2
0
0
0
1
0
1
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
2
3
0
0
1
0
2
0
0
0
0
1
2
0
1
1
0
1
0
2
2
0
0
0
0
1
0
0
1
1
0
0
2
2
0
2
0
1
2
0
1
0
0
2
2
0
1
2
1
1
2
0
1
1
1
0
0
0
0
2
0
0
2
0
1
1
1
0
0
2
0
0
0
0
1
0
0
0
1
1
0
0
2
4
2
1
0
0
1
2
1
1
0
1
1
2
2
0
1
0
0
0
2
1
0
2
2
0
5
1
2
0
2
0
1
1
2
0
1
0
2
1
0
0
0
0
0
0
0
0
0
1
1
2
0
2
2
1
1
0
0
1
0
1
2
1
1
1
0
0
4
0
0
0
2
2
0
1
0
0
1
2
0
0
2
0
0
1
1
1
0
0
0
1
2
0
2
0
1
2
0
1
1
0
2
1
1
1
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
1
0
0
2
1
2
0
1
0
0
2
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
2
2
2
1
2
0
3
0
1
0
0
1
1
0
0
0
1
0
0
0
1
0
1
0
0
0
2
1
2
0
2
0
1
0
0
4
0
2
0
0
0
0
0
1
0
1
0
2
1
0
0
0
0
1
0
0
0
2
0
0
1
1
0
0
2
0
0
1
0
1
1
0
0
0
1
0
2
0
2
2
0
0
3
2
2
0
0
1
1
1
1
0
0
1
0
0
0
2
0
0
1
0
0
1
0
1
1
0
0
4
1
2
0
2
2
0
2
0
0
1
2
2
2
0
1
0
0
2
0
1
2
2
2
0
0
2
1
0
0
2
2
0
0
0
2
0
1
2
0
2
1
2
0
0
2
0
1
0
0
2
1
1
0
0
0
0
3
0
0
0
1
3
0
4
0
2
1
2
0
0
2
2
0
1
0
0
0
0
1
0
2
2
0
1
1
1
1
0
2
0
2
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
2
0
1
0
1
0
1
0
1
2
0
1
0
0
0
0
0
0
0
1
0
2
0
1
0
0
2
0
0
2
0
1
0
1
0
0
0
0
0
0
2
0
0
2
1
0
0
0
1
1
1
0
0
2
0
2
0
0
0
2
0
0
0
1
1
0
2
2
0
1
0
0
0
2
1
0
0
1
0
2
1
3
0
0
0
1
2
1
1
1
0
2
2
0
0
0
1
0
0
0
0
2
0
0
3
0
0
0
2
0
0
1
0
0
2
1
0
2
2
0
1
0
2
0
0
0
0
1
0
0
1
2
1
1
0
2
0
0
0
0
1
1
0
0
0
1
3
0
0
0
0
2
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
2
0
1
0
1
0
0
0
1
0
1
2
1
1
0
3
2
0
2
0
2
2
1
2
0
0
0
1
0
1
0
2
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
3
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
2
2
1
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
2
0
2
2
1
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
2
1
2
0
2
0
2
2
0
2
1
2
2
0
0
0
2
0
0
0
0
1
0
2
2
0
1
0
2
0
1
1
0
1
2
1
0
2
2
2
0
0
2
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
2
1
0
1
0
2
0
0
1
0
0
0
0
1
2
0
1
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
1
1
0
0
1
0
2
2
0
0
0
1
2
0
0
1
2
0
1
2
2
2
0
1
2
0
0
0
1
0
1
0
0
0
0
2
0
0
1
0
2
2
0
0
2
0
2
0
2
1
0
1
1
0
0
0
0
3
0
0
2
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
3
0
0
0
2
0
1
2
0
0
0
0
0
2
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
1
1
0
2
0
1
0
1
2
0
0
0
2
0
0
0
2
1
0
0
2
0
2
0
0
2
2
0
1
0
1
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
2
0
2
0
1
1
0
1
1
2
0
0
2
2
2
2
0
0
0
2
0
3
1
0
0
2
0
1
1
2
0
0
0
0
0
0
1
0
1
1
0
1
0
0
2
1
0
0
2
0
0
1
2
2
0
0
3
2
0
1
0
1
0
0
0
2
1
0
3
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
2
0
0
0
0
1
2
0
0
0
2
0
0
0
0
2
1
0
1
1
0
1
1
1
1
0
1
1
0
0
0
1
2
0
2
1
0
1
0
0
1
2
1
0
1
3
0
1
0
0
0
0
1
0
1
0
2
0
0
0
1
0
2
0
0
0
2
1
0
4
0
0
0
0
1
1
1
0
0
2
0
0
2
2
0
0
0
1
0
1
0
0
0
1
1
0
2
0
0
0
1
0
0
2
1
2
0
0
0
0
0
0
0
0
2
1
0
0
2
1
0
0
2
2
0
1
2
2
1
0
0
2
0
0
2
0
2
1
0
2
1
0
0
1
2
1
0
0
0
0
0
0
3
0
1
1
2
0
1
1
1
0
1
1
0
2
2
0
1
1
2
0
1
0
2
4
0
2
0
1
1
2
0
0
0
0
2
2
0
0
0
1
1
0
0
1
2
0
0
0
2
0
0
0
1
0
0
2
1
2
3
0
0
0
0
0
0
0
1
2
2
0
0
0
0
3
1
0
2
0
0
0
4
2
2
1
1
0
0
0
0
0
0
0
1
0
0
2
1
0
1
1
1
1
0
0
1
0
1
0
2
0
2
1
1
0
1
2
0
0
1
1
0
0
0
0
0
0
2
2
1
0
2
0
1
0
2
1
0
0
0
0
2
0
2
4
0
0
2
0
0
1
0
2
0
0
0
0
1
3
1
1
0
0
1
0
0
0
1
0
2
0
1
1
0
0
0
1
0
1
0
0
2
0
1
2
0
0
1
0
0
0
1
2
0
0
0
0
0
0
1
2
0
2
2
2
0
0
0
1
1
0
0
2
2
0
0
0
2
0
1
1
0
0
1
0
1
0
2
0
1
2
1
0
2
2
1
0
0
1
1
2
1
0
0
0
0
0
2
0
0
1
1
1
0
1
1
2
0
0
3
2
0
0
0
1
2
1
0
0
0
1
1
0
0
0
1
0
0
0
0
1
1
0
2
2
0
0
0
0
0
1
0
1
2
1
0
0
1
1
1
0
0
0
0
1
3
0
0
0
1
0
1
0
0
1
1
0
0
0
2
1
0
0
0
1
1
2
0
1
1
1
0
0
2
0
1
1
0
0
1
0
2
1
0
0
0
0
0
0
2
2
1
0
0
2
2
2
1
1
1
0
2
0
2
0
0
0
2
0
0
0
0
2
0
0
1
0
1
0
0
1
1
0
0
0
2
2
2
2
2
0
2
0
4
0
0
0
1
2
2
0
1
1
0
0
0
0
0
2
1
0
1
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
2
2
3
0
2
1
0
1
0
2
0
2
1
0
0
5
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
5
2
1
1
3
2
0
2
0
0
0
0
0
0
0
2
1
0
0
1
0
0
2
0
1
0
0
0
1
1
0
0
0
2
1
1
1
0
0
0
1
0
1
0
0
0
2
1
5
0
0
2
0
3
0
0
0
0
2
1
0
2
0
0
1
0
0
1
0
2
0
1
0
0
1
2
1
1
0
0
0
2
3
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
2
0
1
0
1
0
1
1
0
0
0
0
0
0
2
0
0
1
3
1
0
1
0
2
1
0
1
0
1
1
0
0
2
0
0
0
2
0
0
0
3
0
2
0
1
0
0
1
0
1
0
0
0
1
2
0
1
2
0
2
1
0
0
0
0
1
0
0
0
2
1
0
1
1
0
2
1
1
1
2
2
1
0
0
0
0
0
1
0
0
2
0
1
0
2
0
2
1
0
1
1
1
0
2
0
2
1
0
0
2
2
0
2
2
0
0
2
0
1
2
1
0
0
1
0
0
0
4
1
0
0
2
0
0
2
2
0
0
1
2
0
0
0
2
1
2
0
1
2
2
1
1
0
0
0
1
0
0
1
2
0
1
0
0
0
0
0
2
0
1
1
0
0
0
1
0
0
2
0
1
1
0
2
0
1
0
0
0
0
2
1
0
2
0
0
0
1
2
0
2
2
0
0
2
0
0
1
1
1
0
0
0
1
0
0
0
1
1
1
0
1
0
1
1
1
0
2
1
0
1
1
2
0
0
0
1
0
0
2
6
0
0
2
0
0
0
0
2
0
0
2
2
0
0
0
0
0
2
3
2
2
0
2
1
0
1
2
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
2
0
1
3
0
1
0
0
2
2
1
2
0
0
2
0
0
0
1
0
2
1
0
0
2
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
1
0
0
2
0
0
1
2
2
0
2
0
1
0
1
1
0
0
1
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
2
2
1
1
0
0
1
1
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
1
1
0
0
0
2
2
0
0
2
2
2
1
2
2
1
0
0
1
2
0
0
1
0
2
1
0
1
0
1
0
0
0
0
2
2
0
2
0
0
2
1
1
1
1
2
0
1
2
0
0
1
2
0
0
2
3
1
0
0
2
0
1
0
3
0
2
0
0
1
2
0
0
1
2
2
0
0
0
1
3
0
0
0
1
0
0
1
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
1
0
2
0
1
0
2
1
0
2
1
0
0
1
2
0
1
0
0
0
2
0
0
0
0
0
0
3
1
0
1
1
0
0
2
0
1
2
2
0
0
2
1
1
0
2
1
0
1
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
3
1
0
1
0
3
2
0
1
1
0
5
0
2
0
0
0
0
0
0
2
1
1
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
2
2
0
2
0
1
2
2
1
0
1
1
2
0
0
1
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
2
0
2
0
1
1
0
0
2
2
0
1
0
0
0
0
1
0
0
0
1
0
2
0
2
0
1
1
0
0
2
0
0
1
1
0
0
1
0
1
0
0
0
0
2
1
0
0
1
0
1
0
0
2
4
1
1
0
0
1
0
0
1
0
0
0
0
6
1
0
1
2
1
1
0
0
0
0
0
1
2
2
2
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
2
2
0
2
1
0
2
0
0
1
2
0
4
0
1
1
1
0
1
2
1
0
2
0
3
0
0
0
0
1
1
2
0
2
1
1
0
1
0
2
2
0
0
0
1
0
1
0
0
2
1
0
0
1
0
1
0
2
0
0
0
1
2
2
2
1
2
0
3
0
0
1
1
0
0
0
1
1
0
0
1
1
0
2
0
1
0
0
1
1
1
2
0
0
0
1
0
2
0
1
1
1
1
0
1
1
0
0
0
0
3
2
2
0
1
2
0
0
2
0
0
0
0
0
3
0
1
0
0
0
2
0
2
2
2
1
2
0
0
0
0
1
1
1
0
0
0
2
0
0
2
1
1
0
0
2
0
1
0
0
0
2
2
0
0
1
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
1
1
1
0
2
2
0
0
0
1
2
0
1
0
2
0
1
0
2
0
0
1
1
2
0
1
1
1
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
1
0
1
0
0
1
0
0
2
1
1
1
0
2
0
1
1
2
0
0
0
0
0
0
2
1
0
2
2
2
0
0
0
0
0
2
0
2
2
1
0
0
0
0
0
2
2
0
0
0
0
1
0
1
0
0
1
2
2
1
0
1
0
0
0
1
0
0
1
1
0
2
0
2
1
0
0
1
1
0
2
0
0
1
0
0
0
0
1
2
2
2
1
0
0
1
2
2
0
2
0
0
3
1
0
1
2
2
1
4
1
0
0
0
1
0
1
1
2
0
1
2
0
1
0
0
1
0
1
0
0
0
0
1
1
0
1
1
2
5
1
1
0
0
2
2
0
1
0
0
0
1
3
0
0
0
1
2
1
0
0
0
0
1
2
0
1
0
1
0
2
0
2
0
0
0
2
2
0
1
0
0
0
2
1
1
2
0
0
0
0
0
1
2
0
0
0
2
0
1
0
1
1
0
0
2
1
1
1
0
2
0
0
0
1
2
0
0
0
0
5
0
7
2
2
2
0
1
1
2
1
4
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
1
0
1
0
0
0
1
2
0
0
0
0
0
1
0
1
1
0
0
1
0
0
2
2
0
5
0
0
0
1
2
1
0
1
0
2
0
0
0
0
1
2
0
2
1
0
0
0
1
2
0
0
2
0
0
1
0
0
2
1
0
1
0
1
0
0
0
0
2
1
0
1
1
2
1
1
0
0
0
0
2
1
0
0
1
0
1
0
1
2
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
2
1
0
1
0
2
0
1
2
0
0
1
0
0
0
1
0
0
2
1
1
0
1
0
2
1
0
0
1
0
1
0
0
0
0
1
0
1
0
2
0
0
0
1
2
0
5
0
0
0
1
0
0
1
1
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
2
0
1
0
0
1
0
1
0
1
2
0
0
0
2
4
3
1
2
2
1
3
0
2
0
3
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
2
1
1
1
1
0
2
2
2
0
2
0
0
0
1
0
0
1
0
0
0
1
4
0
0
1
1
0
0
0
1
0
0
0
0
2
2
1
2
0
0
2
0
0
1
3
0
1
1
2
0
0
0
0
0
0
1
2
2
0
1
1
1
0
0
2
0
2
1
2
3
1
2
1
2
1
2
1
0
0
1
1
2
2
0
1
0
1
2
0
0
0
0
1
0
0
0
1
2
1
1
2
0
0
2
1
0
1
0
0
2
0
1
0
0
0
1
1
0
0
1
1
2
2
2
0
0
0
1
1
0
0
0
0
1
1
1
0
0
3
0
0
0
0
0
1
0
2
0
0
1
0
0
0
1
1
0
2
1
0
0
0
0
0
0
1
0
1
0
0
0
0
2
1
0
0
0
3
0
0
0
0
3
1
1
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
2
0
1
0
2
1
2
2
0
0
1
1
1
1
0
1
1
0
1
2
0
0
0
0
2
2
0
1
1
1
0
0
0
0
0
0
2
0
2
0
1
0
0
1
0
2
4
2
2
1
0
0
0
0
1
2
1
1
2
1
2
0
1
2
0
0
1
2
0
1
0
1
2
1
1
1
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
2
0
0
0
0
2
0
3
1
1
0
0
0
0
0
1
0
2
1
0
0
2
1
0
0
0
0
0
2
1
0
0
0
0
0
2
2
1
0
0
0
2
2
0
0
0
1
2
2
0
0
0
0
0
1
0
0
0
1
0
0
0
2
1
0
0
0
0
3
2
0
0
2
0
2
2
1
2
0
0
2
0
0
0
0
1
1
0
0
1
2
0
0
4
1
0
2
1
0
1
1
2
1
0
1
3
0
0
0
2
1
0
0
0
2
3
0
1
0
0
2
0
1
0
0
0
1
1
1
0
0
2
2
3
0
1
0
0
0
0
1
1
0
0
1
0
0
1
2
0
0
1
0
2
1
1
0
0
0
2
1
0
0
2
1
3
0
0
1
2
0
0
2
0
0
1
0
0
3
2
1
0
0
0
2
2
1
0
2
0
1
1
0
0
2
0
0
1
0
0
0
0
1
1
0
0
0
2
1
0
2
1
2
1
2
0
1
1
1
2
2
1
0
2
0
2
0
1
1
0
0
1
0
0
1
0
0
0
0
2
0
1
2
0
2
0
0
0
1
1
0
6
2
0
2
3
0
1
0
0
0
0
0
2
0
0
1
0
0
1
1
1
0
0
1
2
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
1
1
1
0
0
2
1
0
2
0
2
0
1
1
2
0
0
2
0
2
0
1
1
1
1
2
2
2
0
0
2
0
1
1
0
0
0
2
1
0
2
1
0
1
0
1
1
2
1
2
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
4
0
2
2
0
1
2
0
0
1
0
0
0
0
1
2
2
0
1
0
1
1
1
1
1
0
0
2
0
1
0
0
1
0
2
0
2
1
0
0
0
0
1
2
0
2
0
1
1
0
2
0
0
0
1
1
2
1
0
0
4
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
4
1
2
0
0
1
2
0
0
0
0
0
2
1
0
2
0
0
1
0
1
0
0
0
0
1
2
2
1
0
0
0
0
2
2
0
0
1
0
0
0
1
0
0
0
2
1
0
2
1
0
1
3
0
2
2
2
2
0
0
0
2
0
0
0
0
0
2
0
1
2
0
0
0
2
0
1
0
2
0
1
0
0
0
0
0
1
1
1
0
0
0
2
2
0
0
1
2
0
0
3
0
0
0
2
2
1
1
0
1
1
0
1
0
0
1
1
1
0
2
0
0
0
0
0
0
2
3
0
1
0
0
0
0
0
2
0
0
0
1
2
2
2
0
1
0
2
0
1
2
0
1
0
0
1
2
0
2
0
1
0
0
0
1
0
1
0
0
2
2
1
2
0
1
2
0
1
0
0
1
1
0
0
0
1
0
0
2
1
0
0
0
2
0
2
3
0
1
0
0
0
0
0
2
0
2
1
1
2
0
1
1
2
1
0
2
1
2
0
2
2
0
1
0
0
2
2
2
0
2
0
0
2
0
0
2
0
2
2
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
2
2
1
2
0
0
3
1
0
1
0
0
1
2
2
0
0
2
1
1
0
0
1
1
0
0
1
0
1
0
0
2
2
0
0
0
2
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
2
2
0
0
2
0
3
0
0
0
0
2
0
0
0
2
0
1
1
2
0
0
2
2
1
0
0
1
2
2
2
0
0
0
0
0
0
0
1
0
1
0
0
1
2
1
0
2
1
1
0
0
2
0
0
0
0
1
0
0
2
0
0
2
0
0
1
0
1
0
0
1
2
0
0
0
2
0
0
2
1
0
1
1
0
0
0
0
0
0
2
0
1
1
0
1
1
0
0
0
0
2
0
2
0
1
2
0
0
0
0
0
0
1
1
1
1
0
0
1
1
2
0
1
0
1
1
1
0
0
1
0
0
0
0
0
0
2
1
0
0
0
1
2
1
3
1
1
0
0
0
0
0
1
2
0
1
0
0
0
1
1
0
0
0
0
0
2
0
2
0
1
0
0
1
0
0
0
0
0
0
3
1
0
1
0
0
1
0
0
0
1
0
2
1
2
0
2
0
1
1
0
0
0
1
1
2
2
0
2
0
1
2
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
2
1
1
2
0
2
1
2
0
0
2
2
1
0
0
0
0
2
0
0
1
0
0
2
1
1
1
0
1
0
0
0
2
1
0
0
1
1
0
0
2
0
0
0
1
2
1
0
1
0
1
0
2
1
1
0
0
0
0
1
1
1
0
1
0
0
0
0
0
1
0
2
1
0
2
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
2
0
0
0
0
0
0
2
0
1
0
1
2
0
2
2
5
2
2
0
2
0
0
2
0
1
0
0
0
0
1
0
1
0
0
1
1
0
0
2
2
0
1
0
1
2
0
0
0
0
2
1
0
0
0
3
0
0
2
1
0
0
0
2
0
1
2
0
2
0
0
0
1
0
4
3
1
0
0
2
1
0
2
2
1
0
0
0
1
1
0
0
1
0
1
0
0
1
0
0
1
0
2
2
2
0
0
0
0
0
2
0
3
0
0
0
1
0
0
1
0
0
0
2
3
0
2
1
1
0
1
0
1
0
0
0
1
1
1
0
0
1
1
1
2
0
0
0
0
0
0
0
0
0
2
0
1
0
2
1
0
0
1
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
5
0
2
1
0
0
0
2
0
1
2
0
2
0
1
0
0
1
1
0
1
1
0
0
3
1
2
0
0
1
2
0
0
1
0
1
2
1
0
0
1
0
0
1
0
0
0
0
1
2
0
1
0
0
2
1
1
1
0
0
2
0
1
2
0
0
0
2
2
1
0
0
0
0
0
0
0
2
2
0
2
0
1
2
0
1
0
1
2
0
0
0
0
0
1
0
1
2
0
1
1
0
0
1
2
0
0
0
1
1
1
2
0
0
0
1
0
0
1
0
2
0
2
1
0
0
0
2
0
2
0
0
0
0
0
1
2
1
0
0
0
0
1
2
0
1
0
0
0
1
0
0
1
2
0
1
0
0
0
0
0
2
0
2
2
0
0
0
0
2
0
0
0
0
1
2
1
0
0
0
2
0
0
0
0
0
0
2
2
2
1
0
1
2
0
0
0
3
1
0
1
0
2
1
0
1
0
2
2
0
1
1
1
1
0
0
2
1
1
2
0
0
1
2
1
0
0
0
1
2
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
1
0
2
0
0
0
0
2
0
0
1
0
2
2
1
3
0
1
0
0
1
0
2
0
0
1
0
1
0
0
1
0
0
1
0
2
1
2
1
2
2
3
0
0
0
1
1
0
2
1
0
1
1
2
1
1
1
2
2
2
0
0
4
0
1
0
1
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
1
0
2
1
2
1
0
1
0
0
0
2
0
1
1
0
1
0
2
0
0
3
0
2
0
1
0
0
0
0
0
2
0
2
0
2
0
0
0
1
0
2
0
2
0
0
1
1
2
0
0
0
0
0
0
0
0
0
3
1
0
1
0
0
3
2
2
0
0
0
1
0
0
0
1
3
2
0
0
0
2
2
2
0
2
0
0
0
0
0
0
1
0
2
0
1
0
0
2
1
2
0
1
2
1
2
1
0
0
0
0
0
1
1
1
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
1
2
1
0
1
0
1
1
0
0
0
0
0
1
0
1
0
0
0
5
0
1
0
0
2
0
2
1
0
0
1
1
1
1
0
1
2
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
1
0
0
0
0
1
2
0
1
0
0
1
0
2
1
0
1
0
1
2
2
0
1
0
0
1
1
2
0
2
0
1
2
1
0
2
1
0
1
1
0
0
0
0
3
2
0
1
2
0
1
3
0
0
1
1
0
1
0
0
0
1
1
2
0
3
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
7
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
3
1
1
2
2
0
2
1
0
1
0
0
0
0
0
0
0
1
2
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
1
2
0
2
1
0
1
1
2
1
1
2
0
2
0
0
1
0
2
0
0
0
0
0
2
0
1
1
0
0
2
0
0
1
0
2
0
3
0
1
1
1
2
2
0
0
2
1
1
0
1
0
2
0
0
2
0
2
2
0
2
1
0
1
0
0
3
0
1
0
1
1
1
0
0
2
0
1
0
1
2
2
0
1
0
0
1
0
2
0
0
2
1
0
0
0
1
0
1
0
0
0
0
2
0
0
0
2
2
0
1
2
0
2
2
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
1
2
0
1
1
0
0
1
0
1
0
0
0
1
0
1
0
0
1
1
2
0
0
0
0
0
2
0
0
1
0
0
1
0
2
1
0
0
0
1
0
0
1
0
2
2
0
2
0
0
0
5
1
0
1
2
1
0
1
0
0
2
2
2
0
0
2
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
1
0
1
0
0
0
6
0
0
2
2
0
0
0
0
1
0
2
0
1
1
0
0
0
0
1
0
0
2
0
0
2
0
0
0
2
0
0
2
1
0
1
1
2
0
0
0
0
0
0
2
0
0
1
1
0
2
1
0
0
0
2
0
0
0
1
0
0
2
1
0
1
0
2
2
0
0
0
2
0
0
0
2
2
0
2
2
0
2
0
0
0
1
1
0
0
0
0
2
1
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
1
2
0
1
1
1
0
0
0
2
1
0
0
2
0
0
0
1
1
0
1
1
0
0
1
2
0
2
5
0
1
0
1
2
0
0
1
0
0
2
0
2
2
0
0
1
0
2
2
2
1
2
1
1
0
0
0
2
0
0
0
1
0
0
0
2
1
0
2
1
1
0
0
2
2
0
0
0
0
1
2
2
0
0
0
0
2
1
0
0
0
0
2
5
0
0
0
0
1
1
2
0
2
0
0
1
0
0
0
1
0
0
1
0
1
1
1
0
0
1
0
1
0
1
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
1
4
0
0
0
0
1
0
2
0
1
0
1
1
0
0
0
0
3
0
1
1
0
0
0
2
5
0
1
0
1
2
0
0
0
0
0
1
0
0
2
2
1
0
0
0
2
0
0
2
0
1
1
2
0
0
0
0
0
3
2
1
1
2
1
0
0
1
0
2
0
0
0
0
1
1
0
0
2
0
0
1
0
1
0
2
0
0
0
0
1
0
1
1
1
0
0
0
1
0
2
0
1
0
1
0
1
2
0
0
0
2
2
0
0
3
1
1
2
0
0
0
2
1
0
0
0
0
0
1
1
1
0
2
0
1
0
1
0
0
1
0
0
1
1
0
0
0
1
2
0
0
0
1
0
0
0
0
2
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
1
1
0
3
1
1
0
0
1
0
2
0
0
1
2
1
0
0
1
0
1
1
0
0
1
0
0
1
0
0
0
2
2
0
2
0
0
1
2
0
0
0
2
0
4
0
1
1
0
0
0
1
1
3
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
2
0
0
0
0
2
1
0
0
0
0
1
2
0
1
2
1
1
0
0
1
1
0
1
0
0
2
0
0
1
1
0
0
0
0
0
2
0
0
2
2
1
0
0
2
0
0
0
1
2
0
0
0
0
1
0
0
0
0
2
2
1
2
0
0
0
0
0
1
0
0
1
0
1
0
0
0
2
2
1
1
0
2
2
0
1
0
0
0
1
0
2
1
2
0
0
0
1
0
1
0
0
0
0
0
2
2
0
0
0
0
0
1
0
1
0
0
2
0
0
1
0
0
0
3
1
2
0
0
0
1
1
2
1
2
1
0
1
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
1
0
2
2
1
4
1
0
0
0
0
0
1
0
1
0
0
0
0
2
1
1
2
0
0
0
1
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
1
2
0
0
1
2
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
2
0
1
0
0
0
2
1
0
1
0
1
0
1
2
2
0
0
0
0
0
0
1
2
2
0
1
2
2
0
3
2
2
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
2
2
0
1
0
0
2
0
0
2
0
0
2
0
0
1
0
1
0
1
0
1
2
0
1
1
2
1
0
1
1
0
1
0
0
2
0
0
0
0
2
1
0
2
0
1
0
1
0
1
2
0
0
0
0
1
0
0
0
0
1
0
1
1
0
2
2
1
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
2
1
2
0
1
0
0
1
2
0
0
1
2
2
0
1
0
0
1
2
0
0
2
0
1
0
0
2
1
0
1
0
0
1
0
0
0
0
0
1
3
2
2
0
2
2
0
2
6
0
0
1
2
0
1
0
1
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
2
1
0
1
1
0
1
1
0
0
2
0
1
0
0
1
1
1
0
0
0
1
0
2
2
1
2
0
2
1
0
0
0
1
0
1
1
1
2
2
0
0
0
0
1
1
0
1
0
0
2
0
0
2
1
0
0
0
1
1
0
0
1
0
0
2
0
0
1
1
2
0
0
0
2
0
1
2
0
1
0
0
0
2
1
2
0
1
0
0
1
0
0
1
1
0
1
1
0
1
2
1
0
1
0
2
0
1
1
2
1
0
0
0
0
2
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
2
1
1
0
1
0
0
1
0
0
1
0
2
2
1
1
0
1
0
2
0
3
2
0
2
1
0
0
2
0
0
1
1
0
0
2
0
2
0
0
0
0
0
0
0
0
2
1
2
0
0
2
0
1
2
1
1
0
0
0
0
0
1
0
0
1
1
2
0
2
1
0
0
1
1
2
0
1
1
0
0
3
1
1
1
2
0
1
2
0
0
0
1
1
0
2
2
0
0
0
0
0
1
2
2
0
2
0
0
2
0
2
2
2
0
1
2
2
1
1
1
1
0
0
0
1
1
1
1
1
1
0
2
3
0
2
0
0
0
1
0
2
0
1
0
2
0
2
2
0
1
2
2
0
1
0
2
1
0
0
0
1
0
1
0
0
0
1
1
0
1
0
2
1
1
1
0
0
0
0
1
0
2
2
1
0
0
0
0
1
1
0
1
1
1
0
2
0
0
0
2
0
1
0
1
0
0
2
0
0
0
0
1
0
2
0
0
2
0
0
2
0
1
1
1
2
0
0
0
2
0
1
0
0
0
0
0
0
1
0
4
0
0
0
0
0
1
1
2
0
0
1
1
1
1
0
0
0
0
0
0
0
1
0
2
1
1
0
2
2
0
0
0
1
0
0
0
2
2
0
2
1
0
0
0
1
0
3
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
2
0
0
0
1
0
0
1
0
1
2
0
0
2
2
0
0
0
1
0
0
0
2
0
1
0
0
0
0
1
1
0
2
1
2
0
0
0
0
1
0
1
0
3
2
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
1
2
0
1
2
0
0
0
0
0
0
0
0
0
2
1
0
1
1
0
1
1
0
2
1
0
0
0
0
0
2
0
0
2
1
0
0
3
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
1
1
1
0
0
1
0
2
0
0
0
0
0
1
3
1
0
0
3
0
0
1
0
0
0
0
0
2
0
1
2
0
1
0
0
0
0
1
0
0
0
1
0
0
1
1
3
0
0
0
1
0
1
1
0
0
1
1
1
0
0
1
0
0
0
0
0
2
2
0
1
1
1
1
0
0
1
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
1
3
0
0
0
2
0
0
0
0
2
0
0
0
2
1
0
2
0
0
0
1
0
1
0
0
0
0
0
2
0
1
2
0
0
0
2
0
1
1
0
0
2
0
0
0
0
0
0
0
1
0
1
1
0
0
0
2
1
2
0
0
2
1
0
0
0
1
2
0
0
0
0
0
1
2
1
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
2
1
2
2
2
0
1
0
2
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
1
1
3
0
0
0
1
0
2
0
0
0
0
0
1
1
3
1
0
1
0
2
0
1
1
0
0
1
1
2
0
1
0
0
1
0
2
0
1
0
0
2
0
1
0
1
1
0
2
0
1
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
1
2
0
1
0
2
1
0
2
1
1
0
0
0
1
0
1
0
0
1
0
2
1
0
0
0
3
1
0
1
2
0
0
0
0
0
0
1
0
0
2
0
2
2
1
0
2
0
0
1
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
1
0
1
0
1
2
0
0
1
1
2
2
0
0
0
1
1
1
0
0
0
2
2
1
3
1
1
0
2
1
0
0
0
1
0
0
0
0
2
1
2
1
0
0
0
2
2
0
1
0
2
1
3
1
0
0
1
2
2
0
0
0
1
0
0
2
0
3
0
1
0
0
1
2
3
2
0
0
0
0
1
2
1
0
0
0
0
1
2
0
2
1
0
0
0
1
2
0
0
0
2
2
0
1
1
0
0
0
1
2
2
0
2
2
1
1
1
2
0
1
1
0
0
0
0
2
0
1
0
1
1
2
0
0
0
0
0
0
1
2
1
0
1
0
1
0
0
1
0
0
0
0
0
2
1
0
1
1
0
2
0
0
1
0
0
0
0
0
2
1
1
0
0
1
0
0
0
0
1
1
0
2
1
2
0
1
2
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
1
1
2
2
0
2
6
0
0
1
0
0
0
0
1
0
0
3
1
2
0
0
1
0
1
0
1
1
1
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
4
1
0
0
1
1
1
0
2
0
0
0
1
2
1
1
0
0
2
0
0
2
1
0
1
1
1
1
1
2
1
0
0
2
1
3
0
1
1
0
1
1
0
1
0
0
0
0
1
1
1
1
2
2
1
0
1
1
0
0
0
1
1
1
1
0
0
1
1
0
1
1
1
0
0
1
0
0
1
2
0
3
0
0
1
2
0
0
0
2
0
0
2
1
1
2
0
1
2
1
1
1
0
4
0
0
1
2
1
2
0
0
0
0
1
0
1
0
0
0
0
1
1
0
1
2
0
0
0
0
2
1
1
1
1
0
2
0
0
0
0
1
0
0
0
2
1
1
0
2
1
0
1
1
0
1
1
0
1
2
2
0
0
2
0
4
0
0
0
1
2
0
0
0
2
0
0
2
1
1
0
1
2
2
1
1
1
1
0
0
2
0
1
0
1
0
1
1
0
0
0
1
1
0
0
0
1
2
2
0
2
1
0
0
0
0
0
2
2
1
1
2
0
0
2
1
0
2
1
3
0
1
0
0
2
0
1
0
0
2
1
2
2
0
1
0
2
0
0
0
0
0
0
2
2
5
0
0
0
0
0
0
0
0
0
0
0
1
2
2
1
1
0
0
0
1
0
0
1
0
2
0
0
2
0
2
0
1
0
0
1
2
1
2
0
0
0
0
0
1
1
0
0
0
1
0
0
2
0
0
1
0
0
2
1
1
0
0
1
0
1
2
1
1
1
0
1
1
1
1
0
0
0
0
2
1
0
0
0
0
1
0
2
0
1
0
1
1
0
2
2
0
1
0
0
0
1
2
0
2
1
0
0
1
2
2
1
3
0
1
0
1
0
1
0
1
0
0
0
2
0
2
0
1
0
0
0
1
0
2
0
2
2
0
0
1
0
0
0
1
0
2
0
0
0
0
2
0
1
2
2
0
1
1
1
0
2
0
1
2
0
0
0
2
0
1
2
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
1
2
0
0
1
2
1
0
0
1
0
0
0
0
1
1
0
2
0
1
0
0
3
1
1
0
2
0
0
1
0
1
1
0
0
1
1
4
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
2
1
0
0
0
1
2
3
1
2
1
1
0
0
0
0
0
0
1
2
0
1
0
0
0
1
2
0
0
0
1
0
0
0
0
1
1
0
0
0
2
0
0
0
0
1
1
0
0
1
0
1
0
3
2
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
2
2
0
2
0
2
2
2
2
0
1
2
0
2
0
0
1
3
2
1
2
2
1
0
0
2
0
0
1
0
1
0
0
0
2
0
0
0
0
0
2
0
2
0
0
1
0
0
1
2
3
1
0
0
0
1
2
0
2
2
0
2
2
0
1
2
0
1
0
0
0
2
0
1
2
1
2
1
0
0
0
1
1
2
2
0
0
1
1
1
2
2
0
1
1
0
0
0
0
2
1
1
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
1
2
2
0
2
2
0
0
0
1
0
2
0
0
0
1
0
0
1
0
0
1
0
2
0
0
1
0
2
2
0
0
0
0
1
0
0
2
2
1
2
2
0
0
2
0
0
2
2
0
1
0
2
0
0
0
0
1
0
1
1
0
0
0
2
0
0
6
1
0
1
0
1
0
0
0
1
1
2
0
0
0
0
1
2
1
0
0
0
0
1
1
0
2
0
2
0
2
0
1
0
0
1
2
0
1
0
1
2
0
0
2
2
0
0
0
1
3
1
1
1
0
0
0
0
1
0
2
1
1
2
0
1
0
2
2
2
1
2
1
0
1
2
2
2
0
2
0
1
0
0
0
1
0
1
0
0
1
0
1
0
0
1
0
2
1
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
3
0
0
2
0
0
1
0
2
0
0
1
1
3
2
0
2
0
1
0
0
1
0
0
2
1
0
0
0
0
0
1
0
1
2
2
0
0
0
1
2
0
1
4
0
0
0
0
0
1
2
1
2
0
2
0
0
0
2
1
0
0
2
0
1
0
2
0
1
1
0
0
0
0
0
0
0
0
2
2
1
2
0
0
2
0
2
1
0
2
0
3
0
1
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
1
0
0
0
1
1
1
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
2
1
0
0
1
2
1
0
3
0
0
2
0
2
1
2
0
0
0
1
0
1
0
0
1
1
2
0
0
0
0
2
1
1
0
2
2
2
0
1
2
0
1
2
0
2
1
1
0
0
0
1
0
1
3
0
0
0
1
0
0
2
3
0
2
2
2
1
2
1
0
0
0
2
0
0
3
1
0
2
0
2
0
1
2
0
0
1
0
2
2
0
1
1
0
0
0
1
1
0
0
2
0
0
2
0
0
1
0
0
0
0
1
2
0
1
1
0
0
1
1
0
2
1
0
2
0
1
2
0
2
2
0
2
0
0
0
0
1
0
1
0
2
2
1
1
0
0
2
2
0
0
2
0
2
0
1
0
1
0
1
1
2
0
0
1
1
0
1
2
2
0
0
1
0
2
0
1
1
2
2
0
0
1
0
2
0
1
0
2
0
0
3
0
2
0
0
2
0
0
1
0
0
0
1
3
0
1
2
0
0
0
1
0
0
0
0
0
3
1
0
2
0
2
1
0
0
0
0
1
1
0
1
0
0
2
1
0
2
2
0
0
2
0
0
0
0
0
1
2
0
2
0
0
1
0
0
0
2
2
2
0
0
1
2
0
1
0
0
0
0
2
0
2
1
0
2
1
0
0
1
2
2
0
1
0
0
0
2
2
0
2
2
2
2
4
0
2
0
1
1
0
2
0
0
1
1
1
1
2
0
2
2
1
0
1
1
1
0
0
1
1
2
0
0
1
0
2
0
0
2
1
0
0
0
1
0
2
0
1
0
0
0
0
3
2
1
0
0
0
0
1
0
0
2
1
0
0
0
0
2
0
1
1
0
0
2
1
0
1
0
2
0
1
0
0
0
2
1
0
0
0
1
0
0
1
0
1
0
0
0
0
1
1
0
0
2
0
1
2
1
1
1
1
0
1
0
1
0
0
1
0
2
1
0
0
1
1
1
0
0
0
1
0
0
0
0
2
0
2
0
0
0
1
2
0
2
2
4
0
1
0
2
5
3
0
0
2
0
0
0
0
0
1
1
0
2
2
0
0
0
0
0
1
3
0
2
0
0
0
1
2
2
2
1
1
0
0
0
0
1
2
1
0
1
0
0
1
0
0
0
0
0
3
0
0
0
2
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
2
0
2
0
1
0
0
1
3
2
2
0
2
2
0
1
2
0
1
0
1
1
0
1
0
1
1
0
1
1
0
2
2
1
1
1
1
0
0
1
0
0
2
0
1
1
1
0
0
1
0
1
0
2
1
2
2
0
1
0
1
0
0
1
1
0
2
0
0
2
0
0
1
2
0
0
2
1
1
2
0
0
2
1
0
3
0
0
0
0
2
1
0
1
1
0
1
4
0
0
3
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
1
0
1
0
1
2
0
0
2
2
0
1
2
1
0
0
0
0
2
0
0
2
2
0
0
3
2
1
2
0
0
1
1
0
0
0
0
1
1
1
1
0
2
0
1
1
2
2
0
0
0
0
1
0
0
1
2
0
2
2
1
0
0
1
0
0
0
2
1
0
0
1
1
2
2
0
2
0
0
2
0
0
2
0
2
1
2
0
1
3
0
1
0
0
1
0
2
1
2
2
2
0
3
2
0
1
0
0
0
2
0
2
0
1
2
0
2
0
0
0
0
2
0
0
3
0
1
0
2
0
2
1
1
0
2
0
0
1
1
2
0
1
0
0
2
0
0
2
0
1
0
2
0
0
1
0
2
0
2
0
0
1
0
2
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
1
2
0
0
0
0
0
2
2
0
0
0
2
0
1
2
1
0
0
2
0
0
0
1
0
0
1
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
2
1
0
1
0
2
1
0
1
0
0
1
0
0
0
2
2
2
2
0
0
1
1
0
2
1
0
0
2
0
0
1
3
0
0
0
0
0
0
2
0
1
1
1
0
0
0
1
0
0
0
0
2
0
2
0
1
0
0
2
0
2
0
1
0
0
2
2
2
0
1
2
2
0
2
1
1
1
2
0
0
0
3
0
2
0
3
1
1
2
1
0
1
2
0
1
0
1
0
0
1
0
0
0
2
1
1
2
1
0
1
0
0
0
0
6
0
1
2
0
0
0
2
1
0
0
0
1
0
0
2
1
0
0
1
0
0
1
0
1
0
0
0
1
1
1
0
0
0
0
3
0
3
2
1
0
2
1
0
0
2
2
1
2
0
2
1
0
1
0
0
0
0
1
1
1
2
0
1
0
0
1
2
0
0
0
1
0
0
2
0
1
0
0
1
2
1
3
0
2
0
0
1
1
0
0
1
2
0
0
1
0
2
2
3
1
0
0
0
1
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
2
2
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
2
2
0
1
1
1
0
0
0
0
0
7
0
0
0
2
0
2
0
2
2
1
0
1
1
0
1
0
1
1
0
1
1
1
0
0
2
0
0
0
1
1
2
2
1
0
1
0
1
0
2
0
1
0
0
1
0
2
2
0
1
0
0
1
0
2
0
2
0
0
1
2
1
1
0
0
0
1
0
0
0
2
1
2
2
1
1
0
2
0
2
0
0
1
0
0
1
0
1
0
0
0
2
0
2
1
1
0
0
2
0
2
0
6
0
1
1
1
1
1
1
2
0
2
2
0
0
1
0
0
0
2
0
0
0
2
0
0
0
1
0
1
2
0
0
2
0
0
0
0
0
0
0
1
2
1
0
0
0
0
1
0
2
2
0
0
1
0
0
0
2
1
0
0
0
0
1
0
0
1
2
0
1
4
0
2
2
0
0
0
1
0
0
1
1
0
2
0
0
4
0
0
2
0
0
0
0
0
0
1
0
1
0
0
1
0
1
2
1
0
0
1
0
1
0
0
2
0
2
0
0
0
0
0
1
1
0
1
0
0
1
0
1
0
2
1
0
1
0
2
0
2
1
1
0
1
2
0
0
1
0
1
0
0
1
1
0
1
0
1
0
1
0
2
0
0
0
1
0
2
0
2
0
2
1
0
0
0
1
0
2
0
0
2
2
0
0
0
1
0
0
2
1
0
0
1
0
1
0
0
2
0
2
1
0
0
0
2
1
0
0
1
1
1
1
0
0
1
1
0
1
1
0
0
0
0
1
1
0
0
0
0
0
2
0
0
1
0
0
0
1
1
1
1
2
0
0
2
0
0
2
0
0
1
1
0
2
1
1
0
0
2
0
0
1
0
0
0
0
0
0
2
0
1
1
3
0
1
1
0
2
1
0
1
1
2
1
1
0
0
0
0
1
0
2
0
0
0
0
2
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
2
2
2
2
1
2
0
2
0
3
0
0
0
0
0
2
0
3
2
0
0
2
2
2
2
0
0
0
1
2
0
0
2
2
0
0
1
3
1
2
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
1
0
1
0
1
1
2
0
1
0
1
1
1
0
1
1
0
1
0
1
2
0
0
1
1
0
0
1
2
1
1
0
0
1
0
0
1
1
2
0
1
0
0
0
0
2
2
0
3
1
0
0
0
1
1
3
0
0
1
0
0
0
1
1
2
0
0
0
1
0
1
0
0
1
2
1
0
0
0
1
2
0
0
0
1
0
0
2
2
0
1
0
2
0
2
1
2
2
0
5
0
0
2
0
0
0
1
0
0
0
1
0
0
1
2
0
0
0
1
1
2
0
0
2
0
0
0
1
2
1
0
0
1
0
2
0
0
0
2
1
0
0
2
1
0
3
0
1
2
0
2
0
0
0
2
0
0
0
0
2
1
0
0
0
1
0
0
0
2
0
2
2
0
0
1
2
2
2
0
0
0
2
1
0
2
0
1
0
0
1
2
1
0
2
0
1
1
1
1
0
2
0
0
2
1
0
2
2
2
0
0
1
0
1
2
0
0
0
1
0
0
1
0
1
0
2
0
0
1
1
0
1
0
0
3
0
0
0
0
9
2
2
0
0
0
1
0
2
1
1
2
1
0
1
0
0
0
2
2
0
1
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
1
0
0
0
1
1
0
2
0
1
1
0
2
0
0
1
4
1
2
0
0
0
1
0
0
2
2
0
0
2
1
2
0
1
2
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
2
0
1
0
2
1
0
2
1
0
2
0
1
1
0
2
2
0
0
0
0
0
2
1
1
0
2
0
1
0
1
1
2
0
0
0
1
1
2
2
1
0
1
0
1
1
1
1
1
0
0
1
0
2
0
0
0
2
2
2
1
0
2
0
0
1
2
2
0
1
0
0
0
0
2
2
0
1
2
0
0
6
1
0
1
0
1
1
0
1
0
2
0
0
0
0
2
2
0
0
1
0
0
0
1
0
2
2
1
1
0
1
0
1
0
0
0
0
0
2
1
0
2
0
2
1
1
2
2
0
2
0
0
0
0
0
4
1
0
0
1
0
0
4
0
0
0
0
0
0
0
1
0
1
2
2
0
0
0
0
1
1
0
0
0
1
0
1
0
0
2
0
1
0
0
0
0
2
2
2
1
0
0
0
0
2
0
0
0
2
1
1
0
0
0
1
0
0
0
0
0
1
1
1
0
1
1
0
1
1
1
1
0
0
0
0
1
0
0
1
0
2
1
1
0
0
0
0
0
2
0
0
1
1
0
1
0
2
0
0
0
0
1
0
2
2
0
0
1
0
0
3
1
1
0
2
2
1
0
0
1
0
0
3
0
0
1
0
2
0
1
1
0
3
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
1
2
1
1
1
1
0
1
0
2
0
1
2
0
0
0
1
0
0
0
0
0
1
1
0
0
0
2
0
0
1
0
1
0
1
2
2
0
0
0
2
0
2
0
1
0
1
0
1
0
0
0
1
1
0
2
1
0
0
2
0
2
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
2
0
2
0
1
0
0
1
2
0
0
0
0
0
2
0
0
1
0
1
0
2
0
0
0
1
0
0
1
2
0
0
0
0
2
0
0
0
1
0
2
2
0
0
0
0
1
0
1
1
0
1
0
2
0
1
2
1
0
2
0
1
1
0
2
0
0
1
0
0
0
1
0
0
2
0
1
0
0
0
0
2
0
1
0
0
0
1
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
1
3
2
0
2
2
2
2
0
0
1
2
1
1
2
1
0
0
0
2
1
0
2
1
0
0
2
0
2
0
0
2
0
1
0
1
0
1
0
0
2
0
0
2
0
0
0
0
0
1
0
1
2
1
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
2
3
0
0
0
1
0
1
1
2
2
1
0
0
0
3
0
2
0
0
1
2
0
2
0
2
2
1
1
1
1
2
0
0
1
0
0
1
1
0
1
1
2
1
1
3
2
1
2
0
1
1
0
0
1
0
2
2
1
0
1
0
1
0
2
0
2
0
0
1
0
1
2
0
3
1
1
3
1
1
0
2
1
0
1
1
0
0
0
0
2
1
0
0
1
0
0
1
0
0
2
0
3
2
0
0
0
2
0
0
1
0
2
0
2
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
1
2
2
0
0
0
0
0
2
0
0
3
0
2
0
0
0
0
0
2
0
0
2
1
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
1
1
1
2
2
2
0
1
0
2
1
0
0
0
1
0
2
2
1
1
0
1
1
0
0
0
0
1
3
0
0
1
2
2
2
0
0
1
1
1
0
0
0
0
0
2
0
1
1
3
0
1
0
1
0
0
0
0
2
0
1
0
1
1
1
0
1
1
1
0
0
0
0
2
2
0
0
0
1
0
0
1
3
0
0
0
1
2
1
1
2
1
0
2
2
2
0
1
0
0
1
0
1
0
0
0
2
2
0
0
1
1
1
0
1
1
2
1
2
2
0
2
1
2
2
1
2
0
0
0
2
1
2
1
0
0
0
0
2
1
0
2
0
0
0
2
0
2
0
1
0
1
2
1
0
3
2
1
1
0
2
2
0
2
2
2
1
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
1
0
0
1
2
0
2
0
0
1
1
0
2
2
1
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
2
2
2
0
4
2
0
0
0
1
0
0
0
2
2
0
2
0
1
0
0
0
0
2
2
0
0
0
2
1
1
0
2
0
0
0
2
1
0
2
0
1
2
2
0
0
2
0
0
0
1
0
0
1
2
0
0
0
0
1
0
0
1
1
0
2
2
0
1
1
1
0
0
2
2
0
0
0
0
2
1
2
0
0
0
0
0
4
0
1
0
0
0
0
2
0
1
0
3
2
0
0
1
0
1
0
0
0
0
1
0
1
1
3
0
2
1
1
0
0
0
2
0
2
2
2
0
2
0
0
0
1
0
0
0
1
0
0
2
1
2
0
0
0
1
1
0
0
0
0
0
1
0
4
1
1
2
1
0
2
0
1
2
0
1
0
0
0
0
2
1
0
1
2
0
1
0
0
2
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
1
0
0
2
0
1
1
0
1
1
2
0
0
2
2
0
0
0
1
0
1
2
0
0
1
2
1
1
2
2
1
3
0
0
0
0
1
0
1
2
0
1
0
1
0
1
0
2
0
1
0
0
1
0
0
0
0
0
2
0
2
2
3
0
0
0
1
0
0
0
1
2
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
2
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
1
0
0
0
1
2
0
0
1
1
1
1
0
0
0
2
0
0
0
0
0
2
2
2
1
1
0
0
0
0
0
0
1
0
0
1
0
0
2
1
0
1
1
1
1
0
0
1
1
2
1
2
0
0
0
2
0
2
0
0
1
0
1
0
0
1
1
2
2
2
2
1
0
2
2
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
2
2
3
2
0
0
0
1
0
0
2
2
0
0
1
0
2
1
1
0
0
0
1
1
0
0
1
0
0
1
1
0
0
0
0
0
1
2
0
2
1
0
0
2
1
1
0
1
0
1
2
0
0
1
0
0
0
2
1
0
1
0
1
1
1
2
2
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
1
2
0
0
2
0
1
3
1
1
0
0
2
0
0
0
1
1
2
1
1
2
1
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
2
2
0
2
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
1
2
1
0
0
1
3
2
2
0
3
2
0
2
0
0
4
0
0
0
1
0
0
2
1
2
0
0
0
1
0
0
0
0
0
1
2
1
2
0
1
1
1
0
1
0
0
0
1
1
0
0
2
0
0
2
0
3
0
2
0
2
0
0
0
0
0
1
2
1
0
0
0
1
1
0
1
3
0
1
1
2
1
2
1
0
0
2
2
0
1
2
0
2
0
0
1
0
2
2
2
0
0
2
0
0
2
1
1
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
2
1
1
0
0
2
2
1
0
1
0
0
0
0
2
2
2
2
0
2
2
0
2
1
0
0
2
1
0
3
2
0
0
2
2
0
0
1
1
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
2
0
0
2
0
0
2
0
0
2
0
0
1
1
0
0
0
0
2
0
1
0
0
0
2
1
0
0
0
2
2
0
6
0
2
0
0
1
2
0
0
1
2
0
2
0
0
2
0
0
0
0
0
0
0
0
1
1
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
1
0
0
0
0
0
0
4
1
1
1
2
2
1
0
0
1
0
0
1
0
1
1
2
0
0
1
0
0
2
0
2
0
1
0
0
2
0
0
0
0
0
0
1
1
1
1
0
1
0
3
0
0
0
0
0
0
1
2
1
0
0
0
2
0
0
2
1
0
1
0
0
1
0
0
1
1
2
0
2
0
2
0
0
0
2
0
0
1
3
1
0
1
0
0
2
1
1
0
2
0
1
1
0
0
0
1
0
1
2
0
0
0
1
0
0
2
2
2
0
0
0
1
0
0
1
0
2
2
0
2
0
0
0
0
2
0
0
1
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
3
0
0
0
2
0
2
0
0
0
0
2
2
2
2
2
0
0
0
0
2
2
0
0
1
2
4
0
0
0
0
0
0
0
0
0
0
0
1
1
2
2
1
2
0
0
0
0
0
1
2
0
0
2
0
0
0
0
2
2
0
0
1
0
0
0
0
0
1
0
0
2
2
0
1
1
0
0
3
0
0
3
0
0
2
1
0
0
0
0
0
0
1
2
0
0
0
0
2
3
1
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
1
2
0
0
1
0
0
0
0
1
1
0
2
0
2
4
1
0
0
1
2
2
0
1
0
2
0
0
1
0
1
1
1
0
3
0
2
2
0
0
0
0
1
3
0
2
2
0
2
2
1
0
0
0
0
0
0
1
0
0
2
2
1
2
3
0
0
0
4
2
0
0
2
0
1
0
1
0
0
2
0
1
0
0
0
2
0
1
2
2
2
0
2
3
0
0
0
2
0
2
2
1
2
1
4
0
2
0
0
1
0
1
0
2
1
0
0
1
0
0
0
0
0
0
1
0
1
1
0
1
1
0
1
2
1
0
0
2
1
0
4
0
2
1
1
0
2
1
0
0
1
1
0
0
0
0
1
1
0
0
0
2
0
0
0
0
1
1
0
0
0
0
2
0
0
1
0
0
0
0
1
1
0
2
0
2
0
1
0
1
0
1
1
0
1
0
0
2
1
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
3
1
0
0
2
0
2
1
1
1
2
2
0
0
0
2
1
0
2
1
0
0
0
2
0
2
1
0
0
2
3
1
1
2
0
3
0
0
0
0
2
0
1
2
1
4
0
2
0
2
0
0
1
1
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
1
2
3
0
1
0
0
0
2
0
1
0
0
0
0
1
0
2
1
2
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
2
0
0
2
1
4
2
1
0
1
1
0
1
2
0
0
0
0
0
0
1
0
0
2
0
0
1
1
0
2
0
1
0
1
2
0
0
0
1
2
1
0
0
0
0
0
2
3
0
0
2
0
0
1
0
1
0
2
0
2
1
1
0
0
0
2
0
0
1
2
0
0
2
1
3
1
1
0
0
0
0
2
0
0
1
0
2
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
1
1
0
1
1
0
0
0
0
0
0
1
2
1
1
1
0
0
2
0
2
1
0
1
2
0
0
2
0
2
0
0
0
0
2
0
1
2
1
0
0
2
1
2
1
1
2
2
2
1
0
0
1
1
0
1
0
0
0
0
1
0
1
0
1
2
0
1
0
2
1
1
1
0
1
1
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
1
1
2
1
2
2
0
0
0
2
1
0
0
0
2
0
2
0
1
1
0
0
0
2
0
1
0
2
0
1
1
2
2
0
0
1
3
1
0
0
1
0
0
1
2
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
2
2
0
2
0
2
3
1
0
2
1
1
0
6
0
1
1
1
0
0
0
1
0
0
0
0
1
0
2
1
0
2
2
2
1
2
1
0
2
0
2
0
1
0
1
0
2
1
0
3
1
0
0
0
0
0
2
0
2
1
0
1
1
1
3
2
1
0
1
2
0
0
0
0
2
0
3
2
0
0
0
0
2
1
0
0
0
0
1
1
0
1
2
1
2
1
0
0
1
1
1
0
0
0
2
2
0
1
0
0
2
0
0
1
0
2
0
0
0
0
1
0
2
4
2
1
0
1
1
1
0
2
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
1
0
1
1
1
0
0
0
1
2
0
0
2
0
1
1
0
1
1
2
0
0
1
1
2
1
2
2
2
1
2
2
2
0
0
1
2
0
1
1
2
0
2
0
1
0
0
0
0
1
2
0
1
0
1
0
1
1
0
1
0
1
0
0
0
0
0
0
1
0
3
3
0
0
0
1
0
3
0
0
2
0
0
1
0
1
0
2
1
1
4
0
0
0
0
2
2
0
0
1
0
0
0
1
1
0
0
0
2
1
2
0
2
2
1
0
1
0
1
0
1
1
0
0
0
0
0
0
1
0
0
2
0
2
0
2
0
1
2
2
1
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
6
0
2
1
0
0
0
0
0
1
0
1
0
2
2
0
1
0
2
0
2
0
1
0
0
2
0
1
0
0
1
0
1
0
1
0
1
2
2
0
1
1
0
0
0
0
1
0
0
1
2
0
0
1
0
0
0
0
1
0
2
0
1
0
1
1
0
0
2
0
0
2
0
0
2
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
1
2
1
1
0
0
1
1
2
0
1
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
2
1
1
0
1
2
2
0
0
0
0
2
0
1
0
1
2
0
0
1
0
0
0
0
1
2
0
0
2
1
0
0
0
1
2
2
0
0
0
2
0
0
0
1
1
0
2
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
1
0
0
1
1
0
0
0
2
0
2
0
1
2
0
0
1
2
1
2
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
1
0
0
1
1
0
1
0
0
1
1
0
0
0
0
2
0
0
1
0
0
0
0
2
1
0
0
0
0
2
1
2
0
1
2
0
0
0
1
0
0
0
0
0
0
0
2
0
1
1
1
0
0
0
0
0
1
0
2
2
1
1
1
2
0
0
0
0
0
0
0
2
0
0
2
2
0
0
1
0
2
2
2
2
0
1
0
0
3
2
0
2
1
0
1
0
0
4
1
0
0
0
0
0
3
0
1
0
0
0
0
1
1
2
3
1
1
0
0
2
0
0
0
1
1
1
1
0
0
0
0
2
0
0
2
0
2
0
0
2
0
0
0
0
2
0
2
0
2
3
0
2
0
0
0
0
2
0
1
0
0
0
0
1
2
0
2
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
2
1
1
1
0
0
1
4
0
1
0
0
0
2
2
0
0
3
0
0
0
2
0
2
0
1
0
0
0
2
1
1
2
0
0
1
1
1
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
1
0
0
1
0
1
1
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
1
2
2
2
2
1
2
1
1
3
0
0
0
1
0
1
2
2
0
0
0
0
0
1
0
1
1
0
0
1
2
2
0
2
2
1
0
0
0
2
1
0
0
1
0
1
0
0
0
2
2
0
0
0
0
0
1
0
2
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
2
0
1
2
1
0
0
1
0
0
0
1
0
0
1
1
1
0
0
0
0
1
1
0
2
0
0
0
1
0
1
2
2
2
1
0
0
0
1
1
1
1
2
1
0
0
0
0
2
0
1
1
2
1
0
0
1
0
1
0
0
0
1
1
0
1
0
0
1
0
1
2
0
2
0
2
0
1
2
0
0
3
0
1
0
0
0
1
1
0
0
1
2
1
0
0
0
0
1
1
1
0
2
2
0
0
1
0
0
0
0
2
2
2
0
0
1
1
1
0
0
0
1
0
0
1
0
0
0
1
0
1
1
1
2
0
0
0
0
0
1
1
0
0
0
1
0
1
0
1
2
3
1
0
0
2
1
0
0
0
0
2
1
0
0
2
1
1
0
0
2
0
1
0
1
0
0
1
0
2
0
1
2
1
1
0
1
1
0
0
0
0
0
0
0
1
1
2
0
1
1
0
1
2
0
0
0
2
1
0
0
0
2
0
0
3
0
1
1
0
1
1
0
0
0
0
3
2
3
2
0
0
0
1
0
0
0
0
0
0
1
2
1
3
3
3
2
0
1
1
2
2
0
0
0
0
1
0
0
1
2
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
1
1
0
0
0
0
2
0
1
0
1
1
1
1
0
1
0
0
2
2
0
2
0
1
1
1
0
0
0
0
2
0
1
0
0
0
1
2
1
0
1
0
1
0
1
0
2
1
0
1
1
1
0
0
1
0
0
2
0
1
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
2
0
2
0
0
1
2
0
0
0
2
2
0
1
0
1
0
1
0
1
0
1
0
0
1
0
2
0
2
0
1
1
0
0
0
0
2
2
0
0
2
0
1
1
0
0
5
0
1
1
1
1
0
3
1
1
0
0
1
1
1
0
0
2
1
2
3
1
0
1
0
1
0
0
2
0
0
0
1
1
0
0
1
1
0
0
3
0
0
1
0
3
0
0
1
0
0
2
1
2
2
0
0
2
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
2
0
1
0
1
0
0
2
0
1
1
2
1
0
0
2
0
0
0
1
0
2
1
0
1
1
1
2
0
0
0
0
0
2
1
1
0
0
2
0
0
0
0
0
0
2
0
0
2
2
1
0
2
1
2
0
2
0
1
2
0
2
0
1
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
1
2
0
0
1
0
2
0
1
0
2
1
1
0
0
0
0
1
2
0
1
2
2
0
0
0
0
0
2
0
1
0
0
0
1
2
1
2
2
0
0
1
1
0
0
1
0
0
0
2
0
0
0
0
0
2
1
1
0
2
0
0
2
0
1
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
1
0
0
2
0
2
1
1
0
1
0
0
1
0
0
0
0
2
0
2
0
0
2
2
2
1
2
2
0
0
0
0
0
0
2
0
1
1
0
0
1
0
1
1
0
0
0
0
1
2
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
1
2
0
2
0
0
1
0
1
1
1
0
0
1
1
0
1
1
2
1
1
1
1
1
2
0
1
1
0
0
0
2
0
0
0
0
1
0
1
2
1
1
0
0
1
0
1
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
5
1
0
2
2
0
0
0
0
0
1
0
0
1
2
2
1
2
1
0
1
0
0
1
1
1
1
2
2
0
0
1
0
1
3
1
1
2
0
0
1
0
0
0
2
1
0
1
1
0
2
2
0
1
2
0
3
2
0
3
1
1
0
0
2
0
2
0
0
1
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
2
0
1
2
1
0
1
0
0
1
2
0
0
1
1
0
1
0
1
1
2
0
1
1
0
1
3
0
0
2
1
0
0
0
3
0
1
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
2
0
1
0
0
0
1
0
2
0
3
0
1
2
1
2
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
2
1
0
1
0
2
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
1
1
0
2
0
5
1
1
0
0
1
1
1
1
0
0
1
0
0
1
0
0
0
1
0
1
1
0
2
1
0
0
0
2
0
0
2
1
0
0
0
2
0
0
1
1
2
0
0
2
1
0
0
0
2
0
2
1
0
0
2
0
0
0
0
1
1
0
0
1
0
1
1
0
0
2
3
1
2
0
0
0
0
0
0
0
2
1
2
0
2
2
0
0
1
0
0
0
0
2
1
0
1
1
1
1
0
2
0
1
0
1
0
2
4
0
0
0
0
1
2
1
0
0
0
1
0
2
0
0
1
2
2
0
1
0
2
1
2
0
3
2
0
0
0
2
2
0
2
1
2
1
0
0
1
0
0
1
0
0
0
0
0
2
0
0
2
0
2
0
0
1
0
1
1
2
2
0
1
1
0
3
0
0
0
1
0
0
2
0
0
2
1
0
2
1
2
1
2
1
0
2
1
2
0
0
1
0
0
0
2
1
0
0
0
0
2
1
0
0
0
1
0
0
1
1
1
0
0
1
0
1
0
1
1
0
0
2
0
0
0
1
5
0
0
0
0
1
0
1
0
0
1
1
0
0
0
2
2
1
0
1
1
1
2
2
0
0
0
1
0
1
1
0
0
0
0
0
3
2
1
0
2
0
0
0
0
2
0
1
2
0
2
2
0
2
2
2
0
1
1
2
0
0
0
0
2
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
1
0
0
2
0
2
0
0
0
2
2
0
2
0
0
2
1
2
1
0
0
2
1
3
0
1
1
2
1
0
0
0
1
0
0
1
1
0
0
0
0
2
3
1
0
1
1
0
2
0
1
0
1
0
2
0
2
0
0
0
0
1
0
0
0
0
2
1
2
0
1
2
1
3
1
0
0
2
0
0
1
1
2
0
1
1
1
0
1
0
2
1
2
0
0
0
3
1
3
0
0
1
0
1
2
1
2
0
0
1
0
0
0
0
0
1
1
0
0
0
1
2
0
0
0
0
1
2
0
0
1
1
0
1
0
1
0
0
2
0
0
0
2
2
0
0
1
1
0
2
0
0
0
2
2
0
0
2
1
1
0
1
0
0
2
1
0
4
0
0
1
1
1
0
0
1
0
0
2
0
0
0
0
3
0
1
0
1
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
1
0
2
1
0
2
0
0
0
1
0
0
0
1
1
2
1
2
2
1
2
1
0
0
1
0
2
1
2
1
3
1
0
1
0
1
0
0
0
0
2
0
0
1
0
1
0
1
0
0
0
0
0
2
2
2
0
1
2
0
0
3
2
1
1
0
1
0
2
1
6
2
0
0
1
0
0
0
2
1
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
2
3
0
0
1
0
0
1
0
1
0
1
0
0
1
0
0
0
0
1
3
1
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
2
0
1
0
0
2
1
2
0
1
0
0
1
1
1
2
0
1
1
0
0
2
0
2
2
2
0
0
0
0
2
0
0
1
1
1
2
1
1
0
2
0
2
2
1
1
1
0
2
1
2
0
0
1
1
0
1
1
0
1
2
1
0
0
2
0
2
1
0
1
1
0
0
0
2
0
1
0
0
3
2
1
0
0
2
0
2
1
0
2
1
0
1
1
1
1
1
1
2
0
0
4
1
2
0
0
2
0
0
2
0
1
0
0
0
1
2
2
1
0
0
0
0
0
0
3
0
1
0
1
1
5
0
2
0
1
3
0
0
2
1
2
0
1
1
1
0
0
0
0
0
1
0
0
2
2
0
1
1
1
1
2
0
3
0
0
6
1
0
0
2
0
1
0
2
0
0
0
0
2
0
2
1
0
2
0
0
1
0
1
0
0
1
0
1
2
2
1
0
0
4
1
1
0
0
0
0
2
2
0
0
2
0
0
0
1
2
0
1
0
0
1
0
0
2
1
0
3
0
2
1
0
0
0
0
0
1
0
0
0
0
2
0
2
1
0
2
0
0
0
0
0
1
1
1
0
0
0
0
1
1
0
0
0
1
2
1
0
1
1
0
1
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
1
0
1
0
2
1
1
0
0
1
1
2
4
2
1
0
0
0
0
0
2
0
2
1
0
2
1
2
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
2
2
1
2
0
2
1
0
0
0
2
2
1
0
1
1
2
0
0
0
0
0
1
1
1
0
1
1
1
0
0
0
0
1
2
0
0
1
1
0
4
1
2
0
0
0
0
0
1
1
2
3
1
0
0
0
0
2
0
1
1
0
2
0
2
0
0
0
0
0
0
1
2
1
0
1
0
1
0
1
0
4
0
0
2
1
0
1
0
0
0
1
0
0
1
1
1
0
2
1
2
2
1
1
0
0
0
3
1
0
0
1
2
0
0
0
2
1
2
0
0
0
2
0
2
3
0
0
1
0
2
1
1
2
1
0
0
0
1
1
0
1
0
2
2
2
1
1
0
0
0
2
2
2
1
3
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
1
0
0
0
1
6
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
1
0
2
0
0
1
1
0
1
0
0
0
0
2
0
2
0
0
2
0
1
2
0
0
0
2
2
2
1
0
1
0
1
1
0
0
0
0
0
0
1
0
2
0
1
1
0
1
0
0
0
0
0
2
1
0
0
0
2
1
2
0
0
0
0
0
1
2
0
2
0
0
4
0
1
1
0
0
1
0
1
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
1
1
1
2
2
2
0
0
3
0
2
1
2
0
0
0
2
0
0
1
1
0
1
0
0
0
0
1
1
1
2
0
1
0
0
0
0
2
0
0
1
2
0
0
2
1
3
1
0
2
0
2
0
0
2
1
0
2
1
2
0
0
1
0
2
0
2
0
0
0
0
0
0
1
2
0
0
1
0
2
2
1
0
0
0
1
0
0
0
1
0
0
2
2
0
1
0
1
2
1
1
0
1
1
2
2
0
2
2
0
0
2
0
1
0
0
0
0
1
0
0
0
2
0
1
0
1
0
1
0
0
0
2
1
2
0
1
2
2
1
0
0
1
1
1
1
0
0
0
0
1
0
2
0
1
1
1
1
1
1
0
0
1
0
0
1
0
0
2
0
0
1
1
1
0
1
2
2
0
1
2
4
0
2
0
0
2
1
0
0
0
0
1
0
3
1
0
1
0
0
0
0
0
1
0
2
2
2
0
0
1
0
0
2
4
2
0
1
0
0
0
1
1
1
2
1
0
0
0
0
1
0
1
0
0
1
3
0
1
2
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
1
0
0
0
2
0
2
0
0
2
1
0
0
3
0
0
0
0
2
2
0
0
0
1
0
0
0
2
0
0
1
0
0
0
2
0
2
2
1
1
0
0
2
0
2
2
1
0
1
0
0
0
0
2
2
0
0
0
1
1
0
1
0
0
0
1
1
3
0
2
2
1
0
0
0
1
1
0
0
1
0
2
1
1
0
2
2
0
0
0
1
2
1
2
0
0
2
1
2
0
0
1
1
0
0
2
0
0
2
0
2
0
1
4
1
2
2
0
1
2
0
0
2
1
0
2
2
2
0
0
1
1
1
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
1
1
0
2
1
0
0
0
1
1
1
0
2
2
1
1
1
0
2
1
0
1
0
0
2
1
1
0
0
0
0
1
1
0
0
1
0
1
1
1
2
0
1
3
1
0
0
1
0
0
0
0
1
0
3
0
0
1
1
0
0
0
0
1
1
1
0
3
2
0
1
0
0
2
0
0
0
0
0
2
2
1
0
0
1
0
0
0
2
0
0
1
0
0
0
2
0
0
2
0
3
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
1
0
1
3
0
0
0
1
1
2
0
0
1
2
1
2
0
0
0
0
0
0
0
3
0
0
1
2
0
0
0
1
0
0
0
0
0
1
0
0
1
0
2
2
0
0
0
0
1
1
2
0
0
0
1
0
1
0
0
0
0
1
0
1
1
2
3
0
0
1
0
0
1
1
1
0
0
0
0
1
0
0
2
0
2
1
0
0
1
0
1
1
3
1
0
3
3
0
1
2
0
0
2
0
2
2
0
0
3
1
0
0
2
0
1
0
2
0
0
0
1
2
2
0
0
1
0
0
0
0
0
1
0
0
1
0
2
1
0
0
0
0
0
0
0
2
0
0
1
0
2
2
1
2
2
0
0
1
1
0
0
3
0
2
1
0
0
2
0
1
2
0
0
0
1
0
0
0
0
0
2
1
0
0
0
1
0
1
2
2
0
1
1
1
0
0
1
1
0
0
0
2
2
0
2
0
1
1
0
0
2
1
1
0
1
2
1
1
0
0
0
1
0
1
2
1
1
0
3
0
1
0
0
0
0
0
1
5
0
2
2
0
1
0
2
2
2
0
0
0
1
1
0
2
0
0
1
1
0
1
1
2
0
0
2
0
0
0
0
3
0
0
0
0
2
0
0
0
2
0
2
1
0
2
0
2
0
0
2
0
0
0
2
2
1
0
1
0
2
0
1
0
0
0
0
0
2
0
0
1
0
0
3
0
0
0
0
2
0
0
1
5
0
1
0
1
0
0
1
1
0
1
0
1
0
0
1
0
0
1
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
1
1
0
0
0
1
2
2
1
3
1
1
1
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
2
0
0
1
1
0
0
0
0
7
0
1
2
0
2
0
0
0
1
1
0
1
0
1
2
1
0
0
0
1
1
0
1
0
1
0
2
0
2
1
1
1
1
0
1
2
0
0
0
3
2
0
0
0
1
0
0
0
0
1
1
1
1
1
0
0
1
1
0
1
0
2
2
1
0
0
2
1
0
1
1
2
0
0
0
0
1
0
0
0
0
2
2
1
1
0
0
0
1
0
2
2
0
2
2
0
0
0
2
1
2
1
1
2
0
1
1
2
0
1
0
2
2
0
2
0
0
0
2
0
2
0
0
0
1
0
1
0
0
0
2
0
0
1
0
0
1
2
2
0
1
2
1
1
2
0
2
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
7
0
1
0
1
2
0
3
5
1
0
2
0
2
2
2
0
2
0
2
2
2
2
2
1
2
1
0
1
1
0
0
1
0
0
2
5
0
0
2
0
2
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
1
0
0
1
0
0
1
3
0
0
2
1
0
2
2
0
0
0
2
0
0
0
0
1
2
0
0
0
2
0
0
0
0
2
0
1
1
0
2
0
2
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
2
2
0
0
0
0
0
0
1
2
0
0
2
1
0
1
2
1
0
2
0
1
2
0
0
1
1
0
0
1
0
2
0
2
0
1
1
1
0
0
2
0
0
2
0
1
2
0
0
2
0
1
1
1
2
0
1
1
0
0
0
1
0
2
2
0
1
1
2
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
2
0
0
3
0
0
0
0
0
0
0
2
1
1
0
0
0
1
0
0
0
1
0
2
2
0
1
0
2
0
0
1
2
0
2
0
0
0
2
0
4
0
1
2
2
0
2
0
0
1
0
1
1
0
1
2
1
2
0
0
0
0
0
0
2
1
2
1
0
0
0
0
0
0
0
2
2
0
2
0
0
3
1
2
0
0
13
0
0
2
1
0
0
1
0
0
0
0
1
1
0
1
0
2
0
1
0
1
0
1
0
0
0
0
0
2
0
1
0
2
0
0
0
2
0
0
0
2
1
0
0
1
0
1
0
0
2
0
0
0
2
2
2
0
2
0
0
1
0
1
0
1
1
0
1
2
1
0
0
1
2
2
0
0
2
1
0
2
1
2
0
0
0
0
1
0
1
0
0
0
0
2
0
0
1
0
1
2
0
0
1
0
1
0
0
0
2
0
1
0
2
2
0
1
1
2
1
0
0
1
0
0
0
0
2
1
0
0
2
0
0
2
0
0
2
1
0
2
2
1
0
0
0
0
0
1
2
0
4
0
0
0
0
2
1
0
1
2
1
0
2
1
0
1
2
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
2
2
2
2
0
2
0
1
0
0
0
0
2
0
1
2
1
1
0
0
1
1
2
0
2
1
0
1
1
1
1
0
1
0
0
1
0
1
0
1
0
0
0
0
2
1
0
0
0
1
1
1
2
1
0
0
1
0
5
0
0
0
0
0
1
0
2
0
0
1
1
1
2
0
1
0
1
0
0
0
0
1
0
0
0
1
1
2
0
0
0
1
0
0
1
1
0
0
0
2
0
1
0
1
0
2
2
2
0
0
1
1
1
0
0
0
1
0
0
2
1
1
1
1
0
0
2
2
2
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
2
0
1
0
0
1
0
0
2
0
0
0
1
0
2
3
0
2
1
0
0
0
1
0
0
1
0
0
1
0
1
0
2
2
1
2
0
0
2
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
1
0
0
0
1
0
1
0
0
1
1
2
0
1
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
1
2
0
5
2
0
0
2
2
0
1
0
1
0
0
2
2
0
0
0
0
0
1
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
1
0
0
0
0
2
0
1
1
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
2
2
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
1
0
1
2
1
1
0
0
3
0
2
0
0
0
1
0
0
0
2
1
0
2
1
0
0
0
2
0
0
0
1
0
0
0
1
0
2
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
2
0
0
0
2
0
1
2
2
1
1
2
3
1
0
0
1
0
3
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
2
3
2
1
1
0
1
0
0
0
0
0
0
1
0
2
1
2
0
0
0
1
0
0
0
1
2
0
1
1
0
0
0
0
2
1
3
0
2
1
0
2
0
0
1
0
2
4
0
0
0
0
3
1
1
1
0
0
0
0
0
2
0
0
0
1
4
0
1
0
0
0
0
1
2
1
2
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
1
1
1
1
0
3
2
1
0
2
0
1
0
0
0
0
0
2
1
0
0
0
1
0
0
2
0
0
1
2
0
2
0
1
0
0
0
0
2
0
0
1
1
2
0
0
0
1
1
0
1
2
0
2
0
0
2
0
2
0
0
1
0
0
2
0
2
0
0
1
1
1
0
3
0
2
0
0
1
0
0
0
0
0
2
1
1
1
2
1
2
0
0
1
0
2
2
1
0
0
1
2
2
0
0
2
0
0
0
0
1
2
1
1
2
1
0
0
2
2
2
2
2
0
0
1
1
1
0
2
0
2
5
1
0
2
0
1
0
2
2
0
1
0
1
0
0
1
0
1
1
1
1
0
0
1
2
0
0
0
1
0
0
3
0
0
2
0
2
0
2
1
2
1
2
2
0
1
0
1
2
0
1
0
1
1
2
0
0
0
1
0
1
0
0
1
0
0
1
3
1
0
0
1
2
1
0
0
0
0
2
2
0
2
0
0
1
0
0
1
0
0
2
0
1
0
1
0
1
0
0
0
0
0
1
1
1
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
1
0
2
1
2
4
0
1
1
0
0
0
2
2
0
1
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
2
0
2
1
1
3
0
0
0
1
1
2
2
0
1
0
0
1
0
0
1
1
0
0
0
0
2
0
1
0
1
0
0
0
0
0
1
1
0
0
3
1
2
0
2
1
2
1
0
0
0
0
0
2
1
1
1
0
1
0
1
1
2
1
0
0
0
0
2
1
0
2
3
0
1
1
0
2
0
0
2
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
2
1
1
0
0
1
1
1
0
0
0
1
2
0
0
1
2
0
0
0
0
2
0
0
1
0
0
1
2
0
1
0
0
0
0
2
0
1
0
1
2
0
0
0
0
1
0
2
1
0
2
1
0
0
1
0
1
2
0
0
0
1
0
1
0
1
0
2
0
0
0
0
2
1
0
0
1
0
1
0
2
0
1
0
1
2
1
0
0
1
1
0
0
0
0
0
1
2
0
2
0
1
2
0
0
4
1
2
2
0
2
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
2
2
1
0
1
0
0
0
0
0
0
1
1
2
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
1
3
2
0
1
5
1
2
0
1
1
0
0
0
2
0
0
0
2
0
2
0
0
3
0
2
1
3
0
1
0
1
0
2
1
0
0
0
1
0
0
0
2
1
0
0
0
0
1
1
3
0
2
0
0
1
0
1
0
1
2
0
0
1
1
0
0
0
0
1
0
2
1
0
0
2
0
1
1
0
0
1
0
1
1
0
0
1
0
1
0
0
1
0
1
0
1
2
0
0
0
1
0
2
2
0
0
0
0
2
1
2
0
0
1
2
1
0
2
3
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
2
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
1
2
2
1
1
0
0
0
1
1
0
0
0
0
1
0
0
2
1
2
2
1
0
1
0
0
0
0
1
0
0
1
2
2
1
2
1
1
2
0
2
1
0
0
1
1
0
1
0
0
3
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
1
1
2
0
0
2
2
0
0
0
0
0
1
1
2
1
0
0
2
0
1
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
2
0
2
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
1
0
1
0
2
0
0
0
0
2
2
0
1
3
0
0
0
0
1
1
0
2
2
0
0
0
0
1
0
0
1
0
1
0
0
0
0
3
2
1
0
0
1
0
1
2
1
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
1
1
0
1
0
0
2
0
1
1
0
0
2
0
0
0
1
0
0
2
0
0
0
1
2
1
0
2
2
2
0
2
0
0
1
0
1
1
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
1
0
1
0
0
0
0
3
0
0
0
2
0
0
1
0
0
2
0
2
2
0
1
0
1
1
1
0
1
2
2
2
1
0
0
0
1
1
0
1
1
0
1
1
0
2
0
0
2
1
0
0
0
1
1
1
2
2
0
1
0
0
2
0
1
0
2
0
1
0
2
1
0
0
2
0
0
0
0
2
0
0
0
2
2
0
0
0
1
0
1
0
1
0
1
0
1
2
0
2
0
0
0
1
1
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
2
2
0
2
1
0
0
1
0
0
2
0
0
0
0
2
1
0
0
0
2
0
0
0
1
4
0
1
2
1
0
1
2
0
0
2
0
0
1
1
0
1
2
2
0
2
1
1
2
0
0
2
1
1
0
1
0
2
1
0
0
1
0
2
0
0
2
0
1
0
0
4
2
0
2
1
0
0
2
1
0
0
2
2
1
2
2
0
1
0
2
0
0
3
2
1
4
0
2
4
0
1
0
0
1
0
2
0
3
0
0
1
0
2
2
0
0
1
1
1
0
0
1
0
4
2
1
1
2
0
0
0
0
1
0
0
2
2
0
0
1
0
1
0
0
0
0
2
0
2
1
1
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
2
0
1
0
1
2
2
2
1
0
1
2
0
3
0
1
2
0
0
1
0
0
0
0
0
0
0
0
1
0
4
0
2
0
0
1
0
0
0
1
2
2
2
0
0
1
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
3
0
1
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
1
1
0
1
1
2
2
0
2
0
1
2
0
1
0
2
0
0
1
0
0
0
1
0
1
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
3
0
2
0
2
1
0
0
0
0
3
1
0
0
1
0
0
1
0
1
0
1
2
0
1
0
1
1
2
1
2
2
1
0
0
1
1
0
0
1
0
0
0
0
0
1
1
0
0
2
1
0
2
1
0
2
1
0
0
0
2
0
0
0
0
0
0
0
2
1
1
2
0
0
0
1
0
2
1
2
1
2
0
0
0
0
0
2
2
0
0
0
1
2
0
2
2
0
2
3
0
0
2
2
1
1
2
0
2
2
1
0
1
0
0
0
3
0
0
1
1
0
0
0
0
0
1
1
1
1
3
0
0
1
0
2
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
6
2
1
0
2
1
1
0
0
1
2
1
0
0
0
0
2
1
0
0
2
0
0
3
0
2
1
3
1
2
0
0
2
4
1
2
1
1
0
0
0
0
0
2
2
2
0
2
0
0
2
2
2
0
0
0
2
2
0
1
3
1
1
0
1
0
3
2
1
0
0
3
0
2
1
0
0
1
1
0
2
2
0
0
2
1
0
0
1
0
0
0
0
1
1
0
2
0
0
0
1
0
1
0
0
2
1
0
0
0
3
1
0
0
2
3
0
1
0
0
0
1
0
0
0
0
0
2
0
0
2
2
0
0
0
2
0
0
2
1
0
3
0
0
0
2
0
1
2
0
0
1
0
0
0
1
0
1
1
1
2
0
1
1
2
0
0
0
0
1
0
1
1
0
3
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
2
0
3
0
1
1
1
0
1
0
0
0
2
0
0
0
1
1
1
1
0
0
1
0
2
0
0
0
0
1
0
0
0
0
1
2
0
0
1
0
2
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
1
1
2
0
0
3
0
0
2
1
1
0
1
0
0
0
3
0
2
0
0
0
1
1
0
2
2
1
0
0
1
1
0
1
1
1
0
0
0
2
0
2
2
1
0
1
0
0
0
1
1
0
1
0
0
0
0
0
2
0
0
1
0
0
0
2
1
0
0
1
1
2
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
1
2
2
0
2
1
1
0
1
0
1
2
0
0
1
0
1
1
2
4
2
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
2
1
0
2
0
0
2
0
0
0
2
1
0
3
0
2
0
0
0
0
2
0
1
0
0
0
2
2
0
1
2
1
2
2
2
0
1
0
0
0
0
1
2
1
0
2
0
0
0
1
0
2
1
0
3
0
0
2
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
1
1
1
1
0
1
1
0
0
0
1
0
2
2
2
0
0
0
0
1
0
1
2
1
1
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
2
3
0
0
2
0
0
0
0
1
2
0
0
1
2
2
0
2
2
0
0
2
0
1
0
0
1
2
0
0
1
2
2
0
0
0
1
0
0
0
0
0
2
0
1
0
2
2
1
2
1
0
1
0
0
0
1
1
1
1
1
0
2
0
0
0
2
0
1
2
2
0
0
2
0
0
2
2
1
0
2
0
0
0
1
0
2
0
2
2
1
0
1
2
0
1
0
0
0
2
1
0
2
0
1
1
0
2
0
0
1
1
2
0
1
0
2
0
0
2
0
0
0
0
1
1
2
1
2
3
2
0
2
2
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
2
1
0
0
0
1
1
0
1
6
0
1
0
0
3
0
0
2
0
0
1
0
0
2
2
2
2
0
1
0
0
0
1
0
0
0
1
2
1
0
0
0
0
1
0
1
1
2
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
2
1
2
0
1
0
1
2
2
0
0
3
1
1
0
1
0
0
1
2
0
2
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
1
1
0
0
0
2
0
5
3
0
1
0
2
1
1
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
1
1
0
0
0
0
0
0
1
0
0
2
2
1
1
4
0
1
0
0
0
1
2
1
0
0
1
0
1
2
0
1
0
1
0
0
1
0
1
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
2
0
1
0
2
1
1
0
0
0
2
0
2
0
3
2
5
1
0
0
1
2
1
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
1
0
2
1
0
0
1
2
1
0
0
2
2
1
1
1
1
0
0
0
1
2
0
1
0
0
0
0
1
1
0
0
1
0
0
1
0
2
1
0
0
0
1
0
1
0
0
0
3
1
0
2
1
0
0
0
1
0
2
0
1
0
0
0
1
1
1
0
0
0
0
0
0
2
0
1
3
0
0
2
0
1
0
0
1
0
1
0
1
3
0
1
0
0
1
0
2
1
0
1
2
1
2
2
2
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
2
1
0
0
1
0
1
0
0
0
1
0
2
0
1
1
2
2
0
2
0
2
1
0
0
0
0
1
2
1
1
1
0
1
0
0
0
0
0
0
0
2
1
0
1
0
1
0
1
0
2
1
2
0
0
0
2
2
0
1
1
2
0
0
0
2
2
0
2
0
0
1
0
1
0
1
0
1
0
1
1
0
0
2
0
0
0
3
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
1
2
1
0
1
0
2
0
0
0
2
0
0
1
0
2
0
1
1
0
2
0
2
1
0
1
0
0
2
1
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
6
0
0
1
0
0
1
1
0
1
1
0
0
0
0
2
0
1
3
1
0
0
0
0
1
1
2
0
1
0
1
0
2
1
1
0
1
1
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
2
1
0
0
1
1
0
1
0
0
2
2
0
2
0
1
0
2
0
1
1
1
0
1
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
1
1
0
2
0
1
2
2
0
0
0
1
2
2
0
0
2
0
0
0
1
0
0
0
1
2
0
1
0
2
0
0
0
0
0
1
1
2
2
1
2
0
0
0
1
0
1
0
0
0
1
0
0
2
2
0
0
4
1
2
0
0
1
1
2
1
1
0
1
1
1
0
0
2
0
0
0
1
1
0
2
0
2
2
0
0
1
0
0
2
3
0
1
0
1
0
2
0
0
2
0
0
0
1
1
0
0
0
0
0
2
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
2
2
0
1
1
1
2
0
0
0
1
0
0
1
2
0
1
0
0
0
1
1
0
1
0
0
1
1
2
0
2
2
0
0
1
0
0
2
0
0
1
0
1
0
2
0
0
0
1
3
0
0
2
0
0
0
0
1
0
1
0
0
0
3
0
0
0
0
0
0
0
2
1
2
1
0
2
0
1
2
0
0
0
1
2
2
2
0
0
0
0
0
0
0
2
0
2
2
0
0
2
2
2
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
3
0
3
0
2
0
1
0
0
1
2
0
0
0
0
0
1
0
1
2
1
2
0
1
1
1
1
2
0
1
0
2
1
0
2
1
0
2
0
2
2
1
0
0
1
2
3
0
1
1
0
1
0
0
2
0
2
0
0
1
2
0
0
0
0
0
2
2
0
0
0
1
1
0
0
0
2
0
1
0
0
1
0
2
0
0
0
2
0
0
0
0
1
0
1
2
1
0
1
0
3
1
2
0
0
0
0
1
0
1
0
0
0
0
1
2
0
1
1
1
2
1
0
0
0
2
0
0
0
0
1
0
1
0
2
0
0
0
0
2
0
2
2
0
0
0
0
2
2
0
1
1
0
1
0
1
2
0
1
1
0
0
0
1
0
0
2
0
1
0
2
1
1
0
0
2
1
0
0
0
2
2
2
1
1
0
1
0
0
2
0
0
1
0
0
0
0
1
1
0
0
0
2
0
0
0
1
0
1
0
0
1
0
4
0
1
0
2
2
0
2
1
0
0
0
0
2
2
0
1
0
2
0
0
2
2
0
0
2
1
0
2
2
0
0
1
1
1
2
0
0
0
1
2
0
1
2
0
0
1
1
0
0
1
0
0
1
0
0
1
0
0
2
2
1
0
0
4
1
0
1
0
2
1
0
0
1
0
0
2
0
2
1
0
0
2
2
0
3
1
2
1
0
0
0
1
0
0
0
1
0
0
2
2
2
2
0
0
1
0
0
2
0
0
0
1
1
3
1
1
0
1
0
2
0
1
0
2
2
0
1
0
1
2
1
3
0
0
1
0
1
0
2
1
0
0
0
1
0
0
0
1
1
0
0
0
3
1
1
0
0
1
0
1
0
1
1
0
1
0
1
1
1
2
0
0
0
1
1
2
1
0
1
2
1
1
0
1
0
2
2
2
3
1
0
2
2
2
1
2
2
3
0
0
0
0
1
2
0
0
2
2
2
1
0
1
0
0
2
1
0
2
0
2
0
0
0
2
0
0
1
0
1
1
1
0
2
2
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
1
1
0
0
2
1
0
1
1
0
0
0
0
0
1
0
0
0
2
1
0
0
2
0
0
0
2
2
0
0
0
0
2
0
0
1
0
0
0
2
0
2
2
0
0
0
0
0
1
0
0
1
2
2
0
0
1
0
0
0
0
2
0
0
1
1
2
0
1
0
1
1
0
1
3
0
0
0
0
1
2
0
0
1
1
2
2
0
0
0
0
0
1
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
2
0
0
0
0
2
1
1
1
2
0
1
1
0
2
0
0
2
0
1
2
0
3
0
0
1
0
0
0
1
1
0
0
1
0
0
0
3
2
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
1
4
1
1
2
0
0
0
0
2
2
0
0
0
0
2
0
2
2
1
0
0
0
0
1
0
0
1
0
1
1
0
0
2
0
1
0
1
2
1
1
0
0
0
0
1
1
2
1
1
2
0
1
0
0
0
0
1
3
1
1
0
0
1
0
0
0
1
0
0
0
0
0
2
1
2
0
0
0
0
0
4
1
2
2
0
0
0
0
2
1
0
0
0
0
2
1
1
0
0
0
2
1
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
1
2
1
0
0
0
2
0
0
2
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
2
0
2
0
0
0
1
0
0
1
1
0
1
0
2
0
0
0
1
0
0
0
2
0
1
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
2
0
0
1
2
0
0
2
1
0
2
0
1
2
1
1
0
2
0
2
0
2
2
0
0
2
0
1
2
0
1
2
1
2
0
2
0
0
0
2
0
2
0
0
0
1
0
1
1
0
0
0
0
1
1
2
0
2
2
1
0
0
1
0
0
1
0
0
2
1
2
1
0
0
1
2
0
0
0
0
0
0
0
0
1
1
2
0
1
0
0
0
2
2
2
1
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
1
0
1
0
1
0
1
0
2
0
2
1
0
2
1
0
0
0
2
0
1
2
0
0
0
2
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
1
1
1
2
0
0
1
0
0
0
2
0
1
4
1
0
0
0
1
1
0
1
0
0
1
2
0
1
3
1
0
1
1
2
0
0
0
1
0
2
0
0
1
4
0
2
1
3
0
0
0
1
1
2
0
0
0
0
2
2
0
0
0
0
2
0
1
1
0
2
0
2
3
1
0
2
2
1
0
1
0
1
0
0
0
0
0
5
2
0
0
1
2
0
3
0
1
1
0
2
0
0
0
0
0
1
0
1
2
0
0
1
1
0
0
0
0
2
0
0
0
2
1
0
0
1
2
0
1
0
0
1
0
0
2
0
0
0
2
2
2
0
0
0
0
1
0
2
2
0
0
2
2
2
0
0
0
2
0
1
0
0
2
0
1
0
1
0
0
1
2
3
2
0
0
1
0
0
1
0
2
0
0
0
1
9
1
1
0
0
1
0
2
0
2
0
1
3
0
0
0
0
1
0
1
2
1
0
0
2
1
0
1
0
0
0
0
0
1
2
1
0
0
1
1
0
0
1
2
0
0
1
2
2
0
1
0
1
3
0
0
0
0
2
0
0
2
0
2
1
0
0
0
1
1
0
0
0
0
1
0
0
1
1
1
1
0
0
0
0
2
2
0
2
0
1
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
1
0
2
0
0
0
1
1
0
0
2
2
0
0
2
0
0
0
0
0
0
2
0
0
2
1
0
4
2
0
0
0
2
0
0
0
1
2
1
0
0
2
1
0
0
0
2
1
1
0
1
1
0
0
0
2
1
0
1
0
1
1
1
1
0
0
1
0
2
0
0
0
0
1
3
0
2
2
1
0
2
0
0
0
2
0
0
0
1
0
0
0
2
2
1
2
0
1
2
1
0
2
1
0
0
1
0
0
0
1
0
0
2
0
1
0
4
3
2
0
0
1
0
0
2
0
0
0
1
1
2
0
1
0
0
2
1
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
1
0
1
2
0
1
1
1
2
0
2
0
0
0
0
0
0
1
0
0
1
2
1
0
2
1
0
1
0
0
0
0
2
2
1
0
1
0
2
0
0
1
1
1
0
0
1
0
0
2
0
1
2
1
0
0
1
2
0
0
0
1
0
2
1
1
1
1
2
2
0
0
0
0
0
0
0
2
0
2
0
3
2
0
1
0
0
0
2
1
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
1
1
0
0
1
0
2
0
0
1
0
1
0
1
1
1
2
2
1
2
0
0
0
1
0
0
1
1
1
1
0
1
0
1
0
0
0
1
0
1
0
2
0
1
0
0
1
0
0
0
2
0
1
0
0
0
0
1
1
2
0
0
1
0
0
2
0
0
2
2
0
0
0
2
0
0
1
1
0
0
2
1
1
1
1
0
0
0
0
1
1
3
0
0
1
0
0
0
1
2
5
0
2
0
1
2
0
0
1
1
0
0
2
0
2
2
1
1
1
0
2
0
0
0
0
0
0
2
0
2
1
1
0
2
1
1
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
3
0
0
3
0
2
0
0
0
2
2
1
3
0
0
0
2
0
0
1
0
0
0
1
1
0
0
0
0
1
2
0
0
2
0
0
0
2
1
1
0
0
0
2
1
1
0
0
2
0
1
2
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
2
1
0
2
0
1
0
0
4
2
1
0
0
0
0
1
0
2
1
2
1
2
2
1
0
0
0
1
3
0
0
0
1
0
2
0
0
2
0
0
2
0
0
1
0
1
0
2
0
2
2
0
1
2
0
1
0
3
2
1
0
0
1
0
0
0
0
1
0
2
1
0
0
1
1
0
0
0
1
0
0
1
1
3
0
0
1
0
1
1
2
0
2
0
1
0
0
0
0
1
0
2
0
0
2
2
2
2
2
0
2
2
0
0
0
1
0
0
1
1
1
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
1
2
1
1
0
0
0
2
0
0
0
0
1
0
0
2
2
0
0
2
0
0
1
1
2
0
2
0
2
0
1
0
0
1
0
2
0
0
0
0
0
2
1
0
0
1
1
0
1
1
0
1
0
1
0
0
1
0
2
0
0
0
0
0
0
1
1
1
0
2
0
2
1
2
0
0
0
0
0
1
0
2
0
1
0
0
1
0
1
0
1
0
0
0
3
0
0
3
0
1
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
1
0
1
0
0
2
0
2
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
2
1
2
0
2
0
2
1
1
1
0
0
0
0
1
0
0
0
1
0
2
2
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
4
0
0
1
2
0
0
0
1
0
0
1
0
0
0
2
1
2
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
1
1
2
0
1
0
0
0
0
0
1
0
0
0
3
1
0
1
0
1
4
0
4
0
2
1
0
1
0
2
0
0
0
0
0
2
0
0
1
1
0
0
0
0
2
0
0
0
2
0
2
2
0
1
0
2
0
0
0
3
0
0
0
0
1
0
1
1
0
0
0
0
0
0
2
0
0
0
0
3
0
0
2
2
1
0
1
0
1
0
0
0
2
1
0
0
3
0
2
0
0
0
2
0
0
0
2
2
0
0
2
0
0
1
1
1
0
0
0
1
2
1
1
2
1
3
0
1
2
0
0
0
1
0
0
1
0
1
0
2
0
3
0
1
0
0
0
1
1
2
0
0
2
2
0
0
0
0
1
0
2
3
0
2
0
3
1
1
0
1
1
1
0
1
0
3
0
2
0
0
1
0
0
4
0
2
0
0
2
2
1
2
2
0
1
1
2
0
0
2
0
1
0
1
1
0
0
1
1
0
0
0
0
1
0
0
1
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
1
1
0
1
1
0
0
0
1
0
1
2
0
1
1
2
0
2
0
2
0
0
1
2
0
0
2
2
0
0
0
1
0
1
1
0
2
3
0
0
2
0
0
0
0
2
2
1
2
2
0
0
1
0
0
1
0
1
0
1
0
0
0
1
1
2
1
1
1
1
1
0
1
1
0
0
0
1
1
2
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
2
0
1
0
1
0
0
2
2
0
0
0
2
1
2
0
0
0
0
1
0
2
1
2
2
1
2
3
0
0
0
0
0
0
1
0
2
0
2
2
0
0
0
0
0
1
0
1
0
1
0
0
1
1
2
1
2
0
0
1
3
0
0
1
0
0
1
0
0
0
0
0
0
2
0
3
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
1
1
1
1
0
2
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
1
0
1
1
1
0
0
0
1
1
0
2
0
0
2
0
1
2
2
2
0
0
0
0
0
0
0
2
0
0
2
1
0
1
0
1
1
0
2
0
2
2
0
2
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
1
0
0
0
2
0
1
1
2
2
1
0
0
0
0
0
2
0
0
0
1
1
2
0
2
1
0
2
0
0
3
0
0
1
2
0
0
0
0
2
1
1
0
2
2
0
1
0
1
0
1
0
0
0
1
0
1
2
1
0
0
2
0
0
1
0
0
0
2
0
1
0
2
0
2
3
0
2
2
0
0
0
0
0
0
0
1
0
0
1
1
1
0
1
0
0
0
0
2
0
0
0
0
1
2
0
1
0
0
2
0
2
2
1
0
2
2
0
1
1
0
1
1
2
0
0
1
0
0
1
1
0
0
0
0
1
2
0
0
1
0
0
2
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
3
0
0
2
0
2
2
1
0
1
2
0
0
0
0
2
0
0
2
0
1
0
0
1
2
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
2
0
1
0
2
0
0
0
1
2
1
0
2
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
2
2
0
0
0
1
1
1
0
0
1
0
0
2
0
0
1
0
2
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
3
1
0
0
0
0
0
1
1
0
0
1
3
2
0
1
0
1
1
2
1
0
2
0
0
0
0
2
0
0
0
0
0
2
0
2
1
0
1
1
1
0
0
0
2
2
0
1
2
0
1
0
0
2
1
2
1
1
0
0
0
0
0
2
0
0
0
1
1
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
2
0
1
0
1
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
1
1
0
2
0
1
1
0
2
0
1
2
0
0
0
0
0
2
1
1
2
0
0
0
0
1
2
0
0
2
2
0
0
0
1
0
2
2
0
0
0
1
0
0
1
2
0
1
0
1
1
0
0
2
1
0
0
1
1
2
2
0
0
2
1
0
0
0
3
0
0
0
0
0
0
0
1
2
3
1
0
0
0
1
0
2
0
0
0
0
0
0
0
1
1
0
0
2
2
0
0
0
0
0
0
1
2
0
0
0
0
1
0
1
0
2
0
0
1
0
2
1
0
0
1
2
0
1
1
2
1
1
0
0
2
1
1
0
0
2
2
2
2
2
0
0
2
2
0
0
2
1
1
2
0
0
2
0
2
2
0
0
2
1
2
0
0
3
1
0
0
3
0
1
0
0
0
1
2
2
0
2
0
1
2
1
1
2
1
0
3
1
1
2
0
0
0
2
2
0
2
1
1
0
0
1
1
0
0
0
0
2
0
0
0
0
2
1
0
1
1
0
1
1
0
2
0
0
0
2
0
0
2
2
1
0
0
0
0
1
1
1
0
0
0
0
0
0
1
1
1
0
0
0
0
2
2
2
2
0
0
0
0
1
1
0
0
2
0
0
1
2
0
2
1
1
0
0
0
2
0
0
3
0
3
1
2
3
0
0
0
0
1
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
2
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
2
0
1
0
0
2
0
0
1
2
1
0
2
0
1
0
1
0
2
0
2
2
1
0
0
0
0
2
0
1
1
0
0
2
1
3
1
0
0
1
0
0
0
2
1
2
2
0
0
0
0
0
3
0
2
1
0
0
2
1
0
0
0
0
0
1
1
0
1
0
0
1
0
0
1
0
0
1
2
0
0
2
0
2
2
0
0
0
1
1
2
2
1
0
0
0
1
2
1
0
1
0
0
2
0
0
0
1
1
2
1
0
1
0
1
1
0
1
0
0
2
0
2
0
0
1
0
0
2
2
1
0
2
3
0
2
0
1
2
2
2
4
2
1
0
1
2
0
0
2
0
0
0
1
2
0
0
2
1
1
2
0
1
0
0
1
1
1
2
2
2
0
1
0
1
0
1
2
1
0
2
0
0
1
1
1
0
2
1
0
2
0
0
0
0
0
2
0
1
1
1
1
1
2
0
1
2
2
2
1
0
0
0
2
0
2
5
0
1
0
0
3
2
1
0
2
0
0
1
1
0
1
1
1
0
2
0
0
0
1
1
0
1
0
4
0
0
0
2
0
1
2
0
0
0
0
2
1
0
0
2
1
0
0
0
2
0
1
0
1
1
0
1
0
0
2
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
1
0
0
2
0
1
0
2
0
0
2
1
2
0
1
2
2
0
0
1
0
0
0
2
0
1
0
0
0
0
0
2
0
0
2
2
0
1
1
0
0
0
0
0
1
1
1
0
1
3
4
0
0
0
0
1
0
3
0
7
0
1
1
1
0
0
0
0
0
0
2
0
1
2
0
1
0
0
0
0
0
2
0
0
3
0
2
1
0
0
1
1
0
0
4
1
0
0
0
0
2
0
2
0
0
0
0
0
1
0
1
1
1
1
0
0
0
3
1
0
0
1
0
0
0
0
0
2
0
0
2
1
0
1
0
0
0
0
2
0
2
0
0
0
1
1
1
1
0
0
0
0
2
1
0
0
0
1
0
0
0
0
1
1
2
1
1
1
2
1
0
1
0
1
1
0
1
1
0
0
2
0
2
1
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
1
2
2
0
1
0
0
0
1
2
0
1
0
0
1
1
0
4
0
2
1
2
1
0
2
2
0
0
1
0
0
2
0
1
0
2
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
2
0
0
2
1
1
2
1
0
1
1
1
0
0
2
2
0
0
0
1
2
2
0
0
0
0
0
1
0
2
2
1
0
0
2
2
2
0
0
1
1
2
2
0
1
1
2
0
0
1
0
0
0
0
0
0
0
0
3
1
0
0
0
2
0
0
1
1
2
1
0
0
0
0
0
1
0
1
2
1
2
0
2
2
1
1
0
1
0
1
1
2
0
0
0
0
0
1
0
1
0
0
1
1
1
0
1
1
0
0
1
1
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
2
0
1
0
1
1
0
2
0
0
1
0
2
0
2
1
0
0
2
0
1
1
0
0
0
1
0
2
2
0
2
2
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
2
0
0
2
1
0
0
1
2
0
0
1
1
1
0
1
0
0
2
0
2
0
0
0
0
1
0
2
1
1
0
0
1
0
0
2
0
0
1
3
0
1
1
0
0
2
1
0
0
0
2
1
1
2
2
0
1
2
2
1
0
0
0
0
2
2
0
0
2
1
0
0
3
2
1
0
1
0
0
0
2
1
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
1
1
2
3
1
0
1
2
2
3
0
0
0
0
0
0
2
2
0
0
0
0
1
1
0
1
0
1
0
0
2
1
2
2
0
0
0
2
2
1
0
0
0
0
3
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
2
0
0
2
0
1
1
0
0
1
2
1
1
1
0
2
1
0
2
1
1
2
1
0
0
0
1
2
2
0
2
0
0
1
0
0
0
0
1
1
0
2
1
2
2
0
2
0
1
0
2
0
2
0
1
0
1
1
0
0
1
0
0
0
0
2
0
2
2
2
2
1
0
0
0
0
0
1
2
2
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
1
0
0
2
0
0
1
0
0
4
0
0
0
0
1
2
1
0
0
0
2
2
2
0
0
2
1
0
0
1
0
2
1
0
0
1
0
0
1
2
0
2
1
0
0
0
2
0
0
2
0
2
0
0
1
1
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
2
1
0
0
0
0
0
3
1
2
0
2
0
0
1
2
0
2
0
1
0
1
0
1
1
0
0
0
1
0
2
2
0
0
0
1
0
2
1
1
2
0
0
1
0
0
2
0
0
2
1
0
2
2
1
2
0
2
1
0
0
1
0
2
2
2
0
3
0
0
0
0
0
2
0
0
1
0
0
2
1
0
0
0
2
1
1
1
0
0
0
1
2
1
0
1
1
0
1
1
0
0
1
0
0
21
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
2
1
1
2
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
2
0
3
0
1
0
0
1
1
0
0
1
3
1
0
0
0
1
0
2
2
0
1
2
0
0
0
1
0
1
2
0
0
0
1
2
1
0
0
0
0
0
1
1
1
1
0
0
0
1
1
0
0
0
2
1
0
0
0
0
3
2
1
1
0
0
2
3
2
0
0
0
2
0
1
0
2
0
2
1
0
0
1
0
2
0
1
0
0
0
0
1
1
2
2
2
0
0
0
0
1
1
0
2
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
2
1
0
0
0
2
0
2
0
0
2
2
0
2
1
0
1
1
1
0
1
1
0
0
2
1
1
1
0
0
0
0
1
3
2
0
0
1
0
0
1
0
1
2
0
0
0
0
0
1
2
0
1
0
2
0
0
2
0
1
1
2
1
0
0
0
2
1
0
1
1
0
0
2
2
0
2
0
0
0
0
3
1
1
2
0
0
2
3
0
1
2
1
0
0
1
0
2
0
0
0
0
1
1
1
1
0
2
0
0
0
0
0
0
2
2
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
2
2
1
0
0
1
0
0
0
3
0
2
0
1
1
0
0
0
2
1
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
1
0
1
1
0
0
2
0
2
0
1
2
1
1
0
0
1
1
0
0
0
0
2
0
0
0
0
0
2
1
1
2
0
1
1
1
0
1
0
2
0
1
1
1
1
2
1
0
0
1
0
1
0
1
0
2
0
1
2
1
1
1
3
1
2
1
0
0
0
0
0
1
0
1
2
1
2
0
0
0
2
0
1
0
0
2
0
0
2
0
2
0
0
0
0
1
0
1
1
0
0
0
1
0
0
2
1
1
2
1
0
2
3
0
0
1
0
2
0
0
2
0
2
0
1
0
0
0
2
1
1
2
0
0
0
2
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
1
0
0
2
1
1
0
0
0
0
0
0
2
0
0
0
2
0
2
0
1
0
1
0
1
0
0
1
0
1
0
3
1
2
1
0
1
0
1
2
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
1
2
0
1
0
0
0
2
1
1
0
1
2
2
0
1
1
0
0
1
0
1
2
0
1
1
2
0
0
0
1
2
0
1
0
0
1
0
0
0
1
1
0
0
2
1
0
0
0
0
0
0
4
1
0
0
0
2
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
2
2
0
0
2
0
1
1
1
0
2
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
1
2
2
1
2
0
2
0
0
0
1
0
0
0
0
1
1
2
0
0
0
1
2
1
2
0
0
0
0
1
2
3
1
0
2
0
0
1
0
2
1
1
0
1
2
2
2
0
2
2
0
0
0
0
0
1
2
0
0
1
0
2
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
3
0
1
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
1
1
0
2
2
0
2
0
2
2
0
0
1
0
1
0
0
0
2
0
0
0
1
0
2
0
1
0
1
1
1
0
1
0
0
2
2
2
0
2
0
1
0
0
0
2
0
1
0
1
0
2
0
0
0
0
0
1
0
1
0
1
1
0
0
1
0
0
0
0
6
1
0
1
0
0
0
1
0
1
0
4
0
2
1
1
1
0
0
2
1
1
0
1
2
2
0
1
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
1
0
0
2
0
1
0
0
0
0
1
0
1
0
2
0
0
2
0
1
0
0
0
3
0
2
1
1
0
1
2
0
0
0
1
0
0
1
2
1
0
2
1
0
1
1
0
2
0
1
0
0
2
0
0
1
0
0
2
1
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
3
0
2
2
1
1
0
2
0
0
0
0
2
0
0
1
0
2
0
2
0
0
2
0
2
0
2
2
1
2
0
0
1
0
1
0
2
0
2
1
1
1
0
4
0
0
1
0
1
2
0
0
1
0
0
1
0
0
1
2
1
1
1
0
1
0
0
0
1
2
1
2
0
1
1
0
0
2
2
2
0
1
1
0
2
0
0
0
0
0
0
0
0
0
2
1
2
3
0
1
0
1
2
0
0
1
0
0
0
0
0
0
0
2
0
1
0
1
3
0
1
1
0
3
0
0
1
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
1
1
1
1
2
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
4
1
1
0
0
0
2
0
0
2
0
2
0
0
2
1
0
0
1
2
0
2
2
1
1
2
1
0
0
0
0
0
2
1
2
1
1
1
0
2
0
0
0
1
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
1
3
1
2
0
0
0
0
2
1
0
0
0
1
0
0
2
1
1
2
0
2
1
0
0
0
2
0
3
0
0
0
0
1
0
0
3
0
0
0
0
0
0
2
1
0
1
2
1
0
1
2
1
0
1
0
1
1
2
0
0
0
0
2
0
0
0
1
0
0
0
1
2
1
1
0
1
0
1
0
0
1
0
2
1
0
1
2
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
3
2
1
2
0
0
1
0
0
0
2
0
2
0
2
0
0
1
2
1
0
0
0
2
0
0
0
1
0
0
0
2
0
0
2
3
0
0
0
0
1
1
0
1
2
2
2
2
1
0
1
0
0
2
0
2
0
2
0
0
0
1
0
2
0
0
2
2
2
0
1
0
0
0
1
1
1
0
0
0
1
2
0
0
1
2
0
0
0
1
0
0
0
1
1
2
0
0
1
0
1
1
0
0
0
2
0
2
2
0
2
1
0
1
0
1
1
0
2
0
0
0
2
0
0
1
0
1
1
1
0
0
0
1
0
0
0
0
1
0
0
1
2
2
0
2
1
1
1
0
1
2
0
1
2
0
2
1
1
1
0
1
1
2
1
1
2
2
2
0
0
0
0
0
0
1
1
0
0
2
3
2
0
0
1
2
0
0
0
1
1
0
0
0
1
1
0
2
0
0
1
1
1
0
0
0
0
1
0
1
1
0
1
1
0
0
1
1
1
0
0
0
0
1
2
2
0
1
1
0
0
0
1
0
2
0
0
1
0
2
0
0
1
0
3
0
1
2
1
0
1
1
2
0
0
0
0
0
0
0
1
0
1
1
2
0
1
0
1
0
0
2
2
1
1
0
0
1
0
2
0
0
3
1
1
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
2
2
0
0
2
0
0
2
0
0
0
0
0
0
1
0
1
1
0
1
0
1
0
0
0
1
1
0
1
3
0
0
2
2
0
0
2
0
0
1
0
1
0
1
0
2
1
0
2
2
0
0
0
0
2
0
1
0
1
0
0
1
0
1
0
2
2
0
0
1
0
0
2
1
0
0
1
0
0
1
1
0
0
2
2
1
0
0
0
2
0
0
0
1
0
0
0
0
0
3
0
0
0
2
2
1
0
1
0
2
0
1
1
2
0
0
0
1
0
0
0
0
0
1
0
0
2
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
1
3
0
1
2
0
0
2
0
1
0
0
0
1
1
0
0
1
0
1
1
1
0
2
0
1
0
3
0
1
2
0
2
0
2
2
0
0
1
0
2
0
2
3
1
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
2
2
1
0
0
0
2
0
1
0
0
3
2
1
0
0
0
2
3
0
0
2
2
0
0
0
2
1
2
0
0
0
1
2
0
1
0
2
0
0
1
1
1
0
0
2
2
0
1
1
0
1
1
1
0
0
0
1
1
1
0
0
1
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
3
2
0
1
0
0
2
0
0
0
1
2
1
2
0
0
0
0
0
0
0
0
0
0
4
0
1
0
2
2
0
0
0
0
0
0
0
2
1
0
0
0
1
0
1
0
1
0
0
0
1
0
2
1
0
2
0
1
1
2
2
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
2
1
2
0
0
1
0
2
0
0
0
1
0
0
0
4
2
0
1
2
2
0
0
2
1
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
2
0
1
2
2
0
0
0
1
1
1
0
3
0
0
0
0
0
1
1
0
0
2
0
0
2
0
2
1
0
1
2
1
0
0
2
0
0
2
1
2
0
0
0
0
3
2
2
0
0
2
1
0
1
1
1
0
2
0
1
1
0
0
1
1
2
1
1
0
0
0
0
0
1
0
2
2
0
0
1
0
2
0
0
2
2
2
1
2
0
2
0
2
1
2
0
0
0
2
0
1
0
2
0
0
2
0
0
2
1
0
1
0
2
0
2
0
0
4
0
0
0
0
2
2
1
0
2
0
2
0
1
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
1
2
1
0
0
0
2
0
0
2
0
1
0
0
1
1
1
0
1
1
0
2
0
0
1
0
2
0
0
0
0
0
0
2
0
0
2
2
0
0
0
2
2
0
1
2
0
0
0
0
2
0
0
3
0
0
0
0
0
2
1
2
2
2
0
1
0
2
0
2
0
1
0
0
2
2
0
0
0
1
2
1
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
1
0
0
0
0
2
0
0
1
0
1
0
0
1
0
0
0
0
2
1
0
2
0
0
0
2
2
2
2
2
0
0
1
0
1
1
0
1
1
0
0
0
1
2
0
0
1
0
0
0
1
0
0
1
0
0
1
0
1
0
0
1
2
2
0
0
1
3
0
0
0
0
0
2
0
2
2
0
0
0
2
1
0
2
1
0
1
1
0
2
2
1
0
0
1
0
1
1
0
1
2
1
2
0
2
2
2
0
0
1
0
0
1
0
2
0
0
1
0
0
0
0
1
2
1
1
1
0
3
1
0
1
0
1
2
0
0
1
0
2
0
0
2
0
0
0
0
0
1
2
2
0
0
0
0
0
1
0
2
1
0
0
2
1
0
1
2
1
2
2
0
0
1
1
1
2
1
2
0
0
2
2
1
0
0
0
0
0
0
0
1
0
2
1
0
0
1
0
1
1
0
0
0
3
0
0
0
0
0
2
0
0
1
1
0
0
1
0
0
0
3
0
1
1
2
2
0
0
2
1
2
2
0
0
2
0
0
0
0
0
0
0
2
2
2
0
0
1
2
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
2
2
1
0
1
0
1
2
1
1
0
2
0
0
2
0
1
1
1
2
0
0
0
2
0
5
0
0
2
1
2
0
0
2
0
0
0
0
0
0
2
1
1
1
1
2
2
0
0
0
4
1
1
0
0
1
1
1
1
2
1
0
0
1
2
1
0
0
0
0
0
0
1
0
0
0
0
2
2
1
2
1
0
2
0
0
1
0
2
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
2
0
1
4
1
0
1
3
0
0
0
0
2
1
1
0
2
0
1
0
0
1
2
0
2
0
2
0
1
0
2
0
0
2
0
0
2
0
1
2
1
0
1
0
2
0
0
0
2
1
0
2
0
0
0
1
0
0
1
1
0
1
0
1
1
2
2
0
1
0
2
0
2
1
0
1
0
0
0
2
2
2
1
1
1
2
1
0
0
0
1
1
0
1
0
1
1
0
2
2
0
1
0
0
0
0
0
0
1
0
0
2
1
2
1
1
0
1
1
1
0
1
1
0
2
2
0
0
0
2
0
0
0
1
0
1
2
1
1
0
0
0
1
0
2
0
0
0
0
1
0
2
1
0
2
1
0
0
0
0
1
0
2
0
0
0
0
0
0
2
1
0
1
8
0
0
0
1
0
1
0
0
0
1
0
0
2
2
0
0
1
2
1
0
1
0
1
0
1
0
0
0
2
0
0
1
0
0
1
0
2
2
0
2
0
2
1
1
1
0
2
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
1
0
1
1
1
0
1
1
0
1
0
0
0
1
0
2
1
1
0
1
1
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
2
1
3
0
1
2
2
1
0
0
0
2
0
0
0
1
0
0
0
1
2
1
0
1
0
0
2
0
2
0
2
0
2
2
0
0
0
1
0
2
0
0
1
2
0
0
0
0
0
0
2
0
7
1
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
1
0
0
1
1
0
2
1
2
0
0
0
0
0
0
0
1
0
2
0
1
1
1
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
1
1
0
0
0
0
1
1
1
0
2
1
2
2
0
2
2
1
0
1
2
0
2
0
0
1
0
2
2
1
1
0
1
0
0
1
1
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
1
2
1
2
0
2
0
1
1
1
1
0
1
0
0
2
0
0
0
1
0
2
1
0
0
0
1
0
0
2
0
0
0
0
1
2
0
5
0
0
0
0
2
1
1
0
2
1
2
0
2
0
0
0
0
0
0
1
0
0
0
1
1
2
2
0
0
1
1
0
0
1
0
2
0
1
1
0
0
1
0
1
0
1
0
2
1
1
1
2
1
0
0
0
0
0
1
0
0
1
0
0
2
2
0
0
2
1
0
2
0
2
0
0
1
1
2
0
1
2
0
0
1
1
3
2
1
2
0
0
0
1
0
1
0
0
2
0
0
1
1
0
1
0
1
1
2
0
1
0
1
1
0
0
0
0
2
1
2
0
1
0
0
0
3
1
0
2
2
2
0
0
1
2
0
1
2
2
2
0
0
0
0
0
0
1
2
1
0
1
3
1
0
0
2
2
0
0
4
2
2
1
0
1
0
0
0
2
2
0
0
0
2
0
1
1
2
1
0
0
2
0
2
1
0
0
0
1
2
2
0
2
0
1
0
1
0
0
1
1
0
0
0
0
0
1
1
1
2
0
0
1
0
0
2
0
2
2
1
0
1
0
0
1
2
1
1
1
0
1
0
0
2
0
0
2
1
0
0
1
1
1
0
2
2
2
2
0
1
0
1
2
0
0
2
1
1
0
0
1
0
0
0
2
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
2
2
3
1
2
2
1
0
0
1
0
0
2
0
0
1
2
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
1
0
2
0
1
1
1
0
0
1
2
0
0
2
1
2
0
0
2
1
2
1
0
0
0
0
0
0
1
0
1
2
5
0
2
0
0
0
1
0
2
0
0
1
1
0
1
1
1
0
3
0
0
1
0
0
0
1
0
1
0
0
2
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
2
1
1
0
0
2
0
0
0
1
0
0
2
0
0
6
1
2
0
2
2
0
0
1
0
1
0
0
0
0
2
1
0
0
0
1
2
4
0
1
0
0
1
0
0
0
1
1
0
0
0
0
2
1
0
2
0
0
2
0
0
0
3
2
0
0
1
1
1
2
0
1
0
2
1
0
0
0
0
0
0
1
4
0
0
0
1
0
0
0
1
1
2
1
0
2
0
1
2
1
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
1
1
0
3
0
0
0
0
1
0
0
2
0
0
1
0
0
1
0
1
0
2
0
0
1
0
1
0
0
1
0
1
3
0
0
0
0
2
2
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
2
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
2
4
0
1
0
0
0
2
0
1
0
2
2
1
0
0
0
0
1
0
0
0
0
2
2
0
1
0
2
0
0
2
0
1
0
1
1
0
0
0
0
2
0
1
0
2
0
2
0
0
0
1
1
1
1
0
0
1
1
2
0
0
0
1
1
0
1
0
0
1
0
0
2
0
0
0
0
1
1
1
0
0
1
3
1
0
0
2
0
0
0
0
1
1
1
2
0
1
2
1
3
0
0
1
0
2
0
0
1
1
0
3
0
0
0
1
2
0
0
0
1
2
0
0
0
0
1
0
1
0
0
1
1
2
1
3
0
0
0
2
0
1
0
0
2
0
1
0
0
1
0
3
0
1
1
2
0
0
1
1
0
2
0
2
1
0
2
0
2
0
0
1
0
0
2
0
0
1
0
0
0
2
1
1
0
3
1
0
1
2
0
1
0
5
0
2
2
1
1
0
0
1
0
0
0
0
1
1
1
1
6
0
0
2
2
1
0
2
0
0
1
0
1
1
2
3
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
2
2
0
2
0
0
1
1
0
0
2
0
0
0
1
1
2
2
0
2
0
0
2
1
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
1
1
0
1
0
0
0
0
0
2
3
2
0
1
2
0
1
0
0
0
0
0
0
1
0
2
0
0
2
0
1
0
0
1
1
1
0
1
0
0
0
2
0
0
1
0
2
1
0
0
0
1
0
1
0
1
2
1
0
1
0
1
1
0
1
0
0
1
0
1
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
2
4
0
2
0
0
0
1
1
0
0
0
1
0
0
1
0
0
1
0
0
2
1
1
1
0
1
1
0
0
0
0
1
1
1
2
1
2
0
0
1
2
0
0
0
1
0
2
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
2
1
0
2
1
0
1
0
0
1
0
1
2
0
0
0
1
5
0
0
0
2
2
0
0
0
1
1
0
0
0
1
2
1
0
0
0
0
0
1
2
1
0
0
1
0
1
1
1
2
2
1
0
1
0
1
0
0
0
0
2
1
0
0
0
1
1
0
0
1
1
2
2
0
2
3
0
0
0
0
0
1
0
0
0
0
2
0
1
2
0
0
2
1
1
1
0
0
0
2
2
0
0
0
1
1
2
0
0
1
3
0
0
1
2
1
2
0
1
0
1
0
1
0
0
0
1
1
0
1
1
0
0
0
2
1
2
0
1
0
0
2
1
0
3
0
0
0
0
1
0
0
1
1
0
1
2
0
2
0
2
2
2
1
0
1
0
0
2
1
2
2
0
0
1
0
1
2
0
4
2
1
0
0
0
2
2
2
1
0
1
0
0
0
0
2
1
0
1
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
1
1
2
0
0
0
1
1
3
1
2
0
1
2
2
1
1
2
0
0
0
1
1
0
0
2
0
0
0
0
2
2
0
0
1
1
0
0
1
1
0
1
1
0
1
2
1
2
1
0
1
0
2
1
1
1
0
2
0
0
0
2
1
0
0
2
0
0
0
0
1
2
1
0
1
2
0
0
0
1
0
2
1
1
0
0
0
0
0
1
1
1
2
1
2
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
2
1
1
0
0
1
0
0
2
0
1
0
0
0
1
2
0
3
2
0
0
0
0
2
0
0
0
0
0
2
1
0
2
2
0
1
1
0
1
2
0
1
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
1
1
2
0
2
0
0
0
2
0
1
0
2
0
1
0
1
0
0
0
0
2
1
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
1
2
0
2
2
0
0
1
0
2
0
0
2
2
2
0
0
0
0
0
0
0
2
2
1
0
1
0
0
2
1
2
0
0
1
0
1
2
0
1
0
1
0
0
1
0
0
0
2
2
0
2
2
1
0
2
1
3
1
1
0
0
0
1
0
2
1
2
0
1
0
0
2
0
0
0
2
0
3
0
1
0
0
0
2
1
1
2
0
0
0
0
0
2
1
0
1
1
3
1
0
2
0
2
0
1
0
0
2
0
2
0
0
0
1
0
0
1
1
0
1
2
1
0
0
0
0
1
2
0
1
1
2
1
0
0
3
1
0
0
1
0
0
0
1
0
0
1
0
1
1
0
0
0
0
1
0
0
0
1
0
1
2
0
0
2
0
0
1
0
0
2
0
2
3
0
1
1
0
0
2
2
1
0
2
0
2
1
0
0
0
1
0
0
0
0
1
1
4
1
1
0
1
1
0
0
0
2
1
1
2
2
2
0
0
1
3
2
0
2
1
1
2
1
2
1
2
0
1
1
1
1
1
1
0
3
0
0
2
2
0
1
0
0
0
0
0
2
0
1
0
0
0
2
1
1
0
0
0
0
0
0
1
0
0
2
1
2
0
2
0
0
0
0
0
1
2
0
2
0
0
0
0
2
2
0
0
2
2
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
2
1
0
0
0
2
2
1
0
1
0
2
0
0
0
0
2
2
0
0
0
1
0
2
2
0
0
0
0
0
2
0
0
0
0
2
1
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
2
1
1
0
1
1
2
0
0
0
0
1
0
0
3
0
0
2
0
0
1
1
0
0
0
0
1
0
0
0
2
0
1
0
0
0
1
0
0
0
0
2
0
0
0
2
1
0
0
1
0
2
1
0
1
0
0
0
1
1
0
0
2
1
2
0
0
0
1
2
0
0
2
0
0
1
0
1
0
0
1
0
0
1
2
1
1
1
0
1
3
1
0
0
1
1
0
2
1
0
0
0
0
0
0
2
0
1
1
2
0
0
2
0
2
0
0
1
0
3
0
2
0
1
2
2
0
0
0
1
0
1
0
2
1
0
2
2
2
0
1
2
0
1
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
1
0
0
1
1
0
2
0
0
2
1
0
1
0
0
0
0
2
1
0
1
1
2
2
2
1
2
2
2
0
0
2
1
1
0
0
1
0
0
0
2
2
2
0
0
0
0
0
1
0
1
0
0
1
0
0
0
2
1
1
0
1
0
1
0
0
0
2
1
2
1
0
0
0
1
0
0
0
1
2
2
2
0
0
0
0
0
0
2
0
0
1
1
0
0
1
0
0
0
2
2
0
0
0
0
0
2
1
1
0
0
0
0
1
1
0
2
0
1
1
1
0
2
1
2
2
2
0
0
1
0
0
0
0
0
1
2
1
0
0
0
0
0
1
0
1
0
0
1
0
2
0
0
1
1
2
0
0
0
0
0
4
0
0
3
1
0
1
2
0
0
0
1
0
0
1
0
2
0
0
0
1
0
1
0
0
2
1
0
1
1
0
2
1
1
1
1
1
0
2
0
0
2
1
0
0
0
0
0
2
0
1
0
1
2
0
0
0
0
0
0
0
1
0
0
0
4
1
2
2
4
1
0
0
1
0
0
0
0
0
1
0
1
0
0
1
1
0
1
0
0
0
0
0
1
2
0
0
2
2
2
0
1
0
1
1
1
2
1
0
1
0
2
1
2
0
0
2
1
1
1
0
1
0
1
0
0
1
2
3
2
0
0
0
0
1
2
2
0
1
2
0
3
0
0
1
0
1
0
0
0
1
2
0
0
0
1
1
0
2
0
1
1
1
0
1
0
1
3
0
0
2
0
2
0
0
0
0
1
2
1
2
0
2
0
2
1
0
0
0
0
2
0
0
0
2
0
2
1
2
0
1
0
2
0
2
1
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
1
0
2
2
0
2
0
0
2
1
0
2
1
0
0
0
0
2
1
0
0
1
1
0
2
0
2
2
2
0
1
0
0
2
0
2
0
0
1
1
0
0
1
1
0
0
0
0
2
1
2
1
1
2
0
2
2
0
1
0
0
0
0
0
1
1
1
1
4
3
1
0
1
2
0
2
0
1
1
0
0
0
0
0
0
0
1
0
1
1
2
0
0
0
2
0
0
0
2
2
2
1
3
0
2
1
0
2
0
0
0
0
0
2
0
1
0
2
2
2
0
1
1
0
0
0
2
0
0
0
1
2
0
0
0
1
0
0
2
1
0
2
0
0
0
2
0
1
1
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
1
1
0
0
2
2
0
0
0
2
3
2
0
1
0
2
1
2
0
0
0
1
2
0
0
0
0
0
0
2
1
0
1
5
0
0
2
0
2
0
1
0
0
0
1
0
0
0
0
0
1
0
2
2
0
0
0
0
1
2
0
0
0
0
0
1
2
1
0
1
0
0
1
0
2
2
0
0
0
1
0
2
0
2
0
1
0
0
1
0
4
1
0
1
1
0
0
2
0
0
0
2
2
0
0
2
1
0
0
2
2
0
2
0
0
0
1
1
0
0
1
1
0
0
1
0
1
2
0
1
0
1
3
0
0
2
1
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
1
0
0
1
2
0
0
3
2
1
0
0
1
0
0
1
0
2
0
0
2
2
0
0
1
2
2
0
0
0
0
2
3
1
0
2
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
1
2
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
2
1
1
1
0
0
0
2
2
0
0
0
1
0
0
1
2
0
4
0
0
2
1
0
1
2
1
0
1
0
3
1
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
2
2
2
0
1
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
3
0
1
0
1
1
0
0
0
0
2
0
0
0
2
0
0
3
0
2
0
2
0
2
1
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
2
1
0
0
2
0
0
0
1
0
0
1
0
0
0
2
0
2
1
1
1
0
0
0
0
0
1
0
0
2
0
1
1
3
0
0
1
0
0
2
2
1
0
0
2
0
1
0
1
2
1
2
0
0
1
0
0
0
1
3
0
1
2
0
0
1
0
0
0
0
0
0
1
0
2
0
1
0
1
1
2
0
1
0
1
0
0
1
0
2
0
1
1
0
1
1
1
2
1
0
1
0
2
0
0
0
0
1
0
2
2
0
0
1
0
0
1
1
1
1
0
0
3
0
1
0
0
0
1
1
0
0
0
1
0
1
2
2
0
0
0
1
0
0
0
0
0
0
0
1
3
0
0
0
0
1
0
0
1
1
0
1
2
1
2
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
1
1
1
0
0
2
2
0
1
2
0
1
1
0
2
0
0
1
0
0
1
2
1
0
2
0
1
0
1
0
0
0
0
0
2
1
0
1
1
0
0
0
3
0
0
0
4
1
5
1
1
0
2
0
0
1
0
2
1
2
1
1
0
0
2
0
0
0
2
2
1
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
2
1
0
1
2
0
0
2
1
1
0
0
0
2
0
1
2
0
2
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
1
2
0
1
2
1
0
1
0
0
0
2
0
1
2
0
0
0
0
2
2
1
0
0
0
1
2
1
0
3
2
3
1
1
0
0
0
1
2
2
0
2
0
0
0
1
0
2
0
2
0
2
0
2
0
0
0
1
3
1
1
1
2
1
1
2
2
2
2
0
0
0
0
0
1
1
1
2
2
0
0
3
2
2
1
1
0
2
0
1
2
2
0
0
2
0
1
0
1
2
0
1
0
1
0
1
1
2
0
0
0
0
2
1
0
1
2
0
0
0
1
0
0
0
1
0
0
2
0
1
1
0
2
0
2
1
0
1
2
0
0
2
4
1
2
2
0
1
2
1
1
1
0
0
0
1
0
0
0
0
1
2
2
0
2
0
0
0
0
0
1
0
0
0
0
2
2
0
2
0
0
0
0
1
0
5
1
0
0
2
0
1
1
0
2
0
0
0
0
1
2
1
2
2
0
0
0
0
0
1
0
0
0
0
1
2
1
0
2
0
0
0
0
0
4
1
0
0
0
2
2
1
1
0
0
0
0
0
0
0
1
2
1
0
0
2
1
0
1
0
0
2
2
2
0
2
2
0
4
0
0
1
0
0
1
0
1
0
0
0
1
1
0
2
1
0
1
1
0
0
0
0
0
2
2
0
2
3
0
0
1
2
1
0
1
2
2
0
2
0
2
0
0
0
0
1
4
0
0
1
0
2
1
0
0
2
2
2
2
0
1
0
1
0
2
0
1
2
0
0
0
0
2
2
0
1
0
0
0
1
1
1
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
1
0
2
0
0
0
0
2
0
2
2
1
1
0
0
1
0
0
2
1
0
2
0
0
2
3
0
0
0
0
2
2
0
0
1
2
0
0
0
1
2
0
0
1
1
0
1
0
3
2
0
0
0
2
1
0
1
2
0
0
0
0
0
0
0
0
0
0
1
2
2
0
2
2
2
0
1
1
2
1
0
0
0
1
2
0
0
2
2
2
0
0
0
2
2
1
0
0
0
0
2
2
0
3
0
0
2
2
1
2
1
0
1
1
0
1
2
0
0
2
0
0
0
2
1
0
0
0
1
0
1
0
2
1
0
2
0
0
0
1
1
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
3
0
2
1
0
0
0
1
1
0
2
0
0
1
0
2
0
0
3
0
1
0
0
0
0
0
3
0
2
1
2
0
1
1
1
0
1
0
0
0
2
2
0
0
0
0
0
1
2
2
0
0
0
1
2
1
0
0
1
1
0
1
1
2
1
2
1
1
1
1
0
0
0
0
1
2
2
0
0
1
2
2
2
1
3
1
0
0
0
2
0
1
1
0
3
0
0
2
0
2
0
0
2
0
1
0
0
0
0
3
0
1
0
0
2
2
2
0
0
0
0
0
0
0
1
0
0
0
1
2
0
1
0
0
1
0
0
0
0
0
0
2
1
0
0
1
0
0
2
2
0
1
0
0
0
0
1
0
0
1
0
0
2
0
2
0
0
0
0
0
2
1
1
2
1
0
0
0
1
1
0
0
1
0
0
0
3
1
0
0
2
0
1
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
1
2
0
1
0
0
1
1
0
0
0
0
0
1
1
0
1
0
2
0
1
2
0
2
0
0
0
2
0
0
0
2
1
0
0
0
1
1
1
0
0
0
0
0
1
0
1
0
2
0
0
2
0
0
2
0
1
0
2
0
1
0
1
0
2
1
3
0
2
1
0
2
1
0
0
0
0
2
1
1
1
1
0
0
0
0
0
0
2
0
1
0
0
0
1
2
0
0
2
0
0
0
0
1
0
0
2
3
1
1
1
1
2
0
1
0
0
2
0
0
1
0
1
0
1
0
1
1
0
0
2
0
2
0
0
0
0
1
1
2
0
1
0
0
0
0
2
0
1
1
0
1
0
1
1
2
1
0
0
7
0
0
1
2
1
1
0
0
0
0
2
0
0
1
0
0
0
3
1
2
1
1
0
1
0
0
0
2
2
0
0
0
1
2
1
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
2
1
1
1
0
2
2
1
2
1
0
0
0
0
0
0
0
2
0
1
2
0
1
0
0
3
0
2
2
1
1
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
2
2
0
0
0
0
1
1
1
1
0
3
0
0
0
0
2
0
2
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
2
0
1
0
0
0
0
2
2
1
1
1
0
1
0
0
0
1
2
1
0
0
1
0
0
0
3
2
2
0
1
1
0
1
1
0
0
2
1
0
0
1
0
1
1
1
2
2
1
2
1
3
2
0
0
0
0
0
0
2
0
0
1
2
1
0
0
0
1
0
2
0
2
1
1
4
2
2
0
4
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
2
0
1
0
2
0
0
2
0
1
0
3
0
0
0
0
0
0
1
1
0
0
0
2
2
0
0
0
1
2
0
0
0
1
0
2
0
0
0
0
1
1
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
2
1
0
0
2
0
0
0
0
2
2
2
2
2
4
0
0
2
2
1
0
2
2
1
1
2
0
0
1
0
0
2
0
0
1
0
2
1
0
2
1
2
0
1
2
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
2
1
0
0
1
0
0
1
0
0
2
0
0
0
0
2
1
2
0
0
0
0
0
0
1
1
0
0
0
1
1
0
1
1
0
0
0
0
0
1
0
2
1
2
0
0
0
0
0
1
0
2
0
0
1
0
0
0
1
9
0
1
0
1
1
0
1
0
0
0
0
2
0
1
2
2
0
0
0
1
0
2
2
0
0
2
1
2
2
1
1
0
1
0
0
2
3
0
2
0
2
1
1
1
0
0
1
0
1
0
0
1
0
2
0
0
1
1
3
0
0
1
1
0
0
2
1
0
1
2
0
1
0
1
0
0
1
0
0
1
0
1
1
1
0
0
1
1
0
0
2
0
0
2
2
3
0
1
3
2
0
1
0
0
0
2
1
0
1
2
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
2
0
2
0
2
0
0
1
0
0
1
0
1
0
0
0
1
1
2
0
2
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
2
0
0
2
1
1
1
0
2
0
0
0
0
0
1
2
0
0
1
1
0
1
0
1
4
1
2
2
0
0
2
2
0
0
0
2
0
0
2
0
2
1
1
2
0
0
2
2
0
0
1
0
0
1
0
0
0
2
0
0
0
0
1
0
0
1
0
0
1
2
1
0
0
0
0
1
1
0
0
0
1
1
0
0
2
2
0
0
2
0
0
1
0
0
1
0
0
0
0
2
1
8
0
2
0
1
2
0
2
0
1
0
1
0
0
0
3
2
2
0
0
0
3
1
1
0
1
0
0
0
0
2
1
1
0
0
0
0
0
0
2
0
2
1
0
1
1
1
1
1
2
1
0
3
1
1
0
0
1
0
3
0
1
1
0
2
0
0
0
0
0
2
1
0
0
1
0
2
0
2
0
1
0
1
0
0
1
0
3
0
0
1
1
2
0
2
0
0
0
2
1
0
0
0
0
2
1
2
0
0
0
1
0
0
1
1
0
0
0
1
0
3
1
0
0
0
3
0
2
0
0
1
2
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
1
0
1
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
2
0
1
0
0
1
2
0
1
1
1
0
0
0
0
4
0
0
0
1
0
0
1
0
1
0
2
2
0
0
1
0
2
0
2
0
1
0
0
0
1
0
0
1
0
0
0
2
1
0
0
0
1
2
1
1
1
0
1
1
0
1
1
2
1
0
2
2
1
0
0
2
0
2
0
2
0
0
0
0
0
1
1
2
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
1
0
0
0
2
0
2
1
2
0
0
2
0
2
0
0
1
1
0
1
0
1
0
2
2
0
0
0
2
2
1
0
0
1
0
3
2
1
2
2
1
1
1
1
0
1
0
1
1
0
1
0
0
0
0
1
0
2
0
2
0
0
1
0
2
1
1
1
1
1
0
2
0
2
0
2
0
0
2
1
1
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
1
1
0
0
0
1
1
0
0
1
0
2
2
1
0
0
0
2
2
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
1
0
0
0
1
2
0
2
0
2
0
0
0
1
0
0
0
1
1
1
2
0
1
2
1
0
2
0
0
0
0
2
2
2
0
0
0
1
0
1
2
2
2
1
1
1
2
2
0
2
2
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
1
1
0
1
0
0
0
1
0
0
0
1
2
0
0
0
1
0
2
0
2
3
0
1
1
0
2
0
0
2
1
0
0
0
0
1
1
0
1
1
3
0
0
0
0
0
1
0
1
0
0
2
5
0
2
0
0
1
0
0
2
0
1
0
1
1
0
1
0
0
0
1
0
2
2
0
2
2
1
0
0
0
0
2
1
0
1
1
0
0
1
0
0
3
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
2
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
1
0
1
1
0
1
0
0
0
0
0
1
0
1
1
2
0
0
0
2
3
1
2
0
1
0
1
0
1
0
0
2
2
0
2
0
0
1
1
6
1
0
0
0
2
0
0
0
1
2
1
0
0
0
0
0
2
0
1
0
2
0
2
2
2
0
2
2
1
0
1
1
1
0
1
2
0
2
0
1
2
0
0
0
1
1
2
0
2
2
1
1
2
2
0
1
1
0
1
1
2
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
2
1
1
1
2
1
0
0
0
1
1
1
2
2
2
1
0
1
0
2
0
0
1
1
0
0
0
0
0
2
0
0
0
2
0
0
2
3
0
0
2
0
0
0
0
1
1
0
0
1
2
0
1
1
0
1
0
0
0
0
0
0
2
0
0
1
2
1
0
0
0
2
2
0
0
0
0
0
0
1
0
2
0
2
0
1
0
0
0
1
0
0
2
1
0
0
0
1
1
0
0
1
1
1
0
2
0
0
1
0
2
0
1
2
0
0
1
0
1
0
0
2
0
1
0
0
0
0
1
1
2
0
0
2
1
2
0
0
1
2
1
0
2
0
1
2
0
0
0
0
0
0
1
0
0
0
1
3
2
0
2
2
0
0
0
1
2
0
0
1
0
0
0
2
0
2
1
0
0
2
0
0
1
0
0
1
6
0
0
2
0
0
0
1
0
0
0
1
2
1
0
2
0
0
2
0
1
0
1
0
1
2
0
0
2
0
0
1
0
1
2
0
2
0
1
2
2
0
0
0
0
2
0
1
0
0
0
1
1
1
0
0
1
0
0
1
0
0
2
0
2
1
1
0
1
1
1
2
0
0
0
0
1
0
3
0
1
2
1
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
1
0
1
0
0
2
1
1
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
2
0
2
0
2
1
0
0
0
0
0
2
0
0
2
2
0
1
0
1
1
0
0
0
2
0
2
2
1
2
2
0
2
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
2
0
0
0
2
0
1
0
0
2
0
0
0
1
0
0
1
1
1
0
1
0
2
3
0
0
2
0
1
0
1
2
0
2
0
0
1
0
0
0
2
1
0
0
0
0
0
1
1
2
1
0
0
2
2
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
1
1
0
1
1
1
1
0
2
1
0
0
0
1
0
2
1
0
2
0
1
0
0
1
1
1
0
2
0
0
1
1
2
2
2
2
0
2
0
0
0
0
0
2
0
2
0
1
2
1
0
0
2
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
2
2
0
0
0
0
1
1
0
0
0
2
2
1
0
2
1
2
0
1
1
2
0
1
2
0
0
1
2
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
1
0
2
0
1
1
0
0
0
13
0
3
0
2
0
1
2
1
1
4
0
0
2
2
1
0
0
1
1
0
2
0
0
0
0
1
0
0
0
1
3
10
2
2
0
1
2
1
0
2
1
2
0
1
2
2
0
4
0
2
0
1
2
0
0
1
0
1
0
2
1
1
2
0
2
1
0
1
2
2
0
2
0
0
2
0
0
0
2
1
0
1
0
1
0
2
1
0
0
0
2
0
0
0
2
0
0
0
2
0
1
0
0
0
0
1
2
0
1
0
1
2
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
1
1
1
1
0
0
1
1
2
0
0
0
0
1
2
0
1
1
0
0
0
1
2
0
0
0
1
1
1
0
0
0
2
0
0
0
0
1
1
2
0
2
1
1
2
0
0
0
0
2
0
0
2
0
0
0
2
0
1
0
1
11
2
0
0
0
0
0
1
0
1
0
2
1
1
0
0
0
0
2
0
2
2
2
0
0
2
1
0
0
0
1
0
0
0
1
0
2
0
1
2
0
2
2
1
1
1
1
1
0
2
0
0
0
0
0
1
0
0
0
1
2
2
1
0
4
0
0
0
1
0
0
1
0
0
1
0
0
2
1
1
1
0
2
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
1
1
0
0
1
2
1
1
0
0
0
2
0
1
0
0
0
1
0
0
2
2
0
0
0
0
2
0
0
1
1
0
3
1
0
0
1
1
0
1
0
0
2
0
2
0
0
1
1
0
0
2
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
1
0
1
0
2
1
0
0
3
1
0
2
0
0
1
1
1
0
2
1
1
0
2
0
0
0
2
0
0
0
1
2
0
0
2
0
1
0
0
0
0
0
7
0
0
1
0
0
0
1
0
0
2
3
2
1
0
0
0
0
0
1
1
2
1
1
1
1
0
1
1
0
1
1
2
0
2
0
0
0
0
0
2
2
2
2
0
2
1
0
0
1
1
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
1
2
1
2
0
1
2
1
2
2
0
5
2
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
3
0
1
0
2
1
2
0
0
1
0
0
0
0
2
2
0
1
2
0
0
0
1
0
2
1
0
2
0
2
0
2
0
0
1
0
2
2
0
0
0
0
0
2
1
0
0
0
1
0
1
2
0
0
1
2
0
2
0
1
0
1
0
1
1
0
2
2
0
3
0
0
1
0
1
0
0
0
0
2
1
2
0
1
2
0
0
0
1
0
1
0
0
1
1
2
2
0
2
0
0
0
1
0
1
1
1
1
0
0
0
0
1
0
1
0
1
2
1
0
3
0
2
2
0
0
1
2
0
0
2
2
0
0
0
0
0
0
2
0
1
0
1
0
0
3
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
2
1
1
0
2
0
0
2
0
2
0
2
1
0
1
2
0
1
0
1
0
0
3
1
0
0
1
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
2
0
1
1
0
1
0
1
0
0
1
0
0
0
1
0
1
1
1
1
0
1
0
0
1
0
1
0
1
0
3
0
0
1
1
0
0
0
0
2
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
3
1
1
0
1
1
0
0
2
1
1
1
0
0
0
2
0
0
0
0
2
2
1
0
2
0
0
1
2
1
1
0
3
3
2
0
0
0
0
2
1
0
0
1
1
0
1
0
2
0
3
2
2
0
0
2
0
0
2
1
0
2
0
0
0
0
0
1
2
2
0
2
0
0
2
1
0
0
1
0
0
0
1
0
1
0
0
1
1
0
0
1
0
1
1
0
1
2
1
1
0
0
1
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
1
1
1
1
0
1
1
1
0
0
1
0
2
0
0
2
0
1
2
0
2
1
0
0
0
0
0
0
2
2
0
0
2
1
0
2
1
0
0
0
0
1
2
0
0
0
0
1
1
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
2
0
2
2
3
1
2
0
2
0
0
0
2
1
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
1
2
1
0
0
1
2
0
0
0
2
0
0
0
0
0
0
1
1
0
1
0
0
1
0
1
1
0
0
2
2
1
1
0
0
1
1
1
0
0
2
0
0
0
0
1
0
2
0
0
0
2
2
0
0
1
2
0
0
0
1
2
0
0
0
0
2
1
0
0
0
1
0
1
0
1
2
9
0
0
2
4
0
2
2
1
0
0
0
1
1
1
2
0
0
0
0
2
0
0
0
0
1
1
0
2
1
0
1
0
0
2
1
2
0
0
0
0
1
0
1
0
0
0
0
2
0
1
3
0
3
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
1
0
1
0
1
2
1
0
0
1
2
0
1
0
1
2
0
0
1
1
0
0
2
0
1
1
1
0
0
2
0
0
0
0
0
1
0
1
1
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
2
0
1
0
0
3
0
1
0
0
0
0
0
1
2
1
0
0
0
0
2
2
1
0
0
1
2
2
1
1
1
0
2
0
0
0
1
1
1
1
0
0
2
0
0
1
1
0
0
2
0
0
0
1
1
1
0
0
0
2
2
1
1
1
0
2
0
0
1
1
3
3
0
2
1
2
0
1
0
1
2
2
1
2
0
1
0
1
1
0
2
2
0
0
2
2
0
0
0
0
0
0
2
1
0
0
0
2
2
0
0
2
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
1
0
0
1
2
0
2
0
0
0
0
2
2
1
0
0
0
1
0
0
0
2
0
2
0
2
0
2
1
0
0
0
0
0
2
1
0
0
1
0
0
0
0
3
1
2
0
2
0
0
1
0
2
0
0
2
3
0
0
0
3
0
2
1
2
1
0
0
1
2
1
2
0
0
2
0
1
4
0
1
1
0
1
0
0
1
0
0
0
2
0
2
0
0
1
0
0
1
1
1
0
0
0
2
2
2
1
4
0
1
0
0
2
0
2
1
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
2
0
0
0
0
0
0
0
2
2
0
1
2
0
1
0
3
2
2
2
0
1
0
4
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
1
0
2
2
1
1
0
3
0
2
1
0
2
0
0
1
0
0
0
1
0
0
2
0
2
0
0
0
0
2
0
2
2
2
0
0
1
1
0
1
1
2
1
2
2
0
0
0
0
0
0
0
1
0
0
1
2
0
1
0
0
2
0
1
0
1
1
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
1
2
1
0
2
0
2
0
2
0
2
1
0
2
2
3
0
0
1
1
2
1
1
0
0
2
2
2
0
4
1
1
0
2
1
0
2
1
0
0
2
1
2
0
0
1
0
1
1
0
0
1
1
0
1
0
1
0
0
0
2
0
2
1
0
3
0
0
0
1
0
4
1
1
2
1
0
1
0
0
2
0
2
0
1
1
0
0
0
0
0
0
2
2
0
0
2
0
2
0
0
1
0
1
0
0
0
0
0
1
1
3
2
1
0
2
0
0
2
1
2
0
1
1
0
1
2
2
1
1
0
0
2
0
0
1
0
0
0
0
0
1
1
0
1
0
1
0
1
0
3
1
0
1
1
1
0
1
1
1
1
0
0
0
0
0
2
1
0
1
2
0
2
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
2
1
0
0
0
2
0
0
0
0
0
2
2
2
0
2
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
1
0
0
0
0
2
1
1
1
0
0
1
0
2
0
0
0
1
2
2
0
1
0
1
1
0
1
0
0
1
0
0
0
1
0
1
1
1
1
0
2
1
0
1
1
0
1
1
2
3
1
1
1
1
0
0
0
0
1
0
1
0
1
1
0
1
3
1
0
1
0
0
0
1
1
2
1
0
1
0
0
2
1
1
1
0
0
0
0
0
0
1
1
2
0
0
1
2
2
0
2
0
0
1
1
2
0
2
0
0
0
2
1
1
1
0
0
2
0
2
1
0
0
0
0
1
0
0
0
0
0
0
1
2
1
0
0
1
2
0
0
1
0
2
0
2
0
1
0
0
1
1
1
0
1
0
2
1
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
1
0
1
1
1
0
0
2
1
3
0
0
0
0
0
0
0
0
1
1
0
0
1
1
1
1
0
1
1
1
0
0
1
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
2
2
0
0
0
0
1
0
1
1
1
0
1
0
0
0
0
0
1
1
1
0
2
2
1
0
0
0
0
0
2
1
0
0
2
1
0
1
0
2
0
0
2
0
0
0
2
0
0
0
0
0
1
0
3
0
0
0
2
0
1
0
0
2
0
1
1
0
2
0
0
0
2
0
0
1
0
2
0
1
1
1
1
0
1
0
0
2
1
2
0
1
0
0
0
1
0
1
0
1
2
1
0
0
0
1
1
2
0
0
0
2
1
1
0
0
0
0
0
1
0
1
0
0
0
0
3
2
0
0
0
0
1
2
1
1
1
2
1
0
1
1
0
0
4
0
1
0
0
1
0
1
0
2
0
2
1
0
1
2
1
2
0
0
0
0
2
0
0
1
0
0
0
2
1
1
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
2
1
0
1
0
0
0
0
1
0
0
1
2
1
2
0
1
0
2
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
2
0
1
2
0
2
1
0
1
0
0
0
1
0
0
2
1
1
1
1
2
0
0
1
1
1
0
1
1
0
0
2
1
1
0
1
0
0
2
0
0
0
2
0
0
2
1
0
0
2
0
0
0
1
1
0
0
1
0
0
0
1
2
0
0
0
1
0
0
0
1
2
0
1
2
1
0
0
0
0
0
0
0
1
2
2
1
1
0
0
1
1
0
0
0
0
1
0
0
0
1
1
0
0
0
4
1
0
1
0
1
2
0
0
0
1
1
0
0
1
1
0
0
1
1
1
1
0
1
1
1
0
0
0
0
1
0
0
2
0
0
1
0
1
0
0
0
2
0
0
0
0
2
1
0
2
0
0
2
1
0
2
0
1
0
1
0
0
1
1
0
1
3
0
0
0
2
0
0
0
1
1
2
0
1
0
2
0
2
0
1
0
0
1
1
1
0
1
2
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
2
2
2
0
2
0
2
0
0
0
0
2
2
0
0
0
1
0
0
2
2
1
0
0
1
0
1
0
0
0
0
1
0
0
2
0
2
0
0
0
1
1
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
1
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
2
1
2
2
2
0
0
1
3
0
2
0
0
2
0
0
0
0
2
0
2
6
0
2
0
1
0
2
0
0
1
2
0
2
0
0
0
1
0
1
0
0
1
2
0
0
2
0
1
0
0
0
0
0
2
1
1
0
2
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
1
0
2
0
2
3
4
0
0
0
0
0
2
0
0
2
1
0
0
2
1
0
0
1
0
1
0
0
2
1
0
0
0
0
0
1
0
2
0
0
2
0
2
1
2
0
1
0
2
2
1
1
0
1
0
1
1
0
0
2
0
0
2
1
1
0
0
0
1
1
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
2
1
1
0
0
0
0
1
0
0
0
0
1
0
0
3
0
1
1
0
0
0
0
1
0
0
0
0
0
1
2
1
2
2
1
1
2
2
0
1
0
0
2
0
2
0
1
0
1
0
1
0
2
0
0
2
0
1
1
0
0
0
0
2
1
0
1
1
0
2
0
1
1
0
0
0
0
1
0
0
0
0
1
1
0
1
1
0
1
2
0
0
1
2
0
1
0
1
1
2
0
0
0
0
2
0
1
1
0
2
2
2
2
0
1
0
1
3
3
0
0
1
1
0
0
1
0
0
1
1
2
1
0
1
2
0
0
0
2
0
1
1
1
0
0
0
0
3
2
1
0
0
0
1
2
2
1
2
0
0
0
2
2
0
0
1
2
2
0
0
0
0
0
0
2
0
0
0
0
1
3
0
1
0
0
0
0
1
1
1
1
0
2
0
0
1
2
1
0
1
0
0
0
0
0
1
1
0
2
0
2
1
0
0
1
0
2
0
1
0
2
1
2
0
0
0
0
1
2
0
3
1
0
0
0
2
2
0
0
0
2
1
2
0
0
1
3
0
0
0
2
1
0
0
2
0
0
0
1
0
1
1
2
0
0
0
0
1
2
1
0
1
1
2
1
2
0
2
2
1
1
1
2
0
0
0
3
0
1
0
2
0
0
0
2
0
1
0
0
0
2
1
0
0
1
0
0
0
0
1
1
1
0
0
1
0
2
0
1
2
0
2
2
2
0
1
0
0
1
0
0
0
0
2
0
2
0
0
1
0
0
0
0
1
1
1
0
0
0
0
1
2
0
2
0
1
1
1
0
0
0
0
0
0
2
0
0
0
1
3
1
1
0
1
0
2
0
2
1
1
0
0
2
1
1
1
0
3
1
2
0
0
0
1
0
2
0
2
0
0
1
0
1
2
0
0
1
0
0
2
2
0
0
0
0
0
1
3
3
3
0
2
0
0
0
0
0
0
0
2
0
2
0
0
2
1
2
1
2
0
1
2
1
5
0
2
3
1
0
0
0
1
0
0
0
0
1
0
1
2
1
1
1
1
0
1
0
0
2
0
2
1
2
2
1
2
1
5
2
1
2
2
2
1
1
1
0
0
0
0
0
0
0
2
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
2
0
1
0
0
0
1
0
2
0
1
1
1
0
0
0
2
0
1
1
0
0
0
2
0
0
2
0
0
0
1
0
0
0
1
0
0
0
4
2
0
0
1
3
2
1
1
0
2
0
1
3
2
0
1
2
0
0
1
0
0
0
0
1
0
1
0
1
0
2
2
2
2
0
0
1
0
0
0
2
2
0
2
2
0
0
0
0
1
0
2
0
1
0
0
2
0
0
2
0
0
0
0
0
0
3
0
0
0
0
1
2
0
1
0
1
0
0
2
0
0
2
0
0
0
0
1
1
0
2
1
2
0
0
3
0
0
0
2
0
1
0
0
1
0
1
0
0
0
0
1
0
2
0
2
1
0
0
1
0
0
2
0
0
0
3
0
0
2
2
1
0
0
0
0
0
2
0
0
0
2
1
0
0
1
0
0
0
0
1
1
1
0
0
0
0
1
2
0
0
1
2
1
0
2
0
0
0
2
0
1
0
2
0
0
0
1
1
1
0
1
4
2
1
1
0
0
1
0
0
1
0
0
2
0
0
0
2
1
0
1
0
0
1
0
0
0
0
0
0
0
3
2
0
0
0
0
1
1
0
1
2
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
1
3
0
0
0
1
2
0
0
2
0
0
2
1
2
0
0
1
2
1
2
0
0
0
2
2
2
1
0
0
1
1
0
0
0
0
2
1
1
0
0
0
2
0
0
1
0
1
1
0
0
0
2
2
0
2
1
0
1
0
1
1
0
0
1
0
0
0
2
0
0
0
2
0
0
0
1
0
1
0
0
1
2
0
0
0
0
1
0
1
1
0
0
2
1
1
2
0
0
0
0
2
2
0
0
0
2
0
2
2
0
0
0
0
0
0
2
1
1
0
1
2
0
0
2
1
2
0
2
2
0
0
4
1
1
0
1
2
0
2
0
0
2
2
0
0
0
0
1
0
0
2
0
2
1
1
0
2
0
2
2
2
0
0
0
0
2
2
2
0
1
0
0
2
0
0
1
1
0
2
0
0
1
0
0
1
0
0
0
0
0
2
2
0
1
1
0
0
0
1
2
1
2
1
1
0
1
0
0
2
2
3
1
1
0
0
0
2
1
0
0
2
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
2
1
0
1
2
1
2
1
0
1
0
2
3
1
0
1
0
0
0
1
0
0
1
2
1
0
0
0
0
0
0
1
0
2
0
2
2
0
2
2
1
0
0
0
1
1
0
2
0
1
1
0
0
0
1
0
1
2
0
0
2
0
0
0
2
0
2
2
1
0
1
0
3
2
0
0
0
0
0
2
0
1
1
0
0
2
0
0
0
2
0
0
2
0
0
1
0
3
2
0
0
1
1
2
0
1
0
2
0
0
2
1
1
0
0
1
0
0
0
0
0
0
0
0
2
1
0
1
1
1
0
1
1
0
1
4
1
1
2
0
0
0
0
2
0
2
1
0
1
1
0
2
0
0
2
2
0
1
0
0
2
0
2
0
0
2
0
0
3
1
4
0
0
0
1
1
0
1
0
1
0
0
1
1
1
0
0
0
4
2
1
0
1
1
0
0
0
1
0
2
2
2
1
0
0
2
0
0
1
2
1
2
0
0
2
1
0
2
1
0
0
0
1
2
0
0
1
0
0
1
0
2
0
0
1
2
2
1
1
0
1
0
0
0
0
1
2
1
1
2
2
1
0
1
1
0
2
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
1
1
0
0
0
1
0
1
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
1
0
2
2
0
0
0
0
1
2
0
0
0
2
1
2
0
0
1
0
2
0
1
0
1
0
0
2
0
1
3
2
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
1
0
2
0
0
2
2
1
2
2
0
2
0
0
7
0
0
1
2
1
2
3
1
1
0
2
1
1
0
2
0
0
1
1
0
0
0
0
2
0
0
1
0
2
2
1
0
0
0
2
1
0
0
1
1
0
0
2
0
2
2
0
0
1
0
0
3
0
1
2
1
1
1
0
0
0
2
0
0
1
1
2
1
0
0
0
0
0
0
0
1
0
0
2
1
2
0
2
0
0
1
2
1
0
2
0
1
0
0
1
1
0
1
0
0
0
2
1
0
0
0
0
0
0
3
1
1
0
2
0
1
0
0
1
1
1
0
0
0
0
0
2
1
3
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
2
2
1
2
0
0
0
2
2
0
1
0
0
2
2
0
2
2
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
3
1
1
1
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
2
2
2
1
2
0
2
1
0
0
0
1
2
1
0
0
1
0
2
0
2
1
0
0
1
2
2
2
0
2
0
0
0
2
0
0
2
0
0
0
2
0
1
0
2
0
0
0
0
1
0
1
1
1
1
2
0
1
0
0
0
3
0
0
1
0
1
1
2
1
1
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
1
0
0
1
0
1
0
1
0
1
0
1
2
0
1
0
0
0
0
2
0
0
2
1
1
0
0
0
1
2
1
1
1
2
0
1
0
0
0
1
0
2
1
1
0
1
1
0
2
2
0
4
0
1
0
0
3
1
0
2
1
1
1
2
2
0
2
1
0
1
1
2
0
2
1
0
0
0
0
2
1
0
3
0
0
1
1
1
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
2
2
0
0
1
0
1
1
0
0
0
1
0
1
0
0
0
0
1
1
0
2
0
2
0
0
0
0
1
1
0
1
2
0
4
1
0
1
2
0
4
1
1
2
0
0
0
1
1
0
1
0
0
0
1
0
3
2
0
1
2
0
0
0
0
0
0
0
0
0
2
0
2
2
0
2
1
0
2
0
0
2
0
0
1
2
1
0
2
1
0
2
0
2
0
2
0
2
0
2
1
0
1
1
1
0
2
0
0
0
1
1
0
1
1
1
1
0
0
0
2
0
0
2
2
3
1
1
2
1
0
0
1
1
2
0
0
1
2
0
0
1
2
0
2
0
1
0
0
1
0
2
0
0
0
1
0
0
0
1
2
6
2
0
2
0
0
1
1
0
0
0
0
0
1
1
0
1
1
0
0
2
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
2
0
0
4
0
2
3
0
0
0
0
1
2
1
0
1
5
0
2
2
1
0
2
1
1
0
0
2
0
2
2
2
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
1
0
1
0
2
0
0
0
1
0
1
0
1
2
0
1
0
0
2
2
0
0
0
1
2
1
0
1
3
0
0
2
0
0
1
0
0
1
0
0
0
0
2
2
0
0
2
2
0
1
0
0
1
1
0
1
1
2
2
0
1
1
1
1
0
0
0
0
0
0
1
0
1
0
0
0
2
1
1
0
0
0
0
2
0
0
1
2
0
2
2
0
1
0
0
0
0
1
1
0
2
1
2
0
2
2
1
0
0
2
0
0
0
0
0
2
0
1
4
1
1
0
0
0
1
1
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
2
0
1
0
2
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
1
0
1
0
0
0
0
1
0
0
2
0
0
1
1
0
1
1
1
0
0
0
0
0
1
0
0
1
0
1
0
1
2
1
0
0
0
0
1
0
1
1
0
0
0
1
1
1
0
2
4
0
1
0
1
0
1
0
0
0
0
2
1
0
0
1
0
1
1
0
0
0
0
0
3
0
2
1
0
1
0
1
0
0
2
0
2
0
1
2
1
0
1
1
0
0
0
2
0
0
2
2
0
2
1
1
0
0
3
0
0
0
0
2
0
1
2
0
2
2
1
2
0
2
0
2
0
2
0
0
0
0
1
1
0
1
1
4
0
0
0
2
0
0
0
1
2
0
0
1
1
20
2
2
1
0
0
0
1
0
2
0
0
2
2
0
0
2
0
0
0
0
2
2
0
1
1
2
0
0
1
1
1
0
0
0
2
1
1
2
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
2
0
1
1
0
0
1
2
0
0
0
0
0
1
2
0
0
1
0
2
0
0
0
2
1
1
0
1
0
0
2
1
1
7
2
2
2
0
0
0
1
0
0
2
1
2
0
1
0
0
0
0
0
1
0
0
1
0
1
1
2
1
0
0
2
1
0
0
2
2
1
0
0
0
0
0
0
0
3
2
0
2
1
2
0
0
0
1
0
1
0
0
0
1
1
1
2
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
2
0
1
1
0
0
0
0
0
0
0
0
0
2
1
0
0
1
2
0
0
1
0
2
1
1
0
0
0
0
1
2
0
1
0
0
1
0
0
0
1
0
2
1
2
1
2
2
2
2
0
2
0
2
0
0
0
2
0
0
1
2
0
1
1
1
1
5
0
0
0
0
0
1
0
0
1
1
1
0
2
0
1
1
0
0
0
1
1
0
2
0
2
0
0
2
2
1
0
0
1
0
1
1
0
0
0
1
1
1
0
0
0
1
4
0
0
0
0
1
2
0
0
0
1
2
2
0
0
0
2
1
2
0
0
0
1
0
0
2
0
2
0
1
1
2
0
0
0
0
0
0
1
0
1
0
0
1
2
0
1
0
2
0
0
1
1
0
2
1
1
0
1
0
0
2
0
2
0
2
0
2
0
0
2
0
0
0
0
1
0
0
0
2
0
1
2
1
0
0
1
2
1
0
2
0
2
0
0
2
1
1
0
0
0
0
0
0
0
1
1
0
0
1
2
0
0
0
0
2
2
0
0
1
0
0
0
0
1
0
2
2
2
1
0
1
0
0
1
0
1
2
0
0
0
0
1
1
1
1
0
1
2
1
1
2
2
1
0
1
0
0
0
2
2
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
2
0
0
0
2
1
2
1
0
0
0
2
0
2
0
0
1
1
1
0
0
0
0
0
1
2
0
0
0
1
0
1
0
0
0
2
0
1
1
1
0
2
3
2
0
0
1
2
2
0
1
2
2
2
1
1
0
1
0
0
0
0
1
1
0
1
1
2
0
2
0
0
1
0
0
1
0
0
0
0
1
1
1
0
0
1
1
1
0
0
5
1
1
0
2
0
0
1
1
0
0
1
0
0
1
2
0
2
1
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
2
2
0
0
0
1
0
0
2
0
0
2
2
0
0
1
0
0
0
0
0
2
0
0
2
3
1
1
3
0
0
0
2
1
3
0
0
1
2
0
2
0
0
2
0
0
2
2
0
1
0
0
0
2
2
0
2
0
2
2
0
0
0
0
2
1
1
0
0
0
0
1
1
2
1
2
0
1
0
0
2
0
1
1
0
0
0
0
2
0
0
1
0
0
1
0
0
0
1
0
0
1
0
2
0
1
0
0
0
2
2
0
1
0
0
0
0
0
2
2
0
0
0
0
0
1
1
0
2
1
1
2
0
1
1
0
2
0
2
1
1
1
2
0
0
1
0
0
1
2
0
0
0
0
2
0
0
0
0
0
1
0
2
1
1
0
0
0
2
0
0
0
3
0
0
0
0
2
1
0
2
0
1
1
2
1
1
2
1
0
2
1
0
2
0
0
2
0
0
0
0
2
0
1
1
2
0
0
1
1
0
0
2
2
3
2
0
2
2
0
1
0
1
0
0
2
0
2
4
2
0
2
0
3
2
0
0
0
2
0
0
0
1
1
0
2
1
0
0
2
0
0
3
1
1
0
1
2
0
0
0
1
2
2
6
0
0
2
1
1
0
3
2
1
0
0
1
0
0
1
0
0
2
1
0
0
1
0
0
0
1
2
0
1
1
0
0
0
0
2
0
1
0
0
1
0
0
0
0
1
2
2
0
0
0
0
1
0
0
2
0
1
0
0
0
0
1
0
0
2
1
2
0
0
0
0
2
1
0
1
1
0
0
1
0
1
0
0
1
0
1
2
1
0
0
2
2
0
0
1
2
0
1
0
1
0
0
0
2
2
0
0
0
0
1
1
1
2
4
0
0
1
0
0
0
1
1
0
0
0
1
0
1
0
1
2
1
2
2
2
0
0
0
0
0
0
0
0
0
0
1
1
2
0
1
0
1
1
0
1
0
0
0
0
0
2
0
3
2
2
0
2
1
0
0
0
0
0
2
1
2
0
2
3
1
0
1
0
0
2
0
0
0
1
2
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
2
2
0
0
1
0
1
0
2
1
1
0
0
0
0
0
3
0
2
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
1
1
1
0
0
0
1
2
1
1
2
0
1
0
2
0
0
0
1
0
0
1
0
1
2
1
0
0
0
1
0
2
0
0
1
1
3
2
1
1
0
0
0
1
0
2
0
0
0
1
0
1
0
0
0
2
0
2
1
2
0
1
2
0
0
2
1
2
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
4
2
0
2
1
2
0
2
0
0
0
0
2
0
2
0
1
1
1
0
1
0
1
0
1
0
8
0
3
2
0
0
2
0
2
1
0
0
0
0
1
0
0
0
1
2
2
1
1
0
1
0
2
2
2
0
0
0
0
0
1
0
2
0
2
0
1
1
0
0
0
0
1
1
1
1
2
1
2
2
0
2
0
0
0
0
0
1
2
2
2
0
2
0
2
0
0
0
0
0
0
1
0
1
2
2
0
0
0
0
0
1
0
1
1
0
0
2
0
0
0
0
1
0
2
2
2
2
0
0
0
0
0
1
0
0
2
0
2
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
1
0
0
2
0
2
1
0
2
1
1
0
1
0
0
2
0
0
0
0
2
1
0
3
1
2
2
0
0
1
1
1
0
0
0
2
0
0
0
1
0
2
1
2
0
0
0
2
2
2
1
2
4
1
0
1
0
0
1
0
2
0
1
1
0
0
0
0
0
2
0
0
1
0
0
0
0
1
2
0
0
2
0
0
0
0
0
1
0
2
1
2
0
0
1
0
0
0
2
1
0
1
0
1
0
1
0
1
0
0
2
2
2
0
0
0
1
1
1
2
2
0
1
1
2
0
0
0
0
0
1
1
0
2
0
0
0
0
1
1
0
2
1
2
0
0
0
1
1
2
0
2
1
2
0
0
0
0
1
2
1
0
2
0
2
1
1
1
1
1
3
0
1
2
0
2
0
0
5
0
0
0
1
1
0
0
2
0
1
0
0
0
0
0
3
0
0
1
1
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
2
0
0
1
0
1
0
0
2
0
2
0
1
1
1
1
1
1
2
0
3
1
0
0
2
2
0
2
0
0
0
2
1
2
2
1
0
0
1
0
0
2
2
1
0
0
0
2
0
0
2
2
0
0
1
0
0
0
0
0
2
0
2
0
1
0
1
0
1
3
2
1
0
0
0
1
0
2
0
0
0
2
1
0
0
1
1
0
1
1
0
1
1
0
0
0
1
1
1
0
1
0
1
0
0
2
1
1
0
1
2
2
0
2
0
2
1
1
1
2
1
0
1
0
0
2
2
1
0
1
0
1
0
0
2
0
0
0
2
0
0
1
1
0
1
2
0
0
0
1
0
0
0
1
2
0
0
2
1
1
0
0
2
0
1
2
0
0
0
1
5
0
0
0
0
0
0
1
0
1
0
1
0
1
0
2
0
1
1
0
0
2
0
1
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
2
0
2
0
0
2
1
0
2
0
0
2
2
0
1
0
1
1
0
1
0
1
0
2
0
0
1
0
3
0
0
2
0
2
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
2
1
0
0
0
0
0
0
1
2
0
2
0
0
0
0
1
0
0
0
2
0
2
3
3
1
2
0
1
1
0
1
5
0
1
0
0
2
1
2
0
1
0
1
1
1
0
0
1
2
0
0
0
1
0
1
0
2
0
0
1
1
0
3
2
3
0
1
0
0
0
2
0
0
1
0
0
0
0
2
1
0
1
1
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
1
2
0
1
4
0
0
1
1
0
0
1
3
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
1
0
2
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
1
2
2
1
1
0
1
0
1
1
1
1
1
2
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
2
0
0
2
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
2
1
0
0
2
0
0
1
0
0
0
2
0
0
0
1
2
1
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
2
2
1
1
0
0
0
1
0
2
1
0
0
1
0
1
0
1
0
2
1
1
0
0
1
0
0
0
1
0
0
2
1
1
2
0
0
0
0
0
0
2
3
0
0
0
2
0
2
0
0
0
0
1
0
0
1
1
2
0
0
0
0
0
0
1
0
1
0
2
0
1
0
2
0
1
1
1
0
1
1
0
2
2
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
2
0
1
2
0
0
1
0
2
2
1
1
0
0
2
1
3
0
0
0
0
2
0
1
1
3
1
0
2
0
0
0
2
1
1
0
0
1
0
2
0
1
0
0
0
2
0
0
0
1
1
1
1
2
0
0
0
0
2
2
0
1
0
0
2
0
2
0
0
2
2
1
1
0
2
0
0
1
2
1
0
1
0
2
1
1
1
2
0
0
0
1
2
0
1
1
1
1
0
0
2
0
2
1
2
2
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
1
0
0
1
2
0
0
0
1
2
0
0
0
0
1
0
2
0
0
2
2
1
1
0
2
2
1
1
0
0
0
1
1
1
0
1
0
1
0
0
0
1
1
0
0
0
1
0
0
1
2
0
0
0
0
1
1
0
0
1
0
1
1
0
0
2
0
0
1
0
0
0
2
0
1
0
1
2
0
0
0
2
0
0
2
1
5
2
2
0
1
2
0
1
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
2
0
0
0
0
3
1
1
0
0
0
2
0
0
2
0
0
0
0
2
0
2
0
1
0
0
0
2
0
0
0
1
1
0
2
0
0
3
1
1
0
0
1
0
0
2
0
0
2
0
2
0
0
0
2
1
2
0
0
1
1
1
2
0
1
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
1
1
0
1
2
1
0
2
0
0
1
1
1
1
0
0
0
0
0
2
2
0
1
0
1
2
0
0
2
2
0
1
4
1
0
1
0
0
0
0
0
0
0
1
0
1
3
2
0
0
1
1
0
1
2
1
1
0
0
2
0
0
0
0
0
0
0
2
0
2
2
2
0
0
1
0
0
1
1
0
2
1
2
2
0
2
0
1
0
0
0
2
0
2
0
0
0
1
1
0
1
1
1
0
1
0
1
0
0
2
3
2
0
0
0
0
1
1
1
0
0
0
0
1
0
1
0
0
0
2
1
0
0
0
1
1
0
1
1
1
1
0
0
0
1
1
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
1
0
1
1
0
0
0
2
0
0
0
0
0
1
0
0
1
1
0
1
2
0
2
0
2
1
0
0
1
1
0
0
2
1
0
1
2
0
0
1
0
1
1
1
0
1
0
0
0
0
1
0
0
2
0
0
1
0
0
1
1
1
1
0
0
0
7
0
2
0
2
2
0
0
0
0
0
2
0
1
0
2
0
0
1
0
0
1
2
2
0
0
0
0
1
0
2
2
0
2
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
2
1
1
0
2
1
0
0
0
0
1
2
1
1
0
0
0
2
0
0
0
1
0
0
1
1
0
0
1
0
0
0
1
0
0
1
0
2
1
0
1
2
0
0
0
1
1
2
0
1
0
1
0
0
0
0
1
4
1
1
1
0
0
0
0
0
0
0
0
1
0
0
2
2
2
0
0
2
0
0
1
1
3
2
0
0
1
0
0
0
2
0
3
1
0
0
0
1
2
0
0
0
2
0
0
1
0
0
0
1
7
1
1
1
0
0
1
1
2
0
0
1
1
0
2
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
2
1
1
2
1
0
0
0
1
0
0
0
1
1
1
1
2
1
0
1
1
0
0
0
1
0
3
0
0
1
1
1
0
2
1
1
0
1
2
1
0
0
0
1
1
0
1
0
2
2
0
0
1
1
2
0
0
2
0
3
3
0
0
0
2
1
2
0
0
2
0
1
1
3
2
2
2
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
8
1
0
0
1
0
0
0
2
0
0
2
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
2
0
1
0
1
0
0
0
0
1
0
0
1
0
2
1
2
1
1
0
2
0
2
0
0
2
2
0
0
0
2
2
0
0
1
0
1
2
0
1
1
1
5
1
0
2
0
0
2
1
0
0
1
1
0
2
1
2
0
0
0
0
1
0
0
2
0
1
0
2
1
0
2
1
1
0
2
0
1
0
0
1
0
0
0
0
0
1
1
2
1
1
0
0
1
0
2
1
0
0
0
0
0
1
0
2
3
0
0
2
3
0
0
0
2
0
0
2
0
0
2
0
2
1
0
0
0
0
1
2
2
0
0
0
2
0
0
2
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
1
2
0
1
0
0
0
1
0
0
2
0
2
0
2
0
0
0
1
1
2
0
2
1
0
2
0
2
0
2
0
0
2
0
2
0
0
0
2
1
0
0
4
1
0
2
0
1
1
0
2
0
0
0
3
0
0
2
1
2
1
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
1
0
3
2
1
0
0
1
0
0
0
1
1
2
0
1
0
1
1
0
0
0
0
2
0
2
1
0
1
1
2
0
0
0
1
2
0
0
0
2
1
0
1
1
2
0
0
0
2
0
0
1
0
1
1
1
1
0
0
0
0
3
0
0
1
0
1
3
1
0
1
2
2
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
1
1
0
1
1
0
0
3
1
0
1
2
1
1
1
1
0
0
0
2
0
0
0
3
0
0
1
0
1
0
0
0
0
0
1
1
0
3
0
2
2
2
2
0
0
1
0
2
0
2
0
0
0
0
0
1
1
1
1
0
1
3
1
1
0
2
0
0
1
2
2
0
1
0
1
2
2
0
0
1
1
1
0
0
0
0
0
0
1
0
0
3
1
0
0
2
0
1
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
1
0
2
2
2
2
0
6
0
0
0
0
1
2
0
1
0
2
1
0
0
2
2
0
0
2
0
0
1
0
1
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
2
2
0
1
0
1
0
1
0
0
0
1
1
1
1
1
0
0
1
0
0
1
0
1
0
1
0
1
0
2
2
0
0
0
1
0
0
2
1
2
0
0
1
1
1
0
1
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
2
2
1
0
1
1
1
0
0
2
0
0
1
4
0
2
0
2
0
0
0
0
0
0
2
2
1
0
2
1
0
0
0
0
0
0
0
2
2
3
2
0
1
0
2
0
0
0
2
0
2
0
2
0
2
1
1
0
1
2
1
2
2
2
0
1
0
0
1
0
0
0
2
0
1
2
1
0
0
0
1
1
0
1
0
0
0
0
0
2
1
2
0
0
0
0
2
0
2
0
0
1
2
2
0
0
0
2
0
0
0
3
0
1
0
0
1
0
0
2
2
0
0
3
2
2
0
0
2
0
0
2
0
0
0
0
2
1
0
2
0
0
4
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
1
2
1
1
1
2
0
0
2
1
1
1
1
0
0
0
2
1
0
0
0
2
0
1
0
2
0
2
0
2
2
2
0
0
0
2
0
0
1
0
1
0
1
0
1
0
0
0
2
0
0
0
0
1
1
1
2
2
0
1
0
0
0
0
0
0
0
3
0
1
0
0
1
1
0
0
0
1
0
0
2
0
1
1
3
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
3
1
1
1
0
0
1
0
2
0
0
0
2
2
1
2
1
0
0
2
0
2
1
1
0
1
1
0
1
0
0
1
0
0
0
0
1
0
3
0
0
0
2
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
2
0
2
0
1
1
0
0
0
1
0
0
0
0
0
2
2
0
0
0
1
2
0
1
1
0
2
1
0
0
1
0
0
1
1
1
2
0
0
0
1
0
1
2
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
2
2
2
0
0
0
2
0
1
0
0
0
0
2
0
0
1
0
0
0
0
3
2
0
2
1
2
6
1
0
0
2
0
1
0
1
2
1
0
0
2
0
1
1
1
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
1
1
2
1
0
0
0
0
0
2
2
1
0
9
2
1
0
0
1
0
2
1
1
0
1
2
0
3
1
0
0
0
0
0
0
1
0
1
2
1
1
0
2
0
1
1
2
2
2
0
0
2
0
1
0
0
0
2
0
0
2
2
1
0
0
0
0
1
1
0
2
3
0
3
2
2
1
1
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
1
2
4
0
0
1
0
0
0
0
1
1
3
0
0
2
1
2
2
0
2
0
0
0
0
1
1
0
2
0
1
1
1
0
0
0
1
0
3
0
0
0
0
0
2
0
1
0
0
2
0
1
1
0
1
1
1
2
0
0
2
0
1
0
0
0
1
1
0
1
2
0
1
1
2
0
3
0
0
3
1
0
0
1
0
1
0
2
0
3
2
1
0
0
0
1
1
0
1
4
1
0
0
0
2
0
1
0
0
2
2
1
1
0
1
0
2
0
1
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
1
1
3
0
1
0
0
1
1
4
0
0
1
0
0
0
0
2
0
1
2
0
2
2
0
0
1
0
1
0
0
1
0
0
0
0
0
0
2
1
0
3
0
0
1
0
0
2
0
0
0
0
0
2
0
1
3
1
0
2
0
0
0
1
0
1
1
0
0
1
0
0
1
0
0
1
2
0
0
2
1
1
0
0
0
2
1
1
0
2
0
2
0
0
0
1
2
0
0
0
0
0
1
0
0
0
1
0
1
1
1
0
1
1
2
2
2
2
1
1
2
0
0
0
0
1
0
0
1
1
0
0
1
0
0
4
0
0
1
1
2
2
2
0
0
0
0
1
0
1
1
1
1
0
0
0
2
0
2
0
0
1
0
0
1
0
0
1
2
1
0
1
0
0
2
1
0
2
0
1
0
2
0
0
0
2
0
1
1
1
0
1
1
2
0
2
2
0
2
0
0
1
1
2
0
2
0
0
0
2
0
1
0
2
2
3
2
0
2
1
2
3
0
0
0
0
1
1
0
1
0
0
2
1
2
0
2
2
2
0
0
2
2
1
0
0
2
0
1
3
2
0
2
2
1
3
2
0
2
0
0
0
2
2
1
2
0
0
1
0
0
1
1
2
1
0
0
0
0
1
0
2
0
2
2
1
0
2
0
2
2
0
0
0
0
0
0
1
0
1
2
2
1
2
0
2
0
0
2
0
0
0
0
2
1
0
2
1
1
1
3
0
0
0
2
7
2
1
0
2
0
2
0
2
0
1
0
2
0
1
3
1
1
0
0
0
0
1
1
1
0
0
0
0
0
0
1
1
0
2
0
2
2
1
1
0
0
1
0
2
0
0
2
2
0
0
1
2
0
0
0
1
1
1
0
1
0
0
0
0
1
0
0
2
0
1
2
2
2
1
2
1
0
0
0
0
0
2
0
2
1
2
2
1
3
0
0
0
1
0
0
1
2
0
0
0
0
0
1
0
0
0
2
2
0
4
1
1
0
0
0
0
2
1
2
0
1
1
0
2
1
1
2
1
1
0
0
1
2
0
1
1
0
1
0
0
0
1
1
0
0
0
1
1
0
1
2
1
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
2
0
1
0
0
2
0
0
0
0
1
0
0
2
0
1
0
2
2
2
2
1
0
0
0
0
0
0
3
2
0
0
0
1
0
1
0
1
1
0
0
0
2
2
0
0
1
0
0
1
1
1
2
0
1
0
1
1
1
1
0
2
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
1
1
0
0
2
1
1
1
0
1
1
0
1
0
0
1
0
0
1
1
0
2
1
0
0
1
0
2
2
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
1
0
1
0
0
0
2
2
0
0
0
0
1
2
1
0
0
0
0
1
2
1
2
0
2
2
0
1
1
1
0
7
0
0
2
2
0
1
0
2
2
0
0
0
0
0
2
0
0
2
0
1
2
0
0
0
0
2
1
0
0
1
0
1
0
0
0
1
0
0
0
1
2
0
2
0
0
0
2
2
2
0
1
0
0
0
2
0
1
0
2
0
1
0
1
0
0
1
0
2
0
2
0
0
0
0
0
1
2
0
0
0
1
2
3
1
2
0
2
1
2
0
0
2
2
1
0
2
0
1
0
0
0
3
1
2
0
0
0
0
1
0
0
0
1
0
2
0
1
0
0
1
0
0
0
1
0
0
2
6
1
1
0
0
1
1
1
0
0
2
2
0
2
0
2
0
0
2
1
0
0
1
0
0
1
2
1
1
0
3
0
2
0
0
0
0
2
1
0
1
2
0
0
0
2
0
2
1
0
2
0
0
0
1
1
1
1
2
0
1
0
1
2
0
1
0
2
2
2
0
0
0
0
0
2
0
2
1
0
1
2
0
0
2
0
0
0
0
0
0
1
1
1
2
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
1
2
0
2
0
3
2
0
0
0
0
0
2
0
0
0
0
8
0
1
0
0
0
1
0
2
2
0
1
1
0
0
4
1
1
2
0
0
0
0
2
0
1
0
0
2
2
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
2
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
1
2
0
2
0
1
1
2
1
0
0
1
0
0
0
2
1
0
1
0
0
0
1
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
2
2
0
0
0
0
0
0
0
0
2
0
1
1
1
0
1
1
1
1
0
2
0
0
1
1
0
1
0
2
0
0
0
0
0
2
0
1
2
0
0
0
0
2
0
0
0
0
0
1
0
0
2
1
1
0
2
1
0
1
2
2
2
0
0
0
0
2
0
1
2
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
2
1
1
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
1
2
2
2
2
0
0
8
0
0
0
0
0
0
0
1
1
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
2
2
1
1
2
1
0
0
2
0
0
0
1
2
0
3
1
0
1
1
0
1
0
0
2
0
1
0
1
0
1
0
1
0
2
0
0
0
2
0
0
0
4
0
2
1
1
0
3
0
0
2
0
2
3
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
2
1
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
2
1
1
1
1
1
2
0
0
0
2
1
0
0
3
0
0
0
2
0
1
1
0
2
0
0
0
0
1
0
2
0
0
2
0
2
0
1
2
0
2
0
0
0
1
0
0
3
0
0
1
1
0
2
0
0
2
0
0
1
1
0
0
0
1
0
0
2
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
1
1
0
0
0
0
1
0
0
1
0
2
0
0
0
1
0
1
0
1
0
2
0
0
0
0
1
0
0
1
0
0
2
0
1
1
0
2
2
0
3
0
0
2
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
1
2
1
1
0
0
1
0
0
0
0
0
1
2
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
1
1
0
0
0
0
1
0
2
2
0
2
1
0
0
0
0
3
0
2
0
0
0
0
1
1
0
1
3
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
1
3
1
0
0
2
1
2
0
0
3
0
1
2
0
0
0
0
0
0
1
2
0
0
0
2
1
0
2
0
0
1
0
1
2
2
0
0
0
1
0
4
1
1
0
2
2
2
1
0
0
0
1
0
0
0
0
2
0
0
0
3
2
0
0
1
2
1
0
0
0
0
1
0
2
1
0
1
2
0
0
2
0
1
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
3
2
0
0
0
2
2
2
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
3
1
0
1
0
0
1
0
0
2
0
1
0
2
0
0
0
0
0
0
0
2
0
0
2
1
4
1
0
1
0
2
1
1
1
0
2
0
0
1
0
1
1
3
0
2
0
2
0
1
0
0
0
2
0
1
1
2
0
1
1
0
0
0
2
0
0
0
1
0
1
0
0
1
0
0
1
0
1
0
1
0
2
0
0
0
0
0
0
0
0
1
1
2
0
1
0
0
1
0
1
1
2
0
0
0
1
0
0
0
0
2
0
0
0
0
1
3
1
2
0
0
0
1
2
0
1
0
0
0
2
0
0
1
1
0
0
1
1
0
0
2
0
0
0
0
0
1
0
3
2
0
0
1
1
2
0
0
0
2
0
1
2
0
0
1
2
0
1
0
2
0
1
0
0
0
0
2
0
0
1
0
0
0
2
2
0
1
0
0
0
2
2
1
1
2
0
2
0
0
1
2
0
0
1
1
0
0
2
1
0
0
1
0
2
0
0
0
1
0
1
2
0
1
0
0
0
0
0
2
1
0
1
0
2
1
1
1
2
0
1
3
3
0
0
0
0
1
2
2
0
0
0
2
0
2
2
1
0
1
1
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
2
0
1
2
0
0
0
1
2
2
1
2
0
0
0
7
1
0
1
2
1
0
0
2
0
0
0
1
0
0
0
0
0
3
2
0
1
1
0
0
1
1
0
0
1
0
0
0
1
0
1
0
2
1
2
0
0
1
1
0
1
2
0
2
0
0
1
1
0
3
0
0
1
0
0
0
0
0
1
0
0
0
1
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
2
2
0
2
0
0
0
1
3
1
0
2
2
0
0
2
1
0
0
2
2
0
0
0
2
2
1
1
0
1
1
0
0
0
0
2
1
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
2
2
0
0
1
2
2
1
0
0
0
0
1
0
2
0
1
0
0
1
0
0
0
1
0
1
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
1
0
2
0
1
2
1
0
6
2
1
0
2
0
2
0
1
1
1
1
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
2
1
0
2
0
1
0
1
0
0
2
0
0
1
0
0
1
1
2
0
2
0
1
2
0
0
1
1
2
4
1
0
2
0
2
2
2
0
0
1
0
0
0
1
1
1
1
0
0
0
0
2
0
0
0
0
1
0
0
1
0
2
0
0
0
2
0
1
0
5
2
2
1
0
0
0
1
0
1
0
0
0
1
0
0
2
2
1
0
1
0
1
2
1
0
1
2
1
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
2
1
2
1
1
0
2
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
1
2
2
0
0
0
0
0
0
2
0
1
0
1
0
1
0
0
1
2
2
0
0
1
1
1
0
1
1
0
2
1
1
1
2
1
2
1
3
0
2
0
1
0
1
1
0
0
1
2
1
0
0
0
2
0
0
2
2
0
0
0
0
1
1
0
1
0
2
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
2
2
0
1
0
0
2
2
2
0
2
2
0
0
2
0
0
0
1
2
2
0
1
2
1
2
0
1
1
1
2
4
2
0
1
0
0
0
2
0
1
1
2
0
0
0
1
0
2
2
2
2
2
2
0
0
3
0
0
1
0
3
1
0
0
0
0
0
1
0
1
2
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
2
0
2
0
0
0
1
1
0
0
0
1
1
0
0
1
2
0
1
0
0
0
0
0
2
2
1
0
2
0
1
1
2
0
1
0
0
0
0
0
1
0
1
0
1
1
1
0
0
0
2
1
0
1
1
0
1
0
0
0
0
0
0
1
1
0
0
0
1
2
0
0
0
1
0
0
1
2
4
2
1
0
1
1
0
2
0
2
2
0
1
0
0
1
1
0
2
0
2
1
1
2
2
0
3
0
0
0
1
0
2
2
0
2
0
2
1
2
2
0
1
0
0
0
0
1
0
3
1
0
0
2
1
0
0
1
0
0
2
0
1
2
2
0
0
0
2
1
1
0
3
3
2
0
0
1
0
1
2
0
1
1
0
2
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
1
1
1
0
0
0
1
2
0
0
0
0
0
4
1
0
0
0
0
2
1
0
0
0
1
0
0
0
0
1
1
2
0
0
0
2
0
0
1
2
0
1
1
0
0
0
1
0
0
1
0
0
2
0
0
1
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
2
2
0
2
0
0
0
3
0
1
1
1
0
1
0
2
1
0
0
2
0
0
0
2
2
0
1
2
1
0
0
2
0
0
0
1
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
3
0
2
0
2
0
0
0
2
0
0
0
0
0
1
0
0
1
2
0
1
2
0
0
1
0
0
1
0
0
1
1
0
0
1
1
1
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
1
0
0
2
1
1
0
0
2
0
2
0
0
2
2
2
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
2
0
1
0
0
2
1
0
0
0
0
0
1
0
3
2
2
1
1
0
0
1
1
0
1
2
2
1
1
0
0
0
0
0
0
0
1
2
2
0
2
0
1
1
0
0
2
0
0
2
2
1
0
0
0
1
1
1
1
0
1
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
1
2
2
0
0
1
0
2
0
0
0
0
0
0
1
1
0
2
0
0
0
0
3
0
2
0
2
0
0
0
0
3
2
0
2
0
2
1
0
0
4
4
0
0
0
0
0
0
0
0
1
0
2
4
0
1
1
0
1
0
0
0
0
0
1
0
2
0
0
0
2
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
1
2
0
0
1
2
1
1
0
2
1
0
0
2
0
0
2
2
0
0
1
1
2
0
0
0
0
0
1
2
0
1
1
0
0
1
2
2
2
0
0
0
0
1
2
0
0
1
0
0
0
1
1
0
2
1
2
2
2
0
2
0
2
0
0
3
0
2
0
2
2
0
0
1
0
2
1
0
0
0
2
0
0
0
1
3
1
0
0
0
0
0
2
1
1
1
1
0
2
1
2
0
0
1
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
1
0
1
0
0
0
0
1
0
3
0
0
0
0
1
1
0
1
1
0
1
2
0
0
0
1
0
0
0
0
1
0
3
1
1
0
0
1
0
0
0
0
1
0
2
0
2
1
0
2
1
0
0
0
2
2
2
1
0
2
1
0
2
2
0
0
4
0
2
1
0
1
3
0
1
0
0
1
1
2
1
3
0
1
0
1
1
2
2
1
0
2
1
0
0
1
0
1
0
0
0
1
0
1
2
0
0
1
0
2
1
0
1
2
0
0
0
0
0
0
1
1
2
3
1
0
2
1
2
1
1
1
0
0
1
0
0
1
0
0
1
1
0
1
0
2
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
1
0
1
2
1
2
1
0
0
0
0
1
0
0
1
2
0
1
2
1
0
1
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
3
0
0
3
2
0
2
0
2
1
1
0
0
0
0
0
2
0
1
2
0
1
1
0
1
1
0
1
0
0
2
0
1
2
1
0
0
5
0
0
2
2
0
0
3
0
0
1
1
0
0
0
2
2
2
0
1
0
0
0
2
1
1
0
0
1
2
2
0
0
1
2
1
0
1
0
2
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
2
0
0
2
0
0
1
1
0
1
0
0
1
0
0
1
0
0
1
2
0
2
0
0
2
0
0
0
0
0
0
1
0
2
0
4
0
0
3
0
2
2
0
0
1
0
2
1
2
0
0
0
0
2
1
0
1
1
0
1
0
1
0
1
1
0
2
0
0
0
0
2
3
2
2
1
0
0
3
0
2
1
1
0
0
1
1
0
1
1
0
0
2
1
2
1
0
1
0
1
0
0
1
2
0
0
0
1
0
1
1
0
2
1
0
0
1
0
2
0
0
0
0
0
0
0
2
1
2
0
0
0
2
2
0
3
0
0
0
1
1
2
2
3
0
2
1
2
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
1
1
0
0
0
2
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
2
2
0
0
0
1
0
0
1
2
2
0
2
0
1
0
1
0
0
0
1
0
1
2
1
2
0
0
2
0
2
1
1
0
0
1
0
2
1
1
1
1
1
2
0
1
0
1
2
2
0
2
2
1
2
0
1
0
0
1
0
0
2
1
0
1
2
2
1
0
1
0
1
0
0
0
0
0
0
1
1
1
0
0
1
1
2
0
0
0
0
2
1
2
0
2
1
1
1
0
0
0
0
1
1
0
0
1
0
0
1
1
2
5
1
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
1
0
0
1
1
0
0
0
2
0
0
0
0
0
1
2
2
1
2
0
0
0
1
1
1
0
0
1
0
0
0
0
3
2
0
2
0
1
0
0
2
3
1
1
2
0
0
1
2
0
0
0
0
0
2
1
2
0
0
1
1
3
2
0
3
2
0
0
1
0
0
3
0
0
0
0
0
0
1
0
0
0
2
2
2
2
0
1
2
0
1
2
0
0
1
2
1
0
0
2
0
0
2
0
0
0
1
0
4
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
2
0
1
0
0
2
0
0
0
2
1
2
1
1
0
2
1
0
0
2
2
0
1
1
0
2
1
0
2
1
0
1
0
0
0
0
0
1
0
1
1
2
0
1
0
0
0
2
0
2
2
1
2
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
1
2
1
2
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
4
0
1
2
0
0
0
2
2
1
0
0
0
0
1
2
1
1
1
0
1
1
0
1
1
1
0
1
1
1
2
0
0
2
0
0
1
0
0
0
0
1
0
1
0
2
0
0
2
2
0
0
0
1
0
2
1
0
2
0
2
2
0
0
2
0
0
2
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
1
0
2
0
0
0
0
0
1
0
4
0
3
0
1
0
0
2
0
0
0
0
2
1
1
0
0
4
1
0
2
2
0
1
2
0
2
0
0
0
0
1
1
1
0
0
2
1
1
2
0
0
0
0
1
0
2
0
1
1
0
2
0
0
0
1
2
2
0
2
0
0
0
0
0
0
0
0
3
2
1
0
0
1
2
0
2
0
2
1
1
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
3
2
0
1
4
1
0
0
0
0
0
2
0
2
1
2
2
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
2
0
0
1
0
0
0
1
1
0
1
1
1
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
1
0
0
1
0
0
1
1
2
0
1
2
1
0
0
0
0
1
2
1
1
1
1
1
0
0
1
0
1
0
3
1
0
3
1
1
0
0
1
2
1
2
0
0
0
0
0
2
0
0
2
2
2
0
0
2
0
0
1
0
2
1
0
0
0
0
2
0
0
1
2
1
0
1
0
1
0
2
0
1
0
1
2
1
2
1
1
1
2
4
2
0
1
0
1
1
0
0
1
0
2
1
1
0
0
2
1
1
0
0
2
0
0
2
1
2
1
0
0
1
1
0
0
1
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
2
0
1
2
0
0
0
1
2
0
2
2
2
0
0
0
1
0
0
0
2
2
0
0
0
0
2
1
0
0
1
2
0
2
0
0
2
0
0
0
0
2
2
0
2
0
0
2
1
0
3
0
2
2
0
0
0
0
0
1
0
0
1
0
0
0
3
1
0
0
0
2
2
1
2
0
0
0
2
2
2
1
0
1
0
0
1
0
2
0
1
0
0
1
0
0
0
2
1
2
2
2
0
3
0
1
1
0
0
0
0
2
0
0
0
0
0
0
1
0
2
2
2
0
0
0
0
2
2
0
2
0
0
0
0
0
0
2
1
2
0
3
0
2
2
2
0
0
1
2
1
0
0
2
0
1
2
0
0
1
2
0
0
2
0
1
2
2
1
0
2
2
0
0
0
0
0
2
2
2
0
0
0
1
2
2
0
0
0
0
0
1
0
1
0
2
0
2
0
1
0
0
0
0
0
0
0
0
2
0
1
1
0
1
2
0
0
0
0
0
0
0
1
1
1
0
0
0
1
2
0
0
0
1
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
2
1
2
1
1
0
0
0
1
2
0
0
0
2
0
2
2
0
0
0
1
1
0
0
3
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
1
1
0
1
2
2
0
1
0
0
1
1
0
2
2
0
0
0
1
1
0
1
1
0
0
0
2
0
0
0
2
0
3
4
1
0
0
0
1
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
2
1
0
0
1
0
4
0
2
0
0
1
1
0
1
1
1
2
0
0
0
1
0
1
0
1
1
3
0
0
0
0
2
0
1
0
2
2
1
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
2
0
2
0
0
1
0
0
0
2
1
0
0
0
1
2
0
2
2
0
0
0
0
0
0
2
0
1
1
1
0
0
0
0
0
2
0
0
2
0
1
0
0
0
1
2
2
1
0
1
1
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
2
1
0
3
2
2
0
0
2
2
0
2
3
1
0
0
0
1
1
0
0
2
2
2
1
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
1
0
1
0
1
0
2
0
1
0
2
0
0
1
0
1
1
0
0
0
2
2
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
1
0
0
0
2
0
3
1
1
0
0
0
2
0
1
2
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
2
4
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
1
0
2
2
2
0
1
2
1
2
1
0
0
0
2
1
2
1
0
1
2
3
2
0
1
1
0
0
0
1
0
0
2
2
1
0
2
2
1
0
0
0
0
0
0
1
0
0
0
2
2
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
2
2
1
2
1
2
2
1
1
0
1
0
0
0
0
0
1
2
0
1
0
0
2
0
1
2
0
1
0
2
0
1
0
0
0
0
2
1
0
0
0
2
0
0
1
1
1
0
1
1
0
0
2
1
1
0
0
1
1
0
1
2
2
0
1
0
2
0
0
0
0
0
0
1
1
0
2
0
1
2
1
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
1
1
1
0
2
0
0
2
0
0
1
0
1
1
2
1
0
0
0
2
0
1
2
0
2
1
0
0
0
1
2
2
2
0
1
0
0
2
1
0
1
0
0
0
2
0
2
2
3
1
0
2
1
1
1
1
0
2
0
0
2
0
0
0
0
1
2
3
0
0
0
0
2
1
1
0
2
0
0
0
1
1
2
5
1
1
0
0
0
1
0
2
2
1
0
2
2
0
2
0
0
2
0
0
1
2
1
1
0
0
2
2
1
0
0
1
2
0
0
0
1
0
1
0
0
0
0
0
0
1
0
2
0
2
0
1
2
0
1
0
1
0
1
2
1
0
0
4
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
1
1
2
0
0
0
0
0
0
2
0
0
1
0
0
0
2
1
0
0
0
1
0
0
1
0
0
1
0
0
2
2
0
0
0
1
1
3
0
0
0
2
0
0
0
1
0
0
0
2
0
2
1
0
1
0
2
0
0
2
0
1
1
0
0
0
0
0
1
0
0
1
2
0
0
2
0
0
2
0
1
1
3
0
2
1
3
0
2
1
2
1
0
1
0
1
1
2
1
1
0
0
1
0
1
0
2
0
2
2
0
0
1
0
0
1
1
0
0
1
2
2
0
1
2
2
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
2
1
2
0
0
0
2
1
0
1
2
1
0
0
1
0
2
0
0
0
0
0
1
0
0
2
0
1
2
0
3
0
2
1
0
1
0
0
0
0
1
2
2
1
2
0
0
0
1
0
0
0
2
0
0
0
2
1
0
1
2
0
0
1
2
0
1
1
0
0
0
2
0
0
1
0
0
2
1
0
1
0
0
2
2
0
2
0
0
2
2
0
0
0
0
0
0
0
1
0
1
0
2
0
1
0
2
2
0
2
0
2
0
0
0
0
0
2
1
3
2
2
0
1
3
0
2
0
1
2
1
1
2
0
0
1
1
2
1
1
1
0
1
0
0
2
0
1
0
0
0
0
0
0
1
2
2
0
2
0
0
1
0
0
0
0
1
1
0
0
1
0
1
0
1
0
2
0
0
0
1
2
3
0
1
2
1
0
2
0
0
0
2
0
0
0
0
0
2
3
0
0
0
0
2
0
2
0
1
0
0
2
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
1
0
1
1
0
2
1
0
0
2
0
1
2
0
1
0
1
2
1
0
2
0
1
0
1
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
2
0
1
0
0
1
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
1
1
0
0
1
0
0
0
0
0
2
0
1
2
0
0
0
0
1
1
1
0
1
1
2
1
0
0
0
0
2
0
1
0
0
0
1
1
0
0
0
1
2
0
0
2
3
1
0
0
0
1
2
0
0
0
0
2
0
1
2
0
0
2
0
1
0
1
2
0
2
1
0
1
1
1
2
3
1
2
0
0
1
0
0
1
2
0
2
0
5
0
0
1
0
0
1
0
0
0
2
0
2
2
2
0
2
1
0
2
0
0
0
0
2
0
1
0
1
1
1
2
1
1
0
0
0
1
1
3
0
1
1
0
2
0
4
1
2
1
2
2
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
2
1
3
0
0
2
1
2
0
0
1
0
2
0
0
0
2
0
2
0
0
1
1
0
0
0
1
1
0
0
0
2
0
2
0
2
0
2
0
0
1
0
0
2
2
2
0
0
1
0
1
2
1
1
0
1
1
3
0
0
1
1
2
0
0
0
0
1
0
1
1
0
1
0
0
0
0
2
1
0
0
1
1
0
2
0
0
2
1
2
1
0
1
1
0
1
2
0
0
1
0
1
0
0
2
1
2
1
2
1
1
1
0
2
1
0
2
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
2
2
0
0
1
0
0
5
0
0
3
0
0
0
0
2
0
2
2
0
1
0
0
0
2
1
1
0
0
2
0
0
2
2
0
1
0
0
2
0
1
2
2
0
2
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
2
1
0
1
0
0
0
2
2
0
0
0
0
0
0
0
2
0
2
3
0
0
0
2
0
3
1
0
0
2
0
1
2
0
2
0
0
2
0
0
1
1
0
0
2
0
2
0
1
2
0
2
0
0
4
0
3
0
0
1
0
1
0
2
0
2
2
0
0
0
0
0
0
1
1
0
1
0
0
2
0
0
0
0
2
2
3
0
0
0
1
1
1
0
0
0
1
2
0
0
0
0
0
1
0
1
2
1
0
1
1
0
0
1
1
0
2
0
2
0
0
0
1
0
2
0
0
2
1
0
1
0
1
0
1
0
0
1
0
1
1
0
2
0
0
0
0
2
0
1
0
0
2
2
0
1
1
0
2
0
2
1
1
2
0
0
1
1
0
1
0
0
0
2
0
0
0
0
1
0
2
3
0
1
0
0
0
1
0
0
0
2
0
1
0
0
0
2
2
0
0
0
1
0
1
1
2
2
0
1
2
0
0
2
0
2
0
1
2
0
0
0
1
1
0
1
0
0
2
0
0
0
4
0
0
1
1
1
2
1
0
0
0
1
0
0
0
0
0
0
2
0
0
3
2
0
0
0
0
1
1
0
1
1
0
1
2
1
1
0
0
2
1
0
0
0
2
0
1
1
0
0
0
0
0
2
2
2
0
0
3
0
0
0
0
0
2
2
2
2
0
0
0
0
1
2
1
1
0
0
0
0
0
0
1
2
1
0
1
1
0
1
2
1
2
1
0
0
1
0
0
1
1
2
0
0
2
5
0
0
0
0
2
0
0
0
0
2
1
2
0
1
0
2
0
0
0
2
1
1
1
0
2
0
0
0
0
2
0
0
0
1
0
0
2
1
0
1
2
0
1
1
2
0
0
0
2
0
2
0
0
0
0
0
1
2
1
1
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
2
2
0
0
0
1
0
2
1
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
1
0
0
1
0
2
1
0
0
1
2
0
0
2
1
0
2
2
1
0
0
0
1
0
0
0
0
1
1
1
0
2
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
2
2
0
0
0
1
2
0
2
1
1
2
0
1
1
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
1
0
0
1
2
0
3
2
0
0
0
0
1
1
2
1
0
2
2
1
2
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
1
0
1
0
1
0
1
0
0
0
0
0
2
0
2
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
2
0
2
2
2
2
0
0
0
0
3
0
2
0
2
1
0
0
2
0
2
2
1
0
1
0
2
1
0
2
0
0
0
0
2
1
0
1
2
1
0
0
0
0
0
0
1
2
2
0
0
1
1
6
0
1
0
0
0
0
0
1
0
2
1
0
2
0
0
1
3
2
3
0
0
0
1
2
1
1
1
2
0
0
0
0
0
0
1
0
0
2
1
0
1
0
0
0
2
0
0
1
0
2
0
1
0
0
0
1
0
2
0
0
0
1
0
0
5
0
2
1
0
1
3
0
0
1
0
0
0
2
0
0
3
0
0
0
2
0
0
2
1
0
0
0
2
2
2
1
2
0
0
2
1
0
0
2
1
0
0
0
0
1
2
0
2
0
0
0
1
0
0
2
1
2
0
0
1
0
0
2
0
1
1
0
0
2
0
0
0
0
2
0
0
0
1
0
0
1
2
1
1
1
0
0
1
2
0
0
0
2
3
2
1
0
1
0
0
0
3
1
0
1
1
0
0
2
1
0
1
0
1
0
1
0
2
0
1
1
1
0
1
0
0
0
0
0
0
2
1
0
0
1
1
0
1
1
0
0
0
0
1
0
3
0
2
0
0
0
0
0
0
0
3
1
0
0
0
2
1
0
2
1
0
0
1
0
0
1
0
0
2
0
0
0
0
1
0
1
2
0
1
1
0
0
2
0
2
0
0
2
2
0
1
0
1
0
1
1
0
2
0
1
2
0
2
0
0
0
2
0
0
1
1
1
0
1
0
0
0
2
2
1
0
0
3
3
0
0
2
2
0
1
1
2
0
1
0
1
0
2
1
0
0
0
0
1
0
2
0
0
0
1
0
1
1
0
0
1
0
0
2
1
1
0
2
0
0
0
0
2
2
0
0
0
0
0
2
4
2
0
1
1
1
1
1
2
0
1
0
1
2
0
0
1
0
1
1
0
0
1
2
1
0
0
0
2
1
0
0
0
2
0
2
0
2
0
2
0
0
2
0
0
0
0
2
2
2
0
0
0
0
1
1
0
0
1
0
0
1
2
1
0
2
2
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
2
1
1
2
0
1
0
1
0
0
1
0
0
0
1
0
2
0
1
0
0
0
2
0
0
2
0
2
1
1
0
0
0
1
0
0
0
2
1
0
0
0
2
0
2
1
1
0
0
0
1
1
0
0
0
1
0
2
0
0
0
1
0
0
0
0
1
0
0
2
1
2
0
1
0
0
1
2
0
0
0
0
0
0
1
0
0
0
2
1
0
0
1
1
2
2
0
0
0
0
0
2
0
0
3
0
1
0
1
0
0
2
2
2
0
0
0
2
2
2
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
1
1
0
0
3
0
0
0
1
0
0
1
1
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
1
2
1
0
1
0
0
3
0
0
0
0
2
1
0
2
2
0
0
0
1
0
0
0
1
1
0
0
1
0
2
0
0
0
2
0
2
0
1
2
1
0
2
2
0
2
1
4
0
0
1
0
1
2
0
0
0
1
0
0
1
2
0
2
1
2
0
0
0
1
2
0
0
0
1
0
1
0
2
1
1
1
2
2
1
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
2
1
0
0
0
1
2
2
0
0
2
0
1
0
0
0
0
2
1
2
0
1
0
0
2
2
2
1
0
2
0
0
0
0
0
1
0
0
0
0
0
7
0
0
0
0
1
1
0
0
1
0
0
1
1
0
2
0
2
0
0
0
1
1
1
1
0
1
0
1
2
0
0
0
1
0
2
2
3
0
1
0
0
1
0
0
0
1
1
2
0
0
1
3
0
0
3
2
0
0
0
1
0
1
0
0
2
2
2
0
2
1
2
0
0
1
0
0
1
1
1
0
0
1
1
1
2
0
0
2
0
2
0
0
0
0
1
0
1
0
1
1
1
0
0
1
0
0
0
0
2
2
0
1
0
0
0
2
2
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
1
0
0
0
1
4
2
0
2
0
0
1
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
2
0
1
1
1
0
0
1
0
2
1
2
2
2
1
0
1
0
0
0
0
1
0
0
1
0
0
2
0
0
1
0
2
2
0
1
2
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
2
2
1
2
0
1
0
0
0
0
0
2
2
0
0
1
2
2
1
0
0
0
2
2
1
0
1
0
1
1
3
0
0
2
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
1
0
2
1
0
0
0
0
1
1
0
0
0
0
2
2
1
0
0
1
1
0
2
2
1
1
0
0
2
0
0
0
1
0
0
1
3
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
2
1
1
0
0
1
1
0
0
0
2
0
0
0
0
1
1
1
2
0
1
0
1
1
0
0
2
0
0
0
0
3
0
0
2
2
1
0
2
1
2
0
0
1
1
2
2
1
2
1
1
1
0
0
0
1
1
1
2
1
0
2
1
0
0
0
1
0
0
0
2
0
2
1
2
0
1
0
0
0
0
0
2
2
0
2
2
0
1
0
2
1
0
1
0
0
1
0
0
4
0
6
1
2
0
2
1
1
1
1
0
0
1
0
2
2
2
0
0
2
0
2
0
1
0
1
2
0
0
1
1
0
0
0
0
0
1
2
0
0
1
0
0
0
0
1
0
2
2
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
2
2
1
1
2
0
2
0
0
0
2
2
1
1
0
0
0
0
0
1
1
1
0
0
0
0
0
2
1
2
2
2
1
0
2
2
0
1
2
0
0
0
0
1
0
0
2
0
0
0
1
2
2
0
1
0
2
0
0
0
1
0
1
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
3
0
7
0
0
1
0
0
0
0
0
0
0
2
1
0
2
1
0
0
2
0
0
2
0
0
1
1
0
0
2
0
0
0
0
2
2
0
1
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
3
0
2
0
1
0
2
0
0
2
2
0
0
1
0
2
2
0
0
2
0
2
0
0
0
0
1
1
2
0
1
0
2
0
1
0
1
0
0
0
1
2
3
1
2
1
2
1
2
1
1
0
0
1
0
1
0
1
2
0
1
1
2
0
3
0
0
1
0
0
2
0
0
1
0
0
2
0
3
0
1
0
2
0
1
2
0
0
0
0
0
0
0
1
0
2
0
2
0
1
4
1
0
1
4
1
0
0
0
0
2
2
0
1
2
0
0
0
0
1
1
0
0
0
2
1
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
2
1
0
0
2
1
0
1
2
1
1
1
0
0
0
1
1
0
2
0
1
0
1
0
0
1
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
4
0
2
1
1
0
1
1
2
2
0
0
0
0
2
1
0
0
1
0
0
0
0
1
1
0
1
1
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
6
0
0
1
0
0
0
0
0
0
1
3
1
0
2
0
0
0
0
0
0
0
0
0
1
2
2
0
2
1
2
2
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
1
1
2
0
2
0
0
0
1
2
0
0
1
2
1
0
0
0
1
0
0
0
0
1
1
0
1
2
1
0
1
0
0
1
3
0
0
0
1
0
0
0
1
1
0
0
0
1
0
2
0
0
1
0
0
0
0
2
2
2
1
1
1
1
0
0
0
0
0
1
0
2
0
1
0
1
0
0
0
0
0
0
2
1
2
1
2
0
0
0
1
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
4
2
1
0
2
1
0
2
2
0
0
2
0
1
0
3
2
0
0
0
2
2
2
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
1
0
0
0
1
1
0
0
0
0
0
0
2
0
0
1
0
0
2
1
3
1
0
1
3
1
0
2
0
0
0
0
0
1
0
0
0
2
0
1
3
0
1
1
0
1
1
1
0
0
1
1
0
0
0
1
0
2
1
0
2
0
0
1
0
1
0
0
2
2
0
0
0
0
0
2
0
1
2
2
1
0
0
0
1
0
1
0
2
2
2
0
2
2
2
0
0
1
2
1
0
1
0
0
0
0
0
0
1
2
0
2
0
0
1
0
0
0
0
0
2
1
2
1
0
0
2
2
0
0
2
1
1
0
1
1
1
0
1
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
2
0
4
1
0
0
2
2
2
2
0
1
0
0
0
0
1
0
1
2
1
2
0
1
0
0
0
0
0
1
3
1
0
5
1
0
1
0
0
0
0
1
0
0
1
3
2
0
2
1
0
1
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
1
2
0
1
2
1
2
0
2
2
1
1
1
2
1
0
2
3
0
0
0
2
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
1
0
2
2
0
0
2
0
0
0
0
1
1
1
1
1
1
0
0
0
0
0
1
2
0
0
1
0
1
0
0
3
2
1
2
0
2
1
0
0
1
1
1
2
0
0
0
0
0
0
0
0
2
1
0
1
2
1
2
0
0
0
1
0
2
2
0
1
0
0
0
0
0
1
0
2
0
1
2
1
0
1
0
0
0
0
1
0
0
1
1
0
2
0
0
0
2
1
0
1
2
0
2
0
0
0
0
1
1
2
0
0
1
4
0
2
0
1
0
2
0
0
2
0
1
0
1
0
0
3
0
2
0
0
2
1
1
1
0
1
1
0
1
2
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
2
2
2
0
2
2
2
1
1
1
0
1
1
0
0
2
0
0
0
0
1
0
0
0
1
1
1
0
0
1
0
2
0
1
2
0
0
1
0
2
1
2
1
0
0
0
0
0
0
0
1
0
0
1
0
2
0
2
2
1
0
0
1
0
0
0
1
2
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
3
0
2
0
0
1
3
0
0
2
1
0
2
1
0
1
2
0
0
2
0
2
0
2
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
9
1
0
2
0
1
0
0
0
0
1
0
2
0
0
0
0
0
1
0
1
0
1
1
0
2
0
1
1
1
0
0
2
3
1
0
2
0
1
0
0
1
2
1
0
0
0
0
0
0
1
0
2
0
1
0
0
0
2
0
0
2
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
1
0
1
0
1
0
0
0
0
2
2
2
0
1
0
0
0
0
0
0
1
2
1
2
0
0
2
0
2
0
1
1
0
3
0
1
1
0
1
0
0
0
2
2
0
1
0
0
0
0
0
2
1
2
2
1
0
1
1
0
0
0
1
0
0
1
0
0
0
1
1
0
0
2
0
1
2
0
1
2
2
0
0
2
1
2
0
2
0
0
1
0
3
1
1
2
2
2
0
1
2
1
1
0
0
0
2
0
0
0
1
1
2
0
0
0
0
0
2
0
2
2
2
0
1
0
0
0
0
1
2
1
0
2
0
0
0
0
0
1
0
3
1
1
0
0
2
1
2
0
1
0
0
0
1
2
1
0
0
1
2
0
2
1
2
2
1
0
0
1
0
0
2
0
0
0
0
1
2
0
2
0
1
1
1
0
0
1
2
2
3
2
1
0
1
0
2
0
0
2
0
1
1
0
2
1
0
2
2
2
2
1
1
0
0
1
1
7
0
0
0
0
0
2
0
2
0
0
0
0
1
1
0
0
0
1
0
2
0
1
0
0
0
0
0
2
0
1
1
0
0
0
2
0
0
0
1
2
2
0
0
0
9
1
0
0
2
1
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
1
1
0
2
2
0
0
0
0
0
1
0
0
0
1
1
2
0
1
1
0
0
3
0
2
1
1
1
0
2
1
1
0
2
0
2
1
0
0
2
0
0
1
1
1
2
1
2
0
0
1
0
0
0
0
1
0
0
5
0
0
1
0
1
1
0
1
0
0
2
0
1
0
0
1
1
1
2
0
0
0
0
1
0
0
1
1
1
1
1
2
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
2
1
0
1
1
0
0
2
0
0
2
0
2
0
0
0
2
0
1
2
1
2
2
2
0
2
1
0
0
1
5
1
0
2
2
0
0
2
2
0
0
0
1
0
1
0
0
0
0
0
0
1
2
1
0
0
1
0
2
2
2
0
1
1
1
2
0
0
2
0
2
3
0
0
0
0
0
2
0
0
0
2
0
1
0
0
1
1
0
0
1
0
2
0
2
0
1
2
1
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
2
2
0
0
2
2
0
0
2
0
2
0
1
2
0
0
0
2
0
2
0
1
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
3
0
1
1
1
0
0
2
3
1
1
1
0
0
0
0
0
1
2
1
0
2
1
1
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
1
1
0
2
0
0
1
0
1
2
1
0
2
0
2
3
2
0
1
1
1
2
2
0
0
2
0
0
0
0
0
1
0
0
1
2
1
0
0
0
1
0
3
0
1
0
0
1
1
2
0
2
0
2
3
2
2
0
0
0
1
1
2
0
0
2
1
1
0
2
0
2
1
2
0
1
1
0
2
0
0
2
2
0
0
1
1
0
2
1
0
0
2
1
2
0
1
0
0
0
0
0
1
0
0
2
1
0
0
0
2
1
0
0
0
0
0
1
2
0
1
2
1
0
0
0
1
0
1
0
0
0
1
0
0
0
2
2
0
0
2
0
0
1
0
2
0
0
1
0
1
1
0
0
1
0
0
0
2
0
0
0
1
1
2
0
1
0
0
0
1
0
2
0
1
0
0
2
2
0
0
0
2
0
0
2
0
1
1
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
1
0
1
0
0
0
2
0
1
2
2
0
0
3
0
0
0
1
2
1
0
0
2
0
0
1
2
2
0
0
0
2
1
0
3
2
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
2
0
0
3
1
0
1
1
1
1
0
6
1
1
2
2
0
2
1
0
0
1
2
1
0
0
0
1
0
3
0
2
0
2
0
0
2
1
0
0
0
0
1
1
2
1
0
0
0
0
2
0
1
1
0
2
1
0
0
0
5
1
0
1
0
0
0
2
0
2
3
1
1
0
0
0
0
2
2
2
0
2
0
2
2
0
1
2
1
2
2
0
3
1
0
2
0
0
2
0
0
0
1
0
1
0
0
0
1
2
0
0
1
0
0
0
1
1
2
0
0
0
1
2
1
3
0
1
1
0
1
1
1
0
1
0
0
0
0
0
2
1
2
2
0
2
0
2
1
0
0
0
0
2
1
2
1
0
1
0
2
2
1
1
1
2
0
2
0
1
1
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
2
0
1
0
2
0
0
2
2
0
1
1
1
0
0
0
0
0
2
2
0
0
1
0
2
2
1
0
0
0
0
0
1
1
0
0
1
0
4
0
0
0
0
0
0
0
1
0
2
5
0
0
1
0
0
2
0
0
1
0
1
0
0
2
1
1
0
2
0
1
0
1
0
0
0
0
0
0
2
1
1
6
1
2
2
0
0
1
0
1
0
0
1
0
0
0
1
0
1
0
0
2
2
0
0
2
2
2
2
2
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
2
2
0
1
0
2
0
0
0
2
2
2
0
1
1
1
2
0
0
2
0
4
0
0
1
0
2
1
2
1
0
0
0
0
0
0
1
0
2
0
2
1
0
0
1
1
2
1
1
1
2
0
0
2
2
1
0
0
0
0
0
2
0
1
0
1
0
2
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
1
2
2
1
0
1
1
0
0
0
0
2
1
0
0
2
1
0
0
1
0
0
1
0
1
2
1
2
1
2
2
0
0
1
0
0
2
0
0
1
1
0
0
2
0
0
0
0
0
0
6
2
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
1
1
2
1
0
0
1
0
1
0
1
0
1
3
2
1
2
0
0
0
2
0
0
1
2
0
0
2
1
0
0
0
0
1
0
2
2
1
0
1
0
4
0
2
1
0
0
2
0
0
0
0
0
2
0
0
1
1
0
1
0
4
1
1
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
4
1
0
0
2
2
1
1
2
2
1
2
0
1
1
0
0
1
1
1
0
0
0
0
1
1
0
0
1
0
0
0
0
2
2
1
1
1
0
0
0
0
1
1
2
0
2
0
0
1
0
0
1
0
0
0
0
2
1
0
2
0
0
2
2
0
1
0
0
0
0
1
0
1
2
2
1
1
0
1
0
0
1
1
2
0
1
2
0
1
1
1
0
2
0
1
0
0
3
2
1
1
0
0
1
0
2
0
1
0
1
0
2
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
1
1
1
1
0
2
0
2
1
2
0
0
1
2
0
2
2
1
0
2
1
0
1
1
0
0
0
2
0
1
1
0
2
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
2
1
2
0
0
0
0
0
0
1
1
0
0
1
0
0
1
1
1
0
2
0
0
6
0
0
2
0
2
1
1
0
0
1
2
0
0
0
1
1
0
2
1
3
2
0
1
2
0
1
0
0
2
0
1
0
0
0
2
0
1
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
1
2
0
0
0
1
0
1
0
0
3
0
2
2
0
0
0
0
1
0
0
2
0
2
2
0
0
2
2
0
0
2
0
0
0
0
1
0
0
2
0
0
1
2
2
0
0
1
1
2
0
0
2
0
0
0
0
2
2
2
1
0
0
3
0
2
0
1
0
0
0
0
2
0
0
1
2
0
0
0
1
1
1
0
0
0
1
0
0
1
2
0
1
0
0
0
1
0
2
2
0
1
2
2
0
1
1
0
1
0
0
1
1
0
0
0
1
0
0
2
1
0
0
1
0
2
0
0
0
0
2
1
1
1
0
0
0
0
1
0
1
2
1
0
1
0
2
0
1
0
1
1
2
2
1
0
2
0
0
1
0
1
1
0
1
0
2
0
0
0
1
1
1
0
2
0
0
0
0
1
0
0
1
0
2
5
3
0
0
1
2
0
0
0
2
3
1
3
1
0
2
1
2
0
2
1
0
3
2
1
2
0
0
0
0
0
0
0
1
1
1
0
0
1
2
0
1
0
0
0
1
0
0
1
2
0
2
0
0
0
2
2
0
1
2
0
0
1
2
0
0
0
0
0
2
1
0
0
1
0
2
2
2
0
0
1
0
0
1
0
0
0
0
1
1
2
2
1
0
2
0
1
1
1
2
0
1
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
2
0
1
0
0
2
0
1
2
1
0
0
0
0
2
1
0
2
0
0
0
0
0
0
2
0
1
1
2
2
0
1
0
0
1
2
0
4
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
2
1
1
0
0
0
0
0
2
0
1
0
0
0
0
1
0
1
1
2
0
0
1
0
0
0
2
1
0
1
1
0
0
0
1
0
2
1
1
0
0
3
2
0
2
0
2
0
0
2
0
1
0
1
0
0
1
1
1
2
3
2
0
2
0
0
1
0
0
1
0
0
2
1
0
1
2
0
0
2
0
1
1
0
0
0
2
1
1
2
1
0
1
0
0
0
1
0
0
0
1
1
0
2
2
0
2
0
0
0
2
2
2
0
0
0
0
2
2
2
0
0
2
2
0
1
0
0
0
0
4
0
1
2
1
2
2
0
0
1
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
1
0
2
1
1
0
2
1
1
0
0
2
1
0
0
2
0
0
0
1
0
2
0
0
1
0
0
0
0
1
2
0
1
0
1
1
5
2
2
0
0
0
2
0
1
0
1
1
0
1
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
2
0
1
0
2
2
0
1
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
1
2
0
0
0
0
0
1
0
2
0
2
1
0
0
0
0
0
0
0
2
1
0
0
0
1
0
3
0
0
2
0
1
1
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
1
2
0
0
0
1
0
1
2
0
0
1
1
1
2
0
0
4
0
0
0
1
2
2
1
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
1
3
0
0
1
0
0
0
0
1
0
0
0
1
2
0
0
2
0
1
2
0
0
2
0
1
0
2
2
2
0
0
1
2
0
0
1
2
2
0
0
1
0
1
1
1
1
2
1
0
2
0
0
2
0
0
0
0
0
2
0
1
0
2
2
0
0
0
0
0
0
0
0
1
1
0
2
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
1
0
1
0
0
0
2
1
0
0
0
0
2
1
2
1
2
0
2
0
2
3
2
0
1
0
0
2
1
2
0
2
3
0
0
0
0
1
2
1
0
2
1
2
2
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
2
1
0
0
0
0
2
0
0
2
1
2
0
1
1
1
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
2
2
3
0
0
1
0
0
0
0
0
1
0
2
3
1
2
2
0
0
0
1
0
0
0
1
0
3
0
0
0
2
0
1
1
0
2
0
0
1
0
0
0
0
2
1
0
2
0
0
0
0
0
1
1
0
1
0
2
0
0
0
0
1
0
0
2
0
1
0
1
0
2
0
0
0
0
2
2
3
0
0
0
0
1
0
2
0
0
1
0
0
2
1
4
2
1
2
0
1
1
0
0
2
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
2
0
0
2
2
0
0
1
0
0
0
1
0
1
1
0
0
0
2
1
2
1
2
0
1
0
1
1
0
0
0
0
0
0
1
1
2
2
2
2
0
0
0
0
1
0
2
0
0
1
2
0
0
2
2
2
1
1
0
3
0
0
0
1
1
1
1
0
0
2
1
0
0
0
1
2
1
0
0
0
2
1
1
0
1
2
1
0
2
0
0
1
1
0
1
2
2
0
0
0
1
2
3
0
0
0
0
0
1
0
0
0
1
0
1
1
2
0
1
0
1
0
0
0
0
0
0
0
2
2
3
0
1
2
2
3
3
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
2
0
0
2
0
2
0
0
1
0
2
0
0
1
0
0
2
1
0
0
0
0
1
0
0
2
0
0
0
1
0
1
1
2
2
1
2
2
0
1
1
0
0
0
0
0
2
0
2
0
0
1
2
2
2
2
0
0
2
1
2
0
0
0
0
0
0
0
0
1
0
0
1
1
2
1
2
0
2
0
4
0
0
0
0
2
0
0
0
0
0
1
2
0
1
1
1
1
4
1
2
0
2
0
2
0
3
0
0
0
0
1
1
1
0
2
0
0
0
0
2
0
2
0
0
2
0
0
1
0
2
0
0
0
0
1
2
2
0
0
2
1
0
0
2
1
0
2
0
0
2
2
2
0
0
0
0
2
0
1
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
1
2
0
1
1
2
1
0
0
1
1
0
1
2
0
0
0
0
2
1
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
1
2
2
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
2
1
0
1
0
0
0
2
1
0
0
0
0
2
0
4
0
0
2
0
0
1
1
1
2
2
0
0
0
0
1
2
0
1
0
0
0
0
0
2
0
1
1
2
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
2
0
2
0
1
0
2
2
2
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
1
0
1
0
2
0
1
2
0
1
0
0
1
0
0
0
2
2
1
0
0
0
0
0
3
0
0
2
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
1
0
1
1
0
2
1
3
0
1
0
1
0
1
0
2
0
0
0
1
2
2
1
0
0
2
1
2
4
0
1
0
1
1
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
2
0
0
0
2
0
1
1
0
0
1
0
2
0
0
0
2
0
1
0
0
0
1
0
2
1
0
0
1
1
0
0
2
1
0
0
2
2
0
1
2
1
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
1
1
0
0
0
1
0
2
0
1
4
1
0
0
1
2
1
1
2
1
2
1
0
0
0
0
1
1
0
1
1
1
0
1
0
0
0
0
2
1
0
4
1
0
1
2
0
1
2
1
0
2
0
1
2
0
0
0
0
2
2
1
0
1
1
1
0
0
0
0
1
1
0
1
0
1
0
0
0
1
0
0
1
0
0
0
2
0
1
2
1
1
0
2
0
0
1
0
1
0
2
0
0
0
0
2
1
2
2
0
2
0
2
2
0
0
0
2
0
1
3
2
0
1
0
0
1
3
0
1
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
2
1
0
2
0
0
0
1
0
0
2
2
1
1
1
0
2
0
0
0
4
2
2
0
0
0
2
2
1
2
1
0
0
2
0
0
0
2
0
0
2
0
2
1
0
0
0
0
2
0
0
0
1
1
0
0
0
1
0
0
0
0
1
1
2
2
2
0
0
1
1
0
0
0
0
1
2
0
0
0
0
0
2
1
1
1
0
1
0
3
2
0
0
0
1
1
2
2
0
0
0
1
0
2
0
0
1
0
0
0
1
1
0
1
0
0
0
1
0
2
3
1
2
0
0
0
1
0
0
1
1
0
0
1
0
1
1
1
1
0
0
0
0
2
0
0
0
5
1
0
2
3
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
2
0
0
1
0
0
2
2
2
2
1
0
1
2
2
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
5
0
0
2
0
0
1
1
0
1
1
2
0
0
1
0
0
2
0
0
1
1
1
2
1
5
0
2
0
0
1
0
0
0
1
1
1
2
0
1
1
1
1
0
1
1
0
2
0
1
0
2
1
0
0
0
0
2
0
0
0
1
0
0
1
3
1
3
0
1
12
0
1
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
1
1
1
0
0
0
0
0
0
1
2
0
1
0
0
1
2
0
0
0
0
1
1
1
0
1
0
0
2
0
0
0
2
0
2
1
0
0
0
0
2
0
0
0
0
0
2
1
1
0
1
1
0
0
0
0
0
0
1
0
1
1
0
0
2
0
0
1
0
2
0
1
0
1
2
2
0
0
0
0
1
2
2
0
0
1
0
4
0
2
0
2
0
1
1
1
0
0
1
2
1
0
0
0
0
0
3
1
0
0
0
0
1
0
0
0
0
0
0
1
2
2
1
4
2
0
0
2
0
1
1
2
1
0
0
1
0
0
2
2
0
0
0
0
0
0
2
2
1
0
0
0
0
1
0
0
3
1
0
0
0
0
0
2
2
1
0
0
2
0
0
0
0
0
0
0
3
1
2
1
0
0
0
3
0
0
1
0
1
1
0
2
0
0
0
0
0
0
0
1
1
0
2
0
2
1
0
4
1
0
0
2
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
1
1
2
1
0
0
0
0
1
0
0
0
0
0
4
1
0
1
2
2
0
1
0
2
0
0
2
1
0
0
0
0
1
1
0
0
0
0
1
0
0
2
0
1
0
1
2
0
1
1
0
2
0
0
0
1
0
0
1
0
0
0
0
1
3
0
2
0
3
2
2
0
0
0
2
1
2
0
2
0
0
0
0
3
0
2
0
0
3
0
0
1
1
1
2
1
2
2
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
1
2
0
2
1
1
1
0
1
1
0
0
3
0
2
1
0
0
1
1
0
0
1
1
1
0
0
1
0
2
1
1
0
2
1
0
0
0
1
0
0
0
0
0
1
1
1
2
0
2
0
2
1
0
1
2
0
0
0
0
1
1
1
0
0
1
0
0
2
1
1
0
0
2
0
0
2
0
1
0
1
2
2
0
1
0
2
1
0
0
1
1
1
0
0
2
0
1
1
0
1
0
0
1
0
1
0
1
1
0
2
1
1
1
3
1
1
1
0
1
0
1
2
0
0
0
1
0
0
1
1
0
0
0
0
1
2
1
0
2
0
1
0
1
0
0
0
1
1
2
0
0
0
2
1
0
0
1
0
1
2
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
2
0
1
0
0
0
2
0
0
2
0
1
0
2
0
0
0
0
2
1
2
0
0
1
0
1
0
2
0
0
1
2
2
0
0
0
0
2
0
0
1
2
3
0
2
2
1
2
0
0
0
2
0
0
1
1
0
2
0
1
2
0
0
0
0
0
0
0
1
2
2
1
0
1
0
0
2
0
1
0
1
0
1
0
1
1
1
0
0
0
1
1
1
0
2
0
1
0
3
0
0
2
1
0
1
0
0
1
1
2
0
0
0
2
2
0
0
0
0
1
0
0
0
2
2
0
2
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
1
0
0
0
0
1
0
0
0
2
2
0
0
0
2
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
1
0
0
4
0
0
0
1
0
0
0
0
0
1
3
0
0
0
1
0
1
1
2
1
2
1
0
0
0
2
0
2
3
0
0
0
1
0
0
1
2
0
0
0
0
0
2
4
1
1
0
1
0
0
0
1
0
1
2
2
0
0
2
0
2
0
1
0
0
1
2
2
0
6
1
0
1
0
2
1
1
1
0
0
2
1
1
0
1
1
0
0
0
2
2
0
2
2
1
0
2
2
0
0
0
0
2
0
0
0
0
0
1
1
0
2
2
0
2
1
1
1
0
0
0
1
1
0
1
0
0
1
1
1
0
1
0
1
0
0
0
1
2
2
0
0
1
2
2
0
1
2
0
2
1
1
1
1
1
0
2
1
0
0
0
0
2
0
1
0
2
0
1
0
0
1
0
1
1
1
1
0
1
2
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
3
1
0
0
1
2
0
2
0
1
1
1
1
0
0
0
2
0
0
2
2
0
1
1
0
1
0
0
1
1
0
2
0
0
1
0
0
1
2
0
0
0
1
1
0
0
0
1
1
0
0
0
2
1
0
0
2
2
0
2
0
1
2
1
2
1
1
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
4
2
0
1
0
1
0
2
1
1
0
2
0
0
2
0
1
2
0
0
0
0
0
0
2
1
0
1
0
1
0
0
0
0
1
2
0
1
2
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
2
2
0
0
0
1
2
0
0
0
2
1
2
1
1
0
0
0
0
1
2
0
0
2
0
0
1
1
0
2
0
1
0
3
0
1
0
1
1
1
2
0
2
0
0
2
0
0
1
0
2
2
0
0
2
0
0
1
0
1
1
0
0
0
2
0
1
0
2
2
0
1
0
0
0
0
0
1
1
1
0
2
2
2
0
1
1
1
0
1
2
0
1
1
0
0
0
0
0
2
2
1
0
1
0
1
0
2
0
2
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
1
2
1
0
2
0
0
1
1
0
0
1
1
1
1
0
0
8
0
2
0
1
0
2
1
1
0
1
0
1
1
0
1
1
0
0
2
2
2
0
0
0
0
0
0
1
2
3
1
0
0
0
0
0
2
0
1
0
0
0
0
0
8
0
1
2
1
1
1
0
0
2
1
0
0
1
2
1
1
1
3
0
0
0
1
2
0
0
1
0
2
2
0
0
2
1
0
0
0
3
3
2
0
0
0
1
0
2
2
0
1
1
0
2
1
0
1
1
1
0
0
1
2
0
0
0
1
0
2
0
0
0
1
0
1
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
4
0
1
2
0
1
0
1
0
2
0
2
3
1
1
2
0
1
2
1
1
2
1
2
0
1
1
1
2
0
0
0
1
0
0
1
1
0
0
1
2
0
2
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
2
1
0
1
1
1
1
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
1
0
1
2
1
0
0
0
0
1
1
0
0
2
0
0
1
0
0
0
1
2
0
1
0
0
2
1
0
0
1
0
0
2
0
1
0
2
2
2
1
1
1
0
2
0
0
3
1
0
0
0
1
0
1
0
0
2
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
4
0
0
2
0
0
0
1
1
0
0
0
2
0
1
0
0
0
0
1
0
2
1
0
0
0
0
1
0
0
0
1
0
0
2
2
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
2
0
2
1
2
1
1
1
1
0
1
2
0
0
0
0
2
2
0
0
1
1
2
0
2
0
2
0
0
1
0
1
1
2
2
0
0
0
0
0
1
0
0
2
1
0
1
3
0
0
0
2
2
2
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
3
0
0
3
0
0
2
0
0
1
1
1
2
1
1
2
1
0
2
2
0
0
0
2
1
0
0
0
0
2
3
1
0
2
1
1
1
0
0
0
0
0
0
0
1
0
2
2
2
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
1
1
0
0
1
0
1
0
2
0
0
0
0
0
0
1
2
0
0
0
1
2
0
1
0
0
2
0
0
0
0
3
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
1
1
0
0
2
2
1
1
0
0
0
1
1
0
2
1
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
2
0
0
0
0
0
1
1
0
2
2
1
0
0
1
0
2
0
2
1
1
2
2
0
1
2
1
2
0
0
3
2
0
1
0
0
4
0
0
3
1
1
1
0
0
2
1
0
0
2
2
0
0
2
1
0
1
0
0
0
0
0
0
1
0
0
2
0
2
1
1
0
0
2
1
1
2
2
0
0
1
0
0
0
2
0
2
2
0
4
0
0
0
2
0
2
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
1
1
2
2
0
1
1
0
1
2
0
1
2
2
0
0
0
1
2
1
2
0
0
1
0
2
1
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
1
0
1
0
0
1
0
0
0
1
2
9
1
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
3
0
0
0
2
1
7
2
1
0
2
0
0
0
2
0
2
0
0
2
0
1
1
0
0
0
1
2
1
1
2
0
1
1
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
2
1
0
0
0
1
1
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
2
2
1
2
0
2
0
1
0
1
0
0
0
1
1
0
0
0
2
0
1
0
0
0
1
1
0
0
0
1
0
2
0
0
0
0
2
0
1
0
1
1
0
2
2
0
2
0
1
0
0
0
0
0
1
0
2
0
1
2
0
0
0
0
0
0
1
1
1
1
0
1
1
0
2
0
0
0
0
2
0
0
0
0
0
0
1
1
0
1
0
1
1
2
0
0
0
1
0
0
1
0
0
0
0
0
2
2
0
0
0
1
0
0
0
1
1
0
1
2
2
1
2
2
1
0
0
1
1
2
2
1
0
2
0
0
1
2
0
0
1
1
2
0
0
0
0
0
0
1
1
0
1
1
2
2
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
1
1
0
1
1
0
0
0
0
1
1
0
2
0
1
1
1
2
0
0
0
0
1
2
2
0
0
1
0
1
2
0
0
0
0
0
0
1
0
0
0
1
0
1
2
0
2
1
0
1
1
0
0
1
0
2
2
0
0
0
1
2
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
1
0
1
0
0
1
0
0
2
0
1
1
1
0
0
1
1
1
0
0
2
1
0
2
0
1
0
1
0
2
0
0
5
0
0
1
0
0
0
1
0
1
0
2
2
2
0
0
0
2
0
0
1
0
0
0
2
0
0
0
2
0
2
2
0
0
0
0
0
1
0
2
0
0
1
1
0
0
0
2
1
0
1
2
0
1
0
0
0
0
1
2
1
0
0
1
1
0
1
0
1
0
1
2
0
0
0
0
3
1
0
2
1
2
2
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
2
1
1
0
0
2
0
0
0
0
1
1
0
1
0
0
0
0
2
0
0
0
0
2
0
2
0
2
0
1
2
0
0
1
0
1
1
0
0
2
0
0
2
3
1
0
0
1
1
0
2
1
1
0
1
1
1
0
2
1
0
1
0
1
0
1
0
1
1
0
0
2
3
0
2
0
0
2
0
1
0
0
0
1
2
0
0
0
0
2
0
0
0
0
1
2
1
0
0
2
0
0
0
0
0
0
0
1
2
2
2
0
0
1
0
1
0
0
0
0
2
0
0
0
1
2
1
2
2
0
1
2
2
0
2
0
0
0
0
2
0
0
0
0
0
2
1
0
0
2
0
0
0
2
0
0
0
2
0
0
0
2
0
2
0
2
0
1
1
0
1
0
3
1
1
0
0
0
2
2
0
2
1
1
1
2
0
0
0
1
1
0
0
0
0
0
2
0
0
0
3
0
1
1
2
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
1
0
0
0
2
0
1
3
0
1
0
0
0
1
0
0
2
0
0
0
1
0
0
1
2
0
2
0
1
2
0
2
0
0
0
0
0
1
0
1
1
1
0
2
0
1
1
1
0
2
1
2
0
0
0
0
0
0
1
0
0
1
2
0
2
0
0
1
1
0
1
0
1
1
0
2
1
0
2
1
0
2
0
0
0
0
3
2
0
1
0
0
0
2
2
0
0
2
2
0
2
0
2
1
0
0
2
1
0
2
2
1
2
0
2
0
2
0
0
1
0
2
1
2
2
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
1
0
0
0
0
2
0
1
0
1
0
0
2
0
2
1
3
0
1
1
0
1
2
0
0
0
0
1
0
4
0
0
1
1
0
0
0
0
0
0
0
1
0
2
0
0
0
1
1
0
0
2
2
0
0
0
0
0
0
0
2
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
2
2
0
0
1
1
2
0
0
1
0
0
0
0
2
0
0
0
0
1
0
2
0
2
0
0
0
1
0
1
0
2
0
1
0
0
0
0
1
2
0
0
0
1
2
1
2
0
0
0
0
1
0
0
2
0
2
1
0
0
0
0
2
1
1
0
0
0
2
0
1
2
0
2
0
0
0
0
0
1
0
2
3
0
1
0
1
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
1
2
1
0
0
0
4
0
1
0
0
0
0
0
0
1
0
0
1
0
1
2
1
0
1
0
0
0
2
0
1
3
1
0
1
0
1
0
0
0
0
1
1
4
0
2
0
0
0
0
1
0
0
0
0
0
2
0
2
1
0
0
0
2
0
0
0
1
2
1
0
0
1
0
0
0
0
1
0
2
0
2
2
3
0
0
2
0
0
0
1
1
2
0
2
1
2
0
0
2
1
1
0
0
0
0
2
0
2
1
0
1
0
3
0
1
0
0
0
1
2
0
2
0
1
1
0
0
1
0
1
2
0
0
0
0
0
0
1
0
2
0
1
0
0
1
1
1
2
1
2
0
0
0
1
2
3
0
2
2
1
1
0
0
0
0
2
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
2
1
2
2
0
0
0
0
0
0
2
0
2
0
1
2
2
0
0
0
1
1
1
0
0
1
0
1
0
0
0
0
2
1
0
1
2
0
0
1
2
2
0
0
1
2
2
1
0
0
1
1
1
1
1
0
0
0
1
0
2
1
0
0
0
0
0
0
1
0
2
0
0
1
1
1
0
0
2
2
0
0
1
0
2
0
1
1
2
1
0
0
0
2
2
1
0
1
0
0
1
0
0
2
0
0
0
0
0
1
1
0
2
0
0
0
0
0
2
0
1
0
0
1
1
1
1
0
0
2
0
2
2
2
0
2
0
2
2
0
0
2
0
0
2
2
3
0
0
0
1
0
2
0
1
2
0
1
1
1
1
0
0
1
2
1
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
1
0
2
1
1
0
0
0
0
2
1
0
0
0
1
0
0
1
0
0
3
0
1
0
0
2
1
0
0
2
0
1
0
0
0
0
1
2
0
1
0
1
1
0
0
2
1
0
0
0
2
2
1
0
1
2
0
0
2
2
1
1
1
2
1
1
2
2
2
0
1
1
0
2
1
1
2
2
2
0
1
0
0
0
1
1
0
1
0
1
0
0
0
1
0
1
0
0
1
2
0
0
0
1
0
3
1
2
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
3
1
2
0
0
0
0
1
1
1
0
0
1
2
0
0
1
1
0
0
1
2
0
0
0
0
0
2
0
2
0
1
0
0
0
1
0
1
2
2
1
0
2
0
2
0
1
2
0
1
2
0
0
0
2
2
0
1
0
0
0
0
1
2
0
1
2
0
0
0
0
1
0
0
0
1
0
2
2
1
1
2
2
0
2
1
1
0
0
0
2
1
1
1
0
0
2
0
0
5
2
1
1
0
0
0
1
2
0
0
2
2
1
0
0
2
0
1
0
0
1
0
2
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
1
1
0
0
1
0
0
0
0
2
0
2
1
1
2
0
0
0
2
1
1
0
0
0
2
2
0
1
0
0
2
2
2
1
0
0
2
0
1
2
2
2
0
2
2
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
1
2
1
0
0
0
0
1
1
0
2
1
1
1
2
0
0
0
0
0
1
1
0
1
2
0
0
0
0
0
1
0
0
0
0
0
2
2
2
2
0
1
0
3
1
0
0
1
0
0
1
2
1
2
0
0
1
0
1
2
0
0
0
0
1
2
1
0
0
0
2
0
2
2
0
0
0
1
0
0
0
2
0
2
1
1
0
0
0
0
1
1
0
2
0
1
1
0
2
1
1
0
0
2
2
2
2
0
0
0
0
2
0
0
1
2
0
0
0
2
1
0
0
2
0
1
1
1
0
1
0
0
0
2
0
2
1
1
1
0
1
0
1
2
1
2
1
0
0
2
1
3
1
1
0
0
1
1
0
2
2
0
1
2
1
0
0
2
0
1
2
1
0
2
0
2
0
0
0
2
1
1
0
0
0
2
2
0
0
2
1
0
0
1
0
0
0
0
1
0
7
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
2
0
0
5
0
1
2
2
1
0
0
1
0
1
2
1
1
0
2
0
0
0
1
0
1
1
1
0
0
2
0
0
0
0
0
1
1
1
1
0
2
0
0
1
2
0
1
0
0
2
0
2
0
2
0
0
0
1
0
0
1
2
1
0
2
1
0
0
0
2
1
0
0
1
6
0
2
1
3
1
0
0
0
1
2
2
0
1
0
0
0
0
0
2
1
1
1
2
0
1
2
1
2
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
2
1
1
0
0
1
0
2
0
2
0
0
2
0
1
0
1
2
0
0
0
2
1
0
0
2
0
0
0
2
2
0
1
0
0
0
1
0
0
2
1
0
0
1
0
1
3
0
0
0
0
0
1
0
0
1
0
2
1
1
1
0
4
0
2
2
2
1
2
0
1
1
2
2
1
0
2
0
0
2
0
0
1
0
0
1
0
2
0
0
2
1
1
0
0
0
0
0
1
0
0
0
0
1
2
2
0
1
1
0
2
2
1
0
0
1
0
0
1
0
0
0
1
1
0
1
0
2
0
2
2
2
0
1
2
1
0
0
2
1
0
2
2
0
2
2
0
1
0
1
0
1
0
0
0
0
0
1
1
0
2
0
0
0
2
0
0
0
0
2
0
1
2
3
2
2
0
0
0
1
0
1
0
0
1
2
0
1
2
0
0
1
0
0
0
0
0
0
2
3
0
0
1
0
2
0
1
0
0
0
2
1
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
2
2
0
2
0
0
0
5
0
2
0
1
0
1
0
0
0
0
0
0
2
2
2
0
0
0
0
2
2
0
0
0
1
0
2
2
2
1
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
3
1
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
2
0
1
0
1
1
1
0
0
2
0
0
2
1
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
2
0
0
2
2
0
0
0
0
0
1
2
2
1
2
3
0
1
2
2
2
1
1
1
0
2
0
0
0
0
1
0
0
0
2
2
0
0
0
0
1
1
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
2
1
0
0
0
0
2
1
1
0
1
0
2
0
0
2
0
0
1
0
0
1
0
1
0
1
1
1
1
2
2
0
0
1
1
0
0
0
1
0
0
0
0
0
2
2
2
0
2
0
0
1
0
0
0
1
0
1
1
0
1
2
0
3
0
2
0
2
2
0
1
1
0
2
0
2
0
0
0
0
1
2
1
2
0
0
2
1
0
0
2
0
1
0
0
1
0
0
0
2
0
1
1
1
0
2
2
3
2
0
1
0
2
2
0
1
1
0
0
0
3
1
1
0
0
0
0
1
2
1
0
1
1
1
2
2
0
1
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
2
0
1
0
2
0
0
2
0
2
0
0
0
0
0
2
0
0
0
2
0
1
2
0
0
0
1
1
0
0
2
0
0
1
1
0
2
0
2
1
1
2
2
0
3
0
1
0
0
3
2
2
1
1
1
0
0
0
0
1
2
0
0
1
0
0
1
0
1
2
0
0
0
1
2
0
1
2
0
0
3
2
1
2
2
0
1
0
0
0
0
0
2
1
0
0
1
0
4
1
2
2
1
0
1
3
0
0
1
0
2
0
0
2
0
1
1
1
0
0
5
0
2
1
1
0
0
2
1
0
1
2
0
0
0
0
0
0
0
1
2
1
0
2
1
0
0
0
5
2
1
2
0
0
2
1
1
0
1
1
2
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
2
1
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
2
0
1
0
0
2
2
0
0
0
2
2
0
1
2
0
2
1
0
1
0
2
2
2
0
0
0
0
0
2
0
0
0
2
0
0
0
4
2
1
2
1
2
1
0
1
1
2
1
1
0
0
0
0
2
0
0
0
0
1
0
0
1
1
2
1
0
1
1
1
0
1
1
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
1
2
0
0
1
3
0
0
0
1
0
2
1
2
0
2
2
0
1
2
0
2
0
0
0
2
0
0
0
1
0
0
1
1
0
0
0
1
2
0
0
0
1
1
0
0
0
2
0
2
0
0
1
0
2
0
0
1
0
1
2
0
1
1
0
0
1
1
0
0
0
1
3
1
2
0
0
0
2
1
0
1
0
0
3
0
0
0
0
1
0
1
0
0
2
0
0
0
2
1
0
2
0
1
0
0
0
0
0
0
1
1
1
0
2
2
2
1
1
2
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
2
0
0
2
2
1
0
2
0
0
0
2
0
2
2
1
0
0
2
2
2
0
0
1
2
1
1
1
2
2
1
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
1
2
0
0
0
1
0
0
0
0
2
2
0
0
0
2
2
0
4
0
0
0
0
1
0
0
2
2
1
0
2
1
0
0
0
0
0
0
1
2
0
0
0
1
0
3
0
1
0
0
0
0
2
0
0
0
1
0
0
1
0
0
2
0
1
2
0
0
0
0
0
0
1
0
0
0
1
2
1
1
0
3
1
0
2
2
1
0
2
0
0
2
0
0
1
1
1
1
0
0
0
0
1
2
1
0
2
0
1
0
0
0
0
0
0
2
2
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
2
0
1
1
0
0
2
0
1
0
0
0
0
1
1
0
1
0
2
0
0
1
0
1
1
0
0
1
0
1
0
0
0
2
0
1
0
1
1
2
0
0
0
0
1
1
0
0
0
1
1
2
1
0
1
1
0
0
0
2
2
3
2
2
1
2
0
0
0
2
0
0
0
0
0
1
2
0
0
2
0
0
0
1
0
0
1
0
0
0
1
1
2
0
1
1
0
2
0
1
1
0
0
0
1
0
1
0
1
1
0
1
0
0
0
1
0
2
0
0
0
0
1
0
1
0
1
2
1
0
1
3
1
0
0
0
2
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
2
2
1
0
1
0
1
0
1
0
2
1
0
1
2
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
1
0
1
1
0
0
1
1
0
0
0
0
1
0
1
0
0
1
0
0
0
3
2
0
0
0
1
0
0
1
2
0
0
2
1
0
0
1
1
1
0
2
0
0
0
0
0
1
2
1
1
2
0
0
0
1
0
2
1
2
0
2
1
2
0
2
2
2
0
0
0
1
0
1
0
0
1
2
2
0
1
1
0
1
0
0
1
0
2
0
0
2
1
1
2
0
0
0
0
0
1
2
1
1
2
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
1
2
0
2
1
1
1
0
0
1
1
1
1
1
0
0
0
2
1
2
0
0
0
0
0
2
0
3
0
0
0
1
0
0
0
2
0
1
0
1
2
2
2
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
1
2
0
0
1
0
0
2
0
2
0
2
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
2
0
0
1
1
2
1
2
0
2
1
3
0
2
0
0
2
0
2
2
2
0
2
0
2
3
0
1
1
1
0
0
1
1
0
0
0
0
1
2
0
0
1
1
1
2
0
1
0
0
1
0
0
2
2
1
0
0
0
0
1
1
1
0
0
1
0
0
0
1
0
0
0
2
1
1
0
0
0
0
1
2
2
0
1
2
0
0
1
0
1
1
0
2
1
3
2
0
0
1
1
2
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
1
1
1
2
2
0
8
0
0
2
2
2
1
0
1
0
1
2
0
2
1
1
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
2
1
1
0
0
1
2
0
2
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
2
0
1
0
2
0
2
0
0
4
0
0
1
1
1
1
1
0
0
2
0
0
1
0
0
0
1
1
2
1
2
0
1
1
0
2
1
1
1
0
0
0
0
0
0
0
0
0
2
1
1
1
0
1
1
6
1
2
0
1
0
1
0
1
1
1
0
0
0
0
1
2
0
1
1
2
0
0
0
2
1
0
1
0
2
0
1
0
0
0
0
1
1
0
2
0
2
1
0
2
1
0
0
2
2
0
0
0
0
0
2
1
0
7
0
2
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
2
2
1
1
2
1
0
1
0
1
0
1
2
1
1
1
1
2
0
2
0
0
2
0
0
1
1
0
2
2
1
1
1
0
0
1
0
1
0
1
2
0
1
2
1
0
0
1
0
0
2
0
0
1
0
0
0
1
0
1
0
1
1
0
0
0
1
0
2
2
0
1
1
3
0
0
0
1
0
0
0
1
0
1
0
2
1
2
0
0
0
0
2
0
0
0
1
1
0
2
0
1
0
1
0
0
2
0
0
0
1
0
0
1
1
0
1
2
0
0
0
1
0
0
1
1
1
1
2
1
0
2
1
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
2
0
0
1
1
0
0
0
0
2
0
1
1
0
0
0
0
0
2
0
0
0
0
2
2
0
1
0
1
0
0
0
0
0
0
0
2
1
1
1
1
0
0
0
0
1
1
1
2
2
0
0
0
1
0
0
0
0
2
0
1
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
3
0
2
0
0
1
2
0
0
1
1
0
1
0
2
0
0
0
2
3
2
1
0
0
2
0
2
0
0
2
2
0
1
2
0
0
1
0
0
0
0
0
0
2
0
0
2
1
0
1
0
0
2
1
1
3
1
0
0
1
1
0
0
1
0
0
2
1
0
1
0
0
0
1
1
0
0
0
0
0
2
1
2
0
3
1
2
2
1
0
0
0
2
0
0
2
0
2
2
1
0
1
0
2
2
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
1
2
1
1
0
1
2
1
0
0
0
0
2
0
0
1
0
0
1
1
0
1
1
0
1
1
0
0
2
0
0
1
1
0
0
2
0
0
0
2
1
0
4
2
3
0
2
0
0
0
0
1
0
0
1
0
2
2
0
0
2
0
0
0
1
0
2
0
1
1
1
1
3
0
1
0
1
1
2
0
2
0
0
0
0
1
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
1
0
0
1
1
1
2
1
2
1
1
0
1
1
1
0
2
2
1
2
0
1
0
0
0
1
0
2
2
0
0
0
2
0
0
0
2
0
0
0
2
0
2
1
2
0
0
1
0
1
2
3
0
0
1
0
2
0
1
0
0
2
1
2
0
2
2
2
0
0
0
1
0
1
1
0
2
0
0
0
1
0
1
0
0
0
0
0
0
1
2
1
1
0
1
0
0
0
1
1
0
1
0
1
0
1
1
1
0
2
0
0
2
0
0
0
0
2
2
0
1
0
0
0
1
0
0
1
0
1
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
1
0
1
0
2
1
0
0
2
1
0
2
0
2
2
1
0
0
0
2
0
0
1
1
1
0
0
0
0
0
1
1
2
2
2
0
1
2
0
0
0
0
2
0
0
1
1
1
0
0
2
0
0
0
2
0
0
0
1
0
2
0
2
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
2
0
2
1
0
0
0
2
3
1
0
2
0
0
0
0
0
1
2
3
0
2
0
2
1
2
0
2
1
0
0
1
1
1
1
0
2
0
0
3
0
2
0
2
0
2
0
1
0
2
1
0
0
0
4
0
0
0
0
0
2
0
0
0
1
0
0
0
2
2
0
0
0
0
0
1
0
0
1
1
0
1
0
0
1
0
2
1
1
0
0
0
1
5
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
1
2
0
0
1
0
2
2
1
0
1
0
0
0
0
2
1
2
0
1
0
0
1
0
3
0
0
0
0
0
0
0
0
1
2
1
1
0
0
0
0
1
0
2
0
0
0
2
1
1
0
2
2
2
1
0
0
2
2
0
0
1
0
0
0
0
0
0
2
2
0
1
0
2
0
0
2
0
1
2
2
0
0
1
1
0
1
1
0
0
2
0
0
1
0
0
2
0
1
1
0
0
1
0
1
1
1
1
0
0
0
0
0
2
0
1
0
0
1
0
1
0
1
0
1
0
1
2
0
1
0
0
0
1
0
2
0
0
0
0
1
0
1
1
0
2
0
2
1
0
0
2
2
2
2
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
1
0
1
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
2
2
0
0
0
0
2
1
1
1
0
0
1
1
1
1
1
0
0
0
0
2
1
1
2
0
2
1
1
0
0
2
1
1
2
1
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
2
2
0
0
2
0
0
1
0
2
0
1
0
1
1
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
1
2
1
4
0
0
2
0
1
0
0
1
0
1
1
2
0
1
0
0
1
0
1
0
0
0
2
2
2
0
0
0
0
0
0
0
0
1
0
2
2
0
1
1
0
0
0
0
0
1
1
0
1
0
0
0
1
0
2
2
0
1
0
2
1
3
2
0
1
3
0
1
2
1
2
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
2
0
0
0
1
1
2
0
0
1
1
0
0
0
0
0
0
2
1
1
0
2
1
2
0
0
0
2
0
1
1
0
0
1
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
1
0
2
1
0
1
0
1
0
0
3
0
2
1
0
0
1
1
0
2
0
1
1
0
0
2
0
2
0
1
1
0
0
1
2
1
0
2
2
1
2
0
0
0
2
0
0
0
2
0
0
2
0
0
1
0
0
0
2
0
0
2
2
1
1
0
0
0
0
2
0
0
0
0
2
1
2
1
0
1
0
2
0
1
1
0
2
1
0
0
2
1
0
0
1
2
0
2
1
0
0
2
0
1
1
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
1
1
0
2
2
0
1
0
2
1
2
1
0
1
1
3
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
1
0
1
0
0
2
1
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
1
0
0
2
1
0
1
1
0
2
1
0
0
0
2
0
2
2
0
0
1
0
0
1
0
2
1
0
0
0
0
2
1
1
3
0
0
1
0
0
2
1
2
0
1
0
2
2
1
1
1
1
1
0
0
0
2
1
1
1
0
1
1
2
1
1
0
0
1
0
0
2
1
0
0
1
0
0
0
1
0
2
0
2
1
1
0
2
0
0
0
0
2
1
0
1
0
1
0
2
1
0
1
0
2
0
0
0
1
2
1
0
2
1
0
2
0
0
0
0
0
2
1
2
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
2
2
1
2
2
0
2
5
0
0
1
0
2
0
1
1
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
1
1
1
1
0
0
0
0
0
0
0
1
2
0
0
2
8
1
1
0
0
1
0
2
0
1
1
1
0
0
1
0
0
2
2
0
0
0
0
0
1
1
2
5
0
2
2
0
2
0
0
1
0
0
1
1
0
1
0
2
0
1
0
0
0
0
2
0
0
0
1
1
0
0
0
1
1
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
1
0
2
0
0
2
0
2
1
0
0
0
2
2
0
0
0
0
1
1
2
0
0
0
0
0
0
1
2
0
0
0
1
2
0
1
0
2
0
1
0
0
0
2
2
0
0
2
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
1
0
0
0
1
2
1
1
2
1
0
2
2
0
0
0
0
2
1
2
2
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
5
0
0
1
0
0
1
0
1
0
1
2
0
2
2
2
0
1
0
3
1
0
2
1
0
0
2
0
1
2
0
1
0
1
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
1
0
3
2
2
0
1
1
1
0
2
1
0
0
1
0
1
0
1
0
1
2
0
0
0
2
0
0
0
0
2
0
1
0
1
0
0
1
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
2
2
1
0
1
0
0
0
0
0
1
0
0
0
2
1
0
0
0
2
0
1
0
1
0
1
2
0
0
0
1
2
2
2
0
1
0
0
2
0
0
1
2
1
2
1
1
2
2
0
1
2
0
0
2
2
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
2
0
2
0
2
2
0
1
2
1
0
1
0
2
0
2
0
1
2
2
3
1
0
1
2
0
0
0
1
0
0
0
0
0
3
0
1
0
1
2
0
0
0
0
1
2
2
0
1
0
0
0
1
0
2
0
2
2
0
0
2
0
0
1
0
3
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
2
0
2
1
0
0
0
0
1
0
0
1
0
0
0
0
1
2
0
0
3
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
1
1
2
1
0
0
1
0
0
1
0
0
1
2
0
0
0
1
2
0
2
1
0
0
0
1
2
3
1
0
0
0
2
1
0
2
0
0
0
0
0
2
0
0
2
0
0
1
0
0
2
1
1
1
0
0
1
0
0
0
1
2
1
1
1
0
0
2
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
2
0
2
1
0
1
1
0
2
0
0
1
0
0
1
2
2
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
1
0
1
0
1
1
2
2
1
2
0
1
0
2
0
0
2
1
0
1
0
1
1
2
1
2
1
0
0
0
1
2
1
4
0
2
1
2
2
0
0
0
0
1
0
2
1
1
1
2
1
0
0
1
1
2
0
0
1
2
0
0
0
2
0
1
0
0
0
1
1
1
0
1
0
2
2
0
0
3
1
0
0
0
0
0
0
0
0
0
1
0
0
2
2
1
0
2
0
0
0
0
0
0
1
0
4
1
1
0
0
2
0
1
0
2
2
0
0
1
0
0
0
0
1
0
2
3
1
0
1
2
0
1
0
0
4
0
1
1
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
2
2
0
2
0
1
2
0
0
0
1
0
0
1
0
1
0
1
2
3
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
1
1
1
1
1
1
0
0
0
0
0
1
2
0
0
2
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
2
3
0
2
1
0
0
0
2
1
0
2
0
2
1
0
2
0
0
1
0
0
0
1
0
0
0
0
1
0
0
2
0
1
0
0
0
0
1
1
2
1
1
0
0
1
0
0
0
0
4
0
0
2
0
0
1
0
2
0
0
1
0
3
1
1
1
0
0
2
3
2
0
1
2
1
2
1
2
1
2
0
0
2
2
0
1
0
0
0
1
0
2
0
0
0
2
2
0
2
1
0
0
0
0
1
0
0
0
2
0
0
0
1
1
1
2
0
0
0
0
0
1
8
0
0
4
0
1
2
0
0
2
0
2
1
1
0
0
0
1
1
0
0
1
2
0
0
0
0
0
2
1
0
0
0
2
1
0
2
0
3
0
1
0
0
0
1
2
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
3
1
1
2
0
0
0
3
0
1
0
2
0
1
0
0
1
0
0
2
0
2
2
0
0
0
0
0
0
0
0
1
1
2
3
0
1
3
0
1
0
1
1
0
0
1
2
0
0
1
0
1
2
2
0
1
2
2
0
1
2
0
3
1
0
1
0
0
0
0
0
2
4
1
1
2
0
0
0
0
0
0
0
2
0
2
0
1
1
2
0
2
0
2
1
2
0
2
2
1
0
1
2
3
0
0
1
1
0
1
2
1
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
2
0
0
0
2
3
1
0
1
0
2
1
0
2
0
1
0
1
0
1
0
1
3
0
1
0
0
0
0
1
1
0
0
0
2
2
1
2
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
1
0
1
1
0
2
0
2
0
0
0
0
0
1
0
0
2
0
2
1
0
0
0
1
0
0
0
0
0
0
1
1
0
1
1
2
0
0
0
2
1
0
0
2
0
1
1
0
2
0
0
2
0
0
0
0
1
2
0
2
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
2
0
1
0
0
1
0
0
1
0
0
1
1
0
1
2
0
1
0
1
0
1
0
0
0
1
3
0
0
0
0
0
0
1
0
1
0
2
0
0
0
1
2
0
2
1
0
0
0
1
0
0
0
0
0
2
0
2
1
0
2
0
0
1
0
0
2
2
1
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
1
0
0
0
0
1
1
1
0
2
0
0
0
0
1
0
3
2
2
2
0
3
0
1
0
2
1
2
0
1
0
2
1
0
0
0
2
2
2
0
0
0
1
1
0
0
0
0
2
0
1
2
0
1
0
2
1
0
0
0
2
1
2
1
1
0
0
2
0
2
2
0
0
2
0
0
1
2
0
0
2
0
2
2
1
0
1
1
2
2
2
0
2
1
0
1
0
0
2
0
0
0
0
0
1
1
2
1
0
1
0
0
4
1
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
2
1
1
0
0
1
0
2
1
0
0
1
1
2
1
0
0
1
1
0
0
0
0
0
1
1
1
1
0
1
3
0
2
2
0
2
2
2
2
0
0
1
1
0
0
0
1
0
0
3
1
0
0
1
0
0
0
2
2
0
1
0
0
1
0
0
0
0
2
0
4
0
1
0
0
1
1
0
0
0
0
0
2
1
3
0
1
0
0
0
0
2
1
0
0
1
0
0
0
0
2
0
2
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
3
1
1
2
2
1
4
0
0
0
1
0
0
1
0
1
1
0
0
0
0
2
1
0
1
0
0
0
0
0
1
1
0
1
0
2
0
1
0
0
1
0
2
0
0
2
1
0
2
0
1
0
0
1
0
0
0
1
0
0
8
2
3
2
1
2
1
1
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
1
0
1
0
1
0
1
0
0
0
1
0
1
1
2
2
0
0
0
2
0
0
0
1
1
0
1
0
3
0
0
1
1
2
2
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
1
2
1
0
0
1
2
0
2
2
0
2
0
0
0
2
0
0
0
0
0
1
2
0
0
2
0
0
1
0
0
3
0
0
0
0
0
1
0
0
1
0
0
2
0
1
2
0
3
0
0
0
1
0
0
0
3
0
2
0
2
0
0
0
0
0
0
0
0
1
2
1
0
0
2
0
1
1
0
2
0
2
0
3
0
2
0
1
0
0
1
0
1
2
1
2
0
1
1
0
0
0
0
1
2
0
0
0
2
2
1
4
0
0
0
1
2
1
3
2
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
2
2
1
1
0
0
0
2
2
0
0
2
0
1
2
1
1
0
2
1
0
1
1
0
2
1
2
1
0
2
0
0
0
0
0
2
0
1
2
2
0
0
0
1
1
1
0
1
0
1
0
0
0
2
0
0
1
1
0
0
1
2
0
1
0
2
0
2
0
0
2
0
2
1
0
0
1
0
1
0
0
0
0
1
1
1
2
0
1
0
0
0
0
1
0
2
0
1
0
0
1
1
0
1
0
1
0
0
0
0
0
0
2
2
0
0
0
1
1
1
2
0
0
0
2
1
1
0
1
2
0
1
0
1
2
1
0
2
0
0
0
3
2
0
0
0
0
1
0
1
0
0
0
0
2
1
0
0
5
0
0
0
0
1
0
2
0
0
1
2
0
2
2
0
2
1
2
0
1
2
2
1
0
0
0
1
0
0
1
0
1
0
0
0
2
1
0
0
0
1
1
0
0
1
0
0
0
0
0
2
0
2
1
0
0
0
3
3
1
2
0
0
0
0
1
0
0
1
1
0
1
0
0
0
2
0
0
0
0
1
0
1
0
0
2
0
0
0
0
2
4
0
2
0
1
4
0
0
2
0
0
1
0
0
0
2
0
2
0
0
1
1
1
2
2
0
0
0
1
0
2
0
1
0
0
1
0
2
0
1
1
0
1
2
1
1
0
0
0
1
1
2
2
0
0
2
0
0
1
0
2
2
0
0
2
1
0
0
0
0
2
1
1
0
2
1
0
0
0
0
0
0
0
0
1
1
1
2
1
0
0
2
0
1
0
0
0
2
1
1
0
0
0
1
0
1
1
0
0
0
1
2
3
0
2
0
0
2
1
0
0
0
0
2
1
2
2
0
0
0
1
2
1
2
0
0
0
1
0
0
0
1
0
0
1
0
0
2
1
1
1
0
1
0
1
0
0
0
2
0
1
2
1
1
0
0
0
2
1
1
3
1
2
0
0
1
0
1
1
1
0
2
2
2
0
1
0
1
1
1
2
1
1
0
1
0
5
2
0
0
0
0
0
0
0
3
0
1
1
0
0
0
2
0
0
0
0
1
2
2
2
2
1
2
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
1
0
2
0
0
2
1
0
1
2
0
0
1
0
0
0
0
0
0
0
1
0
2
0
2
1
0
0
0
0
0
1
0
0
0
3
0
0
0
1
0
0
2
1
0
1
0
2
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
1
1
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
2
0
2
0
2
1
0
0
2
0
2
1
0
1
1
2
2
1
2
0
1
2
1
0
0
0
2
2
0
0
1
0
1
1
2
0
0
1
1
2
0
0
0
0
1
1
0
0
0
1
0
1
1
1
1
0
0
1
0
0
0
1
1
0
1
1
0
0
2
1
2
0
1
1
2
0
2
0
2
0
0
0
2
1
1
3
1
0
0
0
0
2
0
1
0
0
2
0
0
0
0
1
2
0
0
1
1
1
0
1
2
0
0
0
0
1
2
1
0
1
1
0
1
0
2
1
2
0
2
0
0
3
1
0
1
0
2
1
2
0
0
0
0
0
2
0
0
2
0
0
0
0
1
1
2
2
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
2
2
2
0
0
4
0
0
2
1
0
2
0
1
2
2
2
0
1
1
2
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
1
0
0
1
0
2
0
0
0
2
0
0
2
2
1
2
0
0
1
0
2
1
0
0
2
2
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
1
0
0
0
0
0
5
2
0
1
3
0
0
1
0
1
1
2
0
1
0
1
0
0
0
0
1
1
0
6
0
0
1
0
1
1
2
0
1
0
2
1
0
0
0
0
0
0
1
1
0
0
1
2
0
2
0
1
0
0
6
1
0
0
0
0
1
0
0
0
1
0
2
2
0
2
0
0
0
1
1
1
0
1
1
2
2
1
0
1
1
1
2
0
2
2
2
1
2
0
2
1
0
0
1
1
0
0
0
1
0
1
2
2
0
0
2
1
0
0
1
2
2
0
0
1
2
1
0
0
1
1
1
1
1
0
0
1
2
2
0
0
1
0
3
1
0
0
0
0
0
0
2
0
0
0
0
2
1
0
1
0
2
1
0
0
0
3
1
3
0
0
0
0
0
2
0
2
0
0
1
0
2
1
1
2
2
0
1
0
0
0
0
1
0
1
2
0
1
0
0
0
0
1
0
2
1
0
0
0
1
1
2
0
0
0
0
0
0
1
0
0
2
1
2
2
1
2
1
2
0
0
2
1
1
1
0
0
1
1
0
0
1
0
2
0
0
0
2
0
0
0
0
1
1
0
0
1
1
1
0
1
2
0
0
2
0
0
0
1
0
1
0
1
2
2
0
1
0
1
0
0
1
1
0
0
1
1
0
1
0
1
0
1
1
0
0
0
0
1
1
2
2
1
2
3
1
0
2
1
1
0
2
0
0
1
0
0
0
1
0
0
0
0
2
0
0
1
1
0
0
0
1
0
0
1
0
2
1
0
2
2
0
0
2
2
0
0
0
1
0
0
0
0
0
2
0
1
1
1
0
0
1
2
2
2
0
1
1
1
2
0
0
1
1
0
3
0
0
1
2
0
1
1
0
0
1
0
0
0
0
2
0
0
1
1
2
0
1
0
1
1
1
2
0
2
0
0
2
1
0
0
1
1
1
0
0
3
1
0
2
2
1
0
0
0
1
0
0
0
1
0
0
1
2
0
1
1
0
0
0
3
0
2
3
2
1
0
0
1
1
1
0
1
6
3
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
2
1
1
1
2
1
0
2
2
2
1
0
2
0
0
2
1
0
0
0
0
0
2
0
0
1
1
1
0
1
0
0
0
0
0
2
1
1
1
1
0
1
3
0
0
0
1
1
0
2
1
0
2
2
0
2
1
0
2
3
1
0
3
3
1
1
1
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
2
2
0
0
0
1
0
1
1
0
0
0
1
1
1
0
1
0
0
3
0
0
0
0
0
0
0
1
2
1
0
0
1
0
0
2
3
0
0
0
0
1
1
1
1
0
0
0
0
0
0
2
0
1
1
0
0
1
0
0
0
0
2
0
0
0
0
1
1
2
1
1
0
0
2
5
0
1
0
1
1
2
1
0
2
1
0
1
0
0
2
1
1
0
0
0
1
1
0
2
2
2
2
0
0
3
0
2
1
0
0
2
0
1
1
0
0
0
0
0
2
1
0
0
0
2
0
0
1
0
0
0
1
0
1
0
2
2
0
0
0
0
2
0
0
2
0
2
0
0
0
2
1
1
1
1
2
1
1
0
0
4
1
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
1
1
0
0
0
0
0
2
1
1
1
0
0
0
2
0
0
2
2
0
1
0
0
0
2
0
2
0
1
2
2
0
1
2
0
0
2
2
0
2
0
1
0
1
0
0
2
2
1
0
0
0
1
0
0
4
0
3
0
2
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
2
1
4
1
0
2
0
1
0
0
2
0
1
0
2
2
0
0
1
2
0
0
0
0
2
2
1
1
0
0
0
2
2
0
0
0
0
0
0
1
2
0
0
1
0
0
2
2
0
0
0
2
0
0
3
0
2
0
0
2
0
2
0
2
0
1
1
1
0
1
2
2
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
1
2
1
2
2
1
2
0
1
0
1
1
2
0
2
0
0
1
1
0
1
0
2
0
0
0
1
1
0
1
0
0
1
2
1
1
0
0
0
1
0
1
0
0
0
1
1
0
1
0
2
0
1
2
0
2
2
0
1
2
0
2
0
0
2
0
0
1
0
1
0
2
1
1
0
0
0
0
1
0
2
0
2
0
1
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
2
1
0
0
0
1
0
1
0
0
0
2
2
0
1
0
0
2
2
0
2
0
0
0
0
0
2
1
0
1
0
0
1
0
1
1
0
0
8
1
0
1
1
0
2
1
1
0
1
0
0
0
0
1
1
0
0
1
1
1
1
1
0
2
0
0
2
1
0
0
2
1
1
1
0
0
1
0
1
2
0
0
2
0
0
0
0
2
0
0
2
0
0
2
2
1
0
2
2
0
0
0
0
1
0
0
0
0
1
0
2
2
1
0
0
2
2
0
0
0
2
2
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
1
1
0
1
0
0
1
1
2
0
0
1
0
0
0
0
2
2
0
2
0
1
1
0
0
0
1
0
1
0
0
0
0
2
1
0
0
1
0
0
0
2
1
1
0
1
2
0
2
2
0
0
1
3
2
2
0
1
0
1
0
0
0
1
0
2
2
2
0
0
0
1
1
0
1
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
2
0
1
0
1
0
1
0
0
2
2
2
0
2
1
2
1
1
2
1
2
0
0
2
0
2
1
0
0
1
2
0
1
2
0
0
0
2
0
2
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
2
2
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
1
0
0
1
2
1
0
1
1
0
2
0
1
0
0
1
0
0
3
0
0
0
0
6
2
1
1
0
1
0
0
1
2
0
2
0
1
2
1
2
0
1
0
0
0
0
0
0
0
0
1
0
2
1
0
2
1
0
0
0
1
0
0
0
1
0
0
2
0
0
0
1
0
2
1
0
1
2
1
0
0
0
0
0
2
0
0
1
1
3
2
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
1
1
0
0
2
0
0
2
0
1
0
0
0
0
2
0
0
0
0
2
1
0
0
2
2
2
1
1
0
0
0
0
0
1
2
1
0
0
1
1
2
5
1
4
1
2
0
0
0
1
2
0
0
0
2
2
0
0
0
0
1
0
0
2
2
0
0
0
0
0
1
0
0
1
1
1
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
1
2
0
0
0
0
0
2
0
0
1
2
0
2
0
1
0
0
0
1
2
2
1
0
0
0
1
0
0
1
0
2
0
0
0
1
2
1
1
1
0
0
0
2
1
1
0
0
1
2
0
0
2
0
2
0
0
0
0
2
2
0
1
0
0
0
1
0
1
1
0
0
0
0
0
2
1
0
1
0
0
0
3
0
2
0
0
0
1
0
1
1
0
0
2
0
0
0
1
3
0
0
0
0
2
0
7
0
1
0
2
0
0
2
2
0
0
1
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
1
2
0
2
0
0
0
0
1
0
3
1
1
0
0
2
2
0
2
0
0
2
1
1
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
2
2
1
0
0
1
0
0
0
1
2
0
0
2
0
1
0
0
2
0
2
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
1
1
0
0
1
0
2
0
1
0
2
0
0
0
2
1
1
1
0
0
0
0
1
0
0
2
1
0
2
1
1
1
1
0
0
1
0
2
0
1
2
0
0
0
0
1
0
0
1
1
0
0
1
1
0
0
1
0
1
1
0
0
0
1
2
1
0
3
1
1
0
2
0
0
0
2
1
1
0
2
2
0
1
0
0
0
2
2
0
0
2
1
0
2
2
0
2
5
2
0
1
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
1
1
0
0
2
1
2
0
0
1
0
0
0
0
0
0
0
2
0
1
2
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
2
1
1
0
1
1
0
0
0
2
1
0
1
1
2
0
0
3
0
0
1
0
1
0
0
0
1
1
1
1
1
1
0
0
0
2
0
2
0
1
1
0
0
0
2
0
0
0
0
1
2
1
0
1
0
0
0
1
2
0
2
2
0
0
0
1
2
1
1
0
1
0
0
2
1
0
0
0
0
2
0
3
0
0
0
1
0
0
1
2
0
0
0
0
2
1
1
0
0
0
0
0
1
2
0
0
4
0
0
0
0
0
2
1
0
0
0
0
1
1
0
0
1
2
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
2
0
1
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
2
1
1
1
1
0
0
2
2
0
0
2
0
1
0
0
1
1
2
1
0
0
0
0
0
2
1
2
3
1
0
2
2
0
2
0
1
0
2
0
2
0
0
0
2
0
0
0
0
2
0
2
0
0
1
0
0
1
0
2
0
0
0
0
1
0
0
0
0
1
2
0
1
1
0
0
0
0
0
1
0
0
0
3
0
2
0
0
0
0
1
0
0
0
1
0
0
2
2
1
2
0
0
0
0
1
0
1
1
1
3
2
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
2
2
0
0
0
0
1
0
3
3
1
0
2
2
1
1
0
0
0
2
2
0
2
0
2
0
0
2
0
1
0
0
0
0
2
1
2
0
0
0
2
2
2
0
1
1
1
2
2
0
0
2
1
2
0
0
0
0
1
0
1
1
3
0
0
1
2
4
0
0
0
0
0
2
0
0
0
1
2
0
1
0
0
0
0
2
0
0
0
1
0
2
1
0
0
0
0
0
1
0
2
2
0
0
0
0
2
0
2
1
1
0
0
1
0
0
0
2
0
1
0
0
2
1
1
0
1
0
0
1
0
0
2
1
1
0
0
2
1
1
0
2
0
0
0
0
2
2
2
0
3
1
0
2
1
0
0
1
0
0
0
1
0
1
3
0
1
0
0
0
0
2
1
0
1
1
0
0
2
1
0
0
1
2
3
1
0
0
1
1
0
0
2
1
0
2
0
5
0
0
0
0
1
0
1
0
4
0
0
2
0
1
0
1
0
2
1
0
0
1
1
1
0
1
0
0
3
2
0
1
0
0
0
1
1
1
2
1
2
2
1
2
1
2
0
0
0
2
1
1
1
0
0
0
1
0
1
1
2
0
2
2
0
0
0
0
1
1
0
1
1
0
2
2
1
0
0
2
0
0
0
2
1
0
1
0
2
1
0
0
0
0
0
0
1
0
2
0
1
2
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
2
1
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
2
2
0
2
0
0
2
0
0
0
0
2
0
2
0
0
0
0
1
3
0
0
1
1
2
1
0
2
0
2
1
2
0
1
1
0
0
0
1
0
2
2
0
0
0
0
1
0
0
1
1
0
1
2
0
0
1
0
2
1
1
0
0
1
0
0
2
3
2
0
1
2
0
0
1
4
2
0
0
0
0
2
0
0
0
0
1
1
0
1
0
2
0
1
0
1
1
1
0
1
0
0
0
0
0
3
1
0
0
0
0
0
0
1
0
0
1
1
1
4
0
0
0
0
1
0
0
2
2
0
0
2
2
1
0
2
2
1
0
2
1
0
2
0
2
0
0
0
0
2
2
0
1
1
0
0
0
1
0
0
0
2
1
1
2
0
0
1
0
1
0
0
2
0
0
0
1
0
1
0
0
0
1
0
0
1
1
2
1
0
1
1
1
2
2
0
0
0
1
0
0
2
0
0
1
0
0
2
0
0
0
1
0
1
1
0
0
0
2
1
2
1
2
0
0
2
0
0
1
0
0
0
0
1
2
1
0
0
0
0
0
1
1
0
0
1
0
2
0
0
0
0
0
1
2
0
0
0
2
0
0
1
1
2
0
2
0
1
0
2
1
0
0
0
0
0
2
1
0
1
1
0
0
0
2
2
2
1
1
2
1
2
1
0
2
0
0
0
1
0
4
3
1
1
2
2
1
0
0
0
3
0
2
0
0
0
0
2
0
0
2
2
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
2
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
2
0
0
2
2
2
0
1
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
2
1
1
1
0
0
0
0
0
2
1
0
2
0
1
1
0
2
1
0
0
1
0
0
2
0
2
2
0
1
0
0
0
0
2
2
2
0
1
0
0
1
1
0
0
0
2
0
0
2
0
1
0
0
0
2
0
0
0
0
1
0
5
1
0
1
7
2
1
1
1
1
0
0
0
0
2
0
0
0
0
0
0
1
3
1
0
0
0
0
0
0
1
2
0
2
0
0
2
2
0
0
0
1
0
0
0
0
0
2
0
0
2
2
1
2
1
0
0
0
0
0
0
1
1
0
2
1
4
0
0
0
0
1
3
0
0
0
0
1
2
2
0
0
3
0
0
0
0
0
2
1
0
1
0
0
2
1
1
0
0
0
0
0
0
1
1
0
0
0
2
2
1
0
2
0
0
1
1
0
0
1
1
1
2
0
0
1
2
0
0
0
2
1
0
0
0
2
0
1
0
0
1
0
1
0
0
0
1
0
2
0
0
0
2
1
0
0
0
1
2
1
0
2
0
0
1
1
1
0
2
0
0
0
3
0
2
0
1
0
1
2
0
0
2
2
0
1
0
1
0
1
5
0
2
0
0
0
1
0
0
0
2
1
0
0
1
0
0
0
2
2
2
0
2
0
0
0
0
0
0
4
2
0
0
2
1
2
3
2
1
3
1
2
0
0
0
1
0
0
0
2
1
0
1
0
0
2
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
2
1
0
0
1
2
2
1
0
0
0
0
2
1
0
0
0
0
1
0
1
2
1
0
1
0
0
1
0
0
1
0
2
0
0
1
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
2
1
0
2
1
0
0
0
1
0
2
2
2
0
1
0
1
3
2
2
0
0
0
1
1
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
6
0
2
2
0
0
0
0
0
0
1
0
1
0
0
2
2
0
0
0
0
0
0
2
1
2
0
0
1
1
1
0
1
1
0
1
3
0
1
0
0
0
1
2
3
2
2
0
2
0
1
0
1
2
1
1
0
0
1
0
2
0
0
0
0
1
1
0
1
2
2
1
0
0
0
1
2
0
1
1
0
2
1
0
1
1
2
0
2
0
0
0
0
0
0
0
1
1
3
0
0
2
0
0
1
2
0
2
0
0
0
0
1
0
0
0
2
0
1
2
0
0
0
0
2
1
1
0
0
0
2
0
0
0
2
0
0
0
0
0
1
1
1
0
0
1
0
0
0
2
2
0
7
0
1
1
0
0
0
0
2
0
0
2
0
0
1
1
0
2
0
0
0
1
4
0
1
2
2
0
0
0
0
0
0
1
1
0
0
1
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
2
0
1
3
0
0
2
0
0
0
0
2
3
0
0
2
2
1
2
2
0
1
2
1
2
2
1
0
0
0
0
0
0
2
2
0
1
2
0
0
1
2
0
1
3
1
0
0
1
1
0
0
1
2
1
0
0
0
1
1
2
1
0
0
0
0
2
0
2
0
1
0
0
0
0
1
0
2
0
0
1
1
1
0
0
1
1
2
1
2
0
1
0
0
0
0
0
0
1
0
1
1
2
2
1
0
0
0
0
0
0
2
2
0
0
1
0
0
2
1
2
2
1
2
1
0
1
0
0
1
0
1
0
1
1
0
1
0
0
1
1
0
1
0
2
2
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
1
1
0
0
1
0
0
0
0
1
1
3
1
1
1
0
0
0
0
1
2
0
2
2
0
1
2
1
0
0
0
1
0
1
1
1
0
1
0
1
2
0
1
2
0
2
2
0
0
0
1
0
2
1
0
1
1
0
0
1
1
0
0
1
2
0
2
3
0
0
0
0
0
0
2
0
0
1
0
0
1
0
2
1
0
0
2
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
2
0
2
0
0
0
1
0
0
2
1
0
2
0
0
0
0
1
1
0
1
1
0
0
0
2
0
1
2
2
0
1
2
1
2
2
1
0
0
0
1
0
0
1
0
0
0
0
2
1
0
1
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
1
2
0
1
0
0
2
0
0
0
1
0
1
2
2
2
1
1
1
2
2
0
1
0
2
0
0
2
0
1
0
0
0
1
2
0
1
0
0
1
2
1
1
2
1
1
0
0
0
2
1
0
1
1
1
0
1
0
0
0
0
0
2
0
0
1
0
2
0
1
0
2
1
1
0
0
0
0
1
0
1
0
0
1
1
0
1
0
0
2
1
0
1
1
0
0
0
0
3
1
0
0
1
0
2
0
0
1
1
0
2
2
0
2
1
2
0
0
0
2
1
0
1
0
1
1
1
0
2
2
1
2
2
0
1
0
2
1
0
0
0
2
1
0
0
0
0
1
2
0
0
0
1
2
1
0
2
0
0
0
6
0
0
0
1
0
0
0
2
0
0
3
0
1
3
0
2
0
0
0
2
1
0
0
2
0
0
0
2
0
0
1
1
0
0
1
0
2
0
0
0
1
0
1
0
2
0
1
0
0
0
1
0
1
0
1
0
0
0
1
1
1
0
1
0
2
2
0
0
0
2
2
0
0
1
0
2
0
0
2
0
0
0
2
2
2
0
1
0
0
0
0
0
0
1
0
0
1
1
0
3
2
2
1
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
3
1
0
0
1
1
2
2
0
1
0
2
0
2
0
1
2
0
0
0
0
0
0
0
0
2
2
1
2
1
0
1
1
0
2
2
1
2
0
0
0
0
0
0
0
1
0
2
1
1
0
0
2
1
0
1
2
2
0
0
1
2
1
0
2
2
1
0
1
0
0
2
2
1
0
0
1
2
2
0
1
1
0
0
0
2
0
0
1
1
0
2
1
0
1
0
0
0
0
2
0
2
0
0
2
0
1
1
1
0
1
0
0
0
0
0
2
0
1
0
1
2
3
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
2
2
0
2
1
0
0
0
1
0
0
0
2
0
2
0
0
0
0
1
0
1
0
0
0
2
0
1
0
1
1
0
0
0
1
0
0
2
1
0
0
1
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
1
1
1
0
0
1
0
2
1
0
0
0
0
2
2
2
0
0
0
1
0
1
1
1
0
0
0
2
0
0
0
0
1
0
0
1
1
0
0
1
1
0
0
2
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
2
0
0
0
0
2
0
2
1
1
0
2
0
1
1
0
0
1
0
2
0
1
0
2
1
0
2
0
0
0
0
1
0
2
0
2
0
0
0
1
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
2
1
1
0
3
0
0
0
0
0
2
0
2
0
0
1
3
0
0
0
0
1
1
1
1
2
0
2
0
0
1
0
0
1
0
0
2
2
0
1
0
1
2
0
0
1
1
1
2
0
1
1
0
0
0
0
0
3
0
2
1
0
2
2
1
0
0
1
0
1
0
0
0
0
0
2
0
0
0
1
2
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
3
1
0
0
0
1
0
0
2
2
0
0
2
2
2
0
1
0
0
0
1
2
0
2
1
0
2
2
0
0
0
1
2
0
0
0
0
0
0
0
0
1
1
0
1
0
2
1
0
0
1
2
0
0
0
1
2
0
1
1
1
1
1
2
0
0
0
1
2
0
1
0
0
0
1
0
0
0
0
0
2
1
3
0
2
0
1
2
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
1
2
1
2
0
0
0
2
2
3
1
0
2
0
0
0
2
0
0
0
0
0
2
0
2
1
0
1
0
1
0
2
1
1
0
0
0
2
2
1
1
0
2
0
0
0
0
0
2
1
0
1
2
1
0
1
2
0
2
0
1
1
0
0
1
0
2
1
0
1
0
2
1
0
1
2
1
0
1
2
2
0
0
1
1
1
0
1
1
0
0
0
0
1
2
2
1
0
0
1
1
0
0
2
1
0
0
1
0
0
1
2
1
0
1
1
1
1
0
0
0
1
1
1
0
2
0
0
2
0
2
0
0
0
0
1
0
1
0
1
0
1
1
0
1
0
1
9
1
1
1
2
1
1
0
0
0
0
2
1
0
0
2
0
0
0
2
2
0
2
0
1
1
0
0
0
2
2
1
2
0
0
2
0
0
2
0
1
0
0
2
0
0
0
0
2
2
0
1
0
1
0
0
2
0
0
0
0
1
0
1
2
1
1
0
0
0
0
1
0
0
0
1
0
1
0
2
0
0
2
1
1
0
0
0
1
2
0
0
0
0
0
1
1
0
1
0
2
2
0
1
0
1
0
0
2
1
0
0
0
2
0
1
2
0
0
0
0
1
2
0
0
1
2
0
0
0
1
0
0
1
0
1
2
0
3
0
2
0
1
0
1
0
0
0
1
2
0
0
0
1
0
0
0
7
0
2
0
2
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
2
2
1
2
0
1
0
0
0
0
3
0
0
2
1
0
2
0
0
0
0
2
1
1
2
2
0
0
0
1
0
0
2
0
1
2
1
0
0
2
0
1
0
0
2
0
0
1
0
0
0
1
0
0
0
1
0
0
1
2
2
0
2
2
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
1
0
3
0
0
2
1
1
1
0
2
2
1
0
1
0
1
0
0
0
1
1
1
0
0
0
0
0
1
0
1
2
1
2
0
0
1
0
0
0
0
0
1
0
0
1
0
0
2
0
2
2
1
0
0
1
2
1
0
2
1
0
0
0
1
1
0
2
0
0
0
1
0
0
1
0
0
2
0
0
1
1
0
0
0
0
0
0
0
1
1
1
2
1
0
2
1
0
0
0
0
1
0
1
0
0
2
0
1
0
0
0
0
3
0
0
0
1
0
1
0
0
0
1
1
0
2
0
2
0
0
1
0
0
2
1
2
0
0
0
0
0
0
0
0
1
0
3
0
0
1
0
0
1
1
2
2
2
1
0
0
1
2
0
1
2
1
0
2
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
1
1
1
0
1
1
0
0
1
4
0
1
1
2
1
3
1
1
0
0
0
0
0
0
1
0
1
2
1
1
0
3
0
1
1
0
2
0
2
2
0
0
2
1
0
0
0
0
0
2
0
0
0
1
0
0
1
0
1
0
2
0
0
2
1
0
1
2
1
0
0
0
0
0
0
0
1
2
1
0
1
0
0
0
2
0
1
1
0
1
0
0
0
1
1
2
1
2
2
2
0
1
1
1
2
1
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
2
2
1
0
1
0
2
2
0
0
2
1
0
0
1
0
0
2
0
0
0
2
0
1
1
0
0
1
0
1
2
2
1
1
0
2
3
0
2
2
0
1
1
0
2
0
1
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
4
1
0
1
0
1
0
3
0
0
0
1
0
0
0
1
0
0
3
0
1
0
0
0
0
0
1
3
2
2
2
0
1
1
1
0
0
1
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
2
0
0
2
0
0
0
0
2
1
1
1
0
1
0
2
0
0
2
0
0
0
0
2
0
0
0
1
2
0
0
1
0
0
2
2
0
1
0
0
2
0
2
2
2
0
2
1
0
0
0
0
0
1
0
0
0
2
2
1
1
0
0
2
2
0
0
0
1
1
0
0
1
0
0
0
2
3
0
2
1
0
0
1
0
2
0
1
0
0
2
2
0
0
0
0
1
2
1
0
0
2
2
0
2
2
2
0
2
0
0
1
2
1
1
0
0
1
0
2
2
1
2
0
0
0
0
0
0
0
2
0
0
0
2
0
2
2
0
0
0
2
0
1
0
0
2
1
0
1
1
0
0
1
2
1
0
0
1
0
2
1
2
0
3
2
0
1
2
2
0
0
2
0
2
1
0
1
0
0
0
1
0
1
0
0
0
1
0
1
0
1
1
0
0
0
1
0
0
0
0
0
2
0
0
2
0
1
0
2
0
0
2
0
0
0
2
2
0
1
0
1
0
0
0
0
1
0
2
0
0
0
2
0
0
1
0
1
0
1
0
2
0
0
0
0
2
0
2
0
0
0
0
0
2
2
2
1
1
0
0
0
0
0
0
2
1
0
2
0
0
0
1
2
0
0
0
0
1
1
0
1
1
1
0
1
2
1
0
0
1
1
2
0
2
2
1
1
0
1
0
0
2
2
0
0
0
0
0
4
0
2
0
1
0
0
0
1
2
0
0
2
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
1
0
2
2
0
0
2
0
1
0
1
1
0
1
1
2
0
2
0
1
2
0
0
0
0
1
1
0
2
0
2
0
6
0
0
0
0
0
2
0
2
2
2
0
3
2
3
0
0
2
2
0
0
1
1
0
0
2
2
1
1
0
0
2
1
0
2
0
0
0
2
0
1
0
1
0
2
0
2
0
0
0
0
0
0
1
1
0
1
0
2
0
0
0
0
0
1
1
0
0
2
0
0
1
1
0
0
0
4
0
1
1
2
0
1
0
1
2
0
0
0
0
1
1
1
0
1
1
0
0
0
0
0
1
3
2
0
0
1
0
0
0
0
0
1
1
2
1
1
2
1
2
0
2
1
0
1
0
5
0
0
1
0
0
2
2
0
0
2
0
0
1
2
0
1
0
1
1
0
2
0
0
0
0
0
1
2
0
2
0
0
0
0
0
1
1
0
2
0
1
0
0
2
0
5
2
0
1
1
1
0
1
2
2
0
3
1
2
1
0
2
0
2
1
0
0
0
1
1
1
2
2
0
1
1
0
0
1
1
2
0
0
1
0
1
2
1
0
2
1
1
0
0
2
0
2
2
1
0
1
1
1
0
0
2
0
1
0
1
0
0
0
1
1
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
1
0
0
2
0
0
0
0
0
2
0
1
2
0
0
2
2
0
0
0
2
7
0
1
0
2
0
3
0
1
0
0
1
0
4
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
1
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
3
1
1
2
0
0
0
3
1
1
0
1
0
0
1
0
1
0
0
0
1
0
2
2
1
2
0
2
0
0
1
2
2
1
2
0
0
2
2
0
0
2
0
0
3
2
2
4
0
0
0
0
1
1
0
2
2
1
1
0
2
0
0
1
0
0
1
0
0
0
0
1
1
0
1
0
1
1
1
1
0
0
0
2
2
0
1
2
0
0
2
1
1
2
2
1
1
1
0
2
2
0
0
2
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
1
2
0
0
1
0
0
1
0
0
0
0
1
1
3
0
2
0
1
0
1
1
0
0
0
1
1
3
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
1
0
1
0
4
1
0
1
0
2
0
1
0
0
0
0
0
0
3
1
1
0
0
0
0
0
0
1
0
0
2
1
2
0
2
1
0
1
1
0
2
0
1
0
1
0
0
0
1
0
1
0
0
2
0
0
1
0
0
0
0
3
1
1
0
0
2
0
2
3
0
0
0
0
1
2
1
0
0
2
1
1
1
1
2
0
2
0
2
1
2
2
2
0
0
0
2
0
1
0
2
0
1
1
0
0
0
0
0
2
1
1
0
1
2
2
2
2
1
2
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
1
0
2
2
2
1
0
2
0
0
0
1
2
0
1
0
0
1
0
0
0
0
2
0
0
1
1
1
1
1
2
0
2
1
0
0
0
2
1
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
2
1
2
0
0
1
0
1
0
2
2
0
1
0
1
0
0
0
0
1
1
0
1
2
0
1
1
0
0
1
1
1
0
0
0
0
2
0
1
0
1
0
2
1
0
0
0
0
2
0
1
1
1
1
0
0
0
1
0
0
2
0
1
7
2
1
0
2
1
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
2
0
2
0
0
0
0
2
0
1
1
1
1
1
0
2
1
0
2
0
0
0
1
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
2
2
0
1
2
0
0
0
1
0
0
1
2
0
0
2
1
1
1
0
1
1
1
1
1
1
0
2
0
0
0
2
0
1
0
0
1
0
0
2
1
1
0
0
2
2
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
1
2
0
1
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
2
1
1
0
1
0
1
1
1
1
0
1
1
0
0
1
0
2
2
0
1
2
1
0
2
0
0
0
0
1
0
0
1
1
0
0
1
0
1
1
2
0
1
0
0
1
0
0
1
2
0
0
0
1
2
2
0
1
2
1
2
2
0
2
2
0
0
0
0
2
1
0
0
0
0
1
0
0
1
0
0
1
2
1
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
3
1
0
1
0
2
1
1
2
1
1
1
2
0
1
0
0
0
1
2
2
0
1
0
0
0
2
4
1
0
2
0
3
1
2
0
0
1
0
2
0
1
0
0
0
1
0
0
0
2
1
0
1
1
1
2
0
1
2
2
0
0
0
1
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
1
1
0
1
1
0
4
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
1
1
2
1
1
1
3
0
0
0
0
0
1
0
1
1
1
0
2
0
0
0
0
2
0
0
1
0
1
0
2
1
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
1
1
0
1
2
2
0
0
0
2
0
0
0
4
0
0
2
2
0
1
0
0
0
0
1
1
0
2
0
0
1
0
2
0
1
0
1
5
1
2
0
0
0
0
1
0
0
0
1
1
0
1
1
2
0
2
1
0
1
2
2
1
0
1
0
1
0
0
2
0
1
0
1
0
1
0
2
0
0
1
0
0
0
0
0
5
2
0
0
1
1
1
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
2
4
1
4
0
2
0
0
2
2
2
0
0
0
0
1
0
2
0
0
0
0
0
2
1
1
0
0
0
3
0
0
2
0
0
0
2
1
1
2
0
1
0
2
0
0
1
1
1
0
0
0
0
2
0
2
2
0
0
0
1
0
3
0
0
0
1
0
0
0
0
0
0
2
0
1
0
2
0
2
2
0
2
0
0
1
1
0
0
0
0
0
3
2
0
0
0
1
0
1
0
1
0
0
1
2
0
0
2
0
0
2
2
1
0
0
0
2
1
0
1
1
0
0
1
0
0
2
1
1
1
0
4
2
0
1
2
2
2
0
0
0
2
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
1
0
2
1
1
0
0
0
1
0
0
0
0
1
2
0
0
0
2
0
0
1
0
0
2
1
0
0
0
1
0
0
0
0
1
2
1
0
0
0
1
0
0
2
0
0
0
0
2
2
0
3
0
1
0
2
1
0
2
1
2
1
2
1
1
0
3
0
1
0
2
0
0
0
2
1
1
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
2
0
2
0
2
1
1
2
0
0
2
0
0
0
1
0
0
0
0
2
2
0
0
0
0
2
0
0
1
2
1
0
0
0
2
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
1
0
0
0
1
0
1
0
2
0
2
0
0
0
0
1
2
0
0
1
2
1
3
0
2
1
2
1
0
0
1
2
0
1
0
0
2
1
0
1
1
0
0
1
1
2
0
2
1
4
2
0
1
0
1
1
2
0
1
2
2
1
1
0
0
1
1
0
0
0
0
0
1
0
0
1
0
1
2
0
3
2
2
3
2
0
0
0
0
2
0
0
2
0
0
2
2
1
0
2
1
3
1
1
1
0
0
0
0
0
1
0
2
3
1
0
0
0
0
0
1
1
0
2
1
0
0
1
0
2
1
0
1
0
1
0
0
0
0
1
2
2
1
0
2
2
2
0
1
0
0
1
0
4
0
0
1
0
0
0
2
1
2
0
0
2
1
0
1
0
3
2
2
0
0
0
0
0
0
2
0
0
0
1
1
1
0
1
1
0
2
1
0
0
0
0
0
1
0
0
2
0
2
0
2
0
0
2
0
0
0
1
0
0
1
0
0
1
0
0
1
6
0
0
1
0
0
1
1
0
1
0
1
0
1
1
0
0
1
0
0
1
1
1
1
1
0
0
0
0
0
0
2
1
0
0
0
1
0
1
2
0
1
2
0
2
0
0
0
0
3
0
3
0
1
2
0
2
0
0
0
0
1
0
1
2
2
1
2
0
0
0
0
3
2
1
0
1
0
0
1
2
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
3
0
0
1
0
0
0
0
0
0
2
0
2
0
1
0
1
1
2
1
0
1
1
1
0
0
2
1
0
3
1
1
0
0
0
0
0
2
0
2
0
2
1
0
1
3
0
2
0
0
0
0
2
2
0
1
0
0
0
0
1
0
4
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
1
2
0
1
0
0
1
0
2
2
3
2
0
0
0
0
0
0
1
1
0
0
0
2
1
0
0
0
0
3
0
2
2
0
0
2
1
0
1
0
0
0
0
0
2
0
0
0
0
1
0
1
0
1
0
0
2
0
1
2
0
0
1
0
0
0
4
0
2
0
1
1
2
0
1
2
0
0
1
2
0
0
1
0
0
1
1
1
2
0
1
0
0
1
2
2
0
0
1
0
0
0
2
1
7
1
0
0
1
2
1
0
0
0
0
2
0
1
0
1
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
2
2
0
0
0
0
1
0
1
0
0
0
2
4
1
1
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
1
0
2
0
0
2
2
2
2
0
0
0
1
1
1
1
2
1
0
2
2
1
2
2
0
3
2
1
2
0
0
2
0
1
2
0
1
1
0
1
0
2
0
2
0
2
0
0
0
0
0
0
2
2
2
0
2
1
1
1
1
1
0
0
2
2
0
2
0
0
1
0
0
1
2
2
0
1
1
2
2
2
0
1
1
2
0
2
0
0
0
0
2
0
0
0
1
0
0
0
1
0
2
2
2
0
0
1
0
0
0
3
0
0
4
0
2
0
2
1
0
1
1
0
0
0
0
0
0
0
2
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
1
0
1
2
0
0
1
1
0
0
0
1
1
0
0
0
1
2
0
0
1
0
2
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
1
2
0
0
0
0
1
0
1
1
1
2
0
0
0
2
1
2
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
1
0
2
0
0
2
0
0
0
1
0
0
0
1
2
0
0
2
2
1
1
0
3
0
2
2
0
2
1
1
1
1
0
0
1
0
0
2
0
1
2
2
1
0
0
0
2
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
1
0
2
1
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
1
0
1
0
2
1
0
0
0
2
0
1
1
1
0
0
1
0
1
1
0
2
0
2
0
0
2
0
2
0
1
0
1
1
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
3
0
2
2
2
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
1
0
0
1
2
1
1
1
0
0
0
1
2
0
2
2
0
2
1
1
1
0
0
1
2
0
2
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
1
0
2
0
2
0
0
0
0
0
2
2
0
1
2
0
0
1
1
1
1
1
2
0
2
0
0
1
1
2
0
1
1
2
1
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
2
2
0
0
2
0
0
2
2
1
2
2
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
1
1
1
0
0
3
0
1
0
3
0
0
1
0
2
0
1
2
0
0
0
0
1
2
3
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
1
0
0
2
1
1
0
0
0
0
0
0
0
2
0
0
1
2
1
0
0
2
1
1
2
1
0
0
0
0
0
0
2
1
0
0
0
1
0
0
1
0
1
0
1
1
0
3
2
2
0
0
2
0
0
1
0
0
1
0
1
2
1
1
0
3
0
2
0
0
1
2
0
0
1
2
0
0
0
0
0
1
1
0
2
0
0
2
0
0
0
0
0
0
0
2
1
1
0
1
1
2
0
0
0
0
2
0
0
1
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
2
1
0
0
1
0
0
0
2
0
1
0
0
0
0
1
0
4
0
1
0
0
2
0
0
0
1
1
0
2
0
1
2
0
2
0
0
2
0
0
0
0
0
2
0
1
1
0
0
2
0
0
0
0
2
1
0
1
2
2
1
0
1
1
0
1
0
0
0
0
0
1
0
2
2
0
2
1
0
1
0
0
0
4
6
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
3
2
1
0
0
1
0
2
1
2
0
1
0
0
0
3
0
2
1
2
1
0
0
0
0
0
0
0
2
0
0
0
2
3
0
0
0
1
0
1
1
1
2
0
2
2
0
0
0
0
2
2
2
2
1
1
0
0
2
1
0
1
0
2
0
1
1
1
0
0
4
2
1
2
0
2
0
2
1
1
1
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
2
1
0
0
0
0
0
2
1
2
0
1
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
1
0
2
0
2
0
2
0
1
1
0
2
0
0
3
2
1
2
1
1
0
1
0
0
0
2
2
1
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
1
0
1
0
1
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
3
2
2
0
0
0
0
0
1
0
0
0
1
2
0
0
0
2
0
2
1
0
0
0
1
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
1
2
0
0
1
0
0
1
1
0
0
0
0
0
2
0
1
0
0
1
2
0
0
1
0
0
1
0
0
0
2
0
2
2
0
2
0
1
0
2
1
1
1
0
1
2
0
1
1
1
0
0
1
0
0
1
2
0
0
1
0
1
0
0
0
0
2
1
0
0
2
2
0
0
0
0
0
0
0
0
1
0
2
2
0
0
2
2
0
0
1
1
2
0
0
2
0
0
0
2
1
1
0
0
1
2
0
2
1
0
0
2
1
0
0
0
1
0
0
0
2
0
2
0
1
1
0
2
1
1
0
0
2
2
0
1
0
0
0
0
0
2
2
0
0
1
0
2
0
2
0
1
0
1
2
0
2
1
0
1
2
0
0
0
0
0
1
0
1
1
1
0
0
0
2
2
0
0
0
2
0
0
2
0
1
1
2
0
0
0
1
2
0
1
0
0
0
0
2
0
0
0
1
2
2
2
0
0
1
0
2
0
2
3
2
1
0
0
2
2
0
0
1
0
1
1
1
1
0
0
0
1
0
9
1
2
0
0
0
0
0
1
2
4
0
0
1
0
1
1
1
0
0
0
1
1
0
2
0
1
0
0
2
0
0
2
1
1
1
0
0
1
0
0
3
1
1
0
1
1
0
2
2
0
0
0
0
1
1
1
1
1
1
0
1
0
0
0
2
0
1
2
0
1
0
0
2
1
2
1
0
0
1
0
0
1
0
0
1
0
0
1
0
2
1
2
0
0
1
0
0
0
0
1
0
1
0
0
2
0
0
0
1
0
0
0
0
3
2
1
1
0
0
0
1
1
2
0
0
0
0
0
1
0
2
2
1
0
0
0
0
1
0
0
1
1
0
0
1
0
1
0
0
0
2
0
0
4
2
0
0
2
0
1
0
0
1
0
0
0
2
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
3
2
0
1
0
2
1
0
1
0
1
1
0
1
0
1
0
1
1
0
2
2
2
0
1
1
0
1
0
0
1
0
0
0
0
1
0
1
2
0
0
2
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
1
0
1
2
2
1
1
1
0
1
0
0
0
1
2
1
1
0
0
1
0
2
1
0
0
2
0
0
0
2
0
1
0
1
2
2
0
2
0
1
1
0
0
0
0
1
0
0
0
2
0
1
1
2
0
2
0
2
0
0
0
2
0
0
0
0
1
0
1
0
1
2
0
0
0
0
2
0
0
1
1
0
3
2
3
0
1
0
1
1
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
2
0
2
0
2
1
0
0
0
2
1
0
1
0
2
0
1
0
0
2
0
3
2
1
1
2
1
1
0
0
0
2
0
1
0
0
0
2
0
0
1
2
1
0
1
0
0
0
0
0
1
1
2
2
1
0
1
2
0
2
0
2
0
0
0
1
0
3
1
0
0
0
0
1
1
0
1
0
2
3
2
0
0
2
1
2
0
1
2
0
2
0
2
0
0
1
0
0
1
1
2
0
1
0
1
0
1
0
2
1
0
2
1
1
0
1
2
1
0
0
1
2
2
0
0
0
2
0
2
0
1
0
0
0
0
2
1
2
2
1
0
1
1
0
2
1
1
2
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
1
1
1
1
0
2
0
0
1
1
1
1
1
1
0
0
0
0
0
0
2
1
0
2
1
1
0
0
0
0
0
2
0
0
1
1
1
1
0
2
0
2
0
1
2
2
0
0
0
0
0
0
2
1
0
1
1
0
2
0
0
2
0
1
1
0
1
1
1
2
2
1
0
0
2
2
0
0
0
1
0
1
1
0
1
1
1
3
2
0
1
0
1
2
0
0
0
0
1
0
5
0
1
1
1
1
0
0
2
1
2
0
0
0
1
2
1
1
0
1
0
3
2
0
0
0
0
2
0
0
1
1
0
2
2
1
2
0
0
0
0
1
0
1
1
0
0
2
0
2
1
1
2
0
0
0
2
2
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
1
1
1
0
0
1
0
0
0
0
1
0
1
0
1
2
0
2
2
0
0
0
0
1
3
2
1
0
2
0
0
2
2
1
2
0
2
0
0
2
0
0
1
0
0
0
1
0
0
2
0
1
1
0
0
0
1
0
2
0
1
1
0
1
0
0
1
0
1
2
2
1
0
1
0
2
2
2
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
2
1
0
2
1
0
0
2
0
0
0
1
0
0
0
2
0
2
0
2
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
1
1
0
1
0
1
2
0
0
0
2
0
2
1
2
0
0
0
0
0
2
1
0
0
0
2
2
1
0
0
0
2
0
1
0
0
2
0
0
0
0
0
1
2
0
2
1
0
0
0
0
0
1
0
2
0
0
0
3
1
1
1
1
0
0
1
3
0
0
2
0
0
0
1
2
0
1
0
2
2
0
0
2
2
0
1
0
3
1
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
2
0
2
1
0
1
0
0
1
0
2
0
0
1
0
1
1
0
0
0
0
0
2
2
0
0
0
1
0
1
1
2
1
0
0
1
2
2
0
2
2
3
0
0
0
0
1
1
2
0
0
0
0
0
1
3
2
0
6
2
2
0
2
0
1
1
0
0
0
0
1
1
1
0
1
0
0
2
0
1
1
0
1
2
2
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
2
2
0
0
1
1
4
0
0
0
0
2
1
0
0
0
2
2
0
0
0
0
1
1
1
0
0
0
1
2
2
1
2
0
0
0
0
1
0
2
0
0
0
0
0
0
2
2
0
0
2
0
0
1
0
0
2
2
1
2
0
0
0
0
2
1
0
0
0
0
2
1
0
2
2
2
0
2
1
0
0
0
1
2
0
2
2
0
0
0
1
0
1
0
1
2
2
2
3
0
2
0
0
1
0
1
1
0
0
2
1
2
0
0
3
0
0
2
2
1
2
3
1
2
0
0
1
0
0
1
2
0
1
4
2
0
2
0
1
1
0
0
0
2
0
0
0
1
2
2
2
0
0
0
0
2
2
0
3
1
1
1
2
0
1
2
0
0
1
1
1
1
2
0
1
6
0
0
2
2
0
2
3
0
1
0
2
2
2
0
0
0
0
2
0
2
0
2
1
0
1
1
0
0
0
0
0
0
0
0
1
1
1
2
2
0
2
2
1
0
2
2
2
1
2
1
2
0
1
1
0
1
0
2
0
1
2
0
0
0
0
2
1
0
0
0
0
1
0
1
0
0
0
1
1
1
2
1
0
1
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
1
1
0
1
1
0
1
0
0
3
0
1
1
0
0
2
1
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
2
0
2
0
2
0
0
2
0
0
0
0
0
0
1
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
1
0
0
0
0
2
0
0
1
1
1
0
0
0
0
0
1
1
0
1
4
0
0
0
1
0
2
2
0
1
2
0
0
0
1
1
0
2
2
0
2
0
1
0
1
0
0
0
1
0
1
1
1
1
0
0
0
1
0
0
2
0
0
0
0
0
0
2
2
0
1
0
2
0
3
2
0
3
1
0
2
0
0
1
2
1
0
1
1
0
2
1
1
2
0
0
2
2
2
0
1
0
0
0
1
0
2
0
0
0
0
0
2
1
0
1
0
0
0
1
1
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
1
3
0
0
1
3
0
1
0
0
0
0
1
1
0
0
2
0
0
0
2
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
1
1
2
1
2
1
2
0
0
2
0
1
0
2
0
0
0
1
2
2
1
0
1
0
1
0
1
0
2
0
2
0
0
1
0
0
2
0
0
0
0
0
1
1
0
1
1
0
0
1
1
1
2
0
2
2
0
2
0
0
0
1
2
0
0
1
2
4
0
0
0
0
3
2
1
0
1
0
0
0
2
1
0
1
0
3
0
1
0
1
0
5
1
0
2
4
0
1
0
0
0
1
0
0
2
2
0
2
0
2
1
0
1
0
1
1
0
0
0
2
0
0
2
0
0
0
1
0
0
0
2
1
0
0
1
1
0
0
0
1
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
1
0
2
1
0
2
0
1
0
1
1
0
0
0
0
1
0
0
1
1
0
1
1
0
1
2
2
0
2
2
2
1
2
1
1
0
0
1
0
0
0
0
2
1
0
1
0
0
0
0
0
0
2
1
1
0
1
2
4
1
0
1
1
2
0
1
2
2
1
0
0
0
2
0
0
0
0
2
0
1
1
0
0
0
4
0
2
4
1
1
0
1
1
2
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
1
3
0
0
0
1
0
0
2
0
2
0
0
0
1
1
0
0
2
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
2
2
0
0
1
0
0
2
2
0
0
0
0
2
0
2
1
0
0
2
0
2
0
0
0
1
0
1
0
2
0
4
0
2
1
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
1
0
1
1
1
2
0
1
1
2
0
0
0
0
2
1
1
0
1
1
1
1
0
2
1
1
0
1
0
1
0
0
0
2
1
0
1
0
2
3
0
2
0
0
2
0
0
2
1
0
1
0
0
0
0
0
1
1
0
0
1
0
0
2
1
0
0
1
1
0
0
0
3
2
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
1
0
2
1
0
0
0
0
1
0
1
0
2
0
0
1
0
2
2
1
0
2
1
2
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
2
0
0
2
0
3
0
2
2
0
1
0
1
1
2
1
0
1
0
1
0
0
0
1
0
1
1
1
2
1
1
0
0
0
1
3
0
0
0
0
0
2
1
2
2
1
0
1
1
2
1
1
0
2
2
2
1
2
2
0
0
0
2
0
2
0
2
2
2
2
0
0
2
1
1
0
0
0
0
2
0
0
1
0
1
0
0
0
1
0
2
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
3
1
1
1
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
2
1
0
1
1
1
0
1
0
0
2
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
2
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
1
0
0
2
0
0
0
2
0
0
0
1
0
1
1
0
1
0
2
1
2
1
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
1
1
2
2
0
0
0
0
1
3
0
0
2
0
3
4
1
0
0
2
1
0
2
0
1
0
2
0
0
0
0
1
2
2
1
0
2
0
0
0
2
1
0
0
0
0
0
2
1
0
2
2
2
0
0
0
3
2
2
0
2
0
0
2
0
1
0
2
1
2
0
0
1
1
0
2
3
2
1
3
1
1
1
2
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
2
2
0
0
0
1
0
2
1
1
2
1
1
0
2
2
0
0
0
0
1
3
1
0
0
0
1
0
1
1
0
1
0
1
0
2
0
2
0
0
0
0
1
2
0
0
0
0
2
1
0
0
1
1
0
0
0
0
1
2
0
2
1
0
2
0
0
0
0
2
1
0
2
1
2
0
0
1
15
2
0
2
0
0
0
0
0
0
1
0
1
1
1
0
2
1
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
1
0
2
1
1
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
1
0
1
1
1
0
0
0
0
1
0
1
2
0
0
0
0
0
2
0
0
1
2
2
0
0
0
1
0
2
0
0
0
0
0
1
0
0
3
1
2
1
0
2
0
1
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
1
2
0
2
0
0
0
0
0
0
1
1
0
0
2
1
0
0
1
0
1
1
1
2
0
0
2
0
0
3
2
0
0
0
2
1
0
1
2
2
0
1
0
0
0
0
0
0
0
0
2
2
2
0
2
1
1
1
0
2
0
0
0
1
0
1
0
0
1
0
0
0
1
0
2
2
0
0
1
0
1
0
0
0
2
0
0
2
0
0
0
1
1
0
2
0
2
2
0
2
1
1
0
1
1
0
1
2
0
0
0
0
0
0
2
1
1
0
1
2
0
2
0
0
0
0
1
0
1
0
1
0
2
3
0
0
2
1
4
2
1
2
1
0
1
2
1
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
2
1
1
0
0
0
0
0
0
0
0
1
1
1
2
2
0
0
0
0
3
1
2
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
3
0
0
0
0
1
0
2
6
2
1
2
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
5
0
0
0
0
1
0
0
1
0
2
2
0
0
0
0
1
1
1
0
2
1
0
0
1
0
0
0
2
0
2
0
0
1
0
0
1
0
0
0
2
1
0
3
0
2
0
2
0
0
1
0
0
0
2
0
2
0
0
0
0
1
1
2
0
1
0
0
0
3
2
0
0
0
1
0
0
0
2
0
0
0
0
2
1
0
0
0
0
1
1
0
0
2
4
0
2
2
1
1
1
0
0
2
1
0
0
1
0
1
1
1
0
0
2
0
0
0
2
0
1
0
0
1
0
2
1
0
0
0
0
2
2
0
0
2
2
0
0
2
0
0
0
2
2
0
0
2
0
2
0
2
1
0
0
0
0
0
1
1
1
2
1
0
1
1
1
2
1
2
1
2
0
0
0
2
1
0
0
0
0
0
1
2
1
0
2
0
1
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
2
1
0
1
1
0
1
0
1
2
2
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
1
1
0
0
2
0
0
0
2
0
2
1
1
0
1
5
0
0
1
0
0
0
2
0
2
0
2
0
0
1
0
0
0
3
0
1
2
0
1
1
2
0
0
1
0
0
1
0
0
0
0
2
2
0
0
1
0
1
0
0
0
0
0
2
0
2
0
0
1
0
1
0
0
0
2
1
0
2
0
1
2
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
2
0
2
0
0
2
0
2
1
0
0
0
0
1
1
2
0
2
2
0
2
0
0
0
0
2
0
2
0
0
1
0
1
1
0
0
0
0
2
0
1
0
2
1
0
2
0
0
1
2
1
0
2
0
1
0
0
0
2
2
0
2
1
0
1
0
0
1
1
1
0
0
0
1
1
2
2
0
1
0
1
2
0
1
0
0
0
0
0
0
2
1
0
2
1
2
1
2
0
0
1
0
0
0
7
0
3
0
0
1
0
2
0
0
0
0
2
0
2
0
0
0
1
0
2
1
0
1
0
1
2
1
2
1
0
1
0
2
1
0
0
0
5
1
0
1
0
2
0
2
1
2
2
0
0
0
0
2
0
0
0
0
0
0
3
0
0
1
0
0
1
0
0
0
1
1
1
0
0
1
2
0
2
2
1
0
0
0
0
1
0
1
0
2
0
0
0
0
0
2
1
0
1
0
2
0
0
0
0
0
0
2
1
0
0
2
0
0
0
1
2
0
2
0
0
0
1
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
2
0
1
1
0
0
1
0
0
0
1
0
0
0
1
2
2
0
0
0
1
0
1
2
1
1
1
0
0
1
2
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
3
1
0
1
0
1
1
1
1
0
0
1
0
1
0
2
0
1
0
1
0
0
0
1
0
6
0
0
1
0
0
1
2
1
0
0
0
2
0
0
1
2
0
0
0
1
2
0
0
0
0
1
2
0
0
0
0
1
3
1
0
1
0
0
2
0
0
0
0
0
0
1
2
0
0
2
1
0
2
0
0
0
0
0
1
2
0
7
2
1
1
1
0
1
1
0
2
2
0
1
2
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
1
1
0
0
1
0
1
2
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
2
0
0
0
2
0
3
0
0
2
2
0
1
1
0
0
0
0
1
2
1
2
0
1
0
0
0
0
0
2
2
0
1
3
2
0
1
0
1
1
0
0
3
1
0
1
2
0
1
1
0
1
0
0
2
2
0
1
0
0
1
0
0
1
0
0
1
0
2
4
2
2
2
2
1
0
0
0
1
0
2
1
2
1
2
1
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
3
1
0
0
1
0
2
0
1
0
2
0
2
2
0
2
2
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
1
0
0
0
3
1
0
0
1
2
0
1
1
0
2
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
2
0
2
0
3
0
0
0
1
1
1
1
2
0
0
0
0
1
0
0
0
0
0
1
2
1
2
1
2
0
0
0
2
1
1
0
0
0
1
0
1
0
1
0
0
1
1
2
0
0
1
0
1
0
0
2
0
1
0
2
0
0
0
1
3
0
2
0
1
0
1
0
2
1
2
1
0
1
0
1
2
2
0
0
0
0
0
1
1
1
0
0
0
0
0
2
0
2
0
2
0
2
0
0
1
0
7
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
1
2
0
0
0
1
2
2
2
2
1
0
0
0
1
0
0
0
0
2
0
1
0
0
0
1
0
0
1
0
1
0
2
2
0
0
0
1
1
1
1
2
0
1
0
3
0
0
1
0
2
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
2
0
1
2
0
1
2
0
1
2
1
2
2
1
0
0
0
2
1
1
3
0
0
1
2
2
0
0
2
1
0
4
0
0
0
0
0
0
0
1
0
2
3
0
0
0
0
0
0
0
0
0
1
2
0
1
2
2
0
0
0
1
0
0
1
2
1
0
0
0
0
1
2
0
0
2
0
0
0
1
0
0
1
2
0
1
0
0
1
2
0
0
0
2
1
0
0
2
0
1
1
1
1
2
2
0
2
0
1
0
0
0
2
0
0
0
0
2
0
1
0
0
0
2
0
0
2
1
0
0
1
1
2
0
0
1
1
0
0
2
0
3
1
1
2
1
0
0
1
1
0
0
0
0
1
0
2
0
2
2
0
2
1
1
1
0
0
0
1
0
2
0
0
2
2
1
0
0
0
0
0
0
0
1
0
1
1
0
2
1
2
0
0
3
0
0
0
0
0
1
0
1
1
1
0
0
0
0
1
2
0
0
2
0
3
1
1
0
0
0
1
0
3
0
0
0
0
0
2
1
1
1
0
2
0
0
1
2
1
5
1
0
2
1
1
0
0
1
1
2
0
1
2
0
1
1
1
1
0
0
1
0
1
1
1
1
0
1
0
0
1
1
0
2
0
1
2
0
1
1
0
1
0
0
0
0
0
0
1
1
1
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
2
1
4
0
1
0
0
0
2
0
2
1
0
1
1
2
0
1
0
0
0
2
0
0
0
0
2
0
1
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
2
0
2
1
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
1
1
1
0
1
0
0
1
0
0
0
1
1
0
0
4
2
1
2
0
0
0
0
0
0
0
0
0
2
0
2
0
5
0
1
2
2
0
0
0
0
3
0
0
2
0
0
0
0
0
0
1
1
0
1
0
1
1
1
1
0
0
0
1
0
0
0
0
1
3
0
2
1
0
0
1
2
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
2
1
3
0
0
0
1
0
1
1
2
0
1
2
0
0
0
0
1
0
0
0
0
0
0
1
2
2
2
0
1
0
2
0
1
2
0
0
1
2
0
2
0
1
0
1
8
1
1
2
0
0
2
1
0
0
2
1
0
0
1
0
0
0
0
0
2
0
0
2
0
0
1
2
2
2
0
1
0
2
0
1
2
2
0
0
1
2
0
1
1
0
0
0
0
1
0
0
1
1
2
1
1
2
1
0
0
3
0
0
0
2
3
0
1
0
2
0
2
2
2
1
3
1
0
0
2
0
2
0
2
0
0
0
1
0
1
1
0
0
2
0
2
0
0
0
1
0
2
1
0
0
0
0
2
0
0
1
2
0
0
1
2
1
2
0
0
0
0
1
0
0
1
0
2
0
0
3
0
3
1
0
1
2
2
0
2
1
1
0
0
0
1
0
0
0
2
2
0
0
0
1
0
0
0
1
3
0
0
0
0
2
1
1
0
2
0
0
1
0
0
2
0
2
0
3
0
0
0
1
1
2
1
0
0
0
1
0
1
0
2
0
0
0
2
0
0
0
0
1
0
1
2
2
0
1
0
1
2
0
1
1
0
1
0
1
2
2
0
1
2
1
0
0
0
2
1
0
0
1
1
0
0
0
0
0
0
0
1
1
0
2
0
2
0
2
1
1
0
0
0
1
1
0
0
0
0
0
0
1
1
0
1
2
0
0
1
0
0
0
1
1
0
0
1
1
2
1
1
1
2
1
0
2
1
0
1
0
0
0
0
2
1
0
1
0
2
2
0
0
0
0
1
0
0
1
1
1
1
0
2
0
1
0
0
1
0
0
0
0
0
3
0
0
0
2
1
0
3
2
0
1
3
0
1
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
1
1
0
2
1
2
2
1
1
2
0
0
2
1
0
1
1
0
1
1
2
0
1
0
1
0
1
1
0
0
0
1
1
2
0
1
1
1
0
2
1
0
0
1
1
0
0
1
1
2
1
2
2
1
0
0
2
1
0
0
2
0
0
1
0
0
1
0
0
0
2
0
2
0
2
0
0
0
0
0
0
2
0
1
0
1
0
0
2
2
0
1
2
0
0
1
0
2
1
1
1
0
2
1
2
0
0
1
0
2
0
3
0
0
0
1
0
1
1
2
1
0
0
0
0
2
0
1
0
0
0
0
7
1
0
0
2
0
0
0
1
1
1
0
0
0
0
1
2
0
0
1
0
0
0
1
0
0
2
0
0
1
2
2
0
0
1
2
2
0
2
1
0
2
1
0
0
0
0
0
2
0
1
0
0
0
1
2
0
0
2
0
1
0
0
0
0
2
2
2
1
0
1
0
1
1
1
0
2
2
0
0
2
0
3
2
0
1
0
1
0
1
0
2
0
1
1
0
0
0
2
0
0
0
0
0
1
0
0
0
1
2
1
0
0
0
0
1
1
0
0
0
2
1
2
0
1
1
0
0
0
0
1
0
2
2
2
0
1
2
1
1
0
0
2
1
0
0
0
0
0
1
0
0
2
0
0
0
0
1
2
1
2
1
2
2
0
0
0
1
1
1
0
0
2
2
0
1
0
0
2
0
0
0
1
1
1
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
1
0
1
2
2
1
0
1
3
0
0
1
1
1
3
0
1
1
0
2
0
0
0
0
1
1
1
0
0
2
2
0
0
2
0
2
2
0
0
2
0
0
2
2
2
0
0
0
0
0
0
1
0
1
2
2
0
1
0
1
0
1
0
0
0
0
2
1
2
2
0
0
0
0
0
0
0
0
0
1
0
1
1
0
2
2
0
2
2
1
2
1
0
0
0
2
1
1
2
0
2
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
2
1
0
2
2
0
0
1
2
1
0
0
1
0
2
0
0
1
0
2
1
1
0
0
0
1
0
0
1
2
1
1
0
0
0
0
4
0
0
1
2
0
1
1
0
2
0
0
0
1
3
1
0
0
0
0
1
0
1
0
0
0
2
1
0
1
0
0
0
1
0
0
0
0
1
0
0
1
1
0
1
0
2
1
1
0
0
0
2
1
1
0
1
1
1
1
0
2
0
1
0
1
2
0
1
0
2
0
0
0
2
0
0
0
0
0
1
0
0
2
1
0
2
0
0
0
0
0
0
2
0
1
0
0
2
2
0
0
0
0
2
1
0
1
0
2
0
0
0
2
0
0
1
0
1
2
1
1
0
0
0
1
1
2
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
2
2
0
0
1
2
0
0
0
0
1
0
0
1
0
2
1
1
0
1
1
0
0
1
2
0
0
0
2
1
0
0
0
1
0
1
2
2
0
0
0
0
1
1
0
0
2
0
2
2
1
0
0
1
0
0
1
1
2
2
0
0
0
1
2
0
0
0
0
2
2
0
0
2
1
2
2
1
1
0
2
0
0
0
1
0
1
0
1
0
0
1
0
0
0
2
2
1
2
2
1
0
2
0
0
0
0
1
0
1
0
0
1
2
0
0
0
0
1
0
0
0
0
1
2
0
0
1
1
0
0
0
2
1
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
2
1
1
1
0
1
0
0
0
0
2
2
1
0
1
2
2
0
0
1
0
2
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
2
0
1
0
0
0
0
1
1
1
0
2
0
0
2
0
0
0
0
0
0
2
0
1
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
1
3
1
0
2
0
0
2
2
0
1
2
2
0
0
1
2
2
0
0
1
1
0
2
2
1
0
0
1
2
1
0
0
0
0
1
2
0
2
0
0
0
0
0
2
2
2
0
0
1
1
1
2
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
1
1
0
1
0
1
0
2
0
2
0
1
0
0
0
2
0
0
1
0
0
3
0
0
0
0
0
1
1
0
2
1
0
1
0
0
2
1
0
0
2
0
0
1
0
1
0
0
1
0
0
0
0
0
2
0
1
0
0
1
2
0
0
1
0
0
0
2
0
1
1
0
0
0
0
1
1
0
0
0
0
0
2
1
2
0
3
0
2
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
2
1
0
0
0
1
1
0
0
2
0
0
0
0
1
0
0
0
1
0
1
1
0
0
2
1
1
2
0
3
0
0
0
0
0
0
2
0
1
0
2
0
2
0
2
0
1
2
0
0
0
0
2
0
1
1
1
2
2
1
2
0
1
3
0
0
0
0
1
0
1
0
1
2
0
1
0
0
0
0
2
2
1
0
0
1
1
1
0
2
2
0
1
1
0
0
0
1
1
2
0
0
4
2
0
0
0
1
0
2
0
1
2
2
0
0
1
0
0
1
0
1
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
1
0
0
1
2
0
2
1
0
0
0
1
0
0
0
0
3
0
1
2
0
2
0
0
0
2
0
0
1
0
0
1
2
0
0
1
1
0
0
0
0
1
0
0
0
0
0
2
0
0
2
2
0
1
1
2
1
0
1
0
0
1
1
2
0
2
4
2
1
1
2
0
0
0
0
1
0
0
2
1
0
0
1
0
0
1
2
2
1
0
1
2
0
1
0
1
3
0
2
1
0
1
0
3
2
2
5
0
0
1
2
0
1
0
1
0
0
0
1
2
2
1
1
0
1
0
1
0
1
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
2
0
1
2
0
0
0
2
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
1
1
0
1
2
2
0
0
0
0
1
0
1
2
2
0
2
0
0
0
0
1
1
1
0
0
1
0
2
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
1
2
0
1
0
3
2
0
0
2
0
0
2
0
2
0
2
1
0
0
1
2
0
1
0
0
1
0
2
2
2
2
0
1
1
0
0
0
0
0
2
0
2
2
0
0
0
1
0
1
1
0
0
0
0
2
0
2
2
1
1
1
1
0
1
2
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
2
2
1
1
2
1
0
0
0
2
1
1
2
3
2
1
0
2
0
0
1
2
2
2
0
0
0
2
0
0
0
2
0
0
2
1
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
1
2
2
0
2
0
13
0
0
0
0
1
2
0
2
0
0
0
2
3
0
0
0
0
1
0
0
1
0
0
2
0
1
0
2
0
0
1
2
0
0
0
2
2
3
0
0
0
0
4
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
1
0
2
0
1
0
0
2
0
0
0
0
2
0
2
0
1
0
1
1
4
2
2
2
0
2
1
0
1
0
2
0
0
0
1
0
1
0
1
1
2
1
0
0
1
2
0
0
0
1
1
0
1
2
0
0
0
0
2
0
1
2
0
1
0
1
0
0
2
2
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
1
1
0
0
1
0
0
1
3
0
0
1
0
0
0
0
2
1
2
0
2
1
1
2
1
1
1
0
0
1
0
2
0
0
1
0
0
0
0
2
2
1
0
1
1
0
1
1
0
0
0
1
2
0
2
0
0
0
1
0
0
0
0
1
0
2
2
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
1
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
3
1
0
0
0
2
0
0
0
1
0
2
2
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
2
1
0
0
1
0
0
3
1
1
0
0
1
1
1
0
0
1
2
1
0
0
1
0
3
0
0
0
0
0
2
2
0
2
1
0
2
0
1
0
2
1
2
2
0
2
0
1
1
0
1
0
1
0
0
2
1
2
0
0
1
1
0
1
1
3
2
1
2
0
1
0
1
2
0
1
0
2
0
0
0
1
1
0
0
1
0
2
1
2
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
1
1
0
2
1
0
0
1
2
0
0
0
0
1
0
0
2
2
0
0
1
0
2
0
3
0
0
0
1
0
0
1
1
1
2
1
0
1
0
2
0
0
0
2
1
2
0
0
0
2
1
0
0
1
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
2
0
2
0
0
1
0
1
0
1
1
1
2
0
0
2
0
0
1
0
1
0
1
2
1
0
0
0
0
0
2
0
0
2
0
0
2
2
1
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
1
2
1
0
0
1
2
0
2
1
2
0
0
2
0
0
2
1
1
0
0
0
0
1
1
2
1
0
2
0
0
0
2
0
2
0
2
3
3
0
1
0
0
0
0
1
0
2
0
0
2
0
0
0
0
2
2
1
1
1
1
0
1
0
0
0
1
0
1
2
1
0
2
1
0
2
0
0
0
0
0
1
0
2
2
2
1
0
0
1
2
0
2
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
2
2
2
3
0
0
1
0
1
0
2
1
0
0
2
1
0
1
2
1
0
0
0
1
1
1
1
0
0
0
1
0
1
0
0
0
1
2
2
0
0
1
0
0
0
1
1
0
1
0
0
2
1
0
3
2
0
2
0
0
0
0
0
0
1
2
0
0
2
0
3
0
0
2
0
1
0
0
0
0
2
0
0
1
0
2
1
1
1
0
1
1
0
0
1
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
1
0
0
1
0
0
0
1
2
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
2
2
1
0
1
0
0
1
0
0
1
0
0
2
0
0
0
0
2
1
2
0
0
0
2
0
0
2
0
2
0
0
0
2
1
0
3
1
1
1
0
0
0
2
1
0
0
0
1
1
0
0
1
0
2
2
0
2
2
0
1
3
0
0
0
0
0
1
0
0
2
1
2
0
3
0
0
0
0
0
2
0
2
2
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
2
2
0
0
2
2
1
2
0
2
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
1
0
2
0
0
0
2
0
0
0
2
1
0
0
1
0
0
2
1
1
1
0
0
1
0
1
1
1
0
0
0
0
1
0
0
1
3
0
1
1
1
0
2
0
0
0
1
2
0
0
2
1
1
1
0
2
1
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
2
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
1
0
4
2
0
2
1
0
2
0
1
0
1
0
0
1
0
1
1
0
1
1
0
0
0
2
2
0
0
2
2
0
0
1
1
0
0
1
0
1
2
1
2
2
0
1
0
0
1
0
2
0
2
4
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
2
1
1
0
2
1
0
0
1
0
2
2
1
0
2
0
0
1
1
1
2
0
0
2
0
0
1
1
0
2
0
2
2
0
3
0
0
1
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
1
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
1
2
0
0
0
1
1
1
0
0
0
1
0
1
0
0
1
2
4
4
0
2
0
1
0
2
2
0
2
0
0
1
2
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
1
1
0
1
0
3
0
1
0
2
1
0
0
1
0
0
0
2
2
1
0
0
0
2
1
0
1
1
1
0
0
0
0
2
1
0
0
0
1
0
1
2
0
0
0
0
2
2
0
1
1
1
2
1
0
0
1
0
0
1
1
1
2
0
0
0
0
2
1
1
0
0
1
2
0
0
2
1
0
0
1
0
2
0
1
0
1
0
0
1
1
0
2
1
0
0
0
1
0
0
1
1
4
3
0
2
0
0
2
0
2
2
1
0
0
0
0
1
0
2
1
0
1
1
1
1
2
0
1
1
0
0
1
1
0
1
2
0
1
0
1
1
0
3
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
1
0
2
1
1
2
0
2
2
0
1
0
0
1
0
0
2
0
1
0
1
0
2
0
0
0
0
1
1
2
2
1
3
2
1
0
0
0
0
2
1
0
2
0
1
1
1
0
2
0
2
0
0
0
1
0
0
0
1
2
0
0
0
0
1
0
0
2
0
1
1
1
1
1
1
0
1
3
0
1
0
2
0
0
2
1
0
2
2
1
1
0
1
1
0
2
0
0
0
0
0
0
2
1
0
2
1
0
0
3
1
0
1
1
0
2
0
1
2
1
2
0
2
0
0
0
1
0
2
0
2
1
0
0
1
0
0
0
2
0
1
0
2
0
0
1
2
1
0
0
0
0
0
0
1
2
1
0
1
1
1
0
2
1
0
2
2
0
2
1
1
0
0
0
1
0
0
2
0
0
1
1
1
2
1
0
0
0
0
1
0
0
2
2
0
0
0
0
0
2
1
0
0
1
2
1
1
0
0
0
0
0
0
1
1
0
0
2
0
1
0
0
1
0
0
2
0
0
0
1
0
0
2
0
1
0
1
0
0
0
1
0
0
0
2
1
0
3
0
1
0
1
0
2
0
2
0
0
1
2
1
0
0
1
0
1
1
0
1
0
0
0
2
0
3
2
2
2
0
2
1
0
0
2
0
0
0
1
0
1
0
0
1
0
0
0
0
3
2
0
2
2
0
0
2
2
1
1
2
0
1
2
1
0
0
1
2
0
0
2
0
1
0
0
1
0
1
0
0
0
1
0
1
2
1
1
1
0
0
0
0
0
0
0
0
1
2
0
1
0
0
2
0
2
0
1
1
2
1
0
1
0
3
0
2
0
0
0
2
1
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
3
2
0
1
0
0
2
1
0
1
0
0
0
1
1
2
0
0
0
0
1
1
1
0
0
2
0
0
2
0
1
1
0
0
0
2
0
0
2
1
1
0
2
0
1
1
0
2
2
2
1
1
1
0
3
1
0
0
0
0
1
2
2
1
0
0
0
0
2
3
1
1
0
0
1
0
3
2
0
0
0
0
0
0
2
1
2
0
2
1
2
0
2
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
2
1
0
2
2
0
0
1
0
2
0
0
0
0
0
4
0
2
2
0
0
0
1
2
2
0
1
0
1
0
2
0
0
2
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
1
0
0
0
1
4
1
0
2
0
0
1
0
0
0
2
0
2
0
0
1
0
0
1
1
0
3
0
0
1
0
1
1
0
0
2
2
0
0
1
1
0
0
2
0
0
1
2
0
0
0
0
0
2
0
0
0
2
0
1
2
0
0
0
0
0
2
2
0
0
1
1
0
1
0
0
1
0
2
2
0
0
0
2
0
0
0
2
2
1
1
0
0
1
1
1
0
2
0
0
0
0
2
2
0
0
1
0
0
1
0
0
0
2
2
2
2
0
1
0
1
0
1
0
0
0
1
0
1
1
0
0
0
2
0
0
2
1
0
2
1
0
0
0
0
1
0
1
0
0
2
0
0
1
0
2
1
0
0
2
0
3
0
0
2
1
0
2
1
0
0
0
0
0
0
0
2
0
0
2
1
0
0
1
2
1
0
1
1
0
0
1
1
0
0
1
3
1
0
1
0
3
1
2
1
0
1
0
0
2
0
1
0
0
0
0
0
2
1
0
2
1
1
1
2
1
0
2
1
1
0
1
1
1
0
1
0
0
0
0
0
2
0
0
0
2
0
0
1
0
3
0
3
1
2
0
0
0
0
1
1
0
0
0
2
0
2
1
2
1
0
1
1
0
0
3
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
1
1
0
2
3
0
1
1
0
0
0
1
0
2
0
1
3
0
2
0
2
0
0
2
0
1
0
0
0
2
0
1
0
0
0
2
2
2
0
1
0
0
2
1
2
2
0
1
1
3
1
2
3
0
0
0
1
2
2
0
2
0
2
0
2
0
1
0
0
0
0
1
0
2
1
1
0
0
0
0
0
1
1
0
0
2
0
0
0
1
0
0
0
0
3
2
1
0
0
2
0
2
0
2
2
2
0
1
1
0
0
1
0
0
0
0
1
0
1
0
0
1
2
1
1
1
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
1
1
2
0
0
1
2
2
1
1
0
0
0
0
1
2
2
0
0
0
0
2
0
1
1
2
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
3
1
2
0
2
2
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
2
0
0
2
3
0
0
0
1
0
2
0
2
0
0
2
0
0
0
0
2
0
0
1
2
0
1
0
0
0
0
1
0
2
0
0
1
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
2
1
1
0
0
1
2
1
0
0
1
0
1
2
0
0
1
0
1
0
2
0
1
2
0
0
2
1
0
2
2
0
1
0
0
1
0
0
0
0
1
1
1
3
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
1
0
0
2
0
0
0
2
0
2
2
0
0
2
1
1
1
0
1
1
0
2
0
0
1
2
2
1
0
1
0
2
1
0
1
1
0
2
1
2
0
2
0
0
0
0
0
1
0
0
2
1
2
0
0
1
0
2
0
1
0
1
0
2
0
2
6
3
0
0
0
2
0
1
1
0
0
0
0
0
0
1
2
1
7
0
0
0
0
2
1
2
1
1
0
0
0
1
0
2
2
1
2
1
0
1
0
1
3
3
0
1
2
0
0
0
0
0
1
2
2
4
0
2
0
1
0
0
0
3
2
0
3
0
0
2
0
2
1
1
0
1
1
2
1
1
0
2
0
1
0
1
0
0
0
2
1
0
0
1
0
0
0
1
1
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
2
1
0
1
0
0
0
0
0
0
0
0
2
1
0
0
2
0
1
0
2
1
1
0
2
0
0
0
0
0
2
0
1
2
0
0
2
0
1
1
0
0
0
0
0
0
0
3
0
0
0
1
0
0
1
0
0
1
0
0
2
1
0
2
0
1
1
0
0
0
0
2
0
2
2
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
2
2
1
1
0
1
0
2
2
1
0
0
0
0
0
1
2
1
0
0
0
0
0
2
1
1
1
0
0
3
1
0
2
2
2
0
0
2
2
0
0
0
1
0
0
0
1
0
0
0
2
0
2
1
0
1
0
2
1
0
0
1
1
1
2
1
0
0
2
0
2
3
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
1
1
2
0
0
0
2
0
0
2
1
0
1
2
0
0
1
2
2
0
1
0
0
2
1
1
0
1
1
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
1
1
0
1
1
2
0
0
0
1
0
0
1
0
6
0
0
0
1
0
0
0
0
2
2
0
1
0
0
0
1
0
0
2
2
1
0
2
0
0
0
0
0
0
0
2
1
0
2
0
2
0
0
0
1
0
0
0
0
1
0
1
0
0
0
2
0
2
0
0
0
1
2
0
2
0
2
1
0
1
0
2
1
0
1
0
1
0
0
2
0
0
2
2
2
0
0
1
1
1
0
0
1
2
2
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
2
0
0
1
0
0
2
1
2
1
0
0
2
0
3
0
2
2
1
0
2
2
0
0
2
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
2
0
1
1
0
2
2
2
0
1
0
1
4
0
1
2
0
1
1
0
1
0
0
2
1
0
2
0
0
2
1
0
2
0
3
0
0
0
1
1
1
0
0
1
3
0
0
1
0
0
0
3
0
0
2
0
2
1
0
2
1
0
0
2
0
0
0
1
1
0
0
0
2
0
0
1
2
0
1
0
1
0
0
0
2
0
1
0
0
1
2
0
1
0
1
0
0
0
0
3
0
0
0
0
0
0
1
0
1
1
1
0
1
2
1
0
0
0
2
1
1
1
0
1
0
0
0
0
0
1
2
1
0
0
0
1
0
0
2
0
0
0
0
0
2
1
0
0
2
0
0
1
0
0
1
0
0
0
1
2
0
0
0
0
0
2
2
1
0
2
0
2
0
0
1
2
0
2
0
0
0
1
1
3
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
1
1
0
0
0
1
0
1
2
0
1
1
2
0
1
0
0
0
0
0
1
2
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
2
1
0
0
2
0
3
1
2
2
0
3
0
1
3
0
0
0
0
0
2
1
1
2
2
1
0
0
2
0
1
0
1
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
2
0
1
0
2
0
1
0
0
2
0
2
0
0
2
0
1
2
0
1
1
0
0
2
0
1
0
2
0
0
0
0
2
0
0
1
0
2
0
0
0
1
2
2
0
1
0
0
1
1
1
2
1
1
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
3
0
1
0
0
2
0
2
0
0
0
2
0
1
1
2
0
1
0
0
0
1
0
0
0
0
0
1
1
2
1
0
0
2
0
0
2
2
2
0
0
0
0
1
1
2
0
0
0
0
1
0
0
1
2
1
5
0
0
1
1
2
0
0
0
0
0
2
2
1
0
2
0
0
0
0
0
0
0
1
0
2
1
0
2
0
1
2
1
0
0
1
2
0
0
2
1
0
1
5
0
0
1
0
0
0
0
2
1
0
1
0
1
0
2
1
0
2
0
0
0
2
0
1
0
1
0
2
0
2
0
0
0
0
2
2
2
0
1
2
0
0
0
1
0
0
0
0
0
0
2
2
0
1
0
3
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
1
0
2
0
0
0
1
0
0
1
0
0
2
0
2
0
2
0
0
1
0
0
0
0
2
0
0
1
0
0
0
2
0
2
2
0
2
2
0
0
0
0
2
1
1
0
1
2
0
0
0
1
0
1
2
0
2
1
0
2
1
0
0
0
0
2
2
0
1
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
3
1
0
0
1
0
0
0
0
1
0
2
0
1
2
1
0
0
1
0
0
0
1
1
1
0
1
1
2
2
0
0
0
1
2
0
0
4
0
0
1
0
0
1
2
1
2
0
1
0
2
0
0
1
0
1
0
1
0
0
1
2
0
3
1
2
1
1
1
0
0
5
1
1
0
1
0
0
0
0
0
0
3
2
0
0
0
5
0
1
0
2
1
0
1
0
1
0
2
1
0
2
1
0
0
2
2
0
0
6
1
2
0
1
0
0
1
1
2
1
0
1
3
0
0
0
1
2
0
0
0
0
0
0
0
2
1
0
2
1
0
2
2
1
0
1
1
0
2
0
1
0
0
0
0
0
0
2
0
2
0
0
2
0
2
0
2
2
1
0
0
1
1
1
2
2
3
1
0
0
1
1
1
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
2
1
0
0
1
0
2
0
0
0
0
2
0
2
1
0
0
0
2
0
3
1
0
1
0
0
1
0
0
0
1
2
0
2
1
0
0
0
0
0
0
1
0
1
1
1
1
1
1
0
1
0
1
0
1
2
1
1
1
0
0
0
1
0
0
0
0
2
2
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
1
0
2
1
0
0
2
3
0
0
0
0
2
3
0
2
0
1
2
1
2
2
0
1
0
1
0
0
1
2
1
0
2
2
0
0
2
2
0
2
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
2
1
0
2
0
2
0
0
0
0
0
0
1
1
2
0
0
0
1
0
0
2
0
0
1
2
2
0
0
0
0
2
0
0
0
0
1
0
0
0
2
2
0
0
1
1
2
0
0
1
1
2
0
0
0
2
0
1
0
2
1
2
1
0
0
2
0
0
0
2
0
2
1
0
2
3
0
0
1
2
0
1
0
1
1
0
2
1
2
2
2
0
0
1
1
2
1
0
0
0
0
1
0
2
2
2
0
0
0
0
2
1
2
1
0
0
1
0
0
0
1
0
2
0
0
0
0
0
2
0
0
3
0
0
1
0
0
0
0
1
1
2
0
2
2
1
0
0
0
1
0
0
0
0
1
1
1
0
1
1
0
1
1
0
0
2
2
1
2
0
1
1
1
0
0
1
0
1
0
1
0
1
0
0
2
2
1
0
0
0
0
1
0
0
0
0
0
2
1
2
0
0
1
1
2
0
1
0
2
1
1
1
1
7
0
2
1
1
0
0
2
0
2
0
0
0
1
0
1
2
7
4
0
0
0
1
2
0
0
0
0
1
1
0
0
0
0
0
2
1
0
1
0
0
2
2
0
1
0
0
0
1
1
2
0
0
0
1
0
1
0
0
0
2
1
0
0
0
1
2
1
0
0
0
0
1
0
2
0
0
0
3
2
0
2
1
0
0
0
1
1
1
0
0
1
1
3
0
0
0
2
1
1
0
0
1
2
0
0
0
1
2
0
0
0
1
2
0
0
0
0
1
0
1
1
1
0
0
1
2
0
0
1
0
1
0
0
0
0
0
1
1
2
0
0
2
0
0
1
0
2
2
2
0
1
0
2
0
0
0
0
0
0
0
2
1
0
1
0
0
2
0
3
0
2
0
0
0
2
0
1
1
0
0
0
2
0
1
0
1
0
1
0
0
2
1
2
1
0
1
1
0
1
2
2
2
1
2
1
0
0
2
0
2
1
1
2
2
0
0
2
0
2
0
0
0
1
3
1
1
1
3
1
0
0
3
1
0
0
0
0
2
2
0
1
0
2
1
0
0
0
2
0
2
0
0
2
0
0
2
0
1
1
1
1
1
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
2
0
0
0
0
0
2
1
1
1
1
2
0
2
0
0
1
2
1
2
2
0
0
1
1
1
0
2
0
2
1
0
2
0
0
1
0
3
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
1
0
0
1
2
0
1
0
2
0
0
0
0
3
0
0
2
1
0
0
1
0
2
3
0
0
0
0
2
1
0
0
1
0
1
2
5
0
0
2
0
0
1
1
4
0
0
2
0
3
0
0
0
2
0
1
0
2
0
2
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
2
1
1
0
2
1
2
2
1
1
0
2
0
0
0
0
1
2
2
2
2
2
0
1
2
1
1
1
0
0
1
0
1
2
0
0
1
1
1
0
2
0
0
0
0
1
2
2
2
0
1
0
0
0
0
2
0
0
1
1
0
0
2
2
0
2
3
2
2
0
2
0
0
0
1
0
2
1
0
1
1
0
1
0
0
0
1
0
1
0
2
1
2
0
0
0
1
0
1
0
1
0
0
1
2
1
0
0
0
2
1
1
0
0
1
0
1
1
1
0
2
1
0
0
2
0
2
0
1
0
2
0
1
2
2
0
0
0
2
0
2
1
0
2
1
0
1
1
0
0
1
2
0
1
0
2
1
0
1
0
2
0
2
1
0
0
0
0
0
2
0
2
3
0
0
0
0
0
2
2
0
0
0
0
1
2
0
2
0
0
1
2
1
2
1
0
2
1
0
0
2
0
3
1
1
0
0
2
0
1
1
1
2
0
1
2
0
2
0
0
1
0
1
0
1
2
0
1
0
2
1
2
2
1
0
0
1
0
1
2
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
2
0
0
0
1
1
0
0
0
1
2
0
1
0
1
0
0
0
0
2
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
2
0
0
0
1
1
0
1
2
1
2
4
0
0
2
0
0
0
3
0
0
0
1
2
0
0
1
1
0
2
1
0
1
2
2
0
0
0
1
1
1
0
2
1
1
0
1
2
1
4
0
0
1
0
0
1
1
2
0
2
0
1
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
2
2
1
1
0
3
2
0
0
1
3
1
0
2
0
0
0
1
3
0
2
0
1
1
2
0
0
0
0
1
2
1
0
2
0
1
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
2
0
2
0
2
0
1
0
1
1
1
0
0
0
0
0
1
1
0
2
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
3
0
0
0
2
0
2
0
2
0
1
0
0
1
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
2
1
0
1
0
2
0
0
0
2
0
0
0
1
0
0
2
1
2
2
1
1
2
0
1
0
0
0
0
1
1
0
0
0
0
2
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
1
2
0
0
1
2
0
0
1
1
1
3
0
0
2
0
0
3
1
0
0
1
3
1
0
0
0
1
0
2
1
0
2
0
1
0
2
0
1
0
0
2
2
1
0
1
0
2
0
0
1
0
0
1
1
1
1
0
2
2
1
0
2
2
1
1
0
0
1
1
0
0
1
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
2
2
0
0
1
1
0
0
1
0
0
0
0
0
2
2
1
1
0
0
1
0
0
0
1
2
2
1
0
2
0
0
2
0
2
1
2
0
1
1
0
2
2
2
2
0
1
0
0
0
0
1
2
0
0
1
0
0
2
2
2
0
0
0
0
0
0
1
0
0
0
0
1
1
2
2
0
1
0
1
0
1
0
2
0
2
0
1
0
0
1
0
2
0
0
1
2
2
0
0
0
1
0
0
1
2
1
0
0
4
0
0
0
0
0
0
0
1
0
3
0
0
2
0
0
1
1
2
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
1
0
0
0
1
1
2
2
2
0
0
1
2
0
0
2
0
0
0
1
0
2
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
1
0
2
0
2
0
0
2
0
0
0
0
2
1
0
0
0
0
1
1
0
1
1
0
1
2
0
1
1
0
1
1
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
1
0
1
0
2
1
2
1
1
1
2
0
0
0
0
0
0
0
2
1
0
0
1
2
2
2
2
0
0
0
2
0
1
0
1
0
0
0
2
0
2
0
0
0
1
0
1
0
0
1
1
0
0
2
1
1
0
0
0
2
0
2
0
0
2
0
1
1
0
2
0
0
1
0
0
0
0
1
2
1
0
1
2
1
0
1
0
2
0
0
0
0
0
1
3
0
2
1
0
1
0
1
1
0
1
0
0
0
2
0
0
0
1
0
0
0
2
3
2
0
0
0
2
0
0
0
1
1
0
2
0
1
1
1
1
1
0
2
0
0
1
0
2
0
0
1
0
0
0
1
0
1
0
2
2
0
0
0
1
0
1
0
1
1
2
0
3
0
0
1
1
0
1
0
0
1
1
1
1
1
2
1
0
0
0
0
2
0
1
1
0
1
1
0
0
0
0
2
0
2
3
2
0
0
0
1
0
0
1
0
0
2
0
0
0
1
2
1
2
1
0
1
2
1
2
2
2
2
2
0
2
0
0
0
2
1
0
1
1
1
0
1
1
0
2
2
0
0
2
0
1
1
0
0
0
2
1
2
0
1
2
0
0
0
0
0
0
2
0
0
0
1
0
2
0
2
0
1
0
0
0
0
2
0
0
0
1
0
0
2
1
1
0
1
0
0
2
0
0
2
2
1
0
1
2
1
0
0
2
1
0
0
0
2
1
0
0
0
0
0
1
0
0
2
0
0
1
0
2
0
1
1
2
2
0
0
0
0
0
0
0
1
1
0
1
1
0
2
0
0
0
4
0
0
2
1
0
0
1
0
2
0
0
1
1
1
1
1
0
0
1
0
0
1
0
0
0
2
1
2
0
0
0
0
2
0
0
0
0
0
0
0
1
2
2
0
0
1
1
2
0
1
1
0
0
0
0
0
0
0
1
0
2
0
1
2
1
1
0
0
0
2
0
0
0
0
0
0
1
1
1
1
1
1
2
0
0
0
2
2
2
0
3
0
1
1
0
0
0
0
0
2
1
0
2
0
0
1
0
0
0
2
0
1
2
0
0
2
1
1
3
1
0
2
2
1
0
1
0
1
0
0
0
1
0
0
1
1
0
0
0
2
2
1
0
1
0
2
0
0
0
1
2
3
1
1
0
0
0
0
1
1
0
0
1
0
1
0
0
2
1
0
1
1
1
2
0
0
0
1
0
0
1
0
0
1
1
2
0
1
1
0
1
2
0
1
2
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
1
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
2
1
0
0
0
1
0
1
1
0
0
0
0
2
1
2
0
2
0
0
2
1
1
1
0
1
1
0
0
0
2
0
1
1
0
0
0
1
0
0
1
0
1
1
0
2
1
2
0
0
1
0
0
0
0
1
0
2
2
1
0
0
1
0
1
0
2
1
0
0
0
2
0
1
0
1
1
1
2
0
0
1
0
0
0
0
1
0
1
0
1
2
0
0
1
0
1
0
0
0
1
1
0
0
2
2
0
0
1
0
0
2
0
1
2
0
0
1
0
1
0
2
2
0
2
0
2
0
0
0
0
2
1
1
0
0
1
0
0
1
0
2
1
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
2
0
1
0
0
0
0
0
0
2
2
2
2
1
1
1
0
0
0
2
2
3
0
3
0
0
0
1
0
0
1
0
0
0
2
2
0
0
0
1
0
1
2
0
0
1
0
0
0
2
1
0
2
2
1
1
0
0
1
0
1
0
1
1
0
0
0
1
1
1
2
0
1
2
0
1
0
0
1
2
0
0
0
0
2
1
0
1
1
2
0
1
0
1
0
0
0
0
2
0
1
0
1
0
0
1
0
1
2
1
1
0
0
0
4
1
0
1
0
0
1
1
0
2
2
1
1
2
2
0
0
0
1
2
1
0
0
0
1
0
0
1
2
0
0
0
0
4
0
0
1
1
1
0
0
4
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
2
2
0
0
0
0
0
0
3
1
0
1
1
1
0
1
2
0
0
0
0
1
0
2
1
0
3
2
1
2
0
0
0
0
3
0
1
0
0
1
0
2
0
0
2
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
3
0
2
2
0
2
0
1
0
2
0
0
1
2
1
2
2
0
1
0
1
2
1
0
0
0
2
1
2
1
0
1
0
2
2
3
0
2
0
2
0
2
1
0
1
0
2
0
2
1
0
1
0
2
2
0
0
0
0
0
0
1
1
2
1
2
0
2
0
0
0
0
0
1
0
2
0
0
0
0
2
1
2
0
0
0
1
1
2
1
1
0
0
2
1
0
0
2
0
0
3
0
0
0
1
0
0
0
1
1
0
0
1
1
2
0
0
1
0
0
1
0
0
1
0
0
1
0
2
2
0
3
0
1
1
0
0
2
0
1
0
0
1
0
0
0
0
0
0
2
2
0
0
0
1
2
0
1
1
1
2
0
1
0
2
0
2
1
1
0
0
1
0
0
1
0
0
3
0
2
2
2
0
0
1
1
0
1
1
3
0
0
0
1
0
0
0
2
1
0
0
1
1
0
0
2
0
0
1
0
0
0
0
0
2
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
1
1
2
1
1
0
0
0
0
0
2
1
1
0
2
1
0
0
1
0
1
0
1
0
2
0
0
2
1
0
0
0
2
0
0
0
0
0
1
2
0
2
1
0
1
1
0
0
0
1
2
1
0
0
0
0
3
0
4
2
0
0
1
0
3
0
0
0
2
0
0
0
1
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
1
1
0
1
0
0
0
2
0
1
1
1
1
2
0
3
1
0
0
0
0
1
1
1
2
1
1
2
0
1
0
0
2
0
0
0
0
0
0
1
1
1
3
0
2
0
2
2
2
2
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
1
1
0
0
1
0
0
1
2
1
0
1
0
3
0
1
2
2
2
1
0
1
1
0
1
0
0
2
3
2
0
1
1
1
0
0
1
0
0
2
0
5
1
0
2
1
0
1
0
0
1
1
0
2
0
0
2
2
1
3
1
1
0
1
1
0
2
0
0
0
0
0
1
0
0
1
2
0
2
3
0
0
2
0
1
0
0
1
1
1
0
0
2
1
1
0
0
0
0
0
1
1
2
1
1
0
0
0
2
0
0
0
1
0
0
1
2
2
0
2
0
1
0
1
1
0
1
0
1
1
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
2
2
0
0
0
0
0
1
2
2
0
0
2
1
0
2
0
1
0
0
2
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
2
2
1
1
2
1
0
0
0
1
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
1
2
2
0
0
1
2
0
0
0
1
0
2
1
0
1
2
0
0
0
2
0
3
1
2
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
2
1
0
1
0
4
0
3
0
0
2
1
2
0
1
2
2
1
1
0
0
0
0
0
0
1
0
1
0
0
1
1
3
2
2
1
0
0
1
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
4
0
0
0
1
0
0
0
0
2
0
0
0
1
0
2
1
0
3
1
0
0
2
1
1
1
0
0
2
1
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
2
1
0
0
0
0
2
0
0
3
1
2
4
1
0
1
0
0
2
0
0
2
2
0
1
0
0
1
0
0
0
0
2
0
2
1
0
0
2
0
0
0
0
0
1
0
0
1
2
0
0
2
0
0
0
0
1
0
2
2
1
0
0
0
0
2
0
1
0
0
0
2
0
1
0
0
2
0
1
0
1
1
1
1
1
1
0
0
0
0
0
0
1
0
2
1
1
0
1
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
2
0
2
0
0
3
3
0
2
0
0
0
0
2
0
1
1
0
0
0
1
1
1
0
0
0
0
0
0
1
1
0
2
0
0
1
2
1
2
2
0
1
2
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
2
0
0
0
1
0
2
1
2
2
0
0
1
0
0
2
1
1
0
0
1
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
2
1
0
3
0
0
2
1
0
0
1
0
0
0
0
2
0
2
0
1
3
0
0
1
0
0
0
1
1
0
0
2
0
0
0
0
0
1
1
0
0
0
1
1
0
1
2
0
2
2
0
0
0
1
0
2
2
2
1
0
1
1
1
1
0
0
2
1
0
0
0
4
0
0
2
0
0
1
1
1
2
0
0
1
0
0
0
2
2
1
0
0
0
0
2
1
0
0
0
0
0
1
2
0
1
1
0
0
2
0
0
2
0
1
2
0
0
0
1
0
1
0
0
1
1
2
0
0
1
0
0
1
0
0
2
0
0
2
0
3
2
1
0
0
0
0
2
1
2
1
1
1
0
0
0
0
0
1
0
0
1
0
2
0
1
0
0
1
2
0
0
0
0
2
2
0
2
2
1
1
0
1
1
1
0
1
1
0
0
0
1
0
1
0
0
0
2
0
0
0
0
2
0
1
0
0
1
0
2
0
1
1
3
0
0
1
0
1
2
0
2
2
0
2
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
1
1
0
0
2
1
0
1
0
2
1
2
0
0
2
1
2
0
2
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
1
1
0
2
0
0
2
2
0
1
0
2
0
1
0
0
2
1
2
0
0
1
2
1
2
0
2
0
0
1
2
1
0
0
2
0
0
0
1
0
1
0
0
0
2
1
0
1
2
2
0
0
0
1
1
0
2
0
0
0
0
0
1
0
0
1
1
0
2
1
1
0
0
0
0
1
2
0
2
0
2
2
0
0
0
0
0
1
1
0
1
1
0
0
1
0
1
2
2
2
0
0
1
1
2
2
0
0
0
0
1
0
0
1
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
2
2
0
0
1
0
2
0
1
0
0
0
2
1
1
1
2
1
0
2
0
1
0
0
0
2
0
0
1
0
2
1
2
2
2
2
0
2
3
0
1
0
0
0
0
0
1
0
0
1
3
0
0
0
1
2
2
0
1
0
0
0
0
3
0
0
1
2
0
0
0
2
0
0
2
2
2
0
0
0
0
0
0
2
0
1
1
0
0
0
0
2
0
0
0
0
0
1
2
1
0
3
0
1
2
0
2
1
0
0
0
2
2
0
2
0
1
2
0
0
2
2
0
0
1
2
0
1
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
1
0
1
2
0
0
0
0
0
0
2
0
0
2
0
0
1
1
0
2
0
2
0
0
0
0
1
1
1
0
0
0
2
1
2
2
0
2
1
1
1
0
2
0
0
2
0
0
2
1
0
0
1
0
1
0
1
1
0
0
1
0
0
1
1
1
1
1
0
1
0
1
0
0
0
2
1
1
0
0
0
0
1
0
0
0
0
2
0
0
0
2
2
0
1
0
2
1
1
0
2
1
2
1
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
2
1
0
0
0
0
0
0
1
0
1
2
0
0
0
2
1
2
0
2
2
0
0
0
2
1
0
1
0
0
0
2
1
0
1
0
1
0
0
0
3
0
0
1
2
0
0
0
0
1
0
0
1
0
0
0
1
2
1
2
0
0
0
0
2
0
0
3
2
0
0
1
0
1
1
0
2
0
0
1
1
1
0
0
0
0
1
2
0
1
1
1
2
0
2
0
1
0
1
0
0
1
0
0
2
1
0
0
2
0
0
0
2
1
1
1
0
0
1
1
0
0
2
0
1
0
0
1
2
5
0
0
1
1
0
2
1
0
1
2
1
0
2
0
2
3
0
1
1
2
0
0
0
0
1
0
2
0
1
2
2
2
1
0
0
1
2
1
0
1
0
1
1
2
4
0
1
1
2
1
0
0
1
0
0
0
2
0
1
1
4
0
0
1
1
1
2
0
0
0
1
0
2
2
1
2
0
1
2
2
0
0
2
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
5
0
1
0
0
0
2
0
0
1
0
0
2
0
2
1
2
0
3
0
1
0
2
0
1
0
0
0
1
0
0
0
2
0
0
0
2
2
3
2
2
0
0
0
0
0
1
0
1
2
1
2
0
1
0
0
0
2
1
0
0
1
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
2
0
1
0
3
0
0
2
0
2
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
2
1
0
0
0
0
1
0
0
1
1
2
0
2
0
0
2
0
0
0
0
0
0
2
0
1
0
2
0
1
1
2
0
2
1
1
0
2
0
0
1
1
0
2
0
1
1
0
2
0
0
0
1
0
2
0
2
0
1
2
2
2
2
1
0
2
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
3
2
0
0
2
0
0
0
1
1
1
1
0
0
2
0
0
0
2
0
1
0
4
2
0
0
0
1
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
2
1
0
0
1
1
0
0
0
0
0
1
0
0
1
2
0
2
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
2
2
1
2
1
0
1
0
2
2
0
1
0
0
0
0
1
0
1
1
0
1
1
0
0
2
1
0
0
0
1
2
0
1
1
0
1
0
0
0
0
0
0
0
0
3
2
0
0
0
0
1
0
2
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
1
1
2
0
1
0
0
3
0
0
0
0
0
0
0
0
2
0
2
0
2
1
0
0
1
2
2
1
1
0
0
0
1
0
1
3
1
0
1
0
1
0
1
0
0
1
1
2
0
1
0
1
1
0
2
1
0
1
0
0
0
2
1
0
0
0
1
2
0
1
0
0
1
0
0
1
2
0
0
1
0
0
0
1
0
2
1
2
0
0
0
0
0
0
1
1
0
0
0
1
2
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
2
0
0
0
1
2
0
0
1
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
1
0
1
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
1
0
2
0
2
1
0
2
0
1
2
1
0
1
2
2
0
0
1
0
0
0
0
0
2
2
10
2
0
2
0
0
0
2
0
0
3
1
2
2
0
0
0
1
1
2
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
1
0
1
0
1
0
0
3
2
2
1
2
0
2
1
0
4
2
1
2
0
1
0
0
0
1
2
1
0
1
0
1
0
2
0
1
0
0
0
2
1
0
0
0
0
1
0
1
0
1
0
0
0
1
0
1
0
1
0
0
1
1
2
0
0
0
0
0
1
0
1
0
0
0
2
0
1
0
0
1
2
2
0
2
1
0
2
0
0
0
0
1
0
2
0
0
2
0
0
0
0
2
0
1
1
0
0
0
0
0
1
1
0
1
2
0
2
0
1
3
1
2
2
0
0
1
1
0
0
2
0
4
0
0
1
0
0
0
0
0
1
1
1
0
0
0
1
0
0
1
0
2
1
0
2
2
1
0
0
0
0
0
1
3
0
1
1
0
2
2
1
1
1
0
0
0
1
1
0
1
2
2
0
1
0
2
0
0
2
0
2
2
1
0
3
3
0
2
0
0
0
0
2
0
0
0
1
1
0
1
0
1
0
0
2
0
3
0
2
0
1
2
1
0
1
1
1
0
2
0
1
0
1
0
1
0
0
0
1
1
0
2
2
2
1
1
0
2
2
0
2
2
2
2
0
0
1
0
0
0
2
0
0
0
0
2
0
0
2
1
1
1
2
0
2
0
1
3
0
0
0
0
0
0
2
0
2
1
0
2
0
2
0
0
0
0
1
0
0
0
1
0
1
0
0
1
2
1
0
2
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
2
1
0
0
0
0
0
1
0
2
1
0
0
0
0
1
0
1
2
0
1
0
2
0
0
0
0
2
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
2
0
2
1
0
0
0
0
1
1
1
1
2
0
2
0
2
0
0
0
1
2
2
0
0
0
0
0
0
1
1
1
2
1
1
2
0
0
0
0
2
2
0
2
0
1
3
1
0
2
2
2
1
0
0
2
0
2
0
1
2
0
2
0
0
1
0
1
0
1
0
0
0
0
1
1
0
1
0
2
1
0
2
0
2
2
2
1
2
0
0
0
2
2
3
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
1
0
0
2
0
1
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
1
0
1
1
0
0
2
1
0
0
0
2
0
0
1
0
1
1
0
0
0
2
1
0
0
2
0
1
0
0
0
1
0
0
2
2
0
0
0
1
1
0
0
2
0
0
0
0
2
0
0
1
0
1
0
0
0
3
1
0
0
2
0
0
2
1
1
1
1
0
0
0
0
0
0
2
1
0
0
0
1
0
1
0
0
0
0
0
1
1
0
1
1
3
1
2
0
0
1
2
0
0
0
1
0
2
0
0
2
1
2
2
0
0
0
0
0
0
0
2
0
0
2
1
0
6
2
1
2
1
0
2
0
0
0
1
0
0
1
1
1
0
2
0
1
0
0
0
1
0
1
1
2
0
0
0
0
0
1
0
1
1
2
0
2
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
1
2
1
0
0
0
0
0
2
2
0
1
0
2
0
0
1
1
1
0
0
4
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
2
2
2
1
0
1
0
2
1
2
0
0
1
1
2
0
0
1
0
1
0
1
0
1
2
2
0
0
2
0
0
0
0
0
1
1
2
0
0
0
0
1
0
1
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
1
2
0
0
0
0
1
2
0
0
1
1
1
0
0
0
2
1
0
0
5
0
1
0
0
0
1
0
1
0
0
0
0
2
0
0
3
1
0
2
0
0
0
1
0
1
1
1
0
1
0
0
0
0
0
1
0
1
0
0
1
1
0
0
2
1
1
0
0
1
0
1
0
2
1
0
1
1
2
0
0
1
0
0
3
0
0
1
0
0
0
0
1
0
1
0
1
0
0
2
1
2
0
2
2
0
2
0
0
0
0
0
0
1
0
1
2
0
2
0
2
0
0
1
2
0
0
2
0
1
0
1
0
1
0
2
0
1
0
0
2
2
0
0
1
0
0
1
0
0
1
0
1
2
0
0
2
1
0
2
0
0
1
0
0
0
0
2
0
1
0
2
0
2
1
2
0
1
2
1
0
1
1
0
1
0
1
2
2
0
2
1
0
0
1
0
0
2
0
0
2
1
1
1
0
1
0
1
0
0
0
0
0
1
2
2
1
1
2
2
3
0
0
0
0
0
0
2
1
1
0
0
2
2
0
0
0
0
0
0
2
0
1
2
2
0
2
0
0
2
1
2
0
1
0
2
0
1
0
0
1
1
1
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
2
2
0
0
0
0
0
1
0
2
0
3
2
0
0
0
3
0
1
1
1
2
0
0
1
0
0
0
0
1
3
0
0
0
0
0
2
1
1
0
1
0
0
0
0
0
1
0
1
2
2
2
0
1
5
0
2
0
1
2
1
0
2
1
0
0
0
0
0
2
0
0
2
1
0
0
1
1
3
0
2
0
2
1
0
0
0
1
0
6
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
1
3
0
3
0
0
0
2
3
0
0
0
0
0
3
0
1
0
2
0
0
1
0
0
1
1
0
0
1
0
2
0
1
1
2
0
0
0
2
1
2
0
2
0
2
0
0
0
0
2
2
1
1
0
0
0
2
2
2
1
0
0
1
0
0
0
0
0
2
0
2
2
1
0
0
2
1
2
0
0
1
1
1
0
1
2
2
1
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
2
1
1
0
2
1
0
2
1
0
0
1
4
2
1
1
0
2
1
0
1
0
0
0
0
0
0
2
0
0
2
0
1
0
2
2
0
2
2
0
0
2
2
1
1
2
0
0
0
0
0
0
0
0
2
0
2
2
0
0
1
0
0
2
0
1
0
0
2
0
0
0
0
2
0
2
1
1
0
2
0
2
0
0
0
0
0
0
1
2
2
0
1
2
1
0
0
0
0
0
1
0
1
1
4
1
1
0
0
2
0
0
1
1
0
0
2
1
0
0
1
2
0
1
1
0
2
0
2
1
2
0
0
0
2
1
0
1
1
0
1
2
1
2
0
0
0
1
1
0
0
0
1
1
0
1
1
0
1
2
0
0
0
2
1
1
0
2
0
2
0
2
2
0
0
1
1
0
0
2
0
1
0
1
2
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
1
1
0
0
0
0
0
1
2
2
1
1
0
1
0
0
0
2
1
1
2
1
2
0
0
0
2
0
2
2
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
1
0
2
1
2
0
1
2
0
0
1
0
0
0
1
1
1
1
0
2
2
1
0
0
0
2
1
1
1
1
0
1
0
1
0
0
1
0
0
2
0
0
1
1
1
2
1
2
0
0
0
0
2
0
0
2
0
2
3
2
1
1
0
1
2
0
0
0
2
0
0
0
0
1
0
1
0
2
0
1
0
0
3
2
1
1
0
0
0
1
0
0
2
2
1
0
1
0
0
1
0
0
1
0
2
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
2
0
1
1
2
1
0
0
1
0
1
0
0
2
2
0
2
0
0
2
0
0
0
2
1
0
1
0
2
2
0
0
1
0
1
0
0
0
2
0
2
2
2
1
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
1
1
2
2
0
1
0
2
0
0
2
1
2
1
1
0
0
0
3
2
1
0
1
2
0
2
1
0
0
0
0
2
1
0
16
0
1
3
3
0
0
0
0
1
0
1
1
1
0
2
0
1
0
1
2
1
2
2
1
0
1
0
0
0
2
1
0
2
0
0
2
1
4
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
2
1
1
0
0
0
0
0
0
0
1
1
1
0
1
2
2
0
0
0
3
0
0
0
0
2
1
2
2
1
0
0
2
1
0
0
0
4
0
0
0
0
0
1
2
0
1
0
3
0
2
2
0
0
0
1
0
2
1
0
1
0
0
0
0
2
1
0
1
0
2
1
0
0
1
0
0
0
1
0
0
0
0
1
0
2
1
0
0
2
1
0
2
0
1
0
1
0
0
1
0
2
0
2
0
2
0
1
0
1
0
0
0
1
0
0
0
0
2
2
0
1
0
2
0
0
1
2
2
1
0
0
1
2
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
1
2
0
0
1
0
2
1
2
0
2
0
0
1
1
1
1
1
2
2
0
0
0
1
1
0
0
1
2
0
1
0
2
6
2
0
1
1
0
0
2
0
0
0
0
0
0
0
2
2
0
0
3
0
2
1
0
1
1
1
0
2
2
0
1
2
2
0
0
1
1
0
0
2
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
3
0
0
1
2
1
0
0
0
0
0
1
1
1
2
0
0
2
1
0
1
0
2
0
2
0
0
0
0
0
2
0
0
0
0
2
0
1
0
2
0
0
0
1
1
2
0
1
0
2
0
0
0
0
2
2
0
0
1
1
0
1
1
0
1
0
0
1
1
1
0
0
0
0
2
0
0
2
0
0
1
0
0
2
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
2
1
0
0
0
2
1
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
1
1
1
0
0
1
0
0
1
0
0
1
0
0
2
2
0
2
3
0
0
0
0
0
1
1
0
0
1
5
2
1
2
1
1
1
0
0
0
1
1
1
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
2
0
1
2
1
0
2
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
3
0
0
0
1
0
1
1
0
2
1
1
2
2
1
1
0
0
0
1
0
1
1
2
1
2
1
0
2
1
0
3
0
0
1
2
0
0
1
1
0
2
2
1
1
0
0
0
2
2
0
0
0
2
1
1
0
1
0
0
2
1
2
2
0
2
3
1
0
0
0
0
0
2
1
0
0
0
2
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
1
2
1
0
0
2
0
0
2
0
0
1
2
2
0
1
1
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
2
0
0
0
0
1
0
0
1
2
1
0
2
1
1
0
0
0
3
0
0
0
1
1
0
1
1
0
2
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
3
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
2
0
1
2
2
1
0
0
1
0
2
0
0
0
0
0
1
2
1
0
0
2
0
0
2
1
1
2
2
0
0
1
1
0
0
1
1
0
0
2
1
0
0
1
2
0
0
1
2
0
1
1
1
1
0
0
0
1
2
0
1
0
0
1
0
2
2
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
1
0
0
0
0
1
0
0
2
0
0
2
0
1
0
0
1
1
0
0
1
1
1
1
0
0
1
1
1
0
1
0
0
2
0
1
1
0
0
0
1
0
0
0
0
3
1
1
0
3
0
0
0
0
0
1
0
3
2
1
1
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
1
1
0
0
0
0
2
0
2
0
0
2
2
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
1
2
0
2
2
0
0
0
0
1
0
0
0
1
1
0
0
0
1
1
0
2
0
1
1
1
0
0
1
2
0
2
0
1
0
0
1
0
1
0
0
0
0
0
2
0
0
1
1
2
0
0
0
1
0
2
2
2
0
2
0
0
2
1
0
0
1
3
1
1
0
0
0
1
1
1
0
0
0
0
1
0
2
1
0
0
1
0
2
1
0
0
2
0
0
1
1
0
2
0
0
2
0
2
0
2
0
3
0
1
1
0
0
0
3
2
1
0
2
0
1
1
1
1
0
1
3
0
0
2
2
1
0
0
2
2
0
2
2
2
0
0
1
0
0
2
0
0
0
1
0
1
3
2
0
2
0
0
2
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
2
2
0
0
1
2
2
0
0
0
2
0
0
1
4
1
0
2
1
0
2
0
0
0
0
0
3
0
0
0
2
2
0
0
0
0
2
0
0
2
1
0
0
0
2
0
1
0
0
0
2
3
0
1
1
1
0
0
0
0
3
0
1
0
2
2
0
0
2
0
0
1
2
0
0
0
2
1
0
0
0
3
0
1
0
0
0
0
0
1
1
2
0
0
0
0
1
1
0
1
1
0
0
2
1
1
1
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
1
0
1
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
3
1
0
0
0
1
2
0
1
2
1
0
0
0
1
2
1
1
1
0
0
0
0
1
1
0
1
1
1
0
0
2
1
1
0
0
0
0
1
0
1
0
0
2
1
0
1
0
0
2
1
0
0
1
0
0
3
2
1
1
0
0
1
0
0
0
0
0
0
2
0
2
1
1
0
0
0
1
0
0
2
0
0
3
0
0
0
0
0
0
0
1
1
1
0
0
1
1
1
3
2
0
1
0
2
1
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
1
0
1
0
0
0
1
2
2
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
1
2
1
1
0
0
1
0
0
0
0
1
0
1
0
0
2
0
1
2
0
1
2
2
0
0
0
2
0
1
0
0
0
0
1
0
0
1
1
0
0
2
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
2
2
0
2
0
1
2
0
0
0
1
1
0
1
0
2
0
0
0
0
0
1
1
1
0
0
1
0
0
1
1
0
0
2
1
2
1
0
2
2
1
2
0
0
1
0
0
0
2
0
1
0
2
0
1
0
1
0
0
1
1
0
2
0
0
2
0
2
2
0
1
0
0
0
0
0
2
1
1
0
2
1
0
0
1
2
1
4
0
2
1
0
0
1
0
2
3
1
1
2
0
1
3
0
1
1
1
2
1
0
0
1
0
0
0
0
1
0
1
1
0
2
0
0
1
1
0
1
0
0
0
0
2
0
1
0
0
0
1
1
3
0
0
0
0
1
0
0
0
0
2
1
1
2
0
1
1
1
1
2
0
2
2
0
0
1
0
0
2
2
1
1
2
0
0
1
0
0
1
0
2
2
2
0
0
0
1
0
0
1
0
0
0
0
2
2
0
1
0
0
1
2
2
0
2
0
2
0
1
1
0
1
1
1
2
2
0
0
0
0
1
2
2
2
0
0
0
0
1
0
0
1
0
1
1
0
0
0
2
0
1
2
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
2
1
0
1
0
2
2
3
0
0
1
1
1
0
1
0
1
2
2
0
0
1
2
1
0
0
2
1
0
1
1
1
0
1
2
2
2
3
0
0
0
1
1
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
2
0
0
1
1
0
0
2
2
0
0
0
1
3
2
1
0
0
0
1
1
1
0
0
0
0
0
0
0
1
1
3
1
2
2
3
0
2
0
1
1
2
1
2
0
1
2
1
2
0
0
0
0
1
1
2
0
0
2
0
0
1
1
2
0
0
1
2
1
0
0
0
1
0
1
0
1
0
0
0
0
2
2
0
1
0
1
2
0
0
0
1
1
1
1
0
1
0
1
2
0
0
0
0
0
2
0
0
2
1
0
2
0
0
1
0
1
0
2
0
2
2
1
0
3
0
2
0
0
1
1
0
1
0
0
1
1
1
0
0
0
0
3
2
1
0
0
1
2
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
2
0
0
0
0
0
2
2
0
4
0
2
1
1
0
0
1
2
2
1
1
2
0
1
0
1
2
2
3
0
0
3
0
0
0
1
2
0
1
1
1
1
2
0
0
0
6
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
1
2
0
2
0
1
4
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
1
2
0
2
1
1
2
0
0
1
2
0
2
2
0
0
2
1
1
0
0
0
1
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
1
0
1
1
0
0
0
1
1
1
0
1
0
2
1
1
2
0
1
0
0
0
2
1
0
1
0
0
1
1
0
0
0
2
1
0
0
0
0
1
1
0
0
0
0
1
0
0
1
2
1
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
2
1
0
0
0
1
0
1
2
3
1
0
0
1
0
0
1
0
0
1
2
2
0
0
1
0
0
1
0
0
0
0
0
2
0
0
3
2
2
0
0
0
1
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
2
1
0
0
0
1
0
0
3
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
1
0
1
2
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
2
0
0
0
2
1
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
2
0
0
2
0
1
0
0
0
0
1
1
1
1
2
0
0
1
3
0
1
0
1
0
2
2
0
2
1
0
2
2
0
2
2
1
1
1
1
1
1
1
0
0
2
0
1
0
1
2
1
1
0
0
0
6
2
1
0
2
2
0
0
2
0
2
1
2
0
0
2
0
0
0
0
0
0
0
0
1
0
2
1
2
0
1
0
0
3
0
0
0
0
0
0
1
0
0
2
0
0
2
1
2
1
1
0
1
2
0
0
0
0
1
3
1
0
1
0
0
1
0
0
0
1
0
1
1
0
1
1
0
0
2
2
0
0
0
2
0
0
1
2
0
1
0
1
0
0
0
0
2
0
1
0
0
0
1
1
0
0
0
1
1
1
2
2
2
1
0
3
0
0
0
0
0
0
0
2
2
0
0
0
0
1
2
0
1
0
0
0
6
0
2
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
1
0
0
2
1
1
0
0
2
0
2
1
1
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
1
0
1
0
0
0
1
2
0
2
0
0
2
1
3
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
2
1
1
2
2
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
1
1
0
1
0
0
1
0
1
0
1
0
0
2
0
0
2
2
0
0
0
0
1
1
0
0
0
0
1
0
2
2
0
0
0
1
2
1
2
0
1
2
0
0
0
1
0
2
1
0
0
0
0
2
2
2
1
2
2
1
1
1
2
2
0
0
0
1
0
0
1
0
2
2
0
0
2
1
2
2
0
0
0
0
1
2
0
0
1
0
0
0
1
0
0
2
0
0
2
0
0
1
2
1
1
0
0
0
1
0
0
0
1
0
1
2
0
1
1
1
1
1
0
0
0
1
0
1
0
2
2
0
1
2
0
1
0
1
0
0
1
1
1
0
0
0
0
2
0
0
0
1
2
1
1
1
1
2
0
1
0
1
1
2
0
0
0
0
0
2
2
1
0
0
0
2
0
0
1
1
3
1
1
0
0
2
4
2
0
1
2
2
0
0
2
0
1
0
2
0
1
1
0
0
0
0
3
2
0
2
0
0
0
0
1
0
0
0
2
0
1
0
0
1
1
0
0
0
1
0
0
0
1
1
1
1
0
1
2
2
2
0
2
1
0
0
2
0
3
1
0
0
0
0
0
0
0
0
0
2
2
1
2
0
0
0
0
0
1
0
0
1
1
0
0
0
3
0
0
2
0
0
1
0
0
2
0
0
2
2
1
1
0
1
1
0
1
1
0
0
0
0
0
1
1
2
1
0
0
0
0
1
2
0
2
0
2
2
1
0
1
2
1
1
0
1
1
0
1
2
0
0
0
0
0
0
1
1
0
0
0
1
0
0
2
1
0
0
0
2
3
2
0
0
3
0
1
0
0
2
1
0
0
0
0
1
0
0
0
3
0
0
0
2
1
0
1
0
0
2
0
2
2
1
1
0
0
0
0
0
2
1
0
2
2
1
0
0
0
1
1
0
0
3
0
0
2
0
0
0
0
2
0
0
1
1
0
2
0
0
2
0
0
1
1
0
1
0
1
0
0
0
0
1
2
1
2
1
0
1
0
2
0
0
0
2
0
1
0
2
2
0
3
0
0
1
0
0
2
0
2
0
0
2
0
2
0
0
0
0
1
1
1
0
0
1
2
1
0
0
1
1
0
1
0
3
0
2
0
0
0
0
2
2
0
0
2
0
1
0
1
1
0
0
1
1
1
2
1
0
0
2
2
1
4
2
0
1
0
1
1
2
0
0
0
0
2
0
0
0
1
3
1
1
0
1
0
1
0
2
0
2
0
0
1
4
0
0
0
2
0
1
0
0
0
1
2
3
0
0
1
2
0
0
1
0
3
0
0
2
0
0
0
0
0
2
0
0
0
2
0
2
3
1
0
0
0
0
3
0
4
0
0
1
1
1
0
0
0
0
0
2
2
0
1
0
0
2
0
0
0
2
0
0
0
0
1
2
0
0
0
0
1
0
0
2
2
1
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
2
2
1
0
1
1
0
2
1
2
0
0
0
2
0
4
1
0
0
0
0
0
1
0
0
0
2
2
2
0
0
0
2
1
1
1
0
0
1
0
2
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
2
1
0
0
0
1
2
0
1
1
0
1
2
2
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
2
2
1
2
1
0
1
3
0
0
0
0
0
2
2
0
0
0
0
2
2
0
2
1
0
3
2
3
2
0
1
2
0
0
0
0
0
0
1
0
0
1
2
4
2
0
0
1
0
2
0
0
0
0
0
1
2
2
1
0
4
1
1
0
0
0
0
0
2
0
0
1
0
1
0
1
0
2
1
0
0
1
1
2
2
0
0
1
1
0
1
1
2
0
0
2
0
1
0
0
0
2
1
1
0
1
1
1
1
0
1
0
0
1
0
1
0
1
0
1
3
0
0
0
0
0
0
0
1
1
2
1
0
0
3
1
1
2
0
0
2
1
1
0
1
0
2
2
0
0
0
0
0
0
0
0
0
1
1
2
0
0
1
0
0
0
0
0
2
2
0
0
2
1
1
1
2
0
0
0
2
0
1
0
0
1
0
2
0
1
0
0
1
0
2
1
0
0
1
1
0
0
0
0
2
2
1
1
2
0
1
2
2
0
0
0
0
1
0
0
0
0
0
0
2
1
0
1
0
2
0
2
1
4
0
0
0
1
0
0
0
0
1
2
0
2
2
0
0
0
0
1
2
0
0
1
1
0
2
2
0
0
1
1
0
0
0
2
0
0
2
2
0
1
3
3
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
1
0
1
0
1
0
1
0
0
0
0
1
1
0
0
1
2
2
0
0
2
0
0
0
0
0
1
1
2
0
1
0
0
0
1
2
0
1
2
2
0
0
0
0
2
0
0
1
1
1
0
1
2
1
0
2
0
0
0
1
0
1
2
1
0
0
0
2
2
2
2
1
0
1
2
0
1
0
0
1
2
3
0
1
0
1
1
0
1
0
1
2
2
2
2
1
0
0
2
0
0
0
2
0
0
1
0
0
0
0
2
0
3
2
0
2
0
0
0
0
0
0
2
0
0
1
2
1
0
2
1
0
1
2
0
0
0
2
0
2
0
1
0
1
0
0
0
0
0
0
1
0
0
2
2
0
0
1
2
2
1
0
0
0
1
2
0
0
1
0
0
2
0
0
1
0
0
0
2
1
1
2
0
0
0
0
0
0
1
1
0
2
0
1
0
0
1
2
1
1
0
2
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
2
0
1
2
0
0
0
1
0
4
0
0
1
1
1
0
1
1
1
1
0
0
1
0
1
0
0
4
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
3
2
0
1
0
0
0
0
1
0
2
1
0
0
0
2
2
0
0
0
1
2
0
0
3
0
1
0
2
0
0
0
0
0
3
0
1
1
0
1
1
1
1
2
0
3
1
0
0
2
2
0
0
1
0
0
0
2
1
0
0
0
0
0
0
1
1
1
0
2
0
2
3
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
1
1
0
0
1
0
0
0
2
1
0
0
0
0
1
0
0
1
0
0
2
0
0
1
0
0
1
2
2
0
2
0
0
0
0
0
0
0
0
2
1
0
0
1
1
6
0
2
0
0
2
0
2
2
0
1
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
1
2
0
1
0
2
0
3
2
0
0
2
0
1
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
1
0
0
0
0
0
0
2
0
0
0
1
2
1
0
2
0
0
1
2
0
1
0
0
0
0
0
0
0
0
1
1
1
1
1
0
2
2
1
0
3
0
1
0
0
0
1
2
1
1
1
0
2
0
2
1
0
1
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
1
0
3
0
1
2
0
1
0
0
2
0
0
0
1
0
1
0
2
0
0
2
1
0
1
1
1
0
0
0
2
0
0
0
2
1
1
2
0
2
2
0
0
1
1
0
2
0
0
1
1
0
0
0
1
0
0
1
3
1
0
1
2
0
0
0
1
0
2
0
0
2
0
0
0
0
0
2
0
1
2
2
2
0
1
1
2
0
0
2
2
1
1
2
0
0
0
1
0
1
1
0
2
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
2
0
3
1
0
1
1
0
0
0
1
0
1
2
2
2
1
0
0
0
0
0
2
0
2
1
2
0
2
1
0
2
1
0
0
1
1
2
1
0
0
1
2
2
0
1
1
0
1
0
1
1
0
0
0
2
1
0
0
0
1
2
0
2
2
0
2
0
0
5
0
1
1
0
0
0
0
0
0
0
1
0
2
2
0
0
1
1
0
0
0
2
1
0
2
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
2
0
2
1
0
0
2
0
2
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
1
0
1
0
2
0
0
0
1
1
2
0
2
0
0
1
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
2
1
2
1
2
1
2
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
4
2
0
0
1
1
0
0
0
0
0
0
1
1
0
1
1
1
0
2
1
0
1
2
1
2
0
0
1
2
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
1
2
0
0
2
2
0
1
0
2
2
2
1
0
0
0
0
2
0
0
0
0
1
2
0
0
1
2
0
0
3
0
0
0
1
2
0
1
1
1
0
2
0
0
0
0
0
2
0
0
0
0
0
2
2
2
0
0
1
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
3
0
1
0
0
0
1
0
2
0
2
4
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
3
2
0
1
0
1
0
0
1
2
0
0
0
1
0
0
0
2
1
0
0
2
1
0
0
0
0
2
0
2
0
1
0
0
2
2
0
0
3
0
0
0
1
0
2
0
0
0
1
1
0
2
3
0
0
2
2
1
1
0
0
2
0
0
2
0
0
0
0
0
0
1
0
2
3
0
0
0
0
2
0
0
1
0
0
3
1
0
2
0
2
2
1
1
0
2
0
0
0
0
1
2
2
0
0
1
0
1
4
0
0
0
2
2
0
1
1
4
0
0
0
0
0
0
2
0
0
2
0
1
0
0
2
0
0
2
0
0
3
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
4
0
0
0
0
0
2
1
0
0
0
1
1
1
0
2
0
0
1
2
0
0
0
1
0
2
0
0
0
1
2
0
2
0
0
0
1
1
0
1
1
0
2
0
2
2
2
0
1
0
0
0
1
1
1
0
1
1
2
0
1
0
1
0
1
0
0
2
1
0
0
0
0
1
2
1
1
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
1
0
1
0
3
2
0
2
0
2
1
2
1
1
0
0
0
1
0
0
2
1
3
0
0
2
1
1
0
2
0
2
0
0
0
0
1
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
2
0
1
3
1
0
1
0
0
1
2
0
1
2
0
1
0
0
1
0
2
2
0
0
0
0
1
0
2
0
0
0
1
0
0
1
2
1
0
0
0
0
0
0
1
0
0
0
2
0
1
1
2
3
0
1
0
0
5
3
0
0
0
0
0
1
1
0
1
2
0
2
0
0
0
0
0
1
1
0
0
2
1
1
2
0
4
1
0
0
0
0
2
0
0
1
0
1
0
0
0
0
2
1
0
0
0
0
1
2
2
1
2
0
2
0
1
1
0
2
2
3
1
2
1
1
0
1
0
2
3
0
2
1
1
0
0
2
0
1
2
0
1
2
1
1
0
1
2
0
0
1
0
0
0
0
2
2
0
0
1
0
0
1
0
1
1
0
0
1
2
2
0
1
0
0
1
1
0
0
0
2
1
0
2
1
0
2
0
2
1
1
0
1
0
0
0
1
0
1
1
1
2
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
2
1
2
1
0
0
1
0
1
0
0
0
2
2
2
0
1
1
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
2
2
0
0
0
2
1
0
2
0
1
2
2
2
1
0
1
2
2
0
2
2
2
1
0
1
0
0
0
0
2
5
0
1
0
2
0
1
0
1
0
1
0
0
2
0
1
0
2
2
2
0
0
2
2
1
0
0
1
0
2
0
1
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
3
3
2
0
0
0
0
0
0
2
1
1
2
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
2
1
0
1
3
1
2
0
0
1
0
0
0
1
0
1
0
0
1
0
0
1
2
0
0
0
0
0
0
1
0
0
1
0
0
2
0
1
1
0
0
0
2
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
2
1
1
1
2
0
0
0
0
0
1
0
0
1
0
2
0
1
0
1
1
0
0
0
1
1
2
0
0
2
0
2
1
1
2
0
2
0
1
0
0
0
0
0
1
2
1
0
0
0
0
1
0
2
0
0
2
0
1
0
0
2
0
2
3
0
2
2
0
0
2
0
0
1
1
1
2
1
1
0
0
2
0
0
0
0
0
0
2
0
0
7
0
0
2
2
0
1
2
0
1
0
0
1
0
1
0
1
0
0
1
0
1
2
1
2
0
2
2
1
0
1
0
1
0
0
0
1
2
0
0
1
1
0
1
1
0
1
0
0
0
0
0
1
1
1
0
0
0
2
0
0
0
0
2
2
0
0
0
0
1
1
0
1
0
1
0
2
1
0
0
0
0
0
1
1
0
2
1
1
0
1
2
0
0
1
0
2
2
0
0
0
2
0
0
1
1
0
0
0
1
0
0
0
2
0
1
1
1
0
0
2
2
0
0
0
0
1
0
0
2
0
0
2
0
0
0
9
0
1
2
0
2
1
2
0
0
0
0
0
1
0
0
0
2
0
1
0
0
1
0
0
0
0
1
2
0
0
2
0
0
0
0
0
1
1
2
1
0
1
0
1
1
0
2
0
1
1
0
1
0
0
0
1
1
0
0
0
0
0
2
1
0
0
2
0
0
1
0
0
2
0
0
1
2
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
1
0
0
0
1
1
0
0
2
1
2
0
0
0
0
0
0
0
0
1
0
2
0
1
0
2
0
0
2
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
2
0
1
0
2
0
1
1
0
2
2
0
1
0
0
2
2
0
1
0
0
1
1
1
0
0
0
2
0
1
0
2
1
1
2
0
0
0
0
1
0
1
0
0
2
1
0
0
0
0
0
2
0
0
0
1
2
0
1
0
1
1
1
0
0
0
2
2
2
0
0
3
0
0
0
2
0
0
0
2
1
1
2
0
1
0
0
0
2
1
0
0
0
5
0
0
0
0
0
1
1
0
0
2
0
1
0
0
1
0
0
0
1
1
2
0
1
0
0
0
2
0
1
2
1
0
2
1
2
2
0
2
2
0
3
1
0
0
1
1
0
0
1
1
0
0
0
2
2
0
2
2
0
0
0
0
1
0
2
0
0
1
1
0
2
0
1
0
0
0
2
0
0
1
1
1
0
0
0
2
1
1
0
2
1
2
2
0
1
1
2
0
2
1
1
0
2
0
1
0
2
0
2
0
0
1
0
1
0
1
1
2
0
2
3
0
1
0
0
0
0
1
0
0
2
0
0
0
3
1
1
0
0
0
2
0
0
0
0
2
2
0
2
0
0
0
1
0
2
0
0
0
2
0
2
1
0
0
0
0
2
0
0
2
0
0
1
2
0
0
2
0
2
0
0
1
0
0
1
0
0
0
1
0
1
0
0
2
1
1
0
0
1
0
0
0
0
0
0
1
1
2
0
0
1
0
0
0
1
2
0
0
1
1
2
3
0
1
0
0
0
1
2
0
2
0
0
8
0
2
1
0
3
0
0
1
0
1
2
1
0
1
1
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
2
2
2
1
0
1
0
0
2
0
1
0
0
0
0
2
1
0
0
0
0
1
1
1
0
0
0
0
2
1
0
1
0
0
1
0
1
0
0
4
1
0
1
0
0
0
1
2
2
0
0
1
0
0
0
2
0
1
2
2
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
2
0
1
2
1
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
2
3
2
1
2
0
2
2
0
1
0
0
0
1
2
0
1
0
2
0
0
0
2
0
3
0
0
1
0
2
0
0
1
1
1
0
0
0
2
0
0
0
2
0
0
2
0
2
0
0
2
0
2
0
1
0
0
0
2
0
1
0
1
0
0
2
2
2
2
0
0
2
0
0
0
1
0
0
1
0
1
0
0
0
2
1
0
0
1
0
1
2
0
0
0
0
1
0
1
0
1
0
0
1
0
2
0
0
1
1
0
0
1
1
0
0
0
1
0
0
0
1
0
0
1
1
0
1
2
1
1
0
0
0
0
0
0
0
2
0
0
0
1
2
1
1
0
0
0
0
1
0
1
2
1
2
1
1
2
2
0
0
0
1
1
3
0
0
0
1
0
1
2
0
4
0
0
2
1
0
0
0
1
2
0
0
2
2
2
0
1
0
0
1
1
0
1
0
1
0
1
1
0
0
0
2
0
0
2
0
0
0
1
2
2
0
2
1
2
0
0
0
1
1
0
0
0
1
0
0
2
2
0
0
0
1
0
0
2
2
1
1
1
0
0
0
1
0
2
2
1
0
2
0
1
0
2
0
1
0
0
2
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
1
2
0
0
0
2
0
0
2
1
0
1
0
1
0
0
0
1
2
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
2
0
0
1
0
0
1
2
0
1
1
0
2
0
1
1
2
2
0
0
2
0
1
0
2
0
1
0
0
0
2
0
0
1
0
0
0
2
0
0
2
0
0
0
1
2
0
0
2
0
0
2
0
1
0
0
0
1
2
1
0
0
0
0
0
2
2
2
0
0
1
1
1
2
1
0
0
0
1
0
0
2
0
1
1
0
0
0
1
1
0
0
2
0
0
0
0
2
0
0
1
2
1
2
2
0
1
0
0
0
1
0
0
0
1
2
0
2
2
2
0
1
1
0
0
1
0
0
2
1
0
0
1
0
2
2
2
2
1
0
0
2
0
0
2
1
0
2
0
2
0
2
1
1
3
2
2
0
0
1
2
1
2
1
0
0
2
0
0
0
1
0
2
2
2
0
0
1
1
2
1
0
0
1
1
2
2
1
1
0
0
1
0
1
2
3
1
0
0
0
2
2
0
0
1
1
0
0
0
3
1
0
0
0
2
0
0
0
0
1
0
2
1
1
0
1
2
0
0
0
0
2
1
0
0
3
1
4
3
0
3
0
0
1
0
0
0
1
0
2
0
2
2
0
0
0
1
0
0
0
2
1
2
2
0
2
0
2
0
1
0
0
0
5
0
0
0
1
0
0
0
0
2
0
0
0
2
0
1
0
1
0
0
1
1
0
0
0
1
0
0
5
0
0
0
1
0
0
0
0
0
0
2
0
1
1
1
0
0
3
0
0
1
2
0
2
0
0
2
0
1
0
1
1
0
0
0
0
0
0
5
0
3
0
0
0
1
1
1
0
2
1
1
2
0
1
0
1
1
0
1
1
0
2
0
0
2
0
0
1
0
2
0
0
0
0
1
1
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
1
2
0
0
0
1
1
0
2
2
0
1
2
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
3
0
3
0
1
0
0
2
2
0
1
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
1
1
3
0
1
1
0
1
0
0
0
2
0
1
1
0
2
0
2
2
0
0
0
0
2
1
0
0
1
4
0
0
0
0
0
0
1
0
1
2
2
0
0
0
0
1
1
0
0
2
0
2
0
0
3
0
2
2
0
0
0
0
2
0
2
0
0
2
0
1
1
0
1
1
0
1
0
0
0
0
1
2
2
0
0
2
2
1
1
0
0
1
1
0
1
1
1
0
0
0
0
0
2
0
0
0
0
1
2
2
0
2
0
2
1
0
0
0
2
0
0
0
1
1
0
0
3
0
2
2
2
1
2
0
2
1
2
0
2
0
1
0
0
0
1
1
0
0
0
0
1
1
0
1
1
1
1
1
2
0
0
0
0
0
0
1
0
2
5
1
0
2
0
0
1
0
0
0
1
1
0
2
0
2
1
0
0
2
0
2
1
2
0
2
1
1
0
0
0
1
0
1
1
2
0
0
0
0
1
0
0
0
1
0
2
0
0
0
2
0
1
0
1
0
1
0
2
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
1
0
2
3
0
0
0
0
2
2
1
1
2
1
0
0
2
0
0
1
0
0
1
2
2
0
0
1
0
0
0
1
1
0
0
0
1
2
0
0
0
0
0
1
0
0
1
1
2
0
0
0
0
0
0
0
1
1
0
1
3
0
0
0
0
0
1
0
0
1
0
3
2
0
1
0
0
0
1
0
1
0
4
1
0
2
0
1
2
0
1
0
1
0
2
0
0
0
0
0
2
0
0
0
1
0
0
2
2
0
4
0
2
1
0
2
1
0
0
0
0
2
0
0
1
2
2
0
0
0
0
0
1
2
0
1
0
1
1
2
2
1
1
0
0
0
0
0
0
0
0
1
3
1
3
0
1
0
0
4
0
2
0
0
0
0
0
2
1
2
0
1
1
2
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
1
1
1
0
1
0
0
2
1
1
0
2
2
0
1
0
1
0
2
1
0
1
1
0
2
1
0
0
0
0
1
0
2
0
2
1
2
0
2
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
2
0
0
2
2
1
1
0
0
0
2
0
1
0
0
0
2
0
0
1
1
0
1
1
1
0
0
1
0
0
1
0
1
1
0
1
0
1
0
2
1
0
1
1
1
0
2
0
0
0
2
0
2
0
0
2
0
0
0
0
0
2
1
0
1
1
1
0
0
0
0
0
1
0
0
2
2
0
0
0
1
2
2
2
1
2
1
0
1
3
0
0
0
1
0
0
2
0
2
2
0
1
2
2
0
2
0
0
2
1
0
0
0
3
1
0
0
0
1
2
1
0
1
3
1
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
2
0
1
2
3
0
0
0
0
0
2
0
0
0
1
0
3
0
0
3
6
0
1
2
0
1
2
1
0
1
0
0
2
1
0
2
0
0
1
0
1
1
1
1
2
2
0
2
0
0
0
2
2
1
0
0
2
0
0
0
2
1
1
2
0
0
1
0
0
1
1
1
1
0
0
0
0
2
3
0
0
0
2
2
2
2
0
1
0
3
0
0
0
1
0
1
2
0
1
0
0
1
0
2
2
0
0
0
0
0
2
0
0
0
1
0
0
0
1
2
2
0
0
2
3
2
0
0
0
0
0
0
2
2
4
2
2
2
0
2
0
2
0
2
2
0
0
1
0
0
1
0
2
0
1
0
0
0
2
1
1
0
0
2
0
0
0
0
0
1
0
1
0
2
10
0
2
0
1
0
0
0
1
2
0
0
1
1
2
0
0
3
2
2
0
1
0
0
0
3
1
0
1
0
0
0
0
2
2
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
3
0
0
0
2
0
3
1
2
2
0
2
2
2
1
0
0
0
0
0
0
1
2
0
0
1
0
1
0
0
2
2
0
0
0
1
0
0
0
1
0
0
1
1
1
0
0
2
0
2
1
0
0
2
4
0
2
2
2
0
2
2
0
0
1
0
2
2
0
0
0
0
2
0
2
1
1
0
0
0
0
0
0
2
0
1
0
0
1
0
2
1
0
1
1
0
1
0
2
1
1
0
0
0
0
0
2
0
0
0
1
0
2
0
2
2
0
2
0
0
0
1
1
0
0
0
0
1
1
0
1
0
0
0
2
2
2
2
1
0
2
3
0
0
0
1
0
0
0
0
2
0
2
0
1
0
1
1
1
2
0
0
1
2
1
2
2
0
0
1
0
0
2
0
2
1
0
0
0
0
1
0
0
1
1
0
0
0
2
0
2
1
0
0
0
2
0
1
1
1
0
0
0
0
0
0
0
0
0
2
2
1
0
1
0
0
0
1
1
0
0
0
0
0
0
1
3
0
1
1
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
2
2
0
0
1
1
2
0
1
0
1
1
2
0
2
1
1
0
2
0
1
0
2
2
0
0
1
0
2
2
1
1
0
1
1
2
0
2
1
0
0
1
0
1
2
2
2
0
0
0
0
2
0
0
0
2
0
1
1
2
0
0
2
3
2
0
1
0
0
0
1
2
2
0
0
0
1
2
1
0
0
0
1
0
1
0
2
2
2
1
0
1
0
0
1
1
2
0
2
0
0
2
0
1
1
2
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
2
1
1
2
0
2
0
2
0
0
2
1
1
0
1
1
1
0
0
0
2
1
1
0
0
0
0
0
0
0
3
0
0
0
1
2
2
2
3
0
1
0
0
2
0
1
1
0
0
4
0
2
2
1
1
0
2
0
1
0
1
1
0
1
1
0
2
0
1
1
0
0
0
0
2
1
0
1
0
0
3
1
1
0
2
1
0
1
1
0
0
2
1
0
0
0
1
0
0
2
0
2
1
2
2
0
1
2
0
1
0
1
0
3
1
2
2
0
0
0
0
0
0
1
0
0
0
1
2
2
1
0
2
0
0
1
2
0
0
2
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
1
0
2
0
0
0
1
0
2
2
0
0
0
0
0
1
0
0
0
0
1
2
1
0
0
2
0
0
1
0
1
1
1
0
2
1
0
0
0
1
0
0
1
0
2
2
0
0
3
0
0
1
1
0
2
0
1
0
0
2
0
1
0
2
0
0
0
0
0
2
1
1
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
2
1
2
1
2
2
2
0
0
0
1
0
2
1
1
1
2
1
0
0
1
1
0
2
0
1
1
1
2
0
1
1
0
0
0
0
0
2
1
1
1
0
2
2
0
0
0
0
0
0
0
0
1
0
2
1
2
0
2
0
0
0
3
0
0
0
0
2
0
0
1
0
2
1
0
0
1
0
2
2
2
2
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
2
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
2
1
0
2
1
0
0
2
0
2
0
0
0
2
0
2
1
1
1
0
2
1
0
0
0
0
0
0
1
0
0
2
2
0
0
0
1
0
0
0
1
0
1
2
0
4
0
0
0
0
0
1
1
2
0
1
1
0
1
1
0
0
0
0
0
0
2
2
1
0
2
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
2
0
1
0
1
2
2
1
0
0
0
0
2
0
1
1
0
0
0
1
1
2
2
1
0
1
1
1
0
0
0
2
0
0
0
2
1
1
1
1
1
1
0
2
2
2
0
0
2
2
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
2
2
1
2
0
2
0
0
0
1
1
0
1
0
4
0
1
1
1
2
2
1
2
0
2
0
0
2
2
0
1
2
0
0
1
2
0
0
0
2
1
2
1
1
0
0
2
0
1
2
1
1
2
3
1
1
0
1
0
2
2
0
0
2
2
1
0
0
1
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
2
1
0
2
0
0
2
1
4
2
1
4
0
3
2
1
0
0
0
0
0
1
0
2
2
0
1
0
0
0
0
0
0
1
1
0
1
0
1
1
1
0
0
0
0
0
1
0
2
1
0
0
0
2
2
1
0
1
1
0
0
0
1
0
1
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
2
1
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
2
2
1
2
0
1
0
2
0
2
1
1
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
2
0
0
1
0
2
0
0
1
0
2
2
1
1
0
0
2
1
2
1
0
0
0
1
1
0
2
1
0
0
0
2
0
0
2
1
0
1
1
2
0
2
3
1
2
1
0
0
1
2
0
0
1
0
3
1
2
0
0
0
1
0
1
0
1
0
0
0
0
1
2
0
2
1
0
1
1
0
0
0
2
2
1
0
1
0
0
0
0
1
1
0
6
0
0
0
1
0
0
1
0
1
2
0
0
0
3
0
1
2
0
2
1
0
0
1
0
0
1
1
0
1
0
0
0
2
0
0
0
0
0
2
1
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
2
1
1
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
1
0
2
0
1
2
1
2
0
2
0
1
2
1
1
0
1
0
0
1
0
0
1
2
0
3
2
1
1
2
2
2
0
1
0
0
1
0
1
2
0
0
0
4
1
0
2
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
2
2
0
0
2
0
2
0
0
1
2
0
0
1
0
0
0
0
0
0
4
1
0
0
1
2
0
0
0
2
2
0
2
0
0
0
0
0
0
2
2
0
1
0
2
1
1
2
1
0
0
1
0
1
0
0
0
0
2
0
0
1
0
0
1
2
2
1
0
0
1
0
1
1
1
0
1
2
2
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
2
1
0
0
0
1
0
2
0
1
1
0
0
0
0
2
0
1
1
2
2
0
0
2
0
2
0
0
1
2
0
0
1
0
0
2
2
1
3
1
1
0
0
0
1
0
2
0
1
0
1
1
2
0
0
0
0
1
1
1
0
1
0
2
0
0
2
0
1
3
1
0
1
1
0
0
0
0
2
1
1
0
0
1
0
4
0
2
1
1
0
0
0
2
0
0
1
0
0
1
15
2
2
2
1
1
0
0
0
0
0
2
5
1
1
1
1
0
0
0
0
1
0
1
0
0
0
0
2
1
0
1
1
1
1
0
0
1
0
2
0
0
0
0
0
0
1
2
0
2
0
1
2
2
0
1
1
0
0
0
0
0
1
0
0
1
1
0
0
0
2
0
2
1
2
2
0
0
0
0
0
1
0
0
0
1
0
1
0
2
0
0
1
2
0
2
0
0
1
2
2
1
0
1
0
2
0
0
1
0
0
0
1
0
2
0
0
0
0
0
1
1
0
0
1
2
1
1
0
2
2
0
0
1
2
1
1
0
1
2
0
0
0
0
0
3
0
0
1
1
0
1
0
1
0
0
0
1
0
1
0
0
2
0
0
1
1
0
0
1
1
0
3
1
2
0
0
0
1
3
1
2
1
1
0
1
0
0
0
0
2
0
0
0
0
0
1
0
2
2
0
1
0
2
3
0
0
2
0
0
2
0
0
2
2
0
1
1
0
0
2
2
0
1
1
0
0
3
2
0
0
0
0
1
1
2
2
1
2
0
0
2
0
2
0
1
0
0
2
3
2
0
0
1
1
0
1
1
0
1
0
2
0
0
2
3
1
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
1
2
1
1
2
0
0
0
2
0
2
0
0
1
0
1
0
2
1
0
2
0
0
0
1
2
2
0
0
1
0
0
0
1
2
2
0
0
1
0
2
0
2
0
0
1
0
2
0
0
2
1
1
0
0
1
2
0
1
0
0
0
2
2
2
1
1
1
0
0
0
0
1
0
2
0
2
1
3
2
0
0
0
0
2
2
2
0
0
0
1
1
0
1
0
1
1
1
1
0
0
0
0
1
1
0
0
1
1
2
0
0
1
0
0
1
2
2
1
0
2
0
2
0
0
1
1
0
3
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
1
1
1
0
0
0
2
0
1
0
1
0
2
0
2
0
1
0
2
2
0
2
0
2
3
1
1
0
0
0
1
0
2
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
1
1
0
2
3
0
1
0
0
1
0
0
2
0
0
0
0
1
0
0
1
2
0
0
0
0
0
1
1
0
0
2
0
2
2
2
0
1
0
2
0
0
0
0
0
2
2
2
1
0
0
0
0
2
0
2
0
0
0
1
0
0
0
2
0
2
2
1
0
0
3
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
1
0
0
0
2
0
1
0
0
1
2
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
1
2
3
2
1
0
0
0
3
0
2
2
1
1
0
0
0
3
0
0
1
1
0
1
1
0
0
0
0
0
2
0
1
0
3
1
1
2
2
2
2
0
1
0
2
0
1
2
0
2
1
0
0
0
0
0
0
1
0
0
0
2
1
0
1
0
0
1
1
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
1
2
0
0
2
0
1
2
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
1
0
2
0
1
1
0
2
1
1
0
0
0
1
2
1
0
0
0
3
1
0
1
2
1
0
0
0
0
0
0
0
2
0
1
1
1
0
1
0
2
1
1
0
2
0
0
0
0
2
1
2
2
2
0
1
2
1
1
0
0
1
1
2
1
2
0
0
2
1
2
0
0
0
1
0
0
0
0
0
1
0
2
0
2
2
3
0
0
0
0
0
0
1
0
1
1
1
0
0
0
2
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
2
1
1
1
0
1
1
2
0
2
1
1
0
0
2
0
2
0
2
0
1
1
0
0
2
0
0
3
0
1
0
1
0
2
0
0
0
0
0
2
2
0
0
0
0
0
1
0
2
0
0
1
0
4
0
2
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
3
1
2
0
0
0
2
2
0
0
1
0
0
1
1
1
0
0
0
1
2
1
1
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
2
1
0
0
2
1
0
0
1
0
0
0
2
2
0
0
1
0
2
1
0
2
2
0
2
3
2
0
0
2
0
1
0
0
0
0
0
1
2
1
0
2
2
0
1
0
1
0
0
0
1
2
0
2
0
1
0
2
0
1
1
0
1
0
1
0
1
2
0
0
0
3
1
0
0
0
1
0
0
1
0
2
0
0
0
2
1
0
2
1
2
1
2
0
2
0
1
0
2
2
1
2
0
0
1
0
0
1
0
1
1
2
1
0
2
0
0
2
2
1
0
0
3
0
0
1
1
1
1
0
2
2
1
2
0
4
3
0
1
0
0
0
0
1
0
0
0
0
0
2
0
1
2
0
0
1
0
0
0
1
0
1
2
2
2
2
1
2
1
1
2
1
0
0
0
0
0
0
2
0
1
1
0
0
0
0
1
0
1
0
0
0
2
1
1
0
0
2
0
0
0
0
1
0
0
1
0
1
0
1
2
1
1
0
1
0
3
0
1
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
2
0
1
0
0
0
1
0
0
0
0
0
0
5
2
3
0
0
0
0
0
2
0
0
0
1
0
1
1
0
2
1
0
0
1
1
2
0
0
2
2
0
1
2
2
0
0
0
0
0
0
0
0
1
0
1
0
3
0
2
1
0
0
0
0
2
2
0
1
0
1
0
1
2
0
0
1
1
1
0
0
0
1
0
1
0
0
0
2
1
0
0
0
0
0
0
0
1
2
1
2
0
1
2
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
2
1
0
2
1
2
0
0
2
1
2
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
3
0
1
0
0
2
0
0
0
0
2
0
1
1
0
0
0
0
1
0
0
0
3
0
0
2
1
2
1
1
1
2
0
2
2
1
2
0
3
1
2
0
2
0
0
0
0
1
2
1
1
1
0
0
0
1
0
0
0
0
0
2
1
1
0
1
0
1
1
0
2
1
0
2
1
0
0
2
0
0
0
0
1
2
0
0
1
1
0
2
0
0
0
1
1
1
0
2
2
3
0
0
0
1
1
0
0
1
2
2
1
1
2
1
1
0
0
0
0
0
3
0
0
1
0
1
0
1
1
1
1
0
1
0
0
2
0
1
0
0
2
0
0
0
2
2
0
2
1
0
0
1
0
0
0
2
4
0
1
1
1
0
1
0
0
1
0
0
0
0
1
2
1
1
2
0
2
3
0
0
2
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
1
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
13
0
3
1
0
2
1
2
1
2
0
2
0
0
0
0
2
0
0
1
0
0
2
0
1
0
1
0
2
0
1
1
1
0
0
0
0
0
0
0
1
3
0
0
0
2
0
1
1
1
1
0
0
1
2
1
0
2
0
0
0
0
0
0
1
0
0
1
0
0
2
1
0
1
1
0
1
0
0
0
0
0
0
1
1
2
0
2
0
2
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
2
0
1
0
1
0
2
0
1
0
1
1
2
1
4
0
1
0
2
1
0
1
2
1
1
0
0
0
0
1
1
0
2
0
4
2
1
0
0
2
0
0
0
0
0
0
2
1
1
2
0
0
0
0
0
1
2
2
0
0
1
0
0
1
0
0
2
1
0
0
0
1
2
0
1
1
0
0
0
1
2
0
0
0
0
2
1
0
0
1
1
1
0
0
2
0
0
0
1
1
1
0
0
0
1
2
0
0
0
3
0
1
1
1
0
2
2
0
0
0
1
2
0
0
0
1
1
0
0
0
0
1
2
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
2
0
2
0
1
2
1
1
2
0
0
0
2
2
0
0
0
2
0
0
0
2
1
1
0
1
1
0
0
0
0
0
0
0
0
2
0
1
0
6
0
0
1
1
2
2
0
0
2
0
0
0
2
0
0
2
0
0
2
1
2
0
2
0
0
0
1
1
1
0
0
1
0
2
1
2
1
0
0
1
2
0
0
1
0
2
0
0
1
2
1
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
1
0
1
2
0
1
1
1
0
0
1
2
0
1
1
0
3
0
0
1
0
2
0
0
1
1
0
2
3
0
0
0
2
0
0
0
0
1
1
0
2
1
0
1
2
0
2
0
0
0
0
2
2
1
2
1
0
0
2
0
0
1
0
0
0
2
1
0
0
0
0
0
0
2
0
2
0
0
1
0
0
1
0
0
1
0
1
0
1
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
2
2
0
2
0
2
0
2
0
0
1
0
0
2
2
2
0
2
0
0
0
2
1
2
1
0
0
2
2
1
0
1
0
0
1
0
1
0
1
1
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
1
1
1
2
2
0
0
0
0
2
0
0
2
0
0
2
0
0
0
1
0
1
2
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
1
0
1
0
0
0
1
2
0
2
0
1
1
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
2
0
1
0
2
0
0
1
0
2
0
0
1
2
1
2
0
1
0
0
0
0
0
0
0
3
0
0
3
1
0
0
1
0
0
1
1
0
1
0
0
2
0
1
0
0
1
2
1
1
0
0
0
2
0
2
2
0
1
0
0
1
0
0
2
0
0
0
0
1
1
1
2
2
0
0
1
0
0
0
0
0
0
2
0
1
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
3
1
1
2
1
2
0
0
1
0
1
0
0
1
0
2
0
2
2
2
0
0
0
2
0
2
0
0
0
0
0
1
0
0
1
2
0
1
0
2
1
0
1
0
1
0
2
1
0
1
1
0
0
0
0
1
1
0
1
0
2
2
0
0
1
0
0
2
0
0
2
0
0
0
0
0
2
1
1
2
2
0
0
0
2
0
2
0
0
0
0
1
2
1
3
1
0
0
1
1
0
0
1
0
0
0
1
2
1
0
0
0
1
0
2
0
1
0
0
0
2
0
2
3
2
0
0
1
0
2
1
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
2
0
2
2
2
2
0
0
0
0
2
1
0
1
0
0
0
0
1
1
0
0
1
1
1
0
0
1
0
0
0
2
0
0
2
2
0
0
2
2
2
0
0
0
2
0
0
1
2
0
1
0
0
1
2
0
2
2
2
0
0
0
1
2
0
0
0
0
0
0
2
0
2
2
0
1
2
0
1
0
1
0
1
4
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
1
0
0
0
1
0
0
0
0
2
0
1
0
1
2
0
0
2
0
0
0
0
0
0
1
2
1
2
1
0
0
4
0
0
0
0
0
2
0
0
1
1
0
0
0
1
1
0
1
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
2
1
0
0
2
0
2
2
1
0
0
0
0
0
0
1
0
0
0
2
2
0
0
2
2
2
0
1
0
1
2
0
0
0
1
2
1
0
1
1
1
0
0
0
0
0
3
0
0
0
0
5
1
0
0
1
1
0
1
2
0
0
1
1
1
1
2
2
0
2
2
2
0
0
0
0
3
0
0
0
0
0
1
1
1
0
2
0
0
1
0
0
0
1
0
0
0
1
0
0
1
1
0
1
2
0
0
2
0
0
0
0
2
1
3
2
0
2
0
0
0
0
0
0
2
0
0
0
2
0
1
1
0
1
0
0
0
1
1
2
1
0
1
0
0
1
0
0
0
1
1
0
0
0
4
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
1
2
2
0
0
0
2
0
0
0
1
0
0
0
3
2
0
0
1
0
1
1
0
0
2
0
1
0
0
0
0
1
1
0
0
0
1
0
2
0
0
1
1
0
1
1
1
1
1
0
0
1
0
0
0
2
0
0
0
1
1
1
1
0
1
0
0
1
1
1
1
1
1
2
0
0
1
0
1
4
2
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
1
1
0
2
1
1
1
0
0
0
0
2
0
1
0
1
2
0
2
0
0
1
0
0
1
0
2
1
0
0
0
0
0
1
1
0
0
0
0
0
1
2
1
0
2
0
0
0
0
1
0
0
2
2
0
0
0
0
2
0
2
0
0
1
2
0
4
0
1
2
0
2
1
2
0
2
1
0
0
0
0
2
2
1
1
1
0
1
0
2
1
0
1
0
2
0
2
0
1
2
1
1
0
0
0
2
2
0
1
1
0
0
0
2
0
2
0
0
0
2
0
0
0
1
2
0
1
0
0
0
1
0
2
0
0
1
1
0
2
1
0
2
2
2
0
1
0
0
1
0
2
0
0
0
1
0
2
1
0
0
1
1
0
1
2
0
0
0
0
1
0
0
2
1
2
2
1
2
0
0
0
0
1
1
1
0
1
2
1
2
0
0
1
0
0
0
0
1
1
2
0
0
0
0
2
0
0
1
0
1
0
1
0
0
2
1
0
0
0
1
2
0
1
0
0
1
2
1
2
0
2
0
2
0
0
0
1
0
0
0
1
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
4
0
0
0
0
0
1
0
0
1
4
0
1
2
1
0
1
0
1
0
1
1
1
0
2
0
2
0
0
0
0
0
2
1
1
1
0
1
0
0
0
1
2
2
1
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
5
2
2
1
0
2
0
0
0
1
2
0
0
0
2
0
2
0
1
0
1
0
1
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
3
1
1
1
2
0
1
0
0
0
0
0
1
0
0
0
2
0
0
1
1
0
1
0
3
0
2
0
0
0
1
0
2
2
0
1
2
0
0
1
0
0
0
0
0
2
2
0
0
2
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
3
2
0
0
1
0
1
0
2
1
0
1
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
2
4
0
1
0
1
0
0
0
0
1
1
1
2
0
3
2
1
2
2
1
0
0
1
1
2
1
0
0
1
0
1
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
1
0
0
2
2
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
1
2
2
0
0
1
0
0
0
1
0
0
0
1
2
0
1
0
1
0
0
1
0
0
1
0
0
2
2
1
0
0
0
0
0
2
0
0
1
0
0
0
0
2
2
0
5
0
0
1
1
0
2
1
0
0
1
0
0
2
0
0
1
1
0
0
1
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
1
0
0
4
2
0
2
1
0
1
0
0
0
0
0
0
0
0
1
0
0
2
1
1
1
1
0
0
1
0
1
0
0
2
2
3
2
0
0
3
2
1
0
0
0
0
1
0
1
0
1
0
1
0
0
2
0
0
0
0
3
0
1
2
2
1
1
0
0
0
2
0
2
0
0
0
2
0
0
1
0
5
2
0
4
0
0
0
2
1
1
1
2
0
0
2
0
0
4
0
0
0
1
1
0
0
2
1
0
1
0
1
0
1
1
1
2
1
1
2
1
1
1
0
0
2
0
0
0
1
1
0
1
1
0
2
0
0
2
1
0
0
0
1
2
0
1
0
0
1
0
2
0
1
1
4
2
0
2
0
0
2
1
1
0
0
2
1
2
2
0
2
0
0
0
0
1
0
0
0
2
1
2
0
0
0
1
0
0
2
0
1
2
0
0
1
0
0
0
1
0
1
0
1
0
3
0
1
0
0
0
1
1
1
0
0
3
1
2
0
0
0
1
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
2
0
0
0
0
0
0
0
1
1
0
2
0
1
2
0
1
1
0
2
2
1
1
2
0
0
1
0
0
0
2
1
0
0
0
1
0
2
2
0
0
0
2
0
1
1
0
2
0
1
0
0
1
1
1
2
3
1
2
2
1
0
0
1
1
2
2
1
1
1
0
2
1
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
2
1
1
0
0
0
1
1
1
0
0
0
0
1
1
0
0
2
0
0
1
0
2
1
3
2
0
0
0
1
1
1
0
0
0
0
1
0
1
2
0
0
2
1
0
2
2
1
1
0
0
0
3
1
1
3
0
0
0
0
1
1
1
0
0
1
0
1
0
0
2
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
2
0
0
1
1
0
3
0
2
0
0
2
0
3
2
1
2
2
0
0
0
0
0
0
1
2
1
2
0
0
2
0
2
2
1
1
0
0
0
0
0
0
0
2
0
0
1
0
2
2
0
0
1
0
3
1
2
0
0
0
0
2
0
2
2
0
0
2
1
2
2
2
0
0
0
1
0
0
0
0
1
0
2
0
2
1
1
0
1
0
0
0
1
0
2
1
2
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
1
1
0
2
0
0
2
0
2
1
0
2
0
0
0
0
0
0
1
1
0
0
2
0
2
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
3
0
2
0
1
2
1
2
8
0
0
0
0
3
2
2
2
0
2
0
1
1
3
1
0
2
0
0
2
2
0
2
0
1
1
0
1
2
0
0
0
0
1
2
2
0
2
1
0
1
0
0
0
2
1
0
2
1
0
0
0
1
0
5
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
1
1
0
0
2
0
0
1
0
0
0
0
2
0
1
1
2
0
0
2
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
1
1
1
0
0
1
2
0
0
0
2
1
0
1
0
0
1
0
1
0
2
2
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
2
0
2
1
0
1
0
1
1
1
1
1
1
0
0
0
0
2
2
0
0
1
0
0
3
0
2
2
0
0
1
2
0
0
0
0
1
2
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
1
0
1
1
0
0
0
2
1
1
2
0
0
2
0
1
0
1
2
0
0
0
1
1
1
1
0
0
0
0
1
2
1
3
2
1
0
0
0
1
1
2
2
1
0
1
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
1
2
0
1
0
0
2
2
1
0
0
0
0
0
0
0
1
1
0
0
2
0
2
0
0
0
0
1
0
0
3
2
0
1
1
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
1
4
2
1
0
0
2
0
1
2
0
2
1
0
1
1
2
0
0
3
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
2
2
0
2
0
1
5
1
0
1
2
1
0
0
2
2
1
0
2
1
0
1
1
3
0
0
0
10
1
1
0
1
0
0
0
0
1
0
2
0
1
0
2
1
0
0
1
2
0
2
0
0
2
0
2
0
1
0
0
1
0
0
3
1
1
0
1
1
0
0
0
0
0
0
0
1
1
2
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
1
2
1
0
1
2
0
0
1
0
1
0
2
1
0
2
0
0
0
0
1
0
0
0
0
1
1
2
6
2
1
0
1
0
1
0
2
0
0
3
2
1
0
0
0
1
0
0
2
1
1
1
1
0
0
0
0
2
0
2
1
0
0
0
3
0
0
0
1
0
0
0
0
0
0
2
0
2
2
0
2
0
0
2
0
0
1
0
0
1
2
0
0
2
0
0
0
0
0
1
2
2
0
2
0
1
0
0
3
0
0
0
2
0
0
1
1
1
0
0
0
1
3
1
1
0
0
2
0
0
1
2
0
0
0
1
3
2
2
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
2
2
0
1
1
0
0
0
0
0
0
2
0
1
2
0
1
1
2
1
0
2
0
2
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
2
0
2
0
0
1
0
0
0
0
0
0
2
0
0
1
1
0
0
1
1
1
1
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
1
1
0
2
0
0
1
1
0
0
2
0
1
0
2
1
0
0
0
1
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
1
1
0
2
1
0
0
0
0
0
1
1
0
2
1
3
0
0
0
3
1
0
0
2
1
1
1
0
4
0
1
2
0
0
0
0
2
1
0
1
2
1
0
0
1
0
0
1
2
0
0
1
0
1
0
0
2
0
1
0
2
1
1
0
0
1
2
1
2
1
0
1
0
1
0
2
2
0
1
0
0
0
0
1
0
0
0
0
1
0
1
1
2
0
1
0
1
0
0
1
0
1
0
1
0
1
0
2
1
0
0
2
0
3
0
1
0
1
0
1
2
1
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
2
0
2
0
2
1
0
0
0
2
2
0
1
2
0
1
0
1
0
2
2
0
0
1
1
0
0
1
1
0
0
1
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
1
0
2
0
0
0
0
0
1
0
0
2
0
0
1
0
2
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
2
0
0
1
1
0
0
0
0
2
0
1
2
0
0
1
0
1
0
0
0
2
0
0
2
0
3
0
0
0
1
0
0
0
0
0
1
0
1
2
0
0
0
0
0
2
0
0
2
0
0
1
2
0
0
0
1
0
0
0
1
2
0
0
1
0
0
0
2
0
0
2
0
0
0
2
1
0
0
0
2
0
1
2
2
0
3
1
0
0
2
1
0
1
2
1
0
2
0
0
1
1
1
1
0
2
1
0
0
1
0
2
1
2
2
2
0
2
2
0
2
0
0
2
0
0
2
2
0
1
1
0
2
1
2
0
0
2
0
2
0
0
0
1
1
0
0
1
2
3
1
2
2
0
0
0
0
0
0
2
1
0
1
1
1
0
0
1
2
1
0
1
1
0
2
0
0
0
0
0
0
1
0
1
0
1
1
0
1
0
0
0
1
1
1
0
3
1
0
3
0
0
0
1
1
0
0
2
0
1
2
1
1
0
1
0
0
1
1
0
0
0
0
2
0
0
0
2
1
0
1
0
3
1
1
2
0
0
2
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
2
2
0
0
0
1
1
3
0
0
0
0
0
0
0
2
0
1
1
0
0
1
2
2
0
0
0
1
1
0
0
1
0
0
2
0
0
1
0
1
0
1
1
0
0
0
0
2
0
1
2
0
2
0
0
1
1
0
0
2
0
0
1
1
0
1
0
0
2
3
0
2
0
1
1
2
1
2
0
2
0
0
2
0
0
0
2
1
1
0
2
1
0
1
2
1
0
2
2
2
1
3
0
1
1
2
3
0
0
0
0
0
0
0
0
0
1
0
1
0
1
2
0
0
1
0
0
0
0
0
1
1
0
1
0
1
0
0
2
0
2
2
1
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
2
1
0
1
1
2
2
0
0
2
1
2
0
0
0
1
0
3
0
2
1
2
0
0
1
0
0
1
2
0
0
1
0
0
1
0
1
1
0
2
0
2
0
2
2
1
0
2
1
0
0
0
0
3
0
0
0
0
2
0
0
0
2
0
1
1
2
0
0
0
0
0
0
0
2
0
1
2
0
4
0
2
1
2
0
1
2
2
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
1
2
2
2
0
0
3
1
0
0
0
0
3
1
2
2
0
0
1
2
0
1
1
0
0
0
1
1
0
1
5
0
0
1
2
0
0
2
3
0
2
1
2
1
2
0
0
1
1
2
1
2
0
0
0
0
1
2
2
0
0
2
0
1
1
0
2
0
1
1
1
2
2
0
0
0
0
1
0
2
0
0
1
0
0
2
0
0
0
2
0
3
0
2
0
2
1
1
0
0
0
0
0
2
1
2
2
0
0
0
0
0
2
1
2
1
0
0
0
0
1
0
2
1
2
1
0
0
2
1
1
0
1
0
0
2
1
1
0
0
0
1
1
2
0
5
1
1
0
0
2
0
0
0
1
0
0
2
0
2
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
2
0
0
0
0
1
0
0
2
1
2
0
1
0
0
2
1
0
0
0
1
2
1
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
1
2
0
0
0
1
0
0
2
1
2
0
0
0
2
0
0
2
0
2
0
0
0
0
1
0
1
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
1
1
1
0
2
0
0
0
0
0
0
0
0
1
4
1
1
1
1
0
2
2
0
0
0
0
0
1
0
0
1
0
0
2
1
0
0
1
0
1
1
2
0
1
2
3
2
2
1
2
0
0
1
0
0
0
2
0
0
0
2
0
2
1
1
0
1
0
0
0
2
0
0
0
0
0
0
2
1
0
2
0
1
1
1
0
0
0
0
0
0
0
1
1
1
0
0
0
3
1
1
0
0
1
0
1
1
0
0
0
1
1
0
2
0
1
0
1
2
1
2
1
1
0
0
0
0
0
0
0
0
1
1
0
0
2
2
2
0
3
0
1
2
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
1
0
2
0
2
1
2
2
1
0
0
2
0
0
2
0
2
0
0
0
2
1
1
1
1
2
0
0
0
0
0
1
0
0
2
2
0
1
0
2
0
0
1
1
0
0
0
0
0
0
0
2
2
0
0
1
2
0
1
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
1
2
0
0
1
0
1
0
0
1
0
1
0
2
0
2
1
1
2
0
0
0
0
0
0
1
0
1
1
0
1
2
0
1
1
1
0
0
0
1
1
0
0
0
1
0
1
0
1
0
3
0
0
2
1
0
0
1
0
0
2
0
1
1
0
2
0
1
0
0
0
0
0
0
1
4
2
2
0
2
0
0
2
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
2
1
1
0
0
0
0
1
3
1
2
1
0
0
1
0
0
3
0
0
0
0
5
0
2
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
1
2
0
1
1
0
0
0
0
0
0
0
2
0
2
0
1
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
2
1
0
2
0
1
0
2
0
0
0
0
0
3
0
0
0
0
0
2
2
0
0
0
2
0
0
0
1
0
1
2
0
0
2
2
0
0
0
1
2
1
0
0
2
1
1
0
1
0
1
1
1
3
0
0
2
1
2
1
1
0
0
0
0
2
1
0
0
2
1
2
2
2
2
0
2
0
1
0
2
1
0
0
2
2
1
0
2
0
2
0
0
0
0
0
1
0
1
1
1
3
0
0
0
2
0
0
2
0
0
1
0
1
0
0
1
1
0
0
2
0
0
0
0
1
0
0
1
1
0
0
0
0
2
0
0
2
0
0
0
2
0
2
0
0
2
0
1
0
3
0
1
1
2
1
0
0
1
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
5
0
1
0
0
1
1
0
0
0
0
1
1
0
0
0
2
0
0
0
0
2
0
0
0
1
2
0
0
2
0
0
1
0
2
0
1
1
2
0
1
0
0
0
0
0
2
1
0
1
0
0
0
1
0
2
0
1
0
2
3
2
2
2
0
0
1
2
0
0
0
0
2
2
0
2
0
0
0
0
0
2
2
0
2
1
2
0
0
1
0
0
1
0
2
1
1
0
1
1
2
1
1
2
1
0
0
1
0
2
0
2
1
2
0
1
2
0
0
2
0
0
0
1
0
0
1
0
2
1
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
1
0
1
1
1
1
0
0
2
0
0
1
1
0
0
0
2
1
0
1
0
1
0
1
0
0
0
0
0
2
1
2
2
0
1
0
0
1
0
0
0
0
1
0
1
2
0
0
0
0
1
2
2
3
0
0
0
2
0
2
0
0
1
0
1
0
1
0
0
1
0
1
0
1
0
2
0
0
0
0
1
0
0
2
2
1
0
0
0
1
0
0
1
0
2
0
2
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
2
0
1
1
1
2
0
0
0
0
0
2
2
0
0
0
1
1
3
0
0
0
2
0
0
1
1
2
0
0
2
2
1
1
1
0
0
2
0
1
3
0
1
0
0
1
0
1
2
2
1
0
2
0
3
2
2
0
2
2
2
1
1
2
2
0
0
0
0
0
1
1
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
2
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
2
1
0
2
2
2
2
0
0
0
0
1
2
0
0
1
2
0
2
2
0
2
0
1
1
0
0
1
1
0
0
2
0
0
0
1
0
3
0
0
1
2
0
0
1
1
2
0
1
2
0
1
2
1
0
0
1
0
0
0
1
0
0
0
0
0
2
1
0
0
2
0
2
0
0
0
2
0
1
0
0
0
1
1
0
0
0
1
0
0
0
2
0
2
2
0
0
0
2
0
0
0
0
0
2
0
2
0
1
0
2
0
1
0
0
2
2
1
0
0
1
2
0
0
0
2
0
0
0
0
2
1
0
0
0
0
5
0
0
2
2
0
1
0
0
1
2
0
1
0
0
0
0
0
1
1
0
0
0
0
1
1
1
1
0
0
0
3
1
1
1
0
0
1
0
0
2
1
2
1
3
0
3
1
0
0
1
0
0
2
0
0
2
0
2
0
0
2
1
0
0
0
1
0
0
5
0
0
1
0
0
0
0
0
1
2
0
1
0
0
1
0
0
1
1
0
0
1
0
1
1
1
1
0
0
2
1
1
1
1
2
0
2
1
0
0
1
0
3
2
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
1
0
1
2
0
0
1
0
0
1
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
2
0
0
0
0
2
0
2
2
0
2
2
1
0
0
0
0
2
2
0
0
0
1
1
0
1
0
2
0
3
0
1
0
0
0
1
2
0
2
0
0
2
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
1
0
0
1
1
1
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
1
0
2
0
1
1
0
0
1
0
0
2
0
0
1
0
1
0
0
2
2
2
0
0
0
0
0
2
0
1
2
1
1
1
2
1
2
4
0
0
2
1
2
1
4
0
0
1
1
1
0
0
0
0
0
0
1
1
1
2
1
0
0
2
1
1
0
0
0
0
2
0
0
1
2
2
0
1
1
2
1
0
0
1
0
1
0
2
0
4
1
1
1
0
2
0
0
2
0
2
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
1
0
1
0
2
1
0
1
1
0
1
0
1
5
0
0
2
0
0
2
0
1
2
2
2
1
0
2
1
0
0
0
2
1
0
1
0
0
2
0
0
0
2
1
0
1
0
0
2
0
1
0
0
1
0
0
0
4
1
0
2
1
0
0
0
1
1
1
2
1
0
2
0
2
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
1
1
0
2
3
0
1
0
1
2
0
0
0
0
1
5
0
0
0
2
0
1
0
0
1
0
0
0
1
1
0
0
0
1
2
2
2
0
2
1
1
2
1
6
0
2
0
5
2
1
0
0
2
0
0
1
0
2
0
2
1
1
0
0
1
2
1
1
1
0
0
1
0
0
0
1
1
0
0
0
2
0
1
0
0
1
2
1
0
3
0
2
0
0
0
0
0
2
0
2
0
1
2
3
0
1
1
0
0
0
0
1
1
0
0
0
1
0
2
0
2
0
0
0
0
0
0
1
2
0
0
1
2
1
0
3
0
2
0
0
0
0
0
0
0
1
1
2
0
0
1
1
1
0
0
0
0
0
1
0
0
0
1
1
3
0
0
2
0
0
1
1
2
1
0
0
0
0
1
2
0
0
1
1
0
0
0
0
0
2
1
2
3
1
0
1
2
0
0
1
2
2
2
0
0
1
0
1
2
0
0
2
1
2
0
1
1
0
1
1
2
1
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
1
0
0
0
2
2
0
1
1
0
0
0
1
0
3
1
0
1
0
0
2
0
1
1
0
0
0
0
0
0
0
1
0
2
0
0
3
1
1
0
0
0
1
1
1
2
3
1
0
0
0
0
0
1
0
0
2
2
0
1
1
1
0
2
2
0
0
0
1
2
0
1
2
2
0
0
1
0
0
0
0
0
2
2
0
0
0
0
1
0
1
1
0
1
0
3
0
1
0
0
0
0
0
0
1
0
0
2
1
2
2
3
2
0
1
1
0
1
1
0
2
0
0
2
0
0
1
0
0
1
0
2
2
1
0
1
2
0
0
0
2
0
1
0
1
1
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
1
0
0
0
2
0
0
2
1
1
3
0
0
0
0
0
2
0
2
1
0
1
0
0
2
0
0
0
0
2
0
0
2
1
0
0
2
1
0
1
1
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
2
1
1
1
1
0
3
1
0
1
1
0
0
0
0
0
1
2
2
0
0
0
2
0
0
1
0
1
0
0
0
3
0
0
0
1
0
0
0
0
0
2
0
0
1
2
2
0
0
0
0
0
2
0
0
1
1
1
0
1
0
2
0
0
0
1
0
0
1
1
0
0
1
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
2
2
0
2
3
0
1
0
3
0
2
2
2
1
1
0
2
0
1
1
2
0
0
2
2
1
0
0
1
0
2
2
0
0
1
0
0
0
6
0
0
0
0
0
2
1
2
0
0
2
2
0
2
0
2
1
2
0
0
0
0
0
0
2
0
2
1
1
0
0
2
1
4
0
0
1
1
0
0
0
0
0
0
0
0
2
1
2
0
2
1
0
0
0
2
1
2
0
1
0
0
1
0
0
2
2
1
0
0
0
2
1
2
1
0
0
3
1
2
1
2
0
0
1
0
0
1
0
1
0
0
0
0
0
1
2
1
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
2
0
1
0
0
1
0
2
1
2
0
0
0
2
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
2
0
1
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
1
3
3
0
0
0
0
1
1
1
0
2
2
0
0
3
0
0
1
0
0
0
0
0
0
0
1
3
3
1
2
1
1
0
2
2
0
2
0
0
0
1
0
0
1
2
1
0
4
0
2
0
0
2
1
1
0
1
0
2
1
0
2
0
2
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
1
2
0
2
0
0
0
2
1
2
0
2
2
0
0
0
0
0
1
1
1
3
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
1
0
1
1
2
2
1
0
1
1
0
1
0
0
1
1
1
0
0
0
1
0
2
0
1
1
0
3
0
0
0
0
0
2
2
1
2
1
0
1
0
1
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
1
0
2
2
1
2
1
1
0
1
0
2
2
0
0
0
2
0
0
2
0
0
0
2
0
3
2
2
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
1
1
2
1
1
1
1
2
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
2
0
2
0
0
0
0
0
0
1
2
1
0
0
0
1
0
1
0
1
0
0
0
1
1
0
2
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
2
1
0
0
0
0
0
1
2
0
2
0
0
2
2
1
0
0
0
0
1
2
0
3
1
2
0
1
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
2
2
0
1
0
0
0
1
1
0
0
1
1
1
0
1
0
2
0
1
0
0
1
0
2
2
0
0
2
0
0
1
0
2
2
1
0
0
1
0
1
0
1
0
2
0
0
0
0
1
0
0
0
0
2
1
0
0
1
2
0
2
1
0
4
0
0
33
0
1
2
0
1
0
0
0
0
0
0
1
1
1
0
1
0
0
1
0
2
0
2
2
1
2
1
0
0
0
1
0
1
2
0
0
2
0
0
5
1
1
1
0
1
0
0
5
2
0
2
1
2
1
0
0
2
0
1
1
0
0
2
0
0
0
0
2
0
1
0
2
2
0
0
0
0
2
2
1
1
2
1
2
2
0
0
3
1
0
0
1
2
2
2
2
0
0
0
0
2
1
1
0
0
1
2
0
0
1
0
2
0
0
1
2
0
2
0
0
1
0
0
1
2
0
0
1
1
1
0
1
2
1
0
2
0
0
0
1
0
4
0
1
2
0
0
2
1
1
0
2
0
0
0
0
1
1
0
0
0
1
0
2
1
0
0
1
1
0
1
0
3
0
0
0
1
3
0
0
2
0
1
2
0
0
1
0
1
0
2
1
0
0
0
2
1
0
1
1
0
0
0
2
2
0
2
0
0
0
1
2
0
0
0
1
2
1
0
1
1
2
1
2
0
0
0
0
0
1
2
2
1
2
0
0
0
2
0
1
1
1
0
0
0
0
1
0
1
0
0
1
2
3
0
2
2
0
2
0
0
0
2
1
1
1
0
0
0
2
0
0
2
0
1
0
1
0
0
2
1
0
0
0
2
0
0
0
0
0
1
0
2
0
2
1
0
0
1
0
0
0
0
0
1
0
1
0
2
0
0
0
1
2
1
0
0
0
0
0
0
1
1
1
4
1
1
2
1
0
2
0
0
2
0
2
0
0
0
0
0
1
0
2
0
1
0
0
0
0
2
1
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
12
0
0
1
2
0
2
0
2
0
0
0
0
0
0
0
0
0
1
3
1
2
2
0
0
1
0
1
0
2
1
1
1
0
0
0
0
0
2
1
0
2
1
0
1
2
2
0
0
1
2
2
1
1
0
0
0
1
0
2
2
2
0
0
1
0
1
0
0
2
1
1
1
0
2
1
2
1
1
1
0
1
1
0
1
1
0
2
0
1
0
0
0
1
0
2
8
2
0
0
2
0
2
1
0
0
2
0
0
1
0
2
0
0
1
0
1
3
0
2
0
0
0
0
2
0
0
1
0
0
2
0
0
1
2
0
0
2
0
2
0
0
1
0
0
0
1
1
0
0
3
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
2
0
3
1
0
2
2
2
1
1
1
0
0
0
1
0
1
1
0
2
0
0
2
0
1
0
0
2
0
1
0
0
0
1
0
1
0
2
2
0
0
1
2
1
0
1
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
1
0
0
0
1
1
0
0
0
0
0
1
1
1
0
1
0
0
1
2
2
2
0
0
2
0
0
0
0
0
2
2
0
1
0
0
1
2
1
2
0
1
0
1
2
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
2
0
0
0
0
2
2
0
1
0
0
0
0
1
2
1
1
0
1
1
2
1
2
0
0
1
2
0
0
1
0
0
2
1
3
1
0
2
1
2
1
0
0
3
1
0
2
2
0
1
0
0
1
1
0
0
0
0
1
1
1
1
0
0
1
0
2
0
0
2
0
0
0
0
0
2
2
0
0
1
2
2
1
0
0
0
0
0
0
0
1
0
0
2
0
1
0
2
0
0
1
0
1
2
2
0
0
2
0
0
1
1
1
2
1
3
0
1
1
0
0
0
0
2
1
1
0
2
1
0
0
0
2
0
2
0
0
2
2
0
0
2
0
0
2
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
1
0
0
2
0
2
1
2
0
0
0
1
0
2
1
1
2
1
1
0
1
1
2
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
3
0
4
0
0
0
0
0
1
1
0
0
0
0
1
2
0
1
0
2
1
0
2
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
2
1
0
0
0
0
1
1
0
0
1
0
0
1
1
1
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
2
0
0
1
3
0
1
2
0
0
0
1
0
1
2
1
0
0
1
0
2
0
0
2
0
4
0
0
0
0
0
0
0
0
3
1
0
1
2
2
0
1
0
0
1
1
1
0
0
0
0
0
1
0
2
1
2
1
0
0
0
0
0
1
2
0
1
0
0
0
2
2
0
3
0
1
0
2
2
0
0
0
1
2
1
0
1
0
0
0
1
2
0
0
0
1
0
0
2
1
1
1
2
0
0
1
0
0
0
0
1
0
1
0
1
0
0
2
2
0
0
1
2
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
1
1
1
0
1
0
2
2
1
1
0
0
1
0
1
1
0
0
2
0
0
4
0
2
1
0
2
2
0
0
2
0
0
2
0
0
0
0
0
0
2
2
0
1
0
0
1
0
0
2
2
2
0
2
0
0
2
0
1
1
0
1
0
0
1
1
2
0
2
0
0
0
0
2
0
0
0
0
1
0
0
1
1
0
0
0
2
0
0
2
2
0
1
0
0
0
1
1
0
2
0
1
0
1
0
3
2
1
0
1
3
2
0
1
0
5
2
1
0
0
0
1
2
0
1
2
2
1
0
2
0
0
1
1
0
0
2
0
0
0
1
0
0
1
2
0
0
0
2
0
2
1
1
1
0
2
0
2
1
2
0
0
0
0
0
0
2
1
0
1
1
0
2
0
0
0
1
2
2
2
0
1
0
2
1
0
1
0
2
1
0
3
0
2
2
0
0
0
0
1
0
1
0
0
0
0
2
1
0
1
0
1
1
2
0
0
2
0
2
0
0
0
1
1
2
0
0
0
0
0
1
1
1
2
0
0
0
0
2
0
2
1
2
0
1
2
0
0
0
0
0
2
0
2
1
0
1
0
2
1
1
0
0
0
0
0
0
0
1
1
1
0
3
0
1
2
0
2
2
1
1
1
0
1
0
0
0
3
2
0
0
0
2
1
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
1
1
1
0
0
1
1
1
0
0
0
0
0
0
2
2
1
2
0
1
0
0
1
0
0
2
1
0
1
1
0
0
0
0
1
1
1
2
1
0
2
0
0
1
2
0
0
1
1
2
2
1
1
0
2
1
1
1
2
0
0
1
2
1
1
0
0
0
0
0
0
1
2
2
0
0
0
0
2
0
2
0
0
2
1
0
0
0
0
0
0
1
0
2
1
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
1
0
2
1
0
1
1
0
0
2
1
2
2
0
2
2
0
0
0
2
2
0
1
0
1
0
0
1
0
2
0
0
1
1
0
0
0
2
1
0
0
1
0
0
0
1
2
0
1
0
0
2
0
0
1
2
1
0
2
0
0
1
0
1
0
1
0
1
2
0
0
1
2
0
1
1
1
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
1
1
1
0
2
2
0
1
0
0
2
0
2
0
4
0
0
1
0
0
2
1
2
3
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
1
1
1
1
2
0
0
1
3
2
1
0
0
0
1
1
1
2
0
2
0
0
1
0
0
0
0
0
0
1
1
0
2
2
1
0
2
2
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
1
4
1
1
3
0
0
1
2
0
1
2
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
1
2
1
0
1
0
0
1
0
0
2
2
1
2
0
1
0
2
0
0
0
2
1
0
1
1
0
0
0
0
0
2
0
2
0
0
2
2
0
0
1
0
0
2
1
0
0
5
0
2
2
0
1
0
2
0
1
2
1
0
0
0
0
1
1
1
2
2
1
0
0
0
0
0
1
0
1
1
0
0
1
2
0
0
0
0
1
0
0
3
1
1
2
0
0
0
1
0
1
0
0
0
2
0
0
3
0
0
7
0
0
0
1
0
1
0
2
2
0
2
2
0
0
0
0
2
0
3
2
2
0
1
1
2
0
0
0
3
2
0
0
0
1
0
0
0
0
0
0
0
0
0
4
2
0
0
2
0
0
2
1
0
1
0
0
1
0
2
1
0
0
0
0
1
1
0
0
0
0
1
2
0
0
1
1
1
2
0
0
0
0
1
0
1
2
1
0
2
0
0
1
0
0
1
0
2
1
0
1
1
0
0
1
1
0
0
0
0
0
1
0
0
4
0
0
2
0
1
2
0
2
4
1
0
1
0
1
1
2
2
1
1
1
2
0
1
2
2
0
0
0
0
2
0
0
2
0
0
0
1
0
0
1
0
1
0
0
1
0
1
0
0
1
2
0
0
0
0
0
0
1
0
0
1
1
1
0
0
1
0
2
0
2
0
0
2
1
0
0
0
0
0
2
0
2
0
0
1
0
0
1
0
0
0
0
0
0
3
0
0
0
1
2
1
1
0
0
0
1
0
0
2
2
0
1
0
0
0
0
4
0
0
0
3
0
0
0
2
0
0
2
0
0
2
2
1
0
0
0
1
0
1
0
3
1
0
0
1
0
0
0
0
1
0
0
0
1
2
1
0
0
2
1
0
0
0
2
0
0
2
1
2
0
0
0
0
0
0
0
2
2
1
0
0
3
0
0
1
0
0
2
3
1
0
1
0
0
0
0
0
2
3
0
0
2
0
0
1
1
0
0
2
0
1
0
1
2
0
0
2
0
1
4
0
1
2
1
2
0
2
0
1
0
2
0
0
0
2
2
1
2
0
1
2
1
1
0
3
2
0
0
0
3
0
0
1
0
2
0
1
1
0
2
1
0
0
2
2
0
0
0
1
1
0
0
0
0
1
0
0
1
2
1
2
0
1
0
0
1
0
1
0
0
1
1
0
1
0
1
1
1
1
0
2
0
0
0
4
0
0
2
1
3
0
0
2
1
6
0
0
3
0
1
1
1
0
0
1
0
0
2
0
2
0
0
0
1
0
0
0
2
0
1
4
0
0
0
0
0
0
1
0
2
2
0
2
3
1
1
0
0
0
1
1
0
0
2
0
0
0
0
1
2
0
0
1
2
1
0
1
2
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
1
0
0
2
2
0
1
0
2
0
0
0
2
2
0
0
1
0
1
0
0
1
0
1
1
0
1
0
1
2
0
0
0
1
0
2
0
1
1
0
2
1
2
0
0
0
1
2
1
0
1
0
0
1
0
3
0
1
3
0
1
1
1
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
1
0
0
1
2
2
3
0
2
0
0
0
0
2
2
0
0
0
1
0
2
0
1
2
1
1
3
3
0
2
0
1
0
1
3
1
1
2
0
0
0
1
0
1
1
4
2
0
0
2
1
1
0
1
2
0
1
0
2
2
0
0
2
0
0
2
2
2
0
1
3
0
0
0
0
2
2
2
2
1
1
0
0
0
0
0
0
0
2
0
2
0
0
0
2
2
0
0
0
1
1
1
1
0
1
2
0
0
1
0
1
0
0
2
0
0
1
0
3
1
0
1
2
1
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
2
0
1
0
1
1
1
2
1
0
1
1
1
2
0
2
0
1
1
0
1
2
1
0
0
0
1
0
0
0
0
1
1
2
0
2
2
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
1
0
0
1
1
1
2
0
2
0
1
2
0
0
1
1
0
0
0
2
0
1
0
0
0
1
0
1
1
0
1
1
2
0
0
1
2
0
1
0
0
2
0
0
1
1
1
0
2
2
0
0
2
2
0
0
0
2
0
2
0
3
0
1
0
0
2
1
0
0
0
0
0
0
0
0
1
1
2
0
0
1
0
1
0
1
1
0
2
1
0
1
1
2
2
1
0
0
0
2
1
0
1
0
0
1
1
0
0
0
2
0
2
3
0
2
0
1
0
2
1
0
2
1
0
0
1
0
0
0
0
1
1
2
2
1
0
10
1
2
2
0
1
1
0
1
0
1
1
0
1
1
0
1
0
0
0
1
2
1
1
0
2
0
1
0
0
0
0
0
2
0
2
0
1
0
2
0
0
1
0
1
1
0
1
1
0
0
0
0
0
0
0
1
0
1
2
0
1
0
0
1
0
0
2
0
0
1
2
1
0
2
1
0
2
1
0
0
0
2
2
0
0
0
0
0
2
0
0
0
2
1
2
1
1
1
0
2
1
0
0
1
2
0
1
0
2
1
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
2
0
0
0
2
0
1
2
0
2
2
0
1
0
0
0
1
1
0
1
2
6
1
0
0
0
0
1
0
0
0
1
0
0
0
2
1
0
1
0
0
0
0
2
0
1
1
2
0
0
0
0
0
0
1
1
0
1
2
0
1
0
0
1
0
0
2
1
2
0
1
0
2
1
0
0
1
2
0
0
2
0
0
0
0
2
2
2
0
2
1
0
1
1
0
1
0
1
0
1
0
1
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
2
2
0
0
2
1
0
1
2
0
2
1
0
0
0
2
0
2
1
0
1
0
0
2
0
0
0
0
0
0
2
0
1
1
0
1
0
1
0
2
0
1
2
2
2
0
3
1
0
0
1
1
0
2
0
2
1
0
0
2
0
0
1
2
0
0
0
0
1
0
2
1
0
0
1
1
3
1
0
1
0
0
0
1
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
3
3
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
2
2
0
0
1
0
1
0
0
2
0
0
2
0
0
0
2
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
2
2
2
0
0
1
0
0
2
0
0
0
1
1
2
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
2
0
2
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
2
4
0
2
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
1
0
1
1
2
1
2
0
1
0
1
0
0
0
1
1
2
1
1
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
2
0
0
0
1
0
1
1
0
1
0
0
1
0
1
0
0
1
0
2
1
0
2
0
2
2
2
0
0
0
0
2
2
0
1
0
2
0
0
2
2
1
1
0
1
2
1
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
2
0
2
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
2
2
0
2
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
2
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
2
2
0
2
0
0
2
0
2
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
1
2
0
1
0
0
0
0
0
1
0
0
1
0
1
2
2
2
0
0
1
2
0
0
2
0
0
2
0
0
0
1
0
2
2
0
0
2
1
1
0
1
0
2
0
0
1
2
2
0
1
0
0
0
0
0
1
1
1
1
2
2
0
0
0
1
0
0
1
0
2
0
1
1
2
0
0
1
1
1
0
0
0
0
1
0
0
0
0
1
0
0
1
2
2
1
2
0
1
2
2
2
0
2
0
0
0
1
0
0
0
0
0
0
0
1
1
0
2
0
0
1
1
0
1
1
0
1
2
2
2
0
0
0
0
1
0
2
0
2
0
2
0
0
2
0
0
0
0
2
0
0
1
1
1
2
2
0
0
1
0
0
2
1
0
0
0
0
4
0
0
0
0
0
0
0
2
2
1
1
0
1
2
0
0
2
0
0
0
0
1
0
2
1
2
1
1
2
0
0
1
2
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
1
0
1
0
2
0
1
0
2
0
0
0
1
1
1
0
0
1
2
0
0
0
0
2
0
2
0
0
2
0
0
0
2
0
0
0
1
0
0
1
2
2
0
0
1
1
0
0
0
1
2
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
3
0
2
0
0
1
0
0
0
2
0
1
2
0
0
1
1
1
2
0
2
1
0
1
0
0
0
1
0
0
1
0
0
1
0
2
0
1
0
0
2
1
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
1
0
2
0
2
0
0
0
2
1
2
0
2
0
2
0
0
2
0
0
0
2
0
0
1
0
0
1
0
0
0
0
1
2
0
4
1
0
0
1
0
0
0
2
0
1
0
1
0
0
0
0
0
2
0
1
0
0
1
2
0
5
0
2
1
2
1
1
1
0
0
2
0
0
2
0
1
1
0
2
1
0
2
1
0
0
3
1
1
0
0
1
0
2
0
0
2
0
0
0
2
0
2
1
1
1
0
0
0
0
1
2
0
0
0
0
2
0
0
2
2
0
0
0
0
1
0
1
1
0
4
0
2
0
0
0
0
0
2
0
2
3
2
1
2
2
1
2
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
3
0
0
1
0
0
3
0
0
2
0
0
0
1
3
1
0
0
0
0
0
3
0
1
2
1
2
1
3
1
3
0
0
0
0
1
0
2
0
1
0
0
0
0
1
2
0
0
2
0
2
0
2
0
0
0
0
1
0
2
1
1
1
0
2
2
0
1
2
0
0
2
0
0
0
1
0
2
0
0
0
1
0
1
0
0
0
0
1
0
7
0
2
1
1
2
0
2
1
1
1
0
0
0
0
1
1
1
0
0
0
2
0
0
0
0
1
0
1
0
1
1
0
2
0
2
1
0
0
0
2
0
0
0
1
1
0
0
2
0
0
2
0
2
2
0
0
0
2
2
1
1
1
0
0
0
0
0
4
0
0
0
0
0
1
1
1
2
0
0
1
1
0
0
0
2
2
2
0
2
0
0
0
2
0
1
1
0
0
0
0
0
1
1
1
1
1
0
0
0
1
0
0
0
0
1
2
0
0
0
3
2
4
0
0
1
0
1
2
2
0
3
0
0
1
0
2
1
0
2
1
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
1
0
2
0
0
0
0
1
1
2
0
0
0
0
0
1
0
0
0
0
0
3
2
2
0
0
0
0
0
2
1
0
0
3
0
0
0
1
0
0
2
1
0
2
0
1
0
1
0
0
0
2
0
0
1
0
0
0
0
1
1
2
0
2
1
0
0
0
0
2
1
1
1
0
4
2
0
1
0
0
0
0
0
2
1
0
0
1
1
2
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
1
1
2
0
1
0
2
2
0
1
1
1
0
1
1
2
0
0
0
0
2
0
2
1
0
2
2
1
2
0
1
1
0
0
0
2
0
1
1
0
0
0
1
2
0
1
0
0
2
0
0
0
0
0
5
0
1
0
2
0
0
0
0
0
4
2
2
0
2
1
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
1
0
2
2
1
0
0
0
1
1
1
0
1
0
0
0
1
0
0
0
2
2
2
0
0
1
0
0
4
1
1
3
1
1
0
0
0
0
1
2
1
2
3
0
0
0
2
0
0
0
2
1
0
0
0
0
2
0
0
2
0
2
1
1
0
2
2
1
0
1
0
0
0
2
1
1
1
1
0
2
0
0
0
2
1
0
1
0
1
1
1
0
0
1
0
1
0
0
0
1
0
0
2
1
0
0
1
0
0
1
1
2
0
0
0
1
2
2
0
2
1
0
1
0
0
0
2
1
0
0
0
0
1
0
0
0
0
1
1
0
0
2
0
0
2
0
0
0
0
1
0
2
1
1
0
0
2
2
3
1
2
0
0
2
0
2
0
1
0
0
1
1
2
0
1
0
0
2
0
2
2
2
0
0
1
0
2
0
2
1
0
1
0
0
0
0
2
0
0
1
0
1
0
1
2
2
0
1
3
0
0
1
0
0
0
0
1
0
0
0
1
2
0
0
0
2
1
2
0
1
0
1
2
1
0
1
2
0
1
0
0
0
1
1
1
3
0
0
0
0
1
0
0
1
2
0
0
0
0
2
2
0
1
2
3
2
0
2
0
1
0
0
0
0
0
2
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
1
0
0
1
3
0
2
1
0
1
1
0
0
0
0
0
1
2
0
1
2
1
1
0
0
0
2
2
1
0
2
0
2
3
0
0
0
1
2
0
0
0
0
0
0
1
0
2
0
2
0
1
1
0
0
1
0
0
0
0
0
0
0
2
0
3
0
1
0
0
2
1
0
0
1
0
0
0
2
0
1
0
0
0
2
0
1
0
0
0
0
3
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
1
0
0
1
2
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
2
0
1
0
0
2
1
0
0
0
1
1
0
0
0
0
0
0
0
5
1
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
2
0
0
2
2
1
1
0
1
0
0
1
0
1
0
1
1
1
0
0
2
2
1
0
1
1
2
1
0
0
1
0
1
2
0
0
1
2
0
2
1
2
0
0
0
0
0
0
1
1
2
0
1
0
1
1
0
1
1
1
2
2
0
0
1
0
0
0
0
2
2
2
0
0
0
1
0
0
0
1
1
0
2
0
1
1
2
3
2
1
2
0
0
3
1
1
0
0
0
0
0
0
0
1
2
0
1
0
1
3
2
1
2
0
0
0
1
0
1
0
0
0
1
0
1
0
0
1
2
0
1
0
0
1
0
0
0
1
1
0
0
0
0
1
1
0
1
3
1
0
0
1
1
2
2
0
0
0
3
2
1
0
1
0
0
1
2
0
0
2
1
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
1
0
2
1
0
2
1
0
0
1
0
1
2
0
1
0
0
0
2
2
1
0
1
0
1
0
1
2
0
2
0
0
2
2
0
2
1
0
0
0
0
0
2
0
0
0
0
0
1
0
1
1
1
0
0
0
0
2
1
1
0
1
0
0
0
0
1
0
1
2
1
0
0
1
1
0
1
1
0
2
1
1
0
2
2
2
0
1
0
0
0
0
0
0
1
2
0
1
2
0
1
0
0
0
0
0
1
0
3
4
0
0
0
1
0
2
1
0
0
0
1
2
2
2
0
0
1
0
2
1
1
1
0
0
0
1
0
1
2
0
0
0
0
0
2
0
2
0
2
2
1
1
1
2
0
2
0
0
2
0
0
0
3
0
0
2
2
2
2
0
0
0
0
1
0
2
0
0
1
1
0
2
1
1
0
0
2
0
1
1
0
1
0
3
2
1
0
1
0
0
0
0
2
2
0
0
1
0
0
2
0
1
2
0
1
0
1
2
0
0
3
0
0
0
0
1
0
1
1
0
0
0
0
0
2
0
0
1
1
2
0
0
0
2
0
2
2
1
0
1
1
0
0
1
0
2
1
0
1
0
2
0
0
0
3
0
0
2
0
2
0
0
0
2
0
1
1
1
0
1
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
2
0
0
0
0
1
3
0
0
2
1
1
0
2
1
1
1
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
1
0
0
2
0
2
0
0
1
0
0
0
1
2
1
0
0
2
1
0
0
2
0
2
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
2
2
0
1
0
0
0
0
0
0
0
1
2
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
1
0
1
1
0
0
2
0
0
0
1
2
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
2
1
0
0
1
1
0
1
2
0
0
0
0
0
2
0
1
1
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
1
0
1
1
0
2
1
0
1
1
1
2
0
0
1
2
2
2
1
0
0
0
0
0
1
1
2
1
0
2
2
1
0
0
2
0
1
1
1
0
2
0
0
0
1
1
3
1
0
1
0
0
0
0
0
1
1
1
0
0
1
0
0
1
0
0
1
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
2
0
2
0
0
2
0
1
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
1
0
0
2
1
0
1
0
1
0
0
0
0
1
0
1
1
0
1
1
0
1
0
0
2
0
0
0
0
2
0
2
0
0
0
2
1
0
0
3
2
1
0
0
0
1
4
1
0
0
0
0
0
0
2
1
2
0
0
2
1
2
0
2
1
0
0
0
1
0
1
2
1
0
2
2
1
0
1
1
0
2
1
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
1
0
0
2
0
1
1
0
0
1
2
0
2
0
0
0
1
1
0
2
1
0
1
0
0
0
2
0
0
1
2
2
0
0
0
1
0
0
1
0
0
0
0
0
1
1
1
1
3
2
2
0
0
0
1
0
1
0
2
0
0
2
0
0
1
0
0
1
0
1
0
2
3
0
2
0
0
1
1
2
2
1
0
0
0
2
0
4
0
0
1
2
1
1
2
1
0
1
0
3
0
1
2
0
0
1
1
0
0
0
0
3
0
0
0
0
1
1
1
0
1
0
0
0
0
1
1
2
2
0
0
1
0
0
0
1
0
0
2
2
0
1
0
0
1
1
0
2
3
0
0
1
0
1
0
1
0
0
1
2
1
2
0
0
1
0
2
0
1
1
0
0
0
1
2
1
0
0
1
1
0
2
1
2
2
0
0
0
0
0
1
1
0
0
1
0
1
0
1
1
0
1
1
1
0
2
0
0
7
0
2
0
0
0
1
0
0
0
1
0
0
0
1
0
1
2
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
2
0
1
0
0
0
2
2
0
1
0
0
1
1
1
0
0
0
2
0
0
0
1
0
2
1
0
2
2
0
1
0
2
2
0
0
2
1
0
1
0
1
0
0
2
0
0
1
1
0
0
1
1
2
0
1
0
0
0
0
2
2
0
0
0
0
1
0
2
1
2
0
1
1
1
2
2
0
0
0
1
0
2
2
1
1
1
0
1
0
0
0
1
2
2
0
0
2
0
2
0
2
1
0
2
0
1
0
2
1
1
0
0
0
0
0
2
0
1
2
1
3
2
0
2
0
2
2
2
0
1
1
1
2
2
0
2
0
0
0
1
0
2
3
0
0
2
1
0
0
2
0
0
0
0
1
0
1
0
1
2
1
2
0
0
0
1
0
0
0
2
2
0
0
0
1
1
2
2
0
0
1
0
0
0
0
1
2
1
2
0
1
0
0
0
2
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
1
0
1
0
1
0
0
1
1
1
1
2
2
1
0
1
2
0
1
0
0
0
1
0
2
0
0
0
1
3
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
1
2
0
0
1
1
1
0
0
0
0
1
2
1
1
0
0
0
0
2
1
0
0
1
1
1
0
1
0
2
3
2
1
0
1
0
0
2
0
0
2
0
0
0
0
3
2
2
3
0
0
2
1
1
0
0
1
0
1
2
2
0
1
0
0
4
1
0
1
2
0
0
0
1
1
0
0
0
3
1
0
1
2
0
0
1
2
0
1
1
1
4
1
0
2
1
1
2
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
1
2
0
0
1
5
9
0
2
0
1
2
0
2
1
0
0
0
0
2
1
0
0
0
0
1
3
1
0
2
2
2
0
1
2
0
0
2
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
1
2
0
2
1
1
0
1
2
2
3
2
1
2
0
1
0
0
1
0
1
0
2
2
2
0
2
1
0
0
0
1
1
0
1
1
1
2
2
0
0
0
0
0
0
1
1
2
1
1
1
0
0
0
0
2
0
1
0
2
0
0
0
1
0
1
1
0
0
0
1
0
2
1
3
2
1
0
0
0
1
2
1
2
0
1
0
0
1
0
0
0
0
2
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
2
2
1
0
0
0
1
0
0
0
1
2
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
1
0
1
0
0
1
1
0
0
0
0
2
0
3
0
0
0
0
1
4
2
0
0
0
2
1
0
0
1
0
0
0
0
0
2
2
2
0
0
0
0
0
1
1
1
0
1
1
1
0
0
2
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
1
1
0
0
3
1
0
0
0
2
0
0
1
0
1
0
1
0
0
1
1
1
1
0
1
2
0
0
1
0
0
2
2
1
1
0
0
0
0
3
0
0
0
0
0
2
0
0
0
2
0
0
1
1
1
0
2
1
0
0
1
0
0
0
0
0
0
1
1
2
0
0
0
2
2
0
2
1
1
0
2
0
0
0
0
1
2
2
1
0
0
3
0
0
0
0
0
0
2
1
1
0
1
2
1
0
1
1
1
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
2
2
2
0
1
2
1
0
2
2
2
2
0
2
2
0
0
0
1
2
1
2
2
2
2
0
1
0
1
0
1
0
0
0
2
2
0
0
0
1
1
0
1
0
0
0
1
0
1
0
0
0
1
2
0
2
1
1
0
0
0
0
0
1
0
0
1
1
2
0
2
1
0
0
1
0
2
0
0
2
1
0
6
0
0
1
0
1
1
3
2
1
0
0
0
2
2
1
1
0
2
0
2
0
0
1
0
1
2
0
0
2
0
1
0
0
0
0
0
0
0
0
1
1
1
0
2
0
0
0
0
1
1
0
0
1
0
0
2
2
0
1
0
0
0
0
2
0
1
2
0
1
1
0
0
1
0
0
0
2
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
1
3
0
0
1
0
2
0
0
0
1
2
2
0
1
0
1
2
0
1
0
2
1
0
1
0
2
0
0
0
1
1
2
0
0
0
0
0
0
1
0
1
1
2
1
2
0
0
2
0
0
2
2
0
0
1
0
0
1
1
2
0
0
0
3
2
0
0
0
1
0
2
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
2
1
1
2
0
0
0
0
0
0
1
0
2
2
2
0
1
0
0
0
0
0
2
1
1
0
2
0
1
2
0
1
0
0
1
2
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
3
0
0
1
0
0
2
2
0
0
1
3
1
0
2
2
0
1
1
1
1
0
0
2
1
0
1
10
2
0
2
2
0
2
1
2
1
0
0
0
2
0
1
2
2
2
0
1
2
2
2
0
0
0
2
0
0
3
2
0
0
0
0
1
0
0
2
2
0
1
0
1
1
0
1
1
0
0
1
0
1
1
1
1
0
0
1
0
2
0
2
0
2
0
1
2
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
2
0
0
1
3
0
0
0
1
0
0
0
2
0
1
1
0
1
0
0
2
0
0
1
0
0
0
0
1
0
0
0
2
2
2
1
0
0
0
0
0
0
0
0
4
2
2
2
0
1
2
0
0
1
2
2
2
0
0
0
0
3
1
0
0
0
0
0
1
2
2
1
1
1
0
0
0
0
0
1
0
0
0
0
0
1
1
2
0
2
1
1
1
0
0
2
2
1
0
1
0
0
0
0
1
3
3
2
2
1
0
1
1
1
0
0
0
0
0
0
1
1
1
0
0
1
0
2
0
0
1
0
0
0
1
1
1
0
0
0
0
1
0
0
1
0
0
2
0
2
0
2
0
0
0
0
1
0
0
0
1
0
0
0
2
2
1
0
0
2
2
0
1
1
0
2
2
0
1
0
0
3
0
0
0
0
0
0
0
1
1
0
0
1
1
0
1
0
2
0
0
0
2
1
0
1
1
2
1
1
0
0
0
2
0
0
1
0
0
1
0
1
1
1
2
1
0
0
0
0
0
2
2
0
0
0
0
0
0
2
1
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
1
0
2
2
2
1
0
0
2
1
0
2
0
1
2
1
2
0
2
1
2
1
1
0
0
0
0
0
0
1
1
0
0
2
3
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
1
0
0
1
2
0
2
2
1
1
1
5
2
1
1
2
2
2
0
2
0
0
2
2
0
0
0
0
0
0
0
0
1
1
0
2
1
0
0
0
0
1
0
0
2
0
1
1
0
1
0
0
1
2
1
0
1
1
1
1
1
2
0
0
1
0
1
1
1
0
1
1
0
0
0
0
0
0
2
1
1
1
0
1
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
1
1
0
0
0
0
2
0
2
0
1
0
0
1
1
1
1
1
0
0
0
0
0
0
0
2
2
0
1
1
0
0
2
2
0
1
1
0
0
2
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
1
2
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
3
0
2
2
0
1
0
1
0
0
1
0
1
1
2
0
1
0
0
0
0
0
0
1
0
0
0
3
0
1
2
1
0
2
0
1
0
0
1
0
0
0
2
0
2
2
0
2
2
0
2
1
1
0
1
1
1
0
2
0
2
1
1
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
2
0
2
0
1
0
0
0
0
0
1
2
2
1
1
1
1
1
1
2
2
0
0
1
2
1
0
0
0
0
2
1
0
0
0
0
0
0
1
1
0
2
1
2
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
2
0
0
0
2
0
2
2
2
0
0
0
0
0
2
0
0
1
0
1
1
1
2
1
2
2
2
2
0
0
2
1
1
0
0
0
0
0
0
0
2
2
1
0
1
1
1
0
2
2
1
2
1
0
2
1
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
1
0
0
0
4
0
4
2
0
0
2
6
2
2
2
1
0
0
0
0
0
1
2
2
0
1
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
2
2
2
0
0
0
1
0
2
1
1
0
0
0
2
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
2
2
2
1
2
0
0
0
4
2
0
0
2
1
2
0
2
0
0
0
1
1
0
5
0
0
0
1
0
0
3
2
2
1
0
2
0
1
0
0
2
0
2
2
0
0
0
0
2
1
0
1
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
1
1
1
0
2
1
0
0
1
0
0
2
1
0
2
1
0
2
0
1
0
1
0
2
0
0
1
2
1
0
0
2
2
0
1
1
1
0
0
2
0
0
0
0
0
1
0
1
2
1
0
0
1
2
0
0
2
0
0
0
0
0
0
1
1
0
1
1
0
0
1
0
0
0
2
0
0
1
0
2
0
0
1
0
1
0
0
0
2
0
2
0
0
1
1
0
0
0
2
0
2
2
0
2
1
1
0
0
2
3
1
0
2
1
1
0
0
1
0
1
0
2
1
0
0
1
0
0
2
0
0
1
1
0
0
0
0
0
3
0
0
0
3
2
1
1
0
0
0
2
0
0
0
0
0
0
2
1
0
1
2
1
1
0
0
1
1
1
0
0
1
0
0
2
2
0
1
2
1
1
2
0
0
1
0
1
0
0
4
0
0
1
0
2
0
0
2
0
0
2
0
0
0
0
2
0
0
5
2
0
0
1
0
1
0
1
0
0
0
2
0
0
0
0
2
0
2
0
2
2
0
1
1
1
1
0
2
2
0
0
0
1
0
0
0
0
0
2
0
1
0
2
0
1
1
2
2
1
0
1
1
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
2
1
1
0
0
2
2
0
1
0
1
2
0
1
1
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
1
0
1
1
0
0
0
0
0
2
0
1
1
0
0
2
1
3
2
1
1
4
2
0
1
0
0
0
0
2
0
0
0
1
1
2
2
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
3
0
0
1
0
0
0
1
0
2
0
0
2
0
0
0
1
0
1
0
2
0
1
1
1
0
2
0
0
1
0
0
0
1
0
0
0
0
2
0
1
1
0
2
0
0
1
2
0
1
2
1
0
0
1
0
0
1
2
2
1
0
2
2
0
1
1
0
2
0
0
0
0
1
1
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
4
0
2
0
0
0
0
0
1
0
1
2
0
0
0
0
1
0
0
2
1
1
1
0
0
2
0
0
0
0
0
2
1
2
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
3
0
0
1
2
0
1
1
1
0
0
1
0
1
1
1
0
0
2
0
0
0
0
2
1
0
1
1
1
1
1
0
1
0
0
0
0
2
0
0
0
0
0
1
0
2
1
1
2
0
0
0
0
1
0
0
2
1
1
0
1
0
2
0
0
0
0
6
1
0
0
1
0
2
4
0
1
1
0
2
0
0
0
1
0
2
2
2
1
1
0
1
0
0
0
2
2
1
2
0
0
0
0
0
1
0
1
0
0
0
2
0
2
3
1
1
0
1
0
0
1
0
0
0
0
0
0
2
1
1
0
0
0
0
5
0
1
0
0
1
0
2
1
1
1
1
0
0
1
0
0
1
0
0
0
0
4
2
0
0
0
0
2
0
1
1
2
2
0
0
1
0
0
5
2
0
0
2
2
2
0
1
0
0
2
1
0
0
0
2
2
0
0
2
0
0
1
0
1
0
1
1
1
2
2
3
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
2
1
2
0
2
1
0
1
3
2
0
0
1
0
2
0
0
0
1
0
0
1
2
0
2
1
1
0
1
0
0
0
4
1
1
0
0
0
0
0
0
2
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
3
1
1
1
0
1
2
1
0
2
0
2
1
0
1
0
1
1
2
1
0
1
2
1
0
0
2
2
0
0
0
0
2
1
2
1
0
2
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
2
2
2
1
1
0
1
0
0
0
0
0
1
1
1
0
0
1
2
0
0
1
1
1
0
0
0
0
2
2
1
0
0
1
0
0
0
0
0
1
1
1
0
1
2
2
0
0
0
1
0
0
0
1
0
0
0
2
0
1
0
0
0
2
1
1
2
1
0
1
2
1
1
0
0
3
1
0
0
1
1
0
1
0
0
0
1
1
0
1
0
2
1
1
2
2
0
1
0
2
0
0
0
0
0
0
0
1
0
1
2
0
0
0
1
1
1
0
0
0
0
1
1
2
0
1
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
1
1
1
2
0
2
0
0
1
0
0
0
2
1
0
0
0
0
1
0
0
0
2
0
0
0
2
0
2
1
1
0
1
1
0
1
2
1
0
1
2
0
1
0
1
0
2
1
1
0
0
2
0
1
0
1
1
0
0
1
3
0
1
0
1
0
2
0
3
0
0
0
0
1
0
0
2
0
2
1
2
0
0
1
1
2
0
0
1
0
0
0
0
0
2
0
0
1
0
0
1
0
3
0
0
0
0
0
1
0
2
0
0
0
0
1
1
2
0
1
1
0
0
1
1
2
1
1
0
1
0
2
0
0
1
2
0
0
4
0
0
1
0
0
0
1
0
1
0
0
1
1
2
2
1
0
1
1
0
0
3
0
1
0
2
0
1
0
2
0
0
1
0
2
0
0
0
0
1
0
2
1
0
0
0
1
2
2
0
2
0
2
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
1
0
0
1
1
0
2
0
2
0
0
0
0
2
0
1
0
0
0
0
0
1
1
0
1
0
1
2
0
0
0
2
1
0
0
0
2
2
0
2
2
0
0
0
0
0
2
1
0
1
0
0
0
0
1
0
1
0
0
0
1
1
1
1
0
0
0
2
1
0
0
0
0
1
0
1
0
2
0
0
1
1
2
2
0
2
0
0
1
1
1
1
0
2
0
0
1
1
0
2
0
1
1
0
0
1
2
0
1
0
0
1
0
0
2
0
1
0
2
2
1
0
0
0
2
0
0
1
0
1
0
1
1
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
2
0
2
2
0
0
1
0
1
1
1
1
0
0
0
1
0
2
1
0
0
2
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
2
1
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
2
1
1
0
0
3
0
0
0
1
0
0
0
0
2
1
0
1
0
2
0
0
2
0
0
2
3
0
1
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
1
2
0
2
1
0
0
2
1
0
1
2
2
0
0
1
0
1
0
1
2
0
1
0
0
1
0
2
2
0
0
3
0
0
0
1
0
2
0
1
0
3
0
1
0
2
0
0
0
0
0
1
1
2
1
0
0
1
0
0
0
0
0
1
0
1
1
1
0
3
2
0
1
2
2
3
1
0
0
0
1
0
2
0
0
0
0
0
0
0
1
1
0
0
1
1
0
2
0
2
0
1
2
2
0
1
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
1
0
0
1
2
0
1
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
1
0
0
2
0
0
1
0
2
0
0
0
2
1
2
1
0
0
0
1
1
0
0
2
2
2
2
0
0
0
0
2
2
1
2
0
3
2
0
0
1
0
1
1
0
1
0
2
2
0
2
1
1
1
1
0
0
0
0
2
0
1
1
0
2
1
0
2
0
1
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
1
2
0
0
1
2
1
2
0
0
0
0
0
0
1
0
0
2
0
0
2
1
0
0
2
0
2
0
0
0
1
0
1
0
0
0
1
0
2
3
0
0
1
1
1
0
0
1
0
0
1
1
0
2
1
0
0
2
1
2
1
1
2
1
0
2
0
1
1
0
1
2
1
1
0
1
0
0
0
2
0
1
0
0
0
0
2
0
1
1
2
1
1
2
0
0
2
3
0
0
1
0
1
0
0
0
0
0
1
2
0
0
2
0
0
0
0
2
0
1
1
1
2
0
0
0
0
1
1
1
1
0
0
0
0
0
1
1
0
1
1
1
3
2
0
0
0
1
2
0
0
2
2
0
0
0
0
0
2
0
0
0
3
0
1
0
0
0
0
1
0
1
0
2
0
0
2
0
3
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
1
1
2
0
0
1
2
0
0
0
2
0
0
0
3
0
2
2
1
2
0
0
0
0
1
0
2
1
0
2
1
0
0
0
2
1
0
0
1
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
2
2
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
4
0
0
2
2
4
0
0
0
0
2
1
0
0
1
0
2
1
0
0
2
1
0
4
0
1
2
1
0
1
1
1
0
0
2
0
2
0
0
0
5
1
2
1
1
0
0
0
1
0
1
1
0
0
0
0
2
0
2
1
2
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
1
0
0
0
0
2
2
0
1
0
0
1
1
0
1
0
0
1
0
2
0
0
0
1
0
0
2
2
0
2
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
2
0
1
0
1
0
2
0
0
1
0
0
2
2
1
2
0
0
0
1
0
1
1
0
0
0
2
1
0
2
1
2
0
0
1
0
0
2
2
0
2
0
0
1
1
1
0
0
2
0
0
2
0
0
0
3
1
1
2
0
1
0
0
0
0
0
2
1
1
0
2
0
1
0
0
1
1
0
1
1
0
0
2
1
1
0
1
1
0
1
0
1
0
0
0
1
1
2
0
0
2
0
0
0
2
1
0
0
0
0
0
0
1
1
0
0
2
1
0
0
1
0
2
2
0
1
1
0
0
1
0
0
2
0
2
2
2
3
2
0
0
2
0
1
0
0
2
1
0
0
0
2
0
0
0
0
4
0
1
1
2
0
1
1
2
0
1
1
0
2
1
0
1
1
2
0
0
0
0
2
0
1
1
0
1
0
0
0
2
1
1
0
2
0
1
1
1
2
2
0
2
0
0
0
0
0
2
0
2
1
0
2
0
0
1
0
0
0
2
1
0
0
0
2
0
0
0
2
0
2
1
2
2
2
0
0
2
1
1
1
0
0
0
0
1
1
0
0
0
2
0
1
4
3
0
0
0
1
1
1
0
0
0
0
0
1
2
1
1
0
0
0
1
2
0
0
1
0
1
0
0
1
1
0
1
2
0
0
0
0
0
1
0
0
0
2
1
2
1
1
1
0
2
0
1
0
0
2
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
3
1
0
2
1
0
0
0
0
0
0
3
0
0
0
0
0
1
4
0
1
2
0
0
0
0
0
2
0
3
0
0
1
0
0
0
0
2
3
1
1
2
2
0
1
1
0
2
1
1
1
0
0
0
0
1
0
2
1
0
1
0
2
2
0
0
0
0
1
2
0
0
1
1
0
0
0
2
2
1
2
0
0
0
1
1
2
1
0
0
0
0
0
0
1
0
1
2
0
1
3
1
0
1
0
2
0
0
2
0
2
1
2
0
2
1
0
0
1
0
1
0
0
0
2
1
0
0
0
0
2
2
1
1
1
0
0
1
0
0
1
1
0
0
0
0
0
5
0
0
2
0
0
0
2
1
0
0
0
0
1
0
0
2
0
1
0
0
0
2
0
3
1
3
1
1
1
2
1
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
1
1
1
1
0
2
0
0
0
1
0
1
2
3
0
0
0
1
1
0
0
2
1
0
2
1
0
0
1
0
0
2
1
1
0
1
3
0
0
0
1
1
0
1
2
1
2
2
0
0
0
1
0
0
5
0
0
1
1
2
0
0
0
0
1
0
0
1
1
0
1
2
2
1
1
1
0
1
1
2
1
0
0
2
1
0
1
0
0
0
0
0
1
1
0
2
1
1
1
0
0
2
1
0
1
1
2
0
0
0
1
1
1
0
2
2
2
0
0
0
1
0
0
1
2
3
0
0
2
0
0
0
1
2
1
1
0
1
0
0
1
1
0
0
2
1
2
1
1
0
0
0
0
2
0
3
1
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
3
1
1
2
1
1
0
1
1
1
2
1
0
0
0
1
2
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
2
0
0
0
1
0
0
2
0
0
2
0
1
0
0
0
0
0
1
1
1
1
0
0
0
2
0
2
0
0
0
0
0
4
0
1
2
0
0
2
0
0
1
0
0
2
1
1
2
0
2
0
0
1
0
0
0
0
1
1
0
1
0
0
1
0
0
1
0
2
1
1
0
2
2
2
1
0
2
1
2
1
0
1
2
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
1
1
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
2
1
1
0
0
0
0
0
0
1
1
2
0
0
1
2
0
0
1
1
1
0
2
1
2
1
0
2
0
1
0
0
0
0
0
2
0
1
0
1
1
2
0
0
0
0
1
2
1
0
0
0
1
1
0
0
0
0
0
1
0
5
0
1
1
0
0
2
2
0
2
1
0
0
1
0
1
1
2
1
0
1
1
2
2
1
0
2
1
1
2
0
0
0
0
0
2
1
1
0
1
2
0
0
2
1
0
2
1
4
1
2
1
0
2
0
0
0
0
1
2
0
1
2
0
0
1
1
0
1
0
0
0
0
1
0
0
0
2
2
0
2
0
1
1
0
2
0
0
0
1
1
2
0
0
2
3
1
1
0
0
1
1
0
0
0
1
0
2
0
2
0
2
0
0
2
0
2
0
1
0
1
0
2
0
0
1
0
0
2
0
1
1
0
2
0
1
2
2
1
0
0
0
0
0
1
0
0
2
0
0
2
0
0
1
2
0
0
1
1
0
1
0
0
0
0
0
1
0
2
1
0
2
0
2
0
0
0
1
0
1
4
1
0
2
0
2
1
0
0
0
2
0
1
0
0
0
2
0
2
3
1
2
2
1
2
0
2
0
1
1
0
1
1
1
0
1
0
4
2
1
1
0
2
2
0
1
0
0
3
1
0
0
0
0
4
1
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
4
1
4
0
0
1
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
2
1
1
0
0
0
1
1
0
3
2
1
2
0
0
0
2
0
0
1
0
0
2
2
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
2
0
2
0
0
0
0
0
1
2
2
0
0
1
1
2
0
0
1
0
1
0
1
0
1
1
2
1
0
1
0
1
3
0
2
0
0
0
3
1
1
0
1
2
0
0
1
0
0
0
1
0
3
0
2
2
0
0
2
2
0
0
2
0
0
1
1
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
1
0
1
0
0
0
2
0
0
1
1
1
0
0
0
2
0
2
0
1
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
2
0
0
1
1
1
2
1
6
1
0
2
3
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
1
2
1
1
1
0
2
2
0
2
2
2
0
2
0
0
0
0
2
2
2
1
0
0
0
0
0
3
1
2
0
1
1
0
0
2
2
0
0
3
0
1
1
2
0
0
0
0
2
0
1
0
0
2
0
0
0
4
0
0
0
0
1
0
0
0
1
2
0
2
1
0
3
1
1
2
0
0
1
0
0
0
0
0
0
1
1
2
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
1
1
0
0
0
1
0
0
2
0
2
2
1
1
1
1
0
0
1
0
2
0
2
0
2
0
0
1
2
0
1
2
1
2
1
0
0
1
2
0
0
0
2
0
0
0
0
0
1
0
1
1
0
1
0
2
0
1
1
0
0
3
1
0
0
2
0
1
1
0
1
0
2
0
0
0
2
0
1
1
0
0
0
1
0
0
1
2
1
0
0
1
0
0
1
0
0
0
2
1
1
0
1
3
0
2
1
1
2
1
1
1
0
1
1
0
0
0
0
0
2
0
2
2
0
2
0
0
0
1
0
1
1
1
1
2
0
0
1
2
1
2
1
2
0
0
0
2
4
2
2
1
2
3
1
2
0
0
0
2
2
0
2
1
0
0
0
0
0
2
2
0
1
0
0
2
1
0
0
0
2
1
1
0
1
0
0
1
1
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
1
2
0
0
0
0
0
1
4
1
0
1
1
0
0
2
1
2
0
0
0
0
0
0
0
0
1
2
1
2
0
2
0
0
0
2
0
0
1
2
0
2
0
1
2
0
2
0
1
0
0
1
1
1
0
2
1
0
1
1
1
0
1
1
1
0
1
0
0
0
2
2
0
1
1
2
0
0
0
1
0
0
1
0
2
2
0
2
2
1
0
1
0
2
1
0
2
2
1
1
2
0
2
1
5
0
2
1
0
0
1
1
0
2
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
1
0
1
0
1
2
0
1
3
0
2
3
0
0
0
1
2
1
0
0
0
2
1
1
0
0
0
0
1
1
0
0
0
0
0
1
2
1
0
3
0
1
0
0
1
0
2
1
0
2
3
0
2
0
0
2
2
1
0
2
1
0
0
0
2
2
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
1
1
0
2
2
2
2
2
0
0
1
1
1
2
2
1
0
1
0
1
1
0
0
1
2
0
2
0
0
1
0
0
0
2
0
0
2
0
0
0
1
0
1
0
2
1
2
0
1
0
1
0
1
0
1
0
0
0
2
0
2
0
0
1
0
2
0
0
0
2
0
0
2
0
0
0
3
0
0
0
0
0
2
2
1
2
0
1
0
1
0
0
0
0
0
1
1
0
0
1
0
1
0
2
2
2
3
2
2
0
1
0
2
0
0
0
0
2
2
2
0
1
0
0
0
0
0
1
1
1
0
2
0
0
1
1
0
0
1
0
1
2
0
0
1
1
1
0
2
0
1
1
0
2
0
0
1
0
1
0
2
0
1
0
0
0
0
0
1
0
1
0
2
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
1
2
0
0
0
1
2
3
1
1
1
0
2
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
2
0
2
2
1
2
1
0
1
1
0
0
0
0
0
0
0
4
0
1
1
1
1
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
2
1
0
0
1
3
2
0
0
1
0
0
1
0
0
2
1
0
0
0
3
1
0
0
0
0
1
0
2
0
0
2
0
0
0
2
0
0
0
0
1
1
2
2
1
2
1
0
0
0
0
0
3
0
0
1
0
2
0
0
1
2
0
2
3
0
1
1
0
0
0
0
1
0
1
0
0
1
0
0
1
1
2
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
2
0
0
1
1
1
3
1
0
1
0
1
0
1
0
0
1
1
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
2
1
0
1
0
0
0
0
1
2
0
1
0
0
4
2
0
0
0
0
0
0
2
3
0
1
0
0
0
0
1
0
0
0
0
0
0
2
1
2
0
1
0
0
1
1
2
0
2
0
2
1
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
2
0
2
0
1
2
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
1
1
1
2
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
2
1
0
2
0
0
0
1
1
0
1
2
3
0
1
0
2
1
2
2
1
1
0
1
0
0
1
2
0
2
0
0
0
0
0
4
2
1
1
0
0
0
2
1
0
1
0
1
2
0
3
1
1
1
0
0
1
0
1
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
1
1
2
0
0
0
0
0
0
0
2
0
0
1
1
0
0
2
1
0
0
3
3
0
2
0
0
1
1
2
2
0
2
0
1
0
1
0
2
1
0
1
2
0
0
1
2
2
1
1
0
0
1
0
0
0
2
0
0
0
2
1
0
2
0
0
0
2
1
0
0
1
1
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
1
1
0
1
1
1
2
0
0
0
0
1
0
2
0
0
2
0
2
0
0
2
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
1
0
2
0
0
0
1
0
2
2
0
1
1
0
1
0
0
1
0
2
0
0
0
0
0
0
2
0
2
1
0
2
0
1
1
2
2
1
2
1
1
0
1
2
0
2
2
0
2
0
0
1
0
2
0
0
2
0
0
0
0
3
1
0
0
1
0
1
2
2
1
0
0
0
0
1
2
0
1
0
0
0
2
0
0
0
2
1
2
0
1
2
2
1
2
0
1
2
1
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
2
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
2
0
2
0
0
0
0
2
0
0
0
0
1
1
2
0
1
1
0
0
0
2
0
0
0
0
0
2
1
0
0
2
0
0
3
2
0
2
1
0
0
0
0
2
0
2
1
0
2
0
0
2
0
2
0
0
1
0
0
1
0
2
0
2
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
3
1
0
1
1
1
0
2
0
0
0
2
1
1
2
0
0
2
1
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
2
2
1
1
0
0
2
2
2
0
2
2
0
0
0
1
2
1
1
0
2
1
0
2
5
1
0
0
0
1
0
1
0
1
0
0
2
1
0
1
1
0
0
0
0
0
0
2
1
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
1
0
0
2
0
0
1
0
1
0
0
1
2
0
0
0
4
0
1
0
2
0
0
2
0
2
1
0
0
0
0
2
1
2
0
2
1
0
2
0
2
1
1
0
0
0
0
2
0
0
0
2
0
1
0
1
0
1
1
0
0
1
0
0
1
2
0
0
0
0
0
1
0
2
0
0
2
0
2
0
0
0
1
1
2
0
2
2
0
0
0
2
2
1
0
0
0
1
0
0
0
1
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
2
2
0
0
2
1
1
0
1
1
1
0
0
1
0
0
1
0
2
0
0
1
0
1
0
1
2
0
2
1
0
1
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
1
1
1
0
1
0
1
0
0
1
2
1
0
2
0
0
0
0
3
0
0
1
2
0
0
0
0
0
1
2
2
2
1
0
0
2
2
0
0
0
2
0
0
3
0
1
2
1
0
2
0
0
0
0
1
2
1
0
0
0
0
1
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
2
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
1
2
0
2
0
1
0
2
0
2
1
0
1
0
0
0
1
0
2
3
0
2
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
1
0
0
0
1
1
3
1
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
1
0
2
0
2
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
2
0
2
0
0
2
0
1
0
1
0
0
0
0
1
0
0
0
0
1
1
2
2
0
1
2
0
0
4
0
1
0
0
1
0
2
0
2
2
0
2
1
1
0
0
1
0
1
0
0
0
0
1
0
1
1
0
1
1
0
1
0
1
1
1
0
1
0
0
2
0
7
2
2
2
0
2
1
1
0
0
2
0
1
1
1
0
2
0
0
0
0
1
0
0
0
0
2
1
1
0
0
2
0
3
1
2
2
2
0
1
0
1
0
0
1
1
0
0
0
1
1
0
0
2
0
0
0
1
0
1
0
0
1
0
0
0
0
0
2
1
0
4
1
0
0
0
0
1
2
0
0
1
4
0
1
1
0
0
0
0
2
1
0
1
1
1
0
0
2
0
0
1
1
0
1
1
0
0
2
0
0
0
0
0
1
0
1
0
0
1
1
0
0
1
0
0
1
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
1
2
1
1
1
1
1
1
0
0
2
3
0
2
2
1
1
1
1
1
1
0
0
1
0
1
0
0
2
0
1
1
0
0
0
2
0
1
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
1
2
0
0
0
2
1
1
0
2
0
0
0
1
1
0
0
0
0
2
0
1
0
3
0
0
0
0
0
2
2
0
1
0
0
1
0
0
2
0
0
2
0
0
0
1
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
2
0
0
1
1
0
0
0
1
0
1
1
0
1
1
1
2
0
2
1
0
0
0
0
0
1
0
1
0
1
1
1
0
1
0
0
0
2
1
0
0
2
0
0
0
2
0
2
1
1
0
2
1
0
0
1
1
0
0
0
3
0
0
0
0
2
2
1
2
1
1
1
2
1
2
0
0
2
0
1
0
0
0
0
2
1
0
0
0
0
2
0
1
0
1
0
1
0
1
0
0
0
1
0
1
0
2
1
0
1
0
1
0
0
2
2
2
0
0
1
0
1
1
0
0
1
2
1
1
0
0
1
2
2
2
0
2
1
2
0
0
0
0
1
0
2
0
1
0
4
0
2
1
2
0
0
2
1
2
0
0
1
1
0
2
0
0
0
0
0
0
2
0
0
0
2
2
1
0
1
1
0
0
0
2
0
1
0
0
0
1
0
0
2
0
1
1
1
0
0
3
2
0
0
1
2
1
0
2
0
0
0
0
0
2
0
1
0
1
1
2
2
0
1
0
0
0
0
0
1
1
1
0
0
2
0
0
0
1
2
0
1
2
0
0
2
0
0
2
1
0
0
0
0
1
1
0
1
0
2
0
1
0
0
2
0
0
1
0
0
1
0
0
1
0
0
0
0
1
1
2
0
1
0
0
2
1
1
2
0
0
0
0
2
1
0
1
4
0
0
0
0
0
1
1
0
0
0
1
2
2
0
0
0
3
0
1
2
0
0
0
2
0
0
0
0
1
1
3
1
2
1
0
0
0
2
0
1
0
1
0
0
0
0
2
1
0
1
0
1
0
0
2
0
1
0
2
1
0
0
1
0
0
0
1
0
0
2
1
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
4
0
0
0
2
1
0
1
0
1
0
1
2
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
1
1
1
2
0
2
0
2
2
0
0
1
1
2
0
0
0
2
1
1
0
2
1
0
2
1
0
0
0
1
0
2
2
0
3
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
1
2
1
0
0
0
0
0
0
3
1
1
0
0
0
1
1
1
0
0
0
0
0
0
1
0
2
0
0
1
2
0
2
1
0
0
0
1
0
0
1
0
1
0
0
0
1
2
2
2
2
2
0
0
0
0
3
0
0
1
0
1
2
0
1
0
1
0
0
1
1
2
0
2
0
1
5
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
2
0
2
0
0
1
2
1
0
0
2
1
1
0
0
0
0
0
1
0
2
1
0
1
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
2
1
2
0
0
1
0
2
1
1
0
1
0
0
0
0
2
0
0
2
2
0
2
2
1
0
0
2
0
1
0
0
0
0
2
2
0
0
1
0
0
0
0
2
0
0
1
1
0
2
1
0
1
0
1
0
0
0
0
1
4
0
2
2
2
0
0
1
0
1
0
0
0
0
2
0
1
1
1
0
2
2
0
12
0
0
0
1
1
1
0
0
1
1
2
1
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
1
0
1
1
0
0
0
2
0
0
1
1
0
0
0
1
2
2
0
0
1
2
0
0
10
1
1
0
0
1
0
1
1
0
0
0
0
0
2
0
0
0
1
2
1
0
2
0
0
0
0
0
0
4
0
2
0
0
1
0
0
1
0
0
2
2
1
1
0
1
1
0
0
0
0
0
1
2
1
2
0
0
2
1
1
1
1
0
0
2
3
1
0
0
1
0
4
0
0
1
0
0
0
4
0
1
0
2
0
0
0
1
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
3
1
1
0
0
0
1
0
0
0
1
1
0
1
0
0
2
0
2
0
2
0
0
2
0
1
2
0
1
1
1
0
1
0
1
2
1
1
0
0
0
0
4
1
0
0
0
1
2
2
0
0
3
2
1
2
2
0
0
1
1
2
2
1
0
1
1
1
2
0
1
1
0
2
0
0
2
2
0
0
0
0
10
1
0
2
0
0
0
1
0
0
0
0
2
0
2
1
1
2
0
2
2
3
1
0
1
2
1
0
0
0
0
0
2
0
0
2
0
3
0
0
1
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
1
0
0
2
0
2
2
1
0
0
0
0
1
0
1
1
1
0
0
0
0
1
0
1
2
1
0
1
0
2
1
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
1
0
0
1
0
0
0
2
0
1
1
0
0
0
1
1
0
2
0
1
0
0
1
2
3
0
2
0
0
1
2
1
1
0
0
0
1
0
1
0
1
1
1
0
1
0
0
0
2
0
0
1
0
1
0
0
0
1
1
0
0
2
2
1
0
0
0
1
0
0
1
0
0
1
0
1
0
1
0
1
0
0
1
0
0
0
2
0
0
0
1
0
0
2
0
0
1
1
0
0
1
1
1
0
2
1
0
0
2
0
1
0
0
1
0
2
0
1
0
0
0
0
0
1
1
1
1
0
2
2
0
0
0
0
0
2
0
3
0
2
0
1
0
0
0
0
0
0
0
1
0
0
1
4
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
1
0
0
1
2
0
1
0
2
0
0
1
0
1
1
2
1
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
1
0
1
0
0
1
0
0
1
0
0
1
1
1
2
2
0
0
0
0
1
0
1
2
1
0
0
0
0
2
0
0
0
1
2
0
0
2
0
0
0
1
0
1
0
2
2
1
0
0
1
0
0
0
1
0
0
2
1
1
2
0
1
0
0
1
0
2
1
1
2
0
2
1
1
0
1
0
0
0
0
1
0
2
0
0
0
0
0
2
0
2
2
1
2
0
0
1
2
2
2
1
1
0
0
0
0
0
1
1
0
2
0
0
1
1
0
1
0
1
1
0
1
0
2
2
2
0
2
1
1
0
1
0
2
1
2
0
0
2
0
0
1
0
0
1
0
0
0
2
1
0
1
0
0
0
1
1
0
0
0
2
0
1
0
1
1
0
0
0
1
2
0
0
0
2
0
1
0
0
0
1
0
2
4
0
2
0
0
0
0
0
2
1
0
0
0
1
0
3
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
1
1
0
1
0
0
2
1
0
0
0
0
0
0
0
4
0
0
1
1
0
2
1
0
0
0
0
0
2
0
0
2
0
0
0
1
2
0
0
0
0
2
0
1
1
0
0
1
1
0
0
0
2
0
0
1
1
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
2
2
5
3
0
1
2
1
1
0
0
0
0
0
0
2
0
0
0
1
1
1
3
0
1
0
0
0
0
1
1
0
2
1
2
0
2
0
0
1
0
0
0
0
2
1
0
0
0
2
2
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
1
3
0
0
0
2
1
0
1
0
2
1
0
0
0
1
0
1
0
2
0
1
0
0
1
2
0
2
2
0
0
0
0
0
0
1
1
2
0
0
1
2
1
0
2
2
1
1
1
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
2
0
0
1
0
1
2
0
1
3
0
0
2
2
2
0
0
0
1
1
2
2
1
1
1
0
1
0
2
0
0
2
3
0
1
0
0
1
1
1
3
1
0
0
2
0
2
0
0
2
1
0
0
0
2
0
0
2
2
2
2
0
1
0
0
1
1
1
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
2
0
1
2
4
1
0
0
0
2
2
0
1
0
1
2
0
2
0
0
1
0
2
0
0
0
0
0
1
1
1
1
0
2
0
0
1
1
1
0
0
1
0
2
1
2
1
0
0
0
0
0
2
0
0
0
1
0
1
1
1
0
0
1
0
0
1
1
0
0
0
1
0
0
1
0
0
2
2
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
2
0
1
1
0
0
2
0
0
2
2
2
0
0
0
1
0
2
1
1
0
1
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
1
1
0
4
0
0
0
0
0
0
1
1
0
0
0
1
2
1
0
0
1
0
0
0
0
0
1
0
1
1
0
2
0
1
1
0
1
2
0
2
1
2
0
1
2
0
1
1
2
1
0
0
0
1
0
1
0
0
0
1
0
1
2
0
2
0
0
2
0
2
2
1
0
0
2
0
0
0
1
1
0
2
0
0
0
0
1
0
2
0
2
2
1
1
0
0
1
0
0
2
0
2
0
0
0
2
5
0
2
0
0
0
1
0
3
2
2
2
0
1
0
0
0
0
0
0
0
1
0
1
0
5
2
2
1
0
0
1
1
1
1
0
0
0
0
0
1
0
1
1
1
0
2
2
0
1
1
0
0
2
2
1
0
0
0
0
0
2
0
0
2
0
0
1
0
1
1
1
2
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
1
1
2
0
1
2
0
0
2
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
1
2
2
0
2
1
2
0
2
0
0
2
1
1
2
1
0
0
2
0
0
2
0
2
1
1
0
0
3
1
0
0
2
0
0
0
0
1
0
0
0
2
0
0
1
0
2
0
0
2
0
0
0
1
0
1
1
0
0
1
0
2
2
0
0
0
0
2
1
1
0
1
0
1
1
1
2
0
1
0
3
0
2
0
2
0
0
0
1
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
2
0
1
0
2
3
0
0
2
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
1
1
2
0
1
1
0
0
1
2
0
2
2
0
2
0
0
0
1
0
1
2
0
0
1
2
0
1
0
0
0
0
1
0
0
1
0
3
0
0
1
2
0
0
2
0
0
0
1
2
1
0
1
0
2
0
1
0
1
0
0
1
0
2
2
1
1
2
0
0
0
0
0
1
0
0
0
1
1
0
2
0
1
0
1
1
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
2
3
2
0
1
1
2
0
2
1
0
1
1
2
2
1
2
0
2
2
0
1
0
2
0
0
0
0
2
1
0
0
3
1
2
0
0
0
0
4
1
4
0
1
0
3
0
0
0
1
2
3
0
0
0
0
0
2
12
0
2
1
1
1
0
1
0
0
2
2
1
0
0
0
0
1
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
3
1
2
1
2
3
2
2
1
0
0
0
0
1
1
0
1
1
0
0
0
1
0
1
1
0
2
1
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
1
0
0
0
2
1
1
0
0
0
1
5
1
0
0
1
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
1
2
0
0
1
2
2
1
2
1
0
0
0
0
0
2
0
2
0
2
0
1
0
2
3
0
0
0
0
1
2
0
0
0
0
0
0
1
1
2
2
1
1
1
1
2
0
2
0
0
0
0
0
0
2
1
0
0
0
0
2
0
2
0
2
0
0
0
2
0
0
0
0
0
1
0
0
2
0
2
2
0
1
0
0
0
0
0
0
0
2
1
0
2
0
2
0
0
2
1
0
1
0
4
2
2
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
2
2
0
1
1
0
2
2
2
0
1
0
1
0
2
0
0
0
0
3
0
0
2
0
2
0
1
0
0
0
1
0
0
0
2
1
2
0
1
0
0
0
0
0
0
0
3
2
0
0
0
1
0
2
2
0
1
2
0
0
0
2
0
0
0
2
2
0
2
0
1
1
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
1
2
0
1
0
1
0
0
0
1
0
0
1
0
1
1
2
1
1
0
0
0
2
0
0
0
0
0
1
0
0
0
1
1
1
0
0
4
2
0
0
1
0
1
3
2
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
1
0
0
0
2
1
1
0
0
1
0
1
0
2
2
1
1
1
1
2
2
1
2
1
0
2
0
0
1
1
0
0
0
2
0
0
1
1
1
1
0
2
0
0
2
1
1
2
1
1
0
0
2
0
0
0
0
2
1
0
0
0
1
0
0
0
0
3
0
1
4
1
2
0
4
0
2
0
0
2
0
1
1
1
1
0
1
0
2
0
1
0
1
0
0
0
0
2
0
2
0
3
0
0
0
1
2
2
0
1
0
2
1
0
0
1
0
0
0
1
2
0
1
2
0
2
0
0
2
1
0
0
1
0
0
1
1
0
1
2
1
0
0
1
0
0
0
1
0
1
1
0
1
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
1
0
0
1
0
1
1
1
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
2
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
1
3
0
0
0
1
0
2
1
1
0
0
2
2
2
0
0
0
0
0
2
1
3
0
0
0
1
0
0
0
2
0
0
2
0
1
0
1
1
1
1
0
2
0
0
1
0
1
0
1
0
0
1
0
2
1
0
2
0
2
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
2
0
0
1
1
0
0
0
0
0
1
1
1
0
0
0
1
0
1
0
2
3
0
2
0
0
0
0
0
0
2
0
0
1
0
1
2
1
0
0
1
0
0
0
0
0
1
1
0
1
0
0
1
0
2
1
2
0
2
1
0
0
1
1
4
1
0
0
0
0
1
2
0
0
2
0
0
2
0
0
0
0
0
2
0
0
4
0
0
3
0
0
0
2
0
1
2
0
2
0
2
0
0
0
0
0
0
1
2
1
0
2
1
1
2
0
2
1
1
0
0
0
0
0
2
0
0
2
0
0
2
0
0
1
0
2
1
0
0
0
0
1
2
0
0
0
0
3
0
0
1
0
1
1
0
1
1
0
0
0
0
0
2
0
0
2
1
2
2
0
2
1
2
2
2
0
2
1
0
1
0
3
0
0
0
0
0
0
0
0
1
0
0
0
2
2
2
0
2
3
0
0
0
0
0
0
0
0
1
2
0
1
2
1
0
2
0
2
1
1
0
0
1
1
0
0
1
2
0
0
1
2
2
0
3
0
1
0
1
2
2
0
1
0
0
1
1
2
2
2
0
0
0
1
2
0
0
2
0
0
1
0
2
2
2
2
0
1
0
1
0
2
0
0
0
1
1
0
0
0
1
0
1
0
1
0
0
1
0
0
1
0
0
0
0
3
2
0
0
4
0
0
1
0
0
1
1
1
0
1
2
2
0
9
0
0
1
2
0
0
2
1
0
0
0
1
0
2
2
0
1
2
0
0
1
0
0
1
2
0
0
2
1
2
0
0
0
0
1
0
0
1
0
3
0
0
0
0
0
0
0
3
0
2
0
1
0
0
2
3
1
0
2
0
0
1
1
1
0
0
1
1
0
2
0
0
0
0
0
0
1
1
0
3
1
0
1
0
1
2
1
0
0
0
2
2
2
0
0
0
0
0
1
0
1
1
0
2
2
1
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
1
0
2
0
0
1
0
0
1
0
0
1
0
0
0
1
0
2
0
1
1
0
0
0
0
0
1
0
1
0
0
2
0
0
1
0
2
1
1
2
0
2
2
0
1
2
0
0
2
0
0
1
2
0
0
0
0
0
1
0
0
2
1
1
0
4
0
0
0
1
2
2
1
0
4
1
1
0
0
1
1
1
0
0
0
1
0
0
0
0
2
0
0
1
0
1
0
0
1
1
2
0
0
1
1
2
0
2
0
0
1
1
1
0
2
0
0
2
0
0
0
1
0
0
0
2
0
0
1
0
0
2
0
1
0
1
1
0
2
0
0
1
0
2
0
0
2
0
0
1
3
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
1
0
2
0
1
0
0
0
0
2
0
0
2
1
0
1
1
0
1
2
1
0
2
2
1
1
2
0
0
0
1
2
2
0
1
0
0
0
2
0
0
0
1
0
0
1
0
1
1
0
0
0
2
0
0
1
2
0
0
1
0
2
1
0
0
2
0
1
1
0
0
1
2
1
0
2
0
0
0
0
1
1
2
0
1
0
0
2
0
0
1
0
0
1
2
2
0
0
1
1
1
3
0
0
3
0
0
1
2
1
0
0
0
1
0
0
2
1
0
1
2
0
2
0
0
2
2
2
2
0
0
1
2
0
1
0
2
0
0
1
0
1
2
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
3
0
0
1
0
1
1
0
2
0
0
0
0
7
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
1
4
1
1
0
1
0
0
0
2
2
0
0
0
0
1
1
2
0
0
1
2
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
1
3
0
0
0
0
0
0
1
1
1
0
0
1
1
2
3
2
1
0
0
1
0
0
2
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
1
1
0
1
1
2
2
1
0
0
2
2
1
3
0
0
1
0
1
1
1
0
2
1
1
0
0
0
2
0
1
0
2
0
0
0
0
0
0
1
1
1
0
0
1
2
1
0
0
0
0
0
0
1
0
0
2
0
2
0
1
2
1
0
2
0
0
1
1
1
1
1
3
1
0
2
1
0
1
1
1
0
2
2
1
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
3
0
0
1
0
2
1
0
1
0
3
1
0
0
0
1
0
1
0
0
1
0
1
1
2
0
0
0
2
0
1
1
0
1
2
1
0
0
0
0
2
0
1
1
0
5
2
0
0
1
0
1
1
1
2
1
0
0
0
0
1
0
0
0
0
2
2
0
0
0
1
0
1
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
1
1
1
1
1
0
0
0
0
2
0
2
0
0
3
1
0
0
2
1
0
2
1
2
1
1
0
1
2
0
0
1
1
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
1
1
0
2
0
1
0
1
0
0
0
2
4
2
1
0
2
0
1
0
0
1
2
1
0
0
1
0
0
0
1
1
0
0
0
2
1
1
2
1
1
1
0
2
0
0
1
0
1
0
0
1
1
0
0
2
1
0
0
0
0
0
2
1
0
1
0
0
1
1
0
1
1
0
1
0
0
2
0
1
1
0
2
0
0
2
1
0
1
0
1
1
1
0
2
2
0
0
8
1
2
0
1
0
3
1
1
0
0
2
1
1
0
2
2
0
3
0
0
0
2
2
1
0
0
0
1
1
1
0
1
1
2
0
0
0
0
0
0
2
0
0
0
0
4
1
0
1
0
0
0
2
0
0
2
0
0
0
0
2
1
0
0
1
0
0
0
2
0
0
0
1
0
1
2
0
0
3
0
0
0
1
0
1
0
0
0
2
1
1
0
0
1
0
0
0
1
2
0
0
0
1
0
0
2
0
1
0
1
0
1
1
0
0
2
0
2
0
0
0
0
0
1
0
2
1
2
0
0
1
2
1
0
0
0
0
0
2
0
0
0
0
0
2
2
2
0
1
0
1
1
1
0
0
2
2
2
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
2
1
2
0
0
0
2
0
2
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
2
2
1
0
1
0
0
0
0
0
0
0
0
0
2
2
2
0
2
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
2
2
0
0
2
2
2
1
2
2
1
0
0
1
0
0
2
0
1
0
1
0
2
1
2
0
0
3
2
0
0
1
0
0
2
0
1
0
0
0
0
0
1
1
0
3
0
0
2
0
2
0
0
1
0
1
0
0
3
3
2
0
2
0
0
0
2
0
1
6
1
0
1
0
0
0
0
0
2
0
1
1
1
1
1
0
2
0
0
0
1
0
0
1
2
1
0
2
2
2
1
0
2
0
1
2
1
0
2
0
0
2
1
1
0
0
1
0
0
1
0
1
0
2
0
2
0
1
1
0
6
0
1
2
1
0
1
0
0
0
2
0
2
2
1
1
0
0
1
0
0
2
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
1
0
2
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
2
0
1
2
1
0
2
0
2
0
2
2
2
0
0
3
2
0
1
0
2
2
2
0
1
0
2
0
1
0
1
0
1
0
0
2
2
2
1
2
2
6
0
1
0
1
1
2
0
0
0
1
0
4
0
0
1
0
2
2
0
1
0
0
0
0
0
3
2
0
0
1
0
0
1
0
0
1
0
0
1
0
0
1
1
0
1
0
0
2
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
2
0
0
1
0
1
1
0
2
1
2
1
0
1
0
1
1
0
0
1
1
1
0
1
0
0
2
0
0
1
0
2
1
0
0
1
2
0
0
2
0
0
0
0
0
2
2
0
0
2
2
0
0
0
0
0
2
0
1
2
1
0
1
1
0
0
0
2
1
2
0
4
2
1
0
0
1
0
0
0
0
1
2
1
0
2
2
0
2
2
0
2
0
0
0
0
1
0
2
1
0
2
0
2
0
0
2
0
0
0
0
2
0
0
0
1
1
1
1
0
0
0
3
0
0
0
0
1
1
0
2
0
0
1
0
0
2
0
0
0
1
0
1
1
0
1
0
0
0
1
1
0
1
1
0
0
2
0
0
2
1
0
0
2
0
0
4
1
2
0
0
0
0
0
0
1
9
1
1
0
0
1
0
0
0
0
1
1
1
0
0
1
2
1
0
1
2
1
0
0
1
3
1
0
2
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
2
2
0
2
0
1
1
1
2
1
0
0
2
0
2
2
1
0
0
1
0
1
2
0
0
0
1
0
0
2
1
2
2
0
0
1
0
1
0
0
1
0
2
2
1
3
0
0
0
1
1
2
0
0
0
0
0
0
0
0
2
0
1
1
2
1
0
1
2
1
0
0
0
3
0
0
0
2
2
2
1
0
2
0
0
0
0
2
0
1
1
1
2
0
2
0
0
0
0
1
0
1
0
0
2
0
2
0
1
0
0
1
2
1
2
0
2
0
3
0
0
0
0
2
1
2
0
0
1
0
0
1
4
0
0
0
1
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
2
1
0
0
2
2
1
0
1
0
0
0
2
2
0
0
0
1
0
1
2
0
1
0
0
2
1
0
0
1
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
1
2
1
0
0
0
0
1
0
1
1
3
0
0
1
1
0
0
2
1
0
0
1
0
1
2
0
0
0
0
2
1
1
7
0
0
0
2
1
1
0
1
0
1
1
0
0
1
0
0
1
2
0
1
1
0
1
0
1
0
0
2
0
0
0
1
2
0
0
1
1
1
0
0
0
0
2
1
0
3
2
1
0
1
1
0
1
0
1
0
1
0
0
2
0
1
0
1
1
1
1
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
1
1
0
1
2
1
0
0
1
0
2
0
6
2
2
1
0
0
1
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
2
2
1
2
0
0
2
0
0
0
0
1
0
2
1
1
0
0
2
0
0
2
2
0
1
0
0
0
2
0
2
0
0
0
0
0
3
1
1
0
0
2
0
0
1
2
0
1
0
2
0
0
0
1
1
0
0
2
0
1
0
0
2
2
0
0
0
1
2
0
0
2
0
0
0
1
0
0
2
5
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
2
1
1
2
1
0
1
1
0
1
0
0
1
1
1
2
0
1
0
0
0
0
1
1
0
1
0
0
0
2
0
0
2
0
0
0
2
1
1
0
0
0
0
2
0
1
0
1
0
0
0
2
0
2
0
1
0
1
0
0
1
0
1
0
1
0
0
1
1
0
1
0
0
0
0
0
3
1
1
2
1
0
0
1
0
0
0
1
1
0
1
2
0
0
1
2
0
1
1
2
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
1
2
1
0
0
1
2
0
0
2
0
0
0
0
0
2
0
0
0
2
2
0
2
4
2
1
0
0
1
3
1
1
0
1
1
0
2
0
0
0
0
0
0
0
1
1
0
0
2
0
6
1
0
0
4
2
1
0
0
0
0
0
0
0
1
1
1
1
1
1
2
2
2
0
1
0
1
2
0
0
0
8
1
0
3
0
0
0
0
0
0
3
3
0
0
0
0
1
1
1
2
0
0
0
1
0
1
1
0
2
0
0
2
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
1
1
2
2
1
2
0
2
1
0
0
0
1
2
1
0
2
0
2
0
0
0
0
2
0
2
0
2
0
0
0
1
0
0
0
0
0
1
0
0
1
2
0
1
0
0
0
2
1
3
1
0
1
0
3
1
0
2
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
1
0
1
0
1
2
2
0
0
0
0
0
1
0
2
0
0
3
1
0
0
0
1
1
1
0
1
0
0
0
0
0
2
0
0
0
0
1
1
1
0
0
2
0
0
0
0
0
0
0
2
1
1
1
0
0
0
0
1
1
2
2
0
0
2
2
0
1
0
2
0
0
0
0
0
1
0
0
2
0
0
2
1
0
1
0
0
1
0
0
2
0
1
3
1
0
0
1
1
0
0
0
0
0
1
1
0
0
0
2
0
0
0
1
0
1
0
1
0
0
1
0
1
0
2
1
2
2
2
1
0
0
1
1
0
0
0
2
1
0
0
2
0
1
0
0
0
0
2
1
2
1
0
0
0
3
0
0
0
0
0
0
0
0
0
2
1
1
0
1
1
2
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
1
2
0
0
0
0
0
3
0
2
1
0
1
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
1
1
2
1
0
0
1
1
0
0
0
0
2
1
1
4
0
0
1
0
0
0
1
1
0
0
1
0
0
1
0
2
1
2
1
1
0
2
0
0
0
2
0
1
0
1
1
1
2
0
0
1
0
0
2
1
0
1
1
0
1
0
0
1
1
0
0
1
1
1
0
0
1
2
0
1
2
1
0
0
1
0
1
2
1
0
2
0
0
0
0
0
1
0
3
1
1
0
2
1
0
1
2
1
0
0
2
0
0
1
0
0
0
0
0
2
1
1
2
1
0
1
0
0
2
2
2
0
0
3
0
1
1
2
0
0
0
0
0
0
1
1
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
4
0
2
0
0
0
0
2
2
1
1
2
0
2
0
0
1
3
2
0
3
1
0
1
2
2
2
1
2
0
1
0
1
0
3
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
1
1
1
1
0
0
0
2
0
3
2
2
0
0
2
2
0
2
1
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
1
0
2
0
2
1
0
1
0
2
1
0
2
0
0
0
0
0
0
3
1
1
1
0
0
0
2
0
0
0
2
0
0
2
0
1
0
2
0
2
0
0
2
2
2
1
0
2
1
0
0
0
1
0
0
0
3
2
0
0
0
3
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
2
2
2
0
0
2
0
0
0
1
0
0
1
1
0
2
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
2
0
0
2
1
1
2
1
2
2
0
0
1
2
0
3
0
0
0
0
2
1
1
0
0
1
0
0
0
0
0
2
2
3
2
0
0
1
0
0
0
1
1
1
1
0
0
1
1
1
1
1
1
0
0
1
1
2
0
2
2
0
0
0
1
0
1
2
1
0
1
0
0
0
0
0
0
0
3
0
0
1
1
1
0
0
1
0
0
0
0
0
1
2
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
1
1
2
0
1
0
0
0
3
0
1
1
0
1
0
0
0
0
0
0
1
2
2
2
0
0
1
0
0
1
2
0
1
0
0
1
0
1
2
2
2
2
2
0
0
0
2
1
2
1
0
0
1
1
0
1
0
0
0
1
1
0
1
0
1
0
0
0
1
3
1
1
1
2
0
1
2
0
0
0
0
0
0
0
0
2
1
2
0
2
0
0
0
2
0
0
1
2
1
0
2
0
1
1
1
0
1
0
0
2
0
0
0
0
0
2
0
2
0
0
1
1
0
0
0
1
0
0
0
3
2
0
0
0
2
0
2
1
2
0
0
1
1
1
1
0
2
1
2
2
0
0
0
1
0
0
0
0
0
2
1
0
2
0
0
0
2
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
1
2
4
2
0
0
0
0
1
2
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
2
0
0
1
2
1
0
2
1
1
1
1
0
2
0
0
0
0
2
0
4
0
0
0
0
0
0
1
2
0
0
2
1
1
2
2
0
0
1
2
0
0
0
2
1
1
0
0
1
0
2
2
0
0
0
1
2
2
0
2
1
0
0
1
1
0
0
2
0
0
0
0
3
1
2
2
2
2
0
0
2
0
1
0
0
1
0
0
2
0
0
2
2
0
3
1
0
0
1
0
1
0
0
1
2
1
1
1
0
1
0
0
0
2
1
0
0
1
1
0
2
2
2
0
1
0
2
0
2
1
0
2
1
1
2
2
0
1
0
0
2
2
0
0
0
3
1
0
1
1
1
0
0
0
2
0
2
0
0
1
2
0
0
1
1
1
0
0
0
0
1
0
0
0
0
2
0
2
1
0
1
1
1
0
0
0
3
0
6
2
0
0
1
2
2
0
0
2
0
0
2
2
0
1
0
2
1
0
0
0
0
0
0
0
1
2
1
1
0
0
0
3
1
0
1
2
4
0
0
1
1
1
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
1
1
0
1
0
0
2
0
0
0
0
1
1
0
0
2
0
2
2
2
3
0
0
0
0
1
0
0
0
3
0
0
0
1
1
0
0
2
2
2
0
0
1
2
0
1
1
0
0
0
2
0
0
2
2
0
0
1
0
4
0
1
0
0
1
0
1
1
0
3
1
1
1
0
1
0
0
0
2
0
0
2
0
0
0
0
2
1
0
2
0
2
0
2
0
2
2
0
0
0
0
1
1
1
3
0
0
0
1
0
1
1
1
0
2
0
2
0
0
0
0
2
2
0
1
0
0
1
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
1
0
0
2
0
2
0
1
0
0
1
0
3
0
2
0
2
0
1
2
2
4
1
1
1
1
0
1
0
1
0
2
0
1
0
0
0
1
2
0
1
0
3
0
2
0
0
0
2
0
1
1
1
1
0
0
0
1
2
0
0
0
0
0
0
2
1
0
1
4
2
0
0
1
2
0
0
1
1
0
3
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
2
0
1
1
0
0
0
0
2
0
1
0
1
2
0
2
0
0
0
0
1
1
1
1
0
0
1
0
0
2
0
1
1
0
0
2
2
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
1
1
0
2
1
2
0
0
2
0
2
0
1
2
0
0
0
0
3
0
1
0
1
2
2
0
0
0
0
0
2
1
1
1
0
0
0
0
1
2
2
0
1
0
2
0
2
0
2
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
2
0
0
0
2
0
0
1
0
2
0
0
0
0
0
2
0
1
2
0
1
1
0
1
0
0
0
0
0
0
0
1
2
1
0
0
0
1
0
0
1
1
0
0
0
1
0
0
1
0
0
1
0
1
0
1
0
2
0
1
1
1
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
2
1
0
1
1
1
0
2
0
2
0
0
0
0
0
0
0
4
0
0
0
1
2
1
0
0
0
0
0
1
1
0
0
0
1
0
2
1
0
0
0
0
4
0
0
0
0
0
2
0
2
0
0
2
0
2
0
0
2
1
0
2
0
0
0
2
1
1
1
0
0
0
0
0
1
1
0
2
1
0
1
0
1
2
1
0
0
2
0
0
2
0
0
0
0
1
2
0
1
0
0
0
2
2
1
0
1
0
0
0
0
0
0
0
1
2
0
0
1
2
0
2
1
0
2
0
0
2
0
1
0
0
2
0
2
1
1
0
0
2
1
0
0
2
0
2
3
0
0
0
0
2
1
1
0
0
2
0
0
0
2
0
0
0
0
0
2
1
1
1
2
1
0
0
1
0
0
2
1
0
0
1
2
1
1
0
0
2
0
0
0
0
0
0
3
0
2
3
0
2
2
0
1
1
0
0
2
0
1
1
0
1
0
0
1
0
1
0
0
0
2
0
1
0
0
0
0
1
1
1
0
1
0
2
0
2
1
0
3
1
0
1
0
2
0
2
0
0
0
0
2
0
0
2
0
1
1
1
1
2
0
0
3
2
0
0
1
0
1
0
0
0
1
0
0
1
1
1
0
0
0
0
0
2
0
0
2
1
1
2
0
0
2
0
1
1
0
0
1
0
0
1
0
1
0
1
2
0
1
0
0
0
0
0
1
1
0
0
1
0
3
3
0
0
0
0
1
0
3
0
1
2
2
2
0
0
1
2
0
0
0
5
0
0
1
0
1
0
2
0
0
0
0
1
1
3
0
0
1
0
0
0
0
2
0
1
1
2
2
0
0
1
2
0
0
0
1
1
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
2
0
1
0
2
1
0
1
0
0
2
1
0
0
2
0
2
1
0
0
0
0
0
1
1
1
2
2
1
0
0
0
1
0
0
0
0
2
0
1
0
0
2
1
0
1
2
0
1
1
1
3
2
1
0
0
0
0
0
0
0
1
1
0
1
2
2
0
0
2
1
0
1
0
3
0
1
0
0
0
1
0
0
1
3
2
0
1
1
0
0
0
0
0
1
1
2
2
0
0
1
0
0
2
2
3
1
0
0
0
1
0
0
2
1
1
2
0
2
1
0
1
2
2
0
1
0
2
0
1
1
0
1
1
0
2
1
1
0
0
1
0
1
0
0
1
1
0
0
0
1
3
0
1
0
2
0
1
0
0
0
0
1
2
0
1
1
1
0
0
0
2
0
1
0
0
1
0
6
7
0
0
0
0
1
0
0
1
0
1
1
1
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
2
0
1
0
0
0
0
1
2
2
1
1
1
2
0
0
0
0
0
2
0
0
1
2
2
4
0
1
2
2
2
0
0
1
2
1
2
0
0
0
1
1
0
0
2
1
0
0
0
2
0
0
0
0
0
2
2
1
0
1
0
1
0
3
1
2
0
1
0
0
2
0
0
2
0
2
1
2
2
1
0
0
0
2
0
2
1
0
0
2
0
1
4
0
0
0
0
0
1
1
2
1
1
1
0
0
0
0
0
0
0
0
1
1
2
1
0
1
2
1
1
2
0
0
0
2
1
0
1
1
1
0
0
4
1
0
1
2
1
2
0
0
0
0
2
1
1
0
0
0
2
2
1
1
2
2
3
2
1
0
3
1
0
0
1
0
1
2
0
0
0
2
0
0
2
0
1
0
0
0
1
1
1
0
1
0
0
1
0
0
1
0
0
1
0
1
0
1
0
2
0
2
0
0
0
2
2
2
0
0
0
0
1
1
0
1
1
0
1
0
0
0
1
0
1
0
0
0
0
2
1
0
1
2
0
0
3
0
2
0
0
1
0
0
1
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
2
1
0
1
0
1
0
0
0
2
0
2
2
2
0
2
1
0
2
0
1
2
2
0
1
0
0
0
0
2
0
2
1
0
1
0
1
0
2
1
0
0
1
0
2
0
2
0
1
0
2
0
0
0
0
2
0
0
0
2
2
2
0
0
0
2
0
0
1
1
2
0
0
2
1
0
2
1
0
1
1
1
0
2
0
0
2
0
0
0
0
1
1
0
2
1
1
1
0
2
2
2
2
2
0
1
0
0
0
2
0
0
1
0
0
0
0
0
2
2
2
0
0
0
2
1
2
0
0
0
0
0
1
0
1
0
2
0
2
0
0
0
2
2
1
0
1
2
0
1
1
0
2
2
0
0
2
1
1
1
0
0
0
1
2
2
2
0
2
1
0
2
0
2
0
1
2
1
0
0
2
0
0
0
0
2
0
0
1
0
0
4
0
0
0
0
2
2
0
2
2
1
1
1
0
0
2
0
0
0
2
0
0
2
0
0
0
1
0
0
1
2
0
0
0
2
1
0
0
0
1
2
2
2
0
1
1
0
1
1
1
0
0
0
1
0
1
0
1
0
2
1
0
1
0
0
0
4
1
1
2
0
0
1
0
0
1
2
0
0
0
1
0
0
0
2
2
1
1
3
2
0
0
1
0
1
0
2
2
0
0
0
0
0
2
0
2
0
0
3
0
2
0
0
0
0
1
1
0
2
0
0
0
0
0
2
0
1
2
0
0
0
2
0
1
0
1
1
1
2
0
0
0
0
2
0
0
0
2
0
0
2
0
1
0
0
0
1
1
0
0
0
2
1
1
0
0
0
2
0
0
1
0
0
2
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
2
1
0
0
1
2
2
1
1
1
1
1
1
2
0
0
1
2
2
0
0
1
4
0
0
1
0
2
2
1
1
1
2
2
2
0
0
2
0
0
0
1
1
2
0
1
2
2
1
0
2
1
0
0
1
0
1
0
1
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
2
1
0
0
1
2
0
4
0
0
0
0
0
0
0
0
0
1
1
2
0
1
2
0
1
0
0
0
0
0
2
1
0
0
1
1
5
0
1
1
2
3
0
3
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
1
1
3
1
0
1
1
0
1
0
0
2
1
0
2
1
0
0
2
0
0
1
0
0
0
2
2
0
0
1
1
0
2
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
2
0
1
0
0
1
0
2
1
0
0
0
0
1
2
1
1
1
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
2
1
0
0
1
1
0
0
0
0
1
0
0
1
0
1
2
2
2
0
0
0
1
0
0
0
0
0
0
2
0
2
2
2
0
1
2
1
1
0
1
0
1
3
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
3
0
2
1
0
0
0
0
0
2
0
2
0
1
0
0
0
1
0
1
0
2
0
2
0
1
0
0
1
0
0
1
0
0
0
0
0
2
1
1
0
0
0
3
2
2
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
2
1
0
0
0
2
1
0
0
0
0
2
1
2
0
1
0
2
0
0
0
2
1
2
0
1
0
1
0
3
2
2
1
1
0
0
1
0
1
0
0
0
1
1
0
0
3
2
1
0
2
0
2
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
2
2
0
0
1
1
1
0
0
2
1
0
1
2
0
1
1
0
0
1
1
2
3
3
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
2
0
6
1
0
0
2
2
0
0
0
2
1
0
2
0
0
0
0
0
0
0
1
0
0
0
3
1
0
1
1
1
0
2
1
1
0
1
0
1
0
0
2
1
0
2
0
2
1
2
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
2
1
1
0
1
1
0
0
0
0
0
0
0
2
2
0
0
1
1
2
1
0
0
1
1
1
0
0
1
0
0
0
2
1
0
0
0
0
0
1
1
1
3
1
0
1
0
1
0
0
0
0
0
1
1
3
0
0
0
0
1
0
0
2
0
1
0
0
2
0
0
3
2
1
0
0
1
1
0
0
1
1
1
0
0
0
0
2
0
2
0
0
2
0
2
0
3
1
0
2
0
0
2
0
0
0
0
1
0
2
0
0
1
0
1
1
0
2
1
2
0
1
0
1
0
2
0
0
0
1
2
0
0
2
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
1
0
1
0
1
0
2
3
0
1
0
0
0
2
2
0
1
1
5
2
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
2
1
2
1
0
0
2
0
1
0
2
0
0
0
2
1
0
1
0
0
0
2
1
0
2
0
0
0
2
0
0
2
1
1
0
2
0
1
2
0
0
0
1
1
0
0
0
0
0
1
0
1
1
0
0
1
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
2
1
0
3
2
0
1
2
1
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
1
0
0
0
2
0
1
1
0
0
0
0
2
0
2
0
0
0
2
1
3
0
1
0
1
0
0
0
2
0
2
0
2
0
0
3
0
2
2
0
0
0
1
0
0
0
1
0
2
0
0
3
1
1
0
0
2
1
1
1
0
3
2
0
0
0
2
1
1
1
0
0
1
1
0
0
2
2
0
2
0
0
1
0
0
1
0
2
0
0
0
0
2
0
0
0
0
1
1
2
0
0
0
0
1
2
0
0
2
0
2
0
0
0
0
0
0
2
3
0
1
0
1
1
0
0
2
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
6
0
1
2
2
1
0
0
1
0
0
0
0
2
0
2
0
0
1
3
0
1
1
0
2
2
0
0
0
1
0
0
1
0
2
0
0
0
1
2
0
1
1
3
1
0
2
0
1
1
0
0
1
0
2
1
2
2
0
0
0
0
1
0
0
2
0
0
0
0
3
1
0
0
1
0
0
0
0
1
2
0
1
0
2
5
0
0
2
0
0
2
0
1
0
1
2
2
2
1
0
0
0
0
0
1
1
0
1
0
0
1
0
0
3
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
1
0
3
2
0
0
1
0
0
2
0
0
0
1
2
0
0
0
0
1
0
0
0
0
1
0
0
1
1
1
0
0
0
2
0
0
0
1
0
0
2
1
0
1
1
0
0
0
0
0
1
0
2
0
1
0
0
1
1
2
0
1
1
0
2
0
0
1
0
2
0
0
0
0
1
0
0
1
1
1
2
0
0
1
0
2
1
0
0
0
0
1
0
1
0
0
1
1
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
2
1
0
1
0
1
0
1
0
0
1
1
1
0
0
1
2
0
2
0
0
0
1
0
0
1
0
0
0
1
1
0
1
0
3
2
1
0
0
1
1
2
0
0
0
0
1
0
0
2
0
1
2
1
2
0
2
0
1
0
0
2
0
0
1
1
1
2
0
0
0
1
1
1
0
0
2
0
0
0
1
0
0
0
1
0
1
2
0
2
1
1
0
0
1
0
0
2
1
2
4
0
2
1
0
2
0
1
0
2
0
0
2
0
2
0
0
0
0
2
1
1
1
2
1
1
3
0
2
2
2
2
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
1
1
2
0
0
0
1
0
0
0
1
0
1
1
0
1
2
0
0
1
0
0
2
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
2
2
0
0
0
0
2
0
1
0
0
0
0
1
1
0
0
1
1
0
0
1
0
0
7
1
1
0
2
1
1
1
0
2
0
0
0
1
0
1
1
1
1
1
1
1
2
0
2
2
0
0
0
0
0
0
1
0
0
2
1
0
1
0
2
0
0
0
1
0
2
2
0
0
0
1
1
1
0
0
2
0
0
1
0
1
0
0
2
1
0
0
0
0
0
0
1
0
1
1
2
0
1
0
2
0
0
0
4
2
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
1
2
0
1
0
0
0
1
0
1
0
2
1
0
0
1
1
0
1
2
3
0
2
2
0
1
0
0
3
1
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
2
0
0
2
0
0
0
0
1
1
2
0
0
1
0
1
1
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
1
0
1
0
2
0
2
0
1
0
1
0
0
2
0
1
0
2
2
0
2
0
2
0
2
0
2
1
0
0
4
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
2
1
0
1
0
0
2
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
2
1
2
0
0
0
0
0
2
0
2
1
0
1
0
0
1
0
1
0
2
2
2
1
0
1
0
0
0
1
0
1
0
1
0
1
1
0
0
2
0
0
1
0
0
1
1
0
2
0
0
0
1
1
0
1
1
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
2
0
0
0
2
2
2
1
0
0
0
1
0
1
0
2
0
2
1
0
1
1
2
2
0
2
0
1
0
0
1
0
0
2
0
0
1
0
2
0
1
1
2
1
0
2
0
0
0
0
3
2
0
2
1
0
2
1
1
1
2
0
1
0
2
1
2
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
2
0
1
2
0
0
0
1
0
0
0
2
0
0
3
0
0
2
0
0
0
0
2
0
1
0
0
1
1
1
0
2
0
3
2
0
0
1
0
1
0
1
0
0
0
0
2
0
2
0
2
0
1
1
0
0
2
0
1
1
2
0
0
1
2
0
2
0
0
0
0
0
0
0
0
2
2
0
1
1
2
2
1
0
0
1
1
3
0
0
0
0
1
1
2
0
0
0
0
0
1
0
2
0
0
1
1
0
1
0
1
1
0
3
0
1
1
0
1
1
0
0
0
2
1
1
0
0
0
0
0
1
3
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
3
0
2
0
2
0
0
0
1
1
2
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
1
0
1
1
0
2
0
0
2
0
1
1
0
0
0
0
0
1
1
0
1
2
0
1
1
0
0
2
2
0
1
1
0
1
0
1
1
2
0
0
0
0
1
0
0
1
1
2
0
0
0
1
1
0
0
2
2
1
0
2
0
1
0
2
0
2
2
0
0
2
1
0
0
0
0
0
1
0
1
2
1
0
0
0
2
1
0
1
0
1
2
0
3
2
0
1
0
0
0
0
1
2
1
0
0
1
3
1
1
0
0
2
1
0
0
0
1
0
2
1
0
0
0
2
0
0
2
2
0
1
2
2
1
0
3
1
0
1
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
1
0
0
2
0
1
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
2
2
1
0
0
2
2
0
1
0
0
1
0
1
0
2
1
1
1
0
0
2
0
1
0
1
0
0
0
2
0
0
0
2
0
2
1
0
0
2
1
2
2
2
1
0
0
1
1
3
2
1
0
0
0
2
2
0
1
0
2
0
0
0
0
12
0
2
1
0
0
1
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
2
2
3
2
1
0
2
0
0
0
0
2
0
0
1
2
0
2
0
0
1
1
1
0
0
1
1
1
0
0
1
1
0
2
2
2
2
0
2
1
2
0
2
2
0
1
0
0
1
0
0
1
0
2
2
1
0
0
0
0
1
1
0
0
0
0
2
2
1
0
0
0
1
0
2
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
1
0
1
1
2
0
0
0
0
0
2
0
2
0
0
0
0
0
1
1
2
0
0
2
0
0
1
1
0
0
2
2
0
1
0
0
0
2
0
1
0
0
0
2
0
1
0
2
2
0
0
0
1
0
0
2
0
0
0
0
2
0
2
0
2
1
0
0
0
0
3
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
1
0
0
0
1
1
1
1
1
0
0
0
1
2
0
1
2
2
4
2
1
0
0
0
0
1
1
0
0
0
2
0
0
0
0
1
0
2
0
1
0
0
0
0
0
1
0
1
0
1
0
4
0
0
2
2
0
2
0
1
0
1
0
0
2
0
2
1
0
0
0
1
1
1
0
2
0
0
2
2
1
2
0
2
0
2
2
0
2
2
2
0
1
0
1
1
0
0
0
2
0
0
1
0
2
0
2
1
2
0
1
0
0
2
0
2
0
0
1
0
1
0
2
0
0
0
0
0
6
2
0
0
0
1
1
0
0
0
2
0
0
0
0
1
2
1
1
2
0
0
2
0
0
2
3
1
2
1
2
1
0
2
1
0
0
2
0
0
1
0
2
2
0
0
0
0
1
2
0
0
0
0
0
0
2
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
2
1
0
2
0
1
1
2
0
2
0
2
1
2
2
1
0
0
2
0
1
0
1
1
0
0
1
2
2
0
1
1
0
0
2
1
2
2
0
0
0
1
0
0
0
0
2
0
0
1
6
0
0
0
0
1
1
0
0
2
1
0
0
3
1
0
0
1
0
2
0
0
2
0
1
0
0
2
0
0
0
0
0
2
1
2
0
0
2
2
0
1
2
0
0
3
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
1
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
1
1
0
2
2
2
2
0
2
0
0
0
0
0
1
1
2
1
1
2
0
1
2
1
0
0
0
0
0
0
0
1
0
0
0
0
1
3
1
1
2
0
0
1
0
2
1
0
1
2
2
0
1
0
0
0
0
1
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
3
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
1
2
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
2
0
1
1
0
0
0
0
1
1
3
1
0
0
0
0
0
2
2
0
1
0
0
2
0
0
1
0
0
1
1
0
0
0
3
1
0
0
1
0
1
1
1
0
1
0
3
0
0
1
0
0
0
2
0
0
1
0
0
4
1
1
0
1
1
0
2
1
4
0
1
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
3
2
2
4
2
0
1
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
4
0
0
1
1
0
0
1
0
1
0
1
0
2
0
0
0
2
0
0
1
0
0
0
2
2
1
1
0
1
0
0
2
0
0
1
0
0
1
0
0
0
2
11
0
0
0
1
2
0
0
0
1
1
1
0
0
0
0
0
0
0
0
2
1
2
0
0
0
1
1
2
4
2
0
0
2
0
0
1
0
2
0
1
0
1
0
0
1
1
2
4
0
1
0
0
0
1
1
0
0
0
1
2
0
2
0
0
1
0
2
0
0
0
0
2
1
0
0
1
1
0
0
2
0
2
1
0
0
0
1
0
2
1
1
0
2
0
0
0
0
2
0
0
0
0
2
2
0
0
2
1
0
1
1
0
0
0
2
1
2
0
0
0
0
0
0
0
2
0
2
0
0
0
3
0
0
2
0
0
1
0
0
2
2
1
4
0
1
0
0
1
1
0
2
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
1
0
2
0
0
2
1
0
2
1
2
0
0
0
0
0
0
0
0
2
0
0
1
1
1
1
0
0
3
0
0
1
0
1
0
0
0
0
0
2
0
0
1
0
1
1
0
0
1
0
0
0
1
0
1
0
2
0
2
0
2
2
0
1
0
0
0
2
1
0
0
2
1
1
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
1
2
2
0
0
0
0
0
0
2
0
0
1
2
0
2
0
0
0
1
0
2
0
0
0
0
0
2
1
0
2
1
2
0
0
0
0
0
0
0
0
2
2
0
1
1
2
2
0
0
2
0
2
0
0
3
0
2
2
0
0
1
0
0
0
1
0
0
1
2
0
0
0
0
0
2
2
0
0
0
0
0
0
3
0
1
1
1
0
0
0
0
0
0
2
0
0
0
4
0
2
2
2
1
0
0
0
0
2
0
0
1
0
1
0
0
1
2
0
0
1
0
0
0
1
1
2
2
1
0
0
1
0
0
0
2
0
0
0
2
0
0
0
1
0
2
0
0
3
0
1
2
0
0
0
0
0
1
0
0
3
1
0
0
0
0
1
0
1
2
1
0
0
0
0
2
0
2
1
0
2
1
0
2
0
0
0
1
0
0
0
1
0
2
0
2
0
0
2
1
0
0
1
1
2
0
1
2
0
1
0
0
2
2
1
2
0
1
0
1
0
0
2
0
0
1
1
0
1
0
0
0
2
2
0
0
2
1
0
2
1
2
1
0
0
0
1
2
0
1
0
1
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
1
0
1
0
0
2
0
2
0
1
1
0
0
0
1
0
2
0
1
1
2
0
0
1
0
0
0
1
0
1
2
0
0
1
1
2
1
0
0
2
0
2
0
2
2
1
1
0
1
1
1
1
0
2
1
0
0
0
0
0
2
0
0
1
0
1
0
1
2
2
1
0
0
0
2
0
0
2
0
0
2
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
1
2
1
2
0
2
0
2
0
1
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
1
3
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
1
0
0
1
2
1
0
0
0
2
0
2
0
0
1
2
1
1
0
0
2
1
1
2
1
0
1
0
1
0
2
2
0
2
2
0
0
1
2
8
1
1
0
0
0
3
0
0
1
1
0
1
1
1
2
1
0
5
0
0
0
2
1
0
3
2
0
0
1
2
1
2
0
0
0
4
3
0
0
1
0
0
5
1
2
0
0
2
3
3
1
2
1
2
1
0
2
2
0
4
0
0
1
0
0
0
0
1
2
1
2
0
2
0
1
0
0
2
2
0
0
3
0
2
3
1
0
2
0
2
2
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
2
2
0
2
2
0
1
0
2
1
2
2
1
0
0
1
0
2
0
3
1
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
1
1
0
1
0
0
3
1
2
0
0
2
1
1
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
1
0
2
0
0
0
0
2
0
1
1
1
0
0
1
0
0
0
0
1
0
0
1
2
0
2
2
0
0
0
0
1
0
1
2
2
1
0
0
1
2
0
0
0
1
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
1
1
2
0
0
0
0
1
0
1
0
2
0
0
0
1
0
2
0
0
0
2
0
0
1
0
0
0
2
2
0
2
0
1
3
1
2
0
1
2
1
1
0
1
0
0
0
0
0
1
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
6
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
1
0
0
2
1
0
1
1
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
2
0
1
0
1
0
2
0
0
2
0
0
0
0
0
1
1
1
0
0
0
1
1
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
1
2
1
0
1
2
2
0
0
2
0
1
1
0
2
2
1
2
2
1
0
0
1
0
0
0
1
0
2
0
2
0
2
1
0
1
1
0
2
0
1
2
1
1
1
0
0
4
0
0
6
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
5
0
0
0
1
0
0
0
2
1
0
1
4
0
0
0
1
2
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
2
0
2
2
1
0
2
0
1
0
0
0
1
2
0
0
1
0
0
0
0
0
1
0
2
0
0
1
1
0
0
1
1
2
0
0
0
1
0
1
1
2
3
0
0
0
0
0
2
2
1
0
1
0
1
1
0
1
2
1
1
0
0
1
0
1
1
0
2
1
2
2
1
0
2
1
2
1
0
0
0
2
3
1
1
2
1
1
0
0
0
1
0
0
2
2
0
1
0
0
1
1
0
1
2
2
0
2
2
0
0
2
2
0
1
0
2
0
0
0
0
0
1
1
1
0
0
1
1
0
1
1
1
1
0
0
2
1
1
0
0
2
0
0
0
0
0
0
0
3
0
0
0
1
1
0
1
0
0
0
0
2
8
1
0
2
2
0
0
1
2
0
0
0
0
0
1
0
0
1
2
0
2
2
0
0
0
2
2
0
0
0
1
0
0
0
2
0
0
0
0
0
4
1
2
0
0
0
1
0
0
1
0
0
0
0
6
0
0
0
1
0
2
0
1
0
1
1
0
0
0
3
0
0
0
2
0
2
0
0
0
2
0
1
0
2
0
1
0
1
0
1
2
2
2
2
0
2
2
0
0
0
2
0
1
2
1
0
0
2
0
2
0
0
2
0
1
0
0
2
0
2
0
0
0
0
1
6
1
0
0
2
0
0
0
2
1
2
2
1
2
0
0
1
0
0
0
2
1
1
1
1
1
2
2
1
2
0
1
1
0
1
0
1
0
0
2
1
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
2
2
0
2
2
0
0
1
0
1
0
2
1
1
2
0
0
0
2
2
1
2
0
2
0
0
2
2
0
0
3
1
0
0
1
0
1
1
2
1
0
2
2
1
1
1
2
0
0
0
1
0
2
1
0
0
0
0
0
0
0
1
0
1
0
2
0
2
0
0
1
2
2
0
0
0
0
1
1
1
2
1
2
2
0
2
0
2
1
1
2
1
0
0
1
2
0
1
0
2
0
3
1
0
2
1
0
0
0
0
0
0
1
0
0
2
0
2
0
0
2
0
2
2
0
0
3
1
0
0
0
2
1
3
5
0
1
0
1
2
0
0
0
0
1
0
0
2
4
0
0
1
0
2
0
2
1
2
1
0
1
1
0
0
1
1
2
1
0
0
0
2
0
1
0
1
0
1
2
0
0
0
1
2
0
0
3
1
0
0
0
0
1
1
1
0
1
1
2
0
0
2
0
2
0
1
2
4
2
2
0
2
1
0
2
2
0
0
2
0
0
0
2
0
0
0
3
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
1
2
0
1
0
2
0
2
1
1
2
1
0
1
1
0
2
0
0
1
0
0
2
4
0
0
1
2
1
0
2
2
0
1
0
0
0
0
1
0
0
0
0
1
0
0
3
0
1
1
1
0
1
1
0
1
2
0
0
1
1
2
2
0
1
3
0
0
2
2
1
0
2
1
0
2
0
1
0
2
2
0
0
1
2
1
0
1
0
0
0
0
0
2
0
1
0
0
0
2
0
2
0
2
0
1
2
2
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
2
0
0
1
0
2
1
1
2
1
0
1
3
0
2
3
1
0
1
0
0
1
1
0
1
0
0
0
0
0
0
2
0
1
2
2
0
0
0
2
0
0
0
2
0
0
1
1
1
2
0
2
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
2
0
0
1
1
1
0
2
2
0
0
0
2
0
0
2
0
0
1
0
1
1
0
1
0
0
0
1
0
0
1
1
0
1
0
0
2
1
0
0
0
0
1
1
0
0
1
0
2
0
0
1
2
1
1
1
1
0
1
0
2
1
0
1
1
0
1
2
0
0
2
0
0
0
2
1
1
0
0
1
2
1
0
4
2
0
1
2
0
0
0
0
0
3
0
2
0
0
0
1
0
1
2
1
0
1
0
1
0
2
0
0
3
1
2
2
0
0
0
0
2
2
1
0
1
1
0
0
5
0
0
0
0
1
0
1
1
0
1
0
0
2
1
1
0
3
0
2
0
2
1
1
1
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
2
0
0
0
0
0
1
1
2
1
0
1
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
1
1
1
1
1
1
2
0
0
1
2
1
0
0
2
1
2
0
0
0
0
0
1
0
1
1
0
1
2
0
1
0
1
2
1
1
1
2
1
1
0
0
0
0
0
0
0
2
1
1
2
0
1
1
2
1
0
0
2
0
1
0
1
0
0
1
2
1
1
0
1
1
2
1
0
0
0
2
4
0
2
1
3
0
2
1
1
1
0
0
0
0
0
0
0
2
0
1
0
1
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
1
1
1
0
1
1
0
1
1
0
0
2
1
0
0
0
0
1
1
1
0
1
0
0
0
0
2
2
0
1
1
2
0
0
1
0
0
1
0
2
1
2
0
2
2
2
4
4
2
0
1
0
1
0
0
0
0
0
2
0
1
0
0
1
0
1
1
0
0
0
1
1
0
0
2
0
0
0
2
2
1
0
0
4
1
5
1
0
0
0
1
0
0
1
1
0
1
0
2
0
3
0
1
0
1
0
1
3
0
2
1
1
2
0
0
0
0
0
0
1
0
0
2
0
2
0
2
0
0
1
0
1
0
2
0
0
0
2
2
0
1
0
1
0
2
4
1
0
1
0
0
0
3
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
2
2
0
1
0
0
0
0
0
0
3
0
0
1
0
0
3
2
2
2
1
0
0
1
0
0
1
1
0
1
0
1
1
0
2
0
0
0
0
0
1
1
1
2
0
0
0
3
0
2
0
5
1
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
1
2
1
0
0
0
0
1
0
1
0
1
0
0
0
1
2
1
0
2
0
1
0
0
2
0
0
2
0
0
0
0
2
0
0
2
1
0
1
0
1
0
0
0
1
0
1
0
1
1
0
2
0
0
0
0
0
0
4
0
0
0
0
0
2
2
0
1
0
2
0
0
0
0
0
1
0
0
0
0
1
0
2
0
2
1
0
1
2
1
0
2
0
2
1
2
0
0
2
2
0
2
0
1
1
2
1
1
1
1
2
2
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
2
1
1
0
0
2
2
1
0
1
2
0
0
0
2
1
0
0
0
1
1
2
0
1
0
2
0
0
0
0
1
1
0
1
0
2
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
2
1
0
0
0
0
1
0
0
0
0
1
2
1
0
2
0
0
4
0
0
0
1
0
1
0
2
1
0
0
2
0
0
2
1
0
0
1
0
0
1
0
0
1
0
2
0
0
0
1
2
0
0
4
1
1
0
2
0
2
0
1
0
1
3
1
0
0
1
1
0
0
2
0
0
0
0
2
2
2
1
2
0
0
0
2
1
2
1
0
2
2
0
2
0
0
0
2
0
1
0
1
3
2
0
2
0
0
1
0
2
1
1
0
0
2
2
1
1
2
1
0
1
0
2
1
0
1
1
0
1
0
0
2
1
5
0
1
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
2
0
1
0
1
2
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
1
0
1
1
0
3
0
0
0
0
1
1
1
0
0
0
3
1
0
1
0
0
0
0
1
0
0
2
1
2
0
0
0
0
1
0
0
0
2
0
2
0
1
1
1
1
0
0
0
1
0
2
0
1
1
1
0
2
2
2
2
1
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
1
0
2
3
2
0
3
2
1
2
0
2
0
0
0
2
0
1
0
1
0
0
1
0
0
0
0
0
0
3
1
2
2
0
1
0
2
0
2
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
2
0
0
1
2
1
0
1
2
0
0
1
2
0
0
0
0
2
1
0
0
2
2
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
1
0
0
1
1
1
2
0
0
2
0
1
1
2
0
2
1
2
0
2
1
0
0
2
1
0
0
0
0
0
0
1
1
0
0
2
0
2
0
2
2
2
1
0
0
0
1
2
1
0
0
0
2
2
2
1
0
2
1
0
2
0
0
2
0
0
1
0
0
1
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
2
0
2
0
0
0
2
2
0
1
0
0
0
2
3
1
0
0
2
0
0
0
1
0
0
2
1
0
2
0
0
1
0
0
1
1
1
1
0
2
0
0
0
1
0
0
0
1
1
2
1
2
0
0
0
0
0
3
0
0
1
2
0
1
0
0
0
2
0
2
0
0
1
0
0
0
2
2
0
2
1
1
0
0
0
0
1
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
2
0
1
2
1
1
0
2
0
0
2
0
1
0
0
3
0
5
1
1
0
0
0
0
0
1
0
0
0
0
0
1
2
2
0
1
2
0
2
0
1
2
0
1
0
1
2
1
0
3
0
0
0
2
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
2
2
2
0
0
0
0
2
2
0
1
0
0
0
2
1
0
3
0
1
0
0
2
2
0
0
1
0
2
0
1
0
2
1
0
2
1
0
0
0
0
0
2
0
1
0
0
0
1
0
2
1
1
0
0
0
0
2
0
1
0
1
0
0
0
2
2
0
0
0
0
0
0
2
3
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
2
1
1
0
2
0
0
1
0
0
0
1
0
1
0
0
1
2
2
0
1
1
0
2
0
1
1
0
0
2
2
2
0
2
2
1
0
1
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
1
1
0
0
0
0
0
0
1
0
0
2
1
1
2
3
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
1
2
1
0
0
1
0
1
0
1
7
0
0
1
0
0
0
0
2
1
0
2
0
0
2
0
0
0
0
0
0
3
1
2
2
0
0
0
0
0
1
2
0
0
2
1
0
2
2
1
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
4
0
1
0
2
0
0
0
1
2
1
0
0
0
0
0
0
0
1
1
1
2
0
0
0
0
1
1
0
1
2
0
0
1
0
2
2
1
0
2
1
0
1
1
0
0
1
1
3
0
0
0
0
0
0
2
0
0
0
2
1
0
2
1
5
4
0
0
0
0
2
2
0
0
1
1
1
1
1
2
1
2
0
1
1
0
1
2
0
0
0
0
0
0
1
1
0
0
0
3
2
1
2
0
0
0
0
1
2
2
1
1
0
0
0
3
0
1
0
3
2
1
0
1
2
2
1
2
1
0
2
0
6
1
0
0
0
2
0
0
2
0
2
0
1
0
2
1
0
2
0
2
0
0
1
1
1
2
0
1
1
0
0
1
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
2
2
1
1
0
0
2
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
2
2
0
0
2
2
0
0
1
0
2
0
1
0
2
0
1
0
0
0
2
0
0
0
1
1
0
0
0
0
2
0
1
0
1
0
1
0
0
0
0
0
0
1
0
2
0
0
1
0
0
2
0
0
0
1
0
0
0
3
0
0
0
0
0
0
1
0
0
4
1
1
0
2
0
2
2
1
0
2
1
1
0
0
2
2
1
2
1
0
1
2
1
1
0
1
0
1
0
0
0
1
0
0
2
0
0
2
1
0
0
0
0
2
0
0
0
3
0
1
1
2
0
0
0
1
2
1
2
1
0
1
0
0
1
0
1
0
1
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
2
1
0
0
0
0
0
1
0
0
1
3
1
0
0
0
4
2
0
1
0
0
0
0
1
2
0
0
0
1
1
2
1
0
2
0
1
2
2
2
0
1
0
0
0
2
2
0
0
0
1
1
0
2
0
0
0
2
0
0
2
0
0
0
2
2
0
1
0
1
2
1
1
0
2
2
0
1
0
0
0
0
0
2
0
2
2
0
0
1
2
0
0
0
0
0
1
1
2
2
0
2
0
1
2
2
0
1
0
1
0
0
1
0
1
0
0
0
2
2
0
0
1
0
0
2
0
0
0
2
2
0
1
0
1
2
2
0
1
1
1
0
0
0
2
0
2
0
0
2
0
0
2
0
1
0
0
1
0
1
0
2
0
0
0
0
0
0
1
2
1
2
0
2
1
2
0
0
0
0
2
0
2
0
0
1
2
0
0
2
1
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
1
0
2
2
0
0
1
0
2
3
0
2
2
0
0
0
1
0
2
0
0
0
1
0
2
0
1
0
0
0
0
0
2
1
0
0
2
0
0
1
0
2
1
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
2
1
0
0
1
0
2
0
1
0
0
1
0
0
0
1
0
1
1
0
2
0
0
0
0
0
0
2
2
0
1
1
2
1
0
0
2
0
2
0
0
0
0
0
1
1
0
2
2
2
1
3
1
0
0
0
2
0
1
0
0
0
0
1
2
0
0
1
0
1
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
1
1
0
0
2
0
2
0
1
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
3
2
0
2
0
0
0
1
1
0
2
1
1
0
1
0
0
0
0
1
0
0
3
0
1
0
0
0
1
0
0
0
1
2
2
0
1
0
1
0
0
0
0
2
0
0
4
2
0
0
0
1
1
0
0
0
2
0
0
0
1
1
1
0
0
0
1
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
3
1
2
0
0
0
6
0
0
0
1
0
0
0
0
2
1
0
0
0
2
0
0
0
0
1
1
2
1
2
1
3
0
1
0
0
2
2
0
2
0
2
0
0
0
0
1
2
2
1
0
3
1
2
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
1
1
0
0
1
0
1
0
0
0
1
0
2
2
0
0
0
1
0
1
0
0
1
1
0
0
0
1
1
0
0
0
2
0
2
0
0
0
2
2
0
2
0
1
0
2
0
2
0
0
0
1
0
2
1
1
1
0
1
0
2
0
0
1
1
1
2
1
0
0
1
1
1
0
2
0
0
2
1
0
2
0
0
2
1
1
1
2
2
0
0
0
2
0
0
0
0
1
0
1
2
0
0
2
0
0
2
1
0
3
3
0
0
2
1
0
1
0
0
1
1
1
1
1
0
0
0
0
0
2
0
0
0
2
2
0
2
1
1
2
2
0
0
2
1
0
1
0
2
0
0
2
0
0
2
0
0
0
0
0
0
1
0
2
0
1
0
2
0
0
0
2
2
0
1
0
0
2
0
0
2
0
0
0
1
0
1
0
0
0
1
1
0
1
1
0
1
1
0
0
0
2
0
0
1
2
0
0
1
0
0
2
0
0
2
1
2
1
0
1
0
0
0
0
1
0
0
0
0
0
2
2
2
1
0
13
2
0
0
0
0
0
0
0
0
0
1
13
0
2
0
2
0
0
1
0
0
1
1
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
1
1
1
0
2
0
0
0
1
0
2
0
0
2
1
0
0
0
1
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
2
0
1
1
0
1
1
0
2
0
0
2
0
1
1
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
2
1
0
0
0
0
0
0
0
0
2
0
0
3
1
0
0
1
1
1
1
0
1
0
2
2
0
0
1
2
0
2
1
0
1
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
2
0
0
2
0
1
1
1
1
0
2
0
1
0
1
2
3
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
1
0
2
0
0
0
2
0
0
1
0
0
1
1
1
0
0
1
0
2
0
0
0
0
1
1
0
2
0
1
2
1
2
0
0
0
0
0
1
2
0
0
0
1
0
1
2
3
0
0
2
1
2
0
2
2
2
0
0
0
0
0
0
0
0
2
2
2
2
3
2
2
0
0
0
2
0
0
1
0
0
1
1
1
0
1
0
0
2
0
2
0
1
0
2
2
0
1
1
1
0
0
0
0
1
1
0
1
0
0
2
2
0
0
0
1
0
1
2
0
7
1
0
1
0
1
0
1
0
2
2
1
0
2
0
0
2
0
3
1
2
0
0
2
1
0
1
2
1
1
0
0
0
0
0
1
2
0
1
0
0
1
0
0
0
2
0
0
1
0
0
0
1
0
0
0
1
0
2
0
1
0
0
2
2
0
0
1
1
0
0
1
2
1
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
1
1
0
2
0
0
2
2
0
2
1
1
0
0
0
1
0
0
2
0
0
1
1
0
1
0
1
0
2
2
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
2
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
2
0
1
0
1
1
0
0
0
0
1
1
2
0
2
1
2
0
1
0
1
2
0
3
1
1
1
2
2
0
0
0
0
0
1
0
1
0
0
1
0
1
1
0
0
0
2
0
1
0
2
0
0
1
1
2
1
0
1
0
0
0
0
0
2
2
0
0
2
0
1
0
0
2
0
0
0
0
1
0
0
0
0
2
0
1
1
0
2
1
1
0
2
2
0
3
0
1
0
0
2
0
0
1
0
0
0
0
1
1
2
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
2
1
1
2
0
2
1
1
0
0
0
0
1
2
1
0
0
3
1
0
0
0
0
2
0
0
0
0
1
0
0
1
2
0
0
0
3
0
0
0
0
0
2
0
1
0
0
0
2
0
1
0
0
0
1
2
0
0
1
3
0
2
1
1
0
2
4
0
0
2
0
0
0
0
1
0
0
2
1
2
1
0
0
0
2
0
1
0
2
0
2
0
0
2
0
0
0
0
1
0
1
1
1
1
1
0
2
2
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
1
0
3
0
1
1
0
0
1
1
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
1
1
0
0
0
0
0
2
1
1
2
0
0
2
0
0
0
2
2
0
0
0
0
2
2
0
0
1
2
1
0
0
1
0
0
1
1
0
0
0
2
0
1
0
0
0
2
1
0
0
1
1
0
1
1
0
2
0
0
0
0
0
2
1
2
0
0
0
0
0
3
2
0
0
0
1
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
2
2
2
0
0
2
0
0
0
1
0
0
0
0
1
0
1
0
0
2
0
0
0
1
0
0
1
1
1
1
0
0
0
4
0
0
2
1
0
1
1
2
2
0
0
0
0
0
2
1
0
0
1
0
1
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
2
0
2
0
0
0
2
5
0
0
2
1
1
0
0
0
0
1
1
0
0
1
2
0
1
1
1
0
1
2
1
2
0
0
1
0
2
0
0
2
2
1
2
2
0
2
0
2
0
2
0
1
0
2
0
0
0
0
2
1
0
1
2
0
0
2
2
0
0
0
1
2
0
1
1
0
0
2
0
1
1
0
0
0
0
2
1
0
1
3
0
0
1
1
0
0
1
2
0
2
0
0
1
0
1
1
2
2
1
0
0
0
0
0
1
1
0
2
0
0
2
2
2
0
0
0
1
1
1
0
0
0
0
2
1
2
2
0
0
0
0
2
0
0
1
0
0
1
2
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
2
1
0
0
1
0
0
2
0
0
1
0
2
2
2
2
0
1
1
0
0
1
2
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
1
0
2
2
2
2
0
0
1
3
1
2
1
0
0
1
0
0
0
0
2
1
1
0
2
0
2
0
0
0
1
0
0
1
0
2
0
1
0
1
2
1
2
0
2
0
1
2
2
0
0
1
0
2
1
0
0
0
1
1
4
2
0
1
1
0
0
1
0
0
1
0
0
0
0
2
2
0
2
2
2
0
1
0
0
0
2
0
1
1
0
2
0
1
1
2
1
1
2
0
0
3
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
1
0
0
0
2
0
1
1
2
3
1
0
0
2
0
0
2
2
1
1
0
2
0
0
0
2
1
0
1
2
0
0
2
0
0
2
1
0
0
1
1
0
0
0
0
0
1
0
0
3
1
0
2
2
0
1
1
0
0
1
0
2
2
0
1
1
0
2
1
1
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
1
0
0
1
0
1
2
2
0
2
1
1
0
0
2
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
1
2
0
1
1
0
1
0
0
0
2
0
0
1
0
2
1
0
0
0
1
0
2
3
0
0
0
0
0
2
2
0
1
1
1
0
0
0
0
0
0
1
1
3
0
0
3
0
0
2
0
1
2
2
3
2
2
1
1
0
2
0
1
2
1
0
1
1
0
1
0
1
1
0
0
0
0
1
0
1
0
0
0
2
0
0
0
1
2
0
1
2
0
0
0
0
0
1
0
1
0
0
2
1
0
0
1
4
2
0
1
0
2
0
2
1
2
1
0
1
0
0
0
0
1
2
2
0
0
2
2
1
0
1
1
1
2
1
0
2
1
0
1
0
2
0
0
0
1
0
2
1
1
0
2
0
0
0
2
4
0
0
0
1
1
0
2
1
10
0
1
0
1
0
1
0
2
1
2
0
1
0
1
0
0
0
0
1
0
1
0
1
0
2
0
0
2
2
0
0
0
0
0
0
2
0
1
0
2
1
0
0
1
1
0
1
1
0
0
1
0
0
0
1
2
1
0
1
0
1
2
2
0
0
2
0
0
0
2
2
0
1
3
1
2
0
2
0
0
0
1
0
1
0
1
0
0
0
1
1
2
0
1
0
2
0
0
3
0
0
0
2
0
0
0
0
2
1
0
2
0
1
0
2
1
1
0
0
0
2
0
0
0
0
1
2
2
0
0
1
1
0
1
1
1
1
0
1
0
0
2
1
2
2
0
0
0
1
0
0
0
0
0
0
1
0
0
4
1
1
0
2
2
2
2
0
0
0
3
0
0
2
2
0
0
0
2
2
2
1
0
0
0
0
0
0
0
0
0
0
0
5
0
1
0
1
0
0
0
1
0
1
0
1
2
1
0
1
0
0
2
0
0
0
1
0
0
2
1
2
2
0
0
0
1
0
0
0
0
0
0
0
0
2
2
2
1
0
1
0
0
0
2
0
0
2
0
0
0
0
2
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
2
0
0
1
0
1
0
3
2
0
0
2
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
1
2
1
1
1
3
0
2
0
0
0
3
2
0
0
0
0
0
2
0
3
0
0
0
1
0
0
1
0
2
1
0
0
0
0
1
0
0
1
0
3
1
2
1
2
0
1
0
2
0
0
0
0
0
2
1
0
2
0
1
0
2
0
0
0
0
2
1
1
1
2
2
0
0
0
0
0
1
3
3
0
0
0
0
2
2
0
0
0
0
1
1
2
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
1
1
0
2
0
0
1
0
1
0
0
1
2
0
1
1
2
1
2
0
0
1
2
0
1
1
0
0
0
0
2
1
1
0
2
2
0
0
2
1
0
1
2
1
0
0
0
1
0
1
1
2
1
2
4
0
1
1
2
0
0
2
0
2
0
0
0
1
0
0
0
1
2
1
2
1
1
0
0
0
0
1
1
0
2
0
0
0
1
2
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
5
0
0
0
1
0
1
2
1
0
0
0
2
1
0
0
1
0
0
0
1
0
0
1
0
1
1
2
2
0
2
0
0
0
1
0
1
0
0
0
1
2
0
1
0
0
3
2
1
0
1
0
0
2
2
0
1
1
0
0
0
1
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
1
1
0
0
0
2
1
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
2
1
2
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
2
0
2
0
0
1
0
0
0
1
1
0
2
0
0
0
0
1
0
0
3
0
2
1
2
3
0
1
0
1
0
1
0
0
0
0
0
3
1
0
0
2
0
1
1
1
1
1
0
0
0
1
2
1
0
1
1
1
0
0
1
1
2
0
0
0
0
2
1
1
1
0
1
2
0
2
0
0
0
0
0
1
1
1
2
1
1
0
0
0
0
1
0
0
0
1
0
2
2
1
0
0
2
2
8
0
0
0
1
2
1
2
0
0
0
0
0
0
0
1
0
2
2
1
1
0
2
0
0
0
2
1
2
1
1
0
2
0
0
0
2
0
0
0
0
0
2
1
1
2
0
0
0
0
1
0
0
0
1
1
1
2
2
1
1
0
0
1
2
0
0
1
0
1
0
3
0
1
2
0
0
1
0
2
0
2
0
2
0
0
0
0
2
2
0
0
1
0
0
0
1
1
3
2
0
3
0
0
0
0
2
0
1
1
2
5
2
1
2
0
0
1
2
2
1
0
0
1
0
0
0
1
0
1
0
1
1
2
3
1
1
1
0
0
1
0
0
0
0
1
0
2
2
0
2
2
2
1
1
0
2
1
2
0
1
0
2
3
0
0
0
0
2
0
0
1
0
0
0
1
0
0
2
2
0
0
1
1
2
0
1
0
0
1
0
0
0
1
0
1
1
0
3
1
0
2
0
0
0
0
1
1
0
0
3
2
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
2
1
1
1
0
1
0
2
2
1
1
0
0
0
1
0
1
0
0
2
0
1
3
0
0
2
2
1
0
0
0
2
0
0
2
1
0
0
0
0
1
1
0
2
1
2
0
2
0
3
0
0
0
2
1
1
0
2
0
0
1
0
0
0
0
0
1
0
2
1
1
0
0
0
0
1
0
1
0
0
0
2
1
1
1
1
0
1
0
0
1
0
2
2
1
0
2
1
1
0
0
2
2
2
0
0
1
0
2
0
0
0
1
0
1
0
1
1
0
0
2
2
2
0
1
0
2
1
0
2
1
0
1
0
2
1
1
2
0
0
0
0
0
0
2
2
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
2
1
0
2
0
1
2
0
0
0
0
0
2
1
1
1
0
0
0
0
1
0
0
2
1
1
0
3
0
1
1
0
0
0
2
0
0
1
1
2
1
1
0
2
0
1
2
0
0
0
0
0
0
2
0
0
1
0
0
1
2
7
2
2
0
2
0
0
0
0
2
0
0
0
0
1
0
1
1
0
0
1
1
0
0
1
1
2
0
0
0
0
1
1
0
1
0
0
1
0
1
2
1
0
2
2
0
0
0
0
2
1
0
2
0
0
2
1
2
0
1
0
1
2
0
1
2
1
2
0
2
0
0
0
3
1
0
0
1
0
1
0
1
2
0
0
0
0
0
1
2
0
1
0
2
1
0
2
2
0
0
0
0
0
1
2
0
0
1
2
0
0
1
0
2
0
0
1
0
0
2
0
0
1
1
3
2
1
0
0
0
0
0
1
1
2
0
0
2
0
1
1
0
0
2
0
0
0
0
2
1
1
0
0
1
0
1
2
0
0
1
0
0
0
0
2
0
2
0
0
0
1
1
0
1
0
0
0
2
1
2
2
2
1
0
0
1
0
0
0
0
2
2
0
0
0
0
0
1
1
0
0
0
0
0
1
2
0
2
0
0
0
1
0
1
0
2
0
0
2
0
0
0
1
0
0
1
1
0
6
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
2
2
1
0
0
1
0
2
0
2
2
0
0
3
0
0
3
0
0
0
1
0
0
0
0
2
1
0
0
1
1
0
1
0
0
0
2
0
0
0
0
1
1
1
0
0
0
0
1
1
1
1
0
0
0
0
0
0
2
0
1
0
1
0
3
0
1
1
0
2
0
2
0
1
1
1
0
0
0
3
0
0
0
1
0
0
0
1
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
4
1
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
1
3
0
1
1
1
0
1
0
2
1
1
0
0
2
2
0
0
0
0
0
1
2
1
2
0
0
1
2
0
1
0
0
0
1
1
3
1
0
1
0
0
0
0
0
0
1
1
2
0
0
1
1
1
1
0
1
0
2
1
1
2
1
0
2
1
0
2
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
1
1
0
0
2
0
1
0
0
1
0
0
4
2
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
1
4
1
1
2
2
0
2
0
0
1
0
0
2
1
1
2
0
0
1
0
0
0
0
2
2
0
1
0
1
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
2
1
0
0
0
2
0
1
1
0
0
1
0
3
0
0
0
0
0
0
0
1
0
2
0
0
0
1
1
1
0
0
0
0
0
0
0
5
0
2
2
0
2
1
1
0
2
1
1
2
1
0
0
0
0
0
2
2
0
0
0
1
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
3
0
1
0
1
0
1
0
0
1
0
0
0
0
0
2
0
0
1
1
1
0
0
0
0
2
1
0
0
1
0
0
1
1
1
2
1
0
0
0
1
1
1
1
1
0
1
0
2
0
1
0
0
0
0
0
2
0
3
0
2
2
0
0
1
0
0
0
1
0
1
1
2
0
0
2
0
0
0
0
0
0
0
1
1
0
5
0
1
0
1
0
0
0
0
1
0
0
1
3
0
0
1
0
2
1
0
0
0
0
2
0
1
0
0
2
2
0
0
1
1
0
0
1
2
2
0
1
2
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
2
0
0
1
1
0
1
2
0
3
0
0
2
0
2
0
1
1
2
0
0
0
0
0
2
0
0
0
1
0
1
2
0
0
2
0
2
1
1
0
1
0
2
0
0
1
2
0
1
0
0
0
0
0
1
1
2
1
0
0
0
0
0
1
1
0
0
2
0
1
1
0
2
1
0
0
1
0
1
4
1
0
0
0
0
1
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
2
1
2
0
0
0
0
1
0
1
0
2
2
0
2
0
0
0
1
0
1
0
1
2
2
1
0
0
2
2
0
1
0
1
0
0
2
0
0
0
1
2
2
0
1
0
1
0
0
0
0
0
1
2
2
3
1
1
0
1
1
1
0
1
2
0
2
2
1
0
2
1
2
1
0
1
1
0
2
2
0
2
1
0
1
2
0
0
0
1
1
0
0
1
0
1
1
3
1
1
2
0
1
0
0
0
0
2
3
1
1
0
0
0
0
1
2
1
0
0
0
0
0
0
2
0
2
0
0
2
1
1
0
0
1
2
0
0
3
0
1
0
0
1
0
0
1
0
0
0
1
0
1
1
1
0
2
0
2
1
1
0
0
0
0
1
0
0
0
0
0
1
0
1
1
1
0
2
0
0
0
0
0
2
0
2
1
2
1
2
0
0
1
0
0
0
2
1
0
0
0
0
1
1
0
1
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
2
1
0
2
1
2
1
2
2
0
0
0
0
1
0
0
1
1
0
0
3
0
2
0
3
0
0
2
3
2
0
0
0
1
0
0
0
3
0
0
0
0
1
0
2
1
0
0
3
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
1
0
1
0
2
1
2
0
0
1
1
0
0
0
3
2
0
0
0
0
0
2
0
0
0
2
2
0
0
0
2
0
0
1
0
1
0
2
0
2
0
0
0
2
0
0
0
2
0
2
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
1
0
2
1
1
0
2
0
0
2
1
1
0
0
0
0
2
1
0
0
1
2
2
0
0
0
1
0
2
2
2
0
1
0
1
0
2
0
0
2
1
2
2
0
1
0
0
0
2
1
0
0
1
2
1
0
0
0
0
0
0
1
0
1
0
0
1
0
2
0
0
2
0
0
1
0
1
0
2
2
0
0
1
0
0
0
0
1
1
0
0
2
0
2
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
2
0
0
0
0
2
0
0
2
2
0
2
2
1
1
2
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
3
0
1
1
0
0
0
1
2
2
1
1
1
2
2
0
0
2
2
0
0
2
0
1
1
1
1
1
2
1
2
2
0
2
0
0
0
0
0
2
0
2
0
1
0
0
1
0
1
0
0
1
1
2
2
0
0
1
1
2
1
2
0
0
1
2
0
2
2
2
1
2
0
0
4
2
0
0
0
2
1
0
2
0
0
1
0
0
1
0
2
1
2
0
1
0
0
2
0
0
1
0
0
1
0
0
3
1
1
1
1
1
2
1
0
2
2
0
1
0
2
1
0
2
0
0
2
1
0
2
1
0
2
0
0
1
2
2
0
2
1
0
0
2
2
3
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
2
0
0
2
0
1
1
0
2
2
0
1
1
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
2
1
1
1
0
1
2
2
1
0
0
2
0
0
0
0
0
0
0
0
2
1
2
0
0
0
2
0
0
1
0
1
1
2
1
0
2
1
0
1
1
0
0
0
4
2
1
0
0
1
0
1
0
1
0
1
1
1
0
1
2
2
0
0
0
1
0
3
1
0
1
1
1
0
0
1
0
1
0
2
2
2
1
0
0
1
0
0
1
0
0
0
0
1
2
2
2
0
0
2
0
2
2
0
2
1
1
2
1
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
1
1
1
0
2
2
0
2
1
0
0
0
1
0
2
0
0
0
1
2
0
1
0
0
0
0
0
2
2
2
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
3
0
1
1
1
0
2
1
1
0
0
2
0
0
1
0
1
0
0
0
0
1
0
0
2
0
0
0
0
1
2
1
4
2
0
0
2
0
1
2
1
0
1
0
1
1
2
1
1
0
1
1
2
0
0
0
0
0
2
0
0
1
1
1
1
0
0
1
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
2
0
2
1
2
0
0
0
1
0
0
0
0
1
0
0
0
2
3
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
2
2
0
0
1
0
0
0
0
2
0
0
1
0
0
1
2
0
2
0
2
0
0
0
1
1
3
0
1
0
1
0
0
0
2
1
0
0
0
0
1
2
0
0
1
1
0
2
2
2
1
0
0
0
0
0
1
5
0
1
2
0
0
0
1
2
1
1
0
1
0
2
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
1
1
0
4
0
1
0
2
1
0
0
2
0
1
3
0
2
0
0
2
2
1
1
2
2
0
0
0
1
1
0
2
2
2
0
2
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
2
0
1
0
0
2
0
0
0
0
1
0
1
0
1
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
1
1
0
0
1
2
2
2
1
0
2
0
2
1
1
2
1
0
0
2
2
1
2
0
2
0
2
0
0
0
1
0
0
2
1
0
0
1
1
2
1
0
0
0
0
2
0
2
0
0
0
1
0
2
1
0
1
1
0
0
0
1
0
2
0
1
0
2
1
0
1
0
1
0
1
2
0
2
2
0
0
0
1
2
3
0
0
1
0
2
0
1
0
1
0
1
2
1
0
1
0
0
1
0
1
6
2
2
0
0
0
1
0
0
0
0
3
1
0
0
0
0
1
2
0
1
0
0
0
0
0
2
0
2
2
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
3
0
0
2
0
0
0
2
0
1
3
0
0
0
2
0
2
1
0
0
0
2
1
1
0
0
2
0
0
0
1
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
2
2
0
2
0
0
0
0
1
0
0
0
0
3
1
2
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
2
1
0
0
0
2
1
0
0
0
0
0
2
0
1
2
0
0
0
1
2
1
4
0
1
1
3
0
0
2
2
1
0
0
1
1
0
0
0
0
0
1
2
0
1
0
0
0
0
3
0
2
2
1
0
1
1
2
1
0
0
1
0
0
2
1
2
1
0
0
0
0
0
1
1
0
0
1
0
0
0
2
0
1
1
2
2
2
1
1
0
0
0
1
0
0
0
1
2
0
2
0
0
0
1
0
1
3
0
1
0
2
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
2
1
1
2
0
1
2
0
1
0
1
1
2
2
0
0
1
1
0
1
1
0
2
3
0
0
1
0
1
0
0
3
0
0
0
1
0
1
1
2
1
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
2
2
1
2
0
1
0
0
0
1
0
0
0
0
1
2
0
2
0
0
0
1
2
0
1
0
0
1
2
1
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
3
0
1
0
1
0
0
2
0
0
0
1
2
0
1
0
1
1
0
0
1
0
1
1
1
0
1
1
0
0
0
2
0
1
2
0
0
1
0
0
1
1
1
1
2
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
2
0
0
2
0
2
3
1
0
1
0
1
0
0
0
0
0
0
1
1
0
3
0
1
1
1
1
0
2
2
2
0
0
2
2
2
0
1
2
0
0
0
2
0
0
0
2
2
2
1
6
1
0
2
0
1
0
0
0
0
1
0
0
1
0
2
0
1
0
0
0
0
2
0
0
0
1
0
0
1
2
1
1
1
1
2
1
0
1
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
3
0
0
0
1
1
1
0
1
2
1
0
0
2
0
2
1
0
0
1
2
0
0
0
0
2
2
0
1
0
0
1
0
0
0
2
0
0
0
2
0
1
1
0
0
0
1
1
0
0
1
2
0
0
1
0
0
0
0
0
0
2
0
1
2
0
0
0
2
0
0
2
0
2
2
0
0
2
1
0
2
1
2
2
2
1
1
0
0
3
0
0
0
0
0
2
1
2
0
2
0
0
2
0
1
0
1
2
1
0
1
1
0
0
0
1
0
1
0
0
2
2
1
0
2
1
1
2
2
0
2
2
0
0
1
0
1
2
0
1
1
0
2
0
0
1
0
1
1
0
1
0
0
0
1
0
0
1
2
0
0
1
1
0
0
2
1
1
0
0
0
0
2
2
0
0
1
0
0
0
1
2
0
0
0
1
1
0
2
1
6
2
2
2
0
0
1
0
0
0
0
0
2
0
1
0
0
1
0
2
0
0
0
1
1
0
2
1
0
0
0
0
1
0
0
1
1
1
0
0
0
3
2
1
2
0
2
2
0
1
0
0
0
0
0
1
0
2
0
1
0
2
0
0
1
0
0
0
0
0
1
1
2
1
1
0
0
1
1
0
0
0
2
0
2
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
2
1
1
0
3
1
2
0
1
2
0
0
2
0
0
0
0
2
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
1
0
2
1
1
0
2
0
0
0
1
0
1
0
0
1
1
0
2
1
0
0
0
0
1
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
1
1
0
0
2
1
2
0
0
2
0
0
0
1
2
0
0
0
2
2
0
1
0
0
0
0
2
0
0
1
1
0
0
1
1
1
0
0
2
0
2
1
1
0
0
0
1
2
0
2
0
1
1
0
1
1
0
0
0
0
0
0
2
2
0
2
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
1
1
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
2
2
1
2
0
0
0
0
1
1
2
0
0
1
2
0
0
0
0
1
1
2
0
0
2
0
2
1
0
0
2
1
0
1
0
0
0
1
2
1
1
2
0
0
0
0
2
0
0
0
0
0
0
0
1
2
1
0
4
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
1
0
0
2
1
2
0
0
2
0
0
3
0
1
0
0
0
1
1
0
4
2
2
1
1
2
0
0
0
1
0
2
1
0
1
2
2
0
1
0
0
2
0
0
2
0
0
1
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
2
0
2
2
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
1
0
0
1
1
0
2
0
2
1
0
2
0
1
2
1
1
1
0
0
2
0
1
0
1
0
0
0
0
1
0
0
0
2
2
1
1
2
0
0
2
2
0
1
0
0
0
2
0
0
2
0
1
0
2
2
1
0
0
0
2
1
0
0
0
0
2
2
1
2
2
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
3
0
2
1
0
0
0
2
0
0
2
0
2
2
2
0
2
1
1
1
1
2
0
0
1
1
0
0
0
1
0
2
0
0
1
0
2
1
2
1
1
0
2
0
2
0
1
0
0
1
0
0
2
2
0
0
0
0
3
0
1
1
1
0
1
0
1
0
1
2
0
0
2
0
0
0
0
0
1
0
2
2
0
1
2
0
0
0
0
1
2
0
0
0
0
1
0
1
2
2
1
0
1
2
2
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
1
0
0
1
2
0
0
1
0
0
1
2
1
1
0
0
1
0
0
0
0
3
1
1
2
0
1
0
2
1
2
0
1
0
0
1
0
1
0
0
1
0
0
0
2
2
1
0
1
0
0
0
1
2
2
3
1
2
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
1
2
0
0
1
0
0
1
2
0
0
2
0
2
0
1
0
1
0
2
0
0
0
2
3
2
0
1
0
1
1
0
1
1
1
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
1
1
0
0
0
1
0
1
0
1
0
0
5
2
2
2
1
0
0
2
1
0
0
1
2
2
0
0
0
0
0
1
0
2
1
0
2
0
0
1
1
0
0
0
0
2
2
2
0
2
0
0
2
1
0
0
0
1
1
1
2
0
0
2
0
1
0
3
0
0
2
2
0
1
1
1
0
0
2
1
2
0
0
1
0
1
2
0
0
1
2
1
0
1
0
0
1
0
0
1
0
0
1
1
0
0
8
0
0
0
1
0
2
0
3
1
1
0
1
0
0
2
0
0
2
0
3
0
1
3
0
2
0
2
0
2
2
2
1
0
0
2
0
0
2
1
0
0
0
0
1
1
0
2
0
2
0
1
0
1
1
2
0
0
0
1
1
2
2
0
0
0
2
0
2
2
1
3
0
0
0
3
1
0
0
0
1
0
0
1
0
1
0
0
0
2
0
1
0
1
0
0
2
0
1
0
0
1
0
1
2
0
0
1
2
1
0
0
1
0
0
2
1
2
2
0
0
0
1
1
2
0
0
1
0
1
1
0
0
0
0
0
3
2
1
2
0
2
1
1
0
1
0
1
0
0
0
0
1
2
0
3
1
1
0
0
0
2
0
1
1
2
0
1
0
0
2
0
1
1
0
0
0
2
0
2
0
0
0
1
2
1
0
1
1
3
0
1
1
0
0
1
0
1
0
0
0
1
0
0
0
1
1
1
0
0
0
1
1
1
2
0
0
1
0
0
2
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
1
0
2
0
1
0
0
2
0
1
0
0
0
1
0
2
1
1
0
1
0
0
0
1
0
0
1
2
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
5
0
0
0
0
0
1
1
2
1
0
2
0
0
1
1
0
1
2
0
2
3
1
1
0
0
0
0
0
1
2
1
1
1
2
2
2
0
2
0
0
0
0
2
1
2
0
1
0
0
1
1
0
1
2
2
0
3
1
0
2
0
2
2
2
0
0
0
0
2
3
0
1
1
0
0
0
1
0
1
1
0
0
2
0
1
2
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
2
0
2
1
2
2
2
1
2
0
0
2
1
0
1
0
0
1
0
0
2
0
0
1
1
1
3
2
1
0
1
0
0
0
0
3
0
0
0
2
0
0
0
0
0
1
2
1
1
1
2
0
2
1
0
2
0
0
0
0
0
2
2
1
0
0
0
4
0
2
0
0
0
2
1
0
0
1
2
0
1
1
0
0
0
2
1
2
1
2
0
1
1
0
0
0
0
1
2
0
1
0
1
0
4
0
0
2
0
0
0
0
0
1
1
1
0
1
0
0
2
0
0
1
0
1
0
2
0
0
2
2
0
0
0
0
2
2
2
1
0
0
0
2
0
2
2
0
1
0
1
0
0
0
1
0
2
0
0
0
0
1
0
0
0
3
2
0
0
1
0
0
0
3
0
2
1
0
1
1
0
1
2
0
1
1
0
2
0
2
1
2
1
2
1
2
3
0
0
1
0
0
1
0
1
1
1
1
0
0
1
0
3
1
2
0
0
1
0
2
3
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
1
3
0
1
0
2
0
0
0
1
1
0
0
2
0
2
2
0
1
2
0
0
0
2
1
2
1
0
0
0
0
0
2
0
0
2
1
0
1
0
0
0
1
0
0
1
0
0
1
0
0
1
1
0
1
1
0
0
1
1
2
1
1
1
0
0
0
1
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
1
2
0
0
1
1
0
1
0
0
0
1
0
1
2
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
2
2
1
0
0
1
0
1
1
0
0
0
0
2
1
1
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
1
0
0
1
0
0
1
2
0
1
0
0
1
0
0
2
0
2
0
0
0
2
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
1
2
0
4
2
0
0
1
1
0
0
0
0
1
0
0
2
2
1
0
0
0
0
0
1
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
2
1
0
2
0
1
1
0
0
0
1
0
2
0
1
4
1
4
0
0
0
0
2
2
1
1
2
0
0
2
1
0
0
0
0
0
1
0
0
0
2
2
0
2
1
0
2
0
2
0
0
2
0
1
0
0
0
2
0
1
0
2
0
0
1
2
1
0
2
0
0
3
0
1
0
0
0
2
1
0
1
0
0
0
1
2
1
1
0
1
1
0
1
2
0
0
0
0
1
1
1
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
1
2
0
0
1
0
0
2
2
1
3
0
0
0
1
0
0
1
2
0
2
1
0
0
0
0
0
2
2
2
2
1
1
2
1
0
2
1
0
2
0
0
0
1
1
0
0
4
1
0
2
0
1
2
2
0
0
0
0
0
0
0
0
1
0
0
3
1
0
2
0
1
0
2
0
0
2
0
1
0
2
1
0
0
2
0
0
1
2
1
1
1
0
0
1
1
0
0
0
0
2
1
0
0
0
2
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
2
0
0
1
0
1
0
0
0
2
1
0
0
1
1
0
0
0
0
0
2
2
0
0
2
2
1
0
0
1
0
1
0
2
0
0
1
0
2
0
0
0
0
1
2
2
0
0
0
1
0
1
0
0
0
0
0
1
0
2
0
0
0
0
1
2
0
1
2
0
1
0
1
1
0
1
0
0
1
0
2
0
2
0
0
0
0
0
2
2
2
1
0
1
1
0
0
2
0
0
2
1
0
0
0
0
0
1
1
0
1
1
0
1
1
0
0
0
0
2
0
2
2
2
2
1
1
0
0
0
0
1
0
0
0
1
0
2
2
1
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
1
0
2
0
0
2
0
0
1
1
2
2
0
1
0
1
0
0
1
0
0
0
2
2
0
0
1
0
0
0
1
0
0
2
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
1
0
0
2
0
0
3
0
1
0
0
0
0
0
0
1
2
1
0
1
0
0
2
1
0
1
0
0
2
0
0
0
0
0
0
1
4
0
0
1
0
1
0
1
1
0
0
2
2
0
0
1
0
1
1
1
0
0
0
0
2
0
0
1
2
0
0
0
1
0
0
2
0
2
0
0
1
1
0
1
1
0
0
0
0
2
0
1
1
0
2
0
0
2
0
0
1
0
3
0
2
2
0
1
1
0
0
0
0
1
0
0
0
0
1
0
2
0
0
2
0
2
2
2
0
2
2
2
0
0
0
1
0
0
0
1
0
0
2
1
4
0
0
0
0
0
0
0
2
1
0
2
0
2
0
0
2
0
1
0
2
0
2
0
1
0
0
2
0
0
0
1
0
0
2
2
0
0
1
0
3
1
2
0
1
0
0
0
0
0
2
0
1
2
1
2
2
1
0
0
1
2
2
1
0
1
1
0
0
1
0
0
0
0
1
2
2
2
2
0
0
2
0
2
1
1
0
1
1
1
1
0
2
2
0
2
0
1
1
0
2
0
1
0
1
0
0
0
0
2
0
0
1
0
1
0
0
3
0
0
2
0
0
0
1
0
0
1
0
0
0
1
3
1
1
0
2
1
0
0
1
2
1
0
0
1
0
0
0
2
0
0
1
1
0
0
0
2
0
1
2
0
0
0
0
3
3
0
0
0
0
0
0
0
2
0
0
2
3
0
0
1
2
1
0
0
1
2
0
0
0
0
1
0
0
1
0
2
2
1
0
2
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
2
0
2
1
2
1
2
0
1
0
1
0
0
4
0
0
0
0
0
2
1
2
0
0
0
1
0
1
0
1
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
1
2
1
1
1
0
0
0
0
1
1
1
0
0
0
1
0
2
3
0
0
2
1
1
0
0
0
0
0
1
0
0
0
2
1
2
0
1
2
1
1
2
2
1
0
1
1
2
2
2
0
0
1
0
1
1
0
2
1
0
1
0
1
0
0
1
1
2
2
0
1
0
2
0
1
0
0
1
3
0
1
1
0
0
1
1
0
0
3
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
2
0
1
0
0
1
1
2
1
0
1
2
2
0
0
2
2
0
1
1
0
0
2
2
1
1
2
0
0
0
1
0
0
0
0
0
0
1
2
0
1
0
1
1
1
0
0
0
0
3
0
0
0
0
0
1
0
1
0
0
0
0
3
1
1
1
2
0
2
0
0
0
4
2
1
0
2
2
0
2
0
0
2
0
0
1
2
0
0
0
1
0
1
1
0
0
2
0
1
1
0
0
0
0
1
0
2
0
0
0
0
2
2
0
2
0
0
2
2
1
0
0
0
0
0
7
0
2
3
3
0
2
1
0
0
0
0
0
0
0
0
0
2
0
1
2
2
0
0
0
1
0
1
0
2
0
2
2
1
0
0
2
1
1
0
1
0
2
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
1
2
2
0
0
0
0
0
3
2
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
2
0
2
2
0
0
0
1
0
0
2
1
2
0
1
0
0
1
0
3
1
0
1
0
1
0
2
2
0
0
0
0
0
1
0
0
1
2
0
0
2
0
1
2
2
0
2
0
1
0
0
0
1
0
2
0
0
0
0
0
1
0
2
2
2
0
1
0
0
0
0
2
0
0
1
2
1
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
3
2
2
0
0
0
0
1
0
1
0
0
2
0
0
1
0
1
0
2
2
0
0
0
0
2
0
0
0
0
2
1
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
2
1
1
1
2
0
0
1
1
1
0
0
1
0
0
0
1
0
0
0
1
1
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
2
2
1
0
2
0
1
0
2
2
0
1
1
0
0
2
0
1
1
0
0
0
0
0
0
0
1
2
0
0
1
2
0
0
0
0
0
2
0
0
2
2
1
0
2
0
0
2
0
0
0
1
1
1
0
0
2
2
0
2
0
0
2
3
0
0
0
1
1
1
0
1
0
1
0
0
0
0
0
0
2
1
2
1
1
0
0
0
0
1
1
1
2
0
0
0
2
0
2
1
2
2
2
0
0
0
1
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
1
1
1
0
2
1
2
2
0
2
0
0
0
0
2
0
1
1
1
0
1
0
0
2
0
1
0
0
2
0
0
0
0
0
0
2
1
0
2
0
1
0
2
2
0
2
0
1
1
0
0
1
2
1
2
0
1
2
2
0
2
0
0
0
1
1
0
0
1
2
0
0
2
0
2
0
0
3
0
2
1
0
3
0
1
2
2
2
2
0
0
0
2
0
0
1
2
0
0
1
0
2
0
2
1
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
1
2
2
1
1
0
2
0
0
0
0
0
0
0
1
2
0
0
2
1
0
0
2
2
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
2
2
0
3
0
0
0
0
0
1
0
0
1
0
0
0
1
2
2
1
0
1
1
0
2
2
1
1
2
0
0
0
2
0
0
0
0
2
1
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
2
1
2
1
0
0
0
1
1
0
0
1
0
0
0
0
0
1
1
0
0
1
2
0
3
2
0
1
1
1
0
1
0
0
0
0
2
0
0
2
1
1
0
0
3
0
1
0
0
3
0
0
0
0
0
1
1
0
0
2
0
1
0
0
0
1
0
1
0
0
0
1
2
2
1
1
0
0
3
0
2
0
0
0
1
0
1
0
2
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
2
1
1
0
1
0
0
2
0
0
1
0
1
0
2
0
0
2
2
0
0
0
1
1
1
0
1
0
2
0
1
2
0
3
0
2
0
2
0
1
2
2
2
0
0
0
2
0
0
3
0
0
0
0
0
0
1
0
1
0
2
1
1
0
1
0
0
2
1
1
0
1
1
0
2
0
0
1
0
0
1
1
0
2
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
1
1
2
0
1
2
0
0
1
1
1
0
0
0
0
2
0
0
0
0
1
1
0
0
1
0
0
0
2
1
1
0
0
1
0
1
0
0
0
2
1
0
0
0
0
1
0
2
0
1
0
2
1
2
0
0
2
1
0
1
1
0
0
0
2
2
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
2
0
1
1
0
1
2
1
1
1
1
2
1
3
0
0
0
1
0
0
0
0
0
1
1
0
2
0
2
1
0
0
0
2
0
0
1
2
1
0
3
0
0
2
1
0
0
0
1
1
0
0
0
2
0
0
0
1
0
1
1
1
2
2
0
0
2
0
3
0
2
0
0
2
2
2
0
0
0
0
1
0
0
2
2
0
0
1
0
0
0
0
1
1
1
0
1
0
0
0
0
1
1
0
1
1
0
0
1
0
2
0
0
2
1
0
0
0
1
2
0
0
0
0
0
0
2
2
1
2
0
1
4
0
0
2
0
2
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
2
1
0
0
0
0
0
2
2
0
1
0
0
1
2
4
1
1
1
2
0
0
0
1
1
1
2
0
0
2
0
0
0
2
0
0
0
0
0
0
4
0
1
1
0
0
0
0
0
1
0
1
0
0
2
2
1
2
1
1
0
0
0
0
1
1
0
2
2
2
0
0
0
0
0
0
0
1
1
1
0
1
0
2
1
1
1
1
0
2
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
2
2
0
2
2
0
0
1
2
2
1
0
0
0
0
1
0
0
0
1
0
2
0
0
1
0
0
0
2
1
2
1
1
0
0
1
2
1
0
0
1
1
0
0
0
2
0
0
0
2
2
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
2
0
2
0
0
1
2
0
0
2
0
0
0
0
1
0
2
0
0
0
1
2
0
0
1
1
0
0
2
1
1
0
0
0
0
0
0
2
0
1
1
0
1
1
1
0
0
1
2
0
3
1
0
2
2
0
0
0
0
2
0
1
2
1
3
1
2
2
2
0
0
1
0
2
3
0
1
0
2
0
0
2
0
0
1
0
1
0
0
0
1
1
0
0
1
2
2
0
0
2
2
0
1
1
0
0
0
0
0
1
2
0
0
2
0
0
1
0
1
0
0
0
2
0
1
2
0
2
0
3
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
1
1
2
3
0
0
0
1
1
1
0
1
1
0
2
2
1
2
0
0
0
0
1
0
2
1
1
0
1
1
1
0
0
2
2
1
2
1
2
1
0
1
2
2
1
0
1
0
2
1
2
0
0
0
2
0
0
0
2
1
1
1
0
0
1
0
1
2
0
0
0
1
2
2
0
0
0
0
1
1
0
1
0
2
1
0
1
1
1
0
3
0
1
0
0
0
2
1
2
0
2
2
1
0
2
0
0
1
0
1
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
1
2
3
3
4
0
1
0
0
1
0
0
0
1
0
1
1
0
0
5
2
2
0
0
1
2
0
0
0
0
1
0
0
2
2
1
1
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
1
1
0
1
2
1
0
0
0
0
0
1
1
1
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
1
0
1
0
0
1
1
2
0
0
1
2
1
0
1
2
0
1
1
2
0
0
1
2
0
0
1
0
0
2
0
0
0
0
2
1
0
0
1
0
2
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
1
2
0
1
0
2
1
0
0
0
1
2
2
2
0
1
1
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
1
1
0
1
0
0
1
2
1
1
0
0
1
1
2
0
0
1
1
2
0
0
0
0
2
2
1
2
0
2
2
0
0
1
1
0
0
2
1
0
0
0
0
2
0
2
1
3
1
0
0
2
0
1
0
0
2
0
0
0
0
0
0
1
0
2
0
1
0
2
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
1
0
0
1
0
0
0
0
1
0
1
0
1
0
1
0
2
0
0
1
0
2
0
0
2
0
5
0
0
0
0
0
1
2
0
0
1
1
0
0
0
1
0
1
1
0
1
1
0
0
2
0
2
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
1
0
1
0
0
0
0
1
0
1
0
0
1
1
0
2
2
1
0
2
2
0
0
0
2
0
2
1
0
1
0
0
1
0
2
1
2
2
0
0
0
0
2
0
1
0
3
0
0
1
2
0
0
0
2
2
0
1
0
2
1
0
1
2
0
1
0
0
0
0
0
2
2
3
1
0
0
1
0
0
2
2
2
1
0
0
0
2
1
0
0
2
0
1
2
0
0
2
0
0
2
0
0
1
1
2
0
2
0
0
1
2
0
0
0
1
0
0
1
1
0
0
1
0
1
0
1
2
0
1
0
1
0
0
2
2
1
0
5
2
1
3
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
1
2
1
1
1
0
1
3
0
0
1
0
0
2
1
0
1
2
0
1
0
1
1
0
1
1
0
3
1
0
0
0
1
0
0
1
1
0
0
1
1
1
1
2
0
1
2
2
0
2
1
0
1
2
2
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
2
3
1
1
0
0
0
0
0
2
0
2
0
1
0
3
0
0
2
0
0
0
1
2
2
0
0
5
0
2
2
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
3
1
0
0
1
1
0
2
0
0
2
2
0
1
1
1
1
1
1
3
0
2
0
0
0
1
0
1
0
1
0
1
1
3
1
0
0
1
1
1
2
1
0
1
0
2
1
0
1
2
0
0
0
2
0
0
1
2
0
0
0
1
2
0
0
1
0
0
1
0
0
1
2
0
0
1
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
1
0
0
0
1
1
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
1
2
0
2
0
2
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
1
0
1
2
1
0
2
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
2
0
0
2
0
2
0
0
0
0
1
0
1
1
0
3
2
3
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
1
2
2
1
1
2
0
0
2
1
0
2
0
2
2
0
1
0
2
1
0
1
0
0
0
2
0
2
0
0
0
0
2
2
2
0
0
3
3
2
0
0
0
1
0
3
0
0
0
0
0
1
1
0
0
3
2
0
2
2
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
2
0
1
0
6
2
0
0
0
0
0
0
1
0
0
1
2
1
2
1
0
2
0
0
0
0
1
1
0
0
0
2
1
0
0
0
1
1
0
0
2
0
3
0
0
1
0
2
1
2
0
0
0
2
0
2
0
0
1
0
0
2
1
1
3
1
1
3
2
1
1
2
0
0
0
0
0
1
0
0
2
0
0
2
0
1
0
1
0
1
0
0
0
0
0
2
0
0
0
1
1
0
0
1
0
0
0
1
2
0
0
1
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
3
1
2
0
3
0
0
2
0
2
0
0
0
2
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
3
1
2
0
1
0
2
1
0
0
0
0
1
2
2
2
1
2
0
0
2
0
0
0
0
1
1
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
1
0
1
0
0
0
3
0
1
1
1
3
0
1
0
2
0
2
0
0
0
3
0
0
0
0
1
0
1
0
1
0
0
1
2
0
0
1
0
1
3
0
2
0
0
2
0
2
1
0
0
0
1
0
0
0
3
0
0
1
0
2
0
2
0
2
2
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
2
1
0
1
1
0
0
0
1
0
1
1
0
0
0
0
0
0
1
1
0
1
0
2
0
2
0
0
0
1
0
0
0
0
1
2
2
0
1
0
0
2
1
2
0
1
0
0
1
0
0
0
0
0
0
1
1
1
2
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
2
2
1
1
0
2
0
2
2
0
0
1
2
2
1
0
0
2
0
2
0
0
1
2
1
2
1
0
1
0
0
0
0
0
0
1
0
1
0
0
2
2
0
0
0
0
2
0
1
1
0
0
0
0
1
1
2
2
3
0
0
0
0
1
3
0
1
1
0
0
1
0
1
0
2
1
2
1
0
0
0
0
4
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
2
1
0
0
1
0
0
0
2
0
0
0
2
2
0
0
2
0
3
0
8
2
0
1
1
0
0
1
0
0
1
2
2
0
0
1
1
2
0
0
2
0
1
1
0
1
2
1
0
1
2
2
0
0
1
0
1
0
0
0
0
2
0
0
0
0
2
0
0
1
0
2
0
1
0
0
1
2
2
0
1
2
1
0
0
0
0
1
0
1
0
0
1
0
0
2
0
0
0
1
0
0
1
1
1
0
1
0
0
2
0
0
1
0
2
1
3
2
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
2
0
1
0
0
1
2
0
0
1
0
2
0
0
1
0
0
1
2
4
2
1
0
0
0
2
2
0
1
0
2
2
1
1
1
0
0
0
0
0
2
2
1
0
0
0
2
1
1
2
2
2
0
2
0
2
0
1
1
1
1
0
2
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
2
1
0
1
2
2
1
0
1
0
0
0
0
2
0
1
2
0
1
0
0
0
2
0
2
0
2
0
0
1
0
0
1
0
0
2
0
0
2
2
0
0
1
0
0
0
0
2
1
0
0
0
2
2
0
0
0
0
2
0
2
0
0
0
0
2
1
0
0
2
0
0
0
0
4
0
0
1
0
2
2
1
1
0
0
2
0
1
0
0
2
1
0
1
0
0
0
0
1
0
0
2
0
0
0
1
4
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
1
1
0
1
0
0
0
0
1
0
2
2
0
1
0
1
1
2
2
0
0
0
0
0
2
2
0
0
2
0
0
1
0
0
1
0
0
2
0
1
1
1
0
0
0
0
1
0
0
2
0
1
1
1
0
0
0
0
2
0
2
0
1
0
1
1
0
1
0
1
2
0
2
0
0
2
0
0
0
2
0
2
0
0
1
1
0
0
1
2
0
0
0
2
1
0
1
1
0
0
0
1
0
0
0
0
3
1
3
1
0
0
2
2
1
0
2
0
1
0
0
0
0
1
2
2
0
0
1
3
1
0
0
1
0
0
0
0
2
1
0
0
1
1
0
0
0
1
1
0
0
0
2
1
0
1
1
0
1
0
0
0
2
0
0
0
0
0
0
1
1
0
1
1
1
0
0
0
2
0
0
1
1
0
0
0
0
1
0
0
3
0
1
0
0
1
0
1
0
1
1
0
0
1
0
2
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
1
0
0
2
0
1
0
1
2
1
1
0
0
0
1
0
1
2
0
1
2
0
0
0
2
0
1
1
1
2
2
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
3
0
1
2
0
1
0
2
1
2
0
2
2
0
0
0
0
0
0
0
0
0
0
1
2
1
2
1
0
0
0
0
0
0
1
0
0
0
0
2
1
2
1
0
0
1
0
1
1
3
1
1
0
1
0
0
0
0
2
1
0
0
2
0
1
1
0
0
0
2
0
2
0
1
1
0
0
1
0
0
0
1
0
2
2
1
0
0
2
0
0
0
1
0
0
2
0
1
0
0
0
1
0
1
1
0
1
0
1
1
2
0
0
0
2
1
2
1
2
1
0
0
0
2
1
0
0
2
0
0
2
1
0
0
0
2
2
0
2
1
0
0
1
0
1
0
1
1
3
0
0
0
2
0
0
0
1
2
2
5
0
0
2
0
0
0
0
2
0
1
2
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
1
2
1
1
1
0
1
0
1
0
2
0
0
0
2
1
0
0
0
1
0
1
0
0
2
1
2
1
1
1
0
1
1
1
1
1
0
1
0
1
2
0
0
2
1
0
0
1
0
2
0
1
1
2
0
1
0
0
1
1
0
1
0
2
0
0
1
0
0
0
0
1
0
0
2
2
0
1
2
0
2
0
1
0
2
1
1
0
0
0
0
0
1
0
0
2
0
2
0
2
1
0
1
0
1
1
1
2
1
5
2
0
2
0
1
0
0
0
1
0
2
0
0
0
2
1
1
1
0
1
1
1
0
2
1
2
0
0
0
0
1
3
2
0
3
2
0
1
0
0
2
2
0
0
1
1
0
2
2
0
1
1
0
1
0
1
0
1
2
0
0
0
0
2
0
2
3
2
0
1
2
0
0
0
0
0
0
0
1
0
0
2
1
0
1
0
0
2
1
0
1
0
1
0
1
0
0
0
2
1
0
3
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
1
0
0
0
2
1
0
2
0
2
1
2
0
0
0
0
0
1
2
0
0
0
0
1
7
1
0
2
1
0
0
0
0
1
0
2
0
0
2
1
1
0
0
0
1
0
0
0
0
2
1
2
1
2
0
2
1
1
2
0
0
0
0
2
1
2
0
3
0
0
1
0
0
0
0
0
1
1
0
1
0
2
0
0
0
0
1
0
2
2
0
0
1
2
1
2
2
0
0
0
0
1
0
2
0
1
2
0
2
0
1
1
0
0
0
2
0
4
1
0
1
0
0
0
2
2
0
2
0
2
1
0
1
0
0
2
0
1
2
2
0
1
0
0
2
0
0
1
1
0
2
3
0
0
0
0
1
1
0
2
0
0
1
0
0
2
1
2
2
0
0
0
0
0
0
1
0
0
1
2
0
2
0
0
1
1
0
1
2
0
2
2
0
1
1
2
0
0
1
0
0
2
1
1
0
0
2
0
1
0
1
0
1
2
0
0
0
0
2
0
4
0
0
2
0
1
0
2
1
0
2
0
9
0
0
0
0
2
1
1
0
2
0
0
1
0
0
2
0
0
1
0
2
1
1
2
0
1
0
2
1
1
0
1
2
0
1
0
1
1
0
0
2
1
1
2
1
2
3
1
2
2
2
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
2
1
1
0
0
0
1
0
0
0
0
0
0
0
1
2
1
0
2
0
1
2
1
0
0
0
0
2
1
2
0
1
1
2
0
0
1
1
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
2
0
0
0
1
0
1
3
1
1
1
0
0
0
1
0
0
0
1
2
0
0
2
0
2
1
0
1
0
1
0
2
1
0
1
0
0
1
2
1
0
1
2
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
2
1
1
1
0
2
1
1
1
0
0
1
0
0
0
3
0
2
0
0
0
2
0
2
2
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
2
1
0
2
0
1
0
2
1
1
0
2
0
0
0
0
0
3
0
2
1
0
0
0
0
0
0
1
1
1
1
0
1
0
0
0
1
2
0
0
1
0
1
0
2
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
1
0
0
2
1
0
0
2
0
1
0
0
1
2
2
3
1
3
0
1
0
0
2
2
0
2
0
2
1
0
0
0
1
0
0
0
0
1
2
0
0
1
0
0
2
0
3
2
0
2
2
0
1
0
0
1
1
0
2
0
2
0
1
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
1
1
0
1
1
0
2
0
1
1
0
0
0
2
2
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
2
0
0
2
0
0
0
0
1
0
0
2
0
0
2
1
0
1
0
0
0
0
1
1
0
0
2
2
2
1
0
0
0
0
0
0
3
0
0
0
0
0
1
0
1
1
0
0
1
2
0
0
2
1
0
0
0
1
1
2
0
2
0
0
2
1
1
2
0
1
1
2
0
1
0
2
0
0
2
0
0
1
0
0
2
1
1
1
0
1
0
2
0
0
0
0
1
1
1
2
0
1
0
1
2
0
1
1
2
0
0
0
2
1
1
4
0
0
0
0
1
2
0
0
0
1
2
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
2
0
2
0
1
0
0
1
3
0
0
0
2
2
2
0
1
2
0
0
0
2
2
2
0
1
0
0
0
2
1
1
1
0
2
0
3
1
1
0
2
1
2
1
0
0
2
1
0
0
0
1
0
0
0
0
1
0
2
2
0
2
2
0
0
0
1
0
1
0
2
0
0
3
1
0
2
0
2
1
1
0
1
1
0
0
0
2
2
1
0
0
0
2
0
0
2
0
0
1
0
2
0
0
0
2
0
1
2
1
0
2
1
2
1
1
0
2
0
0
2
0
1
1
0
0
2
0
0
0
2
0
0
0
1
0
0
2
1
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
1
0
2
1
2
0
2
1
1
2
2
1
0
0
1
0
0
0
0
0
0
1
0
0
1
1
1
0
1
1
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
1
1
2
0
2
2
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
2
2
1
0
0
0
2
2
1
0
0
0
0
0
5
0
0
0
0
1
0
2
0
1
0
2
2
0
0
0
2
2
0
0
0
0
0
0
1
0
2
2
0
0
2
0
0
0
1
0
1
1
0
0
0
0
2
2
1
0
1
1
0
0
0
0
0
0
1
0
0
0
1
2
0
0
1
1
0
0
0
0
0
1
2
0
2
2
2
1
1
2
0
2
0
2
0
0
3
1
0
1
0
0
1
2
0
0
1
0
0
1
1
0
2
1
1
0
0
0
1
0
1
1
1
0
2
0
6
0
0
2
0
0
1
1
0
0
2
1
1
1
0
1
1
0
1
1
0
0
0
0
1
1
1
0
2
1
0
0
0
0
0
1
0
0
0
0
1
2
1
1
0
1
0
0
0
0
1
1
1
0
0
7
0
1
1
2
0
2
1
0
2
1
2
0
0
1
0
1
0
0
2
0
1
0
0
1
1
0
0
1
1
0
0
0
0
2
0
1
0
1
1
2
2
0
0
0
1
0
0
2
0
0
0
0
0
1
2
0
0
0
2
1
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
1
2
1
1
0
0
0
2
0
0
1
0
3
0
0
2
0
0
1
0
0
0
1
2
1
1
1
0
0
2
0
0
3
1
2
1
1
0
0
0
0
1
2
1
1
1
2
0
3
0
0
2
1
0
2
1
1
0
1
0
0
1
0
1
1
2
1
0
0
2
2
1
0
0
0
0
2
2
2
1
2
3
0
1
0
0
0
0
0
1
1
5
0
1
1
0
1
0
0
0
0
2
1
1
1
0
0
0
2
0
2
1
0
0
2
1
0
0
0
5
2
0
0
0
0
0
2
1
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
1
0
1
3
0
0
2
1
1
2
2
0
0
1
0
0
1
1
0
0
1
1
0
0
2
0
2
0
1
0
0
0
0
1
0
2
1
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
1
1
1
0
1
1
0
2
0
2
1
1
1
0
2
1
2
0
0
0
2
0
1
0
0
0
2
0
0
1
0
0
2
2
2
0
1
1
2
0
0
3
0
0
0
0
0
0
0
1
0
0
0
2
1
0
1
1
0
0
2
0
0
7
1
2
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
2
2
1
0
1
0
0
0
0
1
1
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
1
1
0
0
0
1
0
4
0
0
0
1
2
0
0
0
2
1
1
0
0
2
0
2
0
2
0
0
0
2
0
0
0
9
0
0
0
1
0
0
2
2
0
0
2
0
1
1
2
1
1
1
0
0
1
0
1
1
2
0
1
1
0
0
1
0
3
0
1
0
1
0
0
1
1
0
1
0
0
2
0
0
2
0
1
0
1
3
0
0
2
1
1
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
2
0
1
0
2
2
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
2
1
2
0
0
2
0
0
0
0
0
0
1
0
1
1
0
0
2
0
0
1
0
2
1
1
1
0
1
0
1
2
0
0
2
0
2
0
1
0
0
2
0
1
0
1
2
0
2
1
1
0
0
2
0
0
2
0
1
0
1
0
2
2
0
1
0
0
1
0
0
1
0
1
2
0
1
0
1
0
0
0
1
1
2
2
0
2
0
0
0
0
1
1
0
0
0
1
2
0
1
2
2
0
2
3
2
1
0
1
3
0
0
0
0
0
1
2
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
1
0
2
1
2
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
1
0
2
0
0
0
2
5
1
0
0
1
0
0
5
1
1
1
1
1
3
1
0
0
2
0
2
0
0
2
0
1
1
1
1
2
2
2
0
0
1
2
0
3
0
2
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
3
0
0
0
0
0
1
2
1
1
1
1
0
1
0
0
0
1
0
2
0
3
0
1
0
2
0
0
0
0
0
2
2
0
0
0
2
1
0
0
0
1
0
2
0
1
0
1
2
1
0
2
0
0
0
0
2
0
0
0
0
1
0
1
0
0
1
0
2
1
2
3
0
2
0
0
2
0
1
2
2
0
0
0
0
1
0
0
2
0
2
0
0
0
1
0
1
0
0
0
2
2
0
0
0
2
2
1
0
2
0
0
1
0
0
0
0
0
1
0
1
0
0
1
1
1
0
0
2
2
0
1
0
0
0
0
1
2
1
2
0
0
0
0
2
0
1
0
0
1
0
2
1
2
0
0
2
1
1
1
0
1
0
0
2
0
0
1
0
3
0
1
0
0
2
0
1
2
0
0
2
0
2
2
0
1
0
2
0
0
1
0
0
0
2
0
0
1
0
1
0
0
0
1
1
0
1
2
0
1
0
0
1
5
1
0
2
1
0
1
1
0
0
1
0
1
1
1
2
2
0
2
1
0
0
1
0
0
0
0
1
0
2
1
0
3
1
1
0
0
2
1
2
2
1
0
0
0
2
1
0
0
1
1
0
0
0
0
3
0
0
1
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
3
0
1
0
1
0
0
1
0
1
2
1
1
2
0
2
1
2
0
0
2
0
2
0
0
1
0
1
2
2
0
2
1
6
0
0
0
1
0
2
0
1
1
0
2
2
0
2
2
0
1
2
0
0
2
0
1
1
0
0
2
0
1
1
1
0
2
2
0
2
0
0
0
1
0
2
0
1
0
1
0
0
0
1
2
1
0
2
0
1
0
0
1
0
0
1
2
1
0
1
0
2
1
0
1
0
0
0
0
0
2
1
0
0
3
1
0
0
1
1
1
1
1
0
0
2
0
0
2
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
2
0
0
1
1
0
1
0
0
0
0
2
2
0
0
0
3
1
1
1
0
0
2
0
0
0
0
2
2
0
1
1
0
0
2
3
1
1
0
0
0
0
0
0
3
0
1
0
0
1
0
0
0
2
0
0
0
1
0
1
0
0
1
0
0
0
3
2
0
0
1
0
1
2
0
0
0
1
2
1
1
0
2
2
0
2
2
0
0
0
1
0
0
0
1
0
1
2
0
0
0
0
2
1
0
1
1
2
0
1
0
2
1
0
0
0
1
0
1
2
0
0
2
0
2
2
2
2
1
0
0
1
0
0
0
1
2
0
0
2
2
2
0
0
1
1
0
0
1
1
0
1
0
2
2
0
2
0
0
2
0
0
2
0
0
1
0
2
0
0
1
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
1
1
0
0
1
2
2
0
0
0
2
0
2
0
0
0
2
0
0
1
2
0
0
2
0
1
1
0
1
2
0
1
1
0
0
0
0
1
1
2
0
2
1
0
0
0
0
1
1
0
0
0
2
0
0
1
2
0
0
0
0
2
2
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
1
2
0
0
2
0
0
1
0
3
0
0
1
2
0
1
0
0
1
0
1
0
0
0
1
2
0
0
1
0
0
1
0
3
0
2
0
2
1
0
2
1
2
1
2
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
2
3
1
0
0
0
2
2
2
2
2
0
1
0
0
2
1
0
0
0
2
0
1
0
2
2
0
1
2
0
0
1
2
0
0
1
2
0
2
2
0
0
0
0
2
1
3
0
0
0
0
2
1
0
1
0
0
1
1
0
1
0
1
1
0
1
2
0
0
1
2
2
1
1
2
0
3
0
1
2
2
2
2
1
0
0
0
3
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
1
0
1
1
0
2
0
2
2
1
2
0
0
1
1
0
0
0
0
0
0
0
0
1
2
2
0
1
1
0
2
0
0
0
2
0
0
1
1
1
1
1
0
2
2
0
0
0
0
0
0
0
1
1
0
0
1
0
1
1
0
0
0
0
1
0
0
0
2
2
0
0
0
2
0
1
0
0
2
1
1
2
1
3
1
0
2
0
0
1
0
0
1
0
1
2
2
1
1
0
0
2
2
0
0
0
1
1
0
0
2
1
0
1
1
2
1
0
2
1
0
0
0
2
1
0
1
0
1
0
0
0
0
0
0
0
1
2
1
3
2
0
0
0
0
1
0
2
0
0
1
1
0
2
0
0
0
0
0
0
0
3
1
0
0
0
0
0
2
0
2
7
2
2
0
0
2
0
0
2
1
0
0
2
1
0
1
2
0
0
0
0
1
1
0
2
2
1
1
0
0
1
2
2
0
1
0
0
0
2
0
0
3
0
0
2
0
2
0
2
0
0
0
2
0
0
1
0
0
0
1
0
2
2
0
1
1
0
1
0
2
0
0
2
1
2
0
0
1
1
0
1
0
1
0
0
0
0
0
3
2
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
4
0
0
0
1
0
0
0
2
2
1
1
1
1
0
0
0
1
1
2
0
0
0
0
1
0
1
3
0
1
0
0
2
2
0
2
0
0
0
0
0
1
1
1
2
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
3
1
0
1
0
0
1
0
1
2
1
0
1
0
2
1
1
0
1
2
0
0
2
2
0
0
2
2
0
0
0
0
2
0
0
1
2
0
1
0
0
0
0
0
0
0
1
1
0
0
0
3
1
0
0
0
0
2
0
0
1
2
0
2
0
1
0
0
2
2
0
0
0
0
1
0
0
2
0
0
1
0
0
2
2
0
0
0
1
1
3
0
1
1
0
1
2
1
2
0
0
0
0
0
3
0
0
0
0
2
0
1
0
0
0
2
0
1
1
2
0
0
0
0
0
1
1
1
0
1
6
2
2
2
0
0
3
0
0
1
1
0
1
0
0
1
0
0
1
0
0
0
0
0
1
1
0
1
0
1
1
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
2
1
2
2
2
1
2
1
2
2
0
1
0
2
1
0
1
1
0
0
0
2
2
1
0
0
0
0
1
2
0
0
2
1
2
0
3
1
0
0
1
0
2
2
0
1
1
2
0
0
2
1
1
1
0
0
0
1
0
0
1
2
0
0
1
1
0
2
0
2
1
0
0
1
2
0
0
0
2
0
1
0
0
0
0
1
1
1
1
1
2
1
0
0
2
1
1
0
2
0
5
0
1
2
2
0
0
1
0
1
2
0
1
0
0
1
1
1
3
1
2
2
1
2
0
0
0
1
0
0
0
1
0
0
0
3
1
0
2
0
0
0
2
0
1
0
1
1
0
0
2
0
2
0
0
1
1
0
2
0
1
1
0
0
0
0
1
0
1
0
1
1
0
1
1
2
0
0
7
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
1
2
1
0
1
0
1
0
0
0
0
1
1
1
1
2
0
0
1
2
0
2
0
2
1
2
2
0
1
0
1
0
0
1
0
1
0
0
2
0
0
1
0
0
0
0
0
3
0
2
1
0
0
1
0
1
1
0
2
2
2
1
2
2
0
2
0
0
0
0
0
0
0
0
0
1
1
2
1
1
2
0
0
2
1
2
1
0
2
0
0
1
0
0
0
0
0
1
2
2
1
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
2
0
0
1
2
2
0
0
2
0
1
0
0
2
0
0
1
0
0
0
1
1
2
0
0
1
0
3
0
1
0
1
0
1
1
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
1
0
2
0
1
1
2
0
0
1
0
0
2
1
0
1
0
0
2
1
1
1
0
0
0
2
2
1
1
1
2
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
1
1
0
1
0
0
2
0
0
0
2
0
1
2
2
1
0
0
0
0
1
2
0
0
1
0
0
0
0
1
2
0
1
0
0
0
0
2
1
1
1
1
0
0
2
0
0
1
4
0
2
0
2
2
1
1
0
0
0
2
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
1
1
2
1
1
0
0
1
0
0
0
2
2
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
2
0
0
0
2
0
2
1
1
2
0
0
0
1
1
0
0
1
2
0
2
0
1
1
2
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
3
0
2
0
0
0
0
1
2
0
2
0
1
0
0
1
1
0
0
0
2
0
0
0
1
2
0
0
1
1
1
1
0
0
0
0
1
2
0
2
0
0
1
0
1
2
1
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
2
2
0
1
0
2
0
0
2
2
0
2
1
2
0
0
0
1
0
0
0
0
0
0
0
1
3
2
0
0
2
1
0
0
0
0
0
2
0
1
0
0
2
1
0
0
2
0
0
0
0
0
0
4
0
1
2
0
0
0
0
1
1
2
0
0
0
0
0
3
1
2
2
2
0
2
2
1
0
1
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
1
0
0
2
2
1
0
2
4
0
1
1
0
1
1
1
0
2
1
0
0
0
2
1
0
2
2
0
0
1
2
0
0
0
0
1
1
0
1
0
0
0
0
0
2
0
0
1
0
0
1
2
0
2
0
0
0
2
0
0
1
2
0
0
0
0
2
1
0
2
1
0
0
2
0
0
0
1
0
2
0
1
1
1
0
1
0
1
0
1
0
1
2
1
0
0
0
1
0
1
0
1
0
0
1
0
0
1
1
1
0
0
0
0
0
1
2
1
0
0
2
0
0
0
1
1
0
0
0
1
0
1
0
0
0
1
0
1
1
2
2
0
0
0
0
0
0
0
0
1
0
0
2
0
2
2
0
0
1
1
0
0
1
0
0
2
0
1
1
0
1
1
2
0
0
1
1
0
2
0
0
2
0
2
0
1
0
0
0
1
1
2
0
1
2
1
1
1
0
0
2
0
2
4
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
1
3
0
0
2
1
2
2
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
1
0
1
0
1
1
0
0
2
1
0
2
4
0
2
3
1
0
0
2
1
0
0
0
1
1
0
2
2
2
0
0
0
0
0
2
0
0
1
1
0
0
3
0
2
0
1
0
2
1
0
0
0
2
0
0
2
2
1
0
0
0
0
0
0
0
1
0
0
1
2
1
0
1
0
2
2
1
0
0
1
0
0
0
1
0
0
0
0
2
1
1
2
1
1
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
5
1
0
1
0
0
0
1
0
1
1
0
0
0
0
1
2
1
1
0
1
0
2
0
0
0
0
2
0
2
0
1
0
0
1
0
4
1
0
0
1
2
0
2
2
1
1
0
2
0
0
1
0
1
1
0
0
2
0
2
1
0
1
4
0
0
2
1
0
0
1
0
1
0
0
0
0
1
1
1
2
0
2
0
2
0
0
2
0
0
0
0
2
1
0
0
2
0
1
2
2
0
1
2
2
3
0
2
2
0
1
0
1
1
0
0
0
0
0
1
0
0
0
2
1
0
1
2
1
0
1
0
1
0
0
1
0
0
0
2
2
2
2
1
0
1
1
0
0
0
0
0
1
2
0
0
0
0
3
2
1
1
0
2
1
2
2
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
2
1
0
2
0
1
0
0
1
0
2
0
0
2
0
2
0
0
2
2
0
1
0
0
2
0
0
3
0
0
0
0
0
0
1
0
1
1
1
1
1
0
0
1
1
2
0
0
0
0
0
0
3
0
0
1
0
1
1
0
0
2
1
0
0
0
2
0
0
2
1
0
0
0
0
0
2
0
1
1
1
0
0
0
0
0
0
0
0
1
0
2
0
1
0
1
0
0
2
1
2
0
2
0
0
0
1
0
2
0
0
0
0
0
0
2
1
0
1
0
0
0
0
1
2
2
1
0
0
0
2
0
0
1
2
0
1
1
0
1
1
0
2
1
2
2
0
0
0
2
1
0
2
2
0
0
0
0
2
0
1
0
0
0
0
0
2
1
1
0
0
0
0
2
1
0
0
2
0
0
2
0
0
2
0
0
1
1
1
1
2
0
2
0
0
0
1
2
1
0
2
0
2
1
0
0
0
2
0
0
0
0
0
0
1
0
2
0
2
0
0
1
0
0
2
1
0
0
0
0
3
0
0
0
1
1
1
2
1
2
2
1
1
0
0
1
2
0
0
5
1
1
0
0
0
2
1
0
0
1
1
1
0
0
0
1
0
2
2
1
2
0
0
0
2
0
2
0
1
2
1
0
0
2
2
1
4
1
0
0
2
1
1
0
0
0
2
0
2
0
0
3
0
0
2
0
0
1
1
1
0
1
0
1
1
1
2
0
0
0
0
0
0
0
0
2
1
2
2
0
1
1
0
1
0
2
0
0
0
2
3
1
1
0
1
0
0
0
0
2
0
0
1
2
0
0
1
2
0
1
0
2
1
2
0
2
0
0
2
2
2
0
0
0
0
0
0
2
0
0
0
2
0
2
2
0
0
0
0
0
0
1
1
1
0
0
2
2
1
2
0
0
0
0
2
1
0
1
0
0
0
2
2
0
0
0
3
1
0
0
1
2
1
0
0
1
0
1
0
1
0
1
0
0
2
3
0
2
0
1
0
0
0
1
0
0
3
1
0
0
1
1
0
1
0
0
3
1
1
0
0
1
2
1
0
0
2
0
1
1
1
0
1
0
0
2
0
0
1
0
2
0
0
1
0
0
2
2
1
0
2
0
0
1
0
1
1
1
2
1
0
0
0
1
0
1
2
1
0
1
0
0
1
0
1
0
2
0
0
2
0
0
0
0
0
4
0
0
1
0
0
2
0
0
0
2
2
1
2
2
2
0
1
1
1
2
0
1
0
0
1
2
2
0
0
0
4
0
0
0
0
0
0
1
0
0
1
1
2
0
2
0
1
0
0
1
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
3
1
2
1
0
0
0
1
0
2
1
8
0
0
0
1
2
2
0
0
2
0
0
1
0
0
2
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
2
2
0
2
0
1
0
0
6
2
0
0
1
1
0
1
2
0
0
0
0
0
0
1
0
0
1
1
2
0
0
2
0
1
1
0
0
0
0
0
1
0
2
2
2
0
2
1
0
0
0
1
2
0
0
0
1
3
0
0
0
0
2
1
2
2
0
1
1
3
0
0
0
0
2
0
2
0
1
0
0
1
0
1
3
1
0
0
0
0
1
0
1
0
1
1
1
2
1
1
0
0
1
0
1
1
1
0
0
0
2
0
0
1
0
1
0
1
2
3
0
0
0
2
2
0
1
2
0
1
2
0
1
1
0
2
0
0
0
0
0
0
1
0
0
1
0
1
0
2
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
2
0
1
0
2
2
0
0
0
0
1
0
4
0
1
2
1
1
0
0
1
1
2
1
0
2
2
0
0
0
1
2
0
4
2
0
0
1
0
0
1
0
0
1
0
0
0
2
0
0
1
0
0
2
1
1
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
1
2
3
0
0
1
0
1
2
1
1
0
0
1
0
1
1
0
0
2
0
0
0
1
1
1
2
0
0
1
1
0
0
0
1
1
1
0
0
2
2
2
0
1
0
2
0
1
2
0
0
0
1
2
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
2
2
0
1
2
0
0
1
2
1
0
1
1
2
0
0
0
0
1
0
1
1
0
0
0
2
1
0
0
1
2
2
1
1
1
1
0
0
0
0
2
0
2
1
1
3
0
1
2
1
1
0
0
2
1
0
1
1
0
1
2
0
0
0
0
0
0
0
0
3
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
3
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
1
0
1
2
2
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
1
2
1
1
2
0
0
1
0
1
2
0
0
2
1
1
0
0
0
2
0
1
0
1
0
0
1
0
1
1
0
0
2
1
2
0
1
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
1
2
1
0
1
0
1
2
2
0
3
0
0
2
0
1
0
0
1
1
0
1
0
0
0
0
3
0
2
0
1
0
2
2
1
2
1
3
0
0
1
1
2
0
0
1
0
1
2
2
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
1
2
2
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
2
2
1
3
0
0
0
1
0
1
0
1
2
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
2
2
1
0
1
0
0
0
0
0
0
0
0
0
1
7
0
0
0
2
0
1
0
0
1
1
2
1
0
2
0
0
2
0
2
2
1
0
0
2
1
0
1
0
3
2
0
0
3
0
0
1
0
0
1
3
0
1
0
0
0
1
2
0
2
1
2
0
0
0
0
3
0
2
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
1
2
0
0
0
0
1
2
0
3
0
1
1
0
0
2
0
2
2
1
0
2
2
1
0
0
0
4
0
0
0
1
1
1
2
1
1
2
0
0
0
0
0
2
0
0
0
5
1
0
2
1
3
0
2
0
1
0
0
1
2
0
0
0
2
2
1
1
1
1
0
1
3
0
0
0
1
1
1
0
0
0
0
0
0
2
0
0
0
3
1
0
0
1
1
0
0
0
2
0
0
2
0
2
0
1
0
0
0
1
1
2
1
0
0
0
0
0
2
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
1
1
1
1
1
0
0
0
0
0
0
0
1
2
0
0
1
0
0
2
1
0
2
2
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
2
0
1
2
0
2
0
1
1
1
0
2
2
0
0
1
1
0
1
0
0
1
0
2
0
0
1
2
0
1
0
0
1
0
0
1
0
1
1
0
0
0
0
2
0
2
0
0
0
0
0
0
1
1
0
0
1
0
0
1
2
2
0
1
0
1
0
2
0
0
1
0
0
0
1
1
0
0
0
0
2
0
0
0
1
2
1
1
0
0
4
0
2
0
0
0
1
1
1
0
1
0
0
0
1
0
1
1
1
0
0
0
2
0
0
0
1
0
0
5
0
2
0
1
2
1
0
0
0
1
1
1
0
2
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
1
1
0
0
1
0
0
2
0
0
2
0
2
2
2
1
1
0
0
0
0
1
0
0
0
0
1
0
0
1
2
2
0
1
2
0
0
0
0
1
2
0
1
0
0
0
0
2
1
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
1
2
0
0
1
0
0
2
0
0
2
1
0
0
1
0
0
0
0
2
0
0
2
1
0
2
1
2
0
0
0
0
1
0
0
2
0
2
0
0
0
2
1
2
0
2
1
0
2
0
1
2
2
0
2
0
2
1
0
0
0
0
0
1
0
1
2
0
1
0
0
0
0
2
1
3
1
0
1
0
0
0
0
2
1
0
3
1
0
0
0
0
1
0
2
0
0
1
1
1
0
0
2
0
0
2
2
0
2
1
0
2
0
0
0
2
0
1
0
0
0
2
0
2
0
0
0
1
0
0
2
0
0
0
0
0
2
2
0
1
2
0
0
0
0
1
2
1
0
0
4
0
1
1
1
1
2
0
2
1
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
2
2
0
1
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
2
0
2
2
1
0
0
2
0
1
0
1
1
0
1
0
0
1
0
0
1
1
0
1
1
0
0
0
2
0
0
1
1
0
0
0
0
0
0
1
2
0
0
1
2
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
3
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
4
0
0
0
0
0
2
1
2
0
1
0
1
0
1
0
0
1
0
1
0
0
2
2
1
0
0
2
1
0
0
0
0
0
2
0
0
0
4
0
2
1
3
2
0
2
0
0
0
0
1
2
0
0
3
0
1
0
1
1
1
0
0
1
0
1
1
1
1
1
0
0
1
0
0
0
2
1
2
2
0
2
1
0
0
1
0
2
0
0
0
2
2
1
0
2
0
0
0
1
2
1
0
1
0
1
2
0
0
0
0
0
0
0
2
0
1
3
1
1
1
2
2
0
2
2
1
1
2
2
0
0
0
0
1
0
1
1
3
0
0
0
1
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
2
0
1
2
3
0
0
0
0
0
0
1
0
0
1
0
0
0
2
1
1
0
2
2
1
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
1
1
2
0
1
0
0
2
2
0
2
2
0
2
0
2
0
2
2
1
0
0
2
1
2
2
1
0
1
2
1
2
0
1
2
0
2
0
0
0
0
2
0
0
1
0
2
1
1
3
3
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
1
0
1
2
0
0
1
1
1
0
0
0
0
1
0
1
0
2
0
2
0
0
0
0
0
0
1
1
0
0
2
0
1
2
0
0
2
1
0
0
0
0
1
0
1
0
1
0
0
0
0
1
1
1
2
2
0
2
0
1
0
2
2
2
2
0
0
1
2
1
0
0
0
0
2
3
0
0
2
0
0
2
1
1
0
0
1
0
0
2
0
1
2
0
0
2
0
0
0
0
0
0
1
1
1
2
0
0
2
0
0
0
0
0
0
0
1
2
1
1
0
0
1
0
1
0
0
2
0
0
1
0
1
0
0
0
0
0
1
2
0
0
1
1
1
0
2
1
2
0
1
0
1
1
1
0
0
1
1
0
0
1
0
2
0
0
1
2
0
1
1
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
1
0
0
0
3
0
2
1
0
0
1
2
1
1
0
0
0
2
2
3
2
0
0
1
0
1
0
1
0
0
2
2
0
0
0
0
1
1
0
2
0
0
0
0
1
0
0
0
2
1
0
0
2
0
0
0
0
0
1
1
0
0
0
2
1
2
0
0
2
2
2
1
0
0
1
0
0
2
1
0
0
0
2
1
0
1
1
0
0
0
0
0
0
1
0
0
0
1
3
0
0
2
2
1
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
1
0
3
0
0
0
2
0
0
2
0
2
0
2
1
0
2
2
0
1
0
2
0
2
0
1
0
1
0
0
0
0
1
0
0
0
1
0
2
1
2
1
1
0
0
2
0
0
1
2
0
1
2
2
0
0
0
1
0
0
0
0
1
2
0
3
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
1
0
2
0
2
0
0
0
0
2
0
1
0
0
0
1
2
0
0
0
1
2
0
0
2
0
0
0
0
2
0
0
2
2
0
0
2
0
0
1
0
0
2
0
1
2
1
0
0
0
2
3
2
6
0
2
0
1
0
2
0
1
0
0
1
0
2
1
2
0
0
2
0
0
2
1
0
0
1
1
2
2
3
0
2
0
2
2
0
0
2
0
1
1
0
0
0
0
0
1
0
0
0
2
1
0
0
0
2
2
1
0
3
0
1
0
2
2
0
2
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
1
1
0
1
0
0
1
0
1
2
0
0
1
0
0
0
2
0
2
0
1
3
0
0
1
1
1
0
0
2
0
2
2
1
1
0
0
1
0
1
1
2
0
0
2
0
0
0
1
0
0
1
1
0
2
1
0
1
0
1
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
1
2
0
0
0
1
0
2
2
2
1
1
2
2
2
1
3
0
0
0
0
2
2
1
0
1
0
1
0
1
0
0
0
2
1
0
0
1
2
1
0
1
0
1
0
1
1
0
2
0
0
0
1
0
0
0
0
0
0
2
0
1
0
1
0
2
0
1
0
0
0
1
0
2
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
1
0
1
1
0
1
0
0
2
1
3
1
1
1
0
1
0
2
1
0
0
0
0
2
2
1
2
0
1
2
0
1
0
0
1
3
0
0
4
2
1
1
0
0
0
1
0
1
0
1
0
0
1
0
2
1
0
2
2
0
2
2
0
2
0
0
0
0
0
1
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
1
0
0
6
1
0
0
0
1
0
0
2
2
0
2
0
0
0
0
0
1
1
0
2
0
0
0
2
0
1
0
0
2
1
2
1
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
6
0
1
2
0
0
0
0
2
1
0
2
0
0
0
0
0
0
2
0
0
1
1
0
4
1
0
0
2
2
2
0
2
1
0
0
3
0
1
2
0
0
0
1
0
0
1
0
1
1
0
2
2
1
0
2
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
1
2
0
0
0
1
1
1
2
0
0
1
1
0
2
1
0
0
1
2
1
0
2
0
2
0
1
1
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
2
0
0
2
1
0
0
0
1
0
1
2
0
2
2
0
0
1
1
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
2
0
1
2
0
1
1
0
0
0
0
0
1
2
0
3
0
0
1
0
0
1
0
1
7
0
0
3
2
2
0
0
1
1
2
0
3
1
0
0
0
1
1
1
0
1
0
0
0
2
0
1
0
0
0
0
1
0
0
0
2
2
1
2
0
0
2
0
0
1
0
2
1
1
0
0
0
0
0
0
0
1
2
0
0
0
0
2
1
0
1
2
2
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
3
2
2
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
1
2
1
0
0
2
2
0
0
0
1
0
0
1
2
1
2
1
0
0
1
0
2
0
1
1
0
2
0
0
1
1
0
1
0
0
1
1
0
0
1
0
0
0
0
0
2
1
0
0
0
1
0
0
2
1
5
0
2
0
0
1
2
0
0
0
0
1
0
1
0
1
0
0
0
2
1
0
0
0
0
1
1
1
0
2
0
0
1
0
0
1
1
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
2
0
1
0
0
0
1
1
0
3
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
2
0
2
1
0
0
2
1
0
1
1
2
0
1
0
0
5
0
1
0
0
2
0
1
1
0
0
1
0
0
1
1
1
2
2
0
1
1
0
0
3
0
0
3
2
0
1
1
1
1
1
0
0
0
1
1
0
0
0
2
2
0
0
0
0
1
0
0
0
1
0
1
0
1
1
0
2
1
0
1
0
0
0
1
1
0
1
2
1
1
0
1
2
1
2
3
0
2
1
6
2
1
0
0
1
2
0
0
0
0
0
1
0
0
0
2
2
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
3
0
1
0
1
1
2
0
0
2
0
1
0
2
1
1
0
0
2
0
2
2
0
1
2
1
0
0
0
1
2
0
0
0
0
2
0
1
0
0
1
1
0
0
0
0
1
1
0
2
0
0
0
1
0
2
1
1
0
0
0
2
0
0
1
2
0
0
1
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
2
2
0
0
0
0
1
1
0
0
1
3
0
1
0
3
1
0
0
0
0
0
0
0
2
1
0
0
1
0
1
1
0
1
1
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
1
1
1
2
0
2
2
0
0
0
0
0
0
1
2
2
0
0
0
0
0
1
0
2
1
2
2
0
2
2
2
0
2
0
0
1
1
1
0
0
0
2
0
1
1
2
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
1
0
0
1
0
0
0
1
2
0
0
0
1
0
0
0
0
2
1
2
0
0
2
0
1
1
0
0
2
0
0
0
0
0
1
1
1
1
0
0
0
1
1
1
1
2
0
1
1
2
1
0
0
0
0
2
4
0
1
2
1
0
3
0
0
0
2
0
1
0
0
0
3
0
0
1
2
0
2
0
1
0
2
0
2
0
2
1
0
1
0
0
0
1
1
2
0
0
0
0
0
1
0
1
1
0
1
0
0
1
0
1
2
0
0
0
0
0
1
1
0
1
0
0
2
0
1
2
1
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
1
1
1
0
0
0
2
2
1
0
0
0
0
0
0
3
1
0
0
0
1
0
0
0
2
1
1
0
0
0
0
0
1
0
2
0
1
2
2
1
0
0
2
2
0
2
1
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
1
1
1
2
1
1
1
0
0
1
4
1
0
0
0
0
0
2
0
2
1
1
0
2
0
0
2
2
1
0
0
0
0
0
2
2
2
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
2
0
2
2
0
0
2
0
0
1
1
2
0
0
3
0
2
0
0
0
1
1
0
0
1
0
1
2
2
0
0
1
2
0
2
1
2
1
3
1
0
2
0
1
1
0
1
2
0
1
0
0
0
2
0
1
1
0
2
1
0
0
0
1
1
2
0
1
0
0
0
1
2
1
0
1
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
1
2
2
2
1
0
0
0
0
2
0
2
0
0
1
0
1
0
1
0
0
0
1
0
1
2
0
1
2
2
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
1
0
2
1
0
0
0
0
1
1
2
0
1
0
0
1
0
0
0
0
2
4
0
0
0
2
1
0
1
0
2
0
0
1
0
2
0
2
0
1
2
0
1
0
0
0
0
1
1
1
0
0
0
2
1
0
2
0
0
1
0
0
0
0
0
0
2
1
1
0
2
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
1
1
0
1
0
1
0
0
2
0
1
1
1
0
0
2
1
0
0
2
0
0
2
0
0
1
2
2
2
1
0
2
2
0
0
2
0
1
0
0
0
2
1
0
0
0
0
2
0
2
1
0
0
0
0
2
1
1
0
2
0
0
0
2
0
2
1
0
1
0
1
0
1
0
0
2
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
1
1
1
0
0
1
2
0
1
2
0
2
0
0
0
1
1
0
0
2
1
1
1
0
0
1
0
0
0
0
4
1
0
2
1
0
0
0
1
1
0
3
1
2
0
0
1
1
1
2
2
0
2
1
0
2
2
0
0
1
0
0
0
2
1
1
1
0
0
2
0
2
2
0
0
1
1
1
1
0
1
1
1
0
0
3
2
0
2
0
1
1
0
0
0
2
0
1
1
2
0
2
0
2
1
1
0
0
1
2
0
0
2
2
0
0
0
1
0
1
1
2
0
1
1
0
1
0
0
0
0
0
0
0
1
2
1
0
0
1
1
0
0
0
0
0
1
0
2
0
0
1
0
0
0
1
0
1
2
0
0
0
0
0
2
0
0
0
1
0
0
2
1
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
1
2
0
0
2
2
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
1
2
0
0
1
0
0
0
0
0
0
1
0
0
4
1
3
0
1
1
1
0
0
0
3
2
1
0
0
1
2
2
0
1
1
1
1
1
1
2
0
0
1
1
0
2
0
0
0
0
2
1
0
1
0
0
1
0
0
0
0
1
0
0
1
1
2
0
0
2
0
2
1
1
1
3
0
2
0
0
1
0
0
1
1
2
0
0
0
1
0
0
1
1
0
0
1
0
3
2
1
1
0
2
0
0
2
2
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
4
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
2
1
0
0
2
3
1
0
0
0
0
2
0
0
0
2
0
0
0
2
1
0
2
0
0
0
2
2
2
1
2
1
0
0
2
3
0
0
1
1
2
1
0
0
2
2
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
9
0
1
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
1
2
1
1
0
0
1
0
2
0
2
3
1
0
1
0
0
0
0
0
2
0
0
1
3
2
1
2
0
0
0
0
1
0
2
0
0
0
0
0
1
1
0
0
0
1
0
0
1
1
0
1
1
1
1
0
2
1
1
0
0
1
1
1
0
2
0
1
8
0
1
1
0
9
0
2
0
2
0
0
0
0
0
1
1
0
2
0
0
0
1
0
1
0
0
2
2
0
2
0
0
0
2
1
1
0
0
0
2
0
0
1
0
1
1
1
0
0
1
0
0
1
1
0
0
2
0
2
2
0
0
0
0
1
2
0
0
0
1
2
0
1
2
2
0
1
0
1
0
0
0
0
2
0
1
1
2
1
1
1
0
0
0
1
0
0
0
0
1
0
1
0
0
2
0
2
0
2
0
0
0
0
2
0
0
3
0
2
2
1
0
0
2
0
1
1
1
0
0
1
0
0
2
0
0
0
0
2
1
2
0
1
1
1
2
2
0
2
1
2
0
0
2
2
1
0
2
0
3
0
1
1
0
0
2
0
0
1
2
0
0
0
0
2
0
0
0
2
0
1
0
1
2
1
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
2
2
0
0
0
0
3
0
0
1
0
0
0
0
0
0
2
0
1
2
0
1
0
0
1
0
0
0
0
0
0
0
2
2
1
0
3
0
1
2
0
0
0
0
2
0
0
0
2
0
1
1
2
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
1
0
1
0
0
1
0
0
3
0
0
0
2
1
2
0
1
1
0
0
1
0
0
0
0
1
1
0
0
2
0
1
0
2
0
0
1
0
1
0
0
1
0
1
1
0
0
2
1
1
0
0
1
2
1
1
0
1
2
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
1
1
2
0
2
1
0
1
1
0
1
0
0
1
0
2
0
1
2
0
0
1
0
0
2
1
0
1
1
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
2
1
0
1
2
3
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
1
0
2
2
2
2
0
0
1
2
0
0
0
2
1
0
1
1
0
0
0
1
0
0
2
2
0
0
1
1
1
2
0
0
2
0
0
1
0
1
0
1
0
1
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
1
0
1
0
1
1
1
1
0
1
1
0
0
1
0
1
2
0
1
0
0
1
1
0
0
0
1
1
2
0
2
2
2
1
0
0
0
0
0
1
2
2
0
2
0
0
0
0
3
0
0
1
2
3
2
0
1
1
0
0
0
1
1
0
0
0
0
0
1
0
2
2
0
1
0
0
2
0
0
1
1
0
0
4
1
1
2
0
0
2
2
2
0
1
0
0
0
0
0
1
0
2
0
0
0
2
0
1
0
1
0
1
0
1
0
2
0
0
1
1
0
1
1
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
2
0
1
0
0
1
2
0
2
0
0
0
0
0
2
2
1
0
0
0
0
2
0
2
1
2
0
0
0
1
0
0
0
1
0
0
3
1
0
0
0
0
0
2
1
2
2
0
0
0
0
1
0
1
0
2
0
1
1
0
1
2
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
1
0
2
0
0
1
2
1
0
1
0
0
4
2
0
2
2
0
2
0
0
0
0
1
1
1
0
0
0
0
1
1
2
0
0
1
0
2
2
0
1
1
1
1
0
2
0
0
0
0
0
1
0
0
0
2
1
0
2
1
2
2
0
2
2
1
1
2
0
2
1
0
2
0
0
0
0
1
0
1
0
0
0
1
0
0
1
2
0
3
1
2
0
1
0
0
5
1
2
0
0
0
0
0
1
1
2
2
0
0
0
0
1
0
0
0
3
0
0
0
0
2
0
0
2
1
1
0
0
0
2
2
0
0
0
0
1
0
0
1
0
2
1
2
0
1
0
1
0
1
1
2
0
0
0
0
0
2
1
0
2
0
2
1
0
0
1
2
2
0
2
0
1
0
0
0
0
1
1
0
0
1
1
2
0
0
0
0
0
1
1
1
0
2
1
0
0
1
1
1
0
0
2
2
1
0
0
0
0
1
0
0
1
1
2
0
2
1
1
0
0
0
1
0
0
0
2
4
0
0
2
1
0
0
0
1
0
0
0
0
2
0
0
2
5
0
1
1
1
0
2
1
0
0
0
0
2
0
1
0
0
2
1
3
0
0
1
0
2
2
0
0
1
0
1
0
0
0
2
0
0
1
1
2
2
0
1
0
2
0
2
1
0
0
0
1
2
0
1
1
1
0
1
0
0
1
0
1
1
2
1
0
0
1
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
1
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
1
0
1
0
1
0
2
0
0
0
0
0
2
1
0
0
1
0
0
2
0
1
1
0
0
2
0
0
0
2
2
2
2
0
1
1
1
0
2
0
1
0
0
2
2
1
0
0
2
1
2
1
3
2
0
2
0
0
0
3
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
1
1
1
1
0
0
0
0
1
1
0
0
0
0
0
1
0
1
1
0
3
0
2
0
0
0
2
0
1
0
2
1
2
2
1
1
0
1
0
2
0
2
0
0
0
2
0
0
1
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
1
0
2
2
2
1
0
0
0
1
0
1
1
0
1
0
1
2
2
0
2
1
1
1
2
0
0
2
0
0
2
0
0
3
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
2
0
0
1
1
0
0
1
1
0
1
0
0
2
1
1
0
0
0
2
0
1
0
0
1
0
0
0
0
1
0
2
2
1
2
2
0
2
0
2
0
1
1
2
1
1
1
1
2
1
0
1
2
0
0
1
2
0
0
2
1
2
2
1
2
1
2
0
0
0
1
1
0
3
0
0
0
0
0
1
0
1
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
2
1
1
0
0
2
2
2
0
0
0
0
0
2
0
1
0
0
1
0
2
0
2
0
0
2
1
4
0
0
0
0
1
1
0
1
2
0
0
1
0
0
1
1
2
0
0
0
1
1
1
1
1
0
0
2
2
2
0
1
0
0
0
0
0
0
0
0
1
1
1
0
2
1
0
0
1
0
0
1
0
1
0
2
0
0
1
0
0
1
0
0
1
2
0
2
1
0
0
1
1
2
2
0
0
0
2
2
0
1
2
0
1
1
2
0
0
0
0
0
2
3
0
0
1
0
1
0
1
0
0
2
2
0
0
2
0
1
0
0
3
1
2
0
0
1
0
0
1
0
1
1
1
1
0
1
0
0
1
0
1
1
0
0
2
1
0
2
0
0
0
2
0
0
2
2
0
0
1
1
0
0
0
2
2
0
0
2
0
0
0
1
1
1
1
2
2
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
1
1
0
1
2
0
2
1
1
0
0
1
0
2
2
0
0
1
3
1
0
0
2
1
0
2
0
0
1
0
0
1
0
0
3
1
0
2
2
0
0
0
1
0
0
1
1
1
0
1
1
0
0
2
0
0
0
2
0
0
1
0
0
0
0
7
0
0
2
0
2
0
0
0
0
1
1
0
0
1
0
0
1
2
0
2
0
0
6
2
2
0
2
0
1
0
0
2
0
0
1
1
3
0
2
2
1
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
2
0
1
2
0
4
2
0
0
0
3
2
0
0
0
1
0
0
0
0
2
0
1
0
1
0
0
0
0
2
2
0
0
1
0
0
0
0
0
1
1
0
0
0
2
0
0
1
1
0
1
2
0
0
0
0
0
2
0
0
0
1
0
2
1
0
0
0
2
0
1
0
1
0
0
2
1
2
0
1
1
2
0
2
1
0
0
2
1
5
1
0
0
0
2
0
2
0
0
0
0
0
1
1
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
2
1
0
0
0
0
2
0
0
0
1
0
0
1
0
1
0
1
0
0
2
1
0
0
0
0
1
0
0
0
1
1
1
7
2
0
0
0
0
3
1
0
0
0
0
0
1
1
0
2
1
0
0
0
2
1
0
0
0
0
0
2
1
0
0
2
1
0
0
0
0
2
0
0
0
1
2
0
2
1
0
2
0
0
0
0
0
1
2
0
2
2
0
0
0
2
0
1
0
0
0
0
3
0
1
0
0
0
0
1
0
0
2
0
2
2
0
1
0
0
0
0
1
2
0
0
1
0
0
2
2
1
0
0
2
0
1
0
0
0
0
2
0
0
2
0
1
0
0
2
0
0
2
1
0
0
0
0
1
0
1
0
0
0
0
1
0
2
0
0
1
0
0
2
0
0
1
0
0
2
1
0
0
3
0
2
0
0
0
0
0
2
1
0
0
0
1
1
1
0
1
0
0
0
1
0
0
4
0
0
0
0
1
1
1
0
2
0
0
0
2
0
0
2
0
1
1
0
4
2
0
0
2
1
1
0
1
0
0
1
1
0
1
2
2
0
0
0
2
0
1
0
0
1
0
1
1
1
0
2
0
1
0
0
1
2
0
1
2
0
1
2
1
0
0
0
2
1
0
0
0
0
2
2
0
1
0
0
2
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
2
0
2
0
1
2
2
0
0
0
0
0
1
2
2
0
0
0
0
1
1
1
0
0
0
0
0
2
0
0
2
0
0
1
2
0
2
1
1
0
0
1
2
1
0
0
0
2
0
0
0
1
1
2
0
0
0
0
3
1
1
0
2
2
0
0
1
0
1
1
0
0
2
2
1
2
1
2
0
1
1
4
0
0
0
1
2
2
1
1
0
0
1
1
5
0
0
1
1
0
0
0
1
1
2
0
0
1
0
0
0
0
0
1
0
0
1
0
2
1
1
0
0
2
1
0
0
2
1
0
1
0
1
0
1
1
0
2
0
2
1
1
2
0
1
0
1
0
0
1
0
0
0
0
0
0
1
1
2
2
0
0
0
2
1
0
1
0
2
0
0
1
0
0
0
0
3
0
0
0
1
0
0
3
1
1
1
3
0
0
0
2
0
0
2
0
1
0
2
1
0
1
0
0
2
1
0
1
0
2
0
0
0
1
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
1
0
0
0
0
1
0
0
3
0
0
0
0
0
2
0
2
1
0
0
0
0
2
1
0
0
0
2
0
0
0
2
0
1
0
2
0
1
0
1
1
0
1
1
1
2
0
0
2
0
2
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
2
1
1
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
1
2
0
0
1
0
0
2
0
0
1
0
1
0
0
0
2
0
1
0
1
1
1
0
1
2
0
2
0
0
0
2
0
0
5
0
1
2
1
0
4
0
2
2
2
0
0
0
0
1
1
0
0
1
0
0
2
1
0
0
0
1
2
0
3
0
0
3
1
2
1
0
2
1
1
3
0
2
2
1
0
0
0
0
1
1
2
0
1
7
0
1
0
0
6
2
0
0
3
1
0
1
0
0
0
3
2
0
2
0
0
0
0
0
0
0
1
1
2
1
0
0
1
0
0
1
2
0
0
2
0
0
0
1
1
0
2
0
0
0
0
0
2
0
1
1
1
2
0
2
0
1
2
0
0
1
1
2
0
1
0
0
2
0
0
1
1
2
0
0
1
0
3
0
1
2
1
3
1
2
0
0
0
2
1
0
0
0
1
2
1
0
1
0
0
0
1
1
1
0
0
1
0
0
1
1
0
2
0
0
1
0
0
1
0
2
0
2
2
2
0
0
1
0
0
1
0
0
0
0
0
0
1
2
2
1
1
0
0
1
2
2
1
0
0
2
0
2
2
1
0
0
1
0
0
1
0
0
1
0
2
0
2
0
0
1
0
0
0
0
0
2
1
1
0
0
1
2
0
0
0
0
0
0
3
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
2
1
0
1
0
0
0
0
2
1
0
0
1
0
2
1
1
0
1
0
0
1
0
4
1
1
2
1
1
2
0
0
1
1
2
0
2
0
1
0
0
0
2
0
0
1
1
0
1
1
2
2
1
1
2
2
2
1
2
1
0
0
0
0
1
0
0
0
0
0
2
0
0
3
0
0
1
0
1
0
1
0
2
1
0
2
2
2
0
2
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
2
0
0
2
1
0
0
0
0
1
1
0
0
0
0
2
0
1
1
0
1
0
0
0
0
0
0
2
1
1
2
1
0
0
1
0
2
0
0
2
2
0
0
0
2
1
0
1
2
0
0
1
2
0
1
2
0
1
0
1
0
1
2
1
1
0
2
6
0
0
2
0
0
0
0
0
0
0
0
1
1
2
3
0
1
0
1
0
0
0
2
1
0
3
0
2
2
1
2
1
1
1
1
0
0
0
1
0
0
0
0
1
2
0
1
0
0
3
4
0
1
1
0
2
1
0
2
0
1
0
2
0
1
0
2
0
1
0
2
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
3
1
0
0
2
0
1
1
0
1
1
0
1
0
0
2
2
0
2
0
0
2
0
1
2
1
0
1
2
0
0
0
2
1
0
0
0
0
0
0
0
2
3
0
0
0
1
2
3
0
0
0
2
1
0
2
2
0
2
0
0
1
1
2
0
0
0
0
1
0
1
2
0
1
0
0
0
1
0
2
1
0
0
2
0
2
0
0
0
0
2
0
2
2
0
2
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
1
1
2
0
0
0
0
2
0
0
2
0
2
0
1
0
0
0
0
0
2
2
1
1
0
2
0
0
0
1
2
1
0
2
2
0
1
0
0
0
1
0
2
13
1
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
2
0
2
0
1
1
2
0
0
0
1
0
0
0
3
0
1
2
0
2
2
0
0
1
0
2
2
0
0
0
0
2
2
0
0
0
0
0
2
0
1
1
0
1
2
0
0
0
1
1
1
0
0
2
1
0
2
2
2
2
0
1
0
0
0
2
2
1
1
2
2
0
0
0
0
2
0
2
0
0
0
0
1
0
0
1
0
1
1
1
0
3
0
0
0
0
2
0
1
0
2
1
1
3
1
2
1
2
0
2
0
0
0
1
0
0
0
0
1
1
1
1
1
0
1
0
1
0
0
1
2
0
0
0
1
1
2
0
0
1
0
0
0
2
1
0
2
2
0
1
1
0
1
0
0
1
0
0
0
2
0
0
1
0
0
2
1
0
1
1
0
0
0
0
1
0
1
2
0
0
0
1
2
1
2
0
1
2
0
0
0
0
0
2
0
1
0
2
0
0
0
2
0
1
0
1
0
1
0
1
1
2
1
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
1
0
1
1
0
0
1
0
0
0
1
0
0
0
0
2
1
1
2
0
0
0
0
1
0
0
2
1
3
1
1
0
0
0
1
0
0
1
2
0
0
0
0
2
1
0
0
2
0
0
1
0
1
1
0
1
0
0
2
1
1
1
2
0
0
0
0
1
1
0
0
0
0
0
2
2
0
0
1
1
1
0
0
0
1
1
0
0
1
0
0
3
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
1
1
1
0
1
0
1
0
0
0
2
0
2
1
1
0
0
1
1
0
2
2
0
0
0
0
0
2
0
0
0
0
0
1
1
1
2
0
1
1
0
0
0
2
1
0
0
2
0
1
0
1
0
1
0
2
0
0
0
0
0
1
0
0
4
1
3
0
2
1
0
1
0
3
0
0
2
0
1
0
0
0
1
0
0
2
0
1
0
0
1
0
0
0
1
0
2
1
1
1
0
3
2
3
1
0
0
1
4
3
0
0
1
2
0
2
1
0
0
0
1
0
0
0
1
2
0
0
0
0
0
2
0
1
2
2
0
2
0
2
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
3
0
0
0
1
1
1
0
0
2
0
0
2
2
0
0
0
0
2
1
1
0
1
0
0
2
2
0
0
0
1
0
0
0
1
0
0
0
2
0
0
1
0
1
0
2
2
0
0
2
1
1
0
2
0
2
0
0
1
0
1
0
1
0
0
0
1
2
0
0
1
1
0
0
2
1
0
0
2
0
1
1
2
0
0
1
1
0
2
2
1
2
0
1
0
2
0
1
1
1
2
2
1
0
2
1
0
2
0
0
0
1
2
0
1
0
0
0
0
0
2
0
1
0
0
0
1
1
2
0
1
0
0
2
0
1
0
1
0
0
4
0
0
0
0
1
0
2
2
1
0
2
0
1
2
0
0
0
2
0
1
0
1
3
2
1
0
1
0
0
0
2
0
0
0
3
1
0
0
0
1
0
0
2
0
0
0
2
1
0
0
0
1
1
0
0
0
1
1
0
0
2
0
1
0
2
0
1
2
0
2
0
1
0
2
1
1
0
0
2
0
3
1
0
0
0
0
1
1
0
0
0
0
2
2
1
0
1
1
1
2
2
8
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
4
0
1
2
0
1
1
2
0
1
2
2
2
2
1
1
2
0
0
1
0
0
2
1
1
2
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
1
2
0
0
0
0
0
0
1
0
1
0
0
1
0
0
4
3
1
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
1
0
2
1
0
0
1
1
3
0
0
1
1
0
1
2
1
2
1
1
0
1
1
2
1
2
0
1
0
1
2
0
2
0
2
2
0
0
2
0
0
2
2
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
1
1
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
1
0
3
0
0
4
1
0
0
0
0
2
1
2
2
0
2
2
2
0
2
2
0
0
0
0
1
2
1
0
0
0
0
0
0
2
2
1
2
0
1
0
0
2
0
0
1
0
0
1
1
0
2
1
0
0
2
0
0
0
2
2
0
0
0
2
0
2
0
1
2
0
0
0
2
1
2
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
2
0
0
2
2
0
2
1
0
0
0
1
0
1
2
0
0
0
3
1
0
2
1
0
0
0
2
0
1
0
0
0
0
0
1
0
1
2
1
2
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
3
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
3
0
0
0
0
0
0
0
1
1
2
2
0
0
0
1
1
1
0
0
0
1
2
2
0
1
9
0
1
1
0
0
2
1
1
0
1
2
0
0
1
1
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
3
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
2
1
0
0
0
1
0
2
0
0
2
0
1
2
0
1
0
0
1
1
2
1
0
1
0
1
2
0
2
0
0
1
0
0
2
0
0
0
1
1
0
0
0
0
0
2
0
2
3
2
1
2
1
0
1
2
0
1
0
1
0
2
0
2
1
1
0
2
1
1
0
0
1
0
0
0
0
2
2
0
1
2
0
0
1
0
1
0
1
0
1
0
0
1
3
2
0
0
0
2
0
1
1
2
1
0
0
0
0
0
0
2
2
2
1
0
0
0
0
1
1
2
2
0
0
0
0
2
0
2
2
0
0
0
0
2
3
0
0
0
0
0
2
1
0
2
0
2
0
0
1
0
0
0
0
1
0
1
0
0
2
0
2
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
2
1
0
1
0
1
0
0
0
0
1
0
0
2
1
0
0
2
1
0
0
0
2
4
0
0
2
1
0
1
2
1
0
0
0
4
0
0
2
0
1
1
0
0
0
1
1
2
2
1
0
0
1
0
0
0
0
0
2
0
0
0
2
3
0
1
1
0
6
2
5
0
1
0
0
0
2
1
0
0
2
0
0
0
1
1
2
2
0
1
1
1
0
0
0
0
0
0
0
3
0
2
0
0
1
0
1
0
2
0
0
1
0
0
3
0
0
1
1
0
0
1
0
1
0
0
0
1
0
0
2
1
0
0
0
1
1
0
0
2
0
2
2
0
0
2
1
0
0
2
2
0
0
2
2
0
0
0
0
0
0
2
0
0
1
1
2
1
0
0
2
1
2
0
0
0
0
0
0
2
0
0
1
1
0
1
0
1
0
1
0
0
2
0
1
0
0
0
0
2
1
0
1
0
0
0
0
0
1
1
0
0
1
0
1
0
0
2
0
0
2
1
0
3
1
0
0
2
0
2
1
0
2
0
0
1
0
2
0
1
1
0
2
0
2
0
0
0
0
0
0
0
1
2
1
0
2
0
2
0
1
1
2
0
0
2
0
3
2
0
2
1
0
0
0
0
0
2
0
0
2
2
0
0
2
0
0
2
0
0
1
2
0
0
0
1
0
3
2
0
0
2
2
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
1
0
1
0
1
2
0
0
1
2
0
1
0
0
0
0
1
0
0
0
2
2
2
0
0
0
1
0
0
2
0
2
0
0
0
2
0
2
2
2
2
0
0
2
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
1
2
1
2
2
0
0
1
1
0
1
0
1
0
2
2
0
0
1
2
0
0
0
1
0
0
3
0
0
1
1
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
1
2
0
0
0
2
1
0
0
1
0
0
0
2
2
1
0
2
0
1
0
0
0
0
1
0
0
1
1
0
1
2
0
1
2
2
1
0
1
1
0
2
0
2
0
0
0
3
0
0
0
0
0
0
1
1
2
0
2
0
2
0
0
3
0
2
1
0
0
0
2
1
2
1
0
1
0
1
1
0
2
0
1
1
0
0
1
0
0
2
0
2
1
1
1
0
3
0
0
0
1
0
0
1
2
2
0
0
0
0
3
1
0
0
0
0
2
0
1
0
0
2
1
1
1
0
0
0
1
2
2
1
1
2
0
0
2
1
0
2
2
0
1
1
1
2
1
0
0
2
0
1
1
0
0
2
2
0
1
0
1
2
0
1
0
0
1
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
2
1
0
1
2
2
1
0
0
0
1
1
0
2
0
0
2
0
0
1
1
1
2
0
0
0
2
0
2
0
0
0
0
0
0
1
0
2
2
0
2
0
2
0
1
0
1
1
0
0
1
0
2
0
1
0
0
1
0
0
1
2
1
2
2
2
0
1
2
1
0
0
0
2
1
0
0
1
0
2
4
0
1
0
0
1
2
1
0
0
0
2
1
0
1
0
1
2
0
0
1
0
1
2
0
1
0
0
0
0
0
1
0
2
2
2
2
2
1
1
2
2
1
0
0
0
0
0
0
1
0
1
1
0
0
2
0
0
1
0
1
0
0
0
1
1
0
2
0
0
0
0
0
0
1
2
0
0
1
0
0
1
2
0
1
0
0
2
0
0
0
2
2
0
2
1
2
0
1
0
2
0
0
0
1
0
0
0
0
2
2
2
0
1
0
0
0
0
3
0
1
0
1
0
2
0
1
2
0
1
2
0
0
2
2
1
0
1
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
2
2
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
1
2
0
1
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
2
2
2
0
2
2
1
1
0
0
0
1
0
0
0
0
0
1
1
2
0
1
0
0
0
0
2
1
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
2
0
1
1
0
0
1
0
0
1
2
0
0
2
0
0
1
0
1
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
2
0
1
1
0
1
1
1
1
0
0
0
1
0
0
1
0
0
0
2
0
1
0
1
2
0
0
1
1
1
0
1
2
2
0
0
1
0
0
2
1
0
0
2
0
1
2
0
0
0
1
0
1
3
2
1
0
2
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
2
2
1
2
0
0
2
0
1
2
0
0
2
0
0
1
1
2
0
0
0
0
0
0
0
0
0
2
0
0
1
1
1
2
0
0
0
0
2
1
0
0
0
0
2
2
0
2
1
2
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
1
0
1
1
0
1
0
2
0
0
0
0
0
2
1
0
1
0
0
0
0
1
0
2
0
2
0
0
0
1
0
1
0
1
3
1
0
0
0
0
0
0
1
3
1
2
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
1
1
0
2
2
0
0
1
1
0
1
0
0
1
0
2
0
3
0
0
1
1
1
1
0
0
0
2
2
0
0
2
0
0
1
2
1
0
0
0
0
1
1
0
0
4
1
2
0
0
0
1
0
4
1
2
0
2
2
0
0
2
0
2
0
0
1
1
2
1
0
0
0
1
0
0
2
0
0
4
1
2
0
0
2
2
0
1
0
0
0
1
2
2
1
2
2
1
0
2
0
2
0
0
1
1
0
1
0
0
2
0
2
2
1
0
0
2
1
2
0
2
2
0
0
0
0
0
1
3
0
1
2
0
0
3
0
0
0
2
1
1
0
1
2
1
1
0
0
1
0
0
1
2
0
0
2
0
0
0
2
0
0
1
0
2
1
4
2
0
2
4
0
0
0
2
1
2
0
2
0
1
0
2
0
0
1
2
1
0
1
1
0
0
0
1
1
0
1
0
2
0
1
0
2
1
1
0
2
2
0
0
0
0
2
1
1
1
0
3
6
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
1
2
0
0
1
1
0
1
0
2
2
1
2
0
0
2
0
1
1
0
0
0
2
1
0
1
0
1
2
0
0
0
0
0
1
0
1
0
0
0
0
3
1
1
0
0
0
1
0
0
1
0
1
0
0
0
2
2
0
1
2
2
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
2
1
0
0
0
0
0
3
2
0
2
1
0
0
0
2
1
0
0
1
0
2
0
2
0
1
1
2
0
0
0
2
3
1
0
0
0
0
1
1
0
0
2
0
0
0
0
2
0
0
1
0
0
2
0
0
0
1
0
0
0
2
0
0
0
1
0
1
1
0
2
1
2
0
0
0
0
0
1
1
3
0
1
2
0
1
0
2
0
2
1
0
1
0
2
1
0
1
3
0
0
0
1
0
2
0
1
0
0
0
0
0
2
1
0
1
0
2
0
0
0
1
1
2
1
2
2
1
0
0
2
0
0
0
2
2
0
0
2
1
1
0
1
1
1
4
0
1
2
2
0
0
0
0
0
0
0
0
1
0
1
0
2
0
1
2
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
1
1
0
0
3
0
0
1
1
0
0
0
1
0
0
2
1
1
0
1
2
0
2
0
0
2
2
2
0
2
0
0
0
0
1
0
1
1
1
0
1
2
2
3
2
0
0
0
1
2
2
1
0
1
1
0
2
2
2
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
2
0
1
2
2
0
2
0
1
1
2
0
0
0
0
2
0
2
0
0
2
0
1
0
2
0
0
1
1
1
0
1
0
0
2
1
1
1
0
1
2
0
2
0
0
0
0
1
2
0
1
6
0
0
2
0
1
0
0
2
0
0
1
0
0
2
0
0
0
2
1
0
0
2
0
0
0
0
0
0
2
1
0
1
0
1
2
1
2
1
0
0
2
2
0
0
1
2
0
2
0
1
1
2
0
1
0
0
0
0
2
1
0
0
1
1
0
0
0
0
2
2
3
1
0
0
1
0
0
0
1
0
2
0
0
0
2
0
2
1
0
0
0
0
0
2
0
0
0
1
0
0
2
0
1
0
1
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
1
2
0
0
1
1
2
2
0
2
0
1
2
2
2
1
0
0
1
0
0
0
0
1
2
0
0
0
1
1
0
1
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
2
1
0
0
0
1
0
0
0
0
2
0
2
0
0
2
0
1
0
0
1
0
2
0
0
2
2
0
1
0
0
0
0
0
0
2
0
2
0
1
1
1
0
0
0
0
2
0
0
0
2
3
2
1
1
2
2
0
2
0
1
0
1
2
1
0
0
1
0
0
1
2
0
1
1
0
0
0
2
2
2
2
0
1
0
0
1
2
0
0
0
1
0
0
1
1
1
2
0
1
0
0
0
2
1
0
0
0
0
2
0
0
1
5
0
3
3
1
1
0
0
0
1
1
0
1
0
0
0
1
0
0
0
1
2
2
2
0
2
1
0
1
0
3
1
2
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
2
0
1
1
1
0
2
1
1
0
0
0
0
0
1
1
0
2
0
0
0
0
1
0
0
0
0
0
0
3
0
3
2
1
1
2
2
0
0
1
2
0
2
0
0
0
0
0
0
0
0
3
0
0
1
1
1
2
0
1
1
0
1
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
2
0
2
0
1
2
0
1
1
2
0
0
2
1
0
1
0
2
0
2
0
0
0
2
2
1
0
0
0
1
0
0
0
2
2
0
0
1
0
2
1
0
1
0
1
0
0
0
2
0
0
0
0
1
0
1
2
0
0
1
0
0
0
0
0
1
0
1
1
2
1
0
2
0
1
0
2
0
0
0
0
0
0
0
1
0
1
3
1
0
2
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
1
1
1
0
0
0
1
0
0
2
1
1
1
1
2
0
0
0
0
0
2
2
0
0
0
0
2
1
0
0
0
1
4
0
0
3
1
0
0
2
2
0
0
0
1
0
2
1
1
1
0
0
2
0
0
1
0
0
0
1
2
2
2
0
0
2
2
3
0
1
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
2
0
2
0
2
0
0
2
1
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
2
2
2
1
1
0
0
0
2
0
1
1
1
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
2
1
1
1
2
1
1
2
1
1
0
0
0
0
2
2
0
0
0
0
1
0
2
1
1
2
0
0
0
1
0
2
1
1
0
0
0
0
0
0
1
0
1
1
1
2
0
1
1
0
0
2
2
0
1
0
1
1
1
0
0
1
0
1
0
0
2
2
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
2
2
2
0
0
2
0
0
0
0
2
2
0
1
0
0
0
0
0
0
1
0
5
0
0
2
0
0
0
2
0
1
2
0
0
1
2
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
1
1
1
1
2
1
2
0
0
0
2
0
0
0
0
1
1
0
1
0
0
2
1
0
0
0
2
0
0
1
0
0
1
1
0
1
0
0
0
1
1
0
0
0
0
2
2
1
1
0
0
0
2
0
0
2
2
1
1
1
1
2
1
0
2
1
2
0
1
0
0
1
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
1
2
1
0
1
2
0
1
0
1
3
0
4
0
0
1
0
1
0
1
0
1
0
0
5
0
0
2
1
0
1
2
0
0
1
0
2
0
0
0
0
2
0
2
0
0
2
1
1
0
0
1
0
0
1
0
2
0
2
0
2
1
0
0
0
0
2
1
0
0
0
0
0
2
3
0
1
1
0
1
2
1
0
1
2
1
0
0
0
1
0
2
1
1
0
1
1
2
2
2
0
0
2
0
0
1
0
0
0
2
2
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
2
1
0
2
0
1
0
0
0
0
0
0
0
1
1
4
0
0
0
0
0
1
0
1
2
2
2
0
0
0
1
0
0
2
0
0
0
1
0
2
1
0
1
1
0
1
2
1
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
1
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
8
0
0
1
0
0
0
2
1
1
2
2
2
1
2
2
0
0
2
2
2
0
1
2
0
1
1
0
1
1
1
0
0
2
2
0
1
0
0
1
0
1
0
2
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
1
0
1
1
0
0
1
0
1
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
2
2
1
2
1
0
1
5
0
2
0
0
0
0
0
2
0
0
0
0
1
1
1
2
2
0
2
2
2
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
3
1
0
0
0
0
1
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
2
0
1
1
0
2
0
0
2
0
2
2
1
0
2
1
1
1
0
0
1
1
0
2
0
0
3
2
0
1
2
2
0
1
0
0
1
1
0
0
0
0
1
0
0
0
1
1
2
1
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
1
0
0
0
1
1
2
2
0
0
1
0
0
1
0
1
1
0
0
2
2
0
0
0
2
1
0
1
0
1
1
1
0
1
0
1
2
2
1
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
1
0
1
0
2
2
1
0
1
0
0
0
0
0
2
0
2
0
0
0
1
2
1
2
0
2
0
1
1
1
0
0
0
0
1
2
1
1
1
1
2
2
1
1
1
1
0
2
2
0
0
2
2
1
0
1
3
2
0
0
1
1
1
2
1
0
1
0
0
0
0
0
1
0
2
1
1
2
1
1
0
0
2
0
0
1
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
1
0
0
1
1
1
0
1
1
0
0
0
0
0
2
0
1
0
1
2
0
1
0
0
0
0
2
3
0
0
2
0
0
1
0
3
1
0
0
0
0
1
2
0
0
2
0
0
1
0
0
1
0
0
0
0
1
0
1
1
0
2
3
1
0
0
0
0
1
0
0
0
1
2
0
1
0
0
1
2
0
0
0
0
3
0
1
0
0
1
0
0
1
0
0
0
1
2
2
0
0
2
1
2
0
0
0
0
1
2
2
2
0
1
0
0
0
2
2
0
3
0
0
0
0
0
2
1
2
1
0
0
2
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
1
0
2
2
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
3
0
1
0
1
2
0
0
2
0
0
2
0
4
2
0
0
1
2
2
0
1
0
0
1
0
0
0
0
0
2
2
0
0
4
0
2
1
0
2
0
1
2
0
0
0
1
0
0
1
0
2
0
0
0
0
1
0
1
0
0
0
2
2
2
0
2
0
2
6
0
2
0
0
0
0
1
0
0
0
1
0
2
0
0
0
2
1
0
0
0
1
0
2
1
1
0
2
1
0
0
0
1
2
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
1
1
1
0
0
1
2
2
1
1
3
0
0
0
1
1
0
0
0
0
2
1
0
1
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
2
1
2
2
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
2
0
1
2
0
0
0
1
0
2
2
0
1
3
1
0
0
0
0
1
2
1
0
0
0
1
0
1
2
1
0
0
2
0
2
0
2
0
0
0
2
1
1
2
0
0
0
1
0
0
0
0
0
0
0
1
2
1
1
0
0
2
1
0
0
1
0
0
2
1
0
2
0
0
0
0
2
3
0
2
0
0
0
3
0
2
0
2
0
0
1
2
1
1
0
0
0
2
1
0
0
0
1
1
0
0
0
0
1
1
0
0
2
0
1
0
2
0
0
3
1
3
0
1
2
2
2
0
0
1
2
2
2
0
0
0
0
2
0
1
3
0
1
2
0
0
2
0
0
1
2
1
0
0
0
2
1
1
1
2
0
0
0
2
0
2
2
1
0
2
2
1
2
2
0
2
2
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
2
1
1
0
0
1
0
0
2
0
1
1
0
0
1
0
1
0
0
0
1
0
0
0
1
1
1
0
1
1
1
2
0
0
0
2
0
0
0
0
0
0
1
0
0
1
2
0
2
1
0
0
0
1
0
1
1
1
0
0
0
0
0
3
2
0
0
0
0
1
0
1
0
0
0
2
0
0
1
1
0
1
2
1
0
1
0
3
0
0
1
1
0
0
1
1
1
1
2
1
0
0
0
0
1
0
0
1
0
1
0
0
1
2
1
0
0
1
0
0
2
1
0
0
1
0
0
1
0
0
0
0
3
1
1
1
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
2
0
1
0
1
2
0
1
2
1
1
1
1
0
0
0
0
0
0
0
2
0
0
2
0
2
0
1
2
1
0
2
0
2
2
0
1
0
2
1
0
0
1
0
1
2
0
1
0
0
1
2
0
0
0
0
0
1
2
0
0
1
1
2
1
0
0
1
1
0
0
0
0
1
2
0
0
0
0
3
0
1
1
0
0
1
0
1
0
0
0
2
1
1
0
0
1
0
0
0
0
3
1
2
0
3
0
2
0
0
2
0
2
0
0
0
0
0
0
0
1
1
2
0
2
0
0
0
1
1
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
1
0
0
0
1
0
1
0
1
0
0
0
2
0
2
0
12
0
1
2
0
2
0
3
0
1
2
1
0
1
0
2
1
2
0
2
2
0
0
1
2
0
1
2
1
0
0
0
0
0
0
1
2
0
2
0
1
2
0
0
1
3
1
0
2
2
1
1
2
0
3
2
1
0
0
0
0
2
2
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
1
0
2
0
2
1
1
2
2
2
2
0
0
0
0
1
0
1
3
0
0
1
3
0
1
2
0
0
1
3
3
0
0
2
0
0
0
0
0
0
1
2
0
1
0
0
1
0
1
1
2
0
1
1
0
0
1
2
1
0
1
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
1
0
2
0
1
0
0
0
0
2
0
0
0
0
2
2
1
0
2
0
1
2
0
1
1
0
2
0
0
1
2
0
0
0
0
1
2
2
0
0
0
1
0
0
1
0
0
0
0
2
1
0
0
0
1
1
0
0
1
0
2
0
3
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
2
1
0
0
1
0
2
2
0
1
1
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
2
2
1
0
2
1
0
3
0
1
0
2
0
0
1
0
0
2
0
3
0
2
0
0
1
1
1
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
2
0
0
2
2
0
1
2
2
0
0
1
0
1
0
0
1
1
0
2
2
0
1
0
0
0
1
0
0
2
0
0
0
2
1
0
0
1
0
0
1
0
0
0
2
1
0
2
0
1
0
1
0
2
0
1
2
0
1
1
0
2
2
1
1
0
0
0
0
1
2
2
0
2
1
0
1
0
2
1
0
0
0
1
1
0
0
2
0
0
2
2
0
2
0
0
0
0
0
1
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
1
1
0
1
3
2
2
0
2
1
1
0
2
1
1
0
3
1
1
2
0
2
1
1
0
0
0
2
0
2
2
2
2
0
1
0
1
0
2
3
2
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
1
2
0
0
1
1
0
1
0
0
2
1
0
2
0
2
0
1
1
2
2
0
1
2
1
0
0
1
1
2
0
0
1
0
0
2
0
0
0
0
1
2
0
2
2
0
0
0
1
0
0
0
1
2
0
2
0
0
0
0
2
2
0
0
1
0
0
0
0
0
1
1
1
0
2
0
1
1
0
0
0
1
2
0
0
0
2
0
0
0
2
1
2
0
1
1
0
1
0
0
0
0
2
0
0
0
2
2
2
2
1
2
0
0
0
0
0
0
3
0
0
2
0
2
0
0
1
0
1
2
1
1
0
0
0
0
1
2
0
0
1
0
0
0
1
2
2
1
0
1
0
3
0
2
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
3
1
2
0
2
0
0
0
2
2
0
2
1
0
0
0
0
0
0
1
0
0
2
0
3
0
0
1
0
2
0
0
0
0
0
0
1
1
1
1
0
1
2
2
1
0
1
0
0
1
0
0
1
0
0
2
0
2
1
1
0
0
0
0
0
3
2
0
1
0
0
0
1
0
0
0
0
1
1
0
2
0
0
1
0
1
0
1
1
0
0
1
0
1
0
0
0
0
1
1
1
0
2
0
1
0
2
0
0
0
2
2
0
0
0
0
2
1
0
2
0
0
1
0
1
0
0
0
0
0
0
1
2
3
0
1
0
0
2
0
2
0
1
0
1
0
2
1
2
0
0
0
1
1
0
0
2
1
0
0
2
1
2
2
1
1
1
1
1
0
2
0
2
0
0
0
1
0
0
0
1
2
0
0
0
1
2
0
0
0
2
0
1
0
0
1
1
2
0
1
0
0
0
1
1
0
1
1
2
0
0
7
0
1
1
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
2
1
2
0
1
1
0
1
0
0
2
1
1
0
0
1
0
1
0
1
0
0
0
2
2
0
3
0
4
1
0
2
2
0
0
2
0
0
1
0
0
0
0
0
1
0
0
1
2
1
2
0
0
0
0
2
1
2
1
1
0
0
0
2
0
1
0
2
0
0
0
1
2
0
1
0
0
0
0
1
1
2
0
0
0
2
0
0
0
0
2
0
0
1
0
2
0
1
0
4
0
0
1
2
0
0
0
1
0
2
0
1
0
0
1
0
0
2
2
2
2
2
1
2
1
1
2
2
0
0
2
2
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
2
0
2
2
0
2
2
1
2
1
0
0
0
2
0
1
0
0
2
1
0
0
0
0
1
1
1
0
0
0
0
0
1
0
1
0
0
2
1
2
0
0
0
0
0
0
0
0
0
1
0
1
0
2
1
1
0
2
1
0
5
1
0
1
2
0
0
1
0
0
0
2
0
2
0
1
1
1
1
0
2
1
0
1
0
0
1
0
0
1
1
1
1
0
0
0
0
0
1
1
0
2
0
2
1
0
0
1
1
2
0
0
0
1
0
0
0
0
2
0
2
0
0
1
2
2
3
0
0
0
0
1
0
0
1
3
0
0
1
1
0
1
0
1
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
2
1
0
0
0
1
0
1
3
2
0
0
2
1
2
0
3
2
2
2
0
0
1
0
0
3
0
0
1
2
1
2
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
1
1
1
0
0
0
0
3
0
0
0
6
0
0
1
0
0
2
0
1
0
3
1
1
0
0
0
0
1
0
2
1
0
0
2
1
2
0
0
1
3
1
0
0
0
2
1
0
0
2
2
0
0
0
0
2
2
1
0
0
0
0
2
0
1
0
1
0
1
0
0
0
1
2
1
2
0
0
0
0
2
0
0
0
0
0
1
1
0
0
1
0
1
0
1
0
1
1
0
2
0
1
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
1
0
0
1
1
1
1
2
0
0
0
0
0
0
2
1
2
2
0
0
0
0
1
2
1
2
0
1
0
2
0
0
0
0
0
2
0
2
1
0
1
2
0
2
0
0
2
0
1
0
1
0
1
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
2
0
0
0
1
2
1
0
1
2
0
1
0
2
0
2
2
2
2
2
3
0
1
0
0
0
1
0
1
0
2
0
0
0
1
1
1
1
0
0
1
1
1
1
0
0
0
0
0
2
0
0
0
1
2
2
0
0
1
0
0
2
0
0
1
0
1
0
2
0
0
2
0
2
0
0
0
0
1
0
0
2
1
2
1
3
2
0
0
0
0
0
0
0
2
2
0
0
1
1
0
2
0
0
0
0
0
1
0
1
0
2
0
0
1
0
0
2
0
0
1
0
2
2
0
1
0
0
0
0
2
0
0
2
1
0
0
1
1
1
1
0
2
0
3
0
0
2
2
0
0
0
1
0
1
3
0
1
1
2
0
0
0
0
1
2
1
0
0
2
0
2
1
1
0
0
0
1
1
2
0
0
3
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
3
0
0
1
0
1
2
0
0
0
2
1
0
2
2
2
0
1
1
1
0
0
0
0
0
1
0
0
0
2
0
0
2
2
0
0
0
2
0
0
1
2
2
0
0
0
2
2
0
2
0
0
2
2
0
0
0
0
1
0
1
0
0
2
0
1
0
2
0
2
0
0
1
2
0
1
0
2
0
0
0
1
1
0
0
0
1
0
1
0
0
0
1
0
1
1
1
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
2
1
0
2
0
1
2
1
0
0
2
0
1
0
0
0
0
0
0
1
2
0
0
0
2
0
1
0
1
0
0
3
0
0
0
0
0
1
0
0
2
0
0
0
1
0
1
0
0
0
0
2
1
0
0
1
2
0
1
1
0
0
0
2
0
2
0
0
0
2
1
0
0
0
1
0
0
0
2
0
0
2
1
2
0
0
1
0
0
0
1
0
1
0
2
1
1
1
1
1
2
0
0
2
2
0
1
2
0
1
0
1
0
0
2
0
2
2
0
1
0
0
1
1
0
1
1
0
2
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
2
0
1
0
1
0
2
0
1
0
0
0
2
1
0
2
0
0
2
0
1
0
1
0
0
1
2
2
0
0
3
2
0
1
2
0
2
0
1
1
2
0
0
0
1
0
0
2
0
1
0
1
2
1
0
0
0
0
1
1
1
2
6
0
0
1
0
0
0
0
0
1
1
4
2
1
0
0
0
1
0
0
7
0
0
1
0
2
0
0
0
0
0
2
1
2
0
2
1
0
0
1
0
0
0
1
1
0
2
0
1
0
1
1
2
1
0
0
1
1
1
1
0
1
0
1
0
1
0
2
0
1
0
1
0
2
0
0
1
0
1
2
0
2
1
2
0
0
0
0
0
0
0
0
3
1
0
1
0
0
2
0
0
0
2
2
0
3
0
0
0
0
0
2
0
1
1
0
0
0
0
2
2
0
0
0
0
0
2
0
0
1
2
1
0
1
0
0
0
1
0
0
1
1
1
0
1
0
1
0
0
0
2
0
0
0
2
0
0
2
2
1
0
1
1
0
0
1
2
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
2
0
0
0
1
0
0
0
1
1
0
2
1
1
0
0
0
0
0
3
0
0
0
0
0
1
1
1
0
0
0
0
0
0
2
0
2
0
1
2
0
0
0
1
2
1
1
0
2
1
0
0
2
2
2
2
0
0
0
1
2
1
0
1
0
2
0
0
2
2
1
1
2
2
2
0
2
3
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
2
2
0
1
0
1
1
1
0
0
0
1
1
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
2
0
2
2
1
0
1
0
2
2
0
0
0
2
2
2
0
1
1
0
1
1
0
1
0
2
0
0
1
0
1
2
0
0
0
1
1
1
0
0
0
2
0
0
0
0
0
2
0
0
0
2
1
1
1
1
0
0
2
0
2
0
2
1
0
2
1
2
2
1
0
0
0
0
1
0
1
0
2
0
0
0
0
0
1
1
2
1
0
1
3
1
0
3
1
1
0
3
0
0
1
2
1
2
2
2
2
0
0
0
1
1
0
1
0
2
0
1
0
0
0
1
0
2
0
0
1
1
2
0
0
2
2
1
2
0
0
1
0
0
0
0
0
0
2
2
1
0
0
0
1
2
0
1
0
0
0
0
2
0
3
4
0
0
0
1
1
0
1
0
0
2
0
2
0
1
1
0
0
1
0
2
1
0
0
0
2
0
1
1
0
0
0
1
0
0
0
1
1
1
1
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
1
2
2
0
0
0
0
0
1
2
2
0
0
1
1
1
1
0
1
0
1
2
1
2
2
2
1
0
0
2
0
0
2
2
0
0
2
0
0
2
0
2
2
0
1
0
0
2
3
0
1
0
1
0
0
2
1
1
2
0
2
1
0
0
1
0
2
2
0
0
2
0
1
0
2
0
2
0
2
2
0
2
2
0
0
1
0
2
0
0
0
1
2
0
0
0
0
0
1
0
1
0
0
2
0
0
1
0
5
0
0
2
0
0
0
0
0
0
0
3
1
0
2
0
1
0
1
1
0
0
0
0
2
1
2
2
0
2
2
3
1
1
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
3
0
2
0
1
0
1
2
2
1
1
1
0
0
0
1
0
1
0
0
2
1
0
1
1
0
2
2
2
2
0
1
1
1
0
0
0
1
0
2
0
1
1
4
0
2
0
2
2
0
0
3
2
0
2
0
0
2
2
0
0
1
3
4
0
0
0
0
1
0
0
2
0
2
1
0
0
0
1
2
2
1
1
0
0
0
1
0
0
0
0
2
1
0
0
0
1
0
0
4
1
1
0
1
2
1
1
2
1
1
1
1
0
0
0
1
1
1
0
0
0
2
0
2
0
0
2
2
1
0
1
0
0
1
2
2
0
2
2
2
1
0
2
1
1
0
1
2
0
0
0
2
0
1
2
0
2
0
1
0
0
0
3
0
0
2
0
1
0
0
0
0
0
0
2
0
0
1
2
0
2
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
1
1
1
2
0
0
1
2
0
0
0
0
0
0
0
3
0
0
0
1
4
0
0
0
1
0
0
0
2
0
0
1
2
0
1
1
1
0
0
1
0
0
0
0
0
0
0
1
2
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
3
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
3
0
0
2
2
0
0
1
0
1
0
1
1
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
1
2
0
2
0
0
0
0
0
2
0
0
1
1
1
0
0
0
0
0
1
0
0
1
0
0
3
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
1
1
1
0
0
0
1
1
2
1
1
0
0
2
2
0
2
0
3
2
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
2
0
1
1
0
2
0
0
0
0
1
1
0
1
1
0
0
0
1
0
2
1
2
0
2
0
0
0
0
2
1
0
2
0
2
1
0
0
0
0
1
1
0
0
1
0
0
2
0
0
1
0
0
1
2
1
0
0
2
0
0
0
2
0
0
2
0
2
0
0
1
2
0
0
0
0
3
1
1
0
1
0
2
0
2
0
0
0
2
1
0
2
0
0
0
0
0
0
2
1
2
0
0
0
0
2
1
0
2
1
2
0
0
0
1
2
0
0
0
2
1
1
2
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
2
0
2
0
1
1
1
0
0
1
3
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
2
0
0
0
2
1
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
3
0
0
0
0
0
1
0
2
1
2
0
0
2
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
2
2
0
1
0
0
1
1
0
0
0
0
2
1
0
0
1
0
1
0
0
0
2
1
0
2
1
3
0
0
2
0
0
2
2
1
0
0
0
0
1
0
2
0
0
0
2
0
0
0
2
0
1
1
0
0
0
0
1
2
1
1
1
0
1
0
0
1
0
2
1
1
0
2
0
0
1
1
1
1
0
0
0
0
3
1
0
4
0
1
1
1
2
0
1
0
0
0
1
2
2
0
1
2
1
0
1
1
2
0
0
1
0
0
1
0
2
0
0
2
1
2
0
1
0
3
0
0
0
2
1
2
2
0
2
2
0
0
0
0
1
0
0
1
1
2
0
2
2
0
0
0
0
1
1
2
0
0
0
0
1
0
0
0
2
2
2
1
0
0
0
0
0
0
1
1
2
1
1
0
2
1
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
2
0
3
2
1
0
0
1
0
0
0
2
0
1
0
0
2
0
0
1
0
0
0
0
0
0
1
2
1
0
2
0
0
0
0
0
1
1
1
0
0
0
0
2
0
0
0
2
2
0
0
0
1
0
2
0
1
1
0
2
0
1
0
2
0
2
0
2
0
1
0
0
1
1
1
0
0
1
1
1
0
0
1
0
0
1
1
1
1
1
1
0
0
2
1
0
2
2
0
1
0
0
0
2
0
1
0
0
2
2
2
2
0
0
1
1
0
0
1
1
0
0
0
0
0
2
1
0
0
0
0
0
1
1
0
0
0
2
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
2
0
0
0
1
1
1
0
0
1
2
1
2
0
1
0
1
2
0
2
1
0
0
0
1
0
0
2
0
1
0
1
0
0
2
1
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
2
0
0
2
1
0
1
0
1
1
1
0
0
0
1
2
2
2
1
1
2
0
0
2
4
0
0
0
0
0
2
0
0
0
2
2
2
0
0
0
0
0
0
0
2
2
2
1
2
0
0
0
1
1
1
2
0
4
1
0
1
1
0
0
0
0
0
1
2
2
0
1
1
1
1
0
0
0
0
0
0
0
2
2
0
1
2
0
2
0
0
1
0
1
0
0
1
0
0
0
2
1
0
1
0
0
0
1
1
0
1
1
0
1
1
0
0
1
1
2
0
1
1
2
0
1
0
0
0
1
2
1
0
0
1
0
0
2
1
0
0
1
0
1
2
10
1
1
1
0
0
1
0
1
1
2
0
2
1
0
0
2
0
1
0
0
1
0
0
2
0
0
0
0
1
0
0
5
1
1
0
1
1
0
0
0
0
4
0
2
0
1
0
2
1
0
0
2
0
0
0
0
0
1
2
0
1
0
0
0
2
0
0
0
0
0
2
2
2
0
0
1
0
0
0
0
0
1
2
0
1
0
2
0
1
0
0
0
0
2
2
0
0
0
2
2
2
0
1
0
0
0
2
0
0
2
0
1
2
2
0
0
0
1
2
1
1
0
1
2
2
2
1
1
0
0
1
0
0
2
2
0
0
0
0
1
0
1
2
0
0
0
0
1
0
2
2
0
0
0
0
0
0
1
1
0
1
1
1
0
2
1
2
2
2
0
0
4
0
0
1
0
1
0
0
1
2
1
2
1
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
1
0
0
1
2
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
2
0
2
1
0
1
1
0
1
0
0
2
0
1
0
0
2
0
1
0
0
1
0
0
2
1
2
2
1
1
0
0
1
0
0
0
2
1
1
1
1
2
0
1
2
0
1
2
0
2
0
3
0
0
0
1
0
2
0
0
3
0
2
2
0
2
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
2
0
1
0
3
1
1
2
0
0
0
2
0
0
0
1
1
1
0
1
0
0
1
0
0
1
0
2
2
0
2
0
0
2
0
0
0
2
1
0
1
0
2
0
2
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
2
2
1
0
0
1
1
0
0
0
2
0
0
0
0
3
1
0
2
2
0
0
1
0
0
0
2
2
0
2
0
2
3
0
0
1
0
1
2
0
1
1
0
0
0
1
1
1
1
0
0
1
0
2
1
1
2
0
0
2
1
0
0
0
2
0
0
1
0
0
1
0
1
0
0
1
1
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
2
2
0
1
0
1
2
0
2
0
0
2
0
0
3
2
2
0
0
1
1
1
0
1
0
2
1
2
1
0
0
0
1
0
0
0
0
1
0
2
0
1
0
0
0
1
0
1
0
0
0
1
1
1
2
1
0
0
0
1
1
0
1
1
0
1
2
2
0
2
0
0
1
0
0
0
1
1
0
2
4
0
0
1
0
0
2
0
2
3
0
1
0
0
2
1
1
1
0
1
1
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
1
1
0
0
1
0
0
1
0
2
1
0
0
0
1
0
0
0
1
0
1
1
1
0
0
0
0
0
1
2
0
0
2
1
0
0
0
0
2
0
3
5
2
0
2
0
0
0
0
2
0
2
1
0
1
0
0
0
1
0
2
1
0
0
1
0
0
0
0
0
2
1
1
0
2
0
1
0
0
2
2
0
0
0
1
2
2
0
2
0
1
0
0
0
0
1
2
2
0
0
2
1
0
2
1
1
2
0
0
0
2
0
0
1
0
1
2
0
0
1
0
2
0
2
2
0
2
0
3
2
2
0
0
0
2
0
0
2
0
0
2
3
1
0
2
0
1
0
2
0
2
5
0
0
0
1
0
1
0
0
0
0
1
0
0
2
1
2
0
0
0
1
0
2
2
1
0
0
3
3
1
0
2
4
0
0
2
0
0
1
0
2
0
0
0
1
0
3
0
0
0
0
1
0
1
0
2
0
0
0
3
0
0
1
1
0
1
2
2
0
2
0
0
2
0
0
0
0
0
0
0
1
2
2
0
0
0
1
0
0
0
1
0
1
1
2
0
0
1
2
1
0
0
1
0
2
0
0
2
1
1
0
0
0
0
0
1
3
0
0
0
1
1
0
2
1
0
0
3
1
0
1
0
0
0
1
0
1
0
1
1
1
2
0
0
0
0
1
3
1
0
0
1
0
0
1
2
2
1
0
3
2
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
2
0
0
2
0
0
1
1
0
1
0
2
0
0
1
1
1
0
1
2
0
1
2
3
0
0
0
0
2
1
0
2
0
0
0
0
0
0
1
2
0
0
2
1
2
0
1
1
0
0
0
2
0
0
0
0
0
0
0
2
0
2
2
1
0
0
0
0
0
1
0
1
1
1
1
0
1
0
1
0
0
2
1
0
1
2
2
0
0
0
0
2
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
2
0
2
1
0
1
1
0
1
0
0
2
1
1
0
2
0
0
2
1
0
0
2
1
4
0
0
0
2
0
0
0
1
0
2
0
0
0
2
0
0
2
0
0
0
1
1
0
1
0
2
1
2
2
1
0
1
0
0
1
0
1
0
4
0
2
0
3
3
1
1
2
1
1
1
0
0
1
2
1
0
1
1
0
2
2
1
0
0
2
1
4
1
1
0
2
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
2
0
1
0
0
2
1
0
0
2
0
0
0
0
0
1
1
1
0
0
1
1
1
0
2
0
2
2
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
2
2
0
0
0
0
3
2
1
0
0
0
0
2
1
0
1
1
1
0
0
0
2
1
0
0
0
0
0
1
0
1
1
0
1
0
0
2
2
2
0
0
2
0
0
1
0
0
1
2
0
1
0
0
2
2
3
0
0
1
0
1
1
0
1
0
1
2
1
2
0
1
0
0
0
0
1
1
2
0
2
2
0
0
1
1
0
1
3
0
0
1
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
2
0
1
2
1
3
0
0
2
1
0
1
0
1
1
0
1
1
1
0
0
0
2
0
0
0
1
0
0
2
0
2
1
0
5
2
0
0
0
0
1
0
1
3
0
0
0
0
1
0
1
0
0
0
0
0
2
0
1
1
1
1
0
2
1
1
2
1
0
0
0
2
0
0
1
1
0
1
0
0
1
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
2
0
0
1
0
0
1
1
0
0
2
0
0
1
2
2
0
2
0
2
1
0
0
0
0
2
2
0
2
0
0
1
1
0
0
0
0
1
2
2
0
0
0
2
0
0
0
0
0
3
0
0
2
0
2
2
1
0
2
0
2
0
0
0
0
0
1
0
0
2
1
2
1
2
1
2
0
0
2
2
0
0
0
1
1
0
0
1
0
0
2
2
2
2
0
0
2
3
0
0
0
0
0
0
0
2
0
1
0
0
1
1
0
0
0
0
0
0
2
2
0
0
3
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
2
1
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
2
0
0
2
2
0
0
2
1
0
1
0
0
0
0
1
0
1
0
0
0
0
2
1
1
0
4
0
0
0
0
2
0
0
0
1
0
2
3
1
0
0
0
0
0
0
0
1
3
0
0
1
0
0
0
2
0
0
1
1
4
1
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
1
0
1
0
1
2
0
1
0
0
0
1
0
0
0
1
2
0
0
1
0
1
2
0
1
0
0
0
1
0
0
2
1
1
0
0
1
0
1
2
1
0
0
0
1
0
0
0
2
1
1
0
1
0
0
0
2
0
0
1
0
2
1
0
0
2
2
1
1
1
2
1
2
0
0
2
0
0
1
0
1
2
1
1
3
1
0
0
1
0
0
0
0
0
0
0
1
0
2
3
1
0
2
1
1
0
2
0
2
0
0
0
0
0
1
0
0
0
1
1
3
2
1
0
1
2
0
0
0
1
0
0
1
0
2
0
3
1
1
0
0
0
0
0
0
3
1
3
0
1
2
1
3
0
0
1
0
0
1
1
0
2
0
0
2
0
1
1
0
0
0
0
0
1
0
0
1
2
0
1
0
0
0
0
2
1
3
2
1
0
0
0
1
2
0
2
0
0
3
1
1
0
0
0
0
2
2
2
1
0
0
0
1
1
0
0
1
1
0
0
1
0
1
2
2
0
1
0
1
1
1
1
0
0
0
2
0
0
2
1
2
0
1
0
0
0
2
2
0
1
0
0
1
1
0
2
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
2
2
0
0
0
2
2
2
1
1
0
0
2
0
0
0
1
1
0
1
0
1
0
0
0
0
2
0
0
1
0
1
0
1
2
2
0
2
0
1
2
0
0
2
1
0
1
0
2
0
2
0
2
0
1
0
0
2
2
0
1
0
0
0
0
1
0
0
0
0
0
0
2
1
0
1
1
0
2
0
0
0
0
2
1
0
2
1
1
1
2
0
0
1
1
1
0
0
1
0
0
1
1
0
1
0
0
1
1
1
0
1
2
0
0
0
2
2
2
2
2
0
0
0
2
0
0
0
2
1
0
0
2
2
2
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
2
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
2
2
0
1
0
1
1
0
3
0
0
0
1
2
0
2
0
0
1
1
1
1
0
1
0
0
0
0
0
1
0
0
1
1
0
1
0
2
1
0
0
0
1
0
0
4
0
1
1
2
1
1
1
0
0
1
0
1
1
2
2
0
2
1
0
0
0
0
0
1
0
0
1
0
0
0
2
1
2
1
2
0
2
0
0
1
0
0
1
0
1
0
1
1
0
0
1
2
2
0
0
0
1
0
1
0
2
0
2
0
2
0
0
0
1
0
0
0
0
1
2
0
1
3
0
0
0
0
2
1
2
1
2
0
0
4
5
0
1
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
1
1
2
1
1
0
2
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
2
0
1
0
0
0
0
1
1
0
2
1
0
1
1
2
0
0
2
0
0
0
0
0
1
1
2
0
1
0
1
0
0
1
0
0
0
2
2
0
0
1
1
0
2
2
0
0
0
1
1
1
0
1
2
1
0
0
0
2
0
0
1
2
2
0
1
2
0
2
0
0
2
0
0
2
0
0
0
1
1
1
0
0
2
2
1
1
1
2
2
0
0
0
2
1
1
1
2
0
0
1
2
3
1
0
0
0
0
2
1
0
0
0
0
0
2
2
1
2
2
0
0
0
0
0
0
0
0
0
1
2
1
2
0
2
3
1
2
0
0
1
1
1
2
0
0
0
0
0
0
2
1
2
1
2
2
0
0
0
2
1
0
1
0
3
0
1
0
0
1
1
0
1
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
1
0
1
0
0
0
0
2
0
1
0
0
0
0
2
1
1
0
0
0
0
0
2
0
0
2
1
0
2
0
1
2
0
0
2
0
1
1
0
0
0
1
0
0
0
0
1
2
1
0
0
1
0
1
1
0
0
2
1
2
2
1
0
1
1
1
0
2
2
4
0
0
2
2
1
0
0
2
0
0
2
0
0
2
1
0
0
1
0
1
0
0
0
0
2
0
2
0
0
0
1
0
1
1
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
2
0
0
0
2
0
1
1
1
2
0
2
0
1
2
1
2
0
0
1
2
2
1
0
1
1
2
0
0
2
0
0
1
1
0
0
1
0
1
2
2
0
0
0
1
2
0
0
0
0
2
0
0
2
0
1
0
2
1
0
0
0
0
0
0
0
3
1
0
1
1
0
2
3
1
0
0
0
0
1
1
2
0
2
5
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
2
0
0
1
0
0
0
0
0
1
0
0
1
2
1
2
0
0
0
0
1
0
2
0
0
0
0
0
1
0
2
2
2
0
0
0
2
0
0
0
2
2
1
1
0
0
0
1
0
0
0
0
1
1
1
0
2
1
0
0
1
2
0
1
0
1
1
2
0
1
2
1
0
0
0
0
1
2
0
0
0
0
1
3
0
0
0
0
0
1
0
0
2
2
0
0
1
2
0
0
0
1
1
0
1
0
2
0
0
0
0
2
2
0
0
1
0
2
1
0
1
0
2
3
0
0
1
1
2
0
0
0
2
2
1
1
1
0
0
0
0
0
1
0
3
2
2
1
0
0
1
2
2
1
1
0
1
0
0
0
0
1
1
0
1
0
0
0
1
1
2
1
0
0
0
2
0
1
0
0
0
0
0
1
1
1
0
2
2
1
0
1
0
1
2
1
0
0
1
0
0
1
1
1
3
1
0
0
2
2
2
0
0
0
0
1
0
2
0
0
2
0
0
0
1
1
2
0
2
0
0
0
0
2
1
2
0
0
1
2
0
1
1
0
0
1
0
0
1
0
1
2
0
0
1
0
0
2
1
2
0
2
0
0
1
2
2
2
2
0
0
0
0
0
0
2
1
2
0
1
0
2
0
0
2
1
0
1
1
0
2
2
0
0
0
0
0
0
2
0
1
1
2
0
1
0
1
1
0
1
0
0
0
2
1
1
0
0
2
1
0
2
0
0
2
0
0
0
0
2
0
1
2
1
0
0
0
1
0
0
0
0
0
0
0
2
2
1
1
2
1
2
0
2
0
0
2
3
2
1
0
0
1
0
0
1
0
0
1
0
1
2
2
1
0
0
2
0
1
0
3
2
1
2
0
2
0
2
2
0
0
1
1
1
1
2
2
0
0
2
0
0
0
2
0
0
1
1
0
0
3
0
1
2
0
0
0
0
1
1
0
0
1
0
2
2
2
2
1
2
2
0
2
1
0
0
1
1
0
1
2
2
1
0
0
0
1
1
0
3
0
0
3
0
1
0
0
1
1
2
0
0
2
0
2
0
1
1
1
0
1
0
0
2
1
1
0
1
2
0
0
0
1
0
0
0
0
1
0
2
0
0
1
0
0
1
0
1
1
0
1
0
2
0
1
3
1
0
0
1
0
0
1
0
0
1
1
0
0
2
2
0
0
0
0
2
1
0
2
0
2
1
1
0
0
0
0
2
0
1
0
2
1
0
0
2
2
1
0
0
1
1
0
0
1
0
0
2
0
0
0
1
0
0
2
2
2
0
0
0
0
4
0
0
2
0
2
0
2
0
2
1
0
1
1
0
0
0
2
0
2
0
0
0
2
1
2
2
0
0
2
1
0
0
1
0
1
0
2
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
2
0
1
2
0
1
0
3
1
0
0
0
1
0
0
0
0
0
2
1
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
2
1
1
0
1
0
0
2
0
1
2
0
0
1
2
1
2
0
0
0
0
0
0
1
0
0
2
0
3
0
1
0
2
0
0
1
0
0
0
0
1
0
0
1
0
2
0
1
1
0
2
2
1
0
0
1
0
1
0
2
1
0
0
2
0
0
0
0
0
2
3
2
0
1
0
0
0
2
0
1
1
0
0
1
0
0
0
0
2
0
0
1
0
2
2
1
0
0
2
0
0
1
1
0
1
0
0
1
2
0
0
0
1
0
0
0
1
0
0
2
0
0
0
2
0
3
0
0
1
2
4
0
0
1
2
2
1
1
5
0
1
3
0
0
1
1
2
1
0
0
1
0
1
1
1
2
0
3
0
0
0
2
2
1
0
1
0
0
0
0
0
2
1
0
0
1
0
0
1
2
0
0
0
2
1
0
1
0
0
2
0
2
1
0
0
0
2
1
0
0
2
0
2
0
0
1
0
0
0
1
1
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
2
0
2
2
1
2
1
0
0
2
1
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
2
0
0
2
0
0
1
0
0
0
0
0
1
0
1
0
0
1
1
0
1
1
0
1
0
0
0
1
1
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
2
0
2
2
2
0
0
0
0
0
0
0
0
1
2
0
0
2
0
1
2
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
3
0
1
1
0
2
2
1
0
0
1
0
0
1
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
2
1
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
6
0
0
0
1
2
1
0
0
2
0
2
0
0
0
0
0
2
0
0
2
0
0
1
1
1
2
1
0
0
0
2
0
0
0
4
0
2
1
2
0
1
0
0
3
3
0
1
1
0
3
0
0
1
2
1
1
1
0
2
1
1
0
1
0
0
0
2
1
1
0
1
1
1
1
1
0
0
2
1
0
0
0
0
0
0
0
0
0
1
1
2
1
1
2
1
0
0
0
0
0
0
1
1
1
1
1
2
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
1
0
2
0
0
2
0
2
0
4
0
0
0
1
0
2
0
0
0
2
1
0
1
1
0
1
0
0
2
2
1
0
0
3
0
2
0
1
1
2
1
0
1
1
0
0
2
0
1
0
2
1
1
0
1
2
0
2
0
0
1
0
0
1
0
2
0
2
1
0
0
0
0
0
1
0
0
0
0
2
2
1
0
1
2
1
2
2
0
0
0
1
0
2
3
0
0
0
0
1
0
0
1
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
2
1
1
0
2
0
1
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
3
2
0
1
1
0
2
1
2
0
0
1
1
0
0
6
1
0
1
0
0
3
0
2
0
0
1
2
0
0
0
2
3
0
0
0
2
0
0
0
0
2
1
1
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
1
2
2
0
0
1
1
1
2
2
0
0
0
0
0
2
0
2
1
0
1
0
0
0
2
1
2
1
0
0
0
1
1
0
0
1
1
1
2
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
2
0
0
0
2
0
0
0
0
3
0
2
0
1
1
0
0
0
1
2
0
2
1
2
0
2
0
0
1
0
0
0
0
1
0
1
0
0
1
1
1
0
1
0
0
0
2
0
0
0
0
3
0
1
2
2
0
0
0
1
2
1
0
0
0
0
2
0
3
0
0
1
2
0
1
0
2
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
2
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
1
2
1
1
2
0
0
0
0
0
1
0
0
1
0
0
2
0
0
1
1
0
0
3
0
0
0
1
0
0
0
1
2
1
0
0
1
0
0
0
0
2
0
0
0
0
0
2
1
2
1
0
0
0
2
0
1
2
2
6
0
0
11
1
0
2
0
1
0
0
1
1
1
0
3
2
2
1
0
2
2
1
0
0
1
0
1
1
0
0
1
0
2
0
1
2
2
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
1
0
2
1
1
1
1
1
0
0
1
2
0
1
0
0
0
2
0
0
0
1
2
2
0
1
1
2
0
0
2
0
1
1
0
0
0
0
2
0
0
0
1
0
0
2
1
2
1
1
0
0
2
0
0
0
0
3
0
0
1
0
0
0
1
0
2
1
0
1
0
0
0
0
0
2
0
0
1
0
0
0
1
1
3
0
0
1
2
0
1
2
0
0
0
1
1
1
1
1
2
0
1
0
2
0
0
0
0
4
0
1
1
0
0
1
2
0
0
0
2
0
1
0
2
0
0
0
0
1
0
1
0
0
0
0
1
2
0
1
0
1
0
1
0
1
1
0
2
0
0
1
0
0
1
0
0
0
0
1
1
1
2
0
0
2
0
0
1
0
2
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
1
0
2
1
0
0
0
0
2
2
0
0
1
2
0
1
0
0
3
0
2
0
0
2
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
1
0
0
1
2
0
0
0
0
0
2
0
1
0
0
0
1
0
2
3
0
0
2
0
1
0
0
2
2
0
0
1
1
0
1
0
1
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
2
2
0
0
1
4
0
0
0
0
1
1
0
0
0
0
0
1
0
0
2
1
2
2
1
1
1
1
1
1
2
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
2
1
0
1
1
0
1
0
2
0
1
0
1
3
1
3
0
0
0
0
0
0
3
0
0
0
2
0
2
1
0
0
3
0
0
3
0
1
0
0
1
1
0
2
1
2
0
0
0
1
1
0
0
2
2
0
1
0
0
0
1
0
2
0
0
0
1
0
2
2
0
1
1
1
0
1
1
1
0
0
0
2
3
1
0
2
0
0
2
0
0
1
2
0
0
2
1
0
0
1
0
1
1
1
2
1
0
0
0
1
1
0
1
0
2
0
1
0
2
1
0
0
2
0
1
0
1
0
0
2
0
1
1
1
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
2
0
2
0
1
0
0
0
0
0
1
2
3
2
0
0
0
0
2
1
1
0
2
0
0
0
0
2
1
0
1
0
2
0
0
1
0
2
2
2
2
2
0
0
1
1
1
2
1
0
0
2
3
1
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
2
1
0
1
1
0
2
0
1
0
0
1
0
0
1
0
1
2
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
1
1
1
0
1
0
1
2
0
0
2
0
0
0
2
0
3
1
1
0
0
2
3
2
1
1
1
0
2
1
0
0
2
0
1
0
0
0
0
2
1
2
0
0
1
0
0
1
2
0
2
2
0
0
1
0
2
0
0
0
2
0
1
1
0
2
2
0
0
1
0
2
1
0
0
0
1
0
2
2
0
2
0
0
1
1
0
2
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
1
2
0
2
2
0
0
1
1
0
1
2
0
3
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
1
1
0
2
2
2
0
0
1
2
2
0
2
0
1
0
1
0
0
1
2
0
0
0
2
0
0
2
0
2
1
0
1
1
0
0
0
0
0
0
2
0
1
0
2
0
0
0
1
0
0
0
1
1
0
2
0
0
0
1
0
3
0
2
1
0
0
2
0
1
1
0
0
0
1
0
2
2
2
1
1
0
0
2
1
0
0
0
2
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
1
2
2
0
2
0
0
2
0
2
0
1
0
2
2
0
0
0
2
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
2
2
1
2
0
0
0
0
0
1
0
0
2
1
1
1
1
1
1
0
0
0
2
2
0
1
0
0
0
0
2
2
0
2
0
0
0
0
2
1
1
0
1
3
3
0
0
2
1
2
0
0
1
0
1
2
1
1
0
3
2
1
1
0
1
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
3
0
2
0
0
1
1
2
0
1
2
2
0
1
1
0
0
0
0
2
1
0
0
0
1
1
2
1
0
0
2
1
1
0
0
0
0
1
0
1
1
2
2
1
1
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
2
0
2
0
0
0
1
0
2
0
2
0
1
0
1
1
1
0
1
0
1
2
2
1
2
1
0
2
1
0
2
0
0
1
0
0
0
1
1
0
1
0
1
2
2
0
0
0
0
2
0
0
1
0
2
0
2
0
0
2
0
0
2
0
1
2
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
2
1
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
2
1
1
0
0
0
0
2
0
2
0
1
0
0
2
1
0
0
0
0
2
0
0
0
1
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
1
0
1
1
0
1
0
1
1
2
0
0
0
0
2
2
1
0
0
0
0
0
1
0
3
0
0
0
3
0
0
2
2
0
0
0
0
1
0
2
0
0
0
1
2
0
0
0
0
2
0
0
0
2
0
3
0
0
1
0
0
1
1
0
0
1
1
0
0
2
0
0
3
2
2
0
0
0
2
1
1
0
0
0
0
2
2
2
0
0
0
0
1
2
0
0
0
0
1
1
0
0
3
2
0
0
0
2
0
0
0
1
0
1
1
0
2
0
0
0
1
0
0
1
2
1
0
1
0
0
2
0
0
0
1
1
2
1
0
0
1
1
0
0
0
3
0
1
2
0
0
0
0
1
1
1
0
0
0
0
2
0
1
1
0
0
0
1
1
0
0
0
0
0
2
1
1
1
0
2
1
0
2
2
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
1
1
0
1
0
0
0
2
0
0
2
0
0
2
2
1
1
0
1
1
1
0
1
2
0
2
0
0
0
1
0
1
0
0
0
1
2
0
0
1
1
0
2
1
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
1
2
0
1
0
2
0
0
0
2
1
1
0
2
0
2
2
0
0
0
3
2
0
1
0
0
2
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
2
0
0
1
0
0
0
0
2
0
1
1
0
1
0
2
2
1
0
0
0
0
2
1
1
0
0
0
0
1
1
2
0
0
0
0
1
0
1
0
1
0
0
1
1
1
1
0
1
0
2
0
1
0
0
0
0
0
1
0
0
0
0
2
0
1
1
0
1
0
2
0
2
0
1
0
0
0
1
0
1
0
0
2
0
2
2
1
0
1
5
2
1
1
0
1
0
0
0
0
2
0
0
0
1
3
2
0
0
1
0
2
0
0
0
0
0
0
1
1
0
2
0
0
1
2
0
2
0
1
0
0
0
0
2
0
0
1
1
1
0
1
0
0
2
2
1
0
0
2
0
0
2
0
2
0
0
1
0
0
2
2
2
2
1
1
2
3
1
0
0
0
0
0
0
2
0
2
1
2
0
1
8
0
1
1
0
0
1
2
0
0
1
1
0
2
0
3
1
0
0
0
2
0
3
2
0
1
1
2
1
0
0
3
0
0
0
2
0
0
0
0
2
0
1
0
1
0
1
0
0
1
1
0
3
1
0
0
1
0
2
0
0
0
1
1
2
0
2
0
1
0
1
1
0
2
0
1
0
2
0
0
0
1
0
0
1
1
0
0
1
1
1
1
1
0
0
1
0
0
0
2
0
2
1
1
1
1
0
0
0
1
1
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
2
0
0
0
1
0
2
2
1
0
1
1
1
0
1
0
1
0
2
0
2
0
1
2
0
1
2
0
1
0
1
1
0
1
0
1
0
0
1
2
2
0
0
0
0
2
0
1
0
2
0
0
0
2
0
0
0
1
2
0
0
1
0
1
2
0
0
1
0
0
0
0
1
1
1
1
0
1
0
2
0
0
0
1
2
1
2
0
0
0
0
2
1
1
1
1
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
4
0
0
0
0
0
2
2
2
0
0
1
4
0
3
2
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
3
2
0
0
0
0
0
0
1
0
1
2
0
1
0
1
1
0
0
2
1
0
0
2
0
2
0
0
0
0
2
1
2
0
0
0
1
0
0
0
0
1
0
0
4
0
0
1
0
0
0
0
2
2
0
0
0
0
1
0
0
0
1
1
1
0
0
2
0
1
0
2
1
0
0
0
1
2
0
0
2
0
2
0
0
0
0
0
1
2
1
0
0
1
2
0
1
2
0
1
0
0
1
0
0
0
0
1
0
0
0
0
2
0
3
2
2
0
2
0
2
0
2
0
3
0
0
0
0
3
0
2
0
0
2
0
0
0
1
3
2
1
0
2
2
1
0
0
0
0
0
0
1
0
0
0
0
2
1
2
0
0
1
1
1
1
0
0
0
1
1
0
2
1
1
0
0
1
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
1
1
2
2
2
2
1
1
0
2
2
0
0
0
0
0
0
0
0
0
2
1
2
0
4
0
2
0
1
0
2
1
0
1
1
0
0
2
1
1
0
1
2
1
2
1
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
1
1
0
0
0
2
2
3
0
0
0
0
0
0
2
0
1
1
0
0
0
1
1
1
0
1
1
0
1
1
0
0
1
0
1
0
0
1
1
1
0
1
0
0
2
0
0
2
0
0
0
0
1
1
2
0
0
3
1
1
0
2
1
0
0
0
0
1
0
0
0
0
2
2
0
0
0
4
2
1
0
2
2
0
1
0
2
0
0
0
2
1
1
0
1
0
0
0
0
0
0
1
1
2
2
0
2
2
1
0
0
1
2
0
0
2
0
1
0
1
0
0
0
0
0
1
0
1
1
0
0
2
0
1
1
0
2
1
0
0
0
1
2
0
1
0
0
1
1
1
1
2
0
2
0
2
0
0
0
0
0
0
0
0
0
2
2
0
2
2
0
2
2
2
1
0
1
0
0
1
0
0
2
2
0
1
2
0
0
1
0
0
1
1
0
0
0
0
2
0
2
2
1
1
5
0
1
2
2
0
1
1
0
0
0
1
1
0
3
1
0
0
0
2
2
0
1
0
0
1
1
0
1
0
2
1
0
1
1
0
0
2
2
0
0
0
0
0
2
0
0
0
3
0
0
2
2
0
2
0
0
0
0
2
0
1
0
0
2
0
2
0
2
0
0
0
0
0
1
1
0
0
0
0
3
0
0
0
1
0
0
0
2
0
0
0
1
0
1
0
1
0
0
0
2
1
1
2
1
0
2
1
0
0
2
1
0
0
1
1
0
2
0
0
0
1
2
0
4
0
2
0
2
0
0
0
2
0
0
1
0
0
2
0
2
1
2
1
0
0
0
0
0
2
3
1
0
2
1
0
0
0
0
0
0
1
0
1
0
2
1
2
1
0
2
0
0
0
0
0
2
2
0
2
0
1
1
0
0
1
0
2
2
0
2
1
0
0
2
1
0
0
0
2
0
0
2
2
2
0
2
2
0
0
0
2
2
1
1
2
2
1
1
1
1
0
1
0
0
0
0
0
2
0
1
0
2
2
2
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
1
0
1
0
0
0
0
2
1
0
0
0
1
1
1
1
0
0
0
0
0
0
1
0
2
2
2
2
1
0
0
0
1
2
1
1
1
2
0
0
0
0
0
1
0
0
1
1
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
2
0
2
2
1
0
1
0
0
0
1
1
0
1
2
1
0
0
0
0
0
1
0
0
0
2
2
0
0
1
2
0
0
0
0
0
0
2
1
0
0
0
3
1
1
0
0
2
0
2
0
2
1
2
0
3
2
0
0
0
0
2
0
0
2
1
0
2
2
1
1
1
0
0
0
0
0
0
0
2
0
2
1
2
1
0
3
0
1
2
0
3
1
1
1
1
1
0
1
2
0
2
1
0
2
0
0
1
1
0
0
0
0
1
0
1
1
1
2
0
2
1
2
0
2
0
0
1
0
1
0
1
2
2
0
0
0
2
0
2
1
3
2
0
0
1
0
0
0
0
0
0
0
1
0
4
1
2
0
2
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
2
0
0
0
2
0
0
1
2
0
0
0
2
0
0
0
2
0
1
3
0
4
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
2
1
1
0
0
0
1
0
0
0
0
2
1
1
0
0
0
0
2
0
0
0
2
0
1
0
0
2
1
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
2
2
1
2
1
0
1
1
3
0
1
1
2
2
0
0
0
0
0
2
2
1
3
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
2
1
0
1
0
0
0
0
0
0
0
2
1
0
0
0
1
2
2
1
0
2
0
2
3
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
1
0
1
0
1
0
1
1
2
1
2
0
2
0
1
0
1
1
2
2
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
2
0
0
2
0
0
2
1
3
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
2
0
0
1
1
2
0
0
2
1
0
2
0
0
0
0
1
0
1
2
0
1
0
1
0
1
1
2
0
1
0
0
2
2
2
0
0
1
1
0
0
3
2
0
0
0
1
2
1
0
1
0
0
0
2
0
0
0
0
0
3
1
0
1
2
2
0
0
1
0
0
1
1
2
1
0
1
2
0
0
0
2
0
0
1
0
0
1
1
0
0
1
1
0
1
2
2
2
2
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
1
1
0
0
0
0
0
2
1
1
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
1
5
0
0
0
1
1
0
1
0
1
0
0
0
0
0
1
1
0
0
0
1
1
1
2
1
0
0
2
0
0
0
0
1
2
2
2
0
0
0
1
0
0
0
2
2
0
1
1
1
1
1
1
1
0
1
0
0
0
1
0
0
0
0
1
0
2
0
1
0
0
0
2
1
0
2
0
1
0
0
0
0
0
1
2
2
0
2
2
2
1
2
1
2
0
0
1
2
1
0
3
0
2
0
2
2
0
0
2
1
0
1
0
1
1
0
1
1
0
1
0
1
1
0
0
2
0
0
3
0
0
0
0
1
2
0
0
0
2
2
0
0
0
0
0
0
2
2
1
0
2
2
1
0
0
0
0
0
0
1
0
2
3
0
0
1
0
0
0
0
2
0
0
2
2
0
0
1
1
1
2
0
3
2
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
2
0
1
0
0
0
1
0
2
0
1
1
0
0
2
2
2
0
1
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
2
0
2
1
0
1
0
1
0
2
0
0
0
2
0
0
0
2
1
1
2
0
0
0
0
0
2
0
2
1
1
0
2
2
0
0
0
1
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
2
0
0
0
0
1
1
1
0
0
1
1
0
1
1
0
0
0
2
0
0
2
1
1
1
2
0
0
2
3
0
0
0
2
0
0
0
0
1
0
0
1
2
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
2
1
1
1
2
2
1
2
2
2
0
2
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
1
1
0
0
0
0
0
0
1
8
2
0
1
0
1
2
0
0
0
0
2
1
0
0
0
0
0
0
0
3
1
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
1
2
0
0
0
1
2
0
2
1
0
0
0
0
1
0
2
0
0
2
1
0
3
1
1
0
0
0
0
0
1
1
0
2
0
0
1
0
0
1
0
0
2
0
0
0
1
1
2
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
1
1
2
0
1
0
0
1
0
2
1
0
1
1
2
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
1
2
0
0
0
1
2
0
0
1
0
2
0
0
2
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
2
0
0
1
1
2
1
1
1
1
0
0
0
0
1
0
0
0
0
0
2
2
0
0
1
0
1
1
0
2
2
2
1
0
2
0
2
0
0
1
0
0
1
1
1
1
0
0
0
0
0
1
2
0
1
0
0
0
0
0
1
1
0
0
0
0
2
0
0
2
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
1
1
0
0
1
0
0
1
1
4
1
0
1
0
3
0
0
0
0
0
2
0
0
1
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
1
3
0
2
0
0
0
2
1
1
1
0
0
1
0
0
0
0
2
1
0
0
0
1
0
2
1
2
0
0
2
0
2
0
0
0
1
0
1
0
1
1
0
0
0
1
1
1
0
2
2
1
0
1
2
2
0
0
0
2
1
2
0
3
0
0
0
1
2
1
1
2
2
2
0
0
0
0
0
1
0
1
3
1
2
0
0
0
0
0
2
2
0
1
2
0
0
1
0
1
0
2
1
1
0
1
1
0
1
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
1
1
1
0
0
1
0
0
2
1
0
1
0
0
0
0
2
0
1
0
0
0
0
1
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
1
1
2
1
0
1
0
1
1
0
0
0
1
0
0
0
2
2
0
0
0
2
0
0
1
1
0
0
0
0
0
1
2
0
0
1
0
1
1
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
2
2
1
2
1
2
0
2
0
0
0
0
0
0
2
0
0
0
1
0
2
2
2
2
1
1
1
1
1
1
0
2
0
1
1
0
4
0
0
2
2
0
1
0
1
0
0
0
0
2
0
1
0
1
2
1
0
0
0
0
0
0
0
2
0
0
1
1
2
1
1
1
0
1
0
1
0
2
2
2
0
1
0
0
0
2
2
1
0
1
1
2
0
2
0
1
0
2
0
0
1
0
0
0
1
2
1
2
1
0
0
0
2
3
0
3
0
3
2
0
0
0
0
0
0
1
0
0
0
0
2
2
2
1
1
1
0
1
0
0
0
0
0
1
0
0
0
3
2
0
1
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
2
0
2
0
1
0
0
0
2
0
0
0
0
2
0
2
0
0
2
0
2
1
0
2
0
3
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
2
0
1
1
0
0
1
1
2
1
0
2
0
3
1
2
0
0
0
0
0
1
2
1
0
0
0
1
0
0
0
0
2
1
0
1
0
2
0
0
1
0
0
0
0
1
0
0
1
1
0
0
2
2
2
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
1
2
1
0
0
0
0
0
0
1
1
0
1
0
2
0
1
0
2
2
0
1
1
0
1
1
0
2
0
3
0
0
0
0
0
0
0
0
0
1
0
1
2
1
0
0
1
1
2
0
0
0
1
2
0
2
0
0
0
0
0
1
0
0
1
1
2
0
3
1
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
1
2
2
0
0
1
1
2
0
1
0
2
1
0
1
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
2
0
0
2
1
2
3
0
0
2
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
1
1
0
0
0
1
2
0
0
0
1
0
1
1
0
1
0
1
0
0
0
0
0
1
1
0
1
2
0
0
0
1
2
0
1
2
1
1
0
1
2
0
0
0
2
1
0
0
2
0
0
1
2
0
1
0
1
2
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
3
0
2
0
0
0
0
1
1
1
3
1
1
0
0
1
0
0
1
0
2
0
1
0
0
0
0
0
1
1
2
0
0
1
0
2
0
1
2
0
0
1
0
1
0
1
3
2
0
2
0
0
0
2
0
2
1
0
3
0
1
1
1
1
2
4
0
1
0
0
2
0
0
0
0
0
1
2
0
2
2
2
0
0
4
1
0
2
1
0
0
0
0
0
0
1
2
0
0
2
3
1
0
1
2
0
1
1
1
0
1
0
1
2
0
0
0
0
0
2
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
1
2
0
0
1
0
0
0
1
0
2
2
2
1
0
0
0
0
1
2
0
0
0
2
0
0
2
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
1
1
0
1
2
1
0
2
1
1
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
2
2
1
0
0
1
0
1
0
0
2
2
3
2
2
0
1
1
1
0
2
1
0
6
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
3
1
1
1
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
1
0
0
0
0
2
1
1
2
1
1
1
0
0
0
2
0
1
1
2
0
2
1
1
0
1
0
1
2
0
0
2
1
0
1
0
2
1
0
1
0
1
0
1
1
1
0
2
2
2
2
4
1
2
0
1
0
0
0
2
1
0
0
0
0
0
0
0
1
0
1
1
2
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
1
0
1
2
0
1
0
0
0
0
2
0
0
1
0
2
2
0
0
1
0
1
1
2
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
2
2
0
0
2
0
1
0
0
0
3
0
1
2
1
1
0
0
0
0
1
0
0
0
2
0
0
0
0
2
2
0
0
1
2
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
1
1
1
1
0
0
1
1
0
1
3
1
2
0
0
2
2
0
1
1
0
0
0
1
2
0
0
1
2
0
0
0
2
0
2
0
0
0
2
0
0
3
0
1
2
2
2
0
1
0
2
2
1
2
1
0
1
0
1
0
0
1
0
1
1
3
1
1
0
0
1
0
0
0
2
0
1
0
2
0
3
0
1
1
2
1
0
0
2
2
0
0
0
1
0
0
0
2
1
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
4
0
1
0
0
0
1
2
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
1
0
0
2
0
0
1
0
1
1
0
2
1
0
0
0
2
0
2
0
2
0
0
7
3
1
2
2
1
0
0
1
2
1
1
2
0
0
1
1
2
2
0
2
0
0
1
2
0
1
0
0
1
1
0
0
1
0
0
1
0
1
2
1
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
1
1
0
2
2
3
2
0
1
1
3
0
0
1
2
2
2
2
0
1
1
2
0
1
0
0
1
0
0
1
1
0
0
2
3
2
2
0
2
0
0
0
2
1
2
0
1
0
1
0
0
0
0
0
0
2
1
1
1
0
0
2
0
1
1
0
1
2
0
0
1
0
0
0
2
2
0
2
1
0
0
2
0
1
0
0
0
0
0
0
1
0
2
2
1
0
1
2
0
0
0
0
0
0
1
0
0
2
4
0
0
2
0
1
3
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
2
0
1
0
0
3
1
0
1
0
0
0
1
0
0
0
0
1
0
0
1
2
0
0
0
2
0
1
0
2
2
0
0
2
0
0
0
1
0
2
0
0
0
0
0
1
0
0
2
2
0
1
0
1
0
0
1
0
3
1
1
0
2
0
0
0
1
2
1
0
0
2
0
2
0
0
1
2
0
1
0
1
0
1
0
0
1
0
0
1
3
0
1
0
0
0
0
2
2
0
2
0
2
1
0
4
3
0
2
0
1
1
0
1
0
1
3
0
0
0
1
0
1
2
0
1
0
2
0
2
2
2
0
0
0
0
1
0
0
0
2
0
7
2
0
2
2
0
0
0
1
2
0
0
0
0
2
1
2
1
0
0
0
0
0
0
0
2
2
2
0
0
0
1
0
2
2
2
0
1
0
0
0
0
2
0
0
2
0
0
2
1
1
0
0
1
0
0
1
0
2
0
1
2
2
0
0
1
1
1
2
0
0
0
1
2
0
3
3
1
0
0
0
0
1
0
3
0
1
0
0
0
0
0
0
0
1
0
1
2
2
0
1
1
0
0
0
0
2
0
0
1
0
2
0
0
1
0
0
0
4
1
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
1
2
2
1
1
0
0
1
0
3
1
1
2
0
1
2
0
2
0
0
0
2
0
1
1
2
0
1
0
0
0
1
0
1
1
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
3
2
2
2
1
1
1
1
0
2
0
2
2
2
0
0
0
0
0
2
0
6
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
4
0
0
0
0
1
0
1
1
0
0
0
2
2
0
0
5
0
0
0
1
0
0
0
0
0
0
2
0
1
2
0
0
1
0
1
2
0
2
0
0
0
1
0
0
0
0
1
0
0
1
1
2
0
2
0
2
2
0
1
2
0
0
0
0
0
5
1
1
1
2
1
1
1
1
0
0
0
0
2
0
0
0
4
2
0
0
3
2
1
1
0
0
1
0
1
0
1
0
0
1
0
0
0
0
2
2
0
0
0
0
1
2
1
1
0
0
1
1
2
2
1
0
3
1
2
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
2
0
2
1
1
0
1
0
2
0
0
1
2
0
0
1
2
0
0
0
2
0
0
2
1
0
2
1
1
0
0
0
0
3
0
0
0
1
0
0
0
1
2
1
2
0
2
0
0
2
0
0
0
0
1
0
1
0
1
0
0
1
0
0
2
0
0
2
0
0
2
0
0
3
0
0
2
1
0
2
0
0
4
2
3
4
1
0
1
1
0
0
0
2
0
2
1
1
0
0
0
0
0
3
2
0
0
0
2
0
1
0
0
3
0
0
0
0
3
0
0
0
0
2
1
2
0
0
1
2
1
0
1
2
1
2
1
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
1
2
1
4
0
1
2
0
0
0
0
1
0
1
1
2
1
1
0
2
1
2
0
1
1
2
0
1
0
0
0
2
1
1
0
0
0
1
0
4
0
0
0
1
0
1
0
1
3
0
0
0
0
0
0
1
2
2
0
2
1
0
2
2
0
0
2
0
1
0
0
3
0
0
2
2
2
2
0
0
2
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
1
2
0
0
0
1
2
2
1
0
0
0
2
0
0
1
2
0
2
1
0
2
1
1
0
1
2
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
1
0
1
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
3
1
1
1
0
0
3
1
0
0
0
0
1
0
0
2
0
0
2
2
1
0
0
1
0
0
0
0
3
2
0
2
0
1
0
0
1
1
2
1
2
2
0
0
0
0
0
0
2
1
0
0
0
1
1
0
1
0
0
1
0
0
1
2
0
0
0
0
2
2
0
1
0
1
0
2
2
0
1
0
0
1
2
1
0
2
0
0
1
2
2
0
2
0
2
0
1
0
0
0
1
0
0
1
0
0
1
1
0
2
0
0
1
0
0
1
0
0
0
1
0
0
1
1
0
0
2
2
0
1
1
0
2
0
0
2
0
1
0
2
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
2
1
1
1
0
0
1
0
1
0
0
1
0
3
2
1
0
0
2
2
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
2
2
0
0
1
0
0
1
0
2
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
2
0
0
2
0
2
0
2
0
0
2
2
0
0
2
1
1
2
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
2
0
0
1
2
0
0
1
0
0
0
0
2
2
1
0
1
0
0
1
1
2
0
0
0
0
0
2
1
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
1
0
0
1
1
0
2
0
0
1
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
1
3
0
0
1
1
0
0
2
1
0
0
0
2
2
2
0
0
1
2
0
0
0
0
1
1
0
1
0
2
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
1
2
0
1
0
0
0
0
1
1
0
1
0
0
2
1
1
0
1
1
1
2
1
0
0
1
0
0
1
1
1
1
2
0
0
2
1
0
2
0
2
0
2
0
0
2
1
1
1
0
2
0
2
0
0
0
0
2
0
0
1
0
0
0
1
2
0
1
1
0
0
0
2
0
1
1
1
0
0
0
0
1
0
0
0
0
2
0
1
1
0
0
1
0
1
0
0
0
0
0
0
2
2
0
0
0
1
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
3
0
2
0
0
1
0
1
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
2
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
2
1
2
1
2
1
1
0
2
3
0
0
2
0
2
0
0
2
1
0
15
2
0
0
0
0
0
0
2
0
0
0
1
2
0
2
0
0
0
1
0
1
0
2
0
1
1
2
0
2
1
2
2
2
0
1
0
1
0
1
0
0
0
1
2
0
1
1
0
0
0
0
0
0
3
1
0
2
2
1
1
1
3
0
1
0
0
1
2
2
0
1
0
2
0
0
0
2
1
0
1
2
0
1
1
0
0
0
2
1
0
0
0
2
0
0
0
0
1
2
2
0
1
2
0
0
2
1
1
2
2
1
0
0
0
0
0
1
1
0
0
0
0
2
2
2
0
0
0
0
0
0
1
0
2
2
0
0
2
2
0
1
0
1
0
0
2
1
1
0
1
3
1
0
0
0
0
1
1
2
1
0
0
2
2
1
2
1
1
2
2
0
0
1
1
1
2
2
0
1
1
2
0
0
2
0
0
0
1
0
2
0
0
0
1
1
2
1
0
0
0
1
0
1
1
1
2
0
1
1
0
0
2
6
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
1
2
1
1
0
0
0
0
2
1
2
0
0
0
1
0
1
2
0
1
0
1
1
0
0
2
1
0
0
0
2
1
1
2
0
0
0
1
1
1
0
0
2
0
0
0
0
1
0
1
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
2
0
2
0
1
1
0
2
1
0
1
3
0
0
1
0
1
1
0
0
0
1
4
0
1
0
0
0
0
0
1
0
0
2
0
0
0
2
0
1
0
0
0
1
2
1
0
1
0
0
0
0
2
0
2
0
1
0
0
0
0
2
1
1
0
1
1
1
0
0
2
0
0
0
0
1
2
2
0
1
2
0
0
0
2
2
0
0
2
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
2
0
4
1
0
0
2
0
0
1
0
2
2
2
1
1
0
0
2
1
1
0
1
0
0
0
2
0
2
0
0
0
2
3
0
2
1
0
0
1
1
1
0
0
1
1
1
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
1
2
0
0
1
0
2
0
0
0
1
1
0
0
0
0
1
0
2
1
1
0
2
0
2
1
1
0
1
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
3
0
0
1
0
2
1
0
0
0
2
0
0
1
0
0
1
2
2
0
0
1
2
0
1
0
0
0
1
1
1
2
1
0
2
2
0
0
0
1
0
2
1
0
0
2
1
1
0
0
0
0
0
0
0
2
2
0
1
0
0
0
1
0
2
0
1
0
1
3
2
1
1
1
0
0
0
1
0
2
2
0
0
1
2
0
0
1
1
2
0
0
0
0
0
0
0
0
1
2
3
2
2
0
1
1
0
0
1
2
2
2
2
2
2
0
1
1
0
0
1
0
2
0
0
0
2
1
0
0
2
2
1
0
0
0
1
0
0
0
0
0
0
1
1
0
2
0
0
0
2
2
1
0
0
0
3
0
0
0
0
2
0
2
0
0
1
2
2
0
1
0
2
0
0
0
2
1
0
0
0
2
1
2
1
1
2
0
3
2
1
3
0
0
1
0
4
1
0
0
3
2
0
1
0
0
2
0
0
0
1
0
2
0
0
0
0
0
1
2
0
0
1
1
0
0
0
0
1
0
1
2
1
0
0
0
0
1
4
1
1
1
0
1
2
0
0
0
1
2
0
0
0
0
2
2
1
0
0
0
4
0
1
1
1
0
1
0
0
0
2
1
0
0
1
0
2
1
0
0
0
0
1
0
1
0
0
0
2
1
0
0
6
0
1
0
1
1
0
0
0
0
1
0
1
1
0
1
0
0
1
0
0
1
2
0
1
0
2
0
0
0
0
1
0
0
1
2
1
0
2
0
0
0
2
0
0
0
2
0
0
0
0
1
0
2
2
1
0
1
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
2
2
0
0
0
0
0
0
1
0
0
1
1
3
0
0
0
1
0
1
0
1
0
0
0
2
1
0
0
1
0
0
0
0
1
0
0
2
0
1
2
0
1
1
0
2
0
0
1
1
1
0
1
1
0
2
1
0
0
0
0
0
3
0
0
2
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
2
2
1
0
1
0
2
2
0
1
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
2
1
1
0
0
2
2
1
2
0
0
2
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
2
1
0
0
1
2
1
0
1
1
1
0
0
0
1
0
1
1
0
2
2
2
0
0
0
1
0
1
0
0
2
1
0
0
0
4
0
0
0
1
1
0
2
0
0
2
2
0
1
7
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
3
2
2
0
0
0
1
2
0
0
0
0
0
1
0
0
0
1
0
1
1
1
2
0
0
2
0
0
1
1
1
2
2
1
1
6
3
0
0
0
3
0
1
1
1
0
3
2
0
0
0
1
0
2
2
0
2
2
0
1
1
2
3
0
0
0
0
2
1
1
2
2
1
0
1
0
1
0
0
1
2
2
0
1
0
1
1
1
0
0
0
0
0
0
1
0
2
0
2
1
1
0
0
1
0
0
0
2
2
2
1
2
1
2
0
0
1
1
0
2
1
0
0
0
0
1
1
0
2
0
0
0
0
1
1
1
1
0
1
2
1
0
2
3
1
0
1
0
1
0
0
0
3
0
0
1
0
2
1
0
0
0
0
0
1
0
0
2
2
0
0
1
0
0
2
1
0
0
0
1
1
1
0
0
0
0
1
0
2
0
1
2
0
0
0
1
0
2
1
2
1
4
2
0
1
0
0
0
0
0
7
1
0
1
2
0
1
0
3
0
2
1
0
0
1
0
2
1
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
1
0
0
2
0
2
0
3
1
0
0
0
0
3
2
0
5
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
1
2
0
2
0
0
0
1
1
0
0
0
1
0
0
0
0
0
2
1
1
2
1
1
1
1
0
2
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
2
0
1
2
0
1
0
1
0
2
0
0
1
1
2
2
0
0
0
0
1
0
0
0
1
0
1
0
2
0
2
0
0
0
0
0
0
0
3
0
1
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
4
1
0
0
0
0
0
2
3
0
2
0
1
2
2
0
0
0
0
0
2
0
0
1
0
2
0
2
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
1
0
1
0
2
2
1
1
0
1
2
0
2
0
0
1
0
0
0
2
0
0
1
0
0
0
0
1
1
1
1
1
2
3
1
1
0
0
0
3
2
0
0
1
0
0
0
1
2
1
0
0
1
0
2
2
2
2
0
0
0
0
2
1
1
2
0
0
0
0
1
0
1
1
0
0
0
1
0
1
1
0
1
0
0
2
0
0
1
2
0
0
0
2
0
0
1
0
0
0
0
2
0
2
2
1
2
3
0
0
1
2
1
2
0
1
1
0
1
0
0
0
0
2
1
0
0
1
1
0
1
0
0
1
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
1
2
1
1
0
2
0
2
1
0
2
1
3
1
1
0
2
1
1
0
2
0
0
0
0
0
0
2
0
1
2
2
0
1
1
0
0
1
0
0
0
1
0
0
2
0
0
1
2
2
1
1
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
2
1
0
0
2
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
2
2
0
0
0
9
2
0
0
0
0
2
0
2
0
0
0
1
0
1
2
0
2
0
1
2
0
0
1
1
1
0
2
0
0
1
1
0
1
0
0
2
0
2
2
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
2
0
0
2
1
2
0
0
0
1
0
0
2
1
0
0
0
1
0
1
0
1
2
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
2
0
0
2
2
1
1
1
0
1
2
0
2
0
0
1
2
0
1
1
0
1
0
0
2
0
1
2
1
0
2
1
0
0
0
0
0
0
2
2
0
0
0
1
0
0
1
0
0
1
2
1
0
0
1
0
0
0
2
3
1
2
1
0
0
0
2
0
0
0
2
0
0
0
0
3
0
1
1
1
2
1
2
0
0
2
0
1
0
0
1
0
0
0
1
0
0
1
1
2
1
2
2
1
1
2
0
2
0
2
0
0
0
0
0
2
1
1
0
1
0
2
0
0
0
0
0
1
0
0
2
2
1
1
2
1
1
2
1
2
0
0
0
1
0
1
1
0
0
2
1
2
0
2
1
0
0
1
0
0
2
0
0
1
0
2
0
0
0
1
1
0
0
2
1
0
1
0
1
1
0
0
0
0
1
0
0
0
0
1
0
2
0
2
0
1
0
2
0
2
0
2
0
2
2
1
4
1
2
1
2
0
0
1
1
0
0
1
0
0
2
4
1
0
0
1
1
0
2
0
2
0
0
0
0
0
0
2
2
1
0
1
2
2
2
2
4
3
0
2
2
0
2
0
2
0
0
0
0
0
1
1
1
0
1
0
0
1
0
0
2
2
0
0
0
0
2
0
0
0
2
1
0
0
1
0
0
0
0
1
0
0
1
0
1
1
0
1
0
1
0
1
1
1
2
2
0
0
0
2
2
0
2
0
1
0
0
0
1
0
2
1
0
2
0
0
0
0
1
0
1
0
1
1
1
1
2
0
0
1
2
0
0
0
1
0
1
0
2
2
2
0
0
0
0
0
2
1
2
2
2
2
0
0
0
1
0
0
1
0
2
0
2
0
0
0
0
2
0
1
2
1
0
1
0
1
0
0
0
0
0
3
1
0
1
0
1
1
2
3
0
0
2
0
0
1
2
2
1
1
0
1
2
0
1
0
0
0
0
2
2
0
1
1
3
1
2
0
1
3
1
0
1
3
0
0
0
2
2
0
1
0
2
2
1
0
1
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
1
0
0
2
3
0
2
0
0
0
0
1
1
0
0
1
0
0
1
0
0
2
2
1
0
0
1
1
0
1
2
0
0
0
0
0
2
2
1
0
0
0
0
2
0
0
1
1
1
0
0
0
0
2
2
0
0
0
0
1
0
2
1
1
0
0
1
0
0
2
0
2
0
0
0
0
1
2
2
1
0
1
0
1
0
0
2
0
2
1
2
2
1
0
0
0
0
2
0
0
0
0
1
0
0
0
1
1
0
0
2
0
0
0
0
0
0
1
2
1
0
2
0
2
1
0
0
1
0
0
0
2
0
0
2
2
1
0
0
2
0
0
1
0
2
0
0
2
0
1
0
0
0
0
2
0
0
0
1
0
0
1
0
0
2
0
1
0
0
3
1
0
0
1
4
1
2
0
1
2
1
2
0
0
3
2
2
0
0
0
0
1
1
2
0
1
0
0
0
2
2
3
0
2
0
0
2
0
1
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
1
1
0
0
1
1
1
2
1
2
0
1
0
0
0
0
1
0
0
2
0
0
5
1
0
0
2
0
1
0
1
0
0
0
2
1
0
2
1
1
0
2
0
0
0
0
0
0
0
0
1
1
1
2
0
0
2
0
0
1
0
1
1
0
1
2
0
4
2
0
0
1
1
2
0
0
0
0
1
0
0
0
0
1
1
0
0
2
2
3
0
2
1
1
0
2
0
0
0
0
1
0
1
0
0
2
1
4
0
0
0
2
0
1
0
0
1
2
3
0
1
0
0
0
1
1
1
0
2
0
0
1
1
2
0
0
1
1
2
2
0
0
2
1
0
0
0
2
2
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
2
0
2
0
0
2
0
2
0
1
1
1
0
1
0
0
0
1
2
0
0
0
0
0
1
1
0
0
0
1
0
0
1
2
0
0
2
0
2
1
0
0
0
0
1
1
2
0
0
0
0
0
0
0
1
0
0
1
0
3
0
2
2
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
2
2
0
0
1
2
0
0
0
0
0
0
1
0
1
0
4
0
0
2
0
0
0
0
0
3
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
1
1
2
0
1
0
2
0
0
2
0
1
0
0
1
0
0
2
0
0
2
0
0
1
0
0
2
2
2
0
0
0
2
2
3
0
0
2
0
2
1
2
0
1
0
2
0
1
1
0
0
1
0
1
0
1
1
1
1
0
0
0
1
0
0
2
0
2
1
0
0
0
2
0
0
1
0
1
2
1
2
0
1
2
2
0
2
2
1
1
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
1
1
1
1
0
2
0
0
1
0
0
1
0
0
1
2
1
2
0
0
1
0
2
0
1
0
0
1
0
2
1
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
1
2
0
1
1
0
3
0
2
1
1
1
1
2
2
0
0
1
0
0
1
2
1
4
1
1
3
0
0
1
0
0
0
2
0
2
2
0
0
2
1
1
0
0
0
0
1
0
0
2
0
0
0
0
0
2
1
1
0
0
0
1
2
0
1
1
0
0
0
1
2
0
0
3
1
2
1
2
2
1
2
2
0
6
2
0
0
1
0
1
2
3
2
0
1
2
1
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
1
0
1
0
2
0
0
2
0
0
1
0
1
1
0
0
0
0
0
0
1
2
0
0
0
4
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
2
1
0
2
0
2
2
0
0
0
2
0
0
2
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
1
0
1
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
2
0
0
0
2
0
2
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
1
1
0
0
2
1
0
2
1
2
0
0
1
0
0
1
0
0
0
0
0
0
2
0
1
3
0
0
1
0
0
0
1
1
0
0
0
2
0
0
2
0
1
1
2
0
0
0
2
0
1
0
0
0
1
0
0
0
0
2
0
0
0
2
2
1
0
0
2
2
0
0
0
1
1
1
0
0
0
0
0
2
2
0
0
1
0
3
0
2
0
0
1
3
0
1
1
1
0
1
2
0
2
2
1
3
0
0
3
0
0
0
0
0
2
1
2
0
0
1
1
2
0
0
1
0
2
0
1
0
1
0
0
0
1
0
0
2
2
1
2
0
2
3
1
1
0
1
0
0
0
0
1
2
0
2
2
0
0
0
0
4
0
0
0
2
0
1
0
0
4
1
0
0
2
0
0
0
1
1
1
0
1
1
0
2
1
0
2
4
1
0
2
0
2
0
0
0
2
0
1
0
2
0
2
0
0
1
0
1
0
0
0
0
1
2
1
2
0
0
2
0
1
0
1
0
0
0
3
0
0
2
0
0
0
1
0
1
2
1
0
0
0
0
0
2
0
1
0
0
1
1
0
1
1
0
0
0
0
0
2
1
0
1
0
1
2
2
2
0
1
0
0
0
0
0
1
0
2
0
1
0
0
1
1
0
0
0
0
0
2
2
0
0
0
0
0
2
0
1
0
2
0
0
2
2
0
1
2
2
0
1
0
2
0
0
1
0
2
1
0
1
0
0
0
0
2
1
0
1
0
0
1
1
0
2
0
1
1
1
0
1
0
0
0
2
0
1
2
2
1
2
0
1
1
2
2
1
0
0
0
2
0
2
0
0
0
0
1
1
0
0
0
1
1
2
0
1
1
0
1
1
1
2
0
0
2
0
0
1
2
0
1
0
0
1
1
0
1
0
2
1
0
0
1
0
0
0
0
0
1
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
1
3
1
2
2
1
1
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
1
0
1
2
0
0
0
0
0
0
2
2
0
0
0
1
0
1
2
0
0
2
0
0
1
1
0
2
0
2
0
0
2
1
0
0
1
2
0
1
2
2
0
2
0
1
1
1
2
2
0
6
1
0
0
0
1
0
2
0
0
2
0
0
0
1
1
0
0
0
0
0
1
1
2
0
0
2
0
0
1
1
2
1
1
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
1
2
0
1
0
2
2
2
0
2
0
1
1
1
1
0
2
1
0
0
0
0
0
2
0
0
0
0
1
2
1
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
1
0
0
0
0
2
0
0
0
0
1
0
2
0
1
2
1
1
1
1
1
0
2
2
2
0
1
0
0
0
0
0
2
1
0
1
2
2
0
2
2
2
0
1
0
2
0
0
0
0
1
0
2
1
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
1
0
2
2
2
1
1
1
1
0
1
0
0
2
1
2
0
0
1
0
1
0
2
0
2
0
0
1
1
0
1
2
0
2
1
0
0
0
2
0
4
2
0
0
1
0
3
1
2
1
0
0
0
2
0
0
2
1
0
0
1
1
0
2
1
1
0
0
1
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
1
0
1
1
2
0
2
0
2
1
0
1
2
0
0
0
2
0
0
0
1
1
0
2
0
1
2
1
4
1
0
0
0
1
2
1
0
0
1
0
0
2
0
2
2
1
0
0
1
0
0
2
0
0
0
1
2
1
0
0
2
0
2
0
0
0
0
1
1
0
0
1
0
0
2
0
0
0
0
1
1
1
0
0
2
2
3
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
1
0
2
0
0
0
0
0
0
2
1
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
2
1
0
1
0
2
2
0
0
1
3
1
2
0
0
1
2
0
2
0
1
3
1
1
0
0
0
2
2
2
2
0
2
0
0
0
0
0
1
0
0
1
1
2
0
0
1
0
0
0
2
0
0
1
0
2
0
0
1
1
0
0
0
2
0
1
2
0
0
1
0
0
1
2
2
1
0
0
0
1
0
0
0
0
0
1
0
0
0
3
1
2
2
0
0
1
1
1
1
0
0
1
2
0
0
0
2
0
2
0
1
0
1
1
1
1
0
0
2
0
1
1
0
2
2
0
1
0
0
0
0
0
0
2
0
0
0
1
2
1
0
0
0
1
0
0
0
0
1
3
1
0
0
0
2
1
0
0
2
1
1
0
0
0
0
1
1
0
0
0
0
2
2
2
0
0
1
1
0
1
0
2
2
2
0
0
0
0
1
2
0
0
2
0
0
0
1
0
2
1
0
2
2
2
0
1
0
0
1
1
1
0
0
0
1
2
0
1
1
2
0
2
0
0
0
0
1
1
0
1
1
0
0
0
0
1
0
0
0
0
2
2
0
0
1
2
0
0
1
1
1
1
2
2
2
0
0
2
0
1
1
0
0
2
1
1
1
2
1
0
0
0
0
0
1
2
0
1
0
0
1
1
0
0
0
2
0
1
0
1
2
0
1
2
2
0
0
1
0
0
2
0
0
0
1
0
0
0
0
1
0
0
1
1
0
1
2
2
0
2
2
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
1
2
1
0
2
1
1
0
2
0
0
1
0
1
0
1
1
1
0
0
0
1
0
0
2
0
0
0
0
2
1
0
0
0
0
0
1
2
0
0
0
1
1
1
0
0
0
0
2
2
0
0
2
0
0
0
0
0
1
2
0
1
1
0
2
1
0
0
0
0
0
0
3
0
1
0
2
0
1
1
2
0
0
0
0
0
2
2
1
1
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
1
2
2
1
0
0
0
2
0
2
0
1
1
0
1
1
0
0
0
1
0
0
0
0
0
0
1
2
0
3
1
1
1
0
1
2
1
1
2
2
0
0
0
0
1
0
0
3
0
0
2
0
0
1
0
0
2
2
1
2
0
1
0
0
1
2
1
0
1
2
0
0
0
2
0
2
1
1
0
0
2
2
2
0
1
0
2
0
2
0
1
1
0
1
0
0
0
0
0
1
1
0
0
3
0
1
1
0
2
0
0
0
2
0
2
3
2
0
2
0
0
0
2
1
1
0
0
0
0
0
0
2
2
2
0
0
0
1
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
1
1
2
0
0
1
2
1
0
1
2
0
1
0
1
0
1
1
1
0
0
0
0
1
1
1
1
2
1
0
2
0
1
2
2
0
0
3
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
2
1
0
0
1
0
1
2
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
2
1
0
0
1
0
2
0
0
0
0
0
0
0
2
2
0
1
0
2
0
2
1
0
1
2
0
2
1
2
0
0
1
0
0
1
1
0
1
0
1
2
1
0
0
0
1
2
0
0
2
2
2
2
2
0
0
1
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
1
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
1
1
0
2
0
0
0
2
2
0
0
0
0
2
0
0
0
0
1
0
1
2
2
0
0
0
1
1
5
0
1
2
0
1
2
0
0
2
0
0
0
2
2
1
0
0
2
0
0
0
0
0
1
0
1
2
0
0
1
0
0
0
0
2
1
0
0
0
1
0
0
1
0
0
1
1
0
3
0
0
0
3
2
0
1
1
0
1
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
1
0
1
0
1
0
2
0
1
0
0
1
0
1
1
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
2
0
1
9
2
1
0
0
0
1
1
0
1
1
1
1
1
0
0
0
1
1
0
1
0
0
0
3
0
0
0
0
0
0
0
0
3
1
0
0
0
0
1
3
2
0
0
0
0
0
0
0
0
0
0
1
2
0
1
2
0
2
2
0
1
0
0
0
2
1
0
0
1
1
0
0
0
0
2
2
2
0
0
0
0
1
0
0
0
1
1
0
1
0
1
0
0
0
0
1
0
1
0
1
2
2
0
0
0
0
2
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
4
0
0
1
3
1
0
2
2
2
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
2
1
0
0
1
1
3
1
1
0
1
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
2
1
0
0
0
2
0
2
0
0
0
0
0
2
0
0
1
0
2
0
0
2
0
0
0
2
0
1
0
1
1
2
0
0
1
0
2
2
0
3
1
2
1
0
0
1
0
0
1
1
3
0
0
0
2
0
1
1
2
1
2
0
3
1
2
1
0
0
1
0
0
0
0
1
0
2
1
0
1
2
2
0
0
0
0
1
0
1
2
0
0
0
3
1
0
5
2
0
0
2
0
1
0
2
0
0
0
2
2
0
2
0
0
2
1
0
3
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
1
1
2
0
2
1
1
0
2
1
0
0
0
4
0
0
0
1
0
0
2
0
0
1
1
1
2
1
0
0
1
0
2
0
2
0
0
1
0
2
1
3
0
0
0
0
2
0
0
0
0
0
1
2
0
0
1
0
1
0
1
0
1
0
2
1
1
2
2
0
2
1
1
2
1
1
1
0
1
1
1
1
2
1
1
0
0
0
1
0
1
1
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
1
0
0
0
2
0
1
0
0
0
0
1
0
0
2
0
1
1
0
0
0
2
0
2
0
0
0
2
1
0
1
0
0
0
1
0
0
0
2
0
1
0
0
0
1
0
1
1
0
0
0
2
0
0
2
2
2
1
0
1
1
0
1
0
0
1
0
0
1
2
2
0
1
0
2
1
0
1
0
0
0
0
0
0
0
1
4
1
0
0
0
1
0
0
0
0
1
0
2
0
2
0
0
2
0
2
1
0
1
2
1
0
1
0
1
0
0
0
2
2
0
0
5
0
2
1
0
0
2
2
2
0
1
0
0
0
1
0
0
0
0
3
1
1
0
2
0
2
0
1
0
0
0
0
0
2
2
2
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
1
0
1
1
1
0
0
0
0
2
0
0
2
0
0
0
0
2
0
1
2
2
1
0
1
0
2
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
2
0
2
0
0
0
1
1
0
1
1
2
0
0
0
2
2
0
2
0
0
0
0
0
0
2
2
0
0
1
0
2
1
5
4
2
0
0
0
2
3
1
1
1
0
0
0
2
0
0
0
1
3
2
0
0
0
0
2
0
2
1
0
2
2
2
0
0
0
0
0
1
2
0
0
0
0
2
1
0
1
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
2
0
2
1
0
0
2
0
2
1
0
1
1
0
0
1
2
0
0
0
0
0
2
1
0
0
2
2
1
2
2
2
0
0
0
0
0
0
1
0
3
0
1
1
2
1
0
1
0
2
1
0
1
1
0
2
1
0
2
0
2
0
0
0
0
0
0
0
2
2
0
2
0
2
0
1
0
1
2
0
0
1
0
3
0
0
0
3
3
0
1
0
0
1
1
0
2
0
2
1
1
2
1
1
0
2
1
0
0
0
2
0
0
1
0
2
2
0
0
2
1
1
0
3
0
3
0
2
0
2
2
0
0
0
0
2
1
1
0
2
2
0
0
1
1
0
0
0
1
0
2
0
0
1
1
1
1
2
5
0
1
0
0
0
0
0
0
1
2
0
0
2
0
0
1
1
1
2
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
1
1
1
0
1
0
1
2
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
1
3
0
0
1
1
1
1
0
1
0
1
1
0
0
0
1
0
2
0
0
1
0
1
0
1
0
0
1
2
0
2
0
0
1
1
1
2
0
0
2
0
0
2
0
0
0
1
2
1
0
2
0
0
1
0
0
0
2
0
0
0
0
1
0
1
0
0
1
2
0
0
2
0
2
0
0
1
1
0
2
0
1
3
2
0
2
0
2
1
0
1
0
1
1
0
1
0
0
0
0
2
2
2
2
0
0
2
2
0
0
2
0
0
2
0
2
0
1
1
2
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
2
1
0
1
0
0
2
0
2
0
2
0
0
1
0
2
1
1
0
0
0
0
2
1
2
0
0
1
0
0
0
1
0
1
0
1
0
0
0
1
0
2
2
1
1
2
0
0
3
2
0
3
0
0
0
0
1
0
1
0
0
1
3
2
0
1
1
0
1
0
0
0
0
0
0
2
2
0
0
1
1
0
0
1
0
0
2
2
0
0
1
0
2
2
0
1
0
0
1
1
0
2
0
1
0
0
4
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
1
1
0
0
2
1
2
0
0
1
0
0
0
2
1
0
0
0
1
0
1
2
0
2
2
0
0
0
2
1
2
1
1
2
0
2
3
0
1
2
0
0
2
1
0
2
1
0
0
0
0
2
0
0
0
0
0
2
2
0
2
0
0
1
2
0
0
0
1
2
0
0
5
2
2
1
0
2
0
2
0
0
0
2
1
0
1
0
1
0
2
0
0
1
1
0
0
0
2
0
1
2
0
0
1
0
1
0
1
0
0
0
0
0
1
2
0
0
1
1
0
2
2
0
0
0
1
1
1
0
0
2
2
0
0
3
0
1
1
0
0
1
0
2
0
2
0
0
0
2
0
2
2
0
1
0
1
1
1
2
2
0
2
0
0
0
0
1
1
0
0
2
1
0
0
0
1
0
0
1
4
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
1
3
1
0
1
0
0
0
0
0
1
0
1
0
0
0
2
1
0
0
0
0
0
1
1
2
0
5
0
0
2
0
0
0
0
0
1
6
0
0
0
0
0
0
0
0
2
0
2
1
0
0
2
2
1
0
0
0
0
0
2
1
1
0
0
0
0
0
0
1
2
0
0
0
0
0
1
2
2
1
0
0
1
1
1
0
0
3
0
2
0
2
0
0
2
1
0
0
3
0
0
0
0
2
3
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
2
0
1
1
0
0
0
0
1
0
2
3
0
2
0
2
1
2
0
0
0
3
0
0
1
1
0
0
0
3
2
1
0
0
0
0
2
0
0
1
0
0
1
0
0
0
1
0
2
0
1
0
1
0
0
1
1
1
0
0
2
2
1
2
0
0
0
1
0
2
0
1
1
1
0
2
1
1
2
0
1
0
0
0
1
1
2
2
0
0
0
0
0
0
0
2
1
1
0
1
1
0
0
1
0
1
2
0
0
1
1
1
0
1
0
1
0
1
0
2
0
2
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
3
0
1
0
2
0
1
1
3
0
1
0
1
0
0
0
2
1
2
1
0
0
0
0
3
1
0
2
0
3
0
0
0
0
0
0
1
0
1
0
0
2
0
1
2
0
0
0
1
0
0
0
0
2
0
1
0
0
0
1
0
0
0
1
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
2
1
0
0
0
0
1
0
1
0
0
0
0
0
2
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
1
0
0
2
0
0
2
2
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
1
0
2
1
0
1
3
2
1
2
1
0
0
0
0
0
0
0
1
5
0
1
0
0
0
2
0
0
1
0
2
2
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
1
1
0
2
0
0
0
0
0
0
2
1
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
1
0
0
0
2
1
1
2
1
0
0
0
2
1
2
0
0
1
0
1
0
2
0
1
2
0
1
0
0
4
1
0
2
2
0
1
0
2
0
1
0
0
2
0
2
0
2
0
1
2
0
0
0
2
2
0
0
0
3
1
2
0
2
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
1
2
0
0
1
0
1
0
0
0
0
1
0
0
3
1
0
1
0
1
1
2
2
2
2
0
0
2
0
2
0
2
1
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
2
3
0
1
0
0
0
0
1
0
0
1
0
0
0
1
2
1
0
0
0
0
0
0
1
1
2
1
2
3
0
1
1
2
1
1
1
0
1
0
0
1
1
2
2
2
0
0
0
0
0
0
0
1
0
2
0
0
0
2
2
1
2
0
2
1
2
0
0
0
0
1
0
0
0
1
3
0
2
1
0
0
2
0
1
2
2
0
0
0
0
0
0
1
1
0
0
2
0
2
1
2
0
0
0
1
0
0
0
1
1
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
2
2
3
0
1
0
0
0
2
1
0
0
1
0
1
0
0
1
4
0
0
1
1
2
1
1
0
1
0
0
0
0
1
1
0
1
1
1
0
2
0
0
1
0
2
0
0
0
1
1
0
1
0
2
1
1
1
2
0
0
1
2
0
1
1
0
1
0
0
2
1
0
0
1
0
0
1
2
1
0
1
1
1
1
1
0
0
0
0
0
0
1
0
1
1
1
1
0
2
0
1
0
1
1
1
2
0
0
0
2
3
0
2
1
1
0
0
1
1
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
2
0
2
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
1
0
0
0
2
0
2
2
2
1
1
1
0
1
0
4
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
1
2
1
2
1
0
1
0
2
0
2
2
0
0
2
1
2
1
2
0
0
2
0
0
1
0
3
0
0
1
0
0
2
1
1
0
2
2
0
2
1
0
1
0
1
1
0
1
0
0
2
2
2
0
2
1
0
2
0
1
1
0
0
0
1
0
0
0
2
0
0
1
1
0
0
2
0
0
2
0
0
1
1
0
0
0
0
0
2
1
0
2
0
0
1
1
0
1
0
1
2
0
1
1
1
3
1
0
0
1
1
1
1
0
0
1
0
0
0
0
0
0
0
0
2
1
0
2
0
0
1
0
0
2
0
2
2
2
2
1
0
0
2
0
2
1
1
1
1
0
2
1
0
5
1
0
0
2
0
1
0
0
2
1
1
1
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
3
1
1
0
1
0
0
2
0
0
0
1
0
1
0
2
1
0
2
0
1
0
0
0
0
0
0
0
2
0
1
2
0
0
1
0
0
2
0
0
0
0
1
0
0
1
2
0
0
0
0
0
2
0
0
2
0
2
2
2
0
0
0
0
0
1
0
0
2
2
0
3
0
0
0
3
2
0
2
0
0
0
2
1
0
2
0
0
0
0
2
0
0
1
0
0
2
0
1
2
0
1
1
0
0
2
0
0
0
0
2
0
2
3
0
0
2
0
0
1
1
0
0
0
1
0
1
0
0
1
2
1
0
0
1
0
0
2
1
2
0
1
0
0
2
1
0
2
1
0
2
0
0
0
1
0
0
0
0
0
1
2
1
0
0
0
0
0
0
1
1
0
2
7
0
2
1
1
1
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
1
0
0
1
0
0
4
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
1
0
0
2
0
1
1
0
0
0
1
1
0
2
0
0
2
2
0
2
0
2
0
1
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
2
2
0
3
0
1
0
0
2
1
0
1
1
1
3
3
0
2
0
0
1
1
0
0
1
0
1
0
3
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
1
1
1
0
0
2
0
0
2
2
0
1
0
0
0
1
2
0
1
2
1
1
1
2
0
1
0
0
1
0
0
0
1
0
0
1
0
1
0
0
4
0
0
1
0
1
0
1
0
0
0
1
0
0
1
0
0
1
0
3
1
1
0
0
0
2
0
1
0
0
1
0
0
2
2
1
0
0
1
1
1
0
0
1
1
2
0
0
0
1
0
0
0
0
0
0
2
6
0
0
1
1
0
2
3
1
0
2
0
0
1
1
0
1
2
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
2
2
0
1
1
1
2
0
1
0
2
2
1
0
0
1
0
1
0
0
2
1
1
0
1
0
0
2
1
0
1
1
0
2
1
0
2
0
1
1
0
0
2
0
0
2
1
0
0
2
0
0
2
2
2
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
1
0
3
1
1
0
0
1
1
0
0
2
2
0
1
2
0
2
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
2
2
0
0
0
1
2
2
1
0
2
0
0
0
0
0
0
3
0
0
0
0
1
0
1
1
2
3
0
1
2
0
2
0
0
0
0
0
0
1
0
1
0
2
2
1
3
1
1
1
0
1
0
2
0
1
0
4
0
0
0
0
0
0
1
2
0
0
1
0
0
0
2
0
1
1
0
0
0
0
1
2
0
1
1
0
0
0
1
0
1
1
2
1
0
2
2
0
0
1
0
1
0
1
0
2
0
0
0
0
0
0
2
1
1
2
1
0
0
1
0
1
0
0
0
1
2
0
3
2
1
0
2
1
1
0
0
2
1
0
2
1
0
1
2
0
1
0
1
0
1
0
0
1
0
0
0
2
0
0
1
2
0
2
3
1
0
2
0
4
1
1
1
0
0
0
0
0
1
0
2
1
2
0
0
0
2
0
2
0
0
1
1
0
0
2
0
0
2
0
1
0
1
1
0
2
1
0
0
0
2
0
0
0
1
0
0
0
0
0
2
2
0
1
0
0
1
0
2
0
0
1
0
0
2
0
2
2
0
1
0
3
1
0
1
2
0
2
0
0
0
1
2
0
2
0
0
3
0
1
0
1
0
1
0
4
1
2
0
2
1
0
0
0
0
1
2
0
0
0
0
1
0
1
2
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
3
0
0
2
1
0
2
1
0
3
1
0
0
0
2
0
0
2
0
0
1
1
0
2
0
2
0
0
0
2
2
0
2
2
0
0
1
0
0
0
1
1
5
1
2
1
0
0
1
0
3
0
0
1
0
0
0
1
0
1
0
0
0
2
1
2
0
3
0
2
2
1
0
2
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
2
0
1
2
2
1
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
0
2
0
0
1
1
0
1
0
0
2
0
2
2
1
1
0
0
2
0
0
1
0
0
0
1
1
1
1
1
2
1
1
2
2
0
1
0
1
4
2
0
0
0
1
0
0
7
2
0
0
0
2
1
0
0
2
0
0
2
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
1
1
0
1
1
0
0
4
2
0
2
1
2
0
1
0
0
2
2
0
0
0
1
3
1
1
2
1
1
0
0
1
2
2
0
2
2
1
1
0
2
0
4
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
1
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
1
0
0
2
0
1
1
0
0
0
1
0
2
0
0
0
2
1
1
0
0
0
1
0
0
1
0
0
0
0
2
1
1
1
0
0
0
0
0
2
1
0
2
0
0
2
0
0
0
0
2
0
1
1
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
1
1
0
1
0
2
0
2
0
0
0
0
2
2
3
0
1
2
0
2
0
0
1
0
0
0
0
2
0
1
2
0
0
0
0
0
0
1
1
0
0
1
0
0
2
0
2
0
2
0
1
0
1
0
0
0
1
2
0
0
0
0
0
0
2
0
1
1
1
1
0
0
0
0
2
0
0
1
0
2
0
0
0
5
1
0
0
2
0
2
0
0
2
0
2
0
1
0
2
1
0
1
2
2
0
0
1
0
1
0
0
0
0
1
0
0
2
1
3
0
1
0
0
1
1
0
2
0
3
0
0
1
2
0
0
2
0
2
1
0
0
0
0
2
1
2
1
0
0
0
0
2
0
2
1
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
1
1
0
0
0
0
0
1
1
0
0
1
3
0
0
0
1
0
0
1
0
2
2
1
0
0
1
0
2
0
2
0
0
1
0
1
2
0
1
0
0
0
1
0
1
1
0
0
0
0
2
0
1
0
1
1
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
2
0
0
1
0
0
1
0
0
1
0
2
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
2
2
0
2
2
1
0
0
0
0
0
3
0
1
3
2
0
1
2
0
2
0
0
0
2
2
1
0
0
0
0
1
2
1
1
2
0
0
2
0
1
0
0
1
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
3
0
1
2
1
3
0
0
0
1
2
0
0
0
0
2
0
1
0
0
0
1
1
2
2
3
0
0
0
0
0
0
1
3
1
2
2
0
0
0
0
1
1
2
1
2
0
0
0
2
0
1
2
1
0
0
1
1
2
2
0
0
1
0
2
1
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
1
1
0
2
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
2
1
0
0
0
0
0
1
0
1
1
3
2
0
0
1
0
1
0
0
0
0
0
1
2
0
0
0
1
0
0
1
1
2
0
0
1
0
2
0
2
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
2
2
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
1
0
1
0
0
2
2
0
0
2
0
0
0
2
1
2
0
0
0
2
2
1
0
0
1
2
0
1
0
1
0
1
2
0
0
0
0
2
0
0
2
0
1
0
0
2
1
0
1
3
0
0
0
3
2
2
0
0
2
0
0
1
1
0
0
1
0
2
1
1
0
0
0
1
0
0
1
0
1
1
0
1
1
2
2
1
0
0
1
0
0
0
1
2
0
0
2
2
0
0
0
0
1
0
0
0
0
0
1
0
0
2
1
0
1
2
0
0
0
0
0
0
0
0
2
0
1
2
0
0
1
0
0
2
0
0
1
2
2
1
0
2
2
0
1
0
0
1
0
0
0
0
0
0
4
2
0
2
0
0
0
1
0
0
0
2
2
0
0
2
1
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
1
1
0
1
0
0
1
0
2
0
0
2
0
0
0
2
0
2
2
0
0
1
0
1
1
1
0
3
0
2
1
0
1
0
1
2
2
2
0
0
0
1
1
2
1
2
0
0
1
1
1
0
2
0
0
0
0
2
1
0
1
0
0
1
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
2
2
0
1
1
0
1
2
0
1
2
0
1
1
2
0
2
0
1
2
2
5
1
0
1
0
0
0
0
0
2
0
0
0
2
1
0
0
2
2
0
0
0
0
0
0
1
0
2
0
2
0
2
0
1
2
0
2
1
0
0
0
1
1
2
1
0
0
1
0
0
0
0
0
0
1
2
0
2
1
0
0
2
1
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
1
0
1
1
2
0
0
0
0
1
0
0
2
2
0
5
0
1
3
0
2
0
0
2
0
0
0
0
2
0
0
0
1
0
0
2
0
1
0
1
0
0
0
2
0
0
1
0
2
0
0
1
0
0
0
0
2
2
0
1
0
1
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
1
1
1
1
0
1
1
3
1
1
0
0
2
1
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
3
0
2
1
1
0
0
2
0
0
1
0
0
1
1
1
2
0
2
0
2
0
0
0
0
0
0
2
2
0
0
2
2
0
0
1
4
1
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
1
0
1
2
0
0
2
0
0
0
1
0
1
0
0
1
0
0
2
0
0
2
0
2
0
0
1
0
1
1
0
1
1
0
1
2
1
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
1
0
1
0
0
1
1
0
0
2
0
0
2
1
2
2
1
2
0
0
1
1
0
0
0
0
1
0
0
2
0
1
1
1
0
2
0
0
1
0
0
3
2
2
1
1
0
0
1
2
0
2
2
0
0
0
1
0
0
0
0
1
0
2
0
0
1
0
2
0
0
1
0
1
1
2
1
2
0
0
0
1
0
0
0
2
0
0
0
1
0
1
0
0
1
1
2
2
0
0
2
0
2
0
2
0
0
0
0
2
1
2
0
0
0
1
2
0
1
1
0
1
0
1
0
3
2
0
0
0
1
0
0
2
2
0
0
1
2
0
2
0
0
1
0
2
1
0
0
0
1
0
1
1
0
1
0
1
0
2
1
2
1
1
0
1
0
0
0
0
1
0
2
0
0
0
0
0
2
1
2
2
0
2
1
1
0
0
0
1
1
0
0
2
2
2
0
2
1
0
0
2
0
2
1
0
0
2
2
0
1
0
0
0
0
2
2
0
0
0
4
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
1
0
1
0
1
0
0
0
1
1
1
0
1
0
0
0
0
1
0
2
1
2
0
0
0
0
2
0
1
0
1
0
2
0
0
2
0
0
0
2
0
2
1
1
0
0
0
0
0
0
0
0
0
1
2
0
1
0
2
1
1
2
0
0
0
0
0
2
0
0
1
0
0
1
1
2
1
0
0
2
0
0
1
0
2
0
0
0
0
0
0
1
1
2
0
2
0
0
0
0
2
1
0
2
0
1
0
2
3
0
0
1
1
1
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
2
1
0
0
1
1
0
1
0
0
2
0
1
1
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
1
1
0
0
2
0
0
1
2
0
0
2
3
2
0
1
1
1
1
0
1
0
0
0
0
1
0
1
0
2
0
0
2
1
0
1
2
0
0
0
0
0
1
1
0
2
2
0
1
0
1
2
0
2
0
0
1
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
1
0
1
0
2
0
2
1
2
2
1
0
0
0
0
2
0
0
0
1
1
1
0
1
0
2
1
1
2
1
0
1
1
0
2
0
2
0
0
0
0
1
2
0
0
1
0
0
2
1
1
0
1
2
0
1
2
0
1
0
0
2
0
0
2
1
2
0
0
1
1
1
0
1
0
2
1
0
0
1
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
2
4
1
2
0
0
2
1
0
1
2
0
0
2
2
0
0
0
1
2
0
0
1
1
1
0
3
0
0
0
0
1
1
0
1
1
2
0
0
2
0
2
2
2
0
0
5
0
1
0
0
1
0
3
0
2
1
1
0
1
0
1
0
2
0
0
2
1
0
0
2
2
0
0
1
2
0
1
1
0
0
2
1
1
1
2
0
0
0
0
0
0
0
1
0
1
2
2
0
1
2
0
0
1
1
0
1
1
0
0
0
2
2
1
0
0
1
2
0
0
2
0
1
1
1
0
0
0
1
0
0
1
0
0
1
1
0
0
1
0
0
0
0
1
3
0
1
0
1
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
1
2
0
1
2
1
0
0
0
1
1
1
0
1
0
1
0
0
0
2
2
0
0
2
0
2
0
0
2
0
2
2
1
1
3
2
0
0
0
2
1
2
2
0
0
0
2
2
0
1
0
1
1
0
0
0
0
3
1
2
0
2
1
1
0
0
0
0
0
0
2
1
0
1
1
2
1
2
0
0
1
2
1
0
2
0
1
0
2
2
0
0
0
2
0
1
2
0
1
1
0
2
0
1
1
1
1
0
0
1
2
1
0
0
2
1
1
0
0
0
0
0
2
2
1
0
0
0
3
0
2
0
0
1
0
0
2
0
1
0
0
0
0
1
0
1
1
0
1
0
2
1
0
0
2
1
1
0
1
2
0
2
1
2
0
0
1
1
0
2
1
1
0
2
1
0
2
0
0
0
1
0
1
0
0
0
1
2
0
0
2
1
0
0
0
1
1
1
0
2
3
0
1
0
4
0
2
1
1
2
1
0
0
1
2
1
0
0
1
1
0
0
0
2
0
2
0
0
2
1
0
0
0
0
1
0
0
0
1
1
5
0
1
0
0
0
0
0
3
2
0
7
2
1
1
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
1
0
0
1
0
0
1
2
2
0
0
0
1
0
1
0
0
1
2
0
0
0
0
1
0
2
1
0
0
2
0
0
0
0
0
0
2
1
2
0
0
1
0
2
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
1
0
2
0
0
1
0
0
0
0
2
0
0
0
2
0
1
1
0
0
0
1
1
0
0
1
0
0
0
1
1
1
1
0
0
2
1
2
0
0
0
2
0
1
2
0
0
2
0
2
0
0
1
0
0
0
2
0
1
0
2
0
0
1
1
2
0
0
3
0
0
2
0
0
0
2
0
0
0
1
0
0
1
4
0
1
2
0
1
0
0
0
1
2
0
0
1
0
2
0
0
0
0
0
0
0
1
0
2
2
0
0
0
2
1
0
1
1
0
0
1
0
0
2
0
2
0
0
0
0
0
1
1
0
0
0
0
2
0
2
1
0
0
1
1
0
0
0
0
0
0
1
3
0
0
1
2
0
0
0
2
0
1
0
2
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
1
0
0
1
0
0
2
0
1
1
0
0
0
0
0
0
2
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
1
0
2
0
1
0
2
2
0
1
1
1
0
1
0
0
1
0
1
1
0
0
3
0
2
0
2
0
0
1
2
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
2
0
0
0
1
0
0
1
0
0
2
0
0
3
1
0
0
1
1
0
1
1
0
2
2
1
2
0
0
0
0
1
0
1
2
1
1
0
0
1
1
0
0
0
2
0
1
0
1
0
1
0
1
1
1
0
1
1
1
1
0
0
0
1
0
0
2
0
0
0
0
0
0
2
1
0
0
1
1
1
2
0
0
0
3
0
0
0
2
2
0
0
1
1
2
2
0
2
2
1
0
0
0
1
0
2
1
0
0
2
0
2
1
0
0
0
1
0
0
0
7
0
1
0
3
0
2
2
0
2
0
0
1
3
0
0
0
0
2
0
0
0
0
0
2
0
1
1
1
0
0
0
2
0
0
1
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
1
2
2
1
0
0
1
0
0
0
0
2
1
2
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
1
0
3
0
0
0
0
0
3
0
2
0
0
0
0
3
0
1
0
1
1
1
1
1
1
0
1
1
0
1
1
2
0
1
2
2
2
1
0
1
2
1
1
1
1
0
2
0
0
1
0
1
0
1
0
1
1
0
2
2
0
0
1
1
1
2
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
1
2
1
0
2
0
2
1
0
0
1
0
1
2
0
0
0
1
0
0
2
1
1
3
0
0
1
4
0
0
0
0
0
0
1
0
1
0
0
0
2
1
0
0
2
0
0
2
2
0
2
2
2
0
2
1
1
0
2
0
2
0
2
1
0
0
1
0
1
0
1
1
1
0
2
0
2
0
0
0
0
0
0
3
2
0
0
2
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
1
3
0
0
2
0
0
1
1
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
2
2
2
0
0
0
0
0
0
2
0
3
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
2
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
2
0
0
1
0
2
0
0
0
0
1
1
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
1
2
2
0
0
2
1
0
0
0
1
2
1
0
0
1
0
1
1
0
0
2
1
0
2
0
1
0
1
0
1
2
0
2
0
0
1
0
2
2
1
1
0
0
0
2
0
2
1
2
2
2
2
0
1
2
0
1
0
0
0
2
0
0
1
0
1
2
0
1
2
2
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
1
1
0
1
0
0
2
0
1
2
0
1
2
0
0
1
2
0
0
1
0
0
2
0
0
2
2
0
1
0
1
0
2
3
1
0
0
2
0
0
0
0
0
2
1
0
2
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
1
0
1
0
0
1
1
0
1
0
0
1
0
1
0
2
0
0
2
2
1
2
0
0
0
1
0
2
0
0
0
5
0
1
0
0
2
0
1
0
2
1
0
0
1
1
1
2
0
1
0
2
0
0
0
1
1
0
2
0
0
3
2
0
2
0
0
0
0
0
2
0
0
2
0
0
3
2
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
3
2
0
0
1
3
2
2
1
0
0
0
1
1
2
3
2
1
0
1
2
2
0
2
1
1
4
2
0
0
0
0
2
0
1
2
1
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
2
2
0
0
0
1
1
0
0
0
1
1
0
1
1
1
1
0
0
0
0
1
0
0
0
0
0
2
0
2
1
0
0
0
0
2
0
0
0
0
0
0
2
0
2
1
0
2
1
1
0
1
0
2
2
0
2
1
1
0
0
0
2
0
0
1
0
0
0
0
1
0
0
1
1
1
1
1
0
0
2
0
1
1
0
2
0
2
1
0
2
2
3
1
2
0
0
1
2
1
2
0
2
2
2
3
0
0
3
2
2
0
0
0
2
0
1
0
0
3
0
0
0
0
0
1
2
0
0
0
0
2
0
1
0
1
0
0
2
2
0
1
0
0
1
2
0
0
0
1
0
3
0
0
2
0
0
1
0
1
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
2
1
0
1
0
0
0
2
1
0
0
2
0
2
0
2
0
1
0
0
0
2
0
0
0
1
1
2
0
0
1
1
2
3
1
0
1
1
0
0
0
0
0
0
0
2
2
2
0
1
2
0
2
2
1
0
0
0
0
0
0
0
2
2
0
1
0
1
2
2
1
1
0
2
1
0
0
0
0
0
0
0
0
1
1
0
1
1
2
0
2
0
2
2
0
1
1
0
0
1
2
1
0
0
0
2
0
1
0
1
0
2
0
0
1
0
0
0
0
0
2
1
0
0
2
1
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
2
0
2
1
2
0
2
0
1
1
1
0
0
0
0
0
2
0
2
0
2
0
0
2
0
2
0
0
0
2
0
0
2
1
2
1
2
1
3
1
0
0
2
2
2
0
0
1
0
1
3
0
0
1
2
5
2
0
0
0
1
0
2
1
0
2
0
0
1
0
1
2
0
2
0
3
1
0
0
0
2
0
0
1
0
0
1
0
1
1
0
1
0
1
0
1
1
0
1
0
0
0
1
0
1
0
0
0
0
1
2
0
1
0
0
0
0
1
0
0
4
2
0
1
0
0
2
0
1
0
0
1
2
0
0
0
0
0
0
2
0
0
0
2
0
1
0
1
2
0
0
2
0
0
0
0
0
0
0
0
1
15
1
3
1
2
1
1
1
0
0
0
0
1
1
2
0
0
0
0
1
0
0
0
0
0
0
2
1
0
1
2
3
0
0
0
2
0
0
0
2
2
0
1
0
0
2
0
0
0
1
0
2
0
3
0
1
0
1
1
0
0
2
0
2
0
5
1
0
0
2
2
2
2
1
0
2
1
0
2
0
0
0
1
1
1
0
2
0
0
2
1
2
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
1
0
1
1
0
1
1
2
1
1
0
0
0
0
0
0
0
1
2
2
0
0
2
0
1
2
2
0
1
0
0
0
0
1
0
0
1
1
1
0
0
1
2
2
1
0
0
1
2
0
0
0
0
2
0
3
0
2
0
0
2
1
2
0
0
2
0
2
0
0
0
1
0
1
0
2
2
0
0
2
0
0
2
1
0
1
1
0
0
1
0
0
1
1
2
2
1
0
0
1
0
0
2
1
0
7
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
2
2
2
0
2
0
1
0
0
1
1
0
1
0
0
2
0
0
0
2
0
0
0
0
1
1
0
0
2
0
2
0
0
0
0
1
2
0
0
0
0
0
2
0
0
2
0
0
0
2
3
2
0
0
0
0
2
1
1
1
1
0
0
0
0
3
0
2
0
0
0
0
1
1
0
0
0
2
1
2
2
0
1
1
1
1
0
1
2
1
0
0
0
1
0
0
1
2
1
0
0
1
0
0
2
0
1
2
3
0
0
0
0
0
1
1
0
2
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
2
1
2
0
0
2
0
0
1
0
0
1
1
0
1
0
0
0
1
1
1
0
1
0
0
2
1
0
2
0
0
0
0
1
0
0
0
0
2
1
0
0
0
1
0
1
0
2
0
1
0
3
5
1
1
0
0
0
0
1
0
0
0
1
2
0
2
2
0
0
2
0
0
0
0
1
1
2
0
0
1
0
0
2
1
0
0
0
0
2
0
1
0
2
0
1
0
0
0
0
2
0
1
0
0
0
0
0
2
0
1
0
1
0
7
1
0
0
0
0
0
2
4
0
2
0
0
0
0
1
2
2
2
0
1
0
1
0
0
0
0
0
2
2
0
0
0
0
0
1
1
0
1
2
0
1
2
0
1
0
3
0
1
0
0
1
0
1
2
0
0
2
2
1
0
0
0
2
0
2
2
0
2
0
1
0
2
0
1
0
1
1
0
0
0
0
1
0
2
1
0
0
0
0
2
1
1
0
1
1
0
2
0
2
0
0
0
1
1
2
0
0
0
0
0
2
0
1
0
3
1
0
2
2
1
0
0
2
3
1
1
0
0
1
1
2
0
2
0
1
0
2
0
2
2
1
0
0
0
2
2
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
2
2
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
1
1
2
0
4
1
3
0
1
0
0
0
0
1
0
0
0
0
1
2
0
0
2
2
2
1
2
1
0
1
2
2
0
1
0
2
1
2
0
0
1
1
0
0
2
2
1
2
1
2
0
4
1
0
0
2
0
0
2
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
2
3
2
1
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
1
0
2
0
1
0
0
0
1
0
2
2
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
1
2
0
1
0
2
2
0
0
1
0
2
1
2
2
0
1
0
1
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
1
1
0
0
1
0
0
1
1
0
0
1
0
2
0
2
0
0
1
0
3
1
1
0
0
0
0
0
0
1
2
0
1
0
0
0
0
2
2
1
0
0
1
0
2
1
0
0
2
0
0
2
2
0
0
1
0
1
1
1
0
2
1
0
0
0
1
3
0
1
2
3
0
1
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
1
0
0
0
0
2
1
2
0
1
0
1
0
1
0
2
0
0
0
0
2
1
0
0
2
0
1
0
3
0
0
0
0
0
0
3
1
0
1
4
2
0
0
1
1
2
0
1
1
0
0
0
0
0
0
2
0
1
0
1
0
0
2
0
2
0
2
1
1
0
0
2
1
0
2
1
0
3
1
0
1
2
0
1
1
1
2
0
2
1
0
0
1
1
0
0
0
0
2
0
1
2
0
0
0
0
2
2
1
2
0
0
0
1
0
0
0
0
2
1
0
0
0
0
1
0
0
1
0
2
1
1
1
3
0
4
1
0
0
0
1
1
0
0
1
0
1
1
0
0
1
2
1
1
2
2
0
0
1
0
2
2
1
0
1
0
0
0
3
0
0
2
1
1
2
0
0
1
0
0
2
1
1
0
0
0
0
1
0
1
2
0
1
0
0
0
1
0
1
0
1
0
2
1
0
0
0
0
0
1
1
2
0
0
0
0
1
1
1
0
0
1
2
1
1
0
0
1
1
0
1
1
0
0
0
1
0
1
0
0
2
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
2
0
0
0
3
0
1
1
1
0
0
0
2
2
0
2
2
0
0
2
1
0
1
1
2
0
0
0
0
0
0
0
2
0
3
0
1
0
1
0
0
0
1
2
0
1
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
2
0
1
0
0
2
0
1
0
0
0
0
1
0
2
2
0
0
0
0
1
7
1
0
2
2
0
0
1
0
1
2
0
2
1
1
2
2
0
0
0
1
1
0
0
2
1
1
0
0
0
2
0
0
1
2
0
0
0
1
0
0
0
0
2
0
2
0
1
0
2
1
0
1
1
2
0
0
0
1
1
2
1
2
2
0
0
1
0
1
1
0
1
0
0
2
1
0
2
0
0
2
2
1
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
2
2
0
0
0
0
1
1
0
0
0
0
3
0
1
2
0
0
0
2
1
1
1
2
0
2
1
2
0
0
3
1
0
0
0
1
1
0
1
0
0
0
6
1
1
0
0
0
0
3
0
1
0
0
0
0
2
0
0
2
1
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
2
1
0
0
1
1
0
0
0
1
2
0
2
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
3
0
0
0
2
1
2
0
0
2
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
4
1
0
0
1
2
0
2
0
2
3
2
0
2
0
6
2
0
1
2
0
1
0
1
1
2
1
0
0
1
0
1
2
1
0
2
0
1
0
0
0
1
1
0
0
0
0
0
2
1
2
0
0
0
2
2
2
1
0
0
0
0
1
0
0
0
2
0
0
0
1
1
2
2
1
0
0
1
0
1
2
0
0
2
0
0
2
2
0
2
0
1
0
2
1
0
1
1
0
1
1
0
0
1
0
1
0
0
0
0
1
0
1
1
2
0
0
1
0
1
0
0
0
3
0
1
0
2
0
2
0
0
0
0
0
1
0
0
0
1
0
0
1
2
1
2
0
0
5
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
3
0
0
0
2
2
0
0
1
2
0
0
0
0
0
2
3
2
0
1
2
2
0
2
2
0
0
0
2
4
0
0
0
1
0
2
1
0
1
0
1
1
0
2
1
2
2
0
1
0
0
0
0
0
2
0
0
0
2
1
0
0
2
0
0
2
0
2
0
0
2
0
0
0
1
3
0
1
1
1
0
2
2
0
1
0
0
0
1
0
2
0
1
0
0
1
0
1
0
2
0
0
2
1
0
0
2
0
0
0
0
1
0
0
2
0
0
2
2
0
2
0
0
0
2
2
0
1
2
0
1
3
1
0
2
0
0
0
2
0
0
2
2
2
0
0
2
0
0
2
0
1
2
2
1
0
2
1
1
0
1
2
0
1
0
2
0
1
2
0
0
0
3
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
2
2
0
0
0
1
0
2
1
2
0
0
0
1
1
2
1
1
2
1
2
2
0
0
0
1
0
1
1
0
2
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
2
1
0
1
0
1
1
1
1
0
0
0
0
2
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
1
1
0
2
2
1
0
0
0
1
0
1
0
1
0
0
0
2
0
0
2
2
1
0
1
0
0
2
0
0
1
0
5
2
0
0
2
2
2
0
3
0
0
3
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
2
2
0
3
1
0
1
1
0
0
0
0
2
0
2
0
1
0
0
0
3
0
0
0
0
2
0
0
2
0
2
2
0
0
0
0
1
0
0
0
0
0
2
0
0
1
1
0
1
2
1
0
2
2
2
0
1
0
0
1
0
0
2
1
6
0
2
0
0
2
2
5
0
0
0
2
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
2
2
0
2
0
1
0
0
1
2
0
0
1
1
0
0
2
2
0
0
0
2
0
1
0
1
1
0
1
2
0
1
0
1
1
2
2
0
1
0
0
2
0
0
1
1
0
0
0
1
0
1
0
1
1
0
1
2
1
0
1
0
1
0
0
0
0
1
0
0
2
1
1
0
0
1
1
0
2
1
1
1
2
2
1
0
1
0
1
0
0
1
0
1
3
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
2
2
1
2
0
0
1
0
1
1
1
2
0
0
3
1
1
0
1
0
2
0
1
0
0
0
0
0
2
3
0
0
2
2
2
2
0
0
0
0
0
0
0
2
0
1
0
0
0
1
3
1
2
1
0
0
1
0
2
2
0
1
3
0
0
0
0
2
2
0
2
0
0
0
0
0
1
0
1
0
1
0
0
1
2
0
0
0
0
2
0
0
1
0
0
1
0
2
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
2
2
1
1
1
1
0
2
0
1
0
2
0
0
0
0
0
2
0
1
1
1
0
0
2
0
0
0
0
2
0
1
0
0
0
1
0
1
2
2
0
0
2
1
1
1
2
0
0
1
0
3
1
1
0
0
1
0
0
0
1
1
0
0
0
0
1
0
1
1
2
0
2
0
0
0
0
0
2
0
2
0
1
0
1
0
0
1
0
0
0
0
3
2
0
1
0
3
0
2
1
0
0
1
0
0
0
0
0
2
0
0
0
1
0
2
0
1
0
0
0
2
0
0
2
2
2
0
1
1
0
0
0
1
1
0
2
2
1
1
0
0
0
0
0
0
1
0
1
0
2
0
0
0
2
0
0
0
0
1
2
0
1
0
1
1
0
2
0
0
0
0
2
2
1
2
0
0
0
2
0
2
0
1
0
0
2
1
0
0
0
0
2
1
1
0
5
2
1
0
0
0
0
0
0
0
3
2
1
0
1
0
0
2
0
1
0
0
1
1
0
1
2
0
2
0
1
2
0
0
2
0
0
0
0
0
1
1
1
0
2
2
3
1
0
0
0
0
1
3
1
0
1
3
0
0
1
0
0
0
0
0
0
0
0
3
1
0
0
1
0
1
0
1
0
2
0
0
0
0
0
0
0
1
1
0
1
0
2
1
1
0
1
2
0
0
2
0
0
1
0
2
0
0
0
0
0
1
2
3
2
1
0
0
2
2
1
0
0
2
0
0
0
2
0
2
0
1
5
0
2
0
1
2
0
0
0
0
0
2
0
0
1
2
1
1
1
1
2
1
0
0
2
2
2
2
1
0
0
2
1
0
0
2
0
0
1
2
0
0
0
0
0
1
0
2
0
0
1
0
2
1
1
2
1
0
0
0
0
2
3
0
1
1
2
0
1
3
2
0
0
0
0
2
0
1
0
2
0
1
0
0
2
0
1
0
0
1
1
2
0
2
0
2
2
0
0
0
0
0
0
0
1
1
1
0
2
0
1
1
0
0
0
0
1
2
4
0
1
0
3
2
2
2
3
2
0
0
1
1
1
0
1
2
0
0
0
1
2
3
2
0
1
1
0
1
0
0
0
0
2
0
0
0
1
1
0
0
0
1
0
2
3
2
2
1
0
0
0
0
0
0
2
1
2
0
1
0
3
2
0
0
0
0
1
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
2
0
1
0
1
2
2
0
1
0
0
0
2
0
1
0
1
1
0
0
1
1
1
0
1
1
0
1
0
1
2
2
0
0
0
0
2
1
2
1
0
0
1
2
0
1
0
0
1
0
0
2
0
0
1
0
0
3
0
1
0
0
0
2
1
0
0
2
0
2
1
1
0
0
2
0
0
1
1
0
2
1
0
0
2
0
0
0
0
0
2
0
1
1
0
0
1
1
0
2
0
2
2
0
0
0
0
2
0
0
0
0
2
2
1
0
0
0
0
0
0
0
3
0
0
2
0
1
0
0
0
0
2
0
3
1
1
0
0
0
0
1
0
2
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
2
0
0
0
2
1
0
0
0
0
3
0
0
1
2
3
0
1
1
1
0
1
1
0
0
1
2
1
0
0
0
0
0
0
1
4
0
0
0
2
2
1
0
0
0
0
1
1
1
2
0
0
0
0
0
2
0
0
2
0
0
2
0
1
0
0
1
0
0
1
1
2
0
0
0
4
0
0
0
0
0
0
0
1
1
2
2
0
0
0
2
0
2
0
2
1
1
1
0
0
0
0
0
0
0
2
1
0
1
1
0
2
1
1
0
0
1
0
1
1
0
0
2
1
0
0
3
0
0
2
0
2
0
1
0
0
1
0
0
1
0
1
0
0
1
0
0
0
1
2
1
1
0
1
0
0
0
0
2
0
0
0
0
0
2
0
1
0
2
0
0
0
0
1
0
0
0
0
1
0
0
1
0
2
1
0
0
2
0
0
0
2
0
1
0
0
1
0
0
0
1
2
0
0
0
0
2
1
1
0
2
1
2
1
1
0
2
0
2
0
2
0
0
0
2
0
2
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
2
0
0
0
0
1
1
0
0
0
1
0
1
2
0
0
0
1
0
2
0
0
0
2
0
2
1
0
0
0
0
0
0
0
2
0
0
2
0
1
0
1
1
0
0
2
0
0
0
2
0
0
0
1
2
1
1
0
0
0
2
2
1
0
0
2
0
1
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
2
1
4
0
1
2
0
2
0
1
0
0
0
1
2
2
0
2
0
1
1
2
0
2
1
0
2
0
1
0
2
1
2
0
0
0
0
2
0
0
0
1
2
0
0
0
2
1
1
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
2
0
0
1
0
2
1
0
0
0
2
0
1
0
0
0
0
0
0
2
0
1
3
1
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
1
2
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
2
2
0
2
0
2
0
2
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
2
0
0
0
2
1
1
1
1
2
0
0
0
0
0
1
2
1
1
0
1
1
2
2
0
0
0
1
1
0
0
1
1
0
0
0
0
2
2
1
1
2
1
2
0
0
2
0
0
2
2
0
0
1
0
2
1
0
1
0
1
2
3
3
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
1
2
0
1
1
1
2
0
0
1
2
0
0
0
0
1
1
0
0
2
0
1
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
1
2
2
0
1
0
2
1
0
0
3
0
0
0
0
1
0
2
2
0
1
0
0
3
2
1
1
1
1
0
0
1
1
0
0
0
2
2
0
0
1
0
1
0
0
1
0
0
1
0
2
0
0
1
0
0
2
1
1
0
2
2
1
1
1
0
0
2
2
0
2
0
0
0
0
0
0
1
2
1
1
1
0
0
0
2
0
2
0
0
0
0
1
0
2
0
1
1
1
0
1
2
0
2
1
0
0
0
0
1
1
1
0
1
2
0
1
1
2
2
0
0
0
1
0
1
2
0
1
0
0
2
0
0
0
0
2
0
1
1
0
0
1
1
0
0
1
4
4
2
0
0
0
0
1
2
2
0
0
0
0
2
1
0
1
1
4
1
0
0
0
1
0
0
0
2
2
0
2
1
0
3
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
2
0
2
2
0
5
0
2
0
1
0
0
1
1
0
0
0
0
0
0
1
1
1
1
1
1
1
1
0
2
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
2
0
1
0
2
1
0
0
0
0
2
1
1
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
2
1
0
0
0
1
2
1
3
0
1
0
0
1
0
0
0
0
2
1
0
0
0
0
2
1
2
1
0
2
2
0
0
1
2
0
0
2
1
1
0
0
1
0
1
2
1
2
0
1
2
1
1
0
0
0
2
0
0
0
0
2
0
0
2
1
1
1
0
0
1
0
0
2
0
0
0
1
1
0
0
0
1
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
2
0
2
0
3
0
1
0
4
0
0
0
0
0
1
0
1
2
0
4
0
0
1
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
2
1
0
1
1
1
1
0
1
2
0
2
0
1
1
0
1
0
1
2
2
0
0
2
0
0
2
2
1
1
0
0
0
0
0
3
0
0
2
0
0
1
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
3
1
1
1
0
0
0
0
2
0
2
0
0
1
1
0
2
0
1
0
0
1
2
0
2
0
0
0
0
0
2
0
2
1
1
0
0
0
0
0
0
1
2
2
1
0
0
0
0
0
0
0
2
0
1
0
1
1
0
0
1
1
0
0
1
2
0
0
0
2
1
3
0
3
0
2
0
0
1
0
1
1
0
2
0
0
1
0
2
0
0
1
0
0
0
0
1
2
0
0
0
1
0
1
3
1
2
0
2
0
0
1
1
1
1
0
2
0
0
1
0
1
1
1
2
0
0
1
2
1
0
1
0
1
0
2
1
0
0
0
0
2
2
0
0
2
1
1
0
0
0
1
1
0
0
0
1
4
0
0
1
0
2
0
2
0
0
2
2
2
2
1
0
0
0
0
0
0
0
0
0
1
1
0
1
1
2
0
2
0
2
2
0
2
0
1
1
0
0
1
2
0
2
0
1
2
0
1
1
2
1
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
2
2
1
0
0
0
1
2
2
0
0
0
0
0
0
2
1
2
0
2
0
4
1
0
0
1
1
3
0
2
1
2
0
0
0
0
2
2
2
1
0
2
1
1
2
0
0
2
0
1
2
0
0
0
0
0
2
0
3
0
0
1
0
0
0
0
0
2
0
0
2
0
1
2
2
0
0
0
0
2
0
0
0
2
0
1
0
0
1
2
0
2
2
0
2
0
0
0
0
0
2
1
0
0
3
1
0
0
2
1
0
2
0
0
1
0
0
1
1
1
0
0
2
2
0
0
1
0
0
0
0
0
0
0
7
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
1
0
2
0
1
2
1
0
1
0
0
2
2
1
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
1
1
3
0
1
0
0
0
2
0
0
0
2
0
0
1
1
2
0
0
0
0
2
0
1
0
0
0
1
0
2
0
0
1
0
0
1
1
0
1
2
0
0
0
1
0
0
2
0
0
2
0
1
0
0
2
0
2
0
1
0
0
0
0
0
0
1
0
1
1
2
0
1
1
0
2
1
0
1
0
0
2
2
0
0
0
0
2
0
1
2
1
0
1
0
0
0
1
0
2
3
0
2
1
0
1
0
2
0
0
1
2
1
1
1
0
1
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
2
1
1
2
1
0
0
0
0
2
1
1
2
0
1
2
3
0
2
0
0
1
0
2
0
2
1
1
1
2
0
0
3
2
1
2
0
2
0
1
0
0
0
1
0
3
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
1
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
1
0
3
0
0
2
0
0
0
1
0
1
0
0
4
0
2
0
2
0
0
0
0
1
0
0
0
4
0
1
0
0
1
1
2
1
0
4
0
3
1
2
0
2
1
0
2
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
1
2
2
2
0
1
0
0
0
0
1
1
0
0
2
2
0
2
0
1
1
0
0
1
0
0
0
0
3
0
0
0
2
0
2
0
1
0
1
2
2
0
1
2
1
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
2
0
1
2
1
2
0
1
0
2
0
1
0
2
0
0
0
2
0
0
0
1
0
0
2
0
1
0
0
0
1
0
2
0
2
0
0
5
1
0
0
2
1
1
0
0
0
0
1
0
1
1
0
0
0
0
3
2
0
0
0
2
2
0
3
2
0
0
0
2
0
0
0
0
2
0
0
1
2
0
1
1
0
1
1
0
2
0
4
0
1
0
1
0
4
0
0
2
0
1
0
0
0
2
0
0
1
0
1
0
2
2
0
0
0
2
2
0
0
1
0
0
2
1
2
0
1
0
0
1
2
0
0
2
1
0
2
1
2
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
1
0
0
0
0
0
1
2
0
1
0
0
1
1
1
0
0
2
0
0
0
0
1
1
2
0
0
0
0
2
2
0
1
1
1
1
1
1
1
1
1
2
1
4
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
2
2
1
0
2
2
0
0
0
1
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
2
1
1
1
1
2
0
0
0
2
1
2
0
0
0
2
0
0
0
0
1
2
0
2
2
0
0
0
2
1
0
1
1
0
0
2
1
1
0
0
0
0
2
0
2
0
1
0
0
1
0
0
0
0
0
0
2
1
1
2
1
0
2
0
0
0
2
0
0
0
1
1
0
2
1
1
1
2
2
0
0
2
0
3
0
0
0
1
2
0
1
0
0
1
1
0
0
0
2
0
3
2
2
1
0
1
0
2
1
0
0
0
0
1
0
1
0
0
1
1
1
1
0
0
1
1
2
2
2
2
1
1
0
2
1
0
0
0
0
0
1
0
1
1
0
0
1
1
2
0
1
0
2
1
1
0
0
1
1
2
1
1
2
0
1
2
0
0
0
1
0
0
0
2
0
2
1
0
2
1
0
0
0
0
1
0
2
0
0
1
0
1
2
0
0
4
1
1
1
0
0
1
1
0
2
0
2
0
1
1
0
1
1
1
2
0
1
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
1
0
0
2
0
0
1
0
0
0
2
0
0
0
0
2
1
0
2
1
0
0
1
0
1
2
0
2
0
1
0
1
1
0
0
0
0
1
0
0
2
1
0
0
1
0
0
1
0
0
1
0
2
0
0
1
0
0
2
0
4
0
0
2
1
1
0
0
0
1
1
1
0
0
2
2
0
0
1
0
1
1
1
0
1
0
1
2
0
0
0
2
2
2
0
0
0
0
0
0
0
0
1
0
2
0
3
2
3
0
1
2
0
0
0
0
0
0
1
0
0
0
2
0
1
1
1
0
0
0
1
2
1
1
0
0
0
1
0
0
0
1
1
1
2
2
0
0
0
0
0
0
0
1
2
0
2
2
0
0
0
0
1
0
0
0
0
1
0
0
2
2
0
2
2
2
2
0
1
2
0
0
0
0
0
0
0
0
2
6
1
2
0
1
1
2
0
2
0
0
3
3
0
1
0
1
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
1
2
0
0
2
1
0
0
2
0
2
0
2
1
0
0
2
1
0
0
0
1
1
2
1
1
0
0
3
1
0
2
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
1
2
0
0
2
2
0
0
1
0
0
0
2
2
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
1
2
0
0
1
1
1
1
1
2
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
2
0
2
0
2
2
0
2
1
0
1
2
1
1
1
0
0
1
2
0
0
0
2
2
0
0
2
0
0
1
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
1
1
0
0
2
1
1
0
2
0
0
0
0
1
2
0
29
0
0
1
0
0
1
2
0
0
2
1
0
0
2
0
2
1
1
0
0
1
1
0
0
1
0
0
1
1
0
0
0
1
0
0
1
0
1
2
0
1
1
0
1
3
0
0
0
0
0
1
2
0
0
0
2
1
1
2
0
0
3
2
0
1
1
0
0
2
1
0
0
1
1
1
0
1
0
1
0
0
0
2
0
1
0
2
1
1
0
0
0
0
0
2
0
0
1
0
0
2
1
0
1
0
0
1
0
0
0
1
0
0
1
0
0
2
0
0
1
0
1
1
0
0
0
1
0
1
0
2
0
0
1
0
1
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
1
2
0
0
0
0
0
1
1
0
0
0
2
1
0
0
0
0
0
0
2
0
0
3
0
0
1
0
0
1
1
0
0
0
2
2
0
4
1
0
0
2
0
0
0
1
1
2
0
1
0
0
1
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
3
1
1
1
2
0
0
2
0
0
0
1
0
0
2
0
1
1
0
0
2
1
0
0
0
1
0
0
2
0
2
2
1
0
0
0
0
0
0
1
1
2
0
0
1
0
0
0
0
0
0
3
2
1
1
0
0
0
0
1
0
0
0
1
2
1
1
0
2
0
0
0
1
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
2
0
1
0
4
1
0
0
0
1
0
0
1
0
1
0
1
2
1
0
0
2
2
0
0
3
0
1
0
0
1
0
0
0
1
2
0
0
1
0
2
0
0
1
0
2
1
2
0
1
0
0
1
0
0
2
0
0
2
0
0
0
1
0
3
1
2
0
1
0
2
0
1
0
2
0
0
0
0
1
3
2
0
0
2
2
0
2
3
0
0
2
0
2
0
0
0
1
0
0
1
1
2
0
0
0
0
0
0
2
0
2
0
0
2
0
1
0
0
0
2
0
0
1
1
2
0
0
0
1
0
0
2
0
1
0
1
0
0
1
1
0
0
1
1
1
2
0
0
0
1
2
1
2
2
2
2
0
0
2
0
1
1
1
0
2
0
0
0
0
1
0
1
0
1
0
1
1
1
2
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
2
2
1
0
0
1
1
0
2
1
1
2
0
2
2
1
1
2
1
0
0
0
0
2
0
1
1
2
1
0
0
1
2
2
0
0
0
0
0
0
2
2
0
0
0
1
0
0
1
0
1
0
1
0
0
0
1
0
2
0
2
2
0
0
0
0
0
0
0
0
1
1
1
0
1
1
1
0
2
0
2
1
2
1
0
2
1
1
1
1
0
0
0
0
1
0
0
1
2
0
0
1
2
0
0
0
0
0
0
2
1
0
0
2
1
0
0
1
0
0
1
0
2
0
2
0
1
1
1
0
0
0
0
0
2
2
1
1
0
0
0
2
2
1
1
0
0
2
0
0
2
1
2
0
0
1
1
0
1
0
4
0
1
1
0
0
0
2
2
2
1
2
0
0
0
2
1
1
0
0
0
1
0
0
3
2
0
0
0
0
1
0
0
0
2
1
0
0
0
2
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
1
2
2
2
1
2
2
0
0
3
0
2
0
0
2
0
1
2
0
1
4
0
2
0
0
2
0
1
1
2
0
0
2
2
0
2
0
0
0
1
2
0
0
0
1
2
0
0
0
2
0
2
2
0
2
2
0
0
2
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
12
0
2
1
0
1
1
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
2
0
0
2
1
1
2
1
0
0
3
0
1
0
0
2
0
0
0
0
0
0
1
1
2
0
0
0
1
0
1
0
2
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
2
1
0
0
0
1
0
2
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
2
0
2
0
0
2
1
0
0
0
1
1
1
2
0
1
0
0
2
1
1
1
1
0
0
0
0
0
1
0
1
0
0
0
1
1
0
1
0
0
2
1
0
0
0
0
1
0
2
0
0
2
0
1
1
0
0
0
0
0
0
1
0
0
0
0
2
2
1
0
1
0
0
0
0
2
0
0
0
2
1
0
1
2
0
1
0
1
2
0
1
0
2
3
0
0
0
1
0
1
0
2
0
2
2
0
0
2
2
0
1
0
0
0
2
0
1
2
0
0
0
0
2
1
0
0
0
0
0
2
1
0
0
0
2
0
0
1
0
0
2
1
0
2
1
0
1
1
2
2
1
0
1
1
2
0
1
1
1
3
0
0
0
2
0
2
0
2
1
2
2
0
1
0
0
1
0
0
1
0
2
0
2
0
0
0
2
0
2
1
0
2
1
3
1
1
1
2
0
0
0
0
1
2
0
0
0
0
2
0
0
0
1
1
1
0
2
1
1
1
2
0
1
0
2
0
0
0
1
2
2
0
1
0
0
1
0
1
1
0
2
0
0
0
0
0
3
0
1
0
0
0
0
1
3
3
1
2
0
2
1
3
2
1
0
0
2
1
0
1
0
2
1
1
0
0
1
0
0
0
0
0
2
1
0
1
0
2
0
1
1
0
0
0
4
2
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
1
0
2
0
0
0
1
1
0
1
0
1
0
0
0
1
0
0
1
1
1
0
0
0
1
1
0
1
0
1
1
2
0
1
1
0
1
0
0
0
1
1
0
0
0
1
1
1
2
0
0
0
2
2
1
0
0
0
2
0
0
0
2
1
2
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
2
2
0
0
1
0
1
0
0
1
2
1
2
0
1
2
0
2
0
0
1
2
0
0
1
1
1
0
0
0
0
0
0
0
0
1
1
0
2
3
0
2
1
0
0
2
0
0
0
1
2
0
0
1
0
3
0
2
0
2
1
2
0
0
0
0
0
1
0
1
1
0
1
0
0
0
1
2
1
0
0
2
0
0
0
0
1
1
2
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
2
1
2
1
0
1
0
0
0
0
0
1
2
0
2
1
3
0
2
0
1
2
2
0
0
0
2
0
0
1
1
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
3
1
2
1
0
3
0
0
0
1
2
0
1
1
1
0
0
0
1
1
2
0
0
0
0
0
0
0
1
2
0
3
0
1
0
1
0
0
0
1
0
1
0
2
0
1
2
2
0
1
0
1
0
1
0
0
1
1
0
1
1
0
0
3
0
0
0
2
0
2
1
0
2
0
0
0
0
2
2
0
0
0
2
1
0
0
0
2
0
0
0
1
2
2
5
0
1
0
0
1
0
0
1
1
0
1
0
0
0
1
0
0
0
1
2
0
0
0
0
1
2
2
0
0
2
0
0
1
0
0
1
1
0
0
0
2
2
2
1
3
1
0
0
2
0
1
0
1
1
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
1
1
0
1
1
0
0
1
0
1
0
0
3
0
0
0
1
0
2
0
1
0
0
0
1
0
2
0
0
0
2
0
0
2
2
0
2
0
0
0
0
0
0
2
2
0
0
0
0
2
2
0
1
0
0
1
0
1
1
0
0
3
1
1
2
0
0
1
1
0
0
0
0
0
1
1
1
0
0
0
1
0
0
1
0
0
0
1
2
0
1
0
0
2
0
0
1
0
1
2
0
2
2
0
1
0
1
1
0
0
0
2
0
0
0
1
1
1
0
1
0
1
0
1
0
0
2
0
1
2
0
0
2
1
0
0
0
0
4
1
2
0
0
1
0
0
0
0
0
2
0
0
0
0
9
2
0
1
2
0
0
2
0
0
0
2
0
0
0
2
1
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
3
1
0
0
3
1
0
0
2
0
0
1
1
0
2
1
0
1
1
2
0
0
0
0
2
0
1
0
1
1
0
0
1
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
1
1
2
0
0
0
8
2
0
2
2
0
1
0
1
0
2
0
2
0
1
1
2
0
1
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
1
0
1
0
0
1
0
0
2
1
2
0
0
0
1
1
0
0
0
1
1
0
0
0
0
2
1
2
1
2
0
2
1
0
0
0
1
1
0
2
1
1
0
0
1
0
0
1
0
2
1
0
1
2
2
3
1
3
0
1
2
1
0
0
0
1
0
0
0
0
0
1
2
0
1
0
1
3
0
3
1
0
1
0
1
1
0
0
1
0
0
1
2
1
2
1
1
0
0
2
1
0
2
0
0
2
1
2
0
1
0
7
0
0
1
2
0
0
1
0
0
2
2
2
1
1
0
2
2
1
0
0
0
2
2
1
1
1
0
1
0
2
0
0
1
0
1
1
1
0
0
2
0
0
0
1
1
0
0
2
0
0
1
0
0
1
0
0
2
0
4
2
0
0
0
4
1
2
16
0
0
0
0
0
0
1
2
0
0
1
0
0
1
3
0
1
1
0
0
1
2
2
1
0
0
1
0
0
0
1
1
0
2
1
2
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
1
0
1
0
0
2
2
2
0
2
0
0
2
1
2
1
0
0
1
0
2
1
0
0
0
0
2
2
0
1
2
4
1
0
0
0
2
0
0
0
1
0
1
0
0
1
1
1
0
0
0
0
0
1
2
0
0
1
0
1
1
0
0
2
0
1
3
0
0
0
1
0
2
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
2
0
2
2
0
0
0
0
0
0
0
0
1
1
2
0
0
0
2
2
1
1
0
0
0
0
0
0
2
0
1
3
0
1
0
0
1
1
2
2
2
1
0
0
0
1
0
1
0
2
0
1
0
2
0
0
0
1
0
2
0
1
0
0
1
0
1
0
0
0
0
2
2
0
0
0
0
0
0
1
1
0
0
2
2
1
1
0
1
1
0
0
2
2
2
0
1
2
2
2
3
2
2
1
1
2
0
2
0
0
0
0
2
0
0
1
2
1
0
1
0
0
2
1
0
0
2
1
2
0
1
0
0
1
0
1
3
0
2
0
0
3
1
2
0
0
0
1
1
2
1
2
0
0
0
0
1
0
0
4
2
0
0
1
0
2
2
0
0
0
2
0
0
1
1
0
0
0
1
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
2
0
0
0
1
1
0
3
0
0
1
0
0
3
2
2
2
0
0
1
0
3
1
1
1
1
0
2
1
0
1
3
2
1
1
0
0
0
0
0
2
0
0
0
2
1
2
0
0
0
0
0
1
0
2
2
0
2
0
0
0
2
2
1
0
0
0
0
0
2
0
0
0
0
1
3
0
0
14
0
2
0
2
0
0
0
2
2
0
0
3
0
0
1
1
1
2
0
2
0
2
0
2
1
2
0
0
1
0
1
0
0
1
0
1
3
0
1
0
0
1
2
1
0
2
1
1
0
0
2
0
0
2
1
0
1
0
0
1
2
0
0
0
1
0
0
0
0
0
1
2
0
0
2
0
0
1
0
0
0
7
2
0
0
2
0
1
0
0
1
1
0
0
2
0
2
0
0
0
1
1
3
0
2
0
0
2
1
1
0
0
1
2
0
2
3
1
1
0
0
0
2
1
1
1
0
1
1
0
3
1
1
1
1
0
1
1
0
2
0
1
0
2
0
0
1
0
2
0
1
0
0
0
0
1
1
0
1
1
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
1
0
1
0
1
1
2
1
0
0
3
0
0
1
0
0
2
1
0
0
1
2
1
1
1
0
1
0
0
0
0
1
1
1
0
0
2
0
0
0
1
2
0
0
3
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
2
0
0
0
1
3
0
3
2
0
0
1
0
1
0
0
1
0
0
0
1
0
0
1
2
0
1
1
0
2
0
0
2
0
0
2
2
1
0
0
0
0
0
1
0
2
1
0
3
0
4
0
2
0
1
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
2
1
0
0
0
2
2
1
2
0
0
0
1
1
0
0
1
0
0
1
1
2
0
1
0
2
3
0
0
0
2
0
2
0
0
0
1
0
0
0
1
1
0
2
0
0
2
1
0
3
1
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
1
0
2
1
2
0
2
0
0
0
0
2
0
2
0
0
2
0
1
3
2
0
1
0
0
2
1
2
0
0
0
0
0
2
0
1
0
0
1
1
0
0
0
0
0
1
0
0
2
0
3
0
1
0
1
0
2
0
0
2
0
1
0
4
0
0
0
1
1
1
1
1
1
0
2
0
0
0
1
1
1
0
0
2
2
0
1
0
0
0
0
0
0
1
3
0
0
2
0
1
0
2
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
1
0
1
0
1
2
0
0
0
2
0
0
0
0
0
2
0
0
3
1
0
0
1
1
1
0
0
2
0
2
0
0
0
1
1
2
2
1
0
0
0
0
1
0
1
2
0
0
0
5
1
0
0
0
1
1
4
2
0
2
2
2
0
0
0
0
0
0
0
1
0
3
0
0
0
2
0
0
0
0
0
1
1
2
1
1
0
1
1
2
2
0
1
0
2
0
0
0
2
1
1
1
0
2
0
0
1
0
1
2
2
0
0
0
0
0
1
1
0
0
2
1
0
0
1
2
1
0
1
1
0
0
2
0
2
7
0
0
0
0
0
1
2
1
1
0
2
0
2
0
0
1
0
2
0
0
1
2
1
1
1
3
1
1
3
0
0
1
2
1
0
0
0
0
2
2
2
2
0
2
1
0
0
0
2
1
0
1
1
1
1
0
0
0
1
2
0
0
2
1
0
3
0
1
1
0
0
0
1
1
0
1
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
2
1
2
1
1
0
0
2
2
0
0
1
1
0
0
1
0
0
0
0
1
0
1
2
0
2
0
0
0
1
2
0
0
0
0
0
2
0
1
2
0
0
0
1
0
0
2
1
0
1
2
1
1
0
2
0
1
0
0
2
0
0
0
0
0
0
1
0
0
1
0
1
0
2
0
0
0
2
1
0
1
1
3
0
1
1
0
1
1
2
2
0
0
2
0
1
1
1
2
1
1
0
0
0
2
2
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
1
2
2
1
0
0
1
2
2
0
0
1
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
1
1
1
0
0
0
1
0
0
0
2
0
1
1
1
1
1
0
0
1
1
1
0
0
0
2
1
1
1
2
0
0
2
0
1
0
0
1
2
0
1
0
2
0
0
2
1
2
1
0
2
1
1
0
1
1
0
0
0
1
2
2
1
0
2
2
2
2
2
1
0
3
0
0
0
2
0
0
0
0
0
0
0
2
0
1
1
0
2
2
1
3
1
0
0
2
1
1
1
1
0
0
0
0
2
0
0
0
0
0
2
0
1
2
0
0
1
2
0
1
2
0
0
0
1
1
0
0
0
0
0
0
0
0
3
0
1
0
2
0
1
0
2
2
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
1
0
0
0
1
0
1
2
1
1
0
2
0
2
0
0
2
1
0
0
2
1
0
2
2
1
0
0
0
1
1
1
1
0
0
0
1
0
0
1
0
0
0
1
0
1
2
2
2
1
2
0
1
0
1
0
1
0
0
0
0
2
0
0
0
1
1
2
0
0
2
0
1
0
2
0
1
0
0
0
1
0
1
0
1
1
0
0
1
1
0
2
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
1
1
0
0
0
2
0
0
1
1
2
0
1
0
0
0
0
1
1
0
0
2
0
1
0
2
0
2
2
0
0
0
0
2
0
1
0
2
0
2
2
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
1
1
2
1
1
0
0
0
0
0
0
1
1
0
0
2
0
1
0
2
0
2
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
1
3
0
0
1
0
2
0
1
1
2
0
0
2
0
1
0
0
2
0
2
0
1
0
0
3
0
1
2
0
2
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
2
1
0
0
1
1
0
2
0
0
0
0
0
2
0
0
1
0
0
0
1
0
2
0
0
0
0
1
1
0
1
1
1
3
0
2
0
0
0
1
0
1
0
0
2
0
1
2
1
1
0
0
2
2
0
3
0
0
0
1
2
2
1
0
1
0
0
0
0
0
2
0
0
0
0
0
7
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
1
0
0
1
1
2
2
0
0
1
2
0
1
0
1
0
1
0
0
0
0
0
3
0
0
2
0
0
0
1
0
0
0
0
1
2
1
1
0
1
0
0
2
1
0
0
0
1
0
2
0
0
0
0
1
2
0
1
2
1
0
1
1
0
1
0
0
0
2
1
0
4
0
2
1
0
1
0
0
0
0
0
1
2
2
1
2
0
2
0
1
0
1
0
0
2
2
0
1
0
0
0
0
0
0
0
5
2
1
0
0
0
1
0
0
2
0
0
0
1
2
0
0
0
0
1
0
2
0
0
0
1
1
3
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
1
1
1
2
0
0
2
0
0
0
0
0
0
1
1
1
0
0
0
1
1
1
0
1
1
1
0
0
0
0
1
2
2
0
1
0
0
0
0
0
0
0
1
2
0
0
0
1
0
2
0
0
0
3
1
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
1
2
1
0
0
0
0
0
1
0
1
0
0
1
0
1
0
2
1
1
2
0
0
1
2
2
0
1
0
2
0
0
0
0
0
2
2
0
0
0
0
2
1
0
1
0
1
0
0
1
0
1
0
0
0
3
0
2
1
0
0
3
0
1
1
0
2
0
0
0
0
2
0
2
0
0
0
0
2
2
1
2
0
0
0
2
3
1
0
0
0
1
1
0
1
0
0
2
0
0
1
3
1
2
0
0
2
0
1
1
1
1
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
1
0
0
2
1
1
1
0
0
2
0
0
0
0
0
1
2
0
0
1
1
0
1
0
0
0
3
0
2
0
2
4
0
0
0
1
0
2
0
3
0
0
3
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
2
1
0
1
3
1
1
0
0
0
2
0
0
0
0
2
1
2
0
0
0
0
0
1
1
1
0
2
0
1
0
0
0
0
2
2
0
0
0
0
0
1
0
0
1
2
1
0
1
2
1
1
0
2
2
0
1
1
0
0
0
0
0
1
2
1
0
0
1
0
0
0
1
1
0
0
0
0
3
1
0
0
0
1
1
0
0
0
1
2
0
0
0
0
2
1
1
1
2
2
1
2
0
0
0
0
2
1
1
2
0
2
0
0
2
0
0
2
0
0
1
1
0
1
0
0
1
0
0
0
1
2
0
0
2
0
0
0
1
2
1
3
0
0
2
1
0
1
2
0
0
2
0
3
0
2
2
0
0
0
1
0
1
0
0
1
0
1
0
0
2
1
0
0
0
2
2
0
1
1
0
0
1
2
0
2
0
1
0
0
0
0
0
1
1
0
1
0
2
0
0
0
0
0
2
0
2
0
0
1
2
2
1
1
0
2
1
1
1
0
0
0
1
3
1
0
0
2
0
0
0
2
0
1
0
0
0
2
1
1
0
0
0
0
1
0
0
2
2
0
0
0
0
1
0
0
1
2
0
0
1
1
2
1
1
0
0
0
5
0
0
1
0
0
0
1
2
0
1
2
0
1
1
2
0
0
1
1
1
3
2
0
2
1
0
1
0
0
0
1
0
1
1
0
0
2
0
1
1
1
1
1
2
0
0
1
1
0
0
0
0
0
2
1
2
0
1
0
0
2
0
0
1
1
1
1
0
0
2
0
0
0
0
2
1
0
0
0
0
0
3
2
0
0
0
2
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
1
0
0
1
0
0
0
0
1
0
2
1
2
2
2
1
2
1
0
0
2
2
0
2
0
0
1
2
1
0
1
1
0
2
1
1
1
1
0
0
2
0
0
0
2
0
2
0
0
0
0
0
2
0
1
0
1
1
1
0
1
0
1
0
0
2
2
2
0
2
1
0
2
0
0
0
0
0
0
2
2
0
0
1
0
2
0
0
1
1
0
1
0
1
2
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
2
0
0
1
0
2
2
0
0
0
0
2
2
0
0
2
0
0
2
0
0
1
1
2
2
1
1
0
0
0
2
0
0
0
0
1
0
2
0
0
2
0
1
1
2
2
0
1
0
0
1
1
0
1
0
0
1
1
0
0
0
0
0
2
0
2
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
3
0
1
2
0
0
2
2
0
2
2
0
1
0
0
3
1
0
2
2
1
4
0
1
1
0
0
1
1
0
0
0
3
1
0
0
1
0
0
0
0
0
0
1
2
1
1
0
1
0
1
0
2
1
0
2
0
0
0
0
0
2
1
0
0
0
2
1
0
0
1
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
1
0
1
1
2
0
0
1
0
0
0
0
2
0
0
1
0
1
0
2
0
0
1
0
0
3
0
0
1
0
0
0
1
0
0
0
1
2
0
1
2
1
0
0
0
0
1
0
1
2
0
1
0
2
0
0
0
0
2
0
0
2
2
1
3
2
2
2
0
0
0
1
2
1
1
1
0
0
0
0
2
1
0
1
1
2
0
1
2
3
0
0
2
0
1
0
1
1
2
0
1
0
0
1
0
0
0
2
0
1
0
2
0
1
0
0
2
2
0
2
0
0
0
0
0
1
0
0
2
1
0
0
2
0
0
0
1
2
1
0
1
0
1
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
2
1
3
1
1
0
0
1
2
0
0
0
0
2
1
0
2
0
0
0
1
2
4
0
0
2
1
2
0
0
0
0
1
1
0
0
1
0
2
1
1
0
0
1
0
1
1
1
2
1
1
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
1
0
0
2
2
0
2
1
0
0
2
0
2
0
2
1
1
0
0
2
1
0
2
1
0
0
0
0
0
0
1
1
1
0
2
0
0
1
1
0
0
2
0
0
0
2
0
1
2
2
0
0
0
2
1
1
0
0
0
0
1
0
1
2
2
2
0
0
0
1
0
1
0
1
1
1
0
0
0
0
2
1
1
0
1
1
2
1
0
0
4
2
2
0
0
1
2
1
1
0
1
0
0
2
1
0
0
1
1
0
2
1
1
0
0
1
0
2
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
2
1
1
1
1
0
3
1
2
1
0
0
0
2
2
0
3
0
1
1
0
0
0
0
0
0
0
0
3
0
0
0
3
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
1
0
0
2
1
0
0
2
1
1
0
0
2
0
1
1
0
2
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
2
0
0
0
0
0
1
1
0
2
0
1
2
0
0
1
0
1
2
0
0
1
1
0
0
1
0
0
1
0
3
1
1
0
1
0
0
0
0
1
0
0
2
1
0
2
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
2
0
1
0
0
2
1
3
0
0
0
1
2
1
0
0
0
0
0
0
3
1
0
2
0
3
0
0
1
0
1
0
0
2
4
0
2
1
0
0
0
0
0
0
0
2
0
1
1
0
2
1
0
1
0
0
2
0
0
0
1
1
0
0
0
0
2
0
1
0
1
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
2
2
1
1
3
1
0
0
1
0
0
0
1
0
0
1
1
0
1
1
0
1
1
0
0
0
1
0
1
4
0
1
0
1
0
1
2
0
1
0
0
0
2
0
1
0
0
1
2
2
0
0
1
0
1
1
1
1
0
0
0
0
0
0
1
0
2
0
0
2
1
2
1
1
0
1
1
0
1
0
2
0
0
2
2
0
0
0
2
0
0
2
0
0
0
3
2
3
2
0
1
0
0
0
0
1
0
1
0
1
1
1
1
2
2
1
1
0
2
2
2
0
0
0
1
0
0
0
1
1
1
1
1
1
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
2
2
0
0
1
0
0
0
2
0
2
0
2
0
0
1
0
2
0
3
1
0
0
2
0
0
2
0
1
0
0
1
0
0
0
0
1
1
1
2
1
0
2
3
0
2
0
0
0
0
1
1
0
1
2
2
0
0
0
1
0
0
1
0
1
1
1
0
2
0
2
0
0
2
2
0
2
0
1
1
0
0
0
0
0
0
1
2
1
0
0
0
0
3
0
0
0
1
0
0
0
2
0
2
0
2
2
0
0
1
5
0
1
1
1
0
1
0
0
0
1
1
0
1
1
1
0
0
0
1
0
1
2
0
2
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
3
0
0
0
0
1
1
2
1
2
0
1
1
2
2
0
0
1
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
1
2
1
1
0
0
0
0
0
0
0
1
1
1
1
1
0
1
0
0
0
0
2
2
0
1
0
0
0
0
0
0
1
1
0
0
1
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
1
0
2
0
0
0
0
1
0
0
1
2
1
0
0
0
2
1
0
0
1
0
0
1
1
2
2
0
2
1
0
0
1
0
0
2
2
1
0
0
0
0
0
1
1
2
2
2
2
2
1
0
2
0
1
0
2
0
0
1
0
2
0
0
1
2
0
1
0
1
0
0
1
1
1
0
1
1
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
1
1
0
1
0
0
0
2
1
0
0
0
0
0
2
2
1
0
0
1
2
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
2
0
0
1
2
0
0
0
0
0
0
2
1
0
1
0
0
0
2
1
0
0
1
0
0
2
0
1
1
2
1
1
0
2
1
1
0
0
0
0
2
1
2
0
0
0
2
0
0
0
0
1
0
0
1
0
1
1
1
2
0
0
0
1
1
1
0
0
2
1
2
0
1
0
0
0
2
2
0
0
1
0
0
1
0
1
0
0
1
2
0
0
0
0
0
1
1
0
2
1
1
0
2
0
0
0
0
0
0
0
2
0
3
1
1
0
1
1
0
2
1
3
1
2
0
0
0
0
0
1
3
0
0
0
2
0
11
0
0
0
0
3
2
0
0
1
0
0
1
2
1
1
0
1
0
2
1
0
1
1
1
1
1
0
1
1
0
0
2
2
5
0
1
1
0
0
1
1
2
2
0
2
0
0
1
2
0
0
0
0
0
0
0
1
2
2
0
0
1
1
0
1
0
1
1
0
0
1
1
0
0
3
2
0
0
0
1
0
1
1
2
1
2
2
1
2
1
0
0
0
2
0
0
0
0
0
0
0
0
4
1
0
0
1
0
0
0
2
0
1
2
2
1
3
0
0
0
0
0
0
0
0
4
0
2
1
1
1
0
0
0
1
0
1
2
1
0
1
2
0
2
1
2
1
0
0
3
1
1
0
0
2
0
0
1
0
0
1
0
1
2
2
0
2
0
0
2
1
0
0
3
1
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
2
2
1
1
0
1
0
1
0
0
2
1
0
1
0
1
1
1
0
0
2
0
0
0
2
0
0
0
0
2
1
2
0
0
0
2
1
1
0
1
0
0
0
0
1
2
1
2
2
1
2
0
1
2
0
1
0
0
0
0
1
1
1
2
0
1
0
2
0
1
3
0
0
1
2
2
0
1
1
1
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
2
0
0
1
0
1
0
2
0
0
0
1
0
0
0
1
7
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
1
0
0
2
0
0
1
3
0
0
0
0
1
1
1
2
2
0
1
3
0
2
1
0
0
0
1
2
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
2
2
0
1
0
2
0
1
2
0
0
1
2
1
0
2
0
1
0
0
0
0
0
2
0
1
1
0
0
1
0
1
1
1
2
2
0
0
1
2
0
0
1
2
0
0
1
0
0
2
1
0
0
0
0
0
1
1
0
0
0
1
0
2
1
0
0
0
0
2
0
2
1
1
0
0
2
0
2
0
0
0
0
0
1
0
3
2
0
0
0
0
1
1
2
1
1
1
0
0
2
0
1
0
0
1
0
0
1
1
0
1
1
1
2
2
1
0
0
3
1
0
0
1
0
0
0
1
0
0
2
0
0
0
0
2
0
2
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
2
2
0
2
1
2
2
0
2
0
0
2
0
0
0
1
0
1
0
2
2
0
0
1
1
0
0
0
0
0
1
0
1
2
0
1
2
2
1
0
0
1
0
1
2
0
0
2
0
2
0
1
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
2
2
0
1
2
1
2
0
1
0
0
0
1
0
3
0
0
0
1
0
2
0
1
0
0
2
0
0
2
2
1
1
2
0
0
0
1
2
0
0
0
0
2
1
0
1
0
1
0
0
0
1
2
0
0
0
0
1
0
2
0
0
3
2
0
1
0
2
0
0
1
2
1
1
2
1
0
0
1
1
0
0
0
1
0
2
0
0
0
2
1
0
0
1
0
2
0
1
2
0
0
2
0
2
0
1
1
1
0
2
0
0
0
0
0
0
0
1
0
0
2
2
0
3
0
0
0
0
0
1
1
2
0
2
0
1
0
1
0
1
0
1
1
2
0
0
0
0
1
0
1
0
0
0
2
1
2
1
0
0
1
1
1
0
2
0
0
0
0
1
1
0
0
0
3
0
0
0
0
0
0
1
1
0
2
1
1
2
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
2
1
0
0
2
0
0
0
2
0
0
0
0
0
2
0
2
1
0
0
1
0
1
0
0
1
2
1
1
0
1
0
1
0
0
1
2
2
0
1
1
2
1
0
0
1
3
2
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
4
3
1
0
0
1
0
1
0
2
2
0
0
0
2
0
0
2
0
1
2
0
2
0
0
2
2
2
1
1
2
1
1
0
1
1
0
1
1
2
3
0
0
0
0
2
2
0
1
0
0
2
2
0
0
0
0
0
0
1
2
0
0
1
1
0
4
0
2
0
1
1
1
0
0
2
0
0
2
0
0
1
0
1
0
2
0
1
2
1
0
0
0
2
0
1
1
2
0
2
1
0
1
0
0
0
1
2
0
1
0
3
2
0
1
0
0
0
3
1
2
1
0
1
2
0
0
0
0
2
0
0
0
1
2
0
2
1
0
0
0
1
2
0
0
0
3
0
0
0
0
4
0
0
0
2
0
2
0
2
0
0
0
2
0
0
0
0
1
2
2
0
1
0
2
0
0
1
1
1
0
0
2
0
0
0
0
0
1
0
2
1
0
0
2
2
0
0
0
0
4
0
2
1
2
0
1
0
0
1
0
0
0
2
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
2
0
1
0
2
0
1
3
0
1
2
0
2
0
0
1
0
0
0
0
0
1
0
1
2
0
0
2
0
0
1
0
2
0
0
0
2
1
0
0
2
1
1
1
2
2
3
0
0
0
0
3
0
1
1
0
0
0
0
0
2
0
3
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
1
1
0
0
2
2
0
2
0
0
2
0
0
0
0
1
0
0
1
1
2
0
0
1
0
0
1
1
2
0
0
0
0
1
1
0
1
0
1
0
1
0
0
0
2
0
2
2
0
2
2
0
0
0
1
1
1
2
2
0
0
2
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
2
1
0
1
1
0
0
0
2
0
0
0
2
0
0
1
0
2
2
0
1
0
0
0
1
2
1
2
0
0
0
1
0
3
0
0
2
4
0
0
0
2
0
0
3
0
0
0
0
0
2
1
1
2
2
0
0
0
2
1
2
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
2
0
1
0
1
0
0
1
0
0
0
1
2
0
0
0
0
0
0
1
2
0
1
0
0
0
1
0
0
1
0
3
0
1
0
0
1
0
2
0
0
2
4
0
0
1
0
2
2
0
2
1
0
3
2
0
2
0
0
0
2
0
1
0
1
0
1
2
0
0
1
0
2
0
3
9
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
2
1
0
2
0
0
0
2
1
0
1
0
1
2
2
0
1
2
0
1
0
0
0
0
1
0
0
0
0
2
2
2
1
0
1
0
0
0
2
1
0
2
2
1
0
0
0
0
0
2
0
0
0
2
3
2
0
0
0
0
0
0
0
0
0
2
0
2
0
1
2
0
1
0
1
0
3
0
1
0
2
2
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
1
0
1
2
1
1
0
1
0
0
0
0
2
0
0
0
2
0
0
2
0
0
1
1
2
2
2
1
1
1
0
0
0
0
0
0
0
2
0
1
1
2
0
0
0
1
0
0
0
1
1
2
0
0
2
0
3
0
0
2
1
1
0
3
0
1
2
0
0
0
1
1
0
0
0
0
0
2
0
0
1
1
1
0
1
1
1
2
0
1
2
0
1
2
0
1
0
0
0
1
0
0
2
1
1
2
0
0
0
0
0
2
0
2
0
0
0
0
0
1
3
2
1
0
1
1
1
0
1
0
1
0
0
0
2
0
2
2
0
0
0
1
1
2
1
1
1
0
0
1
0
0
1
0
0
0
0
0
2
0
1
2
0
1
0
2
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
2
2
0
2
1
0
1
1
0
0
0
1
1
2
0
0
2
1
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
1
2
0
2
0
0
0
1
0
0
0
1
1
0
1
1
0
0
0
1
0
1
0
1
0
0
0
1
0
2
0
2
0
2
4
1
1
0
0
1
1
0
1
2
1
0
0
0
0
0
1
2
2
0
1
0
1
0
0
0
0
0
0
0
1
0
1
2
2
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
2
1
0
3
0
0
0
2
0
0
0
2
0
0
0
1
1
0
0
0
0
2
0
0
0
0
1
0
1
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
1
0
0
0
0
0
1
1
1
2
2
0
1
2
2
2
2
0
0
0
6
0
0
0
2
2
1
1
1
0
0
2
0
0
1
0
1
0
2
2
0
0
0
0
0
2
1
0
1
0
0
0
1
3
0
2
0
0
0
2
0
0
0
1
0
2
2
0
0
0
0
1
1
0
1
2
0
0
0
2
0
0
0
1
0
0
0
0
2
0
1
1
0
1
1
1
0
1
0
1
0
0
1
0
0
0
1
1
0
1
0
2
2
0
0
2
0
0
2
0
0
2
0
0
1
1
0
0
1
0
3
0
1
0
0
2
0
1
0
0
0
1
0
8
0
0
1
0
1
0
1
0
0
1
2
0
0
2
0
0
0
0
2
3
1
2
0
0
0
0
2
1
1
0
2
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
2
2
1
0
1
0
2
1
2
0
2
0
1
0
1
0
1
0
0
0
0
1
1
0
1
2
2
1
1
0
3
1
2
2
0
0
0
0
0
0
0
3
0
0
0
0
2
0
2
2
1
1
0
0
1
0
0
0
1
1
1
2
0
0
0
0
1
2
0
0
0
0
2
2
2
0
2
1
0
0
0
0
2
1
2
0
0
1
0
1
0
1
0
0
2
2
1
2
1
0
0
3
0
0
1
1
1
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
2
1
0
0
5
0
0
0
0
2
2
0
1
0
0
1
1
0
0
2
1
0
1
0
1
0
0
0
0
0
2
2
0
1
0
0
0
2
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
1
1
1
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
2
2
0
0
2
0
1
0
0
0
0
2
1
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
1
0
1
0
1
0
1
1
0
1
1
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
2
2
0
2
2
1
0
2
1
1
1
0
0
1
0
0
0
0
1
0
0
0
0
2
2
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
2
1
0
0
1
1
0
0
0
0
0
0
0
1
2
2
1
0
0
1
1
0
0
0
2
0
0
0
2
2
0
0
0
2
1
2
2
0
0
0
0
0
0
1
1
0
0
0
1
2
2
0
0
2
0
1
0
0
2
0
0
1
0
0
0
2
0
2
0
0
2
2
0
0
0
0
2
0
0
0
1
0
1
1
0
0
0
0
2
0
0
0
1
1
2
0
0
0
2
0
0
0
0
1
0
1
2
0
1
2
0
0
0
0
1
0
0
1
0
3
1
0
0
2
1
1
0
2
0
1
0
0
1
0
0
0
0
1
0
0
1
2
1
2
0
0
0
0
0
2
0
0
1
2
0
1
1
2
0
0
2
0
0
3
0
0
0
0
0
2
0
2
0
0
0
0
0
1
2
1
0
1
2
1
0
0
0
1
2
0
0
0
0
1
0
0
0
2
2
0
1
0
1
2
0
0
0
1
0
1
1
1
0
1
0
1
0
1
0
1
0
2
0
0
2
0
2
2
0
0
0
2
0
0
0
0
1
1
2
0
0
1
2
1
0
0
2
0
2
0
1
0
0
2
1
2
1
0
1
1
3
2
2
0
1
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
2
0
1
0
1
0
0
0
1
2
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
2
2
0
0
2
0
0
2
0
0
0
0
1
0
4
2
3
1
0
0
2
2
0
0
1
0
0
2
1
2
0
1
2
1
2
1
0
0
0
0
1
0
1
1
0
0
0
1
2
0
0
1
0
2
1
0
0
0
2
0
1
0
2
1
1
0
1
0
1
2
2
0
1
2
0
1
0
0
1
1
0
0
0
0
1
2
1
1
0
0
0
3
2
1
2
0
2
3
2
0
0
0
1
0
0
0
0
2
0
0
0
4
2
0
0
1
0
1
0
0
0
0
2
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
1
1
0
0
1
0
0
2
2
1
3
0
0
1
0
0
0
0
0
1
2
0
2
1
1
1
2
2
0
3
0
2
0
0
2
0
0
0
1
0
1
0
2
0
1
0
1
0
0
1
1
0
0
0
1
1
0
1
1
0
2
0
0
0
0
0
1
1
0
1
0
1
0
2
0
1
2
0
0
0
0
3
1
0
1
1
1
0
0
3
0
0
0
1
2
0
2
0
2
2
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
1
2
2
0
0
1
2
0
0
1
2
0
2
0
0
0
1
2
0
1
0
0
2
0
2
1
1
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
1
1
1
1
0
1
0
2
0
0
0
1
1
0
2
1
2
2
1
2
0
2
0
1
0
1
0
1
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
2
1
1
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
2
0
2
0
0
1
0
1
1
0
0
0
0
1
1
2
0
0
2
0
0
1
0
2
5
1
1
2
0
0
0
1
0
0
2
1
1
1
0
1
0
0
0
0
2
1
2
1
0
0
0
1
0
0
1
0
0
1
2
2
1
0
1
2
0
0
0
0
2
2
2
2
1
0
0
0
0
0
0
0
1
2
1
0
0
0
2
0
3
0
0
0
3
0
0
2
1
0
0
2
0
0
0
1
1
0
0
3
0
1
0
0
2
0
1
2
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
1
2
0
0
0
0
0
1
0
0
1
0
0
2
1
1
2
1
0
0
0
2
1
2
1
0
1
0
0
2
0
0
0
1
2
1
0
1
1
0
0
2
1
0
0
0
1
2
0
0
1
0
1
1
3
1
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
3
0
2
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
2
0
0
0
0
1
3
1
1
2
0
1
0
0
2
0
0
0
3
2
1
0
1
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
2
2
1
0
1
0
2
2
0
0
1
2
0
1
2
0
0
1
1
0
0
0
1
2
0
0
0
1
2
0
0
2
0
1
0
0
1
1
2
1
1
2
2
1
0
1
0
1
0
0
2
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
3
0
1
2
0
1
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
1
1
0
2
0
1
1
0
0
1
0
2
0
2
0
2
0
0
1
1
1
0
0
0
0
2
0
0
2
0
1
0
1
0
1
0
0
0
0
0
0
0
2
1
0
2
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
1
1
0
2
1
2
2
2
0
1
2
1
0
2
0
0
1
0
2
0
0
2
0
0
0
0
1
0
2
1
1
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
1
2
0
0
1
0
2
0
2
1
0
1
2
0
0
0
1
0
4
1
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
2
0
0
2
0
2
1
0
2
0
1
2
0
0
2
1
1
0
0
2
0
0
0
1
0
2
1
0
1
0
1
0
0
0
0
2
5
1
0
0
1
1
1
1
0
0
1
2
0
0
2
0
0
2
2
0
1
1
0
1
1
0
1
1
0
0
0
0
0
2
0
0
0
2
3
1
2
0
0
0
1
0
3
0
2
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
3
0
2
0
0
1
0
0
0
0
1
0
0
0
0
1
2
1
1
0
0
0
2
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
2
1
0
0
0
0
1
0
1
2
0
2
1
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
1
1
1
1
0
0
2
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
4
2
0
0
0
1
1
1
0
1
3
0
1
1
2
2
1
3
0
0
2
2
0
1
0
0
0
3
0
0
0
1
1
0
2
0
1
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
2
1
0
0
0
0
1
2
1
2
0
0
0
0
1
1
1
0
1
2
5
0
1
0
0
1
0
0
1
0
0
1
2
0
1
0
0
0
2
1
0
3
0
0
2
0
0
0
2
0
2
1
2
0
0
0
0
0
0
0
1
1
1
2
0
3
0
0
0
2
1
0
0
0
0
1
0
0
1
0
1
0
1
0
1
2
0
1
2
1
0
1
2
0
1
0
8
0
0
2
0
0
0
1
0
0
0
2
2
0
0
0
0
2
1
0
0
1
1
0
0
2
2
0
0
1
0
2
1
0
0
2
0
1
2
0
2
0
1
0
1
0
0
2
1
0
0
0
0
1
1
0
0
0
2
0
0
0
0
1
0
1
1
0
0
0
1
1
0
0
1
0
1
0
0
1
0
0
2
0
0
2
0
2
0
1
2
1
0
1
1
1
0
0
0
1
0
0
1
1
0
0
0
0
1
1
0
1
2
0
1
0
0
0
0
2
1
2
0
0
2
0
0
1
1
0
0
0
0
0
0
0
2
0
1
1
2
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
2
2
1
1
0
2
0
1
0
0
0
1
2
1
2
1
0
1
1
2
0
1
1
1
1
0
0
0
0
2
0
0
0
1
0
0
1
0
0
1
1
0
2
0
2
0
2
0
0
3
2
1
3
0
0
1
0
1
0
0
1
2
1
0
1
0
2
0
0
0
1
2
2
2
2
2
1
1
0
2
0
1
0
1
2
0
2
2
1
1
0
1
2
1
0
0
0
0
1
1
0
0
2
2
0
1
0
0
0
0
1
1
0
1
3
0
2
0
0
2
1
0
1
0
2
1
0
2
2
0
0
0
0
0
2
0
0
0
2
2
0
1
0
0
0
1
2
0
0
2
2
0
2
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
3
1
2
0
0
1
2
2
0
2
0
2
0
0
1
0
0
0
2
0
0
1
0
0
1
2
2
2
2
0
1
0
0
1
0
0
0
2
2
1
2
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
2
0
0
0
1
2
0
0
1
0
4
0
0
0
1
0
7
0
2
1
0
1
0
0
0
2
0
3
0
2
3
0
1
1
0
1
0
0
0
1
2
0
0
1
0
0
0
2
1
0
0
0
2
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
3
1
0
0
2
0
2
0
0
1
0
1
2
0
2
0
0
2
0
2
1
2
0
1
0
2
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
1
0
0
2
0
0
2
0
0
1
1
2
0
0
0
2
0
0
2
3
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
1
0
5
0
0
0
1
2
0
1
1
1
0
0
0
1
2
2
0
0
1
0
0
0
2
0
1
0
2
2
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
2
0
0
2
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
2
0
0
2
1
1
1
2
0
0
1
2
0
0
0
1
0
0
0
1
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
2
1
1
2
0
1
2
0
0
1
0
2
1
0
1
0
2
0
0
2
0
1
1
0
0
0
1
0
0
0
1
3
2
1
1
2
2
2
0
0
0
1
2
0
0
2
0
0
1
0
0
2
2
2
0
0
2
0
5
0
0
1
0
1
2
0
0
1
0
0
0
0
1
4
0
1
1
0
0
1
2
0
0
1
1
0
1
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
2
2
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
2
2
2
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
1
0
1
2
0
0
0
1
0
2
0
5
0
0
1
0
0
1
0
0
2
0
0
1
1
0
0
0
0
0
0
2
1
0
1
0
0
2
0
2
0
0
0
1
0
3
0
2
0
0
0
1
1
0
0
0
2
2
0
0
1
2
2
0
2
0
0
0
0
0
2
0
0
1
2
0
0
0
0
1
0
2
2
1
0
1
0
0
2
0
0
2
0
1
0
3
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
2
1
0
0
2
0
0
0
2
0
0
1
1
0
0
1
0
0
1
0
0
0
0
2
1
0
0
0
1
0
1
1
0
3
2
2
1
1
0
1
0
1
1
2
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
1
0
2
1
0
0
2
0
0
0
2
1
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
2
0
0
1
1
0
3
1
1
0
0
1
0
3
0
1
1
0
0
0
1
0
1
1
0
1
2
2
2
2
0
1
0
0
0
0
0
1
2
1
1
1
2
2
0
0
0
0
0
2
0
1
3
0
0
1
1
0
0
1
0
0
0
0
0
0
2
1
0
0
1
1
1
0
2
1
2
0
0
2
0
2
2
2
1
0
0
2
0
0
0
0
2
0
0
1
1
0
1
0
0
2
1
1
0
2
1
2
0
0
1
0
0
0
0
0
1
2
1
0
1
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
2
0
2
0
1
1
0
1
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
4
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
2
1
0
2
0
0
0
0
0
0
0
1
2
0
0
1
0
0
2
1
0
2
0
0
0
0
0
1
0
0
2
1
0
1
0
1
1
0
1
2
1
0
1
0
0
0
1
1
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
1
2
0
0
1
0
0
1
1
0
2
0
1
1
2
2
0
2
0
1
0
1
0
1
0
0
0
0
0
2
0
0
0
0
1
1
1
3
2
0
2
0
0
2
0
0
2
1
0
2
2
2
0
2
1
2
1
0
0
0
1
0
1
0
1
0
0
1
3
0
0
2
2
2
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
2
1
0
3
1
1
0
1
0
0
0
1
0
0
0
0
0
0
1
4
0
0
0
1
0
0
1
1
0
2
0
0
0
0
0
0
1
1
1
2
2
0
2
0
1
1
0
1
2
1
1
0
2
1
0
0
0
0
1
0
3
2
0
0
0
1
0
1
0
1
5
1
0
2
1
1
4
1
0
0
0
0
1
0
1
2
0
1
0
2
2
1
2
2
2
0
2
4
0
0
0
2
0
2
1
0
0
0
0
1
0
0
0
0
4
1
2
0
0
2
0
2
1
2
2
0
0
1
1
0
1
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
1
0
0
4
2
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
1
2
2
0
0
1
0
2
0
0
2
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
2
0
1
0
3
2
0
2
1
0
1
0
2
1
2
0
0
2
0
1
0
1
0
1
1
0
0
0
2
0
2
1
0
0
0
0
0
2
2
1
2
1
0
1
0
2
1
0
0
2
1
0
0
0
2
0
1
1
1
2
0
0
1
2
0
2
0
0
1
1
1
4
0
2
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
1
2
1
0
1
0
0
1
0
1
0
2
0
2
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
1
0
2
1
2
0
0
1
1
0
0
0
0
2
0
1
0
1
1
2
0
2
2
0
0
1
0
1
0
1
0
0
0
1
2
0
0
0
1
1
2
0
2
0
2
0
2
0
2
0
1
1
0
0
0
1
0
1
2
0
1
0
0
0
1
1
0
0
0
0
2
2
0
2
4
0
1
0
1
0
0
1
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
1
1
1
0
0
2
1
0
1
0
0
0
1
0
1
2
1
1
1
2
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
2
1
2
0
1
1
1
0
1
1
0
2
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
9
1
0
0
0
2
2
2
2
2
0
2
1
2
0
2
1
2
0
0
0
0
1
1
1
0
0
2
0
1
1
0
0
1
0
1
0
0
0
1
1
0
0
0
0
1
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
2
0
0
0
0
1
1
0
0
0
0
0
0
2
1
1
0
1
0
1
0
0
0
0
0
1
0
1
0
2
1
0
2
2
2
1
1
1
0
0
1
0
2
0
0
0
1
1
2
0
0
0
2
0
0
0
2
0
2
0
2
0
1
0
2
2
3
1
1
1
0
0
0
0
0
0
2
0
0
0
2
2
2
0
2
0
0
2
1
0
0
1
0
1
2
1
2
0
0
0
1
2
2
1
0
0
1
0
1
2
1
0
0
0
1
2
0
0
0
2
0
2
0
0
0
0
2
0
0
2
1
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
1
0
1
0
0
0
0
2
1
1
1
3
0
2
1
0
1
0
0
0
2
0
1
1
1
0
0
0
1
0
1
1
2
1
1
1
0
0
0
3
2
0
0
1
0
0
0
0
2
3
0
0
1
1
0
2
0
2
2
0
0
0
0
0
2
2
0
2
1
1
0
0
0
3
0
1
0
0
0
1
2
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
1
0
1
1
0
2
1
0
0
0
1
0
1
4
2
1
0
0
0
2
0
0
0
0
0
0
0
1
2
0
2
1
0
0
3
1
0
0
0
0
2
0
2
2
0
1
1
0
1
2
0
2
0
0
0
0
1
2
2
0
1
0
4
0
1
0
1
0
1
0
0
1
0
0
0
1
0
0
2
2
0
0
1
1
2
0
0
0
1
2
2
0
0
2
2
2
0
0
0
0
2
0
2
0
1
1
0
0
1
0
1
0
1
2
2
0
0
1
1
0
0
0
0
0
0
0
1
0
2
1
2
0
1
3
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
1
1
2
4
0
1
0
0
2
1
0
1
0
1
0
2
1
1
0
1
1
0
0
0
2
1
0
0
0
0
0
1
2
0
0
0
0
0
1
1
0
1
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
2
0
2
1
0
0
1
0
0
1
0
0
1
0
2
2
0
1
1
0
2
1
0
3
0
0
0
1
1
0
2
2
0
0
1
2
0
1
0
2
1
0
0
1
0
2
1
2
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
1
0
0
1
1
2
0
0
2
1
2
1
3
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
2
1
0
1
0
0
1
0
1
2
2
0
2
2
1
4
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
2
0
2
0
0
0
0
0
1
0
1
2
0
1
1
0
0
0
1
0
2
0
2
2
0
1
0
1
2
0
0
0
0
2
2
0
1
0
0
0
1
0
2
0
2
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
1
3
0
1
0
1
2
0
2
1
1
1
0
0
1
1
0
0
2
2
0
0
0
0
0
0
0
2
1
2
0
0
0
0
1
1
0
1
1
2
0
0
1
0
0
2
1
0
2
0
3
1
0
0
1
2
0
0
1
0
2
2
0
2
1
1
0
1
0
1
0
0
0
1
2
1
0
0
1
1
0
0
0
0
1
0
0
1
2
0
0
0
1
0
1
2
1
2
0
1
3
0
0
0
0
0
2
0
2
0
1
0
2
2
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
1
0
1
0
1
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
2
1
0
1
0
0
2
2
0
1
0
0
1
2
0
0
5
1
0
0
5
0
0
1
1
0
1
1
0
0
0
0
0
1
2
0
0
0
0
1
1
2
0
2
2
2
1
2
0
1
1
2
1
0
0
0
2
2
0
2
2
2
0
0
2
0
0
1
1
0
0
2
0
0
1
0
0
0
2
2
1
2
0
0
0
0
0
0
1
0
0
0
0
2
2
1
0
1
0
0
2
2
2
1
0
0
0
1
0
1
0
1
1
1
1
0
0
0
0
0
1
2
1
1
1
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
1
3
1
1
0
1
2
0
0
0
0
3
0
0
0
2
0
1
0
0
0
1
1
2
1
0
2
0
0
0
2
0
0
0
0
0
0
0
4
0
0
1
1
2
1
2
0
1
2
1
0
0
1
0
0
0
0
0
1
1
2
0
2
0
2
1
0
1
0
1
0
0
2
0
0
0
0
1
0
2
1
0
1
0
0
0
1
0
0
2
1
0
1
0
1
0
2
0
1
0
0
0
0
1
0
0
1
2
2
0
0
0
0
2
0
0
2
1
2
0
0
2
1
0
2
0
0
0
2
0
0
0
0
2
0
2
2
0
1
2
0
0
2
0
0
2
3
0
1
0
1
2
2
1
0
2
0
2
0
1
2
0
0
2
1
1
0
0
0
0
0
1
1
1
0
0
0
0
1
1
0
5
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
1
2
1
0
2
1
0
1
0
0
0
0
0
0
1
0
0
2
2
1
0
0
0
0
0
2
2
0
0
0
0
0
1
1
0
2
0
0
2
2
0
1
1
0
0
0
0
0
0
1
0
1
1
1
0
0
0
1
2
2
2
2
0
2
1
0
0
1
1
0
2
0
1
2
1
0
0
2
0
0
2
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
3
0
0
2
0
2
1
1
0
3
0
1
2
0
2
0
1
1
0
1
2
0
2
0
0
2
2
0
1
0
0
1
1
2
0
0
0
0
0
4
0
0
0
0
0
0
0
3
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
2
0
1
0
0
1
0
2
2
0
2
2
0
0
1
0
0
0
1
0
1
2
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
6
0
1
1
0
0
2
2
1
0
0
0
2
0
1
1
0
2
1
0
0
2
0
0
0
1
0
2
1
2
2
1
0
0
0
2
2
1
1
1
1
1
1
0
0
1
1
2
0
0
3
0
1
3
1
0
0
0
0
1
1
0
0
2
0
0
0
1
0
1
2
1
0
1
0
0
0
1
0
1
2
2
0
2
1
0
0
3
2
1
0
0
2
0
1
0
1
0
1
1
0
0
0
0
0
2
0
2
0
0
0
1
1
1
0
0
1
2
0
2
0
0
0
0
2
0
0
0
1
3
2
0
1
2
1
0
0
0
0
2
0
2
1
0
2
0
2
2
0
0
0
0
1
2
1
0
1
2
2
0
2
0
0
0
2
1
1
2
2
0
0
0
1
1
2
1
0
0
0
0
2
2
0
0
0
1
0
0
1
2
0
0
0
1
0
0
2
1
0
2
0
0
4
2
1
0
2
1
0
0
0
0
0
2
0
0
0
0
1
2
0
0
2
2
0
0
1
1
3
1
0
2
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
1
2
0
2
1
0
1
2
0
0
0
0
2
0
1
0
0
0
1
2
1
0
1
1
2
1
3
0
0
2
0
0
2
0
0
0
0
0
1
2
6
0
0
2
2
0
2
1
2
2
0
2
1
1
0
1
0
1
2
0
2
2
1
0
2
2
1
1
0
1
0
2
0
0
0
1
0
0
0
0
0
0
1
2
0
2
2
0
1
2
2
0
0
0
0
0
0
0
1
1
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
1
1
1
1
2
0
0
0
0
0
0
2
0
0
2
2
0
1
0
0
0
1
1
0
0
0
1
4
0
1
0
0
1
0
1
2
2
0
0
2
0
2
0
0
1
0
1
0
0
1
0
0
1
0
1
1
0
0
0
1
1
1
2
2
0
2
2
0
0
0
0
2
1
1
1
0
0
0
1
0
0
2
0
2
0
0
0
0
2
0
1
1
1
0
0
1
1
2
2
1
0
0
2
2
2
0
2
0
2
2
0
1
0
0
2
0
0
1
1
0
2
0
2
1
1
0
0
0
0
1
1
1
2
2
0
0
0
0
1
2
2
0
1
0
0
0
2
0
0
0
0
1
2
0
0
1
2
2
0
2
0
1
2
2
0
0
1
1
1
0
1
0
1
1
0
1
0
0
0
1
2
1
0
0
1
0
0
2
1
3
0
0
0
0
0
0
2
0
0
0
1
2
0
2
2
0
2
0
0
2
1
1
0
1
0
0
1
0
0
2
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
2
0
1
1
2
1
1
2
2
0
0
0
2
0
1
2
0
2
0
0
0
0
1
1
0
0
0
1
0
0
0
0
2
2
0
0
2
2
0
1
0
0
2
1
0
1
0
2
2
0
0
1
0
0
1
0
0
0
0
1
1
1
0
1
3
2
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
1
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
1
1
2
0
0
0
1
0
2
2
2
0
1
0
1
0
0
2
1
0
0
0
2
1
2
0
0
2
0
1
0
0
2
0
1
0
0
0
2
2
0
0
1
2
2
2
0
0
2
0
1
0
0
0
0
0
0
0
2
1
0
0
0
1
1
0
0
1
0
4
1
2
0
1
0
0
0
0
0
1
0
0
0
1
0
2
1
2
0
1
1
1
0
2
2
1
0
0
0
0
2
0
0
1
2
0
1
0
1
0
1
0
2
2
1
0
0
0
1
1
2
0
0
0
3
1
1
2
0
0
1
0
0
0
0
1
2
0
0
0
0
1
2
2
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
1
1
0
1
0
0
0
0
0
0
2
0
0
1
0
1
0
1
2
1
2
2
1
0
2
0
2
1
0
1
1
0
0
0
0
0
0
2
1
2
0
2
0
0
2
1
1
0
0
1
2
0
4
0
0
0
0
0
1
0
2
0
0
1
1
1
3
1
2
3
0
0
0
2
0
3
0
2
1
2
2
2
1
2
2
0
0
1
0
0
1
0
0
2
2
2
0
0
0
0
2
1
0
1
0
0
0
2
1
1
0
1
0
0
1
1
0
1
0
0
2
2
1
0
2
2
1
0
1
0
0
0
0
1
0
1
0
3
1
0
0
2
0
1
0
0
1
2
0
1
0
2
0
0
1
0
1
2
2
0
3
1
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
1
0
2
0
2
1
2
0
0
1
0
0
2
0
2
0
3
3
0
0
0
2
0
0
3
0
0
1
2
1
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
2
2
0
2
0
1
2
0
0
2
0
1
2
1
0
2
0
0
0
0
0
0
4
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
1
2
1
0
1
0
0
0
0
0
0
2
2
2
1
0
0
0
0
2
1
0
0
0
0
0
2
2
0
0
2
2
2
1
0
0
1
0
0
2
0
1
1
2
0
2
0
0
0
2
2
0
1
0
3
0
2
2
2
2
0
0
0
0
2
2
2
0
1
0
0
2
0
0
0
0
0
1
1
0
1
1
0
2
0
0
1
0
0
0
1
2
0
0
3
0
3
0
0
1
0
0
1
0
0
0
0
0
2
2
0
0
0
2
0
0
2
0
2
1
0
0
0
1
1
1
1
1
1
1
0
0
0
0
3
0
1
0
0
0
2
0
1
2
1
1
0
2
1
0
1
2
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
1
0
1
2
0
0
2
0
0
1
2
1
0
0
1
1
1
2
1
0
1
0
0
0
0
0
0
0
1
1
0
1
1
0
1
0
1
2
2
0
0
1
2
2
0
0
0
0
0
2
0
0
0
2
1
2
0
1
0
0
1
0
0
2
0
0
1
0
3
2
0
0
2
2
0
0
0
1
0
0
0
0
1
0
2
1
2
0
0
2
2
0
2
0
0
0
0
2
0
2
2
2
1
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
2
2
1
2
2
0
0
0
1
2
2
0
0
0
0
0
1
0
0
0
0
1
1
2
0
1
0
1
2
1
2
2
0
0
0
0
0
0
1
0
0
0
2
1
2
0
0
3
0
0
1
2
0
0
2
0
2
1
0
0
2
1
2
0
1
2
0
1
1
1
0
0
2
0
1
1
1
0
0
1
0
1
0
0
0
0
1
1
0
1
1
3
0
0
0
1
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
1
3
0
0
1
2
3
0
1
0
0
2
0
0
1
0
0
2
0
1
1
0
2
0
1
0
1
1
0
1
0
1
1
0
2
0
1
2
0
0
1
2
0
1
2
0
0
2
1
0
0
0
0
0
0
0
1
1
0
1
0
2
2
1
0
2
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
2
0
1
1
1
0
1
0
0
0
0
1
0
1
0
1
2
0
0
0
1
2
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
2
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
2
0
0
1
0
1
2
0
0
1
0
0
0
0
0
3
2
0
0
1
0
0
0
2
0
0
0
2
1
0
1
0
1
2
0
0
1
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
2
2
1
0
1
1
2
2
0
2
1
0
0
1
1
0
2
2
0
2
0
0
1
0
0
0
0
0
0
0
1
1
2
2
0
0
1
0
0
0
0
0
0
0
2
0
2
1
0
0
1
2
1
0
0
1
0
1
1
0
0
1
2
0
1
0
0
1
2
0
2
0
0
0
1
2
0
0
0
2
0
0
2
0
1
1
0
0
0
2
0
1
2
1
0
0
0
0
0
1
1
0
0
2
2
1
0
0
2
2
0
1
2
1
0
3
4
0
1
0
2
1
2
2
0
0
0
0
1
1
0
0
0
0
0
1
0
1
2
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
2
1
2
1
0
0
0
0
2
0
2
0
1
2
0
0
1
2
0
0
0
0
0
0
0
1
1
1
0
2
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
1
2
1
1
0
0
1
0
1
1
2
0
1
2
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
2
0
1
0
2
0
0
1
2
1
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
1
2
0
2
0
1
0
0
0
2
0
0
0
2
1
0
0
1
0
2
0
1
1
0
0
2
1
1
2
1
2
0
1
0
0
0
3
0
1
4
0
0
1
1
0
0
0
0
1
2
0
1
2
0
2
1
0
0
1
1
1
0
0
0
0
0
1
1
1
0
0
0
0
2
1
0
2
2
2
0
0
2
2
1
2
2
0
0
0
0
2
1
4
0
2
0
0
0
0
0
1
0
0
0
0
0
1
2
0
2
1
0
0
2
0
0
1
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
2
0
2
2
0
0
0
0
0
1
0
2
2
0
2
0
0
0
1
0
1
1
1
0
0
1
2
0
1
0
0
1
0
0
2
1
0
0
0
0
0
2
0
0
1
0
0
1
0
1
0
1
0
0
1
0
0
0
1
1
1
2
0
0
3
2
1
0
3
0
0
0
1
0
1
0
2
0
0
0
2
1
0
0
1
2
0
1
2
0
2
1
0
0
0
0
2
1
1
1
2
0
1
1
2
0
0
0
1
1
2
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
1
1
0
1
1
2
1
2
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
1
2
7
1
0
0
2
1
0
0
0
0
2
2
0
0
1
0
0
0
0
0
1
1
2
1
0
1
0
2
1
1
0
0
0
2
0
1
2
0
1
0
0
1
0
0
0
1
0
0
1
2
2
2
0
3
1
0
0
0
2
1
1
1
1
0
2
0
0
2
2
0
2
0
0
0
1
0
1
2
0
0
4
0
1
1
0
0
0
0
0
1
2
2
2
0
2
2
2
0
0
0
2
0
2
0
0
2
1
0
1
2
2
1
1
1
0
2
0
3
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
1
2
0
0
1
0
0
2
2
0
0
0
1
0
2
0
2
0
0
2
2
0
0
0
0
1
0
1
0
1
0
2
0
0
1
0
0
2
1
0
2
2
1
0
0
0
1
1
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
2
0
1
2
0
2
1
0
2
0
1
0
0
1
0
0
0
2
0
0
0
2
1
0
0
1
0
2
1
0
0
0
0
0
0
0
2
2
2
0
0
1
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
1
1
1
0
0
2
4
1
1
0
2
0
2
0
1
1
0
1
2
1
0
2
1
0
0
1
1
0
1
0
0
0
1
2
2
2
0
2
2
1
0
0
1
0
0
2
1
1
3
1
1
1
0
0
1
0
0
2
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
1
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
1
2
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
2
0
2
2
1
3
0
2
0
0
1
1
0
0
0
0
0
1
1
0
0
0
1
0
0
2
0
1
0
0
1
0
4
0
0
0
0
0
1
2
0
1
0
1
0
1
0
1
1
0
1
0
0
1
0
2
2
1
0
0
1
1
2
0
1
5
1
1
0
1
0
0
1
1
2
0
0
0
2
0
0
1
1
0
0
1
0
2
3
1
2
0
2
2
1
1
0
1
1
0
0
0
0
1
0
0
2
2
1
0
0
0
1
0
0
0
1
0
3
0
0
0
1
0
2
2
1
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
2
0
1
0
0
2
1
0
0
0
2
0
0
0
1
1
0
3
2
2
1
0
0
0
2
0
1
1
2
0
0
0
0
0
1
0
1
2
2
0
1
0
0
2
2
0
0
0
0
2
2
0
0
0
2
2
0
0
0
2
0
0
0
1
1
1
0
1
0
0
1
0
6
0
0
1
2
0
0
0
0
0
0
1
1
0
1
2
0
0
0
1
0
1
0
2
0
0
1
0
2
0
1
0
0
2
1
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
1
2
1
1
0
1
2
0
0
2
1
0
0
0
0
0
0
1
2
2
2
0
1
0
0
1
0
0
0
0
0
0
2
0
0
1
0
1
0
2
2
0
2
1
2
1
0
1
1
1
0
1
2
0
6
2
0
1
0
0
1
0
2
1
0
2
1
1
0
2
0
0
1
0
0
2
2
0
0
0
0
2
0
1
2
1
0
2
0
2
1
1
0
0
0
0
3
0
0
1
2
1
0
0
0
0
0
1
1
0
1
0
2
1
0
0
0
1
2
2
1
0
2
0
0
0
2
2
0
0
0
0
0
2
1
2
1
1
0
0
0
0
3
0
0
0
1
2
2
0
2
2
0
2
0
3
0
0
1
0
9
1
0
0
1
0
2
2
2
1
0
2
0
0
3
0
0
2
0
1
0
0
0
0
1
0
1
1
0
0
0
2
0
0
0
0
2
2
1
1
1
0
1
0
2
0
0
1
0
2
2
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
1
0
1
2
0
0
0
2
2
0
0
0
0
0
0
1
0
2
1
0
0
1
0
1
0
0
1
0
1
0
0
1
2
0
1
2
1
2
1
1
0
0
0
0
0
0
0
2
0
1
3
0
0
0
2
1
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
2
0
1
1
1
0
1
0
1
0
0
2
2
1
0
2
0
0
0
0
0
1
2
1
0
1
1
0
0
1
2
1
0
0
0
0
0
0
0
0
1
2
0
1
1
1
0
0
0
1
1
2
0
0
0
2
0
0
2
0
1
0
0
1
0
0
0
2
0
2
0
0
0
1
2
0
1
1
1
0
1
1
2
0
1
0
0
1
1
1
0
2
0
2
2
0
1
1
1
0
0
0
2
0
0
5
1
0
1
0
1
2
0
0
0
0
0
0
0
1
1
2
1
0
0
1
1
2
1
0
0
1
2
1
1
0
0
0
0
0
0
0
4
0
1
0
1
0
0
3
0
0
0
0
0
0
1
0
1
1
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
1
2
0
0
2
4
1
0
0
3
0
0
2
2
0
2
0
0
0
0
0
0
2
1
0
1
0
1
1
2
1
0
1
1
0
1
0
2
0
0
0
1
1
0
0
1
1
1
0
1
3
3
0
0
0
0
2
0
0
0
2
0
0
1
0
0
1
0
0
0
5
1
0
0
0
1
1
0
0
2
0
2
1
1
0
1
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
2
0
0
1
0
1
0
0
1
0
0
0
2
2
0
2
0
0
0
1
3
1
0
0
0
0
1
0
2
0
2
0
1
0
1
0
0
2
1
0
1
0
1
0
2
1
1
0
1
1
0
0
0
2
0
0
1
0
1
0
1
0
0
1
0
1
1
0
0
0
0
1
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
2
1
0
2
0
0
0
0
0
2
1
0
0
0
2
2
1
0
0
2
2
2
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
2
2
1
0
1
0
0
1
0
0
1
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
2
2
1
1
0
2
0
0
1
0
3
0
0
0
1
1
0
0
2
1
0
2
2
0
0
0
1
2
1
1
0
0
0
1
0
0
0
0
1
0
0
0
3
0
1
2
0
0
0
0
1
1
0
0
0
2
1
2
2
1
0
0
1
0
1
0
0
0
0
0
1
1
0
2
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
2
0
1
0
2
0
0
1
2
3
0
2
0
0
0
2
1
0
0
1
2
0
0
1
2
0
2
0
0
2
0
0
1
1
1
0
0
0
0
0
0
1
0
1
1
0
2
0
0
0
2
0
0
0
2
0
0
0
0
2
1
0
1
5
2
0
0
1
2
0
1
0
0
2
5
2
1
0
2
2
0
0
0
0
0
1
2
2
0
1
0
2
0
0
0
0
1
1
0
0
1
1
2
2
1
0
0
2
0
1
0
0
0
1
0
1
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
2
3
2
0
0
0
1
2
2
0
0
0
0
0
2
2
2
0
1
0
0
0
1
1
2
2
0
0
2
0
0
0
1
1
3
0
2
0
0
1
2
2
0
0
0
2
1
2
0
2
0
0
0
0
0
2
0
0
1
1
0
1
0
0
1
0
0
1
0
0
1
0
3
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
2
1
0
0
0
0
0
2
2
0
0
0
0
0
1
0
1
1
0
2
0
0
4
0
1
1
0
0
0
0
1
1
2
0
1
0
0
0
0
2
0
0
0
2
0
0
2
0
1
2
0
2
0
2
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
1
0
0
1
2
1
0
1
1
1
1
1
0
0
0
1
1
2
1
0
0
1
1
0
0
0
1
0
2
2
1
2
0
1
0
0
0
2
0
0
0
1
0
0
1
0
2
0
2
0
0
1
2
0
0
1
0
0
0
3
0
2
0
1
0
0
0
2
0
2
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
2
0
2
1
2
2
0
2
0
5
0
0
0
2
0
0
2
0
1
1
2
0
1
0
2
1
1
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
1
1
0
0
0
0
2
1
0
0
1
0
0
1
0
0
2
1
0
2
2
0
2
1
0
0
1
0
0
0
0
0
1
0
0
0
1
2
2
0
0
1
0
2
0
0
2
0
2
0
1
1
0
0
1
2
1
1
0
2
2
0
1
0
2
2
2
0
0
0
3
0
0
1
0
1
0
0
2
0
0
0
6
0
1
0
1
2
0
1
2
1
1
0
0
0
0
0
1
2
1
0
1
2
1
1
0
0
0
1
1
0
0
0
2
0
2
0
0
1
2
1
0
2
1
1
0
0
0
1
1
1
0
0
0
2
2
0
2
0
0
0
1
0
0
1
1
0
0
1
0
0
2
1
0
1
0
1
1
1
1
0
0
2
2
0
0
1
0
2
0
0
2
1
1
1
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
1
1
0
1
1
3
1
0
2
2
0
0
1
0
2
0
2
0
0
0
1
2
0
1
1
0
2
0
0
2
2
0
0
0
0
0
0
1
1
2
0
0
1
1
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
1
1
2
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
2
2
0
0
0
2
1
1
0
1
0
0
0
1
0
0
2
1
0
0
0
0
0
0
2
5
1
1
0
0
0
1
0
0
0
0
1
2
1
0
0
0
0
2
0
1
2
0
0
2
0
0
2
0
0
1
2
0
1
2
0
2
0
0
2
2
0
0
2
0
2
2
0
0
1
2
0
1
0
0
3
0
1
2
2
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
2
2
0
0
0
0
1
2
2
1
0
2
2
2
2
0
0
0
0
1
0
0
1
1
0
0
0
2
2
2
2
1
0
2
0
0
1
2
0
0
1
0
1
0
0
0
0
0
1
1
0
0
1
1
0
1
1
0
0
2
0
0
0
0
1
1
0
0
1
2
0
0
0
0
1
1
0
1
0
1
0
0
1
1
0
0
1
2
0
2
0
1
0
0
0
1
1
0
3
0
0
0
1
0
0
1
1
2
0
1
1
1
0
2
0
0
0
2
0
0
0
3
0
1
0
0
0
1
2
1
0
1
2
0
2
1
0
2
0
1
0
2
0
2
0
2
1
0
0
0
2
1
1
0
6
0
0
0
0
0
0
0
2
0
0
0
1
1
2
0
0
0
3
2
0
2
2
2
0
0
2
0
2
0
0
0
0
0
1
1
0
2
0
1
1
0
0
0
2
1
1
2
0
1
1
0
0
1
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
2
1
0
1
1
1
0
0
0
0
0
2
1
0
2
0
0
1
0
1
0
1
1
0
2
0
0
0
0
0
0
2
0
1
0
1
0
1
1
0
0
0
2
1
1
0
0
0
0
2
0
1
1
0
1
0
0
0
3
1
1
1
1
2
0
1
0
2
0
2
0
0
0
3
0
0
2
0
2
2
0
1
2
0
0
0
0
2
0
2
0
0
1
2
2
1
1
2
2
0
2
1
0
0
2
2
0
2
1
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
2
0
0
1
0
2
1
0
1
2
1
2
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
3
2
0
0
0
0
2
0
0
3
2
3
1
1
1
1
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
4
0
0
1
1
2
0
2
1
2
0
0
2
0
0
4
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
2
1
0
1
2
0
0
0
1
1
0
0
0
0
2
0
1
1
1
0
2
2
0
0
1
0
2
0
0
0
2
2
0
0
0
0
0
0
2
2
1
0
0
2
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
2
0
1
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
2
0
1
1
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
2
2
1
1
0
0
0
2
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
2
0
0
1
2
2
0
0
0
1
2
1
1
1
2
0
0
2
0
1
0
2
2
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
2
2
0
0
0
1
0
0
2
0
0
0
0
0
1
1
2
3
0
3
2
0
0
3
0
2
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
1
1
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
2
0
0
0
2
1
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
3
2
0
1
0
1
2
2
1
0
1
0
0
0
3
1
1
0
0
2
0
0
0
0
0
0
1
1
2
0
0
1
1
1
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
2
0
1
1
1
0
0
0
1
2
1
0
1
3
0
2
1
2
1
2
0
1
0
1
0
1
2
2
1
0
2
2
2
0
0
2
1
0
1
0
1
1
1
0
0
0
2
0
1
0
0
2
1
0
0
0
0
0
1
0
1
0
1
1
0
2
1
0
1
0
0
1
1
0
0
2
0
2
1
0
1
1
0
0
0
0
0
2
0
0
1
2
0
0
0
2
1
2
0
3
1
2
4
0
0
1
1
0
2
3
0
0
0
1
0
0
1
1
1
1
2
0
0
1
2
0
0
1
0
2
0
0
1
0
0
0
0
1
2
2
0
0
1
1
0
2
0
0
2
1
0
0
0
0
2
2
1
0
0
0
2
0
1
1
2
0
1
0
0
0
0
0
1
1
2
0
1
2
0
0
0
0
1
0
1
2
0
0
1
0
0
1
0
2
1
0
0
2
1
0
2
0
1
4
0
0
0
0
0
1
0
0
0
2
1
0
0
0
1
1
3
1
3
0
0
2
1
0
0
0
2
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
1
2
1
0
2
0
0
1
1
2
2
0
0
1
0
6
0
1
1
0
3
1
0
0
1
0
0
2
0
0
1
2
2
0
0
0
0
2
0
0
1
3
1
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
4
0
1
1
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
2
2
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
1
0
0
2
1
0
1
3
1
0
1
0
1
0
3
0
0
3
0
0
1
0
0
1
0
2
0
1
2
1
2
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
2
1
1
1
0
0
0
0
0
0
0
0
3
0
0
1
0
2
0
0
0
0
0
2
1
0
1
0
0
2
0
1
1
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
2
1
1
1
2
2
2
0
1
0
0
0
2
0
1
0
0
2
0
1
0
0
0
2
0
2
0
0
0
2
2
0
0
0
1
0
1
0
1
0
1
2
2
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
1
1
0
1
3
2
0
0
0
0
1
2
0
1
0
0
2
0
0
2
2
0
2
0
1
2
1
0
1
1
2
0
0
1
3
0
0
2
0
0
0
2
2
2
0
1
1
0
2
1
1
0
0
0
0
2
2
2
1
0
0
2
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
1
2
0
0
0
1
2
0
0
2
0
0
2
0
0
0
0
1
0
2
1
1
2
6
2
0
0
1
0
1
1
1
0
0
2
3
1
2
0
2
1
0
0
0
0
1
1
0
2
0
2
0
2
2
2
0
2
0
1
0
0
0
0
0
2
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
2
2
0
2
1
2
0
0
1
0
0
2
1
0
0
0
1
1
0
1
1
0
0
1
0
0
0
1
0
2
1
0
3
1
1
0
1
0
2
2
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
4
1
0
0
2
0
2
0
1
0
0
2
2
0
0
3
0
0
2
2
1
2
1
1
2
1
2
0
0
3
0
1
0
1
0
0
0
0
0
0
2
2
2
0
2
0
1
0
0
1
0
0
1
1
0
0
2
2
0
0
0
0
0
0
1
1
0
2
0
2
0
1
0
1
0
2
2
0
1
0
1
1
0
0
0
0
0
0
1
0
0
2
2
0
2
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
1
0
3
0
0
1
0
0
0
0
1
0
0
1
0
0
2
0
2
0
2
1
0
1
0
2
2
0
2
0
0
2
0
1
0
1
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
2
1
0
2
1
1
2
1
0
0
0
1
0
0
0
0
2
0
1
1
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
1
2
1
0
0
0
1
0
0
2
1
0
0
0
1
1
2
1
0
1
2
0
1
0
1
0
2
0
0
0
0
0
0
1
0
1
0
1
0
1
3
0
2
2
1
1
0
0
0
0
0
0
1
0
1
2
2
0
0
0
2
2
0
3
0
0
0
0
0
2
0
1
0
0
0
0
1
0
1
0
0
2
1
1
0
1
0
2
0
0
0
2
0
0
2
2
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
1
0
0
0
3
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
2
0
0
0
2
0
2
2
0
1
1
2
0
0
0
2
1
2
0
2
1
0
0
0
0
0
1
1
0
2
0
1
0
3
0
1
1
0
0
2
0
2
1
0
0
0
0
2
0
0
0
0
0
0
5
2
2
0
0
2
0
2
0
0
0
1
0
0
1
0
0
2
1
0
2
1
0
2
0
0
1
1
1
2
0
0
2
0
1
1
0
0
1
0
1
1
1
0
1
0
3
1
0
1
0
2
0
1
0
2
1
0
0
0
0
1
2
2
0
0
2
3
0
0
2
2
1
0
0
0
0
1
0
0
1
2
0
2
0
0
0
0
0
0
2
1
0
0
1
0
1
0
2
0
0
0
0
1
1
0
1
0
2
2
0
1
0
0
0
5
0
2
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
1
0
1
2
0
1
3
0
0
1
2
0
1
3
0
0
0
2
0
0
1
1
0
2
0
0
0
1
0
0
1
0
1
0
0
0
1
0
2
0
2
0
1
0
1
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
2
0
0
2
1
0
0
1
0
1
2
0
0
0
2
0
1
1
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
2
1
2
0
0
0
1
0
1
0
0
2
0
1
2
0
1
2
0
1
0
1
1
0
2
0
0
0
0
0
0
0
1
1
4
1
0
0
2
0
3
0
0
0
0
0
0
0
3
0
2
1
1
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
1
2
0
0
1
0
0
2
0
0
1
0
1
0
0
0
1
2
3
0
1
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
1
0
2
0
0
1
0
0
0
0
2
0
0
1
1
0
0
0
0
1
1
3
0
2
0
0
2
2
0
0
1
0
0
2
1
1
0
1
2
0
1
1
0
0
0
2
0
2
0
0
5
1
0
0
0
1
0
0
0
2
0
0
0
2
1
0
0
0
2
1
3
1
1
1
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
1
0
1
0
1
2
0
0
1
2
0
0
0
0
1
1
0
2
0
2
0
1
0
0
0
1
1
0
0
0
0
1
1
0
3
1
0
0
0
2
0
0
0
0
1
0
0
0
1
2
0
1
2
0
1
1
0
0
1
1
0
1
0
0
0
0
2
0
2
2
0
0
0
1
0
2
0
0
2
0
0
1
0
2
2
0
0
0
1
0
0
0
2
1
0
2
0
1
0
2
0
2
0
0
0
2
0
1
0
1
0
0
0
0
0
0
1
2
0
1
0
1
1
0
0
4
1
2
0
0
1
1
0
0
0
0
2
2
1
0
1
2
0
0
0
5
1
0
0
0
2
2
1
1
0
1
0
2
0
1
0
0
0
0
1
0
0
0
0
1
1
1
0
1
0
4
0
2
0
1
2
0
0
0
1
0
2
0
2
0
0
0
1
0
0
1
1
0
2
2
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
2
0
0
0
5
2
0
0
0
0
0
1
1
0
2
0
1
2
2
1
1
1
2
0
0
2
0
1
0
1
0
1
1
0
0
1
0
1
0
0
2
2
0
1
2
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
2
1
0
1
1
0
1
0
0
1
0
0
1
2
0
2
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
3
0
0
0
1
1
0
0
1
0
0
0
0
2
0
2
1
0
2
0
2
2
0
2
1
0
0
1
0
2
0
1
0
0
2
0
1
0
0
1
0
1
2
1
0
0
0
2
0
0
1
2
0
0
0
1
1
2
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
2
2
1
1
4
3
1
1
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
1
0
1
2
3
0
1
1
3
0
0
0
1
0
1
1
2
0
0
0
0
1
1
4
0
0
2
1
2
0
0
2
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
2
0
1
0
0
1
0
2
0
1
0
0
0
0
1
0
0
1
1
1
0
0
0
0
2
0
2
2
0
0
1
0
2
2
0
2
2
0
0
0
0
0
0
1
0
1
1
0
1
2
2
0
2
0
0
1
2
0
0
1
1
0
0
1
0
1
0
1
0
1
1
3
1
0
0
2
2
2
0
1
0
0
0
0
1
0
4
0
2
0
0
2
2
0
1
0
2
0
1
0
1
0
0
0
0
2
1
0
2
2
1
1
0
0
0
2
0
0
0
0
0
1
0
1
2
0
0
2
2
0
2
0
0
0
0
1
0
1
1
2
0
1
0
0
0
1
1
0
0
0
2
1
1
1
0
0
4
0
0
0
2
1
1
1
0
0
2
2
0
0
2
2
0
0
0
2
1
0
0
0
0
1
0
0
0
0
2
1
2
0
1
2
0
0
0
2
0
0
2
0
0
2
1
0
1
1
0
0
0
1
1
0
0
1
1
0
1
0
2
0
2
0
0
1
1
1
0
0
2
0
0
2
0
0
0
0
1
1
1
0
0
1
0
0
0
1
0
1
0
0
0
1
0
1
0
1
1
0
1
0
0
1
0
0
1
2
0
0
0
1
2
0
1
2
1
1
16
2
0
2
1
0
2
1
1
0
1
0
1
0
0
0
2
0
0
0
0
1
2
1
0
1
1
3
2
0
0
1
0
2
1
0
0
0
1
0
0
6
1
0
1
0
1
2
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
1
2
1
0
0
0
0
1
2
0
1
0
0
2
1
0
0
0
2
0
0
1
2
1
1
1
0
0
2
0
1
1
0
0
0
0
0
0
0
2
1
1
1
0
0
0
0
2
0
1
1
0
3
0
1
2
1
0
0
0
1
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
4
2
1
0
2
0
2
1
0
0
0
0
1
0
1
0
1
1
0
1
3
0
0
0
0
2
0
1
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
2
0
0
2
0
0
1
3
1
0
2
0
0
1
0
0
0
2
1
0
0
0
1
0
0
1
3
2
1
0
0
0
0
1
0
2
2
2
0
1
0
1
2
1
0
0
0
1
1
0
2
0
0
0
2
2
2
3
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
1
2
0
1
0
0
1
0
1
1
0
0
0
1
3
0
0
0
0
2
3
2
0
2
1
1
2
1
0
0
1
0
0
0
2
0
0
1
2
1
0
1
0
1
0
0
0
0
2
0
0
0
1
0
1
0
1
0
0
0
2
0
0
0
3
0
0
2
2
1
2
1
0
0
0
0
2
0
2
0
3
3
1
1
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
2
1
0
0
0
0
4
1
2
0
0
0
2
0
0
0
0
2
1
2
0
2
1
1
0
0
3
0
0
2
0
2
0
1
0
0
2
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
1
1
0
0
2
0
2
0
0
2
0
0
1
0
2
0
2
1
0
0
2
2
2
0
2
0
2
0
0
0
0
2
2
0
0
1
2
1
0
1
0
0
2
0
1
1
2
0
0
1
1
0
0
2
0
0
0
1
2
2
0
2
0
2
1
0
0
0
0
0
1
0
0
2
0
1
0
1
0
0
0
2
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
1
2
0
2
2
0
1
0
2
0
1
1
0
2
1
0
0
0
3
0
2
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
1
1
2
1
0
0
0
0
0
0
0
0
0
0
2
1
2
0
2
0
0
3
0
2
1
2
2
1
1
1
0
0
2
0
0
0
2
2
2
0
0
1
0
1
1
0
1
0
0
1
0
2
0
2
0
2
1
3
1
0
1
2
0
1
0
0
0
0
0
0
2
2
0
0
1
0
0
1
1
3
0
2
0
1
1
1
0
0
0
1
0
0
0
1
1
2
0
1
1
0
0
0
2
2
3
2
2
1
2
0
0
6
0
2
0
1
1
0
0
1
0
1
0
0
0
1
2
0
2
1
0
0
0
2
2
1
0
0
1
3
1
2
0
0
2
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
1
2
1
0
0
0
0
3
0
2
1
0
1
0
2
0
1
0
0
1
2
1
2
0
1
0
0
0
0
0
1
0
0
3
2
0
1
2
1
0
0
1
1
0
0
0
2
0
0
0
0
2
1
4
1
1
1
0
0
0
1
0
1
2
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
1
0
0
2
0
0
1
1
0
0
0
1
0
1
0
0
1
2
0
1
4
1
2
0
0
0
0
0
2
0
1
0
1
1
0
2
0
1
2
2
1
0
1
3
0
0
1
0
1
2
2
0
0
1
2
0
0
1
0
0
1
0
0
2
0
0
1
0
0
2
1
1
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
1
1
1
1
1
0
0
2
2
0
1
1
0
0
0
1
1
1
1
2
1
0
0
1
1
0
0
0
0
1
0
0
1
1
0
0
1
2
1
1
0
2
0
2
2
0
0
0
4
1
0
0
0
2
1
1
1
1
2
2
0
2
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
1
1
1
2
0
0
1
4
1
1
0
1
0
1
0
0
0
1
0
0
1
2
1
0
0
0
2
0
0
2
0
1
3
0
2
0
0
0
0
2
2
1
1
0
1
0
2
2
0
0
1
0
0
4
0
2
2
0
1
0
2
1
0
0
0
1
0
0
0
1
2
2
0
0
1
0
2
0
0
2
2
2
0
0
1
3
2
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
2
3
0
0
2
0
1
1
1
0
3
1
2
0
1
0
2
0
0
1
0
1
0
0
1
0
1
0
1
1
1
0
0
1
0
0
1
2
0
0
0
1
0
2
0
1
2
4
2
0
1
0
1
0
2
0
0
0
0
1
0
0
2
0
1
1
0
3
0
1
2
1
1
2
0
0
0
0
0
2
0
0
0
0
0
1
0
1
3
2
2
2
0
1
1
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
1
2
1
0
0
0
0
0
2
2
0
0
0
2
0
2
2
1
1
0
2
2
0
1
0
0
1
0
0
0
1
0
0
1
2
2
0
1
0
1
1
0
1
0
2
0
1
2
1
1
0
1
2
0
2
5
1
0
8
0
0
0
0
2
0
0
0
1
1
0
1
0
0
0
0
1
0
0
1
0
0
1
1
1
0
0
1
2
0
2
1
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
1
2
2
1
1
1
1
0
2
0
2
2
1
0
0
0
0
1
0
2
0
0
1
0
0
1
1
1
1
0
1
0
0
0
1
1
1
2
1
0
0
0
0
2
0
0
0
2
2
0
0
1
1
1
0
0
0
0
1
0
3
0
0
3
1
0
1
0
2
2
0
0
2
1
1
1
1
1
1
1
1
0
2
1
3
0
0
0
1
0
2
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
3
1
0
0
0
0
0
0
1
0
2
0
2
0
0
2
0
0
0
1
0
1
0
1
0
1
1
0
1
2
0
2
1
0
0
1
2
0
0
1
0
2
0
2
0
1
0
0
1
2
0
3
0
0
0
1
1
0
0
0
1
0
0
0
2
0
1
1
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
2
0
0
0
0
1
2
0
0
1
5
0
0
0
2
2
0
2
0
1
0
2
0
1
2
0
0
0
0
1
0
2
2
1
4
0
1
0
0
2
0
1
1
1
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
2
0
0
2
2
1
1
0
0
2
1
0
0
0
0
0
1
2
2
0
0
5
0
0
1
0
1
2
1
0
1
2
0
0
1
1
2
1
2
0
1
0
0
2
1
1
0
3
1
0
0
2
0
0
0
1
3
1
0
2
0
0
2
0
0
3
0
1
3
3
0
0
1
1
2
0
0
1
0
0
0
0
3
0
2
2
0
0
2
1
0
0
0
0
0
0
1
2
0
2
0
0
1
0
0
0
0
0
2
1
1
0
0
2
0
2
0
3
1
2
0
0
2
2
2
1
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
2
0
0
1
2
0
0
0
0
2
1
1
0
1
0
2
0
0
1
0
2
2
2
0
0
0
0
0
0
2
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
1
0
0
0
0
2
2
1
0
0
0
0
0
0
1
0
0
1
1
2
1
1
2
1
2
1
1
0
0
1
0
0
0
1
0
2
2
0
0
1
3
1
0
2
2
0
2
0
0
0
2
2
0
0
0
2
2
0
3
1
2
0
1
1
1
1
1
0
0
0
2
2
0
1
1
0
0
0
4
2
0
1
0
0
2
0
0
0
1
0
0
1
0
0
1
1
0
1
0
2
0
2
0
0
0
0
0
0
1
0
0
0
2
1
0
1
0
2
0
2
0
2
1
0
1
0
0
0
0
1
3
0
0
0
1
0
0
0
1
0
1
0
0
0
2
0
2
0
0
2
0
0
0
2
0
0
1
1
0
1
2
0
1
1
1
0
0
0
1
1
0
0
1
0
2
2
1
0
1
3
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
2
1
0
2
2
1
0
0
0
2
2
0
1
1
3
2
2
0
1
0
1
0
1
0
1
1
0
2
0
1
1
1
0
0
0
2
0
0
0
1
0
2
0
7
0
0
2
0
0
1
0
0
1
0
2
0
0
2
0
0
0
0
2
2
0
1
0
0
1
2
0
1
0
0
0
1
0
2
0
0
0
0
2
0
1
0
2
2
0
2
0
2
0
2
0
2
0
1
2
1
1
1
0
2
0
0
1
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
1
0
2
0
0
2
0
0
1
1
0
0
2
0
0
0
2
0
0
0
2
2
0
1
1
0
2
1
0
1
2
2
0
2
4
0
1
2
1
2
0
0
0
0
1
2
1
0
2
0
1
1
0
0
0
0
0
1
1
2
2
0
0
0
0
1
1
0
1
1
0
2
0
2
0
0
0
0
0
1
1
1
1
0
0
0
3
0
2
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
2
0
2
0
0
1
0
2
2
0
0
1
0
0
0
0
0
0
0
0
4
0
2
1
0
0
0
0
0
0
2
0
1
4
0
2
1
2
0
0
2
0
0
2
0
0
0
0
0
1
0
2
2
0
2
0
0
0
0
0
2
1
0
2
2
0
1
0
0
1
0
0
2
0
1
0
0
1
0
0
1
1
0
0
0
1
1
0
1
1
0
0
1
3
2
0
0
2
2
1
1
0
0
2
1
0
0
0
1
2
1
1
0
13
2
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
1
1
0
1
0
0
0
1
0
0
1
0
1
2
0
1
1
0
1
1
0
2
0
2
1
1
1
0
0
0
0
1
0
2
1
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
2
1
0
1
0
1
3
2
0
0
0
0
0
2
0
0
0
0
0
0
1
2
1
1
0
1
1
0
2
0
2
2
0
0
0
2
0
0
1
0
0
2
0
1
2
1
0
0
2
1
0
0
3
3
0
0
0
1
0
0
2
0
0
0
5
1
2
0
2
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
1
1
2
1
3
1
0
0
0
0
1
1
0
1
1
2
0
0
0
2
1
0
1
0
0
0
0
1
1
1
2
0
1
1
0
0
0
0
2
1
0
2
0
2
0
0
0
1
0
0
2
0
1
1
0
0
1
0
2
0
0
0
0
0
1
2
1
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
2
3
0
1
1
0
0
0
0
2
0
1
0
1
1
1
1
0
0
1
0
0
1
1
2
0
0
1
0
0
1
0
0
1
0
0
4
0
0
1
2
0
2
0
1
0
0
0
2
1
0
0
1
2
0
2
2
0
1
1
0
0
0
2
1
2
2
0
1
0
0
0
2
0
0
1
0
2
1
0
0
0
0
0
2
2
1
0
0
0
2
0
0
1
1
0
0
2
1
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
1
1
1
2
2
3
2
0
0
0
0
0
0
0
0
0
2
1
0
1
0
4
0
0
0
1
0
0
2
2
0
0
1
0
0
0
0
0
0
3
0
2
1
0
1
0
0
0
3
2
4
1
0
0
0
1
0
0
0
1
2
1
2
1
0
0
0
1
0
0
1
0
0
0
0
2
2
0
0
1
0
2
0
1
0
0
0
0
0
2
2
0
1
0
2
2
2
2
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
3
0
1
0
2
1
1
2
2
0
1
0
1
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
1
0
2
1
2
0
1
1
1
1
1
1
0
0
0
0
0
0
1
0
0
2
2
1
1
0
0
2
0
0
0
0
1
0
0
0
4
0
0
2
0
1
0
0
0
0
1
0
0
1
1
2
1
5
2
0
2
0
1
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
2
2
0
0
0
1
0
0
0
0
0
0
0
1
2
1
2
0
0
2
1
0
0
0
0
2
0
1
0
1
0
1
0
1
2
0
1
0
1
1
1
0
1
0
1
2
1
0
1
0
1
2
0
2
0
0
0
2
2
2
0
1
1
2
0
0
2
2
2
0
0
1
1
0
0
2
1
1
0
0
2
0
1
1
0
0
0
2
0
2
0
0
1
0
1
2
0
0
1
0
1
0
0
2
1
2
0
0
0
2
0
0
0
2
0
0
0
1
1
2
0
0
1
0
0
0
2
0
2
1
0
0
0
2
1
0
1
0
2
2
0
1
0
0
1
0
0
0
0
0
0
0
2
1
1
2
0
0
0
1
1
0
2
0
0
0
0
1
0
2
0
1
0
2
0
2
0
0
0
1
0
0
2
2
0
0
0
2
0
0
0
0
1
0
1
1
0
1
2
0
0
2
3
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
1
2
0
2
1
1
0
1
1
2
2
0
1
1
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
2
0
0
0
0
0
1
0
0
1
0
1
0
2
6
1
0
1
0
0
2
1
2
0
1
0
1
1
1
2
2
0
0
1
0
0
2
0
2
0
0
2
0
2
1
0
1
2
0
0
0
2
0
0
1
0
1
0
1
0
0
3
0
1
0
0
0
2
0
0
2
2
0
0
1
2
1
1
0
0
1
0
2
0
2
1
1
0
2
1
0
1
0
1
1
0
1
1
0
0
1
0
2
0
0
0
1
2
0
0
1
0
0
1
1
0
0
1
1
0
1
0
1
0
0
4
0
2
2
1
1
0
1
0
0
0
0
1
1
2
1
0
1
0
2
0
0
4
2
0
1
0
1
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
2
1
0
2
0
0
0
2
0
0
0
1
0
2
0
0
0
0
1
2
1
0
0
1
1
0
0
1
0
0
0
0
2
1
1
0
0
1
0
1
2
0
0
0
2
0
0
0
0
1
0
0
1
1
1
0
2
0
1
1
1
0
0
1
2
0
2
1
0
3
2
0
0
2
1
0
0
3
0
0
0
0
0
0
1
2
0
0
0
0
1
2
2
0
0
0
0
0
0
1
0
2
0
1
0
1
0
0
0
1
0
0
0
1
1
0
0
1
0
0
1
3
1
3
2
1
0
1
0
2
0
1
0
0
1
1
2
0
0
0
2
2
1
0
0
2
1
0
0
1
1
1
1
2
0
1
1
2
0
2
0
2
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
2
0
2
1
1
2
0
2
0
0
0
0
0
0
1
0
0
0
0
1
2
2
0
0
2
0
2
0
0
0
0
1
0
0
1
0
1
2
0
1
1
0
1
0
0
1
1
0
1
1
0
0
0
0
2
0
1
0
1
2
2
2
2
0
1
0
0
0
0
2
2
1
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
2
0
2
0
1
0
0
0
3
1
0
0
1
1
0
1
0
2
0
0
0
0
1
0
0
0
1
0
0
2
1
1
0
3
0
0
0
0
0
0
2
1
2
0
0
1
4
0
1
0
2
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
1
0
2
0
0
0
1
2
2
0
2
0
0
1
2
2
0
4
0
0
2
1
2
0
0
0
1
2
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
2
0
0
2
1
1
0
0
0
0
1
2
2
0
2
0
0
1
0
0
0
1
2
3
1
2
2
2
2
1
1
1
0
0
0
2
1
2
0
2
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
2
1
1
0
0
3
2
0
0
1
2
0
1
0
0
1
0
1
1
1
0
2
1
1
0
0
1
0
0
0
2
1
2
2
0
1
2
0
2
0
2
0
0
0
0
0
2
0
0
1
0
1
1
2
1
0
1
2
1
2
0
2
1
2
0
0
0
0
0
0
0
0
2
1
0
1
1
0
0
0
0
1
2
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
1
0
1
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
2
0
0
0
0
2
0
0
0
2
1
0
0
2
2
2
0
0
0
2
0
0
1
0
1
1
0
0
0
2
1
2
0
2
1
0
0
0
1
2
2
0
2
0
1
0
2
0
2
1
0
2
2
1
0
0
0
1
0
0
2
0
2
2
0
1
1
5
0
0
0
0
1
2
1
1
0
0
3
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
2
2
2
0
1
1
0
2
0
0
2
0
0
5
1
1
2
0
2
0
0
0
2
0
1
0
0
1
1
0
0
1
1
0
1
1
0
1
0
0
2
0
1
1
1
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
1
1
1
0
1
2
0
0
1
0
0
0
0
2
1
0
1
1
1
1
2
0
0
0
2
0
2
0
0
0
2
2
2
1
0
2
0
0
1
1
0
2
2
2
2
2
1
1
0
1
0
1
2
0
1
7
0
0
2
0
0
0
2
0
0
0
1
0
0
2
0
1
0
0
2
0
2
0
5
2
1
0
0
1
0
0
1
2
0
0
1
0
0
2
0
1
2
0
1
0
0
0
0
1
0
0
0
0
0
1
0
2
0
2
1
0
0
0
0
2
2
0
0
2
1
0
0
0
1
0
2
1
2
3
2
2
1
1
0
1
0
0
2
0
0
1
1
0
0
0
0
0
0
2
2
0
1
2
0
0
1
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
2
1
1
1
1
1
0
0
0
0
1
0
2
0
1
1
2
0
1
0
2
1
0
1
1
0
0
1
2
0
2
0
0
3
0
1
0
1
0
2
0
1
2
2
0
0
2
1
2
1
0
0
0
0
0
0
0
0
0
1
2
0
0
1
1
0
1
0
2
0
1
0
2
3
0
1
0
2
6
1
0
0
0
1
1
0
2
2
0
0
0
1
1
0
1
0
1
1
2
3
2
0
0
1
1
0
0
0
0
0
0
2
0
2
0
0
1
1
1
0
1
2
0
0
1
0
1
0
0
2
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
1
1
4
0
0
2
0
0
0
0
0
0
2
1
0
0
3
0
0
0
1
0
2
0
0
2
2
0
0
1
0
0
1
2
1
0
0
1
1
2
1
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
1
1
0
0
0
0
0
1
2
2
2
0
0
0
0
0
2
0
2
1
0
1
0
0
1
0
1
0
1
2
0
0
2
0
1
0
0
0
2
0
0
0
2
0
2
2
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
2
1
2
0
0
0
2
0
0
2
1
1
0
0
0
0
1
1
0
0
3
0
1
0
1
0
0
1
0
0
2
0
1
1
1
0
3
0
2
0
2
2
0
1
0
1
0
1
0
1
0
1
1
0
0
2
0
0
0
2
0
0
0
0
1
0
2
1
2
0
0
0
0
1
0
1
0
1
0
1
1
2
0
0
0
0
1
0
2
0
1
2
2
1
0
0
0
0
0
1
2
0
2
0
0
2
2
0
0
1
0
1
1
1
0
0
1
0
0
0
0
2
1
0
1
1
1
0
2
1
2
1
0
3
1
2
0
1
0
0
0
0
1
0
3
0
0
0
0
0
1
2
1
0
0
0
0
0
2
0
1
1
2
1
0
0
0
0
2
0
0
0
0
0
0
1
0
2
1
0
0
0
2
0
0
0
1
0
0
1
0
2
0
1
3
0
2
0
1
1
0
0
0
0
1
0
1
0
0
0
0
1
0
2
0
0
2
2
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
2
0
1
2
0
1
0
0
1
1
0
0
2
1
0
0
0
0
2
0
1
0
0
0
1
1
0
0
2
0
0
2
0
0
1
2
0
1
1
0
2
0
0
1
1
2
1
0
0
1
1
0
3
0
0
0
0
0
1
1
0
2
2
1
0
1
0
1
1
2
2
2
0
2
0
0
0
0
0
0
1
2
0
2
0
2
2
0
0
2
2
0
0
0
0
0
0
2
3
0
2
0
0
2
0
1
1
0
0
0
0
0
0
1
2
1
3
2
0
0
2
0
0
0
1
0
0
1
1
0
1
2
2
0
1
0
0
2
2
0
0
0
2
0
1
0
2
0
5
2
2
0
1
0
0
0
1
0
0
1
0
0
2
0
1
0
1
0
1
2
1
1
1
0
1
0
0
0
0
0
0
1
0
1
0
0
2
0
0
1
0
0
1
2
0
2
1
0
0
0
0
1
0
1
2
2
0
0
1
2
0
0
0
0
2
0
2
0
0
0
1
0
1
0
1
0
1
1
0
2
2
0
0
1
0
2
0
0
0
0
0
2
2
0
2
0
1
0
0
2
0
0
0
2
1
0
0
0
0
1
0
1
0
1
1
1
2
0
0
1
1
0
1
0
2
0
0
2
0
0
1
2
0
1
0
0
2
1
0
0
2
0
0
2
2
1
0
1
1
1
1
0
1
0
1
2
0
0
0
2
1
2
0
0
0
0
6
0
1
0
1
0
0
2
1
0
0
2
0
0
0
0
2
0
1
0
2
0
2
2
0
2
2
0
2
0
0
0
0
0
0
0
1
0
0
1
2
0
2
0
2
0
0
2
0
1
0
2
0
0
0
0
1
0
0
0
0
2
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
1
1
2
1
2
2
1
1
0
0
1
1
0
0
0
1
0
0
2
0
0
1
0
0
0
2
1
0
1
0
0
0
2
0
2
0
1
0
0
0
1
0
0
0
1
0
2
2
0
0
2
0
0
4
1
1
0
1
0
2
0
0
0
2
0
2
2
1
0
0
1
0
1
0
2
0
1
1
0
1
1
0
0
2
1
1
1
0
0
2
0
0
0
1
2
0
2
2
0
1
0
0
0
0
0
0
2
1
0
0
0
0
1
1
0
1
2
0
0
0
2
0
0
2
0
1
0
0
2
0
0
2
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
1
1
0
1
0
1
0
0
2
0
1
0
0
2
0
1
0
2
0
1
1
0
0
0
1
0
2
0
2
0
0
2
0
2
0
0
0
0
0
0
1
0
0
2
2
2
2
0
0
0
2
1
2
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
2
0
0
0
2
0
0
0
0
1
0
0
2
1
11
0
0
1
0
2
0
1
2
0
3
2
0
0
0
0
1
2
1
2
0
1
0
0
2
0
0
2
0
2
1
1
2
0
0
2
1
0
1
0
0
1
1
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
1
0
1
0
0
0
0
2
0
0
1
0
1
2
1
1
0
2
1
0
0
0
0
0
1
2
0
0
1
1
1
1
0
0
0
1
0
2
0
1
2
0
0
1
0
0
2
2
2
0
2
1
0
3
0
0
1
0
0
0
0
0
0
1
2
0
2
0
2
0
0
0
1
0
2
2
1
1
0
0
2
1
0
0
2
0
2
0
1
0
0
0
1
1
1
0
0
1
0
2
2
1
0
0
2
0
0
0
2
2
0
1
0
0
1
0
0
2
2
0
0
1
0
0
0
0
1
1
1
2
1
0
1
0
0
0
0
2
0
0
1
2
0
0
2
0
2
2
0
1
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
1
2
1
0
0
0
2
2
0
0
0
1
1
0
2
2
2
0
0
0
0
1
3
0
0
2
0
0
4
1
0
2
0
1
1
0
2
1
0
0
2
0
0
0
1
0
1
1
0
0
2
2
0
0
0
0
2
1
1
1
2
2
2
0
2
0
0
0
2
0
0
1
1
1
2
0
0
0
1
0
1
0
1
1
1
2
1
0
0
0
0
0
0
0
2
2
0
0
0
2
1
0
1
0
1
1
1
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
2
0
1
0
2
0
2
0
1
0
2
1
0
2
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
1
2
1
1
0
1
0
2
0
1
0
0
0
0
0
2
1
0
0
2
0
1
0
0
2
1
2
0
1
2
2
0
0
1
1
0
1
0
1
0
2
0
0
0
0
0
0
2
2
2
0
2
0
2
0
1
0
0
4
2
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
2
0
2
0
1
1
0
0
0
2
1
2
2
2
1
2
1
0
1
0
2
0
4
0
0
0
0
0
0
1
0
1
1
0
0
3
1
2
0
2
0
1
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
1
0
2
2
0
0
0
0
0
1
0
3
0
2
0
0
0
0
0
1
1
0
0
0
0
0
1
2
0
0
0
1
1
0
0
0
0
2
0
0
0
2
0
0
0
0
2
1
0
0
1
0
1
1
1
2
0
0
0
1
0
1
2
0
1
0
0
0
0
2
1
0
1
0
0
0
0
0
1
1
0
1
1
0
0
0
2
2
0
3
2
1
2
0
0
0
0
2
0
0
1
2
1
1
1
0
0
0
0
1
0
2
2
1
0
0
1
0
2
0
1
0
0
1
2
0
0
0
2
0
0
1
0
1
1
1
2
0
1
1
0
0
0
0
0
1
1
0
3
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
3
0
1
2
0
0
2
0
2
1
0
0
1
0
0
1
1
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
1
1
0
1
0
1
0
0
0
1
0
0
0
1
0
2
0
0
0
1
2
3
2
2
0
1
0
2
1
0
1
1
0
1
1
0
0
0
1
1
1
0
0
0
1
0
0
2
1
0
2
0
0
2
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
2
1
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
1
0
3
1
0
0
0
0
2
0
1
0
0
2
1
0
1
2
0
1
0
1
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
1
0
0
1
0
2
1
2
0
2
0
1
0
0
2
0
0
3
0
0
2
0
1
0
2
1
0
1
1
0
0
1
1
1
0
1
0
0
0
2
0
1
0
2
0
1
2
2
1
0
1
0
1
2
0
0
1
0
1
2
0
1
2
1
1
0
0
2
0
1
2
0
0
0
1
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
1
0
2
2
0
0
2
0
0
0
0
1
0
1
0
2
0
0
0
0
2
1
0
0
2
1
0
0
1
1
0
0
0
0
0
0
0
3
1
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
2
1
2
0
0
2
0
2
1
0
0
2
0
0
0
1
0
0
0
0
2
0
1
0
0
0
3
0
2
0
1
2
0
2
0
0
0
2
0
0
1
1
0
1
2
1
1
2
1
2
2
2
0
0
2
0
0
1
2
1
0
0
1
0
0
0
1
2
0
1
1
0
0
0
0
2
0
0
2
0
0
0
1
0
0
2
1
0
0
0
1
0
1
2
0
3
2
1
1
1
1
0
0
0
2
0
0
1
0
0
2
1
2
0
2
0
1
2
0
2
2
2
2
2
0
1
0
0
2
0
1
2
0
0
0
0
0
2
2
2
1
0
0
1
0
1
1
1
0
2
0
2
0
0
0
0
0
2
0
2
1
0
0
0
0
1
1
2
1
0
1
2
0
0
0
0
4
1
0
1
2
0
0
0
1
0
2
1
2
2
0
1
2
3
0
0
2
1
1
2
1
2
0
1
0
0
0
0
0
2
1
0
2
2
0
0
1
1
0
0
0
0
2
1
0
3
2
0
0
1
2
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
2
0
0
0
1
5
3
1
1
0
2
2
2
0
0
2
0
1
1
0
0
4
0
0
5
0
0
0
0
0
1
1
0
2
2
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
2
1
1
0
0
1
1
1
0
2
1
1
2
0
0
2
2
2
0
0
2
0
1
1
1
0
0
2
3
0
2
0
0
1
0
0
1
1
0
0
0
1
2
1
0
0
1
0
0
0
1
0
2
2
0
0
0
0
3
0
0
0
0
1
0
0
1
1
0
1
1
0
0
2
1
2
1
0
0
1
0
1
0
0
1
0
2
0
2
0
0
0
1
0
0
1
0
2
3
0
0
0
0
0
1
2
2
0
2
1
0
2
0
0
0
1
1
3
1
0
1
0
0
0
1
0
0
0
3
0
1
1
4
1
2
0
0
0
1
0
2
1
1
2
1
0
1
0
1
0
0
0
1
0
0
0
3
1
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
1
0
2
1
0
2
1
0
0
2
0
0
0
0
0
0
1
1
1
0
0
1
0
1
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
4
1
3
2
1
1
0
2
0
0
2
2
1
1
0
1
0
1
1
1
0
2
0
1
0
1
0
2
2
0
0
0
0
1
0
0
1
2
0
0
3
0
0
1
0
2
0
2
2
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
2
0
4
0
0
0
0
1
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
1
2
1
1
1
0
2
0
0
2
0
2
1
0
0
0
1
0
1
2
0
0
0
1
0
1
0
0
1
0
1
0
1
0
0
1
2
1
1
0
1
0
0
0
1
0
2
0
1
2
0
0
0
0
0
1
3
1
0
1
4
2
1
1
0
0
0
1
0
0
0
2
1
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
2
1
0
1
2
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
1
1
0
2
1
0
2
0
0
0
2
1
0
0
1
1
0
3
1
1
1
0
1
0
1
1
1
0
2
2
0
0
0
2
0
0
4
0
1
2
1
0
0
0
1
1
5
1
0
12
2
0
0
0
0
2
0
2
1
0
3
0
0
0
0
2
0
0
1
1
2
0
1
0
2
4
2
1
0
1
1
0
2
2
1
3
0
2
3
1
1
2
2
0
0
0
0
2
0
0
0
0
4
2
3
2
0
4
2
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
1
0
1
1
2
0
2
1
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
2
0
2
2
0
0
1
1
0
0
1
0
0
0
0
1
1
0
0
0
1
2
1
2
0
2
2
1
2
0
2
2
2
2
0
0
0
1
2
2
3
3
2
0
2
2
2
1
0
0
1
0
2
0
2
0
2
1
0
0
2
2
0
1
1
1
0
0
3
0
1
0
2
2
0
1
0
0
2
2
1
0
0
0
0
0
1
1
0
3
0
0
0
0
0
0
0
1
2
1
0
0
2
2
1
0
3
0
1
0
1
0
1
0
1
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
1
0
0
1
0
0
1
0
0
0
0
2
0
2
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
2
0
0
0
0
1
0
2
4
0
2
2
0
0
0
0
0
0
1
0
0
2
2
1
0
1
0
0
0
0
2
0
2
0
2
2
0
0
0
0
1
2
0
1
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
1
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
1
0
1
1
0
0
0
2
0
0
0
1
0
1
0
0
1
1
0
1
0
0
0
0
0
1
1
0
0
0
0
2
1
1
1
2
0
0
2
0
0
0
0
2
1
0
0
0
1
2
1
0
0
2
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
1
0
2
0
1
0
1
0
1
2
0
0
4
2
1
0
0
2
0
0
0
0
0
2
0
1
0
0
1
0
0
1
1
2
0
0
1
1
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
1
1
0
0
0
1
0
1
0
1
2
0
1
1
0
0
0
0
0
0
2
1
1
1
0
2
2
0
0
1
1
1
1
1
0
2
0
0
0
1
2
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
2
0
0
2
1
0
1
3
0
1
0
0
1
2
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
5
5
0
1
2
0
0
0
0
1
0
0
0
1
0
1
1
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
2
1
0
1
0
0
2
1
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
6
0
0
0
0
1
2
0
1
0
0
0
0
1
2
2
1
0
2
0
0
2
0
0
3
0
1
0
1
0
2
0
0
2
0
1
0
0
2
1
1
0
0
4
0
0
0
1
0
0
0
1
0
0
2
1
0
1
0
0
2
0
1
2
0
2
0
1
0
2
3
0
0
0
1
0
0
0
2
2
2
0
1
1
1
0
0
0
0
2
0
0
0
0
1
0
0
0
1
1
0
0
2
1
0
0
0
0
2
0
2
0
0
1
0
1
1
3
0
0
2
0
5
0
0
0
1
2
0
1
0
0
0
1
1
0
2
0
0
0
0
1
0
2
2
2
2
2
0
2
1
3
0
0
2
0
0
0
1
0
0
1
1
0
1
1
1
1
1
1
2
2
1
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
2
1
0
1
0
2
0
2
1
0
1
0
0
0
1
1
4
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
1
0
1
2
1
0
0
2
1
0
0
0
2
0
0
0
0
2
0
2
1
1
0
0
0
0
0
1
2
0
0
2
1
2
2
0
1
2
2
2
1
1
3
4
2
0
0
1
2
1
0
1
0
1
1
1
2
0
0
0
0
0
0
4
0
0
0
2
0
0
0
1
0
2
0
1
0
1
1
0
0
1
1
0
1
0
2
1
0
0
1
1
2
0
1
0
1
0
0
0
0
0
1
1
0
0
1
0
3
0
0
0
2
1
1
2
0
0
1
2
0
2
1
1
1
0
0
2
0
0
0
3
0
2
1
1
0
0
1
0
3
1
0
0
1
1
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
2
2
2
0
1
0
1
0
2
2
2
0
2
2
0
1
0
0
0
1
1
1
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
1
0
1
2
0
0
0
0
1
2
1
2
1
0
0
0
0
0
1
1
1
1
1
0
0
0
2
1
0
0
1
1
0
2
0
0
0
2
2
1
1
0
1
0
0
0
2
0
0
0
0
1
1
2
0
2
0
0
0
4
1
0
1
0
1
1
1
0
0
2
0
0
1
0
1
0
1
0
1
0
0
1
2
0
2
2
0
0
0
0
1
0
2
0
1
0
1
1
2
0
0
0
1
1
1
0
1
0
0
0
1
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
1
2
0
0
0
0
3
0
2
1
0
0
0
0
2
0
1
0
2
0
0
0
0
1
1
0
0
2
2
1
0
0
1
0
0
1
0
2
1
0
4
0
0
0
0
0
0
2
0
0
1
1
1
1
0
0
0
1
2
0
0
0
1
0
0
0
1
1
0
1
2
0
1
1
2
0
2
1
0
0
0
0
0
1
1
1
0
0
0
0
0
1
2
0
0
0
2
1
0
0
0
0
0
2
0
2
1
0
1
2
2
2
1
1
2
3
1
0
0
0
0
2
2
3
2
0
0
0
0
0
0
1
0
0
1
0
1
0
0
2
2
1
3
1
0
0
0
0
2
2
0
0
1
0
1
0
2
0
2
0
0
0
2
0
0
0
0
1
0
2
0
1
1
2
1
0
0
1
1
0
2
0
1
2
0
0
2
0
2
0
0
7
0
2
0
0
1
1
0
1
0
0
0
1
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
1
0
1
2
0
0
0
1
1
0
0
2
0
0
1
2
1
1
1
0
0
0
0
2
0
1
2
0
0
1
2
0
0
0
1
0
2
0
1
2
0
0
2
0
0
1
0
0
1
2
1
0
2
2
0
0
0
0
1
1
1
2
0
2
1
0
0
1
0
0
1
0
2
2
0
2
1
0
1
0
2
0
0
1
0
0
1
2
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
1
1
1
1
3
1
1
0
2
0
1
2
0
1
2
0
1
0
1
0
1
1
0
0
2
2
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
1
1
0
0
2
2
2
2
0
0
0
2
1
1
6
2
0
0
2
2
1
1
1
2
2
2
1
0
1
0
1
0
1
0
0
0
2
1
2
0
0
2
0
0
2
0
0
0
1
0
1
2
0
2
0
2
2
0
2
2
2
2
0
0
1
1
0
0
2
1
1
1
1
0
0
0
0
1
2
0
0
0
0
2
1
0
2
0
1
0
0
0
0
2
0
1
0
1
0
0
0
1
0
0
1
0
0
1
0
0
1
0
3
2
1
0
0
1
1
1
2
0
0
1
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
2
1
0
0
3
0
3
1
2
0
1
0
1
1
2
1
1
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
2
1
1
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
2
0
0
0
1
2
0
0
0
0
0
0
1
1
0
0
1
0
1
2
0
0
1
0
2
0
1
0
0
2
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
1
0
0
1
0
2
1
1
0
0
1
1
0
0
0
1
0
0
2
0
0
0
0
0
0
2
2
2
1
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
2
0
1
0
0
1
1
0
5
2
1
1
0
2
2
0
2
0
1
0
1
0
2
2
1
1
0
3
1
2
1
0
1
2
0
1
1
2
0
0
0
2
1
0
2
2
0
0
0
1
0
0
1
2
2
2
0
1
0
2
0
1
0
2
0
0
0
0
0
3
1
0
0
0
2
0
1
0
0
2
0
0
1
2
2
0
0
1
0
0
2
0
0
1
0
2
1
2
1
0
0
1
1
1
0
1
0
0
1
1
0
0
0
0
0
1
0
1
0
2
0
1
0
0
1
0
1
2
2
2
2
1
0
1
0
1
2
2
1
0
0
1
0
0
2
0
2
0
1
1
0
1
0
1
0
1
0
0
0
0
2
0
0
0
0
0
1
2
1
0
0
2
1
2
0
0
0
2
0
0
0
1
0
0
0
1
2
1
1
1
2
1
1
2
1
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
2
1
0
0
2
2
1
1
1
0
1
1
0
0
0
1
0
1
0
2
0
0
0
0
0
2
0
0
0
3
0
0
1
0
1
0
0
2
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
2
1
2
0
0
2
0
0
2
2
0
1
0
0
2
0
0
0
1
0
2
1
0
0
0
0
1
0
1
0
0
1
1
2
1
0
0
1
0
0
0
2
0
0
1
0
1
2
0
0
0
1
0
2
0
1
0
2
2
0
0
2
3
2
3
2
1
2
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
1
2
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
2
1
0
2
1
0
0
1
0
1
0
3
1
0
0
1
0
1
0
0
0
1
0
0
0
0
2
1
3
1
1
0
0
1
0
1
0
0
0
2
0
1
0
0
4
0
0
1
0
1
0
0
0
2
0
0
1
1
0
1
0
1
0
0
2
2
0
0
0
0
2
1
0
0
0
2
2
1
0
0
0
1
0
1
2
0
2
0
0
3
0
0
1
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
1
1
2
0
1
0
1
0
1
1
0
1
2
1
2
0
1
2
1
1
2
0
0
0
1
0
0
0
0
2
3
0
1
2
2
1
0
0
2
1
0
0
2
0
1
0
1
1
0
1
1
0
0
0
0
0
0
1
0
0
1
0
2
0
1
1
0
1
0
0
0
0
0
1
3
0
0
0
2
0
0
2
1
2
0
0
2
0
0
0
0
1
0
0
0
0
2
0
3
0
0
2
0
0
0
0
0
1
2
2
0
0
2
0
0
0
0
2
1
1
0
2
1
2
0
0
0
1
1
0
0
2
1
2
1
0
1
0
0
1
0
2
2
0
2
2
1
2
0
0
2
2
0
0
0
1
0
1
2
0
0
1
3
0
2
1
0
0
0
2
0
0
2
1
0
1
1
2
1
0
0
2
0
1
0
1
0
0
0
0
2
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
2
2
2
0
0
0
2
1
1
1
0
1
0
2
1
1
1
1
2
0
0
0
1
2
0
1
0
1
0
1
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
2
2
2
0
1
1
0
0
0
0
2
0
0
0
2
0
0
4
0
0
0
1
1
2
0
0
1
2
2
0
0
0
2
0
0
3
0
0
0
0
1
0
2
0
2
2
1
1
0
0
0
0
2
0
0
1
2
0
1
0
0
0
0
1
0
0
0
0
2
1
1
0
1
0
1
1
1
1
1
1
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
3
1
0
0
0
0
0
1
0
1
0
2
2
1
1
0
3
1
1
0
0
0
0
2
0
1
2
0
0
0
0
0
1
1
2
2
1
1
0
0
1
0
0
0
0
1
1
2
2
1
0
0
2
0
2
1
2
0
0
0
2
2
1
1
1
2
0
0
2
0
1
0
0
0
0
4
0
1
0
0
2
0
0
1
0
1
0
0
2
0
0
1
1
2
0
0
0
0
1
2
1
2
1
0
1
0
0
0
2
2
0
1
0
0
1
0
2
0
0
0
1
0
1
2
1
0
0
1
0
0
1
2
0
1
2
1
0
0
0
0
2
1
2
1
0
0
2
0
0
2
1
2
0
1
0
1
1
1
0
1
0
1
1
0
0
0
0
1
0
2
0
2
2
1
2
0
0
0
0
0
0
0
2
0
2
2
1
0
1
2
2
2
0
2
1
1
1
0
1
2
2
0
0
1
1
2
0
0
1
1
0
1
0
1
1
0
0
1
1
2
1
1
2
2
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
2
0
1
2
1
2
1
0
0
1
0
0
0
0
0
2
0
0
0
1
1
0
10
0
0
2
2
2
0
0
1
1
0
0
1
1
2
1
0
1
0
0
2
0
1
2
0
1
0
1
0
0
0
0
2
1
0
2
0
1
0
0
1
0
1
0
0
1
0
1
1
2
3
0
1
0
0
2
0
0
0
1
0
0
1
2
0
2
2
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
1
0
0
1
2
0
2
1
1
2
2
1
1
0
2
2
1
0
3
0
0
2
0
1
2
0
0
0
1
0
1
0
0
2
0
0
1
2
0
3
1
0
0
0
2
0
0
2
1
0
0
0
1
0
0
0
0
0
0
1
2
1
1
0
1
2
0
2
0
1
0
0
2
0
0
0
2
0
1
0
0
0
0
0
3
2
1
2
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
2
0
1
0
1
2
1
1
0
2
0
0
0
0
0
0
0
1
0
0
0
2
1
1
2
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
1
1
0
2
1
0
0
0
3
0
1
1
0
2
0
2
2
2
0
0
2
0
1
1
0
0
1
2
0
0
0
0
1
0
0
0
0
1
1
0
0
2
0
0
0
1
2
2
1
2
1
2
0
0
1
0
0
2
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
2
0
1
0
0
0
2
0
0
1
0
1
0
2
1
1
0
0
0
0
0
2
0
2
1
0
0
0
0
0
1
0
2
0
1
0
3
0
3
1
0
0
0
3
0
0
0
2
0
0
1
2
2
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
1
1
2
1
1
0
0
1
2
1
2
0
0
1
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
2
3
1
0
1
0
1
0
1
0
0
2
1
1
0
0
1
0
2
1
0
0
0
0
0
0
2
0
2
0
1
0
2
1
2
0
0
0
1
1
0
2
13
0
0
1
0
0
3
1
1
0
0
0
2
1
0
1
0
0
0
0
1
0
0
0
2
1
0
0
2
2
0
0
0
0
0
0
2
1
0
1
0
0
1
1
1
1
2
1
0
1
2
1
2
0
0
7
2
0
1
0
2
1
0
2
2
0
0
0
1
0
2
1
0
2
0
1
0
2
0
1
3
2
2
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
1
0
0
1
2
0
1
2
2
0
0
0
0
0
0
0
2
0
0
0
2
2
1
0
1
1
0
1
3
1
0
0
0
0
0
0
0
1
2
0
1
0
0
0
2
0
0
1
1
0
0
2
0
1
1
0
0
2
0
1
0
2
0
0
1
1
0
2
0
2
2
0
0
0
0
1
1
0
0
0
2
2
0
0
1
2
0
0
0
0
3
4
0
0
0
0
0
1
2
1
2
2
2
1
2
2
0
1
2
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
2
1
0
0
0
1
0
0
1
0
2
0
0
1
0
1
0
1
0
0
0
2
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
1
0
2
0
0
1
1
4
2
0
0
0
1
1
2
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
2
1
1
3
2
2
0
0
0
1
0
1
0
0
0
1
1
0
2
2
1
0
0
1
0
0
0
0
2
2
1
0
1
0
0
1
0
1
2
2
3
0
2
0
0
3
0
0
1
1
2
1
0
1
0
2
0
0
0
1
1
0
2
0
1
0
0
0
2
0
0
0
0
2
0
2
1
2
1
2
0
0
1
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
2
1
0
7
1
0
1
0
1
0
0
0
0
2
2
0
0
3
0
0
0
0
0
1
0
2
0
1
0
1
0
0
2
0
0
0
1
2
0
1
0
0
2
0
0
1
2
2
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
2
2
0
0
0
1
0
3
1
0
0
0
1
0
1
0
5
1
0
3
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
3
0
1
2
2
1
2
0
0
0
2
0
0
1
0
0
1
1
1
0
0
0
1
0
0
2
1
2
1
1
1
1
0
1
2
2
0
0
0
0
3
0
1
0
0
3
2
0
0
0
0
1
1
2
1
0
3
1
1
2
1
1
1
0
0
0
1
19
0
0
2
0
3
2
1
0
0
1
0
1
1
0
1
0
1
0
0
1
0
1
0
0
1
3
0
1
2
0
1
0
2
0
2
0
0
3
0
2
1
2
1
2
0
1
0
2
0
0
1
2
3
1
0
0
0
2
0
0
0
0
0
2
0
1
0
1
1
0
1
2
1
0
2
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
1
2
0
0
1
0
0
0
2
0
0
0
1
2
0
0
3
0
1
0
1
0
0
0
0
2
1
0
2
0
2
0
0
0
1
0
0
0
4
0
0
1
0
1
0
0
0
0
1
0
2
2
0
2
0
1
0
0
0
0
0
3
2
0
0
0
0
0
1
1
1
3
2
0
2
2
0
0
1
2
0
0
2
0
0
0
0
0
2
2
1
1
0
0
0
2
0
1
0
0
2
0
0
0
0
1
1
2
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
2
1
0
1
0
1
2
1
0
0
2
0
0
1
4
0
0
0
1
0
1
2
0
2
2
0
0
1
2
2
0
2
0
0
0
1
0
0
1
0
2
1
0
2
1
2
0
2
1
0
1
2
1
2
2
0
1
1
0
0
1
0
0
0
3
0
2
0
0
3
0
1
0
0
0
0
2
0
1
0
1
0
0
0
1
0
0
0
1
1
2
0
2
2
2
2
1
1
2
0
3
0
0
1
0
0
0
4
0
0
2
2
1
2
0
0
0
1
0
1
1
0
1
0
1
0
1
0
0
1
0
2
1
0
0
0
2
0
2
1
1
0
0
0
0
0
2
0
0
0
1
1
2
0
0
0
1
0
2
0
1
0
0
0
1
0
0
1
0
1
1
3
0
1
1
0
1
0
0
0
2
1
0
0
0
2
2
0
1
0
0
1
0
2
2
0
0
3
2
2
4
0
4
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
2
2
1
0
0
1
0
2
1
0
2
0
0
1
2
2
2
3
0
2
0
0
2
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
2
0
0
2
0
2
1
0
0
2
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
1
3
1
1
2
2
0
0
1
1
1
2
1
0
0
0
1
0
0
2
2
1
0
0
0
0
0
0
1
2
0
2
2
0
1
2
0
1
1
0
2
0
0
2
4
2
0
0
1
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
3
1
1
2
0
1
2
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
1
0
4
2
0
2
0
0
1
0
2
1
2
0
0
1
1
0
1
0
0
2
0
0
1
1
0
0
1
2
0
1
0
1
0
1
0
0
2
0
0
1
1
1
2
1
0
2
1
3
2
0
1
2
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
2
2
2
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
2
1
3
0
1
0
1
0
1
0
1
0
1
0
4
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
1
2
2
2
2
1
2
1
1
0
0
2
1
0
0
2
2
0
1
0
2
2
0
0
0
0
0
1
0
1
0
0
1
0
0
0
2
0
1
0
0
1
0
0
0
4
0
0
2
2
0
0
1
2
2
0
1
0
0
0
0
1
0
1
1
2
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
1
1
0
0
0
0
1
0
0
0
1
0
0
2
0
0
1
1
0
1
2
0
0
0
0
0
0
6
1
1
1
0
0
2
2
0
0
0
0
0
0
0
0
1
0
1
1
1
2
0
0
1
1
0
2
0
0
2
2
0
3
0
0
0
1
0
1
2
0
2
0
2
0
0
0
0
0
1
0
0
1
0
0
0
2
1
0
2
0
1
0
0
0
2
1
1
0
0
0
0
3
1
0
2
1
2
0
0
0
1
1
2
1
0
1
0
2
0
0
2
0
0
0
1
0
0
0
0
1
0
1
0
2
0
1
0
0
0
0
2
2
1
0
0
0
2
1
0
0
0
0
0
0
3
2
0
1
1
0
2
2
0
0
1
1
0
0
0
0
1
0
1
0
2
1
0
0
1
0
1
3
0
2
0
0
0
0
1
2
0
1
1
0
2
0
1
1
2
0
1
2
0
0
0
1
1
0
0
1
0
1
0
0
0
2
0
2
0
0
0
1
1
0
2
0
1
2
3
2
1
1
0
0
2
0
2
0
1
1
0
1
0
0
0
0
2
2
0
0
2
0
2
2
0
5
1
1
0
1
1
0
2
0
0
0
0
3
2
1
1
5
2
2
2
2
1
2
0
2
0
1
2
1
0
0
2
0
0
0
0
0
2
2
0
1
2
0
1
2
0
0
0
0
0
2
0
0
0
0
1
2
1
0
1
0
1
1
0
0
0
2
0
1
0
2
2
0
1
0
1
2
1
0
1
0
2
2
0
0
1
1
0
0
0
0
1
1
0
2
0
0
2
0
0
1
0
0
0
0
0
0
2
1
0
2
1
0
0
1
0
1
0
2
0
2
0
2
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
2
0
1
0
1
0
0
1
2
0
0
3
2
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
2
0
0
0
0
2
1
0
1
1
0
0
0
1
2
0
2
1
2
0
0
0
2
1
2
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
2
2
1
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
6
0
0
1
2
2
2
0
1
1
0
3
1
2
0
0
1
2
0
3
2
0
0
4
1
1
2
1
0
0
1
0
0
2
1
2
3
0
0
1
0
1
0
2
4
2
1
0
0
0
2
0
0
0
2
1
1
0
0
3
2
0
0
0
0
2
0
1
0
1
0
2
0
0
0
1
0
0
2
1
0
0
2
3
1
2
1
0
1
0
3
0
0
1
1
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
2
1
0
3
0
0
0
0
0
0
0
0
1
1
3
0
0
2
2
0
0
0
0
1
0
0
1
0
1
2
2
0
2
0
2
0
2
0
0
1
0
0
1
2
2
0
1
1
0
2
1
2
0
1
1
2
1
0
0
1
0
1
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
1
1
2
1
0
2
1
0
0
0
2
2
0
1
0
3
0
2
2
2
2
0
0
0
1
1
0
1
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
2
2
1
2
2
2
1
0
1
0
0
0
0
1
1
0
0
2
0
1
0
0
0
1
0
1
1
1
0
0
1
0
1
0
0
2
0
0
0
0
2
0
1
0
0
2
1
2
0
0
0
1
1
2
1
0
0
0
0
0
3
1
1
0
2
0
4
0
2
1
1
2
0
0
0
1
2
1
1
0
0
7
2
1
0
0
1
1
0
0
2
0
4
0
0
0
0
2
1
2
0
1
1
1
0
1
1
0
0
0
0
0
1
5
0
0
0
2
2
0
2
0
1
1
2
0
1
1
0
0
1
0
0
2
0
0
1
0
1
0
0
3
3
2
0
0
1
0
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
2
0
0
2
1
0
1
0
0
2
2
0
0
1
2
2
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
1
1
1
1
0
2
1
1
2
1
0
0
1
0
0
0
0
0
0
1
1
0
2
0
0
2
1
2
1
0
2
0
2
0
2
0
0
0
2
0
1
3
2
0
1
0
0
0
1
1
0
0
1
0
2
0
0
2
0
0
0
0
1
2
1
0
0
0
0
1
2
0
0
0
1
0
1
1
0
2
1
0
0
1
0
2
0
1
0
0
0
1
1
0
2
2
0
1
1
0
0
0
2
1
0
1
0
1
2
1
0
0
1
0
1
4
1
2
0
2
1
0
1
1
0
1
1
2
0
0
0
1
0
1
1
1
1
0
0
1
0
0
0
2
2
0
0
0
0
2
0
2
0
1
2
0
1
2
0
0
0
1
1
0
1
0
1
2
0
1
2
0
1
0
1
2
1
0
1
2
0
3
2
0
1
0
0
0
0
2
0
1
2
1
1
0
0
0
2
0
0
0
0
1
1
0
1
1
1
0
2
1
0
2
2
2
0
0
0
0
0
2
0
1
1
0
0
2
0
0
2
3
2
1
1
2
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
2
0
1
0
16
0
0
3
0
2
1
0
1
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
1
2
2
2
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
2
1
0
2
0
0
0
0
0
1
0
2
2
0
0
0
1
0
2
1
2
0
1
0
1
0
0
2
1
0
0
3
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
1
1
2
0
1
1
1
2
0
0
0
0
1
1
0
1
0
1
2
0
2
2
2
0
0
2
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
2
1
4
0
1
2
3
0
0
0
1
2
0
2
0
0
2
1
0
1
0
2
0
0
0
0
0
1
1
2
1
1
0
0
0
0
1
0
2
0
1
1
0
0
1
0
1
0
0
2
0
0
0
0
2
0
1
2
1
1
2
0
1
2
1
2
0
0
0
0
3
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
2
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
2
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
1
0
2
2
0
1
0
0
2
0
0
0
0
2
1
2
0
2
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
1
0
1
3
0
0
0
2
1
0
1
2
2
1
0
2
0
1
1
0
0
0
2
0
0
0
1
1
1
0
1
0
0
0
2
2
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
2
0
1
0
2
0
2
2
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
2
0
1
2
0
0
0
0
1
1
0
1
1
1
1
0
0
0
0
0
0
0
1
1
0
0
1
0
2
0
1
1
1
0
0
0
0
0
0
3
2
1
0
0
1
1
0
1
2
0
3
0
0
0
1
0
2
0
1
2
2
1
0
0
0
0
1
2
1
0
2
0
2
0
2
0
0
1
1
2
0
0
0
1
2
0
0
1
2
0
0
0
1
2
1
0
2
1
2
2
0
0
2
1
1
0
1
1
0
0
1
0
0
0
0
1
0
0
2
0
3
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
3
0
0
0
3
0
2
1
2
2
0
0
3
0
3
1
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
1
3
1
2
0
2
0
0
0
2
1
1
0
1
0
0
1
1
0
1
1
1
1
0
1
1
0
0
1
0
2
1
0
2
0
1
0
0
0
0
0
1
0
1
0
1
1
1
1
0
1
1
0
2
1
0
2
0
0
2
0
1
0
0
0
2
2
0
1
0
0
0
0
1
0
0
1
2
0
2
0
0
0
0
2
0
0
2
0
0
2
0
2
0
0
2
0
2
0
1
2
0
1
1
1
1
0
1
2
1
1
0
0
0
1
0
0
1
2
0
0
0
2
0
1
0
0
2
0
2
2
0
1
0
2
2
0
1
0
1
2
0
0
0
1
2
1
0
1
1
2
0
0
0
1
0
0
2
0
0
0
1
1
1
0
0
0
0
1
0
2
2
2
2
0
4
0
1
0
1
2
0
2
1
2
0
0
2
0
0
0
0
2
0
0
1
0
0
2
2
0
2
2
1
0
0
0
1
0
0
1
0
0
3
2
2
1
1
1
2
0
0
0
0
0
2
2
1
0
1
1
2
2
0
0
0
0
0
1
0
0
0
0
2
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
2
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
1
0
0
2
0
0
1
0
0
0
0
2
0
3
0
0
1
2
0
0
0
0
1
3
2
0
1
2
2
0
0
1
2
2
2
1
0
2
0
0
0
0
0
0
2
0
2
2
0
2
0
1
1
2
0
1
0
2
0
2
2
0
1
0
0
1
1
1
1
2
0
1
1
0
0
0
0
0
0
1
2
0
1
0
0
0
1
2
1
0
0
2
1
2
1
0
0
2
0
1
0
0
0
0
1
1
0
0
1
2
1
0
0
0
1
0
0
2
0
2
3
0
0
1
1
1
1
2
1
1
1
3
2
2
0
2
0
2
0
0
0
1
0
0
1
0
0
2
0
0
2
0
0
0
2
1
0
2
0
1
0
1
0
0
2
2
1
1
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
1
0
2
0
2
0
0
0
1
0
1
2
0
2
0
2
2
0
1
2
2
0
2
1
3
0
0
3
0
1
1
1
0
3
0
1
0
1
0
2
2
3
2
0
0
1
1
0
0
0
0
1
0
1
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
2
0
2
0
1
0
2
0
1
0
0
0
0
0
0
0
0
2
2
2
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
1
1
0
1
0
0
1
1
1
0
0
0
0
0
1
2
2
5
0
0
1
0
1
0
1
2
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
2
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
2
2
2
0
0
2
0
2
2
2
1
1
2
0
2
1
0
0
1
0
0
1
0
2
2
0
0
1
1
0
2
0
2
0
1
0
0
2
0
1
0
2
0
0
0
0
0
2
0
1
0
2
2
0
1
1
0
0
0
0
1
2
1
0
0
1
1
0
1
0
2
0
2
0
2
2
1
0
0
0
0
2
0
1
0
1
0
0
0
3
0
0
0
1
2
0
1
3
0
1
2
1
1
1
1
0
0
0
0
0
0
1
0
0
1
2
0
0
3
2
0
1
1
0
0
0
0
1
1
0
0
2
1
0
0
1
0
0
1
0
3
1
1
1
1
0
0
2
0
2
0
2
1
2
2
0
0
0
0
1
1
1
1
1
0
0
2
0
2
1
2
2
0
0
2
1
0
2
1
0
0
0
0
0
0
1
0
1
1
2
2
1
0
1
0
1
0
0
2
1
0
1
0
2
2
2
0
0
2
0
0
0
0
0
0
0
0
0
1
2
1
0
0
1
1
1
2
1
0
2
1
1
2
2
1
1
0
1
1
2
0
0
0
0
3
1
2
0
0
0
1
1
0
1
1
2
1
2
2
0
0
1
0
1
0
2
0
0
0
0
0
0
2
0
0
2
2
0
0
1
1
0
0
0
0
1
1
1
2
1
2
2
0
2
0
0
2
0
0
1
0
1
2
0
4
0
2
0
0
2
0
0
1
0
0
2
1
2
0
0
1
2
2
0
1
2
0
1
0
2
0
2
0
2
0
1
0
1
1
1
0
1
0
2
0
0
0
2
1
0
1
1
1
0
0
1
0
0
2
0
1
1
0
0
0
1
0
0
0
3
1
1
0
0
0
1
0
0
0
0
0
1
2
0
2
0
0
2
0
2
0
0
3
0
0
1
0
1
0
1
0
0
0
2
0
0
1
2
1
0
0
0
0
0
1
1
1
0
0
0
0
1
0
1
1
1
0
0
0
0
2
1
0
2
0
0
1
1
0
0
1
0
0
1
1
0
0
0
2
0
0
0
1
1
0
1
1
0
0
2
0
1
0
2
0
0
1
0
2
0
0
3
1
0
0
0
2
0
1
1
0
3
0
1
0
0
3
0
2
0
1
1
0
1
0
1
2
2
0
2
0
0
0
1
0
3
0
0
1
1
0
0
1
0
0
1
1
0
0
1
0
1
0
0
1
1
0
0
0
0
1
0
0
0
1
0
2
0
0
2
0
0
0
1
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
1
2
2
0
0
2
0
1
0
3
0
0
0
1
2
2
0
1
1
1
1
0
2
1
0
1
0
0
0
2
1
1
2
1
1
0
2
0
0
2
1
2
0
0
1
2
0
2
1
0
0
3
2
1
1
2
0
0
2
2
1
1
1
0
0
0
2
0
0
0
0
1
2
0
0
0
2
2
1
1
0
0
0
0
0
2
0
0
2
0
0
0
0
1
1
0
0
0
0
0
4
0
1
3
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
1
0
2
0
0
1
1
0
1
0
0
0
0
1
0
1
0
2
0
0
2
0
1
0
0
1
0
3
0
0
0
2
0
1
0
0
1
1
0
1
0
2
0
0
0
1
0
0
0
0
1
2
0
0
0
2
0
1
0
0
2
1
1
1
0
0
1
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
1
0
2
0
1
2
0
2
2
2
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
1
2
0
0
2
0
0
2
1
0
0
0
0
0
1
2
1
1
1
0
2
1
0
0
0
0
0
2
0
2
0
0
0
0
2
2
0
0
1
1
0
0
0
0
2
2
1
0
0
0
1
0
0
1
0
2
2
0
1
0
0
2
1
0
2
1
0
0
0
1
0
0
0
0
0
2
0
1
2
2
0
1
0
0
0
0
0
1
0
0
2
1
0
0
0
1
1
1
0
2
1
0
0
0
1
4
1
1
1
0
1
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
1
2
0
0
0
0
1
0
0
0
1
0
0
2
1
2
1
2
0
0
0
0
2
1
1
1
1
1
0
2
0
2
0
2
2
0
0
2
2
0
0
1
0
0
0
2
1
1
3
0
2
1
0
1
0
0
0
0
0
1
0
1
0
1
1
1
0
2
0
1
1
0
0
1
1
2
3
1
1
0
1
1
0
2
2
1
0
1
0
2
0
0
1
0
2
0
0
4
0
0
0
0
3
2
0
0
0
1
1
0
0
0
1
2
0
0
2
1
0
0
0
2
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
1
2
0
2
0
0
1
0
1
1
0
1
0
0
0
2
2
1
0
2
0
6
0
0
0
2
0
0
0
2
0
1
1
0
2
2
0
2
0
2
0
0
0
0
2
2
1
0
0
0
1
0
2
0
0
2
0
0
0
0
2
1
1
2
0
0
0
1
0
0
0
2
0
0
1
4
0
1
0
1
1
0
0
0
0
1
0
2
0
0
0
0
0
1
0
1
1
2
2
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
2
1
1
0
0
1
0
1
0
0
3
0
1
1
0
0
1
1
0
0
0
1
1
0
0
1
0
0
2
0
0
0
2
0
0
0
1
1
0
0
0
0
1
2
2
0
1
0
0
0
1
0
0
2
0
0
0
1
1
0
2
2
0
0
2
2
2
0
0
0
0
2
1
0
2
0
2
2
0
1
0
1
0
0
0
0
0
0
0
2
2
0
0
0
1
0
2
0
1
2
0
0
0
2
0
0
1
0
2
0
0
2
0
2
1
2
4
1
0
0
2
0
1
0
2
3
2
1
1
0
1
0
1
2
0
0
0
0
1
0
2
2
0
0
0
0
0
0
2
0
1
3
0
0
1
0
2
0
2
0
0
1
2
0
0
0
1
2
0
2
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
2
0
0
2
2
2
2
0
1
0
0
2
3
1
0
0
2
0
0
0
0
0
0
0
2
2
1
0
0
0
0
4
3
0
0
3
1
0
3
1
0
0
1
2
1
2
2
0
2
1
1
2
0
0
1
0
0
1
0
0
0
2
0
3
2
0
0
0
0
1
0
3
0
1
0
1
2
2
1
3
0
0
0
0
2
1
0
0
1
2
2
0
0
1
1
0
1
0
0
1
0
1
2
2
0
0
0
0
1
2
0
1
2
2
0
0
0
0
2
1
1
2
1
2
1
1
0
0
1
1
0
0
0
0
1
2
0
2
0
0
2
0
1
0
2
0
0
1
0
1
0
0
0
0
0
0
2
0
1
0
0
0
1
2
0
0
0
1
2
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
2
0
0
2
1
0
0
0
0
0
0
2
0
2
0
0
0
1
2
2
1
2
0
2
1
0
0
0
0
2
0
1
1
0
0
0
0
0
1
0
0
1
1
2
0
2
0
1
0
2
0
0
0
1
1
0
0
0
0
1
0
0
2
2
1
0
0
1
0
0
0
0
0
1
2
2
0
3
1
0
1
2
0
0
0
0
1
1
1
0
1
2
0
0
2
1
0
0
1
1
1
0
2
0
0
1
1
0
0
1
1
1
0
1
0
3
1
0
1
0
1
0
1
0
0
2
0
0
0
0
0
1
0
1
0
0
1
0
0
2
0
1
1
0
2
1
1
2
0
0
1
0
2
0
1
1
0
1
0
1
1
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
1
0
0
1
2
0
1
0
1
0
1
1
1
1
2
0
2
0
1
1
1
1
0
0
0
1
0
0
0
0
0
0
2
1
0
1
0
1
0
0
0
0
1
1
3
1
1
0
0
1
2
2
0
2
2
0
1
1
1
2
5
0
0
0
2
0
0
1
0
1
1
0
1
0
1
1
1
1
0
0
1
0
1
0
1
2
0
0
0
0
3
0
0
0
0
0
0
0
2
1
0
2
3
3
0
0
0
2
0
0
0
2
5
1
0
0
3
2
1
1
0
1
2
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
3
2
1
0
0
0
2
1
0
1
0
0
0
2
1
0
0
1
2
2
0
0
0
0
0
1
0
0
0
0
0
2
2
2
1
0
1
0
1
1
0
0
2
2
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
2
1
0
1
2
0
0
0
2
0
0
0
1
0
0
0
0
1
2
2
2
0
2
0
2
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
2
2
0
0
1
3
2
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
1
1
1
0
0
0
2
0
1
0
1
1
2
3
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
1
0
0
1
2
3
0
0
2
1
4
1
0
3
1
1
0
2
1
0
2
0
0
1
0
0
0
1
2
1
0
1
0
2
0
0
0
2
1
1
0
3
1
2
0
1
0
0
0
1
1
1
0
0
1
0
0
0
0
1
0
1
1
2
0
0
0
0
1
2
2
0
0
1
2
2
0
0
0
0
0
1
2
1
2
1
1
0
0
1
1
0
0
2
0
2
1
1
1
0
0
0
3
1
0
1
1
0
0
0
0
0
0
2
2
0
1
2
2
2
2
0
0
0
0
3
0
1
2
0
1
1
1
0
0
2
2
0
2
0
1
0
2
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
1
1
0
0
1
0
0
0
0
1
1
0
0
2
1
1
0
1
1
1
1
1
0
1
2
1
2
0
0
1
0
0
2
0
0
0
1
1
0
0
1
1
0
1
0
1
1
0
1
2
1
1
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
1
2
0
1
1
2
1
1
0
2
0
0
2
0
1
0
1
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
1
2
0
1
1
0
1
2
0
0
0
2
1
2
1
0
0
0
1
0
1
0
1
0
1
2
1
0
1
2
1
2
0
0
0
1
0
1
0
2
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
2
0
1
0
2
1
0
1
0
2
2
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
2
1
0
0
1
0
2
0
2
0
0
0
1
0
0
1
0
0
1
0
2
1
0
1
4
0
0
1
0
2
2
1
0
2
0
0
0
2
0
0
0
1
1
1
2
0
0
1
0
0
0
2
2
0
0
2
2
1
0
0
1
0
2
0
0
0
0
2
1
2
0
0
0
0
0
0
0
1
2
1
0
0
0
1
0
0
0
0
0
2
0
1
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
2
0
0
1
0
1
0
0
0
0
0
2
1
0
0
2
2
0
1
0
2
0
0
2
2
0
0
1
2
0
2
0
1
0
1
0
2
1
0
2
1
0
1
0
1
0
1
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
2
0
0
0
1
0
0
2
2
1
0
0
0
0
0
0
3
0
1
2
1
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
3
0
0
2
0
0
0
1
0
0
0
1
2
0
2
1
1
1
0
0
0
0
1
1
2
0
0
0
0
1
1
0
0
2
2
0
0
0
0
0
0
0
1
1
1
2
0
1
2
1
1
0
1
1
0
1
0
0
0
2
2
1
1
1
1
0
0
3
0
0
2
0
2
1
0
1
1
0
2
1
0
2
1
0
0
1
4
0
0
0
0
0
0
0
1
1
0
2
1
1
0
2
1
1
0
0
2
0
0
0
3
1
0
0
1
2
2
1
2
0
2
1
0
0
0
3
0
0
0
0
1
2
0
0
0
1
0
0
2
0
0
0
1
2
0
0
0
0
1
0
0
2
0
0
0
2
1
1
0
0
0
0
1
0
0
0
0
1
2
0
0
0
1
0
1
2
0
1
1
1
0
1
1
0
0
1
1
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
2
2
1
0
1
2
0
1
2
0
0
0
1
0
0
0
2
4
0
2
1
1
0
0
0
2
0
0
1
0
0
0
2
0
1
2
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
3
0
1
0
1
0
2
2
0
0
0
1
1
0
1
0
0
2
1
1
1
0
0
0
0
0
0
0
2
0
1
2
8
0
2
1
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
3
2
0
1
1
0
1
0
1
0
0
1
1
2
0
0
1
1
0
0
2
2
4
1
2
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
1
1
2
2
0
0
0
2
1
1
0
1
0
0
1
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
1
3
1
1
0
1
0
1
0
0
4
0
0
1
0
0
1
0
0
0
0
0
2
1
2
0
0
2
0
4
2
0
2
0
1
1
2
2
0
0
0
0
2
0
0
0
1
2
0
0
1
0
1
0
1
2
0
3
1
0
0
1
1
2
0
1
0
1
1
0
0
2
0
0
0
0
1
1
0
1
0
0
1
0
1
0
0
0
0
2
0
3
1
0
0
0
2
0
0
1
0
0
0
0
2
0
0
2
0
0
2
0
0
1
0
0
2
2
0
2
0
1
1
0
1
1
0
1
0
0
1
2
1
2
0
1
1
0
0
0
1
0
0
0
2
0
1
0
0
1
2
0
0
1
1
1
2
0
1
1
2
0
0
0
2
2
0
0
1
0
1
2
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
1
1
0
0
2
0
2
1
1
1
0
1
2
0
1
2
1
1
0
0
0
1
1
1
0
2
0
2
0
0
0
1
1
0
0
1
1
0
1
1
2
1
0
0
1
0
0
1
0
0
2
0
1
0
0
1
0
1
2
2
0
0
0
0
0
2
0
0
2
1
1
1
0
0
1
2
2
0
1
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
2
1
0
2
0
1
0
3
4
2
3
0
0
1
1
1
1
0
0
1
1
0
1
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
1
0
0
11
1
0
0
2
0
0
0
1
0
2
0
0
0
0
1
0
1
0
2
1
2
0
2
0
0
2
1
0
0
0
0
0
0
1
0
3
1
2
1
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
2
0
0
2
3
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
1
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
1
2
0
0
0
2
1
0
1
0
0
0
0
0
3
0
1
0
2
0
0
0
0
0
0
0
0
2
0
2
0
2
2
1
0
1
0
0
0
0
1
0
1
0
0
0
0
2
1
2
0
0
1
2
0
1
0
0
2
0
0
1
0
1
0
2
0
2
1
0
1
0
2
0
1
0
2
0
0
1
1
0
0
0
3
0
1
2
0
0
1
0
0
2
0
0
1
0
1
0
0
2
0
0
0
1
0
0
3
2
1
0
0
0
0
2
0
0
1
0
1
2
1
2
2
0
2
2
0
1
2
0
0
2
0
1
1
2
2
0
0
0
3
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
2
2
0
2
0
0
0
0
0
2
2
0
0
2
0
0
1
0
1
0
0
0
0
2
0
1
0
1
2
2
2
0
1
0
3
2
1
0
1
0
0
2
0
0
0
2
0
0
0
0
0
2
0
1
1
0
2
0
2
2
0
1
3
0
2
0
2
0
0
0
2
0
0
0
2
2
0
2
0
0
0
1
1
0
0
0
2
2
0
0
0
2
0
0
0
0
0
3
0
0
0
2
0
3
0
1
1
0
1
1
0
0
1
3
0
2
0
2
1
2
2
0
2
0
0
1
0
0
0
0
2
0
3
2
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
2
1
1
2
1
1
0
0
0
0
0
0
0
0
1
0
1
2
0
1
2
1
0
1
1
0
1
1
2
0
0
2
0
0
0
0
1
1
3
0
0
0
2
2
0
2
0
2
1
2
1
1
0
0
3
0
0
1
0
0
0
1
1
1
1
1
0
0
5
0
1
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
2
1
1
0
0
1
0
2
1
0
0
0
0
0
1
1
1
3
2
0
0
4
0
2
1
0
1
0
0
0
0
0
0
0
1
0
0
2
0
4
0
0
1
0
0
1
0
0
2
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
3
0
0
2
1
0
2
0
1
1
0
0
1
1
0
1
0
0
0
1
2
1
2
1
2
2
0
0
2
2
1
1
2
0
2
0
2
0
0
0
0
2
2
0
0
0
0
0
1
1
0
4
1
2
2
1
0
0
1
1
1
0
2
0
1
1
0
0
1
0
0
0
0
0
0
1
0
1
2
3
2
1
1
2
0
1
0
0
1
1
1
1
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
2
0
0
0
1
1
0
1
1
1
0
0
1
1
0
2
0
1
0
0
1
0
0
1
0
1
2
1
0
0
1
0
0
0
1
1
2
0
0
0
0
0
0
1
2
0
0
0
0
1
2
3
0
2
2
0
1
1
2
2
0
0
0
1
2
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
3
1
0
0
1
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
3
1
0
2
0
0
0
2
0
0
2
0
2
2
0
0
0
0
0
0
1
0
1
1
0
1
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
2
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
1
1
0
1
0
0
0
2
0
0
1
1
2
0
2
0
1
0
0
1
0
2
0
0
1
1
0
2
2
0
1
0
0
0
0
2
0
0
0
0
2
0
1
1
1
2
3
2
0
1
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
2
1
1
0
0
0
0
1
1
2
0
0
0
0
2
2
2
2
0
0
1
2
1
0
0
0
0
0
0
1
2
0
0
1
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
2
3
0
1
0
1
0
2
2
0
1
0
0
0
0
2
0
1
0
0
0
0
0
2
2
2
0
0
0
0
3
0
2
0
2
1
2
0
2
2
1
1
0
2
0
2
0
0
2
1
0
2
2
0
0
0
3
0
2
0
1
0
0
0
0
0
0
0
1
2
1
0
0
0
3
0
2
2
1
0
2
5
0
1
2
0
1
0
2
1
2
1
0
0
0
0
1
0
0
2
1
2
0
0
0
1
0
1
1
0
0
0
2
0
0
0
0
1
0
0
0
0
3
0
2
0
0
2
0
0
2
1
1
1
1
1
2
2
0
0
0
1
1
3
0
1
2
1
0
0
2
0
0
2
1
0
0
0
2
0
1
0
1
0
0
2
0
2
1
0
1
0
0
1
2
2
1
0
0
1
0
0
2
0
1
0
1
1
0
1
0
0
1
0
0
0
1
0
0
2
0
0
2
0
2
0
0
1
0
2
1
1
0
2
1
0
1
0
0
1
1
0
1
1
3
0
1
2
0
1
3
1
0
0
0
0
1
2
0
1
0
0
0
1
0
0
0
1
0
0
1
2
2
0
0
0
0
0
1
2
2
1
0
0
0
1
2
1
0
1
0
2
0
2
0
1
2
0
0
2
0
0
0
1
0
2
2
1
0
0
0
0
0
2
0
0
2
2
0
0
2
1
0
0
2
0
0
1
2
1
1
1
0
3
2
0
0
1
0
0
0
0
0
0
1
2
0
1
1
0
2
0
1
0
2
0
0
0
2
0
0
0
2
1
0
0
0
2
2
2
3
2
0
2
0
0
0
0
2
0
1
0
0
0
3
1
0
0
0
0
1
1
3
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
2
4
1
2
0
0
2
1
0
0
0
0
0
0
0
1
0
1
2
1
1
0
0
1
0
0
0
2
0
0
2
1
0
2
0
0
2
0
0
0
1
0
2
1
2
0
0
0
2
0
2
0
2
0
2
0
0
2
1
0
1
2
1
0
0
0
0
2
2
1
0
0
0
0
0
2
1
2
1
2
2
1
2
1
1
0
0
0
0
2
1
0
1
0
1
1
0
0
0
0
2
1
2
2
3
1
1
1
0
0
1
2
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
1
0
1
0
1
2
0
0
5
2
1
0
0
2
1
2
1
0
1
1
0
0
1
0
0
0
2
0
1
0
0
2
0
2
0
0
0
1
0
1
0
1
0
0
0
0
1
1
2
2
0
2
0
0
0
2
1
0
0
0
0
1
1
2
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
2
0
0
0
2
1
0
2
0
0
1
0
1
0
2
0
0
0
1
1
0
0
0
0
2
1
2
1
0
2
0
0
2
1
1
0
2
0
2
1
0
1
1
2
2
0
0
1
0
1
0
1
1
0
2
0
1
1
0
0
0
2
0
0
1
2
2
3
0
0
1
1
0
0
1
1
0
0
0
1
1
0
2
0
0
1
1
1
0
0
2
2
0
0
1
0
1
1
0
1
0
0
0
2
2
1
0
0
0
1
1
2
0
1
0
0
0
0
2
2
0
0
0
0
0
2
0
0
2
0
1
1
1
2
0
0
2
2
1
0
1
1
0
0
0
2
1
1
1
2
2
0
1
0
0
2
1
0
2
2
0
1
2
0
1
0
0
0
1
0
0
3
0
1
1
0
2
1
1
0
0
0
1
1
0
1
3
0
2
12
1
1
1
0
0
0
0
2
1
0
2
0
0
0
2
2
0
0
0
0
2
1
0
0
0
1
0
0
2
1
0
0
0
3
1
1
0
0
1
2
0
0
0
2
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
2
0
1
0
2
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
2
1
0
1
1
1
0
1
2
0
0
2
3
0
0
2
0
0
1
0
0
1
1
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
1
0
0
1
4
0
1
0
0
0
0
0
2
1
0
0
0
0
1
2
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
7
0
4
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
2
0
1
1
0
0
0
1
2
2
2
0
0
0
1
2
0
1
0
0
2
1
1
0
2
1
2
0
3
0
1
1
0
0
1
0
3
0
0
0
1
1
1
0
1
2
1
0
3
0
0
0
1
1
0
0
2
2
0
2
2
0
2
0
3
1
0
0
0
0
1
0
0
0
0
0
0
2
0
1
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
1
0
2
0
1
0
1
2
0
0
0
2
0
2
0
1
1
0
1
0
1
0
0
2
0
0
2
0
0
0
0
0
0
1
1
1
0
2
0
2
2
0
0
2
0
0
2
0
1
0
1
2
1
1
0
2
2
0
0
2
0
1
0
2
0
2
2
2
0
0
0
0
3
1
1
0
0
1
5
1
0
0
1
0
0
0
1
0
0
0
2
0
0
0
1
2
0
0
0
0
0
5
0
4
0
0
0
0
0
3
2
0
0
1
0
0
1
1
0
0
0
0
0
0
1
1
0
0
2
0
0
1
2
1
0
0
0
1
1
0
2
1
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
2
0
0
0
1
1
0
1
0
2
2
0
2
1
0
1
2
0
0
0
0
1
2
0
0
0
0
0
2
0
2
1
2
1
0
2
0
1
0
1
1
2
0
0
0
0
2
1
0
0
1
2
0
2
0
0
0
0
1
0
0
2
0
0
3
0
1
0
1
1
0
0
0
2
1
1
0
0
2
0
0
2
0
1
0
0
0
0
1
0
1
0
0
0
2
0
2
3
0
1
2
1
4
0
2
0
0
1
0
1
2
0
3
0
0
0
2
0
1
0
2
0
0
1
0
1
0
1
0
0
1
0
1
0
0
0
0
1
0
0
2
0
0
0
1
0
0
1
1
0
2
0
0
0
2
0
0
2
0
2
0
0
2
0
0
0
2
0
1
2
0
0
0
2
1
0
1
0
0
3
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
1
1
2
1
1
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
2
0
2
0
0
3
0
2
3
2
1
0
0
1
1
6
0
1
2
0
1
1
1
0
0
2
2
0
1
1
1
2
3
0
1
2
1
0
0
0
2
1
1
0
0
0
0
0
2
4
0
0
1
0
0
2
0
1
1
0
1
0
2
0
0
0
1
0
0
1
2
0
2
1
2
1
0
1
1
0
2
2
0
0
0
1
0
0
0
1
0
1
2
0
0
1
0
1
1
0
2
0
2
1
0
1
0
0
0
0
1
0
0
1
0
2
2
0
0
0
2
2
0
0
0
0
1
1
0
1
0
2
2
0
1
1
0
0
0
1
0
0
2
2
0
0
0
1
1
0
2
2
0
0
0
0
0
0
2
2
1
0
2
0
0
1
2
0
2
2
0
0
1
0
1
0
2
2
0
0
0
1
0
1
0
2
2
0
1
1
0
0
0
2
0
0
0
0
2
1
1
0
0
0
1
0
0
1
0
0
0
0
0
2
1
1
0
0
0
1
2
1
0
1
1
0
1
2
2
1
1
1
0
1
3
1
1
1
0
0
0
2
1
0
0
0
0
1
2
0
1
2
0
0
0
1
0
1
2
0
0
1
2
1
0
0
0
0
1
1
1
2
0
1
1
0
0
0
0
0
0
0
2
0
2
3
1
2
0
0
0
1
2
0
4
1
1
2
0
1
1
0
2
2
3
0
0
2
1
0
1
1
0
1
2
1
0
0
2
0
0
2
1
1
0
1
0
0
2
0
0
1
0
1
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
2
0
1
2
1
0
2
2
0
0
3
0
2
0
0
0
0
1
0
2
0
0
0
0
2
1
0
1
0
0
0
0
0
1
0
2
1
0
2
1
0
3
1
0
1
1
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
2
1
3
1
0
0
0
0
3
0
0
2
0
0
1
0
0
0
1
0
0
2
0
0
1
1
0
0
0
0
1
0
2
2
1
2
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
1
2
0
0
2
0
0
0
0
1
0
1
1
0
0
0
0
2
0
2
0
1
0
0
0
1
0
2
2
0
2
2
0
1
0
0
0
2
0
2
0
2
1
3
2
1
1
0
0
0
0
2
1
0
0
1
0
0
2
0
2
1
0
0
0
0
2
0
0
0
1
0
0
1
2
0
2
0
1
2
1
0
3
0
3
1
1
1
0
1
0
1
0
0
0
2
0
0
1
2
0
0
0
0
0
1
0
2
0
1
1
0
0
0
0
2
0
0
0
0
2
0
1
2
0
2
0
0
0
0
2
1
2
0
0
2
0
1
0
0
0
2
2
0
1
2
1
1
0
0
0
0
0
1
0
0
0
2
1
1
0
0
1
2
0
0
0
1
3
1
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
2
1
1
0
0
1
2
2
2
2
0
0
0
2
0
2
1
0
0
0
0
0
1
1
2
1
0
2
0
0
2
0
0
3
0
2
0
0
2
1
1
0
0
0
2
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
2
0
1
0
0
0
0
1
0
2
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
2
0
2
0
1
1
0
3
0
0
0
1
1
1
2
1
0
1
1
0
2
0
0
0
0
0
0
0
0
1
2
0
0
1
2
2
0
0
1
0
0
0
1
2
0
0
1
2
0
2
0
2
1
0
2
2
0
1
2
1
0
2
0
0
0
0
1
1
1
2
1
0
0
0
0
0
1
2
0
0
0
1
1
1
1
2
0
2
0
1
0
0
2
1
1
0
1
2
0
1
0
2
0
0
1
0
1
0
0
0
0
3
1
0
0
1
0
1
0
0
0
0
0
0
1
0
2
2
2
0
1
0
1
0
3
0
2
0
0
0
0
0
2
1
0
0
0
0
0
1
3
0
4
0
1
0
1
0
2
1
0
0
0
1
0
1
0
1
2
0
1
1
1
0
0
0
2
0
0
0
1
1
0
2
1
0
1
0
2
2
3
0
1
0
1
1
3
0
2
2
0
0
2
2
0
0
0
1
0
1
0
2
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
1
1
1
0
0
0
2
2
0
0
0
1
0
0
2
0
0
0
1
0
2
1
1
0
1
0
0
1
1
0
1
0
2
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
1
2
0
0
0
1
3
2
1
1
0
0
0
0
1
0
1
0
1
1
2
0
0
1
2
2
2
0
0
1
1
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
1
0
0
0
1
2
0
1
0
1
0
0
1
1
2
2
0
0
1
2
0
2
0
0
1
2
0
0
2
2
0
0
1
0
0
1
2
0
1
1
0
0
1
1
0
0
1
2
0
2
0
0
0
0
1
1
2
1
2
0
0
1
0
0
0
2
0
0
0
3
0
2
0
0
0
1
0
0
1
3
0
2
1
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
2
2
1
0
1
0
0
0
0
1
0
3
0
0
0
0
1
0
0
0
2
1
0
1
0
0
0
0
2
0
1
0
0
2
1
0
1
1
0
0
0
1
1
1
2
0
1
0
1
0
1
0
0
0
0
0
1
1
1
0
1
1
2
0
2
0
0
1
1
0
1
0
0
0
1
2
2
2
0
0
0
0
0
0
0
0
1
0
1
0
2
1
2
0
0
1
0
1
0
2
0
2
0
0
2
1
0
0
0
0
2
2
0
1
0
0
0
2
0
1
2
0
1
2
2
0
0
0
1
0
3
0
0
0
1
2
1
2
2
2
0
1
0
0
1
0
1
0
2
1
0
2
1
1
1
0
1
1
0
1
0
3
1
0
6
0
4
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
2
2
0
1
1
0
1
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
2
1
0
0
0
1
2
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
4
0
1
0
1
2
0
0
2
1
2
0
2
1
0
0
0
0
0
0
0
1
1
1
1
0
2
1
0
2
1
0
1
0
2
0
1
1
2
0
0
2
1
2
0
0
0
0
1
2
1
0
1
0
1
2
2
1
1
0
0
0
2
1
0
2
0
2
0
0
2
0
1
1
2
1
0
0
1
1
0
2
1
0
0
0
2
1
0
2
0
1
0
0
1
0
0
1
1
0
1
2
0
1
2
1
0
2
0
0
2
1
1
2
0
2
3
1
0
0
0
1
1
0
0
2
2
0
1
2
1
0
1
0
0
0
1
2
0
1
0
1
11
2
0
0
1
0
0
2
0
0
0
0
1
0
1
0
0
1
0
1
2
1
0
2
0
0
3
2
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
2
0
0
2
0
0
1
1
2
0
0
1
2
1
0
1
0
0
0
1
0
2
0
0
1
0
0
2
1
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
2
1
2
0
1
0
3
0
1
2
0
4
2
0
1
0
0
1
1
0
0
2
2
0
2
0
0
0
1
2
1
1
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
1
1
1
0
1
0
1
0
0
2
1
0
0
2
0
0
0
1
3
0
1
0
2
2
0
2
0
0
0
0
1
0
1
1
0
1
0
1
1
0
1
0
0
4
0
1
0
0
0
0
2
0
2
0
3
0
0
3
0
0
2
1
0
2
1
0
0
0
0
1
0
2
0
1
2
0
1
0
1
0
0
2
0
0
0
0
0
1
0
1
2
0
1
2
2
2
1
0
0
1
2
0
0
0
0
1
3
1
2
0
0
2
2
1
1
0
3
4
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
2
0
1
1
0
1
0
2
0
1
0
0
0
1
0
1
2
1
1
2
0
0
0
2
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
2
0
1
1
0
0
0
0
1
0
2
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
2
0
0
1
0
0
2
0
1
0
2
0
2
0
1
1
3
0
1
0
0
0
0
0
2
0
0
2
2
2
2
0
0
1
0
0
0
1
1
2
0
3
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
5
2
0
3
0
0
2
1
1
0
0
0
1
1
0
1
0
0
2
0
2
0
0
2
0
0
2
2
0
1
0
0
0
0
0
1
0
2
1
2
1
0
0
0
2
1
2
0
0
1
1
1
2
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
2
1
0
0
1
1
2
1
0
1
1
2
0
0
0
1
0
0
2
0
1
0
2
1
0
1
1
0
0
0
0
1
0
0
3
0
2
0
0
2
0
2
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
1
1
1
0
0
0
0
3
2
2
1
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
2
0
2
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
2
2
0
1
0
0
1
0
1
1
2
0
0
1
4
0
2
2
0
1
1
2
1
0
0
0
2
0
1
0
0
2
1
0
0
0
2
0
0
0
0
0
1
1
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
3
0
0
2
0
2
2
0
0
0
0
0
0
1
1
0
2
0
0
2
1
1
2
0
0
1
0
0
0
0
0
1
1
0
1
0
1
2
0
2
0
0
2
1
0
0
0
0
0
0
2
1
0
2
1
2
2
2
4
2
0
0
1
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
1
1
0
0
0
0
1
0
2
0
0
0
0
0
0
1
2
3
3
1
0
0
1
2
2
0
1
1
1
1
0
0
2
3
0
0
2
0
3
0
0
1
0
0
0
0
0
0
2
0
2
0
0
2
2
1
1
0
0
0
2
1
1
2
1
2
2
0
0
2
3
0
0
0
0
1
0
0
0
0
0
2
0
1
2
1
1
1
1
0
1
0
0
2
1
0
1
2
1
1
3
0
0
0
0
2
1
1
0
1
0
2
0
0
1
0
1
0
0
0
1
0
2
1
1
0
0
0
2
0
0
0
1
2
1
1
0
0
2
1
0
0
1
2
0
0
1
0
1
2
1
2
0
0
1
0
1
0
0
0
2
2
1
0
2
0
0
0
1
0
0
0
0
0
1
1
1
1
0
0
0
2
1
2
0
1
2
0
1
2
0
2
1
1
0
0
0
2
3
1
0
0
0
0
0
0
1
0
2
2
2
0
0
0
1
0
1
0
0
1
0
0
2
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
1
2
0
1
0
2
1
0
2
0
1
2
0
1
1
1
2
2
2
0
0
1
0
2
2
0
0
1
0
2
3
0
1
0
0
0
2
1
0
0
1
0
0
0
2
0
2
1
0
1
0
0
1
2
1
2
0
0
0
0
0
1
1
0
1
0
0
2
1
2
0
0
2
0
1
2
0
0
1
2
0
1
1
0
1
0
0
0
0
2
0
3
0
0
0
0
3
1
1
1
2
3
0
1
1
1
0
0
1
0
0
2
1
0
1
0
0
0
0
2
0
1
0
2
0
0
0
0
2
1
2
0
0
1
2
1
2
2
3
0
0
2
2
1
0
0
0
2
2
1
0
2
0
2
0
2
2
0
1
1
0
0
0
1
1
0
1
1
0
0
2
2
0
0
1
1
2
1
0
0
3
1
0
1
2
1
0
0
0
1
0
0
1
0
0
0
2
1
2
0
1
0
0
2
1
0
0
0
0
1
0
0
1
2
0
2
1
1
0
0
0
1
0
0
2
0
2
2
2
0
2
1
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
4
2
0
0
0
0
0
2
2
0
2
2
0
1
2
2
1
2
0
2
0
2
3
0
1
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
2
2
0
0
2
0
1
0
0
0
0
2
0
1
0
1
0
0
1
0
0
1
0
0
0
1
0
1
2
1
0
0
0
1
0
1
0
2
0
1
0
3
0
0
0
1
0
1
1
1
0
0
1
2
0
1
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
2
0
1
0
2
0
2
1
1
1
0
2
0
2
1
0
0
0
1
1
0
1
1
3
0
2
0
0
1
1
2
2
0
0
2
0
0
0
0
0
1
2
2
0
3
0
0
0
0
0
1
1
0
0
0
1
2
1
2
3
1
2
1
0
0
0
0
0
0
2
1
2
0
0
0
1
0
0
0
0
0
2
1
0
1
2
2
0
0
0
0
0
0
0
0
0
1
2
2
1
0
0
0
1
1
0
0
0
1
0
0
1
0
0
2
0
2
1
0
0
1
0
0
1
2
1
1
0
2
0
1
1
0
2
2
0
0
0
0
0
0
1
2
2
2
2
0
1
0
2
1
0
0
0
0
1
1
0
0
1
0
1
2
1
1
1
0
0
4
0
0
1
0
0
0
0
0
2
0
1
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
1
2
1
0
2
2
1
1
0
0
2
1
1
1
0
2
1
0
2
0
0
1
0
0
2
1
0
1
1
2
0
0
0
1
0
0
1
1
0
1
0
0
1
1
0
0
0
0
1
1
1
3
0
0
0
0
1
0
0
0
0
0
0
2
1
1
0
0
0
2
0
1
2
1
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
2
1
0
2
0
1
1
0
0
1
0
2
2
1
0
0
1
0
2
1
0
2
0
2
2
0
0
0
0
2
0
0
3
2
2
0
2
0
0
2
0
1
0
1
0
3
0
1
2
0
2
2
0
0
0
0
0
0
1
0
0
1
2
0
1
2
0
0
0
2
0
0
2
1
0
3
1
0
2
1
1
1
0
1
0
0
1
0
1
1
0
1
2
0
2
2
1
0
0
0
0
4
1
2
0
0
0
0
0
2
0
2
0
0
0
0
1
1
2
1
1
0
2
1
0
0
0
0
2
1
0
7
2
0
0
2
2
2
2
0
0
0
2
1
1
2
2
2
0
0
0
1
0
0
0
0
2
0
0
0
2
0
1
1
2
2
1
1
0
1
1
1
0
0
1
0
2
1
0
0
0
0
2
2
0
1
0
0
1
0
3
0
0
1
0
0
0
1
1
0
2
1
1
0
4
1
2
0
2
0
0
0
0
0
0
0
1
0
4
2
0
0
1
2
2
0
0
0
2
0
0
0
0
1
2
0
1
0
2
0
0
2
0
0
0
1
1
0
0
1
0
2
0
0
2
2
0
0
0
2
0
0
1
0
1
2
1
2
2
0
2
0
0
0
0
0
0
0
2
1
1
0
0
2
0
0
0
1
1
0
2
1
2
1
0
0
1
1
0
0
0
1
2
2
0
0
0
0
0
1
0
0
2
1
0
0
0
1
2
1
1
1
0
1
0
0
0
2
2
0
0
1
0
0
0
2
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
2
0
1
0
0
1
1
2
0
1
0
0
1
2
1
1
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
2
1
0
0
1
2
0
0
2
0
0
2
0
0
2
0
3
2
2
2
0
0
0
2
0
1
0
0
1
0
0
2
1
0
0
1
0
1
0
0
0
0
0
1
0
0
1
2
0
2
0
0
0
2
1
0
0
1
3
0
2
2
0
1
0
1
2
0
3
2
1
0
2
0
1
0
0
1
2
0
0
1
1
0
2
2
1
1
1
0
0
0
1
1
0
0
0
1
2
0
0
3
2
0
0
2
0
0
0
0
0
0
0
0
1
2
2
2
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
1
1
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
2
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
3
0
0
1
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
1
2
1
0
2
0
0
0
1
0
0
0
1
1
1
0
0
0
1
1
2
1
0
3
0
1
0
2
0
0
0
0
0
2
0
1
2
1
1
2
2
0
0
0
0
2
0
1
1
0
0
0
7
0
0
0
0
0
2
0
2
0
0
1
0
1
0
1
0
0
2
2
0
0
3
2
1
0
1
0
0
0
1
0
2
0
0
2
2
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
2
0
2
0
0
0
0
2
1
0
0
0
2
0
2
0
0
3
1
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
2
0
0
2
2
1
0
0
0
1
0
0
0
0
0
0
0
1
0
2
2
0
0
2
0
1
2
0
0
2
1
0
1
0
2
1
0
2
0
4
0
0
2
0
0
0
1
2
1
2
2
0
1
0
2
0
2
0
0
0
0
2
2
0
1
1
0
2
2
1
0
0
2
0
0
0
0
2
0
1
2
0
1
0
2
1
0
1
0
0
0
2
0
2
1
2
0
0
2
0
0
1
0
0
1
1
0
3
1
2
1
0
0
2
1
0
0
0
1
1
2
1
0
0
2
2
1
1
0
0
0
0
2
2
0
1
1
0
1
1
0
2
0
0
0
0
2
1
0
1
1
0
0
1
0
0
4
0
1
0
0
2
0
1
0
0
0
0
1
0
2
0
2
6
1
2
0
2
2
0
0
2
0
1
0
0
0
2
1
1
0
2
0
2
1
0
0
0
0
0
0
2
0
0
2
1
2
0
1
2
0
2
0
2
2
0
2
1
0
0
1
0
1
0
0
2
1
0
1
0
1
0
0
0
0
0
2
1
0
0
0
0
0
1
2
0
2
0
1
1
0
0
0
0
2
1
0
2
0
1
2
2
0
0
0
1
1
1
0
1
0
0
2
1
0
1
1
1
1
1
0
0
1
2
1
2
1
0
0
1
0
1
0
0
0
0
1
2
0
0
0
1
1
1
1
0
0
0
2
1
0
1
2
0
0
0
0
0
0
1
0
0
1
0
0
1
1
1
1
0
0
2
0
0
0
0
2
0
1
0
1
0
0
0
1
1
0
3
0
0
0
0
0
0
0
1
2
1
1
0
0
1
0
3
1
0
1
1
0
0
1
0
0
2
0
0
0
6
0
2
0
0
0
2
0
2
0
0
2
1
1
1
0
0
1
1
0
0
0
1
0
0
2
0
0
0
0
2
0
0
2
0
1
0
0
0
1
0
0
0
2
0
0
2
2
0
2
1
0
0
4
0
0
0
2
0
1
0
0
1
0
0
0
1
3
3
2
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
2
1
1
0
0
0
0
0
0
0
0
2
0
2
1
10
2
1
0
0
1
1
1
0
2
1
1
1
0
1
2
1
2
0
0
1
0
0
1
1
0
0
0
0
1
1
0
1
0
0
0
1
0
1
2
2
0
0
0
0
0
1
2
0
0
0
1
3
0
0
1
0
1
0
0
1
1
1
2
0
1
1
0
0
0
1
0
0
0
0
1
0
2
1
0
0
1
1
0
0
0
0
0
0
1
1
0
0
1
0
0
2
0
0
0
0
1
0
1
0
0
0
2
0
0
1
0
0
1
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
1
2
0
0
2
0
0
1
0
1
5
0
0
2
0
0
0
0
1
2
1
0
0
1
0
2
0
0
2
1
0
0
0
1
2
1
0
0
0
2
0
2
1
0
1
1
0
1
0
3
0
1
0
0
2
0
1
2
2
0
3
0
0
1
0
0
0
0
0
1
0
2
2
2
1
0
0
0
0
1
0
0
0
0
0
2
2
1
0
0
0
1
0
0
2
2
0
0
1
0
1
0
0
2
0
0
0
2
1
2
0
1
2
0
0
0
0
0
1
0
1
0
0
0
0
1
2
0
0
0
0
2
0
0
1
0
0
2
0
2
1
3
1
0
2
0
0
2
2
1
2
1
0
4
2
2
1
0
0
0
1
0
2
0
0
1
0
1
1
1
2
0
0
1
2
2
1
1
1
0
0
1
0
0
2
0
0
1
0
2
0
0
0
0
0
1
2
0
0
2
0
1
0
1
1
0
0
0
0
2
0
1
0
0
0
2
0
1
0
0
1
0
1
0
1
0
1
0
2
4
0
2
2
1
0
0
2
1
0
1
1
0
1
0
1
0
0
2
0
0
0
1
0
0
1
0
3
0
0
2
3
0
2
0
1
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
2
0
0
0
0
0
1
2
2
0
2
2
3
0
0
0
0
0
0
1
0
3
0
0
0
1
0
1
0
1
1
0
2
1
0
2
0
1
2
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
4
0
0
0
0
1
2
1
0
2
0
2
1
0
2
0
0
0
0
2
0
1
8
0
0
0
0
0
2
1
2
2
0
1
0
2
0
2
0
1
0
0
2
0
0
0
0
1
0
0
0
1
0
0
1
2
0
1
1
1
5
0
0
1
0
2
1
0
0
2
1
0
2
2
0
1
0
0
1
1
0
0
1
2
1
1
0
2
2
1
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
1
1
2
0
0
0
0
1
0
2
0
1
2
1
0
1
0
3
0
0
0
1
1
2
1
1
1
2
1
1
2
0
0
0
1
1
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
1
2
0
0
0
1
0
0
1
2
0
0
0
1
0
1
0
0
0
1
0
0
1
0
2
1
0
2
0
0
0
0
0
0
1
3
0
3
2
2
2
0
2
0
1
0
2
0
0
0
0
0
0
0
1
0
2
2
0
0
1
0
0
2
1
0
0
2
0
0
0
1
0
0
0
0
2
1
1
2
2
2
0
0
0
2
0
1
0
0
0
1
4
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
1
1
1
1
2
0
2
0
2
2
0
1
1
0
0
0
0
1
1
1
3
2
0
2
2
1
0
0
2
0
0
2
0
1
0
0
0
2
2
1
0
1
2
0
1
3
2
0
1
0
2
0
1
0
0
0
1
2
0
0
0
1
2
3
0
1
1
0
0
0
1
0
0
1
0
0
2
0
0
0
1
1
0
2
1
0
0
0
0
0
0
1
0
2
1
0
0
2
1
0
0
0
0
1
2
0
0
0
2
0
0
0
1
0
0
2
0
2
0
1
1
0
0
1
1
3
2
1
0
0
0
2
0
0
0
2
2
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
2
1
2
0
0
0
1
1
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
1
1
0
0
0
0
2
1
0
2
1
2
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
4
0
0
0
0
1
0
3
1
2
0
0
0
0
0
0
0
2
3
2
1
0
0
1
1
0
0
1
2
1
0
2
0
1
1
0
0
1
0
0
0
0
1
1
1
0
1
0
0
0
2
1
0
0
2
2
2
0
0
1
1
0
1
0
0
2
1
0
0
0
0
3
2
0
1
1
0
2
1
0
0
0
1
1
2
0
0
0
0
0
0
1
0
2
0
0
0
2
0
1
2
0
1
1
1
0
0
0
0
2
2
0
0
1
2
0
0
1
1
2
0
1
2
2
2
0
0
0
0
2
0
1
0
2
1
1
2
0
0
0
0
1
0
1
1
0
1
1
1
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
2
0
2
0
2
0
2
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
1
0
0
2
2
0
0
0
0
0
2
0
1
1
1
1
0
1
0
1
2
2
3
0
0
0
1
2
0
2
1
0
1
0
0
0
0
2
1
2
0
0
0
0
1
0
0
0
2
1
2
2
0
0
1
1
0
0
2
1
3
0
1
2
0
0
0
1
0
0
1
1
1
0
1
0
0
0
0
0
1
0
0
1
0
2
0
3
1
2
0
0
0
0
1
0
0
2
0
2
0
2
1
0
0
0
0
1
2
0
1
2
0
2
0
0
2
0
0
0
0
0
0
0
0
1
3
0
0
0
0
1
1
0
0
2
0
2
1
0
0
0
1
2
0
1
0
1
1
1
2
1
0
0
1
1
0
0
2
0
1
0
0
1
2
1
1
0
1
0
1
0
3
0
0
0
0
0
1
3
1
0
1
0
2
2
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
1
1
0
0
0
2
1
1
0
1
1
2
1
1
0
1
0
0
1
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
2
1
0
1
1
0
0
1
1
0
1
1
0
1
0
0
0
3
1
0
0
1
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
1
1
0
1
0
0
1
1
0
0
1
0
1
1
0
0
2
1
0
0
1
0
0
0
2
2
1
0
1
0
1
2
2
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
2
2
1
1
0
1
3
0
0
0
0
0
0
2
2
2
1
0
1
0
0
0
0
2
1
0
0
2
1
0
2
0
0
1
0
0
2
0
0
0
2
1
1
3
2
1
0
1
0
0
3
1
0
0
0
1
0
0
3
2
2
0
1
0
0
0
1
1
2
1
1
1
0
1
3
3
2
1
1
0
1
3
1
1
0
0
0
1
0
0
2
0
1
0
0
0
0
2
0
1
1
2
2
1
0
3
0
1
1
2
4
0
0
0
1
1
2
1
1
4
1
1
1
0
2
0
1
2
2
2
2
1
0
1
0
1
0
0
0
0
2
0
1
0
1
0
0
1
0
0
0
1
0
1
1
2
2
0
1
2
1
1
1
0
1
0
2
2
0
0
1
2
0
1
0
0
2
0
1
0
1
1
0
0
2
0
3
2
0
2
0
0
2
0
0
2
0
0
0
0
0
1
0
1
1
2
0
0
0
1
1
0
0
0
1
0
0
1
0
0
2
0
3
0
0
0
0
1
3
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
2
1
2
0
2
2
1
0
0
0
2
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
1
2
1
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
1
1
0
2
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
1
1
1
2
0
1
1
0
0
0
0
0
0
0
1
2
2
2
2
0
0
0
2
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
1
1
2
0
0
2
2
0
0
0
2
1
0
2
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
2
0
2
1
1
0
1
0
0
2
1
0
1
0
0
2
0
0
0
1
2
0
0
0
0
0
0
2
2
2
0
2
2
1
1
3
0
1
0
0
1
0
2
0
0
0
2
0
0
0
3
0
0
0
2
0
1
1
2
0
0
1
5
1
2
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
1
2
1
0
3
1
0
0
0
2
0
1
0
2
1
1
0
0
0
0
2
2
0
2
0
0
0
0
1
2
0
1
0
1
0
0
2
0
0
0
1
2
1
1
0
0
0
0
0
0
0
3
0
2
0
0
0
1
1
1
0
0
1
0
0
0
2
0
0
0
1
1
2
0
2
0
2
0
1
2
1
0
0
3
0
2
0
1
0
0
0
1
1
0
2
0
1
0
2
0
0
1
2
1
1
0
1
0
0
0
1
0
1
2
0
2
0
0
0
0
0
2
2
0
2
0
2
1
0
0
0
0
0
0
0
0
1
0
2
2
0
1
2
0
2
0
0
0
1
0
0
1
0
1
0
0
0
1
1
1
0
0
2
0
2
1
1
1
1
1
2
0
1
0
2
2
2
1
2
1
1
0
0
2
0
1
0
0
1
1
1
0
0
0
2
0
2
0
0
0
0
0
1
2
0
1
2
0
1
1
2
0
0
3
0
0
1
0
0
0
1
0
0
0
0
3
0
0
2
1
0
1
0
0
0
0
0
0
0
0
3
0
1
0
1
0
2
0
0
0
0
1
0
0
1
1
0
0
1
2
0
2
0
1
0
1
0
0
2
0
0
0
2
1
2
0
2
0
0
2
0
1
1
2
0
0
0
0
0
0
1
0
2
1
1
2
1
0
0
1
1
1
0
2
0
0
2
0
2
1
0
0
1
0
1
0
1
0
2
0
1
1
0
0
1
0
0
1
1
2
2
1
1
2
0
0
1
2
0
1
2
2
0
0
1
1
0
0
2
0
0
1
2
0
0
0
1
0
0
0
0
0
1
0
2
0
0
1
2
2
0
2
0
4
2
1
0
1
0
0
0
0
1
2
1
0
0
2
2
1
1
0
4
0
0
1
2
0
0
2
1
0
0
2
0
0
0
0
0
1
0
1
0
0
2
0
0
0
1
0
0
2
1
1
2
0
1
2
0
2
2
0
1
3
1
0
1
2
0
0
0
0
0
2
2
1
1
0
1
0
0
0
1
1
2
1
2
1
2
1
1
0
2
2
0
1
1
0
0
2
2
0
0
2
0
2
2
1
0
1
0
0
0
1
0
0
1
1
0
0
0
2
0
0
2
0
0
0
2
0
0
2
2
2
0
1
2
0
0
0
0
0
0
1
2
0
1
2
0
0
0
2
0
1
0
0
0
2
1
2
1
0
0
1
1
0
0
1
0
0
0
0
2
0
1
0
2
0
0
0
0
3
2
1
0
0
0
0
0
2
1
0
2
0
2
1
2
2
0
2
0
0
1
0
2
0
1
0
0
0
1
1
1
0
1
0
1
0
0
1
0
2
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
2
0
2
0
1
2
0
0
1
2
2
2
0
0
1
0
0
0
0
0
3
0
1
1
2
2
1
0
1
0
0
0
0
2
2
1
1
0
1
2
3
0
0
0
0
1
0
1
0
1
0
0
0
1
1
2
0
1
2
0
2
1
1
1
0
0
0
1
0
0
2
1
0
2
0
0
2
2
2
2
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
2
1
1
0
2
0
2
2
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
2
0
0
0
2
0
0
0
0
0
2
1
2
1
0
2
0
0
0
0
0
0
1
0
2
0
0
0
1
1
0
0
2
1
0
2
0
2
0
0
3
0
0
1
0
0
0
0
0
0
2
2
2
0
0
0
0
0
1
1
2
0
2
0
0
1
1
1
2
0
0
0
0
2
0
2
0
2
3
2
0
0
2
0
2
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
2
1
1
0
2
0
0
1
1
2
0
0
0
0
3
1
0
0
2
1
0
0
1
1
0
1
2
0
0
0
4
2
0
0
2
0
0
0
0
1
2
2
1
1
2
2
0
0
0
0
2
1
0
3
0
0
4
0
0
0
1
3
0
2
0
0
1
0
5
1
0
1
0
2
0
2
0
0
0
0
0
1
0
1
0
2
1
0
1
1
2
0
0
0
2
0
0
2
0
0
0
1
1
0
0
0
2
0
0
1
0
1
0
0
2
0
0
0
1
2
0
0
1
0
1
0
0
1
0
0
0
2
1
1
0
1
0
0
1
0
0
1
0
1
0
0
0
1
2
1
0
2
1
2
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
2
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
2
1
1
0
0
1
0
1
0
0
2
0
0
0
1
1
3
0
2
1
1
0
0
2
0
1
0
0
1
2
0
0
2
0
0
0
1
2
0
2
2
0
0
3
0
0
0
0
1
0
0
2
1
1
1
0
2
0
1
1
2
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
2
2
1
0
1
0
0
2
2
2
2
1
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
2
0
2
0
1
0
1
0
0
0
2
2
0
1
0
0
1
0
1
0
1
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
2
2
3
2
0
0
0
1
0
0
1
1
0
1
0
0
1
0
4
0
0
0
1
2
0
0
2
1
0
0
0
4
0
0
1
0
1
0
0
0
2
0
0
2
0
1
0
2
0
0
2
0
0
1
0
0
1
0
0
0
1
1
1
1
0
2
2
0
0
0
0
0
1
0
1
0
0
3
0
1
4
0
0
0
1
0
0
2
1
0
2
0
0
0
4
1
1
1
0
1
1
0
0
0
2
2
1
0
0
0
1
0
0
1
1
0
1
0
0
2
2
0
0
2
0
2
0
0
2
1
1
0
0
1
0
1
1
1
1
0
0
0
0
1
0
2
1
0
0
1
2
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
1
0
1
1
2
1
0
0
1
2
0
0
1
0
0
1
0
2
0
0
1
0
1
0
1
0
2
2
0
0
1
1
0
2
1
0
0
1
0
1
0
0
0
0
0
2
2
0
0
1
0
0
1
0
0
0
1
0
2
0
0
0
0
2
0
0
0
1
2
2
0
2
2
2
0
1
0
0
0
0
0
0
0
0
0
2
0
1
1
2
0
1
0
1
0
2
0
2
1
0
0
2
0
0
1
0
0
0
0
1
0
2
1
1
0
1
0
0
0
2
0
1
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
3
0
2
0
0
0
2
0
2
0
1
0
0
1
2
0
1
0
2
2
0
2
2
1
0
0
0
0
0
1
0
2
2
2
2
2
0
0
0
0
3
1
1
0
0
1
1
2
1
0
0
2
1
0
0
2
1
2
0
2
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
2
2
0
0
4
0
0
1
1
0
1
1
1
0
2
2
0
0
2
0
0
1
1
2
0
0
1
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
2
0
0
1
3
2
1
2
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
1
2
0
0
0
3
0
3
2
1
1
0
1
2
0
1
0
0
0
0
0
2
1
2
1
2
2
0
2
1
2
2
1
0
1
1
0
0
1
0
2
1
0
0
0
2
1
0
0
0
1
2
1
0
1
0
2
0
0
0
1
1
1
0
0
2
2
2
0
2
1
1
0
0
1
0
0
0
0
2
0
0
2
1
0
0
0
0
2
1
2
0
0
1
0
0
0
1
2
0
0
2
1
0
0
0
1
0
0
2
2
3
1
2
0
1
0
0
0
0
1
1
0
0
0
3
2
3
0
3
0
0
0
1
2
0
0
0
0
0
1
0
2
0
1
0
2
0
0
1
1
0
0
0
3
2
0
1
0
2
0
0
0
0
2
0
0
2
0
0
0
0
2
2
0
0
1
2
0
0
1
0
2
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
2
0
3
0
1
0
2
0
0
0
0
0
3
0
1
2
0
0
2
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
2
0
0
1
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
2
2
0
2
2
0
1
1
0
0
0
0
0
0
2
0
0
1
0
1
1
1
0
1
0
0
1
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
2
0
2
3
2
2
0
0
2
1
0
0
1
1
2
1
0
0
0
0
2
0
2
1
2
1
1
0
2
0
0
0
0
0
2
0
1
4
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
2
2
2
0
2
1
1
1
0
0
1
1
0
0
1
0
0
0
0
0
0
1
1
2
1
0
0
0
2
1
1
0
0
1
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
2
0
3
0
0
0
2
2
1
1
0
0
1
2
1
0
0
0
0
0
3
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
1
0
0
1
0
0
1
2
2
0
0
0
2
0
0
0
2
1
2
2
0
0
2
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
1
0
2
0
0
0
0
1
1
1
0
2
1
1
0
1
1
0
0
0
1
1
1
2
0
2
1
1
0
0
1
1
0
1
1
0
1
2
0
0
0
0
2
0
0
8
2
2
1
0
1
1
1
0
1
1
0
1
0
0
0
0
0
3
0
0
2
2
1
2
0
1
2
0
0
0
2
1
1
0
0
2
0
2
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
2
1
2
0
0
2
1
0
2
0
0
0
0
1
3
0
2
0
1
0
0
0
1
0
0
2
1
0
1
0
0
1
1
0
2
1
0
1
0
0
0
1
0
0
1
0
3
0
1
1
0
0
0
0
2
1
0
1
2
2
2
0
0
2
2
0
1
0
0
2
0
2
0
1
2
0
0
0
0
1
0
1
0
1
1
0
0
1
1
0
1
0
1
2
0
0
0
1
2
0
1
0
1
0
0
0
0
2
0
1
2
0
1
1
0
0
0
1
2
2
0
1
3
0
1
0
0
0
0
0
0
0
2
0
0
1
1
1
0
0
1
1
0
1
0
0
2
0
0
2
0
0
0
1
2
1
2
0
0
0
0
0
2
0
2
1
0
0
2
0
1
1
0
0
0
1
2
0
0
2
0
0
0
0
1
2
0
0
2
0
1
0
2
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
2
0
1
0
0
0
0
0
1
0
2
0
0
1
1
1
1
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
2
2
2
1
2
0
2
3
0
1
1
2
0
1
1
2
2
0
1
2
0
0
0
2
0
0
0
2
1
0
0
1
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
1
1
0
0
0
0
0
2
0
0
0
2
1
1
0
0
0
0
0
1
2
0
2
3
2
0
4
0
1
0
0
1
0
1
0
0
0
0
2
2
1
2
3
1
1
2
2
0
1
0
0
3
0
0
1
2
0
0
0
2
2
0
1
2
1
1
1
0
0
0
0
1
1
0
1
3
1
2
0
2
0
1
0
0
0
2
0
2
0
0
1
0
1
1
0
0
0
1
2
2
1
0
0
0
2
1
1
1
0
0
0
0
2
0
2
0
0
0
0
0
2
1
0
1
0
0
2
1
0
0
0
0
1
0
2
0
0
0
0
0
1
1
1
1
1
2
0
2
1
1
0
1
1
0
0
0
0
0
2
1
2
1
1
1
2
1
1
2
0
0
2
1
1
1
0
1
1
0
1
0
1
0
1
0
0
0
0
1
1
0
0
1
0
0
0
3
0
1
2
0
1
0
1
0
0
0
0
2
1
0
0
0
2
0
0
1
1
1
0
0
2
0
0
0
0
1
0
2
0
1
0
1
0
1
1
0
0
2
2
2
2
1
0
1
1
1
0
1
0
1
2
0
1
2
0
1
2
0
1
2
0
1
0
2
1
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
1
0
0
2
0
0
1
0
0
2
0
0
1
0
1
1
2
1
1
2
2
2
0
2
2
2
2
2
0
1
0
0
1
0
0
1
0
0
0
0
2
1
0
1
2
0
1
0
1
0
2
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
1
1
0
1
2
2
0
3
1
3
0
0
2
0
2
0
0
1
0
1
1
0
1
0
0
2
0
0
0
1
0
1
2
1
0
0
2
0
1
2
0
0
2
2
0
0
0
0
0
1
1
2
2
0
0
1
3
2
0
0
0
0
1
0
2
0
0
1
0
0
1
0
1
0
0
1
1
1
0
1
1
2
1
0
0
1
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
2
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
2
0
2
1
0
1
0
0
2
2
0
0
0
0
2
1
0
0
1
1
0
0
0
0
0
2
0
0
0
0
2
0
1
0
1
0
1
0
1
0
1
0
2
0
0
2
0
0
1
1
0
2
2
1
1
2
1
2
1
0
0
1
2
1
0
0
1
1
2
0
2
0
1
1
0
1
0
0
0
0
1
1
0
0
1
0
1
0
0
0
1
0
2
0
2
0
1
2
2
0
2
0
0
1
0
1
0
2
0
2
0
1
0
1
0
0
1
0
0
0
0
0
1
0
1
0
2
1
0
1
2
0
2
2
1
2
2
1
4
0
0
0
0
2
2
0
0
1
1
2
0
2
1
1
2
0
2
0
0
0
1
1
0
0
0
2
0
0
0
0
1
0
0
1
0
0
1
3
1
0
1
2
0
1
1
0
0
2
1
0
3
0
0
2
1
0
2
0
1
1
0
0
0
1
1
0
1
0
1
0
0
2
0
0
2
1
1
0
0
0
0
0
0
1
0
0
0
0
3
1
0
0
2
0
0
0
2
0
1
1
0
0
0
0
1
0
0
2
2
0
2
0
2
2
2
0
2
1
1
1
0
0
0
0
2
2
0
2
0
2
1
0
1
1
2
0
0
0
0
0
2
1
0
2
1
0
0
1
1
0
1
0
2
0
2
2
2
0
2
1
2
0
0
0
1
0
1
0
0
2
0
0
0
0
0
2
1
1
0
1
0
1
1
0
0
2
0
0
2
2
2
0
0
0
0
0
0
0
2
0
0
1
2
1
3
0
0
0
1
0
1
1
0
2
2
0
0
1
0
1
2
0
6
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
1
2
2
0
0
0
0
1
0
1
0
0
1
2
1
2
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
1
1
0
1
1
0
1
0
0
0
1
0
2
1
0
0
2
1
0
0
0
1
0
1
2
1
0
0
1
1
0
0
0
2
0
0
1
2
2
0
0
0
0
2
2
0
0
0
2
0
0
1
2
0
1
0
1
0
1
1
0
0
0
1
0
1
2
1
0
0
1
1
0
0
3
0
1
0
0
0
1
1
0
0
1
0
0
1
1
1
2
0
2
1
1
0
2
0
2
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
2
3
0
0
0
1
0
2
2
0
0
0
3
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
2
0
0
0
2
0
0
2
2
1
0
2
0
2
2
2
0
1
1
0
2
1
1
1
0
1
1
1
2
0
1
0
1
0
0
0
0
0
0
2
0
0
0
1
1
0
2
0
0
0
0
1
2
0
0
2
0
0
1
0
0
0
1
0
2
1
1
1
0
1
0
2
2
2
0
0
0
0
0
0
0
1
0
1
2
2
1
0
0
1
0
0
0
1
2
1
0
2
2
0
2
0
1
2
0
4
1
0
0
0
1
2
0
0
0
0
1
0
0
2
2
1
0
0
2
2
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
2
2
0
1
0
2
0
0
1
2
1
2
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
1
0
0
1
0
1
2
2
2
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
10
0
1
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
2
0
0
1
0
0
1
1
2
1
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
1
0
0
2
1
0
2
0
1
2
0
0
1
2
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
1
0
0
2
0
0
1
0
0
0
0
2
1
0
0
0
0
2
2
0
0
2
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
2
0
1
0
0
2
0
0
0
1
1
0
0
0
0
5
0
2
0
1
0
0
0
0
0
1
0
2
2
0
0
2
0
0
0
1
0
0
1
0
0
0
0
1
2
0
2
1
2
0
1
1
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
1
0
0
2
2
1
0
2
2
1
0
1
2
1
2
0
1
2
0
0
0
2
0
2
1
1
0
2
0
1
0
2
1
2
0
0
0
2
0
3
2
0
0
0
0
1
1
2
0
0
1
0
1
0
0
0
1
1
1
0
0
2
0
0
0
2
0
1
2
2
0
0
0
0
1
1
0
0
2
0
4
0
0
1
0
0
2
1
0
0
0
1
2
2
0
2
2
0
0
1
0
0
2
1
0
0
0
0
2
0
0
1
1
0
1
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
2
3
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
3
1
0
0
0
0
2
2
1
0
0
0
1
0
1
0
0
0
2
1
0
0
0
2
2
2
2
0
2
1
2
0
1
2
0
0
0
0
2
2
2
0
3
0
2
0
1
1
0
1
2
0
2
0
0
0
0
0
0
0
1
1
0
1
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
2
1
5
0
1
0
0
2
2
0
2
1
1
0
0
1
0
0
1
0
0
0
1
0
1
3
0
0
0
0
1
2
1
0
1
1
2
0
3
4
0
1
2
0
0
0
0
1
0
0
0
0
0
0
2
2
2
0
0
0
0
1
0
0
2
0
0
2
1
1
0
0
0
0
0
1
0
1
1
0
0
0
1
1
0
1
0
0
2
1
2
1
0
1
0
0
3
0
0
0
1
0
0
1
0
0
1
2
0
0
0
2
2
0
1
2
1
2
2
1
2
1
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
1
0
1
4
0
3
1
0
0
0
0
0
0
0
1
2
1
0
0
2
0
1
1
0
0
2
0
1
0
0
2
2
0
0
0
0
0
0
1
0
1
0
0
0
0
1
2
0
2
0
0
0
1
0
0
0
1
0
0
1
0
0
0
2
2
1
1
1
0
0
2
2
2
0
1
0
2
1
0
1
3
2
0
2
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
2
2
0
1
1
4
1
0
1
0
0
1
0
0
0
2
0
0
0
1
0
0
2
1
0
2
2
2
0
0
1
2
0
0
1
15
0
0
2
2
0
2
0
2
0
0
1
2
1
0
1
2
0
0
2
1
0
0
1
2
1
0
2
0
2
0
0
0
1
0
2
2
2
0
0
2
0
1
2
0
1
1
0
1
0
2
0
0
0
0
0
2
2
1
0
2
2
2
4
2
0
2
0
0
0
0
0
1
0
0
2
2
0
0
0
1
2
1
1
1
1
0
0
2
0
0
2
1
0
2
0
0
0
1
1
0
0
0
1
0
0
0
0
2
0
0
1
0
0
1
1
0
0
0
2
0
0
0
0
1
2
0
0
1
0
0
0
1
1
2
2
1
3
1
1
0
0
0
0
0
1
0
2
0
2
0
0
2
0
1
2
0
0
0
1
1
0
0
0
0
1
0
0
0
0
2
1
0
0
2
2
2
0
0
2
0
2
1
2
0
1
0
0
0
0
2
0
1
0
1
1
1
0
1
0
1
0
0
1
2
0
0
1
1
0
0
0
0
0
0
1
0
0
0
2
2
0
0
2
1
0
0
0
1
1
0
2
0
2
0
0
2
0
0
1
0
0
2
0
2
1
0
0
2
0
2
1
0
0
0
0
0
0
1
2
2
0
0
2
1
0
2
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
1
0
1
1
1
0
0
0
1
0
2
1
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
2
2
0
2
0
0
1
0
1
0
2
2
1
0
2
1
0
0
0
2
0
2
0
0
1
2
0
0
0
2
1
2
0
0
0
0
2
1
1
0
0
1
1
2
1
1
0
0
1
0
0
0
1
0
0
2
0
0
2
0
2
0
1
0
0
1
0
2
4
0
0
0
2
1
1
0
1
0
0
1
1
0
0
0
2
2
0
0
0
1
4
1
0
2
0
2
0
1
0
0
0
2
1
0
0
1
1
1
1
1
0
0
0
2
0
0
0
1
1
1
0
0
0
2
1
0
1
0
0
0
1
0
0
1
1
1
0
3
1
1
2
0
0
0
0
0
1
2
0
2
1
1
0
0
0
0
1
2
2
0
2
0
2
2
2
2
2
0
0
1
0
1
0
1
2
1
0
1
1
0
0
1
1
0
0
2
2
1
0
0
0
3
0
0
0
1
1
0
0
0
0
2
0
0
3
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
1
1
0
2
0
1
1
1
0
2
0
2
0
0
0
1
0
1
1
0
1
1
1
0
0
0
0
1
0
2
2
0
0
1
1
1
0
0
0
1
0
1
0
2
1
0
1
1
1
1
0
2
0
2
0
2
1
0
0
0
0
1
0
0
2
0
2
0
0
0
1
0
0
1
1
2
2
0
0
1
0
2
0
0
0
0
1
0
0
0
1
1
2
0
0
1
2
0
0
0
0
0
0
3
1
0
0
0
2
0
1
0
1
3
2
0
0
1
2
0
1
0
0
2
0
2
0
0
0
0
0
1
1
0
0
1
0
1
0
1
0
0
0
0
1
2
1
0
2
0
0
0
1
1
2
0
0
0
0
0
1
2
0
2
2
0
0
2
0
1
2
0
0
1
0
0
1
1
1
1
0
1
2
0
0
0
0
2
1
0
1
0
0
0
2
1
0
0
0
2
1
0
0
1
0
1
3
2
0
0
1
0
0
1
0
0
1
1
0
2
2
1
0
0
0
0
0
1
0
1
0
1
2
2
0
0
0
2
0
0
0
2
1
0
0
0
2
1
0
0
2
0
1
0
0
2
0
1
1
0
2
1
1
0
2
0
0
1
0
0
2
0
0
2
2
0
0
2
0
0
0
1
0
0
0
0
0
1
2
0
0
5
0
0
2
0
1
2
0
0
2
2
2
0
1
1
0
0
1
1
0
1
0
0
1
0
2
0
0
2
3
1
0
0
0
2
1
2
0
0
0
0
2
0
1
2
0
0
0
0
1
2
1
2
0
1
0
0
0
2
0
0
2
0
0
0
1
1
0
0
1
0
1
2
0
2
2
2
0
2
1
0
0
2
0
0
2
0
0
0
0
2
1
0
2
5
0
1
2
0
1
0
0
2
0
2
0
0
1
0
1
0
2
0
1
1
0
1
0
0
0
0
0
2
0
2
0
1
2
0
2
0
2
0
1
3
1
2
0
0
2
0
2
0
0
0
1
0
0
1
2
0
0
1
0
0
0
0
1
0
0
1
0
4
1
0
0
0
0
1
1
0
1
3
0
0
0
1
2
0
0
0
1
0
3
0
0
2
2
1
0
1
0
0
2
1
1
0
0
0
1
2
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
2
2
1
0
0
0
1
1
0
1
2
0
1
0
1
7
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
1
2
2
1
1
0
10
0
0
1
0
0
1
2
0
0
2
0
2
0
0
0
3
0
0
1
0
0
0
0
2
0
3
0
0
2
0
1
0
1
2
1
2
1
3
0
0
0
0
1
0
2
1
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
1
2
2
1
1
0
1
2
1
1
0
2
1
2
1
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
1
1
2
1
0
2
0
0
0
0
0
1
0
1
0
1
0
1
1
1
0
1
2
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
2
2
2
0
0
0
0
2
2
2
2
1
0
0
1
1
0
0
1
0
1
1
1
1
0
0
1
0
1
0
1
0
0
2
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
1
1
0
1
1
1
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
3
2
0
1
0
0
1
0
0
1
1
0
0
2
1
0
0
0
0
2
2
0
0
1
0
0
1
0
0
0
2
0
0
2
0
0
0
0
1
0
2
0
0
1
3
1
0
0
0
0
1
1
1
0
1
0
0
5
0
0
1
0
1
1
0
1
0
0
0
2
0
2
0
1
1
1
0
0
2
2
0
1
1
0
1
0
3
0
0
2
1
0
1
1
2
0
0
0
0
1
1
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
2
1
0
0
0
0
1
1
1
1
0
1
1
0
1
1
1
0
0
2
0
0
1
1
1
0
1
1
0
2
0
2
0
2
0
1
0
3
0
2
1
0
0
1
1
1
2
2
1
0
0
0
3
0
0
0
0
0
2
2
0
1
0
0
0
0
1
0
2
0
0
1
0
0
2
0
2
0
1
0
2
0
1
0
1
1
0
1
1
0
1
0
2
0
1
0
0
0
2
0
0
0
2
2
1
0
1
0
0
3
0
0
2
0
0
0
0
0
1
0
0
2
1
1
0
0
1
2
0
0
0
1
0
1
0
1
1
0
0
0
1
0
1
0
1
0
0
2
0
1
0
0
1
0
0
0
1
1
1
0
0
0
0
0
2
0
0
2
0
1
0
2
2
1
0
0
0
1
0
0
0
1
0
0
1
1
1
2
2
0
0
0
0
1
0
2
0
1
3
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
1
2
2
0
2
0
2
2
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
3
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
1
5
1
0
0
1
2
0
0
0
2
0
2
0
0
1
0
2
1
1
2
2
1
0
1
0
2
0
0
0
1
0
0
2
1
0
0
1
2
1
3
0
0
0
0
2
2
0
0
1
0
2
0
3
2
2
1
0
0
1
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
2
0
0
0
1
2
0
1
0
1
1
2
0
2
1
1
0
0
0
1
1
1
1
6
0
1
0
0
2
0
1
2
0
0
2
2
1
0
0
2
1
2
0
2
0
1
0
2
1
1
0
0
2
0
0
0
1
0
0
0
0
2
1
0
0
2
1
0
0
2
2
1
2
0
2
0
0
1
0
2
0
1
0
0
0
0
2
2
1
0
0
0
0
0
1
1
0
0
0
0
0
2
2
0
0
1
0
0
1
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
2
0
1
0
1
2
0
0
0
0
0
0
2
0
1
0
1
0
1
2
0
2
0
0
2
0
0
0
2
0
2
1
0
1
0
3
0
1
0
0
0
0
0
1
0
1
0
1
0
1
0
2
0
0
1
0
1
2
1
1
0
0
0
0
0
1
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
2
2
0
0
0
2
0
0
1
1
0
2
1
0
1
2
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
1
2
0
0
0
1
0
2
1
0
2
1
1
1
1
1
1
0
2
0
2
2
1
0
2
0
0
0
1
0
4
2
0
2
1
1
2
0
1
2
0
2
0
0
2
0
2
1
1
2
0
2
0
1
0
0
1
1
0
0
0
1
0
0
2
1
2
0
0
0
0
1
0
0
0
0
2
2
3
2
0
0
0
0
0
0
0
2
1
2
0
1
2
2
0
0
0
0
0
2
2
1
0
1
0
2
1
0
0
0
0
0
2
0
2
1
1
0
1
0
0
1
0
1
1
0
0
0
0
2
1
0
1
0
1
0
2
2
1
0
0
1
0
2
1
0
2
0
0
0
0
3
0
0
0
1
2
2
2
0
2
0
0
0
1
2
0
0
3
0
1
0
1
1
0
2
0
0
0
0
1
1
0
0
0
1
2
1
2
0
2
2
0
2
2
2
0
1
0
0
1
1
0
0
0
0
0
2
1
1
0
0
0
0
0
0
2
3
0
2
0
0
0
0
1
1
0
0
0
0
0
3
0
0
2
1
0
0
1
0
0
0
0
0
3
0
0
0
2
1
0
0
1
0
0
0
0
1
0
0
0
2
0
0
1
2
0
0
0
0
0
2
0
2
2
0
0
1
1
0
1
1
2
0
1
0
0
0
1
0
2
0
0
0
0
1
2
0
0
0
0
2
1
1
1
2
2
1
2
0
0
0
0
0
1
2
2
0
0
2
0
1
0
1
0
1
0
1
0
0
0
2
1
1
0
0
2
1
1
1
0
2
1
2
1
1
0
2
2
2
1
0
3
3
2
0
2
0
0
1
0
0
2
0
0
2
0
1
0
2
0
0
0
0
0
0
2
3
2
2
2
0
2
3
0
0
0
0
0
1
0
0
0
0
1
1
1
1
2
0
1
2
1
0
0
1
1
0
0
2
0
2
2
1
0
1
0
0
4
2
0
2
1
0
2
0
0
0
0
1
0
1
2
0
0
1
0
1
1
4
1
1
0
2
0
0
1
1
2
1
1
0
0
1
1
2
2
0
1
0
1
1
1
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
2
2
1
1
0
1
2
0
2
1
0
0
1
0
0
0
1
1
1
1
0
0
0
0
2
1
0
0
0
2
0
4
1
1
3
0
0
0
1
0
0
2
1
0
1
1
0
0
0
1
2
1
0
0
0
2
0
0
1
0
0
1
0
0
0
0
2
1
0
0
1
1
2
2
2
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
1
0
0
0
3
1
1
2
2
2
0
0
2
2
2
0
0
2
1
2
0
0
2
1
1
0
0
1
1
0
0
0
2
0
2
1
0
0
1
2
2
0
2
2
2
0
1
2
0
0
1
2
1
2
0
1
0
1
0
1
1
0
0
0
0
0
1
2
1
0
0
0
0
0
3
1
1
1
0
3
0
1
1
2
0
2
0
0
2
0
0
0
1
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
2
1
2
1
2
0
0
0
0
2
0
2
0
2
0
2
1
0
1
1
0
0
1
0
2
1
0
0
2
1
2
0
1
2
0
1
1
2
3
2
1
0
1
1
0
0
0
2
0
1
2
2
1
0
0
1
2
0
2
2
0
0
1
0
1
0
0
0
0
2
2
1
2
1
1
0
2
0
0
3
0
1
1
0
0
0
0
0
0
2
2
0
1
2
0
0
0
0
1
1
2
1
2
0
0
0
0
0
2
0
2
0
0
2
0
1
1
0
1
2
0
0
1
0
1
0
0
1
3
3
0
1
0
0
6
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
1
0
2
1
0
1
0
2
0
0
1
2
1
1
2
0
2
1
0
0
1
0
1
1
0
1
0
0
1
2
0
1
0
1
0
2
1
0
0
1
3
2
2
0
1
0
0
2
0
2
1
0
0
0
1
0
1
0
0
4
1
0
0
2
0
0
1
1
2
1
1
0
3
2
0
3
0
0
2
0
1
0
2
0
0
1
0
0
0
0
1
0
0
2
0
2
2
2
0
2
1
0
0
2
0
1
0
1
1
0
0
0
1
0
1
0
0
1
2
1
0
2
0
1
2
0
0
0
0
2
0
0
2
0
2
0
0
0
1
0
0
0
1
2
0
1
0
0
1
1
0
1
0
0
0
2
0
1
1
4
0
1
1
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
1
1
0
1
1
0
2
1
1
2
0
0
0
1
2
0
1
1
0
1
5
0
1
0
0
0
0
0
1
0
0
0
1
2
0
2
1
0
1
2
2
0
0
0
0
2
1
0
0
2
1
0
2
0
0
0
0
0
2
1
2
0
0
0
0
1
0
2
0
0
1
2
1
2
2
1
2
0
3
0
0
2
8
0
1
1
1
1
0
0
1
2
0
2
2
0
0
0
1
0
0
2
0
0
0
0
0
1
2
2
2
0
1
0
0
2
0
0
0
0
0
3
1
2
0
0
3
0
2
2
0
1
2
3
1
0
1
1
2
2
0
0
2
0
1
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
3
0
1
1
0
0
2
1
0
0
0
1
1
0
0
1
2
2
0
0
0
0
1
1
1
2
1
2
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
1
1
2
1
2
0
0
2
1
0
1
0
2
0
0
0
0
2
0
0
2
1
0
1
2
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
5
1
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
1
0
0
2
0
1
2
0
0
2
0
1
2
0
0
0
0
0
2
0
1
2
0
0
0
1
0
0
0
1
2
0
1
0
2
2
1
1
0
0
0
0
0
2
2
1
0
0
1
0
0
0
1
0
1
0
0
2
2
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
1
0
2
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
3
0
1
2
1
2
0
0
0
2
0
0
0
0
0
1
2
0
2
1
0
1
0
1
1
2
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
1
1
0
0
2
2
2
2
2
0
1
0
1
0
0
0
0
0
2
2
0
2
1
0
1
0
0
0
0
1
1
0
0
0
0
0
3
0
1
0
0
0
3
0
0
1
0
0
0
0
0
1
3
0
0
0
0
0
2
0
2
2
1
0
0
2
0
1
2
0
0
1
1
0
1
2
0
0
0
2
0
0
0
0
1
1
1
0
1
2
2
0
2
2
2
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
1
0
1
2
0
0
0
1
0
0
1
2
0
0
0
0
0
2
0
0
1
0
1
0
2
2
0
0
1
0
0
0
1
2
1
1
0
0
0
0
0
0
1
1
2
1
0
1
0
2
0
0
0
2
0
1
0
3
3
0
1
2
0
2
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
2
3
0
1
1
0
0
2
2
0
1
1
0
0
0
0
0
0
0
1
0
1
2
1
2
0
0
2
0
0
2
2
2
2
0
0
0
0
0
0
0
1
0
2
1
2
0
0
3
0
2
0
0
0
0
0
1
2
2
0
2
2
1
0
1
2
3
0
0
1
0
0
1
0
0
0
0
1
0
1
1
0
1
2
2
1
0
1
2
0
0
2
0
2
0
1
0
0
1
0
0
0
0
0
2
2
1
0
0
2
2
0
0
2
0
0
1
0
0
0
2
1
0
0
0
3
1
0
0
1
1
0
1
1
0
0
3
2
0
1
0
1
0
0
0
0
2
0
0
0
1
0
0
2
1
0
1
0
0
1
1
2
0
0
0
2
0
2
1
0
0
0
0
2
2
0
1
1
0
0
0
0
1
1
0
1
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
3
1
0
0
0
0
0
1
2
2
1
0
2
2
0
0
0
0
1
0
1
0
0
1
0
1
0
1
1
1
1
0
0
2
0
2
0
0
1
2
0
0
0
1
0
0
0
0
1
0
0
1
2
0
0
1
2
0
1
2
1
0
0
2
2
0
0
0
0
0
1
1
0
2
0
0
0
0
0
2
1
0
1
1
0
1
2
0
2
0
0
1
1
0
2
0
0
1
2
0
0
0
0
0
1
1
0
0
0
3
0
0
0
1
1
2
0
1
0
0
0
0
1
0
0
0
0
1
1
1
2
0
0
0
0
2
0
1
1
2
1
0
1
0
2
0
0
0
1
0
2
0
1
2
0
0
0
2
0
2
2
2
2
0
1
0
0
2
1
0
0
0
0
1
2
2
0
1
0
1
2
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
1
2
0
0
2
0
0
2
0
2
1
0
1
0
1
2
0
0
0
2
1
1
0
0
2
0
0
0
2
2
3
0
0
1
0
0
2
0
0
0
0
0
1
0
0
2
1
1
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
1
2
0
2
0
0
2
2
0
0
1
0
0
0
1
0
1
0
0
1
0
0
2
0
0
0
1
0
0
2
0
0
1
1
2
1
0
0
0
0
2
1
1
2
0
2
0
0
1
1
0
0
2
0
0
0
0
0
0
2
1
0
0
2
2
3
0
2
1
0
0
0
0
0
1
0
0
0
0
2
2
0
0
1
0
1
0
2
0
0
2
1
0
0
2
2
2
0
1
0
1
2
0
1
2
1
0
2
1
0
0
1
2
0
2
2
0
0
2
0
3
2
0
1
2
0
0
0
0
0
0
0
2
0
0
1
0
0
2
1
0
2
1
2
0
0
2
1
0
0
0
0
2
2
1
0
2
2
1
4
0
0
0
1
0
2
1
0
2
0
0
0
0
1
2
1
0
2
1
0
1
0
0
1
2
1
2
0
0
1
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
2
0
0
0
1
0
0
1
0
1
2
2
1
0
0
0
0
0
1
0
0
2
1
1
0
0
1
1
0
1
2
1
2
2
2
0
2
1
0
0
1
1
1
2
2
0
1
0
1
2
0
1
2
0
2
0
2
2
0
2
0
0
2
0
0
1
1
2
2
2
1
0
1
1
1
0
0
2
0
1
0
2
0
0
0
1
2
0
0
1
0
1
0
1
0
1
2
3
1
0
0
2
0
2
0
3
1
0
2
2
1
0
1
1
0
2
0
1
0
1
0
2
0
0
0
0
2
0
0
0
0
0
2
1
2
1
0
2
0
0
0
1
3
0
2
0
0
1
0
0
0
1
0
2
0
0
2
1
0
2
0
0
1
2
1
0
1
0
3
1
2
0
0
0
0
2
1
1
0
0
0
0
0
0
2
1
0
1
2
0
0
1
1
0
0
0
0
2
0
2
0
2
1
0
1
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
1
0
2
0
1
0
0
2
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
2
1
0
2
1
0
2
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
1
0
0
2
4
0
0
0
1
0
0
1
0
0
1
0
0
1
0
2
0
2
2
2
0
1
1
2
0
2
1
2
2
0
1
0
1
1
0
1
1
0
0
0
0
1
2
2
0
2
0
1
1
0
0
2
0
0
0
0
2
2
0
2
0
0
0
0
0
1
1
0
2
2
2
0
1
2
0
0
1
1
1
0
0
0
0
0
1
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
2
1
0
2
1
0
2
1
0
0
3
0
1
0
1
2
2
1
0
1
1
2
2
0
0
2
1
0
0
0
0
0
0
0
1
1
3
3
0
2
1
0
1
0
2
0
0
2
0
1
0
0
1
1
0
2
0
0
1
0
0
1
2
1
0
1
0
0
0
2
1
0
0
2
0
1
1
2
1
0
0
1
2
0
0
1
2
0
1
1
2
1
1
1
0
2
0
0
2
0
0
0
0
0
2
0
0
2
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
2
2
1
1
1
0
1
1
0
1
0
0
3
1
0
1
2
0
1
2
1
0
0
2
1
0
2
0
0
1
0
1
0
2
1
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
1
1
0
0
1
0
0
0
2
1
0
0
0
2
2
0
1
1
0
0
1
0
0
2
0
0
0
0
1
1
0
0
0
0
1
1
2
0
0
2
0
0
0
0
0
1
0
0
2
1
0
2
0
0
1
0
0
1
0
3
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
1
3
1
1
0
0
1
2
0
1
1
0
0
1
1
2
0
0
0
1
0
0
1
0
0
0
0
2
0
0
1
0
0
0
2
1
0
2
2
0
0
2
0
0
0
1
1
0
1
0
0
0
0
2
0
1
0
1
0
0
1
2
0
0
0
0
1
2
1
0
2
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
1
0
0
0
1
2
0
2
0
0
2
0
2
2
0
0
0
0
0
2
1
0
0
0
2
3
1
2
2
1
0
1
2
0
1
2
0
0
1
0
0
1
2
0
0
1
0
0
1
6
0
0
0
0
2
3
0
2
0
0
1
1
0
4
0
1
0
1
1
0
0
1
2
1
0
1
1
1
0
0
1
0
0
1
2
2
0
0
1
0
1
1
0
0
0
0
1
2
2
0
0
2
1
0
1
1
0
0
1
0
0
0
2
1
1
1
0
0
0
0
1
1
0
0
1
2
0
2
2
0
0
0
2
0
1
3
0
2
2
1
0
0
2
0
0
0
1
1
0
0
1
2
0
0
1
1
1
2
0
0
0
2
2
0
2
2
2
1
0
0
0
2
0
0
1
0
1
2
2
0
1
0
0
1
0
2
0
0
2
0
0
0
0
0
1
0
2
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
2
0
0
2
2
0
1
0
1
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
2
2
0
0
0
1
4
1
2
2
2
1
0
2
0
0
0
0
0
0
1
1
0
0
2
2
0
0
0
0
0
0
0
0
0
2
1
2
0
0
1
0
0
0
2
0
0
0
1
0
0
0
2
1
0
0
0
2
2
1
2
0
0
0
2
0
1
0
1
0
2
2
0
2
1
1
0
0
1
0
0
2
2
0
0
0
2
0
2
0
0
1
2
2
1
2
2
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
2
0
2
0
2
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
1
2
1
0
0
1
0
0
0
0
0
0
2
2
0
1
0
0
0
0
1
0
2
0
0
0
0
1
0
1
1
2
1
0
0
3
0
0
1
1
1
2
1
0
0
3
2
0
2
0
1
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
2
0
1
0
0
1
1
1
0
1
3
0
1
2
0
0
2
1
0
0
0
0
0
1
0
1
1
2
0
2
0
1
2
0
2
2
2
0
1
2
0
0
0
2
0
1
0
2
2
2
0
1
0
1
2
1
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
2
0
0
0
0
1
0
1
0
0
3
2
1
0
0
1
0
2
1
2
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
1
0
1
1
1
0
0
0
0
2
0
0
2
3
0
3
0
1
0
0
1
0
1
0
1
0
2
0
0
0
0
0
1
1
1
0
2
0
1
0
0
0
2
0
3
0
2
0
2
0
0
1
0
0
2
1
0
2
0
1
0
0
1
0
0
0
0
1
0
0
0
2
0
0
2
0
1
0
2
0
1
0
0
0
2
1
1
0
0
2
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
2
1
0
3
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
1
1
0
2
2
0
1
0
1
1
1
2
0
0
1
2
1
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
1
0
2
0
2
0
0
0
1
0
0
2
0
1
0
0
0
2
0
1
1
0
0
2
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
2
0
1
0
2
0
0
0
0
0
0
1
2
0
2
0
1
1
0
0
0
0
0
1
0
1
1
1
0
0
1
2
1
0
1
1
1
5
0
0
1
0
0
7
2
0
1
2
1
0
0
1
0
0
0
1
1
0
0
2
0
0
0
0
1
0
1
0
3
0
0
1
0
1
0
1
0
0
0
0
2
0
0
2
0
0
1
0
0
0
1
1
2
0
1
0
1
0
0
0
0
2
1
1
1
0
3
1
0
0
1
1
1
0
0
0
0
3
0
0
2
1
2
0
0
0
0
0
1
2
1
2
0
0
1
1
1
0
0
1
0
1
0
0
0
0
3
0
2
0
1
0
1
1
0
0
1
0
1
0
0
0
0
0
1
0
0
2
1
0
1
0
0
0
0
0
1
2
0
0
0
0
1
2
1
0
3
1
2
0
0
0
0
1
1
1
0
2
2
0
0
0
2
0
1
0
0
1
0
2
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
1
1
2
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
1
2
2
0
0
0
2
1
1
1
1
0
2
0
1
0
2
0
1
1
0
0
0
0
0
2
2
2
1
2
0
1
0
0
3
0
1
0
1
1
0
2
0
1
1
2
0
0
3
0
1
0
0
1
1
2
2
0
1
1
2
2
1
0
2
2
3
1
1
2
1
3
0
1
1
0
1
3
0
0
2
2
0
2
2
2
0
0
1
2
0
0
0
0
0
2
0
1
3
0
1
1
0
0
1
0
0
2
0
2
0
0
1
0
0
0
1
0
1
1
0
5
1
0
1
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
2
2
0
1
1
2
2
2
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
2
1
0
0
1
0
0
0
0
1
0
0
0
1
2
1
0
0
0
2
2
2
2
0
0
2
0
0
0
0
0
2
2
3
0
0
0
1
0
0
1
0
0
0
0
1
0
2
2
3
1
2
1
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
3
2
2
2
1
1
0
0
1
0
0
1
1
2
0
0
0
2
1
1
0
0
1
0
1
1
1
0
1
1
0
0
0
0
2
0
2
1
0
0
2
0
2
0
0
0
1
1
0
1
2
0
0
2
0
0
1
0
2
1
0
1
1
1
2
0
1
0
0
0
0
0
0
5
1
1
0
1
1
0
1
0
0
0
0
0
2
1
0
0
1
1
0
0
0
1
1
0
0
0
1
0
0
0
1
1
2
2
1
2
1
2
1
0
0
1
0
1
0
0
3
0
0
1
3
1
0
1
1
0
1
0
2
0
0
0
1
1
0
0
1
0
0
2
2
1
1
2
2
0
1
0
0
2
0
2
0
0
0
0
1
1
0
0
0
1
0
2
2
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
2
0
1
0
2
0
1
0
0
0
2
0
1
1
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
1
0
2
2
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
2
0
2
0
1
1
1
0
0
1
0
0
2
0
0
0
1
0
1
0
0
1
0
2
0
0
1
1
0
0
0
1
0
0
2
0
2
0
1
0
1
0
1
2
2
1
0
2
2
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
1
0
2
0
0
1
0
0
1
0
2
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
1
2
0
1
0
2
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
2
2
1
0
0
0
1
1
0
0
2
2
3
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
11
2
0
0
0
1
1
2
1
0
0
0
0
0
2
0
0
1
0
2
0
0
2
0
0
1
2
2
0
0
0
2
0
0
0
2
2
0
2
1
2
0
0
0
0
1
4
0
2
0
0
3
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
2
0
0
0
0
1
1
0
1
1
2
0
0
0
0
0
0
2
0
1
0
0
1
0
2
1
0
0
0
2
1
0
0
2
0
1
2
4
1
2
2
0
2
0
1
2
0
2
3
1
1
0
0
1
1
0
1
2
1
1
0
2
1
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
1
2
2
1
8
2
0
0
1
2
1
2
1
2
0
3
1
0
1
0
3
1
1
2
0
2
1
0
0
1
0
1
2
0
0
1
0
2
0
0
0
1
1
1
0
2
1
0
1
0
2
0
2
0
0
1
1
0
1
0
0
5
1
0
2
1
1
2
1
0
2
2
0
0
2
1
0
0
0
0
2
0
0
1
1
0
1
0
1
0
1
1
1
0
0
3
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
1
1
2
2
0
0
1
2
1
0
1
0
0
0
0
0
0
0
0
2
0
1
1
0
0
1
0
1
0
0
2
1
0
0
2
1
1
0
0
0
1
0
0
1
2
0
0
1
0
2
1
0
0
1
0
0
0
0
2
1
0
2
2
0
0
0
1
0
0
3
0
0
2
0
1
0
1
2
0
0
0
0
2
2
2
1
1
2
1
1
0
0
2
0
0
0
0
2
0
1
1
0
2
0
0
0
2
0
2
0
1
3
1
0
0
2
0
1
2
1
1
0
2
2
1
2
2
0
0
2
2
0
3
2
0
1
0
1
0
1
0
0
0
2
1
3
1
0
2
1
1
2
0
0
2
0
2
1
1
0
0
2
0
0
0
2
0
0
1
0
0
0
1
2
0
0
2
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
2
2
1
2
1
1
0
0
1
2
1
0
0
0
0
1
0
1
1
2
1
0
0
1
4
0
1
2
0
0
1
0
0
0
1
0
1
1
0
0
0
0
1
1
2
1
0
0
1
2
2
0
1
0
0
3
0
0
1
1
0
1
0
2
0
0
1
1
2
2
2
0
1
2
2
1
1
1
2
0
2
1
1
0
2
0
2
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
2
1
0
0
1
1
0
1
0
0
0
0
1
5
0
0
0
2
2
7
2
0
2
0
0
0
0
2
2
1
0
0
0
1
0
0
0
0
0
1
1
1
0
0
1
0
0
1
0
0
1
0
0
0
2
1
1
2
2
0
0
0
1
0
1
1
0
0
0
0
2
2
1
0
0
0
0
0
0
1
1
0
0
1
0
1
1
1
0
1
1
0
0
0
0
0
1
0
1
1
1
1
2
2
0
0
0
2
1
1
0
0
0
0
2
2
0
1
0
0
0
1
0
1
0
0
2
0
1
2
0
2
0
0
1
0
2
0
2
1
0
1
1
0
0
0
0
1
0
0
1
0
0
1
0
2
0
0
2
1
0
2
2
2
0
0
0
2
1
0
1
0
0
1
0
0
0
0
0
1
0
0
3
2
0
0
0
0
1
1
0
2
0
2
2
1
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
1
0
2
0
0
0
0
0
0
0
2
1
1
1
1
1
2
0
1
0
0
0
2
0
1
1
0
0
0
0
1
2
0
0
1
0
0
0
1
1
1
2
1
2
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
2
1
1
3
0
2
0
2
0
0
0
0
0
0
2
0
2
0
0
0
2
2
0
1
0
0
2
0
1
0
0
1
1
0
4
1
0
0
2
0
0
2
1
0
0
1
0
0
1
0
1
0
2
1
0
2
2
0
0
2
1
0
1
1
2
1
0
1
0
1
0
2
2
0
1
0
0
1
2
0
3
0
2
0
1
1
0
0
0
2
2
1
2
0
2
0
0
0
2
0
0
0
0
0
0
2
2
0
0
2
1
0
0
0
0
2
0
0
0
0
0
2
0
0
1
2
0
2
0
0
0
1
0
2
0
0
0
2
1
0
0
0
1
0
0
2
0
1
2
0
0
1
0
2
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
1
2
1
0
2
0
2
1
1
1
0
0
1
2
0
0
2
0
3
0
2
0
0
1
2
2
0
0
0
2
1
0
0
0
0
0
1
0
1
0
1
4
0
0
1
2
0
0
0
2
1
1
0
1
2
0
2
2
2
0
2
0
2
1
2
1
0
1
0
0
0
0
4
0
2
0
1
0
0
3
1
0
0
1
0
0
0
0
0
1
1
1
0
0
1
0
2
1
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
1
0
2
0
1
0
2
0
1
0
0
2
2
1
0
0
0
0
2
1
2
1
2
1
0
2
2
0
1
0
0
0
2
0
0
1
0
2
0
1
1
0
0
1
0
0
0
3
0
1
1
1
0
0
0
0
0
1
0
0
0
2
1
0
6
2
3
0
0
0
0
2
0
0
2
2
0
2
0
0
0
2
1
1
1
0
0
2
1
0
0
1
2
0
1
0
0
0
1
2
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
2
0
3
0
0
1
0
2
2
0
2
0
1
1
0
2
0
0
1
1
0
0
2
0
0
1
2
1
2
1
2
1
2
0
2
1
2
0
0
2
0
2
1
0
0
0
0
0
0
0
2
1
1
1
0
0
2
0
2
0
0
0
0
2
0
0
1
0
1
1
0
2
1
1
0
2
2
0
2
0
0
1
0
0
2
2
0
1
0
1
2
0
2
2
2
0
0
0
2
0
0
1
2
1
1
1
1
2
2
2
0
0
0
1
1
0
2
0
0
0
0
2
1
0
0
2
1
1
0
2
0
1
1
0
2
0
0
0
0
2
1
1
2
1
0
0
0
0
0
0
0
2
2
1
2
1
0
0
0
0
2
0
0
0
1
2
1
2
0
2
0
1
0
2
0
2
0
0
1
1
1
0
1
0
0
0
0
1
0
1
2
2
1
0
0
0
2
2
0
2
2
0
0
1
0
2
0
1
0
1
0
1
0
0
0
0
2
0
1
2
4
0
0
0
0
0
1
0
1
2
0
2
0
0
1
0
0
0
0
0
0
2
2
2
1
2
0
2
1
0
0
2
1
0
0
0
1
1
0
0
1
0
0
1
2
2
1
2
0
2
0
0
1
1
1
1
0
2
0
2
1
0
2
2
0
1
1
2
1
1
0
0
1
0
1
1
0
4
1
2
0
1
0
0
1
1
3
0
0
1
0
2
0
0
0
0
2
1
0
0
1
1
0
0
0
0
3
0
2
0
0
0
0
1
0
2
0
1
2
0
0
2
0
2
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
2
0
2
1
1
0
1
0
0
0
0
2
0
0
0
0
1
2
0
0
0
1
0
0
0
0
1
2
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
4
1
2
2
0
2
1
2
0
0
0
2
0
0
2
0
2
0
0
1
1
0
2
1
0
0
0
0
0
2
1
0
0
1
0
0
1
0
6
0
4
2
0
0
0
0
0
1
0
2
0
0
0
0
2
0
2
2
0
0
0
2
0
0
0
1
2
2
0
0
0
3
2
0
1
1
1
0
1
0
0
0
0
0
1
1
1
0
2
0
0
2
2
1
4
3
1
2
0
1
1
0
1
0
2
0
0
0
0
0
2
1
0
0
0
1
0
0
0
2
2
1
2
0
0
0
1
0
1
0
2
2
0
0
1
0
2
0
1
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
2
2
0
0
2
2
1
0
2
1
2
0
0
0
3
0
1
1
0
1
0
1
1
0
0
0
0
0
1
0
1
0
0
2
0
0
0
2
0
0
0
1
2
0
2
1
0
0
0
3
0
1
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
1
1
0
1
0
1
0
0
0
0
2
1
2
1
1
2
1
1
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
1
2
2
1
0
0
0
0
0
0
2
0
2
1
1
0
2
0
0
1
2
0
1
1
2
0
0
0
1
2
0
2
0
0
0
2
1
0
0
0
0
0
0
1
0
2
0
0
2
2
0
0
1
2
0
2
0
0
0
0
0
0
1
2
2
0
0
1
1
0
2
1
0
0
0
0
2
1
1
0
0
0
0
1
2
0
2
0
0
0
1
0
1
0
0
0
0
1
2
0
0
1
0
1
2
0
1
2
1
0
0
1
0
1
0
2
0
1
0
1
2
0
1
1
0
0
1
2
0
1
2
2
0
0
0
0
1
0
2
0
2
1
0
0
1
0
2
2
0
0
0
0
1
0
2
0
0
0
2
2
1
0
1
1
2
0
1
0
1
0
0
0
1
2
0
0
0
1
2
1
2
0
1
2
0
1
1
1
3
2
0
0
0
1
0
0
0
2
0
0
2
2
1
2
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
1
2
2
2
0
0
0
1
3
0
0
2
1
1
1
0
1
0
1
0
0
2
0
2
1
3
1
2
0
0
0
1
0
2
0
0
0
1
0
0
2
1
1
0
0
0
0
0
0
1
0
2
2
1
2
1
2
0
0
2
0
2
0
1
2
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
2
1
0
1
0
0
6
1
1
1
2
2
0
0
0
1
0
0
1
2
3
2
1
1
0
1
1
0
2
0
2
0
0
0
1
0
1
0
0
1
2
0
1
1
0
0
2
2
2
0
1
1
0
0
0
2
1
2
1
0
0
1
1
2
2
1
1
0
0
0
1
0
1
1
2
2
1
2
0
2
1
0
2
0
0
1
0
2
0
2
1
2
0
1
0
0
2
1
1
0
0
2
0
0
0
0
3
1
2
0
0
1
3
0
0
0
0
2
1
2
0
2
0
2
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
2
1
0
1
1
3
1
0
0
2
0
1
0
0
2
0
0
1
1
0
2
0
1
0
2
0
1
1
0
1
0
2
2
1
0
0
0
0
0
1
0
2
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
2
0
1
2
1
0
0
1
2
0
0
1
1
0
0
2
0
0
0
2
0
1
0
0
0
1
1
1
1
0
0
1
1
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
1
1
1
1
1
0
1
2
2
2
0
0
0
0
0
1
1
0
0
2
0
1
0
0
2
0
0
6
0
1
0
1
0
0
0
1
0
0
0
1
2
1
2
0
0
2
2
0
0
0
2
0
0
0
1
0
3
0
1
1
1
0
1
0
2
1
2
0
0
2
0
2
0
1
0
1
2
0
0
1
1
0
0
1
1
2
0
0
0
0
0
1
0
0
0
1
2
0
0
0
2
1
0
1
1
0
0
0
0
2
0
1
2
0
0
0
1
0
0
1
1
2
0
1
1
0
0
2
1
0
0
1
0
1
0
0
0
0
1
0
1
1
0
2
1
0
0
1
0
0
0
2
0
2
2
0
0
0
0
0
0
4
0
2
1
2
0
2
2
0
0
0
2
0
2
1
3
1
0
0
0
0
0
0
1
1
0
2
0
2
0
0
0
0
3
1
1
0
1
0
2
0
2
1
0
0
0
0
0
0
1
1
0
0
1
0
2
0
0
1
2
0
0
0
0
1
0
2
1
0
1
0
0
2
1
1
0
1
1
1
0
6
0
1
1
2
1
0
0
0
2
0
2
0
2
2
0
0
1
1
2
0
2
1
2
2
0
0
0
0
1
0
0
0
1
2
1
0
2
2
0
0
0
1
0
0
1
2
0
0
2
1
1
1
0
0
2
0
2
1
0
0
2
2
0
0
0
0
0
2
1
0
0
0
0
1
0
1
1
2
0
2
0
2
0
2
1
3
2
0
0
1
2
0
0
0
2
2
2
2
1
2
0
0
2
0
1
1
0
0
2
0
0
1
0
0
0
2
0
0
2
2
1
2
1
2
0
0
0
1
0
0
1
0
0
0
0
5
2
2
0
0
1
0
2
0
0
1
2
0
1
0
0
0
1
0
4
2
2
1
0
0
1
0
1
0
1
0
2
0
0
0
2
0
1
1
1
0
0
0
2
2
2
1
0
2
0
0
2
0
0
2
1
1
0
0
1
2
0
1
0
1
0
0
0
0
0
0
2
0
0
2
1
0
2
0
0
0
2
0
1
2
2
1
0
0
0
1
0
0
2
0
2
0
2
2
0
0
0
0
0
2
1
2
0
2
1
1
0
1
0
1
1
0
1
0
1
2
2
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
1
1
0
1
0
0
1
0
0
0
0
1
1
0
0
1
0
1
0
2
0
0
0
1
0
1
1
3
2
0
0
1
1
0
1
2
0
0
1
0
2
0
0
2
0
0
0
0
1
1
2
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
5
1
2
1
1
2
2
0
0
0
1
2
2
0
0
0
0
0
0
0
0
2
1
2
2
2
0
4
2
1
0
2
1
1
0
1
2
2
0
3
1
0
0
1
1
0
0
0
0
2
0
2
0
0
2
0
2
1
0
0
0
0
1
2
0
0
0
1
0
0
1
1
1
0
2
0
2
0
2
2
2
0
0
0
0
0
1
1
0
1
0
2
1
0
2
0
0
2
0
1
3
1
2
0
0
2
1
0
2
1
1
0
0
2
1
0
0
0
0
0
0
2
0
2
2
2
0
0
1
0
1
2
0
0
2
2
0
0
2
1
0
0
1
0
0
0
2
0
2
0
0
1
2
0
0
0
0
2
1
0
0
0
1
1
1
1
0
0
2
2
2
1
1
0
0
1
0
1
0
0
0
0
2
2
0
0
2
0
0
0
1
2
1
1
1
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
2
2
3
2
2
0
1
0
0
2
2
0
0
0
0
0
2
0
0
1
1
1
1
1
0
0
2
0
1
0
0
2
0
1
2
0
2
2
2
2
0
2
0
0
1
0
0
0
2
0
2
1
1
0
0
0
1
1
0
0
1
1
1
0
0
1
0
0
2
2
0
2
2
1
2
0
0
0
0
1
1
1
1
0
0
2
0
2
1
0
2
1
0
0
0
1
2
0
1
0
2
2
0
0
2
1
0
1
0
0
2
2
0
0
1
2
1
2
0
1
1
1
0
0
2
2
1
0
1
0
0
1
0
0
0
1
1
0
0
2
1
2
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
11
0
0
0
0
0
2
0
0
1
1
2
0
2
0
0
1
1
2
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
2
0
2
0
1
1
0
2
0
0
0
0
1
1
0
0
1
1
1
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
2
1
0
1
0
0
0
0
1
0
2
0
1
2
0
0
1
1
2
0
2
0
0
1
0
1
0
0
0
1
2
0
0
1
2
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
1
1
0
0
1
1
0
0
0
1
0
0
0
3
2
0
0
3
0
2
0
0
3
0
0
0
2
0
0
0
2
1
1
0
2
0
2
0
3
0
0
0
1
0
0
2
0
0
1
0
0
0
1
1
1
2
0
0
0
1
1
0
1
2
1
1
0
0
0
2
0
0
0
2
2
0
1
0
0
0
0
1
1
0
0
2
0
1
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
1
0
2
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
1
0
0
0
1
0
2
3
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
1
0
2
0
0
1
0
1
0
1
0
0
1
0
0
0
2
1
0
1
0
0
0
2
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
2
1
0
1
1
2
0
0
0
2
1
0
1
2
0
0
0
1
0
0
0
0
0
1
2
2
1
1
0
2
1
0
0
0
0
0
0
1
0
0
1
0
2
2
1
0
1
1
0
0
2
1
2
0
2
0
0
4
0
0
1
1
0
2
0
2
1
0
1
0
1
0
0
0
1
1
0
0
0
1
2
2
0
0
2
1
0
1
0
1
1
1
0
0
0
1
1
2
0
0
1
0
2
0
0
0
1
0
0
1
0
2
0
1
0
1
1
0
0
2
0
0
0
1
2
0
0
0
0
0
2
0
0
0
1
1
0
1
2
0
0
1
2
2
0
1
0
1
1
2
0
0
1
1
0
2
0
0
0
2
2
1
0
0
1
1
1
0
0
0
0
1
0
1
0
2
0
1
0
2
8
0
1
1
0
0
1
0
3
1
0
0
0
0
0
0
0
0
1
0
1
0
2
0
3
0
1
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
1
1
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
1
1
0
0
1
1
0
1
0
0
1
0
0
0
1
0
0
1
1
0
1
3
0
0
0
0
2
0
3
1
2
0
2
0
2
2
2
1
0
0
1
1
1
0
0
0
0
2
0
2
0
1
0
0
0
1
1
2
0
0
2
2
0
0
0
1
2
0
0
0
1
0
2
2
0
1
0
1
0
2
0
0
0
0
2
2
0
1
0
0
0
2
1
0
0
2
2
0
0
0
0
0
0
0
1
0
2
2
1
1
0
1
2
1
0
0
0
2
1
0
0
0
0
1
0
2
0
3
0
1
1
2
1
1
0
1
0
0
1
2
2
1
0
1
2
0
4
0
2
0
1
0
0
1
0
2
0
0
2
0
0
1
2
0
2
2
0
2
1
0
1
0
0
0
1
2
1
0
0
1
0
0
2
2
2
0
2
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
3
1
0
0
2
0
0
1
1
0
0
1
0
2
1
2
1
0
0
0
0
2
1
0
2
2
0
0
0
2
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
2
1
0
3
1
2
2
0
3
2
0
0
0
0
1
2
0
1
2
0
0
1
0
1
0
2
0
0
2
1
0
0
1
0
0
1
1
2
0
0
0
0
0
0
1
0
1
1
0
0
2
1
1
0
2
2
0
2
0
2
0
1
1
0
2
0
0
0
0
1
3
0
0
0
1
1
0
0
2
1
0
0
0
1
0
0
0
2
2
2
0
2
0
1
0
1
2
0
0
0
0
0
1
0
0
2
2
0
1
2
1
2
2
1
0
2
0
2
2
0
0
0
1
1
0
1
1
1
1
1
0
0
0
0
1
0
0
2
4
0
0
0
2
0
0
0
0
0
1
0
0
0
3
1
2
1
1
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
1
2
2
0
0
0
0
0
1
0
0
1
0
2
2
2
1
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
1
1
0
1
0
0
2
1
0
0
2
0
0
0
0
0
1
2
2
1
0
1
0
1
0
0
0
0
2
0
2
1
0
0
0
0
0
0
2
0
1
0
0
0
0
1
2
0
1
3
0
0
0
1
1
0
1
0
2
1
1
0
0
0
2
0
0
0
2
2
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
2
1
12
0
1
0
1
0
0
0
0
0
0
1
2
0
2
0
3
0
2
0
0
0
0
2
1
2
1
0
1
0
0
0
3
0
0
1
0
2
0
0
0
0
2
0
1
0
0
0
2
2
1
0
0
1
0
2
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
2
2
0
0
1
0
2
0
1
2
1
2
1
0
0
1
0
0
0
0
2
1
1
0
0
0
1
0
0
0
1
0
0
1
1
1
3
1
0
0
1
1
1
2
0
1
0
2
2
0
0
1
0
0
1
0
0
0
2
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
1
1
1
3
1
0
2
2
1
0
2
0
2
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
3
2
2
0
0
2
0
0
0
0
2
1
1
2
0
1
1
2
0
1
1
2
0
2
0
0
0
0
0
0
0
0
2
1
1
2
0
0
0
0
0
0
1
0
2
0
2
1
0
1
1
1
0
2
0
1
2
1
0
0
0
0
0
1
1
1
0
0
1
1
0
0
0
2
1
0
2
0
0
0
0
0
2
2
0
0
0
0
1
1
0
0
2
2
0
1
0
0
0
0
0
1
0
2
1
0
1
2
0
1
0
2
0
2
2
1
0
1
1
1
0
2
0
1
0
1
0
0
2
1
0
0
2
0
0
1
0
0
1
1
2
0
0
0
0
1
0
0
0
4
1
0
0
0
0
0
0
0
2
1
2
0
0
0
1
1
0
1
2
1
1
3
0
0
0
2
1
0
0
1
0
0
0
3
0
1
0
1
0
0
0
0
1
0
0
2
0
1
0
0
1
1
0
0
0
0
1
2
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
2
0
1
0
0
1
0
2
2
0
2
0
1
0
2
0
0
1
1
0
0
0
2
2
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
2
0
0
3
2
0
1
2
2
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
1
0
2
0
2
0
0
0
0
0
0
2
2
1
2
0
1
1
2
1
1
0
1
1
0
1
1
2
1
2
2
2
0
2
0
1
1
0
0
2
2
1
0
1
1
0
0
2
0
2
1
2
0
2
0
0
0
0
2
0
0
0
0
1
2
0
1
0
0
2
0
1
0
0
1
0
1
1
0
0
0
0
1
0
0
2
0
0
2
0
1
0
2
1
0
1
1
0
0
0
2
2
0
0
1
2
0
1
2
1
1
0
2
0
0
0
0
0
1
2
1
1
0
2
1
2
0
0
2
2
0
0
1
2
0
1
0
2
1
2
2
0
0
0
1
1
0
0
0
1
0
1
0
1
3
0
1
2
0
0
0
0
0
1
0
0
2
1
2
2
2
0
0
2
0
1
0
0
1
0
0
2
0
1
2
0
2
0
0
1
0
0
0
0
1
0
0
1
2
1
0
0
0
2
2
0
1
1
0
0
2
2
0
0
0
0
2
0
1
2
2
0
0
1
0
0
1
0
1
2
0
1
0
0
0
2
0
2
2
0
0
0
0
0
1
1
0
1
0
0
2
1
2
2
1
0
0
0
0
0
2
0
2
0
0
0
1
0
2
0
1
3
0
2
1
2
0
1
2
0
1
0
0
0
2
0
0
2
0
0
0
2
1
0
0
2
0
1
0
0
1
0
1
1
0
0
1
1
2
1
0
1
1
2
0
0
0
2
0
1
0
2
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
2
1
0
0
0
1
2
1
1
1
2
0
2
0
0
0
1
2
0
0
0
0
2
0
0
1
1
1
0
0
0
2
1
0
0
1
0
1
2
2
0
1
2
0
2
2
0
0
1
1
0
3
2
1
1
0
0
0
0
0
1
0
2
1
0
1
0
0
0
0
2
0
0
0
0
1
1
0
0
2
1
0
1
1
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
2
0
0
2
2
0
1
0
0
0
0
1
2
0
0
0
0
0
2
3
0
1
0
0
0
0
1
1
2
2
0
1
1
0
0
0
0
0
1
0
0
1
2
0
3
1
0
0
0
2
0
2
1
1
1
2
0
1
2
0
2
0
0
1
0
0
2
2
3
0
1
1
2
1
0
2
1
0
0
0
7
2
0
2
1
2
0
0
2
0
1
2
0
0
2
1
0
0
0
2
1
1
2
0
1
0
0
0
2
0
2
0
0
2
0
0
1
0
0
1
2
1
1
0
0
1
1
0
0
1
1
0
0
2
0
1
0
1
0
2
1
5
1
0
1
1
0
2
0
0
0
1
0
1
2
0
0
0
0
0
2
0
2
1
0
0
1
1
0
0
0
2
1
0
0
0
0
0
2
0
2
2
1
2
0
0
2
3
0
1
1
3
0
0
0
0
1
0
0
0
0
0
1
2
2
0
1
1
0
0
1
0
2
0
1
2
1
0
0
1
0
0
1
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
1
1
0
2
0
5
0
2
2
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
1
1
2
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
1
1
2
3
0
0
0
2
0
2
1
0
0
1
2
0
0
0
1
0
2
1
2
0
2
0
1
2
0
1
0
2
0
0
0
2
2
2
1
2
0
1
1
2
1
0
0
0
2
0
2
2
0
0
0
1
2
0
0
0
0
0
2
0
0
0
1
1
0
0
1
0
3
2
0
0
2
0
0
2
0
0
2
0
0
0
2
0
0
3
0
1
1
1
0
2
2
0
0
0
0
2
0
1
0
1
0
0
3
0
3
2
1
0
0
0
0
0
0
0
2
1
0
1
2
0
0
0
0
0
2
1
1
0
0
1
2
0
2
2
0
0
2
0
0
2
1
1
2
1
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
1
2
2
0
0
2
1
2
0
3
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
1
0
2
0
0
0
2
2
0
1
0
0
1
0
0
1
0
0
0
0
1
1
1
1
0
0
1
2
0
0
0
2
0
0
2
1
0
0
0
0
0
0
2
1
0
0
0
1
2
0
1
1
0
2
1
0
0
0
1
0
1
1
2
0
0
0
2
0
0
0
2
0
0
1
1
0
0
2
0
0
2
0
1
1
1
0
0
2
0
2
2
1
0
0
0
2
1
0
0
2
0
0
2
0
1
0
1
2
0
0
0
3
1
0
0
0
0
1
2
1
1
1
1
0
1
1
0
0
0
0
0
0
2
2
2
1
1
0
0
0
0
0
0
3
0
1
1
1
0
0
1
1
0
0
0
1
2
3
0
0
0
0
0
0
1
1
0
0
2
2
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
2
0
0
0
0
1
1
0
0
0
0
0
0
0
1
2
0
0
0
2
1
2
2
0
1
1
1
0
0
0
0
0
0
0
2
0
1
2
0
1
0
0
1
0
0
2
1
2
1
2
0
0
2
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
2
1
1
0
1
2
0
0
0
0
0
0
1
0
0
2
0
1
1
0
0
2
0
1
2
2
2
0
0
1
0
0
0
0
0
1
0
1
2
0
0
1
2
1
3
1
0
0
0
2
0
1
1
0
3
0
0
0
0
0
0
3
0
0
0
0
1
0
1
0
0
0
2
0
1
2
1
0
1
0
1
0
0
0
0
1
0
2
1
1
2
2
1
0
1
1
1
1
1
0
0
0
1
0
0
1
0
0
0
0
0
2
0
1
2
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
2
0
2
1
2
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
1
0
0
1
0
2
0
0
0
0
0
0
0
1
3
0
1
0
0
1
1
2
1
0
0
0
2
0
2
0
0
1
0
4
0
0
1
0
0
0
2
2
1
0
0
0
0
2
0
2
1
0
0
0
0
0
1
0
2
2
0
0
3
0
2
5
2
2
1
0
0
2
0
2
3
1
0
0
2
0
0
0
1
0
1
0
0
0
2
3
0
1
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
3
0
2
2
0
0
0
2
0
1
0
0
1
2
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
1
1
0
0
1
3
1
0
3
0
2
2
1
0
0
0
2
0
0
1
0
0
0
0
0
3
2
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
2
2
2
0
0
0
0
2
0
1
0
0
0
1
0
0
0
2
0
1
1
0
0
0
1
0
0
0
0
4
1
0
0
0
0
0
0
0
2
1
0
4
0
0
1
0
2
1
1
0
0
2
0
0
1
1
2
2
0
1
0
0
2
0
1
1
0
1
0
1
1
2
0
2
1
0
1
1
3
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
3
3
2
2
1
0
0
0
2
1
2
0
0
2
2
0
1
0
0
0
2
0
0
2
0
2
0
0
0
0
1
0
0
1
2
0
3
0
0
1
0
1
2
3
0
1
0
0
1
0
0
4
1
1
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
2
1
0
0
1
1
3
1
0
0
0
0
0
0
1
2
0
0
1
2
0
0
3
0
5
1
0
0
0
0
0
0
1
1
1
2
2
1
0
1
0
2
1
0
0
0
0
0
0
0
1
0
0
0
2
0
2
1
0
0
0
1
0
1
0
2
0
0
1
0
0
1
0
0
4
2
1
1
0
0
0
0
0
0
0
0
0
2
3
0
0
1
1
0
0
0
0
0
1
0
2
2
2
0
2
0
0
0
1
0
2
0
1
0
2
0
0
2
0
1
2
0
0
0
0
0
0
1
0
0
1
1
0
2
0
0
0
0
0
2
0
0
0
0
2
2
1
0
1
1
0
0
0
2
2
0
0
0
0
0
1
0
0
1
0
0
1
1
0
2
0
0
2
0
0
0
0
2
0
0
0
1
1
0
1
0
1
2
0
2
1
1
0
0
2
3
2
0
2
2
0
0
0
0
1
0
1
0
1
2
0
0
1
0
0
0
2
1
0
0
0
2
1
0
1
2
0
0
0
0
0
4
2
0
0
0
0
0
0
2
0
1
0
0
1
0
1
0
0
0
0
0
0
2
1
0
2
0
1
0
1
0
2
0
0
1
1
0
0
1
2
0
1
1
1
0
0
0
1
2
1
1
1
0
2
0
0
2
2
0
1
0
0
1
3
1
2
2
0
2
2
0
1
0
2
0
0
0
2
0
0
0
0
1
0
0
0
2
0
2
1
0
0
0
0
2
0
0
0
3
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
1
0
2
1
0
1
2
0
1
3
0
0
0
0
0
1
1
0
2
2
0
0
2
0
0
1
2
1
2
0
0
0
3
0
1
1
0
1
2
0
1
0
0
0
0
1
0
3
0
0
1
0
0
0
0
1
1
0
0
2
0
0
0
2
0
1
0
3
1
2
1
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
1
2
2
0
2
1
1
0
0
2
0
3
0
2
0
2
0
0
2
1
2
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
1
1
2
2
1
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
1
0
1
0
0
2
0
0
0
0
3
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
2
0
0
2
1
0
0
2
0
1
0
1
2
0
0
0
1
2
2
0
0
2
1
0
1
0
1
2
0
3
0
1
1
0
0
2
1
0
0
0
0
1
1
0
0
0
0
0
1
1
1
1
1
0
0
2
1
0
0
1
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
2
2
0
0
2
2
0
0
1
0
2
0
1
0
0
0
0
1
3
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
2
0
2
0
1
1
0
0
0
0
2
0
0
0
0
5
2
2
0
1
0
0
2
2
1
0
0
0
0
0
1
1
1
1
0
0
0
2
0
1
0
4
0
1
0
1
0
2
1
0
2
2
1
2
0
0
0
0
2
4
0
0
0
1
5
0
1
4
2
0
0
0
0
3
0
0
1
0
1
0
0
1
1
0
0
0
1
2
2
0
0
0
0
2
1
1
2
1
0
0
2
0
0
0
1
0
0
2
2
1
2
0
1
0
1
2
0
0
1
0
0
0
0
0
0
1
0
0
2
1
0
0
1
1
0
0
0
1
0
1
0
1
0
1
0
1
0
2
2
0
0
0
0
1
0
0
0
2
2
2
1
0
0
1
0
0
0
0
1
0
0
2
0
1
2
1
2
0
2
5
0
0
2
0
1
1
1
0
2
0
2
0
0
0
2
0
0
2
0
1
2
0
0
0
2
2
1
2
0
0
0
0
0
0
0
1
2
4
0
2
1
0
1
0
1
0
1
1
0
0
0
1
1
0
1
0
1
2
2
2
0
1
2
2
1
0
1
1
0
1
1
0
2
0
2
2
0
0
0
0
0
2
1
2
0
0
1
0
0
1
2
0
0
0
1
0
1
1
1
1
0
0
0
0
0
0
1
2
2
0
0
1
1
0
1
0
1
1
0
0
2
2
0
0
1
0
2
2
1
1
2
1
0
1
0
2
0
1
2
1
0
0
2
1
2
0
2
0
1
3
0
2
1
0
1
0
2
0
1
1
2
0
0
1
1
1
0
0
2
2
1
0
1
0
2
1
1
0
0
1
0
0
0
0
0
1
0
1
0
0
2
0
0
1
0
1
2
0
1
1
0
1
0
0
0
0
1
0
0
1
0
1
1
0
2
1
0
1
1
0
0
0
0
1
1
0
0
0
0
2
2
2
3
1
0
0
0
0
2
2
1
0
0
0
1
0
1
0
0
0
0
2
3
0
0
0
0
3
0
0
2
3
2
1
0
2
1
0
1
0
1
3
2
0
2
2
0
0
1
0
2
0
0
1
1
2
0
0
0
0
0
0
2
0
1
0
1
0
1
2
0
2
2
2
0
2
1
1
1
0
2
0
0
1
1
0
2
0
0
0
0
0
2
2
2
0
3
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
1
1
0
0
2
0
0
0
0
0
1
0
0
2
0
2
0
0
0
1
0
2
0
0
0
0
0
0
2
2
0
2
1
6
1
1
1
1
1
1
1
1
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
2
2
1
2
1
1
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
2
0
4
0
0
1
2
1
0
1
0
1
0
0
2
0
0
2
0
1
0
0
0
0
0
2
1
2
0
0
1
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
1
0
2
2
2
1
0
2
0
2
2
0
1
0
0
1
2
0
1
0
0
1
0
2
2
0
0
1
0
0
1
0
0
1
0
0
0
2
0
2
0
2
0
0
1
0
2
0
1
0
0
0
2
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
2
0
1
2
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
3
0
0
2
2
1
0
2
1
1
1
2
1
3
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
2
2
1
2
0
0
1
0
1
2
0
0
3
2
1
0
2
0
2
0
2
1
0
0
0
2
0
0
1
3
2
3
1
1
0
0
0
0
2
0
5
1
1
0
0
0
1
0
0
1
0
1
0
0
2
1
0
1
0
1
0
0
1
0
0
0
0
2
0
0
2
0
0
0
1
0
0
1
0
0
2
1
0
0
2
0
4
1
0
1
0
0
1
0
0
2
1
0
2
0
0
1
0
2
2
0
0
1
1
2
2
0
0
1
1
2
0
2
0
1
2
0
0
0
0
0
1
0
0
0
1
1
0
1
4
0
0
1
0
0
0
2
0
1
0
2
1
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
1
0
2
0
0
2
1
1
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
2
1
1
0
0
1
0
1
1
0
0
0
1
1
0
0
0
1
0
0
0
2
1
0
0
0
0
1
0
0
1
1
1
0
6
1
0
2
2
2
2
0
2
2
0
0
0
4
1
3
0
2
0
0
1
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
1
2
1
0
0
0
0
0
0
1
1
1
0
0
0
2
2
1
0
0
2
0
2
1
1
0
0
0
3
0
0
0
1
1
1
0
0
2
1
0
0
1
0
3
1
0
0
0
2
2
2
1
1
0
1
0
2
0
1
2
0
2
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
1
1
0
2
0
0
1
1
1
1
0
1
0
0
0
8
0
0
2
2
0
1
2
2
3
1
0
3
0
0
0
0
2
0
3
0
2
1
2
0
2
2
2
1
2
1
2
0
0
4
1
1
0
0
2
0
0
0
0
0
1
1
0
1
1
2
1
0
0
0
1
1
1
1
0
0
0
0
2
0
2
0
0
1
0
2
0
0
2
1
3
0
1
2
0
0
2
1
0
0
1
0
0
0
1
2
0
1
0
0
2
0
0
0
0
4
0
1
1
0
0
0
1
0
2
0
1
2
2
0
1
1
0
1
1
1
2
2
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
2
1
0
1
0
0
0
0
1
2
1
0
1
0
1
0
0
1
0
0
2
0
2
1
1
0
1
0
0
0
0
0
0
1
0
1
2
1
0
0
1
0
2
2
2
0
0
0
0
1
0
0
1
0
2
2
0
1
0
1
0
0
0
1
0
1
2
1
0
1
0
1
3
0
1
0
1
0
0
0
0
0
2
0
2
1
0
0
0
2
1
0
0
0
0
1
0
1
0
0
1
1
2
1
1
2
0
2
0
1
2
2
1
1
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
2
2
1
0
2
0
0
0
1
0
1
1
2
2
0
0
0
0
0
1
3
0
0
0
1
0
2
0
1
1
0
0
0
0
0
2
2
3
2
0
0
2
0
0
0
0
0
0
0
2
0
0
1
1
1
0
0
0
0
2
1
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
1
0
2
0
2
2
0
0
1
0
0
2
1
1
0
1
0
0
0
0
0
0
2
0
1
1
0
0
0
0
2
0
0
1
0
0
0
2
0
1
0
0
2
1
0
0
1
1
0
1
0
0
2
2
0
0
1
3
0
0
0
0
1
2
2
0
2
1
0
0
1
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
1
2
2
1
0
0
0
0
1
0
0
2
0
1
0
0
2
0
0
0
0
3
0
0
2
1
0
0
0
0
3
0
0
3
0
0
1
2
0
0
1
0
0
2
0
1
2
0
0
0
2
0
0
0
0
1
2
1
1
7
0
1
0
0
0
1
2
0
0
2
0
0
2
0
0
0
1
2
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
2
1
0
0
0
3
1
2
0
0
0
0
0
1
2
1
0
0
0
1
0
0
0
0
1
1
1
0
1
2
1
0
0
1
6
0
0
0
1
0
0
1
2
0
0
2
0
2
0
0
0
0
0
0
1
1
0
0
2
2
0
0
0
3
0
0
0
2
0
1
0
1
1
0
0
1
0
1
0
0
0
0
0
1
0
0
2
0
1
0
0
1
0
0
0
1
0
0
0
1
2
0
1
0
1
0
0
0
0
0
2
0
0
0
1
0
3
0
1
0
1
2
0
0
2
0
0
1
0
0
2
0
0
2
1
1
0
1
2
1
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
2
2
1
0
0
3
0
0
0
0
0
0
0
2
2
0
1
3
0
0
1
0
1
0
2
2
0
0
0
1
2
0
1
1
0
1
0
0
0
0
1
1
0
2
0
0
0
2
1
1
0
0
1
0
0
0
0
2
2
1
2
2
0
0
0
0
0
0
0
0
2
0
0
1
0
2
2
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
4
0
0
0
0
1
2
0
1
0
0
1
0
1
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
1
0
2
0
0
1
1
0
2
0
0
0
0
2
1
2
1
0
0
0
1
1
2
3
1
0
0
1
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
3
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
1
1
0
0
2
2
1
2
0
1
1
1
0
0
1
2
0
0
2
0
0
0
0
1
1
0
0
0
1
2
0
1
1
0
2
0
0
1
0
0
2
2
0
1
0
0
0
0
0
0
1
0
0
0
7
0
2
0
1
1
2
2
0
2
2
1
1
2
0
2
0
2
1
0
2
1
1
1
0
2
1
0
1
0
0
1
0
0
0
2
2
0
0
4
0
1
0
0
0
2
0
1
1
1
0
0
0
2
0
0
0
0
0
3
0
0
2
0
1
0
1
0
2
2
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
2
0
2
0
1
0
1
0
1
1
0
1
0
0
0
2
1
0
1
1
0
1
4
0
1
1
1
0
0
0
2
0
0
0
1
2
0
0
0
2
0
2
0
1
2
0
0
1
0
3
0
1
2
2
1
3
1
0
2
0
1
0
1
1
0
1
0
1
0
0
5
0
0
0
0
0
1
2
2
2
0
0
1
0
0
2
1
1
0
2
3
0
1
1
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
1
1
0
0
0
0
0
2
0
0
2
1
0
0
1
0
2
0
1
3
1
2
1
0
0
1
2
1
1
2
1
1
0
0
2
0
1
0
0
0
0
2
0
0
2
1
2
1
0
2
0
1
1
0
0
2
0
1
1
2
0
1
0
0
0
0
2
0
2
1
0
0
1
0
1
1
1
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
6
1
3
0
0
1
2
0
0
2
0
3
0
1
0
0
1
0
2
0
0
3
0
0
2
0
2
1
0
2
2
0
0
0
0
2
2
2
1
0
1
2
0
0
0
0
2
0
2
0
0
0
0
0
2
0
1
3
1
1
1
2
0
1
0
1
0
0
2
1
0
0
0
3
0
0
1
2
0
1
0
0
2
0
2
1
3
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
1
0
2
3
2
1
0
1
0
0
0
0
2
2
0
0
0
6
0
0
1
2
1
0
0
0
0
0
1
0
2
0
0
1
0
0
0
1
0
0
0
0
2
0
0
1
0
0
1
0
0
1
1
1
1
0
2
0
3
0
2
0
1
2
0
1
0
2
0
0
1
2
1
1
2
2
0
0
0
2
0
0
1
0
2
2
2
0
0
2
0
0
0
1
0
0
2
1
2
0
1
1
2
1
0
0
0
0
0
0
0
1
2
0
2
0
0
2
1
2
0
1
0
1
1
0
0
2
0
0
0
1
0
2
2
0
1
0
0
1
2
0
0
0
2
0
0
0
0
0
0
2
0
2
1
0
2
1
0
0
1
1
1
1
0
2
0
1
0
2
0
1
2
0
0
2
2
0
2
0
0
2
0
0
2
0
0
2
2
0
0
1
2
0
0
0
0
1
2
1
1
0
0
1
2
0
1
0
1
0
0
1
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
1
0
1
0
2
0
0
0
0
1
0
0
1
1
0
0
2
2
0
3
0
1
0
2
1
0
2
1
0
1
2
0
1
1
0
0
0
0
2
1
0
0
2
0
2
0
0
2
1
0
1
0
2
0
1
1
2
2
1
0
1
0
1
1
1
0
0
0
0
2
0
0
0
0
2
0
1
1
0
0
0
1
0
0
0
0
2
1
1
0
2
1
2
1
0
2
0
0
0
0
0
0
1
0
2
0
0
2
0
2
1
0
0
2
0
1
1
3
0
1
1
0
0
0
0
0
0
2
0
0
0
1
0
1
2
0
1
1
1
0
1
1
1
0
0
1
0
2
2
1
0
0
0
1
0
0
2
0
2
0
2
0
1
0
0
1
1
1
2
1
2
0
1
0
0
0
0
1
0
0
0
2
1
0
0
0
0
1
2
2
0
2
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
2
2
0
1
0
0
4
0
0
2
2
0
0
2
0
2
0
0
1
0
1
1
0
0
0
0
0
2
0
0
0
0
2
1
1
0
0
0
0
0
0
1
0
0
0
1
0
2
2
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
1
1
0
0
0
0
0
9
0
0
2
2
0
0
0
0
1
0
1
3
0
0
0
0
3
2
2
0
0
0
0
2
0
2
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
1
2
1
0
0
0
1
0
2
0
1
0
2
2
0
0
1
0
1
0
1
0
1
1
0
1
0
1
0
1
2
1
0
0
0
2
0
0
0
1
0
1
0
1
2
2
0
0
1
1
0
0
0
0
2
0
2
1
1
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
2
0
0
1
0
2
0
1
1
1
0
0
0
3
0
0
0
0
2
1
0
0
0
0
1
0
1
0
0
1
0
0
1
1
0
1
2
0
0
0
0
0
2
1
1
0
0
1
0
1
0
0
2
0
0
0
0
1
0
0
1
2
0
1
2
2
2
0
1
0
0
0
0
2
1
0
0
2
3
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
2
0
0
2
1
0
2
0
3
2
0
0
0
2
0
0
0
2
2
1
0
1
4
0
2
1
1
2
2
1
2
1
2
0
0
1
2
0
1
0
1
0
0
2
0
0
0
1
0
1
0
1
1
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
1
0
3
0
2
1
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
1
1
1
0
1
0
1
1
2
1
1
1
0
2
4
1
0
0
2
2
0
0
0
0
0
2
0
2
2
0
0
1
0
2
0
0
0
2
2
0
0
2
2
1
3
2
2
1
2
1
0
0
1
0
1
1
1
1
0
1
2
1
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
2
0
1
2
0
0
2
2
0
2
0
1
2
2
1
1
2
1
1
3
1
2
0
2
0
2
1
2
1
0
0
0
2
2
1
0
1
0
0
2
3
0
2
1
0
0
1
2
0
0
2
2
0
1
1
0
0
3
2
2
1
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
1
0
1
6
1
0
1
0
0
0
0
0
1
0
0
0
0
0
2
1
1
0
0
1
0
2
0
2
0
1
2
0
1
0
0
0
1
0
0
0
0
1
0
1
0
1
0
1
0
1
1
0
0
2
2
0
1
0
0
0
0
2
0
0
2
0
0
2
1
3
1
0
0
0
0
2
0
0
0
0
2
1
0
0
2
1
1
0
0
0
0
1
0
0
0
2
0
2
0
0
2
3
2
0
2
1
0
0
0
0
2
0
3
2
0
0
0
1
0
0
3
0
1
1
0
1
0
0
1
3
0
0
1
0
2
0
0
2
0
0
0
1
2
0
0
0
2
1
2
0
2
3
0
0
2
0
2
0
1
0
0
0
0
2
2
0
1
0
1
0
0
2
0
2
0
0
0
0
0
1
1
0
0
0
0
1
0
0
2
1
0
0
1
1
0
0
0
0
0
0
0
1
1
2
1
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
1
0
2
0
0
0
0
0
1
1
0
1
0
2
1
0
2
0
2
1
2
0
1
0
0
2
2
0
1
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
1
2
0
2
0
2
2
1
0
0
0
0
0
1
0
1
1
1
0
1
0
2
0
2
1
0
2
1
2
0
0
0
2
1
0
1
0
0
1
1
2
0
2
2
2
0
0
0
1
0
0
1
0
0
0
1
0
1
2
1
0
1
2
0
2
0
2
1
1
0
0
0
0
0
1
0
1
2
0
1
2
2
1
0
0
0
0
0
0
0
4
1
0
1
1
1
0
1
0
1
0
0
2
1
0
0
0
5
0
0
0
1
1
1
0
3
0
5
2
0
0
2
0
0
0
1
1
2
0
0
0
0
0
0
0
1
0
0
1
2
0
0
1
1
0
0
1
1
0
2
2
0
2
2
2
1
1
0
0
0
0
2
2
2
1
0
2
2
1
2
0
2
0
0
1
0
1
1
1
0
2
0
1
0
1
2
0
0
0
0
0
0
0
2
2
1
0
0
2
0
0
1
0
0
1
0
0
0
3
2
1
1
0
0
0
0
5
0
0
0
1
1
0
2
0
0
2
2
2
0
2
0
1
3
1
0
1
1
0
2
0
0
0
1
1
2
0
0
0
1
1
2
0
2
0
0
1
0
1
3
0
2
0
0
0
2
0
0
2
0
2
0
2
0
0
2
0
1
0
0
0
0
0
1
0
2
2
0
0
0
0
2
0
2
2
0
2
0
2
0
0
0
0
0
0
1
0
0
1
1
0
2
0
2
0
3
7
0
0
2
0
0
1
1
2
1
2
0
2
0
1
0
0
1
4
0
1
2
0
2
1
1
2
0
0
3
0
0
2
2
0
1
2
0
2
1
0
2
0
1
0
0
0
0
0
1
1
1
0
3
1
2
0
1
1
1
2
0
0
0
0
0
2
0
1
0
2
0
1
1
0
0
2
1
0
0
2
1
0
2
0
0
1
0
1
2
2
5
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
2
1
0
0
2
2
0
0
0
2
0
2
0
0
1
1
1
2
1
1
0
1
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
4
1
1
0
0
1
0
0
2
2
0
0
1
0
0
1
0
0
0
2
1
1
1
1
2
0
1
2
0
0
0
1
0
2
2
2
0
0
0
2
0
1
0
1
0
2
0
0
0
1
1
2
2
0
0
0
1
0
1
1
2
0
0
1
1
1
2
2
1
0
1
0
1
1
1
0
1
2
1
0
0
1
0
1
0
1
1
0
0
0
1
0
2
0
0
5
0
0
3
1
1
3
0
2
1
0
0
0
0
1
0
2
1
1
1
0
1
0
0
0
0
1
0
0
1
2
2
1
0
2
0
0
1
0
1
0
0
2
1
0
0
0
0
0
0
0
3
0
0
2
0
0
1
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
3
1
0
1
0
1
1
0
1
0
3
0
5
0
0
1
0
2
0
2
0
0
1
0
1
0
1
1
0
1
1
0
2
0
2
0
0
0
0
2
0
0
0
2
1
0
0
1
1
2
0
1
0
0
0
0
1
1
0
2
1
2
0
0
1
2
0
2
0
1
0
0
2
0
0
0
0
0
1
1
0
2
1
1
1
0
2
0
1
2
0
0
0
1
1
0
0
2
1
0
1
2
0
0
2
0
2
1
0
0
0
1
0
1
0
0
2
0
2
0
0
1
1
0
0
0
0
0
0
0
2
0
0
1
2
2
0
1
1
2
0
0
0
1
0
0
0
1
1
1
2
2
1
0
0
1
3
2
0
2
0
1
0
1
1
1
0
2
1
0
0
0
1
0
0
0
1
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
2
1
1
0
0
1
1
0
1
2
0
2
0
2
1
0
0
0
0
2
1
3
0
2
1
0
0
0
2
2
1
0
0
1
1
1
1
2
0
1
2
0
2
0
0
0
1
0
0
0
0
1
1
2
3
1
0
1
0
1
1
0
0
0
0
0
2
0
0
1
0
2
2
1
1
0
0
1
0
1
1
2
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
1
0
1
1
2
1
0
0
2
2
1
0
2
0
0
0
1
1
0
1
0
0
0
0
0
0
1
1
0
1
0
0
2
2
0
0
2
0
0
0
0
1
2
0
1
0
2
4
0
1
0
1
1
2
0
2
1
0
2
0
1
0
0
1
0
0
1
0
2
2
2
2
1
0
2
1
0
0
0
0
0
1
0
0
0
0
1
1
0
2
2
2
2
0
1
0
5
1
0
0
2
1
0
0
0
1
2
0
3
0
1
1
2
0
2
2
0
0
1
0
0
0
1
0
0
1
1
1
0
1
0
0
1
2
0
2
2
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
2
0
1
3
0
2
1
1
0
0
0
1
0
1
1
0
2
0
2
0
1
0
1
0
1
5
2
0
2
2
0
2
2
0
0
0
0
0
1
0
0
0
0
2
2
2
0
1
2
0
0
0
1
0
0
0
0
0
0
0
2
0
1
1
0
0
0
1
0
0
1
1
1
2
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
2
0
0
3
0
1
0
0
2
2
1
1
2
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
1
0
0
0
2
0
0
0
0
2
2
0
2
2
2
0
1
1
1
0
0
1
0
0
0
1
1
2
2
2
0
0
0
2
1
2
1
1
1
0
0
1
0
1
2
0
0
0
1
0
1
0
0
0
0
1
0
1
0
1
0
1
0
0
0
2
1
1
0
2
0
1
0
0
1
1
0
0
1
0
2
1
0
1
0
2
0
1
1
1
2
0
1
0
1
2
0
2
0
2
0
2
2
0
2
0
0
1
2
0
1
0
1
0
1
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
2
0
2
0
0
1
0
1
0
2
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
3
0
1
1
1
0
0
0
1
2
1
2
3
1
0
1
0
0
1
2
0
0
0
2
0
1
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
1
1
2
1
0
0
0
0
0
0
2
3
0
0
1
1
0
0
1
1
0
2
0
0
0
0
1
2
1
1
0
0
0
2
1
0
0
1
0
0
2
0
2
0
0
0
0
2
2
1
0
0
1
0
3
2
2
2
1
1
2
1
0
0
0
0
2
10
1
1
0
2
2
1
2
0
0
0
0
2
2
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
2
1
0
0
0
0
0
0
1
0
1
0
1
0
1
1
0
2
0
1
0
0
1
1
0
0
0
1
0
0
0
2
0
1
1
1
3
1
2
1
0
2
0
0
0
2
1
0
0
0
0
8
1
0
1
0
0
0
0
1
2
0
3
0
1
0
0
1
0
2
1
0
1
0
0
2
2
1
0
0
2
0
0
0
0
0
0
0
2
3
0
2
0
0
2
1
1
1
0
0
1
1
1
0
1
0
0
0
0
1
1
1
0
0
2
0
0
1
0
0
0
0
0
0
1
2
0
0
2
2
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
2
2
2
0
0
2
2
0
0
1
0
0
0
1
0
1
1
2
0
1
1
1
1
1
0
2
2
0
0
0
0
1
2
0
2
2
2
0
1
0
2
0
2
2
0
1
0
0
0
1
2
2
0
1
0
2
1
1
3
0
0
0
1
0
1
1
0
0
0
0
1
1
2
0
2
0
0
1
0
1
1
2
0
0
0
0
0
1
0
1
0
1
1
2
0
7
0
0
2
0
1
0
0
0
1
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
2
1
1
0
0
2
0
0
1
0
2
0
1
1
1
0
0
1
2
0
1
0
0
1
0
0
2
0
0
2
0
0
0
1
0
0
0
1
3
1
1
2
1
1
2
1
1
1
0
2
0
1
0
0
0
2
0
0
2
1
2
0
0
2
2
2
0
0
0
0
2
2
0
0
0
0
1
0
0
1
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
2
2
0
0
0
1
3
0
0
0
1
0
0
0
0
0
4
0
0
0
0
2
0
0
0
1
2
1
0
0
0
0
2
0
2
1
0
0
2
1
2
0
0
1
1
1
1
1
1
2
1
0
1
1
2
0
1
0
0
0
2
2
0
0
0
3
2
0
0
1
0
1
0
2
2
0
0
2
1
2
1
1
3
0
0
2
2
0
0
0
1
0
0
0
0
1
0
1
0
1
2
0
0
2
1
2
0
2
0
0
0
1
2
1
1
0
0
2
1
2
0
2
1
1
2
0
0
0
1
0
2
1
1
0
1
0
0
1
0
3
2
1
4
1
0
0
1
2
2
0
2
2
0
0
0
1
2
3
1
2
0
1
0
0
1
1
0
2
0
3
0
1
2
2
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
2
2
2
0
1
1
0
0
1
1
0
1
1
2
0
1
0
0
1
2
0
0
0
0
1
1
0
2
0
0
1
0
0
0
2
0
0
0
0
0
3
0
1
0
0
0
1
2
0
2
0
1
0
1
6
3
1
0
1
0
1
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
4
1
2
0
1
0
2
0
2
0
0
0
0
0
1
0
0
0
1
1
1
0
1
0
0
0
1
0
1
2
2
0
0
0
0
0
2
1
0
0
2
0
1
1
0
1
0
2
0
1
0
0
0
1
1
0
0
2
0
0
0
2
1
1
0
2
0
0
2
2
1
1
2
0
0
0
1
1
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
1
2
0
1
1
2
0
2
2
0
1
0
0
2
2
0
1
0
1
0
0
0
0
0
2
1
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
1
1
2
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
2
0
2
0
0
1
1
0
1
0
2
1
0
1
0
0
1
2
1
0
3
0
0
1
2
2
1
0
0
0
0
0
1
0
0
1
3
2
0
0
1
0
1
2
1
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
2
0
1
1
1
2
2
1
0
0
3
0
0
1
0
8
1
0
0
0
0
0
1
0
2
2
1
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
2
1
1
2
1
2
2
1
0
0
0
0
0
0
2
0
1
0
0
1
1
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
2
0
0
1
0
0
2
2
1
0
0
2
0
1
0
1
1
0
0
0
0
0
0
3
1
0
0
2
0
3
2
0
0
0
1
0
0
0
0
1
1
1
1
0
0
0
0
1
1
0
3
0
0
0
0
0
0
0
0
0
0
2
1
1
0
1
0
2
0
0
0
0
0
1
2
0
0
2
2
0
1
0
2
2
2
1
0
0
0
0
0
2
1
0
1
0
0
1
0
0
1
2
1
0
0
0
1
0
0
1
0
1
0
0
0
3
0
2
1
1
0
1
0
0
1
2
0
2
0
0
2
2
1
2
0
2
0
1
2
2
1
0
0
2
2
1
1
0
1
2
0
0
0
1
0
2
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
1
0
1
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
2
1
0
2
1
1
1
0
0
0
1
0
0
2
0
0
0
2
2
1
2
1
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
2
0
0
0
0
3
0
0
0
0
1
0
0
2
1
0
0
0
1
0
2
0
0
0
0
0
2
0
1
2
1
0
1
0
0
1
0
0
1
0
2
0
0
1
0
1
0
0
0
1
0
1
0
1
1
0
0
0
0
0
1
2
0
1
0
0
0
0
1
1
2
0
0
2
0
2
0
2
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
2
1
0
1
1
1
0
2
0
1
0
1
0
2
0
0
0
0
1
0
1
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
1
1
2
0
0
0
0
2
0
0
0
2
2
2
0
0
0
1
2
3
0
0
0
1
0
1
0
1
0
0
0
1
0
1
0
0
0
1
1
0
1
1
2
1
1
0
1
0
0
2
0
0
0
1
0
2
1
0
1
0
0
2
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
1
1
0
0
1
1
1
1
0
1
1
0
1
2
1
0
0
2
2
0
1
0
0
0
0
0
0
0
0
1
1
0
2
1
2
1
0
0
0
0
0
2
1
1
3
1
0
2
1
0
1
3
0
0
1
2
1
1
0
2
1
2
1
0
0
2
2
1
0
2
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
1
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
1
2
2
0
3
0
0
0
2
1
0
0
1
0
1
0
2
1
2
2
1
1
0
1
2
0
2
0
0
0
0
0
1
1
0
0
0
2
1
2
2
2
2
2
1
1
1
0
1
3
2
0
0
0
2
0
0
0
0
1
1
0
0
0
0
2
0
2
1
1
3
2
2
0
0
1
1
0
0
0
2
1
0
0
0
0
0
0
3
2
0
0
2
1
2
0
0
2
0
0
1
0
0
1
0
0
0
1
1
2
0
0
2
1
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
2
0
0
0
1
0
2
1
0
0
0
2
2
0
0
0
1
1
0
0
0
0
1
0
0
1
1
0
0
2
2
0
1
2
0
0
1
0
0
1
2
1
1
1
1
0
0
1
0
2
0
0
1
0
0
0
0
2
1
0
1
0
0
1
0
0
8
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
3
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
2
0
1
4
0
1
1
0
0
0
1
0
2
2
0
0
0
1
0
0
0
2
0
0
1
1
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
1
2
1
0
0
0
2
3
0
0
2
0
0
1
2
0
1
0
2
1
0
0
2
1
4
1
2
0
0
2
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
2
1
0
1
2
1
0
2
1
0
2
0
1
1
3
2
0
0
2
0
0
0
0
1
0
1
1
2
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
2
0
2
1
1
0
0
1
0
1
2
0
0
0
1
0
2
0
0
0
0
0
0
1
2
0
1
13
0
0
0
0
1
0
0
1
0
0
0
0
2
2
0
0
2
2
0
1
0
2
2
0
1
0
2
2
3
1
0
0
2
1
0
0
0
0
0
0
1
0
0
0
1
0
2
1
2
0
1
0
0
0
0
0
1
0
1
2
0
0
0
2
0
0
0
1
0
3
0
1
0
0
0
0
1
2
2
0
2
0
0
2
0
2
1
1
1
0
0
0
1
2
1
2
2
0
1
0
0
0
0
0
2
0
2
0
1
0
4
1
0
1
0
2
1
2
2
0
0
0
2
0
0
0
0
1
1
0
1
0
0
2
1
0
0
0
2
0
1
0
1
1
3
1
0
1
0
1
0
2
0
2
0
0
2
1
0
2
0
0
5
2
2
2
0
2
0
0
0
0
0
0
0
0
0
1
1
0
1
2
2
0
1
1
1
1
0
0
0
0
2
0
1
0
0
1
1
0
1
0
2
1
0
2
1
0
0
0
3
0
0
0
2
0
0
1
0
0
0
1
0
1
2
2
2
0
2
1
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
1
0
1
0
0
1
0
1
2
0
0
1
0
0
0
1
0
0
0
1
1
0
1
1
1
0
1
1
0
1
2
2
0
2
0
0
2
0
0
2
1
1
1
0
0
0
2
2
2
1
2
0
0
1
0
0
2
1
1
0
2
1
2
0
2
1
0
2
0
0
0
0
1
0
2
0
2
1
2
1
0
0
1
0
1
1
0
0
1
0
0
0
0
1
2
0
1
2
0
0
2
0
0
0
2
0
1
0
2
0
0
2
0
0
1
0
0
0
1
1
3
1
0
2
0
2
0
0
0
0
1
0
1
0
0
1
1
2
0
4
0
0
0
2
0
0
1
0
1
1
2
0
0
2
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
2
1
1
2
0
1
1
0
0
0
1
1
2
0
2
2
0
1
0
1
0
3
2
1
0
0
1
2
0
1
2
2
0
0
0
0
2
2
0
2
1
0
0
1
0
2
1
1
1
0
0
0
1
0
1
0
0
0
0
0
2
0
1
0
1
0
0
2
0
0
0
2
0
1
0
0
0
0
1
1
0
0
2
4
2
0
0
2
0
0
2
0
0
2
0
2
1
3
0
1
0
0
1
0
1
2
1
0
2
1
1
2
0
0
2
1
1
1
0
0
0
2
1
0
0
0
1
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
1
2
2
0
2
0
1
2
2
1
2
2
0
0
0
0
0
0
2
0
0
0
0
0
2
5
2
2
2
0
1
0
0
1
1
0
0
1
2
0
0
1
1
0
1
1
2
0
2
0
0
0
1
0
0
0
2
0
1
2
0
0
1
2
0
2
0
0
0
0
0
0
0
2
0
1
0
1
1
0
0
0
1
2
1
1
1
0
0
2
0
2
0
0
2
2
0
0
0
0
0
0
0
0
2
1
0
1
1
2
1
2
0
0
0
3
1
0
2
1
0
0
1
0
1
0
0
2
1
0
0
0
0
0
0
0
1
0
4
0
0
0
2
0
0
0
0
1
3
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
2
4
0
0
0
0
1
0
0
1
0
1
0
4
0
1
1
0
1
0
1
0
0
1
0
2
1
1
1
0
0
0
2
0
1
0
2
0
0
1
2
1
1
1
0
2
2
0
0
2
2
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
4
3
2
2
0
0
2
1
0
1
1
0
0
1
0
0
2
0
0
0
1
0
2
0
1
0
2
2
1
0
0
2
2
0
3
0
0
0
0
2
1
0
1
0
2
0
0
2
1
0
1
1
2
1
1
1
1
0
2
1
2
1
0
0
1
0
1
2
0
2
0
0
0
1
1
0
1
0
2
0
1
2
1
0
2
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
2
0
1
0
2
0
2
2
3
0
0
0
0
0
2
1
0
0
0
0
2
0
0
1
1
0
1
1
0
0
0
0
0
2
0
0
1
0
0
1
0
1
0
0
1
0
0
1
0
1
0
0
1
0
2
0
1
0
0
2
2
1
1
0
1
0
0
1
2
0
0
0
0
1
2
1
1
0
0
2
0
1
0
0
0
0
0
2
0
0
0
1
1
2
0
0
1
2
3
7
2
0
1
2
0
0
0
0
3
0
2
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
2
0
1
1
0
0
0
2
2
0
0
1
1
0
0
1
0
2
0
0
0
0
1
0
2
0
1
0
2
0
1
0
0
2
0
0
0
2
0
0
1
1
0
1
0
0
0
2
2
0
0
1
1
0
2
0
0
1
3
0
1
3
0
4
0
2
1
2
1
1
0
0
1
1
2
1
0
0
2
0
2
0
1
1
2
0
0
1
2
0
0
1
0
2
0
1
0
0
7
0
1
2
0
0
1
1
1
0
2
0
1
0
1
2
0
1
1
2
0
1
0
0
0
2
0
2
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
2
1
2
2
1
0
1
0
0
1
2
0
1
2
0
1
0
1
1
2
0
2
2
0
0
0
0
0
1
3
1
1
2
2
2
1
2
0
0
0
2
1
0
1
0
1
0
0
1
0
0
2
0
2
0
2
0
0
1
1
0
1
0
1
2
0
0
0
0
0
2
0
0
2
0
2
1
1
2
2
2
0
0
0
0
0
0
2
0
0
0
0
1
1
0
1
0
0
0
2
2
0
0
1
0
0
1
0
2
1
2
2
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
2
0
1
0
1
2
4
1
2
2
0
2
1
0
1
2
0
0
2
2
0
0
2
0
0
1
0
0
1
2
0
0
2
0
0
0
2
0
1
2
2
0
1
0
1
1
0
0
0
0
1
1
1
2
0
1
0
1
1
0
3
1
0
0
2
1
1
0
0
0
0
1
0
0
0
1
0
2
0
2
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
2
1
1
2
0
1
2
0
0
2
2
2
2
1
0
0
0
1
2
0
1
2
0
0
0
0
0
2
2
0
0
0
1
3
2
0
1
1
1
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
1
1
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
1
0
1
1
1
0
2
0
0
0
0
0
2
0
1
0
2
2
1
0
1
1
0
1
0
0
3
2
2
0
0
2
0
1
1
0
2
0
0
0
1
2
1
1
0
0
0
0
0
0
0
0
1
0
0
1
1
1
1
1
1
2
1
1
1
2
2
2
2
0
0
2
0
2
0
0
0
0
2
0
0
3
1
0
2
0
2
2
0
0
2
2
2
3
0
0
0
0
0
0
2
2
1
1
2
0
1
0
2
0
1
0
2
0
1
0
0
2
0
2
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
1
1
0
0
0
2
1
2
1
1
0
3
0
0
3
2
0
2
0
2
1
2
0
0
0
0
0
1
0
0
1
0
1
2
0
2
1
1
0
0
0
2
2
0
2
0
0
1
2
1
1
0
0
1
0
0
0
0
0
1
2
0
1
0
0
0
0
0
2
0
1
0
0
1
4
0
1
0
1
0
0
2
0
2
0
0
0
0
1
1
2
0
0
0
0
0
1
1
2
0
0
0
1
0
0
0
3
2
0
0
0
0
2
0
0
0
2
0
2
0
0
1
1
0
2
0
0
0
0
1
0
0
0
2
0
2
0
0
2
0
0
0
1
0
1
1
0
0
1
0
2
1
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
2
0
2
2
0
0
0
0
0
0
1
0
1
1
2
2
0
1
0
2
1
1
0
0
2
1
0
2
0
0
0
0
0
2
0
0
0
0
2
1
2
0
1
2
0
2
0
1
1
0
0
0
0
0
0
0
0
2
1
2
0
0
0
2
0
0
2
0
0
2
1
0
0
0
0
0
1
2
0
0
2
0
0
1
3
2
0
0
1
0
0
0
0
1
1
1
0
5
1
0
0
2
0
3
0
0
1
2
0
0
0
1
1
2
0
0
0
0
0
0
2
0
1
0
2
0
2
0
0
1
0
0
0
0
1
2
2
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
1
1
1
1
1
0
3
2
1
1
0
0
0
1
1
0
0
1
2
1
2
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
2
0
1
0
0
0
0
0
1
1
0
2
0
2
2
1
2
0
2
1
0
0
2
0
0
0
2
2
2
0
1
0
1
0
0
2
0
0
1
1
1
0
0
2
2
0
0
3
2
1
2
1
2
0
0
1
1
0
2
0
2
0
0
1
2
4
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
2
1
0
0
1
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
2
0
1
1
2
1
2
1
0
0
0
0
0
1
0
1
2
0
2
0
2
0
0
1
0
2
0
1
0
0
1
1
0
0
2
2
3
0
0
2
1
2
1
0
1
0
0
2
0
1
2
0
2
0
1
0
0
0
1
2
1
1
0
2
0
0
0
1
0
0
2
0
1
1
0
0
1
0
0
0
0
0
1
0
3
0
0
2
1
1
0
0
2
0
0
1
0
0
1
4
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
2
0
0
1
2
1
0
0
2
2
2
0
1
2
0
2
0
1
0
0
0
2
2
0
1
0
2
0
2
0
0
0
4
4
0
0
2
1
2
2
0
1
2
1
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
2
0
0
0
1
0
0
0
1
0
0
0
0
2
1
2
0
0
1
1
0
1
1
0
0
1
0
2
2
1
0
0
2
0
1
0
4
0
0
1
0
0
0
2
0
0
2
1
0
0
2
2
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
1
2
1
0
1
0
0
1
2
0
0
1
1
2
0
1
0
0
2
2
0
0
0
0
1
1
0
0
2
2
0
1
1
0
2
0
0
0
1
1
0
0
2
0
0
1
0
2
2
0
2
2
0
0
1
0
0
0
0
2
0
0
1
1
1
2
0
1
0
0
2
2
1
2
2
2
0
0
0
1
0
0
0
1
0
1
0
2
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
1
2
2
0
2
0
2
0
1
0
1
0
2
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
2
0
0
0
1
0
0
1
0
0
1
2
0
0
0
0
0
2
2
1
0
1
0
0
0
2
2
0
0
2
1
0
0
0
0
0
0
0
0
1
1
0
2
2
2
0
0
2
1
0
0
0
1
0
0
0
2
0
2
1
0
0
2
0
0
2
7
2
0
0
0
1
2
2
1
2
1
0
0
0
0
1
0
1
0
0
2
1
0
0
0
0
1
0
0
1
1
1
0
1
0
0
2
0
0
1
1
0
2
0
0
2
0
0
2
3
0
2
1
1
0
0
0
0
1
0
1
0
2
2
0
0
0
0
0
1
0
0
1
0
3
0
0
1
1
1
0
0
0
2
0
1
0
2
0
3
2
0
0
0
0
1
6
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
1
0
0
1
2
0
0
0
1
0
2
0
0
0
1
0
2
0
0
0
1
1
1
0
1
0
2
0
1
0
0
2
1
0
0
1
1
1
1
0
0
0
0
3
0
0
0
0
2
1
1
0
0
0
0
2
2
0
1
0
1
0
0
0
0
0
0
0
2
1
1
0
0
0
0
2
0
0
2
0
1
1
0
0
0
2
2
0
0
0
1
0
2
0
2
3
1
0
0
2
0
2
0
2
0
2
0
0
0
0
0
2
1
0
0
2
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
1
1
0
2
0
3
1
0
0
0
1
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
3
0
2
0
2
0
1
2
0
0
0
1
0
0
1
0
0
1
4
2
0
0
0
0
0
13
0
1
1
2
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
2
3
2
2
1
1
0
2
1
2
1
0
0
0
0
0
0
2
0
0
3
2
1
0
0
1
2
0
0
0
0
0
1
0
1
2
0
1
0
0
0
0
0
0
2
0
1
2
0
0
0
1
1
3
2
0
1
2
0
0
0
0
0
2
2
1
0
2
2
1
0
0
2
2
2
0
0
1
0
0
0
1
4
0
0
1
0
2
2
0
0
1
0
0
0
2
1
2
0
1
0
0
0
0
0
2
1
1
0
0
1
0
0
0
1
0
2
1
1
0
1
1
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
1
1
0
1
1
2
0
2
2
2
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
2
2
0
2
0
0
0
1
1
0
0
0
0
0
1
0
2
0
0
0
2
3
1
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
6
0
1
0
1
0
2
0
0
0
2
2
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
2
0
0
0
2
1
3
3
0
1
2
0
0
2
0
0
1
0
0
0
2
2
0
1
1
0
0
2
3
0
0
2
2
1
0
0
2
0
0
0
1
0
1
2
1
1
2
1
2
0
1
0
0
0
0
2
1
0
2
1
1
0
0
0
0
2
2
0
0
1
1
1
0
0
0
1
0
1
2
0
0
1
0
1
1
2
1
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
1
3
0
1
1
0
0
1
1
1
0
0
1
0
1
0
0
0
0
2
0
2
0
1
1
0
0
0
0
2
1
0
0
0
2
0
1
0
0
1
0
2
2
2
1
1
2
1
0
0
0
1
0
0
2
0
0
0
0
1
0
0
1
0
2
1
1
2
0
0
0
0
0
0
2
0
0
1
2
1
0
0
0
0
0
0
1
1
1
0
1
1
1
1
1
0
1
0
0
0
2
0
1
2
1
2
0
0
2
0
0
0
1
0
0
0
1
1
1
0
0
1
0
2
0
0
0
0
0
0
1
0
1
1
0
0
2
0
0
2
2
0
0
1
1
0
0
0
2
1
0
0
1
0
2
0
0
0
1
1
0
0
0
0
2
0
2
1
0
0
2
0
0
2
0
2
0
2
0
0
2
1
0
0
0
0
1
1
0
0
1
0
0
1
0
0
2
1
0
0
0
1
0
0
2
2
0
1
0
1
2
0
1
0
0
0
2
1
3
2
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
2
2
1
2
0
1
2
0
1
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
2
2
2
0
1
1
2
1
1
2
0
0
0
1
1
0
1
1
2
1
0
0
0
2
1
1
2
1
0
0
0
0
1
0
0
1
1
0
0
1
2
0
2
0
1
0
1
0
2
2
0
1
2
0
2
1
0
0
0
0
0
1
1
2
0
3
0
0
0
0
2
2
0
2
0
0
0
0
1
0
0
0
0
1
0
0
2
2
0
0
1
1
0
0
0
1
2
0
1
1
2
1
0
0
0
0
0
1
0
2
2
0
1
0
1
0
2
0
1
0
0
2
0
1
1
0
0
1
1
1
0
2
2
0
1
0
1
0
0
0
1
1
2
0
0
0
1
0
1
0
1
0
0
2
0
0
1
0
0
0
0
0
3
1
0
4
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
2
1
1
0
2
3
0
2
0
0
0
0
1
2
1
0
0
1
2
0
1
0
0
0
4
0
0
0
1
0
2
0
1
0
1
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
1
0
0
2
0
0
2
0
0
2
0
0
0
2
0
0
1
1
1
0
1
2
0
0
1
0
1
0
0
0
1
0
1
0
2
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
1
2
2
0
1
0
1
1
0
0
0
1
0
0
1
1
0
0
0
0
0
1
2
0
0
2
1
1
0
0
2
2
0
0
0
1
0
2
1
1
0
0
1
2
1
0
0
4
0
2
1
0
0
2
2
0
1
0
2
1
0
8
0
0
1
0
0
2
0
0
0
0
2
0
0
1
3
0
2
0
1
1
2
0
0
0
0
2
1
0
0
0
1
0
1
1
0
1
0
2
2
1
2
2
0
2
0
0
0
2
2
0
2
1
0
0
0
2
1
4
0
1
0
2
0
1
0
0
2
3
0
1
2
0
0
2
0
2
0
2
0
1
1
1
0
0
3
2
1
1
2
1
2
0
1
0
0
0
0
2
0
1
0
0
2
2
0
0
0
1
1
0
0
2
0
0
0
1
0
2
0
3
0
1
1
0
1
0
0
1
2
0
2
0
1
0
1
0
0
0
0
0
0
2
1
0
0
2
2
0
0
2
2
0
1
2
0
1
0
0
0
0
0
1
2
0
1
0
2
1
1
0
0
2
1
1
0
1
0
0
0
0
2
0
2
0
0
0
2
0
0
0
2
1
0
0
0
0
1
1
0
1
0
2
2
0
1
0
0
0
5
1
0
0
2
1
0
0
0
1
0
2
0
1
1
0
0
0
0
2
1
2
0
2
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
1
2
2
1
1
0
0
0
2
0
0
0
1
0
0
0
1
1
0
0
0
3
0
0
0
0
2
2
0
1
1
0
1
1
0
0
0
2
2
0
0
0
1
0
1
0
0
1
2
0
9
2
2
2
2
2
2
0
0
0
2
1
0
0
2
1
0
1
1
0
2
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
2
0
0
1
0
0
2
0
1
0
1
2
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
3
0
1
0
2
1
1
0
0
2
0
1
0
0
1
0
1
0
1
2
0
1
2
1
1
2
3
0
0
0
2
0
0
1
0
0
2
0
0
0
0
2
2
0
0
2
0
0
0
0
0
1
1
2
2
2
0
2
0
3
1
0
1
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
2
0
0
2
0
2
1
0
1
6
2
1
0
0
0
0
0
1
0
2
0
0
0
2
1
2
0
1
1
0
1
1
3
2
1
2
1
0
0
1
1
0
1
1
0
1
0
2
2
0
0
2
0
2
1
0
2
0
0
1
0
2
2
0
0
0
0
1
0
1
1
2
0
0
1
0
1
0
0
0
0
0
0
0
4
0
1
0
2
1
1
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
1
2
0
0
2
0
2
0
0
2
1
0
2
2
1
2
0
1
2
0
1
0
1
1
0
0
0
1
1
0
2
3
1
0
0
0
1
0
0
0
0
2
1
0
1
2
1
1
1
0
0
0
0
0
2
0
2
1
2
0
0
1
0
0
0
1
0
1
0
0
0
0
2
0
0
2
0
0
2
2
0
0
0
2
1
0
0
1
1
0
0
0
1
1
1
0
1
0
0
4
2
0
1
1
0
2
0
1
0
0
2
0
0
1
0
0
0
0
1
0
0
1
0
1
0
1
2
2
0
1
0
2
0
0
0
0
1
0
3
0
1
1
0
2
3
0
0
2
1
2
0
0
0
0
1
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
1
0
0
1
1
0
0
1
0
1
1
0
0
2
0
1
0
2
0
0
1
0
0
1
0
0
1
0
0
1
2
0
0
2
0
0
0
1
1
2
0
0
2
0
1
2
0
0
0
2
0
0
0
0
0
2
0
0
1
0
1
0
0
2
1
0
2
1
0
1
1
0
1
2
1
0
0
0
0
0
0
0
0
0
1
2
1
1
2
2
0
1
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
1
1
1
1
0
1
1
2
0
1
0
0
2
0
3
0
0
2
2
3
0
0
0
0
2
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
1
1
1
0
5
2
0
1
0
0
0
0
2
1
0
0
0
1
1
0
0
1
2
2
0
1
0
6
2
0
2
0
5
1
0
1
1
1
3
0
0
1
1
0
0
0
0
0
1
0
2
0
0
1
0
0
0
2
0
0
2
1
0
0
0
2
0
1
2
0
0
0
1
1
0
4
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
1
2
1
0
0
0
0
1
0
0
2
0
1
0
1
1
0
3
2
2
0
2
1
1
2
3
1
2
0
0
0
1
1
1
1
1
0
2
1
1
0
1
1
0
1
1
0
1
0
0
0
1
0
7
1
0
2
1
0
0
0
0
0
1
1
2
3
0
0
1
1
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
1
0
1
0
2
1
0
0
0
2
0
0
1
1
0
0
0
1
0
3
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
2
2
0
1
0
0
2
0
0
0
0
1
0
0
0
0
1
0
2
0
1
0
1
1
0
2
0
0
0
0
0
1
0
1
2
0
0
2
0
0
2
0
0
0
0
1
3
2
0
2
0
0
3
0
0
0
0
2
0
0
0
2
1
2
0
0
2
0
0
1
0
0
2
2
0
2
2
1
0
2
1
1
2
1
0
0
2
0
0
0
1
0
3
0
2
0
0
1
2
2
0
0
0
0
0
1
1
0
0
1
0
2
0
1
0
0
0
1
0
2
0
2
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
1
2
1
0
0
1
0
0
0
1
2
0
0
1
1
2
0
2
0
0
0
0
2
2
0
0
1
0
1
0
2
1
2
0
0
0
0
0
1
1
2
0
0
2
0
0
0
2
0
0
0
2
0
0
1
0
2
1
2
0
1
1
0
2
1
0
0
0
0
0
0
0
0
0
2
3
0
2
1
0
2
1
0
0
0
2
0
0
0
0
1
0
0
1
1
0
0
0
1
2
2
2
0
0
2
0
0
0
0
0
1
1
1
2
0
1
2
1
0
1
0
0
0
0
0
2
0
1
0
1
1
1
0
0
0
1
1
0
0
0
2
0
0
0
0
2
2
1
0
0
2
4
0
1
0
0
2
1
2
0
0
2
2
0
0
2
2
0
0
3
1
0
0
1
0
0
0
1
0
3
2
4
0
0
2
0
1
0
1
1
2
1
0
1
0
2
1
0
0
0
0
2
1
1
1
0
2
2
0
1
1
2
1
1
0
0
2
0
1
2
0
1
0
0
2
1
0
0
0
0
0
0
2
0
0
2
0
0
0
4
2
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
2
0
2
1
1
0
0
0
2
0
2
0
0
0
0
1
0
3
2
0
0
0
1
0
1
1
0
0
0
2
0
1
0
0
2
0
2
2
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
2
1
1
1
2
0
0
0
1
1
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
2
1
1
0
2
1
0
0
0
1
0
1
2
0
0
2
0
0
1
1
1
1
0
1
0
2
0
1
0
0
0
0
1
1
1
2
0
1
0
2
0
2
1
0
0
0
2
0
2
2
0
2
0
1
1
0
0
1
0
2
0
1
0
1
0
0
1
0
0
2
0
2
0
2
0
0
1
1
1
1
0
0
0
0
0
1
0
0
0
1
2
0
0
0
3
0
0
0
8
0
1
0
0
2
1
1
0
1
0
1
0
0
1
1
2
0
0
0
0
0
1
1
1
0
0
0
1
2
2
0
1
0
0
2
1
0
1
0
0
1
0
1
0
1
0
2
1
2
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
3
1
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
2
2
0
0
0
1
0
0
0
1
0
0
0
0
2
1
0
3
0
0
0
0
2
0
0
1
1
0
0
2
0
0
0
1
0
1
1
2
0
0
0
0
0
1
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
1
2
0
0
1
1
1
0
0
0
0
0
1
1
2
2
2
2
1
0
0
1
0
0
2
2
2
0
0
1
0
0
2
0
2
2
0
0
0
0
2
0
0
1
1
0
1
0
0
2
0
1
0
1
2
0
2
2
2
1
0
0
0
1
2
1
0
0
0
2
0
2
0
1
1
3
1
1
0
2
0
1
2
0
1
0
0
1
0
0
2
2
1
2
0
0
0
1
0
2
1
0
2
0
1
2
0
2
0
1
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
4
2
1
2
0
0
1
1
2
0
0
1
0
2
0
1
0
1
2
0
2
0
1
1
0
0
1
1
0
3
1
6
0
0
0
2
1
1
0
2
1
2
0
0
2
0
1
1
0
0
0
1
0
0
1
0
0
2
2
0
0
2
0
1
0
1
0
0
1
0
0
0
1
0
0
2
0
1
1
1
0
1
1
0
0
0
2
2
0
0
0
0
1
0
0
2
0
1
0
0
0
0
2
2
2
1
0
0
1
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
2
2
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
1
1
0
1
1
0
1
0
0
0
0
4
1
2
0
0
1
0
1
0
1
0
0
0
0
0
1
2
0
2
0
1
0
0
0
2
0
0
0
0
2
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
2
0
0
1
2
2
1
1
1
0
0
0
1
1
0
0
0
1
0
1
1
0
0
0
0
2
0
1
1
0
0
0
1
0
0
0
1
0
1
2
0
0
2
1
0
0
0
0
1
1
2
0
4
1
1
0
1
0
0
0
1
0
0
1
2
0
2
0
1
0
0
2
0
1
0
3
0
0
0
2
0
0
2
1
0
0
2
0
0
1
0
0
0
0
0
1
2
1
1
0
0
0
3
0
0
1
1
1
1
0
0
0
2
0
3
1
0
2
1
2
0
1
0
0
0
1
0
2
1
1
0
0
0
0
0
1
0
0
0
2
2
0
2
0
0
1
0
0
2
1
2
1
2
0
0
0
1
2
0
1
1
1
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
2
0
2
2
0
1
0
0
0
1
0
2
0
0
0
2
2
1
1
2
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
1
0
2
2
0
3
0
2
0
1
1
1
0
0
0
0
0
1
0
2
0
0
2
0
2
0
2
1
0
1
2
0
0
0
0
2
2
0
0
1
0
2
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
2
1
2
0
1
0
2
2
0
2
2
5
1
1
1
0
2
0
1
2
0
1
0
0
0
0
5
2
0
0
0
0
1
0
1
2
0
0
0
2
1
2
0
4
0
0
1
3
2
0
0
0
0
1
2
0
0
1
2
1
1
0
2
2
2
2
0
0
0
0
2
1
1
1
0
0
1
0
0
0
0
0
0
0
0
1
3
2
2
2
0
0
2
2
0
2
1
1
0
0
0
0
1
0
0
0
2
0
0
0
1
1
0
0
0
0
0
1
0
0
2
0
1
0
2
0
2
2
0
3
0
6
0
0
2
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
2
0
0
0
1
0
1
0
0
2
1
1
0
0
2
1
2
0
2
0
0
0
0
0
0
0
1
2
0
0
2
3
0
0
0
2
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
1
2
1
1
0
0
2
0
0
1
0
0
1
1
0
2
0
2
0
1
0
0
2
0
0
0
1
0
2
2
1
1
0
0
2
0
2
0
0
1
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
3
0
2
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
3
2
0
1
0
4
0
4
1
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
1
0
1
0
0
0
0
0
1
1
2
0
0
0
1
2
1
2
0
2
0
1
0
2
1
1
0
1
0
0
0
1
0
2
1
0
0
0
1
1
1
0
2
1
0
2
0
2
2
2
0
3
2
1
2
2
0
1
0
0
1
0
2
0
2
1
0
1
0
2
0
1
0
0
0
1
0
0
0
0
2
1
0
1
1
0
0
0
0
1
0
0
1
0
1
1
1
0
1
1
0
0
0
0
0
1
2
0
0
1
0
0
1
1
0
0
0
0
1
1
0
0
0
1
2
0
0
0
0
0
0
2
1
2
0
0
1
0
0
0
0
0
3
2
0
1
0
0
1
2
0
0
0
1
0
2
2
0
1
2
1
0
1
0
0
0
1
2
0
2
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
1
0
0
1
2
1
0
0
0
0
2
0
0
0
2
2
1
0
1
2
1
0
0
1
2
1
2
0
1
2
0
1
0
2
1
2
1
0
2
0
0
0
0
2
0
2
2
0
1
0
0
1
0
1
0
0
0
6
0
0
1
0
0
1
0
2
0
0
1
1
0
1
0
2
0
0
1
0
0
0
2
0
0
1
2
1
1
0
1
1
0
0
0
0
0
2
1
0
1
1
0
0
0
0
0
1
1
0
2
1
0
1
1
0
2
0
0
0
2
0
0
0
0
1
2
1
0
0
2
0
0
2
4
0
0
0
1
0
1
1
1
0
0
0
0
2
0
1
0
1
1
0
0
0
1
2
0
0
1
0
0
2
2
2
0
0
2
6
0
0
0
1
0
1
0
0
1
1
1
2
0
0
1
0
0
2
0
1
1
0
0
0
2
1
1
2
1
0
1
0
0
0
2
1
5
0
0
0
1
1
2
0
0
2
0
0
0
2
3
0
0
0
1
1
0
2
1
2
0
0
1
0
0
0
0
2
1
1
1
1
0
0
0
2
0
0
0
1
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
2
0
1
2
1
1
0
2
2
0
2
0
0
2
0
0
0
2
0
0
0
1
1
0
2
0
0
0
2
2
0
1
0
2
0
2
0
1
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
2
1
0
0
0
1
2
0
0
0
0
4
0
2
0
0
0
2
0
2
1
0
2
0
0
1
1
2
0
1
2
2
1
2
1
0
0
0
1
0
0
2
2
0
2
2
2
0
0
3
1
1
0
0
2
0
0
0
2
2
0
0
2
0
0
0
0
0
2
1
0
1
0
0
1
0
1
0
0
1
0
0
2
2
0
0
1
2
0
0
0
1
1
1
0
0
0
0
1
0
0
2
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
1
2
1
1
1
2
0
0
0
1
1
2
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
1
2
1
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
1
0
0
2
2
2
0
0
0
0
1
0
1
2
0
0
1
1
2
0
0
0
0
1
2
0
0
0
2
2
0
2
0
1
2
0
0
1
1
0
0
2
0
2
2
0
0
0
1
0
0
2
0
2
1
0
0
2
1
0
0
0
2
2
2
0
0
2
0
0
0
0
3
1
0
0
1
1
0
0
0
2
2
1
4
1
0
1
3
0
0
0
0
0
1
0
1
2
2
1
0
1
0
1
0
0
1
2
1
1
1
0
0
2
0
0
0
2
0
2
3
2
0
2
0
0
1
0
0
0
1
2
0
0
0
1
0
0
2
1
0
1
0
2
0
0
0
0
1
2
1
0
0
0
0
0
0
1
0
1
2
1
2
2
1
0
0
2
1
0
0
0
0
0
0
1
1
1
2
2
0
2
0
1
0
0
1
0
0
2
3
0
2
0
0
2
0
0
3
2
0
1
1
0
0
1
1
1
0
1
1
0
0
0
0
0
1
0
2
1
0
2
2
1
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
2
1
0
0
0
3
0
0
2
1
0
2
1
2
0
1
0
1
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
1
0
2
0
1
1
1
0
0
1
1
0
2
0
0
1
0
0
0
1
2
0
0
0
1
0
0
2
0
1
0
0
0
0
1
0
1
1
0
0
0
0
2
0
1
0
0
0
0
0
1
0
1
0
0
0
2
1
0
0
0
1
2
0
1
1
0
0
0
0
0
1
1
1
1
2
0
0
0
0
0
0
1
0
2
1
0
1
0
0
0
1
0
2
1
0
1
0
0
0
2
1
0
0
0
2
1
0
2
3
2
1
0
2
0
0
0
0
0
1
0
2
0
0
0
0
1
1
0
0
2
0
0
1
1
0
1
0
0
1
0
1
0
1
0
0
2
1
0
2
1
0
1
0
2
1
0
1
0
0
0
2
1
0
4
1
0
6
0
0
2
1
0
2
0
0
2
0
0
2
0
0
0
1
1
0
1
1
4
2
2
0
0
0
2
0
1
2
0
1
0
2
0
0
1
1
0
1
0
0
2
0
0
0
1
0
0
2
0
0
2
1
0
0
1
0
0
2
3
0
2
1
1
2
0
0
1
0
0
0
1
1
0
0
0
1
3
2
0
0
0
0
0
1
0
1
0
1
3
1
1
0
3
0
1
5
0
2
0
0
1
0
2
0
1
0
0
2
1
0
0
2
1
0
1
0
0
1
1
1
0
2
0
1
1
0
1
0
0
1
0
2
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
2
2
0
0
0
0
0
0
1
1
1
0
1
0
2
0
0
1
0
1
2
0
2
1
2
0
1
0
0
2
0
0
0
0
1
1
0
1
0
2
0
2
1
0
0
2
2
0
2
2
0
1
0
1
0
0
0
2
0
3
1
1
0
0
2
1
2
0
2
0
0
0
1
0
0
1
1
0
0
3
0
0
0
1
2
0
0
0
3
1
1
0
2
0
1
0
0
1
0
0
0
0
0
2
1
0
1
0
0
2
0
1
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
1
2
0
1
0
0
0
1
2
1
1
0
1
0
0
1
0
0
0
1
0
0
1
1
3
1
0
0
1
4
0
2
0
0
0
0
0
0
2
2
2
3
0
0
0
0
0
2
0
1
1
0
0
0
3
4
0
0
0
2
0
0
0
0
1
0
2
1
0
0
1
2
0
0
0
0
0
0
1
2
2
1
2
0
0
2
1
0
1
2
1
0
1
1
0
0
1
0
1
1
0
2
0
2
1
0
1
3
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
1
2
1
0
0
0
1
0
0
2
2
0
0
2
0
1
0
0
0
0
1
1
0
2
0
0
0
2
0
0
0
1
0
0
0
0
1
2
0
1
0
0
0
1
0
1
0
0
0
0
0
0
2
5
2
2
0
1
1
0
1
1
0
3
0
0
1
2
0
1
3
1
1
0
0
0
0
0
0
2
0
1
0
0
0
1
2
1
0
0
0
2
0
0
0
3
0
0
0
2
3
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
1
0
1
2
0
1
2
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
1
0
0
0
2
0
1
1
0
1
0
2
0
0
0
2
0
2
1
1
2
2
0
0
0
1
0
0
0
2
0
2
0
2
0
0
0
1
3
0
2
0
0
0
2
1
1
0
2
2
0
0
2
0
0
0
0
0
1
0
0
0
2
2
2
0
0
1
0
2
0
0
0
0
1
0
0
1
2
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
2
5
0
2
0
0
0
1
0
0
0
0
1
2
1
1
2
0
0
0
0
0
1
0
2
1
2
0
0
1
0
0
1
3
1
0
0
0
0
0
0
2
0
2
2
0
0
1
0
0
2
0
1
1
1
1
0
2
0
0
2
0
0
2
2
0
2
0
0
2
0
0
2
0
0
1
0
1
0
1
2
0
2
0
1
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
1
2
1
0
0
0
1
0
0
0
0
0
0
0
1
0
2
4
0
0
2
1
1
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
1
0
0
0
0
0
1
0
2
0
1
1
0
0
2
0
0
0
0
0
0
1
1
1
2
1
0
0
0
0
1
1
0
0
0
0
1
0
2
0
0
0
2
0
2
0
2
2
0
1
1
1
3
0
0
2
0
0
0
0
0
0
0
0
1
2
1
0
0
2
0
1
0
1
0
1
0
0
0
1
0
1
1
0
0
1
0
1
1
0
2
2
0
0
2
2
1
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
1
0
1
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
2
0
1
0
1
0
0
0
1
0
0
0
2
0
1
1
0
0
1
0
1
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
1
2
2
2
0
0
0
0
0
2
0
0
0
2
1
0
0
1
2
0
0
0
2
1
1
0
2
1
0
0
2
0
0
2
2
1
0
1
0
1
1
0
0
0
0
1
0
0
2
0
1
0
2
1
1
2
0
0
0
2
0
0
0
1
1
0
2
0
0
1
1
1
1
0
2
0
1
1
2
0
0
1
1
0
0
2
0
1
0
1
2
2
0
1
3
2
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
1
2
1
0
0
0
3
1
2
1
1
2
1
1
0
2
0
1
2
3
0
0
1
1
1
1
0
2
1
1
0
1
1
0
2
0
0
1
0
0
0
2
2
1
0
0
1
0
0
1
0
0
1
0
3
0
0
0
2
0
2
0
2
0
1
1
0
0
0
0
1
1
1
2
0
0
0
0
1
0
2
1
0
0
0
2
0
0
0
0
0
1
0
1
0
0
1
0
1
1
1
0
0
0
2
1
0
1
1
0
0
2
1
0
0
0
2
1
1
2
0
1
2
1
1
3
0
0
0
0
2
0
1
2
0
0
1
1
1
0
1
0
0
0
1
2
1
1
0
0
0
0
0
0
2
1
1
2
0
0
0
0
1
0
0
0
1
0
3
0
0
0
0
0
0
0
1
2
1
0
0
2
0
1
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
1
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
2
0
1
2
0
0
0
1
1
2
2
1
0
1
0
0
2
1
0
0
0
0
0
1
0
0
0
2
0
0
2
1
2
0
2
0
0
0
3
0
0
0
0
2
0
0
0
1
0
0
1
0
2
2
1
0
0
2
2
0
0
1
0
1
0
0
0
0
1
0
2
0
1
0
0
0
1
0
0
0
2
2
0
0
0
0
0
3
1
2
2
0
2
0
0
0
0
2
2
1
0
0
0
0
4
0
1
1
1
0
0
0
1
0
0
2
1
2
0
2
6
1
0
0
0
0
2
0
2
1
0
1
0
0
1
0
0
1
0
1
0
2
0
2
2
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
1
0
1
0
2
0
0
0
0
0
2
0
0
2
1
1
3
1
0
0
0
0
0
0
0
1
1
1
0
3
0
0
2
0
2
3
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
2
0
3
0
1
3
2
0
0
3
0
0
0
2
0
1
2
0
0
2
1
0
2
0
2
0
1
0
1
1
1
0
0
0
0
0
1
0
0
0
2
1
1
0
0
2
1
0
2
1
2
0
0
1
2
1
0
0
0
0
1
0
2
2
0
0
0
1
0
0
2
0
0
0
0
0
0
2
1
1
0
2
0
2
0
1
0
0
0
2
0
0
2
1
2
0
0
2
0
0
0
1
1
4
0
2
0
2
0
1
3
0
1
0
1
1
0
0
0
0
1
0
1
0
0
1
1
0
1
0
1
0
0
0
0
1
3
2
0
0
1
2
0
1
1
0
0
0
0
3
0
0
2
2
1
0
1
0
0
0
1
1
0
2
1
0
0
1
0
4
1
0
0
3
2
0
0
1
1
3
0
1
0
1
0
0
0
1
1
0
0
0
1
2
0
0
0
1
0
1
0
0
0
0
0
9
1
2
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
1
0
0
4
0
0
1
0
2
0
0
2
2
0
1
0
1
0
0
2
2
0
2
0
2
2
3
0
0
0
0
0
2
0
0
1
2
1
0
0
0
3
2
2
0
0
1
2
1
2
2
1
0
1
0
2
2
0
0
0
2
0
0
3
0
2
0
1
2
0
2
0
0
0
0
0
0
0
2
2
2
0
2
0
0
2
1
0
0
0
0
1
0
2
1
1
1
0
0
0
2
0
0
2
2
0
2
0
0
2
0
1
1
0
3
0
1
0
2
0
0
2
0
1
0
7
1
0
0
2
0
0
2
4
0
0
0
1
0
1
2
0
0
1
0
0
0
1
1
0
1
3
0
0
1
0
1
1
0
0
1
0
0
2
2
0
2
1
1
1
1
1
2
2
0
1
2
2
0
1
1
0
0
3
0
2
0
0
0
3
2
0
0
1
0
0
0
0
2
0
0
0
0
2
0
5
0
1
1
2
1
2
1
1
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
1
2
0
1
0
1
0
2
2
0
0
0
1
0
0
2
1
1
0
0
0
0
0
1
0
1
0
3
2
0
1
0
3
0
0
0
2
0
1
0
1
2
0
2
2
0
0
2
0
0
2
0
0
0
1
0
0
3
1
0
2
2
2
1
0
2
0
0
0
2
0
0
0
2
0
1
2
1
0
0
0
5
0
0
1
1
1
0
1
0
0
0
0
2
0
2
1
2
1
0
0
0
0
2
0
2
0
3
0
0
1
0
0
1
2
1
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
2
2
0
2
0
0
1
4
0
0
1
1
0
1
0
1
3
0
0
0
1
2
0
2
0
0
0
0
0
0
2
2
0
0
0
0
2
0
2
2
2
0
0
1
0
0
0
1
0
0
0
2
2
1
0
3
1
0
6
0
0
1
2
1
0
2
0
0
0
0
0
0
2
0
0
1
0
1
0
1
0
0
1
1
0
2
0
2
0
5
2
0
0
0
0
0
0
1
0
2
0
1
0
1
0
0
0
2
0
0
2
0
0
0
1
2
0
1
0
2
3
2
2
2
1
0
1
0
0
0
0
0
0
0
0
2
1
0
1
1
2
0
2
1
0
2
0
2
0
1
0
1
1
0
0
0
2
1
0
0
0
0
0
1
0
0
1
1
0
0
1
2
0
0
1
1
0
0
1
27
1
1
0
0
2
0
0
0
0
2
0
0
2
1
1
0
2
0
0
0
0
2
0
0
1
2
1
1
1
1
0
0
1
0
1
0
0
2
0
1
2
0
0
1
0
1
3
0
1
0
0
0
0
1
2
1
2
2
2
0
0
0
2
2
0
0
3
0
0
2
0
2
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
2
1
1
2
1
0
2
0
2
1
0
0
0
0
2
1
0
0
1
1
1
1
0
0
0
1
0
0
0
2
2
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
1
1
0
0
2
2
0
1
1
2
4
3
0
0
1
1
2
5
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
1
1
2
0
0
0
2
0
0
2
0
0
2
1
0
0
2
1
0
2
2
0
0
0
2
0
0
1
1
0
1
0
1
1
1
0
0
0
1
2
1
0
0
0
0
0
1
0
1
1
1
2
0
0
0
0
1
2
0
1
2
0
1
2
0
1
0
0
0
0
2
0
0
0
3
0
0
1
1
2
0
0
0
0
1
1
0
0
1
1
0
4
1
1
0
1
1
2
2
2
0
1
3
2
2
0
2
0
0
0
1
2
0
2
0
2
2
0
0
0
0
0
2
0
2
2
0
2
3
1
1
0
0
0
0
0
0
1
1
0
0
0
5
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
1
1
0
2
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
2
2
2
0
2
3
0
0
0
0
0
0
2
0
1
0
1
0
1
2
2
0
0
0
0
3
1
2
0
1
0
0
0
0
2
1
0
2
0
0
1
2
1
0
0
2
0
1
0
1
2
2
0
1
0
2
0
1
0
0
2
2
0
2
0
2
0
0
0
1
1
0
1
1
0
2
0
0
0
0
2
0
2
2
0
1
2
0
0
0
0
1
2
0
0
1
2
0
1
2
1
0
1
0
2
1
1
1
1
2
2
0
2
0
2
2
2
1
0
2
0
0
0
1
1
2
2
1
0
0
1
0
0
1
0
5
0
0
1
0
0
2
0
0
0
0
0
0
1
0
3
0
3
1
0
0
0
2
2
0
0
2
0
0
1
0
0
0
0
0
0
1
1
1
0
2
0
2
0
0
0
1
1
1
0
0
2
2
0
1
0
0
0
0
1
0
0
0
2
0
0
0
1
0
1
0
0
2
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
2
0
1
0
0
2
0
1
0
1
2
0
0
0
0
0
0
0
0
2
9
0
0
0
3
0
2
0
0
2
1
0
1
0
0
1
1
1
0
2
0
0
2
0
0
0
1
1
0
0
1
1
0
1
0
1
0
2
1
2
0
1
1
0
0
1
0
0
0
1
0
0
2
3
1
0
2
0
1
2
0
0
1
0
0
0
0
2
0
0
0
2
2
2
2
2
2
1
1
0
2
1
2
0
0
0
0
0
2
1
1
0
2
1
0
0
1
0
1
0
1
0
0
1
0
2
0
2
2
0
0
0
1
0
2
0
0
2
0
2
0
0
2
0
0
2
1
0
2
2
0
1
0
0
1
2
0
0
0
2
0
0
1
1
2
0
2
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
1
0
0
2
0
4
0
1
0
1
0
0
1
0
3
0
0
1
0
0
1
1
0
1
1
1
0
1
0
0
0
1
0
0
1
0
0
2
2
0
0
1
0
1
2
0
0
0
2
0
0
2
1
0
0
0
1
0
0
2
0
2
1
1
0
0
0
1
0
0
0
0
2
0
1
0
0
1
0
1
0
1
2
1
0
2
2
0
0
1
0
2
1
0
1
0
2
2
0
1
0
0
2
2
2
1
0
0
1
0
1
1
2
0
0
0
2
2
1
1
0
0
0
0
1
0
0
2
1
0
1
0
0
1
2
0
0
2
1
1
0
2
1
0
0
2
2
1
0
0
1
0
0
0
0
0
0
1
0
1
0
3
0
1
0
0
1
2
1
0
1
2
0
0
1
0
0
0
2
0
2
1
0
2
0
1
0
1
0
0
0
0
0
3
2
0
1
2
1
0
1
0
1
1
0
0
0
0
0
0
0
2
0
1
1
1
0
2
0
3
0
1
0
0
0
1
0
1
2
0
1
1
0
0
1
0
0
0
0
0
1
0
2
0
1
0
0
0
1
0
1
0
2
1
1
0
1
1
1
0
0
1
0
0
0
1
0
0
3
0
1
2
1
0
0
1
0
0
0
0
0
0
1
0
1
1
0
7
2
0
1
0
0
0
0
1
0
1
0
1
0
0
0
2
0
2
0
1
2
0
2
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
2
2
0
0
0
1
2
0
2
0
0
2
0
1
0
2
0
1
2
2
2
0
0
1
2
1
0
0
0
2
0
0
0
0
0
0
2
4
1
0
1
2
0
0
0
0
2
2
0
0
0
1
1
0
1
0
1
1
0
1
2
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
2
2
1
1
0
0
0
2
1
1
0
0
2
0
1
2
0
0
0
1
1
0
0
0
1
1
0
2
2
0
0
1
0
0
0
3
0
2
0
2
0
2
0
1
0
1
0
2
1
1
0
1
0
0
4
2
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
1
1
0
0
1
0
0
0
0
1
0
3
2
0
0
1
1
1
1
1
0
0
0
1
1
2
0
0
0
0
0
0
2
0
0
0
1
0
1
1
1
0
0
2
2
0
0
0
2
1
0
2
0
0
1
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
5
2
0
2
0
0
0
0
0
0
0
0
1
2
2
0
1
1
0
1
0
1
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
1
0
0
1
0
1
1
2
0
2
2
2
0
1
0
2
2
2
0
0
1
0
0
0
0
2
0
0
2
1
2
0
0
0
1
0
0
2
0
2
1
0
0
0
0
1
3
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
3
1
1
0
0
0
2
2
2
2
0
2
0
1
0
0
0
1
0
0
0
0
0
2
2
0
0
1
2
0
1
0
1
0
1
0
2
1
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
1
0
0
0
2
1
2
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
2
1
2
0
0
2
0
0
2
2
2
0
1
1
2
0
0
0
0
0
2
2
2
0
0
0
0
0
1
0
0
0
2
1
0
2
1
0
2
1
0
1
0
2
0
0
1
0
2
0
2
2
1
0
0
1
1
0
0
0
0
0
2
0
0
0
0
1
0
0
2
1
0
0
1
0
4
0
0
0
0
2
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
2
2
1
1
0
0
2
0
2
0
0
2
0
0
0
0
0
2
2
2
0
0
1
0
0
0
0
0
0
2
1
0
2
1
0
1
2
0
0
3
0
1
1
2
0
1
1
3
0
0
0
0
0
1
2
0
0
1
0
1
1
0
1
0
0
0
0
2
0
0
2
0
0
2
0
1
3
0
0
0
1
0
0
0
0
0
2
1
2
0
0
0
2
1
2
2
1
1
2
1
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
1
1
0
2
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
1
0
0
0
0
1
0
0
2
2
2
0
0
0
1
0
0
4
2
0
1
2
3
2
0
0
0
0
2
1
2
1
0
0
0
0
1
0
0
0
0
1
0
2
0
1
0
1
0
1
0
2
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
1
1
2
0
2
1
0
0
2
0
0
0
0
0
1
2
0
0
1
0
1
0
2
0
0
0
0
1
0
1
2
1
0
0
2
2
0
1
0
0
1
2
0
0
1
0
0
1
1
0
0
2
2
0
0
1
0
0
2
2
0
0
1
1
0
0
0
0
0
1
2
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
3
0
0
1
1
1
0
0
3
2
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
1
0
0
2
0
2
2
0
0
0
1
2
0
1
1
2
1
2
1
0
2
2
0
2
1
0
0
0
2
1
0
1
3
0
2
2
0
1
0
1
4
0
1
1
0
2
1
0
0
2
0
1
1
1
0
0
5
1
1
2
0
0
0
0
2
2
2
2
0
2
1
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
2
0
1
2
0
2
1
2
0
0
2
0
1
0
1
5
0
0
2
0
0
0
0
0
0
1
0
0
2
0
1
0
2
1
0
0
0
2
0
1
0
1
0
0
1
0
1
0
1
2
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
1
0
1
2
0
0
0
1
1
0
0
2
0
3
0
2
0
1
0
1
0
0
0
2
1
0
0
2
0
0
0
1
2
4
0
2
0
0
1
0
0
0
2
0
2
0
0
2
1
0
0
0
1
0
1
2
0
1
0
0
0
0
0
0
1
0
1
1
0
1
1
0
0
2
1
0
1
6
1
2
1
2
2
2
1
1
0
0
2
2
0
1
0
1
0
0
1
1
0
0
2
2
0
0
1
1
1
0
0
0
0
0
2
1
0
1
0
0
0
0
0
2
0
2
0
0
1
2
2
3
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
3
0
0
0
1
1
0
0
2
2
0
1
0
0
1
1
0
1
0
0
1
0
0
0
0
0
1
1
0
0
2
0
2
0
1
1
1
1
0
2
0
1
0
2
0
0
2
2
2
0
0
1
0
1
2
1
2
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
2
0
0
0
0
0
2
0
1
0
0
2
0
2
0
0
0
0
0
0
1
2
0
0
1
0
0
1
0
0
0
0
1
1
0
2
0
0
2
2
0
0
0
1
1
2
0
2
0
1
0
0
0
3
0
1
2
0
0
0
0
0
0
1
2
0
1
0
0
0
2
0
0
0
2
2
0
0
2
3
0
1
2
3
0
1
0
2
0
0
1
0
0
1
1
1
2
2
2
0
0
0
2
1
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
2
0
2
0
0
2
1
0
0
0
0
0
2
2
0
0
0
4
1
0
2
1
2
0
0
0
0
0
1
1
0
2
0
1
0
0
1
0
0
1
2
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
2
0
1
0
2
1
0
0
1
0
3
0
2
1
2
2
1
0
1
0
0
0
1
2
1
0
0
0
0
0
0
0
0
2
1
0
4
1
1
0
0
0
0
0
0
2
2
2
2
1
0
2
0
0
0
2
0
0
0
0
2
2
0
0
1
1
0
1
0
2
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
3
0
3
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
1
2
1
0
0
2
0
1
0
0
0
1
0
0
1
2
1
0
0
0
1
4
2
0
0
1
0
1
1
0
0
1
1
1
0
2
1
1
0
2
0
2
0
1
0
0
1
1
1
0
0
2
0
0
2
0
2
0
1
2
1
0
0
2
1
2
0
1
1
0
0
0
3
1
0
1
0
0
0
2
1
0
0
3
1
0
1
0
0
1
2
0
0
0
2
0
2
0
0
0
0
1
1
2
0
1
0
2
0
1
0
2
0
0
0
0
0
0
1
0
2
1
1
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
1
1
2
1
2
0
0
0
2
1
0
2
0
0
0
0
0
1
1
2
0
0
0
1
0
1
0
1
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
1
0
0
1
1
0
0
0
2
0
0
0
0
1
1
0
2
0
2
2
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
2
0
1
1
1
0
0
1
0
1
2
0
1
1
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
2
2
2
0
1
0
0
0
2
2
2
0
0
2
0
2
0
0
0
0
1
0
2
2
1
2
0
0
1
0
0
0
2
0
0
0
2
0
1
1
0
1
0
1
2
1
0
0
2
0
1
0
0
1
2
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
1
1
0
2
2
0
0
1
0
1
0
0
0
0
0
1
0
2
2
0
1
0
1
0
1
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
3
2
1
0
0
0
2
0
0
1
0
1
1
2
2
1
1
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
1
1
0
2
0
0
2
0
0
1
0
0
0
1
0
2
0
2
2
1
0
2
1
0
1
0
1
2
1
0
2
2
0
0
0
0
0
0
1
0
2
2
1
0
1
0
2
1
0
0
0
2
2
0
0
1
1
0
0
0
2
0
0
2
0
0
0
3
2
3
1
0
0
0
1
1
0
0
0
0
0
1
0
1
1
0
0
0
1
0
1
0
1
0
0
0
0
2
0
1
0
0
0
2
0
0
3
2
1
2
0
0
0
1
0
0
1
1
0
1
2
1
0
1
1
0
0
0
0
1
0
0
3
1
0
0
0
1
0
1
1
0
0
1
2
0
2
1
0
1
0
1
1
2
1
2
2
1
0
2
0
0
0
0
0
1
1
1
2
0
0
0
1
0
0
1
0
2
0
1
0
0
0
0
2
0
2
0
0
0
0
1
1
0
0
0
0
2
2
0
1
0
1
1
2
0
2
0
1
2
0
1
3
0
0
1
0
0
1
1
0
3
0
2
0
0
2
0
0
0
1
1
0
2
0
1
1
0
2
0
4
1
1
0
2
0
1
0
0
0
0
1
0
2
4
0
1
2
0
3
0
1
2
0
0
1
2
3
0
1
1
1
0
0
2
0
0
0
0
1
0
3
0
0
2
1
2
1
0
0
0
1
0
0
1
0
2
2
2
2
0
0
4
0
0
1
1
2
0
0
0
0
2
2
1
1
0
1
0
0
0
0
2
1
0
2
0
0
1
0
1
1
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
1
1
2
0
0
2
1
1
0
1
2
0
1
2
1
0
1
1
0
0
0
0
1
0
2
0
2
2
2
2
2
0
1
0
0
0
0
0
1
0
0
1
3
0
0
0
0
0
0
0
1
0
1
0
2
0
1
0
0
1
0
0
0
3
0
2
1
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
5
0
0
2
2
0
2
1
3
1
0
1
0
2
1
2
0
0
1
0
0
0
0
1
0
0
2
2
1
0
2
0
0
1
0
1
0
2
1
1
0
0
3
1
0
0
1
0
0
0
0
2
2
0
0
2
3
2
0
0
0
0
3
0
1
0
0
0
1
0
1
0
1
0
2
1
1
0
0
1
0
0
0
2
0
0
2
0
1
1
1
0
0
0
0
0
1
1
0
1
0
1
1
0
0
2
0
0
0
0
0
0
0
0
3
1
1
4
0
0
0
1
0
1
1
0
0
1
0
0
0
1
2
0
1
0
0
1
0
0
0
1
0
0
2
1
0
1
0
1
0
0
0
0
0
1
2
2
0
2
0
0
1
1
0
1
0
1
0
0
2
0
2
1
0
0
0
0
0
1
2
0
0
0
0
1
0
1
0
0
0
1
0
1
1
0
1
0
2
0
0
0
0
0
0
2
1
1
2
0
0
1
0
1
2
1
0
1
1
0
1
2
0
0
1
0
6
2
2
0
1
0
0
0
1
0
1
0
0
2
1
0
0
1
2
0
0
2
1
2
0
0
2
1
0
0
0
0
0
0
3
0
0
0
0
1
2
0
3
2
2
1
0
2
0
0
0
4
0
1
0
0
0
0
0
1
2
0
0
2
2
0
1
1
0
2
1
0
1
0
0
0
2
1
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
2
2
2
0
0
1
0
0
0
0
0
0
1
2
1
0
1
0
1
2
1
2
0
1
0
2
1
0
0
2
0
0
1
1
0
0
1
2
1
0
1
0
4
0
0
2
0
1
1
0
0
0
1
1
2
0
0
1
0
2
0
1
2
0
1
0
0
0
0
0
2
1
1
0
0
1
1
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
1
0
0
0
2
1
1
2
0
0
1
2
0
0
2
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
1
0
1
0
2
0
1
0
2
1
0
0
2
0
0
2
3
0
0
0
0
1
0
0
0
0
0
0
0
2
1
3
1
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
1
0
1
0
0
2
0
3
1
0
1
1
0
0
0
2
0
2
1
1
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
2
0
1
0
0
1
0
2
1
0
0
1
0
0
0
2
1
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
1
2
0
0
1
0
0
0
2
0
0
1
0
0
1
2
1
1
1
0
1
0
1
1
1
0
1
2
0
2
0
1
0
0
3
2
1
2
0
1
2
0
2
2
1
0
0
2
1
1
0
2
0
2
0
0
2
0
2
0
2
2
0
0
0
0
0
0
1
0
1
0
2
1
0
0
1
0
1
1
0
1
0
3
2
1
0
0
1
2
0
2
0
0
2
0
2
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
1
1
2
1
0
0
0
0
1
0
0
0
1
0
0
2
0
3
2
0
2
1
2
2
0
1
2
1
2
0
0
0
2
1
1
0
0
2
0
1
0
1
0
1
2
0
0
0
2
1
1
1
0
0
1
0
0
2
2
0
0
0
0
0
0
0
1
0
2
0
1
2
0
2
1
2
0
2
1
3
0
0
2
3
0
0
0
1
1
0
2
1
0
3
0
0
2
1
2
1
0
1
1
0
0
0
2
1
1
0
0
1
0
0
1
0
2
2
0
2
0
2
0
0
1
1
0
0
0
0
1
0
0
0
2
4
0
2
0
0
0
0
1
0
0
0
7
0
0
1
0
0
0
0
3
0
1
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
2
2
0
0
1
0
1
0
2
0
1
1
0
1
2
0
1
1
2
0
0
1
0
0
0
0
1
3
0
0
1
0
1
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
1
1
1
1
2
1
2
0
0
0
1
0
1
0
1
1
0
2
1
2
1
1
1
1
1
0
0
3
1
1
3
1
0
0
2
0
0
1
0
1
2
2
0
0
1
0
0
2
0
1
0
0
0
0
1
0
1
0
0
0
0
1
1
1
1
0
0
0
0
2
0
0
0
0
2
1
0
0
0
3
0
0
0
1
1
0
1
1
1
0
1
1
0
1
0
0
1
1
0
0
0
2
0
2
0
0
1
0
0
0
0
1
0
2
2
0
0
2
0
0
1
2
0
0
2
0
1
0
0
2
0
0
2
0
1
0
0
0
0
0
1
0
2
1
0
2
1
0
2
1
0
1
4
0
0
1
1
0
1
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
2
0
0
1
2
1
0
0
0
0
0
2
2
0
0
0
0
0
0
5
0
1
0
1
1
1
1
0
1
2
3
0
2
0
0
0
0
0
2
0
0
0
0
8
2
0
2
3
0
1
1
0
1
2
0
0
0
1
0
1
0
0
0
0
2
2
0
1
1
2
0
0
1
0
0
2
0
0
2
0
0
0
2
0
0
0
0
3
0
2
0
1
0
0
1
2
0
0
0
1
0
0
0
1
0
0
0
1
2
0
1
3
2
0
1
0
0
1
1
2
0
1
2
0
0
1
0
1
2
2
1
0
1
0
2
1
1
0
0
0
2
1
0
0
0
2
1
0
1
0
1
0
0
0
2
0
2
2
2
1
1
1
1
0
0
2
0
0
0
2
1
0
1
0
2
1
0
0
0
0
0
2
1
3
2
0
0
2
0
0
1
2
1
0
0
0
2
0
1
1
1
1
0
0
0
1
0
1
1
1
0
1
1
0
2
1
4
0
0
2
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
1
0
2
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
1
1
2
0
0
0
0
1
0
2
0
0
0
1
0
1
0
1
0
1
2
0
0
1
0
1
1
0
0
1
1
0
2
1
1
0
1
0
0
2
0
1
0
1
0
0
3
2
0
0
2
1
0
1
2
0
0
1
1
0
0
1
1
2
1
2
1
2
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
1
1
2
0
3
0
0
1
0
2
2
1
0
0
0
1
1
0
0
2
0
4
0
0
0
2
1
0
2
0
2
2
0
2
1
1
2
2
2
1
0
0
0
0
1
0
2
0
1
0
0
1
0
0
1
0
1
0
0
1
0
1
1
2
2
2
1
0
1
0
0
2
2
0
1
0
0
0
0
2
2
1
2
0
1
1
0
0
3
0
2
2
0
0
2
0
0
0
2
2
0
0
1
2
0
0
0
1
0
0
1
0
0
1
2
2
2
0
0
2
2
0
0
1
1
0
1
0
0
0
2
0
1
2
2
0
2
2
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
1
0
2
2
0
0
0
2
0
2
0
0
2
0
2
0
1
0
0
2
0
1
0
4
0
1
0
5
2
0
0
2
1
0
1
0
0
0
0
1
0
2
2
1
1
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
2
1
0
0
0
0
2
0
0
0
0
0
1
2
0
0
2
1
1
1
0
0
0
1
0
2
0
0
0
2
0
1
3
2
1
0
2
1
1
1
0
0
0
0
2
0
2
0
2
0
1
0
0
1
0
0
0
2
0
1
0
0
0
0
2
2
0
0
2
2
1
0
0
0
0
1
0
1
0
0
0
0
2
0
0
1
4
0
0
2
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
1
0
2
1
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
1
0
1
0
0
1
1
1
0
0
2
1
0
0
0
0
1
2
1
1
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
1
2
0
0
1
0
1
1
0
1
0
2
0
0
0
2
0
0
0
2
2
0
0
2
1
0
0
0
0
1
2
1
2
1
2
0
2
0
0
0
1
1
2
2
1
2
1
1
0
0
0
0
3
0
0
0
0
1
2
0
0
3
0
1
0
1
1
0
0
2
0
1
0
0
0
2
0
2
0
6
0
1
0
2
0
1
1
1
0
0
0
0
0
2
0
1
0
1
1
0
1
2
1
0
2
0
1
0
2
2
0
2
0
2
1
3
1
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
2
2
0
0
0
2
1
0
0
0
1
0
0
2
0
1
0
1
0
0
0
1
0
0
2
1
0
2
0
0
1
0
0
1
0
0
0
0
2
0
0
0
2
0
1
0
0
1
0
0
0
0
1
0
2
0
1
0
0
0
2
0
0
1
2
1
2
0
0
1
2
3
0
0
0
1
0
3
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
2
2
2
0
2
0
0
0
0
0
0
2
0
1
0
2
1
1
0
1
0
0
0
0
0
0
1
2
0
0
0
1
2
2
0
1
2
0
0
0
0
1
1
2
0
0
2
2
0
1
1
0
1
4
0
0
2
0
1
0
0
1
1
1
0
0
0
0
0
0
1
1
2
0
2
1
1
0
2
1
0
0
0
1
2
0
2
0
1
0
0
1
0
2
0
2
0
1
1
2
0
0
2
2
2
0
0
0
0
0
0
2
0
1
1
0
0
1
0
1
0
0
1
0
1
0
0
0
2
0
0
0
3
2
0
0
2
0
1
0
2
1
0
0
1
0
0
0
2
1
0
0
0
1
1
1
0
0
2
0
0
0
0
2
0
0
0
1
1
2
2
0
3
0
1
0
0
2
0
2
2
0
0
0
0
0
0
3
0
2
1
0
0
1
1
0
0
0
0
2
0
2
0
0
0
2
0
2
0
0
0
2
0
1
2
0
0
1
0
0
0
1
0
2
3
0
2
0
0
1
0
0
0
0
3
0
0
1
0
2
0
1
2
1
2
0
2
2
0
1
0
0
1
2
0
0
0
1
0
0
1
2
0
2
0
2
2
0
0
0
0
0
2
0
0
1
1
1
0
2
0
2
0
1
0
3
0
0
2
2
1
0
0
0
1
0
0
0
0
0
0
0
0
2
1
2
0
0
2
1
2
0
0
3
0
2
0
0
1
0
0
0
0
0
2
2
0
0
1
0
1
0
2
0
0
1
1
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
2
0
0
1
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
2
3
0
1
2
2
0
2
0
2
0
0
0
1
0
0
0
2
1
0
1
0
1
0
2
0
0
0
0
0
0
0
3
0
0
1
1
2
0
1
0
0
2
0
1
0
0
3
2
2
1
2
1
0
0
1
0
0
0
0
0
0
1
7
0
1
2
1
1
0
0
0
0
0
2
0
0
0
2
2
0
1
0
0
2
0
1
0
0
1
2
2
1
0
0
0
0
0
0
1
1
2
0
0
0
0
0
1
1
2
0
2
2
0
0
0
0
1
1
1
0
1
0
0
0
2
1
1
2
0
1
0
0
0
0
0
1
2
2
0
2
0
0
0
0
0
2
1
0
1
2
1
1
0
1
0
1
0
2
2
2
2
1
1
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
6
1
2
1
0
0
0
2
1
0
1
0
1
1
1
2
1
0
1
1
0
1
1
0
1
0
0
2
2
0
2
1
0
0
2
0
0
2
0
0
0
2
2
0
0
1
1
0
1
1
2
0
0
0
0
0
2
2
1
0
0
0
1
0
0
0
1
2
0
0
0
1
2
0
0
2
1
1
0
0
0
1
0
0
0
0
1
1
0
0
2
0
0
0
1
0
1
1
0
0
1
1
2
0
0
1
2
1
0
0
0
1
0
1
0
0
0
1
0
1
1
1
3
1
0
0
0
0
1
0
0
1
1
1
0
0
0
1
0
1
1
1
1
0
0
2
0
0
0
0
2
0
1
2
0
1
0
0
0
1
2
1
2
0
1
0
0
0
0
0
0
2
0
1
0
2
0
1
1
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
2
2
1
0
0
0
0
1
0
0
1
0
0
0
1
1
1
0
0
0
0
0
1
1
0
1
0
1
3
1
0
1
0
1
0
3
0
1
1
0
0
0
2
1
1
1
0
0
2
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
2
2
2
1
0
0
1
0
1
2
0
0
2
0
3
0
0
1
0
1
0
0
4
0
0
1
0
0
1
3
1
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
2
2
1
0
1
2
0
2
0
0
0
0
0
0
0
3
0
0
2
0
1
0
2
1
1
0
0
0
2
1
0
1
0
0
0
1
0
0
0
1
1
0
0
0
2
1
0
1
0
0
0
0
0
2
1
0
0
0
0
1
0
0
2
0
0
0
2
0
1
0
1
2
0
1
0
0
1
0
0
2
0
0
1
3
0
1
0
0
0
2
0
0
2
0
0
1
0
2
0
0
1
0
2
0
0
1
0
2
0
0
0
0
1
4
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
2
1
2
0
1
2
1
1
0
0
1
0
0
2
1
1
1
0
0
2
1
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
1
1
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
1
1
2
2
0
1
1
2
1
0
0
0
2
0
2
1
0
0
1
0
0
1
0
1
0
0
2
1
0
0
0
0
0
1
0
0
2
2
1
0
1
0
1
0
0
0
0
0
3
0
0
2
0
1
0
0
0
3
0
2
0
0
0
0
1
0
0
0
0
0
1
1
0
3
2
0
0
0
0
1
1
1
2
1
2
0
0
2
0
1
1
1
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
1
2
1
1
2
2
1
0
1
1
1
1
0
0
0
2
1
2
0
0
2
1
0
1
0
0
0
1
2
0
0
0
0
0
0
1
0
0
1
2
1
0
1
2
1
0
0
0
0
0
0
2
0
2
0
1
0
2
3
0
0
2
0
0
0
0
0
1
0
0
3
0
1
0
0
2
1
0
0
1
0
2
0
0
2
2
0
0
1
2
0
1
1
1
0
2
2
1
5
0
2
3
1
1
0
0
1
0
0
0
1
0
1
0
1
0
0
1
1
2
0
0
0
0
0
1
0
0
0
0
0
0
2
1
2
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
2
1
2
0
0
2
0
1
0
1
0
2
1
2
0
0
0
0
1
1
1
0
0
2
0
0
1
0
0
0
0
2
2
1
0
2
1
2
1
0
0
0
0
0
0
2
0
1
0
2
0
0
1
0
2
0
2
0
2
0
0
1
0
0
1
2
0
2
0
0
2
0
1
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
1
2
0
1
3
1
0
0
1
2
0
0
1
0
1
1
0
1
0
0
2
0
0
0
1
2
0
0
0
2
0
1
1
0
0
0
2
0
0
2
1
0
0
0
0
0
1
1
1
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
1
2
1
2
2
1
0
2
2
0
2
0
0
0
0
2
0
1
1
1
1
1
1
1
1
0
0
1
2
1
0
0
0
0
0
1
0
1
1
2
1
0
2
0
2
1
1
0
1
0
2
1
0
1
2
2
0
0
0
2
0
1
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
1
1
0
0
2
1
2
1
2
0
3
0
1
0
0
0
0
0
1
1
2
1
0
1
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
1
1
0
1
1
0
0
2
2
0
2
0
2
0
2
0
0
2
0
4
1
0
1
3
0
0
3
0
1
1
0
0
0
0
0
1
0
1
1
2
1
2
2
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
1
2
0
1
0
1
2
0
1
1
0
7
0
0
0
1
0
1
0
0
0
2
1
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
2
1
0
0
0
1
1
0
1
0
0
1
2
0
1
1
0
0
0
0
1
1
2
1
2
0
2
0
2
0
2
0
0
0
2
0
0
0
1
0
0
2
0
2
1
0
1
2
2
0
0
0
0
1
0
0
0
1
1
1
0
2
0
0
2
0
0
0
0
2
0
0
0
1
0
0
2
0
0
2
0
1
1
2
0
4
2
2
0
0
2
1
0
0
0
1
0
0
1
0
1
0
1
0
0
1
0
1
0
0
1
0
0
1
0
1
0
1
0
0
0
0
1
2
1
0
2
2
0
0
1
2
0
0
0
1
2
0
0
2
2
5
2
0
0
2
0
0
2
0
1
0
1
0
1
0
0
2
1
2
3
0
0
0
1
0
1
0
0
0
0
0
2
1
0
1
1
0
2
0
0
0
1
1
0
1
1
0
0
2
0
1
1
1
0
0
1
2
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
2
1
1
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
2
2
0
0
0
2
3
2
1
1
1
0
0
0
1
2
0
1
0
0
1
2
4
0
0
0
0
0
0
2
1
1
3
0
2
0
0
2
0
2
0
1
0
0
0
2
0
1
1
1
2
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
1
0
2
2
0
1
0
0
1
0
0
2
1
0
0
2
2
1
0
0
0
0
0
1
1
0
0
0
0
0
3
1
0
0
0
2
0
0
2
1
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
1
2
2
2
0
0
0
0
0
0
0
0
0
2
0
3
1
2
1
0
0
0
2
0
0
0
0
2
0
0
2
1
0
1
0
0
0
0
1
0
6
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
2
1
1
0
0
2
1
2
0
0
0
0
2
1
0
0
0
2
0
0
0
0
2
0
1
2
0
2
1
0
2
0
1
1
1
0
0
2
2
0
1
0
0
0
2
0
0
2
0
0
0
0
0
2
1
0
1
1
2
0
0
0
0
2
0
2
1
0
2
0
2
2
0
0
1
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
2
1
1
0
0
2
1
0
2
3
0
2
1
0
3
0
0
0
0
0
0
0
2
0
2
0
1
0
0
1
0
0
0
1
0
1
1
1
0
1
3
0
0
0
2
0
1
0
0
0
0
2
0
1
2
0
0
0
2
0
0
0
0
0
0
0
1
1
2
0
1
2
2
0
0
0
2
0
2
0
1
1
0
0
6
0
0
0
0
0
0
1
0
1
2
0
0
0
3
2
0
0
1
2
0
0
4
0
2
0
0
0
1
0
0
1
0
0
1
1
2
0
1
0
0
2
0
0
0
0
0
1
0
0
1
1
0
1
2
1
2
1
0
2
3
0
0
0
3
2
1
0
0
0
1
0
0
1
0
0
1
1
1
1
1
2
0
1
0
1
1
1
2
0
2
1
1
1
0
1
1
0
2
0
0
1
0
0
1
0
0
2
2
0
0
1
0
0
0
2
1
0
0
3
0
0
0
1
1
2
0
1
0
1
2
0
2
2
3
0
2
0
2
0
0
0
1
2
2
0
0
1
2
0
0
1
1
0
1
1
1
0
2
2
1
1
0
1
1
1
2
0
0
0
0
0
2
0
1
1
0
0
1
3
0
2
2
0
1
1
2
0
1
1
1
0
0
0
0
1
0
0
0
2
0
0
1
1
1
2
0
0
0
1
0
1
1
2
1
0
0
1
1
1
2
0
0
1
2
1
2
2
1
0
2
1
1
0
1
0
1
1
1
2
0
2
2
1
2
0
2
0
1
0
0
0
0
1
3
0
1
0
0
1
2
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
1
0
2
0
0
0
0
2
1
0
0
0
1
2
0
2
1
0
0
1
0
0
0
1
0
0
1
0
2
1
0
1
1
1
0
0
1
0
2
0
1
5
2
1
0
0
0
0
2
0
0
0
0
1
0
1
0
1
0
0
2
0
2
1
0
0
0
0
2
0
0
0
0
0
1
1
1
2
0
0
1
0
0
1
1
2
2
0
2
2
1
1
0
1
0
2
0
0
2
0
1
0
1
1
0
0
0
0
0
2
2
0
0
0
1
1
2
1
1
0
1
0
0
0
2
0
4
0
2
1
0
0
2
0
1
1
0
3
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
1
2
0
1
2
0
0
4
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
2
1
0
2
3
1
0
2
1
1
0
2
0
0
0
2
0
0
1
1
2
0
0
2
0
0
1
0
0
2
1
0
0
0
0
0
2
0
0
0
2
0
0
4
0
2
0
1
2
0
0
0
0
0
0
2
0
0
1
0
1
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
2
1
1
0
0
1
0
0
1
3
1
1
2
0
2
1
2
2
2
1
0
0
0
0
0
3
0
1
2
0
0
0
0
2
1
0
3
0
0
0
0
0
1
0
0
0
0
2
2
2
2
0
2
2
0
2
2
1
2
2
1
2
0
1
0
2
0
0
1
0
1
0
0
1
0
1
0
2
0
0
2
0
0
0
0
0
1
1
1
0
1
1
1
0
0
0
0
2
1
3
0
1
1
2
0
0
0
0
0
1
1
1
1
0
0
0
2
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
2
1
0
0
0
0
1
0
0
0
0
0
2
2
2
0
0
0
0
2
3
0
0
1
0
2
0
0
1
2
1
0
1
0
0
2
0
2
0
0
0
0
2
1
2
1
0
0
1
3
1
1
1
1
1
0
1
2
2
1
0
1
1
0
0
1
0
2
2
0
0
3
0
2
0
0
0
0
0
0
2
4
2
1
0
0
0
0
0
1
1
0
0
2
2
2
0
0
0
1
0
0
1
1
0
0
1
1
1
0
1
0
0
0
2
1
0
0
1
0
0
2
0
1
1
2
0
2
1
2
0
0
2
2
1
0
0
1
2
0
0
0
0
2
1
0
0
0
3
0
1
2
1
0
0
2
0
0
0
2
2
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
1
1
0
1
0
1
0
1
0
0
0
0
0
2
0
2
1
0
2
1
1
2
3
0
0
0
3
0
0
0
0
0
2
1
1
2
0
0
2
0
0
2
1
1
1
0
2
0
1
1
2
0
2
0
0
2
0
3
0
0
0
1
0
1
2
0
0
2
0
0
2
2
2
2
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
2
0
0
2
1
0
0
0
0
0
1
0
1
0
0
1
1
2
2
1
0
0
0
2
1
0
1
2
0
1
0
1
1
1
0
4
0
0
1
0
0
1
2
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
3
1
0
1
0
0
1
0
0
2
0
0
2
1
1
2
0
0
1
1
1
0
0
0
0
0
1
2
1
0
0
0
0
2
2
0
0
0
1
0
2
1
2
0
1
1
0
1
0
1
0
1
0
1
0
0
1
1
1
1
1
0
2
0
0
0
0
2
0
0
1
1
3
0
1
0
0
1
0
1
0
1
1
0
0
1
3
0
1
1
0
1
0
0
1
0
0
0
2
1
0
1
3
0
0
0
0
0
0
0
1
0
0
0
4
1
0
3
1
2
1
0
0
0
0
0
0
2
2
0
0
2
2
0
0
0
4
2
1
2
2
1
3
2
0
1
0
0
1
2
0
1
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
1
0
0
0
1
2
0
1
0
0
0
0
0
0
1
0
1
2
0
0
0
1
0
2
0
0
0
2
0
0
2
2
2
0
0
1
2
2
2
0
0
0
0
0
0
0
2
1
0
1
0
1
3
0
0
2
2
2
0
1
1
1
1
0
0
0
0
2
0
2
0
1
0
0
0
1
0
1
0
1
1
0
1
0
2
2
2
0
0
0
0
0
2
0
0
1
0
2
0
0
5
0
0
1
0
0
1
0
0
0
2
1
0
0
0
0
1
0
1
0
2
0
2
0
0
0
0
0
1
2
1
0
0
1
0
2
2
0
2
0
0
0
0
0
1
1
0
0
1
2
0
0
0
1
0
1
0
1
0
1
0
0
3
0
1
0
0
0
1
1
0
0
2
2
0
0
3
1
0
0
0
0
0
2
1
1
0
0
0
0
1
0
3
2
0
2
0
0
2
2
4
1
0
0
1
0
0
0
2
0
0
2
0
1
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
2
3
0
0
2
0
1
2
0
1
1
0
0
0
1
1
0
0
0
1
1
0
2
1
0
2
1
0
1
2
1
1
2
0
1
1
0
0
0
2
0
0
0
2
0
3
1
1
0
2
0
0
1
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
2
1
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
1
1
0
1
0
0
1
0
0
0
2
0
0
1
1
0
0
2
0
0
0
1
0
1
2
1
0
0
3
1
0
1
0
1
0
3
2
2
2
2
0
2
1
0
1
0
0
1
0
0
2
0
2
2
0
0
1
0
0
0
1
2
1
1
1
2
2
0
0
2
0
0
1
0
0
3
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
1
0
1
4
0
0
0
0
1
0
2
1
0
0
0
2
0
2
1
0
1
2
0
0
0
2
0
2
0
1
0
1
0
0
1
0
1
3
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
2
0
1
0
0
0
1
3
3
0
1
0
0
0
2
0
2
1
0
0
0
0
1
0
1
0
0
0
1
1
1
1
1
0
0
1
1
0
0
2
0
4
2
0
0
1
1
0
2
1
0
0
0
0
2
0
0
0
0
2
2
2
0
2
1
0
0
2
3
0
2
2
1
1
1
0
1
0
0
0
0
1
1
0
0
0
2
0
0
0
1
0
0
2
0
0
2
1
2
2
1
0
2
1
0
0
1
1
1
1
0
0
2
0
1
0
2
0
0
0
1
0
2
0
0
2
0
2
0
0
0
1
2
1
1
0
0
0
2
0
1
1
0
0
0
0
1
0
2
2
1
0
2
1
1
0
1
0
0
2
1
1
0
0
0
0
0
2
0
0
1
1
2
1
0
0
1
2
2
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
1
0
1
1
1
0
2
2
1
0
0
2
0
0
0
1
0
0
1
1
1
0
1
1
2
2
1
0
0
0
0
0
2
1
0
2
0
0
0
0
1
2
1
0
0
2
0
0
0
0
2
0
3
3
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
1
1
1
1
0
2
0
0
0
2
1
1
0
1
0
1
1
1
0
0
1
2
0
1
1
0
2
0
2
0
1
0
0
0
1
2
0
1
1
1
3
0
0
0
1
0
2
1
0
0
0
0
1
1
1
0
2
0
0
0
2
0
2
2
0
1
0
1
0
0
0
0
0
0
5
0
0
1
0
0
1
1
1
1
0
0
2
1
2
0
1
0
0
0
1
0
0
2
0
0
1
2
1
2
2
1
2
0
0
1
0
0
0
0
2
0
0
1
0
1
1
0
2
1
0
2
1
1
1
2
1
1
0
2
1
0
1
0
0
0
0
0
0
2
2
0
0
1
2
0
1
0
2
0
2
2
3
1
0
2
1
0
0
0
0
0
0
0
1
1
0
0
0
3
2
2
0
2
2
2
1
1
0
0
2
1
1
0
0
0
1
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
1
0
0
1
0
0
1
0
0
1
1
2
2
1
0
2
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
1
2
0
0
2
0
1
2
2
1
0
0
0
2
0
0
1
0
0
0
1
1
0
0
0
2
1
0
0
1
0
0
0
1
0
1
0
1
0
1
0
0
0
2
0
1
0
1
1
0
0
0
0
1
0
1
0
7
0
1
1
0
0
0
0
0
0
1
0
1
7
0
1
1
0
0
0
1
0
2
2
1
0
0
5
0
0
0
0
0
0
0
0
0
2
1
1
2
1
0
0
0
2
0
0
0
0
0
0
0
1
2
1
2
0
2
0
0
2
0
0
1
0
0
0
1
0
0
2
1
0
2
0
0
0
0
2
0
1
1
0
0
1
0
1
2
2
2
0
0
0
0
2
0
1
0
0
2
1
0
1
0
0
0
2
1
0
0
1
0
0
0
0
1
0
0
1
2
1
0
0
0
1
0
0
0
1
1
0
0
0
0
2
0
0
2
0
0
2
0
2
1
1
2
0
1
2
0
0
0
0
1
0
2
0
0
0
2
0
0
1
0
0
0
2
1
0
2
0
0
0
2
2
0
0
0
0
0
2
2
0
0
0
2
1
0
0
3
0
0
1
2
0
0
0
2
0
8
0
0
1
1
0
2
2
1
1
0
1
1
0
0
0
1
0
0
1
0
0
1
0
0
0
2
0
0
1
1
2
1
0
0
0
0
0
0
0
2
1
1
1
0
1
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
1
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
1
0
0
0
0
3
1
0
2
0
2
0
1
1
2
3
0
0
1
0
2
1
1
0
1
0
2
0
2
8
2
1
1
0
1
0
3
1
0
0
1
2
0
0
0
0
0
0
0
1
0
2
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
1
0
0
2
1
2
0
0
0
0
0
0
2
1
0
1
1
0
0
1
0
2
0
0
0
2
0
0
0
0
4
0
1
1
0
1
0
1
0
0
0
1
2
0
0
1
3
0
1
1
0
1
2
0
2
2
1
0
0
2
0
0
1
1
0
0
0
1
0
1
1
0
0
0
2
0
1
0
0
1
1
2
0
0
0
0
0
1
3
1
0
0
0
0
1
2
1
1
0
0
2
1
0
3
1
0
0
1
1
0
0
0
1
2
2
2
0
1
1
0
1
0
2
2
0
0
2
1
1
0
2
0
1
1
1
1
0
0
2
0
2
0
1
2
0
0
0
1
2
0
0
2
0
1
0
2
0
2
0
1
1
0
0
2
1
0
1
1
1
0
2
0
2
0
0
1
2
1
2
2
0
1
1
1
0
1
1
0
1
0
0
0
2
1
0
1
0
0
0
1
1
2
0
2
1
0
2
0
0
0
2
1
0
1
2
0
1
0
1
0
0
0
2
1
1
0
1
0
1
1
0
1
0
0
1
0
2
2
2
1
0
0
3
2
2
0
0
0
0
2
1
1
1
0
3
1
0
0
0
0
1
1
0
0
1
0
0
0
1
1
2
1
1
3
2
0
2
1
0
0
0
0
0
0
1
0
2
2
0
2
1
0
0
1
0
0
2
0
1
1
1
1
0
1
0
0
1
2
0
2
0
2
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
1
4
0
1
0
0
1
0
2
1
2
0
0
0
2
0
1
2
2
0
2
0
0
0
0
0
0
1
2
0
1
1
0
0
1
0
0
0
0
0
0
0
1
2
1
0
0
0
1
1
1
0
0
1
1
2
1
0
2
1
0
0
0
2
0
2
0
1
1
2
0
0
0
0
2
0
0
0
1
1
1
1
1
0
2
1
2
0
1
0
0
0
0
0
0
1
0
3
1
0
2
0
2
2
0
0
1
0
2
1
1
0
0
0
0
2
0
1
0
0
0
1
0
1
2
0
0
0
1
0
0
2
0
0
0
1
0
0
2
1
0
0
1
2
0
0
1
0
2
0
2
1
0
2
0
2
1
0
0
1
0
1
0
0
1
0
0
2
0
0
2
0
3
1
0
0
0
0
0
0
0
0
1
0
2
1
1
0
2
0
2
1
1
1
0
0
0
0
1
1
2
1
0
1
1
0
0
0
0
0
2
1
1
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
1
1
1
1
2
2
0
0
0
0
0
1
0
1
0
2
1
1
0
3
0
0
0
3
2
1
2
1
2
2
2
0
1
1
0
0
0
1
1
2
0
0
2
2
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
1
2
1
2
0
1
0
0
1
2
0
0
1
2
0
0
0
1
0
1
0
0
0
0
0
1
0
1
2
0
0
0
0
1
2
1
0
0
0
0
0
2
0
1
0
2
1
0
1
0
0
1
0
0
0
1
0
2
1
0
2
0
2
2
1
0
0
0
3
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
2
0
2
0
2
0
2
1
0
1
0
2
1
0
0
2
0
1
0
1
0
1
1
0
0
0
0
1
1
1
0
2
0
0
0
2
0
0
1
1
0
1
0
2
2
3
0
0
0
1
0
1
2
0
1
0
1
2
2
0
0
2
1
0
1
0
0
0
1
0
0
0
0
1
1
0
0
1
3
2
0
0
1
1
0
0
6
2
1
1
0
0
0
1
0
1
0
0
0
2
0
1
2
0
1
0
2
0
2
0
0
0
1
0
2
0
1
2
1
1
2
0
1
1
2
1
0
0
0
0
1
0
0
0
0
2
1
1
0
2
0
0
0
0
0
0
2
0
1
1
0
2
1
0
1
0
2
0
0
1
1
2
1
0
0
1
1
0
0
0
0
2
1
1
0
2
0
2
0
1
1
0
0
0
0
1
0
1
1
0
2
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
1
0
2
0
0
0
0
0
1
1
0
1
2
1
1
0
3
2
0
1
0
1
0
1
2
1
0
0
0
0
0
2
2
2
0
2
1
0
1
2
2
0
0
0
0
0
2
0
2
0
0
1
0
1
1
1
0
0
0
1
0
0
0
0
3
0
0
0
0
0
1
0
0
1
0
0
2
0
1
0
2
3
0
1
0
0
0
2
1
1
1
0
0
0
0
2
0
0
0
1
1
0
0
0
2
0
0
2
0
1
0
1
0
0
0
0
0
0
2
0
2
0
0
0
4
0
0
1
2
0
2
2
0
2
2
0
2
2
0
0
1
1
3
1
2
0
0
0
0
0
1
0
0
0
2
2
0
0
1
1
0
0
0
0
2
0
2
0
0
1
1
0
2
1
0
2
0
2
0
0
0
0
0
0
0
1
0
1
1
2
0
2
0
1
2
0
2
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
4
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
1
0
1
2
2
0
0
0
0
0
1
1
0
0
0
1
1
2
0
1
0
1
2
0
1
0
3
0
2
0
1
0
1
1
2
0
0
1
0
0
2
2
0
0
1
0
0
2
0
0
2
0
0
0
2
0
2
2
2
2
2
1
0
1
2
1
0
0
2
0
1
1
4
2
0
0
1
0
2
0
0
1
3
2
0
0
0
2
2
1
0
0
1
0
0
0
1
1
1
0
0
2
0
0
0
0
1
1
0
0
0
2
1
0
1
2
0
0
0
2
1
0
1
0
0
0
0
1
0
2
1
1
0
0
0
0
0
1
1
1
2
1
2
0
1
0
0
0
1
0
0
2
2
1
0
0
0
1
0
0
0
3
0
1
0
0
1
0
1
2
1
1
1
3
0
1
0
2
0
0
0
1
2
2
0
0
1
0
2
0
1
3
0
4
0
2
2
0
1
2
1
2
0
2
2
1
1
0
1
3
0
0
0
1
0
1
0
0
0
0
1
2
2
0
3
0
2
0
2
0
0
0
0
0
2
1
0
0
0
1
1
0
0
0
2
2
4
0
0
0
3
2
2
1
0
0
0
1
2
2
2
1
1
1
1
0
0
0
2
0
2
0
0
0
0
0
0
1
2
0
0
0
0
1
0
2
2
1
0
0
2
0
2
0
1
1
2
2
3
0
1
2
2
1
0
0
0
0
6
0
1
0
1
0
1
0
2
2
1
0
1
0
0
0
3
0
0
2
0
0
0
1
1
1
0
2
0
0
0
0
1
2
0
1
2
1
0
0
0
0
1
0
2
2
0
1
0
2
1
0
1
0
0
1
2
1
0
0
1
1
2
0
1
0
0
0
1
0
0
3
0
2
2
1
1
0
1
0
2
0
2
0
1
1
0
2
1
0
0
2
3
1
0
0
0
0
1
0
0
0
1
1
0
1
2
0
2
0
4
0
0
0
1
0
2
0
0
0
1
1
1
0
2
0
0
0
1
1
2
0
0
0
0
1
2
1
1
0
0
0
2
1
2
2
0
1
1
1
0
2
0
0
0
1
0
0
1
1
1
1
0
0
0
0
1
0
0
0
2
0
0
2
2
0
0
0
2
0
0
2
0
0
1
2
0
0
1
0
0
0
0
0
1
1
2
1
2
0
0
2
1
1
0
3
0
3
1
1
1
2
0
1
0
0
1
1
1
2
0
2
0
0
0
1
2
0
0
0
2
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
1
1
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
1
2
1
2
0
3
1
0
2
0
0
1
0
2
0
0
1
2
1
0
0
0
1
0
0
0
0
1
0
0
1
0
1
2
1
0
0
0
0
0
0
1
0
0
0
0
0
2
3
0
0
0
0
0
1
0
2
1
1
2
0
0
1
0
0
0
1
0
0
2
2
0
0
2
0
2
2
0
2
0
0
2
0
0
0
1
0
2
2
1
2
0
0
0
2
2
1
0
0
0
0
1
1
1
0
1
0
2
2
2
0
0
2
0
1
2
1
0
0
0
1
1
2
0
1
1
0
0
2
0
0
1
1
0
1
1
0
0
1
0
0
1
0
0
0
1
2
1
0
0
2
2
1
0
0
2
0
0
0
1
2
0
1
2
1
0
2
3
2
0
2
0
1
0
1
0
0
2
2
0
0
1
0
0
0
0
1
2
2
0
0
1
0
1
3
1
2
0
0
2
2
0
1
0
0
0
0
0
0
0
1
3
0
2
0
2
0
1
0
2
0
1
2
0
0
0
0
2
2
0
1
0
0
2
4
0
2
2
1
0
3
1
0
1
2
1
0
0
2
1
2
2
0
0
0
2
1
1
0
0
2
4
0
0
0
1
0
1
1
0
1
1
1
0
0
0
0
1
0
2
0
0
2
0
1
1
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
4
0
0
1
1
0
1
0
1
0
1
1
1
0
1
2
0
0
0
2
1
0
0
6
2
2
1
0
1
0
0
0
1
0
0
0
2
1
0
1
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
2
0
1
2
0
0
2
2
0
0
0
0
1
0
0
0
1
2
1
0
1
1
3
1
1
0
1
0
0
0
2
2
0
2
0
0
0
0
2
0
1
2
2
0
1
0
1
0
1
0
1
3
0
0
2
0
0
0
1
2
0
1
0
0
2
2
2
0
0
2
3
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
2
3
2
1
0
1
1
1
1
1
1
0
1
0
0
0
0
0
0
2
0
1
0
2
2
1
0
0
2
0
0
0
0
0
0
0
0
2
0
1
2
0
2
0
1
2
3
0
2
0
0
0
0
2
0
1
2
1
0
1
0
2
0
0
0
0
1
0
0
0
0
0
1
1
0
1
2
2
1
2
2
1
0
2
0
1
0
1
1
0
1
0
0
2
0
2
1
0
2
0
3
1
2
0
0
0
0
2
0
0
1
0
0
2
0
2
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
1
0
2
0
2
2
1
0
1
1
0
0
0
0
1
0
1
0
3
0
1
1
2
2
2
2
2
0
0
0
1
0
0
0
1
1
3
1
2
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
2
1
1
0
0
0
0
0
0
0
0
2
0
5
1
0
0
1
0
1
0
0
0
0
2
2
1
2
0
1
1
2
0
0
2
0
0
2
2
0
0
2
0
1
2
0
1
2
1
0
1
1
0
0
0
1
0
0
0
2
0
0
1
0
1
2
2
0
0
0
0
1
2
2
0
0
1
1
0
0
0
0
0
2
2
0
2
2
0
0
3
0
0
0
1
0
1
0
2
1
0
0
0
0
0
1
2
2
2
2
1
2
2
1
0
0
1
0
1
0
2
0
2
0
1
0
0
1
0
1
2
2
0
0
2
1
0
1
1
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
1
0
1
2
2
2
0
0
1
0
0
2
1
2
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
1
0
1
0
1
0
1
0
0
1
0
1
1
1
0
0
1
0
2
1
0
1
0
0
1
0
2
0
2
1
1
0
1
0
0
2
0
0
0
0
2
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
2
1
2
0
0
0
0
0
2
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
2
2
1
0
0
0
3
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
4
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
1
2
4
2
2
0
1
0
1
0
0
0
3
0
0
0
0
0
0
0
1
1
2
2
0
0
2
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
2
0
0
0
0
0
2
0
1
2
0
0
0
2
1
2
0
0
2
1
0
0
0
0
0
2
1
0
2
0
0
1
0
0
0
0
1
1
2
0
0
0
3
0
0
1
2
0
2
2
0
0
1
0
0
2
0
1
1
1
0
1
0
0
0
0
1
1
0
0
2
2
0
0
0
0
2
0
0
0
2
0
0
3
0
0
0
0
0
2
2
1
0
2
1
0
0
0
0
0
1
0
0
1
0
0
1
2
0
0
0
0
0
0
0
1
3
2
0
1
1
0
2
0
0
0
1
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
3
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
2
2
2
1
0
3
2
0
1
0
0
0
0
0
0
0
2
2
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
1
0
0
1
1
0
0
1
0
0
0
2
2
1
1
0
0
0
0
0
0
1
0
0
0
5
0
1
0
0
2
2
2
0
10
0
0
1
0
2
1
0
0
0
0
0
2
1
0
1
0
2
1
1
0
0
2
1
0
2
0
1
0
0
0
0
2
0
8
0
1
2
0
0
1
0
2
0
2
1
1
1
2
1
0
1
1
1
1
2
0
0
3
1
0
2
1
0
0
0
0
0
1
0
1
1
0
0
2
0
0
0
2
1
0
2
0
1
1
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
2
1
0
0
0
0
1
0
2
2
0
0
2
4
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
1
0
0
1
1
2
0
0
2
2
0
0
1
2
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
1
0
1
1
0
0
1
0
0
2
1
0
4
0
1
1
1
2
2
0
2
2
0
1
1
0
1
0
2
0
1
0
2
1
0
0
0
0
1
4
0
1
1
0
1
2
0
0
2
2
0
2
0
1
1
2
1
1
1
0
2
0
1
0
3
2
0
1
1
4
0
0
1
0
0
0
0
1
2
1
0
1
2
0
2
0
1
0
1
0
0
0
2
0
1
2
0
1
0
0
0
0
0
0
1
1
2
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
1
1
0
6
2
0
0
2
1
1
0
0
0
0
1
0
0
2
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
1
2
1
0
0
0
0
0
0
2
2
0
0
0
1
1
2
1
1
1
2
1
0
1
2
0
1
0
0
0
2
0
0
2
0
3
2
0
0
0
0
0
0
1
1
1
3
0
2
0
3
0
0
0
2
1
1
0
1
2
0
1
2
0
0
1
0
0
2
1
1
0
0
2
1
0
1
0
0
1
2
0
2
1
1
0
1
0
0
1
0
1
2
2
2
0
0
0
0
2
0
2
0
2
2
0
0
1
1
0
1
0
2
0
1
0
0
1
0
1
0
1
1
2
1
0
0
0
0
1
2
0
0
0
2
0
0
0
2
0
1
1
0
1
2
0
2
0
1
2
0
3
0
0
0
2
0
1
0
3
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
1
0
2
1
0
0
2
0
0
0
1
2
0
0
1
0
2
1
0
0
2
0
2
0
2
2
1
2
1
0
0
1
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
2
1
5
2
0
1
0
1
0
2
1
1
2
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
1
0
2
2
0
2
0
0
2
0
2
0
0
1
1
0
1
0
0
0
0
1
0
1
2
0
2
0
0
2
0
2
1
2
2
4
0
0
1
0
3
1
1
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
2
0
2
0
2
0
1
1
1
0
2
0
1
0
0
0
0
2
0
0
0
1
0
2
0
0
1
2
0
1
1
0
2
0
0
0
0
0
1
0
1
1
2
0
2
1
1
2
1
1
0
1
0
1
0
0
0
0
0
0
2
1
0
1
0
0
0
1
2
0
1
0
0
1
0
1
0
1
2
1
3
0
2
0
0
0
0
0
2
1
1
2
1
2
1
1
0
0
0
0
0
0
1
2
1
0
0
0
0
1
2
0
1
0
1
0
0
2
0
0
0
0
2
0
2
2
0
1
0
0
0
0
2
0
1
1
0
0
1
0
0
1
2
0
2
2
0
1
2
2
0
1
0
0
0
2
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
2
2
1
2
2
0
0
1
0
4
0
2
0
0
0
0
0
0
6
0
0
2
0
0
0
0
0
0
1
0
2
2
0
2
1
0
0
0
0
2
0
1
1
0
0
0
1
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
7
0
2
0
2
1
0
0
1
0
0
1
0
0
0
0
0
1
1
1
1
1
0
1
0
1
0
2
0
0
2
0
0
1
2
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
2
1
2
0
0
1
0
0
0
0
2
0
1
0
0
1
0
0
0
0
1
1
2
0
2
1
2
2
1
1
0
3
0
0
0
0
1
0
0
1
0
2
0
3
0
1
2
0
0
1
0
1
0
0
1
2
0
1
2
0
2
0
3
0
0
0
0
0
1
0
1
1
0
0
1
4
0
0
2
0
0
0
0
2
0
0
2
0
0
2
0
2
0
1
0
0
1
1
0
2
0
1
0
1
1
0
0
2
0
1
0
2
0
1
0
0
0
0
0
0
1
2
1
2
0
2
2
1
2
0
0
0
2
0
1
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
1
0
2
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
2
2
0
0
0
1
2
2
1
0
2
0
1
0
2
0
0
1
0
0
2
2
2
0
2
0
0
0
0
0
0
2
0
1
2
2
1
0
1
1
0
0
1
1
0
0
0
0
1
0
1
1
0
1
2
0
0
1
0
0
2
0
2
0
2
0
2
0
0
1
1
1
0
0
1
0
2
0
0
2
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
1
2
1
0
0
2
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
1
0
1
1
0
0
0
1
0
1
0
0
2
1
2
1
1
1
0
1
0
0
2
1
0
0
1
2
0
0
0
1
0
0
0
1
0
0
0
0
1
1
4
1
0
1
2
0
1
1
0
3
2
1
0
0
0
0
0
0
0
1
1
2
2
0
1
0
1
0
0
1
2
2
1
0
0
0
0
1
0
2
0
0
0
2
2
0
2
0
0
2
2
0
2
1
0
0
1
0
0
0
2
0
1
0
0
2
0
1
0
0
2
0
1
1
2
0
0
0
0
1
0
0
1
0
0
0
0
1
2
1
1
0
2
0
0
0
3
0
0
0
0
0
0
0
1
0
1
1
2
0
2
0
1
0
0
0
1
0
0
0
0
1
0
3
2
0
0
2
1
0
2
0
1
0
2
2
0
1
0
1
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
2
1
1
2
1
0
0
0
0
0
0
0
1
0
0
0
1
0
2
1
2
2
2
0
0
2
0
1
0
1
2
0
0
0
0
0
0
1
0
0
0
6
0
1
0
0
0
3
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
1
1
1
1
2
1
0
0
1
1
0
1
0
0
0
1
2
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
2
1
1
2
0
1
1
0
1
1
0
0
0
0
2
1
1
1
0
2
0
1
1
0
1
0
0
0
2
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
2
0
0
0
0
0
1
1
2
1
2
0
2
0
1
1
0
0
2
0
2
2
2
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
1
0
1
1
0
0
2
1
2
0
0
2
1
4
4
0
2
1
2
2
0
2
1
1
1
0
0
2
0
1
2
1
0
0
0
2
0
2
0
1
0
0
2
0
1
0
0
0
1
1
2
0
0
0
2
0
2
0
0
0
1
0
2
0
0
2
2
2
0
0
0
0
1
1
2
1
0
0
0
1
0
0
0
1
0
1
2
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
2
1
2
1
0
0
0
2
0
5
0
1
0
0
0
0
2
0
0
0
2
1
0
0
1
2
0
0
0
0
2
2
2
0
2
0
0
0
1
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
1
2
2
0
1
2
0
0
1
0
1
0
0
2
0
0
2
0
0
0
0
0
2
4
2
2
3
3
2
0
0
1
0
0
1
1
0
0
0
0
1
0
0
1
0
0
2
2
1
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
1
2
0
0
0
0
1
0
1
2
2
0
0
0
0
0
0
2
0
1
0
0
0
2
1
0
2
0
0
0
2
0
1
0
2
2
0
4
1
2
1
0
0
0
2
0
0
1
5
0
1
2
0
1
2
0
1
0
0
2
0
0
1
1
1
0
2
0
0
1
0
0
0
0
1
1
1
0
2
0
0
0
1
2
1
2
2
1
0
1
2
0
1
0
2
0
0
0
1
2
0
0
2
0
0
2
1
0
0
3
1
0
1
0
0
0
1
0
0
2
1
2
0
1
1
0
1
0
2
0
1
1
0
0
1
0
1
2
2
0
0
0
0
2
0
0
1
1
1
1
1
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
1
1
0
1
3
1
0
0
0
0
0
0
0
2
2
2
2
2
1
0
0
0
0
1
1
2
2
0
0
0
2
0
0
2
0
0
1
1
1
0
0
0
0
0
0
1
0
2
0
0
0
1
2
0
0
0
1
0
0
0
1
0
0
1
1
0
4
0
0
1
2
0
1
1
1
0
2
1
0
1
0
1
1
1
0
1
1
1
0
1
2
2
0
0
2
0
0
2
0
0
0
2
1
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
2
0
1
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
2
2
0
0
1
0
0
0
2
1
2
3
0
0
0
0
1
0
3
1
0
0
0
2
1
0
0
0
2
0
0
2
3
1
0
0
1
0
0
0
1
0
0
2
0
0
2
2
2
1
0
0
1
1
0
0
1
3
0
0
2
4
2
2
0
0
0
1
1
3
0
0
0
0
0
0
0
1
1
0
1
0
0
3
0
1
0
0
3
1
3
0
0
1
2
0
0
0
1
0
1
1
2
2
1
0
0
0
2
0
1
1
2
0
0
0
0
0
0
2
0
1
0
0
0
0
1
2
0
1
1
2
2
0
1
0
0
1
0
1
0
1
0
2
1
0
1
1
0
0
0
0
1
2
1
0
2
0
1
0
0
0
1
0
1
0
2
0
0
1
2
0
0
1
0
0
0
1
3
1
0
0
0
1
2
2
1
2
0
0
1
1
2
2
1
1
0
0
0
1
1
0
2
1
0
2
0
0
0
0
0
0
1
0
1
2
0
1
3
2
0
0
1
2
1
2
0
0
1
0
1
0
2
1
0
1
1
0
1
3
2
0
0
0
0
0
0
0
0
3
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
2
0
0
1
1
0
0
2
0
2
0
0
0
0
1
0
0
1
1
2
0
0
0
0
0
0
1
2
0
0
1
0
1
0
1
0
0
1
0
1
0
2
0
0
2
0
0
1
2
0
0
0
1
2
0
0
2
0
0
2
1
1
2
0
0
1
0
1
1
0
0
1
0
0
1
0
1
0
1
0
1
1
1
0
0
1
2
0
0
0
2
2
1
1
0
1
1
1
0
0
0
1
3
2
1
2
0
0
0
0
3
2
1
2
2
0
0
0
2
0
0
2
0
3
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
1
1
1
2
0
4
0
2
0
1
0
1
2
0
0
0
1
1
2
0
1
0
1
0
2
0
0
0
0
2
1
2
2
2
2
0
1
1
0
0
0
0
0
1
1
0
2
2
0
0
1
2
0
1
4
1
0
2
0
0
1
2
0
0
0
2
0
0
0
0
0
0
1
1
0
0
2
2
0
1
0
1
4
1
1
0
1
0
5
2
2
0
1
0
0
0
0
2
0
1
0
0
0
1
0
0
0
2
2
0
0
1
0
0
0
2
0
1
0
2
1
0
1
0
0
0
0
2
0
1
0
2
0
0
0
2
0
1
0
0
1
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
2
2
0
0
2
0
1
0
0
1
0
0
0
0
0
2
0
0
0
1
2
2
0
0
0
2
0
2
0
0
0
1
0
1
4
0
0
0
2
0
0
1
1
1
1
2
0
0
0
2
0
0
0
1
2
2
1
1
0
0
0
1
1
2
0
2
1
0
2
1
0
0
1
1
1
1
0
1
0
4
1
2
1
0
0
0
0
0
0
1
2
0
0
2
0
0
1
1
1
0
1
1
0
2
0
1
0
1
0
1
1
2
3
1
0
2
0
1
0
0
3
0
0
0
1
0
0
1
0
1
1
0
0
0
2
1
0
1
0
0
1
1
0
1
2
1
0
0
1
0
0
0
1
0
0
0
2
2
0
1
2
0
0
1
0
1
0
1
1
1
1
1
1
0
0
2
2
0
0
0
0
0
1
1
0
3
2
0
2
0
1
0
0
2
0
1
0
1
3
6
1
0
0
2
1
1
1
2
2
1
0
0
0
1
1
0
0
0
0
2
0
1
2
0
0
1
3
0
1
0
2
1
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
2
1
3
0
2
0
0
1
1
1
1
0
1
0
0
2
0
0
0
1
0
0
1
0
0
1
1
0
1
0
0
0
1
1
0
1
2
2
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
1
1
0
0
1
1
3
0
1
0
0
0
1
0
0
0
1
1
1
1
0
0
0
1
0
2
0
0
1
0
0
0
2
0
3
0
0
0
2
0
0
0
2
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
2
1
2
0
1
0
0
0
1
0
1
2
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
2
0
0
2
1
1
2
2
0
0
2
1
0
1
0
0
1
0
0
0
0
3
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
1
1
2
0
1
0
0
5
2
0
2
2
0
0
2
0
2
0
1
0
0
2
1
1
4
0
0
1
0
0
0
0
0
0
1
0
0
1
2
0
0
1
0
2
2
2
1
1
0
0
2
1
0
0
0
2
0
0
0
3
0
1
1
1
0
0
1
0
0
0
0
0
2
0
2
0
2
1
4
0
1
0
1
0
0
0
1
0
1
0
0
2
1
1
0
0
0
0
0
1
0
0
1
0
1
0
2
2
1
0
0
0
0
0
2
1
0
0
0
1
1
0
1
0
0
1
0
0
1
1
0
1
1
2
0
0
0
1
0
0
1
2
1
0
1
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
1
0
0
0
1
0
1
1
1
0
0
3
2
2
0
1
0
2
1
4
1
0
1
0
0
2
0
2
0
0
1
1
1
2
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
1
0
2
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
1
0
0
0
1
2
0
0
2
0
1
0
2
2
0
2
2
1
0
0
2
0
0
2
1
0
0
1
0
1
0
0
0
0
1
0
0
0
1
2
0
2
0
0
0
1
0
1
1
0
0
2
0
0
0
0
0
0
0
0
3
0
2
2
1
0
1
2
0
1
2
0
0
2
2
0
1
0
1
0
0
0
0
2
1
2
1
0
0
1
0
1
1
0
2
0
1
0
1
0
2
0
1
0
2
0
0
0
3
0
0
0
0
0
1
0
0
1
0
0
0
2
4
0
0
1
0
1
1
0
0
0
0
0
1
1
0
0
2
1
1
0
1
1
1
1
0
2
0
2
0
0
0
1
0
1
5
0
1
0
1
1
2
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
2
1
0
0
0
0
2
0
2
1
0
0
1
1
0
1
1
1
0
1
2
0
2
0
0
2
1
2
2
2
1
2
0
2
0
0
2
2
2
0
4
1
0
0
2
0
0
1
0
0
0
0
0
1
1
0
1
1
2
0
1
1
0
0
0
0
1
0
1
0
0
1
1
0
0
1
0
0
0
3
0
2
0
1
2
1
1
0
2
2
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
2
1
0
1
1
1
0
1
1
0
1
0
0
1
2
1
0
1
1
0
0
2
0
1
2
0
1
1
0
2
0
0
2
0
0
2
0
0
0
0
0
2
2
2
2
0
0
1
0
0
2
1
1
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
1
0
0
1
1
0
0
3
1
1
0
0
0
1
0
0
2
1
0
1
0
0
2
0
0
3
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
2
2
0
0
2
1
0
0
0
2
0
0
0
0
1
2
2
2
1
0
0
2
0
2
0
1
1
0
2
1
1
0
0
1
0
1
0
0
0
5
0
0
0
2
2
2
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
2
0
1
0
2
1
0
0
2
1
1
0
2
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
2
0
1
0
0
7
2
1
0
0
0
2
0
1
0
0
1
0
1
1
1
0
0
2
3
1
0
0
0
0
0
0
1
1
0
2
0
2
0
1
0
0
0
0
2
1
2
0
0
2
0
0
0
0
0
2
1
0
2
0
0
0
0
0
1
2
1
0
0
0
1
2
2
2
1
2
0
0
0
0
0
0
0
1
0
2
1
2
0
0
1
0
0
0
3
2
0
0
0
0
1
1
1
0
0
0
1
0
1
1
1
0
0
0
0
2
0
0
1
0
1
0
1
0
2
1
0
2
1
0
0
0
1
0
0
0
1
0
0
0
3
0
0
0
2
0
1
3
0
2
0
3
1
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
4
0
1
2
0
1
0
0
0
0
0
1
1
1
0
1
0
2
2
0
0
0
0
1
0
2
0
0
0
1
0
3
4
1
1
1
0
0
1
0
0
0
1
0
0
0
0
2
2
1
2
0
0
0
1
0
1
2
0
0
2
0
0
0
1
1
0
0
0
0
0
1
0
0
1
2
0
1
2
1
0
2
0
0
2
0
0
1
0
2
1
0
1
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
1
0
3
0
0
1
1
2
0
0
0
1
1
2
1
0
0
2
1
1
1
0
2
0
1
0
0
0
1
0
1
0
2
0
0
0
2
0
0
2
0
0
2
0
2
2
2
0
1
1
0
0
2
1
0
1
1
2
1
0
0
2
2
0
1
2
1
1
0
1
0
0
0
0
0
0
0
3
1
3
1
0
0
0
0
0
0
1
2
2
0
2
1
0
1
0
0
0
0
0
2
0
1
1
3
0
2
0
1
0
0
1
17
2
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
1
0
0
0
1
2
0
2
0
1
0
0
2
0
1
2
1
2
1
0
2
0
2
0
2
2
1
0
2
0
5
2
3
0
0
1
0
1
0
0
1
5
0
0
0
1
2
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
2
0
0
2
2
2
0
1
0
0
0
0
1
2
0
2
1
0
2
0
0
0
0
2
1
0
1
0
2
0
0
0
1
2
0
0
1
1
0
0
2
1
1
3
0
0
1
2
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
1
1
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
1
2
0
1
0
1
1
0
0
2
0
1
1
0
0
0
0
0
1
0
0
0
1
0
1
2
0
2
0
0
1
6
1
0
0
0
1
1
0
1
1
0
2
0
0
2
0
0
1
0
0
2
1
1
0
2
0
3
0
2
0
2
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
2
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
5
0
2
1
0
0
0
1
0
1
0
1
0
1
1
1
0
0
1
1
2
0
1
2
0
0
0
0
0
0
1
2
0
2
0
0
2
1
2
2
0
0
1
0
1
0
1
1
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
2
2
0
0
0
0
0
0
2
1
0
2
0
2
1
1
0
0
2
1
2
0
2
1
0
2
2
0
2
1
0
2
0
1
0
0
0
2
0
0
1
0
1
1
2
2
1
1
0
1
2
0
0
1
0
2
1
0
2
0
2
0
3
1
2
0
1
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
1
0
0
2
0
1
0
0
0
2
2
1
2
0
1
2
2
0
2
0
3
0
0
0
0
2
0
1
0
0
1
0
1
2
1
0
0
0
3
2
1
0
0
1
0
0
1
1
1
0
0
0
1
5
0
2
1
2
2
2
0
0
1
1
1
0
3
3
1
1
0
1
1
0
0
1
0
2
0
0
2
0
0
2
2
1
0
0
2
0
2
0
1
1
0
0
0
0
2
1
0
2
0
0
2
0
0
1
0
0
2
2
0
2
3
0
1
2
1
0
0
1
0
0
1
0
0
0
2
0
5
2
2
2
0
0
0
2
0
1
2
0
2
2
0
1
1
0
0
0
2
0
2
0
0
0
1
0
2
0
0
1
2
0
0
0
0
0
1
2
0
0
2
1
0
0
2
0
0
0
0
1
1
1
0
0
3
2
2
0
1
0
2
0
0
2
0
1
2
0
0
2
0
1
1
1
0
0
0
0
0
0
0
0
2
0
1
0
0
1
1
3
1
3
1
2
1
1
1
1
2
3
1
0
0
0
2
0
1
2
2
0
0
0
0
1
1
2
0
0
0
0
0
0
1
1
2
0
0
2
2
0
2
2
1
0
0
0
2
1
2
0
2
1
0
0
1
0
0
0
0
0
1
1
2
0
2
0
0
0
1
0
0
2
0
0
1
0
0
0
1
2
1
0
0
2
0
0
0
2
1
0
1
0
0
1
1
0
0
1
0
0
0
0
1
0
1
1
0
1
2
0
0
0
1
0
0
2
2
0
2
0
2
0
1
0
0
2
0
0
1
1
1
2
0
0
0
0
1
0
2
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
3
2
1
0
1
0
0
1
2
0
0
0
0
0
0
1
0
1
0
1
2
2
1
2
1
1
3
0
0
2
0
1
2
1
0
2
0
2
2
2
1
2
1
2
0
1
0
0
0
0
0
2
0
0
2
4
0
0
0
0
0
0
0
1
2
1
0
0
0
1
1
0
1
0
0
0
2
0
1
1
0
2
1
1
0
0
0
0
2
0
1
2
2
0
1
0
2
2
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
1
2
0
0
0
2
0
0
0
1
1
0
0
2
2
2
1
1
0
1
1
0
1
2
0
0
4
0
0
0
0
2
0
2
0
0
0
1
2
1
1
0
1
0
1
0
0
1
1
0
0
1
2
2
0
0
1
1
2
0
0
0
0
1
0
0
1
0
0
0
1
2
0
0
0
0
2
0
1
0
0
1
0
1
0
0
1
0
3
0
1
0
0
2
0
0
0
0
0
2
2
0
5
2
0
0
2
0
0
0
1
0
0
2
0
0
0
0
1
1
2
0
1
0
1
2
1
0
0
0
0
1
1
1
0
0
1
1
0
2
0
0
1
0
1
1
0
0
0
1
2
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
2
0
2
0
1
1
1
0
2
0
0
1
2
0
1
1
2
0
1
0
1
2
0
0
0
0
0
2
0
2
0
2
1
0
1
1
2
2
0
2
0
0
0
1
0
2
1
3
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
2
1
0
2
2
0
0
0
0
1
2
1
0
1
0
0
0
1
0
0
0
2
1
0
0
2
0
0
0
1
2
0
2
2
0
0
2
0
1
0
1
0
2
2
0
0
0
1
0
1
0
0
1
0
2
2
1
0
0
0
2
2
2
0
2
1
0
1
1
0
1
3
2
2
0
2
3
2
0
2
0
2
1
1
2
1
0
1
1
1
0
1
1
1
0
2
0
0
0
0
0
2
0
2
0
2
1
1
2
1
2
0
2
0
2
0
0
1
0
0
0
0
1
1
2
0
1
0
1
0
0
2
2
1
0
0
1
0
1
2
0
0
0
0
1
0
2
0
1
0
0
1
1
0
0
3
0
0
0
1
2
1
0
0
0
0
2
1
2
0
0
0
2
0
2
1
2
0
0
0
2
0
0
3
0
2
3
1
0
2
2
0
0
0
1
0
1
0
0
1
0
0
0
2
1
1
2
1
1
0
0
1
0
1
2
0
0
0
0
0
2
3
1
1
0
0
1
2
0
0
1
1
1
0
0
0
0
2
0
0
0
2
0
1
1
1
0
2
0
0
0
1
2
3
0
0
0
2
0
1
0
2
0
1
0
1
3
0
0
0
1
1
1
0
0
0
1
0
2
0
2
0
0
1
0
1
1
0
3
2
1
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
1
2
2
0
0
2
2
0
0
0
1
2
0
2
0
2
6
0
1
0
2
2
0
1
0
1
0
0
1
0
1
2
2
1
1
0
0
1
1
2
1
4
1
2
0
0
0
0
1
0
1
0
2
0
1
0
0
1
0
0
1
2
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
2
1
1
1
0
0
2
1
0
1
2
0
2
0
1
1
0
2
0
1
2
0
2
0
0
1
0
0
0
0
2
0
1
0
2
2
0
0
0
2
2
2
0
0
0
1
0
1
1
0
0
0
2
0
1
0
3
0
0
0
0
1
0
0
0
2
0
0
0
1
2
0
0
0
2
1
0
0
2
1
0
0
0
2
0
0
0
0
0
1
0
3
1
2
0
0
0
0
0
0
2
1
0
0
2
2
1
0
0
0
0
2
0
1
0
1
0
0
0
0
1
1
1
2
2
1
1
0
0
2
1
0
1
0
0
0
0
2
0
1
1
0
0
0
1
2
0
0
1
0
1
0
2
0
0
0
2
0
1
2
0
4
2
0
0
0
0
0
2
0
0
1
0
0
0
1
1
1
1
2
0
0
0
0
0
0
0
1
0
2
1
1
0
0
2
2
2
2
2
2
0
2
1
0
4
2
1
0
0
2
1
0
0
2
1
0
0
0
0
1
0
0
0
3
2
0
2
0
0
0
0
0
0
0
2
1
1
0
3
2
0
0
0
0
0
1
0
2
0
0
2
1
2
1
0
0
1
1
4
1
2
0
7
1
0
1
0
1
1
1
0
0
0
1
1
0
2
1
0
1
0
0
0
0
0
1
0
2
0
0
3
0
1
0
1
0
1
2
2
1
0
1
0
1
1
0
2
2
1
0
0
0
0
0
0
1
1
2
0
2
0
0
0
2
0
0
0
2
2
0
0
1
0
0
2
0
2
0
1
3
4
1
1
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
2
1
1
0
0
0
0
1
1
1
1
1
1
0
1
1
0
2
1
0
0
1
1
2
0
0
0
0
0
1
2
2
0
2
0
0
0
1
0
0
0
0
1
1
1
1
0
0
0
1
0
0
2
0
0
2
0
0
2
0
2
4
1
1
0
0
0
0
0
0
2
1
0
1
2
0
1
0
0
0
1
0
1
0
1
2
0
1
0
0
0
0
1
2
0
0
2
1
0
2
0
0
0
0
1
1
1
2
0
2
1
0
0
0
2
0
0
1
2
2
0
1
0
0
0
1
1
0
2
1
2
0
0
1
1
1
1
0
2
0
2
0
0
4
0
0
1
0
0
1
0
0
0
2
0
2
0
0
2
1
0
0
2
0
1
0
2
1
0
0
3
1
0
2
0
2
0
2
0
2
2
2
1
1
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
1
0
1
0
0
2
1
1
2
2
0
0
0
0
0
2
2
2
0
0
1
1
1
2
1
0
1
0
0
1
1
0
2
0
0
0
2
2
0
0
1
0
0
0
0
0
1
2
2
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
2
0
1
1
2
0
1
0
1
0
1
1
0
0
1
2
1
0
0
2
0
1
0
2
0
1
1
0
0
0
0
2
0
0
1
0
0
1
2
0
0
0
0
0
1
0
2
0
0
1
0
1
0
0
0
0
2
1
0
1
2
0
0
2
1
1
0
1
1
3
0
0
2
1
2
2
0
0
1
2
2
0
1
0
0
0
0
2
1
1
1
0
1
3
0
1
0
2
0
0
1
0
1
0
1
0
0
0
0
0
1
0
2
0
0
0
2
0
1
0
0
0
0
0
2
0
1
2
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
2
0
0
1
1
1
0
2
2
0
0
1
0
0
1
1
0
0
0
0
2
2
0
1
1
1
2
0
0
0
0
2
2
2
0
0
1
1
0
0
0
4
2
0
1
0
2
1
0
3
0
0
0
0
1
0
1
1
0
0
1
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
1
2
2
0
0
0
1
0
0
1
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
2
0
1
0
0
3
2
1
1
2
1
1
0
0
2
0
0
2
1
1
0
1
2
1
0
0
3
0
0
2
2
0
0
0
0
2
0
0
0
2
2
1
0
1
1
1
0
0
0
0
2
2
2
0
1
2
1
1
0
0
2
1
2
1
1
1
2
0
3
0
0
2
2
0
0
0
2
0
2
0
0
0
0
0
1
1
2
0
0
1
0
0
0
0
1
0
2
0
2
0
0
1
2
2
0
0
0
0
1
4
0
0
2
2
0
1
3
0
0
0
0
2
1
0
0
0
2
0
3
0
0
1
1
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
1
2
0
1
0
4
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
1
0
2
0
1
0
1
0
0
2
1
0
0
2
0
2
0
2
0
2
1
0
0
0
1
2
0
1
0
1
0
2
0
1
0
1
0
0
0
3
0
0
1
1
2
0
2
1
2
0
0
0
0
0
0
0
0
1
2
0
0
0
2
1
0
0
1
0
0
0
1
1
0
2
0
0
2
0
0
2
3
0
0
1
0
0
2
0
0
1
0
2
1
0
1
0
0
0
0
1
1
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
3
2
0
2
0
2
0
2
0
2
2
0
0
0
2
0
2
1
1
2
0
1
1
1
1
0
2
0
1
0
0
1
1
2
2
0
0
1
2
0
1
2
1
2
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
1
0
0
0
0
0
2
0
0
1
1
2
0
0
1
0
2
2
2
0
2
1
2
0
2
2
0
0
0
1
1
1
1
2
0
1
1
2
0
1
1
0
0
0
0
0
2
0
0
0
0
2
2
2
2
0
0
0
0
1
2
2
1
1
0
3
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
1
0
1
2
0
0
0
0
2
1
1
1
0
0
2
0
4
0
0
0
0
0
0
1
1
1
0
0
0
2
0
0
2
0
1
0
0
0
0
3
0
2
0
1
0
0
0
0
0
1
0
1
0
1
0
2
2
0
0
2
0
0
0
1
2
0
0
1
0
3
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
2
0
0
0
2
0
0
1
0
0
0
2
0
2
0
0
1
0
0
1
0
0
0
0
3
0
2
1
1
0
0
1
1
0
1
1
2
1
0
2
2
0
0
1
0
2
0
2
2
2
2
0
1
1
2
0
2
1
0
0
1
0
0
1
2
1
2
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
2
0
1
1
2
0
1
0
1
1
2
1
1
0
2
0
0
1
2
0
1
2
0
1
1
0
2
1
2
1
0
2
0
2
1
1
1
1
1
2
1
0
0
2
0
0
0
1
1
0
1
1
0
0
0
0
0
1
0
1
0
1
0
0
0
2
0
0
1
0
0
1
2
0
0
0
0
1
0
0
0
1
0
0
0
2
0
1
0
0
1
2
1
1
1
2
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
2
3
2
2
2
1
2
1
1
0
1
2
0
0
0
8
2
0
0
1
2
0
0
0
0
2
0
0
0
1
0
2
0
2
0
0
1
0
1
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
2
2
1
2
1
0
0
0
0
2
0
1
0
2
0
0
0
2
0
1
0
1
0
0
1
0
2
0
0
0
0
0
1
0
0
1
2
0
2
0
0
0
1
1
0
2
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
1
0
0
2
1
3
0
0
0
1
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
4
0
2
1
2
1
1
0
2
0
0
0
1
0
0
0
2
0
0
2
1
0
0
1
0
0
2
1
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
2
1
1
1
0
0
0
0
0
0
0
2
0
1
0
0
10
2
0
2
2
0
2
0
0
1
0
1
2
2
0
1
0
1
0
0
2
1
2
0
0
0
1
2
2
0
3
2
0
1
2
3
4
0
1
0
2
1
0
0
1
1
1
0
1
0
0
0
2
2
2
0
0
0
0
1
0
0
0
1
1
0
2
2
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
1
2
1
0
2
0
1
1
0
2
2
0
1
2
0
1
0
1
1
0
0
1
2
2
0
0
0
0
0
0
2
2
0
1
1
0
0
1
1
0
1
0
1
0
0
0
1
2
0
6
0
1
0
0
0
0
3
0
1
0
0
0
1
0
0
0
0
1
1
0
1
1
1
0
0
0
2
0
1
0
2
1
2
0
1
0
0
0
1
1
0
2
1
2
1
0
1
0
0
2
2
0
0
2
1
1
0
1
1
1
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
1
1
1
3
0
0
0
0
0
1
1
0
0
2
1
0
1
0
0
2
0
0
0
1
2
0
1
1
2
0
2
2
0
2
0
2
2
0
1
1
2
2
2
0
1
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
1
0
2
1
2
0
1
0
0
1
0
0
0
0
2
0
0
1
1
0
0
0
2
0
0
1
1
0
0
2
0
0
0
1
1
2
1
0
0
2
0
2
0
0
0
0
0
0
2
0
0
2
0
0
2
1
0
0
1
2
0
1
0
0
0
0
0
1
2
1
0
0
0
1
1
1
0
0
0
0
1
2
2
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
2
1
0
5
0
0
0
1
2
0
2
0
0
2
2
0
2
1
1
2
1
0
0
1
0
0
1
2
1
0
1
0
0
1
0
0
1
0
1
2
0
1
2
0
0
1
0
0
1
1
1
1
0
2
0
0
0
1
1
0
2
0
2
1
1
0
0
0
2
2
0
2
1
2
1
2
1
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
2
0
1
0
2
0
0
0
0
0
0
1
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
1
0
0
2
0
0
0
2
2
0
1
0
0
0
0
0
3
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
2
2
0
0
0
0
1
2
0
0
7
2
0
0
0
0
1
1
2
0
0
1
0
1
0
1
0
1
0
2
0
2
0
1
1
0
0
0
0
1
1
2
0
0
1
2
1
0
2
0
0
1
1
0
2
1
0
0
1
0
4
0
0
1
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
2
2
0
0
0
0
1
1
0
0
1
2
0
2
0
0
0
1
0
0
0
2
0
2
0
0
1
0
1
0
0
0
2
0
1
1
0
0
2
1
1
2
1
1
0
0
0
1
0
2
2
1
1
0
2
1
0
0
1
0
0
0
0
0
0
1
1
2
0
2
1
0
0
0
0
1
0
1
0
2
2
0
1
2
2
0
0
2
0
0
0
0
1
2
0
0
0
0
2
1
0
0
0
1
0
2
0
0
0
0
1
1
1
2
0
0
2
2
0
0
2
0
0
1
0
0
2
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
1
0
2
0
0
1
1
1
1
0
5
0
2
0
0
0
0
0
1
0
1
2
1
1
3
0
2
1
1
0
1
0
2
2
1
1
0
0
1
0
1
2
0
2
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
2
0
0
1
0
0
0
1
1
0
0
0
2
2
4
1
0
0
0
0
2
1
1
0
1
1
1
0
0
0
1
2
0
0
2
0
1
0
1
0
0
3
3
0
0
1
1
0
0
0
2
2
2
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
2
1
1
0
0
1
0
1
0
2
1
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
2
2
0
0
1
0
0
0
0
0
0
1
2
1
0
1
2
1
0
2
1
0
1
0
1
0
1
1
0
0
1
2
0
1
0
0
0
2
0
0
1
0
0
0
1
1
2
1
0
0
0
5
0
0
1
0
1
2
0
6
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
2
1
2
2
0
2
0
1
0
2
2
0
2
0
0
0
0
0
0
2
2
0
2
2
0
2
0
0
1
0
0
1
0
2
0
0
0
2
2
0
1
2
0
0
0
0
2
1
0
2
0
5
1
0
1
1
3
0
2
1
1
1
0
0
2
0
2
0
0
2
0
2
2
1
2
1
1
2
1
1
1
0
0
1
1
2
1
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
2
2
2
0
1
0
0
0
0
1
0
1
0
0
1
1
0
0
2
1
0
0
1
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
2
0
0
1
0
2
0
0
1
0
2
0
0
1
0
2
0
1
0
2
1
0
0
3
0
0
0
0
0
1
0
0
1
2
0
2
1
1
0
2
1
0
0
1
1
0
0
2
1
0
0
1
0
0
2
0
2
0
0
0
1
0
0
1
0
0
0
1
2
0
0
0
1
0
0
1
0
2
2
2
0
0
0
1
0
0
0
0
3
2
0
0
0
1
1
0
0
1
0
1
0
1
0
1
1
1
0
0
0
0
1
0
0
1
0
1
0
0
0
2
0
2
2
1
1
0
0
1
3
2
0
1
0
0
0
0
1
0
0
1
3
0
0
2
1
0
2
0
0
1
0
0
0
0
2
1
0
4
1
2
0
0
0
0
0
0
0
1
0
0
0
1
2
1
0
1
1
0
1
0
2
0
0
2
0
0
0
0
2
1
2
1
0
1
1
1
0
0
0
0
1
1
0
2
0
0
0
4
0
1
2
0
2
2
1
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
2
1
0
0
0
0
0
1
0
2
2
2
2
0
0
0
0
0
2
0
0
1
0
1
2
1
1
0
0
2
0
1
0
0
2
2
0
1
2
0
0
0
0
0
1
1
2
0
0
0
0
3
1
0
1
1
0
1
1
0
1
1
0
1
2
0
1
0
2
1
2
1
0
0
0
2
0
1
0
2
0
1
1
0
0
1
2
0
0
1
2
0
1
1
2
0
0
0
0
0
1
2
1
2
0
0
0
2
1
3
0
1
0
0
1
1
0
1
2
0
1
0
1
1
0
1
1
1
1
0
2
2
2
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
2
3
2
0
2
0
2
1
0
0
0
0
0
0
0
0
1
2
2
0
1
0
0
0
1
1
2
1
0
0
1
1
0
0
0
1
1
1
2
1
1
1
2
1
2
2
0
0
0
0
1
0
0
2
1
0
2
0
0
1
0
0
0
1
0
1
1
2
0
2
0
1
0
0
0
0
2
0
1
0
0
0
1
2
0
2
1
1
0
0
0
1
1
0
1
1
1
0
1
2
2
2
1
0
1
1
1
0
2
2
1
2
0
0
2
3
1
2
0
3
1
2
0
0
0
2
1
0
2
0
0
2
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
2
5
0
0
0
1
0
0
4
2
1
0
1
0
1
1
1
1
0
0
0
1
1
1
0
0
0
0
1
0
3
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
1
5
0
0
1
1
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
1
1
2
0
0
2
0
2
2
2
0
2
0
0
1
1
0
0
1
0
0
2
0
0
0
2
0
0
2
1
1
1
0
1
1
0
2
0
1
1
2
0
1
0
0
1
0
0
0
0
0
1
1
2
1
2
1
0
0
0
1
1
0
0
0
1
2
0
0
0
2
0
0
2
0
0
1
1
0
0
0
2
0
0
1
2
2
2
1
1
2
0
0
2
1
1
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
2
1
2
0
0
1
0
0
0
0
2
1
1
0
1
0
1
1
0
1
0
0
0
0
0
0
0
2
1
0
0
0
1
1
1
0
0
1
0
0
0
0
0
1
0
1
0
0
2
1
1
0
0
1
0
1
2
0
0
0
0
2
0
0
2
0
1
0
0
0
0
1
1
2
1
0
0
1
0
2
0
0
0
0
2
0
1
0
0
1
2
0
1
0
2
0
0
1
3
1
0
1
1
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
2
1
1
0
1
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
2
1
1
1
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
1
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
2
1
0
0
2
2
1
0
0
0
0
0
0
0
2
2
1
0
0
2
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
1
1
0
1
1
0
0
1
1
0
2
0
1
1
1
2
0
3
2
0
1
0
0
0
1
0
1
1
1
0
0
1
0
0
1
6
0
2
0
0
0
0
0
0
0
1
2
2
1
0
1
1
1
0
0
0
2
0
2
2
2
0
1
0
0
0
1
0
0
1
0
0
0
1
1
1
0
0
1
1
0
2
0
1
0
1
0
0
0
0
0
1
1
0
1
2
0
0
0
0
0
0
0
1
2
1
0
0
1
1
1
1
1
4
0
0
1
0
1
0
1
2
0
0
0
0
2
1
1
1
2
0
0
3
0
1
0
0
2
1
0
1
2
0
0
0
0
1
0
1
2
0
0
0
0
1
1
0
0
0
0
0
2
1
0
0
0
6
2
0
3
0
0
0
2
1
2
2
2
4
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
1
2
0
0
0
1
1
0
0
2
0
1
1
1
2
0
0
0
1
1
0
2
0
0
0
0
0
1
0
0
1
1
0
0
2
3
0
0
0
0
0
1
2
1
0
1
0
0
1
2
0
0
3
0
0
2
0
2
2
2
0
2
0
1
1
0
1
0
1
0
3
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
2
4
0
0
0
1
0
0
1
1
2
0
0
0
0
0
1
0
1
2
1
0
2
2
0
2
0
0
1
0
2
0
2
1
0
0
0
0
0
2
1
0
1
1
0
1
0
1
0
0
0
2
0
2
0
1
1
1
0
2
0
0
0
0
1
0
0
2
0
2
0
0
0
0
1
1
1
0
1
0
3
2
3
0
0
0
0
1
1
0
0
1
0
2
0
2
1
0
1
0
0
1
1
1
0
0
1
0
0
1
2
2
0
2
0
0
0
0
2
1
2
0
0
1
0
1
1
0
0
2
0
0
0
0
0
2
1
0
2
0
0
0
0
2
0
0
0
1
0
2
2
0
2
0
4
2
0
0
0
0
2
1
0
1
2
0
1
1
0
0
1
0
1
0
0
0
0
0
1
0
0
1
1
0
0
1
2
0
0
0
2
2
0
1
0
0
2
0
0
0
1
1
0
2
0
0
0
0
2
0
0
1
0
0
2
3
0
0
0
0
0
3
0
0
1
1
2
1
1
0
2
1
0
2
2
0
0
0
0
0
0
1
2
1
0
0
3
0
0
1
0
1
0
2
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
2
1
0
2
0
1
2
0
0
2
1
1
0
0
0
0
0
2
0
1
0
0
2
2
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
1
1
0
0
0
0
0
0
1
1
0
2
0
2
0
0
0
0
1
0
1
1
2
1
1
0
0
0
0
0
0
0
0
0
0
3
0
1
0
1
0
0
0
0
1
2
1
1
0
1
0
0
0
0
1
0
0
1
1
2
0
0
0
0
0
0
2
1
0
2
1
0
2
0
1
0
0
2
0
0
0
0
1
2
0
1
0
2
0
2
2
1
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
2
1
2
0
0
0
1
1
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
2
1
1
1
1
0
1
0
0
2
0
2
0
0
2
0
1
0
3
0
2
0
1
1
1
2
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
1
2
0
4
0
0
1
1
0
2
1
0
1
0
1
0
0
3
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
1
2
0
0
0
2
0
0
0
0
1
0
2
0
0
0
2
1
0
0
2
2
0
3
0
0
1
2
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
1
0
2
1
0
2
0
0
0
1
2
0
2
0
1
2
4
0
1
0
1
4
0
2
0
0
0
0
2
1
2
0
0
0
0
0
0
0
1
2
1
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
2
0
0
3
2
1
0
0
0
0
0
2
2
0
0
1
1
1
1
1
0
5
1
1
2
2
0
2
0
3
1
0
0
1
1
2
0
1
0
0
3
1
1
0
0
0
0
0
1
0
3
0
1
2
0
0
2
1
0
0
2
0
2
0
0
0
0
0
3
1
1
1
1
2
0
0
0
2
0
1
0
0
1
1
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
2
1
2
0
0
0
0
1
1
2
0
0
0
0
0
1
0
1
2
2
0
0
0
0
0
2
0
1
0
0
0
0
0
2
1
1
1
1
2
0
0
2
0
0
0
3
0
2
0
1
2
0
0
3
2
1
0
0
1
0
1
0
2
1
1
1
0
2
2
0
0
0
1
0
2
1
2
0
2
0
0
0
1
0
0
0
0
0
1
1
2
0
0
2
2
2
1
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
6
0
2
0
0
1
0
2
0
1
1
1
0
0
0
0
1
0
2
0
0
1
0
0
0
2
0
0
1
0
2
0
0
0
2
2
0
0
1
0
0
0
2
1
0
0
2
0
1
0
0
0
0
0
1
1
0
0
2
1
0
2
1
0
1
0
2
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
1
0
2
0
0
1
0
0
0
2
0
0
1
1
1
0
1
0
0
0
2
0
1
0
2
2
2
0
2
0
0
2
0
0
0
1
1
1
0
2
0
1
0
0
1
2
0
2
2
0
0
0
1
0
0
1
2
2
3
0
2
1
0
1
0
0
0
0
2
0
0
0
0
0
1
1
1
0
1
1
0
0
0
0
0
2
0
0
1
2
1
0
2
0
0
1
2
2
3
0
1
1
2
2
1
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
2
2
1
0
4
0
0
0
0
0
0
0
0
0
3
1
0
0
1
0
0
0
1
1
0
2
2
0
0
2
0
0
0
0
0
2
2
0
2
3
0
0
0
1
2
0
1
0
0
0
1
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
2
1
1
0
1
2
0
0
3
0
0
0
0
2
2
0
0
1
0
1
2
2
0
0
2
0
0
1
0
1
2
0
0
1
2
2
1
0
0
0
1
1
2
0
1
0
0
1
1
0
0
1
0
1
0
0
1
0
0
1
0
0
4
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
2
2
0
2
1
0
1
1
0
0
0
0
3
0
0
1
0
0
1
2
2
0
1
0
2
2
2
0
3
1
0
0
1
2
0
0
1
2
0
1
0
1
1
1
2
0
0
2
0
0
1
0
0
1
1
0
0
1
0
0
1
1
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
1
1
0
2
0
2
4
0
1
0
1
0
2
1
0
2
1
0
0
2
0
3
1
0
1
0
1
0
2
1
0
0
2
2
0
0
0
1
1
0
2
1
2
0
1
0
0
1
0
2
2
0
0
0
0
0
0
1
0
1
1
0
1
0
0
2
0
2
0
0
0
0
0
2
2
0
0
1
1
1
0
0
1
0
9
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
1
1
2
1
0
1
1
0
0
0
0
0
2
1
0
0
0
0
2
2
0
0
0
0
2
1
2
2
0
1
1
0
4
0
1
2
0
0
2
2
3
0
0
0
0
0
0
1
0
0
1
1
0
0
2
0
0
0
5
0
1
2
0
0
1
0
0
1
3
1
0
0
2
2
1
0
0
0
0
0
1
0
0
0
1
0
1
1
0
2
1
0
2
0
4
0
2
1
0
2
1
0
1
1
0
2
1
0
1
2
1
0
3
0
0
2
1
0
0
2
1
2
0
0
0
0
0
0
2
0
1
0
0
2
0
0
2
1
0
1
0
0
0
0
1
0
0
4
0
0
3
0
2
0
1
0
0
0
0
0
0
0
3
2
1
0
3
2
0
0
0
0
1
1
0
1
0
0
0
2
0
0
0
1
0
2
0
0
0
1
0
0
0
0
1
0
0
1
1
1
0
0
2
2
1
1
2
1
1
0
0
2
2
0
1
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
2
3
2
0
0
0
0
0
0
2
0
0
2
2
0
0
1
1
0
0
0
2
0
0
1
0
1
0
1
2
0
0
2
0
0
1
1
2
2
0
2
2
0
0
2
2
0
0
1
2
0
0
1
2
0
0
0
1
3
0
0
2
0
1
0
0
0
1
0
0
2
1
2
0
0
0
1
0
0
0
1
1
2
0
2
0
0
7
0
1
2
1
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
2
0
1
0
2
0
0
0
1
2
0
0
1
0
4
0
7
0
1
0
2
0
1
0
2
1
0
0
0
0
0
1
0
0
2
0
0
1
1
0
2
0
0
0
0
0
0
1
1
0
0
2
0
2
2
1
0
0
2
0
0
3
3
0
0
0
0
0
1
0
2
1
2
1
2
0
1
2
1
1
0
1
0
0
1
0
2
2
0
0
0
1
1
1
0
1
1
0
1
0
1
1
0
0
1
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
9
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
2
1
0
0
0
1
0
1
0
2
0
1
1
2
0
0
0
0
2
0
1
1
2
0
0
0
0
0
1
1
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
4
0
0
0
3
0
0
2
0
2
0
0
1
0
1
2
0
2
0
0
0
1
1
1
1
2
2
0
0
0
0
0
0
1
1
0
1
1
1
1
0
0
0
0
0
0
2
0
0
1
1
2
1
0
0
0
1
3
1
0
2
1
0
2
1
0
3
1
2
0
0
0
1
1
0
2
2
1
0
0
0
0
0
0
2
0
1
0
0
1
1
0
1
0
0
0
2
1
1
0
1
0
0
3
1
0
0
0
0
1
1
2
1
0
1
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
1
3
1
1
0
0
0
0
2
1
0
2
1
0
1
3
0
0
2
0
0
2
0
0
0
0
0
2
0
0
1
1
0
0
0
1
0
0
0
0
0
2
1
0
1
0
0
1
1
0
1
0
1
2
1
0
2
0
0
0
0
3
1
0
2
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
1
2
0
2
0
0
0
1
0
1
1
0
2
0
0
1
1
2
1
2
1
0
2
2
1
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
1
0
2
2
1
1
0
0
0
0
1
0
2
2
0
1
0
0
0
0
2
1
2
1
1
0
0
0
1
0
1
0
4
1
0
0
1
1
2
0
0
0
1
0
0
0
2
0
1
0
0
0
1
1
0
0
0
0
0
2
2
0
1
0
0
0
2
5
1
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
1
0
2
0
0
2
0
1
1
0
1
1
0
0
0
0
1
2
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
2
0
0
0
0
1
0
0
1
2
1
0
2
0
0
2
2
3
0
0
1
0
0
2
1
1
0
0
1
1
0
2
0
0
2
2
0
0
1
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
2
2
2
2
0
0
1
0
1
0
1
0
3
0
2
0
0
0
0
0
0
0
1
2
1
0
0
1
2
0
0
0
0
1
0
2
0
2
2
0
2
0
0
1
1
0
2
2
2
0
0
0
0
0
1
0
0
1
0
2
0
0
2
0
3
0
0
0
2
2
0
1
2
0
0
3
0
0
1
0
0
1
2
0
1
0
0
2
4
0
0
1
0
1
0
0
2
0
2
0
0
2
1
2
0
2
0
2
2
0
1
0
2
0
0
0
1
0
1
1
0
1
0
1
0
1
1
1
0
2
0
2
2
2
1
0
0
2
0
0
1
1
2
0
2
0
1
0
0
0
0
2
0
0
1
1
1
0
0
3
0
0
1
0
1
1
0
0
0
1
0
2
0
2
0
0
2
1
0
0
0
0
0
3
0
1
0
1
0
2
0
1
0
0
0
0
1
2
0
1
2
3
1
1
0
0
0
0
0
1
1
1
1
0
0
1
1
2
1
0
2
1
0
2
2
1
0
0
0
1
1
0
0
0
0
0
0
2
0
1
2
0
0
1
0
2
0
1
1
2
0
0
0
0
2
0
2
1
2
1
0
0
1
0
0
0
1
1
1
0
0
0
1
0
1
0
1
1
0
0
1
0
0
0
2
0
0
0
1
0
1
0
0
0
0
1
1
0
2
0
0
0
2
2
0
1
1
0
1
0
1
0
1
1
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
1
0
0
2
0
0
0
2
0
0
0
1
0
1
1
0
1
0
0
0
0
1
2
0
1
0
0
0
0
0
2
0
0
0
1
0
1
2
2
0
1
0
3
1
1
1
0
0
2
0
1
0
0
0
2
0
4
0
0
1
0
2
2
2
0
1
0
2
0
0
0
2
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
1
1
0
0
1
0
2
0
0
0
0
0
1
1
0
1
0
0
2
1
0
0
1
2
0
1
2
2
1
1
0
2
1
1
1
0
0
0
0
0
0
0
1
0
2
0
1
2
4
0
2
0
0
0
1
0
1
2
1
0
1
0
2
0
1
0
0
0
1
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
1
2
1
1
0
2
0
2
0
0
0
0
1
0
0
0
2
1
0
0
1
1
0
1
0
0
2
2
0
0
1
2
2
0
2
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
1
2
2
1
1
0
2
1
1
0
0
0
1
0
0
0
0
3
1
0
0
1
1
0
0
0
0
1
0
0
1
2
0
0
0
0
2
2
2
0
2
1
0
0
0
0
0
0
2
0
0
1
0
2
1
0
2
0
2
0
0
1
1
0
2
1
1
2
0
0
1
2
0
2
1
0
0
0
0
1
1
1
0
1
0
2
0
1
0
0
2
0
0
1
2
0
0
0
0
0
1
0
2
1
1
1
0
0
0
2
0
0
2
1
0
0
0
2
0
0
2
0
0
1
0
1
2
0
0
0
0
1
2
1
1
0
0
1
0
2
2
0
2
2
0
0
1
1
2
1
1
1
1
1
2
0
0
0
2
1
0
0
2
2
1
1
0
0
0
0
2
0
0
1
0
2
1
0
0
1
0
0
2
0
1
0
0
1
3
2
0
0
0
0
0
1
0
0
0
1
2
0
0
2
0
1
0
2
0
2
2
0
3
0
1
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
2
1
0
1
1
1
0
0
0
2
0
1
1
2
0
1
0
0
0
0
2
5
2
0
0
2
0
0
0
0
1
1
1
1
1
0
0
0
0
0
2
1
0
0
0
1
0
0
3
1
1
1
0
1
2
0
0
0
0
0
1
0
2
0
1
1
0
1
0
0
1
1
2
0
0
1
1
2
2
0
3
1
2
0
1
2
1
0
1
0
0
0
0
1
1
0
0
2
4
2
0
0
1
0
1
0
0
0
0
2
1
1
0
1
0
1
0
0
2
1
0
0
0
0
0
2
0
0
0
1
0
0
1
1
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
2
0
1
1
1
1
2
2
1
0
0
1
1
0
1
1
2
2
0
2
0
0
1
0
2
0
0
0
0
4
0
0
0
0
2
2
0
0
2
0
0
0
0
2
1
0
1
0
2
0
0
0
0
2
0
2
0
0
0
1
0
1
1
0
0
2
1
0
0
0
0
2
2
0
1
0
0
0
1
0
2
0
0
0
1
0
0
1
0
2
0
0
0
0
1
0
0
0
1
0
0
0
2
2
0
0
0
0
0
3
0
0
0
0
0
1
0
0
1
0
0
2
0
1
1
0
0
0
1
1
0
1
2
0
1
1
0
1
0
2
0
2
1
1
1
0
0
0
0
2
0
0
2
0
2
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
2
1
1
0
0
0
2
2
0
0
1
0
0
0
1
0
0
0
1
2
0
0
2
0
1
2
1
1
0
0
0
1
0
0
1
1
0
0
1
0
1
1
2
0
0
0
0
1
1
1
0
0
2
0
0
0
0
0
0
0
2
1
0
2
1
1
2
1
2
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
2
1
0
2
2
0
0
1
0
0
1
0
0
0
1
0
0
0
2
3
1
2
0
0
2
0
0
0
3
1
1
0
0
0
1
0
0
3
0
2
2
2
1
0
2
1
0
0
2
1
2
0
1
0
0
6
0
0
2
1
0
4
1
0
1
0
0
2
0
0
0
0
0
2
0
0
0
1
1
0
0
1
0
0
0
1
0
1
3
0
0
2
0
0
0
2
0
0
2
0
0
2
0
0
1
0
2
0
0
0
1
1
4
2
0
0
2
0
0
2
1
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
2
0
2
0
2
1
4
0
2
1
0
1
0
1
0
2
0
0
1
0
2
0
2
0
0
0
1
1
0
0
0
0
0
0
0
2
0
1
2
2
1
3
1
0
1
0
0
0
0
1
1
2
0
0
0
0
0
2
1
0
0
1
2
1
0
2
0
0
0
2
1
0
0
3
2
2
0
1
2
0
1
2
2
1
0
0
0
0
0
2
0
0
1
1
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
2
1
0
0
2
2
3
1
0
3
3
0
0
0
2
0
0
1
0
1
1
0
2
0
2
0
0
0
0
0
1
0
0
0
2
1
1
0
2
0
0
1
2
0
0
0
2
1
1
0
2
2
1
2
0
1
1
0
3
0
1
0
0
0
0
2
0
1
0
0
1
0
2
0
1
1
0
0
0
0
0
2
1
2
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
1
1
0
2
1
0
0
0
0
1
3
0
0
0
2
1
0
0
0
2
1
2
0
1
0
0
0
2
0
1
0
2
0
2
0
0
0
2
0
0
0
1
0
2
0
0
0
0
1
0
1
2
1
1
1
0
2
1
1
2
2
0
0
0
0
0
0
0
2
0
1
1
2
2
0
0
1
2
1
0
1
0
0
0
0
0
2
1
0
0
0
2
0
0
2
0
0
0
0
0
3
0
0
2
2
0
0
1
0
1
0
1
0
1
0
1
1
0
1
1
0
0
0
2
2
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
1
1
0
0
0
1
0
0
2
1
1
0
2
1
0
0
0
0
1
0
2
2
0
1
1
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
2
1
1
0
1
1
0
0
2
1
0
0
0
1
2
0
2
0
0
0
2
0
0
2
0
2
0
0
0
2
0
2
0
0
0
3
0
0
0
0
0
2
1
0
0
2
2
0
0
0
1
2
2
0
0
0
1
0
1
0
0
0
1
1
2
3
0
0
0
3
0
0
0
2
0
0
1
0
0
0
2
0
1
2
2
0
0
1
0
1
2
0
0
0
1
0
1
2
0
0
0
2
0
0
1
1
1
1
0
0
1
0
2
0
1
1
1
0
0
0
0
2
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
1
1
1
0
2
0
0
0
1
1
1
0
2
0
2
0
1
0
0
2
1
1
3
1
2
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
2
2
0
2
0
2
0
0
2
2
0
1
0
0
0
0
0
0
1
2
1
1
1
0
1
1
2
0
3
0
1
0
2
0
5
0
2
0
0
0
0
0
2
1
2
1
2
1
0
0
2
1
1
0
1
0
0
0
2
0
7
0
0
0
0
1
0
1
0
1
2
0
0
0
0
1
1
0
1
0
2
1
0
1
1
0
1
0
0
0
0
1
1
0
1
0
0
2
0
2
0
1
2
2
0
1
1
0
1
2
0
0
0
2
1
2
0
2
1
2
0
2
0
0
1
0
0
0
1
0
1
0
0
1
0
0
3
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
1
0
0
2
0
2
2
0
2
0
1
1
0
1
1
0
0
2
0
1
0
0
0
0
1
0
0
2
0
0
0
0
1
0
2
0
0
0
2
1
0
0
0
3
2
0
1
0
0
0
2
1
0
2
1
0
0
1
2
0
1
0
4
2
0
0
0
1
0
1
1
0
2
0
0
0
7
0
3
1
0
2
1
2
1
1
0
1
2
0
0
0
2
1
0
3
2
0
1
0
2
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
2
2
0
2
0
0
0
1
0
1
0
2
2
1
0
0
0
1
1
0
0
0
0
2
0
0
0
1
2
0
1
1
1
0
1
2
0
1
0
1
0
0
0
1
0
0
0
2
0
2
1
0
2
1
2
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
1
1
1
1
0
0
2
2
0
0
1
3
0
1
2
0
1
0
0
0
1
0
0
2
1
1
0
1
0
0
1
1
2
0
0
1
1
0
0
1
0
0
1
0
0
2
0
0
2
0
2
1
0
2
0
2
2
0
3
0
1
0
1
1
0
0
0
0
1
0
2
2
0
1
2
4
0
0
0
0
0
0
0
0
0
1
1
0
2
0
1
0
0
0
1
0
0
0
0
1
0
0
0
3
2
1
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
1
0
0
0
1
2
1
0
0
0
1
3
0
1
0
0
0
0
1
0
1
1
6
2
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
2
0
0
1
0
1
0
1
1
0
0
0
0
2
2
1
2
0
2
0
0
0
1
0
1
0
0
0
0
3
1
2
0
0
0
2
2
0
1
0
0
1
0
2
0
3
0
1
2
2
1
0
0
1
0
0
0
2
0
1
1
0
0
0
1
1
0
2
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
2
1
1
2
1
1
0
1
0
2
1
1
0
1
0
0
2
0
2
0
0
2
1
2
0
0
0
1
1
0
2
1
0
0
0
0
3
0
0
0
0
1
1
0
0
0
3
2
0
0
1
0
1
0
1
0
0
0
2
0
1
0
0
2
1
0
2
0
0
2
2
1
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
2
0
0
0
2
0
1
0
2
0
0
1
2
1
1
1
2
0
4
0
1
0
0
2
1
0
1
0
0
0
1
1
2
0
0
1
3
0
1
0
0
0
1
0
0
1
0
0
0
1
2
0
1
2
0
1
1
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
1
0
0
0
0
0
2
1
2
0
1
2
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
1
2
1
0
1
0
0
0
0
2
0
3
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
1
0
1
0
2
0
1
0
3
0
0
0
2
0
0
0
0
2
3
0
0
0
1
1
0
0
1
0
2
0
2
1
0
0
0
2
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
2
0
5
0
0
0
2
0
2
0
0
4
1
2
0
0
0
1
1
2
0
0
1
0
0
0
0
0
1
1
2
2
2
1
2
2
1
0
0
0
0
1
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
2
1
2
2
1
2
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
2
1
0
0
0
1
1
0
0
0
0
2
1
1
2
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
1
1
0
0
2
2
0
0
1
1
1
0
0
1
1
0
0
2
0
0
2
0
1
0
1
0
0
0
0
0
1
2
1
0
0
1
1
0
0
0
2
1
4
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
2
1
1
0
0
1
0
0
0
2
0
0
2
1
1
2
2
0
0
1
0
0
1
0
2
0
0
1
0
1
0
2
0
2
0
0
2
0
0
2
0
1
1
0
2
1
0
2
3
0
0
0
0
0
0
0
0
2
2
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
1
0
0
0
2
0
0
0
0
1
1
1
0
2
2
1
0
0
0
2
2
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
2
2
0
0
0
0
1
1
0
2
0
0
0
0
1
1
2
0
1
1
0
0
1
0
0
2
2
1
0
0
0
0
1
1
1
2
2
0
2
0
0
1
0
0
1
0
1
0
1
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
2
0
1
0
0
3
0
0
2
0
0
0
0
1
0
0
0
0
1
2
2
0
2
0
0
0
0
2
0
2
0
2
2
0
1
2
0
2
0
1
1
0
1
0
1
0
3
0
0
2
0
0
0
3
0
1
0
0
1
2
2
0
0
2
1
2
0
3
0
2
1
2
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
1
1
2
0
0
0
0
1
3
1
0
2
0
0
1
2
3
0
2
0
0
1
1
0
0
0
2
1
0
1
1
0
1
0
0
0
1
1
0
3
1
0
0
0
1
0
1
1
0
0
0
1
0
2
0
2
2
1
0
0
0
1
1
0
2
2
0
0
0
2
3
2
0
1
2
0
1
1
0
0
0
1
2
2
2
0
1
0
2
0
1
1
0
0
2
0
1
1
2
0
1
0
0
2
0
0
0
0
0
2
0
0
4
0
2
0
2
1
0
0
1
0
2
0
0
0
1
1
0
0
1
1
0
0
2
0
0
0
0
2
1
1
1
0
1
0
1
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
1
1
1
2
0
0
0
2
2
1
0
1
1
0
0
1
0
0
0
1
2
1
0
0
1
1
0
0
2
0
0
0
2
0
1
1
0
0
0
2
1
1
0
0
2
1
1
0
0
0
0
2
0
2
1
0
0
2
0
0
2
0
2
0
0
2
0
2
0
1
0
2
1
0
0
1
0
0
0
3
0
0
0
1
1
2
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
1
3
0
0
2
1
0
0
0
0
1
0
2
2
0
2
2
1
0
2
2
0
3
0
0
0
0
0
2
1
2
1
0
3
0
1
0
0
1
0
0
3
0
1
2
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
2
1
0
1
0
2
0
0
1
1
0
0
0
0
0
3
1
2
0
0
3
0
0
2
1
1
0
1
2
0
1
0
1
1
0
0
1
1
1
0
0
2
1
0
0
0
1
0
1
0
0
0
1
1
1
0
0
0
0
2
2
0
0
0
0
2
0
0
2
0
3
1
0
1
2
2
0
2
0
0
0
0
0
0
1
2
0
0
3
0
0
2
0
1
1
0
0
0
0
1
1
0
0
2
1
0
1
0
0
2
0
1
0
2
1
0
2
2
0
1
1
1
1
0
0
0
0
0
0
0
1
0
1
0
0
2
1
2
0
0
0
1
0
1
0
1
3
1
0
1
1
0
1
1
0
1
0
0
2
0
3
0
0
1
0
0
0
1
0
0
0
1
0
0
0
3
2
0
1
1
0
1
0
1
0
1
0
0
0
0
0
1
1
0
2
0
1
0
0
1
2
0
1
0
2
1
0
0
1
0
1
0
0
0
0
1
1
4
0
0
1
0
0
0
1
0
2
0
2
2
3
3
0
0
0
0
1
1
0
1
1
1
1
0
0
1
0
0
0
0
0
2
0
1
0
3
0
1
1
0
0
0
0
1
0
1
1
1
0
0
0
1
0
1
0
0
0
2
2
1
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
2
0
0
1
2
0
0
0
2
0
1
0
0
2
0
0
1
1
0
0
0
0
1
0
0
1
0
0
3
2
0
0
0
2
2
0
2
0
1
0
0
1
0
1
0
2
0
0
0
0
2
1
0
0
1
0
0
2
2
0
2
1
0
0
0
0
0
1
4
2
0
2
0
1
0
2
0
0
0
1
0
0
1
0
2
0
0
1
2
0
1
1
0
2
0
1
1
1
5
1
0
1
0
1
0
0
1
0
2
2
0
0
0
0
0
2
1
2
0
2
0
1
0
2
0
1
1
1
1
0
1
0
0
1
0
2
0
0
0
0
0
1
2
2
1
1
0
0
0
0
1
0
2
2
1
2
2
0
0
0
2
0
0
0
0
1
0
1
0
0
2
2
1
2
0
0
2
0
2
2
1
1
2
2
0
1
2
0
0
1
0
0
1
1
2
0
3
0
1
0
1
2
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
2
2
2
1
1
2
0
2
0
0
1
0
0
0
1
0
1
2
2
0
0
0
2
0
1
2
0
0
0
1
0
0
0
1
0
1
2
4
0
0
1
0
0
0
1
0
0
0
2
0
1
1
3
0
0
0
1
0
0
0
0
0
1
0
2
0
1
0
0
1
0
2
1
0
0
0
2
1
1
1
0
2
2
2
1
0
0
0
0
2
1
0
0
0
1
2
0
1
0
1
0
0
0
1
1
0
1
0
1
2
0
0
0
0
1
1
0
0
0
1
0
2
0
0
0
0
1
2
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
2
3
1
1
2
0
2
0
0
3
1
1
0
0
2
0
0
2
0
0
1
0
2
1
0
1
1
2
2
2
0
0
0
1
0
2
0
0
1
0
0
1
0
0
1
0
0
1
1
0
0
1
0
1
2
1
0
1
0
0
0
2
0
0
0
0
0
1
1
1
0
1
1
0
0
1
1
0
1
1
0
1
1
2
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
1
2
0
2
1
0
2
0
0
1
0
1
0
0
1
0
2
3
0
2
1
2
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
2
0
2
2
1
0
1
2
1
2
1
1
0
2
0
2
1
0
1
0
2
0
0
2
0
2
2
0
0
1
0
1
1
1
0
0
0
0
0
0
1
0
2
1
0
0
2
2
0
1
0
1
0
0
0
1
2
1
0
0
2
0
1
7
0
1
0
2
2
1
0
0
1
0
0
2
2
1
1
0
1
0
3
0
0
2
1
1
2
1
0
0
1
0
1
1
0
0
0
0
1
0
1
1
1
2
0
2
0
0
0
1
2
0
0
0
0
1
2
2
0
1
0
0
1
0
0
0
2
1
0
0
0
0
2
0
5
1
0
0
4
2
1
2
0
0
0
0
1
2
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
2
0
2
0
0
0
2
0
0
2
0
1
1
2
1
0
0
2
0
0
0
0
0
3
2
1
0
0
1
2
0
0
0
0
1
1
0
1
0
0
1
2
2
0
0
2
0
4
1
0
1
2
0
0
3
1
0
1
1
0
0
0
0
0
0
1
3
0
0
0
1
0
0
0
0
1
2
1
2
2
0
1
0
2
0
0
0
1
1
1
0
1
2
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
2
1
0
0
0
0
1
1
1
0
0
0
2
1
0
3
2
0
0
0
2
1
0
0
0
1
2
2
1
1
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
2
2
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
2
0
3
0
2
0
2
2
0
0
0
0
0
1
1
1
2
0
0
0
0
2
2
2
1
2
0
0
1
0
0
0
0
2
0
0
1
2
0
0
0
0
0
1
2
2
0
0
0
1
1
0
1
2
2
0
0
4
2
2
0
0
1
0
3
1
0
1
2
1
0
0
0
0
0
2
0
0
0
0
0
4
1
0
0
0
0
1
2
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
1
0
2
0
2
1
0
0
0
1
0
0
1
0
0
1
0
0
0
2
0
2
0
0
0
1
0
2
0
0
2
1
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
1
2
1
0
0
0
1
0
1
1
3
1
0
0
0
0
1
0
0
0
2
0
0
3
0
0
1
2
0
3
0
2
0
1
1
0
1
1
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
3
2
1
0
2
0
2
0
2
1
0
1
1
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
1
0
2
0
1
0
0
0
1
0
0
0
0
1
1
1
0
1
1
0
0
0
0
0
1
1
0
2
1
0
0
0
1
1
1
0
0
0
0
1
2
2
1
0
3
1
1
2
0
0
2
1
1
0
2
2
1
0
0
1
0
2
1
2
2
0
1
1
2
0
2
0
0
1
0
0
0
2
1
0
0
0
1
0
0
1
1
0
0
2
1
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
1
4
1
0
1
0
0
0
0
2
0
2
0
1
1
1
2
3
2
1
0
2
0
0
1
1
0
1
1
0
0
0
0
0
0
2
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
1
2
0
0
2
0
0
0
0
0
2
0
0
1
0
0
2
1
1
0
0
0
1
0
0
0
1
0
1
0
0
2
0
0
0
0
1
0
1
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
2
1
2
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
2
3
1
1
1
1
0
0
0
1
0
0
0
1
1
0
0
1
0
2
0
2
0
1
0
1
1
0
2
0
2
2
0
0
1
2
1
0
2
1
0
0
2
1
0
0
0
0
1
0
0
1
0
2
0
2
0
0
0
1
1
0
1
1
1
0
2
1
0
0
0
0
0
0
2
2
0
1
2
1
0
2
0
2
1
0
1
0
0
1
0
2
2
1
1
4
2
0
0
2
0
0
2
1
0
0
1
1
1
1
0
0
2
0
3
0
0
0
0
1
1
0
0
2
2
1
0
0
2
0
2
0
0
0
0
1
1
0
1
0
0
1
0
2
2
0
0
2
0
2
0
2
0
0
0
0
0
1
0
2
1
2
1
0
0
0
2
0
2
0
0
1
0
0
2
1
2
2
0
0
0
0
0
0
0
0
2
0
1
2
1
1
1
0
0
0
0
1
1
1
1
1
0
0
0
0
0
0
2
0
2
2
0
1
2
1
0
1
1
1
0
0
0
2
0
1
1
0
2
0
2
0
0
2
0
0
0
0
0
1
0
0
2
0
1
1
2
2
0
1
0
0
2
0
0
0
0
1
2
0
0
2
0
2
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
1
1
0
0
2
0
1
1
0
0
0
0
2
1
0
0
0
0
1
1
0
2
0
1
1
0
0
1
0
2
1
0
1
2
1
0
1
1
0
0
1
1
1
0
1
0
2
0
0
0
0
0
0
1
0
1
1
2
0
1
2
0
1
0
2
0
1
2
1
0
0
1
2
0
1
0
0
0
0
0
1
0
0
1
2
1
0
2
2
0
0
1
1
0
0
2
1
0
2
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
2
2
0
2
1
0
2
0
1
0
0
0
2
0
2
9
0
0
0
2
0
1
0
1
1
1
2
0
2
2
0
0
1
0
3
0
0
0
1
0
0
0
2
1
1
0
0
2
1
0
0
0
2
2
0
1
0
0
2
0
0
0
2
1
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
2
1
0
0
1
0
0
1
1
0
0
0
0
0
1
0
3
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
2
0
0
0
0
0
0
4
0
2
2
0
0
0
0
0
1
2
0
0
0
0
0
2
0
1
0
0
0
1
0
2
0
0
0
0
0
1
2
1
0
2
1
2
0
0
0
0
1
0
0
0
0
0
1
0
0
1
2
0
0
2
0
0
0
1
1
0
0
1
2
0
0
0
0
1
2
0
2
0
1
2
0
0
8
0
2
1
2
2
0
0
0
2
0
0
1
0
0
1
1
0
2
0
2
1
1
2
0
0
1
0
0
0
0
0
1
1
0
0
2
1
2
1
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
3
0
0
0
1
0
0
0
2
0
2
0
0
2
0
2
0
0
0
1
2
0
2
0
0
0
1
0
0
0
3
1
0
1
2
1
0
0
0
2
2
1
2
0
0
0
1
0
1
0
0
0
2
1
0
0
0
2
1
0
2
1
0
2
0
0
0
1
1
1
2
0
1
2
1
0
0
1
2
0
1
2
2
0
0
0
0
0
0
1
0
0
0
1
2
1
0
0
1
0
1
2
0
0
1
0
0
0
1
1
0
0
1
0
1
5
0
0
3
0
0
0
0
2
0
1
1
2
2
1
0
1
1
0
0
2
0
0
0
2
0
0
0
1
2
2
1
1
0
0
2
0
0
0
0
1
0
1
0
2
0
2
1
0
0
0
0
2
2
0
0
0
1
0
1
1
0
0
1
2
1
0
1
0
0
0
2
0
0
0
0
1
2
0
1
0
2
0
0
0
3
1
0
0
0
0
1
2
1
2
0
0
1
2
2
0
0
0
0
0
0
2
0
3
0
0
2
0
0
0
3
2
0
1
0
0
1
1
0
2
0
0
2
0
2
1
0
1
0
2
0
0
3
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
12
1
2
1
0
0
1
0
0
0
2
0
0
0
3
1
1
0
0
1
2
0
2
3
0
1
2
1
2
0
0
1
1
2
0
0
2
1
2
1
0
1
2
0
2
3
0
1
0
0
0
0
0
1
1
0
1
0
1
0
4
2
1
1
1
3
0
0
0
1
2
0
2
2
0
0
0
0
0
1
1
0
0
0
1
0
0
0
2
0
1
0
0
0
2
0
1
1
1
0
0
1
0
0
0
0
1
0
1
1
1
1
0
1
0
0
0
2
1
0
0
2
0
2
1
0
0
0
0
0
2
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
2
1
2
0
0
2
2
2
2
2
0
0
0
0
0
1
2
0
1
0
1
0
0
0
1
1
0
0
0
0
0
1
0
1
0
1
0
0
1
0
1
2
1
0
0
2
0
0
1
0
0
0
2
0
0
0
2
0
0
2
2
0
2
1
0
0
2
0
1
1
1
1
0
1
1
0
1
0
1
1
0
0
0
1
0
0
1
0
1
2
0
2
0
0
0
0
1
0
1
1
2
0
1
0
0
2
0
1
1
0
1
0
2
0
0
0
2
0
1
1
2
0
1
0
0
2
2
2
2
0
0
1
0
0
1
2
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
2
1
1
0
1
2
0
0
0
0
1
0
0
0
2
1
0
0
1
0
0
0
1
0
2
2
1
0
0
0
3
0
0
0
1
0
0
0
1
0
0
0
0
2
2
0
0
0
0
3
0
1
0
0
1
1
0
2
0
1
1
0
0
0
0
0
0
3
0
0
2
1
1
0
0
0
0
2
0
0
1
0
0
1
0
0
0
1
1
0
1
1
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
1
1
2
1
0
1
2
1
2
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
1
0
1
0
1
0
1
0
0
1
0
0
0
0
3
2
2
0
0
1
1
0
1
0
0
2
0
2
0
0
0
0
2
2
2
2
1
1
2
0
0
0
1
0
0
0
1
0
2
0
0
0
2
0
0
0
1
0
0
0
3
2
0
1
2
0
2
0
0
0
2
0
2
0
0
2
0
0
1
2
1
0
0
0
0
0
2
0
2
0
1
2
0
0
1
0
0
0
0
0
0
1
3
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
1
0
0
0
0
0
2
0
0
0
1
2
0
0
1
0
0
0
0
0
1
0
1
2
0
0
0
1
1
0
0
1
0
0
2
0
1
0
2
2
0
0
2
2
2
0
0
1
1
1
0
2
3
0
0
0
1
0
2
2
0
0
2
0
2
2
0
2
0
1
0
2
1
0
0
0
2
3
0
0
2
0
0
1
1
0
2
1
0
1
0
0
1
1
0
1
2
0
2
0
1
0
0
0
0
1
0
3
0
1
0
0
1
1
5
3
0
0
2
0
0
2
1
0
0
0
0
0
0
0
1
1
0
0
0
2
2
2
0
1
0
0
0
0
1
0
0
1
1
1
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
4
3
0
3
0
1
0
0
0
0
4
0
0
2
0
1
0
0
0
1
0
1
0
0
0
0
1
1
2
1
0
0
0
1
1
1
0
0
3
0
0
0
1
3
1
2
0
2
0
2
0
0
0
0
0
2
0
1
2
1
1
0
0
0
0
2
1
0
0
1
0
1
2
0
1
1
2
0
1
1
0
0
1
0
0
1
0
0
0
1
2
0
0
0
2
1
0
1
2
1
1
0
1
1
2
2
2
1
0
0
2
1
0
1
0
1
0
2
0
0
2
0
1
2
2
0
1
0
3
2
0
2
0
1
1
0
2
0
0
2
2
0
2
0
1
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
3
0
1
0
1
0
1
1
1
0
2
1
3
1
2
2
0
1
1
1
0
1
0
2
0
1
1
1
2
2
1
0
0
3
0
0
0
0
2
0
0
2
2
0
1
0
1
0
1
2
0
1
0
0
2
2
1
0
0
1
2
0
0
0
0
0
1
0
0
2
0
1
2
0
0
0
0
0
1
1
0
0
1
0
1
2
0
0
0
0
0
1
0
0
3
0
1
0
0
2
2
0
2
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
1
2
1
0
2
3
2
2
0
0
2
0
0
0
1
0
0
0
1
1
2
0
0
1
0
1
1
0
0
1
0
2
1
1
0
2
0
0
0
2
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
1
1
2
0
0
1
1
2
1
1
0
0
0
1
0
0
1
0
0
1
0
2
0
0
0
0
1
0
2
0
0
2
0
0
2
0
2
2
0
2
2
1
2
0
2
2
0
2
2
0
2
1
1
1
1
0
0
0
1
1
0
0
0
0
1
2
0
0
0
0
0
0
2
0
2
0
2
0
0
0
1
0
0
2
0
0
1
1
0
0
1
1
1
1
0
0
0
0
0
2
0
2
0
2
0
1
2
2
0
0
0
0
0
9
0
2
0
1
0
2
2
0
0
0
2
1
2
0
0
0
0
1
1
0
0
1
0
0
2
0
1
0
0
2
0
0
2
2
1
1
0
1
0
0
1
0
0
1
1
0
0
0
0
2
0
1
2
0
0
0
2
2
2
0
0
0
0
0
2
0
2
2
1
1
0
0
0
0
0
0
1
0
2
0
2
1
1
0
0
0
2
0
0
0
1
1
1
0
0
2
2
2
0
0
2
0
0
0
0
1
0
0
2
2
1
0
0
0
0
2
0
2
1
0
0
2
2
0
0
1
1
0
0
2
1
0
1
2
0
0
0
0
0
0
1
0
1
1
0
2
0
0
0
0
0
0
0
1
1
0
2
0
0
1
0
0
2
0
1
2
0
0
0
0
1
0
2
0
0
0
1
1
0
0
0
1
0
0
0
2
0
3
2
0
0
3
0
0
0
1
0
1
0
0
1
2
1
1
2
2
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
1
1
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
2
1
2
2
1
0
0
3
0
0
0
0
0
2
0
1
1
2
2
0
0
2
0
0
6
0
0
1
0
2
0
1
0
0
0
0
3
1
0
0
0
0
1
0
0
0
2
2
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
2
2
2
0
0
0
0
0
0
0
0
4
1
0
0
0
1
2
0
2
1
1
1
1
1
0
1
0
2
2
0
0
2
0
0
0
0
0
1
1
0
2
0
0
0
0
0
2
0
1
0
0
1
0
0
1
0
0
0
1
1
0
0
1
0
0
1
0
1
1
2
1
0
2
4
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
2
2
0
1
2
0
0
0
0
1
2
0
2
1
2
2
0
0
0
0
0
3
2
1
0
0
0
0
0
2
1
1
0
1
0
1
2
2
0
0
0
0
1
2
1
0
0
0
1
1
0
0
1
2
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
2
0
1
1
2
1
0
0
1
0
0
0
0
2
0
0
3
1
0
0
2
1
1
2
1
0
1
0
2
1
0
0
0
2
2
0
0
2
0
2
1
0
1
1
0
0
1
0
0
1
0
0
0
0
1
1
0
1
0
1
0
0
0
2
1
2
0
0
2
0
2
2
1
0
0
2
1
0
0
0
0
0
1
2
0
0
2
2
1
2
1
1
0
2
2
0
0
2
0
0
0
0
2
2
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
2
2
0
1
1
1
0
0
0
2
1
0
0
2
1
1
1
0
2
3
0
0
0
1
1
1
0
0
3
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
2
0
0
2
0
0
1
0
2
0
2
0
1
1
2
1
1
1
1
0
2
0
0
2
1
3
0
4
0
1
1
1
1
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
1
0
0
0
2
2
2
1
5
2
1
0
0
1
1
1
0
0
0
2
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
2
2
1
1
0
0
1
1
1
1
1
3
2
0
1
0
0
3
0
0
2
0
0
0
2
1
0
0
1
1
2
1
0
2
0
0
2
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
2
1
1
1
0
2
0
0
1
1
1
0
0
2
0
0
0
0
0
0
0
0
1
1
1
0
0
0
2
1
1
0
0
0
4
1
2
0
1
0
0
0
1
0
2
0
1
0
0
0
0
1
2
0
0
0
0
1
0
1
0
2
0
2
1
0
0
1
1
0
0
0
1
0
0
2
0
0
2
2
2
0
2
1
2
0
0
2
2
1
0
1
0
1
0
0
1
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
2
1
0
1
0
0
2
1
1
0
0
1
2
1
0
1
1
0
0
0
1
1
0
0
2
1
0
2
1
2
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
1
3
0
0
0
0
2
0
1
0
1
0
1
0
1
2
3
0
0
0
1
0
0
1
0
0
0
2
1
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
1
0
1
2
0
2
0
0
0
0
3
0
0
0
0
0
1
0
1
0
0
0
0
2
2
1
0
0
2
1
1
2
1
0
2
1
2
2
1
1
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
2
0
0
2
1
0
0
1
1
1
2
1
0
0
2
2
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
1
2
1
1
1
0
0
0
2
1
1
0
1
1
1
0
1
0
2
0
0
1
1
0
0
0
0
4
2
1
0
0
1
1
0
0
2
0
2
3
0
0
0
3
0
0
0
1
1
0
1
2
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
2
0
0
2
2
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
1
0
0
1
1
2
0
0
2
0
0
0
1
0
0
0
1
2
0
0
0
0
2
1
0
0
0
2
0
2
0
1
1
1
0
2
0
2
0
0
2
0
1
1
0
0
0
0
1
0
2
0
0
0
0
2
0
2
0
0
2
2
0
0
0
2
0
1
0
2
0
0
2
0
0
0
0
0
1
2
0
1
0
1
0
0
0
0
0
0
0
2
1
2
2
1
2
0
1
0
0
2
0
0
2
1
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
1
1
0
1
1
0
0
1
0
2
1
0
2
1
0
0
0
2
0
2
1
0
2
2
0
0
1
0
0
2
0
0
0
1
0
0
1
0
1
0
0
1
1
2
0
0
1
0
3
2
0
1
0
0
0
1
2
1
0
1
1
1
0
1
1
2
0
2
0
1
0
1
8
0
3
0
1
2
1
2
0
0
0
0
2
1
2
0
0
1
1
0
0
2
0
1
1
2
0
2
0
0
2
1
0
3
1
0
0
1
1
1
0
0
1
0
1
0
2
1
3
0
2
1
0
0
0
0
0
2
0
0
0
2
2
0
1
0
2
0
0
1
0
0
2
2
1
0
0
1
2
2
0
2
1
0
0
0
0
2
2
2
0
0
0
0
2
0
1
0
2
2
2
1
0
0
1
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
2
2
2
0
0
0
2
2
1
2
1
2
0
0
2
2
0
1
1
2
0
2
0
0
3
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
2
0
2
0
1
0
0
0
0
0
0
0
1
0
1
0
1
2
1
0
1
1
0
2
0
1
2
0
0
0
0
0
0
0
0
2
0
2
0
1
1
0
0
1
1
1
2
1
1
0
0
0
0
1
0
0
0
3
2
1
0
0
0
2
0
1
0
2
1
0
2
0
0
0
1
2
0
0
0
0
0
0
0
2
1
0
2
0
0
0
1
0
1
0
0
1
1
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
1
1
1
0
1
0
2
2
0
0
1
0
1
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
3
1
3
0
2
0
1
3
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
2
0
2
2
1
0
0
2
0
1
0
1
0
0
2
0
0
0
1
0
0
0
1
0
1
0
0
0
0
2
1
1
0
0
0
0
1
2
0
0
0
1
1
1
2
0
0
0
0
2
1
0
2
1
1
0
0
0
0
1
1
2
0
0
0
0
2
1
0
2
1
0
2
0
1
0
0
0
1
1
0
0
5
0
0
5
0
0
2
0
0
3
1
0
1
0
0
1
0
0
1
0
1
1
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
2
1
3
1
0
2
0
1
0
1
0
1
2
2
2
0
0
0
0
0
1
0
2
2
0
0
0
0
1
0
0
1
2
0
2
0
1
0
2
2
1
0
0
1
0
1
0
0
0
3
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
5
0
0
0
0
1
0
0
1
0
1
0
1
0
2
2
0
0
0
0
1
0
1
1
3
0
2
0
1
0
0
0
0
1
1
0
2
0
1
0
0
1
1
0
0
0
2
0
2
0
1
1
0
0
2
0
1
1
2
0
0
0
0
2
0
2
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
2
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
1
5
1
2
2
2
0
0
0
2
0
0
1
0
2
1
1
1
0
1
0
0
1
1
2
0
2
0
1
0
0
1
2
0
2
0
1
0
0
0
2
0
0
1
1
0
1
0
0
2
0
1
0
0
0
0
0
1
0
0
0
2
0
2
0
0
1
0
2
0
1
0
1
0
2
0
2
1
0
0
2
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
2
0
0
0
2
0
1
0
0
0
1
0
0
1
1
1
1
0
1
3
0
0
0
0
2
0
1
0
1
0
0
1
0
2
0
0
0
1
0
2
0
0
0
1
1
1
2
0
0
0
0
0
0
1
1
3
3
0
1
2
1
1
0
0
1
0
0
1
0
1
3
0
1
2
0
1
0
2
0
2
2
1
2
2
0
0
0
0
0
2
1
0
0
0
0
1
0
1
0
1
0
2
0
0
1
0
1
1
2
0
0
1
0
0
2
0
0
0
0
0
1
0
0
1
0
0
2
2
2
1
0
0
2
0
0
0
2
0
0
1
0
0
1
2
0
2
0
1
2
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
1
0
0
0
1
1
1
0
0
0
1
0
1
1
0
0
0
0
2
0
2
0
2
1
1
2
1
2
0
0
0
1
0
0
1
2
2
2
0
2
1
1
0
0
2
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
1
2
3
2
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
2
1
0
1
0
2
2
0
0
0
0
2
0
1
1
1
2
0
4
2
0
0
0
0
2
0
1
2
0
1
0
1
1
0
2
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
1
2
1
0
0
2
0
0
2
0
0
2
0
0
0
2
0
0
0
0
1
2
0
2
1
1
2
1
1
1
0
1
2
1
0
1
0
0
0
2
1
2
1
0
0
0
2
0
0
0
0
2
0
0
0
0
2
2
1
0
0
0
0
0
3
0
2
1
2
1
1
2
0
0
0
0
2
2
1
2
0
1
1
2
0
2
0
4
1
2
2
1
1
1
1
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
2
1
0
1
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
2
0
0
1
0
1
0
1
0
0
0
0
0
2
0
0
1
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
2
1
4
1
2
0
0
2
0
2
1
0
0
0
0
0
2
1
1
0
0
2
0
1
0
1
1
0
0
1
0
0
1
1
0
2
1
3
1
1
0
0
0
1
0
0
0
0
1
1
2
2
1
2
1
0
0
0
2
0
0
1
2
0
2
2
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
2
2
1
1
1
0
0
0
0
1
2
1
2
0
0
0
0
0
0
0
2
0
0
1
2
0
2
0
1
2
0
1
0
0
2
2
0
0
0
0
1
1
2
0
0
2
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
1
1
1
0
2
0
0
0
0
1
1
0
0
1
0
0
0
1
2
1
0
2
0
3
1
1
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
2
0
0
2
0
1
2
1
0
0
0
2
2
0
0
0
0
1
2
1
2
0
6
0
0
0
1
2
0
1
0
0
0
0
2
1
0
0
1
0
0
2
0
1
0
0
1
1
1
0
1
1
3
1
0
2
4
1
1
0
0
0
0
1
0
1
2
0
0
1
0
0
0
0
5
1
0
1
0
1
0
1
2
2
1
1
0
0
0
2
0
0
0
0
1
1
2
0
0
1
2
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
1
0
1
2
1
1
1
0
1
0
1
2
2
0
1
0
0
0
1
0
1
0
0
0
0
3
0
0
0
1
1
1
1
0
0
0
1
0
0
1
1
0
2
1
0
0
2
0
0
0
0
2
1
1
2
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
2
1
1
0
0
0
1
0
1
0
0
2
0
0
1
0
1
0
0
1
2
0
1
1
0
1
0
0
1
0
0
0
0
1
2
2
2
2
1
2
0
1
0
2
1
1
0
1
2
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
1
0
1
1
1
0
2
0
1
0
0
0
2
0
0
0
1
0
0
1
0
1
1
1
0
0
0
1
2
0
0
3
0
0
0
0
0
0
1
0
1
0
1
2
0
0
0
2
0
0
0
3
0
0
0
2
2
1
0
2
0
1
0
2
1
2
0
2
2
0
0
0
0
0
1
0
0
0
2
1
1
0
0
0
0
0
0
2
1
0
2
0
2
0
0
1
2
0
0
0
0
2
0
1
0
0
0
2
2
0
2
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
1
0
1
0
0
1
2
0
0
2
2
0
0
0
0
2
0
0
1
0
1
0
0
0
0
1
0
0
0
3
1
1
2
0
0
1
1
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
1
0
1
0
0
1
0
0
0
1
0
2
0
2
0
0
0
1
1
0
0
0
0
1
1
2
2
0
2
1
0
1
0
0
1
2
0
0
1
2
0
2
1
2
0
4
0
0
2
1
1
1
0
2
1
2
2
0
0
1
0
0
0
0
0
2
0
0
1
1
0
1
0
0
0
0
2
2
2
2
0
1
1
1
0
0
0
0
1
1
0
0
1
1
0
0
0
0
2
2
0
0
1
1
1
1
2
0
1
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
2
0
2
2
0
0
0
2
0
0
0
0
1
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
1
0
0
2
2
1
0
2
2
0
0
0
0
2
1
1
2
0
0
1
0
3
0
0
2
2
0
0
0
2
2
1
0
1
0
0
2
1
2
0
0
2
0
0
2
0
0
0
2
2
0
2
1
1
0
0
2
0
1
0
3
0
0
1
2
0
4
2
0
0
0
2
0
1
0
1
0
0
0
1
1
1
1
2
0
1
2
1
0
0
0
1
0
0
0
1
0
0
0
2
0
1
0
0
1
0
0
2
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
1
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
2
1
0
0
0
1
0
0
1
1
0
3
2
1
0
0
1
6
2
2
0
1
0
0
1
2
0
2
2
0
2
0
0
1
0
0
1
0
1
3
0
0
3
1
2
0
1
0
2
1
0
0
1
0
1
0
0
0
0
3
0
3
1
0
0
0
0
0
0
2
0
0
1
4
0
1
0
0
0
0
0
2
0
0
1
1
0
0
1
0
1
0
0
0
0
0
2
0
0
0
2
0
0
1
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
4
1
0
0
0
1
1
2
0
1
2
2
0
0
0
0
2
0
0
0
0
3
0
0
1
2
0
3
0
4
0
0
0
1
0
0
1
0
0
0
0
0
2
1
1
0
3
2
0
0
2
0
1
0
0
0
0
2
1
1
0
2
0
0
0
0
0
1
0
1
1
1
0
1
0
2
0
1
2
0
0
2
0
2
2
0
0
1
0
1
0
1
0
0
0
0
1
0
1
0
0
2
0
0
0
1
0
1
0
0
1
0
0
0
0
1
1
0
2
2
0
1
0
1
2
2
2
0
0
0
0
1
0
0
0
1
2
0
1
0
0
1
2
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
3
0
0
2
1
0
0
0
0
0
2
0
0
1
1
1
0
0
0
3
0
0
1
1
2
1
2
0
1
0
0
2
0
1
2
1
0
1
1
1
0
2
0
0
0
2
0
2
2
0
0
0
0
2
0
0
1
1
0
2
2
1
0
0
1
2
0
1
2
0
0
2
2
1
3
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
2
1
4
2
0
1
2
0
0
1
0
1
1
1
0
0
0
1
1
0
0
2
0
0
0
0
0
2
2
0
2
0
2
2
0
0
2
2
0
0
1
0
0
2
0
0
3
2
0
0
0
0
0
0
0
0
1
0
0
0
2
1
1
0
0
0
3
0
1
0
0
0
0
1
1
4
0
1
0
0
1
0
0
0
0
0
0
1
1
0
2
0
0
0
0
1
0
2
2
1
1
1
1
1
1
0
0
2
1
0
0
1
2
1
1
1
1
0
1
2
2
1
2
2
0
2
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
1
0
1
1
1
1
1
0
0
0
2
0
0
1
2
0
0
0
2
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
1
1
1
0
0
1
1
2
1
1
0
1
0
0
1
0
0
2
0
0
0
0
0
1
0
1
0
0
1
0
0
0
2
1
0
0
2
1
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
1
2
4
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
3
0
0
0
1
2
0
0
0
1
1
1
2
2
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
2
2
0
2
0
0
1
0
0
0
2
0
1
1
0
1
2
0
0
2
1
0
0
0
0
0
1
0
0
0
2
1
0
0
0
2
0
0
2
2
0
0
2
1
2
0
2
0
0
3
0
0
0
2
1
0
0
1
0
0
1
2
0
0
0
2
0
0
0
2
0
0
6
0
0
0
1
0
1
2
0
0
0
0
1
0
1
0
1
0
0
2
2
0
0
0
0
2
0
1
1
1
0
0
0
1
1
0
0
0
0
2
2
0
0
0
0
2
1
1
0
0
0
1
0
2
2
1
0
0
0
0
1
0
1
1
0
0
0
2
2
0
2
1
0
1
0
1
1
0
0
0
1
3
2
1
0
2
2
0
0
0
0
0
1
0
0
0
1
0
2
1
0
0
0
1
0
0
0
0
2
1
0
1
0
2
1
0
0
0
4
0
0
1
0
0
1
1
0
2
0
0
0
0
1
0
0
2
0
1
1
2
0
0
1
0
2
0
0
0
1
1
2
0
2
1
0
1
2
1
1
2
1
1
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
2
3
0
1
0
0
1
0
1
0
0
0
1
0
0
1
1
0
0
0
1
0
2
2
3
2
0
0
1
2
0
2
0
1
0
0
0
2
0
0
1
2
0
0
0
2
2
1
1
0
0
0
1
0
2
3
1
2
0
0
0
0
4
0
0
1
0
0
2
0
0
0
1
2
0
1
0
0
0
2
0
0
2
1
0
1
0
0
0
1
2
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
2
0
2
1
0
0
2
0
0
0
2
0
2
0
1
1
0
0
1
0
0
2
2
0
1
2
1
0
3
0
1
0
2
0
0
2
0
1
1
0
0
2
2
0
0
2
0
0
0
2
0
3
2
0
2
1
0
2
0
2
1
0
0
0
2
0
0
2
0
1
1
1
1
0
1
2
2
0
1
1
0
1
0
1
1
0
0
2
0
2
1
0
1
1
0
1
0
0
0
0
1
1
2
2
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
2
1
0
1
1
1
2
0
0
0
0
0
2
1
1
1
1
0
0
0
3
1
1
0
0
2
0
2
0
1
2
0
1
1
0
0
0
0
0
1
0
3
0
0
0
0
2
1
0
1
0
0
0
0
1
0
0
0
0
1
0
1
2
1
1
2
0
0
0
0
1
0
2
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
2
1
0
0
0
2
1
0
0
0
1
0
0
1
0
0
0
1
0
2
2
2
0
1
0
1
0
0
2
0
0
0
0
0
0
0
2
1
0
0
1
0
2
2
0
2
0
2
1
1
0
0
0
0
1
0
2
0
2
1
0
0
0
1
0
0
1
0
2
0
1
2
0
1
1
2
2
1
2
0
0
2
0
0
0
2
0
0
2
0
0
2
2
1
1
0
0
0
1
0
2
0
0
2
0
1
0
0
2
0
1
1
0
1
0
2
1
0
1
1
1
0
0
2
0
0
2
0
0
1
1
0
0
1
0
0
0
0
0
0
0
2
1
0
1
1
0
0
2
0
0
1
0
0
0
2
0
0
1
2
0
1
0
1
1
0
0
1
0
2
0
1
0
0
0
2
1
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
5
2
2
1
0
2
0
3
0
2
2
1
0
1
2
2
0
0
1
0
2
1
2
1
2
0
0
0
1
2
1
1
1
2
0
1
0
1
0
0
1
0
0
2
0
0
2
0
1
0
0
2
0
0
0
0
1
0
0
0
1
1
2
2
1
0
1
0
1
0
0
2
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
2
0
2
0
0
2
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
2
0
0
0
2
2
3
0
0
0
0
0
0
0
1
0
2
0
1
2
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
2
2
2
1
1
0
0
0
0
0
0
0
0
2
2
2
2
0
2
0
0
2
1
0
0
1
2
1
1
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
2
0
0
0
2
1
1
0
1
2
0
1
0
0
1
1
2
0
1
0
1
0
0
2
0
0
1
1
1
0
0
1
0
0
1
4
0
0
1
1
1
0
0
2
1
0
2
0
0
0
0
0
1
1
1
1
1
2
1
0
1
2
1
2
1
0
0
0
1
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
1
0
0
0
0
1
0
2
0
2
0
1
0
2
1
0
0
0
0
0
1
0
3
0
1
0
0
1
2
0
2
1
0
1
0
2
0
1
0
1
2
0
1
0
1
2
0
1
0
0
0
2
1
0
2
1
0
1
0
2
0
0
1
0
0
0
2
0
0
1
0
0
0
2
0
0
4
2
0
0
0
0
0
1
2
2
2
2
0
0
2
2
0
0
1
0
1
0
2
2
1
0
0
0
0
0
2
0
0
2
0
1
1
0
0
2
1
0
2
0
2
0
0
1
1
1
0
1
2
0
0
0
1
1
0
1
0
3
2
0
1
0
2
0
0
0
1
0
1
0
1
0
1
1
2
0
1
0
1
1
0
2
1
0
0
0
1
0
0
0
2
0
1
2
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
2
1
1
2
1
2
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
2
2
0
0
0
0
1
2
0
1
1
1
0
2
2
2
0
0
2
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
2
2
0
0
0
2
2
1
1
0
0
0
0
1
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
2
1
0
0
2
0
0
1
0
0
0
1
0
2
1
0
1
0
0
1
0
0
2
1
2
0
0
1
0
0
0
0
0
1
0
1
0
0
2
0
0
2
0
1
1
0
0
1
0
0
1
2
0
1
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
1
1
1
2
0
0
0
0
0
0
2
2
0
0
1
2
0
0
0
0
2
0
1
0
0
2
1
0
0
0
1
0
0
1
2
0
0
0
1
0
0
0
2
0
0
2
0
1
1
0
0
1
0
1
2
1
0
2
0
0
0
1
1
2
3
0
2
0
0
0
1
1
1
0
0
3
0
0
0
1
1
0
0
2
0
3
0
2
0
0
0
2
0
0
2
0
0
5
3
0
0
1
6
2
1
0
0
0
0
0
2
2
1
2
0
0
1
1
0
0
1
1
1
0
0
1
1
0
0
0
0
2
0
2
2
1
0
1
0
1
2
0
1
2
3
2
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
2
1
1
3
0
2
1
2
2
0
1
0
0
0
1
1
1
1
0
0
2
0
2
0
2
1
0
0
2
2
0
0
0
0
2
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
1
2
0
1
2
0
2
1
2
0
0
0
0
0
2
0
1
1
0
0
1
0
2
0
2
1
2
0
1
0
2
0
1
0
2
1
0
0
2
1
1
1
3
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
2
1
1
2
3
1
0
0
1
1
1
0
2
0
0
2
2
0
1
0
3
0
0
1
0
0
1
2
0
0
2
2
1
0
2
1
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
1
0
1
0
1
2
0
0
0
2
2
0
1
0
0
0
1
0
3
0
1
1
0
0
2
0
1
2
2
1
0
1
1
1
2
0
1
0
0
1
0
2
0
1
0
0
2
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
1
1
0
1
0
1
2
1
1
0
0
0
0
0
0
2
0
0
1
0
2
1
1
2
2
0
1
1
2
0
0
2
0
0
0
0
2
2
0
1
0
2
1
1
3
0
0
2
0
0
1
0
2
0
0
0
1
2
0
0
0
0
0
1
0
1
0
1
0
2
2
1
2
1
1
0
0
0
0
1
0
0
0
3
1
0
0
0
2
1
0
2
0
0
0
0
0
0
1
1
1
0
1
1
1
2
0
2
0
0
0
1
1
2
1
1
1
2
0
1
2
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
2
1
0
0
2
0
2
1
0
0
0
2
0
0
2
0
2
1
0
2
2
1
2
1
0
0
0
4
0
0
1
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
2
1
0
2
0
0
0
0
0
0
2
0
2
1
2
0
2
0
0
0
0
1
0
1
0
0
0
0
0
2
0
2
0
1
0
3
1
2
1
0
1
2
1
2
1
2
2
2
2
0
2
0
0
1
0
0
0
2
1
1
1
0
2
0
2
0
0
2
0
0
1
0
2
2
0
2
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
2
1
0
1
0
0
0
2
0
0
1
2
1
0
0
0
0
0
0
5
1
0
0
2
2
2
2
0
2
2
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
3
0
1
0
2
0
0
0
0
0
2
0
1
0
1
0
1
0
1
2
0
1
1
1
0
2
0
0
2
0
1
0
1
2
0
1
1
0
0
0
1
1
0
2
0
1
1
1
0
1
1
0
0
0
0
0
2
0
2
0
0
1
0
0
1
0
0
1
1
1
0
0
0
2
1
0
0
3
2
0
1
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
1
2
1
0
2
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
2
2
0
2
3
0
0
0
2
2
2
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
2
0
0
2
2
4
0
0
1
0
0
0
0
0
2
1
2
1
0
4
0
0
1
0
0
0
2
2
0
0
1
0
2
2
1
2
0
1
0
0
1
1
2
0
0
1
0
0
0
0
4
3
0
2
1
0
0
0
1
2
0
1
2
2
4
0
0
1
0
0
1
0
0
0
0
1
1
1
0
0
2
0
1
2
0
0
1
0
0
1
0
0
0
0
1
0
0
1
1
2
2
7
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
1
2
0
0
2
0
0
0
1
1
1
1
0
1
0
0
1
2
2
0
0
1
0
0
2
2
0
1
0
1
0
1
1
1
0
2
1
2
5
0
0
0
1
0
0
2
0
2
0
0
0
2
0
1
2
0
0
1
0
0
2
3
1
0
0
0
0
1
0
0
2
1
1
2
1
0
0
2
1
0
0
1
0
0
0
0
0
0
3
2
0
0
0
0
2
2
2
0
0
0
2
1
0
0
0
0
0
1
0
2
0
1
0
1
0
2
0
0
1
0
2
0
2
0
0
1
0
0
0
0
0
1
4
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
2
0
0
0
2
1
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
2
0
0
0
1
1
2
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
1
3
2
0
1
0
0
0
2
1
0
0
1
0
1
0
2
2
0
2
0
2
1
0
1
1
2
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
1
2
2
0
0
1
1
0
2
2
2
0
0
0
1
0
0
2
0
0
2
1
2
1
0
0
2
0
1
1
0
0
0
0
2
0
0
0
0
0
0
2
2
2
1
1
3
0
0
0
1
0
1
0
2
1
0
2
2
9
2
0
0
2
1
6
0
1
1
1
0
0
1
0
0
0
1
0
0
0
0
2
1
1
2
0
2
0
2
0
1
0
0
0
0
0
0
2
2
0
0
1
0
0
2
0
0
1
0
1
0
1
0
0
2
0
2
0
1
0
2
3
2
2
0
2
0
1
2
0
1
0
1
2
0
0
0
0
1
2
0
1
0
2
2
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
1
0
0
0
0
2
1
0
2
0
0
2
0
1
0
2
0
2
0
1
2
0
0
0
0
0
0
1
0
0
2
0
6
1
2
0
2
2
0
1
1
1
0
2
0
0
0
1
0
1
0
1
1
0
1
0
0
1
0
0
1
2
0
4
1
1
0
0
0
2
1
2
0
0
2
0
2
0
0
0
1
0
0
1
1
0
2
5
1
0
2
0
0
2
1
1
0
2
0
2
2
0
1
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
1
0
0
2
0
0
2
0
0
0
0
1
1
0
2
2
2
0
2
0
0
0
0
1
0
0
2
2
0
0
0
0
0
3
0
0
0
2
0
2
2
3
0
0
0
0
1
0
1
0
0
2
0
2
1
0
0
1
2
0
0
2
0
0
0
0
0
0
1
2
1
0
3
0
0
0
2
0
0
1
2
0
0
2
2
1
0
0
0
1
0
1
4
0
0
1
1
2
0
0
1
0
1
1
2
1
0
0
0
2
2
1
1
0
1
0
1
0
2
1
0
1
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
2
1
0
0
0
0
2
1
0
0
2
0
1
0
0
2
1
0
0
2
0
0
0
0
0
1
0
2
1
0
0
0
1
0
0
0
2
1
0
0
0
0
0
1
0
1
0
2
0
0
0
1
0
2
0
3
1
0
2
2
2
0
0
0
1
0
2
1
0
0
0
0
0
0
0
2
3
0
0
1
0
1
0
0
0
0
0
1
0
1
0
1
0
0
2
0
0
0
2
1
0
0
0
0
1
2
0
0
1
0
1
1
2
0
0
0
0
1
1
0
0
0
0
1
2
1
2
1
2
2
0
0
0
0
2
0
0
0
1
0
0
2
0
1
2
0
0
0
2
0
2
0
0
1
0
1
0
0
1
0
2
1
0
1
1
2
1
0
2
0
0
0
2
1
0
1
0
0
0
0
0
0
0
1
1
0
1
1
1
0
1
0
1
2
1
0
0
2
2
0
1
2
1
0
2
1
2
1
0
2
0
1
2
0
0
2
0
0
1
0
0
2
0
0
1
2
2
0
1
0
1
2
1
0
2
2
0
0
1
1
0
0
0
0
2
1
2
2
0
0
1
0
1
0
0
0
0
2
2
0
1
0
2
0
2
0
0
4
0
0
0
0
0
1
0
2
2
2
0
0
0
2
1
2
2
0
2
1
2
1
2
0
0
0
1
2
0
2
2
0
4
2
0
1
0
1
0
0
0
1
0
0
0
1
0
1
0
0
2
1
0
2
1
0
1
0
0
0
0
0
0
2
0
3
1
0
1
0
1
0
0
0
2
0
0
3
0
2
2
0
0
0
2
1
0
0
2
0
0
1
0
2
0
0
2
0
0
0
0
1
1
0
2
0
1
0
0
2
0
1
0
0
0
1
2
0
0
1
0
0
0
0
0
2
1
0
0
1
1
5
1
0
0
1
0
0
0
1
1
2
0
0
1
0
0
2
0
1
0
0
1
0
2
0
1
1
1
2
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
2
0
2
0
0
0
1
1
0
0
0
0
2
2
0
1
0
2
0
1
0
0
1
0
0
0
1
1
1
1
1
2
1
0
0
3
0
0
0
2
2
0
0
3
0
2
0
0
2
2
0
0
0
2
0
0
0
2
0
0
0
0
1
1
0
1
1
0
0
0
1
0
0
0
0
2
0
0
0
1
1
0
2
1
0
0
0
1
1
0
1
0
0
0
2
2
2
0
2
0
2
2
2
0
0
2
1
2
2
1
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
1
2
1
0
0
0
1
0
2
0
0
2
1
0
3
0
1
0
0
1
1
2
0
2
0
3
0
0
2
0
0
1
2
1
0
0
2
1
0
1
0
1
0
1
1
2
2
0
0
0
0
0
2
1
0
0
1
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
2
0
1
1
0
0
0
0
2
1
1
4
0
0
0
0
0
1
1
0
0
1
0
0
2
1
1
2
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
4
0
0
1
1
2
1
1
3
2
2
0
2
0
1
0
0
2
0
2
1
2
0
0
0
1
0
0
2
0
1
0
1
0
1
0
0
1
0
1
2
0
0
1
2
0
0
0
2
0
0
1
2
0
1
2
0
6
0
2
1
0
0
1
0
1
2
2
0
2
2
0
1
0
1
1
0
0
0
0
2
0
1
1
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
3
1
0
1
1
0
0
0
2
2
0
0
0
0
0
2
0
2
0
1
0
0
2
0
2
1
0
0
2
0
0
0
2
0
0
0
0
1
1
0
2
0
0
0
1
0
0
1
2
0
1
2
1
0
2
0
2
2
0
0
0
2
0
2
1
2
0
1
0
0
0
0
1
2
1
0
0
1
1
0
0
0
1
2
0
0
0
0
2
0
0
0
0
1
0
1
0
1
1
0
2
0
0
2
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
1
0
1
0
0
0
1
1
0
0
0
2
1
0
0
2
0
0
1
0
0
0
1
0
0
0
1
1
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
4
0
2
0
1
1
1
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
1
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
2
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
2
1
1
2
2
1
0
0
0
0
0
1
0
0
0
2
0
0
1
1
3
0
2
0
1
1
2
1
0
1
1
0
2
1
1
0
0
2
2
1
0
0
0
1
2
1
0
0
1
1
0
0
2
0
0
0
0
0
1
0
0
1
1
2
0
2
1
0
0
0
2
1
0
0
1
0
0
0
0
1
0
0
0
0
0
2
1
2
0
1
2
1
0
0
0
0
2
0
1
0
0
2
1
1
1
0
0
0
0
3
0
1
0
1
1
0
0
0
0
0
1
1
0
2
0
1
0
1
0
0
0
0
1
0
0
1
1
0
0
2
0
0
2
0
0
0
2
1
2
0
1
2
0
0
1
2
1
1
2
1
0
0
1
0
2
0
2
0
1
0
0
2
0
0
2
2
1
0
1
0
0
2
0
0
1
0
0
0
0
2
2
0
1
0
0
3
2
1
1
1
2
1
1
2
0
0
0
1
1
1
0
0
1
0
2
2
2
1
2
1
3
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
3
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
2
0
1
0
1
0
0
0
1
1
1
5
0
2
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
2
2
1
2
0
1
1
0
2
0
1
0
2
0
2
1
0
0
0
1
1
0
0
0
2
0
0
0
1
0
2
2
0
2
1
0
0
2
1
2
2
1
1
2
0
1
0
0
2
0
0
2
0
1
0
0
2
2
1
0
0
0
0
0
0
1
0
0
0
1
2
3
0
0
0
0
2
0
0
1
1
0
0
2
0
2
0
0
1
0
1
1
0
0
1
1
0
2
0
2
0
0
0
2
1
2
1
0
0
1
0
1
2
0
0
1
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
1
0
0
0
2
1
1
1
1
1
1
0
0
0
0
0
0
2
0
1
1
2
0
0
0
2
2
0
1
2
0
1
3
1
2
2
0
0
0
0
1
0
1
2
0
0
0
1
2
0
0
0
1
0
1
1
2
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
1
1
0
0
1
0
0
1
2
0
1
1
0
0
1
0
0
0
0
0
2
1
1
0
2
1
0
0
3
0
2
0
0
2
2
1
1
0
0
2
2
0
2
1
1
0
1
2
2
2
0
2
2
2
0
1
0
2
0
0
0
1
1
0
0
0
4
1
0
1
0
0
1
0
1
0
0
2
0
1
0
1
2
1
2
1
0
2
0
1
1
0
1
0
1
1
0
0
0
0
0
0
0
2
1
1
1
2
1
2
1
0
1
1
2
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
3
0
2
2
0
2
0
0
1
0
0
1
0
1
1
0
0
1
2
0
0
2
1
2
2
0
1
3
0
0
2
3
0
0
0
2
0
2
2
0
0
0
0
0
1
0
2
0
0
1
0
0
0
3
0
2
0
0
0
0
0
2
0
1
0
0
1
0
0
0
1
1
1
2
0
0
0
1
0
0
2
0
0
0
2
2
0
0
0
0
0
1
0
2
1
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
2
0
0
1
0
0
0
1
0
1
0
1
0
2
0
0
0
0
0
0
2
1
0
0
0
0
1
1
0
0
2
2
0
2
1
3
0
0
0
3
0
1
0
0
0
1
2
0
0
0
0
0
0
2
2
1
2
0
1
2
0
0
1
0
0
1
2
1
0
2
0
0
0
0
1
0
1
0
2
0
0
3
1
0
1
1
0
1
0
0
2
1
1
1
1
1
0
0
2
1
2
0
0
2
2
0
2
0
4
0
0
1
1
0
0
1
1
0
1
1
0
1
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
1
0
1
1
0
0
1
1
2
0
0
2
0
0
0
0
0
1
0
1
2
0
0
0
0
2
0
0
1
2
1
1
0
1
3
2
1
0
0
0
1
1
0
1
0
0
0
2
1
0
2
2
0
0
0
2
0
2
0
0
0
3
0
2
0
2
1
0
0
3
0
1
0
1
1
0
1
0
1
0
0
1
0
2
0
0
0
0
2
0
0
1
1
1
0
2
0
0
0
2
1
0
0
0
1
0
2
0
0
2
0
0
1
0
0
0
1
0
0
1
0
2
0
2
0
1
1
0
2
0
1
2
0
0
0
0
2
0
0
0
0
1
2
1
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
2
1
0
0
1
2
0
1
2
1
0
0
2
1
2
0
0
0
0
2
2
0
0
1
2
2
1
0
0
0
2
0
2
0
0
2
0
1
0
1
1
2
2
1
0
0
0
0
0
0
1
0
1
0
2
0
0
1
0
1
0
0
0
0
1
2
0
0
0
1
0
0
0
1
0
0
1
0
1
1
3
0
0
2
0
0
0
0
0
2
0
1
0
0
0
1
0
1
0
0
2
2
2
2
2
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
2
2
3
2
1
0
2
1
1
1
0
0
2
2
0
0
1
1
0
2
2
0
2
0
0
0
1
0
2
0
1
2
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
2
1
2
0
2
2
0
0
1
2
2
2
0
0
1
0
3
2
2
0
0
4
0
0
0
0
0
1
1
1
0
1
1
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
2
0
0
2
0
0
1
0
0
0
0
0
2
1
1
2
0
2
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
1
1
0
0
0
0
0
1
0
0
2
0
1
0
1
0
0
0
0
0
2
0
2
0
0
0
1
2
0
1
1
2
1
0
2
1
2
0
0
0
1
0
0
3
1
1
2
0
0
0
0
0
1
1
0
1
2
0
1
0
0
2
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
1
2
1
1
0
2
0
0
1
0
2
0
0
1
1
0
0
0
0
2
0
2
0
1
1
1
1
0
0
0
0
1
1
2
1
2
0
0
0
0
0
0
0
1
0
1
2
0
0
1
2
0
1
0
0
0
2
0
0
1
0
1
0
1
1
0
1
0
1
0
1
1
0
0
0
0
3
2
1
2
0
1
0
0
0
1
0
0
1
0
0
1
1
0
3
0
0
1
0
2
2
1
1
2
0
2
0
0
1
2
1
0
0
2
1
0
0
2
1
1
0
2
1
0
0
2
0
1
2
2
0
0
2
0
2
2
0
1
0
2
0
1
0
2
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
2
1
0
0
0
1
1
0
1
0
1
1
0
1
2
0
0
0
1
2
0
0
1
2
2
0
1
0
0
1
0
1
0
0
0
0
0
0
1
1
1
1
2
1
2
1
1
0
1
1
1
0
2
0
1
1
0
0
0
2
0
0
2
2
2
0
4
0
0
1
0
0
1
0
0
0
0
0
0
0
2
2
0
1
0
0
1
2
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
2
0
0
0
0
2
1
2
2
0
0
0
2
0
1
0
0
1
0
0
0
2
0
1
1
0
0
2
1
0
1
1
0
0
1
2
1
0
0
0
0
0
0
1
2
0
0
0
2
1
0
0
1
2
0
0
0
0
2
0
0
2
0
1
2
2
0
0
1
4
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
1
0
0
1
2
2
1
0
0
0
1
0
1
0
2
0
1
2
1
0
0
0
0
0
0
0
1
1
2
3
2
1
0
1
2
2
0
2
0
0
0
0
2
2
0
0
2
0
2
1
1
0
0
1
0
1
0
1
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
2
3
1
0
1
0
0
0
0
0
0
1
2
1
1
0
0
2
0
0
2
2
0
0
1
1
3
2
0
1
1
2
0
1
0
2
2
0
1
2
0
0
0
0
0
0
0
1
3
0
1
0
0
3
0
1
0
0
1
0
0
2
0
2
1
0
0
2
0
1
1
2
2
2
0
1
1
0
0
0
1
0
0
3
2
0
2
1
0
0
0
0
2
0
0
2
1
0
0
1
2
0
0
0
0
0
1
0
2
0
0
1
0
3
2
0
0
0
0
0
0
0
0
1
0
2
0
1
1
4
1
0
2
3
0
0
0
3
2
0
2
0
1
1
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
2
0
0
1
1
0
0
2
0
0
0
2
1
0
0
1
1
0
1
0
5
0
0
0
0
1
0
2
2
0
0
0
2
2
1
0
1
1
0
0
2
2
2
1
1
0
0
0
1
0
0
2
2
0
2
1
0
0
0
1
1
0
2
1
0
1
0
0
1
2
1
1
1
2
1
0
0
0
0
0
2
0
2
4
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
1
2
1
0
0
1
0
2
0
0
0
0
0
0
1
0
2
0
0
0
2
0
1
0
1
1
1
0
0
1
2
0
0
1
1
0
0
0
0
2
1
0
2
0
0
0
0
0
1
1
0
0
0
0
0
2
0
1
0
0
0
2
4
0
0
2
1
0
4
0
0
2
0
0
0
0
1
0
2
2
0
1
1
0
1
0
1
0
0
0
2
1
2
0
0
1
0
2
0
1
0
2
0
0
1
0
0
0
2
1
1
0
0
0
2
0
0
1
0
1
0
0
0
1
2
0
2
2
0
0
1
0
0
0
0
0
1
1
0
2
2
1
0
1
2
1
2
1
1
0
1
0
0
0
1
0
0
1
0
0
4
1
3
2
0
2
2
2
0
2
2
0
1
0
0
2
0
0
0
2
0
0
0
0
1
2
2
1
3
0
0
0
0
2
2
0
0
2
1
0
0
2
0
0
0
1
0
1
2
0
0
1
0
0
0
0
3
1
1
2
5
1
0
0
0
2
1
1
0
0
0
0
1
1
0
0
0
1
0
1
1
0
1
0
0
0
0
0
2
0
1
1
0
1
0
0
0
0
0
1
0
1
1
1
0
1
0
1
0
1
0
1
0
1
2
1
0
2
0
1
2
1
2
0
1
0
0
1
0
1
2
0
1
2
3
0
0
0
2
0
0
0
0
1
2
0
2
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
1
1
0
0
1
1
1
2
0
1
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
2
2
1
1
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
2
0
0
1
2
0
1
2
1
0
0
2
2
0
0
0
0
0
2
0
1
1
2
0
0
2
2
2
0
0
2
2
0
0
0
2
0
1
0
1
1
0
1
1
1
0
0
2
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
1
0
1
0
0
2
0
0
0
1
0
0
0
1
1
0
1
0
0
1
2
2
0
2
0
0
3
2
0
1
0
1
0
0
0
1
1
2
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
3
1
0
0
0
0
2
1
1
0
1
0
0
0
0
1
1
0
0
0
0
2
0
0
0
1
0
1
2
2
0
1
0
0
0
0
0
1
0
2
0
1
1
0
0
1
1
0
0
2
2
1
0
1
0
1
0
0
0
0
0
0
0
0
2
0
2
2
0
1
0
1
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
2
1
0
0
0
0
1
0
0
0
2
1
1
1
2
1
0
1
1
0
0
1
1
0
0
0
1
0
0
1
1
0
2
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
1
0
2
0
0
2
1
0
1
1
2
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
6
0
1
3
0
0
1
0
0
0
0
0
1
0
2
2
0
2
1
0
1
0
2
1
2
0
2
0
0
1
0
2
1
1
2
0
0
2
1
0
0
0
0
0
0
3
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
1
0
2
1
0
0
1
1
1
2
1
4
0
0
2
1
0
0
0
1
0
0
1
1
1
0
0
0
2
0
2
2
0
0
1
0
0
1
1
0
0
0
0
0
1
0
1
1
4
0
0
1
2
2
0
2
0
1
0
0
1
0
1
0
2
0
2
0
1
0
1
0
0
1
0
2
0
2
2
0
1
0
0
0
1
0
2
2
1
2
1
1
0
0
0
0
1
3
1
1
1
0
2
1
1
1
2
0
1
2
0
0
2
1
0
2
0
1
1
0
2
0
0
1
1
2
2
2
0
2
1
1
0
2
2
0
1
0
0
1
0
0
1
1
1
1
2
0
0
0
0
1
0
1
2
2
2
0
0
2
0
0
1
0
0
0
0
1
2
0
1
2
0
1
0
3
0
2
0
0
0
0
0
2
0
2
0
2
0
0
1
2
0
0
4
0
0
0
1
0
2
0
1
0
1
0
0
0
1
2
0
0
2
0
0
0
2
2
2
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
1
2
2
1
0
0
0
1
1
2
0
1
2
0
1
0
1
0
0
2
0
0
2
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
1
0
2
1
1
0
1
0
2
0
0
0
0
0
0
0
2
1
0
0
2
2
0
0
0
0
0
1
0
0
2
0
3
0
2
0
2
0
1
1
0
0
0
1
0
3
2
2
0
0
0
2
0
4
3
0
0
0
2
3
2
0
0
2
0
1
1
1
0
7
1
7
2
0
0
1
0
1
1
0
0
2
0
2
3
0
0
0
0
0
2
1
1
0
2
2
0
1
0
1
0
2
0
1
2
0
1
0
1
0
2
0
0
0
1
0
1
0
0
1
2
0
1
0
2
2
2
2
1
0
1
1
0
1
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
3
0
1
1
0
0
0
0
0
1
0
0
1
2
3
2
0
0
0
0
1
1
2
0
1
0
2
1
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
1
1
0
0
0
0
3
2
0
2
2
1
0
2
1
2
0
0
0
0
0
0
0
0
0
2
1
0
2
1
1
0
2
1
1
1
2
0
0
0
1
2
0
1
0
0
0
0
1
0
2
1
1
0
0
1
0
0
0
1
1
2
0
2
0
0
0
1
0
2
0
2
0
0
2
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
2
1
0
2
1
0
1
0
0
2
0
2
0
1
1
3
1
0
2
0
0
0
2
0
0
0
0
0
9
0
1
0
0
1
0
2
1
0
0
2
0
2
1
0
0
1
0
0
2
0
1
0
0
1
0
0
0
0
2
0
0
0
1
1
0
0
0
0
1
0
0
2
0
0
0
1
3
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
3
1
0
0
4
0
0
0
1
0
0
0
2
2
2
1
0
1
0
1
0
0
2
0
1
2
1
0
0
0
0
0
3
2
2
1
1
0
2
0
2
1
1
0
3
1
0
1
2
0
0
1
0
0
0
1
0
0
1
0
2
1
0
1
1
1
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
1
0
2
0
3
0
2
0
0
0
0
1
0
1
2
0
0
0
1
1
2
0
0
1
0
2
2
1
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
2
1
0
0
1
2
0
2
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
2
0
1
2
0
0
0
0
1
1
0
0
0
2
0
0
3
1
1
0
5
0
0
1
0
0
1
0
0
0
1
3
0
3
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
1
2
1
0
2
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
2
2
1
0
0
1
1
2
1
1
0
0
10
0
2
2
2
2
2
0
1
0
0
2
0
1
0
0
0
0
0
0
3
0
0
0
0
1
0
2
2
0
2
1
2
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
1
2
0
0
0
0
2
0
2
2
1
2
1
1
2
0
2
1
1
0
0
0
0
0
1
0
1
1
1
1
0
0
0
0
0
3
0
0
2
0
0
0
1
0
0
0
3
0
0
0
0
0
2
0
1
0
1
0
1
0
2
1
1
0
0
0
2
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
2
0
2
0
0
1
0
2
0
0
0
0
2
0
0
0
1
0
1
1
0
1
0
0
0
0
2
0
0
0
1
2
0
1
0
0
1
2
1
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
2
1
0
0
0
0
1
0
0
0
0
0
0
2
0
2
1
0
2
0
0
2
0
0
0
1
1
0
0
1
1
2
0
0
1
1
1
0
0
0
1
1
0
0
1
0
1
1
2
0
2
0
2
0
0
0
0
2
2
0
0
1
0
0
0
1
0
0
0
3
0
0
0
2
2
1
0
1
0
1
3
2
0
2
0
0
1
0
1
2
0
1
0
0
0
1
1
0
2
0
0
0
1
1
0
0
0
0
2
0
2
2
2
2
1
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
1
1
0
2
0
2
0
0
2
2
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
1
1
1
1
0
1
0
0
2
1
0
0
0
1
2
0
1
0
1
0
1
0
1
0
0
0
1
0
7
0
2
0
2
0
1
0
1
0
0
1
1
0
0
0
2
1
0
0
0
1
0
1
2
2
0
0
0
0
1
0
2
0
2
0
0
0
0
2
0
0
2
1
1
0
0
1
1
0
0
0
1
0
0
0
0
2
2
0
0
0
0
1
0
0
1
0
1
2
1
0
1
0
0
1
0
1
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
1
0
2
0
2
0
2
0
0
0
2
0
0
0
1
0
2
0
1
2
1
1
0
1
0
0
0
1
1
2
1
1
1
0
2
0
2
0
0
1
2
0
0
0
1
0
1
0
0
1
1
0
0
1
0
0
0
0
0
1
2
0
0
1
2
0
0
0
1
0
0
0
1
2
1
0
0
1
0
1
0
1
1
1
2
2
0
1
1
2
0
2
2
0
0
2
1
2
0
1
0
1
0
0
0
0
0
1
0
0
5
0
0
0
1
1
0
1
0
0
1
0
0
1
1
0
0
2
0
1
1
0
0
0
0
0
0
0
2
2
4
0
1
0
0
0
0
0
1
1
1
0
1
1
0
2
0
0
6
0
1
0
2
1
1
1
0
0
0
2
0
0
2
0
0
0
0
0
2
1
0
2
0
1
0
1
0
0
0
2
1
2
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
2
1
1
2
2
0
0
0
0
0
2
0
0
2
0
0
1
0
3
2
0
0
2
0
2
0
0
0
0
1
4
0
0
0
3
0
1
0
2
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
1
2
2
0
0
0
0
0
0
0
0
1
1
1
1
1
1
0
0
0
1
4
0
1
2
0
1
2
1
0
0
0
0
0
0
1
2
2
1
1
1
1
1
0
2
0
0
0
0
0
0
1
1
0
1
0
1
1
0
1
1
0
0
0
0
2
0
1
0
0
0
2
0
0
0
1
2
0
0
0
0
1
2
0
0
0
1
0
0
0
2
0
0
1
0
0
0
1
2
0
2
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
3
0
0
2
0
0
0
1
2
1
0
2
0
2
2
0
0
0
2
0
1
0
1
1
2
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
1
1
1
0
0
0
0
1
1
1
1
1
0
3
0
0
0
0
0
0
0
2
0
0
3
1
0
2
2
2
0
0
0
2
0
0
0
0
0
1
0
1
0
0
1
2
0
0
0
1
0
0
0
0
0
3
0
1
2
1
0
1
1
1
0
0
2
0
1
0
0
1
0
1
1
1
0
2
0
0
2
0
0
0
1
2
2
0
0
2
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
3
0
0
1
0
0
0
2
0
0
1
1
0
0
0
2
0
2
1
2
2
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
1
0
0
2
0
1
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
2
3
0
0
0
1
2
0
1
2
2
0
2
0
0
0
1
3
0
1
2
0
2
0
0
0
0
0
1
2
0
0
1
1
0
1
0
1
0
0
0
0
1
0
0
2
1
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
1
1
2
0
0
1
1
0
1
0
0
0
0
2
2
0
1
2
0
2
2
0
0
1
0
0
0
0
0
0
0
1
1
2
0
0
1
1
1
2
2
1
0
0
1
0
0
0
0
1
0
1
0
1
1
1
0
3
4
2
0
4
0
0
0
0
4
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
2
0
1
2
0
0
1
0
0
0
1
0
0
2
0
2
2
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
2
0
1
1
1
0
0
0
0
2
0
2
1
1
0
1
0
0
2
1
2
0
0
0
0
0
0
2
2
0
2
1
1
1
0
2
1
0
0
0
0
2
1
1
1
2
1
1
2
1
0
1
0
0
0
2
2
0
2
0
0
0
1
1
2
2
0
0
0
0
0
1
0
0
0
2
1
0
0
2
0
0
1
0
0
0
1
1
0
0
3
0
1
0
1
0
0
0
0
2
0
0
0
0
1
1
0
1
0
2
1
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
2
1
1
1
1
0
2
0
0
0
2
0
0
0
2
0
2
1
0
1
2
0
0
0
0
1
2
0
1
0
1
0
1
0
0
2
2
0
1
0
1
2
2
0
0
0
2
2
0
2
2
1
2
0
2
1
0
0
0
3
2
1
1
1
2
0
0
0
2
0
2
0
1
0
1
1
3
0
0
0
0
1
0
1
0
0
0
0
1
0
0
2
2
1
3
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
1
0
2
2
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
1
0
2
0
1
0
1
0
0
0
0
0
2
0
3
0
0
2
0
1
0
0
2
0
2
2
0
0
0
2
1
0
0
1
1
1
1
0
2
0
3
1
0
1
0
1
2
1
0
0
2
0
1
1
1
0
0
0
2
0
0
0
0
0
1
1
0
0
1
0
0
1
1
1
0
0
1
0
0
0
1
0
2
0
0
0
0
2
0
0
0
1
0
2
0
0
0
1
0
0
1
2
0
1
2
2
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
2
2
2
0
2
0
0
0
0
2
1
2
2
3
0
1
0
0
0
0
2
2
0
0
0
1
0
0
2
0
2
1
1
0
2
0
0
2
2
1
0
2
0
0
1
2
0
0
0
2
1
0
2
0
2
0
2
1
0
1
1
2
0
1
2
0
1
0
0
0
0
0
2
0
0
2
1
1
0
0
1
2
0
1
0
1
3
0
0
0
3
0
2
0
2
0
0
0
0
1
0
0
0
0
2
0
0
1
1
0
0
2
0
0
1
0
0
2
1
2
0
0
0
2
0
0
2
0
2
0
0
2
0
0
0
1
1
2
2
1
0
2
0
1
2
0
0
0
0
2
0
1
2
1
0
0
0
1
2
0
0
3
1
0
2
0
0
0
2
0
0
1
0
1
0
2
0
1
0
2
0
0
0
0
0
2
0
1
0
0
1
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
2
0
2
2
2
1
1
1
0
0
2
0
0
0
0
0
0
0
2
0
2
0
1
0
2
2
0
0
0
1
1
2
3
0
1
0
1
1
0
0
2
1
0
2
1
0
2
1
0
1
0
1
3
1
0
0
2
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
2
0
0
0
0
1
2
0
1
1
0
2
2
1
0
0
0
2
0
0
1
0
2
1
2
2
3
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
2
0
1
0
1
1
0
0
1
1
0
1
1
2
0
0
1
2
0
0
0
0
1
0
0
0
2
1
0
1
1
2
0
0
0
0
0
3
2
2
1
1
0
0
1
0
1
0
0
1
2
2
2
0
2
2
2
0
0
0
0
0
0
0
0
1
0
1
2
1
2
0
0
0
2
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
1
1
0
0
0
1
0
1
0
1
1
0
2
1
1
0
0
2
0
0
1
1
1
1
2
0
0
0
0
1
2
0
0
0
0
0
1
2
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
2
1
1
0
0
0
0
0
1
2
0
0
0
2
2
0
2
0
1
4
0
1
0
0
1
1
1
1
2
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
2
0
2
0
1
0
0
2
0
0
0
2
0
0
0
2
0
1
2
1
2
0
0
0
0
1
1
0
2
0
0
0
0
1
1
1
0
0
2
0
2
0
0
0
0
0
0
1
1
0
1
1
2
0
1
0
2
2
1
0
0
0
1
0
2
1
0
0
0
0
1
0
2
1
1
0
1
0
0
0
3
0
1
2
0
2
2
0
0
2
1
0
0
0
2
1
0
1
2
1
0
0
0
0
0
1
1
1
0
3
2
2
1
0
0
2
1
1
0
0
1
1
0
0
5
0
0
1
2
0
0
0
0
0
0
1
1
0
0
1
0
2
2
2
0
3
0
1
0
2
2
0
1
0
0
1
0
0
1
0
0
2
0
1
1
0
0
0
0
1
0
0
0
0
3
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
1
0
1
2
0
1
2
0
0
0
1
2
1
1
0
2
0
2
0
0
1
0
2
0
2
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
2
2
1
1
0
1
0
0
1
2
0
1
0
0
0
0
2
0
0
0
2
2
0
0
1
0
2
0
1
0
1
0
1
2
0
0
0
2
2
3
0
0
1
1
1
0
0
2
0
2
0
2
0
0
2
1
0
0
2
0
0
1
0
0
2
0
0
2
1
0
0
0
0
2
4
0
1
1
0
1
2
0
0
2
0
1
0
0
0
0
1
0
1
0
1
1
0
0
0
1
1
0
1
2
2
1
0
2
0
1
2
5
0
0
0
1
0
1
2
0
0
0
1
0
0
2
0
0
1
0
0
1
0
0
0
1
0
2
0
1
0
3
0
2
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
1
0
1
2
0
0
2
0
0
1
1
0
1
1
0
2
1
1
0
1
0
0
1
1
0
1
0
2
0
0
2
2
2
1
2
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
1
0
2
2
0
0
1
1
0
1
1
0
1
1
0
0
0
0
0
0
2
1
0
0
0
0
2
0
2
0
3
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
1
0
0
0
0
1
0
1
2
1
0
0
0
0
0
2
0
1
2
2
1
0
0
0
0
0
1
2
0
1
1
0
0
3
1
0
0
2
2
0
0
0
1
0
2
1
0
1
1
3
0
1
0
0
0
0
1
0
0
1
1
2
0
0
0
2
1
1
0
3
4
0
0
0
1
0
0
0
1
0
0
1
0
2
1
0
0
0
1
0
0
1
0
0
0
0
2
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
2
2
2
1
2
2
0
2
2
0
1
1
0
3
0
0
1
2
0
0
2
0
2
1
0
0
0
0
0
1
1
0
0
1
1
2
0
1
2
2
0
0
0
0
1
0
1
0
0
0
0
2
2
0
0
0
2
0
0
0
1
1
0
0
0
1
2
0
2
2
0
1
2
1
1
1
0
3
1
0
0
0
2
2
2
1
0
0
1
0
4
0
1
1
0
0
0
0
1
2
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
1
1
0
0
0
0
0
2
0
1
0
0
0
1
0
2
1
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
1
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
2
2
0
0
0
0
1
0
0
1
2
1
2
0
1
0
1
1
0
0
0
0
1
1
0
1
2
1
0
0
2
0
2
0
0
3
0
0
0
2
0
0
1
0
0
0
2
2
1
1
2
2
0
0
0
2
1
0
0
1
0
0
1
0
0
0
0
2
0
2
0
0
0
1
1
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
1
1
2
1
1
2
0
0
0
2
0
1
0
1
1
0
0
0
0
0
2
1
0
0
0
0
2
0
0
1
0
2
2
0
1
0
0
2
1
1
2
1
0
2
0
0
0
1
0
0
0
0
9
1
0
2
2
0
0
1
0
2
0
0
2
1
0
2
1
2
0
0
0
2
2
1
1
2
0
0
1
0
0
0
2
0
0
1
2
2
0
1
0
0
0
1
0
1
0
1
0
0
2
0
2
0
2
0
0
0
5
0
0
1
1
0
0
1
0
2
2
0
0
0
2
0
0
1
0
0
0
1
0
0
1
0
0
2
1
0
0
0
2
0
0
1
2
0
0
2
0
0
0
0
0
1
1
2
1
2
0
1
0
0
1
1
0
1
0
1
0
2
2
1
0
0
0
0
1
0
2
0
0
2
0
1
0
2
0
1
1
0
0
0
1
1
1
0
0
0
0
0
0
0
2
0
1
1
0
1
0
0
0
0
2
0
0
2
0
1
0
0
0
0
1
0
0
1
0
1
0
2
1
0
0
1
0
1
0
0
2
0
0
1
0
0
1
0
0
0
2
2
1
2
0
1
0
2
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
2
1
0
1
0
2
2
1
0
1
0
2
0
0
0
2
0
2
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
3
1
1
0
1
1
0
0
2
2
0
0
0
0
2
0
0
0
1
1
2
0
2
1
0
0
2
0
0
0
0
0
1
0
2
0
2
0
0
0
0
2
0
0
0
1
1
0
2
0
0
2
0
0
0
2
0
0
0
1
1
0
2
2
0
2
1
1
0
1
1
0
0
2
2
1
1
0
0
0
0
2
0
1
0
1
3
0
0
0
2
0
2
0
8
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
3
1
0
0
0
2
0
2
2
0
0
0
2
1
0
2
1
0
0
3
0
2
0
0
6
2
2
2
0
0
1
0
5
0
1
0
1
2
0
0
1
2
0
1
0
2
2
2
0
1
2
1
0
0
2
2
1
0
1
0
1
0
2
1
1
1
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
2
2
1
1
0
0
0
0
0
0
0
2
0
1
2
0
3
0
0
1
2
0
0
0
0
1
0
0
0
0
1
0
2
2
1
0
1
0
1
0
1
1
1
1
0
2
0
0
0
0
0
1
2
1
0
0
0
2
1
0
0
0
1
1
0
1
1
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
1
2
2
0
1
2
0
0
0
2
2
0
0
1
0
0
0
0
2
1
2
0
0
0
0
1
1
0
3
0
1
1
1
1
0
2
3
0
0
0
0
1
0
2
2
2
2
0
2
1
2
0
0
0
0
0
2
0
1
0
1
1
1
0
1
0
0
0
0
0
0
1
1
0
0
2
3
2
2
2
2
2
0
0
0
0
0
2
1
1
2
1
0
0
1
0
0
3
0
2
1
0
0
1
0
1
2
1
0
0
1
1
2
0
1
1
0
0
0
1
1
2
1
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
1
0
2
0
0
0
0
1
3
0
0
2
1
2
0
1
0
0
3
1
0
0
2
0
1
2
2
1
0
0
5
0
0
2
0
2
1
0
0
0
0
2
0
1
0
0
1
2
2
2
0
0
1
2
0
1
1
0
0
0
7
0
0
0
3
0
2
0
0
1
1
2
1
1
1
2
1
1
1
2
2
0
0
2
0
1
0
0
0
1
0
0
0
0
1
0
0
2
1
0
0
2
0
2
0
7
0
0
1
0
0
0
0
1
0
0
2
0
2
1
0
1
1
1
2
2
2
1
2
2
2
1
0
2
1
1
0
1
0
0
0
0
1
0
1
0
0
2
0
1
1
4
0
0
1
0
1
2
2
0
1
2
0
0
0
0
1
1
1
0
0
2
2
1
2
0
0
1
2
0
0
1
2
2
1
1
0
0
0
0
1
0
1
2
0
0
0
2
0
2
1
1
2
1
0
1
1
0
2
2
0
0
1
2
0
1
2
0
0
0
1
0
0
2
2
1
2
0
1
1
0
1
1
1
0
2
1
3
0
0
0
0
2
1
2
1
1
0
1
0
0
1
2
0
0
2
0
2
1
1
0
0
0
4
2
0
0
1
0
0
0
0
1
1
2
1
1
1
2
2
0
2
1
0
0
2
0
2
0
0
0
1
0
0
0
0
0
1
2
0
2
0
0
0
0
1
1
0
2
0
0
1
2
1
1
1
2
2
2
0
0
1
0
0
2
0
2
2
1
2
1
0
2
2
1
2
1
0
1
1
0
0
0
2
0
2
1
2
0
0
0
0
0
0
2
0
0
1
0
0
2
1
0
0
0
0
0
2
1
0
0
2
0
0
3
0
1
5
0
1
0
2
0
0
0
0
0
2
1
1
0
1
0
2
2
0
0
0
0
0
1
1
2
0
0
1
1
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
2
0
0
2
0
3
0
0
0
0
0
0
0
0
1
0
1
0
2
2
2
0
1
1
0
1
1
0
0
3
0
0
0
0
2
0
0
2
2
0
0
1
2
0
2
0
0
2
0
0
0
1
0
1
0
0
0
0
0
1
1
0
1
1
0
0
2
1
1
2
1
2
0
0
1
2
0
0
0
2
0
2
1
0
0
3
2
0
0
2
1
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
1
0
0
1
2
2
0
2
1
0
0
0
0
2
0
2
1
0
1
0
1
2
1
1
0
2
1
2
2
0
0
1
1
1
0
0
0
1
0
0
0
0
0
2
1
0
0
0
3
0
0
0
2
1
0
0
1
2
0
1
2
1
1
0
0
2
2
0
0
0
0
2
0
2
2
0
0
2
0
0
0
0
1
0
0
1
0
0
1
0
2
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
3
2
0
1
0
0
0
1
0
0
0
1
0
0
1
0
1
2
0
1
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
1
1
0
0
1
1
2
2
2
0
1
1
0
1
2
1
2
1
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
1
1
0
2
2
1
0
2
0
0
0
0
2
0
0
1
0
1
0
1
0
0
0
0
2
1
2
0
0
1
0
2
0
1
2
2
0
0
1
0
1
0
0
0
0
0
0
3
1
0
1
0
2
0
1
0
1
2
0
0
0
0
0
1
0
1
0
1
0
2
0
0
0
0
0
2
2
0
0
1
0
0
1
0
0
1
0
0
2
2
2
0
1
0
2
1
1
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
1
1
0
1
0
1
1
1
0
1
0
0
0
1
0
1
0
1
1
0
1
1
1
0
1
0
0
0
0
1
0
2
2
0
1
0
0
1
1
1
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
1
1
1
2
1
0
0
1
0
0
1
0
0
2
2
2
0
1
0
0
3
0
1
0
1
2
0
0
1
0
0
0
2
1
0
0
1
1
0
1
0
1
0
0
0
1
2
0
0
0
1
0
0
0
1
1
2
0
0
1
0
1
2
0
0
0
0
0
3
0
0
2
0
0
1
1
0
0
0
2
1
1
0
0
0
1
1
2
2
1
0
0
2
0
0
2
0
1
0
0
0
0
1
0
0
2
1
1
3
1
0
0
0
0
0
0
0
0
0
1
2
2
0
1
2
2
0
2
0
0
2
1
0
0
0
1
1
0
0
0
2
0
1
0
1
1
0
3
0
2
1
1
0
0
2
0
2
0
1
0
2
1
0
2
0
0
0
0
1
0
1
0
0
0
2
2
0
0
0
0
0
0
0
1
0
2
0
1
0
2
0
1
0
2
0
1
1
1
1
1
2
0
2
2
1
1
0
1
0
1
0
0
0
0
2
2
2
0
1
0
3
1
2
0
2
0
2
2
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
2
0
1
0
1
3
0
0
1
1
0
1
0
0
1
1
2
1
0
0
1
0
0
0
1
1
2
0
1
0
0
0
1
1
0
2
2
0
0
1
0
0
2
0
0
0
2
1
0
0
0
1
1
0
0
0
0
2
0
0
1
0
0
2
0
0
1
0
0
0
0
2
0
0
3
1
0
2
0
2
0
1
0
2
2
1
0
0
2
1
6
1
1
2
0
1
0
1
1
1
3
0
0
2
0
1
2
1
1
2
0
0
0
1
0
1
1
5
0
0
1
1
0
1
0
0
0
2
1
3
0
0
0
2
0
0
0
0
2
2
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
2
2
2
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
3
1
0
2
2
1
0
0
1
2
1
1
0
2
0
2
1
0
1
1
0
0
0
2
0
0
1
0
0
2
0
0
1
0
0
0
0
0
2
2
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
2
0
2
0
1
0
0
0
2
0
2
0
0
2
0
0
2
2
1
0
1
1
2
2
1
0
1
0
0
0
0
2
0
0
1
0
2
2
0
2
0
2
2
0
0
1
2
1
0
1
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
2
2
0
0
1
0
1
1
1
0
2
0
2
1
0
1
0
0
0
0
0
2
0
0
2
2
0
0
1
2
2
0
0
0
2
2
0
0
2
0
0
0
1
0
0
0
2
0
0
0
1
0
0
1
0
0
0
1
0
1
5
0
0
1
1
1
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
2
0
1
0
1
1
0
4
1
1
1
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
1
1
0
1
0
0
2
2
0
1
1
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
2
3
0
0
2
1
0
1
0
0
0
2
1
0
0
0
1
2
0
0
0
2
0
0
2
0
2
1
0
1
0
1
1
1
2
2
0
1
2
0
3
0
0
6
0
2
0
0
1
1
1
2
1
0
1
1
0
1
0
0
1
0
3
0
0
0
2
2
0
0
0
1
0
1
0
0
0
2
0
0
1
1
0
2
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
2
0
0
0
0
1
1
1
0
1
0
1
1
1
1
1
0
0
0
2
1
2
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
1
0
0
0
2
0
1
2
0
2
0
1
0
0
2
2
0
0
0
0
1
1
0
2
1
0
1
0
0
0
0
0
2
1
1
0
0
0
1
0
0
0
0
1
0
1
0
2
1
0
0
1
0
0
0
2
0
2
1
0
1
2
0
0
1
1
0
1
2
0
1
2
0
0
2
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
2
1
1
1
1
0
1
3
1
0
0
0
2
0
0
0
0
0
1
1
0
2
0
0
0
0
0
2
2
2
0
2
2
1
1
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
1
2
2
0
2
1
1
0
0
0
0
0
0
2
1
0
0
1
0
0
0
2
2
0
1
0
0
0
1
0
0
1
2
1
0
0
1
0
0
0
0
0
0
1
1
3
2
1
2
1
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
1
0
2
0
1
2
0
2
1
0
0
0
0
0
1
1
2
2
1
0
1
1
0
2
0
0
0
0
0
0
2
1
0
0
1
3
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
1
1
2
0
1
0
2
0
0
0
0
0
0
0
0
1
0
2
1
3
0
0
0
0
1
2
0
0
1
1
0
0
0
0
0
2
2
2
2
0
0
5
0
0
1
1
1
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
1
1
0
2
0
2
2
1
2
0
0
0
0
2
2
0
1
0
2
0
0
1
1
2
0
2
0
0
1
0
1
0
1
1
0
0
1
0
0
0
1
0
0
2
0
0
1
1
0
0
0
2
0
1
0
2
0
0
1
0
0
1
1
1
1
0
1
2
1
0
1
0
0
0
0
0
0
2
1
0
1
0
1
0
1
0
2
0
1
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
2
0
1
2
2
2
0
2
1
0
0
1
0
0
1
1
0
0
2
0
1
1
0
0
2
2
2
1
0
1
0
0
1
1
0
0
1
1
0
1
1
0
0
3
0
0
0
0
0
0
2
3
0
1
0
0
0
5
0
0
0
0
2
2
0
0
2
0
0
0
2
0
1
0
0
1
2
1
0
2
1
1
0
1
0
0
0
2
1
0
2
0
0
2
3
0
1
2
1
0
0
2
0
2
1
0
1
0
0
1
0
0
0
0
0
0
0
0
2
2
1
0
0
0
1
0
1
0
0
0
2
2
1
0
0
0
0
1
0
2
2
2
0
1
0
1
1
0
0
0
0
0
1
0
2
1
0
0
2
1
2
0
0
0
2
2
0
2
2
1
0
2
0
0
0
0
2
0
0
0
1
1
0
0
1
1
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
2
0
0
0
0
2
0
0
2
0
2
1
2
1
0
0
0
0
2
2
2
1
2
2
0
2
0
0
1
2
1
2
0
1
0
1
2
0
2
1
0
1
2
2
0
1
0
0
1
0
1
0
2
0
0
0
2
1
0
0
0
0
2
0
2
2
0
0
0
0
0
1
1
0
1
2
0
1
0
0
2
1
2
2
0
2
0
0
0
2
0
2
2
0
2
1
0
0
2
0
0
1
2
1
0
2
0
0
1
1
0
0
2
1
1
0
2
0
1
0
3
2
1
1
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
2
0
3
0
0
0
0
0
0
1
1
0
1
1
1
1
0
0
1
0
1
1
1
1
0
0
0
2
0
1
1
2
0
2
0
0
0
0
1
3
0
0
0
0
0
1
0
1
1
0
0
0
0
0
2
2
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
1
1
1
2
2
1
0
0
2
0
2
0
2
1
2
0
0
0
0
2
0
0
3
1
0
2
0
1
0
0
1
2
0
0
1
0
0
2
0
0
2
1
1
1
0
1
2
0
0
2
0
2
1
2
0
1
3
0
0
2
0
2
0
0
1
0
0
0
0
0
0
1
1
2
0
1
2
2
1
2
0
0
0
2
0
0
0
0
0
0
2
0
1
0
1
1
3
2
1
0
1
0
0
1
2
0
0
2
0
0
0
0
2
0
0
1
2
0
0
0
1
2
1
0
0
1
1
0
0
0
3
1
0
0
3
0
1
0
2
0
0
1
0
0
0
0
0
2
1
2
1
0
0
0
4
1
0
0
1
0
2
0
0
2
0
0
2
0
0
0
2
2
0
0
1
1
0
1
0
1
2
0
1
0
2
0
0
0
0
0
2
1
2
0
2
0
1
0
2
1
0
0
0
0
0
2
0
0
1
2
0
1
0
0
1
2
2
2
1
0
2
0
2
0
0
0
2
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
1
1
0
0
2
1
0
0
1
1
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
1
0
2
2
0
1
0
0
0
0
0
0
2
3
1
0
1
0
0
0
0
2
0
2
2
2
3
1
0
2
1
0
1
0
0
0
0
0
2
0
1
0
2
1
0
0
0
0
0
2
0
2
1
0
1
1
0
0
0
0
0
0
1
1
0
0
2
0
0
0
2
3
0
0
2
0
0
1
0
1
0
0
1
0
1
0
0
0
1
1
0
0
0
2
1
0
0
0
0
0
2
0
0
1
2
2
4
0
0
0
0
1
0
0
1
0
2
0
1
0
1
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
2
2
2
0
2
1
2
0
0
0
1
2
0
0
2
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
3
0
0
0
1
0
2
0
3
0
0
0
0
0
0
1
2
2
1
1
0
2
1
2
0
0
2
0
1
0
1
0
2
1
0
0
0
2
1
0
0
0
0
2
1
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
2
0
0
1
3
0
0
2
0
0
2
0
1
0
0
0
0
5
1
0
0
0
0
0
2
2
0
0
2
2
0
1
0
0
2
0
0
2
0
3
2
1
0
1
2
1
0
2
0
2
2
1
0
1
0
0
0
0
0
0
0
0
1
2
0
1
1
1
0
1
0
0
1
0
0
2
0
1
0
1
2
0
0
1
0
0
2
2
1
0
0
0
0
0
1
0
2
0
1
1
3
0
0
0
0
0
0
0
2
0
0
1
0
1
1
0
0
2
1
2
0
1
3
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
2
0
1
0
2
1
3
0
1
0
0
0
3
0
0
0
2
1
2
1
1
2
0
2
1
1
0
2
1
0
1
0
1
2
1
0
2
1
1
0
0
3
0
2
1
0
1
2
1
0
1
0
0
2
0
1
1
5
0
2
0
0
0
0
1
1
2
0
0
0
0
0
0
0
1
0
1
0
1
2
0
2
0
0
3
2
0
0
0
0
1
0
0
0
0
1
0
0
0
1
2
0
2
0
0
0
0
0
1
1
0
2
0
0
0
1
2
1
1
0
0
2
2
0
2
2
1
0
0
2
0
0
0
2
2
0
1
1
1
1
0
1
0
0
0
0
1
0
0
0
0
1
3
0
0
1
0
0
2
0
0
1
1
0
0
1
0
0
2
0
2
0
0
0
0
0
0
3
0
1
1
0
0
3
0
0
2
0
0
0
0
0
1
2
0
2
0
0
1
2
1
0
0
1
1
1
2
0
1
1
0
0
0
1
2
2
0
1
0
2
1
0
1
2
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
2
1
0
0
2
0
0
0
0
2
2
1
0
2
0
1
2
1
0
2
0
0
0
0
5
2
0
1
0
2
0
1
2
2
0
0
0
2
0
0
2
1
0
2
0
2
0
0
1
0
1
2
0
2
1
2
0
0
2
0
0
1
1
3
0
0
0
1
0
0
2
0
0
0
1
0
0
2
2
1
1
0
0
0
1
0
1
1
0
0
0
1
0
1
0
2
2
0
0
0
2
0
1
1
2
1
0
2
0
1
0
0
1
0
1
0
0
0
1
1
0
1
1
1
1
0
2
0
0
0
2
0
0
0
3
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
2
1
2
1
2
1
0
1
2
0
0
0
1
2
0
0
1
0
0
0
0
1
0
1
0
1
0
2
0
1
1
2
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
3
1
0
1
0
0
1
1
1
2
0
1
0
0
0
0
0
1
2
2
0
0
0
0
1
1
2
0
0
1
0
0
0
0
2
2
0
1
0
2
2
1
4
2
0
0
0
0
0
0
0
2
2
1
0
0
1
1
0
1
1
0
0
0
0
0
0
2
0
1
1
1
1
2
0
1
0
2
2
0
0
1
0
1
0
2
1
0
0
0
1
2
2
0
0
0
0
0
0
0
1
2
1
0
0
1
0
1
2
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
2
0
1
23
0
2
2
2
0
1
0
1
0
0
0
0
0
0
2
1
2
2
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
2
0
0
0
2
2
2
1
1
0
0
1
0
1
0
2
0
1
0
0
1
0
0
1
0
0
2
0
0
1
0
2
2
2
2
1
2
0
0
1
0
0
0
0
0
1
0
0
0
0
2
2
0
0
1
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
2
1
2
1
1
0
3
2
1
2
0
2
2
0
2
0
0
0
2
2
1
0
1
0
1
0
0
0
0
2
0
1
0
0
1
2
0
1
0
1
1
2
1
1
0
2
0
1
0
0
1
2
0
1
0
0
1
1
0
0
2
0
2
0
0
0
0
0
0
1
1
2
0
0
1
0
1
2
0
0
1
1
0
2
1
1
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
3
1
0
2
0
0
1
0
0
0
6
2
2
1
0
0
1
0
2
1
0
0
0
2
1
0
0
2
0
4
0
0
1
1
0
0
0
2
2
0
1
2
2
0
0
2
2
2
0
2
0
0
0
0
1
0
2
0
0
1
2
0
1
0
1
2
1
0
0
1
1
1
0
0
0
0
2
0
0
0
0
1
0
1
0
1
0
0
0
2
0
1
2
1
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
1
2
0
0
0
1
1
0
0
0
0
1
3
1
2
0
0
0
0
1
0
1
0
0
0
3
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
2
1
2
0
1
0
2
0
2
0
1
2
0
2
0
1
0
0
1
0
0
1
2
0
1
0
1
0
2
0
1
0
0
1
3
0
2
1
2
0
0
1
0
2
0
0
1
1
3
2
0
0
0
2
2
1
0
0
1
0
0
0
0
2
2
2
1
1
0
0
2
0
0
0
0
2
3
0
0
1
0
1
0
0
1
2
0
0
0
2
1
1
0
0
0
1
1
0
0
1
0
2
2
2
0
1
2
0
0
0
0
2
0
2
1
1
1
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
1
2
0
0
0
0
2
0
1
0
2
2
2
1
0
0
0
1
1
1
0
2
0
0
0
0
0
1
0
0
0
1
2
2
0
1
0
0
0
1
0
1
0
0
4
0
0
0
1
2
0
0
2
0
0
0
2
2
0
0
1
0
0
2
0
1
0
1
2
0
0
2
0
2
2
1
0
0
0
0
1
1
0
1
1
2
2
1
0
1
2
0
1
0
0
0
0
1
0
0
0
2
0
2
0
1
0
1
0
0
1
1
0
0
1
2
0
1
0
2
1
0
1
2
1
1
0
0
4
1
0
2
0
0
0
0
0
1
2
0
2
0
0
1
0
0
3
0
0
0
1
1
0
0
1
0
0
0
1
2
1
0
1
1
0
0
3
0
1
0
0
2
0
0
1
4
0
0
0
0
1
1
1
1
0
2
0
1
0
0
0
1
0
0
3
0
2
0
1
2
0
1
1
2
0
0
1
1
1
0
0
0
2
1
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
2
1
2
0
1
0
0
1
0
0
0
0
1
4
0
0
0
0
1
1
0
2
0
1
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
2
0
0
2
0
0
2
1
1
0
0
2
1
0
0
1
0
0
1
2
0
0
1
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
2
2
0
0
0
0
1
1
0
2
0
0
2
2
0
1
0
0
2
0
0
0
0
0
0
2
1
0
0
0
4
2
1
2
0
2
0
1
1
0
2
0
1
0
1
0
1
0
0
0
0
1
2
1
2
1
0
2
2
2
0
1
0
0
2
0
1
0
0
1
0
0
0
3
0
1
1
1
0
0
0
0
0
2
2
1
0
0
2
0
1
1
0
2
0
1
0
0
0
0
1
2
1
2
1
0
1
0
0
0
1
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
2
0
1
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
2
2
0
2
0
0
1
0
0
2
1
2
0
0
0
0
0
2
0
1
1
1
1
0
1
0
1
0
4
1
0
2
0
0
0
0
0
2
3
0
0
0
0
0
0
1
1
0
0
0
1
1
1
0
0
1
2
0
2
0
2
2
0
0
1
1
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
2
1
0
2
0
1
0
0
3
1
0
3
2
2
0
0
1
2
1
0
0
0
0
0
1
0
1
0
0
0
1
2
1
0
1
0
1
0
1
0
0
0
1
2
0
1
2
0
1
0
0
2
1
0
2
2
1
0
2
0
1
2
1
2
0
0
2
0
1
0
0
0
0
0
1
3
0
5
1
0
0
1
1
2
0
0
0
0
0
0
2
0
2
1
0
0
1
0
1
0
1
1
0
0
1
3
0
1
0
2
1
0
0
1
0
0
1
0
0
0
2
0
0
2
2
0
0
1
0
1
0
1
0
2
0
1
0
1
1
0
0
1
2
2
0
0
1
1
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
1
0
0
1
0
0
1
2
0
0
0
1
0
0
1
1
1
2
2
0
0
2
0
0
2
1
2
0
1
1
0
1
0
1
0
0
2
1
2
0
0
0
0
0
1
0
0
2
0
0
0
0
2
1
0
1
0
1
0
0
1
1
0
1
0
1
1
3
0
2
1
0
0
0
0
1
0
1
0
1
0
2
0
0
0
1
1
1
2
1
0
1
0
1
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
4
1
0
2
0
0
2
0
0
2
0
1
0
2
0
0
2
2
2
0
0
0
0
1
0
2
1
0
0
0
0
1
3
0
0
0
0
1
1
1
1
0
1
0
0
2
0
0
2
0
1
1
0
0
0
0
0
1
0
0
2
2
0
2
0
1
1
0
0
1
2
2
0
1
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
2
0
0
0
0
3
1
0
2
2
0
1
0
2
2
1
0
2
0
1
0
2
1
0
0
0
0
0
0
0
2
0
1
2
1
1
0
1
0
1
0
1
2
0
0
1
0
0
2
0
3
0
0
0
1
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
1
1
0
0
0
1
1
2
0
0
1
0
3
1
0
0
1
1
0
0
0
0
1
2
1
1
1
2
0
0
1
0
0
0
0
1
0
2
0
1
0
0
2
1
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
2
0
0
0
0
0
0
0
1
0
2
0
2
2
0
0
2
0
0
1
0
0
2
2
1
2
1
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
2
0
1
0
2
0
0
0
1
0
1
0
0
0
0
2
1
3
0
1
1
0
0
1
0
0
2
0
1
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
2
0
2
0
0
2
0
2
1
1
1
2
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
1
2
2
0
0
1
0
1
0
0
4
2
0
0
0
1
2
1
1
0
0
2
0
0
0
0
2
2
2
1
0
1
0
9
1
1
0
1
0
0
2
1
2
0
0
0
1
0
2
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
1
0
0
0
2
0
0
1
0
1
3
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
1
1
0
2
0
1
0
1
0
1
1
1
3
1
0
1
0
2
0
2
0
0
3
0
5
0
1
2
0
1
0
1
0
0
1
0
1
1
0
1
1
0
0
0
2
2
2
2
0
0
1
0
2
0
0
1
0
0
2
0
1
0
1
0
0
0
0
0
2
2
0
0
1
2
0
0
2
2
0
3
1
1
0
0
0
0
0
0
2
0
2
0
0
2
0
1
1
0
0
3
2
1
0
0
2
0
0
0
0
1
0
1
0
1
0
0
5
1
0
1
0
0
1
3
0
0
0
0
0
0
2
0
0
1
0
1
1
0
0
0
1
1
5
0
0
2
3
1
0
1
0
1
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
1
2
0
0
2
0
0
0
1
0
2
0
1
0
1
1
2
2
0
2
0
2
0
0
1
0
0
0
2
0
0
0
0
2
1
1
0
1
1
0
0
1
0
1
2
1
1
0
1
2
1
0
2
0
0
1
0
1
0
0
2
1
2
0
1
1
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
2
0
1
0
2
0
0
1
0
0
1
0
1
0
0
0
2
1
1
0
1
0
0
0
0
1
0
1
1
0
0
1
1
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
1
0
1
1
0
4
2
2
0
1
0
0
2
0
0
0
0
0
0
0
2
0
1
1
2
0
1
0
1
0
2
1
1
0
2
0
1
0
0
1
0
2
0
2
0
0
1
0
0
2
2
1
2
0
0
2
2
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
2
0
0
0
2
0
1
0
2
1
0
1
2
1
0
2
1
0
2
0
0
0
0
0
0
0
0
1
1
0
2
2
2
0
1
1
0
1
0
0
2
0
0
2
2
2
1
2
2
1
0
0
1
1
1
0
2
1
1
0
1
0
0
0
0
2
0
0
0
0
0
2
1
1
0
2
0
0
0
0
0
0
2
0
0
2
1
3
0
1
0
1
0
1
2
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
2
1
2
2
1
0
1
0
0
0
0
0
3
0
2
1
0
0
2
2
2
0
0
0
2
0
0
2
1
1
1
0
1
0
1
2
2
1
1
0
5
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
2
0
0
0
0
0
2
2
1
0
2
0
2
1
1
2
3
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
2
2
2
0
1
2
2
0
1
0
1
0
0
0
1
0
0
1
0
1
1
2
0
0
0
1
1
0
0
0
1
0
0
0
0
2
2
2
0
1
0
0
0
2
0
0
4
0
0
0
0
1
1
0
1
1
0
0
0
0
2
0
0
1
2
0
2
0
1
0
0
1
0
1
0
0
0
0
2
0
0
0
0
2
2
3
2
1
2
0
2
2
1
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
1
0
1
0
0
2
2
0
0
0
0
2
1
0
1
0
0
0
2
2
3
2
0
0
1
0
0
0
0
1
1
2
1
0
0
0
2
0
0
1
1
0
0
1
0
0
1
0
0
2
1
2
0
2
0
0
0
0
2
0
0
0
0
0
2
0
1
2
0
1
2
1
2
0
1
0
2
1
2
0
0
1
1
2
1
0
2
0
1
1
0
0
0
1
0
2
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
2
1
0
1
0
0
0
1
0
0
1
2
1
0
0
0
0
0
0
2
0
0
1
1
0
0
0
2
1
1
1
1
0
1
2
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
3
0
2
1
0
0
2
0
0
2
1
0
0
1
1
1
0
0
1
0
2
1
2
1
2
0
0
0
0
2
0
0
2
0
0
2
1
0
1
1
2
0
1
2
2
0
2
1
0
0
0
0
1
1
0
0
1
0
2
0
1
0
2
0
1
0
0
0
1
0
0
0
0
1
2
0
0
0
0
1
2
1
2
6
0
2
0
2
1
2
0
0
1
1
1
0
0
0
1
0
1
2
2
0
0
1
0
0
3
2
1
0
2
1
2
0
0
0
0
1
0
1
0
0
0
0
2
2
1
2
0
1
2
2
0
0
1
0
0
1
0
0
0
0
1
2
2
1
0
0
0
1
0
0
2
0
0
0
1
2
0
0
2
2
0
0
0
1
1
0
0
1
2
2
0
2
0
2
0
1
2
0
2
0
3
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
1
1
2
1
0
0
0
0
0
0
0
1
3
0
2
2
0
0
2
3
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
2
1
1
0
0
0
0
0
2
2
2
0
0
2
0
0
0
1
1
0
3
1
0
0
1
0
0
1
0
0
0
2
0
2
0
2
2
0
0
2
0
1
1
2
0
0
1
0
0
0
2
0
0
0
2
1
0
1
1
0
0
2
0
0
0
0
1
0
1
1
0
0
1
1
1
1
0
0
2
1
1
2
0
0
0
0
2
0
1
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
1
0
0
2
0
2
0
1
0
0
1
0
1
2
0
0
1
0
0
5
1
2
1
2
2
2
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
1
1
0
0
0
2
0
2
2
2
0
0
0
1
2
0
0
0
0
0
2
0
0
0
1
2
0
0
0
2
0
0
1
0
1
2
1
0
0
0
0
1
0
2
0
0
1
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
2
1
0
0
0
0
1
0
1
2
0
0
1
0
0
3
0
0
2
0
0
0
0
0
2
0
0
0
0
2
2
1
2
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
2
2
0
1
0
0
0
0
0
1
0
0
0
1
0
1
2
0
1
0
0
0
1
1
1
0
0
1
0
1
0
0
0
0
1
1
0
1
1
0
0
0
2
4
0
2
0
0
0
3
0
0
0
1
2
1
2
0
1
2
0
2
0
0
0
0
1
1
1
1
2
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
1
0
2
0
2
2
1
2
0
0
2
0
0
1
2
1
2
0
2
1
1
0
0
0
2
0
3
0
0
0
0
1
0
1
0
1
0
1
0
1
0
1
1
2
1
0
0
2
1
2
0
0
0
2
2
2
2
0
0
1
0
0
0
0
1
1
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
1
1
0
1
1
3
1
0
1
2
0
0
0
2
2
0
0
2
0
1
1
1
0
0
1
1
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
1
0
2
0
0
0
0
1
0
1
0
2
1
0
0
0
0
0
2
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
3
1
2
0
0
1
1
1
2
1
0
1
1
1
0
2
2
0
0
0
0
1
3
0
0
1
0
0
3
1
1
0
0
0
0
2
1
2
1
0
0
1
0
0
1
1
0
0
0
0
0
1
1
0
2
1
2
1
0
0
0
0
1
0
2
0
0
0
0
1
1
0
2
1
0
1
0
0
1
0
1
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
2
1
1
0
0
0
0
0
1
2
0
1
0
0
1
1
1
0
0
0
0
2
0
0
0
0
0
0
1
2
0
2
0
1
0
0
0
0
0
0
0
2
2
0
8
0
0
0
0
0
0
2
0
1
1
2
1
0
2
0
0
0
1
3
0
0
1
1
1
0
1
1
0
0
0
0
0
1
2
2
0
1
0
0
0
2
0
0
0
2
0
2
0
0
2
3
0
0
0
0
0
0
2
0
1
1
0
2
0
1
1
2
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
2
2
0
0
0
2
0
0
1
3
0
2
0
1
0
0
0
1
0
0
1
0
1
1
0
1
1
0
1
0
0
0
0
0
2
0
0
0
2
0
2
0
1
1
1
0
0
0
1
1
0
2
0
0
0
0
4
2
1
2
0
0
1
1
1
2
0
2
0
0
2
1
0
0
0
2
0
1
5
0
0
0
0
1
2
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
3
1
0
0
1
0
6
0
1
2
0
1
1
2
1
0
0
0
0
2
0
1
0
1
0
2
0
1
0
0
0
0
2
1
2
0
0
0
0
0
1
0
0
0
2
0
0
1
0
1
3
2
2
0
2
1
1
0
0
0
0
1
0
1
0
0
1
2
0
1
1
1
2
1
0
0
5
0
0
0
0
2
0
0
2
0
1
1
2
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
1
0
0
1
0
0
2
0
2
2
2
0
1
1
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
2
1
1
0
0
0
2
1
2
0
0
1
0
0
1
0
0
0
2
0
0
1
0
2
0
1
0
0
1
1
1
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
2
0
0
2
0
2
0
1
2
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
2
2
0
0
0
2
0
0
1
0
2
1
0
0
1
0
1
0
1
2
0
0
0
1
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
3
0
2
0
0
2
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
2
0
0
0
1
3
1
2
1
0
0
2
2
1
2
0
0
2
1
0
2
0
0
0
1
0
3
0
0
1
1
1
0
0
0
0
0
2
1
1
2
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
3
0
2
2
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
1
1
2
0
1
1
1
2
0
1
2
2
0
0
0
1
0
0
0
0
0
0
0
1
1
2
0
0
1
0
2
1
0
1
1
0
0
0
2
0
0
0
4
0
1
0
2
0
0
2
0
0
2
2
2
0
1
2
0
0
0
0
0
0
2
0
2
0
2
0
0
0
2
0
0
1
0
0
1
2
0
1
1
0
1
0
1
1
0
1
2
1
2
1
2
1
2
1
0
0
0
1
0
1
0
2
1
0
0
1
0
0
1
0
1
0
1
2
2
0
0
0
2
0
2
1
0
2
1
0
0
2
1
1
0
2
1
0
0
2
0
2
2
1
0
0
1
2
0
0
0
1
0
2
0
0
2
1
0
1
0
1
2
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
3
0
0
0
1
1
0
0
0
1
1
0
2
2
1
0
1
0
2
2
1
0
1
1
0
2
0
1
1
0
1
0
2
0
0
0
0
0
3
1
0
1
2
0
1
0
2
0
0
0
2
0
0
1
0
0
0
2
0
0
0
1
1
2
1
1
0
1
0
0
1
0
2
0
0
0
2
0
0
0
0
1
1
2
1
0
0
2
0
0
2
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
2
1
0
2
0
0
0
2
0
1
4
1
0
2
0
0
2
0
0
0
2
0
0
0
0
1
0
2
1
1
0
1
1
1
0
1
0
2
1
0
0
2
1
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
3
3
0
0
0
1
1
0
0
2
0
0
0
2
0
1
2
0
1
0
4
0
1
2
2
1
2
0
1
1
2
1
0
0
0
0
1
0
0
1
0
0
0
1
1
1
0
0
1
0
0
2
0
1
2
0
0
0
0
1
1
0
2
0
0
1
0
1
2
2
0
1
2
0
0
2
2
1
0
2
0
0
0
2
2
0
0
2
0
1
0
2
1
1
1
0
2
1
0
1
0
2
2
3
0
0
0
0
2
1
0
0
2
1
0
2
0
2
0
3
1
2
0
0
0
2
0
0
0
2
3
1
0
0
1
0
2
1
0
1
2
0
0
0
1
0
0
0
0
1
2
1
0
0
1
2
0
2
1
1
0
0
2
2
0
2
1
0
0
0
2
1
0
0
1
1
0
0
0
1
1
1
1
0
1
0
0
0
2
0
1
2
2
2
0
0
2
0
1
2
1
0
0
0
0
1
0
1
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
1
2
0
0
0
3
3
0
3
0
0
0
1
1
1
0
1
1
2
0
0
3
1
0
0
0
1
2
0
0
2
1
2
2
0
1
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
1
4
2
0
2
0
0
0
0
1
0
1
0
1
1
1
0
2
2
1
1
1
1
1
1
0
2
1
0
0
0
0
2
0
1
2
0
0
1
0
1
0
0
0
0
1
1
2
1
0
0
2
1
0
1
0
0
0
1
0
0
0
0
0
2
0
1
0
0
1
2
2
1
2
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
2
1
0
0
0
1
0
0
0
0
1
2
2
0
1
1
1
0
0
1
0
2
1
1
2
2
1
1
2
0
0
1
1
0
1
1
0
0
1
1
0
1
0
1
0
2
2
0
2
0
0
1
2
0
1
2
0
2
0
0
2
0
0
2
1
0
1
0
0
0
0
1
2
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
2
0
0
0
1
2
0
2
1
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
2
0
0
2
0
2
0
2
1
0
2
0
0
0
1
0
0
0
4
1
0
0
3
1
0
0
1
0
2
0
0
3
2
2
0
1
0
0
0
2
2
0
0
0
0
0
2
0
0
1
0
0
2
0
0
2
0
1
0
0
1
1
2
2
1
1
0
0
2
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
2
0
1
2
1
1
0
1
2
1
0
1
0
1
0
0
0
0
2
0
1
0
2
0
1
2
1
1
2
0
0
1
0
0
0
0
2
1
3
0
3
2
0
2
0
2
0
0
0
0
2
0
1
2
0
1
0
1
4
0
0
0
0
1
0
0
0
2
2
2
0
0
1
0
0
0
2
0
0
0
0
0
0
3
0
2
2
3
0
0
0
0
1
1
1
0
0
0
0
2
4
0
0
1
2
0
0
1
0
0
0
0
1
1
1
1
0
0
0
0
3
2
1
0
1
1
0
0
0
0
1
0
1
1
0
1
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
3
1
1
0
0
0
0
0
1
1
0
0
1
0
0
1
1
0
1
1
0
0
0
0
0
0
1
0
2
0
0
2
1
0
2
1
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
2
0
1
0
0
2
2
2
0
2
0
2
0
0
0
0
1
1
0
2
2
2
2
1
0
2
2
0
0
2
0
1
0
1
0
0
0
2
0
1
0
2
4
0
0
0
2
0
0
1
0
1
0
0
3
2
1
0
0
1
1
2
2
0
2
0
0
2
1
0
2
2
0
0
1
2
1
1
1
0
0
2
0
1
1
2
0
0
0
0
2
1
0
0
1
0
0
0
0
6
0
0
2
2
3
1
0
1
0
1
0
2
0
0
0
2
0
2
0
0
2
1
0
2
2
0
1
0
0
3
1
0
0
0
0
1
0
2
1
0
0
0
1
1
2
0
4
0
0
2
2
0
2
2
2
1
1
2
0
2
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
1
0
0
2
2
0
0
0
0
2
0
0
0
1
1
1
0
2
0
1
0
1
1
2
1
0
1
2
0
2
2
1
2
0
0
0
2
0
0
1
0
2
1
1
2
0
0
0
1
0
0
1
2
0
0
2
2
0
0
0
1
0
2
0
2
0
0
1
0
2
1
0
0
0
1
1
2
1
2
2
0
1
1
1
1
0
0
0
0
0
0
0
1
1
0
1
1
1
0
0
0
1
2
1
0
0
0
0
0
0
4
0
0
1
0
0
0
1
0
0
0
0
1
0
3
0
2
0
0
0
0
2
0
0
2
1
1
0
2
2
0
2
0
0
1
0
1
0
1
1
0
0
3
1
3
0
1
0
0
0
0
1
0
0
0
2
0
2
0
0
1
0
2
0
0
1
0
3
0
0
0
1
1
0
2
0
0
1
1
2
0
0
0
5
1
1
1
0
0
0
1
0
1
2
1
2
1
0
0
1
0
0
3
2
0
0
3
0
1
2
1
0
0
0
0
1
1
0
0
1
0
0
2
0
2
0
4
1
2
2
2
2
0
1
2
1
0
0
0
2
1
0
0
2
2
0
0
0
2
0
0
1
0
2
1
0
0
0
1
2
4
2
2
0
0
2
0
0
2
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
1
0
3
0
0
2
2
1
0
1
1
0
1
0
1
0
2
1
0
2
1
0
3
3
1
0
0
2
0
0
0
1
0
0
0
0
0
0
2
2
1
0
0
0
0
1
1
0
2
0
0
0
1
1
2
0
1
2
0
0
0
1
1
1
1
1
1
2
0
3
4
0
0
2
0
1
1
0
3
0
2
2
0
1
0
2
1
2
0
2
0
1
0
0
1
0
0
0
0
2
2
2
0
0
0
2
0
0
0
0
2
0
2
1
0
0
0
2
1
0
2
0
0
2
0
3
2
2
0
0
0
1
0
2
0
0
0
2
1
0
0
2
2
1
2
0
1
0
0
2
0
0
0
0
0
2
0
1
0
1
0
1
2
1
1
1
0
0
2
3
0
0
0
1
0
2
2
3
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
1
0
1
0
0
2
1
0
0
1
1
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
2
1
1
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
1
2
0
0
0
0
1
1
0
1
0
0
0
0
2
0
0
1
1
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
1
0
0
2
0
0
1
1
0
2
1
0
1
0
0
0
0
1
0
1
2
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
1
1
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
2
2
0
1
0
0
0
0
1
2
1
0
1
0
0
0
0
0
1
0
1
1
0
0
2
0
0
0
0
1
0
0
1
2
1
0
0
0
0
2
1
0
0
2
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
2
3
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
2
2
0
0
0
2
0
2
0
3
0
0
0
1
0
1
0
0
1
0
0
2
2
1
1
0
1
0
1
0
2
0
0
1
0
0
0
2
1
0
0
2
0
2
1
0
33
2
0
1
0
1
0
0
0
0
0
0
0
2
1
0
0
2
0
1
2
2
0
0
0
0
1
1
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
2
0
1
0
1
0
1
2
1
1
0
0
0
1
2
0
0
0
0
2
0
2
1
0
3
2
0
2
0
0
2
0
0
0
1
0
1
2
0
0
2
0
1
0
1
1
1
0
1
0
0
0
1
1
1
0
2
2
1
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
3
1
2
0
2
0
0
2
0
0
0
1
0
2
0
0
0
0
0
1
1
0
0
2
2
2
3
0
0
0
0
0
0
0
2
1
0
0
1
3
2
0
0
2
1
1
0
0
1
2
2
0
0
1
3
0
0
0
1
1
1
0
1
0
0
1
0
1
0
2
0
2
0
0
0
0
0
2
2
0
2
2
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
1
0
0
2
4
0
0
1
0
0
0
0
0
2
2
0
1
0
2
0
1
0
1
1
1
0
2
0
0
0
2
1
2
0
0
2
2
0
1
0
1
0
1
0
2
0
1
0
0
0
3
1
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
1
2
0
0
2
1
2
0
1
0
0
0
2
2
2
1
2
0
1
0
0
0
0
0
0
1
0
0
1
0
1
4
1
0
2
0
3
0
0
1
2
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
1
1
0
0
2
1
0
0
0
1
1
2
0
0
0
2
0
0
0
0
0
1
0
1
1
0
0
2
2
0
1
2
0
2
1
0
0
0
2
2
0
0
0
2
1
0
0
1
0
0
1
1
1
0
0
1
0
0
3
0
1
1
1
1
2
0
1
0
0
0
0
1
0
3
0
0
0
2
0
0
0
0
0
0
0
1
2
2
1
1
2
0
1
0
1
0
0
0
0
1
2
0
0
1
0
0
0
1
0
2
1
0
0
0
1
0
0
0
2
1
1
2
0
0
1
0
0
1
0
1
3
2
0
2
1
0
0
0
1
0
0
0
2
0
1
2
0
0
0
0
0
0
1
0
1
0
0
0
2
1
0
0
0
2
0
1
0
0
1
3
1
1
1
0
2
1
0
1
0
0
1
2
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
2
1
0
0
2
1
0
2
0
1
0
0
0
1
0
2
0
0
2
1
0
1
0
0
1
0
1
2
0
1
3
0
2
2
1
1
0
2
2
1
0
1
0
0
0
1
0
0
2
7
1
0
2
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
2
1
0
0
0
0
2
2
0
2
0
0
0
0
1
0
2
0
0
0
2
2
1
0
0
1
0
1
0
0
0
0
5
2
2
1
1
0
0
0
0
0
1
0
1
0
1
0
2
0
1
0
0
0
0
2
1
2
0
2
1
0
0
1
0
0
1
2
0
0
1
0
0
0
0
1
1
2
0
0
1
0
0
0
1
1
0
0
1
0
0
1
1
0
2
2
0
1
0
0
0
2
0
0
3
2
0
0
0
0
0
3
0
0
0
1
1
1
0
2
0
0
0
1
2
0
0
0
2
2
0
0
0
0
2
0
2
2
2
2
1
0
2
0
0
0
0
1
0
2
2
0
0
2
0
5
2
0
2
2
1
0
0
1
0
1
0
3
1
1
1
1
0
0
0
0
2
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
4
2
0
0
0
0
0
0
2
0
2
2
0
1
2
2
0
0
0
2
0
0
0
2
1
0
1
1
0
0
0
0
1
0
1
1
1
0
0
0
1
2
1
0
2
1
2
1
0
0
0
0
0
0
0
1
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
3
2
1
0
0
1
0
2
1
0
0
1
0
0
1
0
0
2
0
0
2
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
2
0
0
0
1
2
0
2
0
0
0
0
0
1
0
1
0
2
0
0
3
0
1
2
0
0
2
2
2
0
1
0
0
0
0
0
3
0
2
1
1
0
0
2
2
1
0
1
2
2
1
1
0
0
0
0
1
0
1
0
2
0
0
0
1
2
2
3
1
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
1
0
1
2
0
2
0
0
1
0
1
1
4
2
0
1
1
2
0
2
0
0
0
0
1
1
2
1
0
2
0
2
0
0
0
1
0
0
1
2
2
1
0
0
2
3
1
1
2
0
0
1
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
3
0
0
0
0
0
2
1
1
0
0
0
0
2
0
1
2
0
1
1
1
0
0
1
1
0
0
2
3
0
1
0
0
0
0
0
1
0
1
0
0
0
0
2
1
1
0
1
0
0
1
2
1
0
1
1
0
0
0
2
1
0
1
0
1
1
0
0
1
0
2
0
0
0
1
2
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
1
2
2
0
1
1
1
3
1
1
1
2
2
2
2
0
0
0
1
2
2
2
1
1
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
2
2
0
0
0
2
2
0
0
0
0
1
0
0
0
1
1
0
2
0
0
2
0
1
0
0
2
0
1
0
1
0
2
0
2
2
1
0
2
0
0
0
2
0
1
2
0
0
0
0
0
0
2
0
0
2
1
0
0
1
4
0
0
2
2
1
1
1
1
1
2
0
0
0
0
1
0
2
2
0
0
0
1
0
1
0
0
2
0
0
0
0
0
1
0
2
2
0
1
0
0
2
1
0
2
1
0
1
0
1
2
1
0
0
0
1
0
0
1
0
0
0
2
0
3
1
1
2
0
0
2
0
0
0
1
0
0
0
0
3
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
2
0
2
0
0
0
2
0
0
2
0
0
2
0
0
0
0
1
1
0
0
0
0
1
0
2
1
2
2
0
0
2
1
0
2
0
0
1
1
2
0
0
0
0
4
0
1
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
4
0
2
2
0
0
0
1
1
2
1
0
2
0
0
1
0
2
0
0
0
0
0
0
1
2
0
0
1
0
0
1
0
0
0
2
2
2
0
0
1
0
2
1
0
1
0
1
0
2
1
0
0
2
1
1
0
0
0
0
2
0
3
0
0
1
0
1
0
2
2
0
0
0
0
1
1
2
2
0
1
1
0
0
1
2
1
0
0
1
0
0
2
0
0
1
0
2
0
0
0
2
0
3
0
0
1
0
1
2
0
1
2
0
0
1
1
1
2
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
1
1
1
1
0
1
0
1
0
0
0
1
0
1
0
0
1
2
0
0
1
1
1
4
0
2
2
1
0
0
0
5
0
1
2
0
1
1
0
0
1
0
0
0
2
0
2
0
0
0
0
1
0
0
2
0
1
0
0
0
0
1
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
5
2
1
0
0
2
4
1
3
1
0
0
0
0
1
1
0
1
0
0
2
0
1
0
1
0
2
0
0
1
0
0
1
2
1
0
2
0
0
1
3
2
2
0
0
0
0
2
1
1
0
0
0
0
1
2
0
0
0
0
2
1
1
2
0
0
0
0
3
0
1
0
1
0
0
0
0
0
0
0
2
0
2
0
1
1
0
0
0
0
2
0
0
0
0
1
0
1
0
2
0
0
1
4
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
1
0
1
2
1
0
0
2
0
2
1
2
1
1
0
0
0
0
0
1
0
2
2
1
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
1
1
0
0
2
0
1
0
0
1
2
1
0
1
1
0
2
0
0
2
0
0
0
0
0
0
1
0
2
0
2
0
2
0
0
0
0
1
2
0
2
4
1
8
1
0
0
1
0
0
3
0
2
3
0
0
0
0
0
0
0
2
1
2
1
0
1
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
3
2
0
0
2
0
0
0
0
0
1
0
1
0
0
1
1
2
0
1
0
1
0
0
0
0
2
1
0
0
2
0
2
0
0
0
2
1
0
1
0
0
1
2
0
0
1
0
2
2
2
0
0
1
1
0
2
0
0
1
0
0
0
2
3
2
0
0
0
1
2
2
0
0
0
0
0
0
0
2
0
1
0
0
1
1
0
2
0
0
0
0
0
2
0
1
1
0
2
0
1
0
1
0
2
2
2
1
0
1
2
0
0
0
0
2
1
0
2
0
2
1
0
0
1
0
0
0
0
2
0
0
1
2
0
3
0
0
2
0
1
0
0
0
0
0
2
2
2
0
1
3
0
2
1
2
0
1
0
2
0
1
1
0
0
1
0
2
0
0
0
0
0
0
1
0
1
0
1
0
3
1
0
2
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
3
6
0
2
0
0
2
1
2
0
0
2
1
1
0
1
0
1
1
0
1
0
0
0
1
0
0
1
0
1
1
1
2
0
0
1
0
0
1
1
0
0
0
2
0
2
1
0
1
1
0
0
0
1
1
2
0
2
1
2
2
0
0
2
2
0
0
1
0
3
0
2
0
1
0
2
3
2
1
0
0
0
1
2
1
1
1
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
1
0
0
1
1
2
0
0
0
0
4
1
1
0
1
0
2
1
1
0
0
0
0
0
1
0
0
0
0
2
2
3
1
0
0
3
0
0
0
0
0
0
1
0
1
2
0
1
0
1
0
3
0
0
2
1
1
0
1
0
2
0
3
2
0
1
0
1
0
0
2
2
0
0
0
0
0
2
1
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
2
0
0
2
2
0
2
0
0
1
0
3
0
2
0
1
0
0
0
1
1
1
1
2
0
0
2
1
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
1
0
0
0
2
1
2
1
1
0
0
0
2
0
3
0
2
1
1
1
2
0
0
0
1
1
0
0
0
2
0
2
0
1
1
0
0
0
0
0
0
2
1
1
1
1
0
1
1
0
0
0
0
1
2
0
1
0
2
0
1
1
0
2
0
1
2
1
0
0
0
1
0
2
1
0
0
2
0
0
1
0
0
1
2
2
0
0
1
0
2
2
0
2
1
0
1
2
2
1
2
0
0
1
0
1
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
2
2
1
0
0
0
1
0
2
1
0
0
1
1
5
1
1
0
1
0
2
3
1
0
0
0
2
2
2
0
0
1
0
1
0
0
0
2
0
0
0
1
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
2
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
3
0
0
0
5
0
0
1
0
3
0
0
0
2
0
1
2
0
0
0
2
1
1
0
1
2
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
2
0
0
1
2
1
1
0
0
0
1
2
2
0
0
1
1
0
0
0
2
2
0
0
2
0
0
4
0
0
1
1
1
0
1
0
1
0
1
2
1
0
0
0
0
2
1
0
2
1
0
0
2
0
0
0
1
0
0
0
2
0
1
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
2
2
2
1
2
0
1
0
0
1
1
0
1
0
0
0
0
0
2
2
0
1
1
2
0
2
1
0
0
0
1
0
0
1
0
2
1
0
0
0
1
1
0
0
0
0
0
3
0
2
0
2
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
4
1
1
0
2
0
0
0
0
0
0
0
1
1
0
0
3
1
0
1
0
0
0
0
0
0
0
2
2
1
2
0
1
2
2
2
0
0
0
1
1
0
0
1
0
1
0
0
0
2
1
0
0
0
1
0
2
2
0
4
1
2
0
2
1
1
1
0
0
0
0
0
2
0
0
0
1
2
2
1
2
1
2
1
3
0
1
0
0
0
0
0
2
0
2
0
1
0
0
0
1
1
1
1
4
0
0
3
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
2
1
0
0
2
1
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
1
1
0
0
1
1
1
2
0
2
1
0
1
2
0
0
0
0
4
2
0
0
2
1
2
1
0
1
1
0
0
2
0
0
0
0
1
1
2
0
1
1
1
0
0
1
0
1
0
0
1
1
0
2
1
2
1
2
0
1
0
2
0
0
0
0
0
2
0
1
0
1
0
1
2
2
1
0
1
1
0
0
1
0
0
0
0
2
1
0
1
1
0
1
3
1
4
1
1
0
4
1
1
2
3
2
0
0
0
2
1
0
1
1
0
0
3
0
0
2
2
2
1
1
0
0
1
0
2
0
0
0
2
0
0
2
0
0
1
2
0
0
0
2
1
0
1
0
1
0
1
0
0
0
1
1
0
0
0
0
3
1
0
1
0
1
0
0
1
0
1
2
0
2
0
1
0
0
0
0
0
2
0
0
0
0
2
2
1
0
1
0
2
0
0
1
0
0
0
0
0
1
1
0
1
0
1
0
0
0
2
0
8
2
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
1
0
2
0
2
0
0
3
0
0
1
0
0
0
0
0
1
2
1
0
0
0
1
0
0
1
2
2
2
1
0
0
2
2
1
1
0
0
0
1
1
0
3
0
0
2
0
2
0
1
0
0
2
0
0
0
2
1
0
0
1
0
0
2
2
0
1
1
2
0
0
0
2
0
2
0
2
1
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
3
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
2
2
0
0
1
0
0
2
2
0
1
0
0
2
0
0
0
1
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
2
1
2
2
2
1
2
0
0
0
1
1
0
0
1
0
2
2
0
2
1
0
1
2
0
0
2
1
1
1
0
1
0
2
1
1
0
2
0
0
2
1
0
0
2
1
2
0
0
0
0
1
1
0
1
0
0
1
1
0
0
2
0
0
1
2
0
0
0
0
1
0
0
0
0
2
1
0
0
1
0
0
2
2
0
3
0
2
0
0
0
0
1
2
2
2
0
0
3
3
0
1
0
0
1
0
2
0
1
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
2
0
0
2
3
0
0
0
0
0
0
0
3
2
0
0
0
0
2
0
0
2
0
2
2
0
1
1
0
0
1
0
0
1
1
2
0
0
2
2
1
1
1
0
0
2
0
1
0
0
3
2
0
0
0
2
2
0
2
0
0
0
2
0
0
1
2
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
3
2
2
1
1
0
0
2
0
0
1
1
2
0
0
3
0
0
1
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
2
0
1
3
1
0
1
1
0
1
0
0
2
1
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
2
1
2
1
2
0
3
0
0
0
0
0
0
0
2
2
2
1
1
1
0
1
0
0
0
2
0
1
1
2
1
1
0
0
0
0
1
1
0
1
0
0
0
3
0
2
0
0
0
0
1
0
0
0
2
2
2
0
1
1
1
0
0
1
0
3
0
0
2
1
0
0
1
0
0
0
0
0
2
0
0
1
2
0
2
0
1
2
2
2
2
0
2
0
0
2
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
2
2
0
1
1
0
1
2
0
1
0
2
1
0
0
2
1
1
0
0
0
1
1
0
0
2
0
0
0
2
0
2
2
0
0
3
0
0
0
2
2
0
2
0
0
0
0
0
0
0
3
0
1
1
0
1
1
1
0
2
1
1
1
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
1
1
2
1
1
1
0
0
2
0
1
0
2
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
2
0
2
1
2
1
1
1
0
0
1
0
1
0
1
0
0
1
3
0
1
1
0
1
1
0
1
0
2
0
1
0
0
1
6
2
1
1
0
2
1
0
0
0
0
1
1
0
2
2
2
0
1
0
1
0
0
2
1
0
2
0
0
2
0
1
1
1
1
0
1
1
0
0
1
0
0
1
1
1
0
0
0
0
0
0
1
0
2
0
0
1
1
2
2
0
0
1
0
0
0
0
0
0
0
2
2
0
3
1
0
0
0
1
2
0
0
0
2
1
1
1
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
2
2
0
1
1
0
1
1
1
1
1
2
0
0
0
0
0
3
0
1
1
0
1
0
1
0
2
1
1
1
0
1
0
2
0
0
2
1
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
1
1
1
0
0
2
2
2
0
2
2
1
0
1
2
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
2
1
1
1
0
1
0
1
2
0
2
2
2
0
0
4
1
0
0
1
1
2
0
0
0
0
1
1
1
2
0
2
0
2
2
2
2
2
0
0
0
0
2
1
0
0
0
2
0
2
1
0
1
0
2
1
0
2
0
0
0
0
1
0
0
0
0
0
0
8
1
0
1
0
1
1
0
0
1
0
1
1
0
0
1
0
0
1
0
1
0
1
0
2
0
1
0
0
2
0
1
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
1
0
2
2
1
0
0
1
0
2
1
1
1
0
2
2
0
1
0
1
0
0
0
4
0
0
2
0
3
1
0
2
2
0
2
0
1
0
0
1
1
0
0
0
0
2
0
0
2
2
2
2
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
4
0
1
0
0
0
1
0
0
0
2
2
0
2
1
0
0
0
2
2
0
0
0
2
1
0
2
0
3
1
2
0
2
0
1
0
0
2
0
3
1
1
0
1
0
0
2
2
1
2
0
1
0
0
2
1
1
2
0
1
0
0
1
1
0
2
2
2
0
2
0
0
2
1
1
0
0
0
0
0
0
2
0
0
1
1
0
1
0
2
0
0
2
0
0
2
0
0
1
0
0
0
0
0
2
0
2
1
0
1
0
0
0
0
0
2
1
0
0
2
0
0
2
0
0
0
0
1
0
0
2
2
1
0
0
1
0
1
0
2
0
0
0
2
1
1
0
0
2
1
0
2
1
0
0
1
1
0
0
2
0
1
0
0
0
0
0
1
0
0
1
0
0
0
2
2
2
1
1
2
2
0
0
0
0
0
2
0
0
1
0
1
2
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
1
1
4
0
1
0
1
1
0
0
3
0
2
0
0
0
0
2
0
0
3
2
4
2
0
2
1
0
0
0
0
1
2
0
1
2
2
1
1
0
0
0
1
1
1
0
0
0
0
0
0
1
2
0
0
0
0
0
2
1
1
1
0
0
0
0
1
0
0
2
2
0
2
0
2
0
0
0
0
2
2
0
1
2
1
0
1
1
0
0
0
0
3
0
0
0
1
1
0
0
0
2
1
0
0
2
0
0
1
2
0
0
1
0
1
0
1
0
0
1
2
0
0
0
0
1
0
0
2
2
1
0
1
0
1
1
0
0
0
0
0
2
0
1
2
2
1
0
2
0
0
2
1
2
0
1
2
0
0
0
0
0
1
2
2
1
0
1
1
0
2
1
0
0
0
2
0
2
0
0
0
0
0
2
2
0
0
1
0
1
1
12
1
0
2
0
2
0
0
0
0
0
0
0
1
2
0
0
0
2
2
0
0
2
1
0
0
0
0
0
1
2
0
2
2
1
1
2
0
0
1
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
2
2
1
2
1
1
2
0
0
0
0
1
1
0
0
0
3
2
0
1
0
0
2
2
2
0
0
0
0
2
1
0
2
2
1
2
0
1
0
0
1
0
0
1
1
1
0
2
0
0
2
0
2
1
0
0
0
2
0
2
2
0
1
1
0
2
0
0
1
1
0
0
3
1
0
0
0
0
1
0
0
0
2
2
0
1
0
0
0
3
0
0
1
0
1
0
1
2
2
4
2
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
3
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
1
0
3
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
1
0
0
0
0
0
0
2
1
0
2
1
0
1
0
0
0
0
0
0
0
0
0
1
3
0
0
0
2
0
0
0
1
0
1
0
0
0
0
2
0
1
1
2
2
2
1
2
1
1
2
0
2
0
2
0
1
0
0
0
3
0
0
1
0
0
1
0
1
0
0
0
0
0
2
0
0
0
4
1
0
1
2
0
1
2
2
0
2
0
0
0
2
1
0
2
0
0
0
0
0
1
0
1
1
2
0
4
0
2
1
0
0
0
1
0
1
2
2
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
3
1
0
0
1
1
2
1
1
0
1
0
0
0
0
1
0
1
2
0
1
0
1
0
2
0
2
0
0
2
0
0
1
9
0
0
2
0
0
2
0
0
3
0
0
1
1
0
1
1
1
0
0
0
0
1
4
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
1
2
1
2
1
2
0
0
1
1
0
0
2
1
0
2
0
0
0
1
0
2
2
0
0
1
0
1
0
1
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
1
2
1
0
0
0
0
2
3
0
0
0
0
0
1
0
1
0
0
0
0
1
2
0
0
1
2
0
1
0
0
1
1
0
0
0
0
0
2
1
0
0
0
2
0
2
2
0
0
0
3
1
1
1
2
0
0
0
0
0
1
0
0
4
0
0
1
2
1
0
2
2
0
1
2
1
1
0
0
0
0
1
2
2
0
0
1
1
0
1
0
2
1
2
1
0
0
1
0
1
1
1
0
0
1
1
0
0
0
6
0
0
1
0
2
2
0
1
2
0
1
0
1
0
0
1
1
2
0
0
2
0
0
0
2
0
0
0
1
1
0
0
2
1
0
0
0
0
2
2
2
0
0
1
2
0
0
2
0
1
2
0
2
1
0
1
0
0
2
2
0
1
0
1
0
1
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
1
2
0
2
2
1
0
1
0
2
0
0
0
0
0
2
0
0
0
0
2
2
0
0
2
2
0
1
2
1
0
1
0
0
2
1
0
0
0
0
0
1
0
1
1
2
0
1
1
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
2
0
0
1
1
2
2
0
0
1
1
1
2
7
1
0
2
2
1
0
1
0
3
0
1
1
1
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
2
1
0
1
0
0
0
0
0
1
0
0
0
0
2
1
0
1
0
2
0
0
0
0
0
0
1
1
0
0
0
2
1
1
0
2
0
2
2
0
1
0
1
0
0
0
2
0
0
0
1
1
1
2
2
1
0
0
0
3
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
2
0
2
2
0
2
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
2
0
0
1
0
2
0
0
1
0
0
0
0
1
0
0
2
0
1
1
1
1
0
1
2
0
1
1
0
1
2
3
1
1
0
0
1
0
0
0
0
2
0
0
2
0
0
0
1
2
2
0
0
0
0
1
0
1
0
0
3
1
2
0
0
1
1
1
2
2
1
0
0
0
0
0
2
0
1
0
0
0
0
2
1
2
0
0
0
0
2
0
0
0
0
1
0
2
2
0
0
0
0
0
1
0
0
1
0
0
0
2
2
1
1
0
2
1
0
0
1
0
1
0
0
0
3
3
0
0
0
1
3
0
2
0
2
0
0
0
0
4
1
1
2
0
1
0
0
0
1
0
2
0
0
0
1
0
1
1
1
0
0
1
1
0
0
1
2
2
0
1
2
2
0
0
1
0
2
0
1
0
0
0
2
1
0
0
0
2
0
0
1
1
0
0
0
1
0
0
0
2
0
0
1
0
0
2
2
2
0
2
0
2
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
1
1
0
0
2
0
1
0
2
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
3
1
0
3
1
0
1
0
1
2
0
0
0
0
1
2
4
0
2
2
0
0
0
0
0
1
0
1
0
1
0
2
1
0
0
2
1
1
2
3
0
0
0
0
2
2
1
0
1
0
2
1
0
2
2
0
1
0
3
0
0
1
0
0
0
0
0
2
3
0
0
2
0
0
1
0
2
0
0
0
1
0
2
0
1
0
1
2
0
2
0
0
1
0
1
2
0
2
0
0
0
0
1
0
1
0
1
0
1
0
0
1
0
2
1
0
0
2
1
1
0
4
0
2
0
1
1
1
2
0
0
0
0
0
0
1
1
2
0
1
2
2
0
0
0
0
3
0
0
2
0
0
2
2
0
2
1
1
2
0
1
1
0
0
0
2
3
0
0
0
2
0
0
0
0
1
0
1
0
0
0
1
0
0
2
0
1
1
3
0
0
0
0
0
0
1
0
1
1
2
1
0
0
2
2
0
2
1
0
0
1
1
0
0
2
0
2
0
0
0
1
0
1
2
2
3
2
1
1
2
0
0
1
2
0
1
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
2
0
2
1
1
2
0
0
1
1
1
0
0
0
0
0
1
1
2
0
0
2
0
0
1
0
1
0
1
0
2
0
0
0
0
1
1
2
0
1
1
1
0
2
2
1
0
0
0
0
0
1
1
2
2
1
0
0
0
1
0
0
0
2
4
1
0
2
0
0
0
0
0
2
0
1
1
0
0
0
0
0
2
1
0
0
1
0
1
0
0
2
0
2
2
0
0
0
0
3
2
1
0
1
0
2
0
0
2
2
0
0
0
0
0
2
0
1
0
1
0
1
2
0
0
0
0
0
0
0
2
4
0
0
2
0
0
0
2
1
0
0
0
1
0
2
0
0
0
2
0
1
0
0
6
1
0
0
0
1
2
0
2
0
1
0
0
0
0
0
1
2
1
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
2
0
0
1
2
0
0
2
0
2
0
1
0
2
2
1
0
0
3
1
0
0
0
2
1
0
2
2
1
0
0
1
0
0
1
0
2
1
0
0
0
1
1
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
1
1
0
1
0
0
1
0
0
0
1
1
2
1
0
1
0
2
0
0
1
1
1
3
0
1
0
1
2
0
0
0
3
0
1
1
0
2
0
1
1
0
0
0
1
0
0
2
0
1
2
0
0
0
1
0
1
1
2
0
0
1
2
0
2
3
0
0
0
0
1
1
0
1
0
1
1
0
0
1
0
1
0
2
0
2
0
1
0
2
0
0
1
1
1
0
3
0
0
1
2
1
1
0
0
0
0
0
1
0
1
1
0
0
0
1
1
0
0
1
0
0
2
0
0
0
0
1
2
0
2
0
0
2
0
0
2
0
0
0
2
1
0
2
0
1
0
0
1
0
3
2
0
2
0
0
2
1
0
0
2
2
0
1
0
2
0
0
2
2
0
2
0
1
0
0
2
1
0
1
0
2
0
0
1
1
0
2
2
0
0
2
0
0
0
0
1
1
1
2
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
2
2
0
0
0
0
1
0
3
1
0
1
2
0
0
0
2
1
0
1
3
0
0
1
0
1
1
1
2
0
0
0
1
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
2
0
0
1
0
0
0
1
2
0
2
0
0
2
0
2
0
4
2
1
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
2
2
2
0
0
0
0
1
0
2
0
0
1
0
0
0
0
1
0
0
1
1
0
2
1
0
1
0
2
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
2
1
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
1
1
1
0
2
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
3
2
0
0
0
0
0
0
1
1
0
0
2
0
0
0
1
1
1
1
2
0
0
2
1
0
0
0
1
0
1
2
2
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
1
2
0
2
0
2
0
0
1
0
3
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
2
1
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
1
1
0
0
1
0
1
0
0
1
1
1
0
0
0
2
1
0
0
0
2
0
0
1
1
0
0
0
0
0
0
1
1
0
2
1
0
0
0
2
0
0
2
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
2
1
2
1
1
2
1
0
0
0
0
0
1
2
1
0
1
1
0
0
0
1
1
2
0
0
0
1
0
0
0
1
2
2
0
1
0
0
0
3
0
1
0
0
0
0
0
0
1
2
0
2
2
0
2
0
2
0
0
0
1
0
2
1
2
1
1
0
0
2
0
2
2
1
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
2
1
0
0
1
1
1
0
0
0
0
0
0
0
0
2
2
0
1
0
1
1
1
0
2
2
0
0
2
0
0
1
2
0
0
0
1
0
2
1
2
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
2
2
1
0
0
0
0
0
1
0
0
4
1
1
0
0
0
2
0
2
0
0
0
2
0
0
0
0
2
2
0
0
0
1
2
1
2
1
0
2
0
0
0
2
1
2
0
0
1
1
1
0
2
0
0
0
0
0
1
0
0
0
1
0
1
0
2
3
1
0
1
2
3
1
3
1
1
2
0
1
1
1
2
0
0
2
0
0
1
0
1
0
1
1
0
3
1
0
2
2
2
0
0
1
0
0
2
0
0
0
0
1
2
2
0
1
2
1
2
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
1
0
1
0
1
1
0
0
2
1
0
0
0
2
0
0
1
0
0
1
0
0
1
2
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
1
1
2
0
0
2
6
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
2
0
1
0
1
2
0
0
1
0
0
1
0
0
2
1
0
0
1
2
2
2
0
1
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
1
0
0
1
1
0
0
0
1
0
2
1
0
0
1
0
1
1
2
1
0
0
0
0
0
0
2
2
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
1
1
2
1
0
0
0
0
0
2
0
0
0
0
1
2
0
0
1
0
1
0
1
0
0
0
1
0
2
0
2
0
0
0
1
2
0
1
2
1
0
2
0
1
0
0
0
0
0
2
1
0
1
1
1
0
0
0
1
2
1
2
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
2
2
0
0
0
1
2
0
0
1
1
1
0
2
0
1
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
1
2
0
1
2
0
1
1
0
1
1
5
0
3
2
0
0
0
0
1
0
2
2
0
0
2
2
0
1
0
1
0
0
1
0
2
0
0
0
1
0
0
0
2
0
1
0
0
0
1
1
1
0
0
0
0
2
0
0
2
0
9
0
1
3
0
0
1
0
1
0
1
1
0
0
0
0
2
0
2
1
1
0
2
2
4
1
0
1
2
2
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
2
2
0
0
0
0
1
0
0
1
2
0
2
0
0
2
1
1
0
1
0
0
0
0
0
2
0
1
4
1
0
1
0
1
0
2
0
2
1
0
2
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
2
2
1
2
2
2
1
0
2
0
0
1
0
0
0
2
0
0
1
1
0
0
2
2
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
3
2
0
0
0
0
2
0
1
0
0
0
0
0
0
2
1
0
0
1
2
0
1
0
0
0
2
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
2
2
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
1
0
0
2
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
1
0
1
0
0
0
0
1
0
2
1
0
0
1
1
1
0
2
0
1
0
0
0
0
0
1
1
1
0
0
2
1
1
1
0
0
0
0
0
3
0
0
1
0
0
2
1
1
0
2
1
0
1
0
0
0
1
1
0
2
0
1
0
1
0
0
0
0
1
2
0
2
1
2
1
1
2
0
0
0
2
1
2
0
2
1
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
3
1
0
2
0
1
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
1
1
0
2
0
0
0
2
0
0
2
1
1
0
0
3
1
0
0
0
1
0
1
0
2
0
1
0
0
1
1
0
2
0
2
0
2
0
0
2
1
4
2
1
1
0
0
1
0
1
0
0
0
1
0
4
0
2
1
1
0
1
0
0
1
0
0
3
0
0
0
1
0
0
0
0
0
0
1
1
0
0
3
0
0
1
2
0
0
2
1
0
0
0
0
2
0
0
0
0
0
2
0
1
2
2
1
2
0
0
0
0
1
0
2
2
0
0
1
0
0
0
0
2
2
0
0
1
0
0
0
0
2
2
0
2
1
2
1
0
0
2
0
0
2
0
0
0
0
0
1
1
0
0
1
2
2
1
2
0
1
1
1
1
2
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
1
1
0
2
1
1
0
2
1
0
2
2
0
0
3
2
2
0
0
1
0
2
0
0
2
1
2
0
0
1
2
0
0
0
0
1
0
0
1
0
2
0
2
0
1
2
1
0
1
2
0
0
0
2
0
2
0
3
2
0
0
2
0
2
0
2
1
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
2
3
2
2
0
0
1
1
1
0
0
3
0
0
1
0
0
2
2
1
1
1
1
0
0
1
0
0
0
3
0
0
0
1
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
3
0
2
1
0
1
1
1
4
0
1
0
0
1
0
0
1
2
2
0
2
0
0
0
0
0
1
0
1
0
0
0
0
2
0
1
0
2
1
0
1
0
0
1
0
0
1
1
0
2
0
2
0
0
1
0
0
0
1
0
0
2
0
0
1
0
0
0
1
2
2
2
0
1
1
3
0
1
1
1
2
0
1
2
0
2
0
0
2
3
0
2
0
1
0
1
0
0
0
1
0
2
0
0
1
1
1
0
1
0
2
0
0
1
1
1
0
0
1
0
0
4
0
0
0
0
0
0
1
1
2
0
2
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
3
0
0
0
1
1
1
0
0
2
2
1
0
1
2
2
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
2
2
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
2
0
0
2
2
0
1
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
2
0
0
0
1
2
2
0
0
1
2
0
0
0
1
0
2
1
2
1
0
2
0
0
0
2
0
2
0
0
0
0
0
2
1
0
5
0
2
0
0
0
0
0
1
0
3
2
0
0
0
0
0
0
1
1
0
0
1
1
0
0
2
1
0
0
0
0
1
0
2
0
0
1
1
0
0
0
1
0
0
1
0
2
0
2
1
0
0
0
0
2
0
0
0
1
1
1
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
2
1
0
0
2
0
0
1
0
0
0
2
0
0
1
1
0
2
0
0
3
0
0
0
0
0
0
1
2
0
1
1
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
1
2
1
3
0
1
0
0
4
0
1
1
0
0
4
1
2
0
1
0
0
1
1
0
0
1
1
1
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
2
0
0
0
0
1
1
0
0
1
0
0
0
0
3
0
1
0
0
0
2
0
1
0
0
0
1
1
1
0
1
0
0
0
1
0
2
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
2
1
0
0
0
1
0
0
2
2
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
1
0
0
0
3
0
1
0
0
2
0
0
1
0
0
0
2
0
1
1
0
1
0
0
0
1
1
0
0
0
2
0
1
0
1
0
0
1
2
2
0
0
1
1
2
0
0
0
1
0
0
0
2
0
0
1
2
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
1
1
0
0
0
1
0
1
0
1
0
0
2
4
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
1
0
2
0
1
0
0
0
2
1
2
0
2
0
0
0
2
1
0
1
1
1
0
2
2
0
2
1
2
1
5
0
0
1
2
2
1
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
3
2
0
2
1
0
0
2
2
2
0
0
0
1
1
0
1
0
3
2
2
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
1
1
0
2
1
0
1
0
0
0
0
2
1
0
2
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
1
1
0
1
0
0
1
1
1
0
0
0
0
2
0
0
0
2
0
0
0
0
2
2
0
1
3
0
0
1
0
0
0
0
1
1
0
0
0
1
0
2
0
1
1
1
0
0
0
0
0
0
2
0
0
1
0
1
0
0
1
0
1
0
0
0
0
2
2
1
0
0
1
0
1
0
0
0
0
1
2
0
1
0
1
1
0
1
0
1
2
0
0
0
2
2
1
0
0
2
1
0
0
0
1
2
0
0
2
0
0
0
3
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
1
2
0
0
0
1
2
2
0
0
0
0
0
1
2
2
1
0
0
0
0
0
2
2
1
2
0
0
0
1
1
0
1
0
0
0
1
1
1
0
1
1
1
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
1
1
0
0
3
1
0
1
0
0
0
0
0
2
8
2
0
2
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
1
0
0
1
2
0
0
0
6
2
0
1
2
0
0
0
2
1
0
0
1
0
0
0
1
0
0
1
2
0
0
0
0
0
1
0
0
2
0
2
2
2
0
0
2
0
2
0
0
0
1
0
0
1
1
2
0
2
0
0
2
2
2
0
1
0
0
0
1
2
1
0
0
0
0
0
4
1
0
1
0
0
0
0
0
2
1
2
3
0
2
0
1
0
1
1
0
1
0
0
0
2
0
0
0
2
0
1
1
0
1
0
0
0
0
1
1
0
1
1
1
0
0
0
0
0
0
1
0
1
3
0
1
0
0
0
2
0
0
2
1
1
1
0
2
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
1
2
1
0
0
0
1
0
3
0
1
2
1
0
0
2
1
2
0
2
0
0
2
2
1
0
1
1
0
0
2
1
0
0
0
1
0
0
0
1
0
1
2
2
1
0
0
2
2
0
0
5
0
2
0
1
0
1
0
1
1
0
2
0
0
1
0
0
0
0
2
1
1
0
0
2
1
0
0
1
0
0
1
0
0
1
0
5
1
1
0
0
3
1
0
2
0
1
0
0
1
1
2
2
2
0
0
0
1
0
0
0
2
0
0
0
2
1
0
1
1
1
0
2
3
0
1
0
0
0
0
0
1
1
2
1
1
0
1
0
0
0
2
0
0
2
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
2
0
2
2
0
0
0
1
2
0
0
0
0
0
2
0
1
0
0
2
2
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
1
0
2
2
0
0
2
1
0
1
1
1
0
0
0
2
0
0
0
1
2
0
1
2
1
0
0
1
0
0
2
0
9
0
1
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
1
2
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
2
1
2
2
0
0
0
0
0
1
3
0
2
1
0
0
2
0
1
1
0
0
1
2
1
0
0
2
0
1
2
1
1
2
0
0
3
2
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
1
0
0
0
2
1
0
0
0
0
2
2
0
0
0
3
1
1
1
2
0
2
0
0
1
0
2
0
1
1
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
2
1
0
0
0
1
0
1
1
0
2
0
2
2
0
0
0
0
2
0
1
0
1
1
0
0
2
0
0
1
2
0
0
1
0
1
4
0
0
0
0
1
2
0
0
0
0
1
2
0
0
0
2
0
1
0
2
1
0
0
1
0
1
0
2
1
2
2
2
2
0
0
1
0
1
0
1
1
0
0
0
0
2
4
1
0
0
2
0
0
0
0
0
1
1
1
0
0
0
0
2
2
0
0
2
0
4
1
0
3
0
0
1
0
0
0
0
0
0
1
1
2
0
3
0
0
1
0
0
2
0
1
0
0
1
0
0
2
0
2
2
0
1
0
0
0
0
0
0
0
2
0
2
1
3
1
2
0
2
0
1
0
0
0
0
0
2
2
0
3
2
1
0
3
0
2
0
2
0
1
2
1
1
0
0
0
0
2
1
2
0
1
0
0
1
2
2
3
1
1
2
5
0
0
1
0
0
2
0
0
0
2
2
0
0
2
0
1
0
2
1
0
0
0
1
0
1
2
0
1
0
1
1
2
0
0
0
0
1
0
0
2
0
1
1
0
0
1
0
2
0
1
0
1
1
2
1
2
1
2
0
0
2
2
0
0
1
1
1
0
1
0
0
0
0
1
0
2
0
0
0
2
1
0
0
0
1
2
0
0
0
1
2
1
2
1
0
1
0
0
0
0
2
2
1
0
0
2
0
0
0
1
0
0
1
0
0
3
2
2
2
1
2
2
0
0
1
0
0
0
2
1
0
2
0
1
0
0
0
2
0
1
0
0
3
0
0
0
0
0
2
0
0
0
2
2
2
2
1
1
0
0
0
0
0
3
0
0
2
0
0
1
0
0
0
2
0
1
0
2
1
0
0
0
0
0
1
0
1
1
0
0
0
5
1
0
2
0
0
3
2
2
0
0
0
1
2
0
0
0
0
2
0
2
0
3
0
0
0
0
1
0
1
0
1
2
1
0
2
0
0
3
0
1
1
2
0
2
2
1
0
0
2
1
0
1
0
1
1
2
1
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
3
2
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
2
1
0
0
0
0
0
2
0
1
0
2
1
0
1
2
2
0
0
2
1
0
2
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
1
0
2
0
2
0
1
2
0
0
2
2
0
1
0
0
1
1
2
1
0
1
0
1
1
0
0
0
0
1
0
0
2
0
0
2
1
0
0
1
2
0
3
2
2
0
0
2
0
0
0
0
0
2
1
0
0
1
0
0
1
1
0
0
0
0
1
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
1
2
2
1
1
0
2
1
0
0
0
0
0
0
2
0
0
0
1
2
1
3
3
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
1
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
2
1
1
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
2
0
1
0
1
1
2
2
0
1
0
0
0
2
1
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
2
0
1
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
1
2
0
0
1
0
1
0
1
0
0
2
0
0
2
0
4
0
0
1
1
3
2
1
0
1
1
1
1
1
0
0
1
0
0
1
0
0
0
0
1
0
3
1
0
0
0
1
0
0
1
0
0
0
0
1
2
0
2
0
2
2
0
1
0
0
1
0
0
2
0
2
0
0
2
0
2
0
2
0
1
1
0
2
1
0
2
0
0
0
2
0
1
0
0
1
0
0
1
2
0
2
1
1
2
0
0
1
2
4
2
1
0
1
0
2
1
0
1
0
2
0
0
0
0
0
0
4
0
0
1
0
0
1
2
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
2
1
2
1
0
0
0
0
0
0
5
2
0
2
2
0
0
0
0
2
0
2
0
0
1
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
3
0
2
0
0
0
0
2
0
1
1
0
1
2
0
0
3
0
0
1
1
3
2
0
0
0
1
2
0
0
0
0
2
1
1
0
0
1
0
0
0
1
0
1
0
1
2
1
0
0
0
0
1
2
0
0
2
1
0
0
0
2
1
0
2
0
2
2
1
2
2
0
0
1
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
1
2
0
0
0
2
2
0
0
0
0
1
1
0
0
0
2
0
0
2
2
0
2
0
2
1
1
0
2
1
0
0
0
1
2
2
0
0
0
2
1
0
0
1
0
0
1
0
1
2
6
0
1
2
0
2
0
2
0
2
0
0
1
2
0
0
0
1
1
1
1
1
2
2
1
0
0
0
0
1
0
0
2
1
0
0
0
1
1
1
2
0
0
1
0
0
0
0
0
1
0
1
1
0
0
1
0
1
0
1
2
0
0
2
1
0
2
0
0
3
1
2
1
1
0
0
1
1
0
0
0
0
2
2
2
0
2
0
3
2
1
0
0
0
0
1
1
0
1
2
0
2
2
1
0
0
2
2
0
2
0
0
0
0
1
3
0
2
0
1
0
2
0
0
2
0
0
0
1
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
1
2
1
1
0
0
0
0
0
1
0
0
1
1
0
0
0
1
1
0
1
2
0
1
0
0
0
2
0
2
0
1
0
0
0
1
0
2
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
1
0
1
2
0
0
3
1
2
1
1
2
0
0
0
4
1
2
0
0
2
1
2
0
0
1
1
0
0
1
0
0
4
0
1
2
0
1
0
1
0
0
0
0
2
0
0
2
0
1
0
1
0
0
1
0
0
0
0
2
1
0
0
0
2
2
3
4
0
2
0
0
1
1
0
3
2
0
1
1
0
0
3
0
0
2
2
1
1
0
2
2
1
5
0
1
0
1
1
1
0
2
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
1
0
1
1
0
0
0
0
2
0
1
1
0
0
0
1
2
0
2
0
3
0
0
1
1
0
2
2
1
2
0
0
2
2
0
2
0
0
0
0
0
2
1
3
0
1
0
2
0
0
0
2
0
1
0
1
1
1
0
0
1
2
1
2
0
0
0
1
0
0
2
0
2
2
0
1
0
0
0
0
0
1
0
0
1
2
2
0
1
0
1
2
1
0
1
0
0
1
2
1
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
2
0
2
1
0
2
0
0
1
1
0
1
0
0
2
3
2
0
0
0
1
0
0
0
1
0
1
0
0
2
1
2
0
0
2
1
0
0
0
2
0
0
0
0
2
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
2
0
2
1
0
2
2
0
1
0
0
1
0
2
0
1
1
0
0
0
0
0
0
0
0
2
1
0
1
0
3
2
0
0
9
0
2
2
0
1
0
0
0
0
0
0
0
0
0
1
3
3
0
0
0
1
2
0
1
0
0
2
0
0
0
0
2
0
1
1
0
0
1
0
2
0
0
2
0
0
0
0
0
2
1
0
3
1
0
0
1
2
0
0
2
2
0
0
1
0
2
2
0
1
1
0
1
1
0
3
2
0
0
0
0
2
2
1
0
1
0
2
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
2
1
0
1
1
2
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
2
1
1
1
0
0
2
0
1
1
0
0
0
0
3
0
0
2
0
1
1
0
1
0
2
0
1
2
0
0
0
0
2
1
0
2
0
1
1
0
2
0
0
0
1
0
0
0
2
0
3
2
0
1
0
0
1
0
0
0
2
2
0
2
0
2
0
2
0
1
4
0
0
1
0
1
0
0
0
0
1
2
1
0
1
2
0
2
1
0
2
1
1
2
2
1
0
2
1
0
1
0
2
3
0
0
1
0
2
0
0
1
0
0
2
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
2
0
0
0
1
0
2
2
2
1
1
1
2
1
1
0
1
0
0
0
2
0
1
2
1
2
2
0
1
1
0
1
2
1
1
0
1
0
1
0
2
1
0
2
0
2
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
2
0
2
0
1
2
1
1
0
0
0
0
0
1
2
0
0
1
0
0
0
1
2
0
1
2
1
0
0
1
0
0
0
0
2
0
2
0
2
0
2
1
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
2
2
0
2
0
1
1
0
0
1
0
0
0
2
2
3
1
0
1
0
0
0
1
0
0
0
0
2
0
1
1
0
0
2
0
0
0
1
0
2
0
0
2
2
0
2
0
1
0
1
0
1
1
0
2
1
2
3
1
0
2
0
0
0
0
2
1
0
1
0
2
0
0
2
0
0
0
0
3
0
0
1
1
0
0
1
0
1
2
1
2
2
0
2
1
0
0
0
0
2
0
2
0
2
0
0
0
0
1
1
0
2
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
1
2
1
0
4
2
0
0
2
0
1
2
1
1
0
0
0
1
0
2
0
0
0
2
1
0
0
1
1
0
0
2
2
0
1
0
0
0
1
0
0
0
0
3
0
4
0
2
1
0
0
2
1
2
0
2
0
1
0
1
0
0
0
3
0
1
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
2
0
0
0
1
0
2
2
2
1
0
0
0
0
2
1
0
2
2
0
2
2
0
2
0
0
0
0
0
0
1
0
0
2
3
0
0
0
6
0
3
0
0
0
0
2
0
0
2
0
3
2
0
0
0
1
1
1
0
0
1
0
0
0
0
0
4
0
2
1
0
1
1
2
2
0
0
0
2
0
2
0
2
2
1
1
0
1
1
2
0
0
3
2
0
0
0
0
0
2
0
2
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
1
2
1
2
1
1
0
1
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
1
1
0
0
0
0
2
1
3
0
0
1
0
0
0
0
2
1
2
1
1
0
0
1
0
0
0
0
1
1
0
0
1
2
1
0
1
0
3
2
0
1
0
0
1
0
2
0
0
3
0
1
2
0
2
1
2
0
2
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
7
0
1
1
0
1
1
2
0
2
0
0
0
0
0
2
1
0
1
0
2
0
0
2
0
0
0
0
0
1
0
0
2
0
1
4
2
0
0
0
1
0
0
0
1
0
1
0
0
0
2
0
1
2
2
0
2
0
1
0
0
0
2
0
0
0
0
1
2
0
1
0
0
1
1
0
0
1
1
0
2
1
2
0
2
0
0
2
2
0
0
2
2
0
0
2
2
1
2
0
0
0
0
0
0
1
0
0
0
0
1
2
0
2
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
1
1
0
0
0
0
2
2
2
2
0
2
2
2
1
0
2
0
2
0
2
0
0
1
0
2
0
0
0
1
0
1
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
2
4
0
0
1
0
2
1
0
2
1
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
3
3
0
2
0
2
1
0
0
2
0
2
0
0
2
0
1
0
2
0
1
0
1
1
1
0
0
0
1
0
2
2
2
0
0
0
2
0
3
0
3
1
0
1
0
0
0
2
0
0
1
1
2
1
0
0
0
1
2
2
0
0
0
2
1
0
2
0
2
1
0
2
0
0
0
0
0
0
2
1
0
1
1
0
0
1
0
0
0
1
0
1
0
1
1
0
0
2
2
0
0
1
0
0
1
3
0
2
1
0
0
1
0
0
0
2
1
0
2
2
0
1
0
1
1
0
2
1
2
0
0
0
0
0
0
2
1
0
0
1
1
0
0
0
1
1
0
0
0
2
0
2
2
2
0
2
0
0
0
0
1
0
2
2
0
1
1
0
0
1
1
2
1
0
1
2
2
0
0
2
0
0
0
2
2
1
2
0
2
0
1
0
3
0
0
1
0
0
0
0
2
0
0
2
0
2
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
1
2
0
2
0
1
1
2
1
0
1
0
1
0
0
1
0
1
1
2
2
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
2
0
0
0
1
0
0
0
0
2
0
1
1
1
0
0
0
3
2
1
0
1
1
0
1
2
0
0
0
0
0
1
0
0
1
1
1
0
2
0
1
1
2
1
1
1
1
2
1
0
0
1
2
2
0
2
0
1
0
0
2
1
0
1
0
0
1
0
1
0
0
1
2
0
2
0
2
2
0
0
0
0
1
0
1
2
1
1
0
2
0
0
0
0
0
0
1
0
1
1
0
0
2
1
2
0
0
1
0
0
1
0
2
7
0
1
1
0
0
0
1
0
0
2
2
1
1
0
1
0
0
0
0
0
2
2
1
0
1
0
2
2
3
0
4
1
0
0
0
0
1
0
2
3
2
2
2
0
0
0
0
1
1
0
0
1
2
1
0
0
2
2
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
1
2
2
2
0
1
0
0
0
0
0
0
0
0
2
0
1
1
1
0
1
0
1
1
0
0
2
1
0
1
0
1
1
1
2
0
1
2
2
0
2
2
0
1
1
1
0
1
0
0
0
0
0
2
0
2
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
1
1
0
1
0
1
0
2
2
1
0
0
2
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
2
0
1
1
0
1
0
0
0
1
1
0
0
0
2
0
0
1
2
0
0
0
0
1
0
0
0
0
1
0
0
1
2
1
3
0
0
2
2
2
1
1
0
0
0
2
1
0
0
1
2
0
2
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
2
0
0
0
1
0
0
1
1
2
0
1
0
0
0
0
2
0
1
2
0
0
1
2
0
0
5
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
1
1
2
0
0
0
2
0
2
1
1
0
1
0
0
0
1
1
0
0
1
0
0
0
1
1
0
0
0
0
1
1
1
0
2
1
0
0
0
0
2
0
0
0
0
0
0
1
1
1
1
0
1
0
1
1
0
1
0
0
1
2
1
0
0
2
2
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
2
2
0
0
2
2
1
0
0
0
1
1
0
3
1
0
1
1
3
2
4
0
2
0
0
2
0
0
0
0
1
2
0
0
1
1
2
1
0
0
0
0
0
0
2
0
0
2
0
0
1
1
1
0
2
0
2
0
0
0
2
0
1
0
0
0
2
1
0
2
1
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
1
8
2
0
2
0
0
0
1
0
0
1
1
2
0
0
0
0
0
1
2
1
0
1
1
1
0
2
0
0
2
2
2
1
0
0
1
0
2
0
2
0
0
0
2
1
1
0
2
0
1
0
4
1
0
2
0
2
0
0
0
1
0
1
0
0
0
0
1
0
2
0
0
1
0
1
1
0
0
1
0
0
1
1
1
0
2
1
1
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
1
0
1
0
0
0
0
0
1
2
2
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
2
1
0
0
0
2
0
0
0
2
1
0
0
0
2
0
0
0
2
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
2
1
2
2
2
1
2
0
0
0
0
1
0
0
0
2
0
0
3
0
0
2
0
1
0
0
1
2
0
0
0
2
2
0
0
0
2
0
2
2
0
0
0
0
2
1
0
0
2
2
1
0
0
0
0
0
2
0
1
0
0
1
0
0
2
0
2
1
1
0
0
2
0
0
2
0
0
2
1
0
2
1
2
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
1
0
1
2
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
1
0
2
3
1
0
2
1
0
0
0
0
1
1
2
2
2
2
1
2
0
2
0
1
0
0
0
1
2
3
1
1
0
0
1
0
1
0
2
0
0
0
0
0
0
0
1
0
1
2
0
0
1
1
0
2
1
1
1
0
2
0
2
1
0
1
0
0
0
1
1
0
1
0
1
1
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
1
0
1
2
0
2
0
2
0
1
2
0
3
0
0
0
0
0
0
1
0
0
2
0
0
1
3
2
0
0
1
1
1
1
0
1
0
1
2
2
3
0
0
0
1
0
0
0
2
0
0
1
2
0
2
1
0
0
0
0
0
0
1
0
0
1
0
1
2
0
0
0
0
3
0
0
1
0
0
1
2
2
0
0
2
1
0
0
2
2
0
1
1
0
1
1
2
0
0
2
0
0
0
2
0
0
0
0
1
0
0
1
0
1
1
2
0
0
0
0
0
0
2
3
0
0
1
2
1
1
0
0
0
2
0
0
0
2
2
2
1
0
0
0
0
6
0
0
2
0
1
1
0
1
0
2
1
0
0
0
0
1
1
2
0
0
1
1
1
0
1
0
2
0
0
2
2
0
2
0
0
3
0
0
0
0
0
0
0
0
0
3
0
1
2
1
3
0
2
1
0
0
0
1
0
0
0
0
2
0
1
0
1
1
2
0
1
0
3
0
2
1
0
0
2
0
0
1
2
0
0
0
1
2
0
1
0
2
1
1
0
1
2
1
1
0
0
0
0
3
0
0
0
2
1
1
1
1
1
0
0
0
0
1
0
0
2
1
1
2
0
0
1
0
0
2
1
1
1
0
0
2
0
4
0
0
1
0
2
1
1
2
2
2
2
1
0
2
2
0
0
0
0
1
2
1
0
0
0
2
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
2
6
1
1
2
0
1
0
1
0
1
1
2
0
0
0
0
0
1
0
1
1
0
0
1
1
0
0
2
1
0
0
2
0
1
0
2
0
0
0
0
2
1
2
2
1
2
1
1
0
0
0
0
0
0
2
2
0
0
0
1
0
1
0
0
0
0
1
0
0
2
3
0
1
0
0
1
0
0
1
2
2
0
0
2
0
0
0
0
0
0
1
2
0
0
1
0
0
0
1
1
0
2
0
0
1
1
0
1
1
0
0
0
0
0
1
0
1
1
3
0
0
2
2
0
0
0
0
1
3
1
0
0
1
2
2
0
0
1
2
2
0
1
2
2
0
2
2
2
0
0
0
0
1
2
1
0
1
0
1
0
0
1
0
2
0
1
0
2
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
3
1
0
1
0
0
1
0
2
0
1
0
3
0
0
2
0
0
1
1
0
0
0
0
0
1
0
1
2
2
0
0
0
2
0
1
1
0
1
0
1
2
2
0
1
0
1
0
0
2
2
0
1
1
2
0
0
0
2
0
0
0
1
1
0
0
1
0
0
0
1
2
1
2
2
0
0
0
2
1
0
1
0
0
0
1
0
0
2
0
0
0
2
0
0
0
1
1
1
2
1
0
0
0
0
0
0
2
2
1
0
0
2
1
1
0
1
0
1
0
3
2
0
0
1
1
1
0
2
1
0
0
1
0
2
0
0
0
0
3
2
0
2
1
1
0
0
0
1
0
0
0
0
2
0
1
0
1
0
2
0
2
0
3
1
0
0
0
0
2
1
0
0
0
1
2
0
0
1
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
1
0
0
2
1
0
0
1
0
1
0
0
0
0
2
0
0
1
0
0
1
1
0
1
0
0
1
0
2
0
1
0
0
1
1
0
0
0
0
1
1
0
4
1
0
0
1
0
0
3
0
1
0
2
0
0
1
2
2
2
0
0
1
1
1
0
0
1
1
3
2
2
0
2
0
0
1
0
1
1
4
1
1
0
2
0
1
2
1
2
1
0
0
0
0
0
2
0
1
0
2
0
0
1
2
1
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
2
1
0
2
1
1
0
0
0
0
2
0
0
1
1
0
2
1
1
0
2
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
2
2
2
1
1
2
0
2
0
2
1
2
0
1
1
1
1
1
0
0
0
0
1
0
0
0
8
2
0
2
0
2
0
0
2
0
0
1
2
0
0
1
0
0
0
1
1
1
1
0
1
0
3
2
0
2
0
2
0
0
2
0
0
0
0
1
0
1
0
0
2
2
0
2
0
0
1
2
0
0
2
0
0
0
0
2
1
2
0
1
0
0
0
2
1
2
1
3
0
2
2
1
1
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
2
0
2
2
0
2
0
2
2
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
1
0
2
0
1
0
4
2
2
0
0
0
0
1
0
0
0
2
0
1
0
1
1
1
0
2
2
0
1
0
0
0
2
0
1
1
0
0
1
0
0
0
1
1
0
0
2
0
0
0
0
0
1
3
0
1
1
2
2
2
0
0
0
1
0
1
0
0
1
0
2
1
1
2
1
2
1
0
0
1
1
0
0
2
0
1
0
1
2
0
0
0
0
2
0
0
1
0
0
0
0
1
2
2
0
0
0
2
0
2
1
0
2
0
0
0
0
0
2
0
0
0
1
1
0
0
2
0
2
2
0
0
0
1
0
1
1
0
1
1
0
0
2
1
2
1
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
2
0
1
1
2
1
2
1
2
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
1
1
0
2
0
2
0
3
1
0
0
2
0
0
0
1
2
0
1
0
0
1
2
0
0
0
2
0
1
2
0
2
1
1
2
0
0
2
0
1
2
0
1
0
0
0
2
1
1
0
1
0
1
0
0
1
0
1
1
0
1
0
0
2
0
0
0
0
1
0
2
4
2
0
0
0
0
0
1
0
0
0
1
2
0
0
1
0
1
0
0
2
1
0
1
2
2
1
1
0
0
1
0
0
2
0
0
1
2
0
0
0
0
1
0
1
0
0
1
1
0
0
2
0
1
1
0
0
1
0
2
1
0
0
1
1
1
0
2
2
1
0
1
0
0
1
0
0
0
1
1
2
0
2
2
0
2
1
2
2
0
2
1
0
0
1
0
0
1
0
1
0
2
2
0
0
0
1
0
0
0
2
0
0
0
2
0
1
0
0
2
0
0
1
1
0
0
0
1
0
2
0
1
0
0
0
0
2
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
1
0
2
2
0
1
0
2
0
0
0
0
1
0
0
0
2
0
1
1
2
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
2
2
0
1
0
2
0
0
2
0
0
2
0
0
1
0
0
1
2
2
0
2
1
0
7
2
2
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
1
0
0
1
1
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
3
0
1
1
0
0
0
0
2
0
1
0
0
0
0
1
0
0
1
0
2
0
0
0
2
1
0
0
1
2
0
2
0
0
0
0
1
0
0
0
1
1
2
2
0
1
2
1
0
2
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
4
0
0
0
1
2
0
0
0
0
2
0
0
0
0
1
1
0
1
1
2
0
0
0
2
0
0
5
0
1
2
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
3
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
2
0
1
2
0
0
1
1
0
2
0
0
0
1
0
0
0
0
1
0
0
0
2
0
1
0
2
2
2
0
0
0
2
2
0
0
2
1
0
1
0
0
2
0
2
0
0
0
0
1
0
0
0
0
2
0
1
1
0
0
0
0
1
3
2
0
0
0
1
1
2
0
0
0
0
1
2
1
0
1
2
0
1
0
0
0
3
0
2
1
1
0
0
0
2
0
1
0
0
1
0
0
1
0
0
1
0
0
1
0
1
1
0
0
0
0
1
3
1
0
0
0
2
0
2
1
0
1
2
0
1
1
1
2
0
0
1
0
0
2
1
2
1
0
1
0
2
1
0
0
1
2
1
2
1
2
0
0
0
0
0
0
1
0
1
2
1
0
1
1
0
2
2
0
0
1
0
0
3
1
1
2
0
2
0
0
2
0
2
2
1
2
0
2
0
0
2
0
0
0
0
0
0
0
1
1
2
2
1
0
0
2
0
0
0
1
0
0
0
0
0
1
0
1
2
0
0
0
0
1
2
0
2
2
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
1
0
1
1
2
0
1
0
0
1
0
0
1
0
1
0
0
2
0
0
0
0
1
0
1
0
0
0
1
0
2
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
2
1
0
1
1
0
0
0
1
0
0
1
0
0
0
0
2
0
2
1
0
0
0
2
0
2
0
0
0
1
0
1
0
0
1
1
2
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
2
0
1
1
0
1
0
0
0
0
0
2
0
0
1
0
0
1
6
0
1
0
1
0
1
4
1
0
1
0
0
0
0
0
0
2
1
0
0
1
0
1
0
1
0
0
2
0
2
0
0
0
0
2
1
2
1
3
0
0
2
2
0
0
1
2
0
0
1
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
3
0
2
0
0
1
1
2
0
1
1
0
0
0
0
2
1
1
2
0
0
0
0
1
0
2
0
2
1
2
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
1
2
2
2
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
4
1
0
2
0
2
0
0
0
2
0
2
0
1
1
0
0
1
0
1
1
2
0
0
1
1
1
0
0
1
0
2
0
1
1
0
0
2
0
1
0
0
0
0
1
0
1
1
2
2
1
0
0
0
3
2
1
1
2
0
2
0
0
0
0
1
2
0
1
0
1
0
0
1
2
3
2
2
0
2
0
1
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
1
1
0
0
2
1
0
0
0
0
2
1
0
0
1
0
3
3
0
1
1
2
1
0
0
1
0
0
2
1
0
0
2
0
0
1
0
1
0
0
0
0
1
2
0
0
1
0
0
2
1
1
0
1
1
1
0
2
0
1
1
1
1
0
0
1
0
1
2
0
2
1
1
0
0
2
1
0
0
0
2
0
0
2
0
2
0
2
0
0
2
1
0
1
2
1
0
0
1
1
1
2
0
0
2
0
2
0
0
2
2
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
2
2
1
1
2
0
0
0
0
0
0
1
0
0
0
1
0
1
0
2
1
0
0
0
2
2
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
1
1
1
0
2
2
2
1
0
0
3
1
3
1
0
0
1
0
1
0
0
1
0
2
0
0
0
0
0
1
0
0
1
0
2
0
0
1
1
0
0
1
0
1
1
1
0
1
0
0
1
1
1
0
1
1
2
0
1
2
0
0
1
0
2
0
0
1
0
1
0
0
0
1
1
0
1
0
3
1
0
0
0
2
0
0
1
0
0
1
0
2
0
0
0
0
0
3
1
0
0
1
0
1
2
0
2
0
1
2
0
2
0
1
0
1
0
1
0
1
0
0
1
1
0
3
1
1
0
2
0
0
0
1
0
1
1
0
1
1
2
0
0
0
0
1
6
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
2
0
1
1
0
1
0
0
0
0
1
1
1
0
0
2
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
2
2
0
2
0
2
0
0
1
1
1
2
0
0
1
1
2
1
0
0
0
2
0
0
1
0
0
0
1
1
0
0
0
0
2
0
0
0
2
0
2
0
0
2
0
3
0
0
1
2
1
0
2
1
1
1
2
2
0
1
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
1
0
3
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
2
1
1
0
2
0
0
0
2
0
0
1
2
0
1
0
2
0
0
0
0
0
0
0
1
0
0
1
1
0
2
1
2
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
1
0
0
2
1
2
0
0
0
0
0
0
2
2
1
1
0
0
0
0
0
2
1
0
2
0
1
1
2
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
1
1
0
1
0
0
0
1
2
0
0
2
0
1
0
1
0
2
0
1
0
2
0
2
2
0
0
0
1
4
0
0
2
1
2
0
0
0
0
2
0
0
1
0
1
0
1
1
0
0
1
0
0
2
0
0
1
2
1
1
1
0
2
0
0
2
0
1
2
2
0
2
0
0
2
1
0
0
2
0
0
2
2
0
2
0
0
2
2
0
1
0
0
1
0
0
0
0
4
2
2
1
0
0
0
2
1
0
0
0
0
1
2
2
1
0
0
1
0
0
1
2
0
3
2
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
4
1
1
2
0
1
2
2
0
0
0
0
0
0
1
1
1
0
0
2
0
0
2
2
0
1
0
2
3
0
2
2
1
0
2
0
0
1
1
1
0
0
2
0
1
0
0
0
0
2
0
0
1
2
0
1
0
1
2
1
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
2
1
0
0
2
0
2
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
1
1
0
0
2
2
0
2
0
1
2
1
0
2
1
0
0
0
0
1
0
2
2
1
1
3
2
2
0
1
0
0
0
2
1
0
0
0
2
5
0
2
1
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
3
2
0
2
0
0
0
0
1
1
1
0
2
0
1
1
2
0
0
0
0
0
0
1
1
0
0
0
0
2
1
1
1
0
0
1
0
0
1
5
0
0
1
1
0
1
1
2
0
2
1
0
0
1
1
0
3
2
1
2
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
2
1
2
0
2
1
1
1
0
2
0
0
2
0
0
2
1
2
1
0
1
0
0
0
0
1
2
0
0
2
0
1
3
1
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
2
0
0
0
0
0
0
2
0
2
1
0
2
1
0
0
0
0
1
1
0
0
0
2
1
1
2
0
2
2
1
0
0
2
1
1
0
0
0
1
1
0
0
0
0
2
0
2
1
3
0
1
2
0
0
0
1
0
2
0
2
1
2
0
0
0
0
2
1
0
0
0
2
0
1
0
0
2
0
0
2
0
2
0
0
1
2
0
0
1
0
0
4
0
0
0
0
0
2
2
1
0
2
0
2
2
0
0
0
1
0
0
0
0
1
0
1
2
2
0
1
1
2
1
2
0
1
0
0
0
0
0
0
0
0
2
0
1
0
1
0
1
1
0
1
2
0
1
3
0
2
1
1
0
0
1
2
0
0
0
2
0
0
1
0
0
1
2
0
0
0
0
1
2
0
0
2
0
2
0
1
2
0
1
0
0
0
0
4
0
1
2
1
2
1
0
0
2
1
2
0
0
0
0
1
1
0
0
1
2
0
0
0
1
0
0
0
0
2
2
0
0
1
1
0
1
0
0
1
2
0
0
2
0
2
0
1
0
0
0
1
1
1
2
0
0
1
2
0
1
1
0
1
0
0
0
1
2
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
2
0
0
0
0
1
3
0
2
2
2
0
2
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
3
0
0
0
0
1
1
1
1
1
1
0
0
0
1
2
0
1
2
2
0
0
2
0
2
1
1
0
2
0
0
0
0
0
1
0
1
1
2
4
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
2
2
0
0
2
3
2
0
1
0
1
2
0
2
2
0
0
2
0
0
0
1
0
0
2
0
0
1
0
0
0
0
1
0
2
1
0
0
1
0
1
0
1
2
0
2
0
1
0
0
2
1
2
1
0
3
1
2
2
0
2
1
1
0
2
0
1
1
1
0
1
0
0
1
2
0
0
2
1
0
0
1
0
1
0
0
2
1
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
1
0
1
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
2
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
3
0
1
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
2
0
1
2
2
0
0
1
0
2
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
1
0
0
2
0
0
1
0
2
0
0
0
0
0
0
2
1
1
2
2
0
0
0
2
0
0
0
1
1
1
2
1
2
0
1
0
1
2
1
0
1
2
0
0
1
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
2
0
2
0
0
0
0
2
1
0
0
0
0
1
0
0
2
0
0
1
0
0
1
0
2
0
1
0
0
1
1
0
1
2
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
1
1
0
0
0
0
1
1
1
2
1
0
2
0
0
0
2
0
0
0
0
1
0
1
0
2
2
0
0
1
3
0
1
0
1
0
1
0
2
0
0
3
1
0
1
0
0
2
2
2
1
1
0
0
0
0
0
1
0
1
1
0
0
1
1
1
4
3
2
0
0
2
0
2
2
0
0
0
0
0
0
0
0
1
2
0
0
2
1
0
1
0
1
0
2
2
2
2
0
2
1
2
1
0
1
1
0
0
0
0
2
0
0
0
2
0
0
1
0
0
1
0
0
1
1
2
0
2
0
0
2
0
1
0
0
0
3
1
0
0
0
2
0
0
0
2
0
1
0
1
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
4
0
2
2
0
0
0
2
0
0
1
1
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
2
0
1
2
1
0
1
0
1
0
0
0
0
1
0
0
0
1
0
1
0
2
1
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
1
0
2
2
1
0
1
0
2
0
0
0
2
0
1
2
0
1
1
0
3
0
0
1
0
1
1
0
1
2
0
1
0
2
3
0
1
1
0
2
2
2
0
0
0
0
1
0
2
0
2
0
0
0
3
2
2
1
1
2
2
0
0
3
0
0
0
0
0
0
1
0
0
2
10
1
0
0
0
0
1
1
0
0
1
2
2
0
2
0
1
1
0
0
0
1
0
0
0
0
0
0
1
2
0
0
1
0
2
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
2
1
2
1
0
1
0
1
1
0
2
0
2
0
1
0
2
0
0
0
0
0
0
1
0
0
1
0
3
1
1
0
1
0
1
1
1
0
0
1
0
0
2
0
0
2
3
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
1
1
3
0
1
0
0
1
1
1
0
2
1
0
0
1
2
2
0
0
0
1
0
0
0
1
0
1
0
1
0
0
2
4
0
0
0
1
0
0
0
1
2
1
1
0
1
0
0
0
0
0
1
0
2
0
0
0
0
1
1
3
2
2
0
0
0
2
0
1
1
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
2
0
1
0
1
1
1
0
0
0
4
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
3
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
2
1
0
0
1
0
0
1
2
0
0
0
1
0
0
0
1
0
0
0
1
1
1
2
1
0
2
0
0
0
0
0
1
0
0
2
2
0
0
0
2
1
0
0
2
0
0
0
0
2
2
0
0
0
1
0
0
2
0
0
1
0
0
0
2
0
0
0
2
1
1
0
1
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
2
2
0
0
0
1
2
0
2
0
0
0
3
2
0
1
0
0
0
1
2
1
0
0
0
0
0
0
0
0
2
2
0
2
1
0
0
0
0
0
0
0
2
0
1
3
0
0
1
2
1
1
2
0
1
0
0
1
0
1
0
0
0
2
0
0
1
0
0
1
1
0
0
0
1
0
0
0
2
0
1
1
0
0
1
2
2
0
0
1
0
1
0
1
1
0
0
0
2
0
0
1
1
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
4
1
0
2
3
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
2
2
1
5
1
0
2
2
2
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
1
2
2
0
1
1
0
0
0
1
1
0
1
0
0
0
2
1
0
0
0
1
0
0
2
4
0
0
0
2
1
1
0
0
0
0
1
1
1
0
2
0
0
0
2
3
0
0
2
2
1
1
1
1
1
1
1
0
1
0
0
0
1
2
0
0
1
0
1
0
0
0
1
0
0
0
0
2
0
1
2
1
1
0
0
0
0
0
0
0
0
1
2
0
2
2
0
0
0
2
0
2
0
0
1
0
0
2
0
0
3
1
3
2
0
0
1
0
1
1
0
0
0
2
0
3
2
0
0
1
0
2
2
2
0
2
0
1
1
0
0
1
1
2
1
0
0
1
2
0
2
1
0
0
2
0
0
0
0
0
1
0
0
0
2
0
4
0
2
0
2
1
2
1
0
2
2
0
0
2
2
1
0
0
0
1
2
0
0
1
1
0
0
0
0
1
0
2
0
0
0
0
0
1
2
0
1
1
0
0
0
2
0
0
0
0
0
0
1
0
0
2
1
0
1
1
0
0
2
0
0
1
2
2
1
0
1
0
0
2
3
2
0
0
1
2
0
0
1
3
0
0
2
0
1
1
0
1
0
0
2
2
0
0
1
0
2
0
0
1
0
2
1
1
2
0
0
2
0
2
0
0
0
0
0
0
1
0
2
2
2
2
1
2
1
0
0
1
1
1
0
0
0
0
0
0
1
2
0
1
0
0
0
2
0
0
2
0
0
0
1
0
1
1
1
0
2
0
0
1
0
1
0
2
0
0
0
1
0
0
1
0
0
0
1
0
2
2
0
0
0
0
2
1
0
0
1
0
1
2
2
0
0
1
2
0
1
2
2
0
1
0
2
1
0
0
0
0
3
1
0
0
0
0
1
0
2
2
1
0
0
0
0
2
1
0
0
1
0
0
1
0
4
0
1
2
0
0
2
2
1
0
1
2
1
2
1
0
1
1
0
1
0
0
0
1
0
1
0
1
2
2
0
0
0
0
0
0
2
1
3
0
0
1
0
0
1
0
0
1
1
0
2
2
2
0
1
0
0
2
3
0
2
4
0
1
0
0
2
2
1
0
0
0
2
0
1
0
0
0
1
0
0
0
2
1
0
0
2
0
1
0
2
0
0
1
0
1
0
0
0
0
2
0
0
0
1
2
1
0
0
0
1
0
0
0
1
0
3
0
1
2
0
1
0
0
1
1
2
1
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
3
0
0
1
1
2
0
0
0
0
0
0
0
2
2
1
1
2
1
0
2
1
2
0
1
0
2
0
1
0
1
0
0
0
2
0
1
0
0
0
0
1
2
2
0
1
0
2
0
0
0
3
0
0
0
0
0
2
2
1
0
1
2
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
1
2
0
0
0
0
1
1
2
0
0
1
1
0
0
2
1
0
0
0
1
0
0
1
0
0
0
2
0
0
0
1
2
0
1
4
2
2
1
0
0
0
0
0
0
0
1
0
0
0
2
1
0
2
0
0
0
2
2
1
0
1
0
1
2
0
0
0
0
3
2
0
0
0
1
1
1
2
0
1
1
0
1
0
0
0
0
0
2
2
0
0
1
0
1
1
0
2
0
2
2
1
0
0
0
1
0
1
1
2
1
1
2
0
0
0
1
0
0
2
0
1
0
1
2
0
0
1
2
0
0
0
1
1
0
0
0
2
0
1
1
0
0
3
0
1
0
0
0
0
1
2
0
0
1
0
1
0
1
2
1
0
0
0
1
1
2
0
0
0
0
0
1
0
1
1
1
1
0
1
2
0
0
0
0
2
0
0
1
1
3
0
0
1
2
1
0
0
1
9
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
2
0
1
0
0
0
0
6
2
1
2
1
1
2
0
0
0
1
1
1
0
0
1
2
2
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
2
0
2
0
0
0
1
0
1
0
1
2
0
0
0
1
0
2
0
1
1
0
0
2
0
0
0
0
1
0
0
0
0
2
0
1
0
0
2
1
1
0
2
0
0
1
2
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
2
2
2
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
2
1
0
0
4
2
0
0
2
1
2
0
0
2
0
2
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
4
0
1
0
1
0
1
2
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
1
3
0
1
0
0
1
1
0
1
1
0
0
1
1
2
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
1
0
2
0
0
2
2
0
1
1
2
0
2
1
1
0
2
0
0
2
0
1
0
1
0
0
1
0
1
4
0
1
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
2
1
0
0
1
0
1
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
4
2
3
1
0
2
0
0
0
0
3
0
1
1
2
0
1
0
0
2
0
0
0
0
2
0
1
0
0
3
0
0
1
2
1
2
0
0
1
3
2
1
1
2
1
2
3
0
1
4
0
0
2
1
2
0
0
0
1
1
1
0
0
0
0
2
0
2
1
0
0
0
0
1
0
0
0
2
1
0
2
0
0
2
1
0
1
1
0
5
0
2
0
0
2
0
0
0
0
0
2
2
1
0
0
0
1
1
1
1
2
0
2
0
0
1
1
0
0
2
0
1
2
1
1
1
0
0
2
2
0
0
0
0
2
2
2
0
0
0
1
0
3
2
0
2
2
0
2
1
1
1
0
0
0
0
2
0
1
1
0
0
1
0
0
2
0
2
0
0
0
0
0
1
1
1
2
0
0
1
2
0
1
2
0
1
2
0
1
0
0
3
1
2
0
0
2
1
0
1
0
0
0
1
1
1
2
0
0
1
0
2
1
0
0
1
1
1
1
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
1
1
1
0
0
0
0
0
2
0
2
0
2
0
0
1
0
0
1
0
1
2
1
0
1
0
0
1
0
2
1
0
0
0
0
0
0
3
0
1
0
0
0
2
1
0
0
0
1
1
5
2
3
1
0
2
0
0
1
1
0
1
0
0
1
3
1
0
0
0
1
2
0
0
0
0
1
1
0
0
0
2
2
1
7
0
2
0
0
0
0
0
0
1
1
0
2
1
0
1
1
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
2
2
0
2
0
1
0
0
0
0
0
0
2
1
0
0
0
0
1
2
2
1
0
0
0
0
0
0
2
0
0
3
1
2
2
0
0
1
2
0
1
0
1
1
0
2
0
2
1
2
0
0
0
0
0
2
0
1
0
0
1
0
0
2
1
0
0
0
1
1
0
0
1
2
0
0
0
0
2
0
2
2
0
2
0
0
0
1
0
1
0
4
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
1
0
1
0
0
1
0
0
0
0
1
2
0
0
0
0
1
0
2
0
1
0
0
1
0
0
0
0
2
1
0
2
1
0
0
0
2
1
0
2
1
2
1
0
0
2
0
0
2
0
0
0
2
2
0
0
0
0
0
0
2
0
1
1
1
1
0
2
2
0
0
2
2
1
0
0
0
0
0
1
0
0
0
2
1
0
0
2
1
0
0
1
0
2
1
0
1
0
0
0
1
0
1
0
0
1
0
1
2
0
0
0
2
1
0
0
0
2
0
2
0
1
0
1
1
0
0
0
2
2
2
0
0
1
2
0
0
0
1
0
14
0
1
2
1
0
0
0
0
1
0
0
0
2
1
0
1
0
0
0
2
1
0
0
0
1
0
0
0
1
0
1
0
0
2
0
2
1
2
1
2
0
0
1
0
1
0
4
2
0
0
0
0
0
0
0
2
0
0
1
1
0
2
2
1
0
0
0
1
1
2
0
0
1
2
1
0
3
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
1
1
2
0
0
0
3
0
0
2
0
0
1
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
2
0
1
2
1
0
0
2
1
2
0
1
1
1
1
1
0
2
0
0
0
1
0
0
0
2
2
0
2
2
1
0
0
2
2
0
0
0
0
0
1
2
0
1
1
1
1
1
0
1
0
0
0
1
0
0
0
2
0
2
0
1
0
0
1
0
0
2
1
0
0
0
1
1
0
1
3
0
2
1
1
2
0
1
1
2
1
0
0
2
1
0
0
1
0
1
2
0
1
2
0
2
1
2
1
0
0
2
1
2
1
0
1
0
3
1
0
0
1
0
1
0
0
1
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
1
1
1
0
1
0
0
0
0
0
2
0
1
1
0
0
0
0
2
3
0
1
1
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
1
1
0
0
1
2
0
0
0
0
2
2
1
0
0
1
0
0
0
0
1
1
0
2
0
0
0
0
0
1
0
0
1
1
0
0
0
2
1
0
0
1
0
0
4
2
0
0
0
0
0
2
2
1
2
0
1
0
0
0
0
0
0
0
2
0
1
1
0
0
0
3
2
0
0
0
1
0
2
0
2
0
0
1
0
0
0
4
0
0
2
1
2
0
0
2
0
0
2
1
0
0
0
0
0
1
0
2
0
0
2
1
0
1
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
2
2
2
2
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
1
0
0
1
0
0
1
0
0
0
0
1
0
1
1
1
1
2
0
1
0
0
2
0
1
2
1
0
1
0
1
1
1
2
3
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
1
1
1
3
0
0
0
2
3
1
0
1
0
0
3
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
1
0
3
1
0
0
4
0
0
0
0
0
2
0
2
1
0
0
0
1
0
2
2
0
2
1
2
2
1
1
1
3
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
2
2
2
1
0
2
1
2
0
0
2
2
1
0
1
2
0
0
2
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
1
1
0
1
0
2
0
0
0
0
0
0
1
0
0
1
2
2
2
0
0
1
0
0
0
2
2
0
0
1
0
1
0
1
2
0
0
0
0
2
0
0
0
0
2
0
0
1
0
1
1
0
0
2
1
0
0
0
1
1
0
0
2
1
1
0
1
2
0
1
0
0
0
0
1
0
0
1
0
0
2
0
0
1
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
3
2
1
0
2
0
2
0
1
0
0
0
1
2
0
0
1
2
0
1
0
0
0
0
1
2
0
0
0
0
1
2
2
0
0
1
0
0
1
0
0
0
1
0
1
2
0
0
0
0
6
1
0
0
1
2
0
0
0
0
0
0
0
0
0
2
2
1
0
1
0
2
0
1
0
1
1
1
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
2
1
0
0
0
1
1
0
2
0
2
0
2
0
0
0
0
2
0
2
0
2
0
0
0
2
1
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
1
2
3
1
0
1
1
0
2
0
1
0
1
0
0
0
0
3
0
1
1
0
1
0
0
1
0
0
0
0
0
0
1
1
0
2
0
2
0
2
1
0
0
2
4
0
0
0
0
0
0
0
0
1
2
1
0
2
1
2
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
2
1
0
0
0
2
1
0
0
1
0
1
0
0
1
0
0
0
0
1
0
2
0
0
0
0
2
3
0
0
0
1
0
0
0
2
0
0
1
0
2
0
0
0
2
2
1
0
1
0
0
0
2
2
0
0
0
0
1
2
0
0
0
0
2
0
0
0
2
0
2
2
0
0
1
1
2
2
0
2
0
1
2
0
1
0
1
0
2
0
2
2
1
1
0
0
0
1
3
1
1
0
0
2
2
1
1
0
0
0
0
0
2
2
0
3
1
2
1
0
0
2
0
1
0
1
0
0
1
0
2
0
0
1
0
1
0
0
0
0
1
2
1
1
0
0
2
0
2
0
2
0
1
1
0
0
0
2
0
0
4
0
2
0
0
0
0
0
1
2
0
1
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
1
0
2
0
0
1
0
0
0
1
1
0
1
2
0
0
0
0
0
0
0
0
0
3
0
0
2
2
2
0
0
1
0
1
2
0
0
1
0
0
3
1
0
2
1
0
0
2
0
2
0
0
1
1
2
2
0
2
1
1
0
1
0
2
0
2
2
0
0
0
1
0
2
0
1
0
0
1
1
0
0
2
1
2
1
8
1
2
0
1
0
0
2
0
0
2
2
0
0
1
1
0
1
2
0
2
2
0
0
1
1
0
0
0
1
0
0
2
2
2
0
0
2
0
1
0
1
2
0
1
2
0
0
1
0
0
0
0
2
0
3
1
0
1
0
0
1
0
1
0
0
2
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
2
2
1
0
2
0
1
0
0
2
0
0
2
0
1
2
1
2
2
0
0
1
2
1
0
0
0
0
2
0
0
0
3
1
0
0
0
2
0
0
0
1
0
0
2
2
0
0
0
0
2
0
1
2
1
0
0
1
1
2
0
1
0
1
0
0
0
1
0
0
2
2
0
0
0
0
2
0
1
1
0
0
0
2
1
1
2
0
0
2
2
1
2
1
0
0
1
0
0
2
0
0
1
0
0
1
1
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
1
2
0
0
2
0
1
1
2
0
2
0
1
0
1
0
0
1
1
0
0
0
3
1
0
1
0
2
1
0
0
0
2
0
2
2
0
3
1
0
1
0
1
0
0
0
2
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
2
0
2
2
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
1
1
0
0
0
0
2
1
1
0
3
1
0
2
1
0
1
2
1
0
1
0
0
0
0
2
0
2
0
0
0
1
2
0
0
1
0
2
0
0
1
0
0
1
1
3
0
1
2
0
0
1
0
0
2
0
0
2
0
2
2
2
0
1
0
1
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
2
0
0
0
2
0
0
0
1
0
0
0
1
0
1
0
0
0
1
2
1
0
1
0
0
0
0
4
0
1
0
0
0
1
0
1
0
0
0
1
0
0
1
2
0
1
0
0
0
1
0
0
2
0
0
1
1
0
1
1
0
1
0
1
1
0
0
1
1
0
0
0
1
2
1
0
2
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
2
2
0
2
2
0
1
1
1
0
1
0
0
0
2
1
1
1
2
1
1
0
0
2
1
0
3
2
0
1
0
0
0
1
2
0
0
0
1
1
1
0
0
0
0
0
0
0
1
2
2
0
1
0
0
0
2
2
1
0
2
0
0
0
2
0
0
1
0
1
0
0
2
0
0
0
1
0
0
1
0
0
0
1
0
1
0
1
0
0
1
0
1
0
0
5
3
0
3
1
0
1
2
0
0
1
2
0
0
2
0
2
0
0
1
3
2
1
1
1
0
0
2
0
0
1
0
0
1
2
0
1
0
2
0
2
2
2
0
0
0
2
1
0
0
2
0
2
2
0
2
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
2
1
0
0
1
2
0
0
0
0
0
1
1
0
0
1
1
0
4
0
0
0
0
0
0
0
0
0
2
1
6
1
1
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
1
2
2
1
0
2
0
1
2
0
1
0
0
0
2
0
0
1
0
1
0
1
0
1
0
1
1
2
0
0
1
1
1
1
0
0
0
0
1
2
0
0
0
1
1
2
2
0
1
0
1
2
1
0
3
0
0
2
1
0
0
1
0
2
2
1
0
0
2
0
0
0
0
0
1
0
0
2
2
0
2
0
3
0
0
1
0
0
2
0
0
2
8
1
1
0
1
0
1
0
0
0
1
0
0
0
0
2
0
1
1
0
1
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
2
0
1
0
0
1
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
2
1
0
2
0
1
0
0
1
0
0
0
1
1
1
0
0
1
1
0
0
1
0
0
1
0
0
0
1
0
2
2
0
2
2
0
0
0
2
0
0
0
2
1
0
0
0
0
1
0
0
1
0
2
1
0
1
0
0
0
0
2
1
2
0
1
0
1
0
2
1
0
1
0
0
1
0
0
0
2
0
1
0
1
1
1
0
0
1
0
0
1
0
1
0
0
0
0
1
1
0
0
1
2
2
1
0
0
0
0
0
0
2
0
2
0
0
0
0
2
4
0
2
2
0
1
0
2
1
1
0
1
2
0
1
1
0
1
0
1
1
1
0
2
0
2
1
0
0
1
0
1
0
1
5
0
0
0
0
0
0
1
0
2
2
0
0
1
0
1
0
2
2
0
0
0
0
0
0
1
2
3
0
0
11
2
0
0
3
2
2
0
1
1
0
0
0
0
0
1
0
1
0
2
0
1
1
0
0
0
0
0
0
0
1
0
1
2
0
0
1
1
0
1
1
0
2
4
0
0
0
1
2
2
0
1
0
0
0
1
0
0
0
2
1
2
0
2
2
1
1
1
1
1
1
1
0
1
1
0
0
2
0
0
0
1
0
1
3
0
2
0
0
0
0
2
1
1
0
2
1
0
0
0
0
0
2
1
1
1
1
0
0
0
0
2
2
0
3
0
0
0
2
1
1
0
0
0
0
0
1
2
1
0
1
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
1
0
1
1
0
0
0
1
0
3
0
2
1
0
1
3
2
0
0
0
2
0
0
2
2
2
1
2
0
1
0
1
2
0
2
3
0
2
0
2
0
0
2
2
1
2
3
0
3
0
3
0
0
2
0
0
0
1
1
2
0
2
1
2
0
0
2
0
2
4
2
0
0
0
1
0
0
0
0
1
0
3
0
1
2
0
0
1
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
2
1
1
1
2
0
1
2
0
0
1
1
0
0
0
0
1
2
2
0
1
1
0
0
0
0
1
1
0
2
0
1
0
0
0
1
0
0
0
0
1
0
1
0
2
0
3
2
2
1
0
1
2
0
3
0
2
0
2
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
1
1
0
0
0
0
1
2
1
0
0
0
2
0
0
0
1
0
0
1
0
0
2
1
0
2
0
3
0
0
0
0
0
1
1
0
1
1
0
0
2
0
0
2
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
3
0
0
0
0
0
2
2
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
2
2
0
0
1
2
1
0
2
1
0
0
0
0
0
1
2
1
0
0
0
2
1
0
2
0
2
0
2
0
0
0
0
2
0
0
0
1
0
0
1
1
0
1
0
1
1
0
1
0
3
0
1
0
2
0
0
0
0
1
2
1
1
0
0
0
0
1
0
1
0
0
1
0
1
1
0
1
1
0
2
1
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
2
1
0
0
0
1
1
0
2
2
0
0
0
0
1
0
2
0
1
0
2
0
0
2
0
0
0
0
0
3
0
0
0
2
1
3
0
1
0
0
0
0
0
2
0
0
1
1
0
0
0
0
1
2
1
0
3
1
2
1
1
1
2
0
1
0
4
1
1
1
1
2
2
1
0
0
0
0
3
3
0
1
1
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
1
1
0
2
0
0
0
0
1
0
0
2
0
2
1
1
0
0
0
0
1
2
0
0
0
0
0
1
0
2
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
2
1
2
0
2
0
2
2
0
1
0
1
0
0
2
0
1
0
1
0
2
1
0
1
0
0
2
2
2
0
1
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
3
0
0
1
0
0
0
1
0
0
2
0
2
2
0
0
1
0
2
1
1
2
2
0
0
2
2
1
1
0
1
0
2
0
1
0
0
0
0
0
0
2
0
0
1
0
0
1
0
1
0
0
2
0
1
0
0
1
1
0
1
0
1
0
2
0
1
1
2
0
0
0
0
2
3
0
2
0
2
0
0
2
2
0
2
0
3
1
0
0
0
1
1
1
0
2
1
2
1
1
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
1
2
0
2
0
0
1
0
2
0
0
0
1
0
0
0
0
2
2
0
0
1
2
0
0
0
0
2
0
1
1
1
0
0
1
2
0
0
2
1
0
2
0
1
1
1
2
0
2
0
1
0
1
0
1
0
1
2
0
1
0
1
0
2
1
1
1
1
2
0
0
0
0
2
1
1
1
1
1
4
3
0
0
1
0
1
1
0
2
2
1
0
1
0
2
0
3
1
1
0
0
0
0
1
0
2
1
0
0
1
0
2
0
0
0
0
3
0
1
1
1
0
1
0
1
0
0
2
2
1
0
1
0
2
0
2
0
0
0
0
1
0
0
0
0
2
2
2
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
3
0
0
2
0
0
0
0
1
2
1
0
0
2
0
0
0
1
0
2
0
1
1
0
0
2
0
0
1
0
2
2
0
0
2
0
0
0
0
2
0
0
1
4
0
0
2
0
0
0
0
0
0
1
0
1
0
1
0
2
2
0
2
1
0
0
0
0
0
1
1
2
0
4
0
1
0
2
1
0
1
3
0
1
0
0
0
0
1
1
2
2
0
2
2
2
0
0
0
2
0
2
0
0
0
0
2
0
1
1
0
0
0
2
2
0
2
2
0
0
1
0
0
0
1
0
0
2
1
2
1
2
0
2
1
0
0
0
2
0
0
0
0
2
0
0
2
0
0
1
0
0
3
0
0
1
2
0
1
0
1
1
0
1
0
0
0
1
2
0
0
2
0
3
0
1
0
1
0
0
0
0
2
0
0
1
1
2
0
0
0
2
0
0
0
2
0
1
0
0
1
1
0
1
0
0
0
1
1
2
1
0
2
0
0
2
2
1
0
1
0
2
0
0
0
0
0
2
0
0
0
2
0
1
1
0
0
0
0
0
0
2
0
0
1
1
1
0
2
0
0
2
1
0
1
0
0
2
2
0
0
1
0
0
1
2
0
0
0
1
0
2
0
1
0
2
0
0
0
0
0
0
1
0
0
2
0
1
0
1
1
0
0
2
0
0
0
1
0
0
0
0
2
0
1
0
1
0
0
1
1
0
2
0
1
1
1
0
1
0
1
0
0
2
1
0
1
1
0
0
2
0
1
0
0
0
2
1
0
1
2
0
2
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
2
1
2
2
0
0
3
1
2
0
0
2
1
0
0
3
0
0
2
0
2
0
1
0
1
1
0
0
2
0
0
1
0
0
0
0
1
0
0
0
2
0
11
0
2
1
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
2
0
2
0
1
0
1
0
2
4
2
1
2
0
2
2
0
0
0
0
1
0
0
0
0
2
0
0
1
0
1
0
1
0
1
0
0
1
1
0
1
0
1
0
2
1
0
0
0
1
0
0
1
1
0
0
1
2
1
2
2
0
1
0
1
0
0
0
1
2
1
0
1
2
2
0
1
0
0
0
0
0
0
0
3
0
0
2
2
0
2
1
0
3
0
0
0
0
0
3
1
3
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
1
3
1
1
1
0
2
1
0
0
0
0
0
2
0
0
0
1
1
1
2
1
2
2
2
1
1
0
1
0
2
0
0
2
1
0
0
0
1
0
2
0
2
0
0
0
0
0
0
2
0
2
0
2
0
2
0
0
1
2
0
1
2
0
0
0
1
2
1
0
3
0
0
0
0
1
0
0
1
0
2
1
0
2
0
1
0
1
0
3
0
0
0
1
0
1
2
0
0
2
0
0
0
1
2
2
0
2
0
0
2
1
0
0
0
1
0
2
0
0
1
0
1
2
0
2
1
0
2
2
0
2
1
0
0
1
0
2
3
2
0
0
0
1
0
1
2
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
3
1
0
0
0
1
0
1
2
2
2
0
0
0
2
0
0
2
2
2
1
0
0
0
0
0
0
0
2
1
2
0
0
0
0
1
0
1
0
2
0
1
2
0
0
0
0
0
3
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
2
2
0
1
0
0
0
0
2
0
1
1
0
0
0
0
0
1
0
0
0
0
3
0
0
0
1
0
2
0
0
1
1
1
2
0
0
2
2
0
0
0
2
2
1
3
2
2
0
2
0
0
0
0
1
0
2
0
1
1
0
0
2
0
2
1
1
1
1
0
0
0
0
2
0
0
0
0
1
2
1
0
0
1
0
2
1
0
1
0
1
0
0
0
1
0
0
2
0
0
1
1
2
0
1
2
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
1
0
0
2
0
2
1
2
0
0
0
0
0
1
0
0
0
0
0
0
3
2
0
0
0
1
1
0
0
0
1
2
1
1
4
1
0
1
0
0
0
0
2
0
0
0
0
0
2
2
0
1
0
1
2
1
1
2
1
0
0
2
1
1
1
2
0
2
1
0
1
4
0
0
1
3
0
0
1
0
2
2
1
0
0
1
1
1
2
0
0
2
0
0
0
2
1
2
3
0
0
0
0
0
1
0
3
0
0
0
1
2
3
1
0
0
0
0
1
1
2
0
0
0
1
1
1
1
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
1
0
0
1
2
1
0
0
1
0
0
0
1
2
0
2
0
0
2
0
1
2
1
0
0
2
1
0
2
1
1
0
0
1
0
0
0
2
0
1
1
1
2
1
0
0
2
0
0
2
1
1
1
0
0
0
1
0
0
2
0
0
0
0
2
0
2
0
2
1
0
0
0
0
1
1
2
2
0
2
1
0
0
3
2
2
4
0
1
1
0
0
0
0
2
0
0
2
2
1
1
0
1
0
0
0
0
2
0
1
0
2
0
0
1
0
0
0
1
1
0
2
1
0
2
0
2
2
2
0
0
0
0
0
2
0
2
0
0
2
0
1
0
1
1
1
0
1
1
1
0
1
1
2
1
0
2
2
2
0
0
0
0
0
0
0
0
1
2
1
2
0
0
0
0
2
0
0
2
1
2
2
0
1
1
0
1
0
0
0
1
0
0
0
2
0
2
1
0
2
1
0
0
0
0
0
1
0
0
1
0
1
0
0
3
0
0
0
2
0
2
1
0
0
0
0
4
0
0
2
0
0
0
1
0
0
0
1
0
2
2
1
0
1
0
2
2
0
0
0
0
0
0
0
1
1
0
0
0
2
0
1
0
1
0
1
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
2
1
1
1
1
4
1
0
0
0
2
0
0
0
0
2
1
0
0
0
1
0
1
1
0
2
0
0
2
2
2
2
0
0
0
1
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
2
0
2
1
1
0
2
0
0
2
0
0
0
0
1
2
2
2
0
0
0
0
0
0
1
0
2
1
0
0
0
1
0
6
0
0
1
0
1
0
2
2
0
3
1
2
2
0
0
0
2
0
2
1
2
1
0
0
0
0
0
0
1
0
0
1
1
0
2
0
1
0
1
2
0
0
2
1
0
0
0
1
3
0
0
2
0
0
1
0
1
0
1
0
1
0
0
1
0
0
1
1
0
0
0
3
1
0
0
1
0
0
2
0
1
2
0
0
0
0
1
1
2
0
0
0
2
1
0
0
2
2
0
0
0
1
0
0
1
0
0
1
1
0
0
0
2
0
0
0
0
0
1
2
0
2
0
1
2
2
2
1
0
0
0
1
0
0
0
0
0
0
1
0
2
1
0
2
0
0
0
1
1
0
0
1
0
0
0
1
1
2
0
0
0
0
1
0
2
2
0
2
1
1
0
0
0
0
0
2
2
0
1
1
0
0
1
0
0
2
0
2
2
0
2
0
0
1
1
0
1
1
0
0
1
0
0
2
0
2
1
0
2
2
0
0
0
1
0
0
1
2
1
3
0
0
2
0
1
1
0
0
1
0
0
0
0
2
2
0
0
0
0
0
1
1
0
4
1
0
1
0
1
0
0
1
0
2
0
2
1
0
0
0
1
0
1
3
3
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
1
0
1
0
2
1
0
0
0
3
2
0
1
0
0
0
0
0
0
0
3
0
0
2
0
2
1
1
0
2
2
0
0
0
0
2
1
0
0
0
2
0
0
1
1
0
2
0
0
1
0
1
0
0
0
0
2
2
0
0
1
0
0
1
0
0
0
2
2
0
1
2
0
0
0
0
1
0
1
2
0
1
1
0
0
1
0
0
1
0
2
0
0
0
1
0
1
0
0
0
0
0
1
0
0
2
0
1
0
3
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
5
0
0
1
0
0
2
0
0
3
2
0
0
0
0
0
1
1
0
2
1
0
0
1
0
0
2
1
3
0
0
1
2
2
1
1
0
0
0
2
1
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
1
0
0
0
1
1
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
1
0
2
1
0
0
1
0
0
0
1
0
2
1
0
0
0
1
0
2
0
0
0
0
3
2
0
0
0
0
0
0
0
2
2
0
0
0
3
0
0
0
0
2
0
5
2
1
0
1
0
1
0
1
2
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
2
0
2
1
0
3
0
0
0
0
0
2
0
2
1
0
2
1
2
0
1
0
0
2
0
1
0
2
2
2
1
0
0
0
2
0
0
2
0
0
0
1
1
0
2
0
0
0
1
0
0
1
2
0
2
0
0
2
1
0
0
0
0
0
1
2
1
0
0
1
0
0
0
0
0
0
1
2
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
5
0
2
1
2
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
1
1
1
1
0
2
2
1
3
1
1
2
0
2
2
2
0
1
1
0
1
0
0
1
0
0
4
0
0
1
1
1
1
1
0
1
2
0
0
2
0
2
2
2
0
1
0
0
0
1
0
0
1
2
1
0
0
0
0
0
3
0
2
0
2
1
2
1
1
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
1
2
0
0
0
2
0
0
1
1
1
0
1
1
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
1
2
0
1
1
0
1
0
0
0
0
0
2
0
2
0
0
0
2
1
1
0
0
2
0
0
0
0
0
2
0
0
2
0
2
2
1
0
0
0
1
1
0
0
1
0
1
0
2
0
0
2
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
3
0
0
0
0
0
3
0
0
0
2
0
0
0
1
1
0
0
0
3
0
0
2
1
0
0
0
1
0
0
0
0
0
0
2
0
2
1
0
2
0
0
0
0
1
2
0
2
0
0
1
2
0
0
1
0
1
0
2
2
0
1
0
0
0
2
0
2
0
1
1
1
1
0
0
1
0
0
0
3
2
1
1
1
1
2
0
0
1
3
0
1
0
1
0
2
2
0
0
0
0
2
0
2
2
2
1
0
2
1
0
2
0
0
2
1
0
0
0
0
0
1
1
0
0
0
1
1
1
0
0
0
0
1
0
0
0
2
0
2
1
0
2
0
2
0
0
2
2
0
0
0
2
2
0
1
1
0
1
1
0
0
2
0
2
1
0
1
0
2
2
0
0
0
0
0
0
0
0
2
2
0
1
1
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
2
2
1
0
0
0
1
0
0
0
0
1
0
2
0
0
1
3
0
1
0
1
2
0
0
0
0
1
1
1
0
2
0
3
1
0
2
2
2
1
5
0
0
0
0
0
1
1
0
2
2
1
0
2
1
0
3
0
1
1
0
0
0
0
0
2
2
0
1
1
0
0
2
0
0
0
0
1
0
1
1
3
3
2
1
2
0
1
0
0
0
0
1
1
0
2
5
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
1
0
0
0
3
0
0
0
2
1
1
0
1
2
1
0
4
1
1
0
0
0
0
0
1
2
1
0
0
2
0
0
1
2
0
0
2
1
0
1
2
0
0
2
0
2
0
0
2
0
0
1
0
0
1
0
1
2
2
0
1
1
0
2
0
0
1
1
0
0
1
0
0
0
2
2
0
1
0
1
0
1
1
0
0
2
0
1
0
0
2
0
1
0
0
0
0
1
0
2
0
0
2
0
0
1
0
3
0
0
0
1
0
2
0
0
0
1
0
0
1
0
0
0
1
0
0
0
2
0
0
1
0
0
1
1
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
1
0
1
2
0
0
0
0
1
0
1
0
2
0
0
1
0
1
0
0
1
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
2
2
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
1
2
0
0
0
1
0
0
2
0
0
2
2
1
0
0
0
2
0
0
1
1
0
0
3
1
0
2
1
2
2
2
2
0
0
0
1
2
0
0
0
0
1
0
0
1
1
1
0
0
0
1
2
1
1
1
0
0
1
0
1
0
0
1
0
0
0
0
0
2
2
1
1
0
2
3
2
2
1
3
0
2
2
2
0
2
2
3
0
0
2
0
0
0
0
0
1
2
0
0
2
2
1
0
0
0
0
0
2
1
2
2
1
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
1
0
1
2
0
0
0
2
0
0
0
0
0
3
1
2
0
2
1
2
1
0
1
0
1
1
0
1
0
1
2
1
0
1
1
1
0
1
2
0
1
0
0
0
0
0
1
0
2
1
0
0
1
2
0
0
1
0
1
0
2
1
1
2
0
0
0
2
0
0
1
0
2
0
0
0
4
0
1
0
0
0
0
1
0
0
2
0
1
0
0
2
0
1
0
1
0
0
1
0
0
0
1
0
1
2
1
0
1
2
0
0
1
2
0
0
0
0
0
0
0
2
1
0
0
0
2
1
0
1
0
0
0
2
2
0
0
0
2
1
0
1
0
0
0
0
0
0
1
3
1
2
0
1
1
0
2
0
1
1
0
2
2
1
2
0
0
1
1
1
0
0
2
1
2
2
0
3
2
0
2
2
0
1
0
2
2
0
0
2
0
1
0
0
0
2
0
2
0
1
0
2
1
0
1
2
0
0
1
0
2
0
0
0
0
1
2
0
1
1
1
0
2
1
0
0
0
2
3
0
0
1
0
3
0
2
1
2
1
0
0
2
0
2
0
2
3
1
1
1
0
0
1
0
0
0
2
0
0
1
0
1
0
2
0
1
2
2
0
0
3
1
1
1
2
0
2
2
0
2
2
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
1
0
1
1
0
1
0
2
1
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
2
0
0
0
3
0
0
2
1
2
1
2
1
0
1
0
1
0
0
0
0
2
1
0
2
2
0
2
0
0
0
1
0
0
2
0
2
0
0
0
0
0
1
0
2
2
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
1
3
2
2
1
0
2
1
0
2
2
0
2
1
2
0
2
1
1
1
1
1
2
2
0
2
1
0
0
2
1
0
1
3
0
0
2
7
1
0
0
2
0
0
0
0
1
0
2
0
1
0
2
2
0
0
1
0
1
2
1
0
2
2
0
0
1
0
0
0
0
1
0
2
0
0
2
0
2
1
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
2
1
2
0
2
1
0
0
0
1
0
0
2
4
0
0
0
0
2
0
2
0
0
0
1
0
1
1
0
0
0
0
1
2
1
0
1
0
0
0
0
0
1
0
0
2
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
2
1
1
2
1
0
0
0
0
0
0
0
2
1
2
0
1
0
0
2
0
1
3
0
0
1
0
0
0
2
1
1
0
0
1
3
1
4
2
0
2
3
1
1
1
0
0
0
2
0
0
0
0
0
0
2
1
1
1
2
0
0
1
0
0
0
0
0
1
0
0
0
1
2
0
0
1
1
1
0
0
0
0
2
0
2
0
0
1
0
2
0
0
0
0
0
2
0
1
0
1
2
2
1
0
1
0
0
1
0
0
0
0
0
1
2
3
0
1
0
0
0
2
1
1
0
1
0
4
0
1
2
0
1
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
3
0
2
0
0
0
2
0
1
0
1
0
0
1
0
1
0
2
2
1
0
0
0
2
0
1
0
0
0
0
2
1
2
3
0
1
0
0
1
2
2
2
2
3
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
1
0
0
1
0
0
2
0
1
1
0
0
0
2
0
0
0
2
2
2
2
0
0
0
0
1
2
2
1
2
0
1
1
0
0
1
0
0
0
0
0
1
2
0
0
1
3
0
1
0
0
0
0
1
2
0
0
1
1
0
0
1
0
0
0
2
0
2
0
0
0
0
1
2
0
0
2
2
0
0
0
0
0
2
0
1
0
0
1
1
1
0
0
1
2
0
0
2
0
1
0
2
0
0
1
0
0
1
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
2
1
0
1
1
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
1
0
1
0
1
0
2
2
3
0
0
0
0
2
0
0
2
0
0
2
0
0
1
1
2
2
2
1
0
0
2
1
2
2
0
0
0
0
0
0
0
0
2
0
1
1
1
0
1
0
1
1
2
0
0
0
2
1
1
0
2
1
0
0
0
0
1
1
1
2
0
2
0
0
1
0
2
2
1
1
1
0
0
1
1
0
0
0
0
1
0
1
0
2
0
1
0
0
1
0
0
3
1
0
0
1
1
0
0
2
0
0
1
0
0
0
1
1
1
0
1
0
1
0
1
2
1
2
0
0
0
0
1
0
2
0
0
0
0
0
0
4
1
0
0
0
0
2
1
0
0
2
2
1
0
0
1
0
0
1
0
0
2
0
0
1
0
0
1
0
0
0
2
0
0
5
2
1
2
1
0
1
0
0
1
1
1
1
2
1
0
1
0
2
0
9
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
1
0
2
1
1
0
0
1
0
2
0
2
0
2
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
1
1
1
1
1
0
0
2
0
0
1
0
1
1
0
1
0
1
0
1
0
0
3
0
1
0
0
0
0
0
3
0
2
3
0
0
0
0
0
0
0
0
1
2
2
3
1
0
0
0
0
0
0
1
0
2
3
0
2
0
0
2
0
1
2
1
1
0
0
1
0
1
0
0
0
2
1
1
0
2
2
0
0
1
1
1
0
0
1
1
0
1
1
7
0
1
1
0
0
0
0
2
1
3
2
1
2
1
0
0
2
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
2
1
0
2
2
2
0
0
0
1
2
1
1
2
2
1
2
0
0
0
2
2
1
1
0
0
0
0
2
1
1
0
0
1
1
0
1
0
2
0
0
0
0
0
1
0
2
0
0
0
0
1
1
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
2
2
0
1
2
0
1
2
0
0
2
2
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
1
1
0
1
0
0
0
2
0
0
3
0
2
0
1
0
1
1
0
0
2
2
0
2
0
0
1
0
1
0
2
0
0
0
3
2
0
0
0
2
0
0
1
0
0
1
0
2
0
2
0
0
1
1
0
1
0
1
0
2
0
0
1
0
1
2
1
1
1
0
2
0
0
0
0
1
1
0
3
0
0
0
0
0
2
0
0
0
0
3
2
2
2
0
0
1
0
3
2
1
0
0
0
0
2
0
2
1
2
1
0
1
0
1
0
0
1
0
1
0
0
2
0
0
0
2
1
1
2
2
1
0
1
2
0
1
0
0
0
1
2
0
0
0
2
2
2
3
0
1
0
1
0
0
0
1
0
0
2
0
0
0
2
0
2
0
0
1
1
0
0
0
0
1
0
0
0
0
1
2
0
2
0
1
1
1
1
0
0
2
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
1
3
1
0
0
0
2
0
2
1
0
0
0
1
0
1
1
1
0
1
0
0
0
1
0
2
0
1
2
0
0
0
0
1
1
1
0
0
1
0
2
1
1
1
1
0
5
0
0
0
2
0
1
2
0
0
2
0
1
0
0
0
0
1
0
0
2
0
0
0
2
1
1
1
0
0
2
3
2
2
1
0
1
2
6
2
0
2
0
1
0
0
0
0
1
0
0
4
1
0
1
2
2
2
0
1
0
1
0
0
0
1
0
1
0
5
2
0
0
0
1
0
2
1
0
2
0
1
0
0
0
2
1
0
1
1
1
2
1
0
0
2
0
0
2
2
0
0
0
2
0
1
0
0
2
2
0
0
0
2
2
0
0
0
0
3
1
1
0
2
0
0
0
0
0
1
2
2
0
0
0
0
1
2
0
2
0
2
0
1
0
0
0
0
1
2
0
1
1
0
2
2
0
0
0
0
2
0
0
0
3
1
0
0
2
0
2
1
0
2
1
1
0
0
1
0
0
0
0
1
2
0
2
0
2
0
1
1
0
0
2
1
0
0
0
0
1
2
2
0
0
0
0
0
0
0
2
2
2
0
0
3
1
1
0
0
2
0
1
0
0
1
1
1
1
0
0
2
2
0
1
0
1
1
0
0
1
0
0
1
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
2
1
1
1
0
0
1
1
1
2
0
0
2
1
2
1
1
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
2
2
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
1
0
0
1
1
0
2
0
1
1
2
1
0
1
2
0
1
0
0
1
0
0
0
1
0
2
1
1
0
1
1
0
0
0
1
2
2
0
2
0
0
0
0
3
2
1
0
1
0
0
2
0
0
2
0
1
0
1
0
0
0
0
2
2
2
0
3
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
1
0
2
1
0
0
0
0
2
2
1
0
2
1
0
0
0
0
2
2
0
0
0
3
1
0
1
2
0
0
2
0
0
2
2
1
2
0
0
1
0
0
1
1
1
2
0
0
0
2
0
2
1
2
2
2
0
0
1
1
0
2
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
1
0
0
2
1
2
0
0
1
2
1
0
2
2
0
0
0
2
2
1
0
0
0
1
0
0
0
0
0
0
0
2
1
1
1
0
0
1
0
2
2
1
0
1
0
0
0
2
0
0
1
0
2
1
3
0
1
0
0
0
2
0
0
0
3
0
0
1
2
1
0
1
1
2
1
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
1
0
0
1
2
1
0
0
0
1
0
0
0
0
1
2
1
0
0
0
2
1
0
2
0
0
0
1
2
0
2
1
1
1
1
0
2
1
2
2
0
0
2
0
1
2
0
0
0
0
1
0
1
2
0
2
0
1
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
2
1
1
0
2
2
2
0
0
0
1
0
0
0
2
0
1
0
0
0
1
0
0
1
0
2
0
3
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
1
2
1
0
0
0
1
2
1
0
2
0
0
0
0
1
1
1
1
0
0
2
1
0
0
0
2
2
3
2
0
0
0
0
1
0
2
0
0
2
0
0
2
0
0
0
0
0
1
2
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
2
1
0
1
1
3
0
0
0
0
2
0
0
0
0
1
0
1
0
2
2
2
1
2
0
0
1
0
1
0
1
0
1
2
0
0
0
0
2
0
1
0
1
0
1
0
1
0
0
0
2
0
0
2
0
0
0
1
0
2
0
0
1
0
2
0
2
1
1
2
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
1
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
3
0
0
1
0
2
0
0
0
0
2
1
0
0
1
0
0
0
2
0
1
0
0
2
0
1
0
0
2
0
1
0
0
0
0
0
0
1
1
0
0
3
0
0
1
0
1
2
0
0
1
3
1
2
0
2
1
2
1
0
0
0
2
0
0
1
0
1
0
0
1
1
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
1
0
0
1
0
0
0
1
0
0
2
0
0
0
1
0
1
0
2
0
2
0
0
0
0
2
0
0
1
0
2
1
1
0
1
0
1
1
1
0
2
1
2
1
2
0
3
0
2
3
2
0
0
2
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
2
1
0
1
1
0
2
2
0
0
0
1
0
1
0
1
0
1
0
2
0
1
0
0
1
0
0
0
1
1
0
0
1
2
0
0
1
1
1
0
2
0
2
2
0
0
0
0
0
1
1
1
1
0
0
3
1
1
0
0
0
0
2
1
0
1
0
1
0
1
0
0
0
1
4
0
0
1
0
0
1
2
0
0
0
1
0
0
0
2
1
0
1
0
1
1
0
1
2
0
1
2
2
1
0
1
0
3
2
0
1
1
1
0
0
0
0
0
1
1
0
2
1
0
2
0
1
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
1
0
0
2
0
2
1
0
0
0
5
1
0
0
0
1
0
0
0
2
0
0
1
0
0
1
1
0
1
0
1
2
2
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
2
4
0
1
0
2
0
1
2
0
0
0
0
0
0
1
0
0
0
2
0
1
0
1
0
0
2
1
0
0
0
0
2
0
0
2
0
2
0
0
1
1
1
0
0
1
1
1
0
1
0
0
0
0
0
1
2
1
2
0
1
0
2
0
1
0
0
0
1
0
0
0
0
0
1
0
0
2
1
0
1
0
0
2
1
0
0
0
0
4
0
0
2
0
1
2
0
2
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
2
2
2
4
3
2
0
0
1
1
2
0
1
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
1
1
1
1
0
2
0
2
0
0
0
2
1
0
1
1
0
2
1
0
1
0
1
0
1
0
0
2
1
2
0
0
2
0
0
0
0
0
0
1
0
2
2
0
0
0
1
1
3
0
0
0
0
0
1
2
0
2
0
0
1
0
1
0
1
0
1
1
0
0
0
0
1
2
2
0
0
1
0
0
1
0
0
1
0
0
2
2
0
1
0
0
0
0
1
0
0
1
0
3
1
0
0
1
2
0
1
2
0
0
1
0
0
0
0
1
0
2
0
1
1
0
1
0
0
2
0
0
0
0
1
0
0
0
2
1
0
2
0
0
3
0
0
1
0
1
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
3
2
5
1
0
2
0
0
2
1
1
0
0
1
0
2
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
5
1
0
0
0
1
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
1
0
0
0
0
0
1
0
1
2
0
0
0
0
0
2
0
2
0
2
0
0
0
2
0
1
0
0
0
0
2
0
0
1
0
4
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
1
1
2
2
2
2
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
4
0
1
0
0
0
0
0
0
0
0
1
1
0
2
0
2
0
1
0
0
0
0
2
0
2
2
2
0
2
0
1
1
1
0
2
0
1
3
2
0
1
1
1
1
2
0
1
1
1
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
1
0
0
1
0
7
0
1
1
2
2
1
0
0
0
2
1
0
0
0
0
1
0
0
0
0
1
1
1
0
0
2
0
1
2
0
2
0
0
0
0
1
1
0
2
1
0
0
0
0
4
2
0
1
0
0
1
1
2
1
0
2
0
0
0
1
2
1
0
2
1
1
0
3
0
0
1
1
2
0
1
1
0
1
0
1
0
0
0
2
0
1
0
0
2
3
0
1
2
1
0
0
0
0
0
0
1
2
0
2
0
1
2
0
0
1
0
1
0
0
1
0
4
0
0
0
0
0
2
0
2
0
0
0
2
0
0
2
0
2
0
0
2
1
1
0
2
4
0
1
2
0
1
1
1
2
0
2
2
2
2
2
2
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
1
2
0
0
0
0
1
2
0
1
2
2
2
1
0
0
0
0
2
2
0
0
1
0
2
0
0
2
2
0
0
0
2
1
0
0
3
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
1
0
0
0
1
0
0
2
2
0
0
1
1
0
2
1
0
0
1
0
2
2
2
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
1
2
0
1
1
0
0
1
0
0
0
2
0
0
0
1
1
2
0
0
0
0
4
0
0
0
3
1
0
0
3
0
0
2
0
1
0
0
0
1
0
0
0
0
1
2
2
0
1
2
0
0
0
4
0
0
2
0
1
0
0
1
2
0
1
2
0
0
2
2
0
2
0
0
0
0
0
0
1
1
0
0
0
3
0
1
0
0
1
1
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
1
1
0
2
2
1
1
0
1
1
0
0
0
2
2
0
0
2
0
0
2
1
0
1
2
1
0
1
0
0
3
0
0
0
0
0
2
1
0
2
0
2
2
0
1
1
0
0
0
2
2
1
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
2
0
1
1
1
0
3
1
1
0
0
0
0
2
0
0
0
1
1
0
2
1
0
0
2
1
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
2
0
0
2
2
2
0
0
0
0
0
0
0
2
0
2
2
0
1
0
0
2
2
1
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
3
1
0
0
0
0
1
0
0
0
1
1
2
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
1
0
0
0
1
0
0
1
1
1
0
0
0
0
1
1
0
2
0
0
2
1
0
0
0
3
1
0
1
0
2
0
1
0
1
0
1
0
0
0
0
0
0
1
0
2
0
1
0
0
0
2
0
1
0
1
1
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
2
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
3
2
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
1
0
1
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
1
1
0
1
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
1
0
1
0
2
2
0
0
2
2
2
0
0
0
0
0
2
0
0
0
0
1
0
0
2
1
0
0
1
2
0
1
1
2
1
2
2
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
1
0
2
0
0
1
0
1
0
0
0
0
2
5
2
0
1
0
0
0
1
2
1
0
1
0
1
2
1
0
2
0
2
2
1
0
2
1
1
1
0
0
2
0
0
3
1
1
7
0
2
1
0
0
1
2
0
0
0
1
0
0
0
2
0
0
2
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
5
0
0
2
0
1
0
0
0
2
2
5
0
0
1
2
0
0
0
0
1
0
2
1
2
0
0
2
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
1
2
1
0
2
1
2
2
0
1
2
1
1
0
1
1
2
0
1
0
0
0
0
1
0
1
3
0
1
0
1
0
2
0
0
1
0
0
1
0
2
1
0
0
1
2
0
2
2
0
0
1
1
1
0
2
0
0
0
1
2
0
0
1
0
1
0
2
1
1
0
0
2
2
0
0
0
0
0
2
1
0
0
0
0
1
0
0
1
1
0
0
2
0
0
0
0
2
0
1
2
0
2
0
0
1
0
0
0
0
1
1
2
0
1
1
2
0
1
0
0
0
0
2
2
0
1
1
0
0
0
2
1
0
0
0
0
0
0
1
0
2
0
2
0
1
0
1
1
0
2
2
1
1
0
2
0
0
0
0
0
0
2
0
0
0
1
1
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
1
0
1
1
1
0
0
0
0
1
0
0
0
0
1
0
2
1
0
0
1
0
1
0
0
2
3
1
0
1
0
1
0
0
0
2
0
0
1
0
0
0
2
0
2
1
0
3
0
1
1
1
0
0
0
1
0
0
1
1
2
0
0
0
0
0
0
0
2
1
0
0
0
2
1
3
1
0
0
0
0
0
2
1
0
0
0
2
1
0
0
0
0
1
0
2
0
0
3
0
1
1
2
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
2
2
1
0
0
0
0
0
2
0
0
1
0
1
0
2
1
0
1
1
1
3
1
0
0
0
0
0
2
1
1
0
1
1
0
2
2
0
1
1
1
2
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
7
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
2
0
2
0
1
0
0
1
1
0
0
0
1
2
0
1
0
1
0
0
0
4
1
2
2
0
2
2
0
0
1
0
3
0
0
0
1
2
1
1
2
2
0
0
0
2
0
0
2
1
0
0
1
0
2
0
2
0
0
0
0
2
1
0
0
2
1
2
0
2
0
0
0
0
2
0
2
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
2
0
1
2
2
1
0
0
1
1
2
0
0
0
2
0
1
1
1
1
0
3
2
1
1
1
0
2
0
0
0
1
2
1
2
1
0
0
0
0
0
0
0
1
0
2
2
0
0
2
0
0
0
0
0
0
0
0
4
2
0
1
0
1
1
2
0
1
0
2
3
2
0
0
0
1
0
2
0
1
0
0
2
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
2
1
0
0
0
0
0
0
2
1
0
2
0
0
5
1
1
0
2
1
1
1
0
1
1
0
0
0
0
1
0
2
2
0
1
2
2
0
0
0
0
0
0
0
2
0
0
1
1
0
6
2
0
0
2
2
0
0
0
0
1
0
0
1
2
1
1
1
2
0
1
1
1
2
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
1
2
0
1
0
2
2
0
2
0
0
1
0
2
0
0
1
2
0
0
2
2
2
0
0
3
0
1
0
0
0
0
0
1
1
0
1
0
0
2
2
0
0
2
2
0
0
0
1
0
1
1
1
0
2
2
0
2
0
1
0
2
1
0
0
0
2
0
0
0
2
0
0
0
1
1
2
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
2
0
0
0
2
0
1
1
0
0
0
1
0
0
2
2
2
0
0
0
0
0
2
1
0
0
1
1
1
1
4
0
2
1
0
0
1
0
1
2
2
0
1
0
0
1
0
1
0
0
0
1
1
2
0
0
0
0
1
2
0
0
1
0
1
0
1
0
2
1
0
0
1
2
0
4
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
1
0
0
0
0
1
0
2
0
2
1
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
2
0
0
0
0
2
0
1
0
1
0
1
0
2
0
2
1
0
0
0
0
0
2
1
1
0
0
0
2
2
0
2
0
5
2
4
0
3
0
0
2
2
1
0
0
0
0
2
4
0
0
1
1
0
0
2
2
1
0
0
1
1
1
0
1
0
0
2
0
1
2
0
2
0
0
2
2
1
0
1
1
0
2
0
0
1
0
0
1
1
1
0
0
2
2
1
1
2
1
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
2
2
0
0
2
1
0
0
0
1
2
0
2
0
1
2
0
0
0
0
0
1
1
1
3
2
2
0
1
0
2
0
1
0
1
0
1
2
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
2
2
1
0
2
2
0
1
2
1
1
5
1
0
0
1
0
1
0
0
0
0
0
0
0
1
1
2
2
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
2
0
1
0
0
1
0
2
0
2
0
0
2
1
2
2
2
1
1
0
0
1
0
0
1
1
0
0
1
1
0
0
2
0
0
1
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
1
2
1
1
0
2
0
0
1
0
0
0
2
1
0
1
0
0
0
1
0
0
0
0
1
1
2
0
1
2
0
1
0
0
2
0
0
0
1
2
0
2
0
2
0
2
0
1
0
0
1
0
0
1
2
0
2
1
0
0
0
0
0
0
1
1
0
0
0
0
2
0
1
1
0
0
1
0
1
1
0
0
1
0
2
2
3
1
0
0
0
0
2
0
2
0
2
2
2
0
0
0
0
1
2
0
0
0
0
0
2
2
0
2
1
0
0
0
0
4
1
0
0
0
1
2
1
0
2
1
0
0
3
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
1
0
1
0
2
1
2
2
3
0
1
1
1
2
0
0
0
2
0
0
0
0
1
1
0
0
1
0
1
2
3
1
2
0
2
0
2
1
0
0
1
0
0
0
1
0
0
0
2
2
0
0
2
2
1
0
1
0
2
0
1
0
1
0
1
0
1
0
1
0
0
0
1
0
2
0
0
0
0
0
1
0
1
1
0
0
0
2
0
2
1
2
0
1
1
1
1
0
1
1
1
0
0
0
2
2
0
2
0
0
0
0
2
0
0
2
0
1
0
2
1
1
2
1
1
1
1
1
1
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
1
0
0
1
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
1
2
1
3
0
0
1
2
0
1
0
1
0
1
1
0
0
1
1
0
1
0
0
1
0
1
2
0
0
0
0
0
2
1
0
2
1
1
0
0
2
1
2
3
1
2
0
0
0
1
0
7
0
0
0
2
0
0
0
0
0
2
0
0
0
2
1
2
1
2
2
1
0
0
4
2
2
1
1
0
0
2
1
2
0
2
3
0
0
2
0
0
0
0
1
0
2
1
0
0
0
2
0
1
2
0
1
0
0
0
1
0
1
2
0
0
0
2
0
0
0
0
0
1
0
0
1
0
2
0
0
0
1
2
1
1
0
0
0
1
0
0
0
2
0
0
3
1
1
0
1
1
1
0
1
0
2
1
2
2
1
1
1
0
0
0
0
1
1
2
0
0
1
1
1
1
0
2
0
0
1
0
2
1
2
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
2
0
0
2
0
0
0
1
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
7
1
2
0
1
3
0
1
2
0
0
0
2
1
2
0
1
1
2
1
0
2
0
1
2
0
2
0
0
0
5
0
0
1
0
0
1
0
2
0
0
0
0
2
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
1
2
2
0
1
1
2
0
0
2
0
2
0
1
0
2
0
0
0
0
1
0
0
1
3
2
0
0
1
0
0
2
0
0
2
0
2
0
0
0
2
1
2
2
0
1
0
0
1
0
0
2
1
1
0
0
0
2
1
0
0
2
0
2
0
0
1
1
0
0
2
0
0
2
2
1
0
1
2
3
0
0
2
1
0
2
0
0
0
0
0
0
2
2
1
0
0
2
1
0
1
1
0
2
2
1
0
2
1
0
2
0
2
1
0
0
2
0
1
0
0
0
1
0
0
0
0
0
5
0
0
0
0
0
0
0
1
1
0
3
1
2
0
3
1
1
0
0
0
0
0
2
0
0
2
1
0
0
2
4
2
0
0
2
0
0
1
0
1
1
0
1
1
0
0
0
0
1
0
2
2
0
0
2
0
0
0
0
0
1
0
0
2
2
2
2
0
1
0
0
2
0
1
2
0
1
1
0
1
1
0
0
1
0
0
0
0
0
0
1
0
2
0
0
3
0
1
0
2
1
0
0
0
0
2
2
0
0
0
0
1
0
1
0
0
0
0
1
0
0
2
2
0
2
0
2
0
1
2
0
0
1
0
0
0
0
1
2
2
1
3
1
1
1
0
1
2
2
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
1
0
0
0
1
0
1
2
0
2
0
1
0
2
1
1
2
0
1
1
0
1
0
0
0
1
1
0
3
0
0
0
2
2
1
0
0
1
1
0
1
0
0
0
0
1
2
1
0
0
0
2
0
1
2
0
0
0
1
0
2
0
2
2
0
0
1
1
0
0
2
1
0
0
0
0
0
0
0
1
0
0
1
0
3
2
0
0
0
2
0
2
2
0
0
0
0
2
2
1
0
0
0
2
0
1
2
1
1
0
0
0
0
1
1
2
1
1
2
0
0
0
0
1
0
0
0
2
2
0
0
1
2
0
2
0
1
0
0
1
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
1
1
2
0
0
0
1
4
0
1
1
0
0
0
4
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
1
1
1
0
0
0
1
0
0
0
2
0
0
0
1
2
0
0
2
1
1
0
1
0
0
0
2
2
1
0
0
0
0
0
1
0
1
0
2
0
2
0
0
0
0
0
0
0
0
3
2
0
2
1
1
0
1
2
0
1
2
0
0
0
1
3
0
1
1
0
0
3
5
0
0
0
1
0
2
3
2
0
1
0
0
1
2
1
2
1
2
1
1
2
1
0
1
0
2
0
0
0
1
1
1
0
0
2
2
0
1
0
0
2
0
0
2
0
2
0
0
1
0
2
0
2
0
1
2
0
0
1
0
0
2
0
0
1
0
0
0
1
1
6
0
0
0
0
2
2
0
1
0
0
1
1
1
0
2
1
2
1
2
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
2
0
2
0
1
1
0
1
2
0
1
1
2
2
2
0
2
2
0
0
1
2
2
1
0
1
0
2
0
1
1
0
1
0
0
1
0
0
0
3
2
1
0
0
0
0
0
0
1
0
0
1
0
2
0
1
0
0
2
2
0
0
0
0
2
0
2
2
1
2
2
0
2
1
0
0
0
2
0
0
1
0
0
2
0
1
0
1
2
0
1
0
1
0
0
0
0
1
0
3
0
0
1
0
0
1
0
0
2
0
0
0
0
3
0
0
1
1
0
0
1
2
2
0
0
1
0
0
0
0
0
1
1
1
1
0
0
1
0
0
0
2
0
1
0
0
0
2
1
0
2
0
2
1
0
0
0
2
2
1
1
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
2
2
1
1
4
2
0
0
0
0
2
1
2
1
0
2
1
0
0
0
0
1
0
0
0
1
2
0
0
0
1
0
0
2
2
0
0
1
1
2
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
4
2
0
1
2
2
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
2
1
1
1
0
0
0
1
0
0
0
0
0
2
0
0
1
1
0
2
0
0
2
0
1
2
1
0
0
2
0
0
1
2
0
2
0
1
2
0
1
0
0
1
0
0
0
0
0
0
1
0
2
2
2
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
1
2
1
0
0
2
1
0
1
1
0
2
1
2
0
0
1
1
0
0
0
2
1
0
1
2
1
1
0
1
0
0
1
0
0
0
2
0
1
0
2
0
2
0
1
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
2
1
0
0
0
2
1
0
1
0
2
0
2
0
2
0
1
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
2
1
1
0
1
2
3
2
0
0
0
0
1
0
0
0
2
2
1
0
1
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
2
1
0
0
0
1
0
1
2
0
0
0
1
1
0
0
0
1
0
0
1
0
1
1
2
0
2
1
0
0
0
2
2
0
0
0
0
0
1
0
0
2
1
0
0
3
1
0
0
2
2
2
0
0
0
0
0
1
0
1
2
2
0
0
2
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
1
0
0
2
0
0
0
0
2
2
0
0
0
1
2
1
0
1
0
1
0
0
0
0
0
2
0
0
0
2
0
1
0
0
1
0
1
1
1
0
0
0
0
0
0
2
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
2
1
0
1
0
2
0
0
0
2
1
0
0
0
2
2
0
0
0
0
1
1
1
2
2
0
0
0
1
0
1
0
1
0
0
0
3
1
1
0
0
2
0
0
0
0
1
1
1
1
0
2
2
0
0
1
0
2
2
0
1
0
0
1
0
1
2
0
0
1
2
0
0
2
0
2
1
1
0
0
0
1
0
0
1
0
1
0
1
2
0
3
0
1
0
0
1
1
0
0
2
1
0
0
1
0
1
0
0
0
0
2
4
2
0
0
3
1
1
1
0
0
1
2
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
2
1
2
0
0
0
1
1
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
1
1
2
1
2
2
1
0
0
3
2
0
2
0
0
0
2
0
2
1
0
0
0
2
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
1
2
2
1
1
0
2
1
1
0
2
0
0
0
2
0
0
0
1
0
1
0
1
1
0
1
1
2
0
2
0
1
0
0
1
0
0
0
1
0
0
0
0
2
0
0
3
0
2
1
1
1
0
1
2
0
2
2
0
1
2
1
2
0
1
0
1
0
1
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
1
1
0
1
1
0
1
1
0
2
1
0
0
0
0
2
2
2
2
1
1
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
1
1
2
1
1
2
0
0
0
0
0
0
0
1
1
0
0
1
5
0
0
0
1
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
3
4
0
0
0
0
0
1
0
1
1
0
2
1
0
0
2
0
1
1
0
0
3
0
0
1
1
0
1
2
0
0
0
1
2
1
0
0
0
2
0
1
0
1
1
0
1
0
1
0
2
0
0
1
0
1
0
0
1
1
2
0
0
0
2
0
0
1
1
0
0
0
0
0
1
0
1
0
1
2
0
1
2
0
1
2
2
2
0
0
0
0
0
2
0
2
1
0
1
0
0
1
0
0
2
1
2
0
0
0
1
0
0
0
2
2
0
1
0
0
1
0
2
0
4
2
1
1
0
2
0
0
0
0
1
0
2
1
0
0
2
0
0
1
2
0
0
0
0
1
4
1
1
3
0
0
0
0
0
0
2
1
0
0
1
0
0
2
0
2
1
0
0
0
1
1
0
1
1
0
2
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
2
0
1
2
0
2
0
1
0
1
0
1
0
0
0
1
0
0
0
0
2
2
0
0
2
0
1
0
0
0
1
2
1
1
2
1
0
0
1
2
0
0
0
1
5
0
2
3
2
0
0
0
2
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
3
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
2
1
0
1
0
2
0
1
0
0
0
0
0
0
1
1
0
1
2
0
0
1
2
0
0
0
0
1
0
1
0
3
0
0
0
0
0
1
0
2
2
1
0
0
0
0
3
0
0
1
0
0
0
0
1
0
2
1
0
2
1
0
0
2
0
2
1
0
1
0
0
2
0
0
2
0
0
1
1
0
0
0
0
1
3
2
3
0
2
0
0
2
0
2
0
2
0
0
1
2
0
2
0
0
0
0
2
0
0
1
0
0
2
1
2
0
0
1
1
2
0
1
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
2
1
2
1
0
2
1
2
0
0
0
0
0
1
4
0
0
0
2
0
3
0
0
0
2
5
0
0
1
1
1
0
0
1
0
0
1
0
2
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
2
2
0
1
2
0
2
0
0
0
0
1
0
2
3
0
0
0
0
0
2
1
0
0
0
0
1
0
1
1
0
2
0
2
0
2
0
2
0
2
0
0
0
0
0
0
2
1
0
1
1
0
0
2
0
0
1
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
3
1
1
0
0
5
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
2
0
0
0
1
0
1
2
2
0
2
1
0
2
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
1
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
1
1
1
0
0
0
2
1
0
2
0
1
0
0
0
2
0
1
1
0
2
0
0
1
0
0
1
0
0
0
0
0
2
0
0
2
2
1
0
1
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
1
0
1
0
0
1
0
0
2
0
0
0
1
0
0
2
1
2
0
2
2
0
0
0
0
0
2
0
1
0
0
1
0
1
2
0
0
0
2
0
0
1
2
0
0
0
2
0
0
0
1
1
0
1
2
0
2
1
1
7
2
2
1
0
1
2
2
1
1
0
0
4
0
0
1
0
0
0
0
1
1
2
0
1
0
1
2
0
0
0
1
2
0
1
1
1
0
0
2
0
0
0
0
0
1
1
0
2
2
0
0
2
1
2
0
1
2
0
1
0
1
1
3
0
2
1
0
2
0
0
0
0
0
0
0
0
1
1
0
2
1
0
0
0
0
1
0
1
1
0
1
3
1
1
3
0
0
0
1
2
2
0
0
2
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
2
2
0
0
0
1
1
0
3
1
1
2
0
1
1
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
1
0
0
1
0
2
0
0
0
1
1
0
1
0
2
3
2
0
1
0
1
0
0
1
2
1
1
2
2
1
0
0
1
0
1
2
1
0
1
2
0
0
0
2
0
2
3
2
0
1
0
1
2
0
2
3
2
1
0
0
2
0
1
0
0
1
0
0
0
0
1
0
0
2
0
0
1
1
0
0
2
1
2
0
0
0
0
0
2
0
0
0
0
2
2
0
2
0
0
1
1
0
0
0
2
1
3
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
2
0
0
1
2
2
0
0
2
2
0
0
0
1
1
0
0
0
2
2
0
3
2
0
0
0
0
0
0
0
1
1
0
1
0
0
0
2
0
2
0
0
2
1
0
0
1
1
0
0
0
0
2
0
1
0
0
0
2
1
0
0
3
2
0
0
0
0
0
0
0
0
0
1
1
2
1
2
1
0
1
0
1
0
1
1
1
0
0
0
1
1
1
1
0
0
1
2
1
0
1
3
0
2
1
1
1
1
1
0
0
0
1
0
1
0
3
0
2
0
0
3
1
2
0
0
0
2
0
1
0
0
0
1
0
2
0
0
0
2
1
0
0
0
4
1
0
1
0
0
0
0
1
1
0
1
3
0
1
1
1
1
0
1
2
2
2
2
0
0
2
2
0
0
1
1
1
2
2
0
1
2
1
0
0
0
0
0
1
0
1
2
0
1
1
2
2
0
1
0
0
0
1
1
0
0
0
2
0
0
1
2
0
3
0
0
1
0
2
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
1
1
1
0
2
2
2
0
0
0
0
0
0
1
0
1
2
1
1
1
0
0
0
1
11
0
1
0
0
1
0
0
0
1
0
2
0
0
0
0
1
0
0
1
0
1
0
0
3
0
2
2
0
0
1
2
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
2
0
1
0
2
0
0
0
1
1
0
1
0
2
0
0
1
1
0
0
0
3
0
0
0
0
1
1
1
0
0
1
0
0
0
1
1
0
0
0
0
1
1
0
0
2
0
0
0
0
0
2
1
1
0
0
0
0
2
0
0
1
0
0
1
2
2
1
1
0
2
0
0
1
1
0
0
2
0
1
0
0
0
0
1
2
2
1
1
1
1
0
0
2
0
0
0
1
2
1
1
3
0
0
1
1
0
0
0
0
1
0
0
3
0
0
2
0
2
0
0
1
0
0
1
1
2
0
0
2
0
0
1
2
0
1
7
1
1
1
0
2
0
0
0
0
2
2
0
0
1
0
0
0
1
1
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
1
0
0
0
1
1
0
0
0
2
4
2
0
0
0
0
0
0
0
0
2
0
0
1
0
3
0
0
1
0
0
1
1
1
2
0
0
1
0
0
0
0
2
1
11
1
3
1
0
0
0
0
0
1
1
0
3
0
1
2
1
0
0
2
3
1
1
0
0
0
2
1
0
0
0
1
1
2
0
0
2
0
2
2
0
2
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
1
1
0
2
0
1
0
1
0
2
1
0
2
1
0
1
2
1
0
2
0
1
2
1
4
1
0
2
0
1
0
0
2
0
0
2
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
2
1
0
0
0
1
2
1
0
1
1
0
0
0
2
0
1
2
1
0
0
1
0
0
0
0
2
0
0
2
1
0
0
0
2
0
0
0
1
0
1
2
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
1
2
0
0
1
0
1
0
0
2
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
2
0
0
0
0
0
0
0
2
0
2
0
2
0
1
0
2
1
1
0
0
0
0
1
0
0
2
0
1
0
0
2
2
0
0
0
0
0
1
0
1
1
1
0
3
0
0
0
2
0
0
0
0
1
1
0
0
0
0
2
1
0
1
1
0
1
0
2
2
2
0
1
1
3
2
1
0
0
0
3
2
0
2
1
3
1
0
1
1
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
1
2
0
1
1
0
1
0
0
1
0
0
1
2
1
0
0
0
0
2
1
1
1
2
0
2
0
2
2
0
2
1
0
0
2
1
3
1
0
2
2
0
0
2
2
2
0
0
0
0
1
3
0
0
1
0
2
0
1
0
0
0
0
1
0
2
0
0
1
2
0
0
0
2
2
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
1
0
0
2
1
0
0
2
0
0
1
0
2
0
0
0
3
0
0
1
0
2
1
1
0
1
2
2
2
0
2
0
1
0
2
0
0
0
0
2
2
2
2
0
0
0
0
1
1
0
0
0
1
2
0
0
2
1
0
0
0
0
2
0
0
0
2
0
2
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
2
0
0
1
2
0
1
1
0
0
2
0
1
1
2
0
0
0
1
0
2
0
1
2
0
1
1
0
0
1
2
2
2
0
2
1
1
0
2
0
2
0
0
1
0
0
2
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
3
2
2
1
0
0
2
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
2
1
0
2
0
0
0
2
0
0
2
1
1
0
0
3
2
1
0
1
0
0
0
0
0
1
0
4
0
0
1
1
0
0
1
2
2
2
0
0
1
0
0
0
1
0
2
0
1
1
1
0
1
0
1
2
1
0
0
0
1
0
0
2
1
0
1
0
0
2
0
1
1
0
2
0
0
0
1
0
0
2
0
1
6
1
0
2
0
0
1
0
2
2
0
0
2
1
0
0
2
1
0
0
1
0
0
0
0
2
0
0
2
0
0
1
0
1
0
1
2
1
2
0
0
0
0
1
1
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
1
0
2
0
3
0
0
0
3
0
1
0
2
1
1
1
0
0
1
1
2
0
1
1
2
0
0
0
0
0
0
1
0
2
1
2
0
1
1
2
0
0
0
0
0
0
0
2
2
1
2
1
0
1
0
0
0
0
0
0
2
0
2
0
0
0
1
0
11
1
1
0
0
1
0
0
0
2
0
2
0
0
0
0
2
0
1
0
0
2
1
0
1
0
2
1
2
0
0
0
1
1
0
0
0
1
0
0
0
2
0
0
0
2
0
1
0
0
0
2
0
1
2
1
1
2
0
1
0
0
1
0
1
0
0
1
0
0
1
2
1
1
1
4
0
0
2
1
0
0
2
0
2
0
1
1
0
1
1
1
1
1
0
0
0
3
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
1
2
1
0
0
0
0
0
3
0
0
0
2
1
2
0
0
0
1
2
0
0
2
1
1
1
1
0
0
2
1
1
1
0
2
1
1
1
0
0
0
1
0
0
1
0
2
0
0
0
2
1
1
0
1
0
1
1
4
0
0
0
0
3
0
0
1
2
0
2
0
1
2
1
0
0
0
0
1
2
0
0
1
0
0
0
2
1
2
0
0
0
1
0
0
0
0
0
1
1
0
2
0
1
0
3
1
0
2
0
1
1
1
0
1
0
2
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
2
2
0
1
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
1
0
3
0
0
2
2
2
0
2
0
0
2
0
2
2
2
3
1
0
1
0
1
2
0
0
1
1
0
2
1
2
2
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
2
0
2
1
0
0
2
2
0
0
0
2
0
0
0
3
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
1
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
1
0
0
0
1
2
1
0
2
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
3
0
0
2
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
2
0
3
0
0
0
2
0
0
0
0
0
0
1
1
0
0
1
1
1
0
0
1
0
2
0
0
2
0
1
0
1
0
0
0
0
0
1
1
0
0
1
0
0
1
1
4
0
0
1
2
0
2
0
0
1
0
2
1
1
2
2
0
1
0
1
2
0
0
0
0
0
1
0
2
0
2
0
1
1
2
0
0
0
0
0
2
0
0
1
1
0
0
0
1
1
0
2
2
0
0
0
2
2
0
2
0
0
0
1
1
2
0
2
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
2
0
0
0
2
1
1
0
0
1
0
0
0
0
1
0
2
1
0
0
1
0
2
0
0
1
0
0
1
0
0
0
2
1
1
2
2
0
2
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
2
1
0
0
0
0
1
0
1
0
2
0
0
1
1
2
1
0
1
0
1
0
1
1
1
0
0
1
1
0
0
0
0
0
0
0
2
2
0
0
1
0
2
0
0
0
2
0
1
0
1
2
0
0
1
0
0
2
1
0
2
2
0
0
1
0
1
1
0
4
0
2
0
0
0
0
1
0
2
0
0
1
0
2
2
0
1
0
0
2
0
1
1
2
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
1
0
0
0
1
2
0
2
2
2
0
0
2
3
0
4
0
0
0
3
1
0
0
0
0
0
1
0
0
2
0
1
1
1
2
0
0
0
1
1
0
0
0
0
2
1
1
2
0
1
1
0
0
0
0
0
3
0
1
0
1
0
0
1
0
1
0
0
0
0
0
2
1
0
1
2
2
6
2
0
1
0
1
1
0
0
1
0
0
0
1
1
1
0
0
0
2
1
1
0
1
0
0
0
1
0
0
4
0
0
0
1
0
0
0
2
0
2
0
0
2
0
1
1
0
2
0
0
1
0
0
0
1
0
0
0
0
1
2
1
2
1
0
0
0
1
4
0
1
1
2
1
0
2
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
3
0
0
0
0
1
2
2
1
1
0
1
0
0
0
1
0
2
0
0
2
0
2
0
0
0
0
0
0
0
3
2
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
1
0
0
2
0
2
0
0
0
1
2
1
1
3
1
1
0
1
0
0
0
0
1
0
3
2
1
0
0
1
0
0
1
0
0
2
0
0
2
0
0
2
0
1
2
2
0
1
2
0
3
2
2
1
0
0
1
0
1
0
2
1
2
0
2
0
1
0
0
0
1
1
5
0
2
0
0
1
0
1
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
3
2
1
0
0
0
0
0
2
2
0
0
3
2
2
2
0
0
4
0
1
2
0
1
2
0
0
0
1
2
0
2
0
0
2
1
0
3
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
2
0
2
0
1
0
2
0
1
1
2
0
0
1
2
0
1
2
0
2
0
2
0
2
0
2
0
3
0
0
2
2
3
0
2
0
0
2
1
1
0
0
1
1
2
2
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
1
1
0
2
0
2
0
1
0
2
0
0
2
1
2
0
0
0
0
1
0
0
2
0
0
2
0
0
1
0
1
0
2
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
2
0
0
0
0
0
2
0
1
0
1
0
0
0
0
1
2
1
0
0
1
0
2
0
0
0
0
1
0
0
1
0
2
0
2
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
1
0
0
1
2
1
2
0
2
0
0
1
2
0
0
0
2
0
0
1
2
0
2
0
0
0
0
0
0
1
0
1
0
1
2
0
0
0
1
0
0
0
2
0
2
2
1
1
0
0
0
0
0
0
1
2
2
0
2
0
1
2
0
0
1
0
0
2
2
2
1
2
1
2
0
0
2
0
0
2
0
1
1
1
1
1
1
0
1
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
2
1
2
0
0
0
0
2
1
2
2
0
7
2
0
0
2
0
1
0
2
2
1
0
0
0
0
2
2
1
1
0
2
2
0
1
0
0
3
1
0
0
0
2
1
2
2
1
0
0
1
0
0
1
0
2
0
0
0
1
2
3
0
1
2
1
0
2
0
1
0
0
0
0
2
1
1
1
0
2
0
0
1
1
2
0
0
0
0
2
1
0
2
3
3
2
2
0
2
1
1
0
3
2
1
0
2
1
0
0
2
1
2
1
1
0
2
2
2
0
1
0
0
2
1
0
2
0
0
0
0
0
0
2
0
0
0
2
1
2
1
5
2
0
4
0
1
0
1
0
2
1
1
1
0
0
0
0
1
0
3
0
0
1
1
0
0
1
0
0
2
0
1
0
1
1
1
0
2
0
0
2
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
2
2
0
1
2
2
1
1
2
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
1
0
1
0
0
2
0
4
0
0
1
2
0
0
0
1
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
2
2
2
0
1
2
0
1
0
2
0
3
0
1
0
0
2
0
0
1
1
2
0
0
1
1
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
1
2
1
2
1
0
0
0
3
0
1
2
2
0
0
0
0
2
0
1
2
0
3
1
0
2
0
1
2
2
0
1
2
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
1
0
1
2
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
2
1
1
2
1
1
0
0
2
0
0
1
2
2
0
2
1
3
0
0
0
0
0
0
1
2
1
0
3
0
0
0
0
1
1
0
0
0
0
0
0
3
0
0
2
1
2
0
0
0
1
2
1
2
1
0
1
0
0
2
0
0
2
0
0
1
0
0
3
2
0
2
0
1
0
0
0
0
2
2
0
0
0
0
1
0
1
1
0
0
2
0
2
0
0
1
0
1
0
1
2
1
0
2
0
0
0
0
1
0
1
0
0
1
2
0
1
0
2
1
1
0
2
0
2
2
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
2
5
0
0
0
1
0
1
0
1
0
0
1
0
0
1
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
2
0
0
0
2
0
2
1
0
0
0
0
0
3
0
0
0
0
1
1
0
1
1
1
0
3
0
0
0
0
0
0
2
0
1
0
2
0
1
2
1
0
0
1
0
0
2
0
1
0
0
0
3
2
0
0
2
1
1
4
0
0
0
0
0
0
2
2
1
2
1
0
1
1
0
2
2
1
0
0
2
0
0
1
0
1
2
0
0
1
0
1
1
1
1
0
0
2
0
1
1
0
0
0
1
2
0
1
2
0
1
1
2
1
0
1
1
0
0
0
1
1
0
0
0
0
0
0
1
2
1
0
2
1
2
2
3
0
1
0
0
0
2
2
1
1
2
0
0
0
2
0
0
0
1
0
0
1
2
0
1
1
0
3
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
2
1
2
0
0
0
1
0
0
0
0
0
3
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
2
0
0
0
2
2
1
0
0
0
0
2
1
1
1
0
0
0
0
1
2
2
2
0
0
1
0
0
1
1
1
1
1
2
0
0
1
1
0
2
0
0
0
3
1
1
1
1
0
1
2
0
0
2
1
0
2
2
2
0
0
1
0
0
0
1
2
2
0
0
0
0
0
1
1
1
1
0
1
0
1
1
1
1
0
0
1
1
2
1
0
1
1
0
0
0
0
2
2
0
3
0
0
1
1
3
2
0
1
0
0
0
1
0
1
0
2
2
1
0
0
1
1
0
0
2
0
2
0
0
2
1
1
1
0
1
1
0
2
1
1
2
1
1
0
1
0
0
1
0
0
0
0
0
0
0
2
2
2
2
0
2
0
1
0
1
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
3
0
0
0
1
2
1
2
0
6
2
1
1
0
2
1
0
2
0
0
0
0
0
0
0
0
0
3
1
0
2
2
0
0
2
2
3
2
2
2
0
0
0
1
0
0
1
2
2
2
0
3
1
0
0
0
0
0
1
0
2
0
0
0
0
1
0
1
3
0
0
0
0
2
0
0
3
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
2
1
1
0
2
0
2
0
1
1
1
0
0
0
2
0
0
0
0
0
0
0
6
0
0
1
0
0
0
0
0
1
0
1
0
0
3
0
1
0
2
1
1
1
0
0
2
0
0
1
2
1
2
2
1
2
0
0
0
1
0
1
0
2
2
1
0
0
0
0
2
1
0
2
1
0
0
2
0
0
1
0
1
1
0
0
1
0
1
0
2
0
0
2
0
1
0
1
1
0
0
0
0
0
2
0
0
0
0
2
1
1
0
3
0
0
2
1
0
1
1
0
0
0
4
0
0
0
1
0
0
0
0
2
4
1
1
2
0
0
0
0
1
1
2
1
2
0
0
0
0
2
0
0
0
0
0
1
1
0
1
0
0
1
0
1
0
0
0
2
2
1
2
1
0
0
0
0
0
0
0
1
0
2
1
2
2
0
0
1
0
2
0
0
0
2
2
1
0
2
0
2
0
1
2
2
1
0
2
0
0
0
0
0
0
0
0
0
1
2
1
1
2
1
1
1
1
2
1
2
1
1
2
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
1
1
1
1
1
2
0
0
1
1
0
3
1
0
0
1
0
0
0
1
1
1
2
0
1
0
1
0
4
2
3
0
0
0
2
1
0
0
0
2
1
4
0
0
2
0
1
1
0
0
4
0
0
2
0
0
2
0
1
1
0
0
1
0
0
1
0
1
2
0
0
0
2
0
1
0
0
1
1
1
1
1
0
0
0
0
1
0
0
2
0
1
0
1
0
0
0
1
2
2
2
1
1
0
2
0
1
1
0
1
2
0
2
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
3
0
0
2
0
0
1
0
0
1
2
0
3
0
0
2
0
1
1
0
2
0
1
0
0
0
2
2
0
0
0
1
0
2
0
2
0
4
0
0
0
1
0
1
4
1
3
2
0
2
1
0
0
2
0
2
0
0
1
1
0
0
1
0
0
2
1
1
2
0
1
1
2
0
2
0
2
0
1
0
0
1
2
0
0
0
2
0
1
0
1
0
1
1
2
0
2
1
0
0
2
0
0
1
1
1
0
2
0
1
0
0
0
0
0
1
1
0
0
0
1
2
2
1
0
0
2
0
0
0
1
1
0
1
0
1
1
0
1
0
2
2
0
0
1
0
0
1
0
0
0
2
0
3
2
0
0
0
0
1
2
0
0
4
0
1
2
0
0
0
1
0
0
0
2
0
0
2
1
0
0
0
0
0
2
2
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
1
0
2
2
1
1
0
0
1
1
0
0
0
2
2
0
0
1
0
3
0
2
0
1
1
0
2
1
3
2
0
0
0
2
0
1
0
0
2
1
2
2
1
1
0
1
1
0
1
2
1
0
0
2
4
0
2
0
0
0
0
1
1
0
2
1
0
0
0
1
0
2
1
2
2
1
1
1
1
0
0
0
0
0
6
0
0
2
0
1
2
2
3
0
0
0
0
1
2
0
0
0
2
0
0
2
1
0
2
0
0
0
1
3
0
0
1
2
0
1
0
2
2
0
0
0
2
2
2
1
0
1
1
0
0
0
1
2
1
0
0
0
0
4
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
2
0
2
2
2
0
0
0
1
1
0
1
1
2
0
1
0
0
0
0
2
0
0
2
0
1
0
0
0
1
1
2
0
2
0
0
0
3
0
1
0
1
2
1
0
1
2
1
0
1
2
1
2
1
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
1
0
0
1
2
2
0
2
1
0
2
0
1
1
0
0
2
0
0
1
2
0
0
0
0
2
0
1
2
1
0
1
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
2
2
0
0
2
0
0
0
2
0
0
0
2
1
2
1
0
0
0
0
2
2
1
2
1
2
0
1
0
0
3
1
0
0
0
0
1
2
0
0
0
1
1
2
0
0
0
0
1
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
2
1
0
2
1
0
0
0
2
0
1
0
0
2
0
0
2
0
2
0
0
0
2
2
4
1
2
0
0
2
0
0
0
0
2
2
0
0
1
0
1
0
0
0
0
1
0
0
0
0
2
0
1
0
0
3
0
1
0
0
0
2
0
2
0
0
2
2
2
2
0
1
2
0
1
0
0
0
2
2
2
1
1
1
0
2
5
0
1
0
2
2
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
1
2
0
2
0
0
0
2
0
2
0
0
2
0
1
0
0
2
0
2
2
1
0
1
2
0
2
2
2
1
1
1
2
1
1
1
0
1
0
0
2
0
0
0
1
0
0
1
0
0
1
0
0
4
0
0
0
0
1
0
1
0
0
0
0
2
0
0
2
1
0
0
0
0
1
2
1
2
0
0
0
1
0
2
1
0
0
0
0
1
0
1
0
0
0
0
1
0
1
1
0
1
0
2
1
2
3
0
0
0
0
2
0
0
1
2
2
0
0
0
2
0
0
1
0
2
2
0
2
2
2
1
2
0
0
0
0
0
0
0
1
2
0
0
0
1
1
0
0
2
2
0
2
0
2
1
1
0
0
0
0
1
0
1
0
0
0
0
2
0
2
0
0
0
0
2
0
2
2
0
0
0
1
1
0
0
0
2
0
2
0
0
0
0
0
0
1
0
1
0
2
0
0
0
2
0
1
0
0
0
1
0
1
1
0
2
2
0
1
1
1
0
0
0
0
2
0
1
0
1
1
0
1
1
2
1
1
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
3
0
1
3
4
0
2
2
0
0
1
0
7
0
1
1
0
0
0
2
2
0
1
0
1
0
0
0
0
2
1
0
0
0
0
0
0
2
1
1
2
0
0
1
0
1
0
0
1
0
1
0
1
0
0
1
3
1
1
0
2
0
0
1
0
0
2
1
1
1
0
0
0
0
0
0
2
0
0
2
1
0
0
2
0
0
2
0
0
0
0
1
0
1
2
0
0
0
2
1
0
0
1
0
1
2
0
2
1
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
2
1
0
0
0
0
2
0
0
0
0
0
2
0
1
2
0
1
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
2
0
2
0
1
0
0
1
0
1
0
2
1
0
1
0
2
1
0
0
0
2
1
0
1
0
1
0
2
0
0
2
1
1
0
0
1
2
0
0
2
0
1
0
2
0
0
1
2
0
1
0
0
0
1
1
1
0
2
0
0
0
2
0
2
0
1
0
0
0
0
1
0
0
1
1
1
0
0
1
2
1
0
0
2
0
3
0
0
3
2
1
1
0
2
0
1
0
0
0
2
1
0
1
2
1
0
0
1
0
0
2
0
1
1
1
2
1
0
1
1
2
0
0
0
0
0
2
0
2
2
2
1
0
1
1
1
2
0
0
1
0
2
1
1
0
0
0
2
1
0
0
0
1
2
2
0
0
0
1
0
0
1
0
2
0
0
0
0
0
2
0
1
1
3
2
1
0
1
0
0
0
0
2
5
0
0
0
0
1
0
1
2
0
1
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
1
4
0
0
0
1
0
2
0
0
2
0
1
0
0
0
1
1
0
0
4
0
1
0
1
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
1
0
0
2
2
0
1
1
0
1
1
0
1
1
0
1
2
0
2
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
1
0
0
0
3
0
0
0
2
0
0
1
0
1
0
0
1
0
0
0
1
0
0
3
1
0
0
0
0
0
0
1
0
1
1
0
1
0
1
0
0
0
0
1
2
2
0
0
1
1
0
1
1
1
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
2
0
1
0
0
0
0
1
2
2
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
2
0
1
2
0
2
0
0
0
0
0
0
2
1
0
0
0
0
2
0
1
0
2
2
1
0
0
0
2
0
3
1
1
0
1
0
0
1
0
0
0
0
0
2
1
1
0
2
2
0
0
1
0
3
0
2
2
0
2
0
1
2
0
0
0
2
1
2
0
0
0
2
0
1
2
0
2
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
1
0
1
0
2
2
2
1
0
0
2
1
1
1
1
1
0
2
2
0
0
0
0
1
3
0
0
0
0
0
1
1
1
2
0
0
1
0
1
1
0
0
2
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
2
1
0
1
0
0
0
2
0
1
0
0
2
0
0
0
0
0
2
2
0
1
0
0
0
3
0
0
0
0
1
1
2
0
0
0
0
0
6
3
2
0
0
0
2
0
0
0
3
0
2
0
1
2
0
0
0
0
1
0
0
2
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
2
1
0
4
0
0
2
2
0
0
1
0
1
2
1
1
0
2
1
2
1
2
0
0
2
0
1
0
0
2
1
0
0
0
2
2
2
1
0
1
0
0
0
0
2
0
2
2
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
1
1
0
0
2
2
0
1
1
0
2
1
0
1
0
0
2
0
3
0
2
1
2
1
0
2
2
1
1
2
0
1
0
0
1
0
0
0
0
2
0
2
1
2
1
1
0
0
0
1
0
0
1
0
0
1
0
1
0
1
0
0
1
0
0
1
0
1
1
2
0
0
0
2
1
1
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
1
1
2
2
0
2
0
1
1
0
1
0
0
2
0
0
2
1
0
0
0
0
0
1
0
2
0
0
1
0
0
2
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
3
0
0
0
0
0
3
2
0
0
0
1
0
0
1
1
1
0
1
1
1
0
0
1
0
0
0
1
0
0
1
1
1
0
0
0
1
1
0
1
0
1
0
0
2
1
1
1
0
2
1
2
1
0
3
2
1
0
0
1
2
0
0
2
2
1
0
1
2
0
1
0
1
3
2
0
0
2
2
1
0
0
3
1
2
0
2
1
1
2
0
2
0
0
1
0
2
0
0
2
0
2
1
1
0
0
2
0
0
0
1
0
0
2
0
0
3
0
0
2
2
0
2
0
0
1
1
0
1
0
0
0
0
0
2
2
1
2
0
0
0
0
0
0
0
2
0
0
2
2
1
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
2
1
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
1
0
0
2
1
0
0
0
0
0
1
0
1
1
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
1
2
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
2
1
0
3
0
1
0
1
2
0
0
1
0
2
0
1
0
0
2
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
2
0
1
2
1
2
0
2
0
0
2
2
2
1
0
0
1
1
0
0
0
0
1
2
2
0
1
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
3
1
0
1
2
2
2
1
0
0
0
2
0
1
1
0
0
2
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
2
1
1
0
0
0
1
2
2
0
1
0
0
1
2
0
0
1
0
1
1
2
0
1
0
1
0
1
0
2
1
2
2
1
1
0
0
2
1
0
1
2
0
1
1
0
0
2
1
2
0
0
0
0
1
0
0
0
0
0
1
1
1
2
0
0
0
1
0
1
1
0
1
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
1
0
2
0
0
1
1
0
0
0
1
0
0
0
1
1
0
1
2
2
0
0
0
0
1
1
0
2
0
0
2
0
0
0
1
1
1
2
1
1
0
1
0
0
0
0
0
0
2
1
2
1
1
0
2
1
0
0
0
1
0
1
2
0
0
0
2
2
0
2
1
1
0
0
1
0
0
0
1
2
0
0
0
0
2
0
1
0
0
2
1
2
1
3
0
1
1
0
1
2
1
1
0
2
0
0
0
1
0
1
0
0
1
0
2
1
1
3
1
0
1
0
0
0
2
0
0
1
0
0
0
1
1
0
1
0
0
1
3
0
0
1
0
2
1
0
0
1
0
0
0
0
0
4
1
0
0
0
2
2
0
1
0
2
0
2
2
0
0
0
2
0
2
2
0
2
2
0
0
0
2
2
1
1
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
1
2
0
0
2
0
2
2
1
0
1
2
1
0
1
0
0
1
0
1
0
0
2
0
2
0
1
1
0
0
1
0
0
2
2
0
0
0
2
1
0
0
0
4
0
0
1
1
1
0
0
1
2
0
1
1
1
0
2
0
2
0
0
0
0
0
0
1
0
1
0
1
1
1
0
2
1
2
0
1
0
1
2
2
2
0
0
2
0
0
0
2
1
0
1
2
1
0
1
1
0
4
0
0
1
2
0
2
0
0
0
1
0
0
2
2
2
0
2
0
0
0
0
0
0
0
1
1
0
2
2
0
1
1
1
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
1
0
2
1
0
1
0
1
0
0
0
1
0
0
1
1
0
0
0
1
0
2
0
1
3
2
0
1
0
1
0
0
1
0
0
0
0
1
2
3
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
2
2
2
1
0
1
0
0
0
1
0
0
2
0
2
1
1
0
2
3
0
0
0
0
0
2
0
1
0
0
1
1
2
1
0
0
1
2
1
0
0
0
0
0
2
0
0
0
2
2
2
1
1
0
1
2
1
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
2
1
0
2
0
1
0
1
0
1
1
1
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
2
0
0
0
1
0
3
1
1
1
0
0
0
0
0
1
0
1
0
2
1
2
1
0
1
0
0
0
0
0
0
2
2
1
1
0
1
0
2
0
0
2
0
0
2
0
0
0
2
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
2
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
2
4
0
0
1
0
2
0
0
0
1
0
1
0
2
1
2
1
0
1
0
2
0
2
3
0
1
0
0
0
0
1
3
0
0
1
1
1
1
0
0
0
2
0
0
1
1
0
0
0
2
0
2
1
0
1
0
1
0
0
2
1
1
1
0
2
1
0
3
0
1
2
2
0
1
0
2
1
0
2
2
0
1
1
1
2
0
0
0
0
0
0
0
1
2
0
1
1
2
2
0
2
0
0
0
2
1
0
1
0
0
1
0
0
0
1
0
0
1
1
1
2
0
0
0
0
0
0
0
0
0
2
1
0
2
2
0
0
1
0
0
0
0
0
0
0
0
2
2
1
2
1
1
0
1
0
0
0
2
0
0
0
0
0
1
1
0
0
2
1
0
2
0
1
0
1
2
1
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
1
0
0
2
1
1
2
2
0
1
0
2
0
2
1
2
1
0
1
0
1
1
0
0
0
0
0
1
2
1
1
1
1
0
2
0
2
1
0
1
2
1
0
0
3
1
0
0
0
2
1
1
2
1
2
0
0
4
1
0
0
1
0
0
0
2
0
0
0
1
0
0
2
2
0
0
1
0
0
3
2
1
0
0
2
0
0
2
1
0
0
1
2
2
2
0
0
0
0
1
0
0
1
1
0
0
0
2
0
0
0
0
2
2
2
0
1
0
2
0
1
0
0
0
0
2
0
1
0
0
0
0
1
0
1
2
1
0
0
0
3
0
0
1
1
0
1
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
1
1
1
0
2
1
0
0
0
0
0
0
0
0
1
0
3
1
0
0
1
0
0
2
0
0
0
1
2
0
1
1
0
0
0
0
3
0
0
2
0
0
0
1
1
0
0
2
2
1
2
2
1
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
1
0
3
1
1
0
0
0
0
0
2
0
2
1
1
0
2
0
0
2
1
2
0
1
0
0
0
2
0
2
0
2
0
2
0
0
0
0
0
0
2
3
1
2
0
2
0
0
1
0
0
0
2
0
4
0
0
0
1
1
1
2
1
1
1
1
2
0
0
0
1
1
2
0
0
0
1
2
2
1
0
0
2
2
0
0
0
0
0
2
0
0
0
1
0
4
0
0
1
0
0
2
2
0
3
2
0
1
0
0
1
1
1
1
0
0
1
0
2
2
0
0
0
1
1
0
1
0
0
1
0
1
1
0
0
0
0
2
0
1
1
2
1
1
1
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
1
1
1
0
0
0
0
1
2
0
0
0
0
1
0
1
1
0
0
0
0
1
2
0
2
0
1
2
2
0
0
0
1
0
0
2
0
0
0
2
0
0
1
0
2
0
1
2
0
1
0
0
1
2
1
0
0
2
0
0
0
1
0
2
0
0
2
1
0
0
2
0
0
1
0
1
0
0
2
0
0
0
0
1
2
1
0
0
2
1
1
1
2
0
1
0
0
0
0
0
0
0
1
2
2
1
0
3
1
1
2
0
0
1
1
1
0
0
0
0
1
0
1
0
2
0
2
0
2
0
3
0
0
1
1
0
0
1
1
0
0
0
0
0
0
2
0
3
2
0
2
1
1
1
0
0
1
1
1
0
0
0
2
0
0
0
1
2
1
0
0
0
0
0
1
0
0
2
1
0
2
0
0
0
2
1
0
0
1
1
0
2
0
0
0
2
0
0
0
1
2
2
0
0
2
0
1
0
1
2
0
1
1
2
0
1
1
0
0
0
2
1
0
2
2
1
2
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
1
0
0
1
0
1
2
0
1
0
0
0
0
2
0
0
1
0
1
2
2
3
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
1
0
2
0
0
1
1
0
0
1
2
1
2
0
1
2
1
0
1
1
0
1
1
0
0
0
1
2
2
0
2
0
1
0
0
0
0
1
0
0
1
2
0
1
0
2
0
1
1
0
0
1
2
0
0
0
1
0
0
0
1
1
3
0
2
2
0
0
0
2
2
1
0
0
0
2
0
0
0
2
2
1
1
0
0
0
1
1
1
0
0
1
2
0
2
2
0
0
2
1
1
0
0
0
0
0
0
2
2
0
1
2
1
1
0
0
4
0
3
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
1
1
0
2
0
0
2
0
0
0
0
1
0
0
1
0
1
0
2
0
0
0
0
2
1
0
0
1
1
2
0
2
2
0
2
2
1
2
2
1
0
0
0
1
1
0
1
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
1
1
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
2
0
1
0
2
0
3
0
2
0
2
1
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
2
0
0
2
0
0
0
1
0
3
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
2
1
1
1
0
1
0
2
1
0
2
2
0
0
0
2
3
2
0
0
0
0
1
0
1
2
1
0
1
0
1
0
0
0
1
1
2
8
0
1
0
0
0
2
0
2
0
0
1
0
0
1
1
1
0
1
0
0
0
2
0
1
0
2
1
2
0
0
0
0
0
0
1
1
0
0
0
1
1
1
2
0
2
1
0
0
0
1
2
1
2
0
1
0
2
0
1
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
1
1
0
0
0
3
0
0
0
0
0
2
1
1
0
0
2
1
0
1
1
2
0
1
2
1
0
0
1
0
2
0
0
0
0
0
2
0
1
1
2
0
1
1
0
0
2
1
0
3
1
0
1
0
2
0
1
0
0
2
0
1
0
0
1
1
0
0
1
0
0
1
2
0
0
0
0
1
1
0
0
0
0
1
2
1
0
1
2
0
0
0
0
0
0
1
1
1
0
0
0
2
0
0
0
1
2
0
0
1
1
2
1
1
0
1
0
1
2
0
0
0
1
0
1
1
0
0
0
1
2
0
0
1
0
1
0
2
0
0
0
1
0
2
1
0
1
0
0
4
0
0
0
1
0
2
1
1
0
2
1
2
2
1
0
2
0
2
0
1
0
1
0
2
0
0
0
0
1
1
0
1
0
0
0
0
1
1
0
0
0
1
1
1
2
2
2
0
0
2
1
0
2
0
1
0
1
0
1
0
0
0
1
1
0
1
1
2
0
2
1
0
0
0
0
0
1
0
0
2
1
0
2
0
2
1
0
1
0
0
1
0
1
0
0
0
3
0
0
2
0
0
2
0
0
0
1
2
0
2
0
0
5
0
0
0
0
0
2
1
0
0
1
0
2
0
2
0
2
0
2
0
0
0
0
0
2
1
0
0
3
2
0
0
0
0
2
1
0
1
1
1
0
0
0
0
0
0
1
0
0
0
2
1
1
1
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
2
1
1
0
0
0
0
0
1
1
0
0
1
0
2
0
1
1
1
2
2
1
2
2
0
0
0
2
0
0
0
0
2
1
0
2
0
0
1
1
0
0
0
3
0
0
0
1
0
0
1
1
0
0
1
0
0
1
1
1
0
1
1
2
2
0
0
2
0
3
0
0
0
2
0
2
2
0
0
0
1
0
0
0
1
1
0
1
0
2
0
2
0
0
2
1
0
0
0
0
2
2
0
1
1
1
0
1
2
0
0
0
1
1
0
0
1
0
1
2
1
1
1
0
0
2
1
1
0
1
0
0
2
2
0
0
2
0
2
0
1
0
1
2
0
2
0
2
2
0
0
0
1
1
0
2
2
0
1
0
0
1
2
1
0
1
0
0
1
0
1
0
0
2
0
0
0
0
0
0
1
2
1
0
0
0
1
0
2
2
1
2
0
2
0
1
0
0
4
3
0
2
0
1
0
0
1
0
1
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
1
1
0
1
0
0
1
0
0
3
0
0
0
1
3
0
0
0
0
0
1
0
0
2
2
2
6
0
1
1
0
0
0
1
1
1
0
1
0
1
0
0
0
1
2
2
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
1
1
2
0
2
0
0
1
1
0
0
0
3
2
0
1
0
1
1
2
1
0
0
0
1
0
1
2
0
0
2
3
0
0
0
0
0
0
1
1
0
1
2
0
1
0
0
1
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
2
1
1
0
1
2
0
0
2
0
1
0
0
0
0
1
2
1
0
1
0
0
2
0
0
0
4
1
1
0
0
0
0
0
2
0
2
1
2
1
0
0
0
0
0
1
0
0
1
0
1
2
1
0
2
0
1
0
0
2
0
0
1
2
0
0
2
1
0
2
0
2
1
2
1
2
2
0
0
0
0
1
0
0
0
0
0
0
2
2
0
1
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
2
2
1
0
0
2
0
2
0
0
2
1
4
1
2
1
0
0
2
2
2
1
1
0
1
2
2
1
0
0
3
2
2
2
0
1
2
0
0
0
0
2
0
2
0
0
0
1
0
1
0
0
0
0
3
2
1
1
1
1
0
0
0
0
1
3
2
2
0
1
1
0
1
1
0
0
0
0
0
0
0
1
2
0
2
0
0
2
0
1
1
1
0
0
3
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
2
0
1
0
0
0
0
3
0
0
1
0
2
2
3
0
0
2
1
0
0
1
0
1
0
0
2
2
0
0
0
2
1
0
0
0
1
0
0
0
0
2
1
0
1
2
2
1
1
0
0
1
5
2
1
1
1
0
0
0
1
0
1
2
2
2
0
0
2
0
2
1
0
1
1
0
1
0
0
1
1
2
0
0
1
0
2
1
2
0
0
0
0
0
2
2
2
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
1
1
0
0
2
0
1
1
1
0
0
0
1
1
0
0
1
1
2
2
1
1
0
1
1
0
2
0
0
2
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
2
0
1
2
0
1
2
0
1
0
0
0
0
0
2
2
1
0
1
0
0
1
0
0
0
0
1
2
1
1
1
2
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
1
1
2
0
1
0
1
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
2
1
1
0
0
0
2
0
1
0
2
0
0
0
2
1
3
0
2
0
0
0
1
0
0
2
0
5
0
1
2
2
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
2
1
2
0
0
0
2
1
0
0
1
0
2
1
1
0
0
0
1
1
3
1
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
1
2
5
0
1
0
1
1
0
0
2
0
1
2
2
0
0
1
1
0
0
0
3
0
2
1
2
0
0
1
1
0
0
2
2
2
0
2
0
1
0
0
2
0
0
0
1
0
2
1
0
1
1
0
1
1
0
2
2
0
1
0
0
0
2
0
0
2
0
0
0
0
1
1
2
0
0
0
0
1
3
1
1
0
1
3
0
0
0
0
1
0
0
2
0
0
1
0
0
1
0
2
0
0
0
0
1
1
0
0
2
0
0
1
0
0
2
0
1
0
0
0
0
1
0
0
1
0
2
2
1
0
0
0
2
2
0
2
1
2
0
0
1
0
0
0
0
7
0
0
0
1
0
1
2
0
1
1
0
1
0
0
0
0
2
0
0
1
0
0
0
1
0
0
2
1
2
0
1
1
2
1
1
0
7
0
0
0
0
0
0
1
0
2
0
0
0
0
1
2
0
0
1
0
0
0
0
2
0
0
0
2
1
2
1
0
0
0
1
2
0
0
0
0
1
0
1
0
0
0
0
2
0
1
0
1
0
2
0
0
0
2
0
0
0
1
2
1
0
0
0
3
0
0
2
1
0
0
1
2
1
1
0
0
0
1
1
1
1
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
2
0
0
1
1
2
3
1
0
0
0
1
2
0
0
1
1
0
1
1
0
0
2
0
2
0
0
0
2
0
0
0
1
2
0
1
2
2
1
0
0
0
0
2
0
2
0
1
2
0
0
0
4
0
0
0
1
2
0
0
2
1
0
0
0
1
0
0
0
2
0
0
1
2
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
4
1
2
0
0
1
0
0
0
1
0
0
1
2
0
1
0
0
0
0
0
1
1
2
0
2
1
2
0
1
1
0
1
0
0
0
0
1
0
1
2
0
2
0
2
1
0
0
0
0
0
1
5
1
0
0
0
0
1
1
0
0
0
1
2
2
0
0
0
1
0
0
1
0
1
0
0
1
1
1
0
2
0
2
2
2
0
1
0
0
2
0
1
2
1
0
1
1
1
0
1
0
2
0
0
0
0
0
0
0
0
2
1
0
1
1
0
2
0
0
0
2
0
0
1
1
1
1
0
0
1
1
1
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
1
1
1
0
0
2
0
0
2
0
1
0
0
1
3
0
0
1
0
1
1
0
1
0
2
1
3
1
0
0
0
0
2
2
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
1
0
2
0
0
2
0
0
0
2
1
0
0
0
0
2
1
1
0
0
0
2
1
2
0
0
0
0
0
1
0
4
0
1
1
0
2
2
1
0
1
0
0
0
2
2
0
0
0
0
0
1
0
1
1
0
1
0
1
1
1
1
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
6
0
0
0
0
2
0
0
1
2
0
0
1
1
0
1
0
0
0
0
1
0
0
0
1
0
1
0
2
1
0
0
0
2
0
2
0
0
0
1
2
0
0
1
0
1
2
1
1
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
3
2
2
0
1
1
1
1
1
2
1
1
2
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
1
1
2
0
0
0
0
0
0
2
0
1
0
0
0
1
1
0
3
1
1
0
2
0
2
1
0
0
1
0
0
2
0
1
0
0
0
0
2
2
1
0
0
0
0
2
0
0
2
0
2
0
0
1
2
0
1
0
0
0
0
2
0
0
0
0
1
1
4
0
0
0
0
0
1
1
2
1
0
1
2
0
0
1
1
0
0
1
2
0
0
0
0
1
0
0
0
1
0
5
0
0
0
0
0
1
0
0
2
1
1
0
0
2
0
0
0
0
2
0
0
2
2
2
1
0
0
0
2
0
0
2
1
0
2
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
1
1
1
3
2
0
0
2
2
0
0
0
2
0
1
0
2
1
2
0
1
0
2
0
0
1
0
2
1
1
0
0
0
2
2
0
2
1
0
3
2
0
0
3
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
1
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
2
0
0
2
2
0
0
0
0
0
0
1
0
1
1
2
0
1
0
0
0
2
1
0
2
2
2
0
1
0
0
2
0
1
1
0
0
1
2
0
0
0
0
1
2
0
1
0
2
1
0
1
1
1
0
1
2
1
2
0
0
1
2
0
0
0
0
0
1
1
0
0
1
2
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
1
0
0
1
0
2
1
0
1
0
0
0
0
0
0
0
0
1
2
2
2
2
1
2
2
1
1
0
0
2
0
2
0
0
1
1
0
0
1
0
2
1
0
2
0
0
2
0
2
0
0
1
1
2
1
0
0
0
1
0
2
0
0
0
0
0
0
3
2
1
3
0
0
1
1
1
1
0
0
0
2
0
2
2
1
1
0
1
0
2
0
0
0
0
2
0
2
0
0
0
3
2
0
1
0
2
0
0
3
1
2
1
1
0
0
0
0
1
0
0
1
1
0
2
0
1
3
0
2
0
1
2
1
0
4
0
0
0
2
0
2
3
1
1
0
0
0
0
1
0
2
2
0
1
1
1
1
0
0
0
2
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
2
1
1
2
0
2
1
2
3
2
2
0
2
0
2
1
0
1
1
1
0
0
1
2
0
0
0
0
2
0
3
0
0
2
0
0
0
2
0
0
1
2
0
2
0
1
2
2
0
0
2
1
1
2
0
2
0
1
0
1
0
2
2
2
2
0
1
0
0
0
1
1
2
1
0
0
1
0
0
0
2
2
1
0
0
0
1
2
1
0
2
1
1
1
0
2
1
1
0
0
0
0
0
1
0
0
0
2
2
2
1
2
0
0
0
0
2
2
0
0
2
2
0
0
0
0
1
2
2
0
1
1
3
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
2
2
1
0
0
1
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
1
1
0
0
0
0
0
2
0
0
2
1
0
1
0
0
2
2
2
0
1
1
0
0
0
2
1
4
1
1
0
0
0
1
0
0
9
0
1
0
2
0
0
0
2
0
0
0
1
1
0
2
0
1
2
0
0
0
0
1
2
0
0
0
1
0
0
0
1
1
4
1
0
0
0
1
2
0
1
0
2
0
0
1
0
0
3
0
0
0
0
2
1
1
1
0
0
0
2
1
2
1
2
0
0
0
1
1
0
0
0
1
1
0
0
0
2
2
0
0
0
1
0
0
0
0
0
1
2
2
0
0
2
0
1
0
0
0
2
1
0
0
0
1
1
1
0
0
0
0
1
0
0
0
1
1
2
2
0
0
0
2
2
1
0
0
2
0
2
2
1
0
0
0
3
0
1
1
1
0
0
2
0
2
2
0
2
1
1
0
1
1
1
0
0
0
1
1
0
1
0
1
2
1
0
1
0
0
1
1
0
0
1
1
2
2
1
0
0
1
1
0
0
0
3
0
0
0
1
0
2
0
0
0
0
1
1
2
0
0
0
4
1
1
0
2
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
2
2
0
0
1
0
0
0
3
1
0
0
0
2
3
0
2
0
1
0
2
0
0
2
1
0
0
2
1
2
2
0
1
0
2
0
0
2
2
2
0
3
0
0
0
0
3
1
0
0
0
1
2
1
0
0
0
1
0
1
1
0
0
2
0
0
1
0
0
2
2
1
2
1
1
3
0
0
0
2
0
1
0
1
1
0
1
0
2
1
0
2
3
0
0
0
0
0
0
1
0
2
2
2
1
0
0
0
0
0
0
1
0
0
2
0
0
1
0
2
1
0
0
1
1
0
1
0
1
0
0
1
0
0
0
2
3
0
2
0
0
1
1
0
0
3
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
2
1
1
0
2
2
0
0
1
0
2
0
0
2
0
0
2
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
2
2
1
0
1
2
1
1
0
1
0
0
0
0
0
1
0
1
2
2
0
0
1
0
1
0
0
2
0
0
1
0
1
0
1
0
0
1
1
0
2
1
0
0
0
0
1
0
0
0
2
1
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
1
0
1
0
3
0
1
1
3
0
0
0
5
2
1
2
1
0
2
0
0
0
2
1
2
1
0
2
0
0
0
2
1
0
0
2
0
0
1
0
0
2
0
0
1
1
2
0
1
0
1
0
0
0
0
1
1
1
0
0
3
0
0
0
2
0
1
1
0
0
0
0
2
1
0
2
1
1
1
0
0
0
0
0
0
2
2
0
0
1
1
0
0
3
0
0
0
0
0
0
3
0
0
0
1
0
1
0
0
2
1
0
0
0
2
2
0
2
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
4
0
0
2
0
1
0
2
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
1
2
0
0
1
2
0
0
0
0
1
3
1
1
1
2
1
0
1
0
0
1
0
0
1
0
0
2
1
0
0
1
0
1
0
1
0
0
1
2
2
0
0
0
0
0
0
2
0
0
0
1
1
1
3
0
0
1
5
0
2
2
2
0
0
1
1
2
2
0
0
2
0
0
1
1
0
1
0
0
0
0
2
0
2
2
2
2
0
1
2
0
0
0
2
1
1
2
1
0
0
1
2
0
1
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
2
0
1
2
0
0
1
1
0
0
1
1
2
0
0
2
0
2
1
1
2
0
0
2
1
1
2
1
0
3
1
0
0
0
1
0
2
0
1
1
1
2
2
0
1
0
0
0
2
0
0
2
2
0
2
0
0
0
1
0
2
0
0
1
1
1
1
1
0
0
2
4
3
2
1
1
2
0
0
0
3
3
0
0
0
2
0
2
0
1
1
0
0
2
2
0
2
1
1
2
1
1
1
1
0
1
2
0
0
0
0
1
0
0
1
0
0
0
2
0
1
0
1
0
0
0
0
1
0
0
1
2
0
2
1
1
2
0
0
1
2
2
0
1
0
1
1
2
0
0
0
2
0
0
3
1
1
1
3
0
0
0
1
2
0
2
0
0
0
0
2
2
0
1
0
2
0
1
1
1
0
1
0
4
0
0
0
1
1
2
1
1
2
2
1
2
0
2
0
0
2
0
2
0
0
0
1
0
1
0
0
2
1
0
0
0
0
0
0
1
0
1
0
0
1
0
2
1
1
1
1
1
1
2
0
1
0
0
0
0
0
0
1
1
0
0
0
3
0
2
2
0
2
1
1
0
1
0
0
0
2
0
0
0
0
1
1
1
0
0
0
0
0
1
2
0
1
0
0
1
0
0
1
3
0
0
0
1
1
0
0
0
5
0
1
0
0
0
2
2
0
2
0
1
2
1
1
0
0
3
1
0
0
2
0
0
0
2
1
1
0
0
0
0
0
0
1
1
1
1
2
0
1
0
0
2
0
0
0
2
5
0
0
2
1
0
2
0
2
0
1
1
1
0
0
0
1
0
0
1
1
2
2
0
2
1
0
1
2
2
0
4
0
0
0
1
1
2
1
2
1
1
1
0
1
1
0
1
1
1
0
2
0
0
1
2
0
1
1
1
0
0
0
0
1
0
2
4
0
0
3
2
2
0
1
0
0
0
0
0
0
0
1
0
0
3
1
2
1
2
0
0
0
0
0
0
0
0
2
0
1
1
1
0
1
0
1
0
2
0
0
1
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
2
0
0
1
0
1
2
0
1
0
2
0
1
1
0
0
2
2
0
1
0
1
0
0
1
0
0
0
2
0
0
1
2
2
0
0
0
3
0
0
0
0
1
1
0
0
2
0
1
0
1
0
2
0
0
0
0
0
1
0
1
2
0
0
0
1
1
0
0
2
0
1
0
0
0
0
1
3
0
0
1
1
1
2
1
0
0
0
0
0
0
1
0
0
1
1
0
1
0
1
2
0
1
0
0
0
2
2
1
0
0
0
0
0
0
2
0
1
0
1
2
0
2
0
0
0
1
0
0
1
1
0
1
0
0
2
2
0
1
1
0
0
2
1
2
2
1
0
0
0
0
0
2
0
0
1
0
0
1
1
1
1
0
3
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
4
0
0
0
0
1
0
0
2
0
0
0
1
1
0
2
0
1
0
2
1
0
2
0
2
0
2
2
0
0
0
2
0
0
2
2
1
0
2
0
0
2
1
0
1
0
0
1
2
2
0
1
2
0
2
1
0
2
0
0
1
2
1
2
0
1
0
0
1
1
1
1
0
2
0
2
0
0
0
0
0
0
0
3
0
1
0
0
0
0
2
0
2
2
0
0
1
0
2
0
2
0
0
2
1
0
1
3
0
0
0
0
1
2
1
3
0
0
2
0
1
0
2
0
0
1
2
0
0
0
2
2
0
1
0
1
2
0
1
0
0
0
2
0
2
1
2
0
0
1
2
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
2
2
2
0
2
2
0
0
1
0
1
1
1
1
0
1
0
0
2
1
0
1
0
1
0
3
0
0
1
0
0
2
3
2
1
1
0
0
2
0
0
0
0
0
1
0
0
1
1
1
0
2
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
1
1
0
1
0
1
0
1
0
0
1
0
2
1
0
0
0
0
1
2
0
0
0
0
0
1
0
0
2
0
0
0
0
3
1
0
0
1
0
2
1
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
1
1
0
2
0
1
0
2
5
1
0
0
0
0
1
0
1
2
1
0
0
0
0
1
0
1
0
1
0
2
2
2
0
0
2
2
1
0
2
1
0
0
0
0
1
0
0
1
2
1
0
0
0
0
0
2
1
0
2
1
0
2
0
2
0
0
1
2
2
1
2
1
1
0
0
0
0
0
1
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
2
2
1
2
0
2
1
0
1
2
1
1
0
0
2
1
2
1
4
0
0
3
0
0
0
0
1
0
0
0
0
1
3
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
1
1
0
1
0
1
1
1
0
2
2
0
0
2
0
0
0
0
2
0
0
0
2
2
1
1
0
0
0
2
1
2
0
2
2
0
0
2
1
1
0
1
0
0
2
1
0
3
0
2
1
0
2
2
2
0
2
0
1
0
0
0
0
0
0
1
0
0
2
0
1
1
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
3
0
0
0
0
0
1
0
0
1
1
2
0
0
1
1
3
0
1
2
2
0
1
1
0
4
3
0
0
2
0
0
2
2
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
1
2
0
2
0
2
1
1
1
1
1
1
0
1
0
0
2
0
0
2
0
0
1
0
0
1
0
1
2
0
1
1
0
1
0
1
0
0
0
1
2
0
1
1
2
0
0
1
0
0
0
0
0
3
0
0
0
0
0
2
1
0
0
0
1
0
0
2
0
1
0
0
0
0
0
9
0
1
0
1
0
2
2
2
0
0
1
1
0
1
0
2
2
1
1
1
3
0
1
0
1
1
2
0
2
1
1
0
1
1
1
2
0
0
2
0
1
0
0
1
1
0
0
2
0
2
1
1
1
0
1
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
1
0
3
0
0
0
2
2
2
0
1
0
0
2
0
0
1
0
2
0
2
0
0
0
1
1
0
0
1
2
2
0
0
0
0
1
1
0
3
1
2
0
1
0
0
0
2
1
0
0
0
0
1
2
0
0
0
1
2
0
1
2
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
1
1
2
2
2
0
1
0
1
1
0
2
0
2
1
2
2
2
0
0
2
0
0
1
1
1
2
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
1
2
0
0
1
0
0
2
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
2
1
1
1
2
1
0
0
0
1
2
0
2
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
2
0
0
1
2
1
2
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
2
0
0
0
2
0
1
1
0
1
0
1
1
1
0
2
1
2
0
0
0
0
1
0
0
1
2
0
1
0
2
0
0
1
1
1
0
0
0
2
0
2
0
1
0
0
0
1
1
1
0
0
1
0
0
1
0
2
0
2
1
2
0
1
0
1
0
1
2
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
2
2
0
1
2
0
0
0
0
0
2
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
2
0
0
1
0
0
1
0
1
0
2
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
1
0
1
1
0
0
1
0
0
0
1
2
0
0
1
1
2
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
1
1
2
2
1
0
2
0
0
0
4
1
0
0
1
2
2
0
0
1
2
0
0
1
0
0
0
0
0
0
2
1
0
2
1
0
0
0
2
2
0
0
0
1
0
2
2
2
1
0
0
1
1
0
0
1
2
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
1
0
1
0
2
0
2
1
0
0
0
2
0
0
0
1
0
0
0
1
0
2
0
1
0
0
0
1
2
1
1
0
1
0
2
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
2
1
0
1
0
0
0
0
0
2
1
1
0
0
2
1
0
2
0
0
0
0
2
0
1
2
0
2
0
1
0
0
1
0
1
0
2
1
1
0
0
0
2
1
0
0
1
2
2
0
0
1
2
0
0
2
0
0
2
1
0
0
0
1
0
2
0
0
0
0
2
1
0
1
0
0
1
2
2
0
0
0
0
2
1
0
1
0
1
0
0
1
2
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
2
1
0
0
2
0
0
0
0
2
0
0
1
2
2
0
0
2
1
1
3
0
0
2
2
0
0
1
1
2
0
2
2
0
0
0
2
1
0
0
1
0
0
1
0
2
2
0
4
0
1
0
2
0
0
2
0
0
2
1
0
0
0
1
0
0
0
0
1
3
0
1
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
1
0
1
1
0
1
0
0
4
0
1
2
1
0
2
0
0
0
0
0
1
0
0
0
1
2
0
0
1
0
0
2
2
0
1
0
0
2
0
1
1
0
2
2
0
2
1
0
0
0
0
0
1
0
2
1
0
2
1
2
1
3
0
0
0
0
0
0
1
1
2
0
1
0
0
0
1
1
0
2
0
0
0
1
1
1
2
0
2
0
1
2
2
0
0
0
0
1
2
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
1
2
1
0
1
0
2
0
0
0
2
0
0
0
0
1
2
0
0
1
2
0
0
5
1
1
0
0
0
2
0
0
1
0
2
1
0
0
0
2
1
2
0
0
0
1
0
2
0
0
0
0
0
0
3
2
1
2
2
2
0
2
1
0
0
0
0
0
1
0
0
1
1
2
2
0
0
0
2
0
0
2
1
2
0
1
0
0
1
1
0
1
0
0
1
0
0
0
2
0
0
1
0
1
2
1
2
0
0
0
2
0
0
0
0
4
0
0
2
0
1
2
0
0
1
0
0
0
2
1
0
0
1
3
0
2
0
0
0
2
0
0
0
0
1
2
2
0
0
2
2
1
1
2
0
0
3
1
0
1
2
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
2
0
0
0
1
0
1
0
1
0
0
3
1
2
3
1
1
0
1
0
2
0
2
3
1
0
0
0
0
2
1
0
0
0
2
0
2
0
2
0
2
1
1
2
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
1
0
1
0
0
0
0
0
2
1
0
0
1
0
0
2
6
2
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
1
1
0
3
0
0
2
1
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
2
0
0
0
0
2
0
0
0
2
2
0
0
2
0
1
2
0
2
0
0
0
0
2
2
0
2
3
1
1
0
1
0
0
2
0
0
1
1
0
0
1
2
2
0
1
2
2
2
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
4
1
1
0
0
0
0
0
0
0
1
0
2
2
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
2
1
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
3
0
2
0
0
0
1
1
1
2
0
2
0
0
1
0
2
2
2
0
1
1
0
0
0
1
0
0
0
0
0
4
4
0
1
2
0
0
0
1
0
0
1
2
1
2
1
0
1
0
0
1
1
0
1
0
0
1
2
1
0
2
1
0
2
1
0
0
0
2
0
1
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
2
0
1
2
1
3
0
1
2
2
1
0
3
0
2
2
1
1
0
1
2
0
0
1
0
0
0
2
0
1
2
2
2
0
0
0
0
1
0
1
2
1
2
0
0
0
0
0
0
0
1
1
2
0
1
0
1
0
0
0
1
0
0
0
1
0
0
1
1
0
1
0
1
1
0
0
1
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
1
2
2
0
1
2
1
0
1
2
2
0
3
1
1
3
1
0
1
0
2
0
3
0
1
0
1
1
0
0
0
0
0
1
0
1
0
0
0
1
3
0
0
2
0
0
1
2
0
0
0
0
2
0
0
0
0
1
0
3
0
1
0
2
0
1
0
0
0
2
1
1
0
0
1
0
2
0
2
0
0
2
0
0
1
0
0
3
0
0
0
1
2
0
5
0
0
2
0
0
1
2
0
2
0
1
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
1
0
2
0
3
0
1
0
1
0
1
2
1
1
0
2
0
1
0
1
1
0
0
0
0
0
1
1
1
0
0
0
0
0
2
2
0
2
1
0
0
1
3
0
0
2
0
2
2
0
2
1
0
0
2
0
2
0
0
0
0
0
2
3
1
0
0
1
0
0
0
0
0
3
2
2
0
0
0
0
0
2
0
0
0
1
2
0
0
2
0
0
1
0
2
0
2
0
2
0
0
0
0
0
0
1
0
1
1
2
1
0
0
0
0
2
1
0
1
0
0
2
0
0
2
0
0
1
1
1
1
1
0
4
2
2
1
0
1
0
1
0
1
0
1
2
0
0
2
0
1
0
2
0
2
0
0
0
0
0
0
2
1
0
1
1
2
2
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
2
2
0
2
1
0
2
1
1
0
0
0
2
3
0
0
0
1
1
1
0
2
0
0
0
0
1
2
2
2
2
0
0
0
1
2
0
1
0
0
2
2
0
1
0
1
0
0
1
2
2
0
0
0
0
1
1
2
2
0
1
2
0
2
0
0
2
0
1
2
2
0
0
0
0
0
0
0
2
0
0
2
1
0
1
0
0
0
1
0
1
1
2
2
0
0
0
0
4
2
1
0
0
2
1
0
2
0
1
0
1
3
0
0
1
0
2
1
0
0
2
0
0
1
0
2
0
0
2
1
0
2
2
1
1
2
1
0
1
0
1
2
0
2
0
0
0
0
1
0
2
2
0
0
0
0
2
2
1
0
2
1
0
0
0
0
0
0
2
1
0
0
0
2
0
2
1
0
0
0
0
0
2
1
0
0
2
2
0
0
0
0
2
1
0
0
0
0
2
1
1
2
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
3
2
2
1
2
1
1
1
2
0
0
0
0
0
0
0
1
1
1
0
1
1
0
0
1
3
2
1
0
2
0
0
0
1
0
3
0
1
0
1
0
0
0
0
0
0
4
0
0
2
1
2
0
0
0
0
2
1
0
0
2
2
0
0
0
0
0
0
1
0
0
1
2
1
2
3
2
0
0
1
1
2
0
0
1
3
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
2
2
3
2
0
0
0
1
0
0
0
2
1
0
0
1
0
1
0
0
1
1
0
2
1
0
3
0
0
2
2
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
2
2
0
0
2
1
0
1
2
0
0
1
2
0
1
0
0
0
0
1
0
0
0
1
1
1
1
1
1
1
2
1
1
0
1
2
0
1
0
0
0
1
2
0
0
3
2
0
0
0
0
2
0
1
1
0
2
1
0
0
0
2
1
0
6
0
0
1
0
1
0
0
0
2
3
1
0
2
1
0
0
2
0
0
0
0
1
1
0
0
0
0
2
1
1
0
1
0
1
0
0
1
2
2
1
1
0
0
1
1
0
1
1
1
2
2
0
0
0
0
1
2
1
1
0
2
0
3
1
1
0
0
1
3
0
1
0
0
0
2
0
2
0
0
0
0
1
0
1
0
2
1
0
0
0
1
1
2
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
1
1
1
0
2
0
2
0
1
1
1
0
0
2
2
0
0
0
0
2
1
0
1
0
0
1
0
1
2
0
1
1
0
0
3
0
2
2
2
2
0
2
1
0
0
0
0
1
1
0
1
1
0
2
0
1
2
0
1
2
0
0
0
0
1
0
2
0
0
2
1
0
0
0
0
2
0
2
2
0
2
1
0
2
1
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
1
3
0
0
0
2
0
2
1
2
1
0
2
1
0
0
1
2
0
1
2
0
1
2
0
0
1
1
1
1
1
0
1
0
0
0
3
0
6
0
0
0
1
0
1
0
1
1
1
0
1
1
0
0
1
2
2
1
0
0
1
2
1
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
1
1
1
1
0
1
2
0
0
2
0
0
1
0
1
1
0
0
0
0
0
0
2
2
0
0
2
1
2
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
1
0
2
1
0
2
0
4
2
1
0
0
2
1
0
0
0
1
0
0
2
2
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
2
4
0
1
1
0
2
2
3
1
0
0
0
0
0
1
1
0
1
2
0
0
0
2
0
0
2
1
3
2
0
1
0
0
0
0
0
1
0
0
1
0
1
0
2
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
1
1
2
1
2
1
0
1
2
0
1
1
0
0
0
0
0
0
0
0
1
0
1
1
2
0
0
0
2
1
1
0
1
0
0
0
3
0
0
0
0
0
2
2
0
0
2
1
2
1
1
0
0
0
1
0
2
1
0
0
0
0
1
1
0
2
0
0
1
2
1
1
0
2
0
0
0
2
1
1
0
0
2
1
1
2
0
1
0
0
2
0
1
0
0
2
2
1
0
0
0
0
0
0
0
1
0
0
1
2
2
0
0
1
0
0
0
0
2
0
0
0
1
2
0
0
2
0
2
2
0
2
1
2
2
0
0
0
1
0
3
2
0
0
1
1
1
1
2
0
2
1
1
0
0
0
0
0
1
0
2
0
1
0
2
0
0
2
0
2
0
0
0
2
0
2
0
0
3
0
1
0
0
0
4
0
0
1
2
0
0
0
1
0
4
0
1
0
2
0
1
0
1
0
0
1
1
0
0
2
0
0
0
3
0
0
0
2
1
2
0
0
0
2
0
1
1
0
0
2
1
0
1
0
0
0
1
0
3
1
2
0
1
0
0
2
0
0
0
1
1
0
2
1
0
2
2
0
0
0
0
0
2
0
1
1
1
0
0
0
2
1
0
1
1
1
0
3
1
0
2
0
1
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
2
0
0
0
2
0
0
0
2
2
1
0
1
0
0
1
2
0
2
0
0
0
1
0
0
0
1
0
1
0
0
2
2
0
1
1
2
2
1
2
0
2
2
2
0
0
0
1
0
2
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
1
1
1
0
0
1
2
1
0
0
0
0
0
2
0
0
0
0
2
1
0
2
0
0
2
0
2
2
0
0
1
0
2
0
1
1
0
1
0
0
0
0
2
0
0
0
0
2
1
2
0
2
0
0
1
2
1
1
1
0
0
2
0
2
0
0
0
2
1
2
0
1
0
0
1
1
2
1
0
0
0
0
0
2
0
1
2
0
0
0
1
0
1
0
2
0
0
0
0
1
0
1
0
1
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
2
0
0
2
1
1
2
0
2
0
0
0
0
0
0
0
0
0
2
1
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
2
0
0
2
0
1
0
2
2
2
0
0
0
1
0
0
0
0
2
0
0
1
2
0
0
0
2
1
1
0
0
1
1
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
2
1
0
1
1
0
0
1
0
1
0
0
0
0
0
2
2
1
1
0
0
1
1
0
1
0
1
1
1
1
0
1
0
1
2
1
0
0
1
0
0
0
1
2
0
2
0
0
0
0
1
0
0
0
0
2
1
2
0
0
0
0
1
0
2
2
2
0
0
0
1
0
0
1
0
0
0
0
0
4
2
1
1
1
2
2
1
0
1
0
0
0
2
1
1
0
0
0
0
2
0
0
0
2
1
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
2
1
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
1
0
0
0
0
0
1
0
2
1
0
2
0
0
1
0
0
0
1
1
0
0
0
1
0
0
2
2
1
0
0
0
1
1
0
0
1
2
0
0
0
1
0
0
0
0
0
1
1
0
3
1
2
0
0
0
0
3
0
0
2
2
0
2
1
2
0
2
0
0
0
0
2
2
1
0
1
0
2
1
0
2
0
1
2
1
0
0
1
2
0
1
0
0
0
0
0
0
2
0
1
2
3
0
0
0
1
0
1
2
1
0
0
0
2
1
0
2
1
6
0
1
0
2
0
0
0
1
2
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
2
0
1
1
1
1
0
2
0
0
1
2
2
0
0
2
2
1
1
0
0
0
0
0
0
2
0
1
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
2
0
1
0
2
0
0
2
0
0
3
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
4
1
0
2
0
0
0
1
0
1
0
0
1
0
1
0
1
0
0
0
1
2
0
0
0
1
0
0
0
0
2
0
2
1
2
2
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
2
2
0
0
0
1
1
2
0
2
0
0
0
0
2
0
2
2
0
0
2
0
0
0
0
3
0
0
0
0
0
1
0
2
0
1
0
2
0
0
0
2
1
0
0
0
1
1
0
1
0
2
0
0
2
3
2
0
0
2
1
0
0
1
0
1
0
2
2
0
2
1
0
3
1
0
0
2
1
1
0
0
0
2
2
0
2
0
1
1
1
0
2
1
2
0
1
1
2
0
2
0
0
0
0
0
0
0
0
2
2
2
2
0
0
1
1
0
2
0
1
2
2
0
0
0
0
2
0
0
1
3
2
1
0
2
0
0
0
0
1
0
0
1
1
2
0
0
2
0
2
0
0
0
2
0
0
1
1
2
1
0
1
0
0
0
1
1
2
1
0
0
0
0
0
2
0
0
0
0
3
0
0
1
1
2
1
2
2
1
0
0
0
0
1
1
1
1
0
0
2
2
0
0
0
2
0
1
0
0
2
0
0
1
1
1
0
2
0
1
0
0
0
0
0
0
1
1
1
2
2
0
0
0
1
1
2
0
1
0
0
2
3
1
0
0
0
2
1
0
1
1
1
0
2
0
0
2
1
2
0
0
0
1
5
0
2
1
2
0
1
0
1
0
0
0
0
0
1
1
0
2
1
0
1
1
0
0
0
1
0
1
1
0
0
0
0
2
0
2
0
2
0
0
0
2
2
0
1
0
0
0
1
0
1
0
0
1
1
0
0
0
1
1
0
0
0
1
1
2
1
1
0
2
0
0
1
0
1
1
0
2
0
0
1
0
0
0
2
0
2
0
1
2
0
0
0
0
2
1
2
0
1
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
4
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
3
0
2
0
1
0
1
0
2
0
0
1
1
1
0
0
1
0
0
2
0
2
1
0
0
2
0
2
0
2
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
1
2
1
0
1
0
0
0
0
0
0
0
3
1
1
2
2
0
2
0
1
0
0
0
0
2
2
0
0
0
0
1
0
0
2
1
0
2
2
1
2
0
1
1
0
0
1
0
0
1
1
0
1
1
1
0
0
3
0
1
1
0
0
1
4
0
2
0
0
1
2
0
0
2
0
1
2
0
2
0
2
1
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
1
1
2
0
1
0
0
0
2
1
0
0
1
2
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
1
1
1
1
0
2
1
0
0
2
2
0
1
2
0
2
2
2
0
0
1
1
2
1
0
2
0
0
2
1
2
0
2
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
1
0
0
0
2
3
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
1
0
2
0
0
2
0
1
0
3
2
0
0
2
0
1
0
2
0
0
1
0
0
2
0
0
0
0
3
0
0
0
0
2
1
1
1
0
0
0
1
0
1
0
0
1
2
3
0
0
0
1
2
0
2
1
0
1
0
0
0
1
0
0
2
0
0
1
0
2
2
2
0
1
0
0
2
0
0
0
0
0
3
2
0
0
0
3
0
0
0
0
0
2
1
1
4
1
1
0
0
1
0
0
2
1
0
2
1
0
2
0
0
2
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
1
0
0
0
2
0
0
0
1
0
3
0
0
0
0
0
1
0
1
0
2
0
0
2
3
0
0
0
1
1
1
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
1
1
1
0
0
1
0
0
0
0
1
2
0
0
0
0
1
0
0
0
1
0
2
0
0
0
1
0
0
1
2
0
2
2
2
0
0
1
0
1
0
0
0
1
0
1
0
0
1
1
2
0
0
0
1
1
0
2
0
0
2
0
2
1
1
1
1
0
0
0
2
1
0
2
0
1
0
3
0
0
0
2
0
0
1
1
0
2
1
1
1
2
2
0
0
0
0
0
0
0
1
2
0
0
0
1
2
0
1
0
0
1
1
2
0
2
1
0
0
0
2
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
1
0
0
1
2
2
1
2
0
0
1
0
0
0
1
0
1
0
1
2
0
0
0
0
0
0
0
2
0
0
0
2
1
1
1
0
0
1
2
0
0
2
1
2
2
0
1
2
1
0
0
0
1
0
4
0
0
0
0
0
0
0
1
0
2
1
2
0
1
0
0
0
2
0
3
0
1
0
1
0
2
2
0
0
1
1
0
0
0
1
1
0
2
0
1
0
2
2
1
0
0
8
0
1
0
0
0
0
0
2
1
0
0
0
3
2
1
0
2
0
0
0
1
0
0
0
0
0
1
0
1
0
0
2
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
1
0
0
1
0
2
0
0
2
0
0
1
0
0
1
0
1
0
1
1
1
1
1
1
0
1
0
0
0
0
0
0
2
2
2
0
2
1
0
0
0
0
1
2
0
0
1
1
0
0
1
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
2
0
0
2
0
0
0
0
2
2
1
0
2
2
0
1
0
2
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
2
0
2
0
2
1
0
0
0
0
2
2
2
0
0
0
0
2
1
0
0
3
0
1
1
2
1
0
0
2
2
1
0
0
0
0
1
0
2
1
1
0
0
0
1
1
0
0
1
0
0
0
1
2
1
0
1
0
2
0
0
1
0
0
2
0
0
0
0
2
0
0
0
2
2
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
1
2
0
0
2
1
1
1
0
1
1
1
0
1
0
1
2
1
0
0
0
3
0
1
1
0
0
1
0
2
0
0
1
1
2
2
1
1
0
0
0
1
2
0
1
2
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
2
2
0
1
0
1
0
0
0
0
1
0
2
2
0
1
0
2
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
2
1
0
1
2
1
0
0
0
1
0
0
0
1
0
1
1
0
0
1
0
2
0
0
0
3
0
2
0
1
0
0
0
2
0
1
0
1
0
0
0
0
1
0
1
0
0
1
2
1
1
0
0
2
1
0
0
0
1
0
0
0
0
2
0
0
1
1
0
1
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
1
2
0
1
1
0
0
0
0
0
2
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
2
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
7
0
0
0
0
0
0
3
0
2
1
1
1
0
0
0
0
0
0
1
0
2
0
0
1
2
0
1
1
1
0
2
0
2
1
0
0
0
1
2
2
0
0
1
0
0
0
2
0
0
3
0
0
1
0
0
0
0
1
1
2
1
0
0
0
0
2
1
0
2
0
0
0
0
0
0
2
0
2
0
2
0
0
1
1
0
0
1
0
0
2
1
1
0
0
2
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
1
1
0
0
1
0
1
2
5
1
2
0
0
0
0
0
0
1
2
0
0
0
1
0
1
0
0
2
0
0
1
0
0
0
1
1
0
1
0
0
1
0
1
0
0
2
2
0
0
1
1
0
0
1
0
1
0
1
1
0
0
0
1
0
2
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
3
0
2
0
0
3
0
0
0
0
3
0
0
1
0
0
0
0
1
0
7
1
1
0
0
0
1
0
1
0
2
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
1
1
0
2
0
0
0
2
0
2
1
0
2
0
0
1
1
0
0
2
1
0
1
0
2
0
4
0
1
0
0
1
0
0
0
1
0
0
2
2
2
2
1
2
2
1
0
1
2
1
2
0
0
0
2
0
0
1
2
0
2
2
0
0
2
0
0
2
0
2
2
1
0
2
0
2
0
0
1
0
0
0
0
1
3
0
1
0
1
0
0
0
2
0
0
0
0
1
1
0
2
1
2
0
0
2
0
1
0
0
1
1
2
0
1
0
0
0
0
2
0
0
2
3
0
0
0
1
0
0
0
1
0
0
1
1
1
1
1
1
1
0
0
0
0
0
2
1
2
2
0
2
1
1
0
0
0
0
7
2
2
1
0
0
1
2
0
2
1
1
0
0
2
1
0
1
0
2
0
1
1
2
0
0
0
0
1
0
1
0
0
0
2
0
0
2
0
0
0
1
1
0
2
2
1
0
0
2
2
0
2
0
1
2
0
0
0
1
0
2
0
0
0
1
1
0
0
2
2
0
2
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
2
0
0
2
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
1
1
0
0
2
2
0
0
1
1
1
0
0
0
0
1
2
2
0
1
2
2
0
1
0
1
1
1
2
0
0
2
2
1
4
1
1
1
0
0
2
1
2
0
2
1
0
1
2
0
0
1
2
2
2
2
0
1
0
1
0
0
0
0
1
1
0
0
0
1
0
1
0
0
1
1
2
1
0
0
0
0
0
1
0
2
0
0
2
2
2
0
0
0
0
0
0
1
0
2
2
1
0
0
1
1
2
1
0
2
0
1
0
0
2
0
0
0
0
2
1
0
1
1
2
0
2
1
2
0
0
0
0
2
1
2
0
0
2
0
2
1
1
1
0
0
0
1
0
0
1
0
2
1
1
0
1
2
2
0
0
1
0
2
0
0
0
1
1
0
1
0
1
2
0
0
2
1
0
1
2
1
1
2
0
4
0
0
2
0
2
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
2
1
0
1
2
2
2
2
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
1
0
1
1
0
2
0
0
2
0
1
0
0
2
0
2
2
0
0
1
0
2
1
0
0
0
0
0
1
0
0
2
0
1
1
0
0
0
0
0
2
2
1
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
2
2
0
0
1
0
0
2
1
1
1
2
0
1
0
1
1
0
1
0
0
0
0
0
2
0
0
1
0
0
0
1
0
2
1
1
0
1
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
2
1
0
0
0
0
1
0
2
0
0
0
0
0
2
2
0
2
1
2
1
1
0
0
1
1
2
1
1
0
0
2
0
0
5
0
1
2
0
2
0
1
2
2
4
2
0
0
0
0
0
0
1
1
0
2
0
0
2
1
0
0
7
0
0
0
1
1
0
0
0
0
0
1
0
0
1
2
0
0
0
3
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
2
2
0
0
0
1
0
2
0
0
1
0
0
0
1
0
1
1
0
0
0
2
0
0
0
2
1
2
0
0
1
1
0
0
0
2
0
1
1
0
2
0
0
0
0
2
0
0
0
0
3
0
0
1
1
0
0
0
1
0
2
0
0
1
0
0
3
0
0
2
2
0
1
0
0
0
1
0
0
1
0
1
1
1
0
0
0
0
0
1
1
0
2
1
0
0
0
2
0
2
0
0
2
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
2
2
1
2
0
2
0
0
0
0
2
2
0
1
2
0
0
0
1
1
0
0
0
0
0
0
0
3
0
0
1
0
0
1
1
0
0
1
0
1
0
0
0
1
0
1
0
0
2
0
2
2
0
0
2
2
2
2
2
0
2
0
0
1
2
2
0
1
0
1
0
0
0
0
2
0
0
0
0
0
1
1
2
0
0
0
1
2
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
2
1
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
1
1
2
0
1
0
2
0
0
0
0
1
1
0
0
0
2
0
1
1
0
2
1
1
0
1
1
0
0
0
0
0
1
1
2
2
0
0
1
0
0
1
0
1
0
1
2
0
0
0
2
0
0
0
1
1
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
2
0
2
1
0
1
2
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
1
0
0
1
2
3
0
1
0
1
3
2
0
0
0
0
1
1
0
0
2
1
1
1
0
0
1
0
2
0
3
0
2
3
1
3
2
0
0
0
1
0
0
0
0
0
0
0
3
1
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
2
0
0
0
0
2
0
0
0
1
1
0
2
0
0
1
2
0
0
1
0
0
0
2
0
2
0
0
0
3
0
0
0
1
0
0
0
0
1
2
0
1
0
0
0
0
2
1
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
1
0
0
2
0
1
1
1
0
0
2
1
2
0
0
0
0
3
2
0
0
1
0
0
0
2
0
0
2
0
0
2
2
0
2
1
2
0
0
1
1
0
1
1
0
0
1
2
2
1
2
1
2
1
0
1
2
1
2
2
0
1
0
1
0
1
0
0
0
1
2
0
2
2
0
0
2
0
2
1
0
2
0
1
1
1
1
0
0
1
0
1
0
3
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
1
1
1
1
0
0
0
1
0
0
1
0
0
0
2
0
2
2
0
1
0
2
0
0
2
0
1
0
1
0
0
1
0
2
0
2
0
0
2
0
0
0
0
1
1
1
2
2
0
2
1
1
0
2
2
0
0
1
1
2
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
1
2
2
2
0
0
1
0
0
2
1
0
0
2
1
0
0
0
2
0
1
0
0
1
0
2
0
1
1
0
0
0
0
0
0
0
0
2
0
0
2
0
1
2
2
1
0
0
2
0
2
0
1
2
0
2
0
1
0
0
0
2
12
2
1
0
0
1
2
0
2
1
2
0
0
2
5
1
2
0
0
2
0
0
2
2
1
2
0
0
0
2
2
0
0
1
0
1
0
1
0
0
1
0
0
2
1
1
0
0
0
0
0
0
1
1
1
0
1
0
0
1
1
1
1
2
1
1
0
0
0
1
1
2
1
0
0
0
1
0
0
2
1
0
2
1
0
0
0
0
1
2
0
0
0
0
0
2
0
0
7
0
2
0
0
0
1
0
0
2
0
2
1
2
0
1
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
3
1
0
0
1
0
1
2
1
0
2
1
0
0
2
0
2
0
0
0
1
1
0
2
1
1
0
2
2
1
1
3
2
0
2
0
0
2
2
0
2
0
0
0
0
1
0
0
1
0
0
3
0
2
0
0
0
0
0
1
0
2
2
0
0
1
0
0
2
2
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
2
0
1
0
1
0
1
0
0
2
1
1
2
2
2
0
0
0
0
2
0
0
0
0
1
2
1
2
0
0
0
0
0
0
3
0
0
0
0
1
0
1
1
1
0
0
0
0
1
2
2
0
0
0
0
0
0
1
1
0
0
0
0
1
1
1
1
0
2
1
1
2
0
0
0
2
1
0
0
2
0
2
2
0
2
0
0
0
0
0
2
2
1
1
1
2
1
1
0
3
1
3
2
1
2
0
1
2
2
0
2
1
2
0
2
0
3
2
0
0
1
0
1
0
0
2
1
0
2
2
2
0
0
1
0
0
1
0
0
0
2
2
0
1
1
0
0
0
1
0
0
0
0
0
2
0
1
2
0
0
0
0
0
1
0
2
2
2
0
0
1
0
2
0
1
0
0
0
0
1
1
1
0
0
2
0
0
1
0
0
0
0
0
2
1
1
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
1
1
0
1
0
1
1
3
0
1
2
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
2
1
2
1
1
2
0
0
0
0
0
0
1
3
0
0
1
2
2
1
0
2
2
2
1
5
2
1
0
1
1
1
1
2
0
2
2
0
0
0
0
1
2
0
0
2
0
2
1
1
0
1
0
2
2
1
2
0
0
10
1
0
0
0
0
2
2
1
1
2
0
0
0
2
0
1
2
2
0
2
1
1
0
0
1
0
0
2
2
4
0
1
0
0
0
2
0
2
2
0
0
0
1
0
0
1
0
0
0
1
1
0
2
0
2
0
2
0
0
0
0
1
0
1
0
3
0
1
4
1
0
0
2
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
2
0
2
0
0
1
1
0
2
0
0
0
0
1
0
0
1
0
1
0
0
1
0
1
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
1
2
2
0
0
1
0
0
0
1
1
1
1
0
0
1
0
2
2
2
1
0
2
1
0
1
2
0
1
0
0
2
1
2
1
1
0
2
1
1
0
0
2
0
2
0
1
1
0
0
0
2
1
0
0
1
0
2
0
1
2
0
0
0
1
0
1
0
0
1
1
0
0
0
1
0
2
0
0
0
1
2
0
0
0
1
0
5
2
1
0
0
0
0
0
1
2
0
2
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
1
1
1
0
2
0
0
2
0
1
1
2
1
2
2
0
0
0
0
0
2
1
1
2
0
0
0
2
2
0
2
1
0
1
0
0
2
2
0
0
3
0
0
2
0
2
0
1
0
1
0
2
0
2
1
1
0
0
1
1
0
0
1
0
1
1
2
0
2
0
0
2
1
0
0
0
2
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
1
2
0
0
1
2
1
0
0
1
1
1
1
0
1
1
2
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
1
0
0
0
2
0
0
2
1
0
2
1
0
1
1
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
2
2
1
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
2
0
1
0
0
0
1
1
3
2
1
2
0
1
1
1
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
2
2
0
0
0
2
1
0
0
2
1
0
0
0
0
1
0
2
2
2
0
1
0
0
0
0
0
0
2
1
1
1
1
0
1
0
0
0
1
0
1
1
0
2
0
0
1
0
2
0
2
0
2
0
1
0
0
0
4
0
3
0
0
0
2
0
1
0
2
1
2
0
0
0
0
0
0
2
0
0
0
1
1
0
1
0
0
0
0
2
2
0
1
0
2
0
0
0
2
0
0
2
1
2
0
0
1
2
0
0
2
0
0
0
2
2
0
2
1
0
2
0
2
1
0
0
0
0
0
2
2
1
3
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
1
1
1
0
1
0
1
0
0
0
0
0
1
2
0
2
1
0
1
1
2
2
1
0
2
0
2
1
1
2
0
0
0
0
2
0
0
1
0
0
2
0
2
2
0
2
1
0
0
0
0
0
1
4
0
0
0
2
2
1
0
0
0
2
2
1
1
0
0
0
0
0
1
0
0
2
2
0
0
0
2
2
0
6
1
1
0
1
2
1
0
2
0
1
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
2
0
1
1
0
0
0
1
0
1
0
2
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
1
1
2
2
0
0
0
2
1
0
0
0
2
0
2
1
2
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
1
2
1
0
1
0
1
0
0
2
0
1
1
0
0
3
2
0
2
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
2
0
1
1
1
0
0
2
1
0
0
0
0
2
2
0
2
2
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
3
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
2
0
0
0
2
1
0
0
0
1
2
0
3
2
0
0
1
2
0
1
2
2
0
0
2
0
1
0
1
2
1
0
0
0
2
1
1
1
1
0
1
1
0
2
1
0
0
0
0
1
0
2
0
0
0
0
0
0
2
1
2
0
0
1
1
2
0
2
1
0
2
0
0
3
2
2
0
0
0
2
2
1
0
0
0
0
2
2
1
0
0
0
0
2
2
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
4
1
2
0
0
0
1
0
0
1
0
0
1
0
0
3
0
0
1
0
0
0
1
2
2
2
1
0
0
4
0
2
0
0
0
0
2
1
3
2
2
2
0
1
2
0
0
1
2
0
1
0
1
0
1
2
2
0
0
0
1
0
0
0
1
1
0
2
2
1
1
0
2
0
1
0
1
1
0
0
0
0
0
0
2
2
0
1
3
0
0
2
0
1
0
0
0
1
2
0
0
0
1
2
0
0
1
0
0
2
1
2
2
1
0
1
0
2
2
1
2
0
0
2
0
1
3
1
0
0
0
1
1
2
1
1
0
0
1
0
1
0
0
1
1
0
0
1
1
0
1
0
0
0
2
2
1
0
2
0
2
0
0
0
0
2
0
2
2
0
1
0
1
1
0
2
0
1
1
0
0
0
2
1
0
0
2
0
0
0
1
1
1
0
1
2
2
0
0
0
0
2
1
0
2
0
0
0
1
0
0
2
1
0
1
0
1
2
0
0
1
0
2
2
1
1
2
2
1
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
1
2
0
2
0
0
2
0
0
2
0
1
2
0
2
0
0
0
0
0
0
2
4
0
0
1
0
0
2
1
2
1
1
0
2
1
2
1
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
1
2
3
0
2
0
0
1
0
0
1
0
0
0
0
0
2
0
1
0
1
0
2
0
0
0
0
2
0
0
2
0
0
0
2
1
0
1
2
0
0
0
0
2
1
0
0
0
0
1
0
1
0
0
0
0
1
1
2
2
0
2
1
0
1
0
0
2
0
3
0
2
1
2
0
0
3
0
0
2
1
1
1
1
2
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
1
2
0
2
3
0
0
1
2
1
1
2
0
1
1
0
0
2
1
2
2
0
1
2
0
0
0
2
0
2
1
0
0
0
0
0
2
0
1
1
2
1
0
1
0
1
2
2
0
2
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
2
1
0
0
2
0
2
2
0
0
0
1
0
2
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
1
0
1
0
0
0
2
0
0
2
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
2
1
0
0
2
1
0
0
0
1
0
1
0
0
1
0
0
1
1
0
2
0
0
0
2
0
0
0
1
1
0
0
1
0
2
2
3
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
1
1
0
2
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
2
0
1
1
0
0
2
0
0
0
0
1
0
1
0
0
1
0
0
1
2
0
1
2
2
0
2
0
1
0
0
0
1
0
0
0
1
0
0
0
0
3
2
0
1
0
0
1
0
1
2
2
0
0
0
1
0
0
1
0
0
2
1
0
0
0
0
0
0
0
2
0
0
2
3
2
2
1
2
1
0
0
0
1
2
0
2
0
1
0
0
0
1
1
0
2
2
2
1
1
0
0
2
0
2
0
1
0
2
0
2
0
2
0
3
0
0
1
3
0
1
0
0
0
2
2
0
1
0
2
0
0
0
4
0
2
2
1
0
0
1
1
2
1
0
2
0
0
1
1
1
0
0
1
0
0
1
2
3
0
2
1
0
0
1
1
2
0
0
2
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
1
1
2
0
0
0
2
3
0
0
2
1
0
1
1
0
0
0
0
0
1
1
0
2
0
2
0
2
1
0
1
2
0
0
1
2
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
1
0
2
1
3
0
0
2
0
2
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
1
0
2
0
0
2
0
1
0
0
2
0
0
0
1
1
2
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
1
2
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
2
0
0
0
1
0
2
0
0
1
0
0
1
0
0
0
2
2
1
1
0
1
1
0
0
0
0
1
1
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
1
0
0
0
1
2
0
0
0
1
0
1
2
0
1
0
0
1
1
1
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
2
2
1
0
0
1
2
2
1
1
0
0
0
2
0
2
0
1
1
0
0
0
2
1
0
0
1
0
0
1
0
0
0
0
1
2
1
0
0
0
1
0
0
0
1
1
1
0
3
1
0
0
1
1
0
0
0
0
1
1
0
2
0
0
2
0
2
0
1
0
0
1
0
2
0
0
1
0
0
4
0
1
0
2
0
2
1
0
0
0
2
0
0
0
2
1
2
2
1
1
1
0
0
2
2
0
0
0
1
0
0
1
0
0
0
0
0
2
0
1
0
1
0
0
2
2
0
0
0
1
2
0
0
1
0
1
0
2
0
0
0
2
2
1
2
0
1
1
0
1
0
1
0
0
0
2
2
0
0
0
0
1
0
2
1
0
1
0
1
0
0
0
0
0
0
2
0
1
0
2
0
2
1
0
0
1
0
0
0
0
2
0
1
0
1
1
2
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
1
1
0
2
1
1
1
6
0
1
1
0
2
2
0
0
2
1
0
0
1
1
2
0
1
1
0
1
0
0
0
0
2
1
0
3
0
0
1
0
0
1
1
0
1
1
0
1
0
0
0
0
0
0
0
1
1
2
1
1
2
2
0
2
4
1
0
0
1
1
0
2
0
2
0
0
1
0
0
1
0
0
2
1
1
0
0
0
2
0
0
0
0
2
2
2
0
2
0
0
0
1
0
0
1
1
0
2
0
0
1
4
3
1
0
1
3
1
0
0
2
1
0
0
1
1
0
0
0
0
0
2
2
1
2
0
0
0
1
0
0
7
1
0
1
1
2
2
2
1
2
0
2
2
2
1
0
2
0
0
0
2
2
0
0
1
1
1
2
1
0
1
1
1
0
0
1
0
1
2
0
1
0
2
0
2
1
0
1
0
0
0
0
1
1
0
0
1
2
0
2
0
0
0
2
0
1
3
2
1
2
2
0
2
2
0
3
0
0
1
1
2
0
1
1
0
0
0
1
0
1
2
1
0
0
0
0
0
1
0
0
0
1
0
0
2
1
1
0
0
0
0
3
1
1
0
2
1
0
3
2
1
0
0
0
0
0
1
0
0
2
0
0
2
2
0
2
1
0
0
1
0
2
2
0
1
0
1
0
2
1
0
0
0
1
0
0
0
0
2
0
0
1
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
1
2
0
0
0
2
0
0
0
1
0
1
0
0
0
1
0
0
2
3
0
0
2
0
0
2
1
2
0
2
0
0
2
2
2
0
1
2
0
0
0
0
0
0
1
1
2
2
1
1
0
0
0
0
1
0
0
0
2
1
1
1
1
0
0
0
0
1
1
0
0
0
0
3
0
1
2
0
0
3
0
2
0
0
1
3
0
0
0
0
2
1
1
1
0
1
0
1
1
0
0
0
0
0
0
2
1
0
2
1
0
0
0
0
0
0
0
0
0
1
0
2
1
2
2
0
1
0
0
0
2
0
2
0
1
0
0
2
0
1
0
1
0
2
2
0
2
0
0
1
2
0
0
2
2
1
0
1
0
0
0
0
0
0
0
0
2
1
1
0
0
2
0
1
0
0
0
1
2
2
0
0
0
1
0
0
1
2
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
1
1
0
0
0
1
1
0
1
0
1
2
2
1
0
2
0
0
2
0
2
0
1
2
0
0
0
0
1
0
0
1
1
1
3
0
0
0
0
0
0
0
0
2
2
2
2
2
0
0
0
0
0
0
0
0
2
1
2
0
2
0
1
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
4
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
5
0
0
0
0
2
0
0
2
1
2
0
0
0
0
0
0
0
3
0
0
2
0
0
1
0
0
0
1
0
2
0
0
0
0
1
0
1
0
1
0
2
1
0
0
2
2
1
1
0
0
0
0
2
1
0
0
0
3
2
1
1
0
2
0
0
0
0
5
3
3
0
0
2
1
0
0
0
0
0
1
0
2
0
0
0
2
0
1
0
0
0
0
0
2
0
0
2
2
0
0
2
0
0
0
0
1
0
0
0
1
2
2
0
0
1
0
0
0
2
1
0
0
0
1
3
0
0
0
0
1
3
0
0
0
0
1
0
0
0
1
2
2
0
2
0
0
3
0
0
0
1
2
0
0
1
0
2
0
2
0
3
1
0
1
0
0
2
0
0
0
2
0
0
1
0
2
1
4
1
0
2
0
2
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
2
0
1
0
2
0
2
0
0
2
0
0
0
3
1
1
1
0
0
1
0
1
1
0
1
1
0
1
0
0
3
0
2
2
0
2
1
0
1
1
0
0
2
1
1
2
1
2
0
0
0
0
2
0
0
0
0
0
0
1
2
0
2
1
2
2
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
5
0
0
1
0
0
2
2
0
0
2
0
0
1
0
0
2
0
0
0
2
0
0
0
3
0
1
0
0
0
0
2
0
0
0
2
1
1
1
0
0
2
1
0
0
2
2
0
0
1
0
1
0
0
0
0
0
2
0
1
2
0
0
0
1
2
1
1
0
0
2
0
4
0
1
0
0
2
0
0
0
1
0
0
0
2
1
0
1
0
4
2
0
1
0
2
0
0
1
0
1
1
0
1
0
1
0
1
0
2
1
0
1
1
1
0
0
0
0
1
0
2
0
0
2
0
0
1
1
0
2
0
1
1
2
0
0
0
1
0
2
0
2
1
0
0
1
0
1
0
1
2
0
0
0
1
0
6
2
0
1
0
0
0
0
0
0
0
1
0
2
1
1
2
1
2
0
0
0
0
0
1
2
1
2
1
2
0
0
0
0
0
0
0
0
3
4
1
0
0
0
0
2
0
0
2
0
1
2
0
0
0
1
1
0
0
0
0
0
3
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
2
1
1
2
0
0
2
0
2
1
2
2
0
0
0
1
0
0
0
1
2
0
2
1
0
1
0
0
0
0
0
0
1
2
1
0
0
0
2
0
2
1
2
0
0
0
0
0
0
0
0
1
2
1
0
0
0
1
1
0
0
0
0
0
0
0
0
2
1
0
1
2
0
0
1
2
1
1
0
0
2
1
0
2
0
2
2
0
0
1
2
0
1
0
2
0
1
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
1
1
0
1
0
0
0
2
1
1
0
2
1
1
0
0
2
1
0
1
0
1
0
1
0
1
1
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
2
1
2
0
0
0
0
2
2
0
2
0
0
2
0
0
2
1
1
0
2
0
0
2
0
0
0
0
2
0
0
3
2
1
0
0
0
0
1
0
1
0
2
1
0
0
0
2
0
1
0
0
0
0
0
2
1
1
0
0
1
0
2
0
0
0
0
0
2
2
1
0
0
1
1
2
0
0
0
0
3
2
2
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
2
0
0
0
2
1
0
1
0
0
2
1
1
1
0
1
2
0
1
2
0
0
0
1
1
2
2
0
0
0
0
0
2
1
0
0
2
2
0
1
2
2
0
0
2
1
1
2
0
1
0
0
0
0
2
1
1
0
0
0
1
0
0
0
0
1
2
0
1
2
0
0
2
0
2
0
1
0
0
1
0
0
0
0
2
1
2
2
0
0
0
1
1
2
1
0
0
0
2
1
0
2
0
0
1
0
1
1
2
2
0
0
2
1
1
1
0
2
1
0
1
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
1
0
2
2
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
1
0
0
2
1
2
0
0
1
2
1
0
0
0
1
2
2
0
1
1
2
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
1
0
1
1
0
0
0
2
0
0
2
0
0
0
0
1
0
1
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
2
1
0
1
0
0
0
0
0
0
0
2
2
0
0
2
1
2
0
0
0
0
2
1
2
0
3
0
0
0
0
0
2
2
2
0
1
0
1
2
0
1
2
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
1
2
2
0
0
0
0
0
0
0
2
0
2
0
1
0
2
0
1
1
1
1
2
1
1
0
0
0
0
0
2
1
0
0
1
0
0
1
0
2
0
2
2
0
0
1
4
0
1
1
2
2
0
2
0
2
2
0
1
0
1
0
0
2
2
1
2
0
2
0
0
2
0
2
0
1
0
2
1
0
0
1
0
1
2
1
0
0
0
1
0
0
2
1
2
0
2
0
1
2
0
2
0
0
2
0
1
1
0
2
0
4
0
0
0
0
0
2
1
0
2
0
0
0
3
0
2
1
0
0
2
0
1
2
2
0
1
0
0
1
0
0
2
0
0
0
1
2
1
1
1
1
1
0
2
0
2
0
0
0
0
1
0
1
1
0
0
0
0
1
0
1
0
0
1
1
0
0
1
1
2
0
1
0
0
0
0
0
2
2
0
0
0
0
1
0
2
1
2
0
2
2
2
2
2
0
2
0
0
0
1
1
1
0
0
0
2
0
0
0
1
0
1
2
0
0
1
0
2
1
0
0
0
0
1
0
2
2
1
1
0
0
0
3
0
0
0
0
0
2
0
1
0
0
0
1
2
0
2
0
1
1
2
0
0
0
0
0
1
0
2
0
0
1
0
0
0
2
0
0
2
1
0
1
1
0
0
0
2
1
0
1
2
1
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
2
1
4
0
0
0
0
2
1
0
2
0
0
2
0
0
0
0
2
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
1
2
0
2
1
0
0
0
0
0
0
0
0
1
2
0
0
5
1
0
0
1
2
1
2
0
0
0
0
0
2
0
2
0
1
4
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
2
1
1
2
2
0
1
0
0
2
0
2
0
2
1
2
1
2
0
0
0
0
2
0
0
0
0
1
0
1
2
2
0
0
3
0
0
1
0
1
0
0
1
1
0
0
0
0
1
2
2
0
0
1
1
0
1
0
0
2
0
2
0
0
2
3
0
2
0
1
0
1
0
0
0
0
0
0
2
0
0
0
2
0
1
5
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
2
0
0
2
0
0
1
1
0
0
0
0
2
1
0
0
0
0
3
2
1
1
2
2
1
2
1
0
2
0
0
1
0
1
0
0
0
2
0
1
0
2
0
0
0
1
1
2
1
0
0
0
0
0
1
3
1
2
0
1
1
0
2
0
0
0
1
2
2
0
0
1
0
1
1
1
0
2
0
0
1
1
2
3
0
1
1
0
0
0
2
0
0
1
0
0
2
0
2
2
2
2
0
1
0
0
3
2
0
0
0
4
0
1
0
1
1
2
0
2
1
0
1
1
1
0
0
0
0
1
0
0
0
1
0
1
0
2
2
0
0
0
3
1
0
0
1
0
1
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
2
0
1
0
0
1
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
1
2
1
2
0
1
0
0
1
0
1
0
0
3
0
1
0
0
0
1
2
1
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
1
1
2
0
2
0
1
2
0
0
2
2
2
1
2
2
0
0
0
0
1
0
0
1
2
2
2
1
2
0
2
2
0
0
1
0
0
0
2
1
1
2
0
1
0
0
0
0
1
0
2
1
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
3
0
0
1
2
0
0
0
1
0
1
2
0
0
2
2
3
1
2
0
2
0
1
0
0
1
2
2
0
0
0
1
2
1
2
0
0
0
0
1
0
0
3
1
2
0
0
0
1
0
2
2
0
0
0
1
2
0
2
0
0
0
2
0
0
1
0
0
3
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
2
2
0
0
2
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
1
0
1
2
0
0
1
0
0
1
2
1
2
0
2
0
2
1
0
0
0
0
1
0
0
3
1
0
2
0
0
1
0
1
2
0
1
1
0
1
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
2
1
0
2
0
4
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
1
1
0
2
1
0
0
0
0
0
0
4
0
0
2
1
0
0
0
0
1
0
0
2
1
0
0
0
0
0
3
0
1
2
0
0
0
1
0
1
0
2
0
0
0
1
0
1
0
0
0
0
0
0
1
2
3
0
0
0
3
1
0
0
0
0
2
2
2
2
0
0
1
0
2
0
1
1
0
2
0
0
0
1
2
2
0
0
0
2
2
2
1
0
0
0
4
0
0
0
1
0
1
2
1
2
0
1
1
2
0
2
0
0
0
0
0
3
2
0
0
0
1
0
1
0
0
2
1
0
1
2
1
2
0
2
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
1
0
1
1
0
0
4
2
1
0
2
1
0
0
3
0
0
0
2
2
2
0
2
2
0
0
0
0
0
2
0
0
1
2
2
0
1
0
2
0
2
0
0
1
0
0
2
2
2
1
1
0
0
1
1
0
0
0
2
2
2
2
2
1
0
2
0
0
0
1
0
2
0
1
7
0
1
0
1
1
0
2
1
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
1
0
0
1
0
3
0
2
2
0
0
0
0
2
0
1
2
0
0
0
2
0
1
1
1
1
0
1
1
0
2
0
3
2
1
0
0
0
0
0
1
0
0
3
0
1
1
2
0
0
0
0
0
0
0
0
1
1
2
0
2
1
2
1
1
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
2
1
2
0
0
0
1
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
2
1
1
0
0
2
2
2
0
0
0
1
0
2
1
0
0
1
2
1
1
0
0
0
1
1
2
0
0
0
0
0
1
0
2
1
0
0
2
1
0
0
0
0
3
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
2
0
2
0
2
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
2
1
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
3
0
2
0
0
0
2
1
2
1
2
0
3
0
0
1
0
1
0
1
1
1
1
1
0
2
0
1
1
2
0
2
0
2
0
0
0
1
0
0
0
0
0
3
0
0
2
1
2
0
1
0
0
0
0
1
0
0
0
2
0
2
0
0
0
2
1
2
2
0
2
2
0
1
1
0
2
0
0
0
1
0
0
0
2
0
0
2
2
0
1
1
2
2
0
2
0
0
1
0
0
0
2
2
0
0
0
0
2
0
0
0
1
0
1
2
0
1
0
0
2
1
0
0
2
1
4
1
0
0
2
2
0
1
1
2
1
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
1
2
0
0
1
1
0
0
2
0
2
0
2
1
0
0
0
0
2
2
2
1
1
0
0
2
0
1
2
0
0
0
1
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
1
1
0
2
0
1
0
0
0
0
1
0
0
0
2
1
0
2
1
0
1
0
0
0
0
1
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
1
2
0
1
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
2
0
2
1
2
2
0
2
2
3
0
0
2
0
0
0
2
1
1
0
0
2
0
1
1
1
2
2
1
0
0
3
2
1
0
2
1
1
0
0
1
1
0
2
1
0
1
0
1
0
0
1
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
2
2
2
0
1
2
0
0
0
0
0
2
0
2
0
0
0
0
2
1
2
1
0
2
1
1
1
2
1
2
0
1
2
0
2
2
0
0
1
1
0
0
2
0
0
0
0
2
0
0
0
0
2
2
0
0
2
0
0
0
0
2
0
2
2
1
1
0
0
0
2
0
3
0
0
2
1
0
0
0
0
1
0
0
0
0
2
1
0
0
0
1
2
0
0
0
0
2
0
0
0
1
0
1
0
0
1
0
0
1
1
3
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
2
1
1
2
0
0
1
0
0
0
0
0
1
1
0
0
1
1
0
2
0
1
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
1
2
2
1
2
0
0
1
0
0
2
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
1
1
2
0
0
1
0
2
0
0
0
0
1
2
0
0
0
0
0
1
0
3
1
2
2
2
0
1
0
1
0
1
1
1
1
0
2
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
1
2
2
0
2
0
1
1
0
5
1
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
2
0
1
0
0
0
1
0
2
2
0
0
0
0
1
0
0
2
0
0
2
2
0
3
1
2
2
1
0
1
0
1
1
0
2
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
6
0
2
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
2
2
2
0
1
0
1
0
0
2
2
0
1
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
1
0
0
0
1
1
0
2
0
2
0
1
0
1
0
1
1
1
1
2
0
2
0
0
1
0
0
2
0
0
0
0
0
0
1
0
1
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
2
0
1
0
0
1
0
1
2
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
2
5
0
0
1
2
0
2
0
2
2
0
0
0
1
0
2
0
2
0
2
0
0
2
0
1
0
1
0
0
0
2
3
0
1
0
1
0
2
1
0
0
2
2
0
1
0
0
2
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
3
0
0
2
0
0
1
0
0
0
2
3
0
0
2
1
0
1
0
2
0
0
0
1
0
0
2
0
0
2
1
0
1
0
0
0
0
0
0
2
1
0
0
1
0
2
2
2
0
0
1
0
0
1
0
2
0
1
0
2
0
0
2
2
2
2
1
1
0
0
0
0
0
3
1
1
0
1
0
0
2
1
2
2
0
1
1
0
1
2
1
1
0
2
0
1
1
0
0
0
0
0
0
0
2
0
0
1
2
1
0
1
2
0
0
2
2
1
2
2
2
0
0
0
1
0
2
0
0
0
2
0
0
0
1
2
2
0
0
0
2
1
0
0
1
2
0
0
1
0
0
2
1
0
1
1
3
0
1
0
0
0
1
1
0
3
2
2
2
2
1
2
0
2
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
2
1
1
2
2
1
2
0
2
0
1
0
1
0
2
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
1
1
0
2
0
1
1
0
2
2
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
2
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
1
1
0
0
1
0
0
0
0
0
0
2
1
0
2
0
1
1
0
0
1
1
0
1
0
1
1
1
2
0
0
0
0
0
0
1
1
2
1
0
2
1
0
0
2
1
0
2
0
2
1
0
0
0
1
1
1
0
0
0
2
0
1
0
1
1
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
2
0
0
1
1
0
0
3
0
1
2
2
2
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
2
2
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
3
3
1
1
1
2
2
0
0
0
0
1
1
0
0
0
1
1
2
0
0
2
0
2
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
2
0
1
0
2
0
0
0
0
2
1
0
2
2
0
0
0
0
1
0
0
0
1
1
0
1
1
1
0
1
1
0
2
1
1
0
1
0
1
0
2
2
2
1
0
2
2
1
0
2
0
0
4
2
0
2
0
0
0
2
0
3
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
2
0
1
0
0
1
1
1
0
0
2
2
0
3
2
0
2
2
0
2
0
0
0
1
0
1
0
0
1
1
0
1
0
0
2
0
1
0
0
0
1
1
1
0
2
1
0
0
1
2
0
0
2
0
0
0
0
1
0
0
1
1
1
1
0
1
1
1
1
2
1
0
0
0
0
0
1
0
2
2
1
0
2
0
1
1
1
4
1
0
0
1
1
1
0
0
0
2
1
0
2
2
0
0
0
0
1
1
1
0
0
0
1
0
2
2
1
0
1
1
2
0
2
0
2
0
2
2
0
2
1
0
1
1
0
0
0
0
1
0
0
0
1
0
1
0
1
2
1
0
0
0
0
1
0
0
0
0
1
1
0
1
2
0
1
0
0
0
0
1
0
3
0
0
2
0
1
0
0
0
1
0
0
1
2
2
1
0
0
0
0
1
0
0
2
1
0
0
3
0
0
0
0
2
0
1
0
0
2
0
1
0
2
1
1
2
0
1
0
0
0
0
0
5
0
0
1
0
2
2
0
1
0
0
0
2
1
2
2
0
2
0
1
0
2
0
1
0
0
0
0
2
0
0
0
1
1
0
1
0
2
0
1
0
0
2
0
0
0
1
1
2
2
0
0
2
0
0
0
0
1
0
0
0
1
2
1
2
0
0
0
1
2
0
0
1
1
0
1
0
0
0
0
0
3
0
2
0
0
0
0
1
1
1
0
0
1
0
0
1
0
0
2
1
0
0
2
0
1
0
0
2
1
2
0
0
2
0
0
0
2
0
0
1
0
0
1
1
0
0
0
0
2
0
2
0
0
0
1
1
1
1
7
0
3
1
1
2
0
0
0
0
1
1
2
0
2
0
0
1
2
0
1
0
0
1
0
1
0
2
3
0
0
0
1
0
0
0
2
0
1
1
1
0
0
1
0
0
1
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
1
1
2
1
0
1
0
0
1
2
0
0
0
1
0
1
1
0
1
0
0
1
0
0
0
2
0
0
1
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
2
1
1
2
2
0
2
0
2
0
1
1
0
0
0
1
1
1
1
2
2
0
1
0
0
2
1
0
0
0
1
0
0
3
1
0
2
0
1
1
0
1
2
0
2
0
0
3
0
2
1
1
1
0
1
0
0
1
1
0
2
0
0
1
2
2
1
0
0
0
1
0
1
0
2
0
1
2
0
0
1
2
0
0
0
0
0
0
1
1
1
2
0
0
0
0
1
0
0
1
0
1
3
2
3
0
0
3
2
2
2
0
2
0
0
0
0
0
2
0
1
0
2
1
1
1
1
0
1
0
1
2
1
0
1
2
0
0
0
1
1
2
2
0
0
0
0
1
1
1
0
0
1
0
1
0
0
1
0
0
1
0
2
0
0
0
0
2
2
1
0
0
0
0
0
1
2
0
2
0
2
0
1
2
2
0
0
0
2
2
1
0
0
0
0
1
2
0
2
0
1
0
4
1
2
0
0
0
1
1
1
2
0
1
0
0
1
0
1
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
1
0
2
0
1
0
0
0
1
0
0
0
1
1
2
0
2
2
1
2
0
0
0
0
0
1
0
2
0
0
1
0
0
0
1
0
2
1
0
1
0
0
0
2
1
0
1
0
1
1
1
0
0
2
1
0
0
0
0
0
0
1
2
2
1
0
2
0
0
0
0
1
2
2
0
0
0
1
0
2
0
0
1
1
0
2
0
0
0
0
2
2
0
0
0
3
1
1
1
0
1
2
0
0
2
0
0
0
0
0
2
1
1
3
1
0
0
0
0
2
2
0
2
0
1
0
0
0
1
1
1
0
4
1
0
2
0
3
0
2
0
0
0
2
1
0
0
1
1
1
0
4
2
0
1
0
0
0
0
2
0
0
1
2
0
0
2
2
0
0
0
1
1
2
0
1
0
0
2
1
0
0
0
0
1
0
2
0
0
1
1
1
2
0
0
0
2
1
0
0
1
0
2
0
1
0
1
0
1
0
1
1
0
1
0
1
2
2
1
1
0
0
2
2
1
2
0
0
0
2
0
0
4
0
0
0
2
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
2
2
0
1
0
0
0
1
0
1
2
0
0
0
0
0
0
1
0
4
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
1
2
0
0
1
0
0
0
0
0
1
1
2
0
2
1
1
2
0
0
2
1
2
2
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
2
0
1
0
2
1
2
1
0
0
2
0
1
2
0
0
1
2
1
0
0
1
1
0
0
2
0
0
3
2
0
0
1
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
1
1
1
1
0
0
0
0
1
0
2
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
1
0
1
1
2
0
1
2
0
1
0
0
0
0
3
0
0
0
0
0
1
1
1
1
1
0
0
0
0
0
3
0
1
0
1
0
0
0
1
2
0
0
0
0
1
2
0
0
0
1
0
1
0
1
0
0
2
2
0
0
1
1
0
0
1
1
1
0
0
1
0
1
0
1
0
0
0
1
2
0
0
1
1
2
0
0
0
0
1
1
2
0
2
2
1
1
1
0
0
0
2
0
0
0
0
2
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
2
0
1
0
0
1
0
0
1
0
2
2
0
2
0
1
0
0
2
0
0
2
0
0
1
1
0
0
0
1
1
0
0
1
1
1
0
0
0
0
1
1
0
0
0
1
0
1
0
0
2
0
0
0
1
1
0
2
1
0
0
0
2
1
0
2
1
0
0
0
0
0
1
0
0
1
2
0
2
1
2
2
0
2
1
0
2
0
0
0
1
1
1
0
1
0
0
1
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
1
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
1
2
0
2
1
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
1
0
0
2
0
2
0
1
0
0
1
2
0
0
0
4
1
0
0
1
0
1
0
0
0
2
2
1
2
2
0
0
1
0
0
0
0
0
2
2
0
0
0
1
0
2
2
2
3
0
2
2
0
0
2
0
1
1
0
0
1
1
2
1
1
1
2
0
1
2
0
1
2
0
2
0
0
0
0
2
0
2
0
1
1
1
0
1
0
0
1
1
1
0
2
1
0
0
0
2
0
1
3
0
0
0
0
0
1
0
0
1
0
1
2
5
0
1
0
2
1
2
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
2
1
0
1
0
0
0
0
2
0
2
1
1
0
2
2
0
0
4
2
0
2
3
0
0
2
0
1
1
0
0
0
1
2
0
1
0
1
1
2
0
0
1
0
1
0
0
1
0
2
0
1
1
2
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
2
2
1
0
0
0
0
0
0
1
2
0
2
0
2
1
0
1
0
0
2
1
0
1
0
1
0
0
0
1
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
2
0
0
0
1
0
1
1
2
2
0
0
0
0
0
2
2
0
1
1
0
0
0
0
0
0
2
0
2
1
0
3
1
0
0
0
0
2
1
0
0
1
0
0
1
2
0
1
0
0
0
1
1
0
0
0
1
0
2
1
0
0
1
0
1
1
2
2
0
0
0
0
2
0
0
2
0
0
0
2
2
1
2
2
0
2
0
0
2
1
2
2
0
0
0
0
0
1
0
2
2
2
1
1
0
0
2
0
0
2
1
0
0
0
0
2
0
2
1
0
2
0
0
2
0
0
1
2
0
1
2
0
0
2
0
0
0
2
0
0
0
0
0
1
0
2
0
0
1
0
0
2
1
2
2
2
1
1
1
1
0
1
1
1
0
1
2
0
0
0
1
2
2
2
2
0
2
0
0
1
0
0
0
0
0
1
0
0
2
1
1
0
0
1
1
0
1
3
2
2
0
2
1
0
1
0
0
2
2
0
0
0
0
2
0
0
0
0
0
2
0
0
1
1
0
0
2
0
0
0
0
1
2
0
0
0
2
0
1
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
1
2
0
0
0
1
1
0
0
0
0
2
1
2
0
0
0
3
0
3
0
0
0
0
2
0
1
0
0
0
0
1
1
0
2
1
2
1
2
2
0
1
0
1
0
0
1
0
0
2
0
0
0
0
0
1
1
1
0
2
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
2
0
1
0
0
1
0
0
1
0
2
2
0
0
0
0
0
0
1
2
1
0
2
1
2
0
0
2
0
0
2
0
0
0
1
0
1
1
0
0
2
0
0
0
0
1
0
1
1
0
1
2
2
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
2
2
0
0
2
0
0
3
0
0
0
2
0
2
2
0
0
0
0
1
1
0
0
1
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
2
0
3
2
0
0
0
0
0
0
0
2
0
1
2
1
1
0
0
0
1
0
0
0
0
0
1
1
0
2
0
0
2
0
0
1
0
2
2
0
1
1
1
2
1
0
0
1
0
0
1
0
1
0
1
0
1
0
0
0
0
0
2
0
1
1
0
0
1
0
1
0
0
0
0
0
1
3
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
2
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
2
3
1
0
1
0
0
0
0
0
0
2
0
0
0
1
2
0
1
0
0
2
0
1
0
0
0
2
0
0
0
2
0
0
1
2
1
0
1
0
0
1
1
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
4
1
0
0
0
1
0
0
2
2
1
2
3
1
1
1
0
0
0
0
2
1
0
1
0
2
0
2
0
0
0
2
1
0
0
2
2
0
0
1
0
0
0
2
1
0
0
1
0
0
2
0
1
0
1
0
0
2
0
0
0
0
0
3
0
0
0
0
1
0
0
1
2
0
1
0
1
0
1
2
0
0
0
2
1
0
2
0
0
1
1
4
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
1
2
0
1
0
0
1
0
0
2
2
0
1
0
2
2
0
1
0
0
0
0
1
0
0
2
0
0
2
0
2
1
1
1
0
2
1
1
0
0
1
0
1
1
2
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
3
1
0
2
0
0
2
0
1
0
2
0
2
0
0
2
0
2
1
2
0
0
2
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
3
1
0
0
0
1
0
2
1
2
0
2
1
0
0
0
0
0
0
0
0
0
2
1
1
2
1
1
0
1
0
2
0
0
0
0
2
4
0
0
0
0
0
1
0
0
0
0
0
1
3
2
0
0
0
0
0
0
1
0
0
2
0
1
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
3
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
2
2
0
0
0
0
0
1
0
2
2
2
1
2
0
1
1
2
0
0
0
1
1
1
0
0
0
1
2
0
2
0
2
0
0
1
0
0
0
0
4
2
0
0
0
1
1
1
2
1
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
1
1
1
0
1
0
3
0
0
0
0
0
1
0
1
1
0
1
1
2
0
0
1
0
0
0
0
0
1
1
2
0
0
0
2
0
1
2
1
0
0
1
1
0
0
2
0
0
2
1
0
0
2
0
0
1
1
1
2
0
2
0
1
0
0
0
0
0
0
1
2
1
0
0
0
0
1
0
0
0
1
2
1
3
2
0
0
0
0
1
2
2
0
1
2
0
0
0
0
0
0
1
0
1
1
2
1
0
0
0
2
1
0
0
0
0
1
2
0
1
2
0
0
0
0
0
0
1
0
0
0
1
2
2
1
2
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
2
0
2
1
0
0
1
0
0
0
0
0
0
0
0
2
1
1
1
1
0
2
0
2
0
0
0
0
1
0
1
0
0
0
2
0
0
0
1
0
0
0
0
1
0
3
0
0
1
1
2
0
0
1
1
1
0
1
0
1
0
3
0
1
0
2
0
1
0
0
3
1
2
1
1
0
0
1
2
2
0
0
1
0
0
1
2
0
0
2
2
0
0
0
2
0
1
1
0
0
0
2
0
1
0
0
0
0
2
0
1
2
1
0
2
1
0
0
0
2
0
1
2
0
1
2
0
0
0
0
2
0
1
0
0
1
1
3
1
2
0
2
0
0
0
1
3
0
1
1
1
2
2
0
0
0
0
1
0
2
2
1
1
2
0
0
0
2
2
2
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
1
0
1
0
1
0
5
3
0
1
0
0
0
0
1
1
0
0
1
2
1
0
0
0
1
0
1
1
1
0
0
0
0
0
1
2
0
1
1
0
1
2
0
0
0
0
0
1
0
1
2
0
0
0
1
1
1
0
1
1
1
0
0
1
0
0
0
1
0
0
2
0
0
3
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
2
0
2
0
1
1
0
0
0
0
1
0
2
2
1
1
1
1
1
1
0
0
1
0
2
0
0
1
0
0
1
2
1
0
2
0
1
1
0
0
0
0
1
0
0
0
0
0
2
1
1
0
0
1
0
1
0
0
1
0
0
0
0
0
2
0
2
0
2
0
0
2
2
0
0
1
0
1
3
1
0
1
0
0
0
0
0
0
1
0
1
0
1
1
0
2
2
2
0
2
1
1
2
0
0
0
0
2
2
0
0
0
1
2
0
0
0
2
0
1
2
1
0
0
0
2
1
0
0
1
0
1
0
2
0
1
1
0
2
0
0
2
0
1
2
0
1
2
2
0
0
0
0
2
0
0
0
0
1
0
0
1
2
2
1
0
0
4
0
0
2
0
0
1
0
0
1
0
0
0
0
0
2
0
0
1
2
0
2
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
1
1
0
2
1
2
2
0
1
0
0
2
2
1
1
1
6
0
1
0
0
0
0
0
0
0
0
2
1
2
0
0
0
2
1
0
0
0
0
0
2
1
1
0
0
0
1
0
2
0
2
0
0
0
0
0
2
1
1
2
0
0
0
1
0
0
0
0
1
0
2
0
1
2
2
1
0
0
1
1
0
0
1
1
3
0
0
2
0
2
2
0
1
0
1
1
0
0
0
0
0
2
0
1
2
1
1
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
1
1
2
0
0
1
2
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
2
1
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
1
2
0
0
1
2
0
3
1
0
0
1
0
2
1
1
0
0
0
0
2
0
0
1
1
0
3
0
1
0
0
0
1
0
2
0
0
2
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
1
0
1
1
1
0
0
0
1
1
0
2
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
2
1
1
0
0
2
0
0
2
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
2
1
2
0
1
0
0
0
0
0
1
1
1
0
0
0
2
0
1
1
0
0
2
2
0
0
1
0
1
1
0
1
0
0
1
2
0
0
0
0
1
0
0
2
0
0
2
0
2
0
2
0
0
2
0
1
0
2
0
1
0
0
3
2
0
1
2
0
0
2
0
0
2
0
0
0
2
0
0
0
1
0
2
0
1
0
1
1
0
0
0
0
0
0
1
0
2
1
0
2
1
0
0
2
1
2
2
1
0
0
0
2
0
0
1
0
0
2
0
1
0
0
0
1
1
0
0
1
0
0
2
0
1
0
0
2
0
2
1
3
2
0
2
1
0
2
0
3
0
0
1
0
1
0
0
0
2
0
0
1
0
2
0
0
1
0
0
0
1
2
0
1
0
0
0
2
2
2
2
1
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
2
0
0
2
4
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
1
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
1
1
0
0
2
2
0
1
0
1
1
2
2
2
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
2
0
0
0
2
1
2
0
2
0
2
0
1
0
0
1
2
2
0
1
2
0
2
0
1
1
2
0
1
1
1
1
0
2
1
1
0
2
3
1
0
0
1
0
1
1
0
0
1
1
1
1
1
2
0
1
0
0
0
2
1
0
0
1
1
0
0
2
2
0
0
0
0
2
1
0
0
1
1
1
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
2
1
0
0
2
2
2
1
0
0
1
0
0
1
0
0
1
6
0
0
0
0
0
0
0
0
0
1
0
1
0
2
2
1
2
1
0
0
0
0
0
0
1
0
0
2
0
4
2
2
1
1
0
0
0
0
0
1
0
2
0
0
0
1
1
1
0
0
0
0
0
0
1
1
0
1
0
0
0
2
0
0
0
1
0
0
1
0
1
0
2
0
0
2
1
1
2
0
1
1
1
0
2
1
2
0
0
3
0
1
1
2
0
2
0
0
1
0
2
0
0
0
1
1
1
0
1
2
0
0
2
4
2
1
1
1
2
0
0
0
2
1
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
2
1
0
0
1
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
1
0
2
0
2
0
0
0
2
0
2
0
0
0
1
0
0
0
2
2
0
1
0
2
0
0
2
0
0
0
0
1
0
2
2
2
1
0
0
2
1
0
0
1
2
0
0
0
1
2
0
0
0
0
0
2
0
1
0
0
1
0
1
1
0
1
0
0
0
1
0
2
0
0
2
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
2
1
0
2
1
1
0
0
0
0
1
2
0
1
0
0
2
3
0
0
3
0
1
0
0
1
0
0
0
2
0
1
1
0
0
1
1
0
0
2
3
0
1
0
0
2
0
0
0
0
1
0
2
0
0
0
1
2
1
2
1
0
2
0
1
0
0
1
0
0
2
0
0
1
0
0
0
0
0
2
0
2
1
0
1
1
0
2
0
2
2
2
2
1
1
0
0
0
1
2
2
2
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
2
1
1
0
2
0
0
0
0
1
2
0
0
0
1
3
2
0
0
1
0
0
2
0
4
0
0
0
0
0
2
2
1
1
2
1
0
0
0
0
1
2
0
0
0
0
1
0
0
1
0
0
0
2
1
0
0
2
0
1
0
0
0
0
0
3
0
1
1
2
0
0
0
1
2
0
0
0
1
0
2
0
2
1
0
0
0
1
0
0
1
0
0
3
0
1
2
0
0
1
1
2
0
0
0
0
0
0
1
1
0
2
0
1
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
1
0
1
0
0
0
1
0
1
0
0
1
1
0
3
0
2
0
2
1
2
0
0
0
1
0
2
2
0
0
0
0
0
1
2
0
1
0
1
0
2
1
0
2
1
1
0
0
0
0
2
0
0
0
0
0
2
2
4
0
0
0
2
0
1
0
0
1
0
2
0
0
0
1
0
0
0
0
2
2
0
1
2
2
0
1
0
1
0
2
0
1
4
0
0
2
1
0
1
1
0
0
1
2
2
1
0
2
2
2
0
0
0
3
0
0
0
0
2
0
0
0
0
2
1
0
0
1
0
0
2
0
1
1
1
0
1
2
0
0
0
0
0
2
0
1
1
0
2
0
0
0
0
2
1
0
1
0
1
0
0
0
0
2
1
2
0
2
1
0
1
0
0
0
0
1
2
2
0
1
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
3
0
2
0
0
0
0
2
0
1
0
0
1
0
2
0
2
0
2
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
3
0
1
0
2
0
0
0
1
2
0
0
0
0
1
2
0
0
1
2
0
0
0
1
0
0
0
1
2
0
0
2
0
0
2
0
1
0
0
3
1
0
0
0
2
0
1
0
0
1
0
1
0
1
0
4
0
2
0
0
0
2
0
1
2
0
0
2
0
0
1
0
0
0
0
2
0
1
0
2
0
1
1
0
0
0
2
3
0
0
0
0
1
0
0
0
0
1
2
0
0
0
1
0
0
1
1
0
0
2
0
2
2
0
0
0
1
0
0
3
1
0
0
0
0
0
0
0
0
1
2
2
0
1
0
0
1
1
0
0
1
0
0
4
0
2
0
0
0
0
0
1
0
0
1
2
2
0
0
0
1
0
1
0
1
1
0
1
1
0
1
0
1
1
0
1
1
1
0
0
2
0
0
1
2
0
1
0
0
0
0
2
0
0
0
1
3
0
0
0
0
2
0
1
2
0
2
0
1
2
1
2
2
1
1
0
1
2
0
0
2
1
1
2
0
0
0
2
0
1
2
0
0
3
0
0
4
2
1
2
2
2
0
1
0
2
1
0
1
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
1
0
0
1
0
0
4
0
2
0
2
1
0
1
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
1
2
0
1
0
3
0
1
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
4
0
2
1
0
0
2
0
0
0
5
4
2
2
0
2
0
1
0
0
0
0
1
1
1
3
0
0
1
0
0
0
0
1
3
0
2
0
1
1
2
0
2
2
0
1
1
0
0
0
0
2
1
1
1
1
0
1
0
0
0
0
1
0
1
0
0
2
2
2
0
0
0
1
1
1
0
0
2
0
0
0
1
0
1
0
1
1
0
1
0
0
0
0
0
0
0
2
1
0
1
1
0
0
1
0
0
0
1
2
0
0
0
1
0
0
1
1
2
0
1
0
3
0
2
2
0
0
1
2
1
0
0
0
8
2
0
0
0
1
0
0
1
0
1
0
0
0
2
1
1
0
1
1
0
0
0
0
1
2
0
0
2
0
0
0
0
0
2
0
3
1
0
0
2
0
0
1
1
0
0
2
0
0
0
2
2
1
1
0
0
0
0
0
1
1
2
2
0
0
1
0
0
0
1
3
2
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
2
1
0
0
0
0
0
1
0
1
0
2
1
0
0
0
0
0
0
1
1
0
1
1
1
2
2
1
0
0
0
0
0
0
2
2
1
0
0
0
3
0
0
1
1
0
0
0
0
0
1
2
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
1
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
1
0
1
0
1
0
2
1
0
0
1
0
0
0
0
0
0
2
0
1
0
1
1
0
1
1
0
0
0
0
0
2
0
2
2
2
0
0
1
2
1
2
0
1
1
0
0
0
0
0
0
2
1
0
0
0
0
1
1
0
2
1
0
0
1
0
0
0
0
0
3
0
2
0
0
0
2
0
0
1
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
1
0
3
0
0
0
2
0
2
0
2
1
2
0
2
1
2
2
0
0
0
0
0
0
1
0
0
1
1
2
0
5
0
0
1
3
0
0
0
0
2
0
0
0
1
0
0
2
1
2
1
0
1
0
2
1
0
1
1
0
0
0
0
1
2
0
2
1
2
0
2
2
0
0
2
0
2
2
0
2
2
1
1
0
1
0
0
1
0
0
2
2
1
0
0
1
0
0
0
0
1
0
4
0
0
0
1
0
1
0
1
0
0
0
1
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
2
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
2
1
1
3
0
2
0
0
0
2
0
2
0
2
2
0
1
0
0
1
0
0
2
3
1
1
0
2
2
0
0
0
0
2
2
1
1
0
0
1
1
1
2
2
2
0
2
0
0
2
0
0
0
0
3
2
2
2
0
0
1
1
0
1
0
0
0
1
2
0
1
0
0
0
0
0
1
0
0
0
1
0
1
2
1
0
2
1
1
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
1
0
0
0
2
0
0
0
1
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
7
0
0
0
2
0
1
2
2
1
0
1
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
3
0
2
0
1
0
0
0
0
0
0
0
2
1
0
0
2
0
0
2
0
0
5
1
0
2
0
2
0
0
0
0
0
1
0
0
3
1
1
0
1
0
0
0
1
0
1
2
0
0
0
1
0
2
1
0
2
0
0
0
1
2
0
3
0
0
0
0
0
1
1
1
0
0
0
0
0
2
2
0
0
3
0
1
0
0
2
0
2
2
2
0
1
0
2
0
2
2
0
3
0
0
1
2
0
1
0
0
0
2
0
0
1
0
3
2
2
2
0
0
1
0
0
1
0
0
1
2
1
2
0
0
0
1
0
2
0
3
0
0
0
0
2
0
0
0
2
1
2
0
0
0
2
0
0
1
1
0
1
0
0
2
0
0
1
1
1
0
1
0
0
1
0
0
1
2
1
2
2
0
1
1
1
0
0
2
0
1
0
0
3
0
0
0
0
0
0
2
0
0
2
0
0
1
2
0
2
1
1
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
2
2
0
1
2
1
0
0
2
0
3
0
0
2
1
1
0
2
2
0
0
2
0
0
1
0
1
1
0
0
0
1
1
0
0
0
0
2
1
0
2
1
0
0
0
1
1
1
0
0
0
0
3
0
0
0
0
0
0
1
1
1
1
1
1
1
0
1
2
0
2
0
0
0
0
2
0
1
0
0
1
0
2
0
0
0
1
0
0
2
1
1
1
0
2
0
2
0
0
0
1
0
1
0
0
4
2
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
2
0
3
0
0
1
0
0
2
2
1
0
1
0
0
2
0
2
2
3
3
0
0
0
0
0
2
1
0
0
2
0
0
1
2
2
2
2
0
0
0
0
0
0
2
1
0
0
2
0
0
1
0
0
4
1
0
1
0
0
0
0
0
1
0
0
1
0
3
2
0
0
0
0
0
2
0
0
0
3
0
2
1
1
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
2
0
1
0
0
0
0
1
1
0
0
0
3
1
2
2
0
0
2
2
1
2
2
2
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
2
2
1
2
1
0
0
1
0
1
0
0
1
0
1
1
0
0
2
1
2
0
2
0
1
2
0
1
2
0
0
1
2
2
0
1
0
1
0
0
0
1
1
2
0
0
2
2
1
2
0
1
0
2
0
0
0
2
0
1
0
0
0
0
1
0
2
0
1
0
0
1
0
1
1
0
2
0
0
0
1
0
1
1
2
2
2
2
0
1
2
0
1
1
0
0
3
0
1
1
0
2
0
1
0
0
1
0
1
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
1
1
1
0
0
0
1
0
0
2
1
0
0
0
0
0
0
2
1
2
0
0
2
0
0
0
2
0
2
0
0
2
0
0
0
0
0
1
0
1
0
0
0
2
0
0
2
0
0
0
1
1
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
1
1
0
0
1
3
0
2
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
1
0
1
0
0
0
2
2
1
1
0
1
0
0
1
0
0
0
1
2
0
0
1
0
1
0
0
0
0
0
2
0
2
0
1
2
1
2
1
0
0
1
3
1
0
2
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
1
0
2
0
0
0
0
1
0
0
1
0
2
0
0
2
1
1
2
1
1
1
2
2
2
0
0
2
0
1
0
3
0
2
1
0
0
1
0
0
0
1
0
2
0
1
1
0
1
1
0
0
1
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
2
0
1
2
0
0
0
1
1
2
0
0
1
0
0
0
0
0
2
1
2
0
1
0
2
2
2
0
1
0
0
0
1
1
1
0
4
0
0
0
1
0
1
1
0
2
1
1
0
2
0
0
1
1
1
2
1
0
0
2
0
0
0
1
0
0
0
0
0
2
2
1
0
1
0
1
0
1
0
0
1
1
1
1
2
0
1
2
0
2
2
2
1
0
3
1
2
1
2
1
1
0
1
0
0
1
0
0
0
0
1
0
0
0
2
1
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
1
1
1
0
2
0
1
0
0
0
2
0
2
2
0
2
2
2
0
0
1
0
0
3
0
0
1
1
0
0
1
2
0
0
2
4
0
0
1
0
0
2
0
4
0
1
0
0
2
0
0
0
2
0
0
0
0
1
4
1
1
0
0
0
0
2
0
1
0
1
0
0
0
0
2
0
2
0
0
1
2
0
0
2
1
2
2
2
1
0
1
0
0
0
1
1
0
1
2
3
0
0
1
0
2
0
0
0
1
1
2
0
0
1
2
0
1
1
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
2
1
0
2
0
0
0
3
2
0
2
0
1
0
1
0
0
0
0
2
2
0
1
2
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
4
0
2
0
1
1
0
0
0
0
0
0
0
3
1
0
1
2
2
2
0
0
0
0
1
0
0
0
0
2
0
0
0
2
1
0
0
1
2
2
3
1
0
1
2
1
0
2
1
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
1
0
0
2
1
0
0
0
1
0
0
2
0
2
0
0
0
0
1
0
1
2
0
2
0
0
0
2
0
1
0
1
0
0
0
1
0
1
0
1
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
2
1
0
1
0
0
0
0
1
1
0
0
0
2
0
1
1
2
1
0
0
1
1
1
2
1
2
0
2
0
0
0
0
0
0
2
1
1
0
1
1
0
1
0
2
0
1
0
1
2
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
3
0
0
0
2
0
2
0
0
1
1
0
0
1
2
0
2
0
0
0
0
0
0
0
0
1
0
0
1
1
2
0
0
2
2
0
0
0
0
0
0
1
3
2
0
0
0
2
0
1
1
2
0
0
1
0
1
0
0
0
1
0
0
0
4
0
1
0
1
0
0
0
0
1
0
0
0
0
2
2
1
0
0
0
0
3
0
2
1
2
0
0
0
0
2
1
1
0
0
1
0
1
2
2
0
0
4
0
1
1
0
0
2
2
0
1
1
1
1
0
1
2
3
0
0
2
0
0
2
1
2
0
1
2
0
2
0
0
1
1
1
1
2
0
1
1
0
0
1
0
0
0
2
1
0
0
0
0
2
1
0
0
2
0
0
0
0
1
0
0
0
2
0
1
0
1
0
0
0
1
0
0
0
2
1
0
0
0
1
0
1
1
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
1
2
1
0
3
1
0
4
2
1
2
2
0
0
1
0
1
0
2
1
0
1
2
1
2
1
0
1
2
0
0
0
2
0
1
1
0
1
1
2
0
1
2
1
0
1
0
2
1
0
0
2
2
0
0
0
1
0
1
1
0
1
1
3
1
1
2
2
1
0
1
2
1
0
0
0
0
1
0
0
2
0
2
1
1
0
0
0
0
2
0
2
0
0
2
0
0
0
6
1
0
2
1
2
0
0
0
0
1
0
1
0
0
0
2
1
0
0
2
0
0
0
1
0
0
2
1
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
1
1
0
1
0
2
1
0
2
0
0
0
1
0
0
1
0
1
1
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
1
1
0
2
0
0
0
1
0
0
2
1
0
0
3
1
0
0
1
2
3
0
2
0
0
2
0
0
2
0
0
0
1
0
1
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
1
1
0
1
0
0
0
1
1
0
1
0
0
1
1
0
0
0
2
1
0
1
2
2
0
1
2
0
0
1
2
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
2
0
2
0
1
1
0
2
1
0
1
0
0
2
0
1
2
2
0
0
1
0
0
2
0
2
1
0
0
0
0
0
2
0
1
0
1
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
1
0
1
1
1
2
0
0
1
1
0
1
0
2
0
0
0
0
0
0
0
1
0
2
0
1
1
0
0
0
0
0
0
2
0
2
0
2
1
0
1
2
1
1
0
0
0
0
2
2
1
2
2
2
0
0
0
1
0
1
1
1
1
0
0
1
2
0
0
0
1
1
0
0
2
0
0
0
0
1
0
2
2
0
0
0
0
2
1
3
0
0
1
0
2
4
2
0
0
0
0
0
1
0
2
0
3
0
3
2
0
0
1
2
0
0
0
1
2
0
2
0
1
0
0
1
0
0
1
1
0
2
1
0
1
0
2
2
1
1
1
2
0
1
1
0
2
2
2
0
1
1
0
0
2
0
0
2
0
0
0
1
1
0
0
2
2
0
0
1
1
0
0
0
0
0
0
1
0
1
0
1
0
0
2
1
2
0
0
0
1
0
0
1
2
2
0
0
5
0
0
2
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
2
0
0
2
2
2
0
0
0
1
1
2
0
1
0
1
1
0
1
0
0
0
2
0
1
0
0
1
2
2
1
1
0
0
2
0
0
0
0
0
0
1
0
0
1
4
0
0
0
1
0
1
0
0
0
2
0
0
0
1
1
0
0
0
2
1
0
1
2
1
1
0
0
0
2
0
0
2
0
1
0
1
2
4
0
2
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
2
0
1
0
0
0
0
0
2
0
2
1
1
0
1
0
1
2
1
0
0
2
2
2
0
0
0
0
0
0
1
0
1
0
0
2
1
0
3
0
1
1
1
0
1
1
0
0
1
0
1
0
0
0
0
0
0
4
0
0
1
0
0
0
3
0
0
0
0
0
0
0
1
1
0
0
2
2
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
2
1
0
0
0
0
1
0
1
0
2
1
2
1
1
0
2
2
0
0
0
0
2
0
0
1
1
0
2
0
2
1
0
0
0
1
1
0
1
0
0
0
0
0
2
0
1
0
2
0
0
1
0
0
2
0
0
0
4
2
0
2
1
2
0
0
0
0
0
0
1
1
0
0
1
0
0
2
0
1
0
0
0
0
2
0
2
0
0
0
0
1
1
0
0
1
0
1
0
0
1
0
1
1
0
0
0
0
1
1
0
1
0
2
2
0
0
1
2
0
1
0
2
2
0
0
2
2
0
1
1
2
1
3
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
1
0
0
1
2
0
0
0
2
1
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
1
2
0
0
0
0
2
1
0
0
0
0
0
2
0
0
2
1
0
0
0
2
0
0
2
0
0
2
2
1
0
0
0
0
0
0
2
2
0
0
1
0
2
0
0
1
0
0
1
0
0
2
0
0
3
2
0
0
0
1
0
0
0
2
0
0
1
0
1
0
0
0
0
1
0
0
1
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
2
0
1
0
0
2
2
2
0
0
1
0
0
0
0
0
0
1
0
0
2
1
2
1
0
0
2
0
0
2
1
0
0
0
0
0
0
2
2
0
2
0
3
0
0
1
3
2
2
1
1
1
0
0
2
0
0
0
0
0
0
2
0
0
2
0
1
0
2
0
1
0
0
0
0
0
0
0
1
0
0
1
1
2
3
0
1
0
0
2
2
1
1
2
0
0
2
0
0
0
0
1
2
0
0
1
1
0
0
0
1
1
0
1
0
2
0
0
0
1
1
1
0
2
1
0
2
0
0
0
1
0
2
2
0
0
0
0
1
0
2
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
2
2
0
1
3
0
0
0
0
2
0
1
2
1
1
1
0
1
1
0
0
0
2
0
0
0
0
2
0
0
0
2
0
1
0
2
1
0
0
0
0
1
1
0
2
2
0
0
0
1
1
0
0
1
0
2
2
0
0
0
2
0
1
0
0
2
0
1
1
0
0
2
2
0
1
1
2
1
0
0
1
0
2
1
0
0
2
0
0
0
2
1
0
0
1
1
0
0
1
2
0
0
0
1
2
1
0
0
0
0
2
1
0
0
0
0
0
2
2
0
0
0
2
0
2
0
0
0
1
1
0
2
0
0
0
1
0
2
1
2
0
0
2
2
0
1
1
1
1
1
2
0
0
0
2
1
1
1
0
0
0
0
2
0
2
2
2
0
1
1
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
3
2
2
0
1
0
0
2
0
2
0
0
1
2
0
0
0
1
0
0
0
0
1
2
0
0
0
0
1
0
1
0
2
1
0
0
2
1
3
0
1
0
1
0
0
2
0
0
2
2
0
0
0
0
0
0
0
2
2
0
0
1
0
1
2
1
2
2
1
0
0
3
0
0
0
0
2
0
0
2
3
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
1
2
0
2
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
2
3
2
2
0
1
1
1
2
2
2
2
0
0
0
0
1
0
2
0
1
0
2
0
2
0
0
1
1
2
1
2
0
0
7
1
0
0
2
0
0
0
1
0
0
1
0
0
2
0
2
2
1
2
1
0
0
0
1
2
0
0
1
0
0
1
3
0
2
0
1
0
0
2
0
0
2
0
0
1
0
0
1
1
2
1
2
1
1
0
0
0
2
0
2
2
0
0
1
0
2
0
0
0
0
2
2
0
0
3
0
3
0
0
2
0
1
0
2
1
0
2
0
1
1
0
0
0
1
1
0
0
1
2
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
2
2
0
0
0
1
1
0
1
0
0
0
0
0
0
2
0
2
0
2
0
1
1
0
1
0
1
0
2
0
0
2
0
0
2
0
1
0
1
2
1
0
0
2
0
0
1
1
1
1
0
2
2
1
2
0
1
2
0
1
0
0
0
0
0
0
2
1
0
0
1
0
1
0
0
0
0
2
1
1
1
7
1
0
1
0
0
0
1
0
0
0
1
0
2
2
0
1
1
0
0
2
0
1
1
2
0
2
0
1
0
1
0
2
0
0
0
1
0
0
1
0
1
1
0
1
0
0
3
0
0
2
0
0
1
0
0
1
0
0
0
1
1
1
0
0
0
1
0
3
0
1
0
2
0
0
1
2
1
0
0
0
0
0
0
0
0
0
1
1
2
3
0
0
0
2
0
1
1
0
2
0
0
1
1
0
0
1
2
1
0
0
0
0
1
1
0
0
2
2
0
0
0
0
1
4
0
1
0
1
0
1
1
0
1
0
0
1
2
0
0
2
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
1
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
2
0
2
0
0
0
0
1
1
0
1
0
2
0
2
1
7
0
1
1
0
0
0
1
0
1
1
2
0
1
0
1
2
0
2
0
0
0
0
0
0
1
0
0
1
1
2
0
2
0
2
1
2
2
0
0
2
0
0
1
0
0
0
2
1
0
2
0
0
1
0
0
0
2
2
0
0
2
0
0
1
2
0
6
1
1
2
0
1
0
0
1
0
0
2
3
0
1
0
3
1
0
0
1
2
4
0
2
2
1
2
0
0
0
0
0
0
1
0
1
0
1
0
2
2
0
0
3
0
0
2
0
0
0
0
0
0
1
0
2
1
1
1
0
2
2
0
1
0
1
0
4
0
0
0
0
2
1
2
1
0
0
0
0
0
0
2
0
0
0
0
1
1
2
2
0
1
0
0
1
0
2
1
0
0
1
0
0
0
1
0
2
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
1
1
0
0
0
0
0
2
1
0
2
0
1
0
0
0
0
0
0
2
0
0
0
1
1
2
0
0
0
2
0
1
1
0
0
0
0
1
0
1
1
1
2
1
0
0
0
2
0
2
0
0
0
2
2
0
2
1
0
2
1
0
0
0
1
0
0
2
0
0
0
0
1
0
3
2
1
0
1
0
0
0
0
0
0
0
2
2
1
0
0
0
1
0
2
1
1
3
0
0
2
1
1
0
0
0
0
4
0
0
2
0
0
1
0
0
0
0
0
0
1
1
0
2
2
2
0
0
1
0
0
1
1
1
0
0
1
0
0
0
0
0
1
2
0
0
2
0
0
0
1
2
2
1
0
0
0
1
0
1
0
1
0
0
1
0
0
0
3
0
2
0
0
0
2
0
2
1
0
2
2
1
0
1
0
0
0
0
2
0
1
0
0
2
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
3
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
2
0
1
2
1
0
0
0
0
0
1
0
2
0
1
1
2
1
1
1
1
2
1
0
2
1
1
0
2
0
0
0
0
0
0
1
0
0
1
1
0
2
0
2
0
1
0
1
1
0
0
1
0
4
0
0
0
0
0
0
0
2
0
0
0
2
0
1
1
2
1
1
0
0
0
2
0
2
1
2
1
2
1
0
0
1
0
1
2
0
2
1
2
0
1
2
0
0
0
2
0
1
0
2
1
2
0
2
1
0
2
1
0
2
0
0
0
1
0
2
1
1
3
1
2
0
1
2
1
0
1
2
1
0
2
2
0
1
0
0
0
1
1
1
0
0
1
4
6
1
0
0
2
1
1
3
0
0
0
2
0
0
0
0
0
1
0
0
0
1
1
0
0
0
2
0
0
0
1
2
0
0
0
2
0
1
1
0
1
0
2
0
1
0
0
0
0
0
1
2
0
1
0
0
1
2
2
2
2
0
0
2
0
0
1
0
0
1
0
0
4
0
0
2
1
1
0
2
2
2
1
0
1
3
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
2
0
0
1
1
0
0
0
1
0
0
0
3
0
2
0
0
1
2
0
1
0
1
0
0
2
0
1
0
1
1
0
2
0
0
0
1
0
0
0
0
1
2
0
0
0
2
1
2
0
0
0
0
1
0
2
0
1
0
0
3
0
1
2
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
2
0
0
2
0
0
1
1
0
1
0
2
0
1
1
0
2
1
0
0
0
2
0
1
0
2
1
0
0
0
3
0
1
2
0
0
0
0
0
0
0
0
0
1
0
2
0
2
2
0
0
0
1
0
1
0
0
0
0
2
2
0
1
0
1
2
0
0
0
1
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
1
0
0
1
1
2
0
1
1
2
1
0
0
4
0
3
0
0
2
0
2
0
0
0
0
0
2
1
0
0
0
2
0
0
2
2
0
1
0
0
1
0
0
1
0
0
1
0
0
2
0
0
1
0
0
2
0
0
0
1
2
2
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
2
1
0
0
1
0
0
1
1
1
2
1
2
1
2
0
0
0
0
0
1
2
0
0
0
2
1
0
0
3
2
0
0
1
0
1
0
0
1
0
0
1
1
0
2
0
1
2
0
2
0
2
1
3
2
0
0
0
1
1
1
1
1
0
0
0
0
2
1
1
1
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
1
2
2
2
1
0
0
1
1
0
0
0
0
0
2
0
2
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
4
0
0
0
0
1
1
0
0
0
1
0
1
0
0
2
2
0
3
2
0
0
0
0
4
1
0
1
0
2
1
0
2
2
0
0
2
1
0
0
0
1
0
0
2
0
5
0
0
2
0
0
1
0
0
0
2
2
0
1
1
0
2
0
2
0
0
0
0
1
2
0
0
0
0
1
0
0
2
0
2
1
0
0
0
1
0
0
1
2
0
0
0
2
0
1
1
2
0
1
1
1
0
0
1
0
1
1
0
0
1
0
0
0
1
3
1
0
1
1
0
0
0
2
3
0
0
0
1
0
0
1
0
2
2
0
2
2
1
0
0
0
0
0
0
0
0
0
1
1
1
2
1
2
0
0
0
1
0
0
2
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
1
0
1
0
0
2
0
0
0
2
0
2
0
0
0
0
1
1
2
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
2
0
2
1
0
0
0
0
2
1
1
1
0
0
0
2
0
0
2
1
1
0
0
0
1
0
0
0
0
2
0
0
1
1
2
0
3
2
2
0
0
0
0
2
1
0
10
0
0
2
0
1
0
1
0
1
0
1
0
0
0
2
0
0
0
1
2
2
0
1
0
1
0
0
1
0
0
2
0
0
2
0
2
0
0
1
0
0
1
0
0
3
0
2
1
2
0
0
1
0
2
2
1
0
0
2
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
2
0
1
2
0
2
0
2
0
0
0
0
2
0
2
1
2
0
1
2
0
0
0
0
0
1
0
2
0
0
0
1
2
0
0
2
0
1
2
0
0
2
0
0
0
1
1
1
0
0
0
0
0
3
2
0
0
0
0
0
0
2
0
2
2
0
0
2
0
1
0
0
0
0
0
0
1
2
0
1
1
0
2
1
0
0
0
2
0
0
1
1
1
0
1
1
0
2
4
2
0
0
2
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
2
2
1
2
0
0
0
0
1
2
1
2
0
0
1
1
1
0
1
0
3
0
0
0
1
0
0
0
1
0
0
1
0
0
0
2
1
0
2
0
1
1
1
0
0
2
1
0
1
1
0
0
0
0
0
1
0
2
0
0
0
1
0
0
1
1
0
0
0
0
1
2
0
0
0
1
0
1
0
0
1
0
1
0
0
1
1
0
2
0
0
0
0
2
0
0
1
0
0
0
1
2
0
2
0
0
0
2
0
0
0
1
0
0
2
0
0
2
1
0
2
0
2
0
0
0
0
0
1
2
1
0
0
0
1
4
0
2
0
1
1
0
0
1
0
2
0
2
0
0
1
0
1
0
0
0
0
0
2
0
0
0
1
2
0
0
2
1
0
1
2
0
0
0
2
3
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
1
2
0
0
2
0
2
1
1
0
0
0
0
0
1
0
0
0
1
0
1
1
1
1
0
0
1
0
1
1
1
2
0
2
1
2
0
0
1
0
2
0
0
0
0
0
2
2
0
0
0
0
1
1
2
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
1
0
0
2
2
0
3
2
0
0
0
2
2
0
0
0
0
0
1
1
1
0
0
0
3
0
0
1
1
0
2
2
0
1
2
0
2
0
0
0
0
2
2
0
0
0
1
2
2
1
1
0
0
0
2
0
1
2
0
2
2
5
2
0
0
1
1
0
0
4
2
1
2
0
0
0
0
0
2
0
2
0
0
1
0
0
0
1
3
0
2
0
0
2
0
0
1
1
1
0
2
1
0
0
1
2
1
0
0
0
1
0
1
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
1
0
1
0
0
1
1
0
0
1
0
0
1
2
0
0
3
0
2
1
1
1
1
0
2
0
3
1
0
0
0
0
0
1
0
1
0
0
0
3
0
0
0
2
0
1
1
1
0
2
0
0
2
0
2
1
0
0
0
0
2
2
1
1
0
0
2
0
1
2
1
0
1
0
0
0
1
1
0
0
0
0
1
0
1
2
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
2
2
0
0
0
1
1
3
0
1
0
0
1
0
1
1
0
2
0
0
2
2
0
0
1
0
0
1
0
1
1
1
0
0
2
0
0
0
0
0
2
2
0
2
0
0
0
0
2
1
0
0
2
1
0
0
2
0
2
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
2
2
1
0
0
1
1
1
1
0
0
0
1
2
1
0
2
0
1
0
0
2
0
0
0
1
0
1
0
2
0
0
1
0
0
0
2
2
1
0
0
0
2
2
0
1
0
1
1
0
0
0
0
1
2
0
0
0
0
1
3
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
2
0
1
0
0
0
1
0
0
0
1
0
2
0
0
1
2
0
0
2
3
0
1
2
1
1
0
2
0
0
0
2
0
1
2
1
2
0
0
0
2
1
1
1
0
3
0
1
1
1
0
1
0
1
0
2
2
2
0
0
0
2
1
0
0
1
2
0
0
0
2
0
0
0
1
1
1
0
1
1
0
2
0
0
1
2
0
0
0
0
0
2
2
0
0
1
2
2
0
1
2
0
0
0
0
0
1
0
0
1
1
0
1
2
0
2
0
0
0
2
0
0
0
0
1
0
0
1
1
1
0
0
1
0
2
0
0
0
0
0
0
0
4
0
2
0
0
2
0
1
1
0
0
2
2
0
2
0
1
0
0
0
0
0
2
1
0
0
2
1
1
2
2
0
0
0
0
0
0
1
1
2
1
1
0
0
0
0
2
0
0
0
1
1
0
1
1
0
0
0
0
0
0
1
2
0
2
2
0
1
7
0
2
0
0
0
0
0
0
0
2
0
1
0
2
0
0
2
2
1
0
0
0
1
0
0
0
0
1
0
1
1
0
1
0
0
0
0
1
2
0
2
0
0
1
1
2
0
0
2
2
0
0
1
0
0
2
2
0
0
0
3
0
0
0
2
0
2
0
0
0
2
0
0
1
0
0
1
0
3
0
0
1
0
1
1
0
1
0
2
1
0
0
0
0
0
0
1
2
0
2
1
2
0
0
0
0
0
1
0
1
2
0
1
1
0
0
0
1
0
3
0
4
0
1
0
0
0
0
0
0
2
1
0
0
1
1
2
0
0
0
1
1
0
0
2
0
2
0
0
0
1
0
1
1
0
1
0
1
0
1
1
0
0
0
0
0
2
0
2
0
2
0
0
0
0
2
0
0
1
2
1
1
0
3
0
2
0
2
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
3
1
0
2
1
0
0
0
2
3
1
1
2
2
0
4
0
2
1
0
0
1
1
0
0
0
0
1
0
1
2
1
1
0
0
0
0
2
2
0
1
1
0
0
0
0
2
1
0
0
1
0
2
0
0
0
2
0
2
0
0
0
2
2
0
0
0
1
1
2
0
2
0
3
1
1
0
0
2
2
2
2
0
0
2
0
1
0
0
1
0
1
2
0
1
0
0
0
0
2
0
0
0
0
2
0
2
1
0
2
0
0
1
0
5
2
0
1
1
2
2
0
1
0
0
2
2
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
1
1
0
2
1
2
0
1
0
0
2
1
0
0
1
0
0
0
0
0
0
1
2
0
0
1
2
0
1
0
1
1
0
0
1
0
0
0
1
1
2
0
0
1
1
0
0
1
2
0
2
0
0
0
2
3
2
2
0
0
0
1
1
1
4
0
1
0
1
0
0
0
1
1
0
0
0
2
0
1
0
1
3
2
0
0
2
0
2
0
0
0
1
0
0
0
1
2
0
0
0
1
0
0
1
1
1
1
0
0
0
3
0
0
2
1
0
0
2
0
1
1
0
0
2
0
0
0
0
0
0
1
0
1
0
1
2
1
0
1
2
1
2
0
1
0
0
1
0
1
0
1
1
0
0
0
0
0
2
1
0
1
0
2
0
0
0
2
0
2
0
0
1
0
1
1
0
0
0
2
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
2
0
1
1
0
0
0
0
3
0
0
2
0
2
0
0
2
0
3
0
0
1
0
1
0
0
0
0
0
0
0
2
1
1
4
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
4
1
0
0
2
0
2
0
0
2
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
2
0
1
1
3
0
0
0
1
0
2
1
2
1
0
0
0
1
0
0
0
2
0
0
0
1
1
1
0
1
0
0
1
1
2
2
1
1
0
1
0
0
1
0
1
0
3
2
1
0
0
0
0
1
0
0
2
1
1
2
2
0
0
1
1
1
0
0
1
1
0
1
1
1
0
0
2
0
0
1
0
0
1
0
0
2
0
0
1
2
2
0
1
0
1
0
2
1
1
2
1
0
1
0
2
0
2
0
0
2
0
2
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
1
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
2
2
0
1
0
0
1
3
1
2
1
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
1
0
1
2
0
0
3
0
1
0
0
0
0
0
0
0
3
1
2
2
2
0
0
0
2
0
1
0
2
1
1
0
1
0
2
0
3
2
1
0
0
0
0
1
1
0
0
0
1
2
0
1
0
1
0
0
0
0
1
0
2
2
0
0
0
0
2
0
2
2
1
0
1
1
1
1
0
1
1
0
2
0
0
0
0
1
0
2
0
2
0
0
0
0
2
0
0
2
1
0
0
2
1
2
0
0
0
0
2
0
1
0
2
1
0
0
2
3
1
1
1
0
0
0
0
2
0
2
0
2
0
1
0
2
0
0
1
0
0
1
2
0
2
0
0
1
0
1
0
2
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
2
0
0
0
2
2
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
4
2
1
0
0
0
0
0
1
0
0
0
0
1
1
0
1
2
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
2
1
1
1
0
0
3
1
1
0
0
0
0
0
0
0
0
1
2
4
2
0
1
0
2
2
0
2
0
1
2
0
1
0
0
2
1
0
0
1
4
1
0
0
0
0
2
1
2
0
1
0
1
0
0
0
0
0
1
0
0
0
2
0
0
2
0
3
1
0
0
2
0
0
1
0
2
0
0
1
0
0
1
1
0
0
2
1
1
0
1
2
0
1
0
0
0
0
0
0
2
0
0
1
0
0
1
1
1
1
0
2
0
0
0
1
0
1
2
0
0
1
2
2
2
0
2
2
0
0
0
0
1
0
0
3
1
1
0
1
0
0
0
0
0
0
2
0
0
2
1
0
0
2
0
1
0
1
0
0
0
0
3
1
0
2
0
0
0
0
1
0
1
2
2
0
1
2
2
0
5
1
0
0
0
0
0
0
2
0
0
0
0
0
1
3
0
0
0
0
0
3
0
0
1
3
0
2
0
0
2
0
0
2
0
2
0
0
1
0
2
2
1
0
2
1
1
0
1
1
1
0
1
0
2
1
1
0
1
1
0
0
0
1
1
1
1
0
0
0
2
0
1
0
0
0
0
2
0
0
1
2
0
1
0
2
0
0
2
2
0
1
1
0
0
2
0
0
2
0
0
2
1
2
1
1
0
0
0
2
0
2
2
0
1
1
1
0
0
2
0
2
0
0
0
2
1
1
0
0
0
0
0
0
0
2
2
0
0
1
1
0
2
0
0
0
1
2
0
1
0
1
0
0
0
2
2
0
0
0
0
2
1
0
0
0
0
2
0
1
0
0
0
0
0
0
1
2
1
1
1
1
0
2
0
2
0
0
0
0
0
0
0
0
2
1
1
0
2
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
1
0
2
3
2
1
1
1
0
0
0
0
1
0
1
2
0
1
0
0
0
1
2
1
1
0
0
0
0
1
0
2
2
2
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
1
2
0
0
1
0
0
0
0
0
2
2
0
0
2
1
2
0
0
2
0
1
1
2
0
0
1
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
1
0
1
2
1
0
1
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
1
0
0
0
1
2
2
1
2
1
1
2
1
1
1
1
0
0
0
2
1
1
1
2
1
0
0
1
3
1
0
1
0
2
0
1
0
0
0
0
0
0
0
3
0
0
1
2
1
2
2
1
0
2
2
1
0
0
2
0
2
0
0
0
1
2
1
2
1
0
1
1
2
0
1
1
0
0
1
0
0
1
2
1
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
2
0
2
0
0
0
1
0
1
0
0
2
0
2
2
0
0
0
0
2
0
2
0
2
0
1
0
2
1
0
2
1
0
2
0
0
0
0
1
1
0
0
0
2
0
0
0
4
0
0
1
0
1
1
0
2
1
0
0
0
0
2
1
0
2
1
2
0
2
0
0
2
0
0
2
2
0
1
0
2
1
0
0
0
0
3
0
0
0
1
3
0
1
3
2
0
2
0
1
0
2
2
0
0
0
1
0
1
2
0
0
0
2
1
2
0
0
0
0
2
1
2
0
0
0
0
0
1
1
0
2
1
1
0
0
0
0
0
0
2
2
0
0
2
0
2
1
2
0
0
3
0
2
0
2
4
0
2
0
0
2
0
1
2
1
0
2
0
1
0
0
1
2
0
1
0
0
1
2
2
0
0
0
0
1
1
2
1
0
0
1
0
0
2
3
0
0
1
2
0
0
2
0
1
0
0
0
0
6
5
0
2
1
0
1
1
2
0
1
1
0
1
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
1
2
2
0
0
2
0
2
0
0
0
0
2
2
1
1
2
1
0
0
2
1
0
0
0
1
1
0
2
3
2
0
2
1
1
1
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
1
1
1
0
0
1
0
1
0
3
2
0
3
2
2
1
2
0
0
2
0
0
0
0
0
0
0
0
2
1
2
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
1
0
1
1
0
2
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
1
2
0
0
1
1
0
0
3
0
1
0
2
0
0
2
0
1
0
0
0
0
0
0
1
2
0
0
0
0
2
1
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
1
1
0
1
1
2
0
0
0
1
2
2
1
0
0
0
0
1
1
1
1
0
0
0
4
0
2
1
0
2
1
3
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
4
0
1
2
1
2
0
0
2
0
0
0
0
0
0
2
0
0
0
2
1
0
1
1
1
2
0
2
1
2
2
0
0
0
1
0
2
0
2
2
0
0
0
6
2
1
1
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
2
0
1
0
0
0
0
1
0
0
2
0
0
2
0
2
0
0
0
0
0
1
0
2
4
1
1
0
0
1
0
0
2
0
0
0
0
0
2
1
0
2
2
2
0
1
0
0
1
0
1
0
0
0
0
1
1
1
2
2
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
2
2
1
0
3
0
0
2
2
1
0
0
1
1
2
2
1
1
0
1
3
2
0
1
1
0
2
0
2
0
0
2
1
0
0
2
4
0
0
0
1
1
0
0
0
2
1
1
0
0
0
0
0
0
1
0
1
3
2
1
2
0
0
1
1
2
0
2
0
0
0
0
0
0
0
1
1
0
0
0
1
2
1
1
2
0
2
0
0
1
0
0
1
0
0
2
0
2
0
0
0
0
2
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
1
0
0
2
0
1
1
2
2
0
1
0
0
2
0
0
0
1
0
2
1
1
1
2
0
0
0
2
1
0
2
0
0
0
0
0
0
2
0
0
0
3
0
2
0
2
1
1
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
2
0
2
0
2
0
0
1
5
4
1
1
2
0
0
0
2
0
1
0
0
0
1
2
0
0
2
1
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
1
0
1
2
1
0
0
1
0
0
2
0
0
2
2
0
0
0
2
0
1
1
2
0
0
0
0
0
0
1
0
1
0
0
0
1
4
0
2
0
0
1
0
0
0
0
0
1
1
0
2
1
0
0
0
0
0
1
2
0
2
1
2
1
1
0
0
0
1
2
2
1
3
0
0
2
0
1
2
1
0
0
0
0
0
0
1
0
1
2
0
0
0
1
0
2
0
1
0
2
0
0
0
1
2
0
0
0
0
2
0
0
0
1
1
2
1
0
2
0
1
0
3
0
0
0
0
0
0
0
2
0
1
0
2
0
2
0
0
0
1
2
0
0
0
2
0
0
1
0
0
0
0
0
0
1
2
0
0
2
1
1
0
1
0
1
2
1
1
0
0
2
0
0
0
2
0
0
2
2
0
2
1
0
0
1
1
3
1
1
1
2
0
1
2
0
2
2
4
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
1
1
0
2
1
2
2
1
0
0
2
0
0
2
0
0
1
1
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
1
0
0
2
0
0
1
0
1
0
2
0
2
0
0
0
1
0
1
2
0
0
1
2
0
2
1
1
0
0
2
0
1
0
3
0
1
0
0
1
0
0
1
2
0
0
0
1
2
0
1
2
1
1
0
0
0
0
1
0
0
0
1
1
0
1
2
1
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
3
2
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
2
0
3
1
0
2
1
3
0
0
0
1
0
1
0
0
0
0
1
1
2
0
0
0
3
0
0
0
0
2
0
0
2
0
2
0
1
2
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
1
0
0
1
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
1
0
2
1
0
0
2
0
1
2
0
0
2
0
2
0
2
2
0
2
0
0
1
1
0
0
2
1
1
1
0
1
0
0
0
0
2
0
0
0
1
0
2
2
0
0
0
1
0
0
0
2
0
1
1
1
0
0
0
0
2
1
0
0
0
2
0
0
1
0
1
0
0
0
0
1
1
1
0
1
8
2
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
3
0
0
0
2
1
0
1
0
0
0
0
0
0
2
2
0
1
1
0
0
2
0
2
1
5
0
0
0
1
0
2
2
2
1
0
1
1
0
0
1
0
0
1
0
1
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
1
0
4
0
3
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
2
2
0
2
2
1
0
0
1
2
1
1
2
0
2
2
0
0
0
0
0
0
0
2
0
1
2
2
0
2
2
1
1
2
0
0
0
1
1
0
1
0
2
2
0
0
0
2
4
0
0
2
0
1
0
0
0
1
1
2
2
1
0
0
2
2
1
3
1
0
2
0
1
0
0
4
0
0
0
0
0
2
0
0
0
1
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
2
1
0
0
3
1
1
2
0
5
3
1
1
1
0
1
0
1
0
0
2
0
1
1
2
0
0
0
4
0
0
0
1
0
0
0
0
2
1
1
1
2
0
0
0
0
0
0
0
0
1
1
2
1
0
1
0
0
1
0
0
1
1
0
0
0
1
2
1
0
0
1
0
0
0
0
0
2
1
0
2
2
2
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
2
0
1
1
0
0
0
1
1
0
1
3
0
0
1
2
2
0
0
3
0
0
0
0
1
0
0
0
1
1
0
0
1
2
1
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
1
0
1
1
2
0
0
0
1
0
2
0
3
0
0
2
2
0
0
0
0
2
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
2
2
0
0
0
1
0
0
1
0
2
0
1
2
0
0
3
0
0
2
0
0
1
0
0
0
0
1
2
1
0
1
1
1
2
1
0
1
2
0
1
1
0
1
1
0
0
1
2
0
0
1
1
1
0
0
0
0
0
0
2
1
0
1
1
0
0
2
0
0
0
2
1
2
1
0
0
2
1
2
0
0
2
0
1
0
2
0
2
0
0
1
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
2
0
2
1
2
1
0
2
0
2
2
2
0
1
0
2
0
0
0
1
2
0
0
1
2
0
2
0
2
0
2
0
0
2
2
0
0
3
0
0
1
2
1
2
0
0
0
2
0
0
0
0
2
2
0
2
1
1
0
0
0
1
2
1
1
0
0
1
0
0
0
0
2
0
0
1
1
0
2
0
0
1
2
2
0
0
0
1
2
1
0
1
0
1
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
1
1
2
2
1
0
1
0
0
0
0
1
2
2
0
1
0
0
0
2
2
0
1
0
0
2
1
3
2
0
0
1
2
0
1
2
2
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
1
0
0
0
0
0
2
0
2
0
2
1
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
2
0
0
2
0
1
2
1
0
2
1
1
0
2
0
2
2
1
0
2
0
0
0
1
0
1
2
1
0
2
0
1
2
0
0
2
1
0
0
3
1
0
0
0
0
0
0
1
0
0
0
2
2
2
0
1
0
1
1
0
0
1
0
1
0
0
2
1
1
0
0
3
1
1
0
1
1
0
0
0
1
0
0
2
1
2
2
1
1
1
1
0
1
0
0
0
0
1
0
1
0
2
3
0
0
2
0
0
2
2
0
0
0
0
0
0
1
0
0
0
1
1
0
2
0
0
0
2
1
2
0
0
1
0
0
0
1
2
2
2
0
2
0
3
1
4
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
1
0
0
0
2
1
2
0
1
0
0
0
1
0
0
1
0
0
2
1
2
0
0
2
1
0
0
0
0
0
0
3
1
1
0
0
1
2
1
1
0
0
1
0
1
1
2
0
0
0
0
1
1
0
0
2
1
2
0
0
1
1
1
0
1
0
0
1
0
0
0
0
1
0
2
1
0
2
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
2
2
0
0
0
0
1
1
0
2
0
0
0
1
0
2
0
1
0
0
0
0
0
0
1
2
0
0
0
2
0
2
2
0
0
0
2
0
2
0
2
0
1
1
0
0
0
0
0
0
2
1
0
2
0
0
3
2
0
0
2
0
2
0
3
0
1
0
1
0
2
1
1
0
1
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
2
0
1
2
0
1
1
0
0
2
1
0
1
0
1
0
0
0
2
1
0
2
1
1
2
0
0
0
0
1
0
0
0
2
0
0
0
1
0
1
0
0
2
0
2
0
2
1
0
1
0
0
0
2
1
0
0
1
0
0
0
2
1
1
0
1
0
0
0
2
1
2
0
1
0
0
0
1
0
2
1
0
0
0
0
1
1
0
2
0
1
0
2
1
4
0
1
1
0
2
2
1
0
2
2
2
0
0
0
0
0
0
1
2
1
2
0
0
0
0
0
1
2
0
2
0
0
0
1
2
0
0
2
0
0
0
0
0
2
2
0
1
1
2
0
0
0
0
0
2
1
0
2
0
0
0
3
2
2
1
1
0
0
0
1
1
1
1
2
0
0
1
2
0
0
0
3
2
2
2
2
2
0
1
0
2
2
0
0
0
1
0
1
2
0
0
2
1
0
2
1
0
0
0
0
1
0
0
1
0
1
0
0
2
0
1
0
1
1
0
1
3
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
5
1
0
1
0
2
0
1
0
0
2
0
0
1
0
2
0
0
2
0
1
0
0
1
0
2
0
0
2
0
0
1
2
0
0
0
2
2
1
0
1
2
2
2
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
2
0
1
2
0
0
1
0
2
0
2
2
4
0
0
0
0
0
2
0
2
0
0
0
0
1
1
2
0
0
1
0
0
0
0
0
1
2
0
1
0
0
2
1
1
0
0
2
2
4
0
0
2
0
0
2
2
0
2
0
0
0
0
1
0
0
0
2
0
1
7
1
0
1
1
0
0
2
1
0
1
1
2
0
1
0
0
2
1
0
0
0
0
0
1
0
0
0
1
3
0
0
1
4
1
0
1
1
1
2
0
0
0
1
3
1
1
0
0
1
0
0
0
0
0
0
1
2
3
0
0
0
0
0
0
0
1
0
0
1
1
0
2
0
1
0
0
0
2
1
0
1
0
0
1
2
0
1
2
0
0
2
0
0
2
0
1
0
0
2
2
1
1
2
0
1
0
1
0
0
2
0
1
0
1
2
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
2
3
2
0
0
1
2
0
1
2
0
0
0
0
0
1
0
1
0
0
1
2
0
0
0
2
1
2
2
2
0
0
1
0
0
2
2
2
1
0
1
2
0
1
0
0
0
1
1
1
0
0
0
1
0
0
2
0
2
2
1
0
1
0
2
0
2
2
2
1
0
1
2
0
0
0
1
2
0
0
0
0
0
0
0
1
2
1
1
2
0
0
2
0
1
1
1
0
0
2
0
0
0
0
1
0
1
0
1
0
0
0
0
2
2
0
0
0
1
0
2
2
0
0
2
0
1
1
0
2
0
0
0
0
0
2
1
0
0
0
2
0
0
0
1
1
1
3
1
0
0
2
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
1
2
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
1
1
0
1
0
0
2
0
0
0
0
0
2
0
0
1
2
0
2
0
1
0
1
0
0
0
1
0
2
1
1
0
0
0
0
2
1
1
0
0
0
2
0
1
0
1
0
0
0
1
0
2
0
2
2
2
0
1
1
1
1
0
0
1
1
1
1
2
0
1
2
1
1
2
0
1
0
1
0
0
2
0
1
2
3
0
0
0
0
1
2
0
0
2
0
0
1
0
3
0
2
0
0
1
0
2
2
2
2
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
2
0
2
2
0
0
1
1
0
2
0
3
2
0
0
0
0
0
0
0
1
1
1
0
1
0
2
0
1
1
1
0
0
0
1
1
0
2
0
2
1
1
2
1
2
1
1
1
2
1
1
0
2
0
2
0
1
3
2
0
1
2
0
1
1
1
2
0
0
0
1
1
0
0
0
0
0
1
0
2
0
1
0
0
0
0
2
1
1
1
0
2
0
0
0
1
0
0
2
1
2
0
2
0
0
0
0
0
0
0
1
0
1
0
0
2
1
0
0
2
1
0
1
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
1
1
0
0
0
2
1
0
1
1
6
0
0
0
2
0
0
2
0
1
1
0
2
2
0
0
2
0
0
0
2
0
0
1
2
2
2
0
0
0
0
2
0
1
0
2
0
0
1
0
0
2
0
0
0
0
2
1
1
1
0
1
2
1
0
1
0
1
0
0
2
0
0
2
0
0
0
0
0
2
1
0
2
1
0
0
0
2
0
0
1
1
2
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
1
0
0
3
1
2
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
2
0
1
2
0
1
1
0
0
0
0
0
1
1
1
1
1
0
2
2
1
3
0
2
1
2
1
0
1
0
2
1
0
1
0
2
0
0
1
1
2
1
0
1
0
0
1
0
0
0
1
2
1
2
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
5
0
2
0
0
1
2
0
1
0
0
1
0
0
0
2
0
0
1
2
2
1
0
0
2
0
0
0
2
2
0
3
2
2
2
0
0
0
1
0
2
0
0
2
1
0
0
1
1
0
0
0
0
0
1
1
2
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
2
0
0
2
0
0
4
0
0
2
1
0
0
0
1
1
1
0
0
2
0
0
0
1
0
2
2
0
2
0
0
1
2
0
0
0
0
2
0
3
5
0
0
3
0
2
1
0
1
0
0
1
2
2
2
0
1
1
1
0
1
2
0
2
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
1
2
0
2
1
2
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
1
1
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
3
1
2
0
0
0
1
0
0
0
0
0
0
2
2
1
1
2
0
0
0
0
0
0
0
1
1
2
0
2
2
0
0
1
1
2
0
0
0
0
0
0
0
0
1
1
2
0
0
2
0
0
2
1
2
0
0
0
2
0
0
1
0
2
2
0
1
3
1
2
2
2
0
0
1
1
0
0
0
0
0
0
1
1
1
3
0
0
1
0
3
0
0
0
0
0
0
1
1
1
0
0
3
0
2
0
0
2
0
2
1
5
1
0
1
0
0
0
1
1
2
0
1
0
1
0
0
1
0
2
0
1
1
1
2
1
0
0
2
0
0
0
2
1
1
0
1
3
1
1
2
1
1
2
1
0
0
0
1
0
0
3
0
0
0
0
2
2
1
0
0
0
0
2
2
0
2
2
2
0
0
1
0
1
2
0
0
0
2
1
0
0
1
0
1
0
0
0
0
0
0
1
2
1
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
2
0
0
2
1
0
1
2
1
0
2
3
0
0
0
1
0
0
0
2
0
1
1
1
0
0
2
0
0
1
0
0
1
1
1
3
1
1
0
0
1
0
0
1
0
0
1
1
0
2
2
0
0
2
0
0
0
0
0
0
1
1
1
0
0
1
0
1
1
1
0
2
0
3
1
0
2
1
0
0
2
1
0
1
2
0
2
2
0
2
0
0
0
2
0
0
0
0
2
1
1
0
2
0
0
0
0
0
0
2
1
0
0
1
0
2
2
0
1
2
2
0
2
0
2
1
0
0
0
0
2
0
1
2
2
2
0
1
1
0
0
1
1
1
0
3
0
1
1
0
0
1
0
1
0
0
1
1
1
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
2
0
0
2
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
2
0
1
0
0
0
0
2
1
0
1
2
0
1
1
0
0
0
2
1
0
1
1
0
0
1
0
1
0
0
0
0
2
0
1
0
0
0
2
0
2
2
0
0
0
1
1
2
0
0
2
0
0
3
0
0
1
2
0
1
0
2
0
2
2
1
2
0
1
0
0
0
2
0
0
2
1
0
0
0
1
2
2
0
0
0
1
0
0
0
0
1
0
0
0
0
3
0
0
1
2
2
1
1
1
0
1
0
0
2
0
1
0
1
1
0
0
2
1
0
3
0
1
0
0
0
0
1
1
2
0
0
0
0
0
0
0
2
2
1
2
2
2
0
0
0
2
2
0
0
1
1
2
0
0
2
2
2
1
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
1
0
1
0
2
2
0
0
2
0
2
0
1
2
0
2
1
0
2
1
1
0
1
0
0
2
1
0
2
2
0
0
0
0
1
3
0
1
2
1
1
0
2
1
1
0
0
1
0
0
0
0
1
0
0
2
2
1
1
2
0
2
0
1
1
0
2
2
2
2
2
0
0
0
0
0
2
1
1
0
0
0
1
0
2
0
2
3
0
0
1
0
2
1
1
0
0
2
0
2
0
1
0
0
2
2
2
0
2
0
1
0
0
0
2
0
1
2
0
2
2
2
0
0
0
1
0
0
0
0
0
0
1
1
1
2
2
1
2
0
0
2
0
2
1
0
0
2
1
0
0
2
2
1
1
1
2
0
0
0
1
1
0
0
0
1
1
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
1
2
0
0
1
1
1
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
1
1
0
0
1
2
0
1
0
1
1
0
0
2
1
0
0
0
2
0
1
1
0
2
1
2
0
0
1
1
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
1
0
1
3
1
1
0
0
0
0
2
1
0
0
1
2
2
0
1
0
2
0
0
0
0
2
1
1
0
0
0
2
0
0
2
0
0
1
0
1
0
0
1
2
0
0
0
0
1
1
2
0
1
0
0
1
0
0
0
2
1
1
1
1
2
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
1
1
0
2
2
0
0
0
0
1
1
0
0
0
0
2
2
0
2
2
0
2
2
1
1
0
1
3
1
0
0
0
0
1
0
0
0
1
1
1
1
1
0
2
0
2
0
0
0
0
0
2
2
2
0
1
0
0
0
0
2
0
0
1
1
1
2
1
2
0
0
1
0
0
1
0
0
1
0
2
0
2
2
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
2
0
2
1
2
0
0
0
0
1
1
0
0
2
0
1
0
0
0
0
0
0
0
0
1
2
0
0
2
1
1
0
0
2
0
0
0
0
1
0
1
2
1
0
1
0
1
1
2
1
0
1
0
2
0
0
0
0
0
1
0
0
2
1
2
2
0
0
0
0
0
1
1
0
0
3
2
0
0
0
0
2
0
0
0
0
0
0
2
2
0
1
1
0
2
0
0
2
0
2
0
0
0
2
1
0
1
3
1
0
0
0
1
0
2
0
4
0
0
0
0
1
0
2
1
0
2
0
0
1
0
0
0
0
0
1
0
2
0
2
1
1
0
2
0
1
1
2
0
1
0
0
2
0
2
2
1
0
0
2
1
2
0
0
0
0
0
1
2
0
1
0
0
0
0
0
1
2
0
0
1
0
1
2
0
0
1
1
2
1
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
2
0
0
2
1
1
1
2
0
0
0
0
0
2
0
0
1
0
0
2
0
1
2
2
2
0
2
0
0
0
1
0
0
3
2
2
0
1
1
0
0
0
0
2
1
1
1
1
0
1
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
2
0
1
0
0
0
2
2
0
1
0
1
0
1
1
2
0
1
0
0
2
0
1
0
0
2
0
0
1
0
0
2
2
2
2
1
1
0
0
1
2
2
2
0
2
1
2
2
0
2
0
2
0
1
0
0
0
2
0
0
1
1
0
0
0
2
0
2
0
0
0
1
2
0
0
1
0
0
0
2
2
1
0
2
0
0
0
0
1
1
1
2
2
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
2
0
0
0
2
1
0
0
2
0
0
2
2
2
1
1
0
1
2
0
0
0
0
0
2
1
2
0
0
0
0
0
0
1
1
0
2
0
1
2
0
1
0
0
2
0
0
1
3
0
0
2
1
1
1
0
2
0
3
0
0
1
2
2
2
0
2
0
1
3
2
0
0
0
0
1
1
0
1
1
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
2
0
1
0
2
0
0
0
2
2
0
1
0
0
1
0
1
0
2
0
1
0
1
2
2
0
0
2
2
2
1
1
1
1
0
0
0
1
0
0
0
0
1
0
1
0
2
1
1
0
0
0
2
0
1
1
2
0
1
2
1
0
0
0
1
0
0
1
1
2
1
2
2
1
1
2
0
2
0
0
0
0
0
2
0
0
1
2
2
2
1
0
1
1
0
1
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
1
1
2
0
0
0
0
0
0
2
0
0
1
0
0
2
1
0
0
1
0
0
2
0
0
2
1
0
0
0
0
4
0
0
2
0
1
0
0
0
0
3
0
2
0
2
0
0
3
0
0
0
1
0
1
1
0
2
2
1
0
2
2
2
2
2
2
1
0
0
0
1
0
1
2
1
0
0
1
1
1
1
1
0
1
0
0
2
1
0
0
0
1
1
0
0
2
0
0
2
0
1
0
0
2
1
1
0
0
0
0
1
0
1
1
1
0
2
1
0
0
1
0
0
0
1
1
0
1
2
0
0
1
0
2
0
2
0
0
1
0
1
0
0
0
0
0
1
2
2
4
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
3
0
1
0
0
0
1
1
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
2
0
2
3
1
0
0
3
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
1
1
2
0
0
0
2
0
2
0
0
0
0
0
1
2
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
1
0
0
2
0
0
0
2
0
1
0
1
1
0
0
0
0
0
1
0
2
0
0
0
1
2
0
0
1
0
0
2
1
0
1
0
0
0
0
1
0
0
1
0
3
0
0
0
2
0
2
1
0
2
2
0
0
1
0
0
0
2
0
1
0
1
0
2
1
0
0
2
0
0
0
0
1
0
1
0
2
1
0
1
0
0
0
2
2
1
2
1
0
2
0
1
0
1
1
0
1
2
0
1
0
0
0
2
0
0
0
1
0
0
1
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
1
0
2
0
2
0
1
0
0
0
2
1
1
0
2
2
1
0
1
2
0
1
1
1
0
0
4
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
1
2
0
0
1
0
2
0
0
1
1
0
0
1
3
0
2
2
2
1
0
0
0
0
1
0
2
0
1
1
0
1
0
1
0
0
0
0
0
3
1
1
0
0
1
2
2
2
0
1
0
0
1
0
0
1
0
0
0
0
2
1
0
2
1
1
1
0
1
2
0
1
0
0
1
1
0
1
1
2
0
0
1
2
2
2
2
0
0
2
1
0
0
0
1
2
0
0
0
2
0
0
2
1
1
0
0
0
1
0
1
0
1
0
0
1
1
0
1
1
0
0
1
0
2
2
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
1
0
0
2
0
1
1
2
0
3
0
1
0
0
0
0
0
1
0
0
1
1
0
0
2
2
1
0
0
0
0
2
2
1
0
0
0
1
0
0
0
1
0
0
1
0
0
1
1
2
1
0
1
0
1
1
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
2
1
1
2
1
2
1
0
0
1
0
1
1
0
0
1
0
0
1
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
1
1
0
1
0
2
0
0
1
0
0
0
2
2
2
0
0
0
1
0
0
1
0
1
2
0
2
2
0
1
0
0
2
0
0
0
1
0
0
0
1
2
1
0
1
1
0
1
1
0
1
0
0
0
1
0
2
0
2
0
1
0
1
3
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
2
1
0
2
1
0
2
0
1
1
1
1
0
0
1
0
0
0
1
1
1
0
3
1
2
0
1
0
0
2
0
2
2
0
2
0
1
1
0
2
0
1
0
2
0
0
1
0
0
0
0
0
2
1
0
0
3
0
1
0
2
1
0
0
0
0
2
1
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
1
0
1
0
1
0
1
1
1
0
1
0
0
0
1
1
0
2
0
0
1
0
1
0
1
0
1
0
0
1
0
2
1
0
1
0
0
0
1
1
0
2
0
0
1
2
1
2
0
0
0
1
0
0
1
1
0
1
0
0
0
2
2
0
0
2
0
1
1
2
0
2
0
4
0
0
0
2
2
2
0
1
0
2
1
1
1
0
0
1
0
1
0
0
0
2
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
2
0
1
1
2
0
2
2
0
0
0
0
0
0
1
0
2
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
2
2
0
0
1
1
0
0
2
1
0
2
0
1
0
0
2
0
0
1
0
1
0
0
0
0
1
0
0
0
0
2
0
1
2
2
2
0
1
0
0
0
0
1
2
3
1
0
1
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
1
2
0
0
2
0
0
0
1
1
0
0
0
0
2
0
1
0
0
1
1
2
0
1
0
0
0
0
2
1
1
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
2
2
0
3
0
2
1
0
0
1
1
0
1
1
0
1
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
5
2
2
0
2
0
1
0
0
0
0
0
2
0
2
1
1
4
1
1
1
1
0
0
2
1
0
0
0
1
2
1
2
1
0
0
0
1
0
2
0
1
1
0
1
1
0
2
1
1
0
0
0
0
0
0
0
0
1
2
2
1
0
0
0
0
0
2
2
0
3
0
2
1
1
1
0
1
2
0
1
0
1
0
0
1
2
2
0
0
0
0
0
0
2
2
0
2
2
0
0
2
0
2
1
1
1
3
1
0
0
0
0
0
0
3
0
0
1
2
1
0
2
2
0
5
1
1
0
2
0
0
2
0
1
2
0
0
0
1
0
0
2
0
2
0
4
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
1
0
3
0
0
2
5
0
0
0
0
1
2
0
1
1
0
2
0
0
0
2
1
0
0
1
2
2
0
0
2
0
2
0
1
2
0
1
1
0
0
0
0
1
2
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
1
0
1
0
2
0
1
1
0
1
0
0
0
0
1
3
0
0
2
2
0
0
0
1
0
2
2
1
3
1
0
2
1
2
0
0
0
1
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
1
2
6
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
2
2
0
1
0
0
0
0
0
1
0
0
0
2
3
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
1
0
0
0
0
2
0
0
0
2
1
0
2
0
0
0
0
4
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
1
0
1
0
2
0
2
1
2
4
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
3
0
1
0
0
0
1
0
0
2
0
2
0
0
1
0
2
0
0
3
2
0
0
2
1
0
3
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
2
0
0
1
0
2
0
2
0
2
0
0
1
0
1
1
1
0
0
0
0
0
1
1
0
2
2
0
0
2
2
0
0
2
0
0
0
1
3
2
0
1
0
0
0
0
2
0
2
0
7
1
0
0
2
1
0
0
0
0
0
0
0
2
0
0
2
1
2
0
0
2
1
1
0
0
2
2
1
2
1
0
2
0
1
1
1
1
0
0
2
0
1
0
0
0
1
0
0
0
0
0
2
0
2
0
0
1
7
0
0
0
0
3
0
2
1
0
2
0
1
2
2
0
0
0
1
0
1
0
2
0
1
0
1
2
2
0
0
0
1
1
4
1
1
1
0
0
1
0
0
1
2
0
0
2
0
0
0
1
0
2
0
1
0
0
0
1
0
0
8
0
0
0
1
0
2
0
0
1
0
0
1
0
0
3
2
1
0
0
0
2
2
2
2
2
2
0
1
0
0
0
0
0
0
1
2
0
0
1
0
0
1
0
0
2
0
0
0
0
0
3
0
0
0
0
0
1
3
0
0
1
0
0
2
2
5
0
1
1
0
0
1
0
0
1
0
0
0
0
0
1
1
1
0
0
3
1
0
0
0
1
0
0
2
0
2
0
0
0
1
1
2
0
0
0
1
1
0
0
0
0
2
0
1
1
1
0
0
1
10
0
1
0
1
1
1
2
0
0
1
3
0
0
0
1
0
1
0
0
0
0
2
1
2
0
2
1
0
2
2
1
0
1
1
2
0
0
4
2
0
0
2
1
0
1
2
2
0
0
1
0
0
0
0
1
1
2
0
1
0
4
0
0
0
0
0
0
1
0
0
1
2
0
0
0
2
0
0
0
0
0
1
1
1
0
1
2
2
1
2
1
0
0
0
0
1
0
4
2
1
2
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
2
0
0
2
2
2
0
3
1
1
2
1
2
2
1
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
3
1
1
1
0
0
2
1
1
0
0
1
0
0
1
1
0
1
2
1
1
1
0
1
1
2
0
1
2
0
0
0
0
0
3
1
0
2
0
1
0
0
0
0
0
2
2
1
1
0
0
1
3
0
1
1
0
0
1
1
3
0
0
0
0
0
0
1
1
2
0
0
1
1
0
0
2
2
0
0
2
0
5
0
0
0
2
1
1
0
0
0
2
1
1
0
0
0
1
2
0
0
0
0
0
3
0
2
2
2
0
1
2
2
0
1
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
3
0
1
0
0
0
2
0
0
1
0
0
0
2
2
1
2
0
2
2
1
1
2
0
2
0
0
0
0
0
1
0
0
0
0
2
1
1
0
2
0
0
0
0
2
0
1
2
0
0
1
0
0
0
1
0
2
2
0
4
1
3
0
0
1
0
1
0
0
1
1
1
0
1
2
0
0
1
0
0
1
0
0
0
0
1
0
0
0
2
0
2
0
0
1
1
0
2
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
2
1
1
1
0
0
1
0
1
0
0
0
0
0
0
1
3
1
0
0
1
0
0
0
2
0
1
0
0
0
0
10
0
0
0
1
2
0
0
0
2
0
1
0
2
0
0
0
1
2
3
1
2
0
0
0
3
2
0
0
0
0
2
0
1
0
1
2
0
2
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
1
2
1
0
0
2
0
0
0
0
3
2
0
1
1
1
1
0
0
2
1
0
1
0
0
0
0
1
0
2
0
2
1
2
6
0
2
0
0
1
2
0
2
0
0
0
2
2
1
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
2
0
1
0
0
2
0
0
1
2
0
0
1
0
0
1
2
2
0
1
3
2
0
1
1
0
3
2
0
0
0
0
0
0
0
0
0
0
0
3
1
0
1
0
1
0
0
3
2
0
1
0
0
1
1
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
1
0
1
0
0
0
2
2
0
0
1
0
1
0
2
0
0
1
0
0
0
0
0
1
0
2
0
2
1
0
2
0
0
2
0
2
1
2
0
0
1
0
2
2
1
1
1
0
0
0
1
0
1
1
2
2
0
2
1
0
2
3
0
0
0
0
2
0
1
1
0
0
0
0
2
0
2
0
0
2
2
0
1
2
1
0
2
1
0
0
0
2
2
0
1
0
0
0
1
0
0
1
0
0
2
2
1
1
0
2
0
2
0
0
1
0
0
0
0
1
1
1
0
2
0
1
0
0
2
1
1
1
0
0
0
0
0
0
0
0
2
0
0
0
1
2
2
0
0
2
2
0
0
0
0
1
0
1
0
0
0
2
1
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
2
0
1
3
0
2
0
0
0
2
0
2
1
0
1
0
0
1
1
0
0
0
0
2
0
0
0
1
1
1
0
2
2
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
2
0
0
1
2
1
1
4
0
1
1
2
0
2
0
0
3
1
1
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
2
2
1
2
0
0
0
0
0
1
0
1
1
4
0
1
0
1
1
1
0
1
1
2
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
1
2
2
0
0
0
2
0
0
1
0
2
0
1
1
1
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
2
0
2
0
0
2
0
0
0
2
0
2
1
0
0
3
0
2
0
1
0
0
2
2
0
2
0
1
0
0
1
0
0
0
0
1
1
0
2
0
1
0
2
0
0
1
0
0
0
1
1
0
0
0
1
0
2
1
0
1
0
2
0
0
0
0
2
0
0
1
1
2
0
0
0
0
1
1
0
1
0
1
0
1
0
2
0
0
2
1
0
0
0
1
0
2
0
2
0
2
0
0
2
0
1
0
1
0
2
0
2
0
0
1
2
2
0
1
0
1
1
0
0
1
0
0
0
1
0
0
1
0
0
1
0
1
0
1
0
0
2
1
0
1
1
1
0
0
0
0
6
0
2
1
2
1
2
1
0
0
2
2
2
1
0
2
0
1
0
1
0
0
1
1
0
2
2
1
1
0
0
2
2
0
2
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
2
0
2
0
2
1
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
8
0
0
2
0
2
1
0
1
2
2
2
2
0
1
0
0
0
0
0
1
0
0
0
1
0
2
0
0
2
2
0
0
0
0
0
0
0
0
3
3
2
1
2
0
0
2
2
0
0
0
1
2
2
1
0
2
2
2
2
0
2
0
1
1
0
1
0
0
0
0
0
0
0
0
0
2
1
1
0
1
0
3
2
3
0
0
1
2
0
0
1
0
0
1
0
0
2
1
0
2
0
1
0
1
0
0
0
0
1
0
0
0
2
2
2
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
2
0
0
0
1
0
1
0
2
0
2
2
1
4
1
0
1
0
0
1
2
2
4
0
1
1
1
1
0
2
0
2
0
0
0
1
0
1
2
1
0
0
1
0
1
0
2
0
0
1
0
3
1
0
0
0
3
0
0
0
0
0
1
1
0
1
0
0
1
0
0
2
1
1
0
1
0
2
2
0
1
0
1
2
0
2
0
0
1
1
0
0
0
2
1
0
0
1
5
0
0
2
2
0
0
0
1
0
2
0
1
0
2
0
2
0
2
0
0
0
0
0
1
2
0
1
0
2
0
1
1
1
0
2
1
1
1
1
1
0
0
1
0
0
1
0
0
2
0
1
0
0
1
0
1
2
0
0
3
0
2
0
0
0
0
1
0
1
2
0
1
0
1
1
0
0
0
2
0
2
0
2
0
0
2
0
2
1
0
2
0
0
1
0
0
1
0
2
0
1
1
1
0
0
1
0
0
1
0
1
1
2
1
2
0
0
1
0
2
1
0
2
1
0
1
0
1
0
0
1
0
1
1
0
0
0
1
0
0
0
1
0
2
1
1
0
2
0
0
3
0
0
1
0
3
2
1
0
2
0
0
0
1
1
1
0
1
0
2
2
2
0
0
2
0
1
0
0
1
2
0
1
3
1
0
1
2
1
1
0
0
0
0
0
0
2
2
2
0
2
1
2
0
0
2
0
2
2
2
1
0
2
2
1
0
1
0
0
2
1
0
0
0
2
1
0
2
0
0
0
0
0
0
2
1
0
1
0
1
1
1
0
0
1
1
0
0
0
10
1
1
1
0
0
0
2
1
1
2
1
0
0
2
0
2
1
0
0
0
1
0
2
5
0
0
1
0
0
0
0
0
2
0
2
2
1
0
2
0
2
0
2
2
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
2
0
2
0
2
1
0
2
1
0
0
1
1
0
0
0
2
0
0
2
0
1
0
0
2
2
0
0
0
2
0
1
0
2
1
0
0
1
0
0
1
2
2
2
0
2
0
1
0
0
1
0
0
1
0
0
3
1
2
2
0
0
1
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
3
1
0
0
1
1
0
2
0
0
1
0
0
0
2
1
0
2
2
0
2
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
2
0
0
0
0
1
1
0
2
2
0
2
0
2
0
3
0
1
0
1
0
0
2
1
2
1
0
1
0
0
0
0
0
1
0
2
1
0
1
0
0
0
0
2
1
0
2
2
0
0
0
0
0
1
0
2
2
0
0
0
2
0
2
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
2
1
2
1
1
1
2
0
2
0
0
0
2
0
2
2
1
0
1
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
1
1
0
1
0
2
2
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
3
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
2
1
0
1
2
0
0
2
0
2
0
1
1
2
0
1
0
1
0
1
0
0
0
0
2
0
0
0
1
1
1
0
0
2
0
2
2
2
0
1
1
0
1
0
0
0
0
1
0
0
1
0
1
0
2
0
2
0
1
2
0
2
0
0
1
2
1
0
0
2
0
0
1
1
0
0
0
2
2
0
0
0
0
1
0
0
1
1
1
0
0
0
2
2
0
1
2
2
0
2
0
0
0
0
0
0
2
1
0
1
3
0
2
2
0
0
0
0
0
0
0
0
1
1
0
2
0
2
0
3
0
0
0
2
1
2
1
0
2
1
0
0
2
1
0
0
2
0
0
0
1
0
0
1
1
0
1
0
2
2
1
1
0
2
0
1
0
2
0
0
2
0
0
1
2
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
1
1
0
2
2
1
1
1
2
0
1
1
0
1
2
0
0
0
1
2
0
0
0
0
0
1
2
0
0
2
0
0
2
0
0
2
0
3
0
2
1
0
0
2
2
0
0
0
1
1
2
0
2
1
0
0
5
2
0
0
0
1
2
0
0
1
0
1
2
0
0
0
0
2
0
2
0
0
1
2
0
0
0
0
1
1
1
0
0
2
3
2
0
0
1
0
2
0
0
0
0
2
0
1
2
0
1
1
0
0
1
0
2
2
2
0
0
0
0
1
1
0
0
2
1
0
0
0
1
0
0
0
1
0
1
0
0
0
2
1
1
0
0
2
1
2
0
0
0
1
0
0
2
0
3
1
0
2
1
0
0
0
0
0
0
1
0
0
2
2
1
0
0
0
2
4
1
0
0
2
4
0
1
0
1
0
0
1
1
1
2
2
1
2
0
0
1
0
1
0
2
1
1
0
0
0
0
2
0
1
0
0
1
0
0
2
0
0
0
1
1
0
2
2
3
0
0
0
2
0
2
0
0
1
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
2
2
0
0
1
2
0
1
2
0
0
0
2
0
0
0
0
1
0
1
0
2
0
1
0
0
0
0
2
2
1
0
0
0
3
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
1
2
1
0
2
0
0
1
1
2
0
1
0
1
0
0
0
1
3
0
1
0
2
0
0
2
0
0
1
0
1
0
0
0
2
1
2
1
0
0
1
1
0
1
0
0
0
0
3
0
0
1
1
2
2
0
2
0
1
0
0
0
2
3
0
1
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
2
0
1
0
2
1
2
1
2
2
1
2
2
2
0
2
2
0
1
0
0
1
1
2
0
1
2
0
0
1
1
1
1
0
2
0
1
3
1
1
0
0
3
0
0
0
2
0
2
0
0
2
0
1
1
2
2
1
0
1
0
2
1
0
0
0
1
0
1
1
0
1
0
2
0
0
1
1
2
0
2
0
1
0
2
0
0
0
2
2
1
1
1
0
0
3
2
0
0
0
1
2
1
1
0
0
0
0
1
1
1
1
1
0
0
1
1
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
2
0
0
0
1
0
2
2
0
1
2
0
1
0
0
0
3
2
2
0
0
1
2
0
1
0
1
0
1
0
0
2
0
0
0
0
2
2
0
0
1
1
0
1
1
0
0
2
1
0
0
1
0
2
1
2
1
0
0
0
1
1
0
1
2
0
1
0
0
0
0
0
0
2
1
3
2
0
2
1
0
1
2
2
1
2
2
0
0
2
0
0
0
0
0
2
1
1
0
0
0
0
0
1
2
2
1
0
0
1
0
1
0
3
0
0
0
0
0
0
2
0
0
0
2
2
0
1
1
2
1
0
1
0
0
1
2
1
0
0
0
2
1
0
1
1
0
1
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
2
1
0
1
0
0
0
1
1
0
0
0
3
0
0
1
1
0
0
0
1
2
1
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
1
2
0
0
0
1
2
0
1
0
0
0
0
0
1
1
1
0
1
0
0
0
0
2
0
0
0
0
0
2
2
2
0
1
0
1
0
1
1
0
1
0
0
1
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
1
5
1
0
0
1
2
2
0
1
1
1
0
1
2
1
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
1
2
1
1
1
2
0
2
0
0
1
1
0
2
2
0
0
0
1
1
0
2
2
1
0
0
2
0
2
2
0
0
2
2
1
0
2
2
2
0
2
1
0
1
1
2
1
2
5
1
0
1
0
0
0
0
1
1
2
0
3
2
1
0
0
0
1
1
2
0
1
0
2
1
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
2
1
0
0
0
0
0
1
1
1
0
2
0
0
1
1
0
1
1
0
1
0
2
2
0
0
0
2
0
1
0
2
2
2
2
1
2
0
0
1
0
0
0
0
1
1
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
2
2
0
0
2
1
0
0
0
2
0
2
0
0
1
2
0
1
1
0
2
0
0
2
2
2
0
0
0
2
0
1
2
2
1
0
2
2
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
1
0
2
1
1
0
1
0
2
0
1
1
2
0
2
0
1
2
0
0
0
2
1
0
1
2
2
0
0
1
1
1
0
1
2
2
2
2
2
2
1
2
1
0
1
0
0
1
1
1
0
3
0
2
0
1
0
2
2
1
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
1
1
0
0
0
1
0
0
0
2
1
0
0
2
0
0
1
0
1
0
0
2
1
0
2
0
3
2
0
0
1
1
1
2
0
0
0
0
0
0
1
1
0
1
1
1
0
0
1
0
3
1
1
1
0
0
1
0
0
0
0
0
2
4
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
2
0
2
1
0
0
0
2
1
2
0
0
1
0
0
2
1
0
1
0
0
2
0
0
0
0
1
2
1
0
0
0
0
1
0
0
0
0
0
1
0
1
1
2
0
0
2
0
0
2
1
0
0
2
0
1
0
1
0
5
1
0
2
1
3
1
2
0
0
1
0
0
0
0
0
2
2
1
0
2
1
1
0
2
1
0
0
0
2
0
2
0
2
0
1
0
0
0
0
0
1
1
0
1
2
1
0
0
2
0
0
0
2
0
1
0
0
0
0
0
1
2
0
0
0
1
0
0
0
1
2
0
0
0
2
0
0
0
3
0
0
2
0
0
2
0
0
2
2
0
0
1
1
3
2
0
0
0
0
0
0
1
1
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
2
0
2
2
2
0
1
2
0
0
2
1
2
2
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
3
2
0
0
0
0
0
0
1
1
0
0
1
1
0
2
2
0
1
1
1
2
0
0
0
0
3
1
2
1
1
0
1
0
1
1
1
0
0
0
0
2
1
1
0
0
0
0
0
2
1
0
0
7
0
0
0
1
0
0
1
1
0
0
1
0
0
2
3
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
3
0
0
3
2
2
3
0
1
0
0
0
2
0
0
0
1
2
2
0
1
2
2
1
2
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
1
1
0
1
1
0
2
0
2
1
0
0
0
1
1
2
1
0
0
0
2
0
0
0
2
2
4
2
0
0
3
2
0
0
1
0
0
1
1
0
1
0
0
1
1
0
0
0
1
2
1
0
1
0
1
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
2
0
0
1
1
2
0
1
0
0
1
0
1
0
0
1
0
2
1
0
1
2
0
1
2
0
2
0
0
0
2
0
0
2
1
2
0
1
2
0
1
0
1
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
2
2
0
3
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
1
0
2
2
1
2
2
0
6
2
1
0
2
0
0
0
0
0
2
0
0
1
0
0
2
2
0
0
0
2
2
2
0
2
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
3
1
3
0
2
0
1
0
1
0
2
0
2
0
2
2
1
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
1
2
1
0
1
0
0
0
1
1
1
0
1
1
0
0
0
0
1
0
0
2
1
0
0
2
0
2
2
1
0
1
0
0
2
0
0
0
0
0
0
0
1
0
2
2
2
2
2
2
2
2
2
2
1
0
2
2
0
0
0
1
2
0
2
1
1
0
2
2
0
1
0
0
0
0
0
2
2
0
0
2
2
2
0
1
0
0
0
2
0
2
0
0
0
3
2
0
1
3
0
2
1
0
0
0
2
2
1
0
0
1
0
0
2
2
0
0
0
0
1
0
1
2
0
0
1
0
1
0
0
0
2
0
0
2
0
0
0
2
2
0
0
1
3
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
2
0
0
0
2
1
0
0
0
0
1
0
1
3
1
0
0
1
0
0
2
1
0
0
1
0
1
0
2
2
0
2
0
2
0
0
0
2
0
0
1
0
0
1
2
0
1
0
0
0
2
1
0
0
1
1
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
1
0
0
0
1
0
2
2
0
4
0
2
0
3
2
1
0
0
2
2
2
1
2
1
2
0
2
0
0
0
1
0
2
2
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
1
0
0
0
2
0
0
2
1
1
0
2
1
0
3
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
2
0
2
0
2
0
1
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
3
1
1
0
3
2
1
0
0
0
1
2
3
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
1
0
1
2
0
0
0
0
2
1
0
1
0
0
1
1
1
0
1
2
1
0
0
0
1
2
1
3
2
1
2
0
0
0
0
0
1
0
2
2
0
1
0
0
0
2
2
1
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
2
2
1
0
0
0
0
1
0
2
2
2
2
1
0
2
1
0
0
0
1
1
2
1
2
2
0
2
1
0
1
0
0
0
1
1
1
0
1
1
1
0
0
1
1
2
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
2
0
0
1
0
0
0
0
1
2
1
0
0
0
2
0
0
4
0
0
2
2
0
1
1
0
0
2
1
0
1
2
2
2
0
1
1
0
2
0
1
1
2
0
0
1
1
2
2
1
0
2
1
1
2
0
0
6
2
1
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
2
1
1
1
1
0
1
0
1
1
0
1
0
0
0
1
2
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
2
2
0
1
4
2
1
2
1
1
3
1
1
2
0
0
0
0
1
0
0
2
0
2
0
1
0
3
0
0
0
2
0
0
0
0
0
0
2
1
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
3
0
0
1
1
2
0
0
1
0
4
3
0
0
0
0
0
2
0
1
1
0
0
1
1
0
0
0
0
1
0
0
0
1
2
1
0
0
0
1
1
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
1
0
0
1
1
2
0
1
2
0
1
1
0
0
0
0
1
0
2
1
0
1
0
0
2
0
0
0
2
0
0
0
2
0
0
2
0
2
0
0
0
1
0
1
1
0
2
0
0
0
0
2
0
1
1
0
1
0
0
0
0
0
0
0
2
2
2
2
0
0
0
2
3
0
0
0
2
0
1
0
2
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
1
0
0
1
0
0
0
0
1
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
1
0
0
3
0
0
0
1
0
0
0
1
0
2
1
1
1
0
0
1
0
0
0
0
5
0
1
2
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
1
0
2
3
1
1
1
2
0
0
0
1
0
2
0
2
0
2
0
0
2
1
0
0
0
0
0
1
0
1
1
2
0
2
0
0
3
1
3
1
0
0
2
0
0
0
1
0
0
0
1
1
0
0
0
1
2
1
0
0
0
1
0
2
2
0
1
0
0
2
2
1
0
2
2
0
1
2
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
1
0
2
0
0
2
0
0
0
1
0
0
0
4
2
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
1
0
0
1
1
0
2
0
1
2
2
0
0
1
0
0
2
2
0
1
0
2
0
1
0
0
0
2
2
0
0
1
0
1
1
1
0
3
0
4
0
0
0
0
1
0
2
1
2
0
0
3
1
2
0
2
2
0
1
0
0
3
3
1
0
0
0
1
0
0
0
5
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
1
0
1
0
0
1
1
0
0
0
0
2
0
1
0
0
1
0
0
0
1
1
0
0
2
0
0
1
0
1
0
1
1
0
0
0
1
0
0
2
0
1
0
0
1
0
0
0
2
1
2
0
0
2
2
2
0
1
1
0
0
0
3
0
1
1
0
3
0
3
1
0
0
1
2
2
0
1
0
1
1
1
1
0
1
2
0
0
1
0
0
0
0
1
0
2
0
0
0
2
0
0
1
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
2
0
2
0
0
0
2
0
0
1
0
0
0
2
1
0
0
0
0
2
2
0
0
1
1
2
0
2
2
0
0
0
2
0
0
1
0
0
0
1
0
1
0
0
0
2
0
1
1
0
1
0
2
0
0
1
3
0
2
1
0
1
0
0
0
2
1
0
0
0
2
0
1
2
0
2
1
1
1
0
0
1
1
0
0
1
0
1
0
1
2
0
2
2
1
1
0
0
1
0
0
1
2
2
0
1
1
0
2
0
2
0
1
0
1
0
1
0
0
2
2
1
0
0
0
0
1
1
1
0
0
0
0
2
1
0
3
0
0
2
1
1
0
3
0
0
0
0
0
0
0
2
0
2
1
1
0
4
0
0
1
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
1
0
2
2
2
1
1
0
3
0
1
0
1
0
0
0
0
1
2
0
0
0
0
0
0
2
0
1
0
0
2
2
0
1
0
1
0
0
1
0
1
2
1
0
1
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
2
2
2
0
2
2
0
0
1
0
0
0
1
2
1
0
0
0
0
0
1
2
2
1
1
2
1
0
2
0
1
0
0
0
1
0
1
1
0
2
1
0
1
1
1
0
1
0
1
2
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
1
0
0
2
0
2
1
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
1
2
0
2
2
1
1
2
0
1
0
0
0
1
2
0
0
1
2
2
1
0
0
0
2
0
2
2
1
1
1
0
0
0
0
0
0
2
0
2
0
1
0
0
0
1
1
0
1
0
0
0
2
1
1
0
2
2
0
2
1
0
0
1
0
1
1
0
1
0
2
1
2
0
1
0
2
2
0
0
0
0
2
0
0
0
2
1
0
2
1
1
0
0
4
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
5
0
1
1
0
0
0
0
2
0
1
1
1
2
0
1
0
1
0
2
0
0
2
0
0
0
2
2
0
2
1
1
1
1
0
0
0
0
2
2
0
2
1
2
2
0
3
0
1
0
0
1
2
1
0
0
0
1
2
0
2
1
0
1
0
0
2
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
2
1
2
0
1
1
0
2
0
0
0
0
0
1
0
0
0
1
2
0
2
2
1
0
1
2
0
1
0
0
2
0
0
0
0
2
4
0
2
0
0
0
2
0
2
1
0
0
1
0
1
0
0
2
0
1
0
0
2
0
1
0
1
2
0
2
0
0
1
2
0
1
0
0
0
1
0
1
1
3
0
0
0
0
0
0
0
0
1
1
1
0
0
1
2
0
0
1
0
1
1
2
0
0
0
0
2
1
0
2
0
1
4
1
0
2
0
1
1
0
0
2
1
2
0
0
0
2
0
0
1
2
2
1
1
0
3
0
0
2
0
2
0
0
2
2
0
3
1
0
0
0
3
0
0
0
0
2
0
0
0
0
2
2
1
1
2
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
1
1
2
0
0
1
0
0
0
0
0
0
1
0
0
0
2
2
1
1
1
0
1
0
4
0
1
1
1
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
2
0
0
0
1
0
3
0
0
1
1
0
0
2
2
0
0
0
0
0
1
2
0
0
1
0
2
1
0
0
0
1
2
1
0
0
0
1
0
1
0
2
2
0
3
0
2
0
1
0
0
0
2
0
0
2
0
0
2
0
0
0
1
1
0
0
0
0
1
2
0
0
2
2
0
0
2
2
2
0
1
2
1
0
0
0
2
2
0
0
0
0
0
2
2
2
0
0
0
1
0
0
0
0
0
2
1
1
0
0
0
1
0
0
2
2
1
1
0
0
1
0
0
1
0
3
0
0
0
1
0
2
0
0
1
2
0
0
0
2
2
0
0
2
0
0
0
0
2
1
0
0
2
1
0
2
0
2
0
2
0
2
0
3
0
2
2
0
0
0
1
2
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
2
0
0
0
2
0
0
0
0
0
0
1
2
0
0
1
2
0
2
0
2
1
2
1
1
0
0
0
1
0
0
2
1
1
1
0
0
1
2
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
1
0
0
1
2
1
0
0
0
1
1
1
0
1
1
0
0
0
0
2
1
1
0
1
2
0
1
0
0
2
2
1
0
0
0
0
1
1
0
1
2
1
0
2
0
2
0
0
1
0
2
2
0
2
0
0
1
2
0
0
1
1
0
2
1
1
1
1
1
0
1
2
0
2
1
2
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
1
2
0
0
1
0
2
0
0
0
0
2
2
2
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
2
3
6
2
1
1
0
1
1
0
0
0
0
2
0
0
0
2
0
0
0
2
2
0
1
0
2
0
1
0
0
0
2
2
2
0
2
0
1
1
1
0
2
1
2
1
1
0
0
2
0
2
1
1
2
0
0
2
0
0
0
2
3
1
1
1
2
0
0
1
0
0
0
0
1
0
1
1
0
0
1
1
0
1
0
0
1
1
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
2
0
2
0
1
0
1
0
0
0
0
1
2
1
0
0
2
0
1
3
0
0
0
3
1
2
0
0
2
2
0
2
0
0
0
1
0
0
1
0
0
0
0
1
0
2
1
0
0
1
0
0
0
1
0
0
0
0
1
2
0
0
1
0
1
1
0
0
2
0
0
2
0
1
0
1
0
0
0
1
1
2
0
2
2
0
1
0
1
0
0
1
0
0
1
0
0
0
2
1
2
1
2
0
0
0
0
2
0
1
1
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
3
0
1
1
1
1
2
0
0
0
0
1
2
1
0
0
1
0
2
0
0
0
0
3
1
2
0
0
0
0
2
0
2
0
0
0
1
0
1
1
0
0
0
0
1
2
0
1
0
0
0
0
2
0
1
2
0
0
0
1
0
0
2
0
0
2
0
0
2
0
0
2
0
1
0
0
0
1
1
0
1
0
0
0
2
0
1
0
0
1
2
0
0
0
0
2
0
1
0
0
1
1
0
0
1
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
3
0
0
1
0
0
1
1
0
2
1
0
2
1
0
0
0
0
0
0
2
0
0
0
0
4
2
2
0
0
3
1
2
1
0
0
0
1
0
0
1
2
0
1
2
0
2
0
0
0
0
0
1
1
1
1
2
2
1
1
1
0
4
0
2
0
0
0
1
1
0
1
0
3
0
0
2
2
0
0
1
0
0
2
0
3
2
0
2
1
0
1
0
0
2
0
0
0
0
3
0
0
1
2
2
2
1
1
0
0
0
1
0
2
0
0
0
1
0
0
1
0
0
1
0
2
1
0
0
1
0
0
0
1
0
1
0
0
0
2
2
1
0
0
0
0
2
2
0
1
0
0
2
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
3
0
0
0
2
2
0
0
1
4
0
0
0
0
3
0
0
0
2
1
2
1
0
0
2
3
1
0
0
1
1
3
0
0
1
1
2
1
0
1
0
1
0
0
0
2
0
1
3
0
0
0
1
4
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
2
1
0
0
0
0
2
1
0
2
1
0
2
1
0
2
1
0
2
0
0
2
0
0
2
0
0
0
1
1
0
0
1
0
0
0
0
0
1
2
0
0
2
3
0
2
2
1
0
1
1
0
4
0
2
2
0
2
0
2
2
0
0
0
2
1
1
2
0
0
1
0
1
0
0
1
0
0
2
0
1
1
1
2
0
0
0
0
0
1
4
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
1
0
1
2
1
1
0
2
0
0
0
0
1
0
0
2
0
1
0
1
0
1
0
1
0
1
3
0
0
0
0
1
0
2
2
0
0
2
0
0
1
0
2
1
1
0
2
0
2
3
0
1
1
0
0
0
1
1
0
0
1
0
1
2
2
1
1
0
0
2
2
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
2
1
2
0
2
0
2
0
2
0
0
0
1
2
1
0
0
0
0
0
1
0
0
1
0
0
2
0
2
0
0
0
2
0
0
0
0
0
1
1
1
0
1
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
2
3
0
2
1
2
0
2
2
0
0
1
0
2
0
2
0
0
0
2
1
2
0
1
0
0
0
1
0
1
1
0
3
0
2
2
0
0
0
0
1
2
0
1
1
0
1
1
0
0
1
1
2
0
0
1
1
0
2
0
0
1
0
0
0
0
0
0
0
2
0
2
0
1
2
1
0
0
0
0
2
0
1
0
0
1
0
0
1
1
0
0
0
1
2
0
2
2
2
0
0
1
1
1
2
0
0
1
2
2
0
1
0
1
0
0
2
0
2
0
5
0
1
0
2
2
0
2
3
0
0
1
0
1
0
0
2
0
0
2
3
1
1
2
2
0
0
0
0
0
0
4
0
0
2
1
0
1
2
0
1
0
2
0
1
2
0
0
0
0
1
1
0
0
0
1
2
1
0
0
1
0
0
0
0
0
0
0
0
1
3
0
0
2
2
0
0
0
0
0
1
0
0
0
3
0
0
1
0
2
0
1
0
1
1
0
1
0
0
0
2
0
0
1
1
1
1
0
2
1
0
0
2
2
0
2
0
2
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
2
2
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
1
0
1
2
0
0
0
0
0
0
3
2
0
1
0
0
2
2
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
2
2
0
2
0
0
1
0
0
1
1
1
2
1
0
0
2
0
1
2
1
0
0
3
0
2
1
0
1
1
0
0
3
0
2
1
1
0
0
0
3
0
1
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
2
0
2
0
0
2
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
4
0
0
1
2
0
0
0
2
1
0
2
0
2
1
0
0
2
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
2
0
1
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
3
1
0
4
0
0
0
0
0
2
1
0
0
0
2
0
0
0
1
2
2
0
0
0
0
2
1
0
1
1
0
0
0
0
0
2
0
0
0
0
0
1
1
1
1
0
1
0
0
0
0
0
0
2
2
0
0
2
0
0
2
1
0
0
0
0
1
0
0
2
1
1
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
1
0
2
1
0
1
0
2
0
1
1
0
1
1
0
0
2
0
0
2
0
0
0
2
1
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
1
0
3
0
0
0
0
0
4
0
0
1
0
1
0
0
1
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
1
0
0
1
2
2
0
1
1
2
0
0
0
1
0
1
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
1
1
1
0
0
1
0
0
0
0
1
0
0
1
1
4
1
0
0
0
0
2
2
0
0
1
0
0
0
1
0
1
2
0
2
2
0
0
1
2
0
0
1
1
1
1
0
0
1
1
0
0
3
0
0
0
0
1
0
2
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
2
0
0
3
2
0
0
0
1
0
0
0
0
0
1
2
0
1
0
1
1
0
0
0
2
2
2
0
0
0
1
2
0
0
1
1
0
0
2
2
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
1
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
2
0
0
2
1
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
3
0
2
2
0
0
0
0
0
0
0
2
0
1
3
0
0
2
0
3
0
0
2
2
1
1
0
0
2
0
0
0
1
2
1
1
0
0
0
0
2
0
1
0
0
0
0
2
2
0
0
2
2
2
3
0
0
1
0
0
3
0
1
2
0
1
1
1
2
1
1
2
2
2
0
0
2
0
0
3
2
0
0
1
0
1
0
0
0
2
2
0
0
4
2
0
2
1
0
0
2
0
0
0
2
0
0
1
1
0
1
1
0
0
0
0
2
1
1
0
0
2
0
0
1
0
1
0
0
0
0
0
2
0
2
0
0
1
0
0
1
0
0
1
0
0
6
0
0
0
4
1
0
0
0
2
0
0
0
2
3
0
0
2
0
0
0
1
3
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
2
1
0
2
2
0
2
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
1
0
0
1
2
0
0
2
1
1
0
0
0
0
0
0
0
2
2
2
3
0
2
1
2
2
2
0
1
1
1
1
0
1
0
0
1
3
0
0
1
1
0
1
1
0
0
0
0
1
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
2
0
0
1
1
1
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
1
2
0
0
2
0
1
0
1
0
2
1
0
0
2
2
0
0
0
1
2
0
0
1
0
1
0
0
0
2
0
0
0
2
0
2
0
1
2
1
1
0
2
2
0
0
0
1
0
0
0
2
1
2
2
1
0
0
2
4
2
1
2
1
0
0
1
1
0
0
2
1
2
0
0
0
0
1
1
0
0
0
1
2
0
2
0
0
1
0
0
0
0
0
0
0
1
2
1
0
1
1
2
1
1
0
0
2
0
1
0
3
0
1
1
0
1
1
0
1
0
2
0
0
1
1
1
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
1
0
2
1
1
0
1
0
0
3
0
0
2
2
0
1
0
1
0
0
2
2
0
1
0
0
0
0
0
2
1
0
0
0
0
0
2
2
0
1
0
0
0
0
5
0
0
0
0
1
0
1
0
0
9
0
0
0
2
2
0
1
0
0
1
0
0
1
2
0
0
0
1
2
1
0
2
0
1
0
1
0
0
2
1
0
0
0
2
0
1
0
1
2
0
1
0
0
0
2
2
1
2
2
0
0
2
0
1
0
0
0
2
0
0
0
0
2
0
2
0
1
0
0
2
0
0
0
0
2
1
0
1
1
2
2
0
2
2
0
0
2
0
0
0
0
5
2
0
1
0
1
1
1
1
0
0
2
1
0
2
1
1
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
2
1
0
0
0
1
2
0
1
1
0
0
0
2
1
0
1
0
2
0
0
1
2
1
0
0
0
2
0
2
1
0
2
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
1
1
0
0
1
0
0
2
0
0
2
0
2
0
2
0
1
0
1
4
0
0
0
2
0
2
2
2
0
0
2
1
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
1
1
1
1
0
0
2
1
0
2
0
0
0
2
1
1
3
0
1
1
2
1
1
0
1
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
1
1
0
2
1
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
2
0
1
1
1
0
2
0
0
0
0
3
0
0
0
2
2
0
1
0
0
2
2
1
1
0
0
0
2
0
2
0
2
0
2
0
0
0
2
1
1
1
0
0
2
1
0
0
1
0
1
0
0
0
0
0
3
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
1
1
2
1
0
1
0
2
1
0
1
0
0
0
0
0
1
1
0
1
2
1
0
0
0
0
0
1
3
0
0
2
1
1
2
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
1
2
2
0
0
1
0
1
0
0
0
0
0
1
2
0
0
0
4
0
0
0
1
1
0
1
0
0
0
1
0
2
1
0
2
1
2
0
0
0
0
0
2
2
2
1
2
2
0
0
1
0
0
1
0
2
0
0
1
1
0
1
0
1
1
0
0
2
0
2
0
0
1
1
1
0
2
0
1
2
0
0
1
1
2
1
0
1
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
1
1
0
2
0
0
0
2
0
1
2
0
0
2
2
0
2
0
0
4
0
0
3
0
1
1
1
2
0
1
0
1
0
2
0
0
0
0
2
2
0
0
0
0
4
0
0
0
0
0
1
0
0
2
2
0
1
0
1
2
0
0
0
0
0
3
1
1
1
0
0
0
0
0
2
1
2
0
2
0
3
2
1
0
3
0
1
2
0
0
3
0
2
0
2
1
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
1
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
2
1
0
0
2
0
1
0
1
1
0
0
1
0
0
1
2
0
1
2
0
2
0
2
0
2
2
1
2
0
0
1
0
2
0
0
1
0
0
0
0
9
2
1
2
0
2
1
1
1
2
0
1
0
2
0
0
4
0
0
0
2
1
1
2
0
1
1
0
0
0
0
2
1
1
0
0
2
0
0
2
1
2
0
0
0
0
0
0
0
1
0
1
0
2
1
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
1
2
1
0
0
0
0
2
1
1
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
1
2
1
1
2
2
0
0
1
0
0
0
2
2
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
1
2
1
0
0
0
1
0
1
0
0
0
3
2
1
0
1
2
3
0
0
0
0
2
1
0
2
0
0
2
1
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
1
0
1
0
1
1
1
0
0
1
0
1
0
0
1
0
0
0
0
2
1
0
3
0
0
0
0
0
2
1
2
1
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
2
1
3
0
1
0
0
0
1
0
0
0
0
0
0
2
2
0
1
0
0
2
0
0
1
2
0
1
2
0
1
0
1
0
0
1
0
1
0
0
0
1
0
3
1
2
1
0
0
0
0
2
1
0
2
1
0
1
0
0
0
0
2
0
1
1
0
1
1
2
0
3
0
0
2
0
2
1
2
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
2
1
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
1
1
0
1
0
0
0
1
0
7
0
0
2
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
2
1
0
0
0
0
0
1
2
0
2
2
3
0
2
0
1
1
0
0
2
1
3
0
0
0
1
0
0
7
0
0
0
2
0
0
0
1
1
0
0
1
2
0
2
1
0
0
0
1
3
0
0
0
0
0
2
1
0
0
2
0
0
0
0
2
1
1
0
0
2
2
1
2
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
2
0
1
1
0
0
2
1
1
0
3
3
1
0
0
2
0
0
2
1
0
0
2
1
2
0
2
1
2
0
2
0
0
0
1
1
0
2
2
2
0
0
1
1
2
0
0
5
6
0
0
1
0
1
0
0
0
1
0
0
1
2
0
1
0
1
2
1
1
1
0
1
1
0
2
1
0
1
0
1
2
0
1
2
1
1
0
1
0
2
0
2
0
0
3
0
2
0
10
0
0
2
3
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
2
0
2
1
0
0
0
2
3
0
0
0
0
1
1
0
0
2
1
1
1
1
0
0
1
1
0
0
1
0
0
0
0
2
2
0
2
0
0
1
1
0
0
0
0
1
1
1
1
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
1
1
0
1
2
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
3
0
2
2
1
0
1
0
3
1
0
0
2
0
0
1
2
2
0
2
0
0
2
0
0
2
0
0
0
0
1
2
2
0
1
0
1
0
2
2
0
0
0
0
0
0
1
0
0
0
1
1
2
0
1
1
1
0
1
0
0
1
0
0
0
2
2
0
0
0
0
0
0
2
1
1
2
0
0
0
0
1
2
3
1
0
0
0
1
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
2
1
0
0
0
2
0
0
2
1
0
0
0
0
0
3
2
1
2
2
0
1
1
1
2
1
1
0
1
1
0
2
2
0
0
0
0
2
1
2
0
1
2
0
1
2
0
0
1
0
2
0
1
1
2
2
1
1
0
0
1
0
1
1
0
2
0
0
6
0
2
0
0
2
1
2
0
0
2
1
0
0
0
1
1
3
0
1
0
0
1
2
0
2
0
2
0
0
0
0
2
2
0
0
0
0
0
1
0
1
0
1
0
0
0
2
0
0
0
0
0
3
1
1
0
2
1
0
1
1
0
0
0
0
6
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
2
1
2
1
1
0
0
1
2
2
2
1
2
0
2
1
0
0
0
1
0
0
2
0
2
0
2
0
1
0
0
0
0
0
1
1
1
0
0
0
0
2
0
1
2
1
0
0
1
0
2
0
0
2
1
0
1
0
2
1
0
2
1
0
2
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
1
0
2
1
1
1
0
1
0
0
1
0
1
0
2
2
1
0
0
0
2
0
0
2
1
0
0
1
4
1
2
2
0
1
0
1
2
2
0
2
0
2
0
1
0
1
0
0
1
0
0
2
0
0
2
2
1
2
0
2
0
0
0
0
0
1
1
3
0
0
0
0
2
2
0
0
2
0
0
1
0
4
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
3
0
0
1
2
0
0
0
1
0
1
1
0
3
0
0
0
0
0
2
0
0
2
0
2
1
0
1
0
0
0
0
1
0
1
1
0
1
0
2
1
0
0
1
0
1
3
0
0
0
1
1
1
2
0
0
0
1
2
2
0
1
1
0
0
2
0
2
2
1
0
1
0
0
3
1
0
9
2
2
0
0
1
0
1
0
0
0
0
0
2
0
0
3
0
0
2
1
2
0
0
1
0
3
1
1
0
0
0
0
0
1
2
0
2
0
0
2
0
1
0
2
3
0
2
0
2
0
0
0
0
2
1
0
1
0
0
1
0
1
1
2
0
0
0
1
0
1
1
0
0
0
1
0
0
0
2
0
0
0
2
2
0
0
0
0
2
2
0
2
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
2
1
0
0
2
0
1
0
0
0
1
1
2
0
0
2
3
0
2
1
0
0
0
0
1
0
0
0
0
2
1
0
2
1
0
0
0
0
2
1
1
1
2
1
0
0
2
0
1
0
1
0
0
0
0
0
0
2
2
2
0
0
1
2
0
0
0
2
1
0
1
0
0
0
2
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
2
2
1
2
0
2
0
2
2
0
0
2
1
0
2
0
0
2
1
2
1
1
0
0
0
2
2
0
0
0
1
0
1
0
0
0
2
0
1
1
2
1
1
0
1
0
0
0
1
2
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
1
4
0
0
2
0
2
0
0
1
0
0
0
0
0
1
2
0
0
1
0
0
0
2
2
0
1
0
0
2
0
0
0
2
0
2
2
0
9
1
1
0
2
0
2
0
1
0
1
0
0
1
1
1
2
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
1
2
1
0
0
1
0
0
0
1
0
2
0
0
0
0
2
1
0
0
0
1
2
1
1
1
1
0
0
0
2
2
1
0
1
1
0
2
2
0
0
1
2
1
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
4
0
1
1
0
1
1
0
0
0
0
2
0
0
0
0
1
4
2
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
3
1
2
0
0
1
2
0
0
0
0
0
0
0
0
2
0
1
1
0
0
1
0
0
2
0
1
0
0
0
1
0
3
0
0
2
0
0
2
2
0
0
0
0
0
0
0
1
1
2
0
2
3
0
0
2
0
1
2
1
0
1
0
2
0
0
2
0
0
0
0
0
0
1
1
0
1
0
1
2
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
2
2
1
0
0
1
0
1
2
1
0
0
2
0
5
1
2
0
1
0
2
0
1
1
4
0
0
0
0
0
0
0
2
0
0
0
1
2
0
1
1
0
0
2
1
2
2
1
0
0
0
1
1
0
0
0
0
0
2
1
0
0
0
1
0
0
1
0
0
0
0
0
2
0
1
0
0
1
2
0
0
0
0
1
0
2
1
2
1
0
1
0
0
0
0
1
2
0
2
2
2
2
1
1
2
0
1
2
0
1
0
0
1
0
1
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
2
0
2
0
0
0
0
0
1
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
1
0
0
0
0
0
0
1
2
0
0
2
0
2
0
1
2
0
0
1
0
0
0
0
0
1
0
2
0
2
0
2
2
0
0
0
2
1
1
2
1
0
1
1
0
2
0
0
0
2
1
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
1
0
0
0
0
1
2
0
0
2
2
2
0
2
0
2
0
2
1
0
3
2
1
0
2
0
0
1
0
0
0
0
2
0
0
1
1
2
0
0
1
0
1
1
1
0
2
0
3
1
1
0
2
0
2
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
1
1
2
1
0
2
1
1
0
1
2
2
0
0
0
2
2
0
0
3
0
0
0
0
1
0
0
0
0
2
1
0
1
0
2
1
0
2
0
0
1
1
1
0
0
0
0
1
0
3
1
2
2
1
1
0
1
0
0
0
0
0
0
1
1
0
0
2
0
1
2
0
0
0
0
0
0
0
1
2
1
0
0
1
2
1
1
0
0
0
1
1
2
3
0
1
0
0
1
0
1
1
2
0
0
0
0
0
0
0
2
3
0
1
0
1
0
0
0
1
1
2
2
0
1
0
0
1
0
2
0
0
1
0
2
2
0
0
1
0
0
0
2
0
1
2
0
0
2
0
1
0
1
0
0
0
0
2
0
1
0
1
0
1
0
1
1
1
1
0
0
2
2
1
2
0
0
0
0
1
0
2
0
0
1
0
0
0
0
1
2
2
2
0
0
0
2
0
1
0
0
0
2
1
0
0
0
0
2
1
0
0
2
2
1
1
0
1
2
0
3
2
0
0
2
0
1
2
0
0
0
4
0
0
0
0
2
0
0
1
1
0
1
0
0
1
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
2
0
0
2
0
1
0
0
1
1
0
1
1
2
1
0
0
1
1
1
1
0
1
1
0
1
0
0
2
0
2
1
2
1
0
0
0
0
1
0
0
1
2
0
2
2
2
1
0
0
2
0
2
1
0
2
0
2
2
2
2
0
0
1
2
0
0
0
0
2
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
2
1
0
0
0
2
0
1
0
0
1
0
2
0
0
2
0
0
2
2
0
0
1
0
2
0
0
1
0
1
0
2
2
2
0
0
0
0
0
0
2
0
0
2
0
2
1
0
0
1
2
0
0
0
0
0
1
0
2
0
1
0
1
2
0
0
2
0
0
2
1
1
2
3
0
2
2
0
2
0
0
0
2
0
0
0
0
0
0
2
2
2
0
1
0
0
1
0
0
2
2
1
0
1
1
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
2
0
0
2
0
1
0
1
0
1
2
1
2
0
1
0
1
0
2
0
0
0
0
0
0
0
2
1
0
3
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
1
2
0
2
0
4
1
0
0
2
1
2
0
1
0
2
0
2
1
0
2
1
0
1
0
0
1
0
0
0
1
0
2
0
0
0
2
0
2
0
0
0
0
1
1
0
0
0
0
3
0
0
1
0
0
1
2
0
1
0
0
1
0
0
0
1
0
1
1
0
0
1
2
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
3
0
0
1
1
0
0
0
0
0
2
0
0
1
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
1
2
2
2
0
0
1
3
0
0
0
2
0
0
0
1
1
1
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
2
0
0
1
1
0
0
0
1
2
0
1
2
1
0
1
0
0
1
0
0
1
1
2
0
1
0
1
3
0
1
1
2
3
0
0
0
0
2
0
0
0
2
0
0
2
0
3
0
2
0
0
0
1
2
2
0
1
2
2
2
0
0
3
3
1
0
0
0
0
2
0
0
0
1
0
0
2
0
0
1
3
0
1
0
1
0
0
0
0
1
0
0
0
1
0
1
0
1
0
2
0
0
1
0
1
1
1
0
1
0
0
1
2
0
0
1
2
1
2
0
1
1
1
0
0
0
2
1
0
0
1
0
2
0
1
0
2
0
0
1
0
0
1
0
0
0
1
0
1
0
1
0
1
2
0
5
0
0
0
1
0
0
0
1
2
2
2
1
0
0
0
0
0
1
0
0
0
3
1
0
2
0
0
0
0
0
0
1
0
0
2
1
1
0
2
0
0
1
0
1
1
1
0
0
0
0
1
0
2
0
1
0
0
0
2
2
0
0
0
0
0
3
0
2
0
0
1
0
0
0
0
1
0
2
0
1
1
0
1
0
0
0
1
0
1
3
0
1
0
1
1
0
0
0
1
1
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
1
1
1
1
0
2
1
0
2
2
0
0
0
0
0
0
0
1
2
0
3
0
0
2
0
0
0
2
1
0
1
0
0
1
0
0
3
1
0
1
2
0
1
4
0
0
1
1
0
0
1
0
1
2
2
0
0
1
0
0
1
0
1
2
0
2
2
0
0
0
2
0
2
0
2
0
0
2
0
1
0
0
1
0
0
1
2
0
1
0
0
0
0
0
2
2
0
1
0
0
2
0
0
1
2
1
0
0
1
0
0
2
0
2
0
0
0
0
0
1
0
1
2
1
2
2
2
1
0
0
2
0
0
3
0
1
0
0
1
0
2
2
2
0
0
2
0
1
1
0
2
0
0
1
2
2
0
2
0
0
3
0
0
0
2
0
2
0
1
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
2
2
0
1
2
0
0
2
2
0
0
2
0
2
0
1
1
0
1
2
0
1
1
3
0
0
0
2
0
0
2
1
2
0
2
1
1
0
0
0
1
1
1
0
0
0
0
0
0
2
0
2
1
1
1
0
0
1
0
0
1
2
2
0
0
3
5
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
2
2
1
1
1
2
2
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
2
2
1
0
0
0
1
0
1
2
2
2
0
2
0
2
1
1
3
1
0
1
0
0
0
0
0
2
0
0
1
0
0
0
2
0
1
0
1
0
0
2
1
1
2
0
3
0
1
0
2
1
1
0
2
1
1
2
1
0
2
0
2
0
2
0
1
3
1
0
1
1
0
0
0
0
0
0
0
1
1
0
3
0
0
0
0
0
1
2
1
0
1
1
0
0
2
1
2
0
0
2
1
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
1
0
0
1
2
1
1
1
0
0
0
0
1
0
0
0
1
2
2
0
0
0
1
1
1
1
2
0
0
0
0
0
0
0
2
0
0
2
0
0
1
1
2
0
0
1
0
2
1
3
2
0
0
0
0
2
2
1
0
0
1
2
0
0
1
1
0
0
2
1
1
0
0
0
2
0
2
0
0
0
1
2
0
10
2
0
1
2
1
1
2
0
1
0
0
1
0
0
1
0
0
2
2
1
1
1
0
0
0
0
0
1
0
0
1
1
0
1
0
2
0
2
0
2
2
0
1
1
0
1
0
0
3
1
0
2
1
1
0
1
0
0
4
0
0
0
0
2
1
0
2
1
0
2
0
0
0
0
2
1
0
0
0
2
1
2
2
2
0
0
0
0
0
2
2
0
0
0
1
2
0
1
0
0
0
0
0
1
0
0
0
2
1
0
0
0
1
0
0
0
1
0
3
2
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
1
0
0
0
0
0
2
2
0
0
1
0
2
0
2
0
1
2
0
2
0
0
0
2
1
0
1
0
0
3
0
0
1
0
0
1
2
0
0
0
0
1
1
2
2
0
0
1
1
1
0
0
0
2
2
0
2
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
2
1
2
0
0
0
0
0
2
0
4
0
1
1
2
1
0
1
1
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
3
0
0
0
2
0
0
0
1
0
1
0
0
0
0
2
2
0
1
1
0
0
0
0
0
2
2
2
1
1
3
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
3
2
0
1
0
0
0
3
1
0
0
2
1
0
2
2
0
0
2
1
0
0
0
0
0
0
0
2
1
0
1
0
1
0
0
2
0
0
2
1
2
2
1
0
2
1
0
0
0
0
0
1
1
0
1
0
0
1
0
0
2
1
2
0
0
1
0
1
2
1
1
1
0
0
0
0
0
2
1
0
8
2
2
0
1
2
1
0
0
3
0
2
0
2
0
1
0
2
2
2
1
1
0
0
0
1
0
2
0
1
1
0
0
1
1
0
0
1
0
0
0
2
0
0
0
1
1
2
1
0
0
1
2
2
1
0
0
1
0
0
0
0
0
0
0
1
0
2
1
0
1
0
2
0
1
1
0
0
0
0
1
0
0
1
0
0
0
1
1
0
3
0
1
0
0
0
2
0
3
3
0
0
0
2
0
0
0
0
1
2
0
0
1
0
0
2
2
4
1
0
2
2
0
1
1
0
0
1
0
0
0
1
1
0
2
1
2
1
0
0
1
1
1
2
0
0
0
1
0
0
0
0
0
0
0
2
2
1
1
1
0
1
1
0
2
0
0
1
2
0
0
2
0
1
1
0
0
0
2
0
1
0
0
0
1
2
0
0
0
0
1
0
0
0
0
2
0
2
0
0
1
1
2
0
2
0
0
2
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
2
1
2
2
1
1
0
0
1
0
0
0
0
1
1
1
0
2
2
1
1
0
0
2
0
2
0
1
0
1
0
1
0
1
0
0
0
2
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
1
5
0
0
0
1
0
2
0
0
1
0
0
1
2
0
0
1
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
1
4
1
0
0
0
0
0
0
2
0
0
0
3
2
0
1
0
0
0
1
2
2
0
0
1
0
0
1
2
0
0
1
1
2
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
1
2
0
1
1
0
0
0
1
0
0
2
0
1
0
2
0
0
0
3
2
1
0
0
0
0
0
2
1
2
0
0
1
0
0
2
0
0
0
1
0
1
1
2
2
0
2
0
1
1
3
2
0
0
0
0
1
1
0
1
0
0
1
1
0
0
2
2
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
2
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
3
1
2
2
2
0
1
1
0
4
0
0
2
1
0
2
0
0
0
1
2
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
2
0
1
0
3
2
0
1
2
0
0
0
1
0
2
0
0
1
0
0
0
1
0
0
0
1
2
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
1
0
1
0
0
0
0
3
0
0
1
0
2
0
1
0
1
2
1
1
0
0
1
1
2
0
1
1
2
1
0
0
2
0
0
2
1
1
0
1
0
1
0
0
3
1
2
0
0
0
0
0
0
1
0
1
0
1
2
0
0
1
0
1
2
0
0
2
1
0
2
0
0
2
2
1
0
1
0
0
0
0
4
2
0
2
0
1
3
0
3
0
1
0
0
0
1
1
0
0
1
0
0
0
1
0
2
2
0
1
0
2
0
0
0
0
0
1
2
0
0
0
1
0
0
0
1
0
0
1
1
0
0
2
0
0
0
0
0
1
1
1
1
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
2
0
0
0
1
1
0
0
0
1
1
0
0
0
1
0
0
0
0
2
1
4
0
2
1
1
0
0
2
0
1
0
1
0
0
0
0
2
0
0
0
0
1
0
0
1
2
1
0
2
1
0
0
0
2
0
1
0
0
0
0
2
1
0
2
0
1
1
1
2
1
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
2
1
0
1
1
1
2
0
2
2
0
1
2
1
0
0
2
2
2
0
0
0
0
1
2
2
0
1
0
0
0
1
1
2
2
0
0
0
0
1
2
2
0
1
0
0
0
0
0
1
0
3
0
0
0
1
0
0
0
1
1
0
1
0
0
0
1
2
1
0
1
0
2
2
0
1
0
1
0
0
0
0
0
1
0
0
2
0
1
0
1
2
1
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
1
1
0
0
0
1
2
0
2
1
1
2
1
2
0
0
1
0
0
2
0
1
0
2
0
1
1
1
0
2
0
0
1
0
0
1
0
0
1
0
2
1
0
0
0
2
5
1
1
1
1
0
0
0
0
0
2
1
0
2
0
2
1
2
0
1
0
0
1
1
0
0
0
0
2
2
1
0
1
1
1
1
0
0
2
1
1
0
0
0
1
2
0
0
1
2
1
0
2
1
0
2
1
0
3
0
0
0
0
2
0
0
2
0
0
0
0
0
1
1
0
2
1
0
2
1
1
1
0
1
0
2
0
2
0
0
0
0
0
3
1
0
0
0
1
0
0
0
1
1
0
0
0
0
2
2
2
11
0
1
0
2
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
3
0
3
0
0
1
1
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
1
0
2
2
0
4
0
2
1
1
0
0
1
0
2
0
0
1
0
2
1
1
1
1
0
0
0
0
0
2
0
1
0
1
0
0
0
0
1
0
0
1
1
0
2
0
2
2
0
0
2
0
2
0
0
0
1
2
2
0
0
2
0
2
1
1
2
0
2
0
1
0
3
0
1
2
2
0
0
2
0
0
0
2
0
2
3
1
2
0
0
1
0
0
2
0
2
1
0
0
2
2
1
0
0
0
0
0
0
1
2
0
1
1
0
0
1
2
0
0
0
0
0
0
1
0
2
1
1
0
2
0
3
1
0
2
2
0
0
1
2
0
2
1
1
0
0
0
0
0
1
1
0
0
2
0
0
0
0
1
1
0
0
5
0
0
2
2
1
1
0
1
0
2
0
1
2
2
1
0
0
2
0
0
1
2
0
1
0
0
1
1
0
3
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
1
0
0
2
1
0
2
0
0
0
0
2
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
1
1
0
0
1
2
2
0
0
0
1
2
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
1
0
2
1
0
3
1
0
1
2
0
1
2
0
2
0
0
1
1
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
1
1
1
1
0
0
2
0
0
0
2
2
1
0
1
0
0
0
2
2
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
2
0
1
1
0
0
1
0
0
0
2
0
2
3
0
0
1
0
2
1
0
0
0
2
0
0
0
2
0
0
0
2
0
3
1
1
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
2
0
1
2
2
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
2
2
0
3
0
3
2
2
0
2
2
0
0
0
2
2
0
1
1
1
1
1
0
0
1
1
0
0
0
0
1
2
2
0
1
0
0
2
0
0
0
1
3
0
0
0
2
0
1
1
1
0
1
0
1
0
0
0
2
0
2
1
1
0
1
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
2
0
0
0
3
0
0
1
1
0
0
3
1
1
0
0
0
1
1
0
2
2
2
2
0
0
0
1
0
0
0
0
4
2
0
0
1
0
0
2
2
1
1
2
0
3
0
2
1
0
3
0
2
1
0
0
0
0
0
2
0
2
0
0
0
1
0
0
1
1
1
0
2
0
0
0
0
1
1
1
0
2
2
1
2
1
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
2
2
2
1
0
0
2
1
1
2
1
1
0
1
0
1
0
0
2
1
2
2
1
1
2
2
2
0
1
2
0
0
0
0
2
0
1
0
1
0
0
0
0
2
0
1
2
2
0
2
1
0
0
0
0
3
1
0
0
0
0
0
0
0
0
2
1
1
2
3
1
3
0
3
1
1
0
3
0
2
0
2
1
0
0
1
0
1
1
2
0
0
1
1
0
1
0
1
1
2
0
1
1
2
0
2
0
0
0
2
1
1
0
0
0
1
1
1
0
1
1
1
1
1
0
1
0
1
1
2
0
1
0
0
0
1
0
0
0
0
0
1
0
0
2
1
3
2
0
0
1
0
2
0
0
0
1
2
0
1
0
0
2
0
0
0
3
0
0
0
0
1
4
1
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
1
2
0
0
2
1
0
1
1
0
2
0
0
1
0
1
2
0
0
2
0
2
1
2
3
2
0
2
0
2
1
1
0
0
0
0
2
0
5
2
0
1
1
2
0
1
1
0
2
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
5
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
2
1
0
0
1
1
0
0
0
1
0
0
1
1
0
1
0
2
0
2
0
1
2
0
0
0
1
1
0
0
0
3
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
1
1
0
0
0
0
0
1
1
1
1
0
0
1
0
0
1
2
0
0
0
2
0
0
0
2
2
1
1
0
0
0
0
0
0
1
0
0
2
0
1
2
0
0
0
1
2
1
1
0
0
0
0
1
0
0
7
1
1
2
0
1
2
2
1
0
0
1
0
0
0
0
0
1
1
1
0
0
2
0
1
1
4
0
0
0
2
2
0
1
0
1
3
1
0
1
0
2
0
1
1
0
0
1
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
4
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
1
1
0
1
3
0
1
0
0
2
1
0
0
2
1
0
2
0
0
0
0
0
2
0
0
1
0
0
2
0
0
1
0
0
0
0
1
1
0
0
0
2
0
1
2
2
0
0
0
1
0
1
2
0
0
0
1
0
0
0
0
1
1
0
0
0
3
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
2
0
0
0
0
1
0
1
0
0
0
1
1
0
2
0
2
0
0
0
0
1
2
1
2
0
0
1
1
0
2
0
2
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
2
0
2
0
2
0
1
0
0
4
1
1
1
0
0
0
2
0
1
2
0
0
0
2
0
0
1
2
2
0
0
0
0
0
0
2
1
0
0
2
2
0
0
2
0
0
2
1
0
1
1
1
1
0
0
1
0
1
0
0
0
2
0
0
2
2
0
1
0
2
0
0
2
2
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
2
0
2
1
0
0
1
0
1
0
0
0
1
1
1
0
2
0
0
1
1
0
2
1
0
0
0
0
1
0
2
0
0
2
0
1
0
1
2
0
0
0
0
0
2
1
1
1
0
0
0
2
2
0
0
0
0
0
0
0
2
1
0
0
0
0
1
1
0
1
0
1
2
0
1
0
0
1
2
0
0
0
0
0
0
1
1
1
2
1
3
0
0
0
1
0
1
1
0
2
0
0
0
0
0
1
2
1
0
0
1
2
0
0
0
2
2
2
1
0
0
0
1
0
0
0
2
0
1
0
0
1
2
0
0
0
1
2
0
0
1
0
0
0
2
2
0
2
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
1
1
1
0
0
2
0
0
0
1
2
0
2
0
0
0
1
1
0
0
2
1
0
0
1
0
1
1
1
2
1
1
2
0
0
1
0
0
0
0
0
2
3
0
0
0
0
1
0
0
2
2
0
0
0
0
2
0
2
0
0
0
1
2
0
0
1
2
0
1
1
2
0
2
0
1
1
2
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
1
1
1
2
1
0
1
0
1
0
0
0
1
0
2
1
0
0
0
2
0
1
2
2
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
3
1
0
0
0
2
1
1
2
0
1
2
0
0
0
2
1
0
0
1
0
0
1
1
0
0
0
0
0
3
0
1
1
1
1
0
2
1
0
1
2
2
0
0
0
2
0
0
0
0
1
1
2
1
0
1
1
2
0
0
0
2
1
0
2
0
0
0
0
0
0
1
0
0
1
1
1
2
0
0
0
0
0
2
0
0
2
2
1
1
1
0
0
1
0
0
1
1
0
0
1
0
2
0
0
2
0
0
2
0
0
1
0
1
1
0
2
0
0
0
2
0
2
0
2
1
0
0
1
1
1
1
0
1
1
0
0
1
0
0
0
0
1
1
2
0
0
1
0
1
0
1
0
0
2
2
1
0
2
1
2
1
0
1
2
1
0
1
0
0
0
0
0
0
2
1
0
1
0
0
0
2
0
0
2
0
0
0
0
1
0
1
2
0
1
2
0
1
4
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
1
0
1
1
0
0
0
1
2
1
0
1
0
0
0
0
0
2
1
1
2
1
0
0
0
0
0
0
0
0
1
1
0
1
0
1
2
0
0
1
1
2
0
0
0
1
0
2
2
1
0
1
0
0
0
1
2
1
0
1
0
0
2
0
1
0
1
1
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
2
0
0
0
0
1
0
1
0
0
2
1
0
0
4
2
0
0
0
1
0
2
0
1
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
2
2
1
0
1
2
0
1
0
0
30
0
0
1
1
0
3
0
1
1
0
1
0
0
0
1
0
0
2
2
0
0
0
0
2
0
1
0
2
0
1
1
3
0
0
0
0
2
1
0
0
0
1
1
1
1
0
0
2
1
0
0
0
2
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
2
0
0
2
0
0
1
0
0
2
1
0
0
0
0
1
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
2
2
2
2
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
2
0
0
1
1
2
0
2
0
0
0
0
0
0
2
1
2
2
0
1
0
1
0
1
0
0
0
0
0
0
1
2
0
0
1
1
0
2
0
0
0
0
0
0
0
1
1
2
2
0
0
0
0
0
1
0
3
1
2
2
0
0
0
0
2
1
0
0
0
0
1
0
1
2
0
0
2
2
0
3
0
2
0
1
0
0
0
2
0
0
0
2
0
1
1
2
0
0
0
1
0
1
0
1
1
2
0
0
1
1
0
1
0
0
1
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
1
0
1
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
1
0
1
0
0
0
0
2
2
2
0
0
0
0
1
1
0
1
0
1
0
0
1
1
1
1
2
2
1
0
1
0
0
0
2
1
0
0
1
2
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
1
2
0
0
0
0
2
0
0
1
0
1
0
2
0
0
0
2
0
0
0
2
0
0
1
2
0
2
2
1
0
2
0
0
2
0
1
0
0
0
0
2
0
0
0
0
2
1
1
0
0
1
0
0
2
1
1
0
2
1
2
0
0
1
0
1
2
2
0
2
0
0
0
1
0
2
1
1
3
1
1
1
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
2
1
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
4
2
0
0
0
1
2
1
0
0
1
1
2
0
2
0
1
0
3
0
0
0
0
0
0
1
2
0
0
2
1
2
2
0
1
0
0
2
0
2
0
0
0
1
1
3
1
0
0
1
0
0
0
1
2
0
0
0
1
0
0
2
0
0
2
0
1
2
0
0
0
0
0
0
0
2
0
1
0
1
0
0
3
0
0
0
2
2
1
0
0
2
4
2
0
0
2
0
2
1
0
0
0
0
2
0
0
1
0
0
0
1
3
2
0
2
1
3
0
0
2
1
0
0
1
1
0
2
0
0
2
0
0
0
1
0
0
1
1
0
1
3
0
0
1
0
0
0
0
0
0
2
1
0
1
1
1
1
0
0
1
0
0
1
2
1
0
0
1
0
2
1
0
0
0
1
0
0
0
0
1
0
0
0
0
4
0
0
4
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
1
2
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
1
1
3
0
1
0
2
0
0
1
2
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
1
2
0
2
0
1
0
0
0
5
0
0
2
0
0
0
1
2
2
0
0
1
1
2
1
0
2
0
0
1
1
1
0
1
0
1
0
1
2
2
0
0
0
2
0
3
1
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
1
1
1
0
0
2
0
2
2
1
1
0
1
0
1
2
2
2
0
1
1
2
0
0
1
0
2
0
0
2
0
2
1
0
1
2
0
0
0
1
0
0
0
0
2
2
1
0
0
1
3
0
1
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
3
0
0
0
0
0
2
0
3
2
2
1
2
1
0
0
6
1
2
1
0
0
2
1
0
1
0
1
0
0
0
1
0
0
0
1
2
0
0
3
0
0
2
0
2
0
2
0
1
0
0
0
0
0
0
0
0
1
0
2
1
1
2
1
1
0
1
2
0
1
0
0
0
0
0
2
0
0
1
0
0
1
1
1
0
2
2
2
0
1
0
2
0
0
1
0
2
1
0
2
0
0
0
0
0
0
1
0
0
0
1
0
4
0
0
1
1
1
0
1
1
0
0
1
0
0
0
0
1
0
2
0
2
0
0
0
0
1
1
2
1
2
1
0
1
0
1
2
0
2
0
0
0
1
1
3
0
0
2
0
0
0
2
1
1
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
1
0
1
0
1
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
1
2
2
0
0
0
2
0
0
1
0
1
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
1
0
0
1
1
2
2
1
0
0
2
0
0
1
0
2
1
0
2
0
0
2
1
0
0
0
1
0
1
0
0
1
0
0
0
0
1
2
0
2
0
0
0
2
2
0
1
0
0
1
0
0
3
1
0
1
2
0
0
2
0
0
0
1
0
0
0
2
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
1
2
0
0
2
2
0
0
1
1
0
1
0
1
0
0
0
2
0
0
1
0
0
0
1
1
0
0
0
1
0
0
1
0
0
1
2
2
0
0
0
0
2
1
0
0
1
0
0
0
1
0
0
0
2
1
2
0
2
1
0
0
0
0
1
2
0
2
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
1
0
1
1
3
0
0
0
1
0
1
0
0
1
0
2
0
0
0
1
0
2
0
1
1
0
2
1
0
1
2
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
2
2
0
2
1
1
0
0
0
3
1
0
1
2
0
0
2
0
0
0
0
0
0
2
0
0
0
1
1
2
1
0
1
0
1
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
4
0
0
1
0
2
2
2
0
1
2
0
1
0
1
1
2
0
0
2
1
0
0
0
0
0
0
0
0
1
2
2
2
0
1
0
2
0
0
0
1
1
1
1
0
2
2
1
2
0
2
0
0
2
0
0
1
0
0
2
0
0
0
2
1
0
0
0
0
1
0
1
0
0
0
0
2
0
1
0
1
0
0
0
0
2
0
2
1
1
0
0
0
1
0
2
2
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
1
0
0
0
1
1
0
0
2
0
1
0
2
1
2
0
2
1
0
0
2
2
0
0
1
0
0
1
0
0
2
1
0
1
0
2
0
0
0
1
0
0
1
0
1
0
2
1
0
0
0
2
0
2
0
2
3
0
0
2
0
0
2
0
0
0
0
2
0
0
0
1
0
2
0
2
0
1
0
2
0
0
0
0
0
1
0
1
0
1
2
1
0
0
2
0
0
1
0
1
1
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
1
2
1
2
2
2
0
0
3
1
2
2
0
0
1
0
0
0
0
0
0
0
2
1
2
0
0
0
4
1
0
0
1
0
2
0
1
2
0
0
0
0
0
1
3
1
0
0
1
2
1
1
1
2
0
0
0
0
0
0
1
0
1
0
1
0
0
2
2
7
0
0
2
0
0
1
0
0
1
2
0
2
0
0
0
1
0
0
0
0
2
0
2
2
0
0
1
0
0
1
1
2
0
1
0
0
2
0
0
0
2
0
0
1
0
0
5
2
2
0
2
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
1
2
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
1
1
2
0
0
0
0
1
0
0
2
0
2
0
1
0
1
3
1
0
0
2
0
1
0
1
2
0
0
0
0
2
0
0
0
1
0
0
2
1
2
0
2
0
1
0
0
2
0
1
0
2
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
1
1
1
0
0
0
1
0
2
2
0
1
0
2
0
2
1
0
2
0
1
0
0
2
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
1
2
0
0
2
0
0
2
2
1
2
0
0
0
0
0
0
1
2
1
0
0
0
0
2
0
0
0
0
0
0
2
2
2
0
0
2
0
0
1
0
0
0
0
0
0
2
2
0
0
0
1
0
0
1
1
0
0
1
0
2
0
0
0
0
0
1
1
0
0
1
0
1
2
0
0
2
0
0
1
2
0
0
0
0
0
3
2
1
1
0
0
2
0
0
0
3
0
0
1
0
0
0
0
0
1
1
0
2
0
0
1
0
0
0
1
0
2
0
0
1
1
2
1
1
0
0
0
2
0
1
0
2
0
1
0
0
1
0
0
1
2
0
0
2
2
1
0
1
0
3
2
0
0
0
2
2
0
0
2
5
0
1
0
0
0
0
0
1
0
0
0
1
2
1
0
2
0
2
2
2
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
1
2
0
1
2
0
0
0
2
0
0
1
0
0
2
0
1
1
0
0
2
0
1
1
0
0
0
0
2
0
0
1
1
1
0
2
1
0
2
1
0
2
0
2
0
0
3
2
0
2
0
0
2
2
0
0
1
0
1
0
0
0
1
3
2
0
2
0
2
2
0
0
2
0
0
2
0
0
0
1
0
2
1
2
2
1
2
0
0
0
1
0
0
0
0
1
2
0
2
0
3
1
0
0
1
2
0
1
0
0
1
0
2
1
2
0
1
3
0
0
0
0
0
0
2
1
0
1
2
1
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
1
2
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
1
0
2
1
0
0
1
0
0
1
0
4
0
0
0
0
0
1
1
1
1
0
0
1
2
1
0
2
1
1
1
2
2
2
2
2
1
2
0
0
2
0
2
1
0
0
2
1
0
0
2
0
2
2
0
0
0
0
0
2
2
0
1
3
0
0
1
0
0
0
0
0
1
1
0
0
0
1
2
0
2
0
0
1
1
1
0
0
2
0
3
0
0
0
2
2
2
0
0
0
2
0
1
1
0
2
0
0
0
0
2
2
2
2
0
0
1
0
3
0
0
0
2
2
0
2
0
0
1
0
0
0
0
0
0
2
2
0
0
0
2
1
0
0
0
0
0
1
0
0
1
0
1
0
2
0
2
2
1
0
0
0
1
0
0
0
0
0
0
2
0
1
2
1
0
0
2
2
0
0
0
2
2
0
0
3
0
1
0
0
2
0
0
1
0
3
0
0
1
0
2
0
1
0
0
1
2
0
2
0
0
4
1
0
1
0
0
0
1
1
0
1
0
1
2
1
0
2
1
0
0
0
1
5
2
0
1
2
0
0
0
0
2
1
0
0
0
0
1
0
0
1
1
0
0
0
1
1
2
0
0
1
0
0
0
0
0
0
2
1
0
2
2
0
0
1
2
0
0
1
2
0
1
0
1
2
1
0
0
0
0
3
2
0
2
0
0
0
2
1
0
1
2
2
1
0
2
0
0
2
1
1
0
0
0
1
0
0
1
2
0
1
0
0
0
2
0
0
2
2
2
0
1
1
0
0
1
1
0
2
0
0
0
1
2
2
0
0
1
1
2
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
3
1
0
0
2
0
0
0
2
2
2
1
1
0
1
1
0
2
0
1
0
0
1
3
1
1
2
0
0
0
0
0
1
2
0
0
0
0
1
1
0
1
0
1
2
0
1
0
0
0
0
0
0
0
0
0
1
2
1
0
1
2
0
1
0
2
0
0
2
0
1
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
1
0
2
1
0
0
2
2
2
2
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
2
0
0
3
1
2
0
1
2
0
0
1
0
2
0
2
0
0
1
0
0
2
2
1
1
0
1
2
0
0
2
1
1
2
0
0
1
0
1
1
0
0
0
0
0
2
1
0
1
1
3
0
0
0
0
2
0
0
2
1
2
0
2
2
0
0
0
0
1
0
1
2
0
0
2
0
1
2
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
1
0
0
0
2
2
1
3
2
1
1
1
1
0
0
0
2
2
1
0
2
0
2
1
0
0
0
2
0
1
0
0
1
0
1
1
0
0
0
2
2
2
1
0
1
2
0
0
0
2
2
1
1
0
0
1
3
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
1
1
0
0
2
0
0
1
1
3
1
0
3
0
2
0
0
2
1
0
1
0
2
0
0
0
0
0
1
1
2
0
1
0
0
1
1
3
0
2
0
0
0
0
0
0
2
0
0
1
0
2
1
0
0
0
2
0
0
1
0
0
1
1
0
1
1
0
3
0
0
0
2
3
2
1
2
0
0
1
0
2
0
0
0
0
2
0
1
0
1
0
0
0
0
1
0
2
0
0
0
0
0
2
1
0
1
1
1
1
2
0
0
0
0
0
1
2
0
1
0
1
2
2
2
0
1
0
0
2
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
2
0
1
0
0
0
1
1
1
0
2
1
1
0
0
0
0
0
2
2
0
1
0
0
0
2
0
0
1
0
1
0
0
0
2
0
2
0
3
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
4
0
1
1
1
2
0
2
1
1
2
0
0
0
0
0
0
0
1
1
0
2
0
0
2
1
0
0
1
0
1
3
1
2
1
0
2
0
0
0
1
0
2
0
0
1
1
0
0
0
1
1
0
0
0
2
2
1
0
1
2
2
1
2
0
0
0
0
0
2
1
3
0
0
0
1
0
1
0
2
0
0
0
1
1
0
2
0
1
0
0
2
2
0
2
3
0
0
2
0
3
4
2
0
0
1
1
1
0
0
2
3
0
0
0
0
0
1
0
2
1
0
0
1
0
0
0
3
2
0
0
2
2
0
0
2
0
2
1
2
0
0
2
1
0
1
0
0
0
0
0
2
0
3
2
1
0
3
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
1
0
0
0
1
0
1
0
0
0
0
2
0
0
1
0
0
1
2
1
1
0
0
1
2
2
0
3
1
0
2
0
1
0
2
1
3
1
2
0
1
2
1
1
1
0
0
2
0
1
0
3
0
1
0
0
0
2
0
2
0
1
0
0
0
2
0
0
1
1
2
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
1
2
0
2
0
1
0
1
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
3
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
1
6
0
0
0
1
1
1
0
1
1
1
0
0
0
0
1
1
1
2
1
0
1
0
0
0
0
0
1
1
0
1
0
0
0
1
0
1
1
0
1
2
2
2
1
2
0
0
0
0
2
2
1
0
1
0
0
1
0
0
0
1
1
1
1
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
1
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
1
2
0
0
0
0
0
3
0
1
0
0
1
2
0
1
0
0
0
0
0
0
0
2
0
1
2
0
0
2
0
3
2
1
1
0
0
1
0
2
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
4
2
2
1
0
0
0
0
2
1
1
0
0
1
0
2
0
0
0
1
0
2
1
0
1
0
0
2
4
0
0
1
0
0
0
0
0
0
2
2
0
1
0
0
1
0
1
3
0
2
2
0
2
0
1
0
0
0
0
0
2
2
2
1
1
1
0
2
2
0
2
0
1
0
0
0
0
2
2
0
0
0
2
1
0
1
0
0
1
2
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
2
2
2
0
3
0
2
2
1
0
0
0
0
0
1
2
0
0
0
0
0
1
2
0
2
2
0
0
1
0
0
1
0
2
0
2
0
2
1
1
2
0
1
0
0
0
0
0
3
0
0
2
0
1
1
0
0
0
0
3
0
0
0
0
1
0
1
2
1
1
0
0
1
0
1
0
0
0
2
0
2
2
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
2
0
3
1
0
1
0
0
2
0
0
1
0
2
0
1
0
1
0
0
0
0
2
0
0
0
2
1
1
1
0
0
1
0
0
0
4
0
0
1
1
0
1
1
1
0
2
2
0
1
1
0
0
2
0
0
1
1
0
2
0
0
0
0
0
1
2
1
0
0
1
0
0
2
0
0
1
1
1
0
3
1
1
1
4
1
2
0
1
0
0
0
0
0
1
1
2
2
2
1
0
0
2
1
1
1
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
2
0
1
0
1
1
0
0
0
0
1
0
1
3
0
0
3
1
0
1
2
2
2
0
2
0
0
0
0
0
1
2
0
2
1
0
2
0
1
2
1
2
0
1
0
1
0
1
1
1
0
0
1
2
0
1
0
0
0
0
2
0
0
1
0
0
2
1
1
4
0
0
0
0
0
4
0
0
0
1
1
0
1
1
0
1
0
0
0
0
0
2
0
0
1
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
3
1
0
0
2
1
2
0
2
2
0
2
0
0
0
0
1
0
0
0
0
1
1
0
2
0
0
1
1
0
0
0
0
0
3
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
2
1
0
2
1
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
2
0
0
0
1
0
0
1
0
1
1
2
1
2
0
0
0
0
1
2
1
2
0
0
0
2
0
0
1
0
0
0
0
2
1
2
0
1
0
2
0
0
1
2
0
0
1
0
0
0
0
1
2
0
0
0
0
0
2
0
2
2
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
1
0
0
0
2
2
1
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
2
0
0
2
1
0
1
0
0
0
0
0
1
0
0
1
1
0
2
6
1
0
0
1
2
1
0
0
1
1
0
2
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
1
0
0
3
0
0
0
1
2
1
0
0
2
1
1
0
2
0
2
1
0
1
0
0
1
0
1
1
0
0
1
2
0
0
2
0
1
0
2
1
0
1
2
0
2
2
1
0
0
0
0
0
2
3
0
1
2
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
2
0
0
1
0
0
0
0
3
0
1
0
1
0
0
0
0
0
2
0
0
2
1
0
0
0
0
4
2
0
1
1
1
0
0
0
0
0
0
0
1
0
1
0
2
1
7
0
2
1
2
0
0
0
0
0
2
0
2
1
1
1
0
0
0
1
2
0
1
0
0
2
1
1
2
1
0
2
1
3
0
1
1
0
1
2
0
0
2
0
0
0
0
0
0
0
0
2
0
1
2
1
1
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
1
2
0
0
0
0
2
1
0
1
1
0
1
0
0
1
1
2
1
0
1
1
0
0
0
0
0
1
0
2
2
1
0
1
2
2
2
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
2
2
0
1
0
0
1
1
0
1
0
5
0
0
2
0
1
1
0
0
0
0
0
0
2
0
1
2
2
0
0
0
0
2
0
0
2
0
0
1
1
0
1
2
1
0
0
2
0
2
0
0
0
0
0
0
2
2
0
0
1
1
1
0
0
2
0
0
0
0
0
1
9
0
0
0
2
0
0
1
1
0
1
0
2
0
0
0
0
0
1
0
0
1
1
1
1
2
0
0
5
2
0
1
0
0
2
0
0
0
3
0
0
1
2
3
0
0
1
0
0
0
0
1
1
1
1
1
2
1
1
0
0
0
0
2
0
1
0
2
2
0
0
2
0
1
0
2
0
3
3
0
2
0
1
0
2
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
4
0
2
2
0
1
1
2
0
0
0
0
1
1
1
1
2
2
1
1
2
2
0
1
0
2
0
0
0
1
0
0
2
3
2
0
0
0
2
0
0
0
0
0
0
1
5
1
0
0
1
0
0
0
0
0
1
1
2
0
2
0
0
0
0
0
0
0
1
2
2
1
1
0
2
0
0
0
0
1
0
1
0
0
0
0
3
0
2
2
1
0
0
0
1
0
0
0
0
0
1
0
2
1
0
0
0
2
0
0
0
0
1
0
0
2
2
1
0
0
1
0
0
1
2
1
0
2
0
0
0
2
0
0
2
0
0
1
2
2
1
1
0
2
0
1
0
2
0
0
0
1
2
1
0
1
0
2
0
0
1
2
0
1
1
0
2
0
0
0
0
1
0
2
0
0
1
1
0
1
1
0
0
0
0
1
0
2
1
0
1
2
0
2
0
2
1
0
2
0
1
0
2
2
2
0
0
0
0
0
0
0
6
0
2
1
2
0
0
1
0
2
0
0
2
0
2
1
2
0
1
1
0
2
0
0
1
0
0
2
0
0
0
0
1
0
0
2
0
0
1
0
1
1
1
0
1
0
3
0
0
0
0
2
2
1
0
0
0
2
1
0
0
2
1
1
1
3
0
0
0
1
0
0
0
0
0
0
0
1
2
2
1
1
0
0
2
3
2
0
0
0
0
0
1
0
1
2
0
0
2
0
1
1
0
2
0
0
0
0
2
5
0
2
4
1
0
2
0
2
1
2
0
2
0
0
1
0
2
0
2
0
0
2
0
2
1
0
1
2
2
0
1
2
1
0
1
1
0
0
0
1
0
0
0
0
0
0
1
2
0
0
2
1
0
0
0
1
1
0
1
0
0
0
0
1
1
0
0
0
0
2
0
1
1
0
0
1
0
1
0
0
0
0
1
1
0
1
2
2
2
0
2
2
0
0
0
1
1
2
0
0
2
0
1
1
0
0
2
0
0
0
0
1
2
1
2
0
0
1
0
1
0
0
0
2
3
0
1
2
0
0
2
0
0
0
0
0
0
2
0
0
1
2
1
1
0
0
2
1
0
1
0
0
0
2
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
2
1
0
0
2
0
0
0
0
0
1
0
1
2
0
1
1
2
1
0
1
2
0
0
0
4
0
0
2
1
1
4
1
0
0
3
0
0
0
0
2
0
1
0
0
1
1
2
0
0
0
2
0
1
2
1
1
0
0
0
0
0
2
0
0
2
2
0
1
2
0
1
0
0
1
0
1
2
1
2
1
0
0
0
2
0
0
3
2
2
0
0
3
1
2
1
0
0
0
0
0
0
1
0
2
0
0
1
1
0
0
0
0
0
0
1
1
0
0
1
0
0
3
0
0
0
0
1
2
0
6
2
0
0
0
0
0
1
0
1
2
2
1
1
2
0
1
2
0
0
0
0
0
0
2
12
0
0
1
2
2
0
0
2
0
0
1
3
0
3
1
0
2
0
1
0
2
0
0
1
2
0
3
1
1
0
2
2
2
0
0
1
0
0
0
0
1
0
0
0
1
0
0
2
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
2
1
2
1
0
1
0
2
0
0
0
0
1
0
2
0
0
1
1
0
5
1
0
1
0
2
0
2
0
0
1
0
1
3
1
0
2
0
1
2
0
0
0
0
0
0
0
1
1
2
1
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
1
2
0
0
0
0
0
0
1
0
2
0
0
1
1
0
0
0
1
0
0
2
0
1
0
2
0
1
0
2
2
0
1
0
0
1
1
1
0
1
0
0
1
0
0
0
1
2
1
0
0
0
2
0
2
0
0
0
1
0
1
2
0
2
0
1
0
0
1
1
0
3
2
1
0
3
0
0
0
0
0
2
0
1
0
2
0
0
2
3
0
0
2
0
0
2
0
2
0
0
1
0
0
2
0
0
1
2
2
0
0
0
0
2
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
2
1
1
1
0
0
2
1
0
1
0
0
0
2
0
0
0
0
2
0
0
3
2
0
1
2
1
0
0
0
1
0
1
0
0
1
0
0
0
0
1
2
2
0
0
0
0
1
0
0
1
0
0
1
3
0
2
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
2
2
1
1
1
0
0
0
0
1
0
0
1
3
1
0
0
0
0
0
1
1
2
0
0
0
2
0
0
2
1
2
0
1
0
3
1
2
1
1
3
1
0
0
1
1
1
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
2
2
1
1
1
2
0
0
0
1
2
0
0
2
0
1
0
0
0
2
1
0
0
1
0
0
3
0
0
0
0
0
1
2
0
0
1
2
0
0
1
0
0
0
0
2
0
2
2
0
1
0
0
0
0
0
0
0
1
3
0
0
1
0
1
0
0
0
2
1
0
1
1
0
0
0
0
0
0
0
1
0
2
1
0
0
0
1
0
0
0
0
0
0
0
2
1
2
2
1
1
0
0
0
2
0
0
2
0
0
1
2
2
1
0
0
1
0
0
1
1
0
0
2
0
2
1
1
0
2
1
0
0
2
3
2
0
0
2
1
0
1
0
0
3
2
1
0
1
0
0
1
1
0
2
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
2
0
1
0
1
0
0
0
0
3
0
0
1
1
0
1
2
1
2
1
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
1
0
0
1
2
1
0
0
2
0
2
2
0
0
3
2
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
1
2
0
6
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
1
1
2
0
0
0
2
0
0
2
0
0
0
2
1
2
1
1
2
0
1
2
0
2
0
0
1
0
2
0
2
1
0
0
0
2
0
0
0
1
1
0
1
1
1
0
0
0
2
1
0
0
0
2
0
1
0
1
0
0
0
2
0
0
2
0
0
0
3
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
1
0
1
1
0
0
1
2
0
0
2
0
0
0
0
2
1
0
0
1
0
2
0
4
0
0
1
0
0
0
0
1
2
1
0
0
1
0
1
1
0
1
0
0
0
0
0
0
2
0
1
0
1
0
2
1
1
0
0
0
1
1
1
1
0
0
0
0
3
1
2
0
1
2
2
4
0
3
1
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
1
4
0
2
0
1
0
0
1
2
1
2
0
0
0
0
0
0
0
2
0
0
0
1
2
2
0
0
1
0
0
0
0
0
2
0
0
1
1
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
1
0
1
2
0
2
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
2
1
1
1
2
2
2
1
2
1
2
0
1
2
0
0
0
0
2
2
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
1
0
1
0
0
2
1
0
2
2
0
2
1
0
1
1
0
0
0
2
0
0
1
1
0
0
0
2
0
0
0
0
3
0
2
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
1
0
0
0
3
0
2
2
0
0
2
0
0
0
1
1
2
0
0
0
2
0
2
1
0
0
0
4
0
0
1
1
1
0
0
2
1
0
0
0
1
0
1
0
1
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
1
1
0
0
0
2
1
1
0
2
2
0
1
0
0
2
0
1
0
0
1
1
1
2
0
0
0
0
2
1
0
0
1
0
0
2
0
0
1
0
0
0
0
1
0
2
0
2
0
2
0
2
2
0
1
0
0
0
0
1
1
0
2
1
3
0
1
1
0
3
0
0
0
1
2
0
0
0
0
2
0
0
1
0
0
0
2
1
0
0
0
0
0
2
1
0
2
2
0
0
0
0
0
1
0
0
0
0
1
0
0
2
1
0
0
0
0
2
0
2
2
1
2
1
1
1
0
0
0
2
0
0
0
0
1
1
2
1
0
2
0
0
0
1
1
1
1
3
1
2
0
1
1
0
0
0
2
0
0
0
0
1
0
0
2
1
2
2
0
1
1
0
0
2
1
2
0
2
2
1
0
1
0
1
0
1
0
2
0
0
0
1
0
1
0
0
0
0
2
1
0
0
1
0
0
0
1
0
1
0
0
1
0
1
1
0
0
2
2
1
0
0
1
1
0
0
1
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
3
0
2
0
1
1
1
0
0
0
2
1
1
0
2
1
1
0
0
1
1
0
1
0
0
2
0
1
2
0
1
0
0
2
0
1
3
1
1
0
0
3
3
1
2
0
0
1
1
2
0
1
0
1
0
0
0
2
0
0
0
0
0
0
1
1
2
1
0
1
1
0
0
0
0
0
1
0
0
2
0
0
1
1
2
1
0
1
0
0
0
0
0
2
1
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
2
1
2
0
1
1
0
1
1
0
2
2
0
2
0
0
0
1
0
0
0
1
1
0
0
0
0
1
1
1
1
1
1
0
0
1
1
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
1
2
1
1
0
0
0
0
0
0
1
0
1
1
0
0
2
0
0
0
2
1
0
2
1
0
2
1
2
0
0
2
0
3
2
1
1
0
0
0
0
1
0
2
2
2
1
0
0
0
0
0
2
1
1
0
1
2
0
1
0
1
0
1
0
0
2
1
0
0
1
0
1
1
3
0
1
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
1
1
0
0
4
0
0
0
0
0
0
2
1
0
0
0
0
2
2
0
0
0
0
2
0
1
0
2
0
2
0
2
1
1
0
0
0
0
0
0
1
1
2
0
1
0
0
0
0
2
2
2
0
0
2
1
0
1
0
1
0
0
0
2
1
2
0
2
0
1
0
0
1
2
0
2
1
0
1
0
0
0
1
0
0
2
2
1
0
0
1
0
1
0
2
1
1
0
0
1
0
1
0
0
1
1
0
0
2
2
1
0
1
1
2
0
0
0
0
1
0
1
0
0
0
1
1
0
1
0
2
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
1
0
2
10
0
0
2
2
2
0
2
1
0
2
0
1
1
1
0
1
0
0
1
0
2
2
0
1
2
0
0
1
1
0
1
0
2
2
2
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
1
1
0
2
1
2
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
3
2
1
0
2
0
2
0
1
0
1
2
0
1
1
0
0
2
1
0
0
0
0
2
1
0
0
0
1
0
0
2
1
1
0
0
0
0
0
0
2
0
0
1
2
0
2
0
0
0
3
1
0
0
2
3
0
0
0
1
1
1
0
0
2
1
1
1
1
1
2
0
2
0
0
0
0
0
1
0
0
0
1
0
1
0
2
0
1
0
0
2
0
0
3
0
1
1
0
0
0
0
1
0
2
1
0
2
2
1
0
0
1
0
1
0
0
2
1
2
0
0
1
0
2
2
0
0
1
1
2
1
3
0
1
0
2
2
0
0
0
2
2
1
2
3
0
1
2
2
0
1
2
0
0
1
0
3
2
2
0
0
0
0
1
0
0
0
0
0
1
2
1
1
0
0
1
0
1
0
1
0
2
1
0
2
0
1
1
2
0
0
1
0
2
1
1
1
0
2
0
0
1
1
0
2
0
0
0
0
1
1
0
0
0
2
0
2
0
0
4
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
4
3
0
1
1
1
0
0
0
0
1
2
1
2
2
0
2
2
2
1
1
1
0
0
2
0
0
0
1
0
2
4
1
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
1
0
1
0
2
2
1
0
2
2
0
0
2
0
2
0
0
2
1
3
0
0
1
0
1
1
3
2
1
0
0
2
0
1
2
0
2
1
0
0
1
0
0
0
0
0
1
3
0
1
0
1
0
1
0
1
0
0
0
0
0
1
1
0
0
0
1
1
1
1
2
1
0
1
1
0
0
2
0
3
1
2
1
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
2
0
1
1
0
2
0
0
0
0
0
2
0
2
2
3
1
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
1
2
2
0
1
0
0
1
2
0
1
2
0
2
0
0
1
4
1
1
1
0
0
0
0
1
1
0
1
0
0
0
1
0
1
2
0
2
2
0
2
2
0
0
2
0
0
2
0
0
0
2
2
1
0
1
0
0
0
2
1
2
0
2
5
0
3
1
2
2
1
3
2
0
0
1
0
2
1
2
0
0
1
2
1
0
0
0
1
0
0
1
0
0
0
1
1
2
1
1
1
0
2
2
0
1
0
2
0
0
1
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
1
1
0
0
1
0
1
3
0
0
1
1
0
2
0
1
2
2
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
2
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
3
0
1
0
1
0
1
1
1
0
0
0
0
0
0
0
1
1
0
0
1
2
0
0
1
1
0
1
0
2
0
2
2
0
2
0
4
1
3
0
1
0
0
1
0
0
1
1
2
0
2
2
0
0
1
1
2
0
0
1
2
0
0
2
0
2
1
2
0
0
1
1
0
2
0
0
0
0
0
2
1
0
1
0
1
1
1
4
2
0
0
1
1
0
0
2
0
4
0
1
2
2
0
0
1
2
0
2
0
2
0
0
0
3
0
0
0
1
0
0
0
1
0
0
0
1
0
3
1
0
0
2
0
2
0
0
0
1
0
0
0
1
0
2
0
1
0
1
1
0
2
1
1
2
0
2
0
1
0
1
0
1
2
0
1
2
2
0
0
0
0
0
3
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
2
2
0
0
0
1
0
1
2
0
0
0
1
1
2
0
1
2
0
1
0
0
3
0
2
2
2
2
1
0
0
0
0
0
1
1
3
0
0
1
0
1
2
0
3
0
0
0
2
1
1
0
0
0
2
0
0
1
0
0
3
0
1
0
0
0
1
2
0
1
0
2
0
2
1
3
1
2
4
1
0
0
0
0
2
1
0
0
0
0
1
1
0
0
0
2
2
2
0
0
0
0
1
0
2
2
2
2
2
2
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
1
0
2
0
0
0
0
1
2
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
2
0
0
0
0
0
1
1
2
1
0
0
1
0
2
0
0
2
2
2
0
0
0
0
2
1
0
1
0
2
0
1
0
2
2
0
0
1
1
0
0
2
0
0
2
0
1
1
0
4
1
1
0
1
2
0
0
0
1
1
1
0
1
0
0
2
1
0
3
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
2
1
0
0
1
0
2
0
0
0
1
2
0
1
0
0
2
0
3
3
1
1
0
0
2
1
0
1
0
0
0
1
2
0
2
0
0
2
0
0
2
0
0
1
0
1
0
2
0
0
0
1
0
0
0
0
2
1
0
0
2
0
0
2
0
3
0
1
1
2
0
0
0
0
0
0
2
0
1
1
1
0
0
0
2
2
0
0
1
0
1
0
0
0
0
0
1
2
0
0
3
0
0
0
0
0
0
0
0
0
2
1
2
1
0
0
0
0
1
0
1
2
2
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
1
1
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
2
1
0
0
1
1
1
1
0
0
0
0
0
0
2
1
0
1
0
1
1
0
0
2
1
1
0
0
0
0
0
0
0
2
1
0
1
0
1
0
2
0
0
2
0
0
0
2
3
0
0
2
2
0
0
1
1
0
1
0
1
0
2
0
0
2
0
0
2
0
0
0
0
0
0
3
0
3
0
0
0
1
0
2
1
0
1
0
1
0
1
0
0
0
4
4
2
0
0
0
2
3
0
0
1
1
0
0
2
0
0
1
0
0
1
2
1
0
1
0
1
1
0
1
2
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
2
0
1
2
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
2
0
1
0
0
0
0
0
1
1
1
2
2
0
0
1
0
1
0
0
1
1
2
2
1
0
1
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
11
1
0
0
1
1
0
0
0
1
1
0
1
0
1
0
0
1
0
1
3
2
5
0
0
2
0
1
0
1
0
0
1
2
2
0
1
1
0
1
0
2
2
0
0
3
2
0
0
0
1
1
0
1
2
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
2
0
1
2
0
0
3
0
1
1
2
1
0
0
0
1
2
0
1
0
0
0
0
2
2
0
0
1
1
0
2
1
1
1
0
0
0
2
1
0
0
0
1
0
0
3
0
0
0
0
3
2
0
0
2
4
0
0
2
0
0
1
1
1
1
1
1
0
0
0
2
0
0
1
2
0
2
0
0
2
1
0
0
0
0
2
0
2
0
2
0
0
1
1
2
1
0
0
0
1
2
0
1
0
1
2
2
0
0
0
0
1
1
0
0
0
0
2
0
0
2
2
0
3
0
0
0
0
0
0
1
1
0
2
0
1
0
1
3
2
2
0
0
1
2
2
0
1
0
0
0
0
2
0
0
2
0
0
0
1
0
1
1
1
1
0
0
0
0
2
0
2
1
0
0
0
0
1
0
2
0
1
2
1
0
1
0
2
0
0
0
0
0
2
2
2
0
2
0
0
0
0
3
5
0
2
0
2
0
0
0
0
0
2
2
1
0
0
1
2
0
0
0
0
0
0
0
1
0
1
1
0
0
0
2
2
0
0
0
1
1
2
1
2
0
3
1
2
0
0
0
0
0
0
2
0
0
1
0
0
1
2
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
2
0
0
2
0
0
0
0
0
2
0
0
2
1
2
0
0
0
3
0
1
0
0
1
3
2
2
1
0
2
2
0
0
0
0
0
0
0
1
2
0
2
0
0
1
0
0
2
3
0
2
1
2
0
1
0
1
2
1
0
1
0
1
0
1
2
0
0
1
1
0
0
0
0
0
1
0
0
0
0
2
1
0
0
1
2
0
2
2
3
0
2
1
1
0
0
0
4
0
0
0
0
2
2
1
0
0
0
1
0
1
2
0
0
1
1
1
0
0
0
1
0
1
0
0
0
2
0
1
1
0
1
0
2
0
1
0
0
0
0
0
1
0
2
1
1
0
1
2
0
3
2
1
0
0
0
0
2
0
0
0
0
1
1
0
2
0
0
0
0
0
1
2
0
0
1
1
1
3
1
0
1
0
3
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
3
0
0
2
0
1
0
1
0
1
1
0
2
2
0
0
0
0
0
2
2
0
1
0
1
1
0
1
2
1
0
0
0
0
0
0
0
1
2
2
1
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
1
1
0
0
0
0
2
0
2
0
2
0
0
0
0
3
1
1
1
0
1
0
0
8
1
1
2
0
5
0
0
2
2
1
0
1
0
1
1
0
0
0
0
0
1
1
0
2
2
1
0
0
2
0
2
0
2
0
1
0
0
1
0
2
1
0
1
0
1
0
0
0
0
0
2
0
0
0
1
0
1
2
0
1
1
1
2
0
1
0
1
1
0
1
0
0
0
1
0
0
0
0
3
1
2
3
0
0
0
2
0
0
0
2
1
2
0
0
0
0
0
0
0
2
1
1
0
0
0
2
1
0
2
0
2
0
2
1
0
2
3
0
0
4
0
2
0
2
0
2
1
0
0
0
1
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
2
0
1
1
0
2
0
0
1
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
1
1
1
1
0
2
3
1
0
1
0
0
0
2
0
1
0
2
2
0
0
1
0
1
0
2
1
0
0
0
0
0
1
0
0
0
0
0
2
2
1
0
0
2
0
0
1
0
0
2
1
0
0
0
1
0
1
0
2
0
0
0
0
2
0
1
0
2
0
0
0
0
0
2
1
2
2
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
2
0
2
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
2
0
1
2
2
1
2
0
0
0
0
3
0
0
2
0
1
0
2
0
0
2
1
3
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
2
0
1
2
0
0
0
0
0
2
2
0
0
0
2
2
0
0
0
3
0
0
2
1
0
0
0
1
0
2
0
0
0
0
0
0
2
1
1
0
0
2
0
0
1
4
0
2
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
3
0
1
1
2
0
1
2
0
0
0
0
1
1
1
0
0
1
2
0
1
2
0
2
0
0
1
2
2
1
0
2
2
2
0
0
1
0
2
2
2
2
0
0
0
0
1
1
1
0
1
1
0
0
0
3
2
2
2
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
1
1
1
1
1
1
0
2
0
0
1
1
1
0
0
2
2
0
0
0
1
1
0
2
2
1
2
0
1
2
0
0
2
1
1
3
0
0
0
0
2
1
0
2
1
0
0
2
2
2
0
0
1
0
2
2
0
0
0
0
1
0
0
0
2
1
0
0
1
0
0
2
0
1
2
2
0
1
0
2
0
0
1
0
0
0
0
0
2
0
1
0
0
1
1
1
0
0
0
2
0
0
1
0
1
0
0
2
1
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
2
1
0
2
1
0
1
0
0
1
0
0
1
0
0
1
0
1
0
0
2
0
1
1
0
1
0
0
0
1
0
0
2
2
0
0
0
0
0
0
2
0
1
2
0
0
1
0
1
1
0
0
1
2
0
0
0
1
1
3
1
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
2
1
0
1
1
0
0
0
0
0
2
2
1
1
0
0
0
1
0
0
1
0
0
1
0
0
2
1
0
1
0
2
1
1
0
1
0
0
0
0
1
0
1
0
1
1
2
0
0
1
0
1
2
0
0
0
0
2
1
1
2
2
0
0
1
0
0
1
1
0
1
2
1
0
0
0
0
1
2
1
1
0
0
3
2
2
0
2
2
1
0
0
0
0
0
1
0
0
1
1
2
0
0
0
0
0
1
0
2
1
4
0
2
1
1
1
0
2
2
2
1
0
1
2
2
0
1
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
1
1
4
1
1
1
5
0
0
0
0
0
0
0
0
0
0
0
3
1
1
1
0
2
0
0
1
0
0
0
1
2
1
0
2
0
2
0
2
0
1
0
2
2
0
0
1
0
1
0
2
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
1
0
1
2
0
2
1
1
0
1
0
0
0
0
0
1
2
0
0
0
2
1
1
2
0
1
2
2
2
0
2
0
0
0
0
0
1
2
2
0
0
2
0
1
0
1
1
0
0
1
1
2
1
1
2
4
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
1
2
0
0
1
0
0
1
0
2
1
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
2
2
0
0
0
2
0
0
2
0
1
0
2
0
0
0
0
1
2
0
0
2
1
0
0
0
1
1
0
1
0
0
0
0
1
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
4
0
1
1
1
3
1
0
0
2
0
0
1
2
0
2
1
0
2
2
0
0
0
1
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
2
1
1
1
0
0
0
0
0
0
0
3
0
1
1
0
0
2
2
0
0
0
2
0
1
1
2
0
1
2
0
0
1
1
0
0
2
1
3
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
2
2
0
2
1
0
0
2
0
1
0
0
1
1
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
1
0
3
0
2
0
1
0
0
0
2
0
1
1
0
0
0
2
0
0
0
0
2
0
0
1
2
0
0
0
3
2
2
0
2
0
1
0
0
0
5
0
0
0
3
2
0
1
1
0
0
0
0
0
0
0
1
2
0
4
1
2
0
2
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
2
2
0
1
0
0
0
0
0
1
1
1
0
0
0
1
0
0
2
0
2
0
1
0
1
1
0
2
1
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
2
2
0
0
0
2
2
0
0
0
0
0
1
2
1
1
0
0
0
1
0
1
1
0
1
1
0
0
1
0
0
0
1
0
0
2
2
0
0
2
2
0
1
1
0
0
0
1
0
4
0
1
1
1
0
0
1
0
0
0
0
0
0
1
1
1
1
1
0
2
2
0
0
2
2
0
0
0
2
1
2
2
0
1
0
2
0
0
0
2
0
0
0
2
2
0
1
0
2
0
2
0
3
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
1
0
2
0
2
2
0
2
0
1
0
1
0
1
0
2
0
0
0
1
0
2
0
2
0
2
0
0
0
1
1
1
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
2
0
0
0
0
2
0
0
1
2
1
0
0
1
0
0
2
2
2
0
1
0
2
0
0
1
2
2
1
0
0
1
2
1
1
1
2
0
0
0
0
1
0
0
1
3
0
2
0
0
0
4
0
2
1
0
1
6
2
0
2
0
2
2
2
0
1
2
3
1
0
2
2
1
2
0
0
1
1
0
0
0
1
1
0
1
1
1
2
2
2
1
1
0
0
0
1
0
2
2
2
1
0
1
1
0
1
2
0
2
1
0
1
1
1
0
0
1
0
1
2
0
0
0
0
2
1
4
2
0
0
0
0
2
0
1
2
0
0
1
0
0
0
3
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
2
2
1
0
0
2
1
2
1
0
0
0
0
1
1
1
0
2
0
1
0
1
1
1
0
1
2
1
1
0
3
0
0
2
0
0
1
3
1
2
2
0
1
2
0
0
1
0
1
1
1
0
0
0
0
2
1
2
0
0
2
0
0
0
0
0
0
1
1
2
2
1
1
0
0
0
1
0
2
2
0
0
0
0
1
1
0
2
2
1
0
2
1
0
0
0
2
0
0
1
1
1
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
1
0
1
1
1
1
1
1
1
0
0
0
0
0
1
1
1
2
2
0
0
0
0
0
0
2
0
2
0
1
1
0
0
1
0
0
0
0
0
0
0
2
0
1
1
0
3
0
0
0
2
2
0
0
1
0
1
0
2
1
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
2
0
0
0
1
2
2
0
0
0
1
0
1
1
1
0
0
0
0
2
1
0
1
1
2
2
1
1
1
2
0
1
0
0
0
0
1
0
1
1
1
0
1
2
2
1
1
0
0
2
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
1
1
1
0
0
2
0
1
1
1
1
0
0
0
2
1
0
0
3
0
6
1
2
0
1
2
2
0
2
0
2
0
1
0
0
0
1
0
0
3
1
1
0
1
1
0
0
0
0
0
1
1
1
2
0
0
1
1
0
2
1
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
2
0
1
1
0
0
0
2
0
0
1
0
0
3
2
2
0
0
2
1
1
1
1
0
0
0
0
3
1
0
1
0
0
0
0
4
0
2
0
1
0
2
1
0
0
0
1
0
2
0
0
2
2
2
0
0
0
1
1
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
2
0
1
0
2
0
1
0
1
0
0
0
2
0
2
0
0
1
0
1
0
0
0
0
2
2
0
0
0
3
0
2
0
2
0
0
1
0
1
3
0
0
0
1
2
0
0
1
0
0
1
0
0
0
0
1
0
0
1
2
0
2
0
2
2
0
3
2
1
0
0
0
1
0
0
1
0
0
0
0
1
2
0
0
0
0
1
0
2
0
0
0
0
0
0
2
1
0
1
0
2
0
0
1
0
0
2
0
0
1
0
0
1
1
1
1
2
1
1
2
1
1
2
0
1
0
2
2
2
0
0
0
1
0
2
0
2
1
0
2
2
2
0
1
2
2
0
0
0
0
1
2
0
0
0
2
0
0
1
1
0
3
2
0
0
0
0
1
0
0
2
0
0
2
0
1
2
2
1
1
0
0
2
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
2
2
0
2
0
2
1
0
1
0
0
0
3
0
1
0
0
2
1
2
3
0
2
0
0
0
2
0
0
1
1
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
2
2
0
0
0
0
1
0
0
0
1
1
0
2
1
0
2
5
0
0
2
2
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
3
2
0
1
1
0
1
1
0
0
0
2
0
1
0
1
1
0
1
0
0
1
1
0
0
0
1
2
0
0
1
0
0
0
0
1
0
1
1
1
1
0
0
0
0
0
2
0
2
0
1
0
5
0
0
0
0
0
1
0
0
2
1
2
1
3
1
0
1
1
1
0
0
0
1
0
2
0
0
1
2
1
0
2
0
0
0
0
0
1
1
0
0
1
0
0
2
0
0
0
0
1
0
1
0
0
0
1
0
1
2
0
0
0
0
0
1
2
0
6
0
0
0
0
1
0
0
0
2
0
1
1
2
0
0
2
2
0
0
2
0
2
1
0
5
0
0
0
0
0
2
1
1
1
2
0
1
0
0
0
2
2
0
0
1
1
0
1
0
2
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
2
1
2
0
1
1
0
0
2
0
0
1
0
2
0
0
0
0
1
2
0
0
4
2
1
0
0
0
1
0
0
0
0
0
1
2
1
1
1
2
1
0
1
0
2
2
0
2
0
0
0
1
0
0
2
0
1
1
1
1
0
1
0
0
0
2
1
0
1
0
0
1
2
0
0
0
0
2
1
0
2
1
0
0
2
0
1
0
0
0
0
0
0
0
0
2
2
0
0
1
2
0
1
0
0
1
3
0
1
0
2
0
0
0
1
1
2
1
0
0
0
2
0
0
1
2
0
3
0
1
0
0
0
1
1
0
6
0
0
3
0
1
0
0
0
2
1
0
2
0
0
1
0
0
0
0
2
1
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
3
1
0
0
0
1
2
1
0
0
2
2
0
0
0
1
0
1
1
1
0
1
0
0
0
0
2
0
0
3
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
1
2
2
0
2
0
0
2
1
1
0
0
0
0
0
0
2
0
0
2
0
2
0
0
2
1
2
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
1
2
1
0
2
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
2
1
0
2
0
0
2
0
1
0
0
0
2
0
0
0
2
2
0
0
0
2
2
1
0
1
0
0
2
3
2
1
0
3
0
0
0
0
2
0
0
2
0
2
0
1
0
1
1
1
0
0
1
0
0
1
0
1
1
1
0
0
0
2
0
2
1
0
1
0
2
1
0
0
0
0
0
0
2
0
2
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
1
2
0
0
1
1
0
2
0
2
2
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
2
0
3
6
0
1
1
0
0
0
0
2
0
0
0
1
0
3
0
1
0
2
0
1
0
0
1
2
2
2
0
2
0
0
0
1
0
2
0
0
2
2
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
2
0
2
1
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
1
0
1
0
1
0
0
1
1
0
0
0
1
0
2
0
4
2
0
2
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
2
0
1
0
1
1
1
0
0
0
1
2
2
2
0
2
1
1
1
1
2
0
1
2
2
1
0
1
0
1
1
0
2
1
2
0
0
0
0
0
0
0
0
2
0
0
1
0
2
1
1
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
2
1
2
0
2
0
2
2
0
2
1
0
0
0
3
1
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
2
0
2
1
0
0
2
1
0
0
2
0
0
2
2
1
0
1
0
2
0
0
1
1
2
0
0
1
0
2
0
1
0
0
0
1
4
1
2
0
3
0
0
0
0
0
1
0
1
1
1
4
0
0
0
2
2
0
0
0
1
1
0
0
2
1
0
0
2
1
0
1
2
0
2
0
0
0
2
0
0
0
0
0
1
0
0
1
2
1
0
1
2
0
0
1
0
3
1
0
1
0
0
0
2
0
0
1
3
0
2
0
1
1
0
1
0
0
0
2
0
2
1
2
0
0
2
0
0
2
1
2
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
2
1
0
2
0
1
0
2
0
0
1
0
1
1
0
0
2
0
0
0
0
0
0
2
2
2
0
2
2
0
0
2
2
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
2
2
0
0
1
1
0
1
0
1
0
0
2
0
0
1
2
0
2
58
1
1
0
2
2
0
1
0
2
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
1
1
0
1
2
0
0
0
0
0
0
2
1
1
2
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
1
0
1
2
1
0
2
0
1
1
0
2
1
1
1
0
1
1
0
0
0
0
0
2
2
0
0
2
0
2
2
1
0
1
0
0
2
2
1
2
0
0
1
3
1
0
0
0
2
1
0
0
2
0
0
2
0
2
1
1
0
1
2
0
0
2
0
2
0
2
2
0
1
2
0
2
1
1
1
2
0
0
1
0
2
1
1
0
0
2
0
1
2
0
0
0
1
0
0
0
0
2
1
0
2
0
2
1
1
2
0
0
0
2
2
0
0
0
0
0
0
1
0
0
2
0
2
2
0
0
2
0
2
3
0
0
3
0
1
0
2
0
1
0
1
0
0
2
0
1
2
0
0
1
0
3
2
0
0
2
0
1
0
0
2
1
1
2
0
1
0
0
0
1
1
0
1
0
0
0
0
2
2
0
2
0
1
0
0
0
0
1
2
2
0
0
2
0
0
0
0
0
1
1
0
0
0
0
2
0
1
0
2
2
1
1
0
2
0
0
1
1
0
4
0
0
1
0
1
0
0
0
0
0
2
0
0
4
1
0
2
2
0
1
0
2
0
2
0
0
0
2
0
0
1
1
2
2
0
0
0
0
1
0
2
1
0
2
0
0
1
1
1
0
0
0
0
0
0
0
2
0
1
1
0
1
0
0
2
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
1
0
0
1
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
1
1
0
0
4
2
1
1
1
0
1
2
0
0
0
1
0
0
0
1
0
0
0
3
1
0
1
0
0
2
0
0
1
0
0
2
0
1
1
0
2
1
0
0
0
0
1
0
2
0
1
1
2
1
0
0
0
0
1
1
0
0
0
0
1
0
2
0
0
0
2
2
0
0
1
0
0
2
3
2
2
1
0
1
0
2
1
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
1
0
0
4
1
2
0
2
0
1
0
0
1
0
0
0
2
3
2
2
0
0
1
0
2
0
0
0
0
2
0
0
0
0
1
1
1
1
0
0
2
0
0
1
0
0
2
0
0
1
0
1
0
2
1
1
0
1
0
1
2
0
1
0
0
0
0
8
0
2
1
1
2
0
2
1
2
0
0
2
0
2
2
1
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
1
1
0
0
0
1
1
0
0
0
0
2
0
0
0
1
1
0
0
1
0
0
0
0
0
1
2
0
1
1
0
0
0
2
2
0
1
0
0
1
0
2
2
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
2
2
0
0
0
2
0
0
1
0
0
0
0
2
0
1
0
1
0
2
0
1
1
0
0
2
1
1
2
1
1
0
2
2
1
0
0
0
0
1
1
2
1
0
0
0
1
0
2
1
0
0
0
1
1
0
1
1
2
0
0
2
2
0
0
0
0
0
1
2
0
1
0
1
0
0
0
0
0
2
0
2
1
0
1
2
0
2
2
0
0
1
0
1
1
1
1
0
0
1
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
2
2
0
1
0
0
2
2
0
0
0
2
0
1
0
2
0
1
0
1
0
0
2
0
2
2
1
0
2
0
1
0
0
0
0
1
1
1
0
0
2
0
2
1
0
2
0
0
0
1
1
0
1
0
1
5
0
1
0
0
0
0
1
0
0
0
0
1
3
0
0
2
0
1
1
3
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
2
2
1
0
0
0
0
1
0
1
2
1
2
0
1
0
1
11
0
0
0
0
2
0
0
0
0
2
0
2
1
2
1
4
2
2
0
1
2
0
1
0
0
0
0
2
1
0
2
1
0
0
2
2
0
0
0
1
0
0
0
0
0
0
2
2
1
2
1
2
0
0
0
0
0
1
0
2
0
0
2
2
0
0
2
0
0
0
0
4
0
0
2
0
0
1
0
0
2
0
1
0
0
0
0
0
2
2
0
1
2
1
1
0
0
0
0
0
2
1
0
0
1
2
1
1
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
1
0
0
2
1
0
0
1
0
0
1
1
1
0
3
0
0
0
2
1
0
1
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
1
0
1
0
0
1
2
0
1
0
1
1
3
0
0
2
0
0
0
2
0
1
1
0
1
0
0
2
2
0
1
0
0
1
0
0
0
0
0
1
2
1
0
0
2
0
2
0
0
1
1
0
0
1
0
1
2
0
0
0
2
1
2
0
1
2
0
1
1
2
1
2
0
0
1
1
1
0
0
0
2
1
0
1
0
0
1
0
0
2
1
2
2
2
1
0
2
0
0
0
0
0
4
0
0
0
0
0
2
0
1
0
0
0
0
1
1
0
0
1
2
0
2
1
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
1
0
0
2
2
0
2
0
2
4
1
0
1
0
1
1
1
2
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
1
2
0
0
1
0
0
0
0
2
2
0
1
0
0
1
3
1
0
1
1
2
0
1
2
1
0
0
3
1
1
2
0
1
1
0
2
1
1
0
1
0
1
0
0
0
1
1
2
0
2
0
0
1
2
0
0
0
1
1
2
1
0
2
1
0
2
1
0
0
1
0
2
0
2
0
1
2
0
1
1
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
2
2
2
1
1
0
0
3
0
1
0
2
2
2
0
0
0
1
1
1
0
1
0
0
0
1
1
0
2
0
1
0
1
1
0
1
1
0
1
1
0
0
0
0
0
1
0
0
0
0
1
2
1
0
0
2
0
0
0
2
0
0
1
2
0
0
2
2
0
1
0
0
2
0
1
0
0
0
8
0
1
1
2
0
1
0
0
1
0
0
1
0
0
0
0
1
2
1
0
1
0
1
3
0
1
0
0
0
2
0
0
1
2
0
5
0
2
0
0
1
2
2
0
0
0
0
0
0
0
1
2
1
0
0
1
1
0
0
0
2
0
0
0
1
1
1
1
2
0
0
0
0
0
1
1
2
2
0
1
1
1
2
2
0
2
1
1
2
0
0
0
3
1
0
1
3
0
0
0
1
0
0
1
1
0
2
0
0
0
0
0
2
2
1
0
2
1
0
1
1
0
0
0
0
2
0
3
2
0
1
0
0
0
1
2
0
1
0
2
0
0
0
1
2
0
0
0
0
1
0
1
2
0
0
2
0
1
1
0
1
2
2
2
0
3
2
2
0
2
0
0
0
0
2
0
2
0
3
0
0
0
1
0
0
0
2
0
0
1
0
0
0
1
0
0
2
2
2
1
2
2
0
0
0
0
0
0
2
2
2
0
0
2
0
2
0
1
0
2
0
1
0
0
0
0
2
1
0
0
0
1
0
0
0
0
1
0
2
1
0
2
0
0
2
0
1
0
0
2
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
1
1
2
0
1
0
1
0
0
1
2
2
0
2
0
0
2
1
1
0
0
0
0
1
1
3
0
0
1
2
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
2
0
0
0
0
2
0
0
1
2
1
0
0
2
0
1
1
0
0
0
1
0
0
1
0
1
0
1
1
0
0
0
1
0
0
0
1
0
0
1
1
1
0
2
1
2
2
1
0
0
2
0
0
0
0
2
1
2
0
0
2
0
0
2
0
0
1
0
0
1
0
0
0
2
0
2
1
0
1
2
0
0
0
0
2
2
1
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
1
0
1
1
0
1
0
2
0
0
0
0
0
1
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
1
0
1
2
0
3
0
1
1
0
0
0
2
0
0
1
1
0
3
1
2
0
2
0
0
1
1
0
1
2
1
2
0
1
1
0
1
1
1
1
1
0
0
0
0
0
1
2
0
0
1
2
0
2
1
0
0
0
2
0
3
0
0
2
1
2
0
0
1
0
0
0
0
2
0
0
0
2
1
0
0
2
1
0
0
2
2
0
1
1
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
1
1
1
1
1
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
1
3
0
3
0
0
1
0
0
1
1
1
2
2
2
0
2
1
1
0
0
0
0
2
2
0
0
0
3
0
0
1
1
0
0
2
2
0
0
1
2
1
0
1
2
0
0
2
0
0
0
0
1
0
0
1
0
1
0
0
0
2
0
2
2
2
2
1
0
0
0
0
0
1
2
0
0
0
0
3
0
0
0
0
2
0
0
0
2
0
1
2
2
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
2
2
1
1
0
1
0
0
1
2
0
0
1
1
0
1
0
1
2
0
0
0
0
0
0
1
1
2
0
2
0
0
1
0
0
0
1
0
2
1
2
0
2
0
0
0
0
0
2
2
1
2
2
0
1
2
0
0
0
1
2
0
1
0
0
1
1
0
0
0
0
1
0
1
0
2
2
1
0
0
1
2
0
0
0
2
1
0
2
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
1
1
1
0
0
1
1
0
1
2
0
0
1
0
0
0
1
1
0
2
0
0
2
0
0
2
0
2
1
1
0
0
0
0
2
2
0
0
0
0
2
2
0
1
1
0
0
0
0
1
0
2
2
0
0
0
1
0
1
0
1
3
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
2
1
0
1
1
2
0
0
1
2
0
1
0
1
2
1
0
2
3
0
0
0
0
2
0
0
2
2
1
0
2
0
0
2
1
1
2
0
0
0
0
2
2
1
0
2
2
2
0
0
2
0
2
1
2
0
0
2
1
0
2
1
2
0
0
1
1
0
2
0
0
1
0
2
1
1
1
0
0
0
0
2
2
0
0
2
3
0
2
1
2
1
0
0
0
1
0
2
0
2
0
1
0
0
0
1
1
0
2
2
0
0
0
0
1
0
0
0
1
2
0
2
0
2
2
0
1
2
1
0
0
2
2
0
0
0
1
1
0
0
1
1
1
0
0
0
2
0
1
1
0
2
0
2
1
0
0
1
1
0
0
3
1
0
2
0
2
0
3
0
2
0
0
0
0
0
0
1
0
2
1
0
0
2
2
1
0
0
0
2
1
0
0
0
2
0
0
1
1
0
0
0
0
0
1
0
0
2
2
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
1
2
0
1
9
1
0
0
0
0
0
0
6
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
1
0
1
0
1
1
2
1
2
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
1
0
0
0
3
0
0
0
3
0
2
2
0
1
0
0
0
0
0
1
1
0
0
1
0
0
2
2
1
1
1
0
0
1
0
0
0
1
0
2
2
0
0
2
1
2
0
2
2
0
2
1
1
0
2
0
0
0
1
1
1
0
1
0
0
0
0
1
2
1
0
1
0
0
0
0
2
0
1
0
3
1
1
2
0
0
0
0
0
1
2
0
0
0
2
0
1
0
0
1
0
1
0
1
0
0
2
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
2
0
0
1
0
2
1
0
2
2
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
1
0
2
0
0
1
0
0
1
1
1
2
0
2
0
1
2
0
2
2
1
1
0
0
1
0
1
0
0
2
0
2
1
3
1
0
0
2
1
0
0
3
0
1
1
1
2
0
0
1
1
2
1
2
1
1
2
2
0
2
2
0
2
0
1
0
0
0
0
0
2
0
0
0
0
1
1
1
1
1
1
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
2
2
1
0
0
0
0
0
3
0
0
0
2
0
0
0
1
2
0
1
1
0
0
0
0
0
0
1
0
0
5
0
2
0
0
1
2
2
1
1
1
0
1
1
0
0
0
0
0
0
2
0
2
0
1
2
0
0
2
1
0
0
0
0
0
0
0
1
1
0
0
2
0
0
2
1
1
0
0
0
0
0
0
0
1
2
0
1
1
0
0
1
0
1
1
1
0
0
2
0
0
0
1
1
0
0
1
1
0
0
2
0
1
2
0
1
2
1
1
1
2
1
2
0
0
1
0
0
0
1
0
2
0
0
1
1
2
2
1
0
1
0
0
2
2
0
2
0
2
2
0
1
1
2
0
2
2
0
0
3
2
0
1
0
0
2
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
3
0
1
0
1
0
0
0
0
0
0
1
1
2
0
1
0
0
1
0
0
2
2
0
0
0
0
2
0
0
0
2
2
2
2
1
0
0
2
0
2
0
2
1
1
0
0
0
0
2
0
1
0
1
2
1
0
0
1
2
0
0
2
0
0
0
2
0
1
0
0
0
1
2
0
0
1
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
2
2
1
0
0
0
0
0
1
0
0
2
0
3
0
0
0
0
2
2
0
1
2
1
1
0
0
0
1
4
0
2
1
0
2
2
0
0
3
0
0
0
0
0
2
0
2
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
3
0
1
2
0
2
0
0
0
1
0
2
0
2
2
1
0
2
0
2
1
2
0
1
2
2
1
0
1
1
1
1
2
0
2
0
2
1
0
2
0
1
0
1
0
0
0
1
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
2
2
0
1
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
2
1
0
0
2
0
2
1
0
2
0
1
0
0
0
1
2
0
0
3
0
0
1
0
2
0
0
2
0
2
0
1
2
0
0
0
0
1
2
0
1
0
0
0
1
2
1
2
2
0
0
0
0
0
1
0
0
1
0
3
2
0
0
2
0
1
2
1
0
0
0
1
0
0
0
0
0
2
0
1
1
1
0
2
1
1
0
0
0
0
1
2
2
2
0
0
0
0
2
1
1
1
1
1
0
0
0
0
0
0
0
1
2
2
1
1
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
1
2
0
2
0
0
0
0
2
0
0
0
0
2
0
0
1
1
1
1
0
0
2
1
0
0
0
0
0
1
1
0
0
0
0
2
0
0
2
0
0
0
2
0
1
1
1
1
3
2
0
4
2
2
2
1
0
2
2
0
1
1
0
0
0
1
0
0
0
0
1
2
0
0
1
0
3
1
1
0
1
2
0
0
0
1
2
0
1
2
1
1
1
1
1
0
3
0
0
0
0
0
0
0
2
0
0
0
0
1
1
1
2
0
0
0
1
1
1
1
2
1
1
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
6
0
0
3
1
0
1
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
1
0
2
2
0
0
1
0
0
1
1
1
1
0
0
2
0
1
0
2
0
2
0
0
0
0
3
0
0
0
0
1
1
0
2
0
0
1
1
2
0
0
1
0
0
0
1
0
2
2
2
0
0
0
0
3
0
1
0
2
2
0
0
2
0
1
0
1
0
0
0
1
0
1
2
1
0
1
0
0
2
2
0
0
1
0
0
0
0
2
1
1
1
1
1
2
0
1
0
0
1
0
1
0
0
0
0
2
1
2
0
0
2
0
0
0
2
0
2
1
0
1
2
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
1
1
1
0
0
0
0
0
0
2
1
0
0
0
0
1
0
2
1
0
0
0
1
0
1
1
0
0
0
2
0
1
2
0
0
0
1
2
1
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
1
5
1
0
0
1
1
2
0
2
2
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
1
2
2
1
0
1
0
1
1
0
0
2
0
0
1
0
1
2
0
0
1
0
0
0
1
1
0
2
2
0
0
0
0
0
0
0
1
1
1
0
4
2
0
1
1
1
2
1
0
0
0
0
1
2
1
0
2
2
1
0
0
2
2
0
0
0
0
0
0
0
1
0
3
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
3
0
2
1
2
0
0
2
1
0
0
0
2
1
2
1
1
0
0
2
0
0
0
1
0
2
0
1
3
0
0
0
0
2
1
0
2
0
0
0
0
0
0
2
2
0
2
2
0
0
0
0
1
0
2
0
1
2
0
0
2
0
0
3
0
1
3
2
2
1
0
0
0
0
0
1
1
0
0
0
0
0
0
2
2
2
1
1
2
0
1
0
0
0
0
2
0
1
0
0
1
0
0
1
1
2
1
0
1
0
2
1
0
0
2
0
0
0
0
0
0
2
2
2
1
1
0
1
0
1
1
3
1
9
2
0
0
0
1
0
1
1
2
0
0
0
0
1
0
2
0
0
2
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
2
0
0
1
2
0
2
2
0
0
0
0
5
0
0
1
1
1
3
0
0
0
0
1
1
1
0
2
0
0
0
0
0
2
1
0
1
2
2
0
1
2
1
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
1
0
2
0
1
2
0
0
1
1
0
1
1
2
1
2
0
1
1
2
0
0
1
2
0
2
0
0
0
1
0
1
2
0
2
0
0
0
2
0
0
0
2
0
2
0
1
0
1
1
0
1
1
0
2
0
0
1
2
0
0
0
0
0
2
1
1
1
0
0
0
0
2
1
0
0
0
0
2
0
0
6
0
1
1
0
1
1
0
1
0
2
1
0
0
0
0
1
1
0
1
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
2
1
0
0
2
2
0
0
0
2
2
1
0
1
1
0
0
0
1
0
2
1
1
1
1
2
0
2
0
3
1
1
0
2
0
0
2
1
0
1
0
0
0
3
2
2
0
2
0
1
2
0
0
0
0
2
1
1
0
0
0
2
1
3
2
0
0
2
1
0
0
0
2
0
1
0
0
2
1
0
1
0
1
0
0
0
0
1
2
0
0
0
2
2
0
0
0
0
0
2
1
1
1
0
0
0
0
0
1
0
1
0
0
0
0
2
2
0
2
0
0
0
1
0
0
0
2
1
0
0
1
2
0
1
2
2
0
0
2
0
1
0
0
0
1
1
0
2
2
0
1
0
1
2
2
2
0
2
2
1
0
0
1
0
5
0
0
1
0
2
1
0
0
0
1
0
0
3
0
2
0
1
0
1
2
0
2
0
0
2
1
0
3
0
2
4
2
0
2
0
1
2
2
1
0
0
2
0
0
0
0
0
2
0
0
0
1
2
2
0
2
1
0
2
0
0
1
0
0
0
0
0
4
3
0
0
0
0
0
0
3
2
2
1
0
2
1
1
0
0
0
0
0
0
0
2
0
0
2
2
2
0
2
0
1
1
0
1
0
0
0
1
1
0
2
0
1
0
0
0
0
0
2
0
0
1
0
0
1
0
1
1
1
2
2
0
1
2
0
0
2
2
0
2
2
1
1
0
0
1
0
1
0
0
2
0
0
0
0
0
0
1
0
2
0
2
0
1
1
0
0
0
0
2
0
0
2
0
0
2
0
0
2
1
2
0
0
0
0
0
0
1
0
2
2
0
2
1
0
0
0
1
0
5
0
0
0
2
1
1
1
2
0
0
0
0
3
0
1
1
0
0
2
0
0
0
0
2
2
0
0
0
2
1
0
1
0
0
0
1
0
1
1
0
0
3
0
1
0
2
1
0
0
0
0
0
1
1
1
0
0
1
0
0
3
0
0
0
0
1
0
0
2
0
0
1
0
2
0
1
1
2
0
0
0
1
2
0
0
0
0
2
0
0
2
1
1
0
0
1
2
5
0
2
0
0
0
0
2
1
0
0
2
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
5
0
2
2
0
2
0
0
1
2
0
2
2
2
0
0
0
1
0
0
0
0
0
0
2
1
1
0
0
1
0
0
0
1
1
0
0
0
0
0
2
0
0
2
2
0
2
2
2
0
2
6
0
0
2
0
2
1
0
2
0
1
1
0
1
0
2
0
2
0
2
0
0
0
1
0
1
0
0
1
2
0
1
1
0
1
0
2
2
0
0
0
1
1
2
0
0
2
1
3
1
0
1
3
0
0
2
2
0
0
2
3
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
3
0
1
0
0
0
2
0
5
0
1
1
0
2
1
0
1
0
1
1
0
0
0
0
2
0
0
0
2
1
0
0
0
0
1
0
0
1
1
1
0
0
1
0
0
1
0
1
2
1
0
0
1
0
1
3
0
1
0
1
3
1
2
0
3
1
3
1
0
3
2
1
0
0
0
0
2
0
0
1
2
1
0
1
2
1
1
0
0
0
0
0
0
0
3
0
1
0
0
0
0
1
0
1
0
0
1
0
1
0
1
0
0
0
1
0
5
3
0
0
0
0
0
0
0
0
2
1
1
0
0
0
1
2
3
2
2
0
1
0
2
1
2
0
2
0
2
2
1
0
2
2
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
1
2
0
0
3
1
2
0
3
0
2
2
1
0
0
1
0
1
3
1
0
0
1
1
1
2
0
0
1
1
0
0
2
0
1
0
1
1
0
0
0
2
0
0
2
0
1
2
1
3
0
0
1
1
1
3
0
0
0
1
0
8
1
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
3
0
0
1
0
2
1
1
0
2
0
1
1
0
0
1
1
0
2
2
0
0
2
0
0
0
0
0
0
0
2
0
2
2
2
0
0
1
0
0
1
0
0
0
1
0
1
2
1
1
0
1
0
2
0
0
2
2
0
0
2
1
0
2
0
0
1
2
0
2
1
1
0
0
0
2
1
0
1
2
2
1
0
0
1
0
1
0
0
2
1
0
0
0
1
1
3
2
0
1
0
3
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
2
2
2
0
0
0
0
1
0
1
0
0
2
0
0
1
0
1
1
1
0
0
0
0
1
1
1
2
1
1
0
0
0
0
2
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
2
0
1
1
2
1
2
0
0
2
1
1
1
0
0
0
0
0
0
2
0
0
1
2
2
0
1
1
1
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
1
0
2
1
0
1
0
1
0
0
1
0
0
2
0
0
1
3
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
1
1
2
1
0
0
0
0
0
2
1
0
2
0
1
0
0
0
1
1
0
0
0
1
0
2
1
0
2
2
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
2
0
2
1
0
1
0
4
0
1
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
2
0
1
2
0
1
0
0
0
0
0
0
1
0
2
0
1
0
0
0
2
1
2
2
0
0
2
0
2
2
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
1
1
0
2
1
1
0
0
0
0
1
0
2
1
0
0
0
1
2
2
0
2
2
2
0
0
0
0
0
2
0
2
1
1
0
1
0
0
0
1
0
2
0
2
0
1
0
0
1
0
0
0
0
0
2
0
0
2
1
0
0
0
0
2
0
1
0
1
1
1
0
2
0
0
1
1
1
1
1
0
1
0
2
0
3
0
1
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
2
1
0
0
1
0
1
0
0
0
0
2
0
0
2
1
0
2
2
0
1
0
0
0
0
0
0
2
2
1
1
2
1
0
2
0
1
0
0
0
2
3
1
1
2
0
0
0
1
1
0
0
0
1
1
1
0
0
1
0
1
0
0
2
0
0
0
1
0
3
0
0
0
1
1
2
2
2
2
1
1
1
0
0
0
2
2
0
0
0
0
0
0
1
1
0
0
2
3
1
0
0
0
0
2
2
0
2
0
1
2
0
1
0
0
0
2
1
2
0
0
2
0
1
0
1
0
0
0
0
0
2
0
0
2
1
2
0
2
1
1
1
0
1
0
0
0
0
1
0
0
2
2
0
1
0
0
1
0
0
1
0
2
1
0
0
1
1
0
0
0
1
2
0
2
1
1
0
0
1
0
0
0
2
0
2
0
0
0
0
0
1
0
2
0
0
0
2
1
2
1
0
0
0
2
1
0
1
1
1
1
2
2
0
2
0
0
0
0
0
1
1
0
1
0
0
0
2
0
1
2
0
0
1
0
0
2
2
2
1
0
0
1
0
0
2
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
1
1
3
0
0
0
1
1
2
2
0
1
0
0
3
1
0
0
0
2
1
2
1
0
0
2
0
1
0
0
0
0
0
1
1
0
2
3
0
0
2
2
1
0
1
0
0
0
0
0
2
2
1
1
0
1
0
2
0
1
0
0
2
0
0
2
0
3
1
0
0
1
2
0
1
0
2
0
0
2
2
0
0
1
1
1
1
1
0
0
2
1
0
0
1
1
1
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
2
0
0
1
1
0
2
0
1
0
0
0
2
0
0
0
0
0
2
1
2
1
0
0
1
0
0
0
0
0
0
2
2
1
0
0
1
0
1
0
0
2
0
0
0
1
2
0
2
2
1
1
0
0
0
0
0
2
0
0
2
0
0
1
1
0
0
0
1
0
0
1
1
0
0
2
0
0
1
1
1
0
0
0
0
0
2
1
0
0
2
1
0
0
0
0
1
3
0
0
0
0
0
2
1
0
0
0
0
0
1
1
1
0
2
1
0
1
0
0
0
2
1
2
0
0
1
0
2
0
1
0
0
1
1
0
2
0
0
0
0
1
1
1
1
0
1
0
0
1
2
0
1
2
0
1
2
0
0
3
2
0
0
0
2
0
2
2
1
0
2
0
1
1
0
0
3
0
3
0
0
1
0
2
1
2
1
1
0
0
0
0
0
1
2
0
9
1
0
0
1
0
0
0
0
0
2
1
0
1
1
0
2
0
0
0
0
2
0
0
0
1
2
2
0
0
1
0
6
0
0
3
2
0
2
2
1
0
0
1
0
0
1
1
4
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
2
0
0
0
2
1
1
0
1
0
5
1
0
2
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
2
0
0
2
1
0
0
1
0
1
0
2
0
1
0
1
2
2
0
1
1
0
2
1
0
1
0
1
0
1
0
0
1
2
1
1
2
0
2
0
0
0
2
0
0
0
1
1
0
0
0
2
1
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
1
0
0
2
2
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
3
0
2
0
1
0
1
1
1
0
0
1
1
0
1
1
0
1
3
2
1
0
0
0
2
0
2
0
0
0
0
1
3
2
1
0
1
0
4
2
1
1
0
1
1
2
1
0
1
0
0
1
0
1
0
4
1
0
2
0
0
1
0
0
0
0
1
1
0
0
1
1
0
0
1
0
1
2
1
0
0
0
1
1
2
1
0
0
0
0
0
0
2
0
0
0
0
2
2
0
1
0
0
2
0
1
2
0
0
0
0
0
2
0
0
1
2
0
1
1
1
0
1
2
0
2
1
0
0
2
0
0
0
1
0
0
0
2
0
0
1
1
0
0
2
0
0
0
1
1
0
1
1
0
0
0
0
2
1
0
2
1
1
2
2
2
2
0
1
0
1
1
0
1
0
2
1
0
0
0
2
2
0
0
1
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
1
1
0
0
1
0
0
2
2
0
1
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
1
0
1
1
0
0
10
0
1
0
0
0
0
2
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
1
2
0
0
2
0
3
0
1
0
3
0
0
2
0
1
0
0
0
2
2
0
1
0
1
0
0
0
0
1
0
0
0
0
1
2
1
0
0
0
0
0
0
2
2
1
1
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
3
2
1
2
0
2
1
1
0
0
0
3
1
0
0
2
0
0
0
0
0
1
1
0
0
0
1
1
1
0
0
0
0
0
0
2
0
1
1
2
0
0
0
0
0
1
0
1
2
1
0
1
0
3
0
0
2
0
0
0
2
0
0
0
0
2
2
2
0
1
1
0
0
1
2
0
0
2
2
0
0
0
0
0
0
2
2
0
1
6
1
0
0
0
1
1
0
1
0
0
0
1
0
2
0
2
0
0
1
0
0
0
1
2
1
0
0
0
2
0
2
0
0
1
0
0
2
0
0
0
0
0
2
3
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
1
1
0
0
1
0
1
2
0
0
0
1
2
0
0
0
1
1
0
0
0
1
0
1
0
0
2
2
0
1
1
2
1
0
0
1
0
0
2
1
0
1
0
0
0
1
1
1
3
0
2
2
2
0
0
1
0
1
0
0
0
2
0
1
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
1
2
1
0
1
0
0
0
0
1
0
0
0
2
0
1
1
0
3
2
2
1
2
2
1
0
0
1
0
0
0
2
1
0
1
0
2
1
0
2
0
0
1
1
0
0
0
1
2
1
1
0
2
0
1
2
2
2
1
0
2
1
1
0
4
0
1
1
1
2
1
1
1
1
2
1
1
0
0
1
0
0
1
1
0
0
3
0
2
1
1
0
0
0
1
1
2
0
2
1
0
1
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
2
1
0
2
0
0
0
1
0
1
0
0
2
0
0
0
1
1
0
0
1
2
1
0
0
0
1
2
0
7
1
3
2
2
1
0
0
2
0
0
0
2
0
0
2
0
1
1
0
0
0
0
0
0
2
0
0
0
1
0
0
1
1
2
0
0
0
2
2
2
1
0
0
1
0
0
1
0
1
0
0
1
2
1
2
1
2
2
2
0
2
2
0
1
0
0
0
1
1
2
0
2
0
0
2
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
1
0
0
0
0
2
3
0
0
0
3
0
0
0
4
2
0
0
1
0
0
0
0
1
0
2
2
2
0
0
1
0
2
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
2
0
2
1
1
2
2
0
2
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
1
1
2
0
2
2
0
0
0
0
2
0
0
0
2
1
0
0
0
2
0
0
0
0
1
0
1
0
2
0
0
1
0
1
2
0
2
0
1
2
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
1
1
3
0
0
0
0
0
2
1
1
2
2
0
1
2
1
0
2
0
0
0
0
1
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
7
1
0
1
0
0
2
0
2
1
2
2
1
1
0
0
1
0
0
1
1
0
0
1
2
0
0
0
0
0
2
0
1
1
2
0
1
0
1
0
0
2
2
2
2
1
0
0
0
0
0
2
1
1
0
0
1
1
0
1
2
2
0
1
0
0
1
2
1
0
0
0
2
0
0
0
0
0
0
2
0
0
1
1
0
0
1
1
0
0
0
1
0
2
2
0
0
1
0
0
1
0
2
0
0
0
0
0
1
0
2
0
1
2
2
1
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
1
0
0
3
2
1
0
0
0
0
0
1
1
0
0
1
0
0
2
1
0
3
2
0
0
1
1
0
0
1
0
0
0
2
0
0
0
2
1
0
0
0
0
1
0
2
2
1
2
0
0
1
3
2
0
0
0
2
1
1
0
2
1
2
0
2
2
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
2
1
1
1
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
1
0
2
1
0
1
0
0
0
1
1
0
0
1
1
1
0
0
2
0
1
2
0
0
0
2
0
0
1
0
0
1
0
0
2
1
0
0
0
1
2
0
0
1
0
2
0
2
0
0
0
1
2
0
1
2
1
1
1
0
0
2
0
2
2
0
0
0
0
0
2
0
1
2
0
0
0
2
0
1
2
0
2
0
0
0
0
0
1
1
0
1
2
1
0
1
0
2
0
0
1
0
1
0
0
0
3
0
0
0
2
0
2
0
0
1
2
1
0
1
0
1
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
1
1
1
2
0
0
2
2
0
2
0
2
0
1
0
2
1
0
2
0
1
1
1
0
0
0
0
0
0
2
0
0
3
0
1
2
2
0
0
2
1
1
0
0
2
2
0
2
2
0
0
1
1
0
1
2
0
0
0
0
0
1
0
1
0
0
0
2
0
1
0
1
0
0
2
1
2
0
0
2
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
1
2
0
0
0
1
1
2
0
1
1
0
2
2
0
1
0
0
0
1
2
0
0
1
0
0
0
0
1
0
0
0
2
1
1
0
1
2
1
2
0
1
0
2
0
1
0
0
2
0
0
0
0
1
1
0
2
0
1
0
0
1
1
2
0
1
0
0
0
0
2
1
0
1
0
1
0
0
1
1
1
0
0
1
0
0
1
4
0
1
0
0
0
2
0
0
0
0
1
0
0
0
1
1
1
1
0
0
0
1
2
1
0
0
1
1
2
0
1
0
0
1
2
2
1
0
2
0
2
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
2
0
0
2
1
1
1
1
1
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
2
0
1
0
2
0
1
2
2
0
0
1
0
2
3
0
0
0
2
0
0
2
0
1
1
0
0
0
0
0
0
0
1
0
0
4
1
3
1
1
0
0
0
0
0
2
1
0
1
0
0
0
1
0
2
0
2
2
2
1
2
2
1
0
1
2
1
1
0
0
1
0
1
1
0
0
0
0
2
1
1
0
0
0
2
1
1
0
0
1
2
0
1
2
1
0
0
2
0
1
0
0
0
2
0
0
1
1
2
0
0
0
0
1
2
0
1
0
1
1
1
0
1
1
2
2
0
3
1
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
1
2
1
3
3
2
0
0
0
0
0
2
0
0
1
0
0
2
1
1
1
0
1
0
1
1
2
0
1
0
5
0
2
0
0
0
1
0
0
2
1
0
1
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
1
3
2
2
0
1
0
1
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
5
1
2
1
0
1
2
0
2
0
2
2
0
2
0
0
0
2
2
0
0
0
1
0
1
0
2
0
0
0
4
2
2
0
2
2
0
0
1
2
1
2
0
2
1
0
0
2
0
0
0
1
0
0
0
1
0
0
0
2
0
0
1
0
0
1
0
0
1
1
0
2
2
2
1
0
2
2
0
0
0
0
1
0
0
0
0
0
2
2
2
1
0
2
1
2
0
0
0
0
0
2
1
0
0
2
2
0
0
1
1
0
2
0
1
0
1
2
2
2
2
1
0
0
1
0
0
0
1
1
0
1
0
2
0
1
2
0
1
0
2
2
1
0
0
1
1
2
0
1
0
0
1
0
0
0
0
1
2
1
0
0
2
0
0
1
0
1
2
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
2
2
0
1
1
2
0
2
0
2
0
0
2
0
0
0
1
1
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
2
0
2
0
0
1
0
0
2
0
2
0
3
2
1
0
1
0
2
0
0
1
2
0
1
2
2
2
0
3
0
0
0
0
1
2
0
0
2
1
2
0
0
0
1
0
10
0
2
1
0
1
0
0
1
1
0
0
0
3
0
2
1
0
1
0
2
0
2
1
0
1
1
1
0
0
0
1
1
0
0
0
0
0
0
0
1
2
2
2
0
0
0
1
2
0
0
3
2
3
0
2
0
0
2
2
0
2
2
0
1
1
0
2
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
1
0
0
2
2
1
3
1
0
0
0
0
0
0
0
2
1
0
3
1
0
0
1
2
0
0
0
0
0
0
3
0
1
0
0
1
0
1
0
0
2
0
2
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
2
0
0
1
0
2
0
2
0
0
0
1
1
0
0
0
1
1
1
1
2
2
1
2
0
0
1
1
2
2
2
2
0
1
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
1
0
0
2
1
0
2
2
1
0
1
1
0
0
0
2
2
1
0
1
2
0
0
0
0
1
0
0
1
0
0
1
1
0
1
0
0
0
0
2
0
0
0
2
1
2
0
0
2
0
0
0
1
0
0
4
0
2
1
2
2
0
2
0
3
0
1
1
1
0
0
0
0
1
1
0
1
0
1
1
2
0
1
1
2
2
0
0
0
0
2
2
1
0
0
0
1
2
0
1
2
2
1
2
1
2
0
2
0
2
0
0
1
0
3
0
0
0
0
0
2
0
0
4
1
2
0
2
1
0
2
2
0
0
0
2
0
1
0
0
2
0
0
2
2
0
0
1
1
0
1
0
0
1
1
1
0
0
0
2
0
2
0
1
2
0
1
3
0
1
0
0
0
2
2
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
2
2
2
0
0
0
1
4
1
0
1
3
1
0
2
0
2
1
1
0
0
0
2
2
0
1
1
0
0
0
0
0
1
2
0
0
0
0
1
0
1
0
0
2
0
2
0
0
0
2
0
0
0
0
2
1
0
2
1
0
0
0
0
2
0
0
1
1
1
0
1
2
1
0
0
0
2
0
0
0
1
0
1
0
2
0
0
1
0
2
2
2
0
0
0
0
0
1
1
0
2
1
0
2
2
2
0
0
1
0
0
1
0
0
0
2
1
0
1
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
1
0
1
2
1
0
4
1
1
1
0
1
1
3
0
2
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
1
2
0
3
0
0
2
1
0
0
0
0
2
2
1
0
1
0
0
0
0
0
0
9
1
1
0
0
2
0
0
0
1
0
0
0
0
0
2
0
7
0
0
1
1
0
1
1
0
1
2
0
0
1
0
2
0
0
0
0
0
0
0
2
1
1
0
2
0
0
1
2
2
1
0
0
2
0
1
1
0
0
2
0
0
0
2
0
2
0
0
0
0
5
0
2
0
2
0
1
1
4
1
0
2
2
1
1
0
1
1
0
3
0
0
0
2
0
0
1
1
0
0
0
1
1
1
0
2
1
0
0
2
0
3
1
1
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
3
0
2
0
1
1
0
0
1
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
3
0
2
2
0
2
0
0
2
1
0
1
0
0
2
0
0
2
1
0
0
0
1
1
1
0
0
1
2
2
0
0
1
1
1
1
0
2
2
2
0
0
0
1
0
0
2
0
0
0
0
0
2
0
1
1
0
0
0
0
0
1
0
1
0
3
0
2
0
1
2
0
0
0
1
0
0
3
0
0
0
2
0
0
0
1
0
1
0
0
1
2
0
0
0
0
0
0
0
0
3
0
2
1
0
0
0
1
0
0
0
1
0
0
0
1
2
0
1
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
2
0
0
2
2
2
1
2
0
0
2
1
1
1
0
1
0
0
1
1
1
0
0
3
1
0
1
0
0
4
0
0
0
2
1
1
1
2
0
0
0
2
2
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
2
0
1
2
2
1
0
0
2
1
2
0
1
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
2
0
0
1
0
0
1
0
0
0
0
0
0
1
0
2
2
2
0
1
0
0
2
0
2
2
1
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
2
2
2
2
0
0
2
1
0
2
0
0
1
2
0
1
0
1
0
0
1
2
1
0
1
0
2
0
1
2
0
2
0
0
2
0
0
0
1
2
1
0
1
1
0
0
0
0
0
1
0
1
2
2
0
0
0
0
1
0
2
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
1
1
0
1
1
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
2
2
1
0
0
0
0
2
2
2
2
0
1
2
0
1
0
2
0
0
2
0
2
0
2
1
2
0
0
1
1
0
2
0
0
0
1
2
0
0
2
0
2
0
0
0
2
2
0
1
0
0
0
0
0
2
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
1
3
2
0
1
0
1
1
1
2
0
2
0
0
0
0
0
0
0
0
1
4
0
0
0
1
1
2
1
0
0
1
2
0
0
0
1
0
1
0
0
0
1
0
1
1
4
0
2
1
0
1
0
2
4
1
0
0
0
0
2
0
0
1
0
0
0
1
0
0
1
2
1
0
2
0
2
0
1
1
0
0
1
0
0
2
1
1
0
0
2
1
1
1
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
1
0
0
0
2
0
2
0
1
0
3
0
0
0
0
1
0
2
1
1
1
1
0
1
0
1
0
0
2
0
1
0
1
0
2
1
0
0
1
1
0
0
0
0
0
2
0
2
0
1
2
0
0
0
1
1
1
0
1
0
2
0
0
0
2
0
2
0
0
1
2
0
0
0
0
0
1
0
1
2
2
2
0
0
1
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
1
1
0
2
0
0
0
1
1
0
2
0
1
0
2
1
0
1
0
2
0
0
0
0
0
2
0
1
2
2
0
5
1
0
0
0
0
1
1
2
0
1
2
0
2
1
0
1
0
0
0
2
1
0
2
0
0
0
1
0
0
1
0
3
1
1
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
1
0
0
2
1
0
0
0
1
1
0
1
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
1
0
1
0
0
1
2
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
4
0
0
0
0
0
1
1
0
0
0
0
1
0
3
0
1
1
2
0
0
2
1
0
0
1
0
2
0
0
0
1
1
0
0
2
0
2
1
2
0
3
1
2
2
0
0
0
2
1
0
0
0
0
0
2
1
1
0
1
0
0
2
0
0
1
2
1
0
2
0
0
1
1
0
0
0
0
2
0
0
1
1
2
0
0
0
0
1
0
1
0
2
0
1
2
0
0
0
1
0
1
1
0
0
0
0
0
0
2
2
2
0
0
0
0
1
0
1
3
0
1
1
2
0
1
0
0
1
0
0
1
2
2
0
0
0
2
1
0
0
1
0
0
0
2
0
0
2
0
0
0
2
1
0
0
1
0
0
2
1
2
0
1
1
0
0
3
0
0
0
2
1
0
0
0
0
2
0
2
0
1
2
3
2
1
0
0
1
0
2
1
1
0
0
0
1
0
2
2
0
0
2
0
0
0
0
2
0
2
2
2
0
2
0
0
0
0
0
0
0
0
2
2
5
1
0
1
1
0
1
2
0
0
0
2
2
2
0
0
1
0
0
1
2
1
0
1
0
0
1
0
0
2
2
0
0
0
0
0
0
0
1
2
0
0
1
1
2
2
1
2
2
0
0
1
0
0
0
1
3
0
2
3
0
0
0
0
0
0
1
2
1
0
0
0
2
0
1
0
1
0
0
1
0
0
0
1
0
2
2
2
0
2
0
1
0
1
0
0
0
1
1
0
1
0
1
1
1
0
0
1
0
0
0
0
2
2
0
0
0
3
0
0
2
2
0
0
2
0
1
2
0
1
0
0
1
0
0
0
0
1
0
1
2
0
1
0
1
0
1
0
0
0
0
0
0
2
0
0
2
2
2
0
0
2
0
0
0
0
0
1
0
1
0
2
0
0
0
1
1
0
1
1
0
0
3
2
3
1
2
2
0
1
0
0
0
3
0
0
0
2
2
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
2
1
4
0
0
0
0
2
0
2
0
0
1
0
1
0
1
1
0
0
1
0
0
0
0
0
1
0
1
0
0
1
1
0
2
1
0
0
1
0
0
0
1
2
2
0
0
0
0
1
2
0
2
0
0
1
0
1
0
0
1
2
1
5
0
2
0
0
2
0
0
0
0
1
0
0
1
1
1
1
1
1
0
2
2
0
1
0
0
0
0
0
1
2
0
3
1
0
3
1
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
1
0
0
1
4
2
1
0
0
0
0
2
1
0
1
1
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
1
2
0
2
1
0
0
1
1
2
1
0
1
1
0
0
1
0
2
0
1
2
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
2
1
1
0
1
0
0
0
2
1
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
1
1
0
1
0
0
1
1
0
2
0
1
0
0
1
1
0
0
1
1
2
2
0
0
0
0
2
2
0
0
0
1
0
1
2
2
1
1
1
1
0
0
0
0
1
0
0
0
2
0
2
1
1
1
1
1
1
2
0
2
2
0
0
0
0
2
1
2
0
0
0
0
1
0
1
0
0
0
0
2
1
1
0
2
1
0
0
1
0
0
2
0
0
0
2
0
0
1
0
1
0
0
0
0
1
0
2
2
0
0
1
0
0
0
0
0
0
0
1
0
2
0
1
1
0
4
0
2
2
0
0
0
0
0
2
2
2
1
2
0
2
2
1
0
1
2
2
1
1
1
0
0
2
1
0
0
1
0
2
0
0
0
2
0
2
0
0
0
1
1
0
0
0
2
0
2
0
1
0
0
0
1
0
0
2
0
1
0
2
0
0
0
0
2
0
0
2
0
0
1
2
0
1
1
1
0
0
0
1
1
2
2
0
2
0
1
0
1
1
3
2
2
0
0
0
0
0
2
0
0
1
0
2
0
1
0
0
2
0
0
1
1
2
2
2
0
0
0
2
0
1
0
0
0
1
2
2
1
2
1
0
1
0
1
1
1
0
0
0
2
1
0
0
0
1
0
0
2
3
1
2
2
0
0
0
0
1
0
2
0
0
1
2
1
0
0
2
2
1
2
1
2
0
3
0
0
0
0
0
0
1
0
0
0
0
1
2
1
1
1
0
2
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
1
1
2
0
0
0
0
0
2
0
0
0
0
0
0
1
1
1
0
0
2
2
2
0
1
1
0
0
2
2
0
0
0
0
0
0
0
2
3
1
0
2
0
0
1
2
0
0
0
1
0
2
0
0
0
0
2
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
2
4
0
0
0
0
0
2
1
0
1
0
0
1
1
0
1
0
1
2
0
0
0
1
1
1
0
0
1
0
0
2
0
0
0
1
0
0
1
0
0
2
0
1
0
1
1
0
0
1
2
2
0
2
0
0
2
0
0
1
0
2
1
3
2
0
1
2
2
0
2
1
0
3
2
0
2
0
2
2
0
0
0
2
0
0
0
2
0
0
0
1
0
0
2
0
2
0
0
0
2
0
2
0
0
1
0
1
1
1
2
0
0
2
2
2
0
2
0
0
2
0
0
0
2
0
0
0
2
1
2
0
0
1
0
3
0
0
2
0
0
0
1
2
1
2
1
2
0
2
1
0
1
2
1
2
0
2
2
2
2
1
2
0
0
2
4
2
1
0
2
0
0
0
0
2
0
2
0
1
0
0
0
2
0
2
0
2
0
0
1
2
0
2
1
0
2
0
1
0
0
0
2
2
0
2
3
0
2
1
0
1
0
1
0
0
0
0
1
1
1
1
2
0
1
2
0
1
2
0
2
0
0
1
1
0
1
1
0
0
1
1
1
1
0
0
1
2
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
1
2
1
2
1
2
2
1
0
0
0
1
1
0
0
0
0
0
2
0
2
1
1
2
0
1
0
1
0
1
0
0
0
1
1
1
0
0
2
1
2
1
2
0
0
3
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
2
1
0
0
0
0
0
1
0
0
0
1
2
0
1
0
2
0
2
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
1
0
2
2
0
1
2
0
1
0
1
0
2
0
3
0
2
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
2
1
0
0
1
0
0
1
0
0
2
0
1
1
2
1
2
1
0
1
0
0
0
2
1
0
3
0
0
2
2
1
1
0
0
0
0
0
2
1
0
0
1
0
0
1
0
0
0
1
0
2
1
2
0
1
1
2
1
0
0
2
1
2
3
0
1
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
1
2
1
0
1
2
1
3
0
0
0
0
0
0
0
2
0
0
2
0
1
2
0
0
1
0
0
0
0
0
0
2
1
1
2
0
1
1
0
2
0
0
2
0
2
1
1
0
1
0
0
1
0
1
0
1
0
0
0
0
2
2
0
0
0
1
0
0
2
2
0
0
1
0
3
4
0
0
2
1
0
0
1
2
2
0
0
0
0
1
2
2
2
3
1
1
0
0
1
0
1
0
0
1
0
0
1
0
0
0
2
0
1
2
1
0
0
0
0
0
3
0
0
0
0
0
0
1
1
0
1
0
0
1
1
1
0
5
1
0
0
0
1
0
2
0
1
0
0
1
1
0
1
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
1
2
0
0
1
0
1
0
0
0
1
1
0
1
1
0
1
1
0
1
0
3
1
1
1
1
1
0
0
1
0
1
0
2
0
2
1
2
0
2
1
0
0
0
0
2
1
0
1
0
0
0
1
1
0
2
0
0
1
1
2
1
1
1
0
0
1
2
2
2
0
0
0
3
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
2
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
1
1
0
0
0
3
0
0
0
1
1
3
0
0
0
0
1
0
0
0
1
0
1
2
0
0
1
1
0
2
1
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
1
1
1
0
1
0
0
1
1
0
1
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
1
0
1
1
3
1
1
0
0
2
0
1
0
0
0
0
0
0
0
0
3
0
1
0
1
1
0
1
0
1
0
2
0
0
0
1
2
1
0
2
2
0
0
0
2
1
0
0
0
0
0
0
2
1
1
1
3
2
2
0
0
0
0
0
2
0
0
2
2
1
0
0
0
0
0
2
1
1
1
0
0
0
2
0
1
1
1
0
0
1
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
2
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
3
2
0
0
1
0
0
0
1
0
0
0
0
2
0
1
2
0
2
0
0
1
1
7
1
0
1
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
3
2
1
0
0
0
2
0
3
2
1
2
0
0
0
1
1
2
2
0
0
0
1
0
0
0
2
0
1
0
1
0
0
0
1
0
0
0
0
2
0
1
0
0
1
0
1
0
0
1
1
1
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
2
1
0
0
1
0
2
0
1
1
0
0
0
0
1
1
0
2
0
1
0
0
1
0
0
0
1
2
0
1
1
0
0
1
0
0
2
1
0
3
0
2
0
0
0
0
0
1
0
1
0
0
2
0
0
1
2
2
0
0
0
0
0
2
4
0
0
0
0
0
0
0
1
0
0
0
1
1
1
1
0
0
2
2
2
0
0
0
1
0
0
0
2
1
0
1
0
0
0
2
1
0
0
0
2
1
0
0
0
3
2
3
0
0
1
2
2
1
2
1
1
0
0
1
0
0
0
0
0
0
1
1
1
1
0
2
0
1
0
0
2
0
0
0
1
2
0
2
0
0
0
1
0
0
2
1
1
2
0
0
1
2
1
0
0
2
0
1
1
1
0
2
2
2
0
1
0
1
1
1
0
1
0
0
0
1
0
0
1
2
1
1
0
2
0
1
2
1
0
0
0
1
1
0
2
0
0
0
2
0
2
3
0
0
0
0
0
0
1
0
3
0
0
1
0
1
2
1
0
1
0
0
1
2
0
0
0
0
0
1
0
0
1
0
2
2
0
0
0
1
0
0
1
2
0
2
0
0
0
0
1
0
1
1
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
1
0
0
2
1
1
0
1
2
2
0
0
0
0
0
0
2
0
3
1
0
1
1
2
0
0
0
1
2
0
2
2
1
2
2
0
0
0
1
3
2
1
1
0
0
2
0
1
0
0
2
1
2
0
0
2
1
1
0
0
0
2
0
1
0
0
0
0
0
2
1
2
0
0
0
1
3
1
2
0
0
1
0
1
1
0
0
0
0
0
0
1
1
1
2
0
1
0
0
1
1
0
2
1
2
2
0
0
0
2
1
0
0
0
0
2
2
0
1
0
0
0
1
1
0
0
0
0
1
0
0
2
2
1
1
0
1
0
0
0
0
2
0
0
2
0
2
0
2
0
2
2
0
0
0
2
0
0
0
0
0
2
0
1
0
0
2
2
0
0
2
0
0
1
0
0
0
2
1
1
1
1
0
0
0
1
2
0
0
1
1
0
0
1
0
0
2
1
2
2
0
0
0
2
0
0
1
0
1
1
2
1
0
0
0
2
0
2
0
0
1
2
1
1
2
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
1
2
1
0
0
0
2
0
0
0
1
0
0
1
2
0
2
1
2
0
1
1
2
2
0
1
0
2
0
0
1
0
0
0
1
0
1
0
0
1
1
1
1
1
0
0
2
2
0
3
2
0
0
0
0
0
0
0
0
1
1
0
0
0
1
2
0
0
0
0
0
3
0
1
1
0
0
1
0
0
0
2
0
2
1
0
0
1
0
0
0
0
2
1
0
0
0
2
0
0
1
0
2
0
1
0
0
1
0
2
0
0
2
0
2
0
0
2
0
0
1
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
1
1
2
2
2
1
0
2
0
0
0
0
2
0
0
0
0
0
1
1
2
0
0
1
0
0
0
0
0
2
3
1
1
0
1
1
1
0
1
5
2
1
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
2
2
2
1
2
0
0
1
0
1
1
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
1
0
0
0
0
2
0
0
3
0
0
0
0
1
0
0
2
0
0
0
2
1
0
2
1
0
0
0
0
0
0
0
2
1
0
1
0
0
3
0
0
0
0
1
0
0
0
2
1
0
0
0
2
2
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
4
0
2
0
0
0
2
0
0
3
2
0
1
0
0
0
1
1
3
0
0
1
0
1
1
1
1
0
0
1
2
1
0
0
0
1
0
0
0
0
0
1
2
3
0
0
0
0
5
2
1
2
1
0
0
0
3
0
1
0
2
0
1
1
0
0
1
0
1
0
1
2
2
2
1
0
0
0
0
0
1
1
0
3
0
0
0
2
2
3
1
1
1
0
3
1
1
2
0
0
2
1
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
3
0
2
1
0
0
0
2
0
2
0
0
0
1
0
0
0
1
1
2
1
0
0
2
1
1
2
0
0
1
0
1
1
1
2
0
1
0
1
0
1
1
1
2
2
1
0
0
2
0
0
1
0
0
2
0
0
1
1
2
2
2
0
0
0
0
1
0
0
0
1
0
2
1
0
0
1
1
1
1
0
0
0
2
1
1
0
0
0
2
2
0
0
0
2
0
0
1
5
2
3
0
2
0
0
2
0
1
0
0
0
1
1
0
2
3
0
0
2
0
0
0
2
0
2
2
2
0
0
0
0
0
0
2
0
1
1
0
2
0
0
0
0
2
1
2
2
2
1
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
1
2
0
2
2
2
0
0
0
1
4
0
1
1
1
0
0
1
0
3
2
0
1
0
0
0
1
0
0
2
2
1
1
0
1
0
0
1
1
0
1
0
1
0
0
0
0
0
2
0
0
1
0
3
0
0
1
0
2
1
2
0
0
2
0
0
2
1
0
0
0
0
0
1
1
0
1
2
0
0
1
0
0
0
2
0
2
2
2
0
0
0
1
0
0
0
1
0
0
1
0
0
1
3
0
3
1
0
0
3
1
0
1
0
2
0
1
0
1
0
2
1
1
2
2
0
0
1
2
0
2
3
0
0
1
1
2
0
1
0
2
0
0
1
0
0
0
0
0
0
1
2
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
3
0
0
0
2
2
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
1
1
0
1
1
0
0
0
0
1
0
2
3
1
0
0
3
0
0
0
0
0
2
0
1
0
0
2
0
0
0
1
2
0
2
0
2
0
0
0
1
0
0
1
0
0
0
2
3
1
1
8
0
0
0
1
2
0
1
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
1
2
1
2
0
0
0
2
0
2
3
0
0
0
0
2
0
1
0
0
0
0
1
0
0
2
2
0
2
1
1
0
2
2
0
2
1
0
1
0
0
2
0
1
3
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
2
0
1
1
2
0
0
0
1
0
2
0
2
1
0
0
1
0
0
0
2
1
0
0
1
0
2
0
0
0
1
1
0
0
2
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
2
2
0
1
1
0
1
1
1
3
0
0
2
0
1
1
1
2
0
0
0
1
0
0
0
0
0
1
1
1
0
1
0
0
1
1
0
0
0
2
0
0
1
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
1
4
0
0
1
0
3
0
1
0
1
4
0
2
0
1
0
2
2
0
0
0
0
2
0
1
0
0
0
0
3
0
0
2
1
0
0
2
0
2
0
0
1
2
1
0
0
2
2
1
1
0
2
0
1
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
2
1
0
0
1
2
0
0
0
0
2
0
0
2
1
3
0
0
0
0
0
0
2
2
2
1
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
2
0
2
2
1
0
1
0
0
1
1
1
0
0
1
2
0
0
0
0
0
1
0
1
0
2
1
0
1
1
0
3
0
0
0
0
1
0
0
0
1
2
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
2
1
1
1
1
0
0
0
1
0
0
0
3
0
2
1
1
3
0
6
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
1
2
0
0
0
1
0
2
2
2
0
1
0
3
2
0
1
0
1
1
0
0
1
0
0
0
0
3
0
0
1
0
0
0
1
0
0
3
1
2
1
0
0
0
1
1
0
0
0
0
0
1
2
1
0
1
2
4
1
2
0
0
0
0
0
0
0
2
0
2
0
2
0
2
1
1
2
2
0
0
2
0
5
0
1
1
2
0
0
0
1
0
0
2
0
2
0
0
0
0
1
0
2
1
0
0
0
0
1
0
2
0
0
0
1
1
0
1
1
0
0
0
0
2
0
0
0
1
0
0
2
1
0
2
0
0
0
1
0
0
0
1
2
1
1
0
1
0
2
0
2
0
1
1
2
2
0
0
1
0
1
1
1
0
0
0
0
0
0
1
0
0
2
0
0
2
0
1
3
1
1
0
1
0
2
0
2
1
1
0
2
0
0
2
2
0
3
2
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
2
1
1
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
1
0
0
2
0
1
1
1
1
1
1
1
0
0
2
0
0
0
2
0
1
0
1
0
2
0
2
0
0
0
0
2
1
1
2
2
2
0
0
0
0
2
0
2
2
0
0
0
1
2
2
0
2
0
2
2
2
1
2
1
1
0
0
2
1
2
6
0
0
1
2
1
0
2
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
1
0
0
1
0
6
0
0
1
0
0
1
1
3
2
0
0
2
0
1
1
2
4
0
0
1
0
2
0
1
2
0
0
0
0
2
2
0
0
0
2
2
1
0
0
2
1
1
1
0
0
2
0
1
0
2
0
0
2
1
2
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
1
0
3
0
1
2
2
0
0
0
0
0
1
0
4
0
2
0
1
0
1
0
0
0
1
0
0
1
1
1
0
0
2
1
0
1
0
0
2
1
5
0
0
0
1
1
0
1
0
0
1
0
0
0
2
0
2
0
2
0
2
1
2
0
2
0
0
1
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
1
0
2
1
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
9
1
2
2
0
0
0
1
3
2
2
1
2
0
0
2
1
0
1
0
1
0
1
0
1
2
2
2
0
1
1
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
1
1
1
0
1
1
0
1
2
0
0
0
0
0
3
0
2
0
1
1
1
0
0
0
2
0
2
0
0
2
0
0
2
1
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
2
1
0
0
1
0
0
1
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
1
2
1
0
1
1
0
2
6
2
1
1
1
1
0
2
2
0
2
0
0
2
1
2
0
0
0
0
0
0
2
0
2
0
0
0
1
1
0
2
0
1
1
0
2
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
2
0
2
0
0
0
2
1
0
0
2
1
0
1
0
0
0
1
0
1
0
0
1
0
1
1
0
0
1
0
0
0
0
1
0
2
0
0
1
0
0
2
0
1
0
2
0
0
0
2
1
1
2
0
2
0
0
1
0
0
1
0
0
1
1
2
0
2
1
0
0
0
0
0
0
2
1
2
2
0
0
1
2
1
0
1
1
0
4
2
1
1
0
0
0
1
0
2
0
2
1
0
0
0
0
2
0
1
1
2
1
0
0
1
0
1
0
0
3
0
0
2
0
0
2
2
0
2
0
1
0
0
0
0
2
0
1
0
0
1
2
1
2
2
0
1
0
1
1
0
0
0
2
2
2
0
0
2
0
0
1
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
5
2
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
1
0
0
1
2
1
1
0
0
2
0
2
0
0
2
2
2
2
0
0
0
1
1
0
1
0
0
2
0
1
2
2
0
2
0
1
0
0
1
0
2
0
0
0
0
1
0
0
1
1
2
0
0
0
0
2
0
0
1
0
1
1
0
0
1
0
2
1
0
1
1
0
0
0
0
0
1
0
0
0
0
1
2
2
2
0
1
3
0
1
1
0
1
2
0
0
0
0
1
2
0
0
2
1
2
0
1
0
0
1
0
0
0
2
0
3
1
3
1
5
0
1
0
0
2
1
0
1
0
2
0
1
0
0
2
2
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
1
0
0
1
0
1
0
0
2
0
0
3
1
2
0
0
0
0
1
0
0
1
2
0
0
0
1
0
0
2
0
0
1
0
1
0
1
2
0
0
2
1
0
0
2
1
0
0
0
0
0
0
1
1
0
0
1
0
1
1
2
0
0
0
3
0
0
0
0
0
2
0
0
2
0
1
2
0
9
0
2
0
1
0
1
0
1
0
0
0
0
0
1
2
2
0
2
0
0
2
2
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
2
0
0
1
0
0
0
0
1
2
0
0
0
2
0
0
0
2
0
0
0
2
0
1
1
0
0
0
0
2
1
3
0
0
0
0
2
1
0
1
0
2
0
0
2
0
2
1
1
1
0
0
2
2
1
1
0
1
1
2
2
0
0
1
1
0
1
1
0
0
2
1
2
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
1
0
1
3
0
1
0
2
0
0
0
2
1
2
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
1
2
0
0
1
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
6
0
0
1
2
2
0
0
0
0
1
1
1
0
2
1
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
3
0
0
0
1
0
1
0
0
0
0
1
1
0
0
1
0
0
1
0
0
1
0
1
1
0
0
2
3
2
0
1
0
0
0
2
1
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
3
0
1
0
2
0
0
1
0
2
1
1
0
0
1
0
1
1
0
0
0
0
2
0
0
1
1
0
2
2
1
0
2
0
1
0
0
0
0
2
0
2
2
1
0
1
0
0
0
0
2
2
1
2
2
0
0
0
0
1
2
2
5
0
0
0
1
0
1
0
2
0
1
2
1
3
1
0
2
0
0
0
2
0
2
0
1
0
2
0
0
1
1
1
2
0
1
0
1
0
0
1
0
3
2
1
1
0
2
1
2
2
0
0
0
2
0
1
1
1
3
1
0
0
0
0
1
0
0
1
0
2
1
0
0
0
2
1
1
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
2
1
1
0
3
1
2
2
2
2
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
1
1
0
2
2
0
1
2
1
0
0
2
1
2
1
1
2
2
2
0
0
0
0
2
0
0
2
0
1
0
0
1
1
0
2
0
0
1
1
0
2
2
1
1
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
1
2
0
0
0
0
0
1
0
1
0
0
2
0
1
0
1
0
0
0
0
0
2
2
2
3
0
1
0
0
1
0
0
0
0
0
2
1
0
0
1
2
0
1
2
0
0
0
0
1
2
2
0
0
0
0
0
0
0
2
2
1
1
0
0
2
0
2
1
2
0
0
2
2
2
0
0
1
1
1
2
0
2
0
2
2
3
1
2
0
0
0
0
0
1
0
0
1
1
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
6
1
2
1
0
1
2
0
0
0
0
1
2
1
1
0
1
0
0
0
0
2
2
0
0
1
0
0
0
2
0
1
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
2
2
0
1
0
1
0
4
0
0
0
2
0
2
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
1
0
1
0
7
1
0
1
0
0
0
0
1
1
1
0
0
0
0
2
0
2
1
1
0
0
0
0
0
2
0
2
1
0
0
0
0
1
1
1
1
1
3
0
3
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
3
0
0
0
0
0
0
0
2
0
0
0
1
2
1
0
2
0
0
1
2
1
0
0
0
0
0
2
2
0
1
0
2
0
0
1
0
0
1
0
1
1
3
1
0
0
1
0
2
0
0
0
0
1
0
0
2
1
1
1
0
1
0
0
1
2
0
0
0
1
0
1
0
0
0
2
2
0
2
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
2
2
0
2
1
0
1
0
4
1
0
2
0
0
0
0
0
1
0
0
0
2
2
2
1
1
1
0
0
2
1
0
1
0
0
2
0
0
0
2
0
0
0
2
0
0
0
2
2
2
0
1
2
1
0
0
0
1
0
0
2
4
2
2
0
0
2
1
0
0
2
1
0
0
1
1
0
0
0
0
1
0
3
2
0
0
0
0
1
0
2
0
1
0
0
2
1
1
1
2
0
0
0
0
0
3
2
0
1
2
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
1
0
0
0
1
1
0
0
0
0
3
3
0
2
0
0
0
1
0
1
0
2
0
0
2
2
1
0
0
0
0
0
2
1
2
2
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
2
1
1
0
3
1
0
0
0
0
1
2
1
0
3
0
0
1
1
0
0
2
0
0
0
0
0
0
0
1
1
0
0
1
0
2
1
2
0
1
1
1
4
0
0
2
2
2
0
0
2
0
0
2
2
0
1
0
0
2
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
2
0
0
1
2
0
0
5
0
0
0
0
3
0
0
0
3
1
0
0
0
2
0
0
2
1
1
2
2
1
2
0
0
0
1
0
1
0
1
0
0
2
0
0
1
1
1
0
0
0
0
1
0
0
1
2
1
1
0
0
1
0
0
1
2
1
0
0
1
2
0
2
1
0
0
1
0
4
0
0
1
1
1
0
1
0
1
0
2
0
0
1
0
0
1
2
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
1
0
2
2
0
1
1
2
0
0
2
0
0
0
1
0
0
1
2
1
0
0
1
1
0
2
0
4
0
0
0
0
0
2
1
2
0
0
0
2
2
0
0
0
1
0
2
0
0
0
2
2
2
0
0
1
0
0
0
0
0
0
11
1
2
0
1
0
0
2
2
0
1
0
0
0
0
1
1
0
0
0
0
4
0
1
0
2
0
1
0
0
0
0
0
0
0
2
2
1
0
0
1
0
0
0
13
0
1
1
2
0
0
2
2
0
0
0
2
0
0
1
0
0
0
1
0
0
1
1
2
1
0
0
0
0
1
1
0
1
0
0
0
0
1
1
0
0
2
2
2
1
2
0
0
1
1
3
0
2
0
0
0
1
0
0
0
1
0
1
1
0
0
0
1
0
0
0
2
2
2
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
3
0
2
0
2
1
1
2
1
0
0
0
1
1
0
1
0
0
2
1
2
0
0
0
1
2
0
0
0
2
0
0
0
0
2
1
0
1
0
3
0
3
0
2
1
2
0
0
1
0
0
1
0
1
0
0
0
0
0
2
2
2
2
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
1
1
1
0
2
0
1
0
2
2
1
0
0
1
0
2
0
0
1
2
0
0
2
0
0
0
2
0
2
4
2
0
0
0
0
0
1
1
2
0
0
1
0
0
0
2
0
0
1
2
0
1
0
0
1
2
2
2
0
2
0
2
0
0
1
2
0
0
2
0
0
0
0
1
1
0
1
2
2
2
0
0
2
1
1
0
0
0
0
1
1
0
2
1
1
0
1
0
0
0
0
1
1
0
8
0
0
0
0
0
2
1
0
0
0
0
1
2
0
0
0
0
0
2
0
0
2
0
1
2
0
3
0
1
0
2
1
0
2
0
0
1
0
1
2
0
2
1
2
0
1
0
0
0
0
2
1
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
2
2
0
2
0
1
0
0
2
0
0
0
1
2
0
2
0
1
0
0
2
0
0
0
2
0
2
2
0
0
2
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
1
1
2
0
0
0
1
1
0
1
0
0
1
1
0
1
0
0
2
0
0
1
1
2
1
0
2
1
1
2
1
0
3
2
0
0
0
1
0
0
1
0
1
0
0
2
0
0
1
0
1
1
1
1
0
0
0
1
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
1
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
2
0
1
0
0
1
1
0
0
0
1
2
0
0
0
0
2
0
0
0
1
0
0
0
1
0
1
0
2
0
0
0
0
1
2
0
2
1
0
1
1
2
0
0
2
0
0
0
1
1
1
1
0
2
0
0
1
0
2
0
1
1
0
1
0
0
0
0
0
0
1
0
1
1
1
0
2
2
1
0
1
0
0
0
0
2
0
1
1
1
0
0
5
0
2
1
0
0
0
0
0
0
1
0
2
1
0
2
0
1
0
0
0
0
2
1
1
2
0
0
0
2
0
2
0
0
0
0
1
1
0
2
0
1
2
1
1
2
1
1
0
0
0
0
0
0
1
2
0
0
1
0
0
0
2
0
0
2
0
2
0
0
0
1
0
0
1
0
0
0
2
0
1
0
2
0
3
0
1
2
1
0
0
0
0
5
0
0
1
0
2
0
0
0
1
0
2
0
2
1
0
2
0
2
2
0
0
0
2
0
2
2
2
1
0
0
0
1
0
0
0
2
0
0
2
1
2
0
0
2
0
0
2
0
0
1
0
1
0
0
0
2
0
1
1
0
0
1
1
0
2
0
1
0
0
0
2
2
0
1
0
0
0
2
1
2
0
0
0
0
1
0
0
2
2
0
2
3
0
0
0
2
0
4
2
0
0
2
1
0
0
0
0
1
2
1
0
2
0
2
0
1
0
0
4
2
1
0
0
0
2
0
0
2
0
1
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
4
0
2
0
0
1
0
1
0
0
0
1
0
0
0
1
1
1
0
2
2
0
0
0
0
2
0
0
1
2
0
0
2
2
2
0
2
1
0
0
0
0
2
0
1
0
0
0
1
2
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
1
2
1
0
0
0
0
1
0
2
2
1
1
2
3
2
2
0
0
0
2
1
2
2
2
0
0
2
0
0
1
0
0
0
0
0
2
1
2
0
0
2
0
2
0
0
1
2
2
2
2
1
1
1
0
1
0
2
1
1
1
1
2
0
1
0
0
3
3
1
1
1
1
0
1
1
2
1
0
5
1
0
2
0
0
0
2
0
1
3
0
1
2
0
0
2
0
0
0
2
0
2
2
3
1
1
2
0
1
0
0
2
0
0
2
0
2
0
1
2
0
0
1
2
1
0
1
2
1
1
1
1
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
2
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
1
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
1
0
0
0
0
2
0
0
0
1
2
0
2
2
1
0
0
0
0
0
2
1
0
0
2
1
0
2
1
2
0
1
0
1
0
0
0
0
2
0
2
1
1
0
1
0
0
0
0
0
0
2
2
1
0
0
0
0
1
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
2
0
0
1
1
0
1
0
1
0
2
2
1
0
0
0
2
0
0
0
0
1
0
1
2
1
0
2
2
0
2
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
3
1
2
1
1
2
1
0
0
2
0
1
0
0
6
0
5
1
0
1
0
0
0
0
2
1
2
0
0
0
0
1
0
0
0
1
2
0
0
1
1
0
0
2
0
0
3
2
1
2
0
0
2
0
1
2
2
1
0
0
2
1
0
0
1
1
0
0
2
0
0
0
0
1
0
1
2
1
0
0
1
0
0
2
1
2
1
0
0
0
2
0
1
1
0
0
1
0
0
0
3
1
1
0
1
2
0
3
0
2
0
0
2
1
1
1
0
0
0
0
2
0
0
0
0
2
1
1
0
2
2
1
0
0
1
2
0
1
0
0
2
0
2
2
0
0
0
0
0
0
1
0
0
0
0
2
0
3
2
0
0
2
0
2
0
0
1
1
1
1
0
1
1
0
0
0
1
0
1
1
2
0
0
0
0
1
1
0
0
0
1
0
2
2
1
0
1
0
0
1
1
1
0
2
0
2
2
1
1
0
2
0
0
0
0
1
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
1
2
2
0
1
2
0
0
2
1
0
1
0
1
0
0
0
0
1
0
0
2
1
0
0
1
2
0
1
0
0
0
2
2
0
2
0
0
2
0
0
0
2
0
1
0
2
0
0
0
2
0
0
2
0
2
0
0
0
0
1
1
1
0
1
0
0
0
1
2
0
0
2
0
0
0
0
0
0
2
0
3
1
1
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
1
2
1
0
1
0
0
2
2
0
0
2
0
0
4
0
0
1
2
1
1
2
2
0
0
0
0
1
0
0
2
0
0
3
2
0
2
2
0
0
1
0
0
1
0
1
1
0
1
1
1
0
0
1
1
1
0
0
4
0
0
1
5
0
1
0
0
0
3
0
0
0
0
1
0
0
2
0
1
2
0
0
1
0
2
2
0
0
0
0
2
2
0
1
0
1
0
0
3
0
0
1
2
1
1
3
1
0
0
0
0
2
0
2
0
3
0
3
1
2
0
1
0
3
0
0
0
0
0
1
1
1
1
0
0
0
0
1
2
0
0
1
2
1
0
1
2
3
4
0
1
0
0
0
1
0
1
1
1
2
0
1
1
0
1
0
0
0
0
0
2
0
1
0
0
0
0
1
0
2
0
0
0
1
0
1
0
3
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
2
0
1
1
0
0
0
0
0
2
2
2
0
0
2
2
0
0
2
0
0
2
1
0
0
0
2
0
1
0
2
1
0
0
0
0
2
0
0
0
0
2
1
0
0
1
1
0
1
2
1
0
1
0
2
2
0
0
0
0
1
2
2
1
0
0
0
0
2
0
2
0
2
0
0
0
1
1
1
2
1
1
2
0
2
2
1
1
0
1
0
0
0
1
2
0
2
1
0
0
1
0
2
1
0
2
2
1
0
1
1
1
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
1
1
0
1
0
2
0
0
2
0
1
0
0
0
1
1
0
0
2
0
0
1
0
0
0
1
0
1
0
1
0
0
0
1
1
2
0
0
0
0
2
1
0
0
0
0
1
1
1
0
0
0
1
2
1
1
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
1
0
0
0
1
0
2
3
0
0
0
0
0
2
0
1
1
0
1
2
0
0
1
2
0
1
1
0
0
2
1
1
0
1
1
2
0
0
0
0
0
1
2
0
0
0
0
0
2
1
0
2
0
0
2
2
0
0
0
0
0
2
2
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
2
2
1
0
0
1
1
0
2
2
0
0
0
0
1
0
3
0
0
1
1
0
0
0
2
1
0
0
1
0
0
0
0
2
0
0
2
1
1
2
1
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
2
2
0
1
1
0
0
0
1
0
1
0
0
0
0
2
1
0
2
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
2
0
0
2
0
0
0
1
0
0
2
2
0
0
2
1
0
2
0
0
0
1
0
0
0
0
0
0
0
3
0
1
1
0
0
0
0
0
0
2
2
1
0
1
0
0
2
2
0
0
0
1
0
0
3
0
0
0
0
0
0
2
0
2
2
1
1
1
0
1
2
1
0
2
0
1
1
0
1
0
1
1
2
2
0
1
1
1
2
0
0
1
2
1
0
2
0
3
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
2
1
0
1
0
0
1
1
1
2
0
0
0
0
3
1
2
0
1
2
0
0
0
0
0
0
0
2
1
1
0
0
0
0
2
0
2
0
1
0
1
3
1
0
1
1
0
1
2
0
0
0
0
2
0
0
2
2
0
0
0
1
0
1
0
3
0
2
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
2
0
0
1
0
1
0
2
0
2
0
2
3
2
0
0
1
1
0
1
0
0
0
0
0
0
2
0
0
0
1
0
2
1
0
2
0
0
2
0
1
1
0
0
0
0
0
0
0
1
2
1
2
1
0
2
0
0
1
1
0
3
0
0
0
0
0
0
1
2
0
1
2
2
1
0
0
0
0
1
2
0
0
1
0
1
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
4
1
0
1
1
0
1
0
1
1
1
1
1
2
0
1
0
1
0
0
0
0
2
0
1
0
1
1
0
0
1
0
0
1
1
2
0
1
2
0
0
2
0
1
2
3
2
0
0
0
1
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
5
1
0
1
0
0
2
0
0
0
4
0
1
1
0
2
0
0
0
1
1
0
0
2
0
0
0
2
0
0
2
1
2
2
0
0
0
0
0
1
0
0
0
0
0
6
2
2
0
1
1
3
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
1
2
2
1
2
0
1
0
1
2
1
0
0
0
2
1
1
2
0
0
1
0
2
2
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
1
2
1
0
0
1
0
0
0
0
1
2
2
0
0
0
0
1
0
1
0
0
0
1
0
2
0
0
1
6
0
0
0
0
1
0
0
1
1
0
0
1
2
2
0
0
0
0
0
2
1
1
3
0
1
1
2
0
1
1
2
0
0
0
0
2
2
0
0
1
1
1
2
0
0
1
0
0
2
0
0
1
0
1
2
0
2
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
1
1
2
1
2
1
1
0
2
4
0
0
0
0
0
0
0
2
1
0
0
2
1
0
0
2
0
0
1
0
0
2
2
0
0
1
0
0
3
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
1
1
2
1
0
0
2
2
0
0
1
0
1
2
0
0
0
0
1
2
0
1
1
0
1
0
0
1
0
0
0
0
1
0
0
0
3
0
1
0
2
1
0
1
1
3
0
2
2
0
0
1
1
0
1
0
0
0
0
2
0
2
0
2
0
0
0
1
0
0
1
0
0
1
0
1
0
0
1
0
2
1
2
1
1
1
0
2
0
2
0
0
0
0
0
1
3
0
0
0
0
0
0
1
0
2
1
2
0
0
0
2
0
0
1
0
0
2
1
2
0
0
0
0
0
0
0
1
2
0
0
0
1
1
1
0
2
0
1
0
0
1
0
2
0
1
1
0
0
0
1
1
0
1
0
0
2
2
1
1
0
1
2
0
0
0
0
1
0
0
1
5
1
0
2
0
0
1
0
0
1
0
0
0
1
2
2
2
0
2
1
0
0
0
0
1
1
2
0
0
0
1
0
0
0
0
0
2
1
0
2
0
1
1
0
0
0
1
0
0
0
2
0
1
0
0
0
1
1
2
0
2
3
1
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
2
2
2
0
0
0
0
0
1
0
2
2
0
2
0
0
0
0
2
2
2
0
0
0
0
1
0
0
0
0
0
3
0
2
2
0
1
0
0
1
1
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
1
2
1
0
0
0
0
1
0
2
0
2
2
1
0
1
0
0
0
2
1
2
2
3
2
0
0
1
1
2
0
2
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
1
1
1
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
2
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
1
2
1
0
2
0
1
0
2
0
0
0
1
2
3
3
1
2
0
2
2
1
0
0
2
1
0
0
0
0
2
1
0
1
2
1
0
0
0
0
0
0
2
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
2
0
0
3
1
0
2
2
1
1
1
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
2
0
3
0
0
1
0
0
1
0
0
1
0
2
0
0
0
4
0
2
0
1
0
0
1
0
0
1
2
0
1
0
0
0
0
1
0
1
1
0
0
0
0
1
0
2
0
0
0
1
1
1
1
1
1
0
0
0
1
1
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
1
1
0
2
0
1
2
0
1
2
0
0
0
2
0
0
2
0
2
1
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
3
2
0
0
0
2
0
1
0
0
1
2
1
0
1
0
2
0
2
1
0
0
2
3
0
1
1
0
1
0
0
0
1
0
0
0
1
0
2
0
1
0
0
0
0
1
2
2
0
0
0
0
1
0
1
1
0
2
1
2
0
1
1
4
0
3
0
1
2
0
0
0
0
0
0
2
0
0
2
0
1
0
0
1
0
0
0
0
0
1
2
0
0
0
2
0
0
1
0
1
0
0
1
0
2
0
0
1
1
0
2
1
1
0
0
1
0
0
1
0
2
0
1
1
2
1
2
0
2
0
2
0
1
0
2
0
2
1
0
0
0
1
0
0
0
1
0
0
0
2
1
1
0
0
1
1
3
2
0
0
2
1
1
0
1
0
1
1
1
0
3
1
0
0
1
0
1
0
1
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
1
2
0
1
2
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
2
2
0
0
1
2
0
0
2
0
0
6
1
0
0
1
1
1
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
2
1
0
1
0
1
1
0
1
0
1
0
2
1
0
0
2
0
2
2
2
0
2
1
0
2
1
0
1
0
0
0
2
0
0
0
2
1
1
1
0
2
0
0
0
0
1
0
0
0
0
0
1
0
1
2
0
0
1
0
0
2
0
2
0
2
2
0
0
1
2
2
2
1
2
2
0
0
0
0
0
1
0
0
0
0
0
4
1
0
0
2
2
0
0
2
0
0
2
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
1
0
2
1
0
0
0
1
1
1
2
2
0
2
2
0
2
2
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
1
2
0
0
1
0
0
0
0
3
2
2
1
1
0
1
0
0
2
2
0
0
0
0
1
0
0
2
1
2
1
0
0
1
1
0
2
0
1
1
1
0
3
0
0
2
0
1
0
2
0
0
1
0
1
0
1
1
0
2
1
2
0
0
1
1
2
2
0
1
2
0
0
0
0
0
0
3
0
2
1
0
0
2
0
0
2
1
0
0
2
3
2
0
1
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
1
2
1
0
0
0
1
0
0
0
1
1
2
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
1
0
2
1
0
1
2
0
0
0
2
1
0
0
2
1
2
1
2
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
1
0
1
0
0
0
1
0
2
0
1
2
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
3
0
0
0
1
2
1
2
0
0
0
1
0
0
2
2
0
1
0
1
0
0
0
0
1
2
0
1
0
0
2
0
1
0
2
2
0
0
1
0
0
0
0
0
0
2
0
0
2
2
0
0
2
2
0
2
0
0
0
2
1
0
0
0
0
2
0
2
0
0
0
0
1
1
1
1
2
1
1
1
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
4
0
1
2
0
0
0
0
0
0
1
1
2
0
0
3
1
0
2
12
0
2
0
0
1
0
0
1
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
1
0
3
0
1
0
2
0
0
0
1
0
1
2
0
1
1
0
0
1
0
0
0
1
2
1
2
2
0
0
1
2
0
0
1
0
1
1
1
0
2
0
2
1
2
0
0
1
1
0
0
0
0
1
0
0
0
2
1
0
0
0
2
0
0
0
4
0
1
1
2
1
0
2
1
1
2
2
1
0
0
2
0
1
1
0
1
2
1
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
1
1
1
0
2
0
0
1
1
1
0
2
1
1
0
0
1
2
1
0
0
1
1
1
2
0
1
0
1
0
0
0
0
2
0
0
0
0
2
2
2
0
1
0
2
1
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
2
1
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
2
0
2
2
0
0
0
0
1
0
0
1
1
0
1
0
1
1
0
0
2
1
0
1
0
1
2
1
0
1
2
0
2
0
1
0
0
2
1
0
0
0
0
0
2
0
0
0
2
0
0
0
3
0
0
0
2
1
2
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
2
0
0
0
0
0
0
0
1
0
2
0
1
0
0
1
0
0
0
2
0
1
0
0
0
1
2
0
2
0
0
0
2
0
0
0
1
2
2
2
0
0
0
0
1
2
1
0
2
1
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
1
1
1
2
1
1
0
0
2
1
2
1
0
0
0
0
0
0
0
2
0
1
0
1
1
0
0
0
0
0
2
2
1
1
0
0
0
2
0
1
0
4
0
1
2
1
0
0
0
2
1
0
0
2
2
0
0
0
0
0
0
0
0
0
4
1
0
0
2
0
2
0
1
2
0
2
0
0
0
1
0
0
2
2
0
0
1
0
0
1
0
0
1
0
0
0
2
0
1
2
0
0
0
0
1
1
2
1
0
0
0
2
1
1
1
0
1
2
0
3
0
2
2
1
1
2
0
0
1
0
0
2
2
0
1
0
0
0
2
0
1
0
1
1
0
0
1
1
5
2
1
0
0
0
0
0
2
2
0
0
0
2
0
0
1
0
0
1
2
1
2
2
0
2
0
1
0
0
5
0
1
0
1
1
1
0
0
1
0
0
1
0
0
0
2
0
1
2
1
0
1
2
0
0
2
2
0
0
0
0
1
0
0
0
2
2
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
2
0
2
0
2
3
0
0
0
2
0
0
0
0
0
2
0
0
1
2
1
2
0
2
0
1
0
0
2
2
2
0
0
1
1
0
0
2
0
1
1
0
1
1
1
1
2
1
0
0
1
2
0
1
0
0
3
1
2
0
0
1
0
1
1
0
0
1
0
2
1
0
1
1
0
4
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
2
2
0
0
0
0
1
0
0
2
1
1
0
0
0
0
2
0
2
2
1
0
0
0
1
1
1
0
1
0
0
1
0
2
2
2
1
2
2
0
0
0
0
0
0
0
0
2
2
0
0
2
0
3
0
1
1
2
0
0
2
2
0
0
0
0
0
1
2
2
2
1
0
1
2
0
0
1
2
2
1
0
0
0
2
2
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
1
0
2
0
0
0
2
1
0
3
0
0
0
2
0
1
2
0
0
3
2
2
2
0
0
3
1
0
0
0
1
0
2
0
0
2
0
1
0
1
0
1
2
0
1
2
1
0
2
2
0
0
0
0
0
0
2
1
0
0
3
1
1
1
0
1
2
1
0
1
0
1
1
2
0
1
1
1
0
1
1
0
2
0
1
1
0
0
2
1
0
1
1
0
1
2
0
1
0
2
0
0
0
2
2
0
0
0
0
0
2
0
0
2
1
0
2
0
2
1
0
1
0
0
1
1
1
1
0
2
3
1
0
1
0
0
0
0
0
0
0
0
2
2
0
0
2
2
0
0
1
0
3
0
0
0
0
1
0
0
2
2
0
0
2
0
1
0
0
1
1
1
2
2
1
0
1
0
0
1
0
0
2
0
2
0
1
1
0
0
0
4
1
0
1
2
0
0
0
1
1
0
1
0
0
0
1
0
0
0
1
2
2
2
0
0
2
0
3
2
0
2
2
1
2
0
1
0
1
0
1
0
2
0
1
0
0
0
0
2
2
0
1
2
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
1
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
1
2
2
1
0
0
0
0
0
0
1
0
0
0
2
1
2
0
0
0
0
0
2
0
1
0
0
2
0
0
2
2
2
2
1
1
1
1
0
0
0
0
3
0
0
0
0
1
0
0
1
0
0
2
1
1
0
1
2
0
1
2
0
0
1
1
2
1
2
0
2
0
2
1
0
1
0
0
0
1
0
3
0
0
0
0
0
1
0
0
0
2
1
0
1
0
1
2
0
0
0
0
2
0
2
0
0
0
2
2
1
0
1
0
2
0
0
0
2
1
0
1
0
1
1
0
2
0
0
1
0
1
0
2
0
1
1
0
3
1
1
1
0
1
0
0
0
0
0
0
0
1
0
0
2
0
1
0
1
0
1
1
0
2
0
0
0
0
2
0
0
0
2
0
2
2
1
0
0
2
1
1
1
0
2
0
0
2
2
2
0
2
0
3
1
0
0
0
0
0
0
0
2
0
0
2
0
2
0
1
0
0
0
2
2
2
0
1
1
0
1
0
0
0
0
0
0
0
1
2
1
2
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
1
0
0
1
2
0
2
1
0
1
0
0
0
0
0
0
0
0
5
2
1
0
0
1
0
2
0
0
0
0
2
1
0
2
0
1
0
0
1
0
0
1
1
1
2
0
2
0
0
0
2
0
1
2
2
1
0
0
1
1
2
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
1
1
1
0
0
1
1
1
0
0
0
2
0
0
2
1
0
2
6
0
1
0
2
2
2
1
1
1
0
1
0
0
0
2
1
0
3
1
0
1
0
2
0
0
0
1
1
0
1
2
2
2
0
0
1
1
1
0
1
0
0
0
0
1
0
0
1
2
0
1
0
1
1
0
0
1
0
1
1
0
0
1
1
0
1
2
1
1
1
0
1
0
0
0
1
1
2
2
2
0
2
1
0
0
0
2
1
0
1
0
0
0
0
1
1
0
0
1
2
0
0
0
1
2
0
1
1
0
1
0
0
2
0
1
1
0
1
0
0
0
1
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
1
1
0
0
0
0
1
1
0
0
0
1
2
1
2
5
0
0
0
3
1
0
2
2
1
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
2
1
0
1
2
2
1
1
0
1
2
0
0
0
0
0
0
1
2
0
0
1
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
2
2
0
2
0
0
2
2
0
0
2
0
3
0
0
0
1
2
0
0
1
0
2
0
1
0
0
1
0
2
0
1
0
0
1
0
0
0
0
0
1
1
0
0
2
0
2
0
0
0
0
0
1
0
1
1
2
0
0
0
2
2
1
1
0
2
2
0
1
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
2
0
0
3
2
0
1
0
0
0
2
1
2
0
0
0
1
2
1
2
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
1
1
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
2
2
0
1
1
0
0
0
0
0
0
0
2
0
2
1
1
2
0
1
1
0
1
1
0
0
1
0
2
0
1
0
0
0
1
1
0
1
0
2
1
2
2
2
0
0
0
3
0
0
0
2
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
2
0
2
0
1
0
1
0
2
0
0
0
0
2
1
1
2
0
0
2
1
4
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
4
0
0
0
1
0
0
1
2
5
2
0
2
1
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
2
2
1
0
0
0
1
2
0
0
1
1
2
0
1
1
0
0
0
2
0
0
0
0
0
1
2
0
0
1
2
0
0
0
2
0
0
0
0
2
1
0
0
0
2
0
1
0
2
0
0
0
0
0
1
0
0
0
0
1
0
1
2
1
1
0
1
0
0
0
0
2
0
0
0
2
0
0
1
0
11
0
1
1
0
0
2
1
2
2
0
2
2
0
0
1
1
1
3
0
2
1
0
0
0
1
1
1
0
0
0
0
0
1
1
1
2
1
0
2
0
0
0
0
0
0
2
0
0
1
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
1
1
0
0
0
0
0
2
1
1
0
0
2
1
0
0
0
1
1
1
0
0
0
1
2
2
0
0
0
0
3
1
0
2
2
1
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
1
2
1
0
0
2
2
0
2
0
0
2
2
2
0
1
0
1
0
0
1
0
0
2
2
0
0
0
0
1
1
0
0
1
1
2
0
0
0
0
2
0
0
0
0
1
1
1
0
0
0
0
2
0
0
0
1
0
0
0
1
2
0
2
0
0
0
2
2
0
0
4
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
6
0
2
0
1
1
2
0
0
1
1
0
0
1
0
0
1
1
1
0
2
2
1
0
0
0
2
2
1
1
0
0
0
1
0
0
2
1
1
0
0
0
0
2
2
0
0
0
0
0
2
0
0
1
0
0
1
0
1
0
2
0
1
0
0
0
1
2
1
1
0
0
0
2
0
0
0
2
2
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
1
0
0
2
1
1
1
0
2
0
0
3
2
0
3
0
0
0
0
1
1
0
0
1
0
2
2
0
0
1
1
0
0
0
0
1
0
1
0
0
1
2
1
0
0
1
0
2
1
1
0
1
2
2
2
0
1
1
2
2
0
2
1
1
0
0
0
1
1
1
2
0
1
0
0
1
0
0
2
1
1
0
0
0
2
0
0
2
0
1
1
1
2
0
2
0
0
1
0
2
2
0
0
0
0
1
1
2
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
1
1
1
0
1
0
1
1
0
1
0
0
0
0
0
0
2
4
0
1
0
0
2
0
1
0
0
1
0
0
0
0
2
2
0
0
1
2
0
3
1
0
0
0
2
0
1
0
0
1
2
2
2
1
0
1
0
0
0
0
0
2
2
1
3
0
1
1
0
0
1
0
2
1
0
2
0
1
2
0
1
1
0
0
0
2
0
0
0
1
0
2
1
0
0
0
1
2
0
4
1
1
0
0
0
0
0
0
2
0
2
2
0
0
1
1
0
2
0
1
0
2
0
1
0
0
0
0
3
0
0
5
2
0
0
1
2
1
2
0
0
2
0
0
0
0
0
2
1
2
0
0
0
2
0
2
0
2
1
2
1
0
2
1
1
0
0
2
0
0
0
0
2
0
0
0
1
2
0
0
2
0
0
0
1
1
0
2
0
1
1
1
0
0
0
0
1
0
0
0
2
0
1
0
2
0
1
2
0
0
0
2
1
0
0
1
1
0
0
1
1
0
2
0
0
2
0
0
0
0
2
0
0
2
1
2
1
0
0
1
0
0
1
0
1
0
2
1
0
1
2
1
0
1
2
0
1
2
6
0
0
1
1
0
0
2
0
0
2
2
2
0
1
0
1
0
2
0
0
0
0
0
1
0
0
0
0
1
2
0
2
0
0
2
3
2
0
2
2
0
1
0
0
0
1
0
0
0
1
1
1
0
0
0
0
2
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
3
2
0
1
0
0
2
1
0
0
0
2
0
0
2
0
2
0
0
0
0
1
1
0
0
0
0
0
1
0
5
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
2
1
1
1
0
0
2
0
2
0
0
0
0
0
3
2
1
1
0
0
1
2
0
1
0
0
0
0
0
0
2
0
0
1
2
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
1
0
0
1
2
2
0
0
1
1
0
2
1
0
0
0
3
0
0
0
2
1
1
2
1
2
2
2
1
1
0
1
1
1
2
0
0
0
0
0
1
0
0
0
2
1
0
0
2
1
0
0
0
0
0
0
2
0
2
2
1
0
0
2
2
0
0
0
2
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
2
1
0
0
2
1
0
0
2
1
0
2
0
1
0
1
0
1
0
0
0
0
0
2
2
2
2
1
0
1
1
0
0
2
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
1
1
2
2
0
1
1
0
0
0
2
2
0
1
0
0
2
0
1
1
2
0
1
0
0
2
2
0
0
0
2
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
2
2
0
1
1
1
2
0
2
1
0
0
0
2
1
0
1
1
0
0
2
0
0
0
1
2
1
2
0
1
0
2
4
0
2
0
0
0
0
1
0
1
0
3
0
2
1
0
1
0
2
0
2
3
0
0
1
1
1
0
2
0
0
1
0
1
0
2
0
1
0
2
0
2
8
1
0
0
1
0
2
0
0
0
0
0
1
0
0
2
1
1
1
0
0
0
1
0
1
1
2
0
0
1
0
0
1
3
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
2
2
0
0
1
2
0
0
0
0
0
1
1
2
1
0
0
1
2
1
1
1
0
2
1
1
0
1
0
0
0
0
1
0
1
0
1
2
1
1
1
0
0
0
1
2
0
1
0
1
0
0
0
0
0
2
1
0
0
2
1
0
0
0
1
1
1
0
1
0
2
0
3
0
2
0
0
2
2
0
0
1
0
0
2
0
0
1
1
0
0
0
2
0
0
1
0
0
0
0
0
2
1
0
0
1
2
1
0
0
0
0
1
0
1
0
1
0
0
0
2
0
0
2
0
2
0
1
2
1
0
1
1
2
2
0
1
0
0
1
1
0
0
2
2
0
0
1
0
0
1
0
2
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
2
0
2
0
2
2
0
0
0
3
1
1
2
1
0
0
2
1
0
0
0
0
0
1
0
0
1
2
0
0
2
0
0
0
2
0
1
0
0
4
0
0
2
2
0
0
2
2
0
0
1
0
0
2
1
0
0
0
4
1
0
0
0
1
0
0
0
1
0
1
2
0
1
0
2
0
0
0
0
2
1
0
0
2
1
1
0
0
2
1
0
1
0
0
0
2
0
0
1
0
1
0
2
0
1
2
1
0
1
1
1
0
0
0
2
2
0
1
1
2
1
0
2
0
0
0
0
0
4
2
3
2
1
0
2
0
2
1
1
0
0
1
2
0
0
2
0
0
3
0
0
1
2
2
1
0
0
1
0
0
0
2
0
0
0
0
0
1
2
2
1
2
0
0
0
0
1
0
2
0
0
1
1
0
0
0
2
0
0
0
0
0
1
0
2
2
0
1
0
0
0
2
2
1
0
0
0
0
0
1
1
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
2
1
0
1
4
0
1
0
0
0
2
2
2
1
0
2
0
0
0
2
2
0
1
1
0
0
0
2
2
0
0
0
0
2
0
1
1
0
2
0
0
2
0
2
1
0
0
2
0
0
1
0
2
0
2
1
0
0
3
0
0
1
0
0
0
2
0
0
1
0
0
0
0
5
0
2
0
0
2
2
0
0
0
2
2
0
1
0
2
1
0
0
0
0
0
0
0
0
1
0
0
1
1
1
1
2
1
0
2
0
2
0
0
2
1
0
2
0
0
0
0
2
1
0
0
1
0
0
1
2
2
0
0
0
0
1
0
0
1
0
0
1
3
0
2
0
0
1
0
0
1
2
0
2
1
0
1
0
1
1
0
0
1
1
1
0
0
1
0
2
0
0
1
0
1
0
0
0
2
0
0
1
1
2
1
1
0
1
1
2
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
1
2
0
0
2
0
0
0
2
2
1
0
1
0
0
2
0
0
0
2
1
1
1
1
2
0
2
0
0
0
0
2
1
0
0
0
1
0
2
1
0
1
2
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
1
1
0
0
2
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
3
3
0
3
2
2
0
0
1
0
2
0
0
0
0
2
0
0
0
2
0
0
0
1
2
0
0
0
0
0
2
2
0
2
0
0
0
0
0
1
0
0
0
0
2
1
1
2
0
0
0
1
0
1
2
1
2
0
1
0
1
0
2
0
1
0
2
0
0
1
1
0
0
0
2
1
0
2
0
0
0
0
1
0
1
0
0
0
0
2
0
1
0
2
1
0
1
2
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
2
0
0
0
2
1
1
0
2
1
0
2
0
0
2
2
2
0
2
0
2
1
2
0
0
1
0
2
0
1
0
0
1
0
2
0
1
0
0
0
1
0
2
1
0
0
1
2
0
0
1
0
1
0
2
0
0
1
0
0
0
2
2
1
0
0
0
2
4
0
2
0
1
0
1
0
0
0
1
0
2
0
2
0
3
0
0
0
1
0
0
0
0
0
0
2
1
1
1
1
1
0
1
0
0
0
0
0
6
0
0
0
0
4
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
1
1
2
1
2
0
0
0
0
1
1
0
0
1
2
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
2
0
0
1
0
2
1
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
3
0
1
1
0
0
0
1
0
0
2
2
0
0
0
1
1
1
1
2
5
0
0
0
0
1
0
1
1
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
1
1
1
1
0
1
2
0
2
2
3
2
1
1
0
0
0
0
2
0
0
1
1
0
0
0
0
0
1
0
1
1
1
2
2
2
0
0
0
1
1
2
0
0
1
0
2
0
1
1
1
0
1
0
2
0
0
0
3
1
0
0
0
1
0
2
0
0
0
0
1
0
1
1
1
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
2
1
0
0
0
0
2
0
0
1
1
0
0
2
0
0
1
0
2
2
1
2
1
1
2
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
2
2
0
0
0
0
4
0
1
1
1
0
1
0
0
0
1
0
1
1
0
2
0
1
0
3
0
0
1
0
1
2
0
2
0
2
1
1
1
1
2
2
0
0
0
0
0
0
1
1
0
2
0
0
0
3
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
1
0
2
1
1
1
1
1
0
2
2
0
0
0
1
0
0
1
1
2
1
0
2
2
0
3
0
0
0
1
0
0
0
0
1
1
2
0
1
0
1
0
1
2
2
0
2
0
1
2
1
0
2
0
0
2
0
0
2
0
0
0
2
1
2
0
1
1
1
2
1
0
1
2
0
0
2
2
1
2
0
0
2
1
2
1
0
0
1
1
1
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
2
0
0
2
2
1
0
0
0
0
0
1
0
0
0
1
0
1
2
1
0
0
1
1
0
1
0
2
2
0
0
1
0
1
2
1
2
0
2
0
0
0
0
0
0
2
2
0
1
0
1
2
0
0
3
2
2
0
0
2
0
0
0
1
0
2
2
1
0
1
2
0
2
0
0
2
1
2
1
0
0
0
1
0
0
1
0
1
1
0
1
2
0
2
1
0
0
0
2
1
0
0
0
1
0
1
0
0
0
1
2
0
1
0
0
1
2
0
0
2
0
0
0
0
0
0
1
0
2
3
0
1
0
2
0
1
1
2
2
1
2
0
0
0
0
2
0
0
1
0
2
0
0
0
0
1
0
0
1
0
0
0
2
0
2
0
0
1
3
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
2
0
2
1
1
2
2
3
1
1
0
0
0
1
0
1
0
1
3
0
1
2
0
0
0
2
0
1
1
0
2
1
1
0
0
2
0
0
0
0
0
1
0
0
0
2
1
1
0
1
0
1
0
2
2
1
1
1
0
1
0
2
0
0
0
1
0
0
1
0
2
0
1
0
1
0
0
0
0
1
2
1
0
0
0
1
1
0
0
2
1
2
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
2
2
0
1
0
1
0
0
2
0
1
0
1
0
0
0
0
2
0
1
2
0
0
0
1
0
2
0
1
1
1
2
1
0
2
1
1
0
0
0
0
0
0
0
0
2
0
0
2
0
2
2
1
2
0
0
2
2
0
0
2
0
2
1
0
0
0
0
2
0
0
1
1
0
0
2
1
0
0
0
5
1
0
1
0
2
0
0
1
1
4
0
0
0
0
0
2
1
0
0
1
0
1
2
0
0
1
0
2
0
0
1
0
0
2
1
0
0
0
1
0
0
0
2
0
2
2
0
1
0
1
0
0
2
1
2
0
0
0
2
0
0
0
0
0
1
0
1
0
0
2
0
0
0
2
1
0
0
0
0
1
1
0
2
2
0
0
2
2
1
0
0
2
0
1
0
0
1
0
1
0
0
0
1
0
0
2
0
2
0
1
0
2
0
0
1
1
0
1
1
0
0
0
1
1
2
1
2
2
2
0
1
0
1
0
0
0
0
2
1
2
0
2
2
1
0
0
0
0
1
3
0
1
2
0
0
2
0
0
2
0
0
1
0
0
1
2
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
1
1
2
2
1
2
0
0
1
0
2
0
0
1
0
0
0
0
0
5
1
2
2
0
0
1
2
0
4
0
2
0
0
2
0
1
0
0
0
0
2
1
0
1
1
0
0
2
2
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
1
1
0
0
2
1
1
1
2
0
0
0
1
0
1
0
0
0
0
0
0
2
1
0
0
2
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
2
0
0
1
2
0
0
1
0
0
0
2
0
0
2
0
0
2
2
0
0
0
0
1
1
0
0
1
0
0
1
1
0
0
2
0
2
0
1
1
0
0
0
2
0
0
2
2
3
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
2
2
0
0
0
0
0
0
0
2
1
2
2
2
0
1
1
0
0
0
0
1
0
0
0
1
2
0
2
1
0
2
0
2
2
0
0
0
2
1
0
2
0
0
0
0
0
1
0
1
1
0
0
0
2
2
0
0
2
2
0
1
0
1
1
1
0
0
0
0
1
0
2
0
2
0
1
0
1
1
2
0
1
0
0
1
0
2
0
0
1
2
0
1
1
0
0
0
0
2
0
0
0
1
0
0
2
0
1
0
1
1
2
2
1
0
0
1
2
2
1
0
0
0
0
0
0
0
0
1
2
2
0
2
3
0
0
1
0
2
0
2
2
0
0
0
2
0
1
0
0
2
0
1
0
0
0
0
0
0
0
2
1
0
1
0
0
1
0
0
0
3
3
0
1
0
1
2
1
1
2
2
0
1
0
1
2
0
2
0
1
0
0
0
0
2
0
0
0
0
2
1
1
2
0
1
0
1
2
0
2
0
0
0
0
4
0
2
0
0
0
1
1
1
0
0
1
2
1
0
0
0
0
2
1
0
1
0
2
0
0
0
1
1
1
1
2
0
0
2
0
0
0
0
0
1
0
0
1
0
2
0
1
1
0
0
0
2
2
0
0
0
0
2
0
3
1
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
1
1
1
0
0
0
0
0
0
0
3
0
0
1
1
0
2
0
1
1
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
2
0
0
1
2
1
1
1
3
2
0
0
1
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
1
0
1
1
0
0
0
1
1
2
0
0
0
0
2
0
0
0
0
4
0
2
0
0
2
0
2
0
2
0
1
0
0
0
0
2
0
0
0
0
3
0
0
1
0
0
2
1
2
3
0
2
1
1
0
1
2
0
1
0
0
0
1
1
0
0
0
2
1
0
0
2
1
1
2
0
2
0
0
1
1
0
2
1
1
2
1
0
2
3
1
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
2
2
2
2
0
0
1
0
0
3
0
0
0
0
1
0
1
0
0
0
1
1
1
2
0
1
0
0
1
0
0
0
0
2
0
2
2
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
2
0
0
1
2
6
0
2
1
0
1
1
1
0
0
0
1
0
1
2
2
3
3
0
1
1
0
0
2
0
0
0
2
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
1
0
2
0
0
1
1
1
0
2
2
2
1
2
2
0
2
2
2
0
0
0
0
1
3
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
1
2
0
0
0
2
0
0
1
2
2
0
2
0
0
0
2
0
0
0
2
3
2
1
0
1
2
2
0
1
0
0
2
0
2
0
0
0
1
0
1
1
0
1
2
0
0
1
1
0
2
2
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
1
2
0
1
0
0
2
0
1
0
1
0
0
1
0
1
0
1
0
0
0
0
2
0
1
0
0
0
0
2
1
0
3
0
1
1
2
0
0
0
1
1
0
3
2
2
0
2
1
2
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
1
2
1
2
0
0
0
0
0
0
2
0
0
1
0
0
3
2
0
2
0
2
0
0
1
2
1
1
0
0
0
2
0
1
1
1
0
0
0
0
2
1
1
2
0
0
2
1
0
0
0
1
0
1
0
1
1
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
1
3
2
1
0
2
0
0
0
0
1
1
0
0
0
0
0
1
2
1
0
2
1
0
2
0
2
0
0
0
0
0
0
1
1
1
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
1
0
0
0
3
0
1
0
0
3
0
0
0
0
0
0
0
0
0
1
1
2
1
1
1
0
2
0
1
0
0
0
2
0
1
0
0
1
2
0
0
0
2
0
0
2
0
2
1
0
0
2
0
2
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
1
0
0
0
1
0
2
4
4
1
1
1
0
2
0
0
1
1
2
0
1
2
1
2
0
2
0
5
0
0
0
0
2
0
1
1
0
0
1
0
0
0
0
0
0
0
0
2
2
1
1
0
2
0
0
0
0
2
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
1
2
0
2
2
0
0
1
0
1
0
2
2
1
0
2
0
0
0
0
2
2
0
2
0
0
0
1
2
0
1
0
2
1
1
1
1
0
0
2
0
1
1
1
1
0
0
0
1
2
0
2
0
0
0
0
2
0
0
1
1
1
0
2
1
0
0
1
1
1
0
1
1
0
0
2
1
1
0
1
1
0
0
0
1
1
0
0
1
0
0
2
1
2
0
0
2
2
0
0
2
0
1
1
0
2
1
0
0
2
1
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
2
2
0
0
2
1
0
1
0
0
0
1
0
0
2
0
0
0
0
0
2
1
2
2
1
1
2
0
0
0
1
0
0
1
2
0
1
1
4
1
0
0
0
1
0
0
1
0
3
1
0
0
0
1
0
0
1
2
1
3
1
1
0
0
0
1
0
2
0
0
1
1
1
0
2
0
0
1
0
0
1
1
1
1
0
0
0
0
2
0
1
1
0
0
0
1
2
1
0
2
0
0
0
1
2
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
2
0
0
0
0
0
1
1
1
0
0
0
0
2
2
0
0
1
0
0
0
0
0
2
0
1
2
1
2
0
2
0
2
2
1
2
2
0
2
0
0
0
0
0
0
0
1
2
1
2
2
0
1
1
0
1
0
1
2
1
2
0
2
0
1
1
0
0
0
1
0
0
1
1
0
0
0
1
1
2
1
0
1
2
0
1
0
1
0
1
0
0
0
0
0
0
1
0
1
1
0
2
2
2
2
0
0
2
0
2
2
0
0
0
0
0
2
2
2
1
0
1
1
0
0
0
1
2
0
3
0
1
2
0
0
0
2
0
0
1
1
0
0
0
1
0
0
2
0
2
2
1
0
2
0
0
1
2
0
0
0
1
1
2
0
0
0
0
0
4
0
1
0
1
3
1
1
2
1
0
0
2
0
1
1
0
2
1
2
0
0
0
0
0
0
0
0
0
0
2
0
3
1
0
0
0
1
0
0
0
0
0
9
1
1
0
1
0
0
0
0
0
0
2
0
3
1
3
0
2
1
0
0
0
1
1
2
2
2
1
0
1
0
0
1
1
0
0
1
0
1
3
1
0
0
3
0
2
0
1
0
1
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
2
0
2
0
0
0
2
1
1
3
0
1
1
0
2
0
0
1
1
0
0
2
0
0
0
0
1
1
0
0
0
0
1
0
0
2
0
1
2
1
0
0
0
0
6
0
0
0
0
1
0
2
0
1
0
0
0
2
0
0
1
1
0
0
1
0
2
0
2
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
1
1
0
2
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
2
0
0
0
0
0
1
0
2
0
1
1
0
2
0
0
0
0
0
2
2
1
0
0
1
0
2
0
0
0
2
0
0
1
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
1
1
0
2
2
2
0
2
0
0
2
0
0
2
1
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
2
0
0
0
0
0
1
1
2
0
2
0
0
1
0
2
0
0
0
0
0
0
0
2
1
0
0
0
1
0
2
1
1
2
0
0
2
2
0
1
1
0
0
0
0
0
0
2
2
0
0
0
1
2
0
0
1
1
0
2
1
0
1
1
0
2
0
0
1
0
0
1
0
1
0
2
0
2
0
0
0
1
0
1
0
0
1
1
1
0
2
1
2
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
1
0
2
1
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
2
0
2
0
1
0
0
0
0
2
0
1
0
0
0
1
2
0
0
2
2
1
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
2
0
2
0
0
1
0
1
1
2
0
1
3
0
0
0
1
2
0
1
0
1
2
1
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
1
0
0
2
0
0
2
0
0
0
2
0
1
1
0
0
0
1
1
0
2
0
0
0
0
0
4
0
2
0
1
0
3
1
0
1
0
0
1
2
0
0
2
2
2
0
0
0
0
2
0
1
0
2
1
1
0
0
0
2
0
0
2
0
2
0
1
0
0
1
2
0
2
0
1
1
2
0
1
1
0
1
0
0
0
2
1
0
0
2
0
1
2
0
2
2
1
0
0
0
1
0
0
2
0
0
0
1
1
1
2
3
0
0
0
0
1
1
0
1
0
0
1
0
0
2
0
0
0
0
1
2
0
1
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
2
1
0
0
1
1
0
0
1
0
0
2
0
1
2
0
2
0
2
0
0
1
1
0
0
3
0
1
1
0
0
0
1
1
1
1
2
0
1
0
2
1
0
3
1
1
0
2
0
3
0
0
0
0
0
2
0
0
1
2
2
1
0
0
0
1
0
0
0
0
0
0
2
1
1
1
1
1
2
0
2
1
0
0
1
0
1
0
2
0
1
0
2
1
0
1
0
0
1
0
2
0
1
0
0
0
2
2
1
0
0
0
2
1
0
1
0
0
0
2
0
0
1
0
0
5
1
1
2
1
0
0
0
0
0
0
1
2
1
0
0
1
1
2
0
2
2
0
2
1
0
2
1
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
2
1
1
1
1
0
0
2
1
2
0
0
0
0
2
0
2
2
2
0
2
1
2
1
0
1
0
0
1
1
0
0
0
2
2
2
0
0
0
2
0
1
0
1
0
2
0
0
1
0
1
1
0
0
4
0
0
1
1
1
0
3
0
0
1
0
0
3
0
1
1
0
0
2
1
0
1
0
1
0
1
0
3
0
0
2
1
1
1
0
2
0
0
2
1
2
0
0
0
1
1
1
0
2
0
2
1
1
0
0
0
0
2
0
2
1
1
1
0
0
1
0
0
0
1
1
0
1
2
0
0
2
0
0
3
0
0
0
0
0
1
1
2
0
2
0
0
1
0
2
1
1
2
2
1
0
0
1
1
0
1
1
1
2
0
2
0
2
0
1
0
0
0
1
2
1
0
1
0
1
0
1
2
1
2
2
1
0
0
1
0
0
2
2
3
0
0
0
0
1
0
0
0
2
0
5
0
0
2
2
1
1
1
0
2
0
1
0
1
1
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
2
1
2
0
0
2
1
1
1
1
0
1
2
0
0
0
1
1
2
0
1
1
1
2
1
1
2
0
0
1
0
1
0
0
2
0
0
0
0
1
0
0
2
0
2
1
0
2
2
0
0
1
1
0
1
0
0
0
2
2
1
0
0
0
2
1
2
0
0
0
1
0
0
0
0
0
3
0
1
0
0
0
1
1
0
0
1
2
2
0
0
2
0
5
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
1
1
0
0
1
0
1
1
2
0
2
2
0
1
0
1
0
2
2
0
0
1
1
0
0
2
0
0
1
0
2
2
0
1
0
0
4
0
1
0
0
0
2
0
1
1
0
1
0
2
1
0
0
1
0
0
0
1
2
1
0
0
1
2
0
0
0
1
0
1
1
2
2
0
0
1
2
1
2
0
0
1
0
0
1
2
1
1
2
0
1
0
0
0
0
0
1
2
0
0
0
0
0
1
1
0
2
0
0
0
0
2
1
2
0
1
0
2
0
0
1
0
0
1
0
2
1
0
0
0
0
0
1
0
0
2
5
1
1
0
0
0
0
2
0
0
0
1
0
1
0
2
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
3
0
0
2
0
1
0
1
0
2
0
3
1
4
0
0
0
0
1
2
2
0
0
1
0
1
0
2
0
2
0
1
1
1
1
0
0
0
0
3
0
1
0
1
0
2
2
1
0
1
1
0
2
1
1
1
1
0
2
0
0
1
0
2
1
1
2
1
1
1
0
0
1
2
4
0
0
0
0
0
0
1
1
2
1
0
1
0
0
0
0
2
0
0
0
1
2
1
0
0
0
1
1
0
0
0
2
0
1
0
2
0
0
2
0
2
0
1
1
2
0
0
0
1
0
2
2
0
1
1
0
0
2
2
2
0
0
0
0
0
0
1
1
1
2
0
0
0
2
0
0
2
0
0
0
4
0
0
0
1
0
0
0
1
0
0
2
2
1
1
1
2
1
0
2
0
1
0
1
0
1
1
0
0
0
0
0
0
5
0
0
0
1
2
1
0
3
1
2
0
0
0
1
0
0
1
0
0
1
2
4
2
1
1
0
0
2
0
0
1
0
2
0
1
0
0
0
2
2
0
1
0
1
1
3
2
0
0
0
0
0
1
2
1
0
0
1
1
2
0
1
0
0
0
0
0
0
1
0
4
1
0
1
1
0
0
2
1
1
0
0
2
2
0
3
1
0
0
0
0
0
0
2
0
2
0
0
0
3
1
0
2
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
1
0
0
1
1
2
0
2
1
0
0
1
0
0
0
0
1
1
0
1
0
0
0
2
0
0
2
0
2
0
0
0
0
0
2
0
1
0
0
1
0
2
1
0
0
0
0
0
0
0
3
2
0
0
0
2
0
0
0
0
2
2
1
0
2
0
2
0
1
2
1
0
1
2
1
0
0
0
0
1
0
1
2
0
0
1
1
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
1
0
0
0
1
2
0
2
0
0
0
2
1
0
0
2
2
1
2
1
0
1
0
2
0
0
0
0
2
0
0
1
1
2
1
0
0
2
0
1
1
0
0
1
2
0
1
0
0
2
2
0
2
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
1
0
2
1
0
2
0
0
0
2
2
1
2
1
4
0
2
1
0
0
6
1
0
0
0
2
0
0
1
1
0
1
1
0
1
0
2
0
0
0
2
0
0
0
0
1
2
2
1
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
2
0
0
1
0
0
1
0
0
1
0
0
1
0
2
0
1
0
0
0
0
0
2
0
1
0
0
2
0
0
2
0
0
1
2
0
0
0
0
0
0
2
0
1
1
0
0
0
1
0
0
2
2
0
0
0
0
1
1
0
0
0
4
3
2
1
2
1
1
0
0
1
0
2
2
2
0
0
0
2
0
0
0
0
1
2
0
0
0
1
0
0
0
1
2
1
0
0
0
1
1
2
0
0
0
0
0
0
0
1
3
0
0
0
2
0
0
2
0
1
2
2
0
0
0
2
3
0
2
1
0
0
1
3
1
0
0
0
0
0
1
0
1
2
0
2
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
3
2
0
0
1
1
2
0
2
0
2
0
0
0
0
4
0
1
0
0
0
0
0
0
0
2
3
0
2
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
2
1
2
0
0
0
1
0
3
1
3
0
0
0
2
0
1
3
0
1
0
0
0
1
2
2
1
0
0
1
0
1
1
0
0
1
0
0
2
0
0
1
1
0
0
0
1
2
0
2
1
0
0
0
0
0
0
1
0
0
1
1
0
2
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
1
0
0
1
2
0
0
1
2
0
0
0
1
0
0
1
2
2
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
1
0
0
2
0
1
2
1
0
1
0
2
1
0
1
1
1
0
0
2
0
0
2
1
0
0
0
2
0
2
0
0
1
1
1
3
2
0
0
1
2
0
2
0
1
0
0
0
0
2
2
1
1
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
1
0
1
2
0
0
0
1
0
0
2
0
1
2
1
1
1
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
3
2
2
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
1
2
1
0
0
0
1
0
0
1
1
0
0
1
1
0
1
3
0
0
0
1
1
1
0
2
3
1
1
0
0
0
0
0
0
0
2
0
2
1
1
1
1
0
0
0
1
1
0
0
1
1
0
2
0
0
0
2
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
1
0
1
0
2
1
1
0
1
2
2
0
0
0
0
1
1
0
1
0
0
0
2
0
1
0
0
2
0
1
1
2
0
0
1
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
2
2
2
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
2
0
0
2
0
2
1
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
1
0
0
2
0
0
2
0
2
0
0
0
0
2
1
0
0
2
0
2
2
1
2
0
1
2
0
2
0
2
0
0
2
0
0
1
2
2
0
0
3
0
0
0
0
0
1
1
1
1
0
0
0
2
0
2
0
1
0
0
1
0
1
0
0
1
1
0
0
1
2
0
1
1
1
0
2
0
2
2
2
0
2
0
0
1
0
0
0
0
2
0
0
1
1
0
1
1
0
1
0
0
1
2
0
2
0
1
0
0
0
2
1
0
0
4
0
0
0
4
2
0
0
2
0
1
0
0
0
0
1
2
0
1
0
1
0
2
0
1
1
0
1
0
1
0
3
0
0
0
2
2
0
1
1
1
1
0
1
1
0
0
1
2
0
0
0
1
2
0
0
0
2
2
1
0
0
2
0
0
1
1
0
2
0
1
0
0
0
1
2
0
2
0
0
0
1
1
0
2
0
0
0
1
0
0
5
2
0
1
0
0
0
2
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
2
0
2
0
1
0
1
0
0
1
0
1
1
0
1
0
0
0
0
1
2
2
1
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
1
2
0
0
1
1
3
0
0
1
0
0
3
0
0
0
0
0
0
2
2
0
1
0
2
0
0
0
0
0
1
0
0
2
1
0
0
2
0
0
0
2
0
2
1
2
0
0
0
2
0
0
1
2
2
0
2
2
0
0
0
0
2
0
2
2
0
0
1
0
0
2
0
0
3
0
0
5
0
0
0
0
2
0
0
0
0
0
2
0
2
0
2
0
2
2
1
0
0
0
0
1
1
0
0
2
1
1
0
0
0
2
0
0
0
2
0
0
0
0
2
1
0
1
0
1
1
0
2
0
0
1
2
0
2
1
2
0
0
0
1
0
1
0
0
1
0
0
0
0
1
2
0
0
2
0
0
1
2
0
0
0
1
0
0
0
0
1
1
2
2
0
1
0
2
0
1
1
0
0
1
0
0
2
0
3
0
0
1
2
1
0
1
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
1
0
1
0
2
2
0
0
0
0
2
1
0
0
0
0
1
1
0
1
1
0
0
0
0
1
0
1
0
1
1
0
0
3
3
0
1
0
2
0
1
3
1
1
0
0
1
1
0
0
1
2
0
0
2
1
0
0
0
2
0
0
0
1
0
0
1
1
0
1
0
0
0
0
1
0
2
1
1
0
1
1
2
0
0
1
2
0
1
1
2
0
2
0
0
1
1
3
0
2
1
0
0
2
0
0
2
2
0
2
0
0
0
0
2
1
2
3
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
1
0
1
0
0
1
1
2
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
2
1
1
2
0
0
1
1
2
0
0
1
0
0
1
0
0
1
0
0
1
1
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
1
0
1
1
1
5
2
0
0
0
1
0
0
0
1
0
0
2
0
0
2
1
0
1
2
1
0
1
0
2
2
1
0
1
1
0
0
0
0
1
0
1
0
2
0
0
1
0
0
0
1
2
1
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
1
0
0
1
2
1
0
0
0
0
2
0
0
2
1
0
0
0
2
0
1
2
2
1
1
0
1
0
0
1
0
0
1
0
2
2
1
1
1
0
2
0
0
1
0
0
1
2
0
1
0
2
0
0
0
1
0
0
0
2
0
0
0
1
0
0
1
1
0
0
1
0
0
2
0
0
0
1
1
1
1
1
0
1
2
0
2
2
1
0
0
0
0
1
0
0
0
0
1
1
0
1
0
2
0
0
1
0
0
1
0
0
0
0
0
2
1
2
0
0
1
0
0
0
0
2
0
1
0
1
0
0
0
0
2
0
3
0
0
1
1
0
0
0
0
2
0
2
2
0
0
0
2
0
0
3
2
0
0
0
0
2
1
0
0
0
0
0
5
1
0
1
1
0
0
1
1
2
0
2
2
0
0
2
0
0
2
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
1
1
11
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
3
0
0
1
0
0
1
0
2
0
0
1
0
0
2
0
0
0
0
2
1
0
2
0
1
0
0
1
0
2
0
1
0
0
2
0
1
2
1
1
0
0
0
0
1
2
0
1
2
0
1
0
1
0
0
2
1
1
2
2
0
0
1
3
2
0
0
0
2
1
0
1
1
2
1
0
2
1
1
0
0
0
0
1
0
1
0
0
0
2
0
1
3
2
1
4
0
0
0
2
2
1
0
1
0
0
0
3
0
2
0
1
3
0
3
1
1
0
0
2
0
0
1
0
0
2
0
1
0
0
1
0
3
0
0
0
0
0
1
0
0
1
2
0
0
1
1
1
0
2
1
2
0
1
0
1
2
0
0
0
1
0
1
1
0
0
0
2
0
0
1
1
0
5
0
0
0
2
2
0
0
0
0
1
0
2
1
1
0
3
2
2
1
0
0
1
0
1
1
1
0
1
1
0
0
1
0
0
0
2
1
0
1
0
0
1
2
0
1
0
0
0
0
0
0
1
0
2
0
1
2
1
0
0
2
2
2
1
0
0
0
1
0
2
1
0
0
0
1
2
2
0
2
0
0
0
2
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
2
0
1
2
0
2
0
1
0
0
0
0
0
3
0
2
0
0
2
0
1
1
1
0
2
1
0
0
1
1
0
0
0
0
2
0
2
0
1
0
2
2
2
0
0
0
0
5
0
2
1
1
1
1
0
0
0
0
1
0
0
2
2
2
0
0
1
0
1
0
2
0
0
0
1
0
2
0
0
0
0
1
1
1
1
2
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
3
0
1
0
0
0
0
0
0
0
0
2
0
1
0
1
2
1
0
1
1
2
1
0
2
0
0
1
0
1
1
0
1
0
0
0
0
1
1
0
2
0
1
0
1
0
1
0
0
1
1
0
0
0
2
2
0
1
1
0
0
0
1
3
0
0
1
2
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
1
2
0
2
0
1
2
2
0
0
0
0
0
1
0
1
0
0
2
1
0
0
1
0
0
0
1
0
0
0
0
0
2
2
0
0
2
0
2
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
2
1
0
3
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
1
3
0
1
2
1
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
2
0
2
1
2
1
1
2
1
1
0
1
0
1
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
1
2
1
0
2
1
2
1
1
0
0
0
0
1
1
0
2
0
0
0
1
0
2
0
0
0
1
0
0
0
2
2
1
1
1
0
0
4
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
1
0
1
2
0
0
2
0
1
0
2
1
0
2
0
0
0
1
0
0
0
0
0
1
0
0
2
0
1
2
0
2
0
3
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
3
0
1
1
0
1
0
0
0
1
1
1
0
0
0
2
0
0
0
1
2
1
0
0
0
0
1
2
0
1
0
0
2
1
0
0
0
2
5
2
1
1
0
1
0
0
2
2
0
1
2
0
0
0
1
0
1
2
0
1
0
1
1
1
0
0
0
0
3
0
1
1
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
2
0
0
0
0
1
1
0
0
0
2
1
0
0
0
1
0
0
2
1
1
2
0
0
2
0
2
0
2
0
2
0
2
0
2
1
0
0
0
2
0
0
1
0
0
1
1
0
1
1
1
0
0
1
2
0
1
2
0
2
0
0
0
1
0
0
0
0
0
0
1
2
1
2
2
0
1
0
0
3
2
1
0
0
1
0
0
1
0
1
3
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
1
2
2
1
1
0
2
0
0
0
0
0
0
0
1
1
2
2
1
1
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
1
0
0
1
0
0
2
1
2
1
0
0
1
1
0
2
0
1
0
0
1
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
2
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
5
1
0
2
0
2
0
1
3
0
2
2
0
0
1
0
0
0
0
1
0
0
0
0
0
3
1
2
0
2
2
0
0
0
2
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
4
1
0
0
2
0
0
0
0
1
2
0
0
2
1
0
0
0
0
1
1
1
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
2
0
1
0
1
0
3
0
2
0
1
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
2
0
2
1
1
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
3
2
1
2
0
0
1
2
1
0
2
1
0
1
0
0
0
1
2
1
1
0
0
2
0
0
0
1
1
0
0
0
0
2
0
1
2
2
0
0
0
2
2
1
2
0
0
3
0
0
2
0
1
2
1
1
1
0
0
2
0
1
0
2
2
1
0
2
0
0
2
0
0
2
0
0
0
0
2
2
0
2
0
1
0
0
0
0
0
1
0
0
1
0
3
1
0
0
0
0
1
2
2
0
0
0
0
0
1
0
2
2
0
1
0
1
2
0
3
2
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
2
2
2
0
2
2
1
0
2
2
0
1
0
0
0
2
0
0
2
3
0
0
0
0
0
1
1
2
2
0
0
1
0
1
1
0
2
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
2
0
0
0
0
2
0
1
1
0
0
2
1
2
0
1
2
0
0
0
0
0
0
1
1
0
1
0
0
0
0
2
1
0
0
0
0
0
0
1
1
1
2
0
0
1
1
0
1
0
0
3
0
0
0
2
2
1
1
0
0
0
0
1
2
2
0
2
1
0
0
0
1
2
0
4
0
0
0
0
1
1
2
1
2
2
2
0
0
1
0
0
1
1
0
0
2
0
2
1
1
2
0
0
1
0
0
0
1
0
1
0
0
2
0
0
1
0
0
1
0
1
0
1
1
0
0
0
0
2
0
0
1
1
0
0
0
0
0
2
0
2
2
0
1
0
0
0
0
0
4
0
0
0
1
1
0
1
0
0
0
0
1
1
0
1
0
2
0
2
0
0
0
0
3
0
0
0
2
0
1
0
0
0
1
0
0
0
0
2
0
2
0
0
1
0
1
0
0
0
0
0
3
0
3
0
2
0
0
0
0
2
0
0
0
0
0
0
1
1
1
1
0
1
1
1
1
2
2
0
2
0
0
1
1
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
2
1
1
2
0
0
0
0
3
2
1
0
0
2
0
2
2
1
0
0
0
0
0
2
0
1
0
0
1
1
1
2
0
1
1
0
1
1
0
0
3
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
1
0
0
0
0
1
0
0
1
0
2
0
0
2
3
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
1
0
2
0
1
0
0
0
1
0
2
0
2
0
2
0
0
0
0
0
1
0
0
2
1
1
0
0
1
0
0
0
2
0
0
2
1
0
0
1
0
2
1
0
0
1
0
2
1
2
0
1
0
0
0
2
0
2
0
1
1
0
0
0
0
0
0
1
2
0
0
0
1
0
0
2
1
1
1
0
2
0
2
0
1
0
0
2
0
2
2
0
2
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
2
1
0
2
0
0
0
2
0
0
0
0
0
1
0
2
0
0
1
1
0
0
2
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
1
1
0
1
1
0
1
1
1
1
2
0
0
1
0
0
1
0
3
0
0
0
2
1
0
0
0
2
0
0
0
2
0
0
1
1
2
0
0
0
2
2
0
0
0
0
0
3
2
0
0
0
1
4
0
0
0
0
1
2
2
0
0
1
2
1
0
0
0
1
0
3
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
2
1
1
0
0
0
0
0
2
0
0
2
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
2
0
0
0
0
2
2
0
0
0
0
3
2
0
1
0
0
0
0
0
2
0
0
0
2
1
2
2
2
1
1
0
1
1
0
0
0
0
1
2
1
1
0
0
0
0
0
1
3
2
2
0
1
2
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
2
2
0
0
1
0
0
0
0
1
0
2
0
0
0
2
2
1
0
0
0
0
1
0
0
0
0
0
0
1
2
0
2
1
2
0
0
0
0
0
0
1
2
0
1
0
0
1
0
2
0
0
0
1
0
0
1
0
0
1
0
0
0
2
2
2
1
2
2
0
0
0
2
0
0
2
0
2
1
3
0
0
0
0
0
0
0
0
2
1
0
0
1
0
1
0
2
0
0
0
0
2
2
2
2
1
0
2
2
0
0
1
0
0
1
2
1
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
2
0
2
1
0
1
2
2
0
2
0
2
0
0
1
1
0
2
0
2
1
0
0
0
2
1
0
2
0
1
0
0
2
0
0
0
1
0
0
1
0
0
0
2
2
0
2
0
1
1
0
0
0
0
0
0
2
0
0
1
0
1
0
0
2
1
0
1
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
1
1
1
0
0
0
6
0
0
0
1
0
2
0
1
1
2
1
0
0
1
0
0
0
0
0
0
1
0
0
0
2
1
1
0
0
1
0
1
2
0
1
1
0
0
0
1
0
2
1
0
0
0
2
0
0
2
0
2
0
0
0
4
1
0
0
0
0
1
1
0
0
1
1
1
0
1
2
0
2
0
0
1
0
1
0
1
1
2
0
2
1
0
0
0
1
0
0
0
2
0
1
2
0
2
0
0
0
0
0
0
0
1
0
0
0
2
2
1
0
0
1
1
0
0
1
1
0
1
1
1
2
0
1
0
1
1
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
2
1
0
0
2
1
0
2
0
0
0
0
1
0
1
0
1
2
0
0
1
0
1
0
0
0
2
0
0
0
2
0
1
1
1
0
2
2
0
0
0
0
1
0
0
1
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
2
0
0
2
2
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
2
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
1
0
0
0
0
1
1
0
1
0
1
1
1
0
2
1
2
0
0
1
1
0
1
1
2
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
2
1
0
0
0
0
1
2
2
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
2
2
2
0
2
2
0
0
2
2
0
0
1
1
1
0
0
0
1
0
2
0
0
0
2
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
2
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
1
1
1
2
0
0
2
0
1
0
0
0
0
2
1
2
1
4
0
0
1
4
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
1
2
0
0
0
0
0
3
0
0
1
1
0
1
0
2
0
0
1
1
0
0
1
2
0
1
1
0
1
1
0
0
2
0
2
0
0
1
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
1
1
2
1
0
2
0
0
0
0
1
1
2
0
0
0
0
1
0
1
2
2
1
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
2
0
0
0
1
2
1
4
0
0
0
1
2
0
0
0
0
2
0
0
1
1
0
0
1
0
1
0
1
0
1
0
1
2
1
0
0
2
0
0
0
0
3
0
0
0
2
2
0
2
1
0
0
0
0
1
2
0
0
0
0
0
0
0
1
1
2
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
2
2
1
0
0
2
0
0
0
2
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
1
2
1
2
2
2
0
0
2
0
0
2
0
2
0
1
2
0
2
0
0
2
0
0
0
0
1
0
0
2
1
2
1
0
0
0
2
0
2
0
0
1
0
0
0
1
2
0
2
0
0
1
2
0
2
2
0
0
0
1
3
0
0
3
1
0
1
1
1
0
1
0
0
0
3
2
0
0
1
2
0
4
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
2
2
0
1
0
2
1
4
2
0
0
2
1
0
0
0
5
1
1
1
0
2
0
1
0
1
0
0
2
2
0
2
0
0
1
0
2
0
1
0
1
1
0
0
0
0
2
0
2
2
0
0
0
0
0
0
1
1
0
0
3
0
2
1
0
0
1
0
2
0
2
0
2
2
0
0
0
0
0
2
0
0
0
1
1
1
0
3
0
0
0
0
1
1
1
1
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
1
0
1
2
0
1
0
0
0
0
0
2
0
0
0
1
2
1
1
0
0
1
2
0
2
0
1
2
1
3
2
0
0
0
0
1
1
2
2
0
1
0
1
1
1
2
1
1
1
2
0
2
0
0
1
1
1
0
0
3
0
1
0
0
1
3
0
0
0
0
3
0
0
1
0
2
2
2
1
1
0
0
0
2
1
0
0
2
0
0
0
1
2
0
0
1
2
3
0
0
2
0
0
2
3
0
0
0
1
1
0
1
0
0
1
0
1
3
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
2
1
1
0
2
0
2
1
0
1
0
0
0
0
1
1
2
1
0
0
0
0
1
0
0
0
0
1
0
1
2
1
0
2
1
0
0
1
0
0
0
2
0
2
0
0
3
0
0
0
0
1
0
0
0
0
0
1
2
1
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
2
0
0
1
0
1
0
0
2
1
2
0
1
0
2
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
2
2
3
1
0
1
0
0
0
2
0
3
1
1
2
0
2
0
0
2
2
1
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
1
0
2
0
1
0
0
1
1
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
2
2
0
1
1
1
0
2
0
0
2
1
1
0
2
0
0
2
0
0
0
0
1
2
0
0
2
1
0
1
2
0
2
1
1
1
3
1
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
2
0
0
1
2
3
2
0
0
3
0
2
0
0
0
0
2
2
2
2
2
1
1
0
1
0
1
0
0
0
3
2
0
2
2
0
0
2
0
0
0
2
1
1
1
0
1
0
0
0
0
0
2
0
0
2
0
0
0
1
2
0
0
0
0
0
1
0
1
1
0
2
1
1
0
1
2
0
0
0
2
0
1
0
1
0
2
0
1
0
0
0
1
0
0
1
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
2
2
0
1
2
2
0
0
0
0
1
0
2
2
1
0
1
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
2
2
2
1
0
0
0
0
1
0
2
1
0
1
0
0
0
2
0
2
0
1
2
1
1
0
2
0
0
0
1
0
1
1
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
3
2
1
0
0
1
2
2
2
1
1
0
1
1
2
0
1
0
0
0
0
2
1
0
1
2
0
0
2
1
0
0
0
1
1
0
3
1
0
0
2
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
1
1
1
0
2
1
0
0
2
0
2
0
1
1
2
1
1
0
0
0
1
0
1
0
2
1
1
0
1
0
2
1
0
1
0
0
1
3
0
0
0
1
5
1
0
0
1
2
0
1
0
2
0
0
1
0
0
0
2
1
0
0
1
1
0
0
1
2
0
0
2
2
2
1
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
2
2
1
0
0
0
1
0
0
0
1
1
0
0
1
2
0
2
2
0
0
1
4
0
0
1
3
0
0
0
1
0
0
3
1
0
2
0
0
0
2
0
1
0
2
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
2
1
0
0
0
0
2
0
1
0
0
2
1
0
1
0
0
0
0
2
1
0
0
0
0
3
1
2
0
0
0
2
1
1
2
1
0
0
1
0
1
0
1
0
0
0
0
1
2
0
1
0
0
0
0
0
0
3
0
0
0
0
2
0
0
1
0
1
0
2
1
0
1
0
0
0
0
1
0
2
0
0
2
0
0
1
0
1
1
2
4
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
1
0
1
2
0
0
0
2
1
1
2
0
0
1
2
0
2
0
0
2
0
0
0
0
1
1
0
2
0
2
2
0
0
0
0
2
0
0
2
1
1
0
0
0
1
0
0
2
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
1
0
1
1
0
0
0
0
1
2
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
2
2
0
0
0
2
0
0
2
0
0
2
2
2
0
2
0
0
2
0
0
0
0
0
0
0
2
2
0
0
1
0
0
2
0
0
1
1
0
0
1
1
1
0
1
2
0
0
1
1
1
2
0
0
0
2
0
0
1
1
1
0
2
2
2
2
2
1
0
1
0
1
1
0
2
0
1
1
0
0
2
1
2
0
2
0
0
1
0
0
0
0
1
0
3
0
1
2
0
0
0
0
1
1
0
1
0
1
0
2
2
0
0
1
0
0
0
1
0
0
2
1
0
0
0
2
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
2
2
0
1
0
0
2
0
0
0
0
0
1
2
2
1
2
0
2
0
0
2
0
1
0
0
4
2
1
2
0
0
0
2
0
1
0
0
1
2
1
1
5
2
0
2
2
0
1
2
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
1
0
1
0
0
0
0
1
0
1
0
1
0
2
1
0
1
1
0
2
1
0
0
0
1
0
1
0
1
1
0
0
2
2
2
0
0
2
0
1
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
2
1
1
0
0
2
1
0
0
3
0
0
0
0
0
0
0
0
2
0
2
3
0
0
0
0
0
0
1
3
2
2
0
0
1
1
0
0
0
0
0
0
0
0
1
4
2
2
1
0
0
0
1
0
0
0
0
0
1
2
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
2
0
0
0
1
1
2
0
0
1
4
1
0
1
1
2
1
0
2
1
0
0
1
0
0
0
0
0
0
0
0
2
6
2
3
1
0
2
2
1
1
1
0
2
0
0
1
3
0
0
1
0
0
1
0
1
1
0
0
1
2
0
2
2
1
1
2
0
2
0
2
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
2
1
1
0
4
0
2
1
0
0
0
0
1
0
0
1
0
0
0
0
1
1
2
0
0
0
1
1
0
0
0
0
1
2
2
1
1
0
0
1
2
2
2
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
2
1
0
1
0
0
1
0
2
1
0
2
0
0
1
1
2
2
2
0
0
1
2
0
1
1
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
3
1
0
0
0
0
0
1
0
0
2
0
0
1
0
0
1
0
2
1
2
0
2
0
0
0
0
1
0
0
1
0
0
0
2
0
2
1
0
1
2
0
0
2
1
0
1
1
0
0
0
2
0
0
0
1
0
0
0
0
7
0
2
1
2
0
2
0
1
1
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
2
0
1
1
2
0
0
0
2
2
0
0
2
0
1
1
3
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
1
2
0
2
0
2
0
0
0
1
0
1
0
0
0
0
1
0
3
0
0
1
0
1
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
1
0
2
0
1
0
0
0
0
0
2
0
0
4
0
1
1
2
0
0
0
2
0
0
2
0
0
0
0
0
2
0
1
1
2
0
2
0
1
1
1
0
0
1
1
0
1
0
2
2
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
2
1
0
1
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
1
0
0
0
1
2
0
1
2
2
0
0
0
1
1
1
0
0
0
1
0
0
0
0
1
4
0
0
1
0
0
0
4
0
0
0
0
2
1
2
0
0
1
0
0
1
0
1
1
1
1
0
1
2
2
0
0
0
0
2
2
0
0
2
1
4
1
0
2
0
1
0
0
0
1
2
2
1
0
0
0
2
0
2
2
0
2
0
2
0
0
0
1
0
0
1
0
0
3
0
2
2
1
0
2
0
0
2
0
0
2
2
0
0
1
0
0
2
2
2
0
2
3
0
1
0
2
1
0
0
0
0
0
2
0
2
1
1
1
2
0
2
0
0
1
0
1
0
0
0
0
2
0
0
0
2
2
0
2
2
1
2
1
2
1
2
0
0
1
1
2
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
2
0
1
0
1
0
2
0
0
2
0
1
0
0
1
1
1
0
0
3
0
1
2
1
0
1
2
0
1
0
2
2
0
0
0
0
0
2
2
1
1
0
2
0
0
0
1
0
1
1
0
2
0
0
0
2
1
1
0
0
0
2
0
3
2
0
0
1
0
2
0
0
0
5
0
2
2
0
1
0
0
0
0
0
0
0
0
1
0
2
2
2
0
0
0
0
0
2
1
2
0
0
0
0
0
2
2
1
1
0
0
2
0
0
0
1
0
0
0
0
0
2
2
0
1
1
2
2
1
2
1
1
0
1
0
0
0
0
0
1
3
0
4
1
0
0
0
0
0
0
1
0
1
0
1
0
0
3
0
0
0
1
0
0
0
1
0
0
1
0
1
0
2
0
2
0
0
0
2
0
0
0
0
0
1
0
1
2
1
0
2
0
0
1
1
1
0
0
0
2
0
0
1
0
1
0
0
0
0
0
1
2
0
0
0
1
1
1
1
0
0
1
2
2
1
1
2
0
0
1
0
0
1
0
2
0
0
0
1
0
1
1
1
1
0
2
2
0
0
2
1
2
0
2
0
0
0
0
0
0
0
1
0
1
0
0
2
1
0
2
0
0
3
0
1
0
0
0
0
0
0
0
1
1
2
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
2
0
2
0
1
0
1
0
1
0
0
1
0
1
3
0
0
0
3
0
1
2
4
0
0
0
0
0
0
2
0
0
1
1
2
0
0
0
0
2
1
1
2
0
2
0
1
0
1
0
0
0
0
0
0
0
0
2
3
2
1
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
2
0
1
0
1
1
0
3
0
0
0
1
0
0
0
1
1
2
0
0
1
0
0
2
1
1
0
1
1
2
1
0
1
1
1
1
2
0
0
0
0
2
0
2
0
1
0
0
0
2
0
1
0
2
2
1
1
1
0
0
0
0
1
0
0
0
0
1
0
2
1
1
0
2
2
0
2
0
0
0
0
0
0
2
2
1
0
0
2
1
0
1
0
0
0
0
1
1
1
0
2
1
0
0
1
0
0
0
0
1
0
2
0
0
2
0
1
1
0
0
0
1
1
0
1
0
2
0
0
0
2
0
0
0
0
2
3
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
1
0
1
0
2
0
0
2
2
2
1
0
2
0
0
1
3
1
1
1
0
1
2
1
0
0
0
0
2
0
0
0
0
0
0
0
7
0
0
1
2
0
2
0
2
0
0
0
0
1
0
0
2
0
1
0
1
2
0
0
1
1
0
0
1
0
2
0
0
2
0
0
2
0
2
1
2
0
0
2
1
0
2
2
0
1
0
0
0
0
0
0
2
0
1
1
2
0
0
0
0
0
0
2
0
0
2
1
1
0
2
1
2
0
0
0
2
2
0
1
1
0
0
0
0
0
0
1
0
1
1
1
1
1
0
0
0
0
2
0
0
2
0
1
0
0
1
0
1
0
0
1
0
0
1
5
1
4
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
1
1
0
2
1
1
2
2
2
0
1
0
0
0
0
0
0
1
2
1
0
0
0
2
0
1
0
3
0
1
0
0
0
0
0
2
2
2
1
1
1
0
1
1
0
1
1
2
0
1
0
0
1
2
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
2
0
1
2
3
0
0
0
0
0
2
1
0
1
0
0
0
0
1
1
2
0
1
0
0
0
0
2
0
1
0
0
0
1
0
0
1
1
1
1
0
0
0
1
0
0
0
0
3
0
1
2
1
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
4
0
2
0
1
0
1
0
2
0
0
1
0
0
0
0
0
0
1
0
3
1
0
0
1
0
1
1
0
2
1
0
0
0
2
0
0
1
2
0
0
1
1
2
0
0
0
1
1
2
0
0
1
1
0
0
0
0
2
0
0
0
0
0
2
2
1
0
0
0
2
0
2
1
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
1
0
0
2
0
1
1
0
0
1
2
2
0
1
1
2
0
1
2
1
2
1
1
0
0
0
1
0
0
4
0
0
0
1
0
0
2
3
1
0
0
0
1
0
2
1
0
0
3
0
0
1
0
2
0
1
2
2
0
0
1
1
0
2
0
0
1
2
0
0
0
0
0
0
1
0
0
0
1
2
1
1
2
0
0
0
0
0
0
0
0
1
0
1
2
0
1
2
0
1
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
2
2
2
0
0
1
0
1
2
0
1
1
0
1
0
2
0
1
1
0
1
0
2
0
2
0
1
2
2
0
1
0
1
2
0
1
0
4
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
2
0
1
0
3
0
0
2
1
0
1
2
0
0
1
2
4
2
2
1
3
2
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
1
2
0
0
2
1
0
0
0
0
1
2
2
3
2
0
1
1
1
1
0
0
0
1
0
0
6
2
0
0
1
0
0
2
0
0
0
0
1
2
1
1
0
2
0
2
0
0
0
0
2
0
2
0
1
0
1
0
0
1
0
0
1
0
1
0
1
0
0
0
1
0
0
5
0
0
0
2
0
0
0
1
2
0
1
0
1
0
0
2
0
0
1
1
0
1
0
0
0
0
0
2
0
2
0
2
1
0
1
3
0
2
0
0
0
0
0
1
1
2
0
0
0
1
0
0
0
0
2
0
2
1
0
2
0
1
2
1
2
0
0
1
0
0
0
1
1
0
0
1
0
0
0
2
1
0
2
0
0
0
0
0
2
1
1
0
0
0
0
0
0
2
0
2
0
1
1
0
2
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
1
0
2
0
1
0
0
0
0
1
2
2
0
1
2
2
1
2
2
0
0
0
0
1
2
1
2
2
0
1
1
2
1
0
0
1
0
0
1
0
2
2
2
0
0
0
0
0
1
0
2
0
1
2
2
0
2
1
2
1
2
2
0
0
0
0
1
3
1
2
2
0
0
2
0
0
2
2
0
0
0
2
2
0
3
0
0
1
0
0
0
0
1
1
1
0
1
0
2
2
0
0
1
1
0
1
1
0
0
0
0
0
2
0
0
4
1
0
0
1
0
0
0
0
0
0
2
0
1
1
3
3
0
0
1
2
0
1
4
1
0
0
1
0
1
0
2
1
0
3
0
2
0
1
1
0
1
2
0
0
0
0
0
2
1
0
2
0
1
1
0
0
0
0
1
1
0
2
1
2
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
1
0
0
2
1
0
0
1
1
0
0
0
2
2
1
2
2
1
0
1
0
0
2
1
0
2
0
1
2
2
0
0
1
0
2
1
0
1
0
1
2
0
0
3
0
0
2
2
0
1
1
2
3
1
0
2
2
0
0
0
1
1
0
0
0
0
0
0
1
1
0
1
0
3
0
0
0
2
1
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
1
0
0
3
2
1
2
0
1
2
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
1
2
0
0
1
1
0
1
2
0
1
6
3
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
2
2
1
0
1
0
0
0
0
0
0
0
0
1
0
2
2
1
1
0
0
0
0
0
2
0
1
0
1
2
0
2
1
0
0
2
3
3
0
0
0
0
0
0
0
0
0
2
1
1
2
2
1
2
0
1
1
2
2
0
1
0
0
2
2
0
1
0
1
0
0
0
1
2
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
2
2
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
2
1
0
1
0
0
3
1
0
2
0
0
1
0
0
0
1
0
2
1
0
2
1
0
4
0
0
0
3
0
0
0
2
2
0
2
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
1
0
0
1
2
1
1
2
4
0
1
0
2
2
0
0
0
0
0
1
0
2
2
1
1
0
0
0
2
1
1
1
0
2
1
0
1
1
0
0
2
2
1
0
2
2
0
1
2
0
0
1
0
0
0
1
1
2
0
2
1
2
0
0
2
0
0
0
2
0
2
2
1
1
1
0
1
1
1
0
0
0
0
0
1
1
0
0
3
0
1
0
0
0
0
0
2
2
1
1
0
2
0
1
0
2
0
0
1
0
0
3
0
2
0
2
0
0
0
1
0
2
0
0
0
2
2
0
0
1
0
0
3
0
1
0
0
0
0
0
0
0
0
0
2
1
1
2
0
0
2
2
0
0
0
0
1
2
0
2
0
2
0
0
0
1
0
1
1
0
0
0
2
1
0
0
1
2
0
0
0
0
1
1
0
2
2
1
0
0
0
1
3
0
0
1
1
2
0
0
0
2
1
1
0
0
0
1
2
1
0
2
0
0
1
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
1
0
2
0
1
0
1
5
1
1
3
0
1
2
1
1
0
2
0
1
0
2
0
0
1
0
1
1
0
0
1
0
2
1
0
0
0
2
0
1
2
0
0
2
0
1
1
2
2
1
2
0
0
0
1
1
2
2
0
0
2
0
1
1
0
0
0
0
0
0
1
0
1
0
1
1
0
1
2
0
0
2
0
4
1
2
2
0
1
0
0
2
0
0
0
0
1
0
1
0
1
0
1
1
1
1
0
2
0
2
1
1
0
2
0
0
0
1
1
0
1
1
0
1
0
0
0
1
1
0
2
1
1
2
0
0
2
2
0
0
0
0
1
1
0
0
0
1
1
1
0
0
0
0
0
1
0
1
0
2
0
1
0
0
0
1
0
0
1
0
1
2
1
0
0
0
0
1
0
1
0
0
0
0
1
2
1
0
0
0
2
1
1
0
1
1
0
2
0
2
1
1
0
0
0
1
2
0
0
1
0
1
0
2
1
2
0
0
0
0
0
0
1
1
2
0
2
0
0
0
1
1
2
0
0
1
2
0
0
2
0
1
0
0
1
0
1
0
3
2
0
1
0
2
0
0
1
1
0
0
2
0
1
0
0
3
2
0
0
0
0
0
2
1
0
1
1
0
1
0
0
0
1
0
0
0
0
0
1
0
2
1
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
1
0
1
1
0
0
1
1
1
1
0
0
0
0
2
1
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
2
0
0
2
1
0
0
1
0
2
1
1
1
0
1
0
2
2
1
2
0
0
0
0
0
1
2
1
0
2
0
1
0
0
1
0
0
0
0
0
2
0
1
0
2
0
1
0
1
0
1
0
1
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
2
1
1
0
0
1
0
0
2
2
0
2
0
0
0
0
0
0
3
0
0
0
1
0
1
1
0
0
0
0
0
0
1
1
0
0
2
1
2
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
2
2
1
1
1
0
0
1
2
2
2
0
0
1
0
0
0
0
2
0
0
1
2
0
1
2
0
2
0
1
1
2
2
1
0
0
0
2
0
0
2
2
1
0
0
2
0
0
0
0
0
0
2
0
1
1
0
1
0
1
1
0
0
0
1
0
2
1
2
2
0
0
0
2
0
2
0
1
0
0
0
0
3
2
1
0
0
2
0
2
1
0
0
2
1
0
0
0
1
2
2
1
2
0
0
3
3
2
0
0
0
0
1
2
0
0
0
0
0
3
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
2
2
0
1
1
1
0
1
0
0
1
0
1
0
1
0
0
0
1
1
0
0
2
0
0
0
1
0
0
2
0
3
0
1
0
2
1
0
0
0
1
3
6
0
2
1
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
4
0
0
0
2
1
1
0
0
0
1
0
1
0
0
0
2
0
0
2
0
0
1
0
0
0
0
2
1
0
1
2
0
2
0
2
2
0
1
0
2
2
0
2
0
2
0
1
0
0
2
0
1
1
0
2
2
0
2
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
3
0
2
0
2
0
1
2
0
0
0
5
0
0
0
1
0
0
0
2
0
0
0
2
0
1
1
0
1
0
0
1
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
1
0
1
1
0
0
1
1
0
0
1
0
1
0
1
0
0
1
0
0
1
5
0
2
2
0
0
1
1
1
0
0
1
0
0
0
2
1
2
1
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
1
1
2
0
0
0
0
0
2
0
1
0
1
0
2
1
0
0
1
2
0
1
1
2
0
1
2
0
2
0
1
0
0
0
2
1
1
0
1
0
2
1
1
0
1
0
0
0
2
1
2
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
1
0
2
1
0
2
0
1
0
0
0
0
0
2
2
0
0
2
1
1
0
0
0
2
0
1
1
2
0
0
0
1
1
0
0
2
1
0
0
2
1
1
0
1
1
1
2
0
1
1
0
2
1
2
0
0
0
0
1
0
0
0
2
0
0
0
1
2
1
0
0
2
1
0
0
0
2
0
1
1
0
1
0
2
1
0
1
0
0
0
1
0
0
1
0
0
2
1
0
0
1
0
2
0
0
2
0
2
0
0
2
0
2
0
3
1
0
1
1
1
1
2
0
0
2
1
0
2
0
0
2
2
0
0
2
1
1
1
1
0
1
0
0
1
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
2
2
3
0
0
0
2
1
0
0
0
1
1
0
1
2
2
0
0
2
3
2
0
0
0
0
1
2
0
0
0
1
0
0
1
0
0
2
0
0
0
1
2
1
0
0
1
0
1
2
4
1
0
0
0
0
0
0
1
0
0
0
2
0
2
0
3
2
2
0
0
0
2
0
1
1
1
0
0
1
1
0
1
1
0
0
1
1
0
0
2
0
0
0
1
0
2
1
1
0
1
1
0
2
0
1
0
1
0
1
0
1
0
0
0
1
1
0
1
0
2
0
2
0
0
1
2
0
2
1
0
2
0
0
1
2
0
1
10
0
0
0
0
0
2
2
0
0
1
0
2
2
1
0
1
0
0
1
1
0
0
1
2
1
0
2
0
1
0
2
1
2
0
2
0
0
0
2
0
0
1
0
0
0
1
1
0
1
0
0
2
0
0
1
0
0
0
2
2
0
0
1
0
0
2
0
0
1
0
2
0
0
1
0
0
1
0
1
2
0
0
4
2
0
0
2
0
1
0
1
2
0
1
0
0
0
2
1
2
1
1
0
1
0
0
0
1
0
2
0
0
0
0
0
1
0
2
2
0
0
0
1
0
1
0
1
0
0
1
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
1
2
0
0
1
2
0
1
0
0
2
0
0
1
2
1
0
2
1
0
0
0
1
2
1
0
1
0
1
0
1
0
2
2
0
0
1
0
2
1
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
2
2
0
2
0
0
1
0
0
0
0
4
2
0
3
0
0
0
0
2
0
2
1
0
2
1
1
2
3
1
0
2
1
1
0
2
1
1
0
1
0
1
0
2
0
0
0
0
1
0
2
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
2
2
1
0
2
0
0
0
2
1
0
1
2
0
0
0
1
0
0
0
2
0
2
2
1
0
0
2
2
2
0
2
3
1
0
0
1
0
0
2
1
0
2
0
1
1
1
0
0
0
1
2
0
0
0
2
0
2
1
1
0
0
1
2
0
0
0
1
0
1
2
0
0
0
1
0
1
1
2
2
0
2
0
0
2
2
1
0
0
1
1
2
2
0
3
0
0
0
0
2
0
3
0
1
1
0
0
1
0
1
0
0
0
1
1
2
2
0
1
1
0
1
0
0
1
2
0
2
1
1
1
0
2
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
1
0
2
2
2
1
0
2
2
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
1
0
0
1
0
0
1
0
2
0
0
0
0
0
0
1
1
0
0
2
0
2
2
0
0
0
1
0
0
0
0
0
2
2
0
1
1
0
2
1
0
0
2
0
2
1
0
0
1
0
0
0
0
1
1
1
0
2
2
2
1
1
0
1
2
0
0
3
0
0
0
1
1
2
0
1
0
2
0
0
1
0
0
0
0
1
0
1
2
0
0
0
1
0
1
1
0
0
0
0
2
1
0
0
1
0
0
0
1
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
3
0
3
0
0
1
1
1
2
0
0
1
6
0
0
0
0
0
2
0
0
0
0
1
1
0
2
2
0
1
2
0
0
0
1
0
0
1
0
0
0
0
0
1
4
2
0
0
1
0
2
1
2
2
0
1
1
1
0
0
0
1
3
1
2
1
0
1
1
0
0
1
0
2
1
3
0
0
0
0
2
1
0
0
2
1
2
0
1
2
0
0
2
0
2
1
0
0
0
1
0
0
0
2
1
1
0
1
1
0
2
1
1
1
0
1
1
0
1
1
2
0
0
0
1
0
0
0
1
0
0
1
2
1
0
0
2
0
0
0
2
0
0
1
3
0
3
2
0
2
1
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
1
0
0
1
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
3
0
0
0
2
0
2
1
0
0
0
0
2
2
0
0
0
2
1
0
1
0
1
0
0
0
0
0
0
0
2
1
1
0
2
2
1
0
1
0
1
0
1
0
0
0
1
1
1
0
0
0
0
1
1
0
1
3
3
2
0
1
0
1
0
0
1
1
1
0
1
2
2
1
0
2
0
0
2
0
2
1
2
0
0
0
0
0
0
2
1
0
1
3
0
0
1
0
0
0
2
1
0
0
0
0
0
0
1
0
3
0
0
2
0
2
0
2
0
2
0
1
0
0
2
0
0
0
0
5
0
2
0
0
0
0
1
1
0
0
0
0
0
0
2
1
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
2
2
0
0
0
2
1
0
0
1
2
0
1
0
2
1
0
2
1
0
2
0
2
2
0
1
0
0
0
0
2
0
1
0
0
0
2
0
0
2
0
0
0
0
2
0
1
0
0
2
0
1
0
0
2
0
1
0
0
0
2
0
2
0
1
1
2
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
1
1
1
1
0
0
2
0
1
1
1
0
1
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
2
1
0
0
0
1
0
0
0
2
1
0
0
2
0
0
2
1
2
0
0
2
3
2
1
0
1
0
0
5
2
0
0
0
1
2
0
2
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
2
1
1
2
0
0
0
0
1
2
2
0
2
2
1
0
0
0
0
2
0
0
0
0
3
0
1
0
1
0
0
2
0
2
0
2
1
0
0
5
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
3
0
0
2
2
1
2
0
0
0
1
0
0
0
0
1
2
0
0
0
2
0
0
0
1
1
4
2
1
0
1
1
0
1
1
2
2
1
2
2
1
0
0
0
0
2
1
1
0
1
1
0
1
1
2
0
2
4
0
1
0
2
0
0
0
2
1
0
2
2
0
1
2
0
2
0
0
0
2
0
1
1
0
0
2
0
0
0
1
1
1
0
0
1
2
2
0
0
0
0
0
0
0
0
0
2
1
2
2
4
2
0
0
0
0
2
0
0
2
0
1
2
1
2
1
0
1
0
0
0
1
2
0
2
0
1
1
0
0
0
1
2
0
1
1
2
1
2
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
2
0
1
0
2
1
0
1
1
0
0
1
0
0
0
0
0
1
0
2
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
1
0
0
2
0
1
0
2
0
0
0
2
2
0
0
0
0
1
1
0
0
0
0
0
0
2
1
2
1
1
2
1
0
0
0
0
0
3
0
2
0
0
2
2
0
2
0
0
0
2
0
0
1
0
4
2
0
1
0
0
0
0
1
0
1
0
0
0
0
2
2
0
0
0
2
0
0
2
2
2
0
4
0
0
2
2
1
1
0
1
1
1
0
1
0
0
0
0
0
1
0
0
2
1
2
5
0
0
0
1
2
1
2
0
0
1
0
0
0
0
1
1
2
1
1
0
0
0
1
1
1
0
0
2
2
0
0
1
0
0
2
2
2
0
0
0
1
0
0
0
0
0
0
1
1
2
0
1
1
1
0
0
0
0
0
0
2
0
2
1
0
3
0
0
2
2
0
1
0
0
0
0
2
2
0
0
0
0
1
0
0
2
0
0
0
0
0
1
1
1
0
0
0
0
1
0
5
0
0
1
1
0
0
1
0
0
1
0
0
2
2
1
1
0
0
2
0
0
0
1
0
1
2
2
0
0
1
0
2
0
2
2
0
1
2
2
0
0
1
0
1
2
1
0
0
0
2
1
0
0
0
0
1
0
0
0
3
0
0
1
0
1
0
3
1
4
2
2
0
0
2
1
2
0
2
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
1
0
3
1
0
1
0
0
2
1
0
1
0
2
1
2
1
1
2
0
0
0
1
0
1
2
1
0
0
0
2
0
0
0
2
0
0
0
0
2
1
0
2
1
0
2
1
2
0
0
0
1
0
0
2
0
0
2
0
1
1
2
1
0
2
1
1
2
0
0
1
0
0
0
0
1
0
2
2
0
2
0
2
0
0
3
0
1
0
2
0
1
0
1
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
1
2
2
2
2
2
1
0
0
3
2
0
2
0
2
1
0
2
0
1
2
0
0
1
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
2
0
1
1
0
0
0
2
0
0
1
1
1
1
0
0
0
0
1
0
1
2
3
0
2
2
0
0
1
2
0
0
0
1
0
3
2
0
2
2
3
2
0
1
1
0
0
0
1
1
0
1
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
2
2
0
1
2
2
2
0
0
0
0
0
1
1
1
1
0
0
0
1
1
2
0
0
0
1
1
0
0
0
2
0
0
0
0
0
1
0
0
1
1
0
0
0
1
1
0
0
0
3
0
0
2
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
2
2
0
0
1
0
2
0
2
1
0
2
0
0
1
2
1
1
0
0
0
2
1
0
0
2
0
0
0
0
0
1
0
0
0
2
1
0
2
0
0
0
1
0
1
3
0
0
2
1
0
0
0
0
1
2
0
0
0
1
2
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
2
0
2
0
0
1
2
1
0
2
0
1
2
2
0
0
2
0
0
0
2
1
0
2
2
1
0
1
0
1
0
0
2
1
0
1
3
0
2
1
0
0
0
1
2
0
4
0
0
1
0
2
1
0
0
1
0
0
0
0
4
0
2
1
0
2
0
0
0
1
0
1
0
0
0
3
0
0
1
2
2
0
3
0
0
0
0
2
0
0
2
2
0
1
0
1
2
0
0
1
3
1
2
0
2
2
2
0
0
1
0
1
2
0
0
1
0
2
0
0
0
2
1
4
2
0
0
1
1
2
0
0
2
2
0
2
0
5
2
0
1
0
0
0
1
1
1
0
1
1
2
2
0
0
2
1
0
0
0
1
0
0
1
1
1
0
0
1
2
0
1
0
0
1
0
1
0
1
0
1
0
0
1
1
0
2
2
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
1
1
2
1
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
1
2
0
1
0
2
2
1
0
0
2
0
2
0
1
0
0
1
0
0
2
1
1
1
0
2
0
1
1
0
0
1
0
2
0
0
0
0
1
0
1
1
1
2
0
0
1
0
0
1
2
1
0
2
2
0
1
0
0
0
0
1
0
1
0
1
0
0
2
2
1
0
0
0
2
1
0
0
1
0
1
0
1
4
0
0
0
0
2
0
1
0
2
2
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
2
0
0
0
1
0
4
1
1
0
0
0
0
0
1
2
1
0
1
2
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
4
0
0
1
0
0
1
1
0
1
0
2
0
0
2
1
0
0
2
0
0
2
0
0
1
0
2
1
1
0
0
1
0
0
0
0
0
0
0
1
2
0
0
2
2
0
0
2
1
1
0
0
4
1
2
0
0
2
0
0
0
0
1
2
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
2
0
0
1
0
1
0
4
0
0
1
0
0
0
0
1
3
0
1
0
0
2
0
2
0
3
2
1
0
1
0
0
0
0
0
0
0
0
2
0
4
0
0
0
1
2
0
0
1
0
1
1
0
0
1
0
2
1
0
0
0
0
1
0
1
2
0
1
2
0
2
2
0
0
0
0
3
0
0
1
0
1
0
0
3
0
2
0
0
0
1
0
0
1
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
3
2
0
2
1
0
0
2
0
1
0
0
0
2
2
0
0
1
0
0
0
0
2
0
0
2
0
1
2
1
1
0
0
0
2
0
0
0
0
2
0
0
2
0
1
0
0
2
0
0
1
2
0
1
1
0
2
1
0
0
2
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
2
1
0
2
2
4
1
2
0
0
0
1
0
0
2
0
3
2
0
2
0
1
0
2
4
0
1
1
0
2
0
0
1
2
0
0
0
0
1
1
0
0
2
0
1
0
1
0
2
0
0
1
0
2
1
1
0
1
0
1
0
0
0
1
0
1
0
0
1
0
2
0
0
2
2
0
1
0
1
0
2
0
0
0
0
0
2
0
0
0
2
1
2
0
1
0
0
0
0
2
0
1
2
0
0
2
1
1
2
0
0
0
0
0
0
2
0
2
1
0
0
0
0
2
0
1
2
0
0
1
1
1
4
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
2
1
1
0
0
0
0
2
0
1
0
2
1
0
1
0
0
0
3
2
2
0
0
0
0
0
0
2
0
1
0
1
0
1
0
0
0
1
0
2
0
0
0
0
0
1
1
2
2
0
0
0
0
1
0
0
2
0
3
0
1
0
0
0
2
0
0
1
0
0
0
2
2
2
0
1
1
1
0
0
1
0
1
1
1
0
0
1
1
0
0
0
1
0
1
1
0
1
0
0
2
1
0
0
0
0
0
2
1
2
1
0
2
0
0
3
0
0
0
0
2
0
0
0
1
0
1
0
2
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
2
0
1
1
1
1
2
0
1
1
1
0
2
0
0
2
0
2
0
1
0
0
1
0
2
0
0
1
1
1
0
0
1
0
2
0
2
0
0
0
2
0
0
0
5
1
1
4
0
0
1
1
2
0
0
2
0
0
0
4
0
1
0
0
0
0
2
0
0
1
0
0
0
1
1
0
2
3
1
0
0
0
1
2
2
1
0
2
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
1
2
0
0
1
1
2
0
2
0
0
0
0
1
0
0
2
1
1
2
0
2
0
0
0
1
0
2
1
0
0
0
2
0
0
1
1
0
0
1
1
0
1
1
1
2
0
0
1
0
0
2
0
0
1
0
2
2
0
1
2
0
0
0
0
1
0
1
1
0
0
0
0
0
1
1
0
1
0
1
0
0
3
0
1
1
1
0
1
0
1
0
0
0
0
1
1
0
0
2
0
1
0
0
2
0
2
1
0
0
2
0
0
2
0
0
1
2
0
0
1
0
0
0
1
1
0
0
2
0
3
1
0
0
0
2
2
0
1
2
3
1
1
0
0
0
0
0
0
0
2
2
0
2
0
0
2
0
2
2
0
1
1
2
0
2
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
2
0
2
1
0
0
1
2
0
2
0
2
2
0
0
1
0
2
2
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
2
2
0
0
0
2
0
2
0
1
1
1
1
1
0
1
0
0
0
1
0
0
2
0
0
2
0
1
2
1
0
0
3
1
1
0
0
2
1
3
0
0
0
0
0
0
1
0
2
0
2
0
2
0
0
1
1
0
2
1
0
0
0
1
0
0
1
0
0
0
0
0
1
2
1
2
0
0
1
1
1
1
1
0
0
0
0
1
1
1
1
4
1
4
0
0
1
0
0
0
0
2
0
0
1
1
0
0
0
0
2
1
0
1
1
1
0
0
1
2
0
1
2
0
0
0
0
0
1
1
0
0
0
0
2
0
2
2
1
1
0
0
0
0
0
1
0
0
1
2
1
2
1
0
2
2
1
2
0
0
0
0
0
0
1
0
0
2
0
1
0
0
2
0
1
0
1
2
0
0
2
0
0
0
1
0
2
4
0
0
0
1
0
2
0
1
0
0
2
1
2
1
1
1
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
2
0
2
0
0
2
0
0
2
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
2
2
1
0
2
0
0
1
0
0
0
0
0
1
2
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
1
0
1
2
1
0
3
0
0
1
0
0
0
6
0
0
1
0
2
2
2
1
0
0
0
0
2
0
1
1
0
0
0
0
2
0
0
0
0
0
0
4
0
0
1
0
1
1
0
1
0
0
2
0
2
0
0
2
1
1
0
2
0
2
1
0
1
0
0
0
1
0
0
2
0
1
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
1
0
2
2
1
0
1
3
0
0
0
1
0
1
0
1
1
2
0
0
0
0
1
0
1
0
0
0
0
0
0
3
0
0
0
2
0
1
0
3
1
1
1
0
1
1
2
0
0
1
0
1
0
0
3
0
0
2
1
0
2
0
0
1
0
1
1
2
0
0
0
0
0
2
2
0
0
1
0
0
0
0
1
0
0
4
1
2
0
1
0
1
0
2
0
1
0
0
2
2
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
2
2
1
0
0
0
0
0
0
2
0
1
0
1
2
2
0
0
1
1
2
2
0
0
0
2
0
1
0
1
0
0
0
0
3
2
1
0
2
0
0
1
0
1
1
0
1
0
2
2
1
0
0
1
2
1
0
0
0
0
2
0
0
2
0
0
1
0
0
2
2
0
2
0
0
2
2
0
0
0
2
0
1
0
0
1
2
0
0
0
1
1
0
1
2
0
3
0
1
0
0
0
2
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
1
0
0
0
0
2
2
0
0
0
0
1
0
0
3
0
1
2
2
0
1
0
0
1
0
2
1
0
0
0
0
0
0
1
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
2
2
0
0
0
1
1
2
1
0
0
0
1
0
0
0
2
1
2
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
1
0
0
0
1
2
1
2
0
1
1
1
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
2
0
2
0
0
0
0
1
1
0
1
1
0
0
2
1
0
1
2
1
0
2
1
2
2
0
0
2
2
0
0
0
0
0
0
1
0
0
0
1
1
0
3
1
0
0
0
0
1
0
0
0
1
0
2
0
0
2
1
1
2
4
1
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
2
0
1
1
0
0
0
1
0
0
1
2
1
0
2
0
0
2
1
0
1
0
1
2
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
2
1
0
0
2
1
0
0
0
2
0
0
1
0
1
0
2
1
3
1
0
2
0
1
0
0
0
0
0
0
0
0
0
2
1
2
0
0
2
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
1
2
2
0
1
0
0
2
0
0
3
0
0
2
0
1
0
0
2
0
3
0
2
2
0
1
0
2
2
0
0
0
0
1
2
1
0
0
2
1
1
1
0
1
0
1
2
3
0
0
3
1
3
0
0
2
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
2
1
0
0
0
2
0
2
1
6
0
2
2
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
2
0
3
0
0
0
0
0
0
0
0
1
2
0
0
0
1
1
2
0
2
0
0
0
3
0
2
0
0
0
1
0
0
0
2
1
6
2
0
0
0
0
2
0
0
2
0
2
0
2
2
0
0
0
2
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
4
1
0
1
0
2
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
2
0
2
1
1
0
0
2
2
1
0
0
2
0
0
2
0
2
0
0
0
2
0
0
0
0
1
0
0
0
2
0
2
2
0
0
1
1
1
0
0
0
1
1
0
0
1
1
0
1
0
2
0
2
0
0
0
0
0
0
1
2
4
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
2
2
0
2
0
1
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
2
2
0
2
0
1
0
2
0
0
1
0
2
2
0
0
2
2
0
2
0
0
0
1
0
1
0
2
1
2
0
1
0
0
2
2
0
0
0
1
0
1
0
2
2
0
2
0
0
2
3
1
0
0
0
1
0
0
0
0
0
0
0
2
1
1
1
2
0
0
2
1
2
1
0
0
0
1
2
2
2
1
0
2
1
0
2
1
0
0
0
1
1
1
0
0
0
0
0
0
1
0
2
0
0
2
2
2
1
1
1
0
0
0
0
0
0
2
0
1
2
1
0
2
3
1
0
0
0
0
0
0
0
2
2
0
0
0
2
0
2
0
0
1
0
0
0
0
2
1
2
0
1
0
0
2
1
0
3
0
0
0
0
0
1
0
0
2
0
2
0
0
0
2
0
1
1
0
0
0
0
1
0
0
2
2
0
0
0
1
0
0
0
0
1
0
2
0
1
1
1
1
0
0
0
0
1
0
0
0
2
2
0
1
2
0
0
1
0
0
0
1
0
2
0
0
0
1
2
0
0
0
2
0
2
0
0
0
0
0
0
2
1
0
0
0
2
0
0
2
1
2
0
0
0
1
1
1
1
0
1
1
2
2
1
0
2
0
0
0
0
3
0
1
0
0
0
0
2
0
2
0
0
0
2
0
1
1
0
0
0
0
0
2
2
0
0
1
2
0
0
1
2
2
1
1
0
0
2
2
2
0
0
1
1
0
1
0
2
0
1
0
0
0
0
2
0
1
2
1
0
1
1
0
0
0
1
3
0
0
0
1
0
2
2
0
0
0
0
2
1
0
0
1
0
1
0
1
0
0
1
0
0
0
0
2
3
0
0
1
2
0
1
2
1
0
0
2
0
1
0
0
1
0
0
0
0
1
3
0
1
0
2
0
0
0
2
1
1
2
1
0
1
0
0
1
2
0
0
3
2
0
1
0
0
1
0
0
0
0
0
0
2
2
0
1
1
0
0
0
0
0
2
1
0
1
1
0
2
2
1
0
2
0
2
0
0
0
0
2
2
1
0
0
1
0
0
2
1
1
0
0
2
0
0
3
2
1
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
1
0
2
0
1
1
0
0
2
0
0
0
0
0
0
0
0
1
2
1
0
1
0
0
0
0
0
1
1
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
1
0
1
0
0
0
0
0
1
0
0
1
1
1
2
0
3
0
1
0
0
2
0
0
1
4
0
2
0
0
1
2
0
0
1
0
0
0
2
2
1
0
1
0
0
1
0
0
0
1
1
0
0
1
0
0
0
2
0
0
1
0
0
1
1
1
0
0
0
0
1
1
1
1
0
4
2
0
0
0
0
0
0
1
1
2
2
0
0
0
0
2
0
0
2
2
0
0
0
0
0
1
2
0
0
1
0
2
0
0
1
0
0
1
1
0
0
0
2
0
0
3
0
0
1
0
0
0
0
0
0
0
1
0
3
1
2
1
1
0
0
2
0
0
1
0
2
1
2
0
0
1
1
2
1
2
1
0
1
0
1
2
1
2
2
1
1
0
0
0
1
1
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
2
1
0
0
1
1
0
2
1
0
0
2
1
0
0
0
0
0
0
2
0
3
0
1
1
1
0
0
0
0
2
2
2
0
2
0
2
0
2
0
2
0
0
0
0
0
1
1
0
4
1
0
0
1
1
2
2
0
0
3
2
0
1
2
0
1
0
0
1
1
2
1
0
2
1
0
0
1
0
0
0
1
1
0
1
2
0
0
0
5
0
0
0
0
0
0
0
0
2
0
2
1
2
2
0
0
0
2
2
1
0
1
2
0
0
1
0
1
2
0
0
0
0
1
1
1
0
2
2
1
2
1
0
0
0
1
0
2
0
2
1
0
1
0
0
0
0
0
1
0
1
0
2
2
0
1
0
1
0
2
0
2
0
1
0
0
0
1
0
0
0
2
1
0
0
0
0
1
0
0
1
1
1
2
2
0
0
2
0
0
1
1
2
1
2
0
1
0
0
1
1
0
2
0
2
0
10
0
2
0
0
1
2
2
1
0
3
0
1
0
0
0
0
0
0
0
1
1
1
0
2
0
2
0
1
0
0
2
0
2
1
4
0
0
1
1
0
0
0
0
1
1
0
0
1
0
1
1
0
0
0
1
0
1
0
0
1
0
2
0
0
1
0
0
0
0
2
1
0
0
2
2
1
1
0
0
0
0
0
2
1
2
1
1
1
0
0
0
0
0
0
0
2
0
1
0
0
0
2
2
2
0
1
0
1
0
0
0
0
2
1
0
1
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
3
2
0
3
1
0
2
0
0
0
0
0
1
0
0
0
0
4
1
2
2
0
0
2
0
1
0
1
1
0
2
1
2
2
1
2
0
0
0
0
0
0
1
2
0
0
0
1
0
0
1
1
0
0
1
0
2
1
0
0
1
0
1
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
2
1
1
2
0
0
0
0
0
0
0
2
0
0
0
0
2
2
1
0
1
1
0
0
0
1
2
0
1
0
1
2
0
0
1
1
0
1
0
1
2
2
2
2
1
2
3
0
2
0
2
0
0
0
2
0
0
1
0
2
1
0
1
0
2
0
0
0
1
2
0
0
0
0
0
2
0
0
2
3
0
1
0
0
1
0
0
0
2
1
1
2
1
0
0
0
1
1
2
0
0
0
0
0
1
0
0
2
2
1
0
1
1
0
1
1
1
0
0
1
0
1
1
1
0
0
0
0
0
0
1
1
1
2
2
0
0
1
0
1
2
1
0
0
0
0
1
0
0
1
1
0
0
0
0
3
1
0
2
0
0
1
1
0
1
0
0
0
0
0
0
0
1
2
0
0
4
1
0
1
1
0
1
1
0
0
0
3
0
0
0
0
0
0
0
2
0
2
0
0
1
0
1
1
0
1
0
3
0
0
0
0
2
1
0
0
0
0
1
1
1
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
2
0
1
1
0
0
0
0
0
0
1
0
0
1
2
0
1
0
0
0
0
0
1
0
0
2
2
2
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
6
0
1
0
0
0
0
2
0
0
0
0
1
3
0
0
0
0
0
0
2
0
0
0
0
7
0
1
0
0
1
1
0
0
0
0
3
2
0
1
2
0
3
0
0
0
0
0
0
0
0
2
5
0
1
0
0
2
0
0
1
2
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
2
1
0
0
0
0
1
2
1
2
0
0
1
0
0
2
0
5
0
3
1
1
0
0
1
0
0
0
0
1
1
0
2
0
0
1
0
0
0
1
0
0
0
2
0
0
1
0
1
0
1
0
0
2
0
3
2
5
2
0
2
0
2
0
0
0
0
0
0
1
0
1
9
1
2
0
0
0
0
0
0
1
1
0
2
0
0
1
3
0
0
2
1
0
1
0
2
1
1
2
0
0
1
2
1
1
1
0
0
0
0
0
1
0
0
1
0
0
1
2
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
1
1
2
2
0
1
1
0
2
0
0
3
0
0
0
0
2
1
0
0
0
3
0
1
0
0
0
2
0
1
1
2
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
1
0
0
1
2
1
0
0
0
0
1
2
2
0
0
0
0
2
1
0
0
2
2
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
1
2
2
1
1
1
0
0
1
1
1
0
1
1
1
0
0
0
0
0
3
0
1
1
0
1
1
1
0
0
2
3
1
1
0
1
1
0
0
1
2
2
6
0
0
1
2
1
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
1
1
0
1
0
0
1
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
3
0
0
0
1
0
0
1
0
1
0
0
0
0
2
0
0
2
1
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
2
0
0
2
2
0
0
1
1
0
1
0
1
1
2
1
1
2
1
0
0
0
2
2
0
2
0
0
1
0
0
0
0
1
2
0
0
0
0
1
0
0
1
2
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
2
2
2
0
0
0
0
0
0
1
1
1
2
1
2
0
0
0
1
0
0
2
1
0
0
0
0
0
1
1
1
0
0
1
0
0
2
1
1
0
1
2
0
0
1
0
2
0
1
0
1
0
0
1
1
0
2
1
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
1
1
1
2
0
0
1
0
0
0
0
2
0
0
2
0
0
1
0
1
0
0
1
0
1
3
2
0
0
0
0
1
2
2
0
1
2
2
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
1
0
0
0
0
1
1
0
0
2
0
0
0
0
1
0
3
1
0
1
0
0
0
1
0
2
2
2
1
2
0
1
0
1
1
1
1
1
0
2
1
0
0
0
0
0
1
1
1
0
0
2
0
0
1
0
0
2
0
2
2
0
0
4
0
3
2
1
2
0
2
1
1
1
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
2
0
1
0
0
1
2
2
2
1
2
0
0
0
0
0
1
1
1
0
0
1
0
0
0
2
1
1
2
0
1
1
0
0
1
1
0
1
1
2
2
2
0
0
0
1
0
0
1
2
0
0
2
0
0
2
0
0
0
0
2
0
2
1
0
0
0
3
1
0
0
0
0
1
0
2
1
0
0
0
1
0
2
2
0
1
2
0
0
1
0
2
0
1
1
0
1
0
0
1
0
1
0
0
0
0
0
1
0
2
1
0
4
2
0
2
2
0
1
0
0
0
0
1
1
1
1
2
1
2
0
0
0
2
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
2
1
2
2
0
0
1
0
2
2
2
1
0
1
2
0
0
2
1
1
1
0
4
0
0
0
0
2
0
2
1
2
1
0
2
1
0
0
2
1
2
0
2
0
1
2
1
1
0
0
1
0
1
0
0
0
0
0
2
1
1
1
0
2
2
0
1
0
0
2
0
0
1
2
1
1
1
0
0
0
1
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
2
2
1
0
1
2
0
0
0
1
2
0
0
0
2
0
1
2
0
0
0
0
2
0
0
0
1
2
0
0
2
1
0
2
0
2
0
0
0
2
2
1
1
0
1
0
0
0
1
0
0
0
2
0
1
0
0
1
0
0
2
1
1
1
0
2
1
0
0
0
1
0
0
0
3
0
1
2
0
2
0
2
0
0
0
0
2
0
0
1
1
2
2
0
0
1
2
0
2
1
1
1
1
2
0
0
2
0
0
0
0
0
0
0
1
1
1
0
2
0
0
0
0
1
0
2
1
0
2
0
2
1
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
2
0
5
2
1
0
2
0
0
0
1
0
1
1
1
0
2
1
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
2
1
0
0
1
0
2
0
0
1
0
0
2
0
0
1
2
1
0
0
2
0
0
0
2
0
0
2
0
1
1
2
1
0
0
1
0
1
2
1
0
0
0
0
1
0
0
0
2
0
2
1
0
0
2
1
0
0
0
3
0
0
1
2
2
0
2
0
1
0
0
0
0
0
0
2
1
0
3
1
0
0
0
0
0
1
2
1
2
0
0
0
2
2
1
0
0
2
0
1
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
2
1
1
0
0
0
0
0
0
0
0
1
2
0
0
2
1
0
0
0
1
0
0
0
0
1
0
1
0
3
0
2
2
0
2
0
0
0
0
1
0
0
1
0
0
0
2
2
0
2
2
0
0
0
0
1
0
2
0
0
2
1
0
1
0
1
1
0
0
2
1
0
0
2
0
1
1
1
0
0
0
2
4
0
0
2
0
3
0
0
0
1
0
0
0
0
1
0
0
3
1
0
0
1
2
1
1
0
0
0
1
2
2
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
2
1
0
0
0
1
0
0
2
0
0
0
0
0
1
0
1
2
1
0
0
0
2
0
0
0
1
1
0
2
0
2
0
1
0
1
0
0
2
0
0
2
0
0
0
0
2
0
1
1
1
2
2
1
0
0
1
0
0
0
0
1
0
2
0
0
8
2
2
2
1
0
3
2
0
1
1
0
0
1
1
0
0
0
2
1
0
6
0
0
1
0
0
1
0
0
2
2
0
1
0
0
0
0
2
2
0
1
0
1
0
0
1
0
0
0
2
1
1
0
1
0
2
2
0
0
2
0
0
0
2
0
0
1
0
3
0
2
1
0
0
2
0
1
0
0
1
0
1
2
2
0
2
2
0
0
1
1
1
2
2
1
0
2
0
0
2
0
0
1
2
0
0
1
0
0
0
2
2
0
0
0
2
1
1
2
0
2
0
0
2
1
1
0
0
0
2
0
0
0
0
0
2
0
0
1
0
3
2
1
0
1
0
0
2
0
1
1
1
0
3
1
0
0
1
2
1
0
2
0
0
1
2
1
1
2
0
1
0
0
1
0
1
0
0
1
0
0
1
0
0
1
0
0
1
0
2
0
1
1
2
0
2
1
0
0
0
2
0
0
0
1
0
1
2
0
0
1
0
0
0
0
0
2
1
1
0
2
0
2
0
1
0
0
1
0
1
2
0
1
1
0
0
0
2
0
1
1
0
0
0
3
0
0
0
2
2
0
0
0
0
0
1
2
1
0
0
0
0
0
1
1
1
1
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
2
1
1
0
0
0
1
0
1
1
0
2
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
6
0
1
1
1
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
3
1
0
1
0
0
1
2
0
2
2
0
2
0
0
0
2
2
0
0
0
0
2
1
2
0
0
2
2
0
0
1
0
0
1
2
0
0
0
2
1
0
0
1
0
0
0
6
0
2
0
3
0
2
2
0
1
1
1
0
0
2
2
2
1
0
0
0
2
0
1
1
0
1
0
3
0
2
2
1
0
0
0
1
0
2
1
2
1
3
0
2
0
2
0
1
0
0
0
1
0
0
0
2
0
1
0
1
3
1
0
1
3
1
2
1
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
2
1
2
0
0
1
3
1
0
0
2
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
2
2
0
0
0
1
1
1
0
2
0
0
0
2
2
0
0
0
1
2
0
0
0
0
0
2
2
3
2
0
2
0
0
0
0
0
2
0
1
0
1
4
1
2
0
2
0
2
0
0
1
0
0
0
0
2
0
2
0
2
0
0
1
0
1
0
0
0
2
1
1
0
2
1
0
0
0
0
1
0
0
0
2
1
0
2
0
0
0
1
1
0
2
0
0
0
0
0
0
0
1
2
0
0
1
2
0
1
2
4
1
0
1
1
0
0
0
0
1
2
0
0
0
1
0
0
0
3
0
1
0
0
0
1
0
0
0
0
2
2
0
0
0
1
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
1
2
1
0
3
0
1
0
0
0
0
3
0
0
1
0
0
0
1
0
0
2
0
0
0
1
4
0
0
0
1
0
0
1
0
0
1
0
0
6
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
1
0
2
0
2
0
0
0
1
2
1
0
0
2
0
0
1
0
1
0
1
0
0
2
2
1
2
0
0
0
2
0
0
1
0
1
2
1
0
0
0
1
2
1
2
1
2
0
2
2
0
0
0
1
1
2
1
2
0
0
0
0
0
1
2
0
1
0
0
0
2
0
2
1
1
0
2
0
0
0
0
0
2
0
2
1
0
2
2
0
1
0
0
0
0
0
1
1
0
0
1
0
1
1
0
1
0
0
1
0
0
3
0
1
0
1
2
2
2
2
0
0
0
2
0
0
0
0
0
1
1
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
1
0
1
1
0
0
0
0
2
0
2
2
1
1
0
0
0
0
1
0
1
1
0
2
0
2
0
1
0
0
1
0
1
0
2
0
0
1
0
0
0
0
0
0
0
2
3
1
1
0
1
0
2
2
0
0
2
2
0
0
2
0
0
2
2
2
0
1
0
0
2
1
2
1
0
1
0
0
1
1
0
2
3
2
2
0
3
0
0
0
1
0
3
2
0
2
0
1
1
2
1
2
0
0
0
0
0
0
2
1
1
2
0
0
0
0
0
2
0
0
0
0
1
1
1
0
0
0
1
2
1
0
0
0
0
0
2
1
1
1
2
0
0
0
0
0
0
0
0
2
1
0
1
0
2
0
1
1
0
0
0
2
1
2
0
0
0
1
0
0
0
1
1
2
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
2
2
3
1
1
0
2
0
2
1
0
2
1
1
2
0
2
1
1
2
1
1
3
0
0
0
0
0
1
1
1
0
2
0
0
1
0
2
0
2
2
0
0
0
1
0
0
1
1
0
0
0
0
2
0
2
0
1
1
0
1
0
0
0
3
0
0
2
0
0
4
0
0
1
0
0
2
4
0
2
2
0
0
1
0
2
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
2
2
1
0
0
1
2
1
0
1
1
1
0
2
2
0
2
0
0
1
1
1
0
0
2
3
0
2
1
2
1
3
1
0
0
1
0
1
2
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
2
0
0
0
0
1
2
0
1
1
0
0
0
0
0
0
0
0
1
1
0
8
0
2
0
0
3
0
2
0
2
0
0
2
0
0
0
0
2
0
1
3
0
1
0
2
2
0
0
0
2
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
2
0
1
1
0
0
0
2
2
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
2
0
2
0
0
1
3
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
1
2
2
2
2
0
0
0
0
0
0
0
2
1
1
0
0
0
2
0
2
2
0
0
2
1
1
1
0
0
2
0
1
0
0
1
0
0
1
0
0
0
2
1
1
0
0
0
2
2
1
0
0
0
1
1
1
2
1
0
0
0
0
3
2
0
0
2
1
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
2
2
1
0
0
0
2
2
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
2
0
0
1
0
1
1
0
0
2
2
1
0
1
0
2
0
1
2
0
0
0
1
2
2
2
0
2
1
1
0
0
0
2
2
2
2
0
0
2
0
1
0
1
2
1
0
0
1
0
0
0
1
0
3
0
1
2
1
0
0
2
0
2
0
1
0
1
2
0
0
0
1
0
0
0
2
1
0
0
0
2
0
2
0
0
0
0
1
1
2
0
2
0
0
2
2
1
5
0
0
0
1
0
0
2
2
1
2
0
2
2
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
1
0
1
1
0
2
1
0
2
0
1
0
0
1
2
0
0
0
1
0
1
1
1
1
2
2
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
2
0
3
1
0
0
0
1
1
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
1
1
1
2
0
0
1
0
1
0
1
0
0
2
2
0
2
2
1
3
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
1
0
0
2
1
0
0
0
2
1
1
0
2
1
0
0
0
2
2
0
2
2
0
1
1
1
1
0
2
0
0
2
0
0
1
1
2
1
0
0
1
0
0
2
1
1
0
2
0
1
0
0
2
1
1
2
1
1
0
1
0
0
2
0
1
3
1
1
0
0
0
0
1
0
0
1
2
2
0
0
0
0
0
1
2
0
2
2
0
2
0
2
0
0
1
1
0
0
1
0
0
0
2
0
1
0
1
0
0
1
0
0
1
2
4
0
1
0
0
2
0
0
0
0
0
0
0
2
0
2
0
1
0
4
0
1
1
0
0
0
0
0
1
0
2
0
1
1
2
0
2
2
0
0
0
0
0
0
2
0
1
0
1
1
2
0
2
0
0
0
2
0
0
0
1
0
0
2
0
2
1
0
0
1
1
0
0
2
2
0
1
1
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
1
1
0
0
0
1
1
1
0
0
3
1
0
0
2
0
1
3
2
0
0
0
0
0
0
1
2
0
1
0
1
0
1
0
2
1
2
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
1
2
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
2
1
2
0
0
0
0
0
0
0
2
2
0
1
0
0
1
0
1
1
1
0
0
0
0
1
1
0
3
0
2
0
2
1
1
1
0
0
1
1
1
0
2
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
2
2
0
2
0
0
0
0
1
0
0
0
2
1
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
1
1
0
0
0
0
0
1
3
0
0
2
0
1
1
1
0
0
3
1
0
0
0
0
0
2
0
1
1
0
1
2
1
2
0
1
1
0
0
0
0
0
1
0
0
2
1
1
0
0
0
1
1
0
0
1
0
0
2
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
2
0
0
0
2
2
0
1
2
0
3
2
0
0
2
0
0
1
2
0
0
0
1
0
0
0
1
1
0
1
0
0
0
1
1
1
1
0
1
0
0
0
1
0
0
1
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
2
1
0
2
1
0
0
0
1
0
0
2
2
1
0
3
3
2
0
1
0
2
0
3
2
0
0
0
0
0
0
0
1
2
2
1
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
2
0
0
2
2
0
0
1
0
0
0
2
1
1
2
2
0
1
0
0
0
0
2
2
0
0
0
0
1
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
2
1
1
0
1
2
2
0
0
0
0
0
0
2
0
0
1
0
0
1
1
1
0
2
1
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
3
0
0
0
1
0
0
2
0
1
2
1
1
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
3
0
1
2
0
0
0
0
1
1
1
0
0
1
2
1
0
0
5
1
2
0
1
2
3
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
2
3
0
0
1
1
2
0
2
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
3
0
0
1
0
1
2
0
0
0
0
1
0
0
1
2
0
0
0
0
1
0
1
1
0
2
0
0
2
0
0
1
0
1
2
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
3
0
0
0
0
0
0
1
1
2
2
0
0
1
0
4
0
0
0
2
2
2
1
0
0
0
0
2
2
2
1
2
1
0
2
0
0
2
0
1
0
0
2
0
1
2
0
2
1
2
1
1
1
1
0
4
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
2
0
0
0
0
2
2
2
1
1
2
0
0
2
2
1
1
2
1
2
0
0
1
0
0
0
2
0
1
1
0
2
0
0
0
1
0
0
0
3
0
0
2
2
0
1
1
2
0
1
0
0
0
2
0
0
1
0
0
2
0
2
0
2
0
0
1
1
1
1
0
2
0
0
0
2
2
1
1
2
0
0
0
0
1
0
0
2
2
1
0
0
2
1
0
0
1
0
3
0
1
0
1
0
2
0
1
1
1
0
1
0
1
0
1
0
0
1
0
2
0
0
0
0
0
1
0
1
2
0
0
1
0
0
0
0
0
1
0
2
1
0
0
1
2
1
0
0
0
1
0
1
1
2
0
0
0
0
0
1
0
0
2
1
0
1
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
2
2
0
0
0
1
0
2
0
0
0
0
0
0
2
1
2
0
0
2
0
0
1
1
2
0
1
0
1
3
0
0
0
0
1
1
2
0
0
0
0
2
0
0
2
0
1
0
2
0
0
0
1
0
1
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
1
2
0
1
2
2
0
0
1
0
1
2
2
2
0
0
1
0
0
0
0
1
1
1
0
1
2
2
0
0
0
0
0
0
0
1
0
2
0
2
1
0
1
0
2
0
1
6
1
2
1
0
3
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
2
1
3
0
0
0
0
0
2
4
0
2
0
2
0
0
0
1
1
0
2
0
0
0
0
0
3
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
2
0
0
2
2
1
1
0
2
1
0
0
0
2
2
2
0
2
2
0
2
0
2
0
4
2
0
0
1
0
0
0
0
1
2
0
0
0
1
0
0
2
2
2
1
0
0
0
2
1
0
0
0
0
2
1
2
0
0
0
0
1
1
0
0
0
0
2
2
0
2
1
0
0
2
1
2
0
2
1
0
0
1
2
0
0
0
0
0
1
3
0
0
0
0
0
1
2
0
0
0
1
2
0
2
0
0
1
2
0
1
0
1
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
3
0
0
2
1
0
0
0
0
1
2
0
0
1
2
2
2
0
0
0
2
0
3
2
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
1
1
0
2
0
0
2
0
0
2
0
2
3
2
0
2
0
1
0
0
0
0
0
1
2
0
1
0
0
0
1
0
0
1
1
0
0
0
2
1
0
2
0
0
2
0
2
0
1
0
0
1
0
0
1
1
0
1
0
2
2
1
1
0
0
0
0
0
0
1
1
0
0
0
2
0
0
5
1
0
2
0
2
0
1
0
0
0
2
0
0
0
0
0
0
1
1
0
1
0
0
1
1
0
0
0
1
0
0
0
2
2
0
0
1
0
0
0
1
0
0
1
0
1
2
0
2
2
0
1
2
0
0
0
0
1
0
3
0
0
2
0
0
2
0
0
0
2
2
0
0
1
2
2
0
3
1
0
0
1
0
1
1
0
2
1
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
3
1
0
1
1
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
1
0
1
1
1
2
0
1
1
2
1
0
1
1
4
0
0
2
0
1
2
0
0
0
1
0
0
2
0
0
2
0
3
1
1
1
0
1
0
0
0
0
2
0
0
2
0
2
1
0
0
0
0
2
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
2
0
1
1
1
0
0
1
2
1
1
0
3
0
1
1
1
0
0
2
1
1
1
0
0
1
0
0
1
1
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
1
1
0
2
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
1
2
0
0
0
1
2
2
0
0
2
0
1
0
3
0
0
0
0
0
1
0
1
2
2
0
2
1
0
1
0
0
0
2
0
0
2
0
1
0
0
0
2
0
2
0
1
0
0
0
0
2
0
2
0
0
0
1
0
1
2
0
2
2
0
0
2
2
1
0
2
2
0
0
0
1
0
0
0
0
0
2
1
0
2
0
0
0
0
1
2
0
0
2
0
0
0
0
2
0
0
0
2
0
3
0
0
0
0
1
2
1
0
1
0
0
0
0
0
0
0
4
0
0
1
1
0
1
1
0
0
0
1
0
0
0
0
5
0
2
1
1
0
0
0
0
1
1
3
0
1
2
0
1
1
0
0
2
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
2
0
0
2
3
0
2
0
0
3
0
3
0
0
1
0
1
1
0
2
2
0
0
1
0
2
0
1
0
0
0
0
0
1
0
0
0
0
2
1
1
0
1
0
0
1
0
0
0
0
1
1
2
0
0
0
0
0
0
2
0
1
0
0
0
2
1
0
2
0
0
0
1
1
0
2
1
1
2
0
1
2
0
0
3
1
0
2
0
1
0
2
0
2
0
0
0
1
1
3
1
0
0
1
0
0
1
2
1
2
0
3
0
2
1
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
1
0
1
0
0
1
2
2
6
2
0
1
0
2
2
1
0
0
0
0
0
0
0
0
0
4
0
0
1
1
0
1
1
0
0
2
0
1
0
1
0
0
0
0
0
2
1
0
0
3
0
0
1
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
1
1
1
0
6
0
0
0
1
0
1
1
2
0
0
0
0
1
0
2
0
0
1
1
0
0
0
0
1
0
1
2
0
0
0
3
1
0
1
0
0
1
0
5
0
1
0
2
1
0
2
2
1
0
0
0
0
0
2
0
1
0
1
2
0
0
2
1
0
2
2
1
1
2
0
0
1
0
2
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
1
1
2
1
0
2
0
0
0
2
1
0
1
2
2
2
0
0
1
0
2
0
1
0
2
2
0
0
1
0
0
0
0
0
0
0
1
2
1
2
0
0
3
1
0
0
2
1
1
0
2
0
0
0
0
0
2
1
0
0
0
1
0
0
0
4
0
1
0
0
1
0
0
1
0
0
0
1
0
0
1
1
1
2
2
2
0
0
1
0
1
2
1
1
0
1
2
0
0
0
1
0
0
3
0
1
0
1
2
2
2
2
6
0
0
0
0
2
1
0
1
1
0
0
1
2
1
2
0
1
0
2
1
0
1
1
1
2
0
0
0
0
0
0
0
0
0
0
1
2
1
0
4
5
2
2
3
0
0
0
0
0
2
1
1
0
0
2
0
2
0
0
2
0
0
0
4
0
0
1
1
2
1
0
0
1
0
0
1
3
0
0
0
0
0
2
5
0
0
0
2
1
0
0
1
3
0
1
1
0
0
1
0
0
0
1
1
0
1
3
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
2
2
0
0
1
0
2
2
0
1
1
1
1
1
0
1
0
0
0
0
0
0
0
2
1
1
2
2
0
0
0
1
0
1
0
0
1
3
0
1
0
2
2
0
1
0
0
2
1
5
1
0
0
0
2
0
1
0
0
1
1
0
1
0
1
1
0
1
1
0
1
0
1
2
0
0
0
0
1
0
2
0
1
0
2
0
0
3
0
0
0
1
1
0
0
1
1
0
0
0
1
0
0
0
2
0
2
0
0
1
1
0
0
0
1
0
0
0
1
1
2
2
1
0
2
2
1
2
0
1
2
0
1
1
0
1
0
2
0
0
2
0
1
0
2
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
2
4
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
1
2
0
0
0
0
0
0
2
0
0
2
1
0
2
2
0
2
0
1
0
0
2
0
0
2
2
2
0
2
0
0
3
0
0
5
0
0
0
2
1
0
0
2
0
0
1
0
0
0
1
0
0
0
0
2
0
1
1
4
0
0
1
0
0
0
0
1
2
0
2
0
0
0
3
0
2
0
1
2
2
0
1
1
0
1
2
0
0
0
0
0
0
2
1
1
0
0
2
0
2
0
1
2
0
0
1
0
0
0
2
1
2
0
0
2
0
3
0
0
0
2
1
0
1
0
2
1
2
1
0
0
0
0
0
0
0
1
0
0
0
1
0
2
1
0
0
2
2
0
0
0
0
0
2
0
0
2
1
1
0
0
0
2
0
2
1
0
1
0
2
2
3
0
0
1
0
1
1
1
0
0
0
0
1
2
0
0
2
1
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
2
0
1
0
0
2
2
0
0
0
1
0
2
1
0
0
1
1
0
1
2
2
0
0
2
0
2
1
0
2
0
0
2
1
0
0
2
2
0
0
1
1
0
0
0
0
0
1
1
2
1
0
0
2
0
1
1
0
1
0
0
0
6
0
2
1
0
0
0
0
0
2
0
1
1
0
2
2
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
2
0
0
0
1
1
1
0
0
1
0
0
0
0
2
2
2
1
1
0
0
0
0
1
1
1
1
0
1
0
0
0
0
1
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
1
2
0
1
0
0
0
1
1
1
0
1
1
0
0
0
2
0
1
1
0
3
0
1
1
0
1
0
1
0
0
2
0
2
2
0
0
0
0
0
2
0
0
0
2
0
1
0
5
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
2
1
2
1
0
0
0
0
0
1
1
2
1
1
0
0
1
2
0
2
0
0
1
2
1
2
0
0
1
0
0
0
0
0
2
0
1
1
0
0
0
0
0
1
0
1
3
0
1
0
1
0
0
1
1
1
0
0
0
0
0
1
0
0
0
1
2
0
0
0
1
0
2
0
0
0
2
0
0
3
2
2
0
0
0
0
1
0
0
1
0
0
1
0
0
2
0
0
1
0
0
0
0
2
0
1
1
0
0
0
2
1
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
2
2
0
0
0
2
0
0
1
0
0
0
3
1
1
1
1
0
3
1
0
1
0
0
0
1
0
2
0
0
0
1
0
0
0
1
0
2
2
1
0
0
0
2
0
1
0
3
1
2
2
2
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
2
0
0
2
0
1
2
0
0
1
0
0
1
1
1
1
0
0
4
0
0
0
1
0
2
2
1
2
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
2
0
1
1
1
1
0
0
0
0
1
4
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
2
2
1
0
0
0
1
1
0
0
2
0
0
0
0
1
0
1
0
0
0
2
0
2
0
0
0
0
2
3
0
0
2
3
0
1
0
1
0
0
0
0
1
0
2
0
1
0
2
0
1
1
2
2
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
2
1
0
1
0
1
1
1
0
3
2
2
0
1
2
0
1
1
1
0
2
4
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
1
3
0
0
2
0
0
0
1
0
0
2
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
3
0
1
0
1
0
0
0
0
0
2
0
0
0
2
2
1
0
0
0
1
0
1
0
1
1
0
1
1
2
0
4
0
0
0
0
1
2
1
1
1
0
0
0
1
0
0
0
1
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
1
1
1
1
0
0
1
0
1
1
0
0
0
2
0
0
1
2
2
0
5
0
0
0
2
0
2
2
0
2
2
0
0
0
1
2
0
0
0
0
1
1
1
0
0
0
0
2
0
3
2
0
0
0
0
1
2
1
2
1
3
1
0
0
2
2
2
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
2
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
1
2
0
0
0
2
0
1
2
0
2
1
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
2
0
0
1
1
1
1
2
2
1
0
0
2
1
0
1
0
0
0
1
0
1
0
1
0
0
2
2
2
1
1
0
0
1
0
0
0
0
2
0
0
1
0
0
1
0
2
1
2
0
1
1
1
0
0
0
1
0
2
0
0
0
1
0
2
1
0
2
0
0
1
3
0
1
0
2
0
2
1
1
0
4
0
3
1
2
0
1
1
1
0
0
0
0
1
0
0
0
0
0
1
0
3
1
2
1
1
0
0
0
0
2
2
2
1
0
2
0
2
2
0
0
0
2
2
1
2
0
1
0
1
0
2
1
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
2
0
0
0
2
0
2
2
0
0
1
2
1
0
3
1
1
0
0
2
0
2
2
0
0
1
2
0
3
0
1
2
1
0
2
1
0
0
0
0
0
2
0
2
1
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
2
0
0
0
2
0
1
0
2
0
0
0
0
0
1
0
1
0
0
0
0
1
2
2
0
0
0
2
0
1
2
0
0
0
0
0
0
1
1
0
0
0
2
0
2
1
0
0
0
0
2
1
0
0
0
3
0
2
1
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
2
0
2
3
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
1
0
0
0
1
0
2
2
0
0
2
0
0
0
0
0
0
0
0
1
1
0
1
2
0
0
0
2
2
1
2
0
1
0
1
1
2
0
2
1
0
0
0
0
0
0
0
0
3
1
0
1
0
2
0
2
1
0
0
2
0
0
0
2
0
1
1
0
2
2
1
1
0
0
2
1
0
0
2
0
0
0
0
2
1
0
1
2
5
0
0
0
0
1
0
0
1
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
1
1
0
0
1
2
0
0
3
0
0
1
1
0
0
1
1
1
4
1
0
0
0
0
0
0
1
0
0
0
2
2
1
1
1
0
1
0
0
1
0
0
0
0
3
2
2
0
2
0
0
0
0
1
0
0
1
3
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
1
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
1
0
2
1
2
1
2
0
0
0
0
1
1
0
0
0
0
2
1
0
0
2
2
0
0
1
0
1
0
0
0
1
0
1
1
2
2
0
1
0
0
0
0
1
1
0
0
1
0
2
0
1
0
0
1
0
2
1
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
1
1
2
1
0
0
0
0
2
2
0
0
4
0
0
0
2
1
1
1
0
0
1
0
0
0
1
0
0
1
2
1
1
0
2
0
1
0
0
2
1
0
1
0
0
2
3
2
0
0
2
2
0
0
0
0
0
2
1
2
0
1
2
0
0
1
1
1
0
0
0
0
1
2
1
0
0
0
1
0
0
1
0
2
0
0
2
1
2
2
0
1
1
0
0
0
0
1
0
0
2
1
1
0
0
0
0
1
0
0
2
0
1
1
0
1
2
0
1
0
0
0
1
1
0
0
1
0
1
1
2
0
0
0
0
0
0
0
1
0
0
0
1
1
0
2
0
1
0
1
6
0
1
1
0
2
1
2
3
1
1
2
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
2
1
2
0
2
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
1
0
1
0
1
4
0
0
0
0
1
1
2
0
1
0
0
1
1
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
2
2
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
1
2
0
0
1
0
1
0
0
2
0
0
1
2
1
1
1
0
1
0
0
1
0
0
1
2
0
0
2
2
0
1
1
1
1
0
1
1
0
1
0
0
1
2
0
0
1
1
0
0
0
1
0
2
4
0
0
1
0
1
0
0
0
0
1
2
0
2
0
0
2
3
1
0
0
0
2
1
0
2
1
0
1
0
2
0
0
0
0
1
2
2
0
1
0
2
0
0
0
0
0
1
1
2
1
0
2
1
0
1
0
1
0
0
1
0
2
2
0
1
1
2
2
0
0
0
2
1
0
2
2
0
1
1
0
0
0
1
0
1
2
3
0
1
2
1
0
0
1
2
0
2
2
0
0
1
0
2
0
1
2
1
2
0
0
0
0
1
1
0
0
0
0
1
2
0
1
1
1
2
0
0
1
0
1
0
1
1
0
1
0
0
0
0
0
2
2
0
0
0
1
2
0
0
2
0
0
0
0
2
1
0
1
0
1
0
2
0
2
1
1
2
0
1
1
0
0
1
2
0
2
1
0
1
1
0
0
0
2
1
2
4
1
0
0
1
2
1
0
0
0
0
0
0
0
1
0
2
0
1
0
2
1
0
3
1
2
0
2
0
1
1
2
0
0
1
1
2
0
0
2
1
0
0
3
0
1
2
2
0
0
1
0
0
2
0
0
0
1
6
2
0
3
1
0
0
0
2
0
0
3
1
2
2
0
2
0
1
1
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
1
1
0
0
1
1
1
1
1
2
1
2
0
2
0
2
0
0
1
0
1
0
1
1
0
0
0
0
1
1
0
0
3
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
2
1
3
0
0
0
0
0
0
2
2
0
1
0
2
0
1
0
0
1
2
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
3
2
0
0
0
3
1
0
6
1
0
1
0
0
1
0
0
1
0
0
2
4
0
1
0
0
0
0
1
1
0
0
0
1
2
2
0
0
0
2
1
0
0
0
0
1
0
1
1
1
0
0
0
1
1
0
0
0
0
1
0
0
0
2
0
2
0
1
2
1
3
0
2
0
0
0
1
0
2
0
2
4
1
0
0
0
0
1
0
1
0
0
1
2
0
0
0
0
0
0
0
1
0
2
0
0
1
2
0
1
1
2
0
2
1
2
0
0
1
0
1
0
1
0
1
0
0
0
1
0
2
1
2
0
0
0
0
0
0
2
0
2
0
0
1
2
0
0
0
0
1
2
0
3
1
0
3
2
0
1
2
2
1
0
0
0
0
1
2
2
1
1
1
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
1
1
0
0
0
0
0
0
0
0
1
2
0
0
2
2
0
2
1
0
0
0
0
2
0
0
0
0
2
0
0
0
1
1
0
0
2
2
2
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
1
0
1
0
0
0
0
1
1
3
0
0
3
0
0
3
2
1
2
1
2
0
1
2
0
0
2
0
0
1
0
0
0
0
1
0
1
0
1
0
1
2
2
2
2
2
1
1
1
2
1
0
0
1
1
0
1
0
1
1
2
0
0
0
2
2
0
0
1
2
1
1
1
0
1
3
0
0
1
1
0
0
0
0
0
2
0
0
1
2
0
2
0
0
0
0
1
0
0
1
1
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
1
2
2
0
0
1
0
2
0
0
2
0
0
0
1
0
0
2
0
0
1
0
0
1
2
0
0
1
0
0
0
0
2
1
2
1
0
2
2
0
1
0
0
0
1
0
0
0
0
2
0
2
0
1
2
1
1
1
0
1
0
0
0
0
0
1
0
1
2
0
2
1
1
2
2
1
0
0
0
0
0
2
1
1
2
0
0
1
1
0
1
2
4
1
0
0
0
0
0
0
0
4
1
6
2
2
1
0
2
0
1
0
0
0
1
1
0
0
0
0
2
1
0
0
0
1
1
0
0
1
1
0
0
0
1
1
2
0
0
0
1
0
0
2
0
1
0
2
1
2
0
2
1
2
0
2
0
0
2
0
1
0
0
2
1
2
0
0
2
0
0
0
0
2
0
1
2
0
1
0
2
1
0
1
0
3
0
2
0
0
2
0
2
0
0
1
0
2
2
0
2
0
2
0
0
0
1
2
0
2
2
2
1
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
1
1
0
0
1
2
2
0
0
2
0
2
0
1
1
0
0
1
2
0
1
0
0
1
1
1
2
1
0
1
0
0
2
0
0
2
0
0
1
0
0
0
1
0
2
2
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
1
2
2
0
0
0
2
0
0
1
0
2
0
0
1
2
2
3
0
2
0
0
1
1
0
1
0
0
0
0
0
2
1
0
0
1
2
0
1
2
0
2
0
0
0
0
2
1
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
2
1
1
0
0
0
2
1
0
2
0
0
1
0
3
0
3
0
0
0
1
1
1
1
0
1
0
1
1
0
2
0
0
0
3
0
2
0
1
1
1
0
0
0
0
0
0
0
0
0
2
1
0
1
0
2
2
0
1
0
1
1
0
0
0
1
3
1
0
0
2
2
2
0
2
0
0
0
0
0
0
1
0
0
0
2
1
0
0
1
1
0
1
0
2
0
0
0
2
1
2
2
2
1
2
1
0
1
0
2
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
2
1
0
0
0
1
1
1
0
2
0
1
1
0
1
1
1
0
2
0
0
0
0
1
0
1
0
2
2
0
0
2
1
0
2
0
0
0
0
0
0
2
0
1
0
0
0
1
3
0
0
2
0
1
1
2
0
2
0
0
2
2
2
1
0
0
0
2
2
0
1
1
1
0
2
0
2
1
0
0
0
0
1
2
0
1
0
0
1
1
2
0
0
0
2
5
1
0
0
2
0
0
1
1
1
2
2
0
0
0
2
0
2
1
0
0
2
2
2
1
1
2
2
1
1
2
0
2
0
0
0
0
1
0
0
1
0
0
2
2
0
0
1
1
1
2
0
0
0
2
0
0
1
0
0
0
0
0
2
1
0
0
0
1
2
2
0
2
0
0
0
1
3
1
0
0
0
2
1
2
0
0
2
0
0
0
0
2
2
1
0
2
1
0
0
2
0
1
0
2
0
0
0
2
0
0
0
0
1
1
0
0
1
0
2
6
1
0
0
2
2
0
0
2
0
1
0
0
0
0
2
1
0
2
0
0
2
0
2
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
1
2
0
2
0
1
0
1
0
0
2
0
0
2
3
0
0
0
0
2
2
2
0
2
2
0
1
0
0
0
2
1
2
1
4
0
3
2
0
0
0
1
1
0
0
0
0
2
0
1
2
1
0
1
0
0
0
2
0
0
1
2
0
0
1
1
2
0
0
1
2
0
0
1
0
0
2
0
1
1
0
2
0
0
2
2
0
0
2
0
0
1
0
0
1
0
0
0
1
1
0
2
1
3
0
0
2
0
1
0
2
0
0
2
0
1
0
1
1
0
1
0
0
0
0
2
1
1
2
0
0
0
0
0
0
1
3
0
0
0
0
2
1
1
2
2
1
1
2
0
0
1
0
2
1
0
0
0
1
0
0
1
1
2
0
0
0
0
1
0
0
0
2
1
2
0
0
2
1
3
0
0
1
1
0
0
1
2
1
2
0
0
1
1
0
1
0
1
0
0
0
2
0
0
1
0
0
2
2
0
0
0
2
2
0
0
1
0
0
1
0
0
2
2
1
2
1
2
1
1
0
0
0
1
0
2
1
0
2
2
0
0
0
0
2
1
1
0
1
0
0
2
0
2
2
0
2
1
1
0
2
0
2
0
0
0
2
0
1
2
1
2
1
0
1
0
0
0
1
1
0
2
0
1
0
0
1
0
0
0
2
2
1
2
0
2
1
0
0
2
0
2
0
1
0
0
1
0
0
0
2
0
0
0
2
1
0
1
2
1
2
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
2
0
2
0
0
0
0
0
0
0
1
3
2
0
2
0
0
1
2
0
2
2
3
1
1
0
2
0
0
0
0
0
2
0
0
0
0
2
1
0
0
1
0
0
0
1
0
2
2
0
0
0
1
1
1
2
0
3
1
1
1
0
1
0
3
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
2
0
1
1
0
0
1
0
1
0
1
1
2
1
4
0
3
0
0
0
0
2
0
0
1
2
1
0
0
0
2
0
0
1
0
0
1
2
0
0
0
1
2
1
1
0
0
1
2
0
0
0
0
2
0
2
1
1
0
2
1
1
0
0
1
3
1
1
0
0
0
2
0
2
0
1
1
0
0
0
0
0
0
2
1
2
0
0
1
0
3
1
0
0
1
0
0
1
0
0
1
0
1
2
0
1
2
0
0
0
2
0
0
0
2
2
0
3
0
0
1
0
2
1
1
0
0
0
0
0
0
1
2
1
2
1
0
2
0
0
1
2
1
1
0
1
1
0
1
0
0
2
0
2
0
0
0
2
0
0
0
2
0
3
1
0
0
0
1
0
0
1
2
1
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
1
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
1
1
0
0
0
0
0
0
0
0
1
2
1
0
0
1
0
0
0
2
1
1
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
3
0
2
2
0
1
2
1
0
0
0
5
0
1
2
1
1
2
0
0
0
0
1
0
2
0
1
0
2
1
0
0
0
0
0
1
2
1
2
0
1
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
2
3
1
0
0
0
1
0
2
0
0
0
3
0
2
0
0
0
1
0
0
0
0
0
2
1
2
0
1
0
0
0
0
0
1
0
2
1
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
2
0
0
1
0
0
1
1
0
2
1
0
1
0
0
2
0
2
2
0
0
0
0
1
0
0
0
3
1
0
0
1
0
2
0
0
0
0
0
1
0
0
1
0
1
2
0
0
1
0
0
1
0
0
2
0
0
1
0
0
1
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
1
1
0
0
0
0
1
3
1
0
2
0
1
0
2
1
0
0
1
0
0
1
0
1
0
3
0
2
0
1
1
1
0
2
1
2
0
2
0
2
0
0
2
0
2
0
1
0
1
0
0
0
1
0
0
2
0
2
2
0
1
2
1
2
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
2
1
2
1
3
1
3
0
1
2
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
5
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
1
2
1
0
2
0
0
0
1
0
1
2
1
0
0
1
2
3
0
0
1
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
2
0
0
0
0
0
0
0
1
1
0
1
0
2
1
0
0
0
2
1
0
0
2
2
0
0
0
0
1
0
0
2
0
1
0
0
2
0
0
0
1
1
3
0
0
1
2
2
1
1
2
0
0
1
2
0
2
0
0
0
1
0
0
1
0
0
1
0
0
0
0
2
0
0
2
0
1
1
0
2
2
2
0
0
2
1
0
0
2
0
0
0
1
0
3
0
0
0
0
0
0
0
1
2
2
1
0
0
2
0
3
0
0
0
0
1
1
3
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
1
0
0
1
1
2
0
0
2
2
3
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
2
1
0
0
0
1
1
2
1
2
0
0
0
0
1
0
0
0
0
1
0
0
1
2
1
1
2
1
2
2
0
2
1
0
1
0
0
1
0
0
2
0
1
0
0
2
0
0
1
0
0
1
0
2
0
0
0
0
0
2
1
0
2
0
2
0
2
2
0
2
2
1
0
0
1
0
2
0
0
0
0
0
0
0
0
1
2
0
2
1
2
2
1
1
0
0
1
0
0
0
2
2
0
0
0
0
2
0
2
0
0
0
2
2
0
0
2
0
1
0
1
0
2
1
0
0
0
0
0
0
1
0
1
0
2
0
2
0
0
2
0
0
0
0
0
0
3
0
2
0
2
0
1
4
2
2
0
0
2
0
0
1
0
1
0
2
0
0
1
0
0
1
0
0
0
2
4
2
1
1
2
0
0
0
0
2
0
1
0
1
0
0
0
0
1
1
1
2
2
2
4
1
1
0
0
0
0
0
2
0
1
2
1
0
2
2
1
0
0
0
1
0
0
0
0
0
1
0
2
1
1
0
1
0
1
0
0
0
0
1
1
0
2
0
2
0
2
0
0
0
0
1
0
2
1
0
2
2
2
0
0
1
2
0
0
1
2
1
0
2
0
1
0
1
0
0
0
0
0
1
2
2
0
1
0
0
0
0
1
0
0
0
1
0
2
2
0
0
0
1
0
2
0
0
0
2
0
1
0
0
0
0
1
1
0
0
0
2
0
1
0
2
0
1
0
0
1
3
2
1
1
1
0
1
1
0
0
1
2
0
1
0
2
0
0
1
0
0
1
0
0
0
2
1
2
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
2
1
1
1
0
1
1
2
1
0
0
1
2
0
0
0
0
2
0
1
2
0
0
3
1
0
0
0
0
1
1
0
0
1
2
0
1
0
1
2
2
0
0
1
0
0
0
0
1
0
1
1
1
0
0
0
3
1
0
0
0
0
0
1
0
1
1
0
1
2
1
0
0
0
1
2
1
0
0
0
1
0
2
1
0
2
0
0
0
2
2
2
0
3
0
1
2
0
1
0
2
2
1
1
0
2
0
0
0
3
1
2
0
0
0
0
0
2
0
0
0
0
0
0
2
2
1
0
2
1
0
1
0
1
0
0
0
0
2
0
2
0
1
0
0
0
2
3
1
0
0
1
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
1
1
0
0
0
0
0
2
2
1
0
0
0
0
2
2
2
0
0
1
0
0
0
1
0
1
0
0
1
0
2
0
0
2
0
1
0
0
0
1
0
2
0
1
2
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
2
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
2
0
1
0
2
1
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
1
0
1
0
0
3
2
0
0
1
1
0
2
0
0
1
1
2
0
0
2
0
0
2
2
0
0
2
0
2
1
0
1
1
1
0
1
2
2
0
0
0
2
1
1
1
2
4
0
0
2
2
0
0
0
0
1
0
0
0
0
2
0
2
2
1
0
1
0
0
4
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
2
2
1
0
1
0
1
0
0
0
1
2
1
1
0
3
0
0
0
0
0
1
1
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
1
2
1
0
0
0
0
0
1
0
1
1
0
1
1
2
0
0
0
2
0
0
2
2
1
0
0
0
1
1
0
0
1
1
2
0
1
2
0
0
0
1
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
1
0
1
0
2
0
1
0
0
0
1
0
0
2
1
0
1
1
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
2
0
0
1
0
0
2
1
1
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
1
2
2
0
0
0
1
1
1
0
2
0
1
2
0
1
1
0
0
2
1
1
1
0
1
0
0
0
0
0
3
0
2
0
0
2
2
1
0
2
1
0
1
1
2
2
2
0
0
3
0
0
0
0
0
0
0
1
2
1
2
0
3
2
0
2
0
0
0
2
0
0
2
1
0
0
0
1
0
1
4
3
1
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
6
2
1
1
0
1
1
1
2
0
1
1
0
0
2
0
1
2
0
0
2
0
1
1
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
2
0
1
0
1
0
0
1
0
2
0
1
0
1
0
2
0
2
0
0
0
1
0
0
2
0
2
1
0
0
0
2
0
1
0
2
0
1
0
2
3
0
0
0
0
1
2
1
0
2
0
0
0
0
1
0
0
2
0
0
1
0
0
3
2
1
1
0
2
0
0
1
0
2
1
0
0
1
1
2
0
0
2
0
0
0
1
0
0
0
1
0
0
0
1
0
0
2
2
1
1
1
1
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
1
0
0
1
1
0
0
1
0
1
1
3
0
0
2
0
1
4
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
2
0
1
2
0
0
1
0
1
0
0
0
0
0
2
1
0
0
0
1
0
2
2
2
1
1
1
1
1
0
2
2
2
2
0
0
0
1
2
1
0
0
0
1
2
0
0
2
2
0
1
1
0
2
2
1
0
2
0
0
2
2
0
1
1
0
0
2
0
2
0
3
1
0
1
0
0
0
2
1
0
2
0
0
0
1
1
0
2
2
0
0
0
0
1
0
2
1
0
0
2
2
0
0
0
1
1
0
1
2
1
1
3
1
1
1
0
0
1
0
0
1
1
1
0
0
0
1
2
0
0
0
1
2
1
0
0
1
0
2
0
0
1
0
0
1
0
2
2
0
0
1
0
1
0
0
0
2
1
0
0
1
1
1
0
0
0
0
0
0
1
0
2
0
0
1
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
1
2
0
2
1
0
0
0
1
0
2
2
1
1
0
1
0
0
0
0
1
2
1
7
2
0
0
0
0
0
0
1
0
0
2
0
0
0
2
2
1
0
0
1
0
1
0
1
0
3
0
1
0
0
1
1
0
0
1
0
0
0
0
2
1
0
0
2
0
1
2
1
0
2
1
1
2
1
0
1
2
1
0
0
0
2
1
0
0
3
2
0
0
0
0
0
0
0
0
1
2
0
1
2
1
2
2
0
2
1
2
3
1
0
2
0
2
0
0
0
1
2
2
1
2
0
0
2
0
0
1
0
0
1
0
1
0
0
0
0
1
1
2
0
0
2
0
0
2
0
0
0
0
3
0
0
0
0
2
0
0
1
0
0
0
0
0
3
0
0
1
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
1
0
0
2
0
1
1
2
2
0
0
0
0
2
0
0
0
2
1
1
1
3
0
0
0
0
0
0
1
0
0
0
1
0
1
2
0
1
3
0
1
2
2
0
0
1
1
0
2
2
0
0
2
0
0
1
0
0
1
1
1
1
1
2
2
0
2
1
1
0
0
0
0
0
1
2
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
1
0
1
1
0
0
0
2
1
0
0
0
0
0
2
2
2
1
3
2
0
0
1
0
0
0
0
2
2
0
0
3
0
0
2
2
2
0
1
0
1
0
0
1
0
0
0
0
1
2
0
0
1
0
0
0
1
0
0
2
1
0
0
2
0
1
0
0
0
2
1
1
0
0
1
0
15
1
0
0
0
1
0
0
0
0
2
2
0
2
0
8
2
0
1
1
0
2
4
0
0
0
0
0
2
0
1
1
0
2
0
0
1
0
0
0
0
0
5
0
0
0
0
0
2
0
6
2
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
1
0
2
1
1
0
1
0
0
0
2
0
0
1
0
0
1
1
1
0
0
0
0
0
1
1
0
2
2
0
1
0
2
1
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
1
0
2
0
0
0
2
1
0
2
0
0
0
2
0
0
2
0
0
1
1
0
0
0
2
0
0
3
0
2
2
0
2
0
1
0
2
1
1
1
2
2
1
0
0
0
0
0
1
0
0
0
0
2
1
0
3
0
0
0
0
0
2
0
1
1
1
0
1
0
2
0
2
0
2
3
1
0
0
1
2
0
2
0
1
0
0
0
0
1
0
0
2
0
2
0
0
2
0
0
4
0
0
0
0
2
1
0
2
0
0
1
2
0
1
0
2
2
0
1
0
1
0
0
0
0
1
0
2
1
2
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
2
0
0
1
0
0
0
0
2
2
0
0
0
2
1
0
0
3
2
0
1
2
0
0
1
0
0
2
0
2
0
0
1
0
2
0
1
2
0
0
1
0
1
0
0
0
0
0
0
1
1
5
0
0
0
0
0
2
0
0
0
2
1
1
0
0
0
0
4
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
1
1
0
0
0
0
0
1
0
0
1
0
2
0
3
0
0
1
1
0
2
0
0
0
1
0
2
0
0
0
2
1
0
1
0
0
2
0
0
1
2
2
0
0
0
0
1
1
2
0
1
1
0
0
0
0
0
0
0
3
2
2
1
1
0
1
0
3
1
1
1
0
0
1
0
2
0
1
2
0
0
0
2
1
0
0
1
0
1
1
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
2
0
2
1
0
0
0
0
1
2
0
0
0
0
0
1
1
2
2
1
2
0
0
0
0
2
1
0
2
0
1
0
0
1
0
0
1
1
0
2
2
2
0
1
4
1
0
1
0
1
0
0
1
0
1
1
1
1
2
2
3
4
2
0
2
2
0
0
1
1
2
0
0
0
0
0
0
0
1
1
0
0
2
2
0
0
1
1
0
0
0
1
0
1
0
1
1
0
1
2
1
0
0
0
1
1
1
1
0
0
2
1
2
1
1
1
1
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
1
2
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
1
1
1
1
1
0
1
0
0
0
2
1
0
0
0
0
0
1
3
0
3
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
1
0
0
1
0
1
0
0
1
0
1
0
3
0
1
0
0
2
0
0
0
2
0
2
0
1
1
1
0
1
2
2
1
2
1
1
1
2
0
2
1
0
0
0
1
2
0
2
0
0
1
1
0
2
0
1
0
0
0
1
0
1
2
0
0
2
1
2
0
1
0
1
1
1
2
0
1
0
0
1
0
1
2
2
1
0
1
1
0
0
2
0
0
0
2
1
0
0
0
0
0
1
1
2
1
0
0
0
0
1
1
2
0
0
0
0
0
2
1
2
0
1
0
2
2
0
1
1
0
0
1
1
0
0
1
0
0
2
0
1
0
0
1
1
0
1
0
2
3
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
1
0
2
1
1
0
2
0
2
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
2
0
6
0
0
0
0
2
0
2
1
0
0
1
0
2
1
1
2
0
0
0
0
2
1
2
0
1
0
0
0
1
1
2
2
2
0
0
1
0
2
2
0
1
0
0
2
0
2
0
0
0
0
0
2
1
0
0
0
0
0
1
0
2
0
0
0
1
0
0
1
2
1
1
0
0
2
0
0
1
2
0
0
0
1
1
0
0
0
2
2
0
0
0
0
0
1
2
0
1
0
0
1
0
1
0
0
0
1
0
0
2
1
1
0
2
0
1
0
0
0
1
0
0
1
0
1
2
0
0
0
0
2
1
1
0
0
0
0
0
0
0
2
0
1
0
1
0
1
0
0
1
0
1
0
0
0
0
1
0
1
0
2
2
7
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
1
0
1
2
1
0
0
0
2
2
0
0
1
0
1
0
2
0
0
0
2
0
1
0
1
2
0
0
0
1
0
0
0
0
1
0
1
0
4
0
1
1
0
0
0
1
0
1
0
1
0
1
0
0
2
2
0
0
0
0
0
1
0
1
0
1
1
0
1
1
1
0
3
1
0
0
0
0
0
0
0
0
1
0
0
1
2
3
1
0
1
0
0
0
0
0
1
0
0
0
0
1
3
0
0
1
1
2
0
1
1
2
0
0
0
0
0
1
1
2
0
0
0
0
0
1
1
2
2
0
0
0
1
1
0
1
1
3
0
1
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
3
0
0
0
2
0
0
0
0
0
0
1
0
1
0
2
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
2
1
2
0
0
0
0
0
6
0
0
2
4
0
3
0
0
0
3
3
0
0
1
0
2
0
1
0
0
0
0
3
2
5
0
0
0
1
0
2
1
1
1
2
0
1
0
0
0
0
2
0
2
1
0
3
2
0
2
1
0
2
1
2
1
0
0
2
0
1
0
0
1
1
0
1
0
0
0
0
0
1
1
2
0
0
0
0
1
0
2
0
2
0
0
1
1
2
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
1
2
0
1
0
1
0
2
0
0
0
2
1
1
0
0
0
0
0
1
0
1
2
2
1
0
0
2
0
0
2
1
0
0
0
1
0
1
2
2
0
0
2
2
2
0
0
0
0
1
0
0
2
1
0
2
1
1
1
0
1
1
0
0
0
0
1
0
0
1
0
0
1
2
2
1
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
1
0
0
0
0
0
1
2
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
1
0
2
2
1
1
2
0
0
0
0
2
0
0
2
0
1
2
0
1
1
1
2
0
0
0
0
0
0
0
0
0
1
1
0
2
1
2
0
2
0
0
0
0
0
2
2
0
0
0
0
0
2
2
1
1
0
2
0
0
0
0
0
0
1
0
1
2
1
0
0
1
2
0
0
0
0
0
1
0
3
0
1
0
1
1
1
1
1
0
1
0
0
1
0
1
0
0
1
2
2
1
0
2
0
0
0
0
0
1
1
4
0
0
0
2
0
0
0
0
0
2
2
4
1
0
0
1
0
0
2
0
1
0
0
0
1
0
1
1
2
0
0
1
0
0
2
2
2
0
1
0
0
0
2
0
0
1
0
0
1
0
0
0
0
2
2
1
2
1
2
0
0
2
0
1
0
0
0
0
1
1
1
2
0
1
0
3
0
0
1
0
2
0
1
2
2
0
0
2
0
1
0
0
0
1
0
0
0
1
1
0
0
0
2
2
2
0
0
3
0
2
0
2
0
0
0
0
1
1
0
0
0
1
0
0
1
2
0
0
2
0
4
1
0
0
0
0
0
0
0
0
0
3
0
2
2
2
0
0
0
4
0
0
0
1
1
1
1
1
2
1
1
2
1
1
2
0
0
0
0
0
2
1
1
1
2
0
0
0
0
2
0
2
0
0
0
0
1
2
0
0
0
0
1
2
2
0
2
2
2
0
1
0
0
2
0
1
0
2
0
0
0
1
2
2
0
1
0
1
1
2
0
1
0
0
1
0
0
0
0
0
4
1
0
0
0
0
0
1
2
0
0
1
0
1
1
0
0
2
1
0
0
0
2
1
0
1
1
2
0
2
1
0
2
0
2
0
0
0
0
2
0
3
0
1
1
0
0
0
2
1
0
0
1
2
1
2
0
0
0
3
2
0
2
2
0
0
0
1
1
1
0
2
2
0
0
1
1
0
2
0
0
0
0
0
0
1
1
0
0
0
0
2
1
0
0
0
1
0
3
0
0
1
0
2
0
0
1
1
1
2
1
0
2
1
1
0
1
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
2
0
1
0
0
1
0
0
1
0
1
0
1
0
0
5
2
0
1
0
1
1
2
0
2
0
2
0
1
0
1
2
2
0
0
0
0
0
2
1
0
0
1
1
2
1
0
1
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
2
0
0
0
1
0
1
0
1
1
2
1
1
0
1
1
0
0
0
1
0
0
0
0
1
0
2
0
1
0
2
2
0
0
0
0
0
2
0
0
2
0
2
1
2
2
0
2
0
0
1
0
2
0
2
2
0
1
0
0
0
4
0
1
0
0
2
2
0
1
2
0
0
0
0
1
0
1
0
0
2
1
2
2
2
2
0
2
3
2
2
0
1
0
0
1
0
0
0
0
2
1
0
0
2
0
0
2
0
0
0
2
0
1
0
1
0
0
0
1
0
0
0
0
0
1
1
1
0
1
1
2
0
1
0
2
0
2
1
0
0
0
0
0
1
0
2
1
0
3
0
2
0
0
0
1
2
0
0
1
0
0
1
1
0
2
0
0
0
1
0
0
1
2
0
0
0
0
0
0
1
2
0
1
1
0
1
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
1
1
1
0
0
3
0
0
1
0
0
0
0
0
0
0
1
1
0
2
0
0
2
2
2
0
0
1
1
0
2
1
1
0
0
0
0
1
0
2
1
2
0
0
1
0
0
1
0
1
1
1
2
0
0
0
2
2
1
0
2
0
0
0
2
3
1
0
2
1
0
1
0
2
1
1
1
2
0
0
2
0
0
2
0
0
2
0
1
0
0
1
0
0
2
0
0
1
0
1
0
0
1
0
2
0
1
0
0
1
2
0
2
0
0
0
2
0
0
1
2
0
1
0
1
2
2
0
0
2
1
0
2
1
0
1
0
3
2
1
0
2
0
1
0
0
0
0
1
0
2
1
1
1
0
0
2
0
2
0
0
0
0
2
0
1
1
0
0
2
0
0
2
0
3
1
1
0
2
0
1
0
0
1
2
2
0
2
1
0
2
0
0
0
2
0
0
1
0
0
0
0
0
2
1
0
0
0
0
3
2
0
2
0
0
1
2
1
0
2
0
0
0
0
0
0
0
1
1
2
1
2
0
0
5
1
0
2
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
2
0
1
0
0
2
0
0
2
1
0
0
2
0
0
1
1
2
0
1
0
0
1
1
0
1
0
0
0
2
0
1
0
3
0
2
0
2
0
0
2
0
1
0
0
2
0
0
1
2
1
2
1
2
0
2
0
0
0
1
1
0
1
2
2
0
0
1
0
0
0
0
0
0
0
0
2
0
2
4
1
1
1
1
1
2
0
1
1
0
0
2
0
0
0
2
0
4
0
1
0
0
1
2
0
2
2
0
1
0
0
0
0
1
1
2
2
0
1
0
0
0
4
0
0
1
0
2
0
0
0
1
0
2
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
1
0
0
1
0
0
1
2
0
2
0
3
0
0
4
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
2
0
2
0
1
2
0
2
2
0
0
1
2
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
3
0
2
2
1
0
1
1
0
0
2
0
0
1
1
1
0
2
0
1
0
0
1
0
2
0
2
1
0
1
0
1
2
0
0
0
1
0
0
0
0
1
0
1
0
0
2
1
0
1
0
1
1
1
1
0
1
2
0
0
1
1
0
1
0
2
3
0
2
0
2
0
0
1
2
0
0
1
0
0
0
0
3
0
2
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
2
0
0
1
2
0
1
0
3
0
0
0
0
1
1
0
0
0
2
1
1
0
0
0
2
0
2
1
2
2
0
1
0
1
0
0
2
0
0
0
0
1
0
0
2
1
0
6
1
2
0
0
0
1
1
0
1
2
0
3
0
1
2
0
0
0
0
1
0
0
0
1
1
1
0
2
1
0
2
2
0
0
0
0
3
0
0
0
2
0
1
1
0
0
0
0
1
1
0
0
1
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
1
0
1
1
0
1
0
0
0
1
2
0
2
0
0
0
0
1
1
1
2
1
0
2
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
1
0
0
0
0
2
2
0
1
1
1
2
0
0
2
0
0
2
0
2
0
2
1
0
0
0
2
0
0
2
0
2
0
0
1
2
2
0
1
1
0
2
0
0
0
0
0
0
2
0
0
1
2
0
1
0
0
2
0
0
1
0
0
1
2
1
0
0
0
0
0
1
1
2
1
0
0
0
1
0
0
1
0
0
1
0
2
1
1
0
0
1
2
0
0
1
1
0
0
2
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
1
0
1
1
0
1
0
0
1
1
2
0
0
1
2
0
0
1
0
2
0
0
0
1
0
1
1
0
2
2
0
0
0
3
1
0
2
1
2
1
0
0
0
0
0
1
0
3
0
2
0
0
2
1
2
0
0
0
1
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
1
0
0
1
2
1
0
0
0
1
0
1
1
2
0
1
1
0
0
0
2
3
2
2
0
0
0
1
0
0
0
2
1
0
0
2
0
0
0
2
0
2
0
0
1
0
0
0
1
1
1
2
0
0
0
0
1
1
1
2
1
0
1
2
0
1
0
2
2
1
0
0
0
2
3
2
2
0
2
1
2
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
1
1
0
2
2
0
0
2
0
1
0
1
0
1
1
2
1
1
0
0
0
1
0
0
0
0
0
3
1
0
2
1
0
0
2
0
0
2
2
0
1
1
0
1
2
1
3
0
0
0
1
2
1
1
1
1
2
1
0
1
0
1
1
0
0
0
0
1
2
1
0
0
0
1
1
2
0
2
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
2
2
2
2
0
1
0
2
0
4
0
1
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
3
2
0
2
0
2
1
0
0
2
0
0
2
0
1
1
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
1
2
0
1
0
0
2
2
0
3
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
1
0
1
0
2
1
1
1
0
0
0
1
2
4
2
0
0
0
0
0
1
1
1
0
1
0
0
2
0
0
0
2
1
0
0
2
0
2
1
0
0
0
1
2
0
2
1
0
0
0
0
0
2
0
1
0
0
2
1
2
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
1
0
4
0
0
2
1
1
2
0
0
1
0
0
0
0
1
1
0
2
1
0
1
0
2
0
0
0
0
0
1
3
0
1
2
2
0
0
0
0
0
1
0
3
0
0
1
0
3
2
1
0
2
1
2
0
0
1
0
0
2
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
2
1
0
1
0
0
0
1
1
0
0
0
2
0
0
1
0
2
1
2
0
0
2
0
2
2
2
2
0
0
2
0
0
2
0
0
1
0
1
2
0
2
2
2
0
0
1
0
0
0
0
0
0
1
0
2
0
0
2
1
0
1
0
0
0
0
1
0
1
2
0
0
3
0
0
0
2
2
1
0
2
1
0
0
0
0
1
0
2
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
2
0
2
2
0
0
0
2
2
0
1
1
1
0
1
0
1
1
0
1
2
1
1
4
2
1
0
0
2
0
1
0
0
0
1
0
0
1
0
2
0
0
0
0
0
2
1
2
0
2
2
0
0
1
0
0
1
0
1
0
0
0
0
1
0
2
0
2
0
2
0
0
1
0
1
0
0
1
0
0
0
0
1
0
1
1
0
2
0
1
0
2
0
0
2
2
1
1
0
0
2
0
0
0
0
0
1
0
2
1
1
0
0
0
0
0
1
0
0
1
1
0
1
0
0
1
2
3
0
0
2
0
3
0
1
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
1
2
1
0
1
1
1
0
1
0
0
0
1
1
1
2
0
2
2
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
3
1
0
1
0
0
2
0
0
2
3
2
0
0
2
2
0
0
0
3
0
2
0
1
0
1
0
0
0
0
2
1
0
0
0
2
0
0
1
0
0
0
1
1
0
1
2
1
0
0
0
2
2
2
1
0
1
0
0
2
0
2
0
1
0
0
0
1
2
2
0
1
0
2
1
0
0
0
1
0
2
2
2
2
1
1
0
0
2
1
1
1
0
0
0
0
0
1
0
4
0
0
0
0
0
0
2
0
2
2
0
0
2
0
1
3
0
1
0
1
0
0
2
0
0
1
1
0
2
1
1
1
2
2
1
1
1
0
2
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
2
2
0
2
0
0
0
0
0
0
1
0
1
1
1
2
1
1
0
0
0
1
0
0
1
0
0
0
2
1
0
1
2
0
0
2
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
2
1
0
1
0
0
4
0
0
0
2
1
0
0
0
0
1
2
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
1
0
2
0
0
1
0
0
1
0
0
2
2
2
3
2
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
1
1
0
2
0
2
0
0
1
0
1
0
0
0
0
1
0
2
1
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
1
2
3
0
0
3
0
0
1
0
1
0
2
0
0
2
5
2
0
0
2
1
0
2
0
2
2
0
0
0
1
2
2
1
1
1
0
0
0
0
0
0
0
0
1
0
2
0
2
2
0
0
2
0
0
1
0
1
1
1
2
1
0
1
0
0
1
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
1
4
2
1
1
1
1
0
2
2
0
0
1
0
0
0
0
0
1
0
2
0
1
2
0
0
0
0
1
0
2
2
0
0
2
1
1
0
1
0
1
0
2
1
0
0
1
0
0
1
0
0
0
2
2
0
0
1
2
1
2
2
1
0
0
2
1
0
1
0
0
2
0
1
2
2
0
0
0
2
2
1
1
0
1
0
2
0
1
1
1
1
1
0
1
0
1
0
0
2
1
1
0
1
0
2
0
1
0
2
2
0
2
2
1
0
1
0
0
0
0
2
1
1
1
1
0
0
0
0
0
0
0
0
2
0
1
0
1
2
1
0
2
0
0
0
1
4
2
2
1
0
0
2
0
0
1
0
0
0
0
2
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
2
0
1
0
1
1
0
0
1
1
0
1
0
0
2
0
0
1
0
0
0
1
0
1
2
0
1
1
0
2
0
0
0
1
0
0
0
1
2
0
1
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
2
2
0
2
0
2
0
0
2
0
2
2
0
0
1
2
0
0
1
0
1
0
2
1
0
0
0
1
0
0
0
0
6
2
0
1
1
2
0
2
1
0
1
0
2
1
0
2
0
0
1
1
2
0
0
1
0
2
0
0
1
0
1
2
1
0
2
0
0
0
0
1
0
1
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
1
2
1
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
1
1
1
1
0
0
2
0
1
1
0
0
0
0
0
2
0
1
0
0
0
2
0
2
0
0
2
1
1
1
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
2
0
0
0
1
1
1
0
2
0
2
0
1
0
2
0
0
0
2
0
2
0
0
0
0
1
2
0
0
0
1
1
4
0
0
0
1
0
2
2
0
1
0
1
3
3
0
0
2
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
2
1
2
0
0
1
2
2
1
0
1
0
2
0
1
1
0
3
0
1
1
0
0
0
0
0
0
0
1
0
0
2
0
2
2
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
2
0
1
0
0
2
0
2
2
0
1
0
0
0
0
0
0
1
0
0
1
1
0
1
0
1
1
0
1
0
1
0
0
0
1
2
1
1
1
0
1
2
0
0
0
0
1
0
0
0
1
0
0
0
2
2
1
0
2
1
2
1
0
0
0
3
3
3
1
0
2
1
1
0
0
0
1
0
2
0
1
2
1
1
0
1
3
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
2
0
0
1
2
0
0
1
0
0
1
0
0
3
0
0
0
1
0
0
1
0
0
0
2
2
0
2
0
0
2
0
0
2
2
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
1
2
0
2
1
2
0
0
0
0
0
0
2
0
2
2
1
0
0
1
0
2
0
1
0
2
2
0
2
0
0
0
0
0
2
2
2
2
0
0
2
0
2
1
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
3
0
0
1
0
2
0
0
1
2
2
1
0
0
0
0
0
0
2
2
0
3
0
0
0
0
0
1
0
0
1
0
0
2
1
1
0
0
0
1
1
2
2
0
0
1
0
2
0
0
0
0
1
0
2
2
0
0
0
1
0
2
0
2
2
0
0
1
1
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
2
2
0
1
0
2
1
0
0
0
1
0
0
3
0
2
2
1
2
0
0
0
0
0
2
0
2
1
0
1
0
2
1
0
0
0
0
1
0
0
3
0
0
0
1
2
2
0
0
0
0
1
0
0
0
2
1
2
0
1
0
0
1
2
0
1
1
0
2
2
0
0
1
2
1
0
0
0
2
0
2
2
0
1
2
1
0
2
0
1
0
0
1
1
0
1
0
1
2
1
1
2
0
1
1
2
0
2
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
2
0
0
0
2
1
1
0
0
1
0
0
3
0
0
1
1
0
0
1
2
1
2
0
2
3
1
2
0
7
0
0
2
2
2
0
1
0
0
1
2
0
0
0
1
2
1
1
0
0
1
0
1
1
0
2
1
1
1
0
0
1
0
0
1
0
0
0
0
2
0
0
0
2
1
1
2
0
2
0
1
0
0
0
0
1
2
1
10
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
1
2
0
0
1
1
0
0
1
2
3
0
0
0
0
1
0
2
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
2
1
0
1
0
2
0
0
0
0
0
2
0
0
1
1
1
0
0
0
2
1
1
0
0
0
0
2
2
0
0
2
0
0
0
0
1
2
0
0
1
2
1
1
1
1
0
2
0
1
1
0
0
0
0
0
2
1
1
0
0
0
2
0
0
1
1
3
2
0
0
2
0
2
0
1
1
1
1
1
0
0
0
0
0
2
0
0
1
2
3
0
0
0
2
1
1
2
1
1
0
1
0
0
0
2
0
2
0
3
0
0
3
0
0
1
0
0
0
0
2
1
3
2
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
2
1
1
0
1
0
2
0
0
1
0
0
1
1
0
0
0
2
0
1
1
1
2
1
0
0
1
2
1
2
0
0
0
0
0
0
1
0
2
1
0
0
0
1
1
1
0
0
1
0
0
2
0
0
1
0
2
1
2
1
0
0
0
0
2
1
1
0
0
1
0
0
1
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
1
1
2
0
0
0
2
1
1
2
2
0
0
0
0
1
0
0
1
3
1
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
1
0
2
1
3
1
2
0
0
2
0
0
1
0
0
1
2
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
1
1
1
2
0
2
2
0
0
1
0
0
0
0
1
1
0
0
0
1
1
0
2
0
0
0
1
2
0
0
1
0
0
0
0
1
1
0
1
0
0
1
2
1
1
1
2
1
1
1
1
1
1
0
1
1
0
2
2
0
0
2
2
0
1
0
2
0
0
0
2
0
0
0
1
1
0
2
0
0
1
2
1
1
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
1
0
0
0
2
1
2
0
1
1
0
1
2
1
7
0
1
0
1
0
0
2
1
0
0
1
1
1
0
0
0
1
1
1
0
0
0
2
2
2
0
0
0
1
0
0
0
2
0
0
0
1
0
0
1
0
0
0
2
1
0
1
0
1
1
0
0
0
2
0
2
1
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
2
4
0
0
2
0
2
0
2
0
0
1
1
0
2
0
0
2
1
3
1
0
0
0
2
1
0
1
2
2
0
1
0
2
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
2
2
2
0
1
0
0
0
1
1
0
0
1
0
1
0
2
0
0
1
2
1
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
1
1
1
0
1
2
0
2
0
1
1
0
1
0
0
0
0
0
1
0
0
0
2
1
2
0
1
1
0
0
2
0
1
0
0
0
0
0
0
1
1
0
1
2
1
0
0
0
2
1
0
0
0
0
3
1
2
0
0
0
2
0
1
1
0
1
0
0
0
0
0
0
1
2
0
2
1
0
2
0
0
0
1
0
0
1
0
1
0
1
2
0
0
0
1
0
2
0
1
2
1
1
0
1
1
0
0
2
0
1
0
0
0
1
1
2
0
2
2
0
2
0
0
1
2
1
1
2
2
2
1
0
1
1
3
1
1
0
2
0
0
0
2
2
0
0
0
1
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
2
0
1
0
1
1
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
2
0
3
2
0
1
2
1
0
0
0
0
0
0
2
0
1
0
2
1
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
1
0
1
2
1
0
0
2
0
0
0
0
0
1
1
0
0
1
1
2
0
0
1
0
0
1
0
2
2
1
0
1
1
1
0
2
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
3
0
1
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
1
0
0
0
2
3
0
1
2
0
1
0
2
0
2
2
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
2
1
2
0
2
2
2
0
0
1
0
1
0
1
0
0
1
0
0
0
0
2
0
0
0
3
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
2
0
1
0
1
0
2
0
2
0
2
0
0
0
1
1
2
0
0
1
0
0
1
2
1
0
2
2
0
1
2
0
0
0
2
2
0
2
1
1
1
1
1
2
0
2
0
0
2
1
1
0
0
0
1
0
0
0
0
0
1
2
0
0
2
0
2
2
0
0
0
2
2
0
2
0
0
0
0
1
0
0
0
0
0
1
1
3
0
2
0
0
0
2
1
0
0
0
1
2
1
0
0
2
1
0
1
0
0
0
0
1
0
0
0
0
0
2
2
2
1
0
2
0
0
0
1
0
0
1
0
2
0
1
1
2
1
0
0
0
0
2
2
0
1
0
0
1
0
0
1
0
1
0
0
0
1
1
0
0
2
0
1
2
2
1
0
1
0
2
0
0
2
0
1
0
0
1
2
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
2
0
2
1
0
0
0
1
1
0
0
0
1
0
0
2
2
0
1
1
0
1
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
2
2
0
1
2
0
0
1
2
1
1
0
0
1
0
0
1
3
1
2
2
2
2
1
0
1
0
2
1
0
0
1
0
1
0
0
3
0
0
2
1
2
2
2
0
2
0
0
1
1
0
2
0
0
1
0
2
0
0
0
2
1
0
0
0
0
2
1
0
0
1
2
0
0
0
0
0
1
0
2
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
1
1
1
0
0
2
2
0
2
3
2
0
0
2
2
1
0
0
0
1
0
0
0
1
0
0
2
0
2
0
1
2
0
0
1
2
0
2
0
0
0
0
1
0
0
2
2
0
0
2
1
0
2
0
0
0
0
2
1
0
0
0
0
2
1
0
0
1
0
2
2
0
0
0
2
3
0
0
1
2
1
1
1
1
0
0
2
0
2
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
1
1
2
0
0
0
0
0
0
2
0
3
0
1
1
0
0
1
1
2
0
1
2
0
0
0
0
0
1
1
0
0
0
0
0
2
0
2
0
2
1
0
1
1
1
5
0
0
0
2
2
1
0
0
0
0
0
2
1
1
0
0
0
0
0
0
2
0
1
2
0
0
0
1
1
0
1
2
1
0
0
2
0
0
0
1
0
2
0
2
1
1
0
1
1
1
0
0
0
3
0
1
1
2
0
2
1
0
0
2
0
2
0
0
1
0
2
1
0
0
0
0
2
1
0
0
3
1
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
1
1
3
0
0
1
2
1
0
1
0
0
0
2
2
2
2
0
0
2
2
0
0
1
0
0
2
2
0
1
0
2
2
0
1
1
2
1
0
2
0
0
1
0
2
0
0
0
1
0
2
1
1
1
2
1
1
0
1
0
0
1
0
1
1
1
2
0
2
1
1
2
0
1
0
1
0
1
2
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
2
1
0
2
1
1
0
0
0
2
2
1
2
0
0
0
1
0
0
0
0
1
0
2
2
2
0
0
0
2
1
1
0
1
1
2
1
0
2
0
2
0
2
0
1
1
0
0
0
2
0
0
0
0
1
0
0
3
0
2
2
0
1
0
0
0
1
1
0
2
0
2
0
0
2
0
0
0
0
1
0
0
3
2
1
1
0
1
0
1
1
0
1
2
1
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
1
0
0
0
0
0
1
0
1
0
0
1
0
0
1
2
1
1
0
0
0
0
2
0
3
0
0
0
0
0
2
0
1
0
0
0
2
0
2
0
0
1
1
2
2
0
0
0
0
0
0
1
3
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
2
2
1
1
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
1
0
0
0
2
0
2
0
0
0
2
0
0
0
2
1
0
2
0
0
2
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
1
0
0
2
1
0
0
2
1
1
2
2
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
1
0
1
1
0
0
0
0
0
1
1
0
0
1
1
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
1
2
1
0
0
0
2
2
1
1
1
0
0
1
0
3
1
0
5
1
1
0
1
0
2
1
2
0
0
1
1
1
0
0
0
2
4
1
3
0
1
2
1
2
2
0
0
1
1
0
0
1
4
0
0
0
0
0
1
0
1
0
0
2
5
1
2
2
0
0
0
0
0
1
0
2
0
0
1
0
0
1
0
2
0
0
0
0
4
0
0
0
0
1
0
1
0
0
2
1
3
1
2
2
0
0
0
2
0
0
0
0
1
0
0
1
0
0
1
0
2
3
2
1
0
2
3
0
0
0
0
2
2
1
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
2
3
0
2
2
1
3
1
1
1
1
0
0
0
0
0
0
0
0
0
1
0
1
2
0
1
0
0
0
2
0
0
0
0
1
0
2
1
2
0
0
0
0
0
1
0
1
2
0
1
0
3
0
0
1
2
2
0
2
0
0
2
2
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
2
0
2
0
0
0
0
2
0
2
0
1
0
2
0
0
1
2
1
0
1
0
2
0
0
1
0
0
1
0
1
0
2
1
0
1
0
0
0
1
0
0
2
0
0
0
2
1
1
1
2
0
4
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
2
0
2
1
1
1
0
0
0
0
0
0
2
1
1
2
1
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
1
2
0
1
0
2
2
0
0
0
2
1
0
1
2
1
1
1
3
0
1
2
2
1
0
0
0
0
1
2
0
0
0
0
1
0
3
0
0
0
4
0
0
0
0
2
2
2
1
0
0
1
0
0
2
0
0
0
0
0
0
1
0
2
2
0
0
0
0
2
2
1
2
0
0
0
0
0
0
2
2
0
1
0
0
1
0
1
0
0
0
2
0
1
2
2
1
0
0
0
0
2
0
2
0
0
2
2
2
0
1
0
0
0
1
1
1
0
1
2
0
0
1
0
1
0
1
0
0
0
0
1
2
2
1
0
0
3
2
0
0
0
0
2
1
0
0
1
1
0
1
0
1
0
1
1
0
1
2
0
0
0
0
2
2
2
0
2
0
0
0
1
0
0
0
2
0
2
1
2
0
2
1
1
2
0
0
0
1
1
0
0
1
0
2
0
0
0
0
2
2
1
1
0
1
2
2
1
2
1
2
2
0
0
0
0
0
2
1
0
0
1
2
0
2
0
0
0
2
0
0
0
2
0
0
2
1
0
0
1
0
1
0
0
0
3
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
1
2
1
0
3
2
1
0
1
0
1
0
0
0
1
1
0
0
1
0
2
2
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
2
2
2
1
0
3
2
0
2
2
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
1
1
0
1
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
3
0
1
2
0
1
1
2
0
0
0
2
2
2
0
0
0
0
2
0
2
0
0
2
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
2
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
2
0
1
2
1
0
2
0
1
0
0
2
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
2
0
2
1
1
0
0
1
2
0
0
1
2
0
0
2
0
0
1
1
0
0
2
0
0
0
2
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
2
2
1
0
0
1
1
0
0
0
0
2
1
2
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
2
1
0
0
2
1
0
0
1
0
0
1
2
1
2
4
0
1
0
0
0
0
1
0
0
0
1
2
1
0
0
1
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
2
1
0
1
0
0
0
0
1
2
0
0
0
3
2
0
0
0
2
0
3
2
0
0
2
2
2
4
2
0
0
0
0
0
1
0
0
0
2
0
2
0
0
2
0
0
1
0
2
1
0
1
1
0
2
0
2
2
0
1
0
2
2
0
0
1
1
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
1
1
0
0
0
0
2
1
0
1
0
0
0
0
0
1
0
0
0
0
0
2
1
1
0
0
2
0
0
0
0
0
1
0
0
2
1
1
0
2
1
0
0
0
0
1
2
1
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
2
0
0
0
2
0
2
0
1
2
1
0
1
0
0
3
0
0
2
0
0
1
1
0
0
2
1
0
0
2
0
1
0
0
2
0
2
1
0
0
1
0
2
0
0
1
1
1
0
0
2
0
0
1
2
0
0
1
0
1
1
0
2
0
0
2
2
0
1
2
2
1
0
2
1
0
0
2
1
1
0
2
0
0
0
0
1
1
1
1
0
0
1
0
1
2
0
1
2
1
0
0
1
1
1
1
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
1
1
0
2
0
0
1
2
2
0
0
1
1
1
1
0
0
1
1
0
2
0
0
0
0
0
2
0
2
0
0
2
0
1
0
0
0
1
2
1
0
0
0
2
2
0
2
0
0
0
2
0
0
0
0
2
0
1
0
0
0
2
0
0
1
2
1
0
0
0
2
0
0
2
0
2
1
0
0
2
0
1
0
2
0
0
0
1
0
1
0
0
2
0
0
0
0
2
0
2
0
0
2
1
1
0
0
2
0
0
2
0
0
0
0
0
1
0
1
2
1
2
0
0
1
1
2
0
2
0
0
0
0
0
1
0
2
1
1
0
0
2
0
1
0
4
0
0
0
0
2
1
0
0
2
0
0
2
0
1
1
0
0
0
1
0
2
0
2
0
1
0
3
1
0
1
2
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
1
2
2
1
2
0
0
6
1
1
1
0
0
2
0
12
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
1
0
1
1
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
2
0
1
2
0
0
0
2
0
0
2
2
1
2
2
0
0
1
1
3
1
0
0
1
0
0
2
0
0
0
2
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
1
0
2
0
0
2
0
1
0
0
0
0
0
0
1
1
2
1
0
0
2
0
1
1
2
1
1
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
1
1
0
1
1
0
0
0
4
0
0
1
0
0
0
0
0
1
0
2
0
1
0
1
2
1
0
0
1
0
0
0
0
1
1
0
0
1
2
0
0
0
2
2
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
1
1
0
0
2
2
1
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
2
0
2
2
2
0
2
1
1
0
4
1
1
0
1
1
0
2
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
2
2
1
2
0
0
2
3
0
0
0
1
0
0
0
0
0
2
2
2
0
2
8
1
0
0
1
2
1
0
1
0
0
0
0
1
1
2
2
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
1
0
0
3
0
0
0
0
2
1
0
2
0
2
0
0
2
0
0
3
0
2
2
0
1
0
1
0
2
0
2
0
0
2
3
0
0
0
2
0
2
1
0
0
1
2
0
4
0
0
0
0
0
1
2
2
0
1
2
1
0
1
2
0
0
2
0
2
0
0
1
2
1
0
0
2
0
1
1
1
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
2
1
1
0
1
0
0
2
1
0
1
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
2
0
2
0
0
0
0
1
0
6
0
0
0
1
2
0
0
0
3
0
2
0
0
1
0
0
0
0
2
1
0
0
2
1
0
1
2
2
0
1
1
0
0
2
0
0
2
2
1
0
2
2
1
0
0
0
0
1
0
0
3
0
1
1
0
0
0
0
1
2
2
1
0
1
0
0
1
0
1
0
2
0
2
0
1
0
0
0
0
0
4
0
0
0
2
1
1
0
0
0
2
0
1
2
0
0
1
1
0
1
0
0
0
0
0
0
0
2
3
3
0
0
1
0
0
0
0
0
2
0
0
1
0
1
1
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
2
2
0
0
2
0
1
0
0
0
2
0
0
0
0
0
1
0
0
1
0
2
1
1
1
2
0
1
2
0
0
0
0
2
0
1
0
2
0
0
2
1
0
2
0
2
1
1
0
1
1
0
0
0
1
1
0
2
2
0
0
0
0
1
0
2
1
0
0
0
0
1
2
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
4
0
0
2
0
2
2
0
0
1
0
0
1
2
0
0
2
0
1
1
0
3
0
0
0
1
0
2
0
1
0
2
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
1
0
2
0
0
1
2
0
1
0
0
1
0
1
2
0
0
1
1
0
1
2
0
2
0
0
2
0
2
1
0
2
2
1
2
2
0
0
0
0
2
2
0
0
1
1
0
0
1
1
0
2
0
0
1
0
2
0
0
0
0
0
1
1
1
0
0
1
1
1
1
2
0
0
1
0
1
1
2
0
1
1
0
0
0
0
0
1
0
0
0
1
2
1
1
0
0
0
0
0
1
0
2
2
1
0
2
0
2
0
0
2
1
0
0
0
2
2
0
0
2
0
0
1
3
0
0
0
0
0
0
1
2
2
0
2
0
0
1
2
1
1
2
0
0
1
0
2
1
3
0
0
0
0
1
2
0
0
0
0
4
0
0
2
0
0
1
0
0
0
0
0
0
2
1
0
3
0
0
0
1
1
0
2
0
2
2
0
2
0
0
0
0
0
0
1
2
1
0
0
2
1
0
0
3
0
0
0
0
0
2
1
0
0
2
0
1
2
1
0
2
1
1
2
1
1
0
0
1
0
1
1
0
1
0
0
1
2
0
1
0
2
1
2
0
1
1
2
0
2
0
0
0
1
1
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
1
0
2
0
2
3
1
2
0
1
0
0
0
0
1
2
0
0
0
0
1
0
4
0
0
1
1
0
3
1
0
2
0
1
0
2
1
0
1
2
0
1
2
1
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
2
2
1
0
0
2
1
1
0
1
1
0
0
1
1
1
0
1
0
0
0
2
1
0
2
0
1
2
1
0
1
1
1
0
1
2
0
2
1
2
0
0
1
2
0
0
0
0
1
1
0
0
0
0
0
1
0
1
1
1
2
2
1
0
0
0
2
0
0
0
2
1
0
0
2
2
2
0
0
1
0
1
1
2
1
1
0
0
0
0
0
1
0
1
1
0
0
2
1
0
2
1
0
0
0
0
0
1
0
0
1
2
0
1
0
0
0
0
1
0
0
2
1
0
0
2
0
0
0
1
0
2
1
0
0
2
1
0
0
0
0
0
3
0
0
0
0
1
0
0
0
2
0
1
2
0
1
1
0
0
1
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
1
1
1
0
2
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
3
0
1
0
1
0
0
0
1
1
0
0
0
0
0
2
1
2
0
0
0
0
0
0
1
2
1
1
1
2
0
0
1
0
0
1
1
2
1
5
0
0
0
0
0
2
1
1
2
0
0
1
0
1
2
2
1
1
0
0
1
0
0
2
0
0
0
0
1
2
0
0
2
1
0
1
2
0
1
1
1
0
0
0
0
0
1
1
0
1
0
0
2
1
0
0
1
0
0
1
2
0
0
0
1
0
1
0
1
0
1
0
0
0
2
0
4
1
0
2
0
0
1
0
0
0
0
1
0
1
0
0
0
1
2
1
0
0
1
2
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
1
2
1
0
0
0
0
0
0
1
3
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
2
2
1
1
0
0
0
2
0
0
2
1
0
0
0
1
2
0
1
0
1
0
0
0
2
0
0
1
2
4
0
2
1
1
0
2
0
0
2
0
0
0
0
0
1
0
2
0
2
0
0
2
2
3
0
0
0
0
0
0
3
0
0
0
2
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
2
2
0
0
1
0
0
2
0
1
0
0
0
2
0
1
1
0
2
2
1
2
0
2
0
0
2
1
1
1
0
0
1
0
0
0
0
0
1
1
0
0
2
0
0
1
1
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
3
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
7
2
2
0
0
0
0
2
0
0
0
1
0
1
0
2
0
0
1
0
0
0
1
0
1
2
1
1
0
2
2
0
0
0
0
0
2
0
0
1
0
2
2
1
0
2
0
3
0
1
0
0
0
2
2
1
0
0
0
2
0
0
2
0
0
0
0
0
2
2
2
1
0
0
1
1
1
3
1
1
1
2
1
0
0
0
1
0
2
2
0
1
2
0
2
2
1
0
0
0
1
1
0
0
0
1
0
0
2
1
2
0
2
1
2
1
0
2
0
0
1
2
0
0
0
0
0
1
2
1
0
2
0
2
0
0
1
0
0
2
0
0
2
0
0
1
2
0
0
0
1
0
0
1
2
2
0
0
2
0
0
0
2
0
0
1
2
0
0
2
2
0
2
2
0
1
2
0
0
1
0
0
0
0
0
0
1
0
2
0
1
0
1
1
1
2
0
0
0
0
0
1
0
1
0
0
1
0
0
2
2
0
1
1
0
1
1
0
0
0
0
1
0
1
2
0
2
0
0
1
2
0
0
0
0
0
2
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
2
0
6
2
1
2
0
1
0
3
0
0
0
1
2
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
1
0
0
1
2
0
0
1
0
0
2
2
0
1
1
1
0
0
3
0
0
3
0
2
1
0
2
0
0
0
0
1
0
2
0
0
1
0
2
1
1
2
2
0
2
2
1
7
2
0
0
2
0
0
0
1
1
0
0
0
1
2
2
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
2
2
1
1
0
2
0
1
1
3
0
0
0
2
0
0
0
2
0
1
0
2
0
0
2
1
2
1
2
0
0
3
0
0
2
1
0
1
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
2
1
2
0
1
0
0
0
1
2
0
1
1
4
0
0
0
0
1
2
0
2
2
1
0
1
0
2
0
0
2
0
0
1
0
2
2
0
1
1
0
2
5
2
0
0
2
0
1
0
2
1
0
1
0
0
3
2
0
0
2
0
1
0
1
2
0
1
0
1
0
1
0
0
0
0
2
0
0
0
0
1
2
0
0
2
2
0
1
0
1
1
1
2
0
0
0
2
0
0
1
0
2
1
1
1
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
1
1
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
2
0
1
2
1
1
0
2
0
0
0
3
0
0
2
1
0
0
0
0
0
0
1
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
1
0
2
2
0
0
0
1
0
1
2
2
1
2
2
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
2
2
0
0
0
1
0
0
0
2
0
2
0
0
0
3
0
0
0
2
0
0
0
1
0
2
2
1
1
1
2
1
1
1
0
3
0
0
1
0
0
1
0
1
0
2
0
1
2
0
0
0
0
0
0
1
1
0
0
0
0
2
1
0
0
0
1
0
2
0
0
2
0
1
1
0
0
1
0
1
0
1
1
0
0
0
2
0
0
2
1
1
2
0
1
1
1
0
1
0
0
2
0
0
0
0
0
1
1
0
0
1
1
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
2
0
2
0
2
1
0
0
1
0
1
0
0
1
0
0
2
0
0
1
1
0
0
0
2
1
2
0
0
2
0
1
1
1
0
0
0
1
1
2
2
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
2
0
0
1
2
0
0
1
2
0
0
0
0
0
3
0
0
1
0
0
0
1
1
0
0
2
1
2
0
2
2
0
0
0
2
0
0
2
0
0
0
2
0
1
2
0
2
0
0
2
0
2
2
0
0
0
0
0
1
0
0
0
1
0
1
0
0
3
0
2
0
2
2
2
0
2
0
0
0
1
1
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
1
1
0
2
0
0
0
3
1
0
3
0
0
0
1
0
0
0
2
0
0
1
1
0
0
0
1
0
1
2
3
2
2
0
1
0
1
0
2
0
1
0
1
0
0
1
0
0
1
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
3
1
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
2
1
0
1
0
0
2
2
2
0
0
1
4
1
1
1
0
1
3
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
1
1
0
0
2
0
0
1
0
2
1
2
0
2
1
0
0
3
2
0
0
0
4
0
0
0
0
0
0
0
1
0
0
1
0
0
2
1
2
0
0
0
0
2
0
1
0
0
1
0
0
0
2
0
0
1
1
0
0
2
2
2
0
0
0
1
1
0
0
0
0
1
1
0
2
0
2
2
0
2
1
0
0
1
0
1
2
0
0
1
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
1
0
1
1
0
1
0
2
0
2
1
1
1
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
1
1
0
0
1
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
1
3
1
2
0
0
0
0
0
2
0
0
0
0
0
3
1
2
1
2
0
0
1
0
1
1
0
1
0
1
0
2
0
1
2
0
1
0
0
2
6
2
0
0
0
0
1
0
0
2
0
0
0
1
0
2
1
2
0
0
0
0
2
0
0
0
2
2
0
1
0
2
0
1
0
2
1
0
0
0
0
1
0
0
2
0
0
2
2
0
0
2
2
2
0
0
0
1
0
0
0
2
0
1
0
2
1
1
1
2
2
0
2
0
0
0
1
0
1
0
2
2
0
0
1
0
0
1
1
0
2
1
0
1
0
0
0
0
0
1
0
2
3
0
1
0
0
0
1
3
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
1
0
2
2
2
2
0
0
2
2
0
0
1
1
0
0
2
0
0
0
0
2
0
0
1
1
0
0
0
1
0
2
1
0
0
0
0
2
0
2
1
0
0
2
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
2
0
1
0
3
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
2
0
0
1
0
0
0
0
2
2
0
1
0
0
2
1
3
0
0
0
0
1
0
0
0
0
1
0
2
1
1
2
2
0
0
0
2
0
0
1
0
2
0
1
1
2
2
0
0
0
0
0
1
2
0
1
2
0
0
0
0
0
2
3
0
0
2
0
0
0
1
1
1
1
0
0
0
2
0
0
1
0
0
2
0
0
1
0
0
0
1
0
2
0
0
0
1
1
0
0
2
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
1
1
3
0
0
0
0
0
0
0
2
2
2
1
0
0
1
1
2
0
2
0
2
1
0
0
2
1
0
0
1
2
2
1
0
2
1
1
0
0
0
1
2
0
0
3
2
0
1
0
1
2
2
0
0
0
1
1
1
0
1
0
2
0
0
0
0
1
4
0
1
1
0
1
0
1
2
1
0
0
2
1
0
2
1
0
0
3
1
0
1
0
0
2
0
0
0
3
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
2
1
1
0
1
1
2
0
1
0
0
3
0
0
1
7
0
2
0
0
1
0
1
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
5
2
2
1
0
1
0
1
0
0
0
1
0
0
2
1
0
0
1
2
0
0
2
0
2
1
1
0
2
1
0
0
2
0
2
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
1
0
2
0
2
0
1
0
0
1
0
0
2
0
0
2
1
0
0
0
2
0
1
0
1
0
1
0
0
0
4
1
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
2
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
2
0
0
2
0
0
1
1
0
2
0
1
0
1
0
1
0
3
0
0
0
0
0
1
2
0
0
0
1
0
0
1
0
0
0
0
0
3
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
2
0
1
0
1
0
4
1
0
2
0
0
0
0
4
0
1
0
1
2
2
0
2
0
0
0
0
1
2
0
1
0
0
0
0
0
2
0
0
0
0
1
1
1
0
0
1
0
0
2
1
1
1
0
1
0
0
2
1
0
0
0
0
1
0
2
1
1
0
0
0
0
0
0
0
0
0
2
0
0
1
3
1
0
2
2
0
0
0
2
0
1
0
2
2
0
2
0
0
0
2
2
2
0
0
1
1
1
1
0
1
0
0
0
1
2
0
1
1
0
0
1
1
0
0
0
0
0
1
2
0
2
0
2
0
3
1
0
0
1
1
1
1
0
2
0
1
0
0
0
2
0
2
2
2
2
1
0
0
0
0
1
1
0
0
0
3
1
4
2
0
2
0
1
0
0
1
3
0
1
1
1
0
1
0
1
3
2
0
1
0
0
0
0
0
0
0
0
0
0
3
1
1
1
0
0
0
0
1
0
0
0
2
1
1
3
0
0
0
2
0
0
1
2
2
0
1
1
0
1
0
0
0
0
0
0
2
1
0
0
0
1
0
0
1
0
1
1
1
2
0
1
1
0
0
0
0
1
0
0
0
1
2
0
0
1
0
3
2
2
0
2
2
1
0
0
1
1
0
0
0
0
0
0
1
2
0
0
0
0
0
1
1
2
0
2
1
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
2
1
0
0
0
1
2
0
0
0
0
1
0
0
0
0
1
0
2
1
1
2
0
0
0
1
2
0
0
0
1
0
0
1
1
0
2
2
0
2
0
1
3
0
0
1
0
2
2
2
1
0
0
2
1
2
2
4
0
0
0
0
1
0
0
1
0
2
0
0
0
2
2
1
0
0
0
0
0
1
0
0
0
2
0
2
1
2
0
1
0
2
0
0
0
2
0
0
1
0
0
2
0
2
0
0
1
2
1
0
2
1
0
0
1
1
0
0
0
0
1
0
1
0
1
1
2
1
0
0
0
2
0
1
2
1
0
2
0
2
1
2
2
0
0
0
1
1
1
0
0
0
2
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
2
0
0
1
0
0
1
1
1
0
2
1
0
0
1
2
1
0
0
2
0
0
0
0
3
2
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
1
0
0
1
2
0
0
0
0
2
2
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
2
0
1
0
0
0
0
1
0
0
0
0
1
0
2
0
1
0
1
2
2
0
2
0
2
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
2
2
0
1
1
0
0
0
0
1
1
2
1
0
0
0
0
1
1
0
1
0
0
0
1
0
0
1
0
0
0
2
1
0
1
1
0
0
3
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
1
3
0
1
2
2
2
1
0
0
1
1
0
2
0
0
0
0
2
2
1
0
0
1
0
1
0
0
0
0
0
0
2
0
0
1
0
1
2
0
0
1
0
3
0
0
2
0
1
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
2
2
0
0
0
0
1
2
0
2
3
2
2
0
2
0
1
0
0
1
3
1
0
0
0
1
2
0
2
0
0
0
0
0
1
1
0
1
3
0
0
1
0
1
1
0
2
1
2
0
4
0
0
0
2
1
0
1
2
2
0
0
0
0
1
0
0
2
2
1
0
0
0
2
1
0
1
0
0
0
1
0
0
1
0
0
0
2
1
2
2
0
1
2
2
0
0
1
0
1
0
2
2
0
0
2
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
2
1
2
2
2
0
0
0
0
2
1
1
0
0
2
1
0
0
0
0
2
2
2
0
2
1
1
1
1
1
0
0
1
0
1
0
0
0
0
0
2
0
2
2
0
0
0
2
0
2
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
2
0
5
2
0
0
0
0
2
0
0
1
0
0
0
2
0
0
2
0
0
1
2
0
1
0
1
0
1
0
0
1
0
0
1
1
0
0
0
0
1
0
0
2
0
0
0
0
1
2
2
1
0
2
1
2
2
1
0
0
0
0
1
0
0
0
0
0
0
2
1
0
2
1
2
0
0
0
2
1
0
2
1
0
0
0
1
1
0
1
1
1
0
2
0
0
0
1
1
1
0
2
0
0
2
2
0
0
0
0
1
0
0
0
2
2
2
2
0
0
2
0
0
0
0
0
2
0
0
0
2
2
0
1
0
0
0
0
0
2
2
2
2
0
0
0
2
0
1
0
0
1
1
2
1
2
0
0
0
1
1
1
0
1
0
2
1
0
1
0
1
2
0
1
0
2
0
2
0
0
2
0
2
0
3
2
0
0
0
2
0
1
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
1
2
1
2
1
2
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
1
1
2
2
1
0
0
2
3
1
0
0
0
1
0
1
1
0
0
0
2
2
0
0
1
0
1
0
0
2
0
0
0
0
3
0
0
0
0
3
2
1
2
1
2
2
0
2
0
0
2
2
1
5
2
1
0
0
1
0
0
2
0
2
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
2
1
0
2
0
2
2
0
1
0
0
1
0
1
0
0
0
2
1
0
2
2
1
1
0
0
0
1
1
0
0
0
0
2
0
0
0
1
1
1
0
0
0
0
0
0
1
3
0
2
0
0
0
2
2
1
2
0
0
2
0
0
0
1
0
0
1
0
1
1
3
1
0
0
0
0
1
0
1
2
0
1
1
2
0
2
0
0
2
0
0
0
1
1
0
1
2
1
0
0
0
0
0
0
1
0
0
0
3
1
1
0
0
0
0
0
0
0
3
3
0
2
2
1
0
1
0
0
0
0
1
1
0
0
1
2
0
0
0
2
0
1
1
0
0
0
0
0
0
1
3
2
1
0
1
1
2
1
0
2
0
0
0
0
2
0
3
0
0
0
0
4
2
1
1
0
0
1
2
1
0
0
0
0
0
0
1
0
0
0
0
0
2
3
0
0
0
0
0
1
0
0
0
2
0
1
2
1
2
0
1
0
0
0
1
0
0
0
2
1
0
1
2
2
0
1
0
1
2
2
0
0
2
2
1
0
0
2
0
0
0
1
0
2
2
0
1
0
0
0
1
2
0
2
0
1
1
2
0
2
0
0
0
0
2
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
3
2
2
2
1
0
0
2
0
0
0
1
0
2
1
0
2
2
0
0
4
2
0
1
1
0
2
0
0
0
1
0
2
0
1
1
2
0
2
0
0
0
0
0
0
0
1
0
1
0
1
0
1
1
0
1
0
0
1
2
2
1
0
0
0
0
1
0
0
1
2
1
0
1
0
1
0
0
0
0
1
1
0
1
0
1
0
0
0
2
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
1
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
1
0
2
0
0
0
6
0
0
2
0
0
1
1
0
1
0
0
1
1
2
1
3
2
2
0
0
0
1
0
1
0
0
1
0
1
0
1
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
1
3
0
0
0
1
0
0
2
2
0
0
1
0
0
2
0
2
2
1
2
1
2
2
0
0
0
0
0
0
2
0
1
2
1
0
0
0
0
0
2
2
0
1
0
2
2
0
2
1
0
0
2
0
0
0
2
0
1
0
2
0
2
0
0
0
0
1
2
1
1
0
2
1
0
0
0
1
6
1
0
0
4
0
1
0
0
1
1
1
0
0
1
0
0
0
0
2
1
2
0
0
0
2
2
1
2
0
0
2
0
0
2
0
2
0
0
0
0
1
2
0
0
0
1
1
1
2
1
0
0
0
0
0
0
1
2
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
2
0
2
0
0
0
1
0
2
0
0
0
2
0
1
0
0
0
1
0
0
0
2
0
3
1
1
2
1
1
0
2
0
0
0
0
2
0
1
0
0
2
1
0
0
0
0
0
2
0
1
2
1
2
2
1
0
0
1
0
2
2
0
0
0
1
2
1
0
1
2
0
1
0
1
1
1
1
2
1
0
2
2
0
0
0
0
2
1
1
0
0
1
0
2
0
0
1
0
1
2
2
0
0
0
0
1
2
0
0
0
0
0
0
2
2
2
3
0
0
3
0
0
0
0
0
1
0
0
1
0
0
1
1
1
0
0
1
1
0
0
2
0
0
0
0
2
2
0
1
2
2
2
0
0
0
0
1
0
1
0
0
2
2
2
0
0
0
0
2
0
2
0
1
1
0
1
1
2
0
2
0
0
2
0
2
1
0
0
2
0
0
0
1
0
0
1
0
2
0
3
1
1
0
1
0
2
1
0
0
1
0
0
2
1
2
1
0
1
1
0
0
1
0
0
0
0
1
1
0
0
0
2
0
0
0
1
0
0
0
1
2
0
2
0
0
1
0
0
2
0
0
1
1
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
1
1
0
0
1
2
0
0
0
1
0
2
0
0
1
0
0
0
1
1
0
1
0
2
0
1
0
1
0
2
1
3
0
0
3
0
1
2
0
0
0
0
0
2
0
0
0
0
0
1
1
0
1
2
0
0
0
1
2
0
2
1
0
2
1
2
1
0
0
2
0
1
0
0
2
0
2
2
1
0
2
0
0
2
1
0
1
2
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
1
0
0
1
2
1
2
0
2
0
0
1
1
0
0
0
0
2
0
2
2
0
2
1
0
0
0
1
0
2
0
1
0
1
1
1
2
0
1
1
0
0
0
0
2
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
5
0
1
0
0
0
0
0
0
2
0
2
0
1
2
0
1
3
0
0
0
2
0
2
0
0
0
0
0
0
0
1
1
0
2
7
0
0
2
1
0
1
0
1
2
2
2
0
2
0
1
0
0
3
2
2
0
0
1
1
0
0
0
2
0
1
0
0
3
1
0
2
0
0
1
0
2
0
2
2
0
0
2
1
0
1
0
0
0
1
2
2
0
0
0
0
4
1
2
0
0
0
2
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
1
1
0
0
0
2
1
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
1
0
0
1
0
0
1
0
1
1
1
2
0
0
1
2
0
0
0
0
1
0
2
0
0
0
0
2
1
2
1
0
2
0
0
2
2
0
3
0
1
2
1
0
1
0
1
0
1
0
2
1
0
0
0
0
2
2
2
1
0
1
0
1
2
1
0
2
0
2
0
1
2
1
0
0
0
2
0
0
0
0
0
2
0
1
1
0
0
0
0
1
0
0
1
0
0
0
2
2
0
0
0
1
1
2
0
1
0
4
2
2
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
1
2
2
1
1
0
2
0
0
0
1
2
0
1
2
0
1
2
0
0
1
0
0
1
1
0
2
1
1
0
1
2
0
2
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
3
0
0
2
0
2
0
1
0
3
1
0
0
2
0
1
0
0
0
0
1
1
0
1
0
3
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
2
2
0
0
1
1
0
0
1
0
1
1
1
1
0
0
0
0
0
1
0
0
0
2
0
1
0
1
0
1
0
0
0
0
0
1
1
0
2
0
2
2
0
0
0
0
0
2
1
0
1
0
0
0
0
2
2
0
1
1
1
0
0
0
0
0
1
1
0
1
0
0
2
1
0
4
0
2
0
1
0
0
0
0
0
0
0
2
0
0
2
1
4
0
0
0
1
3
2
0
0
1
0
2
0
1
0
1
0
0
0
2
0
2
1
0
3
0
1
2
0
1
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
2
0
1
2
0
1
0
0
5
0
0
0
1
0
1
0
0
1
1
0
0
2
1
1
0
0
1
0
0
2
0
4
0
0
0
2
1
0
0
0
1
2
0
0
2
0
1
0
0
1
0
0
0
1
0
0
2
0
0
1
0
0
2
0
0
0
0
1
2
2
0
2
0
0
3
2
0
2
0
0
0
1
0
0
0
1
0
0
2
2
0
0
1
2
1
0
1
0
2
1
2
0
2
1
1
0
0
0
0
0
2
2
0
1
0
0
0
1
1
0
0
0
2
2
0
0
0
2
1
2
1
0
0
2
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
2
0
1
2
2
2
2
0
0
0
2
1
0
1
0
0
0
0
2
0
0
2
0
1
1
0
2
1
0
2
0
3
0
2
0
0
1
0
0
0
0
0
0
1
3
0
0
0
2
1
2
0
2
2
2
1
4
2
0
0
0
0
2
2
0
1
1
0
2
0
2
1
1
3
1
3
2
0
2
0
1
0
0
0
0
2
1
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
2
1
2
2
1
1
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
1
0
0
2
1
0
1
2
0
0
2
0
0
2
1
1
1
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
2
0
1
0
0
0
0
0
1
2
1
3
2
1
1
0
1
1
0
1
0
0
2
1
0
1
0
0
2
0
6
1
2
2
0
2
0
0
1
0
1
2
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
2
2
0
0
0
1
1
2
1
2
0
0
3
0
0
0
0
0
1
0
0
2
1
1
1
0
0
0
0
0
0
1
1
0
2
0
0
3
2
0
0
2
0
0
2
3
1
0
1
2
2
2
2
2
1
0
2
1
2
1
0
0
0
0
1
1
0
0
1
1
0
0
0
0
1
0
2
0
0
0
0
3
2
0
1
1
0
0
1
2
0
0
0
0
0
1
1
0
2
2
0
0
1
0
0
1
2
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
2
0
1
1
2
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
2
0
0
1
1
1
0
2
1
0
0
1
0
1
0
0
0
0
2
2
0
0
0
4
2
0
1
0
1
0
1
0
1
0
1
2
1
2
1
0
0
0
0
1
0
0
0
0
0
0
3
0
2
1
2
0
5
1
0
2
0
1
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
1
1
0
2
2
0
2
0
0
2
0
2
0
1
0
2
1
0
0
0
2
0
2
0
1
1
1
0
0
1
1
2
2
0
0
2
2
1
1
2
1
0
0
0
0
2
0
2
2
0
2
0
2
2
0
2
1
0
0
0
0
3
1
0
1
0
0
0
2
1
0
0
2
0
1
0
0
0
1
2
0
2
1
0
1
2
0
0
1
0
1
1
0
1
0
0
0
1
0
2
2
0
0
0
1
2
0
0
1
0
0
0
2
3
0
0
0
0
1
2
1
2
1
0
1
1
0
3
0
1
1
0
2
1
2
0
2
0
0
0
0
0
0
2
0
3
0
0
0
1
0
0
0
1
2
2
0
0
1
1
1
0
1
1
1
0
0
0
1
0
0
1
0
2
3
0
0
1
0
0
0
0
0
0
1
0
2
0
2
0
1
2
1
1
0
0
0
1
0
4
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
2
0
0
1
1
0
1
2
1
2
0
0
0
0
2
0
1
0
1
1
1
5
0
0
0
0
1
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
2
2
2
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
1
0
1
3
0
1
0
0
1
0
0
2
0
2
0
0
1
0
2
0
0
2
0
1
0
1
0
0
0
0
0
0
0
2
0
1
1
0
0
1
1
1
0
0
0
0
0
2
0
0
0
1
2
0
0
1
1
0
0
0
1
0
0
0
0
2
1
1
1
1
1
0
2
1
0
0
0
0
0
1
1
1
0
2
0
2
2
0
1
0
1
0
2
2
2
1
1
1
2
0
0
0
1
0
0
2
1
1
2
1
2
1
2
0
0
0
0
1
2
1
0
1
1
2
0
0
2
1
0
0
1
7
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
2
1
1
1
0
0
0
1
0
0
0
0
0
0
1
2
0
1
0
0
3
1
1
0
0
0
2
2
0
1
0
1
1
0
1
2
0
2
0
1
2
2
0
2
2
2
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
5
1
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
2
0
1
0
2
2
0
0
0
1
2
2
0
1
0
0
0
1
0
0
1
1
1
0
2
1
0
2
1
0
1
1
0
1
0
1
0
0
1
0
2
0
2
2
0
1
0
1
0
0
1
0
2
2
1
1
0
0
0
0
1
2
0
0
1
1
0
0
0
0
0
1
1
2
2
1
1
0
0
0
1
2
1
1
1
1
1
1
2
0
2
2
2
0
0
2
0
2
1
2
1
0
0
2
1
1
0
0
0
1
0
0
2
0
1
0
2
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
2
3
0
0
0
1
2
0
1
1
1
2
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
1
0
0
2
2
1
0
0
0
2
2
0
1
0
0
0
0
1
0
0
0
2
2
0
0
1
2
0
0
2
1
1
1
0
0
0
2
0
2
1
2
0
0
1
2
2
0
0
0
0
0
1
0
0
2
0
0
1
0
2
0
2
0
0
1
1
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
2
0
0
0
0
2
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
1
0
2
2
2
0
0
0
2
0
0
0
0
0
1
2
2
0
3
0
2
2
2
0
0
0
2
2
0
1
0
2
0
2
1
2
2
0
0
0
2
2
0
0
0
0
0
0
2
0
0
2
0
1
0
2
2
0
0
0
0
0
1
0
2
3
0
0
1
1
1
0
0
2
0
0
0
1
1
0
0
1
0
0
1
0
0
0
1
3
1
0
0
0
0
2
0
0
2
0
0
0
1
0
2
0
0
0
2
0
2
3
2
0
0
0
2
0
1
2
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
2
2
0
3
0
0
2
0
2
0
2
0
0
0
0
2
0
0
2
2
0
0
0
0
0
1
1
0
0
2
0
1
0
0
1
0
0
1
1
1
0
0
1
1
0
0
0
0
2
2
2
0
0
0
0
2
1
2
2
2
1
0
2
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
2
0
0
1
0
2
0
0
0
0
2
0
1
1
2
0
0
2
1
0
0
0
0
1
0
2
0
1
1
1
0
0
2
0
0
0
2
0
0
0
0
0
1
0
1
0
0
1
1
0
2
0
1
0
0
1
1
1
0
1
0
2
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
1
0
1
0
0
3
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
2
1
1
0
2
0
0
2
0
1
1
0
0
0
2
0
1
2
0
0
0
0
1
2
0
0
1
0
2
0
1
0
0
0
2
2
0
0
1
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
1
0
0
1
1
0
0
0
1
1
1
1
1
2
0
0
1
1
1
0
5
1
2
2
1
0
0
0
0
1
0
0
0
0
1
0
3
1
1
1
2
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
1
2
0
2
0
0
2
0
0
1
0
1
2
0
1
1
0
2
2
0
2
1
1
2
0
1
2
0
0
0
0
1
2
2
2
3
0
0
0
0
0
0
2
2
0
0
2
0
1
2
0
0
0
1
1
1
1
1
2
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
3
1
2
2
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
2
2
2
0
2
2
0
0
2
0
0
2
0
2
2
2
1
1
0
2
0
0
0
0
1
1
0
0
0
1
2
0
2
1
1
0
2
0
0
1
2
2
1
0
0
0
1
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
1
1
2
1
0
0
0
0
0
0
0
1
0
0
3
0
1
2
0
0
0
0
0
0
2
2
0
2
1
0
2
2
1
1
2
2
0
0
0
0
1
2
0
0
2
0
0
2
1
0
0
1
0
0
0
2
1
0
0
0
2
0
2
0
0
0
0
1
1
1
0
1
2
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
2
3
2
0
3
2
0
2
0
0
0
1
3
2
0
1
0
0
0
2
1
1
0
0
1
0
1
0
4
0
0
0
2
2
1
0
0
1
1
0
0
0
0
0
0
0
2
0
1
0
0
0
1
2
0
2
2
2
0
0
0
2
2
2
1
2
0
0
1
2
0
2
0
1
2
2
0
1
1
3
2
1
2
0
1
0
1
0
2
2
3
2
0
2
2
0
2
0
0
0
0
1
0
0
0
2
2
0
0
0
1
1
0
0
2
0
0
0
1
1
1
1
1
0
2
2
0
3
0
1
0
0
0
0
0
0
0
2
0
1
1
2
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
3
0
0
0
2
0
2
0
2
0
1
1
0
2
0
2
2
1
0
1
0
1
0
3
1
2
0
2
2
1
1
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
1
2
0
2
2
0
0
0
1
1
0
0
0
1
0
1
2
2
0
0
1
0
0
0
1
0
2
0
1
1
1
1
0
0
0
1
0
0
0
2
2
0
1
0
1
1
0
0
2
2
0
1
0
0
0
0
2
0
0
0
1
0
1
2
0
1
0
0
2
2
0
1
2
0
0
0
0
0
0
1
2
0
0
0
1
1
0
2
0
0
2
0
2
0
2
2
0
0
0
2
0
0
1
2
0
0
2
1
2
6
0
4
2
1
0
0
0
1
2
0
0
6
0
1
2
1
2
0
2
1
0
0
1
0
2
2
0
2
0
1
0
0
1
2
0
0
0
1
2
0
1
0
3
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
1
0
2
0
1
0
1
0
1
1
1
0
0
0
0
1
0
1
0
0
0
0
0
1
1
1
0
0
1
2
2
1
2
2
0
1
0
2
1
0
0
1
0
2
0
0
0
2
0
0
1
1
0
2
0
0
2
2
1
0
1
1
2
0
0
2
1
0
0
1
1
0
0
1
1
1
0
0
2
3
0
2
0
1
1
0
1
1
0
2
0
1
0
0
0
2
1
1
1
0
0
0
1
1
2
0
0
0
0
0
0
1
0
0
1
1
3
2
0
0
0
1
4
2
2
2
0
0
2
1
0
0
1
1
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
1
1
0
0
0
0
0
2
3
1
0
0
1
1
0
2
1
0
0
2
0
0
0
0
2
0
0
0
1
0
2
1
3
1
1
0
2
0
0
0
1
0
0
1
0
0
3
0
2
0
1
0
1
0
0
1
1
0
0
2
0
0
0
1
1
0
0
0
0
1
0
0
1
1
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
1
2
1
4
2
0
0
0
0
0
0
1
2
2
2
2
1
1
1
2
2
2
2
0
0
0
2
1
2
1
0
1
0
2
0
1
0
0
0
1
0
2
0
1
1
1
2
1
0
0
1
1
2
1
1
1
0
0
0
0
2
1
0
1
0
0
0
1
0
0
1
2
1
0
0
1
0
0
0
0
2
1
0
0
0
0
1
0
1
1
1
3
0
0
0
2
0
0
0
0
0
1
0
0
2
2
0
0
1
0
0
0
2
1
2
0
2
2
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
1
0
0
0
2
0
1
0
1
1
1
1
0
0
1
0
1
0
2
0
1
1
2
1
2
0
0
0
2
1
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
1
2
0
2
0
2
0
1
0
0
0
1
2
4
0
2
2
2
0
0
0
3
0
0
2
0
0
1
0
1
1
0
1
1
2
0
0
0
0
0
0
0
0
2
1
2
2
0
0
2
0
0
1
2
2
2
4
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
2
1
0
0
2
0
1
3
1
2
0
1
0
0
2
0
1
0
0
1
0
1
1
0
1
0
0
2
0
1
1
1
0
0
1
1
1
3
0
0
0
1
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
1
1
0
0
2
0
0
0
2
0
0
0
2
1
0
0
0
1
0
0
2
0
1
0
0
1
1
2
0
0
0
0
1
2
3
0
0
1
0
0
0
0
2
2
1
0
1
1
2
2
0
0
0
0
0
2
0
2
1
1
2
2
0
2
1
1
1
2
0
0
0
0
1
1
2
0
0
0
0
1
1
0
1
0
2
0
0
0
2
0
2
0
1
0
0
2
2
0
0
0
2
0
2
0
1
0
0
1
0
2
1
1
2
0
1
0
0
0
0
0
1
0
1
1
1
0
0
0
0
1
0
1
2
0
1
0
1
0
0
2
0
1
2
0
0
2
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
2
0
2
0
1
0
0
0
0
0
1
0
0
0
1
1
0
1
2
0
0
1
1
2
2
0
0
2
0
1
2
1
0
0
3
0
2
0
2
1
2
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
2
1
1
2
1
2
0
0
0
0
0
1
0
0
0
0
1
0
3
2
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
1
1
0
2
1
1
0
0
2
1
2
0
1
0
0
0
0
0
3
0
0
0
2
1
0
2
2
0
0
0
0
6
0
1
1
1
1
1
0
0
0
0
1
0
2
2
0
0
0
2
3
2
3
0
0
3
0
0
1
0
0
2
2
0
2
2
2
2
0
0
0
1
0
1
2
0
0
0
0
0
0
1
0
1
2
2
2
1
0
2
0
0
1
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
1
0
1
0
1
0
0
4
1
0
0
0
1
0
0
0
2
0
2
0
0
2
1
2
0
0
1
1
2
0
0
2
1
0
0
2
0
2
0
0
2
1
0
3
0
0
0
0
2
1
0
1
0
0
0
3
0
0
0
0
2
1
0
0
0
0
2
0
2
0
4
0
0
0
0
0
0
0
2
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
1
0
0
0
1
0
1
2
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
1
1
2
0
0
0
2
1
1
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
2
2
0
1
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
1
1
0
2
2
1
0
0
0
0
1
2
1
1
0
2
9
1
1
0
0
0
0
2
0
1
2
0
2
1
0
2
0
1
1
3
1
1
1
2
0
0
1
0
1
0
0
1
1
1
1
1
1
1
0
1
0
1
0
1
6
0
1
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
1
0
1
2
0
2
0
0
0
0
0
2
1
0
0
2
2
2
1
0
0
2
0
0
2
2
1
0
1
1
0
1
0
0
1
1
1
0
2
0
0
0
1
1
1
0
2
0
0
1
2
0
2
0
0
1
2
1
0
2
0
0
0
2
2
0
0
0
0
1
0
1
0
0
2
0
1
0
0
1
0
1
0
0
1
0
2
0
0
5
0
0
0
0
1
0
1
0
0
2
1
0
0
1
3
2
0
0
0
3
0
2
0
2
0
1
0
0
0
2
0
0
0
1
2
1
0
1
2
2
0
2
0
2
2
1
4
1
0
0
2
1
3
2
1
2
2
0
0
0
0
0
0
1
2
0
0
2
0
0
1
0
1
1
0
2
2
0
0
1
0
1
2
0
1
0
2
0
0
1
2
2
1
0
0
2
0
0
0
2
0
1
2
1
0
0
0
0
0
0
0
0
2
0
1
1
0
0
2
0
0
0
1
0
1
2
0
0
0
0
0
2
0
2
0
2
1
1
2
0
0
0
1
1
0
0
0
1
0
1
0
0
2
0
1
2
0
0
1
0
1
0
0
1
0
0
0
2
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
2
1
2
0
0
2
1
0
0
1
1
1
0
1
2
1
3
0
0
0
1
0
1
0
0
2
0
1
2
0
0
0
0
0
2
0
0
2
0
1
1
2
1
2
3
0
0
0
0
1
2
0
0
2
1
0
1
0
2
2
0
0
0
0
1
0
0
2
0
1
1
0
2
0
2
0
0
1
1
0
2
0
0
1
1
2
2
0
0
0
0
0
0
2
1
1
1
0
0
1
0
0
0
1
0
0
1
1
0
2
1
0
0
0
2
1
2
0
0
0
2
0
2
0
0
0
0
1
0
1
0
1
1
0
0
2
0
0
2
0
0
0
0
0
0
2
1
0
0
2
0
0
1
0
0
0
1
1
0
1
0
1
2
0
1
2
0
1
0
0
0
1
0
1
0
0
1
0
1
3
0
0
0
1
1
0
2
1
0
1
0
0
1
0
0
0
2
0
1
2
0
0
3
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
2
2
2
0
1
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
1
1
0
0
0
2
1
0
0
0
0
0
0
2
3
0
0
0
1
1
0
0
1
0
2
0
0
2
1
0
0
1
2
3
2
2
0
0
2
1
0
1
0
0
1
0
1
0
2
0
0
1
1
1
0
1
2
0
0
2
0
0
0
2
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
1
0
1
1
1
1
2
1
0
2
1
0
0
0
0
3
2
2
1
0
1
1
0
0
1
2
1
2
3
0
0
0
0
0
1
1
2
0
1
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
1
0
1
1
0
1
0
2
1
1
0
2
0
0
0
0
0
2
0
1
2
0
0
0
2
0
0
0
1
1
0
0
0
0
0
2
2
2
0
0
0
1
0
0
2
1
0
0
1
2
1
2
0
0
1
0
1
0
0
0
0
2
1
0
0
0
1
2
0
2
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
3
2
1
2
2
0
0
0
1
0
0
0
0
1
0
2
0
0
2
2
0
0
0
1
1
1
2
1
0
2
1
0
0
0
0
2
2
0
0
0
1
1
0
2
0
0
0
0
2
1
2
0
0
1
0
0
2
0
1
0
0
0
1
0
1
0
0
1
0
0
2
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
5
0
4
0
0
0
0
1
0
1
0
2
4
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
1
0
2
2
0
2
0
0
0
0
0
0
1
1
5
2
2
1
0
0
0
1
2
4
2
0
1
1
0
0
0
2
0
1
1
1
0
0
0
0
4
2
2
0
0
0
0
0
1
3
3
0
2
2
1
2
0
0
2
0
2
0
0
2
2
0
1
0
1
0
1
1
0
0
0
1
0
0
0
0
2
0
0
0
1
1
0
1
1
2
1
1
0
2
1
1
0
1
1
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
2
0
2
2
0
0
0
3
0
0
0
1
0
2
0
1
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
1
1
1
0
0
0
1
2
2
0
1
2
1
2
0
1
1
1
0
0
0
0
1
1
0
2
0
1
0
1
1
1
1
0
2
1
2
0
0
0
3
1
0
1
1
2
0
0
0
0
0
0
2
0
0
0
2
0
1
2
1
2
0
1
0
4
1
0
0
2
0
1
0
1
0
0
1
0
0
0
0
0
2
2
0
0
2
0
2
2
4
0
0
2
1
0
0
1
1
0
0
0
0
0
0
0
2
2
0
1
2
3
0
0
1
0
1
0
3
2
1
1
2
0
1
0
2
0
2
0
1
0
0
1
1
2
0
0
0
0
2
0
2
0
0
0
0
2
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
1
0
0
2
0
1
1
0
0
1
1
0
0
1
2
0
2
0
1
0
0
3
0
0
1
0
0
1
0
1
1
1
0
1
0
0
1
0
3
0
0
2
1
1
2
0
0
3
0
2
0
0
0
0
0
2
1
0
0
0
2
2
2
1
0
0
1
0
2
1
0
0
0
0
0
1
0
0
1
0
1
2
0
1
1
0
0
1
0
0
0
2
1
0
1
0
2
1
2
0
2
0
0
0
0
2
1
2
0
0
2
2
1
0
0
0
2
0
0
0
2
1
0
2
0
0
0
2
1
0
0
2
0
1
0
0
1
4
2
0
2
2
1
1
0
0
1
0
1
2
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
1
2
0
2
1
0
2
0
6
0
1
0
1
2
2
2
0
3
0
0
0
0
2
2
0
0
0
1
1
2
2
0
2
0
1
2
0
0
2
1
0
1
0
1
2
1
0
0
1
0
2
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
2
1
0
0
0
0
0
1
0
0
1
0
2
0
0
1
3
2
0
1
0
0
0
0
2
0
0
2
1
0
1
0
2
2
0
2
0
0
0
1
1
0
1
0
1
0
2
0
0
2
0
0
0
0
0
1
0
0
0
2
1
2
2
0
0
0
0
0
0
1
0
3
0
1
0
0
0
0
0
0
0
1
0
3
0
0
2
0
0
0
0
2
0
2
1
0
0
0
2
2
1
0
0
2
1
0
0
2
0
0
1
2
0
2
0
1
0
0
0
2
1
0
1
0
2
1
0
1
1
0
0
0
2
2
2
2
0
0
0
0
0
0
0
0
1
1
1
1
1
2
1
0
1
2
0
0
0
0
0
0
1
0
2
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
1
4
0
0
0
0
0
0
0
1
1
0
0
0
2
2
0
0
0
0
1
2
0
1
1
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
1
1
0
0
0
0
1
0
0
2
0
2
3
0
0
2
1
1
1
1
0
2
0
0
2
3
0
0
0
3
0
2
0
0
0
1
0
1
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
1
1
1
1
0
0
0
2
0
1
0
0
1
0
1
0
0
1
2
0
0
0
0
0
0
0
2
1
0
2
1
0
0
0
1
0
0
1
0
1
0
2
0
1
2
0
1
0
2
0
0
1
0
0
2
0
6
0
0
0
2
1
1
1
1
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
2
2
2
0
0
0
0
0
1
0
2
1
0
2
0
0
1
0
0
0
2
0
1
3
0
1
0
0
3
0
2
2
0
0
0
3
0
1
0
0
2
2
0
0
0
0
0
0
2
0
0
2
1
0
2
0
1
2
2
1
0
2
1
0
0
1
1
2
0
0
0
0
0
2
0
0
0
0
2
1
0
0
1
1
0
0
0
1
0
1
1
0
2
2
0
1
1
1
0
0
2
2
0
0
0
2
0
0
0
0
0
2
1
1
0
0
2
1
2
0
0
0
3
0
1
0
0
2
2
0
1
0
1
2
0
2
0
0
0
1
1
1
2
2
0
0
2
0
1
2
2
3
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
2
0
0
0
1
0
1
0
1
1
2
1
2
0
0
1
2
0
2
2
0
0
0
1
1
2
0
2
0
0
1
0
2
0
0
0
0
0
1
0
0
2
1
2
2
2
0
0
1
0
0
0
0
0
2
1
0
2
0
0
0
0
2
0
0
3
2
2
1
0
1
1
0
0
4
1
0
1
5
0
0
1
2
2
0
2
2
1
1
0
1
3
0
0
0
0
1
2
0
2
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
1
2
0
0
2
2
0
0
0
0
1
0
0
0
0
2
0
3
0
2
0
2
0
0
2
0
2
0
0
0
2
0
0
0
1
0
2
0
2
0
0
0
0
2
0
2
0
2
0
0
2
0
1
1
1
0
2
0
1
2
2
1
1
0
0
0
0
1
2
0
0
1
0
3
2
1
1
0
2
2
1
2
0
0
0
1
2
0
0
2
2
0
0
0
2
1
0
2
2
1
0
0
0
0
3
2
1
2
0
0
1
0
2
0
2
2
1
2
0
0
0
0
2
0
0
0
0
0
1
1
0
1
0
1
0
2
0
2
0
0
1
2
1
2
0
2
0
0
2
0
0
1
2
0
0
0
2
0
0
1
0
0
0
0
0
1
2
1
0
4
0
0
3
0
1
2
0
2
1
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
1
0
0
0
3
0
2
0
0
1
0
0
0
0
0
1
2
1
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
1
0
0
2
0
1
2
0
0
0
1
0
2
0
1
0
2
0
1
0
0
2
0
0
0
0
0
0
2
2
0
0
1
0
2
0
1
1
1
0
0
2
1
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
2
1
0
1
1
2
0
1
1
0
0
1
0
4
0
2
0
1
1
0
2
0
0
1
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
3
0
2
1
0
1
2
0
0
0
3
5
0
1
1
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
1
0
2
1
1
1
1
0
1
2
0
0
0
0
1
2
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
2
0
0
1
0
1
1
0
0
0
0
2
1
2
2
1
0
0
0
1
0
1
1
2
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
1
2
0
2
1
3
1
0
2
1
0
0
0
0
0
0
1
0
0
0
2
2
5
1
2
0
2
2
0
1
1
4
0
2
0
0
2
0
1
3
0
0
0
0
0
1
1
1
0
0
3
0
0
2
1
0
1
1
2
1
0
2
2
0
1
0
0
1
0
0
1
2
3
0
0
0
1
0
1
1
0
0
0
1
1
1
2
0
0
0
0
2
0
0
2
0
2
0
2
0
2
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
1
1
1
1
0
2
1
1
0
0
0
0
0
0
0
0
1
2
6
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
2
0
3
0
1
0
0
1
0
2
1
0
1
3
0
1
0
2
2
0
0
2
0
0
0
0
0
0
1
2
2
0
1
2
0
1
1
0
0
0
0
0
0
0
2
0
2
0
0
1
2
1
0
0
0
0
2
2
2
3
2
0
0
0
0
0
0
3
0
0
0
0
1
0
0
2
0
0
0
2
0
0
1
1
2
0
0
2
0
0
0
0
0
2
2
1
1
2
0
2
2
0
0
0
0
0
1
0
3
0
0
0
3
0
1
1
0
0
2
1
0
0
0
2
0
1
0
1
1
1
0
0
1
2
1
0
0
1
0
2
2
0
1
0
0
0
0
0
0
0
0
1
1
0
0
2
0
1
0
1
0
0
2
0
0
1
0
2
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
1
0
1
0
1
0
0
1
0
0
2
0
1
1
0
1
2
0
1
0
2
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
1
0
0
0
1
0
0
0
1
2
1
0
2
0
0
0
1
1
3
0
0
0
0
1
2
1
1
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
1
2
2
0
0
1
2
0
0
2
0
0
0
0
2
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
4
0
0
0
0
2
2
0
1
0
2
2
1
2
0
1
1
0
0
1
0
2
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
2
2
0
2
1
2
0
1
0
0
0
0
1
2
1
0
1
0
0
0
1
1
1
0
0
2
0
0
0
1
2
2
0
0
0
0
0
0
0
0
1
2
0
3
2
1
0
0
0
1
0
0
0
1
11
1
0
2
1
0
1
0
0
0
2
1
2
2
1
0
0
0
3
0
1
1
2
0
0
0
1
0
2
1
1
0
0
1
0
0
0
2
0
2
0
2
1
0
0
0
0
0
0
2
1
1
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
1
0
0
1
1
0
0
0
1
1
0
0
2
2
2
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
1
2
0
0
2
2
1
1
0
1
0
2
0
0
0
1
0
0
1
2
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
1
0
0
0
5
1
1
0
1
1
1
1
0
1
0
3
2
1
0
0
0
1
0
0
0
2
0
0
3
0
0
0
2
0
0
1
2
1
1
0
1
0
0
1
1
0
1
0
0
0
2
2
0
0
0
0
0
2
0
0
1
0
1
0
0
0
2
0
0
0
0
0
1
0
1
0
1
2
0
0
0
0
1
0
1
2
2
0
2
0
0
0
0
2
1
0
0
0
2
0
0
2
0
0
0
2
0
0
2
2
2
0
0
0
1
0
0
0
0
0
1
1
1
2
0
1
0
3
0
0
0
0
0
2
0
0
0
1
2
1
1
0
0
0
0
1
1
2
1
0
0
2
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
1
0
0
0
2
0
0
2
1
2
1
0
2
0
0
1
0
0
0
0
1
1
0
0
2
0
0
0
0
0
2
1
2
2
0
1
0
1
0
0
0
4
0
2
0
0
3
1
0
1
0
2
0
0
0
0
0
0
0
1
1
0
2
0
0
0
1
2
0
2
2
0
1
1
0
1
1
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
1
0
3
0
0
0
1
2
2
0
2
0
1
1
0
0
2
1
0
0
2
1
1
1
1
1
0
0
0
1
0
0
0
1
0
0
2
0
0
1
0
2
1
0
2
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
2
0
1
0
0
2
1
0
1
1
0
0
0
0
2
2
1
0
0
0
0
0
0
1
0
0
0
0
1
1
1
2
0
0
0
0
1
0
1
2
1
0
2
2
1
2
2
0
0
0
0
1
0
0
0
0
2
2
0
2
0
1
0
1
0
2
1
1
2
0
0
1
0
0
1
1
2
0
0
0
0
0
2
2
0
1
1
0
2
0
0
0
0
0
1
2
0
1
0
1
0
2
0
1
0
1
0
0
0
0
0
0
1
1
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
1
2
1
0
0
1
0
2
0
0
2
1
0
2
0
0
2
1
1
1
2
0
0
1
0
0
0
0
0
1
0
0
2
1
1
0
0
1
2
2
1
0
0
1
0
0
1
0
0
0
0
2
2
2
2
0
1
1
1
0
2
1
0
0
0
0
2
0
0
2
1
0
0
2
2
0
0
0
0
0
2
1
0
2
0
1
0
0
1
0
0
1
0
0
0
1
1
2
0
1
0
0
0
2
0
0
0
0
4
0
1
1
0
0
0
2
0
0
0
0
1
1
0
0
3
2
1
2
0
0
0
2
0
0
0
2
3
2
1
2
2
0
1
0
1
0
0
0
0
0
0
0
0
1
1
2
0
0
1
1
0
0
1
2
0
0
0
1
0
0
0
2
0
1
0
0
1
1
2
0
0
0
1
2
2
0
2
0
0
0
1
1
3
0
0
0
1
0
0
2
0
2
2
1
0
0
1
0
0
2
2
1
3
1
2
0
0
1
1
0
0
2
0
1
2
0
0
2
0
2
0
0
0
0
1
0
2
0
1
1
0
0
0
2
2
0
2
1
1
0
0
2
0
0
0
1
0
0
2
0
2
0
0
2
0
2
1
2
2
0
1
0
2
0
1
0
0
0
0
2
0
3
2
2
0
1
0
0
2
0
0
2
0
0
0
0
0
3
1
1
0
2
0
2
1
0
1
1
0
0
0
0
0
0
2
0
1
0
2
1
2
0
2
0
1
2
1
0
0
0
0
1
0
1
1
2
1
1
1
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
1
1
0
1
0
2
1
1
0
0
1
0
0
1
2
1
1
1
0
1
1
0
0
2
0
0
0
0
0
2
2
0
0
0
0
2
1
0
1
1
2
2
0
0
0
2
2
1
1
1
1
0
0
1
2
1
2
1
0
2
2
0
2
0
2
1
0
0
0
4
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
2
1
0
0
0
2
0
0
0
1
0
0
0
3
1
0
0
0
0
0
0
1
0
2
2
1
1
0
0
0
0
0
0
1
0
5
0
0
0
0
0
0
0
0
2
2
0
1
2
0
0
2
0
1
0
1
1
0
2
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
2
0
0
2
1
0
0
1
0
0
0
1
1
0
0
2
3
1
0
1
0
0
2
0
1
1
1
1
0
1
0
1
2
3
0
0
0
0
0
1
1
0
0
1
0
0
0
0
2
0
0
0
3
0
0
3
1
1
0
2
0
0
1
0
2
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
3
1
1
0
2
2
0
0
1
0
0
0
2
2
2
0
0
0
1
0
1
0
0
2
3
0
0
0
3
2
0
1
0
0
2
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
1
0
2
0
2
5
0
1
3
1
1
0
2
0
0
0
0
0
2
1
0
0
0
1
0
0
1
1
0
0
2
1
0
0
0
0
2
1
1
2
0
1
0
2
3
0
1
0
0
2
0
0
0
2
3
2
0
0
0
2
2
0
2
2
0
0
0
0
2
0
0
2
2
1
1
2
1
1
0
1
1
0
0
0
1
0
2
2
1
0
1
0
0
2
0
2
1
0
0
0
1
2
0
0
0
0
2
2
1
1
0
1
0
1
1
0
2
2
1
2
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
2
0
0
2
1
0
0
0
0
1
0
0
2
2
0
0
0
3
0
0
0
0
0
0
3
0
1
1
0
2
1
1
0
1
1
0
0
0
0
1
1
0
0
5
1
1
1
0
2
0
0
1
0
1
0
0
0
0
0
2
0
0
0
3
0
0
0
2
1
0
0
0
0
0
0
1
1
2
0
1
0
2
0
0
0
0
2
1
0
0
2
0
2
0
0
2
1
0
0
2
0
2
0
0
0
2
1
0
1
0
1
1
0
0
2
0
0
0
1
2
2
0
1
0
0
1
0
0
0
3
0
1
0
0
1
1
1
1
0
1
0
0
2
2
1
1
0
3
1
0
0
2
1
0
0
0
1
0
2
0
1
0
2
0
1
1
0
0
1
1
0
2
1
1
1
0
0
1
0
0
1
0
2
0
1
0
0
0
0
1
0
1
0
2
1
0
0
0
2
0
0
0
2
3
0
0
1
2
0
2
1
0
2
1
1
0
0
0
0
2
0
0
0
0
2
0
0
2
0
1
0
0
0
0
1
0
1
0
0
0
0
0
2
2
1
0
2
0
0
0
0
2
0
2
2
0
1
1
0
0
2
3
0
0
0
0
3
1
0
1
2
0
0
2
0
0
0
1
0
1
0
2
2
2
0
0
2
0
1
1
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
1
0
1
0
1
1
0
0
1
0
1
0
0
0
1
1
2
0
0
0
0
0
1
1
2
2
1
0
0
2
2
2
2
0
0
0
1
0
0
0
0
0
0
0
2
1
1
1
0
1
0
0
1
1
1
0
1
1
0
2
4
0
0
0
0
2
0
0
0
0
0
0
0
0
1
3
0
0
1
2
1
0
0
0
0
0
0
1
0
1
0
6
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
2
0
1
0
0
0
0
0
0
1
0
3
1
0
2
0
0
0
0
0
0
0
2
0
0
1
2
0
2
0
0
1
0
0
2
0
1
0
0
1
1
1
0
1
0
0
0
2
0
0
1
1
1
0
2
0
1
0
2
0
2
1
3
2
2
0
3
0
0
0
0
0
0
1
0
2
2
0
1
1
2
0
1
1
0
1
1
0
0
0
0
1
1
0
2
2
0
0
0
0
0
0
0
1
1
0
1
1
2
1
0
0
2
2
0
1
0
2
0
1
2
2
0
0
0
0
1
1
2
0
0
0
1
2
2
1
0
0
0
1
1
0
0
1
0
2
0
1
2
2
0
0
1
0
0
1
2
2
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
1
2
1
3
0
0
2
0
0
0
1
1
0
0
2
0
1
0
1
1
2
1
0
1
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
2
0
1
0
1
0
1
0
1
0
1
0
2
0
0
0
0
1
1
0
0
1
2
2
2
1
0
0
2
0
0
2
0
1
0
0
0
2
0
2
0
2
1
1
0
0
0
0
1
1
2
1
0
1
0
0
1
0
0
3
0
0
0
0
0
1
0
0
0
2
0
2
1
0
1
0
0
0
1
1
0
0
0
0
0
2
0
0
1
2
0
2
2
1
2
2
0
0
0
0
0
1
1
1
0
0
1
2
2
0
0
0
1
0
1
0
0
0
0
1
0
2
1
1
0
0
1
0
0
1
0
1
2
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
2
0
0
2
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
2
1
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
2
2
0
3
1
0
1
0
0
1
0
2
0
2
1
0
0
0
0
0
0
1
0
2
2
2
0
0
0
0
0
1
2
0
0
0
0
1
1
0
0
2
1
0
0
0
1
0
2
0
2
1
0
1
0
0
0
0
0
0
2
1
2
1
0
0
1
0
1
0
0
1
1
1
1
0
0
1
0
1
0
0
2
2
0
0
1
2
2
0
2
0
2
0
0
0
0
0
1
2
2
0
2
0
2
1
0
0
0
0
0
0
0
2
3
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
2
1
0
1
1
1
0
0
0
1
1
0
2
2
0
0
2
0
1
1
1
0
0
0
0
0
4
1
2
1
0
0
0
0
0
0
0
2
1
1
0
0
0
1
0
0
0
2
0
0
0
0
0
1
2
0
0
1
0
0
0
1
0
0
2
1
0
2
0
0
0
2
0
0
1
2
2
1
3
2
0
1
0
1
0
2
0
0
1
0
0
2
1
2
0
0
0
1
1
2
0
2
0
0
0
1
0
0
1
0
0
1
0
2
0
0
2
0
0
1
0
0
2
6
0
1
2
0
0
2
1
2
0
0
1
0
0
1
0
0
0
0
1
1
0
0
2
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
2
0
0
1
0
2
2
0
0
0
2
0
0
2
1
2
1
0
1
0
0
0
0
0
0
0
1
1
2
1
1
0
1
0
1
6
0
2
1
0
1
2
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
1
0
1
2
2
0
1
0
0
0
2
0
0
0
2
1
0
1
2
7
0
0
0
2
0
0
1
0
2
0
0
2
0
2
0
0
1
1
0
0
2
1
0
2
1
0
0
0
1
0
0
0
1
0
2
0
2
0
2
2
2
0
1
0
0
0
1
0
0
1
2
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
2
1
2
6
0
1
1
0
1
0
0
0
0
0
0
0
1
2
1
0
1
2
2
1
0
0
0
2
0
1
2
2
2
2
0
0
0
0
0
1
1
0
2
0
3
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
1
2
0
0
0
1
1
0
0
1
0
1
0
0
0
2
0
0
1
1
0
0
1
0
0
0
2
2
3
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
2
1
2
0
2
0
1
0
1
1
0
0
0
1
2
2
0
2
2
0
0
1
2
0
0
0
0
0
2
2
0
0
0
1
0
2
1
0
0
0
0
2
0
2
1
1
1
3
1
1
0
2
0
0
2
0
2
1
0
1
1
2
0
0
0
3
3
0
1
0
1
0
2
0
0
1
0
0
0
1
2
0
0
1
0
0
0
1
0
0
0
2
1
1
0
0
0
2
1
0
0
1
2
2
1
0
1
0
0
0
0
0
2
1
0
0
2
2
4
2
0
1
0
2
0
0
0
0
0
2
0
2
0
2
1
2
0
0
0
0
0
0
1
1
2
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
1
2
0
1
0
2
1
0
1
0
0
0
0
1
0
0
2
2
0
0
1
0
0
0
0
0
0
1
2
2
0
0
0
0
1
1
1
3
0
0
0
0
1
3
0
0
1
1
1
0
2
1
0
1
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
2
2
0
1
0
0
0
0
0
1
3
0
0
1
2
1
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
1
0
0
1
0
1
0
2
1
0
3
0
0
1
0
1
2
0
0
1
1
2
0
1
0
0
1
1
3
0
2
0
1
0
2
0
1
0
0
1
0
1
0
0
0
0
1
2
0
1
2
3
1
0
2
0
0
2
0
0
0
0
2
1
0
0
1
0
0
0
2
1
0
0
0
0
0
1
1
0
1
2
0
0
0
0
0
1
0
2
2
0
0
0
0
1
0
1
1
0
1
0
2
0
0
2
1
0
0
1
0
1
0
0
0
0
1
2
0
1
1
0
0
2
1
0
0
0
0
1
1
0
1
0
0
0
0
2
0
2
2
0
0
0
1
0
2
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
2
2
0
2
1
0
2
0
0
0
0
0
1
1
1
2
1
1
1
3
2
0
1
0
1
2
0
1
1
2
1
2
2
0
0
1
2
1
0
1
0
0
0
2
0
1
0
0
1
2
3
0
0
2
0
2
3
1
2
0
0
0
1
3
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
9
0
0
0
0
2
0
0
0
2
2
1
0
0
2
2
1
2
0
0
2
1
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
1
0
0
2
1
2
3
1
0
0
1
2
1
2
1
0
0
1
1
0
0
2
0
1
0
0
1
0
0
0
2
2
1
0
1
2
0
0
0
1
0
0
0
2
2
1
1
0
0
2
0
0
1
2
0
0
0
1
0
1
1
0
1
1
0
0
0
1
0
1
2
0
0
0
2
2
0
0
0
1
0
0
1
1
0
0
0
1
2
0
0
0
2
1
0
0
1
2
5
0
2
1
2
0
0
1
0
0
0
0
0
1
3
2
0
0
0
0
0
2
0
1
1
0
0
2
1
0
0
1
1
0
0
0
0
0
0
2
1
1
0
0
0
1
1
0
0
1
0
0
0
1
0
2
2
0
0
1
0
0
1
0
0
2
0
1
0
0
2
0
1
0
2
0
0
1
1
2
0
0
1
0
0
1
2
0
0
2
0
3
0
0
3
1
0
3
0
0
0
0
1
1
2
0
0
0
0
1
0
2
0
1
2
1
4
2
0
0
0
0
3
2
0
5
1
0
0
0
0
0
0
2
2
1
0
0
2
0
0
0
0
2
1
0
2
0
0
0
2
0
0
0
0
0
0
2
0
2
0
1
0
2
0
0
1
0
0
2
1
2
1
1
0
3
0
0
1
2
0
1
2
0
2
1
0
0
0
1
2
2
1
1
0
2
0
1
1
0
2
0
0
1
1
0
0
0
2
4
0
0
2
0
0
0
0
0
2
0
2
0
0
1
0
0
2
0
1
0
0
1
0
0
0
0
2
1
1
1
1
2
0
0
0
2
0
2
0
0
0
2
0
0
2
0
0
1
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
2
2
0
2
0
0
1
2
0
0
1
0
1
1
0
0
0
0
5
0
2
0
2
1
0
1
0
0
2
0
0
2
2
0
1
0
0
1
0
0
0
0
0
1
2
1
2
0
2
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
2
0
4
1
0
1
0
2
2
2
1
1
0
1
0
0
0
2
0
2
0
3
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
1
3
0
2
0
0
0
2
2
0
0
0
2
1
2
0
0
0
1
1
0
0
0
0
2
0
0
2
0
0
0
0
2
0
2
1
1
1
0
0
0
0
0
1
2
0
0
2
0
1
2
0
0
0
1
2
0
1
0
2
1
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
2
1
1
1
0
0
0
0
2
2
1
0
0
0
2
0
0
1
2
0
0
1
0
2
2
2
2
1
0
1
0
1
0
2
0
1
1
0
1
0
1
2
0
0
1
0
0
0
2
0
1
2
0
2
0
0
0
0
0
2
0
0
0
2
1
0
2
1
0
2
4
2
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
2
1
0
2
0
0
0
0
2
1
1
1
0
0
0
2
0
0
0
0
0
6
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
3
2
2
0
2
0
0
0
2
2
0
0
2
2
2
2
0
1
0
0
0
0
1
0
0
1
2
1
3
0
2
2
0
1
0
0
1
4
0
1
1
2
0
2
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
1
1
1
1
0
0
2
0
0
1
0
0
2
0
1
0
0
2
0
1
1
0
0
0
0
1
2
0
0
2
1
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
1
1
0
1
0
0
1
0
1
2
1
0
0
0
0
0
0
0
0
1
1
0
2
1
1
0
0
0
0
1
2
2
0
2
0
0
1
1
0
1
0
2
1
0
0
1
0
4
0
2
0
2
0
0
1
0
0
2
1
2
0
2
0
0
0
0
0
0
1
1
0
0
0
1
2
0
0
0
0
1
0
2
2
2
0
2
0
0
2
2
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
1
2
1
2
0
0
0
0
0
0
1
1
0
0
2
0
0
1
1
1
1
1
0
0
1
0
2
0
2
0
2
0
1
0
0
2
0
0
1
0
1
0
1
2
0
0
2
0
0
0
1
2
0
1
1
2
0
1
1
0
1
2
0
1
0
0
2
0
0
1
0
2
0
3
1
0
1
0
0
1
2
1
0
0
1
2
2
1
0
1
2
1
0
0
0
2
2
0
1
0
2
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
2
2
1
2
3
1
1
0
1
0
1
1
0
0
1
0
0
2
2
0
1
1
2
0
1
0
2
0
1
1
1
2
0
0
0
2
1
1
0
3
2
3
0
1
0
0
2
0
2
0
0
0
0
1
2
2
2
0
2
0
1
2
1
0
0
0
1
0
2
1
0
0
0
0
3
1
0
0
2
0
0
1
0
0
0
0
0
1
0
0
2
1
0
2
0
0
0
0
2
0
1
1
0
0
0
0
1
0
0
2
0
0
0
1
1
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
1
1
1
0
1
0
0
0
1
1
0
0
2
0
0
1
0
0
0
2
0
0
1
1
0
0
1
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
1
1
0
0
0
0
0
0
0
1
2
0
0
3
2
0
0
1
0
2
0
2
0
2
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
2
2
0
1
1
0
0
0
0
0
2
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
1
2
1
0
0
2
0
1
0
0
2
0
0
0
2
2
0
0
1
0
1
0
2
2
0
1
0
1
1
0
3
0
0
3
0
2
5
0
0
0
0
2
0
1
1
0
0
0
0
2
0
2
0
0
0
3
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
1
2
0
2
2
0
0
1
1
0
1
1
0
2
2
0
0
1
1
2
0
0
2
0
0
1
0
2
0
1
0
1
0
1
0
3
1
0
0
0
0
0
1
2
0
0
2
2
2
0
1
0
0
2
1
2
0
0
0
0
0
0
0
2
0
0
1
1
0
0
2
0
0
0
0
1
0
0
0
0
3
0
2
0
2
1
0
0
0
1
1
2
1
0
0
1
0
1
1
0
1
0
0
2
0
0
2
2
3
0
0
0
0
2
2
1
0
0
0
0
0
4
0
0
2
1
0
0
1
0
1
0
0
0
1
0
0
2
0
1
0
0
0
2
0
0
1
2
0
1
0
0
0
1
0
2
0
0
1
2
0
0
0
1
2
1
0
2
1
2
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
3
0
1
2
2
2
2
0
0
1
0
0
0
2
2
2
1
0
2
2
0
0
2
2
0
1
1
0
2
0
0
1
1
0
2
2
0
1
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
2
3
0
0
0
0
2
0
0
2
2
1
0
0
0
0
1
0
3
0
1
0
2
0
1
0
0
2
1
1
1
0
2
0
0
1
0
0
0
0
1
0
2
0
1
0
2
0
0
2
0
1
1
0
2
0
1
1
2
0
0
0
0
0
2
1
0
0
1
0
0
2
0
0
2
2
0
0
2
2
1
0
1
1
0
0
1
0
0
2
0
1
1
1
0
1
0
2
0
0
0
2
0
0
0
0
2
1
0
0
1
2
0
0
0
0
0
0
1
4
0
0
0
2
0
0
0
0
1
0
1
2
1
0
1
0
2
0
0
1
0
0
1
0
2
0
2
0
0
2
1
2
1
0
0
1
0
0
0
0
0
1
0
0
1
2
0
0
1
0
0
2
0
0
1
0
2
0
2
1
1
2
2
2
2
0
0
0
0
1
1
2
0
2
0
1
1
0
0
0
1
0
1
0
0
3
0
0
0
0
0
0
0
3
0
1
0
0
0
0
2
0
2
1
1
1
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
2
2
0
1
0
2
0
0
0
0
0
0
2
0
0
0
1
3
1
2
0
2
0
0
0
0
2
1
0
1
3
0
0
2
0
0
0
0
0
2
1
0
0
0
1
2
0
1
1
1
0
0
1
0
0
2
1
1
2
1
2
1
0
1
0
1
0
0
0
0
1
0
0
1
2
2
0
1
2
1
0
0
0
0
1
0
0
0
0
0
2
1
1
0
0
1
3
0
0
2
0
1
0
1
1
2
0
0
1
2
0
0
0
0
0
2
0
0
1
0
2
1
1
0
0
0
0
2
0
1
0
0
0
2
2
0
0
0
1
0
1
0
0
1
0
0
0
0
2
0
2
0
1
1
0
0
0
0
0
1
0
1
0
0
2
1
0
0
1
1
0
0
1
0
0
2
0
1
0
0
0
3
0
3
0
0
0
2
0
0
0
1
0
2
0
1
1
0
0
0
0
0
0
0
2
2
1
2
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
1
0
1
0
1
0
0
0
0
2
0
2
0
0
0
2
0
1
0
0
0
1
0
2
0
0
0
0
0
2
2
0
0
0
0
0
2
0
2
1
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
1
2
1
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
4
0
0
0
3
0
0
0
2
0
2
0
0
2
0
0
2
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
2
0
0
2
1
1
1
0
0
0
2
1
0
2
0
0
0
2
2
0
0
0
1
1
0
1
2
0
0
0
2
0
2
2
0
2
0
0
0
2
0
0
1
0
0
1
2
0
0
1
3
0
0
0
1
0
0
0
2
1
2
0
1
1
0
0
0
2
2
0
1
0
2
1
0
0
2
0
0
2
0
2
0
0
1
1
0
1
2
0
1
1
1
0
0
0
0
0
0
0
0
2
1
0
1
2
1
0
0
0
0
0
0
2
2
2
0
3
1
1
0
1
0
0
0
2
0
2
1
0
0
2
2
1
0
0
2
2
0
0
0
0
0
0
1
2
2
0
0
0
1
1
1
0
1
0
0
2
1
0
0
0
1
1
0
1
0
1
1
2
0
2
0
0
0
0
0
1
0
1
0
2
2
1
0
1
1
2
0
0
1
0
0
1
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
1
3
2
1
0
0
0
0
0
2
0
0
0
1
1
0
2
2
2
0
2
1
0
0
0
0
0
0
0
1
1
1
0
1
0
1
0
0
0
1
0
0
2
0
2
1
0
0
1
0
0
0
0
2
1
1
0
0
0
1
1
0
0
2
0
0
1
0
2
0
0
2
2
0
2
2
0
0
1
2
0
0
0
2
0
0
0
3
0
0
2
2
0
2
0
0
2
0
1
0
4
0
0
1
1
1
2
1
2
1
0
2
0
1
2
0
1
0
0
1
0
1
2
0
2
1
0
1
0
2
1
0
5
2
0
0
2
0
0
0
1
0
0
1
2
0
0
0
3
0
1
0
0
2
0
0
1
2
0
0
0
0
0
2
2
0
0
0
2
0
2
0
2
0
0
0
1
2
1
0
0
2
2
0
0
0
0
0
2
0
1
0
0
0
1
0
3
0
2
0
0
0
0
2
0
3
0
1
0
4
1
2
0
2
0
0
1
0
2
2
1
0
0
2
2
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
2
0
0
0
1
1
1
0
0
2
3
0
0
1
0
1
0
2
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
2
0
2
0
0
0
0
0
2
0
1
0
0
2
0
0
3
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
2
0
0
0
2
2
0
0
0
0
2
2
0
1
0
0
0
0
0
0
2
1
0
2
1
0
2
0
1
1
0
0
0
0
0
0
0
1
0
1
1
0
0
1
2
0
0
1
0
0
2
1
0
1
1
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
1
0
1
0
0
1
0
0
0
2
2
0
3
2
2
1
1
2
0
5
0
1
0
0
1
0
0
2
2
0
2
0
0
0
0
1
0
1
1
1
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
3
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
1
2
2
0
0
0
1
0
0
3
1
1
2
1
0
2
0
0
0
1
0
1
0
0
0
1
0
2
0
1
0
1
0
1
2
2
1
3
2
1
0
0
1
0
0
1
0
1
0
1
0
2
1
0
0
0
2
1
0
0
0
2
0
1
0
2
0
0
0
1
2
1
0
4
0
1
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
2
2
0
0
0
2
0
1
1
0
0
1
0
0
2
2
1
1
2
0
1
1
2
0
0
0
2
0
1
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
2
2
3
1
0
1
0
1
0
0
2
1
2
0
2
0
1
0
2
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
1
0
0
0
1
0
2
1
0
0
1
0
2
1
2
2
2
0
1
2
0
0
0
0
1
0
2
1
0
0
0
0
1
0
1
2
2
0
0
0
2
1
0
0
1
1
1
0
2
0
0
0
0
0
0
0
2
1
0
2
0
1
1
0
1
1
1
0
0
0
2
0
0
0
1
2
1
0
0
1
0
0
2
0
0
0
2
2
2
0
0
1
2
0
2
1
0
0
0
1
0
2
0
1
0
0
2
1
1
0
0
0
2
0
0
0
2
2
0
1
1
0
2
0
1
0
0
0
1
2
0
0
2
0
0
1
0
1
0
3
1
0
0
0
1
2
0
2
1
0
1
0
1
0
2
0
0
0
0
2
1
0
0
0
0
1
0
1
0
0
1
0
1
0
2
0
0
0
2
0
0
0
1
0
2
0
0
3
1
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
1
2
2
0
0
0
2
0
0
2
1
0
0
0
0
1
1
0
1
0
0
1
0
0
0
1
2
1
1
2
1
2
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
1
1
1
0
0
0
1
0
3
0
0
0
0
0
1
0
0
2
0
1
0
0
0
2
1
1
1
0
0
0
1
0
0
2
2
0
3
1
1
0
0
0
0
0
1
0
0
2
0
1
0
0
1
0
0
2
0
1
0
0
0
1
1
0
0
1
1
0
0
1
1
0
2
0
1
0
1
1
0
0
3
0
2
1
1
1
0
0
2
0
0
2
0
0
1
2
0
2
0
0
1
0
0
2
1
0
2
1
0
1
1
1
0
1
0
1
1
1
2
0
0
1
1
1
0
0
0
0
0
2
0
0
0
1
2
0
3
2
0
0
2
0
0
0
1
0
1
1
0
0
2
0
2
0
0
1
0
0
1
0
0
2
0
0
2
0
2
0
0
0
1
0
1
0
0
1
0
1
0
1
0
1
0
0
3
2
0
1
1
0
0
1
2
0
0
0
1
0
1
0
0
1
0
2
2
2
1
2
0
3
0
0
0
0
0
2
0
3
2
1
0
2
0
1
0
1
1
2
2
0
1
2
1
0
0
0
4
1
2
1
2
1
1
0
0
0
2
0
0
0
1
0
1
0
1
0
0
0
0
2
0
0
1
0
0
0
0
1
2
1
1
1
0
0
1
0
0
2
2
0
0
4
0
1
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
2
1
0
1
0
0
0
0
0
0
0
0
0
2
2
0
1
1
2
2
2
0
0
0
2
1
0
0
2
0
0
0
1
1
3
1
1
0
1
0
0
0
1
0
0
1
1
2
0
1
0
0
1
1
0
2
2
0
0
0
2
0
0
1
2
0
2
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
1
0
0
0
4
1
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
3
1
0
0
1
0
2
1
0
2
1
2
0
2
1
0
1
0
2
0
0
0
0
3
0
0
2
0
1
1
1
0
1
0
1
0
2
0
1
0
0
0
1
0
2
2
1
2
1
2
0
1
1
3
0
0
0
1
1
0
1
2
0
0
1
1
0
2
5
3
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
1
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
2
0
1
0
0
4
2
1
0
0
0
2
1
0
0
0
2
2
0
0
0
0
1
1
1
0
0
2
1
1
0
1
0
1
0
1
0
0
0
2
0
0
0
1
1
0
3
2
0
2
1
0
0
0
0
2
1
1
0
0
1
1
0
0
1
2
0
0
1
2
2
0
0
1
0
0
0
2
0
2
1
1
0
0
1
0
0
2
0
2
1
0
2
2
2
0
2
2
0
0
0
0
0
2
0
1
1
0
0
0
2
1
0
0
0
0
0
1
0
1
0
1
1
1
0
0
1
0
2
1
1
1
0
2
1
1
0
0
0
0
3
2
0
0
0
0
1
0
0
2
1
0
0
2
2
0
2
0
1
0
2
0
0
2
1
1
1
0
0
0
2
2
3
1
2
1
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
2
0
1
2
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
2
1
0
0
0
0
1
0
2
0
0
0
1
2
0
2
1
2
0
0
1
0
1
1
2
0
1
0
2
1
1
0
1
0
0
0
0
0
2
3
0
0
0
0
0
1
0
0
0
1
0
1
0
2
0
1
2
0
0
0
2
2
0
0
0
1
2
1
1
0
2
2
0
0
2
2
0
3
1
0
2
0
1
4
1
1
0
0
2
2
0
2
0
0
2
0
0
0
2
0
2
0
0
1
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
2
0
2
1
3
0
0
1
2
3
0
0
0
0
0
0
0
2
0
0
0
0
3
0
2
2
0
5
0
0
0
0
0
1
1
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
2
1
2
0
2
1
2
0
1
2
1
1
0
0
0
0
0
0
2
0
0
0
0
1
1
0
2
0
0
0
1
1
0
0
0
3
2
2
0
1
0
0
3
0
0
0
0
0
0
2
0
0
1
2
0
2
0
2
0
2
0
1
1
0
1
1
1
0
1
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
1
2
0
1
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
1
1
0
0
0
4
1
2
2
1
0
0
2
0
0
0
0
2
0
1
1
0
2
0
0
1
2
0
0
5
2
1
0
0
1
0
0
3
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
1
2
0
0
1
0
0
1
1
0
3
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
2
0
1
0
1
1
1
2
0
0
1
0
0
1
1
1
1
2
0
1
2
0
0
1
2
2
0
0
0
2
0
0
1
0
0
0
1
0
0
1
0
0
0
2
0
1
0
2
2
1
1
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
5
0
0
1
0
4
0
0
0
1
1
0
2
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
2
0
0
1
1
2
0
0
0
0
0
1
3
0
0
0
2
2
3
2
1
0
2
1
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
2
0
0
1
2
0
0
2
0
0
0
2
1
0
0
1
0
0
3
0
0
1
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
2
0
1
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
1
0
2
1
0
0
1
1
1
0
0
0
2
0
0
0
2
2
2
3
0
2
2
1
2
0
0
0
0
0
3
0
3
1
0
1
0
1
2
0
0
1
0
1
0
1
1
0
0
0
1
1
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
2
0
2
0
0
0
0
0
2
0
2
1
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
1
0
0
0
0
2
2
0
2
0
0
2
0
0
0
1
0
0
1
0
2
0
2
2
1
1
1
1
1
1
0
1
1
0
1
0
0
1
0
1
0
2
0
0
0
0
1
1
1
0
0
2
1
1
0
1
2
2
0
1
0
3
2
0
0
1
1
1
0
0
0
2
0
0
0
0
0
0
0
2
1
1
0
1
1
0
2
0
0
0
1
5
0
2
2
2
1
0
2
0
3
0
2
0
0
0
0
2
1
0
3
0
1
0
0
1
0
1
0
2
0
0
0
0
1
0
2
0
0
0
1
0
0
0
2
2
1
0
0
0
2
1
4
2
0
1
1
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
1
0
0
3
1
0
0
0
0
0
1
2
0
1
0
0
0
2
2
0
1
2
0
1
0
0
0
1
0
0
0
1
3
0
1
2
0
2
2
1
0
0
0
2
1
0
0
0
0
1
2
1
1
1
1
0
2
0
0
0
0
0
0
2
0
0
1
0
0
2
2
1
1
0
1
1
0
2
0
0
0
0
0
6
0
1
0
1
0
3
0
0
0
1
0
1
1
1
0
2
0
2
2
0
2
2
2
0
0
1
2
1
0
0
0
1
0
0
0
0
0
3
0
0
1
0
0
2
0
1
2
0
0
1
2
0
0
2
2
1
0
2
0
2
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
1
0
2
1
0
1
2
0
1
0
1
0
2
0
0
2
1
1
0
2
1
0
1
0
0
1
1
0
1
2
0
0
1
1
0
0
0
2
1
2
2
0
0
2
0
1
0
2
2
0
0
0
1
2
1
0
1
1
1
0
0
0
0
2
2
1
0
0
7
0
1
1
2
6
2
1
5
0
1
0
1
2
0
0
0
0
0
1
0
1
1
0
1
1
1
0
0
1
2
0
0
0
0
0
0
0
1
0
0
3
1
0
1
1
0
0
0
1
0
1
1
0
0
0
0
0
1
0
1
1
1
0
0
0
0
1
0
2
0
0
2
0
1
0
1
1
0
0
0
0
1
0
2
1
0
2
2
1
0
0
1
0
2
0
1
0
0
0
0
1
1
0
2
0
2
0
1
0
0
1
0
0
0
0
1
1
1
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
1
2
1
1
0
3
0
0
2
0
1
0
2
2
1
2
1
1
0
0
2
0
2
1
0
1
2
0
0
0
0
1
2
2
1
2
0
1
1
2
2
1
0
1
2
1
0
0
0
1
1
0
0
1
2
0
0
0
2
0
0
0
2
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
2
0
1
2
2
0
0
0
0
0
2
1
0
2
0
2
0
1
1
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
2
1
1
0
0
0
1
1
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
2
0
0
2
0
0
1
1
0
0
1
2
3
0
0
0
0
1
1
0
1
0
0
0
1
2
0
0
0
0
0
0
4
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
2
0
0
2
0
0
1
1
1
0
0
1
0
0
0
0
2
0
1
2
0
1
0
2
1
0
0
0
0
2
1
1
0
2
1
0
0
3
0
0
0
0
2
4
0
0
1
0
1
0
2
1
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
1
1
0
0
2
2
0
1
0
0
1
0
1
0
1
0
0
2
0
0
0
1
0
2
2
2
2
0
0
0
1
0
0
3
1
0
0
0
0
2
1
0
0
0
2
0
2
1
0
0
1
2
1
0
0
0
3
0
0
2
1
0
0
1
1
0
10
2
1
0
0
0
0
0
2
0
0
0
1
0
3
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
1
0
2
0
0
0
0
0
1
0
1
0
2
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
1
2
0
0
1
0
2
1
0
0
0
0
1
0
2
0
0
1
0
2
2
0
0
0
1
2
4
2
1
0
0
0
0
0
0
0
0
1
3
0
1
0
1
0
1
0
2
1
0
0
0
0
0
0
2
1
0
1
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
2
0
2
1
0
0
0
0
1
2
0
0
0
2
0
0
0
2
0
0
0
0
1
0
2
0
1
0
0
1
1
1
1
0
0
0
1
1
2
1
1
1
2
2
0
1
2
2
1
0
0
0
0
1
1
1
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
2
1
0
0
1
0
0
0
0
1
0
0
2
1
1
1
0
0
0
2
0
0
2
0
1
0
1
0
0
2
0
1
1
2
1
2
0
0
2
0
0
2
2
2
0
0
2
1
0
0
2
0
2
0
1
0
1
1
2
2
1
0
2
0
0
0
0
1
1
0
0
1
0
0
2
1
0
0
0
1
0
1
0
1
1
2
1
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
1
1
1
0
1
0
0
0
0
1
0
0
2
0
2
0
1
2
0
0
1
0
0
1
4
1
1
1
4
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
1
0
0
1
2
0
1
2
0
1
2
0
0
0
1
2
1
1
0
1
1
1
0
1
2
1
1
2
0
1
0
0
1
1
2
1
2
0
1
2
0
1
1
2
0
1
0
0
1
2
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
2
1
1
0
1
0
0
2
0
1
1
0
1
1
1
0
1
0
0
0
0
0
1
0
2
1
1
2
1
0
1
2
2
1
2
0
1
6
0
1
0
0
1
1
1
1
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
3
0
0
1
0
0
1
0
0
0
0
2
1
5
0
0
0
0
0
0
1
1
1
2
0
0
2
2
1
1
0
0
0
0
0
0
1
0
1
2
1
0
1
1
1
0
0
0
1
2
2
0
2
0
0
0
1
0
0
1
0
0
0
4
1
3
0
0
0
0
1
2
1
0
1
0
2
0
1
0
0
1
3
2
2
0
1
1
0
1
0
0
0
0
1
2
1
1
1
2
1
1
2
1
2
0
0
0
0
2
0
0
0
1
0
2
0
0
2
0
1
0
0
0
0
1
2
0
1
0
0
0
1
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
1
1
0
1
0
1
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
2
2
0
1
0
2
2
0
2
0
0
1
1
0
0
0
0
1
0
0
0
0
2
0
0
1
2
1
0
1
2
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
2
1
2
0
0
1
1
0
0
0
0
0
2
2
0
2
0
1
0
2
2
0
1
2
1
0
1
2
0
0
1
2
2
0
1
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
2
1
0
0
1
1
1
0
0
2
0
0
0
0
0
2
1
1
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
1
2
0
0
1
0
1
0
0
1
2
2
1
0
1
1
1
1
0
1
0
0
1
0
1
1
0
2
0
1
0
1
0
2
2
2
1
2
0
0
2
0
0
1
1
0
1
0
3
0
0
0
2
2
0
1
0
0
2
1
0
2
0
1
1
1
1
1
0
0
0
2
0
0
1
1
0
0
0
0
2
0
2
0
1
1
1
0
0
0
2
1
2
3
0
1
0
1
0
0
0
1
0
0
0
0
0
2
1
0
2
0
0
2
0
0
1
0
0
2
1
0
1
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
2
0
0
2
0
0
0
1
0
1
1
2
0
0
0
0
0
0
0
1
1
0
3
0
0
1
0
0
0
1
2
1
0
2
0
0
0
2
0
0
0
0
0
0
2
0
1
0
2
1
0
2
2
0
0
1
0
0
0
0
0
1
0
0
1
0
1
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
4
2
0
0
0
1
0
0
0
1
0
2
0
0
0
1
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
2
1
1
2
1
0
2
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
3
0
1
0
2
2
2
1
2
0
0
3
0
0
0
0
0
0
0
1
0
0
0
1
1
2
2
1
2
1
0
0
0
0
2
1
0
0
3
1
0
1
2
1
0
0
0
0
2
0
0
0
0
0
3
1
2
0
0
0
1
2
0
1
2
1
2
0
0
1
0
2
0
2
0
0
1
0
0
0
0
2
0
2
0
2
0
0
2
2
1
0
2
0
1
1
0
0
1
1
0
0
0
2
0
1
1
0
0
0
0
2
0
2
2
0
0
0
0
0
2
1
2
2
0
2
2
0
0
2
0
1
0
0
2
0
0
0
0
0
0
1
1
2
1
0
0
0
0
0
0
0
2
2
0
1
0
0
1
0
0
2
1
0
2
0
2
1
1
4
1
1
1
1
3
2
1
0
2
1
0
2
1
1
1
0
2
0
1
0
0
3
0
0
0
2
1
1
0
0
1
2
0
0
1
0
0
1
2
3
1
2
0
0
0
1
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
1
2
1
0
0
2
0
0
0
2
0
1
1
1
1
4
0
0
0
0
2
0
0
1
0
0
2
0
0
1
0
1
2
1
1
0
1
1
0
0
0
0
1
2
4
1
0
0
0
0
0
1
2
0
0
0
2
0
1
1
0
0
0
0
2
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
1
2
0
0
0
0
0
2
2
0
0
0
3
0
0
0
0
1
0
0
0
0
0
1
2
0
0
1
0
0
0
5
0
0
0
0
1
0
1
0
0
1
1
1
2
1
0
1
0
0
0
2
0
0
0
0
0
1
1
1
0
0
0
0
2
1
0
1
0
0
0
2
0
2
1
0
0
1
1
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
2
0
0
2
1
2
2
0
1
6
2
2
2
0
2
2
1
2
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
1
1
1
0
0
0
1
0
1
2
1
1
0
1
1
0
0
0
0
3
2
0
2
0
2
1
1
0
1
0
1
0
1
0
1
1
2
0
0
2
0
0
1
0
1
0
1
0
1
1
0
0
0
0
2
0
2
0
1
1
0
2
0
0
2
0
0
1
2
0
4
1
0
1
1
2
2
1
0
1
0
0
0
0
3
0
2
0
0
2
0
0
0
0
0
0
0
1
0
2
1
0
0
2
2
0
2
2
0
0
0
1
0
0
0
1
0
0
0
1
1
0
2
1
0
3
5
0
0
0
2
2
4
1
0
0
2
2
0
0
0
3
0
0
0
2
1
1
2
0
2
2
0
0
0
0
2
3
0
1
2
1
0
1
0
1
1
0
0
1
1
0
2
2
1
0
2
0
1
1
2
0
2
1
0
0
1
0
0
2
0
0
1
0
0
0
0
4
2
0
0
1
2
0
2
0
1
1
0
2
0
0
0
0
0
0
2
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
1
1
2
0
0
0
1
1
1
0
2
0
2
0
1
0
1
0
0
0
1
0
0
0
0
2
2
0
1
2
0
0
0
1
0
0
0
1
1
0
1
1
0
0
2
1
1
0
1
0
0
0
1
0
0
2
0
1
0
0
0
0
2
0
3
1
1
0
2
1
0
0
1
1
3
0
0
0
0
2
0
0
0
0
3
2
0
0
1
0
2
3
0
2
0
2
1
1
0
1
1
0
0
2
0
1
0
1
0
1
0
1
0
0
0
2
0
1
1
0
0
1
0
2
3
0
0
0
0
0
2
2
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
1
1
2
0
0
0
2
0
0
2
1
0
0
0
2
1
0
1
0
0
2
0
0
0
1
0
0
0
4
0
0
0
0
1
0
2
0
0
0
2
1
0
2
0
0
1
2
2
0
3
0
0
0
0
1
0
0
1
1
1
2
0
0
0
2
0
1
2
0
0
1
1
0
0
0
0
2
0
0
0
2
0
0
2
1
1
0
0
2
0
2
2
0
1
1
1
0
2
1
1
0
0
0
0
0
0
0
0
0
2
1
2
0
1
0
0
2
1
0
0
0
2
2
2
2
2
0
2
1
0
0
0
2
1
0
0
3
2
0
0
2
0
3
1
0
1
0
0
0
0
2
0
2
0
0
0
0
5
1
1
2
0
0
2
1
0
1
0
0
0
2
2
1
0
1
0
0
2
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
2
3
1
1
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
3
1
2
1
1
0
2
3
0
2
2
0
0
1
0
0
2
1
1
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
1
1
1
0
0
2
0
1
0
1
0
0
0
0
0
0
2
0
0
1
0
0
2
2
2
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
1
0
0
1
1
2
1
0
0
0
0
0
4
0
0
0
6
1
2
0
1
0
0
1
1
1
1
1
0
1
0
2
2
1
0
0
0
0
0
2
1
0
2
0
2
2
1
0
0
0
0
1
0
0
1
0
0
0
2
1
0
1
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
1
2
1
2
1
0
1
0
0
2
1
0
0
0
0
0
2
0
1
2
0
0
2
0
0
0
0
0
0
0
2
1
0
0
1
0
1
1
0
0
0
0
2
0
0
0
0
2
0
0
1
2
1
2
0
0
1
0
2
0
2
1
0
0
1
0
0
0
1
1
1
1
1
0
1
2
0
2
0
2
0
0
1
0
2
2
0
1
1
0
2
0
0
0
1
0
2
0
1
1
0
2
0
1
0
0
1
2
1
0
0
0
1
2
1
0
0
0
2
0
2
0
0
2
0
0
0
0
1
3
1
0
1
0
0
0
2
2
1
0
2
0
0
0
0
3
0
2
1
0
2
0
1
0
2
2
2
0
0
0
0
0
1
0
0
0
0
0
0
1
2
2
0
0
0
1
0
0
0
2
0
0
1
2
0
0
2
0
0
0
1
0
1
0
0
1
0
0
0
2
0
2
1
0
2
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
1
1
2
0
1
0
1
0
2
2
0
0
1
0
1
1
2
1
0
2
2
0
0
1
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
2
2
1
0
2
2
0
0
0
1
2
1
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
1
0
0
1
1
2
0
1
0
2
2
0
0
0
2
0
0
2
0
1
0
1
0
3
0
0
1
2
1
0
1
1
0
0
0
2
0
0
0
0
1
1
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
2
1
0
0
2
0
0
0
1
0
0
0
0
2
2
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
2
2
2
2
0
0
0
0
2
1
2
0
2
0
0
0
1
0
2
0
1
2
1
2
2
0
2
0
2
0
0
2
2
1
2
1
1
0
0
1
1
0
2
2
0
0
0
0
0
2
1
1
0
1
1
0
2
1
2
1
0
0
2
0
0
0
0
0
1
0
1
2
0
1
1
0
0
1
0
0
0
0
0
0
2
1
1
1
1
0
2
0
0
2
2
0
1
0
1
1
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
4
0
0
0
1
0
0
0
1
2
0
4
1
0
2
0
0
2
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
1
1
2
1
0
0
2
1
0
0
1
0
0
0
0
2
0
0
1
2
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
2
3
0
1
0
1
0
2
0
0
1
1
0
2
2
2
2
0
1
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
1
0
0
2
2
0
2
0
0
1
1
0
2
2
0
0
1
0
0
1
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
1
0
1
2
0
1
1
2
0
1
1
1
0
1
0
0
2
0
0
0
2
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
1
2
0
1
2
1
0
0
2
0
2
1
1
1
0
2
1
1
2
0
1
0
2
1
0
1
2
0
2
0
0
1
1
0
0
0
0
1
0
0
1
2
2
0
2
2
0
0
0
1
1
2
0
0
1
0
2
2
1
1
2
0
2
1
0
0
2
0
0
2
0
0
2
0
0
3
1
0
0
1
2
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
1
0
1
0
0
0
0
0
2
1
0
1
2
1
0
0
0
0
0
0
2
2
0
0
1
2
0
0
0
1
1
0
0
1
0
0
0
2
0
3
1
0
5
2
2
0
0
0
0
0
0
0
0
0
0
1
2
0
1
1
2
1
1
2
0
0
0
0
2
2
1
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
1
1
2
1
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
2
1
0
1
0
0
0
0
1
5
1
0
1
0
3
1
1
0
2
0
0
0
0
0
1
1
0
1
0
0
2
2
0
2
2
0
0
0
0
2
0
1
2
0
0
1
0
2
0
0
1
1
0
1
0
0
2
2
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
3
0
2
1
1
2
3
1
0
0
2
0
0
1
0
0
2
0
0
1
0
3
0
0
0
2
2
0
0
0
2
0
0
1
2
0
0
0
2
0
2
2
0
1
1
0
1
0
2
2
0
2
0
1
0
1
0
2
0
0
0
0
3
0
0
0
0
1
0
0
1
0
2
1
0
2
0
2
2
1
1
0
1
3
1
0
1
0
0
0
3
2
0
1
0
0
1
1
4
0
2
2
2
0
0
0
0
0
0
0
1
1
1
2
1
0
3
1
0
1
0
0
0
1
0
0
0
2
0
1
0
0
2
2
1
0
1
1
0
2
0
1
2
0
2
0
0
0
1
0
0
2
0
1
0
1
0
2
2
2
2
0
0
0
0
1
1
1
0
0
0
0
0
0
0
2
2
2
0
2
0
0
0
1
2
0
0
1
1
1
0
0
0
0
1
3
0
1
0
0
2
0
1
0
0
1
0
2
1
0
1
1
2
1
0
3
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
1
2
2
1
0
0
2
0
0
0
0
1
1
0
2
0
0
1
0
0
0
0
0
2
0
3
2
2
2
1
0
1
2
0
0
0
3
0
2
1
0
0
0
0
2
1
1
0
1
0
1
0
0
0
0
1
2
1
2
1
2
1
2
0
0
2
2
1
0
1
0
0
1
0
1
0
0
2
0
0
0
0
0
0
1
2
1
0
0
0
2
0
0
0
0
0
0
1
1
2
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
2
1
1
1
1
1
0
1
0
1
0
0
0
0
3
1
0
1
1
0
0
0
0
1
0
1
1
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
2
0
1
0
0
1
0
0
0
2
0
0
1
0
0
1
2
1
2
0
2
2
1
1
0
0
2
2
2
0
0
2
0
2
1
0
0
2
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
2
0
0
2
2
0
2
0
0
1
1
0
2
1
0
1
0
1
0
1
0
0
0
1
0
2
0
0
2
1
0
1
0
1
0
2
0
1
0
2
1
0
1
2
0
2
2
1
0
8
1
0
0
2
1
0
1
0
2
3
1
0
2
0
2
2
0
1
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
2
2
2
2
2
0
2
0
1
1
0
1
1
0
0
0
3
0
0
2
1
1
2
0
1
0
1
0
0
0
1
0
1
5
0
0
0
2
2
1
0
1
1
0
1
0
2
0
2
0
1
2
0
0
0
1
0
0
1
2
1
1
0
1
2
0
0
0
0
2
0
1
0
0
1
0
2
0
0
2
0
1
0
1
0
0
0
0
1
0
1
2
0
0
1
2
0
0
0
1
1
0
1
0
1
1
0
0
2
2
1
0
1
0
1
0
0
2
0
1
0
1
0
2
0
0
2
0
2
2
0
1
2
0
2
0
2
0
0
1
0
1
0
2
1
0
0
0
0
1
0
0
0
0
0
0
2
1
1
0
0
0
1
0
2
0
4
2
1
1
0
1
1
0
1
1
0
0
1
2
2
2
9
2
0
3
0
0
2
0
0
0
2
0
1
0
0
1
2
0
0
1
2
2
1
0
0
0
0
2
0
2
1
0
2
0
0
1
0
0
2
1
0
0
0
0
0
3
0
1
0
1
0
0
0
0
1
0
2
0
0
0
2
2
2
0
0
1
0
0
1
0
1
0
1
1
1
0
2
0
1
0
0
1
0
1
1
1
0
2
0
0
1
0
1
2
1
1
0
0
1
2
0
2
0
0
0
0
1
2
0
2
1
1
0
0
2
2
1
0
1
0
0
0
0
0
0
1
1
3
0
0
0
0
0
2
0
2
1
2
0
1
0
0
2
1
2
0
0
1
1
0
2
0
1
1
1
3
1
0
0
0
1
1
1
0
0
1
0
0
0
1
1
0
0
0
0
1
0
2
0
0
0
2
0
2
0
1
1
0
0
0
2
0
0
1
1
0
2
0
2
0
0
0
0
0
0
0
5
0
2
0
0
1
3
1
2
2
0
0
0
1
1
0
1
0
0
0
2
1
0
0
0
1
1
1
2
1
1
0
1
0
0
2
0
0
0
1
0
2
1
0
0
0
0
3
0
0
0
1
2
0
0
2
0
0
1
2
0
3
1
0
2
0
1
1
1
0
2
2
0
1
0
1
0
2
2
0
0
2
0
0
0
0
0
0
1
0
0
1
1
1
2
1
0
1
2
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
2
1
0
0
0
0
2
1
0
0
2
0
1
0
0
2
0
0
1
0
0
1
2
0
1
1
0
0
0
0
0
0
1
0
2
0
0
0
0
2
1
1
0
2
0
0
2
0
2
0
0
1
1
1
1
0
0
0
0
2
2
2
2
0
0
0
2
1
0
0
1
1
0
0
0
0
3
0
3
1
2
1
2
2
0
0
2
0
2
1
0
0
1
1
2
0
0
0
2
1
0
1
0
2
2
0
0
0
0
0
0
1
0
1
0
2
2
0
2
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
1
0
1
1
1
1
2
3
1
1
0
0
0
0
0
0
1
1
0
0
1
6
2
1
1
1
2
1
2
1
0
0
0
0
1
0
2
1
1
0
1
1
0
1
0
0
1
3
1
2
0
0
1
0
2
0
0
1
2
0
0
0
0
1
2
0
0
0
0
2
2
0
0
0
1
2
0
1
0
1
0
0
1
0
0
1
2
0
2
0
0
0
1
0
1
2
0
0
0
1
2
0
1
0
1
1
0
0
2
1
0
0
0
0
2
2
0
0
1
0
1
0
0
0
0
0
0
0
1
2
1
0
0
1
0
0
0
2
2
1
0
2
2
0
0
0
3
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
1
1
1
0
1
0
0
0
1
0
2
2
0
0
1
0
1
1
0
0
0
0
1
2
0
2
0
1
2
2
0
0
4
1
0
0
0
0
1
0
1
2
0
0
0
1
0
2
0
0
0
0
0
2
0
2
2
2
1
1
0
0
1
0
0
2
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
1
1
0
0
0
0
2
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
1
2
1
0
0
0
2
0
1
1
2
0
0
0
1
2
0
0
0
0
0
0
0
2
1
5
0
0
2
0
0
0
0
1
0
2
1
2
0
2
0
1
0
0
2
1
2
0
0
2
0
1
1
1
0
0
0
0
0
0
1
0
2
0
0
0
0
1
2
3
1
0
0
2
0
2
1
0
0
0
0
1
1
0
2
5
0
0
1
0
0
0
0
2
2
1
0
2
0
1
0
0
1
0
0
0
3
0
1
0
2
2
0
2
1
0
2
0
0
0
0
0
1
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
2
2
0
0
1
0
1
0
0
2
2
0
1
0
0
1
2
0
0
1
0
2
1
1
0
2
2
0
1
0
0
0
0
0
0
1
0
0
3
0
2
1
0
2
2
2
2
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
1
0
1
2
2
0
0
0
0
2
0
1
0
0
0
2
0
0
0
3
1
0
1
0
1
2
0
1
0
0
1
0
2
0
0
1
1
2
2
0
0
1
1
0
0
0
2
0
0
2
0
0
1
1
0
1
0
0
0
0
1
1
1
1
1
0
0
0
0
2
0
0
0
0
0
1
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
3
0
0
1
0
2
2
0
1
0
1
0
2
2
1
0
2
0
1
2
2
0
0
2
0
1
1
0
1
0
0
0
0
1
2
1
2
0
0
0
1
0
0
0
0
2
2
0
0
1
1
1
0
2
0
1
0
0
0
0
0
0
2
1
3
1
1
1
1
2
1
0
1
2
0
1
0
0
2
0
2
0
1
2
0
0
1
0
0
2
1
1
1
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
1
2
1
0
0
2
1
0
0
0
0
2
0
1
0
0
1
0
0
1
0
0
0
0
0
0
2
2
0
2
2
0
0
3
0
0
0
2
0
1
0
0
0
2
0
1
2
0
0
0
0
0
2
0
1
0
0
2
1
0
0
3
0
2
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
1
0
2
0
0
2
1
7
0
0
0
1
2
0
1
1
2
2
0
0
3
3
0
0
1
0
0
0
0
2
0
0
2
1
0
0
1
0
0
1
0
2
1
2
0
0
0
1
0
2
1
0
0
2
0
1
0
0
0
0
1
2
0
1
0
0
1
0
0
2
0
1
1
0
2
2
0
0
0
0
0
0
2
2
0
0
0
2
1
2
0
1
0
1
1
0
1
2
0
0
0
0
0
2
0
0
1
0
1
2
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
2
1
2
2
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
2
1
2
0
1
1
2
0
0
1
1
0
0
1
0
2
0
0
0
0
1
1
2
2
0
0
2
0
2
1
0
2
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
1
0
0
2
1
2
2
0
1
2
2
1
2
4
0
0
2
2
0
2
0
1
2
0
0
0
0
0
0
0
0
0
1
1
2
0
2
0
0
1
0
1
2
1
0
0
0
0
2
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
2
1
2
1
2
2
0
0
0
1
2
1
2
0
0
0
0
0
1
2
1
0
1
1
0
0
1
0
0
0
2
0
1
0
1
2
0
0
0
1
0
0
2
0
2
1
0
0
0
0
0
1
1
1
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
5
1
0
0
1
0
0
0
2
2
0
0
0
0
0
2
1
0
0
0
1
0
1
0
0
0
0
0
2
1
2
0
0
1
2
1
0
1
0
0
1
0
1
0
0
0
0
2
2
0
2
0
0
0
0
1
0
0
0
1
2
1
0
0
0
0
0
0
0
1
1
0
1
0
1
2
0
1
2
0
1
1
2
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
3
2
2
0
2
1
0
2
0
0
0
0
0
0
0
0
1
2
0
1
0
1
0
0
0
1
1
2
1
1
1
0
1
2
1
2
0
0
1
2
0
2
2
0
2
0
0
0
0
2
0
2
3
0
1
3
0
2
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
2
1
0
0
0
0
1
0
0
1
0
1
0
0
2
1
0
3
2
1
0
2
0
0
0
1
2
2
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
2
0
1
2
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
1
1
2
1
3
0
0
1
1
0
2
2
1
0
0
2
0
1
1
0
0
2
0
0
1
0
0
2
0
0
1
0
1
1
1
2
0
0
0
1
0
0
2
0
1
0
1
2
0
1
1
0
2
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
4
2
1
0
0
0
1
0
0
0
1
2
2
1
2
1
0
2
0
2
7
0
1
0
1
2
1
0
0
0
2
0
0
0
0
1
0
1
2
2
2
1
0
2
0
0
0
1
2
0
1
1
2
0
1
0
1
3
0
1
0
0
0
1
2
0
0
0
1
0
0
1
0
0
1
2
0
0
2
0
0
0
0
0
1
1
0
2
0
1
0
2
0
0
0
2
0
0
0
1
0
1
0
0
2
0
0
2
0
2
0
0
0
0
0
0
2
0
1
3
0
0
0
0
1
2
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
2
0
0
1
0
0
0
3
1
1
0
1
1
1
0
1
1
2
1
0
0
1
0
0
0
2
1
3
0
0
0
1
1
0
1
0
0
1
1
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
2
1
0
2
0
0
1
3
0
2
0
0
0
0
0
2
2
0
3
1
0
0
0
1
0
1
0
2
0
1
0
1
1
2
0
0
0
1
0
2
0
0
0
0
1
1
0
2
1
1
0
1
0
1
2
1
2
1
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
2
0
0
0
2
2
0
0
0
0
0
1
0
2
0
1
1
0
1
2
0
0
0
1
2
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
1
0
0
0
2
2
1
0
2
1
2
2
0
0
2
1
2
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
1
1
1
1
0
4
1
2
0
0
0
2
0
0
0
0
0
1
0
1
1
0
1
2
0
2
0
0
0
0
0
2
1
0
1
0
1
0
1
0
0
2
0
4
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
1
0
0
2
0
2
0
1
1
1
0
2
0
0
0
2
1
1
0
0
1
0
0
0
0
0
0
0
0
3
0
3
0
0
1
0
1
0
0
1
0
0
1
0
2
2
1
0
0
1
0
1
2
0
2
0
0
0
0
0
0
0
1
2
2
0
0
1
1
2
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
2
1
0
1
1
0
1
0
1
1
0
0
1
0
1
0
0
1
1
0
1
0
1
0
1
0
1
2
0
1
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
2
1
1
2
0
0
1
2
1
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
1
2
0
0
0
2
4
0
0
0
2
1
0
2
2
0
1
0
0
1
1
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
1
2
0
2
0
2
0
0
0
0
0
0
0
1
0
1
2
2
2
0
0
0
1
0
0
1
0
0
1
0
1
0
2
0
0
0
0
2
1
0
2
2
1
0
0
3
0
0
0
0
0
0
2
1
1
0
0
0
0
0
1
2
0
2
3
0
0
0
1
2
0
0
1
0
3
0
0
0
0
0
3
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
2
1
0
0
1
2
0
0
0
1
0
2
0
2
1
2
1
2
0
0
0
1
0
4
2
2
0
1
0
2
2
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
2
0
0
2
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
2
2
0
2
0
2
0
2
2
0
1
0
2
1
2
2
0
0
0
0
0
0
1
1
0
0
0
2
2
1
0
0
0
3
0
0
0
0
2
0
1
1
2
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
1
0
0
1
0
2
0
1
0
1
1
0
2
0
2
0
0
0
0
0
1
2
1
0
1
0
2
0
0
1
0
0
2
0
2
0
0
2
1
0
1
2
2
2
0
0
1
2
0
0
1
0
0
0
0
0
2
0
0
1
1
0
1
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
3
2
0
2
2
0
0
0
0
0
0
2
2
2
1
0
1
0
0
0
0
2
0
0
0
1
0
2
2
3
2
2
0
1
0
0
2
2
2
0
0
0
2
0
2
0
1
0
2
1
1
0
0
1
2
0
1
1
0
0
1
0
0
0
0
2
0
0
2
0
1
0
0
2
0
0
2
2
0
0
2
0
2
1
0
2
1
3
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
2
0
3
0
1
2
2
2
0
2
0
1
1
0
1
0
0
1
0
0
1
0
2
1
1
0
1
0
0
0
0
2
0
2
0
0
1
1
0
0
2
0
0
0
1
2
2
0
0
0
0
2
1
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
1
1
2
1
2
1
1
0
1
1
1
1
0
2
0
0
0
1
1
1
0
0
0
0
2
0
1
0
1
0
0
0
3
0
1
0
2
2
0
1
0
0
0
0
0
1
0
1
1
0
1
0
1
2
1
1
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
2
1
1
2
1
0
0
2
1
0
2
0
1
0
1
0
0
0
1
2
1
1
1
1
0
2
0
1
0
1
0
0
1
0
1
2
1
1
0
0
1
1
1
0
2
0
0
1
0
0
2
0
1
0
0
0
1
0
2
1
0
1
0
0
0
0
0
0
2
1
0
2
0
0
1
0
1
0
2
1
0
1
0
0
0
0
0
0
0
0
2
3
1
2
0
1
0
2
0
0
0
1
0
2
2
0
1
1
0
0
0
1
2
2
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
2
0
0
1
2
1
2
0
1
0
0
1
1
0
1
1
0
1
0
0
2
0
1
2
0
2
2
2
2
2
0
1
0
2
0
0
0
0
2
0
0
0
1
1
0
0
0
2
0
1
0
0
0
0
1
2
0
0
0
1
2
0
1
0
2
0
0
3
2
2
0
3
0
2
0
0
1
0
0
0
0
0
0
0
2
0
1
2
2
0
0
2
0
0
0
0
0
3
0
1
0
0
1
0
0
0
0
2
0
1
0
0
0
0
2
0
1
0
1
0
0
2
0
0
0
0
1
0
0
0
1
1
2
2
2
2
0
1
0
0
0
0
0
0
0
0
1
1
2
2
0
1
1
0
0
0
0
3
0
0
0
0
0
0
0
0
2
2
0
1
2
0
2
2
2
0
0
1
0
0
0
0
1
1
1
0
1
0
1
0
2
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
1
2
0
0
1
0
2
1
0
1
0
0
2
1
2
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
2
0
0
0
0
0
1
1
1
0
2
0
0
2
2
0
1
3
2
0
1
1
1
2
0
1
0
0
2
0
1
0
4
2
0
0
0
0
0
2
0
0
2
0
0
0
1
2
0
2
0
0
0
0
0
0
1
0
0
2
0
2
0
1
0
2
0
1
0
0
0
1
2
1
0
0
0
1
1
0
0
2
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
1
0
1
1
1
0
2
2
0
0
0
1
0
2
1
2
0
1
0
0
2
0
1
2
0
0
0
0
1
2
1
0
0
0
1
0
1
0
0
2
0
0
2
1
0
0
1
3
0
0
1
0
0
0
1
0
0
1
0
1
0
1
0
0
1
0
3
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
2
0
2
0
1
2
0
0
2
1
0
0
1
2
0
1
0
2
0
0
0
1
0
0
0
2
0
1
1
1
1
0
0
0
2
2
2
0
0
3
2
0
0
0
0
1
0
0
0
0
0
1
0
2
1
0
0
2
0
0
0
0
0
1
0
0
1
0
1
2
3
0
0
0
2
1
2
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
2
2
0
0
1
0
0
0
1
0
0
0
0
0
2
1
1
1
0
0
1
2
0
0
0
0
0
3
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
2
0
0
1
1
0
0
0
0
0
0
0
1
0
2
2
0
0
0
1
1
1
1
2
0
0
3
1
0
0
1
2
2
1
2
2
1
2
0
0
2
1
0
0
2
2
2
1
1
2
2
0
0
0
2
2
2
1
1
0
2
0
2
1
2
1
2
0
2
2
0
0
0
0
0
0
0
0
0
2
1
0
1
1
0
0
1
0
0
1
0
2
1
0
2
0
1
2
0
1
0
0
0
0
1
0
1
2
0
0
0
1
0
2
2
0
0
2
0
0
0
2
1
0
0
1
2
1
0
2
1
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
1
1
0
0
1
1
2
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
1
1
0
2
0
0
1
2
0
1
2
0
0
0
2
0
2
2
0
0
0
0
2
1
0
1
1
2
0
0
2
0
1
2
4
0
0
0
1
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
1
3
1
2
0
0
0
0
0
0
2
0
2
0
1
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
2
0
2
1
1
0
2
0
0
0
0
0
0
2
1
0
0
1
0
0
2
0
1
0
0
2
0
2
2
1
0
2
1
0
2
0
3
0
1
1
1
1
0
0
1
2
1
0
0
0
0
3
1
5
1
1
0
1
0
0
1
2
1
1
0
0
2
2
1
0
2
0
2
2
2
1
1
0
0
2
2
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
1
1
2
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
2
2
2
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
1
0
1
0
2
2
0
2
1
1
0
2
0
0
0
0
0
0
1
1
1
0
1
0
2
0
2
1
1
0
3
0
1
2
0
0
0
2
1
0
0
0
0
0
1
0
1
0
2
2
0
1
0
0
0
0
1
0
0
0
1
3
1
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
2
2
0
2
0
2
1
2
1
0
1
0
1
0
1
2
1
0
1
2
2
2
1
0
0
2
0
0
0
0
0
1
0
1
0
1
1
1
0
0
2
1
0
1
2
1
1
1
0
2
0
1
0
0
0
0
0
2
1
0
2
0
0
1
0
2
2
3
2
0
1
0
0
0
1
0
0
0
2
2
1
1
1
0
0
1
0
3
0
1
0
1
2
1
0
0
0
0
1
2
0
2
2
2
0
0
0
1
1
0
0
0
0
1
0
1
2
0
1
2
0
0
2
0
0
0
2
0
0
0
0
2
0
0
1
0
0
2
0
0
0
2
1
1
0
0
0
0
2
2
1
2
0
0
0
0
1
0
0
0
1
2
0
1
0
0
0
1
0
0
0
0
1
1
4
0
0
0
0
0
1
0
2
0
0
0
1
1
2
0
2
2
0
0
0
0
2
1
0
0
1
0
2
0
0
2
0
1
0
1
1
1
2
0
0
0
1
0
1
1
0
0
0
5
0
0
0
0
1
1
1
2
1
1
2
0
0
0
0
0
3
0
2
1
0
3
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
1
0
0
0
2
1
0
2
1
0
0
0
1
0
0
1
1
0
0
0
2
1
1
1
1
0
1
1
1
0
2
1
0
2
0
0
0
1
1
1
0
0
0
2
0
0
0
1
2
0
0
0
0
2
0
2
1
2
2
2
1
0
1
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
2
2
2
0
0
1
1
0
0
0
0
0
1
1
1
0
0
0
0
2
0
0
1
0
2
1
0
1
0
0
2
0
1
1
2
2
0
1
1
0
2
0
0
1
0
0
0
0
2
0
0
1
3
0
0
1
1
0
0
0
1
0
2
1
0
1
0
0
0
0
3
0
2
0
2
1
0
1
0
0
1
0
2
0
0
0
0
0
2
1
1
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
1
0
1
1
1
1
1
0
0
2
0
1
0
0
0
0
0
0
0
1
0
1
1
2
2
1
0
0
0
0
0
0
2
2
0
2
0
2
1
0
0
1
3
2
3
1
2
1
1
2
1
2
0
0
0
0
1
0
0
0
0
0
0
0
2
2
1
1
1
2
0
1
2
2
2
3
0
1
5
1
2
0
2
0
2
1
1
2
2
0
0
1
0
0
0
2
3
0
1
0
0
2
2
0
1
0
0
0
1
0
0
0
0
1
0
0
2
1
0
0
1
0
0
0
2
0
1
0
0
0
0
0
1
2
0
0
0
1
1
0
0
0
0
2
0
1
0
0
2
0
1
1
0
4
1
0
3
0
0
1
1
1
0
0
2
1
0
0
0
1
2
0
1
0
3
2
1
2
0
0
0
0
0
0
2
1
0
0
0
2
0
2
1
3
0
1
0
0
0
0
1
1
1
0
1
2
0
0
2
0
2
1
1
1
0
0
0
2
2
1
1
0
0
0
0
0
1
0
0
0
2
0
0
2
1
0
0
0
1
0
2
1
2
0
1
0
0
2
0
0
2
0
0
1
0
0
2
3
2
2
0
1
0
0
2
0
0
1
1
1
0
2
2
2
0
0
4
2
0
3
2
0
0
0
0
1
2
0
0
0
0
2
0
0
0
2
1
1
0
2
0
1
1
1
1
2
1
0
1
0
0
0
0
1
0
2
1
1
2
1
2
0
0
2
0
2
0
2
2
0
0
0
1
0
3
1
2
1
3
0
0
0
0
0
0
2
2
1
1
2
0
1
2
0
0
0
1
0
0
0
0
0
0
1
1
0
0
2
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
2
0
2
2
1
0
2
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
2
2
0
0
0
2
2
0
1
2
0
0
2
0
0
2
0
2
0
0
1
0
1
2
2
0
1
1
0
1
2
1
0
1
1
2
0
1
1
1
3
0
2
0
0
0
0
0
0
3
2
0
1
0
0
2
0
2
0
1
0
0
0
0
1
0
2
1
1
0
0
2
0
0
1
1
0
1
1
0
1
0
0
0
0
1
1
0
0
2
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
3
2
0
0
1
1
3
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
1
1
1
1
2
2
0
0
0
0
1
2
1
1
0
0
1
2
0
0
0
0
2
0
0
0
1
1
0
0
0
0
2
2
1
2
0
2
0
1
1
0
0
2
0
1
2
0
0
0
1
2
1
2
1
1
1
0
1
0
1
0
1
2
0
0
0
0
0
1
3
0
2
0
0
0
1
0
0
1
0
2
1
1
0
0
0
0
1
0
0
0
2
0
2
2
2
2
0
0
1
0
1
1
1
0
0
0
0
1
0
0
1
1
0
0
2
2
1
1
1
0
1
0
2
0
2
0
1
0
0
0
1
1
0
0
1
0
2
1
0
0
2
2
0
3
0
0
1
2
0
1
0
1
2
0
2
0
0
0
0
1
0
1
0
0
1
1
0
0
0
1
0
1
0
0
1
1
1
1
0
0
0
0
1
0
0
0
0
0
1
1
1
1
0
0
0
2
2
0
1
3
2
0
0
1
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
1
7
1
2
1
0
2
0
1
0
0
3
0
2
0
0
2
0
1
1
0
0
0
0
2
0
0
1
0
1
2
1
1
1
0
2
0
2
0
1
2
1
0
2
0
1
0
1
0
0
0
1
0
0
1
0
1
2
0
1
2
0
0
2
0
0
4
1
0
0
1
0
1
0
0
0
1
0
4
1
2
0
0
0
0
3
0
0
0
0
0
1
0
2
2
3
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
1
2
0
0
0
0
0
2
0
1
0
1
3
0
0
0
1
2
0
3
0
1
1
1
0
2
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
1
2
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
1
1
0
1
2
0
0
0
2
2
0
0
0
0
1
1
0
1
0
0
2
0
0
0
0
0
0
0
1
0
2
0
2
0
2
0
1
1
1
2
2
0
0
0
0
0
1
1
2
2
0
1
2
2
2
0
0
2
0
2
2
0
2
3
0
0
0
1
1
0
0
0
0
0
0
0
2
2
0
1
2
0
0
0
0
1
0
1
0
2
1
0
0
0
0
1
1
0
0
1
1
0
1
0
0
0
0
0
2
1
0
0
0
2
0
0
1
3
2
0
0
0
0
0
0
0
1
0
2
2
0
2
0
0
0
3
2
1
1
0
2
1
0
2
0
0
2
1
1
0
0
0
0
0
3
0
0
2
0
2
0
0
0
0
0
2
0
1
1
0
1
0
1
1
1
0
0
1
0
1
0
0
0
0
1
2
0
2
0
2
0
0
1
0
2
0
2
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
1
1
0
1
1
1
1
2
1
0
2
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
2
0
0
1
0
0
1
0
1
0
1
1
0
0
1
0
3
0
2
1
2
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
2
0
0
0
1
1
1
2
2
0
2
2
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
2
0
1
0
0
2
0
0
1
0
2
1
1
1
0
0
2
0
1
0
0
1
2
0
0
0
0
1
1
1
0
1
1
2
2
0
0
2
1
0
2
1
1
1
1
0
1
2
0
0
0
2
0
0
0
2
2
2
0
0
1
0
1
0
2
0
2
1
0
0
2
0
1
0
1
2
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
2
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
2
0
0
2
2
2
0
0
1
2
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
1
0
0
0
1
0
1
1
3
2
2
0
0
0
0
0
2
0
1
1
1
0
1
1
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
4
0
2
2
0
0
2
2
0
2
0
3
1
0
0
2
0
0
0
1
0
0
0
1
0
0
1
2
5
2
2
1
1
0
2
0
2
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
3
0
2
1
2
0
2
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
1
0
0
2
0
1
0
2
0
0
1
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
4
0
0
2
2
0
2
0
2
0
2
2
0
3
1
0
2
0
0
0
0
2
2
1
0
1
2
0
0
0
1
0
0
0
2
2
0
1
0
0
0
1
0
0
2
1
2
0
0
0
0
0
0
2
0
1
2
0
2
2
3
3
2
3
1
1
4
0
0
0
0
1
0
0
0
2
0
1
1
1
0
0
2
2
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
1
0
0
0
2
1
0
0
2
0
2
0
1
1
1
0
1
2
1
1
0
0
1
0
1
0
2
0
1
0
1
0
0
0
2
0
0
1
0
2
1
0
0
0
2
2
0
0
0
0
2
1
0
4
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
1
2
1
2
0
1
1
0
1
2
0
0
1
2
0
0
0
0
1
0
1
1
0
1
2
0
1
0
0
6
0
1
1
1
0
0
0
0
0
0
1
1
1
0
1
1
1
0
0
0
7
0
0
0
2
1
0
0
0
0
1
0
1
1
0
2
0
0
0
2
0
0
3
2
0
0
0
2
2
3
0
1
0
0
3
1
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
2
0
0
2
0
1
0
0
2
0
1
0
1
0
2
1
0
0
0
0
1
0
1
0
0
1
4
0
2
0
1
1
2
1
2
2
0
0
2
0
0
2
1
1
0
0
0
0
1
2
0
0
0
1
0
1
2
0
2
0
1
1
1
1
0
0
0
0
0
1
0
1
0
1
1
1
6
0
0
1
0
0
0
2
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
1
1
0
1
1
2
0
1
1
2
1
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
2
0
2
1
0
0
1
1
0
0
1
1
0
0
1
2
2
0
0
1
0
1
0
0
0
1
1
4
2
1
1
0
0
2
0
0
0
0
2
0
2
1
2
0
0
2
0
0
0
0
1
3
0
2
0
1
1
0
2
0
0
1
1
0
2
1
3
0
2
0
2
0
1
1
1
0
2
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
2
0
0
0
0
1
2
2
1
0
1
2
2
0
0
1
2
0
0
1
0
1
0
0
2
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
2
1
0
0
2
2
2
1
0
0
2
1
1
0
0
1
1
1
0
1
2
0
1
2
0
0
0
1
1
0
0
0
0
2
3
0
0
0
1
0
0
0
1
0
0
2
1
0
0
1
1
0
4
0
2
0
1
2
0
0
0
2
0
0
0
0
2
0
0
3
0
1
2
1
1
1
3
0
1
0
0
0
0
0
0
1
1
1
0
1
0
1
1
0
1
0
0
2
0
2
2
0
0
0
0
1
1
2
0
0
2
0
0
0
0
2
0
2
0
0
1
2
0
1
0
0
3
1
0
0
0
2
0
0
1
4
0
0
0
1
2
0
0
1
2
0
0
0
1
0
1
0
1
2
0
1
0
0
1
0
0
0
2
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
3
1
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
2
0
2
0
0
0
0
0
1
2
0
0
0
0
2
0
1
1
0
1
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
1
1
0
1
0
0
0
0
2
1
0
2
0
3
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
1
0
0
0
2
1
0
1
2
2
0
0
0
0
0
0
1
2
0
0
0
0
2
2
0
1
1
1
0
0
0
0
1
1
0
0
1
1
1
2
0
0
1
1
0
0
1
0
2
1
1
0
0
2
0
0
0
0
0
0
0
3
0
0
1
2
0
0
0
1
1
0
0
1
0
0
2
1
0
0
0
0
0
0
2
1
3
0
0
1
1
2
1
0
0
1
0
0
3
3
0
2
0
0
1
0
0
0
0
0
2
0
1
2
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
1
0
2
0
0
2
0
2
1
2
0
0
0
0
0
1
0
2
0
0
0
0
2
0
1
1
2
0
0
0
2
0
2
2
1
1
2
0
2
1
1
0
2
1
0
0
2
0
0
2
1
0
1
0
2
2
1
1
0
1
0
0
0
0
0
1
1
0
0
0
0
2
1
0
0
0
1
0
1
0
0
0
0
2
0
2
0
2
0
1
0
0
0
0
2
0
1
0
0
0
2
0
2
1
0
1
0
0
1
1
0
0
1
0
0
1
0
2
0
0
0
1
0
2
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
2
2
1
4
0
0
0
2
0
0
0
1
2
0
4
2
2
2
2
3
0
1
0
0
2
2
2
0
0
0
0
1
2
0
2
2
2
0
2
1
0
2
1
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
1
2
0
0
0
0
2
0
0
1
1
1
0
0
0
0
1
0
1
1
0
2
0
0
0
1
0
0
2
0
1
0
0
2
2
2
0
1
0
0
1
2
2
1
1
0
0
1
0
0
0
0
0
0
1
1
2
2
1
0
0
0
1
0
0
2
0
2
1
0
1
0
0
0
2
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
1
0
2
2
0
0
0
0
0
0
1
1
1
0
3
0
0
0
0
0
1
1
1
2
0
0
2
1
0
2
0
0
1
0
1
0
1
0
0
0
2
0
1
0
2
1
0
1
1
0
0
0
0
0
1
2
2
0
0
1
0
0
1
0
0
0
1
0
0
1
1
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
3
0
2
0
2
1
0
1
2
1
2
0
0
0
3
0
2
0
0
0
0
0
1
0
1
0
0
1
0
0
0
2
0
2
1
0
1
0
2
0
1
0
0
1
0
1
0
1
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
2
2
1
1
2
3
2
1
0
0
2
2
0
2
0
0
0
0
0
1
0
2
0
2
2
0
1
2
0
0
0
0
0
2
3
0
0
0
0
0
0
0
3
2
2
0
1
0
0
3
0
2
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
2
0
1
1
0
2
0
0
2
0
0
0
0
0
1
0
1
0
0
1
0
1
3
0
0
0
0
2
0
0
1
3
0
0
0
2
0
2
2
0
0
0
0
1
0
0
2
2
1
0
0
2
0
0
1
0
2
2
0
1
1
0
2
1
0
0
1
0
0
1
0
2
3
0
1
0
1
1
0
1
2
0
1
3
0
0
0
1
2
0
2
0
1
0
2
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
2
2
1
2
0
0
0
2
0
0
0
0
0
0
0
1
0
2
1
1
0
0
2
0
2
0
0
0
0
0
0
3
1
0
2
1
2
0
0
0
0
0
0
2
2
0
0
0
0
0
2
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
2
1
0
0
0
0
0
0
2
0
1
0
2
0
0
2
0
0
1
1
0
0
1
0
0
1
2
1
1
0
1
0
0
1
1
2
1
0
2
0
1
0
0
2
0
0
0
0
2
0
0
1
1
0
1
0
1
0
0
1
0
2
0
0
1
3
0
0
0
1
0
0
1
2
3
0
0
0
1
0
2
1
1
0
0
0
2
0
0
1
0
2
0
0
0
0
1
0
1
0
1
1
0
0
0
1
2
1
2
0
1
0
2
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
1
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
1
0
0
2
0
0
5
0
0
0
0
0
0
0
0
0
1
0
0
1
2
2
0
1
0
2
0
0
2
1
1
0
1
1
0
1
2
2
1
0
2
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
1
0
0
0
2
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
1
0
0
0
1
1
2
0
1
0
2
2
1
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
3
4
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
2
0
2
2
1
0
0
0
0
1
0
0
1
2
0
0
0
2
1
0
0
1
0
1
1
1
0
0
0
1
0
1
1
0
0
1
1
0
0
0
1
1
0
1
1
0
2
2
3
0
1
0
1
0
0
0
0
1
0
1
0
1
0
0
0
1
1
1
1
0
0
1
0
2
0
1
2
1
0
0
1
1
0
0
0
2
2
0
0
0
0
0
0
0
1
0
2
2
2
0
1
2
2
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
1
2
1
0
1
1
0
1
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
2
1
1
2
1
1
0
0
3
0
0
1
0
1
0
0
1
0
2
1
0
0
1
1
3
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
2
0
2
0
2
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
2
0
1
0
0
2
2
0
1
0
1
2
2
1
0
0
0
0
0
0
0
1
0
2
0
1
0
1
3
0
2
1
2
0
0
2
2
0
0
1
0
0
2
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
1
0
2
1
0
0
0
0
0
0
0
0
2
0
2
0
2
1
3
1
1
1
4
1
0
0
2
0
0
0
1
0
1
0
0
0
1
2
2
2
0
1
1
0
2
0
2
0
0
2
2
2
1
2
2
0
0
0
2
1
2
2
2
1
0
0
0
1
0
1
1
0
2
2
0
1
3
0
2
0
2
4
2
0
3
0
0
0
0
0
0
1
2
0
2
0
2
0
0
0
0
1
0
1
0
0
0
0
2
0
1
1
1
0
1
2
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
2
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
2
1
2
2
0
0
0
0
0
2
2
0
0
0
1
0
0
0
1
0
2
2
1
0
0
0
2
1
0
2
0
2
0
0
0
0
2
2
2
0
1
0
0
2
0
2
0
0
1
2
0
0
2
1
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
1
2
2
3
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
2
0
2
0
0
1
1
0
2
0
0
0
0
2
0
0
1
1
0
1
2
2
2
0
0
0
2
1
2
0
0
1
1
1
0
0
0
0
2
0
1
0
0
2
2
1
2
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
2
3
0
2
0
0
2
0
0
1
2
0
0
2
2
1
1
0
1
0
0
0
0
1
0
0
1
1
0
2
2
1
1
2
0
0
3
0
2
2
2
0
0
2
0
0
0
2
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
1
1
2
0
0
0
2
1
1
0
1
0
2
2
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
1
2
1
0
0
0
1
1
0
2
0
2
1
1
0
0
1
0
1
1
2
0
2
1
0
2
0
2
0
1
1
0
2
1
0
0
1
0
0
0
1
0
0
0
0
0
0
3
7
3
1
1
2
0
1
2
0
1
1
1
0
0
0
1
0
1
0
2
0
1
2
0
0
0
1
0
1
0
0
1
1
1
1
0
0
0
1
1
0
2
0
0
1
2
0
0
0
0
1
2
1
2
0
2
2
0
0
0
2
2
2
2
1
0
0
0
2
1
1
1
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
1
1
2
0
0
0
1
1
1
1
2
2
0
1
0
2
1
1
0
4
2
0
0
0
0
0
0
0
0
2
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
1
2
0
2
1
2
2
0
1
0
2
0
1
1
0
2
0
2
2
1
0
0
0
2
2
2
0
2
0
2
0
2
0
3
2
0
0
0
2
1
0
1
2
2
2
0
2
1
1
0
0
1
0
1
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
2
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
2
1
0
0
0
0
2
0
0
2
1
1
0
2
0
0
0
2
0
0
1
0
2
2
1
3
0
0
0
0
0
0
0
1
0
0
0
1
1
2
1
1
0
0
0
1
2
0
0
1
2
0
0
1
0
0
1
0
1
2
0
0
2
0
0
1
0
0
1
0
0
0
2
1
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
2
1
0
0
0
0
2
0
4
0
0
0
0
0
0
1
1
3
1
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
1
1
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
1
1
2
1
0
0
1
0
0
1
1
1
0
0
0
2
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
1
0
1
0
0
1
0
0
1
0
1
0
0
1
0
0
2
0
1
0
0
0
0
0
1
1
2
2
2
0
1
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
1
1
2
0
1
1
0
1
1
3
2
1
1
2
0
0
0
0
2
2
1
1
0
0
0
1
0
2
0
0
1
1
0
1
0
0
1
1
0
0
1
0
0
1
0
1
0
2
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
2
0
1
0
0
0
0
0
0
0
0
2
2
0
1
2
2
0
0
0
2
0
1
1
0
1
1
0
0
1
0
2
0
1
0
1
0
0
1
0
0
1
0
0
2
1
0
0
4
1
2
0
0
1
1
1
1
2
1
2
1
0
3
0
1
0
0
0
0
2
0
0
2
0
1
0
2
0
0
0
1
0
0
0
0
1
0
2
2
1
1
2
2
0
0
3
3
1
1
0
0
1
0
2
0
0
1
0
0
2
3
1
0
2
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
1
2
0
0
1
0
0
0
0
2
0
0
1
0
0
2
2
2
3
0
3
1
0
0
0
0
1
0
0
0
0
1
2
2
0
0
0
0
3
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
2
0
0
0
2
2
0
1
1
0
0
2
0
0
1
0
0
0
0
2
1
1
0
0
0
3
1
0
0
2
0
0
0
1
0
0
1
2
0
1
0
2
0
2
0
1
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
2
2
0
0
2
0
1
0
0
0
0
1
1
1
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
1
2
2
0
2
1
0
0
1
0
0
1
0
0
0
2
1
0
2
2
0
0
3
0
0
0
1
0
0
0
1
0
2
1
1
1
2
1
0
0
1
0
2
0
0
0
0
2
0
1
0
0
2
1
0
0
0
0
0
0
0
1
0
0
2
0
1
2
0
0
1
0
0
1
0
1
0
1
2
1
0
1
0
0
1
1
1
0
0
0
0
0
2
0
0
1
0
0
1
0
0
2
0
0
0
0
2
0
0
2
2
2
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
1
0
0
2
2
0
0
0
0
1
0
0
2
2
1
1
0
2
1
0
0
1
1
2
1
0
0
2
0
0
0
0
1
2
0
0
2
0
0
0
0
2
0
0
1
0
1
1
1
0
1
0
2
0
1
0
1
0
1
1
1
0
0
0
0
0
1
1
2
1
0
2
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
1
1
0
0
0
0
1
0
0
0
0
2
1
0
0
0
1
0
0
0
0
1
2
0
2
1
0
0
0
2
1
0
1
0
1
1
2
1
2
0
0
0
1
2
0
2
2
2
0
0
0
0
1
2
0
0
2
0
1
1
0
2
0
1
2
0
0
0
0
2
0
0
0
1
1
1
0
0
0
0
0
1
2
0
8
2
2
0
0
0
0
0
2
2
0
0
1
0
1
0
0
0
0
1
0
0
1
1
0
0
1
0
0
1
0
1
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
1
2
0
1
0
0
2
2
1
2
0
0
0
1
2
0
2
1
2
1
0
0
2
2
0
2
0
0
0
1
0
0
0
2
0
2
0
2
1
0
0
0
0
0
4
0
0
0
2
0
1
0
0
2
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
2
0
1
0
0
0
0
4
0
0
0
0
2
0
1
1
0
0
2
0
0
2
1
1
0
0
0
1
0
2
0
0
0
0
1
1
1
0
2
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
2
0
0
0
1
0
0
2
0
2
1
0
0
0
0
0
0
0
0
1
2
1
1
1
0
1
0
2
2
0
1
1
0
1
0
0
0
2
0
1
1
1
0
0
0
2
1
0
2
1
0
2
2
0
0
0
0
0
0
2
0
0
2
2
3
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
2
1
0
2
0
3
0
2
1
1
0
1
1
0
1
0
0
0
2
2
2
0
0
1
0
1
1
2
0
0
0
0
0
2
0
2
0
2
1
0
2
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
1
0
0
2
0
0
2
1
0
2
1
1
0
0
2
2
0
1
0
2
2
0
0
1
0
0
0
0
2
1
0
0
0
1
0
1
1
0
0
1
0
1
0
0
0
0
1
0
0
2
0
0
2
0
2
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
2
6
2
0
2
1
0
0
1
0
2
0
0
1
1
0
2
0
0
2
2
0
0
2
1
2
0
0
1
1
0
2
0
0
2
0
0
2
1
0
1
1
2
0
0
0
0
0
0
1
2
0
2
1
2
0
0
0
0
0
0
1
1
0
0
1
0
2
1
1
2
0
0
0
2
0
1
0
0
1
1
1
2
0
0
0
0
4
1
2
0
0
0
0
1
0
2
0
1
7
1
0
2
1
1
0
2
1
0
0
1
1
2
0
0
0
0
0
1
2
5
0
0
0
0
2
1
2
0
0
1
0
0
0
1
0
0
0
1
1
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
2
2
2
0
1
1
0
0
2
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
1
1
1
2
0
0
0
0
0
1
0
0
2
1
0
0
2
3
2
2
5
2
0
0
0
2
0
0
1
0
2
2
0
2
1
2
1
2
1
1
2
0
0
2
1
2
0
0
1
0
0
0
0
0
0
1
2
0
1
0
0
1
1
0
3
1
1
0
1
2
1
1
0
0
0
0
2
2
0
2
1
0
0
1
0
0
1
1
0
2
1
0
2
0
0
0
0
0
2
1
1
3
0
2
0
0
2
0
0
0
1
0
0
0
0
0
2
0
2
1
2
0
0
2
1
0
1
2
1
1
1
0
2
0
0
0
1
0
0
2
1
1
0
0
0
0
0
0
2
0
2
2
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
1
0
0
0
2
0
1
0
0
2
0
2
0
0
1
2
2
0
2
1
0
0
0
0
0
1
0
0
0
2
2
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
1
1
0
1
2
0
2
0
2
0
0
0
0
2
0
0
0
5
0
2
0
3
0
1
2
1
1
0
0
2
1
0
0
0
2
2
0
0
1
0
1
1
1
0
0
0
0
1
0
1
0
0
2
1
1
0
1
2
0
0
0
0
0
0
0
1
0
1
1
0
2
0
2
1
2
1
1
0
1
2
0
1
0
2
1
1
2
0
2
1
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
1
1
0
0
1
0
0
2
0
0
0
0
1
2
0
1
0
0
2
0
2
2
0
2
0
0
2
1
1
0
0
0
1
2
2
0
0
0
0
0
1
2
1
0
0
0
1
0
0
1
0
0
0
0
0
2
1
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
1
2
2
0
0
0
0
0
0
0
2
2
1
0
1
2
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
1
2
2
0
1
0
0
0
2
0
0
0
0
0
2
1
2
0
0
1
0
0
0
1
2
1
2
1
0
1
1
1
2
2
1
0
2
0
1
0
0
0
2
0
0
0
1
0
0
0
0
2
1
2
0
0
0
0
0
0
0
1
0
1
0
0
2
1
0
1
1
1
1
0
0
2
0
0
0
0
0
0
0
1
1
1
0
2
0
0
0
2
2
1
0
2
0
0
0
0
1
1
2
1
1
3
1
1
0
0
0
1
2
0
2
0
0
1
0
1
0
2
1
0
0
1
2
0
0
1
2
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
2
1
2
0
1
1
0
0
0
1
0
2
1
0
8
0
1
2
0
1
0
0
0
0
0
2
1
2
0
0
0
1
0
0
0
1
1
2
2
1
0
0
0
2
0
0
1
1
1
1
0
2
0
0
0
0
3
0
0
1
1
1
0
1
1
0
0
0
0
0
0
1
0
1
1
0
3
0
1
1
1
4
0
1
1
0
2
0
2
1
2
1
2
2
0
0
1
2
0
8
0
0
0
2
0
0
3
0
1
2
0
3
1
0
2
0
1
1
0
2
0
0
0
0
1
1
0
2
0
1
2
0
0
0
1
0
3
1
0
1
1
1
2
1
0
1
2
2
0
0
2
2
0
0
1
1
1
0
2
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
2
0
3
0
0
0
0
0
0
0
0
3
1
0
1
0
0
0
0
0
0
0
3
2
0
0
1
5
0
0
1
0
2
0
0
1
0
2
2
2
0
0
0
0
2
0
2
1
0
0
0
1
2
0
1
0
2
1
0
1
1
1
1
1
1
0
2
0
0
1
0
1
0
0
2
2
0
0
0
2
2
1
0
2
1
2
2
1
2
1
2
1
0
0
0
0
0
0
1
1
0
0
2
1
2
1
2
0
0
1
0
2
0
1
0
1
0
1
1
1
3
1
0
0
1
2
1
0
0
0
0
0
2
3
0
0
0
1
1
2
0
0
0
0
0
0
0
1
0
0
1
1
0
0
2
1
0
2
2
0
1
1
1
1
0
2
1
0
0
0
0
1
0
3
0
2
2
0
0
0
0
2
0
0
0
1
0
1
1
1
0
0
0
0
1
1
0
1
2
1
0
2
0
1
0
1
2
2
2
2
0
2
0
2
0
0
0
0
1
0
0
3
1
0
0
0
2
0
2
0
0
0
0
0
2
1
2
2
1
0
0
0
0
0
0
0
1
1
2
1
0
0
0
2
0
1
0
0
0
2
0
1
0
1
1
0
2
1
1
0
0
0
0
2
0
0
0
0
1
0
0
2
1
5
0
0
1
0
1
0
2
0
0
0
0
1
0
1
2
3
0
0
1
0
0
2
0
0
2
1
0
0
1
1
2
2
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
2
1
1
1
0
7
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
2
1
2
2
2
2
0
0
2
0
0
0
0
1
1
0
2
0
1
0
0
0
1
0
0
0
0
1
0
2
0
2
2
1
0
0
0
0
0
1
1
0
0
1
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
1
0
0
1
0
0
0
0
0
2
0
1
0
0
0
2
0
0
1
0
0
2
1
0
2
0
2
1
0
1
1
0
2
0
1
0
0
0
0
0
2
2
0
0
1
2
2
1
2
0
1
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
3
1
0
0
1
0
1
0
0
0
0
2
2
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
2
0
0
1
1
0
0
0
0
2
2
2
0
1
0
2
0
0
0
1
0
2
0
0
2
0
1
1
2
0
1
0
2
2
2
0
0
0
0
0
0
1
0
2
1
1
1
1
0
1
2
2
1
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
1
1
0
1
0
0
0
2
0
0
0
0
2
2
1
1
1
1
0
3
0
2
2
1
0
1
0
0
1
0
0
0
1
0
2
0
2
0
1
0
0
2
0
0
0
1
0
1
1
2
1
1
0
2
0
2
3
0
2
0
0
0
0
3
0
0
0
0
2
1
3
0
1
2
1
0
2
0
0
0
1
0
0
0
0
1
1
1
0
1
0
0
0
2
0
1
0
0
2
0
2
3
0
0
0
0
1
0
0
0
2
1
3
1
0
0
0
0
2
0
0
1
1
0
1
2
0
0
0
0
2
1
0
0
0
0
2
1
2
0
0
0
0
1
4
1
0
2
0
0
2
1
1
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
2
1
0
1
0
1
0
0
0
2
0
0
0
2
1
0
0
0
0
0
1
0
1
0
2
0
1
0
1
2
2
1
0
1
2
1
0
1
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
4
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
2
2
2
1
1
1
0
0
0
0
2
1
2
0
0
0
0
0
1
0
0
0
0
2
1
0
1
3
2
0
2
0
1
1
1
0
0
0
2
0
1
0
1
1
0
0
0
1
1
2
0
2
1
0
0
0
1
0
0
1
2
3
0
0
0
0
1
1
4
0
1
0
0
0
0
0
2
0
2
2
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
1
1
0
2
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
2
1
6
0
2
0
1
1
0
2
2
0
0
1
0
1
2
0
1
0
2
5
1
0
2
0
0
0
1
0
0
0
0
0
1
1
2
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
2
0
0
0
0
0
0
0
0
0
1
1
0
3
0
2
0
2
0
0
2
1
0
1
4
0
1
0
0
2
0
1
0
0
0
1
0
1
0
2
0
0
1
1
0
3
0
0
0
2
0
0
2
1
0
0
2
0
0
1
1
1
1
0
2
0
0
0
2
2
1
0
1
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
1
2
0
0
0
1
6
1
1
0
0
5
0
2
2
1
0
3
1
0
0
0
2
0
0
0
1
1
1
1
2
1
1
0
1
1
0
0
0
0
1
0
0
0
0
2
0
0
0
1
4
1
2
0
0
0
1
2
2
0
0
1
1
0
1
0
2
1
2
0
0
1
0
1
0
1
1
2
2
0
0
0
1
0
0
2
1
2
0
0
2
0
3
0
0
1
2
1
0
0
0
0
2
0
0
1
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
2
1
1
1
2
2
0
1
2
2
0
1
1
2
1
2
0
0
1
0
0
1
0
2
0
1
0
1
2
0
2
0
0
1
0
0
1
0
0
1
0
1
1
2
1
0
1
0
0
1
2
8
0
1
0
0
0
2
0
1
1
0
0
2
1
1
2
0
2
0
0
1
0
0
0
0
0
1
0
0
1
1
1
1
0
3
1
5
0
0
0
0
1
0
0
2
0
2
2
0
2
0
2
0
0
1
0
1
0
0
2
0
3
2
2
2
0
1
0
0
1
1
2
2
1
1
0
0
2
0
2
1
0
1
3
2
0
1
1
1
2
2
0
1
0
0
0
2
2
0
1
1
1
0
0
1
0
1
0
0
0
2
0
0
0
0
1
2
0
3
0
0
0
0
2
0
1
0
1
0
2
0
0
1
0
2
0
0
0
0
0
1
1
0
4
0
2
0
2
2
0
0
0
0
0
0
0
2
1
0
3
2
1
0
0
2
2
0
0
0
0
2
0
0
2
2
0
0
0
0
0
1
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
1
0
2
0
2
0
1
1
0
2
0
0
0
1
1
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
2
0
1
2
0
1
0
0
0
1
0
2
4
0
0
0
0
2
0
0
0
0
2
2
2
0
0
2
0
2
2
0
0
0
0
0
1
0
0
0
0
2
2
1
0
0
1
0
0
0
2
1
2
1
0
1
0
0
2
0
2
0
0
0
2
0
2
1
5
0
2
0
0
0
1
7
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
2
0
0
0
0
1
2
1
0
1
0
0
0
0
1
0
0
2
1
0
0
0
0
0
2
0
1
0
2
0
2
0
2
0
1
0
1
0
0
1
1
0
2
0
0
1
0
0
0
2
2
1
1
0
0
2
0
1
2
3
0
0
2
0
2
1
2
0
2
2
1
1
0
0
2
1
0
0
2
1
2
0
0
0
1
1
0
1
0
2
1
0
0
0
2
1
0
0
2
1
2
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
3
1
0
1
2
0
0
0
0
0
0
1
3
1
0
1
0
1
0
1
2
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
2
0
2
0
1
1
0
2
0
0
1
0
1
0
0
0
2
0
0
0
0
2
1
2
1
2
1
0
2
0
0
0
1
0
1
2
0
0
0
1
2
1
0
1
1
2
0
0
0
1
0
2
1
0
1
1
0
0
0
1
2
0
0
1
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
1
0
0
1
0
2
2
1
1
0
0
1
0
0
2
1
0
0
0
2
0
2
0
0
1
2
0
1
0
2
1
0
1
0
0
0
0
2
1
1
2
0
0
0
1
0
1
2
2
0
0
2
2
1
0
0
1
0
1
2
1
1
1
0
0
0
0
0
1
2
0
1
1
1
0
0
1
0
0
3
0
1
0
0
1
2
0
0
0
0
1
0
1
0
0
0
1
1
0
0
2
0
2
0
0
3
0
0
0
0
1
0
1
3
0
0
0
2
0
0
0
2
1
2
1
1
1
0
0
0
2
0
1
2
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
1
2
3
0
0
2
1
2
0
1
0
0
0
1
0
1
0
2
0
0
1
0
0
1
0
0
1
1
0
0
0
0
2
0
0
2
2
0
0
1
0
0
0
0
1
0
2
2
2
0
0
2
0
1
0
0
0
1
0
0
1
2
2
0
0
0
2
0
0
2
0
1
3
1
1
0
0
0
0
0
1
0
2
0
1
2
2
0
0
1
1
2
0
1
0
2
0
0
0
0
0
0
0
0
1
0
4
1
2
2
0
0
0
1
0
2
1
1
1
0
1
0
0
0
1
0
1
0
0
1
1
0
0
1
2
0
1
2
2
0
2
0
2
0
0
0
0
1
0
0
0
1
1
0
2
1
0
2
1
0
1
0
0
2
0
0
0
0
0
0
5
1
0
1
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
2
0
2
0
0
0
1
2
0
4
1
0
1
0
0
0
0
0
1
0
23
1
0
0
0
1
1
0
1
1
1
0
1
0
1
2
0
1
1
0
2
1
1
0
2
0
0
0
0
0
1
0
1
0
2
0
2
2
2
0
0
2
0
0
1
0
0
0
0
1
2
0
0
0
1
0
0
0
0
1
0
0
0
2
0
2
2
0
1
2
0
0
2
1
0
0
2
0
0
2
1
0
0
0
2
0
0
2
0
1
1
2
0
2
0
2
0
2
0
0
1
0
0
2
0
3
2
2
0
1
0
0
2
0
1
0
2
0
0
0
1
2
3
0
0
0
1
2
0
0
0
0
0
1
1
0
1
1
2
0
0
1
1
1
0
0
1
1
0
0
1
1
2
0
1
1
0
1
2
2
3
0
1
0
0
1
0
0
2
0
2
0
0
1
0
1
0
2
0
1
0
3
0
0
0
1
2
0
0
1
0
2
0
0
1
2
9
2
0
0
1
0
0
2
1
0
0
0
0
2
1
1
2
1
2
2
1
1
0
0
1
1
0
2
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
2
3
0
2
0
0
0
2
2
0
0
0
0
1
2
0
2
0
0
1
2
1
0
0
1
0
0
2
2
0
1
0
0
2
0
2
2
0
0
2
2
0
0
4
2
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
2
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
1
0
1
3
0
1
1
0
1
4
0
1
2
2
0
2
1
0
0
0
1
0
0
2
1
0
2
5
2
0
0
0
2
2
2
0
0
0
0
0
0
1
2
2
0
0
0
0
0
1
1
0
2
0
0
2
2
0
1
2
1
3
0
0
0
0
0
0
0
2
0
0
1
0
0
1
2
2
0
1
1
1
2
1
0
0
0
0
2
1
2
2
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
2
1
3
1
0
0
0
2
0
1
0
2
0
2
0
2
0
0
0
3
2
1
0
0
1
0
1
2
0
0
2
0
0
0
0
0
1
0
2
2
1
0
0
0
0
0
1
1
2
2
0
3
0
1
0
0
1
1
0
0
0
1
1
0
1
0
0
0
1
1
3
0
0
0
0
0
2
0
0
0
0
0
3
0
2
0
0
2
1
0
1
0
1
0
3
0
0
0
0
0
2
0
0
2
1
1
1
2
0
0
0
1
2
2
1
0
1
1
0
1
0
1
0
1
0
4
2
0
0
0
0
1
0
0
0
2
2
0
0
2
0
0
2
0
1
0
0
0
0
0
0
1
2
1
0
0
1
1
0
2
2
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
1
1
0
0
0
0
0
1
2
0
4
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
2
2
1
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
4
2
2
0
0
2
2
0
0
0
0
2
0
0
2
4
0
1
1
0
2
0
0
0
0
1
0
2
0
1
0
0
0
1
0
1
1
0
0
0
0
1
0
1
1
0
0
0
1
0
1
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
1
1
2
0
0
1
0
0
0
2
0
0
2
1
1
1
2
0
1
1
0
1
1
0
2
0
0
0
0
0
0
2
4
0
3
1
0
2
0
0
0
0
0
2
0
2
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
2
1
0
0
0
0
0
0
1
0
2
0
0
1
1
1
0
1
1
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
4
0
1
0
2
0
2
0
1
1
2
0
0
0
2
0
1
1
2
1
2
0
1
2
0
2
0
0
3
2
0
0
0
0
0
2
2
3
0
1
0
0
0
0
0
1
0
3
1
1
1
0
2
0
0
0
1
0
0
0
2
1
2
1
0
0
0
3
0
2
1
0
0
0
2
2
0
2
0
1
0
0
0
1
2
0
1
0
2
0
0
0
1
1
2
0
0
1
0
0
2
1
2
2
0
2
0
0
0
2
0
0
1
2
3
2
0
1
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
2
1
0
1
0
0
0
0
2
3
0
0
1
1
0
1
2
0
0
1
1
0
2
1
0
1
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
2
1
0
1
1
0
2
1
0
1
0
0
2
1
0
2
1
0
1
0
1
0
0
3
1
1
1
1
0
0
1
2
3
0
0
2
0
1
1
2
0
0
0
2
1
0
2
1
0
1
0
0
0
2
1
0
0
0
6
1
2
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
1
0
0
2
1
0
0
0
2
1
0
1
2
2
0
0
1
0
0
0
0
1
2
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
2
1
0
0
1
0
0
1
0
1
0
0
0
0
2
0
0
0
0
1
0
0
1
1
1
0
0
1
1
1
0
0
2
1
2
0
0
1
0
0
1
1
0
0
0
0
0
0
3
1
2
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
1
1
0
2
0
0
0
0
0
0
0
1
1
1
0
0
0
1
2
0
1
0
0
0
0
2
0
2
2
0
2
0
1
0
0
2
0
0
2
1
0
1
0
3
0
0
0
0
0
1
2
2
2
2
0
2
2
1
2
1
0
0
1
0
0
2
0
2
1
3
0
2
0
0
0
1
2
0
0
0
2
0
0
0
2
2
0
0
1
0
0
2
2
2
1
0
1
2
0
0
0
1
1
0
2
2
1
0
0
0
1
0
0
0
2
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
2
1
1
0
2
0
0
2
0
0
0
0
0
0
1
0
1
0
2
0
3
1
2
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
1
1
0
0
1
2
0
0
2
1
0
2
2
0
1
1
1
0
1
1
1
1
0
0
0
1
2
1
1
0
1
2
2
0
0
0
0
1
2
0
0
0
0
0
0
1
2
0
0
0
1
0
0
3
0
0
0
0
2
2
2
1
0
0
0
0
2
0
2
0
0
1
0
2
0
0
0
0
0
0
0
1
0
1
0
2
0
1
0
0
3
2
2
2
2
1
2
0
0
4
0
1
0
0
2
0
1
1
2
0
1
0
1
0
1
1
0
0
2
0
1
0
1
2
1
2
1
1
1
0
0
0
0
1
2
0
2
0
1
0
2
0
2
1
3
0
0
0
0
1
1
1
0
0
0
1
1
5
1
1
2
2
1
0
2
0
0
0
0
0
1
1
1
2
0
0
0
0
4
0
2
0
2
0
2
0
1
0
1
0
0
2
0
1
1
1
2
0
1
3
1
0
1
0
1
0
0
2
1
0
2
0
1
0
0
2
1
0
0
0
0
2
2
0
1
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
2
2
0
0
2
1
1
1
0
0
0
1
0
0
3
2
0
0
0
0
2
1
0
0
2
1
0
0
0
1
0
1
0
0
0
0
2
0
0
1
0
0
0
0
1
3
2
1
2
1
1
1
0
2
0
0
0
2
1
1
2
0
0
0
0
0
1
0
1
2
0
1
1
0
0
1
0
0
2
1
2
2
0
1
0
0
0
1
1
0
2
3
0
1
0
2
0
2
0
2
2
0
1
2
0
0
0
2
0
2
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
3
1
0
2
0
0
0
1
1
1
1
0
0
2
0
0
0
0
1
1
0
0
1
0
1
2
0
0
0
0
0
0
1
1
1
2
0
0
1
2
0
0
0
0
2
0
0
0
1
0
2
0
0
0
1
0
1
2
2
2
3
1
0
0
0
0
1
0
0
0
0
2
1
0
0
2
0
2
1
3
0
3
0
0
1
0
0
2
0
1
0
2
0
2
0
0
0
0
2
0
2
0
0
1
0
0
0
2
0
0
3
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
1
4
0
0
2
0
1
0
1
1
1
0
1
0
2
1
1
1
0
1
0
0
0
2
1
0
0
0
2
2
1
2
0
1
2
0
1
2
0
1
0
0
1
1
0
2
0
0
1
0
0
0
0
1
0
2
0
0
1
0
0
2
1
1
0
2
2
1
2
0
2
0
0
0
2
0
0
0
1
0
2
0
1
0
0
0
0
2
0
0
2
1
2
0
0
0
1
1
2
0
1
2
0
1
2
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
1
0
0
4
0
0
1
0
2
0
2
2
0
0
2
0
1
0
2
2
0
0
1
1
0
0
0
1
0
0
0
1
2
1
0
0
1
1
0
2
0
1
0
2
0
0
1
2
1
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
1
2
1
2
0
0
2
0
0
0
1
0
2
0
2
0
0
2
0
0
1
2
0
1
0
0
0
0
1
1
0
0
2
1
0
0
2
0
1
2
1
1
2
0
0
2
0
1
0
0
2
1
0
0
0
0
0
0
2
2
0
2
0
0
0
0
1
0
0
0
0
1
2
1
3
0
0
1
2
1
2
1
2
1
0
0
0
0
0
2
0
0
0
1
0
1
1
2
2
1
1
0
0
1
1
0
0
0
0
1
2
0
0
1
0
1
0
0
2
2
0
2
0
1
2
0
2
0
2
0
1
1
2
2
0
0
1
0
0
0
0
0
0
1
1
1
0
0
1
2
0
0
1
2
1
1
1
2
0
0
0
1
0
0
0
1
0
0
2
0
0
1
1
1
2
1
2
0
3
2
2
0
0
0
0
1
0
0
0
2
0
2
0
2
1
0
4
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
1
1
1
0
0
1
0
0
2
1
2
2
2
1
1
1
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
2
0
0
1
0
0
2
1
0
0
2
0
2
1
0
1
0
2
0
1
0
0
3
0
2
2
1
0
1
0
0
1
0
0
0
0
0
3
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
2
0
0
2
0
1
0
2
1
0
1
3
0
0
1
0
2
1
0
1
2
0
2
0
0
0
1
0
0
2
1
2
0
0
1
0
1
0
0
2
2
0
2
0
1
2
1
2
1
2
1
0
0
0
0
0
0
2
2
1
0
0
0
1
1
1
0
1
0
2
0
1
0
1
0
0
0
1
0
0
2
0
1
2
1
0
0
2
0
2
2
2
0
0
0
1
0
0
2
1
1
2
2
0
0
0
0
1
0
0
0
2
1
0
2
0
1
1
1
0
1
0
0
0
3
0
0
2
1
2
1
0
0
0
1
2
1
0
0
0
2
0
1
1
1
1
1
0
2
0
0
0
0
0
1
1
1
1
0
2
1
4
1
0
0
0
0
0
2
1
2
1
0
2
1
0
0
0
2
3
0
2
0
2
2
0
1
1
0
0
0
0
0
0
0
0
2
2
2
1
1
0
0
0
2
2
1
0
0
1
0
1
2
0
0
0
0
0
2
1
2
0
1
0
2
1
0
0
0
1
0
0
1
0
2
0
0
0
1
0
0
0
1
1
0
0
2
3
0
0
0
0
0
0
2
1
1
0
0
2
0
3
0
1
1
0
2
0
0
0
0
0
2
0
2
1
2
1
0
2
1
2
0
2
0
0
1
0
0
0
1
1
1
0
0
0
1
1
0
0
1
0
1
1
2
1
0
1
2
2
0
0
0
1
1
2
0
0
0
0
0
0
4
2
1
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
2
1
1
1
0
0
0
0
0
2
0
0
2
2
0
1
3
1
0
0
0
1
2
0
0
0
1
0
0
0
1
1
1
3
0
1
2
0
0
2
1
0
0
1
0
0
0
0
0
2
0
0
0
2
2
0
2
1
0
2
1
0
1
0
1
0
3
0
0
2
1
0
2
2
0
1
0
0
1
0
0
0
1
0
3
0
0
2
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
2
0
0
2
0
0
1
0
2
1
1
2
0
0
1
0
0
1
0
1
3
0
2
0
1
0
0
0
1
0
0
1
0
0
0
2
1
0
2
0
1
0
0
0
1
0
0
0
1
3
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
1
0
0
2
1
0
0
0
1
0
2
0
2
0
0
0
0
0
1
1
1
0
1
0
0
1
1
0
2
0
0
0
0
1
1
0
0
1
2
1
0
0
2
0
1
0
0
1
0
2
0
0
0
1
0
0
0
2
1
0
0
2
0
2
2
2
0
0
1
0
0
0
0
1
1
0
0
1
1
0
0
1
0
0
0
0
2
2
0
0
2
2
0
0
1
2
0
2
1
2
0
0
0
2
1
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
3
0
0
0
1
2
0
3
1
0
1
1
0
0
4
0
1
0
0
1
0
0
0
2
0
0
2
0
0
2
0
0
2
0
0
2
1
0
0
0
1
2
0
0
1
2
2
1
2
1
0
2
2
1
1
1
1
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
1
1
0
2
0
0
1
2
0
1
0
0
0
0
0
0
1
0
1
0
0
2
0
2
0
0
0
1
1
0
0
1
0
1
1
0
1
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
2
1
0
0
0
0
1
2
0
0
0
2
1
0
0
1
0
1
0
1
0
0
2
2
0
1
0
2
1
0
0
0
2
1
0
1
0
1
1
0
0
0
0
1
2
0
0
2
0
0
2
0
0
0
1
2
1
0
1
1
2
2
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
2
1
1
0
0
0
3
0
0
0
0
1
2
1
0
0
0
0
0
1
0
1
0
0
1
0
0
1
2
0
1
0
0
0
0
0
2
0
0
1
1
0
0
0
1
0
1
0
0
2
2
2
1
0
1
0
0
1
0
0
2
0
0
2
2
0
1
1
2
0
2
0
5
0
0
1
0
0
0
0
2
0
1
0
0
1
2
0
0
0
2
0
2
0
0
1
2
0
0
0
1
0
1
0
2
1
0
0
1
0
1
0
1
0
0
0
0
0
2
1
2
0
0
1
0
0
0
2
1
2
2
0
0
0
0
0
1
0
1
1
0
0
1
0
0
1
0
0
0
0
0
2
0
1
1
1
0
2
0
0
0
0
0
0
1
1
2
0
0
0
0
0
1
0
1
0
0
1
2
1
0
1
0
2
0
0
2
1
2
0
1
4
2
1
0
0
0
1
0
0
2
0
2
2
1
1
1
1
0
0
0
0
0
0
2
0
1
1
0
2
2
0
0
0
2
1
0
2
0
2
0
0
0
2
0
0
1
0
0
0
2
2
0
0
0
1
0
1
1
0
1
0
1
2
0
0
0
1
3
0
2
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
1
1
2
0
0
0
0
0
2
0
0
1
1
0
0
3
2
2
1
0
0
0
0
0
5
0
1
1
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
1
2
0
2
0
0
0
0
4
1
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
1
0
1
0
3
1
0
0
0
0
0
1
2
2
0
0
0
0
2
1
0
0
0
1
0
0
1
1
1
0
1
0
0
2
0
0
0
0
2
0
0
0
2
2
0
2
1
0
1
2
0
0
2
2
1
0
0
0
2
1
0
0
1
0
0
0
1
2
0
0
0
0
0
2
0
1
1
1
0
1
1
0
0
0
0
0
1
0
1
0
1
0
1
2
1
0
0
2
0
0
0
0
2
1
0
1
0
6
2
2
0
0
1
0
1
0
2
2
2
1
0
0
2
1
0
0
0
2
1
0
2
1
2
0
1
0
1
0
1
0
1
0
2
0
0
0
0
0
0
2
0
2
0
0
2
0
2
0
0
0
0
1
1
0
0
0
0
0
1
0
2
1
0
0
2
0
0
1
0
0
0
1
2
1
3
0
3
0
0
0
1
0
0
0
0
1
2
3
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
1
0
1
0
2
2
0
1
1
0
1
0
0
1
1
2
0
0
2
0
0
0
0
0
0
0
2
1
0
0
2
0
1
0
2
0
0
2
1
2
2
1
0
0
0
0
2
0
0
2
0
2
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
4
1
0
1
1
2
0
0
0
1
0
0
0
0
1
0
2
2
0
1
0
0
0
2
2
2
0
0
1
0
0
0
1
0
0
0
0
0
4
0
0
1
0
1
2
0
0
0
1
0
1
0
0
2
1
1
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
2
0
0
1
0
0
0
0
1
1
0
0
2
0
0
2
0
0
2
0
0
1
1
0
0
0
0
1
0
0
0
1
1
0
0
3
2
1
0
0
0
1
2
0
0
1
2
0
1
0
1
1
0
0
1
0
2
1
1
0
1
1
2
0
0
1
0
0
4
0
1
0
1
0
0
2
0
0
6
0
1
2
0
0
1
1
0
2
1
0
0
1
0
0
0
1
1
0
0
3
1
0
0
1
0
0
0
0
2
2
0
1
0
0
0
1
2
0
0
0
1
0
2
1
1
0
0
1
0
0
0
2
0
0
1
0
0
2
0
0
0
0
2
0
2
2
1
0
0
1
0
0
2
2
0
0
0
1
2
0
0
1
0
0
0
1
0
1
0
0
1
0
0
1
1
0
2
0
1
0
0
1
2
1
1
2
0
0
0
2
0
0
0
0
0
0
1
0
2
2
1
0
0
2
2
0
0
0
2
1
2
2
2
0
2
1
1
0
0
0
1
0
2
0
1
0
2
1
0
1
2
0
0
2
0
2
0
1
1
0
1
0
0
1
0
0
2
1
0
0
2
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
2
1
2
2
0
1
0
0
0
1
0
0
2
0
0
0
0
1
1
1
0
0
1
0
2
0
1
0
1
0
1
2
0
0
0
0
1
1
0
1
0
2
2
0
0
2
0
2
0
0
0
0
1
2
2
1
0
0
0
0
1
0
1
0
0
1
2
1
1
1
0
0
2
2
0
0
0
0
1
1
2
1
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
2
1
0
2
1
0
0
2
0
0
0
0
0
1
0
1
0
2
2
2
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
1
2
0
0
0
1
1
0
0
0
0
0
2
1
0
0
1
0
2
1
0
0
0
1
0
2
1
0
2
2
2
0
0
0
2
0
2
0
2
0
0
0
2
2
0
1
0
2
3
2
0
0
1
0
0
0
0
1
0
0
3
2
0
0
1
0
0
1
0
2
1
1
1
6
0
0
3
2
1
0
2
0
2
0
0
3
1
0
1
0
2
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
2
2
0
1
0
0
1
0
0
1
1
1
1
0
0
0
0
1
1
0
0
1
0
1
0
0
0
2
0
2
0
2
0
2
1
0
0
0
1
2
0
0
1
0
2
0
1
0
0
0
1
0
0
0
0
0
2
1
0
0
1
1
0
0
2
1
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
3
2
2
1
0
0
2
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
2
3
1
0
0
1
1
0
4
0
0
1
0
2
0
1
0
1
2
0
0
0
1
0
0
0
0
1
0
0
0
2
0
3
1
0
0
1
0
1
0
0
1
0
0
1
1
1
0
1
0
0
2
1
0
0
0
0
1
0
0
2
0
1
3
2
0
0
0
1
2
2
2
2
2
3
1
2
1
0
0
0
2
2
1
0
0
0
0
0
1
0
1
2
0
0
0
2
0
2
0
3
0
2
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
2
1
1
0
2
0
0
0
3
2
1
0
0
0
0
0
2
4
0
0
0
0
2
0
2
0
2
0
2
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
1
0
0
0
3
0
0
0
1
2
0
0
0
2
2
3
0
0
1
0
0
0
1
2
0
0
3
0
1
0
0
1
1
2
0
0
0
1
0
2
0
0
0
0
2
0
0
0
2
0
0
1
2
1
2
0
0
1
0
0
1
0
0
1
0
0
2
2
2
1
0
1
0
2
2
1
2
1
0
0
0
0
2
1
1
0
2
2
0
1
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
1
3
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
6
0
0
1
0
0
0
1
0
0
0
2
1
2
0
0
1
2
0
0
1
2
0
1
1
1
2
1
0
1
2
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
1
1
0
1
0
3
1
0
2
1
0
1
2
1
2
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
1
0
0
1
0
2
2
3
1
1
0
0
1
2
1
2
0
0
1
1
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
3
0
2
1
0
0
0
1
0
2
1
1
0
0
0
1
0
1
0
1
0
1
0
1
0
1
2
2
1
2
2
0
0
0
2
1
0
0
0
2
1
0
0
1
2
0
0
1
1
0
0
0
0
1
0
3
2
2
1
2
0
0
0
1
1
2
0
0
2
4
1
0
0
2
0
0
1
0
0
0
2
0
1
0
0
1
1
0
2
2
1
0
2
0
0
2
2
0
0
2
0
0
0
0
2
1
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
3
1
0
2
0
2
0
0
0
0
2
0
1
0
0
1
1
0
0
1
0
0
1
0
0
2
2
0
0
0
0
0
1
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
1
1
0
2
0
1
0
2
3
0
0
0
2
1
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
1
1
0
1
1
1
0
0
0
0
2
0
1
2
0
0
0
0
0
2
1
1
0
0
0
3
2
0
0
0
2
0
0
0
1
2
0
1
0
0
0
1
2
2
2
2
0
2
0
0
0
0
2
3
0
1
2
1
0
1
0
2
0
0
1
0
0
0
0
0
3
3
0
0
0
0
0
2
0
1
0
0
1
0
1
0
1
1
0
0
0
2
2
0
1
0
2
0
1
0
0
2
0
0
1
2
0
0
0
0
2
1
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
1
2
1
1
0
0
0
2
0
0
0
0
0
0
0
1
1
2
0
0
1
0
2
2
0
2
2
0
0
0
1
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
2
2
2
1
2
2
0
0
0
0
2
2
0
0
2
0
0
0
2
2
0
1
1
0
3
0
2
0
0
1
0
2
0
0
1
1
1
0
0
2
0
0
5
0
0
0
1
2
1
2
1
1
2
1
2
1
1
2
1
1
0
0
0
0
0
0
0
2
1
2
0
2
1
0
0
2
0
2
0
1
2
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
1
0
1
2
0
1
0
1
0
0
0
0
2
0
0
0
2
0
2
0
2
1
0
0
0
0
1
0
0
2
0
2
0
1
1
1
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
1
1
1
1
1
0
0
0
0
0
2
2
0
0
0
3
0
1
0
0
0
2
1
1
2
2
0
1
2
0
2
0
0
0
2
0
0
0
0
0
0
0
2
2
2
1
0
2
0
0
0
1
0
0
0
1
0
2
1
0
2
0
0
0
0
2
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
1
3
0
1
2
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
2
0
0
0
2
0
0
2
1
1
0
0
1
1
0
0
1
0
2
1
1
0
2
4
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
1
1
2
0
0
2
1
0
1
0
0
1
0
0
2
2
2
1
2
1
2
2
0
0
0
0
0
0
2
0
0
1
1
0
2
0
0
0
0
2
0
0
1
3
0
3
0
2
0
0
0
0
2
1
3
1
0
0
3
1
0
0
0
0
0
0
1
2
1
2
0
0
2
1
2
0
2
2
0
0
2
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
1
1
0
0
3
0
1
2
1
1
0
1
0
1
2
0
0
0
0
1
0
1
0
0
0
0
0
1
2
2
0
1
0
1
0
0
0
0
0
2
2
0
3
1
0
0
0
0
0
0
0
1
1
1
0
1
2
2
1
0
0
2
2
0
0
1
0
0
2
1
0
1
1
0
0
1
1
1
1
0
2
0
1
1
0
0
0
0
0
0
1
1
1
0
0
2
0
0
1
1
0
3
1
1
0
1
1
2
0
1
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
1
0
0
2
1
1
0
0
0
0
1
0
0
2
0
1
2
2
0
0
0
0
1
0
0
2
1
1
0
0
1
0
3
0
0
0
1
0
0
1
2
1
2
0
0
2
0
0
0
2
0
0
0
0
1
0
1
0
1
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
1
2
0
2
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
3
0
0
1
0
1
0
0
0
1
0
1
0
0
3
1
2
1
0
1
0
2
2
2
2
0
0
0
1
0
0
0
0
0
1
0
1
2
1
2
1
0
3
2
0
0
0
0
0
1
0
0
1
0
0
0
2
2
2
0
0
1
0
1
0
2
0
1
0
0
3
0
1
2
1
0
0
0
0
0
1
0
0
1
1
0
0
2
0
0
0
1
2
1
2
0
1
0
2
1
0
0
2
0
0
0
0
0
1
3
1
2
2
0
0
0
2
0
0
0
0
0
0
0
0
2
1
1
1
0
1
0
0
1
0
1
0
1
0
0
0
2
2
2
0
1
0
4
0
2
0
1
0
1
2
0
2
0
1
1
0
0
0
0
0
0
0
1
1
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
2
1
1
2
1
2
2
0
0
0
2
0
0
1
0
2
1
0
0
2
2
0
0
1
0
0
2
1
2
1
1
1
2
0
0
1
2
2
0
2
0
0
1
0
0
0
0
0
1
2
1
1
0
0
0
1
0
0
0
0
0
1
0
0
1
2
2
0
1
2
0
0
2
0
1
1
0
0
0
0
0
0
1
0
1
2
1
0
0
2
0
0
2
1
0
1
0
0
0
0
0
0
3
1
0
0
1
2
0
2
0
13
2
0
0
1
0
3
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
1
0
0
1
1
0
1
0
0
8
0
3
2
2
0
0
0
1
0
0
0
5
1
0
0
0
0
0
0
0
1
1
2
0
2
2
0
1
2
0
3
0
1
2
0
0
2
0
2
0
0
1
0
1
1
0
1
0
0
0
0
1
0
1
0
2
0
0
0
1
0
3
0
0
0
2
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
1
1
2
2
3
0
2
0
0
1
0
0
1
0
0
0
1
0
1
0
0
3
1
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
3
1
0
0
0
0
2
0
1
0
2
0
0
0
0
1
1
0
0
2
1
1
1
0
0
0
0
0
2
1
0
1
2
1
3
0
1
0
0
0
0
0
2
2
1
1
1
0
0
2
2
0
0
0
1
0
1
0
0
0
0
0
0
3
0
1
1
0
0
1
0
1
0
0
0
0
0
1
2
1
0
0
2
0
1
0
0
2
0
1
1
0
2
0
0
0
2
1
1
0
2
1
0
2
2
0
2
0
2
0
0
0
0
1
0
0
0
2
1
2
1
0
0
1
0
1
0
0
0
1
0
1
0
1
2
0
1
0
0
2
0
1
0
0
0
2
0
2
0
0
2
1
1
1
2
1
4
2
0
0
3
2
0
1
1
1
0
1
0
2
0
0
1
1
1
2
1
2
3
0
0
1
0
2
1
1
2
0
1
0
0
0
0
0
1
1
2
1
2
0
5
1
0
2
2
2
0
2
0
0
3
1
0
2
0
0
4
1
2
0
0
0
0
0
1
0
0
2
0
0
0
3
2
0
0
0
2
0
2
0
0
0
0
3
0
0
0
0
2
1
0
0
1
0
0
1
0
0
0
0
2
0
0
1
0
0
0
1
1
0
0
1
2
1
1
0
0
2
0
0
2
0
1
0
4
0
0
1
0
5
0
2
1
2
0
1
1
0
2
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
2
1
0
4
2
0
0
2
2
2
1
0
0
0
0
2
0
1
0
1
0
0
2
2
1
0
0
1
3
2
0
0
0
4
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
5
0
1
1
1
0
0
2
0
0
0
1
0
2
0
1
0
2
0
0
1
0
0
1
2
0
0
0
1
0
2
2
1
0
0
0
0
1
1
2
1
0
3
1
1
0
0
2
2
1
2
1
0
0
0
0
1
0
1
0
0
0
1
1
0
0
1
2
2
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
1
2
2
2
0
0
0
0
2
0
1
0
0
2
2
0
0
0
3
0
0
2
0
2
0
0
0
0
1
2
1
1
1
1
0
2
1
0
2
1
2
2
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
1
1
1
1
0
0
0
2
0
0
0
0
0
0
2
2
2
1
1
2
0
1
0
2
0
1
3
2
0
2
0
1
0
0
0
0
0
1
0
0
0
0
2
1
2
0
1
0
2
0
0
2
2
2
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
1
0
2
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
3
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
1
0
0
1
0
0
0
0
0
1
0
1
2
0
2
0
1
0
0
0
0
1
0
2
0
2
0
1
2
0
2
0
0
0
0
0
0
0
1
0
1
0
2
2
0
1
1
2
0
0
1
1
2
2
0
2
2
1
2
0
0
2
1
0
1
2
0
0
1
0
0
0
0
0
1
0
1
0
0
1
1
1
0
0
1
1
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
1
0
1
2
2
0
0
0
2
0
1
1
1
0
2
1
0
0
0
0
0
0
0
0
0
0
1
2
0
1
1
0
0
0
0
1
1
0
0
1
0
0
0
1
1
0
1
0
2
1
1
0
0
0
1
5
0
0
1
1
2
2
2
0
0
2
1
0
2
2
0
0
0
0
0
0
1
1
0
0
1
2
0
0
1
0
0
0
0
0
2
1
0
0
2
0
2
0
1
1
0
1
0
0
1
0
1
0
0
1
0
1
0
1
0
1
2
0
2
1
2
1
0
0
0
0
0
0
0
2
0
0
3
1
2
0
2
0
0
2
1
0
0
0
0
1
0
2
0
0
1
0
2
1
0
0
0
0
1
0
1
2
0
1
0
2
0
0
2
1
4
0
2
0
1
0
1
0
0
0
2
0
0
2
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
1
0
0
0
1
2
0
2
2
0
0
1
0
0
1
1
0
0
0
1
0
2
0
0
2
1
4
2
0
0
0
0
0
1
1
1
0
0
0
0
3
0
0
0
0
3
2
2
0
0
1
0
0
1
0
0
0
0
2
0
0
0
2
1
2
3
0
0
2
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
1
0
0
1
0
4
0
1
0
0
2
2
2
0
1
2
0
0
0
2
0
2
0
2
0
2
0
2
0
0
0
2
1
0
0
2
0
0
2
3
0
1
0
0
1
0
1
0
1
1
2
0
1
0
1
0
0
1
2
2
0
2
0
1
1
2
0
0
0
8
2
1
0
1
0
1
1
1
0
0
0
1
0
0
1
0
1
2
0
1
1
1
0
0
0
1
0
1
0
0
2
0
0
2
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
1
2
0
1
0
2
0
1
2
0
0
0
0
1
2
1
1
0
2
0
2
2
0
0
0
2
0
0
2
0
0
0
2
1
0
2
1
0
0
0
1
0
0
3
0
0
3
1
0
0
2
0
2
0
0
0
1
0
1
0
1
0
1
2
0
1
1
1
2
1
0
0
2
0
1
0
0
1
0
2
0
2
0
0
0
0
0
2
1
0
1
1
0
0
2
0
0
0
1
0
0
0
0
0
2
1
2
1
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
2
1
1
0
0
0
0
1
0
1
0
0
0
2
0
2
0
0
0
1
0
1
1
0
0
2
2
0
1
0
1
0
0
0
0
3
1
1
0
0
1
0
2
0
0
1
0
2
2
3
1
0
2
0
3
0
0
2
2
2
0
2
1
0
1
0
0
1
1
1
0
0
0
2
0
0
1
1
1
0
0
0
0
0
0
0
1
0
2
1
1
0
2
2
1
1
0
0
1
0
2
1
0
0
0
2
0
1
2
1
0
1
0
2
0
1
0
0
0
0
2
0
0
1
0
2
2
0
0
0
0
0
0
0
0
2
0
0
1
1
1
1
0
0
1
2
0
0
0
0
1
1
0
0
1
0
2
1
1
2
0
0
0
0
0
1
1
0
3
0
2
0
2
3
0
1
2
0
2
0
3
0
0
1
2
0
0
1
2
1
1
0
0
1
0
1
0
0
0
2
2
2
0
0
0
0
3
0
1
0
0
1
0
1
0
0
1
0
1
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
1
2
0
0
2
0
2
0
1
0
0
0
1
1
0
0
1
1
0
2
1
1
0
0
1
0
0
0
2
2
0
0
1
0
2
2
2
2
1
1
0
0
0
0
0
0
1
2
1
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
1
1
0
0
1
2
0
0
1
0
1
1
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
2
1
0
0
0
2
0
0
2
0
0
0
0
0
0
2
1
1
1
2
1
1
0
1
1
2
1
0
0
0
2
0
0
0
1
2
0
1
0
1
0
0
0
3
0
1
0
1
0
0
0
0
2
0
0
0
0
1
2
0
0
1
1
0
1
2
0
2
0
0
1
0
0
0
0
0
0
0
0
1
1
2
1
1
0
1
0
0
0
1
2
2
0
0
1
1
1
1
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
1
1
2
1
0
0
0
0
2
1
1
3
0
0
1
2
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
1
0
0
0
1
2
0
2
2
0
2
0
1
2
0
0
1
2
1
0
0
4
2
0
1
1
0
0
0
1
0
2
0
0
0
0
0
0
2
0
2
0
1
0
1
2
0
1
0
0
0
1
0
1
2
0
0
2
1
0
0
0
0
1
0
1
2
0
0
1
0
0
0
0
1
0
0
0
2
2
2
2
0
0
0
0
0
2
1
0
0
2
0
0
2
1
0
2
0
1
2
1
2
0
0
1
0
2
1
0
0
0
0
1
2
2
0
2
0
1
4
1
0
0
0
0
0
0
0
2
2
1
0
0
2
0
1
2
0
0
0
0
1
0
0
0
2
0
0
1
0
2
0
3
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
1
1
1
2
0
0
1
2
0
0
0
0
0
1
0
2
0
1
0
2
0
0
0
2
0
0
2
2
1
0
0
1
2
0
0
0
0
0
0
5
1
2
0
0
0
0
2
1
0
0
1
1
2
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
1
2
0
0
1
0
1
1
1
0
2
1
0
1
0
0
1
1
2
1
0
1
1
2
1
1
2
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
2
0
1
0
1
0
0
0
1
2
0
0
0
1
0
1
0
2
0
3
0
2
2
2
0
0
0
0
1
0
1
0
0
1
0
2
1
1
1
2
0
0
0
0
0
2
0
2
1
1
1
0
0
0
0
0
2
0
1
0
1
0
1
0
0
0
1
0
0
0
2
1
0
0
0
0
0
1
0
3
0
1
0
2
0
1
2
0
0
0
0
6
2
0
0
2
2
0
0
0
0
2
2
1
0
2
0
0
0
0
1
0
0
0
1
0
0
1
0
2
0
0
0
2
0
0
0
1
0
0
1
0
1
1
0
0
1
1
1
0
2
0
1
2
0
0
3
0
0
0
0
0
1
0
1
1
1
2
2
0
2
0
0
2
1
0
1
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
1
1
2
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
1
1
0
0
0
0
0
0
2
1
2
1
0
0
0
2
2
0
1
1
0
2
0
1
2
0
1
2
1
0
0
2
0
6
0
2
2
0
2
0
1
1
0
1
2
0
0
1
3
0
0
0
1
0
0
0
1
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
2
0
2
0
3
2
0
0
0
1
0
0
0
0
2
1
2
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
1
2
0
1
0
2
0
0
1
0
0
1
2
0
0
1
1
0
0
1
4
0
2
0
1
0
0
0
2
0
0
0
0
2
0
0
0
1
2
2
1
0
0
2
1
0
2
0
1
0
1
0
1
0
2
2
0
0
0
0
2
0
0
0
1
0
1
0
0
0
1
1
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
1
3
1
3
0
1
1
1
0
2
0
0
0
1
0
0
0
1
0
0
0
2
0
1
0
0
0
1
0
1
2
1
1
1
1
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
2
2
0
0
0
1
0
1
0
0
1
1
0
0
1
0
1
0
0
1
0
0
0
0
1
2
1
1
0
0
0
1
0
0
1
0
0
1
1
0
2
0
1
0
0
0
1
1
0
1
1
0
2
0
0
2
2
0
1
1
2
1
0
0
0
0
1
3
2
1
0
1
0
2
1
3
0
0
1
1
2
0
0
0
1
2
0
0
0
0
1
0
2
0
2
0
0
2
0
1
0
0
0
1
2
0
1
0
1
0
0
0
0
1
0
2
0
0
0
2
2
0
0
0
2
0
0
0
0
0
1
1
1
1
0
0
0
0
2
1
0
0
0
1
1
1
2
0
2
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
1
1
0
2
0
0
0
0
0
1
0
0
1
0
0
2
0
2
1
0
0
1
0
1
0
0
0
0
1
1
0
4
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
1
1
0
0
2
2
2
1
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
2
1
0
0
0
2
0
2
0
0
0
0
0
0
1
0
1
0
2
1
0
1
1
2
2
0
4
0
0
0
0
1
0
2
1
1
0
0
0
2
0
0
0
1
2
0
0
0
2
1
0
0
0
0
2
0
1
1
1
1
0
0
1
2
0
1
2
0
1
0
1
0
0
0
0
0
0
2
2
2
0
1
1
2
1
1
0
1
2
1
0
0
0
2
1
1
0
2
0
1
3
0
0
2
1
0
1
1
1
0
0
0
0
1
1
2
1
2
1
1
1
2
2
1
0
1
1
0
2
1
2
0
0
0
0
2
2
1
1
1
2
1
1
0
1
0
0
2
0
1
1
1
2
0
1
0
1
1
0
4
0
0
1
1
0
0
1
0
2
0
1
0
2
0
2
1
2
0
0
1
2
0
1
0
2
0
2
2
1
0
0
1
0
3
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
3
0
2
0
2
3
0
0
0
0
1
0
0
1
0
0
0
0
0
1
3
0
2
0
0
2
2
2
0
0
1
0
1
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
2
0
0
2
0
0
1
2
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
2
2
2
2
2
0
0
0
0
0
2
0
1
0
0
2
2
2
0
0
2
0
0
2
0
0
2
1
0
1
1
0
0
2
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
2
1
0
2
1
0
2
0
1
2
0
0
1
1
0
0
0
0
0
2
0
1
1
0
0
0
0
1
0
0
0
0
3
0
0
0
1
0
0
1
1
0
1
0
1
0
1
0
0
0
3
1
0
0
0
0
2
2
0
3
1
0
1
1
0
0
0
0
1
2
0
2
0
1
0
0
0
0
8
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
4
0
0
0
1
1
2
2
2
1
2
0
0
0
0
0
1
2
0
1
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
3
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
1
0
0
0
14
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
2
0
1
0
0
1
0
0
0
4
0
2
1
0
1
1
0
0
0
2
0
0
3
1
0
3
0
2
1
0
1
0
1
0
1
1
1
2
0
0
0
2
2
2
1
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
1
2
2
0
0
1
2
0
0
2
0
0
0
1
1
0
0
0
2
0
0
0
0
2
1
0
1
0
0
0
1
2
0
0
2
0
1
2
1
1
2
2
3
0
0
2
0
2
2
0
1
1
0
0
0
0
3
0
0
0
1
1
2
0
1
2
0
0
0
0
2
0
3
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
1
2
0
0
0
2
1
0
0
1
0
0
0
2
2
0
0
0
0
0
0
1
0
0
1
1
1
0
2
0
0
0
0
0
0
2
0
0
1
0
1
0
6
0
2
0
1
0
0
2
0
0
1
0
0
0
1
0
0
0
2
1
1
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
1
2
0
0
0
0
0
1
2
0
0
1
0
0
0
1
2
0
2
0
0
0
2
0
2
1
0
0
2
0
2
2
0
0
0
2
0
1
0
1
1
0
0
1
0
0
0
1
1
0
0
0
0
1
1
0
2
2
0
2
0
0
1
0
2
0
1
0
1
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
1
1
0
1
0
1
0
0
0
0
0
1
1
0
0
1
0
1
2
0
0
0
1
1
0
1
1
1
0
0
0
0
0
0
0
0
2
1
0
1
2
0
2
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
4
0
0
1
1
2
0
0
0
2
1
0
1
1
0
0
0
2
0
1
1
0
1
0
0
1
1
0
0
2
0
0
0
1
2
1
0
1
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
1
1
0
0
0
0
0
0
1
2
1
2
0
0
0
0
0
0
1
2
1
0
1
1
1
2
0
0
1
0
2
1
2
0
0
0
2
2
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
2
2
0
0
2
0
1
1
1
1
0
2
0
5
0
0
0
0
1
0
2
0
0
1
1
0
1
0
2
2
1
1
0
2
0
0
0
0
0
1
1
0
1
0
0
0
0
2
0
1
1
1
0
0
1
0
0
0
1
0
0
0
1
0
0
2
0
0
0
1
2
3
0
0
2
0
0
1
0
0
1
1
0
0
2
0
0
0
1
1
2
0
0
0
1
0
0
2
2
0
0
2
1
2
1
0
1
0
0
0
0
0
2
1
1
0
0
1
2
0
0
0
2
1
0
2
0
0
1
0
0
1
1
1
0
0
1
1
0
0
0
2
0
0
0
2
0
0
1
5
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
2
0
1
0
2
0
0
2
0
0
1
3
0
0
1
0
6
0
0
1
0
0
0
0
2
0
1
2
0
0
0
1
0
0
0
2
1
1
0
1
0
2
0
0
0
0
0
0
1
0
0
1
0
2
3
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
3
2
1
1
0
2
2
2
1
0
1
2
0
0
0
1
0
0
1
0
0
1
0
1
2
1
0
1
1
0
1
0
0
0
2
2
1
1
0
1
0
0
0
1
1
0
0
1
0
0
1
0
0
1
0
2
0
0
2
1
1
0
0
2
1
0
0
3
0
1
1
1
0
2
0
1
1
0
1
0
0
0
1
1
2
0
1
2
0
0
0
0
2
0
1
0
1
1
1
0
1
0
0
0
0
0
0
2
0
0
1
0
2
0
2
2
0
0
1
2
2
0
0
2
0
2
0
3
0
0
0
2
2
1
1
0
0
0
1
2
1
1
0
0
0
0
0
0
0
1
0
0
1
0
2
2
2
0
0
1
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
2
1
0
0
0
0
0
0
0
2
1
0
2
2
1
0
0
1
0
2
0
0
4
0
0
1
1
0
2
1
0
0
2
1
0
0
0
0
2
0
0
0
0
1
0
1
1
0
0
0
2
2
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
1
2
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
2
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
1
2
0
0
0
0
0
1
2
1
1
1
0
0
0
2
1
0
0
0
0
2
0
0
0
3
0
0
0
2
0
0
0
2
1
1
1
0
2
2
0
0
0
2
0
0
1
2
0
1
0
1
0
0
0
2
0
1
0
1
0
0
1
0
1
1
0
2
0
0
0
1
0
0
0
0
3
0
1
1
4
0
0
0
0
0
1
3
0
2
2
1
1
2
1
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
1
0
1
0
0
2
2
0
0
2
0
2
0
3
1
0
0
0
1
0
1
1
0
1
0
2
1
0
4
0
0
0
1
1
0
0
0
2
0
3
1
0
0
1
0
0
2
1
2
0
5
0
1
0
0
2
0
1
2
0
0
0
0
0
2
1
0
2
0
2
0
0
2
2
0
0
2
0
2
3
0
1
0
0
0
0
0
0
1
0
1
0
1
2
2
0
2
1
0
2
0
0
0
2
0
0
1
1
0
0
1
0
1
2
1
0
0
2
0
2
0
0
1
0
0
0
0
0
1
2
2
0
0
1
0
0
0
1
2
0
0
0
0
0
1
0
1
0
1
0
2
0
1
2
2
1
0
0
2
0
2
0
0
1
1
0
2
2
0
1
2
0
2
0
0
0
2
1
0
2
0
0
0
0
0
2
0
0
1
1
2
2
0
2
2
0
0
2
0
2
0
2
1
0
1
0
2
0
0
2
0
0
0
1
0
2
0
0
1
0
1
0
0
1
2
0
0
0
0
0
2
1
2
0
0
1
2
0
2
0
1
2
0
1
0
0
0
1
0
0
1
0
0
0
0
0
2
0
3
2
1
2
1
0
0
2
1
0
0
2
1
1
0
4
0
1
0
0
1
0
0
0
1
0
2
1
0
0
0
0
1
0
2
2
1
1
0
1
2
1
0
1
0
1
2
0
1
0
0
0
0
1
0
2
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
2
0
1
1
2
0
1
2
0
0
2
0
2
0
0
0
0
1
0
1
2
1
0
0
0
0
1
2
0
2
0
0
0
2
0
2
0
1
0
0
1
0
2
1
0
0
0
0
3
0
0
0
0
1
3
0
0
0
2
1
0
0
1
0
0
1
2
0
1
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
1
1
2
0
0
1
0
0
1
0
0
1
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
2
1
0
2
0
0
0
0
0
0
0
0
3
0
1
1
0
0
0
0
1
0
0
0
1
0
2
0
1
2
1
0
0
0
0
0
1
0
2
0
2
2
0
0
1
2
0
0
0
1
1
0
0
2
0
1
0
0
1
2
6
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
1
0
0
0
1
2
0
1
0
1
0
2
2
1
2
0
2
0
0
2
0
0
2
1
0
1
0
0
1
0
1
0
0
1
1
0
1
1
0
0
0
0
0
1
1
1
0
1
1
2
1
2
0
1
1
1
0
0
2
1
0
0
1
0
0
2
1
3
1
2
5
0
2
0
1
0
0
0
0
0
2
0
3
2
4
0
0
0
0
2
1
1
2
0
0
1
0
2
0
0
0
2
0
0
0
0
0
1
2
0
0
0
2
2
0
0
1
0
0
1
1
1
1
0
2
0
0
0
1
0
0
1
0
1
0
1
2
0
0
0
0
0
0
0
3
1
0
0
0
2
0
0
0
0
2
0
0
3
2
2
0
0
0
2
0
0
1
0
2
0
0
0
0
1
0
2
2
0
0
2
1
0
0
1
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
1
0
0
0
2
0
0
1
2
0
0
0
2
0
0
1
2
1
1
0
0
2
0
0
2
0
1
0
2
0
0
0
3
0
1
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
4
10
1
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
1
0
2
0
0
2
2
2
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
2
2
2
0
2
0
0
2
0
1
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
2
0
1
2
1
0
0
0
0
0
1
0
0
0
0
1
1
0
1
2
2
0
1
1
0
1
0
1
0
0
0
2
0
1
0
0
1
0
1
1
1
0
2
1
0
1
0
0
0
1
2
1
0
0
0
0
1
1
0
1
1
2
1
0
1
0
0
2
1
0
0
0
2
0
1
0
1
0
2
0
0
2
2
0
1
1
0
1
1
1
2
0
2
2
1
6
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
2
0
1
0
1
0
1
0
0
1
0
0
0
2
1
1
0
1
0
0
1
0
2
0
2
0
2
2
1
0
1
0
0
0
2
1
1
0
2
0
2
0
0
0
0
2
0
2
2
1
1
0
0
0
4
0
1
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
1
0
0
2
0
0
1
0
1
2
0
2
1
0
0
1
1
0
1
2
2
0
3
2
2
0
0
0
2
0
0
0
2
0
0
2
1
2
2
0
1
0
0
1
0
0
0
0
1
1
0
0
1
1
0
0
0
0
1
2
1
0
0
0
1
1
2
1
0
0
0
2
1
0
1
0
1
0
2
0
0
0
0
2
2
2
0
0
0
0
1
0
0
1
0
1
2
0
0
2
0
1
0
1
0
2
0
2
1
0
0
0
0
2
1
1
2
0
0
1
1
0
0
0
1
0
1
2
2
2
0
0
0
1
1
0
0
0
0
1
0
0
1
0
1
0
2
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
1
0
2
0
0
0
2
3
2
0
0
0
0
1
0
0
1
0
2
0
0
2
0
0
1
1
0
0
2
0
0
0
0
0
0
1
1
0
1
2
1
0
0
1
0
1
2
1
0
0
2
1
0
0
2
0
0
2
0
0
0
0
1
0
2
2
0
0
0
1
2
0
0
0
0
0
0
2
2
1
0
1
0
0
0
1
0
0
0
2
0
2
0
1
2
1
2
5
0
1
1
0
2
4
0
0
1
0
0
0
0
0
0
2
0
0
1
2
0
0
0
1
0
1
0
0
0
1
2
3
0
0
0
2
0
0
0
6
2
1
2
0
0
0
0
1
1
1
0
0
0
2
0
1
2
1
1
2
3
0
0
1
0
0
1
0
0
0
0
2
0
2
0
3
0
0
0
0
1
0
0
0
2
0
0
0
0
1
1
2
0
0
0
0
0
2
1
0
2
0
0
1
0
0
2
2
3
0
1
2
2
0
0
0
0
0
1
2
1
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
2
0
0
0
2
0
2
0
0
2
0
0
1
0
1
0
2
0
1
0
0
0
0
2
2
0
1
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
3
1
0
0
0
2
0
0
1
1
0
0
0
0
1
0
0
2
0
1
1
0
2
0
0
1
0
1
0
0
2
0
2
1
1
1
1
0
0
0
0
0
0
1
2
2
2
2
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
1
1
1
1
2
1
0
2
1
0
0
1
0
0
1
2
0
2
2
0
0
2
2
1
0
1
1
3
0
2
0
1
2
0
0
2
0
1
1
0
0
0
0
1
1
2
1
3
1
0
1
1
0
0
5
0
1
0
0
2
0
1
0
2
0
0
2
2
0
1
0
0
0
1
0
1
2
0
2
0
1
0
1
1
1
1
1
0
0
0
0
0
1
0
0
2
2
0
1
2
2
1
2
2
0
0
0
0
2
0
2
1
0
0
1
0
0
0
0
2
2
0
2
1
2
2
0
0
0
0
0
0
1
0
0
0
2
0
1
2
0
1
0
0
0
0
0
0
2
0
0
2
2
0
2
2
0
2
1
0
2
0
1
0
1
0
2
1
0
0
0
0
0
1
0
0
1
1
0
1
0
2
0
0
2
0
0
1
3
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
1
2
1
0
0
0
0
2
1
0
1
0
0
0
0
0
2
1
0
0
0
0
1
1
0
0
0
0
2
0
0
2
0
0
0
0
0
1
1
0
3
1
0
0
0
2
4
2
0
1
0
0
0
0
0
0
1
1
0
1
2
0
1
0
0
2
1
1
0
0
0
4
0
1
0
0
2
0
2
1
0
0
0
1
0
0
1
0
0
0
0
1
1
0
2
1
0
2
2
0
0
0
1
0
1
1
0
0
2
0
1
0
2
0
0
0
0
1
1
3
0
0
0
0
1
0
1
0
0
1
0
0
0
2
0
2
0
1
0
1
0
0
1
1
0
1
1
0
0
2
2
1
0
2
0
0
0
0
0
0
2
0
4
1
2
1
0
0
1
0
0
0
1
0
2
1
0
0
3
2
0
2
0
1
0
0
2
1
0
0
0
2
1
0
2
2
1
2
1
0
0
0
2
0
1
0
2
0
2
0
0
0
1
2
0
0
1
0
0
0
0
2
2
0
2
0
0
0
0
0
2
0
0
1
0
0
2
0
2
0
0
2
0
0
1
2
0
0
0
0
1
0
1
0
0
3
0
2
0
1
0
0
0
1
0
2
0
0
2
2
0
1
0
0
0
0
1
1
2
0
2
1
0
2
3
2
1
1
0
1
0
0
1
2
0
0
0
0
0
1
2
1
1
1
2
2
0
2
1
0
2
0
1
0
3
2
0
1
0
0
0
1
1
1
1
0
0
0
0
0
0
1
0
1
0
2
0
0
1
2
0
0
2
0
1
0
0
0
0
2
1
0
0
2
2
1
3
1
2
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
2
1
0
0
0
1
1
0
2
0
0
2
0
1
1
1
2
0
1
2
2
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
2
1
1
0
0
0
0
1
0
2
0
0
2
1
0
1
0
0
1
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
2
1
0
0
0
0
1
0
0
0
0
1
0
0
1
2
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
1
0
0
3
0
0
1
0
0
0
0
1
1
0
0
0
1
0
1
0
1
1
0
1
0
1
2
2
0
0
0
2
0
2
0
1
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
2
0
5
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
1
0
0
1
1
0
0
0
1
1
0
0
1
1
0
1
2
1
1
2
0
0
0
0
0
0
1
0
5
0
1
0
0
1
0
0
0
0
0
0
2
0
0
1
1
0
0
1
1
0
0
1
1
1
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
1
0
2
0
2
0
1
0
0
0
0
1
2
0
1
1
1
0
0
2
0
0
0
0
0
0
1
0
1
2
1
0
0
0
0
0
0
1
0
1
0
2
2
0
0
0
0
1
0
1
0
1
0
1
2
1
2
0
0
1
0
0
2
0
0
0
2
2
1
0
0
1
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
2
2
0
0
0
0
0
1
0
0
1
1
2
2
2
0
1
0
0
0
2
0
2
0
1
0
0
0
1
0
0
0
1
0
2
1
0
0
0
0
0
0
2
2
1
1
2
1
0
1
0
0
2
0
0
0
2
0
0
1
2
0
2
0
1
0
2
4
0
0
0
0
1
1
1
0
2
1
0
0
1
1
2
0
2
2
1
0
0
0
1
3
2
0
0
0
2
0
1
0
0
0
1
0
0
1
2
0
0
0
1
0
2
0
2
0
0
0
2
0
0
1
0
0
1
2
0
2
0
2
1
2
0
0
2
1
0
0
2
0
2
0
0
0
0
2
0
0
0
0
2
2
1
1
1
1
0
0
0
2
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
2
0
0
1
0
0
0
0
2
0
0
2
1
0
2
3
2
0
0
1
0
0
0
2
1
0
2
0
0
0
2
2
0
1
2
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
2
1
1
0
2
0
0
0
0
2
3
0
1
2
0
2
3
0
2
0
0
0
0
2
0
0
0
4
0
2
2
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
6
2
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
1
1
0
0
2
0
0
0
1
1
0
0
1
2
0
0
1
1
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
1
0
0
2
2
2
1
0
0
1
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
2
1
0
1
0
2
0
0
2
2
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
3
0
0
0
2
2
1
0
0
2
2
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
3
1
2
0
2
1
0
1
0
1
0
0
0
0
1
1
0
2
0
0
1
0
0
2
1
2
4
2
0
1
1
0
1
1
1
2
2
2
0
2
0
2
0
0
2
0
0
0
2
1
1
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
1
1
1
1
0
2
2
1
0
1
1
0
0
2
0
2
1
0
0
2
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
2
0
2
0
1
0
1
0
0
1
0
0
0
1
0
0
0
2
0
0
0
2
2
0
0
1
0
0
2
0
1
2
1
0
0
0
3
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
2
1
0
1
1
1
0
3
0
0
0
0
1
1
1
2
2
0
0
0
3
0
2
1
1
1
0
0
0
1
0
2
0
0
1
1
1
0
0
3
0
2
2
0
3
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
2
0
1
0
2
0
1
0
1
2
2
1
1
1
0
1
0
0
0
1
0
2
0
0
0
1
1
2
1
1
1
1
2
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
1
0
2
1
1
0
0
2
3
2
0
1
1
0
0
0
1
0
1
0
2
1
2
0
0
0
1
2
3
0
0
0
0
1
1
0
1
2
1
2
0
2
1
0
2
0
0
2
0
0
0
0
0
0
1
2
0
1
0
0
0
2
0
2
0
0
1
0
2
0
1
0
0
0
2
0
0
2
0
2
2
0
1
2
1
0
1
0
1
2
1
1
0
1
1
0
1
2
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
1
0
1
0
2
2
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
2
0
0
1
0
0
0
0
1
1
1
0
0
0
3
0
1
2
0
0
0
0
2
0
2
3
0
1
0
0
0
2
0
0
0
3
0
0
1
0
0
3
1
0
1
0
0
1
0
0
0
8
0
2
1
0
0
0
0
0
2
2
0
1
1
1
1
0
0
0
2
0
2
1
0
1
0
1
1
1
1
2
0
0
0
1
0
2
1
0
1
0
2
1
0
1
0
0
1
1
1
0
0
0
0
1
2
0
0
2
1
0
0
1
0
0
0
2
0
0
2
1
0
1
1
0
0
2
0
0
1
0
0
0
1
0
0
2
0
1
1
1
0
2
0
2
0
0
2
2
0
2
0
2
2
0
0
0
0
1
0
2
0
1
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
1
0
0
2
1
2
0
1
0
0
0
2
3
0
0
0
1
3
0
0
0
0
4
1
1
0
0
0
0
0
2
0
2
2
2
0
1
1
1
0
2
0
1
0
0
1
1
0
2
0
0
0
0
2
0
1
0
2
0
0
1
5
2
2
0
0
0
0
2
2
0
0
0
0
0
2
1
0
1
0
1
2
2
0
0
1
0
2
1
3
1
0
0
1
0
0
2
0
2
0
0
1
0
1
0
0
2
1
2
1
2
5
2
0
2
3
0
2
2
0
0
0
0
0
2
1
2
0
2
0
1
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
2
0
2
2
0
1
0
1
1
2
0
0
1
0
2
0
1
1
0
0
0
0
1
0
2
0
0
1
0
0
1
0
0
0
0
0
0
1
6
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
1
2
0
1
2
1
0
0
0
0
0
0
1
2
1
2
2
1
0
1
0
0
1
0
0
0
0
0
1
1
1
0
2
2
1
0
0
1
0
1
0
3
0
0
2
1
0
1
1
1
1
2
2
0
0
1
1
1
2
0
0
1
1
0
0
2
0
1
0
1
1
0
0
1
0
0
0
3
1
0
1
0
2
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
2
1
2
2
0
0
2
0
2
0
0
2
0
0
1
1
2
0
1
1
0
1
0
0
0
0
3
2
0
0
0
0
1
1
0
2
1
1
3
0
0
1
0
0
2
0
2
1
0
1
0
2
1
0
2
0
0
1
0
0
1
0
0
0
0
0
0
5
1
0
2
2
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
2
2
0
3
1
1
1
0
0
0
1
0
0
3
0
0
1
0
2
0
0
0
2
3
0
0
0
1
2
0
1
0
0
1
0
0
2
0
1
0
3
0
1
1
2
0
0
0
2
0
2
1
2
0
0
0
0
0
0
2
2
2
1
0
1
1
0
2
0
1
0
0
0
2
0
0
1
0
0
0
1
0
1
0
0
1
2
0
0
0
2
1
0
0
0
0
2
0
0
1
2
0
0
2
2
1
0
0
0
0
0
0
2
0
1
1
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
2
0
0
1
0
1
1
0
0
0
0
2
2
0
1
0
1
2
2
1
1
0
1
1
0
0
0
1
0
0
0
0
0
2
0
2
2
0
0
2
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
2
2
0
0
2
0
0
2
2
2
2
0
2
0
0
0
2
2
0
0
0
2
0
0
0
1
0
1
2
0
0
0
0
0
0
2
1
3
0
0
1
0
1
0
0
1
0
0
1
2
2
0
2
0
2
0
2
0
2
0
0
0
0
2
2
1
3
0
0
2
0
0
1
2
0
0
0
2
2
0
0
0
2
0
1
0
1
0
2
1
0
0
0
0
0
1
0
0
0
2
1
0
0
2
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
2
2
2
0
0
0
2
0
0
1
1
0
0
0
0
0
0
2
0
2
1
1
0
2
0
1
2
2
0
1
0
0
0
0
0
0
0
0
0
2
1
0
2
0
1
1
0
0
1
2
1
0
0
1
1
0
0
0
0
1
2
0
2
2
1
0
0
1
0
0
0
0
0
0
0
2
2
1
2
1
2
1
0
2
0
1
0
1
2
0
0
0
0
2
1
0
1
0
0
0
2
1
0
1
2
0
0
1
1
0
0
0
0
1
0
1
1
1
0
0
1
0
3
2
3
1
1
2
0
0
1
0
2
0
2
0
0
1
0
2
3
0
1
1
0
0
0
3
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
1
2
0
1
0
0
0
1
2
0
0
0
1
0
0
0
0
1
1
0
1
0
2
1
0
0
0
0
2
2
1
0
0
0
2
0
1
0
0
0
0
2
1
1
0
0
2
2
1
1
2
1
2
2
1
0
2
0
0
1
0
1
0
1
0
1
2
0
0
0
0
1
0
0
2
0
2
1
0
0
1
0
0
0
0
2
1
0
2
0
1
0
0
0
1
2
1
0
0
0
0
0
0
0
2
1
0
2
1
2
1
4
0
2
0
1
1
0
0
1
0
0
2
0
0
2
0
1
0
2
0
0
1
1
0
2
2
2
0
0
0
1
0
1
0
0
2
2
2
0
0
0
0
1
1
0
0
1
1
0
2
0
0
2
1
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
2
2
0
1
2
2
2
2
0
2
1
0
0
0
0
0
0
0
1
2
2
0
1
1
0
2
0
0
2
1
2
1
0
0
2
1
1
1
2
0
2
1
0
0
1
3
0
0
0
0
1
3
0
0
0
1
0
2
0
0
1
2
0
0
2
0
0
2
2
0
2
0
0
1
0
0
4
0
0
0
2
1
0
0
0
0
1
0
0
0
0
1
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
2
1
1
0
0
0
0
0
0
1
0
1
3
0
1
0
0
1
2
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
1
0
1
1
2
1
0
5
0
1
1
0
0
2
2
2
0
1
0
0
2
1
1
0
1
1
0
2
0
2
0
0
0
0
0
0
0
2
0
0
2
0
1
1
1
0
0
0
0
1
0
1
0
0
1
0
0
2
3
2
0
1
2
2
0
0
0
1
1
0
2
0
0
2
0
0
0
1
0
1
0
1
1
0
1
1
0
0
0
1
0
2
4
3
0
1
0
0
1
2
2
2
1
0
6
3
0
0
1
1
0
2
0
0
1
0
0
0
0
0
1
0
0
1
2
0
0
1
1
3
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
2
1
1
0
0
0
1
2
1
1
1
1
0
1
0
0
1
0
1
0
0
1
1
1
0
2
0
2
1
1
0
0
0
0
0
2
1
0
2
0
0
1
3
0
0
0
0
0
0
0
1
2
0
0
1
0
1
0
0
0
1
0
1
0
0
0
2
1
0
0
0
1
1
0
3
2
1
0
2
0
0
0
0
1
0
0
2
1
0
0
2
0
2
1
0
0
0
0
2
1
0
2
2
0
1
0
0
1
1
0
1
1
0
0
1
0
0
0
2
2
0
1
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
2
1
0
1
2
1
0
2
0
1
2
2
1
1
1
0
2
2
1
0
0
0
0
2
2
1
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
1
3
1
2
0
1
0
0
1
0
1
0
0
0
0
2
1
2
1
0
0
0
0
1
0
0
0
0
1
1
0
0
2
0
1
2
0
0
0
2
2
1
0
0
1
1
0
0
0
0
0
1
1
0
2
1
2
1
0
0
0
0
1
0
1
0
1
1
2
1
1
0
0
0
1
0
1
0
1
0
1
1
0
1
0
0
1
2
1
1
0
0
0
0
0
1
0
0
2
0
1
0
0
2
1
2
0
1
0
0
1
0
2
1
0
0
0
1
0
1
0
0
1
0
1
0
1
0
0
1
0
0
1
0
0
2
0
2
2
1
1
1
0
1
1
0
1
0
0
1
1
0
0
0
1
1
0
2
2
0
1
1
2
1
0
1
1
1
0
1
0
1
1
0
2
1
0
0
2
1
2
1
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
1
2
0
2
1
0
0
0
0
3
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
2
2
0
0
1
3
0
0
1
0
1
1
1
0
0
1
0
0
2
0
0
0
0
1
0
1
2
1
0
2
0
2
0
2
2
1
0
5
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
2
1
0
2
0
0
1
2
0
0
2
0
0
2
2
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
1
1
0
0
2
1
1
0
2
0
0
1
0
1
0
0
2
3
2
1
0
0
0
2
0
1
0
0
0
0
2
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
2
1
0
2
0
0
0
1
2
2
1
0
0
0
1
0
0
0
1
0
2
2
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
2
0
2
0
2
0
2
1
0
0
0
2
1
2
0
1
0
0
0
1
0
0
0
1
2
3
0
2
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
3
0
1
0
0
2
0
0
2
0
0
1
0
2
0
2
0
1
0
1
2
2
1
0
1
0
0
2
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
1
0
0
0
1
0
1
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
1
2
0
0
1
1
0
0
0
0
1
0
1
0
1
1
3
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
1
2
0
2
0
1
1
1
0
0
0
0
0
0
0
1
2
3
2
0
1
0
0
0
0
2
2
1
0
0
1
0
0
0
0
0
2
0
0
1
0
2
1
0
2
0
1
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
2
1
1
1
0
2
1
1
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
2
1
0
0
1
1
2
1
0
0
2
1
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
2
0
0
0
2
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
2
0
1
1
0
2
2
0
0
1
0
0
0
0
1
0
1
2
0
0
0
0
0
2
0
0
0
0
2
1
1
1
1
0
0
0
0
1
1
0
0
0
0
1
0
1
2
0
0
0
2
1
2
0
0
1
0
1
2
1
0
1
0
2
0
1
0
1
0
0
1
2
0
0
0
0
2
0
1
0
0
0
2
0
2
1
1
1
1
0
0
2
1
1
0
0
1
2
1
0
0
2
0
0
0
0
2
0
2
0
2
2
0
0
0
1
0
0
1
0
0
0
1
1
1
2
0
0
4
1
0
0
2
0
0
1
1
0
1
0
0
1
0
1
0
1
1
0
0
0
0
1
1
0
1
0
2
0
0
2
3
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
2
1
2
0
2
0
0
0
0
0
0
1
1
0
0
0
1
2
1
0
1
0
1
2
0
2
1
0
0
1
2
1
0
0
0
0
0
2
0
1
0
0
0
0
2
2
0
1
1
2
1
0
2
0
0
1
0
0
2
0
0
1
1
2
0
2
0
0
0
2
0
1
0
0
1
1
0
2
2
0
2
1
1
0
0
0
0
0
1
2
1
0
0
1
0
0
1
1
1
0
0
1
0
0
0
0
1
1
1
2
1
1
0
0
1
0
0
0
0
0
1
1
1
2
0
3
0
2
1
2
0
0
3
2
2
1
0
1
0
2
0
2
0
0
2
2
0
0
0
2
0
0
0
0
0
1
1
2
0
1
1
0
0
2
0
0
0
1
2
2
0
0
0
0
0
0
2
0
2
0
0
2
1
1
3
0
1
4
0
0
0
0
2
2
0
2
2
0
0
0
0
0
0
1
0
0
2
2
0
2
1
0
1
0
0
0
0
1
0
0
2
2
0
0
1
0
0
2
1
1
0
0
1
0
0
3
3
1
0
0
1
1
2
0
2
0
0
0
0
0
0
2
2
2
1
1
0
1
2
0
0
0
2
0
1
1
0
3
0
0
2
0
0
0
0
0
1
0
2
2
0
2
0
2
0
0
1
0
0
0
1
0
2
0
2
2
0
1
0
0
0
0
2
0
1
0
1
1
0
0
0
3
0
1
0
0
1
1
2
0
0
0
0
0
0
3
2
0
0
0
1
0
2
0
0
2
0
1
1
0
0
0
0
2
0
0
2
1
0
0
0
1
0
0
4
2
2
0
1
0
2
2
2
0
0
0
2
0
0
1
0
0
1
2
1
2
1
0
3
0
1
1
0
0
0
0
0
0
0
3
0
0
0
0
1
2
2
0
0
1
0
1
1
0
0
0
0
0
1
2
1
1
2
0
2
0
1
1
0
4
2
1
0
2
0
0
1
0
0
1
0
0
1
2
1
0
0
2
2
0
0
0
0
0
2
0
0
1
1
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
2
0
2
2
0
1
0
1
2
2
0
0
0
0
0
0
0
2
0
0
1
1
2
2
3
0
0
1
0
0
2
2
0
1
0
0
0
1
0
0
1
0
0
0
0
2
2
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
2
1
1
0
0
0
0
0
0
2
0
0
0
3
1
0
0
1
0
0
0
1
2
2
1
1
0
2
0
1
0
0
0
0
1
0
0
2
2
1
0
2
0
0
0
1
0
0
2
0
2
0
2
2
1
0
1
1
0
1
1
0
1
0
0
0
3
1
0
0
2
0
0
0
1
0
0
0
1
0
0
2
2
0
2
2
0
0
0
0
1
0
0
0
0
1
0
2
1
0
0
0
4
0
0
2
1
0
2
2
0
0
0
2
0
1
0
1
0
0
0
0
1
0
0
1
2
0
1
1
0
0
2
2
2
0
1
0
0
1
0
0
1
1
2
0
0
0
0
0
4
0
0
0
2
2
0
0
0
0
2
0
0
0
1
1
0
0
1
0
0
0
0
2
0
0
1
2
2
2
2
0
0
0
0
1
0
1
1
1
0
1
1
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
2
1
1
0
2
0
1
0
0
0
1
0
0
0
0
0
0
2
7
0
0
0
0
0
2
0
0
0
2
0
0
0
1
2
0
2
1
2
1
2
0
1
0
1
2
0
0
0
0
0
2
0
0
0
0
0
1
3
1
2
1
0
1
1
0
2
1
1
1
0
1
2
0
1
0
1
2
1
1
0
1
2
0
2
2
2
2
0
0
0
0
1
0
0
0
0
0
0
1
1
0
3
1
1
0
1
0
1
0
0
0
1
0
0
1
0
0
0
2
2
0
2
0
0
0
1
1
0
1
1
0
2
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
2
1
1
1
1
0
2
0
1
0
1
0
2
1
0
2
0
2
1
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
1
1
0
2
0
1
1
2
0
1
1
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
2
1
0
1
0
1
1
0
0
0
2
1
1
1
0
1
0
0
0
1
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
2
0
0
2
1
0
1
0
0
0
1
1
1
1
0
1
3
1
0
0
2
0
1
2
1
0
0
2
0
0
1
3
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
2
0
1
0
0
1
1
0
0
0
1
2
0
1
2
2
0
1
2
1
0
2
2
1
2
2
1
0
0
0
1
1
2
0
0
2
0
0
1
1
1
0
0
0
0
3
0
2
0
0
0
0
0
0
0
2
0
1
3
2
0
1
0
0
1
0
0
0
0
0
2
0
2
2
0
0
1
0
1
1
0
1
0
2
0
0
0
1
1
2
0
2
1
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
4
0
2
1
1
0
0
3
2
0
0
3
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
2
0
0
1
0
2
1
1
0
2
0
2
0
0
0
3
1
1
0
0
0
2
0
0
2
1
1
1
2
0
2
0
0
0
0
0
0
0
0
2
0
1
3
0
0
0
1
1
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
1
1
0
1
0
2
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
1
0
2
0
2
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
2
1
0
2
0
1
0
0
0
1
0
1
0
2
0
0
0
2
0
1
0
1
0
0
0
0
1
2
0
1
1
0
0
2
1
0
0
1
3
0
2
1
5
1
0
0
0
0
2
0
0
2
1
0
1
0
1
1
0
2
0
1
0
0
2
0
0
1
0
0
2
0
2
2
1
1
0
1
0
1
0
0
2
0
2
2
0
2
0
2
1
0
1
2
1
2
1
1
1
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
1
0
2
2
0
2
2
1
0
0
0
2
0
1
2
2
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
1
2
0
0
0
2
0
0
1
0
1
1
1
0
3
0
0
0
1
0
2
1
0
1
1
0
1
0
0
2
1
2
2
2
0
0
0
2
0
0
0
1
0
1
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
2
1
0
0
0
3
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
2
0
1
2
1
0
0
0
2
0
0
1
1
2
0
1
1
1
0
0
1
1
0
1
1
1
0
1
1
0
0
0
2
2
2
0
0
1
0
1
1
0
2
0
3
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
2
0
0
0
1
0
0
1
2
0
0
2
0
0
0
1
0
0
2
1
1
0
2
2
1
0
0
1
2
1
0
1
1
0
0
1
1
0
0
0
0
0
1
0
0
1
0
2
2
0
1
0
1
0
0
2
1
4
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
1
0
1
1
0
1
0
2
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
2
0
1
0
0
0
1
0
0
1
0
0
0
0
2
1
2
0
0
0
0
1
0
1
0
0
4
1
0
0
1
0
1
1
1
2
0
0
0
0
0
6
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
1
1
2
1
1
2
0
0
1
2
0
1
0
1
0
2
1
0
0
0
0
0
0
1
0
1
0
0
0
1
2
2
0
0
0
2
0
0
2
2
0
2
0
2
1
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
1
2
0
1
1
2
0
1
0
0
0
0
0
0
2
0
2
1
1
0
2
0
0
0
2
1
0
0
0
1
0
2
0
0
1
0
0
0
1
1
1
0
0
0
2
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
2
1
1
2
0
0
0
0
0
0
1
0
2
1
0
1
0
0
0
0
0
2
0
0
1
2
1
1
0
0
1
2
0
2
0
2
2
1
2
0
0
0
1
0
2
2
1
0
2
0
0
1
1
0
1
0
0
0
0
2
0
1
0
0
2
0
0
2
2
0
0
1
0
0
1
0
0
3
0
0
1
1
2
1
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
1
1
1
1
2
0
0
0
0
0
0
0
0
0
0
1
2
0
1
2
2
0
1
1
0
2
0
0
1
0
0
1
1
0
1
0
0
0
0
2
2
1
0
1
0
1
1
0
1
0
1
0
0
2
0
0
3
1
0
0
1
0
2
0
0
1
0
1
2
0
1
1
0
1
0
0
2
1
0
0
1
0
0
2
1
3
0
0
0
0
1
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
2
1
0
0
0
1
1
1
1
0
0
0
1
0
0
1
0
0
1
0
0
2
2
0
1
0
2
0
1
0
0
1
0
0
0
2
1
0
2
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
1
1
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
1
0
1
2
0
0
1
0
2
0
2
2
0
0
0
0
0
2
2
0
0
0
2
2
0
0
2
2
0
0
1
1
0
1
0
0
2
3
0
1
0
2
0
1
0
2
0
0
0
0
0
1
1
0
2
1
2
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
1
1
0
0
0
1
1
1
0
1
0
0
0
0
0
0
1
0
2
0
1
1
0
0
2
0
2
2
0
0
1
2
2
1
0
1
1
2
1
1
1
0
0
0
0
2
1
3
0
0
2
3
0
4
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
2
0
0
3
0
0
0
0
0
0
0
2
2
2
0
1
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
2
0
3
0
1
0
0
1
1
0
1
0
1
3
1
0
2
1
0
1
0
1
0
0
1
0
1
1
0
0
3
0
1
0
0
0
2
1
2
0
1
0
0
2
0
0
0
1
0
0
0
2
0
1
0
0
0
1
2
0
1
0
0
2
1
1
1
0
1
0
0
2
0
0
2
0
0
0
0
0
1
2
0
0
2
0
3
0
0
0
1
1
0
0
0
1
2
1
0
2
2
0
0
0
0
1
0
0
1
1
1
2
0
0
1
0
1
0
2
2
0
2
2
0
1
1
0
1
0
2
1
2
0
0
2
0
1
0
1
2
0
0
0
1
1
0
2
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
2
2
0
0
0
0
0
1
2
0
0
0
0
2
0
0
1
0
2
0
1
0
0
1
0
0
0
1
0
2
0
1
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
2
0
1
0
3
0
0
1
0
2
1
0
1
2
0
0
1
1
0
0
0
1
1
1
0
1
0
2
0
2
0
0
1
0
0
1
0
0
2
1
1
0
2
2
0
0
2
0
0
0
2
1
0
2
0
0
1
0
2
2
2
1
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
2
1
1
0
0
0
0
0
1
0
0
0
0
0
2
0
1
2
1
1
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
7
0
2
2
0
2
2
0
3
1
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
1
1
2
0
1
1
1
0
4
2
2
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
1
1
0
1
1
2
0
0
1
1
0
2
0
0
0
0
0
0
0
2
0
0
1
2
0
0
3
0
0
0
0
0
0
2
0
1
1
0
0
0
0
1
0
1
0
1
0
2
0
2
1
0
2
0
2
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
3
1
2
0
2
0
0
0
0
0
1
8
0
2
0
2
2
1
0
0
1
2
2
1
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
3
0
2
0
0
0
0
1
0
0
0
1
0
0
2
2
1
0
1
0
0
1
0
0
1
0
0
1
1
1
0
3
0
0
1
1
0
0
2
1
0
0
0
2
1
0
0
1
1
2
2
0
0
2
0
0
1
0
2
2
2
0
0
1
2
2
0
2
0
1
0
0
1
2
3
0
0
2
2
2
0
0
1
1
2
0
0
0
2
0
2
1
0
0
1
2
2
0
0
0
1
2
2
1
1
2
0
1
0
0
1
0
1
1
1
2
0
0
1
1
2
2
0
2
0
0
0
0
0
0
1
1
0
0
1
0
1
0
1
2
1
2
1
0
0
1
1
1
0
0
0
0
2
2
0
0
0
1
1
3
1
0
0
3
0
1
2
0
0
0
2
1
0
0
1
1
2
0
2
2
1
0
1
0
0
0
0
2
1
1
0
0
1
0
0
1
0
0
0
0
0
2
0
0
8
0
2
2
0
1
1
0
0
0
3
0
0
0
0
0
1
0
2
0
0
0
1
0
0
1
0
0
0
0
2
2
2
0
0
1
0
0
0
1
2
2
0
2
2
1
0
1
0
0
1
0
0
2
0
1
2
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
3
2
2
2
0
1
0
0
0
3
1
1
1
0
0
0
0
0
0
0
1
0
2
0
0
1
1
0
0
0
2
2
1
2
1
0
2
0
0
2
2
0
1
0
0
1
1
1
0
1
0
1
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
2
1
0
0
0
2
0
0
2
0
0
0
1
0
0
0
1
3
2
0
0
2
0
1
0
1
2
2
0
3
2
0
0
1
1
1
0
2
2
0
0
0
2
0
1
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
2
0
3
0
0
2
0
0
2
0
1
0
1
2
2
0
2
0
1
1
3
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
2
2
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
2
0
3
0
1
0
2
2
1
1
1
1
0
3
0
0
0
2
0
2
1
0
0
0
2
0
2
2
0
0
2
0
0
1
0
2
1
1
0
0
0
0
2
0
1
0
2
0
0
0
0
2
0
1
0
0
1
1
1
2
2
0
0
2
2
0
2
2
1
1
1
1
0
0
1
0
0
0
0
1
1
2
0
0
1
0
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
2
0
0
0
1
1
1
0
1
0
0
0
0
2
0
1
0
0
0
0
0
1
2
2
2
0
0
1
0
1
0
1
0
0
1
1
1
2
0
0
0
0
0
1
0
2
0
0
0
0
1
0
1
0
0
2
0
2
0
0
2
1
0
0
2
0
0
0
0
0
1
2
3
0
0
0
0
0
2
1
0
1
0
1
1
1
0
0
1
1
0
1
0
2
1
1
0
0
0
3
2
0
1
0
1
0
1
2
0
1
0
0
0
0
0
1
1
0
0
1
0
2
0
0
4
1
1
1
2
0
0
6
0
0
1
0
1
0
0
1
2
2
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
2
0
2
1
2
0
0
0
0
0
0
2
2
0
0
1
1
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
1
1
0
2
0
2
1
1
1
0
0
0
0
0
0
1
0
3
2
2
0
0
0
0
1
0
1
2
1
2
0
2
1
0
2
0
0
2
1
1
0
2
1
1
2
0
0
1
2
0
1
0
0
1
0
2
0
1
0
0
1
0
2
0
0
2
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
2
0
0
1
2
0
0
2
0
0
1
2
0
0
0
0
0
2
0
2
0
1
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
1
2
0
2
0
1
0
2
1
2
0
0
1
0
0
1
0
2
1
0
2
1
2
2
0
1
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
2
0
2
0
1
0
2
0
1
0
1
0
0
0
1
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
1
0
0
2
2
0
1
0
0
0
0
0
2
2
2
0
0
1
0
0
2
0
1
0
1
0
1
0
0
0
2
0
0
1
2
1
1
7
2
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
1
0
0
0
0
0
2
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
2
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
1
1
2
0
1
1
1
1
0
0
0
1
0
1
0
2
2
2
0
2
0
0
0
0
0
1
0
0
2
0
1
0
0
0
2
2
1
0
0
0
0
0
0
1
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
5
1
0
0
0
1
0
0
0
1
1
0
0
2
0
0
0
1
1
2
0
0
2
2
0
2
3
0
0
0
4
0
0
0
2
0
0
0
1
0
0
1
1
0
2
1
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
2
1
0
0
1
1
0
0
2
1
0
1
1
0
1
2
0
0
0
0
2
1
1
0
2
0
0
1
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
1
0
0
2
4
0
0
1
0
2
1
0
2
1
0
1
0
0
0
1
4
1
0
2
0
0
0
0
1
0
1
1
0
1
0
2
1
1
0
2
2
0
0
2
2
0
3
0
0
0
0
0
0
2
1
2
0
0
4
0
1
1
0
1
1
0
0
1
0
2
0
0
2
1
2
0
0
2
1
0
0
2
0
0
0
0
2
1
1
0
2
0
2
1
0
0
2
1
1
1
0
3
7
0
1
2
1
1
1
0
1
8
0
0
0
0
0
0
0
2
2
2
2
1
0
0
4
0
0
0
1
0
0
1
1
0
0
0
3
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
2
0
0
1
0
0
1
2
0
0
1
0
0
0
1
0
3
1
1
1
2
2
0
0
1
0
1
2
0
1
0
0
1
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
2
0
0
1
0
1
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
1
2
0
1
0
3
0
1
0
0
2
1
0
2
1
0
0
1
2
1
1
1
1
0
0
2
0
1
0
1
2
0
0
2
1
0
1
0
1
0
1
0
0
3
3
3
1
2
0
0
0
0
0
0
1
4
0
0
0
1
1
1
0
0
0
2
0
0
2
3
1
0
0
1
0
0
1
0
1
1
0
1
3
2
0
1
1
1
2
1
0
0
2
0
1
0
0
1
1
2
1
0
0
2
2
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
3
0
0
0
1
2
1
0
1
2
0
0
1
0
2
2
0
1
1
2
1
0
0
0
1
2
0
0
0
2
1
1
1
0
1
3
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
2
0
2
0
0
1
0
0
1
0
1
0
1
2
1
2
2
2
0
0
0
0
0
1
2
0
0
0
0
2
0
1
0
0
1
0
0
1
4
1
0
0
2
0
1
3
0
0
1
0
1
0
0
1
0
2
0
0
0
0
2
0
0
1
0
1
0
0
0
1
1
1
0
0
0
1
1
0
0
2
1
0
2
1
0
1
0
1
0
0
2
0
0
1
0
1
2
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
2
1
0
1
0
2
0
2
1
2
2
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
2
0
0
2
1
0
2
1
0
5
0
0
0
0
1
0
3
0
0
0
2
2
0
2
2
0
1
0
1
0
0
1
3
0
1
0
0
0
0
2
0
3
0
1
0
2
1
0
0
0
1
2
1
2
1
0
1
2
1
1
1
0
0
3
3
0
0
2
0
0
1
1
1
0
1
0
0
0
4
0
2
1
0
0
0
0
0
0
0
0
1
2
2
0
2
0
1
0
0
0
2
0
1
0
0
1
0
1
0
0
0
0
0
1
1
0
2
2
0
2
0
1
0
2
0
0
0
0
1
3
0
0
0
0
1
0
0
0
2
0
0
1
0
1
0
2
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
2
2
0
1
1
1
0
0
0
0
0
1
0
0
0
1
3
0
0
1
0
0
1
1
3
1
0
0
0
0
2
0
0
0
0
2
2
2
2
2
0
1
0
0
0
0
1
0
0
1
1
1
3
0
0
0
0
0
0
0
0
2
0
2
1
0
2
1
2
0
1
0
2
1
2
0
0
1
2
1
0
0
2
0
0
0
0
2
0
0
2
1
0
1
1
0
0
0
2
0
1
0
0
0
0
0
1
0
1
1
0
0
2
2
1
1
2
1
2
1
0
1
1
0
1
0
0
2
0
2
0
0
0
1
0
1
2
0
0
0
1
0
0
1
2
1
0
1
2
0
1
0
1
0
0
2
0
0
0
1
1
0
1
2
0
1
0
2
1
0
1
0
1
0
2
0
0
1
0
0
1
0
2
0
1
1
0
0
0
0
1
0
0
2
0
1
0
0
0
2
0
0
1
0
2
1
0
2
2
0
2
0
0
0
1
0
2
0
0
2
2
1
1
2
0
1
0
1
0
0
1
0
1
0
2
0
2
1
2
0
0
0
0
0
2
0
2
0
1
1
1
0
0
0
1
4
2
1
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
1
0
0
0
2
1
1
0
0
1
0
3
2
0
0
0
1
0
1
1
0
2
2
0
1
0
0
1
2
1
0
0
1
2
0
0
0
0
1
0
0
0
2
1
2
0
0
1
0
0
1
0
0
0
1
1
1
2
2
0
2
0
1
0
1
2
0
2
0
0
0
0
0
1
2
1
0
0
1
0
0
2
1
2
0
0
0
1
0
0
0
1
0
0
0
2
0
2
0
2
2
0
0
0
0
0
0
2
0
0
1
0
1
0
0
1
0
0
1
1
2
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
1
2
2
1
2
0
2
0
2
2
0
0
1
1
0
1
0
0
0
0
2
0
0
2
1
0
0
2
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
1
0
3
0
1
0
0
2
0
0
0
0
0
5
2
1
1
2
0
2
0
1
1
2
0
0
0
2
0
0
0
2
0
1
2
0
1
0
0
0
0
3
0
0
1
2
0
2
1
2
0
0
0
0
0
1
0
0
1
0
1
2
0
0
1
0
0
0
0
1
2
1
0
0
0
3
0
0
2
0
0
0
0
0
0
3
1
0
0
0
2
0
2
0
0
0
0
0
1
0
0
1
0
0
1
1
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
1
2
0
0
1
0
0
0
1
0
2
0
1
1
6
2
0
0
1
0
0
2
0
0
1
1
0
1
0
0
0
2
0
0
2
0
0
0
0
1
1
1
2
2
2
0
0
2
0
2
0
0
1
2
2
0
0
1
0
1
2
0
0
0
0
0
0
0
0
2
2
1
0
1
0
1
0
2
0
0
0
1
1
0
3
0
2
2
0
0
2
0
0
1
3
0
0
1
0
3
0
0
0
0
2
1
0
1
2
1
0
0
2
2
0
1
0
1
0
2
1
2
1
2
2
0
2
0
0
0
2
4
0
0
1
2
0
0
1
0
0
1
0
0
2
0
1
5
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
1
0
2
0
2
0
1
2
0
0
0
1
0
3
1
0
0
2
1
0
0
0
0
0
0
1
1
0
0
1
1
2
1
1
2
0
0
0
2
0
1
0
0
1
0
1
0
0
0
0
1
2
0
0
0
0
0
1
1
1
0
2
0
2
1
0
0
1
0
1
2
1
1
0
0
1
0
0
2
1
0
0
0
0
1
0
1
0
6
0
0
0
2
0
0
0
0
1
0
0
1
1
0
0
0
2
0
0
0
2
0
1
0
0
0
2
0
2
0
0
1
0
1
2
2
0
1
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
2
1
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
1
0
2
1
0
1
0
0
0
0
2
0
1
0
0
1
0
2
0
1
1
1
1
0
2
0
1
0
1
1
0
1
0
2
1
0
1
0
0
2
0
0
1
0
0
0
2
0
0
2
2
0
0
0
1
0
1
0
0
0
2
1
0
0
0
0
1
2
0
1
1
3
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
1
1
2
0
1
2
1
1
0
0
1
0
0
0
4
2
0
1
2
0
0
2
1
0
0
0
2
1
2
0
0
0
0
0
2
0
0
1
2
0
0
0
1
2
0
2
0
0
0
1
1
0
0
0
1
1
1
1
0
1
0
2
0
1
1
0
0
2
1
0
0
1
2
1
1
0
0
1
1
2
1
5
2
0
0
1
0
0
0
0
0
0
1
0
0
1
1
1
0
0
2
0
1
0
1
0
0
1
0
0
1
0
1
0
1
0
1
1
0
1
0
2
0
1
2
1
0
0
0
0
1
1
0
0
0
2
0
1
1
1
0
2
0
0
0
8
0
0
1
0
1
2
1
0
2
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
1
1
0
2
0
1
1
0
1
1
0
0
3
0
0
0
0
1
0
1
0
0
0
1
2
0
2
1
0
0
3
1
1
0
0
0
0
0
1
2
0
0
0
1
0
2
1
0
0
0
1
0
0
0
0
1
0
1
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
1
2
0
2
1
2
0
0
1
0
0
0
1
1
0
0
1
0
0
1
2
1
2
0
0
1
2
0
2
2
0
0
1
0
1
2
1
0
0
0
2
2
2
1
5
0
0
2
0
1
0
2
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
2
0
0
2
0
2
2
0
0
0
0
2
0
0
1
0
0
1
3
0
5
0
3
0
0
2
0
1
3
2
1
1
2
2
0
1
0
0
1
1
0
0
0
2
2
0
0
1
2
4
0
3
0
0
2
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
1
2
0
0
1
0
2
0
0
1
0
0
0
2
1
2
0
1
2
0
0
0
2
0
0
0
0
2
1
1
0
0
1
1
0
0
1
0
1
2
1
0
0
4
0
0
0
0
0
1
0
0
2
2
2
0
0
0
2
0
1
0
1
1
0
1
0
0
0
0
0
3
0
2
1
0
0
3
1
2
0
0
0
2
0
0
0
0
2
1
1
0
0
0
3
0
0
2
1
1
2
2
0
0
0
0
1
0
0
2
2
0
2
0
0
2
1
1
1
0
1
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
2
1
1
0
1
0
1
0
0
0
1
0
1
0
0
0
0
3
0
1
2
0
1
0
0
2
0
1
0
2
1
2
0
2
0
0
2
0
0
1
1
0
1
2
0
0
0
2
0
0
0
1
0
2
0
2
0
0
3
1
1
0
0
0
0
0
1
0
0
0
2
0
2
2
3
0
2
1
0
0
0
1
0
1
1
1
0
2
0
0
1
2
1
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
2
0
1
1
0
0
0
1
0
0
0
0
3
0
0
1
0
0
1
0
1
0
0
0
0
1
0
1
1
0
1
2
0
2
0
0
1
1
0
0
1
0
0
0
2
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
1
1
0
0
1
2
0
2
1
1
1
3
0
0
0
0
1
0
2
0
1
2
0
1
2
0
1
2
2
0
0
1
0
2
2
1
0
0
3
1
0
0
0
1
3
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
2
0
2
0
0
0
0
0
1
2
2
1
2
0
1
0
0
1
1
0
1
0
1
0
0
0
0
1
0
1
0
2
2
0
1
0
0
0
1
1
2
1
0
1
2
0
0
1
0
0
0
2
0
2
0
0
0
0
0
2
1
3
0
0
0
1
0
1
0
0
1
2
0
0
2
0
0
0
0
0
1
0
0
2
2
0
0
0
0
1
0
2
1
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
3
0
0
0
1
2
0
0
0
2
1
4
2
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
4
0
2
0
0
0
0
0
1
0
0
0
0
0
1
3
1
2
1
0
2
0
0
0
1
2
0
1
1
0
2
2
0
1
0
2
0
0
1
0
0
2
1
0
0
1
0
0
0
0
2
0
0
0
0
3
1
0
1
1
0
1
0
0
0
0
1
0
1
3
0
0
1
0
0
0
1
2
0
0
0
1
0
0
1
1
0
0
1
3
1
2
2
0
0
2
2
0
1
0
3
0
0
0
0
2
3
0
0
2
0
0
0
0
2
0
1
2
0
2
2
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
2
2
1
1
2
1
0
2
1
1
0
0
0
1
2
1
0
1
1
1
0
0
0
2
0
0
0
7
1
2
0
0
0
1
2
0
0
0
2
0
1
0
0
0
0
0
0
1
0
2
2
0
1
0
0
2
1
1
0
1
0
0
0
0
2
2
0
1
1
0
0
0
1
0
2
1
0
0
0
0
1
2
0
0
1
1
1
2
1
0
0
1
0
0
0
0
2
0
0
2
0
2
2
2
0
0
2
0
0
0
1
0
1
0
2
0
0
1
0
0
1
0
0
0
0
2
0
1
1
1
2
1
0
1
0
2
0
0
2
0
2
0
1
0
1
0
3
2
2
0
2
2
0
0
0
1
1
1
0
1
1
0
0
1
1
1
2
0
0
0
1
2
4
0
0
1
0
1
0
2
0
1
1
0
2
0
0
2
0
0
1
0
0
0
0
2
0
1
1
2
0
2
1
0
0
0
2
0
0
0
2
1
1
1
2
1
1
0
2
2
0
0
1
0
4
0
0
2
0
1
0
1
2
0
0
1
0
0
0
1
0
4
0
2
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
1
1
2
2
2
2
1
0
0
1
0
0
0
0
1
0
2
1
1
1
0
0
0
0
0
1
1
0
0
0
0
0
2
2
0
0
0
1
3
0
0
3
0
0
0
1
0
0
1
0
0
0
0
0
2
2
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
1
2
0
0
1
0
0
6
0
1
0
1
2
1
1
2
1
0
1
0
0
1
0
1
0
0
0
0
1
2
2
1
0
0
2
0
1
0
1
3
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
1
0
2
2
1
0
0
3
0
2
2
1
0
2
2
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
1
0
2
1
0
0
1
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
2
0
0
1
2
0
2
1
0
2
0
2
3
0
0
0
0
0
3
1
0
0
2
1
0
1
0
1
0
2
1
0
2
0
1
2
0
0
0
2
1
0
1
0
0
0
0
1
0
0
2
1
1
1
0
3
0
0
1
2
0
1
1
2
0
1
1
0
0
0
1
0
0
0
0
0
1
1
0
0
2
2
0
0
0
0
0
0
1
0
0
1
2
0
1
1
0
0
0
1
2
0
0
0
0
0
1
0
3
1
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
1
1
0
0
0
1
0
0
0
0
1
1
1
0
0
0
3
0
2
0
1
0
2
1
1
0
1
0
0
0
2
0
2
0
0
0
2
0
0
1
2
2
1
0
2
0
0
1
1
0
1
2
2
2
0
2
0
2
2
0
0
2
2
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
1
0
1
0
1
1
0
0
2
2
1
1
0
0
0
2
0
0
1
2
2
0
0
0
1
1
0
0
0
1
0
0
1
0
2
2
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
2
0
1
0
0
0
2
0
1
2
1
1
0
0
0
1
0
0
1
0
0
2
0
0
0
0
1
2
0
1
0
0
1
0
1
0
0
1
1
0
2
0
2
0
0
0
1
0
2
1
0
2
0
0
2
2
0
2
1
2
2
0
1
0
2
2
0
0
1
2
0
0
2
0
1
0
0
2
1
1
1
1
0
1
1
0
0
2
0
2
0
0
1
1
0
0
1
2
1
0
0
0
3
1
0
1
0
0
0
0
0
0
2
0
1
1
1
0
2
0
0
0
0
0
0
0
1
0
2
0
2
0
0
1
1
0
0
0
0
0
1
2
0
2
2
1
1
2
2
0
0
2
1
0
1
2
0
0
2
0
1
0
0
2
0
2
1
1
0
0
0
0
1
0
0
0
2
1
1
2
0
0
0
2
2
0
2
0
1
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
2
2
1
1
1
0
0
0
1
1
0
0
0
2
0
2
1
2
2
0
0
0
2
0
1
1
0
1
1
0
2
0
2
1
0
0
0
0
1
1
1
0
0
0
0
0
1
2
1
0
1
1
0
0
0
0
0
0
0
0
2
1
1
1
0
0
1
0
0
1
0
0
0
1
1
1
2
0
0
2
0
0
0
1
2
0
0
2
0
1
2
2
0
1
0
1
0
2
0
1
0
2
2
0
0
0
0
0
0
1
1
1
1
0
2
1
0
0
2
0
2
0
0
0
1
0
1
0
1
0
0
0
2
0
0
2
3
1
2
1
2
0
0
0
1
1
1
1
0
1
0
0
0
1
0
1
0
1
0
2
9
1
1
0
1
0
2
0
0
2
0
1
2
1
2
0
0
2
0
0
2
1
1
0
0
0
0
1
0
1
0
1
0
0
1
2
0
1
1
1
0
0
0
2
0
1
0
1
0
0
0
2
0
2
1
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
1
2
0
2
0
0
0
1
2
0
0
6
0
1
2
0
0
0
1
0
0
0
1
1
1
1
2
1
0
1
0
1
3
2
1
0
0
0
0
1
1
1
1
4
0
0
1
2
0
0
1
1
0
0
0
1
0
2
1
1
1
3
2
0
0
1
0
0
0
1
1
0
2
0
0
2
0
1
2
1
1
0
2
4
0
1
1
2
0
2
2
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
2
1
1
2
0
0
0
0
0
0
1
0
2
1
1
0
0
0
2
0
1
0
2
2
2
0
0
2
0
0
0
2
2
1
0
2
0
0
0
1
0
3
0
0
1
2
0
0
0
1
0
0
2
0
1
1
0
0
1
1
1
1
0
0
2
0
2
0
1
0
2
0
0
0
1
2
0
0
1
1
1
0
1
0
0
3
2
0
2
0
0
0
0
0
1
1
1
2
1
1
2
0
1
0
1
0
6
0
0
2
2
2
0
2
0
2
1
1
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
2
0
0
0
0
1
0
0
2
0
0
1
1
0
1
0
0
0
1
0
1
1
2
2
0
0
2
0
0
0
2
1
2
0
0
0
1
1
2
0
0
0
0
2
2
0
1
0
1
2
0
1
0
2
0
2
0
1
1
1
0
0
1
2
0
2
0
1
0
3
0
1
0
0
2
1
0
0
2
2
1
1
0
1
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
1
2
0
1
4
2
0
0
0
0
0
1
0
0
0
2
3
0
0
0
0
0
0
1
0
0
1
2
2
1
0
2
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
1
1
0
1
0
1
0
1
2
0
1
0
1
1
2
1
0
2
0
0
0
0
2
0
0
1
0
1
1
0
0
0
2
0
1
1
0
2
0
0
0
2
0
0
0
0
0
0
1
2
0
0
2
0
0
4
1
0
2
2
1
0
2
1
7
0
1
0
1
2
1
1
1
0
0
1
0
0
0
1
1
2
0
0
0
0
1
1
2
1
0
0
0
1
2
0
2
0
1
0
1
1
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
1
0
0
1
0
0
2
2
0
2
0
2
2
0
0
1
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
3
2
0
0
0
1
1
1
0
0
1
0
2
0
0
0
1
0
0
2
1
0
0
0
2
0
0
1
1
0
0
0
3
0
1
0
2
1
0
0
0
0
0
0
0
1
1
1
2
0
0
2
1
0
0
2
1
1
0
2
1
0
2
0
1
0
2
2
1
0
0
1
1
0
0
2
0
0
1
0
2
1
2
2
1
2
1
1
0
1
1
2
0
0
0
0
0
1
1
2
0
0
0
0
0
1
2
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
2
2
1
1
0
2
1
0
1
0
1
0
0
2
0
1
1
0
0
1
0
2
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
2
1
1
0
2
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
1
1
2
1
0
1
1
1
2
0
2
0
2
1
0
1
0
0
2
2
2
2
0
0
2
0
0
0
1
6
1
0
0
1
2
3
0
0
1
0
1
0
1
0
2
2
2
2
0
0
2
0
2
2
0
0
2
0
0
1
2
0
0
3
0
0
1
0
0
0
0
1
1
0
8
0
0
1
0
0
0
0
1
1
0
1
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
2
2
1
0
1
2
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
3
0
0
0
0
0
3
0
0
0
2
0
2
0
0
2
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
2
0
1
1
0
2
0
2
2
1
0
2
2
0
0
2
2
0
0
4
0
0
2
0
1
0
1
1
1
1
0
0
2
0
1
0
0
0
0
2
1
0
0
1
0
0
0
0
1
0
0
1
0
2
0
2
0
0
0
2
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
2
0
1
2
1
0
2
0
0
2
0
2
0
0
0
2
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
2
0
1
0
0
1
1
2
3
2
0
0
0
1
0
0
1
0
1
0
2
0
0
0
1
0
0
2
0
1
0
0
1
2
1
2
0
1
0
0
2
0
2
0
1
0
2
0
2
0
1
0
0
0
0
0
2
1
0
2
2
0
0
1
1
1
2
0
0
2
1
0
0
1
0
1
0
0
2
0
1
0
1
0
0
2
1
0
2
0
0
1
0
2
0
1
0
0
1
0
0
0
2
0
1
0
2
1
0
0
0
0
2
0
3
0
0
0
0
2
0
0
1
0
0
2
2
0
0
2
2
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
1
2
0
0
0
1
2
1
2
1
1
2
2
0
1
0
0
1
0
0
0
0
0
1
0
0
1
1
1
2
0
0
1
0
2
0
0
1
0
4
0
0
0
0
0
0
2
0
0
0
1
0
0
2
3
1
0
1
0
0
0
0
0
0
2
0
1
1
0
0
2
0
0
0
1
0
2
1
2
1
0
1
0
2
0
2
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
1
0
0
0
1
0
1
0
0
0
1
2
1
2
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
2
0
1
0
0
2
1
0
0
1
0
0
2
2
0
1
0
0
0
2
0
0
2
0
1
0
3
0
1
1
0
2
0
0
0
1
0
0
1
0
0
0
1
1
2
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
5
0
3
0
2
0
1
0
3
1
0
2
1
0
0
0
2
0
2
0
2
0
2
0
0
1
0
2
2
0
1
1
0
0
0
2
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
1
1
2
1
0
2
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
2
0
1
0
1
0
1
0
0
2
1
0
2
0
1
0
0
2
0
0
1
1
2
0
0
0
1
0
0
0
1
0
2
0
1
1
0
0
1
1
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
1
1
2
0
0
2
0
2
1
0
1
3
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
1
2
1
0
1
1
2
0
0
0
0
0
0
0
0
2
2
2
0
0
2
2
1
0
1
1
2
1
2
2
1
2
0
2
0
0
0
0
1
0
0
0
0
1
0
1
1
0
2
1
1
0
2
0
0
0
0
2
1
2
0
0
1
1
0
0
0
1
0
1
0
2
0
0
0
1
0
2
0
1
0
0
1
2
0
1
0
1
0
0
1
1
0
1
0
1
1
1
0
0
1
0
1
1
0
0
1
2
0
2
2
0
1
0
0
0
0
1
2
0
1
0
0
0
2
2
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
1
0
1
2
2
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
1
0
2
1
0
2
0
0
1
1
0
0
0
2
0
1
2
1
1
2
0
1
1
0
1
0
0
1
0
0
0
0
2
1
0
0
0
1
1
0
1
2
1
0
0
0
2
2
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
1
1
2
2
2
0
0
0
2
1
2
2
0
2
2
0
0
0
2
0
0
1
0
0
1
0
1
2
0
2
0
0
0
0
0
1
0
0
3
0
1
0
0
1
0
2
0
0
0
2
1
0
0
2
0
0
1
0
2
4
0
0
0
0
0
1
1
2
1
0
1
2
0
0
0
1
0
0
0
1
2
1
2
4
0
0
0
2
0
0
1
1
0
2
0
2
0
3
0
1
0
0
1
1
0
2
0
2
0
2
0
2
0
2
0
2
0
0
1
0
1
0
0
1
0
0
0
2
0
1
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
2
1
0
2
2
0
1
2
1
0
0
3
0
1
2
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
1
2
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
2
0
0
0
1
1
0
1
1
0
0
1
2
0
2
0
0
0
2
0
0
0
2
2
2
0
2
0
0
3
2
1
0
1
0
2
1
0
0
0
0
2
2
1
2
0
1
0
0
0
1
0
0
1
0
2
0
2
0
0
0
2
0
3
0
1
2
0
1
0
0
0
1
1
2
1
0
0
0
1
0
3
1
0
1
1
0
1
2
0
1
2
1
2
0
0
2
1
0
0
1
1
0
0
1
0
2
1
1
3
1
2
0
1
0
0
0
0
0
0
1
1
0
1
0
3
0
1
0
0
0
5
0
0
2
1
0
0
2
1
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
0
0
2
1
1
0
0
0
0
0
0
0
1
0
2
2
2
2
1
1
1
0
0
2
1
0
0
0
0
2
0
3
0
0
0
2
2
2
2
0
2
1
1
1
1
0
0
0
2
1
2
0
0
1
0
0
1
0
1
2
0
2
1
2
1
1
0
0
1
2
0
2
0
0
0
1
2
3
0
0
0
0
0
1
0
1
1
0
2
0
0
0
0
0
2
2
0
2
0
1
1
2
0
0
1
1
2
1
0
0
1
0
0
0
2
0
1
0
0
1
0
0
1
1
1
0
0
0
1
0
2
0
2
0
0
1
0
0
0
1
0
1
0
0
1
0
3
3
0
2
0
0
0
2
0
0
0
3
1
0
0
2
1
0
0
1
0
2
2
1
1
1
0
2
2
1
0
1
1
1
0
1
1
0
0
0
1
2
0
0
0
0
1
1
0
0
0
1
0
0
1
0
3
2
2
0
0
2
0
0
0
0
1
1
3
0
1
0
1
1
0
2
0
0
1
0
0
0
1
2
1
0
0
0
0
0
0
2
1
0
0
1
0
0
1
2
2
0
0
0
1
0
0
0
1
0
0
0
2
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
2
1
0
1
0
1
0
2
1
0
2
2
2
1
0
0
1
0
0
1
2
0
0
0
0
2
0
0
0
1
0
0
0
2
0
1
0
2
0
2
2
0
1
2
0
1
0
0
0
0
2
0
0
6
1
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
1
0
2
0
0
0
0
0
1
0
1
2
0
1
0
1
1
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
1
1
0
1
1
1
0
0
2
1
0
2
0
0
0
0
0
2
0
0
0
7
2
0
0
0
2
2
0
0
0
0
0
0
2
0
0
1
0
1
1
0
0
0
3
0
0
1
0
0
0
1
0
2
0
0
2
0
0
2
0
5
0
0
0
2
0
1
0
0
1
0
0
1
0
0
2
1
0
0
1
1
5
0
1
1
0
0
0
0
2
3
1
0
0
0
0
1
0
0
2
0
4
1
0
0
1
1
0
2
0
2
0
1
1
0
0
1
0
0
0
3
0
2
0
0
1
0
1
0
0
0
1
1
3
2
1
0
1
1
0
3
0
0
1
1
0
0
2
1
2
0
0
0
0
0
1
0
1
0
0
1
0
2
1
0
0
0
1
0
0
0
0
0
1
0
1
0
1
2
2
0
0
1
1
1
1
2
0
1
1
0
0
0
0
2
0
0
2
1
2
0
0
1
0
2
0
0
1
1
0
0
0
1
0
1
1
0
0
0
0
0
0
4
2
2
2
0
2
1
0
6
0
0
2
0
0
2
3
2
0
1
2
2
1
1
0
1
0
2
0
0
0
0
2
1
1
0
0
0
0
2
1
3
0
1
1
0
2
0
0
1
0
0
0
0
2
2
0
0
1
2
2
2
0
0
2
1
2
2
0
1
2
2
0
2
0
0
2
1
0
0
2
0
2
0
0
0
2
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
1
2
2
0
1
0
2
0
1
2
0
0
2
0
0
0
0
2
0
1
2
0
0
2
0
1
0
1
0
0
0
0
1
0
2
2
0
1
2
1
2
0
0
2
0
1
0
1
0
1
0
1
0
0
0
0
2
0
2
1
1
3
0
2
0
0
0
0
0
1
2
1
0
0
2
0
3
0
0
0
2
1
2
0
0
2
1
0
1
0
0
0
0
2
2
0
0
0
0
1
0
0
2
1
0
0
0
0
0
1
0
1
1
0
2
1
2
0
0
0
1
0
0
2
2
1
0
1
0
3
0
1
0
1
0
2
2
2
0
0
1
1
2
0
0
1
2
2
0
1
1
1
0
2
0
0
2
1
1
0
1
0
1
0
2
0
1
0
2
1
2
0
0
3
0
0
1
2
2
1
2
0
1
0
0
0
0
0
1
0
1
0
0
0
2
0
3
0
1
1
0
2
0
1
2
0
2
0
2
1
1
2
2
0
0
0
3
2
0
0
1
0
2
0
0
1
0
1
0
0
1
2
0
0
1
0
0
0
1
0
2
0
0
2
0
1
1
0
0
0
0
0
0
0
0
1
1
5
2
2
0
1
2
0
1
1
0
2
0
1
2
0
0
2
1
2
0
2
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
1
0
1
2
2
2
1
2
1
2
1
2
1
0
0
0
0
0
1
2
1
0
0
1
0
0
0
1
0
0
1
0
0
2
0
2
0
0
0
1
1
2
0
0
0
0
0
0
2
2
1
0
1
0
0
2
0
2
0
1
0
1
5
0
2
1
0
1
2
0
2
0
0
1
2
0
2
0
1
1
0
0
0
0
0
0
0
2
1
1
1
1
2
1
0
0
0
0
0
0
1
1
0
1
0
2
0
1
3
2
2
0
0
0
1
0
2
1
2
1
0
0
1
0
0
0
2
1
0
2
2
2
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
1
2
0
1
2
2
0
0
0
0
0
2
2
1
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
1
0
1
0
0
0
2
0
0
1
0
1
2
1
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
1
3
0
0
0
2
1
2
0
1
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
1
0
4
1
0
0
1
0
0
1
0
0
2
0
0
2
0
0
0
2
1
0
1
2
0
1
1
1
0
0
0
0
0
0
2
0
2
1
2
0
0
0
0
2
1
1
2
0
0
0
0
2
0
0
1
0
1
1
0
0
2
0
1
0
0
0
2
2
2
2
0
3
1
0
0
0
0
0
0
0
2
0
1
0
0
0
2
1
0
1
0
0
0
0
0
0
0
2
2
2
0
0
0
0
2
2
1
0
2
0
0
0
0
0
0
2
0
0
2
0
0
1
2
0
0
0
0
2
0
0
1
1
2
2
2
0
0
0
3
0
2
0
0
2
1
0
0
1
1
1
2
0
0
1
1
3
0
0
1
0
1
0
0
0
2
0
1
0
1
0
2
0
0
2
1
1
0
2
2
0
2
1
0
2
2
0
1
1
1
0
2
0
0
2
0
1
0
0
2
0
0
1
0
2
0
0
0
0
1
1
0
0
1
1
0
0
1
1
0
1
0
2
0
0
5
0
0
1
0
2
1
2
0
1
0
2
0
0
0
2
1
0
2
0
1
2
0
0
0
0
4
2
0
0
3
2
0
0
0
0
1
0
2
1
0
0
0
0
1
0
0
0
0
0
1
1
0
2
3
2
1
2
0
0
0
1
0
0
0
2
0
1
0
2
0
0
2
0
1
0
0
0
1
1
0
0
0
0
0
0
0
2
1
2
0
1
2
1
1
0
0
2
0
0
0
2
1
1
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
2
0
0
0
0
1
0
0
0
2
2
0
1
2
2
0
0
0
1
0
0
0
1
0
2
2
0
1
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
2
0
0
0
1
2
0
0
2
1
0
1
1
0
0
0
0
0
0
0
2
0
0
1
1
1
3
0
1
1
0
1
0
0
0
1
0
0
0
0
3
1
0
1
0
0
0
1
1
0
1
0
0
2
0
2
1
0
2
0
1
0
0
0
0
0
1
2
0
0
0
3
1
1
0
1
0
0
1
0
2
0
0
2
0
2
0
0
2
0
0
0
0
5
1
0
0
2
0
1
0
1
0
1
0
2
0
0
0
2
1
0
0
1
1
0
1
1
1
2
1
0
1
1
0
1
0
0
1
0
0
1
2
0
0
1
0
0
0
2
0
1
0
1
0
1
1
0
0
0
0
0
1
1
0
1
0
1
2
0
0
1
0
0
0
0
2
1
0
0
0
1
1
1
0
2
2
0
2
0
2
0
0
0
0
0
1
0
0
1
0
1
2
0
1
2
0
0
2
1
0
1
0
0
1
2
0
1
0
0
0
0
0
0
0
1
0
2
1
0
2
0
2
1
0
1
0
0
0
1
0
3
0
0
0
1
0
2
0
3
1
0
1
1
1
1
0
1
0
2
0
2
0
0
0
1
0
2
0
2
1
0
1
0
0
0
0
2
1
2
0
1
2
2
0
0
0
0
0
2
1
0
0
0
0
0
2
3
0
0
0
2
1
0
1
0
0
0
0
2
0
0
1
1
0
0
0
2
0
0
0
0
1
7
3
2
0
0
0
2
2
0
1
1
0
0
0
0
1
2
0
0
0
0
2
1
0
0
0
1
1
2
0
0
1
1
0
0
0
0
0
2
1
0
3
0
0
2
0
0
1
3
2
1
0
0
1
2
0
0
1
0
0
0
0
2
1
0
2
0
0
1
1
1
0
2
0
0
0
0
0
0
0
2
1
0
0
1
0
3
2
2
0
0
3
0
2
0
0
0
0
0
0
2
0
2
0
1
0
1
1
2
0
2
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
2
1
0
2
0
0
1
2
0
0
0
2
0
2
0
0
1
2
1
1
0
2
0
0
1
0
1
0
2
0
1
2
0
1
0
2
2
0
1
0
0
1
0
1
0
0
0
1
1
2
0
1
0
0
4
3
0
0
1
1
1
2
1
0
0
1
1
0
1
1
0
5
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
1
1
3
1
0
0
2
0
2
1
0
0
0
2
2
0
1
0
0
1
0
0
0
2
0
2
0
1
2
0
1
0
0
0
1
1
2
0
0
2
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
1
0
2
1
0
0
0
0
1
0
2
0
0
1
2
0
0
2
1
1
0
1
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
1
2
0
1
0
0
1
0
0
0
0
1
0
2
0
0
2
0
1
0
0
1
2
0
2
1
1
0
0
0
1
0
0
0
0
0
2
0
2
2
1
0
0
1
0
0
0
0
1
0
0
0
2
1
2
0
1
0
1
1
0
13
0
0
1
0
0
1
0
2
0
0
2
0
0
2
0
0
2
1
0
2
0
2
1
1
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
1
1
0
1
0
0
0
2
2
1
3
2
0
1
0
0
1
2
0
1
2
0
2
0
1
0
1
0
0
0
0
2
2
2
0
0
0
0
0
1
0
1
0
0
0
2
0
1
0
1
1
2
1
0
0
0
2
2
0
0
1
1
0
1
3
0
1
0
1
2
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
1
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
2
0
2
0
1
1
2
0
0
2
0
2
0
1
0
0
0
0
0
3
2
0
0
2
2
1
2
1
8
1
0
1
2
1
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
1
1
1
0
0
1
1
1
1
1
0
5
2
0
2
2
0
2
0
0
0
0
0
1
0
0
0
0
1
2
2
0
2
0
0
0
1
0
0
0
1
2
2
0
0
0
0
1
0
2
0
0
2
1
0
3
0
0
0
1
2
0
0
1
1
0
0
1
0
1
0
2
2
1
0
1
2
1
0
0
0
1
0
2
2
0
2
0
0
0
1
0
0
2
0
0
1
0
0
0
1
2
2
0
0
1
0
0
0
0
0
0
0
0
1
0
1
2
0
1
1
1
1
2
0
2
0
0
0
0
0
0
2
2
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
1
1
0
0
2
3
0
0
0
0
0
2
0
0
2
1
0
0
5
1
0
2
1
0
0
0
0
0
0
0
2
1
0
2
0
0
1
1
0
0
2
2
1
0
0
1
0
0
1
0
1
2
0
0
0
2
2
0
0
1
0
0
0
1
2
2
0
0
0
0
2
0
0
1
1
0
2
1
1
1
0
1
1
0
0
0
4
1
0
0
1
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
1
0
0
0
1
2
0
0
1
1
1
0
0
1
0
0
2
0
0
0
1
0
0
0
2
0
1
0
0
3
0
0
2
2
0
1
1
1
1
2
1
1
0
0
2
0
0
2
0
0
2
0
2
0
0
0
0
0
2
2
0
1
0
1
0
2
2
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
4
1
2
0
0
1
1
1
0
0
2
0
0
0
0
0
0
2
1
0
2
1
0
0
0
0
0
1
1
1
1
0
0
0
0
1
1
1
0
0
0
0
2
0
0
1
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
2
1
0
0
1
0
1
2
0
0
0
3
2
1
0
0
2
0
0
2
0
0
1
0
0
0
2
0
1
0
0
0
0
0
1
2
0
0
0
0
1
0
1
2
0
0
1
3
0
1
1
2
0
0
2
0
2
2
1
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
2
0
0
1
0
2
2
0
3
0
0
0
2
2
0
1
2
0
0
0
1
0
0
1
0
2
1
0
2
0
2
1
0
0
0
1
1
1
2
2
0
2
1
0
2
1
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
1
0
1
1
1
0
1
0
0
0
0
2
0
0
1
2
0
0
2
0
2
2
1
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
1
1
2
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
2
0
0
0
1
0
2
1
1
1
1
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
2
1
0
0
0
1
0
4
2
0
1
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
2
1
1
2
0
1
0
1
4
1
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
2
0
1
0
1
2
0
2
1
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
2
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
2
1
1
0
0
1
0
1
2
1
1
2
1
0
1
2
0
0
0
0
1
0
0
0
0
1
0
1
0
3
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
1
1
1
0
0
0
2
2
1
1
2
0
0
0
0
2
1
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
2
1
1
0
2
1
0
2
0
2
2
1
0
0
2
0
0
2
0
2
1
0
1
0
0
2
0
2
0
0
0
1
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
3
0
0
0
0
0
0
0
1
2
0
1
0
3
2
0
0
1
2
1
0
0
0
1
0
0
0
1
1
0
0
2
0
1
0
0
0
0
0
2
0
1
2
0
0
1
0
0
0
0
1
1
0
0
0
0
2
0
0
1
0
1
0
2
2
0
0
0
2
2
2
2
0
2
1
3
2
0
0
0
1
0
0
1
0
0
0
0
1
1
1
1
1
0
1
0
0
1
1
1
2
0
0
2
0
2
0
0
2
2
0
3
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
2
2
1
0
0
0
0
0
0
2
0
0
1
3
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
2
0
3
0
1
1
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
2
0
0
0
0
1
2
0
3
1
1
0
2
1
0
0
0
0
0
1
1
0
1
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
1
0
3
0
0
1
2
0
0
0
0
0
1
0
1
0
1
2
1
0
0
2
0
0
1
0
0
0
0
1
1
1
1
2
0
1
0
1
0
0
1
0
0
1
3
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
1
1
2
1
0
0
0
0
0
0
1
0
0
0
2
2
1
2
0
0
0
1
0
0
1
1
1
0
0
2
0
0
2
1
0
0
2
0
1
2
0
1
1
1
2
0
0
1
0
0
1
1
0
0
0
0
0
2
0
1
0
2
0
0
0
0
1
0
0
0
2
1
0
0
1
1
1
0
0
2
2
0
1
0
1
0
0
0
0
0
0
0
0
0
1
2
0
2
2
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
2
0
0
2
0
1
0
0
1
1
2
2
0
1
2
0
0
2
0
0
0
0
0
2
1
0
2
0
1
0
2
0
1
0
1
0
0
1
0
0
0
0
1
0
2
0
2
1
0
0
1
0
1
0
0
2
0
0
2
0
1
2
3
4
0
1
0
0
1
0
0
0
0
0
2
0
0
1
0
2
2
0
0
0
0
0
2
0
0
0
1
0
2
0
2
0
2
2
0
0
1
1
0
1
1
0
1
0
1
0
0
0
0
0
3
1
0
2
0
0
1
0
0
0
2
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
2
0
1
0
0
2
2
0
1
1
0
0
1
1
0
0
0
2
0
1
0
0
0
1
2
1
0
1
1
1
1
0
0
2
2
0
0
1
0
1
0
0
1
1
0
1
2
0
2
1
1
0
1
1
1
2
0
2
0
0
1
2
0
0
3
1
0
0
2
2
0
0
0
0
1
2
0
2
2
0
0
2
0
1
0
2
0
1
2
0
2
3
0
1
0
2
0
0
2
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
1
1
0
0
0
0
1
2
0
0
0
1
2
0
1
0
0
2
0
1
0
0
0
2
2
1
0
0
0
1
0
0
2
0
0
0
2
2
0
1
1
0
0
0
2
0
1
2
2
0
1
1
2
0
1
0
0
2
1
0
2
0
2
1
1
0
0
0
2
0
0
1
1
1
1
0
1
1
0
0
0
0
2
3
0
0
0
3
0
0
0
0
0
1
0
0
0
2
1
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
1
3
0
0
2
0
1
0
1
0
1
2
0
0
0
0
1
0
2
2
1
0
0
0
1
0
0
0
0
1
1
2
0
0
0
0
0
3
0
1
0
0
0
1
2
0
0
0
1
0
1
1
3
0
0
0
0
0
2
2
0
1
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
1
0
0
1
0
0
0
2
0
2
0
0
0
1
0
2
2
1
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
2
0
1
0
2
0
2
2
2
0
0
2
0
0
0
0
2
2
0
0
1
0
3
0
1
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
1
0
0
0
2
2
0
0
0
1
0
0
1
0
0
1
1
1
0
0
1
1
1
0
0
0
0
2
0
0
2
1
1
0
0
2
0
1
1
0
2
0
0
2
1
0
0
0
0
0
0
1
2
0
1
0
0
2
2
2
0
2
0
0
0
0
2
2
2
0
0
1
1
2
2
1
0
1
2
0
1
0
4
0
2
0
0
0
2
0
0
2
1
0
1
0
0
1
0
0
0
0
0
2
1
1
2
0
2
3
0
0
2
0
0
1
0
0
2
0
0
0
1
0
3
1
0
0
2
0
0
1
0
0
1
2
0
2
0
0
0
0
0
0
1
1
0
1
2
2
2
0
0
0
0
1
1
0
1
0
1
0
1
2
2
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
3
1
1
0
0
0
0
0
0
1
0
0
2
1
2
0
0
2
0
0
0
0
1
0
0
0
0
1
0
1
1
2
2
0
2
1
1
0
0
0
2
0
0
1
0
1
1
0
2
2
0
0
0
0
1
1
0
2
0
0
0
0
0
0
1
0
1
0
0
2
0
0
2
2
0
0
0
1
0
1
0
0
0
1
2
1
2
0
0
0
0
0
2
0
2
1
0
0
1
1
0
1
2
2
1
0
0
0
0
2
1
0
0
2
2
1
2
0
0
0
2
0
0
0
1
1
0
1
0
1
3
0
0
0
0
0
2
2
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
3
0
0
1
0
1
1
1
0
2
1
2
1
0
1
0
0
0
1
0
1
1
0
1
0
0
1
0
1
1
2
0
3
1
1
0
0
0
0
0
0
0
2
1
0
1
0
1
0
1
0
0
1
0
1
1
0
0
1
0
0
0
0
0
2
0
0
0
2
2
0
2
2
0
0
1
1
0
2
0
0
0
2
2
0
1
0
2
2
1
1
1
2
2
0
1
1
2
0
0
0
0
0
0
2
1
0
1
0
0
0
2
1
0
3
0
2
2
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
2
1
0
3
0
0
2
2
2
0
2
1
2
0
1
0
0
0
2
0
2
0
2
0
0
0
1
0
0
1
0
0
1
0
1
2
2
2
0
0
2
0
0
0
1
0
0
2
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
2
0
0
0
2
1
0
0
1
0
1
1
1
0
2
0
2
0
0
1
0
2
0
1
0
0
1
0
1
0
0
1
0
2
1
0
0
2
0
0
0
2
1
2
1
0
1
0
0
0
1
0
2
1
0
1
1
0
2
0
0
0
2
0
0
0
0
0
1
2
2
0
0
1
2
0
1
0
0
1
0
2
4
2
1
1
2
1
2
0
0
2
1
0
2
1
1
2
0
0
0
1
0
0
1
0
1
0
0
2
0
0
2
2
0
2
1
1
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
2
2
0
1
0
1
0
1
0
0
0
1
0
0
2
0
2
1
0
0
1
0
0
0
2
0
0
0
0
1
0
2
1
0
0
0
0
2
0
2
2
2
0
0
0
1
1
2
0
0
2
1
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
2
1
1
0
1
0
0
0
0
0
0
0
2
0
1
1
0
3
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
1
1
1
2
2
2
1
2
2
0
1
0
0
0
0
0
1
0
2
0
2
1
1
0
0
0
2
1
3
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
1
0
0
3
2
0
0
1
0
0
0
2
0
1
0
0
0
1
0
0
2
1
0
0
1
0
0
2
0
0
0
1
0
1
0
1
1
0
0
0
0
2
2
0
0
0
2
0
1
1
1
0
1
0
2
0
1
2
2
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
2
2
0
0
0
0
2
0
0
1
1
2
1
0
1
1
0
0
3
0
0
1
1
1
0
3
1
2
0
0
2
1
0
0
0
1
1
1
1
1
0
2
0
0
2
0
0
1
0
0
1
0
2
1
1
0
0
4
1
4
1
2
1
3
1
0
0
1
0
0
3
2
0
2
1
0
1
0
1
1
1
0
0
0
0
0
0
1
0
0
2
1
0
1
2
1
0
0
0
0
0
0
0
0
2
0
0
1
1
0
2
1
3
2
1
0
0
0
0
1
0
2
1
0
2
0
0
1
0
2
0
0
0
2
2
1
2
2
0
0
0
2
0
4
0
0
1
2
2
0
0
0
0
0
0
1
0
1
1
1
2
0
0
0
1
1
0
2
2
2
0
2
0
2
2
0
3
0
2
0
0
1
2
0
0
0
2
0
0
0
0
0
1
0
0
1
1
0
0
2
2
0
0
0
0
0
0
0
0
1
1
2
1
0
0
1
0
2
0
0
2
0
1
0
2
0
0
0
2
0
0
0
0
0
1
1
0
1
0
0
0
1
1
1
0
1
1
0
1
2
0
1
0
0
0
1
1
0
0
0
0
2
1
2
0
0
0
2
0
0
0
0
0
0
0
1
2
1
0
0
2
2
0
1
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
2
0
0
0
1
1
0
1
1
2
0
0
0
1
0
0
1
3
0
1
0
0
2
0
1
1
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
2
2
0
1
0
0
0
0
0
1
0
1
2
0
1
1
0
0
0
1
1
2
2
0
2
1
0
2
1
0
0
4
0
0
0
0
2
2
0
0
1
0
0
1
2
2
0
2
2
0
0
1
2
2
0
0
0
0
1
0
2
0
2
0
0
0
2
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
2
2
0
0
2
0
0
0
0
0
2
2
1
1
2
2
0
0
0
0
1
3
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
1
2
0
0
2
1
0
0
2
2
0
0
1
0
0
0
0
2
1
0
1
0
2
0
0
0
0
2
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
3
1
0
2
0
0
3
1
0
2
0
2
0
2
0
1
0
0
1
1
1
2
2
0
0
1
0
1
2
1
0
0
1
2
1
1
2
3
0
2
1
1
1
0
2
1
0
0
1
0
2
2
0
0
1
0
1
2
0
2
0
0
2
0
2
0
2
0
1
0
1
1
1
2
4
1
2
1
1
2
2
1
0
2
0
1
1
2
1
0
0
0
1
0
2
0
0
1
1
1
0
1
0
0
0
2
1
2
0
1
0
0
2
0
0
1
1
0
0
0
0
2
0
0
0
2
0
0
0
2
1
0
2
1
0
3
2
0
1
0
0
1
0
0
0
1
3
0
0
1
1
0
2
0
0
0
0
0
0
1
1
2
0
1
0
1
0
0
0
0
0
2
0
1
1
0
0
1
1
0
0
2
0
2
2
0
2
0
0
0
0
0
0
0
0
2
0
1
1
0
2
2
0
0
2
2
0
0
0
0
1
2
0
0
2
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
2
1
0
1
0
2
0
1
2
1
2
0
0
1
1
1
2
0
0
0
0
0
0
0
0
0
1
0
1
1
1
1
0
0
2
0
0
0
0
1
1
0
1
0
0
1
0
1
0
2
0
0
1
0
0
1
0
5
1
0
0
0
0
2
2
0
0
0
1
0
0
0
0
2
0
0
2
2
0
2
2
0
0
2
0
2
2
1
0
1
0
0
0
0
1
1
0
0
1
0
1
2
0
0
0
2
0
2
0
0
6
0
0
2
0
2
1
2
3
0
1
1
1
0
2
0
1
1
0
0
1
0
0
2
2
1
2
2
1
1
1
0
1
0
1
0
1
0
0
0
0
2
0
2
0
0
0
1
1
2
0
0
0
0
0
1
1
1
0
2
2
1
1
0
0
0
0
0
0
0
0
2
2
0
2
2
0
0
0
2
0
0
1
0
0
0
0
0
1
2
0
0
0
0
1
0
4
2
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
1
2
0
0
1
0
2
0
1
0
0
2
0
0
0
0
0
1
1
0
2
0
0
0
0
0
1
1
4
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
1
2
0
1
0
1
0
0
0
0
0
0
1
0
2
0
3
0
1
0
1
0
1
1
0
1
1
1
0
0
0
0
0
2
2
2
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
1
2
0
0
0
1
0
1
1
0
2
1
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
1
0
2
1
0
2
0
0
0
2
0
0
0
3
0
2
1
0
2
2
0
1
1
2
2
1
1
0
2
1
0
0
0
0
0
0
0
0
2
2
3
0
1
0
0
0
1
2
0
1
0
0
1
0
2
0
0
0
0
0
1
0
2
0
2
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
2
0
1
0
0
0
2
0
0
0
2
2
0
3
1
0
0
1
0
0
0
0
0
0
1
2
0
1
0
1
0
1
0
0
0
0
2
2
0
0
0
0
1
3
2
0
1
2
2
1
0
3
3
0
0
0
1
2
0
0
0
1
0
0
0
0
0
1
3
0
1
0
3
2
0
1
0
0
1
0
1
0
0
1
1
0
2
2
2
0
0
1
0
2
0
1
0
0
1
1
0
0
2
0
0
0
1
0
2
2
0
1
0
1
1
0
1
0
2
0
0
0
0
2
2
2
0
1
0
0
2
2
1
0
0
2
0
1
0
0
0
1
0
0
0
1
2
0
1
1
2
0
1
0
1
0
0
1
1
0
0
4
1
0
0
1
0
0
1
0
0
0
0
2
0
1
1
1
0
1
0
0
2
0
2
0
0
0
2
0
2
0
2
2
0
2
1
2
0
3
0
0
0
0
2
0
0
1
0
1
1
0
0
0
0
2
0
1
0
1
0
0
2
1
0
0
0
1
2
1
2
3
0
0
0
0
1
2
0
0
0
1
2
1
0
2
1
2
0
0
2
1
1
0
0
2
1
0
2
0
0
1
0
2
0
1
0
0
0
0
2
2
0
0
1
0
2
1
0
0
2
0
0
1
2
0
2
0
2
0
1
1
1
0
1
0
1
0
0
1
0
2
1
0
2
2
0
0
2
0
0
1
1
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
1
2
1
0
1
1
0
0
0
1
0
0
0
1
2
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
2
2
0
1
0
0
0
1
1
0
1
2
0
0
0
0
0
1
1
1
2
0
0
0
0
0
1
1
0
0
2
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
2
2
2
1
2
1
4
2
0
0
0
1
0
0
1
0
0
0
1
0
0
1
3
0
0
0
1
2
0
0
0
0
0
2
2
1
0
2
1
2
2
1
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
1
3
0
0
1
0
2
1
1
1
1
1
0
2
1
2
0
3
1
0
1
1
1
1
0
0
0
0
2
0
2
0
0
0
0
1
1
0
3
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
1
0
1
1
0
0
2
1
1
0
0
0
0
0
0
0
1
2
2
2
1
2
0
0
0
1
2
1
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
2
0
0
2
1
0
3
0
0
0
0
1
2
0
1
0
2
2
1
0
2
0
0
2
1
0
0
0
2
0
1
2
0
0
2
0
0
0
0
2
0
0
0
2
1
0
0
2
1
0
1
0
1
0
1
0
0
0
1
1
1
0
2
1
0
1
0
2
0
0
1
0
0
0
0
2
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
2
1
0
0
0
0
1
0
2
0
0
1
0
1
1
0
2
0
0
1
2
0
0
0
1
0
1
0
0
1
2
1
0
2
0
1
1
0
1
0
3
0
0
0
1
0
0
0
0
2
2
2
0
0
3
0
1
5
0
2
0
1
1
1
0
2
1
0
0
2
1
0
1
0
0
1
0
0
0
1
0
2
3
2
0
2
0
0
0
2
2
2
1
1
0
2
0
1
1
1
0
1
2
1
0
2
1
2
0
2
2
2
0
0
2
2
0
0
0
0
0
2
2
2
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
1
2
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
2
1
2
0
2
0
0
1
1
0
1
2
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
1
0
0
2
7
2
0
2
1
0
2
0
2
0
0
2
2
0
0
2
1
0
2
0
0
0
2
0
0
0
7
0
2
1
0
2
3
0
0
0
0
0
0
0
1
1
0
2
0
0
0
2
1
0
0
2
2
1
2
1
2
1
0
0
2
2
0
0
0
0
1
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
7
1
0
0
1
0
1
1
1
2
9
1
0
2
0
0
0
0
1
1
0
0
0
0
4
2
3
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
2
0
1
0
0
0
2
0
1
0
0
0
2
0
2
0
0
1
1
0
1
0
2
1
0
1
0
2
0
2
0
0
0
3
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
2
0
3
2
0
1
1
2
2
0
3
1
0
1
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
2
0
3
0
1
0
0
2
2
0
0
2
1
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
1
0
0
0
0
0
2
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
2
3
0
0
0
1
0
1
1
0
1
0
0
2
0
1
1
2
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
2
1
1
2
2
2
0
1
2
0
0
0
0
2
0
2
1
1
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
2
1
2
1
1
2
0
1
0
0
1
1
2
0
2
1
1
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
1
1
1
0
1
1
2
2
2
2
0
0
1
2
0
0
0
2
1
2
1
0
1
1
1
1
1
0
0
0
0
2
0
0
1
1
0
0
2
0
3
0
0
0
0
0
2
0
1
1
0
1
2
0
2
2
2
0
2
1
0
0
1
1
0
1
0
1
3
2
0
0
0
2
1
0
0
0
0
1
1
0
0
0
1
0
1
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
2
1
0
1
0
0
1
2
0
2
0
0
0
2
2
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
1
2
2
0
0
0
0
1
0
1
3
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
2
0
2
0
0
1
0
2
0
0
0
2
2
0
0
1
0
0
0
0
0
1
0
1
1
0
0
1
1
2
0
1
0
1
0
0
0
2
2
0
1
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
1
0
0
0
1
1
0
2
1
2
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
4
2
2
2
1
0
0
0
1
0
0
2
1
1
2
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
1
0
0
1
0
0
0
2
0
0
0
0
1
0
1
2
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
2
2
3
0
2
1
1
0
2
1
0
2
0
0
0
0
0
0
2
2
0
0
1
2
1
1
0
1
0
1
2
1
0
0
0
2
0
0
2
2
0
0
1
1
1
0
0
0
0
0
1
1
0
0
0
2
1
1
0
0
2
1
0
0
1
0
2
0
2
0
0
2
0
0
0
2
0
0
0
0
0
3
0
0
3
2
0
0
0
0
0
1
0
0
3
1
2
0
0
0
1
1
3
0
0
0
0
2
0
0
0
1
0
2
0
0
2
0
0
1
1
0
0
2
1
2
1
0
2
1
0
2
0
1
0
3
1
1
0
2
0
0
2
0
0
0
1
1
1
0
0
2
0
0
2
1
0
0
0
0
1
0
1
0
1
0
0
0
1
0
2
2
0
0
0
0
1
0
0
0
2
1
0
1
2
2
2
1
0
0
0
2
0
1
2
1
0
1
1
2
0
2
0
0
2
1
0
0
0
2
1
3
1
0
0
0
0
0
0
2
2
1
0
3
0
2
0
0
0
2
1
0
2
3
0
0
0
1
0
1
0
1
2
0
0
0
0
0
2
0
2
0
1
1
3
1
2
2
0
0
0
0
1
1
0
0
0
0
0
5
2
0
0
0
1
1
0
0
0
0
1
0
1
0
0
2
1
2
0
0
1
0
0
1
0
2
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
1
2
0
2
1
0
0
3
0
0
0
2
0
0
0
0
1
2
0
0
0
1
0
1
0
0
1
1
0
1
0
0
0
1
0
1
0
0
0
2
1
0
0
2
0
2
2
0
0
0
0
1
0
0
0
2
0
0
2
0
0
1
1
2
0
0
0
0
0
0
2
1
0
1
0
0
2
0
0
0
0
2
1
1
2
0
1
2
0
1
1
1
1
1
0
0
2
0
0
0
1
1
0
1
1
0
1
0
0
2
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
2
2
0
1
1
0
2
0
1
0
2
0
2
0
0
1
1
1
1
0
0
0
2
2
2
0
2
1
1
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
2
0
1
0
3
1
0
2
2
0
1
0
2
2
2
0
0
1
0
2
1
0
1
2
1
0
2
2
0
1
2
0
0
2
1
2
0
1
2
0
0
0
0
0
1
0
1
2
0
2
2
2
1
0
0
0
1
0
0
0
0
2
0
2
0
0
2
0
1
3
0
0
0
0
0
0
1
1
0
0
0
1
1
1
1
1
1
2
1
1
1
0
1
1
0
1
1
0
0
0
2
0
1
0
1
1
1
0
4
1
0
2
0
0
0
0
2
0
0
0
1
0
1
1
1
2
0
2
1
0
0
3
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
2
0
2
0
1
1
2
0
0
0
2
0
0
1
0
0
1
0
0
1
0
0
0
0
0
3
1
2
0
0
2
0
1
1
2
2
2
0
1
12
2
0
0
1
0
0
0
1
0
1
1
2
0
2
1
2
2
0
1
0
0
3
0
0
1
0
2
0
0
1
1
0
0
0
1
0
0
1
5
1
0
0
1
1
0
0
2
0
2
0
0
1
0
0
0
2
0
2
0
0
0
1
0
0
1
2
0
2
0
0
0
1
0
1
0
1
0
1
0
2
0
1
0
0
2
0
0
0
0
1
0
0
2
0
1
0
0
1
0
2
0
0
0
0
0
2
0
0
2
0
1
0
0
0
1
0
1
1
0
0
0
0
2
0
0
2
0
0
0
0
1
1
0
0
0
0
0
2
0
1
0
1
1
0
0
0
0
0
2
1
0
0
0
0
0
0
1
2
1
0
0
0
1
1
1
0
0
0
0
0
1
0
1
3
0
0
0
0
0
0
1
0
2
2
1
0
0
0
0
1
0
2
2
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
3
0
1
0
1
0
1
0
0
0
0
0
1
1
0
1
0
0
2
0
0
0
0
2
0
0
1
1
2
1
1
0
0
0
2
2
0
0
0
1
1
2
1
3
0
1
1
0
1
0
0
1
0
2
0
0
2
1
0
1
2
0
3
2
3
0
2
0
0
1
1
0
0
0
0
1
2
1
0
1
0
0
2
0
1
1
0
1
0
2
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
2
2
1
0
0
0
2
2
0
0
0
1
0
0
1
0
0
1
1
0
0
2
1
0
0
2
2
2
0
0
0
1
0
1
0
2
0
0
2
0
0
0
1
0
2
0
1
2
0
0
0
0
0
3
2
0
1
0
0
0
0
1
1
0
0
2
0
2
1
1
0
0
0
0
1
0
2
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
1
1
0
1
0
0
0
3
2
0
0
0
2
0
2
0
1
0
0
3
0
0
0
0
0
0
0
1
2
2
1
2
1
1
2
0
0
1
1
0
2
1
0
3
0
0
0
0
1
0
2
0
2
1
1
2
0
0
1
2
0
0
2
0
0
0
2
0
1
0
2
0
0
2
0
1
0
2
0
0
1
0
1
1
2
0
0
0
0
0
0
0
1
0
0
0
0
1
2
2
0
2
0
0
1
0
2
1
1
1
0
1
0
0
1
0
0
2
0
0
0
0
2
1
0
2
0
2
3
1
0
1
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
2
1
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
1
0
0
0
2
2
2
0
1
0
0
1
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
3
0
2
1
0
0
1
2
1
0
1
1
0
2
0
1
0
1
0
2
0
0
0
1
0
3
1
0
0
0
0
1
1
0
1
0
0
3
0
1
0
2
0
0
2
0
2
0
2
0
2
1
0
2
2
3
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
2
3
0
0
1
2
0
0
1
0
0
1
1
1
2
1
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
1
1
0
2
1
0
0
0
0
1
0
2
3
1
2
2
0
0
5
1
1
2
2
9
1
0
0
0
2
0
0
0
0
4
0
2
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
1
1
2
1
0
0
0
1
0
0
2
1
0
0
1
0
0
0
0
3
2
2
1
0
0
2
1
1
0
0
1
0
0
0
1
0
1
0
2
0
1
1
2
1
2
0
1
1
2
1
2
0
0
0
2
2
0
2
0
0
0
1
0
0
0
1
0
2
0
0
0
0
1
0
2
1
0
1
3
0
1
0
0
0
2
0
1
0
2
0
2
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
2
0
0
1
0
1
1
1
0
0
2
0
0
1
0
0
0
1
1
0
0
2
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
1
2
0
0
2
2
2
1
2
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
2
0
1
2
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
1
0
0
2
0
1
0
2
1
0
0
0
5
1
1
2
0
0
0
0
0
0
1
0
0
1
0
1
3
2
2
2
2
0
2
0
0
1
1
0
2
0
0
0
2
2
0
0
0
1
1
0
0
0
2
1
1
0
1
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
1
2
2
0
0
0
1
0
0
2
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
2
0
2
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
2
2
2
0
0
0
2
1
2
0
0
0
0
0
0
6
2
0
1
0
0
1
0
1
0
1
0
2
1
0
0
1
0
0
0
3
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
1
1
1
4
2
0
0
1
2
0
1
0
0
1
1
1
1
1
0
1
0
0
0
0
3
1
0
3
0
0
0
2
0
1
0
0
0
2
2
0
0
2
2
0
0
2
1
2
2
0
1
1
2
0
1
0
2
1
1
0
0
2
2
0
2
0
0
2
0
0
0
2
1
1
2
0
2
0
3
0
2
0
1
0
2
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
1
2
0
1
1
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
1
2
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
4
0
0
1
0
3
0
1
1
0
0
5
0
0
0
1
0
0
1
0
1
2
1
0
2
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
2
1
0
0
2
0
0
1
1
0
1
0
0
0
0
0
0
0
2
0
0
2
1
2
1
0
1
1
1
2
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
2
0
1
0
0
0
0
2
0
1
2
0
0
2
0
1
0
1
3
0
1
0
0
0
2
1
0
0
0
0
1
2
0
2
0
0
1
0
0
0
1
0
0
2
0
0
1
0
2
0
1
2
0
0
0
1
0
1
0
1
0
1
0
1
0
0
2
2
1
0
0
0
2
0
1
0
1
0
0
1
0
0
2
1
3
0
2
0
0
2
1
1
0
0
0
1
0
1
2
1
2
0
1
0
2
0
2
0
3
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
3
2
2
1
0
1
2
0
0
0
2
2
0
2
2
0
1
1
0
1
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
1
2
0
1
2
2
2
0
0
1
0
1
0
2
0
1
0
1
0
1
2
0
1
0
0
1
0
2
0
0
0
0
0
1
3
0
2
0
2
0
0
0
1
0
0
1
1
4
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
1
2
1
0
0
0
0
0
2
0
2
0
1
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
2
1
1
0
1
1
2
0
0
0
0
0
1
0
0
0
2
0
0
0
3
1
0
0
1
1
1
0
0
0
2
0
0
1
1
0
0
0
0
1
2
1
0
1
0
2
0
0
0
3
0
0
1
0
0
0
2
1
0
0
0
2
2
1
1
6
0
1
0
0
1
1
1
2
1
1
2
2
1
2
1
0
0
0
1
0
0
0
1
0
0
2
0
1
2
0
0
0
0
1
2
0
0
1
0
2
0
0
0
0
2
0
2
1
0
1
0
2
0
0
2
1
0
0
1
5
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
2
1
2
0
0
0
1
0
2
0
2
0
1
0
0
2
2
2
0
0
0
2
0
1
1
2
2
0
1
0
0
2
1
2
0
2
0
0
1
2
1
0
1
0
0
0
0
1
2
0
2
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
2
1
0
1
0
2
0
2
0
3
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
2
0
0
2
0
0
1
0
1
1
0
0
0
1
1
2
0
1
2
1
0
2
2
2
1
3
0
0
0
2
1
1
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
1
1
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
2
0
2
0
0
2
1
0
2
1
0
1
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
2
0
2
2
0
0
0
1
0
0
0
0
0
1
0
0
2
1
1
2
0
0
0
1
1
0
0
0
1
0
0
0
2
0
1
0
3
2
0
2
2
2
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
2
1
2
0
1
0
1
0
0
0
0
2
1
0
0
0
1
0
0
0
0
2
0
0
0
3
0
2
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
3
0
4
0
0
0
0
1
2
2
0
0
2
0
0
1
0
2
0
2
0
0
1
0
0
0
0
0
0
0
1
1
0
2
1
0
0
1
1
0
0
4
0
1
0
0
2
3
0
1
0
0
0
2
0
0
0
2
2
1
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
1
0
0
0
2
0
0
2
0
1
0
2
0
1
0
0
1
0
0
1
0
2
1
0
3
0
0
0
1
1
1
0
0
0
0
0
0
1
1
0
1
2
2
0
0
1
1
0
1
0
0
0
1
2
1
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
1
2
0
2
0
0
0
0
1
0
0
1
0
1
0
2
2
0
0
0
0
2
0
1
1
2
0
0
0
0
0
2
3
0
2
0
1
1
2
0
1
2
1
0
0
0
0
0
0
2
0
0
2
0
0
0
1
3
2
2
0
2
0
0
0
0
1
2
2
0
1
0
2
0
0
0
0
1
2
2
1
0
2
0
1
2
0
0
1
2
0
0
0
1
0
0
1
2
0
0
0
1
0
0
1
2
0
0
1
2
0
1
1
3
0
1
0
0
0
1
2
2
3
1
2
0
1
1
0
1
1
1
0
0
2
4
1
1
2
1
2
2
0
2
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
2
0
2
0
2
0
0
0
0
1
0
0
2
0
1
0
0
2
1
0
0
2
1
1
1
0
0
1
0
0
2
0
0
0
0
1
0
1
2
0
2
0
0
1
1
3
0
2
0
0
1
0
0
1
0
2
0
0
0
0
0
1
2
2
0
1
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
2
0
4
1
0
2
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
1
1
1
0
2
2
0
0
2
0
0
0
0
1
2
1
0
0
1
0
0
1
2
3
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
1
2
0
2
0
0
2
2
0
0
0
1
0
0
2
0
2
0
0
0
2
0
0
1
2
0
0
0
2
0
1
1
0
2
0
3
2
2
0
0
0
0
0
1
0
2
0
1
2
0
2
0
0
0
0
2
0
1
2
0
0
0
0
1
1
2
2
0
0
2
0
0
1
0
1
0
0
1
0
2
0
0
0
0
1
2
2
1
0
0
0
0
0
1
1
0
0
0
1
2
1
2
0
1
0
0
0
2
0
0
0
1
2
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
1
2
0
2
0
0
0
2
0
2
1
0
1
2
0
0
2
1
1
0
2
1
0
0
0
2
0
0
1
2
1
0
0
0
2
0
2
2
0
0
0
1
1
0
2
0
0
1
0
0
1
2
0
3
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
2
0
1
2
0
0
2
2
0
1
6
2
0
1
2
2
2
0
0
1
1
2
2
2
0
0
0
2
1
1
1
0
1
2
2
0
1
0
0
2
0
1
0
2
0
1
1
1
2
0
1
3
0
1
0
1
0
0
1
0
1
0
2
2
0
0
1
1
0
0
1
0
1
2
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
1
2
0
0
1
0
2
0
0
3
0
0
2
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
2
1
0
2
1
2
0
0
2
0
0
0
1
1
2
0
1
2
0
1
0
0
2
0
0
2
0
1
1
0
1
0
0
0
0
0
1
2
0
0
0
2
0
2
0
2
1
1
0
0
0
1
0
0
0
1
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
2
0
2
0
0
1
1
0
0
2
0
0
0
0
0
2
2
0
0
2
0
0
0
1
2
1
0
2
0
2
0
1
1
1
0
0
0
0
1
2
2
0
0
0
2
0
0
0
0
1
2
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
1
1
0
1
0
0
0
0
0
0
1
2
1
1
0
1
0
0
0
0
2
0
2
2
3
0
0
1
0
1
0
0
0
0
2
0
5
0
0
0
1
2
2
0
0
2
0
1
0
0
2
0
0
1
0
0
0
0
0
0
2
2
0
2
0
1
0
0
2
1
0
0
2
0
1
1
0
0
1
0
0
1
0
0
0
0
2
2
0
0
0
2
2
0
2
0
2
1
1
5
0
2
1
2
0
0
0
0
2
0
1
1
1
2
1
0
1
0
1
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
1
1
0
1
0
0
1
0
3
1
1
0
0
0
0
0
1
1
1
2
1
2
0
0
2
0
2
0
0
1
0
0
0
0
0
2
2
0
0
1
1
0
0
1
1
0
0
2
0
1
0
0
0
1
0
2
0
1
1
0
0
0
2
1
1
1
2
3
1
0
0
0
2
1
0
0
0
2
1
1
1
5
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
2
1
0
1
1
0
3
2
2
0
0
0
1
0
0
0
0
2
1
1
0
2
2
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
1
1
0
1
2
0
0
0
0
2
1
0
0
2
0
0
0
1
1
1
0
0
2
2
0
1
0
0
1
0
1
1
1
1
2
0
0
1
2
0
0
0
1
0
0
2
0
0
1
0
0
1
0
0
0
1
1
0
0
0
2
1
0
0
3
0
0
1
0
0
1
0
2
2
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
1
0
0
2
1
0
2
2
2
1
2
0
0
2
1
0
2
1
2
0
0
2
1
0
1
0
0
0
2
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
1
1
0
1
0
0
2
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
1
2
0
0
2
2
0
0
1
0
2
0
0
0
1
2
0
1
2
2
1
0
1
0
0
0
0
0
1
0
0
2
2
1
0
0
1
0
1
1
0
1
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
2
0
3
2
1
2
0
2
1
0
1
0
1
0
1
0
1
0
0
1
0
1
0
1
2
1
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
1
2
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
1
0
2
1
0
0
0
1
0
0
2
4
0
0
2
2
0
3
1
2
1
0
2
1
3
0
1
1
1
0
2
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
2
1
2
2
2
1
2
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
2
1
0
1
0
0
0
0
0
1
2
2
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
1
2
0
0
0
0
2
0
0
0
1
1
4
2
2
2
1
2
0
0
0
0
0
1
1
2
9
2
2
0
2
0
0
2
0
0
2
1
0
2
2
0
2
1
2
0
1
0
1
0
0
2
3
1
0
1
3
1
1
0
1
0
0
1
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
2
0
3
0
1
1
0
0
3
0
0
0
0
0
2
0
1
0
2
0
0
1
1
0
1
0
0
0
0
1
2
1
0
1
1
0
0
0
2
0
0
0
0
2
1
1
0
2
0
0
2
0
2
0
2
0
0
1
2
1
0
0
2
1
1
1
0
2
2
0
0
1
1
0
0
0
0
1
0
0
2
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
2
0
0
1
0
2
2
0
1
1
3
0
1
0
2
0
2
1
0
1
0
1
0
0
3
1
0
0
1
1
2
0
0
2
0
1
0
0
2
0
0
0
1
0
2
1
0
0
0
2
0
1
0
0
0
2
1
1
2
1
0
0
2
1
1
2
0
2
0
0
0
0
0
1
0
0
3
1
0
2
0
2
1
1
0
1
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
4
2
0
0
0
0
0
0
2
0
0
0
0
2
2
1
0
1
0
0
0
0
1
1
2
0
1
0
0
2
0
1
1
1
0
2
2
1
0
0
2
2
0
0
0
2
0
1
0
1
0
0
1
0
0
1
0
0
1
0
2
2
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
1
3
0
0
0
0
0
2
1
0
2
1
0
0
0
0
2
1
0
0
0
0
2
1
0
0
0
0
1
0
2
0
0
1
1
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
2
3
1
0
2
2
0
0
0
0
0
0
0
1
0
2
1
0
0
1
1
0
3
0
0
1
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
2
0
0
0
1
0
0
0
3
1
0
0
0
0
1
0
2
0
1
2
0
2
1
1
1
2
0
1
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
1
1
2
1
0
1
0
0
0
2
0
0
0
2
2
0
1
2
0
0
0
2
2
0
0
1
1
1
0
2
2
2
1
3
0
2
0
0
0
0
3
0
2
0
2
0
0
2
0
0
3
2
1
0
0
0
2
1
2
0
0
0
0
0
2
0
0
1
0
1
0
0
1
1
2
0
0
0
0
1
1
2
0
0
0
0
0
2
1
0
0
5
0
0
1
0
0
2
0
0
0
0
0
6
0
1
1
0
1
2
0
0
2
0
0
1
2
1
0
0
0
0
0
0
1
0
0
1
1
0
1
2
0
1
0
0
2
0
1
0
0
1
2
1
1
0
0
2
1
4
0
0
2
0
1
2
0
0
1
0
0
1
0
2
2
0
0
0
1
0
1
0
0
1
2
0
0
0
0
1
1
1
0
1
1
0
0
1
2
0
0
2
1
4
1
0
0
1
0
0
0
0
0
2
2
2
1
0
0
0
0
0
0
1
1
0
0
0
0
2
3
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
1
0
2
0
1
0
0
1
1
0
0
2
1
0
0
1
0
0
1
1
1
0
1
0
2
0
0
0
0
2
0
1
0
0
1
0
3
1
0
0
0
1
2
1
2
1
1
0
2
0
0
0
0
2
2
1
1
2
0
2
0
1
0
2
1
1
0
0
2
0
1
0
0
1
0
1
0
0
1
4
2
2
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
1
2
0
0
0
1
3
1
1
1
0
0
2
2
0
0
0
1
0
0
0
0
2
1
0
0
0
1
1
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
2
2
0
1
0
2
0
0
0
0
0
0
1
0
1
0
0
3
0
3
1
1
1
0
2
1
0
0
1
0
2
0
2
0
1
0
0
2
0
0
2
0
1
1
0
2
0
1
0
1
0
1
1
0
0
0
1
1
2
0
0
1
0
2
0
0
0
0
0
2
0
2
2
0
0
1
0
0
0
2
0
0
1
0
2
1
3
0
2
1
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
2
0
2
0
2
1
1
0
0
1
1
2
0
1
0
0
0
0
0
0
0
0
0
2
2
1
1
0
0
0
1
0
1
0
0
1
0
2
0
2
0
2
0
5
0
0
0
1
0
0
1
0
1
0
0
0
0
0
2
1
2
0
0
2
2
2
0
2
0
2
0
1
0
1
0
2
0
3
1
2
0
1
2
2
0
0
2
0
0
0
1
0
0
0
2
2
0
0
2
0
2
1
1
0
0
2
2
1
1
0
0
0
0
1
1
2
1
0
2
0
2
0
1
2
0
1
0
0
0
0
0
1
2
1
1
0
0
0
0
1
1
0
0
0
1
0
1
1
0
0
0
0
0
2
0
0
0
0
1
1
0
1
2
0
2
2
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
1
2
2
0
1
0
1
0
0
1
0
0
3
0
0
0
0
0
2
0
0
1
0
0
0
0
2
1
0
2
0
2
0
0
0
0
0
2
4
1
0
0
0
0
2
1
2
3
1
1
0
1
0
1
0
1
0
0
0
0
0
3
0
0
0
1
0
1
1
1
2
0
0
0
1
0
0
0
1
0
0
1
0
0
1
1
2
0
0
0
2
0
0
1
0
0
0
1
2
0
2
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
1
0
0
0
1
1
0
2
0
0
0
0
2
0
0
0
1
0
1
0
0
2
0
2
0
0
0
2
0
0
0
1
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
1
0
0
0
1
2
1
1
1
1
0
0
0
0
0
1
2
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
1
2
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
1
2
0
0
0
0
1
0
0
2
2
0
2
0
0
2
0
2
1
0
1
0
2
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
2
2
0
0
2
2
0
3
2
0
0
1
0
0
0
1
1
0
0
0
0
0
1
1
0
2
3
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
3
2
2
1
1
0
1
2
1
3
0
2
0
0
1
0
1
2
0
2
0
0
2
2
1
0
2
2
0
0
0
2
0
0
2
0
0
1
0
1
2
0
0
0
0
0
0
0
2
2
0
1
0
1
1
0
1
0
2
1
1
1
0
1
0
0
1
0
0
0
0
3
2
1
1
1
0
1
1
0
0
2
2
1
1
1
1
2
1
1
0
0
0
1
2
0
0
0
0
2
0
0
1
0
1
0
1
2
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
1
2
1
2
0
2
1
0
2
0
1
0
0
1
1
2
1
1
0
0
2
1
0
0
0
1
3
1
1
0
2
0
0
1
1
0
1
2
0
0
2
0
1
0
0
1
1
0
2
1
2
2
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
1
1
1
1
0
2
1
0
1
2
1
0
2
0
0
1
1
0
0
0
0
0
1
2
3
1
1
0
0
1
0
0
1
2
0
0
0
0
0
0
1
0
2
0
2
0
2
0
2
1
0
0
0
0
0
0
1
0
1
1
0
2
2
0
2
0
1
2
2
0
1
2
2
0
0
2
1
0
2
0
0
0
2
2
1
2
0
0
0
2
0
1
0
0
0
5
0
1
0
0
3
0
0
1
0
2
0
1
0
0
0
2
0
2
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
2
2
0
2
2
3
1
1
0
3
2
0
0
0
0
0
0
1
1
2
1
0
1
0
2
0
1
0
0
0
2
1
0
0
2
1
0
0
0
0
0
1
0
0
1
0
1
2
1
0
0
2
0
1
0
0
2
1
1
0
0
2
0
0
1
0
2
2
0
0
0
2
0
0
0
2
1
0
0
0
1
1
1
0
0
0
1
1
0
1
2
1
0
2
1
0
1
1
2
0
2
0
0
1
3
0
0
0
0
0
0
0
0
1
1
1
0
2
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
2
1
0
0
0
1
1
2
0
1
0
0
1
1
0
0
1
0
0
1
0
1
2
1
2
3
1
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
1
1
0
0
0
0
2
2
0
0
0
1
0
0
2
0
1
0
2
0
2
0
0
0
0
1
0
2
1
2
0
0
0
1
1
0
2
0
0
0
0
0
0
1
0
1
0
2
2
0
0
0
0
4
0
3
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
3
1
2
0
1
0
0
1
0
0
2
1
2
0
0
0
2
1
2
0
0
1
0
0
2
1
0
1
0
0
0
1
1
1
0
2
0
2
0
1
1
2
0
1
0
3
0
2
1
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
2
1
2
2
1
0
1
0
2
0
1
1
0
1
1
1
2
0
0
2
0
0
2
3
0
0
0
0
0
2
0
5
0
0
0
2
0
0
1
0
0
0
0
2
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
2
2
2
0
1
0
2
0
0
1
0
0
1
0
0
0
0
0
0
2
1
0
0
2
1
0
0
1
2
3
2
1
0
0
0
0
0
0
2
0
2
1
0
1
2
0
0
0
1
0
2
2
1
0
1
0
0
0
1
0
0
2
0
4
0
1
2
1
2
0
0
0
0
0
1
0
0
2
1
0
0
2
1
0
0
0
2
2
0
0
1
1
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
2
0
0
1
1
0
2
0
2
0
2
2
0
0
0
1
0
0
0
1
1
1
0
2
1
1
0
0
0
3
0
1
0
2
3
1
0
0
1
1
0
2
1
0
0
2
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
6
2
1
0
2
1
0
3
2
0
0
2
3
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
2
0
0
0
2
3
1
0
0
0
2
1
1
0
1
0
0
0
1
1
0
1
0
0
0
0
2
2
1
0
1
0
2
2
0
1
0
0
1
6
0
1
0
0
0
1
1
1
1
0
0
2
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
1
0
3
2
2
3
1
0
0
0
2
0
0
0
3
0
0
2
1
1
0
1
1
1
0
0
0
0
2
1
0
2
1
2
1
0
0
0
0
2
1
2
0
0
2
0
0
0
0
0
1
0
1
0
0
1
0
2
0
2
1
0
0
2
1
0
1
0
0
0
0
0
1
2
1
0
1
1
2
0
0
1
2
0
0
1
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
1
2
0
0
0
2
2
2
0
1
0
0
0
2
0
1
0
0
0
2
3
0
0
0
1
2
0
0
0
0
0
2
2
1
3
0
1
0
3
2
3
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
2
0
2
1
0
1
0
0
0
0
2
0
1
0
2
0
0
2
0
0
1
0
1
0
3
0
1
2
1
0
1
2
1
2
2
0
0
2
0
0
0
2
0
0
1
0
0
0
2
2
0
1
0
0
2
2
0
2
0
0
0
2
0
0
3
3
1
0
2
0
0
0
0
0
1
1
0
1
2
0
0
3
1
1
0
1
1
0
0
0
0
1
0
2
1
0
1
0
1
0
1
1
0
0
1
0
1
3
1
0
1
2
0
0
0
0
0
0
1
0
2
0
0
1
2
0
0
0
1
0
0
1
0
0
0
2
0
2
0
2
1
0
2
0
0
2
0
0
2
0
1
0
0
2
1
0
0
0
2
1
1
2
1
0
1
0
0
0
0
2
0
1
0
0
1
0
2
1
0
3
0
0
2
0
0
1
0
0
0
0
1
1
2
1
0
0
0
1
0
0
2
2
1
2
0
0
2
1
1
1
3
2
1
0
1
1
1
0
1
0
1
1
0
0
0
0
1
0
1
2
0
2
0
0
5
1
1
0
1
0
0
0
1
2
2
1
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
2
2
2
0
1
0
0
3
0
0
0
1
0
0
2
3
2
0
0
0
0
2
0
0
0
1
0
1
2
1
0
0
0
2
1
0
2
1
0
2
0
0
2
2
2
2
0
0
2
2
1
1
1
0
3
2
2
0
1
0
1
0
1
0
0
0
1
0
0
1
1
1
1
2
0
0
2
2
1
2
0
0
2
0
0
3
0
0
1
2
1
4
0
1
1
0
0
2
0
0
1
0
2
0
0
1
0
0
0
1
2
2
2
2
3
3
0
0
0
1
2
2
0
2
0
2
0
0
1
2
0
1
0
0
0
0
0
0
0
1
1
0
0
2
1
0
0
1
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
1
2
0
0
0
0
2
0
2
2
0
1
0
2
1
0
1
0
1
0
0
2
0
0
2
0
0
0
0
1
0
1
1
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
1
1
0
2
1
0
0
0
1
1
1
0
1
1
0
1
0
0
0
0
0
3
0
2
2
0
2
1
0
1
2
1
0
2
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
2
0
2
1
1
0
0
0
1
1
0
2
0
0
3
0
1
1
0
1
1
0
0
0
0
2
0
1
0
2
1
0
0
1
0
1
0
1
0
2
1
0
2
0
0
0
1
2
0
1
1
1
0
2
1
0
0
0
2
1
0
0
0
2
0
0
0
0
0
2
2
2
2
0
0
1
1
0
0
0
0
2
0
2
0
0
1
1
0
1
1
0
0
0
0
1
0
0
1
0
2
1
2
0
0
0
0
0
0
0
1
1
2
2
0
1
1
2
0
0
1
1
0
0
2
1
0
1
2
2
2
2
2
0
0
0
0
2
0
1
0
0
0
1
0
0
1
0
2
0
1
0
1
0
1
0
1
1
0
2
0
2
0
1
1
1
0
0
2
0
0
1
0
0
1
0
0
0
2
0
1
2
1
0
1
2
0
0
0
2
0
0
0
0
1
2
0
2
0
2
3
1
0
0
4
0
1
0
0
1
1
0
2
0
0
2
1
0
1
0
0
0
1
1
2
0
2
1
1
0
2
2
0
0
0
0
1
2
0
0
1
0
2
0
2
2
0
1
1
0
0
0
0
2
0
2
0
0
1
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
2
2
0
0
2
0
0
1
0
0
0
2
1
2
0
1
2
2
0
0
0
2
0
0
0
2
0
1
0
0
0
1
2
0
1
1
0
1
0
0
1
0
0
0
0
0
0
2
1
0
2
1
0
0
0
0
2
0
1
0
0
0
1
0
1
0
1
4
0
0
0
2
2
0
1
0
0
2
1
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
2
0
2
2
1
0
1
0
2
0
0
2
0
0
0
2
0
1
0
1
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
3
0
0
0
0
1
0
1
0
0
0
0
0
1
2
2
0
2
1
2
0
2
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
2
1
0
0
0
0
0
2
1
1
2
0
2
0
0
1
1
1
0
0
0
1
0
0
1
1
3
0
1
0
0
0
2
0
2
0
0
1
0
2
2
0
3
1
0
1
0
1
0
0
0
0
0
0
1
1
2
0
0
0
0
2
0
0
1
1
0
1
2
0
0
0
0
0
2
1
1
4
2
0
2
1
1
0
1
0
0
0
1
2
1
0
0
2
0
0
0
1
0
2
2
0
1
3
1
0
0
0
2
0
1
0
0
2
0
0
2
1
0
1
2
2
2
1
0
0
2
0
0
1
0
1
2
0
1
2
0
0
0
0
0
1
2
0
0
0
4
2
0
0
0
1
0
0
0
0
1
1
1
0
0
0
3
1
0
2
0
2
0
2
2
1
0
1
1
0
1
1
2
0
0
0
2
0
1
1
0
0
2
1
0
0
0
1
1
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
1
0
1
3
0
0
0
0
0
0
2
0
3
0
0
0
0
3
0
0
0
2
4
0
0
0
0
0
2
1
0
0
0
1
0
1
0
2
0
0
2
0
0
1
0
1
0
0
0
1
1
0
2
0
0
0
0
1
0
1
0
2
0
2
0
0
0
2
0
1
0
0
1
2
2
1
0
2
0
1
0
2
0
2
2
0
0
0
0
1
0
4
1
1
2
2
1
0
0
1
1
0
2
0
5
0
0
0
0
0
2
0
0
0
2
1
2
0
2
0
0
0
0
0
2
1
2
0
1
0
0
0
1
1
0
1
1
0
2
3
1
2
1
0
2
2
0
0
0
1
1
2
0
4
1
0
0
1
0
1
0
0
0
1
1
0
1
1
0
0
1
1
1
0
2
1
1
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
1
0
1
2
1
0
0
0
0
1
1
0
0
0
2
0
1
2
0
0
0
0
0
0
2
2
0
2
0
0
2
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
2
2
1
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
2
0
0
0
0
1
3
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
1
0
1
0
0
0
4
1
0
0
0
0
1
2
0
0
3
0
0
2
2
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
1
1
1
1
0
0
0
0
0
0
0
2
3
0
0
0
0
0
1
0
0
0
0
2
2
0
1
1
0
0
1
0
0
1
0
0
2
2
0
1
1
0
0
2
3
1
2
2
2
2
0
0
1
0
0
3
0
0
2
0
0
2
0
0
2
1
0
1
1
0
0
3
2
2
0
2
0
0
0
2
2
3
1
0
0
0
2
0
0
1
0
0
1
2
2
1
2
2
0
0
0
0
0
0
2
1
1
2
0
1
0
1
3
0
0
0
0
0
0
0
0
1
1
2
0
1
2
2
0
1
0
2
0
1
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
1
0
0
2
2
1
0
0
0
1
1
1
0
2
0
2
0
2
2
1
2
0
0
1
0
0
0
0
1
0
2
0
0
0
1
0
0
1
1
0
1
0
0
0
1
2
2
2
0
2
0
0
0
0
0
2
2
1
0
0
0
2
1
0
1
0
1
0
2
1
1
1
1
1
2
1
2
0
0
0
0
0
1
1
0
2
1
0
0
0
1
2
0
0
1
0
0
1
0
0
2
0
0
1
0
0
1
1
1
0
0
0
1
0
0
1
0
0
1
0
0
2
1
0
0
0
0
0
0
0
2
0
1
2
1
0
2
2
1
0
1
1
1
1
0
0
0
1
0
1
0
1
2
0
1
0
0
2
1
0
1
0
0
1
0
0
0
1
1
0
0
0
2
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
1
1
1
0
0
0
2
0
1
2
1
1
0
1
1
1
0
0
0
2
0
0
0
0
0
0
2
0
2
2
1
0
0
0
0
0
0
1
0
0
1
0
7
1
1
0
0
0
0
1
0
1
0
2
1
1
1
0
1
4
0
1
0
3
0
0
2
1
0
2
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
2
0
0
0
2
1
0
0
0
2
1
0
1
4
2
3
1
2
0
0
0
0
1
0
1
1
0
0
0
2
2
1
2
0
2
0
0
2
0
0
1
1
0
2
0
1
1
0
1
2
0
1
0
0
0
1
1
0
0
3
1
3
0
1
0
1
0
2
0
0
0
2
0
0
2
1
0
0
1
0
0
0
2
1
0
0
1
0
3
0
0
2
2
2
0
0
0
1
0
1
0
0
0
2
0
0
1
0
0
0
0
0
3
2
0
0
0
0
0
3
1
1
1
0
2
2
1
0
3
2
2
2
1
0
1
0
1
0
0
1
1
1
0
0
2
0
0
2
1
1
1
0
1
1
3
0
0
0
1
0
0
1
2
0
2
2
2
0
0
0
2
2
1
1
0
1
2
0
0
1
0
0
2
0
2
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
2
2
0
2
0
1
0
0
0
1
0
2
0
1
0
0
0
1
2
0
0
1
0
0
0
1
0
0
2
0
1
2
1
0
0
2
1
1
2
1
0
0
0
0
0
2
1
2
1
2
0
1
1
0
0
2
0
2
3
1
3
1
0
0
1
0
1
2
0
2
0
0
0
3
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
1
0
0
1
0
2
1
1
0
1
1
2
2
1
0
0
1
0
1
2
0
0
0
0
0
1
0
0
0
1
2
0
2
0
0
1
2
1
0
0
0
0
0
0
2
2
2
0
0
1
2
0
0
0
2
1
1
3
0
2
0
0
2
2
0
2
0
2
1
0
2
0
0
0
0
1
2
0
0
2
0
1
2
2
0
2
0
0
0
2
0
1
1
0
1
1
0
1
0
0
2
0
0
0
0
1
0
2
1
1
0
2
1
0
2
1
2
1
2
0
0
0
2
0
1
0
2
1
1
1
1
2
1
0
0
1
1
1
0
0
1
2
1
0
3
0
2
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
2
1
3
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
1
2
2
0
1
0
1
2
1
2
2
0
1
2
0
0
2
0
3
0
0
0
0
0
0
0
0
7
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
2
2
0
1
0
0
2
1
0
1
1
0
1
0
3
2
0
0
1
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
1
1
0
1
0
0
0
0
1
0
1
0
2
2
0
0
0
0
0
0
2
0
0
0
1
1
0
2
4
2
0
1
2
3
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
1
1
0
3
1
0
1
2
1
0
0
0
0
1
0
2
2
2
0
2
2
2
2
2
1
2
0
0
0
1
1
0
1
0
0
0
0
2
1
1
0
0
0
0
0
1
0
0
0
0
0
2
2
1
0
2
0
1
2
0
0
0
0
1
1
2
0
0
2
1
2
0
0
0
1
0
1
1
0
0
1
0
2
0
2
0
1
0
2
2
0
1
0
0
0
0
1
0
0
1
1
1
2
0
1
1
1
0
0
1
0
2
0
2
1
1
0
0
0
0
2
0
0
0
2
1
0
1
0
0
0
0
0
0
0
2
2
0
0
2
0
2
0
2
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
2
2
0
0
0
0
0
0
0
2
1
2
1
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
2
0
0
0
0
0
2
2
2
1
1
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
1
0
0
3
1
0
1
2
0
2
0
1
0
1
0
0
0
0
0
2
0
0
2
2
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
1
0
2
0
2
1
0
2
2
0
1
1
0
1
1
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
1
2
0
0
0
0
1
1
0
2
1
0
0
1
0
0
0
2
0
0
2
1
0
3
1
1
0
0
1
0
0
2
0
0
0
0
1
0
0
2
2
0
0
3
0
1
0
1
0
0
0
2
0
2
2
1
0
0
0
0
0
1
0
1
2
0
0
0
0
1
2
0
1
0
2
1
0
0
0
0
0
1
0
0
1
3
0
2
3
0
1
2
0
1
0
0
2
0
0
0
0
0
1
0
1
2
1
2
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
1
0
1
0
1
2
0
0
1
1
0
1
0
0
0
2
0
0
0
1
1
2
0
0
2
2
0
0
1
1
0
4
0
0
1
0
1
0
1
1
0
0
0
0
0
3
2
2
0
1
1
1
1
2
2
0
1
0
0
0
2
1
0
1
2
1
1
0
2
0
1
0
0
2
1
0
2
0
1
2
3
0
0
2
2
1
0
0
0
1
1
0
0
1
0
0
2
0
0
1
0
0
0
0
0
4
0
0
0
1
0
0
1
0
0
2
2
2
0
2
1
0
0
1
1
0
0
2
1
0
0
1
1
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
3
2
0
2
2
3
3
2
0
0
2
1
0
0
0
0
0
0
0
0
2
1
0
1
1
0
1
2
0
2
0
1
1
0
0
0
1
2
0
0
0
2
0
1
0
0
2
0
0
1
2
2
0
0
1
0
1
0
1
2
0
1
0
0
0
0
0
2
0
1
1
0
0
1
2
1
0
1
0
0
0
0
1
0
0
0
1
0
3
0
1
1
0
0
2
0
2
0
0
0
0
0
2
0
0
0
1
2
0
0
0
1
1
1
0
0
1
0
1
0
0
2
0
0
0
2
0
1
1
1
0
0
1
0
0
0
0
3
2
1
1
0
0
2
0
1
1
0
1
0
2
3
0
0
1
0
2
2
0
2
0
1
0
0
2
1
0
0
1
0
2
0
0
0
0
1
1
2
1
1
2
0
1
0
1
0
0
0
0
1
0
2
0
0
2
0
2
0
1
0
1
0
0
2
0
0
1
0
0
1
0
0
2
2
1
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
1
0
0
2
1
1
0
1
0
2
0
2
0
0
0
1
0
0
2
0
1
1
2
2
0
0
1
0
3
2
2
1
2
0
0
2
0
1
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
2
1
0
0
0
0
0
0
1
0
0
1
0
2
1
2
0
2
0
1
0
1
0
1
0
1
0
0
0
0
0
0
2
1
2
0
0
1
2
1
0
1
0
0
0
0
0
0
1
2
0
0
1
0
0
1
0
2
2
1
1
2
0
0
0
0
0
0
2
2
0
2
0
3
2
0
0
2
0
0
1
0
0
0
2
0
1
0
1
1
1
0
0
0
0
2
2
0
2
1
2
0
1
0
1
2
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
1
2
1
0
1
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
1
1
2
2
0
1
2
0
1
1
1
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
1
0
0
1
0
0
1
2
0
0
0
0
1
0
0
0
1
0
2
2
0
0
0
1
1
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
2
2
2
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
1
0
3
1
0
0
1
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
4
1
2
0
0
0
0
0
1
2
0
1
0
0
0
2
0
0
0
0
0
2
1
0
0
1
1
2
0
0
0
0
0
1
0
0
1
4
2
2
0
0
0
0
0
0
0
0
0
3
0
0
3
0
0
0
0
2
0
1
0
0
1
0
0
1
0
1
0
0
1
1
1
2
0
2
0
1
1
2
1
2
0
0
1
0
0
2
2
0
0
0
0
2
0
1
1
1
0
1
0
2
2
1
0
1
0
0
0
1
0
2
1
0
0
1
0
0
0
0
1
0
0
2
2
0
1
1
2
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
2
0
1
0
0
2
1
0
2
0
1
2
2
2
1
0
1
2
2
0
0
1
0
1
2
0
3
0
0
1
0
0
0
1
0
0
1
2
0
0
2
0
0
2
0
0
2
0
0
0
1
0
0
1
0
2
0
2
0
0
0
1
0
0
0
2
0
0
0
1
0
1
0
0
0
0
1
1
0
1
3
0
0
3
0
0
0
0
1
0
1
0
0
0
0
1
0
4
0
1
0
0
1
0
0
1
1
1
1
0
2
0
0
0
2
0
1
0
0
0
0
1
1
0
0
1
0
0
1
1
0
0
1
0
2
1
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
1
0
1
2
0
0
0
2
0
1
0
0
0
1
0
1
0
0
0
2
0
1
0
2
1
0
2
0
0
0
0
2
2
0
2
2
2
2
2
1
0
0
0
1
0
2
0
0
1
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
2
2
4
0
2
0
2
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
3
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
1
1
1
1
2
0
0
2
0
0
2
0
0
1
0
1
2
1
0
2
0
0
0
1
0
3
1
1
0
0
3
1
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
1
2
1
0
0
0
0
2
3
2
0
2
1
0
0
0
0
0
1
0
0
0
2
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
2
3
1
0
1
1
0
2
1
0
2
0
1
0
1
3
0
0
0
2
4
0
0
0
0
1
2
0
1
1
0
2
0
1
0
0
0
0
2
1
0
1
0
1
0
0
1
2
0
1
0
0
1
1
0
2
0
1
0
0
1
1
0
0
2
2
1
0
0
0
2
2
1
1
2
1
1
0
2
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
1
1
2
0
0
0
1
1
2
0
0
1
0
0
0
0
0
1
1
1
1
0
3
0
2
1
1
2
1
1
1
2
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
2
2
1
1
1
0
0
0
0
0
0
0
3
3
0
0
2
2
2
0
1
1
0
0
0
0
0
1
0
0
0
0
0
2
1
2
0
4
2
0
2
0
0
1
0
0
0
0
0
0
0
2
0
2
1
0
2
0
2
0
2
0
2
0
0
0
2
2
0
0
2
0
2
1
1
0
1
0
0
1
0
2
1
0
2
0
1
0
0
1
0
0
0
0
0
0
0
1
1
3
0
0
2
0
1
1
2
1
0
0
1
0
0
1
0
0
0
1
1
2
0
1
0
0
0
1
1
1
2
2
1
2
2
0
2
1
0
1
3
2
0
2
0
3
2
1
1
1
0
0
1
1
2
0
1
1
0
2
0
0
1
1
2
2
1
0
2
1
2
1
0
0
0
0
0
2
0
0
1
2
0
0
2
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
2
0
2
4
2
0
1
0
0
1
1
0
2
0
0
2
0
0
1
0
2
0
0
1
1
1
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
3
1
1
0
2
0
1
2
0
0
0
0
1
2
0
2
1
3
0
2
0
1
1
1
0
0
0
0
0
0
1
0
0
2
2
0
2
2
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
1
1
2
0
0
0
1
2
0
1
0
2
1
1
0
1
0
0
2
2
0
1
0
2
1
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
3
1
0
1
1
1
0
0
0
0
0
2
0
2
0
1
0
0
1
0
0
0
0
0
1
1
1
1
0
0
0
0
1
3
1
0
2
1
0
2
1
0
0
0
1
3
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
2
1
1
2
3
0
1
0
0
1
1
0
1
1
2
0
0
1
3
1
0
0
0
1
0
0
0
0
3
1
1
1
0
0
0
0
0
0
2
1
0
0
2
3
4
0
1
1
0
0
0
1
0
0
2
2
0
3
0
0
2
0
0
0
1
2
0
0
0
3
0
0
0
0
1
2
0
2
1
2
0
0
0
1
1
0
2
2
1
0
1
0
2
1
1
5
0
2
2
2
0
2
0
0
2
0
0
3
3
1
0
2
1
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
2
0
1
2
2
0
0
0
0
1
0
0
0
2
0
2
0
0
2
2
1
2
0
3
1
1
2
1
0
1
0
0
1
2
2
1
0
1
0
0
0
0
0
2
1
2
1
0
0
0
1
1
0
1
1
1
0
0
0
0
0
0
0
2
0
1
0
0
0
1
2
0
0
2
2
0
1
0
0
0
2
0
2
0
0
0
0
0
1
0
2
1
0
2
0
0
0
1
1
0
2
1
0
6
2
0
0
0
0
0
2
0
1
0
1
2
0
0
1
1
0
1
0
0
0
0
0
0
0
2
0
1
0
0
1
3
0
0
1
1
1
0
0
0
0
1
1
0
0
1
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
3
0
0
0
0
0
0
0
1
0
0
1
3
0
0
1
0
1
0
2
0
0
0
0
2
0
2
1
0
1
2
0
0
1
0
1
0
0
0
1
0
0
0
1
0
2
1
2
2
2
0
2
0
0
0
1
0
1
0
0
0
17
0
2
0
0
0
2
1
0
0
2
0
0
0
0
0
1
2
2
0
0
0
0
2
0
1
2
2
0
0
1
0
0
0
0
0
1
0
0
1
2
0
1
1
1
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
5
0
1
0
1
0
1
2
0
0
0
1
1
1
0
0
1
1
0
2
0
0
1
0
1
0
1
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
2
0
0
0
1
0
0
1
1
0
0
2
0
1
2
0
1
2
1
2
1
0
0
0
0
1
5
0
0
2
1
1
0
0
2
0
1
1
1
0
2
2
0
1
0
0
0
2
0
1
0
0
2
0
0
1
2
0
1
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
1
0
0
0
0
3
2
2
1
0
0
0
0
1
0
0
3
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
2
0
1
1
0
0
1
2
0
0
1
1
0
0
0
1
2
0
1
0
0
1
0
2
1
0
2
0
0
0
1
1
1
0
0
0
2
0
0
0
0
2
0
0
3
0
0
0
0
1
0
2
3
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
1
1
0
0
2
0
0
2
2
5
2
1
0
0
1
2
0
0
0
0
1
2
0
7
0
1
0
1
2
2
0
0
0
1
1
0
0
0
0
0
2
1
2
0
0
1
0
0
1
0
0
1
0
2
1
0
0
0
0
0
0
0
1
4
0
1
0
0
0
2
0
3
0
0
0
0
6
0
2
0
2
0
1
0
0
2
0
1
0
2
0
2
0
0
0
2
0
0
0
0
0
1
4
0
2
2
1
0
1
2
0
1
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
2
1
0
2
0
0
1
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
2
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
1
0
0
2
0
0
0
2
0
1
1
2
0
2
0
0
0
1
0
2
0
0
0
1
2
1
0
0
0
0
1
2
0
0
0
0
0
0
2
2
1
0
0
0
1
0
0
2
2
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
1
2
1
0
0
2
0
0
1
1
0
0
1
2
1
1
1
0
1
0
0
1
0
2
0
0
1
0
1
5
1
0
2
2
1
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
2
1
1
0
0
3
1
0
1
0
1
1
0
0
2
0
3
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
2
0
1
0
0
2
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
1
2
1
0
1
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
1
0
1
2
1
1
1
1
0
2
0
0
1
0
0
1
1
2
0
0
0
1
0
0
0
0
0
0
1
2
2
0
1
2
2
0
1
0
2
0
2
0
0
2
1
0
0
0
2
0
1
0
1
0
2
0
1
0
0
2
1
0
0
1
0
0
0
1
1
0
0
0
1
0
0
2
2
1
3
0
1
0
1
2
1
1
0
0
2
2
0
2
0
2
2
0
0
1
2
0
2
0
1
2
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
4
2
0
2
0
0
1
0
0
3
0
1
0
1
0
2
1
2
1
0
0
0
1
1
2
0
1
0
2
1
0
0
1
0
0
0
0
0
2
1
0
2
2
3
2
0
0
1
2
0
0
0
0
0
1
2
1
2
2
0
1
2
0
0
0
0
0
0
1
2
2
0
1
1
1
0
1
0
1
2
0
0
0
0
2
1
2
0
0
0
0
2
2
0
0
0
2
0
0
0
0
1
0
0
1
0
0
2
0
1
2
1
0
0
2
1
0
1
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
1
2
0
0
1
0
0
0
0
1
0
0
2
0
0
0
2
0
2
1
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
1
0
0
0
1
0
0
2
0
0
2
3
1
0
0
2
0
0
2
0
3
0
1
1
0
1
1
1
1
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
2
2
2
0
0
1
0
0
0
2
1
2
0
0
2
1
0
2
3
1
2
0
1
0
0
1
2
0
0
4
0
0
0
0
2
0
1
2
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
1
0
2
2
0
1
1
0
1
1
1
1
0
0
0
0
0
0
1
0
2
0
0
1
1
1
0
2
0
0
1
1
2
1
0
2
0
0
0
0
0
0
1
1
1
0
0
2
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
2
1
0
0
0
0
2
0
1
0
0
0
2
0
0
2
1
3
0
0
2
3
0
0
1
0
0
0
0
2
3
0
0
0
0
0
0
1
0
1
1
0
2
0
0
0
1
0
2
1
1
0
0
0
1
0
2
1
0
2
0
1
2
0
0
4
0
0
1
1
0
0
0
0
2
0
1
0
0
1
2
1
1
1
1
2
2
0
2
1
0
0
0
1
1
0
0
2
0
0
1
2
0
1
2
0
0
0
1
0
2
1
0
2
0
1
1
2
1
0
2
0
2
0
0
0
0
1
2
2
0
2
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
3
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
2
1
2
0
2
2
2
2
0
0
0
1
2
1
1
2
0
1
0
0
1
0
1
1
0
2
0
0
0
0
1
0
0
0
1
0
0
1
2
0
0
0
2
1
0
0
0
3
0
0
1
2
0
1
1
0
1
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
1
2
0
2
0
1
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
3
3
0
2
0
0
0
1
0
0
0
0
2
1
2
2
0
0
0
0
0
1
2
0
0
0
0
1
1
0
0
1
0
0
2
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
2
2
0
0
0
0
0
1
1
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
2
1
1
0
0
0
0
0
0
0
1
1
2
0
0
1
0
0
0
2
0
2
2
1
2
0
1
0
0
0
1
1
1
1
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
1
1
0
0
1
1
0
1
0
1
2
1
2
0
0
0
0
1
0
2
2
0
0
0
2
1
0
0
0
2
0
0
0
2
0
2
2
0
1
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
2
0
0
0
1
0
0
0
0
2
0
2
0
0
2
1
1
0
0
0
0
0
0
2
0
2
1
2
0
0
0
1
1
1
0
2
0
2
1
0
2
0
2
1
0
2
0
0
0
0
0
1
0
0
0
0
0
2
2
1
2
0
2
0
0
1
0
0
2
1
0
0
0
0
0
4
0
0
0
0
0
0
0
1
2
0
0
1
2
2
0
0
1
1
2
2
2
1
0
0
0
0
1
0
0
1
0
2
0
0
2
0
0
0
0
2
0
2
2
0
0
0
0
0
1
1
0
0
0
2
1
0
1
0
1
0
2
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
2
0
0
1
1
0
0
2
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
1
1
0
1
0
0
1
0
0
0
0
0
2
0
1
1
0
0
0
0
0
1
0
2
2
0
3
0
0
2
0
2
1
1
0
1
0
3
0
0
0
0
0
0
2
0
1
0
0
1
0
1
0
1
0
2
0
2
1
1
0
1
0
0
0
2
0
0
3
0
0
0
2
4
0
2
1
0
0
2
2
0
0
2
1
0
11
2
1
2
0
0
0
0
1
0
0
1
4
2
2
1
0
1
0
1
0
1
1
0
2
0
0
0
0
0
1
0
0
0
0
1
0
2
2
1
0
1
2
0
0
1
0
1
1
0
0
1
1
1
0
0
1
2
0
0
2
0
2
1
0
0
1
0
3
1
0
2
1
1
1
0
1
0
1
2
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
1
1
0
1
1
0
1
0
0
0
0
0
1
2
0
0
0
0
0
2
0
1
0
1
1
0
0
0
1
1
1
0
0
0
0
1
2
0
1
0
0
0
2
0
7
0
0
0
1
0
0
0
2
0
1
0
1
0
0
0
0
2
1
0
0
0
0
0
2
1
1
0
0
0
2
2
0
2
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
1
0
0
1
0
0
0
1
0
0
0
2
0
2
0
1
1
2
0
1
1
1
0
2
2
0
0
1
0
1
0
2
1
2
0
1
2
1
2
0
0
0
0
0
0
2
0
0
12
0
0
0
2
2
0
2
1
2
2
0
0
2
0
0
0
0
0
1
0
0
1
1
2
1
0
0
0
0
0
3
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
2
0
0
0
0
1
4
0
0
0
2
2
1
2
2
0
0
1
1
0
2
0
0
0
0
0
0
0
0
2
0
1
0
2
0
1
0
0
0
0
0
0
1
0
1
2
0
0
0
1
0
2
0
0
0
1
0
1
0
1
1
0
1
0
2
0
3
0
1
0
0
2
1
1
2
0
1
1
0
0
0
1
0
2
0
2
0
1
0
2
0
1
0
0
0
0
2
0
2
0
0
2
3
2
0
0
2
0
0
0
2
0
1
0
1
0
0
2
0
2
0
0
0
0
2
0
1
0
2
0
0
0
0
0
2
1
0
1
0
0
0
0
2
3
1
1
1
2
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
1
2
1
0
0
2
2
1
1
0
0
1
0
2
0
0
1
0
1
0
0
0
3
0
0
2
0
2
0
0
0
0
3
1
1
0
0
0
0
0
2
1
0
0
1
2
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
1
1
0
1
0
1
1
1
0
0
1
3
0
2
2
0
2
2
2
0
0
0
0
1
0
0
1
0
1
0
0
0
2
1
2
1
0
0
2
1
2
1
3
0
2
0
0
0
0
0
2
2
0
1
0
2
3
2
0
0
1
0
2
1
1
1
0
1
0
0
0
0
0
0
2
1
1
0
2
2
3
2
2
2
0
1
0
0
0
0
1
1
0
0
0
0
0
0
2
1
0
0
0
0
0
2
1
2
0
0
0
0
2
1
2
0
0
2
3
2
0
0
2
1
2
0
2
2
1
0
0
0
4
1
2
1
2
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
1
0
2
0
0
0
1
1
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
1
3
2
0
0
0
0
0
0
0
3
0
1
1
0
0
1
2
0
1
0
0
0
0
1
1
0
2
1
0
2
0
0
0
2
2
0
0
2
0
0
1
0
0
1
0
2
0
2
2
0
0
2
0
0
1
2
0
1
2
0
0
2
0
0
1
1
0
0
0
1
0
0
0
0
1
2
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
1
0
0
0
2
2
0
0
2
0
0
2
0
2
1
2
2
0
1
0
0
2
1
0
0
2
1
0
0
1
1
1
2
0
2
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
1
0
2
2
1
0
0
1
0
0
0
0
0
5
0
2
1
1
1
2
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
3
1
0
0
0
0
0
2
0
0
2
2
0
1
0
0
0
0
1
2
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
2
1
0
1
2
0
2
2
0
0
1
0
1
0
0
1
1
0
1
0
0
2
2
1
0
0
0
0
1
0
0
1
0
1
1
1
0
0
2
0
2
2
0
0
0
0
1
1
0
2
2
0
0
0
0
0
0
0
3
1
0
1
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
3
0
0
0
2
2
1
1
2
0
0
0
0
0
0
2
1
0
2
0
0
0
0
1
1
1
0
0
0
0
1
1
1
2
0
1
0
0
2
0
2
0
0
0
2
2
0
2
2
0
1
2
2
0
1
2
0
0
2
1
0
0
0
0
1
0
1
2
0
1
0
1
1
0
0
1
0
2
0
2
0
1
0
0
0
1
0
0
0
1
0
0
1
2
0
1
0
0
0
1
1
2
0
0
2
0
0
0
0
0
2
0
2
0
0
0
1
0
1
0
0
0
2
0
1
1
0
0
0
2
0
0
0
1
0
1
1
0
0
1
0
2
0
1
2
0
0
0
0
0
1
1
1
0
0
1
1
1
0
0
1
0
0
1
1
1
0
0
0
0
0
1
2
2
1
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
1
1
2
0
0
0
1
0
2
2
1
2
0
2
1
0
0
2
0
1
0
1
0
0
0
2
2
1
1
0
1
0
0
0
2
0
2
1
0
0
1
1
2
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
3
1
1
0
2
0
0
0
0
0
2
0
2
0
0
2
1
0
0
1
0
0
1
1
2
1
0
2
2
0
0
2
0
0
0
2
0
0
1
0
0
0
0
1
0
2
0
0
2
2
0
1
1
0
2
1
0
0
0
0
0
1
1
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
1
0
1
1
0
3
0
0
0
0
2
0
2
2
2
0
0
0
0
1
0
1
2
0
0
0
0
2
0
0
1
1
0
1
2
1
1
0
1
1
1
1
3
0
0
0
0
1
0
2
1
0
0
0
1
0
0
0
0
1
2
1
0
0
1
0
0
0
1
0
0
0
3
0
0
0
2
1
0
2
0
2
1
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
3
0
0
2
1
0
0
0
2
0
0
2
1
1
0
0
0
0
0
0
0
0
2
2
1
0
1
2
1
2
3
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
3
2
0
2
1
0
0
0
2
0
2
1
1
0
1
2
0
1
2
0
0
1
0
0
0
2
0
0
0
2
0
2
1
1
1
0
0
3
1
0
0
0
0
1
0
2
1
0
1
0
0
0
0
0
2
1
0
2
0
0
2
0
0
1
2
0
0
1
1
0
2
0
2
0
1
0
2
2
0
0
0
2
0
0
1
0
2
0
2
1
0
2
0
2
0
0
0
0
0
2
2
2
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
2
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
2
1
3
0
0
1
1
1
1
1
1
2
1
1
1
1
2
0
0
0
0
0
1
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
2
2
1
1
1
0
0
0
0
0
2
3
0
0
0
3
0
0
2
0
0
0
1
0
2
1
0
0
0
3
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
2
0
0
0
1
3
1
0
0
0
0
2
0
1
0
0
0
1
0
0
0
1
2
3
3
2
2
1
0
1
0
0
0
1
1
0
0
1
1
0
0
0
1
2
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
1
1
0
0
0
2
1
0
0
0
0
1
1
0
1
2
0
1
0
1
2
3
0
0
0
0
1
0
2
2
0
1
1
0
0
2
1
0
2
1
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
2
0
0
0
0
1
0
2
0
1
1
0
1
2
0
2
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
1
2
0
1
0
2
0
0
1
0
0
0
0
0
1
0
0
2
0
0
1
1
1
0
1
2
1
0
4
1
0
0
1
2
2
0
0
0
1
0
0
0
0
1
0
0
1
2
0
0
2
0
0
0
0
2
2
0
0
0
2
0
2
2
1
4
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
1
0
0
1
0
1
1
0
0
1
2
0
2
0
0
1
0
0
0
0
1
2
1
0
0
0
2
2
0
0
2
2
1
2
0
0
2
1
0
0
0
0
0
1
2
2
1
0
1
2
0
1
1
0
2
3
0
1
0
0
1
0
1
0
0
0
1
2
0
1
0
0
0
0
2
0
0
0
0
1
0
1
1
2
0
0
2
0
2
0
1
1
2
1
1
0
2
1
1
0
0
0
0
1
0
2
0
0
1
0
0
1
2
2
0
2
1
2
2
0
1
1
2
0
2
0
2
0
0
3
1
0
0
0
1
2
0
1
2
0
0
0
0
1
0
2
0
1
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
1
2
2
0
0
0
1
1
2
1
0
0
1
0
1
0
2
0
1
0
2
3
0
1
0
0
0
0
1
0
1
1
0
0
1
1
0
0
0
0
1
2
0
0
2
0
0
0
0
2
0
0
1
2
0
0
0
1
1
2
2
0
0
1
1
0
0
0
1
0
0
2
1
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
2
0
2
1
1
1
0
1
0
2
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
2
0
1
0
2
3
0
0
1
0
0
0
0
0
2
1
0
0
1
0
0
2
2
1
0
2
0
1
0
2
0
0
0
0
0
0
0
1
1
2
0
6
0
0
0
0
0
2
0
0
2
0
1
0
0
2
1
1
0
0
2
1
0
1
1
0
1
0
2
0
2
0
0
0
0
0
2
0
0
0
0
3
2
0
0
0
0
0
0
1
0
0
0
0
0
3
0
1
0
2
2
0
3
0
2
0
0
0
1
0
0
0
2
0
0
2
0
0
1
1
0
0
0
0
0
2
0
0
0
0
1
1
0
2
0
0
0
0
1
2
1
0
2
2
0
0
0
0
0
2
0
0
1
0
2
2
1
1
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
1
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
1
1
2
0
0
0
0
1
1
0
2
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
2
1
1
0
2
1
1
1
0
0
0
1
1
0
0
0
2
0
1
0
0
0
2
0
2
0
0
1
0
4
2
1
0
0
0
0
0
0
0
2
0
0
1
0
1
0
2
2
0
2
0
1
0
1
1
0
0
0
1
3
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
3
0
2
1
0
1
1
0
1
2
0
2
0
0
0
1
1
0
0
1
1
1
0
0
0
0
2
1
1
1
0
1
1
1
2
2
0
1
0
0
2
2
3
1
3
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
2
0
0
0
0
0
1
0
0
0
0
1
1
0
1
1
0
0
0
2
0
2
0
2
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
1
2
0
0
0
0
0
4
0
1
0
0
0
1
2
0
0
1
0
0
0
0
2
1
1
0
0
1
2
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
4
2
0
1
0
0
0
0
0
0
0
1
1
0
2
1
0
0
0
2
0
0
1
0
0
1
0
0
1
2
0
0
1
0
1
0
0
0
0
1
1
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
2
1
0
2
0
0
2
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
1
0
4
0
0
0
0
1
0
1
0
0
1
2
2
2
2
0
0
0
0
2
0
1
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
1
2
0
0
2
0
0
0
0
2
0
0
0
1
0
1
1
0
2
0
0
0
0
0
0
1
0
0
0
0
2
3
1
0
2
1
0
1
1
0
1
0
0
1
0
0
0
2
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
9
0
0
0
1
1
0
1
2
0
1
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
1
2
1
1
0
0
2
0
0
0
0
2
1
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
2
0
1
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
1
1
1
2
1
1
2
1
0
0
0
0
2
0
0
1
0
0
2
0
0
1
0
0
0
1
2
2
0
2
0
0
0
2
0
0
0
0
0
1
1
1
1
0
0
0
0
2
0
1
0
0
2
0
2
0
0
0
0
1
2
0
0
1
0
1
0
1
0
0
0
1
0
0
2
1
0
2
1
0
2
1
1
2
1
0
0
0
2
2
6
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
2
0
0
2
1
0
1
0
0
0
1
0
2
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
2
0
0
2
1
2
0
0
0
2
0
0
1
0
0
0
1
0
0
0
2
2
0
1
0
2
2
0
0
0
0
2
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
2
1
0
2
0
2
0
0
0
0
2
2
2
0
0
0
0
1
2
0
2
0
1
2
1
1
2
0
1
2
0
0
2
0
0
2
0
1
1
2
0
1
3
2
0
0
0
0
0
0
3
0
1
0
0
1
0
0
0
2
1
1
2
1
1
0
2
0
0
1
0
2
0
4
2
0
2
0
1
1
1
0
0
0
1
0
1
2
2
0
0
0
0
1
2
2
0
2
2
0
0
2
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
1
1
0
1
0
1
0
2
0
0
0
0
0
0
1
1
0
1
2
2
2
0
1
0
0
0
0
3
0
0
2
0
1
0
1
0
0
2
2
3
1
1
1
1
0
2
0
0
0
1
0
0
2
1
0
1
0
1
0
3
0
2
1
2
0
1
2
2
0
0
0
1
2
0
1
2
0
0
0
0
0
2
0
0
2
0
2
0
0
0
2
0
0
0
0
2
0
3
0
1
1
0
2
0
0
0
0
0
1
0
1
0
2
1
1
1
0
0
1
2
1
2
2
2
1
1
1
2
0
2
2
1
1
0
0
0
1
0
1
1
0
0
1
0
0
0
2
0
2
0
0
1
0
1
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
1
2
2
0
1
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
2
1
0
2
0
0
0
1
1
2
2
1
0
0
5
2
1
0
2
0
1
2
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
1
2
0
0
0
2
0
0
1
2
0
0
1
0
1
1
1
3
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
2
0
2
0
0
3
0
0
0
0
0
1
0
2
0
0
0
0
0
2
1
0
1
1
1
0
0
0
2
0
1
2
1
0
0
1
1
0
0
0
2
0
1
0
0
1
0
0
0
2
0
0
0
0
1
0
0
2
0
1
0
2
0
0
2
2
0
1
1
1
1
1
0
0
1
0
0
2
0
0
0
1
0
0
0
1
1
2
0
0
0
0
1
0
0
0
1
2
0
0
1
0
1
0
0
1
2
1
2
0
0
1
0
0
2
0
1
0
1
2
0
0
0
1
0
1
2
2
0
0
1
0
1
0
2
1
0
0
0
1
0
0
0
1
1
0
2
2
2
0
1
0
1
4
0
0
0
0
0
0
0
1
2
2
2
1
3
2
0
2
0
0
3
2
0
0
0
0
0
0
1
0
1
0
0
0
2
1
2
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
1
1
0
0
1
1
0
1
0
1
1
0
0
2
1
0
1
1
0
2
1
2
0
0
0
0
0
0
0
2
1
2
2
2
0
0
2
0
0
0
0
0
0
1
0
1
0
0
2
0
3
2
1
2
2
1
0
1
0
1
2
0
0
0
0
2
1
1
1
2
0
0
1
1
0
0
0
0
1
2
0
0
0
0
0
0
1
3
0
0
2
0
1
1
4
1
1
2
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
2
2
0
1
0
1
1
1
0
0
0
2
1
0
0
1
0
0
2
0
2
2
1
0
0
1
0
2
2
0
0
2
1
2
1
1
2
0
1
1
0
1
2
0
0
1
1
0
2
1
0
1
0
2
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
2
0
0
0
1
2
1
2
0
2
0
0
0
2
1
0
0
0
0
0
1
2
0
0
0
0
1
1
0
2
0
0
0
1
0
1
0
0
2
0
2
0
1
0
0
0
2
0
0
0
0
0
0
2
1
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
1
1
1
3
0
2
0
0
1
2
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
1
2
0
1
0
0
2
0
0
2
0
0
1
1
0
1
1
1
0
0
0
0
0
0
0
0
2
1
0
1
2
1
2
2
0
0
1
1
0
0
0
0
0
2
0
0
0
0
2
2
0
1
0
0
0
1
0
0
0
0
2
1
0
1
2
2
0
0
1
0
0
2
0
2
0
0
0
2
0
5
0
0
1
1
1
0
1
0
0
0
1
0
0
1
0
2
3
0
0
0
0
0
1
2
1
2
0
0
1
0
2
2
0
0
0
1
2
2
0
0
0
0
2
0
1
0
3
0
2
0
3
0
0
1
0
0
0
0
0
0
2
2
0
1
0
0
0
0
3
0
1
1
0
0
1
0
1
0
1
2
0
1
0
1
0
0
2
0
0
2
1
0
2
0
0
2
1
0
1
2
0
0
0
2
2
0
2
1
0
0
0
2
0
1
0
0
0
1
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
1
0
1
2
0
0
0
0
2
2
0
0
1
2
1
4
0
1
1
0
2
0
2
0
2
0
1
0
2
0
0
0
0
0
0
0
1
0
0
4
0
2
0
1
2
0
1
0
0
1
0
3
2
0
0
1
2
0
0
0
1
0
2
0
0
0
2
1
0
0
0
1
0
2
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
1
1
0
2
0
0
0
2
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
1
2
0
1
1
3
2
0
0
2
2
0
1
0
0
0
1
0
2
2
1
0
0
0
2
0
2
0
0
0
1
0
3
1
2
2
2
0
0
2
0
0
0
0
0
1
0
2
0
2
2
0
1
1
0
1
0
2
0
2
0
2
0
0
1
0
2
0
0
4
1
0
1
2
0
0
1
0
0
0
1
2
0
0
1
0
0
2
0
0
0
1
2
2
2
2
0
1
1
1
1
0
0
0
1
0
0
1
1
0
2
1
1
2
0
0
0
0
0
0
1
1
0
0
1
1
0
3
2
0
2
0
0
0
1
0
3
0
1
0
2
0
1
2
1
0
0
1
1
0
1
1
1
2
0
0
1
0
1
0
0
0
0
0
1
1
2
1
0
4
0
0
1
0
0
0
0
0
1
0
0
1
0
2
0
1
0
0
3
0
2
0
0
0
0
2
2
0
0
2
1
1
2
0
0
1
0
0
0
0
0
0
0
0
1
1
1
1
0
1
2
0
2
0
1
0
0
3
0
0
0
2
1
0
1
1
1
2
1
1
2
0
2
0
0
0
1
2
2
0
0
1
2
1
0
0
0
0
1
0
2
0
3
1
0
0
1
0
0
0
2
1
0
1
0
0
0
1
1
2
1
2
6
1
2
0
0
1
0
1
2
0
0
0
0
0
1
1
2
2
0
1
0
1
0
1
3
0
1
1
0
0
2
0
0
0
2
0
1
2
0
2
1
0
2
0
0
2
0
2
0
1
0
0
0
1
1
0
0
2
2
1
0
1
0
2
8
0
0
0
0
2
0
2
2
3
0
0
2
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
1
1
0
2
0
1
2
2
0
0
0
0
0
0
0
0
2
0
1
1
3
1
2
1
0
0
1
1
0
0
2
0
0
2
2
0
0
2
1
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
2
0
0
2
1
1
0
0
1
0
2
1
0
0
0
0
0
2
0
1
0
2
2
1
0
0
0
1
1
2
0
0
0
1
0
2
0
2
2
1
0
0
3
0
1
2
0
1
1
2
1
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
2
1
1
0
0
2
0
3
1
2
1
2
2
0
1
0
2
0
0
0
0
1
2
2
0
0
0
1
0
0
0
0
2
0
2
1
1
0
2
1
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
2
1
2
0
1
0
0
0
2
1
0
0
0
2
3
0
1
0
2
0
0
0
0
2
0
0
1
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
1
0
2
2
0
0
2
0
0
0
0
2
2
2
0
0
0
1
2
2
0
0
0
0
2
1
0
2
3
0
0
1
0
2
0
0
1
0
0
0
0
1
0
0
3
0
1
0
1
0
2
0
2
2
3
1
0
0
2
0
0
2
3
0
0
2
0
1
0
1
2
0
0
2
0
1
1
1
0
2
0
1
0
1
5
0
2
1
0
1
0
2
1
0
0
1
1
0
0
1
2
0
0
3
3
0
1
0
0
2
0
1
1
0
1
2
1
0
0
0
1
0
0
2
2
2
0
0
1
0
2
0
0
0
0
1
2
1
0
0
1
1
1
0
0
6
1
0
2
0
0
1
0
0
1
1
0
0
1
2
0
0
2
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
2
0
1
0
0
2
2
2
0
0
2
0
0
2
1
0
1
1
1
0
2
0
2
2
0
0
0
0
0
0
0
0
2
0
1
0
3
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
2
0
0
1
1
0
0
1
1
2
1
1
2
1
1
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
2
2
2
0
1
0
0
0
0
0
1
0
2
2
0
0
2
2
0
2
1
0
0
1
2
0
0
0
1
1
2
0
2
0
0
2
0
0
0
0
0
2
0
1
0
0
1
0
0
2
1
0
0
2
0
0
2
0
0
2
0
2
2
3
3
1
0
0
2
1
2
1
0
1
1
1
0
0
0
0
0
0
2
1
1
2
0
2
0
1
0
0
1
2
0
2
0
1
0
1
0
0
2
0
2
0
0
0
1
1
0
0
0
1
0
1
2
0
0
0
0
0
0
1
1
1
2
1
0
0
1
0
2
1
2
0
2
0
0
1
0
0
2
0
1
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
1
1
1
2
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
2
2
1
1
0
0
0
0
1
0
0
2
0
0
0
0
2
1
0
0
0
0
2
0
2
0
0
0
2
2
1
0
1
0
1
1
0
2
1
2
0
1
1
2
1
0
0
0
1
1
0
0
1
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
4
1
0
1
1
0
2
1
1
0
2
0
0
4
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
1
0
2
1
2
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
2
1
0
2
0
2
0
1
0
0
0
1
1
0
0
0
0
1
0
0
2
1
1
0
0
1
0
2
0
1
0
2
1
0
0
2
1
0
0
3
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
3
0
0
0
1
2
3
1
0
1
0
0
0
1
0
0
1
1
1
2
1
2
0
3
0
2
0
2
0
0
0
1
0
1
0
0
0
3
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
1
1
1
1
2
0
1
1
0
2
1
1
2
2
0
0
4
1
1
1
0
1
0
3
0
0
0
1
0
0
2
2
0
2
2
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
2
0
0
0
2
2
2
1
0
0
1
0
0
1
0
0
0
3
0
0
0
0
0
1
0
1
0
0
3
3
2
0
2
2
2
2
0
2
2
0
0
0
1
0
2
0
1
1
0
0
0
0
0
2
0
4
2
1
2
2
0
2
0
0
0
3
1
0
0
1
1
0
1
1
0
1
2
0
1
1
0
0
0
0
1
0
0
1
0
1
0
0
0
2
1
1
2
2
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
1
1
2
0
2
0
0
1
2
2
0
0
0
1
2
2
0
1
1
2
0
0
0
1
1
1
0
2
0
0
0
0
0
1
0
1
1
2
0
0
0
0
2
0
0
0
1
2
0
0
0
1
0
0
0
1
0
2
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
3
0
1
2
2
0
0
0
0
1
1
0
0
0
3
0
0
0
2
0
1
0
0
1
2
0
0
0
0
1
2
1
3
0
1
0
1
0
0
2
1
0
2
1
0
0
0
1
2
1
0
1
0
1
1
0
0
0
0
0
2
0
0
2
1
3
0
0
0
0
0
1
0
0
2
0
2
2
0
1
0
0
0
1
0
1
0
1
2
0
1
2
0
2
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
1
0
2
0
0
0
1
0
1
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
2
0
0
2
2
0
0
2
0
0
0
2
0
0
0
0
1
2
1
3
0
0
2
2
2
0
0
0
0
1
1
0
0
0
2
0
1
0
0
0
2
2
0
1
0
0
3
4
2
1
1
0
2
1
0
0
2
0
2
0
0
2
1
0
6
0
0
0
0
0
0
2
0
2
3
1
0
0
3
2
0
0
1
0
1
0
0
1
1
0
2
2
1
0
0
0
0
1
1
0
0
1
0
2
2
0
1
0
1
1
0
0
0
0
0
1
0
0
0
1
1
1
1
0
1
3
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
2
0
0
2
2
1
2
0
1
1
0
1
0
0
0
0
0
1
1
0
0
2
1
0
0
0
5
1
0
2
0
1
0
2
2
3
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
2
0
0
0
0
0
2
2
0
0
0
0
0
1
2
1
0
1
0
2
2
1
1
2
2
2
1
0
0
1
0
1
0
1
0
0
0
0
0
1
0
1
0
2
1
1
0
0
1
2
0
0
1
2
0
0
1
1
2
2
2
1
0
0
0
0
3
0
0
2
0
0
0
0
1
0
4
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
3
0
0
0
0
0
1
1
1
0
0
0
1
0
0
1
0
2
0
3
1
2
0
0
0
1
1
1
0
0
0
0
0
1
1
2
0
3
2
1
1
0
0
0
4
0
1
0
1
0
1
0
0
0
1
2
0
0
0
0
0
1
0
0
2
0
2
0
0
0
1
3
1
0
0
1
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
2
1
0
1
0
0
0
2
0
1
0
0
2
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
3
0
0
1
0
1
0
1
0
0
0
2
1
0
1
2
1
0
1
1
2
0
0
0
0
0
0
1
0
1
0
2
0
1
0
0
0
0
3
0
1
0
0
0
0
0
1
2
0
1
0
1
0
2
1
0
0
1
0
0
0
0
0
0
0
0
1
0
2
1
0
0
1
1
0
0
1
0
0
0
5
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
2
0
1
1
2
2
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
2
1
1
3
0
2
0
2
2
2
0
2
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
3
1
1
0
1
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
7
0
2
1
1
1
0
0
1
2
0
0
2
1
2
0
0
2
2
0
2
0
0
0
2
3
2
0
0
2
1
1
2
1
0
3
1
0
0
1
1
2
1
0
0
0
0
1
0
1
3
0
2
2
0
1
0
2
0
1
0
0
2
2
0
0
0
0
2
0
0
0
0
2
1
0
1
1
1
1
0
2
0
1
0
1
0
1
0
2
1
0
2
0
2
1
0
0
2
0
2
0
1
0
2
0
1
0
0
2
0
0
1
1
0
1
0
1
2
0
1
0
2
0
2
2
1
0
0
2
1
0
0
2
0
0
1
1
2
2
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
2
2
2
0
0
0
0
0
0
2
0
2
1
1
1
0
2
0
0
0
0
0
0
0
2
1
2
1
2
1
2
0
0
0
2
0
2
0
2
0
0
0
2
0
1
2
0
0
0
1
0
0
1
0
3
0
0
1
0
1
1
0
1
1
0
0
1
1
0
0
2
0
0
0
0
2
0
1
0
2
2
0
0
1
0
0
1
1
0
2
2
0
2
0
2
0
2
0
2
0
0
0
2
0
1
1
2
0
0
0
0
0
4
0
1
0
3
2
0
0
0
1
1
0
3
0
1
1
0
0
0
2
1
0
0
1
0
0
2
0
1
1
0
0
1
0
0
0
0
0
4
3
1
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
2
2
2
0
1
0
0
0
0
0
1
2
1
0
2
1
0
0
2
0
2
1
2
1
0
0
1
2
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
2
2
0
0
0
0
1
0
1
1
0
0
0
0
1
0
2
2
1
1
0
2
2
0
0
0
0
1
0
3
0
0
1
1
2
1
0
0
0
2
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
2
0
0
1
1
1
2
0
0
0
2
0
0
2
1
0
0
1
1
0
0
0
1
0
0
0
1
0
1
1
0
2
1
0
0
1
0
0
0
0
0
0
0
0
2
3
1
0
0
1
1
3
0
3
1
0
0
0
3
0
0
2
2
1
0
0
0
2
1
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
2
0
0
0
2
1
2
2
0
0
0
1
0
1
0
2
0
0
2
0
0
2
2
0
3
0
0
0
0
1
0
0
0
0
2
0
0
1
2
0
0
0
0
0
2
1
2
0
0
0
2
1
1
0
0
0
1
1
0
2
2
1
0
1
1
0
0
1
0
0
0
3
0
2
0
2
2
2
0
0
0
0
2
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
1
0
1
0
2
0
0
0
1
0
1
2
0
0
1
2
0
0
0
0
0
2
1
2
1
0
0
3
0
0
2
2
0
2
1
0
0
0
0
1
0
0
0
1
1
0
3
0
1
1
0
0
0
4
1
0
1
0
2
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
4
0
1
2
1
0
0
2
3
0
2
0
0
0
0
0
0
0
1
1
0
1
1
0
0
1
1
0
0
0
1
0
2
2
0
0
1
1
0
1
0
0
1
0
0
0
0
1
1
1
1
0
1
1
1
0
0
0
0
0
1
0
3
0
0
0
0
0
0
2
1
1
0
0
0
2
0
1
0
1
1
1
2
0
1
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
1
4
2
0
0
0
1
2
0
0
1
0
1
2
0
0
1
0
2
0
0
1
1
1
0
1
0
0
1
0
0
0
1
2
2
2
2
0
1
0
0
1
0
0
0
2
0
0
2
2
0
0
0
0
1
0
1
4
4
0
1
0
19
1
3
0
0
0
0
0
0
1
0
2
0
2
2
0
0
1
1
3
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
3
0
1
0
0
0
2
0
1
2
0
1
0
0
0
2
1
1
0
1
1
2
0
1
0
0
1
2
1
0
0
4
1
0
2
2
2
0
2
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
1
1
3
1
0
0
0
0
1
2
2
1
0
1
0
1
0
1
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
3
1
1
1
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
2
0
0
2
1
0
0
1
1
0
0
0
0
0
0
2
0
1
2
2
0
2
2
1
0
0
2
4
2
1
0
1
0
0
1
0
2
1
0
2
2
2
2
3
0
2
0
1
1
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
1
0
0
0
1
2
1
0
0
0
0
2
2
0
0
0
1
0
0
1
0
2
0
0
0
2
1
1
1
2
0
1
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
2
0
0
1
1
2
1
1
1
0
1
0
1
0
1
0
1
0
0
3
1
2
0
0
0
1
0
0
1
1
0
0
0
0
2
2
0
2
0
2
0
0
1
0
0
2
0
1
0
2
0
0
1
0
0
2
0
0
1
1
1
0
0
0
0
2
0
2
0
0
2
0
2
1
1
2
0
2
0
0
0
0
1
2
0
2
2
0
0
0
3
1
0
1
0
1
0
2
0
0
0
1
1
1
2
0
4
2
1
0
0
2
2
1
0
2
1
2
0
2
0
0
1
0
1
0
0
0
0
0
1
2
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
2
0
2
2
0
0
0
0
0
3
2
0
0
0
0
1
1
2
0
0
1
1
0
1
0
0
0
1
3
1
1
2
0
0
1
0
2
0
2
2
0
1
1
0
1
0
1
2
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
2
0
2
1
2
0
7
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
2
0
0
0
0
0
2
0
0
1
1
0
1
0
0
2
3
0
2
0
1
1
0
1
2
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
1
0
0
2
2
0
2
2
1
0
2
0
2
2
0
0
0
0
0
0
0
2
0
1
0
1
1
1
1
3
2
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
1
2
0
0
2
3
0
2
0
0
1
2
2
0
1
2
1
1
1
0
0
2
3
0
1
0
1
0
0
0
0
1
0
0
9
0
2
0
0
0
0
0
1
0
0
0
0
2
2
0
1
0
0
0
2
0
1
0
1
0
0
0
0
2
2
0
0
0
2
0
0
2
1
0
1
0
1
0
1
0
0
0
0
2
0
1
5
0
2
2
0
0
0
3
1
0
0
3
1
1
1
1
1
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
2
0
2
0
1
3
0
1
0
0
0
1
0
0
2
2
1
1
1
2
1
0
0
0
2
0
0
0
1
0
1
0
0
0
2
0
0
1
0
0
0
0
0
1
2
0
1
0
0
1
3
0
0
2
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
4
1
0
0
0
0
0
1
1
1
0
0
2
0
2
0
0
2
0
0
2
1
0
0
1
1
0
0
2
2
0
0
0
0
1
0
0
1
2
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
3
0
1
0
0
2
2
0
0
1
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
1
1
1
2
0
0
0
3
1
1
0
0
0
1
1
0
0
0
0
2
2
0
2
0
1
1
1
1
1
2
0
0
1
0
0
0
2
0
0
0
0
0
1
1
0
1
0
0
3
1
0
0
1
2
0
0
1
0
0
1
2
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
2
1
1
0
1
0
1
0
0
0
1
0
0
0
2
0
0
2
0
2
2
0
0
0
2
0
0
0
0
2
0
2
2
1
1
0
2
0
1
0
1
0
0
1
2
0
2
2
0
0
5
1
0
0
0
3
0
0
1
2
0
1
0
0
0
0
0
2
0
2
0
0
0
0
1
1
0
2
0
2
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
1
2
0
2
0
0
1
1
0
0
1
0
0
0
1
0
0
0
1
1
1
0
2
0
1
0
0
0
0
0
0
2
1
0
2
0
0
1
2
1
2
0
0
2
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
1
0
1
1
2
2
0
0
0
0
0
1
1
1
6
1
1
0
0
2
0
1
2
0
1
2
0
0
0
1
1
0
0
1
2
0
0
2
1
0
0
1
2
1
2
0
1
0
1
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
3
1
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
2
0
2
2
1
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
2
2
2
0
0
0
2
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
2
1
0
0
0
2
0
0
0
2
0
1
1
1
1
2
1
0
1
1
0
1
0
0
0
0
2
1
2
2
1
2
0
1
2
1
1
0
0
0
1
1
0
0
0
0
2
0
2
0
1
1
0
0
0
0
0
2
2
2
0
1
0
2
0
2
1
1
1
0
0
0
0
1
1
1
0
0
0
2
3
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
2
1
0
2
0
0
0
0
0
0
0
1
0
2
1
2
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
2
1
1
0
0
1
1
0
2
0
0
0
0
0
0
1
3
1
0
0
0
0
1
1
0
3
0
2
1
2
0
2
2
2
0
1
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
2
1
0
1
1
2
3
2
1
1
1
0
0
1
2
0
0
0
0
1
2
0
2
0
0
0
0
2
0
0
3
2
0
2
1
0
2
1
0
1
0
0
2
0
0
1
0
0
1
0
0
0
1
0
0
0
0
2
2
0
0
1
0
0
0
0
1
0
0
1
0
0
0
2
0
1
1
1
2
0
1
1
0
1
1
0
2
0
2
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
2
0
2
0
0
0
0
0
2
2
0
2
2
0
1
1
0
1
2
1
0
2
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
1
0
1
2
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
2
1
1
0
0
2
2
2
0
0
0
1
2
0
0
0
1
0
0
1
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
1
0
0
1
0
1
0
1
4
0
2
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
2
0
1
0
1
0
0
3
2
2
0
0
0
0
0
0
0
2
2
0
0
0
1
2
0
0
2
0
1
0
1
0
0
2
2
1
0
1
0
1
0
0
0
0
0
1
2
2
0
0
0
2
0
0
0
2
0
0
0
0
2
2
0
0
0
1
0
2
1
0
0
0
1
0
0
2
2
2
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
1
1
1
0
0
2
0
2
0
2
0
2
1
0
0
0
1
0
0
1
2
0
1
1
0
0
0
2
1
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
2
1
0
2
0
2
0
0
0
0
1
2
0
0
2
1
1
0
0
0
0
0
0
2
2
0
2
1
1
0
0
0
0
0
0
0
0
0
1
0
0
5
1
0
0
1
3
2
0
1
3
1
1
0
2
2
0
2
0
1
1
1
0
0
2
2
2
0
3
1
0
0
0
0
0
0
1
1
1
0
0
2
1
1
0
0
0
0
0
2
1
0
0
1
0
0
1
0
2
1
2
0
2
0
1
0
0
0
1
1
0
0
2
2
1
0
0
0
1
2
2
0
2
0
0
2
1
0
0
0
1
2
0
0
0
0
0
1
0
2
1
1
0
0
1
1
1
2
1
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
1
1
0
2
0
1
2
1
0
0
0
1
2
0
0
0
2
0
0
2
2
0
0
1
0
2
0
0
1
1
2
2
0
0
0
0
0
0
0
0
1
2
1
0
1
2
0
2
0
0
0
1
0
0
0
2
0
1
0
1
1
0
0
0
1
0
0
0
2
0
1
0
0
0
0
3
0
1
1
0
0
0
0
0
0
2
1
1
1
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
1
1
3
2
1
1
0
2
0
0
0
0
1
2
1
2
1
0
1
0
1
1
1
0
1
0
0
0
1
1
1
2
0
1
2
0
1
0
2
1
0
1
1
0
0
1
0
2
1
0
0
2
0
2
1
2
0
2
1
0
2
1
2
0
2
2
0
2
2
0
0
0
0
2
1
0
0
0
0
0
0
0
2
2
1
0
2
0
0
0
1
1
1
0
0
0
0
1
0
2
1
2
0
2
0
0
1
0
2
2
2
0
1
1
0
2
0
1
2
0
0
0
1
1
2
2
2
2
0
0
0
0
1
0
1
0
0
0
0
0
0
3
0
2
1
0
0
0
0
0
1
2
1
0
0
0
0
2
0
0
0
0
1
0
2
0
1
2
2
0
0
1
1
2
2
2
0
0
1
0
1
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
2
1
0
1
2
1
2
0
2
0
0
1
0
0
1
2
1
1
1
2
2
0
1
0
0
0
0
2
1
2
0
0
0
2
0
12
0
2
0
2
1
1
0
0
1
0
0
0
2
0
2
2
2
1
0
1
2
1
1
0
0
1
0
0
0
0
0
0
0
2
0
1
1
0
1
0
0
0
0
2
0
0
0
0
0
2
1
0
0
2
1
2
2
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
2
2
1
1
0
0
0
0
0
2
0
0
1
0
1
2
0
1
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
2
1
2
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
2
0
1
0
1
0
0
1
0
1
0
0
1
0
1
0
0
0
2
0
0
1
1
0
2
0
1
0
0
0
2
0
0
0
0
0
1
1
1
0
2
0
1
0
1
0
2
0
0
1
0
1
2
2
1
2
1
1
0
0
0
0
1
0
0
2
2
0
0
0
1
2
0
2
0
0
0
2
0
0
0
0
1
2
1
0
0
1
0
0
2
1
1
0
0
0
0
1
0
0
1
1
1
0
1
0
0
1
1
1
1
1
2
1
1
0
0
3
0
0
1
0
0
1
0
0
0
0
1
0
0
2
0
0
0
2
0
2
0
0
1
0
1
0
0
1
2
0
0
0
1
0
2
0
1
2
2
0
2
0
2
0
2
0
2
1
1
0
2
1
2
1
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
2
2
0
0
1
0
1
2
2
0
0
2
0
0
2
1
2
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
2
0
2
0
1
0
0
1
1
1
0
2
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
2
0
0
0
1
2
2
0
1
1
0
0
0
0
0
0
0
1
0
0
1
1
0
2
1
1
0
0
1
2
0
2
0
4
2
0
0
0
0
1
0
0
0
1
0
0
0
2
0
1
2
0
0
0
0
3
1
2
2
2
2
0
0
0
1
2
1
0
0
0
1
0
0
0
1
0
1
2
0
0
2
1
0
2
1
2
2
0
0
0
0
0
1
0
1
2
0
0
0
0
2
0
1
0
2
0
0
1
3
2
0
0
1
1
0
0
2
0
2
0
0
2
1
0
2
2
0
0
1
0
0
0
0
2
0
1
0
2
0
2
1
1
2
0
0
3
2
0
2
0
1
0
2
2
0
2
0
2
2
1
2
0
2
0
2
0
0
0
0
2
0
0
2
0
0
0
1
1
0
0
0
2
0
1
1
2
0
0
0
2
0
0
0
0
0
2
0
0
1
1
0
0
0
3
1
2
2
2
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
2
1
0
0
0
0
1
0
1
0
2
2
0
2
0
0
0
1
2
2
2
1
2
1
2
0
0
0
1
0
1
2
1
0
1
1
2
0
1
1
0
0
0
2
0
1
2
0
0
2
1
0
2
2
1
2
0
1
2
0
1
0
2
0
0
0
0
2
1
0
0
0
0
0
1
2
1
0
0
1
1
2
1
1
2
2
0
1
0
0
0
2
1
0
0
2
0
0
0
1
0
0
1
0
2
0
1
0
0
0
0
0
0
2
1
0
1
1
2
0
1
0
0
0
0
3
0
0
0
0
0
0
1
2
1
1
2
0
0
2
2
2
1
0
0
0
0
0
0
0
0
0
1
1
2
0
2
1
1
0
1
0
0
0
0
0
0
0
0
1
2
0
1
2
0
0
0
1
0
0
1
1
2
1
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
3
1
2
1
1
1
1
2
0
0
0
0
0
0
2
0
0
0
0
2
2
2
1
1
0
1
0
2
0
0
2
0
1
2
0
0
2
2
2
0
1
2
2
0
1
2
1
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
1
1
0
0
0
0
0
0
2
0
0
1
1
0
1
1
0
1
1
0
1
2
1
0
1
0
0
0
0
0
0
1
2
0
1
0
0
1
0
0
0
0
2
0
1
2
2
0
1
0
1
0
0
1
1
0
0
2
0
0
0
1
0
1
2
0
0
0
0
0
0
0
2
2
2
3
0
1
2
2
0
0
2
0
0
0
1
1
0
1
0
0
0
0
2
0
0
1
1
0
1
0
0
0
2
1
3
0
0
1
0
1
0
0
0
1
0
2
0
0
2
2
0
3
1
0
2
0
1
0
2
2
0
0
0
0
2
0
0
0
1
0
2
0
1
0
2
0
0
2
0
0
0
1
0
0
4
0
2
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
1
2
0
0
1
1
0
1
0
0
0
3
0
0
0
0
2
0
0
0
2
1
1
1
2
0
0
2
0
0
0
2
0
1
1
0
0
0
1
1
0
2
2
0
0
0
0
0
3
1
1
0
2
0
2
0
0
2
0
0
2
1
0
1
0
1
0
0
1
0
0
0
2
0
2
0
2
0
0
0
0
0
2
1
2
0
2
0
0
0
0
0
2
2
0
2
0
0
1
1
0
2
0
0
0
0
2
2
2
1
0
1
0
0
0
0
0
3
2
0
2
2
1
0
2
2
0
1
0
0
0
2
1
0
1
2
0
0
1
0
0
1
2
0
0
0
2
0
3
2
0
0
0
0
2
1
0
0
2
2
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
1
2
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
2
2
1
0
0
0
1
1
0
0
0
2
0
1
0
0
2
0
0
3
2
0
0
1
1
0
0
0
3
1
0
0
0
5
1
0
0
0
2
0
0
0
2
0
0
0
1
0
0
1
0
2
1
2
0
2
3
0
0
1
1
1
0
0
2
2
1
2
0
2
0
0
0
0
0
0
1
0
1
0
0
0
1
2
2
1
0
2
1
0
0
0
0
0
0
0
2
0
0
3
2
0
1
0
1
0
2
2
1
0
1
1
0
0
0
1
1
0
0
2
0
0
0
0
2
1
2
2
0
1
2
0
1
1
0
0
0
1
7
2
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
2
0
2
1
0
0
2
1
0
1
2
0
1
0
0
2
0
3
3
2
1
0
0
0
4
0
0
0
0
1
1
0
0
0
0
0
1
1
1
0
0
0
1
0
0
2
0
2
0
2
2
0
0
1
1
0
0
0
1
0
2
1
0
0
0
1
2
0
0
3
0
0
2
0
1
0
0
2
2
1
1
1
2
0
0
0
0
0
1
0
0
0
1
0
0
2
2
0
1
1
0
1
0
0
0
0
0
0
0
1
2
2
0
0
1
2
0
2
1
2
0
1
0
0
2
0
0
0
0
1
0
1
0
0
0
1
0
1
0
2
0
0
0
4
1
1
0
2
0
0
0
1
0
1
0
2
0
2
1
0
1
0
0
2
0
0
2
0
2
0
2
0
0
1
2
0
0
1
0
0
2
0
2
0
0
0
2
2
0
3
1
0
0
2
0
0
2
0
0
2
0
0
2
2
0
2
1
2
0
0
1
0
1
1
0
2
0
0
0
0
0
2
0
0
2
0
2
0
0
0
1
0
0
0
1
0
0
2
0
2
0
1
2
0
0
0
3
1
1
2
1
2
0
1
0
0
0
0
0
1
1
1
0
2
0
2
0
0
1
0
1
1
0
0
0
3
3
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
1
0
0
1
0
1
0
0
2
0
2
0
0
1
0
2
0
0
2
1
0
0
0
1
0
0
2
0
1
1
0
4
0
1
0
0
0
0
1
0
2
0
0
0
1
0
0
0
3
1
0
1
0
0
3
1
3
0
1
1
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
3
0
1
0
1
0
1
0
0
1
0
1
1
0
0
0
0
1
2
0
1
2
2
1
1
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
1
1
0
2
0
1
0
0
0
1
2
2
0
2
0
0
2
1
1
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
1
1
2
0
1
0
2
1
0
0
2
2
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
2
1
1
0
0
2
0
2
0
0
0
0
0
2
0
0
1
2
0
0
0
2
0
2
1
0
0
2
1
1
0
0
0
2
1
1
0
0
0
2
0
1
0
2
1
0
0
0
0
1
0
1
2
3
0
2
0
1
0
0
0
0
1
2
0
0
0
2
0
1
0
0
1
2
1
1
1
0
1
0
2
0
1
1
0
0
0
0
0
0
2
0
0
1
0
0
0
4
0
0
0
1
2
2
2
0
2
2
1
0
1
0
1
0
0
0
0
2
0
1
0
1
0
1
0
0
0
0
0
0
0
1
2
1
1
1
1
1
1
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
2
0
0
3
0
0
0
0
0
0
0
1
0
0
0
1
2
2
0
2
0
0
2
0
0
0
0
1
1
2
1
0
0
1
0
5
2
0
0
1
2
3
1
0
0
0
0
2
0
0
0
1
0
0
1
1
0
0
0
0
2
2
0
1
1
0
0
0
1
0
0
2
0
0
0
0
0
0
1
1
2
1
0
2
1
1
9
0
0
1
3
1
1
0
0
0
0
0
0
2
1
0
0
0
0
0
3
1
2
2
0
2
2
0
0
0
0
1
1
0
0
1
2
1
2
0
0
0
0
2
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
1
2
0
2
0
1
0
0
1
0
1
0
0
2
0
0
0
2
0
0
2
2
0
1
2
0
0
0
2
0
0
2
1
0
1
0
0
0
0
0
1
2
0
0
0
0
1
0
2
1
0
0
1
1
0
0
0
0
2
0
0
3
1
0
0
0
0
0
1
0
2
0
2
0
0
0
0
2
0
0
1
1
1
1
0
1
0
1
0
0
0
1
0
3
2
2
0
0
2
1
1
0
0
2
0
1
2
1
0
1
2
0
2
1
1
2
1
0
0
1
2
1
0
0
1
0
1
0
1
0
2
0
0
0
0
0
1
2
2
1
0
1
2
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
1
0
0
2
0
1
1
0
1
2
0
0
0
1
1
0
2
2
0
1
0
0
0
0
3
0
0
1
0
0
2
0
4
0
2
3
3
0
2
0
1
0
0
1
2
0
2
1
2
1
3
3
0
0
0
3
0
1
0
0
0
0
0
0
2
2
0
1
0
1
0
0
0
0
2
1
0
1
1
4
0
0
0
3
0
3
0
0
0
3
1
0
1
1
0
0
0
2
0
2
1
0
0
0
1
2
0
2
2
2
0
0
1
1
1
1
2
4
0
2
0
2
0
0
1
2
0
0
0
2
0
1
0
1
0
2
1
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
1
0
0
1
1
0
1
1
0
2
1
1
0
2
0
0
2
1
0
0
0
0
0
2
0
1
2
0
0
1
0
1
2
2
2
0
1
0
2
0
0
2
1
0
1
1
0
1
0
0
1
0
1
0
2
0
2
2
3
0
0
0
2
2
0
0
0
2
2
1
0
2
1
2
0
0
1
0
0
1
0
1
1
0
0
1
7
0
1
2
0
0
0
1
0
2
0
2
0
0
0
0
3
0
0
0
0
0
1
2
1
1
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
2
0
1
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
1
1
0
0
2
0
0
1
0
0
2
1
0
0
0
0
0
2
2
0
0
0
1
1
0
2
0
0
1
0
2
2
2
1
0
1
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
1
2
0
1
0
0
1
2
1
0
1
0
2
0
2
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
2
0
0
1
0
3
0
0
2
0
2
2
0
1
2
0
1
1
1
0
0
1
2
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
5
0
0
1
0
0
0
1
2
0
1
2
0
0
1
0
0
0
0
0
0
0
2
2
2
0
0
0
0
2
1
1
1
1
0
1
1
0
2
0
0
0
0
0
0
0
1
0
1
0
2
1
0
0
0
2
0
0
0
0
2
0
2
0
2
0
0
2
0
1
2
0
2
0
0
1
0
2
1
0
2
0
0
1
1
0
0
0
0
2
0
1
0
1
1
2
2
1
0
2
0
2
0
0
0
0
0
0
2
2
2
0
0
2
0
0
1
0
0
0
0
2
0
2
1
0
1
1
0
2
2
0
0
2
1
0
1
2
0
0
1
1
1
0
0
1
1
0
0
0
1
2
1
1
0
1
1
1
0
0
2
0
1
0
0
2
2
0
0
0
1
1
0
0
0
1
0
1
2
2
1
1
0
0
1
1
2
2
0
0
0
2
1
2
0
0
1
0
0
6
1
0
1
0
0
0
0
1
1
0
1
2
0
1
0
3
0
2
0
1
1
0
0
3
0
0
0
0
2
0
0
1
1
0
0
1
0
2
0
0
1
1
1
0
0
0
0
2
1
1
2
1
0
1
0
3
2
0
0
1
0
1
3
0
0
1
0
1
0
0
1
4
2
2
1
0
0
0
0
3
0
1
2
0
0
0
0
2
0
2
0
1
1
2
1
0
0
0
0
2
2
0
1
2
2
0
0
0
3
1
1
0
2
0
0
0
1
0
0
1
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
1
1
0
1
0
2
0
0
1
0
1
1
2
2
0
0
0
0
0
1
2
2
2
0
0
0
2
3
0
1
0
0
2
0
0
1
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
2
0
0
0
1
0
1
0
2
0
0
0
2
2
0
0
0
0
0
2
2
1
0
0
2
2
2
1
2
0
2
0
0
0
0
2
1
0
1
0
0
0
3
0
0
2
1
0
1
2
0
0
0
0
0
0
0
2
1
1
1
1
0
0
1
0
0
1
0
0
2
2
1
1
0
0
1
0
1
0
0
1
1
0
0
0
2
0
2
0
0
2
1
2
0
0
0
0
0
0
0
0
0
1
2
0
2
0
1
2
0
0
2
0
1
2
1
0
1
1
0
0
0
0
2
0
1
2
0
0
0
0
1
0
2
0
2
0
1
2
2
2
1
0
2
0
1
0
0
1
0
0
0
0
0
1
1
1
0
2
0
0
1
0
0
0
0
3
0
0
0
0
2
0
2
1
0
0
1
2
1
0
1
0
0
2
0
1
1
1
0
2
1
3
0
1
0
2
0
0
2
0
0
2
0
1
1
0
2
1
2
0
2
0
1
1
0
0
1
0
2
3
0
2
2
0
2
2
0
1
1
0
0
0
0
0
0
0
1
1
0
1
1
0
0
2
0
2
1
1
0
0
0
3
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
1
2
0
0
2
0
0
0
1
2
2
1
0
0
0
2
1
0
1
1
1
0
2
0
1
0
0
0
1
3
0
1
1
2
2
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
1
0
1
1
0
0
1
2
0
0
1
0
0
0
1
0
0
0
1
2
0
1
2
2
1
0
0
1
0
2
2
1
1
2
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
3
1
1
0
0
3
2
0
1
0
1
0
2
0
0
0
0
1
1
0
0
1
0
1
0
1
0
0
2
1
0
0
2
0
1
0
1
0
1
0
0
0
0
2
2
0
6
1
0
0
4
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
2
0
1
2
2
0
0
0
0
1
2
0
0
0
1
0
1
0
0
2
0
0
0
0
0
2
0
1
0
0
0
5
1
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
2
0
1
4
1
2
0
0
0
0
0
0
3
0
0
0
1
0
0
1
0
0
0
2
0
2
2
0
1
2
2
0
1
0
1
0
2
0
0
2
1
0
0
0
1
1
0
0
1
0
2
2
1
1
1
0
0
1
0
1
0
0
0
0
5
1
0
2
2
1
1
0
1
2
2
1
0
2
0
0
1
1
2
0
2
1
1
0
0
0
0
2
0
0
2
1
0
2
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
2
0
0
2
0
2
0
0
0
4
1
1
1
0
0
0
3
0
0
0
2
0
2
1
1
0
2
0
0
0
1
0
1
0
0
0
1
0
2
0
0
1
1
0
0
0
1
1
0
1
2
1
0
0
0
0
0
0
1
0
0
1
0
2
2
0
1
0
1
0
2
1
0
0
0
0
1
0
0
0
2
2
1
0
2
0
0
0
0
2
1
2
0
1
0
1
0
0
0
0
0
2
1
0
0
0
0
1
2
1
2
1
0
0
1
2
1
0
1
0
1
1
0
1
1
1
1
2
2
0
2
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
2
1
2
1
0
0
1
1
2
0
3
0
0
0
0
1
0
2
1
0
2
2
1
0
0
2
0
2
2
0
0
0
1
0
0
0
0
2
1
1
2
0
1
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
1
0
0
0
0
0
4
0
0
1
1
0
0
0
1
1
2
0
0
0
0
0
2
1
2
0
0
0
1
0
2
0
2
0
1
1
1
2
3
2
1
2
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
2
1
2
2
1
0
2
0
0
2
0
0
0
0
2
0
1
0
0
1
1
1
1
1
1
0
2
0
0
0
0
0
0
0
0
1
1
3
0
2
1
0
0
0
1
2
1
0
0
0
0
0
1
0
1
0
0
1
0
0
1
1
0
2
0
0
0
1
0
0
0
4
0
0
0
0
1
0
0
2
1
0
2
0
0
0
3
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
1
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
4
0
2
1
2
0
0
0
2
0
1
1
1
1
2
0
0
1
1
1
2
3
0
1
1
2
1
0
0
1
4
0
0
1
0
0
1
2
0
2
0
2
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
2
0
0
1
0
0
1
0
1
2
0
0
2
0
0
2
2
1
0
0
2
1
0
1
2
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
3
1
1
0
0
2
1
0
0
2
0
0
0
0
1
2
1
1
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
2
0
2
0
2
2
0
0
0
0
0
0
1
2
2
0
0
0
0
0
1
1
0
0
0
0
1
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
1
2
0
2
1
2
0
0
1
2
0
0
0
0
0
1
0
0
2
2
0
3
1
1
2
0
0
0
0
1
1
0
0
0
0
1
0
1
2
0
0
0
1
2
1
0
1
0
0
0
0
7
0
0
0
0
2
0
0
1
2
1
0
1
0
2
1
0
1
1
2
0
0
0
1
1
0
1
1
0
1
1
0
1
2
1
0
0
2
1
1
0
0
0
2
0
2
1
0
0
3
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
2
1
0
1
0
0
2
0
0
0
0
2
3
2
0
0
1
1
0
1
2
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
1
1
0
1
1
2
0
0
2
0
0
0
0
0
0
1
2
0
0
1
2
2
2
1
1
1
0
1
2
0
0
1
0
2
0
1
1
0
4
3
2
1
0
1
0
1
0
1
0
0
0
0
5
1
0
0
0
0
4
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
2
0
1
0
0
1
0
2
0
2
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
1
0
0
0
0
1
0
2
0
1
0
0
0
0
0
1
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
1
1
0
1
1
1
0
2
0
0
0
2
0
0
0
1
0
1
1
1
0
0
1
1
0
0
1
0
0
1
0
2
1
0
1
0
2
2
2
2
0
1
0
0
2
0
0
1
0
0
0
1
1
2
2
1
1
0
0
2
0
0
0
2
1
2
0
0
1
1
0
1
0
0
0
1
1
2
1
0
0
0
0
1
3
1
1
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
2
1
2
0
2
0
0
2
1
2
2
1
4
2
0
0
0
0
0
2
2
2
0
2
2
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
1
2
2
2
0
1
0
1
0
0
1
1
0
0
0
0
0
1
1
0
1
0
2
2
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
1
5
0
0
2
1
0
1
2
0
0
1
1
1
1
0
1
1
2
0
0
0
0
1
1
0
2
1
0
0
2
2
0
0
0
1
2
1
0
0
0
2
2
0
0
2
0
0
1
4
2
2
0
0
2
0
0
0
1
0
0
0
2
0
0
2
0
0
0
2
1
1
2
0
2
0
0
0
0
5
2
0
0
2
0
1
0
0
1
1
2
0
2
1
1
2
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
2
0
0
0
1
2
0
1
1
2
1
0
0
3
2
0
0
1
1
0
2
0
0
2
0
0
0
0
1
0
0
1
1
0
1
0
2
0
0
0
0
0
2
2
0
1
2
0
0
0
1
0
0
1
0
3
0
0
2
2
2
0
0
0
0
1
1
2
0
2
0
0
2
1
0
0
1
1
0
2
0
2
0
0
2
0
2
1
0
0
2
1
0
0
0
0
1
0
0
1
1
0
0
2
3
0
0
1
0
1
0
0
7
2
0
0
1
0
2
0
0
0
0
0
1
0
0
1
2
0
0
1
1
1
0
0
1
0
2
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
2
0
0
0
0
0
0
0
2
1
2
2
0
2
0
0
1
0
0
1
1
0
1
2
0
1
0
0
0
2
0
1
1
1
0
0
0
2
2
0
0
0
1
0
2
2
0
1
2
0
0
7
2
0
2
1
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
1
0
1
0
0
0
0
2
2
2
0
0
0
3
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
2
0
1
1
0
1
0
2
1
1
0
0
0
0
0
0
0
1
0
0
2
0
1
0
1
1
1
2
0
1
1
1
2
0
2
0
2
2
1
2
0
0
0
1
1
2
2
0
0
0
0
0
0
0
0
0
2
2
2
2
1
0
0
0
0
1
2
2
0
2
0
0
2
0
2
1
2
1
0
0
1
0
0
0
1
0
1
0
1
0
0
0
3
0
3
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
1
1
0
0
1
0
2
0
0
0
1
0
0
2
2
0
0
1
2
0
2
0
0
0
0
0
0
3
1
0
0
1
0
1
2
0
0
1
2
0
0
1
2
2
0
1
0
0
0
2
1
0
1
0
1
2
1
0
1
1
1
0
1
0
0
0
2
0
1
0
2
0
0
2
0
0
0
1
1
0
1
0
0
0
2
1
0
1
0
4
2
0
1
0
0
1
1
0
3
2
0
0
0
1
0
1
0
0
0
1
1
0
1
0
1
1
0
0
0
1
2
1
0
0
0
0
0
2
0
2
2
1
2
2
0
0
2
0
0
2
2
0
1
0
0
1
2
0
1
0
1
0
1
0
2
2
0
0
1
0
2
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
2
0
2
1
0
2
0
0
1
1
0
0
2
2
0
1
1
1
0
0
0
1
0
1
0
1
2
2
1
2
0
0
2
0
3
1
2
1
0
1
0
0
2
1
0
3
2
2
1
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
2
3
0
0
2
0
0
2
0
0
0
0
1
1
0
0
0
1
2
1
0
1
0
0
2
0
2
0
2
0
1
0
1
0
1
2
0
2
1
1
0
2
1
0
1
2
3
2
2
1
0
0
0
2
0
1
2
3
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
3
0
2
1
0
0
2
1
0
0
0
2
0
0
0
0
0
1
0
0
1
1
1
1
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
4
0
0
0
0
1
2
0
0
0
1
0
1
0
1
1
0
1
2
0
0
1
2
0
1
0
2
1
1
2
4
0
0
1
1
1
0
0
0
0
2
2
2
1
2
0
0
1
1
1
0
2
0
2
0
1
1
1
0
0
2
0
0
0
2
2
0
0
4
2
0
0
0
1
2
0
0
0
0
0
0
2
2
0
0
2
0
2
1
1
0
0
2
0
1
1
0
0
2
1
0
2
0
2
2
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
2
2
0
0
1
2
0
0
2
2
1
0
0
0
0
1
0
0
1
0
0
1
1
0
0
1
0
0
1
0
0
1
0
0
2
0
0
0
2
0
0
0
3
1
2
0
2
2
1
0
1
0
2
0
0
0
0
3
3
0
1
0
1
0
1
0
0
0
1
0
0
2
0
1
0
0
0
0
2
0
0
1
0
1
1
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
1
1
2
0
1
0
0
0
0
1
0
0
0
1
0
1
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
1
1
1
0
1
2
0
0
0
0
1
0
0
1
0
1
0
0
0
0
5
1
0
0
2
0
0
1
0
2
0
1
1
1
0
1
0
0
1
0
0
0
2
2
1
0
0
0
1
1
0
1
0
0
0
2
1
0
0
0
1
0
0
1
2
0
1
0
1
2
1
0
0
0
1
0
0
0
0
0
1
1
1
2
2
0
0
0
0
1
2
0
1
0
2
0
1
0
0
0
1
0
2
1
0
0
1
0
2
0
1
0
2
0
0
0
0
0
1
0
1
0
2
2
1
0
0
0
0
0
2
1
0
0
2
0
2
2
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
3
2
2
1
1
1
1
1
0
4
1
3
0
0
1
0
0
1
1
1
0
1
0
0
0
0
0
1
0
1
1
0
1
1
2
0
1
0
1
2
1
1
0
2
0
1
0
0
0
0
0
0
0
2
1
1
1
0
0
2
0
1
0
2
0
0
2
1
1
2
0
2
1
2
0
0
2
0
0
1
2
0
0
2
0
1
1
0
0
0
0
0
2
1
0
0
0
0
1
3
0
0
1
0
0
0
1
0
0
0
2
2
2
0
0
0
1
0
2
0
0
2
2
0
3
0
0
0
0
0
0
2
0
1
3
2
1
1
0
1
1
1
0
1
0
1
0
0
3
0
1
2
0
2
0
2
2
0
2
0
2
0
2
0
2
1
0
0
0
0
1
1
2
1
2
1
2
2
2
0
1
0
1
1
0
2
2
0
0
0
1
0
2
0
2
0
2
1
0
0
0
2
0
0
0
1
0
1
0
0
2
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
2
2
0
0
0
0
1
0
1
0
8
0
1
0
1
2
0
0
1
1
0
0
0
0
2
1
0
0
1
1
0
2
1
0
0
0
0
1
3
0
2
0
0
1
2
2
0
1
2
0
0
1
0
0
1
0
1
0
2
1
1
2
2
1
0
1
2
0
2
0
0
2
0
0
0
1
0
1
1
5
0
2
0
3
0
1
1
1
1
0
0
1
0
1
0
0
0
0
2
0
0
1
2
1
0
2
0
0
2
0
0
0
0
2
2
0
1
0
0
0
0
1
0
0
0
3
0
2
2
0
0
2
0
2
1
0
2
1
0
1
0
0
0
2
0
0
0
2
0
2
0
1
2
1
3
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
1
1
0
0
0
0
0
0
0
1
1
0
2
0
0
2
0
1
1
1
0
2
0
2
0
1
4
1
0
1
0
0
0
0
0
0
1
1
0
0
0
2
1
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
2
0
2
0
0
1
0
0
1
0
0
1
0
0
2
3
0
2
0
1
2
1
0
0
1
0
0
0
0
2
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
1
2
1
0
0
0
0
1
0
1
1
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
2
3
1
1
1
0
1
1
0
0
3
0
2
1
1
2
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
2
1
0
2
1
0
0
2
0
0
2
2
0
1
1
1
0
1
0
0
0
0
0
2
1
0
2
0
1
1
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
2
2
0
1
1
0
1
0
1
1
0
0
1
0
0
0
1
0
0
2
0
0
0
2
0
1
0
0
1
0
1
1
2
6
0
1
0
3
2
0
2
0
2
1
0
0
2
0
0
0
2
0
1
0
1
2
2
0
0
0
0
1
0
0
0
0
1
0
1
2
2
0
1
0
0
1
2
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
2
2
1
0
0
0
2
1
0
0
0
1
0
0
2
1
0
0
0
1
1
0
2
0
0
1
0
2
0
0
0
0
2
0
0
1
0
2
0
0
2
0
0
0
2
0
0
2
2
1
0
2
0
0
0
0
0
2
0
0
0
1
2
0
1
1
0
0
2
0
0
0
0
4
1
4
0
2
0
0
0
1
1
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
2
0
0
0
0
0
0
0
1
1
2
1
0
0
0
1
0
0
0
2
0
0
3
0
0
0
0
0
2
0
2
0
1
2
1
2
0
0
0
0
2
1
2
0
1
2
2
1
0
2
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
2
0
1
4
0
1
0
1
1
0
0
1
0
2
1
1
1
0
1
3
0
2
0
0
0
0
0
1
2
0
0
0
0
2
0
2
1
1
0
0
0
3
1
1
2
0
1
0
0
1
0
1
1
0
1
0
1
0
1
2
1
0
0
0
2
0
1
0
0
1
0
0
0
2
2
0
0
0
0
0
0
1
2
0
2
0
1
0
0
1
0
0
0
0
2
3
0
1
0
1
0
2
0
1
2
0
1
0
0
2
1
0
0
1
2
0
1
2
0
1
2
2
0
0
2
1
0
0
0
1
0
1
0
1
1
0
0
0
0
0
1
0
2
0
2
1
0
0
0
2
0
1
1
0
0
0
0
0
1
0
0
1
0
1
0
0
2
0
0
0
2
0
0
0
1
1
1
2
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
2
1
1
0
2
2
0
0
2
2
1
0
1
1
0
2
2
2
0
0
2
2
1
1
0
1
1
0
0
0
0
0
2
0
1
0
0
0
0
0
1
1
2
0
1
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
1
0
1
2
0
2
2
0
2
0
1
2
2
2
0
0
1
1
1
2
0
1
0
0
0
0
0
0
2
1
0
0
0
1
0
0
1
1
0
1
0
1
0
0
1
0
0
0
2
0
0
0
2
0
2
0
2
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
2
1
0
0
2
0
0
0
0
2
1
0
0
1
0
3
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
2
0
0
0
0
0
1
0
1
0
0
0
4
0
2
1
1
2
1
2
1
0
0
1
0
1
0
3
0
2
0
0
1
0
0
0
1
1
1
2
3
0
2
0
0
2
2
2
0
0
2
1
1
0
1
3
0
1
0
1
0
0
0
1
0
0
1
0
0
2
0
4
3
1
0
0
2
1
1
1
0
0
4
0
2
0
1
0
2
0
0
0
1
0
1
0
2
0
0
1
0
0
1
0
0
2
1
0
2
2
0
3
1
1
0
0
0
0
2
1
1
0
0
0
1
0
1
2
0
1
0
0
1
2
0
0
0
0
2
2
2
1
0
0
1
1
0
2
0
0
3
0
0
0
1
0
0
2
2
0
0
3
0
0
0
0
1
0
2
2
1
1
0
0
2
2
0
2
1
0
1
1
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
1
1
0
1
2
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
1
0
2
0
0
0
1
2
0
2
0
0
1
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
2
0
1
3
0
1
1
2
0
0
1
0
2
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
1
0
1
1
2
1
0
0
2
0
2
2
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
1
0
1
1
1
0
1
0
1
2
0
0
1
0
0
0
0
0
1
0
0
1
1
0
2
0
2
0
1
0
1
1
0
2
2
1
0
1
2
0
2
0
1
0
0
2
1
0
0
0
1
0
2
3
0
1
0
1
0
0
1
0
0
0
0
2
0
0
0
1
0
1
1
2
0
0
0
2
0
0
1
2
1
0
0
1
2
1
1
0
0
1
3
2
0
1
0
0
0
0
1
0
0
0
5
0
0
3
0
0
2
1
2
2
0
2
0
0
1
2
1
0
2
0
1
2
0
0
1
0
0
0
1
0
0
2
0
1
0
0
0
1
2
0
2
1
0
0
0
2
0
2
2
0
0
0
0
0
2
0
0
0
1
0
0
1
1
2
1
0
0
0
1
0
3
0
1
0
0
0
1
2
0
0
0
2
0
1
0
2
1
0
2
0
2
2
1
1
0
0
0
2
0
2
0
1
0
1
0
1
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
2
0
0
0
0
2
0
0
0
0
0
2
1
0
1
0
1
0
0
0
1
2
2
2
5
2
0
0
0
0
0
0
0
1
1
2
0
2
0
0
0
0
3
0
0
0
1
0
0
0
2
0
0
0
2
0
0
2
0
2
0
0
1
9
0
1
1
2
0
0
1
0
1
0
0
1
0
0
2
0
1
2
2
0
0
2
0
2
0
0
1
2
0
1
1
1
0
0
0
2
0
0
0
0
0
1
2
0
0
1
0
1
1
0
0
0
0
0
2
0
1
2
0
4
1
2
0
2
0
0
0
0
2
2
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
1
0
0
2
1
1
0
0
0
2
2
2
0
0
0
0
1
0
2
1
0
2
0
2
1
0
0
2
3
0
0
0
2
1
0
0
1
0
0
1
0
0
2
0
0
0
0
2
0
3
0
1
0
2
2
1
2
2
0
2
1
0
0
1
0
0
0
2
2
2
0
0
0
1
0
0
2
2
0
2
0
2
0
0
1
0
0
0
1
2
2
0
0
0
0
1
0
0
2
0
0
0
0
1
1
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
2
0
1
0
0
0
1
0
1
2
2
1
0
1
2
0
0
0
2
0
1
2
0
1
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
1
2
0
0
0
2
0
1
0
0
0
1
0
0
2
1
0
2
2
0
0
0
0
0
1
1
2
0
0
0
2
0
2
1
1
0
0
1
1
1
2
0
3
2
0
0
1
0
0
2
0
1
0
3
0
0
1
0
0
1
1
2
0
0
3
2
0
0
2
0
0
2
0
0
1
2
1
0
2
1
0
2
0
0
0
2
1
1
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
5
2
2
2
0
0
1
3
1
0
1
1
1
0
0
2
0
0
1
2
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
2
3
0
2
0
0
0
0
0
2
0
1
0
0
0
2
1
2
2
1
0
0
1
1
3
0
0
0
1
0
0
2
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
1
2
0
1
1
2
0
0
1
2
0
1
1
1
0
0
0
0
0
2
2
2
1
2
0
0
0
0
2
0
0
1
1
1
0
0
0
0
1
1
0
1
0
2
0
0
0
0
1
1
0
2
1
3
2
2
1
2
2
1
0
2
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
1
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
2
0
2
0
0
1
1
0
0
0
0
1
2
0
1
0
0
0
2
0
1
1
0
1
0
0
0
0
1
1
0
0
0
1
0
0
2
0
1
0
1
0
2
1
1
0
0
0
0
0
1
0
0
0
2
1
0
3
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
1
0
0
0
0
2
1
0
0
0
0
2
0
0
1
0
3
2
0
2
1
0
0
2
0
1
2
1
1
0
1
0
2
2
1
1
0
2
0
0
0
0
2
1
0
1
2
0
2
0
5
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
1
2
0
0
0
2
0
0
0
2
1
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
1
0
0
1
2
0
0
1
0
2
3
0
1
0
1
4
0
0
0
1
1
0
2
0
2
1
0
2
1
0
2
0
2
2
0
1
0
0
0
0
2
0
2
0
1
0
2
0
0
1
0
0
0
0
0
2
0
2
1
1
2
1
0
0
2
0
2
0
1
0
1
0
0
2
0
0
0
0
0
1
1
0
0
3
0
1
2
0
1
0
0
0
2
2
1
0
0
1
0
0
2
1
1
0
0
0
0
1
1
0
1
1
0
2
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
1
0
0
0
1
0
3
0
0
2
1
0
0
1
1
2
0
0
1
0
0
0
2
0
1
1
0
8
0
0
0
2
1
0
0
1
0
1
0
0
2
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
5
0
0
2
2
2
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
1
2
0
0
2
0
2
2
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
1
0
0
1
0
1
1
2
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
1
2
1
0
2
0
0
1
0
2
0
3
0
0
0
2
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
2
1
0
0
3
0
0
0
3
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
1
0
0
1
0
1
1
1
1
0
0
1
1
1
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
1
2
0
2
2
0
0
2
4
0
0
0
0
1
0
2
0
0
0
2
1
0
0
0
1
0
0
0
1
0
0
2
1
1
1
2
0
0
0
0
2
0
0
1
2
0
2
0
2
0
0
0
1
0
0
1
0
0
2
0
2
0
1
0
0
2
0
0
0
0
1
0
0
0
1
0
2
0
0
0
2
1
1
3
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
2
1
0
0
1
0
0
0
1
0
1
1
1
0
1
1
1
0
1
1
0
0
1
0
1
0
0
0
1
2
1
0
0
0
0
2
0
1
0
0
0
0
1
2
1
0
0
3
5
0
0
2
2
0
0
1
1
1
1
0
2
2
0
0
0
0
1
0
0
0
1
1
2
2
0
0
0
0
0
1
2
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
3
0
0
0
0
1
0
0
2
0
1
0
0
1
0
1
0
0
1
0
2
2
2
0
8
1
0
0
0
0
0
0
1
2
0
0
2
0
1
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
2
2
5
2
1
2
0
1
0
0
1
0
0
1
2
0
1
3
0
2
0
0
0
2
1
1
0
0
0
0
0
0
2
0
0
1
0
1
0
2
2
0
1
2
0
0
0
2
0
0
0
0
0
2
0
0
1
2
0
0
0
2
0
1
0
0
3
0
0
0
2
3
1
2
2
0
2
2
2
0
0
0
0
3
0
1
2
2
2
0
2
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
2
2
1
0
0
1
2
0
2
1
0
0
1
0
0
0
0
1
0
2
0
0
1
0
0
2
1
8
1
2
0
0
0
0
0
1
2
2
0
1
1
0
1
0
0
0
0
1
3
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
2
0
1
0
1
0
0
0
1
0
1
2
2
2
0
0
3
2
2
1
1
0
1
0
0
2
0
0
2
2
0
0
0
0
1
2
0
0
0
0
1
0
1
0
2
0
1
2
0
0
0
0
0
1
0
0
1
0
1
1
0
0
2
2
1
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
2
1
1
0
1
1
0
0
1
1
0
0
0
0
0
0
2
1
1
0
0
0
7
0
0
1
0
0
1
2
1
1
0
0
0
2
0
2
0
0
2
1
2
1
1
2
0
1
1
0
0
0
0
3
0
1
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
2
2
0
0
1
0
0
2
2
2
0
0
1
2
2
0
1
1
2
1
2
1
0
0
1
0
0
1
0
0
0
0
1
1
0
2
0
0
0
1
2
1
0
0
0
0
2
1
0
0
0
2
0
2
2
0
2
0
0
2
0
0
0
1
1
1
0
2
1
2
0
0
2
2
0
0
0
1
1
1
0
0
0
1
1
2
1
1
0
0
2
0
1
1
2
0
0
0
2
0
0
0
2
0
0
2
1
0
0
0
1
0
1
0
0
2
2
1
0
1
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
2
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
1
1
0
0
1
1
1
2
2
2
0
0
1
0
2
0
0
2
1
1
2
1
2
0
1
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
1
0
3
0
0
2
2
0
0
0
0
0
2
0
0
2
2
0
0
2
1
2
1
0
3
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
1
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
2
1
0
1
1
1
0
0
0
1
0
1
1
2
0
1
2
0
0
2
2
0
0
0
1
2
2
0
0
2
0
0
0
0
0
1
0
2
1
2
2
2
0
2
0
0
0
0
1
1
1
0
0
1
2
0
1
2
0
2
0
1
0
0
1
2
1
1
1
2
0
0
0
0
0
0
1
2
0
0
1
0
0
2
0
0
2
0
0
0
0
2
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
1
2
1
1
0
2
1
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
1
1
0
0
0
1
1
1
0
0
1
0
2
1
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
2
1
0
0
0
1
0
2
2
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
2
0
1
2
2
1
0
0
2
0
0
2
0
4
0
0
0
2
0
2
1
0
2
1
2
1
2
0
0
0
0
0
2
0
1
0
1
1
0
3
1
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
2
1
0
1
0
3
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
1
1
0
2
0
0
0
0
0
0
2
0
2
1
1
0
1
0
0
2
0
2
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
2
1
1
0
1
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
1
0
0
1
1
1
2
0
0
2
2
2
2
1
0
0
0
0
0
0
2
1
1
2
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
2
0
1
0
1
0
1
1
0
0
0
0
0
2
0
1
1
0
0
0
1
2
0
0
0
3
0
1
0
0
0
0
0
1
0
1
2
0
2
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
1
0
0
2
3
0
0
1
1
0
0
0
1
0
2
2
0
2
0
0
0
0
0
0
1
1
1
0
0
1
1
0
0
0
1
1
1
1
0
0
0
0
0
1
0
0
0
1
0
1
2
0
1
0
1
2
0
1
3
0
0
0
2
1
3
0
1
1
1
0
0
2
0
0
0
1
1
0
0
1
0
0
2
1
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
1
0
0
0
0
1
2
2
4
1
1
2
0
1
0
2
0
0
0
0
2
2
0
0
1
0
2
0
0
1
1
3
0
1
0
2
2
0
0
1
0
1
1
1
0
0
1
1
0
1
2
1
1
0
1
0
2
1
1
2
0
0
0
0
0
0
0
2
1
2
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
1
2
0
0
0
1
1
0
0
2
2
0
1
0
2
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
1
1
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
1
2
2
0
0
6
0
0
2
0
1
1
0
1
1
1
2
0
0
1
3
1
0
2
1
2
1
0
1
0
0
2
2
0
1
2
0
2
0
0
0
1
2
0
0
1
1
0
1
0
3
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
1
2
2
0
0
2
0
2
0
1
1
1
0
2
0
0
1
1
0
0
0
3
2
0
0
1
0
1
0
1
1
2
0
0
0
0
0
0
1
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
3
0
0
1
1
2
2
0
0
2
0
3
1
2
1
0
2
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
2
0
1
0
1
1
0
0
1
1
0
2
0
2
0
3
0
0
0
0
0
0
0
2
1
1
2
2
0
1
3
0
1
0
0
0
0
1
0
0
0
2
0
0
0
2
1
0
0
1
0
0
1
2
0
0
1
2
0
0
0
2
2
0
0
1
0
0
0
0
0
1
1
0
0
2
0
2
2
2
0
0
1
0
0
0
2
0
0
2
0
2
0
0
0
0
0
2
2
0
0
0
1
0
1
0
0
0
0
2
1
2
0
1
0
0
0
2
1
2
2
1
0
0
1
2
1
2
1
0
0
0
1
0
0
2
0
0
0
3
1
1
2
0
0
0
0
0
1
0
1
0
2
0
0
0
0
1
1
2
2
0
0
1
0
0
2
1
0
6
0
0
0
0
0
0
1
2
0
0
2
0
0
1
0
2
0
1
0
2
0
0
2
1
0
0
0
0
0
0
1
0
1
2
2
0
0
1
0
2
2
0
0
0
0
0
0
1
3
0
1
0
0
0
2
2
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
1
0
2
2
0
2
0
5
1
2
2
2
0
0
0
0
2
2
0
2
0
0
1
9
0
2
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
2
2
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
2
3
0
0
1
0
0
0
0
2
0
1
2
1
3
0
0
1
0
2
0
0
0
0
0
2
1
0
2
0
0
0
0
2
0
0
2
0
0
0
1
0
2
0
1
0
0
2
0
1
0
0
0
2
2
0
2
0
0
0
1
0
0
0
2
0
1
1
0
1
2
0
1
1
0
2
0
1
0
0
1
0
2
1
2
0
2
2
0
1
0
0
0
0
0
0
0
0
1
1
1
0
1
1
2
0
0
2
0
0
0
1
0
0
2
0
0
1
2
0
0
1
1
1
0
0
0
0
0
0
2
0
0
2
2
0
2
0
1
0
0
0
1
1
1
2
2
1
0
2
2
0
0
0
1
0
0
1
1
0
1
1
0
2
0
2
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
1
0
2
0
0
3
0
2
0
2
0
1
1
0
1
0
2
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
2
1
2
2
0
0
1
2
1
1
0
0
0
2
0
1
2
0
2
3
2
1
0
0
1
0
0
0
2
2
0
1
0
0
0
1
0
0
2
2
2
0
2
0
2
0
0
2
0
2
0
1
1
0
0
0
1
1
0
2
0
2
2
0
0
2
0
0
1
0
0
2
0
0
2
0
0
0
0
1
1
2
0
0
0
0
2
1
0
1
0
2
0
2
1
1
2
2
1
1
1
1
0
0
0
1
2
1
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
1
0
2
2
0
2
0
1
0
0
1
0
0
0
2
0
0
0
1
0
0
0
2
2
3
3
4
0
0
1
0
0
1
2
0
0
1
0
1
1
0
0
2
2
2
1
0
0
0
3
0
2
0
0
1
0
2
1
1
0
0
2
0
0
0
0
0
0
2
0
2
1
0
2
1
0
0
0
0
0
0
3
1
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
2
0
0
0
1
0
0
2
0
0
2
1
1
0
0
1
2
0
1
0
1
1
0
0
1
2
1
0
0
0
2
1
2
0
0
0
0
2
1
1
0
0
0
2
0
0
0
0
0
0
1
1
1
1
0
1
0
1
0
0
0
0
0
2
2
2
0
2
2
2
1
0
1
0
0
2
1
0
0
2
0
0
0
3
0
0
0
1
1
0
2
0
0
0
0
0
2
2
2
2
0
0
0
0
0
2
0
4
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
2
1
1
0
0
0
1
1
0
3
0
0
0
0
2
0
0
2
2
0
5
3
2
1
0
1
0
1
0
2
1
0
1
0
0
0
0
0
0
2
0
0
0
1
1
1
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
2
0
2
1
1
1
0
1
0
1
0
0
2
1
0
0
0
3
0
2
2
0
0
0
1
1
0
0
0
2
0
0
2
1
0
1
0
0
0
1
2
0
1
1
0
0
1
1
0
0
0
2
0
1
0
0
0
1
0
2
1
0
0
1
0
0
2
2
0
0
1
0
1
0
1
1
0
0
0
0
0
0
1
1
1
0
1
2
2
0
2
0
0
1
0
1
1
0
1
0
0
0
0
0
1
2
0
0
0
2
0
1
0
2
0
2
0
0
1
0
2
1
0
0
0
0
0
0
1
0
1
1
0
2
0
1
1
1
1
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
1
0
2
0
0
2
0
1
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
3
0
0
1
1
0
0
0
1
0
0
4
1
1
0
0
1
0
2
19
0
1
0
0
0
0
0
0
0
2
1
0
1
3
1
0
1
0
1
0
0
0
0
1
2
2
1
2
0
0
0
1
0
0
1
0
1
0
1
0
2
0
0
2
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
2
1
1
0
1
0
1
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
1
2
0
1
1
2
0
0
0
1
2
0
1
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
2
2
2
2
0
1
0
0
0
0
2
1
1
2
2
2
2
0
0
0
2
0
1
0
1
0
5
0
0
3
0
1
0
3
2
0
0
1
2
1
2
0
1
2
1
0
0
1
0
1
3
0
1
1
1
0
0
0
0
0
0
1
0
2
0
1
1
0
7
0
2
1
1
0
0
1
0
0
0
0
1
0
0
1
0
1
2
1
2
0
2
2
0
1
2
0
3
0
1
0
1
1
1
0
1
2
0
0
0
1
0
0
0
2
0
0
0
1
1
3
0
0
2
0
0
0
0
23
1
0
0
1
2
0
0
0
0
0
0
0
0
1
0
2
1
0
2
0
1
0
0
0
0
2
1
0
1
0
0
0
0
0
1
0
1
2
1
1
1
2
2
0
1
1
0
0
0
0
3
0
0
0
2
1
1
1
0
1
2
1
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
1
0
1
1
0
0
0
0
1
2
1
0
1
1
2
1
0
0
0
2
1
2
0
0
2
2
1
0
0
2
1
2
1
2
0
0
3
0
0
1
0
0
0
1
2
6
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
2
1
0
0
0
2
0
0
0
1
1
2
0
0
2
0
1
2
1
1
1
1
0
2
0
0
0
1
0
2
2
0
1
0
1
1
1
0
2
1
0
2
0
0
2
0
0
0
2
0
1
0
0
2
0
0
2
0
4
0
0
2
1
1
0
0
1
0
0
0
2
0
2
0
0
0
1
0
0
2
1
0
1
1
0
1
0
0
0
2
0
0
1
0
2
0
2
1
1
1
0
1
0
1
1
0
0
0
0
0
0
0
1
2
0
1
3
1
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
1
0
0
1
2
0
0
2
0
1
0
0
2
0
0
0
0
1
1
2
4
1
1
0
2
0
3
0
0
2
1
0
0
2
2
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
1
2
0
0
1
0
0
0
0
2
0
2
1
0
0
1
1
1
2
2
0
0
1
2
0
0
0
1
0
0
2
2
0
1
1
0
4
0
0
1
0
1
0
0
1
1
0
0
2
2
1
1
1
2
2
1
0
3
1
0
1
0
1
2
0
0
0
0
2
0
0
1
2
2
1
1
0
10
1
0
0
1
0
0
0
0
0
1
1
1
2
0
0
2
0
0
3
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
1
0
2
0
2
2
1
1
0
2
0
0
1
0
1
2
2
1
0
1
0
2
0
0
2
0
0
0
1
1
2
0
2
1
0
0
0
0
1
0
0
0
2
0
0
3
2
0
0
0
0
0
1
0
1
2
0
1
0
0
0
0
0
1
1
0
2
2
2
0
1
3
0
2
1
0
3
0
0
0
2
1
0
0
0
1
0
1
0
0
0
0
0
2
0
2
0
4
0
0
0
0
0
1
2
0
2
0
2
0
2
0
0
2
0
2
0
0
1
1
1
1
0
0
1
1
0
0
0
1
0
1
2
0
0
0
0
3
1
0
2
1
0
1
0
0
1
1
0
0
1
1
2
1
1
4
2
0
0
0
0
0
2
0
0
1
2
2
3
4
1
0
0
0
0
2
1
0
0
2
0
0
0
2
0
2
1
0
1
1
1
1
0
0
0
1
0
0
0
3
2
0
0
1
0
1
0
0
0
0
1
0
1
2
0
0
1
2
1
2
0
2
0
0
0
0
0
0
1
0
0
0
1
2
0
2
0
0
1
1
0
1
1
0
1
2
2
1
0
1
1
0
1
1
0
2
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
1
0
0
1
1
2
0
0
0
0
0
1
0
0
4
0
0
2
0
0
1
2
0
2
1
0
0
0
1
0
1
1
2
0
0
1
0
0
1
1
0
0
0
2
0
2
0
0
1
0
2
0
0
0
0
0
0
2
1
1
1
1
0
2
1
0
2
0
0
0
1
0
0
0
1
3
1
1
0
1
1
1
0
0
0
0
0
0
3
2
0
0
5
2
2
0
2
0
1
1
0
1
0
2
1
0
0
2
0
1
2
1
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
2
0
0
1
2
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
2
2
0
0
2
2
0
2
2
1
0
0
0
0
0
0
2
0
0
0
1
2
0
2
0
0
2
2
0
0
0
0
1
0
0
1
2
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
1
1
0
2
0
0
0
1
1
1
0
0
0
0
3
1
0
0
0
1
1
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
2
1
0
0
0
1
2
0
1
1
0
1
0
0
1
0
1
0
0
0
1
2
1
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
2
0
2
2
2
2
2
0
0
2
11
2
2
2
0
3
0
0
3
3
2
2
4
0
3
2
1
0
0
0
1
1
0
0
2
1
1
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
3
0
0
0
0
0
0
2
0
2
0
1
0
0
0
1
1
0
0
0
2
2
0
2
1
1
1
0
1
1
1
0
1
2
0
0
2
0
0
0
0
0
0
1
1
0
0
2
2
2
1
0
2
2
1
1
0
0
0
0
0
0
2
3
0
1
1
0
0
2
2
0
0
0
0
2
1
1
0
0
0
0
0
1
0
1
2
0
0
0
1
1
1
1
0
2
0
0
2
0
0
0
3
0
1
0
2
1
1
2
2
2
0
0
1
2
0
1
0
0
2
0
1
1
0
0
0
2
1
1
0
6
2
0
0
0
0
0
1
0
2
2
0
2
0
0
0
1
3
2
1
0
0
2
0
2
0
0
2
0
0
0
0
0
0
2
1
0
2
1
1
0
0
0
1
0
2
0
0
0
1
0
1
0
2
0
2
0
2
0
0
2
0
2
0
0
2
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
2
2
1
2
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
1
0
2
1
0
1
1
0
0
2
2
0
1
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
3
0
1
1
0
2
0
0
0
0
2
0
0
0
1
2
2
0
2
0
4
0
2
0
1
0
0
0
0
1
0
1
1
0
0
2
1
1
2
0
1
0
0
1
2
3
1
2
0
1
2
1
2
1
2
0
0
0
0
1
0
0
1
0
2
0
0
0
1
1
0
0
1
1
0
2
1
0
1
0
0
1
0
0
1
2
0
0
0
2
0
0
0
0
3
0
0
2
0
1
1
0
0
0
2
3
0
2
0
2
1
1
0
1
0
2
1
2
0
0
0
0
0
1
0
0
0
0
0
1
2
1
2
1
0
1
2
0
0
0
0
0
1
2
0
1
1
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
2
1
0
0
1
1
0
1
1
0
0
2
2
3
0
2
1
2
2
0
0
0
1
1
0
0
0
1
2
1
1
0
1
1
0
2
3
0
0
1
1
1
0
0
1
0
0
1
0
0
0
0
0
0
2
1
2
0
0
2
2
0
1
0
0
0
0
1
0
2
0
0
0
0
1
0
2
0
0
2
0
0
0
0
1
0
2
1
0
2
0
0
0
1
0
0
1
3
3
2
0
2
0
0
2
0
2
0
0
0
1
4
0
0
0
1
0
0
2
0
2
0
1
1
2
2
1
0
1
2
0
2
2
2
0
0
0
0
0
1
0
2
0
1
0
2
0
1
0
1
1
0
2
0
1
0
0
0
0
1
0
1
1
0
1
1
1
2
0
2
0
2
2
1
0
1
1
0
2
2
1
1
1
1
0
2
1
1
0
0
2
1
1
2
0
2
0
1
0
1
0
0
1
0
0
2
1
0
0
0
0
0
2
3
0
1
1
0
1
0
1
1
0
0
2
2
2
0
2
1
0
0
0
0
0
2
1
0
0
2
0
3
0
0
0
0
0
0
0
0
2
2
1
0
0
1
0
0
1
2
0
2
0
0
0
0
0
1
2
2
1
1
0
0
2
2
0
1
0
0
1
2
0
0
0
0
2
3
0
1
1
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
1
0
2
2
2
1
0
1
0
1
1
1
0
2
0
0
2
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
1
0
0
3
0
0
0
0
0
2
1
2
0
0
2
1
0
0
0
2
0
2
0
0
0
1
2
1
1
0
0
2
0
2
0
0
0
0
1
1
2
0
1
0
1
2
1
0
1
0
0
2
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
2
2
2
0
0
0
1
0
1
0
0
0
0
0
0
4
0
1
3
0
0
2
0
1
0
0
2
0
1
2
2
0
2
0
0
0
2
0
0
2
2
1
2
0
2
2
0
0
0
1
0
1
1
0
0
0
2
0
0
0
1
1
1
0
0
0
0
1
0
1
0
2
2
1
0
0
0
1
0
2
0
0
1
2
1
0
0
0
2
2
0
0
1
1
1
0
2
0
2
0
1
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
1
0
0
0
1
1
2
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
1
2
0
0
0
2
1
0
1
0
0
0
4
2
2
0
0
0
0
0
0
2
1
0
1
3
2
0
2
0
0
0
1
0
0
2
1
1
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
3
2
2
2
0
2
2
0
2
0
0
0
1
1
3
0
0
0
2
1
0
1
0
0
1
0
0
4
2
0
0
0
2
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
1
0
1
0
2
0
0
0
2
2
2
0
0
2
0
3
0
1
1
1
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
2
1
2
0
1
0
0
1
0
0
0
2
0
2
0
1
2
0
0
0
0
2
1
1
0
1
0
1
4
0
0
0
2
0
0
0
0
0
0
0
0
1
1
2
0
3
0
0
0
0
1
0
1
1
3
0
3
2
1
0
1
2
0
0
0
3
1
2
0
0
2
0
1
0
0
0
0
0
1
0
0
0
1
1
2
2
1
0
2
0
2
0
0
0
0
1
0
3
0
2
2
2
0
0
1
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
2
0
1
0
2
1
1
0
0
2
1
2
0
1
0
1
1
2
0
0
0
1
1
2
1
0
1
0
2
0
0
1
0
0
0
0
0
3
0
0
2
0
1
0
0
0
2
0
0
1
2
7
0
0
0
1
2
0
0
2
2
0
0
1
1
2
0
0
2
0
0
0
4
0
0
0
0
0
0
2
0
0
1
1
0
1
0
0
2
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
2
2
1
0
2
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
2
0
0
0
2
0
0
1
0
1
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
2
0
0
1
0
0
0
0
1
1
0
0
0
0
1
2
0
2
0
0
0
0
0
2
0
0
2
0
2
1
2
0
1
0
1
1
1
1
0
0
2
1
0
1
1
0
0
2
2
1
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
2
1
0
2
0
0
0
1
0
2
0
1
0
0
0
1
1
0
1
1
0
1
0
1
0
0
2
2
2
0
1
2
0
0
1
1
2
0
0
0
2
1
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
2
2
2
0
1
0
1
3
0
0
0
0
1
0
1
0
1
2
2
1
0
2
2
2
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
1
2
0
1
0
1
1
1
1
0
0
1
0
0
0
3
0
1
0
0
0
2
2
0
1
1
0
0
1
0
5
2
0
0
1
2
1
0
1
0
0
0
2
2
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
2
0
0
0
2
0
1
0
2
0
2
4
0
2
0
0
1
0
1
0
1
2
0
0
0
0
1
1
0
0
1
1
2
0
0
0
0
1
0
2
2
0
2
1
1
0
0
1
1
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
4
0
1
0
0
1
0
1
1
0
2
1
2
1
2
0
1
2
4
0
1
0
1
2
0
1
0
0
0
2
2
1
0
2
0
1
0
0
0
1
0
0
1
0
0
1
1
0
0
2
0
0
0
1
2
1
0
1
0
1
3
2
1
2
0
0
1
1
1
2
1
1
1
0
1
1
0
5
0
2
0
2
0
2
0
2
0
2
0
1
0
2
1
2
0
2
0
2
2
0
1
0
1
1
2
1
0
0
1
0
0
0
2
0
1
0
1
2
0
2
0
1
1
2
0
2
0
0
0
5
2
2
2
0
3
1
1
7
0
2
0
0
0
2
0
2
0
0
0
2
0
0
2
1
1
1
0
1
0
1
2
1
0
0
0
1
0
0
0
0
3
0
0
2
0
2
1
1
1
2
2
2
1
0
1
1
0
0
1
2
0
0
0
2
2
1
1
1
1
2
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
1
1
0
1
0
1
0
0
0
1
0
2
0
2
1
1
2
0
0
2
0
2
2
0
1
2
2
1
0
0
0
1
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
5
0
1
2
1
2
0
0
2
0
0
2
1
0
0
2
0
0
2
0
1
2
0
1
0
2
1
0
0
0
0
0
0
1
0
2
2
2
2
0
0
1
0
0
0
1
1
0
1
3
1
0
0
0
1
0
0
1
1
0
0
0
2
0
2
1
1
3
1
0
0
2
0
1
0
0
1
0
0
1
2
1
0
1
0
1
0
1
1
1
0
1
1
0
0
0
1
0
2
1
1
0
2
2
1
0
0
0
0
0
0
0
3
2
0
2
2
2
0
1
0
0
1
2
0
1
1
1
2
1
2
0
0
2
0
0
2
1
0
2
0
0
1
0
0
0
2
0
0
1
0
0
0
0
1
0
1
0
0
0
1
1
0
1
0
0
0
0
2
0
0
2
2
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
2
0
0
2
0
0
1
2
0
0
0
0
1
0
0
0
0
1
1
0
0
1
2
1
1
0
0
1
0
1
0
0
0
0
1
0
0
0
2
1
2
1
2
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
2
0
0
1
0
0
1
2
1
0
2
1
0
2
0
0
0
1
1
1
0
0
0
0
0
1
2
0
0
0
0
1
0
2
0
0
0
2
2
0
3
0
2
0
0
2
1
0
0
2
0
1
1
2
0
2
0
1
3
0
1
0
2
0
0
0
0
0
0
0
0
0
2
2
2
1
2
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
2
1
0
0
1
2
1
0
2
1
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
1
1
2
2
0
0
1
0
0
0
0
0
2
2
6
0
0
0
1
0
1
1
2
0
2
1
0
2
1
0
0
0
2
2
2
3
0
0
0
1
0
1
0
0
3
2
0
1
2
1
2
2
0
1
0
0
0
0
2
0
2
0
1
2
0
2
4
0
1
0
0
0
0
2
0
0
1
2
0
0
2
0
1
0
0
2
0
0
0
1
2
0
2
0
0
0
1
6
1
1
2
3
1
1
0
2
0
0
1
0
1
2
0
0
2
1
2
0
1
0
1
0
0
1
2
0
0
2
2
1
1
1
0
2
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
2
0
1
2
2
0
2
0
0
0
2
0
0
1
0
0
1
0
0
0
1
0
0
0
4
0
0
2
0
0
1
0
0
0
2
0
0
1
1
1
0
1
0
1
0
0
1
0
1
0
0
0
0
0
1
2
0
1
0
1
2
2
0
0
1
1
1
0
0
1
0
1
0
0
0
0
0
0
1
2
0
0
0
0
4
0
2
0
0
1
0
1
0
0
2
2
0
0
2
0
1
2
0
1
0
0
0
1
1
1
0
0
0
0
1
0
0
2
0
0
2
0
0
2
0
0
0
0
2
0
2
0
2
2
0
0
0
0
0
0
1
0
1
0
0
0
2
0
2
0
4
0
0
0
1
0
0
0
0
1
2
0
1
0
0
2
0
0
0
0
0
1
0
0
3
0
1
0
1
2
2
0
1
0
1
0
2
0
2
0
0
0
1
0
0
1
1
0
0
1
1
2
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
2
0
0
1
0
1
1
0
1
0
2
0
3
1
0
0
0
0
0
0
1
3
1
1
0
0
1
0
0
0
0
0
1
0
1
0
2
0
1
1
0
1
0
0
1
2
1
0
0
0
0
4
0
2
0
0
0
0
0
1
0
1
2
0
0
0
0
0
1
0
0
0
1
0
1
1
1
1
1
0
0
0
1
0
1
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
1
2
0
0
1
0
0
3
2
1
0
0
0
1
0
1
0
2
1
1
0
0
0
2
0
2
0
0
0
3
0
0
1
2
0
2
0
0
3
0
0
0
1
0
1
2
1
1
1
2
0
1
0
0
3
1
2
0
0
0
1
0
0
0
0
0
2
0
2
1
1
2
0
0
1
0
2
0
0
2
0
1
2
1
1
1
0
0
0
0
2
1
0
0
1
0
1
0
2
0
0
0
1
1
0
0
0
0
0
1
2
0
0
1
0
1
0
2
0
1
1
0
0
0
1
2
2
1
4
1
0
0
1
1
1
1
1
0
0
1
0
1
0
0
3
0
0
1
0
0
2
1
0
0
0
1
1
0
1
0
1
0
0
1
2
2
0
0
0
0
0
1
1
2
0
0
2
0
0
1
2
2
2
0
0
0
1
0
0
0
0
2
1
2
0
0
1
0
0
2
0
2
0
0
0
2
1
1
2
0
0
1
1
0
0
0
1
1
0
1
0
0
0
2
0
0
0
1
0
1
0
0
2
2
1
0
0
2
0
0
0
0
0
0
0
1
3
0
0
1
2
0
0
1
2
1
0
0
0
1
0
0
1
0
1
0
2
2
1
0
0
1
0
2
0
2
0
0
1
0
2
0
2
1
1
0
0
1
0
0
2
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
1
0
0
2
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
3
2
2
0
2
1
0
1
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
1
0
1
0
0
0
0
2
1
0
0
0
0
0
2
0
1
0
1
0
1
2
0
0
0
0
0
2
0
0
2
1
0
0
0
1
0
0
1
0
1
2
1
0
0
0
1
0
0
0
0
2
0
2
0
1
1
2
0
0
0
3
1
0
0
0
2
0
0
0
0
0
0
2
0
1
0
1
0
0
1
0
3
0
2
0
1
0
0
0
2
1
0
0
0
1
0
3
0
0
1
1
0
0
0
0
0
0
2
0
0
4
1
0
0
0
2
2
2
0
1
3
0
1
2
0
0
0
0
1
0
0
2
0
1
0
1
0
0
1
2
0
2
0
0
0
0
1
2
2
1
2
0
1
0
0
1
1
0
0
0
1
2
2
0
1
0
2
0
0
0
1
0
1
0
0
1
0
0
2
2
2
0
0
0
0
1
1
1
1
2
0
0
2
0
3
0
1
2
2
0
0
0
1
2
2
1
2
1
0
1
0
0
2
1
0
1
0
2
0
0
1
0
0
2
0
0
0
2
2
0
2
1
1
0
0
0
2
1
0
0
1
2
1
1
0
1
2
0
1
0
2
1
0
0
2
1
1
0
2
0
0
2
0
0
0
1
0
1
2
4
0
1
0
0
0
0
0
1
1
1
0
0
0
0
2
0
1
0
0
2
0
0
1
1
2
1
2
0
2
0
0
1
1
0
0
0
0
0
0
0
1
0
2
1
2
2
0
0
0
0
2
1
0
0
2
0
1
0
2
1
1
2
1
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
2
1
0
1
1
0
0
0
2
0
0
3
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
1
2
0
0
2
2
0
0
0
2
2
0
0
0
0
2
2
0
0
1
2
0
0
0
0
2
0
0
1
0
2
0
2
0
2
0
0
2
0
1
0
0
0
0
1
0
2
0
0
2
1
1
0
1
2
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
1
1
1
1
0
2
2
1
0
0
2
1
2
1
1
0
1
0
2
0
0
0
0
2
0
1
0
1
1
0
1
0
0
2
0
1
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
2
0
0
0
2
2
0
2
0
0
1
3
1
1
1
2
0
0
0
0
1
0
1
0
0
0
1
2
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
1
0
2
1
2
2
0
0
0
0
2
0
1
2
0
0
2
1
1
1
1
0
1
0
0
0
2
2
1
0
2
2
0
0
1
2
0
0
0
0
0
1
0
0
2
0
1
2
1
1
0
0
0
1
1
2
1
1
2
2
2
0
1
1
1
2
0
0
0
2
2
4
0
0
0
1
1
2
2
0
2
0
0
0
1
1
0
0
0
2
1
3
0
1
1
0
1
0
1
1
1
4
1
0
1
3
0
2
0
1
0
2
1
0
0
0
1
2
1
2
1
0
0
1
0
1
0
2
0
1
0
2
3
1
0
0
0
0
2
2
0
0
0
0
1
2
0
0
0
1
0
0
0
0
3
2
2
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
2
0
2
0
0
0
0
2
0
1
0
0
0
2
0
1
1
0
2
2
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
2
1
2
0
1
0
1
2
1
2
0
0
0
0
0
2
0
1
0
2
0
0
1
0
2
1
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
2
1
1
0
1
0
1
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
2
2
2
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
1
4
1
0
0
0
0
0
2
0
1
2
0
0
0
1
0
0
0
2
0
2
2
0
0
0
2
0
2
0
0
0
1
1
0
0
0
0
0
1
1
1
0
0
1
1
0
0
2
0
3
0
0
2
1
0
2
1
0
0
0
0
2
0
0
0
0
2
0
0
2
0
2
1
0
0
1
1
1
0
0
0
0
0
0
0
6
2
1
4
0
2
0
0
0
2
1
0
0
2
0
0
0
2
2
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
2
2
1
0
0
0
0
0
2
1
2
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
1
2
1
0
2
0
1
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
1
0
2
0
0
0
1
2
0
2
0
0
1
0
0
0
1
0
2
1
0
2
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
2
1
1
0
0
0
0
2
2
1
0
0
2
1
2
0
1
2
2
0
0
0
0
1
2
0
2
1
0
2
0
2
0
0
0
0
0
1
1
0
2
0
0
0
2
2
1
1
0
2
0
2
0
0
1
0
1
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
3
0
1
0
2
1
0
1
2
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
5
0
1
0
0
0
1
0
0
0
2
1
0
0
1
2
1
1
1
0
0
0
2
0
2
0
0
0
0
1
0
1
1
2
0
1
12
1
2
0
0
0
1
0
0
2
0
0
1
0
1
1
1
1
0
0
0
0
0
0
0
2
0
1
1
0
4
1
1
1
0
1
0
1
0
0
1
0
0
0
1
0
0
3
2
0
1
0
0
2
0
2
1
0
5
1
0
0
0
2
1
1
0
2
1
0
0
0
1
1
1
1
0
1
1
2
0
0
0
0
1
0
0
0
0
2
1
0
0
0
2
2
0
1
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
1
0
2
1
2
2
0
0
0
0
1
0
0
0
0
0
1
2
3
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
3
0
1
1
0
0
1
2
1
1
0
0
1
0
0
1
0
2
0
0
1
1
0
2
1
1
0
2
0
0
1
0
0
0
2
0
0
4
0
0
0
2
0
1
1
2
0
0
0
1
0
0
0
0
1
1
2
0
1
2
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
8
0
0
0
0
0
0
1
0
0
2
1
1
0
0
0
0
1
0
2
2
0
2
0
1
2
3
0
0
2
1
0
0
2
0
1
1
0
0
1
0
1
0
0
1
0
0
0
0
0
1
1
0
1
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
2
1
0
0
0
0
2
0
1
0
2
1
0
0
0
0
0
0
1
0
2
0
1
0
0
1
2
1
2
0
0
0
1
2
0
2
0
0
0
0
0
2
1
2
1
2
2
3
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
1
5
0
0
0
0
0
1
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
2
3
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
1
0
0
0
2
0
0
0
0
1
1
0
2
0
2
0
0
0
0
0
2
2
0
0
0
1
2
2
0
0
0
1
2
0
1
0
0
0
0
1
1
0
0
2
0
1
2
1
1
1
2
0
1
0
0
1
0
2
0
1
0
2
0
1
0
0
0
0
0
1
0
0
2
2
2
1
0
0
1
0
2
0
0
0
0
2
1
0
2
0
0
0
2
0
2
2
0
1
0
0
1
1
0
0
1
0
2
0
0
1
1
0
1
0
2
2
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
1
2
1
1
0
0
2
0
2
2
0
1
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
1
2
0
2
1
0
0
2
0
0
1
2
0
0
1
0
1
2
2
0
0
3
0
1
0
0
0
2
0
1
1
0
0
0
2
1
0
0
0
1
2
2
0
0
1
0
2
0
2
0
0
2
1
1
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
3
0
1
2
0
0
1
1
0
0
0
1
0
2
0
0
0
0
3
0
3
0
2
3
0
0
1
0
0
1
0
0
2
0
2
1
0
2
0
0
0
0
0
2
0
1
0
0
2
0
1
0
0
2
1
0
1
0
0
1
2
0
1
0
1
0
0
2
0
1
1
3
0
0
0
0
0
1
1
0
2
2
0
2
1
1
2
2
0
2
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
2
0
1
1
1
2
2
2
0
2
0
1
0
3
1
0
0
0
1
2
3
1
1
2
0
1
0
1
0
0
1
0
1
0
2
0
0
0
1
0
0
0
2
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
2
0
1
2
1
0
0
0
3
0
0
1
2
1
0
0
0
1
0
1
2
1
1
0
2
0
2
1
0
2
0
1
0
1
0
1
0
0
2
0
0
0
0
1
1
1
0
1
1
1
1
0
3
0
0
0
2
0
2
0
2
2
0
0
0
0
0
0
0
16
2
1
0
2
2
0
0
0
0
0
1
1
1
1
2
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
1
0
0
2
0
1
1
0
1
0
1
1
0
0
2
0
2
0
0
0
0
1
2
1
2
0
0
4
1
0
0
3
0
1
1
2
3
3
0
1
0
2
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
1
0
1
0
1
0
0
2
2
0
0
1
0
1
0
0
0
0
1
0
1
0
2
1
1
0
2
0
2
2
1
0
0
0
0
2
1
2
1
0
1
1
0
1
0
0
2
0
0
2
0
0
0
1
0
0
1
1
0
0
1
0
1
2
1
0
0
0
2
2
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
2
1
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
1
1
0
2
0
1
1
2
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
2
1
0
0
2
0
1
1
0
0
0
1
2
2
0
3
2
1
4
0
7
0
2
0
0
0
2
2
3
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
1
2
1
1
0
0
2
2
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
2
0
1
0
0
0
0
0
2
2
0
2
0
1
0
0
1
1
1
0
2
2
0
0
0
0
0
2
1
1
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
1
2
0
1
2
0
3
1
2
0
0
0
2
0
2
1
1
0
0
1
0
1
1
1
2
0
2
0
0
0
2
2
3
0
0
0
0
0
2
0
2
0
1
0
0
1
0
0
0
1
1
0
0
1
0
1
1
0
0
1
0
1
1
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
1
0
1
0
2
0
0
0
0
2
0
2
0
2
2
0
0
0
2
0
0
2
2
1
0
0
0
1
0
0
0
1
0
1
0
0
1
2
0
2
2
0
0
0
1
1
0
0
0
0
0
0
0
2
0
3
0
1
0
2
3
0
0
2
1
1
0
0
0
0
1
2
0
0
1
0
2
0
1
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
1
1
0
1
0
0
1
2
2
0
0
1
0
1
0
0
0
1
0
0
0
0
2
2
1
0
0
0
2
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
2
0
0
0
1
0
2
1
0
0
1
0
1
0
0
2
0
0
1
2
2
0
2
0
2
2
1
1
1
0
0
0
0
0
0
2
0
0
1
0
2
2
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
1
0
0
1
0
0
2
0
2
0
0
1
1
0
1
0
0
1
0
1
1
0
1
0
0
0
0
0
0
2
2
2
0
0
1
1
1
0
0
1
0
1
0
0
1
2
0
2
0
0
0
0
0
0
2
0
2
1
1
0
1
2
0
1
1
2
0
0
2
1
1
1
0
0
1
0
2
0
0
0
0
2
1
2
2
1
0
0
0
0
0
1
1
1
1
0
3
0
0
0
0
1
2
0
2
0
0
0
1
8
1
1
0
0
1
0
2
2
0
2
0
2
2
0
0
0
1
2
1
1
0
1
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
3
1
1
0
0
2
2
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
2
2
1
0
1
0
0
1
2
0
3
2
0
0
0
2
2
0
0
0
2
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
1
0
2
3
0
1
1
0
2
2
0
0
2
1
1
2
0
0
2
0
0
2
0
1
0
0
1
0
0
0
1
1
0
0
0
0
2
2
0
0
0
0
0
1
0
0
2
0
2
0
1
0
1
0
2
0
2
1
0
0
0
2
0
0
0
0
0
0
0
2
2
1
0
1
0
0
1
2
1
0
2
3
0
0
0
0
1
2
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
1
0
2
0
4
0
1
3
1
0
1
1
1
0
1
1
0
2
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
2
0
1
0
2
1
2
0
0
1
0
1
0
0
0
2
0
2
2
1
1
0
0
1
1
0
0
2
2
1
1
0
0
1
0
1
2
1
0
0
2
0
0
0
3
1
0
1
0
0
0
0
2
1
0
0
0
0
1
0
0
0
3
0
0
0
1
0
0
0
1
1
1
0
0
2
2
2
0
1
0
0
1
2
1
2
0
2
0
0
0
1
2
0
0
2
0
1
2
2
1
2
1
2
1
3
0
0
0
0
1
0
2
0
0
0
3
1
0
0
0
0
0
0
0
2
2
1
0
2
0
0
0
1
2
0
0
0
0
0
0
0
1
2
0
2
0
1
1
1
2
0
2
1
0
0
2
0
0
0
2
0
2
0
1
2
0
0
0
0
3
0
0
1
0
2
0
0
1
2
0
0
0
0
0
1
0
1
0
0
1
2
0
2
0
0
0
0
1
0
2
1
0
1
1
0
0
0
1
0
0
0
1
1
1
2
0
2
0
1
1
0
1
0
1
2
0
0
1
0
1
2
0
0
0
2
3
0
2
1
1
2
0
2
0
1
0
2
1
2
2
0
0
1
0
0
0
0
0
0
2
0
0
1
0
1
2
0
2
0
0
3
0
0
0
0
0
2
0
0
0
7
1
1
1
0
0
0
0
0
3
2
0
0
0
3
0
0
0
0
0
0
0
0
0
1
1
0
1
2
2
0
0
0
1
2
0
0
1
0
0
0
1
1
0
0
0
0
1
0
4
2
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
1
1
0
0
2
0
1
1
0
2
1
0
0
0
0
0
0
2
0
1
1
1
1
0
0
1
1
13
1
0
2
2
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
2
1
1
0
1
0
1
0
1
0
1
0
1
0
0
0
2
1
0
1
0
1
2
1
1
0
1
4
0
2
0
0
0
1
0
1
0
0
0
0
2
0
2
2
0
2
0
1
0
0
0
0
2
0
0
0
1
0
1
0
2
0
1
0
2
0
0
0
0
0
0
1
2
0
1
1
1
0
0
1
1
2
1
0
1
0
0
3
2
0
0
1
0
1
0
0
0
1
2
0
2
0
0
2
0
1
2
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
2
0
3
1
0
1
0
2
0
0
2
2
0
0
0
0
0
3
0
2
0
2
1
2
0
2
0
0
2
3
0
1
2
0
0
4
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
2
2
2
0
1
0
0
0
2
2
2
0
0
1
2
1
2
1
1
2
1
0
1
1
1
0
1
2
0
0
2
1
0
0
0
0
1
0
1
1
0
1
0
0
0
1
0
0
0
2
0
0
1
1
1
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
2
1
1
1
1
0
1
0
0
0
1
1
2
1
0
3
1
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
1
2
1
1
0
0
1
0
2
0
1
0
1
0
0
0
2
1
0
0
0
0
0
1
0
2
0
0
1
2
0
0
2
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
1
2
0
0
0
1
1
1
0
0
0
0
2
0
1
1
1
0
0
0
0
0
2
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
1
3
0
3
1
0
0
0
2
2
2
3
0
1
0
1
1
2
0
2
0
0
0
0
1
2
1
0
2
1
0
0
0
2
0
1
2
1
0
0
2
0
0
1
0
0
2
0
0
1
0
0
2
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
1
2
3
2
0
0
0
2
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
1
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
2
2
0
2
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
2
1
1
0
0
0
1
2
0
1
0
0
2
0
0
2
0
0
0
2
0
0
0
1
1
2
0
1
0
2
0
0
0
2
1
0
1
0
0
1
1
0
1
1
0
0
0
0
0
2
4
0
0
0
0
3
1
0
0
0
0
2
0
2
0
0
0
2
0
2
0
1
1
1
0
0
2
0
0
0
1
0
2
0
2
0
1
1
0
0
0
2
2
0
1
0
0
2
1
1
1
0
0
0
0
1
0
1
0
0
0
0
1
2
1
0
0
4
1
2
0
0
1
2
2
0
1
1
0
0
0
1
1
0
2
1
0
0
2
0
2
1
0
1
0
0
0
1
0
1
1
0
1
2
2
0
1
1
0
1
0
2
0
0
1
0
0
2
1
0
0
0
1
0
0
1
2
0
1
1
1
1
0
3
0
0
1
1
0
0
1
3
1
0
0
0
0
0
0
0
0
1
2
0
0
2
3
0
0
2
0
1
2
1
1
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
2
1
0
3
2
0
0
0
0
0
1
2
0
2
0
1
0
0
0
0
0
3
0
1
0
1
2
0
0
1
0
0
2
0
0
2
0
0
2
2
2
1
0
0
2
0
0
1
0
1
3
0
0
2
1
0
0
1
4
1
0
3
0
0
0
0
1
0
0
1
0
1
2
0
0
1
1
0
2
0
1
2
0
2
2
0
0
1
0
0
1
1
0
0
0
0
2
0
2
1
0
0
0
2
2
1
0
0
1
0
0
2
0
0
4
2
0
0
0
0
2
0
2
0
3
0
1
0
1
0
2
0
1
0
0
0
0
2
0
1
0
2
0
0
0
0
1
1
0
2
0
0
0
0
1
1
0
1
2
0
2
0
2
0
2
2
1
1
1
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
2
2
0
1
0
0
0
0
2
1
0
2
0
0
1
2
0
0
0
0
2
0
0
1
0
0
0
2
0
1
1
0
0
2
2
1
0
0
0
2
0
1
0
0
0
1
1
0
1
0
1
0
0
0
0
1
0
2
2
2
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
1
0
1
0
0
2
1
2
0
0
0
6
0
0
0
2
4
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
1
0
3
0
1
0
2
0
0
1
0
2
0
0
2
2
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
1
0
0
0
1
0
0
0
0
0
0
1
2
0
0
1
0
1
2
3
1
0
2
0
2
0
6
0
1
0
1
1
0
1
1
2
1
1
0
1
0
0
0
0
2
0
1
0
0
2
2
0
0
0
0
1
0
1
2
2
0
0
0
0
0
2
2
0
0
0
0
1
2
0
1
0
0
0
0
0
0
1
1
0
1
1
0
2
0
0
2
2
0
1
1
0
0
0
1
4
1
3
0
1
1
1
1
1
0
0
0
0
0
2
2
1
1
0
2
0
2
0
0
0
0
0
0
2
2
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
3
1
0
2
1
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
2
2
0
0
0
2
1
0
1
2
1
0
0
0
0
2
2
1
0
0
0
0
6
2
0
1
0
2
0
1
0
1
1
0
0
2
2
0
0
3
0
0
0
0
2
0
0
1
0
2
1
0
0
0
1
0
0
1
0
0
0
0
2
2
0
0
1
0
0
0
0
2
0
0
0
0
1
2
0
1
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
2
0
2
1
3
0
0
2
0
0
3
0
0
0
0
0
2
1
0
0
1
1
0
0
0
0
0
1
2
0
1
0
1
1
0
0
0
0
1
1
2
0
1
0
1
1
2
0
0
1
0
0
3
0
1
1
1
0
1
1
0
0
0
0
1
0
1
0
1
2
0
2
0
1
2
0
2
2
0
1
0
2
0
1
3
2
3
0
0
1
1
0
0
0
2
0
0
1
0
2
1
2
1
0
0
2
0
0
1
0
1
0
0
0
2
0
0
0
2
2
0
0
1
2
1
2
0
0
0
2
1
1
2
1
2
1
0
1
2
3
0
0
0
2
0
1
0
1
1
0
1
0
2
3
0
0
0
2
2
0
0
0
0
1
0
0
1
0
0
0
2
0
1
2
0
3
0
0
1
1
1
1
0
1
0
0
0
0
1
0
0
0
1
0
1
0
2
0
3
0
0
0
0
1
0
1
0
2
2
1
0
0
0
0
0
0
0
1
0
1
0
1
0
2
2
0
1
0
0
1
0
0
3
0
1
0
1
1
0
0
0
2
1
5
0
0
0
0
1
0
0
1
0
0
0
1
3
2
1
0
0
1
3
2
3
0
0
0
0
0
1
2
2
1
0
0
1
0
0
0
2
0
0
0
0
2
1
2
0
0
3
0
2
2
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
2
0
1
0
0
0
0
0
2
2
4
1
0
0
1
1
2
0
0
2
2
0
2
1
0
0
1
1
0
1
2
0
1
2
0
0
0
1
2
1
0
3
0
2
0
1
0
3
2
0
1
0
1
0
1
1
0
0
3
0
2
2
0
0
1
0
2
1
0
0
1
1
0
0
0
0
2
0
0
1
0
0
8
1
1
0
0
2
1
1
0
1
2
0
2
1
0
0
0
0
0
0
2
0
1
0
2
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
1
0
0
0
2
0
0
0
2
0
0
0
1
2
0
0
2
0
1
0
2
3
1
1
2
2
2
0
1
0
0
0
0
0
0
1
0
0
1
0
2
0
1
1
1
2
1
0
0
0
1
2
0
0
0
2
1
0
1
2
0
0
1
2
0
1
1
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
3
1
0
1
2
1
0
0
2
0
2
0
0
1
1
0
0
0
0
0
0
2
0
1
0
2
2
0
2
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
2
0
1
0
0
0
1
0
2
1
1
0
0
0
1
0
0
0
1
2
1
2
0
1
0
1
1
0
0
0
0
0
1
1
0
0
0
0
2
0
1
1
1
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
2
1
2
2
0
1
0
2
0
2
0
0
0
0
0
1
2
0
0
0
2
2
0
0
1
0
1
1
1
1
0
1
2
0
1
1
0
0
0
0
0
0
0
2
0
2
0
1
1
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
1
2
0
1
2
2
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
1
0
0
3
0
0
1
0
0
0
0
2
0
2
0
0
1
2
1
0
0
0
0
1
0
1
2
3
0
0
2
1
2
1
0
0
0
0
0
2
0
0
2
2
1
0
1
1
0
0
1
0
5
2
0
0
1
2
0
0
0
1
0
0
1
1
2
2
0
4
2
0
0
0
0
2
2
2
0
2
0
1
1
3
0
0
1
0
1
1
1
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
1
2
3
0
1
0
2
0
2
0
0
0
0
1
0
0
2
1
2
0
2
1
0
0
0
0
0
0
1
1
1
0
0
2
0
2
0
1
2
0
0
3
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
2
0
1
0
0
0
1
2
0
0
2
1
0
0
1
2
0
1
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
1
0
0
0
0
0
1
0
0
0
1
2
0
1
0
1
0
0
0
2
0
0
1
1
2
1
0
0
2
0
2
2
0
0
2
1
2
2
2
0
0
1
0
0
0
0
2
2
0
0
0
2
2
0
2
0
0
2
0
0
3
1
0
1
3
0
0
0
0
1
0
4
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
1
2
0
0
0
0
1
0
1
0
0
0
0
1
2
0
0
0
0
0
0
2
0
1
0
0
5
3
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
2
1
2
0
2
0
0
1
0
0
0
0
0
1
2
1
0
1
2
1
0
1
0
1
2
1
0
0
0
0
1
0
0
0
2
0
0
1
1
1
0
2
0
0
0
0
2
0
2
2
0
0
2
0
0
2
2
1
1
0
2
2
2
0
1
2
0
0
1
2
1
0
0
2
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
2
2
0
0
1
1
0
2
1
0
1
0
0
1
1
0
0
0
2
0
4
0
1
1
0
0
1
1
1
0
0
0
0
2
1
0
1
1
0
3
1
1
0
2
2
1
3
1
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
1
2
0
0
1
0
1
1
1
0
0
0
0
0
0
0
1
2
3
1
0
0
0
3
0
0
0
1
0
0
1
0
2
0
2
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
2
2
0
0
0
2
0
0
0
0
2
0
1
0
0
1
0
0
1
0
0
1
0
3
0
1
0
0
2
1
1
2
0
2
0
3
0
1
0
0
1
0
2
0
0
0
2
0
0
0
0
1
1
0
0
0
2
2
1
2
0
1
0
0
1
2
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
3
2
0
0
0
1
2
1
8
0
2
1
0
0
1
1
0
2
2
0
1
0
0
0
1
0
0
0
0
2
1
2
2
0
0
0
1
0
0
2
2
0
0
1
1
0
0
2
2
0
2
1
2
2
0
0
1
0
0
2
0
1
0
0
0
1
1
1
0
2
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
3
0
2
0
0
0
0
0
0
0
1
0
2
2
1
0
1
0
1
0
2
1
0
0
0
1
0
0
0
2
0
2
1
1
0
0
0
1
1
2
0
0
0
0
0
1
2
0
1
1
0
2
0
1
0
1
0
0
2
0
0
1
0
1
0
0
0
0
2
2
0
0
2
2
0
2
1
2
0
1
0
0
2
1
0
1
1
2
1
1
1
0
0
0
0
0
0
0
1
2
1
1
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
1
2
1
1
1
0
2
0
2
2
0
0
0
0
0
1
2
0
0
0
0
2
1
0
0
1
1
0
1
0
1
0
1
0
1
0
0
0
0
0
2
0
2
2
0
0
0
1
3
0
1
0
0
3
0
0
1
0
0
2
1
0
2
1
1
0
0
0
2
0
2
0
0
1
1
1
1
0
2
0
0
1
2
0
2
0
2
1
2
2
0
0
0
0
2
2
1
0
0
0
0
1
0
3
1
0
0
3
0
0
0
0
1
0
1
1
0
1
0
0
1
0
1
0
3
0
0
0
1
0
1
0
0
1
0
0
1
0
2
1
0
2
1
2
0
2
1
2
0
1
0
1
1
1
0
2
1
3
0
1
0
1
0
0
0
2
0
1
2
0
2
0
1
1
0
0
0
0
0
0
0
0
2
2
0
0
1
1
0
0
0
0
0
1
0
2
0
0
2
1
1
0
0
0
1
1
0
0
1
0
0
2
0
1
0
1
1
2
0
1
0
0
1
0
0
1
0
0
2
0
0
1
0
2
0
0
2
1
0
0
0
0
2
1
0
3
2
0
2
1
0
0
0
2
0
1
0
0
0
2
2
0
1
2
1
1
0
2
0
0
0
0
0
2
2
1
1
0
0
2
0
3
0
2
0
0
1
1
0
1
2
1
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
1
0
1
7
2
2
4
2
0
2
1
1
0
0
0
2
0
0
1
2
0
0
0
0
1
2
0
2
1
0
0
1
1
1
2
2
2
0
0
1
0
1
0
0
2
1
1
2
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
1
1
0
0
2
3
0
1
1
0
0
0
2
0
0
0
1
2
1
0
0
1
2
0
0
0
0
1
2
0
2
0
1
2
0
1
0
0
0
1
0
0
1
1
1
0
0
2
2
1
0
1
0
1
0
0
2
0
0
1
2
0
1
0
0
0
0
1
1
0
0
2
1
2
0
0
2
0
0
0
0
1
2
1
0
2
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
2
0
1
2
0
2
2
1
0
1
1
1
0
2
2
0
0
2
2
0
1
2
0
0
0
1
0
0
0
0
0
0
1
0
2
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
2
0
0
0
1
0
1
2
1
2
0
2
0
0
1
0
0
0
0
0
0
0
0
1
1
2
0
0
7
0
1
1
0
1
0
0
2
0
0
1
0
1
0
0
1
1
1
1
0
1
0
0
3
2
1
0
0
1
0
1
0
0
1
2
2
0
0
0
0
2
2
2
1
1
0
0
0
0
0
2
0
0
1
0
0
0
2
2
1
2
0
0
2
0
0
0
2
0
0
0
2
1
2
0
2
2
0
0
2
2
2
2
1
4
0
0
1
1
2
0
2
0
0
0
2
1
2
1
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
2
1
0
3
0
0
0
0
0
0
1
0
1
0
0
2
0
1
0
0
0
0
2
0
2
0
0
0
0
2
1
0
0
0
2
0
0
0
0
1
0
1
1
0
0
1
1
1
0
0
0
0
1
0
0
1
2
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
4
1
1
0
0
0
1
0
0
0
2
2
1
0
1
0
0
2
0
1
2
1
0
0
0
0
0
1
0
0
0
2
2
1
2
0
1
0
0
0
2
0
0
2
2
1
0
0
2
2
0
2
0
0
0
1
0
2
0
0
2
2
2
1
0
3
0
0
0
2
3
0
0
1
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
2
0
1
1
2
2
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
2
0
0
2
0
1
2
1
1
1
0
2
0
1
0
0
0
2
0
2
1
1
1
1
1
0
2
0
1
0
0
0
2
1
2
0
2
1
0
0
2
2
0
2
2
0
1
0
0
0
1
0
0
0
2
0
0
1
0
3
2
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
1
2
0
0
0
2
1
0
2
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
5
1
0
2
0
3
0
0
2
2
2
1
0
0
0
0
1
0
2
1
0
0
0
2
1
0
0
0
1
2
0
2
1
1
1
0
0
2
0
0
0
0
1
2
0
1
0
1
0
0
0
2
0
2
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
2
0
2
0
0
0
0
2
0
0
0
2
0
2
2
1
0
0
0
1
0
0
1
0
2
2
2
2
0
0
1
2
0
2
1
0
0
0
1
1
0
2
0
0
0
0
0
1
1
0
2
0
2
0
2
0
0
1
2
0
0
0
0
1
1
2
0
0
0
0
1
2
0
0
0
0
0
0
6
0
0
1
0
0
0
0
0
0
1
2
0
0
0
2
0
0
1
0
0
1
0
0
2
2
3
0
0
0
1
0
1
0
2
0
1
0
1
2
2
1
2
2
0
1
0
1
0
1
0
1
0
0
2
0
1
1
0
2
1
1
0
1
0
1
0
0
0
1
0
0
0
0
0
2
1
0
0
1
0
2
0
0
0
0
0
1
0
3
1
0
0
1
1
2
0
1
2
0
0
1
0
1
0
2
0
0
0
1
1
0
1
0
0
1
0
2
1
0
2
0
1
0
0
0
0
1
0
1
1
0
0
1
0
0
1
0
0
2
0
0
0
0
1
2
0
0
0
1
0
0
1
0
0
1
0
0
1
2
3
0
2
1
0
0
0
2
1
0
1
0
0
1
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
1
2
0
1
2
0
0
0
0
1
2
1
0
0
0
0
1
0
0
0
2
0
1
0
0
2
1
0
2
0
2
1
2
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
3
0
2
0
0
0
0
0
1
0
1
1
2
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
2
2
0
1
1
1
2
0
0
0
1
0
1
2
0
0
0
0
0
0
1
0
0
1
2
0
0
0
1
0
0
0
0
0
1
2
2
1
1
1
1
0
0
2
1
0
2
0
0
2
2
2
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
1
1
0
1
1
1
0
0
0
1
2
0
1
0
0
0
1
1
0
0
0
1
2
0
2
0
0
0
0
0
0
2
2
2
2
0
2
0
1
1
0
0
0
2
1
2
1
0
0
0
0
0
0
1
0
0
1
1
1
2
0
0
1
2
0
0
2
0
0
0
1
0
0
2
0
3
0
0
2
2
2
0
2
0
0
0
0
0
0
0
0
3
0
1
0
0
4
0
0
0
2
0
0
0
0
2
0
1
0
2
0
0
1
2
0
1
2
1
0
2
0
3
2
0
0
1
2
0
4
1
0
0
2
1
2
3
0
0
2
0
0
1
0
2
0
0
0
1
2
0
2
0
0
0
2
1
0
0
0
0
0
0
4
1
3
0
2
0
1
1
0
0
0
0
1
0
0
2
2
1
2
0
0
0
1
2
2
1
1
2
2
0
0
0
0
0
1
0
2
2
2
0
0
1
1
0
1
4
0
2
0
1
1
0
1
0
1
2
0
0
1
0
0
0
2
0
2
0
0
2
0
1
2
1
0
0
0
2
0
2
0
2
0
2
0
0
0
2
1
0
0
0
2
0
0
0
2
2
0
0
0
0
1
0
1
1
0
0
2
0
0
0
0
2
2
2
0
0
1
3
2
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
2
2
0
1
0
2
2
1
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
2
1
0
2
1
1
0
0
1
0
1
2
1
1
0
1
0
0
0
1
0
1
1
0
0
2
0
2
2
1
0
0
0
0
1
2
1
0
1
1
0
0
0
2
8
2
2
0
0
1
0
1
1
2
2
0
1
0
0
2
0
1
1
1
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
1
0
0
1
0
0
0
0
2
0
0
2
0
0
0
2
0
1
2
2
0
0
0
2
0
0
0
1
2
0
2
0
0
1
1
0
2
0
1
1
1
1
0
2
0
2
0
0
0
0
1
1
1
1
0
1
0
1
2
2
2
0
1
2
2
2
2
0
0
0
0
0
1
2
0
2
0
0
2
0
0
2
2
0
1
0
0
0
0
1
0
2
0
1
1
0
0
1
0
0
2
0
0
0
2
0
0
0
2
0
1
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
2
1
1
0
2
0
2
0
0
0
0
3
0
0
0
1
0
0
1
0
0
2
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
2
0
2
1
0
2
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
1
2
1
0
2
0
2
2
0
2
0
0
0
0
0
1
1
2
2
0
2
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
1
2
0
2
2
0
1
1
2
0
0
0
0
1
0
1
1
1
1
0
0
0
0
0
1
0
0
0
0
1
1
2
1
0
0
0
1
0
0
0
2
1
0
0
0
1
2
0
2
2
1
0
2
0
0
0
0
0
0
1
0
0
2
1
0
1
0
0
0
0
0
0
1
0
0
4
0
1
2
0
0
0
0
1
0
1
0
0
1
0
0
0
0
2
0
0
0
0
2
2
2
1
1
1
1
0
1
0
2
0
0
0
1
1
0
1
1
0
0
1
2
0
2
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
2
0
0
1
1
1
1
0
1
0
0
2
1
0
0
2
1
0
0
2
1
0
1
0
2
0
0
0
0
0
1
0
2
2
1
0
1
0
0
0
1
0
0
1
0
1
1
0
0
2
2
0
1
0
1
0
0
3
0
1
1
1
0
0
0
1
1
1
2
1
0
1
1
0
0
0
1
1
0
0
0
2
2
0
1
0
0
0
1
2
0
2
1
0
1
0
0
0
1
0
0
1
0
2
2
0
1
0
2
0
0
1
2
2
2
1
0
0
1
0
0
0
0
1
0
2
2
1
2
0
1
0
2
1
0
0
2
0
0
0
0
0
2
0
0
0
0
1
2
0
0
2
2
0
2
0
0
1
2
0
0
0
1
1
4
1
2
0
2
1
2
1
0
0
1
3
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
1
1
0
2
2
0
0
0
0
0
0
2
1
0
0
1
3
0
2
0
1
0
0
0
1
0
0
0
1
2
1
2
0
0
0
0
2
0
1
0
0
1
0
2
3
2
0
0
0
1
0
0
0
0
1
0
0
2
0
0
2
0
0
0
1
0
0
0
0
2
1
2
2
2
0
0
0
1
2
2
0
2
0
2
1
0
0
2
0
1
1
1
2
1
0
1
0
0
2
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
1
3
0
4
0
1
0
2
1
1
2
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
1
0
0
0
1
1
2
2
1
1
2
0
0
1
1
0
0
3
0
0
0
0
3
3
2
2
0
0
0
2
1
1
1
0
2
0
0
0
2
1
1
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
2
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
1
0
1
2
0
2
1
1
1
0
0
0
2
1
1
0
0
0
1
1
0
0
1
1
0
0
0
1
0
2
0
2
0
0
0
2
0
1
1
2
0
0
0
1
0
0
2
1
0
2
1
0
2
0
0
1
0
5
0
0
1
0
0
2
1
2
0
2
2
0
0
0
0
0
0
1
2
2
1
0
0
1
0
1
1
0
0
2
0
0
2
2
1
0
0
0
1
2
0
0
0
0
0
1
1
0
0
1
2
1
2
2
1
2
2
0
0
0
0
0
0
1
1
1
3
0
1
0
1
1
0
1
0
0
0
0
2
3
0
0
0
0
0
1
2
0
2
2
0
1
0
0
0
2
1
0
0
1
0
0
2
2
0
1
0
0
2
0
1
1
0
2
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
2
2
2
0
0
0
0
2
0
0
1
2
0
0
2
1
1
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
2
0
0
0
3
0
1
0
0
0
0
0
0
1
0
1
1
2
0
0
2
1
0
0
2
1
1
0
0
0
0
1
1
0
2
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
1
2
0
0
1
0
2
0
2
0
0
0
0
2
1
0
0
0
0
1
0
1
0
2
0
0
2
0
2
0
1
0
3
2
0
0
1
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
2
2
0
1
0
0
0
1
0
0
2
0
1
0
0
0
0
0
1
2
3
1
0
0
0
4
2
0
0
1
2
1
0
0
0
0
0
1
0
1
1
1
0
0
2
1
0
0
2
0
1
0
3
0
0
0
0
0
0
0
1
2
2
0
0
2
2
0
1
0
0
2
0
2
1
0
2
1
1
0
0
0
1
0
0
1
2
0
0
0
0
1
2
1
0
1
1
0
0
1
1
0
0
0
1
1
0
2
0
0
1
0
0
0
2
0
0
0
1
2
0
0
0
0
1
0
0
1
0
0
0
0
1
3
0
0
0
3
1
3
0
1
0
1
0
0
1
2
0
1
2
0
2
0
0
0
0
0
2
3
0
2
0
0
0
0
2
0
0
2
0
1
0
0
2
2
2
2
0
0
0
0
1
0
0
1
1
0
0
0
1
0
1
0
1
0
0
1
2
0
3
0
1
0
0
1
2
1
0
0
2
2
0
0
0
0
0
1
0
1
3
1
2
0
2
0
0
0
1
1
0
1
0
0
2
0
0
1
2
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
2
0
0
0
0
1
0
2
2
0
1
0
0
0
2
0
0
1
0
1
0
2
0
0
2
0
1
0
1
0
0
0
0
1
2
1
0
1
0
0
1
2
0
1
1
0
1
1
0
2
2
0
0
0
0
1
0
0
2
1
1
1
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
2
0
0
0
1
0
1
1
1
0
1
0
0
0
0
4
2
0
5
1
0
2
1
0
2
0
1
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
3
0
1
0
0
2
0
3
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
2
0
1
0
0
0
1
0
2
0
0
0
2
1
0
0
0
0
0
0
1
2
0
1
2
2
1
0
1
0
1
0
0
2
1
0
1
0
1
0
0
0
0
1
0
2
0
0
0
0
2
0
1
0
2
0
0
0
0
0
2
0
1
0
2
3
0
0
0
1
2
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
1
2
1
1
0
0
2
2
0
2
2
0
0
0
0
2
0
2
1
0
1
0
0
0
0
0
0
2
1
0
0
0
0
1
2
0
0
0
1
0
1
0
1
0
0
1
1
0
0
0
1
2
0
0
1
0
1
0
0
0
0
1
0
0
0
1
2
1
0
0
0
0
1
2
3
0
2
2
0
0
0
0
0
0
2
2
0
1
0
0
2
0
0
1
1
0
0
0
1
0
1
1
0
0
0
1
2
1
2
1
2
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
1
0
1
1
2
2
1
0
1
0
0
2
2
2
1
1
0
0
2
2
2
0
2
2
0
0
0
1
2
0
1
0
1
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
1
2
1
2
0
0
3
0
0
1
0
0
1
1
0
0
0
0
0
3
1
0
1
0
0
1
0
0
1
1
2
0
0
2
2
0
0
0
2
2
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
2
0
1
0
1
2
1
2
0
2
2
0
0
0
0
0
1
1
1
1
0
0
0
0
0
2
1
0
1
1
0
0
0
2
0
0
2
2
0
0
1
0
1
0
2
0
2
2
0
0
0
0
0
2
0
1
1
0
0
1
0
0
0
3
1
2
0
0
1
0
0
0
1
0
0
1
1
0
3
0
0
0
1
1
0
1
2
2
0
0
0
0
2
1
2
2
0
0
0
2
0
1
1
1
2
1
1
0
0
1
0
1
2
0
0
0
0
0
0
3
2
0
1
0
3
1
1
0
0
0
2
1
0
0
1
0
0
1
2
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
2
2
0
1
2
2
0
0
0
5
0
0
0
0
1
1
0
0
1
0
2
0
0
0
2
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
2
0
1
2
1
1
0
0
0
0
0
2
0
0
2
1
0
0
0
1
2
0
2
0
2
2
1
0
0
0
0
0
2
1
0
0
3
0
0
0
0
1
0
0
0
0
1
0
0
2
1
1
1
0
3
0
0
2
1
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
1
0
1
0
0
0
2
1
0
0
2
0
1
0
0
0
0
1
2
2
0
2
0
0
0
0
2
0
0
0
0
4
1
1
0
0
0
1
2
1
0
2
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
2
0
0
0
2
2
0
1
0
1
0
2
2
0
0
0
0
0
0
3
0
0
2
1
0
0
0
1
0
0
2
2
0
0
0
0
0
1
2
0
1
0
1
0
2
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
2
0
1
1
1
2
2
0
0
0
0
1
0
2
2
0
0
0
0
0
1
2
1
2
0
0
2
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
1
2
0
0
1
0
0
0
0
0
2
2
1
2
1
2
0
0
3
1
0
0
1
0
0
0
0
3
0
2
2
1
2
1
1
1
0
1
1
2
1
0
1
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
2
2
1
1
1
0
2
0
1
0
1
0
0
0
1
1
0
1
0
2
0
2
0
0
1
2
0
0
0
0
1
0
0
1
0
0
2
2
0
0
1
0
0
0
2
2
0
0
3
0
1
0
0
0
0
1
0
2
0
0
0
0
1
0
1
2
3
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
7
1
0
0
1
2
2
0
0
0
2
0
1
0
0
0
5
1
1
0
0
0
4
1
0
0
2
0
0
0
0
2
0
1
0
0
2
0
2
1
1
0
0
2
0
1
0
0
0
0
3
0
0
0
0
2
1
2
0
0
2
0
1
3
1
1
1
2
0
1
1
1
2
0
1
0
2
0
1
1
0
2
0
0
3
0
2
2
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
3
0
2
1
1
2
2
1
0
0
2
0
2
2
0
1
0
2
3
1
0
1
1
1
0
0
1
0
1
1
0
4
1
0
0
0
0
1
2
1
1
0
0
0
1
2
0
0
0
0
2
0
1
1
0
0
1
2
1
1
1
0
2
0
1
0
0
0
0
2
1
1
0
0
0
1
0
0
0
1
0
0
0
2
0
0
2
0
2
2
2
0
1
1
2
0
0
0
1
0
1
0
2
2
1
1
2
2
0
0
1
0
0
0
2
0
2
2
0
1
0
1
0
0
1
0
0
0
1
5
0
0
2
0
0
1
2
0
3
0
1
0
2
0
2
2
2
1
0
0
0
0
0
0
2
1
0
0
1
0
4
3
2
0
0
1
2
0
0
0
0
0
1
3
1
0
2
0
1
0
0
0
1
0
0
3
1
0
1
0
0
0
0
1
1
0
0
0
1
1
0
0
1
1
1
0
1
0
0
2
1
2
1
1
1
3
0
2
0
0
0
1
0
0
0
0
1
2
0
0
0
0
1
2
0
1
0
1
2
2
2
1
6
1
0
0
1
0
0
0
1
0
1
2
0
2
0
0
2
2
0
1
0
1
0
1
2
0
0
2
2
1
0
0
0
0
1
0
0
0
1
1
1
1
0
0
0
2
0
0
0
1
0
0
0
2
0
3
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
2
1
2
0
1
1
0
1
0
1
1
2
0
0
0
0
0
1
0
1
0
2
2
1
2
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
2
0
1
0
1
1
1
2
0
0
1
0
2
1
1
0
5
0
0
2
0
0
2
2
0
0
1
0
0
0
2
0
0
1
1
0
1
1
2
0
0
0
0
0
2
0
1
1
0
0
0
1
0
2
0
1
8
0
2
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
1
2
0
1
1
0
1
0
2
1
0
0
0
0
0
3
2
1
0
1
0
0
0
2
0
0
1
2
0
0
2
0
0
2
0
0
1
0
0
0
1
1
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
2
3
0
0
2
1
2
0
0
0
2
0
0
2
1
0
2
0
0
2
2
2
0
0
1
0
2
0
0
0
0
1
1
0
0
2
1
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
1
3
0
1
2
2
2
0
1
0
1
0
2
2
0
2
0
0
0
1
0
2
2
0
2
0
2
0
0
0
5
3
2
0
0
0
0
0
1
0
2
0
0
2
0
1
0
0
1
3
2
0
1
0
0
3
1
1
1
0
1
1
1
0
0
3
1
2
2
2
1
0
0
2
1
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
2
1
2
1
1
0
0
2
1
3
2
0
1
0
0
1
2
0
2
2
0
0
2
1
2
1
0
0
1
4
0
2
1
0
0
1
0
0
0
1
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
2
1
0
0
0
0
0
0
0
1
1
0
0
2
5
0
0
0
0
0
1
2
2
0
0
0
1
0
1
1
0
1
0
2
0
2
1
0
1
0
0
0
2
0
1
0
1
0
1
2
0
0
0
2
1
0
2
0
0
2
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
1
2
1
2
0
1
1
0
0
0
0
1
1
0
0
1
3
2
1
1
1
0
2
0
1
0
0
0
2
0
0
1
2
0
0
0
0
0
0
1
0
0
0
2
2
3
0
0
1
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
2
0
2
2
2
0
2
1
0
0
2
0
0
0
0
1
1
1
0
0
2
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
2
0
3
0
0
2
0
6
0
0
0
0
0
0
0
0
0
0
2
6
2
0
0
1
1
0
0
0
2
0
1
0
1
2
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
1
0
1
0
2
2
3
1
0
2
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
2
0
0
0
2
0
0
2
2
0
0
0
2
2
0
2
2
1
1
2
0
0
1
2
2
2
1
3
0
2
0
0
0
0
1
2
2
0
0
1
1
0
2
0
0
1
0
1
0
1
0
1
2
1
1
1
0
0
0
2
0
0
0
0
0
0
1
1
1
0
2
0
0
0
0
1
1
2
5
2
1
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
1
2
0
1
0
2
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
1
2
1
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
2
2
1
1
0
0
2
0
0
0
1
2
2
0
2
1
0
1
0
0
0
0
0
2
1
1
0
0
2
0
0
3
0
1
0
0
0
1
1
1
0
2
1
1
0
0
0
0
2
2
0
1
0
0
0
1
0
0
0
0
1
0
2
2
0
0
0
0
0
1
0
0
2
2
2
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
1
2
0
1
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
2
1
3
1
0
2
0
0
2
0
0
0
1
2
1
1
0
2
2
0
0
1
2
3
1
1
1
2
0
0
1
0
1
0
0
2
0
2
1
2
0
0
0
0
2
2
1
1
0
3
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
2
2
1
2
0
0
2
2
0
0
0
0
1
0
2
2
0
0
0
3
1
1
0
1
1
1
0
3
0
0
2
0
1
0
0
0
0
0
1
1
0
0
0
1
0
2
0
1
0
2
0
2
0
0
1
0
0
0
2
1
0
0
0
0
0
0
1
2
0
0
2
0
2
0
0
1
1
0
0
1
0
2
0
0
0
1
0
0
0
1
2
0
2
0
1
0
1
0
1
1
1
1
0
0
0
2
1
0
0
0
1
1
2
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
3
0
2
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
1
1
1
1
1
0
2
0
0
1
0
0
0
0
0
1
2
0
0
0
1
1
1
1
0
0
0
0
2
1
0
2
0
0
0
0
2
1
0
1
0
0
2
0
1
0
2
0
2
0
1
2
1
0
1
0
0
0
1
0
2
2
2
0
0
2
0
1
0
1
2
0
1
0
0
0
2
2
0
0
2
0
0
1
0
0
2
0
2
0
0
1
0
1
0
1
2
0
0
0
0
0
0
0
2
0
0
2
1
2
0
1
0
1
0
0
5
1
1
0
0
2
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
2
0
1
0
0
2
1
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
2
1
0
2
0
0
0
2
1
0
1
1
2
0
0
0
0
0
2
1
2
1
1
2
0
0
2
0
0
2
0
2
0
0
0
0
1
0
2
0
1
0
1
2
0
0
1
0
1
0
0
1
0
3
1
2
0
1
0
0
0
1
0
2
2
1
2
0
2
0
2
0
1
0
1
0
2
1
1
0
1
0
0
0
0
0
1
2
2
3
1
1
0
4
1
2
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
2
1
1
1
2
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
1
1
1
1
0
1
2
0
2
2
0
0
0
0
0
2
1
0
0
0
0
2
2
2
0
0
0
1
0
1
0
2
0
0
0
5
0
1
2
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
1
1
0
0
2
0
0
0
1
0
2
0
0
1
1
0
0
0
2
0
0
1
0
0
1
0
0
0
2
1
0
0
1
0
2
1
0
0
0
0
0
3
1
0
0
2
0
0
0
0
0
0
0
2
2
1
2
0
1
0
0
1
2
0
3
0
4
0
0
2
2
2
0
0
2
2
1
4
2
0
1
0
0
0
0
0
2
2
1
2
0
2
2
0
0
3
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
2
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
1
0
1
0
0
0
0
0
1
1
1
0
0
0
3
1
0
2
2
1
0
1
0
0
0
2
0
2
0
0
2
0
0
0
2
1
0
1
1
2
0
1
0
1
0
2
1
2
1
0
0
1
0
0
1
0
2
0
2
0
1
1
0
2
1
0
0
1
0
0
2
1
1
1
1
0
0
2
1
1
0
1
0
1
0
1
0
0
1
0
2
0
0
1
1
0
0
0
0
1
0
2
1
2
0
2
1
1
0
0
0
0
2
3
2
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
2
1
1
0
0
2
0
0
1
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
1
0
1
0
2
1
0
0
1
1
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
2
2
0
1
1
0
1
0
1
1
0
0
0
1
0
0
0
1
1
2
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
1
0
2
0
2
0
1
0
2
1
0
1
0
0
0
1
0
2
1
2
0
0
1
0
0
0
3
0
0
0
0
0
2
0
2
1
2
1
0
1
2
0
0
1
1
0
0
0
0
3
1
0
1
2
0
1
0
0
2
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
2
0
0
1
7
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
1
1
0
0
0
1
0
2
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
1
2
1
2
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
1
1
1
0
1
1
0
2
0
0
0
0
1
2
1
2
1
1
1
2
1
0
0
0
1
0
0
0
1
0
0
2
0
0
1
0
1
2
0
0
0
1
0
2
0
2
0
1
1
1
0
0
2
0
0
0
2
0
0
0
1
2
1
2
0
0
1
0
0
1
0
0
2
0
0
2
0
0
1
2
2
1
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
1
10
2
2
1
0
2
0
0
1
0
1
2
2
0
1
0
1
0
2
0
2
1
2
0
0
0
3
3
0
4
0
2
6
0
1
0
2
4
0
0
0
0
0
0
0
1
1
1
1
1
0
0
2
1
0
0
0
2
0
0
1
2
0
0
2
1
0
0
0
0
4
0
0
0
1
0
3
0
2
0
1
1
3
2
1
0
0
1
1
0
0
2
0
0
1
0
0
1
0
0
0
0
0
1
2
0
0
2
0
1
2
0
0
2
0
1
0
2
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
2
1
0
1
0
0
0
0
0
0
1
3
2
0
0
1
1
0
1
0
2
0
0
0
2
1
0
0
0
2
0
0
0
0
2
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
2
0
0
1
0
0
0
0
2
0
0
2
2
0
1
0
1
0
1
2
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
2
1
2
0
2
3
1
1
2
0
0
1
3
1
0
0
0
2
0
0
0
0
0
1
0
1
0
0
2
0
1
0
1
1
0
0
0
0
1
2
0
2
0
0
2
2
3
2
0
0
1
2
0
2
0
2
2
0
0
0
1
0
1
0
0
2
2
0
0
0
1
0
0
2
1
0
3
0
0
0
2
0
1
0
2
1
1
1
1
0
0
2
0
2
1
0
0
2
0
2
0
0
0
0
2
0
1
1
0
1
0
1
1
0
2
0
0
0
2
2
1
2
0
1
1
2
2
1
0
1
4
1
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
2
3
2
0
0
0
2
0
0
0
0
0
5
1
0
0
2
0
1
0
0
2
0
1
1
1
0
0
0
0
1
0
1
1
2
0
2
0
2
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
2
2
0
0
2
1
0
0
2
0
0
1
2
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
2
0
0
2
1
1
2
0
1
0
1
1
0
0
1
2
0
2
2
0
1
0
1
1
0
1
1
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
1
1
0
0
3
0
0
2
0
2
2
0
4
2
0
2
0
1
2
1
3
2
0
0
1
0
0
3
1
0
1
0
1
0
1
0
2
2
2
2
1
0
1
0
0
2
0
2
2
2
3
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
2
0
2
0
0
1
0
0
0
0
0
0
0
1
1
0
1
2
2
0
1
0
1
1
0
0
1
0
1
0
0
3
0
0
1
2
0
0
2
0
1
0
0
2
2
0
0
0
0
2
0
0
1
0
1
0
1
0
0
0
0
1
0
0
4
0
0
1
0
3
1
1
2
0
0
0
0
0
2
1
0
2
0
1
1
0
2
3
0
1
1
1
0
0
0
2
1
1
3
2
0
0
0
0
2
0
0
0
0
2
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
3
2
1
2
0
1
2
0
0
2
0
0
0
1
0
0
0
0
1
0
0
1
0
2
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
2
0
3
2
0
0
1
2
1
1
0
2
1
0
0
1
0
0
2
1
0
0
2
1
2
0
2
0
0
0
0
1
2
0
0
1
0
0
0
0
0
2
1
0
1
0
0
0
0
0
1
0
0
4
0
3
2
0
0
0
0
0
0
0
1
1
0
0
0
2
2
1
0
2
1
0
1
1
1
2
0
1
1
0
2
0
1
2
0
0
2
0
0
0
0
2
0
7
2
1
2
0
0
1
2
0
2
0
0
2
0
0
0
1
2
1
0
0
0
0
0
0
2
2
1
0
0
0
1
1
0
0
1
1
0
1
0
1
0
0
0
2
0
2
1
0
0
1
1
0
0
2
1
0
0
1
0
0
1
0
1
4
0
0
0
0
1
1
2
2
2
0
2
0
0
0
0
2
0
2
0
2
0
0
1
0
0
2
0
0
2
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
2
1
1
0
1
0
0
0
2
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
1
0
1
3
2
1
0
0
0
1
0
0
0
0
1
2
1
0
0
7
1
0
0
0
0
1
0
2
0
0
0
2
0
0
2
1
3
1
0
2
1
1
0
2
0
0
1
1
1
0
0
0
0
1
2
2
2
2
0
0
0
0
1
0
0
2
1
0
0
0
1
0
2
0
1
2
0
1
0
2
0
1
0
1
2
0
0
0
2
0
2
0
0
0
0
0
0
4
1
1
1
2
2
0
0
2
0
2
0
0
0
1
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
2
2
0
2
2
0
0
0
0
0
0
2
0
1
1
0
1
1
0
0
0
1
0
0
1
1
0
1
0
0
1
2
1
0
2
2
1
0
0
1
0
0
0
0
1
2
2
0
1
0
0
0
1
0
0
1
0
1
2
0
2
3
0
1
0
1
0
0
0
3
0
2
0
0
0
0
2
0
0
0
1
2
2
1
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
1
2
0
0
0
0
0
0
4
0
0
2
0
0
0
3
0
0
0
1
0
1
2
0
0
0
0
0
2
0
1
1
0
0
2
0
1
2
1
0
0
2
0
1
0
0
0
0
0
1
1
0
1
1
1
1
2
2
1
1
0
2
0
1
0
2
2
1
2
0
1
0
0
0
2
1
1
0
0
2
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
1
0
1
2
2
2
2
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
1
0
0
0
1
1
1
0
1
0
0
2
2
0
0
0
0
0
2
0
0
4
1
0
2
1
0
0
0
1
1
2
1
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
2
0
3
1
1
2
2
0
1
2
0
2
1
0
1
0
2
0
3
0
2
1
0
0
0
2
0
0
0
1
0
0
0
0
0
1
2
2
0
0
0
0
0
2
0
0
0
0
0
2
1
0
2
0
0
1
2
1
0
0
2
0
1
0
1
0
3
1
0
0
1
0
0
2
2
0
0
0
2
2
0
0
2
1
1
1
0
1
1
2
0
0
1
1
0
0
0
1
0
1
2
2
0
1
2
0
0
0
0
2
0
0
2
2
0
2
0
0
1
2
1
0
1
1
0
0
1
0
2
0
2
0
0
1
1
2
1
0
1
0
1
0
0
1
0
1
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
2
2
2
0
1
0
0
0
0
0
1
2
0
2
1
1
2
1
0
0
0
1
2
2
0
1
0
1
3
1
0
1
0
1
1
0
2
2
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
2
1
1
0
0
2
1
0
1
1
0
0
1
1
0
2
0
0
1
2
2
0
1
2
0
1
2
0
1
0
0
1
0
1
1
0
2
0
0
1
1
0
0
0
2
0
0
2
1
1
1
0
0
0
2
1
0
0
2
0
0
2
0
2
0
0
2
0
0
0
0
0
0
1
1
0
2
0
2
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
2
1
1
0
1
2
0
1
0
1
0
0
2
1
1
0
0
0
2
0
1
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
2
1
0
2
1
1
0
0
0
1
0
1
0
1
1
2
3
0
1
0
2
0
0
1
0
0
0
0
1
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
1
1
2
0
0
1
1
0
0
0
1
0
1
2
2
0
2
2
0
1
0
0
0
1
1
1
1
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
1
1
0
2
0
0
0
0
2
2
1
0
2
1
2
1
0
0
0
2
0
0
0
0
1
0
0
1
0
1
0
2
0
0
0
0
0
1
2
2
1
1
2
0
2
1
1
1
0
2
2
0
2
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
2
2
1
0
0
2
0
2
0
0
0
2
0
0
3
2
4
1
0
1
0
2
1
0
0
0
0
1
0
0
1
0
2
0
0
0
0
1
2
0
1
0
0
0
2
0
0
0
1
2
0
0
1
0
0
0
2
0
0
0
0
2
2
0
1
0
0
0
0
0
0
2
2
1
2
1
0
2
1
1
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
3
2
1
1
0
0
0
0
0
2
5
1
0
0
2
0
2
1
0
1
0
2
0
0
0
0
0
2
0
1
0
1
0
2
2
2
0
1
1
0
0
0
2
1
0
0
0
0
0
2
1
0
2
0
0
1
2
0
0
0
0
0
0
0
4
0
0
1
1
0
0
1
2
0
1
0
0
0
2
0
0
2
0
1
0
0
0
1
1
2
0
0
1
2
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
2
1
0
0
2
0
1
1
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
2
0
0
0
2
0
2
0
0
0
1
0
2
0
0
2
0
3
2
0
0
0
1
0
0
0
0
2
2
2
1
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
2
1
0
2
0
0
1
2
2
0
0
0
2
2
1
1
0
0
0
0
0
0
2
2
0
1
2
0
1
0
2
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
1
5
1
0
0
0
1
0
0
2
1
2
0
0
0
0
1
0
0
2
0
1
1
0
1
1
0
2
2
1
0
1
2
0
0
1
0
1
0
0
0
2
1
0
1
0
0
1
0
0
0
0
0
1
2
1
1
0
2
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
2
3
1
1
0
0
0
2
1
1
0
2
0
0
0
1
0
0
0
1
0
0
2
1
0
0
0
1
0
0
1
0
0
0
3
3
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
1
0
0
1
0
1
1
2
2
0
1
0
2
0
3
0
2
0
0
0
0
2
0
2
1
1
1
0
2
2
0
2
0
0
1
0
5
0
0
0
0
2
0
0
3
0
1
0
0
2
0
0
0
0
1
0
1
0
0
2
1
0
2
0
1
1
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
3
0
0
1
1
0
1
0
1
0
0
1
1
0
0
0
0
0
0
1
0
2
0
2
1
2
2
0
0
2
3
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
2
0
1
2
2
1
0
0
0
0
0
1
0
0
2
1
0
0
0
1
0
3
0
1
2
1
0
1
2
0
0
0
2
0
0
0
2
1
1
0
2
0
0
2
0
0
2
2
0
0
0
0
2
1
1
0
2
0
2
0
1
2
2
2
0
1
1
1
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
2
0
1
0
0
1
1
1
2
0
0
1
1
0
0
0
2
1
0
1
2
3
0
0
1
0
4
0
0
0
0
0
0
0
2
4
1
2
0
0
2
1
0
0
0
0
0
1
0
1
0
0
0
1
0
1
3
1
0
0
1
0
1
1
2
0
1
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
1
1
0
0
1
0
1
1
2
2
0
2
2
0
0
2
2
0
0
0
0
1
2
1
0
0
0
0
1
2
0
1
0
0
0
0
0
0
1
0
2
2
1
1
2
2
1
0
0
0
1
4
0
1
0
0
0
0
0
1
1
0
2
2
1
0
2
0
1
1
0
0
0
0
0
0
2
3
0
0
0
0
3
0
2
2
0
1
1
2
0
1
1
0
1
0
2
1
0
0
1
0
0
1
0
0
0
0
4
0
1
1
1
0
0
0
0
0
0
0
0
1
2
0
0
0
2
2
2
0
1
0
2
3
3
1
0
0
0
2
0
0
0
0
1
0
0
2
1
1
0
0
2
1
1
0
2
0
4
4
1
2
1
0
0
3
0
0
2
0
2
1
0
2
0
1
3
2
2
0
0
0
1
0
0
2
1
1
1
0
1
0
0
1
0
0
1
2
0
1
0
0
1
1
0
0
1
0
0
1
0
2
0
0
2
2
0
0
0
0
0
1
0
0
1
0
0
1
1
0
2
0
0
0
0
0
1
2
1
0
2
8
0
0
2
0
2
2
3
1
0
1
2
1
0
2
0
1
0
0
0
0
0
1
1
2
0
1
1
1
0
0
2
0
0
0
0
1
0
0
1
0
2
2
0
2
2
1
0
2
1
2
1
0
0
0
0
2
0
1
0
0
4
1
0
0
0
0
1
0
1
0
0
0
0
0
1
2
1
2
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
2
0
3
1
2
1
2
3
1
0
1
0
0
2
0
1
0
0
2
0
1
0
1
1
1
2
1
1
0
0
0
0
0
0
2
0
1
0
2
0
1
0
0
0
1
0
0
1
0
0
1
0
1
0
0
1
1
2
0
0
2
2
0
0
2
0
0
2
0
0
0
2
0
0
2
1
2
1
0
1
0
2
0
0
4
0
0
1
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
1
1
2
1
1
1
0
0
2
1
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
1
2
0
0
1
0
0
0
1
0
0
0
0
0
3
2
0
0
2
0
1
0
2
0
2
0
0
1
1
1
0
0
1
0
2
0
1
0
1
1
2
3
1
0
0
1
0
0
1
1
0
1
0
0
0
0
1
0
0
0
2
0
1
2
1
0
1
0
1
0
1
0
0
2
0
1
0
0
0
0
0
2
2
2
1
2
0
0
0
0
0
0
0
0
2
0
2
0
2
0
2
2
1
0
0
2
1
0
0
1
2
0
2
1
2
0
0
0
0
0
1
0
0
1
5
0
2
2
0
0
2
2
2
0
0
0
1
0
0
1
2
0
0
1
0
0
0
1
0
0
1
1
1
0
2
1
1
1
1
0
1
2
1
2
1
2
2
1
2
2
1
1
0
2
1
0
4
0
0
1
2
0
2
4
0
0
1
0
2
0
1
1
1
0
2
0
2
1
0
0
0
0
0
1
2
1
2
0
1
1
2
1
0
1
0
1
0
0
0
0
1
0
0
1
1
2
0
1
0
2
2
2
2
0
1
0
1
0
1
2
0
0
1
0
0
0
0
2
0
0
1
2
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
2
0
0
0
0
0
0
0
0
2
0
0
2
2
1
0
0
0
0
1
0
1
0
0
3
0
1
1
0
0
0
0
0
2
2
0
0
1
0
0
2
2
1
1
2
1
0
0
0
2
3
0
0
0
1
0
0
0
0
0
3
0
2
0
0
0
2
0
0
2
1
0
1
1
0
0
0
1
2
1
0
0
0
0
2
1
2
0
0
2
0
1
0
2
0
1
1
0
0
0
2
0
0
1
0
0
0
2
0
2
0
0
0
2
0
0
1
0
1
0
1
1
0
0
0
0
0
0
2
2
1
0
0
2
0
0
0
1
1
2
2
2
1
0
0
0
1
0
0
2
0
0
1
2
0
2
0
1
0
0
2
1
1
2
0
0
1
0
2
0
0
2
0
1
1
2
0
0
1
0
0
1
0
2
0
1
0
0
0
2
1
0
0
2
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
2
2
0
0
2
1
0
0
2
2
0
0
0
0
0
2
2
2
0
2
2
2
0
0
0
2
2
0
1
2
2
0
0
0
0
1
0
0
0
0
0
1
3
0
1
0
0
1
0
1
3
0
0
0
0
2
2
0
0
1
0
0
0
1
1
0
1
2
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
2
0
2
1
0
0
1
0
1
0
2
0
1
1
0
0
0
0
2
0
0
0
2
1
0
2
0
2
0
0
0
2
0
1
0
2
2
0
1
1
1
0
1
0
0
0
1
0
1
0
1
0
1
2
2
2
0
0
1
1
2
0
0
0
0
0
2
0
1
1
1
0
0
0
1
0
0
0
1
0
2
0
0
0
0
1
0
0
0
1
0
0
1
1
0
2
1
0
0
1
2
0
0
1
1
1
0
1
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
2
2
2
2
2
0
0
0
1
0
2
0
2
2
0
0
0
1
0
1
2
2
1
0
2
0
0
2
0
0
0
1
0
0
2
1
0
0
0
0
1
0
1
0
0
1
0
3
0
0
1
2
0
0
0
1
2
2
0
2
0
0
1
1
0
2
0
0
0
0
0
0
0
2
0
1
2
0
2
0
2
0
0
0
0
0
0
2
3
0
0
0
0
0
1
0
2
2
1
0
1
0
0
2
0
0
1
2
0
1
2
2
0
0
2
1
0
1
0
2
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
2
1
0
1
0
0
1
2
1
0
2
0
0
0
1
0
2
0
0
4
0
0
0
2
0
0
1
1
2
0
2
1
0
2
2
0
1
0
2
0
2
2
0
0
0
0
0
0
2
0
1
0
2
0
0
2
0
0
0
1
1
0
1
2
0
1
0
0
2
1
0
2
0
2
0
0
2
0
2
0
0
1
2
0
2
1
0
0
0
1
0
0
0
1
0
0
1
0
0
1
1
0
0
1
0
2
0
2
2
1
0
0
1
2
3
1
2
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
1
0
1
1
2
2
1
0
2
2
0
0
0
1
0
2
2
0
1
0
0
0
1
0
2
1
2
1
2
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
2
1
0
0
0
0
0
2
2
4
0
0
1
0
0
3
0
0
0
0
1
1
2
0
1
0
0
2
2
0
0
0
1
0
1
0
1
1
2
1
0
0
0
1
0
2
0
0
2
0
2
0
0
2
1
0
0
1
1
1
2
0
0
2
0
2
0
1
1
0
1
2
0
0
2
0
2
0
0
1
0
0
2
2
1
1
1
1
0
0
0
2
0
2
1
0
0
1
2
1
2
0
0
0
2
1
1
2
0
1
0
0
0
1
2
10
0
1
0
0
2
0
0
2
0
1
0
0
4
1
0
2
0
1
1
0
2
0
0
1
0
1
1
0
0
2
0
0
1
0
0
0
0
0
0
0
1
1
4
0
1
0
1
2
0
2
0
0
3
0
0
1
0
0
1
1
0
0
1
0
0
0
2
1
0
1
0
0
0
1
0
0
2
0
0
0
1
1
1
0
2
0
0
0
0
0
0
4
1
0
2
0
1
1
2
0
2
2
0
0
2
2
1
2
1
0
0
0
1
1
1
0
0
1
1
1
0
0
1
1
0
0
0
2
0
2
0
1
1
1
0
1
0
1
1
1
0
3
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
1
0
2
2
2
3
2
2
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
1
0
2
0
2
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
2
1
1
0
0
3
0
4
1
0
0
2
1
0
0
0
2
0
1
0
1
0
2
0
0
1
0
2
0
1
1
2
1
0
0
2
2
1
0
6
2
0
1
2
0
0
1
2
2
0
1
2
2
2
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
4
2
0
2
0
0
3
1
2
0
0
1
1
0
0
0
2
0
0
0
0
0
1
0
1
0
0
3
0
3
1
1
5
1
0
0
0
0
1
1
1
0
0
0
2
1
2
2
0
1
1
2
0
2
0
0
2
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
2
2
0
3
0
2
1
0
1
0
2
0
0
3
0
0
1
0
1
0
0
1
2
1
0
2
1
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
1
0
2
0
0
1
0
0
0
0
0
2
0
1
1
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
3
2
0
0
0
2
1
0
0
1
0
0
2
1
0
1
1
2
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
2
1
2
1
2
0
0
2
1
0
0
0
0
0
1
0
0
1
0
1
2
2
1
1
0
0
1
0
0
0
0
2
0
2
0
0
2
0
1
0
1
0
0
0
2
2
0
0
6
0
0
1
0
1
0
0
2
0
1
0
0
2
1
1
0
1
2
0
0
0
4
0
0
1
0
0
2
1
0
1
0
0
0
1
0
2
0
0
2
0
1
0
0
2
1
1
3
0
0
0
0
1
1
0
0
0
2
2
0
0
0
0
0
0
2
3
1
0
0
0
2
0
1
0
0
0
2
1
0
1
0
1
0
0
0
0
0
0
2
2
2
0
3
0
2
1
0
1
2
1
2
2
0
0
2
0
0
0
0
1
0
0
2
1
2
3
0
0
2
1
0
0
1
0
1
1
4
1
2
1
1
0
0
0
1
3
0
1
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
2
2
0
1
1
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
2
1
0
0
0
0
2
4
1
0
2
0
0
1
1
1
0
1
1
0
0
0
0
0
1
2
2
1
0
2
0
0
1
0
2
1
0
0
1
0
0
0
1
0
0
1
0
2
0
1
1
0
0
2
0
0
0
0
0
0
0
2
0
2
0
1
0
0
2
0
0
0
1
0
0
0
0
1
1
2
2
0
0
0
0
2
0
2
0
1
0
1
2
1
0
0
1
1
0
0
2
1
0
1
1
0
2
1
0
4
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
1
0
2
1
1
0
1
2
1
1
0
2
0
0
0
2
1
0
0
2
0
0
2
0
1
1
3
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
1
0
2
0
3
1
0
0
0
0
0
0
1
0
2
0
0
2
1
1
1
1
0
1
0
0
0
0
0
1
0
1
0
0
0
3
1
0
0
3
6
2
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
3
2
0
2
2
2
0
2
0
0
0
0
3
2
0
1
2
3
0
0
1
0
0
1
1
0
1
0
0
1
2
0
0
1
0
0
0
0
0
0
1
1
2
0
2
0
1
3
0
0
0
0
2
0
0
0
1
0
0
0
0
1
1
2
0
0
0
0
0
0
2
0
1
0
2
2
0
2
0
0
0
1
0
0
0
2
2
0
0
0
0
1
0
1
0
0
0
2
0
1
1
1
0
1
2
1
2
1
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
2
0
1
0
1
2
1
2
2
1
0
2
0
2
2
0
1
2
2
1
2
0
0
0
2
1
1
1
1
1
1
1
0
1
1
0
1
0
2
0
0
1
1
0
1
2
2
0
0
0
1
1
0
2
3
2
0
0
0
2
1
0
0
0
0
2
0
1
0
0
0
0
1
2
2
0
2
1
2
0
2
2
2
0
0
0
3
2
2
0
0
1
1
0
0
0
1
0
0
2
7
1
1
2
0
1
1
0
2
0
0
1
0
0
1
1
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
1
0
0
1
0
0
1
2
0
0
1
0
1
1
1
1
1
0
0
0
2
2
1
0
0
1
0
1
2
0
0
1
2
2
0
1
0
0
2
2
0
0
0
3
0
2
2
4
1
1
1
0
0
1
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
2
1
0
0
0
2
0
1
0
1
4
0
1
1
1
0
3
0
0
0
0
3
0
0
0
2
0
1
1
2
0
3
0
0
3
1
0
2
2
1
0
2
2
5
1
0
1
0
0
1
0
0
1
0
1
0
2
0
2
0
2
0
1
0
0
2
2
0
1
0
1
1
1
0
0
2
0
0
0
0
0
2
0
0
1
0
0
2
2
1
0
0
0
2
0
1
0
0
0
1
0
1
3
0
0
0
0
0
0
0
1
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
2
0
0
1
1
0
0
1
0
2
1
0
2
0
1
0
0
2
1
0
0
1
2
2
1
0
2
0
0
0
0
0
0
2
1
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
2
1
0
0
0
2
2
0
0
2
0
2
0
1
2
0
2
0
0
0
0
1
0
0
2
0
0
2
1
0
0
1
0
0
1
1
0
2
0
1
0
1
1
1
0
0
0
2
2
0
0
0
1
0
0
1
0
0
1
1
0
0
0
2
0
0
1
2
1
0
2
2
0
0
0
2
2
0
0
2
2
0
1
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
1
2
2
0
0
1
0
1
0
2
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
1
0
1
1
1
0
0
1
0
2
1
0
0
0
0
1
1
1
0
0
0
0
2
0
0
0
1
0
2
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
3
0
0
1
0
1
0
1
2
2
0
0
0
1
0
1
0
1
0
2
2
1
0
0
0
0
0
0
2
2
1
2
0
2
0
0
2
0
0
0
0
0
1
2
2
0
2
0
1
0
0
1
0
1
1
1
0
0
0
0
0
0
0
1
1
2
0
2
2
2
0
0
0
3
0
2
1
0
1
0
1
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
2
0
0
2
1
0
1
0
0
2
0
0
0
1
0
0
1
0
0
3
0
0
0
2
0
1
1
0
0
0
0
0
2
2
0
1
1
0
0
0
1
2
0
2
0
0
1
0
2
1
0
1
0
0
1
0
1
0
0
0
0
1
2
0
0
2
0
2
1
1
1
2
2
0
0
2
0
0
0
2
1
1
1
2
0
0
0
0
1
2
1
1
0
0
1
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
2
2
0
1
0
0
0
0
3
0
3
1
1
1
2
0
0
2
0
0
0
0
0
0
1
0
0
0
2
2
0
0
1
0
0
1
0
1
1
2
0
0
0
1
2
0
0
0
1
0
0
1
2
0
0
1
1
4
1
0
3
1
2
1
0
0
2
0
2
0
0
0
1
0
1
0
2
0
2
0
2
1
0
2
0
0
2
0
0
1
2
1
1
0
0
0
0
1
2
0
1
0
0
1
0
0
0
0
0
3
0
0
2
0
1
2
0
0
2
0
2
0
2
1
0
0
4
1
0
0
0
0
1
0
1
1
0
0
0
2
0
2
2
1
0
3
2
0
0
0
0
0
0
0
3
1
1
2
0
0
0
0
1
1
0
1
0
0
2
0
1
0
1
3
0
2
0
0
0
0
1
2
1
0
0
0
0
0
3
3
0
2
0
1
1
0
2
0
0
0
2
2
0
0
1
1
0
2
0
2
0
1
3
0
1
2
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
2
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
1
1
0
2
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
2
1
0
0
1
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
2
0
0
2
1
0
0
0
0
2
2
1
1
1
2
1
1
0
1
0
0
0
0
2
0
0
0
0
1
1
0
1
2
1
0
1
0
0
0
0
0
0
2
0
0
2
2
0
1
0
1
0
2
0
0
0
2
0
2
0
0
0
0
0
0
1
3
0
0
1
1
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
2
0
0
3
0
0
1
0
1
0
2
1
0
0
0
1
1
0
0
0
1
0
0
3
0
1
2
1
1
1
0
2
2
0
0
2
0
0
0
1
0
0
1
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
3
2
1
1
0
1
0
0
0
0
1
2
0
0
2
1
0
0
0
2
0
1
0
1
0
3
0
0
1
0
0
0
1
0
1
0
0
2
2
2
1
0
2
1
0
0
0
0
0
2
2
1
0
2
1
2
1
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
3
0
0
0
0
0
2
2
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
2
2
0
1
0
0
1
0
2
1
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
1
3
0
0
0
2
0
1
0
0
1
0
0
2
0
2
0
0
2
0
2
0
0
0
2
0
0
0
0
1
0
1
1
0
0
1
0
0
0
2
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
2
1
2
0
2
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
2
0
1
0
0
1
1
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
2
0
0
0
0
1
1
1
2
0
0
1
0
0
0
0
0
0
0
0
0
2
1
7
1
0
2
2
1
0
0
2
1
2
1
1
4
1
1
0
1
1
0
0
0
0
0
0
0
0
3
1
1
1
1
1
0
2
1
2
0
0
1
1
0
0
0
2
1
2
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
1
0
3
0
1
1
3
0
0
0
0
2
2
2
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
2
2
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
1
1
0
2
0
0
0
0
0
0
0
2
2
0
1
2
2
0
0
2
2
2
0
0
0
2
0
1
0
1
2
0
2
0
0
2
0
0
0
0
0
0
1
0
3
0
0
2
0
3
0
2
0
1
0
0
0
0
0
0
1
1
0
2
0
0
2
1
1
0
0
0
0
1
0
1
0
0
1
2
1
0
1
0
2
1
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
1
3
2
0
2
0
3
1
0
0
0
1
2
2
0
0
0
0
1
0
0
0
0
0
2
1
0
1
1
0
2
0
1
2
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
2
1
0
3
0
0
0
1
1
1
0
0
1
2
0
0
2
1
2
0
0
0
2
0
2
0
1
0
0
0
2
0
2
0
0
0
0
2
1
0
0
0
0
0
2
2
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
2
1
0
0
1
1
1
0
1
1
1
1
0
3
0
0
0
0
0
0
2
1
0
3
2
1
1
0
1
0
0
1
0
0
1
0
1
0
0
2
2
0
0
1
0
0
1
3
0
0
2
1
0
0
0
0
1
0
2
1
0
2
1
0
2
0
1
2
0
0
0
2
0
1
0
0
0
0
2
1
2
0
1
0
2
0
0
1
0
0
2
1
0
2
0
2
0
0
1
0
0
1
4
2
1
0
0
0
0
0
0
0
0
2
0
2
1
0
2
0
1
1
1
0
0
0
0
0
0
1
2
0
3
0
2
0
0
0
1
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
1
2
0
2
0
1
2
1
2
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
2
2
3
0
0
0
2
1
2
0
2
0
1
1
0
2
1
3
0
0
1
0
0
0
0
0
0
0
0
4
1
0
0
1
0
0
1
0
2
0
1
0
1
0
1
0
1
2
0
0
0
0
1
1
1
1
0
0
0
1
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
1
1
0
2
0
0
1
1
0
2
1
1
0
1
0
0
0
0
0
0
0
2
0
2
0
2
2
0
0
0
0
2
2
0
1
0
1
2
2
0
0
0
1
0
0
0
1
1
1
0
1
0
0
0
1
0
0
1
1
2
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
1
3
2
2
0
2
0
2
1
0
0
0
3
1
1
0
1
0
0
1
1
0
1
0
2
0
2
1
0
1
0
2
0
0
2
0
0
0
1
0
1
0
0
0
3
0
3
0
0
0
1
0
0
2
2
0
0
2
0
2
0
0
0
1
0
1
2
2
1
2
2
0
2
0
0
1
2
1
2
0
1
1
0
0
0
2
0
0
0
0
0
2
0
2
0
5
1
0
1
0
0
0
1
2
1
1
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
1
0
3
1
0
0
0
0
1
0
1
0
0
1
1
1
1
0
1
0
0
1
0
0
0
2
0
0
2
0
0
2
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
2
1
0
0
0
2
2
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
1
2
2
2
0
12
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
1
0
1
1
2
0
1
2
0
1
0
0
0
0
2
0
0
2
1
1
0
0
0
1
0
0
2
0
0
0
1
1
0
2
1
0
0
2
0
0
0
2
4
1
0
0
1
0
0
1
0
0
1
0
0
1
2
0
2
3
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
1
0
2
3
0
0
0
2
1
2
1
0
1
0
1
0
2
0
0
1
0
1
0
1
0
2
2
2
0
0
0
1
1
0
2
2
0
0
2
2
0
0
0
2
0
0
0
2
2
1
1
2
0
1
3
2
1
1
0
0
0
2
1
2
0
0
0
0
1
1
0
0
0
0
1
0
2
0
2
0
0
11
1
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
2
1
1
0
1
1
0
1
0
1
2
2
1
0
0
0
2
1
1
0
2
1
0
0
2
1
2
0
0
1
0
0
2
1
0
1
1
0
1
0
0
2
0
0
0
0
1
3
2
0
2
0
0
1
0
2
1
1
0
0
6
0
1
0
0
0
0
0
0
0
0
2
2
0
3
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
2
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
2
2
1
0
0
0
1
0
0
0
0
0
0
2
2
0
0
1
0
1
0
0
0
1
0
0
0
1
0
2
1
0
0
0
1
0
0
1
1
0
2
0
2
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
3
0
0
0
0
0
1
1
1
1
0
0
0
1
2
0
2
1
0
2
0
0
2
0
0
0
1
0
0
0
0
0
2
1
1
0
0
2
1
0
1
1
2
1
1
0
0
0
2
0
0
1
0
0
1
0
1
2
1
0
0
2
2
0
2
0
0
0
0
1
1
1
1
0
2
0
0
0
0
1
1
1
0
0
0
2
0
0
0
2
1
1
1
2
1
0
0
2
0
0
2
2
0
0
0
0
0
0
0
1
2
2
0
0
3
0
1
0
1
0
0
0
2
0
0
0
0
0
1
0
0
1
1
0
1
0
4
0
0
0
0
0
0
0
1
1
2
2
0
0
1
0
1
0
0
3
0
0
2
0
0
0
1
0
1
2
1
1
1
1
0
0
1
1
0
0
0
2
0
0
1
0
0
1
2
2
0
0
0
1
1
2
0
2
0
2
1
1
0
0
0
2
1
0
0
0
2
1
1
0
1
0
1
1
0
1
1
0
0
0
2
1
1
0
0
2
1
0
2
0
0
0
0
0
1
0
0
0
0
3
0
0
1
0
0
4
0
0
0
0
0
0
0
1
1
0
0
1
0
1
2
0
1
0
2
0
0
0
0
0
2
0
0
2
2
0
1
3
0
2
1
2
0
0
0
0
2
1
0
0
0
1
2
1
0
2
0
2
1
0
2
0
1
0
0
0
0
1
0
0
0
0
4
0
0
3
0
2
2
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
1
1
0
1
0
0
1
1
1
1
0
1
0
2
0
2
1
0
0
2
3
1
0
0
0
2
0
2
0
0
2
0
0
1
0
0
0
0
1
2
2
2
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
2
2
1
0
0
0
0
0
1
0
0
1
2
0
1
1
0
0
1
1
1
0
0
0
0
0
1
1
0
0
1
2
1
1
0
0
2
0
0
0
0
0
0
0
5
1
2
0
0
0
1
2
0
0
0
0
1
0
2
1
4
2
1
0
0
0
0
4
1
2
1
0
0
0
0
2
0
2
1
0
0
0
0
0
2
0
2
1
1
0
2
1
0
0
0
0
0
2
4
0
0
0
0
1
1
1
1
2
0
0
0
2
1
0
0
0
0
2
0
2
1
2
0
0
0
0
0
2
1
2
0
0
2
4
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
2
4
1
0
2
0
0
0
1
0
2
1
0
1
0
0
0
1
0
1
0
0
0
1
2
0
0
2
1
0
2
0
0
0
2
0
1
0
0
0
0
2
0
0
1
1
1
1
0
1
1
1
1
0
0
0
1
2
0
0
0
1
1
2
0
0
1
1
0
1
0
0
3
1
0
0
0
0
1
0
0
0
0
0
1
0
2
1
2
0
1
4
0
0
1
0
0
2
0
0
0
2
0
0
0
2
0
2
1
1
0
2
0
1
0
2
0
1
1
0
2
0
1
0
0
1
0
0
0
1
2
1
1
2
4
0
1
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
1
0
2
0
1
2
0
1
2
1
0
0
0
2
1
0
1
0
1
1
0
0
0
0
0
1
2
1
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
2
0
1
0
0
1
2
0
1
1
2
2
0
0
1
2
2
0
0
1
2
0
0
0
2
0
2
0
0
0
0
1
0
1
0
0
2
1
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
2
0
2
3
1
1
2
0
0
0
2
0
3
1
0
0
0
0
0
0
0
2
0
0
0
1
0
1
2
1
0
2
1
0
0
1
0
0
0
3
1
0
2
0
2
0
0
0
1
0
1
0
0
0
0
0
1
1
2
1
0
1
0
2
0
3
0
0
0
1
0
0
0
1
1
0
0
0
2
0
1
0
2
0
2
0
1
0
0
2
0
2
2
1
0
0
1
0
0
1
0
2
2
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
1
2
1
0
3
0
2
1
0
0
3
0
2
1
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
2
2
1
2
2
0
0
1
2
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
1
2
1
0
1
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
1
0
2
2
0
1
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
3
0
0
1
2
0
0
0
1
2
0
0
2
1
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
1
1
1
2
0
1
1
2
3
2
0
0
0
0
0
0
1
0
0
2
0
1
1
0
2
2
2
2
2
0
0
0
1
0
0
3
0
1
0
0
0
5
1
0
0
1
2
0
0
0
0
0
0
1
2
1
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
2
4
2
0
1
0
0
0
0
1
2
0
0
0
1
1
1
1
0
0
2
1
0
0
0
2
0
1
2
0
2
2
0
2
2
0
0
1
0
0
1
0
0
1
2
0
0
1
0
0
0
2
0
0
1
0
0
0
0
2
0
2
1
1
0
2
2
2
0
2
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
2
2
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
2
0
0
0
1
0
2
0
0
1
0
1
0
0
1
0
1
0
0
0
1
3
0
0
2
0
0
0
0
3
1
2
0
2
0
1
0
0
0
1
1
1
0
0
0
0
0
2
0
2
2
0
4
2
1
0
1
2
0
1
0
3
0
2
0
1
1
0
0
0
2
0
1
0
2
0
2
0
1
2
0
2
2
1
0
0
1
3
1
0
0
0
0
0
0
1
0
2
0
1
0
1
0
2
1
0
0
0
2
0
0
0
1
0
0
0
1
0
1
2
1
1
1
0
0
1
2
1
0
1
1
0
2
0
0
1
0
0
0
1
2
0
0
1
0
1
0
1
0
0
1
0
0
4
0
2
1
0
0
0
1
2
0
0
2
1
2
0
1
2
0
0
2
2
0
0
1
0
1
0
0
0
2
0
1
0
0
1
1
2
0
0
1
2
0
0
1
0
0
0
1
0
0
0
1
2
0
0
2
0
0
0
1
0
0
0
0
0
2
2
1
0
0
2
1
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
2
2
1
0
2
0
0
1
0
1
2
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
1
0
0
0
2
0
2
0
2
0
0
2
0
0
0
2
1
2
1
2
0
0
0
0
2
1
0
2
2
0
0
0
0
0
0
1
2
1
1
0
0
0
0
1
2
0
1
0
2
2
0
0
0
2
0
0
0
2
2
0
1
0
0
1
2
0
2
0
0
0
1
1
0
0
4
0
0
0
2
0
0
2
1
0
2
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
1
1
2
1
1
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
3
0
2
1
0
0
2
0
0
2
2
0
0
0
0
2
2
0
1
0
1
0
0
1
1
0
0
0
0
2
2
0
0
0
0
5
1
0
1
0
0
2
1
0
1
0
1
2
1
0
1
0
0
1
0
0
2
2
0
2
0
0
2
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
1
2
0
2
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
2
0
1
0
0
0
2
0
0
2
1
1
0
1
0
1
0
0
2
0
0
1
1
0
0
0
1
0
1
0
0
0
1
1
0
1
0
0
2
0
0
0
2
2
1
1
1
0
2
2
1
0
0
0
0
2
0
0
0
2
0
0
0
2
2
0
2
8
2
0
0
1
0
2
2
1
2
0
1
0
0
0
3
0
0
0
2
0
0
0
0
0
2
2
2
0
1
0
0
0
0
1
1
0
1
2
0
2
0
2
0
0
1
0
0
1
0
0
2
1
0
1
1
0
2
0
2
1
0
1
0
1
2
0
0
0
3
0
1
0
1
0
0
1
0
0
0
0
0
1
0
2
0
1
1
1
2
2
2
0
0
0
0
0
2
2
0
2
0
0
0
1
0
0
0
0
2
2
2
1
0
0
0
0
0
1
0
2
1
0
3
0
0
2
1
0
0
0
1
2
0
1
0
0
0
0
1
0
2
2
0
1
1
0
2
0
0
1
0
0
2
2
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
1
0
1
0
2
0
2
0
0
2
0
2
0
1
1
2
0
1
2
0
0
0
1
2
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
3
0
0
1
0
2
2
0
1
0
0
0
0
2
0
0
3
0
1
1
0
1
2
0
0
0
0
0
0
0
2
0
2
2
2
0
2
0
1
0
2
1
1
0
0
0
1
0
0
0
0
0
0
1
1
3
1
0
2
1
1
0
0
2
12
1
0
0
0
0
0
1
0
2
2
0
0
2
0
2
2
1
1
0
0
2
1
2
2
0
0
0
0
0
0
1
0
1
1
0
0
1
1
2
1
0
0
0
0
0
0
2
0
1
0
0
1
1
1
0
0
1
0
0
0
4
1
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
1
5
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
2
2
1
0
1
0
0
0
0
1
4
0
5
2
0
1
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
1
0
0
3
0
0
1
1
0
1
0
0
0
0
0
0
0
1
2
0
0
1
2
1
1
1
0
1
2
2
0
0
1
3
0
0
0
0
0
2
0
0
0
1
2
0
1
0
0
1
0
0
1
0
1
0
3
2
0
1
1
0
0
3
2
2
0
0
0
1
0
1
0
0
0
2
0
2
1
2
1
2
0
0
0
2
0
0
0
0
0
2
0
1
0
0
4
0
0
0
2
0
0
0
2
2
2
0
0
0
1
0
0
0
0
5
0
0
2
0
2
2
0
2
0
0
1
2
0
0
0
1
0
1
0
0
2
2
0
3
2
2
0
1
0
2
2
0
1
2
0
0
0
0
0
1
0
0
0
0
2
0
2
1
0
3
0
1
1
1
0
2
1
1
0
1
1
1
0
2
0
0
2
1
0
3
1
0
2
0
0
3
1
2
1
1
1
1
2
0
2
1
0
1
0
0
0
0
0
0
1
2
0
0
1
1
2
0
1
0
2
0
2
2
0
2
0
0
2
0
1
2
0
1
2
0
0
0
1
0
0
0
1
0
0
0
0
1
1
1
0
2
0
3
0
0
0
2
2
0
0
1
2
2
0
0
2
1
2
0
0
0
2
2
0
0
0
1
0
0
2
0
1
1
4
4
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
2
0
0
1
1
0
0
0
8
0
0
0
0
0
1
1
0
2
0
0
2
0
1
0
0
0
0
0
2
0
1
3
0
1
0
3
2
1
0
0
1
1
1
2
1
2
0
0
0
0
0
1
0
1
0
0
1
0
1
0
1
0
1
2
1
2
0
0
0
0
0
0
0
0
2
2
0
1
2
2
0
0
0
0
2
2
1
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
12
0
1
0
2
0
2
0
1
1
0
0
0
0
0
1
0
0
2
2
0
2
0
1
0
1
0
1
0
1
2
1
1
0
0
1
0
0
1
0
0
0
0
1
0
2
1
2
2
0
1
0
0
2
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
2
3
0
3
1
2
1
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
2
0
0
0
1
0
1
0
0
1
0
0
2
1
2
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
3
0
1
2
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
1
0
0
1
5
2
0
2
0
0
2
0
2
0
2
0
0
2
0
1
0
0
0
2
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
1
0
3
0
0
0
2
1
1
1
0
0
2
0
2
1
0
0
2
0
0
2
1
0
0
0
1
4
2
0
0
0
1
0
0
0
2
0
1
0
2
2
0
0
0
1
0
1
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
2
0
0
0
2
0
1
4
0
2
0
2
0
0
2
0
0
1
1
0
0
1
0
0
0
0
0
3
0
0
0
2
0
0
2
0
1
0
2
0
1
0
0
3
0
0
2
1
1
2
1
1
0
0
1
1
17
0
1
0
2
1
1
1
0
0
0
2
2
1
0
1
2
0
0
2
0
0
0
0
0
2
1
0
0
0
0
1
0
2
1
1
0
2
0
0
0
0
1
1
0
1
1
2
2
1
0
2
1
0
0
1
0
0
0
2
0
0
0
2
0
0
1
2
0
0
0
0
0
1
0
0
0
1
2
2
1
1
1
0
0
1
3
0
0
0
2
0
1
0
3
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
3
1
0
0
2
0
0
0
0
0
2
2
1
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
1
2
2
1
1
2
0
2
0
2
1
2
0
0
0
0
3
0
0
0
1
0
0
0
1
2
0
1
0
0
1
0
2
3
0
3
0
2
0
3
1
1
1
2
5
0
1
1
0
2
0
2
0
1
2
2
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
1
0
2
0
0
1
0
0
1
0
2
3
1
2
0
1
0
0
0
1
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
2
1
1
0
0
1
0
0
1
0
0
1
1
0
2
0
2
0
0
0
0
5
2
2
1
2
0
2
2
0
1
0
0
0
3
2
2
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
1
1
0
0
0
0
0
2
2
0
0
2
0
2
0
1
0
0
0
1
0
1
2
0
1
2
0
1
1
0
1
0
1
1
2
1
0
2
0
0
2
0
1
0
2
1
0
2
0
0
0
1
1
2
0
1
0
0
0
0
0
0
0
1
2
2
2
0
0
2
1
1
1
0
0
0
0
0
0
1
2
0
3
1
0
0
0
0
2
1
0
2
0
2
2
2
0
1
0
1
2
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
2
1
0
1
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
2
0
2
2
0
3
1
1
0
0
0
0
0
0
2
0
0
1
0
0
1
0
2
0
0
0
1
1
0
0
1
1
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
1
0
0
1
0
1
0
0
0
1
2
1
0
1
2
8
0
1
2
0
0
0
0
2
0
2
4
1
1
0
0
0
2
1
0
0
0
1
0
1
0
0
0
2
0
0
0
0
1
0
0
3
0
0
0
0
0
1
0
0
2
2
0
2
0
0
1
2
2
2
0
1
0
0
0
2
0
2
2
0
1
0
2
1
0
0
0
1
0
1
1
0
1
0
2
0
0
0
1
2
0
1
0
0
0
1
0
1
0
2
0
1
0
0
0
1
0
0
2
2
1
0
2
6
0
3
0
0
0
0
1
1
1
1
1
0
2
0
2
1
2
1
0
0
0
1
1
0
0
1
0
0
2
0
0
1
0
0
1
0
3
1
1
0
0
0
1
2
2
1
1
1
0
0
0
0
0
2
0
0
1
2
0
2
1
0
0
0
2
0
0
1
2
2
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
1
2
0
0
0
0
0
2
0
0
0
0
5
1
0
0
0
0
0
2
0
0
0
0
2
0
3
2
1
0
3
0
1
0
0
0
1
1
0
0
0
0
0
1
1
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
2
0
0
1
0
1
0
0
0
0
1
1
0
1
0
1
2
1
0
0
0
2
0
0
0
0
1
0
0
0
1
2
0
1
0
0
0
2
1
2
2
0
0
1
0
2
2
0
0
0
2
1
0
0
0
1
1
1
0
0
1
2
0
2
2
0
0
2
2
0
1
0
1
0
0
0
0
2
2
1
1
0
0
0
1
2
0
0
0
0
0
2
1
2
2
1
1
0
0
0
1
0
0
0
0
0
1
2
2
0
1
0
0
1
2
0
2
0
0
0
0
0
1
0
3
2
0
0
2
0
2
0
0
0
1
1
0
2
1
0
1
0
0
1
1
0
1
0
1
2
0
2
0
0
0
2
0
1
0
2
0
0
1
1
1
1
1
0
1
0
7
1
0
0
2
1
2
0
0
0
0
0
1
0
1
0
2
0
0
1
1
1
0
0
1
1
3
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
1
1
0
1
0
0
1
0
1
0
2
0
0
0
1
0
0
1
0
2
0
1
0
1
0
0
1
0
2
0
1
0
0
1
0
3
3
0
0
0
0
2
1
2
1
1
1
0
0
0
2
0
2
1
0
1
0
2
0
0
17
2
0
0
0
0
0
0
0
0
3
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
1
1
0
1
0
2
0
0
2
0
2
0
0
0
2
0
0
2
0
0
0
2
0
2
0
0
1
1
0
0
1
0
0
0
0
0
2
0
1
1
2
0
0
1
2
1
0
0
1
0
0
1
2
1
3
2
6
0
0
1
0
1
1
1
2
0
2
0
1
1
1
2
1
2
0
0
2
3
0
1
2
5
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
1
1
1
0
1
0
2
0
1
1
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
1
2
0
2
1
0
0
0
0
0
0
2
0
0
2
0
0
2
1
1
0
0
0
0
0
0
0
0
0
2
2
0
2
2
0
1
2
0
0
2
0
0
0
0
0
1
0
1
0
1
2
1
0
0
0
2
0
0
0
0
1
2
0
0
1
0
1
0
2
2
2
0
2
1
3
0
1
0
0
0
2
2
0
2
0
0
0
2
0
0
2
0
0
0
1
1
0
0
0
1
2
0
1
0
1
0
1
0
1
1
1
0
1
1
1
0
1
2
0
0
0
0
3
2
0
2
2
1
0
1
0
0
2
1
0
1
1
0
0
4
1
0
0
0
0
1
0
0
1
0
0
1
2
0
1
0
0
0
0
0
2
2
0
0
1
0
1
2
2
2
1
2
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
2
2
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
1
0
1
0
0
2
1
2
0
0
0
0
0
0
2
0
1
1
0
0
0
0
2
0
4
0
1
1
2
0
1
0
0
0
0
0
0
0
0
2
0
0
2
1
1
0
1
2
0
0
0
0
0
0
1
2
0
0
1
2
0
0
0
0
0
0
1
2
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
1
0
0
1
1
1
0
0
1
0
1
2
1
1
0
1
2
2
0
0
0
0
2
0
1
0
0
0
2
1
3
0
1
1
0
0
0
3
1
1
2
2
0
1
1
0
0
1
3
1
0
2
0
0
0
2
1
0
1
0
2
0
0
1
0
2
0
0
0
0
0
1
0
0
2
0
1
0
0
1
2
1
1
0
0
1
1
1
2
0
0
0
1
0
0
2
0
0
0
1
2
0
0
2
0
1
0
2
0
0
0
0
2
0
0
2
0
0
2
0
0
2
0
1
0
0
1
2
0
0
2
0
1
0
1
2
0
0
0
0
0
0
0
1
0
1
0
1
1
0
2
2
1
0
0
0
1
1
1
1
0
1
0
2
1
2
1
1
0
2
0
1
0
0
3
1
1
0
0
0
1
0
1
0
0
0
2
2
0
1
0
1
1
2
2
0
1
0
0
1
2
0
0
0
1
0
0
0
1
2
2
0
0
0
0
0
0
2
0
0
1
0
1
2
0
2
0
0
0
1
1
0
0
1
3
2
0
2
1
0
1
0
2
2
0
2
0
0
0
3
0
2
0
1
0
0
2
0
1
0
0
1
2
2
2
0
1
0
0
1
0
0
0
2
0
1
2
1
0
0
0
2
1
1
0
0
1
1
1
0
0
2
0
0
1
1
0
0
0
0
1
0
5
0
2
0
0
0
0
2
0
0
1
0
0
2
0
1
0
0
0
0
0
1
1
0
0
2
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
2
1
0
2
0
8
1
1
1
1
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
2
2
2
1
2
2
0
2
0
0
0
2
0
1
0
0
0
2
0
1
1
0
0
2
0
2
0
1
0
0
1
0
0
2
0
1
0
1
0
0
2
3
1
0
0
1
1
2
2
2
0
0
0
2
2
0
2
1
2
0
0
0
0
1
0
2
0
2
0
1
3
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
1
0
2
0
0
2
3
1
0
0
0
0
0
2
3
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
2
1
2
0
1
2
0
1
2
0
0
0
0
1
0
0
0
0
1
0
0
0
1
2
0
0
0
2
0
0
1
0
1
0
1
1
0
0
1
0
1
0
0
0
3
2
0
1
0
0
0
2
1
0
0
0
0
1
1
3
1
2
1
2
1
0
0
0
0
0
4
0
0
0
0
0
0
1
2
0
0
0
1
1
0
0
1
1
1
0
2
0
0
1
0
1
0
0
2
0
0
0
0
0
0
1
0
0
2
2
1
1
1
2
3
1
0
0
1
1
1
1
0
0
1
2
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
2
0
1
0
1
1
1
0
2
0
2
0
2
2
0
1
0
0
1
0
0
0
0
0
0
2
2
1
2
0
0
2
0
1
0
0
0
1
1
1
1
0
2
0
0
2
0
0
1
0
0
1
3
2
0
0
0
2
0
1
1
0
0
0
2
2
0
0
2
1
2
0
2
0
0
0
1
0
1
1
2
0
2
3
0
0
0
1
2
2
2
0
2
1
0
1
0
2
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
1
1
0
2
0
0
2
1
2
1
0
0
0
1
0
0
0
0
0
1
0
1
1
2
3
0
1
0
0
2
0
0
0
1
1
2
1
0
0
1
2
0
0
0
0
1
0
2
0
0
0
2
0
2
1
0
1
0
0
0
1
2
0
0
2
2
4
3
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
2
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
2
0
1
0
1
1
0
0
0
0
1
3
2
0
0
2
0
1
0
0
0
0
0
0
0
1
2
0
0
1
1
2
1
0
0
1
0
1
0
0
0
2
1
0
2
0
2
0
2
0
0
3
2
0
0
1
2
0
0
0
1
2
0
1
0
0
0
0
1
1
2
0
0
2
2
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
2
0
2
2
1
0
0
0
2
2
2
0
0
0
0
1
0
0
0
1
1
1
1
2
0
0
0
0
1
0
2
0
1
1
1
0
0
1
0
1
0
1
2
0
1
2
1
2
1
0
0
2
4
2
1
0
0
1
3
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
1
1
0
1
1
1
0
1
2
0
0
0
2
0
2
0
0
0
0
1
0
1
2
0
1
2
1
1
0
1
0
0
2
0
0
2
0
0
2
2
0
0
0
2
1
0
2
0
1
2
0
0
3
2
2
2
0
1
2
2
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
1
3
0
0
2
0
0
1
0
0
2
1
1
1
1
0
0
0
0
0
0
0
0
1
2
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
1
0
0
0
0
0
0
2
2
3
1
1
0
0
0
0
1
1
2
0
0
3
2
0
0
0
0
0
2
0
0
0
0
2
2
1
0
1
2
2
1
0
1
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
1
0
0
2
0
0
0
1
2
0
1
0
0
0
2
0
0
0
0
4
3
0
0
3
0
1
0
2
0
0
0
2
0
2
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
1
0
0
1
0
0
3
1
0
2
0
0
0
2
0
0
1
1
0
0
1
1
1
1
0
1
0
0
0
1
1
0
1
2
1
2
0
0
2
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
1
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
2
2
1
0
0
0
0
2
0
2
1
0
2
1
0
0
0
1
0
3
0
2
0
0
0
1
1
0
1
1
2
1
0
0
2
2
2
0
2
1
1
2
1
1
0
0
0
0
1
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
2
0
2
1
0
2
0
1
1
0
1
2
0
1
3
1
0
1
1
1
1
0
0
0
0
1
0
1
0
1
0
0
1
0
1
0
1
2
0
2
1
1
0
0
0
2
1
1
2
0
1
2
1
1
1
0
0
0
0
0
2
0
1
2
1
0
0
0
1
0
0
0
1
3
1
2
0
1
0
1
0
2
1
2
0
2
0
0
1
0
0
1
0
0
2
1
1
1
1
2
2
0
0
0
1
2
0
1
0
0
1
2
2
0
1
0
2
0
0
0
2
0
0
0
2
0
1
1
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
1
0
0
2
2
0
0
1
0
2
0
2
0
2
0
0
1
0
0
0
0
2
0
2
0
0
0
0
2
1
1
2
0
0
2
0
1
0
0
0
0
1
0
0
2
0
3
1
0
0
1
1
0
0
0
0
1
0
1
0
2
0
0
1
0
1
0
1
2
1
1
2
0
0
1
1
2
1
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
2
1
1
1
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
1
0
0
2
1
2
0
2
1
0
1
2
1
1
0
2
3
2
0
0
0
1
0
1
0
0
0
0
0
1
0
2
0
0
0
0
1
2
2
1
0
0
2
0
0
0
1
0
0
2
0
0
1
0
0
0
2
0
0
1
2
0
0
0
2
1
2
0
1
1
2
0
0
0
2
2
2
2
0
0
0
0
1
1
0
0
0
1
2
1
1
0
1
0
0
1
2
0
0
0
2
0
0
2
0
0
2
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
2
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
2
0
2
0
0
2
2
0
0
0
0
0
1
0
0
0
2
0
3
0
0
1
0
0
0
0
0
1
0
2
0
0
1
0
1
0
0
0
1
0
3
0
0
0
0
1
0
0
0
1
0
0
1
0
3
0
0
0
0
0
0
1
0
1
0
1
0
0
2
1
0
0
0
1
0
0
0
0
0
0
1
1
0
2
0
0
2
1
2
0
0
1
0
0
0
0
0
0
1
0
0
2
2
1
2
0
0
1
0
1
1
0
0
0
0
2
0
0
2
0
0
2
0
0
2
0
2
0
0
0
1
10
0
0
0
0
0
1
1
0
1
0
0
2
0
0
0
0
1
0
0
0
2
0
3
2
0
0
1
0
0
1
2
1
0
2
0
2
0
0
2
1
0
0
0
0
0
2
0
0
0
2
0
0
2
0
1
1
0
2
1
0
0
0
0
0
0
1
2
0
2
2
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
5
0
0
0
0
0
1
0
0
0
1
0
0
0
2
1
2
1
0
0
2
0
0
0
2
1
1
2
0
1
1
0
1
1
0
0
0
0
0
2
2
0
0
2
0
0
0
2
0
0
1
1
2
1
0
1
0
0
0
0
2
1
0
1
0
0
1
1
1
0
3
0
1
0
0
1
0
0
1
0
0
2
0
1
0
0
0
2
1
0
0
2
0
2
1
2
0
1
1
0
2
5
0
1
0
0
1
1
0
1
0
0
0
1
2
2
2
0
0
0
0
0
0
2
2
2
1
0
0
0
2
1
0
1
0
2
0
0
0
3
1
0
1
0
0
2
1
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
2
3
2
2
2
0
1
0
2
1
1
0
2
0
0
2
0
2
2
0
0
0
0
1
0
0
0
2
1
0
0
0
2
1
1
2
1
0
1
1
0
1
0
0
0
1
0
1
0
7
0
2
0
2
0
0
0
0
0
0
0
0
1
1
1
0
2
1
0
0
2
1
2
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
1
0
1
1
1
0
0
1
0
1
1
2
0
0
0
2
0
0
0
0
0
2
0
2
0
2
0
1
2
0
2
1
1
1
0
0
1
0
0
0
2
0
1
0
0
2
1
1
0
0
0
2
0
0
0
0
2
0
2
0
4
2
1
0
2
2
2
0
0
1
0
1
1
0
2
0
2
0
0
1
2
0
0
0
0
0
1
2
0
0
1
2
0
1
2
1
0
1
2
1
0
0
0
0
0
0
2
3
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
1
0
0
0
0
0
0
2
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
2
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
1
1
1
0
1
1
1
3
0
2
0
2
0
0
0
2
0
0
0
0
1
2
2
0
2
0
0
0
0
0
1
1
0
1
0
0
2
0
2
0
0
2
1
1
0
1
1
0
0
2
1
0
0
1
1
0
0
0
0
1
0
2
0
0
1
0
1
2
0
2
1
0
0
1
0
0
2
0
0
2
0
1
2
0
0
0
2
4
2
0
0
2
1
0
0
0
0
1
1
0
0
1
2
2
2
0
2
0
0
0
1
0
0
0
2
0
1
0
1
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
1
2
0
0
1
0
2
1
1
1
1
1
0
0
0
0
0
0
2
0
1
0
1
0
2
0
0
1
2
1
1
2
0
1
3
2
2
1
0
0
0
1
1
0
0
1
2
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
2
0
0
2
2
0
0
2
2
1
0
1
0
0
0
1
0
1
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
1
1
1
0
2
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
2
2
2
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
1
1
0
0
2
0
0
1
2
10
1
0
0
1
0
1
1
2
0
1
1
1
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
2
2
2
1
0
2
2
2
1
0
0
2
1
1
3
0
0
2
0
0
2
0
1
1
0
2
1
3
0
0
0
0
1
1
2
2
1
1
0
0
0
0
0
0
0
2
0
1
1
0
0
0
1
2
2
2
0
0
0
1
0
2
1
2
0
0
1
1
0
2
2
0
1
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
2
1
0
0
1
0
1
0
0
1
1
0
0
1
0
0
0
1
0
0
2
1
1
2
2
1
2
1
0
0
4
0
1
0
0
0
0
1
1
0
0
2
0
1
1
0
1
2
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
1
1
0
2
1
0
0
0
0
0
2
1
0
1
0
2
2
1
1
1
0
2
2
1
1
0
1
0
0
2
2
0
0
1
0
0
0
1
0
0
0
0
0
1
1
2
0
0
1
1
1
0
0
0
1
0
5
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
2
0
1
0
1
1
0
0
1
1
0
1
0
2
0
2
0
1
0
0
0
1
2
2
0
0
0
2
2
0
0
2
0
2
2
0
0
0
0
0
0
3
2
0
0
0
2
2
0
0
1
1
0
0
0
0
0
0
0
2
0
0
2
4
1
2
1
1
2
2
0
1
0
0
0
1
2
2
1
0
0
2
0
0
0
2
2
1
2
0
0
0
2
1
1
0
0
1
0
2
0
0
3
2
2
1
2
0
0
1
2
2
1
0
1
0
1
1
2
1
0
2
1
0
1
0
0
1
0
1
1
0
0
0
0
1
1
0
1
1
1
0
2
1
1
0
2
0
0
0
0
1
0
1
0
0
2
0
0
0
0
2
0
1
0
2
1
0
0
0
0
0
1
1
0
1
0
2
0
0
3
0
0
0
2
1
1
0
1
0
0
0
2
0
2
2
1
0
0
1
0
0
0
0
2
0
0
0
5
0
0
0
1
1
0
2
0
1
1
1
0
1
0
0
2
0
0
0
2
0
2
2
1
1
1
0
0
0
0
0
1
1
1
1
1
0
0
2
0
2
0
1
1
0
0
2
2
2
0
1
1
0
2
0
2
0
2
0
0
1
0
2
1
2
0
0
1
3
2
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
1
1
2
0
1
0
1
0
1
0
0
1
0
1
0
0
0
2
1
2
0
0
0
0
2
0
0
1
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
1
0
1
1
2
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
1
1
0
2
0
1
0
0
1
1
0
2
1
0
0
1
3
0
0
0
0
0
0
0
0
2
1
1
0
0
2
0
1
0
2
0
1
0
1
0
1
1
0
0
1
2
0
0
2
0
0
2
1
0
2
1
2
0
2
0
1
0
1
0
2
1
1
2
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
2
0
2
3
2
0
1
34
1
0
2
0
1
1
0
1
0
1
2
1
1
0
1
0
0
2
0
0
2
0
0
1
2
0
0
0
1
2
2
0
0
0
2
0
2
2
0
0
0
1
0
1
0
2
1
0
0
3
0
0
1
0
0
0
2
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
2
0
2
1
0
1
0
0
1
2
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
3
1
0
1
0
2
1
1
0
0
2
0
0
1
1
0
0
0
0
0
1
0
0
0
0
2
1
0
0
2
1
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
1
2
2
0
0
2
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
2
0
3
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
2
0
0
1
2
0
2
2
1
0
1
2
0
1
1
0
1
0
2
1
2
0
0
0
0
1
0
1
2
0
0
0
1
0
0
2
0
0
0
0
0
0
2
1
1
1
0
1
0
1
2
1
0
0
0
2
2
1
0
0
0
2
0
0
1
1
2
0
2
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
1
1
0
0
1
0
2
0
0
1
1
1
0
3
2
0
0
1
0
2
0
2
0
0
0
0
0
1
1
0
1
0
2
0
0
0
0
8
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
2
2
0
0
0
0
0
2
2
0
0
2
2
1
2
2
1
0
0
0
1
2
0
0
0
0
0
1
1
2
1
2
1
0
0
1
0
1
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
1
1
0
0
1
2
0
0
2
0
0
1
1
0
0
1
0
2
0
2
1
2
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
1
0
0
1
0
0
0
0
1
2
2
1
1
0
0
0
1
0
2
0
0
0
1
0
0
0
0
2
0
1
2
2
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
1
0
1
0
1
0
2
1
1
0
0
0
2
1
0
0
1
0
1
0
1
0
0
0
0
4
0
1
0
0
0
3
0
0
0
1
1
1
2
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
2
1
0
0
0
1
2
0
0
0
0
1
1
1
1
0
0
1
1
0
1
1
0
0
0
0
0
2
1
0
0
2
0
2
0
1
0
1
0
2
1
2
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
1
1
2
1
0
0
1
1
0
0
1
3
0
1
0
1
1
0
0
0
1
0
0
0
0
2
0
1
0
0
2
0
1
1
0
0
1
3
1
0
1
0
0
2
2
0
0
0
0
2
0
0
0
2
0
0
0
2
0
1
0
0
0
2
0
0
0
2
4
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
1
2
3
0
0
1
1
0
0
0
2
2
1
0
0
0
0
0
1
1
0
0
0
1
0
2
2
1
0
0
0
0
3
0
0
1
2
3
2
0
2
0
0
2
1
0
0
1
0
1
2
0
0
1
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
2
1
0
0
2
2
0
0
1
0
0
0
0
1
0
2
1
1
5
1
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
3
2
0
1
2
0
1
0
0
0
1
0
2
0
2
1
0
1
0
2
0
2
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
2
0
0
0
1
1
0
4
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
2
0
3
1
0
2
0
3
2
2
0
0
1
0
2
0
0
2
0
0
1
0
2
0
0
2
0
0
1
0
1
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
3
0
2
0
3
0
0
0
0
2
1
0
0
0
1
1
0
1
2
3
0
0
2
1
2
0
0
0
1
0
0
2
1
4
2
1
2
1
2
0
2
1
2
1
0
0
1
0
1
1
0
1
0
0
0
0
0
1
0
2
0
0
0
0
2
2
0
1
1
2
1
0
0
2
0
0
1
0
0
0
1
0
2
0
1
0
0
2
2
2
3
0
0
0
0
2
1
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
7
2
0
0
1
0
0
1
0
1
2
1
0
0
0
0
0
1
0
1
0
0
0
0
1
2
0
0
3
2
0
1
1
2
1
0
0
0
0
2
2
0
0
0
1
0
0
1
2
1
0
0
2
0
1
0
0
0
2
1
2
0
0
0
1
1
2
0
2
0
1
1
0
2
0
1
0
1
2
3
1
0
1
1
0
0
0
0
2
0
1
0
1
1
1
0
1
0
0
0
0
2
1
0
0
2
4
3
0
2
2
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
2
0
1
0
0
0
0
1
2
1
1
2
1
3
1
0
0
2
1
1
0
2
0
2
3
1
0
1
0
1
0
0
0
0
0
0
0
2
1
1
0
0
3
0
0
0
0
0
0
0
0
1
1
2
2
1
0
1
2
0
0
1
0
0
1
2
1
0
1
0
0
0
2
1
1
0
0
0
0
0
1
2
2
1
0
0
1
2
0
0
0
2
0
0
1
2
0
0
0
1
2
1
0
0
2
1
0
0
2
0
2
1
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
4
1
0
0
1
1
0
1
0
0
2
1
0
4
0
0
4
0
2
1
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
1
1
0
1
0
2
0
1
0
0
0
0
0
2
0
2
2
2
1
0
1
1
2
0
0
0
1
2
2
2
0
0
0
4
2
0
1
0
1
0
1
0
0
2
1
1
1
0
0
1
0
0
1
0
0
0
4
0
0
0
0
0
1
0
1
0
0
1
0
0
2
1
1
2
1
0
3
1
0
1
0
1
3
2
0
0
0
1
1
1
0
0
1
1
1
1
1
0
1
0
1
0
0
2
2
0
0
0
0
1
0
0
0
1
1
2
1
0
2
2
0
0
0
0
1
1
0
0
2
0
0
1
0
1
1
1
1
1
2
1
2
0
0
0
2
2
1
0
0
0
2
1
1
1
0
2
1
1
1
2
2
0
0
1
0
2
0
0
0
0
0
1
2
1
2
0
0
2
0
0
0
2
0
1
1
2
1
0
1
0
2
0
0
1
1
1
0
2
0
1
1
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
3
0
0
1
0
0
0
0
0
0
0
1
1
0
2
0
0
0
1
0
0
0
0
2
2
0
2
3
0
0
0
2
0
0
0
0
1
1
1
0
0
0
4
0
0
0
0
1
0
0
1
0
2
1
0
1
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
2
0
1
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
2
0
0
0
0
1
1
0
0
2
1
0
0
2
0
0
0
0
0
0
2
2
0
2
0
2
0
0
2
3
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
2
3
1
4
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
1
0
1
1
2
1
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
2
2
0
1
1
0
0
0
0
0
0
1
2
0
0
1
2
1
0
0
1
2
0
1
1
1
0
1
1
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
2
1
0
0
1
0
0
0
0
3
0
1
0
1
0
0
0
2
0
1
1
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
1
1
0
2
0
2
0
2
0
3
0
0
0
0
0
0
0
2
0
0
0
0
1
1
1
0
0
0
0
0
2
0
0
0
1
2
0
2
0
2
0
3
1
0
0
2
2
1
0
2
3
0
0
2
0
1
0
0
0
0
0
1
2
0
0
0
2
0
2
0
2
1
0
3
0
1
0
2
1
0
0
2
2
2
0
2
0
1
2
0
0
1
2
1
0
2
0
1
0
1
1
0
0
2
0
0
2
2
0
0
0
1
0
1
0
0
1
0
2
0
2
0
1
1
0
0
1
0
0
1
0
0
1
0
0
1
0
2
1
0
0
0
0
0
1
0
0
0
1
0
0
0
3
0
0
0
0
1
1
2
0
2
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
2
1
3
0
2
1
3
2
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
2
2
1
1
8
0
0
0
2
0
0
2
0
2
0
0
0
1
1
2
1
1
1
7
3
0
0
0
1
0
1
0
0
2
2
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
2
0
0
0
0
2
0
0
1
0
1
2
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
2
0
2
0
0
1
0
1
2
2
0
0
0
2
0
2
0
0
0
1
0
0
2
0
0
0
1
0
0
1
0
0
0
0
2
0
2
0
0
3
0
0
0
2
0
0
2
0
0
0
0
1
1
2
2
0
0
2
2
0
0
0
2
2
1
0
2
1
0
0
1
2
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
1
0
0
2
1
0
0
1
1
1
1
4
2
2
0
0
0
0
1
0
2
1
1
0
0
0
0
2
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
1
1
1
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
3
0
1
0
3
0
2
0
0
1
1
1
0
0
0
1
3
0
0
0
1
0
0
2
2
1
2
0
1
2
2
1
1
0
0
1
2
0
0
1
0
2
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
1
0
2
0
2
4
2
1
0
1
0
1
2
0
2
1
2
1
0
2
2
2
0
1
0
1
0
1
0
0
0
1
0
0
0
0
2
0
2
0
0
1
1
0
0
4
0
0
0
1
2
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
1
2
1
0
3
0
1
1
2
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
2
0
1
0
0
0
0
1
0
2
0
0
0
1
0
0
0
1
0
1
0
0
2
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
1
0
1
1
5
0
0
0
0
1
1
0
1
0
2
0
0
1
1
0
0
0
0
2
0
0
0
2
1
2
1
0
2
2
0
0
0
1
0
1
0
0
0
0
1
2
0
1
2
1
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
1
1
1
2
1
0
2
1
0
1
0
0
2
0
2
0
0
0
0
0
1
0
0
1
1
2
0
0
1
0
1
0
0
2
0
1
0
0
2
0
2
0
3
0
0
0
0
0
1
0
0
0
0
1
1
0
2
1
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
2
1
1
1
0
0
0
0
0
1
0
0
0
0
2
2
3
0
2
0
2
2
2
2
0
0
0
0
1
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
1
0
1
0
0
1
0
0
2
0
0
2
0
0
0
1
1
0
1
0
2
0
0
0
2
0
0
2
1
2
5
2
0
2
0
0
0
4
0
0
0
1
0
2
0
1
2
1
0
1
0
0
0
2
0
0
0
0
1
0
0
3
1
0
0
0
1
1
2
0
1
0
2
0
0
1
1
2
2
2
1
0
0
0
0
0
0
1
1
0
0
1
0
0
2
0
0
1
0
1
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
2
1
0
0
0
1
0
1
0
0
3
0
0
0
2
0
0
0
0
2
0
2
0
2
2
2
0
1
0
0
1
2
0
1
1
0
1
0
3
0
1
0
2
0
0
2
2
0
0
1
0
0
1
0
0
1
0
2
0
4
2
0
0
0
0
0
2
0
0
0
0
0
4
2
0
1
0
0
3
0
2
1
2
0
0
1
1
0
0
0
0
0
2
2
0
0
0
2
0
0
2
1
0
0
1
0
0
1
1
1
0
0
0
0
1
0
0
0
2
2
1
2
0
1
2
0
1
0
1
1
0
1
1
0
1
0
0
2
1
0
0
1
0
0
0
0
0
0
0
2
0
2
0
1
0
0
2
1
3
0
1
2
1
0
0
0
0
2
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
4
0
2
0
1
1
0
1
0
0
0
1
0
0
0
1
1
1
0
0
0
1
1
1
1
1
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
1
1
1
1
2
0
1
0
0
0
2
0
1
0
0
0
1
0
0
1
0
0
3
0
3
0
1
1
1
0
1
3
0
4
0
0
2
2
0
1
2
2
1
0
1
2
0
1
0
0
4
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
2
0
1
0
1
2
1
2
1
1
1
0
1
0
0
1
1
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
2
1
0
0
0
3
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
2
0
0
2
1
2
1
0
3
0
0
0
2
1
0
0
3
1
1
1
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
2
1
1
0
0
1
1
0
0
0
0
0
2
0
2
0
1
2
2
1
2
0
0
0
1
0
2
1
1
1
3
0
0
0
2
2
0
1
0
2
0
2
0
2
1
0
1
0
0
1
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
2
0
1
2
0
0
1
2
0
1
3
0
0
2
2
0
0
0
2
0
0
1
0
0
0
2
1
2
0
0
1
0
2
1
0
2
2
0
0
2
0
0
0
2
1
0
1
2
0
0
0
2
1
0
0
0
5
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
1
2
1
0
1
0
0
0
0
2
0
0
0
0
1
0
0
2
1
0
0
0
0
1
2
3
3
0
1
1
0
0
1
0
0
0
0
0
1
0
0
3
0
1
2
0
2
2
0
0
2
0
0
0
2
0
0
2
0
1
0
0
0
3
2
0
3
0
0
0
0
3
0
0
1
0
0
1
2
2
1
2
0
0
2
1
1
1
0
0
0
0
0
0
0
0
1
1
0
1
2
0
2
1
2
0
1
1
2
0
0
1
1
1
0
0
0
2
2
0
1
0
1
0
0
2
2
1
0
1
2
1
0
0
2
1
0
1
2
1
0
0
1
0
0
0
1
0
0
0
1
1
2
0
0
0
2
0
2
2
2
2
0
0
0
0
0
0
2
1
1
0
2
0
0
0
0
0
2
0
2
0
1
1
2
0
0
0
0
0
0
0
2
1
1
0
0
2
1
0
0
0
1
1
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
2
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
2
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
1
3
0
0
0
2
0
0
0
0
1
0
2
1
0
0
0
0
0
1
1
0
0
1
1
0
1
1
0
0
2
2
0
0
2
2
0
0
1
0
1
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
1
2
0
1
0
0
0
0
2
1
5
1
0
0
2
0
1
2
0
2
0
0
2
2
1
0
0
0
2
2
0
2
1
2
0
2
0
1
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
1
0
0
2
3
0
0
1
1
1
4
1
1
2
2
0
2
0
1
0
2
2
0
0
0
0
0
1
0
1
2
0
1
2
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
2
1
0
1
0
5
0
1
0
0
0
0
0
1
2
1
1
0
0
1
0
0
0
0
0
0
0
2
0
2
0
1
0
3
3
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
2
3
0
0
2
0
0
1
1
0
1
0
1
0
0
0
0
0
1
1
0
2
0
1
0
1
0
0
0
2
0
2
0
2
1
2
0
0
1
0
0
0
0
1
1
2
0
0
1
1
0
0
1
0
1
1
3
0
0
2
0
1
2
0
1
0
1
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
1
1
2
1
2
2
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
1
1
0
0
0
2
2
0
0
1
2
1
0
1
1
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
1
4
0
1
1
1
0
0
0
1
1
0
0
0
3
2
2
0
1
0
0
2
2
1
1
0
0
4
0
1
0
0
2
0
0
1
0
2
0
2
0
0
0
2
0
2
1
1
1
0
2
1
2
1
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
2
0
2
2
2
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
2
0
3
0
0
2
2
0
1
0
0
1
0
1
2
2
2
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
1
1
2
0
0
2
0
1
0
2
5
0
3
0
0
1
0
0
1
0
2
0
2
2
1
1
1
0
0
2
1
0
0
1
0
0
1
2
0
0
0
1
2
0
0
1
1
0
2
1
1
0
0
2
0
0
0
2
0
1
0
1
1
2
2
2
1
1
2
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
2
0
0
3
0
1
3
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
2
2
2
2
1
2
0
0
1
2
2
0
0
1
2
0
0
0
0
1
0
0
0
1
0
0
1
1
0
2
0
0
0
0
0
0
0
2
0
0
2
1
2
0
2
0
2
0
2
0
2
1
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
1
1
0
1
2
0
2
0
0
2
1
0
0
2
2
6
1
1
0
1
2
0
0
0
2
2
0
0
4
2
2
1
1
1
2
0
1
0
0
1
1
0
0
1
0
1
2
0
0
1
0
0
2
1
0
0
1
0
0
2
0
0
2
2
0
0
1
0
0
1
1
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
2
0
0
1
0
0
0
0
4
1
0
1
1
0
1
0
0
2
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
2
2
2
0
3
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
1
0
0
2
0
0
1
2
0
1
0
1
0
0
0
0
0
0
0
1
2
1
1
0
2
0
2
1
0
1
1
1
0
1
0
2
0
1
0
0
0
1
2
5
2
1
2
0
0
2
0
0
0
5
0
0
1
0
0
0
0
2
0
1
1
0
1
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
1
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
1
1
0
0
0
1
0
0
0
2
1
0
2
0
0
0
0
0
0
0
1
1
1
1
2
4
0
0
0
1
0
1
0
2
0
3
0
0
0
2
0
0
0
4
0
2
0
1
0
0
0
0
0
2
0
0
2
1
2
1
2
0
2
0
0
1
0
0
0
0
0
1
2
0
1
0
0
2
0
1
2
0
1
0
1
1
0
0
1
0
3
1
0
2
0
0
0
2
1
2
0
1
1
0
1
0
1
0
0
2
0
1
2
2
0
0
0
2
0
1
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
2
0
1
1
0
0
0
0
0
1
0
1
2
0
0
1
0
0
1
2
0
1
0
0
1
1
0
2
0
2
4
1
0
2
0
2
2
0
3
2
2
1
0
0
2
1
0
0
0
0
1
1
0
1
0
2
0
0
0
0
1
0
1
0
1
0
1
1
0
0
1
0
2
0
2
0
0
0
0
0
0
1
0
1
2
0
2
0
2
0
1
0
2
1
2
0
0
1
0
1
2
1
0
0
0
1
1
2
0
0
2
0
0
1
0
1
0
2
0
0
1
0
1
1
0
0
2
0
0
1
2
0
0
0
0
2
2
0
0
0
0
3
0
0
0
0
0
1
2
2
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
3
0
1
3
0
0
2
2
1
2
0
0
2
0
0
0
2
1
0
0
0
2
0
0
1
2
1
2
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
1
0
2
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
1
1
0
1
0
1
0
0
1
0
0
1
0
2
0
2
1
0
1
3
1
0
1
0
2
1
0
1
1
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
2
0
1
2
2
0
0
1
0
1
0
0
1
1
0
0
0
0
1
0
0
1
0
1
1
0
0
1
0
1
0
0
1
2
0
0
1
0
1
0
3
1
0
2
0
2
0
0
0
1
1
1
0
2
0
1
0
1
2
2
0
1
0
0
0
2
1
0
1
2
0
0
2
1
0
0
2
0
1
0
1
0
0
0
0
0
3
0
0
0
1
2
2
3
0
1
0
2
1
0
1
1
1
0
2
1
0
0
0
0
0
0
0
2
2
1
2
1
0
1
0
0
1
1
0
0
0
0
0
2
0
0
0
1
2
1
0
0
0
1
1
3
1
1
1
0
0
0
2
0
0
0
0
0
1
0
3
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
2
0
0
1
0
0
1
2
1
0
0
0
0
0
2
1
0
0
2
2
0
0
1
2
2
0
1
0
0
0
0
0
0
0
1
2
0
2
1
2
4
1
0
1
1
0
0
2
1
1
0
2
1
2
0
0
1
1
2
0
0
0
1
0
0
0
2
2
0
0
0
0
0
2
0
0
0
1
1
1
0
2
0
2
1
2
1
0
2
1
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
1
0
0
2
1
0
2
0
2
1
2
0
0
0
0
2
1
0
0
1
0
2
0
0
0
0
0
0
2
1
0
1
0
2
0
2
0
1
1
0
1
2
0
0
0
0
0
0
3
0
1
0
1
0
0
1
1
2
0
1
0
0
0
0
0
1
0
0
0
1
3
1
0
1
0
1
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
2
0
1
0
1
1
2
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
1
2
0
1
1
0
3
0
0
0
0
0
0
2
1
2
2
1
0
2
0
0
0
0
0
0
1
1
0
1
2
0
2
4
1
0
2
2
0
1
1
0
0
0
1
0
7
1
2
1
2
0
1
2
0
1
0
0
0
1
2
1
1
2
1
0
2
1
0
0
2
0
0
2
0
3
0
0
1
0
0
1
0
0
0
1
0
2
1
1
1
0
0
1
2
0
0
2
2
2
0
2
1
2
1
0
1
1
0
0
2
0
0
3
1
0
0
2
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
1
1
0
2
0
4
0
2
0
0
1
0
1
0
0
1
0
2
2
0
0
1
1
0
0
2
0
1
0
1
2
0
2
0
0
0
0
0
1
1
2
0
1
1
0
1
1
2
0
2
1
0
0
0
2
0
2
0
1
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
2
2
0
0
1
2
1
2
1
2
1
0
0
0
0
0
0
2
2
1
1
2
0
0
0
0
0
0
0
1
2
1
1
1
0
0
0
2
0
2
1
1
2
0
2
0
1
2
0
2
0
0
1
1
0
0
1
1
0
0
0
0
0
0
2
2
1
1
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
1
0
1
2
1
0
0
0
0
2
1
1
2
2
0
0
0
4
0
0
1
1
0
0
0
0
2
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
3
1
1
0
0
2
0
0
0
2
2
0
0
1
0
1
0
0
2
0
0
2
1
2
0
0
1
0
0
2
0
1
0
2
0
1
0
0
0
0
2
0
1
0
2
0
2
0
0
0
0
1
1
0
0
1
0
2
3
0
0
2
0
2
0
2
0
0
2
0
1
1
0
0
2
0
0
0
2
0
1
0
2
0
1
0
0
1
0
2
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
1
1
0
0
0
0
2
0
2
1
2
1
0
0
2
0
0
0
1
1
0
0
2
2
0
1
0
2
2
0
0
2
0
2
0
1
2
1
0
0
1
0
0
1
0
2
0
0
0
1
1
0
0
5
2
1
4
2
1
0
1
1
0
0
0
1
0
0
0
0
0
2
1
2
1
0
0
0
2
1
0
0
1
2
1
2
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
2
0
0
0
0
0
3
0
1
0
0
1
1
2
1
2
0
0
0
0
0
0
1
0
2
1
0
4
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
2
1
2
1
1
1
0
2
0
0
0
0
1
0
0
1
0
0
0
0
2
0
1
1
0
2
0
1
0
1
0
0
0
2
0
0
0
2
2
0
1
0
0
2
0
0
1
0
0
0
2
1
0
0
1
0
1
1
2
1
0
0
0
1
1
4
1
0
0
0
0
0
0
0
0
0
1
2
0
0
2
2
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
1
2
0
1
0
2
0
0
1
0
2
4
1
2
0
2
0
2
1
1
0
0
0
0
3
0
0
2
1
0
0
0
1
0
0
0
0
1
0
2
0
0
3
0
1
0
0
0
0
0
1
0
5
1
0
2
0
1
0
1
2
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
2
1
1
1
0
2
0
2
0
1
2
0
1
0
1
2
0
0
2
2
0
1
0
1
0
0
1
2
0
0
0
1
1
0
0
1
0
0
0
0
0
1
1
0
2
1
0
2
0
0
2
2
4
0
0
0
0
2
0
2
0
1
0
0
1
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
2
0
0
0
0
0
1
1
0
1
0
2
0
2
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
2
0
0
3
2
0
0
0
0
1
0
0
0
2
0
1
0
2
0
0
0
0
0
0
1
0
15
0
0
0
1
0
0
0
0
1
0
1
0
2
0
2
1
0
0
0
2
1
0
0
1
0
0
3
0
0
0
0
0
0
1
0
0
1
1
0
2
0
0
0
0
5
0
0
2
1
1
2
1
2
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
3
2
0
3
1
0
0
0
0
0
0
1
0
2
0
0
10
0
0
2
0
1
0
0
0
2
2
0
0
1
0
2
1
0
0
2
0
0
2
0
0
1
1
0
0
0
0
0
0
2
2
1
0
0
1
0
1
0
0
0
0
0
1
0
0
2
1
1
0
1
0
1
0
1
0
2
1
2
1
1
0
1
1
3
0
0
0
0
1
1
1
1
0
0
0
0
1
0
0
0
2
0
2
0
1
1
3
1
2
0
0
0
1
2
0
1
0
1
2
1
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
2
0
1
0
0
0
4
0
0
0
0
0
2
0
6
2
0
1
0
0
1
1
1
0
1
2
2
1
1
0
1
1
2
0
0
0
2
2
0
2
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
2
4
0
4
2
0
0
2
1
0
0
1
0
0
0
2
1
2
0
0
0
0
0
2
0
0
1
2
2
0
1
0
2
0
0
0
0
1
1
0
0
0
0
0
2
4
4
3
1
0
1
0
0
0
1
2
0
2
0
1
0
0
1
0
1
0
0
0
0
2
0
0
2
0
0
1
0
2
0
1
0
2
0
0
2
0
0
1
1
2
2
1
1
0
0
0
2
1
0
0
1
1
0
1
1
1
0
2
0
2
1
1
2
0
0
2
2
1
2
1
1
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
1
1
0
1
0
0
1
1
1
0
0
1
0
2
0
0
0
0
1
0
0
1
2
0
0
3
0
0
0
2
1
0
4
1
0
0
0
0
0
1
11
0
0
1
0
2
2
1
0
2
0
2
0
0
2
1
1
2
0
0
1
0
1
1
2
2
0
0
1
3
2
0
0
0
2
2
1
1
1
0
0
1
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
2
1
0
0
0
2
1
0
0
0
0
0
1
1
1
0
1
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
1
2
0
0
1
1
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
2
0
0
1
1
1
0
0
1
1
0
2
1
0
1
0
1
0
0
0
0
1
1
1
1
0
2
2
0
0
2
0
0
1
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
1
2
1
1
0
0
0
1
0
0
0
2
2
0
1
0
0
1
0
2
0
0
2
0
2
2
0
0
0
0
2
0
0
2
0
0
2
1
0
2
0
0
3
1
0
2
1
0
0
2
0
0
0
0
0
0
0
2
1
3
1
2
1
1
0
0
3
1
0
0
0
0
0
2
0
0
2
0
1
2
0
1
1
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
2
1
1
1
0
1
0
1
2
0
2
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
2
2
3
2
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
3
2
2
1
0
2
0
2
0
1
0
0
0
0
2
2
0
0
3
2
0
4
0
1
0
0
0
0
1
1
2
0
0
0
1
1
1
0
0
2
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
1
0
2
1
0
0
2
0
0
0
0
2
0
0
2
0
1
1
0
0
1
0
0
0
0
1
1
0
6
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
2
0
1
2
0
0
0
0
1
0
0
2
1
0
0
2
1
0
2
1
0
0
2
1
1
1
0
1
0
0
3
0
0
2
0
0
0
1
2
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
2
1
0
0
5
2
0
0
0
6
0
0
0
3
0
1
1
1
1
2
0
0
0
0
0
1
1
0
0
0
0
0
1
2
1
0
0
0
1
0
0
1
0
1
0
1
1
2
0
0
1
1
0
1
1
0
1
2
0
2
0
0
0
3
2
1
0
1
0
1
0
1
0
2
1
0
2
0
2
0
0
0
1
1
2
1
0
0
2
1
0
0
1
0
2
1
0
1
1
2
0
2
0
1
0
2
0
0
0
0
0
1
0
2
0
1
1
2
0
2
0
1
0
0
0
1
2
0
2
0
2
1
2
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
2
0
1
2
2
2
2
0
0
0
0
4
0
0
1
1
0
0
0
0
0
2
1
2
0
1
2
0
2
2
1
1
0
0
2
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
1
2
0
0
0
1
4
1
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
1
1
0
0
0
0
0
1
0
2
0
0
1
0
0
1
2
0
0
0
1
2
0
0
0
2
0
1
0
1
1
0
2
2
2
2
0
0
0
0
1
1
1
0
0
2
0
0
0
0
0
3
0
2
0
0
2
2
0
0
2
0
1
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
1
1
2
0
2
1
0
0
1
0
0
0
0
0
2
0
0
0
0
2
1
1
0
0
4
0
1
0
2
0
0
0
0
0
0
1
2
2
1
0
0
0
0
1
2
0
2
0
1
0
2
0
0
1
0
2
0
0
0
0
1
3
0
1
1
0
0
1
0
0
0
2
0
1
0
1
0
2
0
0
0
1
1
0
0
0
1
0
0
0
2
1
0
1
1
0
0
2
0
1
7
1
0
1
0
2
0
1
1
0
0
0
0
0
0
1
1
0
1
0
2
1
0
1
1
1
0
1
0
0
1
0
1
2
0
0
2
1
2
2
1
0
0
2
0
0
0
2
0
0
2
2
0
0
2
1
1
1
1
0
0
2
0
0
1
2
0
2
1
0
0
1
0
2
2
1
0
0
0
2
0
6
3
0
0
2
2
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
1
2
2
1
0
2
2
0
0
0
2
2
2
0
2
2
0
1
1
0
0
1
1
0
0
1
2
0
0
2
1
0
0
0
1
0
1
0
2
0
1
0
0
0
0
0
1
3
2
0
0
2
1
1
0
0
2
0
1
2
2
0
1
1
0
0
3
1
1
0
0
0
0
2
1
0
0
0
0
0
1
0
0
1
0
2
0
0
1
0
1
0
2
2
0
0
0
0
1
1
2
1
2
0
0
0
2
0
2
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
1
0
0
2
0
0
0
0
0
0
0
1
0
2
1
1
0
1
0
2
2
0
0
0
1
0
0
0
2
1
0
1
0
0
2
1
0
0
2
0
1
0
1
0
0
1
0
1
0
0
2
1
1
1
0
0
2
2
0
0
0
1
0
5
0
0
0
0
0
2
1
1
0
0
1
0
2
0
0
2
0
3
1
2
0
0
1
2
0
0
0
2
0
1
1
0
0
2
4
0
2
1
0
0
0
0
2
1
0
0
1
0
2
0
1
1
0
0
2
2
0
0
1
2
0
0
1
0
1
0
0
0
0
4
2
2
0
0
1
0
2
0
0
2
0
0
0
0
0
0
1
0
2
0
0
2
0
1
2
1
0
0
1
0
2
0
0
0
0
0
1
1
0
2
0
1
2
0
0
1
0
1
1
0
3
1
0
0
2
0
1
0
0
0
0
0
1
0
1
0
4
1
2
1
0
0
2
2
0
2
2
2
2
1
0
0
0
0
0
0
0
2
1
0
2
1
1
1
0
2
0
1
0
1
2
0
0
2
0
0
2
0
0
0
1
0
1
2
0
0
1
0
1
0
0
0
0
1
1
2
0
0
0
2
3
0
0
1
0
1
0
2
0
0
0
0
1
1
0
0
0
0
2
0
2
1
1
3
0
0
0
1
0
2
0
0
2
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
2
0
1
0
0
0
0
1
0
1
0
2
0
0
2
0
2
2
1
1
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
1
1
0
0
0
2
0
0
0
3
0
0
2
0
1
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
2
0
0
0
0
2
3
2
1
2
2
1
0
2
0
0
2
2
0
0
0
0
1
0
0
2
2
0
2
2
1
0
0
1
0
1
1
0
0
1
1
1
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
2
0
1
0
0
1
1
1
1
2
3
0
0
0
1
0
0
0
1
1
0
1
1
0
1
0
2
1
0
0
0
0
0
1
0
2
0
0
0
2
0
1
2
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
2
1
0
0
1
0
0
0
1
0
2
1
0
0
0
2
1
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
1
0
1
2
0
0
0
0
1
0
0
2
1
0
0
0
0
0
2
0
0
2
0
0
0
2
2
0
0
0
0
0
1
0
0
1
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
5
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
3
0
2
0
1
2
1
1
0
2
2
1
1
0
1
1
0
0
1
0
1
1
2
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
2
1
3
0
0
1
2
1
0
2
0
0
0
0
0
0
2
1
0
2
0
1
0
2
1
0
2
0
0
2
2
2
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
2
2
0
1
0
2
0
0
0
0
0
0
1
0
2
0
1
2
0
2
0
1
0
2
0
0
0
0
2
0
1
0
2
0
0
1
0
0
0
0
3
0
0
0
0
1
0
1
0
0
1
0
0
0
3
2
0
1
2
0
1
0
0
0
0
0
2
0
2
0
1
0
2
1
0
0
0
0
1
1
2
0
0
0
0
0
1
1
1
0
2
2
1
0
0
0
0
0
1
0
2
0
0
0
2
0
1
0
0
1
1
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
1
6
2
0
0
0
0
2
0
1
0
0
0
1
0
2
0
0
1
0
0
2
0
1
2
2
0
0
0
2
1
0
0
1
0
2
0
0
0
1
0
1
1
2
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
2
1
0
0
2
0
0
0
4
0
0
1
0
0
5
0
1
0
1
0
3
0
1
1
2
2
0
0
1
0
0
1
1
1
0
2
1
0
4
2
2
0
0
0
0
1
0
0
0
1
0
0
0
2
1
0
1
0
1
1
1
0
0
1
2
2
0
2
0
0
0
0
4
0
1
0
2
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
1
0
0
0
2
0
2
0
0
0
0
2
1
0
0
0
1
0
0
4
3
2
0
0
0
1
0
2
0
0
0
0
1
0
0
2
0
0
0
2
0
2
0
0
1
1
1
9
0
0
0
1
0
1
2
0
0
2
0
1
2
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
2
1
0
0
0
3
1
1
2
0
0
0
2
0
0
0
0
2
1
2
0
1
0
2
2
0
0
1
0
1
0
0
0
4
2
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
2
0
0
0
0
0
0
1
1
0
0
0
0
2
0
1
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
3
1
0
1
0
2
0
2
0
0
0
0
2
0
2
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
2
3
2
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
2
0
0
0
0
1
1
0
0
0
2
0
1
0
2
0
0
1
2
0
0
0
1
0
1
0
0
0
1
2
0
0
2
2
0
1
0
0
2
0
2
0
0
2
2
1
0
0
1
2
0
1
0
1
0
2
1
0
0
0
0
1
0
2
0
0
1
0
1
2
0
1
0
1
2
1
0
0
1
2
1
0
1
0
0
0
0
0
0
1
0
4
0
0
1
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
2
1
0
0
0
0
0
1
1
0
0
1
1
1
0
0
1
0
0
0
0
0
0
2
0
2
0
2
2
1
1
1
2
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
2
1
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
3
2
0
1
0
0
0
1
2
0
0
0
1
0
2
0
0
2
2
0
1
0
1
0
2
0
0
2
0
1
0
2
0
2
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
4
2
0
2
0
1
0
0
2
0
1
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
1
0
0
2
0
1
0
0
0
1
0
1
0
1
1
0
0
0
1
0
2
0
0
0
2
0
0
1
0
1
0
0
0
0
0
2
2
1
1
2
2
0
0
1
0
0
2
1
2
0
1
0
1
2
0
0
0
0
1
1
0
0
2
1
1
0
2
2
2
0
1
0
1
1
0
1
0
1
0
0
0
0
2
0
0
0
3
0
0
0
2
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
1
0
1
2
0
1
0
0
1
1
1
1
0
0
2
0
1
0
0
0
0
0
1
1
3
0
1
1
2
0
0
1
1
1
0
0
2
2
0
0
2
0
0
2
1
1
0
1
0
0
0
1
0
2
2
1
1
0
1
0
0
1
0
0
0
1
1
1
1
0
1
2
4
1
2
0
0
0
0
2
0
0
0
0
1
0
0
0
1
2
0
0
2
3
2
0
0
2
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
1
1
2
1
0
0
0
0
0
2
0
1
1
0
2
0
1
1
0
0
1
1
1
2
0
1
0
0
0
2
1
0
1
3
2
0
2
5
0
2
1
1
0
0
1
0
0
0
1
0
0
0
0
1
2
2
2
1
0
0
2
0
2
0
0
2
0
2
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
2
0
0
1
0
4
0
1
2
0
2
2
2
0
2
2
0
2
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
2
1
2
0
0
0
0
0
0
1
1
2
0
1
0
0
0
2
0
1
0
0
1
2
1
1
1
1
1
0
1
0
1
0
2
2
0
2
2
2
1
1
0
0
0
0
0
0
1
0
2
1
0
0
1
1
1
1
0
1
1
0
0
0
1
0
2
1
0
0
2
0
0
0
0
2
1
0
0
1
0
0
0
6
1
0
2
0
2
0
1
1
1
0
2
0
0
0
0
0
0
2
1
0
0
0
1
0
2
0
0
2
2
0
0
0
2
0
0
0
1
0
0
3
0
0
0
0
0
2
0
0
1
0
0
3
1
0
1
1
0
3
0
1
0
0
0
2
0
2
4
2
1
0
1
0
2
1
2
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
2
2
0
2
0
0
1
0
0
0
0
0
0
1
2
0
2
1
0
0
2
1
0
0
0
0
0
0
1
2
0
2
0
0
0
1
2
0
2
2
0
0
2
2
2
0
1
0
0
0
0
2
1
0
2
0
1
0
0
0
2
0
1
0
0
0
2
0
0
4
2
0
0
2
1
1
0
2
2
0
1
2
0
1
1
1
0
1
0
2
2
0
1
1
1
2
2
0
1
2
2
0
3
0
2
0
2
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
2
2
2
0
1
1
0
2
0
2
0
1
0
0
0
1
1
0
0
0
1
0
2
0
2
2
1
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
1
2
0
2
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
2
1
0
0
2
1
0
1
0
0
0
1
2
0
0
1
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
1
1
1
0
2
1
0
0
0
0
2
2
0
0
0
1
3
0
2
0
2
2
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
1
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
3
2
0
0
0
0
0
0
2
1
0
2
0
2
0
0
0
2
2
0
2
0
0
0
0
0
0
1
0
1
0
2
1
2
0
2
0
2
2
0
1
0
0
0
2
0
0
2
2
0
2
2
1
1
0
1
1
1
0
2
0
0
2
2
2
0
2
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
1
2
1
0
2
0
0
0
2
0
0
0
1
1
0
0
0
0
2
2
1
0
0
1
2
0
0
0
0
0
0
0
0
0
1
1
0
2
4
0
0
1
1
0
0
0
2
0
5
0
1
1
0
2
0
0
0
1
2
1
0
0
0
2
1
0
2
0
2
2
2
0
0
2
0
0
1
1
1
0
1
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
2
2
1
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
2
0
1
1
0
1
4
0
0
0
0
0
0
1
0
4
0
0
1
0
0
1
0
0
1
0
0
1
2
2
0
0
0
0
0
2
2
1
0
0
0
1
1
0
0
1
0
0
1
2
1
0
0
1
1
0
1
2
2
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
1
1
2
0
1
1
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
1
0
2
0
0
1
3
0
1
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
1
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
2
1
2
0
2
2
0
0
0
1
0
0
0
1
0
1
0
0
1
2
1
0
1
0
0
0
0
0
0
0
0
2
2
1
2
1
0
0
0
2
0
1
0
0
0
1
0
1
2
1
0
0
0
2
2
0
1
1
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
2
1
0
0
2
1
0
1
0
0
2
0
0
0
0
2
1
0
2
1
0
0
0
0
0
0
2
2
0
0
0
2
2
3
0
0
2
0
0
1
1
3
2
0
2
1
1
0
0
1
1
2
1
2
0
0
0
1
0
0
1
0
0
2
2
0
2
0
0
2
0
1
0
1
1
0
1
1
0
0
0
2
0
0
2
1
1
0
1
2
0
1
1
2
2
2
1
0
0
0
0
0
1
2
1
0
3
0
2
1
2
1
2
0
7
1
0
1
0
0
1
0
0
1
0
4
2
0
2
0
0
0
0
0
0
4
0
0
1
2
1
0
0
1
0
0
0
0
0
0
2
2
0
0
1
1
0
2
0
1
2
0
1
0
0
10
0
0
0
2
1
0
1
2
1
1
1
2
0
2
0
0
1
1
0
1
0
0
0
0
1
0
0
2
1
0
0
1
0
0
1
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
1
1
0
1
0
1
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
3
0
0
2
1
0
0
1
0
1
0
0
0
1
2
2
1
0
0
0
0
0
0
2
4
0
0
1
0
1
0
0
0
1
0
0
0
4
0
0
0
0
0
0
2
0
0
0
1
0
0
2
2
0
2
1
1
1
0
1
2
2
0
1
0
0
0
1
0
1
1
1
1
0
2
0
1
0
0
1
0
2
2
0
0
3
0
2
0
2
0
1
0
2
2
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
1
0
2
0
0
2
0
0
0
2
2
0
0
1
2
0
1
0
2
0
4
1
0
0
3
0
0
2
0
2
2
1
0
0
0
1
2
2
3
1
0
2
0
0
1
2
2
2
2
0
2
2
0
3
2
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
2
0
0
0
0
0
2
1
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
2
2
0
0
1
1
0
0
2
1
0
2
2
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
1
1
0
2
0
0
0
0
0
2
0
1
0
0
2
0
6
3
0
1
2
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
2
1
0
0
0
3
0
0
0
0
2
0
2
2
1
0
0
0
1
2
2
0
0
3
1
0
1
0
1
1
1
0
0
1
0
0
1
2
2
0
0
0
0
0
0
2
0
0
0
0
2
1
1
1
0
1
2
0
1
1
0
0
0
0
0
0
1
2
0
0
1
1
3
1
2
1
1
0
0
1
0
1
2
0
0
1
0
0
1
0
0
1
0
0
0
2
0
1
0
1
0
0
1
0
1
2
0
0
2
2
1
1
1
1
2
1
0
0
0
0
0
0
0
0
2
0
0
1
2
2
2
2
0
2
0
0
2
0
0
1
1
0
0
0
3
1
0
1
1
0
2
2
0
1
0
1
2
2
0
0
0
1
0
0
3
1
0
0
0
0
0
0
2
1
1
0
0
1
0
1
0
2
0
2
1
1
0
0
0
0
3
0
0
2
1
1
1
0
0
2
2
1
1
0
0
1
0
0
1
2
1
0
0
1
2
0
0
0
0
0
0
0
1
1
0
0
3
1
2
0
2
0
0
1
0
0
0
1
0
1
0
0
0
1
1
0
1
0
0
1
0
1
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
3
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
2
0
2
0
0
1
0
0
0
0
2
2
0
1
0
0
1
6
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
2
0
0
2
0
0
0
0
2
1
0
1
3
1
0
2
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
2
0
0
0
1
1
2
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
2
2
1
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
1
1
2
2
1
2
0
0
0
0
3
1
0
0
2
0
1
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
2
0
1
2
0
2
1
0
1
0
2
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
1
2
1
1
5
1
0
1
0
1
0
0
2
0
0
0
2
2
0
0
2
1
0
0
0
1
0
0
0
0
0
2
0
2
1
0
0
2
3
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
2
2
0
0
1
1
2
0
0
0
1
2
1
0
0
2
0
1
0
2
2
0
0
1
1
0
2
0
1
2
1
1
0
1
1
0
2
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
1
1
1
0
0
0
0
1
1
0
0
0
0
1
2
0
1
0
2
1
0
0
0
2
0
0
1
0
0
0
1
1
0
1
2
0
2
1
0
0
2
1
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
1
0
0
5
2
0
0
0
0
1
4
1
1
0
0
0
0
3
0
0
0
0
0
1
2
0
0
0
0
2
0
0
2
0
1
2
2
0
1
0
0
1
1
0
3
1
1
0
2
0
1
0
2
0
0
2
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
2
2
0
1
0
1
2
1
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
3
1
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
2
2
0
0
0
0
3
1
0
3
2
0
0
1
0
1
0
1
3
2
0
0
0
1
0
0
2
0
2
0
0
0
2
1
1
1
2
1
0
0
0
0
3
3
0
0
0
0
0
0
0
1
0
1
2
1
0
2
1
0
1
0
0
0
2
0
0
0
0
1
0
0
0
1
0
1
0
1
1
1
0
2
1
0
0
0
0
0
0
2
0
1
2
2
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
1
2
2
0
1
2
0
1
0
0
0
1
0
1
0
0
0
1
0
0
2
2
3
0
0
1
0
0
1
0
0
0
0
1
0
0
2
0
0
0
2
1
1
0
2
2
0
1
1
1
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
2
0
1
0
2
1
0
0
0
0
0
0
1
1
0
0
0
2
0
1
3
1
1
1
1
2
1
2
1
0
1
2
2
0
1
2
0
1
2
0
0
1
1
1
0
0
1
2
0
0
1
0
0
2
0
2
2
1
0
0
1
2
0
0
1
0
0
0
3
0
1
1
0
2
0
1
0
0
1
0
0
0
0
0
2
0
1
0
0
0
2
0
2
0
2
0
0
0
1
1
0
0
2
1
0
0
0
0
0
0
0
2
1
0
0
1
0
2
0
0
0
0
1
1
0
2
1
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
1
0
0
0
0
1
0
1
0
0
2
1
2
0
2
2
1
2
0
0
1
0
0
0
0
1
0
0
1
3
2
0
0
0
0
1
2
1
0
0
0
1
0
2
0
2
2
2
0
0
2
1
1
0
6
0
2
0
0
2
0
1
0
1
1
0
0
0
0
0
1
1
0
0
1
0
1
2
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
1
0
0
0
2
0
1
0
1
0
0
0
0
3
0
1
1
0
1
0
1
1
1
0
0
0
0
0
2
0
0
0
2
0
2
0
1
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
2
0
1
2
2
2
2
1
0
1
1
0
0
2
2
1
1
0
0
0
1
0
1
0
0
2
2
0
1
0
0
2
3
2
0
1
2
2
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
1
0
1
0
1
0
1
2
0
1
0
1
0
0
0
3
1
1
2
0
0
2
0
0
0
1
0
2
1
0
2
0
2
1
1
1
1
0
1
0
2
1
1
0
0
2
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
1
1
0
2
2
0
0
2
0
2
1
0
1
2
2
0
0
0
0
0
0
1
1
0
1
1
0
0
2
2
0
0
2
1
2
1
1
0
2
1
2
0
0
0
1
0
2
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
2
1
2
0
3
1
1
0
1
2
0
2
0
0
2
1
2
0
0
1
1
0
2
0
1
1
0
1
0
0
0
0
2
1
1
0
1
0
1
0
0
1
0
0
0
0
0
0
1
2
1
0
0
1
2
1
0
0
0
1
2
1
0
1
2
4
1
0
4
1
0
0
1
0
0
0
1
0
0
3
0
1
0
1
0
0
0
2
2
3
0
2
0
0
1
2
1
2
1
1
0
0
1
2
1
0
2
0
0
1
0
0
1
2
0
0
1
0
1
0
1
2
0
0
1
3
2
0
0
0
0
2
0
0
0
0
2
0
0
2
2
2
1
0
1
1
0
0
0
1
0
0
0
1
1
2
1
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
4
0
2
0
0
0
3
0
0
0
2
0
1
0
3
0
1
0
0
0
0
0
1
2
0
0
0
2
0
2
0
0
0
0
2
0
0
0
1
0
1
2
0
0
0
2
0
0
2
0
2
0
0
2
0
0
2
0
2
2
3
0
0
0
0
0
0
1
1
1
0
2
1
1
0
0
0
0
2
0
0
1
0
0
2
0
1
0
0
0
2
2
0
0
1
1
1
0
0
0
2
2
0
0
1
2
0
2
0
1
0
1
1
0
0
2
1
1
1
0
1
1
2
0
0
1
0
0
0
0
2
1
1
0
2
0
0
1
0
1
2
0
0
0
0
2
0
0
0
1
1
0
0
0
2
0
5
1
2
0
0
0
0
0
0
1
0
1
0
0
0
1
1
1
0
4
0
0
1
2
0
0
0
2
2
0
2
0
0
0
0
2
2
0
2
0
0
0
2
2
1
1
2
2
0
1
0
0
0
0
0
1
4
0
0
1
0
0
0
1
1
0
2
0
2
1
0
2
2
0
0
0
3
0
0
0
0
0
0
2
0
3
0
2
0
1
2
2
1
0
0
0
0
0
0
2
0
0
1
0
0
1
2
2
0
2
0
0
1
0
0
0
2
2
0
4
0
0
0
2
2
0
0
0
0
0
0
2
1
2
0
1
0
0
0
0
0
3
1
1
0
0
0
1
2
3
0
1
0
0
0
0
1
0
1
2
0
1
0
1
1
0
2
0
0
0
0
0
1
1
2
2
2
0
0
0
1
0
0
0
1
0
0
0
0
0
3
0
1
0
2
0
1
0
0
2
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
1
0
2
2
0
0
0
0
1
0
2
0
0
0
0
1
0
1
0
1
0
0
1
0
2
1
0
0
0
0
1
0
0
2
1
2
0
0
2
1
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
1
0
1
1
3
0
0
2
0
0
2
1
1
1
1
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
2
2
0
0
2
2
0
2
2
0
0
2
1
1
1
0
0
0
0
2
0
1
0
0
2
3
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
1
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
1
1
0
0
1
0
0
0
0
1
1
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
2
0
0
1
0
1
0
0
0
1
0
2
0
2
0
0
0
2
1
1
2
0
0
0
0
0
2
2
0
0
0
1
0
1
0
0
1
0
1
0
0
0
2
0
1
0
0
2
1
0
1
0
2
0
0
1
1
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
2
0
1
0
7
2
2
0
0
1
1
1
0
2
1
1
2
0
2
0
0
0
1
0
2
1
0
0
0
0
0
2
0
0
0
0
0
2
2
0
1
2
1
1
2
0
0
0
0
0
0
0
1
1
1
2
0
0
0
2
2
0
1
0
3
1
2
0
0
1
0
1
1
0
0
2
1
2
2
0
2
0
0
0
0
0
0
1
0
0
3
0
2
0
0
0
3
0
1
2
0
0
0
2
0
0
2
0
0
2
0
1
0
2
0
2
0
0
1
0
0
2
2
1
0
2
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
2
1
0
2
0
0
2
0
0
0
0
2
0
0
1
1
0
4
0
1
0
1
1
2
1
2
2
2
0
0
0
0
0
0
1
0
0
2
2
2
1
0
2
0
1
2
0
2
0
0
0
2
0
1
0
1
0
3
0
0
0
0
1
2
0
2
2
0
0
0
1
0
2
0
0
1
0
0
0
1
2
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
1
1
2
0
1
1
1
1
0
1
2
0
0
2
0
0
2
0
0
1
0
1
1
1
2
1
0
0
2
1
1
2
2
2
0
1
0
0
0
2
1
0
1
0
2
2
1
0
2
1
0
3
0
1
0
2
0
0
0
1
2
0
2
0
0
2
0
0
1
1
0
2
0
2
0
0
0
2
0
0
0
2
0
0
0
2
0
1
0
2
2
0
1
0
0
0
0
1
2
2
1
1
2
0
1
2
0
0
0
0
0
0
0
1
0
1
0
1
1
1
0
0
0
1
0
0
0
1
0
0
0
2
0
0
1
2
0
0
2
2
0
1
1
0
1
0
0
2
0
2
0
1
0
0
1
0
0
0
0
2
0
0
1
1
0
1
0
0
0
0
2
1
1
1
0
0
0
2
0
2
0
2
0
0
2
0
0
0
1
1
1
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
1
0
2
1
2
2
1
0
1
2
1
1
0
1
0
1
0
2
1
1
0
0
0
1
2
0
0
1
0
0
2
0
0
2
3
0
1
0
1
1
2
0
2
0
0
2
1
0
0
0
2
0
0
0
0
0
1
1
2
0
0
1
2
0
2
2
0
0
0
1
0
2
2
1
0
1
0
1
0
2
2
0
2
0
1
2
0
0
0
0
2
1
0
1
2
0
0
0
2
1
0
1
0
0
2
1
0
0
2
0
1
0
2
0
0
0
1
1
2
2
3
2
2
2
1
0
2
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
2
2
1
2
1
0
3
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
4
0
0
1
2
0
0
1
2
0
0
1
2
2
0
0
1
0
1
0
0
3
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
1
1
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
3
1
2
1
2
0
0
0
1
0
0
0
1
0
1
0
0
0
1
1
0
2
0
2
0
0
1
1
0
0
2
0
2
0
0
1
0
1
0
2
0
0
3
0
1
0
0
0
4
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
1
1
1
2
2
2
1
2
0
1
1
2
2
0
1
0
0
0
1
0
0
1
2
0
0
0
0
1
2
0
0
0
1
0
1
2
1
0
0
0
1
0
2
0
1
0
0
0
0
0
0
1
1
1
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
1
2
2
0
1
0
0
0
0
0
3
0
1
2
0
2
0
0
0
0
1
2
0
0
0
1
0
1
0
2
1
1
0
0
0
0
2
1
0
0
2
1
0
3
0
1
1
0
1
0
0
1
2
0
0
0
1
0
0
0
2
1
0
1
0
2
0
1
0
0
0
2
0
0
1
0
2
2
2
0
0
0
2
0
3
0
2
2
1
0
2
0
0
0
2
0
2
0
2
2
0
3
0
0
0
0
0
0
2
2
2
0
4
0
0
1
0
0
0
1
0
2
2
0
2
0
1
0
0
0
0
0
2
1
0
0
0
1
2
0
0
0
0
2
1
1
2
2
0
0
0
0
2
0
0
0
0
1
2
2
0
1
0
1
0
0
0
1
1
0
2
2
1
2
0
0
0
2
2
2
0
0
1
0
1
0
0
0
0
0
0
1
0
0
2
0
2
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
2
2
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
3
0
0
2
1
2
0
0
1
0
0
1
0
0
2
2
0
0
0
0
1
2
1
1
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
1
0
2
2
1
0
0
0
1
2
0
1
0
0
0
0
0
1
4
3
0
0
0
1
3
1
0
0
2
0
0
0
1
1
1
0
0
1
0
0
2
1
0
0
0
2
0
1
0
1
0
0
0
0
1
0
1
0
3
0
1
0
1
0
0
1
0
1
1
0
1
0
2
0
0
0
0
0
2
0
0
1
0
0
1
0
1
1
0
1
0
2
0
1
1
2
0
1
2
1
0
2
1
0
2
1
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
1
1
1
0
0
0
0
0
0
3
0
0
0
0
0
1
1
0
2
0
1
0
0
2
0
0
0
0
1
0
2
1
1
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
1
0
0
2
1
2
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
1
2
0
2
0
0
0
2
2
0
0
0
0
0
2
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
2
1
0
0
0
2
2
0
3
1
0
0
1
0
1
2
1
0
0
0
0
0
1
0
1
1
1
0
1
0
1
0
0
0
0
0
2
0
1
1
1
0
0
2
0
3
0
2
0
0
0
3
0
1
0
2
2
0
1
1
0
0
0
1
0
1
2
1
1
0
0
5
2
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
2
0
1
1
2
2
1
0
0
3
1
0
0
0
2
0
0
3
0
0
0
2
2
2
0
0
0
0
3
0
2
0
1
0
0
0
1
0
2
1
0
0
0
1
0
2
0
1
0
0
1
0
1
0
1
1
1
0
0
1
2
1
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
3
2
0
0
0
2
1
0
1
0
2
1
1
0
1
0
0
0
0
0
0
0
0
2
1
2
0
2
0
0
2
2
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
1
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
3
1
0
0
0
0
1
0
2
0
1
0
0
0
1
1
0
0
0
3
0
0
2
2
0
0
0
0
0
0
2
0
2
0
1
0
1
0
1
0
0
0
1
1
1
0
0
0
0
1
0
1
0
0
0
1
0
0
2
0
0
2
0
1
0
1
1
2
0
0
0
1
0
0
0
0
2
0
0
3
1
2
0
0
0
0
0
2
1
1
0
1
0
0
1
0
0
1
0
0
1
1
0
0
2
0
2
2
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
3
3
0
0
0
1
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
1
0
0
0
3
2
3
3
0
0
0
2
3
0
1
2
0
2
2
0
1
0
0
0
0
1
0
0
3
1
0
0
0
0
1
2
0
2
1
2
0
3
0
2
1
2
1
1
1
0
1
0
0
0
2
0
0
2
1
1
0
2
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
1
1
1
0
0
3
1
0
0
1
0
1
1
0
0
0
1
0
0
2
2
1
0
2
0
2
1
4
0
2
0
2
0
2
0
1
0
0
0
0
0
1
0
2
2
0
0
1
0
3
0
0
0
0
1
0
0
0
0
1
2
1
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
1
0
0
0
1
0
0
1
0
0
0
2
2
0
1
0
0
0
1
0
0
0
0
0
1
2
0
0
2
0
0
1
2
0
1
1
0
0
0
2
1
0
0
2
1
0
2
1
0
0
0
0
2
1
1
1
0
1
1
1
2
0
2
0
0
0
2
0
1
0
0
1
0
2
0
0
0
1
2
1
2
0
1
0
2
1
0
1
0
0
3
1
3
1
1
0
0
11
0
0
0
1
1
0
0
1
3
2
0
0
0
0
0
0
1
0
1
0
2
2
0
0
1
0
2
0
1
0
1
0
1
1
0
0
3
0
0
0
2
2
2
0
0
0
1
0
2
2
0
0
2
0
0
0
0
0
2
0
0
1
1
0
2
1
0
1
1
0
2
1
2
2
0
0
0
0
1
2
0
0
1
1
0
0
0
1
1
2
0
2
1
2
2
0
0
0
1
2
2
0
0
1
0
1
0
2
0
0
0
1
2
0
0
0
0
2
0
0
0
2
0
1
2
0
1
0
0
0
0
1
0
0
2
0
0
1
0
0
0
1
0
0
0
1
2
1
0
0
0
2
2
2
0
1
1
0
0
0
0
1
0
0
0
2
0
0
2
0
2
0
2
0
0
0
2
1
2
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
3
1
1
1
2
2
1
0
0
0
0
0
1
0
2
2
0
0
0
1
0
1
0
0
0
2
0
1
1
1
2
2
2
0
0
1
0
0
1
1
1
0
0
0
0
2
0
0
1
1
0
1
0
0
1
1
2
0
1
2
0
0
0
0
3
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
2
0
1
2
0
0
1
1
0
2
1
0
1
1
0
0
0
1
0
1
0
0
1
0
2
1
0
1
0
0
0
0
1
2
0
0
1
1
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
3
1
0
0
2
0
1
0
0
2
0
1
0
1
3
1
0
0
2
1
2
2
0
2
0
2
1
0
0
1
0
0
1
0
0
2
0
2
0
0
0
0
0
0
3
0
1
2
0
0
0
2
0
0
2
0
2
2
0
0
1
3
0
2
1
0
0
1
1
1
0
1
0
0
1
0
1
1
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
3
0
0
0
1
7
0
0
0
0
0
0
0
1
2
0
2
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
2
0
0
0
2
2
0
1
0
2
0
1
3
0
0
2
0
1
0
0
0
1
0
2
0
0
1
0
2
2
0
0
0
0
0
1
0
0
1
0
2
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
2
2
2
1
2
0
0
0
1
1
0
1
1
1
0
0
0
0
1
0
0
0
0
0
1
0
2
0
1
1
2
2
0
0
3
0
0
3
2
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
1
0
1
1
0
0
1
1
1
0
2
0
0
1
0
2
0
0
0
3
0
0
0
0
2
1
2
0
0
2
0
1
0
1
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
2
1
1
0
1
0
0
0
0
1
0
1
0
1
0
0
2
0
2
0
0
1
2
1
0
0
1
0
0
1
1
1
0
3
0
1
1
0
2
0
3
0
0
1
0
0
0
0
2
0
1
1
0
1
1
2
0
1
0
0
2
0
2
1
1
3
0
1
2
0
1
2
2
0
0
0
1
2
0
0
0
2
0
0
1
2
0
0
0
2
2
1
0
1
0
2
1
1
0
0
0
0
1
2
1
0
2
0
2
0
0
1
0
0
0
1
0
0
0
2
0
0
1
0
1
0
2
2
2
0
0
1
0
0
0
1
0
2
0
2
0
1
2
0
0
0
0
0
0
0
0
2
1
0
1
2
0
0
0
1
1
0
0
2
1
0
0
0
1
1
0
0
0
0
0
2
1
0
1
0
2
0
0
2
0
1
1
1
0
0
0
0
0
2
0
1
1
0
1
1
0
0
2
0
0
0
0
2
0
1
2
1
0
1
1
0
0
1
0
0
0
0
1
0
0
0
2
2
0
1
1
0
1
2
1
0
0
0
0
0
0
0
1
0
2
2
1
0
0
2
1
1
0
0
0
0
2
0
2
2
1
1
0
1
0
0
0
1
0
0
0
0
1
0
0
2
0
0
1
1
0
0
2
0
0
0
2
1
2
0
2
0
1
0
2
1
2
0
0
0
0
1
0
1
1
1
0
1
1
0
1
0
0
0
2
0
0
0
0
1
0
2
2
0
0
0
1
1
0
0
0
2
2
2
0
0
0
2
0
0
0
1
0
1
1
1
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
3
2
1
0
0
0
2
0
0
0
0
2
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
1
2
0
1
0
0
1
3
1
0
2
0
1
2
1
2
1
1
1
6
1
1
0
0
0
0
0
0
3
2
1
2
0
0
2
3
0
8
0
0
1
0
0
0
0
0
2
0
1
0
2
0
0
2
0
0
1
2
0
0
1
0
0
0
4
1
0
1
0
2
0
0
0
0
0
1
0
2
2
0
0
2
1
2
1
0
2
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
1
1
2
0
3
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
1
0
0
2
1
0
1
1
0
2
0
1
0
0
1
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
1
0
1
1
1
0
0
0
1
0
2
1
0
0
0
0
1
1
1
2
0
0
2
0
1
0
1
0
1
2
0
0
1
0
0
0
0
1
0
0
1
2
0
0
1
2
0
0
0
1
0
0
0
2
2
1
0
0
0
0
2
1
0
0
0
2
3
0
0
0
1
1
1
0
1
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
2
2
0
2
1
0
0
1
2
2
0
0
0
0
0
2
0
0
0
1
0
2
0
1
0
0
0
0
0
1
0
1
0
0
0
0
2
1
0
1
0
0
0
1
2
2
1
1
1
1
1
0
0
0
0
1
0
2
6
0
0
1
0
1
0
1
0
0
0
1
4
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
1
1
0
0
0
1
0
1
0
0
0
0
0
2
2
0
0
0
1
0
1
1
1
1
2
1
0
0
0
4
2
0
0
0
1
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
1
0
2
0
0
2
2
2
0
0
0
2
0
0
0
0
2
0
1
5
0
2
0
1
0
0
1
2
2
0
0
2
0
1
2
0
0
0
0
0
0
2
0
1
0
3
0
0
1
1
0
0
2
0
2
1
0
0
2
0
0
2
0
0
0
2
1
0
2
2
2
2
0
0
0
0
0
0
1
0
1
0
1
0
2
2
1
1
0
1
2
2
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
2
1
1
0
1
0
0
1
2
0
1
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
1
1
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
2
2
2
2
2
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
4
3
1
1
0
0
1
1
0
2
2
0
0
0
4
2
3
0
0
0
0
1
0
1
2
2
0
0
2
0
1
2
0
2
0
0
0
1
1
0
2
0
1
1
0
0
0
0
2
0
1
0
2
0
0
0
2
0
2
0
0
0
1
1
2
1
2
0
0
1
1
1
2
0
0
0
0
1
1
1
0
0
0
1
1
1
0
2
0
2
1
0
2
0
0
0
0
2
1
1
1
2
0
0
0
0
0
1
2
0
0
1
0
0
1
7
1
0
5
0
0
0
0
0
0
2
1
0
0
1
0
0
2
0
0
0
2
0
0
0
0
3
0
1
0
0
0
2
0
1
2
0
0
0
2
0
0
2
1
2
0
2
0
1
0
2
2
0
1
2
0
1
2
0
2
0
0
0
0
1
2
1
0
0
1
2
1
3
2
0
2
0
0
0
0
0
0
0
2
0
1
0
1
2
0
0
0
0
3
2
0
0
3
0
0
0
0
1
2
1
1
1
1
1
1
2
0
0
2
0
0
0
0
2
1
1
0
0
0
0
2
0
1
0
0
0
0
2
0
2
0
2
0
2
0
0
2
0
2
0
0
2
2
2
0
0
0
1
0
1
2
1
0
2
1
2
2
1
0
0
0
0
1
2
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
1
0
2
0
1
1
1
0
0
2
2
1
0
0
1
1
0
2
3
0
0
2
0
1
2
0
0
0
2
0
1
0
1
2
0
0
0
0
2
2
0
1
3
1
2
0
1
1
0
0
5
0
1
0
2
0
0
0
1
0
1
0
1
0
2
0
0
0
0
1
0
0
0
1
0
0
1
3
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
1
2
1
0
2
3
0
2
0
0
0
0
1
0
1
2
0
0
0
0
0
2
0
3
1
0
0
1
0
1
1
0
1
0
0
0
0
0
0
2
1
0
2
0
0
1
0
0
0
1
1
0
0
0
1
0
4
1
1
1
1
2
2
1
0
0
2
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
1
2
0
0
3
1
0
0
0
0
0
1
0
3
0
0
2
0
2
1
0
2
1
0
1
2
0
0
0
0
1
1
0
1
1
0
1
1
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
3
0
0
0
1
0
1
0
0
1
0
0
0
4
0
1
0
1
0
0
1
0
0
0
0
3
1
2
0
0
0
2
1
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
3
2
0
0
0
0
1
0
2
0
1
0
0
2
0
0
0
2
0
0
1
2
0
0
0
0
0
1
0
1
1
2
0
0
0
2
2
2
1
2
0
3
2
0
0
2
0
2
2
1
7
2
3
1
1
0
0
0
0
0
0
1
1
0
2
2
1
0
0
0
0
1
0
1
2
2
2
0
0
2
1
1
0
0
2
0
0
2
0
0
0
2
0
2
0
2
1
0
1
0
0
0
2
0
0
1
0
2
1
3
1
0
0
0
0
0
0
0
0
2
1
0
1
1
0
0
5
0
0
2
0
0
2
1
0
0
0
1
0
0
1
3
2
1
3
0
0
0
2
1
2
1
0
0
0
0
2
0
0
0
0
0
2
0
3
2
0
1
0
1
0
1
0
0
1
0
2
0
1
0
1
0
0
0
0
0
2
0
2
0
0
1
2
2
0
0
2
0
0
2
0
1
2
2
2
1
2
0
0
0
1
0
1
0
2
0
0
0
2
1
2
1
0
1
1
0
0
2
0
2
1
0
0
1
0
0
0
0
1
1
3
2
0
2
2
0
1
0
0
2
2
1
0
0
1
2
0
2
0
0
1
1
1
0
0
1
0
0
0
0
2
0
0
1
0
2
0
0
0
0
2
0
2
0
0
0
2
1
0
0
2
1
1
0
0
1
2
0
1
0
1
1
1
0
0
0
0
0
0
1
2
2
0
0
2
1
0
2
1
0
0
1
1
1
0
0
2
0
0
1
2
2
0
1
0
0
0
0
0
4
0
1
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
4
0
0
1
1
0
0
0
0
0
1
2
0
2
1
0
0
0
0
2
0
0
1
0
1
2
1
0
1
0
2
1
1
0
2
0
2
0
1
0
0
2
2
0
0
2
0
1
1
1
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
3
0
1
2
1
2
0
2
0
0
0
0
0
2
1
2
2
0
0
2
2
1
0
0
1
0
0
0
0
0
0
1
1
0
0
2
2
1
0
0
1
2
0
1
2
1
0
1
3
0
0
0
0
1
2
0
0
1
0
0
1
2
0
0
1
1
0
2
2
0
3
3
1
1
0
1
0
2
0
0
0
2
2
0
0
1
1
0
0
0
0
0
1
1
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
3
0
0
1
0
0
0
2
0
6
2
1
0
1
0
0
0
0
0
2
0
0
1
0
2
2
0
2
0
0
0
2
3
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
2
2
0
2
0
0
2
1
0
0
1
0
0
0
1
0
0
2
0
0
1
1
0
1
1
0
2
0
1
2
0
2
0
1
0
0
0
0
0
0
0
1
2
0
2
0
0
2
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
2
0
1
1
0
9
1
2
0
1
0
1
0
1
0
0
1
0
1
0
1
0
2
0
0
2
0
0
2
0
2
1
2
0
1
0
0
2
0
0
0
0
1
0
0
1
1
0
1
0
2
2
1
0
0
1
1
2
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
2
0
0
0
0
1
2
1
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
2
2
0
2
1
0
0
1
4
0
0
0
0
1
0
2
0
2
0
0
0
0
1
3
0
1
0
0
0
1
2
2
2
0
0
2
2
0
2
0
0
0
0
0
0
0
2
1
1
0
1
0
1
0
0
0
1
2
0
0
1
0
0
1
1
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
3
2
2
2
3
1
1
0
1
1
2
0
3
0
0
1
0
0
0
2
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
1
2
2
2
3
0
0
0
2
1
0
0
2
5
0
2
1
0
0
0
4
0
0
0
0
0
0
3
0
0
1
0
1
1
2
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
2
0
0
0
2
1
3
0
2
2
1
0
3
0
0
0
1
1
2
0
0
2
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
1
1
0
2
1
0
0
0
0
1
1
1
2
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
2
1
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
1
1
1
1
0
2
2
0
0
0
0
0
0
0
1
0
0
1
0
2
0
1
0
0
0
0
2
2
0
1
2
2
0
2
0
0
1
1
0
1
0
2
0
1
0
0
0
0
0
0
1
2
0
1
2
2
1
1
0
1
0
0
4
0
0
0
3
4
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
3
0
0
0
0
0
1
2
0
0
0
0
2
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
2
3
0
0
0
1
0
1
0
1
3
1
0
0
2
2
0
2
2
1
0
0
0
0
2
0
2
0
1
0
1
0
2
0
2
0
0
0
1
1
0
1
0
0
0
0
2
2
0
0
0
0
0
1
0
0
1
2
0
0
0
1
0
0
2
1
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
1
3
4
1
0
1
0
1
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
2
0
2
2
0
2
1
0
1
2
2
1
0
0
0
0
1
0
0
0
1
1
2
0
0
0
0
0
2
0
0
0
0
0
0
1
1
2
0
2
2
0
1
1
0
0
1
2
0
0
0
0
0
1
0
1
0
2
0
2
0
2
1
2
1
0
0
2
2
0
0
0
0
0
2
0
1
1
3
1
0
0
0
1
0
4
2
0
1
0
2
2
2
0
0
0
2
0
2
0
1
0
1
1
1
1
0
1
0
0
2
0
0
0
0
0
1
1
0
1
1
0
0
1
0
1
1
0
0
4
0
0
1
0
3
0
1
0
0
0
0
0
2
1
2
2
0
0
1
2
1
0
0
0
0
1
0
1
1
1
2
0
0
0
2
0
1
0
0
2
1
2
2
0
1
0
1
0
0
0
0
2
1
0
2
0
1
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
2
0
2
0
1
1
1
0
0
1
2
2
0
0
1
0
1
0
0
1
0
0
2
1
0
0
0
0
2
0
2
1
2
2
2
0
0
0
0
2
1
0
0
0
2
0
0
0
2
1
1
0
2
0
0
0
0
0
1
0
0
0
3
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
1
2
2
0
0
0
0
2
2
1
2
0
0
0
0
0
1
2
0
0
2
0
0
2
0
0
1
1
0
2
1
2
0
4
0
0
2
3
2
0
1
0
0
0
1
1
2
0
1
2
0
0
1
0
0
3
2
0
1
0
0
0
0
2
3
0
0
1
0
0
0
0
2
1
1
2
0
1
0
1
0
0
1
1
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
1
0
1
0
2
0
0
2
2
1
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
2
1
0
3
2
0
0
0
1
0
1
2
0
2
4
0
0
0
0
2
0
2
0
0
2
0
2
2
1
1
2
0
0
2
0
0
0
0
2
0
1
1
0
2
0
0
2
0
0
0
2
2
0
2
0
2
0
1
0
0
2
1
0
0
1
1
2
0
1
0
1
1
0
0
2
5
0
0
2
0
0
0
2
0
0
2
1
0
2
1
0
1
2
0
1
0
2
0
0
1
1
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
2
0
2
1
1
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
1
2
0
0
0
1
2
1
0
2
0
1
0
1
0
1
1
0
0
0
2
3
0
2
0
0
0
0
1
0
0
2
0
0
0
1
0
0
2
0
1
2
0
0
1
0
2
0
2
2
0
0
3
3
1
0
0
1
1
1
2
1
1
0
0
0
1
0
0
2
2
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
1
2
0
0
2
0
2
2
0
0
0
1
0
0
0
0
1
1
0
2
0
0
0
0
2
0
2
0
0
2
2
0
0
0
0
2
0
1
2
0
2
0
0
0
1
1
0
0
2
0
2
0
0
0
1
0
2
0
1
0
3
1
0
1
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
1
0
2
2
0
1
2
0
0
0
0
2
0
2
0
0
0
0
0
0
2
1
2
1
0
2
0
1
1
2
0
0
1
2
0
0
1
0
0
0
2
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
2
2
0
1
2
2
2
0
0
1
2
0
0
1
0
0
0
0
2
1
0
2
0
0
2
0
0
0
2
0
2
0
0
0
0
0
1
1
1
0
1
1
0
2
0
0
0
3
0
2
0
0
4
0
0
1
2
0
0
2
0
0
2
2
0
0
2
3
0
0
2
1
2
0
0
0
0
0
1
0
2
1
1
2
1
0
0
1
0
1
2
0
1
0
0
0
0
0
1
0
2
1
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
1
1
1
1
2
1
0
1
1
2
0
1
0
0
1
0
2
0
0
1
1
0
1
2
0
2
2
1
0
0
1
2
0
0
0
0
0
1
1
1
0
0
3
0
0
2
0
1
1
2
1
2
0
1
0
0
0
0
0
1
0
0
0
1
1
0
1
0
1
1
0
0
0
0
0
2
1
1
0
0
1
0
0
1
0
0
1
2
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
1
0
0
1
0
2
2
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
2
0
0
2
0
1
0
1
0
0
1
2
1
0
0
0
1
2
0
3
2
1
0
0
0
1
2
2
0
0
0
3
0
0
2
1
0
0
1
0
1
0
0
0
2
0
0
2
0
0
0
0
2
0
2
0
0
0
2
1
1
0
1
1
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
1
2
1
3
1
0
1
1
0
2
1
0
1
0
1
0
0
1
1
0
0
1
0
1
1
0
2
0
2
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
1
1
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
1
0
0
1
2
1
0
0
0
2
0
1
0
1
0
0
1
1
0
2
0
3
0
0
2
1
1
1
0
2
2
1
2
2
1
1
0
0
2
0
0
0
1
2
0
0
0
2
3
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
2
2
1
0
0
2
2
0
0
2
0
0
0
0
0
2
2
0
0
1
0
1
1
1
0
0
0
2
2
0
0
0
0
3
3
2
1
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
1
0
1
1
0
2
0
2
1
0
0
0
2
1
1
1
0
1
0
0
2
0
2
0
2
0
0
2
2
0
0
0
2
0
1
0
0
2
0
2
0
2
2
0
0
2
0
1
0
0
1
0
1
0
0
1
0
0
0
2
0
1
0
1
1
0
0
2
0
0
0
0
0
0
2
1
1
0
2
1
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
2
0
0
1
0
1
0
1
3
0
0
0
2
1
0
1
1
2
0
0
0
2
0
0
1
0
0
0
0
2
1
1
1
2
0
1
1
1
0
0
0
1
0
0
0
0
0
1
0
1
1
1
1
0
0
1
0
0
0
1
0
2
1
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
2
0
1
2
5
0
0
0
0
0
0
1
0
1
1
1
1
0
2
0
0
0
2
0
0
0
2
2
0
2
1
0
1
1
1
0
1
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
2
2
0
0
1
1
0
0
2
0
1
0
1
0
0
0
1
0
1
1
0
1
3
0
0
2
0
0
0
0
2
2
2
2
0
0
0
1
0
0
0
2
1
1
1
2
2
0
0
1
0
0
0
0
0
2
1
0
3
1
0
1
1
0
0
0
2
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
1
1
1
0
0
1
0
3
0
0
2
2
0
1
1
0
0
0
0
0
1
0
1
0
1
0
0
1
2
1
0
1
0
0
0
1
1
2
5
2
0
0
0
1
1
0
2
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
2
0
0
1
0
3
0
0
0
1
0
0
0
1
2
0
2
0
0
2
0
0
0
0
2
0
0
2
0
1
0
1
0
0
0
1
2
1
2
0
1
2
0
0
0
0
1
0
0
0
2
0
0
1
0
1
1
1
0
1
0
1
0
2
0
1
0
1
1
0
2
1
0
0
0
0
1
1
0
0
1
0
1
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
2
0
1
2
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
1
0
0
1
1
2
1
2
2
0
0
0
2
0
0
0
3
2
0
1
0
1
0
1
1
0
0
1
1
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
1
6
1
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
1
0
2
2
0
0
0
1
0
1
1
1
0
0
2
1
0
0
3
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
3
0
0
1
2
1
0
1
2
0
0
0
0
1
0
0
0
3
2
0
0
1
1
0
0
1
2
1
0
0
0
2
2
0
2
0
2
2
0
0
1
2
0
1
0
1
1
0
0
0
2
2
1
0
2
0
0
0
0
2
0
1
0
2
4
0
1
0
2
0
1
0
0
2
2
2
0
1
2
2
2
0
0
1
0
0
0
1
0
1
0
0
2
0
1
1
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
1
2
2
0
1
0
2
0
3
1
1
2
2
8
0
0
0
2
0
0
1
0
1
1
0
1
0
0
0
1
4
1
0
0
0
0
1
0
0
0
0
0
1
1
0
2
0
0
2
0
0
1
0
0
0
2
3
2
1
2
0
0
0
1
0
0
0
0
1
3
2
0
1
0
0
0
1
0
1
2
2
2
0
2
0
0
0
0
0
2
2
0
0
0
1
0
2
0
0
1
0
1
1
0
1
1
0
1
0
0
2
0
0
2
0
2
2
1
0
2
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
2
0
1
0
0
1
1
0
0
1
1
2
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
2
2
0
2
0
2
0
2
2
0
0
0
1
0
2
1
2
2
0
0
1
0
1
0
1
2
1
1
1
0
0
0
0
0
2
0
1
2
2
1
2
1
0
1
2
0
1
3
2
3
1
2
0
0
1
0
2
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
6
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
1
2
1
2
0
0
0
1
1
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
1
0
1
0
2
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
2
1
0
0
1
1
0
1
0
1
1
0
0
1
3
1
1
0
0
1
1
0
1
1
0
0
0
1
0
0
1
0
0
0
1
2
0
0
0
0
0
1
1
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
2
1
0
0
1
0
2
0
0
1
0
2
2
0
1
1
2
1
1
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
2
0
0
1
0
2
2
1
1
0
0
2
2
0
0
1
0
0
2
1
0
0
0
2
2
2
2
0
3
0
2
1
0
2
2
1
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
2
1
2
1
2
2
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
1
1
1
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
1
0
0
2
1
1
0
1
1
1
0
0
0
0
2
0
2
3
0
0
2
0
1
0
0
0
0
3
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
1
0
2
3
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
1
1
1
0
1
2
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
1
0
2
2
0
0
1
0
0
2
0
0
1
2
1
0
0
2
2
0
0
0
2
0
0
0
0
0
1
1
1
3
0
1
2
0
0
0
0
2
1
1
2
2
2
2
0
1
0
1
2
1
0
0
0
0
2
2
1
0
1
0
1
2
1
0
0
1
0
0
0
3
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
3
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
3
2
1
1
0
0
0
2
2
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
1
1
1
0
1
1
0
1
1
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
2
0
0
3
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
2
1
0
2
0
0
0
0
1
2
0
2
0
0
0
0
0
1
1
1
0
0
0
0
1
1
1
0
0
0
0
0
1
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
1
2
0
1
0
1
1
0
0
0
0
2
2
1
2
2
1
0
0
0
0
0
1
1
1
0
1
0
0
1
0
0
0
1
0
1
1
2
2
0
1
0
0
1
1
2
2
0
0
1
1
0
1
0
0
0
0
1
2
0
2
0
0
0
0
2
2
0
1
0
1
1
2
0
0
1
1
0
2
0
0
1
0
0
1
2
0
2
0
0
0
1
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
1
1
0
1
1
0
0
1
0
0
0
0
2
1
4
0
1
2
0
0
0
0
1
0
0
2
1
1
0
2
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
1
1
2
1
0
0
0
0
3
0
1
0
1
2
0
0
1
0
1
0
2
0
0
1
0
0
0
0
2
0
1
1
2
0
4
0
0
0
0
1
0
1
1
1
2
0
0
0
0
0
2
0
0
0
1
2
1
2
2
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
2
0
0
0
2
0
2
0
2
0
1
2
2
4
0
0
0
0
1
0
3
2
0
0
0
1
2
0
2
1
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
1
1
2
1
0
0
1
2
2
1
2
1
0
0
0
2
2
0
2
1
2
0
0
0
1
0
1
0
0
0
0
2
1
0
0
0
0
2
1
0
1
2
1
1
0
0
0
0
0
1
5
2
1
0
0
1
0
0
3
1
1
1
2
1
0
0
1
1
2
1
0
0
0
1
2
1
2
1
0
0
2
2
0
0
1
0
0
2
0
1
1
2
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
2
0
0
0
0
1
0
1
1
0
2
2
0
1
2
1
0
1
1
0
2
0
0
0
0
0
2
2
2
0
0
1
1
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
2
2
1
1
0
0
0
0
2
1
1
1
2
0
0
2
0
0
2
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
2
1
0
2
0
2
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
2
2
0
0
0
0
1
0
2
2
0
0
0
0
1
2
1
1
2
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
2
0
0
0
0
2
0
0
1
1
0
0
0
0
2
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
2
2
0
0
1
0
2
1
0
0
2
0
1
0
2
2
2
2
2
1
0
0
0
1
2
2
0
0
0
0
1
0
2
1
1
0
1
2
1
2
0
2
0
0
1
0
2
1
3
0
0
2
0
0
2
2
1
1
4
1
0
1
1
1
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
3
0
1
2
0
2
2
0
0
2
0
2
0
0
1
1
0
0
2
1
0
1
0
3
2
0
0
0
0
2
1
0
0
0
1
1
3
2
0
2
1
2
0
0
0
0
1
0
0
0
0
2
0
0
1
1
2
2
2
0
0
1
0
0
1
0
0
1
2
1
0
1
0
1
0
1
2
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
1
2
1
0
2
0
0
1
2
0
0
0
1
1
2
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
2
0
1
0
0
0
1
0
0
0
1
0
0
2
1
0
0
1
0
0
0
0
0
1
2
1
0
0
0
0
0
3
0
0
0
1
1
2
0
2
0
0
1
2
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
1
1
2
0
2
1
1
0
1
2
2
0
0
0
0
0
0
0
0
2
1
1
2
0
0
0
0
0
1
2
2
0
0
0
0
2
0
2
0
0
1
1
0
2
2
2
1
1
0
0
2
1
1
0
2
0
0
1
0
1
0
0
0
2
0
2
1
0
1
0
0
1
1
2
2
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
1
2
0
1
0
0
0
0
2
0
0
0
0
1
0
2
1
0
2
0
0
0
0
2
0
0
1
1
1
1
0
3
0
0
1
1
2
0
0
2
2
2
2
1
1
0
2
4
0
2
0
1
0
2
1
0
1
0
1
2
0
1
0
0
0
1
0
1
0
0
0
1
1
1
4
1
1
2
0
0
1
0
2
0
0
3
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
1
2
2
0
2
1
2
0
0
2
2
3
0
1
0
0
1
0
2
0
3
0
0
0
0
3
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
2
0
1
2
0
2
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
2
1
0
0
0
0
1
2
0
0
0
2
1
0
0
0
0
2
2
0
0
1
2
0
1
0
1
0
2
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
3
2
0
0
2
2
2
1
0
0
1
1
2
0
1
0
1
2
0
1
0
0
0
0
1
0
1
0
0
2
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
1
0
1
0
0
2
0
2
1
0
1
2
4
2
1
1
0
1
2
2
2
0
0
2
0
1
0
0
0
0
0
2
0
1
2
0
0
2
2
1
0
0
2
1
0
1
2
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
1
2
0
1
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
1
3
0
0
0
1
0
0
0
3
0
1
1
1
0
0
1
0
0
0
0
0
0
2
0
2
0
1
2
1
2
0
1
1
0
0
0
0
1
1
0
0
2
2
0
0
0
0
1
0
1
0
2
0
2
1
1
1
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
2
0
0
0
2
2
4
1
0
0
2
1
0
2
0
1
1
0
0
0
0
0
0
1
0
1
0
1
5
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
2
0
0
0
0
0
0
2
2
0
2
0
2
3
1
0
0
0
1
2
0
2
1
2
0
2
2
0
2
1
0
0
2
0
0
0
0
2
0
2
0
0
2
1
2
2
0
2
0
0
0
0
1
0
0
1
1
2
0
1
0
1
1
0
0
0
0
2
0
1
2
1
1
0
0
0
0
2
1
1
4
0
0
0
2
2
1
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
1
0
2
0
0
2
0
2
2
0
0
0
2
0
1
0
0
2
0
1
0
1
0
1
0
0
1
0
0
1
1
0
0
1
1
0
2
1
1
0
2
1
0
1
1
0
0
0
3
0
0
2
0
2
0
2
0
1
2
2
1
0
0
1
0
1
1
0
1
0
0
1
1
0
0
0
2
2
0
0
2
4
2
2
1
0
0
0
0
1
0
2
0
0
0
0
0
1
1
0
2
1
2
2
1
0
0
0
1
0
0
3
0
0
0
0
2
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
1
0
2
0
2
1
0
0
1
0
0
1
2
2
1
2
1
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
1
0
0
2
0
0
0
1
1
1
1
2
1
0
0
0
0
0
1
1
0
1
1
2
0
0
0
1
0
1
0
1
0
1
1
0
0
0
2
1
1
2
0
1
2
0
0
1
1
0
0
0
0
0
0
0
0
2
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
2
2
0
1
0
0
1
0
1
2
0
0
1
0
1
0
1
1
0
1
2
0
1
2
0
2
0
2
2
0
0
2
0
0
0
0
3
0
0
1
0
2
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
2
0
1
2
1
0
0
0
2
0
0
1
1
1
2
0
0
0
1
1
1
0
0
0
0
0
0
1
1
1
0
0
2
2
2
0
0
0
0
0
1
0
1
1
1
0
0
1
1
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
2
0
0
2
0
1
1
1
1
0
0
0
0
0
1
2
2
0
0
0
0
1
1
0
1
0
2
0
2
1
2
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
2
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
1
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
2
0
1
2
2
5
1
0
0
0
0
0
1
1
0
2
0
0
0
3
0
1
1
0
1
0
0
0
0
2
0
0
2
0
2
0
1
1
0
2
0
0
0
0
0
0
1
0
2
1
0
1
2
0
0
1
0
2
0
0
1
2
3
0
1
0
0
0
0
0
0
3
0
1
0
0
0
1
2
0
0
0
0
0
1
0
3
0
0
1
2
0
1
2
0
1
2
0
0
0
2
2
0
1
0
1
2
0
1
0
0
2
1
0
2
0
0
0
0
0
0
0
1
0
2
0
0
2
0
1
0
1
0
0
3
1
1
0
1
1
0
0
1
0
0
2
0
1
2
1
0
0
1
1
0
0
2
0
0
2
0
2
0
0
0
1
1
0
0
2
0
0
0
1
1
3
2
0
1
1
0
1
0
1
1
1
0
0
0
1
0
1
1
1
0
1
0
1
0
0
0
0
1
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
2
2
1
1
0
0
2
1
2
0
0
0
1
0
0
0
0
1
1
2
0
1
0
0
0
0
1
0
1
0
0
2
0
2
0
1
0
0
0
0
1
0
1
0
0
0
1
0
2
0
0
1
1
0
3
0
5
0
0
2
0
1
0
0
1
1
0
0
0
0
2
0
2
1
2
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
1
3
1
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
1
0
0
2
0
2
0
0
0
1
0
1
1
1
0
2
0
2
0
0
0
0
0
2
2
0
0
2
1
0
0
1
2
0
1
0
1
0
1
0
1
2
0
0
1
1
2
0
0
0
0
0
0
0
0
2
0
1
0
1
1
0
0
0
0
1
3
1
0
2
0
2
1
2
0
0
0
0
1
2
1
1
2
1
0
2
0
1
3
1
0
1
2
2
0
0
2
0
1
0
2
0
0
0
1
1
1
1
1
1
2
2
0
0
0
0
2
0
1
2
0
0
2
0
0
0
1
0
2
1
1
0
0
0
0
0
0
0
2
0
2
1
0
0
1
0
4
0
2
1
0
1
0
0
2
2
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
2
2
0
0
0
0
1
1
1
0
0
0
1
0
3
1
0
3
0
1
2
1
2
0
0
1
2
0
0
0
0
0
0
1
1
0
2
0
0
0
2
0
0
0
0
1
0
2
0
0
0
1
0
3
0
0
0
0
0
0
0
3
0
0
0
2
1
0
2
0
2
2
0
0
2
2
2
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
1
0
1
2
0
0
0
2
0
1
1
0
0
0
0
2
2
2
2
2
0
0
0
1
2
1
0
1
0
0
3
1
1
0
0
2
0
1
1
1
1
1
0
0
0
0
2
1
1
1
2
0
3
0
0
0
1
1
1
0
0
0
0
0
0
0
3
1
0
2
0
1
1
2
4
1
2
2
1
1
0
0
2
0
0
0
0
2
1
1
0
0
2
0
0
2
0
1
1
0
0
0
2
2
0
0
0
2
0
1
2
1
0
0
1
0
0
0
0
1
0
1
2
0
0
1
1
0
1
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
1
1
2
2
0
1
0
2
0
0
1
0
1
0
3
0
0
0
0
2
0
0
1
0
1
1
0
1
3
0
0
2
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
1
0
0
1
0
2
0
0
2
0
0
0
0
1
0
1
0
0
1
0
1
1
0
0
0
1
0
0
0
0
1
1
0
1
1
0
0
0
1
0
1
1
1
2
1
1
1
0
0
0
0
0
1
3
0
0
0
0
1
0
1
1
4
0
0
1
0
1
1
1
0
1
0
0
0
0
1
1
0
2
2
2
0
0
1
2
0
0
0
0
0
0
0
2
0
1
0
0
2
0
1
0
0
1
0
0
2
1
1
0
1
1
0
0
0
1
1
0
0
0
0
0
0
1
0
2
0
1
1
2
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
2
0
1
0
0
0
0
2
2
0
1
1
0
2
1
0
2
0
1
0
0
0
2
1
2
1
2
0
1
0
0
2
2
0
2
0
0
0
2
0
1
1
0
0
2
0
2
1
2
0
1
2
1
0
2
1
1
0
1
2
0
0
0
0
1
0
2
0
0
1
2
0
1
0
0
2
1
1
0
0
0
1
0
0
0
0
1
0
0
1
0
2
1
0
2
1
2
0
0
1
0
1
0
2
0
3
1
0
0
0
2
0
0
0
0
1
1
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
3
0
1
1
2
0
1
2
0
1
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
2
2
1
2
0
2
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
1
1
2
0
3
1
0
3
0
0
0
0
0
2
0
0
2
0
0
0
2
0
2
0
2
1
0
0
1
1
2
0
0
2
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
1
2
0
1
2
0
0
1
1
2
2
0
0
1
2
0
0
2
1
1
0
0
0
2
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
2
1
0
0
0
1
1
0
1
1
0
0
0
1
0
0
1
2
0
0
2
1
1
2
1
0
0
0
0
0
2
0
0
3
1
1
0
0
2
0
1
0
0
1
0
0
0
1
0
2
2
0
0
1
3
0
0
0
1
6
0
1
0
1
0
2
0
0
0
2
0
1
0
1
1
0
0
2
0
0
0
0
1
0
0
2
0
0
2
0
0
2
1
0
0
2
0
3
1
1
0
0
0
1
2
1
2
3
1
1
4
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
1
1
0
1
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
9
0
1
2
0
0
1
0
0
0
0
0
2
1
0
0
0
0
1
0
0
1
1
1
0
1
0
1
0
0
1
0
0
0
0
2
2
2
2
0
0
0
0
2
0
1
1
0
1
0
0
2
0
0
1
2
0
2
0
0
0
2
0
0
2
1
0
1
0
1
0
0
1
0
0
2
1
2
1
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
2
0
0
1
1
0
0
0
1
0
0
1
0
0
2
0
1
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
2
0
0
2
2
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
2
0
0
1
0
1
0
1
1
0
2
0
0
0
1
0
2
0
0
0
0
0
0
2
1
0
1
0
0
1
0
0
0
0
2
0
0
1
2
1
0
0
2
0
0
1
0
1
1
0
0
0
1
0
2
0
0
0
1
0
1
0
0
1
1
0
1
2
0
1
2
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
4
0
0
2
1
2
0
0
0
1
1
0
0
0
0
0
0
1
0
6
0
1
1
1
0
2
0
0
0
0
2
0
0
0
1
1
0
0
2
2
0
1
0
0
0
2
1
0
0
0
0
0
2
0
2
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
1
1
1
0
0
1
2
2
2
2
0
1
0
2
0
0
0
1
2
0
2
2
0
0
1
2
0
2
0
2
0
0
0
0
1
2
0
0
0
1
0
0
2
1
1
0
0
2
0
2
0
0
1
1
0
2
0
0
0
0
1
1
1
0
0
0
1
0
1
0
0
0
2
2
0
1
0
2
2
1
2
0
1
1
0
1
0
0
0
0
0
2
0
0
2
0
1
1
1
2
0
0
1
0
0
0
0
0
3
0
0
3
0
1
0
0
0
0
0
0
1
1
0
3
0
1
1
0
1
0
0
0
1
0
0
2
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
1
1
0
1
0
0
0
0
1
0
0
1
2
0
0
0
2
1
2
0
0
0
1
1
0
1
0
1
3
0
0
0
3
0
0
0
1
0
0
1
2
0
1
0
0
1
1
2
1
3
0
0
2
0
0
2
2
1
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
2
2
0
1
0
0
1
0
0
2
0
1
2
2
0
0
0
0
0
0
0
0
0
0
3
0
0
1
2
0
0
2
0
0
0
4
0
2
1
1
1
0
1
1
0
0
0
2
1
1
0
0
2
0
0
1
0
0
0
2
0
1
1
1
0
0
0
0
2
2
0
1
2
1
1
0
0
0
0
0
0
0
2
0
0
2
1
2
2
0
2
0
2
0
0
0
1
0
0
0
2
2
2
2
0
1
0
0
2
0
3
2
0
0
0
0
0
0
1
0
0
2
2
0
2
0
1
1
0
1
2
2
1
1
0
0
0
0
1
1
0
0
0
0
1
0
1
2
0
0
2
1
1
1
2
1
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
2
1
1
1
0
0
0
2
1
0
2
0
2
0
2
0
0
1
1
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
1
1
0
0
2
0
0
0
4
2
2
0
0
2
0
0
0
0
2
3
0
0
1
0
0
2
2
0
0
0
0
0
1
0
0
2
2
3
0
0
0
0
1
0
0
0
1
0
1
1
2
0
0
1
0
2
0
1
0
0
0
0
1
0
1
1
0
0
1
0
0
1
0
0
0
1
0
0
0
2
0
0
1
0
0
0
1
2
2
0
0
0
2
1
0
0
2
0
2
2
0
1
1
2
0
1
2
0
3
2
0
2
0
0
0
1
2
0
0
0
0
3
2
0
0
1
0
0
0
0
0
0
0
2
0
1
1
5
2
1
0
0
2
0
1
2
1
0
1
2
1
1
1
0
0
1
0
1
2
2
0
0
1
0
2
1
2
0
2
0
1
1
0
1
1
0
0
1
1
2
0
0
0
1
0
0
2
0
0
2
0
0
1
2
0
2
0
2
2
0
2
0
0
0
2
1
0
0
0
0
1
0
0
1
0
0
0
2
2
0
1
0
0
0
2
1
0
0
0
2
1
1
0
1
1
1
1
2
2
1
2
0
0
2
0
1
0
2
0
0
3
2
0
0
1
0
0
1
0
1
0
0
1
0
0
0
2
0
1
1
2
3
0
1
0
1
0
0
0
2
1
0
0
1
0
0
1
0
0
1
1
0
0
0
2
0
0
0
0
2
1
0
2
0
0
0
0
0
1
2
1
2
0
1
0
0
1
0
2
1
0
1
2
0
0
0
0
0
0
0
1
1
0
0
2
0
2
2
0
0
0
0
0
2
1
0
1
2
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
2
0
0
2
0
1
2
0
0
1
0
0
0
0
2
0
1
1
1
1
2
0
0
1
0
0
1
0
0
1
1
1
2
0
3
0
3
2
2
0
3
0
0
2
1
0
1
1
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
2
1
0
1
0
1
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
2
0
3
2
0
1
0
0
0
0
0
0
1
1
2
0
0
1
0
1
0
0
0
2
0
0
2
1
0
0
0
1
0
1
0
0
1
1
2
0
0
0
0
1
0
0
2
0
0
0
2
0
3
1
0
0
3
2
2
1
2
0
2
1
2
2
0
2
0
0
4
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
2
0
0
0
2
1
0
1
1
0
0
0
2
0
2
0
0
0
2
2
0
1
0
1
1
0
0
2
2
0
0
0
0
0
0
2
2
3
0
0
1
0
1
0
2
0
0
0
0
1
3
0
0
2
2
2
0
1
1
0
0
0
0
0
2
1
0
0
0
2
0
0
0
1
0
0
0
0
1
0
2
1
0
1
1
1
2
0
1
0
2
0
2
2
0
0
0
0
0
0
2
2
0
1
0
0
2
1
0
1
0
0
0
1
1
1
0
2
0
0
0
2
2
1
0
0
0
0
0
0
2
2
1
0
2
0
0
1
0
0
0
2
1
0
2
0
1
0
1
0
0
1
1
0
0
1
2
0
1
0
0
0
2
0
0
3
1
0
1
2
1
0
1
1
1
2
0
1
2
0
2
0
0
0
0
0
0
2
0
2
0
0
3
0
2
0
0
0
0
0
0
0
1
0
0
2
1
0
1
2
2
0
1
0
0
0
0
2
0
1
1
0
0
0
0
0
2
0
1
0
1
0
0
0
2
2
0
0
1
1
0
0
0
2
1
0
0
2
0
0
1
2
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
1
0
0
2
1
1
0
0
0
0
0
0
0
2
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
2
2
0
0
0
1
2
1
0
0
1
0
0
0
0
1
1
0
0
2
0
2
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
1
0
0
1
2
0
0
0
0
0
0
2
2
0
1
2
0
0
0
3
0
0
0
1
0
0
1
2
0
2
1
0
0
0
2
0
0
1
2
2
0
0
2
0
1
0
0
0
1
0
1
2
1
1
0
0
2
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
1
1
0
0
0
1
2
2
0
0
0
1
2
2
0
1
2
2
0
2
1
1
0
2
0
0
2
0
0
0
1
0
0
0
0
1
2
0
1
0
0
0
0
2
0
0
0
0
1
1
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
2
0
1
1
2
0
2
4
0
1
1
1
2
0
0
0
0
1
0
0
1
2
0
0
0
1
2
0
0
0
2
0
2
0
0
1
0
1
2
0
1
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
2
1
2
0
2
2
0
0
2
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
3
0
0
0
0
1
1
2
0
1
1
1
1
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
2
0
2
1
2
0
0
0
0
2
0
0
1
0
1
0
0
0
0
2
0
1
0
1
0
0
0
0
1
0
0
1
1
0
0
2
0
1
0
0
0
2
4
1
1
0
2
2
0
1
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
2
2
2
0
0
0
0
0
0
1
0
0
1
0
2
0
1
0
0
1
1
0
1
3
1
0
0
0
0
2
1
0
1
0
0
1
0
1
0
1
1
2
2
0
2
0
1
1
0
0
1
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
2
2
1
1
0
0
0
4
1
0
1
0
0
0
0
0
0
1
0
0
2
1
2
0
0
2
0
0
0
0
0
0
2
0
3
1
0
0
0
0
2
0
2
0
0
2
2
0
0
1
1
0
1
0
1
3
2
0
2
1
0
2
0
2
2
0
0
0
0
0
2
0
0
1
0
0
0
2
1
1
2
1
2
0
0
2
1
0
2
2
0
0
0
0
1
0
2
0
0
1
4
0
1
0
0
1
1
0
0
2
0
4
0
0
2
0
1
1
0
0
0
0
1
0
0
0
1
2
0
0
2
0
0
0
1
0
2
2
1
2
1
0
1
0
2
2
2
1
0
0
2
0
2
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
2
2
0
0
1
2
5
0
2
0
0
0
2
1
1
0
0
0
2
0
0
0
1
0
0
1
0
0
1
2
2
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
1
0
2
0
2
0
2
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
1
0
0
3
0
2
2
2
2
2
0
0
1
0
0
2
0
2
0
0
2
2
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
2
1
1
0
1
3
0
0
1
0
1
0
1
0
2
1
0
1
0
0
0
0
1
0
0
3
2
1
0
0
2
0
2
1
0
0
2
2
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
2
0
1
0
0
2
2
0
0
0
0
1
1
0
1
1
0
1
0
0
1
0
0
2
0
0
1
1
1
0
2
0
4
0
0
0
0
0
2
0
0
0
1
2
2
0
0
0
0
0
2
0
0
1
0
1
0
0
1
1
0
2
0
1
0
0
2
0
2
0
0
0
2
2
0
0
3
0
2
0
1
0
0
0
0
0
0
0
0
1
2
0
2
1
0
0
0
1
0
0
1
0
2
1
2
0
2
2
0
0
0
0
2
1
2
0
0
0
0
1
0
0
1
0
2
0
0
1
0
0
0
1
2
1
0
1
0
1
0
0
0
3
0
0
1
0
0
0
2
1
0
1
1
1
0
2
0
2
0
0
1
0
1
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
2
0
2
0
0
0
2
2
1
0
0
1
1
0
0
0
0
1
0
0
2
1
0
0
0
2
0
1
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
1
0
2
0
2
1
1
2
3
1
0
2
1
0
0
0
2
0
2
0
0
0
0
2
2
0
1
0
0
1
0
1
0
0
1
1
1
0
0
0
0
2
0
0
1
1
2
0
0
0
0
3
0
0
0
2
0
2
0
2
0
0
2
0
0
1
0
3
1
0
2
5
2
2
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
2
0
1
2
2
1
0
1
0
2
2
2
0
0
0
2
1
1
1
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
2
2
0
0
1
2
0
0
0
0
2
1
0
0
2
3
0
0
0
1
0
0
2
1
1
2
0
0
2
0
2
0
0
0
0
1
1
0
2
0
2
2
1
0
1
0
3
2
1
2
2
1
0
2
2
1
0
0
0
2
0
2
0
0
1
0
2
0
1
0
1
0
2
0
0
1
2
0
1
1
0
0
0
1
0
0
1
0
0
2
2
0
2
0
1
0
0
1
2
0
1
1
1
0
1
2
0
0
1
1
0
0
0
1
0
1
0
0
1
0
1
2
2
1
0
0
1
0
0
0
1
0
1
0
1
0
2
0
1
1
2
2
1
0
0
1
0
0
0
1
1
1
1
2
0
0
1
0
0
1
0
0
1
1
0
0
0
1
1
1
0
2
0
2
2
2
0
4
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
2
1
0
1
0
0
0
0
0
0
1
0
0
2
0
2
1
2
0
0
1
1
2
0
2
2
1
0
0
0
1
0
1
0
0
0
0
0
0
0
2
1
2
0
0
0
1
0
0
1
0
0
0
0
0
2
1
2
0
0
1
0
0
2
0
1
0
1
2
0
0
2
0
0
0
1
0
1
2
0
0
0
1
1
1
0
1
0
1
0
0
1
1
0
0
0
2
0
0
0
0
0
0
1
0
3
0
1
0
0
2
0
0
0
0
1
2
0
0
0
2
0
1
2
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
2
0
2
0
1
0
0
2
0
2
2
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
2
2
1
0
0
2
1
0
0
0
0
0
0
1
2
0
0
0
0
2
0
1
1
0
1
2
0
1
0
2
0
1
0
1
0
0
0
1
0
0
0
1
1
1
0
0
1
0
0
1
2
0
1
0
0
2
0
1
0
0
1
0
2
2
0
0
0
0
0
0
1
0
2
0
0
0
1
0
1
3
0
0
2
1
1
0
1
0
0
1
2
0
1
2
0
1
0
0
0
2
1
1
2
1
0
0
0
2
2
1
0
2
0
1
2
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
1
0
1
0
0
2
2
0
0
2
1
0
1
2
0
0
0
1
0
2
0
1
1
1
1
0
0
2
2
0
0
0
2
0
0
0
0
0
1
1
0
1
0
2
1
1
0
0
0
1
1
1
0
1
0
2
1
0
2
1
0
1
1
3
0
0
0
1
0
2
0
0
0
2
1
0
2
0
0
1
0
1
0
0
2
0
0
3
0
3
0
1
2
0
0
1
0
1
1
1
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
1
2
2
0
0
1
0
0
3
1
0
0
0
0
1
0
0
0
0
0
3
0
0
3
0
2
0
2
0
2
1
3
1
0
2
2
1
0
0
1
1
4
0
2
5
0
0
0
1
0
0
1
1
0
1
0
2
0
0
0
2
1
0
0
2
2
1
4
2
1
1
1
2
0
0
1
1
0
0
2
0
0
2
1
0
0
2
0
1
2
0
0
1
1
1
0
2
0
0
0
0
0
0
3
0
1
0
0
0
2
0
1
0
0
0
1
2
0
0
0
2
1
0
0
0
1
0
0
0
1
2
1
0
0
0
0
0
0
1
0
0
0
2
2
1
0
1
0
0
0
0
0
0
1
0
0
0
2
2
0
2
3
1
0
2
0
0
3
1
0
0
1
0
4
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
1
0
0
1
0
0
2
0
0
2
0
0
1
0
2
0
1
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
1
0
2
3
0
0
0
0
0
2
4
0
0
0
0
0
1
0
0
1
0
1
0
1
1
2
1
1
0
0
2
0
1
0
0
1
1
1
0
2
2
0
2
2
1
1
0
1
0
0
0
1
0
1
0
0
2
5
2
2
2
0
0
3
0
0
0
1
0
0
1
1
0
1
0
0
3
7
1
2
0
0
0
1
0
0
2
1
2
1
0
0
0
0
1
1
2
0
0
0
0
1
0
2
1
0
2
0
1
0
0
1
0
0
2
0
1
1
0
1
0
0
0
0
0
2
0
0
1
4
0
0
0
1
1
2
2
0
0
0
2
1
0
2
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
2
2
0
0
1
0
5
0
0
0
1
0
2
1
2
0
0
0
2
0
1
0
1
0
0
1
1
0
0
1
0
0
1
0
0
3
2
1
0
0
2
0
1
1
0
1
0
0
0
0
0
1
2
0
0
2
0
2
0
2
0
1
0
1
0
1
2
0
0
1
2
2
1
2
1
0
1
1
0
0
1
1
0
0
0
0
2
0
0
1
2
2
0
0
0
0
0
2
1
0
0
4
0
0
0
1
4
2
2
0
2
1
0
0
0
1
2
2
0
0
0
1
0
0
0
2
0
2
1
2
1
1
2
0
1
0
1
0
1
0
1
0
3
0
0
1
0
0
2
1
0
1
1
0
1
0
0
0
0
1
0
0
2
3
2
0
1
2
2
0
1
2
0
0
2
0
2
0
2
0
0
1
1
1
2
1
0
0
0
0
2
0
1
0
2
0
0
0
2
0
1
0
1
0
1
0
0
1
0
0
2
0
0
0
0
0
3
1
0
0
0
2
2
1
1
2
1
1
1
0
2
0
2
1
2
0
2
2
0
0
0
0
0
1
0
0
0
1
0
0
0
2
1
0
1
1
0
0
1
0
0
1
1
1
0
0
1
1
0
0
2
5
1
0
1
0
0
0
0
2
0
0
1
0
0
0
1
2
2
1
0
4
1
0
0
0
0
0
0
0
0
0
1
2
1
2
0
0
0
0
1
0
0
0
0
0
1
0
1
3
0
1
0
0
1
0
0
1
0
0
2
0
1
0
2
0
0
0
0
0
2
1
0
1
1
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
1
0
2
0
2
1
1
1
1
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
1
0
1
2
0
2
0
0
3
0
2
3
1
0
0
0
3
2
0
0
0
0
0
0
0
2
0
0
0
1
0
1
1
0
1
0
0
2
0
1
0
0
0
3
2
0
0
1
1
0
0
0
0
0
0
1
0
0
2
1
0
3
0
0
0
0
0
2
2
0
0
0
1
0
2
1
0
0
0
0
0
0
1
0
0
1
1
2
0
1
1
1
1
0
1
0
2
0
0
0
0
2
0
1
0
0
2
2
3
1
0
1
0
1
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
2
2
2
0
0
0
0
1
0
2
0
2
1
0
2
0
1
0
0
0
0
0
0
1
1
0
0
0
0
2
1
1
0
0
0
0
0
0
1
0
0
1
3
0
0
0
0
0
1
0
1
0
1
0
1
2
0
0
1
1
1
0
3
1
1
3
0
0
0
1
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
2
1
2
0
1
0
2
0
0
0
1
0
0
1
2
0
1
1
0
0
1
1
0
0
0
0
1
1
1
0
1
0
0
0
2
1
0
0
0
0
0
0
1
1
0
0
1
0
1
0
2
2
1
0
2
0
0
2
0
2
1
1
0
3
0
0
0
2
0
1
0
0
0
1
0
0
0
3
2
2
0
1
1
0
2
0
1
1
1
0
0
0
0
0
0
0
2
0
2
2
1
0
2
1
0
1
1
1
1
0
0
0
0
4
0
0
0
3
0
0
2
1
0
5
0
0
0
0
3
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
3
0
0
0
0
1
2
1
1
1
0
1
2
0
0
0
0
0
0
1
0
1
4
0
2
2
1
2
2
0
1
0
0
0
0
2
1
0
2
1
0
1
0
2
2
1
2
0
0
0
0
2
0
3
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
1
1
2
0
0
1
4
2
0
0
0
4
0
2
0
1
0
0
0
2
2
2
0
0
0
1
2
1
0
0
1
0
0
0
2
2
0
0
1
1
0
1
0
2
0
0
0
2
0
0
0
0
2
0
2
1
0
0
0
2
2
0
0
0
0
2
2
0
2
2
2
0
1
0
1
0
0
2
1
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
1
4
2
2
0
2
4
2
1
1
2
0
1
0
1
0
0
1
0
0
0
0
0
4
1
0
1
1
1
0
2
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
2
2
2
1
1
1
0
1
1
0
1
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
2
0
3
2
0
0
2
0
3
0
0
0
2
0
2
1
3
2
0
0
0
2
0
2
0
0
0
0
0
0
2
1
0
0
0
2
1
1
0
0
0
0
1
1
0
1
1
1
1
1
1
0
1
0
0
0
0
2
0
0
0
1
0
1
0
2
0
0
0
1
2
0
0
0
0
0
1
0
1
0
0
2
0
1
2
2
0
2
0
1
2
0
0
0
0
2
2
0
0
0
2
3
0
2
4
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
1
3
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
2
1
0
0
2
2
1
0
0
0
0
0
0
0
1
0
2
0
0
1
0
2
4
0
3
1
0
2
0
2
0
2
0
2
1
2
0
1
0
0
0
2
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
1
1
0
0
2
2
0
0
0
0
1
0
2
2
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
1
0
1
0
1
1
1
1
2
0
1
0
1
2
0
2
3
0
0
0
1
0
0
1
1
0
2
0
0
0
1
2
0
0
1
0
0
1
0
0
2
0
0
2
0
0
0
1
1
0
2
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
2
0
0
1
0
2
0
0
1
0
0
0
1
1
2
0
0
1
0
0
1
0
2
0
0
0
2
2
0
2
1
1
0
2
0
2
0
0
1
1
2
1
1
0
2
0
0
0
0
0
1
0
1
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
1
1
0
3
0
2
1
2
0
1
0
0
0
0
0
1
0
0
2
1
2
0
0
1
0
0
0
0
2
1
0
1
0
2
0
0
0
2
1
0
2
2
0
1
0
0
0
2
1
0
1
0
0
0
1
0
0
0
1
0
0
1
0
2
0
0
0
2
1
0
1
0
0
1
0
2
0
1
1
0
1
0
0
1
5
0
0
0
1
0
1
0
1
1
1
1
0
2
0
0
0
1
0
1
1
0
1
2
1
0
0
0
0
2
1
2
0
0
0
2
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
1
1
0
1
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
2
1
0
2
0
0
2
0
2
0
1
0
0
0
0
0
2
0
0
0
0
1
2
0
2
0
0
0
1
0
0
0
0
1
0
1
0
3
0
0
2
1
2
0
2
0
0
0
0
1
1
0
0
2
1
1
2
0
1
2
0
0
0
0
1
1
0
0
0
0
0
2
0
1
1
1
1
2
1
0
2
0
1
1
1
2
1
0
0
0
0
3
0
2
0
2
0
2
0
2
2
0
2
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
1
1
0
2
3
0
0
0
0
1
0
2
1
0
0
0
1
1
0
2
0
0
0
1
0
0
2
0
2
2
0
0
4
1
1
0
0
2
0
2
1
1
0
0
2
0
0
0
0
0
1
2
0
0
0
0
1
1
1
1
0
0
0
3
0
0
0
2
1
2
1
0
0
0
2
0
0
0
2
0
1
1
2
2
0
0
3
0
1
1
4
0
0
0
1
0
0
0
0
1
2
2
1
0
2
1
0
2
0
1
2
0
2
0
1
1
1
2
3
0
0
2
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
1
0
0
2
1
1
0
2
0
0
0
2
0
2
0
0
1
0
1
0
0
0
0
0
0
2
0
1
2
0
0
1
2
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
1
0
0
2
2
2
0
2
0
0
2
0
0
0
1
0
0
0
1
0
0
1
2
1
0
0
2
2
0
1
3
0
0
0
0
0
1
0
0
0
2
1
2
0
2
0
2
0
0
0
0
0
2
2
0
0
3
1
0
1
1
0
1
1
2
1
0
0
2
1
0
2
0
1
0
2
2
1
0
0
0
0
2
2
0
0
0
2
1
0
2
2
2
1
0
2
0
0
1
3
0
0
1
2
0
1
0
0
2
0
0
2
0
0
0
0
2
2
2
0
0
1
0
0
2
1
3
0
0
1
2
1
0
1
1
0
0
0
1
2
1
2
2
0
1
1
0
0
0
2
0
1
0
1
0
0
0
2
2
1
0
0
0
0
0
0
3
0
2
2
1
2
0
0
0
2
1
0
0
0
1
0
0
0
1
0
0
0
2
3
2
1
2
1
1
1
0
0
0
0
0
1
0
1
1
1
0
2
0
0
1
2
1
0
0
1
0
0
0
0
0
0
3
2
0
0
0
2
1
2
0
0
2
0
0
0
1
1
2
0
0
0
0
2
1
1
0
1
0
0
0
2
2
1
0
1
2
0
0
1
0
1
2
0
0
1
0
0
2
1
2
0
2
0
1
1
1
0
2
1
0
3
0
1
0
0
0
2
2
0
0
0
0
1
1
1
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
1
2
1
2
0
5
0
0
0
0
2
2
0
1
0
0
0
0
1
2
0
0
0
0
0
2
1
0
0
2
0
2
0
1
0
2
1
2
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
1
2
1
0
0
0
2
1
0
0
1
1
0
0
0
0
3
2
0
0
0
0
0
1
0
1
0
2
0
0
2
1
1
0
0
2
0
0
0
0
3
0
2
0
2
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
1
0
2
2
2
1
2
0
0
0
0
0
1
2
0
0
0
4
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
2
0
0
0
0
0
2
0
1
2
0
1
0
0
0
0
0
0
2
0
0
1
1
1
0
0
0
3
0
0
2
1
0
2
0
0
2
1
0
0
0
1
2
2
0
3
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
1
2
0
0
0
0
0
2
1
0
0
1
1
0
1
0
1
0
2
0
0
1
0
2
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
2
1
0
0
1
2
0
1
1
0
0
2
0
0
2
0
0
0
2
0
0
0
0
2
0
3
5
1
2
0
1
0
0
0
2
0
2
2
1
1
1
0
1
2
0
0
0
0
2
0
1
0
0
0
1
0
1
5
2
0
1
0
2
2
0
1
0
0
0
1
0
0
1
1
0
0
2
1
0
0
0
0
0
2
2
1
0
1
0
2
2
0
2
2
2
0
2
1
0
0
2
2
1
0
2
1
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
3
1
1
1
1
0
0
0
2
2
2
0
0
1
0
1
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
2
0
2
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
1
2
0
0
0
0
1
4
0
2
0
1
0
0
0
0
0
0
1
2
1
1
0
0
2
1
0
2
1
2
0
2
0
0
0
0
1
0
2
1
0
0
0
0
1
3
0
1
0
1
1
1
0
1
1
0
0
0
2
1
0
0
0
0
1
0
2
1
1
0
2
2
0
1
0
1
0
0
2
0
1
2
2
2
2
0
0
0
0
1
0
2
0
1
0
0
0
1
0
0
0
2
1
1
0
2
0
0
1
1
0
0
0
0
0
2
1
0
2
1
0
1
2
2
2
2
2
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
2
0
0
2
1
0
1
0
1
0
0
0
2
0
0
2
1
2
1
1
0
2
0
0
0
0
1
0
1
1
0
0
1
1
1
2
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
2
0
0
1
1
1
1
2
0
0
0
0
0
1
1
1
0
0
0
0
0
0
2
0
1
0
0
0
0
2
2
1
1
0
1
0
0
0
4
1
1
0
0
0
0
0
2
0
0
0
1
0
0
2
0
1
0
0
1
0
0
0
1
0
1
1
0
0
0
2
0
0
0
1
0
0
2
0
0
2
0
2
2
2
2
1
0
0
0
0
0
0
0
0
0
0
0
3
0
2
1
1
0
0
1
1
1
1
2
0
4
2
2
0
0
1
0
0
0
2
1
0
0
1
2
0
3
0
0
0
0
1
1
0
0
0
2
1
1
0
0
1
1
0
1
0
3
1
0
1
0
1
0
0
1
0
0
0
1
0
1
2
0
0
0
0
2
1
2
0
0
0
2
2
0
0
2
0
0
1
0
1
0
0
0
0
0
0
3
0
1
0
0
2
0
2
0
2
0
0
0
3
0
0
0
0
0
0
2
0
1
0
1
2
0
1
0
0
2
0
2
0
0
2
2
0
0
1
1
0
0
4
0
1
1
1
0
0
0
0
0
1
1
0
0
1
0
0
1
2
4
1
2
0
1
2
0
1
1
0
0
1
2
0
0
0
0
0
1
0
2
0
2
0
2
0
0
2
1
1
0
0
0
1
0
0
1
0
0
2
2
0
0
0
0
2
0
1
0
0
0
0
0
1
0
2
1
2
0
0
0
1
0
0
2
1
0
1
0
0
2
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
2
0
1
1
0
0
0
2
1
0
0
2
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
2
2
0
0
1
0
2
1
0
0
0
1
0
1
2
0
0
0
1
13
0
1
0
0
0
2
0
0
1
2
0
0
0
0
1
0
0
0
0
2
0
0
1
0
1
1
1
1
0
0
2
0
1
2
1
0
2
0
2
0
0
0
0
0
0
0
0
1
1
2
2
1
0
1
2
0
1
2
1
1
2
1
1
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
1
3
1
0
0
0
1
2
0
0
1
0
0
1
2
2
0
1
0
2
2
0
0
1
0
1
1
0
0
0
2
0
2
1
0
1
2
0
0
1
0
0
0
0
0
0
0
2
0
2
2
1
0
0
0
1
0
2
0
0
0
0
2
1
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
2
0
0
2
0
5
1
0
0
0
0
0
2
0
2
0
1
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
2
1
2
2
0
2
1
0
2
1
2
1
1
3
0
0
0
1
0
1
0
0
0
2
0
1
2
0
0
0
0
0
3
1
0
1
2
0
0
0
2
0
0
2
0
0
0
0
1
2
1
1
2
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
1
0
1
0
0
0
2
1
1
2
0
4
2
0
1
2
0
0
2
2
0
2
0
0
1
1
0
0
0
1
1
0
1
0
0
0
2
0
0
1
0
1
0
2
2
0
2
0
2
0
1
2
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
1
1
1
0
0
0
1
2
2
0
1
0
0
0
0
1
0
0
0
1
3
1
0
2
2
0
1
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
1
1
2
2
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
1
0
1
0
2
0
0
0
0
2
0
0
2
2
2
1
0
2
0
3
0
0
1
1
1
1
2
2
0
1
2
0
0
0
1
2
1
0
1
2
0
2
0
2
2
0
1
0
1
0
2
1
0
1
0
0
1
2
3
1
0
3
1
1
0
0
0
0
2
2
2
0
0
0
0
2
0
0
1
12
0
2
0
1
0
0
0
1
1
0
2
2
0
1
0
0
1
1
0
2
1
2
0
1
0
0
0
0
0
0
1
1
1
1
1
0
2
0
1
3
2
0
0
3
1
2
0
2
1
2
0
0
0
3
0
1
0
0
0
0
0
1
2
0
2
0
2
2
2
0
0
0
0
0
0
1
0
2
0
0
0
1
2
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
2
0
0
2
1
0
0
0
0
0
2
2
0
1
0
2
0
0
0
0
0
0
1
0
0
1
2
0
0
2
0
0
0
0
1
1
2
0
1
0
1
2
1
0
1
2
0
0
1
1
0
0
2
0
2
1
2
1
0
3
1
0
0
0
0
0
1
2
0
0
0
0
5
0
1
0
2
0
1
1
1
0
0
1
0
0
0
0
0
1
0
3
0
0
2
0
1
0
2
0
2
0
2
0
1
2
0
3
2
0
0
0
1
1
0
0
0
2
0
0
0
0
0
3
1
2
0
1
0
0
1
0
2
0
0
0
0
1
0
0
2
0
1
0
0
0
2
0
0
1
0
1
1
0
0
0
2
0
0
0
2
2
2
0
0
0
1
0
2
0
1
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
1
0
1
1
0
1
1
0
0
2
0
0
1
0
2
1
1
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
3
0
1
2
0
2
1
0
1
0
0
0
0
0
0
2
1
0
1
0
2
0
0
1
0
2
3
1
0
0
0
1
0
0
0
0
1
0
0
4
0
1
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
1
2
0
1
0
1
0
0
1
0
0
0
0
1
1
3
1
0
0
0
0
2
1
0
0
0
0
0
0
0
1
1
2
1
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
2
2
0
2
1
2
1
0
0
0
2
0
0
2
0
0
2
2
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
1
0
1
0
0
2
0
2
0
1
0
0
1
0
1
0
0
0
2
1
0
0
2
0
0
0
2
0
0
0
0
3
0
1
0
0
0
0
0
0
1
0
2
2
1
0
0
0
2
0
1
0
1
0
0
0
0
0
2
0
0
2
1
1
0
2
0
2
2
1
2
0
1
0
3
2
0
0
0
0
1
2
2
0
0
0
2
0
0
2
0
1
2
2
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
1
0
1
2
0
0
0
1
2
0
0
0
2
0
1
1
0
0
0
0
0
0
0
2
1
0
1
0
2
1
1
0
0
0
1
0
0
0
0
1
2
0
0
1
1
2
0
1
1
0
0
0
2
2
0
1
2
1
0
1
1
0
3
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
1
0
0
2
1
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
1
0
0
1
1
2
0
0
0
2
0
0
1
0
1
2
0
0
1
0
0
0
0
0
4
1
0
0
0
0
0
1
0
5
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
1
1
0
1
0
2
0
2
1
0
1
1
1
1
0
0
0
2
0
0
0
1
0
1
2
1
1
0
2
1
0
0
0
0
1
2
2
2
0
0
0
0
2
0
0
2
0
0
0
0
1
0
2
1
0
1
0
0
2
2
2
1
0
0
0
1
1
0
2
0
0
1
0
3
0
0
1
0
2
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
2
2
0
2
0
2
0
0
1
0
1
0
1
1
0
0
1
1
0
0
0
0
1
0
0
2
0
1
0
0
1
2
0
0
1
0
13
0
2
0
0
0
0
0
2
0
0
1
0
0
0
2
1
2
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
2
2
0
0
0
1
0
1
0
0
0
0
0
0
0
2
2
0
3
0
2
0
0
0
3
1
1
1
0
2
0
2
1
2
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
1
1
3
1
0
2
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
1
2
2
0
0
2
0
0
0
1
2
0
0
0
2
0
0
1
0
1
1
0
2
2
0
2
0
1
1
0
0
0
0
0
0
0
0
2
2
0
1
0
0
1
1
3
2
1
2
0
1
3
1
2
0
1
0
2
0
0
0
0
0
0
3
0
0
2
0
0
2
0
1
1
0
0
2
1
1
2
0
1
0
4
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
1
0
0
2
0
0
2
1
0
0
0
0
1
0
0
1
0
0
2
0
2
0
1
1
0
2
0
0
0
2
0
2
2
0
0
0
0
0
0
3
0
0
0
2
0
0
1
0
0
0
0
0
3
0
0
5
0
3
0
1
0
0
0
0
0
1
0
1
0
0
0
2
1
0
0
1
0
1
0
0
1
0
0
2
2
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
1
0
0
1
0
0
2
1
1
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
1
0
0
1
2
1
0
0
0
0
2
0
0
0
0
1
0
0
0
7
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
3
1
0
1
1
2
0
1
0
0
0
2
0
0
2
0
0
0
1
0
2
0
2
0
0
2
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
2
2
0
1
0
0
0
0
0
0
2
1
0
0
1
2
0
0
2
2
0
0
2
0
0
2
0
0
2
0
1
2
0
2
0
1
0
0
1
1
1
0
2
2
2
0
1
1
1
1
0
1
1
2
0
1
0
2
1
0
1
0
1
0
1
1
1
0
0
0
0
1
1
1
0
3
0
1
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
2
1
0
1
2
0
0
0
1
1
0
1
0
1
0
0
0
2
0
0
0
0
1
2
0
1
0
1
0
0
1
0
0
2
0
0
1
0
1
0
0
0
2
2
0
0
1
0
0
2
0
0
1
0
2
0
1
1
1
0
0
2
1
0
1
0
0
0
2
1
4
2
2
0
0
1
0
0
1
0
1
0
1
0
1
2
1
0
2
2
1
2
1
0
0
1
1
2
2
0
3
0
1
0
1
0
0
0
2
1
1
0
0
0
0
1
0
2
0
2
2
0
0
0
1
2
0
1
2
0
0
1
0
0
1
2
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
3
0
1
1
1
2
0
0
2
0
2
0
0
0
0
1
1
3
0
0
0
0
0
1
1
0
0
0
1
2
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
2
1
0
0
0
0
2
1
0
2
0
1
1
0
0
0
0
0
1
5
0
0
0
0
0
1
2
2
2
1
0
0
0
1
0
1
0
1
0
1
0
0
2
2
2
0
0
2
0
2
2
2
0
0
0
2
0
2
0
2
2
1
0
0
2
0
0
0
0
1
1
1
0
0
0
1
1
0
2
1
0
1
0
0
2
0
2
1
0
0
0
0
1
0
0
0
2
0
1
0
1
0
0
2
0
0
0
0
0
0
0
1
1
0
0
2
1
0
0
1
1
0
0
0
0
0
0
0
2
2
0
2
0
0
0
1
2
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
2
0
0
1
0
0
1
1
0
3
0
1
2
0
1
1
1
2
0
0
2
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
3
0
1
4
0
1
0
0
0
2
5
0
0
0
2
1
1
2
0
1
0
1
1
0
2
2
0
1
0
0
0
2
0
0
2
0
1
0
0
0
2
0
0
1
0
0
1
0
1
1
1
2
0
2
2
1
2
1
0
0
3
0
0
3
1
0
0
1
0
2
1
3
2
2
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
2
1
0
0
1
0
0
2
1
2
1
0
2
0
2
0
0
0
0
2
1
0
3
0
1
0
0
0
2
2
1
0
1
0
0
0
2
0
2
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
2
0
3
0
2
0
2
2
0
0
0
1
1
0
1
0
2
2
1
2
0
1
1
0
2
1
2
2
0
1
1
0
1
0
0
0
0
0
2
0
0
0
0
0
2
4
0
1
0
0
2
0
1
2
0
2
0
1
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
2
0
2
0
0
2
0
0
1
1
0
0
0
0
0
1
0
1
2
0
0
2
0
1
0
0
0
2
1
0
0
1
1
2
1
1
0
0
0
0
1
0
1
0
0
2
1
0
1
2
1
0
0
5
2
0
0
0
0
0
1
0
1
0
0
2
0
0
1
1
2
0
0
0
0
2
2
1
0
0
1
2
1
1
2
0
1
1
0
0
1
0
0
0
2
0
0
1
2
1
0
1
0
0
0
0
2
0
2
0
1
2
0
2
0
0
0
0
0
0
0
0
1
0
1
2
0
1
0
0
0
1
0
1
1
1
1
0
0
0
0
0
1
0
1
2
0
0
2
2
2
1
0
0
0
0
1
2
1
1
3
1
1
1
0
0
2
0
2
0
2
0
0
1
0
0
1
0
1
0
1
0
1
0
2
0
0
0
0
1
0
1
0
1
1
0
0
2
1
0
0
0
0
1
2
0
0
1
0
0
0
3
0
3
1
0
0
0
2
0
0
2
0
1
1
2
0
0
0
2
1
1
0
0
0
0
1
1
0
0
1
0
0
2
1
2
0
0
0
0
0
0
2
2
1
2
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
2
1
2
0
2
0
1
1
1
2
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
2
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
1
3
0
0
2
1
1
2
0
0
4
2
0
1
0
0
0
0
0
0
0
2
1
0
3
2
2
2
0
2
1
0
0
0
0
0
1
0
0
1
2
1
0
2
1
0
2
0
1
1
0
0
0
1
0
0
1
0
0
1
2
0
0
0
2
2
2
1
0
0
0
0
1
0
0
1
0
2
1
0
2
0
2
1
0
2
0
0
1
2
0
0
0
2
2
0
0
2
2
1
1
0
0
1
1
0
0
0
2
0
0
0
0
0
1
0
1
1
2
1
1
0
1
2
0
0
2
0
0
0
1
2
0
0
0
2
0
1
0
2
0
2
0
2
0
0
0
0
1
0
0
0
0
1
2
2
5
1
0
0
1
0
1
2
1
0
0
1
0
0
1
0
1
0
0
0
1
0
0
1
0
2
1
0
2
2
0
0
0
1
1
1
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
1
2
0
1
1
0
2
0
1
0
1
2
2
2
0
0
0
1
1
0
1
2
2
1
0
0
0
0
0
0
0
2
0
0
2
1
0
1
2
1
0
0
0
0
1
0
0
0
0
1
2
0
1
0
2
1
2
2
1
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
1
1
0
1
2
2
0
1
2
0
1
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
1
0
2
1
1
0
0
1
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
1
2
0
2
0
1
0
0
0
0
1
2
0
0
0
1
1
0
0
1
0
1
0
2
0
1
0
0
0
0
0
2
1
0
0
2
5
0
1
0
1
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
1
0
1
1
1
0
0
2
1
0
0
0
0
0
0
1
1
0
0
0
2
0
1
3
0
1
0
0
0
1
2
1
2
1
1
0
2
2
0
2
1
0
0
2
2
0
0
0
1
0
0
0
0
0
0
1
2
2
1
0
0
0
1
0
1
1
0
2
0
2
2
1
0
1
0
0
1
0
0
0
0
1
0
3
1
3
0
0
1
0
0
0
1
0
0
1
2
0
0
1
0
0
0
0
1
2
1
0
1
2
0
0
0
1
0
1
0
2
0
0
1
0
0
0
2
2
1
4
0
1
0
0
0
0
1
2
2
0
1
0
0
0
0
0
0
2
0
2
1
0
1
0
1
0
3
1
1
0
0
0
0
2
1
0
0
0
1
0
0
1
0
2
1
0
0
0
0
0
2
0
1
0
0
0
2
0
3
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
2
0
2
1
0
2
0
0
0
2
3
1
2
1
0
0
0
0
0
0
1
2
0
1
1
0
2
2
2
1
2
2
0
0
1
1
1
1
0
0
0
0
0
0
0
2
0
2
1
0
1
0
0
0
1
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
2
1
1
2
0
1
0
0
0
0
1
0
2
0
0
1
0
1
2
0
3
1
0
0
0
2
0
0
0
0
1
0
0
1
0
1
0
0
2
0
2
2
0
2
2
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
5
0
0
0
2
0
1
2
0
1
2
1
0
2
2
1
0
1
0
0
1
1
0
2
0
2
0
2
0
2
1
0
0
0
1
1
0
1
0
0
0
1
0
0
0
1
1
1
0
0
1
0
0
0
0
0
2
2
0
0
0
2
0
0
1
3
0
0
0
0
0
3
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
1
1
1
0
0
0
0
2
0
2
0
0
2
0
1
3
0
1
0
0
0
1
0
1
1
0
2
0
0
1
0
0
0
2
0
0
1
1
0
2
0
0
1
1
0
1
0
2
0
0
0
2
1
1
0
0
0
0
0
2
0
1
0
2
1
1
5
1
1
1
0
0
1
0
1
0
2
0
0
0
0
0
0
1
0
1
2
0
0
1
0
0
1
3
1
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
3
3
1
2
0
1
0
1
0
0
2
0
2
0
1
0
2
0
2
0
0
0
3
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
1
2
2
0
2
2
3
1
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
2
0
1
0
1
1
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
1
0
2
2
0
0
0
2
0
0
0
0
1
1
2
0
0
0
0
1
1
2
5
1
1
1
2
2
0
2
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
2
0
0
1
0
0
1
0
1
1
0
1
1
0
0
2
1
2
0
1
2
1
1
1
0
1
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
1
0
2
0
1
0
1
0
1
0
0
0
0
0
2
0
2
2
1
0
0
0
2
2
1
2
0
1
0
0
0
0
0
0
0
0
0
0
2
1
2
1
1
2
0
2
2
0
0
0
1
0
2
0
0
0
2
0
0
0
0
2
2
0
0
1
2
1
0
0
2
2
0
0
0
0
2
1
0
0
0
0
2
0
1
0
1
1
0
0
0
0
0
2
0
0
1
0
1
2
0
0
1
1
0
0
0
2
0
1
0
0
2
1
0
1
0
0
1
0
0
0
1
0
1
0
1
1
0
0
0
0
2
0
1
0
1
0
2
0
0
1
1
0
0
0
0
0
1
1
0
1
0
2
2
1
0
1
0
0
2
1
0
2
1
0
2
0
0
2
2
2
2
0
3
0
0
1
0
1
0
1
0
0
0
0
0
1
2
0
2
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
1
1
0
2
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
1
0
2
2
2
0
0
1
2
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
2
0
0
1
2
4
0
1
2
2
0
0
2
2
1
2
1
0
0
1
0
2
0
0
0
2
1
3
1
2
0
1
1
0
2
2
2
0
0
1
1
0
0
0
1
1
1
1
1
0
1
0
2
0
2
1
3
0
0
0
2
0
2
0
0
1
0
0
0
1
1
0
0
3
0
0
0
2
0
0
2
2
0
1
1
0
2
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
1
1
0
1
0
1
0
0
1
3
0
0
0
1
0
0
0
1
0
0
1
0
2
0
1
2
0
1
0
0
2
0
2
0
4
0
0
0
0
2
0
0
1
1
0
0
0
0
1
0
1
0
0
0
1
0
0
2
2
0
1
1
0
0
2
0
0
0
1
2
0
0
1
1
1
0
0
0
0
0
2
0
1
0
1
0
0
1
0
0
5
0
1
0
1
0
0
1
0
0
0
2
0
0
0
1
1
2
0
0
0
0
1
0
0
1
0
0
0
0
2
1
0
0
1
0
0
1
0
1
2
0
0
1
0
0
2
0
3
0
2
0
0
2
1
2
0
1
0
0
2
0
0
1
0
2
0
0
2
0
0
0
0
0
2
0
0
2
0
0
2
0
1
0
1
0
0
1
0
0
2
2
0
0
0
1
0
2
0
1
2
0
1
1
0
0
2
2
0
1
1
0
0
1
1
0
2
3
2
1
1
1
1
0
1
2
1
2
0
0
2
0
0
0
0
2
2
0
1
0
1
1
0
2
2
1
1
1
2
3
0
0
0
0
2
2
0
0
1
0
1
2
2
1
1
2
1
2
0
2
0
0
2
2
2
1
1
2
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
2
1
2
1
0
0
0
0
0
0
2
1
0
1
1
0
3
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
1
1
0
1
1
0
1
2
1
0
0
1
0
2
0
1
0
0
2
2
2
4
1
0
1
1
0
2
0
0
0
2
0
1
0
2
1
0
0
1
1
0
1
2
0
0
1
0
1
0
0
2
0
0
0
0
1
0
2
2
0
0
0
0
2
0
0
0
0
0
2
2
1
0
0
0
1
0
0
0
0
2
0
2
2
2
0
1
0
1
0
0
0
0
0
2
0
1
0
0
0
2
2
0
1
0
2
0
0
0
0
2
1
0
2
1
1
0
1
0
0
0
1
0
2
0
1
0
0
0
0
2
0
3
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
2
0
1
2
1
0
0
0
2
1
2
0
0
0
2
0
0
2
0
2
0
2
0
3
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
2
0
0
1
2
1
2
0
0
1
0
1
0
2
0
0
0
2
0
2
0
0
1
1
1
0
1
0
0
0
0
2
0
0
1
0
0
0
0
1
0
2
0
0
2
2
1
0
0
0
2
0
0
2
0
0
1
1
0
0
1
2
2
0
1
2
0
0
1
0
2
2
2
2
1
0
2
1
3
1
0
2
0
0
0
0
1
0
2
1
0
5
0
2
0
1
0
0
0
0
0
0
1
1
2
0
2
0
1
0
0
0
2
0
1
0
1
2
0
0
0
1
4
0
0
2
0
2
2
1
0
0
2
1
0
0
0
2
0
0
1
1
2
0
0
0
0
0
0
0
0
1
0
1
1
1
2
1
0
1
0
0
0
0
0
1
0
2
0
2
0
1
1
0
2
0
0
2
1
0
0
0
1
0
0
2
2
0
1
0
2
0
0
0
2
0
0
0
1
2
2
1
0
2
0
0
2
0
1
2
0
2
1
1
0
0
0
2
0
0
2
0
0
0
0
1
1
0
0
0
0
2
0
0
0
2
1
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
2
0
0
1
0
1
0
1
0
0
0
2
0
0
0
1
0
3
2
0
1
1
2
2
1
0
0
1
2
0
0
2
0
1
0
0
0
0
2
0
1
2
0
1
3
1
0
0
0
0
0
0
0
0
0
2
1
1
1
0
2
1
0
0
1
2
2
0
0
0
0
1
0
0
0
1
1
0
3
0
0
0
2
0
0
1
0
0
1
0
0
0
0
1
0
0
2
0
0
1
0
1
0
1
0
0
1
2
2
2
1
1
2
1
1
1
0
1
1
0
2
1
2
0
2
2
1
0
2
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
2
0
2
2
0
0
2
1
1
1
0
0
0
2
0
1
1
0
0
2
3
0
2
1
0
0
0
0
2
0
1
0
0
0
1
0
0
1
1
0
0
0
2
1
1
1
2
2
0
1
2
1
2
0
2
2
2
0
0
0
0
2
1
1
2
2
0
2
0
0
0
2
1
0
2
1
0
7
0
0
0
1
1
0
1
0
2
1
0
1
0
0
1
0
0
1
0
0
1
2
0
2
2
2
0
1
2
0
2
2
0
0
0
0
1
0
6
1
1
1
1
0
0
1
0
2
2
1
0
1
2
0
0
1
0
0
0
0
0
0
1
2
1
0
0
0
2
0
0
0
0
0
2
0
0
1
0
2
2
0
0
2
0
0
1
1
0
2
0
0
0
0
0
0
2
0
0
2
0
2
0
0
3
2
0
2
0
0
0
1
2
0
4
1
0
0
0
0
0
0
1
2
0
0
1
0
0
1
3
2
0
0
0
0
2
0
0
0
1
0
1
0
0
2
0
0
0
0
2
0
2
0
0
2
2
2
2
0
0
0
0
1
0
0
0
2
2
0
1
1
0
2
0
2
0
4
0
0
1
0
0
2
0
2
0
1
1
2
0
1
1
0
0
0
1
1
2
0
0
1
0
0
0
0
2
0
2
0
2
2
2
0
0
0
0
0
1
0
2
1
0
0
0
1
0
1
1
0
1
0
0
1
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
1
0
0
2
0
0
0
2
0
1
2
0
2
1
0
1
1
0
0
1
0
0
1
2
1
0
0
0
0
1
2
0
1
1
0
2
2
1
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
1
1
0
2
2
2
0
0
0
0
1
1
1
0
1
0
0
1
1
2
0
0
1
0
0
1
0
2
0
0
0
2
0
0
0
1
1
2
0
0
0
1
0
1
2
0
0
2
1
0
0
1
0
2
2
1
1
2
0
1
2
2
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
1
2
0
0
0
0
0
2
0
0
1
0
2
2
0
0
2
0
0
2
0
2
0
0
0
1
2
8
1
0
5
0
0
0
1
0
2
0
1
1
5
0
0
2
2
2
0
2
2
0
1
0
1
2
0
0
2
0
0
2
0
1
0
0
0
2
1
0
1
0
2
0
2
1
0
3
1
0
0
1
0
0
0
0
2
1
2
0
2
0
0
1
2
0
0
2
0
0
2
0
1
0
0
1
1
2
0
1
0
2
0
2
0
0
2
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
1
0
1
1
0
0
2
0
0
0
0
0
1
0
1
0
0
0
2
0
0
1
2
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
1
2
1
0
1
2
0
1
1
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
2
0
1
0
1
2
0
1
0
1
0
0
0
0
1
0
2
0
2
2
2
0
2
0
0
1
0
1
0
0
2
1
2
2
0
0
2
0
0
0
2
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
1
1
0
0
0
2
0
1
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
2
0
2
0
0
2
1
1
0
1
1
1
0
1
5
0
1
0
0
1
1
0
1
1
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
1
2
2
1
0
0
0
2
1
1
2
0
0
0
0
0
0
2
0
1
1
0
0
0
0
1
1
0
1
0
2
3
0
0
2
1
1
1
1
0
0
0
0
1
0
0
1
0
0
1
1
2
0
2
2
0
0
2
1
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
1
2
2
0
0
2
1
2
0
0
0
2
0
1
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
2
0
0
2
0
0
2
0
2
0
0
4
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
1
2
0
0
1
2
0
2
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
2
2
0
0
0
0
0
2
0
0
0
0
1
2
0
0
2
0
0
1
2
0
0
0
0
1
0
0
0
2
1
1
0
1
1
0
0
0
2
0
0
1
0
0
1
0
0
0
2
0
0
2
0
0
0
0
2
1
0
1
1
1
0
2
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
1
0
1
1
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
1
1
3
2
0
0
0
0
0
5
1
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
1
0
1
2
2
0
0
0
2
0
0
2
0
0
0
2
0
0
2
1
2
0
0
0
1
1
2
0
0
2
2
0
0
0
0
0
0
2
2
2
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
1
1
0
1
1
2
0
0
2
3
2
0
0
0
0
1
0
1
0
0
0
1
2
1
1
0
0
0
0
2
1
0
0
1
2
0
0
2
0
0
0
1
2
0
1
1
0
1
1
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
2
0
2
0
0
0
2
1
0
1
0
1
0
2
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
1
0
2
0
1
4
0
0
0
0
1
2
0
0
0
0
2
0
0
1
0
0
3
0
1
3
0
0
1
0
0
1
2
1
0
2
1
1
0
0
1
0
0
1
0
0
3
2
0
1
1
0
1
1
0
1
0
2
0
1
1
0
0
0
0
0
2
0
0
0
0
0
1
1
0
3
0
0
2
0
0
0
2
0
0
0
0
0
1
1
0
0
1
1
0
1
1
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
2
1
0
2
0
2
0
1
1
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
2
0
0
2
3
0
0
2
0
1
0
3
1
1
0
1
0
0
0
0
1
0
2
2
0
1
0
0
2
0
0
3
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
2
0
1
0
0
1
1
0
0
1
0
0
0
1
0
1
0
2
1
0
1
1
1
1
0
1
0
0
2
1
1
0
0
3
0
1
0
0
0
1
1
0
0
0
1
1
0
0
0
0
1
0
0
2
2
2
1
2
1
1
1
0
0
0
0
1
0
0
2
0
5
0
1
3
1
1
0
0
0
0
1
0
0
1
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
1
1
0
2
1
2
0
1
2
2
0
0
0
1
0
0
2
0
0
0
1
2
2
0
0
1
2
0
1
0
0
0
0
0
2
0
0
0
2
0
1
1
2
0
1
0
1
1
0
0
0
0
1
1
0
0
3
0
0
0
0
1
1
0
0
1
0
2
1
1
0
0
0
0
1
2
0
0
1
2
0
0
1
0
0
2
1
2
0
1
1
1
2
2
0
2
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
1
0
1
1
0
2
1
2
0
0
0
1
1
2
1
0
2
0
1
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
1
0
2
2
0
1
2
1
2
0
0
0
2
0
2
0
0
0
0
0
0
2
0
2
2
0
0
0
0
1
1
0
0
0
0
0
0
4
0
1
0
2
0
2
0
1
0
0
0
0
1
0
1
0
0
0
0
2
1
1
2
2
0
0
4
1
1
2
2
1
0
1
1
0
0
0
1
0
2
0
0
4
1
1
1
0
2
2
0
0
0
2
0
0
1
0
0
1
1
2
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
1
2
0
1
3
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
2
0
0
0
2
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
2
0
2
0
0
0
1
2
1
2
0
0
1
2
3
1
1
0
0
1
2
0
0
0
1
0
0
0
1
2
0
0
2
0
0
2
1
0
0
0
0
1
0
0
0
0
0
1
1
1
1
1
0
1
1
0
2
0
0
1
2
1
0
0
0
0
1
1
1
0
0
0
1
0
0
0
1
0
2
0
0
0
0
2
0
0
2
2
0
1
0
0
0
1
0
2
1
0
2
0
2
1
1
2
0
0
0
2
0
2
1
0
1
2
2
1
0
0
0
2
0
2
0
1
0
0
0
0
4
0
1
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
2
1
1
0
0
0
1
1
0
0
2
0
0
2
1
1
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
2
2
1
1
1
2
0
0
0
0
1
2
0
2
0
1
2
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
1
1
0
2
0
0
1
0
0
0
1
0
2
0
0
1
2
0
0
2
1
0
4
0
0
1
1
1
0
0
0
1
1
0
0
0
2
1
0
0
1
1
1
0
0
1
0
2
1
1
4
0
0
0
1
1
1
0
0
0
2
1
0
0
0
1
1
1
1
2
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
1
0
0
2
0
0
4
2
0
1
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
2
1
0
0
0
1
2
0
2
0
2
1
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
5
0
0
0
0
0
0
1
0
0
0
2
2
0
2
0
2
2
0
1
0
2
0
1
1
2
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
2
0
1
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
2
0
2
0
2
0
0
1
0
0
1
1
0
0
0
0
1
0
2
2
2
1
0
1
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
1
0
9
0
0
0
0
0
1
0
0
2
1
2
1
1
2
0
0
0
1
0
0
2
0
0
3
0
0
0
2
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
2
2
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
2
1
0
1
0
0
0
0
2
0
0
1
2
0
1
0
0
1
1
1
1
0
0
2
0
1
0
1
0
0
0
1
0
0
1
0
0
2
0
0
2
0
2
0
0
2
0
1
0
0
2
0
1
0
0
0
1
1
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
2
1
2
0
0
0
0
0
2
2
1
0
0
0
1
1
1
1
0
1
0
2
2
0
0
0
1
0
2
0
0
1
0
0
0
2
0
0
0
2
1
2
1
1
0
2
0
2
0
2
1
1
2
0
1
0
0
2
0
0
1
0
1
1
1
0
0
2
1
0
0
2
2
0
2
0
0
1
0
2
0
0
1
2
0
0
0
1
0
2
0
0
0
0
0
1
3
1
1
0
2
2
0
0
2
0
2
1
1
0
0
0
1
1
1
2
0
0
0
0
0
0
0
0
0
0
3
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
1
0
2
0
0
1
1
1
2
0
0
0
1
1
0
2
0
1
0
2
0
0
1
0
0
0
1
0
1
1
2
0
0
0
3
0
0
0
2
0
0
0
0
2
1
2
2
0
2
0
0
1
0
0
0
0
0
1
0
1
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
2
1
0
0
2
2
0
1
1
1
1
0
0
0
2
0
0
0
0
1
0
2
0
1
1
1
1
1
0
0
0
1
0
0
1
2
2
1
0
1
2
0
2
1
0
2
0
2
0
0
0
0
0
1
0
0
2
0
0
1
0
1
0
0
1
2
0
0
3
1
0
0
1
2
0
2
0
0
0
5
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
1
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
1
0
2
1
0
2
1
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
3
1
0
0
1
0
0
1
0
0
1
1
1
2
0
2
0
0
0
2
0
0
2
1
0
1
0
2
0
3
0
2
0
0
2
0
0
1
0
3
0
1
2
2
1
0
0
2
1
0
0
0
0
3
0
0
0
0
0
2
1
0
0
0
1
1
0
1
1
1
1
0
1
2
0
0
0
1
0
0
2
0
2
1
2
2
0
1
2
2
0
0
1
0
2
0
0
0
2
0
1
0
0
0
1
2
2
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
1
0
1
0
2
3
0
0
2
0
0
0
2
0
0
0
3
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
2
1
0
0
0
1
0
2
1
0
1
0
0
2
0
0
0
0
0
2
2
2
1
1
0
0
1
0
0
0
2
0
0
1
0
1
0
1
0
0
1
1
0
0
4
1
1
0
3
1
0
0
1
0
0
0
1
2
0
7
0
0
1
0
0
2
0
2
0
1
0
0
0
2
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
1
0
1
0
2
0
1
1
0
0
0
0
1
0
0
0
0
0
0
2
1
0
2
0
2
2
0
0
0
0
0
0
1
1
0
1
0
1
0
1
1
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
1
0
0
1
2
2
1
0
0
2
0
0
1
0
0
2
2
1
0
0
0
1
0
0
0
1
0
0
2
0
1
0
0
1
2
0
1
1
0
0
0
0
0
4
1
0
0
0
0
0
2
1
1
1
0
0
0
1
1
0
2
2
1
2
0
0
2
1
1
1
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
2
2
0
0
1
0
1
1
0
4
2
0
2
1
2
0
0
1
0
1
0
0
0
0
0
1
0
0
1
1
4
0
1
1
0
0
2
0
0
0
1
0
0
2
0
0
2
2
0
0
0
0
0
2
1
1
0
0
1
0
0
0
0
1
1
0
1
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
1
1
0
1
0
0
2
0
0
0
0
0
0
0
1
2
1
0
2
0
1
1
1
0
8
2
0
1
1
0
0
0
3
0
2
2
2
1
1
0
0
0
0
0
0
0
2
1
0
1
0
2
1
0
2
0
1
1
0
0
1
2
0
0
0
1
1
1
0
0
0
0
0
0
0
3
0
0
0
1
0
0
2
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
1
2
3
1
2
0
2
2
2
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
2
2
0
0
2
3
0
1
1
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
2
1
0
1
1
1
1
0
1
2
0
2
1
2
1
0
1
0
2
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
3
0
0
2
0
4
0
1
0
0
0
0
0
1
0
0
0
2
1
0
0
0
1
0
1
0
0
1
1
0
1
0
0
0
0
1
0
0
1
0
0
2
1
2
2
1
0
1
1
1
1
1
0
2
0
1
1
0
0
0
0
0
1
3
0
0
0
0
2
0
2
2
2
1
0
2
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
2
0
0
1
0
2
0
0
0
2
0
0
0
0
0
2
0
1
0
0
1
0
1
1
2
1
1
0
0
0
1
2
1
1
0
1
1
0
0
2
1
1
0
0
0
1
2
3
1
0
1
1
0
0
1
0
0
0
0
1
0
3
3
0
2
0
2
2
0
0
0
0
1
0
0
0
0
1
0
2
1
0
2
0
0
3
2
0
0
0
0
1
1
1
0
0
0
0
0
2
1
1
0
0
0
1
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
1
2
2
2
0
0
1
0
2
0
0
0
2
0
0
3
0
1
0
0
2
1
1
0
0
0
0
0
0
0
0
2
1
1
2
1
0
0
0
1
1
0
0
0
0
0
2
0
0
0
12
0
2
0
0
0
0
1
1
1
0
2
1
0
0
1
1
0
1
2
0
1
1
0
2
0
0
1
0
0
0
0
1
3
0
0
2
0
1
0
1
1
0
1
0
0
0
1
0
2
0
2
0
2
2
0
1
1
0
0
0
1
1
2
0
0
1
1
2
1
2
0
0
0
2
0
0
2
2
0
1
0
1
3
0
1
2
0
0
0
0
0
1
0
1
0
1
2
0
2
0
1
0
0
1
0
2
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
1
0
2
0
0
0
0
1
0
0
0
1
0
0
0
3
0
2
0
2
0
2
0
2
1
1
2
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
1
1
0
1
1
0
0
0
1
0
0
2
0
2
1
0
0
0
0
0
3
0
2
2
2
0
0
0
0
1
1
4
0
0
0
2
2
2
0
0
0
0
0
0
0
0
2
0
1
1
2
0
0
0
0
1
0
1
1
1
0
2
2
1
0
0
0
0
0
2
2
0
0
1
0
1
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
1
1
2
0
0
0
2
1
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
2
1
0
1
0
0
3
2
0
0
2
0
0
0
0
0
0
1
0
1
2
0
1
0
0
0
0
0
2
2
1
1
0
2
0
1
0
2
0
0
0
0
2
0
2
1
0
0
0
2
0
0
0
1
1
0
1
0
0
0
0
1
0
2
0
0
0
0
2
2
1
1
0
0
0
0
2
0
0
0
0
0
0
3
2
1
0
0
0
0
3
0
1
0
0
0
0
0
0
1
2
0
2
0
0
1
2
2
0
1
0
2
1
0
0
0
0
1
1
0
0
2
0
2
0
0
2
0
2
0
1
0
3
2
2
0
1
0
1
2
0
2
0
2
2
0
1
0
0
1
0
0
2
0
2
1
2
2
0
2
0
1
1
0
3
0
1
2
1
2
1
0
0
1
2
2
0
0
1
1
3
2
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
2
2
0
2
0
2
0
0
0
1
1
2
1
0
2
0
0
2
0
0
0
0
2
2
0
1
0
0
0
0
1
1
0
0
0
1
0
2
0
1
0
0
0
2
0
0
0
1
0
2
1
0
2
0
0
1
1
0
0
0
1
2
0
1
0
3
2
3
0
0
0
2
3
1
0
0
1
3
1
0
2
0
0
2
2
0
0
0
0
0
1
1
2
0
1
1
2
0
0
0
0
0
0
1
0
1
2
0
0
1
2
0
1
2
0
1
0
0
1
0
3
0
1
1
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
1
0
0
2
1
0
0
0
0
2
1
1
0
0
0
0
0
2
1
0
0
0
1
1
0
2
0
0
0
2
1
0
1
0
0
0
4
1
0
0
1
2
1
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
2
0
0
2
0
3
0
2
0
0
0
0
0
0
2
0
1
1
0
1
0
2
2
0
0
2
2
0
0
0
2
0
0
0
3
1
1
2
2
0
0
2
1
0
0
0
0
1
0
1
1
1
1
1
1
0
1
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
1
2
1
0
0
2
0
1
3
0
2
0
0
1
0
1
2
0
0
2
0
0
1
2
0
0
1
0
0
1
1
1
1
0
0
1
1
1
0
0
0
1
2
0
1
1
0
0
1
0
3
4
0
0
1
2
0
1
1
0
0
2
1
2
0
2
0
0
0
1
0
0
1
2
0
0
3
0
0
0
0
1
0
0
0
3
0
0
3
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
2
0
4
0
0
1
2
0
1
0
0
0
1
0
1
1
1
0
0
0
1
0
0
0
0
2
0
0
2
2
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
1
0
4
0
0
0
0
0
0
1
1
2
2
3
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
2
1
2
0
1
3
0
2
0
2
1
0
0
1
2
0
0
1
1
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
2
1
1
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
1
1
0
1
0
0
1
1
0
2
0
0
0
1
0
0
1
0
0
1
0
0
2
1
0
4
0
0
2
0
2
0
0
1
0
2
0
2
1
1
1
1
0
0
2
0
2
2
2
0
0
2
0
2
3
2
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
2
0
0
3
0
0
0
2
0
1
2
1
1
0
0
0
2
0
0
1
2
2
2
0
0
0
1
1
0
0
0
2
2
0
0
0
0
0
0
2
0
2
1
0
2
0
1
2
0
2
0
0
1
1
0
0
1
2
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
1
0
2
0
0
2
1
0
2
1
1
1
2
2
0
0
2
1
2
1
0
0
2
1
2
1
2
0
0
1
0
0
2
0
0
0
1
2
0
1
1
2
1
0
0
0
0
1
0
0
2
1
1
1
0
0
0
0
0
1
0
1
3
0
2
0
0
0
1
0
1
0
6
0
3
3
0
1
0
0
0
0
1
1
2
1
2
0
0
0
0
1
0
0
2
0
1
2
0
2
1
0
1
2
0
2
0
0
0
1
3
0
0
1
1
0
0
0
0
0
0
0
0
3
0
1
1
0
2
2
0
1
1
2
1
1
0
0
0
0
0
1
0
1
0
0
1
0
2
2
0
0
0
2
0
4
1
2
0
0
0
2
0
0
0
0
2
2
1
0
0
0
0
0
1
0
2
2
2
0
0
0
2
0
0
0
0
2
1
0
0
1
0
0
0
0
0
2
3
0
1
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
2
1
0
0
2
0
0
1
0
0
2
0
0
0
0
1
1
1
0
0
0
2
0
1
2
2
0
0
2
0
0
1
2
2
0
0
0
1
0
2
0
0
0
0
0
0
3
0
0
0
2
2
2
0
0
2
0
0
0
2
0
1
0
1
0
1
0
2
1
0
0
0
0
0
2
0
0
0
3
2
0
0
1
1
0
0
4
1
1
1
0
0
1
0
2
0
1
2
1
1
2
2
3
1
2
1
1
0
1
0
3
0
0
2
0
0
0
2
2
1
0
0
3
0
1
0
0
1
0
0
0
2
0
0
0
0
1
4
2
8
0
2
0
0
1
0
0
2
2
1
1
2
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
3
0
2
0
1
2
0
0
0
0
1
2
1
2
0
1
0
0
0
0
2
0
0
2
1
0
1
1
1
2
0
0
0
0
0
0
2
0
2
2
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
1
0
2
0
0
2
2
2
2
2
2
0
0
0
3
2
2
0
0
2
4
0
0
0
0
0
0
1
2
0
0
2
0
0
1
0
0
0
1
2
0
1
0
2
0
0
2
0
0
2
0
2
0
0
2
2
0
2
1
1
0
0
1
2
0
0
0
0
2
2
0
1
1
0
1
0
2
0
1
2
0
0
0
0
2
0
2
0
1
0
2
1
0
3
2
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
2
2
1
0
1
0
0
0
2
1
0
2
1
0
2
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
2
0
0
2
0
2
0
0
0
2
0
0
0
0
1
0
0
0
1
2
1
1
0
0
3
0
1
0
1
0
0
0
0
2
2
1
0
0
0
0
0
0
0
2
1
3
2
0
0
1
2
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
2
0
0
0
2
1
0
1
0
2
0
0
3
0
2
1
1
0
0
0
1
0
0
0
0
3
2
2
0
0
0
1
1
2
0
0
1
0
1
0
2
2
2
0
0
2
0
0
0
1
0
0
2
0
0
3
1
0
1
0
0
0
0
0
1
0
0
2
2
0
0
1
0
0
2
1
0
0
0
0
2
0
2
0
0
0
0
0
1
1
0
1
1
0
1
0
0
2
0
0
2
0
2
0
0
2
0
1
2
0
0
2
0
1
0
0
0
0
1
1
0
0
0
2
2
0
2
1
1
2
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
2
0
1
0
2
2
2
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
2
0
0
1
0
2
0
0
0
4
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
3
0
1
2
2
0
1
0
0
0
0
1
0
0
0
1
0
0
3
0
0
0
2
0
2
0
1
0
0
0
1
0
2
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
1
2
0
0
4
2
0
2
2
0
0
3
2
0
0
2
0
0
0
0
0
0
1
0
1
1
2
6
0
0
0
2
1
3
0
2
2
0
4
1
0
0
0
0
2
2
0
0
1
2
0
0
1
0
0
0
0
0
1
1
1
1
0
2
0
0
1
0
1
0
1
1
1
2
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
2
1
2
0
0
0
0
0
0
0
1
0
3
2
2
0
1
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
2
2
1
0
2
1
0
0
0
1
0
2
1
1
0
0
1
1
1
2
2
0
0
0
1
2
0
0
0
0
1
2
4
0
0
0
0
1
0
0
1
1
0
0
0
1
0
2
0
1
1
0
2
0
2
1
0
1
0
0
0
0
0
2
1
0
0
1
2
1
1
1
0
2
0
2
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
2
0
0
2
2
0
0
1
0
0
0
0
0
0
0
1
0
2
0
1
1
0
0
0
1
2
0
0
1
0
0
2
1
0
2
0
0
2
5
1
1
2
0
0
0
0
2
1
0
0
0
0
0
3
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
1
0
0
2
1
0
0
2
0
1
0
2
0
2
1
1
0
1
1
0
0
0
0
1
0
2
0
0
2
0
0
1
0
0
1
1
1
2
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
3
1
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
2
0
1
2
1
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
2
0
1
0
0
2
0
0
0
1
1
0
0
0
2
0
7
1
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
2
1
0
0
0
2
3
1
1
2
1
0
0
1
0
7
0
0
2
0
3
1
0
0
0
2
1
1
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
2
0
0
2
1
0
2
1
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
2
2
1
0
1
2
0
1
1
0
2
1
0
1
2
0
2
0
1
0
0
3
1
0
2
0
0
1
1
0
1
1
0
1
1
1
0
2
0
0
2
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
2
0
0
1
0
0
0
0
2
0
0
2
2
1
0
0
1
0
1
0
0
0
1
1
0
0
0
0
4
2
0
9
0
1
0
1
0
0
1
0
0
0
0
1
2
2
0
1
0
1
1
0
0
1
0
3
0
0
2
0
2
0
0
2
1
1
0
0
0
0
0
0
0
0
0
2
1
0
1
2
2
0
2
0
1
2
0
3
2
0
0
0
1
0
1
2
0
1
3
2
0
0
1
0
0
0
0
0
1
2
2
1
1
0
1
2
0
2
0
2
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
1
0
1
0
0
1
0
1
0
1
0
1
0
0
1
0
0
0
1
0
2
0
2
0
1
0
0
2
0
0
0
1
2
2
0
0
3
0
1
1
0
0
1
0
0
1
0
0
0
1
1
1
1
3
0
0
0
2
1
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
1
2
0
2
2
0
2
0
0
2
1
0
1
0
2
1
0
2
0
0
2
2
2
0
1
0
0
2
0
2
1
0
2
2
2
0
0
3
2
0
2
0
0
0
2
0
2
2
1
1
0
0
0
1
3
0
1
0
0
0
0
2
0
2
0
1
0
2
0
1
1
0
2
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
1
2
0
0
0
0
2
0
0
2
0
1
1
1
0
0
0
3
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
3
0
2
0
0
0
0
2
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
2
1
1
0
2
1
1
1
1
0
1
1
1
1
0
1
0
2
0
2
2
0
0
0
0
4
1
0
0
0
1
1
0
0
0
0
2
0
1
1
2
0
0
1
0
0
0
0
0
0
0
0
1
0
2
1
2
0
1
0
3
0
1
0
0
1
1
0
0
0
0
0
1
0
0
2
1
0
2
0
0
2
0
0
0
2
0
2
0
1
1
0
0
0
0
1
0
2
0
0
1
0
1
2
1
0
0
0
0
0
2
1
0
0
0
1
1
0
1
0
1
0
2
2
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
3
0
0
0
2
1
0
0
0
0
0
1
0
2
0
0
1
0
0
2
0
2
0
1
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
1
1
2
0
2
0
0
0
3
0
1
2
2
1
1
0
0
0
1
0
0
2
1
0
0
0
0
2
0
0
0
1
0
0
0
1
2
2
0
0
3
1
2
1
1
0
1
0
0
0
0
0
0
0
2
2
0
0
2
1
1
1
0
0
1
1
1
2
0
0
1
2
2
0
0
2
1
2
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
1
1
0
0
2
1
5
1
2
0
1
2
1
0
0
0
2
1
1
0
3
0
1
0
0
0
2
1
0
1
2
1
0
0
1
0
0
0
0
1
2
1
2
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
1
0
1
0
0
1
2
0
1
0
0
1
2
0
0
1
0
1
0
0
0
2
2
1
0
1
2
1
1
0
0
2
0
0
0
0
1
2
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
3
0
0
3
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
1
2
1
0
0
0
0
0
0
2
2
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
3
1
0
2
0
0
0
0
1
0
1
0
1
0
1
2
0
0
0
0
1
0
0
2
0
2
1
0
0
0
0
0
0
0
0
2
0
0
1
1
0
2
2
1
0
0
0
0
0
0
2
1
1
1
2
0
2
0
1
0
0
2
1
0
0
0
1
0
2
0
0
1
1
1
0
0
3
0
0
0
0
1
0
0
0
0
0
4
2
2
0
1
0
0
0
0
0
2
0
0
0
2
1
2
0
1
2
0
1
2
0
0
2
2
0
2
0
1
1
0
1
0
0
2
1
0
1
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
2
0
0
1
0
1
2
0
2
0
0
0
1
0
0
0
0
3
0
2
2
0
0
2
2
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
1
0
0
0
2
0
2
0
1
0
0
1
0
2
1
0
2
0
0
1
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
2
1
0
1
0
0
1
3
0
1
2
0
2
2
2
0
2
0
0
0
1
1
0
0
1
1
0
1
0
0
0
1
0
3
0
0
0
2
2
2
1
1
1
0
0
0
2
1
0
1
2
0
1
1
0
0
0
2
0
0
0
0
3
2
2
1
2
0
0
0
0
0
2
2
1
0
0
3
2
2
0
1
2
1
0
0
3
0
1
0
0
0
3
2
0
0
0
0
0
2
0
1
0
0
0
0
0
1
2
2
0
0
0
2
2
2
0
2
1
2
2
0
0
0
0
0
1
1
1
1
0
0
0
0
1
1
0
0
0
0
0
2
0
1
0
1
2
2
0
2
0
0
0
0
0
0
2
0
0
0
3
1
0
0
0
2
0
3
0
0
0
0
0
0
0
2
2
1
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
2
0
2
0
0
0
2
1
0
0
0
0
0
0
1
0
2
0
0
1
1
1
2
0
2
2
0
1
2
0
0
1
0
1
0
0
0
1
2
0
2
0
0
2
2
0
0
2
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
2
1
0
1
1
2
2
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
2
0
1
0
2
2
0
2
0
3
0
1
0
0
0
0
2
2
2
0
0
2
0
0
1
1
2
1
0
1
0
0
1
2
0
0
0
1
1
0
2
0
1
1
0
0
2
0
0
1
0
5
0
0
0
0
2
2
0
1
0
0
0
0
0
1
1
2
1
1
0
0
1
0
0
2
0
0
0
0
1
0
1
0
1
1
0
1
2
1
0
0
0
0
1
1
0
0
5
1
3
1
0
2
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
3
2
0
1
0
1
0
0
0
1
0
0
0
1
2
1
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
2
2
0
2
2
0
1
2
0
1
0
2
1
0
1
0
1
1
4
0
1
0
0
0
0
0
1
0
0
2
2
0
0
2
0
1
0
0
1
0
0
0
2
0
3
0
2
0
1
0
0
1
0
1
0
0
0
2
0
2
2
0
0
1
2
0
0
2
0
0
2
0
0
0
0
1
0
2
0
0
0
2
1
0
0
0
2
0
0
0
1
2
0
0
2
0
0
2
0
2
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
2
1
1
2
0
1
1
0
0
0
0
0
2
2
0
0
1
1
1
0
1
0
0
0
0
1
0
3
1
0
1
0
0
1
2
1
0
1
1
1
0
1
1
0
1
2
1
2
0
0
1
0
1
1
0
1
0
0
2
1
0
0
2
2
0
0
2
1
1
1
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
2
0
0
1
2
0
1
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
2
0
0
0
2
2
2
0
1
0
0
0
0
0
4
1
1
0
1
1
2
1
2
0
0
0
0
0
0
1
1
0
1
2
2
0
0
0
1
0
1
3
0
0
1
1
0
0
0
0
2
0
0
2
1
2
0
1
0
1
0
0
2
0
0
0
1
0
0
2
2
1
0
2
0
1
0
0
0
0
0
0
2
0
3
0
0
1
2
1
0
2
1
3
0
0
0
0
0
1
2
0
2
1
1
0
1
2
0
0
2
0
0
2
0
0
1
5
0
0
2
0
0
0
0
0
0
0
0
2
0
1
1
0
2
0
2
0
0
0
1
0
1
3
0
1
0
1
0
1
0
0
2
2
0
3
2
0
2
1
1
0
2
0
0
2
0
0
1
2
0
0
2
0
0
2
1
1
1
0
0
1
1
0
2
2
0
0
0
0
2
0
0
1
1
0
2
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
3
2
0
3
1
0
0
0
0
2
0
0
0
10
0
2
0
1
1
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
2
1
4
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
1
0
0
1
2
0
1
0
2
0
1
1
3
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
1
0
2
0
2
2
0
0
0
0
1
1
2
0
0
0
2
1
0
1
2
2
0
0
0
0
1
0
0
1
0
2
0
0
0
1
0
2
0
2
0
0
1
0
0
0
1
1
2
0
2
2
2
0
0
1
0
3
0
0
2
1
0
2
0
2
0
0
1
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
3
2
1
1
3
0
1
2
1
0
0
0
1
1
0
0
1
2
0
1
2
0
0
0
0
1
0
1
0
1
0
0
2
0
1
0
0
0
0
0
0
2
0
2
0
0
2
0
0
2
0
0
1
0
0
0
1
0
0
0
1
0
1
0
2
0
2
4
1
0
2
1
0
2
2
1
0
0
2
1
1
0
2
2
2
1
0
1
1
0
1
0
0
0
2
0
2
0
0
1
1
0
0
0
0
0
2
0
0
2
0
3
0
0
0
2
0
0
2
0
0
1
2
0
0
0
0
0
2
0
0
1
0
0
1
0
1
0
2
0
1
0
2
0
1
2
1
1
0
0
1
1
0
0
0
0
2
0
0
0
0
0
1
2
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
2
0
2
1
1
0
0
1
2
2
0
0
0
1
1
0
2
0
2
1
0
0
3
0
0
1
0
2
0
2
0
1
1
0
0
2
1
0
1
0
0
1
1
1
0
1
0
0
0
0
2
1
0
1
3
0
2
1
1
0
2
0
2
1
0
0
0
0
1
0
0
2
0
0
0
1
1
0
1
0
2
1
2
2
0
0
0
1
0
0
0
0
2
0
0
3
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
1
1
2
1
0
2
0
1
1
0
1
1
1
2
1
1
3
0
1
0
1
0
0
0
0
1
1
1
1
0
2
2
2
0
0
0
0
0
2
0
2
1
0
1
2
0
0
0
0
2
0
1
0
0
1
1
2
0
0
0
0
2
0
2
0
0
0
0
0
0
3
0
0
0
0
1
0
2
2
0
2
0
0
0
2
0
1
1
1
0
0
1
1
1
1
0
1
0
0
0
1
1
1
0
0
0
3
1
1
0
0
1
2
0
1
0
1
0
2
0
0
0
0
1
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
3
2
0
1
1
2
0
0
0
0
0
2
2
2
0
1
1
0
0
0
0
0
1
1
2
1
0
0
1
2
0
0
0
2
0
4
1
0
2
0
0
2
2
0
0
0
0
0
0
0
2
0
0
2
1
2
0
0
1
0
2
0
0
0
0
0
0
2
1
1
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
1
0
0
4
1
0
0
2
2
0
0
0
0
4
0
1
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
1
2
0
1
0
0
0
0
1
1
0
2
0
1
3
0
1
0
1
0
0
1
2
0
0
1
0
0
1
0
0
0
1
1
2
0
0
0
0
0
1
1
1
0
2
0
0
0
1
0
0
1
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
2
0
0
2
1
1
0
0
0
0
0
0
0
0
0
1
0
1
1
2
2
0
0
1
0
0
0
1
0
1
0
0
1
1
0
2
0
0
0
3
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
2
1
1
0
0
0
0
1
2
0
0
0
0
0
0
3
0
1
2
0
1
1
2
2
1
0
1
0
1
0
0
0
1
0
1
1
1
2
0
0
0
2
1
0
2
2
0
0
2
0
1
0
1
1
0
1
2
2
0
1
0
0
1
0
0
0
1
0
1
1
2
0
1
0
1
0
0
0
0
2
1
0
0
0
1
1
0
0
2
1
2
0
0
1
1
0
2
2
0
0
2
0
3
0
0
0
2
1
0
0
2
0
2
0
1
0
3
0
1
0
0
1
0
1
0
0
0
2
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
2
0
2
0
0
0
1
0
0
0
0
1
0
2
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
2
0
0
1
0
1
2
0
0
0
1
0
3
1
0
0
2
1
1
2
0
2
0
1
1
1
0
0
0
0
2
1
0
1
1
2
0
0
1
0
1
0
2
2
0
0
0
2
2
1
0
0
1
1
0
2
0
3
2
1
2
1
1
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
1
0
2
0
0
0
3
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
3
1
0
1
2
2
0
2
0
1
2
0
1
0
2
1
0
0
0
0
0
5
0
0
0
0
2
1
1
2
0
2
0
0
1
0
2
0
1
1
2
0
0
0
2
0
1
0
0
0
0
0
0
1
0
3
0
0
0
2
2
0
1
1
0
0
0
0
0
0
0
2
0
0
1
1
1
0
0
1
0
2
0
0
2
0
0
0
1
1
0
3
1
0
1
0
0
2
0
2
0
0
1
0
1
0
1
2
0
1
0
0
1
1
0
0
0
1
1
0
0
1
1
0
1
0
0
0
0
0
1
0
1
2
1
0
2
2
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
3
0
0
0
0
0
1
0
1
2
0
0
2
0
2
0
1
2
2
0
2
0
1
0
2
0
2
0
0
0
2
0
5
0
0
0
0
2
2
0
0
1
0
0
0
1
2
0
2
2
3
0
0
0
0
0
2
1
1
0
0
0
0
1
0
1
0
1
0
2
5
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
2
2
1
0
0
3
0
0
0
0
1
1
2
1
1
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
2
2
2
0
0
0
0
0
0
0
1
2
2
1
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
2
1
0
2
1
0
2
2
1
0
0
1
2
0
2
2
0
0
2
0
0
1
1
3
1
0
2
0
0
0
0
0
0
0
0
2
2
0
0
1
0
2
2
0
2
0
2
0
0
3
1
0
0
0
0
0
1
2
1
1
0
0
1
2
1
1
2
0
0
1
0
0
0
0
2
1
1
0
0
3
0
2
0
2
0
1
1
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
2
1
0
0
1
1
0
0
0
0
1
1
2
0
1
0
1
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
1
0
1
0
0
0
1
2
2
2
0
0
0
2
0
0
1
2
0
0
2
0
2
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
1
0
2
0
0
2
0
3
0
0
0
2
1
0
0
0
0
1
1
0
0
2
0
1
2
0
0
1
0
0
0
0
1
0
2
0
2
1
1
2
0
0
1
0
2
2
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
1
0
0
0
2
2
0
1
0
1
1
1
0
0
0
0
2
1
1
0
0
0
2
2
0
0
0
0
1
1
0
1
1
0
0
2
0
1
2
0
2
0
1
0
1
1
0
0
0
0
0
1
2
1
2
0
2
1
0
2
0
0
0
0
2
0
0
0
1
0
2
0
0
0
2
0
1
0
1
0
1
1
1
1
0
2
0
0
0
1
0
2
0
1
1
2
0
1
1
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
2
2
0
0
0
1
1
0
0
0
0
1
1
0
0
0
2
1
2
0
0
0
0
2
0
2
0
0
2
0
1
0
0
0
2
1
0
0
0
1
0
1
0
1
0
1
2
0
0
0
0
0
0
2
1
0
0
0
2
0
1
0
0
0
0
0
2
0
1
3
0
2
4
0
2
0
0
2
0
1
1
0
0
1
0
2
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
1
0
1
0
0
2
0
1
0
0
1
2
0
2
0
0
0
1
0
1
0
0
0
2
1
0
2
2
0
1
2
0
0
0
1
1
1
0
2
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
9
0
1
0
0
1
1
0
1
2
0
0
1
0
3
0
1
0
0
1
0
0
1
2
0
0
1
0
3
0
1
1
0
1
0
1
0
1
1
1
0
0
2
0
0
0
0
2
2
0
4
2
2
0
0
0
1
0
0
0
1
0
0
2
1
2
0
0
2
1
1
1
0
0
1
1
0
2
2
2
0
0
0
0
2
0
1
2
0
2
0
2
1
0
0
1
2
0
0
0
3
0
0
1
0
1
2
1
0
0
1
0
2
0
0
2
0
0
2
1
0
1
0
1
1
1
2
1
1
2
1
1
0
0
2
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
1
1
2
1
1
0
1
2
0
2
0
1
0
0
2
1
0
1
2
1
2
2
0
0
2
1
0
0
0
0
0
0
2
1
1
0
0
0
1
1
1
2
1
1
0
3
1
0
1
0
0
0
0
0
0
0
2
0
0
1
2
1
0
2
0
0
3
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
2
2
1
0
0
1
0
0
0
0
2
3
0
1
2
0
0
2
0
1
2
2
2
0
2
2
2
0
0
0
2
0
0
1
1
2
3
0
0
1
2
0
0
0
2
0
0
2
0
0
0
0
3
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
1
0
0
0
0
0
2
2
0
0
1
2
2
1
0
1
0
0
0
1
2
0
0
0
0
3
2
0
0
0
0
0
1
1
1
1
1
1
0
0
2
1
1
0
2
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
1
0
0
0
0
1
1
1
0
2
1
0
0
2
0
0
1
0
2
0
1
0
0
0
0
1
0
0
0
0
2
1
0
0
2
0
1
0
2
2
0
2
2
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
1
2
1
3
1
0
0
1
0
0
1
1
0
0
1
2
1
0
2
2
0
0
1
3
2
0
2
1
0
0
1
2
1
0
1
0
1
0
2
0
1
0
0
2
0
1
1
2
0
2
2
0
1
1
0
0
2
1
2
0
2
1
0
0
0
1
2
2
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
1
1
1
1
3
0
0
0
2
0
0
2
0
1
0
0
0
0
2
0
1
2
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
2
3
1
2
1
0
1
2
0
0
0
0
0
2
1
1
0
1
0
1
1
1
0
1
1
0
0
0
2
0
0
1
0
0
0
0
0
0
2
3
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
1
0
2
0
2
0
0
0
0
1
0
0
2
2
0
1
0
3
0
0
0
0
1
0
0
1
1
6
0
2
1
4
0
0
2
3
0
1
0
1
1
1
0
0
0
2
0
0
0
0
1
0
2
0
0
1
0
1
0
1
1
0
0
1
0
0
0
0
0
0
2
1
0
1
0
0
2
0
0
1
0
0
1
1
0
0
0
2
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
2
0
2
1
0
0
0
0
0
0
0
0
1
1
1
1
0
1
2
1
0
0
0
0
1
0
1
1
0
1
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
1
1
1
1
1
0
2
1
0
2
0
1
0
0
0
0
0
0
0
0
2
3
0
0
0
0
1
2
3
0
0
1
0
0
1
1
0
0
1
0
2
0
0
2
0
0
0
1
0
0
1
1
1
1
1
0
1
0
2
1
1
0
3
5
2
2
0
0
0
2
0
0
0
3
0
2
1
1
0
2
0
0
0
0
1
0
0
0
0
3
0
2
0
0
0
1
0
0
0
1
0
0
0
1
0
2
1
1
0
0
0
3
0
0
2
1
0
0
0
0
0
1
1
0
0
1
0
0
1
2
0
2
0
0
2
1
2
1
1
0
0
1
2
3
0
0
2
0
2
1
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
1
2
0
1
2
1
0
0
1
8
2
0
0
2
0
0
0
2
2
0
1
1
0
0
2
0
1
0
0
1
1
0
2
1
2
1
0
1
0
3
1
1
0
0
2
1
0
0
0
2
0
0
0
2
2
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
1
2
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
2
1
1
0
0
0
3
0
5
1
0
0
0
1
2
2
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
2
2
1
0
2
0
2
1
0
1
2
0
0
0
1
2
0
2
0
0
1
3
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
2
0
0
1
0
0
0
0
2
1
2
2
1
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
1
2
0
0
0
1
0
0
1
0
2
0
0
0
1
0
0
0
1
0
0
0
3
2
1
0
2
0
0
0
0
0
0
2
1
0
0
0
0
1
1
0
2
0
0
1
0
1
4
2
0
0
0
0
10
0
0
1
1
0
1
0
0
2
0
0
0
0
2
2
1
0
2
1
0
0
2
0
1
1
0
1
1
0
0
0
1
0
2
1
1
0
0
0
1
1
1
0
0
0
0
1
0
0
2
2
0
0
1
0
0
1
2
0
0
2
0
0
3
0
1
1
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
2
1
0
0
2
0
0
1
0
0
0
2
0
1
0
1
0
1
2
0
0
1
1
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
4
1
0
1
0
0
1
1
0
0
3
2
1
0
2
3
0
0
1
1
2
0
0
2
2
0
1
0
0
0
0
0
1
1
1
0
0
1
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
1
2
2
0
0
2
0
2
1
0
0
2
1
0
0
2
1
2
0
2
0
0
0
0
0
2
1
2
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
1
1
2
1
0
1
2
0
0
0
0
2
1
2
2
2
2
0
1
1
0
0
0
2
2
0
1
0
1
1
0
0
3
0
2
1
0
0
0
1
1
1
0
2
0
2
0
2
0
0
0
1
0
1
0
1
2
0
1
0
0
0
1
2
0
0
2
2
2
0
2
0
1
0
1
0
0
1
2
0
2
0
1
1
2
0
0
0
0
2
1
0
0
0
0
2
2
0
0
0
1
2
1
0
0
0
1
0
0
0
0
2
0
1
0
0
2
1
0
0
0
1
0
0
1
1
1
0
0
1
0
0
1
0
0
0
2
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
1
1
2
0
2
0
0
0
0
2
2
0
1
1
2
0
0
1
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
1
0
0
1
1
1
1
2
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
1
1
0
1
2
2
8
1
0
0
0
1
2
0
3
0
0
0
0
0
1
1
0
0
1
0
1
2
0
0
0
0
0
0
2
2
1
2
0
0
0
0
5
3
0
0
1
0
0
0
0
4
2
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
3
2
0
2
1
0
0
1
0
1
1
0
0
1
1
2
0
0
0
0
0
2
0
0
2
2
0
2
0
0
0
0
0
1
0
3
1
0
0
0
1
3
1
0
2
0
2
0
0
2
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
1
2
0
1
0
2
0
1
1
2
0
0
2
0
0
1
3
1
0
0
0
0
2
2
1
2
0
1
0
2
3
2
0
1
0
0
0
0
0
0
0
1
2
2
0
0
0
0
1
0
1
2
1
0
2
0
2
0
0
0
1
1
0
0
0
1
0
2
1
1
0
0
0
0
0
0
0
2
1
2
1
0
0
2
2
0
0
1
2
0
1
1
0
2
1
1
2
0
0
2
1
1
0
0
0
0
0
0
0
0
0
7
1
2
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
2
0
0
0
0
1
0
0
2
0
1
1
1
0
0
0
0
0
1
0
0
1
0
3
2
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
1
2
0
2
2
0
2
0
0
2
3
0
1
2
0
1
0
0
0
0
0
2
1
0
0
0
0
2
0
0
1
2
0
0
0
1
1
1
0
2
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
1
0
1
1
0
0
2
0
1
0
1
0
0
0
1
0
0
0
1
1
0
0
2
0
0
1
0
2
1
0
0
0
2
0
0
1
2
0
0
0
1
1
0
0
0
0
1
1
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
2
2
0
2
1
0
1
0
0
2
0
0
0
1
0
0
0
0
3
2
1
1
3
0
0
0
0
2
1
2
0
2
2
1
2
1
0
2
0
0
0
1
3
0
0
2
0
1
0
2
1
1
0
0
0
0
0
0
1
1
0
2
1
0
0
0
2
0
2
0
1
0
2
1
0
0
1
0
1
0
2
1
0
0
0
0
2
2
2
2
0
0
2
2
0
1
0
0
2
0
1
0
2
0
0
0
0
2
1
2
0
1
0
0
0
0
1
1
0
2
1
0
0
0
0
0
2
1
0
2
1
1
0
2
1
0
0
1
0
0
0
2
1
1
0
0
0
0
1
2
2
0
3
0
1
0
1
0
6
0
0
0
0
0
0
0
2
0
1
0
0
0
2
2
0
0
0
1
0
0
0
0
0
3
2
0
2
4
1
1
0
0
0
1
2
0
2
0
0
1
0
0
0
0
2
1
0
1
0
1
1
1
0
0
0
1
2
1
1
0
0
0
0
2
2
0
1
0
0
2
0
1
0
2
2
2
0
1
0
2
0
0
1
0
0
1
0
0
1
0
0
2
0
3
1
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
2
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
2
3
3
1
0
0
1
0
1
1
1
0
1
2
0
0
0
0
0
1
0
0
0
0
2
1
1
0
0
0
1
3
2
0
1
0
1
0
1
0
0
3
0
0
0
2
2
2
0
0
0
0
0
0
0
2
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
1
0
0
1
1
1
0
0
0
2
0
0
1
0
0
2
2
0
0
0
2
0
0
0
0
1
1
0
0
0
2
0
0
0
1
1
2
2
1
0
0
1
1
1
2
0
0
0
0
0
2
0
0
2
0
0
0
1
0
2
1
0
2
2
1
0
0
1
0
0
2
2
1
1
2
0
2
0
2
1
0
0
3
0
0
1
0
1
2
1
0
0
0
0
0
1
1
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
12
0
3
2
2
1
0
0
8
0
1
1
0
0
0
2
1
0
1
2
2
0
2
0
2
0
2
0
0
4
0
0
0
2
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
1
2
1
2
0
1
2
0
1
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
1
0
2
0
0
2
0
0
2
0
1
0
0
0
0
3
0
0
1
0
2
2
2
0
1
0
0
1
0
0
0
2
0
0
0
0
0
2
1
0
1
0
0
1
0
2
1
4
3
1
2
0
1
0
1
1
0
0
0
0
2
0
1
0
0
1
0
0
2
0
0
1
0
0
2
0
0
0
2
0
0
0
0
1
0
0
1
0
2
2
2
0
2
0
0
0
1
1
2
2
1
0
1
1
2
0
2
2
0
1
1
0
1
1
1
0
1
2
2
2
0
3
2
1
0
0
0
1
0
0
0
1
2
2
0
0
2
2
0
1
0
0
0
0
0
1
2
0
4
0
1
1
0
1
0
2
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
2
0
1
1
0
2
2
1
0
0
2
0
1
0
2
1
0
0
2
0
0
2
2
0
1
0
1
0
2
0
0
0
0
0
1
2
0
1
0
1
0
0
2
0
0
1
0
0
0
1
0
1
0
1
0
1
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
2
2
1
0
2
2
1
0
0
0
0
0
0
0
0
1
2
1
0
0
2
0
0
0
0
1
1
0
0
1
1
0
0
0
1
0
0
0
0
2
0
0
2
1
0
0
1
0
0
1
1
1
0
1
2
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
1
0
0
0
0
2
1
0
0
1
0
1
3
1
2
2
0
0
0
2
1
1
0
0
0
1
2
2
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
1
2
2
0
0
0
0
2
2
1
0
0
0
0
2
0
0
2
3
2
1
1
2
2
1
0
2
0
0
0
1
1
2
0
1
2
0
2
0
0
0
0
0
0
0
1
1
0
2
0
0
1
0
1
2
2
2
0
2
0
0
1
0
2
0
0
0
3
1
0
0
0
1
0
2
0
0
3
0
2
0
0
0
2
0
1
0
2
0
1
2
2
0
0
0
0
0
0
1
2
0
1
0
2
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
2
0
1
2
0
0
0
0
2
0
1
0
0
0
0
0
1
1
3
1
1
0
2
0
0
2
0
1
2
0
0
0
5
1
1
0
0
2
0
0
0
0
0
2
0
2
0
2
0
1
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
1
2
0
0
0
2
0
2
1
0
0
0
2
0
0
1
0
0
2
0
0
1
0
0
0
0
0
1
1
0
1
2
0
1
1
1
2
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
1
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
3
1
3
1
6
2
1
1
0
0
2
2
0
2
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
1
0
2
1
0
0
1
1
0
1
0
0
0
0
0
1
2
1
1
0
0
2
1
2
0
0
0
2
0
0
2
2
0
0
0
2
1
0
2
0
0
2
0
1
1
0
2
0
2
1
0
1
1
0
2
0
0
0
0
0
1
2
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
1
2
0
0
0
1
0
0
2
0
2
0
0
1
1
1
2
1
0
1
0
2
1
2
0
2
0
0
0
1
0
3
1
1
1
1
0
1
2
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
1
2
1
0
0
1
1
0
1
1
1
0
2
0
0
0
0
1
2
0
4
1
1
2
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
1
2
1
1
2
1
2
2
1
1
1
2
0
0
0
0
2
0
2
1
2
1
2
1
1
2
0
1
1
2
2
0
0
3
0
3
0
0
0
0
0
1
2
0
0
1
0
1
0
0
0
0
0
2
2
2
0
0
2
0
0
2
2
0
2
2
1
0
2
0
0
2
0
0
1
2
1
2
0
0
1
1
0
0
1
0
2
0
1
1
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
2
0
0
0
1
0
1
0
1
1
0
2
0
0
0
1
1
1
0
1
1
0
0
1
0
1
1
2
1
0
0
0
1
0
0
1
2
0
1
0
2
0
2
2
0
2
0
0
0
0
0
2
1
0
1
0
0
1
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
3
2
0
2
0
0
0
0
1
0
0
1
1
1
1
0
2
0
0
0
0
1
1
2
0
0
2
0
0
2
0
2
0
1
1
0
1
0
1
0
0
1
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
1
1
0
2
2
0
0
1
2
0
2
2
0
1
0
1
2
0
0
0
0
0
2
2
1
0
0
0
0
2
0
2
0
0
0
0
2
0
1
0
2
0
0
1
0
1
0
0
2
0
0
1
2
0
0
0
0
1
0
0
0
0
2
0
1
0
2
2
0
1
2
0
1
0
1
3
0
1
0
0
0
1
2
0
0
0
0
1
1
0
0
0
1
0
1
1
0
2
0
2
1
1
2
2
0
0
1
2
0
1
1
0
0
0
0
1
0
1
0
0
0
0
2
1
0
2
2
0
1
2
1
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
2
0
2
0
1
0
2
1
0
0
0
0
2
2
0
2
1
1
0
0
1
0
0
1
2
0
0
0
0
2
0
0
1
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
1
1
0
2
0
2
0
0
0
0
1
0
0
0
2
1
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
2
1
0
3
1
0
0
1
1
1
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
1
2
1
2
0
0
0
2
1
1
0
0
0
0
1
2
2
0
0
2
2
0
0
1
0
1
1
0
0
0
2
0
1
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
1
2
1
0
0
0
0
1
0
0
0
1
2
6
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
2
1
1
0
0
0
1
2
3
0
1
0
0
0
2
0
2
0
0
2
0
0
1
1
1
1
0
2
1
0
0
0
1
0
4
0
0
1
0
0
0
0
0
1
2
0
0
1
1
2
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
2
0
0
2
1
0
2
1
1
0
0
2
1
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
1
0
2
2
2
2
0
0
2
0
0
0
1
0
2
0
0
2
1
2
3
0
0
0
1
0
0
1
0
0
1
0
0
3
1
0
0
0
2
1
2
0
0
0
2
0
1
0
0
2
0
1
0
0
2
0
0
1
2
0
2
1
2
1
1
3
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
2
0
2
1
4
0
0
1
0
1
0
1
0
3
0
0
1
0
0
1
1
0
0
0
1
0
0
2
2
2
1
0
1
1
1
1
2
2
0
0
2
0
2
0
0
0
1
2
1
2
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
2
1
0
1
0
1
2
2
1
0
2
2
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
2
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
1
1
1
0
0
2
0
0
2
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
1
1
1
1
0
1
1
0
2
0
0
1
0
2
2
2
0
0
0
0
0
0
0
0
0
1
1
0
1
1
2
2
1
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
1
1
0
0
1
2
1
0
1
1
1
2
1
2
2
0
0
2
3
2
1
0
2
2
0
1
0
0
0
1
0
6
1
0
0
0
0
0
0
1
1
1
2
0
1
2
1
0
2
1
2
1
0
0
0
0
0
0
1
0
2
0
0
1
1
1
2
0
2
1
2
0
0
0
3
0
3
0
2
0
0
0
0
0
1
0
2
0
1
0
0
1
0
0
2
0
2
1
0
4
1
4
2
0
0
0
1
0
0
0
1
2
2
1
0
1
2
0
1
1
0
0
0
0
1
0
0
2
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
2
1
0
0
1
0
1
0
0
0
2
0
1
2
0
2
0
2
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
2
1
0
0
1
0
1
0
2
0
0
0
1
2
0
0
0
1
0
2
1
0
0
1
0
1
2
1
2
0
0
1
0
0
0
1
0
0
0
1
1
1
4
0
2
2
2
0
0
2
0
0
2
2
0
0
0
2
1
4
1
0
0
2
0
0
1
0
0
0
1
2
0
1
1
0
0
0
0
0
0
0
6
0
0
2
0
0
3
1
1
3
0
2
1
0
0
2
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
1
2
3
0
0
1
0
0
0
0
2
0
1
4
0
0
2
0
0
0
3
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
1
2
1
0
2
2
2
0
1
0
0
0
1
0
1
0
1
0
0
0
2
2
1
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
2
0
1
0
0
1
0
0
0
1
0
2
1
2
1
0
1
0
0
2
0
1
0
0
1
1
0
0
2
1
0
0
0
0
0
2
0
0
0
0
1
2
0
1
1
0
0
0
0
1
0
4
0
0
1
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
1
0
0
0
0
0
0
0
1
1
0
2
0
2
0
2
0
2
0
0
0
2
0
2
0
0
2
0
0
1
0
0
1
0
0
1
1
0
4
0
2
1
0
1
0
0
0
2
0
0
1
0
0
0
2
1
0
0
3
0
0
1
2
0
5
2
0
1
0
1
0
0
0
1
0
1
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
2
0
0
0
2
1
0
1
0
0
2
0
0
2
0
0
1
0
0
0
0
1
0
0
1
2
1
0
1
2
0
1
2
1
0
0
1
1
2
2
0
1
1
0
2
0
2
0
0
2
2
0
0
0
0
1
0
2
0
0
2
2
1
0
2
1
1
1
0
2
0
0
0
1
0
2
2
1
0
0
1
0
2
1
0
0
0
0
0
0
1
0
1
2
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
1
1
2
0
0
2
2
2
0
1
1
2
1
0
0
2
2
1
2
2
0
0
1
1
1
2
0
0
1
1
0
0
1
2
2
0
0
1
0
2
2
1
0
0
1
1
0
0
2
1
0
0
0
1
0
2
0
0
0
2
0
1
1
0
0
2
4
0
2
0
2
0
2
1
2
0
0
0
1
2
2
0
0
1
0
1
2
1
2
0
0
0
0
1
0
2
1
1
0
1
1
1
0
0
0
2
0
0
0
2
0
0
0
0
0
1
2
0
2
2
2
0
0
0
2
0
0
0
1
0
0
0
1
0
0
1
1
0
1
0
0
0
0
1
1
2
1
0
2
1
0
0
0
0
0
1
1
1
0
2
0
0
2
2
0
0
0
0
0
1
0
0
0
0
1
1
3
2
0
0
2
0
0
0
0
0
2
1
1
0
1
2
0
2
0
0
0
1
0
1
2
2
0
0
1
1
0
1
0
0
0
3
1
1
1
0
1
0
0
2
0
0
0
0
2
2
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
1
0
1
0
1
2
1
2
2
2
0
0
0
1
0
0
1
0
1
2
1
0
0
2
0
2
0
0
0
1
2
1
0
2
0
1
0
1
0
0
0
0
1
0
2
0
1
0
3
1
0
1
2
2
2
0
0
0
1
0
0
1
0
2
0
2
0
0
1
0
1
0
0
2
1
0
0
0
0
0
0
2
2
0
2
0
2
1
0
0
0
2
0
3
1
0
0
1
0
0
0
0
0
0
2
2
1
1
1
2
2
2
0
0
0
0
1
0
1
0
0
2
0
0
0
1
1
0
2
0
0
2
0
0
0
2
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
3
1
2
1
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
2
0
1
0
0
0
1
1
0
0
4
2
0
0
1
0
0
0
2
0
2
2
0
1
0
0
0
0
0
0
8
0
1
0
0
0
0
2
0
2
0
1
1
0
0
2
0
0
3
2
0
0
1
2
0
0
2
0
0
1
0
1
0
0
1
0
2
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
1
0
1
1
0
0
0
0
1
1
0
0
2
0
1
0
0
0
1
1
1
0
2
2
1
0
0
2
2
0
2
0
1
1
0
1
0
1
0
1
0
0
1
1
1
1
1
0
0
0
0
1
2
0
0
1
0
0
0
0
1
2
0
2
2
0
2
0
0
1
0
1
0
1
2
2
0
1
0
0
1
2
0
1
1
0
0
0
0
0
1
2
0
0
1
0
2
0
0
2
0
0
0
0
1
2
0
1
0
0
0
2
0
0
1
1
1
4
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
3
0
0
0
0
1
2
0
1
1
1
0
1
2
0
0
0
0
0
3
0
0
0
0
0
1
0
2
2
2
0
2
0
2
0
0
1
0
0
0
1
2
0
1
1
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
3
0
1
2
0
2
0
0
2
0
0
0
2
0
2
2
3
0
1
1
0
1
0
0
0
2
2
0
1
0
2
0
0
1
1
2
0
0
3
0
0
0
1
0
0
0
0
0
3
0
0
1
1
0
0
0
1
0
1
2
0
2
0
0
2
1
0
1
0
2
2
0
0
0
0
0
1
0
0
1
1
2
0
0
2
0
0
2
1
1
0
0
2
1
1
1
0
0
1
0
0
0
0
1
2
1
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
2
2
0
0
0
1
0
0
1
0
2
0
0
2
0
0
0
0
2
0
2
0
0
0
2
2
0
0
2
0
0
1
1
0
1
0
3
2
2
2
0
1
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
2
3
0
2
0
2
1
1
0
1
0
0
0
1
0
0
1
1
2
2
3
2
1
0
0
0
2
0
1
2
3
2
1
0
1
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
1
2
0
2
0
1
2
1
1
1
1
0
0
0
0
0
8
0
2
0
1
3
2
1
1
1
0
0
0
0
1
2
2
0
1
0
0
0
0
0
3
0
2
5
2
2
0
2
0
1
0
0
0
0
7
0
2
1
1
0
0
0
1
0
2
1
2
0
2
0
2
1
0
0
1
0
1
2
1
0
0
2
2
1
2
0
1
0
2
0
0
1
1
0
2
2
2
0
0
0
0
0
2
3
2
0
0
1
2
0
0
0
0
0
0
2
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
2
2
0
0
0
2
0
0
0
1
2
0
2
2
0
0
0
0
2
1
2
1
2
0
1
1
1
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
1
1
2
2
0
0
0
0
0
2
0
2
0
1
1
0
0
2
0
1
0
0
1
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
1
0
2
2
0
2
0
0
0
0
0
1
2
0
0
1
0
1
0
0
2
2
1
2
1
0
0
0
0
0
2
0
2
0
3
2
0
0
0
0
0
0
1
1
0
0
2
0
1
1
2
1
1
2
2
0
1
1
0
0
0
0
0
2
0
0
1
1
0
0
0
1
0
1
2
0
0
1
0
1
0
0
0
1
2
0
0
3
1
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
4
1
0
0
2
0
0
4
2
0
0
1
1
0
0
1
0
0
0
1
1
2
1
0
2
2
0
0
1
0
0
0
2
0
0
0
1
0
1
1
0
1
0
0
2
0
0
0
0
0
0
1
0
1
0
2
1
0
1
0
0
2
0
1
0
2
0
0
0
1
0
1
1
0
1
0
1
0
1
0
0
2
1
0
1
0
0
2
0
2
2
0
1
2
0
2
2
2
0
1
0
0
1
1
1
0
2
1
2
2
0
1
0
0
1
2
0
1
0
2
0
0
2
0
1
0
0
0
1
2
1
2
0
0
1
1
1
1
2
0
2
1
3
1
0
2
0
0
1
1
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
2
2
0
0
1
0
2
0
1
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
2
0
0
2
0
1
0
0
0
2
0
1
1
2
0
0
3
0
2
0
0
1
0
0
2
1
0
0
0
0
2
2
0
2
0
1
0
0
0
1
0
1
0
2
0
0
2
2
0
0
0
1
2
0
0
2
2
4
0
0
2
1
1
0
2
0
1
0
0
1
1
0
1
2
0
0
0
0
0
1
2
0
0
2
0
0
0
1
0
2
0
0
2
1
2
0
0
0
0
1
0
0
2
0
2
2
0
1
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
2
0
2
0
2
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
2
1
1
0
1
1
0
0
0
1
1
0
2
1
0
0
0
0
2
0
0
2
0
0
0
1
0
0
1
2
1
0
1
0
3
2
0
1
2
2
0
0
0
0
2
0
0
1
1
1
0
1
2
1
1
0
1
0
0
1
1
0
0
0
1
0
0
2
1
0
0
1
0
1
2
1
0
0
2
1
1
0
0
0
0
1
0
1
0
2
0
0
0
2
0
1
0
0
0
0
3
0
1
0
0
0
2
0
2
3
0
0
2
2
2
0
0
0
0
1
2
0
2
0
0
0
0
0
3
2
2
0
0
0
0
2
2
1
0
0
0
1
1
0
1
1
1
0
2
0
0
1
0
0
2
0
0
0
2
1
2
0
0
0
1
0
0
0
0
0
1
3
1
0
2
0
1
0
0
2
0
1
0
2
2
0
1
0
1
2
0
1
1
0
2
2
0
0
0
2
2
2
2
1
0
0
0
0
0
0
1
1
1
1
1
1
0
2
0
0
0
1
1
0
2
0
1
0
2
0
0
2
0
0
1
0
1
1
0
0
0
1
0
2
0
2
2
1
0
0
0
2
2
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
1
0
2
1
0
0
0
0
0
0
0
0
1
0
3
2
0
1
0
0
2
1
1
0
0
0
2
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
3
0
1
2
0
0
1
1
2
0
2
0
0
1
2
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
2
0
0
0
1
0
1
0
0
1
0
0
2
1
0
0
2
0
0
1
0
1
2
0
1
1
0
2
0
0
1
3
1
0
0
0
2
1
0
1
1
1
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
2
1
0
0
0
0
1
0
0
1
0
2
0
0
1
1
1
0
0
1
0
1
1
0
2
0
3
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
2
1
0
2
1
0
1
0
0
0
0
1
1
0
0
0
0
3
0
0
0
2
0
2
1
0
2
1
0
2
0
0
0
0
0
0
1
1
0
0
0
1
0
2
0
2
2
1
2
1
2
0
0
1
0
1
2
0
0
0
2
0
0
0
2
2
0
1
0
2
1
3
0
2
0
2
0
1
0
0
0
0
2
0
0
0
0
1
0
3
0
1
1
0
0
0
0
0
1
0
2
2
0
0
1
0
0
2
0
0
0
0
0
0
1
1
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
2
1
0
2
1
1
1
0
1
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
2
2
1
0
0
0
0
0
1
0
0
2
0
0
2
0
1
2
0
1
2
2
1
1
1
0
0
0
2
0
0
0
3
0
1
0
0
2
2
2
0
2
0
1
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
1
2
1
0
0
0
0
0
1
1
0
1
0
0
2
2
1
0
4
0
2
0
0
0
0
1
0
2
0
1
0
1
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
5
0
1
0
1
0
1
0
0
0
1
1
0
0
0
2
0
1
1
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
2
2
0
0
1
0
1
0
0
1
0
1
2
0
0
0
1
0
0
1
0
0
0
0
0
1
2
0
0
0
2
1
0
0
2
0
1
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
1
1
0
2
1
0
0
1
0
0
0
0
2
0
0
1
2
1
0
2
1
1
3
2
0
1
1
0
0
0
0
2
0
2
0
0
0
0
2
2
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
1
2
1
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
2
2
2
1
0
0
0
0
2
0
0
0
0
2
0
0
0
2
2
0
1
2
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
2
1
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
2
0
0
0
1
0
0
1
0
0
0
0
5
2
1
0
1
0
0
2
0
0
0
0
2
2
0
0
1
0
2
0
0
0
0
1
0
2
1
0
0
2
2
0
0
0
2
2
1
3
0
0
2
0
0
1
1
0
2
0
0
1
1
1
0
2
2
0
0
2
0
2
0
0
0
2
0
1
0
0
0
1
1
1
0
1
0
1
0
0
0
1
2
2
1
2
0
1
2
2
0
0
0
0
3
0
1
2
2
1
1
1
0
0
3
0
2
2
0
2
1
1
2
0
0
2
0
2
2
1
0
0
1
3
0
0
2
2
1
0
0
1
0
1
1
2
0
1
2
1
1
0
0
1
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
3
0
0
1
0
0
1
2
1
2
0
3
0
0
1
0
2
1
0
2
1
1
0
1
0
1
1
1
2
0
0
0
0
1
2
1
0
0
0
0
0
0
0
1
0
1
2
0
0
1
3
0
2
0
0
1
2
0
1
2
0
1
0
1
2
0
0
0
1
0
0
1
0
0
0
1
0
1
1
0
2
0
0
1
0
0
0
0
0
1
2
0
0
2
0
0
0
0
1
0
1
0
3
2
1
1
0
0
1
0
0
1
2
0
0
0
0
2
1
0
0
1
2
0
0
0
0
0
0
2
2
1
0
0
1
2
0
1
0
1
2
2
0
1
0
0
0
1
1
0
1
0
0
0
0
0
1
0
2
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
1
2
2
0
0
2
0
2
0
0
2
0
1
1
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
1
1
3
0
1
1
0
2
0
1
3
0
0
1
1
2
0
1
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
2
0
1
0
0
0
1
2
0
1
1
0
0
1
0
2
0
0
0
0
0
4
0
1
2
2
1
0
1
0
0
1
2
0
2
2
0
2
0
1
1
0
0
2
0
2
1
1
0
0
0
1
2
0
1
0
0
0
1
0
4
0
0
1
0
0
0
0
2
2
1
0
0
1
2
0
2
1
0
3
0
1
2
2
0
1
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
2
0
0
1
0
0
2
0
0
2
0
2
0
1
2
0
0
1
1
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
2
0
0
0
1
0
0
1
0
0
0
2
0
1
2
0
1
2
0
2
3
2
0
1
2
0
0
1
2
0
0
0
0
0
1
0
3
0
2
0
2
0
0
0
0
5
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
2
1
0
2
0
0
0
1
1
0
0
0
1
0
0
0
2
2
0
0
0
0
2
0
1
0
0
0
2
2
2
1
2
0
1
0
2
0
0
0
0
0
0
0
1
0
1
2
2
0
1
0
1
0
0
1
0
1
1
2
0
2
2
2
0
0
2
1
0
1
1
2
2
2
2
0
0
3
0
1
0
1
0
0
0
2
2
2
2
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
2
1
0
1
0
0
0
0
2
0
0
0
1
2
3
2
0
0
0
1
4
0
0
0
2
0
0
0
0
2
1
0
0
0
1
0
1
0
0
1
0
0
0
0
2
0
1
2
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
1
1
1
0
0
2
2
1
0
1
0
0
0
1
1
2
0
0
1
2
0
0
2
1
0
1
0
1
0
0
0
0
0
1
0
0
2
15
1
0
0
0
0
0
2
0
2
0
1
0
0
0
3
0
2
0
0
0
0
0
0
0
0
1
1
0
1
0
0
2
0
0
4
0
0
0
0
1
0
2
0
2
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
3
1
0
0
0
2
0
1
0
0
0
0
0
0
1
1
0
1
1
0
2
0
1
0
0
0
1
0
0
0
0
0
1
0
4
1
0
1
0
0
0
1
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
1
0
0
2
2
2
0
0
1
1
2
0
0
0
0
2
1
1
2
2
1
1
0
1
2
1
0
1
1
0
0
0
0
0
0
0
2
2
1
2
0
2
1
1
0
0
1
0
2
3
0
0
0
1
2
2
0
0
0
1
0
2
2
0
0
2
0
2
0
0
0
0
0
0
2
2
0
2
0
2
1
0
2
1
0
2
2
1
0
0
1
2
0
0
2
1
3
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
2
2
1
2
2
2
2
0
0
0
0
1
0
3
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
1
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
3
0
1
2
0
2
1
0
1
1
0
1
3
2
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
2
2
0
2
0
2
2
0
0
1
4
1
0
0
0
2
1
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
2
2
1
0
0
0
1
0
1
1
1
0
1
0
0
0
2
2
0
1
0
0
2
0
3
0
0
0
0
1
2
0
0
0
4
0
0
0
3
0
0
0
0
2
2
0
1
0
0
1
1
0
2
0
2
0
2
1
1
2
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
2
0
1
0
1
0
1
0
0
2
0
0
0
2
1
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
1
0
2
2
1
0
0
1
2
1
0
1
0
0
1
2
1
0
0
2
0
0
0
0
2
1
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
3
0
0
0
1
1
0
1
2
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
2
1
0
1
0
2
2
0
1
2
0
0
1
2
0
1
3
1
3
2
0
1
1
0
0
0
2
2
2
0
1
1
0
0
1
2
1
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
1
0
0
0
1
0
1
0
0
2
2
0
1
0
1
2
0
0
1
0
3
0
2
2
0
1
0
0
1
0
2
1
2
1
0
1
0
0
0
1
2
0
0
0
2
0
1
2
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
1
2
0
1
0
2
0
2
0
0
1
1
1
2
0
0
0
2
0
1
2
0
0
2
1
2
0
1
1
0
0
0
1
1
0
0
1
0
0
2
0
2
2
0
1
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
2
1
1
0
0
2
0
0
0
1
1
0
0
1
1
2
1
0
2
0
0
0
0
0
1
0
1
0
2
0
1
0
0
1
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
1
0
0
2
1
0
0
1
0
1
0
1
0
1
1
1
5
1
1
1
0
0
2
0
0
2
2
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
2
1
0
0
1
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
2
0
0
1
1
0
1
0
1
2
0
2
2
0
1
0
1
2
2
0
0
0
2
0
0
0
1
0
1
0
2
2
0
0
0
2
0
0
1
2
0
0
2
0
0
1
1
0
1
0
2
0
0
2
2
0
1
0
2
0
0
1
1
0
5
0
0
0
0
0
0
0
3
2
2
1
4
2
0
2
2
0
0
2
4
0
0
0
1
0
0
0
0
0
2
1
2
0
1
0
0
0
0
1
1
0
1
2
0
0
0
1
0
0
0
3
0
0
1
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
1
0
1
1
0
0
0
0
2
1
0
0
0
0
1
0
0
0
2
2
1
0
0
1
2
0
1
0
0
0
0
1
0
0
2
0
1
0
1
2
1
2
1
1
2
0
0
0
1
0
0
1
1
0
0
2
1
1
2
0
0
0
2
0
3
0
0
1
2
1
0
0
2
0
0
0
0
0
2
0
2
1
0
0
0
1
0
3
0
1
1
0
2
2
0
0
2
0
0
1
1
0
1
2
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
2
1
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
2
1
0
1
1
0
1
2
0
0
0
0
1
1
2
2
0
0
1
0
0
0
2
0
1
0
0
1
0
0
1
1
0
2
1
1
0
0
2
0
2
0
1
0
0
0
1
0
3
0
1
0
2
0
0
3
2
0
0
0
0
1
0
0
0
0
0
1
1
1
2
0
1
0
1
0
2
2
1
0
3
0
1
0
1
0
3
0
0
0
1
0
0
0
0
0
0
2
1
1
1
0
0
0
0
0
0
0
0
2
2
0
1
1
1
0
2
0
2
1
1
0
0
0
1
0
0
1
2
2
0
0
0
0
0
0
1
0
2
0
2
1
0
0
0
2
2
1
0
0
2
1
2
0
1
0
0
1
2
0
0
0
1
3
1
0
2
2
0
2
0
2
0
1
1
0
0
2
0
0
0
0
0
1
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
4
2
2
0
0
1
1
1
0
3
0
0
0
0
1
1
0
2
0
2
0
1
1
0
1
0
2
0
0
0
2
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
1
2
0
2
1
1
0
0
3
0
1
0
0
1
2
0
1
0
0
0
0
0
0
0
2
1
0
0
1
0
1
1
0
0
1
0
1
0
1
0
1
2
2
0
2
0
0
0
2
0
0
1
0
0
0
2
3
2
0
2
0
2
0
0
1
2
0
1
0
0
0
1
2
0
0
2
0
0
1
0
0
0
3
1
2
0
0
0
1
1
1
1
1
1
1
0
0
1
1
0
0
0
1
0
0
2
1
0
1
0
0
0
0
1
0
1
2
2
1
0
2
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
3
1
1
0
0
0
0
1
0
1
0
1
1
0
2
1
0
1
3
0
0
0
2
1
2
0
0
0
1
0
1
1
0
3
0
0
0
1
0
0
2
2
0
0
0
2
3
2
2
0
0
1
0
0
2
0
2
0
2
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
1
1
0
0
1
1
0
3
0
2
0
0
0
0
0
2
0
2
1
2
2
0
0
0
0
2
2
1
0
1
0
1
0
1
0
0
1
0
1
2
1
0
2
1
0
0
2
0
1
1
2
3
0
1
1
1
0
0
0
0
1
0
1
1
0
1
0
0
5
3
0
1
0
0
1
1
2
0
0
0
1
0
0
0
0
0
0
2
0
1
1
0
1
0
0
0
1
1
1
0
2
1
0
1
0
0
0
2
1
0
0
1
0
2
2
0
0
0
0
0
0
1
1
2
1
0
0
2
1
0
0
1
1
1
0
1
0
1
0
1
1
1
0
0
1
0
1
0
0
0
1
0
1
0
2
0
0
2
0
1
0
0
0
0
0
1
2
1
0
0
2
2
0
0
2
2
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
1
1
1
0
2
0
1
2
2
2
0
1
1
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
1
1
0
0
0
0
2
2
1
2
0
0
0
3
0
1
2
0
0
0
1
0
0
2
0
0
2
0
1
0
0
1
0
1
1
2
1
0
1
0
2
0
1
0
1
2
0
0
1
0
0
1
1
2
0
0
0
0
0
0
0
2
2
0
0
2
0
0
1
1
1
0
0
0
0
0
0
0
1
2
0
1
0
4
0
0
0
1
0
1
5
2
2
2
2
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
2
0
0
0
1
0
0
1
0
0
1
1
2
0
1
0
3
0
2
0
2
2
0
2
0
0
1
1
3
2
0
1
1
0
2
0
0
0
3
0
2
0
0
1
0
0
0
1
1
1
0
1
1
0
0
0
0
0
1
1
0
0
2
1
0
0
0
3
1
0
2
2
0
2
0
2
0
2
0
0
2
1
0
2
1
0
1
0
0
2
2
0
0
0
0
0
1
2
1
0
1
0
0
1
1
2
1
1
2
0
2
2
0
0
0
0
2
2
1
2
2
0
0
1
0
1
0
2
0
1
2
0
0
0
2
0
0
1
0
1
0
0
3
0
0
0
0
0
1
0
0
0
2
2
0
2
0
0
2
0
2
1
0
0
0
0
0
0
2
1
0
1
0
0
4
0
0
0
1
0
2
0
0
2
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
2
2
2
1
0
0
0
1
0
2
1
0
0
1
0
2
1
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
2
0
2
0
1
1
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
2
0
3
2
1
0
10
0
4
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
2
1
0
2
0
1
0
3
1
2
2
1
2
2
2
0
1
1
0
0
0
0
0
1
0
2
2
2
0
0
1
1
0
0
2
3
0
1
1
0
0
1
2
0
0
0
1
0
1
0
2
1
0
1
0
0
0
0
2
0
1
2
0
0
0
2
0
0
0
2
0
2
0
2
0
0
0
2
0
0
0
2
1
0
2
0
2
1
0
1
0
1
1
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
2
1
1
2
1
1
0
0
2
3
0
0
3
2
2
0
0
1
0
2
0
1
0
0
2
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
2
0
0
2
0
0
0
0
1
2
1
2
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
1
2
2
1
0
0
0
0
0
0
0
0
0
0
1
1
0
4
0
0
0
2
0
0
0
0
0
0
0
2
0
1
2
0
1
0
1
0
2
0
1
0
0
0
1
2
2
0
2
0
0
0
0
0
4
2
0
2
2
0
0
2
1
1
0
0
2
1
0
0
0
0
1
0
0
0
2
0
2
1
0
2
1
1
2
0
2
0
0
0
1
0
1
0
1
0
0
2
0
0
0
0
0
0
2
1
1
1
1
0
0
0
0
1
0
0
0
0
0
2
0
1
1
0
2
1
2
1
2
1
0
2
1
0
1
0
0
0
0
0
1
0
1
1
0
2
0
1
0
2
0
0
2
1
0
0
2
0
2
0
0
0
0
0
0
1
0
0
2
2
0
2
0
0
0
0
1
2
0
0
1
0
0
2
0
2
0
1
0
7
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
1
0
0
3
0
0
0
0
2
0
2
1
2
2
0
0
2
2
0
1
0
0
0
2
0
0
2
0
2
0
1
1
0
0
0
0
1
2
2
0
0
2
0
2
1
1
0
1
1
0
0
1
2
0
2
0
2
2
0
0
0
1
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
2
0
0
0
0
1
5
0
3
0
0
2
1
0
0
0
0
1
1
0
0
0
2
0
2
1
0
0
1
2
0
0
0
0
1
0
0
2
0
0
1
2
0
2
2
0
0
0
0
0
0
0
1
1
1
0
0
2
1
3
2
0
0
1
1
0
0
1
0
0
2
1
2
2
1
0
1
0
0
0
1
1
0
0
1
0
1
3
0
1
1
2
0
1
2
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
2
1
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
2
1
1
1
2
0
2
0
1
2
0
0
2
2
0
1
0
1
1
1
1
0
2
1
0
0
0
2
0
0
0
1
0
1
2
1
2
0
0
0
1
1
1
1
0
1
1
0
2
0
0
1
0
1
1
0
0
0
2
0
1
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
1
2
0
1
1
0
2
0
3
5
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
1
0
1
0
2
1
2
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
2
0
1
0
1
0
1
0
0
0
1
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
2
0
1
1
1
1
0
0
1
0
1
1
0
0
1
0
2
0
0
0
1
0
0
0
0
1
0
0
2
0
0
2
1
0
2
1
0
2
1
1
0
0
0
1
1
0
0
0
2
0
0
2
1
2
0
0
0
2
0
1
1
0
2
0
0
1
0
0
0
0
0
0
1
3
0
0
1
0
0
0
2
0
0
0
0
0
2
2
1
1
0
0
2
2
0
1
0
0
2
2
1
1
2
0
0
0
0
0
1
1
0
2
0
0
2
1
1
0
0
1
0
2
2
1
0
2
2
1
2
1
1
1
0
2
0
1
0
1
0
2
2
0
0
1
0
1
0
0
0
1
0
0
0
1
0
2
0
0
2
0
2
2
0
0
2
0
0
0
2
2
0
0
0
0
2
0
1
1
0
1
0
2
1
0
0
0
0
0
1
1
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
2
0
0
2
0
5
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
2
0
2
1
2
3
0
0
1
0
0
0
2
2
1
0
1
2
0
0
2
1
1
0
0
0
0
0
1
0
0
0
0
2
0
0
2
2
0
2
3
0
0
1
2
2
0
1
0
0
0
2
0
2
1
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
1
1
1
0
1
1
0
1
2
1
0
0
0
2
1
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
1
0
1
0
0
1
0
0
1
2
0
2
1
0
0
1
0
2
1
0
0
0
1
2
2
2
1
0
0
0
2
1
1
2
0
0
1
2
0
2
0
1
0
0
0
0
0
0
0
1
0
0
2
1
1
1
2
0
1
2
0
0
4
0
0
2
1
0
1
1
1
0
0
0
0
0
1
1
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
2
2
1
1
2
1
0
0
2
0
0
0
2
1
1
0
0
2
1
0
1
0
0
0
0
0
1
0
3
2
0
0
0
0
3
0
1
1
0
0
0
0
2
0
0
1
0
1
0
3
0
2
0
2
1
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
1
2
1
0
0
3
0
1
0
2
2
1
2
2
0
0
0
1
0
1
0
0
0
1
0
2
0
0
0
0
0
2
1
0
0
2
0
1
1
1
1
0
0
0
0
0
2
2
0
1
0
1
0
0
1
3
0
0
0
2
1
0
1
2
2
1
2
2
1
0
2
0
0
1
2
2
0
2
0
0
1
0
0
1
0
0
1
0
0
1
1
0
1
2
0
1
0
3
1
0
2
0
0
0
0
1
0
0
1
1
1
0
0
0
1
1
0
0
2
2
2
2
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
2
0
0
1
1
0
2
2
0
2
0
0
0
1
0
2
2
0
0
2
2
1
0
1
0
0
2
1
0
1
0
1
1
0
0
2
0
0
1
0
0
0
1
0
1
0
1
0
2
2
1
0
0
0
0
0
0
3
2
3
0
1
0
0
0
0
0
0
2
0
0
1
0
1
0
1
0
0
3
0
0
1
0
0
1
1
2
2
2
2
0
0
0
0
0
2
0
3
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
3
1
0
0
0
1
0
0
1
0
1
2
0
1
0
0
2
1
1
0
0
0
0
0
0
0
2
1
2
0
0
1
0
0
1
1
1
0
2
1
0
2
0
3
0
0
2
0
1
0
0
1
1
2
1
0
0
1
0
0
0
0
1
3
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
7
1
0
1
1
0
0
1
1
2
1
0
0
2
0
1
0
1
1
0
1
0
2
2
2
0
2
0
1
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
2
2
0
0
0
0
0
1
2
0
2
2
1
2
0
0
0
1
0
0
2
0
1
0
0
1
0
0
0
1
0
2
0
2
2
0
0
0
2
2
0
1
2
0
0
0
3
2
1
2
0
0
0
1
2
2
0
0
0
0
0
2
0
3
0
0
0
1
1
2
2
1
0
0
1
0
2
0
0
0
3
0
2
0
0
0
1
2
0
2
0
0
0
1
1
0
0
0
1
2
0
1
1
0
0
1
0
0
1
1
2
1
0
0
2
0
1
1
1
2
1
1
0
0
0
0
1
2
1
0
1
1
0
0
1
1
0
0
2
0
0
0
0
1
0
0
0
0
1
1
2
0
1
0
1
0
0
0
3
1
0
0
2
0
1
4
0
0
0
0
2
0
2
0
1
0
0
0
1
0
1
0
0
1
1
1
0
0
2
0
0
0
1
0
0
1
2
1
2
0
1
0
1
1
0
0
1
1
0
2
0
4
0
0
0
0
2
1
0
0
1
0
1
0
4
0
2
2
0
0
0
1
0
2
0
2
0
0
1
0
2
2
0
0
0
0
0
0
0
2
0
0
2
2
0
1
2
0
0
0
0
1
0
0
2
2
1
3
1
0
0
2
0
1
1
2
2
0
1
0
1
0
0
0
0
2
1
1
0
1
0
1
2
0
2
0
1
0
0
1
3
0
3
0
2
0
1
1
0
1
0
1
2
1
0
0
0
2
0
2
2
0
0
0
0
1
2
0
0
0
1
0
0
0
1
2
2
0
0
0
2
0
2
0
0
2
0
1
0
2
0
0
2
1
0
0
0
0
1
0
1
0
0
2
2
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
2
0
0
1
2
1
1
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
1
0
0
1
1
1
2
0
0
2
1
1
0
1
0
2
2
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
1
1
0
0
1
0
0
0
2
0
0
2
0
1
0
0
0
0
0
2
0
0
1
1
0
0
3
0
1
0
0
2
0
3
1
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
2
2
2
0
0
1
1
0
4
0
0
1
0
0
0
0
0
1
1
1
2
0
2
0
0
2
0
0
1
0
0
0
1
0
1
0
1
2
3
0
1
1
1
2
1
0
0
0
0
1
0
0
1
0
0
0
1
2
0
2
1
2
1
0
0
0
1
1
2
2
0
0
0
1
0
2
0
0
1
1
2
1
1
0
0
2
0
3
0
0
0
2
0
1
1
2
2
1
0
0
0
0
1
0
0
2
0
0
0
2
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
2
0
1
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
2
2
0
1
0
0
0
0
3
0
0
0
0
2
0
0
0
0
2
0
1
0
0
1
1
0
0
0
1
0
0
0
1
2
1
0
0
0
1
0
1
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
2
0
0
0
0
1
1
1
2
0
1
1
0
0
1
0
0
1
5
0
0
0
2
0
1
1
0
0
0
0
0
1
0
2
0
0
2
1
0
0
1
1
0
2
0
2
0
3
1
0
2
0
1
0
0
1
0
1
0
1
1
2
0
0
0
0
0
2
0
0
0
0
2
2
2
1
3
0
0
0
0
2
0
3
1
0
1
0
0
0
2
1
0
1
0
0
1
2
0
1
0
1
0
0
2
1
1
0
2
1
1
0
2
0
0
0
0
2
1
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
3
0
0
1
2
0
1
0
2
0
2
3
0
0
0
1
2
2
0
0
0
0
2
1
0
0
0
0
0
1
2
0
1
0
3
2
0
0
0
0
1
2
0
0
1
0
2
0
1
0
0
1
0
0
0
2
0
0
2
0
1
0
0
2
0
0
2
0
0
2
1
0
1
1
0
0
2
0
0
0
0
3
0
1
0
0
0
0
0
0
2
0
0
1
0
0
2
0
1
0
1
0
0
0
0
2
28
0
0
0
2
0
0
1
0
0
0
0
2
1
2
1
0
0
0
0
0
0
2
0
2
0
1
0
1
0
2
2
2
0
2
0
0
2
1
0
2
1
0
0
0
0
0
1
0
0
2
0
0
2
0
1
0
0
0
0
2
3
1
0
1
0
0
0
0
0
1
0
0
1
1
0
0
1
1
0
0
0
0
1
1
1
2
0
0
0
2
3
0
2
11
0
1
1
2
1
0
2
1
0
0
1
0
0
0
0
1
0
1
2
0
1
1
0
0
2
1
1
2
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
1
1
2
0
2
0
0
0
0
2
1
0
1
0
1
0
0
1
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
2
0
2
0
1
0
1
0
0
0
0
2
0
3
1
0
1
1
0
0
0
0
0
0
0
1
1
0
0
1
1
0
2
2
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
4
0
0
0
0
0
2
0
1
2
0
1
1
0
0
2
0
0
0
0
0
1
2
0
2
0
0
1
1
2
0
0
0
0
0
0
3
0
1
0
2
2
5
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
2
1
0
0
0
0
0
2
0
2
1
0
0
1
0
0
0
0
5
0
0
1
1
0
0
1
0
1
1
0
0
0
5
0
0
0
2
1
0
1
0
1
0
0
1
2
2
1
1
1
0
0
1
2
1
0
0
0
0
0
0
1
1
0
2
3
0
0
0
0
0
1
0
0
2
0
0
1
0
3
1
0
0
0
1
0
0
0
0
1
1
1
2
1
0
0
2
1
0
1
2
2
0
0
0
1
0
0
0
0
0
2
2
2
3
1
0
1
1
1
1
2
0
1
1
0
0
0
2
2
2
0
1
2
2
0
0
2
2
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
2
0
0
0
2
2
6
0
2
8
0
0
2
1
2
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
2
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
5
1
1
1
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
1
2
2
0
1
0
0
0
1
0
0
0
0
0
1
0
2
0
2
1
2
0
0
3
1
1
0
0
1
0
0
0
1
1
1
0
0
2
1
0
2
0
0
1
2
0
0
0
0
1
3
0
2
0
0
1
0
1
0
0
0
0
0
2
0
0
2
2
0
0
1
0
1
0
1
0
0
1
2
1
0
2
0
1
0
0
1
0
1
0
1
0
1
0
2
2
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
2
1
1
0
0
1
0
0
0
1
0
1
0
0
0
2
0
1
2
1
1
2
2
2
2
0
0
0
0
0
2
0
1
1
0
0
3
0
1
2
3
0
0
0
0
0
2
2
0
0
0
0
0
1
1
0
0
2
2
0
0
0
1
0
0
3
0
1
2
2
0
1
2
1
0
0
1
2
0
1
1
0
0
1
0
2
0
0
2
2
0
0
1
0
0
1
2
0
2
2
0
0
1
0
1
0
1
1
0
0
0
2
1
0
0
1
0
2
1
0
0
2
0
0
1
2
2
2
0
0
0
1
2
2
2
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
2
0
0
0
3
2
0
1
0
0
2
2
2
1
2
2
2
0
1
0
1
2
5
1
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
1
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
2
0
1
0
0
0
1
1
0
0
0
0
2
0
2
0
0
0
1
0
0
0
1
2
0
1
2
0
0
0
0
1
0
0
1
2
2
0
2
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
1
2
1
0
0
2
0
0
0
1
0
2
1
0
0
2
0
1
1
0
3
1
0
1
0
0
2
1
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
2
0
2
0
2
2
0
1
0
2
0
2
0
0
0
2
0
1
0
0
1
1
0
5
1
0
1
2
0
1
0
0
1
2
2
0
2
1
2
1
0
2
0
2
1
0
0
0
0
0
0
2
0
2
0
1
0
1
1
1
3
0
0
0
0
1
1
1
2
1
0
1
0
2
1
0
2
0
0
0
0
0
0
1
2
0
0
1
0
1
0
0
1
1
1
0
0
1
0
0
0
2
0
0
2
0
1
2
1
2
1
0
1
1
1
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
1
0
0
0
0
0
2
0
0
2
2
0
0
0
2
2
1
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
1
0
2
0
1
1
1
3
0
0
2
0
0
0
0
0
2
0
3
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
3
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
1
0
0
1
2
1
0
2
0
0
0
1
0
0
0
0
2
1
0
0
1
1
0
2
0
0
2
1
0
0
0
2
1
0
0
1
0
1
0
0
1
0
2
3
0
0
0
0
0
0
1
0
1
4
0
1
0
1
0
1
1
0
2
3
2
0
1
0
0
0
3
0
0
0
1
1
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
1
1
2
0
0
0
1
2
2
0
1
0
0
0
1
0
0
2
1
2
1
0
1
0
0
0
0
1
1
0
1
0
3
0
0
0
1
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
2
1
2
0
1
1
2
1
0
1
2
0
0
0
0
0
2
1
2
0
1
0
0
0
0
0
0
0
1
0
1
0
0
2
0
1
2
0
0
2
2
0
2
1
0
1
1
0
0
5
0
0
2
0
1
0
0
2
1
0
1
0
0
1
2
0
0
0
0
2
1
2
0
0
1
1
0
2
0
1
2
0
1
0
0
1
2
0
0
0
3
0
0
1
1
2
1
1
1
0
1
0
0
0
0
2
0
1
2
0
0
0
0
1
0
2
1
0
0
0
2
0
0
0
0
0
0
0
1
0
1
1
0
1
2
0
2
0
0
0
0
0
2
0
2
0
1
1
0
0
0
1
0
1
0
0
0
0
2
1
2
0
2
0
1
1
1
2
1
0
0
2
0
2
0
0
0
0
2
2
0
0
1
1
1
1
0
0
1
0
0
0
0
0
2
0
0
2
2
0
2
0
2
0
2
0
0
0
0
0
0
1
2
0
0
2
2
0
0
1
0
0
0
0
0
1
1
1
1
2
0
0
2
2
0
0
1
1
1
1
0
0
2
4
1
1
0
2
1
0
0
2
0
0
0
2
1
1
0
0
0
3
1
1
0
0
0
0
0
1
1
2
0
0
0
1
2
2
0
0
0
0
0
1
0
1
1
2
0
0
1
2
0
1
1
0
0
2
0
1
0
0
0
1
2
0
2
0
0
2
1
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
1
3
0
0
0
1
0
0
1
2
0
1
1
1
0
0
2
0
2
2
0
2
3
0
0
1
0
0
0
1
4
0
0
1
0
2
1
0
0
0
5
3
0
3
0
0
0
1
0
1
1
2
2
0
0
1
2
2
2
0
0
0
3
2
0
0
0
0
2
1
1
0
1
1
0
1
3
1
0
2
0
0
3
0
0
1
0
0
0
0
0
2
1
0
1
0
1
2
0
0
0
1
2
1
2
2
0
0
0
0
2
0
1
0
2
0
2
0
0
2
0
2
4
1
2
2
2
2
0
2
2
0
2
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
1
0
0
1
0
1
1
2
1
0
1
1
2
1
0
0
0
1
1
3
0
1
0
1
0
2
1
0
2
1
0
0
1
2
1
0
0
1
0
2
0
0
0
0
1
1
0
1
0
2
1
0
2
0
0
0
0
5
2
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
1
1
2
1
0
0
0
0
0
0
2
2
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
2
0
0
0
0
1
1
4
0
0
0
0
1
1
1
2
0
0
2
1
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
3
0
0
1
2
1
0
0
2
0
0
0
2
0
2
0
1
0
0
0
2
0
1
0
0
1
0
0
0
1
0
0
0
2
2
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
1
0
0
1
2
1
0
0
0
1
2
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
1
0
0
0
1
1
0
0
2
0
0
1
0
0
0
1
1
1
5
0
0
0
0
1
2
0
0
0
1
1
0
0
1
0
0
2
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
2
2
2
1
2
2
2
0
2
0
0
0
0
0
0
0
2
1
1
1
0
1
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
1
0
1
0
3
0
1
1
0
2
1
2
0
0
1
0
1
2
0
1
0
2
2
1
0
2
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
1
0
0
0
1
0
0
0
2
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
1
2
1
0
1
0
1
0
1
0
2
0
0
0
1
0
0
0
0
0
1
1
2
2
0
1
0
0
1
0
0
2
2
0
0
0
2
0
2
1
1
0
0
0
0
0
0
2
0
1
1
0
1
2
2
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
1
0
0
0
1
1
0
0
0
2
0
2
2
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
2
0
0
1
0
0
1
1
1
0
0
0
0
2
2
0
1
2
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
3
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
2
2
1
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
1
2
0
2
0
0
1
2
1
1
1
1
0
2
2
1
1
2
0
0
1
0
2
0
2
0
0
1
2
0
0
1
4
0
1
0
2
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
2
0
2
2
0
0
0
0
2
0
0
0
0
3
0
3
0
0
2
0
0
0
2
2
1
0
0
0
0
2
1
0
1
0
0
1
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
1
3
2
0
0
1
0
0
0
1
2
0
2
0
3
2
1
0
3
0
0
0
1
0
0
0
2
0
0
1
1
0
0
2
1
2
2
0
0
0
0
0
1
0
2
0
2
2
0
0
0
2
2
1
0
0
2
0
0
0
0
3
1
0
0
1
0
0
2
2
0
0
4
2
1
0
0
1
1
0
0
2
0
0
2
0
2
1
1
2
2
1
3
2
0
1
0
0
2
0
0
0
0
0
0
1
1
0
0
0
2
2
1
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
1
1
0
0
0
2
2
0
1
0
2
0
0
0
1
0
0
1
0
2
2
0
0
1
0
1
1
0
1
1
1
1
2
0
0
2
1
2
1
0
0
3
2
0
1
2
0
2
0
2
2
1
0
2
1
0
2
1
0
0
1
0
0
1
0
1
0
1
0
3
0
1
0
0
1
2
0
0
0
0
0
0
0
3
1
0
0
1
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
2
1
2
1
0
0
1
3
0
0
0
0
1
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
2
0
0
1
0
1
0
0
2
2
0
0
0
0
1
0
2
1
2
0
0
1
3
0
0
0
1
0
1
0
0
0
0
0
2
0
2
3
1
0
0
0
0
1
1
1
0
1
0
2
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
2
0
1
1
2
0
0
0
0
2
0
1
2
0
2
3
1
0
0
0
0
0
0
0
1
0
1
1
1
2
1
1
2
2
1
0
2
2
2
0
2
2
0
2
1
0
1
0
0
1
0
0
2
0
2
2
1
1
0
2
1
2
1
0
0
2
0
1
0
0
0
2
0
1
0
3
0
0
0
0
2
0
0
0
2
0
0
1
1
0
1
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
2
1
2
0
0
1
0
0
0
0
0
0
0
2
0
1
1
2
0
0
2
1
0
0
5
0
1
1
2
1
0
1
1
0
0
0
0
2
0
2
1
1
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
1
2
0
0
1
0
0
1
0
0
0
0
0
0
2
1
2
0
0
0
1
0
2
0
0
0
1
0
2
1
0
0
2
0
1
0
0
0
1
1
0
1
1
0
0
3
0
1
0
0
1
0
0
0
0
0
1
0
0
1
1
0
1
0
2
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
2
2
1
1
0
1
0
3
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
3
1
0
0
1
0
0
1
0
0
0
2
0
0
0
2
1
1
1
0
1
1
0
0
0
0
0
1
1
0
0
2
0
2
1
0
2
2
1
0
1
1
0
1
0
0
0
0
0
3
1
0
0
1
0
0
0
1
0
0
0
1
2
1
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
1
0
0
2
2
2
0
2
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
1
1
0
0
1
0
0
2
0
0
1
2
0
0
4
0
0
2
1
1
0
0
1
1
0
0
1
1
0
0
0
2
0
1
1
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
2
1
2
1
1
1
0
0
2
0
0
0
2
1
2
0
0
0
2
2
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
3
1
0
0
0
1
2
0
0
0
0
0
0
1
0
2
2
1
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
1
2
0
0
1
0
0
0
2
1
0
2
0
0
0
0
0
0
2
0
1
2
0
1
3
0
0
1
1
0
2
0
1
0
0
1
1
1
0
1
0
0
0
1
1
0
2
1
2
0
0
0
1
2
0
0
0
2
0
1
0
0
2
1
0
0
2
0
2
1
1
0
0
0
0
0
2
0
0
1
2
0
0
0
2
0
0
0
0
2
1
1
0
0
0
1
0
2
1
0
0
0
1
1
1
3
0
2
0
2
0
0
0
0
2
0
0
1
2
0
0
1
2
0
0
0
1
0
0
1
0
0
0
1
1
1
1
0
1
0
0
1
2
0
0
1
0
0
1
0
1
0
0
1
0
2
0
0
2
3
0
2
1
1
0
0
0
0
0
0
1
2
0
0
2
2
0
1
1
0
2
0
0
0
0
0
1
1
0
3
0
1
1
2
4
1
1
2
0
1
1
0
3
0
0
0
0
0
1
1
0
0
0
2
1
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
1
1
0
1
1
0
1
1
0
0
3
0
2
0
0
0
0
1
1
0
3
1
2
0
0
0
1
2
2
1
0
2
0
0
1
0
1
1
1
0
0
2
2
2
0
1
0
0
0
1
0
1
0
1
1
0
0
0
1
0
2
1
0
1
2
2
0
0
2
0
0
0
0
0
1
1
1
0
0
0
0
2
2
1
1
0
0
0
0
0
2
0
1
0
2
2
0
0
2
0
2
0
0
0
1
0
0
4
0
1
0
0
0
1
3
0
0
0
0
2
0
0
1
3
0
0
0
1
0
2
0
0
0
0
0
0
3
0
1
4
1
0
0
0
0
1
0
1
0
0
1
0
0
0
2
1
0
1
1
1
0
3
1
0
0
2
0
0
0
1
1
0
3
0
0
1
1
0
1
3
1
2
0
1
0
0
0
0
0
0
0
0
2
1
2
1
0
0
0
0
0
0
0
0
2
1
1
0
2
2
0
0
0
0
2
1
0
2
2
0
2
1
0
1
0
2
2
0
0
2
0
0
0
1
1
0
2
1
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
2
1
0
2
1
1
0
0
2
0
0
2
0
2
0
2
2
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
1
2
1
1
1
0
0
0
2
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
2
0
0
2
1
1
2
0
0
1
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
2
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
2
2
0
0
1
0
1
1
0
1
3
1
0
0
0
0
2
2
0
0
0
2
0
0
1
0
0
0
1
0
1
2
0
1
0
0
2
0
1
0
1
0
0
1
0
0
1
1
0
0
0
0
1
2
1
0
1
0
0
2
0
0
1
0
0
1
0
0
0
0
0
1
1
1
2
0
1
3
0
0
0
0
0
1
0
1
0
0
1
0
1
0
1
0
1
1
0
2
0
0
0
1
1
2
0
2
2
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
2
2
0
0
1
2
0
0
2
0
0
1
1
0
0
0
1
3
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
1
0
2
0
1
0
1
2
2
2
1
0
2
2
0
1
2
2
0
1
0
1
0
2
0
0
1
1
2
0
0
2
1
0
0
0
2
0
0
1
0
0
1
0
0
2
0
0
2
2
0
2
1
0
0
0
1
0
0
2
0
1
1
0
2
2
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
2
2
0
0
1
0
2
1
0
0
0
0
2
0
0
1
2
0
0
2
0
0
1
3
0
1
0
0
0
0
0
1
0
1
4
0
0
1
1
0
0
0
0
2
0
2
0
2
0
2
2
0
0
0
0
4
3
1
0
2
0
2
3
1
0
0
0
2
0
0
0
0
2
2
0
1
0
1
1
0
0
0
1
2
1
1
0
2
4
0
1
0
0
0
2
0
1
2
1
0
1
0
0
1
1
0
2
0
0
2
2
0
2
0
2
0
1
1
0
0
0
2
1
0
0
2
1
0
2
1
0
2
2
2
0
0
0
6
4
0
0
1
1
1
2
0
0
0
1
0
2
0
1
0
0
0
0
0
2
0
2
0
2
1
0
0
0
0
1
1
0
2
0
1
1
0
0
0
0
0
0
0
0
2
1
1
0
0
1
0
0
0
0
0
1
1
1
0
0
1
1
0
1
1
1
0
2
0
1
0
2
0
0
0
0
0
0
0
0
2
1
2
0
1
0
1
2
2
2
0
0
2
0
1
0
0
0
0
1
0
2
0
2
0
1
0
0
0
1
1
1
0
0
2
1
2
0
0
2
0
0
0
0
1
2
2
0
2
1
0
0
0
0
1
0
1
0
2
1
0
2
0
1
0
0
2
1
0
2
1
1
0
1
0
0
0
0
0
2
2
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
2
1
2
1
0
3
0
1
2
0
0
0
0
2
0
2
2
3
1
0
1
2
0
1
1
0
0
2
0
0
0
0
0
0
0
0
1
2
2
1
0
1
1
0
4
0
0
0
2
2
0
0
0
1
0
2
3
1
0
2
0
2
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
2
0
2
1
2
2
2
1
0
0
0
0
0
2
0
2
2
0
0
0
0
2
0
0
0
3
0
0
0
0
1
0
1
1
0
2
0
0
2
1
2
2
0
0
2
0
0
0
0
1
0
0
2
2
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
2
0
2
2
0
0
0
0
0
0
0
1
2
1
0
1
0
0
2
1
0
2
0
0
0
0
0
2
1
0
2
2
1
1
0
0
2
2
0
2
0
0
0
0
1
0
2
2
0
0
0
0
2
2
0
0
0
1
0
1
1
0
1
0
1
0
2
1
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
5
2
0
0
0
2
2
0
2
1
0
1
0
0
2
0
0
0
1
0
1
1
0
0
0
2
0
0
1
2
0
0
0
2
1
0
1
1
1
0
1
0
2
1
0
0
0
1
1
2
0
0
0
1
0
0
2
1
2
2
0
0
0
0
0
0
0
1
2
1
0
1
0
0
0
0
4
2
1
2
1
1
2
0
0
0
3
0
1
1
1
1
0
2
0
1
2
2
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
2
1
0
0
0
0
1
0
2
0
0
0
1
2
0
0
2
0
1
0
0
1
0
0
0
0
1
1
2
0
2
0
0
2
0
0
0
0
1
0
1
1
0
0
1
2
1
0
0
0
1
1
0
0
2
0
1
0
2
1
0
0
1
2
1
3
1
0
0
2
0
0
0
2
1
0
1
1
0
0
0
0
1
0
0
2
1
0
2
1
0
0
0
2
0
0
2
0
0
2
0
2
0
1
0
1
0
0
0
0
2
1
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
2
0
2
0
1
0
0
0
1
0
1
0
0
0
0
0
2
2
1
1
0
1
1
2
4
0
1
0
0
1
0
0
0
0
0
1
1
2
2
0
0
1
0
1
2
0
0
2
0
2
0
2
1
0
1
0
0
0
0
1
0
0
1
0
1
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
3
0
0
1
1
0
0
1
2
0
0
0
0
3
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
4
0
0
2
2
1
0
0
0
0
0
2
0
2
0
2
1
0
0
2
2
1
2
0
0
0
0
6
0
0
1
2
0
1
1
2
0
0
0
0
0
0
0
2
0
1
1
0
1
2
0
0
0
2
0
0
0
1
1
0
0
0
2
0
0
0
1
4
0
0
1
0
0
1
0
1
1
2
0
0
1
1
0
0
2
0
0
2
0
1
2
0
1
0
2
0
2
0
0
0
0
0
0
1
1
1
1
1
0
2
0
1
1
0
0
1
1
1
0
3
0
1
0
1
1
0
1
1
0
0
2
0
0
1
0
0
2
2
2
2
0
0
0
0
0
0
0
2
2
2
1
1
1
0
0
0
0
0
0
1
0
2
0
0
1
0
2
2
2
1
2
1
0
0
2
0
2
1
0
2
0
2
0
2
0
2
0
1
2
0
2
0
0
2
0
1
0
1
1
0
2
2
0
0
0
2
1
0
0
0
3
1
2
0
1
0
0
0
0
1
2
0
1
1
0
1
1
0
1
2
0
0
0
0
0
2
0
2
2
2
0
1
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
3
0
0
1
0
1
0
0
0
1
1
3
0
0
0
1
0
0
1
2
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
1
1
0
2
0
0
1
0
2
1
0
2
2
0
2
2
0
1
1
1
0
1
0
1
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
2
1
2
1
0
1
0
3
1
1
0
0
0
0
1
0
1
2
0
1
0
0
1
1
0
0
0
2
1
0
0
0
0
0
0
1
2
0
0
0
0
0
2
1
3
0
0
2
2
0
1
1
0
0
1
0
0
0
2
0
0
0
0
1
2
0
1
1
0
0
1
1
0
0
0
0
0
2
0
0
1
0
0
2
3
1
1
0
0
2
0
0
2
0
0
1
0
0
2
2
0
3
0
0
2
0
2
2
0
0
0
0
1
0
0
0
2
0
2
0
3
0
1
0
2
0
2
2
0
0
0
2
2
0
0
0
2
2
1
0
2
1
3
0
1
0
0
0
0
1
2
0
0
0
1
1
0
0
2
0
0
0
1
0
1
0
2
0
0
0
0
1
0
0
0
0
0
4
1
0
0
1
0
0
0
3
2
0
0
1
0
0
1
0
2
0
0
0
0
1
0
1
0
2
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
2
0
4
1
0
0
0
1
0
0
1
2
2
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
1
1
0
0
1
0
1
1
0
0
0
0
0
0
0
1
2
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
2
1
1
1
0
0
0
0
3
5
0
0
2
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
2
0
2
0
0
1
0
1
0
2
0
1
0
0
2
0
1
0
2
0
0
0
4
0
0
0
0
2
2
0
2
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
1
2
0
1
2
0
2
0
0
0
2
0
2
2
0
1
2
1
0
1
1
1
0
0
0
0
0
0
2
0
0
2
0
0
1
1
1
1
2
1
2
2
2
0
3
2
1
1
2
2
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
2
1
1
1
0
1
1
0
2
0
1
0
0
0
0
1
0
2
2
0
0
0
3
0
1
0
0
0
3
0
1
1
1
0
0
1
0
1
0
0
0
2
0
0
0
0
0
1
1
0
1
1
0
1
2
0
0
2
2
2
2
1
0
2
0
0
0
1
1
2
1
1
3
1
3
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
1
0
0
1
0
2
1
1
1
0
1
0
2
0
0
0
2
2
0
0
0
2
2
2
2
0
0
0
0
2
1
1
0
1
0
9
0
0
0
0
0
0
0
0
0
2
1
3
0
0
2
0
1
0
0
0
0
2
2
2
1
0
0
1
0
2
0
0
0
2
1
0
0
2
0
0
0
0
2
0
0
1
0
0
2
1
1
0
2
1
0
0
0
1
0
1
2
0
2
0
2
0
0
0
3
3
0
0
0
1
1
0
0
1
1
0
2
1
0
2
0
0
2
2
1
0
2
2
2
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
1
1
1
0
1
0
0
1
0
2
1
0
1
2
0
0
0
0
3
2
1
1
2
0
0
2
0
1
0
4
0
0
1
1
0
0
1
0
0
1
2
0
2
1
2
0
1
0
0
0
0
1
0
0
0
0
2
0
3
0
1
0
0
1
0
0
2
0
1
2
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
3
1
1
0
0
1
1
1
2
0
3
1
3
0
2
0
0
0
2
1
0
0
0
2
4
0
0
0
0
1
2
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
1
2
0
0
1
0
0
1
0
0
2
0
0
1
2
2
1
1
1
0
0
0
0
0
1
0
1
2
0
0
1
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
1
0
1
1
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
1
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
3
2
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
1
0
2
1
0
0
0
1
0
0
2
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
3
7
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
2
0
0
0
2
0
1
0
1
0
1
0
2
1
0
2
2
1
0
0
1
0
0
1
2
0
0
2
0
2
0
0
0
0
0
2
2
2
0
0
1
0
0
0
0
1
0
0
0
2
1
1
1
1
0
0
1
0
2
1
0
1
0
1
0
0
0
1
2
2
0
0
0
1
1
1
2
0
0
2
1
1
2
2
0
0
1
2
0
0
1
2
2
0
1
2
0
2
0
1
0
1
1
1
0
0
2
0
2
0
2
0
0
0
0
0
5
0
1
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
2
1
0
2
2
0
1
1
0
1
4
0
1
2
0
2
0
1
0
2
1
0
1
0
4
1
1
0
0
0
1
0
3
0
2
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
2
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
2
0
0
0
0
2
1
0
0
0
2
0
2
0
0
2
1
0
1
2
0
0
0
0
2
0
2
0
0
0
0
0
2
1
1
0
0
0
0
0
0
2
0
0
2
1
2
0
2
1
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
1
0
0
0
2
1
2
0
1
0
3
1
0
0
0
0
2
0
0
1
2
0
0
1
0
0
2
0
0
0
1
1
0
0
0
0
3
0
1
1
0
1
2
2
1
0
2
0
1
0
1
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
1
2
0
2
1
0
0
1
0
2
0
2
0
0
2
0
1
1
1
1
0
0
0
0
1
0
0
2
2
1
0
0
2
0
1
0
2
0
0
1
0
0
0
0
0
0
1
0
3
1
0
0
0
0
1
0
0
0
1
2
1
2
0
2
2
1
0
0
2
2
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
1
1
0
0
0
0
1
1
0
3
1
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
1
1
0
0
2
0
0
1
0
1
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
2
0
2
1
0
0
0
0
0
1
2
0
0
2
1
1
1
0
0
1
2
2
1
0
0
1
0
0
0
0
1
0
1
2
1
1
2
0
1
1
2
0
2
3
0
0
0
0
0
0
0
0
1
0
2
0
2
2
0
1
1
0
0
2
1
0
0
0
2
2
6
2
0
0
2
2
1
3
0
1
0
1
1
0
1
3
0
2
1
0
0
2
0
2
1
0
2
0
0
0
0
0
2
0
1
1
0
0
2
1
1
1
2
0
0
1
0
2
2
0
2
0
0
0
0
2
2
0
0
1
0
1
4
1
2
2
1
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
1
0
0
1
0
0
0
0
0
1
3
0
0
1
0
0
1
0
1
1
0
1
0
1
0
0
0
1
2
2
0
1
1
0
1
0
0
0
0
3
2
0
2
0
1
1
0
0
0
1
0
0
4
1
2
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
2
1
0
1
0
0
1
0
0
2
1
0
0
2
1
0
2
0
2
0
1
0
0
2
0
0
0
0
0
0
0
2
1
1
2
2
0
2
0
0
0
0
0
3
1
3
2
1
1
0
2
2
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
1
1
1
0
0
3
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
1
0
0
0
2
1
2
0
0
0
1
0
2
0
0
0
1
0
0
2
1
0
0
0
0
0
2
2
0
0
2
0
0
1
2
3
0
0
0
1
2
0
3
2
0
1
0
1
0
1
0
0
1
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
1
0
0
0
0
1
5
0
3
4
3
0
2
0
0
1
0
1
2
0
1
0
2
0
2
2
0
2
2
1
3
0
0
1
0
2
0
1
0
1
1
0
0
0
2
0
1
0
1
0
1
0
0
0
2
2
0
4
1
0
0
1
0
0
0
2
1
3
0
0
1
0
0
2
1
2
2
0
2
2
0
2
2
0
2
0
0
1
1
0
2
1
0
1
0
0
0
0
0
2
0
0
0
0
2
1
1
1
0
2
1
2
0
1
0
0
1
0
2
0
0
0
1
2
1
0
2
1
0
0
0
0
0
0
0
2
0
0
0
1
1
0
2
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
2
2
0
0
1
0
0
1
0
0
2
1
2
0
0
1
0
0
0
0
0
0
2
0
2
1
0
0
1
2
0
0
0
2
2
1
0
1
1
0
2
2
0
1
0
0
0
0
0
2
1
2
2
2
0
0
2
0
0
0
0
0
2
2
1
0
1
0
3
0
0
0
3
2
0
2
1
1
0
1
0
1
2
0
1
1
0
0
0
0
0
0
0
2
1
0
0
0
0
1
1
0
3
0
0
0
0
0
1
0
1
1
0
0
1
0
2
0
0
0
0
1
0
1
0
1
0
1
0
1
1
0
1
0
0
0
0
1
0
1
0
1
1
0
0
1
0
0
0
2
0
1
0
0
1
0
0
0
1
0
2
0
0
0
0
1
1
0
0
0
0
2
0
1
1
0
0
0
0
0
0
2
1
2
0
0
0
1
1
0
1
2
0
0
1
0
0
0
2
1
2
0
0
1
0
0
1
1
0
0
0
1
0
4
1
0
2
0
1
2
0
0
2
1
1
2
0
1
2
0
0
0
2
1
3
0
0
0
0
1
1
0
0
2
2
0
2
0
1
2
2
2
0
1
0
0
1
1
2
0
1
2
0
0
1
2
0
0
0
2
0
0
0
0
1
1
2
0
1
1
1
0
0
0
0
1
0
1
0
0
0
0
0
2
2
0
0
0
1
0
1
2
0
0
2
1
2
0
0
2
0
0
0
2
0
0
1
0
2
0
1
0
0
2
1
0
0
2
0
0
1
1
2
0
2
0
1
1
0
1
3
0
2
0
0
2
0
0
0
0
0
1
1
0
0
1
2
2
0
3
1
0
2
0
1
0
2
1
1
0
0
4
0
0
0
0
0
1
0
2
0
1
0
0
0
0
1
3
0
0
1
0
0
2
2
1
0
1
2
2
0
0
2
1
0
0
2
2
0
0
1
2
2
0
0
2
0
0
1
1
1
2
0
0
2
0
1
0
1
0
0
0
0
3
1
0
2
0
0
0
3
1
3
0
0
0
0
0
1
0
1
1
2
1
0
2
0
0
0
0
0
2
2
0
0
0
0
2
0
1
0
0
0
1
2
2
1
0
0
1
2
0
1
1
0
2
1
0
0
0
0
0
0
0
1
0
2
0
0
1
1
1
3
0
9
2
0
0
2
0
0
0
2
0
2
1
1
1
0
0
0
1
1
0
1
2
1
0
2
0
1
0
1
0
0
1
0
2
0
0
0
0
2
2
0
2
0
2
0
1
1
2
0
0
0
0
1
0
2
0
1
2
1
0
2
1
1
0
2
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
2
2
1
0
0
2
0
0
0
0
2
0
2
0
1
0
1
0
0
0
0
2
0
0
0
1
1
1
1
1
0
1
2
1
0
3
2
2
1
0
0
1
0
0
0
2
1
0
0
0
1
0
2
1
0
0
0
0
0
1
1
0
0
0
3
0
0
0
0
2
2
0
1
2
0
2
1
2
2
1
0
0
0
2
0
1
0
1
1
0
1
1
0
1
0
0
0
0
0
0
2
0
1
0
1
0
0
1
0
0
1
2
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
1
1
1
0
1
1
1
0
0
0
1
1
1
1
2
1
1
1
2
2
1
2
1
0
0
2
3
0
0
0
1
0
0
0
0
2
0
3
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
3
1
1
0
0
0
1
1
1
0
1
0
2
2
1
1
0
0
0
0
1
0
0
1
2
0
2
0
1
0
0
2
1
0
1
1
2
1
1
2
0
1
0
0
0
2
0
1
0
0
1
0
2
0
0
0
2
0
2
0
0
0
0
0
2
0
1
2
0
1
0
0
2
0
1
1
0
0
2
0
0
0
2
1
2
0
2
1
0
1
2
1
2
0
0
0
0
0
0
1
2
1
0
0
1
2
0
1
0
0
0
1
2
0
0
2
0
1
1
2
1
0
0
1
0
2
0
2
2
0
0
2
0
0
11
0
0
1
0
0
1
0
0
2
0
0
0
0
1
0
2
0
2
0
0
0
1
1
0
1
0
0
0
0
0
1
1
0
1
0
2
0
3
0
2
0
3
0
0
1
0
0
1
1
0
1
2
0
1
0
2
0
0
2
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
3
2
2
1
1
1
1
0
1
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
2
0
0
0
2
1
0
0
1
0
0
0
1
0
0
1
0
2
0
0
0
0
0
2
0
0
2
0
0
4
0
0
0
0
1
0
2
1
2
0
2
1
0
2
2
0
0
0
2
0
0
0
1
0
0
2
0
2
1
0
3
0
0
0
0
1
0
0
1
0
0
1
2
0
1
0
0
0
0
0
0
2
1
1
1
2
0
1
0
0
2
0
1
0
1
0
1
0
0
0
0
0
1
2
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
2
0
1
0
1
1
0
0
2
0
1
0
2
0
0
1
2
0
0
0
2
0
0
1
0
0
0
0
2
0
1
1
0
0
1
1
0
0
2
0
0
2
0
1
0
0
0
1
1
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
2
2
0
1
0
1
1
0
0
1
0
1
0
0
2
0
0
0
2
0
3
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
2
0
2
3
0
1
2
0
3
0
0
0
0
2
0
1
0
2
1
2
0
1
0
2
1
2
0
0
1
3
0
1
0
0
2
1
1
0
1
3
2
2
0
0
0
0
2
2
0
2
1
2
1
1
1
0
2
0
0
0
1
2
0
0
0
0
0
2
0
0
2
0
0
0
2
1
2
0
2
0
2
0
2
0
1
0
0
0
2
1
2
2
0
2
0
1
2
0
2
2
0
0
0
0
0
0
0
0
1
0
2
1
0
1
1
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
2
0
1
0
0
0
0
1
1
1
0
0
2
0
0
0
0
0
0
1
2
0
0
0
2
0
1
0
1
1
0
0
3
0
1
1
1
1
0
5
2
1
1
2
1
0
0
2
2
0
0
2
2
1
0
0
0
0
1
0
2
0
0
0
1
0
2
1
0
0
1
2
1
1
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
1
0
0
1
2
2
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
2
0
0
2
0
1
1
2
1
0
0
0
1
2
0
1
1
0
0
0
1
1
0
2
0
1
0
1
0
0
0
0
0
0
0
1
2
2
0
1
0
2
2
2
1
0
0
2
0
0
1
0
1
1
1
0
0
0
1
1
1
1
0
1
0
0
0
3
0
1
2
0
4
0
0
0
2
0
0
0
0
1
2
2
0
1
2
0
2
1
1
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
1
2
2
1
1
0
0
2
0
0
1
2
0
0
1
0
0
1
0
2
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
2
1
0
0
0
1
1
2
2
1
2
0
2
3
1
1
0
0
0
0
2
0
2
0
0
0
2
0
0
0
1
2
2
1
2
1
0
0
0
0
0
1
1
1
0
0
2
1
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
1
0
0
2
0
1
0
0
0
2
4
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
3
0
0
0
2
0
0
1
0
0
0
0
2
1
0
0
2
0
0
0
1
0
3
1
1
0
0
1
1
0
0
1
0
0
1
1
1
0
0
0
2
1
2
1
0
0
1
0
1
0
1
0
2
0
0
2
0
0
0
0
2
2
0
1
0
1
2
0
1
0
1
1
2
1
2
0
0
0
1
0
2
2
0
0
2
1
0
1
1
1
0
0
0
1
0
0
2
0
1
0
0
1
0
2
0
1
0
1
0
0
0
1
1
0
0
0
2
1
0
1
2
1
0
0
0
0
2
2
1
1
2
2
0
0
0
1
2
1
2
0
0
1
0
2
0
1
0
1
0
2
2
0
0
1
2
0
0
1
0
2
0
5
2
0
1
1
0
0
2
1
1
1
1
0
0
0
0
0
0
2
0
0
0
1
13
0
1
2
1
1
0
0
2
0
2
2
2
0
0
0
0
1
2
2
2
0
0
2
0
0
0
1
3
0
0
0
1
1
0
1
0
2
1
2
0
2
1
0
0
2
2
0
0
1
0
1
0
2
5
0
0
2
1
0
0
3
0
1
1
2
0
0
1
2
0
1
2
0
4
0
0
2
1
2
0
2
1
2
0
0
0
0
0
1
0
1
0
0
1
3
0
0
1
0
1
2
1
1
0
0
0
1
3
3
1
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
1
1
0
2
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
2
0
0
0
0
1
1
1
2
0
2
0
1
0
2
1
0
2
0
1
1
0
1
3
0
0
0
0
1
0
1
2
0
1
0
0
3
0
0
2
0
0
0
1
0
0
0
2
0
0
0
1
1
0
1
0
2
1
1
1
1
0
0
0
0
1
1
0
0
2
1
2
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
2
1
0
1
1
0
0
0
2
0
2
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
3
0
0
0
0
1
1
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
2
0
1
1
2
3
1
1
0
1
0
1
0
0
0
0
2
1
1
0
2
0
1
1
0
0
0
1
0
2
5
0
0
1
0
1
1
0
0
0
1
0
1
2
0
1
1
0
1
0
1
0
0
1
2
1
0
0
0
0
3
2
0
0
0
0
0
1
2
1
0
0
2
0
0
0
0
1
0
1
0
1
0
1
2
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
2
0
2
2
0
1
1
1
0
1
0
2
2
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
2
0
1
1
0
2
0
1
1
2
1
2
0
0
0
0
2
2
0
2
0
1
0
1
0
0
0
2
1
0
0
1
2
0
0
1
0
1
0
0
0
2
0
0
0
1
1
0
0
0
1
2
0
1
0
0
0
2
0
1
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
2
1
0
0
0
0
1
1
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
1
2
0
0
1
0
0
0
1
0
1
1
2
0
1
2
0
1
0
0
2
2
0
0
1
0
0
0
4
0
1
0
1
0
2
1
1
2
1
0
0
0
0
1
1
2
1
1
1
1
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
1
1
0
2
0
1
0
2
0
0
0
0
0
2
0
2
0
1
0
0
1
0
2
1
2
0
1
0
1
1
0
0
0
0
2
1
1
1
2
2
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
1
3
0
1
0
1
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
1
0
0
1
2
0
1
1
0
1
2
2
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
2
0
0
2
1
1
0
0
2
1
0
1
0
0
2
2
1
0
1
0
2
0
0
0
0
0
2
0
1
1
0
2
0
0
0
2
0
1
0
0
2
2
0
2
0
2
0
1
2
2
0
0
0
2
1
0
0
1
0
0
0
1
1
0
0
2
0
1
0
0
1
0
2
0
0
3
0
0
0
2
0
2
0
0
0
0
0
0
2
0
1
0
1
2
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
2
1
0
0
0
0
1
0
3
1
2
0
1
2
2
0
1
2
1
0
0
0
0
0
0
4
0
2
0
0
0
1
0
1
1
0
1
0
0
2
2
0
1
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
1
2
0
0
4
0
1
1
0
0
1
0
0
0
1
0
0
0
1
1
0
2
0
0
0
3
0
0
0
0
1
0
0
0
1
1
2
2
0
2
2
0
1
1
0
0
1
0
0
6
1
0
2
0
0
0
0
0
0
0
0
0
1
0
1
2
1
2
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
2
0
0
1
1
1
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
1
1
2
2
0
0
1
0
1
0
0
0
1
3
2
2
2
0
1
2
1
2
0
2
1
2
0
2
0
0
0
0
0
6
2
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
2
0
2
2
0
0
0
2
0
0
0
0
0
2
1
1
1
0
1
0
0
0
0
0
0
1
1
0
0
0
1
1
0
1
0
2
0
2
2
0
1
2
0
0
0
0
0
0
1
0
2
0
2
0
1
2
0
0
0
0
0
0
1
1
0
2
2
0
0
0
0
0
2
0
1
0
2
1
1
2
0
0
0
0
2
2
0
2
0
0
0
1
2
0
0
2
2
0
1
2
0
0
0
8
2
2
0
3
0
0
0
1
0
0
2
0
0
0
1
1
1
0
5
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
1
0
2
0
1
0
0
1
0
2
2
0
0
1
0
0
1
0
1
0
2
1
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
3
2
2
1
0
0
2
1
0
2
0
0
0
2
0
0
1
0
2
0
0
0
1
2
2
0
0
0
1
0
1
0
0
2
0
0
0
1
0
0
0
2
1
2
0
0
2
0
0
0
2
1
2
1
0
1
1
0
2
0
0
1
1
0
0
0
0
0
1
1
1
0
0
0
1
1
1
0
2
0
0
0
1
0
1
2
0
0
0
1
0
0
1
0
0
0
1
0
2
1
0
1
0
1
0
0
1
0
0
1
1
1
2
1
1
0
0
1
0
2
0
0
0
0
0
2
2
0
0
3
2
1
2
0
0
7
2
0
1
0
0
0
0
1
2
0
2
2
0
2
2
0
0
0
1
0
0
0
0
0
2
0
1
1
0
0
1
0
0
2
1
0
3
1
0
0
0
0
1
0
0
2
1
0
0
1
0
2
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
1
0
1
0
1
1
0
1
0
1
1
2
2
0
0
1
0
2
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
2
2
0
2
0
2
2
0
1
0
1
0
0
2
0
0
0
1
1
0
2
0
0
2
2
1
2
1
1
0
1
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
2
1
2
3
0
1
1
1
0
2
1
0
0
2
1
0
1
0
1
0
1
0
1
1
1
0
1
2
2
0
0
2
0
1
0
0
2
0
1
0
3
0
0
0
2
1
2
0
3
0
1
0
2
0
0
0
0
0
2
0
1
11
1
1
0
1
0
0
0
3
0
0
0
0
0
2
0
2
0
2
0
1
1
0
1
0
1
0
2
0
1
0
0
0
2
1
2
0
2
1
2
0
1
2
0
2
2
0
0
2
2
0
0
2
0
0
0
0
3
1
1
0
2
0
4
2
0
0
0
0
0
0
1
0
0
0
3
2
0
2
2
0
0
0
2
1
2
0
0
1
0
0
2
1
0
2
0
0
0
0
1
1
4
1
0
0
2
2
0
2
0
1
0
2
0
0
2
1
2
1
0
2
2
2
0
0
2
1
0
0
0
0
1
1
1
0
3
2
1
2
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
2
0
1
0
0
0
0
2
0
2
0
0
0
0
3
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
2
2
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
1
1
2
2
1
0
0
0
1
0
2
0
3
2
0
2
0
0
0
0
0
0
1
0
1
0
2
2
0
1
0
1
0
1
0
1
0
0
1
0
2
0
0
1
2
3
0
1
0
0
0
1
1
0
1
0
1
0
0
2
0
1
0
0
0
2
0
0
0
1
1
0
0
0
0
0
1
0
2
0
0
2
2
0
1
0
0
0
2
0
0
0
0
1
0
1
2
2
0
0
0
1
0
0
0
2
1
0
2
0
1
0
2
0
0
0
0
0
0
2
1
1
0
2
0
0
0
2
0
1
0
0
0
0
2
0
0
1
0
0
0
0
1
1
0
6
2
0
0
2
0
0
2
1
0
3
0
0
2
0
2
0
3
0
0
0
0
0
2
0
1
1
0
2
1
0
0
0
0
2
0
0
1
1
0
0
0
2
2
0
1
0
1
0
0
0
3
0
1
0
0
1
2
0
0
0
2
1
0
2
1
0
2
0
2
2
0
0
2
1
0
1
4
0
0
1
0
1
0
2
0
1
0
1
0
0
1
0
0
1
0
2
2
0
0
1
2
0
1
0
0
0
0
1
2
0
0
2
2
0
0
1
2
3
0
0
1
0
1
0
2
0
1
0
0
2
1
0
1
0
0
1
0
0
0
1
1
1
4
1
0
2
0
0
0
8
0
0
0
0
0
2
0
0
0
1
2
1
1
0
0
0
1
1
0
0
1
0
0
0
0
1
1
0
0
0
2
0
1
0
0
2
2
0
1
2
0
0
1
2
0
1
0
0
0
1
0
0
1
0
2
0
2
0
1
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
1
2
1
0
0
0
1
2
0
1
0
2
0
0
0
0
1
0
0
1
1
2
0
2
2
2
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
2
0
0
0
0
0
1
1
0
1
2
0
0
2
2
0
2
0
0
1
1
0
0
1
0
1
2
1
1
1
0
2
2
0
0
0
0
0
0
0
1
0
0
2
0
6
2
0
1
1
0
1
1
1
0
0
1
2
1
2
0
0
0
1
1
0
0
1
1
0
0
2
0
0
2
0
1
2
1
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
1
1
0
1
0
1
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
2
0
1
1
0
0
0
2
4
0
2
0
0
1
1
0
3
0
0
1
1
2
2
0
3
0
0
2
0
2
1
2
1
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
2
0
1
0
0
0
0
1
2
3
0
1
2
0
0
1
0
1
0
0
0
0
2
2
0
2
0
0
2
2
0
2
2
0
0
0
0
0
1
2
1
2
0
0
1
0
0
0
0
2
0
0
1
0
2
0
0
0
1
0
2
0
3
0
1
2
0
1
1
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
1
2
0
2
3
0
0
0
1
1
1
2
2
0
0
0
0
0
2
2
1
0
0
2
1
1
3
0
1
1
2
2
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
1
0
1
0
1
1
0
0
1
0
0
2
0
0
2
0
0
0
1
0
1
0
0
0
1
2
2
1
1
2
2
1
1
0
0
0
1
0
2
3
2
2
3
0
2
2
0
0
1
1
2
0
2
0
2
2
0
0
1
1
1
0
0
0
0
1
1
2
0
1
2
0
0
0
2
1
0
1
2
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
1
0
3
2
0
0
0
0
1
0
2
0
2
1
2
0
1
0
0
1
0
1
0
0
0
0
1
2
2
0
1
1
3
0
0
0
0
1
0
0
2
0
1
1
0
1
0
0
0
0
2
0
1
0
1
0
0
2
1
2
0
0
1
1
1
0
0
0
0
2
0
1
0
0
0
1
1
0
1
2
2
2
2
5
0
0
1
2
0
0
1
1
0
0
0
0
0
1
1
2
1
1
1
0
0
0
2
2
0
2
0
2
1
2
0
2
2
0
0
0
2
0
0
2
0
1
1
2
0
0
1
0
0
2
0
2
0
0
0
0
1
0
3
0
0
0
2
1
2
2
0
0
0
1
0
1
1
1
0
0
0
0
0
0
2
1
0
0
0
0
2
1
1
2
2
0
2
0
1
1
0
0
2
2
0
1
1
0
0
0
0
1
0
1
0
1
0
2
0
0
1
0
0
3
1
1
0
2
1
0
1
0
2
2
0
2
0
2
0
2
0
1
2
0
1
0
1
1
0
1
0
1
0
0
0
0
0
0
1
1
0
2
1
0
2
0
1
0
0
2
0
0
1
2
0
0
0
1
0
1
1
1
0
0
0
0
0
0
1
0
2
0
1
0
1
2
0
0
2
0
0
2
1
0
1
1
1
0
1
0
0
0
0
1
1
0
1
2
0
0
0
1
0
2
0
0
1
1
0
2
1
0
1
0
0
0
1
0
0
1
1
0
0
0
2
0
0
0
0
0
2
0
2
2
0
0
0
0
0
1
1
1
0
1
1
0
0
1
1
2
1
1
0
1
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
2
2
1
0
0
0
2
2
1
2
0
0
0
0
0
1
0
1
0
3
0
1
1
0
0
0
2
2
1
1
2
0
0
0
0
0
0
1
0
0
1
0
2
0
2
1
0
0
0
0
2
0
0
2
0
0
1
0
0
0
2
1
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
1
2
0
1
2
0
1
1
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
3
2
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
1
3
0
0
0
0
1
2
1
0
0
0
2
0
2
0
0
0
2
1
1
0
0
1
0
0
0
1
0
1
1
0
1
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
2
0
1
1
1
1
2
0
2
1
2
2
0
1
2
0
0
2
0
1
0
6
1
0
0
4
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
2
2
1
2
1
2
0
0
0
2
0
2
0
1
5
0
0
0
2
0
0
0
1
1
0
2
0
0
2
1
2
1
1
1
0
0
1
1
2
1
1
0
2
1
0
0
0
0
0
0
0
0
2
0
1
2
1
2
1
0
0
0
2
4
2
1
1
1
0
0
2
0
0
1
0
0
0
1
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
2
1
0
0
1
0
1
1
0
1
1
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
6
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
3
0
2
2
0
0
0
1
2
2
2
2
0
0
0
0
1
0
0
0
1
2
1
0
0
2
1
0
0
0
2
0
0
2
0
0
1
0
0
1
1
1
2
1
0
0
0
1
1
2
0
0
2
2
0
0
1
0
0
1
0
1
2
2
0
0
0
0
0
2
0
0
2
2
0
0
0
0
2
0
0
0
1
1
0
1
5
2
0
2
0
2
1
0
2
1
2
0
0
0
0
0
0
1
0
2
0
0
0
0
1
1
0
2
2
7
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
2
2
0
0
2
0
0
0
0
2
1
0
0
2
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
3
0
1
0
0
1
0
1
0
0
2
0
0
0
1
0
1
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
1
0
2
0
0
1
0
1
0
0
0
0
1
2
0
2
0
0
0
0
1
0
0
0
2
0
2
2
0
3
1
2
2
0
0
0
1
0
2
1
0
0
1
0
0
0
0
0
0
0
2
1
1
0
0
2
1
2
2
0
1
0
0
1
0
0
0
1
2
0
0
3
0
1
1
2
1
0
1
2
2
2
0
0
0
3
0
1
1
1
0
0
0
0
2
2
2
0
0
1
3
3
3
2
0
1
0
0
2
2
0
0
3
1
2
1
1
1
0
2
6
0
0
1
0
2
1
2
1
2
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
1
0
2
1
0
0
2
2
0
0
1
0
1
0
0
0
0
0
1
0
2
2
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
2
1
2
1
0
1
2
2
0
1
1
1
0
0
0
0
2
0
2
2
0
1
1
0
0
0
2
0
0
0
2
0
1
1
0
0
2
1
0
0
0
0
0
0
1
2
0
0
0
2
1
0
1
2
0
0
0
0
1
0
2
1
0
1
0
0
1
1
1
2
1
2
1
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
5
0
0
0
1
1
0
0
0
0
2
2
0
0
0
1
0
1
0
0
0
2
2
0
0
0
2
0
1
0
0
1
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
2
0
0
1
0
1
0
2
0
0
1
0
0
0
0
2
2
2
0
0
0
1
1
0
0
1
2
1
0
0
1
0
0
0
2
3
0
1
0
0
1
0
0
2
1
2
1
0
1
2
0
1
2
1
0
2
0
3
0
1
1
0
1
2
0
0
1
2
2
1
2
0
2
1
0
2
0
1
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
3
2
0
0
0
0
1
0
2
0
2
1
0
0
1
0
0
2
0
1
2
1
1
2
0
0
2
1
0
1
0
0
1
0
0
0
2
1
0
2
2
0
0
1
1
2
0
0
0
0
0
1
1
2
0
1
0
0
1
2
0
2
1
2
2
1
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
2
0
2
2
1
2
0
1
0
0
0
2
0
1
0
1
1
2
0
0
2
0
3
2
0
1
0
0
0
0
0
0
0
2
1
1
0
0
0
0
1
1
0
1
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
1
0
2
2
1
2
2
1
0
1
0
0
8
0
2
0
0
0
1
2
0
2
2
0
0
2
1
0
0
0
2
1
0
0
0
0
0
1
2
2
0
2
1
2
1
1
0
0
0
0
2
0
0
0
1
0
0
0
2
2
1
0
1
0
2
0
1
3
1
0
1
2
1
0
1
0
1
0
0
0
1
1
0
0
1
0
0
0
0
2
3
0
0
0
0
0
1
2
0
0
2
2
2
1
1
0
1
2
0
1
2
0
0
0
0
0
0
0
1
1
0
1
2
2
0
1
2
2
0
0
1
0
0
0
0
2
2
1
0
2
0
0
0
0
1
0
0
0
0
1
0
3
0
1
0
0
0
0
1
1
0
1
1
0
0
8
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
2
1
0
0
2
2
0
1
2
2
0
1
0
1
0
0
1
0
0
0
0
2
2
0
1
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
2
2
1
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
2
1
0
0
0
0
0
1
0
1
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
3
1
0
0
1
2
3
3
0
2
2
0
0
1
2
0
0
1
0
0
1
2
0
0
0
1
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
2
1
0
3
1
0
2
2
0
2
0
0
0
0
1
0
1
1
2
1
2
0
0
1
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
4
1
1
0
0
2
0
1
0
0
1
0
1
0
0
0
2
1
0
0
0
0
1
0
0
1
0
2
1
0
0
0
2
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
3
0
0
2
0
1
0
2
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
1
0
2
2
2
0
3
2
1
0
0
0
0
1
0
0
0
1
0
1
2
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
1
0
0
1
0
3
2
2
0
1
1
0
0
0
0
1
1
0
1
1
0
0
0
0
2
0
1
2
0
0
1
0
1
0
1
1
0
2
2
1
2
1
0
2
2
2
1
1
2
0
2
0
2
2
1
0
0
3
1
1
0
0
0
0
1
1
0
1
1
1
0
1
0
0
0
0
0
2
0
0
2
0
0
1
0
2
3
0
0
0
0
0
0
2
1
2
3
2
0
1
1
2
1
0
1
2
2
0
1
1
0
1
0
2
0
0
0
0
0
0
2
0
0
1
0
2
1
2
1
0
0
0
2
1
0
0
0
1
1
0
1
0
0
0
1
2
1
0
0
0
0
1
0
0
0
1
2
0
0
0
2
1
2
0
0
0
1
0
0
1
0
1
1
0
2
0
0
4
1
2
0
0
0
2
1
0
1
0
0
1
2
0
0
0
3
0
1
1
0
0
1
0
1
0
0
2
1
2
0
2
0
0
1
0
0
1
3
2
0
3
0
0
1
0
0
0
0
0
0
1
0
2
1
0
2
0
0
1
0
0
0
0
1
0
0
0
2
0
2
0
2
0
0
0
2
1
2
0
0
1
0
1
0
1
0
1
0
1
1
0
1
0
2
0
1
0
0
0
1
2
2
1
2
0
0
2
0
2
0
0
1
1
0
0
1
0
0
0
2
0
0
1
2
1
6
1
0
2
0
2
1
0
2
0
0
0
2
0
5
2
0
0
0
3
2
0
0
0
0
1
0
1
1
2
0
2
1
2
1
2
0
0
0
1
0
2
0
0
0
2
0
0
1
0
1
0
1
2
2
0
0
1
0
0
0
2
0
0
2
0
0
2
0
0
2
0
0
0
1
2
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
2
0
1
0
2
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
3
0
0
2
1
1
0
1
2
2
1
2
0
1
0
0
2
0
0
1
0
0
0
0
1
0
0
0
2
0
0
2
0
0
1
0
0
0
1
0
0
0
0
1
1
0
2
0
7
1
0
0
0
2
2
1
0
0
1
0
1
0
1
1
0
0
0
0
0
1
1
1
0
2
2
0
2
1
1
0
0
0
0
1
0
1
0
0
0
1
1
1
0
3
3
1
0
3
0
0
1
1
0
2
0
0
1
0
0
0
2
0
1
1
2
0
1
1
0
0
0
0
1
0
2
0
0
0
1
0
0
2
0
2
0
0
0
1
2
2
1
4
0
0
1
0
0
2
0
2
0
1
0
0
0
0
1
1
1
0
0
2
0
1
0
2
0
2
0
1
1
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
2
1
0
0
2
1
0
3
0
2
1
0
1
1
2
2
1
1
0
0
0
3
1
0
0
0
0
0
0
1
2
2
0
0
0
3
2
0
0
2
0
0
0
0
2
1
0
2
3
2
1
0
2
2
1
0
0
2
0
0
1
0
0
0
1
1
0
2
2
1
2
2
0
0
1
0
0
0
0
2
0
1
1
0
0
0
0
0
1
2
0
1
0
1
0
2
0
1
2
1
0
1
0
1
2
0
3
0
1
0
0
0
0
0
0
0
0
1
0
0
2
9
1
0
2
1
0
0
1
1
0
0
0
0
1
2
0
0
1
0
1
0
1
1
2
0
1
1
0
1
0
0
1
0
0
0
0
0
0
1
0
2
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
1
2
0
2
2
0
0
0
2
2
0
0
0
0
2
1
2
2
2
2
2
0
0
0
1
0
2
1
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
1
1
0
1
0
2
1
0
1
2
1
0
0
0
1
1
2
0
2
1
0
0
1
0
1
1
1
0
1
0
0
2
3
0
0
2
0
1
0
0
0
2
0
0
0
1
2
2
0
0
1
0
0
0
1
2
1
1
0
0
0
0
1
0
2
0
2
0
0
2
2
0
0
2
0
1
0
0
0
2
1
1
1
2
0
0
0
0
0
0
0
0
0
3
2
0
0
2
0
0
0
0
1
1
0
0
2
0
1
1
2
0
1
0
0
1
0
1
2
2
1
2
1
0
0
0
0
1
0
0
0
2
0
0
2
0
0
2
2
1
1
0
0
0
2
3
0
0
0
2
0
2
0
0
1
0
3
2
2
0
0
0
2
3
1
2
2
2
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
1
0
2
0
5
2
0
2
0
2
2
0
0
1
0
1
0
1
0
1
0
3
0
0
1
0
3
0
0
0
0
0
2
1
0
0
1
0
0
0
0
1
1
0
1
3
0
0
1
2
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
1
0
3
0
1
0
0
1
1
0
1
0
0
0
3
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
1
2
0
2
6
0
0
2
0
1
0
0
0
0
2
0
1
0
0
1
1
0
2
0
0
0
1
2
2
0
0
2
0
1
0
0
2
2
2
0
4
3
2
2
1
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
1
1
2
2
1
0
0
0
2
0
0
1
1
7
1
0
1
0
2
0
0
0
1
2
1
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
2
1
0
2
0
1
0
1
2
0
0
2
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
2
1
0
3
0
0
0
0
0
0
2
0
1
0
1
2
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
1
2
0
1
0
0
1
2
0
2
0
0
0
0
1
0
0
0
1
1
0
1
0
3
2
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
2
0
1
2
1
0
2
1
0
0
0
0
0
0
0
1
1
0
1
0
2
0
0
1
0
0
0
0
0
2
1
2
0
0
1
0
0
1
1
0
0
2
0
2
2
0
0
0
1
0
2
0
0
0
1
0
2
0
0
0
0
2
2
1
1
0
0
2
2
1
0
0
0
0
1
1
1
0
0
0
3
2
0
0
2
0
0
1
0
0
1
0
0
1
0
0
0
0
0
2
2
0
3
0
0
2
0
0
1
0
0
2
0
0
1
0
1
1
1
2
2
2
4
0
2
0
5
0
2
1
0
0
2
0
0
0
2
1
0
0
1
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
2
1
0
0
0
0
0
0
2
0
1
0
1
1
0
0
0
0
0
0
0
4
2
2
1
0
0
0
2
1
0
2
0
2
2
1
0
2
0
1
1
1
0
0
1
1
0
0
1
0
2
2
0
1
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
2
1
0
2
3
0
0
0
2
0
0
0
0
1
1
0
2
0
0
0
0
0
1
1
0
2
0
0
1
0
0
0
0
0
3
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
3
2
2
0
0
2
0
0
1
0
0
0
1
0
1
0
2
0
0
0
1
0
0
2
2
2
1
0
0
0
0
2
0
0
0
2
4
0
0
2
2
0
2
0
3
0
0
0
0
0
0
2
1
1
1
0
1
0
0
0
1
0
1
0
0
0
1
0
0
4
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
1
1
2
1
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
2
0
2
2
2
2
0
2
0
0
0
1
0
1
2
2
2
0
0
0
2
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
1
2
0
2
0
1
0
1
1
2
1
0
0
2
0
2
0
0
0
0
0
2
0
0
1
0
0
2
0
3
2
2
0
1
1
2
4
0
0
2
0
2
0
2
0
2
2
0
0
0
2
0
2
0
0
0
2
0
0
0
1
2
0
0
2
2
0
2
2
1
2
0
2
0
1
1
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
1
0
1
1
2
0
0
0
0
1
0
0
0
1
0
1
2
0
0
3
2
1
0
0
1
1
0
1
2
0
0
0
2
0
2
2
2
0
0
2
0
0
0
0
2
0
1
0
2
0
2
1
0
0
0
0
1
1
2
0
0
0
1
0
0
3
0
2
2
0
1
1
0
0
0
1
0
1
0
1
1
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
1
0
0
1
1
0
1
1
0
1
0
0
1
2
1
6
0
1
1
0
2
0
0
0
0
3
1
0
0
0
1
0
1
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
1
2
1
1
1
0
2
0
0
0
0
1
1
1
0
2
2
0
0
0
0
0
4
0
2
1
0
1
0
0
0
2
0
0
1
0
0
0
0
1
2
2
0
2
0
0
0
0
0
3
1
2
1
1
0
0
2
1
0
0
2
2
1
1
1
0
0
0
0
1
0
0
1
0
2
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
1
1
2
1
0
0
1
0
0
3
0
0
3
0
0
0
2
0
0
0
0
0
0
2
2
1
0
0
0
0
1
2
0
0
0
0
0
0
2
1
0
1
0
1
0
2
1
0
0
0
0
1
1
2
0
0
2
1
0
0
0
2
1
2
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
1
0
1
0
0
1
1
0
0
0
2
1
2
0
2
1
4
0
0
0
0
2
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
2
0
9
0
0
0
1
0
2
0
2
0
1
4
2
0
0
2
2
0
0
2
2
0
1
1
0
0
0
2
0
0
2
1
0
1
0
1
0
0
0
0
0
1
0
3
0
0
0
1
0
0
2
2
0
2
2
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
1
2
1
0
2
0
2
1
0
0
1
1
0
0
0
2
0
0
0
2
0
0
0
2
0
2
0
0
0
2
1
0
0
1
2
0
0
1
3
0
0
1
1
2
1
2
2
1
2
2
2
0
1
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
2
3
1
2
2
0
0
0
0
1
3
1
0
0
2
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
4
4
0
0
2
0
0
0
0
0
1
2
0
0
2
2
0
0
1
0
0
0
0
2
2
0
0
0
0
1
2
0
2
2
0
0
2
0
0
2
2
0
0
2
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
2
0
1
0
0
1
0
0
0
0
1
1
0
0
2
2
0
0
2
0
1
0
2
0
1
0
1
1
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
1
2
0
1
1
1
0
2
0
0
0
0
1
2
0
1
0
2
0
0
0
2
3
0
2
0
2
2
0
2
0
1
0
0
2
0
1
0
1
0
0
0
1
1
2
0
0
1
0
1
1
0
0
1
1
0
0
2
0
0
0
0
2
1
2
0
0
0
0
1
0
0
0
0
0
1
1
0
2
1
0
0
0
2
1
0
3
0
2
1
0
2
0
2
1
0
0
0
1
0
0
1
2
0
2
0
2
2
0
0
0
2
0
2
1
0
0
1
2
2
0
0
0
0
0
2
0
1
0
0
1
1
0
1
0
2
0
0
0
0
0
1
0
0
1
1
0
0
1
1
2
0
0
0
0
2
2
2
0
0
1
1
1
1
0
0
2
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
4
0
0
1
2
3
2
0
0
0
1
1
0
2
2
0
1
0
2
0
1
2
0
1
1
2
0
1
2
0
2
1
0
0
0
2
0
2
0
0
0
0
1
1
2
0
1
0
0
0
2
0
0
0
0
0
1
2
0
0
0
1
0
0
3
2
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
1
2
0
2
5
0
0
0
2
1
0
1
2
0
0
2
0
2
2
2
2
0
0
0
0
3
1
0
0
0
2
2
2
0
0
0
0
1
0
0
0
1
0
0
1
0
2
0
2
0
1
3
0
1
2
0
1
2
1
1
2
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
2
1
1
0
0
2
1
2
0
2
0
4
0
0
0
0
2
0
2
0
1
0
2
2
1
0
2
1
2
0
2
0
0
0
2
2
0
0
0
0
2
2
0
0
0
0
1
2
2
0
1
0
2
1
4
2
0
0
0
0
1
1
0
0
0
0
0
1
2
1
3
0
0
2
0
2
0
0
0
0
1
0
0
0
1
2
2
2
1
0
0
0
1
1
0
0
2
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
2
0
0
0
1
1
0
2
2
0
1
2
0
1
0
0
0
2
1
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
1
2
1
1
1
2
2
0
0
0
0
1
0
0
1
2
0
0
3
0
2
1
0
3
2
0
1
1
1
0
0
0
2
2
0
1
0
1
0
1
0
1
0
1
1
2
0
0
0
2
1
0
0
2
1
0
0
0
1
0
0
1
0
1
1
0
1
1
0
1
0
0
0
0
1
2
0
1
2
0
0
1
0
2
0
0
1
1
2
0
0
1
2
2
2
0
0
2
0
0
2
0
0
1
2
1
0
2
2
2
2
0
0
0
0
0
0
0
1
0
0
0
2
4
0
2
1
0
0
0
0
0
0
0
0
2
0
1
0
2
2
0
0
1
2
2
2
1
2
2
2
2
0
1
1
2
0
0
0
0
1
0
3
2
0
2
0
2
1
1
2
2
2
0
2
0
2
2
6
1
0
2
1
2
2
1
1
2
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
2
1
0
3
0
0
1
0
0
0
0
1
0
0
2
1
0
0
0
0
1
0
0
2
0
1
0
0
2
0
2
2
0
0
0
1
2
0
0
0
1
0
2
0
2
2
0
2
0
2
2
0
1
0
0
0
0
0
0
0
2
0
1
1
0
0
2
2
2
0
0
0
0
0
2
1
2
0
0
1
0
0
1
1
1
0
2
0
0
1
0
0
4
0
1
0
1
0
0
2
0
0
1
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
2
2
2
1
3
1
0
2
0
0
0
1
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
1
0
2
1
0
3
0
2
1
0
2
0
2
2
1
1
1
2
0
1
0
0
0
1
2
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
1
0
1
2
1
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
1
0
0
1
0
1
1
0
0
0
3
2
0
1
0
1
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
1
2
0
0
1
3
2
0
0
0
2
0
0
2
2
0
0
0
0
1
0
2
0
0
2
0
2
1
1
0
1
0
2
1
0
0
2
2
1
0
0
2
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
1
7
0
0
0
1
1
2
1
1
0
1
1
2
0
0
1
1
4
1
2
2
0
0
0
0
0
2
0
0
0
0
0
2
0
1
2
1
2
0
1
0
0
0
0
2
0
0
2
2
1
2
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
2
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
1
2
1
0
0
1
0
2
2
1
1
2
0
0
2
2
1
1
1
0
2
0
2
1
0
0
2
0
0
1
2
0
1
0
0
0
0
2
0
2
2
0
0
2
2
2
0
0
0
0
0
0
0
0
1
2
0
1
1
0
1
0
0
2
1
0
1
0
0
0
0
2
0
0
2
2
0
2
0
1
0
1
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
1
2
0
0
0
2
1
0
3
0
0
2
2
0
0
0
0
0
0
2
0
0
0
2
1
0
1
0
0
0
1
1
1
0
2
2
0
0
1
0
1
0
1
0
1
1
0
0
0
0
0
2
0
1
1
0
1
3
0
1
3
2
1
1
2
1
0
7
0
1
0
0
2
1
1
2
0
3
0
1
0
0
1
0
0
1
0
2
0
1
1
0
2
2
1
2
1
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
1
1
2
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
1
2
0
1
0
0
2
0
0
0
0
0
2
0
0
2
0
0
2
0
0
2
0
1
0
0
2
0
2
0
0
0
1
2
0
0
0
0
1
0
4
0
0
1
2
1
0
10
0
1
0
1
0
0
1
2
0
0
0
0
2
0
0
0
1
1
0
2
1
0
2
1
1
1
0
0
1
0
1
0
1
0
0
1
2
2
0
2
0
0
0
2
0
0
2
1
1
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
2
1
0
2
0
2
2
0
0
0
0
2
0
1
0
1
2
0
0
3
4
1
0
0
0
0
0
2
0
2
3
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
1
0
0
2
2
1
0
2
0
0
0
1
0
1
2
1
1
0
0
1
0
1
2
1
2
2
1
1
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
1
2
0
0
2
2
0
0
0
1
2
1
2
0
3
0
1
1
2
0
1
0
4
0
0
0
1
0
0
2
1
2
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
2
1
0
2
1
2
1
1
0
2
0
0
1
0
3
0
0
0
2
0
1
1
0
1
2
0
0
0
0
0
0
0
0
3
0
0
0
1
1
0
0
2
0
0
4
0
2
1
0
3
1
1
0
0
0
5
1
1
0
0
2
1
0
0
0
0
0
0
0
1
0
1
1
1
0
1
0
2
0
2
0
1
2
2
0
1
0
1
0
0
2
1
0
1
2
2
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
1
0
1
0
0
0
2
0
0
1
0
0
3
2
1
2
0
0
0
0
1
0
1
0
0
0
0
1
2
0
2
2
1
0
0
0
0
0
0
0
2
0
0
0
1
0
2
1
0
2
0
2
2
0
0
2
0
0
0
1
0
0
0
1
0
0
3
0
1
0
1
1
2
0
0
0
0
0
0
0
2
2
1
0
2
2
0
0
0
1
0
0
0
0
0
0
2
0
0
1
2
0
0
1
1
0
0
1
1
2
2
0
2
2
1
1
2
1
2
2
2
1
2
0
0
0
2
0
0
2
1
2
0
1
0
0
1
1
2
0
0
0
0
2
1
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
1
2
2
0
0
2
2
3
2
0
0
0
0
0
0
2
1
0
0
0
1
1
0
0
2
1
1
1
1
1
0
0
2
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
2
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
1
0
1
3
0
0
2
1
0
2
2
0
0
0
0
0
0
0
1
0
3
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
4
2
2
0
2
2
0
0
2
0
0
0
2
6
2
0
0
0
0
0
0
0
2
0
0
2
0
2
2
0
0
3
0
0
2
1
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
3
0
1
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
6
0
2
0
0
1
1
0
0
0
1
2
2
0
0
0
0
0
0
2
0
0
0
2
0
0
1
1
0
0
1
0
0
1
2
0
0
0
2
1
2
0
2
1
2
3
0
0
0
2
0
0
1
1
2
0
0
0
0
2
2
0
3
1
2
0
2
4
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
2
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
1
1
2
2
1
0
0
1
2
0
0
1
1
0
2
1
0
0
1
0
0
1
1
1
0
1
0
1
0
1
0
0
3
1
0
1
1
0
0
2
0
0
2
0
0
0
0
2
4
0
1
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
2
2
2
1
1
0
0
0
0
0
2
2
2
0
0
1
0
1
2
1
1
1
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
2
1
1
0
0
0
1
3
2
0
0
0
0
0
2
2
1
0
1
0
0
0
0
0
2
0
0
1
2
0
0
0
1
3
0
0
2
2
2
0
1
0
0
0
2
1
1
2
2
0
0
1
3
1
0
0
0
0
1
0
2
1
2
0
0
0
1
0
0
0
2
1
0
1
0
1
0
1
0
2
0
1
2
0
1
2
1
2
0
0
0
1
2
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
1
3
2
2
2
0
2
1
2
1
1
2
0
1
2
2
0
1
3
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
6
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
1
0
2
0
1
1
2
0
1
1
2
0
0
1
1
1
0
0
0
2
1
0
0
2
2
0
0
0
2
0
0
0
0
0
2
2
0
1
0
0
0
0
0
1
0
0
0
1
1
0
1
1
0
0
1
0
0
0
1
3
1
1
2
0
0
0
2
0
0
6
0
0
0
0
1
0
1
0
1
0
0
3
2
0
1
1
0
0
2
0
0
0
0
1
0
1
0
4
0
0
2
0
0
0
1
0
0
0
2
1
0
2
1
0
0
1
0
1
0
1
2
0
0
0
1
0
0
2
2
0
2
0
2
2
1
0
1
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
2
0
3
0
0
0
0
2
1
2
2
1
0
0
1
0
1
0
0
0
1
1
1
0
2
0
0
1
1
1
0
7
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
1
0
0
1
0
1
1
1
3
1
0
0
0
1
0
0
0
0
1
1
0
0
0
3
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
2
0
2
0
0
2
1
1
0
1
0
0
0
0
1
0
1
6
1
0
0
0
0
4
1
0
0
0
0
0
0
0
4
1
0
0
0
1
0
1
2
1
0
0
0
2
0
0
0
0
1
0
0
0
1
0
2
2
2
0
1
0
0
2
2
1
1
2
0
2
0
1
0
1
0
2
0
0
1
0
0
2
1
0
0
0
0
2
2
1
0
1
0
1
2
0
0
0
1
0
0
0
1
0
0
0
0
1
0
2
0
0
1
2
0
0
1
0
0
2
0
2
1
2
3
2
0
0
2
0
2
0
0
1
0
1
0
2
0
1
0
2
0
3
2
1
2
0
0
1
3
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
1
2
0
2
0
0
0
3
2
0
3
0
0
0
0
0
0
0
2
0
1
1
1
1
0
2
0
0
0
1
0
1
1
0
1
1
0
0
0
1
0
1
2
0
1
0
1
0
1
1
1
0
1
0
0
0
0
0
1
0
1
0
0
1
0
2
0
0
0
1
2
1
0
1
0
0
0
1
1
0
0
0
2
0
0
0
1
2
1
0
0
0
1
0
1
2
0
1
1
0
1
1
0
0
2
0
2
0
0
0
0
0
0
3
2
0
1
2
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
2
2
0
0
1
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
1
0
1
0
2
0
2
2
0
0
0
0
0
2
0
0
0
1
1
1
0
1
1
0
0
0
0
0
3
0
0
0
2
0
1
0
1
0
1
2
1
2
1
2
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
2
0
0
0
2
0
2
1
2
0
1
2
0
1
0
0
1
0
2
0
0
2
0
1
2
1
0
0
2
0
2
1
1
0
2
2
2
0
0
0
0
0
1
0
2
0
0
0
1
2
0
0
0
0
1
3
0
1
0
0
0
1
0
0
2
0
0
2
2
0
2
0
3
0
0
0
0
1
0
0
2
2
0
1
0
1
1
0
0
1
0
1
0
0
0
2
2
0
0
0
7
0
2
0
1
2
0
0
0
0
4
2
2
0
0
1
0
0
0
1
0
0
0
1
2
0
0
0
1
0
0
0
1
1
0
2
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
1
1
0
2
0
0
0
1
0
2
1
0
0
1
4
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
1
1
0
2
2
2
1
0
0
0
0
2
1
0
0
3
0
0
0
0
0
0
3
1
0
0
1
1
0
1
2
0
0
0
2
1
2
0
1
0
0
0
0
2
0
3
1
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
2
0
2
1
0
0
0
1
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
4
0
1
1
0
0
0
0
1
1
0
1
1
0
2
0
3
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
2
1
0
0
1
0
0
0
2
0
1
1
1
1
1
0
1
0
0
0
1
0
2
0
0
2
0
0
2
0
1
0
1
2
0
0
0
1
1
2
0
0
0
0
2
2
3
1
0
0
1
1
0
0
0
0
1
2
0
0
2
0
0
2
0
2
0
2
1
0
1
2
2
0
1
0
3
1
1
0
0
0
2
2
0
0
2
0
0
2
0
0
2
0
1
0
2
0
0
0
0
1
0
0
0
2
0
2
2
1
1
1
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
2
0
0
2
0
0
0
1
0
2
2
0
0
0
0
1
0
2
0
1
0
1
0
0
1
0
2
1
0
0
0
1
0
0
0
1
1
0
0
0
0
2
1
0
1
0
0
0
0
0
2
0
2
0
3
0
0
0
0
0
1
0
0
0
2
0
2
1
0
1
0
0
0
1
0
0
2
0
0
0
2
1
0
2
0
1
1
0
0
0
0
2
1
1
0
2
2
0
0
0
2
1
0
0
0
1
0
0
1
0
0
0
1
1
0
0
2
2
0
2
2
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
1
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
1
1
0
0
0
0
0
1
2
2
0
0
0
0
2
0
2
0
2
0
2
0
1
1
0
0
2
0
0
2
0
1
0
1
0
0
2
3
1
0
2
0
0
0
1
0
2
0
0
0
2
2
1
2
0
0
2
0
0
0
1
1
1
1
1
1
0
0
2
1
1
0
0
2
0
1
0
0
3
0
0
0
0
0
1
2
0
0
0
0
0
0
2
2
2
0
2
1
0
0
2
1
0
0
1
0
3
0
0
0
0
0
0
2
0
2
2
0
0
2
1
1
0
0
1
0
3
1
0
0
2
0
0
0
1
0
1
2
0
1
0
2
1
0
2
1
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
2
0
0
0
3
0
0
2
1
0
0
1
0
2
2
0
2
0
0
1
2
1
2
0
2
1
1
0
1
2
1
0
2
0
2
0
0
0
1
2
4
1
1
0
0
0
1
0
0
0
0
2
0
3
1
2
0
0
0
0
1
1
0
1
2
1
0
1
1
0
2
0
1
0
1
1
0
1
0
0
1
2
1
1
1
0
2
2
2
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
1
2
2
3
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
1
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
1
1
0
2
0
0
1
0
9
0
0
0
2
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
2
0
0
0
2
2
2
0
0
0
0
0
1
0
0
0
2
3
1
1
0
4
0
2
2
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
2
0
0
2
0
2
0
0
0
0
1
1
3
1
0
1
0
2
0
0
0
0
1
1
1
0
1
0
2
2
0
0
2
0
0
0
1
4
0
0
2
1
2
0
0
2
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
1
0
0
2
0
2
1
2
1
0
1
0
0
5
0
0
0
0
1
1
2
2
0
0
0
2
0
0
1
0
1
2
0
1
0
1
2
2
0
0
0
1
1
0
0
0
0
2
0
1
2
0
2
1
2
0
0
1
0
3
1
2
1
0
0
0
0
1
1
0
0
2
0
1
1
0
2
0
0
2
0
0
0
0
0
1
1
0
0
0
1
1
0
1
0
0
0
1
0
0
1
0
0
1
0
0
2
0
0
1
0
0
1
0
2
1
0
0
2
0
0
2
0
0
2
0
3
1
0
0
0
2
1
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
1
0
0
2
1
1
0
0
2
2
1
1
0
0
0
1
2
0
0
1
0
0
0
1
2
0
0
2
1
0
2
1
1
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
1
1
0
0
2
0
1
0
2
2
2
0
0
0
1
0
1
0
1
1
1
1
0
0
0
0
3
2
0
2
0
1
0
2
1
0
1
0
0
0
0
1
0
1
0
0
2
1
1
2
2
2
0
2
0
0
1
0
2
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
3
0
0
0
4
0
0
2
1
0
1
2
0
0
0
1
0
1
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
2
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
2
1
0
2
0
3
1
0
1
4
2
1
0
0
2
2
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
2
0
1
1
1
2
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
2
1
0
0
0
1
2
2
1
1
2
1
1
0
0
0
2
0
0
1
2
0
2
0
0
0
3
0
0
0
1
1
1
2
0
0
1
1
0
0
0
2
0
2
0
2
0
1
1
0
0
1
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
3
2
0
0
0
0
1
4
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
1
0
0
0
0
2
2
1
2
0
0
1
2
1
1
0
0
2
1
0
0
1
2
0
2
0
0
0
0
1
0
1
1
0
2
1
2
0
0
0
0
0
0
1
2
0
1
1
2
1
0
0
2
0
1
0
0
1
0
0
0
0
0
0
1
2
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
4
1
0
0
1
0
2
0
0
0
1
2
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
1
2
0
0
1
2
1
2
0
0
0
0
0
0
0
0
0
0
0
2
6
2
0
0
0
1
0
1
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
2
0
1
2
1
0
1
0
0
0
0
1
1
0
0
0
0
1
1
0
0
2
0
2
1
0
1
2
0
2
1
0
2
1
0
0
0
0
3
2
0
0
1
0
2
3
0
0
2
4
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
1
0
1
0
0
0
0
0
0
1
0
2
2
0
2
1
0
0
0
0
0
2
0
1
2
0
2
1
0
0
0
0
0
0
1
2
2
0
1
0
0
2
2
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
1
2
0
0
1
0
0
2
0
0
2
1
1
0
0
0
0
1
0
0
0
5
1
0
0
0
2
2
0
0
1
0
0
2
0
0
0
0
1
1
2
1
0
0
1
2
1
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
1
0
2
0
2
1
0
0
0
1
0
0
2
0
0
0
0
2
1
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
1
2
0
0
0
0
0
0
0
2
0
1
1
1
1
1
0
0
2
1
1
0
1
0
1
1
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
1
1
0
1
1
1
1
0
0
2
0
1
1
0
0
0
1
3
2
0
0
0
1
0
0
2
0
1
3
0
0
0
1
2
0
1
1
0
0
1
1
0
0
1
0
1
0
0
1
0
0
2
2
1
2
0
0
0
1
1
2
0
0
1
2
0
0
0
1
2
0
0
0
0
2
0
1
0
1
0
0
0
0
6
2
0
1
0
0
2
0
2
0
3
2
1
1
0
0
0
0
0
0
1
1
0
0
1
1
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
1
0
0
0
1
0
1
0
0
0
1
1
0
0
2
1
1
1
1
0
0
0
0
0
1
2
0
0
1
1
0
1
1
1
1
0
2
0
0
0
0
0
0
2
0
1
3
2
0
1
0
2
0
0
0
4
2
0
1
2
2
0
2
0
0
0
0
2
0
0
0
0
0
1
1
1
0
1
0
0
0
0
2
2
1
1
0
0
0
0
1
0
2
0
0
0
2
3
3
1
1
0
1
0
1
2
1
0
0
0
0
1
0
0
0
3
1
0
0
0
1
0
0
1
0
0
1
2
2
1
0
0
0
0
0
2
1
1
1
0
0
1
0
0
0
2
0
0
1
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
2
1
1
0
0
0
4
0
0
0
0
1
1
2
3
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
1
0
0
2
2
0
0
1
1
1
2
0
0
2
2
0
0
1
2
1
1
0
1
1
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
1
1
0
1
3
0
0
0
0
0
1
2
1
2
0
0
1
1
0
1
0
2
0
2
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
2
2
2
1
0
0
0
0
1
2
2
2
0
0
0
0
1
1
0
0
0
0
0
0
2
0
2
0
1
1
0
0
2
2
0
0
2
2
2
2
1
0
0
0
1
1
0
0
0
0
2
0
0
1
0
0
1
1
1
1
2
1
0
2
0
0
4
2
0
0
1
0
0
0
0
1
2
2
0
2
2
2
0
0
0
1
1
1
0
0
0
1
2
1
0
0
0
0
1
1
0
0
1
1
0
0
1
2
0
2
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
1
0
0
0
0
0
1
0
1
2
1
1
1
2
2
2
1
1
1
0
0
0
2
0
2
0
0
0
1
0
1
1
0
0
0
0
0
0
2
1
1
0
2
0
1
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
2
0
0
2
0
1
0
0
2
0
2
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
2
3
1
2
6
0
2
1
2
0
0
0
2
0
1
1
1
1
2
2
0
2
1
1
0
2
2
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
1
0
1
0
0
2
2
0
0
2
0
0
1
1
2
0
0
0
2
0
0
1
1
1
1
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
2
1
0
1
0
0
4
2
2
1
0
0
0
0
2
2
1
0
1
0
0
0
2
0
1
0
0
2
0
0
2
2
0
2
0
1
2
1
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
1
1
2
0
0
0
0
0
0
2
0
1
1
0
0
2
2
0
0
0
2
0
1
0
0
0
1
1
0
0
2
1
1
0
2
0
2
0
0
0
1
1
0
0
0
1
0
0
1
0
1
1
0
0
0
2
0
0
0
2
1
1
2
0
0
0
1
1
2
0
0
1
0
0
2
0
2
0
1
0
0
0
2
0
0
0
0
0
2
1
1
2
0
0
1
2
1
1
2
0
1
0
0
0
1
1
0
0
0
2
2
0
0
0
1
0
1
1
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
2
1
0
0
1
6
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
2
0
0
0
0
0
2
1
2
0
0
0
0
0
0
2
1
0
2
0
0
1
0
0
0
1
0
0
0
0
2
1
0
2
0
0
0
2
2
2
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
2
2
2
0
0
0
0
1
2
1
1
3
0
2
0
0
1
0
0
0
0
0
2
1
0
0
1
0
0
1
0
2
0
1
2
0
0
0
1
0
1
1
2
2
0
4
1
0
0
1
0
0
1
0
0
2
0
0
2
0
0
0
1
0
2
0
0
2
3
1
1
2
0
0
0
1
2
0
2
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
2
1
0
2
2
1
2
0
1
0
1
1
2
2
0
2
0
0
1
0
0
0
1
1
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
1
3
0
0
2
1
0
2
0
0
1
0
1
0
3
2
2
0
0
2
3
2
2
2
1
0
2
0
0
0
1
0
2
0
1
2
0
0
0
0
1
0
0
0
2
0
2
2
2
1
0
2
0
1
0
2
0
0
1
1
1
2
9
0
0
1
1
0
2
0
2
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
2
2
1
2
2
0
2
1
0
1
0
1
2
0
0
1
0
0
2
0
2
1
1
0
0
1
0
1
2
0
2
1
2
0
0
0
0
1
0
2
2
0
2
2
0
2
0
0
1
0
0
0
0
1
3
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
2
1
1
0
0
2
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
1
1
0
0
0
0
2
0
1
1
2
0
0
0
0
1
1
1
2
2
0
2
2
0
0
2
0
1
0
1
0
0
2
0
1
1
2
0
0
2
1
0
0
3
1
1
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
2
0
1
0
0
0
0
4
0
2
1
2
2
2
0
0
1
0
2
0
1
0
1
1
0
1
0
0
1
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
2
0
2
1
1
0
1
2
0
0
0
2
0
1
0
2
0
0
2
0
0
3
0
0
0
0
1
2
0
2
0
0
0
1
2
1
2
0
0
0
2
0
0
0
0
2
2
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
1
1
3
2
0
0
1
0
0
0
0
2
0
0
2
1
2
0
0
0
1
0
0
3
2
2
0
0
0
1
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
2
1
0
2
1
0
1
0
2
0
1
1
0
1
1
1
2
0
0
0
0
2
0
4
2
0
1
0
0
1
2
0
0
0
0
0
0
1
0
0
1
0
0
3
0
1
0
2
2
0
2
0
1
0
2
1
0
6
2
0
1
0
0
1
1
0
0
1
3
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
1
2
0
1
0
0
0
1
1
0
0
2
2
2
0
0
0
0
1
2
0
2
0
0
0
0
3
0
1
2
0
0
0
2
1
1
0
1
2
3
1
0
2
0
0
2
0
0
0
0
0
1
2
2
1
2
0
0
0
2
0
0
0
0
1
0
0
0
2
0
1
3
0
0
0
1
0
0
1
1
0
2
0
0
0
0
1
0
0
0
3
2
0
1
0
0
0
0
2
0
0
1
0
2
2
0
0
0
0
1
0
2
0
2
1
0
1
0
1
2
1
2
0
1
0
0
0
1
0
1
0
0
3
2
1
1
1
1
0
0
2
0
0
0
2
1
0
1
1
0
0
0
1
1
0
1
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
1
0
2
1
1
0
0
2
1
0
2
2
0
0
2
1
1
0
2
2
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
2
2
1
0
1
2
0
1
0
0
2
0
0
2
0
0
0
1
0
1
0
1
0
0
0
0
1
0
2
0
0
0
2
13
1
0
0
2
2
0
0
0
0
3
2
2
1
1
1
0
0
2
1
0
0
1
0
0
2
3
0
0
1
3
0
1
0
1
0
2
0
0
3
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
2
0
0
0
2
1
0
0
0
1
0
2
0
2
0
2
0
0
0
0
2
0
0
0
0
2
0
0
1
1
0
0
2
2
2
0
0
2
0
0
3
1
0
0
0
0
0
1
2
0
0
0
1
0
1
1
1
1
0
1
0
0
0
0
0
0
1
0
0
1
0
1
1
0
1
0
0
1
0
0
0
0
1
1
0
0
2
1
0
0
0
2
2
2
0
0
0
2
0
0
1
1
0
2
0
0
1
0
0
0
1
1
2
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
1
0
0
3
0
2
0
0
0
1
2
0
0
1
0
1
0
0
2
1
0
0
1
0
0
0
1
1
1
2
0
2
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
2
2
0
2
1
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
1
2
2
0
0
0
0
2
2
0
2
0
0
0
2
0
1
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
1
0
0
1
1
2
0
0
0
0
0
0
2
1
1
1
1
0
0
0
1
2
1
1
1
0
0
0
1
0
1
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
1
0
0
0
0
1
0
3
1
0
1
1
1
0
1
0
0
0
2
0
1
2
3
2
2
0
2
0
0
0
0
1
2
1
0
0
0
0
1
1
2
0
0
1
0
1
1
0
0
2
2
1
2
2
0
2
2
1
0
0
3
0
0
0
0
0
1
1
0
0
1
0
0
1
1
0
0
0
2
0
0
2
0
2
1
0
1
0
2
0
0
2
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
1
0
1
3
0
0
0
1
1
2
2
0
1
1
2
0
0
0
0
1
6
0
1
0
0
1
1
1
0
0
2
0
3
3
0
0
0
1
0
0
0
1
0
0
0
0
2
2
0
0
2
0
0
2
1
0
2
0
0
3
0
2
0
0
0
0
1
2
0
2
0
1
0
2
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
2
0
1
1
2
1
1
2
0
0
0
2
0
1
0
2
0
0
2
0
0
3
0
0
2
2
0
1
1
0
0
0
2
2
0
1
0
2
2
2
1
0
2
0
0
0
0
0
0
2
2
0
1
2
2
0
1
1
0
0
2
0
0
0
1
3
2
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
3
0
1
0
2
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
1
0
1
0
1
0
0
0
0
3
0
0
1
3
2
0
0
0
0
0
2
0
0
0
0
0
2
1
0
2
0
2
0
2
0
2
1
0
1
0
2
0
0
0
1
0
0
0
1
0
0
0
1
2
0
0
0
1
2
0
0
2
0
1
2
0
0
0
2
2
1
0
0
1
1
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
1
2
0
1
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
1
2
0
1
0
0
0
3
1
1
0
0
1
0
0
0
0
0
0
2
1
1
0
1
1
0
0
0
2
0
1
2
0
1
0
1
2
0
0
0
0
2
0
0
2
0
3
1
0
0
1
0
0
0
0
1
0
0
0
1
0
1
3
0
1
1
2
2
0
0
1
1
1
2
2
2
0
0
0
0
1
0
0
0
2
0
1
2
2
0
2
2
0
1
0
2
1
0
0
2
2
0
0
0
1
0
0
1
0
0
2
2
2
1
0
0
0
0
2
1
0
0
0
2
2
0
0
0
0
2
0
1
0
0
0
2
1
1
1
1
2
1
0
2
2
0
0
0
3
2
1
0
0
2
2
1
2
0
3
1
0
0
0
0
1
1
1
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
3
1
2
0
1
2
0
1
0
0
2
0
1
0
0
0
0
2
0
0
0
1
1
0
0
0
3
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
1
3
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
1
0
0
2
0
1
1
1
5
0
0
0
2
2
2
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
2
0
2
1
0
0
2
2
1
2
0
1
0
0
0
0
0
0
0
2
1
0
2
0
2
1
0
1
0
0
0
0
0
0
1
1
2
0
2
2
0
0
0
2
0
1
1
1
1
1
0
0
1
0
2
1
0
1
1
0
0
2
1
0
0
0
0
1
1
1
0
1
1
0
0
2
2
0
0
0
2
1
1
0
2
2
1
1
0
2
1
2
0
0
1
0
0
0
0
0
0
1
1
2
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
3
0
0
1
1
0
2
0
0
2
0
0
0
0
2
0
2
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
2
0
2
2
0
0
2
1
0
2
2
1
3
3
0
0
2
1
0
1
0
2
0
0
1
3
2
1
1
0
2
0
0
0
0
2
2
0
0
0
0
0
1
0
2
1
0
2
1
0
0
0
0
1
0
0
0
0
0
1
2
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
4
0
3
0
0
2
0
0
2
0
2
0
0
0
0
4
2
1
1
1
0
0
2
0
0
0
0
2
2
1
0
0
0
0
0
2
1
0
0
0
0
1
0
2
1
0
0
0
1
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
3
0
2
1
0
2
0
0
0
1
2
2
1
0
0
0
1
0
2
0
0
2
4
0
0
1
1
2
0
0
0
1
2
2
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
2
1
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
1
1
1
2
1
2
1
0
1
0
0
0
0
3
1
1
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
1
1
1
0
1
0
2
2
0
0
2
1
2
0
0
0
0
1
0
0
0
2
2
2
2
2
2
0
0
1
0
0
0
0
0
2
1
0
2
0
0
2
1
0
0
1
0
0
1
0
0
0
1
1
0
2
0
0
0
0
0
2
1
2
0
1
0
2
0
0
0
0
0
0
1
0
0
1
0
1
2
1
0
0
1
0
2
0
0
0
0
1
3
0
0
1
1
2
0
2
0
1
0
2
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
2
2
0
0
0
0
0
0
2
0
1
2
1
0
0
0
0
1
0
0
0
1
0
5
0
1
1
0
2
1
0
0
0
0
0
0
1
0
1
0
0
0
0
2
1
1
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
1
1
0
0
2
0
0
1
0
0
0
2
0
0
0
1
2
0
0
1
0
2
1
0
0
0
1
0
0
0
0
0
1
1
2
0
0
1
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
1
2
1
0
2
0
1
2
1
0
0
0
1
2
2
0
0
0
0
0
0
0
0
1
1
0
0
0
1
2
1
0
0
1
0
0
0
1
0
0
0
0
0
3
1
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
2
8
0
0
1
2
0
0
0
0
0
0
2
0
2
0
0
1
0
1
2
0
1
0
0
0
0
2
0
0
2
0
1
0
1
0
1
0
2
0
2
0
1
0
1
0
1
3
0
0
1
0
0
1
0
0
2
0
1
0
2
0
0
0
0
1
0
0
2
0
1
1
0
1
2
0
0
0
1
2
1
2
0
2
2
0
0
0
1
4
0
1
0
0
2
0
0
0
0
3
2
0
1
1
0
2
0
1
0
2
0
0
2
1
1
1
1
0
0
0
0
0
0
1
0
1
2
2
0
0
1
0
0
2
0
1
0
0
1
0
1
0
0
2
0
0
0
2
0
0
1
1
0
0
1
1
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
2
0
0
2
1
2
1
1
1
1
2
1
0
0
1
1
2
1
1
0
0
2
1
2
0
0
0
2
2
1
0
0
1
0
2
0
0
0
0
0
0
3
0
2
0
0
0
1
0
2
2
1
0
0
2
0
0
1
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
1
0
0
2
2
0
0
0
1
1
1
1
2
0
2
0
1
0
2
2
0
0
0
0
1
1
2
2
2
0
1
0
2
1
0
0
2
0
1
0
7
0
0
2
1
1
0
2
2
0
2
1
1
3
0
0
2
0
0
1
0
0
1
0
1
1
0
0
1
0
0
2
2
0
0
1
1
1
0
0
0
0
0
2
2
2
2
0
0
0
0
0
0
0
1
1
2
1
1
0
0
0
0
0
3
0
0
1
0
2
1
1
0
0
0
2
1
2
0
3
1
1
0
0
2
0
0
0
0
2
2
0
2
1
0
1
0
0
0
2
2
3
0
0
0
0
0
1
0
0
0
1
2
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
1
0
2
0
0
1
1
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
4
0
0
0
0
1
0
0
0
2
2
0
0
0
0
2
0
3
0
2
2
2
0
0
0
1
1
0
1
1
2
0
1
0
2
0
0
2
0
0
0
0
1
2
0
1
0
0
0
0
0
1
2
0
2
1
0
0
1
2
1
0
2
3
0
2
0
0
0
0
0
2
0
0
3
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
3
0
0
2
2
2
0
0
0
0
2
1
0
2
1
0
0
0
0
2
2
1
1
0
2
0
2
0
2
2
2
0
2
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
2
0
0
1
0
1
0
1
1
2
0
4
4
0
0
1
1
3
1
0
0
0
0
1
1
0
1
1
2
1
0
0
0
0
2
0
1
0
2
1
0
0
1
0
0
0
0
1
0
2
0
0
2
2
2
1
0
1
0
0
0
0
0
3
0
2
0
1
1
2
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
1
1
1
0
1
0
3
1
0
1
0
0
2
0
0
0
1
0
2
0
0
1
0
0
1
2
0
2
1
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
1
0
0
0
2
2
0
0
1
1
1
0
0
0
2
0
0
2
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
3
1
0
0
0
0
0
0
1
0
1
0
5
0
0
0
0
0
2
0
2
1
0
0
2
1
0
2
0
0
1
0
2
0
1
0
1
0
0
1
2
1
0
0
0
1
0
3
0
1
0
2
3
2
1
1
0
1
1
2
2
0
0
0
2
0
0
0
1
0
0
0
0
2
1
0
2
2
0
0
0
0
1
0
1
0
0
0
1
1
2
0
0
0
2
1
0
0
0
0
1
0
0
0
0
1
3
0
0
0
0
1
0
4
0
0
1
5
0
0
0
1
2
0
0
1
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
2
0
0
2
2
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
1
0
0
1
2
0
2
2
0
0
0
0
0
1
2
0
0
2
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
2
2
2
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
4
3
0
0
4
1
1
2
0
1
0
1
0
0
1
0
0
1
1
0
1
0
0
0
2
1
0
0
3
1
1
2
4
0
1
0
0
2
0
2
0
2
2
1
0
0
0
0
1
0
0
0
1
1
1
0
0
1
1
2
1
0
0
0
2
1
0
0
0
0
1
0
1
2
1
1
0
1
2
2
1
0
0
1
2
1
2
2
0
0
0
2
0
0
1
0
1
1
0
3
0
2
0
2
3
1
0
2
2
1
0
1
1
0
0
0
2
0
1
0
0
1
0
2
0
2
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
2
1
0
0
0
1
0
0
0
2
2
0
2
0
0
0
0
0
0
0
1
0
2
0
0
1
2
1
0
0
2
0
0
0
0
0
0
0
2
0
0
2
2
2
0
0
2
0
0
0
2
0
0
0
2
0
1
0
0
2
0
0
0
5
3
1
2
0
0
0
0
0
2
0
0
0
0
1
0
1
1
0
0
0
2
0
0
2
0
0
1
1
0
2
3
1
2
0
0
1
2
0
0
0
0
0
0
2
0
1
0
2
0
0
0
1
0
1
0
1
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
2
1
2
0
1
0
1
2
1
0
2
0
0
2
0
0
1
0
0
2
2
1
0
0
2
1
1
0
0
0
1
0
2
1
2
2
0
0
1
0
1
0
0
0
0
0
1
3
0
0
0
0
2
0
2
0
3
0
0
0
0
0
0
0
0
1
2
1
0
2
1
1
2
1
1
2
2
2
2
1
2
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
1
0
2
0
0
2
0
5
1
0
0
0
2
2
2
2
2
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
1
0
2
1
0
2
0
0
0
1
0
0
0
3
0
1
0
0
0
0
2
1
0
1
1
1
1
1
1
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
1
2
0
0
0
0
2
0
1
2
0
2
0
1
0
2
0
2
1
0
0
3
2
0
0
1
0
1
0
0
0
1
0
0
1
1
1
1
0
0
1
0
2
2
0
0
0
1
0
0
0
0
0
1
2
1
1
1
0
0
0
0
1
0
0
0
5
0
2
2
0
0
0
1
0
1
1
0
1
2
0
0
0
0
0
0
2
3
0
0
2
1
1
1
5
1
0
1
3
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
1
0
0
2
0
0
0
0
0
2
4
0
2
2
0
0
0
0
2
0
0
0
2
0
2
1
0
0
1
0
2
1
0
0
1
2
1
2
3
2
2
2
2
0
2
0
0
0
1
3
0
0
0
0
0
0
1
0
1
0
2
0
0
1
2
0
0
0
1
1
0
2
0
2
0
1
2
0
2
0
0
0
3
0
0
0
2
0
2
0
2
1
0
0
0
0
0
0
2
0
1
0
1
0
2
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
2
0
1
0
0
1
1
1
0
0
1
0
0
0
0
1
2
0
1
1
1
0
0
0
1
0
1
0
2
0
1
0
4
0
0
0
1
1
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
1
2
0
1
0
2
2
1
2
0
1
0
0
0
1
0
1
0
0
2
1
0
3
0
0
0
1
1
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
2
0
0
0
2
0
0
2
1
0
0
2
2
1
0
1
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
1
1
0
0
2
1
1
0
0
0
0
2
1
1
2
0
0
2
1
1
0
1
1
2
1
2
1
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
3
2
0
1
1
1
0
0
2
1
0
1
5
1
2
0
0
1
2
2
1
0
0
0
3
0
0
0
1
0
0
0
1
2
0
2
0
2
0
0
0
0
2
1
0
2
0
0
2
0
0
0
0
0
2
0
1
2
0
1
1
1
1
2
0
0
0
2
0
0
0
2
2
2
2
2
0
1
1
2
0
1
0
0
1
1
0
3
2
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
2
0
0
1
0
2
3
2
0
2
2
1
0
0
2
0
0
0
0
0
0
0
0
0
2
2
1
2
2
0
0
0
1
2
0
0
0
0
1
1
0
1
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
1
0
0
3
0
2
1
1
2
0
0
0
0
4
0
2
0
2
0
0
2
2
0
0
0
0
1
2
0
0
0
2
0
1
1
2
0
2
1
0
2
0
0
0
0
1
1
0
0
0
2
0
2
0
1
0
0
0
2
0
1
1
0
0
1
2
0
0
0
1
0
2
2
1
1
1
1
0
0
0
0
0
2
2
0
1
0
1
1
0
2
0
1
0
2
0
0
0
1
0
0
1
0
0
2
0
1
0
0
2
0
0
0
1
0
1
0
1
2
2
1
0
0
0
0
2
0
1
0
2
2
1
0
2
0
0
0
0
0
1
1
0
0
0
1
2
0
0
0
0
0
1
2
0
0
0
2
4
2
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
1
1
0
0
0
1
2
0
1
1
0
0
0
0
0
1
0
1
0
0
2
2
3
2
2
2
0
0
0
0
0
1
0
2
2
6
0
0
0
0
2
2
2
2
2
2
0
2
1
1
0
0
0
2
0
0
2
3
1
2
2
0
0
0
0
2
2
1
0
1
0
2
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
1
2
0
0
1
0
1
0
1
0
0
0
2
3
3
1
0
2
3
2
0
1
0
0
2
2
1
0
2
0
2
0
0
0
0
2
1
0
0
1
0
2
0
2
0
0
1
0
0
1
0
1
3
1
0
2
1
0
0
1
0
0
0
0
0
0
0
1
2
1
1
0
0
1
1
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
2
0
0
1
2
1
0
2
2
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
2
1
1
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
1
2
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
2
0
1
0
2
1
0
0
2
2
0
3
2
1
2
2
0
0
0
0
1
2
0
2
0
0
2
1
1
0
1
1
2
1
0
0
1
1
1
0
2
2
1
1
2
0
1
1
0
2
0
0
0
1
2
0
4
0
0
0
2
0
2
0
2
1
0
0
0
0
0
2
0
1
0
0
4
1
2
0
0
2
0
0
0
1
2
1
0
0
2
1
0
1
1
0
2
0
0
0
1
0
0
0
0
0
2
1
1
2
1
0
0
1
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
1
0
1
0
0
2
2
0
0
0
1
0
0
2
0
1
0
2
0
0
1
0
0
2
2
2
1
0
0
0
1
0
1
0
0
2
0
0
0
3
3
0
0
0
0
0
0
0
0
0
2
0
0
2
1
1
1
0
0
0
2
0
1
0
0
0
2
2
0
0
0
0
1
2
0
0
0
1
0
2
0
0
0
1
2
2
0
2
2
2
2
0
1
0
0
0
2
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
2
2
1
0
0
0
0
2
1
0
0
0
2
2
0
0
0
1
0
0
0
0
1
0
2
3
0
0
0
0
0
1
0
0
0
0
1
1
1
0
1
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
4
0
1
2
0
0
2
1
2
0
0
2
0
0
0
1
1
1
0
0
0
2
1
0
0
1
0
0
0
2
2
2
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
2
0
0
2
2
3
0
0
0
0
0
0
2
2
0
0
2
0
2
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
2
2
1
0
0
1
0
0
0
1
0
1
0
0
0
0
1
5
0
0
0
0
1
2
0
0
0
2
1
0
1
0
3
0
0
0
1
0
1
0
0
2
1
2
0
0
2
1
0
0
0
0
0
2
0
2
0
0
2
0
0
1
0
2
0
0
0
0
2
0
1
1
0
2
1
0
1
0
2
1
0
0
0
0
1
2
1
0
0
2
2
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
2
2
1
1
2
1
1
0
2
1
0
1
1
0
0
1
0
0
1
0
0
0
0
2
0
1
0
0
1
1
0
0
0
5
0
0
2
1
0
0
0
0
2
2
1
1
2
0
0
0
2
2
0
0
1
1
0
0
0
2
2
0
0
0
3
2
0
0
0
1
2
0
0
0
1
3
3
1
0
0
1
0
3
2
0
2
0
0
0
2
2
0
0
2
2
0
0
0
1
1
1
0
1
1
0
0
0
1
1
1
0
2
1
0
0
1
0
0
0
2
0
0
0
2
1
0
1
1
0
0
2
1
0
0
1
0
0
0
0
0
2
0
2
0
2
2
2
0
0
1
0
0
1
3
1
0
0
2
0
6
0
1
0
2
2
1
2
1
0
2
1
0
1
0
0
1
2
1
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
2
1
0
0
0
0
2
0
2
0
2
1
0
0
0
0
0
0
0
0
2
1
1
0
2
0
0
0
1
1
0
1
0
2
2
0
0
0
1
1
0
0
1
1
0
0
0
2
0
0
2
0
1
0
1
0
1
0
0
0
0
2
0
2
0
0
0
0
1
0
2
1
0
0
0
0
1
0
0
0
2
2
2
2
0
0
2
0
2
1
2
1
0
1
0
0
2
0
0
1
0
1
0
0
3
0
0
0
0
1
2
1
0
1
0
2
1
0
0
0
1
0
2
1
0
0
2
1
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
1
1
0
0
0
0
1
1
0
0
0
1
0
0
0
2
2
0
2
2
3
1
0
2
0
0
1
0
0
0
0
0
1
0
1
3
2
3
1
2
3
2
2
1
1
1
0
0
1
2
4
0
0
3
0
0
0
0
9
0
3
0
0
0
2
2
0
2
0
2
0
0
0
2
1
0
0
2
1
0
1
1
1
0
0
0
2
0
0
0
2
1
0
0
1
1
1
2
0
2
1
2
2
1
0
0
0
1
0
0
0
0
2
0
2
0
1
0
0
0
3
0
0
1
0
0
0
0
1
1
0
1
1
2
2
1
1
0
1
0
3
0
2
0
0
0
0
0
2
1
0
0
0
0
2
0
12
0
1
0
2
0
0
0
2
0
1
0
1
2
2
1
1
0
2
0
0
0
0
1
0
0
0
2
0
0
1
1
0
1
0
2
0
1
1
2
0
2
1
0
0
2
0
0
0
1
0
2
1
0
2
2
0
0
0
1
0
1
0
0
0
2
2
2
0
1
0
0
0
2
0
0
2
1
0
1
0
0
2
1
0
2
0
0
0
0
0
0
2
0
1
0
1
0
2
2
2
2
3
0
1
0
2
0
2
0
1
1
0
1
1
0
2
0
0
0
1
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
2
0
2
2
0
1
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
2
0
2
2
2
0
1
0
0
1
2
1
2
2
2
2
0
0
0
0
0
0
0
0
0
2
2
0
0
2
1
0
0
2
0
1
2
0
0
1
0
0
0
0
1
1
0
0
3
0
1
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
2
0
0
1
2
0
0
1
2
0
1
1
0
1
0
0
0
2
2
0
0
1
0
1
2
1
1
2
1
0
2
0
2
0
3
0
0
0
1
0
0
0
2
2
1
2
0
0
0
0
2
0
0
1
2
1
0
0
1
1
0
1
2
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
1
2
0
0
0
0
1
0
1
1
1
0
0
1
1
1
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
3
0
0
1
1
0
1
0
1
0
1
0
2
0
2
0
0
0
1
2
0
1
0
0
1
1
1
1
0
0
0
0
1
0
2
2
0
1
0
1
0
0
0
0
1
0
0
3
0
2
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
4
1
0
0
3
2
1
4
0
0
2
0
2
0
2
1
1
0
0
0
0
2
1
1
0
0
0
1
0
0
0
1
2
0
1
2
0
0
3
1
1
0
0
1
2
1
0
0
0
1
0
0
3
2
0
0
1
0
2
0
2
0
0
1
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
2
1
1
0
2
1
1
0
0
0
0
1
1
2
0
0
0
1
0
1
0
3
0
0
0
2
0
2
2
1
0
0
0
1
1
0
0
2
1
2
0
1
0
0
0
1
0
0
0
3
2
2
1
1
1
1
1
1
0
0
1
0
0
0
1
0
0
1
0
0
2
0
3
0
1
0
0
0
1
0
1
1
1
3
1
0
1
0
2
2
6
1
0
5
0
0
0
0
2
1
0
0
1
0
1
1
0
1
0
2
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
1
2
4
1
1
0
2
0
1
0
1
0
0
0
2
1
0
1
0
0
0
0
0
0
0
1
0
2
1
0
2
1
0
0
1
2
0
0
2
0
0
2
0
2
0
4
0
1
2
1
0
0
0
0
1
1
0
1
1
2
1
2
0
0
0
2
1
0
1
0
0
1
2
0
0
0
2
0
0
3
0
0
1
0
0
2
0
2
0
1
2
0
0
0
1
1
2
1
0
0
0
0
0
2
1
1
0
1
0
0
1
0
0
1
1
1
1
0
1
0
0
1
1
0
0
0
0
0
0
2
2
0
1
0
2
0
1
0
0
0
0
0
1
0
1
2
1
0
2
0
0
0
0
0
2
2
1
0
2
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
2
1
0
1
1
0
0
2
1
0
1
0
2
0
1
0
1
0
0
0
0
0
1
0
2
1
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
2
2
2
0
0
0
0
2
1
1
0
2
1
1
0
1
0
2
0
0
0
0
2
0
0
0
0
2
0
2
1
0
0
0
0
0
1
0
0
1
0
0
2
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
1
0
0
2
2
0
0
1
0
0
2
0
1
0
1
0
0
1
1
2
0
0
0
0
1
0
3
2
2
0
0
2
1
0
0
0
1
0
0
1
2
0
0
1
2
0
0
2
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
1
0
1
0
2
2
0
0
0
2
0
0
2
2
1
2
2
2
2
0
0
1
1
0
1
0
1
1
0
0
0
2
1
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
1
0
0
1
1
2
0
0
0
0
1
2
0
0
0
2
0
0
1
0
0
0
1
0
2
0
2
0
0
1
0
0
1
2
0
0
0
0
0
0
2
0
1
1
0
3
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
3
0
0
2
0
2
0
2
1
0
0
0
0
0
1
1
0
0
2
0
1
0
2
0
0
0
2
3
1
1
2
1
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
6
2
0
0
0
0
1
0
1
1
0
1
0
0
0
1
0
0
1
0
1
0
3
0
1
0
3
0
0
0
0
2
0
0
0
0
1
1
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
2
2
0
0
1
0
2
1
1
2
1
1
0
0
0
1
0
2
0
1
0
1
3
1
1
0
0
0
0
2
3
0
1
1
2
1
1
1
0
0
2
0
0
1
1
2
2
0
1
0
0
0
1
2
1
1
0
0
1
2
1
2
1
0
0
0
0
0
0
0
0
0
2
4
2
1
0
0
1
2
0
0
0
0
1
2
0
1
0
0
0
2
1
0
0
0
2
1
0
0
0
1
0
1
0
0
2
2
1
0
0
1
0
0
1
1
0
0
1
1
0
2
0
0
0
2
2
0
2
1
1
0
0
0
1
1
0
2
1
1
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
2
1
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
2
1
1
0
0
0
1
0
0
1
0
0
2
0
0
0
2
0
1
1
2
1
0
0
0
2
1
1
0
2
0
0
0
1
1
2
1
0
0
0
3
2
0
2
0
1
2
0
0
0
0
1
0
1
1
0
0
0
1
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
2
1
1
0
0
0
1
2
2
0
2
0
0
0
0
2
0
1
2
0
0
3
0
8
1
2
1
0
0
0
0
0
0
1
0
0
0
2
5
0
0
2
2
0
0
0
0
0
2
1
1
0
1
2
0
0
0
0
2
0
1
0
0
0
3
0
0
1
0
0
0
0
1
0
0
1
5
2
1
2
0
0
0
0
0
0
2
1
0
0
1
1
3
2
1
0
0
0
0
0
2
0
0
0
1
1
0
0
1
0
0
1
0
0
0
1
0
0
2
2
2
1
1
0
1
0
0
2
0
2
1
0
1
0
1
2
0
1
1
1
2
0
2
0
1
0
0
0
0
0
0
2
2
0
1
2
4
2
1
1
0
0
0
0
0
0
1
1
0
4
1
1
2
0
0
1
1
1
1
0
0
2
0
0
2
0
0
0
0
0
1
0
1
2
1
0
1
0
2
1
1
1
0
1
0
0
1
1
0
3
1
0
2
2
2
0
0
2
0
0
0
0
1
0
1
1
0
0
0
1
0
2
0
2
2
1
2
0
2
2
0
0
0
0
0
1
2
2
3
2
0
1
0
2
1
0
0
1
0
1
0
2
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
1
1
0
2
1
0
1
1
0
2
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
1
0
0
1
2
0
1
2
0
1
0
0
2
1
0
0
2
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
1
1
0
0
0
0
1
1
0
0
1
0
0
3
0
1
2
2
2
1
0
2
4
2
0
0
1
2
0
0
1
0
1
0
1
0
0
1
2
0
0
1
0
1
0
0
1
1
0
1
3
0
0
0
2
0
1
0
0
0
0
0
2
0
1
1
0
0
2
1
0
0
0
0
0
0
0
2
0
0
2
0
0
1
2
1
1
0
0
0
0
0
2
1
2
2
3
2
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
1
0
0
1
2
0
0
0
1
3
0
0
2
1
0
0
2
0
0
1
0
0
0
2
1
0
2
0
2
0
0
0
1
1
0
1
0
1
0
0
0
2
1
1
0
2
0
2
2
4
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
1
2
0
2
0
0
0
2
0
1
1
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
3
0
2
0
2
2
1
0
2
0
2
0
0
2
0
1
1
1
1
3
1
0
0
3
0
1
1
0
0
1
0
0
1
0
0
1
1
0
0
0
2
2
2
0
2
0
1
0
0
2
2
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
1
1
0
2
0
0
0
2
0
1
1
0
1
2
1
0
1
1
2
0
0
0
0
1
1
1
1
2
1
0
0
1
0
0
0
1
1
0
0
0
0
0
1
2
2
0
2
0
1
0
2
0
1
1
0
0
1
0
1
1
2
1
0
2
0
1
0
0
0
2
1
0
2
0
1
0
2
0
0
0
0
2
0
1
1
1
0
2
0
0
2
2
0
1
0
0
2
0
0
0
0
0
1
2
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
3
2
0
0
0
2
0
0
1
2
0
0
0
0
0
0
1
1
0
2
0
2
0
0
1
0
0
0
1
1
0
2
1
0
2
0
2
0
0
2
0
0
0
1
1
2
0
0
0
2
3
0
0
0
2
1
1
1
0
1
1
0
0
0
0
0
0
1
1
2
0
0
1
0
0
1
1
0
1
0
1
1
1
2
0
0
0
0
1
1
2
2
0
0
2
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
2
2
1
2
2
2
1
0
0
0
2
2
2
0
0
1
0
0
0
3
0
1
0
0
0
2
1
1
1
2
1
0
0
0
1
1
0
0
1
1
1
0
0
2
2
2
1
0
2
1
1
1
0
0
0
2
1
0
0
0
0
0
1
0
0
1
1
1
2
0
3
0
0
2
0
1
2
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
2
0
0
2
0
0
0
0
2
1
1
2
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
2
1
1
0
0
0
2
0
0
1
2
0
1
0
0
0
0
2
1
0
0
3
0
0
2
0
2
0
0
2
0
2
2
0
0
0
0
0
0
0
1
0
2
2
0
0
1
0
0
0
2
2
0
0
1
1
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
2
1
2
0
0
0
1
0
0
0
0
0
0
0
2
0
1
2
1
0
2
0
1
1
0
0
0
4
0
0
0
1
0
1
1
2
0
1
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
2
0
0
0
2
1
0
0
0
0
1
0
0
0
2
2
2
0
1
0
1
1
2
0
0
0
2
0
0
0
0
1
0
1
2
0
0
0
0
2
2
1
0
1
0
0
0
2
0
0
0
0
1
2
0
0
2
0
0
0
2
0
0
0
0
1
0
1
0
0
2
1
1
0
1
1
0
0
0
1
2
1
0
0
1
0
0
1
2
1
2
0
0
0
2
0
2
0
0
0
0
0
3
0
0
0
1
0
1
0
1
2
1
0
1
0
0
0
0
1
0
0
1
2
0
1
2
0
2
0
1
1
1
0
0
1
1
0
1
2
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
1
1
0
0
0
1
0
1
0
1
2
1
2
2
2
2
1
2
2
2
2
1
0
0
1
0
0
0
1
2
0
2
0
0
2
1
1
0
2
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
1
0
1
1
0
0
0
1
0
2
0
2
0
2
0
2
1
1
1
0
0
0
2
0
1
0
0
6
1
0
1
0
1
0
0
0
0
2
0
0
0
3
0
0
0
0
0
2
0
0
0
1
0
2
2
1
0
2
0
2
0
0
1
1
1
2
0
0
0
1
1
0
0
2
0
0
0
0
0
2
1
1
0
0
0
0
1
0
3
0
2
0
0
1
0
1
1
0
0
0
0
0
2
0
2
1
0
1
1
0
0
0
0
1
0
1
1
2
0
2
1
1
0
0
2
1
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
2
2
2
1
0
0
1
1
0
1
0
0
1
1
1
0
0
1
2
0
0
0
2
1
2
0
0
0
2
2
0
2
0
0
0
0
1
0
0
0
2
0
0
0
2
5
0
0
0
1
1
3
2
0
2
0
1
0
0
2
0
0
0
1
0
1
4
0
0
2
2
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
2
0
2
0
0
2
2
0
0
2
2
0
2
2
0
0
0
2
2
1
0
0
4
0
0
0
1
0
0
2
2
3
0
0
0
0
0
0
1
1
1
0
2
2
0
0
2
0
0
2
2
0
2
0
0
0
0
0
1
1
0
0
2
2
2
0
1
2
2
0
1
1
0
0
1
1
0
0
0
2
0
2
0
0
0
0
1
0
1
0
2
1
2
1
1
0
0
0
0
0
0
2
0
2
0
0
2
1
0
1
0
0
0
0
3
2
0
1
3
0
2
0
1
0
0
0
1
0
1
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
2
0
0
0
3
2
1
1
0
0
0
2
2
0
2
2
2
1
2
0
2
0
0
0
0
1
2
2
0
0
1
0
0
1
1
2
2
0
3
0
0
0
0
2
1
0
4
2
3
0
2
0
2
2
1
0
2
1
0
0
0
0
1
0
3
2
0
1
0
1
1
0
0
0
2
1
0
2
1
0
0
0
2
0
0
0
2
0
2
3
2
1
2
2
0
0
1
0
0
2
0
3
1
0
1
1
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
2
2
0
0
1
0
2
1
0
0
2
1
0
2
2
1
0
0
1
2
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
2
0
0
0
2
1
0
0
2
0
0
0
2
0
2
0
2
2
0
0
1
0
0
0
0
0
1
0
1
2
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
1
0
2
0
2
2
1
0
1
0
0
1
0
0
2
1
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
1
0
0
3
1
0
0
2
0
0
0
2
1
1
1
0
4
1
2
0
0
2
1
0
0
0
1
1
1
2
0
0
0
0
1
0
0
2
0
0
0
1
1
0
0
0
0
1
0
0
1
2
1
0
0
2
0
2
2
1
0
1
0
0
0
2
0
0
0
0
2
1
2
2
0
0
0
0
0
2
0
0
0
0
0
1
2
0
1
1
0
1
2
2
0
3
0
1
1
0
0
0
1
2
0
0
0
1
2
0
3
2
1
1
2
0
1
3
0
0
1
2
1
2
2
0
2
2
0
0
2
0
0
0
2
1
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
1
2
0
3
1
2
0
0
0
0
0
0
2
0
2
2
1
3
1
0
0
2
0
3
0
1
1
0
2
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
1
0
0
0
0
0
1
0
0
2
1
3
1
1
0
0
0
0
1
1
0
0
1
0
2
0
1
1
2
1
3
0
2
0
0
0
2
0
0
0
0
1
1
1
0
0
2
0
0
0
0
0
1
0
3
0
0
1
0
0
1
0
0
2
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
2
2
0
1
0
0
0
2
1
3
0
0
0
2
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
3
1
0
0
5
0
1
0
0
0
1
2
0
0
1
0
1
0
1
1
0
0
1
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
1
0
2
1
2
0
0
0
1
0
0
2
0
0
0
1
2
1
0
0
2
1
1
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
3
1
1
1
2
0
0
2
1
0
2
2
1
0
2
0
0
0
3
0
1
0
1
0
1
0
1
0
0
0
1
0
1
0
2
1
2
0
1
1
0
0
0
2
0
0
2
2
0
0
0
1
0
2
0
1
0
2
1
2
0
0
0
0
0
1
0
0
0
0
2
1
0
2
0
0
0
0
1
0
0
1
0
2
2
1
2
2
2
0
1
2
0
1
0
3
1
0
0
0
3
1
0
2
1
1
0
0
0
0
0
0
2
0
2
0
0
0
0
2
2
0
0
0
0
0
0
1
0
1
1
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
2
2
1
1
2
1
0
2
0
1
0
1
1
0
1
0
0
2
0
1
1
3
2
1
3
1
0
0
0
2
1
0
0
3
2
1
2
1
0
0
0
2
2
1
0
1
0
2
2
0
0
2
0
1
0
1
0
0
3
0
1
0
0
0
2
0
0
2
2
0
0
1
0
0
1
2
0
0
1
0
1
0
2
1
0
0
2
4
2
1
0
0
0
1
0
1
2
1
0
0
0
1
0
2
2
2
2
0
4
0
0
0
0
0
0
1
2
0
2
1
0
0
1
1
0
0
0
1
1
1
2
2
0
1
0
0
0
2
2
2
1
2
2
1
0
1
0
2
1
2
0
2
0
1
2
0
1
1
0
0
1
0
3
0
2
0
1
0
2
1
0
0
1
1
0
0
1
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
1
1
0
1
2
1
0
1
1
1
0
1
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
1
0
2
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
2
0
2
1
0
1
0
1
1
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
1
2
0
0
1
0
1
1
2
0
0
2
0
1
0
1
2
1
1
0
0
0
1
2
0
2
0
0
2
0
3
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
1
0
0
0
0
0
2
1
0
0
2
2
0
0
0
1
2
0
2
0
0
1
0
2
0
2
0
1
0
0
2
0
1
2
0
0
2
1
2
0
0
1
1
0
0
2
0
0
0
1
0
0
0
2
1
2
0
0
0
2
0
1
0
0
2
1
0
0
1
0
0
1
0
0
1
2
0
1
0
0
0
0
1
0
1
0
0
1
0
1
1
1
0
0
0
0
2
0
2
0
2
0
0
0
0
2
0
1
0
1
1
0
2
0
0
1
0
1
0
1
0
0
0
2
0
0
0
0
2
2
0
0
1
1
1
2
0
0
2
1
2
2
0
2
0
0
1
2
1
0
2
1
0
0
0
0
0
2
2
0
2
1
0
0
0
0
0
0
0
0
0
2
1
2
1
3
2
0
2
0
0
0
0
2
0
0
1
0
1
0
2
2
0
0
1
0
0
0
0
0
0
3
0
0
0
2
0
1
0
1
1
2
1
0
0
2
1
1
1
0
0
0
0
2
1
2
1
1
1
0
2
0
0
0
0
2
3
0
0
0
2
0
0
0
2
0
0
0
0
0
1
4
0
0
1
0
1
0
0
2
0
1
3
0
0
1
0
0
1
0
1
2
0
0
0
2
0
2
0
0
1
0
0
0
1
0
0
0
0
2
1
0
0
0
0
2
0
1
0
2
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
2
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
1
2
2
0
1
0
0
2
1
0
1
0
0
3
2
0
0
0
2
3
0
1
0
0
0
1
0
1
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
2
1
3
1
0
0
0
0
2
0
3
0
0
0
1
1
2
0
0
2
0
0
1
2
0
0
0
0
1
2
2
2
0
0
0
0
0
0
0
1
0
0
2
2
0
1
0
2
0
0
0
0
0
2
0
1
1
2
0
2
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
2
1
1
0
0
1
0
2
2
0
0
0
2
0
1
2
1
1
0
0
1
0
1
0
0
0
0
1
2
0
1
0
0
0
0
1
0
0
0
0
1
0
2
2
0
2
0
0
0
2
0
0
0
1
0
0
1
1
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
3
3
0
1
2
1
0
0
1
0
1
0
0
1
3
0
0
0
2
0
1
0
0
1
0
2
0
2
1
2
0
1
1
1
0
1
5
1
0
2
0
0
2
0
2
0
0
2
1
1
0
2
0
3
0
0
0
0
1
0
1
1
1
0
2
0
1
0
2
1
0
0
1
0
2
1
1
2
0
1
0
2
0
0
0
1
1
1
0
0
0
2
1
2
1
0
0
2
0
0
0
0
1
0
0
0
2
1
0
0
0
2
2
0
0
1
1
1
0
2
2
0
3
1
1
0
2
0
0
2
0
1
0
2
0
0
0
0
0
1
1
0
1
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
2
1
1
0
0
2
1
0
2
0
0
0
0
0
2
1
0
0
0
1
0
0
1
0
2
0
0
0
2
1
0
1
1
1
0
1
0
0
0
1
0
0
0
2
0
0
0
2
0
0
1
0
0
0
1
0
1
0
0
2
1
0
0
0
2
0
2
2
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
1
2
0
0
2
0
0
0
2
2
0
0
0
1
1
0
2
0
0
1
2
0
1
0
1
0
0
0
2
0
0
3
0
0
1
0
0
1
0
0
1
0
2
2
2
0
0
2
1
0
0
0
3
0
0
0
1
0
0
4
1
0
0
3
2
0
0
1
1
0
2
1
2
1
0
2
0
0
0
0
0
1
0
0
2
1
0
0
0
0
1
2
0
2
0
0
0
2
1
1
1
0
3
2
1
0
1
0
0
0
2
0
0
6
1
2
2
2
3
0
0
1
0
0
0
2
0
0
0
1
1
1
1
0
2
0
2
0
0
0
0
1
1
0
0
3
0
2
0
0
0
1
2
0
1
0
0
0
0
0
2
0
2
1
1
0
1
2
0
1
0
1
2
0
0
0
1
1
0
2
0
0
2
0
0
0
2
0
0
1
2
0
0
1
0
1
1
0
0
0
0
0
2
0
2
0
2
1
2
0
1
0
0
2
0
1
1
0
1
1
0
2
1
0
1
2
1
1
0
2
1
0
0
0
0
2
0
0
0
0
1
1
1
0
0
2
0
0
2
0
1
0
1
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
1
0
0
0
0
0
0
2
2
0
2
0
2
1
0
1
0
1
0
0
0
1
1
0
2
1
0
0
2
0
0
0
2
0
0
2
1
0
0
0
0
1
1
0
0
0
2
0
0
1
0
0
1
0
1
2
2
0
3
1
0
0
0
0
1
0
0
0
1
0
1
1
2
1
1
0
0
0
1
0
2
0
1
1
1
0
0
0
1
0
2
0
0
1
1
0
1
0
2
2
2
1
2
0
0
0
2
0
2
1
2
1
0
1
0
2
1
2
0
0
0
0
0
1
1
1
0
0
2
2
0
1
2
0
0
3
2
0
0
1
2
0
0
2
0
0
2
0
1
0
0
0
1
0
0
1
0
2
0
2
4
0
0
0
2
0
2
0
2
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
2
0
2
0
0
0
0
1
2
0
0
1
0
0
1
1
0
1
0
2
0
0
1
1
1
0
1
1
0
1
0
0
0
3
1
0
0
0
0
2
2
2
1
0
0
0
0
0
1
0
0
1
2
2
0
1
0
0
3
0
1
1
0
2
0
0
0
1
0
0
1
0
0
2
0
0
3
0
0
1
1
1
1
0
0
0
1
2
2
0
0
0
2
1
0
0
0
1
0
0
2
2
2
2
0
1
1
2
2
0
0
1
1
2
0
1
0
0
0
0
1
0
0
0
2
1
0
0
0
0
1
0
0
1
0
0
0
1
0
1
1
3
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
2
1
0
2
0
1
0
0
1
0
0
0
0
0
1
0
0
0
3
2
0
2
0
0
0
0
0
0
0
0
1
0
1
1
1
3
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
2
0
0
1
1
0
0
0
0
2
0
1
0
0
1
0
0
0
0
1
1
0
0
0
2
2
1
0
0
0
0
0
2
1
1
1
0
1
0
2
0
2
1
0
0
0
1
0
0
0
1
0
1
0
2
0
0
2
0
2
0
1
0
1
0
0
0
0
0
1
1
0
1
0
0
1
1
0
2
2
0
0
1
2
0
0
2
0
1
0
2
0
2
0
2
2
2
0
0
0
1
0
0
0
0
2
0
1
0
0
1
0
2
1
0
0
0
0
0
0
1
2
0
0
3
1
0
1
0
0
0
0
0
2
0
1
1
2
3
0
2
0
0
0
1
2
0
0
0
1
0
0
0
1
1
3
2
0
1
1
0
1
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
1
1
0
2
0
0
0
0
0
0
0
0
0
2
2
2
2
0
1
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
2
1
0
0
0
0
0
0
0
2
0
2
0
2
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
1
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
1
2
1
1
1
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
1
2
2
0
2
0
4
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
1
0
3
0
1
0
1
0
0
3
0
0
2
1
2
0
2
0
0
0
0
1
2
0
1
0
1
0
1
0
2
0
1
0
1
1
0
0
2
2
0
1
2
0
2
0
0
0
0
0
4
0
2
0
0
0
0
0
1
2
0
1
0
0
1
1
2
1
0
2
0
0
0
1
2
0
0
2
0
0
0
0
1
1
0
0
0
0
0
1
2
1
0
1
3
0
1
0
2
1
1
1
1
0
1
0
0
0
1
0
0
0
0
2
2
2
1
0
0
0
0
0
1
0
0
2
0
0
2
3
0
0
1
1
1
0
1
2
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
2
2
0
1
0
0
0
0
1
0
0
2
2
1
0
1
1
0
0
2
0
1
1
0
0
2
1
0
1
0
0
2
0
0
0
0
0
2
1
0
0
1
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
2
2
1
0
0
0
0
0
0
3
0
0
3
0
0
2
0
0
0
1
1
0
1
0
0
1
0
0
1
2
1
0
0
1
0
0
0
0
0
2
2
1
0
1
0
0
0
1
1
3
0
0
0
1
1
0
0
0
0
0
2
1
0
0
2
1
2
0
0
0
2
2
2
0
0
1
0
0
1
1
0
2
2
0
0
1
0
1
0
2
2
0
0
0
0
0
2
0
0
1
0
1
0
1
0
1
2
1
0
1
0
0
1
1
1
2
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
2
1
1
4
0
0
0
2
1
2
2
0
3
0
3
1
0
2
0
1
2
0
2
1
0
1
1
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
1
1
0
0
1
1
2
2
2
0
0
1
1
0
0
0
0
1
0
1
0
2
0
1
2
1
1
1
2
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
1
2
2
0
1
1
2
0
0
0
0
1
1
0
2
1
0
0
0
0
0
0
0
0
2
2
0
2
0
3
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
2
2
1
0
0
0
2
0
0
2
0
0
0
0
1
2
0
1
0
2
0
2
1
0
0
1
0
1
0
1
0
0
2
0
0
0
1
0
1
0
0
1
0
0
1
1
1
0
0
0
0
1
0
1
1
0
2
0
0
0
0
1
0
2
1
2
0
1
0
0
0
2
2
0
0
3
2
0
1
1
1
2
0
0
0
0
0
0
2
0
2
2
0
1
0
0
0
1
2
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
2
0
0
2
0
0
1
0
0
1
1
2
1
2
1
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
1
3
1
1
0
3
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
1
0
2
1
0
0
3
0
0
1
0
0
0
2
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
1
0
0
1
2
2
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
1
1
1
0
0
3
0
1
1
0
1
1
0
2
0
0
1
2
0
0
0
2
0
0
0
0
2
2
2
1
0
0
1
0
1
2
1
0
1
0
1
0
0
0
1
0
0
0
1
3
2
0
2
1
0
0
1
1
0
1
0
2
0
0
0
0
0
1
0
0
2
1
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
3
0
1
0
0
2
0
0
2
1
0
0
2
0
0
0
2
1
0
1
0
0
0
0
0
1
0
0
0
2
1
2
0
0
0
0
1
0
0
1
0
0
1
1
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
2
2
0
0
2
0
0
1
0
0
0
2
1
0
0
0
1
1
2
0
0
2
0
0
0
0
1
0
0
0
3
1
0
2
1
0
1
0
0
2
1
1
1
0
2
1
0
0
0
0
1
2
2
1
1
3
0
0
1
0
1
1
0
1
0
2
0
0
3
3
0
0
0
0
1
0
0
0
0
1
0
0
0
1
2
1
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
2
2
0
1
1
0
1
0
0
0
0
0
3
0
0
1
0
0
2
2
0
0
1
1
2
0
2
1
2
4
0
0
0
2
1
0
2
0
0
0
0
0
0
2
1
2
1
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
1
1
1
0
0
0
0
0
0
0
2
1
0
0
0
2
0
1
0
2
2
0
2
2
0
2
0
1
2
0
0
1
0
2
0
1
0
2
0
0
0
2
1
0
1
0
0
2
0
0
0
0
0
1
1
1
0
0
0
0
1
2
2
2
0
1
0
0
0
0
1
0
2
1
1
0
2
2
1
1
0
1
0
1
2
0
1
1
1
2
0
1
1
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
3
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
1
0
1
0
2
0
0
0
0
0
2
0
0
1
2
0
0
1
0
2
0
1
0
0
0
0
2
0
1
0
2
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
1
1
0
0
0
1
2
0
0
1
0
0
0
1
1
0
1
3
0
1
1
0
0
0
2
1
1
2
0
0
0
1
0
0
0
0
2
0
0
3
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
2
1
3
0
2
0
1
0
1
1
0
0
2
2
2
3
1
0
2
0
1
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
2
1
1
0
1
2
0
1
0
2
0
0
0
2
0
0
0
0
8
2
2
0
0
0
2
2
1
0
1
2
2
0
2
1
0
1
1
0
2
0
0
0
1
1
0
2
0
0
0
0
0
0
1
2
1
0
0
1
2
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
1
0
0
1
1
1
2
2
0
0
0
2
2
1
2
0
0
0
1
1
1
0
2
2
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
1
0
1
2
1
0
3
2
2
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
1
0
2
0
2
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
2
0
1
0
1
2
0
0
0
0
2
1
0
0
0
0
2
0
0
2
0
0
3
1
0
2
0
0
0
0
0
2
2
1
0
1
1
2
0
2
1
1
1
1
0
6
0
0
1
0
0
1
0
1
1
0
2
3
0
1
0
1
0
1
1
0
1
2
2
0
0
1
0
0
2
0
1
0
1
1
0
2
1
0
1
0
0
1
0
1
1
0
2
0
0
2
2
4
0
1
0
0
0
0
0
0
1
2
0
2
0
0
0
1
2
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
1
2
1
0
0
0
0
0
1
1
0
1
1
0
0
0
0
2
2
0
1
0
1
1
0
1
0
0
0
1
0
3
0
2
1
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
1
3
0
1
2
3
0
0
2
0
1
1
0
0
0
0
2
0
0
0
0
1
2
1
0
2
2
1
0
0
1
2
1
0
0
0
0
1
2
1
1
2
0
0
0
2
2
0
0
2
2
0
0
2
0
1
0
0
0
1
1
1
0
0
1
0
2
0
3
1
0
1
0
2
0
2
0
0
0
0
0
1
2
0
0
0
2
2
2
0
0
0
0
1
0
1
0
0
0
2
2
0
1
2
1
1
0
0
2
1
0
0
0
0
2
1
2
0
0
0
1
0
2
0
0
1
0
0
0
0
0
3
2
4
1
2
1
0
0
1
0
2
1
0
1
0
2
0
2
0
0
3
1
0
0
0
1
0
1
0
2
2
1
1
0
2
1
0
0
2
2
1
0
0
0
0
0
0
4
0
1
0
0
1
1
1
2
0
1
2
0
2
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
2
0
0
2
0
1
0
2
1
0
2
1
1
0
0
1
1
0
2
0
1
2
0
0
1
1
0
1
0
1
0
0
0
1
3
2
0
2
0
2
0
1
1
1
0
1
0
2
2
0
1
1
0
2
0
2
2
2
0
1
1
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
2
1
0
1
2
0
0
0
2
2
0
0
0
2
1
1
0
0
2
0
0
2
1
0
1
0
2
0
0
3
0
0
0
1
0
3
2
0
0
0
1
0
2
0
2
0
0
0
0
0
0
1
0
0
0
2
0
2
0
2
5
2
0
0
0
0
1
0
0
0
0
0
1
0
1
0
2
0
0
0
1
0
0
0
0
0
0
2
3
0
1
2
1
0
3
1
0
0
0
2
0
1
1
0
0
2
1
0
0
0
0
1
0
0
0
1
1
0
2
1
2
0
0
2
0
1
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
2
0
1
2
2
1
0
2
0
0
2
2
0
2
1
0
2
0
1
0
0
1
0
1
0
1
0
0
0
0
0
1
1
0
0
0
2
0
3
2
0
2
0
2
0
2
0
6
0
1
0
0
2
1
0
2
0
0
0
0
0
0
2
2
0
1
0
0
0
0
2
1
2
0
1
0
2
3
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
2
0
2
1
0
0
0
1
0
0
1
1
0
1
0
0
1
0
0
2
0
2
0
0
0
0
2
0
0
0
1
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
8
1
0
0
0
2
2
1
0
0
0
0
2
1
0
0
0
0
2
0
0
0
2
0
2
1
0
2
0
0
1
1
3
1
2
0
1
2
0
0
0
0
2
0
2
1
0
0
0
2
0
1
0
1
0
1
0
1
1
2
1
1
0
0
0
0
0
1
2
0
1
1
2
0
6
0
0
0
0
2
0
0
0
0
0
1
0
1
1
0
1
0
0
1
0
0
0
2
1
0
3
0
0
0
1
1
0
2
0
0
2
0
1
2
1
0
1
2
0
0
0
0
1
2
0
1
0
0
0
1
1
0
2
0
0
2
0
0
2
0
0
2
0
2
0
1
0
0
0
0
0
1
0
1
5
0
0
0
0
0
0
1
0
1
0
2
0
2
0
2
2
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
1
3
0
0
0
0
0
0
2
0
1
0
2
0
1
0
1
1
0
1
2
0
2
0
0
0
1
0
0
2
0
0
2
2
0
1
2
0
0
0
0
0
1
0
2
1
0
0
0
1
0
1
2
2
0
0
0
1
1
0
1
0
1
0
2
0
0
1
2
2
1
2
0
2
0
0
0
0
0
0
2
2
1
2
0
1
1
1
4
0
0
0
0
1
2
0
0
0
0
2
2
2
0
1
2
2
0
0
2
0
0
0
0
0
2
0
0
0
1
1
1
2
0
0
2
2
1
1
0
0
0
1
0
1
1
1
0
0
1
2
2
0
0
0
0
0
2
2
0
1
1
0
0
0
1
0
1
1
2
0
0
0
0
1
0
0
0
0
0
2
1
4
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
7
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
2
2
0
2
0
0
1
0
0
0
0
1
2
1
0
0
1
0
0
0
0
1
0
1
0
0
1
0
2
1
0
1
1
0
1
0
1
1
0
0
0
0
0
1
2
0
1
0
2
0
0
1
0
3
0
2
1
2
0
0
0
2
0
0
1
0
0
0
0
2
5
0
0
0
1
1
0
1
0
0
0
0
1
1
1
1
1
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
1
0
3
0
0
2
0
1
2
0
0
0
1
1
1
2
1
0
0
1
0
2
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
1
1
2
0
0
2
1
1
2
1
2
0
0
1
2
3
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
2
0
0
0
2
0
1
2
0
0
0
1
0
2
0
0
0
1
2
0
2
1
0
1
0
0
1
0
2
1
0
0
1
1
1
0
0
0
0
0
4
2
2
0
1
0
0
2
1
1
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
2
1
2
4
0
0
0
0
1
0
0
2
0
0
0
0
2
0
3
0
0
0
1
2
5
2
0
0
0
0
1
2
2
1
1
1
1
0
0
0
0
1
0
1
1
1
1
2
1
0
2
2
0
0
0
0
0
0
1
1
2
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
2
0
0
0
1
2
1
0
0
6
0
1
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
2
1
0
1
2
0
0
0
0
2
2
0
0
0
0
0
0
1
0
1
0
0
3
1
0
1
2
0
0
2
2
0
0
0
1
0
0
0
0
0
1
2
1
1
0
0
2
0
0
2
2
1
1
0
0
0
0
1
0
0
0
0
1
4
0
1
2
0
0
0
0
1
0
0
2
2
1
0
0
1
0
2
2
0
0
0
0
0
1
0
0
1
0
2
0
0
0
1
1
3
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
2
0
0
1
0
0
1
0
2
0
0
2
2
0
2
0
0
0
1
2
0
1
0
0
2
2
2
0
0
0
0
1
0
2
0
0
1
1
0
3
0
0
2
2
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
1
1
0
1
2
0
0
0
0
0
0
0
0
2
2
0
1
0
2
0
1
0
0
1
0
1
1
2
0
2
0
0
0
1
4
1
2
2
0
0
0
0
1
2
0
0
0
2
1
0
2
0
1
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
2
0
0
0
1
0
2
0
1
1
1
0
1
2
1
2
0
1
0
0
0
0
1
0
1
0
0
1
1
0
0
0
1
0
0
2
0
0
0
0
0
2
1
1
1
0
0
0
2
0
0
2
0
0
2
0
1
0
0
0
0
1
2
0
0
0
0
2
2
2
0
2
0
2
0
0
0
0
1
0
2
0
0
0
1
0
1
0
2
0
2
0
0
0
0
1
0
1
1
0
2
0
0
0
0
0
0
0
2
0
0
2
1
2
0
0
1
0
2
1
1
2
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
2
0
2
0
0
2
1
1
0
0
0
0
0
0
0
0
2
2
2
0
0
2
1
0
0
0
0
1
0
0
0
1
0
0
0
2
0
2
1
0
2
0
0
0
2
0
2
0
2
2
0
0
0
0
2
0
0
0
3
2
2
0
1
2
0
0
0
1
2
0
0
0
1
1
0
0
0
1
0
2
0
2
2
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
2
0
0
2
1
0
3
0
1
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
2
1
0
0
0
1
2
0
0
0
2
2
0
0
1
1
1
2
0
2
1
3
2
1
2
0
1
0
0
1
0
0
0
0
0
0
2
0
1
0
0
2
0
1
0
1
2
0
1
0
1
1
0
1
1
0
2
0
0
2
1
0
0
0
0
0
2
0
2
0
1
2
1
0
0
2
0
0
0
2
0
0
1
2
2
0
0
3
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
1
0
0
0
2
0
1
0
0
0
3
0
0
0
2
1
0
0
0
0
0
0
1
2
3
0
2
3
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
1
2
1
2
1
0
0
2
2
0
0
0
0
0
0
1
1
0
0
1
0
1
2
0
0
0
0
2
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
1
3
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
2
1
0
0
2
0
1
2
1
0
0
1
0
0
1
1
0
0
1
0
0
2
1
0
1
0
2
0
2
0
2
5
2
1
0
0
0
0
0
0
1
0
0
0
2
0
1
2
0
2
0
0
0
1
1
1
2
0
2
2
0
0
0
2
1
1
1
2
0
0
2
1
0
0
1
2
0
2
1
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
4
0
2
0
0
1
2
1
0
1
0
2
2
2
0
0
0
2
2
0
0
0
1
2
0
1
1
0
0
1
1
0
1
0
0
1
2
2
2
0
0
0
2
1
0
0
1
0
0
1
0
1
0
0
1
0
2
0
1
1
0
0
0
0
2
0
0
1
0
0
1
0
2
1
1
1
0
1
1
0
1
1
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
1
0
0
2
0
0
0
1
2
0
0
0
1
2
1
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
2
0
1
0
2
0
0
0
6
0
0
2
0
4
0
2
1
1
0
2
0
0
0
1
0
1
0
2
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
2
1
1
0
1
1
0
2
0
1
0
1
0
0
1
0
0
1
2
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
2
0
2
0
0
1
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
1
1
0
1
1
2
2
1
0
1
2
0
0
1
0
0
0
0
0
3
2
1
0
0
2
2
0
0
2
0
0
0
0
1
2
0
1
0
0
0
0
0
0
1
2
2
0
1
5
1
0
0
2
3
1
0
2
3
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
2
0
2
0
0
0
0
0
0
2
1
0
0
1
1
1
0
2
0
0
2
0
0
0
0
0
0
1
1
1
0
0
0
2
1
2
0
0
0
0
1
2
0
1
2
0
4
1
0
2
0
0
1
1
2
0
2
2
0
3
0
0
0
0
2
0
0
3
2
0
0
0
0
1
0
0
1
0
0
1
1
2
0
1
1
1
0
0
1
1
0
0
1
1
0
0
0
2
0
0
2
2
2
3
0
1
2
0
2
0
1
2
2
0
0
0
0
0
2
2
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
2
1
1
0
0
1
1
2
0
0
0
0
0
0
1
1
2
1
0
1
2
2
2
1
0
3
0
0
0
1
0
1
0
1
0
0
0
0
0
3
1
0
0
1
1
0
0
1
0
1
2
1
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
1
0
0
1
2
1
0
2
0
0
0
2
0
0
0
0
1
0
0
2
0
1
2
2
0
0
0
2
3
1
0
1
2
1
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
1
0
1
0
0
2
2
1
0
3
2
1
2
1
0
0
2
2
0
0
0
0
0
1
1
1
0
2
0
1
1
2
1
2
2
0
1
2
2
0
0
2
0
0
1
2
0
2
0
0
1
3
1
0
0
2
1
0
2
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
1
0
0
2
2
0
1
1
0
2
0
0
0
0
1
1
2
0
1
0
0
0
0
0
2
0
2
0
0
2
0
0
2
0
0
1
1
2
1
0
2
2
0
0
0
0
0
0
0
0
0
1
0
1
2
2
1
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
4
2
0
1
1
0
0
0
0
0
0
1
2
2
1
1
0
0
2
0
2
0
0
0
0
2
0
0
0
1
0
0
1
0
2
1
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
1
1
1
1
0
0
0
0
0
1
0
1
0
0
1
0
0
3
2
0
1
0
1
0
0
0
2
0
2
0
1
0
0
1
1
2
1
2
2
0
0
0
2
0
0
1
2
0
0
0
2
0
2
1
1
2
0
0
0
0
1
2
0
0
2
1
3
0
0
0
2
1
0
0
2
1
0
1
0
1
0
2
2
0
1
1
3
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
2
2
2
1
0
2
0
1
0
2
0
1
2
0
2
0
0
2
0
2
0
1
0
2
2
2
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
5
0
1
1
2
0
0
2
1
2
0
0
0
1
3
0
2
2
0
0
0
2
0
2
1
0
0
1
2
0
1
0
0
0
0
1
0
0
0
2
2
0
0
0
0
2
1
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
1
1
0
0
0
1
0
0
0
1
2
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
1
1
2
0
0
0
1
2
1
1
0
1
1
1
2
2
0
0
0
2
1
0
1
0
1
2
0
1
1
2
0
0
0
2
2
1
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
2
0
2
1
2
0
0
1
3
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
2
0
0
0
0
2
2
0
2
0
0
0
0
1
1
0
0
1
0
0
1
2
2
0
0
2
0
1
0
1
0
0
0
0
1
1
0
1
0
0
0
2
1
0
1
0
1
0
0
0
2
0
0
0
0
1
0
0
0
1
1
2
0
0
0
0
0
0
0
0
2
1
0
0
1
0
1
0
1
0
0
0
2
0
2
2
0
0
0
0
1
2
0
0
0
1
1
0
0
0
2
1
0
0
1
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
2
2
1
2
1
1
2
0
2
1
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
3
0
2
0
2
0
0
0
1
0
0
0
1
0
2
0
0
1
1
1
2
1
0
1
0
0
1
2
0
0
0
2
2
1
1
0
1
0
1
0
2
0
1
1
1
0
0
0
2
2
2
3
1
1
0
0
0
4
0
3
0
0
2
0
0
0
1
1
1
2
0
1
0
1
2
1
2
2
0
0
0
2
2
2
1
1
0
0
3
2
0
0
0
0
0
1
2
1
0
0
0
2
1
0
0
1
2
3
0
2
0
2
0
1
0
0
1
1
0
0
2
2
0
2
1
0
2
0
1
2
1
2
0
1
0
0
1
0
0
1
0
2
1
2
0
0
0
0
0
2
0
3
2
1
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
1
0
2
0
2
0
1
1
0
2
0
0
0
2
0
1
0
1
2
1
0
0
0
1
1
0
0
1
0
0
2
0
2
2
0
1
2
1
1
0
2
1
1
2
0
1
0
0
0
0
2
0
2
0
0
0
0
2
0
0
2
0
1
2
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
2
0
1
1
2
4
0
0
1
2
1
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
2
0
1
3
1
1
1
1
0
2
0
2
2
0
1
0
0
0
2
3
2
0
0
0
0
1
1
0
0
2
0
0
0
1
0
0
2
1
2
0
0
2
0
0
2
1
0
1
2
0
1
0
2
1
0
1
1
0
2
2
2
0
1
0
0
1
2
1
2
2
0
0
0
0
0
2
0
0
0
2
0
0
1
2
2
0
1
1
0
0
2
0
1
0
0
2
0
1
0
1
0
1
0
0
0
0
0
0
0
1
2
3
0
2
2
0
0
0
0
0
0
2
1
2
2
0
0
2
0
2
1
0
0
0
0
1
1
0
0
0
1
0
6
0
0
2
0
1
1
1
0
1
1
0
2
0
0
3
0
0
2
0
0
0
0
2
2
0
2
2
1
0
0
1
0
0
1
0
2
0
0
1
0
1
0
2
0
0
0
1
2
0
0
1
0
0
0
1
0
9
1
3
0
0
0
2
2
0
0
0
1
2
2
0
2
1
1
0
1
1
1
0
0
0
1
0
0
0
2
0
2
2
0
0
0
0
2
3
0
1
0
0
0
0
2
2
0
0
0
1
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
3
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
1
0
1
0
1
0
2
1
0
0
0
0
0
0
1
0
1
0
2
0
0
0
2
0
1
2
2
0
0
2
0
0
0
1
0
0
1
0
0
0
1
2
0
0
1
0
0
3
0
0
0
0
1
1
0
2
0
0
1
2
1
1
0
0
0
0
2
0
0
1
1
0
0
0
3
0
1
0
0
0
1
2
0
3
0
2
0
0
1
0
0
2
1
0
0
1
0
1
1
1
0
2
0
1
0
2
0
0
0
0
0
0
0
2
0
2
0
1
1
0
0
2
0
0
0
1
2
0
2
2
1
1
0
0
0
0
0
2
0
0
0
2
0
3
0
1
2
0
2
0
0
0
0
0
2
1
1
2
1
0
0
0
0
1
3
0
1
1
0
0
1
1
0
2
0
0
2
0
0
2
0
0
0
0
1
0
0
0
1
1
2
0
0
1
0
1
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
1
0
1
2
0
1
0
0
0
1
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
2
0
0
2
1
1
1
1
0
2
1
1
0
3
0
1
3
2
2
0
1
0
2
2
0
0
3
1
1
0
0
0
1
0
0
1
1
0
0
1
1
0
0
1
0
0
0
1
0
0
0
2
0
0
1
0
0
1
1
1
2
2
0
0
0
1
0
2
1
2
1
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
2
2
0
0
0
0
0
1
0
2
1
0
0
3
0
0
1
1
0
0
1
0
2
1
1
0
1
1
3
1
0
1
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
1
1
0
2
1
1
0
0
2
2
1
2
0
0
2
0
2
0
1
1
2
1
0
1
2
0
0
0
0
4
2
1
1
0
1
1
2
2
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
2
0
2
0
2
2
0
0
2
0
0
0
0
0
3
0
0
0
2
1
2
1
2
1
0
0
1
0
0
1
0
2
0
0
0
1
3
0
2
0
0
0
0
0
1
0
0
3
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
2
0
2
0
0
0
0
1
0
1
0
0
2
0
1
1
0
1
0
2
0
0
0
2
2
0
1
0
0
0
0
0
0
3
0
0
0
2
1
0
0
2
1
0
0
1
0
0
2
2
1
1
0
0
0
2
0
0
0
0
0
2
0
0
3
0
0
0
0
3
0
0
0
1
0
2
0
1
0
0
1
0
0
2
1
0
2
0
0
0
0
0
3
2
1
0
1
0
0
0
0
0
1
2
2
2
1
2
0
1
1
0
0
1
1
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
3
0
0
1
1
0
1
2
0
2
1
0
0
0
0
0
1
1
1
0
2
1
0
1
0
0
0
0
1
0
1
0
1
0
0
2
0
4
2
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
5
1
0
1
0
0
0
1
2
2
1
1
0
1
0
0
0
3
0
2
2
0
0
2
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
1
0
0
2
0
0
0
0
0
0
2
2
0
0
2
0
0
1
0
2
0
0
0
0
1
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
2
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
1
0
2
2
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
1
0
1
1
1
0
2
1
0
1
0
0
2
0
0
1
0
0
2
1
2
1
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
2
2
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
2
0
0
0
2
0
1
0
1
1
1
0
0
0
0
2
0
0
0
2
0
1
2
0
3
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
1
0
0
1
1
1
0
0
1
2
0
1
0
0
2
0
0
1
0
2
1
0
0
2
0
2
2
0
2
0
0
0
1
0
0
0
2
0
1
0
0
0
1
1
0
0
1
0
1
1
1
1
1
0
1
0
2
0
0
0
0
0
2
2
0
0
0
3
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
1
1
0
1
2
0
0
1
2
0
0
0
1
0
0
1
0
0
5
0
0
0
0
2
1
0
0
0
2
0
0
0
1
0
1
1
0
0
0
0
1
0
0
1
0
2
1
0
0
1
2
2
0
0
0
0
0
0
2
0
1
0
0
2
1
1
0
0
0
0
0
2
2
0
0
1
1
0
0
0
1
0
0
0
1
0
2
5
1
0
0
1
1
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
2
1
0
3
1
0
0
0
2
0
1
0
0
1
0
0
2
1
0
1
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
1
0
0
1
1
3
1
1
0
0
0
0
2
0
1
0
0
2
0
2
0
0
1
1
0
0
0
2
1
0
0
1
1
0
1
0
0
2
0
0
1
0
0
0
1
1
2
0
0
2
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
4
1
2
0
1
2
0
1
2
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
1
0
1
2
0
0
0
2
2
1
0
0
0
0
1
0
0
0
0
0
0
4
2
0
0
4
1
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
2
0
0
2
0
2
2
2
0
0
1
0
0
0
2
0
2
2
0
0
0
0
2
1
0
2
1
1
0
0
2
1
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
2
1
2
0
0
1
0
0
0
0
1
1
2
0
0
1
0
1
0
0
0
1
7
1
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
1
1
1
2
2
2
2
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
2
1
1
0
0
0
2
2
0
2
1
2
2
2
1
0
0
0
0
2
1
2
0
0
0
0
1
1
2
0
1
0
0
2
0
0
0
0
0
3
1
0
4
1
0
0
0
1
0
1
0
2
0
1
2
1
1
0
2
0
2
0
0
2
0
0
2
0
0
2
2
2
2
1
0
0
1
0
1
2
0
1
2
0
0
2
1
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
2
0
0
1
0
0
1
0
0
0
2
0
0
2
2
3
1
1
0
0
0
0
0
2
2
0
2
2
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
1
2
2
0
0
2
0
0
0
1
2
0
0
0
0
1
0
2
0
0
1
2
1
1
0
0
2
0
2
0
1
0
1
2
1
0
0
2
1
0
1
1
0
0
0
2
0
1
2
0
0
0
1
1
1
1
0
0
1
0
1
0
1
4
0
0
2
2
0
0
1
0
0
3
0
0
1
2
0
1
0
0
2
0
0
0
0
0
0
0
1
1
2
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
2
0
0
1
2
1
0
2
0
0
1
2
0
0
4
0
0
1
1
0
0
0
0
0
1
1
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
2
0
0
2
1
0
1
2
0
0
2
0
0
1
0
1
0
1
0
0
1
0
0
1
1
0
0
1
1
0
0
0
1
2
0
2
2
1
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
1
0
0
0
1
2
2
0
1
0
1
0
0
0
1
2
0
0
0
1
1
0
1
2
0
1
0
4
1
0
0
1
0
1
1
0
2
0
1
2
1
1
0
0
0
1
2
0
0
1
0
3
0
2
0
1
0
0
2
1
0
2
3
0
0
2
0
1
0
0
0
0
2
2
0
0
1
1
2
1
1
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
4
0
2
2
1
0
0
0
2
0
1
0
6
0
1
0
1
0
3
0
0
0
2
2
0
1
0
0
4
0
0
2
0
0
0
0
0
1
1
1
1
1
0
0
0
1
0
0
0
1
2
1
0
0
2
0
0
0
2
0
1
0
1
0
0
0
1
0
0
2
0
1
2
2
1
2
0
0
0
1
1
0
2
0
2
2
0
1
1
0
0
0
0
0
1
1
1
0
0
0
0
0
2
0
0
0
0
1
2
2
2
0
0
2
3
0
0
1
0
0
0
1
2
2
1
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
2
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
1
1
1
0
2
0
0
0
2
0
2
2
2
0
1
2
0
0
0
2
0
0
0
0
0
0
2
0
1
0
2
0
1
0
0
1
0
0
1
2
0
1
2
0
0
0
0
0
0
1
2
0
1
0
2
0
0
1
2
0
1
0
0
0
0
2
0
0
2
0
0
2
2
0
0
0
2
0
0
0
0
0
1
0
2
2
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
2
2
0
2
2
0
2
0
0
0
2
0
0
0
2
0
0
1
0
0
0
1
0
1
2
1
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
3
2
1
2
0
0
1
0
1
1
0
2
0
2
1
0
0
0
1
1
0
0
2
1
0
1
2
2
0
1
2
0
2
0
1
0
2
2
0
1
0
1
0
1
1
3
2
2
0
0
0
0
0
3
0
0
0
2
0
2
2
0
2
0
0
0
0
0
0
0
0
1
0
0
3
2
0
1
0
0
0
1
2
0
0
0
0
1
0
0
2
2
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
1
0
0
2
0
1
2
0
0
0
1
2
1
3
0
0
0
3
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
1
0
2
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
2
1
0
2
0
0
2
1
0
0
1
2
1
1
0
0
0
0
2
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
1
1
0
1
0
1
1
1
1
0
2
2
0
0
0
0
2
0
0
0
0
0
2
0
2
0
2
0
1
0
1
2
1
0
0
0
2
0
0
0
0
1
0
1
2
2
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
2
2
0
2
0
0
0
0
1
0
2
1
2
0
0
2
0
0
0
0
0
0
2
0
1
1
0
0
1
0
1
0
0
3
2
0
0
1
2
0
0
0
2
0
1
0
0
0
0
1
0
1
0
0
1
1
0
0
0
1
1
0
1
0
0
0
0
1
1
2
0
0
2
0
2
2
1
1
0
0
1
3
1
0
0
0
0
0
0
0
0
4
2
2
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
2
1
1
1
0
0
0
0
2
2
0
2
0
0
2
0
2
0
0
2
0
1
0
1
1
1
0
0
0
2
0
0
1
0
0
2
1
0
1
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
1
1
2
0
0
0
0
0
2
1
1
1
0
0
0
2
2
0
0
0
0
0
0
0
2
1
1
0
0
1
2
1
1
2
0
0
0
0
2
1
0
0
0
1
0
1
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
1
0
0
1
2
0
1
1
0
0
1
2
0
0
0
0
1
2
0
1
0
0
0
1
0
5
0
1
0
1
1
0
0
0
0
1
0
0
0
0
1
0
1
2
1
1
0
0
0
0
1
0
1
0
1
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
1
1
0
0
1
1
0
2
2
0
2
0
0
0
0
0
0
1
0
0
2
0
1
0
1
1
1
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
3
1
0
0
2
0
0
2
0
0
0
1
1
0
2
0
0
0
1
0
2
0
1
2
0
0
0
0
0
0
2
0
0
0
0
1
0
3
0
0
0
0
2
2
1
0
0
2
2
2
2
0
0
0
1
0
3
0
0
0
0
0
1
0
1
0
1
0
1
0
0
1
1
2
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
1
0
0
1
0
2
0
1
1
0
1
0
0
0
2
0
0
2
0
0
2
2
0
1
0
0
3
0
1
0
2
0
1
2
1
0
2
1
0
1
0
0
1
0
1
0
0
1
0
1
2
1
0
0
1
0
0
1
0
0
1
0
0
1
0
0
1
0
0
2
0
1
0
1
0
0
0
0
0
0
0
2
1
1
0
2
2
1
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
2
0
1
0
1
0
1
0
0
1
3
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
1
0
0
0
1
2
0
0
1
0
0
1
0
0
0
0
0
0
0
3
0
1
0
0
1
0
0
0
2
0
1
0
0
2
0
1
1
0
0
1
1
1
0
0
0
0
0
0
2
2
0
0
1
1
1
0
0
0
0
0
0
0
1
4
0
2
1
1
2
0
0
1
0
2
3
1
0
0
1
2
0
1
0
0
0
2
0
2
0
0
0
2
2
0
0
0
2
0
1
0
0
0
2
1
1
0
0
0
0
0
0
3
2
0
2
2
0
2
1
0
1
0
2
1
1
1
2
0
0
0
0
0
1
2
0
0
0
0
0
1
1
2
0
1
0
0
0
1
0
2
0
0
0
0
1
2
0
0
0
0
1
2
0
1
2
0
3
0
1
2
1
0
0
2
1
0
2
0
0
0
0
0
0
0
1
1
2
2
0
1
0
1
0
0
2
2
1
2
1
1
0
0
2
0
0
0
1
0
1
0
0
1
2
1
0
2
0
0
0
0
0
0
0
2
1
1
0
0
0
0
2
2
0
2
0
0
1
2
0
2
0
4
0
0
0
2
1
0
0
0
1
0
1
0
0
1
1
0
0
0
2
2
0
0
0
0
0
2
1
0
0
0
0
0
1
2
2
0
1
0
0
0
0
0
2
2
0
0
0
1
2
1
0
0
0
0
0
1
0
0
1
0
0
2
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
3
0
0
1
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
1
0
2
1
0
0
0
1
0
0
0
2
0
2
0
1
0
0
0
3
0
2
1
1
1
1
0
1
0
2
0
1
1
2
1
0
0
0
1
0
0
0
2
2
2
0
3
0
0
1
0
0
1
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
2
1
3
0
1
0
0
0
0
3
1
0
1
2
2
1
2
0
0
0
2
1
1
2
1
2
2
1
0
0
0
1
2
1
0
0
0
2
3
0
3
0
1
0
0
1
1
0
1
0
0
0
0
1
0
0
0
2
0
1
1
0
1
0
3
2
2
0
0
2
0
2
3
1
0
2
0
1
2
2
2
1
2
3
0
1
0
0
0
1
1
2
0
0
1
0
1
0
2
0
0
1
2
1
1
0
0
0
1
0
2
0
2
0
0
1
0
0
0
2
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
1
1
1
0
0
0
2
0
0
1
0
1
0
1
0
0
1
1
0
0
2
2
2
2
0
3
2
0
3
1
1
1
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
2
0
1
2
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
5
0
1
1
0
1
1
1
0
0
0
3
1
0
0
1
0
0
0
0
0
2
0
0
0
0
2
1
1
0
0
1
1
2
1
1
0
0
0
0
2
0
0
2
0
0
2
0
3
0
0
1
2
0
0
1
2
0
2
1
0
1
1
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
1
0
2
2
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
1
0
0
0
2
0
1
1
2
0
0
0
0
0
4
1
0
3
2
1
1
2
0
0
1
2
0
1
2
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
1
0
0
0
2
0
0
1
0
0
0
0
1
1
0
0
1
0
2
0
0
1
0
0
0
2
2
0
0
0
0
0
0
1
1
0
2
1
0
1
3
2
0
2
1
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
1
0
0
0
1
0
0
0
2
0
1
2
1
0
0
0
0
0
0
0
1
0
1
0
2
0
2
2
2
1
0
0
0
2
1
0
0
0
0
0
1
2
0
0
1
1
2
2
0
2
2
0
0
1
0
0
2
0
1
0
3
0
0
1
0
0
0
0
1
0
1
1
1
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
2
0
0
0
0
0
1
1
0
1
0
0
2
0
0
1
2
0
0
1
1
2
1
1
1
0
2
1
1
0
0
3
0
1
0
1
1
0
0
2
1
0
0
0
0
0
0
1
0
2
2
2
1
1
0
0
0
1
0
2
0
1
0
2
0
0
1
0
0
0
0
2
2
0
2
0
0
0
0
0
1
0
0
0
2
0
0
2
0
2
2
1
1
0
1
0
0
1
0
1
0
1
2
0
0
0
0
0
1
1
1
0
0
0
0
1
0
1
1
0
1
3
0
2
0
0
0
0
2
0
2
1
1
2
2
0
1
2
0
0
1
0
2
0
0
1
2
1
0
0
2
2
2
2
2
5
0
1
0
0
0
0
0
0
1
0
0
2
0
1
1
0
2
1
0
0
0
2
0
0
1
0
1
1
2
1
0
2
0
0
0
0
0
0
0
2
0
1
0
2
0
1
2
0
0
0
0
0
2
0
0
2
0
1
0
2
1
1
0
0
7
0
1
6
0
0
0
1
0
0
0
1
0
1
1
0
0
2
0
0
3
0
1
0
0
0
0
0
1
0
2
0
2
0
0
0
2
0
2
0
0
0
1
0
0
1
2
0
1
0
1
0
0
0
2
0
0
7
0
0
0
0
1
0
1
0
2
0
2
0
0
4
0
3
1
0
0
0
0
0
2
0
0
0
3
0
0
0
0
2
1
1
0
4
0
2
0
0
1
1
0
1
2
0
2
0
2
1
2
0
0
2
0
2
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
2
0
1
0
1
0
1
0
1
0
1
2
2
0
0
0
2
0
1
0
0
1
0
0
0
0
0
1
2
0
0
2
0
0
3
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
2
0
2
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
2
2
1
1
0
1
0
0
2
2
0
0
1
1
5
1
1
1
0
0
2
0
0
0
1
0
0
0
2
0
0
2
1
2
1
2
1
2
1
0
2
1
3
0
2
0
0
1
0
2
0
0
2
1
0
0
1
0
1
0
1
2
0
0
0
2
0
2
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
2
0
0
0
2
0
1
1
0
0
2
0
0
1
2
0
0
2
1
0
0
2
2
0
0
1
0
0
2
0
0
0
0
1
2
2
2
0
1
2
1
2
0
0
0
2
0
0
2
1
0
1
0
0
0
1
0
1
0
2
2
0
2
3
0
0
0
2
1
2
0
1
0
2
2
0
1
0
2
0
0
0
0
0
0
1
1
2
0
0
3
0
1
2
0
0
0
1
2
0
2
3
0
2
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
3
0
1
0
0
1
1
0
0
0
0
1
1
0
0
0
0
2
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
1
1
0
0
1
1
2
2
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
2
0
1
1
0
1
0
0
2
0
0
2
0
1
1
2
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
2
1
0
1
2
2
0
0
0
0
0
2
0
1
2
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
2
1
1
0
1
2
2
0
0
1
0
1
0
2
1
2
1
0
0
1
1
0
0
1
0
1
2
1
0
2
0
1
1
2
0
0
2
1
1
2
0
0
0
0
1
0
0
0
1
0
3
0
0
1
0
0
2
0
1
0
0
2
0
1
1
1
1
2
0
0
1
0
2
2
0
0
0
1
0
1
0
0
0
1
0
0
1
0
1
0
0
0
3
0
0
1
2
1
2
1
0
2
1
2
0
2
1
0
0
1
0
0
1
0
0
1
1
0
0
2
0
1
1
1
1
2
1
0
1
0
1
2
0
0
0
0
1
2
0
1
0
0
0
0
0
0
1
4
0
0
1
0
1
0
0
0
2
1
2
2
2
0
0
2
1
0
0
1
0
0
1
0
2
0
1
0
0
1
0
0
2
0
2
2
1
0
0
0
2
1
1
1
1
0
0
0
1
0
1
2
0
1
0
0
0
0
2
3
1
1
0
0
1
2
0
1
3
2
1
1
2
0
1
1
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
2
2
0
3
0
0
2
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
2
0
0
0
1
2
2
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
2
1
0
0
0
0
1
0
0
2
0
0
1
1
0
0
1
0
2
1
2
1
0
0
0
0
2
0
1
1
0
2
2
0
0
0
0
0
0
0
0
1
0
0
3
1
0
0
0
1
5
0
0
1
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
1
0
0
2
2
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
2
4
0
2
2
0
0
0
1
1
1
0
0
1
0
2
1
2
1
1
0
0
0
0
0
2
2
2
0
0
2
3
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
1
0
1
0
2
0
3
1
1
2
0
0
1
0
0
1
0
1
1
0
0
0
1
1
0
0
1
2
0
0
0
0
0
1
1
0
2
0
2
0
0
0
0
0
2
1
0
0
2
0
2
0
1
0
1
0
0
0
2
1
0
0
0
0
2
0
1
1
0
3
2
0
1
1
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
2
0
0
0
0
1
0
0
3
0
1
0
3
0
0
0
2
0
0
0
1
0
0
0
2
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
2
2
1
2
0
0
1
0
0
1
0
1
0
0
1
0
1
0
2
2
1
0
0
0
1
0
0
0
0
0
1
0
0
2
0
1
2
2
2
1
2
0
2
0
1
0
0
0
0
2
0
2
0
1
0
1
2
0
0
0
2
0
0
0
0
2
0
1
1
0
0
2
1
0
0
2
2
1
0
0
0
2
0
0
0
1
0
1
0
1
0
1
0
2
2
2
2
0
0
2
0
2
2
0
0
1
0
0
2
1
2
0
0
0
0
0
0
2
1
0
0
1
1
0
1
1
1
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
2
1
0
0
0
0
2
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
2
2
1
1
0
2
0
0
1
2
0
2
0
2
0
1
1
1
0
0
0
1
0
0
2
1
0
0
1
2
1
0
0
2
1
0
1
0
1
0
1
0
4
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
1
1
1
0
1
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
2
2
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
1
2
1
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
2
0
1
1
0
1
1
1
2
0
1
0
0
0
1
0
0
1
3
2
0
1
2
1
0
2
0
1
0
0
1
1
1
0
0
0
0
0
1
1
1
2
2
1
2
0
1
1
2
0
0
0
2
0
0
0
0
2
0
0
2
0
0
1
0
1
0
0
1
2
2
0
0
3
2
1
0
0
1
0
0
0
2
0
0
0
1
0
2
2
0
1
0
0
1
2
1
0
1
1
1
2
0
0
2
1
1
0
0
1
0
0
0
0
0
1
0
2
2
2
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
2
1
2
0
2
0
0
2
0
1
0
1
0
1
0
1
0
1
2
1
0
0
2
4
0
2
1
1
0
0
5
1
1
0
0
1
2
0
0
3
0
1
0
1
2
0
0
1
1
0
0
0
0
1
0
1
2
0
1
1
0
0
0
0
0
1
0
0
2
0
1
1
0
1
3
0
0
0
2
0
0
1
0
2
0
1
2
0
2
2
0
0
2
0
1
1
0
0
0
0
0
1
0
2
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
2
0
0
2
1
0
1
2
1
1
1
3
1
0
2
0
3
0
0
0
0
2
2
1
1
0
0
1
0
1
0
0
0
1
0
2
2
0
2
0
1
2
0
1
0
0
0
1
0
1
2
0
0
2
0
0
1
0
2
0
1
1
0
0
1
0
0
0
2
0
0
0
2
3
0
0
0
2
0
0
1
0
0
2
2
2
0
0
1
2
0
2
2
1
0
0
2
1
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
2
2
0
0
0
0
1
0
0
0
0
0
2
0
0
2
1
0
0
0
0
1
1
2
1
0
2
0
0
0
2
0
0
0
0
0
1
0
2
0
0
1
0
2
0
0
6
0
0
1
1
2
0
0
2
2
0
34
0
0
2
0
0
0
2
2
2
0
0
3
0
0
0
2
0
1
2
0
2
0
0
0
1
0
0
1
1
0
0
0
1
0
2
0
0
0
0
0
1
3
2
1
2
0
0
0
0
1
0
0
0
2
0
2
0
1
0
1
1
0
4
2
2
0
0
2
0
0
1
0
1
0
0
2
0
2
1
0
0
0
0
1
1
1
1
2
2
0
1
0
2
0
0
2
2
2
0
6
0
0
0
0
1
0
0
2
2
2
0
0
0
1
1
2
2
0
1
0
2
1
0
2
0
1
0
0
2
0
0
0
0
0
2
0
2
2
0
0
2
1
2
0
0
1
0
1
1
0
1
0
0
0
0
6
1
0
0
0
2
2
0
0
1
0
0
1
0
2
0
0
2
1
0
0
2
0
0
1
1
0
1
1
0
3
1
0
0
0
0
2
0
2
2
1
0
0
1
2
0
2
0
0
0
1
1
0
0
1
0
1
0
0
0
1
0
0
2
2
2
0
1
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
1
2
0
3
0
1
1
0
2
2
0
0
0
0
0
0
0
1
2
2
2
2
0
0
0
3
0
0
0
2
0
0
1
0
0
0
1
1
1
0
0
0
3
0
0
1
2
0
1
0
1
0
1
0
2
0
0
1
0
0
0
0
0
2
0
0
2
0
3
0
0
1
1
1
2
2
1
0
1
1
0
2
2
1
0
0
2
0
0
0
0
0
2
1
0
0
1
0
2
1
2
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
1
0
1
0
0
1
0
0
0
0
0
0
0
2
1
2
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
2
1
2
0
0
0
0
0
0
1
4
2
0
1
3
0
1
0
0
2
1
2
1
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
3
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
1
0
0
2
2
1
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
2
1
0
2
0
0
1
1
0
2
0
0
2
2
1
1
1
1
0
0
0
0
1
1
0
0
1
2
0
0
1
0
1
0
1
1
0
1
2
2
2
0
0
1
0
1
1
1
0
0
0
0
2
1
2
4
0
2
0
0
4
1
1
0
0
0
1
0
1
1
1
0
1
0
0
0
3
2
0
2
0
0
1
0
0
2
0
0
1
0
2
2
0
0
0
2
0
0
0
0
2
3
2
2
2
2
0
0
2
0
0
1
0
0
0
3
1
2
0
0
1
2
0
2
1
2
2
0
0
0
0
2
0
5
0
1
0
1
2
2
1
0
1
1
0
1
1
3
1
2
0
0
1
1
0
0
0
1
0
2
0
0
0
1
2
0
0
1
0
0
0
2
0
1
2
0
0
0
1
0
0
1
2
5
3
2
1
0
0
1
0
0
0
2
0
0
1
0
2
1
1
2
2
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
2
0
0
0
0
0
0
0
1
0
8
1
0
0
5
0
2
0
1
0
0
0
2
0
0
0
0
0
1
1
1
0
0
1
0
2
1
2
0
0
0
0
2
0
2
2
0
0
0
2
0
0
1
2
0
1
0
0
0
2
0
2
1
2
1
2
0
0
1
2
2
1
2
1
0
0
1
0
0
2
0
2
2
0
0
0
0
2
2
0
1
0
0
2
0
0
1
0
2
2
0
0
2
2
2
1
0
2
0
1
1
1
1
0
1
0
0
0
0
0
0
0
1
1
0
2
0
1
2
0
0
2
1
1
2
0
1
2
0
1
0
1
0
2
0
0
1
0
1
2
0
3
0
0
0
0
4
0
2
0
1
0
2
0
0
0
2
1
1
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
13
0
1
0
2
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
2
1
3
0
0
0
1
0
1
0
0
0
0
0
1
1
2
0
2
0
0
0
2
0
0
2
1
2
0
0
0
0
0
0
1
0
0
1
0
0
1
0
2
2
2
1
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
2
2
0
0
2
1
1
0
0
1
2
1
0
0
2
0
2
0
0
0
0
1
3
1
0
2
0
0
0
2
2
1
0
0
0
2
2
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
1
0
1
1
0
0
1
0
2
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
1
2
2
0
2
1
0
2
1
0
0
0
0
2
2
0
1
0
1
2
0
2
1
0
0
1
0
0
0
0
0
1
0
0
1
0
3
0
0
2
1
1
2
2
2
2
1
2
0
2
0
0
0
1
0
2
0
0
0
0
0
0
2
2
1
2
0
0
0
0
1
0
2
2
2
2
2
2
0
2
0
2
1
2
1
0
1
0
1
0
0
3
1
0
0
0
2
0
1
0
0
2
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
2
0
2
0
2
2
0
1
0
0
0
3
1
0
1
1
0
0
0
0
0
0
1
0
0
2
2
0
2
0
1
0
0
0
0
1
0
0
0
2
2
0
4
1
0
1
0
0
1
0
0
3
1
1
0
0
2
0
0
0
2
0
1
0
0
0
0
2
0
0
2
0
2
0
0
0
1
1
1
2
0
0
0
0
2
0
0
1
0
1
1
2
2
0
0
0
0
7
0
0
0
0
1
0
1
0
1
0
0
0
0
2
1
1
0
1
2
2
0
0
0
2
2
2
2
0
0
1
0
0
0
2
1
0
0
0
0
0
0
1
2
0
2
0
0
1
2
0
0
1
0
0
2
2
0
2
2
0
1
0
2
0
0
0
0
0
1
0
0
2
1
0
1
0
0
1
0
0
0
3
0
2
1
2
0
1
1
0
0
0
1
0
1
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
4
2
0
0
1
0
0
0
2
2
0
0
0
2
0
0
0
1
0
2
1
1
0
0
1
0
0
3
0
0
1
0
0
1
2
0
0
2
1
0
0
0
2
2
2
0
1
2
3
1
1
1
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
2
0
2
0
0
1
0
0
1
0
0
2
0
2
0
0
1
2
2
0
1
0
1
0
2
0
0
0
0
1
1
0
2
0
1
0
0
2
0
2
0
0
1
0
2
0
0
0
0
1
0
0
0
2
0
2
2
0
0
0
0
0
0
2
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
3
1
1
0
0
1
0
1
2
0
0
3
0
2
0
2
0
0
2
2
0
0
1
1
0
0
0
2
2
0
0
0
1
2
0
2
0
1
1
0
1
1
1
2
0
0
0
0
0
2
0
0
1
0
0
1
2
1
0
0
1
0
1
2
1
0
2
0
1
2
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
3
0
1
0
1
2
0
0
0
2
1
2
0
0
1
0
2
0
0
0
0
0
1
0
2
0
0
2
0
1
1
0
1
0
0
1
1
2
1
0
1
0
0
2
0
0
0
0
0
2
0
0
0
2
0
2
0
0
1
1
0
1
0
0
0
0
1
2
0
0
0
2
1
1
0
1
0
0
0
1
1
3
0
2
2
2
1
0
2
1
0
0
0
0
0
0
0
0
2
1
1
0
3
1
0
0
0
0
2
1
1
0
2
1
0
0
1
0
2
2
0
1
0
1
1
0
0
0
0
2
1
0
1
1
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
1
1
0
0
0
1
0
2
1
0
2
0
0
0
1
0
2
2
0
0
0
2
0
0
1
1
0
1
0
1
1
0
1
0
2
0
1
2
2
0
0
0
0
1
2
0
0
0
2
0
0
0
0
1
1
0
0
0
1
0
2
1
0
0
1
0
2
0
1
0
2
0
2
1
0
5
0
0
2
1
3
0
0
0
2
0
0
0
1
2
2
0
2
0
1
0
0
0
1
0
0
0
1
0
1
1
0
0
0
1
0
3
0
1
0
0
0
1
3
0
2
0
0
0
0
0
1
1
0
1
0
2
0
2
2
0
2
0
1
2
0
0
2
0
1
0
2
1
0
1
1
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
1
1
0
0
0
2
2
0
1
1
1
2
0
0
2
0
2
0
1
0
0
1
1
0
0
2
0
2
0
2
0
0
2
1
0
0
1
0
2
0
0
0
0
1
0
0
2
1
0
1
1
0
0
1
0
0
0
0
2
2
1
0
2
1
0
0
0
0
0
1
0
1
1
0
1
1
3
2
0
1
0
0
0
0
0
0
2
1
1
0
1
2
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
2
0
0
1
0
1
2
0
0
0
0
0
0
2
0
1
0
0
0
1
1
0
0
0
2
0
0
0
0
2
1
0
1
0
0
1
1
2
1
0
4
2
13
0
1
1
2
0
0
0
2
1
0
0
0
3
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
3
0
2
2
0
1
1
4
0
1
0
0
1
0
0
0
0
0
2
1
0
2
3
0
0
0
1
1
1
1
1
0
1
2
0
0
0
1
0
0
3
1
0
0
1
0
0
0
2
0
0
1
0
1
1
0
2
2
0
2
0
1
0
1
1
1
0
4
0
3
2
0
2
1
1
1
1
2
1
0
2
1
2
1
0
2
1
2
0
2
1
1
0
0
2
0
0
2
0
0
3
0
5
0
0
3
1
0
0
0
2
1
0
0
0
0
0
0
2
0
1
0
0
1
0
2
2
3
0
0
1
1
0
2
2
0
3
0
2
0
0
0
0
0
2
0
1
2
0
0
0
1
2
1
1
2
0
1
1
1
0
0
0
0
2
1
0
1
0
0
1
1
0
0
0
2
1
1
2
0
2
2
0
0
1
0
0
1
0
0
1
0
1
1
2
2
0
0
2
0
0
1
1
0
1
0
1
0
1
2
2
0
1
0
0
1
0
0
0
0
0
0
0
1
2
1
0
2
0
0
0
2
3
2
2
0
0
2
1
0
2
0
2
0
0
0
2
1
0
2
0
0
2
1
0
0
0
1
0
1
1
0
0
0
0
1
0
0
2
2
1
2
1
0
1
0
0
0
0
0
0
0
0
0
3
1
1
0
0
0
0
0
1
0
0
0
0
0
0
2
3
0
0
0
0
1
0
0
0
0
1
1
0
0
2
3
0
2
2
1
1
1
0
2
1
0
0
0
0
2
0
1
1
0
2
1
2
0
0
0
2
0
0
3
1
1
2
0
1
0
1
10
3
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
1
0
1
2
0
0
2
4
2
0
1
2
0
0
0
1
2
0
1
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
2
1
1
0
2
1
2
1
2
0
0
0
0
1
0
0
0
1
0
2
2
0
0
1
0
3
1
1
0
1
1
1
2
0
1
0
0
0
0
0
2
0
0
0
4
0
0
1
0
0
0
0
2
0
2
0
0
2
3
0
2
2
2
0
0
0
2
0
0
2
1
0
2
0
2
0
0
2
0
2
2
2
0
0
0
0
0
0
2
1
2
1
2
0
0
2
2
0
0
0
2
0
2
0
0
1
0
0
0
0
0
1
0
1
0
2
0
1
0
0
2
3
0
0
0
2
0
0
0
2
0
1
0
0
2
0
1
1
0
2
1
1
0
1
1
1
0
0
0
1
0
1
0
0
1
1
1
2
0
0
0
0
0
2
0
0
0
1
0
0
0
1
2
1
3
1
0
0
1
0
0
2
2
1
1
0
1
0
0
0
0
0
0
0
2
1
0
1
2
0
0
0
0
0
2
1
1
1
1
0
0
0
0
1
0
0
0
0
0
2
2
0
0
1
2
0
0
1
0
0
0
0
0
1
1
2
0
0
2
1
0
0
0
1
0
2
0
2
0
1
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
3
0
0
1
1
0
2
1
0
0
0
1
0
2
0
0
0
1
2
0
0
0
2
1
0
1
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
2
1
0
1
2
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
2
0
6
0
1
1
0
4
0
0
1
0
2
2
0
2
0
0
0
0
0
0
0
0
1
1
1
2
1
0
0
1
0
0
0
2
0
0
0
0
0
1
2
0
1
0
2
0
0
0
2
0
0
0
0
0
1
0
0
1
2
0
1
1
0
0
0
0
0
0
2
2
0
0
2
0
0
2
0
2
1
0
0
1
2
1
1
0
1
0
0
0
1
0
0
0
2
0
1
0
0
0
0
1
2
1
2
0
0
0
0
3
0
2
1
0
2
1
0
0
1
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
1
0
2
1
0
0
2
2
0
0
2
2
0
0
0
1
1
1
2
1
0
1
0
1
0
1
0
0
0
0
1
0
0
1
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
4
0
1
0
1
0
2
0
0
1
0
0
2
0
0
0
0
1
0
0
2
0
0
1
1
1
0
0
0
4
1
0
0
2
0
1
0
2
1
2
0
0
2
2
1
2
0
1
0
0
0
0
0
0
2
0
2
1
2
0
1
0
1
1
2
0
1
0
0
0
1
1
1
1
0
1
0
0
0
0
1
2
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
1
0
2
1
0
0
1
0
1
2
0
2
0
1
0
0
1
1
0
2
0
2
0
0
0
0
1
1
0
3
0
1
1
2
0
0
1
0
0
0
0
0
0
1
1
1
0
2
0
0
0
0
0
0
1
1
1
1
0
1
0
0
1
0
0
0
0
2
0
1
0
0
1
0
2
0
2
0
0
1
0
0
0
0
1
0
0
0
1
2
0
1
1
0
2
0
0
1
1
0
0
1
0
0
0
0
0
0
1
1
0
2
2
0
0
2
1
0
2
0
0
1
1
0
2
1
0
0
0
0
1
0
0
2
4
2
0
0
0
1
0
0
0
0
2
0
1
1
0
0
0
1
1
0
0
1
1
1
0
0
2
0
2
0
0
0
0
2
1
0
0
2
0
0
0
1
0
1
0
1
1
0
1
0
0
0
2
0
0
0
2
1
1
2
0
1
0
0
0
0
1
2
0
2
0
1
0
1
0
2
2
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
1
0
1
1
2
2
0
2
2
1
2
0
2
0
2
0
2
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
2
1
1
4
2
0
4
0
2
0
2
1
0
0
0
0
0
0
0
2
1
0
2
0
0
0
2
0
1
2
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
1
1
0
0
1
1
1
0
0
1
0
0
1
0
2
2
0
0
0
2
0
2
2
2
0
1
0
0
0
0
0
0
1
0
1
1
0
1
0
2
1
0
0
2
0
0
0
2
1
0
0
2
0
0
1
2
0
1
2
0
0
5
1
0
0
1
1
1
2
1
1
0
0
0
0
0
0
0
1
0
0
5
0
1
3
1
0
1
0
1
0
1
0
1
0
0
0
2
1
1
0
0
0
1
2
0
0
1
0
0
0
1
0
1
0
3
0
2
1
2
0
0
2
2
0
0
0
0
0
1
0
1
0
1
0
0
2
0
0
1
0
0
0
1
1
2
2
0
2
0
0
1
1
1
0
0
1
4
1
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
3
1
1
1
1
0
0
0
0
1
1
1
1
0
1
0
0
0
0
1
0
2
1
2
1
1
2
0
0
0
1
0
1
2
0
1
3
1
0
2
0
0
0
3
2
0
2
1
0
0
2
0
0
0
1
2
0
0
0
0
2
1
0
2
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
2
0
1
0
0
0
0
2
0
0
2
0
0
1
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
1
0
0
0
1
0
2
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
2
2
0
1
1
0
3
0
1
2
1
0
0
0
2
1
1
0
0
0
0
0
0
2
0
1
1
1
0
1
0
2
0
0
3
0
0
0
0
0
0
0
0
4
1
0
3
0
0
1
0
1
1
0
1
2
1
0
0
0
0
2
0
1
0
0
0
1
2
0
0
0
2
2
0
0
2
0
0
0
0
2
0
4
2
0
3
0
0
3
0
0
0
2
0
3
1
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
1
1
0
1
2
0
0
2
0
0
2
2
0
0
1
1
0
2
1
0
0
0
1
0
2
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
1
2
0
2
3
2
1
0
1
0
0
1
0
0
2
0
0
0
0
1
0
2
0
2
0
2
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
1
0
2
0
0
1
1
0
0
2
0
0
0
1
0
1
11
1
1
1
0
2
1
2
2
2
0
1
0
0
2
0
0
2
0
0
1
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
1
0
0
1
0
0
4
2
1
2
0
2
0
2
0
0
0
0
1
0
0
1
2
1
1
1
0
0
1
1
1
0
0
0
2
0
0
0
0
1
1
2
1
0
0
0
0
0
0
1
2
0
0
2
0
0
1
2
0
0
0
0
1
1
2
2
1
0
1
0
0
0
0
1
0
0
3
1
0
1
1
1
0
0
2
2
0
1
0
2
2
1
0
0
0
0
1
1
0
2
0
0
0
1
0
0
2
0
0
0
1
0
7
0
0
2
2
0
2
1
0
0
0
0
0
0
0
1
1
0
2
1
0
0
0
0
0
2
0
0
1
1
0
0
0
0
1
0
0
2
1
0
0
1
0
2
2
2
1
0
1
2
1
0
0
1
2
1
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
1
0
0
0
2
1
0
0
1
2
0
2
0
0
0
0
4
1
0
0
0
0
1
0
1
0
1
2
2
1
0
1
2
0
0
0
0
1
1
2
1
2
0
0
1
0
1
0
2
0
0
0
0
0
0
2
0
0
1
2
0
0
1
0
0
0
0
0
1
0
0
1
1
1
2
0
1
0
0
0
2
1
0
1
0
0
0
0
2
0
1
2
2
1
1
2
0
1
0
1
0
0
0
0
1
2
2
0
2
0
2
1
0
1
0
2
1
0
0
0
1
0
1
1
1
0
2
2
2
0
2
1
0
0
0
0
0
1
2
0
0
0
1
0
1
1
2
1
1
0
0
0
2
1
0
1
0
0
0
1
0
1
0
1
0
2
1
0
0
3
2
0
2
2
0
0
2
0
1
2
1
2
0
0
0
1
0
0
1
1
0
0
0
0
1
0
2
1
0
0
2
2
0
0
1
2
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
1
0
1
0
0
1
2
2
0
0
2
0
1
2
0
2
2
0
0
0
0
0
0
0
1
0
1
0
0
1
2
0
1
0
0
0
0
0
2
0
1
0
2
0
0
3
1
0
0
2
2
2
0
2
0
2
3
2
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
3
0
2
0
2
0
0
2
0
3
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
1
0
0
1
0
3
3
0
3
0
0
1
1
0
1
2
2
0
2
1
2
0
0
0
0
0
0
2
2
0
0
1
2
0
1
0
2
1
1
0
1
1
1
1
1
0
0
0
0
1
2
0
1
0
1
0
1
0
2
0
2
1
2
0
0
1
0
0
0
1
0
1
0
1
0
0
1
0
1
1
0
3
0
0
0
2
2
2
0
1
0
0
0
0
0
0
0
2
0
0
2
0
2
1
0
0
0
1
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
3
0
1
6
0
0
1
1
1
0
0
2
0
0
0
0
1
0
0
1
0
2
2
0
1
0
1
0
0
0
0
1
1
0
0
0
2
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
1
1
0
1
0
0
0
2
0
1
0
1
0
0
2
0
0
2
0
1
0
0
0
0
1
0
2
0
0
0
1
0
0
2
0
0
0
0
1
0
0
2
0
0
0
2
0
1
2
0
0
0
2
1
2
2
0
2
0
2
0
1
0
0
1
0
0
0
2
1
2
1
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
2
1
1
1
0
0
1
1
2
0
2
1
0
0
0
0
0
2
0
0
2
0
1
0
2
2
1
1
0
1
0
1
2
1
0
0
3
0
1
0
2
3
0
0
0
0
1
0
1
0
0
0
2
2
2
0
0
2
0
0
1
2
0
1
0
0
2
0
0
1
2
2
0
2
0
0
0
2
2
0
1
0
1
0
1
0
1
2
2
0
0
0
1
0
1
1
0
4
2
0
0
2
0
1
0
0
0
0
0
1
0
0
0
2
0
1
0
1
2
1
0
0
0
2
0
1
0
0
0
1
0
2
0
1
0
0
0
1
0
0
1
0
0
1
1
0
1
2
0
0
1
0
0
1
2
1
0
0
2
0
0
0
0
0
2
1
0
0
2
0
2
0
2
0
2
0
0
2
2
0
2
2
0
3
3
2
1
2
0
0
0
2
1
0
2
0
0
0
0
1
1
0
0
0
1
1
0
0
2
0
0
0
0
1
2
0
0
0
1
1
0
2
1
0
2
0
0
1
1
1
1
2
0
2
0
2
0
1
2
0
1
0
0
2
0
0
0
0
0
0
1
0
2
0
1
4
0
1
2
0
0
0
1
2
0
0
0
0
0
2
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
1
0
0
0
0
1
0
1
3
1
1
2
2
0
2
1
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
1
2
0
0
1
0
0
0
0
2
0
3
2
1
0
0
0
2
0
2
1
0
0
1
0
0
0
0
0
1
0
2
0
1
0
1
1
3
0
1
2
1
3
0
2
1
0
0
0
1
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
1
0
0
0
1
0
0
0
0
2
1
2
1
0
0
1
2
0
2
2
1
0
1
1
4
0
0
2
1
0
0
2
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
1
0
0
0
0
0
0
2
2
0
0
1
2
0
0
1
0
1
1
1
4
1
0
1
1
1
0
2
2
0
0
2
0
1
0
0
2
0
0
1
2
0
1
2
0
1
0
1
0
0
3
0
0
0
0
1
2
2
2
0
0
2
0
0
0
0
0
0
1
0
1
2
0
0
2
1
1
0
1
0
2
1
0
0
2
1
0
0
2
0
2
0
0
1
2
2
0
0
0
1
0
3
2
1
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
2
2
0
0
0
2
0
1
2
1
1
2
2
2
2
0
1
0
1
0
3
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
2
3
2
1
1
2
1
0
0
0
1
1
1
1
0
1
2
1
0
0
2
0
0
2
1
0
0
1
2
0
1
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
2
0
0
1
0
0
0
2
0
0
2
0
0
0
0
2
0
0
1
0
1
0
0
1
0
0
1
2
1
0
0
0
0
1
0
2
1
1
0
0
0
2
2
1
0
1
2
0
2
2
0
1
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
1
0
2
1
2
0
0
0
2
1
0
0
0
0
0
1
2
0
0
0
2
1
0
2
2
0
0
1
1
0
0
0
2
0
2
1
2
1
1
0
0
0
0
1
1
0
2
1
2
1
0
0
0
0
0
0
2
0
0
0
1
1
1
0
0
2
0
1
0
0
0
1
0
1
2
4
2
0
1
0
0
2
0
0
0
1
0
1
0
2
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
2
0
1
0
0
0
0
0
1
0
1
0
3
0
0
2
0
1
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
2
2
0
0
0
1
0
0
0
1
1
2
1
1
0
2
2
0
1
2
1
0
2
4
1
1
1
0
0
0
0
0
0
2
0
1
0
0
1
1
1
0
1
0
1
0
0
2
0
1
1
0
0
1
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
3
0
0
0
1
1
0
2
0
1
0
0
2
2
1
0
1
0
2
2
1
1
0
0
1
2
1
0
2
1
0
2
0
1
1
0
0
1
1
1
0
0
0
1
0
0
2
2
0
2
0
2
1
1
0
0
1
1
0
0
0
1
2
0
0
2
0
0
1
2
0
2
0
1
0
0
2
0
2
0
0
2
0
2
1
2
0
2
0
0
1
0
0
1
2
0
1
0
1
0
2
2
0
0
1
0
4
1
0
0
0
2
0
0
0
1
0
1
2
0
1
0
0
0
0
2
0
2
0
1
0
2
1
0
2
0
0
1
0
2
4
0
1
1
0
2
1
2
2
0
0
2
1
0
0
0
0
2
1
1
0
0
1
0
1
0
0
0
0
1
0
0
1
0
1
1
2
0
2
1
2
0
2
0
0
0
0
0
1
0
2
0
0
0
1
2
2
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
2
0
1
0
2
0
1
2
1
0
0
2
1
0
0
1
0
0
1
2
0
0
3
1
2
1
0
0
1
0
1
1
0
0
0
0
1
0
1
0
0
2
0
0
0
1
0
1
2
0
1
0
1
1
0
0
0
0
0
2
0
2
0
0
1
2
0
2
0
0
1
0
2
1
1
0
0
2
6
1
2
1
0
0
0
2
0
1
2
0
1
0
0
1
0
0
0
1
3
0
1
0
0
0
2
0
3
0
0
0
0
2
0
0
0
1
2
0
0
2
1
0
0
1
0
0
1
2
1
0
0
0
1
2
2
1
0
2
2
0
0
0
1
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
1
2
2
1
1
0
2
0
0
1
0
1
0
1
1
0
1
1
0
0
2
0
0
1
2
0
0
1
1
2
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
3
0
0
0
0
0
1
2
5
0
0
0
1
0
1
1
0
0
1
0
0
0
2
0
0
1
4
0
2
0
1
0
1
0
0
0
1
1
2
0
0
0
0
0
1
2
0
1
0
2
1
0
0
0
0
0
0
2
1
0
2
0
0
0
1
0
1
2
1
2
2
2
2
0
0
0
0
0
1
0
0
2
2
0
0
0
1
0
0
1
2
1
1
2
1
0
1
2
3
1
2
2
0
0
2
2
1
0
2
0
2
2
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
2
0
0
0
2
0
2
0
0
0
0
1
1
1
1
0
0
1
0
2
1
2
0
2
1
3
0
0
0
0
3
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
2
0
0
0
2
2
0
1
1
3
2
0
1
0
1
2
0
2
0
1
0
0
0
2
0
0
0
0
0
0
2
2
0
0
2
3
0
1
0
0
1
1
0
1
1
0
0
0
5
2
0
0
0
2
0
1
0
1
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
2
0
1
2
2
1
0
0
0
0
2
1
0
2
1
1
0
0
0
1
1
0
0
1
0
0
0
2
1
1
1
3
0
2
0
2
1
0
0
2
0
1
0
0
0
0
0
2
0
0
1
0
0
2
2
2
1
1
0
2
0
2
0
0
0
0
1
1
2
0
0
0
0
1
0
0
2
0
0
1
0
1
3
1
0
2
0
0
0
1
0
0
0
0
0
1
0
0
1
1
2
0
0
1
1
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
1
1
0
1
1
0
0
1
0
0
2
1
0
1
2
0
0
0
2
1
0
0
0
2
0
1
1
2
2
0
2
2
0
1
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
2
0
5
1
0
3
0
0
0
1
0
2
1
0
0
1
0
4
0
1
0
0
0
2
0
1
0
2
0
0
1
1
0
2
2
1
0
0
2
1
0
1
0
0
0
2
0
0
1
0
3
2
0
0
2
3
0
0
0
1
0
1
0
1
1
0
0
2
0
0
0
0
2
1
0
1
2
0
2
0
0
0
1
0
1
2
1
2
0
1
1
1
0
0
2
0
0
0
0
0
2
1
0
0
2
0
1
0
0
0
2
0
0
1
2
0
0
1
0
1
3
0
1
0
2
0
0
0
1
0
1
0
0
1
0
0
1
0
0
1
2
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
2
0
1
0
1
1
1
0
0
0
0
0
1
2
3
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
3
1
0
1
1
0
2
1
2
0
1
0
2
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
2
0
1
2
0
0
0
2
0
0
0
1
1
1
0
1
0
0
2
0
0
0
0
1
0
0
1
1
0
1
0
0
0
2
0
0
1
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
1
2
1
2
0
1
2
0
0
0
1
2
0
0
2
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
3
0
2
1
0
0
0
0
1
3
0
1
0
0
1
0
0
0
0
2
0
2
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
2
0
0
0
0
0
0
1
4
2
1
0
0
4
2
2
1
0
0
2
2
2
0
0
0
0
2
0
1
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
2
3
2
2
0
0
0
2
0
0
1
3
3
0
1
0
0
0
0
0
2
1
2
0
0
1
0
1
0
0
1
1
0
0
0
1
0
3
0
1
0
1
0
0
0
0
0
0
2
0
2
0
0
2
0
2
1
0
0
0
2
0
0
0
0
0
2
0
0
1
2
0
0
2
1
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
2
0
1
1
1
0
2
0
0
0
0
0
0
2
1
0
0
0
2
0
1
0
0
0
1
0
1
0
0
0
1
0
0
1
1
0
3
1
0
0
1
1
2
0
2
1
1
2
0
2
0
1
0
0
1
0
2
2
0
0
0
0
1
0
0
2
0
3
1
0
1
1
1
1
2
0
0
2
2
1
1
0
0
0
0
0
2
1
0
0
0
1
0
2
1
1
1
0
1
0
0
0
3
0
0
0
0
1
0
0
0
2
1
0
1
1
0
0
2
1
1
4
1
1
2
3
0
1
0
0
2
2
0
0
1
1
1
0
0
0
2
0
2
0
0
2
1
3
2
1
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
3
0
2
0
1
0
2
3
0
2
1
1
1
2
1
1
0
0
0
2
0
2
0
0
1
0
1
1
0
0
0
0
2
0
1
2
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
3
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
2
1
1
0
1
0
2
0
1
0
0
0
2
0
2
0
0
0
2
0
0
0
1
0
2
0
0
1
0
0
1
0
1
0
0
1
0
0
0
2
1
0
0
1
0
0
2
0
0
3
1
0
2
0
0
0
0
2
1
0
2
2
0
0
0
1
0
1
0
1
1
0
1
0
0
0
0
2
2
0
2
1
0
0
0
0
2
1
0
0
1
0
0
1
0
0
2
0
0
0
0
0
6
0
0
0
1
1
1
1
0
0
0
2
1
0
0
1
1
1
1
1
2
1
0
0
0
0
0
1
0
0
0
2
0
3
0
1
0
0
2
1
0
2
0
0
0
2
1
0
0
1
2
2
2
3
2
0
0
0
6
0
0
0
0
0
0
0
1
2
2
2
2
2
0
0
1
0
1
2
1
0
0
2
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
3
0
2
0
0
0
0
1
1
1
1
0
1
1
0
0
0
0
2
0
2
0
0
0
2
0
0
1
2
2
0
2
0
1
0
2
0
0
1
0
1
0
0
0
0
0
0
0
2
2
0
2
2
0
1
1
2
1
0
0
0
0
1
0
2
0
2
0
0
0
2
2
1
0
0
0
0
1
2
1
0
0
1
2
0
1
1
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
1
1
1
0
0
1
0
0
0
0
2
4
0
0
0
2
0
0
0
0
0
2
3
2
0
0
0
0
1
0
1
0
0
0
2
2
3
0
0
1
2
2
2
1
0
0
1
0
1
2
0
0
0
0
0
0
1
3
0
0
1
0
2
0
2
1
0
0
1
2
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
2
2
0
2
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
1
0
1
2
1
2
0
0
2
2
0
0
1
0
4
1
2
2
0
2
0
0
1
2
0
0
0
0
1
0
0
0
0
2
0
2
2
2
1
0
3
0
0
0
0
0
0
0
2
3
0
2
2
0
2
0
0
2
2
0
0
0
1
2
0
2
0
0
2
0
2
0
2
2
0
4
0
2
2
2
0
1
2
0
0
0
1
3
2
2
1
3
3
0
1
2
0
0
1
0
0
1
1
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
1
1
0
9
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
2
1
0
2
0
2
1
13
2
0
0
0
0
0
0
0
1
1
1
0
2
2
0
0
1
0
0
0
0
0
2
0
1
1
1
3
1
0
0
1
0
1
0
0
2
0
0
1
0
0
1
0
0
0
2
0
0
0
0
2
1
1
1
0
0
0
1
0
0
0
0
2
1
0
1
0
0
0
3
0
2
0
0
1
1
0
0
1
0
0
0
0
0
2
0
1
1
0
1
0
1
2
2
1
1
0
0
1
0
0
0
2
0
1
1
0
1
0
1
0
0
0
1
1
1
3
0
1
0
1
0
0
0
2
1
2
1
0
0
2
2
0
0
2
1
2
0
0
0
2
3
0
0
0
1
0
0
0
1
0
1
2
2
1
9
2
2
2
0
2
1
0
1
0
0
1
2
1
0
0
2
1
1
0
0
0
1
0
0
2
1
1
0
2
0
0
0
2
2
1
2
0
2
1
0
0
1
0
0
1
1
0
0
0
0
0
7
1
1
0
3
0
0
0
0
0
2
0
1
0
0
2
0
0
0
2
0
1
1
1
0
0
0
2
0
2
0
0
0
0
0
2
1
2
0
0
2
2
1
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
2
0
0
0
0
2
3
0
0
0
2
1
0
0
0
0
2
2
0
0
0
1
1
0
0
1
1
1
0
0
0
2
0
0
2
0
0
0
0
0
0
1
1
0
2
0
0
0
1
1
2
0
0
1
0
2
0
1
0
1
2
1
0
0
0
0
0
2
0
0
2
0
1
2
2
1
2
0
0
0
1
0
0
0
0
0
0
2
0
4
0
0
0
1
1
0
1
0
0
0
1
2
0
0
0
2
0
0
0
1
0
1
0
2
0
0
0
0
2
2
2
0
0
0
1
1
0
2
1
0
2
0
0
0
0
2
1
2
0
0
0
2
0
1
0
2
1
0
1
0
1
1
0
0
2
0
0
1
0
1
2
0
0
0
0
0
1
1
0
0
1
2
1
0
0
0
2
0
0
1
0
0
1
0
0
3
0
0
0
3
0
0
1
0
2
2
3
1
2
0
2
1
1
0
0
1
0
0
2
2
2
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
1
2
1
1
1
2
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
2
0
0
1
2
1
2
0
0
0
0
0
1
0
2
0
0
0
1
0
1
0
0
2
0
0
1
2
2
1
0
0
2
2
2
0
2
0
1
0
0
1
0
1
0
3
0
1
0
1
0
1
2
0
0
0
2
1
5
2
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
1
1
0
1
0
1
0
0
1
0
0
0
0
1
2
0
1
1
1
2
4
1
0
1
1
0
0
2
0
1
0
1
0
1
0
0
0
1
0
0
1
1
0
1
0
0
1
0
3
2
1
0
0
2
0
0
1
0
0
1
0
0
0
2
0
0
1
1
0
0
0
0
2
0
2
0
0
0
1
2
0
0
2
0
0
0
1
0
0
0
0
0
0
3
0
0
2
1
2
0
0
0
2
3
2
1
0
1
2
0
0
0
1
0
0
0
0
2
0
0
0
0
3
0
0
1
2
0
2
2
2
0
0
0
0
2
0
2
0
2
2
2
1
2
0
0
2
1
1
1
0
0
0
0
0
4
0
0
0
2
0
1
5
0
0
0
0
0
2
0
0
0
1
1
0
0
1
0
0
1
0
0
1
0
1
1
0
0
0
2
2
1
0
0
2
3
0
0
0
0
1
0
0
0
0
0
2
2
1
0
1
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
3
0
2
0
3
0
1
1
0
0
0
0
1
2
1
0
0
1
2
1
2
0
0
1
1
0
1
0
2
0
1
0
1
2
2
0
0
0
0
0
0
0
0
0
1
4
0
0
2
0
2
0
0
2
1
1
0
0
0
0
1
0
2
0
0
0
3
0
2
1
2
0
3
0
0
0
0
3
0
2
0
0
0
0
2
1
2
0
0
0
2
1
0
0
1
0
0
0
1
0
0
2
0
2
0
0
0
0
1
0
1
0
0
2
0
1
0
0
3
0
0
0
2
2
0
0
0
5
0
0
0
0
2
1
1
0
0
1
0
0
0
1
1
0
0
0
0
4
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
1
1
2
2
0
1
0
2
1
0
1
1
0
0
1
0
0
2
0
2
1
1
2
1
0
0
1
0
1
1
0
2
0
0
2
1
1
2
0
1
0
0
1
1
0
0
0
0
3
0
1
0
0
1
1
0
0
2
0
1
0
0
0
1
0
0
0
0
1
2
0
0
0
1
2
1
0
0
0
2
0
0
0
0
2
1
2
2
0
1
0
2
0
0
1
0
2
1
0
0
0
1
0
2
0
0
1
0
0
0
2
0
0
2
0
2
0
0
1
0
2
0
3
0
1
0
0
0
1
0
2
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
1
1
0
0
1
0
0
0
2
0
0
0
1
2
2
0
1
0
2
2
2
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
1
0
0
0
2
2
0
0
1
2
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
2
0
0
0
1
2
1
0
1
1
0
2
0
0
2
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
1
0
0
0
2
1
0
1
2
1
2
0
0
0
0
0
0
3
2
1
1
0
0
0
0
0
3
0
0
0
0
2
0
1
0
1
2
2
2
2
2
0
1
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
2
0
2
0
1
0
0
0
0
1
2
1
0
1
2
0
0
0
0
1
1
2
0
1
0
0
0
0
0
0
0
1
0
5
0
2
0
2
0
2
0
2
0
1
0
1
2
0
1
0
0
1
0
0
0
0
2
0
0
2
0
0
2
0
0
1
1
0
2
0
0
0
0
2
2
2
0
0
1
0
1
2
1
2
0
0
0
0
0
1
0
1
0
0
0
1
0
2
1
0
0
0
0
0
0
1
1
0
0
2
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
3
0
2
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
1
0
0
0
1
0
5
0
0
1
0
0
0
0
0
0
0
2
1
1
1
0
0
1
0
0
0
0
1
0
2
0
1
0
0
2
1
0
0
1
0
3
1
0
1
0
0
2
2
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
2
0
3
2
0
0
2
0
0
0
1
1
3
0
0
1
0
0
1
0
0
2
1
0
0
0
1
1
0
0
3
0
2
1
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
2
0
0
1
0
0
1
2
0
0
2
0
0
0
0
1
1
0
0
0
3
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
2
2
0
2
0
0
0
1
3
2
1
0
1
1
0
0
0
1
0
0
0
0
2
0
0
0
1
0
2
2
1
1
1
2
3
1
2
0
0
0
0
1
0
0
0
0
1
1
0
0
1
1
0
0
0
0
2
0
1
8
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
2
2
1
2
0
1
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
1
0
1
0
0
2
0
2
0
1
0
0
1
2
1
0
1
2
1
0
0
0
0
2
0
1
2
2
0
0
2
2
0
2
1
1
13
0
1
0
2
0
0
0
1
0
0
0
0
0
2
1
0
0
2
0
2
0
1
0
0
1
0
2
1
0
0
0
0
1
1
1
0
0
0
1
0
0
2
1
0
1
0
0
0
0
2
0
1
2
0
1
2
0
2
0
1
0
0
1
0
0
0
0
3
2
0
1
1
0
2
0
1
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
1
1
2
0
0
2
0
0
0
1
0
0
2
0
2
0
0
1
0
0
1
0
2
0
2
2
0
1
0
2
0
1
2
2
0
2
0
0
2
2
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
1
0
0
0
1
0
2
0
1
0
0
2
0
1
1
2
0
0
2
0
2
2
1
0
0
0
2
1
0
0
0
1
0
0
0
0
2
1
1
1
0
0
0
0
0
0
2
1
6
0
0
2
0
1
1
2
0
1
1
0
0
0
0
2
1
2
1
0
1
0
0
0
0
0
1
1
1
0
0
2
0
2
2
0
0
1
2
0
1
0
1
2
0
2
1
0
0
3
0
0
0
1
1
0
3
0
0
0
0
1
1
0
0
0
1
0
1
1
0
0
2
0
1
1
2
0
2
0
0
1
1
3
2
1
2
0
0
0
0
2
0
1
0
0
0
0
0
1
0
1
0
0
0
1
2
1
1
0
0
0
1
1
3
0
1
1
0
2
0
0
1
2
1
1
0
0
0
0
0
1
0
0
2
0
1
2
0
1
0
0
0
0
0
1
0
0
0
2
1
1
0
0
2
2
1
2
2
0
1
0
1
2
0
2
0
1
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
2
1
0
1
1
0
0
2
0
1
1
0
0
0
0
2
2
0
2
1
1
0
1
2
0
0
0
1
1
0
0
0
1
0
1
0
1
0
0
0
0
2
0
0
1
1
0
1
0
0
0
1
0
1
0
2
0
0
1
2
2
1
2
0
1
0
0
0
1
3
0
0
0
0
0
0
0
1
0
1
1
1
0
1
2
2
0
0
1
0
1
1
2
0
2
0
0
0
0
0
2
1
0
2
0
1
1
0
0
1
1
1
2
0
0
0
1
4
2
0
2
2
2
0
1
0
0
0
3
0
2
2
2
1
2
0
0
0
2
2
2
3
0
0
0
1
3
2
0
1
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
2
1
1
0
0
0
2
2
2
0
0
0
0
1
1
1
1
1
0
2
1
1
0
0
0
0
0
2
2
0
0
2
2
0
1
0
1
0
1
0
0
0
0
0
2
0
2
1
2
2
0
1
5
0
0
2
0
0
0
2
2
2
1
0
0
0
1
1
1
2
0
0
2
0
0
0
1
0
0
2
2
0
0
1
0
0
0
1
0
1
2
0
1
3
0
0
0
1
0
2
2
1
0
0
1
0
0
0
2
0
0
0
1
2
2
1
2
0
0
1
0
0
0
2
1
2
1
0
2
0
2
0
1
0
3
1
2
2
0
0
0
0
0
1
1
2
0
0
0
0
0
0
2
2
0
0
0
0
2
0
1
2
0
1
0
0
0
0
0
0
0
1
0
1
1
1
1
0
2
0
2
0
0
0
1
0
0
1
3
2
2
1
0
1
0
0
0
2
1
1
0
0
0
8
0
2
0
0
2
0
2
0
0
2
0
2
0
0
2
8
1
2
2
0
0
2
0
2
0
1
1
0
0
1
2
4
1
6
0
0
2
1
1
1
0
1
0
0
0
1
0
0
1
1
0
0
1
0
2
0
1
1
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
2
1
0
2
1
0
1
1
0
0
1
1
2
0
0
2
0
0
0
2
0
2
1
0
0
1
0
0
0
0
0
2
0
1
0
0
2
2
0
2
0
0
2
0
2
0
0
2
0
0
0
1
0
2
0
0
2
0
0
1
0
2
2
2
1
0
0
0
0
1
0
1
0
2
0
1
0
0
1
0
0
0
2
2
0
0
0
0
0
1
0
2
0
2
0
0
1
0
0
0
2
1
0
1
0
0
1
1
2
0
2
0
1
0
2
0
0
0
2
0
0
0
2
0
1
2
2
0
0
0
2
2
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
2
1
0
1
0
0
0
0
0
0
2
0
3
0
0
0
1
0
1
1
2
1
2
2
0
1
1
2
1
2
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
5
0
2
1
0
0
1
1
1
0
1
1
1
0
0
1
0
0
2
0
1
1
3
0
0
0
0
0
0
0
1
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
2
1
0
0
0
0
0
0
2
0
1
2
0
1
0
0
2
0
0
2
1
0
2
2
2
0
0
0
1
2
0
0
2
1
1
1
1
1
0
0
0
0
1
2
0
0
1
2
0
0
0
2
2
2
1
0
0
1
2
1
0
0
0
0
0
0
0
1
0
2
1
2
0
2
0
0
1
0
1
0
2
5
0
0
0
0
1
0
0
1
2
1
0
0
0
1
2
0
0
2
2
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
2
1
0
0
0
0
0
2
3
0
0
0
2
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
2
2
0
2
1
2
0
0
1
2
0
0
2
0
0
0
2
0
0
0
1
0
2
0
1
2
0
0
0
2
0
0
2
0
2
0
1
1
0
1
0
2
0
0
0
1
0
1
1
1
1
2
1
2
1
1
0
0
1
2
0
0
0
0
1
0
0
2
0
2
2
0
1
0
0
0
1
0
1
0
0
0
2
1
1
0
2
0
0
1
1
1
1
0
1
0
0
0
0
0
0
1
2
0
1
0
5
2
0
2
2
1
1
2
2
2
0
0
0
2
2
2
1
1
0
2
0
1
0
0
0
1
0
0
2
0
1
2
0
0
0
0
1
2
2
0
2
2
0
0
0
0
1
0
2
0
0
0
1
1
0
0
2
0
3
0
1
2
1
2
0
0
1
0
0
1
1
2
0
2
0
0
0
0
0
0
0
1
1
0
1
0
0
1
1
0
2
0
0
0
0
1
2
1
0
1
0
1
2
0
3
1
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
3
1
0
2
1
0
0
0
0
1
1
2
0
2
2
1
1
0
0
0
0
1
1
0
1
1
2
2
2
2
2
0
1
2
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
3
1
0
0
0
1
2
0
1
0
0
0
0
0
0
2
0
0
0
2
0
1
2
2
1
0
0
2
1
1
1
0
1
2
1
2
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
1
0
1
1
2
0
0
0
0
0
2
1
1
0
1
0
2
0
0
0
0
0
0
0
2
0
0
2
1
0
2
0
1
1
0
0
1
1
2
2
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
1
0
2
1
0
0
1
1
2
2
1
0
1
0
2
0
1
1
0
0
0
0
0
2
0
0
0
2
1
0
0
1
0
0
0
2
3
0
0
2
1
1
0
0
0
0
1
0
2
0
2
1
2
1
3
2
2
0
0
0
1
0
1
2
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
2
2
1
1
0
0
0
1
0
0
2
0
1
0
0
1
2
0
0
0
0
0
1
2
1
1
1
0
0
2
0
1
0
0
0
2
2
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
1
0
2
7
0
2
1
0
0
1
0
0
0
2
2
0
1
2
0
0
0
1
0
0
2
1
3
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
1
2
0
0
1
1
0
0
3
0
0
0
0
2
2
0
2
0
0
2
1
3
0
0
0
0
1
2
0
0
2
0
2
1
4
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
2
2
0
0
1
1
0
4
1
1
0
1
0
0
0
0
2
1
0
2
0
0
1
2
0
0
0
0
1
0
0
1
1
2
0
2
2
1
2
0
2
2
0
0
0
2
2
0
0
0
1
0
0
0
0
1
0
1
1
0
1
1
0
2
0
0
2
0
4
1
0
2
0
0
1
1
0
1
1
1
0
1
2
1
0
0
2
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
2
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
1
0
0
0
0
0
2
2
2
1
1
0
1
1
1
0
0
1
0
0
1
0
1
2
1
1
0
1
0
1
2
0
2
0
0
1
0
0
0
2
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
2
1
0
2
1
1
1
1
2
1
1
1
0
1
2
2
1
0
1
2
0
2
0
1
0
2
1
1
1
0
2
0
0
2
0
0
0
0
1
0
0
2
1
0
1
2
0
1
0
2
5
0
0
0
0
0
0
0
0
0
2
0
1
1
1
0
2
3
0
0
1
0
1
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
2
0
1
0
1
0
0
0
1
1
0
2
0
0
0
2
2
0
2
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
1
0
1
1
2
1
2
2
1
2
0
0
2
2
0
0
0
8
1
0
0
1
0
2
1
0
0
0
1
2
1
1
0
2
1
0
1
0
0
0
1
1
0
2
0
1
0
1
2
1
0
1
0
0
0
0
0
2
0
0
0
0
0
1
5
0
1
0
2
2
2
0
0
0
1
0
2
2
1
0
0
1
2
1
3
0
0
0
0
2
0
0
1
0
0
1
0
0
1
0
0
0
1
0
3
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
1
0
3
2
2
2
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
2
0
0
0
1
2
2
0
1
0
2
0
0
0
2
0
0
1
0
1
2
0
0
1
0
1
0
0
0
2
0
2
1
0
1
1
1
2
2
0
1
0
0
1
0
1
0
1
2
1
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
2
1
0
0
1
0
0
0
2
1
0
1
0
0
0
0
1
0
1
0
1
0
1
2
2
0
0
1
1
0
1
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
2
0
2
0
2
2
0
1
0
1
2
0
2
0
0
0
1
0
0
2
1
0
0
0
0
2
1
2
0
1
4
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
1
1
1
0
0
1
0
0
2
0
1
2
0
2
1
0
0
0
2
3
2
2
0
0
0
0
1
0
0
2
1
0
0
2
1
0
1
1
0
0
0
0
0
0
1
0
2
1
0
2
0
0
1
1
2
1
0
2
0
2
0
0
2
0
0
0
0
0
2
0
0
2
0
1
0
0
2
3
0
2
2
1
1
1
1
1
0
1
0
2
0
0
1
0
2
1
0
3
0
1
0
0
1
1
1
1
2
0
2
0
0
0
0
1
2
1
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
4
2
0
0
0
0
0
0
0
0
2
2
1
1
2
2
0
2
2
1
2
3
1
1
0
0
2
0
0
3
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
1
0
0
2
2
1
0
0
0
0
2
0
2
1
0
0
0
0
0
4
0
2
0
0
0
0
2
0
0
2
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
2
0
0
1
0
0
0
0
1
0
0
1
0
2
0
1
1
0
1
0
0
2
3
0
1
2
0
0
0
1
1
1
1
2
0
0
2
2
2
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
2
0
0
0
1
0
0
0
2
1
0
0
0
0
1
0
1
1
1
0
0
0
1
0
3
0
2
2
0
0
2
0
1
0
2
0
2
0
0
0
2
0
1
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
3
0
4
0
0
0
0
0
0
1
1
2
1
0
0
1
0
1
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
1
1
1
2
0
2
0
1
0
0
0
2
0
0
0
0
0
1
1
1
2
1
2
0
0
0
0
0
0
0
3
1
0
2
0
0
0
1
0
1
2
0
1
0
0
1
0
2
1
1
0
1
1
0
0
1
0
2
0
1
0
1
1
1
0
0
2
0
2
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
3
2
0
0
0
0
1
0
3
1
1
2
0
0
1
2
1
0
0
2
0
0
0
0
1
0
1
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
1
0
2
2
0
1
1
0
0
2
0
0
2
2
0
1
0
1
0
1
1
0
1
0
0
0
0
0
3
2
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
1
0
1
0
0
0
2
0
0
1
1
2
0
1
0
0
0
0
0
2
0
0
1
0
0
2
0
0
1
0
0
0
0
2
0
0
1
2
1
0
1
1
1
2
2
1
0
1
0
2
2
0
0
0
1
0
0
0
0
1
0
0
0
1
1
1
0
5
1
0
0
0
0
0
0
1
0
0
0
2
0
3
0
0
0
0
1
0
2
0
2
2
0
1
0
0
0
0
0
1
1
0
3
0
3
1
0
1
0
1
0
1
1
0
2
2
0
0
0
2
0
2
0
0
1
2
0
0
0
2
0
2
2
1
2
0
0
0
0
2
0
0
0
0
1
0
0
2
0
1
0
0
0
1
0
1
0
0
4
0
2
0
0
1
3
2
1
0
1
1
0
0
0
1
1
1
2
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
1
2
2
2
1
0
0
0
0
0
2
1
1
2
2
0
2
2
0
1
0
0
1
1
1
0
0
0
0
2
0
2
3
0
0
0
0
2
1
1
1
1
0
0
0
1
0
0
1
0
0
0
2
0
0
2
2
0
3
1
2
0
2
0
0
0
1
0
1
0
0
2
1
0
0
1
0
0
1
1
1
0
0
0
1
0
2
0
0
1
0
4
0
1
1
0
0
0
0
0
0
2
1
0
1
0
2
2
0
0
0
0
1
1
1
0
0
0
1
0
0
2
1
2
0
0
1
2
0
1
0
2
0
0
1
0
0
3
0
1
2
0
1
1
1
1
0
0
2
0
0
0
0
0
0
0
0
1
1
1
2
0
1
0
2
0
1
0
0
4
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
3
3
2
2
0
0
2
1
0
1
1
0
0
1
0
1
0
0
1
0
0
0
0
2
2
0
1
0
1
1
0
0
0
0
1
0
1
0
0
1
1
0
0
1
0
0
0
0
2
0
3
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
4
0
0
1
0
1
0
0
0
1
2
0
0
1
0
0
0
1
0
1
0
1
0
0
2
0
2
0
0
1
2
0
0
0
0
3
0
0
2
2
0
2
0
0
0
2
2
0
3
2
2
1
0
0
2
0
2
0
0
0
0
0
5
0
1
0
1
2
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
2
1
2
0
0
0
0
0
1
1
0
0
0
1
1
1
2
0
1
0
0
0
0
0
2
0
1
2
2
0
0
1
0
2
0
1
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
3
0
1
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
2
0
1
1
0
0
3
2
2
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
1
1
2
2
1
1
0
1
1
0
0
2
0
1
0
2
1
1
0
12
0
1
1
2
0
0
2
0
1
2
1
0
1
0
0
0
0
1
1
1
0
0
1
0
1
0
0
0
0
2
0
1
1
1
0
2
1
2
1
0
0
2
3
0
1
0
0
2
2
2
0
0
0
2
2
1
0
0
2
0
0
0
0
2
0
0
0
1
0
0
1
0
2
2
0
0
0
0
1
1
0
0
0
1
0
2
0
0
0
1
0
2
0
1
0
0
0
0
0
2
2
0
0
2
0
0
2
0
1
0
2
2
0
1
0
0
0
0
1
0
0
0
1
1
1
2
0
1
2
1
3
0
2
0
0
0
1
1
0
0
2
0
0
0
2
2
1
0
0
2
0
1
6
0
0
1
0
1
0
2
1
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
2
0
2
1
1
2
0
0
2
0
0
0
3
2
1
2
1
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
5
2
1
0
0
0
2
0
1
0
0
2
1
0
0
1
1
4
0
0
2
2
1
1
0
0
0
1
2
0
0
0
0
0
0
1
1
0
2
0
0
2
0
0
1
1
0
0
0
0
2
0
0
2
0
2
0
0
1
1
2
1
0
2
0
0
1
0
0
0
1
0
1
3
0
1
1
0
1
3
2
2
0
2
1
0
1
0
1
2
3
0
0
0
0
2
1
2
1
0
0
1
0
0
1
0
2
1
1
0
1
2
1
0
2
0
0
0
0
0
1
0
2
2
0
0
2
6
2
0
0
0
2
2
1
0
0
0
0
0
1
0
0
0
1
1
1
2
1
0
0
1
0
0
0
1
0
0
0
2
1
1
4
0
0
0
0
1
0
5
1
2
0
0
0
2
2
2
0
1
1
2
2
0
2
1
0
0
0
0
0
0
3
1
1
0
0
0
2
0
1
1
0
0
0
1
1
1
2
2
1
1
0
1
0
2
0
0
1
1
1
0
1
0
0
0
0
0
2
2
0
0
1
1
0
0
2
0
2
0
0
0
2
1
1
0
2
0
0
1
1
2
0
1
0
0
2
0
0
1
0
3
2
2
0
0
2
1
1
0
0
1
2
0
0
2
2
0
2
3
0
0
0
1
0
1
2
0
0
0
0
0
1
2
2
0
0
1
0
2
2
0
0
0
1
4
1
2
0
0
0
0
3
0
2
0
1
2
0
0
0
0
0
2
2
1
0
2
3
0
1
0
2
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
2
0
0
2
1
2
0
0
0
0
0
0
0
1
0
0
2
0
2
2
0
2
2
0
0
0
1
1
0
1
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
1
1
2
0
0
1
0
0
0
0
0
1
1
0
0
2
2
0
0
0
2
0
0
1
0
1
0
0
0
1
1
0
0
2
0
0
0
0
1
0
0
1
1
0
0
0
2
0
1
0
1
0
1
0
2
2
0
1
0
0
1
0
2
1
1
0
0
0
0
0
0
0
0
2
0
2
0
1
2
0
2
1
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
1
1
2
0
0
0
1
2
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
1
2
1
3
0
1
0
0
3
0
0
1
0
0
2
2
0
0
0
0
0
0
0
1
2
2
0
2
0
2
0
1
0
0
0
0
0
0
1
1
0
3
0
0
1
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
1
0
2
2
1
0
0
2
1
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
2
1
0
0
0
2
2
0
1
0
0
2
0
2
0
1
1
0
1
0
0
3
1
3
2
0
2
0
2
0
1
0
0
3
0
0
1
2
0
1
1
1
0
0
2
1
0
0
0
0
0
1
0
2
1
2
0
0
0
1
0
2
0
0
0
8
0
2
0
0
2
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
2
0
0
0
1
0
0
1
1
0
1
2
1
0
2
1
2
0
1
1
1
0
2
0
2
0
0
0
0
1
0
0
2
0
0
2
0
2
2
0
0
0
0
0
0
1
2
0
2
0
0
2
0
0
1
2
0
1
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
1
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
2
1
1
1
0
0
1
0
2
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
1
0
3
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
1
0
0
1
0
2
1
0
0
0
0
0
0
1
1
2
2
0
2
2
0
2
0
0
0
0
0
2
0
1
0
1
0
0
0
2
0
2
1
0
1
2
0
0
1
0
0
2
1
0
2
1
2
0
2
0
0
0
0
1
1
0
0
0
1
2
0
2
2
1
1
2
1
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
1
0
1
0
2
0
1
1
3
0
2
0
2
0
0
0
0
0
0
0
2
2
2
2
0
1
2
0
0
0
0
2
2
0
0
0
0
0
2
1
0
0
2
0
1
2
2
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
2
0
1
0
0
0
0
1
0
1
0
1
0
0
0
2
1
0
2
1
0
1
0
0
0
0
2
0
2
0
2
0
4
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
1
0
0
2
1
2
1
2
0
0
2
0
0
6
0
1
0
0
1
3
1
0
0
2
0
0
0
0
1
2
0
0
2
0
0
2
2
0
0
0
1
0
1
1
2
1
1
2
1
0
2
2
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
3
0
0
0
1
2
0
1
1
0
1
0
2
0
0
0
3
0
0
3
0
2
2
0
2
0
0
2
0
2
0
0
2
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
3
0
0
2
0
0
0
1
2
0
2
0
2
1
2
1
0
0
1
0
0
2
1
1
0
0
1
0
0
1
0
0
2
0
0
1
1
0
0
1
2
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
1
2
0
2
0
1
0
0
1
2
0
0
0
1
1
1
0
0
0
1
0
2
2
1
2
1
0
1
2
0
1
0
2
0
0
2
0
0
0
1
1
0
0
1
0
1
0
0
1
0
0
1
2
1
0
0
0
2
2
3
0
1
0
0
1
2
0
0
1
6
0
0
0
0
2
0
2
2
0
0
2
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
2
2
1
1
0
3
0
1
0
0
0
1
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
1
0
2
0
0
1
0
1
1
0
2
1
0
1
1
0
0
2
2
0
1
0
0
0
0
2
0
0
0
2
2
0
0
1
2
0
0
1
0
0
0
5
1
1
0
0
2
0
1
2
3
2
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
5
0
0
1
0
0
0
1
1
0
2
2
2
1
1
0
0
0
0
0
1
2
0
1
2
2
0
1
2
0
1
2
1
2
2
0
1
1
1
0
0
0
0
2
0
2
0
0
0
0
0
1
1
2
1
1
0
1
0
0
1
1
0
0
0
2
0
0
0
0
0
2
2
0
1
5
1
2
0
0
0
1
2
2
0
1
0
0
1
2
1
0
3
1
0
0
0
2
1
0
0
0
0
0
2
1
0
1
2
2
0
0
2
1
0
0
1
0
0
1
0
1
0
0
0
0
2
0
0
2
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
2
1
0
0
1
2
1
0
1
0
5
2
2
0
0
2
2
0
4
0
0
0
0
0
1
1
0
0
0
2
0
0
1
2
0
4
0
1
3
1
2
1
1
1
1
2
0
0
0
0
0
1
0
0
0
0
2
0
1
0
1
0
0
0
0
0
1
1
2
1
0
0
3
0
0
2
0
0
0
2
2
0
2
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
2
0
0
0
1
0
1
0
2
0
2
2
0
0
2
1
2
2
1
0
1
1
0
0
1
2
1
2
1
3
0
0
2
2
2
1
1
0
2
0
1
2
0
1
1
1
0
0
0
2
0
0
0
2
0
0
0
2
1
1
2
0
0
0
0
0
0
0
0
2
0
0
1
1
2
8
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
2
0
1
0
0
1
2
0
0
0
0
0
2
0
0
2
0
0
1
0
1
0
0
0
2
1
1
2
3
0
0
0
0
0
0
0
0
1
1
0
2
0
1
1
0
2
0
0
1
0
2
0
0
0
2
3
1
0
0
1
0
0
2
0
1
0
1
0
1
1
2
1
2
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
1
0
1
0
0
2
0
0
1
2
1
0
1
1
1
2
1
2
1
0
0
0
0
0
0
0
0
2
0
1
0
1
1
0
1
2
2
2
2
1
0
0
0
0
0
2
1
2
1
2
0
0
0
1
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
2
0
0
0
0
1
1
0
1
0
1
0
1
0
3
0
1
0
1
1
0
0
0
2
0
2
1
0
1
1
2
0
0
1
2
0
0
1
3
2
0
2
1
2
2
2
0
1
0
0
0
0
0
1
1
1
1
3
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
1
2
1
1
0
0
0
0
2
0
1
1
0
0
0
2
0
0
3
2
2
0
0
1
2
0
0
2
0
0
0
1
2
3
0
0
1
2
0
2
2
0
0
2
0
2
1
0
1
0
0
0
1
1
2
0
1
2
1
0
0
0
2
0
1
0
1
1
2
0
1
1
0
0
0
2
1
2
1
0
0
0
2
1
0
2
1
0
1
0
0
0
2
1
1
2
0
0
0
2
2
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
2
0
3
2
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
5
1
1
0
1
1
2
0
0
0
3
1
1
0
0
0
0
1
0
0
0
0
0
0
3
0
0
3
2
1
3
2
0
0
1
0
1
0
2
1
0
0
1
1
1
0
1
1
0
1
0
0
0
0
0
0
0
1
2
0
0
2
13
0
1
0
0
0
2
0
1
0
0
1
0
0
0
2
0
2
2
0
2
0
0
0
2
0
1
0
1
0
1
2
0
0
1
0
0
0
0
2
0
1
0
0
1
0
0
0
2
1
0
0
0
0
2
0
0
1
1
0
0
0
0
2
0
2
0
1
0
2
0
2
1
1
1
0
2
2
1
0
0
2
0
2
2
1
0
0
2
0
0
0
0
2
1
1
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
1
0
0
0
2
0
0
1
1
2
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
1
0
2
0
0
0
0
2
0
0
0
0
1
0
1
1
2
1
0
0
0
1
1
1
1
2
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
2
1
0
0
0
2
1
1
0
0
0
0
1
2
0
0
1
1
0
1
0
0
2
0
2
1
1
0
0
0
2
0
0
2
0
2
1
1
0
0
1
0
0
0
2
0
0
0
1
1
0
0
0
0
1
2
0
0
0
2
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
1
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
3
0
2
1
5
0
0
1
2
0
2
0
0
1
4
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
2
0
0
1
0
0
0
0
1
0
0
2
0
1
4
0
0
0
0
0
0
0
2
0
0
2
5
1
0
2
0
0
0
0
2
1
1
2
1
0
0
3
0
0
1
0
1
0
0
0
2
2
1
2
0
1
4
0
1
0
0
2
0
0
0
0
0
0
1
2
0
0
1
0
1
1
0
0
0
0
2
0
0
0
1
2
1
0
2
0
2
0
0
0
0
0
1
0
0
2
0
0
1
3
1
0
0
0
2
1
1
0
0
2
0
0
0
0
0
2
0
0
0
0
2
2
0
2
2
1
0
0
2
0
0
2
2
0
0
0
5
1
0
0
1
2
1
0
0
0
2
1
2
0
2
1
2
0
2
0
0
0
1
0
0
0
0
2
4
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
2
0
0
1
0
1
0
3
0
0
1
0
0
2
2
1
0
0
0
0
0
0
1
2
0
2
2
0
0
2
1
1
0
2
0
0
0
0
1
0
0
1
1
0
2
0
0
0
0
1
0
0
1
0
2
0
1
2
0
0
1
0
0
0
0
2
1
1
0
0
0
0
2
0
0
3
1
0
0
0
0
1
2
1
1
1
1
0
0
3
1
0
0
2
0
0
0
2
1
1
1
0
3
0
1
2
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
2
1
3
0
0
0
0
0
3
1
2
0
0
0
0
2
0
0
0
2
1
1
0
0
0
3
0
2
2
0
1
0
1
3
1
0
0
0
0
0
1
0
2
0
2
1
2
1
2
2
0
0
1
0
0
0
3
1
2
0
0
0
0
1
2
0
0
0
1
2
0
0
0
0
0
2
0
2
1
1
2
1
1
0
0
0
2
0
0
0
1
0
1
1
2
0
0
0
2
0
0
1
0
2
1
1
1
1
0
0
0
0
0
0
2
3
2
0
0
0
0
1
0
0
2
0
0
0
0
0
1
2
0
0
0
2
1
0
0
0
0
0
2
2
0
0
0
0
1
0
2
2
1
1
1
0
0
1
0
2
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
2
2
1
0
1
1
0
2
0
2
0
0
0
1
2
2
1
0
0
0
1
1
0
1
2
2
0
0
0
0
1
0
0
0
2
2
0
0
2
0
0
0
0
2
1
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
2
2
2
2
1
0
0
1
2
1
3
0
0
0
1
1
2
1
0
0
0
1
0
1
0
0
0
4
0
0
3
2
0
0
0
0
1
0
0
0
0
1
0
4
2
2
2
2
2
0
1
0
2
2
2
0
2
0
2
2
0
0
2
0
0
1
2
0
0
0
0
0
0
0
1
0
0
1
2
0
3
1
1
2
0
1
0
0
2
1
0
1
0
0
0
0
0
1
0
0
1
0
2
0
1
0
1
0
0
1
2
1
2
1
0
1
0
0
0
0
1
1
0
1
1
2
0
0
0
2
0
0
0
2
3
0
0
0
1
1
2
0
1
0
0
0
3
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
3
1
2
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
2
1
1
0
0
0
0
0
2
0
1
1
1
2
0
0
1
0
2
2
1
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
2
0
0
0
2
1
0
0
0
0
1
1
0
0
1
1
0
2
0
1
1
2
0
2
0
1
0
0
0
2
0
1
0
0
2
0
0
1
2
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
2
2
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
2
2
0
0
2
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
1
2
2
0
0
0
2
0
1
0
0
2
0
1
2
2
2
1
0
2
0
0
4
1
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
2
1
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
2
2
2
2
1
1
1
0
2
1
2
0
0
1
0
0
0
2
0
2
0
0
2
0
2
0
0
0
2
2
0
0
0
1
3
1
0
0
0
2
0
0
2
2
1
3
1
3
2
2
0
0
0
0
1
2
0
1
1
0
0
1
1
2
0
1
0
3
0
2
1
0
1
0
1
0
1
2
2
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
1
0
2
1
0
0
1
1
0
1
0
0
0
2
3
1
0
2
0
0
0
2
0
1
0
2
0
0
0
0
0
0
1
0
1
2
0
1
1
0
0
6
0
2
0
0
0
1
2
0
0
2
0
1
0
1
0
1
0
1
0
0
0
0
0
2
1
0
2
2
1
1
0
1
1
2
1
2
3
2
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
1
2
2
2
1
3
2
0
1
0
1
1
2
0
0
2
2
0
2
0
2
1
2
1
1
0
0
0
0
0
0
0
2
1
1
2
0
0
3
1
2
0
0
0
1
0
0
1
0
0
1
0
1
1
1
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
1
1
0
1
0
1
0
1
2
3
2
0
0
1
0
2
0
0
1
3
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
2
3
1
1
0
0
0
2
0
1
0
0
0
2
3
0
0
1
0
2
0
2
2
2
0
1
0
0
0
0
0
2
0
2
1
0
1
1
0
1
0
1
1
2
0
0
1
2
2
2
0
0
1
0
1
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
1
0
2
5
1
0
2
0
0
0
1
0
0
1
1
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
2
0
0
1
0
0
1
0
2
1
3
1
0
2
1
0
0
0
1
2
0
0
0
0
0
1
1
2
1
0
2
2
2
0
2
0
2
1
1
1
1
0
0
1
0
0
0
1
1
0
1
0
1
0
1
0
0
0
1
0
0
0
2
2
0
0
2
0
2
0
0
2
0
0
1
0
0
3
0
0
0
0
0
0
1
2
2
0
0
1
2
0
0
2
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
2
0
0
1
0
0
0
1
0
2
1
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
2
1
0
0
2
0
0
0
2
0
0
0
0
0
0
1
2
0
2
2
1
1
0
0
3
0
2
0
2
2
0
0
0
0
2
0
1
1
2
0
0
0
2
2
0
2
2
0
2
0
1
0
2
0
0
0
0
1
2
0
0
2
0
0
1
1
0
0
0
0
0
0
2
0
2
0
2
0
0
2
0
0
1
0
2
1
0
0
0
0
2
1
0
7
0
0
0
1
0
0
2
0
1
0
1
0
0
0
2
1
0
3
1
0
0
1
0
0
0
1
0
2
0
0
1
0
0
0
1
2
0
0
3
0
0
0
0
0
2
1
0
3
1
2
2
1
2
0
2
2
1
0
0
1
0
3
1
0
0
0
0
0
1
0
0
0
1
0
0
2
1
0
1
0
0
1
2
0
0
0
0
0
3
0
0
1
3
0
0
1
1
1
1
1
1
0
2
1
0
0
0
1
0
1
1
0
0
0
0
2
0
0
1
0
1
0
2
0
0
2
0
0
0
1
0
0
1
1
1
2
0
1
0
1
0
0
1
0
0
1
0
0
0
2
0
0
0
1
2
1
1
0
1
2
0
0
1
2
1
1
0
0
0
0
0
0
0
2
0
0
2
2
0
1
0
2
0
0
0
0
0
1
0
1
0
1
2
1
0
1
1
1
2
1
2
2
0
1
1
0
1
3
0
1
0
1
2
2
0
0
10
0
2
0
0
0
0
0
0
0
0
1
1
2
1
0
1
0
1
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
1
2
2
1
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
1
1
0
1
1
1
0
1
0
2
0
0
1
2
0
0
0
0
1
0
0
0
2
0
0
0
2
0
2
0
0
2
2
0
0
1
0
2
0
0
0
0
1
0
3
1
2
0
1
1
0
0
1
0
0
1
0
1
0
0
0
2
0
0
1
0
0
0
2
0
0
0
3
2
0
0
2
1
0
0
0
1
0
2
1
2
0
0
1
0
0
1
0
0
0
0
2
2
2
2
0
0
0
0
0
1
2
0
0
0
0
1
0
0
2
0
2
2
0
0
0
0
0
3
1
2
0
2
1
0
1
0
0
0
1
3
0
0
2
0
0
1
0
0
2
0
3
0
1
2
0
0
2
0
0
0
2
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
2
0
0
2
1
2
0
0
3
0
0
1
0
2
0
2
0
1
0
0
0
1
0
0
1
0
1
0
0
1
1
1
2
0
2
2
1
0
2
2
0
0
1
0
0
1
0
1
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
2
1
2
0
0
2
0
1
2
1
1
1
0
1
0
0
0
1
2
1
0
0
1
0
0
0
0
0
0
0
0
0
7
0
0
2
0
0
0
1
1
0
0
1
1
0
1
2
1
0
2
1
2
0
0
0
2
0
0
1
2
0
1
1
1
2
0
0
1
2
1
0
2
0
0
2
0
0
0
1
0
1
2
0
1
0
1
0
0
2
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
1
1
0
1
0
1
0
1
2
0
0
0
0
0
0
0
1
3
1
1
0
0
4
1
1
1
2
1
0
0
2
0
0
1
2
0
1
0
2
2
0
1
0
1
2
0
0
0
0
0
0
2
2
1
1
1
0
0
0
0
1
0
2
1
0
0
2
0
2
0
0
0
0
3
1
0
0
0
0
0
0
2
1
0
1
0
2
0
2
1
0
0
2
0
1
0
2
2
0
1
1
0
1
0
1
0
2
0
0
2
0
1
0
0
1
1
1
4
1
0
1
0
0
1
0
1
0
0
2
0
0
1
0
0
0
2
0
2
0
1
0
0
0
0
0
2
1
0
1
2
0
1
0
0
0
0
0
1
0
0
1
2
1
0
0
2
1
0
0
2
0
0
0
0
0
1
1
1
3
0
0
2
2
0
1
1
0
1
1
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
2
4
0
0
1
0
0
2
0
0
1
0
1
0
0
0
2
0
0
0
1
2
0
0
0
1
0
1
0
1
1
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
2
1
2
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
1
3
0
1
0
0
0
0
2
1
0
1
2
0
2
0
2
1
1
0
1
0
2
0
2
0
2
0
0
1
0
2
2
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
2
1
3
0
0
1
2
0
0
0
1
0
0
1
0
0
0
0
2
1
2
2
2
0
1
1
2
1
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
2
3
0
1
0
0
1
0
0
0
1
1
0
0
0
0
2
0
1
0
0
1
2
0
0
1
2
1
1
1
5
0
1
2
0
2
0
2
0
0
1
0
0
0
1
1
0
1
0
0
1
0
0
0
0
2
0
1
0
2
0
0
0
1
0
2
0
0
1
0
1
2
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
3
0
2
0
2
1
1
0
0
0
2
0
0
1
2
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
2
1
0
0
1
1
1
2
0
0
1
0
0
1
0
0
1
0
1
0
1
1
1
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
2
0
0
0
0
1
2
1
0
1
1
2
1
1
2
0
0
0
0
0
1
1
1
0
0
1
0
0
2
0
1
0
1
0
0
0
2
0
1
0
1
0
1
0
0
0
1
1
1
0
0
1
0
0
0
2
1
0
1
0
1
0
1
0
0
7
0
0
0
0
0
0
0
1
2
0
1
0
2
0
0
0
2
0
2
1
2
0
0
1
0
1
0
0
0
1
1
1
0
0
1
0
2
5
1
1
0
0
0
1
0
0
0
0
1
0
2
1
0
0
1
1
0
0
1
1
1
0
0
2
0
0
1
1
0
2
1
0
2
2
2
2
0
1
1
0
2
1
0
1
0
2
2
0
1
0
1
0
0
1
2
0
0
1
2
0
1
0
2
1
0
2
3
0
1
2
2
1
2
2
0
0
1
0
0
0
0
1
1
1
1
0
0
0
2
0
0
1
0
1
0
1
1
0
3
1
1
2
2
2
2
1
1
2
1
0
0
0
0
0
1
3
2
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
1
0
0
0
2
0
1
0
0
2
1
2
0
0
0
0
2
1
0
0
2
0
0
0
2
2
2
2
2
0
0
1
2
2
0
2
0
0
2
3
0
2
0
0
0
1
0
2
1
0
0
2
1
2
0
0
0
0
2
0
0
0
0
2
1
2
1
1
0
0
0
0
0
1
1
0
0
1
3
0
0
2
0
2
1
1
0
0
0
0
0
1
1
1
0
0
0
1
1
1
1
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
2
2
0
2
1
2
0
0
1
0
0
0
2
0
1
0
1
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
2
0
0
0
1
1
0
1
0
2
0
0
0
1
0
1
0
1
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
2
1
1
2
0
2
0
0
1
1
0
1
0
1
0
2
0
1
0
1
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
2
1
0
2
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
1
0
0
1
2
0
1
2
2
2
0
0
1
0
2
1
0
0
0
2
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
2
1
0
0
2
2
1
0
0
0
0
2
2
0
0
3
0
0
2
1
1
0
0
0
0
0
0
0
2
0
1
0
1
1
0
2
0
1
2
0
2
1
0
1
0
1
0
0
2
1
1
1
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
2
1
0
1
1
0
1
0
0
0
0
0
0
0
2
0
0
0
3
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
1
2
1
0
0
0
0
0
1
0
2
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
1
0
0
0
1
1
1
0
0
0
2
2
1
2
1
0
0
2
0
0
0
1
3
0
0
0
2
2
1
0
2
2
2
0
1
1
0
0
1
2
0
0
0
0
2
2
0
2
2
0
1
0
0
3
1
1
2
0
1
0
0
0
0
0
2
1
0
1
0
0
1
0
1
0
1
0
0
0
2
1
0
0
0
0
0
3
0
0
0
0
3
0
1
0
2
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
2
2
2
1
1
0
1
0
0
0
3
1
2
2
0
0
0
0
0
0
1
2
1
0
0
0
2
0
0
0
0
1
2
2
0
1
0
0
0
1
0
1
1
1
1
0
1
1
0
0
2
1
0
3
2
2
0
0
0
2
0
0
0
0
2
0
1
0
0
2
2
0
1
0
0
0
3
1
0
1
0
1
0
0
2
1
2
0
0
0
2
0
0
0
0
0
0
0
2
2
2
0
1
0
1
0
0
1
2
0
0
0
0
0
0
0
1
5
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
2
1
1
2
0
2
2
1
1
1
0
2
0
2
1
0
1
0
1
2
0
2
0
0
1
2
2
2
0
0
3
0
1
0
0
0
2
0
1
0
1
0
0
1
0
0
0
0
0
2
0
2
2
0
2
0
0
0
1
1
2
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
1
1
0
0
0
2
0
0
0
0
0
0
1
0
2
0
2
0
0
0
2
0
0
0
2
0
0
2
1
1
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
2
0
2
0
0
1
1
0
0
4
0
2
0
0
0
1
0
0
1
0
3
1
1
0
2
0
3
1
1
2
1
0
0
0
0
0
2
2
0
1
0
0
0
1
4
2
0
0
2
0
0
3
0
1
0
0
2
0
1
2
2
1
1
2
1
0
0
0
0
0
0
1
1
0
2
0
3
2
0
1
0
0
1
0
0
0
0
0
1
0
2
0
0
1
0
0
1
0
0
0
0
0
2
1
0
0
2
0
1
2
2
2
0
1
0
0
2
1
0
0
3
1
0
0
0
0
0
0
6
1
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
2
3
0
2
1
0
0
2
0
2
1
0
0
1
3
0
0
0
2
0
1
2
0
1
0
0
0
0
1
1
1
0
2
0
1
0
2
1
2
0
0
2
0
1
1
2
0
0
0
0
2
0
1
0
2
0
0
0
2
2
0
0
3
0
0
0
1
2
0
0
2
1
2
2
2
0
1
2
0
1
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
1
0
1
0
1
0
0
1
0
0
0
1
1
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
2
0
0
0
0
1
0
1
1
2
0
3
3
0
0
1
0
0
0
0
0
0
0
2
1
1
1
0
1
0
0
0
0
0
0
0
2
1
0
4
0
2
0
0
0
1
2
1
0
0
0
2
0
1
1
2
1
0
2
0
0
0
2
0
0
1
1
0
0
1
0
0
2
0
2
0
0
0
0
2
1
2
0
2
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
1
0
1
1
0
2
0
2
2
0
2
0
1
1
1
2
0
2
0
0
0
0
0
2
0
1
1
1
0
0
0
0
0
2
0
0
0
1
2
1
0
0
0
0
2
2
1
0
0
0
1
0
0
1
1
0
2
1
0
0
0
0
0
1
0
0
0
0
0
1
1
2
0
1
2
1
0
0
0
2
2
1
0
3
1
0
0
2
0
1
1
2
1
1
2
1
2
0
1
1
0
0
0
0
0
0
2
2
0
1
1
0
1
0
1
1
0
0
0
1
2
0
2
1
0
0
0
1
2
0
0
1
2
5
2
1
1
0
0
2
0
1
0
0
0
1
2
0
0
0
0
2
1
0
0
0
0
0
1
1
1
0
0
2
0
0
2
0
0
2
2
2
1
0
0
0
0
1
1
1
0
0
1
3
1
1
3
0
2
0
1
0
1
0
0
1
0
0
0
0
0
1
0
2
1
2
0
0
2
1
1
0
2
0
0
0
0
0
0
3
0
1
1
1
0
1
2
0
0
1
0
0
2
0
0
1
0
0
0
0
2
1
1
0
0
0
0
1
0
0
0
0
4
1
0
0
2
0
2
0
0
0
2
0
3
1
0
2
0
0
1
0
3
2
0
0
1
0
2
2
2
1
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
2
0
0
2
2
0
0
1
1
0
0
1
0
0
2
0
2
1
2
0
1
0
0
0
1
2
1
0
0
1
2
0
0
0
0
0
1
0
1
1
1
0
0
1
0
2
1
2
0
0
0
2
2
2
0
0
1
0
1
1
0
0
0
0
0
1
1
0
0
1
0
1
1
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
1
2
1
0
0
1
0
2
0
1
0
0
1
0
0
2
2
0
0
0
2
0
1
2
0
2
0
1
0
1
1
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
3
0
0
0
1
0
1
0
0
3
2
1
1
2
0
1
0
0
1
1
2
0
1
0
2
2
3
0
0
0
2
0
0
1
1
1
2
1
1
0
0
2
0
3
2
2
0
3
0
2
1
0
0
1
4
0
1
0
0
1
1
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
1
1
0
1
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
1
2
2
0
2
1
2
0
0
1
0
0
0
0
0
1
0
2
0
0
2
0
1
0
0
1
2
1
2
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
2
2
0
1
2
0
2
0
0
0
0
0
2
0
1
0
0
2
1
0
1
0
1
0
0
0
2
0
1
2
0
2
0
1
2
0
2
0
1
2
0
0
0
2
1
0
0
0
1
0
0
0
0
2
2
1
1
0
2
1
1
0
2
0
0
2
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
2
0
1
1
3
0
0
2
2
1
2
0
4
0
1
1
2
0
0
0
2
2
1
2
0
0
1
1
0
2
0
0
1
1
0
2
0
0
1
0
2
0
0
0
0
1
0
2
0
2
2
0
2
0
0
0
0
1
1
0
0
2
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
2
0
1
0
0
2
0
0
0
2
0
2
0
0
0
0
1
0
2
2
1
0
0
0
0
2
1
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
2
0
1
0
0
0
2
0
0
0
2
1
0
2
2
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
1
2
1
0
1
2
0
2
0
0
2
1
2
0
0
2
2
0
1
0
1
0
0
0
1
1
2
0
2
0
0
0
1
0
1
0
2
0
0
2
0
0
0
0
0
1
0
4
0
0
0
1
0
0
0
0
2
1
1
0
1
2
0
0
0
0
0
3
1
0
2
2
0
2
0
0
0
0
1
2
0
2
2
1
0
0
0
0
0
0
0
1
0
7
0
3
1
1
0
0
0
1
0
2
2
0
1
1
1
0
0
3
2
1
0
0
2
0
0
1
2
2
0
0
0
9
0
0
0
0
2
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
2
0
1
0
0
2
0
0
2
0
0
1
1
0
1
0
0
0
2
0
0
1
1
0
2
0
1
2
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
2
0
2
2
1
2
2
1
0
2
0
1
2
0
0
2
0
1
1
0
0
1
0
2
1
1
2
0
0
0
0
0
2
0
2
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
1
2
0
2
1
0
0
0
1
0
0
0
0
1
0
0
0
2
1
0
0
1
1
1
2
0
0
0
1
0
1
0
0
0
0
1
2
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
1
2
1
1
0
0
1
0
1
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
2
0
2
1
0
0
0
0
1
1
0
0
1
0
0
0
2
1
2
1
0
0
1
0
0
0
2
0
0
0
0
0
0
2
2
0
1
2
2
0
2
0
1
1
0
0
0
0
0
1
0
0
0
0
2
4
1
0
1
2
0
0
0
0
0
0
0
1
2
0
1
0
0
2
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
1
0
0
1
0
2
1
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
1
2
0
0
1
0
0
0
0
1
1
0
0
1
0
4
0
0
4
1
0
0
0
0
2
1
0
0
1
1
2
0
0
0
1
0
1
2
2
1
1
0
0
0
0
0
2
0
0
0
0
2
1
0
2
0
0
1
2
1
0
0
2
1
1
0
1
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
2
0
1
0
0
0
0
1
0
1
0
1
3
2
1
0
1
1
2
2
0
0
1
1
0
1
2
0
1
0
1
0
0
2
0
0
1
2
0
4
0
2
2
1
0
1
1
0
2
1
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
1
1
1
0
0
2
0
1
1
0
0
1
2
1
1
0
2
0
0
1
0
2
0
1
1
0
1
0
0
0
1
2
0
2
2
1
2
0
1
1
0
0
1
2
0
1
0
0
1
1
1
0
0
1
1
0
1
0
1
1
1
1
0
0
1
0
2
1
0
1
1
0
1
1
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
1
0
1
1
0
2
0
1
1
0
0
0
0
0
2
1
2
0
0
1
1
0
0
1
2
0
0
3
1
3
0
0
6
1
0
0
2
0
1
0
1
0
2
0
0
0
1
1
0
0
0
0
0
1
0
1
0
1
0
0
1
3
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
2
1
2
1
3
0
1
0
0
0
2
4
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
1
0
2
2
0
2
0
2
1
0
0
1
2
1
1
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
1
2
0
1
0
0
0
0
2
0
3
1
0
1
0
1
0
0
0
2
1
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
1
0
0
1
0
2
1
2
2
0
1
0
2
0
0
0
0
0
1
0
1
0
3
2
0
2
0
0
0
0
0
0
1
2
0
2
0
0
0
2
0
1
0
1
2
0
0
0
1
0
1
0
0
0
0
0
2
0
0
1
1
0
0
1
0
2
0
0
1
0
1
0
0
0
2
0
0
0
1
1
0
0
2
0
1
1
0
0
0
0
0
7
1
2
0
2
1
1
0
2
0
0
0
1
0
2
1
2
2
0
2
3
1
0
0
0
0
1
1
0
1
0
0
2
0
2
1
1
0
1
0
0
1
1
1
0
1
0
2
0
2
0
2
2
0
1
1
0
0
1
0
1
1
1
1
0
0
1
0
1
0
0
0
0
0
0
3
0
0
0
2
0
0
0
2
0
1
2
0
2
0
0
0
0
0
0
0
2
0
1
0
0
1
1
0
1
1
2
2
1
0
2
0
0
1
0
0
2
0
2
0
4
1
0
0
2
2
0
2
0
0
2
0
0
1
0
0
0
0
0
2
0
2
0
1
2
1
2
0
0
0
0
0
2
0
0
1
0
1
0
0
2
0
2
0
0
0
0
2
0
1
0
0
1
0
2
0
2
2
2
2
0
0
2
1
2
0
1
0
1
0
1
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
2
2
2
1
2
0
0
0
0
2
2
0
2
0
2
1
0
2
2
0
0
2
0
0
0
0
0
0
2
0
0
0
3
0
2
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
1
2
1
0
0
1
0
1
0
1
1
0
0
0
0
0
2
0
2
0
0
2
2
0
0
2
6
1
0
2
0
0
0
0
1
0
0
1
0
1
2
0
0
0
1
1
1
0
0
0
1
0
0
0
0
2
0
0
2
0
0
2
0
1
0
0
0
1
0
0
0
1
0
3
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
2
1
1
1
0
1
1
2
0
0
1
0
0
0
1
0
2
0
0
0
1
2
0
1
0
0
0
1
2
1
0
0
0
0
0
1
0
1
2
2
1
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
2
0
1
0
1
2
0
1
0
1
0
2
1
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
3
0
0
0
0
0
0
1
0
1
1
0
0
0
2
2
0
0
3
0
0
2
0
2
2
0
0
0
1
1
2
1
0
1
0
0
1
0
2
0
1
0
1
0
0
0
0
1
0
2
0
0
0
1
0
2
1
0
0
0
0
0
0
0
2
1
0
1
2
2
1
2
0
1
0
1
1
0
1
0
0
2
1
0
2
0
1
2
0
0
0
3
0
2
0
0
2
0
2
1
1
2
0
0
2
0
0
2
0
0
2
0
1
2
0
1
0
1
0
0
1
0
0
0
0
0
1
2
0
3
0
2
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
1
2
0
2
2
2
0
1
0
0
0
0
1
0
2
0
1
0
0
0
0
1
0
2
0
1
0
2
0
0
0
0
2
0
1
0
2
0
1
1
0
0
1
0
0
1
1
0
0
1
0
0
3
0
0
0
0
1
3
2
1
0
0
0
1
0
0
1
0
0
1
0
0
1
2
0
2
2
1
0
0
0
0
0
1
0
0
1
0
1
0
2
1
1
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
1
2
2
2
1
2
1
0
0
0
1
3
0
1
0
2
0
0
4
0
0
0
1
1
2
0
2
0
1
0
0
0
0
2
2
2
0
0
1
0
2
1
0
0
1
0
2
0
0
0
0
2
0
0
0
1
0
2
0
2
1
0
1
0
2
0
3
1
1
1
1
0
0
1
0
1
0
0
2
0
1
0
1
2
1
0
1
0
0
2
1
2
0
2
0
0
1
1
1
0
1
0
0
0
0
4
0
0
2
0
1
2
0
0
0
1
0
0
1
0
0
1
0
0
0
0
2
1
0
0
0
0
0
1
1
1
0
1
0
0
0
2
0
2
0
0
0
0
2
2
0
0
2
0
2
1
1
0
0
2
2
0
2
2
0
0
0
0
2
0
0
1
1
0
1
1
1
1
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
2
2
0
1
0
0
2
0
1
0
0
2
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
1
1
3
2
0
0
1
0
0
1
0
1
0
0
0
0
2
1
1
0
0
0
0
2
2
2
0
1
1
0
0
2
0
1
0
0
0
0
2
2
2
2
0
0
2
0
0
2
0
1
0
0
2
0
0
0
0
0
1
2
0
3
0
1
1
1
2
1
1
0
0
0
0
2
0
1
0
0
0
2
2
0
1
2
1
0
2
0
0
0
1
2
0
0
2
0
1
0
0
2
1
0
1
0
0
0
0
0
0
2
4
0
3
1
0
2
0
3
1
0
0
0
2
0
2
0
0
1
0
0
1
0
1
2
3
2
0
0
2
0
0
0
1
1
0
1
1
0
2
0
1
1
0
0
0
0
2
0
1
0
0
0
1
2
0
2
0
2
5
1
1
0
0
2
1
2
0
2
2
0
0
0
1
1
2
2
2
0
2
0
0
1
1
0
2
3
0
1
1
0
2
0
1
1
0
0
1
0
0
3
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
1
0
4
2
0
0
0
0
0
1
2
1
1
0
0
0
1
0
0
1
0
0
1
1
0
2
0
2
0
1
0
0
2
1
0
0
2
0
0
0
0
0
1
2
0
1
0
0
0
0
1
0
0
0
3
1
2
0
1
0
0
2
0
3
5
1
0
1
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
2
2
0
2
0
0
2
0
1
0
5
2
0
0
0
2
0
1
0
1
1
1
2
1
0
0
0
1
4
1
0
0
2
2
0
0
0
1
0
0
0
0
0
2
1
0
1
0
0
0
2
2
2
1
1
0
0
0
0
2
2
0
1
0
2
0
3
0
1
0
1
1
1
3
2
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
3
0
1
0
0
0
0
0
0
1
2
3
1
2
0
2
0
2
0
0
0
0
0
1
2
0
1
0
0
0
0
2
1
1
0
0
1
0
0
0
1
0
0
2
3
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
2
0
0
0
2
0
0
1
0
0
1
1
1
0
0
0
0
0
2
1
0
0
0
0
1
0
1
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
2
2
0
1
0
0
2
1
1
0
0
2
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
1
0
1
2
2
2
0
0
2
0
0
0
0
1
1
2
2
0
0
1
0
1
0
0
1
1
1
0
2
2
0
0
1
1
0
0
0
0
2
0
0
2
0
2
0
1
3
1
1
1
3
0
0
0
0
1
1
1
0
0
1
1
0
0
0
0
0
0
1
0
1
2
0
1
0
1
0
0
0
1
0
0
0
1
2
1
1
2
1
0
2
3
1
0
0
0
2
0
0
2
2
3
1
1
1
0
1
0
2
0
1
2
0
2
1
2
0
0
0
1
0
1
2
0
0
0
0
0
0
2
2
2
0
0
4
0
0
4
2
1
0
0
1
1
2
0
0
0
3
0
0
0
2
0
0
1
2
0
2
1
0
1
0
1
2
0
2
0
2
1
0
0
1
0
0
1
0
0
2
0
1
0
2
0
0
0
2
1
0
0
0
0
0
2
2
0
1
0
1
1
1
0
2
2
0
1
0
2
0
0
0
1
4
0
0
0
2
1
0
1
0
0
2
1
0
0
0
0
0
2
0
1
0
0
2
1
2
0
0
0
1
0
0
0
0
0
1
0
1
2
2
0
1
2
1
0
0
1
0
2
0
0
2
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
2
2
1
1
0
0
0
1
1
2
1
1
0
2
1
0
0
0
0
0
2
0
4
0
1
0
1
1
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
1
0
4
0
0
0
1
1
0
0
0
0
2
0
1
0
2
1
1
0
0
1
0
0
0
2
2
1
0
0
1
1
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
1
0
2
0
1
1
0
2
2
1
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
2
1
1
0
0
0
0
0
1
0
2
0
0
2
0
1
0
2
0
0
0
1
0
0
0
1
1
4
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
1
1
0
0
1
2
2
1
2
1
1
0
2
0
0
1
0
0
1
1
2
0
2
3
1
2
0
3
1
3
0
0
2
0
2
0
1
1
0
0
0
1
0
0
1
0
2
0
0
3
0
0
1
0
2
2
0
1
0
1
0
1
2
0
1
0
2
1
0
1
0
0
0
0
0
1
0
0
0
2
1
0
0
0
1
0
0
1
0
0
1
0
1
0
1
0
3
2
1
1
0
0
1
0
0
0
1
0
1
0
1
2
0
1
0
0
0
2
0
2
2
1
0
0
0
2
0
0
2
0
1
0
1
2
0
2
0
0
1
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
2
1
6
0
2
1
0
0
0
0
2
0
2
0
0
2
0
1
0
0
0
2
1
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
1
1
1
0
2
2
3
1
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
3
2
0
1
0
2
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
1
1
2
0
0
0
0
0
2
3
0
0
2
2
0
0
0
0
2
2
0
2
1
0
0
0
1
2
2
0
1
2
2
2
1
0
1
1
0
1
0
0
0
0
2
0
1
1
1
0
2
0
1
1
1
2
0
2
2
1
0
1
1
2
1
1
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
2
0
0
0
2
0
0
2
0
0
2
2
0
1
0
0
0
1
0
0
2
1
0
0
0
1
2
1
0
0
0
0
1
0
0
0
1
0
0
1
1
1
0
1
0
1
2
2
1
0
0
1
0
0
2
0
0
1
0
0
3
0
1
2
3
1
0
0
2
0
0
0
0
1
2
0
0
0
3
1
1
0
2
0
0
0
2
2
0
1
1
0
2
0
1
2
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
1
0
1
0
0
0
0
1
1
0
1
2
0
1
0
2
0
0
0
0
3
0
0
0
0
1
0
0
0
0
2
0
1
0
1
1
0
1
2
1
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
2
0
1
0
0
3
0
0
0
0
2
2
2
0
0
1
0
0
1
2
0
1
0
2
2
1
0
0
0
1
1
0
2
0
0
1
1
0
0
1
2
2
2
0
0
0
1
0
0
0
1
0
0
0
1
2
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
1
2
0
0
0
0
2
0
1
0
0
0
1
0
1
0
0
0
1
0
2
7
0
1
1
0
1
0
0
0
2
1
1
0
1
0
2
2
0
1
2
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
1
1
0
0
1
2
0
0
3
0
1
0
2
1
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
1
0
2
0
1
1
0
3
0
0
0
2
1
2
0
0
2
1
0
0
1
0
1
0
0
1
0
0
0
0
1
2
0
1
0
1
0
1
2
1
0
1
2
0
0
1
0
2
1
1
2
0
0
0
0
2
2
0
0
1
2
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
1
2
0
1
0
1
0
1
2
1
3
1
1
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
3
1
1
0
1
0
1
0
2
0
1
0
2
0
2
2
2
0
0
2
1
2
0
0
2
2
2
1
1
0
2
0
2
2
2
1
0
1
2
0
0
1
0
1
2
0
2
1
0
1
1
0
2
2
0
0
1
1
2
0
0
2
0
0
0
0
1
0
1
0
0
1
0
0
0
0
2
1
2
0
1
1
2
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
1
0
2
1
0
1
1
2
1
0
1
2
1
0
0
1
0
1
0
2
1
1
0
0
0
0
0
2
2
0
2
1
1
1
0
0
1
0
0
0
1
0
0
2
0
0
1
0
1
0
0
0
1
0
1
0
0
0
2
2
2
0
1
0
0
0
0
0
0
1
0
1
0
2
1
0
2
0
1
1
0
0
1
0
0
0
2
0
1
2
0
0
1
0
0
1
0
2
0
1
1
0
0
2
2
0
1
11
2
2
2
0
0
0
0
0
0
1
2
3
2
2
2
1
0
0
0
0
1
1
1
1
3
0
2
0
0
0
1
1
1
0
1
1
1
0
1
0
0
2
2
1
0
0
1
0
0
0
0
2
0
1
0
2
2
0
0
1
0
0
0
0
1
0
0
3
1
0
0
0
1
2
0
1
1
1
0
2
0
0
0
0
1
1
0
0
0
0
0
2
0
0
1
1
0
2
0
0
0
2
2
1
0
0
2
0
1
2
3
0
0
0
0
2
1
1
0
2
2
0
1
0
0
0
0
0
1
3
0
2
2
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
2
1
0
0
1
2
0
3
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
2
2
1
2
0
0
0
0
2
2
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
1
2
0
0
0
2
2
1
0
2
1
1
1
2
0
1
3
1
0
1
0
0
1
0
0
0
0
0
1
2
0
2
0
1
0
0
2
0
1
0
0
0
0
1
1
2
0
0
0
2
1
0
0
2
1
2
0
0
0
0
0
0
1
2
0
1
0
0
0
0
2
0
0
2
0
0
2
0
2
1
0
2
0
0
1
0
0
0
0
2
0
2
0
1
2
1
0
1
0
0
0
0
1
2
0
1
1
0
6
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
2
1
0
2
1
0
1
1
2
0
0
0
1
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
1
0
1
0
0
1
0
2
2
0
1
0
0
0
0
2
1
0
1
0
2
0
2
1
1
0
1
1
0
2
0
0
2
2
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
1
0
2
0
0
1
0
0
2
1
0
0
1
0
0
0
0
1
2
0
0
0
2
2
2
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
1
2
2
0
0
0
0
1
1
0
2
0
1
1
1
0
0
2
0
1
2
0
0
0
1
2
1
0
0
0
2
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
1
1
1
1
1
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
3
0
2
0
1
0
2
2
2
0
0
0
1
0
0
0
1
0
0
1
0
2
0
0
1
0
1
0
1
1
2
0
2
0
1
0
1
0
1
2
1
0
0
2
0
0
0
1
0
2
0
0
1
0
0
0
2
0
0
0
2
0
0
0
2
1
1
1
0
1
0
2
0
0
0
2
1
0
0
2
2
1
0
1
1
2
0
0
2
0
2
1
0
3
0
2
0
0
2
0
3
2
0
1
0
0
0
0
0
1
0
0
0
0
2
1
1
1
0
1
0
1
0
0
0
1
0
1
0
1
5
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
2
2
1
2
2
0
0
2
0
2
0
0
1
0
1
0
2
0
0
1
1
0
2
0
0
0
1
0
0
1
0
0
2
2
0
0
2
0
1
0
1
1
0
2
2
0
1
1
0
2
0
2
0
0
1
2
0
1
0
0
0
2
0
1
0
0
1
0
0
0
1
1
0
3
0
2
0
0
0
1
0
2
2
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
1
0
2
2
3
0
0
0
2
1
0
0
0
0
1
1
3
0
1
0
0
0
0
0
0
0
2
1
2
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
1
0
0
0
2
0
2
0
3
1
0
2
0
0
0
2
1
0
0
0
2
0
2
2
1
0
0
2
0
2
0
0
1
1
0
0
0
0
0
2
0
1
1
1
2
2
0
0
0
1
0
0
2
1
0
2
2
0
0
0
0
0
2
1
0
0
0
1
0
0
0
3
1
0
0
0
1
0
0
1
2
1
2
0
2
2
0
5
0
0
0
1
2
2
0
2
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
1
1
3
1
0
2
1
0
1
1
1
0
1
0
0
3
0
2
1
2
0
2
1
2
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
2
1
1
0
1
0
0
2
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
1
1
0
1
2
0
0
1
0
0
2
1
0
0
0
2
0
2
0
0
0
0
0
0
1
1
2
1
0
0
0
2
0
0
0
0
0
0
2
2
0
2
2
0
0
0
1
2
2
0
0
0
1
0
1
1
2
0
2
0
0
1
0
0
0
1
1
0
0
0
1
2
2
0
0
1
0
0
0
0
1
2
0
1
0
1
2
0
2
0
0
0
3
0
0
2
0
1
0
2
1
2
0
1
0
1
1
0
2
0
0
0
1
0
1
1
1
0
0
0
2
0
1
0
0
1
0
0
0
1
0
0
0
1
0
2
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
2
2
1
1
2
1
1
1
0
0
0
1
0
2
0
0
0
2
1
1
0
0
1
1
0
2
2
1
1
0
0
0
0
2
0
1
1
2
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
1
1
0
0
2
0
1
0
0
0
0
1
1
1
2
0
1
0
2
0
1
0
1
1
0
1
3
0
0
1
0
2
0
0
0
2
0
4
0
0
2
1
2
1
0
0
0
1
2
2
0
0
0
0
0
2
0
0
2
1
1
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
2
0
2
1
2
2
0
0
2
0
0
0
0
2
0
2
1
1
0
0
1
0
2
1
0
1
1
0
0
0
2
0
0
2
1
0
1
1
0
0
0
1
0
0
0
4
0
0
0
1
0
2
1
1
0
2
0
0
1
0
0
0
0
0
0
1
0
1
0
0
2
0
0
1
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
1
2
0
1
0
0
1
0
3
1
0
0
0
0
1
2
0
2
0
0
2
0
0
0
2
2
0
0
1
1
1
4
0
1
0
2
1
0
2
2
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
3
0
1
0
0
2
2
1
0
1
1
0
0
0
1
0
0
2
1
0
0
0
1
2
0
2
0
2
0
0
1
0
1
0
0
0
2
1
0
0
0
1
0
1
1
1
2
0
1
1
1
0
0
1
2
0
0
0
0
0
0
0
0
1
0
2
1
0
2
2
0
0
0
0
7
0
2
2
0
2
1
0
0
2
2
0
1
1
0
0
3
0
2
0
0
0
1
0
0
2
0
0
2
1
2
2
0
1
0
0
2
2
0
0
2
0
0
1
1
1
2
0
0
0
0
0
1
0
1
1
1
1
0
0
0
0
0
1
0
0
2
1
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
2
2
1
0
0
1
1
1
0
0
2
1
0
0
1
0
2
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
2
0
1
0
0
2
0
1
3
0
0
0
1
1
0
0
0
2
0
0
1
0
1
1
0
0
1
2
2
0
0
0
2
0
0
0
1
1
0
0
1
0
0
1
1
0
1
2
0
0
0
2
2
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
1
0
1
0
0
0
0
1
0
0
0
1
2
1
1
0
0
1
0
2
0
0
0
1
1
2
0
1
1
0
2
1
0
1
0
1
0
2
0
2
0
2
0
1
0
1
0
0
2
0
2
1
2
0
2
2
1
2
0
0
0
0
1
0
1
0
0
3
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
2
0
2
0
2
0
0
1
1
1
1
0
0
0
1
0
1
0
2
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
1
0
0
0
2
0
0
0
1
1
0
0
2
2
3
1
2
0
0
1
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
1
1
2
1
0
2
3
0
2
0
3
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
2
1
0
0
2
0
0
0
0
0
2
0
1
0
0
0
2
0
2
1
2
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
1
2
3
1
0
1
0
1
2
1
2
0
0
0
0
0
1
1
0
0
0
1
2
0
2
0
2
0
1
2
0
0
0
2
0
0
2
1
0
0
1
0
0
1
2
1
0
1
1
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
1
2
0
0
0
0
1
0
1
2
2
0
5
1
0
1
0
0
0
0
2
1
2
1
0
0
2
0
0
0
0
0
0
2
0
0
2
0
1
0
1
0
1
0
2
2
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
1
1
2
0
1
0
1
2
2
1
0
1
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
1
0
0
0
1
2
0
0
2
0
1
0
2
2
0
0
0
1
1
0
2
1
0
2
0
0
0
0
0
0
1
0
1
0
1
3
0
0
2
0
0
1
0
1
2
0
0
0
2
2
1
0
0
0
0
0
1
0
3
2
0
0
0
2
0
0
2
0
0
2
1
2
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
1
1
2
2
3
1
2
0
1
0
0
1
0
0
2
0
0
0
2
2
0
1
0
1
1
0
0
1
2
0
0
1
1
2
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
2
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
2
1
1
0
1
1
0
0
0
1
1
0
0
0
2
1
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
2
0
1
0
2
2
0
1
0
0
1
0
0
0
1
2
1
0
0
1
0
0
0
0
1
0
0
1
1
1
0
2
1
1
0
1
0
0
0
0
0
0
0
2
0
2
1
1
2
2
1
0
1
2
2
1
7
0
0
3
0
0
2
2
0
2
0
0
1
0
0
0
1
0
0
1
1
0
1
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
2
0
0
2
0
2
0
0
0
2
1
1
0
0
0
1
1
0
1
0
0
0
2
2
0
0
1
1
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
2
0
0
1
1
3
0
0
0
2
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
1
0
2
0
2
2
2
1
0
0
1
0
0
1
0
1
0
1
0
1
3
0
0
1
0
1
1
0
0
2
2
0
0
1
0
0
0
2
0
1
0
1
2
0
2
0
0
1
0
0
0
2
2
0
2
1
0
0
3
0
0
0
0
2
1
0
1
0
0
1
2
0
2
0
1
0
2
0
1
0
0
2
1
2
0
0
2
2
1
2
1
2
0
0
0
0
0
0
2
2
0
1
2
0
1
1
0
1
0
2
1
1
0
0
0
0
2
0
0
0
2
0
1
1
0
0
2
0
1
2
0
1
1
0
2
0
0
0
0
0
1
3
2
1
1
0
0
0
0
2
1
2
2
2
4
2
0
2
0
0
1
1
0
0
1
0
0
2
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
1
1
0
1
1
2
2
2
2
1
0
0
0
0
0
2
1
3
0
0
0
2
0
0
0
0
2
2
1
0
0
0
1
1
0
0
0
0
1
1
0
0
0
1
0
0
2
0
2
0
0
1
5
0
0
1
2
0
0
1
1
1
0
2
1
0
1
3
0
2
1
0
0
0
2
2
2
1
0
0
1
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
2
0
2
1
0
0
2
1
0
0
0
1
2
3
0
0
2
0
0
1
2
0
1
0
3
1
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
1
2
0
0
0
1
0
1
1
1
0
0
1
2
2
0
0
0
1
2
0
0
0
0
0
1
0
0
0
1
0
0
2
2
0
2
3
0
1
1
0
0
0
3
0
0
0
2
0
1
0
0
2
0
0
0
0
0
1
0
1
0
2
2
1
1
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
2
0
0
2
0
2
0
0
0
0
1
0
2
1
0
2
0
0
0
2
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
2
0
0
2
0
2
2
0
1
0
1
2
2
2
2
0
0
1
0
6
1
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
1
2
1
1
2
1
0
0
0
0
1
0
0
0
0
2
0
0
0
2
3
0
0
0
0
0
0
1
1
1
0
1
2
0
0
0
0
1
0
0
0
0
2
1
0
1
0
0
1
0
1
0
0
0
1
0
1
0
0
1
0
0
0
3
1
0
1
1
1
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
1
0
1
0
1
2
1
1
0
1
0
1
1
0
0
1
1
0
2
0
1
0
0
1
1
1
1
0
1
2
0
1
0
3
0
1
1
2
0
0
1
0
0
0
0
0
0
2
1
2
2
0
1
2
1
0
3
3
1
1
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
1
1
2
1
1
1
0
0
0
2
0
1
2
2
0
2
1
1
1
3
0
2
0
2
2
0
0
1
0
2
1
1
2
0
0
2
0
1
0
0
1
0
0
0
0
2
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
1
0
1
0
0
0
0
2
2
1
2
2
2
0
6
1
1
0
0
0
0
0
1
0
0
0
1
0
2
2
0
1
2
1
0
2
1
0
1
1
1
0
2
0
0
0
0
2
2
1
0
0
2
0
0
0
2
0
0
2
0
3
0
1
0
0
0
1
0
1
1
0
1
1
0
0
1
0
1
0
0
1
0
0
0
0
1
1
1
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
2
0
0
0
0
0
0
0
0
2
2
2
2
0
0
0
0
8
1
2
0
1
0
0
2
1
2
0
0
0
1
2
0
0
0
1
0
1
2
1
0
0
0
1
1
0
2
0
0
1
1
2
2
1
2
0
0
2
0
1
1
0
1
0
1
0
1
2
3
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
2
0
1
0
1
1
1
1
0
0
1
2
0
0
1
1
0
0
1
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
1
2
1
0
0
1
2
1
1
0
1
1
2
0
0
0
0
1
2
0
1
2
0
0
1
0
2
1
0
0
1
1
2
2
2
0
0
0
2
1
0
2
1
3
1
1
0
1
0
0
2
2
0
0
0
0
1
2
0
0
2
1
1
0
1
2
0
0
0
0
2
1
0
0
3
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
1
2
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
1
1
2
1
0
0
0
1
0
0
0
0
0
0
0
2
1
0
1
0
0
2
3
0
0
0
0
1
0
0
1
0
1
0
2
1
0
2
1
0
0
0
0
1
2
0
0
1
2
1
0
0
0
0
0
1
0
0
0
2
0
2
1
0
1
0
2
0
0
1
1
0
0
3
1
0
1
0
0
0
0
2
0
2
2
0
0
2
0
0
0
0
0
2
0
1
2
0
0
0
1
0
0
0
0
3
0
0
0
1
0
2
1
0
0
0
2
0
0
0
0
0
2
0
1
2
2
1
0
0
0
2
1
0
1
0
1
1
2
0
0
1
0
0
0
2
2
2
0
1
2
0
0
1
1
2
2
0
1
0
0
1
0
0
0
1
2
1
0
0
2
1
0
0
0
0
3
0
2
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
1
1
2
0
0
2
0
0
2
0
0
1
1
2
1
1
1
1
0
0
0
0
0
0
2
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
1
0
2
0
2
1
1
1
0
0
0
0
0
1
0
1
0
0
2
0
0
2
0
0
2
0
0
0
1
1
0
2
0
0
1
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
2
1
0
2
0
1
2
0
0
2
2
0
2
2
0
0
0
0
1
0
0
0
1
1
1
0
0
0
1
0
2
0
0
0
0
0
1
0
0
1
0
1
1
1
0
2
0
0
0
0
1
0
0
1
0
2
0
1
0
0
0
1
0
0
0
0
0
2
0
0
1
0
1
0
2
0
2
1
0
2
1
3
0
0
0
1
1
1
2
2
0
0
2
0
2
1
0
0
0
0
2
1
0
2
1
1
0
1
2
1
1
0
0
0
2
0
2
2
0
0
0
1
0
0
0
2
1
2
0
0
0
1
1
2
1
0
0
0
2
0
0
0
2
0
0
2
2
0
1
2
0
2
2
1
2
0
1
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
2
0
0
5
2
0
1
0
2
0
1
0
0
0
2
0
1
0
2
1
0
3
0
1
0
2
0
0
0
0
1
0
0
0
2
2
0
1
1
2
1
3
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
2
2
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
1
0
1
0
1
0
0
0
0
0
1
2
3
2
2
0
0
1
0
2
0
0
0
1
0
0
0
0
2
0
7
0
2
0
2
1
0
3
0
0
0
1
1
0
0
0
0
0
1
0
2
1
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
2
3
1
0
0
2
2
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
1
0
2
1
0
2
0
0
2
2
2
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
2
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
1
2
0
0
0
1
0
0
0
0
2
1
2
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
2
0
0
3
0
1
0
0
2
2
2
0
1
0
1
0
1
1
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
2
0
2
2
2
1
0
0
0
0
2
2
0
1
1
1
2
1
0
2
2
0
0
0
2
0
0
1
1
0
2
0
0
0
1
2
0
2
3
0
0
0
0
1
0
1
0
0
0
0
2
2
1
0
2
0
2
0
2
0
0
1
0
0
0
1
0
0
1
2
1
0
0
0
1
2
0
4
0
1
1
1
2
1
0
1
0
0
0
0
1
0
0
2
0
0
3
1
0
1
1
0
0
1
0
0
2
1
1
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
1
2
0
1
0
0
1
0
4
2
0
0
0
2
0
1
0
1
0
0
0
1
0
0
2
2
0
1
2
0
1
0
0
1
0
0
1
0
3
0
0
2
0
0
0
0
1
0
1
2
0
0
0
2
2
0
1
1
2
2
0
2
2
0
2
0
0
2
0
0
2
0
2
0
2
0
1
2
2
1
0
0
1
2
0
2
0
0
0
2
0
0
0
2
2
1
0
0
0
0
0
0
2
1
0
0
1
1
2
0
3
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
2
0
1
0
0
0
0
2
0
0
2
0
0
1
0
2
2
2
1
0
2
0
1
0
0
2
2
0
2
0
1
0
0
0
0
0
1
0
2
0
0
1
2
0
0
0
0
0
2
1
2
0
2
1
0
1
2
0
1
2
0
0
2
0
3
0
0
2
0
0
1
2
0
0
0
0
1
2
7
0
2
2
0
0
0
1
2
1
1
1
1
1
0
0
0
0
2
0
1
2
1
1
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
1
0
2
0
0
0
0
0
2
0
1
0
0
0
1
0
2
2
1
0
0
0
0
0
2
2
2
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
1
0
2
0
0
2
0
0
2
1
0
2
0
1
0
1
0
3
0
0
1
1
0
0
0
2
0
0
0
1
1
2
0
0
2
0
2
0
0
0
1
0
1
0
1
0
2
0
1
0
0
0
0
2
0
0
0
0
4
0
2
0
2
1
0
0
0
0
2
2
1
3
0
2
1
0
1
0
0
0
0
0
1
0
3
1
2
1
0
0
0
2
0
0
1
0
1
2
0
0
1
0
0
1
1
1
0
0
0
0
1
0
0
0
0
1
0
1
0
8
0
1
0
1
0
1
1
0
0
2
0
1
2
0
2
1
0
0
2
2
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
2
0
0
2
1
0
2
0
2
1
1
2
0
0
1
0
3
0
0
0
0
0
0
2
1
0
0
0
2
0
2
0
0
0
1
0
0
0
2
1
0
0
0
0
2
1
0
0
2
0
0
1
1
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
1
0
2
0
2
1
2
0
0
0
0
2
0
0
0
0
1
0
0
1
0
1
1
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
2
2
1
0
0
2
0
1
1
2
0
0
0
0
2
2
0
1
2
0
2
0
0
2
0
0
1
2
0
2
0
0
2
1
0
2
0
2
0
0
1
0
0
0
0
0
0
0
2
0
1
1
0
0
1
0
0
0
2
0
0
0
2
1
1
2
1
2
0
0
0
0
3
0
1
1
0
1
0
1
0
1
0
1
1
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
2
2
2
0
2
1
2
1
0
3
4
1
0
0
1
0
0
2
2
0
1
0
0
2
2
0
0
1
0
0
0
2
3
2
0
1
1
0
3
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
1
2
0
0
2
0
2
0
0
0
0
2
0
2
0
0
0
4
0
1
0
0
1
2
2
1
0
0
0
0
5
1
2
0
1
2
1
0
1
0
2
1
0
1
1
0
1
0
1
0
0
1
0
0
2
0
0
1
2
0
0
1
0
2
2
0
0
0
0
1
3
1
2
0
1
2
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
2
0
1
2
0
0
0
0
1
0
2
2
0
1
0
1
0
0
0
0
2
1
1
0
1
1
1
0
2
0
0
0
0
2
2
0
0
2
1
1
2
6
1
0
0
2
2
2
0
0
2
0
1
1
0
0
1
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
1
0
2
1
2
0
0
0
2
0
1
1
1
1
1
1
0
0
2
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
1
2
0
1
0
2
0
0
0
1
0
0
0
0
0
1
0
0
2
2
2
1
0
0
1
0
2
0
0
0
0
0
1
2
0
0
1
0
2
0
2
0
0
0
2
0
0
2
1
0
0
0
2
2
0
1
0
0
0
1
0
0
0
0
1
2
0
2
2
0
0
0
2
2
0
3
0
0
0
0
2
1
0
0
2
1
0
2
2
0
2
0
1
0
2
0
0
0
0
2
2
1
0
1
1
0
3
0
0
1
0
1
0
0
0
0
0
0
0
5
1
1
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
1
0
0
0
0
1
1
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
1
2
1
1
0
0
0
1
2
0
2
0
0
2
0
2
0
3
0
2
2
1
0
1
0
1
2
2
1
1
0
0
1
0
0
2
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
2
0
0
2
1
0
0
0
0
0
0
1
1
0
1
2
2
0
0
0
0
0
0
2
1
2
0
0
1
0
0
1
0
0
1
2
1
1
0
0
1
2
1
0
0
0
0
2
2
1
2
0
2
0
0
0
1
0
0
0
0
0
2
0
4
0
0
0
0
0
0
2
1
0
0
1
1
0
0
0
0
0
2
2
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
2
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
1
2
0
0
0
0
2
2
0
0
0
0
1
1
0
2
0
0
0
1
1
0
0
2
0
2
1
0
0
0
1
1
0
0
1
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
1
0
2
1
0
1
0
0
1
1
0
2
0
2
1
1
0
1
0
0
0
1
0
1
0
0
4
0
2
2
0
1
0
0
0
0
0
2
0
0
1
1
0
0
2
0
2
1
0
1
1
1
0
0
2
1
0
0
0
2
0
0
2
0
1
0
1
2
2
0
2
0
0
2
1
1
0
1
0
0
0
0
1
1
1
2
0
2
1
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
1
1
1
0
0
0
0
2
0
1
1
0
2
0
0
1
2
2
0
1
1
3
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
2
0
0
2
2
0
0
0
2
0
0
1
1
2
0
0
0
0
2
2
0
0
2
0
0
0
0
3
1
0
0
2
0
2
3
0
0
0
0
0
0
2
0
1
0
0
1
2
0
0
2
0
0
0
0
0
2
2
3
0
0
0
4
0
1
0
1
2
0
0
0
0
0
2
2
0
2
0
0
2
0
0
1
0
0
2
1
1
1
1
0
0
2
0
1
0
0
2
0
1
1
2
2
0
0
0
2
1
3
0
2
2
0
0
2
0
0
1
0
0
0
0
2
0
1
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
2
0
0
1
1
0
1
2
2
0
1
1
0
1
0
2
1
0
3
0
2
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
3
0
1
1
0
0
2
0
0
1
2
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
2
1
0
0
0
0
0
1
0
0
0
2
0
1
0
1
1
0
0
0
0
3
2
0
1
2
0
0
1
1
1
3
0
1
1
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
2
0
0
0
0
1
2
1
0
2
0
0
1
0
1
1
1
0
0
0
2
1
2
2
0
0
2
0
2
3
0
1
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
2
0
0
2
0
2
0
0
3
0
1
0
0
0
0
2
2
1
1
1
1
0
3
2
0
0
0
1
2
0
0
0
0
0
2
0
0
0
2
0
1
1
1
2
0
0
0
0
0
0
0
0
0
1
1
1
0
1
2
0
0
1
0
0
0
2
2
0
1
0
2
0
1
0
1
0
1
0
2
2
0
0
0
1
2
1
0
0
2
0
2
1
0
0
0
0
0
1
1
1
0
0
1
0
0
2
0
0
1
1
1
0
0
2
1
0
0
0
0
1
0
1
0
0
0
1
0
1
2
1
2
0
0
0
2
2
2
0
2
0
0
1
0
2
0
0
2
2
0
0
2
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
1
0
1
0
1
1
1
0
1
2
0
0
1
2
2
1
0
0
0
0
1
1
0
1
0
0
0
0
0
1
2
2
1
1
0
0
0
0
2
1
1
1
2
0
0
1
0
0
0
0
1
2
2
0
0
0
0
2
2
1
1
0
0
0
3
0
0
1
0
0
0
2
1
1
1
1
0
2
0
0
0
0
0
2
0
0
2
0
1
0
0
2
1
0
0
0
1
1
0
0
1
0
1
0
1
2
0
2
0
1
2
1
0
1
0
2
0
2
0
1
2
2
0
3
1
2
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
1
0
1
0
0
3
2
0
0
0
2
0
2
1
2
0
2
1
2
0
3
1
0
2
0
0
1
0
1
0
2
0
0
0
1
0
2
1
0
2
1
1
2
0
1
2
2
0
0
1
1
2
1
1
2
0
1
0
0
0
1
2
1
1
0
2
0
2
2
2
1
3
0
2
0
2
1
0
0
0
1
1
0
1
2
0
0
0
0
1
0
0
2
2
0
0
1
2
2
0
0
0
3
0
2
0
0
0
4
0
1
0
0
1
0
0
1
2
0
0
1
1
0
2
0
0
0
2
0
0
0
1
0
0
0
2
0
1
0
0
1
1
1
1
2
0
0
1
1
1
2
0
0
0
1
0
0
0
1
3
5
0
1
0
0
2
0
1
0
0
1
0
1
1
2
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
2
1
0
0
0
1
2
0
0
0
0
0
1
2
1
0
1
2
0
0
2
0
0
0
0
0
0
1
0
1
0
0
1
0
2
1
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
1
2
0
0
3
2
0
0
0
2
4
0
1
2
0
0
0
0
0
0
0
1
2
0
1
0
1
0
0
0
1
1
1
0
0
0
0
2
0
0
1
1
0
0
0
2
2
2
0
0
1
0
0
0
2
1
1
1
0
1
1
0
1
0
0
0
1
2
0
0
0
0
0
1
0
1
2
0
0
1
0
0
1
1
2
0
1
0
0
2
0
2
2
1
0
0
0
0
0
2
2
0
0
1
0
2
0
0
0
2
0
0
7
1
2
0
0
3
2
2
0
1
0
1
0
0
3
0
2
0
2
2
0
2
2
1
1
0
0
2
1
0
2
2
2
0
2
0
2
1
0
0
1
0
1
1
0
0
1
0
2
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
3
0
0
0
1
0
1
2
2
0
1
1
0
2
0
2
2
0
0
0
1
0
1
0
0
0
3
1
0
2
0
0
1
0
1
0
0
2
0
0
0
1
0
1
2
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
2
1
0
0
4
0
1
0
0
0
1
0
0
2
0
2
2
0
0
1
5
0
1
0
0
0
2
3
2
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
1
2
1
1
0
2
2
1
1
1
2
2
0
0
0
2
0
1
1
1
0
1
0
0
0
0
1
0
0
0
1
0
2
2
0
5
2
0
1
1
0
0
1
0
1
0
2
0
0
1
1
0
0
2
0
2
2
0
0
1
0
0
1
0
0
0
2
0
1
1
0
2
2
1
1
2
1
0
0
2
0
0
0
3
0
0
2
0
0
0
1
0
0
0
0
2
1
0
1
2
2
0
1
3
0
1
0
0
1
0
0
2
0
4
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
1
0
3
0
1
1
1
1
1
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
2
0
4
0
0
0
2
2
0
0
0
1
0
0
0
1
2
0
2
2
0
0
0
0
0
0
0
2
2
2
2
1
0
1
0
0
2
0
0
0
0
0
1
2
0
1
0
1
0
0
2
0
1
1
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
1
2
1
0
0
0
0
0
2
0
2
1
2
0
0
0
0
0
0
1
0
0
1
0
2
1
0
0
0
0
0
0
3
1
0
1
0
1
0
0
0
2
0
1
1
0
0
2
0
1
2
1
2
0
2
0
0
0
1
2
0
0
2
0
0
0
0
0
2
0
0
1
1
0
2
1
1
0
0
2
0
0
1
0
0
0
1
0
0
2
0
0
0
1
1
0
1
4
1
0
0
2
0
2
1
0
1
0
0
1
1
0
1
0
0
0
0
1
1
0
2
2
3
0
0
0
1
0
0
2
1
0
0
0
0
2
1
1
0
0
1
2
0
0
0
0
0
0
1
1
0
2
1
2
0
0
0
2
0
2
0
0
0
0
1
1
0
1
3
0
0
2
0
0
0
0
0
1
0
2
0
3
0
1
2
0
0
0
0
0
0
0
1
0
2
2
1
0
0
0
0
0
2
0
0
2
0
2
1
0
0
1
0
0
0
1
0
1
0
1
1
0
0
0
0
0
2
0
2
0
0
1
0
0
0
2
5
0
0
2
0
0
1
0
0
0
0
0
3
1
2
1
1
0
0
2
0
2
0
0
0
2
0
0
0
2
0
0
0
0
1
2
0
2
2
0
0
0
0
3
0
0
3
0
0
2
1
0
1
0
0
0
0
0
0
2
2
1
1
1
2
1
0
1
0
0
0
1
0
1
0
0
0
1
1
0
0
2
1
1
0
1
0
1
1
1
0
0
0
0
0
3
0
3
0
1
2
2
4
0
3
0
0
0
0
0
0
2
1
0
0
0
0
1
1
0
1
0
1
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
1
0
2
0
0
0
2
0
1
0
0
0
0
2
1
0
0
0
1
2
1
0
0
0
2
2
1
0
2
0
0
1
0
0
1
0
3
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
1
1
1
1
0
1
0
0
2
1
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
2
2
0
1
0
0
1
0
0
2
0
0
0
0
2
2
1
2
2
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
1
0
2
2
0
2
0
0
1
2
0
3
0
0
1
0
2
0
1
0
1
2
2
1
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
1
0
1
1
0
0
2
1
0
1
0
2
3
0
0
2
0
3
1
0
2
2
0
1
0
0
0
1
1
0
1
0
1
1
0
0
0
2
0
0
0
1
2
6
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
1
0
2
0
0
0
1
1
0
2
0
0
1
2
1
0
0
0
0
0
4
0
2
0
1
0
2
1
3
1
2
2
1
0
0
0
0
0
1
0
1
0
1
0
0
2
1
1
0
2
2
0
1
1
0
0
0
0
2
6
0
0
0
0
1
1
0
0
2
1
2
0
1
2
0
2
0
1
0
0
1
0
0
1
0
0
1
1
2
2
2
2
0
1
0
1
1
0
1
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
2
1
1
1
0
0
0
0
2
0
3
2
1
0
0
0
1
0
0
0
0
2
2
1
0
1
1
0
3
1
2
0
2
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
1
2
0
2
0
0
1
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
1
3
2
0
0
0
0
0
1
0
0
1
1
0
0
1
2
0
2
0
0
1
0
0
1
1
1
1
0
2
0
0
0
1
2
0
2
0
0
1
5
0
1
1
0
0
2
1
0
0
0
1
3
2
0
1
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
2
0
0
2
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
2
0
1
0
2
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
1
1
2
0
0
1
0
1
0
0
1
4
0
0
1
0
2
2
0
2
0
2
2
1
2
0
0
0
1
2
1
0
3
0
0
0
2
2
2
1
2
0
2
2
0
2
0
0
0
0
0
0
1
0
2
0
0
1
1
0
0
2
2
4
0
2
2
2
0
0
0
0
2
1
2
0
0
0
0
2
0
2
1
1
2
2
0
1
0
0
0
0
0
0
0
2
1
0
1
1
1
0
0
0
1
1
0
0
0
1
1
0
0
0
1
0
1
2
0
0
2
0
1
1
1
1
0
1
0
1
0
2
1
0
0
0
0
2
0
1
1
1
0
0
1
0
1
0
0
2
0
0
0
0
0
0
1
1
1
2
1
0
1
0
0
0
0
2
0
0
2
2
0
0
0
1
0
2
2
0
0
0
1
2
2
1
2
0
0
0
1
0
0
0
2
2
1
2
0
0
0
0
1
0
0
2
1
0
0
2
1
0
0
0
0
2
0
0
0
1
2
0
0
2
3
0
1
0
0
0
2
2
2
0
1
0
1
0
2
0
0
0
3
2
2
0
2
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
2
1
1
0
1
0
0
1
0
1
0
0
1
1
1
1
2
2
1
0
0
2
0
0
0
1
0
0
0
1
2
0
1
1
0
0
2
0
1
0
1
1
0
0
0
2
2
0
0
0
2
1
0
0
6
3
1
0
2
0
1
3
2
0
0
0
1
0
0
0
0
0
1
0
0
1
0
2
0
2
0
0
0
0
1
1
0
1
0
0
1
1
0
0
2
1
2
3
0
0
0
1
0
1
2
0
0
0
1
0
1
0
0
1
0
2
5
0
0
1
0
0
1
1
0
0
0
1
0
2
2
0
1
0
0
0
0
1
1
0
1
0
3
1
0
0
0
0
0
0
0
2
0
0
1
0
2
1
0
0
0
0
0
6
0
0
0
0
1
1
0
0
1
0
1
0
1
1
1
0
0
0
1
1
0
2
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
3
0
1
0
0
0
0
0
0
0
1
2
0
2
1
0
0
0
2
2
0
0
0
1
0
0
1
0
3
0
0
1
0
0
0
1
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
2
0
1
0
0
0
0
3
2
2
0
0
1
0
0
0
0
0
2
0
2
0
0
0
2
1
1
0
0
1
0
0
0
0
1
0
0
1
0
3
1
0
0
2
0
2
2
0
0
2
0
1
2
1
0
0
3
0
0
1
2
0
0
2
0
2
1
0
2
1
0
0
0
0
0
0
1
0
0
0
1
2
1
0
0
2
0
0
0
2
0
0
1
1
0
0
1
0
0
1
0
0
1
0
1
2
0
0
0
2
1
0
2
0
0
3
1
0
0
3
1
1
1
1
2
0
0
1
0
1
2
2
0
0
0
0
0
1
0
2
0
0
0
2
0
0
1
1
1
0
0
0
0
2
2
1
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
3
0
1
0
2
0
0
0
0
1
0
1
2
1
0
2
0
0
0
1
0
0
0
2
2
0
2
2
1
1
3
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
2
0
0
2
0
2
2
1
2
2
0
0
2
0
2
0
0
0
2
2
0
1
0
0
0
1
1
1
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
1
0
2
0
2
0
0
0
1
1
2
0
0
1
0
2
0
2
0
0
0
1
0
2
2
2
0
1
0
0
0
0
0
1
0
0
1
0
2
1
0
0
0
2
0
0
2
1
0
0
0
0
0
0
1
2
3
0
0
0
0
2
0
2
0
1
1
0
0
0
1
1
1
0
0
0
0
0
0
1
0
2
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
2
1
1
0
1
0
1
1
0
1
0
0
0
0
2
0
0
1
0
0
1
0
2
0
1
1
0
2
1
0
0
2
0
0
2
0
1
0
0
0
2
0
0
0
1
0
0
2
1
0
1
0
1
1
0
1
4
1
2
0
0
1
2
0
1
1
1
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
1
0
1
0
0
0
1
2
0
0
0
0
0
0
1
2
1
1
2
2
0
0
0
0
1
2
0
0
2
0
0
0
2
2
1
0
1
2
0
0
8
0
1
0
1
0
0
1
2
2
2
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
4
4
2
0
0
0
0
2
0
0
1
1
0
2
0
0
0
0
0
0
1
0
0
2
1
0
0
1
2
0
0
2
0
0
2
2
0
0
0
2
2
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
1
2
2
0
2
0
3
1
0
1
0
0
2
1
0
2
1
0
0
0
0
0
1
2
0
3
1
1
1
1
4
1
2
2
0
0
1
1
0
1
1
1
1
0
0
1
0
0
1
3
0
0
0
1
1
1
1
2
2
2
1
0
0
0
2
2
0
0
0
0
0
1
0
0
2
1
2
0
0
1
0
1
0
0
0
0
0
7
0
1
1
0
2
0
1
1
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
1
1
0
0
1
3
0
5
0
0
3
2
1
0
2
0
1
0
0
1
0
1
2
0
0
1
0
0
0
1
0
2
0
0
0
0
0
3
0
2
0
0
0
1
1
1
1
2
1
2
1
0
2
0
1
0
1
2
0
0
0
0
0
0
1
0
1
0
1
1
1
0
0
1
1
0
1
0
1
1
1
0
1
2
1
0
2
1
1
0
0
1
0
0
1
0
0
0
2
2
2
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
1
2
0
2
0
2
0
2
0
0
0
1
0
0
3
2
0
0
1
0
1
0
2
0
0
2
0
0
0
2
1
0
1
1
0
2
0
2
2
2
1
1
3
0
2
0
1
1
2
1
0
1
1
0
0
0
0
0
1
2
0
2
0
1
0
0
1
0
0
0
0
1
2
0
0
4
0
1
1
1
0
0
0
2
0
0
2
0
0
2
2
1
2
0
1
2
0
2
2
0
0
0
0
0
0
2
0
0
1
1
1
0
0
0
0
0
3
0
2
1
0
2
1
1
0
1
0
1
1
0
1
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
2
1
0
1
2
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
3
0
0
0
1
0
0
0
0
3
0
2
9
1
0
2
0
0
1
0
0
0
2
0
0
0
0
1
2
0
4
4
2
2
0
2
1
1
0
0
0
0
0
0
1
1
2
0
0
1
0
0
0
0
0
0
2
1
1
1
0
0
0
0
2
0
0
0
2
0
1
1
1
0
0
1
2
2
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
1
1
1
1
4
0
2
0
1
2
0
0
0
2
1
1
0
0
2
1
1
0
1
1
0
0
3
0
0
2
2
0
1
0
0
0
3
1
2
0
1
3
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
1
1
0
0
3
0
0
1
2
0
1
0
0
0
0
1
0
0
1
0
0
2
3
0
0
2
2
0
0
0
0
0
1
0
0
0
2
1
1
1
2
1
0
0
2
1
0
0
0
2
9
4
1
0
1
1
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
1
0
2
0
1
2
0
2
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
2
0
1
0
0
1
1
0
2
0
0
1
2
0
0
0
0
0
0
3
0
1
1
0
2
0
2
0
2
0
2
0
0
0
0
0
1
1
2
2
1
0
1
0
0
0
1
2
1
1
2
2
0
0
0
0
0
2
1
1
2
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
1
2
0
0
2
0
1
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
4
2
2
0
1
0
0
0
2
0
0
1
0
2
2
0
1
2
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
2
0
1
0
0
0
0
1
1
1
0
1
0
0
2
0
0
3
0
1
2
1
0
0
0
2
0
1
1
2
1
0
2
0
0
0
2
0
0
0
0
0
1
0
2
1
0
1
1
1
0
2
0
2
1
0
1
0
0
1
0
0
0
0
0
0
0
3
0
0
1
2
2
0
0
0
0
0
0
1
2
0
0
2
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
1
1
0
0
2
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
2
2
0
1
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
1
0
2
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
1
0
0
0
1
2
1
0
1
0
1
1
0
1
1
0
0
1
0
0
1
2
0
0
1
0
2
0
3
2
0
0
0
0
1
2
2
0
2
4
0
0
2
0
2
2
2
1
0
0
0
0
1
4
0
1
1
1
0
1
0
0
1
4
0
0
0
0
2
2
0
2
2
0
0
2
2
2
2
0
1
0
2
0
0
1
1
0
0
0
2
1
1
0
1
0
0
1
1
1
0
1
0
1
1
0
0
0
2
0
0
1
0
0
0
1
2
0
1
0
1
1
2
0
0
2
2
1
1
2
1
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
2
0
1
1
0
1
0
0
2
0
2
2
0
0
0
0
1
0
0
2
1
1
0
0
0
0
3
0
1
1
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
1
0
0
2
0
2
0
3
2
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
2
0
1
0
1
1
0
2
2
2
0
1
0
1
0
0
1
2
1
0
0
2
0
0
1
2
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
1
0
1
0
2
0
2
0
0
0
0
2
0
0
2
1
0
0
1
1
0
1
0
1
0
2
0
0
0
0
3
0
0
0
1
0
0
0
2
0
1
0
1
1
1
2
2
1
1
0
0
0
0
0
1
0
0
1
3
2
0
1
0
0
2
0
0
2
2
1
0
1
2
2
1
1
0
0
0
0
0
0
2
1
0
0
1
1
0
1
1
0
2
0
0
0
1
0
0
1
0
1
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
2
0
1
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
1
0
2
1
2
0
4
0
2
0
1
0
1
0
0
2
0
1
1
1
2
0
1
0
1
0
1
1
0
2
0
1
1
1
3
0
2
1
2
0
0
1
0
2
0
0
0
0
0
2
0
1
2
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
1
2
0
0
1
1
2
2
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
2
4
2
0
0
1
0
0
2
1
0
1
0
2
0
0
0
1
0
1
1
2
0
1
1
2
0
2
0
0
0
2
0
0
0
1
2
1
0
0
0
0
0
0
0
1
0
2
1
1
0
0
1
2
2
2
0
0
2
0
2
0
2
0
2
0
1
2
0
0
0
0
1
1
1
0
2
1
1
2
1
0
0
2
0
1
0
0
1
1
0
0
2
0
0
0
1
0
3
0
0
2
0
1
0
0
1
0
0
2
1
2
0
1
2
2
0
0
0
2
0
0
0
0
1
1
1
1
1
0
0
0
1
0
0
0
0
0
0
1
2
1
1
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
2
2
2
0
1
0
0
0
1
0
0
2
1
1
0
1
0
2
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
2
0
1
1
2
0
1
0
0
1
0
3
0
0
1
2
2
0
0
2
0
0
0
0
1
1
0
0
0
0
0
2
1
0
1
1
1
0
0
6
0
0
0
2
1
1
0
0
0
0
1
0
1
2
0
0
1
2
0
2
0
0
0
0
1
0
0
0
0
0
0
4
1
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
1
0
0
0
0
0
1
2
1
1
0
0
0
1
0
2
0
1
0
0
1
1
0
0
2
0
1
1
1
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
1
1
0
0
0
0
2
0
0
2
0
1
3
1
0
0
1
0
0
2
0
0
1
0
0
2
0
2
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
2
1
0
2
1
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
9
0
0
1
0
1
1
0
0
0
0
2
0
0
2
1
2
2
0
0
0
1
2
2
4
0
0
0
1
1
0
2
0
0
1
0
0
0
0
2
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
1
1
0
1
0
0
2
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
2
2
0
0
0
2
1
0
3
0
1
0
0
0
1
0
0
0
1
2
0
0
0
1
0
2
3
2
0
2
0
0
0
1
0
0
3
2
0
1
0
0
0
1
2
2
2
0
0
2
0
0
1
0
0
0
4
2
0
0
1
0
2
1
0
2
2
0
2
0
1
0
2
1
0
0
0
0
1
2
0
0
0
1
0
0
2
0
0
0
0
0
2
3
0
2
0
2
0
3
0
0
0
0
2
0
0
0
0
1
0
0
0
1
1
6
0
0
9
0
1
4
0
0
1
0
0
2
0
0
2
0
0
4
1
0
0
2
0
0
0
1
0
0
0
2
2
0
1
2
0
1
2
1
0
0
1
0
8
1
0
0
1
0
0
0
0
0
1
0
2
0
0
2
1
0
0
1
0
0
2
0
1
0
0
0
1
1
0
0
0
2
0
0
1
0
2
1
2
1
1
1
0
2
3
0
1
0
1
0
0
0
2
0
2
0
2
0
2
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
2
0
3
0
1
2
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
2
0
1
1
2
1
0
1
0
1
0
0
0
1
0
5
0
0
2
0
0
1
0
2
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
1
2
1
0
0
2
1
0
1
1
1
2
0
0
1
0
0
0
2
0
1
0
2
3
0
0
0
0
0
2
0
0
0
2
1
3
0
1
2
1
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
2
0
1
0
0
1
0
0
2
0
2
1
7
2
0
2
2
0
1
1
1
1
1
0
0
0
1
1
0
0
0
0
2
1
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
1
2
2
0
2
1
0
0
1
2
1
1
2
0
3
1
2
0
0
2
0
0
0
0
0
0
0
1
1
2
0
0
0
0
4
0
1
0
2
0
1
0
2
2
0
1
1
0
0
0
0
1
2
0
0
1
1
2
0
0
0
1
0
1
0
0
0
0
0
5
0
0
1
1
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
1
2
0
0
2
0
2
1
0
0
3
0
0
0
2
0
0
0
1
2
1
1
0
0
0
0
1
0
0
2
2
0
0
0
2
0
0
2
1
0
0
1
0
0
1
0
0
0
0
2
2
0
1
0
2
1
0
2
1
2
1
1
0
0
1
1
0
1
0
0
2
2
1
0
1
1
0
2
0
0
0
2
0
0
0
1
0
2
0
0
0
2
2
1
2
2
0
2
0
0
0
0
0
1
0
0
0
2
0
1
0
2
0
2
0
0
0
1
0
1
2
1
0
2
2
0
3
0
3
1
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
2
0
0
2
0
3
0
2
0
0
0
1
1
0
0
0
0
2
1
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
1
0
0
0
1
1
2
0
1
0
1
0
0
1
0
2
0
0
0
2
2
0
0
0
0
3
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
1
0
2
0
1
0
0
0
2
1
1
0
1
1
1
0
1
1
0
0
2
2
2
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
3
2
0
0
1
1
2
0
1
2
0
1
0
0
2
1
0
1
0
0
0
1
0
0
0
0
2
0
1
0
0
0
2
0
2
0
2
3
0
0
0
0
0
0
0
0
2
2
0
1
0
1
1
0
1
0
1
0
0
0
2
0
0
2
0
0
2
0
0
0
1
5
2
0
1
2
3
0
3
1
2
0
0
2
1
1
0
0
0
0
0
2
0
2
0
0
1
0
0
1
0
1
1
1
0
0
0
2
0
1
2
0
0
0
2
0
0
2
0
2
2
1
0
0
0
0
0
2
1
2
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
5
0
0
0
0
0
1
1
0
0
1
0
0
2
0
0
1
1
2
1
1
0
1
0
0
2
0
0
0
0
0
0
0
1
1
0
2
0
0
0
1
1
1
0
2
0
0
2
1
0
0
0
0
6
0
2
1
2
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
3
0
0
0
1
1
0
2
1
0
1
0
1
0
4
0
2
0
0
0
0
1
0
0
1
0
1
0
1
0
1
0
1
2
0
1
1
0
1
1
2
0
0
0
0
0
0
1
1
2
1
2
0
0
4
1
2
0
0
0
3
0
2
0
0
0
0
0
0
2
0
1
0
0
1
0
0
2
0
0
0
1
2
0
0
0
1
0
0
2
0
0
1
0
1
0
1
0
2
0
0
2
1
1
0
0
1
0
0
1
1
0
0
0
1
1
0
0
1
2
0
0
1
1
0
1
0
0
1
1
0
1
0
2
0
0
2
0
2
1
0
1
1
1
1
2
1
0
0
0
0
0
2
0
2
0
1
0
2
0
0
1
0
2
0
2
0
1
0
0
1
0
2
0
0
1
1
1
0
0
0
0
0
0
2
0
0
0
2
1
1
2
2
0
2
0
2
0
0
0
0
2
0
2
0
0
0
1
2
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
2
0
0
2
0
1
1
0
0
0
1
0
0
0
0
2
0
0
0
1
0
1
1
2
0
0
0
0
1
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
2
0
1
1
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
2
0
1
0
0
0
0
2
1
0
0
0
0
1
5
2
1
0
0
1
0
0
0
1
0
0
1
0
2
2
0
1
0
0
1
0
1
0
0
0
0
0
0
1
2
1
2
0
2
0
2
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
1
0
1
1
1
1
2
1
0
2
0
2
2
0
1
0
1
0
0
1
0
1
2
2
1
2
1
1
0
2
0
2
0
1
0
0
2
0
1
0
0
0
0
0
0
1
0
0
2
2
0
0
2
0
2
0
2
0
0
1
2
0
0
0
1
1
0
0
1
4
0
1
0
0
1
0
1
0
0
0
0
1
0
1
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
2
0
0
1
1
2
0
0
0
0
2
0
1
2
1
0
1
1
2
1
0
2
0
0
0
2
0
2
0
2
0
0
1
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
1
1
0
0
2
0
2
1
2
2
0
1
0
0
2
1
0
0
2
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
1
0
0
0
1
1
0
0
0
1
1
1
0
1
2
0
0
0
0
0
0
0
0
0
0
2
1
1
2
1
1
0
1
0
0
2
0
0
0
0
2
0
3
1
1
0
1
0
2
0
1
0
0
1
0
0
0
0
1
1
2
1
0
2
0
0
0
0
2
2
1
0
0
1
0
0
1
1
3
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
2
0
1
2
0
0
2
2
0
0
2
0
0
0
2
0
0
2
4
0
1
1
0
0
2
0
1
0
2
0
2
0
1
1
0
1
0
1
2
0
1
1
0
0
0
0
2
2
3
0
0
0
0
0
0
0
0
2
0
1
4
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
1
3
0
1
0
0
1
2
0
2
0
0
0
2
0
1
0
1
1
1
0
2
0
0
1
2
1
2
0
1
1
0
1
2
0
0
0
0
0
2
1
1
0
0
0
0
2
0
0
1
0
0
0
0
1
0
1
0
2
0
1
0
0
0
0
1
0
2
0
1
2
1
2
2
0
0
0
0
0
1
0
0
7
0
0
1
2
1
0
2
0
0
0
0
2
0
2
0
1
2
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
1
1
0
1
2
1
0
0
2
1
0
2
0
2
0
0
0
0
1
1
0
0
0
1
0
3
2
0
0
1
0
0
0
0
2
1
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
2
5
1
0
1
1
0
0
0
2
1
0
0
0
2
2
1
0
0
0
5
0
0
0
1
0
0
0
0
2
0
2
0
3
0
1
2
0
2
0
0
0
2
2
0
0
3
0
0
0
0
0
2
0
1
0
0
1
0
2
0
1
0
0
0
2
2
0
0
2
1
0
0
0
2
0
1
0
1
0
0
2
2
2
0
2
1
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
1
1
0
0
0
0
0
2
2
1
3
1
0
0
3
0
2
0
0
1
1
0
2
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
4
1
0
2
0
0
1
1
0
0
2
1
0
0
1
0
2
0
0
2
2
0
1
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
1
1
0
4
1
2
2
2
0
2
1
0
0
0
0
0
0
1
0
0
0
1
2
3
1
0
0
2
0
0
0
0
2
0
0
2
2
0
0
0
0
1
0
0
2
0
0
2
2
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
1
2
1
0
2
2
2
0
0
1
0
1
1
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
1
0
1
1
0
0
2
0
0
0
2
0
0
1
3
1
2
0
0
0
1
0
1
0
1
0
0
2
2
0
1
1
2
0
0
0
0
1
0
0
1
1
1
1
0
1
0
1
2
0
0
0
3
1
0
0
1
0
1
2
0
0
0
1
2
1
0
0
2
0
0
2
0
0
2
1
0
0
0
2
2
0
0
0
1
1
0
2
1
0
0
0
0
0
7
2
0
2
2
2
2
2
2
1
0
1
0
0
1
0
0
0
0
2
0
0
1
0
1
1
0
0
0
0
1
2
0
0
0
1
1
2
0
0
0
2
2
1
2
0
0
2
0
0
1
0
3
0
1
1
2
2
0
0
3
1
2
0
0
1
0
0
0
0
2
2
0
0
1
2
1
1
0
1
0
0
2
0
0
1
1
0
2
0
1
0
0
1
1
0
1
1
0
1
1
2
1
0
0
1
3
0
0
0
0
0
1
3
0
1
0
1
0
2
2
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
1
0
1
2
0
0
0
2
2
2
0
0
0
2
2
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
2
0
2
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
1
2
0
2
0
0
0
1
0
0
0
0
1
0
0
3
0
1
0
1
0
2
1
1
2
0
1
1
0
0
1
1
0
2
0
1
1
1
0
1
2
1
0
6
2
0
0
1
0
0
1
2
0
0
0
0
0
1
1
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
1
2
1
0
0
1
0
0
0
0
2
0
0
1
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
1
0
0
2
0
1
1
1
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
1
1
0
2
0
2
0
1
2
0
2
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
2
3
0
0
0
0
2
0
0
2
0
1
1
2
0
1
2
2
2
2
2
2
0
1
2
1
2
2
1
0
2
0
0
0
0
1
0
0
0
0
1
2
2
0
2
0
1
0
0
0
1
1
0
0
0
1
0
2
0
0
0
2
1
0
1
2
1
1
2
1
2
2
0
1
2
2
0
0
0
2
0
0
2
1
0
0
0
0
1
1
0
0
2
0
0
2
0
0
1
2
0
0
0
0
0
1
0
0
2
2
0
1
0
0
0
0
0
0
0
1
0
2
0
2
1
1
3
0
0
2
0
0
1
0
2
2
0
0
0
2
0
0
0
1
1
0
0
0
0
0
2
1
1
0
0
1
1
2
1
2
1
0
1
1
1
1
1
0
2
1
1
0
2
1
2
0
0
2
1
0
0
0
2
1
0
2
0
0
0
0
1
2
0
3
0
0
1
0
0
0
1
0
2
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
2
2
2
0
1
0
0
1
0
0
1
2
0
1
0
1
0
0
0
0
3
0
0
0
2
0
0
1
0
0
0
0
0
2
0
2
0
0
2
0
2
0
0
1
1
1
0
0
0
2
0
1
1
0
0
0
2
0
0
2
0
0
4
2
0
0
3
0
0
3
1
1
1
0
0
0
0
0
1
2
0
0
2
3
2
2
2
1
0
2
0
0
0
0
1
0
0
0
0
2
1
1
2
0
1
0
0
2
2
1
0
0
0
0
0
2
2
0
2
0
1
0
1
0
1
0
0
0
0
0
1
2
0
0
0
2
1
0
0
2
3
0
0
1
0
0
0
0
1
0
1
1
1
0
0
0
1
0
0
0
0
1
1
1
0
2
1
0
1
0
0
1
2
0
0
2
0
2
0
0
0
1
2
0
2
0
0
0
0
0
1
0
1
0
1
0
0
1
0
3
0
0
0
0
1
0
1
1
1
2
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
1
2
0
0
1
4
0
0
0
2
0
1
2
0
1
0
0
0
0
1
0
0
0
0
1
2
1
0
2
0
0
0
0
1
0
0
1
0
0
2
1
1
0
1
2
0
2
1
0
0
0
1
1
0
0
4
0
0
2
1
2
2
1
0
0
0
2
2
2
0
2
2
1
0
1
0
0
2
0
2
0
1
0
0
0
1
0
2
1
0
1
0
0
0
0
3
2
0
2
0
2
2
2
2
0
0
1
0
0
2
0
0
0
2
0
1
0
2
2
0
0
3
0
1
2
0
1
0
2
0
1
0
2
0
0
0
1
2
1
0
0
0
1
1
0
2
0
1
2
1
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
2
0
0
0
3
0
0
0
0
2
2
0
1
0
2
1
1
1
0
0
0
0
1
2
2
2
1
1
0
2
0
0
0
1
0
0
0
1
2
1
2
2
0
1
0
0
0
1
0
0
0
2
1
0
0
1
2
3
1
0
1
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
2
0
2
0
0
1
0
2
0
2
1
1
0
0
0
2
0
2
0
1
1
1
0
0
0
0
0
0
0
0
1
0
2
1
0
1
0
0
0
0
0
0
1
0
1
0
1
1
1
2
1
0
0
0
0
0
2
0
0
2
0
1
0
2
0
2
1
0
2
0
1
0
0
2
1
2
1
0
1
0
1
1
0
1
0
0
0
0
0
0
2
0
1
0
0
1
1
0
0
0
1
2
1
0
0
1
0
2
0
0
1
2
0
1
2
1
2
2
1
1
0
0
1
1
2
0
0
1
0
0
0
0
1
1
0
0
2
1
0
0
0
1
1
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
2
4
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
1
3
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
1
1
1
0
2
2
0
0
0
0
0
1
1
0
0
0
0
1
2
1
1
0
0
0
2
0
1
0
1
1
1
0
1
0
0
2
0
0
0
0
1
1
2
1
0
0
3
0
2
0
0
1
2
0
1
0
0
1
0
0
0
0
0
1
2
0
0
2
1
0
2
0
0
0
2
1
1
0
2
0
1
2
1
2
1
0
0
2
0
0
2
0
2
0
2
1
2
2
0
2
0
0
0
0
1
1
0
3
0
1
0
1
1
2
2
2
0
0
0
0
2
0
0
2
2
0
0
1
1
0
0
0
0
2
0
1
0
0
1
0
0
0
0
1
1
0
0
2
0
0
1
0
0
0
1
0
1
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
1
0
2
1
1
0
0
0
2
1
0
0
3
1
0
1
0
0
0
0
0
1
0
1
0
0
2
1
0
0
0
0
1
0
0
2
1
0
0
0
0
1
0
1
1
0
2
2
1
0
0
1
2
0
0
2
1
2
2
2
0
1
0
0
0
0
0
2
0
1
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
1
0
0
1
1
0
0
2
2
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
1
1
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
2
0
1
1
0
0
1
2
2
2
0
2
0
0
0
2
1
0
0
0
0
0
0
2
0
1
0
0
3
2
2
1
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
1
1
0
1
0
1
1
0
1
0
2
0
0
0
1
1
2
0
0
0
1
1
0
2
1
0
0
2
1
1
2
0
1
0
0
0
2
0
0
0
2
0
0
1
1
0
1
0
0
1
0
0
0
0
2
2
1
2
2
1
1
2
0
0
2
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
2
2
1
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
1
0
0
3
0
20
0
2
0
0
0
0
2
1
0
0
2
0
2
1
1
2
0
2
0
0
0
0
1
0
1
2
1
1
0
0
2
0
0
2
0
2
0
0
0
2
0
0
0
1
2
0
0
1
2
0
0
2
0
0
0
1
0
0
0
0
0
2
2
1
0
1
0
0
3
1
0
2
1
0
0
0
0
0
1
2
2
0
0
2
0
0
1
1
0
0
1
2
0
0
1
1
0
1
2
0
0
2
2
0
1
0
0
0
1
0
2
2
0
0
0
0
1
0
0
0
2
2
0
2
0
0
3
2
1
0
0
0
4
2
0
0
0
1
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
1
0
1
0
0
0
0
0
2
1
3
0
2
0
0
1
2
1
1
2
1
0
0
0
2
2
1
0
1
0
1
0
1
0
0
2
0
2
1
1
0
1
0
0
0
0
0
0
2
0
2
1
1
0
1
2
2
2
0
0
1
1
1
0
1
1
2
0
0
0
2
1
0
0
2
1
0
2
0
0
0
0
0
1
0
1
0
1
0
0
1
0
1
2
0
2
0
0
1
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
2
1
3
1
2
0
0
1
0
0
1
0
1
1
0
2
1
1
0
0
0
0
0
2
1
2
0
1
0
0
2
0
3
0
1
1
0
0
0
0
1
1
2
0
2
0
1
0
0
0
0
0
0
1
1
1
0
2
1
0
1
2
1
1
0
0
0
0
2
0
1
0
0
0
2
0
3
0
0
1
1
1
0
0
0
0
2
1
0
0
0
2
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
2
1
0
0
0
1
0
0
1
2
2
0
0
0
1
0
0
2
2
1
0
1
3
1
1
0
1
1
2
0
2
0
1
0
2
0
0
0
0
2
1
0
0
0
3
5
0
1
0
0
2
0
2
2
0
0
0
1
1
0
0
1
3
2
1
2
0
0
2
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
2
2
0
0
2
1
0
3
0
0
2
0
0
0
2
0
1
2
0
2
0
0
0
0
0
2
1
2
0
0
0
1
0
2
0
0
2
0
2
0
0
2
0
0
1
0
0
2
0
2
0
0
2
1
0
1
1
0
0
0
0
0
2
2
1
2
2
0
0
0
0
0
0
2
1
0
2
0
1
1
0
0
0
1
2
2
2
1
0
0
0
1
0
0
0
0
2
0
0
0
1
3
0
0
0
0
2
0
0
1
0
0
1
0
0
0
1
2
1
1
0
1
0
0
1
0
1
2
0
0
0
0
1
1
0
0
0
1
0
0
1
0
2
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
1
1
0
1
1
3
1
0
0
0
2
2
0
0
2
0
2
1
0
0
0
2
1
0
0
0
1
1
1
0
0
1
0
2
1
1
2
1
2
2
0
1
0
2
0
2
1
1
0
0
2
0
2
0
0
0
0
0
0
2
0
2
0
0
1
0
2
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
2
0
1
1
2
0
0
0
0
0
1
0
1
2
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
2
2
0
0
0
0
0
0
2
2
0
2
2
2
0
1
1
2
2
0
1
0
0
0
2
0
0
1
2
1
0
0
2
0
2
0
0
1
0
0
1
1
0
0
0
2
0
1
1
0
1
0
0
1
2
0
0
1
0
0
0
1
1
0
0
0
2
2
0
2
2
0
0
1
0
0
0
0
1
2
0
2
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
2
3
0
2
2
0
0
0
0
0
2
0
0
1
0
0
2
0
0
1
0
0
1
0
0
0
0
0
2
2
1
1
2
0
1
0
0
0
1
0
1
0
1
1
1
0
0
1
1
0
0
0
1
0
2
0
0
1
1
2
1
0
1
1
0
1
0
3
0
0
0
0
2
0
1
0
1
1
1
1
1
2
4
2
0
0
0
2
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
2
2
1
0
0
0
0
2
0
0
0
0
1
0
2
0
2
0
2
1
0
1
1
0
1
0
1
0
0
0
0
1
2
0
0
0
0
0
1
2
0
2
0
0
0
1
0
1
1
1
1
0
2
1
1
0
1
0
2
0
0
0
2
0
0
0
1
0
1
2
1
1
1
1
1
2
1
0
0
1
1
0
2
0
2
2
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
2
2
0
2
0
2
0
0
1
0
1
1
1
0
0
1
2
2
2
0
2
1
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
1
1
0
0
0
1
0
0
1
0
0
2
1
9
1
1
0
0
1
0
0
0
0
2
0
1
1
1
2
0
0
0
1
1
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
2
0
1
0
1
2
0
0
2
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
1
0
0
0
1
0
1
1
2
0
0
2
2
0
0
1
1
0
0
0
1
3
1
1
2
0
2
0
0
2
0
0
0
0
0
1
4
2
0
0
2
0
1
1
2
0
0
0
1
3
1
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
1
0
2
2
0
3
1
0
1
0
0
0
0
0
1
4
0
0
1
1
0
2
1
0
2
0
0
0
2
0
0
0
0
0
1
1
0
0
2
0
0
0
0
3
1
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
4
2
2
1
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
1
0
0
1
0
2
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
3
0
0
0
0
1
2
1
0
0
0
0
0
1
0
0
2
2
1
0
0
5
2
1
0
1
0
0
0
1
2
2
0
2
2
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
2
1
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
1
2
1
0
0
0
1
0
0
3
2
2
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
1
0
1
0
0
1
0
0
1
1
0
0
0
2
2
0
0
2
0
0
0
2
0
1
0
3
2
0
2
1
1
0
2
0
0
0
0
0
1
0
2
1
0
0
0
0
2
0
1
1
0
1
0
2
0
0
2
1
1
2
0
0
0
1
2
1
0
0
0
0
0
2
1
0
3
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
1
0
1
0
2
0
2
2
2
0
0
0
2
0
2
1
1
0
0
0
0
0
1
0
0
0
2
0
2
1
0
0
0
0
2
1
1
2
8
1
0
0
1
1
1
0
0
0
0
1
0
2
0
2
0
1
1
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
2
1
2
1
0
1
1
1
0
1
0
3
0
1
0
3
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
2
2
0
2
1
0
0
0
0
0
1
0
3
1
2
0
0
0
0
1
0
0
0
0
3
2
0
0
0
2
0
1
0
0
0
2
0
0
0
0
1
1
0
2
1
0
3
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
3
2
0
2
0
0
0
1
2
0
1
0
0
2
1
0
0
1
0
1
0
0
4
2
2
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
1
0
0
1
0
1
0
1
1
0
3
2
0
2
0
1
0
0
0
0
0
0
3
0
2
0
0
0
0
0
1
0
1
2
2
3
0
0
2
0
2
0
2
2
0
0
1
0
1
2
0
1
0
0
1
1
1
0
0
0
1
1
1
1
0
0
2
0
0
0
1
0
1
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
1
0
0
1
2
2
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
2
2
1
0
0
1
1
0
1
2
2
0
0
0
1
2
0
0
5
0
0
1
0
2
2
2
2
2
0
0
0
1
2
1
0
0
0
2
3
1
1
0
2
0
0
2
2
1
0
0
1
1
0
0
0
0
1
0
1
0
2
2
1
0
2
0
0
2
2
3
1
0
4
1
2
0
2
0
1
0
0
0
0
2
0
3
1
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
2
2
1
0
1
0
0
1
0
0
0
0
0
4
1
0
0
2
0
2
1
2
1
1
0
2
0
0
0
1
2
0
0
2
0
0
0
2
1
1
1
2
0
0
0
0
0
0
0
0
0
2
2
0
0
1
1
0
0
0
2
2
0
2
2
1
1
1
1
0
0
1
2
0
0
0
1
0
2
1
0
2
1
0
1
0
2
0
0
0
2
2
0
1
0
0
0
0
0
1
2
0
1
0
2
1
0
0
0
1
0
1
2
2
0
1
0
0
1
0
0
0
2
1
1
1
0
0
3
0
2
0
0
3
2
1
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
1
0
0
0
0
2
0
0
2
3
1
1
0
0
0
0
0
0
2
2
0
2
0
2
1
0
3
0
1
0
0
2
0
2
1
1
0
0
0
0
3
1
1
2
0
0
2
0
0
0
0
2
0
0
0
0
1
2
0
0
1
0
2
2
1
0
0
3
0
1
0
2
0
4
0
0
0
0
2
0
2
0
1
0
2
0
0
0
0
0
1
0
2
0
0
4
2
0
0
0
1
0
1
1
0
0
0
0
0
0
0
2
0
1
0
2
0
3
2
0
0
0
0
0
1
0
0
2
2
2
1
0
1
1
2
1
2
0
1
0
1
2
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
2
0
1
0
0
2
0
0
0
0
0
2
0
0
2
0
0
1
0
0
2
0
2
0
1
2
0
0
0
0
2
0
1
3
0
2
2
1
1
0
1
0
0
1
2
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
2
0
0
0
1
0
5
0
0
0
1
2
0
1
1
0
0
0
0
2
1
0
2
1
0
2
0
2
2
0
0
0
1
1
0
0
0
0
2
0
0
0
1
1
0
1
2
0
0
1
1
0
2
0
2
0
2
1
2
1
0
0
0
0
1
2
2
1
1
0
0
0
0
0
5
0
0
1
0
2
1
0
1
0
0
2
0
0
0
1
1
0
0
0
0
0
0
1
1
1
0
0
0
2
1
2
0
0
0
0
1
0
0
0
0
0
1
0
2
2
0
0
2
0
2
2
0
1
0
0
0
2
0
0
0
1
1
0
1
1
2
0
0
0
0
1
2
2
1
1
0
5
0
0
1
0
0
1
0
1
0
0
0
1
1
1
1
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
1
0
0
2
0
0
1
2
2
0
1
0
4
0
2
0
0
2
0
0
1
0
0
3
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
2
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
4
0
0
0
0
0
1
2
1
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
1
2
1
0
2
1
0
0
0
0
0
2
0
1
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
2
2
0
0
0
1
0
1
1
0
0
1
4
0
0
2
2
0
2
0
0
2
0
0
1
0
0
2
1
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
2
0
2
0
2
1
2
3
0
0
2
1
2
0
1
2
0
1
0
1
0
0
1
0
2
2
0
0
0
0
2
0
3
1
0
0
0
0
1
0
0
2
0
1
0
1
3
0
1
0
0
1
0
0
0
0
0
0
1
0
2
0
3
0
0
0
2
0
1
2
0
3
1
1
2
0
1
4
1
0
0
1
0
0
2
1
0
2
0
0
2
2
0
0
1
0
4
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
1
0
1
0
1
0
0
0
1
2
4
0
2
2
2
0
1
1
0
2
0
1
2
0
0
0
0
0
0
1
0
0
1
1
0
1
1
1
0
1
2
1
1
1
0
1
2
2
1
1
0
0
2
0
1
0
0
0
0
0
3
2
0
2
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
3
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
2
0
2
1
0
2
0
1
0
2
0
1
0
0
1
0
0
2
0
0
0
1
0
0
2
0
2
0
2
2
2
1
2
1
0
0
1
0
0
2
2
1
2
0
0
0
0
1
0
3
3
1
2
0
0
0
1
2
1
0
1
2
0
0
2
0
1
0
2
0
0
0
0
1
1
5
0
0
1
2
3
2
0
1
0
0
1
0
0
0
1
2
0
0
1
0
2
0
0
0
0
1
0
1
1
0
0
0
0
1
2
0
0
2
2
2
0
0
0
2
0
0
2
0
0
0
2
1
2
0
0
0
0
0
2
1
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
2
0
2
0
0
0
2
2
0
1
0
1
1
0
1
2
0
1
2
0
1
0
0
0
1
1
1
0
1
0
4
2
0
2
0
0
0
2
1
2
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
1
1
2
2
1
1
0
0
0
2
1
1
1
0
0
0
0
0
0
2
0
1
2
0
0
0
0
2
0
2
2
0
1
0
0
1
0
0
0
0
2
2
0
1
0
3
0
0
0
0
0
1
0
0
0
0
1
1
2
0
3
0
0
0
2
1
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
1
1
0
0
0
0
2
0
1
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
2
1
0
2
1
0
0
0
0
3
0
0
2
0
0
1
2
0
1
0
1
1
2
2
0
0
1
0
2
1
2
0
2
0
0
0
2
1
1
0
0
0
0
3
0
0
1
3
1
1
0
1
0
1
7
0
0
0
1
3
0
1
0
1
1
3
0
0
2
1
1
1
0
1
2
0
1
2
0
0
0
1
1
0
0
0
0
1
2
1
2
1
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
2
2
0
2
1
1
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
2
2
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
2
0
0
1
0
0
2
1
1
0
0
0
2
2
2
1
0
4
2
0
0
0
0
0
0
0
1
3
0
0
1
0
1
1
2
2
0
5
0
1
0
0
0
0
0
2
0
0
0
2
2
0
0
0
1
1
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
3
1
1
0
0
1
0
0
3
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
2
1
2
1
0
1
0
0
2
0
0
0
0
1
0
1
2
1
1
2
0
0
2
0
2
2
2
0
2
0
0
2
0
0
2
2
0
0
0
1
0
1
0
0
0
1
1
1
1
0
0
0
0
0
0
3
2
2
0
0
0
0
0
0
0
0
1
0
1
0
1
2
2
0
1
0
0
2
2
0
0
3
2
1
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
1
0
0
0
3
0
0
0
0
2
2
0
1
0
2
2
1
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
2
0
0
0
1
2
0
0
5
0
0
2
1
0
0
0
1
2
2
1
0
0
1
0
0
1
0
1
0
0
1
0
0
2
0
0
2
0
1
0
2
1
0
2
0
0
0
0
2
2
0
0
1
2
0
2
0
0
0
1
2
0
2
1
1
1
0
0
2
1
0
0
1
0
2
0
0
2
2
1
1
2
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
3
0
0
1
1
0
0
0
1
0
0
0
2
1
2
0
2
0
1
1
1
0
0
0
0
0
0
2
1
0
1
2
10
0
0
0
1
0
0
1
0
1
2
0
0
0
0
0
2
2
1
1
0
0
1
0
0
2
0
0
0
0
0
2
0
2
2
1
2
0
0
0
1
1
0
2
1
0
0
2
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
2
1
2
1
0
0
2
2
0
1
2
1
0
0
1
1
2
1
2
1
1
0
0
2
2
0
1
3
1
0
0
0
0
2
1
0
5
1
0
1
2
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
3
0
0
0
3
0
2
0
1
3
1
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
2
0
0
3
1
0
0
0
0
0
2
0
0
2
2
1
1
0
0
1
0
0
0
1
0
1
0
1
2
0
0
0
2
2
2
2
0
2
0
1
2
0
2
0
1
2
0
0
0
1
4
0
0
1
0
1
1
0
0
1
0
1
1
0
0
1
0
2
1
0
0
0
2
1
0
0
2
1
0
0
0
1
0
2
2
2
2
0
0
0
0
0
0
1
0
0
0
2
2
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
1
2
0
1
1
0
0
0
0
2
2
4
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
2
0
2
2
0
0
0
2
0
1
0
1
0
2
0
2
0
0
1
1
0
0
0
0
2
2
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
1
1
0
3
0
2
0
0
0
0
2
0
0
0
0
1
2
2
0
1
0
0
2
2
1
0
1
2
0
1
2
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
1
0
1
0
1
1
0
0
0
1
0
2
2
0
0
1
0
0
1
0
2
1
1
0
0
3
2
0
0
0
1
1
0
0
0
1
0
0
2
1
0
0
0
2
3
1
0
0
0
1
1
0
0
0
2
2
0
1
0
0
0
0
0
0
0
1
0
1
1
0
1
1
1
2
0
0
1
1
0
0
1
2
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
2
0
0
1
0
2
2
2
0
0
1
0
2
1
0
0
2
1
1
1
2
1
0
0
0
0
0
1
1
1
0
2
0
0
0
0
1
1
0
0
2
0
2
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
1
0
2
1
0
0
0
0
2
0
0
0
0
0
2
1
0
1
2
1
0
1
2
0
0
0
0
2
0
2
1
0
0
0
1
0
0
0
2
0
2
1
2
1
0
0
1
1
3
1
0
0
1
0
0
0
0
0
1
2
0
0
0
1
3
0
0
0
1
0
1
0
1
0
0
1
3
0
3
1
0
0
2
0
2
0
0
2
0
2
0
1
2
0
1
1
0
1
1
0
1
0
0
0
0
2
1
0
0
0
1
0
0
0
0
1
2
0
2
0
0
1
0
0
0
0
0
1
0
1
1
0
2
0
0
2
0
1
2
1
1
0
1
0
0
0
0
0
0
2
0
0
0
2
1
0
1
1
0
0
2
2
1
1
1
0
2
1
1
0
0
0
2
0
4
1
0
2
2
0
1
0
0
2
0
0
0
0
0
2
0
2
1
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
2
1
0
0
1
0
0
1
0
2
0
0
0
2
0
2
2
0
0
0
0
0
0
1
2
1
0
1
0
0
1
0
0
0
2
0
0
0
2
0
0
1
3
1
0
0
0
2
1
1
2
0
0
0
2
0
0
2
2
0
1
2
0
0
2
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
2
2
0
2
0
0
0
2
2
0
0
0
0
1
0
2
0
3
0
1
0
0
2
0
2
1
0
1
0
0
2
0
2
2
0
0
2
1
1
3
1
0
2
0
0
1
0
0
2
0
1
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
1
1
0
1
2
2
1
1
0
1
0
0
2
0
1
2
1
1
0
0
0
0
0
3
1
1
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
1
2
4
0
2
1
1
2
2
0
1
0
0
0
2
0
1
1
1
1
1
0
0
2
1
0
2
2
0
1
0
1
2
0
0
0
0
2
1
0
0
5
0
2
0
0
0
1
0
0
0
0
0
1
0
0
2
2
0
0
0
1
0
0
1
0
1
0
1
0
1
2
0
0
0
2
0
0
0
0
0
1
2
0
0
1
0
2
1
1
2
0
2
2
0
1
2
0
0
1
0
2
0
0
0
0
2
0
2
0
1
0
3
0
3
0
0
1
0
2
0
0
0
0
1
1
2
0
0
0
0
0
0
1
1
0
2
2
0
0
2
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
1
0
1
0
2
1
1
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
2
0
0
1
0
0
1
2
1
0
0
0
1
0
2
2
0
1
0
0
1
0
1
0
0
0
0
0
1
0
2
0
1
2
2
0
0
0
0
2
1
1
1
1
1
1
2
1
1
1
1
1
0
1
0
1
0
0
0
0
2
1
0
1
0
1
0
0
1
2
1
0
5
0
0
2
2
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
2
0
2
0
0
2
1
1
0
2
0
0
1
2
2
1
0
0
0
0
0
0
0
0
0
1
1
0
1
2
0
0
0
1
0
2
0
2
0
1
1
0
2
0
0
1
1
0
0
0
1
0
2
3
2
2
0
0
0
0
0
3
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
1
2
0
2
2
2
0
0
2
0
1
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
1
0
3
0
0
1
0
0
2
0
0
1
0
0
0
0
1
0
0
0
2
2
0
1
0
2
1
2
1
1
1
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
1
0
3
2
2
0
0
0
0
0
1
0
0
0
5
1
1
0
0
2
4
0
0
2
0
0
0
2
1
0
1
0
0
1
0
2
2
0
0
1
0
1
1
1
0
0
0
2
0
0
0
0
1
2
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
3
0
4
0
0
0
2
9
0
0
1
0
0
1
0
1
0
0
3
1
0
0
1
0
0
2
0
0
2
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
2
1
0
0
1
0
1
1
0
1
2
1
0
0
0
2
0
1
0
0
2
0
3
0
1
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
3
4
1
0
1
0
0
1
2
0
0
1
2
0
4
0
2
0
0
0
1
1
0
0
0
0
1
1
0
1
0
1
0
0
3
1
0
0
0
0
1
0
0
1
0
0
2
0
4
0
0
0
1
0
0
2
1
0
0
2
0
3
0
1
0
0
0
0
0
3
0
0
1
0
0
1
0
2
0
2
2
0
0
1
0
1
4
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
1
4
0
0
2
0
0
0
0
0
0
2
0
2
2
1
2
1
1
1
0
0
2
1
0
0
2
0
2
0
1
1
1
0
0
0
0
1
1
2
0
0
0
0
1
0
0
2
1
2
0
0
0
2
1
0
2
1
2
0
1
1
0
0
0
2
1
1
0
3
1
0
0
0
0
0
0
0
2
0
1
1
1
0
1
0
0
1
1
2
0
0
1
0
0
0
1
0
0
0
1
0
1
1
0
0
1
0
0
0
2
0
0
0
0
0
0
2
1
1
2
2
2
1
0
1
0
1
1
0
1
2
0
0
1
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
1
1
0
1
0
0
1
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
1
0
2
2
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
3
1
0
0
1
2
0
0
0
0
0
0
0
2
2
0
0
0
0
1
1
0
0
0
0
2
0
1
2
1
1
0
2
0
1
0
2
1
0
2
1
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
2
1
1
0
0
0
1
2
3
1
1
1
0
2
0
0
0
0
0
1
2
2
2
0
0
0
0
1
0
0
1
1
0
1
0
0
0
1
2
1
2
0
1
0
0
0
0
0
2
2
0
2
0
1
2
0
0
0
1
0
1
0
2
0
0
2
2
0
0
0
1
0
1
0
1
0
1
0
0
1
1
0
0
2
0
1
0
1
2
1
0
2
0
2
0
2
1
0
1
0
0
1
0
2
1
2
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
2
2
0
0
2
0
0
2
1
0
2
0
2
1
0
2
1
1
1
0
0
1
1
0
1
0
0
0
0
0
1
0
1
1
4
1
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
1
0
0
0
2
0
0
1
2
2
2
1
2
0
1
2
0
0
2
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
1
2
0
0
0
5
0
0
0
1
1
0
0
1
1
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
1
2
0
1
1
2
0
1
1
0
1
2
0
1
0
1
0
2
0
1
0
6
0
0
3
2
2
2
0
0
2
1
1
0
1
1
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
1
1
3
0
0
0
0
0
2
0
0
1
3
1
1
0
1
1
2
2
0
1
1
1
2
1
0
0
0
1
0
0
0
0
3
0
0
0
1
0
0
1
2
1
0
0
0
1
1
2
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
1
2
0
2
0
0
2
0
0
0
0
0
2
3
1
1
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
2
2
0
0
0
1
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
1
2
0
0
1
1
0
2
0
3
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
1
0
0
2
1
0
0
1
0
1
0
1
0
2
2
0
0
1
0
0
1
0
2
2
2
1
0
0
0
2
1
2
0
1
0
2
1
0
0
1
1
4
1
2
0
0
1
0
2
0
1
0
2
0
0
2
0
0
0
1
0
0
2
0
0
0
2
0
2
1
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
2
2
3
0
0
2
0
0
0
0
1
2
0
2
2
0
2
1
2
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
1
1
0
2
0
2
0
0
0
0
1
1
1
2
0
2
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
1
0
2
0
3
0
0
2
1
0
2
0
0
2
1
0
0
2
1
1
1
2
0
0
0
1
1
0
1
0
1
0
0
1
0
1
0
0
0
0
2
0
3
0
1
0
0
0
0
2
0
2
1
0
0
1
1
1
0
1
2
2
0
0
0
0
0
0
0
1
5
2
0
2
1
1
1
1
1
0
1
1
2
2
0
1
1
2
0
0
0
2
2
0
0
0
0
1
0
2
0
0
2
0
1
0
0
0
1
0
0
0
0
2
1
1
0
0
0
0
0
0
1
4
0
0
2
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
1
2
1
0
0
0
2
0
0
0
1
0
0
1
0
0
1
2
2
0
2
1
0
1
2
0
0
0
2
0
0
2
2
1
1
0
0
0
0
0
1
1
0
0
0
0
2
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
3
1
1
2
1
1
2
2
0
0
0
1
0
0
1
2
0
2
0
0
1
1
0
0
1
0
1
0
0
1
2
0
0
0
1
0
1
1
0
0
0
0
0
0
1
1
0
0
0
1
0
2
0
1
0
0
2
0
2
1
0
0
0
1
2
2
0
0
0
2
0
0
0
0
0
2
1
2
1
0
0
1
3
0
0
0
2
0
0
0
1
0
2
0
0
0
2
1
0
2
2
0
0
0
0
2
0
2
2
1
0
0
0
0
0
0
0
0
1
2
2
0
0
0
2
1
2
0
2
2
2
0
0
0
0
0
2
1
0
1
0
0
0
1
0
0
3
2
1
1
1
1
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
1
0
0
1
0
2
0
0
1
0
0
0
1
2
0
1
3
2
0
1
0
0
0
0
1
2
0
0
0
0
0
2
0
2
0
2
1
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
1
0
4
2
0
0
1
1
2
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
4
0
0
0
0
0
0
0
1
0
0
4
3
0
1
0
1
2
1
0
0
0
0
0
0
0
0
1
0
2
2
1
2
0
0
0
0
0
0
1
0
0
0
0
1
0
2
1
0
0
0
0
0
0
2
0
3
2
1
0
1
0
0
2
0
0
0
0
0
3
1
0
1
0
2
0
0
0
0
1
1
2
0
0
2
0
2
1
0
0
0
2
2
0
1
0
2
2
0
0
1
0
2
0
1
2
0
0
1
0
0
0
2
1
0
2
2
0
0
0
1
0
0
0
4
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
1
0
1
2
1
2
0
0
1
1
0
1
0
0
0
2
2
2
1
0
0
0
0
1
0
1
1
0
0
0
0
1
1
2
0
0
1
0
1
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
2
2
1
0
2
1
1
0
0
0
0
2
2
2
0
1
0
0
0
2
1
1
0
1
0
0
0
2
0
0
2
0
1
0
2
0
2
2
0
2
2
1
2
0
2
0
0
0
0
0
0
1
0
0
1
5
0
0
0
2
0
2
1
0
0
0
0
0
0
1
2
0
2
1
1
2
2
1
0
1
0
1
2
0
2
1
0
0
0
0
1
0
0
2
1
0
2
2
0
0
2
1
0
0
0
2
0
1
0
2
0
0
0
0
1
0
1
0
0
1
3
0
0
0
1
1
0
2
0
1
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
2
1
2
0
2
1
1
0
0
2
3
2
2
1
2
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
2
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
2
0
7
0
0
1
2
1
0
0
0
0
2
3
1
1
0
1
1
2
0
0
0
2
0
0
0
2
0
0
1
1
1
0
2
0
2
0
0
0
1
1
0
0
0
1
1
0
0
0
0
2
1
0
1
0
2
0
2
1
1
2
2
0
0
2
0
2
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
2
1
0
0
0
1
2
0
1
0
0
0
0
1
2
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
5
1
0
1
0
0
0
0
2
9
0
0
0
2
0
0
0
0
0
1
0
0
2
2
0
1
2
2
0
0
0
0
0
0
0
2
0
0
0
7
0
1
1
1
2
3
0
1
1
1
2
0
0
0
0
0
0
2
0
0
2
2
2
0
2
0
0
0
1
0
0
1
0
0
2
0
1
2
0
0
0
0
0
1
1
1
0
0
1
2
0
1
1
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
1
1
1
2
0
1
1
1
0
2
0
2
0
0
0
0
2
0
2
0
0
0
0
1
1
0
1
0
0
2
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
2
0
1
1
0
1
0
0
2
0
0
2
0
2
0
0
1
0
1
0
2
0
0
1
0
2
1
0
0
0
0
0
1
1
0
2
1
0
0
1
2
2
0
0
2
1
2
0
2
1
0
0
1
0
0
0
0
0
1
3
0
0
0
3
1
0
0
0
1
1
0
0
1
0
2
2
0
0
0
0
3
2
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
2
0
1
1
2
0
2
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
1
2
0
0
2
0
2
0
1
0
1
0
2
0
0
0
0
0
1
1
0
0
1
0
1
1
0
0
1
0
2
0
2
0
1
0
3
0
0
2
1
0
0
0
0
2
0
0
2
3
2
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
1
0
0
0
2
2
2
0
0
0
0
0
0
0
0
1
2
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
2
0
1
0
0
1
1
0
2
1
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
1
0
2
0
2
0
0
2
0
0
0
1
1
0
1
1
2
0
0
0
0
3
2
0
1
1
0
0
1
1
0
0
0
1
1
0
0
0
0
1
0
0
0
2
0
1
1
0
1
0
2
0
0
2
2
0
0
1
1
0
1
0
0
0
2
0
0
0
0
1
1
1
0
0
0
1
0
1
1
1
0
0
4
0
0
0
2
0
1
0
0
0
2
1
0
1
0
2
1
0
1
1
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
2
0
0
1
0
0
0
1
2
1
2
0
0
1
1
1
1
0
0
2
1
0
0
1
0
0
0
2
0
0
2
1
0
0
0
2
0
2
0
0
0
1
0
0
0
2
2
1
1
1
0
1
0
2
0
0
0
1
0
0
1
2
1
2
0
1
1
0
0
1
1
0
1
0
1
1
0
1
0
0
2
2
0
0
0
2
0
0
0
0
4
3
0
2
0
0
1
0
1
0
1
2
0
0
0
2
1
2
1
0
0
3
1
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
1
4
1
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
1
0
0
0
2
2
0
0
1
1
2
0
1
1
1
0
0
0
0
1
1
0
0
0
0
0
2
1
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
2
0
1
1
1
1
0
0
1
1
0
2
3
0
0
0
0
0
0
0
0
2
0
1
2
1
0
1
1
0
0
0
0
0
0
0
1
0
1
1
5
3
0
1
0
1
0
0
3
1
2
0
1
1
0
0
1
0
0
0
0
2
0
1
2
0
0
0
2
1
0
0
0
0
1
0
0
1
0
4
0
0
1
0
0
0
2
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
1
0
4
0
3
1
1
2
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
1
2
0
2
0
0
2
1
2
0
2
2
2
0
2
3
1
0
0
2
0
0
0
0
3
0
2
0
0
0
0
0
1
1
1
0
0
0
0
1
0
1
0
2
0
0
3
1
1
0
2
0
0
2
1
1
0
2
0
4
2
2
1
2
0
0
0
2
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
1
2
0
0
1
0
2
1
0
2
0
1
0
2
2
2
2
0
2
0
1
0
1
2
2
0
0
0
0
2
2
1
0
2
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
1
0
1
0
2
0
0
0
2
1
1
0
2
0
0
2
2
1
0
2
0
1
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
1
1
0
0
1
0
2
1
0
0
2
1
0
0
1
0
0
0
0
0
0
3
2
0
3
0
0
1
0
0
2
1
0
0
1
3
0
1
0
2
1
2
2
0
0
1
0
2
0
0
2
0
0
2
0
0
4
2
0
2
2
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
1
0
0
0
1
0
1
0
1
2
2
2
2
0
0
0
0
0
0
1
0
0
2
0
2
2
1
1
6
2
1
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
2
1
0
0
1
1
1
0
0
0
0
0
0
5
0
1
0
0
0
2
0
1
0
3
2
1
3
1
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
3
1
2
1
0
0
1
1
0
2
1
3
0
2
2
1
2
0
0
2
1
0
0
0
0
3
0
0
2
0
0
1
0
0
2
0
2
0
2
1
0
0
0
0
1
1
1
0
0
0
0
1
2
2
0
2
0
2
1
0
3
0
0
1
0
1
2
2
0
0
0
2
0
0
3
0
0
0
0
0
2
2
0
0
1
2
0
2
2
0
3
0
0
0
0
0
0
1
1
0
1
0
2
0
1
0
1
0
2
0
1
1
0
1
0
0
1
0
0
2
0
2
0
1
0
0
4
1
0
2
0
0
0
0
0
1
1
0
0
1
0
0
1
2
1
0
1
0
0
0
1
0
1
0
0
0
0
3
2
1
0
1
1
1
0
1
1
0
0
0
0
2
2
0
0
0
0
2
0
1
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
2
2
0
1
3
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
2
1
1
0
1
2
2
1
0
1
0
0
1
1
0
0
0
2
1
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
2
4
0
2
0
1
1
0
2
0
0
1
1
0
0
0
0
1
2
0
0
0
1
0
3
0
2
0
0
0
0
0
2
1
0
0
0
2
0
0
2
0
2
0
0
1
0
2
2
0
2
2
0
2
2
0
0
0
3
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
2
4
0
1
2
3
2
1
2
0
2
0
0
0
1
1
1
0
1
3
0
0
1
0
2
0
2
0
1
0
1
0
1
2
0
0
0
0
0
1
0
0
1
1
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
1
0
2
0
0
2
2
0
2
0
0
1
0
1
0
1
0
2
1
1
0
1
2
0
0
1
0
0
1
2
0
0
0
0
0
2
2
2
0
0
2
5
0
3
1
2
1
0
0
1
0
0
0
1
0
0
2
0
0
1
0
2
1
0
1
1
2
1
5
0
0
0
0
1
1
2
1
1
1
0
0
1
2
0
0
0
2
0
0
2
2
0
0
2
0
0
0
1
0
0
2
0
1
0
0
0
0
0
1
0
1
0
0
1
0
1
1
0
0
2
0
2
1
0
0
2
1
2
1
0
2
0
1
1
0
2
1
1
0
0
0
1
0
0
0
0
1
1
0
0
2
5
0
0
1
0
1
0
0
0
0
0
1
0
0
2
1
0
0
2
0
1
1
0
1
2
0
0
2
2
0
0
1
0
0
0
0
1
0
1
1
0
1
0
0
0
0
2
1
0
0
1
1
2
0
0
2
2
0
0
2
0
1
1
2
1
2
0
0
1
2
0
2
4
0
0
0
1
0
5
0
0
2
0
0
0
1
2
1
0
0
2
1
0
0
0
1
0
0
0
1
2
0
0
0
2
1
2
0
1
1
0
0
0
2
2
0
0
0
0
2
0
0
3
2
0
0
5
0
0
0
0
0
0
1
0
2
1
1
0
0
0
2
2
0
2
0
1
2
2
1
2
1
0
0
0
2
0
1
1
0
2
0
0
0
1
0
0
2
1
0
0
0
0
1
2
1
0
0
0
0
1
0
1
0
1
0
1
1
2
1
2
0
0
2
0
0
1
0
0
2
1
0
0
2
0
0
1
0
0
0
0
0
0
2
1
0
0
1
0
0
1
1
0
0
1
0
1
0
0
2
0
0
0
1
0
0
1
0
0
2
1
2
1
0
0
3
0
1
1
3
1
1
0
1
0
0
1
2
0
0
0
0
2
1
0
2
0
0
1
0
0
0
0
2
2
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
1
0
0
4
2
0
1
0
0
0
1
2
0
0
0
0
1
2
0
2
0
0
1
2
1
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
3
2
2
1
0
0
0
0
0
1
0
1
2
0
0
0
0
0
2
0
1
1
0
0
2
0
0
0
0
1
0
0
1
2
0
1
0
0
0
2
0
0
1
2
1
1
0
0
2
1
0
0
0
2
0
0
0
0
2
2
2
2
0
2
0
1
2
0
0
2
0
3
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
1
2
1
0
0
1
1
0
2
1
1
1
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
2
2
0
0
0
0
2
0
0
1
0
2
0
0
0
0
2
1
0
1
0
0
0
1
1
0
0
2
1
0
1
0
1
0
0
2
0
0
0
1
0
1
1
2
0
0
1
0
2
0
2
0
1
0
2
0
2
0
0
0
2
0
0
0
4
2
0
0
2
0
0
0
0
3
0
2
0
2
1
0
2
1
1
1
0
0
0
1
0
0
0
0
1
1
1
2
1
0
0
0
0
1
1
2
2
0
0
1
1
0
0
0
3
0
0
1
1
0
0
0
0
0
4
1
1
2
0
1
0
0
1
1
0
0
0
1
2
0
0
0
1
0
3
1
1
0
1
0
0
0
1
1
0
0
0
0
2
1
1
2
0
0
0
2
2
0
2
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
1
2
3
0
0
1
0
1
0
2
0
1
2
1
0
2
0
0
0
0
0
0
2
0
2
1
1
0
4
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
1
0
1
2
0
0
2
2
0
2
0
1
1
0
0
0
1
0
3
0
0
1
2
1
0
0
0
0
0
0
0
1
2
1
0
0
2
1
1
2
2
0
0
2
0
1
0
2
0
1
0
0
1
0
2
3
2
0
2
0
2
0
0
0
1
1
0
3
1
2
0
3
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
1
0
0
0
0
2
2
0
0
0
0
1
1
1
0
1
1
2
0
2
0
1
2
0
0
0
2
0
0
0
1
1
0
2
2
0
1
0
0
1
0
0
2
1
1
0
0
0
1
0
3
0
1
1
0
0
0
0
0
0
0
1
3
1
2
0
2
0
0
1
1
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
1
0
4
1
0
0
1
1
1
2
2
0
1
0
0
2
0
10
0
0
0
0
2
0
0
0
0
1
1
0
0
2
2
1
1
1
0
0
1
0
2
3
2
0
1
7
0
0
0
1
0
0
0
0
2
0
2
2
2
2
2
0
1
0
0
0
0
1
0
3
1
1
1
1
2
2
0
0
0
0
0
1
0
0
2
1
0
0
0
1
0
2
2
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
1
1
2
0
0
2
0
3
1
0
0
0
2
2
1
0
0
2
0
0
0
1
0
2
1
0
0
0
0
0
0
1
1
0
0
1
0
0
2
0
0
2
0
0
0
1
1
0
0
2
2
0
0
1
0
0
0
0
0
3
0
0
0
1
3
0
0
0
0
2
0
0
1
1
0
1
2
0
0
0
0
3
2
0
0
2
2
0
0
2
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
2
1
1
2
2
0
1
1
2
0
1
0
0
0
2
0
1
0
1
0
1
1
1
0
0
0
0
1
0
1
1
1
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
1
1
2
1
1
2
0
0
0
0
0
0
3
0
0
0
1
0
2
2
2
1
0
2
0
0
0
0
1
1
0
2
0
0
1
0
1
2
2
1
1
2
1
0
0
0
0
1
2
0
0
0
0
0
1
2
1
2
0
1
0
3
2
1
0
0
1
2
0
0
2
2
2
2
0
2
2
2
1
0
2
0
0
5
2
2
0
0
1
0
0
1
1
1
2
1
2
2
1
1
1
0
1
0
0
1
0
0
0
1
0
1
1
0
1
0
1
2
1
2
0
1
0
2
0
1
0
1
0
2
0
0
0
1
2
0
1
3
0
0
1
0
0
0
2
2
4
1
1
0
5
0
1
0
0
0
1
0
0
0
0
3
2
1
0
0
0
1
0
0
0
0
0
2
1
0
0
0
2
1
0
0
1
1
0
0
1
0
0
0
0
0
2
1
0
2
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
1
0
1
0
0
0
0
2
3
1
2
0
0
3
2
2
2
2
0
1
2
0
0
1
0
0
0
0
0
0
3
0
1
0
0
0
2
1
0
0
0
0
1
2
0
0
2
0
0
0
1
3
1
0
0
0
1
0
0
0
1
0
2
1
0
1
0
1
0
2
1
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
2
0
2
2
0
0
0
0
7
1
2
0
0
0
1
0
1
2
0
0
1
0
1
1
2
0
2
1
0
1
0
0
2
0
1
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
4
0
0
2
1
1
0
0
0
1
0
0
0
1
0
0
2
0
1
0
1
0
0
2
1
2
0
0
0
0
0
1
2
0
0
1
1
0
0
0
1
1
1
2
0
0
2
0
0
0
0
0
0
0
1
2
2
1
2
2
1
1
0
2
1
2
0
2
1
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
1
2
0
2
0
0
0
1
0
1
0
1
0
0
0
0
2
2
1
0
0
1
2
1
1
0
1
1
0
3
0
0
2
0
0
0
0
1
2
0
1
0
0
3
3
2
0
2
1
1
0
0
0
4
4
1
0
1
0
1
1
0
2
0
0
2
0
0
1
0
2
3
1
2
3
0
1
0
0
0
2
1
0
0
0
0
2
1
0
1
2
0
1
2
0
1
2
0
2
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
1
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
3
0
0
2
0
2
0
0
2
0
0
0
0
0
2
1
0
0
2
0
1
0
0
0
2
1
0
0
2
0
2
0
1
1
0
0
1
1
0
0
2
0
0
0
2
2
0
0
0
1
1
2
1
0
1
0
0
0
2
2
1
2
0
1
0
0
2
0
2
0
0
2
0
0
2
2
2
2
0
0
0
0
2
3
0
0
1
0
2
0
0
1
2
0
1
1
1
2
3
0
0
0
1
2
1
0
0
0
2
2
1
0
0
0
0
0
0
0
0
1
2
1
0
1
2
0
2
0
0
0
0
0
0
2
2
1
0
0
2
0
1
2
1
0
0
2
2
0
2
0
3
1
2
0
1
0
0
0
1
0
0
0
0
0
2
0
1
2
1
0
1
0
0
0
0
1
0
0
0
1
2
2
0
1
0
0
0
1
0
0
0
2
2
0
0
0
0
2
2
0
0
1
2
4
0
0
0
2
0
0
2
1
0
0
2
0
0
0
0
1
4
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
2
0
1
0
0
2
2
0
0
0
0
0
0
2
2
2
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
2
2
0
0
0
1
0
0
1
0
1
0
1
0
0
0
1
1
3
0
1
0
0
0
1
0
0
0
2
0
2
2
2
1
0
2
2
1
0
0
0
1
0
1
0
0
2
1
0
0
1
0
2
2
1
1
0
0
0
0
0
1
0
2
1
0
0
1
2
1
0
1
0
0
1
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
4
0
2
2
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
1
0
0
1
0
0
1
0
1
2
0
1
1
2
0
0
0
0
0
0
2
0
1
0
0
1
1
0
2
2
2
0
0
1
0
0
0
1
1
0
0
1
0
2
0
0
0
0
0
0
2
1
2
0
2
1
0
2
1
0
1
1
2
0
2
0
0
1
0
0
1
2
0
0
1
0
0
1
0
2
2
0
1
2
1
0
0
0
0
2
0
0
2
0
0
0
2
0
1
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
2
0
0
2
1
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
2
2
0
2
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
3
0
0
0
0
2
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
2
1
0
0
1
1
1
0
2
0
0
0
2
1
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
2
1
2
0
0
2
2
0
0
0
0
1
1
1
1
2
3
0
2
1
1
1
0
0
0
1
0
2
1
1
0
0
0
3
1
0
2
2
0
2
1
1
0
0
0
0
1
0
0
0
1
2
0
0
1
0
2
1
1
0
0
1
2
0
3
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
2
0
0
0
1
0
1
2
0
0
0
3
0
2
0
1
0
0
1
0
0
0
0
1
1
0
1
0
2
0
0
2
0
0
0
0
0
0
0
1
1
0
2
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
3
1
0
2
0
2
1
0
0
1
0
0
0
7
0
0
0
1
0
0
1
0
1
1
1
0
0
1
0
2
0
1
2
0
1
0
0
1
0
0
2
0
2
2
0
2
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
2
2
2
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
3
4
2
0
1
0
0
0
2
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
1
0
2
0
1
1
1
0
0
1
0
1
3
0
0
0
1
0
1
2
0
0
1
0
1
1
0
1
1
0
0
0
1
0
0
1
0
0
1
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
3
1
0
0
2
0
0
0
1
0
0
2
0
0
2
1
0
0
1
0
0
7
1
0
0
1
0
0
1
0
0
0
1
1
2
0
1
2
2
2
0
1
1
1
0
2
0
0
0
2
0
1
0
0
1
0
0
0
2
2
0
0
1
1
1
0
0
0
0
0
0
0
2
1
0
0
2
0
1
1
1
0
0
2
2
0
0
2
1
0
0
0
2
2
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
2
1
2
2
1
1
1
2
0
1
0
0
2
0
1
0
1
2
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
2
1
1
0
2
0
0
0
0
1
0
1
2
0
0
1
0
0
0
0
3
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
1
1
0
0
0
1
1
1
0
0
1
0
0
0
0
6
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
1
0
1
2
0
0
0
1
1
0
1
1
0
2
1
1
4
2
1
2
2
3
0
6
0
0
0
0
2
2
0
2
1
2
0
0
2
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
6
2
0
0
2
0
1
0
0
2
0
0
0
0
0
2
1
1
1
0
1
0
2
0
1
0
1
0
1
1
2
0
1
1
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
1
2
0
1
0
0
2
1
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
2
0
4
0
0
0
0
2
0
1
1
1
2
0
1
0
0
0
0
0
0
0
0
0
0
2
2
2
0
2
0
2
0
1
2
0
2
2
0
2
1
0
1
0
1
1
0
0
0
2
0
0
0
2
1
1
0
0
2
0
1
0
1
0
2
1
2
0
0
0
0
0
1
2
0
1
2
0
1
0
0
0
2
0
2
0
0
0
0
0
0
1
0
2
1
1
2
0
1
0
0
0
0
0
1
0
1
1
2
0
0
1
4
0
0
0
0
2
0
0
2
0
1
0
1
0
2
0
2
3
0
0
2
0
2
0
0
0
0
2
1
0
0
2
2
0
1
0
1
2
0
1
0
1
0
1
3
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
1
0
0
3
0
0
2
0
0
2
0
2
0
0
0
0
2
1
0
1
0
1
2
0
0
0
2
1
2
3
0
0
0
1
0
1
2
0
1
0
0
0
0
1
0
2
0
2
2
1
1
0
0
2
0
2
0
0
1
0
1
0
0
0
0
0
2
1
1
1
2
2
2
1
0
0
1
0
0
2
0
2
0
0
0
2
3
0
0
1
1
2
0
0
0
0
0
2
0
1
0
0
1
1
0
0
0
0
2
0
2
0
0
1
0
0
0
0
1
0
1
0
0
0
0
2
0
1
0
0
0
2
0
0
2
0
1
0
1
2
2
0
0
0
1
2
0
0
0
1
0
0
1
0
1
0
1
0
0
1
4
1
0
0
1
0
0
0
0
0
1
0
2
2
2
0
2
1
0
0
2
1
0
2
0
1
1
1
2
2
0
1
0
0
2
2
0
0
2
0
0
1
0
0
0
0
0
0
4
2
1
1
2
1
0
0
0
1
0
2
0
1
0
0
3
1
2
0
1
0
0
0
0
1
1
0
0
0
1
0
1
0
0
2
1
1
1
1
0
0
0
1
1
0
0
0
1
1
1
1
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
1
0
1
0
0
1
0
0
0
0
0
1
1
0
2
0
1
0
0
1
2
2
0
1
0
2
0
0
1
1
1
0
1
1
1
0
0
2
2
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
1
0
2
0
0
2
0
0
0
1
0
0
1
2
2
0
0
0
2
2
2
0
1
1
0
0
1
0
1
0
2
0
1
0
0
1
2
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
2
2
1
0
2
0
0
0
0
0
0
0
0
1
1
1
1
0
0
1
2
2
2
1
0
0
1
0
0
0
0
1
4
0
1
0
2
0
0
1
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
1
0
0
1
1
0
3
8
2
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
1
2
1
2
0
0
2
0
3
2
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
2
2
0
0
2
1
0
1
2
0
0
2
0
0
0
0
2
0
0
0
0
1
0
1
0
2
0
0
0
1
1
0
0
0
5
1
0
1
1
0
0
0
1
0
0
0
0
0
1
2
1
1
0
0
3
2
0
0
0
2
1
1
2
1
0
0
0
1
0
2
0
0
0
0
1
0
0
0
1
0
2
1
0
2
0
1
0
0
1
0
1
0
0
0
1
0
0
1
0
3
0
0
0
3
1
0
0
0
0
2
0
2
2
2
0
0
2
0
0
2
1
0
2
1
0
2
1
1
0
2
0
1
0
2
0
1
0
0
0
1
2
0
0
0
1
0
0
0
0
0
1
1
2
1
0
1
1
0
1
2
0
1
2
1
0
0
0
0
0
0
1
1
1
2
2
2
0
2
0
2
0
3
4
1
1
1
1
0
1
2
0
0
0
2
1
2
0
2
0
2
2
2
0
2
1
2
1
0
0
0
0
2
0
0
1
1
2
1
2
0
0
0
0
0
2
1
0
0
0
2
0
1
0
0
1
0
0
1
1
0
0
2
1
0
0
3
0
0
2
2
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
1
2
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
1
1
0
0
0
2
0
1
1
2
1
1
1
0
2
1
0
0
1
0
0
0
1
1
2
0
0
0
1
0
2
1
2
1
0
4
0
0
0
0
2
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
2
0
0
0
2
4
0
0
3
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
2
0
0
0
0
2
0
2
0
1
1
0
0
2
0
0
0
1
0
0
2
2
0
0
0
1
1
0
0
0
0
1
0
2
1
0
0
0
2
0
3
1
0
1
2
0
1
0
0
0
1
0
0
2
0
0
3
0
0
1
0
0
1
1
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
1
0
0
0
1
1
0
0
0
0
2
2
0
0
1
0
2
1
0
1
0
0
0
2
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
3
1
0
0
0
1
1
2
0
0
0
2
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
1
0
1
1
0
0
1
1
2
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
2
0
2
2
1
0
2
0
0
0
1
0
2
0
0
0
0
1
1
1
1
1
0
1
0
0
0
2
0
2
1
0
2
1
1
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
1
0
1
0
1
1
0
0
0
2
0
1
1
0
0
1
0
2
2
0
0
1
0
0
0
0
0
2
1
0
1
0
0
0
0
1
0
0
0
3
1
0
2
0
0
2
3
0
1
2
0
2
2
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
3
0
1
0
0
2
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
1
0
2
2
0
0
0
0
0
1
0
0
0
0
2
0
1
1
0
1
0
2
0
2
2
0
0
0
0
0
0
0
0
3
2
0
0
2
1
0
0
0
0
2
0
1
0
2
0
2
1
0
0
0
0
2
0
2
0
2
2
0
0
0
0
1
0
0
1
2
0
0
1
2
0
0
3
2
0
2
2
0
0
2
0
0
0
0
2
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
1
0
1
0
0
0
2
10
0
0
0
0
2
0
0
0
2
1
1
1
1
1
1
0
0
3
0
1
1
0
0
0
0
0
3
0
0
0
2
0
0
0
2
2
0
0
0
1
0
0
1
1
0
0
1
0
0
1
0
0
1
1
1
0
2
0
0
0
0
1
0
0
0
0
0
1
2
2
0
1
0
0
0
0
0
1
0
0
0
1
1
1
0
0
2
1
0
0
1
3
0
0
0
1
0
2
2
0
2
0
0
0
2
0
0
0
1
0
0
0
2
0
2
2
0
0
2
0
0
2
1
0
0
1
0
1
0
0
0
0
0
2
0
3
0
0
1
0
2
0
0
2
2
0
3
0
0
0
0
0
2
0
0
0
1
0
1
1
0
2
2
0
0
0
1
0
0
0
0
1
0
2
2
0
0
1
0
2
2
0
2
0
0
2
0
0
2
1
0
0
1
0
0
3
2
2
2
1
0
1
0
0
0
2
1
2
0
1
1
0
0
1
2
2
0
0
0
0
1
2
0
0
0
1
0
0
0
2
2
0
0
0
0
0
1
4
3
2
0
0
2
1
0
1
1
0
2
0
1
0
0
2
1
0
0
1
0
0
0
2
1
0
2
0
1
0
0
0
0
0
1
0
0
0
1
2
0
1
0
2
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
3
1
0
2
0
0
0
0
1
0
2
2
0
1
0
0
1
2
0
0
2
0
0
1
2
2
2
0
2
0
0
1
0
0
0
1
0
1
1
0
2
0
0
0
0
3
0
2
1
0
1
2
1
1
0
0
0
1
0
0
1
1
2
0
1
0
1
2
2
0
1
2
1
0
2
0
0
0
0
0
2
0
2
2
1
1
0
0
1
2
0
0
2
0
0
1
0
0
0
0
0
1
1
1
1
0
2
0
0
3
0
1
0
0
0
0
1
2
0
0
1
0
1
2
1
1
0
1
1
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
3
0
0
2
0
0
0
0
0
1
0
1
3
1
0
0
2
2
0
2
2
1
0
0
1
1
0
0
0
1
2
1
0
0
1
2
0
1
1
0
1
0
1
0
0
0
2
0
1
1
0
0
2
1
0
0
0
0
1
0
0
1
3
2
3
0
0
1
0
2
0
0
0
0
0
0
1
2
2
1
1
0
0
2
0
2
2
0
0
1
1
0
0
2
0
1
0
0
0
0
0
1
0
1
0
1
1
0
0
1
0
2
0
2
2
2
1
2
0
0
1
2
0
1
0
0
0
0
2
0
0
0
0
2
2
0
2
2
0
2
0
3
1
0
1
2
7
4
0
0
2
0
2
2
0
0
2
1
1
1
0
1
0
1
2
1
1
2
0
1
1
1
0
0
0
0
4
0
0
1
1
2
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
1
1
0
0
1
0
0
0
2
0
2
0
2
0
0
2
0
2
0
0
1
0
0
0
1
0
1
0
2
2
2
0
2
0
2
0
2
2
2
0
1
0
0
0
1
0
1
0
0
0
2
0
0
1
0
0
3
0
0
0
0
0
1
0
0
1
0
1
1
0
2
2
0
0
1
3
1
1
2
0
1
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
2
0
2
0
0
1
0
1
0
2
2
2
1
2
0
3
0
1
0
2
0
2
2
0
2
0
0
0
0
1
0
0
0
3
0
0
0
1
0
0
0
0
0
2
0
1
2
2
2
1
0
1
0
2
0
0
0
1
0
1
1
0
2
0
1
1
2
0
1
2
0
0
0
1
0
1
0
0
0
2
0
0
0
1
1
0
2
0
2
2
0
0
0
1
1
0
0
1
0
1
2
0
1
0
0
1
2
0
0
0
2
1
0
0
0
2
1
2
1
0
0
1
0
1
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
2
2
0
0
0
2
1
0
1
0
0
0
0
1
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
2
1
1
0
1
0
2
1
2
0
2
1
1
2
1
0
2
0
0
0
2
0
1
1
1
0
1
1
0
0
2
2
2
1
0
2
0
0
2
2
2
0
0
2
1
0
0
0
1
0
1
0
2
0
2
0
0
0
0
0
0
2
0
1
0
0
3
0
0
2
3
0
0
2
0
2
1
3
1
0
2
0
0
1
1
0
1
1
0
0
2
0
2
0
2
2
0
0
0
0
0
1
0
1
2
4
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
1
2
2
0
0
1
0
0
0
2
0
0
0
1
1
0
2
1
1
0
0
0
2
0
1
0
2
0
0
2
2
1
0
2
0
2
2
1
0
1
0
0
1
0
0
0
2
1
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
1
0
1
0
0
0
0
0
1
3
0
0
0
0
1
0
2
0
0
0
0
0
1
4
0
0
0
0
1
0
1
1
0
0
0
2
1
1
2
1
0
0
0
0
2
1
2
0
0
0
0
1
1
0
1
2
2
0
2
1
0
2
0
2
0
0
1
0
1
0
0
0
1
0
1
2
2
0
0
0
0
0
1
0
2
0
0
1
2
0
1
1
1
1
0
2
1
0
0
0
0
1
2
1
0
2
0
0
0
0
2
0
1
0
2
0
2
0
2
0
1
1
1
1
0
0
0
2
0
0
1
0
0
0
0
1
2
0
0
2
2
7
4
3
0
1
0
1
0
1
1
0
1
2
3
0
2
0
0
1
0
0
0
1
2
1
3
0
0
0
0
0
0
0
0
0
1
0
7
2
0
3
0
0
0
2
1
0
1
0
1
2
0
2
2
2
2
1
1
2
0
1
1
0
0
0
0
2
1
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
1
2
0
0
0
0
1
1
2
1
2
1
2
1
2
2
0
0
1
2
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
1
1
1
0
0
0
0
1
1
2
1
1
2
1
3
0
0
0
0
1
0
2
0
0
0
0
0
1
2
0
1
1
0
2
0
1
0
1
0
2
0
5
1
1
1
2
2
3
0
0
0
2
1
0
0
2
0
2
1
0
1
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
2
2
0
2
0
0
0
1
0
0
0
2
1
0
2
0
0
3
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
1
0
2
1
1
1
2
1
0
0
2
0
1
2
0
1
0
0
0
0
0
2
2
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
1
2
1
0
0
1
0
0
0
2
1
1
0
0
2
0
0
0
0
3
2
2
0
1
1
2
0
2
2
2
1
1
0
2
1
0
1
0
0
1
0
2
1
0
0
2
0
2
1
0
2
2
0
0
0
2
0
1
0
0
1
0
1
1
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
3
0
1
1
0
0
0
1
2
0
0
0
2
0
0
0
1
0
1
0
1
0
0
2
0
0
1
0
2
0
0
0
0
1
0
0
0
0
1
2
0
1
1
0
0
0
1
0
2
0
0
1
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
1
1
0
2
0
1
1
0
0
0
0
0
1
0
0
1
2
0
0
0
0
1
0
2
0
0
2
0
0
0
2
1
0
1
1
3
2
1
0
2
1
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
1
2
0
2
0
0
0
0
0
0
0
1
0
0
2
2
0
0
2
1
0
1
0
2
2
2
1
0
0
0
0
1
0
1
1
2
0
0
2
0
1
0
0
0
0
0
1
2
0
3
0
1
2
0
0
1
2
0
0
0
0
2
0
0
0
0
0
3
2
2
2
1
0
0
2
0
1
2
0
6
2
0
3
1
0
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
1
1
2
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
2
1
1
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
1
0
0
1
1
0
0
1
2
0
1
0
1
2
1
0
2
2
1
0
1
2
0
2
0
2
0
2
1
0
2
0
0
0
1
0
0
2
2
0
0
0
1
1
1
0
2
0
0
0
1
2
1
0
0
1
0
0
0
1
0
0
0
0
2
0
2
2
0
0
0
0
2
1
0
0
1
0
1
0
0
0
0
2
0
2
0
1
2
0
1
1
1
1
0
0
0
0
0
2
2
0
0
1
3
0
2
0
0
1
1
0
1
1
0
1
0
0
2
0
0
0
0
1
0
3
1
2
0
3
0
1
1
1
0
0
1
0
1
0
1
0
0
2
2
0
0
0
1
0
2
2
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
1
2
0
2
3
2
0
0
0
1
1
1
3
1
0
2
0
0
0
0
2
1
0
0
1
1
2
0
0
0
0
0
1
1
1
2
0
0
0
1
0
0
2
0
0
2
0
0
0
1
0
0
1
0
0
0
0
1
2
0
2
2
0
0
2
0
1
0
0
2
0
0
0
1
2
0
0
1
0
0
0
0
2
0
0
0
2
1
0
2
0
0
1
0
1
1
0
1
1
0
0
0
0
0
1
2
1
0
0
2
0
3
0
2
0
1
1
0
1
2
0
1
2
1
2
0
1
1
1
2
1
0
0
0
0
1
0
2
0
0
1
2
0
2
2
1
6
1
0
0
1
0
2
0
0
1
2
0
1
5
0
0
0
2
5
2
2
0
2
2
0
0
0
1
1
0
1
0
0
1
0
1
1
0
0
0
0
0
0
2
0
1
0
0
0
1
0
2
2
1
1
0
1
1
0
2
0
0
2
3
0
0
0
0
1
2
0
1
0
1
2
2
0
1
1
0
1
0
2
0
0
0
2
0
1
1
0
2
0
2
0
1
0
0
1
2
1
0
1
1
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
2
1
2
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
1
0
0
1
2
0
1
0
0
0
0
0
2
0
0
1
0
0
2
0
1
2
2
0
2
1
1
0
0
1
0
0
0
0
2
2
1
0
0
1
1
0
1
1
0
0
0
0
0
1
2
2
0
0
1
0
0
0
2
2
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
3
0
2
1
0
0
0
2
0
1
2
2
2
0
0
1
2
0
1
1
0
0
0
0
0
0
1
0
0
0
0
2
0
2
1
2
0
1
1
0
1
0
2
1
1
0
0
0
2
2
2
0
0
0
1
0
0
0
0
1
2
2
0
1
1
2
0
0
1
0
2
0
0
0
0
2
0
0
0
0
1
2
1
2
0
0
2
1
0
0
1
1
1
2
0
2
0
0
0
0
0
1
3
0
0
0
0
0
0
0
1
1
0
1
2
2
0
1
1
1
2
0
0
1
1
0
0
0
1
2
1
1
1
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
2
1
0
0
1
2
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
2
2
4
2
0
0
2
1
1
1
0
2
0
2
0
0
0
0
1
0
0
0
0
0
1
0
3
0
0
2
0
0
0
2
0
0
2
2
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
2
1
2
0
1
0
2
2
1
0
2
2
1
1
0
0
3
0
0
1
0
2
0
0
0
2
2
0
0
0
2
0
0
1
0
2
0
2
0
0
1
0
1
0
0
2
1
0
0
0
2
0
2
0
2
0
1
2
0
0
1
0
2
0
0
0
1
2
2
0
0
0
2
0
3
0
3
2
2
0
2
1
2
1
0
0
2
1
1
0
2
0
2
2
0
1
0
0
0
2
0
2
1
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
2
2
2
0
2
0
0
2
2
0
0
0
0
2
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
1
2
1
0
0
1
0
0
0
0
2
1
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
1
0
2
1
1
1
2
1
0
2
1
0
0
1
0
1
2
0
0
2
1
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
1
1
2
0
1
0
0
0
0
1
1
0
1
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
2
2
2
0
1
1
0
1
2
0
0
2
0
0
1
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
2
0
1
2
0
2
2
1
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
2
0
2
0
0
1
2
0
0
1
0
0
1
1
0
1
0
0
1
0
0
0
1
2
1
1
1
0
0
0
0
1
0
0
0
2
0
1
0
0
0
1
0
0
1
2
1
0
1
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
2
2
1
1
2
0
0
0
0
0
0
0
2
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
2
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
1
2
1
1
0
1
1
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
1
1
0
0
0
2
1
1
2
0
0
2
2
0
2
0
0
2
0
3
0
0
0
0
5
2
2
4
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
1
0
0
0
0
5
2
0
1
0
1
2
0
2
2
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
2
1
0
1
0
1
0
1
2
1
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
2
1
1
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
1
2
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
2
1
1
1
0
1
2
0
0
0
2
0
2
0
0
2
2
2
0
0
1
1
0
2
0
0
0
2
2
0
0
2
2
0
0
2
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
1
1
0
1
0
2
2
0
2
0
1
0
0
0
1
0
0
1
0
1
0
0
1
0
0
2
1
3
0
0
0
0
0
0
1
0
2
1
1
0
3
2
0
0
0
2
0
0
0
0
0
0
2
1
1
1
2
0
0
2
0
2
1
0
0
0
1
1
0
2
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
2
2
1
1
1
0
0
0
2
0
0
2
0
0
2
1
0
2
1
0
4
1
0
1
1
0
2
1
1
0
2
0
0
1
2
1
2
2
0
0
2
2
0
0
0
0
0
2
1
3
0
2
1
2
1
0
1
2
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
3
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
4
0
1
0
1
2
0
0
2
0
0
0
1
3
0
2
1
1
0
0
0
1
1
2
0
0
0
0
0
1
2
1
0
2
0
0
2
2
1
0
3
0
1
1
0
0
0
0
0
0
0
0
2
0
0
1
2
1
0
0
2
0
2
0
1
0
0
0
0
2
0
0
0
0
0
3
1
0
0
0
0
1
1
2
5
0
0
2
0
0
2
5
0
2
0
0
0
0
0
2
0
0
3
0
0
0
0
0
1
0
3
3
2
0
1
0
1
1
1
0
1
1
0
2
0
0
0
0
0
0
2
0
1
1
1
0
1
0
1
1
0
0
1
2
0
2
1
2
0
3
2
2
0
0
2
0
3
1
0
0
0
2
0
0
1
0
0
0
2
0
0
2
2
0
0
0
2
2
0
0
0
0
0
2
0
0
1
1
0
1
0
2
0
2
0
0
0
1
1
0
0
2
2
0
0
1
2
0
1
0
0
0
2
0
1
0
0
0
1
0
0
0
2
0
0
0
1
0
0
2
0
2
1
1
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
1
0
3
0
1
0
0
1
1
1
0
0
1
1
0
0
2
0
0
2
2
0
0
1
4
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
2
1
1
0
1
0
0
0
0
0
0
2
1
1
0
0
0
0
0
1
0
0
2
2
1
0
0
0
0
0
2
0
0
1
0
2
1
0
2
1
0
1
0
0
0
0
0
0
0
0
2
2
2
0
0
0
1
2
2
0
2
0
0
0
1
2
2
1
0
0
0
0
3
2
0
1
1
0
0
0
2
0
2
2
0
3
0
1
2
0
2
4
0
2
1
1
0
2
1
0
0
1
0
0
0
0
1
0
1
1
1
1
1
0
0
0
0
1
0
0
2
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
1
1
1
0
1
0
0
1
4
2
0
0
0
0
1
1
0
0
0
3
4
0
0
1
0
0
0
0
2
2
2
0
2
1
0
0
0
0
0
0
0
0
0
0
2
2
2
1
1
0
0
5
0
2
0
3
1
0
0
2
2
0
0
0
1
0
1
0
0
0
0
2
0
2
1
0
0
0
1
0
0
0
1
0
2
1
1
0
3
0
2
0
1
0
0
0
1
2
0
0
1
2
0
2
0
0
0
0
0
0
0
1
1
0
0
2
1
0
1
2
2
2
0
2
1
0
1
2
2
0
2
2
0
1
2
0
0
2
1
0
2
2
0
0
0
0
0
0
1
1
1
0
0
2
0
0
2
0
2
2
0
2
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
1
1
2
2
2
0
0
0
1
1
3
1
2
1
0
0
0
0
0
0
1
0
1
0
1
0
1
1
0
1
1
1
2
0
0
2
1
2
1
2
1
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
2
0
0
1
0
0
1
0
1
1
1
0
0
1
0
1
0
1
1
0
1
0
1
0
0
1
1
0
0
0
0
0
0
1
1
0
2
1
1
1
2
1
0
1
1
0
0
2
1
0
0
4
2
0
2
0
0
0
2
0
0
2
0
0
0
2
0
0
0
2
2
0
3
2
0
0
1
2
1
1
0
1
0
0
1
0
1
0
2
1
1
0
2
1
0
0
0
0
1
0
1
2
0
0
0
0
0
2
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
1
7
0
1
0
2
0
1
0
2
2
0
1
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
2
1
0
2
0
1
0
2
2
0
0
2
0
2
1
0
0
0
0
2
0
0
0
0
1
2
1
0
1
2
2
2
0
2
0
0
1
0
2
1
2
0
0
2
0
0
0
0
0
0
1
1
1
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
1
1
0
2
2
0
2
0
1
0
2
0
2
1
0
0
0
0
1
0
2
0
0
1
0
1
2
0
0
2
0
1
0
2
0
1
1
1
2
1
0
0
2
2
0
2
1
1
0
0
0
0
1
0
0
1
0
0
1
1
0
3
0
0
1
0
3
0
0
1
0
1
0
0
0
2
2
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
2
2
2
0
1
2
2
1
0
1
0
2
1
0
1
0
0
0
0
0
0
2
1
2
1
0
1
0
2
1
6
1
1
0
0
0
2
0
1
1
0
1
2
0
0
0
0
0
0
0
0
2
2
1
2
0
2
0
0
0
2
0
0
0
0
1
2
1
0
1
0
0
0
0
1
0
0
3
0
0
1
0
0
1
0
3
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
1
2
0
1
0
0
2
0
0
0
0
0
3
2
0
2
0
0
2
0
0
2
2
0
2
0
2
1
0
1
0
0
2
0
0
0
0
0
0
1
2
2
0
1
0
0
2
1
0
0
0
0
1
1
2
1
0
0
0
0
0
1
1
0
1
0
0
5
2
2
0
0
1
0
0
0
0
1
0
0
2
0
0
0
2
1
0
0
1
2
1
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
3
0
1
0
0
0
0
2
1
1
0
0
1
2
2
0
0
0
1
2
0
1
0
1
1
0
0
2
0
1
0
0
1
0
2
0
0
3
0
4
0
1
0
0
0
3
0
0
1
0
0
1
3
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
3
0
0
0
0
1
0
0
0
2
1
0
0
1
0
0
0
0
2
0
0
0
0
1
1
0
1
1
2
0
0
1
1
2
0
0
0
1
0
0
0
0
2
1
2
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
1
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
2
0
2
0
0
2
2
2
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
1
1
1
1
0
0
1
0
1
1
0
1
0
2
1
1
0
0
0
0
3
0
0
0
0
0
1
1
1
1
0
2
1
0
0
1
0
2
3
3
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
2
1
1
0
2
0
2
3
0
0
0
0
0
0
0
0
1
0
2
0
0
2
1
2
2
0
0
0
0
0
1
1
0
0
1
1
0
0
2
0
0
1
0
2
0
1
0
1
2
0
0
0
0
2
1
1
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
1
2
1
0
0
0
0
0
0
2
1
0
1
0
0
2
0
3
0
2
0
2
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
1
0
3
1
1
1
1
0
0
0
0
0
2
2
0
1
2
0
2
0
0
0
0
2
0
0
0
2
2
0
0
0
1
0
0
0
1
0
0
0
1
1
0
1
0
2
0
2
0
2
0
0
0
0
2
1
2
0
0
0
2
1
2
0
2
0
0
0
0
1
1
0
0
0
2
2
0
0
0
0
0
1
0
0
0
1
2
0
2
0
1
0
1
0
0
0
1
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
1
1
1
2
1
0
2
0
0
0
0
2
1
1
2
2
2
0
0
0
0
1
2
0
0
2
0
0
1
0
0
1
0
0
0
0
2
0
1
1
1
0
2
0
1
0
0
1
0
0
2
2
0
1
0
2
1
0
2
0
0
0
0
2
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
1
0
2
0
0
0
1
0
2
3
0
2
1
1
1
1
0
0
0
2
0
0
0
0
0
2
1
0
2
1
0
2
2
0
0
2
0
0
1
0
0
0
3
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
3
2
0
1
0
0
2
1
0
1
1
0
0
1
2
1
0
0
0
1
2
0
0
0
2
0
0
2
0
0
2
3
1
2
0
1
0
0
0
1
0
2
0
0
2
0
0
0
1
0
0
0
1
0
2
0
2
0
0
0
0
0
0
1
1
0
0
1
0
1
5
0
0
0
0
0
0
0
2
1
0
1
2
1
1
0
0
0
1
0
1
0
0
2
1
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
1
2
0
1
1
2
2
2
2
0
0
0
2
2
1
1
1
2
1
0
0
0
0
0
0
2
2
0
2
0
0
1
0
1
0
0
2
1
0
0
0
2
2
0
0
1
0
1
2
2
0
0
2
0
0
2
1
2
0
0
0
0
0
2
1
0
1
0
0
0
0
0
2
0
0
0
2
0
2
0
0
2
0
0
0
0
1
0
1
1
0
0
1
2
1
0
0
1
2
0
0
0
2
1
0
0
0
0
2
1
1
1
0
0
1
1
0
2
1
0
2
0
0
0
0
2
0
0
0
0
2
2
2
2
1
2
0
0
0
0
1
0
0
0
1
0
2
1
0
0
2
0
0
0
1
0
0
0
0
2
0
2
1
0
0
3
0
0
1
0
1
1
0
1
1
1
2
0
0
0
2
0
0
2
0
0
2
1
0
1
0
2
1
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
1
0
1
0
0
1
0
1
1
0
0
0
0
2
1
0
2
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
2
1
0
0
1
0
2
0
1
1
2
1
1
0
0
0
1
0
0
0
1
0
2
0
1
0
0
0
0
2
1
1
0
1
0
0
0
1
0
1
1
0
0
1
0
1
0
1
0
0
1
0
1
0
0
0
0
1
2
0
2
1
1
1
0
0
2
0
1
0
1
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
2
2
0
0
1
0
0
0
0
1
0
2
0
0
1
1
2
0
2
0
1
0
0
0
1
0
0
10
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
2
0
0
0
0
1
0
1
2
0
2
0
2
0
1
1
1
0
0
1
1
0
0
0
2
0
1
1
0
2
2
2
0
0
3
0
0
2
3
0
2
2
1
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
1
1
0
0
1
0
0
0
0
2
1
2
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
5
1
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
2
1
2
3
2
0
0
2
0
0
0
0
1
1
1
0
0
0
2
2
0
0
1
0
2
0
0
0
0
1
0
0
0
1
0
2
0
0
1
2
2
1
1
0
0
1
0
1
1
0
1
0
0
2
0
0
2
0
0
0
0
1
1
1
2
1
1
1
1
0
0
1
0
1
2
0
2
1
3
2
0
0
0
0
1
0
1
1
0
1
0
0
0
1
0
0
2
0
0
0
0
0
2
1
0
1
1
2
2
0
1
0
0
1
0
0
0
2
0
2
2
0
2
0
0
1
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
2
2
0
2
1
0
0
0
3
0
1
0
0
1
2
4
0
0
0
0
1
1
0
1
2
0
0
2
0
0
0
2
3
2
0
1
0
0
1
2
2
0
3
0
0
0
1
1
0
0
0
2
0
0
0
0
2
0
1
2
1
1
1
1
1
1
1
0
0
0
2
0
0
2
0
2
1
0
1
0
0
1
1
0
1
0
0
0
0
0
2
0
0
0
4
0
1
1
0
1
1
2
4
1
1
0
0
0
0
0
2
0
0
1
0
1
0
1
2
1
1
1
1
2
2
1
1
2
0
0
0
1
0
0
0
1
0
0
0
2
1
0
1
0
0
0
2
1
0
1
2
2
1
0
2
0
0
1
0
0
0
0
0
0
2
0
0
2
1
1
0
2
1
1
0
2
0
3
0
0
1
0
0
2
0
2
2
0
0
0
2
0
1
1
1
0
2
2
0
0
0
2
1
0
0
0
1
0
1
0
1
0
0
1
0
3
1
2
0
2
0
0
2
0
2
0
0
2
0
0
1
0
3
1
0
0
0
0
0
0
2
3
1
2
2
0
0
2
0
2
0
0
0
0
3
1
3
1
0
0
0
0
0
1
2
0
1
1
1
0
1
2
0
0
1
1
2
1
0
0
0
1
0
4
1
0
0
1
1
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
3
2
2
2
0
0
1
0
1
0
0
0
2
0
0
0
1
0
0
1
0
0
2
0
2
1
2
2
1
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
1
2
1
0
0
0
0
1
1
0
2
0
0
0
0
0
1
3
0
5
1
1
0
3
0
0
0
0
0
1
0
0
1
0
0
1
0
2
0
2
0
0
0
0
1
0
1
0
0
0
2
0
1
0
0
2
0
2
0
1
2
0
0
2
0
1
1
2
0
1
0
1
0
1
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
1
1
2
0
2
0
2
0
1
0
2
2
0
1
1
1
0
1
1
0
3
0
0
0
0
2
1
0
0
0
4
1
2
0
1
0
0
0
0
0
1
2
0
2
0
2
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
2
0
1
0
0
2
1
1
0
2
0
0
1
1
1
0
0
1
1
2
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
1
1
0
0
0
5
1
0
1
1
1
0
2
1
0
1
1
0
1
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
2
0
0
0
1
1
1
1
1
0
0
0
0
1
0
2
0
0
3
0
1
0
1
0
0
0
0
2
0
1
0
0
0
0
2
1
0
0
0
2
1
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
3
1
0
0
0
2
2
0
2
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
1
1
0
0
1
0
0
0
0
1
1
5
0
0
0
0
0
1
0
2
2
2
0
0
0
1
2
1
0
0
2
0
0
0
1
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
2
1
0
0
2
2
0
1
0
1
2
1
0
2
0
0
0
0
2
1
0
0
2
1
0
0
0
0
0
0
0
1
0
2
2
0
0
0
1
0
2
0
1
0
0
0
2
0
1
0
1
0
0
1
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
1
2
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
1
2
0
3
0
1
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
1
3
1
1
1
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
2
1
0
2
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
2
0
1
0
0
1
0
1
0
1
0
0
2
0
1
1
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
2
0
2
1
0
1
5
1
0
0
0
0
0
0
2
0
1
1
0
1
0
2
0
0
0
2
0
1
1
2
0
1
2
1
0
2
1
0
0
0
1
1
0
2
1
1
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
1
0
2
0
0
0
2
0
2
0
0
0
0
0
0
2
1
0
2
0
0
2
1
0
2
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
1
1
0
0
2
0
2
2
0
0
1
0
0
0
0
0
0
0
0
2
2
0
2
0
0
1
1
1
0
2
2
0
0
0
0
2
1
0
0
1
1
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
1
0
1
2
0
1
0
0
0
1
2
0
0
2
0
1
1
0
0
0
0
1
1
0
1
0
0
1
2
0
1
1
0
2
0
2
1
0
0
0
0
0
1
0
1
1
2
1
0
1
0
2
1
3
1
1
0
1
0
2
0
0
0
0
2
0
0
2
0
0
0
1
1
0
0
0
0
0
1
1
2
0
1
1
2
0
1
1
0
2
1
0
0
2
0
0
0
1
0
1
2
0
0
0
1
2
2
1
1
0
0
2
0
0
0
0
0
2
2
0
0
1
2
1
0
2
1
4
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
1
1
0
0
1
0
0
0
1
0
2
2
0
2
0
2
0
0
2
0
2
1
0
3
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
1
1
0
1
2
0
1
1
1
0
2
0
0
0
0
1
1
0
0
0
2
0
1
0
0
0
0
2
0
0
1
0
2
1
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
3
0
2
1
1
0
0
0
0
2
2
0
1
0
0
0
0
0
0
1
0
1
0
2
0
0
1
0
0
1
0
0
0
0
0
1
1
0
1
0
1
1
1
1
1
1
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
2
2
0
0
0
0
1
0
0
2
0
0
2
0
2
0
0
0
0
2
0
1
2
0
0
0
1
0
0
0
0
1
1
0
2
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
3
2
1
0
0
1
2
5
2
2
0
0
1
1
0
0
1
0
2
2
0
0
1
0
0
0
0
1
1
0
2
0
2
0
0
2
2
0
0
0
0
0
1
0
2
0
0
0
1
2
0
2
2
2
0
0
0
2
1
2
0
2
0
1
1
0
1
2
0
0
2
0
1
0
0
0
3
0
0
2
0
0
2
0
0
0
0
3
2
2
2
0
1
0
0
0
1
0
1
2
1
0
2
0
0
0
1
2
0
0
0
0
1
0
4
0
0
0
2
0
0
1
2
0
0
0
2
0
2
1
0
0
0
0
1
0
2
1
0
0
0
0
1
1
0
0
0
3
1
0
7
1
0
0
2
0
1
1
0
0
0
0
0
0
1
0
1
2
0
2
2
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
9
0
0
0
1
0
2
1
0
0
0
0
2
0
0
0
0
1
2
0
2
0
0
0
2
0
0
0
0
2
1
3
1
0
0
1
0
3
1
0
0
0
0
0
0
0
1
0
1
0
1
2
1
1
1
1
1
2
2
2
0
1
0
0
1
0
1
0
0
0
0
0
2
0
0
2
0
2
1
1
0
1
1
0
0
2
1
0
0
0
2
2
0
2
0
1
0
1
0
0
2
0
1
0
0
2
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
2
0
0
1
0
0
2
0
3
0
2
0
0
1
1
1
0
0
0
2
0
2
2
0
0
1
0
0
0
0
0
1
0
2
2
0
0
2
0
3
2
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
2
1
0
2
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
2
0
1
2
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
1
0
2
1
1
2
2
1
2
0
0
0
0
0
0
0
0
2
0
1
0
0
2
2
2
0
0
1
1
3
0
1
1
2
2
2
0
2
2
0
0
0
0
0
1
2
1
0
1
0
0
1
0
1
0
1
0
2
2
3
1
0
0
2
0
1
1
2
0
2
0
1
0
0
0
1
2
0
0
0
0
1
2
3
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
1
1
0
2
0
0
0
0
2
2
1
0
0
0
0
2
2
1
0
0
3
0
0
2
0
0
2
0
2
0
3
1
1
0
0
1
2
1
0
0
0
2
0
3
1
1
0
0
0
0
0
1
1
0
0
1
0
1
3
0
1
0
0
0
0
3
1
0
2
2
1
1
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
2
0
1
0
1
0
1
1
0
0
1
0
2
1
0
3
0
0
1
0
1
0
0
0
2
0
0
1
1
1
2
1
2
1
2
0
0
0
1
0
0
0
0
2
1
0
1
1
0
0
1
0
0
0
0
2
1
2
0
1
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
1
0
0
0
1
1
0
1
0
2
0
1
0
0
2
0
1
0
2
1
2
0
0
2
2
0
0
0
2
0
0
0
2
2
0
1
1
0
2
0
1
0
0
0
2
2
0
1
0
1
0
0
1
0
1
3
2
1
0
0
0
1
0
2
2
0
2
0
1
1
2
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
3
0
0
0
0
0
0
1
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
1
0
0
2
2
0
2
1
0
2
0
0
2
0
0
0
0
0
2
0
1
0
1
0
2
0
4
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
2
0
2
1
0
0
2
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
1
0
0
0
0
3
0
0
0
0
2
2
0
0
1
0
0
1
2
0
1
0
0
0
0
0
0
1
0
1
0
0
1
1
1
0
0
1
0
1
0
0
0
2
1
0
2
0
0
0
0
0
0
0
2
0
0
1
0
2
2
0
1
0
1
2
2
2
1
0
1
1
0
0
0
0
2
0
0
3
0
0
4
0
2
2
0
1
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
1
1
4
0
0
0
0
0
0
3
0
1
2
2
2
0
0
0
2
0
0
0
1
0
1
0
2
0
2
0
0
0
0
2
0
0
0
1
0
0
2
1
0
0
0
0
1
0
0
0
0
0
1
2
2
0
1
2
2
6
0
0
0
2
2
2
0
0
2
0
0
1
0
2
0
1
1
2
1
1
0
0
1
1
1
0
0
0
0
1
0
0
2
0
0
0
3
0
1
1
2
1
0
0
0
0
2
1
0
0
1
0
1
0
0
1
0
2
3
1
1
0
2
0
1
2
2
2
0
0
0
0
0
0
1
2
0
0
2
0
2
1
0
1
0
0
0
0
6
0
1
1
0
0
0
1
1
0
0
0
1
2
1
2
0
0
1
1
0
0
0
1
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
2
0
2
0
0
1
1
0
1
0
0
1
1
1
1
0
0
0
0
0
1
0
0
2
1
0
1
0
0
0
1
0
1
0
0
0
11
0
0
1
0
0
0
2
0
1
0
1
2
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
2
0
0
2
1
0
0
2
0
2
0
2
0
0
0
1
0
1
1
0
1
0
1
0
1
0
0
2
2
2
0
1
0
0
1
0
1
0
0
4
1
1
0
2
2
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
1
3
2
2
0
0
2
0
0
3
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
1
0
0
1
0
0
0
1
0
0
1
0
1
0
1
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
2
0
2
0
1
0
0
1
2
3
0
2
0
0
2
0
0
2
1
0
2
0
4
0
2
1
0
0
0
0
2
0
1
0
1
0
0
0
2
2
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
2
2
1
0
0
0
1
0
2
0
1
0
0
2
1
0
0
2
1
0
0
1
0
2
0
0
0
0
0
0
1
0
0
1
2
2
2
1
2
0
1
0
2
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
1
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
2
1
0
0
1
0
1
0
0
0
0
0
0
0
2
0
1
0
1
1
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
2
0
0
0
3
2
0
0
0
2
1
0
0
1
0
0
3
1
0
0
0
1
0
0
0
1
0
0
2
1
0
0
0
1
0
0
1
1
0
1
1
0
0
2
2
0
3
2
0
0
1
2
0
0
0
0
1
0
3
0
0
0
1
1
0
2
1
2
2
1
1
0
0
2
2
1
1
0
0
1
0
0
0
1
0
0
2
1
0
0
2
2
2
2
1
0
0
0
2
2
0
1
0
0
0
0
0
0
2
0
0
1
1
1
1
2
0
1
2
0
1
0
1
0
2
2
0
0
0
0
0
2
2
0
2
2
0
0
0
0
0
1
1
1
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
5
1
2
1
0
2
0
0
0
0
2
0
0
2
1
0
0
2
1
0
1
2
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
1
0
1
1
1
2
4
0
1
1
2
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
2
0
0
2
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
2
2
0
2
2
0
1
0
0
2
1
0
1
0
2
1
0
0
1
0
2
1
1
1
0
3
3
0
0
0
0
1
2
1
0
0
0
0
2
0
0
0
0
2
1
1
0
2
0
0
0
2
0
0
1
0
0
1
0
0
2
0
1
1
0
2
0
0
0
2
1
0
0
0
2
0
1
0
2
1
0
0
0
1
0
0
1
0
0
0
1
0
1
3
1
0
0
0
2
1
0
5
4
1
0
1
0
0
0
0
0
2
0
3
2
2
1
1
1
0
2
1
1
0
1
0
1
0
0
1
2
0
0
0
0
2
1
0
2
0
0
0
1
2
1
1
0
0
2
1
0
0
1
0
1
0
2
1
0
0
0
0
2
2
0
0
4
0
2
1
0
0
1
0
1
0
0
0
2
0
0
4
1
1
0
0
2
1
1
0
0
2
2
2
0
1
2
2
0
0
0
1
0
0
2
0
2
2
0
0
2
0
0
0
0
0
1
1
0
2
0
1
1
0
0
1
2
0
0
0
2
0
0
1
1
0
1
0
2
2
0
2
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
3
2
0
0
0
0
0
0
0
0
1
1
0
1
0
1
2
0
2
0
1
0
1
0
0
2
0
2
1
1
0
0
1
2
0
2
2
0
1
0
0
2
0
2
2
2
0
0
2
2
1
0
0
0
2
1
0
0
1
0
1
0
0
1
2
1
0
0
2
0
1
0
0
1
0
0
2
1
1
3
0
0
0
0
2
2
2
0
0
0
0
0
1
0
0
2
1
1
0
0
2
2
4
0
0
0
0
2
2
0
0
0
2
1
1
0
1
1
0
0
7
2
0
4
0
2
0
3
0
1
2
2
0
0
0
3
0
1
0
0
1
0
0
3
1
2
0
1
0
0
0
0
0
2
0
0
1
1
2
0
2
0
0
0
0
2
1
0
0
1
0
0
0
0
0
1
2
0
0
0
2
0
0
0
2
0
2
2
1
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
2
1
0
0
0
0
0
1
0
2
0
0
2
0
0
1
2
0
1
0
2
0
0
2
1
0
0
0
0
3
1
0
1
0
0
2
1
0
0
2
2
2
1
1
0
0
3
0
0
0
0
0
1
0
2
0
3
1
0
2
0
0
0
4
0
0
1
2
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
2
0
0
2
0
2
0
0
0
2
0
0
2
0
2
1
0
2
1
2
0
0
0
0
0
1
0
1
2
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
2
0
0
0
0
1
0
1
0
3
2
0
2
0
0
0
1
0
1
0
0
1
0
0
1
2
0
1
1
2
0
0
0
0
0
1
1
0
1
0
0
1
0
0
1
0
1
2
2
0
0
2
0
1
0
2
0
0
0
0
2
1
0
0
1
1
3
1
1
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
2
0
0
1
2
3
2
0
1
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
2
2
0
2
1
1
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
1
0
1
1
0
1
1
0
0
0
0
0
1
0
1
0
0
1
0
4
1
2
0
0
0
1
0
2
2
2
0
0
1
0
2
0
1
0
0
1
0
1
0
0
2
0
1
1
0
1
2
1
0
1
1
0
0
0
2
1
0
0
0
1
2
1
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
1
1
1
1
2
4
0
0
2
1
0
1
2
0
0
0
1
0
1
2
0
0
0
0
0
0
0
2
2
1
0
0
0
1
0
0
5
0
0
4
2
2
0
0
1
0
1
0
2
1
1
1
0
0
0
1
0
0
0
1
2
2
0
0
0
0
0
0
0
1
0
2
2
0
3
0
2
0
0
1
1
0
0
2
0
1
0
0
1
2
2
2
0
0
2
0
0
0
2
0
1
2
0
0
0
1
0
0
0
0
2
0
2
1
2
0
2
0
0
1
0
2
1
0
0
1
0
0
1
0
0
1
0
2
0
2
0
0
1
1
0
2
0
0
0
2
3
0
0
0
0
1
0
2
2
0
0
0
0
0
1
1
0
0
2
0
0
1
2
0
0
1
2
0
0
0
1
5
0
0
1
2
0
2
1
0
0
1
2
1
0
1
0
0
2
0
0
0
0
0
1
0
0
1
0
0
1
0
2
0
1
1
0
0
2
1
0
2
2
0
0
0
0
0
1
0
2
1
2
0
0
0
0
2
1
2
0
0
0
0
3
2
1
1
1
0
0
0
1
0
1
0
0
1
2
0
0
1
0
1
2
0
1
0
1
1
0
0
0
0
2
1
0
1
0
1
2
0
1
2
0
3
0
0
1
1
0
1
0
0
0
1
0
1
0
1
2
0
0
0
0
2
0
0
1
0
2
0
0
0
1
0
3
0
1
2
0
0
0
0
1
0
0
0
2
1
0
1
1
1
0
0
0
1
0
0
1
0
0
2
1
0
0
0
2
2
0
0
0
2
0
2
0
1
0
1
0
0
3
0
1
1
1
0
0
2
2
1
1
2
1
0
0
0
0
2
2
1
1
1
0
3
0
0
0
0
2
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
1
1
2
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
2
2
0
0
2
0
1
2
0
1
0
1
1
0
0
1
1
1
1
2
0
2
0
0
0
0
1
1
0
0
0
1
0
3
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
1
0
0
1
0
2
0
0
0
2
1
1
1
0
1
0
4
0
0
2
1
0
0
1
0
1
1
3
0
0
1
2
0
0
1
2
0
0
0
0
1
0
0
2
0
0
3
1
0
1
0
2
3
1
0
0
2
2
0
0
0
0
0
2
1
0
0
1
2
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
2
0
0
1
0
0
0
0
2
0
0
0
3
0
0
2
0
1
2
1
0
0
0
1
0
0
0
0
2
2
0
0
1
0
1
0
0
2
1
0
2
2
0
1
0
0
2
0
2
0
0
0
2
0
1
2
1
0
1
2
2
1
1
0
1
2
1
2
2
1
0
1
2
0
0
2
1
0
2
3
1
0
1
1
2
1
0
0
0
2
2
1
0
2
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
1
1
1
1
0
2
0
0
2
0
0
0
0
0
2
0
0
2
0
0
1
1
0
2
1
0
0
0
2
0
0
1
2
1
0
0
0
2
0
1
1
1
2
0
0
0
0
0
0
1
0
1
1
0
0
0
0
2
0
3
0
0
2
0
1
0
0
2
0
2
1
0
0
1
0
0
0
1
1
0
0
1
0
0
2
0
0
0
0
0
0
1
0
2
2
2
0
1
0
1
0
0
0
1
2
0
0
0
3
2
2
0
0
2
0
2
0
0
0
0
2
1
1
2
1
0
0
0
0
1
2
0
1
2
1
0
0
0
0
0
0
2
0
0
0
1
2
2
1
1
1
2
0
1
1
1
0
1
2
0
0
0
0
1
1
2
0
3
0
0
1
0
1
0
0
0
0
0
1
2
0
2
0
1
0
0
0
1
2
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
2
1
0
0
0
0
2
1
1
0
1
2
1
0
0
1
2
0
1
0
0
0
0
1
1
0
2
1
1
0
0
1
2
0
0
0
0
2
0
0
2
2
1
1
0
0
0
3
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
2
0
0
1
0
0
2
1
0
0
0
1
2
0
2
0
1
0
1
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
2
1
0
0
0
0
0
2
0
1
1
2
0
2
0
2
1
4
1
0
0
1
0
0
0
2
0
0
2
2
0
0
1
0
1
0
0
2
0
0
1
1
0
0
0
2
0
1
2
0
2
1
0
0
0
2
1
3
0
0
1
2
1
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
1
0
1
2
0
2
1
1
0
0
1
1
0
0
1
0
4
1
0
1
0
0
0
0
1
0
1
3
0
1
0
0
0
0
0
0
0
1
2
0
0
2
2
2
0
0
0
2
0
0
0
0
0
2
0
1
0
2
0
1
0
0
0
0
0
0
2
0
0
0
1
1
0
1
0
0
0
2
0
0
0
0
2
1
0
1
0
0
1
0
1
0
0
0
1
2
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
2
3
3
0
1
1
0
2
1
0
0
0
0
1
0
2
0
2
0
2
0
0
0
1
1
2
0
0
0
1
0
0
0
0
0
2
2
1
0
1
0
2
0
0
0
2
0
2
0
2
0
0
1
1
0
1
2
0
0
0
1
0
0
2
1
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
2
1
1
0
2
0
2
0
0
0
1
0
1
1
0
4
1
1
1
2
0
0
0
0
2
2
0
2
2
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
2
1
0
2
4
0
0
1
3
0
1
0
0
1
0
0
0
4
2
1
0
1
1
0
0
0
1
1
1
2
2
0
0
1
1
0
0
1
2
3
0
0
2
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
1
2
0
0
2
0
1
0
1
0
0
0
0
0
0
1
0
1
0
2
2
0
0
2
1
1
1
0
2
1
0
4
1
0
1
3
0
0
2
0
0
2
2
0
0
0
0
2
0
0
1
4
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
2
0
0
2
0
0
0
1
1
2
1
0
0
0
0
0
0
2
3
0
0
0
0
1
0
0
0
0
3
1
0
2
0
1
0
0
0
2
0
1
1
1
2
1
2
2
3
0
1
0
1
0
1
1
0
3
1
0
0
2
0
0
0
0
0
1
0
0
1
0
2
0
1
1
0
2
1
0
2
1
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
1
1
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
1
1
0
0
0
3
0
0
0
3
0
1
0
0
0
2
2
0
0
2
1
2
0
0
0
0
0
2
0
1
0
1
1
0
0
0
0
1
0
2
2
2
0
0
0
0
2
1
1
1
0
1
1
0
1
0
2
0
0
0
0
1
0
1
2
0
0
0
1
1
0
0
0
2
0
1
1
0
0
0
2
0
0
0
2
0
1
0
1
0
0
1
0
2
0
0
0
0
1
0
2
0
1
0
0
2
0
1
2
0
0
0
0
2
1
0
0
1
0
1
2
0
0
1
0
1
0
0
2
0
1
0
7
0
0
0
0
1
0
0
1
0
2
0
5
2
1
2
2
0
2
0
0
0
1
1
0
0
2
0
2
0
2
0
1
0
0
0
1
0
0
1
1
3
2
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
2
0
0
2
0
2
0
2
2
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
5
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
3
0
0
0
2
3
2
1
0
0
0
0
1
2
0
4
2
1
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
1
0
0
0
2
1
3
0
0
0
1
2
1
0
0
2
1
0
1
0
2
1
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
1
0
1
0
0
2
1
0
0
1
0
1
0
0
0
0
2
0
1
0
1
0
1
1
2
0
0
0
2
0
0
0
2
2
3
0
0
0
0
2
0
1
2
0
2
1
2
0
1
1
1
0
1
1
2
0
1
0
1
2
1
2
2
1
1
0
0
0
1
0
2
0
0
2
0
0
0
2
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
2
1
0
2
0
2
0
0
0
0
0
0
2
0
1
1
0
2
2
1
0
0
0
0
2
3
0
0
0
2
2
0
1
1
0
1
0
2
0
2
1
0
1
2
0
1
0
0
0
0
1
2
1
1
0
2
2
1
0
0
1
0
1
0
2
0
1
0
1
0
0
0
0
1
0
2
0
0
0
1
0
2
0
0
1
0
0
0
1
1
0
0
0
1
0
1
0
0
1
1
0
0
2
0
2
0
0
0
0
1
0
2
0
0
0
3
2
0
0
0
0
0
0
1
0
0
0
1
2
0
1
0
1
1
2
1
1
0
0
0
1
1
2
3
1
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
1
2
4
0
1
0
0
1
1
1
0
0
0
1
2
0
0
0
1
1
0
0
3
0
0
1
1
1
1
1
0
0
0
0
0
0
0
0
2
1
0
1
0
1
0
1
0
1
0
2
1
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
2
0
1
0
2
0
0
0
2
1
1
1
0
0
1
2
0
0
0
0
1
0
0
0
2
0
2
0
0
2
0
0
1
0
3
1
0
1
0
0
0
2
2
1
1
0
1
2
0
2
0
2
0
0
1
2
0
2
1
1
1
0
0
2
0
0
0
0
1
0
2
2
0
1
0
1
0
2
0
1
0
0
0
1
1
1
0
2
0
0
3
0
1
1
1
1
2
0
0
0
1
0
0
2
1
2
0
0
1
0
0
0
1
0
0
2
0
1
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
2
0
0
2
2
1
1
0
1
1
2
1
0
2
0
2
0
1
0
1
0
0
2
0
0
2
1
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
3
2
1
1
2
2
0
0
2
1
2
2
0
2
0
2
1
0
0
1
0
2
0
0
1
2
0
0
1
0
0
2
0
0
2
0
1
1
0
1
2
0
2
0
1
2
0
0
1
1
0
2
1
1
1
0
0
0
0
1
2
2
2
0
2
0
0
6
0
1
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
2
2
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
1
1
1
0
0
0
1
0
2
0
0
2
0
1
0
2
0
0
2
2
2
0
1
3
0
1
2
3
0
2
2
1
0
1
0
0
0
0
1
0
2
0
1
1
0
0
0
2
4
0
0
1
7
0
1
0
3
0
0
2
0
0
2
0
2
0
0
0
0
0
2
2
0
0
2
0
1
2
0
2
0
0
0
1
0
2
0
0
0
0
2
1
0
0
1
0
0
1
1
2
1
6
0
0
0
1
0
0
0
0
0
1
2
2
7
2
0
1
0
1
0
0
2
0
0
1
2
0
2
0
0
0
0
0
3
1
1
0
2
2
0
0
1
0
2
0
1
0
0
1
2
0
0
0
0
1
1
0
1
0
0
0
1
2
1
1
2
0
1
1
1
0
0
0
1
0
0
2
0
0
1
1
0
1
0
2
2
0
0
1
0
1
1
2
1
0
0
5
2
1
0
0
2
1
0
0
0
0
3
0
2
1
0
1
0
0
0
0
2
2
0
0
2
1
0
2
1
2
0
0
0
0
0
1
3
1
0
0
0
2
0
1
2
0
1
0
0
1
0
0
1
2
0
0
2
0
0
1
0
0
0
0
0
0
1
2
0
1
2
1
1
0
0
0
0
1
0
2
0
2
0
0
0
0
0
2
0
1
1
1
2
2
1
0
0
0
0
0
0
0
2
2
2
1
0
0
0
0
1
0
0
0
1
0
0
0
1
2
0
0
0
0
0
1
2
1
0
2
2
0
0
0
1
1
0
1
0
0
0
0
2
2
2
0
0
1
0
0
0
0
0
1
0
0
0
2
1
2
0
1
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
2
2
1
0
0
2
0
0
0
0
0
2
0
2
2
0
1
0
2
0
0
2
3
0
0
0
2
0
1
1
1
1
0
2
2
1
0
0
0
2
2
0
2
1
1
0
2
0
2
1
1
0
0
0
0
0
0
2
2
0
4
0
1
0
1
0
2
2
0
1
0
0
0
0
2
0
0
0
3
0
0
2
2
0
0
0
0
0
1
0
0
1
1
0
0
3
2
0
2
1
2
0
1
2
2
1
1
0
2
0
2
1
0
0
2
1
0
1
1
0
0
0
1
0
2
0
0
2
0
2
1
0
0
0
1
6
0
0
0
0
0
3
0
1
0
0
0
2
2
0
0
1
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
1
2
0
1
1
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
1
1
1
0
2
0
1
2
1
0
2
0
3
0
2
2
1
0
1
1
0
2
3
0
2
0
2
0
2
0
1
1
5
0
1
0
1
0
0
0
0
0
0
0
1
2
0
2
1
3
0
0
1
2
2
0
1
0
1
1
0
0
0
0
1
2
1
0
0
0
0
0
1
0
2
0
1
2
0
0
0
2
1
2
0
0
0
1
0
2
0
1
0
0
0
1
2
2
2
0
2
0
1
0
0
1
2
0
1
0
2
0
0
0
1
2
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
2
1
0
2
1
0
0
1
0
0
0
1
2
1
0
0
0
0
2
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
1
2
1
1
0
0
1
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
1
0
2
2
0
0
0
1
1
1
1
0
1
0
1
0
1
0
2
0
0
0
1
1
0
8
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
1
0
1
2
0
0
1
0
0
2
2
0
0
0
2
0
0
1
0
0
1
2
0
0
2
1
2
0
0
0
2
0
1
0
0
0
0
0
1
0
1
1
0
2
0
0
0
2
0
0
1
0
1
0
2
0
0
0
0
0
1
0
2
2
1
0
0
2
1
0
0
0
0
1
2
0
2
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
1
2
0
1
0
0
0
0
0
2
0
2
2
1
2
0
0
0
2
0
0
0
0
0
1
2
0
0
0
1
0
1
0
0
0
0
2
0
0
0
1
2
1
0
1
0
0
0
2
1
2
0
0
2
0
0
1
2
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
2
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
3
2
1
2
0
2
0
2
1
2
0
1
0
1
0
1
1
1
1
0
0
1
0
0
2
0
1
1
1
0
1
0
0
1
0
0
2
2
3
3
2
0
1
0
0
2
0
2
2
3
1
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
2
0
2
1
0
0
2
0
0
0
0
0
0
1
1
0
0
0
2
4
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
2
0
1
3
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
2
0
0
1
0
1
1
0
2
0
1
0
0
0
0
0
0
1
0
2
0
2
1
1
0
0
1
1
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
2
3
0
0
0
0
1
0
1
2
0
0
0
2
0
0
0
1
0
1
1
2
0
1
0
2
1
0
0
2
0
0
0
0
0
1
1
0
2
0
0
0
0
1
1
1
1
2
0
0
0
0
1
0
0
0
3
2
0
1
0
2
2
2
1
2
0
2
0
0
0
0
1
0
0
0
1
0
0
0
2
0
1
0
0
0
0
2
1
1
0
0
2
2
0
1
0
2
0
0
1
2
0
0
0
2
3
0
1
0
0
0
1
0
1
1
2
0
3
2
1
0
0
0
0
0
0
0
1
3
0
2
2
2
6
0
0
0
0
0
2
1
0
1
0
0
0
1
0
1
0
0
0
0
0
2
2
0
0
0
1
0
1
2
0
0
0
0
1
0
0
0
1
0
0
1
1
1
1
0
0
0
0
1
0
2
0
0
1
0
1
0
2
0
4
0
2
1
1
1
2
0
2
0
1
0
1
2
0
0
0
0
0
2
0
0
0
3
0
1
0
0
1
0
0
1
1
0
0
2
2
0
0
0
1
1
2
2
0
2
2
0
0
0
1
0
0
0
2
1
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
2
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
2
0
0
1
0
0
0
1
0
1
0
1
2
2
2
2
0
0
1
1
1
0
1
0
0
1
1
0
0
1
0
2
1
1
3
0
2
2
2
0
0
1
0
2
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
1
1
1
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
1
1
2
0
0
0
0
0
2
0
1
1
0
1
1
0
0
0
0
1
1
0
0
0
1
2
0
2
2
0
0
0
0
0
2
1
1
0
0
0
0
0
2
1
1
0
1
0
0
2
0
0
2
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
2
0
2
0
0
0
1
0
0
0
0
1
0
0
1
2
0
0
1
1
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
1
2
0
0
2
0
1
3
0
0
1
0
2
2
1
1
0
1
2
0
0
3
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
2
0
0
0
2
3
2
0
0
0
0
1
0
0
0
1
0
0
1
0
1
1
2
0
0
1
0
1
0
0
1
1
2
2
1
0
0
2
0
0
0
0
0
0
0
0
1
0
2
2
2
0
2
2
0
1
0
1
2
0
0
1
1
0
0
1
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
2
2
0
1
2
1
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
3
2
0
0
0
1
0
0
0
2
1
1
0
0
2
0
1
0
2
0
2
0
0
2
1
0
0
0
1
1
0
2
0
0
0
0
0
0
0
2
2
1
0
2
1
1
0
2
2
0
2
3
5
1
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
1
2
0
3
0
0
1
0
0
2
0
0
0
1
1
1
1
1
1
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
3
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
2
0
0
2
1
1
2
0
0
0
1
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
4
0
2
0
1
0
0
0
0
2
2
0
2
0
0
0
2
1
2
0
0
1
0
0
1
1
1
0
1
0
1
0
2
1
1
1
5
0
0
0
1
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
1
3
1
0
0
2
0
0
0
0
2
0
0
0
2
2
0
0
2
0
0
0
2
2
0
0
0
0
0
1
0
1
1
2
0
0
0
2
1
0
0
0
2
0
1
1
0
0
1
1
2
4
0
1
0
0
2
1
0
0
2
0
2
0
1
0
0
2
1
0
0
0
0
2
1
2
2
0
0
0
2
0
3
0
1
1
2
0
1
0
1
1
1
0
0
1
0
1
1
1
0
0
2
2
0
1
0
2
1
0
2
0
0
0
1
0
3
4
0
1
2
0
0
2
0
2
0
0
1
2
1
0
0
2
1
1
0
0
0
1
2
2
2
0
0
1
0
2
0
0
2
1
0
0
0
0
0
0
1
2
0
0
0
0
0
1
2
0
2
2
1
0
0
1
0
0
0
0
0
0
0
2
1
2
0
0
0
0
1
0
1
0
1
1
0
1
0
0
0
0
0
2
2
1
2
0
0
0
1
1
0
1
1
0
2
2
0
2
1
0
1
0
2
0
0
0
1
0
0
2
0
3
1
1
0
3
0
1
0
0
2
0
0
0
2
6
6
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
3
0
0
1
0
0
0
0
0
2
1
0
0
2
1
0
2
0
1
3
0
2
0
0
0
1
2
0
0
0
0
0
0
2
2
2
0
2
0
2
0
0
1
1
0
1
1
1
0
0
0
0
0
1
1
0
2
0
2
0
2
1
0
0
0
2
0
0
2
0
0
1
0
1
0
0
0
0
0
1
1
0
1
0
1
0
0
0
2
2
0
2
1
0
0
1
0
0
1
0
1
0
2
2
2
0
0
2
1
0
1
1
2
0
0
2
1
0
1
2
1
2
2
0
1
2
3
0
0
1
1
0
2
1
0
0
1
0
0
1
0
2
0
0
0
2
0
0
0
0
0
2
0
0
2
1
0
1
0
0
1
0
0
2
0
0
1
2
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
2
1
0
1
2
2
0
1
0
1
0
0
0
0
0
1
0
0
0
1
1
0
1
1
0
2
1
0
0
0
1
0
2
2
2
0
1
4
2
2
0
0
2
0
0
0
1
1
0
0
2
1
0
0
1
0
1
1
0
0
2
0
0
0
2
0
2
3
0
0
2
2
2
0
1
0
0
0
0
1
0
0
1
0
2
1
2
0
0
1
0
0
1
0
0
0
1
0
2
0
2
0
0
0
1
0
0
2
4
2
0
1
0
0
0
1
0
2
0
0
1
1
0
0
0
1
0
3
0
1
0
0
0
2
2
1
2
0
0
0
0
0
0
2
0
0
0
4
0
2
2
2
0
1
0
0
1
0
0
1
0
0
2
0
0
3
0
0
2
1
0
0
1
1
1
1
1
0
0
0
3
0
2
0
0
0
1
1
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
1
0
0
2
2
3
0
0
0
0
2
0
0
0
0
0
0
0
1
2
1
0
2
0
0
1
1
0
2
0
1
2
0
0
0
0
0
1
0
0
0
1
2
0
1
0
0
1
1
0
2
1
0
0
0
1
1
1
0
0
2
0
1
1
2
0
0
2
1
0
1
2
0
0
1
0
0
0
0
1
2
2
0
0
0
2
1
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
2
0
0
2
0
0
2
0
0
0
1
2
0
1
2
1
1
1
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
2
0
2
2
0
0
1
1
0
0
0
0
1
0
0
2
2
0
1
0
0
1
2
0
0
1
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
4
1
2
0
0
2
2
0
0
0
1
0
2
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
2
2
1
2
0
1
0
1
1
1
0
0
2
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
2
4
2
0
0
0
0
0
2
0
0
1
2
2
0
0
0
1
0
0
0
1
0
2
0
0
2
0
2
0
0
2
0
1
0
0
0
0
0
0
3
0
0
2
1
0
2
0
0
0
2
0
0
0
1
1
2
1
0
0
0
0
1
0
0
0
1
0
0
0
1
1
2
0
2
0
0
0
2
0
1
0
0
2
1
0
1
0
2
0
0
0
0
0
1
3
1
0
4
0
0
1
0
2
0
2
2
2
0
1
0
0
2
1
1
1
1
0
0
2
0
2
4
0
1
1
0
1
1
2
0
0
0
0
0
0
1
0
0
2
2
0
1
2
0
0
1
1
0
0
1
0
0
0
0
0
1
2
1
0
1
3
2
1
0
0
0
2
0
0
1
1
0
1
2
1
2
0
0
1
1
0
0
0
0
1
0
2
2
0
0
0
0
1
1
0
1
0
0
1
0
1
2
1
1
2
0
0
1
1
1
3
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
1
2
0
0
0
2
0
0
1
1
0
0
0
4
0
1
0
2
0
1
0
0
3
0
0
0
1
0
0
2
0
1
1
1
1
0
1
0
2
0
0
3
2
2
0
2
0
0
0
0
0
2
2
0
0
0
0
1
1
0
0
0
0
0
1
2
2
0
2
0
0
2
1
0
3
1
0
0
0
1
1
0
1
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
2
2
0
0
1
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
1
0
1
0
2
2
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
1
0
0
1
0
1
0
0
2
2
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
1
1
0
2
2
0
0
0
0
0
2
0
2
0
0
0
1
0
2
2
1
2
1
0
1
0
1
0
0
0
4
0
0
2
0
0
0
1
0
2
0
2
0
1
2
0
0
0
1
2
0
2
1
1
2
0
1
0
2
2
0
0
2
1
1
2
1
0
0
1
1
0
0
0
1
1
0
0
1
2
0
1
0
0
0
0
0
0
0
2
3
0
0
0
0
2
0
0
0
0
1
0
0
2
1
1
0
0
0
0
1
1
1
1
0
0
0
0
0
4
0
1
2
0
0
2
2
0
2
2
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
1
0
0
1
2
0
1
3
0
2
0
0
1
1
0
2
0
0
0
1
1
1
0
0
2
2
1
0
0
1
1
1
1
1
2
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
1
0
1
0
1
0
0
2
1
2
1
0
0
0
1
2
0
1
0
0
1
0
1
0
1
0
0
0
0
0
2
0
2
1
2
1
2
1
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
2
0
0
0
0
1
2
0
2
0
1
0
0
1
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
3
0
1
1
0
0
2
0
0
0
1
0
0
1
0
0
0
0
1
3
2
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
2
2
0
1
0
0
0
2
0
1
1
2
0
1
0
0
2
3
2
0
2
0
0
1
0
1
0
0
0
2
2
0
0
1
0
0
1
0
0
1
0
0
2
1
0
0
1
0
1
0
1
0
1
1
0
2
0
1
1
2
0
3
0
2
0
0
1
0
1
0
2
1
1
2
0
0
2
0
0
2
0
2
2
0
0
0
0
2
1
0
0
2
0
0
1
0
0
0
1
0
1
2
0
2
1
0
0
0
0
1
1
2
0
1
0
0
1
0
1
0
0
0
0
1
5
0
1
0
2
2
0
3
0
0
0
0
0
2
2
0
1
1
0
2
2
0
0
0
0
2
1
1
2
1
1
2
0
1
1
1
0
2
0
0
0
0
0
0
2
0
3
0
0
2
0
0
2
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
1
0
0
0
0
0
0
1
2
0
1
0
0
0
0
2
0
0
1
0
0
1
0
0
1
0
0
1
2
0
1
1
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
2
1
0
1
0
1
1
1
0
1
2
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
4
2
0
1
0
0
2
1
1
0
4
2
0
0
2
1
1
0
1
0
0
1
1
0
2
0
0
0
2
1
2
0
0
0
2
0
1
2
0
1
9
2
0
2
0
0
0
0
0
1
2
0
0
1
1
0
2
0
1
2
2
0
0
0
0
1
0
3
1
0
3
0
0
2
1
2
0
2
0
0
1
2
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
2
1
1
0
2
0
1
0
0
0
2
0
0
2
3
0
0
0
1
0
0
1
2
0
0
2
3
1
2
0
0
4
0
0
0
2
0
0
1
0
0
0
1
0
0
2
1
4
1
2
2
0
1
0
2
0
1
1
2
2
0
1
0
1
0
1
1
0
4
0
0
0
0
0
2
2
0
2
0
1
1
0
0
0
0
2
1
0
0
1
0
1
1
0
2
0
0
0
0
0
2
0
0
2
2
2
1
0
0
0
1
0
0
0
0
2
1
0
0
0
2
2
2
0
0
0
0
2
1
1
0
0
0
0
0
1
3
0
1
1
1
2
1
1
0
0
2
0
0
0
0
0
1
0
2
0
0
2
1
0
0
1
0
0
0
1
0
1
0
0
1
1
0
1
1
0
0
0
1
1
1
0
2
1
2
0
0
0
1
0
0
0
1
0
0
1
1
2
2
0
0
0
1
2
0
0
0
0
1
0
2
0
3
0
0
2
1
2
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
3
0
3
1
0
0
0
2
0
1
2
0
3
0
0
0
0
2
2
2
0
2
2
1
2
0
1
1
1
2
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
1
2
2
0
0
0
1
2
0
3
0
2
1
0
0
0
0
1
0
0
0
0
1
0
0
1
2
2
0
3
1
0
1
0
0
0
1
0
0
0
0
0
3
0
0
2
0
0
0
2
0
1
1
1
2
1
2
2
0
0
2
1
0
0
1
0
0
0
1
0
0
0
2
1
2
1
1
0
0
0
0
1
0
0
0
2
0
0
2
0
1
2
0
0
0
0
0
1
1
1
0
0
0
1
2
0
0
2
0
0
0
1
1
1
2
0
1
0
0
2
2
1
0
2
0
2
1
1
0
0
2
1
0
2
0
1
0
0
3
0
2
0
0
2
1
0
2
0
0
0
1
2
0
0
0
1
0
2
0
0
2
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
2
1
1
1
0
0
1
2
3
1
0
0
0
0
2
0
2
1
0
0
0
2
0
1
0
0
0
1
2
0
2
0
1
1
1
0
0
1
1
0
2
0
0
1
0
0
1
2
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
2
0
0
2
0
0
2
0
3
0
2
0
0
1
0
0
0
1
0
1
2
1
2
0
10
0
1
0
2
0
0
1
2
3
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
1
1
1
0
1
0
1
2
0
0
2
0
0
0
2
0
0
2
1
2
0
0
1
1
0
1
1
0
0
2
3
0
1
0
4
0
0
1
1
0
0
2
0
0
1
2
0
0
0
0
0
0
1
0
0
2
3
2
0
0
1
0
0
0
0
0
2
1
1
0
0
0
2
2
0
1
1
0
0
0
0
0
0
0
1
0
2
0
1
0
0
2
2
0
0
0
0
0
2
0
1
3
0
2
0
1
1
0
1
0
0
1
0
1
2
2
2
1
0
1
1
0
0
0
2
0
1
0
0
0
1
0
0
0
1
2
2
0
2
1
1
0
0
1
0
0
0
3
1
0
0
0
1
0
2
1
0
0
2
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
2
0
2
0
2
0
2
0
0
0
1
0
1
2
1
0
2
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
1
4
1
0
0
2
1
0
2
1
0
1
2
1
0
1
0
0
0
1
2
0
0
2
3
0
0
1
0
0
0
0
2
0
0
1
0
2
0
0
3
1
0
2
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
2
1
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
2
1
1
2
0
0
1
0
0
0
2
1
0
0
1
1
4
0
0
1
2
0
0
0
0
0
0
1
0
3
1
0
0
0
0
2
2
0
2
0
0
1
3
0
1
1
0
1
0
0
0
1
3
2
2
1
0
0
0
2
0
4
1
0
2
0
0
0
1
0
0
0
2
0
1
1
0
0
0
0
3
0
0
0
0
2
1
2
0
0
0
2
0
0
0
0
1
0
1
1
1
0
2
1
1
1
0
0
0
1
2
1
1
0
0
0
1
0
0
1
0
0
1
2
0
1
1
0
1
0
2
0
4
2
0
1
2
0
1
0
2
0
0
0
0
0
0
0
0
1
2
1
0
1
0
0
0
0
2
2
1
1
0
2
1
0
0
0
1
0
1
0
0
2
0
2
0
0
1
1
1
2
3
1
0
1
0
1
1
1
0
1
0
0
0
2
1
1
1
0
0
1
0
0
0
0
0
1
1
0
2
1
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
3
0
2
2
2
1
1
0
0
0
0
2
1
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
2
0
1
1
0
2
2
0
0
0
1
0
2
0
0
2
1
0
2
0
0
0
2
0
0
0
0
2
1
0
1
0
0
0
0
0
1
0
0
0
1
2
2
0
2
2
0
1
1
0
0
1
0
0
0
2
0
0
0
0
0
1
2
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
2
1
2
0
3
0
0
2
0
2
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
3
0
0
2
0
1
1
0
0
0
0
2
2
0
0
0
1
4
1
0
1
0
1
2
1
0
0
0
2
2
0
2
1
1
0
2
0
0
0
0
1
0
0
0
1
0
0
1
0
2
3
1
0
1
0
0
0
2
0
2
0
0
1
1
0
0
2
2
1
0
0
0
1
0
1
0
0
2
1
0
0
0
1
0
1
0
0
0
2
0
0
0
1
1
0
2
1
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
1
0
0
0
0
1
2
0
2
1
0
0
0
0
0
0
0
1
2
2
1
0
0
1
1
1
2
0
0
1
1
0
0
1
0
2
0
0
1
2
0
0
1
1
0
1
0
0
1
0
0
2
2
1
0
0
0
0
0
2
0
1
0
0
1
0
0
1
1
2
2
0
1
0
2
0
0
1
2
1
2
1
2
0
0
0
1
0
1
1
2
0
0
2
2
2
2
1
0
0
0
1
1
0
0
0
2
1
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
2
1
0
0
2
0
2
2
0
1
0
0
0
2
0
0
1
1
2
1
0
2
0
0
0
2
0
0
0
0
1
0
0
2
2
0
2
0
0
2
0
0
0
0
1
0
0
1
0
1
0
0
2
0
0
2
0
0
2
1
1
0
1
1
0
0
0
1
1
2
0
0
0
0
0
0
0
3
0
0
0
1
2
1
0
2
0
0
1
0
4
2
1
0
0
0
0
1
0
1
0
0
1
0
0
1
0
1
2
0
2
0
0
3
0
1
1
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
1
2
0
1
13
2
0
0
4
0
0
1
2
0
0
0
0
1
0
1
2
1
0
1
0
0
0
0
2
2
2
0
1
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
2
1
1
0
0
1
1
0
1
0
4
0
1
0
1
0
1
0
0
0
1
2
0
0
0
2
0
0
1
0
0
0
2
0
1
0
0
0
2
1
0
2
1
0
2
0
0
0
0
2
1
1
2
0
1
0
0
0
1
0
0
0
0
0
0
0
1
3
1
0
1
1
2
0
0
1
0
2
1
2
0
0
0
1
0
0
2
0
0
0
2
2
0
2
1
2
1
0
1
1
1
0
0
0
1
4
2
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
1
0
1
2
1
2
0
1
1
0
0
2
0
1
1
1
1
2
0
1
2
0
1
1
2
1
1
0
3
1
0
0
1
1
2
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
1
1
2
0
0
0
1
1
0
2
1
1
1
0
0
0
0
0
0
1
1
0
0
2
1
0
0
3
2
0
0
0
0
0
2
2
0
1
0
1
0
2
0
2
1
2
0
1
0
2
2
2
5
2
0
2
2
0
2
1
1
2
0
1
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
1
1
1
1
0
1
1
0
2
3
1
2
1
2
1
0
1
0
1
0
0
2
0
0
2
1
0
0
1
0
1
2
0
0
2
0
2
2
1
2
0
0
0
1
0
0
2
0
2
0
0
2
1
1
0
0
0
2
2
0
1
0
1
1
2
0
2
1
0
0
2
0
0
1
0
0
1
2
0
0
0
0
1
0
0
0
0
1
2
2
0
0
1
1
2
0
2
0
0
2
2
1
0
2
2
1
0
0
0
0
2
0
2
1
0
0
2
0
1
0
0
1
0
0
3
0
1
2
1
0
2
2
1
0
0
0
1
1
0
1
0
0
2
0
0
0
2
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
1
3
0
0
0
2
0
2
2
0
1
0
0
0
1
0
1
0
1
0
2
2
0
0
0
1
0
1
1
0
2
2
0
1
2
0
0
0
0
0
2
0
0
1
0
1
1
0
0
1
1
1
0
2
0
0
1
2
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
2
0
0
4
1
0
0
1
0
1
0
2
0
0
2
1
2
1
0
1
0
0
0
0
1
1
0
1
2
1
0
2
0
0
0
1
0
1
2
1
0
0
0
0
2
0
0
2
0
0
0
0
0
1
2
0
0
1
2
0
3
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
2
1
2
0
0
2
2
1
1
0
0
1
1
1
1
0
2
0
1
1
0
0
0
0
2
1
2
0
1
0
0
1
0
0
2
1
2
2
0
0
1
0
0
0
0
1
0
0
1
0
0
2
0
0
2
0
1
1
2
0
1
1
0
0
2
0
1
0
0
0
0
0
2
2
1
0
4
0
0
0
2
1
1
0
0
1
0
2
2
0
0
0
0
0
1
1
1
0
0
0
0
3
1
2
0
0
2
1
0
0
1
2
0
0
0
1
2
0
2
1
0
1
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
2
1
0
1
1
1
0
2
2
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
2
1
1
0
1
2
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
1
3
1
1
1
2
1
1
2
0
0
0
0
0
2
1
2
0
0
0
1
0
1
2
0
0
2
0
0
0
0
2
1
0
1
2
3
0
0
2
0
1
0
0
0
2
4
1
2
1
0
0
0
0
0
0
0
0
0
1
1
0
2
1
2
0
0
0
1
0
0
0
2
0
1
0
0
1
0
0
1
0
0
2
0
0
0
0
0
1
1
2
0
0
1
2
0
2
0
0
2
0
0
1
0
2
0
0
0
0
0
1
4
1
0
6
1
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
3
2
0
6
0
1
0
2
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
3
0
0
1
0
1
2
0
1
2
2
0
2
0
0
0
1
0
0
2
0
1
2
0
0
0
1
0
0
0
2
0
0
0
2
2
0
0
1
1
0
1
1
1
0
1
3
2
3
1
0
0
2
0
0
0
1
1
2
2
0
1
1
2
0
0
0
0
2
1
0
0
0
2
1
2
2
0
0
2
0
2
0
0
2
0
3
2
2
4
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
2
2
1
2
0
0
0
0
0
1
1
0
0
1
0
2
0
2
0
0
0
2
0
0
0
0
0
1
2
0
1
1
1
2
1
2
1
0
2
0
0
2
1
4
1
0
0
0
1
0
0
2
2
1
2
1
0
0
0
0
0
1
0
0
0
2
2
1
2
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
1
0
0
2
2
2
0
0
0
0
0
2
0
0
0
0
2
1
2
0
1
1
1
0
2
0
1
0
1
2
0
0
1
0
0
0
1
2
1
2
1
0
0
1
0
0
1
0
1
0
1
0
2
0
1
0
1
2
0
0
0
2
0
0
1
0
0
0
2
0
1
0
1
1
2
2
0
0
0
0
0
2
0
0
0
2
1
1
1
0
2
1
0
2
1
0
2
2
1
2
0
0
0
2
0
0
2
0
2
0
0
1
0
3
2
0
0
0
0
4
1
2
0
0
1
1
2
0
0
0
0
0
0
0
0
0
1
1
1
0
1
2
2
2
0
0
0
1
1
0
0
1
2
0
1
1
0
0
1
0
0
1
1
0
0
1
1
0
1
0
0
0
0
1
2
1
0
2
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
1
0
1
0
1
0
1
0
1
2
1
1
0
1
0
0
1
0
0
0
2
0
1
1
0
0
1
0
0
0
1
2
2
0
0
0
0
0
3
0
0
2
1
2
1
0
0
0
0
1
1
0
0
1
1
0
0
0
1
1
0
0
2
0
1
0
2
0
1
0
2
0
0
0
0
0
0
0
2
2
2
0
0
0
0
1
0
2
2
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
1
1
0
1
1
0
0
0
1
0
0
0
0
2
0
0
0
0
3
1
2
0
0
0
2
0
0
1
0
0
0
0
0
1
1
0
0
2
0
1
0
1
2
0
3
0
0
1
2
0
0
1
2
1
1
1
0
0
1
2
2
0
0
0
0
2
2
1
2
1
0
0
0
2
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
2
2
0
1
0
2
0
1
0
0
0
1
0
0
0
1
0
0
2
0
1
0
0
0
0
5
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
3
0
0
0
0
0
0
2
0
0
0
1
2
2
0
0
1
0
1
2
0
0
0
2
2
1
1
0
1
0
0
0
1
0
0
2
0
0
2
0
2
0
1
0
0
1
0
3
0
1
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
2
0
1
2
0
1
2
0
2
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
2
2
2
1
0
0
2
3
1
2
0
0
1
0
0
1
0
0
0
1
1
0
0
1
0
2
0
2
1
0
0
2
1
0
1
1
1
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
3
1
2
0
0
0
2
0
1
0
1
0
1
2
0
0
0
0
0
1
3
2
0
1
1
1
3
2
2
0
1
0
3
0
0
0
0
1
2
0
0
0
0
0
0
1
0
2
0
0
1
1
2
0
1
0
0
1
0
0
2
2
1
0
2
1
0
0
1
2
0
2
0
2
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
1
0
2
2
2
0
0
0
0
0
0
0
3
1
1
0
0
0
0
0
0
2
0
2
0
0
3
0
0
0
0
0
0
0
0
0
2
0
3
0
2
0
0
0
0
0
0
0
0
1
1
2
2
0
1
0
1
0
1
2
2
0
0
1
0
2
1
0
1
1
0
0
1
0
0
0
2
1
1
1
0
1
7
0
1
1
0
1
1
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
2
0
2
0
0
0
0
2
1
2
2
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
4
1
0
0
2
0
0
2
0
0
0
1
0
2
1
0
0
0
0
2
0
2
0
1
0
0
2
2
0
0
1
1
0
0
1
0
2
1
0
2
2
0
1
2
0
2
1
2
0
0
1
1
1
0
0
0
0
0
2
3
2
0
0
1
1
0
0
1
0
0
1
1
1
1
2
0
0
0
1
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
1
0
1
2
2
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
3
0
1
1
0
2
2
2
2
1
0
1
0
0
0
1
0
1
0
0
0
0
0
2
0
0
1
0
0
4
0
1
1
0
3
1
0
0
0
1
0
0
0
0
0
0
0
2
2
2
1
0
0
0
2
0
0
1
0
1
3
2
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
1
1
2
0
2
0
0
2
0
0
0
2
0
1
1
0
1
0
2
0
1
1
0
0
0
0
2
0
0
0
2
3
4
1
1
1
0
0
1
0
2
0
1
0
1
0
0
0
0
0
0
0
2
2
1
2
1
2
1
0
0
0
0
1
2
0
1
2
2
2
0
1
1
1
1
1
2
1
0
0
1
0
1
2
2
0
2
0
0
0
1
0
0
2
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
2
2
2
0
0
0
2
0
2
0
0
0
1
1
1
1
0
0
0
2
1
0
0
1
1
0
0
0
0
2
3
1
0
0
1
0
0
0
4
0
1
2
2
0
3
1
0
0
2
0
0
0
0
1
1
0
1
0
0
2
0
0
1
1
2
0
3
0
0
0
0
0
1
1
0
0
0
2
1
2
1
0
1
1
0
1
0
2
1
0
0
2
0
2
0
0
1
1
2
0
0
0
1
0
1
1
0
0
0
0
1
0
2
2
2
0
0
0
0
0
1
1
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
1
0
0
2
0
1
1
0
0
1
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
2
0
1
2
0
2
1
0
2
0
1
5
1
0
0
0
0
0
0
1
1
2
2
1
0
0
2
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
7
2
0
1
1
0
2
0
2
0
0
0
0
1
1
0
0
3
0
2
1
2
1
2
1
1
0
0
0
0
0
0
2
3
0
0
2
0
0
0
0
1
0
1
1
0
0
0
2
2
0
1
0
1
1
0
0
1
6
1
1
0
0
0
0
0
0
0
0
2
1
0
2
1
0
0
0
0
2
0
0
0
1
2
1
0
2
1
0
0
2
0
2
0
0
0
4
0
0
0
2
0
0
0
2
0
1
0
0
0
0
2
2
1
1
0
0
0
2
2
0
4
1
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
1
1
1
0
0
1
1
1
2
0
0
0
0
0
1
0
2
1
0
0
0
0
1
0
0
0
3
0
0
0
1
0
1
0
0
1
0
1
0
0
2
0
0
2
0
1
1
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
2
1
3
0
0
0
1
0
0
0
1
2
0
2
0
0
5
0
0
2
0
2
2
0
0
0
0
0
1
0
0
2
1
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
2
2
1
0
1
0
0
0
2
0
0
0
0
1
1
2
2
0
0
0
0
0
0
0
0
0
1
0
0
2
1
1
0
0
0
0
0
2
1
0
3
1
2
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
2
2
1
0
2
0
0
0
0
0
1
2
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
1
2
0
0
1
4
1
0
0
0
1
0
0
1
0
0
1
1
1
0
0
1
1
0
2
0
0
1
0
0
1
0
0
0
2
1
2
0
1
2
0
0
2
0
2
2
1
0
0
0
0
0
0
1
1
0
1
1
0
1
0
0
2
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
1
0
2
2
0
1
0
0
0
0
2
2
0
0
0
0
2
0
0
0
1
0
0
0
2
1
0
0
1
0
0
2
1
1
0
1
1
1
0
0
0
1
1
0
2
1
0
0
0
1
0
1
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
2
0
1
1
0
2
1
0
0
1
0
0
3
0
1
1
0
2
1
2
0
0
1
1
0
0
0
0
0
0
0
0
0
2
4
0
0
0
1
0
0
0
2
2
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
2
0
4
1
0
0
5
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
2
0
1
1
0
0
0
0
1
0
0
0
1
0
1
0
0
1
1
0
0
0
1
0
0
1
0
1
0
0
1
1
0
0
0
0
1
0
1
0
2
0
3
0
1
0
0
0
0
2
1
0
0
0
0
1
0
0
2
0
0
2
0
2
2
1
0
1
0
2
0
1
0
0
1
0
2
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
1
0
2
1
2
0
0
0
1
0
1
0
2
2
0
0
0
0
0
0
1
2
2
0
1
1
0
2
0
0
0
0
1
0
0
0
0
0
1
0
1
0
6
0
1
2
0
2
1
0
3
0
0
0
2
0
0
0
0
0
0
0
1
0
2
1
0
0
0
1
0
0
1
0
1
0
0
0
0
2
5
2
0
0
0
0
1
0
2
1
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
2
0
1
0
0
1
1
0
0
0
2
0
2
0
2
1
1
1
0
0
2
0
1
2
2
0
0
1
2
0
0
1
1
2
2
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
2
1
2
0
0
0
0
2
0
1
2
0
0
1
0
0
2
1
0
1
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
1
0
0
0
2
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
2
0
0
1
2
0
1
0
1
0
0
0
6
0
0
0
0
2
0
0
1
2
0
0
1
0
0
1
1
0
0
2
2
0
0
0
1
0
0
1
1
1
0
0
0
0
1
1
0
2
0
0
2
0
0
2
0
0
0
0
1
1
2
0
2
1
1
0
0
0
3
0
0
0
1
0
0
0
1
1
1
2
0
0
1
1
0
1
0
0
1
0
1
1
0
1
0
0
0
1
1
1
0
0
1
0
1
0
0
1
0
2
1
0
0
0
2
1
1
0
0
0
1
0
1
1
0
1
1
1
0
0
2
0
2
0
0
2
0
2
0
2
1
2
1
3
1
2
0
2
0
1
0
0
1
0
0
2
1
0
1
0
2
1
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
2
1
2
4
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
1
0
0
0
1
0
2
0
0
0
0
0
0
0
1
1
2
0
1
0
0
0
2
2
2
0
0
0
0
0
1
0
2
0
0
0
0
1
1
0
2
0
0
2
0
2
0
0
0
0
0
0
2
1
1
2
0
2
0
0
0
2
0
0
0
0
0
1
0
1
2
0
2
0
1
0
2
0
0
2
2
2
1
1
0
1
1
0
0
0
0
3
2
2
0
0
1
2
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
1
0
1
0
0
0
3
2
0
0
1
1
1
2
1
0
0
0
0
2
0
1
0
0
0
2
0
0
0
2
0
0
1
1
0
0
0
2
1
1
1
1
1
2
1
0
0
0
0
0
2
0
0
1
1
0
0
0
0
1
2
0
2
3
0
0
0
2
0
0
1
1
2
0
0
0
2
0
0
0
1
0
0
0
1
0
2
3
0
0
1
0
1
0
0
1
0
0
1
0
0
2
0
0
0
1
0
0
0
2
0
1
1
1
0
0
2
0
0
0
0
0
1
0
0
0
0
2
3
0
1
0
2
2
0
0
0
1
0
2
2
0
3
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
2
0
1
2
0
0
0
2
1
2
2
1
1
0
1
2
0
2
2
0
1
1
0
1
0
0
2
0
1
2
0
0
0
1
1
1
0
0
2
0
2
1
0
0
0
0
1
0
0
2
1
2
0
2
0
0
1
3
1
2
2
1
1
0
1
0
0
3
2
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
3
0
0
0
0
2
0
2
0
1
0
1
0
1
1
2
0
0
2
2
0
0
0
0
1
0
2
5
1
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
3
1
0
2
3
0
0
2
1
0
1
0
2
0
1
2
2
0
0
1
0
2
2
0
0
0
0
2
2
0
0
0
0
0
0
0
1
1
2
0
2
2
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
2
2
1
0
0
0
0
1
1
0
0
0
0
2
2
1
0
1
0
0
0
1
0
0
0
2
1
0
0
0
0
0
2
0
1
1
0
1
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
1
2
0
2
1
0
0
0
0
1
2
0
1
3
0
2
0
2
1
0
0
2
1
2
0
0
0
1
0
2
3
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
1
1
0
0
1
2
0
7
0
2
0
1
1
0
0
2
1
0
0
3
1
1
0
1
0
1
0
0
0
2
0
0
1
2
0
1
0
1
2
1
0
1
0
0
1
0
0
0
0
3
0
2
0
1
2
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
2
2
0
0
1
0
0
0
1
0
0
0
3
0
0
0
0
1
2
2
0
1
0
0
0
2
1
0
0
0
1
2
1
0
2
0
2
1
2
0
0
0
0
1
0
1
0
1
2
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
1
2
0
2
0
2
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
2
0
2
0
0
4
1
0
0
0
2
0
0
0
1
2
1
1
1
0
1
0
0
0
0
0
0
0
0
1
1
2
0
0
0
2
0
0
0
2
0
1
0
2
0
0
1
0
0
1
0
0
0
2
3
0
0
2
1
0
2
0
0
1
0
0
0
0
0
0
0
1
2
2
0
0
0
0
3
0
0
2
1
0
0
2
0
0
2
0
0
1
0
1
0
2
0
1
0
2
1
2
0
1
0
2
1
1
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
2
2
0
0
1
0
0
2
0
0
2
2
1
3
0
2
0
1
1
1
0
1
0
0
1
0
0
3
0
0
0
0
1
0
0
0
2
1
1
1
0
0
0
0
1
0
0
1
0
2
1
0
0
0
0
0
0
0
0
1
0
2
0
0
1
1
0
0
0
1
1
0
0
0
0
1
2
2
1
1
0
0
2
0
1
2
0
0
0
1
0
0
1
2
0
1
0
1
2
2
0
2
0
1
0
1
1
1
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
1
1
2
0
0
0
0
0
2
0
0
0
3
1
0
2
1
1
0
0
0
4
0
2
0
0
0
0
1
1
0
0
0
2
1
2
2
0
0
2
1
0
0
1
0
0
1
0
1
1
1
0
0
0
1
1
1
0
2
1
1
2
1
0
3
0
0
0
0
1
0
0
1
0
1
0
2
2
0
0
0
2
0
1
0
0
2
1
1
0
1
0
0
0
3
0
2
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
2
2
0
0
0
2
0
3
1
1
1
1
0
1
0
1
2
1
1
0
0
1
1
1
0
0
0
1
0
0
1
1
1
1
1
0
1
0
0
1
0
0
2
2
0
2
2
0
1
1
2
0
0
2
0
0
0
1
2
0
1
0
0
1
2
0
1
0
0
3
0
1
1
2
0
0
0
1
2
0
0
1
1
0
0
0
0
0
1
0
1
0
0
2
0
2
1
0
1
0
1
2
1
3
0
0
2
1
0
2
1
3
0
0
1
2
0
2
0
2
0
2
0
0
0
1
0
2
1
0
1
0
1
0
0
0
0
1
0
1
0
0
2
0
0
0
0
1
1
2
0
2
1
2
2
0
0
0
0
0
2
1
0
0
0
2
1
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
1
0
1
0
0
2
0
0
0
2
2
1
0
0
2
0
1
0
0
1
1
2
2
0
2
0
0
0
2
14
0
0
0
1
2
0
1
1
0
0
1
0
0
0
1
0
2
0
0
0
2
0
0
0
0
2
1
1
1
0
0
1
0
0
2
0
0
0
2
0
0
1
0
1
0
2
0
0
0
2
0
2
1
0
0
1
0
0
1
0
2
2
2
0
0
0
0
2
2
0
1
0
0
0
2
0
0
0
0
0
1
0
1
0
1
2
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
1
2
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
1
1
1
2
2
0
1
0
1
0
0
1
0
0
0
0
0
0
0
2
2
1
2
0
1
0
0
0
1
0
2
0
0
0
4
0
0
0
0
0
0
1
2
2
0
1
0
0
0
0
0
1
3
0
1
0
0
1
0
1
0
2
1
0
2
3
1
0
2
0
2
0
0
2
1
0
2
0
2
2
1
1
2
0
2
0
0
1
0
0
1
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
2
1
2
1
1
0
0
1
0
0
0
2
2
0
1
2
0
0
0
0
2
0
1
0
0
0
2
1
0
1
0
1
0
2
0
1
1
2
2
2
1
2
0
0
0
0
0
0
0
2
2
0
1
0
1
0
0
2
0
0
0
0
0
0
1
0
0
2
2
1
0
1
1
1
0
0
0
0
0
1
0
0
1
1
1
2
2
1
0
0
1
0
1
0
0
1
1
1
0
0
0
2
0
1
1
0
0
2
1
0
0
0
0
10
2
0
0
3
2
0
1
2
1
0
1
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
2
0
1
0
2
0
2
1
0
1
1
0
0
0
0
0
1
0
0
1
0
0
1
1
1
1
2
0
0
1
2
1
0
0
2
0
0
0
0
1
0
0
0
3
2
2
0
2
1
1
0
0
2
1
1
0
2
1
2
1
0
1
0
2
0
0
0
0
0
0
2
8
0
2
0
1
1
0
0
1
1
0
0
1
0
2
0
5
0
1
0
1
0
1
0
0
1
0
0
1
0
2
0
0
2
0
0
0
1
2
1
0
0
1
4
0
0
2
0
2
0
1
0
2
1
1
2
2
1
0
1
0
1
2
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
2
0
1
2
1
0
1
1
2
1
0
1
3
0
0
2
0
0
0
0
0
0
0
0
2
3
0
0
2
0
0
0
2
0
2
1
3
0
2
0
0
1
0
5
1
2
0
0
0
1
0
0
0
1
0
0
0
2
0
1
1
2
0
0
0
2
1
0
0
0
0
0
2
0
2
0
0
1
1
1
0
1
1
0
0
0
1
1
0
3
2
2
0
0
0
0
0
0
0
1
2
1
1
1
2
2
1
2
2
0
0
1
0
4
0
0
0
0
0
0
3
0
0
0
1
3
2
0
2
0
0
1
0
0
0
1
0
0
1
0
0
2
1
0
0
0
1
0
0
0
2
0
0
1
1
1
1
1
2
0
1
1
0
2
3
1
0
0
0
0
0
0
0
2
1
1
0
0
0
1
1
0
1
0
0
0
0
1
3
2
2
0
0
2
0
0
1
0
2
0
0
0
3
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
1
0
2
0
0
0
2
0
0
2
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
1
2
0
0
2
2
1
2
2
2
0
4
0
2
0
0
0
1
0
0
0
3
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
2
0
0
3
2
1
1
2
0
0
0
0
0
0
0
0
1
0
2
2
0
1
1
0
2
0
0
0
0
0
0
2
1
0
1
2
0
0
1
2
3
1
0
1
0
2
0
0
1
1
0
1
0
2
0
0
0
0
3
0
0
0
0
0
0
3
2
2
0
0
2
0
2
1
0
0
1
0
0
0
1
1
4
0
0
1
0
0
1
1
2
2
0
0
0
4
0
0
0
0
2
0
0
2
0
0
2
1
0
2
0
0
1
1
1
0
0
0
2
2
0
1
2
0
1
0
0
1
5
0
0
0
0
1
0
0
2
0
1
2
0
0
0
0
1
0
2
0
0
0
1
1
1
0
0
0
0
0
0
2
0
2
0
0
0
1
0
1
2
0
1
0
1
0
0
1
0
2
0
0
1
1
2
0
2
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
2
0
2
1
0
2
0
0
2
2
0
2
2
0
0
0
2
0
0
1
0
0
2
0
2
0
5
0
3
0
2
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
2
1
0
2
0
0
0
0
0
0
1
2
0
2
2
2
0
2
1
0
3
1
0
1
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
2
1
0
0
2
1
0
0
0
1
0
0
2
0
0
0
0
2
2
0
2
2
0
0
0
1
0
0
0
0
0
0
0
2
1
2
0
0
2
0
2
2
0
0
0
1
0
0
1
0
2
2
2
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
2
1
0
0
0
1
0
2
0
2
0
2
1
3
0
2
0
0
1
0
2
2
2
0
1
0
1
0
1
0
1
1
0
0
0
0
2
0
0
1
0
1
0
0
0
0
3
0
0
0
2
0
0
2
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
1
0
0
1
1
0
0
0
2
0
0
0
1
0
0
0
1
2
2
0
0
0
0
2
1
0
2
2
0
0
0
1
1
1
0
3
0
0
0
0
1
2
0
0
2
0
2
1
1
0
0
2
0
0
0
1
2
0
1
1
2
3
0
2
2
2
0
2
1
0
1
0
1
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
2
0
2
1
1
0
2
2
0
0
3
2
0
1
0
1
2
2
1
0
0
1
2
0
2
0
1
0
1
2
0
0
1
2
1
0
0
0
0
0
1
1
0
3
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
2
1
0
2
0
0
2
0
0
1
2
0
0
2
0
0
1
0
2
0
0
0
2
1
0
0
0
0
0
2
0
1
2
0
2
0
1
0
1
0
0
0
0
1
0
1
0
1
0
0
1
1
2
1
0
1
0
1
2
0
0
0
2
0
1
0
0
0
0
0
1
0
2
1
0
2
1
2
1
0
1
0
0
0
2
0
2
0
2
0
2
1
0
1
0
0
0
2
0
1
0
2
0
0
0
0
0
2
2
0
0
1
1
0
0
1
0
0
0
3
3
0
0
0
0
1
0
0
1
0
0
2
2
2
0
0
0
2
0
0
1
0
0
0
0
0
1
1
0
2
0
2
0
0
2
1
1
0
1
0
2
1
2
2
0
0
2
0
0
0
0
0
1
0
0
0
1
0
1
1
0
1
0
1
2
1
0
0
2
2
2
1
0
1
2
0
2
3
1
0
0
3
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
2
1
1
1
0
2
0
0
3
0
0
2
1
0
2
1
2
1
0
0
0
2
0
0
2
0
2
0
0
0
2
0
0
2
1
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
2
2
2
0
2
0
0
0
4
0
0
2
0
0
1
0
1
0
1
0
0
0
1
0
0
0
2
0
0
0
0
1
1
0
2
0
1
0
2
0
0
1
0
0
0
1
1
1
0
0
0
0
2
0
0
2
3
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
2
1
0
2
0
2
0
0
0
0
0
0
1
3
0
1
0
2
0
0
1
1
1
3
2
0
0
0
0
3
0
0
0
1
2
0
0
2
1
0
0
0
0
0
1
7
1
0
0
1
1
0
1
0
0
0
2
0
0
0
1
2
1
1
0
0
1
1
0
1
0
2
0
0
1
0
0
1
1
2
1
0
0
0
0
0
0
0
0
0
0
2
0
1
2
2
1
0
0
0
0
2
0
0
2
0
0
2
0
0
0
1
0
0
0
2
2
0
0
0
0
0
2
0
1
0
1
2
2
0
2
0
0
0
1
2
2
1
2
0
4
0
0
0
0
0
0
1
1
0
0
0
0
1
2
0
0
1
0
0
0
1
0
0
1
0
1
1
2
1
5
0
2
2
0
1
0
1
0
1
0
0
0
2
1
1
5
0
0
0
2
1
0
2
0
0
1
0
0
0
1
0
0
0
1
1
0
1
0
0
0
1
1
0
0
0
2
0
0
0
0
1
0
0
0
2
2
1
1
0
0
0
0
1
1
0
1
1
3
0
0
2
0
3
0
1
2
0
0
1
0
0
0
0
1
2
2
0
0
0
0
0
1
1
0
0
2
0
1
0
3
0
1
0
1
1
4
1
1
0
2
2
0
1
1
0
0
0
0
2
1
0
2
0
1
1
1
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
3
2
0
2
1
0
0
0
0
0
4
0
1
1
0
2
0
1
1
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
3
0
0
0
1
1
0
1
0
0
1
0
0
1
0
0
0
0
2
0
2
0
0
0
1
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
1
2
0
2
0
2
0
0
2
1
0
0
0
0
1
2
1
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
2
1
2
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
3
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
2
1
0
2
0
0
1
0
0
0
1
0
2
0
0
2
1
0
2
1
0
0
2
2
2
0
0
0
0
1
2
3
1
0
0
2
2
1
2
1
0
0
3
0
1
1
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
2
2
0
2
1
0
0
0
2
0
3
2
0
0
0
1
0
0
1
1
0
2
0
0
0
2
0
0
0
2
0
3
0
0
0
0
0
1
1
2
0
0
2
0
0
1
0
2
0
0
1
2
0
2
1
0
0
0
1
0
1
1
0
3
2
0
2
0
0
2
0
0
0
0
0
2
2
0
0
0
1
1
2
1
2
0
1
0
0
1
0
0
0
1
0
2
0
0
0
1
1
2
2
0
0
0
1
1
0
0
1
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
1
2
2
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
1
0
0
3
0
1
1
2
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
2
0
1
0
1
0
2
0
1
2
0
0
2
2
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
3
0
1
0
0
0
1
1
2
5
2
2
0
0
0
4
2
0
0
2
2
7
0
0
0
0
0
1
1
0
0
0
1
0
1
1
1
0
1
0
3
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
1
1
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
1
0
0
2
1
0
0
0
2
0
0
0
0
0
2
0
1
0
2
0
1
0
0
0
0
1
1
0
0
0
0
1
0
1
2
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
2
0
2
0
1
2
0
2
0
0
3
1
1
2
0
0
1
2
1
0
0
0
1
0
1
0
0
1
0
1
1
1
0
0
0
0
0
1
2
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
2
2
0
1
1
0
1
0
1
0
2
0
0
0
0
0
0
2
0
0
1
0
0
3
1
0
1
0
2
0
2
0
2
1
0
0
0
1
0
0
1
1
0
0
2
1
0
0
1
0
0
0
0
0
0
1
2
0
0
0
1
1
0
1
1
1
0
1
0
1
2
0
0
0
1
1
0
0
0
0
0
2
0
1
1
1
0
2
0
5
1
0
1
1
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
3
0
1
1
1
0
1
0
0
0
2
0
0
2
2
0
0
2
2
1
2
0
4
0
4
2
0
1
0
0
2
2
0
0
0
3
1
2
1
0
0
0
0
0
2
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
1
0
0
0
1
1
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
1
0
1
2
0
0
0
2
2
0
1
1
2
2
1
0
0
0
1
0
0
0
0
0
2
2
1
0
0
2
1
3
2
1
0
0
0
0
1
2
0
2
0
2
1
0
0
0
0
0
2
1
1
0
1
0
2
0
1
0
0
1
1
0
0
2
1
0
1
0
1
0
0
0
0
0
0
1
0
2
2
0
0
0
1
0
0
1
0
0
0
0
0
0
3
0
2
2
1
2
2
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
2
0
3
1
1
2
1
1
1
0
0
0
0
0
0
0
0
0
0
1
2
0
2
3
0
2
0
0
0
0
0
0
1
0
0
0
2
2
0
2
0
0
0
2
0
0
1
2
1
1
0
2
0
2
0
1
0
0
0
0
0
1
0
2
1
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
2
1
1
3
0
2
0
0
0
2
0
0
0
2
2
0
3
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
3
0
0
2
2
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
2
0
1
3
1
2
0
0
0
0
1
0
0
0
0
0
1
2
0
1
0
0
0
1
0
0
1
0
0
0
1
0
1
2
1
0
0
2
0
0
0
0
0
1
2
1
1
0
0
1
0
1
1
1
0
1
0
2
2
2
0
0
0
0
0
3
0
0
1
2
0
0
1
1
0
2
1
0
2
1
3
0
0
0
2
0
0
2
0
0
0
2
0
3
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
2
0
1
0
0
1
1
2
2
0
0
0
0
0
1
0
2
2
0
0
2
2
2
0
0
0
2
0
0
1
0
0
2
0
0
1
0
2
0
0
2
0
0
2
1
0
1
0
0
0
1
1
2
1
0
0
1
0
1
1
0
0
0
2
0
2
1
2
0
0
2
1
0
0
1
3
2
0
0
0
0
1
0
2
0
0
2
1
0
0
0
2
1
2
0
0
0
1
2
2
0
1
0
1
3
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
1
0
0
1
2
2
1
0
0
0
0
2
0
0
1
0
0
0
3
0
0
0
0
0
1
1
0
0
0
0
0
1
2
2
1
1
0
0
0
0
0
1
0
0
2
0
1
0
0
2
2
0
0
0
0
2
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
1
2
2
2
0
1
1
1
2
0
0
1
1
0
3
1
0
0
0
1
1
0
1
0
0
3
1
0
1
0
0
0
0
1
0
0
2
0
2
0
0
0
2
0
0
2
0
1
0
1
0
0
1
0
1
1
0
0
2
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
3
0
1
0
0
0
0
2
1
2
2
0
1
1
0
1
0
0
0
1
0
0
1
0
0
0
0
2
0
1
0
2
0
1
0
0
0
1
0
2
0
0
0
1
0
0
2
0
0
1
1
1
1
0
1
0
0
1
0
1
1
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
2
2
0
1
0
2
2
0
0
2
0
0
0
0
2
1
2
1
0
2
0
0
1
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
2
0
2
0
1
2
0
2
0
0
2
0
1
1
1
0
0
0
2
0
0
2
1
0
1
1
1
0
1
1
1
0
0
0
2
1
0
1
2
0
2
1
1
1
1
0
0
2
1
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
1
2
1
0
0
1
1
1
2
1
1
2
0
0
1
1
0
0
1
0
0
1
0
1
0
1
1
0
0
0
1
0
0
1
1
1
0
2
0
0
0
0
0
0
0
1
2
0
0
2
0
2
1
5
0
0
2
1
0
0
0
2
0
1
0
1
0
2
0
0
3
1
0
2
0
0
0
2
0
0
2
0
0
0
1
0
2
1
0
1
0
0
0
0
0
1
0
2
0
0
0
2
0
1
2
0
0
0
2
3
0
1
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
2
1
0
1
0
4
2
1
2
2
1
0
2
1
1
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
1
2
0
0
0
1
1
0
2
0
0
1
0
2
2
1
0
0
1
2
1
0
1
1
0
1
0
1
0
0
0
0
0
0
2
0
2
4
0
0
1
1
2
0
2
0
0
0
0
1
0
2
0
0
1
2
0
1
2
2
2
0
2
0
0
0
0
1
1
0
2
1
0
2
2
0
0
0
2
1
2
0
1
0
0
1
0
0
2
0
0
2
0
0
0
2
0
0
0
1
1
0
0
1
1
0
0
2
2
3
0
1
0
1
0
1
0
0
0
1
0
0
0
0
1
1
3
0
0
2
0
1
0
2
0
1
0
0
0
0
0
0
2
0
2
1
0
1
0
0
2
0
1
3
0
0
0
1
2
0
0
0
0
1
0
0
2
2
0
1
2
3
1
0
0
0
1
2
0
1
2
1
2
1
0
0
0
2
0
2
0
0
2
1
1
0
3
0
0
0
1
2
2
1
0
0
0
0
2
0
0
0
1
1
0
0
1
1
0
0
3
0
2
1
2
1
0
0
0
0
0
0
0
2
1
0
2
1
1
0
1
1
0
2
0
0
2
0
0
0
1
1
2
0
0
0
2
0
0
1
2
1
0
0
0
0
0
0
1
2
0
1
1
2
0
0
0
1
2
2
0
0
2
0
2
0
1
0
0
0
2
0
1
2
2
0
0
0
0
2
1
1
2
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
2
1
1
0
2
0
1
0
1
1
0
0
0
0
0
2
0
0
2
0
0
0
0
1
1
0
2
2
0
0
1
1
0
1
1
0
3
1
1
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
2
2
0
0
2
0
2
0
0
1
0
0
0
1
0
2
1
0
0
0
0
0
0
0
2
0
4
2
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
2
1
2
1
2
2
0
1
0
1
0
1
0
1
0
0
0
0
3
2
0
1
0
0
0
0
0
0
1
2
0
0
2
0
1
0
1
2
0
1
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
2
2
0
0
0
1
1
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
2
1
0
2
1
1
0
0
0
0
0
1
1
1
0
1
0
0
0
3
0
1
0
1
0
0
0
1
1
0
2
0
0
0
0
0
1
2
0
0
2
2
0
0
0
1
0
0
0
0
1
0
0
1
0
2
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
2
2
0
0
1
0
2
2
0
0
2
2
1
0
0
0
1
2
0
0
0
0
1
0
1
2
1
0
2
0
0
2
0
1
0
0
0
2
1
0
0
2
0
0
0
0
0
0
2
1
2
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
2
0
2
1
0
2
2
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
1
2
0
0
0
1
0
0
1
0
2
1
0
0
0
1
0
2
0
0
0
0
3
0
1
0
0
1
1
2
0
1
4
2
0
0
0
1
0
1
1
0
0
0
0
2
0
0
2
2
2
0
0
0
1
0
0
0
0
0
1
1
0
2
0
1
0
2
1
0
0
0
0
0
1
0
1
0
0
0
1
0
1
1
2
0
0
2
1
4
1
0
1
1
0
0
0
2
0
1
1
0
2
0
0
1
1
0
0
0
0
0
2
1
2
0
3
1
0
0
0
0
0
0
2
0
2
0
0
0
0
2
1
2
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
2
0
2
0
0
0
0
1
0
0
0
0
1
1
1
2
2
2
1
0
1
0
0
1
0
0
0
0
4
1
2
0
0
0
0
3
3
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
1
0
1
2
0
0
0
1
0
0
1
0
1
2
0
2
0
1
1
2
1
0
1
0
1
0
0
0
2
0
0
1
0
0
2
1
2
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
1
1
0
0
2
0
1
1
0
0
0
0
1
0
0
0
1
1
0
2
0
2
2
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
2
0
0
2
2
0
1
0
0
0
1
0
1
0
2
1
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
1
0
1
0
2
0
2
1
0
2
2
1
2
0
0
4
2
0
2
1
1
0
0
0
2
1
0
0
2
1
0
2
0
1
2
0
2
1
0
0
2
0
0
0
2
0
0
4
2
1
1
1
0
0
0
1
2
1
1
0
0
0
0
0
0
0
2
0
1
0
0
1
1
1
2
0
1
0
2
2
0
0
2
2
0
0
0
1
2
1
1
2
0
0
4
0
0
1
0
1
0
1
0
0
2
2
0
1
1
0
0
0
1
0
1
2
0
0
0
0
2
0
0
1
0
1
0
1
0
0
0
1
0
0
0
2
0
0
1
0
0
0
2
0
0
0
1
0
0
1
3
0
0
1
2
0
0
0
0
0
2
0
2
0
2
2
1
0
0
0
2
0
0
0
0
1
2
2
1
0
0
3
2
0
0
1
0
0
0
1
1
0
2
2
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
2
0
0
1
0
2
4
0
0
2
0
1
0
2
2
1
1
0
0
2
0
0
1
0
0
0
0
0
0
3
0
1
1
0
0
2
0
1
0
0
2
0
0
2
0
0
0
1
0
0
0
1
0
1
2
0
0
0
0
0
3
0
0
1
2
0
0
2
0
0
2
0
0
2
0
0
1
0
0
0
0
1
2
0
1
0
0
1
1
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
3
1
0
0
0
0
1
0
0
1
0
0
0
0
2
1
1
1
0
0
5
2
2
2
2
0
0
0
0
0
1
2
4
0
0
1
0
0
0
1
2
0
2
0
0
0
2
0
0
0
2
1
2
1
1
0
1
1
1
0
2
2
0
7
0
1
0
0
0
1
0
0
3
0
1
0
0
0
0
2
2
0
1
0
1
2
4
1
0
0
0
2
1
0
0
2
1
0
3
0
0
0
0
0
2
1
0
0
0
0
3
0
1
0
2
0
0
1
0
1
2
1
0
2
0
0
2
0
2
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
1
2
0
0
1
0
0
0
0
2
2
0
0
0
1
0
2
1
1
0
0
2
1
0
0
0
0
2
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
1
0
0
0
0
1
0
1
1
1
0
3
2
0
0
0
0
0
2
1
0
1
2
0
0
0
0
0
0
0
2
0
1
1
2
0
0
1
1
0
1
0
0
0
1
0
2
0
1
0
0
1
0
1
2
4
0
0
0
0
0
0
3
0
1
0
0
2
2
2
0
0
0
1
1
0
1
0
0
1
0
0
0
2
0
0
0
6
1
2
0
0
1
2
0
0
0
1
0
0
2
0
1
0
1
2
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
3
2
0
1
2
1
1
0
0
0
0
2
1
0
1
0
1
0
1
3
0
0
0
0
2
0
0
1
0
0
0
1
1
0
0
1
2
1
2
0
0
2
0
0
2
1
1
0
0
1
0
0
0
0
0
0
2
3
0
0
0
0
4
2
0
0
2
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
4
2
2
1
2
0
0
0
2
1
2
0
0
1
1
0
0
0
0
0
0
0
2
0
2
0
0
0
2
1
0
0
2
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
1
1
1
0
1
1
0
0
1
1
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
1
1
1
2
4
2
0
1
0
2
0
2
0
0
2
1
0
1
2
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
2
0
0
1
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
2
1
0
2
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
2
1
0
0
0
2
1
2
0
0
0
1
1
2
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
3
1
0
0
0
0
2
0
0
2
0
1
2
2
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
1
0
2
0
1
2
2
1
0
0
2
0
2
0
2
0
0
0
0
0
3
2
2
0
0
2
0
0
2
0
0
0
0
3
0
0
2
1
0
0
1
1
1
3
0
1
0
1
0
2
2
1
1
1
1
1
2
0
2
0
2
1
1
0
0
2
4
0
0
1
0
1
0
0
0
0
2
3
0
1
2
0
0
0
0
0
3
2
2
0
2
2
1
0
0
2
0
0
1
0
0
0
0
4
0
2
0
0
0
2
0
0
1
0
0
2
2
1
1
0
0
1
1
2
0
0
0
0
0
2
1
1
0
2
0
1
0
1
0
2
1
0
0
2
0
1
2
0
0
2
0
0
0
2
0
0
0
1
4
0
3
2
1
1
0
0
1
1
1
1
2
0
0
0
0
0
0
2
1
0
0
0
0
1
0
2
1
2
1
0
0
1
1
0
0
0
0
0
1
0
1
0
2
0
2
0
2
0
0
0
0
2
1
2
4
0
0
0
1
0
2
2
0
0
0
0
0
0
0
2
0
1
1
0
1
1
1
0
1
0
1
0
0
1
0
1
2
0
1
0
1
4
2
0
0
0
1
0
0
1
0
0
1
0
0
1
1
2
0
0
0
1
0
1
2
1
2
1
0
0
0
0
1
0
0
3
0
1
0
0
3
2
0
0
0
0
1
0
1
2
0
1
2
1
0
0
0
1
0
0
2
0
0
2
0
1
1
3
0
0
2
2
0
0
0
2
2
0
0
0
0
0
0
2
0
3
0
2
0
1
1
1
2
2
0
1
0
0
2
0
0
0
1
1
0
1
0
2
0
0
0
0
0
0
1
1
0
0
0
2
0
1
0
0
2
0
3
0
0
2
0
0
2
2
1
0
0
0
0
2
0
0
0
0
0
2
4
2
2
0
1
0
2
0
2
2
0
0
0
1
0
2
0
0
2
0
0
2
1
0
2
1
0
2
0
0
0
0
2
2
3
0
1
1
0
0
2
2
0
0
0
2
0
1
2
2
1
4
2
1
0
0
1
1
0
0
0
0
0
2
0
1
1
0
2
1
2
1
2
0
2
2
0
0
1
0
1
2
0
0
1
2
0
1
3
1
0
0
0
2
0
0
1
2
0
0
0
0
2
1
0
0
0
2
0
2
0
0
0
0
0
0
2
1
1
2
0
0
0
3
0
0
0
0
2
2
2
1
0
2
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
1
1
2
0
0
0
1
2
0
0
0
0
0
2
0
1
1
2
1
1
2
0
0
2
0
0
2
0
0
0
0
2
1
0
1
2
0
0
2
1
1
0
0
1
0
4
1
3
1
0
2
0
2
1
1
0
0
2
1
0
0
0
1
1
2
0
1
4
0
1
2
0
0
0
0
1
0
0
2
1
3
2
2
0
0
1
1
2
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
1
5
2
2
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
1
0
0
1
0
0
0
0
0
2
2
0
1
2
1
2
0
0
2
2
0
2
0
0
1
1
1
0
0
2
1
0
0
0
2
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
1
2
0
1
2
0
2
2
0
0
1
2
0
0
0
0
0
0
0
2
1
1
2
2
6
0
2
0
0
2
1
2
0
2
0
0
1
0
0
0
1
0
2
0
0
0
0
0
1
1
1
0
0
1
0
1
1
0
1
0
1
2
0
0
0
2
0
2
0
1
2
2
0
0
2
2
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
2
0
1
2
1
0
1
0
0
2
2
2
1
0
2
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
1
0
0
2
2
0
0
0
0
1
0
0
5
1
0
0
0
0
0
0
1
0
2
0
0
0
2
0
2
0
2
0
2
1
1
2
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
2
2
2
1
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
2
2
1
1
0
0
0
2
0
1
0
0
0
0
0
3
0
0
1
1
0
0
0
1
0
1
1
0
4
1
2
0
0
1
0
0
0
0
0
1
2
0
0
0
1
0
0
2
0
0
2
0
0
0
2
1
1
1
0
1
1
1
0
1
0
2
0
1
1
0
1
0
2
0
0
0
0
3
2
0
0
1
0
0
1
0
0
0
0
0
2
1
1
0
1
0
0
1
2
1
0
2
2
0
2
1
2
1
0
2
0
0
2
0
0
0
0
2
0
0
1
2
1
1
0
0
0
2
0
0
0
2
0
0
0
0
1
4
0
1
1
1
2
0
0
1
0
0
1
0
0
2
0
0
2
0
2
1
0
0
0
2
1
0
0
1
2
0
0
0
0
3
1
0
1
2
1
0
0
0
0
0
1
0
0
1
1
1
8
1
0
0
0
2
1
0
2
0
0
0
0
0
1
0
0
2
2
2
0
1
0
1
0
3
1
2
0
2
2
0
1
1
0
0
0
0
1
0
0
0
1
0
0
2
1
0
1
2
0
1
0
0
2
0
1
1
2
2
2
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
2
1
2
0
0
2
0
3
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
1
0
2
0
0
1
0
0
1
1
0
0
1
1
1
0
1
0
1
1
0
0
0
0
0
1
1
2
2
0
0
1
1
0
1
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
1
2
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
1
4
1
0
1
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
1
0
1
3
2
0
2
2
0
0
0
0
2
2
0
0
1
0
2
0
0
1
0
0
3
1
0
0
1
2
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
1
2
2
2
0
0
0
2
2
0
1
0
0
2
2
0
0
0
0
2
1
0
0
0
1
1
0
0
0
0
0
0
0
3
1
0
0
0
1
0
0
2
1
0
0
2
0
0
2
0
0
2
0
2
0
0
0
0
1
0
0
1
0
0
1
1
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
1
0
2
2
1
0
1
0
0
0
1
0
0
0
2
1
0
1
2
2
0
0
2
0
2
0
0
1
0
1
1
0
0
0
0
2
0
2
0
0
0
0
2
2
0
1
2
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
1
1
0
0
0
0
1
0
1
1
2
0
0
1
2
0
1
0
0
0
2
0
0
2
2
0
1
2
0
2
1
2
1
0
1
0
1
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
2
0
0
2
2
1
2
2
2
2
0
0
1
1
1
2
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
2
0
1
0
1
2
0
2
0
1
0
0
1
2
2
1
1
1
0
2
0
3
1
0
0
0
0
1
2
2
1
2
0
1
0
0
1
3
0
1
0
2
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
3
0
0
1
0
1
2
1
1
0
1
1
1
1
2
2
0
2
0
2
2
0
0
2
2
1
0
1
0
2
1
0
0
0
0
0
1
1
1
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
1
0
2
0
0
0
0
3
2
1
0
0
1
1
0
0
2
0
2
0
2
0
1
0
1
0
1
1
0
2
2
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
4
0
0
2
0
2
0
1
0
0
2
0
0
0
0
1
0
3
0
2
0
1
0
0
0
0
2
2
3
0
0
1
1
1
0
0
2
1
0
0
0
0
0
0
1
1
0
1
1
2
0
0
0
0
2
2
0
0
0
0
1
1
2
2
1
1
2
0
2
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
3
0
0
1
2
0
1
0
0
0
1
1
2
0
1
0
1
1
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
3
0
0
2
1
0
1
0
0
1
0
1
0
0
0
1
2
1
1
0
0
2
3
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
2
0
0
1
0
1
1
1
0
0
1
0
0
2
0
0
1
0
1
1
0
2
1
0
1
1
1
0
0
0
0
2
1
1
0
2
0
0
0
2
2
0
1
1
0
1
0
1
2
2
3
2
0
0
2
2
0
0
1
0
0
1
1
1
2
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
2
1
1
0
1
3
8
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
1
2
1
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
2
0
1
0
2
0
2
0
0
1
0
2
1
2
0
0
2
1
1
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
2
1
1
2
1
0
0
2
2
1
0
2
1
0
3
0
1
1
0
0
1
0
2
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
3
0
1
1
0
0
0
0
0
0
1
0
2
0
2
0
2
1
0
2
0
0
2
0
0
1
0
0
0
0
2
0
0
1
0
0
2
2
1
0
2
0
0
2
0
3
0
0
1
0
1
0
2
0
0
2
0
0
0
2
0
3
0
2
0
0
1
2
0
0
2
0
0
0
2
3
0
2
2
0
0
2
1
2
1
0
1
0
1
0
1
0
3
1
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
1
0
0
2
2
1
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
1
1
0
2
0
0
0
1
1
2
0
0
2
0
2
1
0
3
2
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
2
0
2
0
1
1
1
2
2
0
1
0
0
2
1
0
1
2
0
1
1
1
1
0
0
0
1
0
3
1
1
0
0
0
0
1
0
3
2
0
1
2
2
0
1
0
0
0
1
0
0
0
1
1
2
0
0
0
1
1
0
0
0
0
2
0
2
0
0
2
0
1
1
1
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
1
1
0
0
2
0
1
2
0
1
0
1
0
0
3
2
4
0
0
2
1
2
0
0
1
0
0
2
0
0
0
1
0
1
0
3
1
0
0
7
3
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
2
1
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
1
0
0
1
2
0
1
2
2
0
0
2
0
0
0
1
0
0
2
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
2
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
1
2
1
0
0
1
0
0
0
1
0
0
1
0
2
1
1
0
0
0
0
2
0
0
1
1
1
0
0
0
2
0
0
2
2
1
0
1
0
2
2
0
0
4
1
1
0
0
1
1
0
0
0
0
2
0
1
1
0
1
0
2
0
2
0
0
0
0
1
0
0
1
2
0
1
2
0
2
0
2
3
0
2
0
2
0
2
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
2
2
0
1
2
1
0
0
1
0
2
3
1
2
1
0
2
2
0
1
0
1
0
0
0
0
0
1
2
2
0
1
0
0
0
0
1
0
1
1
2
0
0
0
0
1
0
2
1
1
0
0
0
1
0
0
1
0
1
1
0
2
1
2
0
0
0
2
0
0
1
0
1
2
2
0
0
1
1
0
0
0
1
0
0
2
1
1
2
0
0
1
0
1
0
0
1
0
0
0
1
1
1
0
2
2
1
1
2
0
2
0
0
0
1
0
1
0
0
0
0
3
0
2
0
0
2
0
0
0
2
1
0
1
5
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
2
0
1
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
2
2
1
2
0
1
0
3
0
0
1
0
0
0
0
0
0
0
2
1
0
0
2
0
2
1
0
0
0
0
0
0
1
2
0
0
0
1
0
0
1
0
1
2
0
1
0
0
1
2
0
0
0
0
0
0
2
0
0
0
2
0
2
1
0
1
2
0
0
2
2
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
3
2
0
0
1
0
0
0
0
2
0
0
0
1
1
0
2
0
1
0
0
1
1
0
2
0
1
2
0
2
1
0
1
1
0
0
2
0
2
0
0
0
0
2
1
2
0
2
2
0
0
1
1
1
1
1
1
1
0
0
0
1
0
0
2
1
0
0
2
0
0
2
2
1
0
0
0
0
0
1
1
2
2
0
0
1
0
0
2
0
1
0
1
2
1
0
2
0
2
0
2
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
1
1
0
0
2
0
2
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
2
1
0
0
2
0
0
2
1
1
1
1
0
1
2
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
2
1
0
0
2
0
1
0
1
2
1
2
3
0
0
0
2
1
2
1
0
0
2
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
2
0
1
0
0
1
0
0
0
0
1
2
2
0
0
0
0
1
0
2
0
2
0
0
2
2
1
1
1
0
2
0
2
0
0
0
0
0
0
0
0
0
3
0
2
1
1
0
1
1
0
0
1
0
0
1
2
1
0
1
3
1
0
0
0
0
1
0
2
1
2
1
0
2
1
0
0
0
0
2
0
0
2
0
2
1
0
1
0
2
0
0
1
0
0
2
1
0
1
0
0
0
0
1
1
2
0
0
1
0
1
1
0
2
1
2
0
0
0
0
0
0
2
1
2
0
0
2
1
2
1
2
2
0
2
0
0
0
0
2
2
1
0
0
0
2
0
0
0
2
3
0
2
1
0
2
0
2
0
0
0
1
0
0
0
1
2
0
2
0
0
2
0
0
1
0
0
0
0
1
2
0
0
0
2
1
0
0
0
2
0
2
0
2
0
0
0
1
0
0
1
0
0
0
0
3
0
0
0
0
0
0
1
0
0
1
0
1
1
0
3
0
0
1
3
2
1
0
0
1
1
1
2
0
0
0
2
0
0
1
0
2
0
1
0
1
0
1
1
0
1
0
1
1
1
0
0
0
1
0
0
0
1
0
1
2
0
0
0
1
0
2
0
0
2
0
2
1
2
0
1
0
0
0
1
0
0
1
1
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
2
1
0
1
0
0
1
1
1
0
1
1
0
0
3
1
0
0
1
1
0
1
0
0
0
2
2
0
1
0
1
0
0
0
0
1
0
2
0
0
0
1
0
1
0
1
0
0
0
0
1
0
2
2
1
1
0
2
0
0
0
0
0
0
2
1
2
0
3
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
2
0
0
0
0
2
1
0
0
2
1
0
0
2
0
0
0
0
0
1
0
1
0
0
0
1
0
1
2
0
2
1
1
2
2
1
1
2
2
1
2
0
1
0
1
1
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
2
0
0
2
2
0
2
0
0
0
0
1
2
1
0
2
0
0
1
0
0
1
2
2
0
0
2
0
0
0
0
0
1
0
2
0
0
1
1
0
2
1
0
0
2
2
0
0
0
0
1
2
2
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
1
0
1
0
0
1
0
0
0
2
2
0
2
0
2
0
0
0
0
4
1
1
2
1
1
0
0
0
2
1
1
1
0
1
2
0
0
0
2
2
0
2
2
1
1
1
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
1
2
0
3
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
1
1
2
2
0
0
1
0
2
1
2
0
1
2
0
1
0
1
1
0
1
0
2
1
0
1
0
0
2
1
2
1
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
4
0
2
0
0
13
0
0
0
0
1
1
1
3
1
1
0
2
0
0
0
1
2
1
1
0
0
0
1
2
1
0
2
0
0
0
1
1
0
0
0
0
1
2
1
1
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
2
2
1
2
0
0
2
1
1
0
0
2
3
1
0
0
0
1
1
2
0
0
0
2
1
0
0
0
0
0
0
0
1
1
0
2
0
1
2
1
1
1
0
0
2
2
1
2
0
1
2
2
0
1
2
2
2
1
2
0
2
1
0
1
0
0
0
1
0
2
2
0
1
1
2
0
0
0
1
1
0
1
0
2
0
0
0
1
0
1
2
0
0
0
0
2
1
2
2
0
2
1
1
1
0
0
1
2
0
0
0
5
0
0
1
1
2
2
0
2
2
2
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
1
1
2
2
2
0
1
2
0
2
1
0
0
2
1
1
0
2
0
1
0
0
0
0
4
1
1
0
0
0
0
0
1
2
1
0
1
0
1
0
2
0
0
0
0
0
0
2
1
2
1
0
0
2
2
1
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
2
2
2
2
0
0
2
0
2
1
2
2
2
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
1
0
2
0
0
1
0
0
1
0
1
1
0
0
0
2
0
0
0
0
1
0
2
0
1
1
0
0
0
0
0
1
0
1
2
0
1
0
1
2
1
2
0
0
1
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
1
0
2
3
0
0
1
0
1
1
1
2
1
2
0
0
1
2
0
0
2
1
0
1
1
2
1
0
1
0
1
0
0
0
1
0
1
0
2
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
3
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
3
0
2
0
1
1
2
2
1
0
0
0
0
2
0
2
0
1
0
2
1
1
0
0
0
2
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
2
2
0
0
0
2
0
0
0
0
0
1
1
0
0
2
0
0
0
1
0
2
0
0
0
0
1
0
1
2
0
2
0
2
1
1
0
4
1
0
0
0
0
0
2
2
0
0
2
0
0
1
2
1
0
2
1
4
2
0
1
1
2
1
1
2
0
3
2
2
1
0
1
0
0
0
0
0
1
0
2
0
0
0
2
2
0
0
0
0
0
1
0
1
2
2
2
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
2
0
0
0
0
0
0
1
0
0
2
0
1
0
2
0
1
0
0
0
0
0
0
2
0
1
0
0
1
2
2
1
2
0
2
0
0
0
0
3
0
0
0
0
1
0
0
1
0
0
2
0
0
1
0
2
1
0
2
2
0
0
0
2
0
2
2
1
1
0
0
0
1
0
0
0
2
0
1
0
0
1
0
0
0
1
0
2
1
1
0
0
0
0
0
0
2
0
2
0
0
1
0
1
1
0
2
1
1
1
0
0
0
0
0
2
0
0
0
0
0
1
1
1
1
1
0
0
1
2
0
2
0
2
2
0
0
1
0
0
0
0
2
2
2
1
2
2
0
0
0
0
0
2
2
0
0
0
0
1
0
0
1
1
1
0
2
0
1
1
0
0
0
0
1
0
2
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
1
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
4
2
1
0
0
0
0
1
0
1
0
2
2
0
1
0
0
0
1
0
2
0
0
2
0
0
0
1
0
0
0
0
0
2
0
1
1
2
1
0
0
1
1
2
2
0
0
0
0
0
1
2
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
1
0
0
0
2
1
0
0
1
0
1
1
2
0
0
0
2
1
2
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
2
1
2
0
0
0
1
0
0
2
2
0
1
0
1
2
0
0
0
0
1
0
1
0
0
1
2
0
0
1
2
0
2
2
0
1
1
2
0
0
1
0
1
0
2
2
0
0
2
0
1
1
2
0
1
1
0
0
1
0
0
0
2
0
0
0
0
0
1
1
0
0
0
1
1
2
0
1
2
2
0
1
0
0
3
2
0
1
1
3
2
0
0
0
0
0
1
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
1
1
1
0
0
0
0
1
0
2
0
0
0
0
0
0
2
2
2
1
1
0
0
1
0
2
0
1
2
0
1
1
0
0
0
2
0
0
1
0
1
0
0
2
2
0
2
0
0
2
1
0
0
0
1
2
0
0
2
2
0
0
0
1
0
1
0
0
0
0
0
0
2
2
0
2
3
0
0
0
2
1
0
2
2
1
2
2
1
2
0
1
2
1
2
0
0
1
0
2
0
1
0
2
0
0
0
0
0
1
1
0
2
5
2
2
5
0
0
0
1
1
0
1
1
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
2
2
2
0
2
1
3
1
1
1
0
0
1
0
1
4
2
2
3
2
0
0
0
0
0
0
2
1
2
0
1
1
0
0
2
0
2
0
0
0
0
1
2
0
0
3
1
0
1
1
1
2
0
0
0
0
0
0
2
2
2
2
0
2
1
1
0
0
1
0
0
2
0
0
0
0
3
0
0
0
1
0
0
0
2
0
1
0
0
1
1
0
2
1
2
0
1
0
2
0
1
0
0
0
1
2
2
0
0
1
0
2
0
0
1
1
0
1
2
0
0
1
0
0
2
0
1
1
1
0
1
0
1
1
0
1
0
0
1
2
1
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
1
1
1
1
0
0
1
1
0
0
1
0
2
2
0
0
1
0
0
2
1
1
0
0
0
1
2
0
2
0
2
0
0
0
1
0
2
1
1
0
0
0
0
1
0
1
0
2
0
0
0
1
1
1
0
0
2
0
0
0
0
0
0
1
2
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
1
1
0
1
2
0
0
2
0
1
2
0
2
1
0
2
0
2
0
0
0
2
0
0
0
2
0
0
1
2
0
1
1
0
0
0
2
1
0
2
0
0
0
0
2
2
0
2
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
1
0
1
1
2
0
1
0
2
0
1
2
0
1
0
1
0
0
0
2
0
0
1
0
0
2
1
0
0
2
1
0
0
2
0
0
2
0
0
1
1
2
1
0
0
0
2
0
0
0
0
2
0
0
2
3
0
0
2
8
1
0
0
0
0
1
0
1
0
0
0
2
1
0
0
0
2
0
0
2
0
1
0
1
2
1
0
1
3
0
1
0
0
1
1
0
0
0
0
0
2
0
2
2
0
1
0
0
0
0
0
0
0
2
0
2
0
1
0
2
2
0
0
0
0
2
1
0
0
0
2
1
1
0
1
2
0
0
1
2
0
0
0
3
2
0
0
0
0
0
2
3
0
0
0
3
2
2
0
1
1
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
3
0
0
0
1
2
0
0
0
0
1
2
0
1
1
1
2
1
2
1
0
1
1
2
2
0
0
1
0
0
2
0
2
0
1
0
0
0
0
1
0
0
2
2
0
1
0
0
2
0
0
0
1
0
0
3
0
1
0
2
0
0
0
2
0
2
1
0
0
1
0
1
0
0
4
2
0
1
0
1
0
1
1
0
2
2
2
0
2
0
0
0
0
0
1
2
1
0
0
0
0
2
0
0
0
0
0
0
2
0
1
2
0
2
0
1
0
0
4
1
2
0
0
0
0
0
0
0
1
1
1
2
1
0
0
0
1
0
0
1
1
1
0
1
2
1
1
0
0
0
0
0
3
0
2
1
2
2
2
1
3
0
1
2
1
2
0
0
0
1
0
0
0
2
2
1
0
1
0
1
0
1
0
1
0
1
0
2
1
0
1
2
1
0
0
0
0
0
0
1
0
0
0
2
0
1
1
0
0
0
0
0
0
1
1
1
0
0
2
1
2
0
2
0
0
0
0
1
1
1
0
0
0
0
0
2
0
2
0
0
0
3
2
0
1
0
0
0
0
0
0
0
4
0
0
0
1
0
0
1
1
2
0
0
0
1
1
1
1
2
2
0
0
1
0
0
0
0
0
2
0
0
0
1
2
1
1
0
0
1
0
0
0
0
0
1
1
2
0
1
2
2
2
0
0
0
0
0
3
1
0
0
0
0
0
0
3
1
1
0
2
2
1
0
0
3
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
1
0
2
1
0
0
6
0
1
0
0
0
1
2
0
0
0
2
0
0
0
2
2
2
0
2
0
2
2
0
1
0
0
1
0
0
1
0
2
0
0
2
2
2
0
0
0
1
2
0
2
2
0
1
3
2
2
1
2
1
2
1
0
0
2
0
2
2
0
2
2
2
1
0
0
2
0
1
0
0
0
0
1
0
0
1
0
2
3
0
1
0
0
0
0
1
0
0
0
2
0
0
2
2
0
0
1
1
1
0
1
2
1
0
0
0
2
2
1
1
0
0
0
0
2
2
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
1
1
0
0
0
0
0
0
1
2
0
0
0
0
0
3
0
2
1
0
0
0
0
0
2
0
1
0
0
0
2
1
0
0
1
1
0
0
0
0
0
1
4
1
0
0
1
0
0
0
0
2
0
2
2
1
0
0
2
2
0
1
1
1
0
1
1
0
0
1
1
1
0
0
0
0
0
0
1
2
2
2
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
1
0
1
2
0
1
0
1
2
2
2
0
1
0
0
2
2
1
2
0
0
0
2
0
3
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
1
0
0
0
1
0
0
1
0
2
2
0
0
0
0
0
0
1
1
3
0
1
0
0
0
1
1
2
0
0
2
0
1
0
0
0
1
0
0
1
0
0
2
1
0
0
1
2
0
2
1
3
1
0
0
2
0
0
2
0
0
1
0
4
0
0
2
0
1
1
0
0
3
0
0
1
0
2
2
0
0
2
2
1
1
0
0
1
0
2
0
1
0
2
2
2
2
2
0
0
0
2
0
0
0
0
0
2
2
0
1
1
1
1
1
0
2
1
0
0
1
2
0
0
1
4
0
2
0
0
2
0
1
1
0
1
0
3
1
0
2
1
0
2
1
0
0
2
2
0
2
0
1
0
1
0
2
1
0
0
1
0
0
0
0
2
1
0
0
0
1
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
1
0
0
1
1
2
0
1
0
2
2
2
0
0
0
2
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
1
1
0
2
0
1
0
1
0
0
0
0
0
0
0
2
0
1
2
0
2
0
0
0
0
0
0
0
2
2
1
1
1
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
2
0
2
0
0
0
0
0
1
1
0
1
0
0
2
1
0
0
0
1
1
2
0
0
2
1
2
1
2
1
1
0
2
0
2
3
2
2
0
0
1
0
1
1
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
2
1
1
2
0
1
0
2
2
0
0
0
1
0
2
0
1
2
0
2
0
0
2
1
1
1
0
2
0
0
0
0
0
0
1
0
0
2
1
0
1
0
1
2
1
0
0
0
0
0
2
0
2
2
1
0
0
2
1
0
2
0
0
2
1
0
0
2
2
0
0
3
1
0
1
0
2
0
0
0
2
3
0
0
0
2
0
2
0
0
1
1
1
1
0
0
0
0
1
0
0
1
0
1
1
0
2
2
0
1
1
2
0
0
0
1
0
0
0
0
0
1
2
1
0
4
0
1
0
0
1
0
2
0
0
0
2
2
1
0
0
1
0
1
0
0
0
2
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
2
0
0
2
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
2
1
0
1
0
2
2
1
0
0
1
0
0
0
0
0
0
1
0
2
0
2
0
0
0
1
2
1
0
2
2
0
0
2
4
0
1
0
1
1
0
0
0
1
0
0
0
0
2
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
1
2
1
0
1
1
0
1
0
0
0
0
2
0
0
0
1
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
1
1
2
1
1
1
0
0
0
1
2
2
0
0
0
0
2
0
1
0
0
1
0
2
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
1
1
0
1
2
0
0
0
0
1
2
2
0
0
1
0
0
0
0
0
2
0
0
0
0
1
2
0
0
2
1
0
0
2
0
0
0
1
0
0
0
0
2
0
1
1
2
0
0
2
2
0
1
1
0
1
0
1
0
0
2
0
0
0
0
0
0
2
0
1
0
2
0
2
2
0
2
0
1
1
0
0
0
0
0
1
2
1
0
0
0
0
1
0
0
0
2
0
1
0
0
2
1
0
0
2
1
1
0
2
1
0
0
0
1
0
0
0
1
0
1
2
1
2
0
2
1
1
2
0
0
0
0
0
1
1
0
2
0
3
1
0
1
1
0
1
2
0
0
0
0
0
1
2
0
0
0
1
0
0
2
0
0
0
2
0
0
1
0
2
2
2
0
1
1
1
0
2
0
2
0
1
0
0
0
2
0
1
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
2
0
2
0
0
0
1
0
1
1
0
1
1
1
2
0
1
2
2
0
0
0
0
1
0
0
2
0
0
0
2
1
0
0
1
1
0
0
2
0
2
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
2
0
3
4
0
1
0
0
1
0
0
0
1
2
0
1
0
2
0
0
2
0
0
0
0
0
2
2
2
0
0
0
0
0
2
0
1
0
0
0
0
0
5
0
0
1
0
0
0
0
2
3
1
1
0
2
0
1
0
0
0
0
0
3
2
0
1
0
2
1
0
0
0
0
0
2
0
3
0
0
0
1
2
1
0
0
1
1
2
0
2
0
2
0
0
0
1
0
1
0
0
0
0
0
1
0
2
1
0
0
0
1
3
0
0
0
1
0
1
1
0
0
0
0
0
0
2
0
2
2
2
0
0
1
0
0
2
2
0
0
0
0
0
0
1
0
1
0
1
0
2
2
0
0
0
0
2
0
0
1
1
0
1
3
0
0
1
0
2
0
2
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
1
1
2
0
1
0
0
0
0
1
1
1
0
0
1
6
0
0
2
2
0
2
0
2
1
1
0
0
1
1
0
2
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
3
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
1
1
0
1
0
0
0
0
0
0
1
0
1
0
2
0
1
0
2
0
0
0
1
0
2
0
0
1
0
1
3
0
0
0
0
0
0
1
1
2
2
0
1
2
2
0
0
0
0
0
0
1
0
0
1
0
1
0
2
1
0
0
2
2
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
1
2
0
0
2
0
0
0
0
0
0
0
1
0
2
2
0
0
0
1
0
0
1
0
0
0
0
3
0
0
0
2
2
0
0
1
0
1
0
0
1
0
0
0
0
2
0
0
1
0
1
0
0
1
4
0
0
0
1
1
1
2
0
0
1
0
0
0
0
0
0
1
0
1
1
1
1
2
0
0
0
2
1
2
0
0
0
0
2
0
0
0
1
0
0
0
1
1
0
2
1
0
0
0
0
2
2
0
1
1
2
0
0
0
0
1
2
0
0
2
1
1
0
0
0
0
2
2
1
0
0
0
0
2
0
0
2
0
0
2
2
0
2
1
2
1
1
1
1
1
0
0
1
0
1
0
3
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
1
3
0
0
1
0
9
2
1
0
2
0
0
1
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
2
2
2
0
1
0
1
0
0
0
0
0
1
2
0
0
2
0
2
2
0
1
0
0
0
1
0
0
0
0
0
3
0
0
2
0
0
0
2
2
0
0
0
0
1
1
1
0
0
1
1
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
1
2
2
2
0
0
0
1
1
1
1
2
2
1
2
0
0
2
2
0
0
1
2
1
0
0
0
0
0
0
1
0
0
3
0
0
1
0
2
0
0
0
1
1
3
1
0
0
1
2
1
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
2
0
3
0
0
1
1
1
0
0
0
0
0
0
1
1
1
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
2
1
1
0
0
0
1
2
0
1
0
0
0
1
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
1
2
0
2
2
0
0
2
0
0
1
1
0
0
2
0
1
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
2
2
2
1
0
0
0
0
0
2
0
0
0
3
1
0
0
0
0
2
1
0
2
0
0
0
2
1
1
2
0
0
0
0
0
0
0
0
0
1
2
2
1
1
3
0
0
0
2
0
0
1
2
0
1
0
3
0
1
0
2
0
0
2
0
0
0
1
0
1
0
0
1
0
0
2
0
0
0
2
1
0
3
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
2
2
0
0
0
0
0
0
1
0
0
2
0
0
1
0
2
1
0
1
0
2
0
0
2
0
2
0
0
0
0
3
0
0
1
1
1
0
0
2
0
2
2
0
0
0
1
0
1
0
0
2
0
0
2
0
0
0
2
0
1
0
1
0
0
1
1
0
1
0
0
1
0
1
1
2
2
2
2
0
0
1
0
1
0
1
0
0
1
2
0
3
0
1
0
0
0
1
2
0
0
1
0
0
1
2
1
0
0
1
0
1
0
1
1
2
2
1
1
0
3
0
0
1
0
1
0
0
0
0
1
0
2
1
0
0
2
0
0
0
0
2
2
0
1
1
0
1
1
0
2
0
0
1
0
2
0
0
2
0
0
0
0
0
0
1
1
0
0
1
0
2
3
1
0
0
0
2
0
0
0
0
0
2
1
1
2
0
2
0
1
0
0
1
0
2
2
1
1
0
0
1
2
0
0
1
0
0
1
2
0
1
0
0
0
2
2
0
1
0
1
0
0
0
0
1
1
0
2
0
3
0
2
0
0
1
1
2
0
0
0
0
0
1
0
0
1
2
1
0
0
2
0
0
0
0
1
0
0
0
0
0
2
3
0
1
1
0
1
2
0
0
1
1
0
0
1
2
0
1
0
2
1
0
0
0
1
2
2
1
0
0
2
0
5
1
1
0
0
2
0
0
0
0
2
1
0
0
0
0
0
2
0
0
2
0
0
0
1
0
2
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
1
0
0
1
1
0
2
1
1
1
0
1
0
0
2
1
2
3
2
0
2
2
0
0
0
0
0
0
0
2
0
0
1
0
2
2
1
0
0
0
0
0
1
2
1
1
2
2
1
0
0
0
0
0
0
0
0
2
1
1
2
0
2
1
0
0
0
1
0
2
0
2
2
0
0
2
2
1
0
0
2
1
0
0
2
2
2
0
1
1
1
0
0
0
1
2
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
1
0
1
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
2
2
2
0
2
2
1
1
0
1
0
0
0
0
0
0
2
2
0
1
1
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
2
1
0
2
0
0
0
0
1
0
0
0
2
2
0
0
0
0
1
1
1
3
0
0
0
1
0
0
0
4
0
0
0
0
1
1
0
1
2
0
0
1
0
2
0
2
2
2
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
2
0
1
0
0
0
0
1
1
2
1
0
0
0
0
0
2
0
1
0
2
0
1
1
1
1
0
0
1
0
2
0
0
2
0
3
0
1
1
0
1
1
2
0
1
1
2
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
1
3
0
1
0
2
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
3
2
2
0
2
1
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
1
0
3
0
0
1
0
1
0
0
1
1
2
1
0
0
2
0
1
0
0
0
2
0
3
1
2
0
2
0
0
0
1
0
0
2
0
2
0
0
0
1
0
0
1
0
1
1
2
0
0
0
1
0
2
2
0
0
0
2
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
2
0
0
1
0
2
0
2
0
0
2
2
2
1
0
0
2
2
2
0
1
1
0
2
0
2
1
0
1
0
0
0
1
0
2
2
0
0
1
1
1
0
2
2
2
0
0
0
0
0
1
0
0
1
1
1
0
1
0
0
0
0
0
0
2
0
1
0
1
1
1
1
0
0
0
1
0
0
1
0
1
1
0
0
0
0
2
0
0
0
0
1
0
2
1
2
0
2
1
2
2
0
0
2
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
2
2
0
0
0
0
1
1
1
0
2
2
1
0
0
1
1
0
2
1
0
3
0
0
0
1
2
2
2
0
0
1
1
0
1
1
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
2
3
0
1
1
0
0
0
0
0
0
1
2
0
0
2
0
1
0
0
0
0
0
1
1
0
0
1
2
0
5
0
1
0
0
2
0
0
2
1
0
1
0
1
0
0
0
2
2
2
1
0
1
0
0
0
0
0
1
0
0
1
2
0
1
1
0
2
0
0
2
1
0
0
0
1
1
1
1
0
0
4
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
2
1
0
0
0
0
0
0
2
0
1
1
1
0
0
0
0
0
2
1
0
0
0
0
1
1
0
0
0
3
0
1
0
0
3
1
0
0
0
0
1
3
2
0
0
0
2
1
1
1
0
0
2
0
0
0
1
1
0
0
0
0
0
1
0
1
2
0
0
1
2
2
0
0
0
0
0
0
0
0
0
2
1
1
1
0
0
1
2
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
1
2
0
2
2
0
0
0
0
0
1
1
0
0
1
1
0
1
1
0
0
2
0
0
0
0
2
0
0
1
1
0
0
1
0
1
0
0
0
2
0
2
0
0
2
0
2
0
2
2
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
2
0
1
1
0
0
0
0
0
2
0
0
3
0
0
3
0
4
0
0
1
0
2
0
0
1
0
0
1
0
0
0
1
0
1
0
1
2
1
0
0
0
0
0
0
0
1
0
1
0
0
0
2
2
1
2
1
0
0
0
2
0
0
0
2
0
2
2
1
3
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
1
1
0
0
2
1
0
0
0
0
1
1
0
3
0
0
0
0
1
0
0
0
2
2
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
2
1
2
1
2
2
0
0
0
1
1
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
1
0
0
0
1
2
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
1
2
1
0
0
0
2
0
2
2
1
0
0
2
0
0
0
1
0
2
0
0
1
2
1
0
0
1
0
0
0
0
2
0
2
0
1
0
2
0
2
2
0
2
2
2
2
0
0
1
2
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
2
0
1
0
1
0
2
2
1
0
1
0
0
0
1
2
0
1
0
1
0
1
0
0
1
0
2
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
2
0
0
2
2
0
1
0
0
1
0
2
0
2
0
0
0
0
1
1
0
0
0
2
0
0
1
0
0
0
0
0
0
2
2
2
1
0
2
2
0
0
1
0
0
0
0
0
0
1
1
0
2
1
0
0
0
1
0
1
5
0
1
1
1
3
2
1
1
0
0
2
0
0
0
0
0
2
1
0
0
0
0
2
0
1
0
1
0
1
0
1
2
2
1
0
1
0
2
0
2
0
1
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
1
2
0
0
2
0
1
2
1
0
1
0
0
2
1
0
2
1
1
0
1
2
0
0
0
0
2
0
0
0
1
1
0
0
0
0
1
1
0
2
1
2
2
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
2
0
1
0
0
1
0
1
2
0
0
0
0
0
1
0
1
2
0
1
2
0
0
1
0
1
1
1
1
0
0
2
0
0
0
3
2
1
0
1
0
2
1
2
5
0
2
0
0
2
1
0
1
8
0
0
2
1
0
0
0
0
0
0
2
0
1
1
0
0
0
0
2
2
1
0
0
0
0
2
0
1
1
0
0
1
0
2
0
0
1
0
0
2
2
2
1
1
1
0
1
0
2
0
0
1
0
0
2
0
0
0
0
2
0
2
0
1
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
2
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
2
2
0
1
0
1
1
0
0
2
0
2
0
1
0
1
2
0
0
0
3
1
2
0
2
0
0
0
2
2
1
1
1
3
0
0
1
0
1
0
2
2
2
1
1
2
0
2
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
2
0
1
0
0
1
2
0
0
0
1
0
0
0
0
3
0
1
0
0
0
0
0
1
0
1
2
0
0
2
0
2
2
2
0
0
2
0
0
0
0
0
0
1
0
0
3
0
1
2
0
1
0
0
1
1
0
1
1
2
0
0
0
2
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
1
0
1
0
0
1
1
0
1
1
0
2
0
1
0
3
0
1
2
1
0
0
1
2
0
0
0
0
1
0
2
0
1
1
0
0
1
0
2
1
0
0
0
2
1
2
0
1
2
0
0
0
0
2
1
2
1
0
0
1
0
0
2
0
0
2
0
0
0
0
1
0
2
1
0
0
1
3
2
1
1
0
1
2
1
0
2
2
0
0
0
0
1
0
0
0
2
0
0
2
2
0
0
0
0
1
0
2
0
0
0
0
0
2
1
2
0
0
0
1
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
1
2
1
1
0
0
0
2
0
2
0
0
2
0
0
2
1
0
1
1
1
0
3
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
2
0
0
0
2
0
1
0
2
2
0
0
1
0
1
1
1
0
1
0
0
1
1
1
0
0
1
0
1
1
1
0
2
0
0
2
1
0
0
2
1
0
1
0
0
3
0
2
0
0
1
2
0
1
2
0
0
0
1
0
0
2
1
1
0
0
2
0
1
0
0
1
0
2
0
1
2
0
1
0
0
2
1
0
0
0
0
0
4
1
0
0
0
0
1
1
1
0
0
2
0
0
0
0
0
0
2
0
3
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
1
2
0
2
0
2
0
0
0
0
0
2
0
3
0
0
0
1
0
1
0
1
2
1
0
1
2
2
0
0
0
0
2
1
0
1
1
0
1
2
2
0
3
0
0
0
0
1
0
1
0
0
0
0
0
0
1
2
15
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
3
0
0
2
0
1
0
1
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
1
2
0
1
0
0
0
2
0
1
0
1
0
0
0
1
1
0
2
2
0
0
1
0
0
1
1
0
0
6
0
2
0
3
1
0
0
0
1
0
0
2
0
0
1
1
2
0
2
0
0
0
0
0
1
2
1
2
0
0
0
2
0
0
0
1
0
2
1
2
1
0
1
2
0
1
0
0
0
0
0
0
2
0
2
2
2
0
2
2
0
1
1
0
1
0
0
2
2
0
1
2
0
2
2
1
0
0
0
0
2
0
0
2
2
1
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
1
0
3
0
3
2
1
0
0
0
0
2
1
1
0
0
1
1
2
0
0
1
0
2
0
2
0
0
0
0
0
4
0
0
1
0
0
1
2
0
0
0
0
0
0
1
0
1
0
3
0
0
0
0
0
0
2
1
0
3
0
1
0
0
0
0
1
0
0
1
0
1
1
0
0
1
2
0
2
2
0
0
3
0
1
2
0
1
1
0
0
1
3
1
0
1
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
2
0
0
1
3
1
0
2
0
2
0
1
0
1
2
0
0
2
2
0
0
2
1
2
0
1
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
2
0
4
0
0
0
1
2
0
2
0
0
2
0
0
0
0
2
0
0
2
1
0
0
2
0
0
0
1
0
1
0
1
0
0
0
1
1
1
0
2
0
1
2
0
0
0
0
2
0
0
1
0
0
0
0
0
1
1
0
0
1
2
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
2
1
1
0
0
1
0
0
0
1
1
1
0
1
1
3
1
1
2
1
0
0
1
1
0
5
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
2
0
2
0
0
1
0
0
0
2
0
1
0
1
1
1
2
0
2
1
0
0
1
0
2
0
0
2
2
3
0
0
0
1
0
0
0
1
1
0
0
1
0
2
0
0
0
0
1
0
0
0
0
1
0
1
0
2
1
0
0
0
0
0
0
1
1
0
0
0
0
0
2
6
1
0
1
2
1
2
0
0
0
0
2
0
0
0
1
3
0
0
1
0
2
0
2
0
0
0
0
2
1
1
2
0
0
2
1
2
0
0
1
1
2
2
1
2
1
1
0
2
0
2
0
0
0
2
2
0
0
0
1
3
0
1
0
0
1
1
1
0
2
0
0
0
0
1
0
1
0
1
0
1
2
1
0
1
0
1
0
2
2
1
2
1
0
1
0
1
1
1
0
0
1
2
0
0
0
2
0
0
2
0
0
0
0
1
0
1
2
0
1
0
0
0
0
0
0
2
0
1
0
2
1
0
0
0
1
0
0
1
1
1
2
2
1
0
2
0
0
0
0
0
2
0
1
0
5
0
1
0
0
3
0
0
0
2
0
0
2
2
0
0
0
1
0
0
1
0
2
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
2
0
1
1
2
0
0
2
0
0
0
1
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
2
0
1
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
1
0
1
0
2
0
2
2
0
2
2
0
0
0
0
0
2
0
0
1
1
0
2
0
0
1
0
0
0
0
1
0
2
2
1
1
1
0
0
2
0
0
0
0
0
0
1
1
0
0
2
0
2
0
0
0
0
0
0
1
2
0
1
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
1
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
1
0
1
0
0
1
3
1
0
0
0
2
1
0
0
0
2
1
0
1
1
0
0
0
0
0
0
1
1
0
1
0
0
0
1
1
0
4
2
2
1
0
0
0
2
1
1
1
1
0
2
0
0
1
2
0
0
2
2
0
0
0
0
0
0
0
1
3
2
1
0
1
0
2
2
1
2
0
1
0
0
1
0
2
2
0
1
0
0
0
0
1
0
2
0
0
0
2
0
0
1
0
1
1
1
1
0
0
0
1
2
0
0
1
0
1
1
1
2
3
0
0
0
2
2
0
0
0
0
2
0
0
1
0
0
2
3
0
3
5
0
1
0
1
2
6
0
0
0
0
0
2
2
2
1
0
0
2
0
0
1
1
0
1
0
0
0
2
0
0
1
0
1
0
0
0
2
0
2
1
0
1
0
1
0
0
0
1
0
0
0
0
2
1
0
2
0
0
1
2
0
0
1
1
0
2
0
1
0
1
0
2
1
1
0
0
2
0
0
0
2
2
2
2
2
1
0
0
2
2
0
0
0
0
0
0
2
2
0
0
2
0
1
1
0
1
0
0
1
0
0
1
1
0
2
1
0
2
0
1
0
0
6
0
2
0
2
1
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
2
2
0
2
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
3
0
2
2
0
0
1
0
0
2
1
0
0
0
3
0
2
2
1
2
1
0
0
0
0
1
0
0
2
0
2
1
2
0
1
2
0
0
0
2
1
0
1
0
2
0
0
2
2
0
0
0
2
0
0
0
0
1
2
2
0
0
0
1
0
3
2
0
1
0
1
0
0
1
0
0
0
2
2
0
0
0
2
1
0
2
1
0
1
0
0
0
1
0
1
0
1
1
1
0
0
1
0
0
0
2
1
2
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
1
0
0
1
1
2
2
4
0
0
2
2
0
0
1
1
0
2
0
1
0
0
0
0
0
1
0
3
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
1
0
0
0
1
0
0
2
0
2
1
1
2
0
1
0
2
1
0
1
1
0
0
1
0
1
0
0
0
4
0
1
3
2
0
0
2
0
0
1
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
1
1
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
1
2
0
0
0
0
2
0
2
2
1
0
0
1
2
1
2
0
0
0
0
1
0
1
2
0
0
0
1
0
0
2
0
0
0
0
0
0
1
2
1
0
0
1
0
1
2
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
1
0
2
0
1
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
1
0
1
1
0
0
2
0
0
1
0
2
1
1
0
1
0
2
0
1
0
0
0
0
1
0
1
2
1
0
0
0
2
1
0
2
1
0
0
0
0
3
0
1
0
2
0
0
2
0
1
1
1
0
1
2
0
0
0
0
3
0
0
2
2
0
2
0
1
0
2
0
2
1
1
2
0
0
1
1
3
2
0
1
0
0
1
1
1
0
2
0
0
1
1
0
1
0
1
0
1
1
0
0
0
0
1
0
2
0
1
2
1
1
0
0
0
0
2
1
0
2
0
1
0
0
0
0
0
1
0
2
0
0
4
0
0
0
2
0
2
2
0
0
0
0
1
2
1
2
2
1
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
1
0
1
0
0
2
3
2
0
0
4
0
6
1
2
0
0
2
2
1
0
2
0
0
0
0
1
2
0
0
7
0
2
0
3
0
0
2
0
0
0
0
0
0
0
2
1
0
0
1
0
3
1
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
1
1
1
0
0
0
1
0
1
0
0
1
0
1
0
3
3
0
1
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
2
1
1
0
0
0
1
2
2
0
0
1
0
0
1
0
0
0
1
0
2
0
1
0
0
0
0
0
2
1
0
0
1
0
2
0
2
1
2
0
0
2
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
2
2
4
0
0
0
0
0
2
0
1
2
1
2
1
0
0
0
0
2
2
0
0
0
0
0
0
0
1
1
1
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
1
2
1
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
1
0
0
2
2
1
0
1
1
1
1
3
0
1
0
0
2
2
2
0
1
0
1
0
0
0
0
3
1
1
2
1
0
2
1
1
2
0
1
0
2
0
0
1
1
2
0
1
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
3
0
1
2
1
0
0
0
0
0
2
2
0
0
0
2
2
0
0
0
0
3
0
0
1
0
0
0
2
0
1
0
2
0
2
0
0
1
1
2
3
0
1
1
0
1
0
0
2
2
2
0
0
0
0
0
0
2
0
2
1
1
0
1
0
1
1
2
0
0
0
1
0
0
2
0
0
0
1
1
0
0
4
2
1
1
1
2
0
0
0
2
2
1
0
0
0
0
0
3
2
1
3
0
0
0
0
0
1
0
1
0
0
0
2
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
3
3
0
0
0
0
5
0
1
0
6
0
2
0
2
0
2
0
2
0
0
0
0
0
0
0
2
0
1
1
2
0
1
0
0
2
1
0
0
0
2
0
0
0
1
3
0
1
0
2
1
0
2
0
0
1
2
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
2
1
0
1
2
0
0
0
0
1
0
3
1
0
0
0
0
0
0
0
0
1
0
2
1
0
1
2
1
0
0
2
0
0
0
2
0
2
1
0
0
2
1
0
0
0
2
0
0
0
0
4
1
3
1
2
3
3
1
0
6
2
1
1
0
0
0
0
0
0
0
2
3
1
1
2
0
0
1
0
2
3
0
1
0
0
2
0
1
0
0
0
2
0
0
0
0
1
2
0
0
0
0
1
1
0
2
0
3
0
1
0
0
0
0
0
2
0
1
1
2
0
0
0
0
0
0
0
1
2
1
0
0
0
1
0
0
0
2
0
2
2
2
0
2
1
2
0
2
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
1
3
2
0
2
2
2
1
0
0
1
2
0
0
2
2
1
0
0
0
2
0
0
2
0
1
0
0
1
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
2
1
4
1
0
1
1
1
2
0
2
0
0
0
2
0
0
2
0
1
0
1
1
1
1
0
0
0
0
0
2
0
0
1
0
2
2
0
3
2
0
1
0
1
0
0
0
1
0
0
0
0
2
1
2
0
0
1
0
0
2
0
0
0
1
1
0
1
0
0
0
1
0
0
0
1
1
0
1
0
2
0
0
2
0
2
0
0
0
0
2
0
0
2
3
1
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
1
1
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
2
0
3
3
0
0
0
1
0
0
0
0
2
2
1
0
1
0
0
1
0
0
1
0
1
3
0
0
0
2
0
0
2
1
0
0
0
0
1
0
1
0
2
3
0
0
1
0
0
0
2
3
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
2
0
0
2
1
2
1
0
1
0
0
2
0
0
6
0
0
0
1
2
2
2
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
1
0
2
2
2
1
0
0
0
0
0
3
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
2
2
1
0
0
0
0
2
2
2
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
2
2
0
2
1
0
1
1
2
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
2
0
1
1
0
0
0
2
2
0
0
0
0
2
2
1
0
0
0
1
1
2
2
1
2
2
0
1
0
0
0
3
0
0
0
2
0
0
2
1
2
0
1
0
1
1
1
3
2
1
1
1
0
1
0
0
1
0
0
1
2
2
0
1
0
0
1
2
0
0
2
0
1
0
1
0
0
1
0
1
2
0
1
1
1
0
0
1
0
1
0
2
0
0
0
0
1
0
0
1
1
0
0
2
1
0
2
0
0
4
1
0
0
0
0
0
1
1
2
0
2
0
0
2
0
0
1
0
0
1
0
0
0
2
0
0
2
0
1
2
1
2
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
1
1
0
0
2
0
1
0
1
1
1
0
1
1
0
0
0
2
2
0
0
0
0
0
2
1
0
0
1
0
2
0
0
0
0
0
0
1
2
1
1
0
2
1
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
1
1
0
0
1
0
1
0
1
0
0
0
0
2
1
0
2
0
2
2
0
0
0
2
1
1
1
1
0
1
2
0
1
0
0
1
2
0
0
0
0
0
0
4
1
1
2
0
0
0
1
0
0
4
2
0
2
0
0
1
2
0
0
0
0
0
1
1
1
0
1
0
1
1
0
1
0
3
2
2
2
0
2
0
2
0
0
0
0
1
2
0
0
0
0
2
0
1
0
0
1
0
1
1
0
0
1
1
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
2
1
0
0
0
2
0
0
0
2
2
2
1
2
3
2
1
0
0
0
2
0
0
3
0
0
0
1
0
0
2
0
1
2
0
0
0
0
0
2
1
2
0
0
3
0
2
0
1
0
0
2
2
1
0
0
1
1
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
2
0
0
1
0
2
0
2
0
0
0
2
0
0
2
1
1
0
0
1
2
0
0
1
2
0
1
0
2
0
0
0
0
0
1
0
0
1
1
2
1
0
1
0
0
0
0
1
2
0
1
0
0
1
1
3
0
0
0
0
0
0
0
1
1
2
1
2
0
3
1
1
0
0
0
2
0
2
2
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
2
1
0
2
2
0
0
0
0
0
0
1
4
0
0
0
0
0
3
0
2
0
2
3
0
0
0
1
2
0
2
0
2
0
0
2
0
0
4
3
2
2
2
0
0
0
0
0
0
0
1
2
0
1
1
1
0
0
0
0
0
0
0
2
0
0
0
1
0
1
2
0
2
1
0
0
0
3
0
0
1
0
0
1
0
0
0
0
0
1
2
0
0
2
0
0
0
0
2
0
0
1
2
1
2
0
0
0
2
2
1
0
0
1
1
0
0
0
0
2
1
0
0
2
0
2
1
0
0
0
2
2
0
1
0
2
4
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
2
2
0
0
1
1
0
2
0
0
0
1
2
1
1
0
0
0
0
1
0
0
2
1
2
0
0
1
0
0
2
0
0
1
1
0
0
0
0
0
2
0
0
0
0
1
0
2
0
1
1
0
1
0
1
1
1
0
0
0
0
0
0
0
0
1
0
1
0
2
1
0
0
0
0
1
2
0
3
0
1
2
0
0
0
2
2
0
0
0
0
2
0
1
0
1
0
0
0
0
2
1
0
2
0
0
0
0
0
1
1
1
3
0
0
0
2
0
0
0
0
0
0
0
1
1
1
1
1
1
0
3
2
1
0
1
1
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
3
0
0
2
0
2
2
0
1
1
0
0
0
1
0
2
2
1
2
2
0
0
0
1
0
0
0
0
2
0
0
1
1
0
1
0
0
2
2
0
0
0
0
0
2
0
0
1
0
0
2
2
0
2
0
2
2
2
3
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
1
1
0
1
0
0
2
0
1
0
0
0
0
0
0
0
2
1
2
0
1
0
0
2
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
2
0
1
2
0
1
0
0
0
0
1
0
0
2
0
1
0
3
0
0
2
0
0
1
0
0
1
1
1
0
1
0
0
3
1
0
0
2
0
0
0
1
1
0
0
0
0
0
2
1
0
0
0
0
0
2
0
2
2
0
0
1
1
2
0
2
1
2
2
0
1
2
0
0
0
1
2
0
0
1
1
0
0
0
0
1
0
1
2
0
0
2
0
0
1
0
2
0
0
1
0
1
0
1
0
0
0
0
2
2
2
0
0
0
0
1
2
0
0
2
2
0
3
1
0
1
0
1
0
0
0
2
2
2
0
0
0
1
0
0
0
0
0
0
2
1
0
2
1
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
2
0
0
1
0
0
1
0
0
2
0
1
0
2
2
0
0
0
1
0
0
2
2
0
0
0
1
1
1
0
0
0
2
2
0
0
0
1
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
1
0
0
2
0
1
1
1
2
1
1
0
1
0
1
2
0
0
1
1
0
0
0
2
1
0
0
1
0
2
2
0
0
1
2
2
1
0
1
1
2
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
1
1
0
0
0
0
2
2
0
1
0
0
2
0
2
0
0
2
0
0
0
0
0
2
1
0
2
1
2
0
1
0
2
1
0
0
0
2
0
2
1
2
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
2
3
0
0
3
2
0
1
1
1
1
0
0
0
2
2
0
0
2
1
1
1
0
0
2
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
1
2
0
0
1
1
2
0
0
0
0
0
1
0
2
2
0
0
2
0
1
0
0
0
0
2
0
0
0
0
2
1
1
0
0
1
0
0
2
1
1
0
2
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
1
2
2
0
0
0
1
1
0
0
0
0
0
0
1
1
2
0
0
0
1
0
0
0
2
2
2
0
1
1
1
1
1
1
0
2
1
0
1
1
0
0
2
0
0
1
0
3
0
1
0
2
0
0
0
0
0
2
0
2
2
2
0
0
3
1
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
2
1
0
1
1
1
1
0
2
0
2
1
0
0
0
0
0
2
0
2
2
2
0
0
2
0
2
0
1
2
0
0
0
1
0
0
2
0
0
0
0
2
0
2
0
0
1
1
0
0
2
0
0
0
0
1
2
0
0
1
0
0
1
0
1
0
2
1
0
0
1
2
0
1
0
0
0
0
1
1
1
0
1
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
3
1
1
0
0
0
1
1
2
0
1
1
1
2
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
1
1
0
1
0
0
0
0
2
0
2
0
3
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
1
2
2
1
2
0
0
0
0
0
0
2
1
0
0
0
1
3
0
2
1
0
1
1
2
0
0
0
1
0
1
0
0
0
2
4
1
2
1
0
0
1
2
0
3
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
2
2
1
1
3
0
0
2
0
0
3
2
1
0
2
0
1
0
0
2
2
1
3
1
0
0
2
1
1
0
3
0
0
0
0
0
1
1
0
0
0
3
1
0
0
2
0
0
4
1
1
0
0
0
0
0
1
0
0
2
0
2
0
1
0
0
0
1
2
1
0
0
1
0
0
1
0
0
1
2
2
0
0
0
0
0
0
0
2
0
0
2
1
1
0
1
2
1
1
0
0
4
0
1
3
0
4
3
1
0
0
0
0
0
0
2
2
0
0
2
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
2
1
0
0
0
0
1
0
0
2
2
0
1
2
0
1
2
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
2
0
1
2
1
2
0
1
0
0
0
0
0
0
0
0
0
1
3
0
0
2
0
0
2
0
1
2
2
3
2
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
2
0
2
1
0
0
0
0
0
3
2
0
3
0
1
1
0
1
2
4
2
1
0
0
1
0
2
0
0
1
0
1
1
1
1
0
1
2
0
0
0
0
1
0
0
0
0
1
1
2
0
0
2
2
0
2
2
0
0
0
0
0
0
0
0
1
2
1
0
1
2
0
0
0
2
2
1
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
1
0
2
0
2
2
0
0
0
1
0
0
1
0
0
1
1
0
1
2
0
1
2
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
2
2
0
0
0
0
1
0
0
1
2
0
1
2
2
0
1
2
0
0
0
2
0
0
2
3
0
0
1
0
0
5
1
1
1
0
0
0
1
2
0
1
2
0
1
0
0
1
1
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
1
3
0
1
1
0
1
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
1
2
0
2
0
1
4
1
0
2
0
0
0
2
1
2
0
0
0
1
0
2
1
0
0
0
1
0
0
2
0
0
1
0
1
1
0
0
1
0
1
0
0
2
2
0
1
1
1
1
0
0
1
0
1
0
3
1
1
0
2
2
0
0
0
0
0
2
2
1
2
2
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
1
2
1
0
1
2
0
1
0
0
0
1
1
0
0
0
0
1
2
0
0
0
0
0
0
2
1
0
2
2
1
0
2
0
0
3
0
0
0
2
1
0
0
0
0
1
0
2
0
1
1
1
0
1
6
2
0
2
0
0
1
0
0
0
1
0
1
0
1
1
0
1
0
1
0
0
2
3
0
0
0
0
0
1
0
0
0
2
1
0
1
2
0
2
3
2
0
0
1
1
1
0
0
1
2
1
0
0
0
0
0
0
2
0
0
0
2
0
0
1
1
0
1
0
0
1
1
0
1
0
1
2
0
3
0
0
1
0
2
0
0
0
3
0
0
3
0
0
2
0
0
0
0
0
0
0
0
1
0
3
2
0
0
0
0
0
1
1
0
0
0
0
0
1
1
1
0
0
0
1
0
3
3
0
1
1
0
2
0
0
0
1
1
0
1
2
1
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
2
0
1
0
1
1
1
0
0
0
2
2
0
1
2
0
2
0
0
0
0
0
0
1
3
0
0
0
0
0
2
2
0
1
0
2
0
0
0
2
0
2
0
0
0
1
1
1
2
1
0
0
2
0
0
2
0
0
0
2
0
0
0
1
0
2
0
0
0
0
1
2
0
0
1
1
0
1
1
0
2
2
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
1
1
0
0
2
0
2
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
1
1
0
1
1
1
1
0
0
2
1
0
0
0
2
1
0
0
2
0
0
2
1
2
1
0
0
1
1
2
0
0
1
0
2
0
1
0
0
0
1
2
0
1
1
0
1
2
0
0
0
0
0
0
0
0
2
2
0
1
1
0
2
3
0
2
0
2
1
0
1
0
0
0
0
0
0
2
3
2
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
2
0
1
0
1
0
0
2
0
3
2
0
2
2
0
1
0
0
0
1
0
2
1
0
1
1
0
1
1
0
0
1
1
0
0
2
0
2
0
0
0
0
0
1
0
1
0
2
1
0
0
1
0
0
2
0
0
9
0
0
0
1
2
0
2
1
2
1
2
1
2
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
2
0
1
1
1
0
0
2
1
0
0
2
0
0
0
0
0
0
1
1
0
0
3
0
1
1
0
0
3
0
0
0
0
1
0
2
0
0
2
0
0
1
0
0
0
0
4
1
0
2
0
0
2
4
0
3
0
0
0
2
4
2
0
3
1
2
1
1
0
0
2
1
1
0
0
1
0
0
2
2
2
0
0
0
1
2
0
1
0
1
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
1
0
2
0
1
1
2
0
0
2
2
0
0
0
0
0
0
0
2
2
2
0
1
0
0
0
0
0
0
1
0
1
0
2
0
1
0
0
2
2
2
0
0
0
1
0
0
1
1
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
2
1
0
2
0
1
1
0
0
2
1
0
0
1
0
1
0
1
0
2
0
1
2
0
1
1
0
0
0
0
1
1
2
0
0
2
0
0
0
2
0
2
2
1
0
0
1
1
0
0
0
2
0
0
1
0
0
0
0
2
0
2
0
2
1
2
0
4
1
0
0
2
0
1
2
0
1
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
2
5
0
0
2
1
1
0
1
2
0
0
0
2
0
2
2
0
1
0
3
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
1
0
0
1
1
1
0
0
0
2
0
1
0
0
0
1
0
2
0
2
0
2
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
3
0
0
1
0
0
0
1
2
0
2
0
6
0
0
2
0
0
1
2
1
0
1
1
2
0
0
0
0
2
0
0
0
0
0
2
2
1
1
0
0
0
0
0
0
1
2
0
0
0
0
1
2
1
0
1
2
2
0
2
0
0
0
0
3
1
2
2
0
0
1
1
0
0
0
0
3
0
2
1
1
2
1
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
2
1
1
0
2
2
2
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
1
1
0
0
0
2
0
0
2
1
0
0
2
0
2
2
0
2
0
0
2
0
0
2
2
0
0
0
1
0
0
0
0
2
1
1
2
2
0
2
0
2
1
0
0
1
0
1
0
1
0
0
0
0
0
2
0
0
1
0
1
0
1
0
0
3
2
1
1
2
0
2
0
0
0
2
2
0
0
2
0
0
0
0
0
0
6
0
0
0
2
2
2
0
1
1
2
2
2
0
2
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
2
1
2
0
0
1
1
1
1
0
0
0
0
2
1
2
0
2
0
0
0
0
1
0
1
2
0
1
0
1
0
1
2
3
3
0
0
2
2
0
0
1
0
2
0
0
0
1
0
0
2
2
0
1
0
1
0
0
0
0
0
1
0
2
3
0
0
0
1
0
1
0
0
1
0
2
0
2
0
0
1
1
0
2
0
1
0
2
0
1
2
1
1
0
0
1
1
2
0
0
2
2
2
0
2
0
2
1
0
0
0
2
0
2
2
2
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
2
0
1
0
3
1
2
1
0
2
0
2
0
1
0
8
2
0
0
1
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
2
0
0
1
0
1
1
0
2
3
2
0
4
0
1
1
0
2
1
2
0
0
0
0
1
0
0
1
2
1
0
0
0
0
1
1
2
0
0
0
1
2
1
1
0
0
0
1
0
0
0
2
0
0
2
0
1
2
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
1
0
0
1
0
2
1
0
2
1
0
0
0
2
0
0
0
2
0
0
1
2
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
1
0
0
3
0
0
0
0
2
0
0
0
2
2
3
0
0
1
0
2
0
4
0
2
1
0
0
1
1
1
0
1
0
0
0
2
3
4
2
1
1
0
0
2
0
0
0
0
0
1
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
1
0
0
0
0
1
2
2
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
2
2
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
1
2
0
2
0
1
0
0
2
2
2
0
0
2
0
1
1
0
2
0
0
0
3
1
1
1
1
2
0
0
0
1
2
0
0
2
0
2
0
0
1
0
2
0
0
0
1
2
1
2
0
1
1
1
1
0
2
1
0
2
0
0
2
1
1
1
0
0
0
0
0
2
1
0
0
0
2
0
0
1
0
1
0
0
2
0
0
0
1
1
0
2
2
0
1
1
0
0
2
2
0
0
0
1
1
1
0
0
0
0
2
0
0
0
0
0
0
2
2
1
0
0
0
2
0
0
0
0
0
3
0
1
0
1
2
0
0
2
0
0
0
0
1
2
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
2
1
1
0
1
1
1
0
0
1
2
2
0
1
1
0
0
0
3
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
4
0
0
0
0
0
2
2
2
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
1
0
0
0
0
1
1
1
0
0
0
0
5
0
0
1
0
0
0
1
3
0
0
1
1
1
0
0
1
2
1
0
0
0
0
1
0
0
0
0
1
2
0
1
2
2
0
0
1
0
0
0
0
2
0
0
1
1
0
3
0
2
0
4
0
0
1
2
0
0
2
0
0
2
0
0
1
0
1
0
1
0
2
0
0
1
0
0
0
0
0
1
0
0
0
1
2
0
0
0
2
0
0
1
1
0
2
0
0
0
0
1
2
2
0
1
0
2
0
0
1
2
0
1
1
0
2
0
0
0
0
1
0
0
0
0
0
1
2
1
0
1
0
5
2
1
0
1
0
0
1
0
1
0
1
1
0
2
0
0
0
0
1
0
0
1
0
4
1
0
0
1
3
1
2
0
2
2
1
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
2
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
1
2
2
0
0
0
2
0
1
1
2
0
0
0
1
2
2
1
0
0
2
2
0
1
0
4
0
0
0
0
0
1
0
1
0
0
1
1
0
1
0
0
1
0
0
2
0
0
0
0
1
0
0
1
2
0
2
0
0
0
4
1
1
2
1
2
0
0
1
1
0
0
1
0
0
0
0
1
1
0
2
0
1
0
0
0
1
2
2
2
0
1
2
0
0
1
3
0
0
0
0
0
1
2
1
1
0
2
0
1
0
2
1
0
4
1
4
0
1
1
0
0
1
0
0
0
0
0
0
2
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
2
0
2
1
0
0
0
0
2
1
1
0
0
2
0
2
2
0
1
0
0
2
1
1
2
0
0
0
0
0
0
0
2
1
1
0
0
0
1
0
1
2
1
2
2
1
1
2
0
3
1
0
0
2
0
2
0
0
0
3
0
0
1
0
0
1
0
0
0
1
1
1
2
0
0
0
0
0
2
0
2
0
0
1
0
2
0
0
2
2
0
1
0
0
0
1
2
3
1
1
1
0
1
2
0
1
1
2
0
0
0
1
0
0
1
1
0
1
0
2
0
2
2
2
2
0
0
1
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
1
4
0
2
1
1
2
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
1
0
0
0
5
0
0
0
0
0
1
0
1
2
0
0
2
2
0
0
0
1
0
0
0
0
2
0
1
0
0
0
2
1
0
2
0
1
0
2
0
2
1
2
0
0
0
1
0
2
0
2
0
2
1
0
0
0
0
0
0
1
2
1
0
0
0
0
1
1
1
2
0
0
0
0
2
0
1
0
0
0
0
1
0
2
0
1
0
1
2
2
0
1
1
0
0
0
3
0
0
0
0
2
2
0
4
1
0
0
1
0
0
0
2
0
0
0
2
3
0
2
0
1
0
0
0
2
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
1
1
0
0
0
1
0
1
0
0
0
2
0
1
2
2
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
1
0
0
1
0
1
0
2
2
0
0
1
0
0
2
0
1
1
2
0
1
1
0
0
1
2
2
0
0
2
0
0
1
1
2
1
2
2
2
0
0
1
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
2
2
0
1
1
1
0
0
1
1
0
3
0
1
2
2
0
2
2
0
0
0
1
0
0
0
0
1
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
2
1
0
2
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
2
2
0
0
2
2
2
1
2
0
1
2
0
2
0
0
1
13
0
0
2
2
0
1
0
0
0
0
1
0
1
2
0
0
0
0
0
2
1
0
0
8
0
0
0
2
0
0
1
0
0
0
0
2
4
3
1
0
2
1
0
2
2
1
0
2
1
1
0
0
0
1
2
1
0
1
0
0
0
1
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
2
0
2
1
2
0
0
0
0
2
2
1
1
0
0
0
1
0
2
0
0
2
1
0
1
0
0
2
0
2
0
2
0
0
2
1
0
0
1
0
2
1
5
0
1
1
0
0
2
1
2
1
3
0
2
0
0
0
0
0
2
0
1
0
2
2
0
0
7
0
0
1
0
0
1
1
0
0
1
0
0
0
1
0
0
1
0
0
2
1
0
1
2
0
0
0
0
0
0
2
2
0
1
2
0
0
0
0
0
0
0
2
1
2
1
0
0
0
0
0
1
0
0
0
2
3
0
1
0
0
0
0
1
2
0
0
3
0
2
0
1
0
1
0
0
1
1
1
0
1
2
1
1
0
0
2
0
1
2
0
1
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
2
0
0
1
2
2
2
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
1
0
2
2
0
2
2
1
0
0
1
1
0
0
1
1
0
1
1
2
1
0
0
1
2
0
0
0
0
2
2
0
1
0
3
0
2
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
2
2
0
0
1
0
0
1
0
6
2
0
2
2
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
2
1
0
0
1
0
0
0
0
2
0
0
0
2
2
0
1
1
2
0
1
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
2
0
1
2
2
1
0
0
0
1
1
0
3
2
0
0
0
0
1
1
2
0
0
0
0
0
2
0
0
0
2
0
2
1
0
0
0
2
1
0
1
1
1
1
0
1
1
1
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
2
0
0
0
3
0
2
0
0
2
0
0
0
3
2
1
0
0
0
1
1
1
0
0
0
0
2
2
0
0
0
0
4
0
0
1
0
1
1
0
1
0
0
2
1
0
0
0
1
1
0
2
0
1
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
1
0
1
2
0
1
0
0
1
0
0
2
0
0
0
1
0
0
1
0
0
2
0
0
2
1
0
0
1
2
0
0
2
0
0
2
0
1
2
1
0
1
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
2
0
0
0
0
0
2
1
0
0
1
0
1
2
0
0
1
0
0
1
2
0
0
0
0
2
1
2
0
0
1
0
2
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
2
1
0
2
0
1
2
0
1
2
2
1
1
1
0
2
0
2
0
1
0
0
0
1
1
0
0
1
1
1
0
0
1
2
0
0
0
7
0
0
1
2
1
0
4
1
1
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
1
1
0
2
0
2
2
2
2
0
0
0
3
0
1
0
0
2
0
0
0
0
1
0
1
2
2
1
0
0
3
2
0
0
0
0
2
0
0
0
2
0
0
0
6
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
2
2
2
1
1
0
0
2
2
0
0
0
1
0
1
1
1
2
0
1
0
4
1
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
2
0
0
2
1
1
0
0
1
0
0
0
2
0
0
2
1
0
0
1
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
1
0
2
2
1
0
1
0
0
0
0
1
2
1
0
1
2
4
8
2
0
1
0
1
1
2
0
1
0
2
0
0
0
0
0
0
0
2
0
1
2
0
0
0
3
0
1
0
0
0
0
0
0
2
1
0
0
1
1
1
1
2
1
0
0
0
1
1
0
2
0
0
2
0
0
1
2
0
2
2
0
0
0
0
1
0
0
0
2
0
0
2
0
1
2
1
1
1
1
2
0
1
2
0
0
0
1
0
2
0
1
2
0
0
0
0
0
0
2
0
0
2
0
2
2
0
2
0
1
0
0
1
0
0
0
1
1
0
1
1
1
0
0
2
2
0
1
1
1
0
1
2
2
0
2
0
0
1
1
1
0
1
0
1
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
1
1
0
0
0
1
0
1
0
0
0
1
2
0
1
0
0
0
0
2
0
1
0
0
0
2
1
0
0
0
1
1
2
0
3
2
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
2
1
0
1
0
2
0
0
1
0
0
2
2
2
1
0
1
0
1
2
0
2
0
0
0
0
1
1
0
2
0
0
1
2
0
0
0
0
0
0
1
0
2
2
0
2
0
0
2
0
2
1
1
0
1
0
1
0
0
1
0
1
1
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
2
1
0
2
4
0
0
0
0
0
1
0
1
1
1
2
0
0
0
0
0
0
0
1
2
1
1
0
2
0
0
1
0
0
0
0
0
2
1
0
0
0
2
1
0
2
0
0
1
2
0
0
2
0
0
1
2
4
2
0
2
0
0
0
1
2
1
1
0
1
1
2
1
1
0
0
1
0
0
0
0
3
0
2
0
0
0
2
0
1
0
0
2
0
2
2
0
0
0
3
4
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
1
1
0
1
0
0
0
1
1
1
1
2
0
0
0
1
2
0
0
0
2
0
0
2
0
0
0
1
0
0
1
0
1
1
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
2
0
0
0
0
2
2
2
0
0
2
0
0
2
0
2
3
1
1
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
1
1
2
0
2
2
0
3
0
0
0
0
2
1
0
0
2
0
0
0
1
2
2
0
2
2
0
1
0
1
0
0
2
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
1
0
2
1
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
1
4
0
0
0
2
0
2
0
1
0
1
0
0
2
0
2
2
2
0
0
2
0
0
0
0
1
2
2
2
2
1
3
2
0
2
0
0
1
0
0
0
0
2
0
2
2
2
0
0
0
2
1
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
1
0
1
0
0
2
2
1
0
3
2
0
1
1
2
0
0
0
1
0
2
1
1
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
1
1
0
1
0
2
1
1
0
1
0
0
0
2
1
1
1
0
1
1
2
0
0
0
0
0
1
2
0
0
0
2
0
0
0
1
2
1
0
0
0
0
0
2
0
0
0
2
0
1
2
1
0
0
2
0
1
1
2
1
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
1
0
0
2
0
0
0
1
2
2
2
0
0
1
1
1
0
1
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
1
2
1
0
0
0
2
1
1
0
0
0
1
0
0
0
0
2
1
1
0
2
1
2
2
2
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
3
0
1
0
2
0
2
0
0
0
0
2
0
1
1
2
2
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
1
0
1
1
0
0
1
0
0
1
0
2
2
7
0
1
3
1
2
0
1
0
0
0
1
2
0
0
0
0
0
1
1
0
0
0
0
1
2
0
0
1
0
0
0
2
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
1
2
0
2
1
0
0
2
1
0
1
0
1
0
0
1
2
2
1
0
0
0
0
2
0
2
3
2
1
0
1
0
1
2
2
0
0
1
2
1
1
1
1
1
0
0
1
1
0
0
0
0
2
0
0
2
2
0
0
0
1
1
2
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
5
0
0
3
0
0
1
0
2
0
1
0
0
2
2
2
0
0
0
1
0
0
0
0
0
1
1
2
1
1
0
1
0
1
0
0
1
0
0
0
0
2
0
1
0
0
0
0
1
0
1
1
0
2
0
1
2
0
0
0
1
1
0
2
0
1
1
0
1
1
0
0
0
1
0
0
0
1
0
2
2
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
1
0
0
8
0
1
2
0
2
0
0
0
2
0
0
0
0
1
0
0
2
0
2
0
0
0
2
0
0
0
2
1
0
0
3
0
0
2
1
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
1
2
0
2
0
0
2
2
0
0
0
0
0
0
3
0
0
0
0
1
0
2
2
0
0
2
0
0
0
1
1
0
0
0
2
0
0
2
2
0
0
0
1
1
0
1
0
0
0
0
1
3
1
2
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
1
0
0
0
1
2
0
0
1
3
0
1
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
2
1
0
1
0
0
2
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
2
0
2
0
0
0
1
0
2
0
0
2
0
0
0
0
0
1
1
0
2
0
1
0
2
0
0
0
0
2
0
0
2
0
2
2
0
0
1
0
0
1
1
1
0
0
1
4
0
0
0
0
2
0
0
2
0
2
2
0
0
0
0
0
0
0
3
0
0
0
2
1
2
2
0
2
0
0
0
2
0
0
2
4
0
1
1
0
1
0
0
2
1
0
0
0
2
0
0
0
0
2
0
2
0
0
0
2
2
1
1
0
0
2
4
0
2
0
1
1
0
0
0
2
0
0
1
2
0
2
0
1
0
0
0
0
0
0
0
1
1
0
1
1
2
0
0
1
0
1
2
0
0
0
0
1
1
1
0
0
0
1
2
0
0
0
2
0
2
0
1
0
0
2
0
0
0
2
1
1
2
0
0
0
0
1
0
2
0
0
2
2
1
0
0
2
0
1
1
1
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
2
0
0
0
2
0
1
0
0
2
1
0
0
0
0
1
1
2
0
0
0
0
0
2
0
1
1
0
0
1
2
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
2
0
0
1
0
1
0
0
2
0
1
0
0
1
0
2
0
0
0
2
0
1
0
0
2
2
0
1
0
0
0
2
2
0
2
0
2
0
0
0
0
0
0
1
0
2
1
0
2
2
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
2
0
0
0
0
0
0
1
1
0
1
0
0
1
5
2
0
2
0
0
0
0
0
0
1
1
1
1
1
0
0
2
2
0
2
0
2
2
3
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
1
1
0
2
0
0
2
2
0
0
1
2
2
2
0
1
2
0
0
0
0
0
2
0
0
0
0
0
1
0
2
2
1
2
0
0
0
0
1
1
0
0
0
0
0
1
2
0
0
0
0
1
0
0
1
4
1
0
0
2
0
0
0
2
1
0
1
1
2
2
1
2
0
1
0
0
1
2
2
1
1
0
0
0
0
1
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
1
0
0
2
1
0
2
2
0
0
1
1
2
0
0
2
1
0
0
0
1
0
0
0
0
0
0
2
2
1
0
0
0
1
0
2
0
0
0
0
2
1
2
0
1
0
2
2
0
2
0
1
0
0
0
0
0
0
3
0
0
0
0
0
2
1
2
0
1
0
0
0
2
0
0
3
0
0
0
0
0
1
0
0
0
0
2
1
2
1
2
0
0
0
0
0
0
1
1
0
0
0
2
3
1
0
0
2
1
2
1
2
1
1
0
2
0
0
0
0
0
0
0
0
1
0
2
0
1
2
1
0
0
2
1
1
2
0
1
0
0
0
1
1
0
0
0
1
0
0
2
0
2
1
1
0
0
2
0
3
0
0
0
1
0
0
0
3
1
0
0
2
0
0
0
0
1
0
0
2
2
0
1
1
0
0
0
2
0
0
0
1
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
1
2
2
1
0
0
1
2
0
0
1
1
0
0
1
0
1
1
0
2
0
0
2
0
0
2
0
0
0
3
2
0
0
2
0
2
2
2
0
1
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
1
0
0
0
0
0
0
1
1
1
0
1
0
2
1
3
0
0
0
0
0
0
1
1
2
0
0
1
0
3
0
0
2
2
0
1
0
1
1
0
0
2
2
0
0
0
3
0
1
1
0
0
1
0
0
0
0
2
1
0
2
1
1
0
2
1
0
1
1
1
0
1
0
1
1
0
2
2
8
0
2
0
0
3
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
2
0
1
1
0
0
0
1
2
1
1
2
0
0
0
0
1
1
0
0
1
1
0
1
0
1
1
2
0
0
1
1
1
0
0
2
1
1
0
0
2
0
1
1
0
0
1
1
2
1
1
1
0
1
0
0
1
0
2
0
1
2
0
0
1
2
0
0
0
0
0
1
0
1
0
1
1
0
1
0
0
1
1
0
0
0
0
0
0
1
2
0
1
0
3
2
2
1
1
0
0
1
2
2
0
1
3
0
1
0
1
0
1
0
0
2
0
1
0
0
0
0
0
2
0
1
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
2
0
1
1
4
0
2
0
2
2
1
2
1
0
2
1
0
1
2
1
1
0
2
1
2
0
0
0
1
1
1
2
1
1
0
0
2
1
0
0
1
0
1
0
0
1
0
2
1
0
0
0
2
1
2
3
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
2
0
1
1
0
0
5
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
1
0
0
0
0
2
0
0
1
0
0
1
0
1
0
0
1
2
0
0
0
2
0
2
0
0
0
0
1
0
0
2
0
0
1
0
2
0
1
1
0
0
0
1
0
2
1
0
1
0
0
1
0
0
2
0
0
1
0
0
1
0
2
0
0
0
0
0
0
3
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
3
0
2
0
0
1
0
0
2
0
2
2
1
1
1
0
0
2
0
0
0
0
0
0
1
1
2
0
3
1
0
4
0
1
0
2
0
0
2
0
0
0
0
1
0
1
3
2
0
3
0
0
1
0
1
2
0
0
0
0
2
0
7
0
0
0
0
0
0
2
2
0
0
0
1
1
0
0
1
0
4
0
0
0
2
2
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
2
2
1
0
0
2
0
1
1
0
0
1
0
1
0
2
0
0
0
2
0
0
0
3
2
1
2
2
1
0
0
1
0
0
0
1
2
0
0
2
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
1
0
1
0
0
0
2
0
0
0
2
1
0
1
3
0
0
0
0
1
1
2
2
1
0
2
0
0
1
0
0
0
0
2
1
0
0
0
1
1
1
0
1
0
0
0
2
0
0
1
0
1
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
2
0
1
0
1
0
0
0
0
0
0
0
1
0
3
0
0
0
1
0
0
0
0
0
2
0
1
2
1
1
1
0
0
0
1
0
0
2
1
2
1
1
3
2
0
1
0
0
1
1
1
2
2
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
2
0
0
1
2
1
1
0
0
2
0
1
0
0
1
1
0
2
0
1
1
0
0
2
1
0
0
0
0
2
1
0
2
0
1
4
2
1
0
0
0
2
0
1
2
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
1
0
0
1
2
0
0
1
0
0
0
1
0
0
1
3
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
1
1
0
0
0
0
1
0
0
0
1
2
0
0
0
0
2
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
1
2
0
0
1
0
0
2
1
0
0
2
0
0
0
2
2
0
2
1
0
0
1
0
0
0
1
3
0
1
0
0
1
0
2
2
2
0
1
0
0
2
0
1
2
0
2
1
1
2
3
1
2
0
0
1
1
0
0
2
0
2
0
0
0
0
2
0
0
0
0
1
0
1
0
3
1
0
0
0
1
1
0
0
1
0
2
2
0
0
3
1
0
2
0
0
0
0
1
0
1
2
0
1
1
0
0
3
0
0
0
0
0
2
1
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
2
1
1
1
1
0
2
1
0
1
2
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
1
0
0
1
1
2
2
1
0
1
1
0
1
0
1
0
0
2
0
2
0
0
0
1
0
1
0
0
0
0
2
0
0
1
0
2
2
2
6
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
2
2
1
1
0
1
1
2
1
0
1
0
2
2
1
0
0
1
0
0
1
1
0
1
1
1
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
3
1
0
1
0
0
0
1
0
0
1
0
1
0
2
1
2
0
1
1
0
1
0
2
1
0
0
1
2
1
0
0
0
3
0
3
1
2
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
1
0
1
0
2
0
0
0
2
0
0
2
0
2
0
0
2
0
0
1
0
1
0
0
1
0
2
0
2
0
0
0
0
0
0
0
1
0
2
2
0
2
0
1
0
0
1
0
1
0
0
1
0
0
1
0
2
2
2
2
2
2
1
1
0
1
0
2
0
2
0
0
2
2
0
0
0
1
1
0
2
2
2
0
0
2
0
1
1
0
0
1
0
2
0
0
1
0
3
2
1
0
1
0
3
0
0
1
1
2
0
2
2
0
0
0
2
2
0
1
0
2
0
1
1
0
0
1
0
2
0
0
1
2
0
1
0
1
2
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
2
2
1
0
0
0
2
0
0
0
2
0
1
0
0
1
2
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
2
0
1
0
2
2
2
0
0
0
0
2
1
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
2
0
1
2
2
0
0
2
0
0
1
2
1
0
1
0
0
0
0
0
2
0
1
0
2
0
1
0
1
0
2
0
1
2
0
0
2
2
0
0
2
1
0
1
0
1
0
0
0
1
1
0
2
0
0
2
0
1
0
0
1
0
0
0
1
0
2
2
0
0
0
2
0
0
3
1
0
1
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
1
1
1
0
2
3
1
0
0
0
0
1
0
0
0
2
2
0
0
1
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
1
1
0
1
2
0
2
0
1
0
0
0
2
1
2
2
2
0
1
2
1
1
0
2
0
0
1
2
1
2
2
0
1
0
0
1
2
1
0
2
2
2
2
1
1
1
2
2
0
0
0
2
0
0
0
0
0
2
2
1
0
0
2
2
0
0
1
0
0
0
1
0
2
0
2
0
0
3
0
2
0
0
0
0
2
0
0
0
0
1
2
3
0
0
0
0
2
2
2
2
0
0
1
1
3
0
0
0
2
0
2
0
0
0
1
2
0
0
1
0
0
0
0
1
0
0
0
2
0
2
0
0
1
1
0
3
2
0
0
1
2
0
2
0
0
2
1
0
0
1
2
0
0
0
1
0
0
2
2
0
0
0
1
2
2
0
1
0
0
0
0
0
1
2
0
1
0
0
0
1
0
0
0
2
0
1
0
0
2
0
0
0
2
2
1
2
2
0
0
0
1
2
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
2
0
0
1
0
2
0
0
2
1
0
0
0
0
1
0
2
1
0
0
1
0
1
0
1
2
0
1
0
4
0
2
0
2
0
1
0
1
0
0
1
1
0
1
0
0
1
0
0
0
3
2
2
1
0
1
0
0
2
2
0
0
0
0
0
0
1
0
2
1
0
0
1
2
0
0
0
0
3
1
2
0
2
0
2
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
1
0
3
0
1
0
1
1
1
2
0
1
0
1
1
2
1
0
0
2
0
0
2
0
0
2
0
0
2
0
0
1
1
2
1
2
2
0
0
0
1
0
0
0
0
2
0
0
0
2
2
0
0
2
2
2
0
0
0
0
1
0
0
1
1
2
1
0
0
0
1
0
0
0
1
0
0
0
2
1
0
0
0
0
2
1
0
0
0
1
0
2
0
1
0
0
0
2
1
0
0
0
0
2
0
0
0
2
1
0
1
2
0
1
2
1
1
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
1
1
2
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
1
1
1
2
1
0
2
2
0
1
1
2
0
2
1
0
1
2
1
0
1
0
1
1
0
2
2
0
0
0
0
2
0
0
0
1
0
3
0
0
2
0
1
0
0
1
0
0
0
2
1
1
2
0
2
0
0
0
1
1
0
0
0
0
2
2
2
3
1
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
1
1
0
0
1
1
0
1
0
1
0
1
1
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
2
0
1
0
1
1
0
2
2
2
2
0
0
0
0
0
0
0
0
3
2
0
0
2
0
0
2
1
0
0
0
0
6
0
2
0
0
0
3
0
0
1
1
0
0
0
1
0
0
2
0
4
1
1
0
0
0
0
1
2
2
0
0
0
0
0
0
2
0
1
2
0
1
0
2
1
0
1
0
1
0
0
0
1
0
0
3
0
0
3
2
0
0
0
0
1
2
0
0
0
0
2
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
2
1
2
0
1
0
1
0
2
1
1
0
1
0
0
2
2
0
1
0
1
0
0
1
1
0
0
1
0
0
1
0
0
2
0
0
0
0
0
1
2
2
1
0
1
0
0
2
0
0
0
0
1
2
0
0
1
0
0
0
2
1
1
1
2
0
0
0
0
1
0
2
2
0
0
2
1
0
0
0
0
0
3
0
0
0
1
0
1
0
2
2
1
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
1
1
1
1
2
2
2
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
1
2
0
0
0
0
2
1
0
1
1
0
0
0
1
0
0
0
0
2
2
2
0
1
2
0
0
1
2
0
0
0
3
0
1
0
0
0
0
2
0
0
0
0
0
3
1
2
1
1
2
0
2
2
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
1
1
1
0
0
2
0
0
2
3
2
0
0
1
0
0
0
0
7
1
1
0
0
1
0
0
1
0
0
1
3
0
0
0
2
0
0
0
0
1
0
1
0
0
0
2
1
0
0
1
0
1
1
2
0
0
2
0
2
0
2
0
0
1
1
1
0
0
0
2
0
1
0
0
2
0
1
2
1
0
1
0
0
0
0
1
1
2
1
0
1
0
2
0
2
0
1
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
2
0
0
2
0
2
0
3
0
1
2
1
0
1
0
0
0
0
0
1
2
2
0
1
0
0
0
0
0
1
0
1
1
0
0
1
1
0
1
1
0
0
0
0
0
0
1
0
1
1
2
0
0
2
0
1
2
1
0
1
0
0
0
2
0
2
0
0
2
0
0
2
0
0
1
0
1
2
0
0
0
0
0
0
1
0
0
2
2
0
1
0
1
0
0
2
2
1
2
0
0
0
0
2
3
0
1
1
1
2
0
0
0
0
2
1
4
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
2
2
2
0
1
1
0
1
0
0
2
2
1
0
1
0
0
0
2
1
2
0
0
2
0
0
0
1
1
3
1
0
0
2
2
2
0
0
2
0
2
1
1
0
1
0
0
0
1
0
0
0
1
0
2
0
0
2
0
1
1
0
1
1
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
2
0
2
2
0
4
1
0
2
0
2
3
1
0
1
2
0
0
1
0
1
2
0
0
2
0
0
0
0
0
0
0
0
5
0
2
3
0
1
2
0
1
0
0
0
2
0
0
0
2
2
1
0
1
0
1
2
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
1
3
1
2
2
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
2
0
1
0
0
2
2
2
2
0
1
1
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
1
3
0
0
0
0
2
2
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
2
1
0
0
0
2
0
0
1
0
2
0
0
0
0
1
2
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
1
0
2
3
1
0
2
1
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
1
0
0
0
0
0
0
2
2
0
0
2
0
2
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
1
1
2
0
0
2
1
1
0
0
0
1
2
1
1
1
0
0
0
0
0
0
0
0
1
1
2
1
0
0
0
2
0
0
2
0
1
0
1
0
0
0
2
0
0
0
0
1
1
1
0
2
0
2
0
2
0
0
0
0
1
1
0
2
0
1
0
0
1
0
1
1
0
0
1
0
0
0
2
0
0
0
2
0
0
3
2
0
1
0
1
1
0
1
2
0
0
2
0
0
0
0
1
2
0
2
0
0
1
1
0
0
2
0
0
0
0
0
1
0
0
2
1
0
2
1
2
0
2
1
0
0
0
0
1
0
2
1
0
0
0
0
1
2
2
1
2
0
2
0
0
1
1
1
0
1
2
1
0
2
0
0
2
0
0
0
2
0
1
0
3
1
0
0
0
2
1
2
0
2
0
1
2
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
2
0
7
2
0
0
0
0
1
0
1
1
0
0
0
0
1
1
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
2
0
0
1
2
0
1
1
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
2
1
3
0
2
0
2
0
0
1
1
0
1
0
0
0
2
2
2
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
1
2
0
1
0
2
1
1
0
0
1
2
2
0
1
2
1
1
0
3
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
1
1
0
0
0
1
1
0
0
1
0
0
0
0
2
0
2
0
0
3
1
0
0
0
0
0
1
0
2
1
1
2
1
0
0
1
2
1
1
1
0
1
2
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
2
1
1
0
0
0
4
0
0
1
1
0
0
1
2
0
0
2
3
0
0
2
1
0
0
1
2
1
0
0
1
0
1
1
0
2
0
0
0
0
1
0
1
1
1
1
0
0
1
0
0
0
0
2
2
1
1
2
2
0
2
0
1
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
2
0
0
0
0
2
2
2
1
0
0
0
0
0
1
0
1
2
2
1
2
0
0
0
0
0
0
0
0
2
0
0
2
1
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
1
2
0
0
1
0
0
2
0
0
0
0
3
1
1
1
2
0
0
2
0
2
0
0
2
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
1
0
1
2
0
2
0
2
0
0
1
0
1
0
0
1
1
0
0
2
1
1
1
3
0
2
0
0
0
0
0
3
0
2
0
0
2
2
0
0
0
0
2
0
0
2
1
2
2
0
2
1
1
1
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
1
1
2
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
2
0
0
0
2
1
0
1
0
0
0
0
0
0
0
2
1
3
1
1
0
2
2
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
4
1
0
1
0
0
0
1
0
2
1
0
1
1
1
2
0
2
0
2
0
0
3
2
0
2
0
0
0
0
0
1
1
0
1
1
2
0
0
0
0
0
1
0
1
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
1
0
1
2
0
1
0
1
1
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
1
2
1
0
0
0
2
0
3
1
0
2
1
0
0
0
1
0
1
0
2
0
1
0
0
1
2
0
1
0
0
0
1
2
2
0
0
0
1
1
0
2
1
1
0
1
0
0
1
0
0
1
2
1
0
0
1
0
0
1
0
0
1
0
1
0
1
0
0
2
1
0
0
0
2
0
0
1
0
0
0
0
0
0
1
2
0
1
0
0
0
2
0
3
0
1
2
0
0
1
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
1
0
2
0
0
0
1
2
3
2
0
0
0
0
0
2
0
0
0
0
0
0
4
0
2
1
1
0
1
2
0
0
0
0
0
0
1
0
3
0
0
0
1
0
1
1
2
2
1
0
1
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
1
1
0
0
0
2
0
0
2
0
0
1
0
0
2
0
0
0
3
1
0
0
2
0
2
0
1
0
0
0
0
0
0
2
0
0
0
2
1
1
0
1
1
0
0
0
0
0
0
2
1
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
4
0
2
1
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
2
1
0
0
2
0
1
0
0
0
1
3
0
1
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
2
2
0
0
2
1
0
0
0
0
1
1
0
2
4
0
1
0
0
0
0
2
1
1
2
0
1
3
0
1
1
0
0
0
0
1
1
1
0
2
0
2
0
2
4
1
2
1
0
2
0
1
1
0
1
1
0
0
0
0
0
0
0
0
1
1
2
3
1
3
0
0
0
0
1
0
0
1
0
1
2
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
2
1
0
1
2
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
2
0
1
2
0
0
1
0
1
3
2
1
0
0
0
2
0
0
1
1
1
1
2
0
0
0
0
0
1
1
0
1
0
1
1
1
0
2
0
0
0
2
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
3
0
0
0
0
1
0
0
2
0
0
0
0
0
0
3
0
0
0
2
0
0
2
1
0
0
2
1
0
0
0
0
0
0
1
3
1
2
1
0
0
0
1
0
2
1
0
1
0
0
0
0
2
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
1
2
1
0
2
2
2
1
1
1
2
0
0
2
0
0
0
0
0
0
0
0
2
1
0
1
1
1
2
0
0
0
2
0
1
0
0
2
1
0
1
1
1
0
0
0
0
0
1
0
1
2
0
0
0
0
2
1
1
0
0
0
1
0
0
0
0
1
0
0
1
2
0
0
1
1
0
0
0
0
1
0
2
1
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
3
0
1
0
0
2
4
0
0
1
1
1
0
2
2
1
2
0
0
1
0
1
0
2
0
2
1
2
1
0
0
1
0
0
0
1
0
0
0
2
0
1
2
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
2
4
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
2
2
1
0
0
1
0
2
1
0
0
1
2
1
1
0
1
0
0
2
0
2
1
1
1
1
0
2
2
0
2
2
0
0
0
0
0
0
0
1
0
2
0
0
2
2
0
0
0
0
0
2
0
2
0
0
0
0
0
1
1
0
1
0
1
0
1
0
2
0
0
1
0
0
0
0
2
3
1
0
0
1
3
0
0
0
0
0
0
0
0
0
1
1
0
2
1
0
0
0
0
0
2
0
2
0
2
0
2
0
2
3
2
0
0
0
0
0
1
1
2
2
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
1
0
1
2
0
0
1
1
0
0
0
2
0
0
0
0
2
0
0
1
0
2
0
0
1
1
0
1
0
0
1
0
2
0
0
2
0
0
2
0
1
0
0
0
0
1
0
2
3
0
0
0
0
2
0
0
0
0
4
1
0
0
1
0
0
0
0
0
0
2
0
2
0
0
1
0
1
1
1
0
0
0
2
0
0
0
1
0
0
2
1
0
0
1
0
2
0
0
4
1
0
0
0
2
0
1
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
2
1
0
0
1
0
2
1
0
2
0
2
2
1
0
1
2
4
0
1
2
2
0
1
1
1
0
0
0
1
0
0
2
3
1
0
2
1
1
0
0
1
2
0
1
0
0
2
0
2
0
0
0
0
1
2
0
2
0
2
2
1
1
0
0
1
2
1
0
2
0
0
0
1
0
1
0
1
1
0
0
0
0
0
1
0
0
1
1
0
0
1
0
1
0
1
0
0
0
2
1
0
1
1
0
0
1
1
1
0
0
0
1
0
1
0
0
0
1
1
0
1
0
1
0
0
0
0
0
1
0
1
2
0
1
0
1
0
0
0
0
0
0
1
2
1
0
0
0
1
1
0
1
1
0
0
0
0
1
0
1
0
2
2
1
1
2
0
2
0
0
0
0
2
2
2
0
1
0
0
1
1
0
0
1
2
1
1
0
1
1
1
1
2
2
0
0
0
0
2
1
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
2
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
1
0
2
1
1
1
2
1
0
2
2
0
2
0
1
0
1
0
1
0
0
0
2
0
0
0
2
0
2
0
2
2
1
1
0
0
1
1
3
0
0
0
0
0
0
0
3
0
1
1
0
1
1
0
2
0
0
0
0
0
1
0
2
1
0
1
0
1
0
1
0
2
2
0
1
0
0
0
0
2
0
2
0
0
1
0
0
0
0
2
1
0
0
1
2
0
2
1
0
1
1
0
0
0
0
0
0
1
1
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
2
1
0
0
2
1
0
2
0
0
0
0
0
2
0
1
2
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
2
2
0
0
0
2
0
0
1
0
0
1
0
1
0
0
1
0
2
3
1
1
0
0
0
0
2
2
1
0
2
0
2
0
0
0
1
0
1
0
1
0
2
1
2
1
0
1
1
0
0
2
2
0
0
2
2
1
0
0
2
0
0
0
1
0
0
0
1
3
0
1
0
0
1
0
2
3
0
1
0
0
2
2
1
0
2
0
0
0
0
2
0
1
0
1
1
0
0
1
2
1
0
0
0
2
0
1
2
0
2
0
0
0
2
0
2
0
0
0
0
1
1
2
0
0
0
2
0
0
0
0
2
2
3
0
0
0
1
0
2
0
0
4
0
4
2
0
0
0
1
3
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
2
0
0
1
0
0
0
0
1
1
2
0
2
0
1
0
4
0
1
0
0
1
2
1
4
0
2
0
0
0
0
0
0
0
1
0
0
0
2
2
0
1
1
3
2
0
1
1
1
0
0
1
2
0
0
1
0
0
1
2
2
1
0
0
0
0
0
0
1
0
2
0
1
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
1
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
1
0
1
1
0
1
0
0
1
2
0
0
2
2
0
0
1
0
1
2
0
2
2
1
0
0
1
1
1
0
0
2
2
1
0
2
2
0
0
2
0
0
2
2
0
0
0
0
2
2
0
0
0
1
0
2
0
0
1
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
1
1
4
1
2
0
2
0
0
0
1
0
0
0
0
0
0
1
0
2
2
2
1
0
0
2
0
0
0
0
2
1
0
2
3
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
2
2
0
1
0
0
0
0
0
0
2
0
1
0
1
0
1
1
0
2
1
0
0
0
1
1
2
1
2
0
0
0
0
1
2
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
2
2
2
1
2
2
0
2
1
0
0
0
1
0
1
0
3
2
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
2
2
0
0
0
0
0
0
1
2
1
1
2
0
1
0
0
2
0
0
2
3
0
1
0
0
2
2
0
1
1
0
0
2
2
0
0
0
2
0
0
1
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
2
1
0
1
0
0
2
1
0
0
2
1
0
0
0
0
2
1
1
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
1
1
0
0
0
0
1
1
3
0
2
0
0
1
0
1
1
0
0
1
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
3
1
1
1
2
0
1
1
0
2
2
0
2
0
0
1
0
0
2
0
3
1
3
2
2
0
2
0
0
1
0
0
3
0
0
1
0
0
2
0
0
0
1
0
1
0
2
0
0
0
0
2
1
1
0
0
0
0
2
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
1
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
3
0
1
0
1
0
2
1
2
2
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
2
2
0
1
0
1
3
1
7
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
1
1
0
0
0
1
2
3
3
1
3
0
0
0
2
0
0
2
2
0
2
0
0
2
0
0
0
0
1
0
0
1
0
2
2
2
0
0
0
2
0
0
1
1
0
1
2
1
0
0
0
0
0
1
0
0
0
4
2
2
0
0
2
3
2
0
0
1
0
1
2
2
0
0
3
0
1
0
2
0
0
0
0
0
2
1
2
1
0
0
2
1
0
0
0
0
2
1
1
2
0
2
1
0
0
0
2
2
1
2
0
0
1
2
0
1
3
0
0
1
2
2
0
1
1
2
1
0
0
1
2
0
0
0
0
1
0
1
2
0
1
0
0
0
1
0
0
0
1
2
0
0
0
1
0
0
0
0
0
1
1
1
4
0
0
0
0
2
2
0
0
2
1
0
0
0
1
2
1
2
0
0
2
2
0
0
1
0
0
2
0
1
1
0
0
0
0
1
0
0
0
2
0
2
2
1
0
0
0
0
2
0
0
0
2
2
0
2
1
3
0
0
2
0
2
0
0
2
0
4
0
1
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
2
0
0
1
2
0
0
0
1
0
2
1
0
0
2
1
1
0
2
1
2
0
0
1
1
2
1
2
2
0
0
1
0
0
0
0
0
1
0
1
1
0
0
2
1
2
1
1
0
0
1
0
0
2
1
0
2
0
1
1
0
0
2
0
0
0
1
0
2
0
0
2
1
1
0
0
0
0
1
0
0
1
2
1
0
0
0
0
1
1
0
0
1
2
0
0
2
0
0
0
1
0
0
0
0
0
0
1
3
0
3
2
0
1
0
0
1
0
1
0
0
2
0
0
2
0
2
0
1
1
0
0
2
0
0
0
1
2
0
0
0
0
0
0
1
0
0
1
0
2
1
2
1
1
0
2
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
2
1
0
2
4
0
6
0
0
0
2
2
2
2
3
0
0
0
0
0
0
0
1
1
0
2
2
0
0
1
0
2
0
0
2
1
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
1
2
1
2
1
1
2
2
1
0
0
0
1
0
0
2
1
0
2
1
0
0
0
0
0
2
0
0
3
1
0
1
0
0
0
0
0
2
0
0
0
0
2
0
1
0
2
1
2
0
1
0
2
0
0
0
1
0
0
1
3
0
2
1
2
1
0
0
2
0
0
0
1
1
4
0
0
0
1
0
0
2
0
1
1
0
0
0
1
2
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
2
0
1
1
2
0
1
2
0
0
0
2
3
0
2
0
2
0
2
1
1
1
0
0
0
0
0
1
2
0
0
1
0
3
2
0
3
2
1
0
0
0
2
0
1
0
0
2
2
0
0
1
1
1
0
0
0
0
2
0
0
1
1
0
0
1
2
0
0
2
2
2
0
1
1
0
2
0
1
2
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
1
2
0
0
1
0
1
0
0
0
1
1
0
0
0
2
1
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
1
0
1
1
2
0
0
0
0
0
1
0
1
1
0
2
2
2
1
2
0
1
0
1
0
1
3
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
1
0
0
1
0
1
0
1
2
1
1
0
2
3
1
0
0
2
0
2
1
0
1
0
1
0
0
0
1
0
1
1
1
0
0
0
2
0
1
1
0
1
2
1
2
0
0
0
1
1
0
2
0
2
1
0
1
0
0
0
1
0
1
0
1
0
1
2
0
2
1
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
3
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
2
0
1
0
2
0
1
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
1
2
1
2
0
1
0
5
2
0
4
0
0
1
0
0
0
1
0
1
2
0
0
2
1
0
0
0
1
1
2
0
1
1
0
0
0
0
1
0
0
2
0
0
0
1
1
0
1
1
1
0
2
1
0
0
2
1
2
0
0
0
2
1
1
0
0
1
1
2
1
0
0
0
1
2
1
2
0
2
0
0
0
2
1
0
2
0
0
0
2
1
0
0
0
1
0
1
0
0
0
1
0
2
0
0
2
2
0
0
0
2
2
1
0
1
1
0
0
0
0
0
0
2
0
2
1
0
0
0
1
2
1
1
1
0
2
1
0
0
0
0
0
1
2
0
0
3
0
0
0
0
0
0
0
1
0
0
2
2
0
1
2
0
2
2
0
1
1
0
0
0
0
0
1
2
0
0
1
0
0
0
2
0
1
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
6
0
0
0
2
2
0
0
0
2
0
0
2
2
1
2
2
0
0
1
0
2
0
0
2
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
2
0
1
0
0
0
0
2
2
2
0
2
0
0
0
0
0
0
0
2
2
2
2
2
0
0
1
0
2
3
2
0
0
0
1
0
0
1
2
2
1
3
0
0
0
1
1
3
0
0
0
2
0
2
2
4
0
1
1
0
0
0
1
0
0
0
2
0
2
2
1
0
2
0
2
1
1
2
0
0
0
2
2
0
2
2
0
0
0
0
1
1
0
4
0
1
1
0
2
1
0
1
0
0
1
0
0
0
2
0
0
1
0
0
1
2
0
0
0
1
0
0
0
0
2
0
0
1
3
0
0
0
0
2
2
0
1
3
0
0
0
0
0
0
2
2
2
0
0
0
1
0
4
0
0
0
0
0
1
0
0
1
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
1
1
1
0
0
0
0
1
2
1
0
2
0
1
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
3
0
0
0
1
0
0
2
2
0
0
1
0
2
0
2
2
0
0
1
0
1
0
0
1
0
0
0
0
0
1
1
1
2
0
1
2
0
0
0
0
1
0
0
0
1
1
0
1
0
0
2
0
0
0
0
0
2
2
2
0
2
2
0
3
0
0
0
1
1
2
1
1
0
0
0
2
2
2
0
1
0
4
0
0
0
0
0
0
2
2
1
0
1
0
2
0
0
0
0
1
2
1
2
2
0
0
2
1
0
0
0
0
2
1
0
1
0
0
0
1
0
0
1
0
0
1
2
0
3
2
0
0
2
0
0
0
2
0
0
0
0
1
0
1
1
0
1
2
2
1
2
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
2
1
0
0
2
1
0
1
0
1
3
0
1
1
0
0
0
0
1
2
2
1
1
1
0
0
0
0
1
1
1
0
1
0
1
1
0
1
0
0
0
0
2
1
0
1
2
0
0
1
0
0
0
1
1
1
0
2
0
0
2
0
0
1
0
2
2
2
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
2
0
0
1
0
0
2
0
0
0
3
1
2
0
0
0
0
0
2
0
0
2
2
0
0
3
2
1
0
1
1
0
5
1
2
3
0
0
2
0
1
2
1
2
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
2
0
2
1
0
1
0
2
0
0
2
0
0
0
2
3
0
0
0
2
2
0
1
0
1
0
0
0
0
2
1
0
1
0
1
2
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
1
1
0
2
0
4
0
0
2
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
1
0
0
1
0
0
0
2
2
2
0
0
1
0
1
0
4
2
0
1
0
1
1
0
1
1
2
0
0
1
0
0
2
2
0
1
0
0
2
0
1
1
1
0
0
0
0
2
0
0
0
2
0
0
1
1
2
0
0
0
0
0
1
0
1
0
1
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
2
0
4
1
0
0
2
1
0
2
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
2
0
3
2
1
1
0
2
0
0
0
2
3
3
1
1
1
0
2
0
0
0
1
1
1
0
2
2
0
1
0
1
0
1
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
2
0
0
2
3
1
0
0
1
0
1
0
2
1
2
1
0
0
0
0
0
2
0
0
1
1
0
2
0
1
0
0
1
1
2
2
2
0
0
2
1
0
0
0
0
1
2
0
1
0
0
1
2
1
2
0
0
1
0
1
0
0
0
0
1
3
0
0
0
0
0
1
0
2
0
0
3
0
0
1
1
0
0
0
0
0
0
0
2
1
0
1
2
0
3
0
1
0
1
0
1
1
0
0
0
0
1
0
0
0
0
5
0
0
0
1
1
2
1
1
0
1
1
0
0
0
0
0
3
2
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
1
2
1
1
0
0
0
2
3
2
0
1
0
0
0
1
1
0
2
0
0
0
0
0
3
0
1
0
0
0
1
0
1
2
1
2
0
0
0
1
0
0
0
0
0
3
4
1
0
0
1
2
0
0
0
0
0
2
2
2
1
0
0
1
0
2
0
0
1
1
0
0
0
1
0
0
1
0
2
0
0
1
0
2
2
1
0
0
0
0
0
2
2
1
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
1
2
0
2
1
2
0
0
2
0
3
0
0
2
0
0
0
1
0
1
0
0
0
2
1
0
0
2
2
0
0
2
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
3
1
0
1
1
1
0
1
0
0
0
2
2
0
0
2
1
0
1
0
4
0
0
0
0
0
0
0
0
2
2
0
0
1
0
1
0
0
1
0
0
2
2
0
2
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
2
1
1
0
2
1
0
0
0
1
0
0
0
0
0
1
0
2
2
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
2
1
1
0
0
0
0
0
1
2
2
1
3
0
1
1
0
2
0
0
2
0
0
0
1
1
0
0
2
0
0
2
0
1
0
1
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
1
0
2
1
1
0
0
1
2
1
1
0
0
0
0
2
0
2
1
0
3
1
1
2
0
1
0
0
0
0
2
0
0
0
1
1
1
0
0
0
0
3
0
0
3
1
0
0
0
4
0
2
0
0
0
0
0
2
0
1
0
0
0
2
1
1
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
2
0
0
2
1
2
1
0
1
2
1
2
2
0
1
0
0
2
0
1
2
0
1
0
0
0
0
0
2
1
1
0
1
2
1
1
1
1
0
0
0
1
0
0
1
2
1
2
0
2
0
0
2
1
0
3
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
3
1
0
2
0
1
0
0
0
1
2
0
0
0
0
0
0
2
2
0
1
1
0
0
0
1
0
2
0
0
2
0
0
2
0
1
2
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
1
1
0
0
1
1
0
0
1
0
0
0
1
1
1
1
0
0
2
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
1
0
2
0
0
2
0
0
0
2
1
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
2
0
0
0
2
0
5
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
2
0
2
0
0
0
1
2
1
0
0
0
1
0
2
0
0
2
0
0
1
0
0
1
0
0
2
1
0
2
2
1
1
0
0
0
0
0
1
1
0
0
1
1
0
1
0
2
0
0
0
0
0
2
0
0
1
0
0
0
2
1
0
0
0
0
1
1
0
2
0
0
0
2
1
0
1
2
0
1
0
0
2
0
1
2
0
2
0
1
0
0
0
2
0
0
1
2
0
1
0
0
0
0
0
0
1
1
0
0
1
1
2
0
0
0
0
0
0
0
0
1
1
0
0
1
3
7
1
0
0
2
0
2
0
0
2
0
4
0
2
0
0
2
2
2
0
0
0
1
2
0
0
1
0
0
0
1
2
0
1
0
0
0
0
0
2
0
0
1
1
0
1
1
0
0
0
0
2
0
1
0
0
0
0
2
0
0
2
0
1
0
1
1
0
0
0
0
0
0
1
1
0
0
0
2
0
2
0
0
0
2
0
0
1
2
0
0
1
0
0
1
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
2
2
2
0
1
0
0
0
0
0
2
1
1
1
3
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
3
0
1
1
0
0
0
1
2
2
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
2
2
2
1
1
2
1
2
0
0
1
2
2
1
2
0
0
2
0
0
0
0
1
2
1
1
1
2
0
0
2
0
0
1
1
1
2
1
1
2
2
1
2
1
0
0
0
1
0
0
2
2
0
0
0
1
0
0
2
1
0
1
0
0
1
0
2
0
1
1
2
1
5
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
1
1
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
3
0
0
2
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
2
1
0
0
1
0
2
2
0
0
0
0
2
0
0
0
2
0
0
1
0
1
16
0
0
1
0
0
0
2
0
0
2
0
1
1
2
2
0
4
0
1
0
0
2
0
0
0
0
0
1
0
0
2
0
1
2
2
1
0
0
1
2
0
0
0
0
2
0
0
0
2
1
0
2
0
0
0
2
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
2
2
1
0
1
2
0
2
2
0
1
0
0
0
0
1
2
1
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
2
2
0
1
0
2
2
1
0
1
2
0
2
0
0
1
2
1
2
3
2
1
2
0
2
0
0
1
2
0
1
0
2
0
0
0
0
0
0
1
2
1
1
0
1
2
1
1
1
0
2
0
1
0
2
2
0
0
3
0
0
0
0
1
2
1
1
1
0
2
0
0
1
1
1
2
1
2
1
0
0
2
1
0
0
2
1
0
1
0
0
0
2
2
0
1
0
0
1
0
2
0
1
0
0
1
0
0
0
1
2
1
2
0
0
0
2
2
0
0
0
1
0
0
0
1
0
1
4
0
2
1
0
0
0
0
0
2
0
2
2
0
1
1
2
0
2
0
5
0
0
1
1
1
0
1
1
0
0
0
0
1
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
2
0
3
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
2
0
1
0
1
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
2
0
2
2
2
0
1
0
0
0
0
2
2
1
4
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
1
0
0
2
0
0
1
0
0
0
1
0
0
2
1
0
0
0
0
1
0
1
0
0
1
2
0
1
0
0
2
1
0
0
2
1
0
0
2
0
0
0
2
0
0
0
2
0
1
0
1
3
3
2
0
0
1
0
0
1
4
0
0
1
0
0
1
0
2
1
0
0
0
0
2
0
1
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
2
1
0
0
0
0
0
1
1
0
2
0
2
1
0
0
3
0
2
0
0
2
2
1
2
1
3
1
1
0
2
0
0
0
0
0
0
0
1
2
1
1
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
2
2
0
0
0
0
0
1
2
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
2
0
2
1
1
2
0
0
2
0
0
0
0
0
0
1
2
0
0
2
0
0
2
1
0
0
1
0
0
0
1
0
0
1
1
0
1
0
0
0
2
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
3
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
3
0
0
1
0
3
0
0
1
2
0
1
0
1
2
1
0
0
0
0
0
0
2
1
0
2
0
4
0
1
0
1
2
0
2
0
0
3
0
0
0
2
0
0
0
5
1
2
0
0
1
1
0
1
0
2
2
0
1
1
0
0
2
0
0
0
0
1
1
0
0
1
1
2
0
0
0
1
0
0
1
3
1
2
2
0
0
0
0
0
1
1
0
0
2
0
0
0
1
0
0
1
1
0
0
0
0
2
0
0
1
0
1
2
0
0
3
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
2
0
0
1
0
0
1
1
0
1
1
1
0
1
0
0
0
2
3
1
0
2
0
2
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
2
0
2
2
0
1
2
1
0
2
0
0
0
1
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
2
0
1
2
0
0
2
0
0
0
1
0
1
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
1
2
0
0
8
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
2
1
0
0
1
0
0
1
1
0
1
1
0
0
2
1
1
0
0
0
0
0
0
0
0
4
2
2
0
0
0
1
0
2
0
0
0
1
1
1
1
0
0
1
1
0
0
1
0
0
1
0
1
0
2
0
2
1
0
2
0
1
0
0
0
0
0
0
0
1
0
0
1
1
2
3
2
1
0
1
2
0
0
0
0
1
0
2
1
0
2
2
1
0
2
0
0
0
0
0
4
1
1
0
3
1
0
0
3
0
1
0
0
0
0
2
0
0
0
0
0
1
0
2
0
2
0
2
1
1
2
1
2
0
0
0
0
1
1
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
2
2
0
0
2
0
1
0
1
0
0
1
0
2
0
2
0
0
0
0
1
0
2
0
0
1
1
0
2
0
0
0
1
0
1
2
2
1
1
1
0
0
0
0
0
0
1
2
0
2
3
0
1
0
0
0
0
2
2
0
1
1
0
1
0
1
0
1
0
2
1
2
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
2
0
1
1
0
1
2
2
1
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
2
2
1
1
2
2
0
0
1
0
1
0
1
0
0
0
0
0
2
2
1
0
0
0
1
1
0
0
2
0
0
0
2
1
1
0
0
0
0
2
0
0
0
2
2
0
0
0
2
2
0
0
0
2
2
0
3
0
0
1
0
0
0
0
0
1
2
0
0
0
1
0
1
0
1
2
1
0
1
3
2
1
0
1
2
0
0
0
0
0
0
3
0
1
0
0
1
0
0
0
2
1
2
0
2
0
1
1
1
1
0
1
1
1
0
0
1
0
0
0
1
0
1
0
1
3
0
0
0
0
1
0
1
0
0
2
0
1
2
0
1
1
1
0
0
0
0
2
0
2
0
0
1
0
0
0
2
1
0
2
2
1
0
1
2
0
0
2
0
2
0
2
0
2
2
1
2
2
0
0
0
1
5
0
1
0
0
0
1
2
1
0
0
2
1
1
1
0
0
2
2
0
1
0
0
0
1
0
1
0
0
0
0
0
1
1
2
2
2
1
0
2
0
0
0
0
2
0
0
1
1
0
1
1
1
0
0
0
0
2
0
2
0
2
0
0
0
0
2
0
0
1
0
1
2
2
1
0
0
0
1
0
0
1
0
0
2
0
0
0
1
0
1
0
1
1
0
1
1
3
2
0
0
0
1
2
2
0
0
0
0
0
0
1
0
1
0
1
3
0
0
0
0
0
1
2
0
0
1
1
0
2
0
2
1
2
0
0
0
2
1
0
0
0
2
0
1
0
3
0
0
0
0
2
0
0
0
0
1
2
1
1
0
0
1
2
1
0
0
1
0
2
0
0
0
2
0
2
0
1
0
1
6
2
0
0
1
0
1
1
0
1
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
2
2
0
1
0
0
0
0
0
2
0
1
2
0
0
0
2
0
2
0
2
6
0
0
0
1
1
1
1
0
2
2
2
0
0
0
2
0
0
1
0
2
1
0
0
0
0
0
0
2
2
1
1
1
1
0
0
1
1
1
1
0
0
0
2
0
1
0
1
1
0
0
2
0
0
1
0
2
0
0
0
0
0
2
0
2
0
0
2
0
2
0
0
0
1
0
2
0
1
2
1
1
0
0
2
0
0
0
1
0
0
0
1
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
1
2
0
0
0
0
0
0
4
1
0
0
1
0
1
0
1
0
2
1
0
0
0
0
0
0
0
2
0
0
0
1
1
0
2
0
1
2
0
1
2
0
2
1
2
0
0
0
2
1
2
1
0
1
2
1
0
0
4
3
2
1
1
0
0
0
0
0
1
0
3
1
0
0
2
0
1
2
0
0
2
0
1
2
3
2
0
0
2
0
2
0
1
0
0
4
1
0
0
0
0
0
2
0
0
0
0
2
1
0
2
0
0
2
1
2
2
0
2
2
1
1
0
0
0
0
0
2
0
2
2
2
0
0
0
0
0
1
0
0
1
0
1
1
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
1
1
0
0
2
0
0
0
0
1
2
0
0
0
2
0
1
0
0
2
0
0
0
1
0
0
2
0
0
0
1
0
0
2
1
0
0
2
1
2
0
0
0
0
1
0
4
1
0
0
0
2
0
1
1
0
1
0
0
1
2
1
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
2
1
0
0
4
1
0
0
0
0
1
0
0
1
0
2
0
0
1
0
0
2
2
0
0
1
0
0
4
0
2
0
0
0
2
0
0
1
0
0
2
1
1
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
2
0
1
0
0
0
0
0
4
0
1
0
0
0
1
1
0
1
0
2
1
0
2
0
1
1
1
0
0
0
0
0
0
0
2
1
1
2
1
2
0
3
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
1
2
0
1
0
2
1
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
1
0
1
2
0
1
0
1
0
2
0
1
1
2
2
1
1
0
1
0
0
2
0
0
1
2
2
0
1
0
0
0
0
1
1
2
0
1
2
0
2
2
0
0
2
0
0
0
1
0
0
0
0
1
0
1
1
0
1
0
1
0
2
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
1
0
1
0
2
0
0
1
2
2
0
0
2
0
0
2
0
0
1
0
1
2
0
1
1
1
0
2
2
0
8
2
1
0
3
3
0
1
0
0
0
1
0
0
1
1
1
2
0
2
2
1
0
0
0
0
0
2
0
0
0
2
3
1
0
0
0
1
0
1
0
0
2
1
2
0
0
6
0
0
1
0
1
0
1
0
0
0
0
0
0
2
0
1
0
1
1
0
0
0
0
0
1
2
0
0
0
0
0
2
0
2
0
0
2
0
1
0
2
0
0
0
0
1
2
0
0
1
0
0
4
1
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
1
0
0
1
2
0
2
0
3
2
1
0
0
1
0
0
0
2
1
1
2
2
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
2
2
3
0
2
1
0
0
0
0
1
3
0
0
0
2
1
3
0
1
1
2
0
1
1
1
2
0
1
0
0
0
0
2
1
0
1
0
1
0
0
2
0
1
0
2
1
2
2
0
0
0
0
0
0
0
2
1
1
3
1
2
1
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
1
0
0
1
2
2
0
1
2
2
0
0
1
1
0
2
2
2
1
0
0
0
3
0
0
2
2
0
0
1
0
2
0
0
1
1
1
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
3
0
1
0
0
0
1
4
0
0
0
1
1
0
0
2
1
1
0
0
1
0
1
1
0
1
1
0
0
0
0
2
0
0
1
0
0
0
1
2
0
1
0
0
0
4
0
0
1
0
0
0
0
2
0
0
0
2
2
0
1
0
2
0
0
0
2
2
2
1
1
2
0
0
0
0
0
1
1
0
0
0
0
0
1
3
0
0
0
0
1
2
0
1
2
1
1
0
2
0
0
0
1
2
0
1
1
1
2
1
2
2
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
2
1
1
2
1
2
2
2
0
0
2
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
1
2
0
2
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
2
0
0
0
0
1
1
0
0
2
3
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
2
0
2
0
0
0
0
2
0
3
0
0
0
2
0
2
1
1
2
0
2
0
0
0
0
0
3
0
0
2
0
0
1
0
0
0
2
0
1
0
0
2
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
2
1
0
0
0
0
3
0
2
2
0
2
1
0
0
0
0
0
0
0
0
2
0
1
4
3
0
0
0
1
1
0
2
2
0
2
1
0
2
0
1
4
1
1
0
0
2
4
0
0
0
2
1
1
5
1
0
0
0
1
2
0
2
0
0
0
1
0
0
0
1
0
0
2
1
0
0
0
0
2
0
0
2
0
1
0
0
0
1
0
0
1
2
1
0
0
0
0
0
0
3
0
0
0
1
0
1
0
6
1
0
4
0
0
0
0
0
2
0
1
2
3
0
1
0
0
0
1
0
1
0
0
1
0
0
0
1
1
2
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
2
0
1
3
0
0
1
2
0
2
0
0
2
3
0
1
1
6
2
2
2
0
0
0
0
0
0
1
2
0
1
1
0
1
3
0
2
0
0
2
0
1
0
0
0
0
1
0
1
0
0
2
2
0
0
0
1
2
0
1
0
1
0
1
0
0
1
0
0
1
0
2
1
0
0
0
2
0
0
0
0
0
0
1
2
2
1
0
0
2
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
1
0
2
0
0
1
0
2
1
2
0
0
0
0
0
0
2
1
0
0
1
0
3
0
1
3
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
2
1
0
2
2
2
2
0
0
2
0
2
0
2
0
0
0
0
1
1
0
1
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
2
0
1
1
0
1
0
0
0
0
3
0
0
0
2
0
2
0
2
0
2
0
0
0
0
0
1
2
1
2
2
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
2
0
0
3
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
1
3
0
1
0
0
0
0
0
2
0
0
0
2
0
0
1
0
1
1
1
0
0
0
0
1
0
0
0
0
1
0
2
0
0
2
1
0
1
1
0
1
2
1
2
0
2
1
0
0
0
0
0
0
1
0
2
0
0
0
1
0
1
0
0
2
0
0
1
1
0
1
0
1
0
2
0
0
0
1
0
0
0
0
0
0
3
1
1
1
0
0
0
1
0
0
1
0
0
2
0
0
2
2
1
0
0
1
0
6
0
1
2
2
0
0
0
3
0
0
0
1
0
0
2
2
3
0
1
0
0
1
0
0
4
2
2
0
0
0
2
0
3
0
0
0
2
1
0
2
0
1
0
2
1
2
2
0
2
1
0
1
0
0
2
0
0
0
0
2
0
3
0
2
0
1
0
2
2
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
2
0
0
1
0
0
0
2
0
0
5
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
2
0
2
0
0
1
0
1
0
1
0
0
0
1
2
0
3
5
0
1
0
1
0
0
0
1
0
0
1
1
2
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
1
0
0
0
0
1
0
2
1
0
0
0
0
0
0
1
0
0
0
1
0
2
1
0
1
1
0
1
0
0
3
3
1
0
0
2
0
0
0
0
2
2
1
0
1
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
2
0
0
1
0
0
1
2
0
0
2
2
1
0
2
0
1
0
1
0
1
0
2
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
1
0
2
0
0
0
0
0
2
0
2
0
0
0
0
1
0
1
0
1
0
0
1
1
1
1
0
0
1
1
2
0
0
1
1
0
0
1
0
0
0
0
2
2
1
0
0
0
0
2
0
0
0
1
1
0
1
0
0
1
1
0
0
0
0
0
1
0
2
2
1
2
2
0
0
0
1
1
0
0
0
0
1
2
0
1
1
2
2
0
0
2
0
2
0
0
1
0
0
1
0
2
0
1
2
0
2
1
0
0
0
1
0
0
1
2
0
0
0
0
2
0
0
3
0
0
0
4
2
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
3
0
2
0
0
0
1
0
0
0
0
0
1
0
2
0
5
0
0
0
0
0
1
0
0
0
0
0
2
0
2
2
1
1
1
2
0
2
0
2
0
1
0
0
0
0
1
5
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
2
0
2
1
0
1
2
0
0
1
1
2
1
1
0
0
2
0
0
0
1
1
0
0
1
1
2
2
1
0
0
0
2
1
1
0
2
0
1
1
0
0
1
1
1
0
0
1
1
0
1
0
0
0
1
2
0
0
0
2
1
0
0
1
0
0
0
0
1
1
0
2
2
0
0
0
2
0
0
1
0
0
0
1
0
0
2
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
3
1
0
0
0
1
0
1
2
0
2
0
0
0
0
2
2
1
0
0
0
0
0
2
2
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
1
0
0
0
1
0
1
0
1
1
0
2
2
1
0
1
2
0
0
0
0
0
2
1
0
1
1
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
2
1
2
0
0
0
0
1
0
0
0
1
2
1
0
0
1
2
0
0
1
0
0
0
2
1
0
2
0
0
1
1
2
2
1
0
1
0
2
0
0
2
1
1
0
0
0
1
1
0
1
0
0
1
2
0
0
1
1
2
1
0
1
1
0
1
1
1
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
1
0
2
2
0
0
1
0
1
0
2
0
1
0
0
0
1
0
0
3
0
2
1
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
1
0
2
0
0
0
0
1
1
2
0
0
1
1
1
0
0
2
0
0
0
0
0
0
2
0
1
0
2
0
2
0
0
0
1
0
1
2
1
2
2
0
0
3
1
0
0
0
1
0
1
1
0
0
2
1
1
0
0
1
0
2
0
3
2
0
2
0
0
0
2
2
0
0
2
0
0
0
2
0
0
1
1
0
1
0
1
1
1
0
0
0
0
0
0
1
0
2
0
1
0
1
1
2
0
2
1
0
0
1
2
2
0
2
1
0
2
0
0
1
1
0
0
0
1
0
0
2
0
0
0
0
0
2
0
2
1
0
0
0
0
2
0
2
0
0
0
1
1
2
0
1
0
3
7
1
0
0
2
1
0
0
0
2
1
1
1
0
0
0
0
0
0
0
2
0
1
0
1
1
0
2
1
2
1
0
2
0
0
0
1
0
0
0
2
1
0
1
0
1
0
0
0
0
0
2
0
2
1
2
1
2
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
1
2
1
1
1
2
0
0
0
1
2
0
3
2
2
0
0
0
0
4
2
2
2
1
3
1
2
2
0
2
2
0
0
0
2
0
0
2
0
3
0
0
0
0
0
2
2
0
1
0
0
2
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
1
0
1
0
0
1
2
0
1
2
1
0
1
0
0
1
0
0
2
1
0
1
0
0
2
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
1
2
0
0
0
1
0
2
0
0
0
1
0
0
0
1
0
0
0
1
0
0
2
4
0
1
0
2
1
1
0
0
0
1
0
2
1
0
0
1
0
0
0
2
0
0
0
1
2
2
1
0
0
2
0
2
0
0
0
0
1
1
0
1
0
0
2
2
2
1
1
0
0
1
1
3
1
0
1
1
0
2
2
1
2
1
0
2
2
0
2
0
0
1
0
0
0
0
2
3
0
0
1
2
0
1
0
2
1
0
0
2
2
0
0
0
2
1
0
0
2
0
2
1
0
1
0
1
1
1
0
0
0
1
0
1
0
0
2
3
0
2
1
1
0
2
0
1
0
0
0
0
2
1
0
1
2
2
1
2
2
2
0
0
2
1
0
1
1
0
3
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
1
0
2
2
1
0
0
0
0
2
1
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
2
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
4
0
1
0
0
0
0
1
0
0
0
1
2
1
1
0
1
1
0
0
1
0
0
0
0
0
2
1
1
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
1
0
1
0
0
0
1
0
0
2
1
0
2
0
2
2
2
0
0
1
1
0
0
0
2
1
1
0
2
1
1
1
1
2
0
0
0
0
0
0
1
0
1
0
0
0
0
2
2
2
12
2
0
0
0
0
0
0
1
0
2
0
1
0
0
0
2
2
0
0
2
0
0
2
0
0
0
1
0
1
0
2
1
1
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
1
1
1
0
2
1
0
0
1
0
2
1
0
0
0
0
0
1
0
0
0
0
0
2
1
2
0
0
1
0
0
0
1
1
1
0
2
2
0
2
1
0
1
0
0
0
1
0
3
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
2
2
2
0
0
0
0
0
1
1
1
0
0
0
1
0
1
2
0
0
0
1
0
0
0
1
0
1
0
0
2
2
1
1
0
0
0
0
2
0
0
1
0
1
0
0
1
2
0
0
1
0
1
0
0
0
0
1
0
0
1
1
2
1
1
0
0
0
2
0
2
2
0
1
3
0
0
3
2
0
0
1
0
1
0
0
2
0
1
1
0
1
2
0
0
3
0
0
1
2
0
2
1
2
0
0
0
0
0
1
2
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
3
2
1
0
0
2
0
0
0
0
2
1
0
0
0
0
0
2
0
1
0
0
0
0
1
1
0
3
0
0
2
1
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
2
2
1
2
0
1
0
0
0
0
0
0
1
0
2
1
0
1
2
0
0
2
0
0
0
0
0
2
0
1
2
0
2
2
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
2
1
2
0
0
0
0
0
0
0
0
1
2
0
1
2
0
0
1
2
0
2
0
0
1
1
0
1
0
1
1
0
2
0
0
0
0
0
0
0
1
0
1
0
1
2
0
0
0
1
1
0
0
0
2
0
2
2
1
0
2
2
1
0
1
0
0
1
0
2
0
0
2
0
1
1
1
0
0
0
2
0
2
0
1
0
0
0
1
1
0
3
0
0
0
0
0
0
0
0
3
0
0
0
0
1
2
0
0
0
1
3
0
0
2
1
1
1
0
0
1
0
0
2
1
2
0
3
1
1
0
0
0
2
1
0
2
0
0
1
1
0
0
0
1
1
0
0
0
0
1
1
1
0
0
0
0
2
1
1
1
1
0
0
0
0
1
1
1
0
0
0
0
0
0
3
0
2
0
2
0
0
0
0
2
0
1
0
0
1
0
0
2
0
0
0
1
0
2
0
1
2
1
2
0
2
1
0
0
0
0
0
2
3
0
0
1
0
0
0
0
2
2
0
1
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
1
2
2
1
0
0
1
2
0
1
0
2
1
2
0
0
0
1
0
2
0
1
0
0
1
1
0
0
0
0
0
1
1
0
1
0
5
2
0
1
0
1
0
0
1
0
2
1
1
0
0
0
2
0
0
0
1
2
1
0
0
0
0
2
1
0
0
0
0
0
2
1
0
0
0
1
2
0
0
0
0
1
0
0
0
1
1
0
2
0
1
1
0
2
0
0
0
1
1
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
1
0
0
2
0
0
2
3
0
2
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
2
1
1
0
3
0
2
0
0
2
0
1
0
0
2
2
3
0
0
1
0
0
0
0
0
1
0
2
1
0
2
0
1
2
0
0
1
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
2
0
0
0
2
0
8
2
0
0
0
2
2
0
1
0
0
1
1
0
0
1
0
0
0
2
0
1
1
2
0
0
1
0
0
0
0
1
0
1
2
1
0
1
0
0
0
0
1
1
0
0
0
2
1
0
0
0
0
3
3
1
1
0
2
0
1
3
2
0
0
1
0
0
0
1
1
0
2
0
1
1
2
0
2
0
0
1
0
2
0
1
1
2
0
0
0
2
0
0
0
0
1
0
1
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
1
2
2
0
0
1
0
2
0
0
2
2
0
0
0
0
0
0
0
0
3
1
0
0
2
1
0
0
0
1
1
0
0
0
1
0
2
1
0
0
3
0
0
1
0
0
0
2
0
2
1
0
0
0
1
1
2
2
0
0
0
2
1
0
0
0
0
1
2
4
1
2
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
2
0
1
0
0
1
0
0
2
1
2
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
2
2
0
2
0
1
0
0
1
1
0
1
0
0
0
1
4
0
1
1
1
0
0
0
0
2
0
2
0
0
0
1
0
1
0
0
0
0
2
0
0
0
2
0
1
0
0
1
2
2
2
2
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
1
1
1
0
0
0
0
1
0
0
0
1
0
2
0
0
2
1
2
0
1
1
0
2
0
0
2
0
0
0
4
0
0
0
0
0
0
0
1
1
0
0
1
1
1
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
3
0
2
1
0
2
0
0
0
2
0
0
0
1
1
0
0
0
0
1
0
0
0
2
2
0
2
0
0
0
0
0
2
1
2
0
0
2
1
0
0
0
0
2
0
2
0
1
0
2
1
2
0
2
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
2
0
0
0
2
0
1
2
0
0
0
2
1
1
2
0
1
4
2
1
0
0
0
0
0
0
2
0
0
0
1
1
0
0
2
2
0
0
1
2
2
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
3
0
1
1
1
2
1
0
2
2
1
2
1
2
2
1
1
1
2
0
0
1
0
1
2
1
2
1
1
0
3
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
1
0
2
2
1
0
1
0
1
0
0
0
1
0
2
1
1
1
0
2
1
0
0
0
0
0
2
0
1
2
0
1
0
0
0
1
3
2
2
2
2
1
0
0
2
0
0
2
1
0
0
2
2
1
1
0
0
1
1
0
0
1
0
0
0
1
2
0
1
0
2
1
1
1
2
0
2
1
0
1
0
2
1
0
0
1
0
0
2
0
0
0
1
0
1
1
0
1
0
2
1
0
0
0
0
0
2
0
2
0
1
0
0
0
0
1
2
0
0
2
0
1
3
1
2
2
2
1
0
0
1
0
2
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
3
1
0
0
0
0
0
1
0
1
1
0
0
0
2
0
0
0
1
1
3
2
0
0
3
0
1
2
0
2
0
2
0
4
0
1
0
1
2
2
2
0
0
0
0
0
0
0
1
0
0
0
0
1
2
1
1
1
0
1
0
1
2
0
1
0
0
0
0
2
0
2
0
1
0
2
0
1
0
1
2
0
0
2
1
0
0
0
0
1
0
1
0
2
1
0
1
0
0
0
2
0
0
0
0
0
1
0
2
0
2
0
0
1
0
2
0
1
0
0
0
2
0
0
1
0
1
2
4
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
1
0
0
1
0
0
1
2
0
0
0
0
1
1
0
0
1
2
2
0
0
0
2
1
0
1
0
4
0
1
0
0
2
0
2
1
0
0
0
2
2
0
0
2
0
0
2
0
0
1
0
2
1
2
2
0
1
0
0
1
0
0
0
0
2
0
0
0
2
0
1
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
2
1
0
0
2
0
0
0
0
0
1
2
2
0
0
1
0
1
2
2
0
2
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
2
0
1
1
0
0
0
2
0
0
0
0
0
0
2
1
0
1
1
0
0
0
1
1
1
1
1
1
0
0
4
0
0
1
1
1
1
1
1
0
0
2
0
0
0
1
2
1
2
0
0
0
0
1
0
0
1
0
0
0
2
1
0
2
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
2
2
0
0
0
0
2
2
0
1
0
0
0
1
2
0
0
2
1
3
1
2
1
1
2
2
0
1
0
0
1
1
0
5
1
0
1
0
1
2
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
1
0
0
0
2
0
1
0
0
1
0
0
1
1
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
1
1
0
0
0
2
2
1
2
0
0
1
1
0
0
1
2
2
0
1
1
0
0
3
0
0
0
0
1
0
0
0
1
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
1
0
0
2
0
0
0
0
0
0
1
0
1
1
2
1
1
1
1
0
2
1
0
0
1
1
0
1
1
2
0
0
0
1
0
2
1
0
0
0
1
0
0
0
2
1
2
2
2
0
0
2
0
0
0
0
0
2
1
0
2
0
1
0
0
0
1
0
2
1
0
0
1
1
0
0
1
2
0
0
1
0
0
0
0
0
1
0
1
2
1
1
0
0
0
0
1
1
0
2
2
1
0
0
2
0
0
2
1
0
1
0
0
1
0
0
0
1
1
0
0
2
0
2
1
1
0
2
0
2
0
0
2
0
0
0
2
2
0
0
0
0
0
2
1
1
0
0
1
0
3
0
0
2
0
0
4
2
2
0
1
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
2
1
0
2
0
1
0
3
0
1
0
0
2
2
1
0
0
1
1
0
0
1
0
1
0
0
2
1
2
0
0
2
1
2
2
0
1
2
2
1
2
0
0
0
0
0
2
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
2
1
0
2
3
0
0
0
8
0
1
0
2
0
0
0
0
0
2
2
0
0
2
2
0
3
1
0
0
3
3
2
0
1
0
0
0
0
0
0
0
2
1
1
1
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
1
1
0
0
1
0
2
2
0
1
0
0
0
1
0
0
0
0
1
2
0
0
1
0
1
2
5
0
1
0
0
2
1
0
0
0
0
2
0
2
2
0
1
0
2
3
0
3
1
0
1
3
2
0
0
1
0
1
0
3
3
1
0
1
2
0
0
1
0
0
1
1
0
0
0
0
0
1
0
2
0
0
1
0
0
0
2
2
2
0
0
1
0
0
0
0
0
0
2
2
0
0
2
0
1
0
1
0
2
0
2
2
0
1
0
2
4
0
0
1
1
0
3
0
2
0
0
2
2
2
0
0
0
1
0
0
0
0
0
2
0
2
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
1
1
1
2
1
1
2
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
1
2
0
1
0
2
0
0
0
2
2
1
1
0
0
2
0
0
0
2
5
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
5
0
1
2
1
1
0
1
0
1
0
0
0
2
0
0
0
0
1
0
0
1
2
2
0
0
1
0
1
0
1
0
0
2
0
1
1
0
0
0
1
1
0
1
1
2
0
2
2
0
1
0
0
0
1
0
2
2
2
0
0
1
0
1
2
1
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
2
0
0
0
2
0
0
2
0
0
0
2
1
1
0
0
0
1
1
2
0
2
0
1
0
0
0
0
2
0
2
2
1
2
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
1
0
2
3
0
1
2
1
2
0
3
1
1
1
0
1
0
0
0
0
1
0
1
1
0
0
2
0
0
0
0
0
2
2
2
0
0
0
1
2
2
0
1
0
0
0
1
0
2
1
2
0
0
1
0
0
0
0
0
0
2
1
3
2
0
0
3
1
1
0
2
1
2
0
2
0
0
0
0
1
0
1
1
3
1
0
1
2
1
0
0
0
0
0
1
1
0
1
0
0
1
0
0
1
1
0
0
0
0
0
1
1
0
0
5
1
1
0
1
0
0
0
0
2
0
3
1
2
0
1
0
0
0
1
1
1
2
0
0
1
0
0
0
0
0
2
0
0
0
1
2
2
0
0
0
1
0
2
0
0
0
0
0
1
2
0
1
0
0
2
0
0
0
0
13
2
0
1
2
0
0
0
2
2
0
0
0
0
1
0
0
2
1
0
0
4
1
0
0
0
1
0
0
1
0
0
0
0
0
0
2
2
1
2
2
0
0
2
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
1
0
1
0
1
0
2
1
2
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
3
1
0
0
0
0
2
0
1
2
0
0
2
2
0
0
0
3
1
0
0
3
0
0
1
0
0
2
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
1
0
2
0
1
0
0
0
1
0
0
0
2
0
0
2
0
0
0
2
2
1
0
0
0
0
2
2
0
0
0
0
0
0
1
1
2
0
2
0
0
1
0
0
0
0
0
2
1
0
2
0
2
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
3
0
0
1
1
0
0
1
1
0
0
0
1
0
2
0
0
1
0
2
0
2
2
1
0
1
0
0
0
0
2
2
1
0
0
1
2
0
2
0
0
0
2
1
0
2
1
0
1
0
0
1
1
0
0
2
0
1
0
0
2
0
0
0
1
0
0
0
1
2
2
0
0
2
0
0
0
1
0
2
0
0
0
1
2
0
0
0
0
2
2
0
2
0
0
0
0
0
1
1
0
0
2
2
0
2
0
2
0
0
0
0
1
1
1
1
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
1
0
2
0
0
1
0
0
1
2
1
2
0
1
0
0
0
2
1
0
1
1
2
0
2
2
0
0
0
0
1
0
2
2
1
0
0
0
0
0
1
1
0
1
0
2
2
0
1
0
1
7
0
1
2
0
2
0
1
5
2
0
0
1
0
0
0
0
1
0
1
0
0
2
0
0
0
1
1
1
0
0
2
1
0
1
0
1
1
0
2
0
0
0
0
0
1
0
0
0
0
0
1
2
1
0
5
0
0
1
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
2
0
1
0
0
2
0
1
0
0
1
2
0
1
2
0
3
1
0
0
0
0
2
0
1
0
2
1
0
1
2
1
0
0
1
0
1
0
2
0
1
1
1
0
2
0
2
0
2
0
0
0
0
0
0
2
0
0
1
0
0
2
2
0
0
0
1
0
0
0
3
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
2
1
0
0
2
0
1
0
0
0
1
0
2
0
0
0
2
0
0
2
2
1
2
1
1
6
0
0
1
0
2
2
0
0
0
1
1
3
0
0
0
0
1
1
0
0
0
2
0
1
2
0
0
0
0
2
1
0
1
0
1
1
0
0
2
2
0
2
0
0
0
2
1
0
0
0
0
0
0
1
1
0
0
0
0
2
0
2
0
0
0
1
3
0
0
1
0
2
0
0
1
1
0
0
0
1
0
1
0
2
0
3
1
2
0
1
0
0
0
1
0
0
1
2
1
1
0
2
2
1
0
0
1
2
0
1
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
1
2
0
0
0
1
1
5
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
2
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
2
1
0
0
0
2
2
1
1
1
1
2
0
0
0
1
0
2
0
0
2
0
0
0
0
0
2
2
0
4
0
0
0
0
0
0
0
1
2
2
0
0
0
1
0
0
0
0
0
0
2
1
1
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
2
0
1
2
0
2
0
0
0
1
0
2
2
0
0
4
1
2
1
2
0
0
0
0
0
1
1
1
1
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
1
1
1
0
1
0
0
0
0
1
0
1
0
1
0
0
0
2
1
1
2
0
5
0
0
0
1
2
0
0
2
0
2
0
3
0
0
0
2
0
0
1
2
0
1
2
0
0
1
1
0
1
0
2
0
0
1
1
0
1
1
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
2
0
1
0
0
2
0
0
2
1
0
2
2
1
1
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
3
0
0
0
1
0
0
2
0
0
0
1
0
0
1
2
1
1
2
1
0
1
1
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
2
1
0
2
0
2
0
0
1
1
0
2
2
0
2
2
0
1
1
0
2
0
0
0
0
2
1
0
0
1
0
0
0
0
4
1
0
2
0
0
2
1
2
2
0
0
0
1
0
0
2
0
2
2
0
0
2
0
0
0
1
0
0
1
1
0
0
1
1
2
0
0
0
0
2
0
1
0
0
2
0
2
0
0
2
0
0
2
0
0
1
0
0
1
0
2
0
0
0
1
1
0
0
0
1
1
0
0
1
0
0
0
0
0
2
2
0
0
2
0
0
0
0
1
0
3
2
0
0
1
1
0
0
1
0
1
0
1
0
0
0
0
0
1
0
2
2
2
0
1
0
2
1
1
0
0
1
1
0
2
0
2
0
2
0
0
1
1
2
2
1
0
0
0
0
0
0
1
1
1
0
1
1
0
0
0
1
0
2
0
0
0
0
2
0
2
0
1
0
1
0
0
1
1
2
1
0
0
0
1
0
0
0
1
1
0
0
3
2
1
1
2
0
2
0
2
1
0
0
0
2
0
0
0
0
0
1
0
2
1
3
2
0
0
1
0
0
0
0
0
0
0
1
1
2
0
0
2
0
1
2
3
1
2
2
0
0
0
0
0
0
3
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
1
1
0
2
1
2
2
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
2
2
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
2
0
2
0
0
1
1
1
2
0
1
0
0
0
0
0
1
0
2
1
0
0
0
0
2
0
4
2
1
0
0
0
0
0
0
1
0
1
2
2
1
0
0
0
0
1
1
0
1
0
0
1
1
1
2
0
0
0
2
0
0
0
1
2
0
1
1
1
0
1
1
0
0
1
1
0
0
0
1
1
0
2
0
0
1
0
1
2
0
2
2
2
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
2
0
2
2
0
0
0
0
2
0
1
0
0
0
0
0
1
1
12
0
0
1
2
1
0
0
1
1
0
0
0
1
1
2
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
2
1
1
0
2
0
1
0
2
0
0
1
2
0
2
2
0
0
0
0
3
0
0
1
0
0
2
0
2
0
0
1
0
1
0
1
2
1
0
2
0
0
0
0
1
1
2
0
0
1
1
2
0
2
0
0
2
0
2
3
0
0
0
0
0
1
3
2
0
1
0
0
1
0
3
0
0
0
0
2
1
1
0
0
0
0
0
1
0
1
1
2
0
0
0
0
0
2
0
1
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
2
0
0
2
1
0
0
1
2
0
0
2
1
0
2
1
0
0
1
0
0
2
3
2
0
0
0
0
0
1
0
0
0
0
1
0
2
2
2
0
0
0
0
1
0
1
1
0
0
1
0
0
0
1
2
1
0
0
0
2
2
2
0
2
0
1
0
1
0
2
0
2
1
0
0
1
2
0
2
0
0
1
1
0
0
0
1
0
0
2
2
0
0
0
1
1
0
0
0
0
0
0
1
0
2
0
0
2
1
0
0
1
0
0
0
0
0
1
0
0
2
1
1
0
0
0
0
0
3
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
1
2
2
0
0
0
2
1
1
1
1
0
3
0
0
2
0
0
1
1
0
0
0
0
1
0
0
1
0
1
1
2
0
0
0
0
0
0
0
0
0
1
0
1
0
1
2
0
0
2
0
0
2
1
0
1
2
0
1
0
2
0
0
2
1
2
0
0
0
0
0
1
2
1
0
1
1
0
0
0
2
1
1
0
1
0
1
0
4
0
0
0
2
0
0
0
1
2
0
0
0
0
5
0
2
0
4
0
0
2
0
1
2
1
2
0
2
1
1
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
2
0
0
2
0
2
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
1
0
1
2
2
1
1
0
1
2
0
1
0
0
1
0
2
2
2
0
0
0
1
0
2
0
1
0
0
0
0
0
0
1
4
0
0
1
1
2
0
2
0
1
2
3
2
0
2
0
0
1
0
0
2
2
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
1
2
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
2
0
1
1
0
1
0
0
2
0
3
1
0
0
0
0
2
0
2
1
2
2
0
2
0
1
0
2
1
0
1
0
0
0
0
0
0
2
1
1
0
0
2
0
0
1
3
1
0
0
0
0
0
0
2
2
2
1
0
1
0
0
0
0
0
1
2
0
1
0
0
0
0
1
1
2
0
0
0
0
1
0
1
0
0
0
2
1
2
1
0
0
0
0
1
2
0
4
2
0
1
0
0
0
0
2
0
0
2
2
0
1
0
1
1
0
1
1
0
1
0
0
0
1
1
0
2
0
0
0
2
2
1
0
0
1
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
2
2
1
0
2
0
1
1
2
0
0
0
1
0
0
0
2
0
1
0
2
2
0
0
2
0
2
1
2
0
1
2
1
2
0
0
1
0
2
1
0
0
0
1
2
1
0
0
1
0
2
0
2
1
0
0
1
1
0
0
1
1
1
2
0
0
1
1
0
0
0
0
0
2
0
2
2
0
0
0
0
1
0
1
0
0
1
0
1
1
0
1
2
0
0
0
1
0
1
0
1
1
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
1
1
1
0
1
1
0
0
1
1
2
0
1
0
1
0
0
0
0
1
1
1
1
2
1
0
3
0
1
0
0
2
1
0
1
1
0
0
0
1
0
3
0
0
0
0
0
1
0
0
0
1
2
1
2
0
0
1
0
0
2
0
1
2
0
0
1
2
1
1
2
0
0
0
2
3
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
2
0
2
1
0
0
0
1
1
2
1
0
2
0
0
1
0
0
1
0
0
1
1
0
2
0
0
2
0
2
0
2
0
0
1
0
2
0
0
0
0
2
0
2
0
1
0
2
2
0
0
0
2
0
0
0
0
1
0
0
3
0
0
0
1
0
0
0
1
1
0
2
1
0
2
2
1
0
1
0
0
0
1
2
1
2
1
0
0
1
1
0
2
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
2
1
1
0
2
0
2
0
1
0
0
2
0
0
0
0
0
0
1
0
0
2
0
2
0
0
1
0
0
0
0
0
1
2
1
2
0
1
2
1
0
0
2
4
1
1
1
0
0
0
2
0
3
1
1
0
0
0
3
0
1
1
1
0
1
2
0
0
0
0
0
1
2
0
1
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
1
1
0
2
0
2
0
0
1
2
0
0
0
2
2
0
2
0
0
1
0
2
0
1
0
0
1
6
1
1
2
0
2
0
0
1
0
0
0
1
2
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
2
0
1
0
2
1
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
2
0
0
0
0
2
1
0
2
0
2
0
0
0
0
1
1
3
0
0
2
0
0
0
0
0
4
0
1
0
0
2
0
0
0
0
1
0
1
1
0
1
0
0
1
0
1
1
0
0
2
3
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
2
0
0
0
0
1
2
0
0
2
0
0
0
2
2
0
0
2
0
0
1
0
2
0
0
0
0
0
0
3
0
1
0
0
0
0
1
0
2
1
0
0
1
1
0
0
0
2
1
0
1
0
0
0
0
2
0
0
2
0
0
1
1
1
0
0
2
0
0
0
1
0
1
1
0
0
3
1
0
1
0
1
1
1
0
2
2
0
0
1
2
2
2
0
0
0
0
1
0
2
0
0
1
2
2
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
2
0
0
1
0
0
0
0
1
0
1
0
1
1
2
0
2
0
0
0
1
1
2
0
0
1
1
0
0
0
2
0
0
1
2
2
0
0
0
2
0
0
1
1
0
1
1
0
0
2
0
0
2
0
4
0
0
0
0
2
0
1
2
0
2
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
2
2
1
0
1
2
0
1
0
1
2
0
1
1
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
1
1
1
0
0
3
0
0
1
2
4
0
0
0
0
0
0
0
1
2
0
0
0
2
2
0
0
1
0
0
0
1
2
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
2
2
1
0
0
2
0
0
0
0
1
1
0
2
0
0
0
2
0
1
2
2
0
0
1
0
2
1
0
1
0
0
2
4
2
0
0
0
1
1
2
1
1
3
0
1
1
1
0
0
2
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
2
2
0
0
0
1
0
1
0
0
1
1
0
0
1
0
1
2
0
0
2
0
0
0
0
2
1
0
0
0
1
0
1
4
0
1
3
1
1
0
0
1
0
1
0
0
0
0
0
1
1
1
1
0
2
0
0
1
0
0
1
0
1
0
0
2
1
0
0
0
0
0
0
2
2
2
1
2
0
0
2
0
0
0
1
0
0
1
1
2
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
2
5
0
1
1
0
0
1
2
0
0
3
0
1
0
1
2
0
1
0
0
0
0
0
1
1
1
0
2
0
2
2
1
2
0
0
0
2
2
0
1
0
1
1
0
0
2
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
2
2
1
1
2
0
0
2
0
0
2
0
2
0
0
0
0
0
1
0
1
0
0
0
0
1
2
2
1
0
0
0
2
0
2
1
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
2
0
2
0
1
0
1
2
1
1
0
0
0
0
0
0
0
0
0
0
2
2
1
0
2
0
0
1
0
0
2
1
4
0
2
2
2
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
4
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
2
0
2
2
0
0
0
0
0
2
0
0
0
0
1
0
2
2
2
0
0
0
0
0
0
1
0
0
1
1
2
0
0
2
0
2
0
0
1
1
0
0
0
0
0
0
0
2
0
2
0
1
0
4
0
1
0
1
0
2
0
0
0
2
0
1
0
2
0
0
2
0
0
0
1
2
0
0
0
1
0
0
0
0
1
0
0
1
2
0
2
0
0
1
2
4
0
1
1
1
0
2
2
0
1
0
3
0
2
1
1
0
0
0
2
0
1
1
0
1
1
0
0
0
0
1
0
0
0
1
2
0
0
1
1
2
0
0
2
0
0
0
0
2
1
1
0
1
1
0
1
4
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
2
1
2
2
0
0
0
1
1
1
1
2
0
0
1
3
0
2
0
1
0
0
1
1
0
0
0
2
1
1
0
0
0
2
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
2
0
2
2
0
1
0
2
0
0
0
0
1
0
2
1
2
0
2
0
1
0
0
1
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
1
2
0
0
1
0
0
0
0
2
0
0
2
0
1
2
0
2
2
1
2
0
1
0
0
4
1
0
1
1
0
2
1
0
1
0
0
0
2
1
2
0
0
2
2
2
0
1
0
0
0
2
2
0
2
1
0
0
0
0
0
2
0
0
1
0
1
1
0
0
1
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
3
0
0
2
0
0
2
0
0
0
0
0
2
1
1
0
1
0
0
1
2
0
0
0
0
1
0
0
2
1
0
0
0
2
0
2
1
1
0
0
1
2
0
0
1
0
0
0
1
1
0
1
2
1
1
2
0
2
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
1
1
0
0
1
0
0
2
0
2
0
2
1
0
0
0
0
0
0
3
1
0
0
2
0
0
0
0
2
2
2
1
0
1
0
0
0
1
2
3
1
1
0
1
0
2
0
3
1
0
1
0
1
0
0
3
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
2
0
0
0
0
1
0
1
0
1
0
2
1
1
2
0
1
0
5
1
0
1
0
0
0
1
0
0
0
0
1
2
2
1
0
1
1
2
1
0
2
0
1
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
3
0
1
3
1
0
2
2
0
0
1
0
0
2
0
1
0
2
0
0
2
1
1
0
2
0
1
2
0
0
0
3
0
0
0
2
0
4
1
0
1
0
1
1
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
1
0
0
2
2
1
0
1
1
1
1
0
0
0
2
0
0
0
0
1
0
0
1
0
2
0
1
2
0
0
0
2
2
1
1
1
2
2
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
2
0
0
5
1
0
0
2
0
0
2
1
0
0
0
2
0
0
0
1
4
1
2
2
0
0
0
0
0
0
1
1
1
2
0
2
0
0
0
0
2
0
0
0
2
0
1
0
0
0
1
0
0
2
0
1
2
2
0
0
0
0
0
0
1
1
0
0
2
0
0
1
1
0
0
0
0
2
0
0
1
2
0
0
1
2
0
1
1
0
1
0
0
1
0
2
2
1
2
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
2
0
0
0
0
3
0
0
0
1
0
0
2
0
1
2
0
2
0
2
0
0
1
0
0
0
0
3
2
0
0
0
2
1
0
0
0
1
2
0
0
1
0
0
0
3
0
1
0
0
0
2
0
0
0
2
0
2
1
0
1
1
0
1
0
0
0
2
0
0
0
0
2
2
0
2
0
0
5
1
1
2
0
2
1
2
0
0
0
1
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
1
0
1
2
0
0
0
0
1
0
1
0
1
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
1
0
0
0
2
1
1
0
1
1
2
1
1
0
0
0
1
0
1
0
2
0
2
0
1
2
0
0
1
0
1
0
0
1
1
0
2
0
0
1
0
2
0
3
0
2
2
0
0
0
2
0
2
0
0
2
0
0
0
1
1
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
3
0
2
1
0
0
1
0
1
2
0
1
0
1
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
2
0
0
1
0
1
0
1
1
0
1
2
0
0
0
1
0
2
0
4
0
1
1
0
0
2
0
2
0
0
1
0
1
0
0
0
1
0
1
2
0
0
0
2
0
1
0
0
1
2
2
0
2
0
0
2
0
0
1
1
0
0
1
1
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
2
0
3
2
0
1
2
2
2
0
0
2
1
0
0
1
0
1
0
3
1
0
2
2
4
0
1
0
1
0
0
0
2
1
1
0
0
2
2
2
1
1
1
0
2
2
4
0
0
0
0
2
1
0
1
2
0
0
1
0
1
0
0
1
2
1
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
2
1
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
1
1
0
1
0
0
1
0
2
1
0
0
0
2
0
1
2
2
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
1
2
1
1
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
1
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
2
1
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
1
0
0
0
0
1
0
0
0
2
1
1
0
2
0
0
1
1
2
0
2
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
6
0
0
0
1
0
1
1
0
2
1
0
0
0
1
0
1
2
0
0
0
1
0
2
0
1
0
0
1
0
0
2
4
0
0
0
0
0
2
2
0
1
1
0
0
0
0
0
0
2
1
0
1
0
3
2
1
0
0
0
1
2
0
1
1
1
1
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
1
2
2
2
1
0
1
0
2
0
2
0
1
1
0
0
0
1
0
1
2
2
0
0
0
0
2
2
0
0
1
1
0
0
0
2
0
0
1
0
1
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
2
3
0
0
2
0
0
0
0
0
2
1
0
2
0
0
2
1
0
0
2
2
1
0
1
0
2
1
0
0
0
0
0
0
0
1
1
0
0
2
1
1
0
0
0
1
0
0
0
0
2
0
0
2
0
2
0
0
1
0
0
1
1
0
0
0
2
0
1
0
0
0
1
0
2
1
0
0
0
0
0
1
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
1
0
1
2
0
0
2
1
2
2
0
0
1
0
0
0
0
0
1
1
2
1
0
0
0
2
0
0
1
0
0
1
0
1
0
2
0
0
0
0
2
1
0
0
4
0
0
0
0
1
1
0
0
0
3
2
2
0
0
1
0
1
0
2
0
2
1
2
1
0
0
1
0
0
0
2
0
0
1
1
0
2
2
0
3
0
2
0
0
0
0
2
0
0
0
0
1
1
5
0
2
2
1
0
0
0
0
0
2
2
1
0
0
0
0
0
1
0
0
0
0
2
1
1
1
0
1
1
0
0
0
0
2
0
0
2
0
0
0
1
2
1
0
1
0
0
0
0
1
2
1
0
0
1
0
0
0
2
3
0
1
1
0
0
0
2
0
0
0
1
1
2
1
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
1
2
1
2
0
1
2
0
0
0
0
0
0
1
2
1
1
0
3
0
0
0
0
2
0
0
1
0
1
0
2
0
1
1
1
0
1
0
0
2
2
2
0
0
2
3
2
0
1
0
1
0
0
0
1
0
2
1
1
2
0
0
0
0
2
0
1
1
1
0
0
4
2
2
0
0
0
0
0
0
2
0
0
1
1
0
1
0
0
1
0
0
0
0
1
1
0
0
2
1
2
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
2
0
1
0
2
0
0
0
0
0
1
1
0
2
0
2
1
1
0
1
0
1
1
1
0
2
2
0
0
0
0
1
1
1
0
0
2
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
2
2
0
0
0
1
0
0
2
5
0
6
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
2
2
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
2
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
2
0
1
1
0
0
0
1
2
0
2
2
0
2
0
2
0
0
0
2
1
0
2
0
0
0
0
0
1
0
0
0
0
0
1
2
0
1
0
0
0
0
0
2
0
1
1
0
0
1
0
0
0
3
2
0
2
0
0
2
0
1
2
0
0
0
1
2
0
1
2
1
1
0
2
1
0
0
1
2
0
1
0
0
0
1
2
1
0
1
2
0
1
0
1
2
2
1
0
2
0
0
1
0
2
1
1
2
0
0
1
0
0
2
2
0
0
2
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
3
0
1
2
1
2
6
0
2
0
1
0
0
2
1
1
2
2
1
0
0
2
2
0
0
2
0
0
0
0
0
2
1
1
4
2
0
1
0
2
2
0
0
1
0
0
0
0
0
0
2
2
1
0
0
0
2
2
0
0
1
0
0
0
0
1
0
0
2
2
1
0
0
1
1
1
0
0
1
0
0
0
2
0
0
0
1
0
0
2
1
0
2
0
0
0
0
0
0
1
0
0
2
2
3
2
1
0
0
0
1
2
2
0
1
2
2
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
2
1
0
0
0
3
0
2
2
0
0
0
0
1
1
0
0
0
0
1
0
1
1
0
0
2
0
0
2
1
0
2
2
0
0
0
0
0
1
0
0
0
1
1
3
0
0
0
2
2
0
0
0
2
2
0
1
0
0
1
0
1
0
2
0
4
0
0
0
1
0
0
0
1
0
2
0
0
1
0
2
2
0
2
1
0
0
0
0
0
0
0
2
1
0
1
2
1
1
1
0
0
2
1
2
0
1
0
0
0
0
0
1
1
2
1
0
2
2
0
3
1
0
0
1
1
0
0
1
1
2
1
0
0
1
0
0
0
2
0
0
0
1
0
3
2
1
0
1
0
1
2
3
1
0
1
0
2
0
0
0
0
0
2
2
0
0
2
0
0
0
2
1
0
0
1
0
0
6
2
0
1
2
1
1
1
1
1
0
0
2
2
1
1
0
2
1
2
2
0
0
2
1
1
3
1
2
0
0
0
0
1
0
2
1
0
0
1
0
2
0
0
0
1
3
1
1
1
3
2
0
0
0
0
0
1
2
1
1
1
2
1
2
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
2
1
0
0
0
0
0
0
1
1
2
0
0
0
1
0
0
3
0
1
1
1
0
2
0
1
0
2
0
0
1
0
0
0
1
2
0
2
0
0
0
2
1
1
0
1
0
0
2
0
2
1
0
1
0
0
1
0
0
0
2
2
0
1
2
0
1
0
1
0
3
0
0
0
1
0
0
0
0
0
1
2
1
1
0
0
0
1
0
0
1
0
2
1
3
0
1
0
0
0
2
0
0
0
4
0
0
1
5
0
2
2
0
6
2
0
1
1
0
0
0
2
1
2
2
0
0
0
0
1
1
2
1
0
0
1
2
0
1
1
0
0
2
0
0
2
1
0
1
1
2
0
1
1
2
0
0
0
1
0
2
0
2
0
0
1
0
0
2
1
2
0
0
0
0
0
1
0
0
1
0
0
2
1
0
1
0
0
0
2
0
2
1
2
2
0
0
0
1
0
0
0
0
0
1
0
0
1
2
0
2
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
2
2
0
0
1
2
2
0
0
1
5
0
0
2
0
0
1
1
2
0
2
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
1
2
0
2
1
1
2
0
1
1
2
0
0
1
0
2
0
1
0
2
1
0
0
0
0
0
2
1
2
0
2
0
0
1
0
0
0
1
1
1
0
0
0
2
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
1
1
3
0
2
2
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
2
0
2
1
2
0
0
2
0
0
0
2
0
2
2
0
0
2
0
0
0
1
0
2
0
1
0
0
0
0
2
2
0
0
0
1
0
0
0
0
1
0
9
0
0
1
0
0
0
3
0
0
2
1
2
2
1
0
0
0
2
0
0
1
2
0
1
0
0
0
0
0
0
1
2
1
2
0
0
2
0
0
0
4
0
0
1
0
0
0
2
1
2
1
0
0
0
0
1
0
0
1
0
1
0
0
2
0
1
1
0
0
0
1
0
0
0
1
0
1
2
0
0
0
1
0
2
0
0
0
2
2
0
1
0
1
0
0
0
2
0
0
2
0
0
0
0
0
2
0
1
1
0
0
0
0
1
1
0
1
0
0
2
0
0
0
2
1
0
1
0
1
0
0
1
0
2
2
0
2
2
0
0
0
1
0
1
0
0
0
4
4
1
0
0
0
0
0
2
2
0
1
0
0
2
1
2
0
0
0
0
1
0
2
0
3
1
0
0
0
1
0
1
2
0
0
0
2
0
0
0
1
0
0
2
2
0
3
1
0
0
1
0
0
2
0
0
0
0
3
0
2
0
0
0
0
2
0
0
0
0
1
2
1
0
0
0
2
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
2
0
0
0
0
1
2
0
0
5
0
0
1
1
0
2
0
0
0
1
0
1
2
0
1
0
2
2
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
1
0
2
0
1
0
0
0
2
0
0
0
1
0
0
0
1
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
2
1
1
0
0
0
2
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
2
2
1
0
0
1
0
0
2
0
0
3
1
0
0
0
1
1
0
0
0
2
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
1
2
2
2
0
0
1
3
0
2
0
0
0
0
2
1
1
1
0
0
0
1
2
0
0
0
0
1
2
1
0
1
0
0
1
2
0
0
2
1
2
1
0
0
0
1
1
0
0
0
0
1
0
0
0
1
2
0
0
2
0
2
0
0
2
0
1
0
0
1
0
0
0
2
0
0
2
1
0
0
1
0
0
0
0
2
1
2
0
1
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
2
0
1
2
1
0
0
0
1
2
2
0
1
0
1
0
0
1
0
0
0
2
0
2
1
0
0
0
0
1
0
0
0
2
4
1
1
0
1
0
0
0
2
1
1
2
2
1
0
0
2
0
1
0
0
0
2
1
1
0
1
4
0
2
1
0
0
0
1
0
0
2
0
1
0
1
1
3
0
0
1
2
1
2
0
1
0
0
1
1
0
1
0
1
1
0
0
1
0
1
0
1
0
2
1
3
1
0
0
1
0
2
0
2
1
0
2
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
1
1
3
0
2
0
4
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
3
1
0
0
2
4
0
0
1
0
0
0
1
0
0
0
2
0
1
0
0
0
0
1
3
0
2
0
0
0
0
0
1
3
1
4
1
0
0
2
0
1
1
2
2
0
0
1
2
0
0
0
1
1
2
0
1
1
12
3
1
2
0
0
0
0
1
0
0
0
1
0
2
1
0
2
0
2
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
2
2
1
1
0
2
0
1
0
0
1
0
0
0
0
2
0
2
0
2
1
1
0
0
0
2
2
2
0
0
0
0
0
1
4
2
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
2
0
1
0
0
1
1
0
0
0
0
1
2
0
0
0
0
1
2
0
4
0
1
2
0
1
1
1
0
0
0
3
0
1
0
0
0
2
0
3
1
0
1
0
0
0
0
0
0
2
2
2
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
2
1
1
1
4
0
1
1
0
0
0
3
0
0
1
0
2
2
3
0
0
3
0
0
2
0
0
0
1
0
1
0
1
0
1
0
0
0
2
1
0
1
0
0
2
2
2
2
1
0
0
0
2
0
0
3
0
1
0
0
0
3
0
0
1
0
0
0
0
0
0
2
0
0
0
1
2
0
1
0
0
1
0
2
1
0
2
0
1
0
0
2
0
0
0
0
2
0
2
2
0
2
0
0
0
2
0
6
1
0
0
1
0
0
0
0
1
0
11
0
1
0
3
0
1
2
0
1
0
2
1
1
0
0
0
0
1
0
2
0
0
0
3
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
1
2
2
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
2
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
1
0
1
1
0
0
0
0
1
0
1
1
1
2
0
1
0
0
0
0
1
2
2
0
0
1
0
2
0
3
2
0
0
2
0
0
0
1
1
0
2
0
0
0
1
1
0
0
0
0
1
0
2
0
0
0
0
0
0
1
2
1
2
2
2
0
1
0
1
2
2
0
0
1
2
0
0
0
0
0
0
2
0
2
2
1
2
0
1
0
0
0
2
0
0
0
0
0
0
0
1
1
3
1
0
0
2
0
0
2
1
0
0
3
0
0
0
1
1
1
0
1
0
1
0
1
0
1
2
2
0
0
1
0
0
0
1
0
0
1
0
0
0
1
1
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
2
0
2
2
1
0
1
0
1
2
2
1
0
0
0
2
0
1
2
1
1
0
0
2
1
1
5
0
1
0
1
1
0
0
0
0
0
1
2
0
1
0
0
2
0
0
4
0
0
1
5
0
0
0
1
3
0
0
0
1
0
0
2
0
1
0
3
0
1
0
0
0
1
1
0
0
0
0
1
0
2
0
0
1
0
0
1
0
2
0
8
2
0
1
0
1
2
0
0
0
1
2
0
1
1
0
1
0
0
0
0
2
1
2
0
2
2
1
3
2
1
0
0
0
0
1
1
1
0
1
0
2
2
0
0
1
0
0
0
0
0
0
1
0
0
1
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
2
2
5
0
1
0
0
2
0
0
0
0
0
2
2
0
0
2
2
0
0
0
0
0
0
0
0
2
1
2
1
0
0
0
1
0
1
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
2
0
1
0
0
0
2
2
2
0
0
0
0
1
0
2
2
0
2
0
0
0
0
0
3
0
0
0
1
0
0
2
1
1
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
1
1
0
0
0
0
2
0
1
0
1
2
0
0
0
1
2
1
1
0
1
0
2
1
0
0
2
0
0
0
0
1
0
0
0
0
1
1
0
1
2
2
0
1
0
2
1
0
0
1
0
0
0
1
0
0
2
0
2
0
2
0
2
0
1
0
1
0
1
0
0
1
1
2
0
0
1
0
0
0
0
1
0
0
1
0
2
2
3
2
1
1
1
1
0
0
2
1
1
1
0
0
1
1
0
0
0
3
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
4
0
0
0
0
2
0
0
0
1
1
0
0
1
1
1
0
1
2
0
0
0
2
1
2
0
0
1
2
0
0
2
1
0
0
0
0
2
4
0
2
0
1
1
1
0
1
0
0
0
0
2
0
2
1
3
0
1
0
0
0
2
0
0
0
1
0
0
2
2
0
0
1
0
1
2
1
0
2
0
3
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
1
1
1
1
2
1
1
1
1
0
0
0
0
2
0
0
1
0
0
0
2
0
0
1
0
2
0
1
3
0
0
3
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
3
0
1
0
0
1
0
0
0
1
0
0
1
2
0
2
2
2
0
0
2
1
1
0
0
0
0
1
0
0
1
2
0
2
1
1
0
1
0
0
2
2
1
2
0
0
2
0
2
0
1
1
0
0
0
2
2
1
0
1
0
1
0
2
0
0
1
0
0
2
0
0
0
0
0
2
2
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
1
2
1
3
1
0
0
3
2
1
2
0
2
2
2
0
0
1
2
0
1
0
2
0
2
0
2
0
0
0
1
0
2
0
1
0
0
1
0
2
0
1
0
0
1
0
0
1
0
3
2
1
2
0
1
2
1
3
2
0
1
0
0
1
0
0
0
0
0
1
0
0
2
2
4
0
0
0
0
2
0
0
0
0
0
0
0
3
1
1
0
0
0
2
1
0
1
0
0
0
2
0
0
2
0
0
1
2
0
0
0
1
1
1
0
2
2
2
1
2
3
0
2
0
0
0
0
0
2
0
0
1
3
3
0
2
1
2
2
0
0
1
3
0
0
1
1
0
0
0
2
0
1
1
2
0
0
0
0
0
0
0
2
0
0
1
0
1
1
1
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
1
0
0
1
0
0
0
0
1
0
2
0
0
0
2
0
0
2
1
0
1
0
0
0
2
2
2
0
1
3
0
0
0
0
1
0
1
1
0
0
0
0
0
0
2
0
0
1
0
2
1
0
1
1
0
0
1
2
0
0
0
2
0
1
2
0
0
1
2
2
0
0
0
1
0
0
0
2
0
2
1
2
0
2
1
0
1
0
0
0
1
3
2
3
1
2
2
0
1
0
0
0
0
2
2
0
2
2
1
0
0
0
0
0
0
2
1
1
0
1
0
0
0
1
0
0
0
1
1
0
2
0
0
0
0
1
0
0
0
1
2
2
2
2
1
0
0
0
0
1
0
0
0
0
0
3
1
0
0
0
2
0
1
0
2
1
0
1
0
0
1
1
0
2
1
0
0
1
1
0
0
0
2
2
0
2
0
0
2
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
1
2
1
2
0
1
0
2
2
1
0
1
0
0
1
0
0
0
2
1
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
1
0
0
1
0
1
2
0
0
1
2
0
1
0
3
3
2
0
1
4
1
0
0
0
0
1
0
0
1
0
0
0
1
1
1
0
0
0
0
2
2
5
1
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
2
1
0
0
0
0
2
2
1
2
0
0
1
0
0
2
2
0
0
0
3
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
2
0
0
0
2
0
1
0
0
0
1
0
0
1
3
0
3
0
2
0
0
2
0
3
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
1
2
0
2
0
0
1
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
1
3
0
0
2
0
0
0
1
0
2
0
0
1
2
0
0
0
0
1
1
2
1
2
1
0
0
0
0
1
2
0
0
0
2
0
0
1
0
0
1
2
0
0
1
0
0
0
0
0
0
0
2
1
1
1
0
0
0
0
0
0
0
2
0
0
0
1
1
1
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
2
2
0
1
1
1
0
0
0
0
1
2
1
0
2
0
1
0
0
0
0
2
0
2
3
2
0
1
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
2
1
0
0
0
2
2
0
0
0
1
1
0
2
2
0
0
1
1
0
0
0
0
2
1
0
0
0
0
2
1
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
1
0
0
0
1
2
0
0
1
1
0
1
0
0
0
0
0
0
0
2
2
0
2
0
0
0
1
1
1
2
0
0
0
2
0
0
1
0
0
1
0
0
1
0
2
0
2
0
0
1
1
0
1
0
0
2
1
2
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
2
1
1
0
0
0
2
3
2
1
1
0
0
0
0
0
0
0
2
0
2
0
1
2
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
1
0
0
0
1
1
1
0
0
0
2
1
0
1
0
0
0
0
1
2
1
1
0
1
1
1
0
1
1
0
3
0
0
1
0
0
1
0
0
1
0
1
0
1
0
1
2
0
2
0
0
0
2
0
0
2
0
1
2
0
1
0
0
0
1
1
0
0
1
1
4
1
2
1
2
0
1
0
0
0
0
2
0
0
2
1
0
2
0
0
0
1
1
0
1
2
0
0
0
0
2
2
3
2
0
0
2
0
0
2
1
1
0
1
1
0
0
0
0
0
0
0
1
0
2
0
3
1
0
1
2
1
0
2
0
2
0
2
2
2
2
0
1
0
2
2
0
1
0
1
2
0
0
0
2
0
0
1
1
0
0
0
2
0
2
0
0
0
1
3
0
0
2
0
0
0
0
0
2
0
0
0
1
1
0
1
0
2
0
1
2
0
2
2
1
2
0
2
2
0
3
0
0
0
1
0
2
2
1
0
0
2
1
0
0
2
3
2
1
1
0
0
0
0
0
2
2
0
0
0
2
1
2
2
0
0
0
0
2
1
0
0
2
0
0
1
0
3
0
0
0
2
0
0
0
0
0
1
1
0
1
0
0
1
0
1
2
0
1
0
0
0
2
2
2
0
0
0
0
3
0
2
0
0
1
0
2
0
1
0
0
0
1
0
0
1
0
0
0
2
1
0
1
1
0
0
2
0
1
2
0
1
1
1
3
0
1
0
0
0
1
0
0
2
0
0
2
1
0
0
0
0
0
1
0
0
0
0
1
3
0
0
0
1
0
2
0
0
2
0
2
1
0
0
0
2
2
0
0
1
2
0
1
0
2
1
0
1
2
0
0
1
1
0
0
0
2
0
1
0
3
0
0
1
1
1
0
1
0
1
0
1
1
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
1
1
0
0
2
1
0
0
0
0
2
3
0
1
2
1
0
2
0
1
0
0
0
2
0
2
0
0
0
0
0
0
2
1
2
1
2
0
0
0
0
0
0
1
0
0
2
1
2
0
0
2
0
2
0
2
0
2
0
0
0
2
0
0
1
0
2
1
0
1
1
0
1
1
1
2
2
0
0
2
0
0
0
0
0
2
2
0
0
0
1
0
0
1
1
0
0
1
0
1
0
0
0
1
0
0
1
2
0
2
0
2
0
0
0
1
1
0
0
0
0
1
0
1
2
2
0
1
0
3
0
0
0
2
1
1
2
1
0
0
0
2
1
1
0
1
0
0
0
0
0
0
1
2
0
0
2
1
0
1
1
0
1
0
0
1
0
0
0
0
0
1
0
0
1
1
2
0
0
0
0
1
0
0
0
1
1
0
0
0
2
1
0
1
0
0
0
3
0
1
0
0
0
2
0
2
0
0
0
0
1
0
1
1
0
2
1
0
2
0
0
0
1
2
0
0
0
0
1
0
0
0
2
1
2
0
0
0
0
1
0
0
0
0
1
0
2
2
0
0
0
0
0
2
1
0
0
0
2
1
0
0
0
1
0
2
2
1
1
3
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
2
1
0
3
1
0
0
0
0
2
2
0
2
2
0
2
0
1
0
0
0
2
0
2
4
0
0
2
0
2
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
2
3
0
0
2
1
0
0
0
1
0
2
0
3
1
0
0
0
0
0
1
0
2
1
2
0
2
2
2
1
0
0
0
0
0
2
0
2
0
1
0
1
0
0
0
0
0
0
1
2
1
0
0
0
0
3
1
1
2
0
2
0
1
0
1
1
0
0
2
0
1
2
0
2
0
0
1
1
0
1
0
1
0
0
0
1
0
2
0
0
1
0
2
0
2
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
2
0
1
2
2
2
2
2
2
0
2
0
0
0
0
1
0
0
2
0
0
1
0
2
0
1
2
1
0
0
0
1
0
0
0
1
0
0
0
1
1
2
2
2
2
1
2
1
0
0
0
1
0
1
2
0
2
0
1
0
0
1
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
3
0
2
0
0
2
1
0
0
0
0
3
1
0
1
0
0
1
1
2
1
0
0
1
2
0
0
0
1
2
0
0
0
0
1
2
0
1
2
1
1
0
1
2
0
1
0
2
0
1
0
2
0
0
2
1
2
0
2
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
1
0
0
0
1
0
1
0
1
0
1
5
0
0
1
2
0
2
0
0
1
0
2
1
1
0
0
0
0
0
0
0
1
0
2
2
0
0
0
2
0
0
2
0
1
0
0
0
0
1
1
1
0
0
0
0
1
0
0
2
0
1
1
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
2
0
0
2
2
2
0
0
0
1
0
1
2
2
0
0
0
2
0
0
0
0
1
1
10
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
2
1
1
1
2
0
0
1
0
0
0
0
0
1
0
0
3
0
0
0
0
0
2
1
0
0
1
0
0
0
1
2
1
2
0
2
0
0
2
1
0
0
2
1
2
0
2
1
2
2
0
0
1
1
2
2
0
0
0
0
0
1
0
0
0
2
1
0
2
1
2
1
0
0
1
0
1
0
1
0
0
2
2
0
2
0
0
0
2
3
2
1
0
0
0
2
0
2
0
0
0
1
0
1
0
2
2
2
2
0
0
0
1
0
1
1
2
0
1
0
0
0
1
0
1
1
0
0
1
2
1
0
4
0
1
2
2
0
0
0
0
0
0
2
0
2
2
0
2
0
0
0
0
0
0
1
0
1
6
1
0
2
0
2
0
0
0
2
2
0
0
2
0
2
0
1
0
2
0
0
1
0
2
0
2
1
0
0
0
1
0
2
0
2
0
1
0
0
0
1
3
0
2
1
0
1
2
0
0
2
1
1
0
0
1
0
0
2
2
1
0
0
2
0
1
0
2
2
0
0
1
1
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
2
3
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
4
0
3
1
3
0
2
2
2
0
2
0
2
0
0
1
0
0
2
1
0
1
0
1
2
0
0
1
2
1
0
0
0
2
0
0
0
0
0
0
2
0
2
0
1
0
0
2
0
4
1
0
0
0
0
1
2
0
1
0
0
0
0
1
2
3
0
2
2
3
0
0
1
0
1
2
0
0
0
0
0
0
2
1
0
2
2
0
1
1
1
1
0
1
2
0
1
1
0
0
0
4
0
1
2
1
2
0
0
0
0
0
0
1
0
0
0
2
1
0
1
2
0
1
0
1
0
0
0
1
1
3
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
1
1
0
2
0
0
0
0
0
0
1
2
1
0
1
0
0
1
0
0
1
2
2
0
1
0
1
0
0
0
1
0
0
1
1
0
0
0
2
4
0
2
1
0
2
2
0
0
0
0
0
0
1
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
2
1
2
3
0
1
0
0
0
1
1
0
0
1
2
0
0
0
0
0
0
0
0
1
0
3
0
1
0
2
0
0
1
0
0
0
2
0
2
2
2
0
0
1
0
1
0
1
2
2
2
1
2
0
0
2
0
0
2
0
0
0
0
0
1
0
1
0
1
2
0
3
1
3
0
0
1
2
2
2
2
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
3
0
2
0
1
0
1
0
0
0
0
1
0
2
1
0
1
3
0
0
0
2
1
2
1
0
2
1
2
0
0
2
3
0
0
3
0
0
1
0
1
1
1
0
0
1
0
3
1
0
0
0
1
0
0
1
0
2
0
0
0
0
2
0
0
0
1
0
2
0
0
3
0
0
0
0
0
1
0
0
2
0
1
0
0
2
0
0
1
2
0
0
0
0
0
2
0
1
0
1
0
0
2
1
1
0
0
0
2
2
2
0
2
0
0
1
0
0
0
1
0
0
0
4
0
0
0
0
1
0
1
0
0
2
0
0
2
1
1
0
0
0
0
2
2
2
0
0
0
0
2
0
0
0
0
1
0
3
1
0
0
0
0
1
0
1
1
0
0
1
2
0
0
1
0
0
0
0
0
1
2
1
0
0
1
0
2
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
1
1
1
2
1
2
1
0
2
0
2
0
2
0
0
1
0
2
0
0
0
1
2
0
1
1
2
1
0
0
0
0
0
2
1
0
0
0
1
0
0
2
1
2
0
3
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
1
2
0
0
0
0
4
0
0
1
0
2
0
2
0
0
1
2
0
2
2
0
0
1
0
2
2
2
0
1
2
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
2
1
0
0
0
0
0
0
2
0
0
0
1
2
1
0
0
1
2
2
0
1
2
0
2
3
0
0
1
0
0
0
2
0
2
0
0
0
0
1
2
1
1
1
0
0
0
0
2
0
0
0
1
1
1
0
1
1
0
2
1
0
0
0
1
2
0
0
0
0
2
0
0
0
2
1
0
2
1
0
1
0
0
1
0
0
2
0
1
0
1
0
0
0
2
2
0
0
0
0
1
1
0
0
1
1
0
2
0
0
1
0
1
2
0
0
2
0
0
1
0
1
0
1
2
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
1
2
0
1
1
2
2
0
0
0
0
0
1
0
1
1
0
0
0
0
0
2
0
2
0
0
2
2
0
0
0
2
0
0
0
0
0
0
2
0
2
0
2
0
2
0
2
0
1
0
0
2
2
0
0
0
0
1
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
1
2
2
0
0
2
0
0
2
2
2
0
2
0
0
2
2
0
0
2
0
0
0
0
1
1
2
0
0
1
0
0
2
0
0
2
2
2
0
2
2
1
2
1
1
1
0
0
0
1
0
1
1
0
0
2
1
1
1
0
2
1
0
1
0
1
1
1
1
0
2
0
0
1
0
2
0
0
0
0
0
0
1
1
0
0
7
0
0
0
0
0
1
0
0
0
1
0
0
2
1
0
1
0
1
1
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
1
2
1
0
1
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
3
0
0
0
0
0
1
1
0
1
0
0
2
1
0
2
1
1
0
3
0
1
1
0
1
2
0
0
0
0
0
0
3
0
0
1
1
0
2
2
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
2
0
1
0
1
0
1
2
2
0
1
1
0
0
1
0
1
0
1
0
6
0
0
0
0
0
0
0
1
0
1
0
1
2
0
3
0
2
1
1
1
2
0
1
1
0
1
0
0
0
3
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
1
3
0
0
1
2
0
0
0
0
0
5
0
0
1
1
0
0
1
2
0
0
2
0
2
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
3
0
2
0
1
2
2
2
0
0
1
0
2
0
0
2
0
2
2
0
1
0
1
0
0
0
0
0
1
0
0
0
1
2
0
0
2
1
2
0
1
2
1
0
0
0
0
0
1
0
2
1
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
1
1
0
1
2
0
0
2
0
0
0
0
1
0
2
1
0
0
0
1
0
0
0
0
0
1
0
1
0
2
0
2
0
0
0
0
0
1
0
2
1
2
0
0
2
0
0
1
2
3
0
3
0
1
0
1
1
1
0
2
2
0
0
0
0
1
0
2
0
1
0
0
1
0
2
2
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
1
1
2
0
0
1
0
0
0
2
2
2
0
0
0
0
2
0
0
3
0
2
0
1
0
0
1
0
0
0
1
2
0
0
1
1
1
1
0
0
0
0
1
1
0
0
2
2
2
0
0
0
0
0
0
2
0
0
0
2
0
1
0
1
0
1
0
1
1
0
2
2
0
1
0
0
1
0
0
2
0
0
2
0
1
0
2
2
1
0
1
0
0
1
0
1
0
0
0
2
2
0
0
2
0
0
0
1
0
0
0
0
0
0
2
1
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
2
2
0
2
1
0
0
1
1
1
0
1
0
0
1
1
0
1
0
1
1
0
2
0
0
2
1
0
0
0
0
2
2
1
1
0
0
3
0
0
2
1
1
2
0
2
0
0
2
0
2
0
0
2
1
0
1
1
1
0
1
2
1
2
2
1
0
0
1
1
0
1
2
0
2
0
0
0
0
1
0
2
2
0
0
2
0
2
1
0
2
2
1
0
0
2
0
0
0
0
1
0
0
1
2
2
1
0
0
1
0
0
0
0
0
1
0
0
1
0
2
0
2
0
3
0
1
0
2
3
0
1
0
0
1
0
0
0
0
0
1
3
1
0
0
1
1
0
0
0
0
2
2
1
1
0
0
0
1
0
3
0
0
1
0
2
1
1
1
1
0
0
0
1
2
0
2
0
0
0
0
0
2
1
2
2
0
40
2
0
0
0
0
2
0
2
2
0
0
0
0
1
0
1
0
0
1
2
0
0
1
1
0
1
0
0
0
1
1
0
3
0
0
0
0
1
0
0
0
0
0
0
1
2
1
0
2
0
0
0
0
2
0
0
0
0
0
0
2
1
1
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
2
0
3
0
0
0
1
0
0
0
2
1
0
2
0
0
0
1
1
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
3
0
0
2
0
0
0
1
0
0
0
1
0
0
0
2
2
2
0
1
0
0
1
1
2
0
1
2
0
1
1
0
0
0
1
0
0
2
0
0
1
0
2
0
0
0
1
2
2
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
3
2
0
0
1
0
0
0
2
0
0
1
2
0
0
0
0
0
0
7
0
0
0
2
0
0
1
0
0
2
2
0
0
0
0
2
2
0
2
2
0
2
0
0
3
1
1
2
0
0
1
1
0
1
0
0
0
0
2
0
0
0
1
3
0
0
0
1
1
0
3
0
0
0
2
0
0
1
0
0
1
0
2
0
2
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
2
1
1
0
2
1
1
2
0
0
1
0
0
0
0
1
2
0
2
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
2
1
0
2
1
1
0
2
0
0
1
2
2
0
1
0
0
2
1
0
0
0
2
0
0
0
1
0
0
0
0
2
0
2
0
1
1
1
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
2
0
1
0
0
0
1
2
0
0
2
1
0
0
1
0
0
2
0
2
2
2
0
1
0
0
2
2
0
0
2
2
0
0
0
1
0
2
0
0
0
0
1
0
2
0
0
2
0
1
1
1
1
2
0
1
0
0
1
0
0
1
1
0
0
2
1
0
0
1
0
1
0
2
2
0
1
1
0
0
1
0
0
3
2
1
0
1
1
4
0
0
1
0
0
2
0
0
1
0
0
0
0
2
2
7
0
0
0
0
0
0
0
2
1
0
2
2
1
2
2
3
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
1
0
1
0
1
1
3
0
0
1
0
0
1
0
0
0
0
1
1
0
1
0
0
0
2
0
1
0
1
0
2
0
0
1
2
0
3
0
1
1
1
0
2
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
2
3
2
0
1
0
0
0
0
2
2
2
0
0
2
0
0
1
2
1
0
1
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
1
0
2
0
2
0
2
1
0
0
0
2
2
1
2
0
0
0
0
2
1
2
0
3
1
0
2
1
1
2
0
0
1
0
0
0
0
0
1
2
1
0
0
2
0
2
1
0
1
0
0
0
1
3
0
0
0
2
1
0
0
2
1
2
2
0
0
0
0
0
0
0
1
1
0
0
2
0
1
2
1
2
0
0
1
0
3
2
2
0
2
2
0
0
1
0
1
2
0
1
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
3
3
5
1
1
0
0
2
1
0
1
1
0
3
1
3
1
0
2
1
0
1
1
0
0
0
1
0
0
1
1
2
2
1
0
3
0
1
0
3
0
2
0
1
0
1
0
0
0
0
0
0
2
0
1
1
2
0
2
0
0
0
0
2
0
1
1
0
0
0
0
2
1
2
1
2
0
1
1
2
0
0
0
0
2
0
1
1
0
2
0
0
2
0
0
0
0
0
1
2
1
0
0
0
0
2
2
0
0
0
0
1
1
1
0
2
1
1
0
0
0
0
0
1
2
2
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
2
2
2
0
1
2
0
2
1
2
0
0
1
2
0
1
0
2
1
0
0
1
3
0
0
2
2
1
0
0
0
0
2
0
0
0
1
2
0
1
1
0
0
1
7
0
2
2
0
0
1
0
0
0
0
0
2
0
0
1
0
0
2
2
2
0
0
0
2
1
0
0
0
3
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
9
0
0
0
0
0
0
1
2
1
0
0
0
1
0
1
1
1
0
1
1
0
0
0
3
0
1
0
0
2
0
3
0
1
2
2
0
2
1
2
0
2
0
0
0
2
0
3
2
0
1
2
0
2
0
0
1
0
1
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
2
0
2
0
1
2
0
0
0
2
1
0
2
3
0
0
0
1
2
0
2
1
0
1
0
0
2
0
0
0
0
2
2
0
0
0
1
2
0
1
0
0
2
1
0
3
2
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
1
0
1
1
1
0
0
0
1
2
2
2
1
0
0
3
0
1
2
1
1
0
0
0
3
0
2
0
0
0
1
0
0
2
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
1
1
0
0
0
2
0
0
2
2
2
2
0
2
2
1
0
0
0
2
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
4
0
1
0
2
2
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
2
1
0
0
0
1
1
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
1
0
2
0
1
2
0
2
0
0
1
2
0
1
0
1
2
0
2
0
1
0
0
0
2
0
0
1
1
1
0
0
1
0
2
0
0
1
1
2
0
0
0
2
2
2
1
0
0
1
0
1
0
0
0
0
1
3
0
1
0
0
0
1
0
1
0
1
0
0
0
0
2
2
2
0
0
1
0
0
2
1
0
1
0
2
2
0
2
0
1
0
0
1
1
1
1
0
1
0
1
1
0
0
1
2
0
1
1
0
0
0
2
1
0
0
2
1
1
0
1
2
0
0
0
2
2
2
2
2
0
1
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
2
2
0
1
2
3
0
3
0
2
0
2
0
0
0
1
0
0
1
0
2
1
1
0
0
2
0
0
1
1
0
3
2
1
0
1
0
0
0
0
0
2
0
1
1
3
0
1
1
0
0
2
0
1
0
1
0
1
2
1
2
1
0
0
1
0
2
1
0
0
1
2
0
0
1
0
1
0
0
1
2
2
2
0
2
2
0
1
1
1
0
3
1
0
0
0
1
1
0
0
0
0
0
0
2
0
1
1
0
1
2
1
0
0
0
0
2
0
2
0
1
2
3
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
2
0
0
2
0
0
2
0
1
0
1
2
0
2
0
2
0
0
2
1
0
0
0
0
2
0
0
2
1
0
2
1
1
2
1
2
0
2
0
2
0
0
1
1
0
0
1
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
2
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
2
2
0
2
0
0
0
0
2
1
1
1
0
0
1
2
1
1
0
0
0
0
1
0
1
0
3
1
1
0
0
1
2
0
0
0
1
2
1
0
0
3
2
0
0
1
0
0
0
0
2
0
0
2
0
2
2
0
0
0
0
2
1
2
2
0
2
0
0
1
1
0
2
2
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
1
2
0
1
1
0
1
1
0
2
0
0
0
2
1
0
0
2
2
1
3
3
0
0
1
1
0
0
1
1
2
0
0
0
1
0
0
0
0
1
2
0
2
2
2
3
2
0
0
2
0
1
0
0
1
3
0
0
0
2
0
2
0
2
0
1
0
0
2
2
1
1
0
2
2
0
0
0
1
1
0
0
1
1
0
1
1
0
0
1
1
0
1
0
0
1
0
0
0
2
0
0
0
0
2
1
0
0
0
1
1
0
0
0
2
2
0
1
0
0
0
0
0
0
2
0
0
1
0
0
2
0
1
0
0
1
1
3
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
2
2
0
0
0
2
2
1
0
0
0
0
0
0
0
0
1
8
1
0
0
2
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
2
2
1
1
0
0
0
0
2
1
0
0
0
0
1
0
0
0
1
0
2
0
1
0
0
1
1
1
0
3
0
0
0
1
0
1
1
0
0
2
2
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
2
0
0
2
0
0
0
1
0
1
0
1
0
0
1
1
0
1
2
0
1
0
0
1
2
2
1
0
0
0
0
0
3
0
3
1
1
3
0
0
0
0
0
3
1
0
0
1
1
0
0
0
2
0
0
1
2
0
2
3
2
1
0
2
0
0
1
1
0
0
1
0
0
0
0
0
0
1
1
1
0
1
0
1
0
2
1
0
4
0
0
1
0
0
1
0
0
1
1
0
1
0
2
0
0
2
0
0
0
2
0
2
2
1
0
0
2
0
1
0
1
1
0
2
2
0
1
0
0
2
1
2
1
0
0
1
0
0
2
1
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
2
2
2
1
0
0
2
2
0
0
0
0
0
1
0
0
0
2
0
1
0
2
0
0
2
0
0
0
0
0
0
0
1
0
2
2
2
1
1
0
2
0
1
2
0
0
0
2
2
1
0
2
1
0
0
1
0
2
0
1
0
0
1
0
1
0
0
1
2
2
0
1
0
0
0
0
0
0
0
2
1
1
0
0
0
2
0
1
0
0
1
0
1
1
1
0
0
0
0
0
3
0
0
0
0
2
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
2
0
0
0
1
0
1
0
2
1
0
0
1
0
1
0
2
1
1
0
2
0
0
0
1
0
4
1
0
1
0
2
0
0
1
0
0
1
0
0
0
0
1
1
2
0
1
1
1
1
2
2
2
0
0
0
0
0
1
1
2
0
1
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
1
0
2
0
0
1
0
1
6
0
0
1
0
1
0
1
1
0
0
2
0
0
2
2
1
0
0
2
0
0
1
0
0
0
0
2
0
0
1
1
0
1
0
2
0
0
2
0
1
1
1
0
2
0
2
0
0
0
1
0
0
0
0
1
0
2
0
0
2
0
0
0
0
2
0
0
0
0
1
2
0
0
1
1
0
0
1
0
2
0
1
0
2
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
1
1
0
0
2
0
0
0
4
2
0
2
0
2
0
2
2
2
2
0
1
2
2
1
0
0
1
0
1
0
1
1
2
0
0
1
0
1
0
1
0
4
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
1
0
1
0
0
0
1
0
2
0
1
1
2
0
0
2
2
1
1
2
4
0
0
0
0
0
2
0
0
1
1
1
0
2
2
0
2
0
0
1
0
1
0
0
1
2
1
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
2
1
2
1
0
1
1
0
1
2
0
0
2
0
0
2
0
0
0
1
2
0
1
2
2
0
1
0
1
0
1
1
2
1
1
0
0
1
0
0
1
0
0
0
1
0
1
2
2
0
1
0
0
0
0
0
1
0
0
0
2
3
0
1
0
2
0
0
1
0
0
0
0
1
0
0
1
2
2
2
0
2
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
3
1
2
0
1
0
0
3
1
1
0
0
0
1
0
0
0
0
0
0
0
1
2
0
2
2
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
2
0
1
2
0
1
0
0
2
0
1
0
1
0
0
0
1
0
0
0
1
0
1
0
2
0
0
3
1
0
0
1
2
0
0
0
3
0
2
0
0
0
0
0
0
6
1
0
1
2
1
0
0
0
2
1
1
0
1
1
0
2
0
0
1
0
2
1
0
1
1
2
0
0
2
0
1
0
1
2
0
0
2
0
1
0
2
1
0
0
2
2
2
0
1
2
1
0
1
0
1
0
2
1
0
1
0
3
0
2
2
0
2
1
0
0
0
0
0
2
1
1
2
0
0
0
0
0
2
2
0
1
2
1
0
0
0
4
2
0
2
0
2
0
1
2
1
0
0
2
1
2
0
0
1
2
2
0
0
0
0
0
2
0
1
3
3
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
1
1
1
1
0
0
0
1
0
1
0
0
0
0
0
2
1
1
0
0
0
1
0
0
0
2
0
0
0
1
2
0
0
0
1
2
2
2
1
0
1
0
0
1
0
0
0
1
2
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
3
0
0
1
1
2
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
1
2
0
1
2
0
0
1
1
2
1
0
0
1
1
3
0
1
0
2
0
0
1
1
0
2
0
0
2
0
0
0
0
0
0
0
4
7
0
0
2
1
0
0
9
0
1
1
0
0
0
2
0
2
0
0
1
0
0
0
0
1
1
1
0
0
0
0
5
0
0
1
0
2
0
1
2
0
1
0
0
1
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
2
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
3
1
2
0
1
1
0
1
0
0
1
3
0
1
2
2
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
2
0
1
0
2
0
1
0
0
1
0
1
2
0
1
2
1
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
1
2
1
2
0
0
0
0
0
2
0
2
1
0
0
2
0
0
1
2
0
0
0
0
0
0
1
1
0
0
2
1
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
1
0
0
2
1
0
0
0
2
1
2
1
1
1
0
2
0
1
0
1
0
0
2
0
0
0
1
0
2
2
0
0
2
0
2
0
0
0
0
0
2
1
0
0
0
1
0
2
0
1
0
0
2
0
1
2
0
2
0
1
0
0
1
0
0
2
0
0
0
0
1
1
2
0
0
1
0
1
0
0
0
0
0
1
0
1
2
1
0
1
2
2
0
0
4
2
0
2
1
2
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
2
2
0
0
1
1
0
2
1
0
1
0
0
2
0
0
2
3
0
1
2
0
0
0
0
0
2
2
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
1
2
1
0
0
6
1
0
0
0
0
1
0
2
0
1
2
0
0
2
1
1
0
0
0
0
4
0
0
1
0
0
1
0
1
2
0
0
3
0
0
0
0
2
0
2
1
0
1
1
0
2
2
0
0
1
1
0
2
0
0
1
1
0
1
1
2
2
0
0
0
2
0
1
0
3
2
0
0
0
1
0
0
0
2
0
1
0
1
1
1
2
1
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
1
0
0
0
2
3
2
0
0
1
2
0
0
0
0
1
4
0
0
1
0
2
0
2
0
1
7
1
0
0
2
0
1
0
2
2
0
0
0
2
1
2
0
2
0
1
1
0
0
0
2
0
0
0
1
3
1
0
2
0
2
0
0
2
2
0
2
0
2
1
0
1
2
2
0
0
1
0
0
0
0
0
2
2
0
1
0
1
1
0
2
1
0
1
0
0
1
0
2
0
0
2
0
0
1
0
0
0
1
0
0
1
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
2
1
1
1
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
2
0
1
1
0
0
2
1
2
0
1
1
1
0
1
0
0
1
0
2
0
0
0
1
0
0
2
1
0
2
0
0
1
0
0
0
0
0
0
0
2
0
1
1
0
1
0
2
0
2
0
1
0
0
2
0
0
0
2
0
0
1
0
0
1
1
3
0
0
0
0
1
0
2
2
2
0
0
1
1
0
1
0
2
0
0
2
0
2
2
1
0
0
0
2
0
2
2
0
0
1
2
1
0
1
1
0
0
0
0
2
1
1
3
0
0
1
0
4
1
0
0
0
0
0
0
0
1
0
0
2
0
1
0
3
0
0
1
1
0
0
0
1
0
0
0
1
2
2
0
0
0
0
0
2
0
0
0
1
4
0
2
0
2
0
1
0
0
2
0
0
2
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
1
0
1
0
0
0
0
2
1
0
2
2
1
1
0
1
1
2
0
0
0
1
0
0
4
1
0
1
1
2
1
2
1
1
0
2
0
0
0
2
0
0
0
1
0
0
1
4
2
0
1
0
0
0
0
0
3
1
0
2
2
0
0
0
0
0
2
1
1
0
0
0
2
0
0
0
1
0
1
2
0
1
0
1
0
0
0
0
0
0
2
1
0
1
2
0
1
0
0
2
1
2
0
0
0
2
0
0
1
1
0
0
0
2
0
0
0
0
0
2
2
0
0
1
2
0
0
0
0
0
2
1
1
0
0
1
2
1
0
1
1
0
2
1
0
1
1
1
2
0
0
0
2
0
0
0
2
0
0
0
1
1
0
2
1
0
2
1
3
2
0
0
0
1
0
2
1
0
2
0
0
0
1
0
0
0
1
1
0
1
0
0
1
0
0
2
0
0
1
0
0
0
2
2
0
1
0
0
0
0
2
0
0
0
2
0
5
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
2
0
0
0
1
1
2
2
2
0
2
0
0
0
0
2
0
0
0
0
0
2
2
2
0
2
0
1
0
1
0
0
1
0
0
2
1
0
0
1
0
0
0
0
2
2
2
0
0
0
2
2
0
0
0
1
2
0
1
0
0
0
2
3
0
0
0
2
0
0
0
0
0
0
1
0
2
1
0
2
0
1
1
0
2
1
1
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
1
1
0
1
0
1
0
0
2
0
0
0
0
1
1
2
1
0
0
0
0
2
1
0
0
1
0
0
0
0
0
1
2
2
0
0
0
2
2
0
0
1
0
2
0
1
0
1
2
1
2
0
2
0
2
0
0
2
3
0
0
2
0
2
2
0
2
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
3
0
1
0
2
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
2
0
0
0
2
1
2
2
1
1
0
2
2
0
0
1
0
0
2
1
3
2
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
1
0
1
0
0
0
2
0
1
1
2
0
2
0
0
2
0
1
0
0
1
0
0
0
1
2
0
0
0
1
0
0
0
1
0
0
2
1
0
0
0
0
0
2
2
0
2
0
0
1
2
0
0
0
3
0
1
0
0
1
2
0
1
0
1
0
1
0
0
1
0
1
0
2
0
1
1
2
1
0
1
0
0
2
2
0
0
0
2
2
0
0
2
1
2
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
1
2
2
0
0
1
0
2
2
1
1
0
1
2
0
0
1
2
0
2
0
1
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
2
0
0
1
0
2
1
0
0
0
0
0
2
0
0
0
1
2
1
0
0
0
0
0
0
2
0
0
0
0
1
0
1
1
0
0
1
2
0
1
0
2
0
0
1
1
1
1
2
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
1
2
1
0
0
0
1
0
0
0
0
2
0
0
2
0
0
2
2
1
0
2
1
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
1
0
2
0
0
0
1
0
0
1
0
2
0
1
0
3
0
1
2
0
0
2
0
0
0
0
1
2
1
0
2
1
1
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
1
2
1
0
1
2
0
0
0
1
0
1
2
0
1
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
1
1
1
0
0
0
2
1
2
4
1
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
3
0
7
1
4
0
0
0
1
1
1
2
0
0
1
0
0
1
0
2
1
0
0
2
2
0
0
0
2
0
1
2
1
3
0
0
1
0
1
1
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
2
1
2
0
2
0
2
0
0
0
1
0
1
0
0
2
0
1
0
0
1
2
2
0
1
1
3
2
0
0
0
0
0
2
0
1
2
2
1
0
0
1
0
0
2
2
0
0
2
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
2
2
0
1
0
0
1
2
0
2
2
1
0
0
0
0
2
0
1
2
0
0
0
0
1
1
1
3
0
0
0
1
0
0
2
1
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
10
0
1
0
0
0
1
0
0
2
0
0
1
0
0
1
1
0
2
0
2
2
2
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
1
0
0
0
2
0
0
1
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
1
0
0
0
0
4
2
1
0
0
0
0
0
0
0
0
1
2
2
0
0
0
2
0
0
0
1
1
0
0
0
0
2
1
2
0
0
0
0
0
0
0
1
2
2
0
2
0
2
2
0
0
2
1
0
2
0
0
1
1
0
0
0
2
0
0
1
0
0
0
1
0
0
4
1
2
0
0
2
0
0
0
0
2
0
0
1
2
0
2
2
0
0
2
0
0
0
0
1
0
1
0
0
2
2
0
1
0
2
1
0
1
0
1
0
0
0
0
0
0
1
1
0
1
0
0
1
0
2
0
0
0
0
1
0
0
2
1
0
0
2
0
0
2
2
1
0
0
1
0
1
1
1
0
0
2
1
0
1
0
0
1
0
0
0
1
1
1
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
2
1
0
0
0
2
0
0
1
0
1
0
0
0
0
0
3
2
0
1
0
1
0
2
2
1
0
0
0
0
0
0
2
2
0
0
2
0
0
0
1
1
0
0
2
2
0
0
1
0
2
2
1
1
1
2
0
0
0
2
2
2
2
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
2
2
2
0
0
0
0
1
0
3
0
2
0
0
0
0
0
0
2
3
0
0
3
0
0
2
0
3
2
2
1
0
0
1
0
0
2
0
1
0
1
0
1
0
3
0
1
0
2
0
1
0
0
0
0
0
2
0
0
0
6
1
0
0
0
0
0
3
2
0
0
0
0
2
0
0
2
0
1
3
0
0
0
1
2
0
1
0
2
0
0
2
1
1
0
1
0
1
0
0
0
1
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
1
2
0
0
2
2
0
0
1
0
0
0
1
2
2
0
0
0
0
1
2
0
0
0
1
1
0
0
0
1
1
0
0
0
1
0
0
0
2
0
1
0
0
0
1
0
2
0
0
0
1
1
0
0
0
1
0
0
2
2
0
2
0
0
1
0
0
2
1
1
2
0
0
0
0
0
0
0
3
0
2
1
0
0
2
0
1
1
0
0
0
2
2
2
0
4
0
2
3
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
1
3
1
1
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
2
1
1
1
1
0
0
0
1
0
0
2
0
2
0
0
0
1
0
0
1
0
2
0
1
2
0
4
0
0
0
0
2
0
0
1
0
0
0
2
1
2
0
0
0
0
0
1
1
2
0
2
1
0
0
2
0
0
0
1
0
0
1
0
0
0
2
1
2
0
2
0
2
0
1
1
1
0
1
1
0
0
0
0
0
0
2
0
1
1
0
0
2
1
2
1
0
2
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
1
0
0
0
2
0
2
0
2
0
0
1
0
0
1
1
2
0
2
0
0
2
0
0
2
0
1
1
1
1
2
0
0
0
0
0
2
0
2
2
0
2
2
0
2
1
0
1
0
0
0
0
2
0
3
3
0
2
1
0
0
0
0
0
1
1
0
1
0
2
1
2
0
0
1
2
0
0
0
2
0
1
0
1
1
2
1
0
1
2
1
1
0
1
0
1
1
2
0
3
0
0
0
0
0
0
0
0
0
1
2
2
1
0
1
0
0
2
1
2
0
0
0
0
1
0
0
1
0
3
0
1
1
0
0
1
0
1
2
0
1
0
0
1
0
0
1
1
1
0
0
0
1
2
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
3
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
2
1
0
1
0
0
0
1
0
0
3
2
0
0
0
1
0
0
2
1
0
0
0
0
2
0
0
0
0
1
0
1
0
2
2
0
1
0
2
0
0
1
0
1
1
1
1
1
0
0
0
1
0
0
2
0
0
0
0
0
1
0
1
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
1
1
0
4
0
0
0
2
0
1
0
0
0
0
2
0
0
0
2
0
0
1
2
0
1
2
0
0
0
0
2
0
0
3
1
0
1
0
0
0
2
2
0
0
0
0
1
0
1
1
0
0
0
2
2
0
0
0
2
0
2
0
0
0
0
2
0
0
0
2
1
1
0
1
3
2
0
2
0
0
2
1
0
0
0
3
0
2
2
0
0
2
0
0
1
0
1
2
2
0
1
1
1
2
0
0
0
2
0
0
0
1
2
0
0
1
1
0
1
0
1
1
1
2
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
1
2
1
0
0
1
0
0
2
0
1
0
1
0
0
1
0
0
0
2
0
4
0
0
0
0
1
0
2
1
0
0
0
0
0
2
0
0
1
0
2
0
0
2
1
0
0
0
0
0
1
2
0
0
1
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
3
1
2
1
0
1
3
0
0
2
1
1
1
0
1
0
0
0
0
0
0
0
0
0
2
1
0
2
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
2
0
2
1
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
2
2
0
1
0
0
1
0
0
0
1
0
0
0
2
1
0
0
2
0
1
3
0
2
2
0
0
0
3
1
1
0
1
0
1
1
0
0
2
1
0
1
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
2
2
0
2
1
1
2
1
2
0
1
2
2
1
0
0
0
2
2
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
1
1
2
0
1
0
1
0
0
1
0
2
1
1
0
0
0
0
0
0
0
1
1
0
2
0
1
0
0
2
0
0
1
1
1
0
0
0
1
1
1
0
1
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
2
0
2
2
2
0
0
1
0
0
3
2
0
0
0
0
0
0
1
0
0
2
0
2
1
0
0
0
1
2
0
0
0
0
2
1
3
1
2
2
1
0
0
1
0
0
0
0
2
0
0
2
0
0
2
0
0
0
2
0
1
1
1
2
0
0
2
0
0
0
0
0
1
0
1
0
0
0
2
2
1
1
1
0
0
2
0
1
2
0
2
1
1
1
3
1
0
2
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
3
0
0
1
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
3
2
0
0
2
0
0
2
0
0
0
2
0
0
0
3
1
1
2
0
0
0
1
1
0
0
0
0
3
2
0
2
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
2
2
0
0
0
3
1
1
1
0
2
2
2
0
2
0
1
2
1
1
0
1
0
2
0
0
0
1
1
0
0
2
2
0
1
0
2
0
1
1
0
0
2
2
0
1
0
0
1
2
0
1
0
0
0
2
0
1
0
1
2
0
2
1
0
0
2
3
0
0
0
2
0
0
0
1
1
0
0
1
2
1
0
1
1
0
0
1
0
0
0
0
3
2
0
0
0
0
0
2
2
1
0
0
0
1
2
0
0
2
0
0
1
0
2
0
0
1
0
0
0
2
0
0
0
2
1
3
2
1
1
1
0
0
0
0
0
0
2
1
0
0
0
0
0
1
1
0
2
0
0
1
1
0
0
0
0
0
1
0
2
2
0
0
0
0
0
1
0
2
1
1
2
3
2
1
0
0
0
0
2
0
0
1
2
0
0
0
1
0
2
2
0
0
0
0
1
0
0
0
2
0
1
1
1
2
2
0
0
3
2
0
3
0
0
1
0
2
0
0
0
1
0
2
0
1
0
0
0
1
0
5
0
0
2
0
0
0
0
0
1
1
0
2
2
0
0
0
0
1
0
2
0
1
0
0
1
0
2
2
0
0
1
2
0
0
1
1
0
1
0
3
0
1
0
1
2
2
0
0
1
0
1
0
1
0
0
2
1
1
0
0
0
1
0
1
2
0
0
0
0
1
0
1
2
1
0
1
0
0
2
2
0
2
1
0
2
1
0
0
0
0
2
0
0
0
2
1
1
0
2
1
2
0
0
0
0
0
0
0
1
1
0
0
0
0
2
2
0
0
2
0
2
1
1
3
1
0
0
0
0
0
2
0
0
1
0
1
0
0
1
0
2
1
0
0
1
0
0
0
0
2
1
1
2
1
2
3
0
0
2
0
0
1
2
0
2
0
0
2
0
0
0
0
2
0
0
1
0
0
1
0
0
1
2
0
2
2
0
1
2
0
1
1
0
1
1
0
0
0
0
3
0
2
0
1
0
0
2
0
2
1
4
2
0
0
2
0
1
2
2
1
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
2
0
1
2
1
0
0
1
2
0
0
0
0
1
2
1
0
1
0
2
0
1
0
0
0
0
2
0
0
1
0
0
0
0
1
2
0
0
2
2
0
0
3
0
0
0
0
1
0
2
0
0
0
1
0
2
0
0
2
0
0
2
1
2
1
0
2
0
2
1
0
2
1
2
0
2
1
2
0
1
2
0
2
2
1
0
2
2
3
1
1
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
1
2
1
0
0
2
0
2
0
0
1
0
2
0
0
0
0
0
0
0
1
1
2
1
0
0
0
1
2
0
0
0
1
0
1
0
0
1
0
1
1
1
0
1
0
0
1
0
0
0
2
0
0
1
0
0
2
1
1
0
0
2
0
0
0
0
0
1
2
0
1
2
2
1
1
1
1
1
3
0
0
0
2
1
4
0
0
2
2
0
0
0
1
2
0
0
0
0
0
0
0
2
0
3
0
0
0
1
2
0
0
2
0
0
1
1
0
1
0
2
0
1
2
0
2
2
0
2
1
0
1
2
0
1
1
2
0
2
2
2
0
0
0
2
1
0
1
0
1
1
0
0
1
1
1
0
0
1
1
0
0
2
0
1
3
1
0
3
2
0
2
0
1
0
0
0
0
0
0
1
2
0
2
2
2
1
0
2
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
1
2
1
0
0
1
0
1
0
2
1
0
2
0
0
0
0
0
2
0
2
1
0
1
0
2
0
0
2
2
2
1
2
2
0
0
0
2
0
0
0
2
2
0
0
1
2
0
2
0
1
0
2
0
2
0
2
0
0
0
0
0
0
2
1
0
4
1
2
0
0
1
1
0
2
0
0
0
2
0
0
0
2
1
0
1
1
2
0
0
0
0
0
0
1
0
0
2
2
2
2
0
1
2
1
0
1
2
0
0
0
1
0
1
0
1
2
0
0
0
0
2
0
0
0
0
2
2
1
0
2
0
1
2
1
2
1
0
0
0
1
2
1
1
0
0
0
1
0
0
0
1
0
2
0
0
1
0
2
1
0
1
1
0
0
0
2
1
0
0
1
0
0
2
2
0
0
0
0
2
1
2
0
0
1
0
0
0
1
2
0
1
0
0
1
0
0
2
0
0
0
0
1
0
1
0
0
1
0
1
2
0
0
0
3
1
0
1
1
1
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
1
4
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
1
2
2
1
0
1
0
2
0
0
0
0
2
0
2
2
0
0
0
2
0
0
1
0
0
2
1
0
0
1
1
0
2
0
0
2
0
0
0
1
0
0
0
2
0
0
0
1
1
0
5
1
1
0
2
0
0
0
0
2
2
1
2
0
0
0
1
0
0
2
0
0
0
0
2
0
0
1
0
1
0
0
0
0
2
0
1
0
0
0
1
0
2
0
0
1
0
2
0
0
2
0
0
2
0
0
1
2
0
0
0
0
0
0
1
2
0
0
1
0
2
0
2
0
2
1
0
0
0
0
0
2
1
0
0
1
0
0
0
0
1
0
1
6
2
0
0
0
1
0
1
0
0
2
0
2
1
0
1
0
0
0
0
2
0
2
1
0
2
0
1
2
0
0
1
1
1
0
0
0
0
1
1
0
1
0
2
0
0
1
1
0
1
2
0
0
0
2
0
6
0
1
0
1
2
0
0
1
1
0
2
2
0
0
0
0
0
2
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
2
1
3
1
0
0
1
2
0
3
2
0
2
0
0
0
1
0
0
0
1
1
1
0
0
0
0
1
0
3
0
2
0
1
2
0
0
2
0
0
0
0
0
2
2
0
0
1
1
2
2
0
1
1
0
0
0
1
1
0
0
0
2
0
1
1
2
0
0
0
2
0
3
0
0
0
1
0
2
0
2
0
1
2
0
0
3
0
0
0
0
0
0
0
1
0
1
2
2
2
0
1
2
1
0
0
0
2
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
2
1
1
0
1
2
0
1
0
1
2
1
0
0
0
0
1
0
0
0
1
1
1
0
0
1
1
0
0
2
0
0
1
2
0
0
0
0
0
1
1
0
2
0
0
1
0
0
2
0
1
1
2
0
0
0
3
2
0
0
0
0
0
2
1
1
2
1
0
2
1
0
1
0
1
0
0
2
2
2
0
0
0
0
1
0
1
0
2
2
1
0
2
0
0
0
1
1
0
0
1
0
3
0
1
1
0
2
0
0
2
0
0
0
0
1
1
2
1
1
1
2
0
1
0
2
1
5
0
2
0
0
1
0
0
0
1
2
0
0
2
2
0
0
0
0
1
0
0
1
1
1
0
1
0
0
0
1
1
1
0
0
0
0
2
0
1
0
0
0
0
3
2
0
0
1
1
1
3
0
0
0
0
0
0
0
1
0
0
1
1
1
0
2
0
0
1
1
0
0
3
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
2
0
1
2
1
0
1
2
0
2
0
1
0
0
2
0
2
3
0
1
1
0
0
1
0
0
2
0
1
0
0
2
0
0
0
1
0
2
0
1
2
0
0
2
0
0
0
0
0
0
0
2
0
3
0
0
0
2
2
0
3
2
1
0
2
0
2
0
1
2
0
2
0
0
2
1
0
0
0
0
2
0
2
2
0
1
0
0
0
2
0
0
1
2
0
0
0
0
1
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
3
0
1
1
1
1
0
0
0
2
0
0
1
1
2
1
1
1
0
0
0
0
1
0
2
0
0
1
2
0
0
0
0
2
0
1
1
0
1
1
1
3
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
2
1
0
0
2
2
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
2
0
0
2
0
1
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
2
1
1
0
0
1
0
0
0
0
2
0
1
0
2
1
0
0
0
0
1
2
2
0
3
2
1
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
2
0
0
1
1
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
2
0
1
0
0
0
2
1
1
0
2
1
0
1
0
0
3
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
1
1
0
2
1
2
2
0
0
0
0
0
0
0
0
0
1
2
3
2
2
0
2
2
1
2
0
2
0
0
1
0
0
0
0
0
2
2
0
0
0
1
0
1
1
1
1
0
0
2
2
2
0
1
0
1
2
0
0
0
0
0
4
1
0
0
0
0
0
2
0
0
0
2
1
0
0
1
0
0
0
1
1
0
0
0
2
0
0
1
2
0
0
2
0
0
1
0
0
2
2
1
1
0
0
0
3
0
0
0
0
0
2
0
1
1
0
1
1
0
0
1
0
0
0
0
2
2
0
2
0
0
2
0
2
0
0
0
1
0
2
0
0
1
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
1
0
1
0
0
1
1
1
2
0
0
1
1
0
1
0
0
0
1
0
0
0
2
1
2
0
2
0
0
1
2
0
0
0
0
0
0
0
3
1
2
0
1
0
2
0
2
0
0
0
0
2
6
1
2
0
0
0
0
1
2
1
1
1
0
2
0
0
2
0
1
0
0
0
0
0
1
2
1
1
0
0
0
0
0
0
0
0
0
1
1
2
1
2
0
2
0
0
0
0
0
2
0
0
2
1
1
0
0
2
0
2
0
0
1
0
1
0
0
0
0
3
1
0
0
2
2
0
0
1
0
1
0
2
0
0
3
0
0
1
0
2
0
1
1
0
3
0
2
0
2
3
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
1
0
0
1
0
1
0
2
1
0
0
2
0
1
1
2
2
1
3
2
2
0
0
1
0
4
1
1
1
0
0
2
0
0
0
1
0
3
0
0
0
0
0
5
0
0
1
0
2
0
0
0
2
1
2
0
0
2
2
0
1
1
1
0
1
1
0
2
1
0
0
0
0
2
0
0
3
1
2
0
5
0
0
1
0
0
0
1
0
0
0
0
2
1
1
0
0
2
1
0
0
0
0
2
2
2
1
0
2
0
0
0
0
0
0
0
0
2
2
0
0
1
2
1
1
0
0
0
0
0
0
0
1
2
0
1
0
0
0
1
2
2
0
2
2
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
1
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
2
2
2
0
0
1
2
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
2
1
0
0
2
0
1
0
0
0
2
0
2
2
0
2
2
1
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
3
0
0
0
1
0
0
0
0
2
0
0
1
1
0
0
0
1
0
0
1
0
1
0
2
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
1
1
0
0
0
0
0
0
4
0
0
2
0
1
2
0
1
0
2
0
2
0
2
0
1
0
2
1
0
2
2
0
0
1
2
0
0
0
0
2
0
0
0
1
1
0
2
0
2
0
1
1
1
0
0
0
0
0
0
1
1
0
1
0
0
1
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
2
1
1
0
3
0
0
1
1
0
0
2
2
0
2
0
0
0
1
1
0
0
0
0
0
0
0
1
0
2
0
1
0
1
2
0
2
1
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
2
2
1
2
0
1
0
2
0
0
0
0
2
0
0
1
0
2
0
1
1
0
2
0
0
1
0
0
2
2
0
0
2
0
0
2
0
0
1
2
0
2
0
0
1
0
2
1
1
2
1
0
0
1
0
1
0
0
0
0
0
2
1
0
0
2
0
1
1
1
2
0
0
1
0
1
1
0
0
0
0
0
1
0
2
1
0
0
0
2
1
1
2
2
2
0
0
0
0
0
2
1
0
0
2
0
2
1
1
2
0
0
1
0
2
1
1
2
0
3
1
1
1
0
0
2
0
0
0
2
1
2
0
2
0
0
1
3
2
0
1
0
2
1
0
0
0
1
0
1
1
0
1
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
1
2
0
0
0
0
1
0
0
2
0
0
0
1
0
1
1
3
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
2
0
1
0
2
0
0
0
0
2
0
1
0
0
0
2
2
1
0
0
1
0
0
0
0
0
1
0
1
0
0
1
1
2
1
1
0
0
0
0
0
1
1
2
0
1
0
0
1
0
0
2
0
0
0
1
0
0
1
1
1
0
2
0
2
1
0
2
4
0
1
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
2
2
0
1
0
0
0
0
1
0
1
0
1
1
0
2
4
0
2
0
1
1
0
2
0
1
0
0
0
1
0
1
0
0
0
1
0
1
1
1
0
2
0
0
0
1
1
0
0
0
1
0
2
0
0
2
0
2
1
2
2
0
0
0
2
1
2
1
3
1
0
0
0
0
0
3
0
0
2
0
0
0
0
7
0
2
0
1
0
0
0
0
0
0
0
1
2
0
2
1
0
0
0
0
1
1
1
2
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
1
1
5
0
0
0
1
2
0
0
0
0
2
0
2
1
1
1
1
0
0
1
0
1
0
2
0
0
1
0
0
0
2
0
0
0
2
0
1
0
0
1
0
2
1
0
0
2
0
2
0
1
0
0
0
2
3
1
1
0
0
0
2
2
2
0
0
0
1
1
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
1
2
1
0
1
0
0
1
0
2
0
0
0
0
1
0
1
2
0
2
0
0
1
0
1
2
0
2
0
0
0
0
1
0
0
0
0
1
0
0
1
2
0
2
0
2
0
2
0
0
0
2
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
2
1
1
0
1
1
0
2
1
1
0
0
0
0
0
0
0
0
0
2
0
2
1
2
0
1
0
3
2
0
0
1
0
1
1
1
0
0
0
0
1
1
1
0
0
1
1
0
1
2
0
0
1
0
4
0
0
0
1
0
1
0
0
1
1
0
0
1
0
1
2
0
0
1
1
0
0
2
1
0
0
0
1
0
0
2
3
0
0
1
1
2
0
1
2
0
1
1
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
1
0
2
0
2
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
2
3
0
0
2
0
0
1
1
1
1
0
0
0
0
0
0
0
1
0
1
0
1
2
0
0
2
0
2
0
0
1
0
1
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
1
0
0
2
0
2
1
1
2
0
0
1
0
1
0
0
1
1
1
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
1
0
1
0
1
1
2
1
1
0
0
1
3
0
3
0
0
0
0
1
4
0
0
0
0
1
1
0
2
1
1
0
0
0
2
0
1
2
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
1
0
2
2
1
1
1
0
2
0
0
0
2
2
0
1
0
0
1
0
2
2
1
0
1
0
0
1
2
1
0
1
0
0
3
0
1
0
1
0
0
0
0
2
0
0
2
0
1
0
2
2
0
0
2
0
0
0
1
2
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
1
0
2
0
0
2
0
0
0
0
2
1
0
0
0
0
1
1
0
0
0
0
1
0
3
2
0
0
0
4
2
0
0
0
0
0
0
1
0
0
0
2
2
1
0
2
0
0
1
1
0
1
0
0
2
1
2
0
0
2
1
0
0
0
0
2
0
0
2
0
0
0
1
0
0
2
0
2
4
1
0
0
2
0
1
0
1
0
2
2
2
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
1
1
0
0
2
1
0
2
1
0
0
0
0
1
1
0
0
1
1
0
0
1
0
0
0
3
0
1
0
0
2
0
0
2
0
0
0
0
1
1
0
1
1
0
0
0
1
2
1
3
0
0
0
1
1
2
0
0
1
2
2
0
0
0
0
2
0
0
1
0
0
1
0
0
2
1
0
0
0
1
0
0
8
2
1
0
0
0
0
0
0
2
0
2
0
2
0
0
0
2
1
1
0
0
0
0
3
1
2
0
5
0
0
1
0
1
0
2
0
0
0
1
0
1
1
0
2
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
1
0
3
1
0
2
1
0
2
1
0
0
0
0
0
0
2
0
0
1
1
3
0
2
1
0
0
0
0
0
0
1
2
0
0
2
2
0
1
0
2
0
0
0
0
1
1
0
2
2
1
0
0
0
0
1
1
2
2
0
1
0
2
0
2
1
1
1
0
0
0
2
0
1
0
0
0
1
0
1
0
0
2
0
3
0
1
0
2
0
1
0
0
1
1
0
2
1
0
0
0
3
0
0
4
0
0
0
1
2
2
0
1
2
0
0
0
0
3
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
1
0
1
2
1
1
0
0
1
0
0
0
1
0
0
0
1
3
1
0
0
0
0
2
1
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
2
2
2
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
1
2
0
2
1
2
0
0
2
0
1
0
0
1
0
0
2
1
1
0
0
0
1
2
2
0
0
0
0
0
0
2
1
1
0
0
0
1
2
2
0
0
1
1
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
1
1
2
0
0
3
2
2
2
0
0
2
0
0
0
0
0
1
0
2
2
2
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
2
1
0
2
2
0
2
1
2
0
0
1
1
0
0
0
1
1
1
2
0
2
0
0
2
1
0
2
0
0
2
1
0
0
1
4
0
0
1
1
2
2
1
0
1
1
3
0
0
0
3
1
0
1
2
0
2
5
0
2
0
0
0
1
1
2
0
1
0
0
0
1
2
0
0
1
1
4
0
1
1
0
0
0
3
1
1
0
1
0
1
1
1
0
0
0
0
0
0
1
0
0
1
2
0
1
3
1
2
0
2
0
0
0
0
0
0
0
1
2
0
2
0
1
1
2
2
0
2
1
0
0
2
0
0
0
1
1
1
1
2
2
0
2
2
0
0
0
1
0
1
1
0
0
0
1
2
0
2
2
1
0
0
2
1
0
2
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
1
0
1
0
2
0
1
1
1
1
1
0
0
0
1
1
1
1
0
0
1
1
2
0
1
0
1
2
1
0
0
0
0
1
0
0
0
1
0
0
0
2
0
2
1
0
2
2
0
0
0
1
0
2
1
2
0
1
0
0
0
4
0
0
0
1
1
0
2
0
0
0
2
4
0
0
0
0
0
0
0
1
1
2
0
1
1
0
1
0
2
0
0
0
0
0
3
1
0
2
0
0
2
0
0
0
1
0
0
0
0
0
2
2
0
0
1
3
0
1
4
0
0
0
2
2
0
0
2
0
1
0
0
0
2
0
2
0
1
1
0
0
2
2
2
0
2
0
2
0
0
0
2
10
0
1
0
2
2
1
0
0
1
0
2
2
2
1
1
0
1
0
0
0
0
2
1
0
2
1
0
2
1
0
0
0
1
2
1
0
2
0
0
2
2
0
0
0
0
2
0
0
2
2
0
0
2
0
0
0
0
0
2
0
0
2
1
1
1
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
2
1
1
0
1
0
1
0
5
0
0
0
0
3
1
0
2
0
0
0
0
2
0
1
0
2
1
0
0
0
0
2
2
0
0
0
2
1
0
2
0
1
2
2
1
0
1
0
0
0
0
0
1
3
0
0
1
1
0
0
0
1
0
1
0
0
0
0
2
1
0
0
0
0
2
2
1
0
0
1
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
4
0
3
0
0
2
0
0
0
2
1
0
1
0
0
2
2
0
0
0
1
0
0
0
0
0
0
1
2
1
2
0
0
1
0
1
0
3
0
0
2
2
0
0
0
1
3
0
0
4
1
1
0
0
1
0
0
0
2
0
0
0
2
3
1
0
2
1
0
0
2
0
0
1
2
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
1
1
1
1
0
2
1
2
0
0
0
0
2
2
1
0
0
0
0
0
0
2
1
0
1
2
0
0
0
0
1
1
0
1
0
0
2
0
2
0
1
0
1
0
0
1
1
1
0
0
0
0
0
1
1
0
2
2
0
1
2
0
0
0
2
2
2
0
0
2
0
2
2
1
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
1
1
0
0
1
2
1
1
2
0
2
1
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
1
3
1
0
1
0
1
2
0
0
2
0
2
2
0
1
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
1
0
1
2
0
1
1
0
1
0
1
0
2
0
2
0
0
0
2
0
0
3
0
0
0
1
0
0
0
1
0
0
2
2
0
2
0
0
1
0
0
0
0
0
3
1
0
0
1
1
0
0
0
0
0
0
0
0
1
2
0
0
1
0
2
2
0
0
1
1
0
1
1
2
0
2
0
0
2
0
0
0
1
0
0
0
0
1
1
2
0
0
2
0
0
2
0
2
2
2
1
0
0
2
1
0
1
1
0
1
0
1
2
0
2
0
0
0
0
0
1
0
0
1
0
2
0
2
2
0
0
0
0
2
0
0
0
0
2
1
1
0
2
1
0
1
2
1
1
0
0
1
1
0
2
1
0
2
0
0
0
1
1
0
2
0
1
0
0
0
0
2
0
0
0
0
0
1
1
1
0
0
0
0
0
2
2
1
2
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
1
0
1
0
3
2
0
1
0
1
2
0
0
2
1
1
0
2
0
0
0
0
0
0
2
0
1
1
1
0
2
1
2
1
0
2
2
0
0
1
0
0
2
2
0
2
2
1
0
0
2
2
2
0
2
1
1
0
0
0
1
0
2
0
2
0
1
2
0
2
0
0
2
0
0
1
0
0
0
0
2
1
0
1
0
1
0
0
0
1
0
1
0
2
1
0
0
0
0
2
0
2
1
0
2
0
1
2
2
3
2
0
0
0
0
1
0
1
3
0
0
0
0
0
0
1
1
2
1
0
0
1
0
0
1
0
0
1
1
0
0
2
0
0
0
0
0
1
0
0
0
0
3
1
0
0
1
1
2
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
1
0
0
0
0
2
2
0
2
0
0
1
4
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
3
0
2
2
2
0
0
1
0
1
2
0
1
1
0
0
0
0
1
0
0
0
0
0
0
2
4
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
1
0
2
1
0
0
0
0
0
0
0
2
2
1
0
0
0
1
2
1
0
0
0
0
1
0
0
1
0
2
2
0
0
0
1
0
2
3
0
1
4
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
3
1
1
0
1
0
0
0
0
0
1
0
0
2
1
1
0
0
1
0
2
0
0
1
1
0
2
2
0
0
1
1
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
2
2
0
0
1
1
2
0
0
1
0
1
0
0
0
1
0
1
1
2
0
0
1
0
1
0
0
0
0
0
2
2
1
0
0
0
0
0
2
0
5
0
0
1
1
1
0
2
1
1
1
1
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
6
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
3
1
0
0
1
0
0
0
1
0
2
0
0
1
0
2
1
0
2
0
0
2
0
1
0
1
1
2
1
0
0
0
0
2
1
1
2
2
2
0
0
1
0
1
2
0
1
1
0
0
1
0
0
1
0
0
0
1
1
2
1
0
0
1
0
1
0
0
1
2
2
1
2
1
0
0
1
0
1
0
2
0
0
1
0
0
0
2
0
0
0
1
1
0
0
0
1
2
0
0
2
1
1
1
2
0
0
0
0
0
2
0
0
2
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
2
1
0
0
2
0
0
1
0
2
1
0
0
0
2
0
1
2
0
0
0
0
0
0
0
3
1
0
2
0
1
0
1
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
2
5
0
1
2
1
2
0
1
1
2
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
3
1
0
1
2
0
2
1
0
2
0
1
0
0
1
0
0
1
0
0
0
0
2
0
1
2
1
0
1
1
0
2
4
2
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
1
0
2
0
1
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
2
0
0
2
1
0
0
0
2
0
2
2
0
0
0
2
0
0
0
0
3
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
1
2
0
0
0
1
2
0
0
0
2
0
0
0
2
1
0
1
1
0
0
0
1
0
4
0
2
0
0
2
0
1
1
1
0
0
0
0
1
1
2
4
1
0
0
1
1
0
0
2
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
3
0
0
0
0
3
0
5
0
0
2
2
2
0
3
0
0
2
0
1
0
0
2
1
0
0
0
0
2
1
1
1
1
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
2
2
1
0
3
0
2
0
2
0
0
0
2
0
2
0
0
1
1
0
0
2
3
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
1
0
2
0
1
0
0
2
1
0
0
2
0
1
0
0
1
2
2
0
0
1
2
0
0
1
0
2
0
0
1
0
0
0
0
1
0
0
1
0
0
2
1
0
0
0
0
2
0
0
1
2
2
0
0
0
0
1
0
2
0
3
3
0
0
2
0
1
2
0
2
1
0
2
0
0
0
0
0
0
1
4
1
0
0
0
2
0
0
0
2
2
0
1
1
0
0
1
2
1
1
0
1
0
10
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
1
1
0
2
0
2
0
2
0
1
3
0
1
0
1
2
0
0
2
1
0
0
0
0
0
2
1
2
2
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
4
0
0
2
0
0
0
1
0
2
2
2
1
0
2
0
2
0
0
0
0
2
2
0
0
0
0
0
0
2
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
1
2
0
0
3
2
0
0
2
0
0
0
0
1
1
0
1
2
0
0
0
1
2
0
0
0
0
0
2
2
3
1
1
1
1
0
0
0
0
0
0
2
3
0
2
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
2
1
0
0
2
0
0
0
2
1
1
0
1
0
0
1
2
1
0
0
0
0
2
0
1
2
2
1
0
0
0
0
1
2
0
0
0
0
0
0
1
0
1
2
0
0
2
1
1
0
1
0
2
0
0
1
1
0
3
0
2
2
0
0
2
1
0
0
0
0
0
0
6
0
0
0
0
0
0
1
1
0
2
2
2
2
1
2
0
1
0
2
2
0
1
1
2
0
0
0
0
3
0
0
0
1
2
0
0
0
0
1
2
1
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
1
1
0
1
1
2
0
1
0
0
0
0
1
2
0
0
0
0
1
0
0
2
1
2
0
0
0
0
2
2
0
0
2
0
0
0
2
0
0
0
0
1
0
1
1
0
0
0
2
1
0
2
0
0
2
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
2
0
0
0
0
1
1
1
0
2
2
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
1
2
2
0
0
0
0
3
2
2
0
0
1
4
0
0
0
0
0
2
0
0
0
1
0
2
2
1
0
0
0
1
2
0
0
1
2
0
0
2
2
1
0
2
1
2
1
5
0
0
0
2
0
2
1
0
0
1
0
2
0
1
0
0
2
2
1
2
1
0
0
0
0
0
1
2
1
3
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
3
0
0
0
0
1
0
1
0
1
0
1
2
1
0
0
1
0
1
0
0
0
2
1
0
0
0
2
2
0
0
1
1
1
1
0
1
0
1
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
2
1
0
0
2
0
1
0
2
0
1
2
1
0
0
2
0
0
0
0
0
1
2
0
1
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
1
1
0
2
1
0
2
0
0
0
0
0
1
0
0
1
0
0
1
0
1
2
0
1
0
0
1
0
0
0
1
1
1
0
2
1
2
6
0
0
0
0
0
0
2
1
1
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
2
1
0
1
1
0
1
1
0
1
0
0
0
0
0
1
1
0
0
1
1
2
1
1
0
1
0
1
0
0
2
0
2
0
0
0
2
2
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
2
0
2
0
0
1
2
2
0
0
0
0
0
2
2
0
0
0
1
0
0
3
1
1
1
2
1
0
1
1
0
0
2
2
0
0
2
0
2
1
0
2
0
1
0
0
1
0
0
1
3
2
2
2
1
2
0
0
0
2
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
2
0
1
0
0
0
0
2
0
2
2
1
1
0
0
1
0
2
0
0
0
0
0
3
0
0
0
0
0
1
0
2
0
0
0
3
0
0
1
0
2
1
0
1
0
2
1
1
0
0
0
0
2
1
0
0
1
2
0
0
2
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
2
2
2
2
1
0
1
0
0
0
2
2
0
2
0
0
2
0
0
0
0
0
1
2
0
0
1
0
2
2
0
1
2
1
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
2
1
2
2
0
1
0
1
0
1
1
0
0
0
0
0
0
0
1
1
0
2
2
2
1
0
1
1
1
0
0
2
0
0
0
2
0
0
0
1
0
0
0
1
1
0
0
2
1
0
0
2
1
2
2
0
2
2
1
1
0
0
0
0
0
2
0
1
0
0
1
0
0
2
0
2
0
1
2
0
2
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
1
1
0
0
2
2
0
2
0
0
0
1
0
1
1
2
0
0
0
1
4
0
1
0
0
1
2
0
1
1
0
0
0
1
1
1
0
0
0
2
0
1
1
0
2
2
0
3
0
0
0
2
0
1
0
1
1
0
0
0
1
0
0
2
0
1
2
2
0
0
0
0
0
2
2
0
0
2
0
0
2
2
1
0
1
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
1
0
1
2
0
0
0
0
0
0
1
2
2
0
1
0
2
0
0
2
0
1
1
1
2
1
0
2
0
0
0
1
0
0
0
0
2
0
0
2
1
2
2
0
2
1
0
0
0
0
2
1
0
0
1
0
2
0
2
2
2
1
0
2
2
2
1
0
2
0
2
0
0
1
0
0
2
0
1
0
0
0
1
3
0
0
0
0
0
0
1
0
2
0
2
0
2
0
2
1
0
1
0
2
0
1
0
0
0
0
0
1
0
2
1
0
2
1
1
1
0
2
2
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
2
0
0
1
1
2
1
2
2
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
2
0
2
2
0
0
0
2
0
0
0
0
0
0
0
1
2
1
0
2
0
1
0
1
1
0
0
2
1
1
0
1
2
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
1
1
1
0
0
0
0
0
0
3
0
2
2
0
0
2
0
2
0
0
2
0
0
0
0
0
1
1
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
1
1
1
2
0
0
0
0
0
1
0
0
0
1
2
0
0
2
0
0
0
0
2
0
0
3
0
1
0
1
0
0
2
0
0
0
0
0
0
1
0
0
2
1
1
0
0
0
0
3
2
1
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
2
0
0
0
0
2
0
1
0
2
0
0
0
0
0
2
1
2
2
0
0
2
1
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
1
0
3
2
2
0
0
0
2
0
0
0
1
1
0
2
0
3
0
0
0
0
0
1
0
0
1
1
0
2
2
1
0
0
0
0
2
0
1
0
0
1
0
1
2
0
1
0
2
2
1
0
1
2
1
0
2
0
0
0
0
1
0
0
1
4
0
1
0
0
0
0
3
0
0
0
1
2
0
0
1
0
2
1
0
1
1
2
2
0
0
2
1
2
1
0
0
0
1
0
1
0
0
0
3
0
0
0
0
2
1
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
2
1
1
0
0
0
0
1
2
1
1
2
0
0
0
0
0
0
0
1
0
0
2
2
0
0
1
5
0
2
3
2
2
1
0
0
0
0
1
1
1
0
0
1
0
0
0
1
0
2
2
0
2
1
0
0
0
2
0
2
0
3
0
0
2
1
0
1
0
0
2
0
2
0
2
0
0
0
2
0
0
2
0
0
0
1
2
4
0
2
0
1
0
0
0
0
0
0
0
2
2
0
3
0
2
2
2
0
2
1
0
0
0
1
0
1
0
1
0
2
0
0
0
2
0
2
0
0
2
0
0
0
0
0
1
2
0
0
0
2
2
0
0
0
0
0
0
2
1
0
0
2
1
2
0
0
0
1
0
2
2
3
0
0
2
0
1
0
2
1
0
0
1
0
1
2
0
0
1
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
2
2
0
0
0
0
0
2
0
0
3
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
2
1
2
1
0
0
0
0
0
0
2
2
0
2
0
2
0
0
2
3
2
2
0
0
0
0
3
2
0
0
2
1
1
0
0
1
0
2
0
1
1
0
1
2
0
2
0
2
1
0
0
0
1
0
1
0
2
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
1
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
2
3
0
0
0
2
0
2
0
5
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
2
0
1
0
2
2
0
0
1
2
0
1
0
0
1
0
0
0
0
0
1
2
1
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
1
0
0
1
0
0
1
0
1
2
0
0
0
2
2
1
0
1
1
1
2
0
0
1
2
1
0
1
1
2
1
1
2
1
0
0
2
2
0
1
1
3
0
0
2
0
0
0
1
0
4
0
2
0
2
3
2
0
0
0
1
0
4
0
0
3
2
2
0
0
2
1
0
1
0
2
1
0
0
0
1
1
1
2
0
0
1
1
0
0
0
1
0
1
1
0
0
0
0
3
2
0
0
0
1
2
1
0
0
2
0
2
1
2
1
1
0
0
1
0
1
0
2
1
1
0
0
0
1
0
0
1
2
0
0
0
3
0
2
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
1
1
0
3
0
0
3
3
2
1
0
0
0
0
1
1
1
0
3
0
0
0
0
0
2
2
0
1
1
0
0
1
0
2
2
0
2
1
2
1
1
0
1
1
0
2
0
1
0
3
0
0
2
0
3
1
0
2
2
0
1
1
1
0
1
0
2
2
0
2
1
0
2
0
1
2
2
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
2
1
2
0
1
0
0
0
0
2
0
1
0
0
0
1
0
2
2
0
0
2
3
0
1
1
0
1
0
0
0
0
0
1
2
0
0
0
1
0
0
1
2
0
1
0
0
3
1
0
0
0
0
0
1
0
0
0
1
0
2
1
0
0
2
0
2
0
0
1
0
0
1
1
2
2
0
0
2
1
2
0
1
0
0
0
1
0
0
0
0
1
3
1
0
1
0
1
0
0
2
0
0
1
0
0
2
3
0
1
0
1
0
2
0
1
1
0
0
1
0
0
0
0
1
1
0
0
0
0
3
2
2
2
0
1
0
0
0
2
0
1
0
0
1
0
0
0
2
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
2
2
0
0
1
0
2
0
2
0
0
0
1
0
2
0
0
0
1
1
0
0
1
3
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
1
1
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
1
0
0
2
0
0
0
2
1
0
0
2
0
0
0
1
2
1
1
0
0
0
0
0
1
0
0
1
0
0
0
2
0
2
1
0
0
0
0
2
1
0
1
0
2
0
0
0
0
0
1
1
2
0
0
1
0
0
0
2
0
0
2
0
5
2
0
0
2
0
1
2
0
1
0
1
0
1
0
1
1
0
0
2
0
0
1
1
2
1
0
5
0
2
0
1
0
2
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
1
0
2
1
1
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
5
0
3
2
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
2
2
1
0
0
2
0
0
0
2
0
0
0
0
1
1
4
2
2
2
0
5
0
1
1
1
1
0
1
1
0
2
2
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
1
0
1
0
3
2
1
2
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
1
2
1
1
2
0
1
1
2
0
0
0
0
0
0
1
0
0
0
0
2
0
1
1
0
1
1
0
0
0
0
0
0
2
0
1
0
1
2
0
2
0
0
0
0
0
1
2
0
0
1
2
2
0
0
0
2
0
1
2
1
0
2
0
2
0
2
0
0
0
0
0
2
0
2
0
1
0
0
2
0
1
1
1
1
0
0
2
2
2
2
0
1
1
0
2
1
0
0
0
1
0
1
2
2
0
0
0
0
0
0
1
1
0
1
2
2
2
0
0
2
1
0
0
1
0
1
2
0
0
0
0
2
0
1
1
0
0
3
2
2
0
1
1
2
1
0
0
1
0
1
2
0
0
2
0
1
1
0
2
0
0
0
0
2
1
0
0
0
0
2
0
1
2
2
2
0
1
0
0
0
1
1
0
1
2
3
0
0
0
1
0
0
0
0
1
2
0
0
0
2
0
1
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
2
1
0
1
2
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
2
1
0
0
0
1
0
0
0
0
0
1
1
1
0
1
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
1
1
1
2
0
0
1
0
0
0
0
0
0
2
0
1
2
0
0
0
2
1
1
1
0
1
1
0
1
2
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
2
1
1
0
0
2
1
2
0
1
0
2
0
0
0
1
0
0
1
0
2
0
1
0
2
0
0
2
1
2
0
1
0
2
0
1
2
0
1
0
0
0
0
3
0
0
0
0
0
2
0
2
0
3
0
1
2
1
0
0
2
2
1
0
0
0
0
0
0
2
0
0
2
0
1
0
1
2
1
2
1
0
0
0
2
2
1
0
0
1
0
1
2
2
0
2
0
1
1
1
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
2
0
0
0
3
0
2
0
0
0
2
1
2
2
0
1
3
0
1
0
0
3
0
2
0
0
2
2
1
0
0
4
0
1
0
0
0
0
1
0
0
1
0
0
2
2
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
2
0
2
2
0
2
0
0
2
1
0
2
0
2
0
0
1
0
2
0
1
1
0
1
0
0
1
0
0
0
2
0
0
0
0
0
3
2
0
1
0
1
0
0
0
2
1
0
0
1
0
2
1
1
2
0
0
0
0
0
1
2
1
0
2
1
1
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
2
1
2
1
0
1
0
0
0
0
0
1
0
2
2
0
0
0
1
1
0
0
0
1
2
0
3
0
1
1
0
0
0
0
1
0
0
5
0
2
3
0
0
0
0
0
0
1
0
0
0
0
2
2
1
1
0
0
0
1
0
2
0
0
0
0
1
0
0
1
2
0
0
0
0
2
1
0
1
0
0
1
2
0
0
0
0
1
1
0
0
0
1
2
0
0
0
0
0
0
2
0
0
1
0
1
1
0
0
0
2
1
0
1
0
0
3
2
0
2
1
0
1
1
0
0
0
0
0
2
1
1
0
0
0
0
0
3
0
0
0
0
0
1
1
1
1
0
0
0
2
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
1
0
0
2
2
0
0
1
2
0
0
1
0
0
0
0
0
0
2
2
1
0
1
0
2
2
0
0
2
2
1
0
0
2
1
0
0
0
0
0
2
1
1
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
2
0
0
1
1
0
1
1
3
0
0
2
1
0
0
2
0
0
0
1
2
0
1
0
1
0
1
0
1
2
1
0
0
0
2
0
0
2
0
0
0
2
1
1
0
2
1
1
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
1
0
2
0
0
2
0
0
0
2
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
1
1
1
0
1
0
2
0
0
0
1
1
1
0
0
1
1
2
1
1
1
0
1
0
1
0
1
0
1
2
0
0
2
2
2
0
0
0
1
0
0
0
0
0
0
1
2
2
1
0
2
0
0
0
1
0
0
0
1
2
0
0
0
1
0
2
2
2
1
0
0
0
0
1
0
2
1
0
1
1
1
2
1
2
2
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
1
1
0
0
2
0
1
3
2
2
0
2
0
0
0
0
0
1
2
1
0
1
2
0
2
0
1
0
0
0
1
0
2
1
0
0
0
2
0
0
0
1
0
0
0
2
1
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
1
0
2
1
0
1
2
0
1
0
2
2
3
2
0
2
0
2
2
1
2
1
2
0
0
0
0
2
3
0
0
0
0
2
0
1
2
0
2
0
0
2
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
2
2
1
1
2
0
2
0
2
0
0
0
1
0
0
1
0
0
0
1
0
0
1
1
2
0
2
0
1
0
1
0
1
0
1
2
0
1
0
0
3
4
0
0
0
2
0
0
0
0
2
1
0
2
0
1
0
0
0
0
2
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
1
2
2
2
0
0
1
0
0
1
0
2
2
1
0
1
1
1
1
1
0
1
0
1
1
0
0
1
1
0
0
0
2
0
0
2
0
0
2
0
0
2
3
0
0
0
0
0
2
0
2
2
0
0
0
2
0
2
0
0
0
0
0
0
0
2
1
1
1
1
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
1
2
2
0
0
0
0
2
0
0
2
1
1
2
1
1
0
1
1
1
1
0
1
0
0
4
0
0
2
0
0
0
0
0
2
0
0
0
1
0
2
0
0
1
2
0
0
0
0
0
1
1
0
1
0
1
0
0
1
1
0
0
3
0
2
1
2
1
0
1
0
0
0
1
0
1
2
0
0
0
0
2
0
0
0
1
0
0
0
2
1
0
2
0
0
0
0
1
1
0
0
2
0
1
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
1
0
2
1
1
2
1
2
0
0
0
0
0
0
1
2
2
0
0
0
1
1
2
0
1
0
1
0
2
0
2
0
0
2
1
0
2
2
0
2
0
2
2
1
0
1
0
0
0
1
0
2
0
0
1
0
2
0
0
1
1
0
0
0
1
1
2
0
0
0
0
0
0
2
1
2
1
0
1
0
2
0
2
0
0
0
2
0
0
0
2
3
0
0
0
0
2
0
2
0
2
1
2
0
1
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
1
0
0
1
0
0
0
0
0
1
2
1
0
0
0
2
1
0
1
0
2
0
0
0
0
1
0
2
0
1
2
2
0
2
0
0
2
3
0
0
1
0
2
2
1
1
0
0
2
0
0
0
2
1
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
2
2
0
1
1
0
0
0
0
1
1
2
0
1
0
0
0
2
0
0
0
0
0
1
0
1
1
0
1
0
2
0
0
1
1
2
0
2
2
0
0
0
2
0
0
0
0
0
1
0
0
5
0
1
0
1
1
0
2
1
2
0
1
0
0
0
0
0
0
0
0
0
2
1
0
2
2
0
0
0
0
0
0
0
1
1
0
0
0
0
1
2
2
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
2
0
2
0
1
1
0
0
2
1
0
1
2
0
0
3
0
0
3
0
0
0
0
1
0
3
1
1
0
0
1
0
0
0
0
1
1
1
0
2
2
0
0
0
1
2
0
0
0
0
2
0
0
2
0
0
2
2
0
2
0
1
2
0
2
0
2
1
2
2
2
2
2
0
2
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
5
1
1
0
1
0
0
0
0
1
0
1
0
0
0
2
0
0
2
0
2
1
0
1
0
0
0
1
0
0
1
0
1
2
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
2
0
0
1
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
2
0
1
0
1
1
2
0
2
1
2
3
0
1
0
0
0
2
0
2
1
3
2
2
0
0
0
0
0
1
0
1
1
0
2
0
0
0
0
0
0
1
1
0
2
0
2
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
2
0
0
0
2
0
0
0
1
1
0
0
0
2
0
0
0
0
1
0
0
3
0
0
0
0
1
0
0
1
2
1
0
0
0
1
3
0
1
1
0
1
0
1
1
2
2
0
0
2
1
0
1
0
0
0
2
0
2
0
2
0
0
0
0
1
0
1
0
0
3
0
1
0
0
1
0
2
0
0
2
1
1
1
1
1
0
2
0
0
0
0
2
1
0
0
2
1
2
2
0
1
2
1
0
1
3
0
2
0
2
0
0
0
0
0
3
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
2
5
1
1
0
1
0
1
1
2
1
1
2
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
1
5
2
0
0
3
1
1
1
0
1
0
0
2
0
0
2
0
1
2
2
0
0
0
0
0
3
0
0
2
2
2
0
0
0
0
0
2
0
0
2
0
0
0
2
0
2
0
0
1
0
0
2
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
1
1
1
0
0
2
0
0
0
0
0
0
0
1
1
2
0
0
0
0
2
1
0
0
0
0
0
0
0
1
1
1
1
1
0
1
1
7
0
2
0
0
2
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
2
1
0
0
1
0
0
0
2
0
0
0
1
0
1
0
1
0
1
2
0
2
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
1
0
2
0
0
0
1
0
1
2
0
0
1
0
0
0
1
0
1
2
2
2
0
0
0
0
0
1
1
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
2
0
0
2
2
0
0
0
0
1
0
0
0
2
0
0
2
0
0
2
0
3
0
2
1
0
0
0
1
0
1
0
1
0
1
1
2
0
0
0
2
3
0
1
0
2
1
1
2
0
0
0
1
1
1
2
0
0
2
1
0
0
0
0
3
0
0
1
2
0
0
0
1
0
1
0
1
2
2
0
0
0
0
1
0
0
0
2
2
2
0
3
2
1
0
0
2
0
2
2
0
1
0
0
0
0
1
0
0
0
1
1
0
2
2
0
0
0
0
1
2
0
0
0
1
0
0
0
1
2
0
0
1
2
0
2
0
0
0
0
0
0
2
0
0
2
0
2
0
4
0
0
2
0
2
0
0
2
2
2
2
0
0
0
2
2
2
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
2
2
2
2
0
1
1
0
0
0
2
0
2
0
1
0
2
1
0
1
2
0
3
3
1
2
0
1
0
2
0
0
0
0
2
2
0
1
0
1
0
0
0
2
0
0
1
0
0
0
2
0
0
1
2
0
0
1
1
2
0
1
2
0
0
2
0
0
2
1
2
1
0
0
0
2
1
0
2
0
0
0
1
1
0
2
1
1
3
3
1
1
0
2
2
0
0
0
1
0
0
2
0
0
0
1
1
0
0
0
0
2
0
1
0
1
0
0
0
0
2
2
0
0
2
1
0
1
0
2
1
0
0
0
1
1
2
2
2
0
1
1
2
0
0
0
3
0
1
1
1
0
0
0
2
0
0
0
0
1
1
1
0
1
0
0
1
0
0
2
0
0
1
2
1
0
0
1
1
1
0
1
1
0
0
1
1
0
0
0
0
2
0
0
1
0
0
0
1
0
0
5
0
1
0
0
0
1
5
0
0
0
2
0
0
2
0
2
0
0
1
1
1
1
0
1
0
0
0
2
0
0
1
1
0
0
1
1
0
3
0
0
2
0
1
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
1
1
0
0
0
0
1
1
1
0
2
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
1
1
1
0
0
2
0
0
0
1
0
0
1
1
1
0
3
0
1
2
2
0
0
0
1
2
1
0
0
0
0
1
0
0
1
2
0
2
0
1
1
0
5
0
0
0
0
0
2
1
0
1
0
3
2
1
0
0
2
0
0
2
2
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
1
1
2
0
0
2
0
2
0
0
0
0
1
0
0
0
2
0
1
0
1
2
2
0
0
0
0
0
0
1
0
1
0
0
0
1
1
1
0
3
2
0
0
0
1
1
7
4
1
0
2
2
0
1
2
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
2
2
0
0
0
0
0
1
0
0
1
2
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
2
1
2
0
0
0
1
2
0
0
2
2
0
0
1
0
1
0
0
0
0
0
3
0
0
1
0
2
2
0
0
1
1
0
2
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
5
0
1
0
1
2
2
0
0
0
2
0
0
0
2
1
0
0
0
1
0
1
1
0
2
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
2
1
0
0
1
0
1
2
0
0
2
1
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
2
2
1
1
2
1
2
0
0
0
0
0
2
1
0
3
1
0
1
0
0
1
0
1
0
0
0
1
1
0
0
0
0
1
0
1
0
2
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
2
0
1
2
0
1
0
0
2
1
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
1
0
1
0
1
1
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
2
0
1
0
2
2
2
1
2
0
2
2
1
0
0
0
1
0
0
0
1
1
1
1
0
0
0
0
0
1
0
2
0
0
2
1
0
0
1
2
0
0
2
3
0
0
0
0
1
1
2
0
2
0
0
2
0
1
2
0
1
0
1
0
2
1
0
1
2
0
1
0
0
1
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
1
0
2
0
1
0
1
0
0
0
0
2
1
0
1
1
2
2
0
2
1
2
2
1
0
0
0
0
0
0
1
0
1
2
0
0
0
0
1
1
2
1
1
0
0
2
0
0
0
1
1
1
1
0
0
2
0
3
1
0
0
1
0
0
0
0
1
0
1
0
0
0
2
2
1
0
0
0
1
0
0
0
0
0
2
1
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
1
0
1
2
0
2
1
1
1
0
0
0
2
1
0
0
0
0
0
2
0
0
0
2
1
2
0
0
0
1
0
0
0
0
1
0
6
2
0
0
0
0
0
1
0
0
2
0
0
2
1
0
1
1
1
0
0
0
0
0
0
2
2
0
1
1
1
2
0
0
2
2
0
0
2
0
0
0
0
1
0
0
0
0
2
0
2
2
0
0
2
2
1
1
1
3
1
0
0
1
0
2
1
0
2
2
0
0
0
1
0
1
2
0
2
0
2
0
0
0
1
2
0
1
1
0
0
1
0
2
0
0
0
1
13
2
0
1
0
0
0
1
0
0
0
0
0
3
0
0
1
1
0
0
0
1
0
2
0
0
1
1
0
1
0
0
1
2
2
2
1
0
2
0
1
1
1
1
2
0
2
0
3
0
1
0
0
0
0
1
0
2
0
1
1
1
0
1
1
1
1
0
0
0
1
1
0
0
0
2
0
3
0
1
0
0
1
0
0
1
0
0
0
2
1
0
1
0
0
0
0
2
0
1
0
1
1
2
1
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
2
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
2
0
2
0
0
0
0
2
1
0
0
0
2
0
0
1
0
2
1
0
1
1
2
2
2
0
2
0
0
0
0
0
1
0
0
0
1
0
0
2
7
0
0
0
1
2
0
0
1
0
2
0
0
0
1
4
0
1
0
0
0
3
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
3
1
0
0
0
0
2
0
1
0
1
0
0
0
2
0
0
2
0
2
0
0
0
1
0
0
0
3
0
0
2
0
2
0
0
0
1
2
1
1
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
1
1
0
2
0
0
0
0
1
0
2
0
2
1
1
0
2
0
0
2
1
2
1
0
0
1
1
0
0
1
1
1
0
0
1
2
1
0
0
0
0
0
0
1
0
0
0
3
2
1
0
1
0
1
0
0
0
2
1
0
0
2
0
0
2
0
2
2
3
1
0
1
0
0
1
0
2
0
2
0
0
2
2
1
0
0
0
3
0
2
0
0
0
0
0
0
0
0
2
0
1
0
1
2
0
0
0
2
0
1
0
0
1
0
1
1
1
4
1
2
0
2
0
2
0
0
1
0
0
1
2
1
2
0
0
0
2
0
1
2
2
0
0
0
2
0
2
0
0
2
2
0
0
1
0
0
0
0
6
2
1
1
0
2
0
0
1
2
1
0
0
0
0
2
0
2
0
0
2
2
1
0
0
1
0
1
0
1
0
1
2
0
0
1
1
0
2
0
0
0
2
0
1
0
2
1
1
2
2
2
0
1
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
1
0
2
0
0
2
0
1
0
2
0
0
2
0
0
2
0
2
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
2
2
0
1
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
2
2
2
1
1
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
1
0
0
2
1
1
0
0
0
0
3
0
0
1
0
0
0
2
0
2
2
0
1
0
2
2
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
1
1
1
0
0
0
1
1
1
1
1
2
1
0
0
0
1
1
2
0
2
0
0
0
1
0
0
2
0
0
2
2
1
1
0
2
0
1
2
3
0
1
2
0
0
2
0
0
0
1
0
2
0
0
0
2
1
2
0
2
1
1
0
2
0
0
1
1
2
1
2
0
1
1
0
1
0
1
0
0
0
0
1
3
0
2
1
0
1
0
1
0
0
0
2
0
1
1
2
2
1
1
0
0
0
0
0
0
0
1
0
0
1
2
0
0
2
0
0
0
2
2
1
0
0
0
0
0
0
1
2
0
0
3
1
0
0
0
0
1
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
3
2
1
1
0
1
0
1
0
0
0
0
2
1
1
0
2
0
0
1
2
0
0
0
0
2
0
0
0
1
2
1
0
1
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
2
0
0
2
1
0
2
0
0
2
0
2
0
1
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
1
3
0
0
2
0
3
0
0
2
0
2
0
0
2
0
0
1
0
2
0
0
0
0
2
0
1
1
0
0
2
0
0
0
2
2
1
1
0
2
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
1
0
0
1
0
0
0
2
0
0
0
1
0
2
0
0
0
2
1
0
0
1
0
0
2
0
0
0
2
0
0
0
0
1
2
0
0
0
0
1
1
0
1
0
0
2
2
2
0
0
0
0
1
1
1
0
1
0
0
0
0
1
0
1
0
2
0
2
0
0
2
1
0
1
1
0
0
0
1
0
1
2
1
2
0
2
0
2
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
1
1
1
0
1
0
0
2
2
0
0
0
0
0
1
0
0
1
0
0
1
2
1
0
1
2
0
0
0
2
1
2
0
1
1
0
1
1
1
1
0
2
1
2
1
2
0
2
0
0
1
0
0
0
0
1
2
0
1
1
0
2
0
1
0
2
1
2
1
2
0
0
1
2
1
0
2
1
0
1
0
1
1
0
2
1
0
2
0
0
0
0
0
1
0
2
1
1
0
1
0
0
0
2
0
0
1
2
2
0
0
0
0
2
1
0
0
0
1
2
0
0
0
0
0
0
2
0
2
0
1
1
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
1
1
2
1
0
0
1
0
2
0
2
1
2
0
1
0
0
1
1
2
0
0
1
1
3
0
0
1
1
0
0
0
2
0
0
1
0
0
1
0
1
3
0
2
1
2
1
2
1
1
2
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
2
1
1
1
0
1
0
0
0
0
2
0
1
0
0
1
0
0
0
0
1
0
0
0
2
1
1
0
1
0
0
0
0
4
3
1
2
1
0
2
1
1
1
1
0
0
0
0
1
0
0
1
2
1
2
0
0
2
1
0
1
0
2
1
0
0
0
1
0
0
2
2
0
1
1
1
0
0
0
0
1
0
2
0
0
0
2
0
1
0
1
2
1
1
0
0
2
1
2
1
0
2
1
0
0
0
0
2
1
0
1
0
1
0
2
0
0
2
0
0
0
0
0
0
0
1
1
1
0
1
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
2
1
0
0
1
0
0
2
0
1
0
0
0
0
0
0
2
0
1
3
0
2
0
1
2
1
1
1
0
0
1
0
1
0
2
1
0
0
0
0
1
0
1
0
0
0
1
0
1
1
0
0
0
1
1
0
2
1
2
0
1
2
0
1
2
0
1
1
11
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
1
0
2
2
0
1
1
2
0
0
0
0
0
1
0
0
1
0
3
0
0
0
0
0
2
0
0
1
2
0
0
0
1
2
0
0
0
0
1
2
0
2
1
0
1
1
0
0
2
1
1
1
1
0
1
2
0
0
0
0
0
1
1
0
0
1
1
0
1
2
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
1
2
2
0
0
1
1
0
1
0
0
0
0
0
0
0
0
2
1
2
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
2
2
0
0
2
2
0
0
0
0
1
0
2
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
2
1
1
1
1
1
1
1
0
2
1
0
1
2
0
0
1
2
2
0
0
1
0
0
1
1
0
2
0
0
1
0
2
0
0
0
1
1
1
0
2
0
0
1
0
2
0
0
2
0
0
0
4
0
2
2
0
1
1
2
2
0
0
0
0
2
0
0
0
0
0
0
2
2
1
0
1
0
0
1
0
0
2
1
1
1
0
2
0
0
0
0
2
0
0
0
0
2
2
1
0
2
0
0
2
1
1
2
3
0
2
2
0
1
0
2
0
2
1
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
4
1
0
1
1
0
0
2
0
0
1
0
0
0
0
2
0
0
1
0
0
0
2
1
1
1
1
1
3
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
3
0
1
0
1
0
0
0
0
1
1
0
3
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
2
1
1
0
0
1
0
0
2
0
2
2
0
0
1
0
0
3
0
0
2
0
0
0
2
0
0
1
2
3
1
0
0
0
0
0
0
1
0
1
2
0
0
1
1
1
1
0
0
1
0
2
2
1
2
0
1
1
0
0
0
0
0
0
1
2
1
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
1
0
0
1
0
1
0
2
0
0
0
2
1
1
1
1
0
2
2
4
2
0
3
0
0
2
0
1
0
2
0
0
0
0
1
0
1
1
0
0
0
2
0
1
0
1
3
0
1
0
1
0
2
0
1
0
0
1
1
1
0
0
2
0
2
0
0
1
1
0
0
0
4
1
0
2
0
0
0
0
0
2
1
0
1
0
1
0
0
1
1
1
2
0
1
0
1
0
1
0
0
0
0
0
2
0
0
1
3
1
2
2
2
0
0
1
2
0
2
0
1
0
0
0
1
0
1
1
0
0
1
0
0
3
0
0
1
0
1
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
1
2
0
4
0
1
0
0
2
2
2
2
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
2
1
0
1
0
1
0
1
2
0
1
0
0
1
0
2
0
2
0
0
0
0
1
0
0
1
0
0
0
0
1
0
2
1
0
1
0
0
0
1
2
0
1
0
1
0
1
2
0
0
0
0
0
1
0
2
0
0
0
0
1
1
2
0
0
2
0
0
0
1
0
0
2
0
0
1
0
1
0
0
0
1
1
0
0
1
1
0
0
0
0
0
1
1
2
0
0
2
2
0
0
0
0
0
2
0
0
1
1
1
0
0
2
0
0
0
2
3
2
2
2
0
1
2
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
2
2
0
2
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
2
2
2
0
1
1
0
1
0
0
0
0
2
1
1
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
2
1
2
0
0
0
3
0
4
1
0
1
1
0
0
0
0
0
0
1
2
0
2
0
0
0
0
1
0
0
1
1
0
0
2
0
0
0
0
0
2
1
1
2
1
1
0
2
1
1
0
2
0
0
0
0
2
2
0
0
1
0
1
2
0
0
1
0
0
2
0
0
2
1
0
0
1
0
0
0
0
0
1
0
1
0
0
2
1
9
1
0
2
0
1
1
0
2
3
1
0
1
0
0
1
0
1
2
1
2
0
1
0
0
0
3
2
0
0
1
0
0
2
0
2
1
0
2
0
2
1
0
2
0
0
0
0
2
2
2
0
2
0
2
0
0
1
2
2
0
2
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
3
1
1
1
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
2
0
3
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
2
3
0
0
2
1
1
0
0
0
2
2
0
0
2
0
3
0
1
0
2
0
1
0
2
0
0
0
1
0
0
0
1
0
1
2
1
0
0
0
2
0
0
1
0
1
1
0
1
1
0
2
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
1
2
2
0
1
0
1
0
0
0
1
1
0
2
1
3
0
0
0
1
0
1
1
0
1
2
0
2
1
0
0
0
0
0
0
0
0
1
1
4
0
0
1
0
1
0
1
0
1
2
0
1
2
0
2
2
2
1
0
0
0
0
1
0
2
0
2
0
0
2
1
0
0
2
0
0
1
0
2
0
0
0
0
0
1
0
2
0
0
5
0
1
9
0
1
1
2
0
1
0
2
2
1
2
0
0
0
1
0
0
0
1
2
1
0
0
1
3
0
1
0
0
1
0
0
1
1
2
0
0
1
1
1
0
0
2
0
0
3
1
0
0
2
0
0
2
2
2
1
0
1
0
2
3
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
2
1
0
2
2
1
2
0
0
1
4
0
1
0
0
1
0
0
1
0
1
0
1
2
0
0
2
0
1
2
2
0
0
1
1
0
1
0
1
2
0
0
1
0
0
2
0
1
1
0
0
0
3
0
0
0
0
0
2
0
1
0
0
1
0
0
0
1
1
0
1
2
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
1
0
1
0
2
2
3
2
0
2
2
1
2
0
0
2
0
1
0
0
0
0
0
0
3
1
1
2
1
4
0
0
1
0
1
2
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
2
4
1
0
0
1
2
0
0
2
0
0
1
0
0
1
0
2
0
1
0
0
2
0
1
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
1
2
0
0
0
0
1
0
0
2
1
1
1
0
0
2
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
2
1
0
1
2
0
2
1
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
2
1
1
2
2
0
0
1
0
2
1
0
1
0
0
1
1
1
0
1
2
0
0
0
2
0
0
1
2
1
0
1
0
0
2
0
1
0
0
0
0
1
0
0
0
0
1
2
0
2
1
1
1
0
0
0
0
0
0
0
0
0
0
1
2
2
1
0
0
0
2
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
1
2
1
1
0
0
0
0
0
2
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
2
1
0
0
0
0
0
0
0
2
1
0
0
1
0
0
1
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
2
2
0
0
2
1
0
0
1
1
0
2
0
0
1
0
1
0
1
1
2
2
0
1
0
0
2
0
0
0
1
1
1
0
0
0
0
1
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
1
0
1
0
0
1
0
0
1
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
1
0
0
0
1
1
0
0
0
2
3
0
0
0
4
0
0
0
0
0
2
0
1
0
0
2
0
0
0
1
2
0
1
1
0
1
0
0
0
2
0
2
2
0
0
0
1
1
0
0
0
0
0
0
1
0
1
2
2
0
0
1
0
2
0
1
1
0
0
0
0
1
0
2
0
0
0
0
1
1
0
0
0
0
1
1
0
0
1
0
1
0
4
0
0
0
0
0
2
1
2
2
1
0
0
0
2
2
0
1
1
0
2
0
0
2
2
0
1
0
0
0
2
1
4
1
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
1
1
2
2
0
4
0
0
2
0
0
2
1
2
0
1
1
0
4
1
0
2
0
1
1
1
0
0
1
0
1
2
1
0
1
0
0
2
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
2
2
0
1
0
0
2
1
2
0
2
0
0
0
2
1
2
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
2
2
0
1
1
1
0
0
1
1
1
0
0
2
0
2
2
0
0
2
2
0
0
0
2
2
0
1
1
1
0
1
2
1
0
0
0
2
1
0
2
2
0
0
1
1
0
2
1
0
0
1
0
0
0
0
0
2
0
0
0
4
0
0
0
2
3
1
0
0
2
1
0
0
0
1
1
0
2
2
1
0
0
2
0
2
2
0
0
1
0
2
0
0
1
0
0
2
2
0
0
0
2
0
1
0
2
2
0
0
0
1
1
0
0
0
0
2
1
2
0
1
1
0
1
0
0
0
0
2
0
1
0
0
0
0
1
0
2
1
1
0
1
1
0
2
1
0
0
1
1
0
1
3
0
0
0
0
2
2
2
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
2
1
0
1
1
2
1
1
0
1
1
2
0
1
1
0
2
0
2
2
1
2
0
4
0
0
1
0
0
2
0
0
1
2
0
0
1
2
1
0
2
0
2
2
1
1
2
0
1
0
0
0
0
0
0
0
0
2
0
2
1
1
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
2
2
0
0
0
0
0
2
0
2
0
0
1
2
0
0
1
0
0
1
0
2
0
0
0
0
0
0
1
2
3
0
0
0
1
0
0
0
1
2
0
0
0
0
1
0
1
2
1
0
0
0
0
2
2
0
1
2
0
0
0
0
2
0
2
0
0
0
0
0
2
0
2
0
2
0
0
0
1
1
1
1
0
2
0
0
1
1
1
0
0
0
2
2
0
2
1
0
3
0
0
0
0
1
2
0
1
1
0
0
1
0
0
0
0
2
2
2
1
2
1
0
0
0
0
1
0
0
1
2
0
0
0
0
2
0
0
0
0
2
0
2
1
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
1
0
1
0
0
2
2
2
0
0
0
0
0
1
1
0
0
0
0
0
0
2
2
1
0
1
2
0
0
0
0
0
2
1
0
0
0
0
2
1
0
0
0
0
0
1
1
2
0
0
0
0
2
1
1
0
0
2
0
2
2
0
1
1
0
2
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
2
0
2
1
0
2
2
0
0
1
0
1
0
1
0
0
0
0
0
0
1
1
0
0
2
0
0
0
1
1
2
0
0
2
3
1
0
1
2
1
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
2
0
1
0
2
1
1
1
1
0
0
4
0
2
0
0
1
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
1
0
2
0
2
0
2
1
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
1
2
0
0
2
0
0
1
0
0
2
1
0
0
2
1
0
2
1
0
1
0
2
0
1
0
0
1
1
0
1
1
2
0
2
0
0
3
0
0
1
1
0
1
2
1
0
0
0
1
0
0
1
0
1
0
1
0
1
0
0
0
0
0
1
0
2
0
1
0
0
0
0
2
3
0
4
0
0
0
1
0
0
0
0
2
1
2
0
0
0
0
3
2
11
1
1
0
0
2
1
1
0
0
1
0
1
1
0
1
1
0
2
1
0
0
1
1
0
0
0
0
2
2
0
0
0
0
0
0
0
2
1
2
1
0
0
0
1
0
0
0
0
0
0
0
2
2
2
2
0
0
0
0
3
2
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
1
0
0
1
0
3
2
1
0
2
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
1
1
0
0
0
1
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
3
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
1
2
0
1
2
0
1
2
3
0
0
0
0
2
0
0
2
2
1
2
0
0
2
0
2
2
0
0
1
0
0
1
0
0
0
0
0
0
1
1
1
1
0
4
0
2
0
0
1
0
1
1
1
0
1
1
3
0
0
0
0
0
0
0
0
1
1
0
0
2
0
2
1
0
0
0
2
0
0
0
0
2
2
1
2
2
2
1
0
1
1
0
0
0
0
2
1
1
1
0
0
0
0
0
0
2
0
1
2
0
2
0
0
0
0
1
0
1
0
2
1
1
1
0
0
1
0
2
0
2
0
0
0
2
0
0
1
2
2
0
1
1
1
0
0
2
0
1
0
0
2
0
1
1
0
0
1
2
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
1
0
1
2
2
2
0
0
2
1
0
0
0
0
0
0
1
1
0
0
2
0
0
1
0
0
2
0
1
0
1
2
1
2
0
1
2
0
2
4
0
1
2
0
1
0
0
0
1
0
0
2
0
1
0
1
1
0
0
2
0
0
0
0
2
1
1
0
4
0
1
0
5
2
1
0
1
2
1
1
0
0
1
0
3
0
0
0
0
2
2
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
1
0
2
1
0
0
1
1
0
1
0
2
0
2
0
1
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
2
0
1
1
0
0
0
1
2
0
1
1
1
0
0
2
0
2
0
0
0
0
0
0
1
1
0
2
0
0
0
1
2
1
0
0
1
1
1
2
0
1
2
0
1
1
0
0
0
1
0
0
1
2
0
0
2
0
3
0
0
0
1
2
1
0
0
1
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
1
1
0
0
2
0
0
2
2
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
1
2
1
2
0
0
0
1
2
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
2
0
2
0
0
1
0
2
0
0
2
0
0
0
2
0
0
0
0
0
1
4
5
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
3
1
0
0
0
0
0
1
2
1
2
1
0
1
0
0
0
0
1
0
0
0
0
2
2
0
0
1
2
0
0
1
0
0
0
0
0
0
2
0
1
1
0
1
1
2
2
0
0
1
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
2
0
2
2
1
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
1
1
1
2
0
0
3
1
0
0
2
2
0
0
1
0
0
2
1
1
0
0
0
0
1
3
1
0
0
1
2
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
2
0
1
0
2
0
2
0
0
1
0
1
1
0
1
1
0
0
0
1
1
0
0
1
1
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
10
0
1
1
0
0
2
2
0
0
0
0
2
0
0
1
1
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
2
0
1
0
0
0
2
1
1
0
1
1
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
1
0
1
1
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
2
0
0
0
0
0
0
1
0
1
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
1
0
0
1
2
0
0
2
0
0
1
0
0
0
1
0
0
0
0
1
2
0
7
0
0
0
2
2
1
2
0
0
0
0
0
0
0
2
1
0
1
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
1
1
2
0
0
1
0
1
0
0
0
0
0
2
0
2
0
0
1
0
0
2
3
0
2
3
1
1
2
0
0
0
0
1
0
2
0
0
0
0
0
0
1
1
0
1
1
1
1
0
1
1
3
2
0
1
0
0
0
2
3
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
2
0
0
1
1
2
2
1
1
0
0
0
1
1
1
1
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
2
2
0
2
1
2
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
2
0
0
2
1
1
2
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
2
0
1
4
2
0
0
0
1
1
1
0
1
0
1
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
1
1
1
1
2
0
0
1
0
1
0
2
1
0
0
1
0
0
1
0
0
1
0
0
2
1
2
2
4
2
1
1
0
0
0
1
0
0
2
0
1
0
2
1
0
0
0
1
0
0
2
0
2
1
0
0
1
0
0
2
2
1
0
0
2
2
1
0
1
0
0
0
0
0
0
1
0
0
2
2
2
1
1
0
0
0
2
1
2
1
2
2
0
0
2
0
1
1
0
1
0
0
0
1
2
3
1
1
2
1
0
1
2
1
0
3
0
0
0
0
0
0
0
2
1
1
0
3
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
1
0
3
2
1
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
2
0
0
2
0
2
3
2
0
1
2
1
0
0
0
0
2
0
0
0
2
0
2
0
2
0
0
1
1
2
3
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
2
1
2
0
0
0
0
0
1
0
0
0
0
0
0
2
2
2
1
1
2
0
0
1
0
0
1
2
2
2
1
2
0
2
0
0
0
1
2
0
2
1
0
0
0
1
0
0
2
0
1
2
0
0
0
1
0
4
1
2
0
0
2
2
1
0
0
0
0
0
1
3
0
0
0
1
1
1
0
0
2
0
2
2
0
3
1
0
0
0
1
0
2
0
1
1
0
1
0
1
0
0
0
2
1
3
2
0
2
0
1
2
1
4
0
2
0
0
1
0
0
2
0
0
1
0
2
0
0
1
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
1
2
0
2
1
1
1
0
0
2
0
0
0
0
1
0
0
1
0
0
0
1
0
1
2
3
2
2
0
2
0
2
1
0
1
1
0
0
0
0
1
0
1
2
2
2
2
0
0
0
0
2
0
0
2
0
0
1
0
0
0
2
1
1
2
0
0
0
0
0
4
3
0
0
0
1
0
2
0
0
1
0
0
0
0
1
0
0
1
0
1
2
2
0
0
0
0
2
0
0
2
0
0
0
1
0
2
2
1
1
1
0
0
0
1
0
0
0
1
1
0
0
2
0
2
2
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
1
0
0
1
1
0
0
0
0
0
1
0
2
1
0
1
1
4
1
2
1
0
2
0
0
0
0
0
1
2
0
1
1
2
0
2
0
1
0
2
1
2
0
1
0
0
1
1
4
1
1
1
0
0
2
2
2
1
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
2
1
0
2
0
2
1
1
2
1
0
1
2
0
5
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
2
0
3
3
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
1
2
2
0
0
2
0
1
0
1
2
2
0
0
0
6
1
0
1
1
0
2
0
0
1
0
0
1
0
0
2
1
0
0
0
0
1
0
0
1
3
1
1
0
1
2
0
0
0
0
0
0
0
2
2
2
0
0
1
0
2
1
0
0
0
0
0
2
0
0
0
2
1
2
2
0
0
2
0
0
0
8
0
0
2
1
0
0
0
0
0
2
0
0
1
0
0
0
0
2
3
0
0
0
1
1
0
0
0
2
2
0
0
0
0
1
2
1
0
1
0
0
2
0
0
2
1
0
0
2
0
0
0
0
0
2
0
1
0
0
0
1
1
1
1
0
2
2
0
1
1
2
1
0
0
1
0
0
1
2
0
1
0
0
0
0
2
0
1
2
0
2
0
1
2
0
0
0
1
2
2
3
2
0
1
0
0
0
2
1
2
2
0
0
2
0
1
0
1
0
0
0
1
1
0
1
0
0
0
2
0
1
1
0
0
1
2
1
1
0
1
2
0
0
0
1
0
0
2
0
0
1
2
0
1
0
0
2
1
2
1
0
3
0
0
2
1
1
0
2
2
0
0
1
2
0
0
1
0
2
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
2
0
0
0
0
0
2
0
1
0
0
0
2
1
0
1
2
1
1
0
0
1
0
2
2
0
2
0
1
0
1
0
2
1
0
0
1
0
1
0
0
0
3
2
1
0
1
1
0
1
0
0
0
2
1
0
1
1
0
2
0
2
2
0
0
1
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
1
1
2
0
0
2
1
0
0
2
0
2
2
0
1
1
1
1
0
1
0
0
1
1
0
0
0
0
0
1
0
2
0
0
0
0
2
0
1
1
0
2
1
1
0
1
0
0
0
0
1
2
1
0
2
1
0
0
0
2
2
0
1
2
1
0
2
0
1
0
2
0
0
0
1
2
0
0
0
0
0
0
4
1
0
0
0
0
0
1
1
0
2
2
2
1
2
0
1
2
0
1
0
0
0
0
0
1
0
0
0
1
1
2
0
1
0
0
1
0
1
0
0
1
2
0
0
2
2
0
2
0
0
2
0
2
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
2
1
2
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
2
3
2
1
2
2
2
0
3
1
0
0
3
2
1
0
0
0
3
0
1
0
0
0
0
0
2
0
2
0
0
0
1
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
1
0
0
0
3
0
0
0
0
1
1
0
0
0
0
2
2
0
1
0
0
2
0
0
0
0
1
1
5
0
2
0
1
2
0
1
1
2
1
0
0
2
2
0
0
0
0
0
0
1
2
1
1
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
1
1
0
1
2
2
0
0
2
0
0
0
2
0
0
1
0
0
0
1
0
1
2
1
0
0
1
0
2
0
1
0
0
0
0
0
2
0
0
0
2
2
0
1
0
1
0
0
2
0
0
3
5
1
2
0
2
1
0
0
0
0
1
0
1
2
2
0
0
0
0
2
0
2
0
1
0
0
1
0
0
1
1
2
1
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
1
0
2
0
0
1
0
1
2
0
0
0
2
0
0
0
0
0
1
1
1
1
1
0
0
1
0
1
1
0
0
1
0
1
2
0
0
0
1
0
2
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
2
1
0
0
2
0
0
0
0
1
1
0
1
0
0
0
0
2
0
4
2
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
2
0
0
1
0
2
1
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
1
1
1
0
2
0
0
0
0
0
2
1
0
0
0
1
1
2
0
2
0
2
0
0
1
2
2
2
1
2
1
0
1
0
0
0
2
4
1
1
2
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
1
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
2
0
0
0
0
1
0
0
0
1
0
0
0
2
2
0
0
0
1
1
0
1
2
0
0
0
1
0
0
2
0
1
1
0
2
1
2
0
0
2
0
1
0
0
1
0
0
0
0
1
0
0
1
2
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
2
0
2
2
2
0
2
2
0
0
2
0
0
2
0
1
0
0
0
0
0
2
0
0
1
2
0
2
2
0
2
0
0
2
0
0
0
0
0
0
2
0
0
1
0
2
1
2
2
0
2
0
0
1
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
1
1
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
1
2
0
0
0
0
2
1
2
1
0
0
0
0
1
0
1
1
0
0
3
0
0
0
0
2
2
0
0
2
0
0
1
0
0
0
4
1
0
1
3
0
1
0
2
2
1
0
0
0
0
1
0
0
2
1
0
0
0
0
2
2
0
2
2
2
0
0
0
2
2
2
2
0
2
0
0
0
2
2
1
0
0
0
0
0
0
2
0
0
2
0
0
0
2
1
1
1
2
1
0
0
0
0
1
0
1
0
2
0
0
0
0
2
0
0
3
3
0
2
0
0
2
0
2
0
3
2
0
0
1
0
0
0
1
1
1
1
0
0
0
2
1
0
0
0
0
0
1
1
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
4
1
0
0
0
0
0
3
1
2
0
0
0
0
0
0
0
1
2
2
0
2
4
0
2
1
0
0
2
0
2
0
0
2
0
0
0
3
2
0
1
0
0
0
2
0
2
0
0
3
1
2
1
0
0
0
1
0
2
2
0
0
0
0
0
0
0
2
2
0
0
1
2
0
0
0
0
1
0
0
0
1
1
2
1
1
0
1
1
1
0
0
2
0
0
0
0
2
0
1
2
0
0
2
0
0
1
0
0
2
1
1
0
0
2
0
0
0
1
0
0
1
2
0
1
0
1
0
0
0
0
2
0
1
2
0
0
0
1
0
2
1
1
0
0
1
2
1
0
0
4
2
0
0
0
0
1
0
0
1
2
1
1
0
0
1
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
1
2
0
0
0
0
0
2
1
1
0
0
1
1
0
0
0
0
2
1
1
2
1
1
0
0
0
0
1
0
0
0
1
0
0
0
1
2
2
0
0
1
1
0
2
3
1
0
0
2
1
0
0
0
2
2
1
0
0
1
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
3
1
1
0
0
0
1
0
0
2
0
2
0
1
0
3
0
0
0
2
2
0
0
0
1
1
0
1
2
0
1
0
1
0
0
1
1
2
0
2
0
0
0
0
0
0
2
1
1
0
0
0
2
0
0
3
0
2
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
1
1
1
0
1
0
0
1
1
1
0
0
0
0
2
0
0
0
1
0
2
0
1
0
1
0
0
2
1
0
1
2
1
2
3
0
1
0
1
0
0
2
0
2
0
0
0
1
0
1
1
2
2
0
1
0
0
1
0
2
0
1
0
3
0
1
2
2
1
0
0
0
2
0
4
0
0
0
0
2
0
2
5
0
2
1
1
2
0
0
0
0
2
0
1
4
1
0
0
0
0
0
1
0
0
1
2
0
3
0
2
0
0
2
0
0
0
1
0
2
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
3
0
0
0
1
1
0
2
2
1
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
1
0
2
0
0
0
0
1
1
1
1
0
0
1
1
1
0
0
0
2
1
0
1
0
0
0
0
0
2
0
1
2
1
0
0
0
3
2
0
0
0
0
1
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
1
2
0
0
3
0
2
1
0
0
1
0
0
2
0
2
1
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
1
0
1
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
2
2
1
0
2
0
1
0
1
0
0
0
0
0
0
0
2
1
1
1
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
4
1
0
2
0
0
2
0
0
0
2
1
0
1
2
0
0
0
1
0
0
0
2
0
0
0
2
2
0
0
0
1
1
0
2
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
2
0
2
0
0
2
1
1
0
1
1
0
1
0
2
1
0
2
1
0
1
0
1
0
0
0
0
1
0
1
0
0
1
1
0
2
1
2
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
2
0
0
1
2
0
0
0
0
2
1
1
0
0
1
0
1
2
0
0
0
0
2
1
0
3
0
0
0
2
2
1
1
2
0
2
0
1
1
0
0
0
0
1
0
0
0
3
0
1
0
0
0
0
0
0
1
1
1
2
0
1
1
2
0
0
1
0
1
0
0
0
0
1
1
0
4
2
0
2
0
1
1
1
2
0
1
2
0
0
1
2
1
0
0
2
2
0
1
2
2
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
1
2
2
0
0
0
0
0
0
1
0
5
0
1
0
0
2
0
1
0
0
2
0
0
0
0
0
2
2
0
0
1
1
2
2
1
0
0
0
1
2
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
1
2
0
1
2
0
1
0
0
0
0
0
0
1
1
0
0
0
2
2
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
6
1
0
0
2
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
1
0
0
3
1
2
0
2
0
1
2
3
0
0
0
1
1
0
2
0
2
0
0
0
1
1
0
1
0
0
2
0
0
0
2
0
0
2
3
0
1
0
2
0
1
0
0
0
0
1
0
0
0
0
2
1
2
0
0
0
0
0
2
1
0
0
2
2
1
0
0
0
0
2
0
0
1
0
2
2
0
0
0
0
0
0
2
1
0
0
1
0
0
1
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
2
2
0
1
0
0
0
0
0
0
1
0
2
0
0
0
3
0
0
0
0
0
1
0
2
1
0
1
0
2
1
0
0
1
0
1
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
2
0
2
0
1
0
0
0
0
1
0
0
1
1
0
1
2
0
2
1
0
2
2
1
2
0
0
0
1
1
1
2
0
0
2
1
0
0
0
0
1
2
1
2
0
2
0
2
1
1
0
2
0
2
0
1
1
1
0
0
0
1
0
0
2
0
0
1
2
0
0
0
0
0
1
1
2
1
2
0
0
2
0
1
0
2
0
0
1
2
0
0
1
0
0
2
0
1
0
0
0
1
0
2
2
1
1
2
1
1
1
0
0
0
0
0
0
2
1
2
2
0
0
1
0
1
4
0
1
0
0
0
1
0
2
0
0
0
1
2
0
1
2
0
0
0
0
0
0
1
1
1
0
1
0
0
1
2
1
1
0
1
0
0
1
0
0
2
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
1
2
2
1
0
0
0
0
1
0
0
0
2
2
0
1
0
0
0
1
1
0
0
1
0
2
0
0
1
0
2
0
0
0
0
0
0
1
1
0
1
0
2
0
0
0
1
2
0
0
0
1
2
1
1
1
0
2
0
0
0
2
0
2
1
0
1
1
0
0
0
0
1
1
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
1
1
0
2
1
1
1
0
0
0
0
0
1
0
2
0
0
2
0
1
0
0
0
2
1
0
0
0
2
0
2
0
0
1
1
0
0
2
0
0
2
0
1
0
2
1
0
2
0
1
0
0
0
0
2
2
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
2
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
2
0
0
0
0
2
1
0
0
0
1
2
1
0
3
3
0
0
0
2
1
1
1
0
0
2
1
1
0
0
1
0
0
0
1
1
0
0
2
0
0
0
2
1
0
0
1
1
0
0
0
1
0
1
0
0
2
2
1
0
0
0
0
2
0
0
0
1
0
0
6
0
1
0
1
2
0
0
2
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
2
2
0
2
1
0
2
0
1
0
0
1
0
1
3
2
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
1
2
1
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
2
0
2
0
0
0
0
1
2
0
0
0
1
2
1
0
1
0
1
1
2
1
0
1
2
2
0
2
0
0
0
0
0
0
1
0
3
0
2
1
0
1
0
0
1
0
1
0
0
0
1
1
1
2
0
1
2
1
0
1
0
0
0
2
0
0
0
1
1
0
2
0
0
0
0
2
0
1
3
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
2
1
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
2
2
0
0
0
0
0
2
0
1
0
0
0
0
1
1
2
0
1
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
1
1
0
0
0
2
0
1
0
2
0
2
1
0
0
0
1
0
1
0
2
0
0
0
2
2
2
0
1
1
0
2
0
1
0
0
0
0
3
0
0
0
0
0
2
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
1
2
2
1
1
1
0
0
0
0
2
0
1
1
0
1
1
1
0
0
0
1
1
1
0
1
0
2
11
0
1
0
0
2
0
2
0
1
2
2
0
0
0
2
0
0
0
0
6
3
0
0
1
0
0
2
0
0
0
4
0
0
2
0
0
0
0
1
2
0
0
1
0
0
0
2
1
1
2
2
4
2
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
1
0
0
2
1
0
0
1
0
1
0
0
0
0
0
0
2
2
1
0
2
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
1
1
0
1
2
2
1
0
0
0
0
0
0
3
0
0
0
1
4
0
1
0
0
2
0
2
2
4
0
0
2
2
2
2
0
1
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
3
1
1
2
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
1
1
0
2
2
0
1
0
1
0
0
0
1
0
0
1
2
2
0
2
2
0
1
0
0
2
0
1
2
0
3
0
0
0
0
0
0
1
0
0
0
2
1
2
1
0
0
0
0
2
1
1
1
1
2
2
2
0
4
0
2
2
0
0
0
1
1
0
1
0
1
0
2
2
0
0
1
0
0
0
2
2
0
0
1
0
1
1
2
1
2
2
0
2
1
0
0
0
0
0
0
1
0
0
2
1
1
0
0
0
0
0
0
1
1
2
0
0
1
1
0
0
1
0
0
0
0
0
2
2
0
0
2
0
2
1
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
5
0
2
1
2
0
0
0
0
0
0
0
0
1
0
1
2
0
0
2
2
1
0
0
0
0
1
0
2
0
0
0
1
0
2
2
1
1
0
0
1
1
1
0
0
1
0
1
2
2
0
2
0
0
1
0
0
0
3
1
2
0
2
2
1
2
2
0
0
0
0
0
2
0
0
0
1
0
0
1
1
3
2
0
1
0
0
0
0
2
1
0
1
1
0
1
0
0
0
0
0
0
0
0
2
0
2
2
1
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
1
1
0
0
2
0
0
0
4
2
0
2
0
0
0
2
2
0
1
1
0
0
0
1
0
1
2
2
0
0
0
2
0
1
0
0
1
0
0
0
0
2
0
0
1
0
1
2
0
2
0
0
2
1
2
0
3
0
1
0
0
0
2
1
1
1
0
1
1
1
1
1
2
0
0
0
0
2
1
0
1
0
2
1
0
1
0
2
0
2
1
1
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
2
1
0
0
0
2
0
1
0
0
0
0
2
1
0
0
0
0
2
0
2
0
1
1
0
0
0
1
1
0
2
2
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
1
1
0
1
0
1
0
2
0
0
0
0
0
0
1
0
1
1
2
1
1
1
2
3
0
0
0
1
0
1
0
0
1
2
0
1
0
0
2
1
0
2
2
2
0
2
2
0
0
0
0
1
0
0
2
3
0
2
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
1
0
2
0
0
0
1
1
0
0
1
1
0
1
2
0
0
1
1
0
0
2
0
1
1
2
1
0
1
2
2
0
0
0
1
0
0
1
0
2
0
1
0
0
2
0
0
2
0
2
0
0
1
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
2
1
0
0
0
1
0
0
1
0
2
1
1
0
1
0
0
0
0
0
1
0
0
0
2
2
0
1
2
2
0
0
0
0
1
0
0
2
1
0
0
2
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
1
1
1
0
0
0
0
1
2
1
1
0
0
0
0
0
1
0
0
2
2
0
0
2
0
0
0
2
0
0
0
0
0
1
0
2
2
1
0
1
0
1
0
0
0
0
0
2
2
0
0
2
2
0
1
0
0
0
0
2
2
0
1
0
2
0
2
0
0
1
0
0
0
0
1
0
1
1
0
0
2
0
0
0
1
1
0
0
0
0
0
2
2
1
0
0
0
0
2
2
1
2
1
0
2
2
2
0
1
1
0
2
2
0
0
0
0
0
0
1
1
2
1
4
0
2
0
0
2
2
1
0
2
1
0
0
1
2
1
0
1
0
2
0
1
1
0
1
0
0
3
0
0
0
0
0
0
0
0
2
0
2
2
1
1
0
1
2
0
0
0
0
1
1
0
0
0
1
1
0
1
1
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
1
1
1
0
0
2
0
2
2
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
1
2
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
1
2
0
0
1
0
0
1
0
1
1
1
0
0
0
1
0
0
1
2
0
1
1
0
0
0
2
2
1
0
0
0
0
2
0
0
0
0
2
2
0
1
2
0
0
0
2
1
0
1
1
0
0
0
0
1
2
0
0
1
1
1
0
1
0
0
2
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
2
1
2
0
0
0
0
2
0
0
0
0
0
1
2
1
0
0
2
1
5
1
1
0
0
1
0
0
1
0
0
0
1
3
0
0
0
1
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
1
1
0
2
2
0
1
0
2
0
0
2
0
0
2
1
0
0
0
0
1
1
2
1
0
0
0
0
1
2
0
0
0
0
0
0
2
0
1
1
0
0
2
0
0
0
1
2
0
0
0
2
0
0
1
1
0
0
0
1
0
1
0
0
2
0
1
0
2
1
1
0
0
0
0
2
1
0
2
0
0
2
1
0
0
0
1
0
1
2
1
1
1
0
0
0
1
0
2
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
1
1
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
1
1
0
0
1
2
1
0
1
1
0
2
1
2
2
0
0
0
0
1
2
1
0
0
2
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
3
1
0
2
0
4
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
3
2
0
2
2
0
0
0
0
5
0
2
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
2
0
0
0
0
0
0
0
0
2
0
2
2
1
2
0
1
0
0
2
0
2
0
1
0
0
4
0
0
1
0
0
0
0
2
2
0
1
3
2
0
0
0
1
1
3
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
4
0
1
0
2
0
2
0
1
2
2
2
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
2
0
0
1
0
1
0
0
0
3
1
2
0
0
2
0
1
1
2
2
1
0
2
1
0
0
0
1
1
1
0
0
0
1
4
1
0
2
0
1
1
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
1
2
0
1
1
0
1
1
0
1
2
0
0
0
0
2
0
1
0
2
0
0
0
1
0
0
0
0
0
1
2
1
1
0
0
0
5
1
2
0
2
2
0
0
0
2
0
1
1
2
2
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
1
0
2
2
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
2
2
1
0
0
0
1
0
0
0
0
1
1
1
1
0
2
1
1
0
0
1
0
0
2
1
2
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
4
0
0
3
0
0
1
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
2
1
2
0
2
0
2
1
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
2
0
3
2
1
0
0
1
1
2
0
0
0
0
0
0
0
0
1
0
0
1
2
2
0
0
1
2
0
3
2
1
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
3
2
0
0
0
0
1
1
0
1
0
0
0
2
2
0
0
1
0
2
0
2
1
1
2
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
1
3
1
0
1
0
0
1
1
0
1
1
0
0
2
2
0
1
0
2
2
1
0
1
1
1
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
1
1
0
2
0
0
2
0
0
2
1
0
0
2
1
0
0
2
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
2
2
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
1
0
2
2
1
2
0
1
0
0
0
0
0
0
0
0
1
1
0
2
0
4
2
0
2
1
1
1
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
2
3
0
0
2
0
0
2
1
0
0
1
1
0
0
1
2
0
1
0
0
1
1
1
0
0
0
3
0
1
0
2
0
0
2
0
0
1
0
0
0
2
0
1
1
0
0
1
0
0
0
0
0
1
1
0
3
0
0
2
0
0
0
0
1
0
0
0
2
1
1
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
2
2
0
1
2
2
1
0
2
0
0
2
2
2
0
0
0
0
0
1
0
1
1
0
2
0
0
0
0
0
1
2
2
0
1
0
1
0
2
0
1
1
4
0
0
1
1
0
0
0
2
0
0
0
2
2
0
1
2
0
0
1
0
1
2
0
0
1
0
0
0
0
2
0
1
1
1
0
0
2
2
0
0
0
0
0
1
0
1
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
2
2
0
0
0
0
2
1
1
1
1
2
0
0
1
0
1
1
0
0
1
0
0
0
0
0
1
0
1
1
1
3
0
0
1
0
2
2
0
1
0
1
1
1
2
0
2
1
2
0
1
0
0
0
0
2
0
1
1
1
1
0
0
0
2
1
1
0
0
1
1
2
1
1
1
0
1
2
2
0
0
2
0
1
0
2
2
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
1
0
2
0
2
1
1
0
0
1
1
0
0
0
2
1
0
0
0
4
0
1
0
0
0
0
3
0
1
0
0
0
1
0
0
1
2
0
1
0
2
2
1
0
2
0
0
0
0
0
0
0
0
0
2
2
2
1
1
2
1
0
0
0
1
1
0
0
0
1
0
1
2
1
1
0
0
2
2
1
0
2
0
0
1
0
0
2
0
0
0
0
1
0
1
0
1
0
0
1
0
2
0
1
0
0
2
0
0
0
0
1
2
1
1
1
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
2
1
1
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
2
2
0
1
0
0
0
0
1
1
0
1
2
2
1
0
0
0
1
0
0
1
0
0
0
0
1
3
0
2
0
0
0
0
2
1
1
0
2
0
0
0
0
0
1
1
0
0
0
1
0
6
0
0
0
0
2
0
2
1
0
0
2
2
0
2
0
0
2
0
2
3
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
2
0
0
1
0
1
0
0
2
0
1
2
1
0
1
0
0
2
1
2
1
0
2
0
0
0
0
0
0
1
0
2
0
2
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
1
0
2
0
2
2
0
1
5
0
0
2
0
2
1
0
2
0
2
0
2
1
1
2
0
0
2
0
0
2
0
2
0
0
0
1
1
1
0
1
0
2
1
1
0
1
0
1
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
2
0
2
2
1
0
0
0
0
2
0
3
1
2
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
2
0
0
1
0
0
0
0
1
0
1
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
1
0
3
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
2
0
0
0
2
0
0
0
0
2
0
2
1
1
0
0
3
4
0
2
5
0
0
0
0
1
1
2
1
0
0
0
1
0
0
0
1
0
0
0
0
2
2
2
1
0
1
2
0
2
1
1
0
0
1
0
0
2
1
0
0
0
1
0
2
1
2
2
1
1
1
0
0
0
2
0
0
2
0
0
0
1
3
1
0
0
0
1
0
0
0
2
0
1
0
0
1
0
1
0
0
0
0
0
0
0
2
0
1
0
2
0
0
2
0
1
2
0
2
0
0
0
0
0
1
2
2
0
2
0
0
1
0
2
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
2
0
0
2
0
1
1
0
0
2
0
0
0
0
0
0
1
3
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
1
0
2
0
0
2
1
0
0
0
0
0
2
0
0
0
0
1
0
0
1
2
2
0
2
0
2
0
0
0
0
0
1
0
1
3
2
0
0
1
0
0
2
2
1
1
0
1
2
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
2
0
2
0
0
1
0
0
1
1
2
0
0
0
0
0
1
1
2
0
1
0
1
2
2
2
2
0
2
0
2
1
3
0
3
2
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
2
1
0
0
2
0
1
0
0
0
0
2
1
1
0
2
0
0
0
1
0
1
1
2
0
1
1
0
0
1
0
1
0
2
1
0
2
1
1
0
2
0
2
0
0
0
0
2
0
1
0
1
0
0
2
1
1
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
3
1
0
2
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
1
2
0
2
0
1
0
0
2
1
1
1
0
1
0
1
0
1
1
0
1
0
1
0
1
0
1
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
1
0
1
0
2
0
4
0
0
0
1
3
1
0
2
1
1
0
0
1
0
2
0
0
0
2
3
0
1
2
1
0
0
0
1
0
0
2
1
1
1
0
4
1
0
0
0
0
0
2
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
2
1
0
1
0
0
3
0
0
0
0
0
2
0
1
0
2
1
1
0
2
0
1
0
2
0
0
0
0
2
2
2
0
2
0
1
1
0
0
0
0
2
0
0
1
2
0
1
0
0
2
0
2
1
0
1
0
0
1
0
0
0
0
1
2
0
3
0
0
0
2
1
0
1
6
0
0
1
0
2
1
0
2
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
2
2
2
0
1
2
0
1
2
1
0
2
1
4
2
0
0
0
1
0
0
0
0
0
2
0
4
0
0
0
0
0
1
1
1
0
2
0
2
0
2
0
0
2
1
0
2
3
1
1
0
0
0
2
0
0
0
2
1
0
0
1
0
2
0
1
0
9
2
2
0
0
1
2
0
1
0
2
2
1
4
0
0
0
1
0
2
2
0
0
0
2
2
2
0
0
0
0
1
0
0
2
2
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
4
0
3
2
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
1
0
0
2
2
3
2
1
0
0
2
0
1
2
9
0
0
0
0
0
2
2
0
2
0
1
1
0
2
0
0
4
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
2
2
0
0
0
2
2
1
0
2
2
0
0
0
0
0
2
0
0
0
0
2
1
0
2
0
1
1
1
0
0
1
1
0
0
0
0
0
0
1
3
0
0
1
2
0
0
2
0
0
0
0
1
1
0
2
2
0
0
0
0
2
2
0
2
2
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
2
0
3
2
2
0
2
0
0
2
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
1
0
0
1
0
0
2
0
1
0
0
0
2
0
1
0
1
2
0
0
0
0
0
0
1
0
2
2
0
0
0
0
2
0
0
0
1
0
1
1
0
0
0
0
1
0
0
2
0
0
0
0
0
3
0
0
0
0
1
0
0
2
2
0
1
1
2
1
0
0
1
2
0
2
2
0
1
0
0
2
0
0
1
0
0
0
0
0
0
5
2
0
2
0
0
1
0
2
0
0
1
0
0
0
1
2
1
0
0
0
0
1
0
2
1
1
1
2
1
2
1
0
0
2
1
0
1
0
0
1
0
0
0
0
0
1
2
0
2
0
1
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
2
1
0
1
0
0
2
0
2
1
1
0
0
2
0
0
0
0
1
0
2
0
0
2
2
0
0
1
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
2
2
0
0
2
1
0
0
0
1
0
0
2
0
0
1
1
2
0
0
0
2
0
0
0
0
2
1
1
0
0
1
2
0
2
0
0
1
0
0
0
2
0
2
0
0
1
3
2
0
1
1
0
0
0
2
0
0
2
0
0
0
1
0
1
0
0
3
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
2
0
0
0
0
2
1
2
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
1
2
0
1
2
1
0
0
0
0
1
3
0
2
2
0
0
0
0
0
1
0
0
0
1
1
0
1
2
0
0
0
1
0
0
0
1
1
1
1
0
2
0
0
0
0
0
0
1
0
0
0
1
0
1
0
4
0
1
0
0
0
0
2
0
2
0
0
2
0
0
2
0
1
0
0
1
2
0
1
0
0
0
0
2
0
1
0
1
0
0
0
4
1
1
0
1
0
2
1
0
0
1
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
3
2
0
2
0
1
0
1
0
2
0
0
2
2
1
0
1
2
0
0
1
0
1
0
0
1
0
1
0
1
1
0
0
5
1
2
0
0
0
2
0
1
0
0
2
0
2
2
1
1
1
1
0
1
0
2
0
0
0
2
0
6
0
0
0
2
0
0
0
1
1
1
0
2
1
2
1
0
0
1
0
1
1
2
1
0
1
1
2
0
2
2
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
1
1
0
1
0
2
0
2
0
0
1
2
0
1
0
0
0
1
0
0
0
0
0
0
0
2
1
1
2
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
2
0
1
0
1
1
2
0
1
0
0
3
1
1
2
0
0
0
1
0
0
0
1
0
0
1
1
1
0
0
2
2
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
1
0
2
2
0
1
0
0
2
0
2
0
2
0
0
0
0
0
2
2
0
0
1
2
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
1
2
1
1
2
0
1
0
2
0
0
1
0
0
0
0
2
0
0
0
0
1
2
3
0
2
0
2
0
0
0
1
1
0
1
0
2
0
1
0
2
0
2
0
0
1
0
0
2
0
1
1
2
0
2
0
1
0
0
0
2
0
0
0
2
0
2
1
0
2
0
0
0
0
1
0
0
0
1
1
0
0
0
0
2
0
1
0
1
0
1
2
0
0
1
0
1
0
1
1
0
1
1
0
1
0
0
1
0
3
0
0
1
1
0
0
0
0
2
1
0
2
2
1
1
0
0
1
0
0
0
1
2
1
2
0
1
1
1
0
0
0
0
2
0
0
0
2
0
0
0
1
0
1
0
0
0
1
1
0
0
2
0
0
1
1
0
4
0
1
0
2
2
2
1
0
1
1
0
0
0
2
0
0
0
0
1
1
1
1
1
1
0
1
2
1
0
0
0
2
1
0
2
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
1
0
0
2
0
0
1
2
0
0
2
0
0
1
2
0
1
0
0
2
0
0
2
0
0
0
0
1
4
0
1
0
1
1
0
2
0
0
0
3
0
3
1
4
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
2
1
0
2
0
0
0
1
0
0
2
0
2
0
0
0
0
4
1
1
0
0
2
0
0
0
1
0
2
1
2
0
1
2
0
0
2
0
0
0
1
1
1
2
1
0
2
0
0
1
0
0
0
0
2
0
1
0
1
0
0
0
2
1
0
0
0
0
2
2
2
0
2
2
1
2
0
0
0
0
0
0
1
1
0
0
0
1
0
0
2
1
2
2
2
1
0
2
2
0
1
0
0
0
0
2
0
0
1
1
0
2
0
0
0
2
0
0
2
0
1
1
0
0
1
0
1
1
0
2
0
2
1
2
0
1
0
0
2
0
2
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
2
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
1
0
1
2
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
1
0
1
0
0
0
4
0
0
0
1
1
1
0
1
2
0
2
0
0
0
0
2
1
2
2
2
1
1
0
1
0
0
0
1
0
0
1
0
1
0
1
0
2
0
0
1
0
1
0
0
0
0
5
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
2
0
1
1
1
0
0
0
2
0
2
1
0
1
0
2
0
1
1
0
1
0
1
0
0
0
1
1
0
1
0
1
2
2
0
1
0
2
0
2
1
1
2
0
0
0
1
2
1
1
0
0
0
0
0
2
1
2
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
2
1
0
1
0
0
0
0
0
1
0
0
1
0
1
0
1
1
0
1
2
2
0
0
0
0
1
2
2
5
0
0
0
1
0
0
0
3
0
0
0
0
3
0
2
2
2
1
0
2
1
0
0
0
0
0
1
3
0
0
0
0
1
1
1
1
2
0
1
0
0
0
2
2
1
2
0
1
1
2
0
1
0
0
2
0
0
0
1
1
0
1
0
2
1
0
1
0
0
0
0
2
0
0
0
0
2
0
2
1
1
1
2
1
1
0
1
2
0
2
0
0
0
1
2
0
1
1
0
0
1
2
0
2
1
2
0
0
2
0
0
0
0
0
1
0
0
1
2
1
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
2
2
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
2
1
2
0
0
0
0
0
0
1
1
0
1
0
0
1
2
0
0
1
0
0
0
1
0
1
0
0
0
0
1
1
0
0
2
0
0
0
3
0
0
0
0
0
0
0
1
1
1
0
0
3
1
0
0
0
1
0
0
0
0
0
2
2
2
2
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
3
0
3
2
0
0
0
1
0
1
2
0
0
0
2
2
0
2
1
1
0
1
0
1
2
0
0
1
0
0
1
0
0
0
1
0
0
0
2
0
2
0
4
0
2
0
0
0
0
0
0
0
1
5
0
0
0
1
1
0
0
0
1
1
2
1
0
0
0
0
0
0
0
2
1
1
0
0
2
1
1
0
1
0
2
1
0
1
2
0
2
2
1
0
0
1
2
0
0
0
1
0
2
2
1
0
2
0
1
2
0
0
1
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
1
0
2
2
0
0
0
0
1
2
0
1
0
2
2
0
1
2
0
0
1
0
1
2
0
0
0
0
0
2
2
0
0
0
2
0
0
0
3
0
2
1
0
2
0
0
0
0
0
0
1
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
2
0
3
0
2
0
0
1
0
0
0
4
1
1
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
1
0
0
1
0
0
1
0
2
0
1
0
1
0
1
0
1
2
2
2
0
0
1
2
0
0
2
0
2
2
0
1
0
2
0
1
1
0
1
0
2
0
0
0
0
0
0
1
0
1
1
1
0
0
0
1
1
0
0
0
2
7
3
0
0
0
0
0
0
1
2
2
0
0
1
0
0
1
0
0
2
0
2
1
0
0
1
2
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
2
2
1
0
2
2
2
2
0
2
1
0
0
3
2
1
1
0
0
0
0
0
0
0
0
2
0
1
2
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
2
0
1
2
1
1
0
0
0
5
1
1
1
2
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
1
1
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
1
0
0
4
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
1
1
1
1
0
2
0
0
2
0
2
0
0
0
0
0
0
7
0
1
1
2
0
0
0
1
1
0
0
0
0
0
0
1
1
0
1
0
0
1
0
1
0
0
0
4
1
0
0
2
0
0
1
0
0
0
0
1
2
0
0
0
1
0
0
0
0
2
0
2
0
1
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
1
0
0
1
17
0
2
0
0
0
0
0
0
0
2
0
2
0
1
2
2
1
2
0
0
0
2
1
0
0
0
1
1
0
0
0
1
0
1
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
2
2
0
0
1
1
0
0
0
2
0
0
2
0
1
0
4
1
1
2
1
0
0
0
1
7
0
1
1
1
1
3
0
6
2
0
0
1
0
0
1
1
0
1
0
0
0
0
2
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
1
1
1
0
0
0
0
2
0
0
2
0
0
2
0
0
1
0
1
1
0
0
2
1
1
2
2
0
1
1
1
0
1
0
0
0
0
0
0
5
1
1
1
1
0
0
1
0
1
0
0
2
1
0
1
0
1
0
1
0
0
0
1
0
2
1
0
0
0
2
2
1
0
0
0
2
0
0
0
0
1
2
2
0
0
1
0
2
1
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
2
2
0
0
0
0
0
1
0
0
2
1
0
1
0
0
1
0
2
1
1
0
0
0
0
2
0
1
0
0
0
0
0
2
0
2
0
2
0
0
0
0
1
0
0
1
0
2
0
0
2
0
0
1
0
2
0
2
6
0
0
2
0
0
0
0
0
0
1
1
2
0
0
2
0
1
2
0
1
0
0
2
1
0
2
0
1
0
1
0
0
0
1
1
2
3
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
1
1
2
0
1
0
0
0
0
1
0
2
0
1
0
0
1
1
5
1
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
2
2
1
0
0
1
2
0
0
1
1
2
1
0
0
1
1
2
1
0
0
2
1
1
0
1
2
0
5
1
0
0
1
0
2
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
1
1
0
1
1
0
1
0
0
0
2
3
2
0
2
0
0
0
1
1
0
3
0
0
0
1
0
0
0
0
0
0
0
1
2
1
0
1
0
0
2
2
0
0
1
0
2
0
0
2
0
1
0
0
0
0
1
0
0
0
1
0
2
0
2
0
0
0
1
1
0
2
0
1
0
1
0
1
2
0
0
2
0
0
2
0
2
0
0
3
0
0
2
0
1
0
0
1
0
3
0
0
1
1
2
2
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
3
0
0
0
2
0
1
0
0
1
1
1
1
2
0
2
2
0
2
0
0
1
0
0
1
1
0
0
1
0
2
3
0
1
2
2
0
1
3
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
4
2
0
2
0
0
0
0
0
0
1
2
2
2
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
1
2
1
0
0
0
0
0
0
0
0
0
2
0
1
2
0
1
0
1
0
0
1
0
1
2
0
0
1
0
1
0
2
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
2
1
1
2
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
3
0
1
0
1
0
1
2
0
0
2
1
2
2
0
1
0
0
0
1
0
1
0
3
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
2
2
3
0
1
2
0
0
1
0
0
0
1
0
0
1
0
1
1
0
0
0
0
1
1
0
0
0
2
2
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
1
1
0
0
0
0
1
1
0
0
2
1
1
0
2
0
0
0
1
0
2
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
1
0
0
1
2
0
2
1
2
0
0
0
1
0
2
2
1
2
2
0
1
1
0
2
1
1
0
0
2
0
0
0
2
0
2
1
1
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
1
1
0
1
0
0
1
1
2
0
2
0
0
0
0
1
0
0
1
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
1
2
1
1
2
2
0
0
1
0
0
0
1
0
2
0
3
0
2
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
1
0
0
0
1
0
0
2
2
0
0
2
1
0
0
2
1
0
2
2
2
0
0
0
0
1
0
0
2
0
1
2
2
1
2
2
0
1
0
2
0
2
1
1
2
0
0
0
0
2
1
0
2
2
0
0
1
0
2
0
2
0
1
0
2
1
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
3
0
0
0
1
0
0
6
0
0
2
1
0
1
0
1
0
2
2
0
0
1
0
2
0
1
0
2
1
2
0
0
0
2
0
0
1
0
0
0
1
1
0
2
0
2
1
1
1
3
2
0
0
0
2
2
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
1
2
0
0
2
2
0
2
0
2
0
2
4
3
0
1
0
0
1
2
2
0
0
2
0
2
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
2
1
1
0
1
0
0
0
0
0
0
3
0
0
0
0
0
2
0
2
0
0
1
0
1
0
0
1
0
0
1
1
0
1
0
2
1
1
2
1
2
0
0
0
0
0
0
0
0
0
5
0
2
0
0
1
0
0
0
1
2
2
2
0
0
1
2
0
0
1
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
2
0
0
0
0
3
0
0
1
2
0
0
1
0
0
0
4
3
1
0
0
1
0
0
0
1
0
0
0
0
2
0
3
0
0
0
1
0
1
0
2
0
0
1
0
0
0
1
0
0
1
0
3
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
2
2
1
0
0
1
0
1
0
1
0
1
0
2
0
1
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
1
2
0
1
0
1
2
0
1
1
0
2
1
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
6
1
0
0
0
0
0
2
0
0
0
1
0
0
1
1
0
0
1
0
0
0
1
0
0
1
2
1
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
3
2
0
1
0
0
1
0
1
2
1
0
0
2
0
0
0
0
0
1
0
0
1
0
0
1
1
1
0
2
1
0
1
2
0
0
0
1
0
0
1
0
0
0
0
1
2
1
1
0
0
1
0
0
0
1
0
2
3
0
2
2
2
1
2
0
0
0
1
0
1
0
0
0
0
2
2
2
0
1
0
0
0
0
1
0
1
0
2
0
2
1
0
2
0
1
1
2
2
0
0
0
1
0
0
1
0
1
2
0
1
1
2
0
0
0
2
2
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
1
1
2
1
0
2
2
2
0
0
1
2
0
2
0
2
0
0
0
1
2
2
1
0
1
1
0
1
1
1
2
1
0
2
2
0
1
0
1
2
1
0
2
2
0
2
1
1
0
0
1
2
0
0
0
0
2
0
0
0
1
0
0
0
2
2
1
2
3
0
1
2
1
1
0
2
0
0
2
0
1
2
0
0
0
2
1
1
0
1
0
0
2
2
0
0
0
2
0
1
2
0
0
0
2
0
0
0
0
0
2
2
2
0
2
0
1
2
0
0
0
1
0
0
2
0
2
0
0
0
2
2
0
2
2
3
3
2
1
1
0
0
0
0
0
1
0
1
2
1
1
2
2
0
1
0
1
0
0
0
1
0
1
0
2
0
0
0
0
0
1
0
2
1
0
2
0
0
0
1
0
0
0
1
2
0
1
0
1
2
0
0
1
0
0
1
2
0
2
0
0
0
0
0
0
0
0
1
1
2
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
4
0
0
0
0
0
4
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
1
2
0
1
0
2
0
0
0
0
2
1
1
2
2
1
0
2
0
0
0
0
0
3
0
0
0
0
0
3
0
0
1
2
0
2
1
0
1
0
1
1
0
1
2
3
1
2
0
0
2
0
0
0
0
0
0
1
1
0
0
0
2
1
1
2
0
1
2
0
1
0
0
0
0
1
0
1
1
0
1
2
1
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
2
0
0
1
1
0
1
0
0
0
0
1
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
1
0
1
0
0
0
2
1
2
1
2
0
0
2
0
0
0
0
0
2
1
0
0
1
1
2
0
0
1
1
0
0
1
0
2
0
2
2
0
3
0
0
1
0
1
0
2
1
0
0
2
0
0
0
0
0
0
0
2
0
2
0
5
1
1
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
1
0
1
2
2
2
0
0
1
2
0
1
1
0
2
0
0
0
1
2
0
0
3
0
0
0
2
2
0
1
1
0
0
0
3
0
0
2
1
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
2
1
0
0
2
0
1
0
0
0
2
0
0
0
2
0
0
0
2
4
0
1
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
1
0
2
0
1
0
3
0
0
0
2
0
2
0
2
1
2
0
0
1
0
0
0
0
2
0
3
3
0
0
0
2
0
0
2
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
2
2
0
0
3
0
0
0
0
1
0
3
0
1
0
2
0
1
0
2
2
1
1
1
2
1
0
2
0
2
0
1
1
0
0
3
0
0
0
1
1
0
2
3
0
2
0
1
0
1
0
0
1
0
0
1
1
0
2
0
0
1
1
0
0
1
2
0
0
1
0
0
0
0
0
0
1
1
1
0
0
2
0
0
1
0
0
2
0
0
1
0
0
0
0
1
0
1
0
1
1
2
0
2
0
0
0
0
0
0
0
1
0
0
0
1
2
0
2
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
3
0
0
2
1
0
2
2
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
2
0
0
2
0
0
1
0
0
1
1
2
0
0
1
2
2
0
2
2
0
1
0
0
0
0
0
2
1
0
1
0
1
2
0
1
0
2
2
0
0
0
0
1
2
1
0
1
0
2
2
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
2
1
0
0
1
2
1
0
1
0
0
0
1
0
1
1
0
0
2
0
0
2
0
1
0
2
2
0
0
0
2
1
1
0
0
0
1
4
1
0
0
0
1
1
6
0
1
0
0
0
0
2
1
0
2
1
0
0
0
0
2
1
2
0
0
0
0
0
1
1
0
0
0
0
0
2
0
2
1
1
1
1
0
0
2
1
1
2
0
2
0
1
0
0
0
2
0
2
2
0
0
1
1
0
2
0
2
3
0
2
0
0
0
0
0
2
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
1
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
1
0
0
3
2
0
0
0
0
2
0
0
1
0
0
0
0
1
1
0
0
2
3
1
2
0
0
1
0
2
0
0
0
0
3
0
0
3
0
2
1
1
0
2
0
1
2
2
0
1
1
0
0
0
1
0
0
0
1
0
1
0
1
0
2
1
2
2
0
0
2
2
0
0
0
2
0
0
0
2
0
1
2
1
1
0
1
0
2
0
1
1
2
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
2
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
2
0
0
0
1
0
1
0
0
0
0
2
0
0
0
1
2
0
0
0
2
0
1
1
0
0
2
1
0
1
1
0
0
1
0
2
1
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
1
0
1
0
6
1
0
0
0
2
0
0
1
0
2
0
1
2
0
1
0
1
2
2
2
0
3
0
1
0
0
0
0
0
0
1
2
2
0
2
0
2
0
0
1
3
1
0
2
1
2
2
0
0
0
0
0
3
0
0
2
0
2
0
0
2
1
0
0
0
0
0
1
2
2
1
1
0
0
0
0
0
2
1
0
1
0
2
0
2
0
0
0
1
0
1
0
0
0
2
0
1
1
0
0
0
1
0
1
1
0
0
5
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
2
1
2
0
1
2
0
1
2
0
0
0
1
2
0
1
0
2
0
0
0
0
2
0
3
0
0
0
2
0
0
0
0
0
0
0
0
1
2
2
2
1
0
2
0
2
0
0
0
0
0
1
1
0
0
1
2
1
2
0
2
1
2
0
0
0
1
0
2
1
0
0
1
0
0
0
2
0
0
0
0
2
4
0
0
0
0
0
2
0
1
4
0
0
2
0
1
1
0
0
0
1
0
1
0
0
0
2
2
1
2
0
0
1
0
2
0
0
0
2
2
0
1
0
2
0
0
0
2
1
0
0
1
0
4
2
4
0
3
0
0
0
0
0
2
9
0
1
0
0
0
3
0
0
1
0
0
0
2
1
1
1
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
1
2
1
1
0
0
0
1
1
1
1
1
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
3
3
2
0
0
0
0
2
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
2
0
0
1
2
2
0
0
0
0
0
1
0
0
1
0
1
1
0
0
1
0
1
0
0
0
0
0
5
1
0
0
2
2
0
1
1
2
1
2
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
1
1
3
2
0
0
0
1
0
0
1
2
2
3
0
0
0
0
0
0
0
1
2
1
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
1
0
0
1
1
1
2
1
2
0
0
2
1
0
1
5
0
0
0
2
0
0
2
0
2
2
2
1
1
1
0
0
0
1
2
0
1
0
1
0
0
2
2
0
0
2
0
1
0
2
0
0
0
2
0
0
0
2
0
1
2
0
0
0
0
0
1
0
2
0
0
0
0
0
2
2
0
1
2
0
0
1
0
0
2
0
0
0
2
2
1
0
2
2
1
0
0
0
1
2
0
2
0
2
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
2
0
1
0
2
0
1
1
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
1
0
0
2
0
0
3
2
2
0
2
0
3
0
0
2
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
3
2
0
0
2
0
0
1
1
0
0
0
0
1
0
0
0
2
1
0
0
0
1
2
1
0
0
0
0
0
0
2
0
0
1
0
2
0
1
0
1
2
2
2
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
2
1
0
1
2
0
2
1
2
1
2
1
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
2
0
0
1
0
2
2
1
0
0
0
0
0
2
1
2
0
0
1
1
0
2
1
0
0
1
2
0
0
0
0
0
1
2
2
1
0
0
0
0
2
0
0
1
0
1
0
2
1
1
1
2
0
0
2
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
2
0
0
1
2
0
0
0
2
0
0
0
1
2
3
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
3
0
0
0
0
2
1
2
2
2
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
1
0
0
0
2
0
0
0
1
2
0
2
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
2
2
0
1
2
0
0
0
0
1
0
0
2
2
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
2
0
2
0
0
0
0
0
1
1
0
3
0
1
0
1
0
0
1
1
0
0
0
0
1
2
0
0
0
0
0
4
1
0
0
2
2
2
0
0
2
0
0
1
1
0
2
1
0
2
1
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
2
2
0
1
2
0
1
1
0
0
2
0
1
0
1
0
1
0
1
1
2
0
0
2
1
1
3
0
1
1
1
1
0
1
1
0
0
0
1
0
0
2
2
0
2
0
0
0
1
0
2
1
1
0
0
0
1
1
0
0
0
1
1
0
1
0
1
0
0
0
2
0
1
1
2
0
1
0
0
0
0
0
2
2
0
1
1
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
3
0
1
0
0
2
0
0
0
0
1
2
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
2
3
0
2
0
0
1
1
1
0
0
1
0
0
1
3
0
0
2
0
0
1
0
0
2
2
2
0
1
0
0
0
0
0
1
0
0
0
0
0
1
3
0
0
0
0
0
2
0
0
2
1
1
0
4
0
2
2
0
0
1
1
1
2
0
0
2
0
0
2
1
0
0
2
1
0
0
0
3
1
3
0
0
0
0
2
0
0
0
0
2
0
1
0
0
2
0
0
0
1
1
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
2
1
0
0
0
2
0
2
2
0
1
0
1
0
0
1
0
1
0
0
0
2
1
2
2
1
2
2
1
0
0
1
1
0
0
1
2
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
2
1
0
2
0
0
0
2
2
3
0
0
2
0
3
1
2
0
1
3
2
0
0
0
0
0
2
1
0
2
0
2
0
0
0
2
0
2
1
1
0
1
0
0
2
0
0
0
0
1
1
0
0
0
0
3
6
2
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
1
2
0
2
1
1
0
1
0
0
3
0
1
2
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
2
0
0
2
0
0
0
3
2
0
2
2
2
2
0
2
0
1
2
0
2
0
0
1
0
2
0
0
0
2
0
1
1
2
0
0
0
0
1
0
0
2
3
1
1
2
0
0
0
0
1
0
1
2
1
2
1
0
2
2
0
0
1
0
2
1
0
0
0
0
1
0
0
0
1
0
2
2
2
2
0
0
0
1
0
0
0
1
0
0
2
0
0
1
0
1
0
0
0
0
1
2
1
2
1
0
1
0
0
0
1
0
0
2
2
0
0
0
0
1
2
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
2
2
0
0
2
0
1
0
2
2
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
2
0
0
0
0
0
2
2
2
0
2
0
0
3
1
0
0
0
0
2
0
2
0
0
0
2
0
1
0
0
0
2
1
0
0
2
0
0
0
1
0
2
0
0
1
0
2
1
0
2
0
0
1
0
1
0
0
2
0
0
0
0
0
0
1
2
0
1
1
0
0
2
2
0
0
2
1
2
0
0
0
2
0
0
1
0
0
1
0
2
0
2
0
2
0
0
0
3
2
0
2
0
1
0
2
2
2
1
2
1
0
0
5
2
0
0
0
0
0
2
0
1
0
1
0
0
2
0
1
0
1
2
0
1
0
1
2
0
0
2
0
0
1
0
3
0
1
2
2
1
1
2
0
2
0
1
0
2
0
0
0
2
0
0
0
0
1
1
0
0
2
0
0
0
1
0
1
2
0
0
0
1
0
1
0
2
3
1
3
0
0
0
0
1
0
0
1
0
0
0
1
1
0
3
2
0
0
1
0
0
2
0
0
0
0
0
2
2
0
0
2
1
1
1
0
0
1
0
0
0
0
0
0
2
2
0
2
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
1
0
0
1
2
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
2
2
1
1
3
2
0
0
1
2
2
0
1
0
0
0
0
0
2
0
1
0
2
0
1
1
0
1
0
0
0
1
1
1
2
0
0
0
2
0
5
2
2
1
1
0
2
0
1
0
1
1
0
1
0
2
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
2
0
2
0
0
2
0
0
0
0
2
2
0
2
0
2
1
0
0
0
1
1
0
0
2
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
1
0
1
0
1
2
2
0
0
0
2
2
0
0
1
0
1
0
0
0
2
0
1
0
0
0
1
1
1
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
1
1
0
0
2
1
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
1
0
1
2
0
0
2
0
0
1
1
0
0
1
0
0
1
1
2
1
0
0
2
2
0
0
2
0
0
0
2
1
0
0
0
0
1
0
1
0
2
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
2
0
0
1
0
0
1
0
3
0
0
1
1
2
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
3
0
0
1
2
1
2
0
0
0
2
1
1
0
0
2
0
1
2
0
2
0
0
0
0
2
0
0
0
1
1
0
0
1
0
0
1
2
1
1
2
1
1
0
0
2
0
0
1
2
2
0
0
0
1
0
1
0
0
0
1
0
0
0
0
2
2
2
0
0
0
1
2
1
1
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
2
0
0
0
1
2
2
0
0
1
2
2
0
0
0
1
0
0
0
0
2
0
0
2
0
0
1
0
1
0
0
0
2
1
0
1
0
0
1
0
1
1
0
0
0
2
1
0
1
0
0
0
0
0
2
0
1
1
0
2
1
0
7
0
0
0
1
0
1
2
2
0
1
1
4
2
0
3
4
0
0
2
2
0
0
1
0
2
3
1
1
0
2
1
0
1
2
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
1
1
1
0
2
0
0
1
0
0
0
0
2
0
0
1
0
0
3
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
2
1
0
2
1
0
0
0
0
1
0
2
2
2
1
1
2
0
0
2
0
1
1
0
1
2
1
0
0
0
0
2
0
0
2
1
0
1
0
0
2
0
2
3
2
0
1
0
2
0
1
0
3
1
1
1
0
0
2
0
2
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
1
1
0
2
0
2
0
0
0
0
1
0
0
0
2
1
0
4
0
2
0
1
0
0
0
0
0
0
0
0
2
1
0
1
1
2
2
0
0
2
0
0
0
1
2
2
2
0
3
0
2
2
2
0
0
0
0
1
0
0
2
1
0
0
0
2
0
1
0
2
0
0
0
1
1
2
0
2
0
3
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
1
1
0
0
0
1
2
4
0
0
3
1
2
0
0
1
2
2
0
2
0
0
0
0
1
0
0
2
2
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
1
0
1
2
0
0
1
0
0
2
0
0
3
0
2
1
0
0
1
2
0
1
2
1
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
1
2
0
1
2
2
0
3
0
0
0
0
0
0
2
0
3
1
1
2
0
2
2
0
0
0
0
0
0
0
0
0
1
1
2
0
0
1
2
2
0
1
0
0
0
0
1
1
2
0
0
1
0
0
0
2
2
0
1
2
1
0
0
1
0
1
0
2
0
2
0
1
0
2
0
1
1
0
2
1
0
1
0
2
1
1
2
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
2
1
0
0
2
1
0
0
0
0
2
0
2
0
0
1
1
0
1
0
1
2
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
2
2
1
2
2
1
0
4
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
1
0
1
1
0
0
1
0
2
0
0
0
0
3
0
0
0
0
0
1
1
0
0
0
1
2
0
3
1
0
1
0
0
1
1
2
0
0
1
0
1
0
0
0
0
0
1
0
1
1
0
0
1
2
2
0
0
1
3
2
0
0
2
1
0
2
0
0
1
0
0
0
0
0
0
1
3
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
1
1
0
0
0
0
4
2
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
2
0
0
0
1
2
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
3
0
0
0
1
0
0
1
1
0
0
1
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
1
0
0
2
2
2
3
0
0
2
2
4
0
1
0
1
0
1
2
0
0
1
3
0
0
0
2
0
0
0
3
1
1
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
1
2
1
0
0
1
0
0
0
0
2
0
2
0
0
0
1
1
0
2
2
1
1
0
1
0
0
0
1
0
0
2
1
0
0
2
0
0
0
0
1
2
2
0
1
0
2
0
0
0
0
4
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
1
0
1
1
0
2
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
3
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
1
0
0
2
0
0
0
0
0
0
2
0
1
0
0
2
0
0
1
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
2
0
1
0
0
2
2
3
0
1
0
2
0
1
0
0
1
0
3
2
0
1
1
1
0
0
0
0
0
0
1
0
1
0
2
0
0
1
1
0
0
0
1
0
0
2
1
0
1
0
0
2
1
0
1
0
0
1
0
0
0
0
0
1
0
1
1
0
2
0
0
0
2
2
2
0
0
2
0
0
0
1
1
1
0
0
0
0
1
0
2
0
2
1
1
6
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
2
0
1
0
0
0
0
0
0
1
0
1
0
0
2
0
1
0
2
0
0
0
2
2
0
1
3
1
0
0
2
0
0
0
1
0
0
1
0
0
3
0
0
1
1
2
0
2
1
0
0
2
1
0
0
0
1
0
2
2
0
2
1
0
3
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
2
2
2
1
2
0
1
0
2
1
0
0
0
0
0
0
1
1
0
0
3
1
2
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
1
0
0
2
0
0
1
0
0
0
1
0
2
0
1
0
0
0
2
0
1
0
2
0
1
0
1
0
0
0
0
1
2
0
1
2
1
2
0
0
0
0
0
1
1
0
0
0
0
1
0
2
2
2
0
0
1
1
1
0
0
2
0
2
2
0
0
3
1
1
0
2
1
1
0
0
0
1
2
0
0
0
1
0
0
3
0
0
1
0
1
0
0
1
1
0
0
0
1
1
0
1
1
0
0
1
0
0
1
0
3
0
0
0
0
0
2
0
2
0
1
1
0
2
1
0
0
0
0
1
1
2
0
0
0
2
0
2
0
0
0
1
0
0
0
1
1
0
2
0
2
2
0
0
0
0
0
1
0
0
0
0
1
2
0
0
2
1
1
0
1
0
0
1
2
0
0
0
0
1
1
0
0
1
2
2
0
0
0
0
1
1
2
2
2
0
1
1
0
0
0
0
0
1
0
1
2
0
1
0
0
0
0
0
2
0
0
0
2
0
0
1
1
0
0
0
0
0
1
0
1
3
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
1
1
2
1
1
1
0
0
0
0
2
2
1
1
3
0
0
2
0
1
2
2
0
0
0
0
0
1
2
0
2
1
1
0
0
1
0
1
0
0
1
0
0
1
2
0
0
0
2
1
0
1
1
1
1
1
0
0
0
0
2
1
2
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
3
0
1
0
1
0
0
0
1
2
0
1
0
0
1
0
0
0
0
2
0
1
0
0
0
1
2
2
0
1
2
0
2
1
0
0
0
0
0
0
2
2
2
1
1
1
1
0
1
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
1
2
0
1
2
2
0
1
0
0
0
1
0
0
1
0
1
2
1
0
1
0
0
0
2
1
0
0
1
2
0
1
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
3
2
0
0
0
0
1
2
0
0
0
0
0
1
0
1
0
2
1
0
1
2
1
0
1
0
2
1
1
0
2
0
2
0
0
0
1
0
2
1
0
1
0
1
2
0
0
0
1
1
1
0
2
2
2
1
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
2
0
1
2
2
1
1
0
0
1
0
1
1
2
0
0
0
1
0
2
0
0
0
2
0
0
1
0
0
0
3
0
2
0
0
0
0
1
0
2
0
1
0
0
0
0
0
1
1
0
2
1
0
0
0
2
0
0
2
1
0
2
0
0
0
1
0
0
0
2
0
1
0
1
0
0
2
2
1
0
0
1
0
0
2
0
1
0
0
0
0
2
2
0
3
0
0
0
0
1
0
0
2
0
2
2
0
0
2
2
1
0
0
1
0
0
2
1
0
1
0
0
0
0
0
1
0
2
1
0
0
0
1
1
0
0
1
0
0
1
1
0
3
2
2
0
0
2
1
0
2
0
2
2
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
1
0
0
0
2
0
1
0
1
3
0
2
0
1
0
1
0
0
0
1
0
0
1
1
0
0
0
0
2
0
0
2
0
1
1
1
0
0
0
2
1
0
1
2
0
0
0
0
0
1
1
0
0
2
1
0
1
0
0
0
0
0
0
2
1
0
2
2
0
0
0
1
0
1
0
1
1
0
0
1
0
2
0
0
0
1
0
0
0
0
2
0
1
2
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
3
4
1
1
2
0
0
1
0
0
0
0
1
1
0
0
0
2
1
1
0
1
0
0
1
1
0
0
1
0
2
0
2
0
0
2
0
0
1
0
0
0
2
2
0
1
1
0
0
0
0
0
2
0
2
2
0
0
2
0
2
2
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
1
2
0
1
1
1
0
0
0
2
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
2
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
2
0
2
2
2
0
0
2
0
0
0
0
0
0
1
1
0
0
0
1
0
0
2
0
2
0
0
0
1
0
0
2
1
2
0
0
1
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
2
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
3
1
2
1
1
0
0
0
0
0
0
0
2
2
0
0
0
0
1
1
2
2
0
2
0
2
2
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
3
2
0
2
1
2
0
0
1
0
0
2
2
0
2
0
2
5
0
0
0
0
2
2
1
0
1
0
2
0
0
2
1
0
0
1
2
1
0
1
0
1
2
1
0
1
0
0
1
1
1
1
1
0
0
2
0
2
2
0
0
0
0
0
2
0
0
0
0
5
0
1
0
2
0
0
0
1
0
0
0
0
2
6
2
1
2
2
1
2
0
0
1
0
2
0
1
0
2
0
2
1
0
0
0
0
1
1
2
0
0
0
0
0
2
1
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
1
1
0
1
1
1
0
0
0
0
1
0
1
0
0
2
0
0
0
2
0
0
2
0
0
1
0
0
1
0
0
1
0
0
1
0
2
1
0
0
0
1
0
0
0
2
0
3
0
2
1
2
0
0
0
2
0
1
0
1
1
2
0
1
0
0
2
0
0
1
0
0
0
0
2
0
1
0
2
0
1
0
1
0
0
0
1
0
0
1
2
2
2
0
0
0
2
0
0
1
0
1
0
0
2
0
2
0
1
2
0
0
0
1
1
1
1
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
2
1
0
0
0
1
2
2
0
0
0
0
0
0
0
2
1
0
1
0
0
2
1
0
1
2
0
2
2
0
2
0
0
1
1
0
0
0
1
0
0
1
0
0
1
1
0
0
2
0
0
0
0
1
0
1
1
0
1
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
2
0
0
1
2
0
2
2
1
1
0
0
2
0
0
0
0
1
0
1
1
0
1
1
1
0
0
1
0
3
2
0
0
1
1
0
2
0
2
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
1
0
3
0
2
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
1
1
0
2
0
1
2
2
2
0
0
2
0
0
0
1
1
2
0
2
0
0
0
0
0
0
0
0
0
0
2
3
0
0
1
0
0
1
1
2
0
1
1
2
0
2
0
1
0
0
0
0
1
1
0
0
2
1
0
0
1
0
0
0
1
0
0
0
1
0
1
1
1
0
1
2
1
4
0
1
2
0
2
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
3
0
0
0
0
1
0
0
2
1
2
0
1
0
0
0
1
1
0
0
0
1
2
1
2
1
0
2
0
0
3
0
2
2
1
0
0
0
0
0
0
0
1
1
1
1
1
0
0
0
2
0
1
0
0
0
1
0
2
0
1
3
2
1
2
0
1
0
1
0
0
0
1
2
0
2
0
0
0
1
0
0
0
0
0
2
1
2
2
1
0
1
2
0
1
6
0
1
0
1
1
0
1
0
1
2
2
0
0
0
0
0
0
1
1
0
1
0
0
1
2
0
2
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
1
0
0
1
3
0
1
2
2
1
0
2
3
2
0
3
0
0
0
0
3
1
2
0
0
2
1
2
0
0
0
2
1
0
1
2
1
0
0
0
0
3
1
0
1
3
1
0
1
0
0
0
3
0
0
2
0
0
2
1
2
2
0
0
0
0
2
2
0
2
1
0
1
0
2
1
2
2
2
2
0
0
0
2
0
0
0
0
0
0
5
0
1
0
0
0
0
0
1
1
2
0
1
2
1
0
1
1
1
0
1
0
0
0
0
1
0
0
1
3
0
0
0
0
1
0
1
0
0
1
0
1
2
1
0
0
2
1
0
0
0
0
0
0
1
5
0
0
1
2
2
1
0
2
0
0
2
1
4
0
1
0
0
1
1
0
0
0
1
0
0
0
8
0
0
1
0
0
2
1
0
2
2
0
1
2
1
0
0
0
5
0
1
2
0
0
1
0
0
1
2
0
0
0
0
2
2
1
0
0
1
2
1
0
5
0
0
0
0
0
0
2
0
0
0
0
0
0
0
5
0
0
0
0
0
0
1
0
1
1
2
1
2
0
0
0
0
0
1
2
1
0
0
0
1
0
0
2
2
1
0
0
0
0
2
0
0
0
0
0
1
2
2
0
1
0
0
4
1
2
0
2
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
1
0
0
1
2
2
1
0
0
2
0
1
0
0
1
2
0
0
1
1
1
0
2
0
1
2
2
2
1
0
0
0
0
2
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
2
0
2
0
0
1
1
2
0
5
0
1
2
1
0
1
1
2
1
0
0
1
0
0
2
2
1
0
0
0
0
2
0
0
0
0
1
0
1
0
0
2
2
0
0
0
0
0
1
0
2
0
0
2
2
2
0
1
0
0
0
1
0
0
0
0
1
1
0
0
2
0
0
1
0
6
0
1
0
3
1
0
0
0
2
0
0
2
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
2
2
2
0
0
2
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
1
2
0
2
0
0
0
0
1
0
0
2
1
1
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
1
2
1
0
1
3
0
0
2
1
2
0
0
1
1
0
0
0
0
0
0
0
0
2
1
0
1
0
2
0
0
1
1
0
0
1
2
1
0
0
3
0
0
2
1
1
1
1
0
0
0
2
0
0
1
1
0
2
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
2
2
4
1
0
0
2
0
0
2
0
2
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
2
0
2
0
0
1
0
1
1
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
2
0
0
1
0
0
2
4
1
0
0
0
0
1
2
3
1
0
0
0
0
1
0
0
2
1
0
1
0
0
1
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
2
0
2
0
0
1
0
0
4
1
2
2
0
0
0
1
2
2
2
1
1
0
2
2
2
1
0
0
1
2
0
1
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
1
1
1
0
2
1
0
1
0
0
0
1
2
2
1
1
0
0
0
0
0
1
0
0
9
2
0
0
1
0
0
0
2
2
1
4
1
0
1
2
2
0
2
0
0
0
1
2
0
0
1
1
1
0
0
2
0
0
0
0
1
4
0
3
3
1
2
1
0
0
1
0
1
2
2
1
1
0
4
0
0
0
1
0
0
0
2
0
0
0
1
0
1
0
2
1
2
2
1
3
0
1
0
0
1
0
0
0
0
0
0
1
3
2
2
2
0
0
0
1
0
0
0
0
0
2
1
0
4
4
1
0
0
1
1
0
0
0
0
2
2
1
1
1
0
1
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
3
1
0
1
1
2
1
0
2
1
2
0
0
0
0
1
2
1
0
0
1
1
0
0
0
1
0
0
0
0
0
2
0
0
3
0
0
1
2
0
0
0
0
2
1
0
0
1
2
0
2
1
1
2
0
1
2
0
1
2
0
1
0
0
2
0
1
0
1
2
1
2
1
1
0
2
0
0
0
0
1
0
0
0
0
1
0
0
2
1
0
0
0
2
0
1
0
0
1
1
1
0
2
0
0
0
2
0
0
0
1
1
1
0
0
1
0
2
0
0
4
0
0
0
0
0
0
2
0
0
2
2
3
1
1
2
1
1
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
1
0
1
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
1
0
0
0
2
1
1
1
1
2
0
2
0
1
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
1
1
2
2
0
1
1
0
0
1
0
0
2
1
1
2
0
1
1
1
0
2
1
0
0
1
0
0
2
3
0
0
0
0
1
1
0
0
0
0
0
0
2
0
2
2
0
0
0
0
1
1
0
0
0
2
1
2
0
0
0
1
1
0
0
0
0
1
2
0
0
0
0
0
2
0
1
0
0
0
2
0
1
0
0
0
0
2
0
2
0
1
0
2
0
0
0
0
6
0
0
0
1
0
0
1
0
0
3
0
0
0
0
0
0
0
2
0
1
0
1
2
2
0
0
0
0
2
0
0
0
0
0
3
1
2
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
2
2
2
1
0
0
0
3
2
0
0
0
0
0
1
0
0
0
0
0
1
2
1
0
0
0
2
0
1
0
0
1
1
2
0
2
0
1
0
2
0
2
0
2
0
2
2
1
1
0
2
2
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
1
2
0
0
0
2
2
0
1
2
1
0
2
0
0
1
0
1
2
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
1
1
1
0
0
0
1
0
1
0
0
0
0
0
3
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
2
1
0
1
2
0
2
1
1
1
0
0
2
0
0
0
0
0
2
0
2
1
2
1
0
0
1
2
0
0
1
0
0
0
0
0
1
0
0
0
2
0
2
2
3
2
0
0
0
0
1
2
1
1
0
1
0
1
2
0
2
0
1
0
0
0
0
0
2
1
2
0
2
2
3
0
0
0
1
0
0
0
0
1
2
0
0
0
1
0
1
1
0
0
0
0
0
2
0
1
0
2
2
0
1
1
0
2
0
0
1
0
1
2
0
0
0
0
1
0
0
2
0
1
0
0
2
2
2
0
0
2
0
1
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
1
1
2
2
0
1
0
2
0
0
1
0
2
1
0
0
0
2
0
1
0
0
0
2
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
2
2
0
1
0
0
0
0
1
0
0
2
1
1
0
0
1
0
3
1
2
0
0
2
0
2
1
3
0
1
0
1
2
0
0
1
1
2
1
2
0
0
1
0
0
3
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
2
1
1
0
0
0
0
0
0
2
1
2
0
0
0
0
1
0
0
1
0
0
2
1
1
0
1
1
2
0
2
1
2
0
1
1
1
0
0
0
0
0
0
1
2
0
1
1
1
0
0
1
0
0
2
2
0
0
1
1
0
0
3
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
1
2
2
1
1
2
0
0
2
0
1
0
0
2
2
0
0
1
1
1
0
2
0
0
2
0
0
0
0
0
1
0
1
0
4
1
0
0
1
0
1
0
0
1
1
0
0
1
0
1
0
1
2
0
1
2
2
0
0
1
1
2
1
0
0
1
1
0
1
0
0
0
0
1
2
2
0
0
0
0
0
2
0
0
0
2
2
0
0
1
0
0
2
0
0
2
0
2
1
0
1
0
0
0
0
0
1
1
0
0
0
2
4
0
0
2
0
1
0
1
0
0
0
2
2
2
0
0
1
0
0
2
0
1
2
0
2
0
0
0
2
0
7
0
0
2
0
2
1
1
1
0
0
0
0
0
2
2
0
0
2
0
1
2
2
0
2
0
1
0
0
2
1
2
0
1
0
0
0
2
0
0
0
0
1
1
0
1
0
2
2
0
1
0
0
0
1
0
0
2
0
0
1
0
0
2
5
0
1
1
0
0
0
1
0
0
2
2
0
2
0
1
2
0
0
0
2
1
0
1
2
2
1
0
0
0
1
2
1
1
2
0
0
0
0
0
1
0
0
2
1
0
4
0
2
0
0
2
0
2
1
0
0
0
0
1
1
0
0
0
1
0
1
2
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
2
0
1
0
0
0
0
2
0
0
0
0
1
1
0
0
0
1
0
0
2
1
0
0
2
2
0
0
0
0
0
0
0
2
1
0
0
0
0
2
2
0
2
0
0
0
1
1
1
3
0
1
1
1
0
0
1
0
1
2
0
0
1
0
0
0
1
2
0
1
0
0
1
1
2
0
0
1
2
1
1
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
1
1
1
1
2
0
0
2
0
0
0
0
1
3
2
0
3
0
2
0
0
1
0
2
1
1
0
2
1
2
0
2
0
0
0
0
0
2
2
0
0
1
0
0
0
1
0
0
1
0
0
0
2
0
0
3
0
1
1
0
1
1
2
1
0
1
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
2
1
0
2
0
0
0
2
1
0
1
0
1
0
0
0
2
2
1
1
0
1
0
1
2
0
0
0
0
0
0
0
2
0
3
0
1
0
1
1
1
0
0
0
2
2
0
0
0
2
0
1
0
0
2
2
0
1
1
1
0
1
0
0
0
0
0
1
2
0
0
2
0
0
0
1
2
0
2
0
0
0
2
1
0
0
0
1
1
0
0
1
3
0
0
2
2
0
0
0
0
2
1
0
2
0
0
0
0
3
2
0
0
0
0
0
1
0
2
0
0
1
0
2
0
0
0
3
1
1
0
2
2
0
2
0
2
1
0
0
2
1
2
0
0
0
2
0
2
0
1
0
0
0
0
0
2
2
1
0
0
0
0
1
1
2
3
0
0
0
0
0
2
0
2
1
0
0
0
0
0
1
0
2
2
0
0
0
1
0
0
2
1
0
1
0
2
1
0
1
3
1
0
0
0
0
0
1
0
0
1
1
0
0
0
2
0
2
2
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
2
0
0
1
2
2
0
1
0
3
0
0
1
0
0
0
1
1
2
0
0
2
0
1
0
1
2
0
2
0
0
2
2
0
2
0
0
0
1
0
2
1
2
1
2
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
4
2
0
0
0
0
0
2
0
0
2
2
0
1
1
0
0
0
0
2
0
1
1
2
0
0
2
0
1
0
1
0
2
0
2
0
1
1
2
0
1
0
1
0
0
0
0
0
2
0
0
1
1
2
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
1
1
3
0
0
3
0
2
1
2
0
0
0
1
1
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
4
2
1
2
0
0
1
0
0
2
0
1
0
1
0
1
0
2
0
2
2
0
5
1
0
0
0
0
2
0
0
0
0
0
3
0
1
0
0
0
0
0
1
0
0
0
2
2
0
2
2
0
0
0
0
0
0
1
4
0
0
0
0
0
0
2
2
0
1
0
1
0
1
2
2
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
1
1
1
0
2
0
0
0
1
0
0
1
0
0
0
0
2
5
1
0
2
2
1
2
2
0
0
1
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
1
0
1
0
2
0
0
0
0
2
2
0
0
0
1
2
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
2
1
1
0
0
1
0
0
1
2
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
2
1
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
1
2
2
1
10
0
0
1
0
2
2
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
2
0
2
0
0
2
0
0
0
0
1
0
2
1
0
1
1
1
1
0
0
1
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
2
2
0
1
0
0
1
0
1
1
0
0
2
1
1
1
1
2
0
0
0
0
0
2
0
1
0
2
0
0
1
0
1
1
1
2
2
2
0
2
2
1
0
1
0
1
1
2
0
0
1
0
0
1
0
0
2
0
0
1
0
0
0
2
0
1
2
0
0
0
0
0
0
0
1
0
0
1
0
0
2
2
0
1
0
0
2
1
2
0
2
0
0
1
0
0
0
0
0
0
2
0
1
3
0
1
0
0
1
0
0
0
0
2
2
0
1
0
1
0
0
0
0
0
1
0
1
1
0
1
1
0
1
0
0
0
0
0
1
0
0
2
0
0
0
1
1
0
1
0
0
0
1
0
2
0
2
0
2
2
0
2
1
0
1
2
0
1
0
0
0
0
0
1
1
0
1
0
1
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
1
0
4
1
1
0
0
2
0
2
0
0
0
28
0
1
0
1
0
2
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
3
2
0
0
0
1
0
1
0
1
1
0
2
0
2
0
1
2
1
0
0
1
0
2
0
0
0
2
0
2
0
0
0
2
0
0
1
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
2
0
0
1
0
0
0
0
2
0
0
2
2
1
0
0
1
1
2
2
0
2
2
0
0
0
0
1
0
1
0
0
1
0
0
0
3
2
0
0
2
1
2
0
0
0
0
2
3
0
0
0
0
0
0
1
1
0
1
4
3
0
2
1
2
2
0
2
1
0
1
0
0
0
1
1
0
1
0
0
1
1
1
0
1
0
0
0
1
1
1
2
0
0
2
2
4
2
1
2
1
0
1
3
1
1
2
0
2
0
0
1
0
1
0
2
0
0
0
0
1
0
0
0
1
0
2
1
0
0
0
0
0
1
1
1
2
3
1
1
1
3
1
1
2
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
2
0
1
3
0
0
1
1
2
2
0
0
1
2
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
2
2
0
0
1
2
0
1
1
1
0
2
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
2
0
3
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
2
1
1
0
2
0
2
1
2
0
0
0
2
1
0
0
0
1
0
0
0
0
1
3
0
2
0
0
0
0
1
1
0
0
0
0
0
0
1
2
0
1
0
1
0
0
0
0
2
1
2
0
2
0
0
1
0
0
2
3
2
0
0
0
0
1
0
0
0
1
0
0
0
1
0
2
1
0
2
1
0
1
1
1
0
3
1
0
0
0
1
0
0
2
0
2
1
3
2
2
0
0
3
0
0
2
0
0
1
0
2
0
1
1
0
1
0
0
1
0
0
0
1
2
0
1
0
1
0
0
3
2
0
0
0
0
2
0
0
0
1
0
1
0
2
0
1
0
3
0
1
1
0
0
0
0
0
0
0
0
1
0
2
0
1
0
1
0
2
0
2
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
2
2
2
0
0
1
0
0
1
2
0
2
2
0
3
2
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
1
5
1
0
0
1
2
2
0
2
1
0
1
0
0
2
0
2
0
0
0
2
0
2
0
0
0
2
1
0
2
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
2
2
1
1
1
0
2
1
2
2
0
2
0
0
2
0
0
1
0
0
1
2
2
0
2
0
0
0
0
1
2
0
0
0
1
1
0
1
0
0
0
1
0
0
0
1
0
0
2
0
0
2
9
0
1
0
3
2
0
2
0
1
0
0
1
0
1
0
0
0
1
0
1
0
1
1
0
2
1
0
2
0
1
0
2
0
0
0
2
1
1
1
2
1
2
1
1
1
0
0
1
2
4
1
0
0
0
2
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
1
0
1
1
2
1
2
2
2
1
0
2
0
0
0
0
2
0
2
2
2
0
0
0
1
1
0
0
0
0
2
0
0
1
0
0
0
2
0
0
1
1
0
0
2
0
2
0
1
2
0
0
0
0
2
0
0
0
0
0
1
0
3
1
0
1
0
1
1
0
3
2
0
2
0
0
0
1
0
2
4
2
1
0
1
2
1
0
0
0
0
0
0
0
0
0
3
0
0
1
1
2
0
0
2
0
1
0
0
0
1
2
0
0
1
0
0
2
0
0
0
2
2
2
0
0
2
0
0
3
1
1
2
2
0
2
1
0
1
1
0
1
0
0
0
1
1
2
0
0
1
1
1
2
3
2
0
2
0
15
0
2
1
1
1
3
1
0
0
0
0
2
0
1
1
1
0
1
0
1
2
1
0
0
1
1
0
0
2
0
0
1
1
0
1
1
2
0
0
1
1
1
0
2
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
1
0
1
0
0
0
1
0
0
0
1
2
0
2
1
0
0
1
1
3
2
2
0
0
2
1
1
2
1
3
0
3
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
1
0
0
1
0
0
0
2
0
0
2
0
1
1
1
0
0
1
0
3
0
0
0
0
1
0
0
0
0
1
2
1
1
2
0
1
0
2
0
1
0
0
0
0
0
0
0
0
1
1
2
0
1
0
0
1
0
0
2
0
0
0
0
0
1
0
3
1
0
0
0
2
2
1
1
1
1
0
0
0
0
2
0
1
0
0
0
2
1
1
2
0
1
0
2
2
0
0
0
0
0
1
1
0
0
0
0
3
1
0
0
1
0
1
0
0
2
0
0
0
0
2
0
1
0
0
0
2
2
0
0
2
0
0
2
0
1
2
0
2
0
1
0
0
1
0
1
0
2
0
0
2
0
1
1
0
2
1
0
0
0
1
2
0
2
0
2
0
0
1
0
1
0
0
0
2
0
0
0
1
1
1
0
1
0
0
1
0
0
2
0
0
0
1
0
1
1
1
0
0
0
2
1
0
2
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
1
0
2
2
0
0
0
0
0
1
0
2
1
0
1
0
1
0
0
1
2
2
1
1
0
1
1
2
2
0
2
1
2
1
0
0
1
0
0
1
0
0
2
0
0
0
2
2
1
2
0
2
2
1
0
0
1
1
0
2
0
0
0
0
2
1
1
1
0
0
0
2
2
1
0
2
0
2
1
0
2
1
0
0
0
0
2
1
0
0
0
1
2
0
1
2
1
0
0
1
0
2
0
1
0
2
1
0
2
2
1
1
0
2
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
1
2
0
2
2
1
1
0
0
0
0
0
4
0
1
1
1
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
2
1
0
0
0
0
0
1
0
2
0
0
0
2
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
2
0
1
0
0
1
1
2
1
0
0
0
1
0
0
0
0
2
0
2
1
2
0
0
1
1
0
0
2
2
1
0
0
2
0
2
0
1
0
0
0
0
0
0
0
2
1
1
1
2
0
1
1
2
0
0
0
2
0
0
2
1
2
0
1
0
1
4
0
2
0
0
0
0
0
0
0
1
1
2
1
2
1
0
0
1
2
2
0
0
0
1
2
0
0
0
2
1
2
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
1
0
0
1
2
0
0
2
2
0
1
2
0
0
2
0
1
1
0
0
0
0
0
1
2
0
0
0
0
0
2
1
2
1
0
0
0
0
1
2
3
0
0
0
0
2
3
2
1
0
0
1
0
0
0
0
0
0
0
2
0
1
1
2
0
0
0
2
2
2
0
1
0
0
2
0
1
0
1
0
0
0
2
2
1
0
0
0
2
0
0
1
1
0
0
0
2
0
0
1
2
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
2
1
1
1
1
0
0
1
1
1
0
0
0
2
1
2
0
3
0
0
2
1
3
0
0
0
2
1
2
1
0
0
2
1
1
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
2
0
0
0
1
0
3
1
1
0
0
0
2
0
2
0
2
2
1
0
2
0
0
0
1
0
1
1
2
0
2
0
1
1
2
0
0
2
1
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
1
2
0
0
2
0
0
0
0
0
0
0
1
0
5
0
0
0
0
2
2
1
3
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
1
1
2
2
0
0
0
1
0
1
0
0
0
2
0
2
0
2
1
4
0
0
2
0
2
3
0
0
0
0
2
2
1
0
0
1
0
0
0
0
0
0
0
1
1
0
1
2
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
1
1
0
0
0
1
0
0
1
1
1
0
0
0
0
2
1
2
0
2
0
3
2
0
0
0
1
2
0
2
0
1
0
2
1
0
0
0
0
0
1
2
0
0
0
0
0
1
0
2
2
0
0
0
1
1
1
2
0
1
1
0
1
0
2
2
2
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
2
2
2
0
0
1
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
1
1
0
2
1
1
1
2
0
2
1
0
0
1
1
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
2
0
0
0
2
1
1
0
2
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
4
2
0
0
0
2
0
0
0
0
0
2
1
0
2
0
1
2
0
0
2
2
1
2
0
2
1
1
0
0
2
0
0
0
2
0
0
2
0
2
0
0
1
1
2
0
1
0
1
0
2
0
1
0
0
1
0
0
0
0
2
0
0
0
3
0
0
0
0
4
0
1
2
1
1
2
0
1
2
0
0
2
0
0
2
1
1
0
2
1
0
0
1
0
0
2
1
0
1
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
1
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
1
0
0
1
0
0
0
0
2
1
1
0
1
0
6
0
1
0
0
0
5
0
3
1
2
0
1
1
0
2
0
0
2
0
0
2
0
0
1
3
0
0
1
0
0
2
1
0
1
0
0
0
0
2
3
1
0
1
0
0
0
1
0
1
0
0
2
2
0
0
1
0
1
1
0
0
0
1
0
2
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
2
2
2
0
1
2
2
0
0
2
1
1
3
0
1
0
0
0
0
0
0
2
0
1
0
2
2
0
0
0
0
1
3
2
0
1
2
0
1
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
1
0
0
0
0
0
0
3
0
0
0
0
0
0
1
2
0
0
1
1
2
0
1
0
0
1
0
0
1
0
0
0
2
0
0
1
1
2
0
2
0
0
0
1
1
2
0
0
1
0
0
1
1
1
1
0
0
3
0
2
0
0
0
1
0
1
0
0
1
1
2
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
2
0
2
1
0
0
0
0
1
1
0
0
2
1
2
2
2
0
0
0
0
1
2
1
0
0
2
0
0
0
2
2
0
0
1
2
0
2
0
0
2
0
1
1
2
0
1
1
1
0
0
0
0
0
2
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
1
2
0
0
3
1
1
1
2
1
1
0
0
0
0
2
0
0
0
0
1
0
2
0
2
0
0
1
1
0
2
0
0
1
1
0
0
2
2
0
2
0
3
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
1
1
0
1
1
2
1
0
0
2
0
2
0
0
1
2
0
0
0
1
2
0
0
0
0
1
0
0
1
1
0
1
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
1
2
2
1
0
0
0
0
1
0
1
0
1
0
2
0
0
1
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
1
3
0
0
0
0
3
2
1
2
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
2
2
0
0
0
1
0
0
0
0
0
1
1
1
0
3
0
0
0
2
0
0
0
0
2
1
2
0
2
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
2
2
0
1
2
0
1
2
0
0
1
0
0
2
0
3
0
0
0
0
0
2
1
2
0
0
0
0
1
2
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
2
1
0
0
0
1
0
0
2
1
0
1
0
1
2
0
0
0
0
2
1
0
1
0
1
1
0
0
1
2
0
2
0
0
2
1
0
1
2
0
0
1
1
0
0
0
0
0
2
2
2
0
0
2
1
0
0
0
1
0
3
3
1
0
2
1
2
0
0
2
3
0
0
2
0
1
0
0
0
0
0
0
2
2
2
0
0
1
1
2
3
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
3
0
1
0
1
1
0
2
0
1
2
1
0
0
0
0
1
0
2
0
0
2
0
0
0
0
2
0
3
0
0
0
1
2
2
1
1
0
1
0
0
0
0
0
0
1
2
1
0
0
2
2
0
1
0
1
1
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
1
0
1
2
0
0
0
0
3
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
1
2
0
2
0
0
1
0
2
5
0
0
1
3
2
0
1
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
3
0
0
1
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
1
1
2
0
1
1
2
2
0
2
0
0
0
2
0
1
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
1
2
0
0
1
0
0
2
0
0
0
0
1
1
0
1
0
0
0
0
0
1
3
2
0
0
0
0
2
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
1
0
0
2
0
0
1
0
2
0
2
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
1
0
1
0
2
0
0
2
0
2
0
1
0
1
2
2
0
1
1
0
1
0
1
0
1
0
1
2
0
0
0
0
2
0
0
0
0
2
0
0
0
2
1
2
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
1
3
0
0
1
2
0
0
2
0
1
0
1
0
2
0
2
1
3
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
3
1
0
0
0
2
2
1
0
2
0
0
0
0
0
2
0
2
1
1
1
2
0
0
0
1
2
0
0
0
0
3
0
0
1
0
1
0
1
2
2
1
2
0
1
0
0
1
2
0
0
1
1
0
0
1
0
0
0
2
0
0
0
1
0
2
2
0
0
1
0
0
3
1
2
0
0
2
0
0
2
0
0
0
1
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
2
1
0
1
0
0
0
0
1
1
1
0
1
2
2
1
0
2
0
2
0
1
0
2
2
0
3
0
0
1
1
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
2
0
1
0
1
1
1
1
1
0
0
0
2
2
0
0
2
0
0
0
1
1
0
1
0
2
0
2
0
1
0
0
0
0
2
2
3
1
0
1
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
1
2
1
0
2
1
0
2
1
1
0
0
3
0
2
2
0
2
0
0
1
0
0
0
2
0
2
0
1
2
0
1
0
1
0
0
2
0
0
1
1
2
0
1
0
0
0
0
0
1
0
0
0
2
1
1
0
0
2
0
0
6
2
0
1
2
1
0
2
0
0
1
3
0
2
1
0
0
0
0
0
0
0
2
2
5
0
0
0
0
0
3
1
0
1
0
0
1
1
1
0
2
0
0
2
0
1
0
0
2
2
0
0
0
0
1
0
1
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
2
1
0
2
0
4
1
0
2
0
1
0
0
1
2
1
0
0
0
1
0
1
0
2
0
0
1
0
1
0
0
1
0
0
2
0
1
0
0
0
2
2
0
0
0
2
0
1
0
2
1
1
0
1
0
0
0
1
0
0
2
0
1
1
2
0
2
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
2
1
1
1
0
0
0
1
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
1
2
2
0
0
0
2
2
0
0
1
0
1
0
2
0
2
0
1
0
0
0
1
1
1
2
0
0
0
2
0
1
0
1
0
3
1
0
2
1
1
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
1
0
1
2
0
1
1
1
1
0
1
0
1
0
0
1
0
0
1
2
0
1
1
0
0
1
0
0
2
0
0
1
1
0
0
0
0
0
1
1
2
1
0
0
0
0
2
0
6
0
0
0
2
0
0
0
1
0
0
2
0
0
0
1
0
0
1
0
0
0
1
2
2
0
2
0
1
1
1
0
2
0
0
0
0
0
1
0
0
0
2
2
0
0
0
1
1
1
0
1
0
2
1
2
1
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
1
0
0
0
0
0
0
2
2
0
2
0
0
2
0
2
3
0
2
0
2
0
0
0
1
1
2
0
0
2
1
0
0
1
2
0
1
0
0
0
2
0
1
2
1
0
0
1
1
3
1
0
1
0
1
0
0
2
3
0
0
1
0
0
2
2
0
0
0
0
0
0
2
2
0
1
1
1
1
2
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
2
0
2
1
1
3
1
1
0
0
0
1
0
0
0
1
0
0
2
1
3
0
1
0
0
2
1
0
0
0
0
0
0
2
3
0
2
2
2
2
0
3
0
0
1
0
1
0
1
0
1
0
2
0
0
0
1
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
1
0
1
2
0
0
0
0
2
0
0
0
0
5
1
0
0
0
0
1
1
2
0
1
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
1
1
1
0
3
0
0
3
2
0
2
0
1
0
0
0
1
0
1
1
0
1
1
0
3
0
1
0
0
1
0
1
0
0
0
5
0
1
2
0
0
2
0
1
1
0
2
2
1
0
1
0
0
0
0
2
0
2
2
0
0
0
2
0
2
0
0
2
2
0
1
1
0
2
0
2
0
1
0
2
1
1
2
0
0
1
2
2
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
2
2
2
2
0
0
0
1
0
0
0
0
0
2
0
2
0
3
0
0
2
0
0
2
1
1
2
0
0
2
0
0
0
0
0
1
0
2
3
1
2
0
0
1
0
2
0
0
1
0
0
2
1
1
0
1
0
1
0
1
2
0
0
0
0
0
2
1
0
0
0
0
2
2
2
1
2
0
1
1
1
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
1
1
2
0
2
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
3
1
0
0
1
2
0
2
2
0
2
0
0
0
1
1
2
0
0
0
0
1
0
1
0
0
0
2
0
2
1
0
0
3
0
0
0
0
0
2
0
0
0
1
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
7
0
0
0
0
1
1
0
1
0
1
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
1
2
2
1
1
0
1
0
0
0
0
1
0
0
3
1
1
2
0
0
0
1
0
0
0
0
0
2
0
0
2
2
0
2
2
0
0
2
2
0
1
1
1
0
0
1
2
0
0
0
0
0
2
0
0
2
1
1
1
0
0
1
1
1
2
2
0
4
1
0
2
0
1
1
0
0
2
1
2
0
0
0
1
0
1
0
2
3
1
2
0
3
0
0
1
0
0
0
2
0
2
0
1
0
3
1
0
0
0
0
0
0
0
0
0
0
2
2
0
2
1
0
0
1
2
0
2
1
0
0
0
2
0
0
0
0
1
0
0
1
1
0
2
1
0
1
0
0
1
1
2
0
0
0
0
1
1
0
0
2
0
1
1
2
1
3
0
2
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
2
1
1
1
0
0
0
0
1
0
1
1
0
2
0
2
0
1
0
0
1
0
0
2
1
1
0
0
1
2
0
0
1
0
1
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
1
0
1
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
1
1
2
0
2
2
0
1
0
1
0
0
2
2
0
0
0
0
0
0
2
1
0
2
2
0
0
0
1
2
0
0
0
0
2
0
0
0
0
1
2
2
0
0
1
1
0
0
1
2
0
1
0
0
0
2
0
0
0
2
2
0
0
3
2
1
0
0
1
0
1
0
0
0
0
2
2
0
1
1
0
2
3
0
0
1
0
0
0
1
0
0
0
0
0
2
0
2
1
0
0
0
0
0
2
0
0
0
2
1
1
0
0
0
1
1
0
0
0
1
0
2
2
0
0
2
2
0
0
0
0
0
0
0
0
3
0
0
2
0
1
0
0
2
2
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
1
1
3
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
2
1
2
2
0
2
0
0
2
0
1
0
0
0
0
0
1
0
1
0
3
0
2
0
2
0
2
2
0
0
1
1
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
1
0
0
2
2
0
0
2
0
2
0
2
0
0
1
0
0
0
1
2
0
2
0
0
0
2
2
0
2
0
2
0
2
1
2
3
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
3
2
0
0
2
2
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
1
1
0
0
1
3
9
0
0
2
0
1
0
0
1
0
0
3
2
0
0
0
2
0
1
1
1
0
1
1
1
0
2
0
1
1
0
1
0
2
0
1
1
0
1
2
0
1
0
2
0
0
0
1
0
1
0
1
0
0
2
0
0
1
0
0
0
1
0
2
2
2
0
2
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
2
3
2
0
2
0
0
0
1
1
2
3
1
0
0
1
0
0
0
1
0
0
1
2
0
0
0
0
1
0
1
2
0
0
0
1
2
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
2
0
0
1
2
2
1
1
0
1
0
0
0
0
0
1
0
0
2
0
0
1
2
1
1
2
2
0
0
0
0
0
2
0
0
0
0
1
0
2
2
4
1
0
0
1
2
2
0
1
0
0
2
0
0
1
0
0
2
0
1
1
0
1
0
1
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
2
1
1
1
1
1
3
0
0
0
0
1
1
1
0
1
1
0
0
0
0
0
0
0
2
1
0
2
2
1
0
0
0
1
0
2
1
2
0
0
1
0
3
1
0
0
0
1
1
1
0
2
0
0
4
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
2
0
0
0
0
2
2
0
0
0
0
2
1
2
0
0
0
0
1
2
0
0
1
2
0
0
1
1
1
0
0
0
2
1
0
0
1
0
2
0
0
2
0
0
0
2
1
0
0
0
2
2
0
0
0
1
1
1
1
2
2
0
2
1
2
1
2
0
0
2
0
2
0
0
0
0
0
0
0
1
2
1
0
2
2
1
0
0
1
2
2
1
1
1
0
0
0
0
1
0
0
0
1
0
0
1
0
4
0
0
0
0
1
0
0
1
0
0
2
2
0
2
0
0
2
1
1
0
0
0
0
0
2
0
2
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
1
0
2
1
1
0
0
2
0
0
0
0
1
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
1
2
0
0
0
0
0
0
0
2
0
0
0
2
2
2
0
1
1
0
0
0
2
1
0
0
0
1
1
0
2
0
0
0
2
1
0
1
0
0
2
0
2
0
0
0
0
4
0
0
2
13
0
2
1
0
0
0
1
0
3
1
0
0
2
0
1
2
0
2
0
0
0
0
1
1
0
1
1
2
2
0
2
2
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
2
2
0
1
1
1
0
0
1
0
1
2
0
1
0
0
0
0
0
0
1
0
0
0
1
2
1
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
1
1
2
2
0
2
0
0
0
2
0
0
1
0
0
1
0
0
2
0
0
0
0
1
2
2
2
0
2
0
0
2
0
1
0
0
0
2
0
2
0
1
1
0
0
2
0
0
0
0
0
2
3
0
0
0
3
0
0
2
0
1
0
0
0
0
1
0
2
1
0
0
0
1
4
1
0
0
1
0
3
0
0
0
0
0
0
0
1
1
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
2
0
0
2
0
1
0
0
2
0
0
1
0
0
0
0
0
1
0
2
0
0
2
0
1
0
0
0
1
2
0
1
0
1
0
1
0
1
2
0
2
1
0
0
0
0
0
0
0
0
0
3
2
1
0
1
0
0
2
0
0
2
0
0
1
1
2
0
0
0
0
0
0
1
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
2
0
1
1
2
0
2
0
0
1
1
1
0
0
0
2
0
1
0
0
0
0
0
0
2
0
2
1
0
0
0
1
0
2
1
2
0
1
0
0
0
0
0
1
2
0
0
2
0
1
0
3
0
0
0
0
1
0
0
0
2
1
0
0
3
0
1
2
0
0
3
2
0
0
2
0
0
0
0
2
1
0
1
0
2
0
0
2
1
1
2
0
1
2
0
0
2
2
0
1
0
0
0
0
0
3
1
1
2
1
0
2
0
1
0
2
2
0
0
0
0
0
2
3
3
0
2
0
1
0
0
0
2
1
0
2
1
0
0
0
2
2
1
1
0
0
2
0
0
0
0
1
0
0
1
0
2
1
0
0
0
0
0
0
0
1
1
0
1
0
2
1
1
0
0
0
0
0
0
2
0
1
0
3
0
1
1
0
0
0
0
1
0
1
2
0
0
1
1
2
0
2
0
2
1
0
0
1
2
0
0
0
3
0
0
0
0
0
2
0
1
0
2
1
1
0
2
0
0
2
0
0
0
0
0
1
2
0
0
0
0
1
1
0
0
0
2
0
2
0
0
1
0
2
1
3
0
1
0
0
0
0
0
1
2
2
2
0
0
1
1
0
2
0
1
0
0
2
0
0
2
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
2
1
0
0
0
1
0
0
0
2
2
1
0
0
2
2
0
0
0
2
1
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
3
0
2
0
0
1
1
2
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
1
1
2
0
2
0
2
2
0
1
0
0
0
2
2
0
1
2
0
0
0
0
0
2
0
0
0
0
0
1
0
2
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
2
1
0
2
0
0
0
0
1
3
0
0
2
1
1
1
2
0
2
0
2
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
4
2
0
1
1
0
0
0
0
0
0
1
1
0
2
0
1
0
0
1
0
2
0
2
3
0
0
1
0
0
0
2
1
2
1
0
2
0
0
2
0
1
1
1
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
2
1
2
0
0
0
0
0
1
0
0
1
2
0
0
0
1
2
0
0
1
2
0
0
1
2
0
2
3
1
0
0
2
0
0
2
0
0
1
0
0
0
2
0
2
0
1
0
0
0
3
0
0
0
0
2
0
0
0
2
0
1
1
0
2
0
0
0
0
0
0
0
1
1
2
2
1
1
1
0
0
0
0
0
0
2
0
1
2
0
1
0
0
0
6
0
1
2
0
0
2
2
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
1
4
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
1
1
1
0
2
0
0
1
0
0
1
2
0
1
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
2
0
2
2
2
2
0
1
0
0
0
0
0
0
0
0
0
2
0
1
2
1
3
0
1
0
3
0
0
1
0
0
0
1
0
0
2
1
0
0
1
0
1
0
0
2
0
0
0
0
2
0
1
1
0
0
2
0
1
2
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
2
0
2
1
0
0
0
0
1
0
2
0
2
0
0
1
2
2
1
0
1
2
1
0
2
1
1
0
0
2
2
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
3
2
3
0
1
0
1
2
1
0
0
1
0
0
2
0
2
0
0
3
2
1
1
0
0
2
0
0
0
0
0
0
0
1
1
1
0
2
2
1
0
1
0
0
0
0
1
0
0
0
2
0
0
2
1
2
2
2
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
2
1
1
0
0
0
0
1
0
0
2
0
0
1
0
0
1
0
0
1
1
1
2
2
0
1
1
0
0
0
2
0
1
0
2
0
0
0
1
0
0
0
1
0
0
0
0
2
0
2
1
3
2
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
1
2
2
0
1
1
0
0
3
2
0
1
0
0
3
0
0
0
2
2
1
0
0
1
0
2
2
0
2
1
0
0
0
4
2
1
1
2
1
0
0
0
1
0
2
0
0
0
2
0
1
1
1
0
0
0
0
1
1
0
0
1
2
0
0
0
0
0
3
1
0
0
0
1
0
0
2
0
1
2
0
2
2
2
3
2
0
0
0
0
1
1
3
0
2
0
2
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
3
1
2
2
1
0
1
0
0
0
1
1
0
2
0
2
2
0
2
3
0
0
1
0
1
0
0
1
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
1
1
0
2
2
1
2
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
1
0
0
0
1
0
2
1
0
0
4
0
0
3
0
0
3
0
0
2
0
0
0
2
2
0
0
1
0
2
2
1
1
2
0
2
1
0
0
1
2
2
1
0
0
1
2
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
2
0
0
0
1
0
0
2
1
0
1
1
0
0
2
2
1
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
2
5
2
1
2
1
0
0
0
0
2
0
0
2
3
2
0
1
0
0
0
1
1
0
2
0
0
0
1
0
2
0
0
2
1
3
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
2
1
1
0
0
0
0
0
0
0
2
0
2
2
0
2
0
1
2
0
0
2
2
0
1
1
0
2
0
0
0
1
0
2
0
0
1
0
0
0
0
0
1
3
2
1
2
0
0
1
0
2
0
1
2
2
2
2
0
1
0
0
2
2
0
2
0
1
1
0
0
0
1
0
0
0
0
0
1
0
1
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
1
2
0
1
0
0
2
0
2
1
2
0
0
0
0
2
0
0
1
0
1
0
2
0
0
2
0
0
0
1
1
0
0
2
2
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
1
0
0
0
1
1
0
2
2
0
0
0
1
0
0
0
2
0
2
0
0
2
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
1
0
0
2
1
2
2
0
1
0
0
1
1
0
0
1
1
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
1
1
0
1
0
2
1
0
0
0
0
1
0
0
1
0
0
0
1
2
1
0
1
1
0
1
0
0
0
2
2
0
0
0
1
0
0
0
2
0
1
2
2
2
2
2
2
1
0
1
0
1
0
2
0
1
0
2
2
2
1
1
1
2
0
2
2
0
0
0
1
1
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
2
3
0
0
0
0
1
1
0
0
0
0
2
1
0
0
2
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
1
1
1
0
0
2
0
3
2
0
2
1
2
3
0
2
0
0
0
0
1
2
0
0
2
2
2
2
0
2
0
0
2
3
0
2
0
2
4
1
0
2
0
1
2
1
2
0
1
0
3
2
2
1
0
0
0
2
1
0
0
2
0
3
1
2
0
0
0
0
2
0
1
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
1
3
0
1
0
0
0
1
1
0
0
0
0
4
0
2
0
0
0
0
2
2
0
2
0
0
3
1
0
2
0
2
1
0
1
1
1
1
1
1
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
2
0
0
0
2
1
0
1
1
2
0
0
0
0
0
0
2
1
0
0
1
0
0
2
0
0
1
0
0
0
1
0
2
0
2
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
1
0
1
0
0
1
1
0
2
1
0
1
2
1
0
1
1
0
0
1
0
0
2
0
2
0
0
1
0
1
1
1
0
0
1
0
0
0
0
0
0
2
0
1
1
0
0
0
0
2
1
0
2
0
1
0
0
0
0
0
2
1
0
2
0
0
2
1
0
0
0
2
0
0
2
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
2
2
0
0
0
0
0
1
2
1
0
1
2
1
0
0
3
2
1
1
1
0
0
2
2
2
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
1
2
2
0
0
0
0
1
0
0
0
0
0
0
0
2
3
0
0
1
0
2
0
1
0
0
0
0
1
0
1
0
1
0
0
0
2
1
0
0
0
2
0
0
0
1
0
1
1
0
1
2
0
0
2
0
0
0
0
0
0
2
3
1
0
2
2
1
2
0
0
0
0
0
0
1
1
0
4
0
0
0
0
1
1
2
0
0
0
0
0
0
0
1
1
1
1
0
0
2
2
0
2
0
0
1
0
2
2
0
0
0
0
0
0
3
2
1
0
1
1
1
1
2
0
1
0
0
0
3
2
0
1
2
1
1
1
2
0
1
0
2
0
1
0
2
2
0
1
0
0
1
0
2
0
1
0
0
1
0
0
0
1
0
0
1
1
1
1
2
2
0
0
1
2
2
2
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
1
1
0
1
0
2
0
3
0
0
0
2
0
1
1
4
0
0
2
0
0
0
2
1
1
2
0
0
2
0
0
0
2
0
0
1
0
0
5
0
0
3
0
0
1
2
0
1
0
2
0
0
2
0
0
1
0
1
0
0
1
1
0
1
0
0
2
0
0
0
0
1
2
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
2
2
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
1
1
2
0
0
2
0
0
0
0
2
0
0
4
1
2
1
2
0
0
0
0
0
2
0
0
2
0
2
1
0
0
1
2
0
0
0
0
1
1
1
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
1
0
2
0
2
0
0
0
0
3
2
1
1
1
2
0
0
2
0
0
0
0
0
1
0
0
1
1
0
1
0
1
0
0
0
2
0
0
4
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
1
0
2
0
2
2
0
2
0
0
0
1
0
1
0
7
0
0
2
0
0
0
0
1
0
2
2
0
0
1
0
0
2
2
0
0
1
2
2
2
1
0
0
0
1
0
2
0
0
0
2
0
2
0
0
1
1
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
2
0
0
2
3
0
0
0
0
0
0
3
1
3
0
1
0
1
0
1
2
2
1
0
0
0
0
0
0
2
1
2
1
0
2
0
1
0
0
1
0
0
2
0
0
0
1
2
2
0
0
0
7
0
0
2
3
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
2
2
0
1
2
2
0
5
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
2
0
2
2
1
1
1
0
0
1
1
0
0
0
0
0
1
1
0
0
2
3
1
0
2
0
0
2
0
0
1
0
0
0
0
1
1
1
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
2
0
2
0
0
0
0
2
2
1
0
0
1
0
0
0
0
0
0
1
0
1
1
1
1
1
0
0
1
2
1
0
0
3
0
0
2
0
2
1
2
0
2
0
0
2
2
2
0
2
1
0
1
0
3
2
1
0
0
2
0
0
1
0
0
2
0
4
0
0
1
0
2
1
2
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
2
2
0
1
0
0
0
0
0
0
2
1
3
0
0
0
0
0
1
2
2
0
0
1
0
0
0
0
2
2
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
1
3
0
2
0
0
0
0
3
0
0
0
2
0
1
0
0
0
0
2
0
0
0
1
0
0
0
2
1
3
0
2
1
2
1
0
2
2
1
0
1
0
0
2
1
2
2
0
1
0
0
0
0
0
0
0
0
2
1
0
1
0
3
2
0
1
0
0
3
2
0
2
0
0
0
2
1
1
1
1
0
1
0
0
0
0
5
0
2
2
2
3
0
0
0
0
0
2
2
1
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
1
2
0
1
2
0
0
0
0
0
3
0
0
0
0
0
1
0
2
0
0
0
0
1
1
0
0
1
2
2
0
1
2
0
0
1
0
0
0
2
0
1
0
2
0
0
1
2
1
2
0
2
0
1
0
0
0
1
0
0
0
2
0
0
0
2
1
0
0
1
0
1
2
0
1
1
2
2
0
2
0
0
1
0
1
1
1
0
1
0
0
1
0
1
1
0
1
0
0
0
1
0
0
0
1
2
0
0
1
2
0
1
1
2
1
2
0
0
1
0
0
2
2
1
0
0
5
0
0
2
0
0
0
0
0
1
0
2
0
0
1
2
0
2
2
0
1
0
0
1
0
0
0
1
2
0
2
0
0
1
0
0
0
0
1
1
0
2
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
14
0
2
0
0
0
2
0
1
0
0
1
0
1
0
2
2
2
0
0
1
2
0
1
1
0
0
0
2
2
1
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
1
2
0
1
1
0
0
0
0
2
0
1
2
0
0
0
2
2
0
2
1
1
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
2
0
0
0
1
0
0
2
0
0
0
0
2
2
0
0
1
0
0
5
1
0
0
2
0
0
2
0
2
0
2
1
0
2
1
2
0
2
0
0
0
0
0
0
0
0
0
2
0
1
1
3
0
2
0
2
1
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
1
1
2
0
0
0
0
0
1
1
0
2
2
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
1
1
0
0
0
1
2
0
0
0
0
1
2
0
1
2
1
2
0
2
0
0
1
0
0
2
0
0
0
1
0
0
2
2
0
0
0
0
1
0
1
0
0
2
0
1
2
0
0
0
2
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
1
1
1
2
0
0
0
2
2
2
1
1
2
2
3
0
1
0
2
0
1
0
0
0
0
2
0
0
4
0
2
1
2
0
0
1
2
0
1
1
0
2
1
0
0
2
1
0
1
2
0
0
0
2
2
0
1
2
2
2
0
0
0
0
2
2
2
1
1
0
1
0
2
0
3
0
2
0
0
0
1
0
0
0
1
1
3
0
1
0
0
0
0
3
0
2
1
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
2
0
0
0
0
1
1
2
0
1
0
1
0
0
0
0
0
0
2
1
1
2
1
0
0
0
0
3
0
0
0
1
1
2
2
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
3
1
0
0
0
1
2
0
1
1
0
0
2
2
0
1
0
0
0
0
0
2
0
1
1
0
0
2
0
0
0
0
0
0
0
2
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
1
2
0
1
0
3
0
1
0
0
1
0
1
1
0
0
1
3
0
1
1
0
1
2
1
0
0
2
1
0
1
0
0
0
2
0
2
2
1
0
1
2
0
1
0
2
0
0
0
0
2
2
0
0
1
2
1
2
1
0
0
0
0
0
1
0
0
1
0
0
0
1
1
2
2
0
0
1
0
1
2
0
0
0
2
0
0
1
0
0
0
0
0
1
1
2
0
0
0
0
0
1
0
0
0
0
0
1
0
2
3
0
0
0
0
1
0
1
0
0
0
2
0
1
0
0
3
0
0
2
1
1
2
0
2
2
0
1
1
1
2
0
0
0
1
2
0
1
1
0
0
0
1
1
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
2
0
2
0
0
0
2
0
0
0
2
1
1
0
2
0
0
2
0
1
0
0
1
0
0
0
2
1
0
0
1
0
2
0
2
1
1
0
2
2
1
0
0
0
0
1
0
0
0
0
0
2
0
0
4
2
1
0
0
1
1
2
0
1
0
0
0
1
0
0
0
0
1
2
2
1
0
1
2
2
2
0
1
0
0
1
0
0
1
1
2
0
0
0
0
0
0
0
3
2
2
1
0
1
2
0
1
2
1
0
0
1
0
0
0
2
0
2
0
2
0
0
1
0
0
0
1
1
1
2
0
0
1
0
0
1
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
3
0
3
0
0
2
0
1
0
1
1
0
0
0
1
2
2
1
0
1
0
0
0
2
0
0
0
1
1
0
4
1
2
0
0
0
0
1
0
2
1
0
1
0
0
2
2
1
2
2
0
1
0
0
0
0
2
1
1
0
0
1
1
2
2
0
0
0
0
2
0
0
0
2
0
0
2
2
2
1
1
0
1
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
1
1
0
12
1
0
0
1
0
2
0
0
0
0
0
0
3
0
1
0
0
2
0
0
4
1
0
1
1
0
0
2
0
2
0
2
1
0
0
1
0
1
2
0
0
2
1
0
1
1
0
1
0
3
2
0
0
0
5
2
1
1
0
0
0
0
1
2
0
2
0
1
0
2
0
0
1
2
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
1
1
2
1
0
1
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
1
0
0
0
1
0
1
1
0
0
1
2
2
0
0
0
0
0
0
2
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
1
2
0
1
0
1
2
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
1
2
0
2
0
0
0
2
0
1
0
1
1
0
0
0
1
1
0
0
1
0
1
0
2
0
0
1
1
0
1
0
0
2
0
2
1
1
0
0
2
0
0
0
3
0
1
0
0
1
1
0
1
0
0
2
2
0
1
2
1
1
0
1
1
0
1
1
0
0
0
0
1
1
0
0
1
0
1
1
0
0
0
2
2
0
1
1
0
1
0
1
1
1
1
0
0
0
0
3
0
0
0
0
2
0
1
0
1
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
2
3
0
0
3
2
0
1
0
0
1
3
1
2
0
0
2
0
1
1
0
0
0
1
0
1
0
0
0
0
0
2
2
1
0
0
0
2
0
0
0
0
1
2
0
0
0
0
1
0
0
0
1
0
2
0
0
0
2
4
1
1
1
0
2
0
2
0
0
2
0
2
0
1
0
2
0
0
0
0
2
1
2
0
0
1
2
0
0
2
2
0
0
0
2
0
0
2
1
0
0
2
1
0
0
2
1
1
1
0
0
0
2
2
0
2
0
0
1
2
1
0
0
0
0
1
0
1
2
0
1
0
1
0
2
0
0
0
1
0
0
0
0
3
2
0
2
0
1
0
0
0
1
2
2
0
0
0
2
0
0
0
2
1
1
0
0
0
2
0
0
1
0
0
0
0
0
2
2
0
2
0
0
0
2
2
1
0
1
0
0
0
0
2
0
0
1
2
2
1
0
0
2
0
0
0
0
0
0
2
0
5
0
0
0
0
0
0
1
0
0
0
0
2
1
1
0
2
0
0
1
2
0
2
0
0
2
0
2
0
0
2
0
2
0
0
0
0
2
0
0
0
0
1
3
0
0
1
1
0
1
0
3
2
0
0
0
1
0
2
0
0
0
1
0
0
1
1
0
0
0
0
0
2
0
1
0
0
1
2
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
1
0
2
0
0
1
0
2
0
2
0
0
0
0
2
2
1
1
0
0
0
0
0
1
0
1
2
0
2
2
2
0
0
0
1
2
1
0
0
1
3
0
0
2
0
0
2
2
2
0
2
0
1
1
2
0
2
1
2
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
3
2
0
1
0
0
0
1
1
0
0
1
1
0
2
0
1
1
0
1
2
0
1
2
1
0
1
0
0
2
0
0
1
1
1
0
0
0
2
1
2
0
1
2
1
0
2
2
2
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
2
2
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
3
0
3
1
2
0
0
0
0
0
1
0
1
0
2
0
0
0
1
0
0
1
0
0
0
0
1
0
2
0
1
0
3
0
0
0
0
0
0
0
0
0
1
1
0
0
3
1
1
0
0
2
2
0
0
0
0
0
0
2
1
2
2
2
0
0
1
1
0
0
1
0
0
0
1
1
0
2
2
0
1
4
0
2
0
0
2
0
0
3
0
0
0
0
1
2
0
0
3
0
1
0
0
0
0
0
0
0
1
0
1
1
2
1
1
0
0
0
2
2
0
1
1
1
0
0
2
1
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
2
0
0
1
0
0
0
0
3
2
2
1
0
1
1
2
1
0
2
2
0
0
1
0
2
1
0
0
2
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
1
2
2
1
0
0
2
0
3
0
2
1
1
0
1
0
0
3
0
1
1
0
0
1
1
0
0
2
2
2
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
2
0
4
0
0
2
0
2
1
0
2
1
0
0
1
1
0
0
0
1
0
0
0
0
2
0
0
1
2
0
1
0
1
0
2
2
0
0
0
0
0
2
2
0
0
2
0
0
0
0
3
0
1
0
0
0
0
0
2
0
1
2
0
0
0
1
2
2
1
0
0
0
0
1
0
2
1
1
0
1
1
0
2
0
0
0
0
3
2
0
1
0
1
0
0
0
0
0
0
0
0
1
1
1
1
2
0
0
1
0
1
2
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
2
1
1
0
0
0
0
1
0
0
0
0
0
0
2
2
1
2
0
0
2
0
1
1
2
0
0
0
0
0
1
0
0
0
1
2
1
2
1
0
0
2
2
0
0
0
1
0
2
0
0
0
0
0
0
0
1
1
0
0
0
1
0
2
0
0
2
1
2
0
0
1
2
1
0
2
0
1
0
1
1
0
1
0
4
0
0
0
0
2
0
0
0
0
0
0
5
1
0
0
0
2
2
3
0
2
0
0
0
0
1
0
0
1
0
0
0
1
2
0
1
1
0
3
0
0
1
2
1
2
2
1
2
2
0
2
2
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
2
0
0
1
3
2
2
1
0
0
0
1
0
0
1
0
2
0
2
2
1
0
2
0
2
0
2
1
1
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
1
0
0
2
0
2
0
0
0
1
0
1
0
2
0
2
1
2
0
0
0
1
2
0
0
2
0
2
1
0
0
1
0
0
0
0
2
0
0
2
0
0
2
3
0
0
2
0
1
1
0
2
1
1
2
0
2
0
2
2
0
0
1
2
0
0
2
0
2
0
0
1
0
0
0
2
0
1
0
0
0
0
0
1
3
4
0
1
1
2
0
0
1
1
2
0
2
0
3
0
0
0
2
1
0
2
2
0
0
0
0
0
2
0
2
0
0
0
2
0
1
1
0
0
1
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
1
2
0
0
0
0
0
1
0
1
0
0
3
0
2
0
0
0
2
0
1
0
1
1
0
0
0
0
0
1
0
0
1
0
0
2
1
0
0
0
0
0
2
2
2
2
0
0
0
0
2
0
1
0
0
2
0
0
1
2
0
0
1
0
1
1
2
0
0
0
0
1
2
1
0
1
0
2
1
0
0
0
1
2
1
0
0
1
0
4
0
2
2
0
0
1
0
0
0
2
2
0
1
1
2
1
0
0
1
2
0
1
0
2
1
0
0
0
1
1
1
1
2
1
3
2
0
2
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
2
2
1
0
0
1
0
1
0
1
0
0
0
1
0
0
0
2
0
2
0
3
0
0
0
0
1
1
0
1
2
2
2
2
2
1
0
2
0
0
0
2
0
3
0
0
2
0
2
0
2
1
0
0
0
2
8
0
0
1
0
0
0
0
2
0
0
1
0
2
0
1
2
0
0
1
0
0
0
1
1
0
0
1
1
1
1
0
2
0
0
1
0
0
0
0
0
2
0
1
1
2
0
0
2
1
0
1
1
1
1
0
0
0
1
0
1
0
2
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
1
0
0
1
2
1
1
0
1
2
2
0
0
1
2
2
0
0
1
0
0
2
0
1
2
0
0
0
2
0
0
0
2
0
0
1
1
0
1
0
0
0
1
2
2
0
0
2
0
3
2
0
0
2
1
3
1
0
1
0
1
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
1
0
0
2
0
1
0
0
2
1
0
0
2
2
1
2
0
1
0
0
2
0
2
0
2
0
0
2
1
0
2
1
1
3
1
0
1
0
2
0
1
0
1
0
0
0
0
1
0
0
2
0
1
1
2
0
0
0
0
0
0
0
2
0
2
0
0
1
0
1
1
1
1
0
0
1
0
2
0
0
0
1
0
0
0
11
0
0
0
0
1
0
0
1
1
1
2
0
0
1
1
2
0
1
0
2
0
0
0
1
1
1
0
0
0
1
1
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
2
0
0
1
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
3
0
1
2
0
0
1
0
0
0
2
0
1
1
0
1
2
0
2
2
0
2
1
2
1
0
2
0
2
0
0
1
1
2
0
0
2
0
0
0
0
0
2
0
0
0
2
1
0
0
1
0
1
0
0
0
3
1
0
0
0
1
1
1
0
1
0
1
2
0
0
2
1
0
2
1
0
0
2
2
2
1
1
1
0
0
0
0
2
0
0
0
0
2
0
1
2
2
0
1
0
1
0
0
0
0
1
0
0
2
0
1
0
0
1
3
0
1
1
1
0
0
0
0
0
2
0
0
1
0
0
0
0
1
2
0
1
2
2
1
0
1
0
1
2
0
0
0
1
3
0
0
1
1
0
0
0
1
0
0
0
0
2
0
1
1
0
0
1
0
0
1
2
2
0
0
1
0
1
2
0
0
0
0
0
0
2
0
2
0
0
1
1
0
7
0
1
0
0
0
0
2
0
1
2
1
0
0
0
0
0
0
0
4
0
2
2
1
1
2
2
3
1
2
1
0
1
0
0
2
2
0
3
2
0
0
0
0
0
1
0
1
1
2
2
2
0
0
0
1
2
1
2
0
2
2
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
2
0
1
1
0
2
0
0
0
0
1
0
1
1
2
0
1
0
1
1
0
0
2
2
1
0
1
0
0
2
4
0
2
0
0
2
0
0
1
0
1
1
2
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
2
0
0
2
1
0
1
0
0
0
2
0
1
1
0
2
2
2
1
0
0
2
0
1
1
0
1
0
1
1
0
0
0
0
0
0
0
1
2
2
0
1
0
0
0
0
0
1
0
2
0
0
1
0
0
0
2
2
1
2
2
2
0
0
1
0
2
2
0
0
0
1
1
0
1
0
0
1
0
2
0
1
0
0
1
1
0
0
1
0
2
1
2
1
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
1
1
1
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
2
1
3
0
0
0
3
0
3
0
0
0
2
0
0
0
0
1
1
1
0
3
0
0
1
0
1
0
0
0
0
1
1
1
0
0
0
1
0
1
0
0
0
0
1
0
2
2
0
0
0
0
1
0
2
1
6
0
0
1
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
2
0
1
0
1
0
0
0
0
2
0
0
2
1
0
1
0
1
0
1
0
0
0
3
1
0
0
2
1
0
1
0
1
0
4
2
0
0
2
0
7
4
5
0
0
2
2
0
0
0
0
0
0
0
2
1
0
0
1
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
1
0
2
1
0
1
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
1
2
2
0
2
0
2
1
0
0
0
1
0
0
0
1
1
0
1
0
2
0
2
0
0
2
2
0
0
2
0
0
0
1
1
1
0
0
0
0
0
2
0
1
0
0
1
0
1
0
1
0
1
0
1
2
0
0
2
0
0
0
0
1
3
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
5
1
1
0
0
1
0
0
2
2
0
0
1
0
1
2
2
1
0
0
1
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
1
0
1
1
1
0
0
0
2
0
0
0
0
2
2
0
2
1
1
0
1
1
0
1
0
0
0
1
2
1
1
2
2
1
0
2
0
0
0
2
0
2
2
0
4
1
0
1
0
1
1
0
0
2
0
0
2
1
0
0
2
0
2
0
2
0
0
2
0
5
0
0
0
0
1
1
0
0
2
0
6
1
2
2
0
2
0
0
0
0
2
0
1
0
1
0
1
2
1
2
1
1
0
0
2
0
0
1
1
0
1
2
2
0
0
2
0
0
1
1
1
1
0
0
0
0
2
0
1
1
0
0
0
0
0
0
2
2
1
0
1
0
2
1
0
0
0
2
2
0
0
2
0
2
1
0
1
2
2
0
2
1
0
0
0
0
1
0
0
2
0
1
0
0
2
0
0
1
0
2
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
3
2
2
0
2
0
1
0
0
0
0
0
0
0
0
0
5
1
2
0
0
0
0
2
0
0
0
0
2
0
0
1
0
1
1
1
2
0
0
0
1
0
0
2
1
1
1
1
1
0
0
0
1
0
0
0
2
2
0
1
0
0
2
0
2
0
0
0
0
1
0
1
1
0
0
1
0
1
0
0
0
0
1
1
1
0
1
0
0
0
2
0
0
0
1
1
1
2
1
1
0
2
2
0
0
0
0
0
1
0
0
2
2
1
1
1
0
1
0
0
1
2
1
0
0
0
2
0
1
1
0
1
1
2
1
0
1
0
0
1
0
0
2
0
2
1
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
2
1
0
0
1
0
1
1
0
2
0
2
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
6
2
1
2
1
0
1
0
1
1
0
1
0
0
1
4
0
0
0
0
0
2
1
2
2
0
0
0
1
2
0
2
2
1
1
0
0
1
2
0
0
2
0
0
0
0
0
0
1
1
0
0
1
0
0
3
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
3
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
2
0
1
2
0
2
2
1
0
0
0
1
0
0
0
0
2
0
1
1
0
2
1
0
0
0
1
0
3
0
0
0
0
2
0
2
0
1
0
0
0
0
0
1
0
2
2
0
0
2
1
2
2
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
3
0
2
0
0
0
2
0
2
0
0
0
1
0
2
2
2
0
0
2
0
0
0
0
1
4
0
3
0
2
0
0
0
0
0
0
0
0
1
2
1
2
0
0
2
0
1
1
1
0
4
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
2
1
0
2
0
1
0
0
0
0
0
2
0
0
2
0
0
1
1
0
4
1
0
0
1
1
2
1
1
0
1
0
2
2
0
0
0
4
1
0
1
0
1
2
0
1
0
1
0
0
2
1
1
0
2
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
2
2
1
1
5
2
2
0
0
0
0
0
0
1
0
3
0
0
2
2
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
2
1
0
0
0
1
2
0
1
0
0
0
0
0
0
1
1
0
1
0
1
2
2
0
0
0
0
0
0
2
0
0
1
0
0
1
1
1
0
3
0
0
1
1
1
0
0
0
1
0
0
2
0
1
0
1
0
0
2
2
0
0
1
0
2
2
1
2
0
0
0
0
1
2
0
0
2
2
3
0
0
1
0
0
0
2
2
2
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
3
0
1
0
0
1
0
0
0
0
3
0
0
0
2
0
1
1
0
2
0
1
1
1
0
0
2
0
0
0
0
0
1
0
0
2
2
0
0
0
1
0
0
0
1
0
0
1
2
0
2
1
2
0
0
0
2
1
3
0
2
0
2
0
1
1
0
0
1
2
1
1
1
2
2
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
1
1
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
1
0
0
1
1
0
2
0
0
2
1
0
0
0
1
0
1
1
0
1
0
1
0
0
1
0
0
0
0
0
2
1
2
0
0
2
0
0
1
2
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
1
1
2
0
0
1
0
0
0
1
1
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
1
1
0
2
0
0
0
1
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
2
2
0
0
1
2
0
0
3
0
0
0
2
0
1
0
2
0
0
1
0
0
1
1
0
2
1
0
0
0
1
0
0
0
1
0
2
0
2
0
0
0
0
1
0
0
2
0
2
1
0
1
0
1
2
2
0
0
2
0
0
0
0
1
0
1
1
3
1
0
0
0
0
0
0
0
0
0
1
1
1
2
0
1
2
0
2
1
2
2
1
0
0
0
0
1
0
1
0
0
0
0
1
2
0
0
2
1
0
0
1
0
0
2
0
2
2
0
2
0
0
0
0
0
0
0
2
0
1
1
0
0
0
1
0
0
0
1
0
2
5
0
0
0
1
0
2
0
0
0
0
0
0
2
0
1
0
0
1
0
0
1
1
0
1
2
2
0
2
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
2
2
2
0
0
0
0
0
0
1
0
0
1
2
1
0
0
0
0
0
0
3
2
1
0
0
0
0
1
0
2
1
0
0
1
0
0
1
0
0
1
0
0
0
2
0
0
2
0
0
1
2
0
0
2
1
1
1
0
0
1
2
1
0
0
0
0
0
0
0
1
2
1
0
1
2
0
0
0
0
0
0
2
1
1
1
0
1
0
1
2
0
2
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
1
1
2
0
0
0
0
0
0
0
0
2
1
2
1
1
0
0
0
0
1
0
2
0
0
2
1
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
1
0
0
1
2
0
1
1
1
0
2
2
0
1
2
2
1
1
0
0
2
1
0
1
0
1
0
2
2
1
1
0
1
0
0
0
0
2
0
2
0
0
1
1
0
0
5
2
0
0
1
0
1
1
0
2
2
1
0
0
0
1
2
0
0
0
0
1
1
1
0
0
2
1
3
1
0
2
2
0
1
0
2
0
0
0
0
2
2
0
2
0
0
0
0
1
0
2
0
2
0
0
1
0
2
0
1
1
0
1
1
2
2
1
0
0
0
2
0
1
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
2
3
0
0
0
0
0
0
3
0
1
0
0
0
1
0
0
1
0
0
2
1
1
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
1
2
0
1
0
2
2
0
2
2
1
0
1
0
0
0
0
1
1
0
11
0
0
0
0
0
0
2
1
1
0
2
0
0
2
1
0
0
0
1
1
0
1
0
1
1
0
0
0
2
1
1
0
0
0
0
1
0
0
1
1
1
0
1
1
0
2
1
2
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
1
1
1
1
1
0
1
3
0
0
2
0
0
1
0
0
1
1
0
0
0
2
5
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
1
1
3
1
1
0
0
1
0
0
0
0
2
2
0
0
0
0
1
1
0
2
0
1
1
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
3
2
0
0
1
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
1
0
0
1
1
0
0
1
0
1
0
1
0
0
0
0
1
1
1
2
1
2
0
0
1
0
0
2
1
0
0
1
1
2
2
4
0
1
0
0
0
0
2
0
2
0
2
0
0
1
0
3
0
1
2
0
1
2
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
2
1
1
0
0
1
0
0
2
0
1
0
1
0
2
0
0
1
2
0
0
0
0
2
0
0
3
1
1
0
0
0
1
0
2
1
0
1
0
1
3
0
1
2
0
2
0
1
1
2
2
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
1
2
2
0
2
0
1
0
1
2
3
1
0
1
3
2
1
1
0
0
1
2
0
0
0
0
0
1
1
0
0
0
0
2
4
0
1
1
0
2
2
0
0
2
0
0
1
0
1
0
0
4
0
0
0
2
0
1
1
0
0
1
2
0
1
0
2
0
0
0
0
0
0
1
2
0
2
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
1
0
0
1
1
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
3
0
1
2
2
0
0
1
0
0
2
0
0
0
0
1
2
0
0
2
0
0
10
0
1
1
0
0
0
0
2
1
1
0
0
0
0
1
1
3
0
1
0
0
0
0
0
0
1
0
0
2
0
1
0
1
1
1
0
0
0
1
2
3
1
0
2
0
2
0
0
2
1
0
0
2
2
0
0
0
1
1
0
3
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
5
0
1
1
0
2
0
1
0
0
2
0
0
2
2
1
0
0
0
0
1
2
2
0
0
2
0
1
1
1
0
2
0
2
0
0
1
0
1
2
1
0
1
0
3
0
0
2
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
2
1
0
1
0
2
0
0
0
0
0
1
1
1
3
0
0
0
2
0
0
2
0
0
0
1
0
1
2
0
0
0
1
0
2
0
0
2
2
0
0
1
2
0
1
0
0
0
0
0
0
2
0
0
0
1
2
1
0
0
3
2
1
2
1
0
0
0
0
1
0
0
1
0
1
1
1
2
0
2
1
0
1
2
0
0
1
2
0
1
1
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
1
0
1
1
0
0
2
0
0
2
0
0
0
0
0
0
0
1
1
1
0
0
0
0
2
0
0
1
0
0
0
1
1
0
0
0
0
3
0
2
0
0
0
1
1
0
0
0
0
0
1
0
2
0
1
0
1
0
2
1
0
0
0
1
3
0
0
0
0
1
0
0
0
0
0
4
2
0
2
1
0
0
0
0
3
2
1
0
0
0
2
1
0
1
0
1
0
1
2
1
0
0
0
0
2
0
2
0
0
3
0
0
0
0
0
0
0
1
1
2
0
1
0
2
1
2
1
0
3
2
0
0
0
0
2
1
0
0
0
1
0
0
0
1
2
0
1
0
0
1
0
0
0
1
0
2
2
2
0
0
1
1
1
0
1
2
2
0
0
0
2
0
2
4
2
2
2
0
1
2
1
0
0
0
0
0
2
2
1
0
0
1
1
1
6
0
0
0
0
1
0
0
0
0
0
1
0
2
0
1
0
1
2
0
0
0
2
2
0
0
1
1
0
0
0
2
2
2
1
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
2
0
0
2
1
2
0
2
1
1
0
0
2
7
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
1
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
11
1
0
0
0
0
2
0
0
2
1
0
0
0
0
0
1
1
0
1
0
0
1
0
1
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
3
2
1
0
2
0
0
0
1
0
2
0
1
0
1
1
2
0
0
2
0
1
0
0
0
3
2
1
0
0
0
1
0
2
2
2
1
1
0
0
0
0
1
0
0
2
0
1
2
0
1
0
0
0
0
1
0
2
1
0
2
1
0
0
0
0
1
2
1
0
0
2
2
8
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
1
1
0
1
1
1
0
0
0
0
2
4
1
0
0
0
0
2
0
1
0
1
0
0
0
1
2
2
1
1
2
2
2
0
0
2
1
0
0
2
1
1
0
1
0
1
0
2
0
0
2
2
3
2
1
0
0
0
0
0
0
0
1
0
1
1
0
1
2
0
0
1
1
1
1
0
0
2
1
3
2
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
2
1
1
0
1
0
1
2
2
1
1
0
0
0
1
0
0
0
0
1
0
2
1
0
1
1
0
1
0
2
2
0
0
0
0
0
2
0
0
1
1
0
1
1
0
0
0
0
1
1
2
1
0
0
0
2
0
0
1
0
3
0
2
1
2
1
0
1
0
2
0
1
0
1
0
0
2
1
0
2
0
0
1
0
0
0
2
0
0
0
1
1
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
1
1
0
0
2
0
0
1
0
2
1
0
0
0
1
0
0
1
1
2
1
2
2
0
0
1
0
0
2
0
1
0
0
1
0
1
2
0
0
0
2
0
1
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
2
0
0
0
4
0
2
1
0
0
1
0
2
3
2
0
2
0
0
0
1
0
0
0
0
0
1
0
0
2
2
2
0
1
0
0
0
1
3
0
1
0
0
0
2
2
0
0
0
0
0
2
3
2
0
0
4
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
4
0
2
0
0
2
0
3
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
1
0
2
2
2
0
0
0
2
0
0
0
0
2
0
4
0
0
1
2
2
0
2
1
0
1
0
2
2
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
1
0
4
0
0
0
1
0
0
0
0
1
0
0
1
0
2
0
1
0
0
0
1
2
0
2
0
0
2
0
2
2
0
1
0
0
2
1
1
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
1
1
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
3
2
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
1
1
1
2
0
0
1
0
1
3
0
0
0
0
1
3
0
0
0
0
0
2
0
1
1
2
0
0
0
0
0
1
0
0
2
0
2
1
0
2
1
1
0
1
1
0
1
0
0
1
2
0
0
1
0
2
0
1
0
2
0
0
1
0
0
1
2
0
0
0
0
1
3
4
2
0
0
1
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
1
0
2
2
2
0
0
2
1
2
1
2
0
2
1
2
0
2
0
0
1
1
1
1
0
2
0
0
1
1
0
0
0
0
1
2
0
0
0
2
0
2
2
0
2
1
0
2
0
0
2
2
0
0
0
0
0
1
1
0
0
0
0
0
2
0
2
0
0
2
0
0
2
0
1
0
0
1
1
0
0
1
2
0
0
0
1
0
1
0
0
0
0
2
0
0
1
1
0
1
1
1
1
0
1
2
0
0
0
0
0
1
0
1
1
2
1
2
2
0
2
1
0
2
1
1
0
0
1
0
0
0
1
1
0
1
2
2
0
2
0
0
0
0
1
0
0
1
0
0
3
0
0
0
2
1
2
0
2
0
0
0
1
0
0
0
2
2
0
0
0
2
1
0
0
0
2
0
4
0
0
2
0
0
2
0
2
0
1
0
1
0
1
0
2
0
1
0
0
0
1
2
0
2
1
0
1
2
3
2
0
0
0
0
0
1
1
2
0
0
0
1
0
0
0
0
0
2
0
1
2
0
0
1
0
0
2
0
1
0
0
1
0
1
0
2
5
1
0
0
0
0
2
1
1
0
0
1
0
2
0
2
0
1
0
2
0
0
0
0
0
0
0
0
1
0
2
1
2
0
0
0
1
0
1
1
2
0
0
0
2
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
1
0
0
0
2
1
0
0
0
0
0
0
1
0
0
2
2
0
0
2
0
0
1
1
1
2
1
2
0
1
1
0
1
1
1
0
0
1
0
1
2
0
0
0
1
0
1
1
1
0
0
2
1
1
0
0
0
2
1
0
0
1
1
0
1
0
1
0
2
0
2
4
0
1
0
0
0
0
0
0
1
2
0
0
0
1
2
2
0
0
1
2
0
2
1
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
1
0
0
0
0
0
2
2
1
2
1
1
2
1
0
0
0
0
2
0
1
0
0
0
1
0
0
3
0
2
1
1
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
1
0
0
2
1
0
0
1
0
0
2
0
0
1
2
1
1
1
1
0
2
0
0
0
0
1
2
1
2
1
0
0
3
0
0
0
1
0
2
2
1
1
2
1
1
2
1
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
2
0
0
1
1
2
0
0
2
0
0
2
0
0
0
2
0
2
1
0
0
0
2
1
0
0
0
0
1
3
0
2
0
0
2
0
1
0
0
1
0
0
0
0
1
0
2
0
2
0
0
1
0
0
0
1
1
1
1
0
0
1
2
3
2
0
2
1
1
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
1
1
0
0
1
0
1
1
0
0
0
0
0
0
2
0
0
0
1
2
1
0
2
2
0
0
0
0
1
1
0
0
1
1
0
1
1
0
0
0
0
2
1
0
0
0
1
1
0
1
0
0
0
1
0
2
0
2
0
0
1
1
0
1
1
0
1
0
0
1
0
0
0
1
0
0
2
1
0
0
1
2
0
4
1
2
1
0
0
0
0
1
0
0
0
1
2
0
2
0
0
1
0
0
1
0
0
2
0
2
2
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
1
0
0
0
2
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
3
1
0
0
2
0
2
2
0
0
2
2
0
2
3
0
0
0
0
2
0
2
0
0
0
0
0
2
1
0
1
1
0
1
1
1
1
0
0
0
1
0
0
1
1
1
1
0
0
0
0
0
0
0
2
0
0
2
2
0
1
1
0
0
2
0
0
0
0
2
0
0
4
1
1
0
0
2
1
2
1
0
0
1
1
0
0
0
0
2
0
0
0
2
1
0
1
1
2
0
1
0
0
2
0
0
1
2
8
0
0
0
1
0
1
0
1
0
0
0
1
0
0
1
0
1
1
0
1
0
0
0
2
2
0
0
2
0
0
1
1
0
1
2
0
2
0
2
2
0
0
0
0
1
0
0
0
3
0
2
0
1
2
0
0
1
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
4
1
2
0
0
2
2
0
0
1
0
1
3
0
0
0
0
0
1
0
1
0
0
1
2
2
0
2
2
2
2
1
0
2
1
1
2
0
2
0
0
0
2
0
2
2
0
0
1
0
0
0
1
0
2
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
1
2
3
2
2
1
1
2
0
1
1
0
0
1
0
0
0
0
1
1
1
0
0
1
0
0
0
0
2
1
1
0
0
0
1
0
2
1
0
0
0
1
0
0
0
1
2
1
0
0
0
0
0
2
0
0
2
2
0
2
2
0
0
0
0
1
0
1
1
0
0
0
0
0
1
1
0
2
0
0
1
2
0
0
0
0
0
0
1
0
4
2
0
0
0
0
3
0
2
0
0
0
2
0
1
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
3
0
2
0
0
1
1
2
1
0
0
0
1
0
1
0
2
0
1
0
0
1
1
2
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
2
1
2
0
1
0
0
0
1
2
0
1
1
1
0
2
0
1
2
0
2
0
1
2
0
1
0
1
0
2
0
0
1
1
2
2
2
1
0
2
0
0
1
0
0
0
0
0
1
0
0
0
1
0
2
2
0
0
1
2
1
1
0
0
0
3
2
0
0
0
0
1
0
0
0
1
0
1
1
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
3
0
2
0
0
0
0
0
0
0
0
1
1
0
2
0
0
1
0
0
0
0
0
1
0
0
5
1
0
0
0
0
1
2
0
0
0
0
0
3
2
1
0
1
2
1
1
0
1
2
1
0
1
0
0
0
0
0
0
1
1
1
0
2
0
0
0
2
2
2
0
1
0
1
2
0
0
2
0
1
0
2
0
0
1
0
2
1
2
1
0
2
1
0
3
0
0
0
0
5
0
0
2
1
0
0
0
0
1
3
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
2
3
0
0
0
0
0
0
2
0
0
0
0
2
1
0
2
0
3
0
2
0
0
0
1
0
0
0
2
0
0
3
2
0
0
1
2
0
0
1
0
0
0
0
1
0
0
1
0
1
1
0
2
0
1
0
3
1
0
0
0
1
0
2
0
1
0
0
0
0
0
2
0
2
1
0
1
0
1
1
0
2
1
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
1
2
0
1
1
0
1
0
2
2
1
4
0
0
0
0
0
0
0
1
1
2
2
1
2
1
0
2
0
1
0
0
1
2
0
0
1
1
0
0
0
0
2
0
1
1
0
0
2
0
1
1
0
0
1
0
0
2
0
2
2
1
1
0
1
0
0
1
2
0
0
1
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
1
0
4
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
1
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
1
2
2
0
1
0
0
0
0
0
0
1
4
1
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
2
0
0
1
2
0
0
2
1
0
0
0
0
0
0
3
0
1
1
1
1
1
0
0
0
1
2
0
1
1
0
1
0
3
0
0
0
1
0
0
1
0
2
1
1
2
0
0
0
1
1
1
0
0
0
0
2
1
0
2
1
0
0
3
0
0
0
1
0
1
0
1
0
1
6
0
0
0
2
4
2
1
0
1
0
0
1
0
0
0
2
0
0
0
0
0
1
0
1
2
1
0
0
1
2
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
1
1
0
2
0
1
2
0
1
0
0
1
1
1
0
0
2
2
1
0
1
0
0
0
1
0
1
0
0
1
0
2
0
2
0
0
1
0
0
2
0
2
1
1
1
0
2
4
1
0
0
0
2
0
1
0
2
0
2
2
0
0
0
3
0
1
2
0
1
0
1
0
0
0
2
1
1
2
0
0
1
2
1
1
0
0
0
2
0
1
2
0
0
0
2
2
1
2
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
2
0
1
1
1
0
0
0
1
2
2
0
2
0
0
1
0
2
0
0
2
1
0
0
0
1
1
2
0
0
0
2
3
0
0
0
0
0
2
0
0
1
0
1
1
0
0
2
3
0
0
0
0
0
3
0
1
2
0
1
2
3
0
0
0
2
0
0
0
2
0
1
0
1
0
0
0
0
2
1
1
0
1
0
0
0
1
0
0
1
1
1
0
0
0
1
2
0
0
1
0
0
1
0
1
1
2
0
1
0
2
0
0
2
0
0
1
0
0
1
0
1
0
0
0
0
0
2
1
0
1
0
2
1
0
1
1
2
0
2
0
0
0
0
2
2
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
2
0
0
1
2
1
1
1
2
1
2
0
0
2
2
1
0
0
5
1
0
0
1
0
0
1
0
0
1
0
0
0
1
2
0
2
3
1
2
2
0
2
0
1
2
0
1
1
0
0
0
0
1
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
1
0
1
0
1
0
1
0
0
0
2
0
2
3
2
0
2
0
0
0
1
0
0
0
0
1
0
0
1
2
0
1
0
0
0
1
2
1
1
1
2
1
0
0
0
0
0
0
0
2
0
1
1
3
0
0
0
0
2
0
0
1
2
2
0
2
1
1
0
0
0
0
0
0
0
0
2
1
0
0
0
2
1
0
0
2
0
0
2
0
0
3
2
0
1
2
1
0
1
0
0
0
1
0
0
1
1
1
2
0
0
1
0
1
0
0
2
0
0
1
1
0
1
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
4
0
1
0
2
0
2
0
2
2
0
2
0
2
2
0
2
1
0
2
0
3
1
0
2
0
0
2
0
0
0
0
0
0
6
0
0
0
1
1
1
1
0
1
1
0
0
0
1
0
0
2
0
2
0
2
0
2
1
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
1
0
1
0
2
0
0
2
0
1
2
1
0
2
0
1
2
0
0
0
0
0
2
0
0
2
1
3
0
2
0
0
0
1
0
1
2
1
3
0
1
0
1
0
0
0
0
0
0
0
4
0
0
0
3
0
0
0
2
2
2
0
0
1
2
0
1
1
0
2
0
0
2
2
1
0
1
0
0
0
0
0
0
1
1
1
4
2
0
0
0
1
1
0
2
0
1
0
1
0
0
0
1
1
0
0
0
2
1
0
2
2
2
0
1
1
0
4
3
0
1
0
2
2
1
2
3
0
0
0
0
0
2
0
0
0
2
1
2
1
0
1
0
2
1
0
0
2
0
0
0
0
1
1
1
0
0
2
1
1
1
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
1
0
0
1
2
0
1
0
1
0
1
1
0
0
0
1
1
2
0
1
0
0
2
1
0
0
2
0
1
0
1
2
0
2
0
0
1
2
0
1
2
1
0
1
0
0
0
1
0
0
0
1
0
0
1
1
0
0
5
1
2
0
0
1
0
2
0
0
0
2
1
1
0
2
1
2
0
0
1
2
0
0
0
2
1
0
0
0
0
0
2
0
0
0
3
2
0
0
0
2
2
1
0
1
1
0
1
1
0
2
2
0
2
2
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
2
2
1
0
0
0
2
0
1
0
1
0
1
0
2
0
2
2
0
0
2
0
1
1
2
0
0
2
0
0
2
2
2
0
0
0
0
0
1
1
0
0
0
0
0
1
2
0
0
0
1
1
1
2
1
0
2
0
3
2
0
0
0
0
0
1
1
0
1
2
0
2
1
0
0
2
0
1
2
0
0
2
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
1
1
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
3
0
0
2
0
0
1
0
1
0
1
1
0
1
2
0
0
1
0
1
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
3
3
0
1
0
0
0
4
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
2
1
1
3
2
1
2
0
2
0
0
1
0
1
0
0
0
1
1
0
0
3
0
1
1
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
2
0
1
0
0
2
1
0
1
1
0
0
2
2
1
1
0
2
0
8
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
2
0
0
1
0
0
1
2
0
0
2
0
1
1
1
2
0
0
0
5
1
0
2
3
0
0
0
1
2
2
0
0
0
2
0
0
0
1
1
2
2
0
2
0
0
1
0
0
2
0
1
1
2
0
2
0
3
1
0
0
0
2
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
1
0
0
0
2
0
0
3
1
0
1
1
3
0
1
0
2
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
1
1
0
2
2
1
1
0
0
0
0
0
2
1
2
1
0
2
0
0
1
0
0
1
0
3
1
0
0
0
0
0
1
2
2
2
1
0
0
1
0
2
1
0
0
0
0
1
0
2
0
0
1
2
0
0
2
0
0
0
0
2
0
2
1
2
0
1
2
0
0
2
0
2
3
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
2
1
0
0
1
0
0
0
2
0
0
2
1
0
0
2
0
0
2
0
0
0
0
0
0
1
2
0
1
0
2
1
0
2
0
0
0
2
2
0
0
0
0
1
2
2
1
1
0
0
0
2
1
0
0
2
0
0
0
0
2
0
0
0
3
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
2
1
4
0
0
0
2
0
0
2
0
1
0
0
0
0
2
0
0
2
1
0
1
0
0
0
0
0
1
0
0
0
1
2
0
3
1
1
2
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
1
0
2
1
0
0
1
0
0
0
1
1
2
1
2
0
1
0
0
0
0
1
0
2
1
0
0
1
1
0
1
0
0
0
1
1
1
0
1
2
0
0
2
1
0
1
1
1
0
0
1
0
2
0
0
0
2
0
0
3
0
0
0
1
0
0
2
1
0
1
1
2
0
0
0
1
1
0
2
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
1
2
0
0
1
0
2
2
0
2
1
2
0
0
2
1
0
1
1
2
2
0
1
2
0
1
0
0
3
3
1
2
1
1
0
0
0
2
2
1
0
0
1
0
2
1
1
2
1
0
0
2
0
0
1
0
0
2
0
2
0
3
0
2
0
2
0
0
0
2
1
0
0
0
1
1
0
2
1
0
0
0
0
2
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
2
0
0
0
0
0
1
1
0
1
2
2
1
0
0
2
2
1
1
1
0
0
0
0
0
1
0
1
0
0
1
0
0
2
0
0
2
0
2
0
1
0
0
0
3
1
0
0
1
0
2
0
2
2
0
0
0
2
1
0
0
0
6
0
1
0
3
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
1
2
1
0
2
0
0
2
1
2
1
2
1
0
1
0
0
0
0
0
2
0
0
0
0
2
2
0
0
2
0
0
0
0
2
0
0
1
2
0
1
5
0
0
0
0
0
1
3
0
0
1
2
0
1
0
2
0
0
0
0
0
0
1
0
0
2
0
0
1
0
1
0
2
1
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
2
0
0
1
1
0
2
0
0
1
2
0
1
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
1
0
0
2
3
1
0
3
0
0
2
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
2
0
0
0
0
2
1
0
0
2
2
1
2
0
2
2
2
2
0
0
2
0
2
0
2
0
1
0
0
1
2
0
0
1
0
0
3
1
0
0
1
0
1
2
0
0
0
2
1
0
0
0
0
1
0
0
0
0
1
2
0
2
1
0
1
0
1
0
0
0
1
0
2
0
0
0
2
1
0
2
0
1
0
0
0
0
0
1
2
2
0
2
0
5
0
0
1
0
4
1
0
0
0
0
0
1
0
0
0
1
2
0
1
0
1
0
1
2
1
1
2
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
2
1
0
1
0
1
0
2
0
0
0
3
0
0
2
0
0
0
0
0
1
0
2
1
0
0
0
2
1
0
2
0
2
1
0
0
0
1
0
2
0
0
0
3
1
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
1
4
2
0
0
0
0
0
1
1
0
1
3
0
0
0
0
1
0
0
0
0
2
2
2
1
0
4
0
1
0
0
1
2
0
2
1
2
0
0
5
0
0
0
0
0
0
0
3
0
0
2
0
0
0
1
2
2
2
0
5
0
4
0
2
0
0
0
1
0
2
0
2
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
1
0
1
0
0
1
0
1
1
0
0
2
0
1
1
2
0
0
0
1
0
0
0
2
0
0
2
2
1
0
0
0
0
1
0
2
2
3
1
0
1
0
1
2
2
0
1
1
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
1
0
1
0
0
0
1
1
0
1
2
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
1
1
1
2
0
1
0
2
0
0
0
1
1
0
1
0
0
2
0
0
2
2
0
2
0
2
0
2
0
0
0
0
1
0
0
2
1
0
0
1
2
0
1
1
1
0
2
1
1
0
1
0
1
0
0
1
1
3
0
0
2
0
0
2
0
1
0
3
0
0
1
0
0
1
0
1
2
0
2
0
0
0
2
0
1
0
1
0
1
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
1
0
2
2
2
0
1
0
2
0
0
0
0
2
1
0
0
2
1
1
0
1
0
2
0
2
2
0
1
0
0
1
2
1
0
2
0
0
0
0
0
0
0
0
0
2
0
1
1
0
14
0
0
0
3
1
0
0
0
0
0
2
1
2
0
1
0
1
0
0
1
0
0
1
2
1
0
0
2
2
0
0
0
2
2
0
0
3
1
1
2
1
1
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
3
1
0
2
1
0
0
2
0
0
2
0
0
2
2
0
1
0
4
0
0
0
1
0
2
0
0
0
0
2
1
0
0
2
2
2
0
0
0
1
1
2
2
0
0
2
2
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
1
2
0
1
1
2
0
0
0
0
2
1
1
0
0
0
0
0
0
1
0
0
0
0
1
2
0
1
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
1
2
0
0
2
0
0
1
1
0
0
1
0
2
0
0
2
2
0
0
2
2
0
1
0
0
2
0
0
1
2
0
0
0
1
2
0
1
0
0
1
0
1
2
0
2
0
0
1
1
0
0
0
0
0
1
1
2
0
2
1
2
0
0
0
1
1
1
2
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
1
2
0
0
0
0
0
2
0
0
2
0
1
2
0
0
0
1
0
0
1
2
1
3
2
0
0
0
0
1
2
2
0
2
0
0
2
0
1
0
0
0
0
0
0
2
1
1
0
0
0
0
0
1
0
0
1
0
1
0
0
1
1
2
0
2
0
1
0
2
1
0
1
2
0
0
3
0
1
1
1
1
0
2
0
0
0
0
1
5
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
2
0
0
0
0
2
1
0
0
0
1
0
0
1
1
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
2
0
0
0
1
0
0
1
2
2
0
0
0
0
0
0
0
1
2
1
1
3
2
2
0
0
4
0
0
1
0
0
0
3
0
0
2
0
0
0
0
0
1
1
0
0
1
0
0
1
0
2
0
0
2
1
1
0
0
1
0
2
0
2
2
0
0
1
1
0
0
0
0
2
2
0
0
0
0
0
2
0
0
1
1
1
0
0
0
0
2
2
0
2
0
0
2
0
2
0
1
2
0
1
2
2
1
0
0
0
2
2
0
2
2
2
1
2
0
0
0
2
1
1
1
0
0
2
1
0
0
1
1
0
2
2
0
2
0
2
0
2
0
0
1
0
0
1
0
1
0
2
0
0
0
1
0
1
0
0
1
2
0
2
2
1
1
0
0
0
0
0
1
0
2
2
1
0
0
1
0
2
0
2
1
1
0
0
2
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
3
0
0
2
0
1
0
1
0
0
0
0
0
0
1
0
0
1
1
2
1
2
1
0
2
2
0
2
2
1
0
0
1
0
1
0
2
1
2
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
2
0
1
0
0
2
0
1
1
0
1
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
2
1
0
0
0
0
0
0
0
0
2
2
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
2
1
1
1
0
0
2
0
3
1
0
0
2
0
0
0
2
0
2
2
0
1
2
2
2
0
1
0
0
2
0
0
0
2
2
0
2
2
2
0
3
0
0
0
0
1
2
0
0
1
1
1
1
0
0
3
0
1
0
2
2
0
2
0
0
0
0
1
1
0
0
2
0
3
2
0
1
2
0
1
1
0
2
0
2
0
0
0
1
0
1
1
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
2
1
1
1
2
0
0
0
0
0
0
2
1
0
1
0
0
2
3
1
0
0
0
0
1
0
2
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
2
2
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
1
0
2
0
1
2
1
1
2
8
0
2
0
0
2
0
0
0
1
1
0
1
0
1
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
2
0
0
2
2
0
2
0
0
1
0
1
1
0
0
2
1
0
0
0
1
0
1
1
2
2
1
0
0
2
0
0
1
0
2
1
2
0
0
0
0
0
1
1
0
1
1
1
0
0
0
1
0
0
2
0
0
1
3
0
0
0
1
0
2
0
0
1
2
1
0
0
0
1
0
1
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
1
2
1
1
0
2
0
5
0
0
0
0
4
0
0
0
2
0
0
0
1
2
0
2
2
1
1
0
0
3
1
0
0
0
0
0
1
0
0
0
0
1
1
0
1
1
0
0
0
0
0
2
0
0
0
0
0
2
0
1
1
0
0
0
1
1
0
0
2
0
0
0
0
0
3
0
0
0
0
2
0
2
3
1
0
0
0
0
1
0
2
0
1
0
0
0
0
1
0
0
1
0
2
0
4
0
0
2
0
1
0
0
0
2
0
1
1
0
2
0
1
0
0
0
1
0
0
2
0
2
1
1
0
0
0
0
0
0
2
1
0
0
0
0
0
2
1
0
2
0
2
2
2
0
0
0
0
0
0
2
0
0
0
5
0
2
0
1
1
1
1
1
3
0
2
1
0
0
0
0
2
2
0
1
3
0
1
0
1
0
1
0
2
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
1
2
0
5
6
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
2
0
0
2
2
1
0
1
1
2
0
0
0
0
2
1
0
0
1
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
1
0
0
1
0
1
1
0
2
0
0
0
0
1
0
0
1
1
0
2
0
1
0
2
0
0
0
1
0
1
0
2
0
1
2
0
1
1
1
0
1
1
2
0
0
1
1
1
0
0
1
0
0
0
2
1
2
1
0
0
0
0
0
0
0
0
0
1
1
0
0
3
0
0
0
1
0
2
0
0
0
1
2
0
1
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
1
0
0
2
0
0
0
2
2
0
0
0
0
0
2
0
1
0
0
0
2
0
1
0
1
1
2
2
0
0
1
0
0
1
1
0
0
1
0
0
1
0
0
0
0
3
0
1
0
1
4
2
5
0
1
0
0
2
0
0
2
2
1
0
1
2
2
0
0
0
0
1
0
0
0
2
2
1
0
1
1
1
1
2
0
0
0
2
2
0
0
1
1
1
2
1
1
2
3
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
2
1
0
2
0
0
2
2
0
0
2
0
0
2
0
1
1
0
2
0
0
0
1
1
1
1
0
2
0
1
0
0
1
0
0
1
0
1
1
0
1
4
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
1
0
1
0
0
0
1
2
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
2
0
0
0
1
2
1
1
1
0
0
0
0
0
0
1
2
1
2
0
0
1
0
2
1
0
2
2
0
1
2
3
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
1
0
1
0
0
0
0
1
1
0
2
0
0
2
0
0
0
0
2
0
3
1
0
0
0
0
0
0
1
0
0
1
1
0
0
1
1
1
0
1
0
2
1
0
0
2
0
0
0
0
0
2
0
1
0
0
2
0
2
2
2
0
0
0
2
2
1
1
0
0
2
2
0
2
0
0
0
1
0
0
0
2
0
0
2
0
2
1
0
0
0
0
2
0
2
0
0
0
1
2
0
1
0
0
1
0
1
2
3
2
0
0
0
2
0
0
0
0
2
0
1
1
0
0
0
1
1
0
0
0
2
0
2
0
0
0
0
2
1
1
1
1
1
0
0
0
2
1
2
0
0
0
1
0
1
1
0
1
0
2
1
0
0
2
1
1
0
1
2
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
3
1
2
0
0
0
0
3
3
0
1
0
1
2
0
1
0
2
0
2
0
3
0
1
0
1
0
0
1
2
0
0
2
1
1
0
0
0
0
0
1
3
0
0
0
2
1
0
0
0
1
1
0
0
0
2
2
0
1
0
2
0
1
1
1
1
0
2
0
1
1
0
0
2
2
0
1
0
2
0
0
0
0
2
0
0
0
0
2
0
2
2
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
3
2
0
1
2
1
0
1
2
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
2
0
0
2
0
1
0
0
0
0
0
2
2
5
0
0
0
2
0
0
0
2
0
2
1
0
0
0
1
0
0
0
2
2
0
1
2
2
0
1
2
0
0
0
0
0
0
1
1
1
2
0
2
0
2
2
1
0
0
1
0
1
2
0
0
0
0
1
0
2
0
0
1
0
0
2
2
0
1
0
3
1
1
2
0
2
2
2
1
1
1
0
2
0
0
0
0
0
0
2
0
2
0
3
2
2
1
0
1
0
1
2
0
0
3
1
0
0
2
0
1
0
3
0
0
1
0
1
1
0
1
0
0
2
0
1
0
0
2
1
2
1
0
0
2
0
0
0
2
1
1
1
0
0
0
0
2
2
2
0
2
0
1
0
0
3
0
1
1
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
2
0
1
1
0
0
0
0
2
2
0
0
1
1
0
0
4
1
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
1
0
0
0
0
2
1
0
0
0
1
0
2
1
0
0
1
0
2
0
1
0
1
1
1
0
0
0
1
0
0
1
0
2
0
0
0
1
0
1
0
0
2
1
1
0
2
1
0
1
2
0
0
0
1
0
1
1
2
0
1
0
0
2
0
1
0
0
0
1
0
0
0
0
2
0
1
0
0
0
1
1
1
2
1
0
0
2
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
1
0
1
0
2
2
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
1
1
0
1
0
1
0
0
2
0
0
0
2
2
0
0
0
0
1
0
0
1
0
1
2
2
0
0
0
1
1
2
0
0
2
1
2
0
1
0
0
2
2
1
1
3
0
2
0
0
2
2
1
0
1
1
0
1
0
2
0
0
0
0
0
0
0
2
0
1
0
2
0
1
2
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
3
0
0
0
0
2
3
0
0
0
0
2
0
0
0
2
2
1
0
1
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
2
1
1
0
2
0
0
1
0
1
0
0
2
4
2
0
0
0
0
1
0
2
1
2
2
0
0
2
0
0
2
0
1
1
2
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
1
2
3
0
0
0
1
0
2
0
0
1
1
2
0
0
0
0
0
0
2
0
0
0
0
0
2
2
1
0
1
2
1
0
0
0
2
0
0
0
2
1
0
13
0
0
1
0
0
0
0
0
0
1
2
1
1
0
0
0
1
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
1
0
1
2
0
0
0
1
1
0
2
0
0
0
0
0
1
0
0
2
1
0
0
0
2
1
1
0
0
0
0
1
0
1
1
0
1
2
0
0
0
1
0
3
0
0
0
1
0
0
2
0
0
2
0
1
1
1
1
0
0
0
0
2
1
0
2
1
2
0
1
2
1
1
2
1
0
0
1
0
0
0
0
0
0
0
2
1
1
1
0
1
0
0
0
0
2
0
0
2
2
2
0
2
2
0
1
1
1
0
1
1
1
0
0
0
1
1
1
1
2
1
0
0
1
1
0
0
0
2
0
1
3
0
0
2
0
0
1
1
0
1
0
1
0
1
1
0
0
1
0
0
0
0
1
2
2
2
2
2
0
0
0
1
2
2
1
0
0
0
0
1
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
1
1
0
0
0
0
2
0
1
3
0
1
1
0
0
1
0
0
0
0
4
2
0
2
0
0
1
2
1
1
0
0
0
1
0
0
3
0
2
0
0
0
0
3
0
1
0
3
0
2
4
0
0
0
0
2
2
0
1
2
1
0
0
2
1
0
3
3
1
0
0
0
0
0
0
0
2
0
1
4
2
2
1
0
0
0
0
0
0
1
2
0
0
1
0
0
0
1
1
1
0
0
2
0
0
0
2
0
0
0
2
0
2
0
0
7
0
0
2
1
0
1
0
2
1
0
1
0
0
2
0
2
2
0
7
1
0
0
0
2
0
0
0
1
0
0
0
1
2
1
0
1
0
1
2
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
3
0
3
0
0
2
0
0
0
0
0
1
0
1
1
2
2
1
2
0
1
2
0
0
1
0
0
0
0
0
2
2
2
0
0
0
2
2
2
0
0
1
0
0
0
0
0
2
0
1
0
1
0
0
1
1
0
2
2
0
2
1
0
0
2
0
0
0
1
0
0
0
0
1
1
0
0
0
1
2
1
1
0
0
0
0
0
1
0
0
0
1
0
2
0
0
2
1
0
0
2
0
0
0
1
1
2
2
1
1
0
0
0
0
0
1
1
0
2
2
2
0
0
0
2
0
0
2
2
1
0
0
0
0
0
2
0
0
0
0
1
2
0
0
2
0
1
0
2
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
1
0
0
2
0
1
2
0
0
0
0
3
0
0
0
0
1
2
3
1
1
0
0
0
0
0
0
1
0
2
1
1
1
0
2
1
1
0
0
1
1
0
2
0
0
1
0
2
0
0
0
0
2
0
0
1
0
1
0
1
0
0
2
1
0
2
0
1
0
0
1
0
1
2
1
0
0
2
0
0
3
1
0
0
0
0
2
0
1
1
2
2
0
0
0
0
0
0
1
0
1
1
0
0
2
0
2
2
0
0
3
0
0
0
1
2
0
0
1
1
1
1
1
0
0
2
0
1
0
1
0
1
0
0
2
0
0
0
1
1
0
2
0
1
0
0
0
0
1
1
0
1
0
7
0
0
1
1
0
0
2
0
0
1
2
0
1
1
2
1
0
0
0
0
0
2
1
0
0
0
0
0
1
0
1
0
0
0
0
1
1
1
0
2
2
0
2
0
0
1
0
1
0
0
0
0
0
0
0
2
2
0
0
1
2
2
1
1
0
0
2
3
1
0
0
0
0
0
0
0
1
0
2
1
0
0
0
2
0
0
1
0
2
0
0
0
0
1
0
0
1
0
1
0
1
2
0
0
0
0
0
2
1
1
0
2
2
0
0
0
1
1
1
0
0
0
2
0
1
0
0
2
0
0
0
0
1
2
0
0
2
2
0
2
2
0
0
0
0
2
2
0
0
0
0
3
0
1
0
0
0
4
0
2
0
0
1
1
0
1
0
3
2
1
0
2
2
2
1
2
0
2
1
0
0
1
0
2
2
1
1
0
1
0
2
2
0
1
2
0
0
4
1
2
2
0
0
0
2
2
0
0
0
0
0
0
0
1
2
1
0
2
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
1
0
1
2
0
0
0
1
0
0
1
1
1
0
1
2
1
0
1
0
0
1
0
0
1
2
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
2
1
0
0
0
0
1
0
0
0
0
2
0
1
1
0
2
0
1
2
0
0
1
0
0
1
0
0
3
0
2
0
0
0
1
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
1
1
0
1
2
1
2
0
0
1
0
0
0
0
1
0
2
1
0
2
1
0
1
2
0
1
1
2
0
0
1
1
1
0
0
0
0
1
1
0
0
0
2
2
0
0
1
1
0
0
1
0
2
1
1
1
2
2
0
0
0
2
0
2
0
1
0
0
1
2
2
1
0
1
0
6
1
2
1
0
2
0
1
0
0
0
2
1
2
0
0
2
1
2
2
2
0
2
0
0
2
0
1
2
1
2
0
0
1
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
3
5
2
1
1
0
0
0
1
0
1
0
2
0
2
0
2
0
2
0
0
0
2
2
0
1
2
0
3
0
0
0
0
0
0
2
0
0
0
1
1
1
1
2
1
0
0
0
0
1
0
0
0
1
2
1
0
0
0
2
2
0
0
1
0
1
2
0
2
0
0
3
1
1
1
2
2
0
1
0
2
0
0
0
1
0
0
0
1
2
0
0
1
2
0
0
1
1
1
0
0
1
0
2
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
1
0
0
2
0
3
2
1
1
0
0
1
0
0
1
0
0
0
0
0
1
2
0
0
0
2
2
1
0
0
1
0
2
0
0
0
1
1
0
0
0
0
0
1
0
1
0
1
1
2
0
1
1
0
2
0
1
2
2
2
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
1
2
0
0
0
2
0
1
0
1
0
0
0
0
0
2
2
0
0
0
0
0
1
0
2
0
0
1
0
1
0
0
1
0
0
0
2
0
0
0
2
3
0
0
0
0
2
1
0
0
0
1
0
2
2
0
0
0
0
2
0
0
0
0
0
1
0
2
0
1
0
2
0
0
0
0
1
4
1
2
0
2
0
1
0
1
0
0
0
0
1
0
3
1
2
2
0
1
0
0
0
0
0
2
0
0
0
2
2
0
0
0
1
0
1
2
1
0
1
0
0
1
0
0
0
1
0
1
2
0
0
0
2
1
0
1
0
0
0
0
2
1
0
0
1
2
0
1
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
1
0
0
4
0
1
0
2
1
2
1
5
0
1
2
0
1
0
0
0
0
1
1
0
1
0
2
2
1
1
2
0
0
0
0
0
1
0
0
0
0
0
1
0
1
2
0
3
1
0
1
2
2
1
0
0
1
0
1
0
1
2
1
0
2
0
0
0
1
2
2
0
0
0
1
1
0
1
0
1
0
0
0
1
1
0
1
1
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
1
0
2
0
1
0
0
0
0
0
0
3
0
2
0
0
0
1
0
1
0
2
1
0
0
0
0
2
0
0
2
0
0
1
1
1
2
1
0
1
1
0
0
0
1
1
0
3
1
0
2
5
0
0
1
0
0
2
0
0
1
0
0
2
1
0
0
1
0
1
0
0
0
1
0
0
0
1
1
1
0
0
1
1
0
0
0
0
1
1
0
0
2
2
2
2
0
2
2
0
0
0
1
1
0
1
0
0
2
1
0
2
0
0
2
0
2
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
1
0
0
0
0
2
0
0
0
1
2
1
0
0
0
2
0
0
0
0
1
0
1
0
2
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
1
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
2
1
2
0
0
3
0
0
0
0
0
0
0
0
0
0
1
3
1
0
0
2
0
0
0
1
0
0
2
0
1
0
0
1
2
0
2
0
2
0
1
2
2
0
2
2
1
0
1
0
1
0
0
0
1
1
0
0
0
2
2
2
0
0
2
2
0
2
1
0
1
0
2
0
0
2
1
0
0
1
0
0
0
0
0
2
0
1
0
0
2
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
1
2
2
0
0
1
0
2
1
0
2
0
0
0
0
0
2
2
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
1
0
1
0
0
0
0
0
2
1
1
0
1
2
0
2
0
0
2
1
2
0
0
0
2
0
2
0
2
0
0
0
0
0
0
1
0
0
0
1
0
1
2
0
0
1
0
1
2
0
0
2
1
0
1
2
2
1
0
0
0
0
0
0
0
2
0
1
0
0
2
1
1
0
0
1
2
0
0
0
0
0
1
1
1
1
2
1
2
0
1
0
0
0
0
2
0
1
1
0
1
0
1
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
1
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
1
0
0
1
0
0
1
0
1
2
0
2
1
0
0
1
0
0
0
0
1
1
1
2
0
2
0
0
0
0
1
1
0
1
0
1
0
1
1
0
1
2
0
1
1
1
2
2
0
2
2
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
2
1
2
2
0
0
1
0
0
0
0
1
0
0
1
2
3
1
0
0
0
1
0
2
1
0
0
0
1
1
2
0
2
0
0
2
0
0
1
0
1
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
2
0
0
2
2
2
0
0
0
2
1
0
1
1
0
0
0
0
0
2
0
0
1
2
2
0
1
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
2
0
1
2
0
0
0
1
2
0
0
1
0
2
0
0
1
1
2
3
1
3
1
0
1
0
2
1
0
2
9
1
0
0
0
0
1
2
3
2
2
2
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
1
0
1
2
2
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
3
1
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
1
0
0
1
0
0
0
2
1
0
0
0
0
0
1
1
2
1
0
1
0
0
0
1
2
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
1
0
1
2
1
0
0
0
0
1
1
1
0
4
0
0
0
0
1
0
0
2
0
1
0
0
1
0
0
1
0
0
2
0
0
0
1
0
1
1
0
0
2
1
0
1
1
2
2
0
0
0
0
0
0
0
1
2
1
1
0
0
0
2
0
0
2
2
2
0
0
0
0
2
1
2
0
0
1
2
2
1
0
0
1
0
1
2
1
0
0
0
0
0
2
2
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
2
0
0
0
0
2
2
0
1
1
0
1
2
2
0
0
1
0
2
1
0
2
0
0
0
1
1
0
1
0
2
0
0
0
0
1
0
0
0
0
1
0
2
0
1
2
0
1
0
1
6
0
0
1
2
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
2
0
1
1
0
0
1
0
2
0
2
1
1
2
0
0
0
1
2
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
1
1
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
1
1
0
0
1
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
2
1
0
1
0
0
1
0
0
0
2
1
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
3
0
1
0
0
2
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
1
1
1
1
1
0
0
2
2
0
0
0
0
2
0
0
0
1
0
2
1
2
1
1
0
0
2
0
0
2
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
3
0
0
2
0
0
0
0
2
0
2
0
0
0
1
0
0
4
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
1
2
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
2
0
0
2
0
0
0
0
2
1
0
0
3
0
0
0
1
1
0
1
2
2
0
0
0
1
2
1
0
0
0
0
0
0
2
2
0
2
2
0
0
0
0
0
0
1
1
1
0
1
0
0
1
0
2
0
2
0
0
0
2
0
0
1
2
2
0
0
1
0
0
0
0
1
2
0
0
0
2
0
0
1
4
0
2
1
0
1
1
0
2
3
2
1
2
3
0
0
0
2
2
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
2
1
2
0
0
1
0
0
0
0
2
0
1
1
1
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
1
0
1
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
1
2
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
2
1
0
0
1
3
0
3
0
0
0
1
0
1
2
0
3
1
1
0
0
0
2
2
2
2
1
2
0
0
0
1
0
1
2
0
0
0
0
0
0
2
0
0
0
0
1
0
3
1
1
2
0
2
0
0
0
1
0
0
0
0
1
0
0
2
0
0
1
1
0
2
2
0
0
0
1
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
1
1
0
0
2
2
0
0
1
0
0
0
1
0
2
1
1
0
0
0
2
0
0
1
0
1
0
1
0
0
2
1
3
0
2
0
0
0
0
1
0
0
1
1
2
1
1
0
0
0
1
0
0
0
0
6
0
0
0
0
0
2
0
2
0
0
2
2
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
2
0
0
0
1
0
3
2
1
0
0
0
0
0
2
2
0
0
3
0
0
1
3
0
2
2
0
1
0
0
1
2
0
0
0
0
1
1
0
0
0
2
2
1
1
1
0
1
0
2
0
0
0
1
0
2
0
1
0
0
0
0
0
3
0
1
0
2
0
1
0
0
0
0
0
0
1
1
0
0
2
0
2
0
4
0
0
0
1
2
0
2
1
0
0
0
2
0
2
2
0
0
0
0
0
0
1
1
0
1
0
0
0
2
1
1
0
2
0
0
2
0
2
1
1
0
1
0
2
2
2
2
1
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
2
0
2
0
1
0
2
0
2
1
0
2
0
0
0
1
1
3
1
0
2
0
0
0
0
0
0
1
2
1
0
1
1
0
0
0
1
0
0
0
0
0
0
2
1
0
1
0
0
0
0
1
0
0
1
2
0
2
0
0
2
0
2
0
0
1
0
0
0
2
0
0
0
1
1
0
0
1
1
2
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
2
1
2
1
0
2
0
0
0
0
0
0
1
2
1
2
0
0
0
0
0
1
1
0
1
0
0
1
2
1
0
1
1
0
0
1
0
1
0
1
0
0
2
1
0
0
1
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
2
0
1
1
0
2
1
0
0
1
0
2
1
0
0
2
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
1
0
0
2
0
2
0
2
1
0
2
0
2
0
0
2
0
2
0
0
0
0
1
1
1
0
1
0
0
0
0
2
1
2
0
0
0
0
1
2
0
1
0
2
0
2
1
2
0
2
2
0
0
0
0
0
1
0
0
0
1
0
0
2
2
1
0
1
0
0
0
0
2
2
2
2
0
0
0
2
0
0
0
1
1
2
0
1
3
0
1
1
0
1
2
0
2
1
0
0
1
0
0
1
0
0
0
0
1
2
1
0
3
2
1
0
0
0
0
0
0
1
1
0
1
0
1
2
1
0
1
0
0
1
2
1
0
0
2
0
1
0
1
2
0
2
1
3
0
0
0
1
0
0
1
0
0
0
1
0
0
2
0
3
2
0
0
0
0
0
2
0
0
0
0
0
2
3
0
1
0
0
0
0
7
0
0
1
0
0
0
1
0
0
2
0
0
2
0
0
1
1
2
0
1
0
2
0
0
2
1
1
0
0
2
0
1
1
0
1
0
3
1
1
2
0
0
0
0
2
2
1
1
0
0
2
1
0
1
0
1
0
0
0
2
0
0
0
2
0
2
0
1
0
0
0
0
0
2
0
2
2
0
0
0
1
0
2
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
1
0
0
0
0
0
1
0
0
2
2
2
0
0
0
1
0
1
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
3
2
2
0
1
0
0
1
1
3
0
1
1
1
0
1
1
0
0
0
1
0
1
0
2
0
2
0
1
0
1
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
2
0
1
0
1
3
1
1
1
1
1
3
0
2
2
0
0
0
1
0
0
0
3
2
2
0
0
0
1
0
0
0
2
0
0
0
0
2
2
0
0
1
3
0
0
0
2
0
0
1
2
1
0
0
2
0
0
1
0
0
2
0
1
0
0
0
3
2
2
2
1
0
2
0
0
2
0
0
1
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
2
1
1
2
0
2
0
2
1
2
0
1
0
0
2
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
1
1
0
0
0
1
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
3
0
2
1
0
1
1
2
6
0
1
1
2
0
0
0
1
1
0
1
2
1
1
1
0
3
0
0
0
2
0
0
0
2
2
0
1
1
0
0
1
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
1
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
2
0
0
0
1
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
5
0
0
0
1
0
0
0
1
0
0
1
0
0
2
2
1
1
2
0
0
2
1
1
0
1
0
1
1
2
0
0
0
2
0
2
0
0
0
1
0
0
0
0
2
0
2
1
0
1
0
1
0
2
3
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
1
2
2
3
0
1
0
0
0
0
3
0
1
0
2
2
3
0
0
0
2
0
1
0
2
0
0
0
2
0
0
1
0
1
2
1
0
0
2
0
1
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
2
1
1
0
0
1
0
0
2
0
0
1
0
0
1
2
0
0
0
0
2
0
1
2
0
0
0
0
0
0
1
0
0
1
0
1
2
1
2
0
0
1
0
2
0
4
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
2
0
0
1
0
1
1
2
2
0
0
1
0
0
0
0
0
0
2
0
1
0
0
2
1
0
0
1
0
0
2
2
0
0
2
0
1
2
0
0
0
4
1
0
0
0
0
2
0
0
5
4
0
2
0
1
0
0
0
2
0
2
0
0
0
1
0
2
0
0
0
0
1
2
1
0
0
1
0
0
0
1
0
0
0
2
1
0
0
2
0
2
0
1
1
0
0
1
1
0
4
0
0
1
0
0
0
0
0
0
0
3
1
2
2
0
0
2
0
0
0
0
0
0
2
2
0
1
2
0
1
0
1
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
1
0
2
0
0
1
1
1
1
2
0
0
2
2
1
0
2
0
1
0
0
1
0
1
0
1
1
2
0
0
0
1
1
0
1
0
1
0
2
0
0
1
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
1
2
3
0
4
1
1
0
0
0
2
1
0
0
0
0
0
1
0
0
0
1
1
1
1
0
2
0
0
0
1
0
0
1
1
0
0
1
1
2
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
2
2
2
0
1
1
2
0
0
0
0
1
2
1
0
0
2
2
2
0
0
0
0
2
0
0
0
0
0
0
1
2
0
1
2
0
2
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
1
2
2
1
0
2
1
0
1
0
0
1
1
0
2
0
2
0
0
0
0
0
0
0
1
2
1
0
0
3
2
2
1
0
0
1
0
0
0
1
0
2
2
0
0
2
4
0
3
2
0
1
0
1
2
4
1
0
0
0
0
0
1
1
0
1
1
0
2
0
1
1
0
2
0
0
0
0
0
0
1
1
0
0
1
1
0
2
0
0
3
2
0
0
2
0
0
0
2
0
0
1
0
0
0
1
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
1
0
2
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
3
0
0
0
0
2
0
0
0
1
0
0
1
1
0
0
0
2
0
0
0
0
1
0
0
2
2
1
0
0
2
0
0
0
1
0
1
0
0
2
0
1
3
0
1
1
0
0
1
1
0
0
0
2
0
0
1
0
1
1
2
0
0
2
2
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
1
0
2
0
1
0
0
2
0
0
0
0
3
0
0
0
2
0
0
0
0
1
0
1
0
0
1
0
0
4
0
3
0
1
0
2
0
1
1
2
0
0
1
0
2
0
0
2
0
2
2
0
2
0
1
0
2
2
0
2
0
1
1
2
2
1
2
1
1
0
0
0
0
0
0
0
0
1
1
1
0
2
2
1
0
2
0
2
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
1
0
2
0
0
0
1
0
0
1
2
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
1
2
2
0
0
0
1
1
0
0
2
2
1
0
0
0
0
0
0
1
2
2
0
0
0
0
2
2
0
0
1
2
0
0
1
0
0
2
2
1
2
0
0
0
0
0
0
1
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
2
1
0
0
1
2
0
2
0
0
0
0
0
1
1
3
0
2
0
0
0
2
2
3
0
0
0
1
1
0
0
0
2
0
0
3
0
0
0
0
2
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
3
2
0
0
2
0
0
1
2
1
1
0
0
1
1
0
0
0
0
0
1
0
1
1
0
2
1
0
1
0
1
0
2
0
0
1
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
2
0
2
0
1
2
0
1
0
0
0
0
1
0
1
2
1
1
0
0
2
0
1
0
0
0
1
0
0
0
0
1
0
1
1
0
0
1
1
0
1
0
2
0
0
2
1
0
0
1
0
2
0
0
1
1
1
1
0
0
0
1
2
0
0
0
1
2
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
5
1
0
0
0
0
0
0
2
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
1
1
2
0
1
0
1
0
2
2
0
0
0
0
1
0
2
0
1
0
0
0
1
0
1
2
2
2
0
0
0
2
1
0
0
2
1
0
1
1
0
0
4
1
0
0
0
0
0
0
2
1
1
2
0
0
1
0
0
0
1
2
0
1
2
1
0
0
0
1
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
2
0
2
0
1
2
1
0
0
0
0
0
3
0
0
0
0
1
2
0
1
0
2
1
1
0
2
0
0
2
1
1
2
0
0
1
1
0
3
2
0
0
0
0
1
1
0
1
0
3
1
2
0
0
1
0
0
1
2
0
0
1
2
0
0
0
0
2
0
0
2
0
0
0
0
2
2
1
0
2
0
0
0
4
0
0
0
2
2
1
2
1
0
0
0
0
2
2
0
0
0
2
1
0
2
0
2
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
2
0
1
0
0
0
0
3
0
1
0
2
2
1
1
0
0
0
2
0
1
0
0
1
1
0
0
0
0
3
0
0
0
0
2
1
1
0
0
2
1
0
0
0
1
0
1
3
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
1
2
0
2
0
0
0
1
2
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
2
1
0
2
0
0
0
1
1
0
0
2
1
0
1
0
2
0
0
0
2
2
2
2
1
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
1
0
2
0
0
1
0
1
0
0
1
0
4
0
1
0
0
0
0
0
0
2
0
1
0
0
2
0
0
1
0
1
1
0
0
0
0
2
1
2
1
1
1
2
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
2
1
0
0
1
0
0
1
0
1
1
0
0
2
0
1
0
2
2
0
2
0
1
1
0
0
2
0
0
3
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
3
0
1
1
2
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
3
2
0
0
0
0
0
0
2
0
1
1
2
1
0
1
0
3
0
1
0
1
1
0
1
0
0
3
0
0
1
2
0
1
2
2
2
0
2
0
1
0
1
0
1
1
1
0
2
0
1
2
2
0
0
0
0
0
2
0
0
0
2
0
0
2
0
2
2
2
0
0
2
0
0
0
1
1
0
2
2
0
1
0
0
3
2
0
2
0
0
0
1
0
0
0
0
0
1
1
0
0
1
1
0
1
1
0
2
0
1
0
2
0
1
2
1
2
2
1
2
0
1
0
0
2
1
1
1
0
2
0
0
1
1
0
1
1
2
0
0
0
0
2
0
0
0
1
1
1
2
1
2
0
0
1
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
2
0
0
1
2
0
0
2
1
0
1
2
2
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
1
3
2
2
1
1
1
0
0
1
0
0
1
0
2
2
0
1
2
1
0
0
1
0
0
1
0
2
0
0
0
0
1
1
0
0
0
0
2
0
0
2
2
0
0
0
3
1
1
0
2
0
0
0
0
1
0
1
0
0
0
3
0
0
2
2
1
0
0
0
0
5
0
0
2
2
0
2
1
0
2
1
2
0
0
0
0
0
0
0
0
1
1
1
2
0
0
0
0
1
2
1
1
0
2
1
0
1
7
2
0
0
0
0
2
0
0
2
0
1
1
1
0
1
0
0
0
0
3
0
1
1
2
0
1
1
1
2
2
1
0
0
1
0
0
0
2
1
0
1
0
2
1
2
2
0
0
0
1
0
2
0
1
3
1
2
0
0
0
0
0
3
1
1
2
1
0
1
1
0
0
0
1
2
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
2
0
0
1
0
2
1
1
2
0
0
0
1
1
0
0
2
0
0
1
1
0
0
2
0
1
0
2
2
3
0
0
0
1
0
3
0
0
0
0
1
0
0
2
2
0
1
0
0
1
2
0
0
0
0
2
1
0
1
1
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
1
1
2
3
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
2
3
1
2
0
0
0
1
0
1
2
0
1
0
0
0
0
0
0
2
1
0
1
0
0
1
0
1
0
0
2
2
2
0
0
0
0
0
0
0
1
0
1
1
0
0
2
1
0
0
0
7
1
2
0
0
0
3
0
0
1
1
2
1
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
1
1
0
0
0
0
0
2
1
1
0
0
0
2
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
1
1
1
1
0
0
1
0
0
1
0
0
2
1
2
2
1
0
1
2
0
0
0
0
3
0
1
0
1
0
0
2
1
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
2
1
0
3
0
2
0
0
0
0
0
0
1
0
1
1
0
0
0
2
2
0
3
1
0
0
0
0
1
0
0
2
0
0
2
1
2
0
0
2
0
1
0
0
0
2
0
0
2
2
0
1
2
1
2
0
0
0
0
0
1
0
3
1
0
1
0
0
0
0
0
0
1
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
2
0
0
2
0
0
0
1
0
2
0
1
0
0
0
0
3
2
1
2
0
0
1
1
0
0
0
1
1
0
0
1
2
0
1
0
1
1
0
0
0
2
0
1
0
0
0
1
0
0
0
2
2
0
0
0
2
1
0
0
0
2
1
0
2
0
2
1
2
1
0
0
0
0
0
0
2
1
1
0
0
0
2
1
1
0
0
0
1
0
0
0
0
0
1
2
2
2
0
2
2
0
1
0
3
0
1
2
1
0
2
2
0
0
1
0
0
0
2
2
0
0
2
0
0
1
0
0
1
0
0
1
1
0
0
1
0
1
0
1
2
0
0
0
0
1
0
2
1
0
2
0
0
8
0
1
1
0
0
1
0
0
1
0
2
0
2
0
1
0
1
0
1
0
1
0
0
2
0
0
0
0
1
0
0
0
1
0
0
3
2
2
2
2
2
0
0
0
1
0
1
2
0
0
0
0
0
2
2
0
0
0
0
1
0
0
1
1
0
0
0
1
1
0
0
0
1
0
2
1
0
0
2
2
0
0
2
0
0
1
2
2
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
1
0
1
0
1
0
0
2
2
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
1
1
0
1
0
1
0
0
1
0
1
0
0
0
2
2
0
0
2
2
1
2
0
0
1
0
0
1
0
1
1
0
0
0
0
0
1
2
1
3
0
1
2
3
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
1
2
2
1
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
2
1
0
0
0
1
0
0
2
0
0
0
2
2
1
1
1
1
0
1
3
2
2
0
0
0
2
0
2
1
0
0
1
1
0
0
0
1
0
0
1
2
0
1
0
2
1
0
0
0
0
4
0
1
4
0
0
3
0
1
5
0
2
3
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
2
2
3
0
0
2
1
2
0
5
0
5
2
1
2
0
0
0
2
0
0
0
0
0
1
0
0
0
2
1
0
0
2
0
0
1
0
2
0
0
0
0
1
1
0
1
0
0
2
0
1
0
0
0
0
0
1
0
4
0
0
0
0
0
0
1
2
1
0
0
1
0
2
0
2
1
1
0
0
0
0
2
1
0
0
1
0
2
0
1
0
0
1
1
0
0
3
1
0
2
3
2
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
2
0
2
0
0
0
0
2
3
1
2
1
0
2
1
0
1
0
2
0
2
0
0
0
0
0
0
0
1
1
0
1
2
0
1
1
0
0
2
1
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
1
2
0
0
0
1
0
0
2
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
2
0
1
1
0
2
1
0
0
0
0
1
0
1
0
0
2
0
0
2
0
1
0
0
2
0
0
2
0
0
2
0
0
0
0
2
2
1
2
0
1
1
2
0
0
0
2
0
0
0
0
0
0
1
0
0
3
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
2
3
1
0
0
0
0
3
2
0
0
0
0
1
0
2
1
1
0
0
2
0
2
2
0
2
1
0
0
0
1
2
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
2
1
0
2
1
0
1
3
0
0
0
0
0
0
0
2
0
1
1
0
0
2
0
2
2
2
0
1
5
1
0
0
0
1
1
0
0
2
0
0
1
2
0
1
1
2
2
0
2
0
2
0
2
0
0
0
0
1
0
0
2
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
2
0
0
2
2
0
0
1
3
2
0
2
0
0
0
0
1
2
1
0
1
0
0
0
0
2
1
0
0
1
0
1
0
1
0
0
0
0
0
0
1
1
0
0
1
2
1
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
2
2
0
0
0
2
0
1
2
0
1
0
0
0
1
2
2
0
2
1
2
0
0
0
0
1
1
1
0
0
1
0
1
1
0
0
0
3
0
0
0
1
1
1
0
0
0
0
0
0
1
1
0
3
0
0
0
1
0
1
1
0
0
0
1
0
0
1
0
2
0
0
0
0
0
2
1
0
0
0
1
0
0
0
1
2
1
0
0
0
1
1
1
0
0
2
0
0
0
0
0
3
1
0
1
0
0
1
0
1
1
1
0
0
0
0
1
0
2
0
0
0
1
2
0
0
1
2
2
0
2
2
0
0
0
0
2
0
1
2
0
1
0
0
1
3
0
2
1
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
2
0
1
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
2
0
0
2
2
0
2
0
0
2
0
0
0
0
2
1
2
2
1
0
2
0
0
1
1
1
1
2
0
1
0
1
2
0
0
1
2
3
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
1
0
2
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
1
0
0
2
0
0
2
1
0
2
1
0
0
1
0
0
0
2
1
1
0
1
7
1
1
0
2
0
0
0
0
1
0
0
1
2
0
0
4
0
0
0
0
1
0
0
0
1
1
0
1
0
2
0
0
0
1
1
2
2
0
1
1
0
1
0
0
0
2
0
0
1
0
2
0
2
0
1
2
0
2
1
2
0
0
0
0
2
0
0
1
0
2
0
2
2
1
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
3
0
2
0
2
0
2
1
1
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
2
1
0
0
1
2
0
0
0
0
1
1
0
2
0
0
1
0
0
0
1
0
1
0
1
0
0
2
0
0
1
0
0
1
2
0
1
2
0
0
0
1
2
1
0
2
2
0
0
0
0
0
0
2
2
2
0
1
0
0
1
0
0
1
0
0
0
2
2
2
0
1
0
0
0
0
0
0
1
0
0
1
1
2
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
3
2
3
2
0
1
2
0
0
0
2
0
1
1
2
1
0
2
1
0
0
0
2
2
1
0
0
0
1
0
0
2
2
0
0
0
0
3
0
2
1
1
0
0
0
0
2
2
1
2
2
0
1
0
1
1
1
0
8
2
0
2
2
1
6
1
0
0
0
0
0
1
0
1
0
2
0
0
1
0
0
1
2
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
2
1
3
2
1
1
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
2
0
2
1
0
0
1
0
0
2
1
1
1
2
0
0
0
1
1
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
2
0
0
1
1
2
0
0
0
0
1
0
0
0
0
0
0
2
0
1
2
1
0
2
2
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
2
2
0
0
0
2
1
0
0
0
1
0
0
0
1
1
2
2
1
0
1
1
0
1
0
2
0
2
0
0
0
0
0
1
1
2
2
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
2
0
2
2
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
1
1
0
0
2
2
2
0
0
0
1
1
1
0
0
0
0
2
0
0
5
2
0
1
0
0
2
0
1
2
0
0
1
1
0
1
1
0
0
2
0
1
0
2
0
0
0
0
0
0
2
1
3
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
3
0
1
2
1
2
0
2
0
1
0
2
1
1
2
0
1
1
0
0
1
1
0
0
0
2
0
2
2
2
1
0
0
0
0
2
0
1
1
1
1
0
1
0
1
0
0
0
1
0
0
2
0
2
0
2
2
1
0
0
1
0
1
0
0
2
0
0
0
0
1
0
2
0
0
0
0
2
1
0
1
0
1
1
1
1
0
1
0
2
0
0
2
0
0
0
0
0
0
2
2
1
0
0
0
2
0
1
0
1
1
0
1
2
0
0
0
2
0
0
2
0
3
0
1
0
0
1
0
0
0
2
1
1
2
0
1
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
1
1
0
0
3
2
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
2
2
4
0
0
0
0
0
1
1
0
1
1
0
0
1
1
0
0
0
0
2
1
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
3
0
2
0
0
0
1
0
1
2
1
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
2
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
2
2
1
0
0
2
0
0
3
2
1
0
1
0
0
1
2
0
0
0
0
0
0
2
0
1
0
1
0
2
1
1
1
0
2
0
0
0
1
2
0
0
2
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
1
2
0
0
1
0
0
0
1
0
2
0
0
0
0
2
0
2
0
1
2
1
2
2
0
1
1
0
1
0
1
1
1
0
1
1
0
2
0
2
2
1
2
0
0
0
0
0
0
0
0
0
1
2
1
1
0
0
1
1
0
0
0
0
0
1
2
2
1
0
0
2
0
0
1
0
0
2
0
2
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
2
1
2
1
4
0
0
0
3
1
0
1
1
0
1
0
0
0
1
0
1
1
0
1
0
0
1
0
0
0
0
1
1
1
0
0
7
0
0
0
0
3
0
0
1
0
2
1
0
1
0
2
0
2
0
0
0
0
0
0
0
0
2
1
1
1
1
0
1
2
0
0
0
1
2
0
0
2
0
0
0
0
0
1
0
1
0
2
2
0
1
0
2
1
0
0
0
1
2
2
0
1
2
0
0
1
1
0
0
0
0
0
1
0
1
2
1
1
0
0
0
0
0
2
0
0
0
0
1
1
3
0
1
2
1
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
3
0
2
1
1
2
0
1
1
0
0
0
1
0
1
0
0
0
0
2
0
1
0
0
0
1
0
0
1
1
0
0
2
2
0
0
0
1
0
1
2
0
1
2
0
1
0
0
2
0
1
0
0
0
0
2
2
1
0
2
4
2
0
2
0
0
0
1
1
1
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
4
2
1
0
0
0
1
1
0
0
1
2
1
2
2
0
1
2
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
1
2
1
0
1
0
1
0
1
1
2
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
1
0
1
0
1
1
1
0
0
1
0
0
2
0
3
2
0
0
0
0
2
0
0
0
0
2
0
0
0
2
1
2
2
0
0
1
1
0
0
1
2
0
2
0
2
2
0
0
0
0
0
2
2
1
1
1
0
1
1
3
1
2
0
2
1
2
2
0
1
0
2
0
0
0
3
0
0
1
1
0
0
0
0
0
1
1
2
1
2
1
0
0
2
0
2
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
1
3
0
2
0
1
1
1
3
2
2
0
0
0
0
3
0
2
0
0
0
0
2
2
0
0
0
2
0
0
0
2
0
0
1
0
2
0
0
0
0
3
0
0
1
2
0
0
4
0
0
1
2
0
1
1
2
1
0
3
1
1
0
0
0
0
3
0
0
0
0
0
1
0
0
0
2
1
0
2
0
0
0
1
0
0
2
2
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
1
2
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
1
2
1
2
0
0
1
1
0
0
1
0
0
0
0
1
1
1
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
3
1
1
0
0
0
1
0
0
0
0
1
5
0
2
0
0
0
2
2
2
0
0
1
0
2
1
0
0
1
0
0
0
0
2
2
0
0
1
2
4
2
1
0
0
0
1
2
0
0
1
0
0
1
0
2
0
1
1
0
0
2
0
0
0
0
0
2
0
0
2
1
2
1
2
2
0
0
0
2
0
0
0
1
0
0
2
2
2
0
0
1
2
1
0
1
0
0
1
0
1
0
0
0
0
1
0
0
1
2
0
0
4
0
2
0
1
0
2
1
3
0
0
1
0
2
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
2
0
1
1
0
1
2
1
0
0
0
0
0
1
0
0
3
0
0
2
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
2
0
0
0
2
1
0
1
1
0
0
0
0
0
1
2
1
0
1
0
0
2
0
1
0
2
1
1
0
0
0
0
0
0
0
0
1
2
0
0
2
2
0
1
2
2
0
0
1
3
0
2
0
0
1
1
0
0
0
0
0
0
2
0
1
1
1
1
1
0
2
2
1
2
0
1
2
0
2
1
0
2
0
2
1
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
3
0
3
1
0
2
2
0
0
2
1
0
0
1
0
1
1
2
2
1
1
2
0
0
0
0
1
2
1
0
0
0
2
0
1
0
0
2
0
1
0
0
2
0
0
0
0
3
0
0
0
2
1
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
1
0
3
0
1
1
1
0
2
0
2
2
0
3
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
1
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
1
0
2
2
2
0
0
0
0
0
0
0
1
0
0
0
2
2
2
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
2
0
2
0
0
0
2
2
0
2
0
0
0
1
0
0
0
0
1
2
0
1
2
0
2
0
0
1
0
2
0
2
0
2
0
3
0
1
2
2
0
2
0
0
0
1
0
0
2
0
1
0
0
2
1
1
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
2
0
2
2
1
0
2
0
0
1
0
0
0
0
0
0
1
0
5
2
1
1
0
2
0
2
0
0
0
1
1
5
1
2
1
0
0
1
0
1
1
1
2
2
0
2
1
1
0
0
0
2
1
0
1
0
1
0
1
0
0
1
2
0
0
0
0
0
1
0
1
2
0
0
2
0
0
0
2
1
0
0
0
0
0
1
0
0
2
0
2
0
0
0
2
0
2
0
0
0
0
0
0
3
0
1
0
3
0
0
0
0
0
0
0
1
0
2
0
2
0
1
0
0
0
2
2
0
0
2
1
2
0
0
0
1
0
0
1
2
0
1
0
0
0
1
0
4
2
2
1
1
1
0
0
0
1
0
2
0
1
0
0
0
0
1
1
2
2
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
3
0
1
0
0
2
2
1
0
0
1
0
0
0
2
0
2
0
0
0
0
1
0
1
1
1
0
2
2
1
0
2
1
0
0
0
2
1
0
0
0
0
1
3
0
0
0
2
0
2
0
0
1
0
0
0
1
1
0
1
0
0
2
2
0
1
0
1
2
0
0
1
1
0
0
3
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
1
2
1
1
0
0
0
0
0
1
1
0
0
2
1
0
2
0
1
0
1
1
1
2
0
1
1
0
0
2
2
1
3
0
0
1
0
1
0
0
2
2
2
0
1
0
2
2
0
2
0
0
0
0
0
2
0
0
1
1
0
0
0
0
2
2
0
0
0
0
1
1
2
0
0
0
1
0
0
0
1
2
0
0
0
1
0
3
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
2
0
0
1
1
2
0
6
2
0
0
5
1
3
0
2
0
0
0
0
1
1
0
2
0
0
0
0
0
2
2
2
0
0
2
2
0
0
0
1
1
1
1
0
2
0
0
1
0
0
2
0
1
0
0
0
0
2
0
0
1
2
1
0
0
0
0
0
1
0
0
0
2
2
2
0
0
0
2
0
0
2
2
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
2
1
0
0
2
2
2
0
2
0
2
0
0
1
0
0
0
0
1
0
0
0
0
2
1
0
0
1
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
2
0
0
0
0
0
2
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
2
0
3
0
1
0
1
2
0
0
1
1
1
0
0
2
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
2
1
0
4
0
2
0
2
0
0
1
0
0
0
3
0
0
0
1
0
0
0
3
0
0
0
0
2
0
1
0
0
0
0
0
2
0
1
2
0
1
2
2
0
0
1
2
0
2
1
0
0
0
2
0
1
0
0
0
0
0
0
2
2
0
0
1
1
0
2
0
0
0
1
0
1
1
0
0
2
0
1
0
0
1
0
0
1
0
1
2
0
1
1
0
1
0
0
1
0
0
1
0
2
0
0
2
2
0
0
1
1
0
0
1
3
1
2
0
2
0
0
0
0
2
1
0
0
0
0
1
1
2
1
2
0
0
1
0
2
1
1
0
1
1
0
0
3
0
0
0
0
0
0
0
1
3
0
1
0
0
0
0
0
0
0
2
1
0
0
2
0
2
0
0
2
0
0
0
1
0
3
0
0
4
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
1
2
0
0
0
2
1
1
0
1
0
1
2
2
0
2
0
1
0
1
1
1
0
2
0
0
1
1
0
0
1
1
0
0
0
1
2
0
0
1
0
0
0
2
0
2
0
2
1
0
2
2
2
2
0
3
2
0
0
1
0
2
0
0
1
2
3
1
0
0
1
1
0
0
0
1
1
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
2
2
0
0
1
0
1
1
1
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
2
0
2
0
0
0
2
0
0
0
1
0
0
1
0
0
3
2
2
0
0
0
1
0
0
0
0
2
0
0
1
0
1
0
2
3
0
0
0
2
2
2
1
0
2
4
2
1
1
2
2
0
1
0
1
2
0
0
0
0
0
0
2
2
0
0
2
0
0
0
1
2
0
1
0
2
1
1
0
2
2
2
0
0
0
2
0
0
0
4
0
0
0
1
1
0
0
0
1
0
2
0
1
0
0
0
1
0
0
0
1
2
0
0
1
0
0
1
2
1
0
1
1
0
0
0
1
2
0
0
0
0
0
1
0
2
1
2
1
0
0
0
0
0
1
0
0
1
0
1
2
0
2
1
0
2
0
0
0
0
2
0
1
0
2
0
0
0
1
0
0
2
2
0
2
0
0
0
0
2
0
1
0
0
0
1
1
2
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
1
1
0
0
2
0
0
1
2
1
0
0
0
0
1
0
1
0
0
0
0
0
2
1
2
1
0
2
2
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
2
0
0
0
0
0
0
1
2
2
0
0
0
1
1
1
1
1
0
0
1
0
1
0
0
0
2
1
2
2
0
0
0
1
0
0
0
0
2
2
0
2
1
0
1
1
2
1
1
0
0
0
2
0
1
2
1
0
0
0
1
2
0
2
0
1
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
2
2
2
0
2
1
0
1
0
1
0
1
0
0
0
0
1
2
1
0
2
1
0
0
2
0
0
0
0
1
0
2
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
1
1
1
0
1
1
2
1
0
0
1
1
2
1
0
4
0
2
2
0
1
2
0
0
2
3
0
0
0
0
1
2
0
0
0
0
1
1
0
2
0
1
2
3
0
0
1
0
1
0
0
1
0
0
0
0
0
2
0
0
3
0
0
0
0
0
2
2
0
1
0
0
0
2
1
0
1
0
0
2
1
0
0
0
0
1
0
2
1
2
0
2
0
2
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
5
0
0
0
0
0
2
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
1
0
0
2
0
2
2
0
0
1
0
2
1
0
0
0
0
1
0
3
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
1
1
2
1
0
0
0
1
1
0
1
0
2
1
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
2
0
0
0
1
2
0
0
0
2
0
2
1
2
0
0
2
2
0
0
0
0
1
2
0
0
1
0
1
0
1
2
0
0
0
2
1
0
0
2
0
0
0
0
0
2
2
0
1
0
1
2
0
0
3
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
1
0
2
0
2
1
0
0
1
0
1
0
2
1
0
0
4
0
1
0
0
4
1
0
0
0
1
0
0
2
0
0
2
0
1
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
2
0
1
0
0
2
0
2
1
2
1
0
2
5
0
0
1
0
0
1
1
0
0
4
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
1
0
0
2
0
1
0
0
0
2
1
2
0
0
0
0
2
0
1
1
2
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
1
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
2
1
0
2
1
2
1
1
2
1
0
0
0
0
2
2
0
0
0
0
0
0
3
0
3
0
2
0
0
0
1
2
0
0
1
0
2
0
0
1
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
1
0
2
2
0
0
1
0
1
0
1
0
0
0
2
0
0
1
1
0
0
2
0
0
0
0
0
0
1
0
1
1
0
2
2
1
0
0
0
2
2
0
1
2
1
1
0
0
0
1
0
0
0
1
2
2
2
2
0
0
0
1
0
2
0
0
0
2
1
0
1
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
1
0
1
0
0
1
0
1
0
2
1
0
2
0
0
0
1
0
2
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
1
2
1
1
1
0
0
1
1
0
0
0
1
1
1
0
1
0
0
0
0
1
1
0
0
3
0
0
0
0
3
0
0
0
0
0
0
0
2
1
0
1
0
1
0
1
0
0
2
0
2
1
2
1
0
0
0
1
2
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
2
0
2
0
0
0
1
1
2
2
1
0
0
0
0
0
0
0
2
1
1
1
0
1
1
2
2
0
0
0
0
1
1
2
9
1
0
2
1
0
1
2
0
1
2
0
0
0
0
1
0
2
1
0
0
0
0
1
1
0
1
0
0
1
0
1
0
0
0
1
0
0
0
3
0
0
2
3
2
0
2
0
2
2
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
1
2
3
0
4
0
0
1
0
0
0
0
0
0
2
2
0
1
0
2
0
0
1
0
3
0
2
1
1
0
1
0
2
0
0
0
1
0
0
0
0
0
1
2
0
0
1
0
1
1
0
1
2
0
0
2
1
0
0
2
2
2
0
1
2
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
1
2
0
1
0
0
2
2
1
0
0
0
0
1
0
0
2
0
1
0
1
0
0
2
3
1
1
0
3
0
2
0
1
1
0
0
0
0
0
2
2
1
0
0
1
1
0
0
0
1
0
2
0
1
1
0
0
0
0
0
0
0
0
4
0
0
0
1
0
2
0
1
0
0
1
1
0
0
0
0
1
1
0
0
0
2
1
0
1
0
0
0
0
1
0
0
0
2
1
0
1
0
0
0
1
0
3
0
2
2
0
0
0
0
1
0
0
0
0
1
2
0
2
1
0
1
0
1
2
0
2
1
1
1
0
0
0
0
0
1
0
0
0
4
0
1
0
0
2
0
0
0
1
2
0
0
0
1
0
0
0
0
0
2
1
3
1
0
1
1
0
0
0
1
0
0
0
0
0
2
1
2
0
1
0
0
0
0
1
0
0
0
2
1
0
0
0
0
1
0
1
2
0
1
0
0
0
1
2
0
0
2
0
0
0
0
1
1
0
1
0
0
0
2
1
1
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
4
3
1
0
1
0
0
0
2
0
0
2
1
1
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
1
2
0
1
1
0
0
0
2
1
0
1
0
0
2
0
2
2
0
0
0
2
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
1
1
2
0
0
2
1
0
0
1
3
1
1
1
1
0
1
2
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
1
2
0
1
0
2
0
0
1
0
0
0
1
0
2
2
0
0
0
0
2
2
1
0
0
0
2
2
0
3
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
1
2
0
1
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
2
1
1
1
1
0
2
0
0
2
0
2
0
0
1
0
0
0
0
1
2
0
0
0
0
0
2
1
0
2
1
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
2
1
2
1
0
2
1
0
1
1
0
1
2
2
3
3
2
0
0
0
0
3
1
1
1
0
0
0
1
1
1
0
0
0
0
1
2
1
0
1
0
0
0
0
0
0
0
0
2
2
3
2
0
1
0
2
0
0
7
2
1
0
0
0
2
2
2
3
0
0
2
0
0
0
2
1
0
0
1
0
0
2
1
2
0
3
0
0
0
1
0
0
1
0
1
1
2
1
0
1
0
2
1
0
2
1
0
0
0
3
0
0
0
2
2
1
0
1
1
0
1
0
0
2
0
0
2
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
2
1
0
0
1
0
0
0
0
0
0
0
1
0
0
2
2
0
2
1
0
0
0
2
2
0
2
2
1
0
0
0
0
0
1
2
2
0
2
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
1
0
1
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
3
3
0
1
0
0
2
0
0
0
0
1
0
0
2
0
0
2
1
0
1
2
0
0
0
0
0
0
2
1
2
0
1
2
0
2
0
2
2
1
2
0
0
1
1
0
1
0
0
2
0
0
0
0
0
0
2
1
0
1
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
2
0
1
0
2
0
1
0
0
0
2
2
2
0
2
0
1
1
1
0
0
2
1
0
0
1
0
1
0
3
4
1
1
0
0
0
0
0
1
1
2
0
1
0
0
0
2
0
1
3
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
5
0
0
2
1
0
2
0
0
1
0
2
0
2
0
2
2
0
1
0
0
0
0
2
1
1
1
0
0
0
0
0
0
0
1
1
0
2
0
0
2
0
1
2
2
1
1
0
0
1
0
9
0
0
0
1
0
0
0
1
0
0
2
0
2
2
2
0
0
0
2
2
1
0
0
0
1
0
1
0
1
2
1
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
2
1
0
0
3
1
0
0
0
1
2
0
1
2
0
0
0
1
2
2
1
0
2
0
0
0
0
2
0
1
0
2
0
1
0
0
0
0
2
0
0
0
3
1
0
1
0
0
3
1
0
1
0
0
0
1
0
0
0
1
0
0
0
2
4
0
2
0
0
0
0
0
1
2
1
0
0
2
0
2
1
0
0
0
0
2
0
2
0
0
1
0
0
0
1
0
0
1
0
0
0
2
0
0
2
0
0
2
2
0
0
0
0
0
2
0
0
2
0
1
0
1
2
0
2
1
1
0
1
1
0
0
0
0
2
0
1
0
2
2
0
0
0
2
0
0
1
2
1
0
1
0
0
0
2
0
0
0
4
0
0
2
1
0
0
2
1
0
1
0
0
0
0
2
1
2
0
0
0
0
0
1
0
1
2
0
0
0
1
0
2
3
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
2
1
0
1
0
4
0
1
0
1
0
1
2
1
0
1
0
0
0
0
2
0
0
1
1
0
7
2
0
2
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
1
2
0
0
1
0
2
0
0
0
1
0
1
1
0
2
2
0
0
0
1
2
0
1
1
0
0
0
0
2
0
2
1
0
0
0
0
2
1
0
1
1
2
1
0
2
0
0
1
0
0
0
2
1
0
0
0
0
2
2
2
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
1
0
0
1
0
2
0
0
0
1
0
0
0
1
1
0
1
0
1
0
0
0
0
2
1
0
1
0
0
1
2
0
1
1
0
0
1
0
2
1
2
0
0
0
1
0
0
1
1
1
0
1
2
0
1
0
2
0
0
0
0
0
1
0
0
2
1
0
0
0
0
3
0
2
0
1
0
2
0
0
0
2
0
0
1
2
0
0
1
2
0
0
0
0
1
1
0
2
2
0
0
2
0
0
0
0
0
2
1
0
1
0
2
0
2
0
0
1
2
0
1
1
2
1
3
1
1
2
0
0
0
0
1
0
1
0
0
2
0
0
1
0
0
0
2
1
1
1
0
0
2
0
0
0
0
0
1
2
1
0
1
1
2
0
0
1
0
2
1
0
2
2
0
0
2
1
0
0
2
5
2
2
1
0
1
1
0
0
0
0
1
1
0
1
1
0
2
0
0
0
3
0
0
0
0
3
0
2
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
2
2
0
0
0
1
0
1
0
1
0
0
0
1
0
2
0
0
0
2
0
1
2
0
1
0
2
2
1
0
1
0
2
3
1
2
0
0
0
1
0
0
0
0
0
2
2
0
1
0
1
2
1
3
0
0
2
0
3
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
1
0
2
0
2
0
0
2
0
0
0
0
0
2
0
1
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
1
1
1
0
0
0
1
0
1
0
0
0
1
1
0
0
0
2
2
0
0
1
2
0
1
0
0
1
1
0
6
0
2
0
1
1
0
1
0
1
2
0
0
0
0
0
1
0
0
1
0
0
0
1
1
1
2
0
0
1
0
0
0
0
0
0
0
1
0
0
2
1
2
0
0
1
0
2
0
0
0
1
0
0
3
0
1
0
1
1
1
2
1
2
0
1
2
0
0
1
3
0
0
2
0
0
0
0
0
1
1
0
2
0
0
2
1
1
1
2
0
0
1
1
0
0
0
2
0
0
0
0
1
0
0
2
0
0
3
3
2
1
1
2
1
0
0
0
0
1
0
0
0
2
2
1
0
0
0
2
0
0
0
2
1
2
0
2
0
0
0
0
0
1
3
0
0
0
1
0
1
2
1
0
1
0
1
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
1
2
2
2
1
2
0
3
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
2
5
2
0
0
0
2
1
0
0
0
0
2
1
0
2
0
0
0
1
2
0
0
1
0
0
2
0
0
1
0
2
1
0
0
2
0
2
0
1
0
0
0
2
0
0
0
0
2
0
1
1
0
2
1
0
0
0
1
0
0
2
1
0
0
0
0
2
2
2
1
1
0
0
0
0
2
0
1
2
1
0
1
0
0
0
0
2
0
3
1
1
3
0
0
2
0
0
1
0
1
0
1
0
1
2
1
2
0
2
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
2
3
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
4
1
2
1
0
2
2
0
1
1
2
1
2
0
1
0
0
2
0
1
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
1
0
1
0
1
1
2
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
1
2
0
0
0
0
1
2
0
0
0
1
0
0
0
1
0
0
2
2
1
0
0
0
1
4
2
0
0
0
0
0
1
0
0
0
2
0
1
2
0
1
2
1
0
1
1
0
1
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
2
0
1
0
2
0
2
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
2
1
0
1
0
1
1
0
0
2
0
2
2
1
0
0
0
4
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
2
0
1
0
1
2
0
0
0
2
1
2
0
0
0
0
2
1
0
1
2
1
0
1
0
1
0
0
0
0
2
1
1
2
1
0
0
0
1
0
0
0
0
2
0
0
0
1
1
1
0
2
0
0
0
0
1
0
1
1
0
2
2
0
0
2
0
0
0
0
2
0
0
1
2
0
1
0
1
2
0
2
0
0
1
0
2
0
0
1
0
0
0
2
0
1
1
2
0
0
2
1
0
2
1
0
3
1
3
0
2
0
2
0
0
0
0
0
1
0
1
1
1
2
0
3
0
0
2
0
1
1
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
2
2
2
0
1
0
2
0
0
0
2
1
2
0
1
2
2
0
1
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
1
0
1
0
1
2
0
2
0
0
2
1
0
0
0
0
2
0
0
0
1
2
2
2
0
1
0
1
0
2
2
0
1
1
1
0
0
0
2
0
0
1
0
2
0
1
1
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
2
0
1
0
0
0
2
0
1
1
0
2
2
0
0
2
0
1
1
0
0
0
0
0
4
0
0
2
1
0
0
2
5
0
0
1
0
0
0
2
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
1
2
3
0
2
1
0
2
0
0
1
2
0
0
0
0
0
0
0
3
0
0
2
0
0
2
0
0
0
0
2
0
0
3
3
0
0
0
0
0
2
1
2
2
0
0
0
1
0
0
2
1
1
0
0
0
1
1
0
1
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
2
0
1
0
1
2
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
1
1
0
0
2
0
1
3
0
3
2
1
0
1
1
0
1
2
1
0
0
2
0
0
1
0
0
0
1
1
0
0
0
2
0
2
1
0
0
1
0
0
3
2
0
0
1
1
0
1
0
0
0
1
0
1
0
2
2
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
2
1
1
1
0
0
0
1
1
0
0
1
2
0
2
0
2
0
0
1
0
0
0
0
1
0
2
1
0
3
1
2
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
2
0
0
1
1
1
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
1
0
0
2
3
2
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
2
2
0
1
0
0
1
1
2
2
0
1
2
1
4
0
0
2
0
0
1
1
0
0
2
0
0
1
0
0
0
1
1
0
0
0
2
0
2
0
2
2
2
2
0
1
1
0
2
2
0
2
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
3
2
2
0
2
0
0
0
2
5
1
1
0
2
0
0
1
1
0
1
2
0
2
0
0
1
0
1
2
0
0
0
0
0
1
2
0
1
0
1
0
0
1
0
1
0
1
0
0
0
0
1
1
0
1
0
2
0
0
2
0
0
0
0
0
2
1
1
1
0
1
0
2
0
2
1
1
0
3
2
0
1
0
0
1
2
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
2
1
3
2
2
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
1
0
0
0
2
2
2
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
1
0
3
0
0
0
2
0
0
1
0
1
0
2
1
2
2
1
2
0
1
2
0
0
1
2
2
1
2
1
0
1
0
1
0
1
0
1
1
1
0
0
0
0
0
0
0
1
0
1
0
2
2
1
1
2
2
1
0
0
0
0
0
1
1
0
0
1
1
0
0
1
2
1
0
0
1
0
0
2
1
1
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
3
0
0
2
2
0
0
1
0
0
0
0
1
1
1
0
0
0
2
1
1
1
0
0
0
0
2
0
1
0
0
0
3
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
3
0
2
0
1
1
0
0
0
0
0
2
0
0
2
1
0
0
3
0
0
2
1
1
0
0
0
0
2
0
3
2
0
0
0
0
2
0
1
2
0
2
0
1
0
1
0
2
0
1
0
1
2
1
0
2
0
0
0
1
0
0
1
1
3
0
0
0
0
0
1
0
0
0
0
2
0
0
1
2
1
1
0
0
0
4
1
0
0
0
0
1
0
1
1
0
1
0
0
4
2
0
1
1
1
0
2
0
2
0
1
0
2
1
0
1
3
1
0
2
0
0
0
0
0
0
0
1
2
2
0
2
2
1
0
0
0
2
0
0
0
1
7
0
2
2
0
1
2
2
1
1
0
0
2
1
0
1
0
0
0
0
0
0
1
0
2
2
0
0
0
1
0
2
0
1
1
2
2
2
0
1
0
0
2
2
1
4
2
0
4
1
2
0
1
1
2
2
2
4
0
1
2
2
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
1
0
2
1
1
0
1
0
2
0
1
1
1
0
2
0
0
0
1
0
0
2
1
0
0
1
0
2
1
2
2
2
0
0
0
0
0
0
0
0
1
0
0
1
2
1
0
1
0
0
2
1
0
0
0
0
2
2
0
1
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
1
2
2
1
0
2
0
0
1
2
0
1
1
0
1
1
1
2
1
2
0
0
0
1
0
0
0
2
0
0
1
2
2
2
0
2
1
0
0
0
0
0
0
0
0
4
1
0
2
0
0
0
0
1
2
1
0
0
1
0
0
0
0
1
0
1
2
0
2
1
0
1
1
1
1
0
2
0
0
0
1
0
2
0
0
2
0
2
0
2
0
0
0
1
0
2
1
2
0
0
0
0
0
2
1
0
0
1
2
2
2
0
0
1
2
1
0
0
1
1
0
1
1
0
0
1
0
0
2
1
0
1
0
1
0
0
0
0
0
2
1
1
0
1
0
1
2
0
0
4
1
1
0
0
1
1
0
0
1
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
3
0
0
0
1
1
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
1
2
1
0
0
1
2
0
0
1
0
0
0
1
1
0
2
0
0
1
0
0
0
2
0
1
2
1
1
2
0
0
0
0
0
1
0
0
0
2
2
1
0
0
0
1
0
0
0
2
2
1
0
1
1
0
1
0
0
1
0
1
2
0
1
0
0
0
0
2
2
0
2
1
0
0
1
1
0
0
0
1
1
0
2
0
0
0
1
1
0
0
2
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
2
1
2
1
0
2
1
0
2
2
1
0
1
1
1
3
0
2
1
2
0
0
0
0
0
0
0
0
2
0
2
2
0
1
0
0
0
2
1
1
0
2
2
0
2
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
2
0
1
1
0
2
0
1
3
0
0
1
0
0
3
2
0
5
2
2
0
1
0
2
2
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
2
3
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
1
0
2
0
0
0
0
0
2
0
2
0
1
0
0
2
0
1
0
0
2
0
2
0
0
1
2
1
2
0
0
0
0
1
2
0
0
0
0
0
0
0
2
1
2
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
2
0
1
0
2
1
0
2
0
0
1
1
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
3
1
1
0
0
0
0
2
1
2
0
1
1
0
0
0
2
0
1
0
0
0
0
1
0
1
1
0
0
0
1
0
0
1
0
1
1
0
0
1
0
1
0
0
0
1
0
2
0
0
0
1
0
1
1
0
0
0
0
0
1
2
0
0
2
0
2
0
0
0
0
0
0
0
2
4
1
0
0
1
0
2
0
2
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
1
0
2
2
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
1
0
3
0
2
0
2
1
0
0
0
1
0
0
3
3
2
1
0
1
0
0
0
0
0
2
2
0
2
0
1
0
2
0
0
3
0
0
0
1
0
0
1
0
1
0
1
1
0
0
1
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
2
2
0
1
1
0
0
1
0
0
0
0
1
1
0
2
1
0
0
2
0
0
0
0
1
3
0
0
1
0
0
2
2
1
0
0
1
2
3
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
4
0
0
0
0
3
1
0
0
0
2
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
3
0
1
0
0
3
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
2
1
2
1
0
0
0
0
0
0
0
5
2
3
2
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
2
0
0
1
0
4
1
0
0
1
0
0
0
2
1
4
0
0
0
0
2
1
0
1
2
0
1
0
0
0
2
1
0
0
0
0
0
2
2
0
0
1
0
1
0
0
0
2
0
2
0
0
0
3
0
2
0
1
0
0
1
1
0
0
0
0
1
1
0
0
1
0
2
0
2
0
2
0
0
0
1
0
0
2
1
1
0
2
2
0
0
0
0
1
3
0
0
0
1
0
0
0
1
0
2
1
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
1
2
3
0
0
0
1
0
0
1
0
2
0
1
2
0
1
0
0
2
0
2
0
0
1
1
0
0
3
0
0
0
2
0
0
0
0
0
1
1
0
0
2
3
1
0
1
2
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
2
1
0
1
2
2
1
2
0
2
0
1
0
2
0
0
0
1
2
4
1
0
2
1
3
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
1
1
1
0
0
0
1
0
0
1
1
2
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
4
1
0
0
0
1
0
0
0
1
0
0
2
1
0
1
1
0
0
2
0
2
0
1
0
2
0
0
0
0
0
0
1
2
2
0
0
1
0
1
0
0
0
0
1
1
1
0
0
2
0
0
1
0
0
1
1
0
0
0
0
0
1
0
2
2
0
2
1
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
1
2
2
0
0
2
0
0
1
0
0
0
0
0
0
0
1
2
1
0
0
0
2
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
2
1
0
0
2
0
0
2
2
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
2
0
2
2
1
0
2
1
1
2
1
0
0
2
1
0
0
1
1
0
0
0
2
0
0
0
0
1
2
0
0
2
0
0
1
0
0
0
1
0
2
2
1
0
1
2
2
0
0
0
0
1
1
0
1
0
1
1
1
0
0
0
1
0
1
0
0
0
0
3
0
2
0
0
2
0
0
1
2
0
1
2
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
1
0
0
2
2
0
0
2
0
0
1
1
0
0
0
0
2
2
1
0
1
0
0
0
0
0
1
0
0
2
1
0
0
2
1
0
0
0
1
0
1
0
0
0
0
0
0
2
2
1
1
2
0
1
0
1
0
0
0
1
0
0
1
1
0
0
0
2
1
2
1
2
2
0
0
1
0
0
0
0
0
0
3
0
1
0
2
0
0
0
0
0
0
0
0
0
1
1
1
0
3
0
1
1
2
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
2
0
1
0
2
0
0
0
0
0
0
0
0
2
2
0
1
1
1
1
0
0
0
2
0
6
1
0
1
0
0
1
0
0
2
0
2
0
1
0
0
2
0
0
0
1
0
0
0
1
2
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
3
2
0
2
0
0
0
2
1
1
1
2
2
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
2
1
0
0
2
1
0
0
1
2
1
1
0
1
0
0
0
0
0
2
2
1
0
0
0
0
0
0
1
0
0
0
1
2
2
0
1
0
7
0
0
2
0
0
0
0
0
0
0
0
2
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
2
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
3
0
1
1
1
0
0
1
1
0
0
1
2
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
2
1
0
0
0
2
0
0
1
0
0
0
0
1
0
1
2
1
0
2
1
1
2
0
0
4
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
1
2
1
1
1
0
2
2
0
0
0
0
1
2
2
0
0
1
3
0
0
0
3
2
2
0
0
0
1
0
2
2
0
1
3
3
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
2
0
2
1
0
0
4
2
2
0
1
0
0
0
0
0
0
0
2
1
0
0
0
2
2
0
0
0
0
0
2
1
1
0
1
1
2
1
0
2
0
1
0
2
0
2
2
0
0
0
0
0
3
0
0
1
0
0
0
0
2
2
1
1
0
0
0
0
0
0
1
2
1
1
0
0
0
0
0
2
0
0
1
1
0
0
1
0
0
1
0
0
0
1
0
0
1
2
1
0
0
1
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
1
2
1
1
0
1
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
5
0
1
0
2
4
1
0
1
1
0
2
1
2
1
2
1
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
1
0
0
0
2
0
0
1
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
2
0
1
2
1
0
1
0
0
1
2
4
0
1
0
1
1
1
0
2
0
0
1
0
0
0
1
0
1
1
2
0
1
2
3
0
2
0
0
1
1
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
3
1
0
0
1
0
0
2
2
0
2
1
1
2
2
3
0
0
1
5
0
2
2
2
2
0
2
0
2
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
2
1
0
0
0
0
2
2
0
0
0
1
0
0
0
2
1
2
0
0
1
0
0
2
0
0
1
0
0
0
2
1
0
0
2
0
0
0
2
0
1
0
4
2
1
0
0
0
0
0
0
2
1
0
0
1
1
3
0
2
2
0
1
1
0
1
1
0
2
0
2
0
1
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
2
0
0
1
0
2
0
2
1
0
0
1
0
0
0
1
2
0
1
2
0
0
1
1
0
0
1
1
0
1
2
0
1
1
2
1
0
1
0
0
0
2
0
0
2
0
0
0
0
2
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
1
1
0
0
0
1
0
0
0
0
2
0
0
2
0
1
0
1
0
2
2
1
0
1
0
1
0
0
0
0
0
0
0
0
2
1
2
0
1
0
0
0
0
0
2
0
0
0
1
0
0
2
1
0
0
1
2
0
0
2
2
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
2
1
0
0
3
0
2
1
0
1
0
2
2
0
0
0
2
0
0
0
2
1
2
1
0
0
1
2
2
0
2
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
2
0
0
0
1
4
2
0
2
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
1
0
0
0
1
3
1
2
1
1
1
2
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
2
1
2
0
0
0
0
2
0
3
2
2
0
0
0
2
0
1
0
2
2
0
0
1
1
0
0
1
0
2
2
1
2
0
1
0
2
2
2
0
2
1
0
0
0
0
0
1
1
1
0
0
1
0
0
1
1
0
0
0
0
1
0
1
0
1
1
0
1
0
1
2
0
0
0
0
0
2
0
0
0
0
2
0
0
1
1
1
0
1
2
0
0
0
1
0
1
0
0
1
0
0
0
0
1
1
0
0
2
0
0
0
2
0
1
1
1
0
1
0
1
2
0
1
0
0
0
0
2
2
2
0
0
0
0
1
0
0
0
1
1
1
3
0
2
0
2
1
1
1
0
0
0
2
0
1
2
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
3
1
0
0
3
2
0
0
1
0
1
1
0
0
2
0
2
1
0
0
0
1
0
0
1
0
2
0
1
0
1
1
0
0
1
0
0
2
1
1
0
2
1
2
0
1
0
0
1
0
0
1
0
0
0
1
2
0
1
1
1
0
0
1
0
1
0
0
1
0
1
0
1
0
2
1
1
1
2
0
1
0
1
0
1
0
0
2
1
0
2
2
1
0
0
1
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
2
0
0
0
2
2
2
0
1
0
1
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
1
2
2
0
0
0
1
2
2
2
0
0
0
0
1
2
1
0
0
0
0
1
0
0
2
4
0
0
1
0
1
0
0
0
0
1
3
2
0
1
1
3
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
2
1
0
1
2
0
1
2
0
0
0
0
2
0
1
1
1
1
2
1
0
1
0
1
0
0
2
2
0
0
0
1
0
2
2
0
0
4
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
1
1
0
1
1
1
0
3
2
0
0
1
0
1
1
2
1
0
2
2
0
1
0
3
2
0
1
2
2
1
2
2
1
0
1
0
0
0
1
0
1
0
0
1
1
1
0
0
1
2
2
0
0
1
0
1
1
0
0
1
0
1
0
0
0
0
0
1
0
0
2
0
1
1
0
1
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
4
0
0
0
0
1
0
0
0
2
0
2
0
2
1
0
0
2
0
1
0
2
0
1
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
2
1
0
0
0
0
0
3
1
0
0
1
1
0
0
1
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
1
0
0
0
1
0
1
1
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
2
1
0
2
0
1
2
1
1
2
1
3
1
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
2
0
1
0
1
1
1
0
0
0
2
0
0
0
0
1
0
2
0
1
0
0
0
2
2
0
1
1
0
0
3
0
2
0
1
0
1
2
0
0
1
2
0
0
0
0
0
2
0
0
1
0
0
1
2
0
0
0
0
0
2
1
1
0
1
0
0
2
0
1
3
1
2
2
0
0
2
0
0
0
1
0
2
3
1
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
1
0
0
0
1
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
2
0
2
0
0
0
1
0
0
1
3
0
0
0
0
1
1
0
0
1
0
2
1
1
1
0
2
0
0
2
2
2
0
2
1
0
1
2
1
0
0
9
0
0
0
2
1
2
1
0
0
0
0
0
0
0
2
0
0
1
0
2
0
1
2
0
0
0
0
0
1
2
2
1
0
2
1
0
0
2
2
1
0
1
2
0
0
0
1
0
1
1
0
0
2
0
0
2
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
1
0
0
20
0
2
0
0
2
0
0
2
0
0
0
0
1
0
0
1
0
0
0
1
1
0
2
0
1
2
2
0
0
0
0
0
1
0
2
0
2
1
1
0
1
0
1
2
2
0
0
1
0
0
0
0
0
1
2
2
0
3
2
0
1
0
2
2
1
0
1
1
1
0
1
0
1
2
0
1
2
1
1
2
0
0
0
0
1
0
1
0
2
0
2
1
2
0
1
0
2
0
2
1
1
0
0
0
0
5
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
1
0
0
2
0
2
1
1
0
2
0
0
1
0
0
2
0
1
0
3
0
1
0
1
0
0
0
0
2
1
0
0
1
1
0
2
3
0
1
0
0
2
0
1
1
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
2
0
4
1
1
0
1
1
1
0
2
1
2
2
0
2
2
0
0
0
2
0
0
0
1
2
0
1
2
1
1
0
0
1
2
0
1
0
0
0
0
1
1
1
0
1
1
2
2
0
0
1
0
2
0
0
2
1
2
0
0
2
1
0
0
2
0
0
2
0
0
0
0
1
1
1
0
0
0
0
0
2
0
1
0
0
0
0
0
2
1
1
0
1
0
0
0
0
1
1
0
0
0
1
0
1
0
0
2
0
0
1
0
0
2
0
2
0
2
0
0
2
0
1
0
0
0
1
0
2
0
1
0
2
0
0
0
1
1
3
3
0
2
2
0
0
1
1
1
1
2
0
1
0
0
1
0
0
0
0
1
1
1
2
2
0
0
0
2
1
0
2
0
0
0
0
0
1
3
1
2
0
0
4
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
2
2
2
3
0
1
0
0
0
0
0
0
2
0
0
0
1
1
1
0
1
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
3
2
0
0
0
0
0
0
0
0
2
0
3
0
0
1
2
0
1
0
0
0
0
0
0
1
1
0
0
0
1
1
0
3
0
1
0
1
2
1
0
0
2
0
0
2
0
0
0
1
0
2
0
2
0
0
2
1
1
0
2
1
1
0
0
0
0
0
0
0
0
0
1
0
0
2
1
1
0
0
0
2
1
0
0
0
2
0
2
0
0
0
1
0
0
0
0
3
2
1
0
0
2
0
0
0
0
2
1
1
0
0
0
0
0
0
1
1
1
1
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
2
0
0
0
6
0
1
0
2
1
2
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
1
0
0
2
0
0
0
2
2
0
0
2
2
0
0
0
4
1
2
0
1
0
0
0
0
3
0
2
2
0
0
0
3
0
1
0
0
2
0
0
0
1
0
2
0
1
0
1
1
2
2
0
0
1
0
1
0
0
1
1
1
0
2
0
0
1
2
1
0
2
1
0
0
2
0
2
0
1
0
0
2
2
1
1
1
0
2
2
2
2
1
0
0
0
2
0
2
2
1
0
0
0
3
2
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
1
3
0
0
0
2
1
0
0
0
4
0
0
1
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
2
3
1
1
0
0
0
0
0
1
1
0
2
0
1
2
1
0
1
2
0
2
1
0
0
0
2
2
1
0
2
0
2
0
2
0
1
1
0
1
1
1
2
1
0
0
0
0
2
0
1
0
0
1
2
0
2
0
0
2
0
0
0
1
1
0
0
1
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
1
2
1
2
0
0
1
0
0
2
1
1
2
2
0
1
2
2
0
0
0
0
1
0
1
2
0
0
0
9
1
0
0
0
1
0
1
0
2
2
0
0
0
0
0
0
2
0
1
2
0
0
0
0
1
0
1
0
2
1
0
0
0
0
0
1
1
2
0
0
0
0
2
1
1
0
2
1
0
1
2
0
1
0
0
0
2
0
1
1
0
2
0
0
0
0
0
0
0
2
1
2
1
0
0
2
1
0
2
0
0
1
1
0
3
0
0
0
1
0
0
0
0
1
2
0
3
2
0
0
1
0
2
0
0
1
2
0
0
0
0
1
2
1
0
0
0
1
0
1
0
1
0
0
1
0
1
0
0
0
2
0
0
0
0
1
2
0
0
2
2
3
2
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
2
0
0
3
0
0
1
0
0
0
0
0
0
0
2
0
1
2
0
1
0
1
0
0
0
2
0
1
0
1
0
1
0
0
0
2
0
2
0
0
1
1
1
1
1
0
2
0
2
0
2
2
0
0
2
0
1
0
0
0
1
0
1
2
0
0
0
0
0
0
1
1
0
0
0
2
1
0
1
0
0
0
1
0
3
2
2
0
0
0
0
0
2
0
3
0
0
2
1
0
0
1
1
1
1
1
0
1
0
0
1
0
0
2
0
1
0
0
0
0
2
1
0
0
1
4
0
1
0
0
1
2
2
0
0
0
2
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
1
0
2
0
2
2
2
2
0
0
0
0
0
0
0
2
0
0
0
0
2
2
2
2
2
0
0
1
0
1
1
2
2
0
0
0
2
2
0
2
0
1
1
0
0
0
2
0
1
1
0
2
0
1
0
0
0
0
0
3
1
1
1
1
0
0
2
2
2
2
0
0
2
0
0
1
1
2
1
0
3
0
1
0
1
1
0
2
0
1
0
2
0
0
0
0
0
2
0
1
1
0
3
1
0
0
0
0
0
0
0
5
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
2
1
0
1
1
2
0
0
0
0
0
0
0
1
0
1
1
0
0
1
1
0
0
2
1
0
0
1
1
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
2
0
0
1
0
0
1
0
3
0
2
2
1
0
0
0
0
0
0
0
0
0
1
1
2
1
0
0
0
1
0
2
0
1
3
0
0
1
1
1
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
1
2
2
0
0
0
0
1
0
1
2
3
0
0
0
2
1
2
0
0
0
0
2
1
0
0
0
0
0
0
3
3
0
0
2
0
2
0
1
0
1
2
0
0
2
1
0
1
1
1
0
1
2
2
0
0
0
3
0
2
1
1
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
2
1
0
0
2
2
1
0
2
0
1
0
1
2
2
0
0
1
2
0
0
1
0
0
0
0
1
0
1
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
1
1
1
1
2
2
0
3
0
0
2
1
0
0
0
2
0
2
0
2
2
0
2
0
0
1
0
2
0
0
0
0
1
1
0
2
1
0
0
1
1
1
0
0
1
0
0
2
0
1
1
0
0
0
0
0
1
0
1
3
0
1
0
0
1
0
0
5
0
1
1
0
0
0
1
0
1
0
0
0
8
1
0
2
0
1
1
0
2
0
0
0
2
0
0
1
2
0
2
0
0
2
1
3
1
2
0
1
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
2
1
0
2
1
0
0
0
2
2
0
0
1
0
0
2
0
0
1
1
1
0
2
2
2
2
0
0
0
0
0
0
0
2
0
0
3
0
0
1
1
3
2
1
1
0
2
1
0
0
0
0
1
0
0
2
2
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
3
0
2
0
0
1
0
0
0
1
0
0
2
1
0
1
0
0
2
2
0
0
1
0
1
2
3
0
0
0
1
0
0
0
1
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
1
0
0
0
0
1
0
2
1
1
0
0
0
0
1
1
1
0
2
0
1
0
0
0
1
0
1
0
1
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
2
2
2
2
1
1
0
2
0
1
0
0
0
2
2
2
1
1
1
1
1
0
1
0
1
0
0
2
0
1
0
0
1
1
1
0
2
0
1
0
0
2
0
1
0
1
1
0
0
0
0
0
0
0
2
2
0
0
3
0
0
2
0
0
2
0
0
2
0
0
2
0
0
1
1
0
0
0
1
0
2
0
2
0
2
0
0
0
1
1
0
0
0
0
0
3
2
2
1
0
0
1
0
0
0
0
0
0
2
0
1
1
0
0
1
0
2
0
0
0
0
0
0
2
0
1
2
0
0
0
1
0
0
1
0
0
1
0
2
0
1
0
0
0
0
0
2
0
0
0
2
2
2
2
0
2
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
1
3
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
1
1
0
0
0
0
0
0
0
0
1
3
0
0
0
1
2
3
0
0
1
0
0
1
1
0
0
0
1
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
1
1
2
1
2
2
1
1
0
2
0
0
0
0
0
0
1
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
6
1
0
2
2
0
0
0
2
0
1
0
0
0
2
0
0
2
0
2
2
1
1
2
1
0
0
1
0
0
1
1
0
1
0
1
0
0
2
1
0
1
0
3
0
0
0
0
2
1
0
1
2
0
2
0
0
0
0
2
2
1
0
1
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
1
1
0
0
2
1
0
0
1
1
1
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
3
0
0
0
2
0
1
1
0
1
2
0
0
1
0
0
1
2
0
1
0
1
0
0
0
1
1
0
0
1
2
0
2
0
0
4
0
0
0
0
1
2
0
5
0
2
2
0
2
0
0
0
0
0
0
0
1
0
0
1
0
2
2
2
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
1
0
1
1
2
0
1
1
0
0
1
2
1
0
0
1
2
2
0
2
0
0
1
0
0
2
2
0
2
0
1
2
0
0
0
1
0
0
2
2
2
0
1
0
1
0
2
0
2
0
1
0
2
0
1
1
0
1
0
1
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
2
2
0
2
0
0
1
2
0
0
0
2
0
1
0
2
2
1
1
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
2
0
0
3
0
2
0
0
2
0
0
0
1
0
1
0
2
1
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
1
3
1
0
0
0
2
1
0
2
0
0
0
0
0
0
0
1
1
1
1
1
0
0
0
0
0
1
2
1
1
0
0
0
1
0
0
1
2
0
2
1
2
0
1
0
2
2
0
1
0
1
1
0
2
0
0
2
0
0
0
1
0
1
0
0
2
2
0
0
2
1
0
0
0
0
1
0
0
0
2
1
0
0
2
1
1
1
0
1
0
1
2
0
2
0
0
1
0
0
0
0
0
1
0
0
0
2
3
2
0
0
1
1
2
0
0
1
0
0
1
1
0
0
1
0
0
2
0
0
0
0
2
0
1
1
1
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
4
1
0
0
3
0
1
0
0
0
0
0
1
0
1
0
0
1
1
0
2
1
1
2
1
1
0
1
0
0
0
2
0
2
0
0
0
1
0
0
0
2
0
0
2
0
2
0
0
0
0
1
0
0
1
0
2
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
1
2
2
1
0
1
0
0
0
2
1
0
2
0
0
0
0
1
1
0
0
0
2
0
0
1
2
2
2
0
0
0
1
2
1
0
2
1
0
2
0
1
1
0
0
1
1
0
2
0
2
1
0
2
1
0
1
2
0
0
0
0
0
0
1
2
1
0
3
0
0
1
2
1
0
0
0
1
0
0
2
1
0
1
0
0
0
2
0
0
1
1
2
1
0
1
1
0
2
1
1
0
0
1
0
0
1
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
2
3
0
0
1
2
0
0
0
0
1
2
0
0
1
2
0
0
0
1
0
0
0
0
2
1
0
0
1
0
0
0
1
2
0
0
1
4
0
0
0
0
0
0
2
2
2
0
0
1
0
0
1
2
0
1
1
1
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
1
0
3
0
0
0
2
0
0
1
0
0
0
0
1
0
0
3
1
1
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
2
3
0
0
1
1
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
1
0
1
2
2
1
1
2
0
0
0
3
0
0
0
0
1
0
2
0
0
0
0
0
0
1
1
9
2
1
0
1
1
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
1
2
1
0
0
0
2
0
0
2
0
1
0
2
0
2
2
1
0
0
0
1
0
0
2
0
0
0
3
0
0
0
1
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
2
2
1
1
1
0
0
0
1
3
0
1
0
1
0
0
2
0
2
1
2
0
0
2
1
1
0
0
0
2
2
2
1
0
0
0
0
0
0
0
0
1
1
0
0
2
0
1
0
2
0
1
0
0
1
0
0
0
0
0
2
0
0
0
2
2
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
1
1
0
0
1
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
1
0
0
1
2
2
0
0
0
2
2
1
0
1
0
0
0
0
2
0
0
2
1
0
0
0
0
1
2
2
0
0
2
2
0
0
2
0
2
0
0
1
0
2
0
0
0
0
2
0
1
0
0
1
0
0
2
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
1
0
1
2
0
0
0
1
0
1
0
0
1
0
1
0
2
1
1
2
0
0
2
0
0
1
2
0
3
0
0
0
1
2
0
0
0
0
0
2
0
2
1
0
0
0
1
2
0
0
1
0
1
0
2
1
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
1
0
0
1
2
0
2
0
2
2
1
0
3
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
1
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
2
1
1
0
0
0
1
2
0
0
0
0
0
3
0
0
0
0
0
1
2
0
0
2
9
1
0
0
1
0
1
0
0
0
0
1
2
0
1
0
0
0
0
1
1
1
0
2
1
0
1
0
0
1
0
0
0
0
0
1
1
0
0
2
0
0
0
0
1
1
0
0
2
1
0
1
0
2
0
0
0
0
3
1
0
2
0
0
0
0
2
0
0
0
0
1
2
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
1
0
0
1
0
0
0
0
0
1
2
1
0
0
1
1
1
0
1
1
1
0
0
0
0
2
1
0
0
0
1
1
0
1
0
2
3
0
0
3
0
0
0
0
1
0
0
0
2
0
0
1
1
0
0
0
1
0
0
0
0
0
2
0
1
0
1
0
1
1
0
0
1
0
1
0
2
0
1
0
0
0
0
2
0
3
1
0
0
2
0
0
0
0
2
0
0
1
0
0
2
2
1
0
0
0
1
1
0
0
1
0
0
0
0
0
2
0
2
1
0
0
0
2
0
0
0
1
0
0
2
0
1
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
1
1
0
0
0
2
0
0
1
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
3
0
0
0
2
0
1
2
0
1
0
1
0
0
2
0
1
0
1
2
0
1
0
1
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
2
1
0
2
0
0
0
1
0
2
0
1
0
2
0
1
0
0
0
1
0
0
0
0
1
0
2
0
3
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
2
0
0
2
2
0
2
2
2
1
1
0
0
4
0
0
1
0
1
0
2
0
1
0
1
2
0
0
0
0
0
0
1
2
1
0
0
1
0
0
1
2
1
0
2
1
2
1
1
0
1
0
0
2
0
2
0
1
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
4
1
0
0
0
0
1
0
2
0
0
1
0
0
1
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
2
2
0
1
0
0
0
1
0
0
2
0
2
0
0
2
2
0
0
0
0
0
0
1
1
0
2
0
1
0
1
0
0
1
0
1
0
0
1
0
0
1
1
1
2
0
2
2
0
0
0
2
2
1
1
2
0
2
0
0
2
0
0
0
0
3
0
2
0
1
0
1
0
0
0
2
0
0
1
0
0
1
1
0
1
0
0
2
0
0
0
0
0
1
0
0
3
0
0
0
2
0
1
3
0
0
2
0
0
1
0
0
1
1
0
0
1
0
2
1
0
1
2
0
0
1
0
0
1
1
1
2
0
0
1
0
0
0
0
2
1
2
0
2
0
0
0
0
2
0
2
0
0
2
0
0
0
3
2
0
2
0
1
1
0
2
3
2
2
1
0
0
0
0
0
1
0
0
1
1
2
1
2
0
2
0
1
2
2
1
0
0
0
2
2
0
0
1
1
1
0
1
0
0
0
1
0
0
1
0
1
2
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
1
1
1
0
0
0
2
0
0
0
1
0
0
0
1
0
2
2
0
2
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
2
2
0
1
1
2
0
3
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
2
0
2
2
0
0
1
0
1
0
0
0
0
0
0
1
0
1
2
3
1
0
0
2
0
0
2
0
0
0
0
1
0
1
1
0
0
1
0
2
0
0
0
2
0
4
2
0
0
2
0
0
1
1
2
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
1
2
0
0
0
1
0
2
0
3
0
0
2
1
2
1
0
0
0
0
0
1
0
0
0
1
3
2
0
2
0
0
0
1
1
2
0
1
0
0
2
0
2
0
2
2
0
3
2
2
0
0
1
0
1
0
0
0
0
1
1
1
1
4
2
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
1
0
2
2
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
2
2
0
0
0
0
2
0
0
1
0
1
1
1
0
0
2
0
0
0
0
0
1
1
0
1
2
0
1
0
0
2
0
2
1
0
0
0
2
0
0
2
0
1
1
2
0
3
0
1
0
2
2
0
1
0
0
1
0
2
0
1
0
1
2
1
0
0
0
0
2
0
1
1
1
0
0
2
0
0
1
2
0
2
0
0
0
0
0
0
1
0
0
0
2
1
1
0
1
0
1
0
0
0
2
2
0
1
0
0
0
2
2
1
0
1
0
2
1
0
2
0
0
1
0
0
0
2
0
2
0
0
1
3
1
2
2
1
0
1
0
0
0
1
2
0
0
1
1
1
0
0
0
1
0
0
0
0
0
2
1
0
1
0
1
0
0
0
1
0
0
1
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
1
2
2
0
1
0
2
0
1
1
0
2
0
2
0
2
1
0
0
0
1
2
0
2
0
0
0
2
0
0
0
2
0
0
2
2
1
1
0
0
0
0
1
0
0
0
1
0
2
2
1
1
0
2
0
0
2
0
0
0
1
1
2
0
0
1
1
0
1
2
2
0
0
0
0
0
0
0
0
1
3
0
2
0
0
2
0
2
0
3
0
4
0
1
0
2
0
0
0
0
0
0
0
0
2
1
3
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
2
0
1
0
1
0
2
1
2
1
0
0
2
0
0
0
0
0
1
0
0
0
1
2
0
0
2
2
2
0
2
0
10
0
3
1
0
0
0
0
0
1
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
4
0
0
2
1
0
0
0
2
2
0
0
0
0
1
2
0
6
1
0
0
2
0
0
0
3
0
0
0
0
1
1
0
0
1
2
2
1
2
1
1
1
2
0
1
1
0
0
0
0
0
2
0
1
1
1
2
0
2
0
0
0
1
2
0
0
0
1
0
0
1
1
0
0
0
2
0
1
0
0
0
0
0
0
1
0
1
0
2
2
0
2
1
1
1
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
2
1
2
0
0
0
0
1
0
0
0
1
0
0
0
1
2
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
1
2
0
1
2
0
2
0
2
1
0
0
0
2
0
1
0
0
1
0
2
0
0
0
2
2
0
0
5
1
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
1
2
1
2
1
0
0
1
1
2
0
1
0
0
0
1
2
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
2
0
0
0
2
2
1
0
1
0
0
0
0
0
1
2
2
2
0
3
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
2
2
0
0
4
0
0
2
0
0
2
0
0
1
0
0
1
0
1
0
2
0
1
2
2
1
1
0
0
0
0
0
2
2
2
1
0
2
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
1
1
1
1
0
0
1
0
0
0
0
0
0
0
2
0
2
0
2
1
2
0
0
3
0
0
0
0
1
0
1
0
2
0
1
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
3
3
0
0
0
0
0
0
1
2
2
1
0
0
0
1
3
1
0
1
0
0
0
0
0
1
0
0
1
2
0
1
0
2
1
0
1
2
0
3
1
0
2
0
0
2
2
0
0
0
1
0
2
1
0
0
0
0
0
2
0
1
0
1
1
0
2
0
0
0
1
1
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
2
0
2
2
0
1
1
1
1
0
2
0
0
1
1
3
0
0
0
0
2
2
0
0
0
0
1
2
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
2
0
2
0
2
2
0
0
1
0
1
1
0
1
0
0
1
0
0
0
0
0
0
1
1
1
0
1
0
0
0
1
0
2
2
1
3
2
0
0
1
1
3
0
0
0
0
0
1
0
1
0
0
0
0
1
2
0
0
1
0
0
2
2
0
0
2
0
0
0
0
1
0
2
0
0
0
3
0
1
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
1
0
0
2
0
2
0
0
0
2
0
1
0
0
1
0
0
0
3
2
0
1
1
0
0
0
1
0
0
0
1
0
0
1
1
2
1
2
0
0
1
2
0
1
1
0
0
1
3
1
1
0
1
1
1
0
0
0
2
1
0
1
2
0
0
0
0
2
1
0
0
2
0
0
0
0
1
2
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
1
0
1
1
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
2
3
0
0
2
2
0
0
0
1
0
1
1
2
2
1
2
0
2
1
2
1
0
1
3
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
2
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
2
1
2
1
0
0
1
1
1
1
1
0
1
1
0
0
0
1
1
2
1
0
0
0
2
0
0
0
0
1
0
0
1
2
0
0
2
0
0
0
2
2
0
0
1
0
0
0
0
0
3
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
2
2
0
0
0
2
0
2
2
0
0
0
2
3
2
0
0
0
2
0
0
0
2
1
0
0
0
0
2
0
2
0
0
1
1
0
2
0
0
0
3
1
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
1
2
0
1
0
0
4
1
0
2
0
2
1
1
2
0
0
1
0
1
0
2
0
0
1
1
0
2
2
0
1
0
0
2
0
0
1
0
0
1
1
2
0
0
0
2
0
0
0
2
0
1
2
2
1
0
0
1
3
2
2
0
2
2
0
0
0
0
0
0
2
1
1
0
0
1
0
0
2
2
1
0
0
1
0
2
0
1
0
2
1
2
0
0
0
3
1
0
0
1
0
0
0
1
0
0
0
2
0
2
0
1
0
2
0
2
1
2
2
2
1
0
0
2
0
0
1
0
0
0
0
0
0
1
2
2
1
1
0
0
1
2
0
1
1
0
0
2
2
0
1
1
0
0
0
0
0
2
0
1
1
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
2
2
0
0
0
2
0
2
0
0
1
2
0
0
1
2
1
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
1
2
0
1
2
0
0
0
0
2
0
1
1
1
0
0
0
1
0
0
0
0
1
0
1
0
1
0
2
2
1
6
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
2
0
0
2
0
0
0
0
1
2
0
2
2
2
1
0
0
1
1
0
0
1
0
2
2
1
0
0
0
0
0
2
0
0
0
1
0
1
1
0
2
2
0
0
0
1
1
0
0
0
1
0
2
0
0
0
2
0
0
0
3
0
1
0
0
2
0
1
2
0
0
1
2
0
2
0
2
2
0
2
2
0
0
0
1
2
0
0
0
1
2
1
0
0
0
0
0
0
3
2
0
1
2
2
0
0
2
0
0
1
0
3
0
1
1
0
1
2
2
0
0
2
1
0
0
1
2
0
0
1
0
1
1
2
2
0
0
1
0
0
0
2
0
1
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
2
1
0
1
2
1
0
2
0
2
2
1
0
1
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
1
0
2
2
0
2
0
1
2
0
2
1
0
0
0
1
1
1
0
0
1
0
0
4
1
0
0
2
0
6
0
3
2
0
1
2
2
0
2
2
0
0
2
2
1
1
0
1
2
7
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
3
2
0
1
0
0
0
0
2
0
1
0
1
2
0
0
1
0
2
0
0
0
2
1
2
2
0
1
2
1
0
0
0
0
0
0
0
0
2
2
0
2
2
1
2
1
2
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
2
2
2
0
0
1
0
0
0
2
0
0
0
1
0
0
1
0
1
2
0
1
0
0
0
0
2
0
4
0
0
0
1
0
0
0
3
2
0
0
0
0
0
1
1
2
0
1
0
0
2
1
0
3
0
1
1
0
0
0
0
0
1
2
0
0
1
0
2
1
0
2
2
0
0
0
0
0
0
1
0
1
0
1
0
1
0
2
0
0
0
0
0
1
1
2
0
1
2
1
0
0
0
0
0
2
0
2
0
0
0
0
0
1
1
2
0
1
2
0
1
0
0
1
0
1
1
1
2
2
0
2
0
0
0
1
2
3
2
0
0
0
1
0
2
0
0
0
1
1
1
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
3
0
1
0
2
0
2
0
1
2
0
2
2
0
0
2
1
0
1
1
0
2
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
2
0
1
0
0
2
1
0
0
0
2
0
0
2
0
0
1
0
2
0
0
1
2
0
0
0
0
0
0
1
2
2
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
1
1
0
1
0
0
0
0
2
2
0
2
4
1
0
0
1
0
0
1
0
0
1
0
2
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
2
10
1
3
0
0
0
1
0
0
0
0
1
1
0
2
1
1
0
0
0
0
0
1
1
0
0
3
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
3
4
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
2
1
0
0
0
1
0
0
1
2
1
0
0
1
2
0
0
1
0
0
0
0
0
0
2
2
2
2
3
0
2
1
0
0
0
0
1
0
2
2
0
1
0
1
0
2
1
0
0
0
0
2
0
1
0
0
2
1
1
0
2
0
0
0
0
1
0
1
0
0
0
0
0
1
1
1
2
0
3
1
0
0
2
0
2
0
0
0
1
0
1
0
1
1
5
2
0
0
1
0
0
1
0
0
0
1
0
2
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
2
1
0
0
0
1
0
1
0
2
0
0
0
2
0
2
0
1
2
0
0
0
1
2
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
1
2
1
0
0
1
0
0
0
0
2
1
0
1
0
1
1
1
0
1
1
0
1
1
0
0
0
2
0
0
2
2
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
1
2
0
0
1
2
0
1
1
0
0
2
0
0
2
3
0
2
0
0
0
1
0
2
2
0
0
2
2
2
1
0
1
4
0
1
0
2
3
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
2
0
0
0
1
0
0
1
0
2
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
1
2
0
1
1
0
3
0
1
0
0
0
2
0
1
1
2
2
1
0
0
0
1
0
0
1
0
0
0
2
2
0
0
2
1
1
1
2
0
0
0
1
0
0
0
0
2
1
0
0
1
1
1
0
1
1
1
0
0
2
0
1
0
0
1
0
0
0
0
0
2
0
2
0
0
0
1
0
0
1
2
2
6
1
0
0
0
0
0
2
1
0
1
1
2
0
0
5
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
1
0
2
0
0
1
0
0
0
1
2
0
2
0
1
1
0
0
1
0
1
0
0
0
0
1
1
0
0
1
3
2
0
2
1
1
0
0
0
0
0
2
2
2
1
0
1
0
0
2
0
0
0
0
0
1
0
1
0
0
0
3
1
0
0
2
0
1
0
4
0
1
1
0
1
0
0
0
2
2
0
2
0
1
0
2
0
0
0
0
1
0
1
2
1
0
2
2
0
0
0
0
2
2
1
0
1
1
2
2
2
0
0
2
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
1
1
0
0
1
2
2
1
1
0
0
1
0
2
1
0
1
1
0
0
0
0
0
0
1
1
0
0
2
0
0
1
1
2
2
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
2
1
0
0
2
0
2
1
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
2
2
0
0
0
0
2
2
3
2
0
0
0
0
3
2
0
2
0
1
0
2
7
0
1
3
1
2
0
0
0
0
0
2
0
0
2
2
1
3
0
0
0
1
1
2
0
1
2
0
0
1
0
0
1
2
1
0
0
0
0
2
0
0
0
0
2
1
2
0
0
0
0
0
2
0
1
2
0
0
0
1
0
0
0
1
1
0
2
0
3
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
1
1
0
2
0
0
0
1
0
0
1
0
5
0
0
0
0
0
0
2
1
1
2
0
2
1
0
2
0
0
2
0
1
1
2
1
1
1
0
2
0
0
0
1
2
3
0
1
0
1
0
0
0
5
0
0
0
0
0
1
0
2
2
0
0
0
2
0
0
0
0
1
0
0
1
0
1
0
0
0
2
1
0
1
0
0
0
0
2
0
2
1
0
4
0
0
0
1
0
0
0
0
0
1
0
2
0
2
0
1
0
1
1
1
1
0
0
1
0
2
0
2
0
1
1
0
1
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
2
0
1
1
0
0
0
1
0
0
0
0
0
2
2
1
0
1
2
0
0
1
0
2
0
0
2
0
0
1
0
0
2
2
1
0
0
1
1
0
0
2
1
0
2
2
2
0
0
0
0
0
0
1
0
0
2
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
2
0
0
2
0
0
1
0
1
0
0
3
0
0
0
0
1
0
0
1
1
0
0
2
0
1
0
0
0
0
0
0
1
0
1
1
0
2
0
0
0
0
1
1
0
1
1
0
0
2
0
0
1
3
1
2
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
2
1
0
2
1
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
2
2
2
0
0
0
0
0
2
1
0
2
1
2
0
2
0
0
2
0
0
5
0
0
1
0
0
0
0
1
0
1
0
1
0
0
2
1
1
2
0
0
2
1
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
3
0
2
0
0
2
0
0
1
0
2
0
1
3
2
0
0
1
0
0
1
2
1
0
0
3
0
2
0
0
1
2
2
2
0
0
2
0
0
0
0
0
4
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
1
0
2
0
0
0
2
1
0
1
1
0
0
1
2
0
2
2
0
2
0
1
1
0
1
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
2
2
2
0
0
1
2
0
1
1
0
0
2
0
2
0
2
2
1
0
1
0
0
0
1
0
0
1
0
1
0
0
0
2
0
0
0
1
2
1
0
0
2
0
0
6
0
0
1
2
0
2
0
0
1
1
0
0
2
0
1
2
1
0
0
1
1
0
0
0
2
2
0
0
1
0
4
0
1
2
1
2
2
0
2
0
0
0
1
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
1
0
1
1
0
0
0
0
1
2
2
0
1
2
0
0
0
1
0
2
0
0
2
0
2
0
0
1
0
0
1
1
0
1
2
0
1
0
3
3
0
0
0
0
0
0
0
1
0
0
0
0
2
1
1
0
3
2
2
0
2
0
0
0
1
1
1
0
2
1
0
0
0
0
0
1
2
2
2
1
2
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
2
1
0
1
0
2
2
4
0
2
0
0
0
0
0
0
2
1
0
0
1
0
0
2
0
0
0
0
0
0
1
2
0
1
1
2
0
1
0
0
1
0
0
0
2
0
0
0
0
1
1
0
3
0
2
0
0
0
2
2
2
0
0
0
0
2
0
0
2
1
0
3
1
0
1
1
0
1
2
0
0
1
0
0
0
1
0
1
0
1
0
0
1
0
0
1
2
1
0
0
0
2
1
0
0
2
2
0
1
1
0
0
1
2
1
0
1
2
0
0
0
0
1
0
0
0
1
1
2
0
0
1
0
0
0
0
0
1
2
0
0
2
0
0
0
1
0
0
0
1
2
5
0
1
1
0
2
0
0
0
2
0
0
0
2
0
2
0
0
1
0
0
1
2
0
0
0
0
0
2
0
2
2
1
0
0
0
2
0
0
0
0
1
0
1
3
0
1
0
1
0
0
0
0
0
1
2
0
0
0
2
2
1
0
0
0
1
1
2
0
0
2
0
0
0
1
0
3
0
3
1
2
0
0
0
2
0
0
4
0
0
0
2
2
0
0
1
0
1
0
2
2
0
1
0
2
0
0
0
0
1
0
2
2
0
1
0
3
0
0
0
0
2
2
0
0
2
2
1
0
0
0
2
1
0
1
1
3
0
0
0
1
2
1
0
0
0
0
0
0
1
0
1
0
0
2
0
0
1
0
0
1
0
0
0
1
0
0
1
0
2
0
0
1
0
2
1
1
0
0
0
1
0
0
2
0
2
1
0
0
1
0
1
2
0
1
2
0
0
0
0
1
1
0
0
1
2
0
1
1
0
2
0
0
1
0
0
2
2
0
0
0
0
0
0
1
1
0
0
0
0
2
2
0
0
0
0
2
0
2
0
0
0
0
2
2
0
1
1
0
0
0
1
0
1
1
3
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
2
1
1
0
0
2
0
0
1
1
0
2
0
1
2
2
0
0
2
0
2
0
0
2
0
1
1
0
1
0
0
0
7
0
0
0
0
0
1
3
0
0
0
0
1
0
0
2
0
2
0
2
0
1
0
0
2
0
1
0
1
0
1
3
1
2
1
2
0
0
1
1
2
0
2
2
1
0
1
2
0
0
0
1
0
1
0
1
0
0
1
1
0
1
0
0
0
2
0
0
0
1
4
0
1
1
0
0
0
0
2
2
2
0
0
0
0
0
1
0
0
1
2
0
0
0
0
1
1
0
0
2
0
0
1
3
1
0
1
0
0
1
0
1
0
1
0
0
0
1
0
1
2
0
0
0
2
0
1
2
0
1
0
1
0
0
1
0
0
0
1
0
1
2
1
0
0
0
2
0
0
0
0
0
2
2
0
2
0
2
0
0
0
0
1
0
2
2
0
2
3
1
2
0
0
2
1
2
2
1
1
0
2
1
0
2
0
0
0
1
0
0
3
1
0
0
0
0
2
4
0
0
1
0
2
2
0
2
0
2
0
0
0
0
2
0
0
0
0
0
1
1
0
5
0
0
0
0
0
0
1
0
0
0
3
0
0
2
2
3
1
1
0
0
0
2
0
1
2
0
0
0
0
0
0
1
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
1
0
3
0
0
1
0
0
0
0
0
0
2
3
0
0
0
1
1
0
0
0
1
2
0
1
0
1
0
0
2
2
1
2
0
0
0
2
0
0
1
0
0
0
1
0
2
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
1
0
0
1
0
1
1
0
2
3
0
0
0
0
0
0
1
0
0
0
0
1
1
0
2
2
0
1
0
0
0
0
0
0
1
0
3
0
0
0
3
1
0
0
0
0
0
0
0
1
0
1
2
1
0
0
0
1
0
0
0
0
2
0
2
0
2
2
2
2
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
2
2
1
0
4
2
0
3
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
2
0
0
0
0
2
2
0
0
1
1
1
0
0
0
0
2
1
0
1
0
1
0
1
0
1
1
1
0
0
2
1
2
0
0
1
1
0
0
2
0
0
0
0
0
2
1
1
0
0
0
0
0
0
2
0
1
0
1
1
1
0
1
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
2
0
0
1
0
1
0
0
3
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
1
1
1
0
0
0
0
2
0
0
2
2
1
0
1
0
2
2
2
0
1
1
2
0
3
0
0
0
0
2
0
1
0
0
1
0
1
2
0
0
0
0
3
1
0
2
2
0
0
0
0
0
1
0
2
2
0
1
0
0
0
1
0
1
1
0
0
1
2
1
0
1
2
0
1
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
1
2
2
0
0
0
3
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
2
0
0
0
1
0
0
0
2
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
1
0
0
2
2
0
0
1
2
2
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
2
2
0
0
0
1
0
2
0
0
0
1
2
0
2
1
0
0
1
0
0
1
3
0
0
1
0
0
0
1
0
0
0
0
0
1
2
0
0
2
0
0
1
1
3
1
2
0
0
0
1
0
2
2
2
0
0
0
2
1
1
0
0
0
0
2
0
0
0
2
2
1
0
0
2
0
0
2
2
0
2
1
1
0
2
0
0
2
2
0
1
0
0
0
0
0
2
1
0
0
0
1
2
1
2
1
0
0
0
2
1
1
1
1
0
1
1
0
0
0
0
1
3
0
0
1
0
0
1
0
0
0
0
2
2
2
0
0
0
0
0
2
0
0
2
0
2
0
2
1
2
0
0
2
0
0
0
0
0
0
3
1
0
0
1
0
0
2
0
1
0
1
2
2
1
0
0
2
1
0
2
0
0
0
3
1
1
0
2
3
1
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
2
0
0
1
1
2
1
0
1
0
1
1
2
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
1
1
1
0
0
1
0
0
1
1
0
0
2
0
0
2
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
1
0
0
0
2
0
0
0
0
0
2
0
1
0
0
2
0
0
1
0
0
2
0
0
0
1
1
0
0
1
1
2
0
0
2
0
0
0
0
0
0
0
2
0
4
0
0
1
5
2
2
2
1
0
1
2
2
0
0
2
0
0
0
1
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
1
1
2
1
0
1
0
0
1
1
0
3
1
0
2
1
2
0
0
0
0
1
2
0
1
3
0
0
2
0
2
1
1
0
2
0
1
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
2
2
3
0
0
3
2
0
1
2
5
0
0
0
0
0
2
1
0
0
1
0
0
2
0
1
0
1
1
1
2
0
0
1
0
2
0
0
2
0
2
2
1
2
0
0
3
0
1
2
0
0
0
0
0
1
0
2
0
1
0
2
1
0
2
0
0
0
1
1
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
3
2
0
0
0
0
1
0
0
1
2
2
0
1
0
0
0
2
0
0
2
0
2
0
1
2
0
0
0
0
1
2
0
1
0
0
0
2
2
0
2
1
1
1
0
0
1
0
0
1
0
2
2
0
1
2
0
0
1
0
0
0
0
0
0
2
1
2
0
0
1
0
1
0
0
0
2
1
0
2
0
1
0
1
0
1
0
2
1
0
2
0
0
0
0
2
1
3
8
0
1
1
1
1
0
0
0
1
2
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
1
0
2
1
1
0
1
0
0
0
1
2
0
2
0
0
0
2
0
0
2
2
0
1
1
0
0
1
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
2
2
0
3
0
1
1
0
0
1
0
0
1
0
0
1
0
2
1
0
0
0
0
0
9
0
2
0
0
2
0
0
1
2
2
2
0
0
3
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
1
2
0
1
1
2
0
0
0
1
0
2
1
0
0
0
2
0
1
0
0
8
1
2
0
0
0
1
0
2
2
0
0
0
0
1
0
0
0
1
3
1
1
0
1
0
0
1
2
1
2
0
0
0
0
2
1
2
1
0
0
2
2
2
1
2
2
2
0
0
0
0
0
0
0
1
1
0
0
0
1
0
2
0
1
0
3
0
0
0
3
4
1
1
1
1
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
2
0
0
0
1
0
1
2
1
2
1
1
1
0
0
0
0
1
1
1
2
4
2
2
0
0
0
0
0
0
1
0
0
0
0
3
0
0
1
1
0
2
0
1
2
0
0
0
1
1
2
0
2
0
2
1
0
0
0
2
0
0
1
1
0
1
0
1
0
0
2
0
2
0
0
2
0
2
1
0
0
1
1
0
0
1
1
0
1
4
0
0
2
0
0
1
0
1
0
0
0
0
1
2
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
1
2
1
0
0
1
0
0
1
0
0
0
1
1
1
1
1
2
2
0
0
0
2
0
1
1
2
0
0
2
0
0
2
1
1
0
0
0
2
2
1
1
3
0
2
2
1
0
0
2
0
1
0
3
2
0
0
2
0
0
0
1
0
1
2
1
0
0
0
0
2
0
0
1
2
0
0
1
0
1
1
0
2
1
0
0
0
1
1
0
1
1
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
2
0
1
1
1
1
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
2
0
1
0
0
0
2
1
2
0
0
2
0
1
0
0
0
0
2
1
2
0
1
1
0
0
0
0
1
0
1
0
0
2
0
2
0
1
3
0
0
0
0
1
0
0
0
1
0
0
0
0
2
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
2
1
0
1
0
2
0
0
2
0
0
1
0
0
1
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
1
0
1
0
1
0
2
0
0
0
1
0
2
1
2
1
0
0
2
2
0
0
0
0
0
0
0
6
0
0
0
1
1
0
1
0
0
0
1
2
2
0
0
0
2
1
0
1
0
0
0
1
0
1
0
1
1
1
0
2
0
0
0
1
1
0
2
0
0
0
2
1
0
2
2
0
1
0
0
1
2
0
1
1
0
0
1
0
2
0
1
1
1
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
3
0
2
2
1
1
0
1
0
2
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
2
3
0
0
2
1
0
1
0
0
0
2
2
0
0
0
0
1
0
2
0
2
2
0
0
0
1
0
0
0
0
0
1
2
2
1
1
0
1
1
0
1
0
1
1
0
2
0
0
1
1
0
1
2
0
0
1
0
1
1
1
0
2
2
0
0
2
2
1
2
4
2
2
2
0
2
2
0
0
1
0
0
0
0
2
1
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
2
2
0
0
1
0
0
1
0
0
0
0
0
2
1
2
0
0
0
1
0
1
0
0
2
0
0
1
1
1
0
0
0
0
0
1
1
2
0
0
2
2
2
0
0
2
2
2
0
0
0
0
1
2
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
1
1
0
1
1
0
0
2
1
0
0
0
2
0
1
0
0
1
0
0
2
0
0
2
1
0
2
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
1
1
2
1
2
2
0
0
0
6
0
2
0
2
1
1
0
0
0
0
0
0
2
0
0
1
1
0
0
0
2
0
0
0
0
2
2
1
0
2
0
1
0
2
0
2
1
0
0
0
1
0
2
2
0
0
0
0
0
1
0
0
2
0
0
1
0
1
0
0
1
1
1
3
0
0
0
0
3
0
0
1
2
1
1
0
2
1
0
3
0
0
2
0
0
0
0
1
0
0
0
2
2
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
3
0
1
1
1
0
2
0
0
2
1
1
0
1
0
1
3
0
0
0
0
1
1
0
1
1
0
0
0
1
2
2
0
1
1
2
0
0
0
0
1
0
0
0
2
1
0
0
1
2
2
0
0
0
0
1
2
0
0
1
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
2
0
0
0
1
0
2
1
0
1
1
0
0
2
0
0
0
2
1
1
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
1
2
0
0
1
2
0
1
1
2
1
0
2
0
0
0
4
0
3
4
2
0
0
0
1
2
0
0
0
1
1
0
0
0
0
0
0
2
0
2
0
0
0
1
2
0
1
4
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
2
2
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
2
0
0
0
1
0
0
0
1
0
1
0
2
0
1
1
1
3
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
3
0
0
2
1
0
0
0
1
0
0
0
0
0
1
1
1
2
3
2
0
2
4
1
1
1
0
0
0
2
2
0
2
2
1
1
1
0
2
2
1
2
0
0
0
2
1
0
0
0
0
2
2
2
1
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
2
2
2
0
0
0
2
0
0
0
2
0
1
2
0
0
0
0
0
0
2
0
1
2
1
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
2
0
2
0
0
0
0
0
0
0
0
1
1
1
0
2
1
0
0
0
1
0
0
0
0
0
2
2
0
2
1
2
0
0
0
2
0
0
0
2
2
0
0
2
0
1
2
2
1
0
0
0
0
1
0
0
1
0
2
0
1
0
1
0
0
0
1
3
0
2
1
0
1
0
0
0
1
0
0
1
0
2
2
2
2
2
0
2
0
2
1
2
1
0
1
1
0
2
0
0
0
1
1
0
0
1
0
2
1
1
3
0
0
1
0
0
0
2
2
0
0
1
0
0
2
2
0
0
0
0
1
0
2
0
0
0
0
1
1
0
1
2
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
2
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
1
0
2
0
0
2
0
2
0
0
0
0
1
2
0
1
0
0
0
1
0
1
0
0
0
2
0
1
0
1
1
1
1
0
0
1
1
0
1
0
0
0
0
0
2
0
0
0
0
0
2
2
2
0
1
0
0
1
0
0
4
1
1
2
0
1
1
0
2
2
0
0
0
1
1
0
0
2
1
1
0
0
0
0
1
0
0
1
0
2
0
2
2
0
0
0
0
0
0
0
0
1
0
0
2
2
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
2
1
0
0
1
1
1
1
0
0
0
0
2
2
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
2
0
2
1
0
0
2
0
2
1
2
2
1
0
0
2
1
0
0
0
0
0
1
2
1
2
0
0
2
0
0
0
3
0
1
1
1
0
1
2
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
2
0
0
0
0
0
1
1
1
1
0
1
0
0
0
0
1
1
1
2
0
0
0
1
0
0
2
1
0
1
3
0
1
0
0
2
0
0
0
0
1
0
0
1
0
2
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
2
2
1
0
1
1
0
0
0
0
1
0
1
2
1
0
0
2
0
4
0
0
0
0
1
0
2
2
0
1
0
0
0
1
0
1
1
0
0
1
2
0
0
0
1
0
0
1
1
0
0
0
2
1
0
0
1
2
0
1
1
0
0
1
0
1
0
0
1
0
0
0
1
0
0
2
1
4
0
1
1
1
2
0
1
2
0
0
0
1
1
1
2
2
0
0
0
0
2
0
0
1
0
0
0
0
2
0
2
0
1
0
0
3
2
0
0
0
0
0
0
0
2
0
0
0
1
2
2
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
2
1
0
0
0
0
0
2
0
0
1
1
0
0
0
2
0
0
0
2
0
0
0
5
0
2
0
0
0
0
0
0
0
2
1
2
0
2
3
0
1
0
0
1
1
1
0
2
0
1
3
0
0
0
1
0
2
0
1
0
0
1
0
1
0
2
0
2
0
2
0
0
2
1
0
2
2
0
0
0
2
2
0
2
0
0
0
2
0
2
2
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
2
1
0
0
1
2
0
0
0
0
2
0
0
0
0
2
0
1
2
0
0
0
0
2
1
0
1
0
0
0
2
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
2
0
1
2
0
2
2
1
0
0
1
0
0
0
0
0
2
1
0
0
0
1
1
0
0
2
0
2
1
1
2
0
0
0
0
0
0
2
0
2
0
1
0
1
0
0
1
0
1
0
2
0
0
1
0
0
0
0
0
1
1
2
2
2
0
0
0
0
1
3
0
1
6
1
0
1
1
0
1
1
0
0
1
0
0
2
0
2
0
0
2
0
2
1
0
1
1
1
0
0
1
0
1
1
1
0
1
0
1
0
0
2
0
1
0
1
0
2
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
1
2
0
1
0
0
2
0
2
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
1
1
2
1
2
0
0
1
0
2
0
4
1
2
1
0
0
2
0
1
2
0
0
0
4
0
1
2
3
0
0
0
0
1
0
0
0
0
2
0
2
1
0
0
0
0
2
0
1
0
0
1
0
0
0
2
1
0
2
2
1
0
0
3
0
1
0
0
1
1
2
0
1
0
0
1
2
0
0
0
0
0
1
1
1
0
0
0
2
0
1
1
0
0
2
0
1
0
0
2
0
0
2
0
2
0
2
0
0
0
2
1
0
0
0
0
0
2
2
0
1
1
0
0
0
0
0
2
3
0
2
0
2
2
0
0
1
2
1
2
0
1
0
1
2
2
2
0
0
0
2
2
2
0
2
2
0
0
2
1
0
0
0
2
1
2
0
1
3
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
2
0
2
0
0
1
1
0
2
2
2
2
1
0
0
0
2
2
0
0
0
1
0
2
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
1
0
0
2
1
0
0
0
0
1
1
1
0
0
1
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
2
2
0
0
2
2
0
0
0
2
1
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
2
4
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
2
0
2
1
1
0
1
1
0
0
0
0
1
1
0
0
0
2
2
0
0
1
0
2
0
3
0
0
0
0
0
2
0
0
0
2
0
1
0
1
0
0
2
1
0
0
0
0
1
1
1
2
2
2
0
0
2
0
1
0
0
2
0
0
0
1
0
0
0
0
0
3
0
1
0
1
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
1
0
2
1
1
2
0
1
2
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
2
1
0
1
2
0
0
2
0
1
1
0
0
0
0
2
2
0
3
3
0
1
1
3
0
0
0
0
0
1
1
2
0
2
0
0
2
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
2
2
0
1
1
0
1
1
2
0
2
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
2
1
2
1
0
1
0
1
1
1
0
0
0
2
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
2
1
0
1
0
2
0
1
1
0
0
1
0
1
1
2
0
0
0
2
3
2
2
0
1
2
0
0
1
1
2
0
0
1
0
0
0
1
0
1
0
1
1
0
1
2
0
0
1
2
0
0
1
0
1
1
2
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
2
1
0
1
0
0
2
2
1
0
1
1
2
1
2
0
0
2
0
0
0
1
1
2
0
2
0
0
0
0
0
1
2
2
1
0
0
0
0
2
2
0
1
0
0
0
2
2
0
0
0
1
0
0
0
2
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
2
1
0
1
0
2
2
0
0
0
0
0
1
0
0
0
0
1
1
2
0
1
1
0
0
1
0
0
0
2
0
0
0
1
1
1
0
0
1
2
0
0
0
1
2
1
0
1
3
0
1
1
0
1
1
0
0
1
2
0
1
1
0
1
0
0
2
0
0
1
1
0
0
0
0
0
1
0
2
2
0
0
1
1
0
2
0
1
0
2
0
1
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
1
3
1
0
1
2
3
0
0
2
0
0
0
2
2
1
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
2
1
1
1
2
0
0
2
0
2
0
1
0
2
1
0
0
1
0
0
0
0
2
0
1
0
0
1
0
2
0
2
0
0
1
0
0
2
0
1
2
0
1
0
1
0
1
1
0
1
0
0
0
0
2
0
0
0
0
0
2
2
0
1
0
2
1
2
0
0
0
2
2
1
0
2
0
1
3
0
0
2
2
2
2
0
0
2
0
0
1
0
0
0
1
3
1
0
0
1
0
0
2
0
0
2
0
2
0
0
0
1
2
0
3
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
3
0
1
2
1
0
0
2
1
1
0
0
1
0
1
1
0
0
1
1
0
2
2
0
3
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
2
0
0
2
0
2
0
0
1
2
2
0
1
0
2
1
2
1
0
0
0
0
2
0
0
0
1
0
0
0
1
1
0
0
2
2
2
0
0
0
0
2
0
0
0
2
0
2
0
0
1
0
0
2
2
3
0
2
0
0
0
0
0
0
1
1
0
0
0
2
0
1
0
1
0
1
1
0
2
0
2
0
1
0
1
1
0
0
0
1
0
0
1
1
0
0
2
3
0
2
0
0
3
1
0
1
0
0
1
1
0
2
1
2
0
0
2
0
2
2
0
2
2
0
0
0
0
0
0
2
3
1
0
0
0
1
0
0
0
0
1
2
1
0
0
0
0
0
0
1
0
1
0
0
0
2
2
1
0
2
0
1
2
0
2
0
0
1
2
0
2
0
0
1
0
0
1
0
0
1
0
0
2
1
1
0
0
1
2
1
0
1
0
0
0
2
0
2
2
0
1
2
0
1
0
2
1
1
2
0
1
0
1
0
0
0
0
0
2
2
0
2
0
2
1
0
0
1
1
0
0
0
0
0
1
0
2
1
0
0
2
1
1
1
0
0
0
0
0
1
0
0
0
0
2
1
1
0
0
1
0
0
0
2
1
2
0
0
0
0
0
0
0
1
1
1
0
2
0
0
0
1
3
0
2
1
0
0
0
3
0
0
0
0
0
0
0
3
1
1
1
0
0
0
1
0
0
0
0
2
2
2
1
0
0
0
0
0
0
0
0
1
1
0
0
0
3
0
2
2
0
1
0
0
0
0
0
2
2
0
1
1
1
0
1
0
0
1
2
1
0
0
0
0
0
0
0
2
2
2
1
0
0
0
2
0
3
1
0
0
1
0
2
0
0
0
2
2
2
0
1
1
0
0
0
1
0
0
0
2
2
2
1
1
0
0
2
2
1
2
2
0
1
0
2
0
2
0
0
0
2
0
0
0
0
2
0
1
0
2
2
0
1
0
0
0
0
0
0
2
1
1
1
0
1
0
2
0
0
1
0
2
1
1
1
0
2
0
0
2
0
1
0
0
1
0
0
0
1
0
0
2
1
0
0
0
0
1
2
2
0
0
0
0
0
1
1
0
0
1
0
0
0
2
1
0
1
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
1
2
0
0
1
1
1
0
1
0
0
0
0
0
1
1
0
1
0
0
0
1
0
1
0
1
1
0
1
0
0
1
0
2
2
0
2
4
0
1
0
2
1
0
2
0
0
0
1
0
0
0
0
2
0
4
0
0
2
2
0
0
0
0
1
0
0
1
1
1
0
1
1
2
2
2
0
0
1
0
0
2
0
1
0
1
2
2
3
2
2
0
0
0
0
1
0
0
1
0
1
0
0
2
2
0
1
0
0
0
0
0
0
0
1
1
0
2
0
0
2
0
0
2
2
2
0
2
1
0
2
0
2
0
2
0
3
0
0
2
0
2
1
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
2
1
0
0
0
2
0
0
1
0
0
0
1
0
0
1
0
2
1
0
0
0
0
2
1
0
3
2
1
0
1
0
0
2
2
0
0
1
0
1
1
1
3
0
2
0
0
0
2
0
5
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
1
0
0
0
1
1
0
2
2
0
2
1
0
1
0
1
1
0
0
0
2
0
2
0
1
1
0
0
0
1
0
1
1
0
0
0
1
1
2
2
0
0
2
1
0
1
0
1
0
2
0
0
1
0
3
0
0
0
0
1
2
1
0
1
1
1
0
0
0
0
1
2
0
0
2
1
1
0
0
0
1
0
0
0
1
3
0
0
5
0
0
0
0
1
1
0
2
2
0
0
0
0
1
0
1
1
1
0
1
0
0
0
0
2
0
2
0
0
2
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
2
1
0
0
0
1
2
0
0
1
2
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
1
0
0
0
1
2
0
0
0
2
1
1
2
0
2
3
0
0
1
1
0
0
2
0
1
0
1
0
0
1
1
0
2
0
0
1
1
0
2
1
0
0
0
0
0
0
0
0
2
1
1
0
0
4
1
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
2
0
1
1
1
0
0
0
0
0
0
1
0
0
2
0
0
0
1
1
1
1
0
0
0
0
1
2
1
0
1
0
1
2
1
2
1
0
0
3
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
2
2
0
0
1
2
0
0
0
2
0
0
0
0
2
0
0
1
2
0
2
1
2
0
3
0
0
0
0
2
1
3
1
0
0
0
0
1
1
2
0
1
3
0
0
1
0
2
0
1
1
1
0
2
0
0
2
0
0
0
0
2
2
1
0
0
0
2
0
1
0
0
0
1
1
0
1
0
1
1
1
1
2
0
1
0
1
0
0
0
1
0
1
2
0
2
0
0
2
1
0
0
2
2
2
2
0
0
0
1
2
1
2
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
1
0
1
0
0
2
0
1
2
0
0
1
1
1
0
0
2
0
1
1
3
1
2
2
3
0
0
2
1
1
2
0
0
0
0
0
0
0
0
0
0
1
2
2
2
2
0
1
0
2
0
0
1
0
0
0
2
0
0
1
0
2
0
0
1
1
0
0
0
2
1
1
3
2
1
3
0
0
0
0
1
0
1
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
2
0
0
0
1
1
1
1
2
1
1
0
0
0
1
0
0
0
0
0
1
0
1
1
1
0
2
0
1
0
0
2
2
3
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
3
1
1
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
1
0
1
0
2
1
2
0
0
0
0
0
0
1
0
2
2
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
1
0
2
0
1
0
0
2
2
0
1
1
0
0
0
0
0
2
0
0
0
1
1
0
1
0
2
1
1
0
1
2
2
0
0
1
1
0
0
0
1
2
1
1
2
0
0
2
1
1
0
0
0
0
1
1
0
2
0
0
0
1
0
1
0
1
0
1
1
0
0
0
2
2
0
0
1
1
0
2
0
2
0
2
0
0
0
0
2
0
1
2
0
2
0
0
0
0
2
0
0
0
2
0
2
0
2
0
0
0
2
1
0
2
1
2
0
0
0
1
0
1
1
0
0
1
0
1
1
0
0
2
2
1
1
0
0
1
1
2
0
0
0
0
0
1
0
2
2
0
1
0
3
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
2
0
0
0
1
2
2
2
1
2
1
0
0
0
2
1
2
0
1
0
1
0
0
1
2
2
0
0
0
0
1
2
0
2
0
1
1
0
0
0
1
0
0
0
0
2
0
1
2
1
2
2
2
0
0
0
0
0
0
2
2
2
2
1
0
0
1
0
0
2
2
0
0
0
0
0
0
2
0
0
2
0
0
1
2
1
0
0
0
0
0
0
1
0
2
0
2
0
2
2
2
1
1
0
0
0
0
3
0
0
1
1
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
7
1
0
0
0
0
1
2
0
0
0
2
0
0
2
0
2
0
1
2
0
0
2
1
1
1
0
1
0
1
0
0
1
0
0
0
1
1
1
1
2
0
0
0
0
0
2
2
0
2
1
0
0
0
0
0
0
0
1
1
0
2
2
0
0
0
0
0
0
1
0
1
0
0
2
1
0
0
0
1
1
0
0
0
0
0
2
0
0
0
2
1
2
0
1
0
0
3
1
0
0
1
0
0
0
0
0
2
2
0
0
0
0
2
0
1
0
0
0
0
2
0
0
1
0
1
1
0
0
0
0
0
0
2
1
0
3
2
0
1
0
0
0
0
0
0
1
1
0
1
1
0
1
0
1
0
0
0
1
2
1
1
1
2
1
1
0
0
2
2
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
2
2
0
0
1
1
0
0
0
0
0
2
0
1
0
1
0
2
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
2
0
0
0
1
0
2
0
1
1
0
0
0
2
0
0
0
0
0
1
1
0
0
2
1
0
0
2
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
2
0
2
0
0
0
2
1
0
1
0
0
0
1
2
0
1
0
1
0
5
1
1
1
2
1
0
1
0
0
0
0
0
0
2
0
2
0
0
0
3
0
0
0
2
0
2
2
0
1
2
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
1
0
1
0
0
2
0
1
1
0
1
0
0
2
1
0
0
2
2
0
2
1
0
0
0
1
1
2
2
2
1
0
1
1
1
1
1
0
1
0
0
0
0
1
2
2
0
1
0
0
0
0
0
1
0
2
1
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
2
2
0
0
0
0
2
1
2
0
1
0
0
0
0
0
1
0
0
2
2
0
2
1
1
3
0
1
0
0
2
1
0
0
0
1
0
0
1
0
0
0
0
0
1
2
1
2
0
2
0
0
0
1
0
0
1
0
0
0
2
0
2
0
0
1
0
1
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
4
1
0
0
2
0
0
0
0
0
0
2
0
0
2
0
1
1
2
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
2
0
2
0
2
0
2
0
4
0
0
1
0
2
0
0
1
0
2
0
2
2
0
0
0
2
0
1
1
0
0
0
0
1
1
2
1
0
0
0
0
0
2
6
0
0
0
0
0
0
2
0
0
3
1
0
0
0
2
1
1
0
1
0
0
2
0
0
0
1
0
0
2
0
0
2
2
0
0
0
0
0
0
2
0
0
2
2
2
0
2
1
0
0
0
0
2
0
1
1
0
1
0
0
1
0
1
0
2
0
1
0
1
1
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
3
0
0
0
1
0
0
1
0
1
3
2
0
0
0
0
0
0
2
1
1
0
0
0
2
0
4
2
2
0
0
1
1
0
0
0
0
0
0
0
0
2
3
0
1
2
1
2
0
1
0
1
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
1
2
1
0
1
0
2
0
2
0
2
1
0
1
2
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
1
8
2
1
1
0
0
0
0
1
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
1
1
0
0
0
3
0
0
0
0
2
1
1
1
0
0
0
2
2
0
0
0
0
1
0
0
0
1
1
0
0
0
2
0
0
2
2
0
0
0
0
0
0
5
0
2
2
0
0
1
0
0
0
0
0
1
0
0
2
1
0
0
2
0
0
2
1
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
2
1
2
1
1
0
2
1
0
1
1
0
3
1
1
1
0
2
0
1
0
0
0
1
2
0
0
0
1
0
0
0
1
2
1
0
0
2
0
2
0
0
0
1
1
1
2
2
0
1
1
2
0
1
3
1
0
0
0
0
2
2
0
0
2
1
2
0
0
0
2
2
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
2
1
1
1
1
0
0
2
2
0
2
0
0
0
0
0
2
0
0
0
3
1
1
1
0
0
0
1
1
2
0
1
0
0
0
0
0
1
0
1
1
0
0
1
0
0
1
2
0
0
0
0
1
0
2
1
0
0
2
0
0
0
0
2
2
2
0
0
0
0
1
1
1
0
2
2
2
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
3
3
0
0
0
0
0
2
1
0
0
1
2
0
2
0
0
0
0
0
0
2
4
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
2
1
2
2
0
1
0
2
3
0
1
0
0
0
1
0
0
0
1
6
0
0
2
1
1
1
0
0
0
0
4
2
1
1
1
0
1
2
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
2
2
0
1
0
0
0
0
2
0
1
0
0
1
1
1
1
0
1
1
1
0
2
2
1
0
2
0
1
0
0
0
1
1
1
1
2
0
0
2
0
2
0
0
0
0
1
1
0
0
0
1
2
2
2
1
0
2
0
0
2
2
2
0
2
0
2
0
0
0
0
0
0
0
1
3
0
4
0
1
2
0
1
0
0
0
0
2
1
0
0
1
0
0
0
0
2
5
0
0
1
0
2
0
0
0
2
0
0
0
0
0
1
1
2
0
0
0
1
0
1
0
1
1
0
0
2
1
0
0
0
1
0
0
0
0
0
0
1
1
0
2
1
0
0
1
0
2
0
2
1
0
0
1
1
0
1
0
0
2
0
0
0
0
0
2
1
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
1
1
0
0
0
0
0
1
3
0
0
0
1
0
0
0
0
0
1
4
0
0
0
0
2
0
1
0
0
0
1
0
1
1
0
2
1
2
2
2
0
1
0
0
1
0
2
1
3
2
1
0
0
1
0
0
2
0
0
2
1
1
2
1
0
0
0
1
2
1
2
0
1
0
0
0
0
1
0
1
0
1
2
0
1
1
2
1
0
0
1
0
0
2
1
0
3
1
2
1
0
1
0
0
0
1
0
0
0
0
3
0
0
0
0
1
2
0
2
2
0
1
0
0
1
0
0
0
2
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
1
0
2
0
0
0
1
1
1
0
2
1
1
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
2
0
0
0
2
0
1
0
1
0
0
2
1
0
2
1
2
0
0
0
0
0
2
1
0
2
1
2
1
2
1
0
1
2
1
3
0
0
0
0
0
2
0
0
1
2
0
0
1
1
0
0
0
0
0
2
0
0
0
1
1
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
2
2
0
0
2
2
7
0
2
0
1
2
0
1
0
1
2
0
0
0
0
2
1
1
1
0
0
0
0
1
0
0
0
2
0
1
0
0
0
1
0
0
2
1
0
0
0
0
0
2
1
1
0
0
0
0
0
1
2
1
0
0
1
1
0
0
0
0
0
0
1
2
0
0
0
0
1
1
3
2
0
0
0
2
1
1
0
2
0
0
0
1
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
2
2
0
0
2
1
0
0
0
2
0
0
0
0
1
0
2
0
1
0
2
1
0
0
0
0
2
1
0
0
1
2
1
1
0
0
0
0
1
0
0
2
0
2
1
0
2
0
0
0
1
0
0
0
0
2
2
0
0
0
1
0
0
0
2
0
0
1
1
0
2
1
0
0
0
2
1
1
2
1
0
0
0
0
0
1
2
0
0
0
2
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
2
1
0
0
0
0
0
2
0
0
0
1
4
1
0
2
0
0
0
0
2
0
1
2
1
2
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
3
2
2
2
0
1
0
1
0
0
3
1
1
0
1
0
1
2
2
2
0
2
0
0
1
0
0
0
1
0
0
1
0
2
0
1
1
0
1
0
0
1
0
2
1
2
1
0
0
0
2
2
1
2
2
0
1
0
0
1
0
0
0
0
0
1
2
1
0
1
0
0
2
1
0
2
0
0
2
0
0
0
0
0
0
1
0
2
0
2
0
2
0
1
2
1
0
1
0
0
0
2
2
0
0
1
0
0
0
0
0
5
0
0
1
1
1
0
0
0
2
0
1
1
0
0
2
0
1
2
1
0
1
2
0
0
1
1
0
2
3
0
1
0
2
1
0
1
0
0
0
1
0
2
1
0
2
1
0
0
0
0
0
0
2
1
0
0
0
0
1
2
0
0
0
1
0
0
0
0
1
1
0
0
2
1
2
0
4
2
0
2
0
0
0
0
1
0
1
2
0
0
1
0
1
0
2
0
0
0
0
1
0
2
0
2
2
0
2
2
2
0
1
2
1
2
0
1
0
0
0
1
2
0
1
0
2
0
0
0
10
1
2
0
0
1
0
0
2
1
0
0
2
0
0
0
1
0
0
0
0
0
2
3
0
0
2
0
0
2
2
2
0
2
1
0
0
0
2
0
0
1
0
0
0
1
2
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
1
0
1
0
0
0
2
2
0
0
2
0
0
1
1
2
2
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
1
2
0
1
0
2
1
2
0
1
1
0
0
1
0
1
1
0
1
0
2
0
0
1
2
0
0
1
1
0
0
0
0
2
1
5
2
0
2
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
2
2
0
0
0
1
0
0
1
0
0
0
0
1
0
1
2
0
0
1
0
0
0
1
0
2
0
1
2
0
0
0
0
0
0
0
1
2
0
1
1
0
0
0
2
0
0
2
1
2
2
0
0
0
0
0
0
0
1
0
2
0
1
1
1
0
0
0
0
0
2
2
2
0
2
2
0
0
0
2
0
0
2
4
2
0
0
0
0
0
0
1
1
1
0
1
0
1
2
1
1
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
2
1
1
1
0
0
0
0
1
0
0
0
1
0
2
2
0
1
2
0
0
0
0
1
0
0
1
1
0
2
2
0
0
0
1
0
0
0
0
1
0
1
2
1
1
1
0
0
1
2
2
2
0
1
0
0
1
0
2
2
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
2
1
0
0
1
0
0
0
0
1
0
2
1
0
0
1
0
0
0
3
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
3
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
1
0
0
0
2
2
2
0
0
0
0
3
0
2
1
1
2
0
0
1
1
2
1
1
0
2
0
1
0
0
0
0
0
0
0
0
0
1
2
2
0
2
0
0
0
1
0
0
0
1
0
1
2
2
1
0
0
0
2
2
2
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
1
0
1
1
0
2
0
0
1
0
0
0
1
0
2
1
1
0
2
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
1
0
0
1
4
0
0
2
1
2
0
0
0
2
0
1
0
1
1
0
2
0
0
2
0
0
1
2
1
0
1
2
0
0
0
0
2
1
2
1
2
2
0
1
0
1
0
2
0
1
2
1
2
2
0
0
0
0
0
2
0
2
0
0
1
1
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
1
1
0
0
1
0
1
0
0
0
2
0
0
1
0
1
2
3
0
1
2
1
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
1
0
3
1
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
2
0
1
0
1
1
0
0
0
0
2
0
0
0
1
0
1
1
0
2
2
2
1
0
0
0
1
0
0
2
2
2
2
1
1
1
2
1
2
1
2
0
0
1
0
0
0
0
0
1
0
2
0
1
0
0
2
0
0
1
0
0
0
0
1
2
2
0
0
0
1
0
0
2
2
1
0
4
0
0
0
0
1
0
0
0
0
3
0
0
0
0
2
1
0
2
0
0
0
2
0
0
1
0
3
2
1
1
1
1
0
2
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
1
2
0
0
1
1
0
0
1
1
0
0
0
2
0
2
2
0
2
0
0
1
0
1
0
2
0
1
1
0
2
0
0
0
0
1
0
1
0
0
0
2
0
0
2
0
2
0
2
2
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
2
3
2
1
1
0
0
0
2
0
2
0
2
0
0
1
1
0
2
0
3
0
0
0
2
1
1
0
0
0
0
2
0
1
0
0
2
2
0
0
2
0
2
0
2
2
0
2
0
1
1
2
2
6
1
0
1
0
0
1
1
2
0
2
2
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
1
3
1
0
2
0
0
2
0
0
0
1
0
0
0
2
0
0
0
1
3
1
2
2
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
2
0
0
1
1
1
0
1
0
1
2
0
0
0
1
0
1
2
1
2
1
0
1
0
0
2
2
0
0
0
0
1
0
0
0
2
0
2
1
0
0
2
0
2
1
2
0
0
0
1
1
1
0
0
0
0
1
0
0
1
0
0
2
0
0
1
1
1
1
1
1
1
0
0
0
0
0
2
0
0
2
0
0
2
0
2
1
3
2
0
1
0
0
1
0
0
0
0
2
2
0
0
0
1
2
3
1
0
2
2
1
1
3
1
2
0
0
1
0
2
1
0
1
1
0
0
0
2
0
0
0
6
0
0
0
0
1
0
0
0
0
2
2
1
2
1
0
1
1
0
2
1
1
1
2
0
1
0
0
0
0
1
0
0
0
4
0
0
2
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
1
1
0
0
2
0
2
0
0
0
2
0
1
0
0
2
0
0
0
0
1
0
2
0
0
1
2
0
3
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
2
0
1
2
1
1
0
2
0
0
3
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
1
2
2
0
0
1
0
2
1
1
1
0
0
0
0
0
1
1
1
1
0
0
2
0
0
0
0
2
0
0
0
0
0
1
2
0
0
2
2
1
3
0
1
1
0
0
0
2
1
0
0
1
2
2
2
0
1
0
1
0
0
0
1
1
0
2
0
4
0
1
0
0
2
0
2
0
0
0
2
0
0
0
0
0
1
1
0
1
2
2
1
2
3
0
2
0
0
0
2
0
0
2
0
0
0
2
1
0
0
2
0
0
0
1
0
0
0
0
0
2
1
2
2
2
0
3
0
0
2
1
2
0
0
0
0
2
2
0
0
0
2
0
0
1
0
0
1
2
0
0
0
1
0
0
1
2
0
1
5
0
2
1
0
2
0
2
1
1
1
0
1
0
0
1
2
1
0
0
0
2
0
0
0
0
2
0
2
2
0
0
3
0
2
1
1
0
2
2
0
0
0
1
1
1
0
0
0
2
0
0
0
1
0
1
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
1
0
1
0
0
0
2
1
0
2
0
0
2
0
2
0
2
9
0
0
0
2
0
0
0
0
1
3
1
1
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
2
1
2
0
1
2
0
0
0
1
0
2
2
0
0
0
2
0
2
2
0
0
2
0
2
0
0
0
3
0
0
1
0
0
0
0
0
2
0
0
0
0
1
2
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
6
0
2
0
1
2
0
0
0
1
2
0
2
2
0
1
2
1
0
0
2
0
1
2
1
2
0
2
0
1
2
0
1
0
0
0
0
0
0
1
2
0
0
2
0
2
0
2
2
3
0
0
2
2
3
0
0
2
0
2
0
0
2
1
0
0
2
1
1
0
0
0
2
0
0
1
2
0
0
2
2
1
1
0
1
0
0
1
1
2
0
2
0
0
0
0
1
0
0
0
0
1
0
0
2
0
2
0
1
2
1
0
0
2
2
2
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
3
0
0
0
2
0
0
0
0
3
7
0
1
0
1
0
2
0
0
0
0
0
3
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
2
0
1
0
0
0
0
0
1
1
0
1
0
1
0
2
1
0
0
1
0
0
0
1
0
0
3
0
0
1
1
2
0
1
2
0
2
1
0
0
0
2
0
0
0
0
1
0
2
0
0
1
0
1
0
1
0
2
2
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
1
0
1
2
0
2
0
2
0
0
0
1
2
1
0
0
2
0
0
1
1
2
2
2
1
0
0
0
0
0
1
0
0
0
1
1
2
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
1
2
4
0
0
1
0
2
0
0
2
0
0
2
0
1
2
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
3
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
1
0
2
1
0
0
0
0
0
2
0
2
0
0
0
0
2
0
1
0
0
2
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
1
0
0
2
0
2
2
0
1
0
0
0
1
1
1
1
0
2
0
0
1
0
0
0
1
0
0
0
0
2
0
2
0
2
1
1
0
1
0
0
1
2
0
1
0
0
0
0
0
2
1
1
0
0
1
0
0
0
2
1
2
0
0
1
1
1
1
1
2
1
1
2
1
0
1
0
0
0
0
2
0
0
2
0
0
1
0
0
2
0
1
0
2
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
3
0
2
0
2
0
1
2
1
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
2
1
0
2
0
0
0
1
1
0
1
1
0
0
1
0
2
0
2
0
1
1
1
0
0
2
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
3
0
2
2
0
1
0
0
0
0
1
1
0
0
0
2
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
6
0
1
1
0
2
0
0
0
0
0
0
0
1
0
2
0
1
0
0
2
0
0
0
2
0
1
0
0
0
1
0
2
0
0
1
0
0
2
0
1
1
2
0
0
0
0
2
1
0
0
0
0
0
0
2
2
0
1
1
0
0
0
0
0
0
2
0
1
0
0
1
1
1
0
0
1
1
0
1
0
1
2
2
0
0
1
5
0
1
1
1
1
1
1
0
0
0
0
2
0
0
2
0
0
2
1
1
1
0
0
0
0
1
0
0
1
2
1
2
1
1
1
1
0
2
1
0
2
0
1
2
0
2
0
2
1
0
0
2
1
0
0
0
2
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
1
3
0
0
0
4
3
1
1
1
0
0
0
2
0
2
0
1
0
1
0
0
1
0
2
0
2
0
0
2
0
2
1
1
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
15
0
2
2
0
0
0
0
2
1
0
0
0
1
0
0
0
2
0
5
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
1
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
1
1
0
0
2
0
0
1
2
1
0
1
0
2
0
0
0
2
0
0
2
0
2
3
1
1
0
2
1
1
0
3
1
2
1
2
2
2
2
1
0
1
0
1
4
0
2
0
2
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
1
0
1
0
2
0
0
0
1
0
2
0
0
1
0
1
0
1
0
1
0
2
1
1
1
0
0
2
2
0
2
0
1
2
0
0
1
0
0
0
0
0
1
0
0
2
0
1
0
0
0
1
0
0
1
0
0
1
0
0
2
1
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
2
1
0
2
1
1
0
2
0
2
0
0
1
0
0
0
0
0
2
0
2
2
2
0
0
0
1
0
0
0
1
0
1
2
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
1
0
1
0
0
0
0
2
0
0
2
2
0
0
2
0
0
1
0
2
1
0
0
2
0
0
0
0
0
0
2
0
2
0
2
0
0
0
1
0
0
0
0
0
0
1
2
2
0
2
0
0
0
3
1
0
1
0
0
2
0
0
0
0
0
2
1
0
1
2
1
0
2
0
2
0
2
0
2
1
0
1
0
0
0
0
1
0
0
0
1
0
0
2
0
2
0
0
2
0
0
2
0
0
2
0
2
1
0
0
0
0
0
0
0
2
1
0
0
2
0
2
0
0
2
0
0
0
1
0
1
0
0
0
0
2
2
0
0
2
0
1
1
2
0
0
0
1
2
2
0
0
0
1
0
1
1
2
0
2
0
0
0
2
0
0
0
1
0
1
0
0
1
1
0
0
2
0
1
2
3
0
0
2
1
0
1
0
1
0
1
2
0
0
1
1
0
0
0
1
1
0
0
2
2
0
0
1
0
0
0
2
0
2
0
0
0
0
3
0
0
0
0
2
0
0
1
0
1
0
0
1
0
2
1
2
0
1
0
0
0
0
0
0
0
2
0
2
1
1
0
1
0
0
2
1
0
4
2
0
0
0
0
0
2
0
0
6
1
1
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
2
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
2
0
0
0
0
2
0
0
1
0
0
1
0
1
1
0
0
2
1
0
0
0
0
2
0
1
2
0
1
0
0
0
0
1
0
2
0
2
2
0
3
2
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
1
0
2
0
0
0
1
1
3
0
0
2
0
1
1
1
2
0
0
1
2
1
0
1
1
0
0
0
0
2
1
1
0
0
2
0
2
0
0
0
1
0
0
0
2
1
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
2
0
0
0
2
2
0
1
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
2
1
0
0
0
0
1
0
0
1
0
2
0
0
1
1
1
0
0
1
1
0
0
4
0
1
2
0
0
0
0
0
2
0
0
0
2
0
0
0
2
5
0
0
1
0
0
2
0
1
0
2
0
0
0
2
0
0
0
0
0
1
0
1
0
0
1
0
0
0
2
0
2
1
0
0
0
1
2
1
1
0
0
2
0
0
2
0
2
0
1
2
0
0
0
1
0
0
0
0
0
2
0
2
1
0
0
2
0
0
1
1
0
3
0
0
1
0
0
1
0
0
0
0
3
1
1
0
1
0
3
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
2
2
2
0
2
1
1
0
3
0
1
0
1
1
2
0
0
0
1
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
2
1
1
5
0
0
1
2
0
0
0
0
0
0
0
2
1
0
0
1
1
0
3
0
2
0
0
0
1
0
2
1
2
2
2
0
1
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
2
1
0
0
0
0
1
1
0
2
2
0
0
2
0
1
2
0
0
0
0
0
0
0
0
1
2
0
0
1
0
2
1
1
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
1
0
0
1
0
2
1
0
1
0
0
1
2
0
0
0
1
0
0
0
0
1
2
0
0
1
2
0
0
0
0
1
0
0
0
2
0
2
0
1
0
2
2
1
0
2
0
0
1
2
1
2
2
1
0
2
0
1
2
0
0
0
1
0
1
0
3
0
1
0
2
0
0
1
0
0
0
0
2
0
1
0
1
0
2
0
0
0
0
0
4
0
0
2
0
2
1
0
3
0
0
1
1
0
1
2
0
0
2
0
1
2
1
1
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
1
1
1
0
2
1
0
3
1
1
2
1
0
0
1
0
2
0
0
1
0
0
2
1
0
2
2
0
2
2
0
0
0
2
2
0
2
2
0
2
0
2
0
0
1
1
1
1
1
1
0
0
2
0
0
0
2
0
2
2
0
2
0
0
0
3
0
0
0
0
1
0
0
1
2
0
0
0
4
0
1
2
2
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
3
2
0
0
0
0
1
1
0
2
1
0
0
1
4
0
2
3
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
2
2
2
0
0
0
1
0
0
0
0
0
1
0
2
0
0
1
1
1
1
0
0
0
2
2
0
0
1
0
1
1
1
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
2
1
0
1
2
0
2
0
3
0
2
1
1
0
0
0
0
3
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
2
1
0
0
1
1
2
0
1
1
1
1
0
2
0
1
3
3
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
2
0
1
1
0
0
2
1
0
1
2
0
0
2
2
0
0
2
0
0
1
0
0
0
2
0
1
1
0
0
0
1
1
0
1
0
2
1
0
0
0
1
0
0
2
0
1
0
2
2
0
0
1
0
2
0
0
0
0
0
0
2
2
4
0
1
0
1
0
1
0
1
2
1
0
2
2
2
1
2
0
0
0
1
1
0
0
0
1
0
0
1
1
2
1
0
0
1
3
0
1
0
2
0
1
0
2
0
0
2
0
0
1
0
1
3
0
0
0
0
2
1
2
2
0
0
0
2
2
0
0
1
0
0
2
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
2
0
1
1
1
0
0
0
0
2
0
2
1
0
1
0
0
0
0
2
0
2
1
1
2
0
0
2
2
0
0
0
1
0
0
0
0
2
2
0
1
0
0
1
1
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
2
1
0
0
0
0
4
2
1
0
1
1
2
2
2
2
0
1
0
2
1
2
0
0
2
2
0
0
2
0
2
0
0
0
0
1
2
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
1
0
3
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
1
1
0
1
2
0
1
1
2
0
0
0
0
1
0
0
1
1
0
2
0
2
2
0
0
0
0
3
0
2
0
3
0
0
0
1
0
0
1
1
0
0
0
0
0
2
2
1
0
0
0
0
1
0
1
0
0
0
0
2
0
1
1
0
0
6
0
1
1
0
1
1
0
0
0
1
0
0
0
1
0
2
0
1
2
0
2
1
1
2
0
1
0
2
0
2
0
1
2
0
0
4
4
0
0
0
0
1
0
0
1
0
1
0
0
0
2
2
0
0
0
0
1
2
0
0
2
0
0
3
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
2
1
1
0
3
0
0
3
1
0
3
0
1
0
0
0
0
0
2
0
2
0
3
1
0
0
0
0
0
0
1
2
1
0
0
0
0
0
1
0
2
2
1
0
0
2
0
0
0
0
2
0
0
2
0
3
0
0
0
0
1
0
0
0
0
2
1
0
1
0
0
0
0
0
0
2
1
2
2
0
0
1
1
2
0
0
3
0
2
2
0
0
0
1
0
0
2
0
1
0
1
1
2
1
0
0
1
0
0
0
5
2
0
0
2
0
0
0
0
0
0
1
0
1
2
0
0
2
0
0
0
1
1
0
2
0
1
0
0
0
1
0
3
0
1
3
2
1
0
2
0
0
0
2
1
2
2
0
0
1
0
0
0
0
2
0
0
1
0
0
2
0
5
1
0
1
1
0
0
0
0
0
2
1
0
2
1
2
0
1
0
1
1
1
1
0
2
0
2
0
0
0
1
0
0
0
0
1
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
1
1
0
1
0
0
0
0
0
2
0
2
0
1
0
1
1
0
0
0
2
0
0
0
1
2
0
0
2
0
0
0
0
1
0
0
0
2
2
0
0
0
2
0
2
0
1
1
0
0
0
0
1
2
0
0
0
1
0
0
0
0
1
0
2
0
2
2
0
1
1
3
0
2
0
1
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
4
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
2
1
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
1
0
2
1
2
0
0
2
0
2
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
2
1
1
1
0
0
0
1
0
0
0
0
0
0
0
2
2
1
0
1
0
0
2
0
0
0
1
0
2
0
2
0
0
1
0
2
0
2
1
2
0
0
1
1
1
0
0
3
2
0
2
1
0
1
2
0
0
0
2
0
0
0
1
2
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
2
1
0
0
0
0
2
0
1
2
0
0
0
0
2
1
0
3
0
3
1
1
0
0
0
0
2
0
1
2
0
0
0
0
1
0
0
0
2
0
0
1
0
1
0
3
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
2
2
2
1
2
0
1
1
1
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
1
1
0
1
0
3
1
0
0
1
2
0
0
0
0
1
0
0
0
0
3
2
0
1
0
0
0
0
0
0
0
0
2
0
6
2
1
0
0
0
1
0
2
0
1
1
0
2
0
1
2
0
2
2
2
3
1
1
1
0
0
0
0
3
0
0
2
1
4
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
2
1
2
0
2
2
1
0
0
0
1
0
0
0
0
0
2
0
2
3
0
0
1
0
0
1
2
1
0
0
0
0
2
0
0
1
0
2
0
0
0
1
0
0
0
0
0
1
2
0
2
1
0
0
2
0
1
3
0
2
0
0
0
0
0
2
0
3
1
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
2
2
0
2
0
1
1
0
0
1
0
0
0
0
1
0
1
0
0
2
0
0
2
0
0
0
1
2
0
0
2
2
0
1
0
1
0
1
1
1
0
0
2
1
2
1
0
2
0
0
0
0
0
0
0
2
0
1
0
0
1
0
2
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
3
2
0
1
2
2
2
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
2
0
0
3
1
0
0
1
2
0
0
0
2
2
2
3
1
0
0
0
2
0
2
1
2
0
0
0
2
0
0
1
2
0
0
2
0
1
2
1
1
1
1
0
1
6
0
0
0
0
0
2
0
1
0
1
2
2
2
0
0
0
2
1
2
1
0
0
0
2
2
0
2
0
1
2
0
2
0
0
1
0
0
1
2
0
0
2
0
0
2
1
0
2
0
0
0
0
1
1
1
0
0
2
2
1
0
0
1
0
0
0
0
0
0
0
2
2
0
0
1
0
0
1
1
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
1
0
0
1
2
0
0
0
0
0
0
1
2
0
0
2
0
1
0
3
0
2
0
1
1
0
1
0
2
0
0
2
0
2
1
0
1
1
1
0
3
0
0
1
0
1
2
0
0
1
1
2
0
1
2
1
0
0
2
0
0
0
1
0
2
2
3
0
0
0
1
1
1
0
2
0
3
0
2
1
0
0
1
0
1
1
4
0
1
2
1
0
1
2
0
0
3
0
1
1
1
0
0
0
1
1
0
0
0
2
2
0
0
0
1
0
0
0
2
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
2
0
1
0
1
1
0
0
0
1
1
2
2
0
2
1
2
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
1
2
0
0
0
2
0
1
0
2
0
0
1
0
2
1
0
0
2
2
1
0
1
0
2
3
0
0
3
1
0
0
2
1
1
1
0
0
1
2
1
2
0
1
1
0
0
0
0
1
0
1
2
0
0
2
2
2
0
0
2
0
0
1
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
1
1
0
0
2
0
2
1
0
0
0
2
0
0
0
1
0
0
1
0
2
0
0
0
1
1
0
0
0
0
1
1
0
1
3
3
0
0
0
0
1
1
0
2
1
0
0
1
0
1
1
0
0
0
2
0
2
2
0
1
0
2
0
0
0
0
0
1
2
2
0
0
1
1
2
0
0
1
1
1
0
0
2
0
1
0
1
0
0
0
0
0
2
0
0
0
0
2
0
1
0
2
1
0
2
1
3
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
2
0
2
0
2
1
0
1
1
0
2
1
2
1
1
0
1
0
0
0
1
0
0
0
2
0
0
0
1
2
0
0
2
2
0
3
1
0
0
1
0
0
2
1
0
2
2
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
3
0
0
1
4
0
0
0
0
0
0
1
0
0
0
2
0
1
2
0
2
0
3
0
0
2
0
0
1
2
3
0
0
0
2
0
0
0
0
0
0
0
0
1
0
3
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
2
0
1
2
1
2
0
0
0
2
3
1
2
1
2
0
0
2
0
0
2
2
1
1
1
6
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
2
2
0
0
2
2
1
0
0
1
1
0
0
0
1
1
1
0
0
0
0
2
0
2
1
0
2
0
0
1
0
1
0
0
1
2
0
0
0
1
2
0
1
2
1
1
0
2
2
1
0
2
1
0
2
2
0
1
2
0
0
0
0
1
2
0
0
0
2
0
2
2
0
1
0
1
1
0
4
2
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
2
1
0
0
1
0
0
0
1
0
0
0
0
2
0
2
0
0
2
0
1
2
0
0
0
1
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
2
0
1
1
0
1
1
1
2
0
0
0
0
3
0
2
0
1
1
0
0
2
2
2
2
0
0
1
2
2
1
2
1
0
2
0
2
0
0
2
0
0
0
0
0
0
1
2
0
1
1
2
2
2
1
1
2
0
0
1
0
0
0
1
0
0
2
0
0
2
0
1
0
0
0
0
0
0
2
0
1
2
1
2
1
0
0
2
0
1
0
0
0
0
0
2
1
0
0
0
0
1
1
0
3
0
1
0
0
0
0
0
2
2
0
2
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
1
2
1
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
2
0
3
0
2
0
0
2
0
0
0
0
1
0
1
1
0
1
0
2
2
2
2
2
0
1
1
0
0
0
0
0
2
1
0
1
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
1
4
0
0
2
1
0
0
1
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
2
1
0
0
2
0
2
0
2
0
2
1
0
2
2
0
1
1
1
0
1
0
0
2
0
2
0
0
0
0
1
0
0
0
0
1
0
2
1
0
1
0
0
2
0
0
0
0
0
2
1
0
0
0
0
1
0
0
2
0
0
0
2
0
1
0
0
2
0
1
0
0
0
0
0
2
0
0
0
2
2
0
0
1
1
0
0
1
0
0
0
0
1
1
0
2
0
0
1
0
2
0
0
0
2
1
0
1
1
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
5
0
0
0
0
2
0
0
1
1
0
0
0
0
1
0
1
0
0
0
4
0
0
0
1
2
1
1
0
0
1
2
1
3
0
1
1
1
2
2
0
0
1
0
0
2
0
1
0
2
0
1
0
0
0
2
0
2
1
2
2
0
0
1
0
1
0
0
0
1
0
2
0
0
1
2
0
2
0
1
3
0
0
2
0
0
2
0
0
0
0
1
1
2
1
3
0
1
2
0
1
0
3
0
1
0
0
1
1
0
1
0
1
1
0
0
0
1
0
1
0
1
0
0
1
0
2
2
2
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
1
2
0
0
0
0
1
0
2
0
2
1
0
1
0
0
0
0
2
2
0
2
1
0
2
1
0
0
1
0
3
2
0
1
1
1
1
0
0
2
1
2
0
0
1
2
1
0
0
0
1
0
0
0
0
1
0
1
2
0
0
0
2
0
2
0
1
1
2
2
0
0
2
1
0
0
1
3
0
1
1
2
0
0
0
0
2
0
0
1
1
0
1
0
0
0
2
0
1
0
0
0
1
1
0
2
1
0
0
0
1
0
0
0
1
0
0
2
0
2
1
1
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
2
2
0
0
0
0
2
1
1
1
1
2
1
1
2
0
0
1
0
0
0
3
0
0
0
0
1
1
0
1
0
2
0
2
0
2
0
2
0
0
0
0
1
1
0
0
2
0
2
0
0
1
3
1
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
1
0
2
1
1
0
1
0
1
0
1
2
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
1
0
3
0
0
1
1
0
0
0
0
0
3
0
0
1
2
1
1
1
0
0
2
2
1
1
0
0
0
1
2
0
0
0
0
0
0
1
1
0
2
0
0
0
0
1
2
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
2
0
2
1
1
1
0
1
0
2
0
4
0
0
0
0
0
0
2
0
0
0
1
0
0
0
4
0
0
2
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
2
0
1
0
2
0
0
1
1
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
1
1
0
4
0
0
0
2
2
1
2
2
3
0
0
2
1
1
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
2
0
0
3
0
2
0
0
2
1
1
0
0
2
2
0
1
2
2
0
0
2
0
2
0
2
0
1
0
1
2
0
0
2
0
0
0
0
2
1
0
0
2
0
1
1
1
0
0
0
0
1
1
2
1
1
2
0
0
1
2
0
1
1
0
0
0
0
1
1
2
1
0
0
0
1
0
1
0
0
0
0
2
0
0
2
0
0
1
1
0
0
0
0
4
1
0
0
0
1
0
1
1
0
2
0
2
1
1
1
2
0
0
0
2
0
2
0
0
0
2
2
0
0
0
1
2
0
2
0
0
0
2
0
4
2
2
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
3
2
0
2
0
1
0
2
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
2
1
2
0
0
0
1
3
1
2
0
0
0
2
0
0
0
0
1
1
1
0
0
1
1
0
0
0
0
2
1
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
2
0
1
1
1
1
2
0
0
2
0
1
1
1
2
2
2
0
0
0
2
0
2
0
6
0
1
0
0
1
0
1
0
0
1
0
0
0
0
1
1
0
0
2
0
2
1
0
0
0
0
2
0
0
1
0
2
0
2
1
0
0
2
0
0
1
0
0
0
1
0
0
0
0
2
1
0
0
1
1
0
0
0
0
1
0
0
2
0
0
0
2
1
2
0
0
3
1
0
0
2
2
0
1
0
2
0
0
2
0
0
0
1
1
2
0
0
1
0
0
0
0
0
2
0
0
1
2
0
2
0
1
0
2
0
0
0
0
0
0
2
1
0
1
0
0
3
1
0
0
0
0
0
1
1
1
0
0
1
1
0
0
0
2
3
0
1
0
0
1
3
1
0
0
1
0
0
1
1
0
0
3
1
0
0
1
2
0
3
0
2
0
2
0
0
2
0
2
0
2
1
2
0
2
1
0
1
1
0
1
0
0
1
2
1
2
0
0
0
2
1
1
0
0
0
1
0
1
0
0
0
2
0
2
1
1
2
0
0
2
2
0
0
2
0
2
1
0
2
0
0
2
0
1
0
0
0
2
0
0
0
1
1
0
0
2
2
0
2
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
1
0
2
0
0
1
0
0
0
2
0
2
2
2
0
0
0
0
1
0
1
0
2
0
2
2
0
0
1
1
0
1
1
0
2
0
0
2
2
0
1
1
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
1
0
2
1
0
2
1
0
0
1
2
0
0
0
1
1
1
0
0
2
0
0
1
0
0
0
0
2
0
0
2
0
1
0
2
0
1
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
3
0
2
1
0
1
1
2
1
0
0
2
0
1
0
1
1
0
2
2
0
0
0
1
1
0
0
3
0
0
0
0
1
0
0
1
0
1
3
0
0
0
0
0
2
1
0
2
1
1
1
0
0
0
1
0
0
3
1
0
0
0
1
0
2
2
0
1
1
1
0
0
2
1
0
0
2
0
1
0
0
0
0
1
1
0
6
2
1
2
1
2
0
0
0
0
0
1
1
2
0
0
1
2
1
0
2
0
0
2
0
0
0
0
0
0
0
0
2
2
0
2
0
1
0
2
0
0
0
0
1
0
1
0
3
2
2
1
0
1
1
1
1
2
2
2
0
2
2
2
0
2
1
2
2
0
1
0
0
0
1
1
0
0
2
0
2
1
1
6
1
0
0
2
0
0
2
0
0
2
2
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
1
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
2
0
1
3
0
0
2
0
1
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
3
0
0
0
2
3
0
0
1
0
2
2
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
2
0
0
1
0
0
0
2
1
1
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
2
1
2
2
1
0
2
2
1
1
1
0
2
0
2
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
2
1
0
2
1
0
0
2
0
1
0
0
0
1
0
2
0
1
0
0
0
0
1
0
1
0
0
0
2
0
0
2
0
2
0
0
1
0
0
2
1
2
1
1
0
0
2
0
2
1
0
1
0
2
0
0
0
0
0
1
2
0
2
11
0
0
1
1
0
2
2
0
0
2
1
1
0
0
1
0
1
1
0
0
2
0
0
0
1
1
2
0
0
0
0
1
0
2
0
0
0
0
1
0
2
1
0
0
1
0
1
1
2
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
2
1
0
0
0
2
0
2
1
0
0
0
0
0
0
2
0
3
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
1
1
2
2
0
1
0
1
2
2
3
0
1
0
0
0
2
0
0
0
0
0
0
2
2
1
2
0
2
2
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
2
2
1
0
0
0
2
0
2
1
0
2
1
0
0
3
0
0
2
0
0
1
2
2
1
0
1
2
0
2
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
3
1
1
0
2
0
1
0
1
1
0
0
0
0
0
0
2
0
0
2
3
0
0
2
0
1
1
0
1
0
0
1
0
0
0
1
1
3
0
0
0
0
0
1
1
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
2
2
0
1
2
4
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
2
2
0
0
0
2
0
0
2
2
2
0
0
0
2
1
2
0
0
0
0
0
0
0
2
1
1
0
0
1
0
2
0
2
0
0
2
2
0
0
0
1
0
0
0
0
0
0
2
0
0
1
2
0
2
0
0
0
3
0
0
2
2
0
0
0
0
0
0
0
0
0
2
1
0
2
0
2
0
1
0
0
1
0
1
0
2
1
0
0
0
0
0
0
0
2
1
0
0
2
0
1
0
0
0
0
2
0
1
1
0
2
0
1
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
1
0
0
0
2
0
0
0
2
1
1
0
0
1
0
1
2
0
1
0
1
1
0
1
0
2
0
1
0
3
1
0
1
1
0
0
2
1
0
1
0
0
2
0
0
1
0
1
0
0
0
0
0
0
2
0
0
2
1
0
2
2
0
2
0
0
0
0
0
1
0
0
1
1
2
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
2
1
0
1
0
0
0
1
0
0
2
2
1
0
1
1
1
0
0
0
1
3
2
2
2
1
0
2
2
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
2
0
0
1
1
1
0
0
0
0
0
2
0
0
2
0
2
0
2
2
3
1
2
0
0
0
0
1
1
1
0
2
0
0
0
1
0
0
1
0
0
0
1
0
0
0
2
0
1
1
1
0
2
1
0
0
0
0
0
0
0
0
2
2
0
1
0
0
1
2
2
1
0
0
1
0
0
2
0
0
0
2
0
0
2
0
0
0
1
2
1
2
1
0
1
0
0
0
1
1
3
0
0
5
0
1
1
1
0
0
1
0
0
0
0
0
0
2
6
0
1
0
0
1
1
2
0
2
0
0
0
0
2
0
2
0
0
0
1
0
0
0
1
1
0
0
1
0
2
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
1
2
2
0
0
2
1
0
0
0
0
0
1
1
0
1
2
2
0
0
1
2
0
0
1
0
0
2
0
0
2
2
3
0
2
2
0
0
0
0
1
0
1
3
0
0
0
2
0
2
1
0
0
0
1
2
1
0
0
3
0
0
4
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
2
1
1
0
0
2
0
2
0
0
0
2
1
2
0
0
0
0
2
1
1
0
0
0
2
1
0
2
0
3
1
0
1
0
0
1
0
0
0
0
0
2
1
1
0
1
2
0
0
0
0
2
1
0
4
2
0
0
0
0
0
1
0
2
1
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
1
1
0
1
0
0
1
0
1
0
0
2
0
0
2
1
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
2
1
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
2
0
3
2
0
0
0
1
0
2
0
0
0
2
0
2
1
1
0
0
1
1
0
0
0
0
1
2
0
5
2
2
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
1
0
1
2
1
2
4
1
0
2
1
1
2
2
0
1
2
1
1
0
0
0
0
1
0
0
0
0
1
1
2
0
6
0
0
1
0
0
0
1
1
0
0
0
1
0
1
2
0
0
0
0
1
0
0
3
0
0
2
1
0
1
0
2
1
2
3
0
1
0
0
2
0
2
0
0
0
0
1
0
1
1
0
2
0
2
0
2
0
1
0
3
1
0
0
0
0
1
2
3
0
1
2
0
0
0
1
0
0
0
0
1
0
1
0
1
2
0
0
0
1
0
2
0
1
0
0
0
4
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
1
2
1
0
0
1
0
0
1
1
1
2
1
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
3
2
2
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
1
1
0
2
0
1
1
0
2
1
0
0
0
0
0
0
3
2
1
0
0
0
4
2
0
3
1
0
0
2
0
2
0
2
0
0
0
3
0
0
1
0
0
1
0
2
0
0
1
1
0
0
2
2
0
1
0
0
3
0
1
3
2
0
0
3
0
0
0
0
0
1
2
0
2
0
0
0
0
0
1
0
2
0
0
0
0
2
0
2
0
1
0
0
0
0
0
2
1
2
1
1
0
0
2
1
0
2
0
2
0
2
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
2
2
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
3
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
2
2
0
2
2
0
0
1
0
1
4
0
2
0
0
0
1
0
0
0
2
0
2
0
2
0
2
0
2
0
0
0
0
1
0
0
0
0
1
3
1
1
0
0
0
2
1
0
1
0
1
0
1
0
0
0
1
1
2
0
0
0
0
1
2
2
0
1
0
0
0
1
0
2
1
0
3
0
2
0
0
1
2
2
1
0
0
2
0
0
1
2
2
0
0
0
2
1
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
3
0
0
0
0
0
0
1
0
0
2
1
0
0
2
1
3
0
0
0
2
0
0
0
0
0
0
1
1
2
0
0
0
2
0
1
0
2
0
2
1
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
1
0
2
1
2
0
1
1
0
2
2
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
2
0
2
1
0
0
0
2
0
1
0
2
2
0
1
0
1
0
0
0
1
1
1
2
0
1
0
0
0
0
1
0
0
2
0
1
0
0
0
0
2
0
0
0
0
1
0
2
0
2
0
0
2
0
2
1
0
0
0
0
2
0
1
0
1
2
1
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
1
1
1
0
0
0
1
2
0
0
1
1
0
2
0
1
2
0
0
0
2
0
1
0
1
1
1
0
2
0
0
0
2
1
0
0
0
0
1
0
2
2
0
0
0
0
0
0
2
0
0
1
2
0
2
2
0
0
2
0
0
1
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
1
1
1
0
0
0
0
0
2
6
1
0
0
1
0
1
0
0
1
2
0
1
0
1
1
0
1
0
0
0
1
0
0
2
0
0
0
0
2
2
0
1
0
1
0
0
2
0
0
0
0
1
0
0
1
1
0
1
0
2
1
1
1
1
1
2
1
0
2
0
0
2
1
2
0
0
0
0
2
2
1
0
0
0
0
1
1
1
0
0
1
0
0
1
0
1
1
0
0
0
0
2
0
0
2
2
0
0
1
0
0
1
2
0
1
2
1
2
1
2
0
1
0
0
0
0
0
2
2
2
1
0
0
0
0
2
2
0
2
0
0
1
0
1
2
1
0
2
1
2
1
0
0
1
0
0
1
0
0
0
0
2
1
3
0
1
0
0
0
0
0
0
0
1
0
3
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
1
0
0
1
2
0
0
0
0
0
2
2
0
2
1
0
0
0
2
0
2
0
2
4
0
3
1
0
0
2
1
0
0
0
0
0
0
2
2
1
1
0
0
2
0
0
2
1
0
0
0
1
4
1
0
0
0
0
1
0
0
0
1
0
1
0
2
0
2
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
1
2
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
3
1
0
0
1
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
1
1
0
1
0
1
0
0
0
3
0
0
2
0
0
0
0
1
0
2
0
3
0
2
0
0
0
0
1
2
1
0
0
0
2
3
2
0
2
1
2
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
1
1
2
1
0
2
0
0
0
0
0
0
0
1
2
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
2
0
1
1
0
0
2
0
0
0
2
1
1
0
1
0
2
2
0
13
0
1
0
0
2
1
1
0
1
0
0
0
2
0
0
0
0
1
2
0
0
2
0
1
0
0
1
1
1
0
0
1
0
1
0
0
0
0
1
1
0
0
2
0
2
0
1
0
0
1
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
1
0
1
1
1
2
0
0
0
0
0
2
1
0
1
0
1
1
0
0
0
1
0
0
1
0
0
3
0
0
1
0
1
0
0
1
0
0
2
0
0
0
2
1
1
0
0
1
1
0
0
0
2
0
1
1
0
2
0
0
0
3
0
1
1
0
0
1
1
2
0
0
0
1
0
2
1
0
1
1
0
0
2
1
2
0
0
0
2
0
1
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
1
2
2
0
3
0
0
2
1
0
8
0
0
0
2
0
0
0
1
3
2
2
0
0
0
2
0
2
0
0
0
1
0
0
2
2
0
0
1
0
1
1
0
2
0
2
1
0
0
0
2
1
0
0
1
0
3
0
2
0
2
0
0
0
0
2
0
2
0
1
0
0
0
0
2
0
1
1
2
1
11
0
0
2
2
0
1
0
0
0
0
0
0
2
0
1
0
0
0
1
1
1
2
0
0
0
0
1
1
2
1
0
2
0
0
0
2
1
0
0
1
0
1
2
1
2
0
1
0
0
0
0
0
0
0
0
1
2
0
2
0
0
1
0
0
0
0
1
2
1
2
2
0
1
0
1
2
0
0
0
1
2
0
1
1
3
0
1
1
0
0
1
0
0
2
2
0
0
0
1
0
1
1
0
2
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
2
4
0
0
0
0
0
0
1
1
2
0
0
0
0
0
2
2
0
1
0
0
0
1
2
0
2
1
0
0
0
0
1
0
3
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
1
0
0
0
4
1
0
0
1
0
1
0
2
0
1
2
0
2
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
2
0
0
0
0
0
0
0
2
2
0
1
1
0
0
4
0
2
0
0
0
2
3
2
0
0
0
0
0
2
0
1
0
2
1
0
0
0
1
0
0
1
2
0
0
0
1
0
0
2
0
2
2
0
1
0
2
2
0
0
2
1
1
0
1
0
0
1
0
2
1
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
2
1
1
0
0
0
1
1
0
1
2
1
1
0
2
0
1
1
0
1
0
0
0
1
0
0
1
2
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
2
0
3
0
2
1
0
0
0
1
0
0
0
2
0
1
0
0
1
1
1
1
1
0
0
1
1
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
4
2
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
1
0
0
2
1
0
0
1
0
1
2
0
0
0
1
0
1
2
2
0
0
0
0
1
0
0
0
2
0
1
0
0
0
2
0
0
0
1
2
0
0
0
0
1
0
1
0
2
0
0
0
2
0
1
2
2
1
1
0
0
0
0
0
2
2
0
0
0
1
0
1
2
0
0
0
0
0
1
2
2
0
0
1
0
0
0
0
0
0
1
0
1
5
0
0
0
0
1
1
1
0
0
1
2
2
2
0
2
2
2
1
0
1
2
2
0
0
0
0
2
0
2
2
1
0
0
1
0
0
0
1
1
0
0
0
0
2
1
1
0
0
1
0
2
2
2
0
0
2
1
0
0
2
1
2
2
0
0
0
1
0
0
0
0
0
2
3
0
0
0
3
0
2
0
0
1
1
1
1
0
2
1
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
2
1
0
2
2
0
0
0
2
1
4
0
0
2
0
1
0
0
4
0
0
2
1
0
1
0
0
0
1
0
0
0
0
1
0
0
2
2
0
0
0
1
1
0
1
1
1
0
2
1
1
2
1
0
0
2
0
0
2
1
2
0
0
0
1
0
0
2
1
1
1
0
2
0
0
0
1
1
0
0
0
0
0
2
1
0
1
0
0
0
0
1
2
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
1
3
0
0
1
1
0
0
0
0
0
0
0
2
0
0
1
0
1
0
2
0
0
1
1
2
1
1
1
1
0
0
0
0
0
0
0
0
2
3
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
1
0
0
1
1
0
0
0
1
1
1
0
0
2
0
0
4
1
0
2
2
2
0
2
2
0
0
0
0
0
2
2
0
0
0
0
0
1
0
1
0
0
0
2
2
2
0
0
0
1
1
0
1
0
2
2
0
1
0
1
0
1
2
0
0
1
0
0
0
0
0
0
0
2
1
1
1
0
1
0
2
0
1
0
0
0
0
0
0
2
2
3
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
3
2
0
2
2
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
1
2
0
0
2
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
1
1
0
0
1
2
2
0
0
1
0
1
0
1
0
1
0
2
0
0
2
1
0
1
0
0
2
0
0
0
0
0
0
2
1
2
0
0
0
2
1
2
1
0
0
0
0
0
0
3
1
0
0
1
0
0
0
0
0
1
1
2
2
1
1
0
0
1
0
0
0
0
0
2
0
0
1
0
0
2
2
3
0
0
0
2
0
0
1
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
1
2
3
0
1
0
0
0
1
0
0
2
1
1
0
2
0
0
0
2
0
1
2
0
0
1
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
1
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
2
2
0
2
0
0
0
0
0
0
0
2
1
0
0
1
0
2
0
0
1
1
0
3
0
2
1
2
2
0
0
0
0
1
1
0
2
0
1
0
1
2
2
2
0
1
1
0
2
0
0
0
0
0
2
0
0
2
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
1
0
3
0
0
0
0
0
2
0
2
1
0
1
1
0
0
0
0
1
0
0
0
2
0
1
0
0
1
0
0
1
0
1
2
0
0
2
0
0
2
0
0
2
1
0
2
0
1
0
0
0
0
2
0
0
1
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
2
1
2
0
0
1
1
0
0
0
0
1
1
2
0
0
1
0
2
1
1
1
0
3
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
1
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
1
0
0
2
0
1
0
2
1
0
0
0
0
0
2
0
0
0
1
1
2
2
0
0
1
0
1
1
0
0
0
2
0
0
0
1
0
1
0
0
1
2
2
0
0
0
0
0
0
1
2
0
0
0
0
1
0
2
2
0
3
2
0
0
0
2
0
0
0
1
2
1
0
0
1
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
1
1
0
0
2
0
1
0
0
1
1
1
1
2
0
0
0
0
0
2
1
1
0
2
0
0
0
2
2
0
1
2
0
0
0
0
0
2
0
1
0
0
0
0
1
0
2
0
2
0
0
2
0
0
0
1
1
1
2
0
1
1
0
0
0
0
0
2
0
0
0
1
0
1
1
0
2
0
2
0
1
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
4
2
2
2
1
0
0
0
2
0
0
3
0
6
2
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
1
1
2
0
0
1
0
1
1
0
0
0
0
0
0
3
1
0
1
0
2
1
1
0
0
0
2
0
0
1
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
2
0
2
1
1
0
0
0
0
2
6
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
3
2
0
1
0
0
0
0
2
0
0
0
1
0
1
0
0
2
1
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
1
0
0
0
1
0
0
2
0
1
1
2
0
2
0
0
0
0
2
0
0
2
1
0
0
0
0
0
1
0
0
0
1
0
0
2
0
1
1
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
1
0
2
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
2
2
2
0
0
0
0
0
0
1
0
1
2
1
2
2
1
0
3
0
0
0
0
2
1
0
0
1
0
0
0
0
1
2
0
0
0
0
1
0
0
1
0
2
2
0
0
0
2
0
0
0
16
0
2
0
0
0
1
0
0
0
2
2
0
1
2
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
1
0
0
2
1
0
1
0
2
0
0
0
2
1
0
2
3
1
0
0
0
0
0
2
1
2
2
0
1
0
0
0
3
0
0
0
2
0
0
1
0
1
1
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
2
0
1
1
2
0
0
2
0
0
2
0
0
2
0
0
0
2
2
0
0
2
0
0
0
1
2
0
2
0
0
0
0
1
0
1
0
0
0
1
0
0
2
3
1
0
0
0
1
0
0
2
0
0
1
0
2
2
1
0
0
0
0
0
1
2
0
1
2
0
0
0
1
0
1
0
0
2
0
0
2
0
1
0
0
0
0
0
2
1
0
1
0
2
0
0
0
0
0
2
0
2
0
0
2
0
2
0
0
1
2
0
0
1
0
0
2
2
0
0
0
1
0
0
2
2
1
1
0
0
2
1
0
1
0
3
3
0
1
0
1
0
0
0
4
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
1
1
2
0
2
0
0
1
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
1
1
1
2
0
0
7
0
0
1
0
0
0
0
2
0
0
2
0
0
1
3
0
2
0
2
0
2
2
0
0
0
0
1
0
6
0
1
0
1
1
2
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
1
0
0
0
1
0
1
0
1
1
0
0
2
2
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
3
1
1
2
0
0
0
0
1
0
0
0
1
1
2
0
0
0
0
2
0
2
0
0
0
1
0
0
0
1
0
0
0
1
0
1
1
0
0
1
0
1
0
0
2
0
0
0
0
1
0
0
1
1
1
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
1
0
0
0
1
0
1
1
0
6
0
0
0
2
0
0
1
2
0
0
2
2
1
3
0
0
0
3
0
0
0
0
1
2
0
0
0
0
0
0
2
2
1
0
0
0
1
2
0
0
1
0
1
0
0
1
0
1
0
0
0
0
2
1
0
0
0
0
2
2
2
0
0
0
0
2
1
0
0
0
0
0
2
1
0
0
0
0
1
0
1
1
0
1
2
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
2
0
0
0
2
0
0
1
2
1
0
2
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
2
0
2
1
1
2
2
0
2
1
0
0
0
0
2
0
0
2
0
1
0
0
0
0
1
0
1
0
0
0
2
0
0
1
2
0
2
0
0
0
0
0
1
0
0
2
0
1
0
0
2
1
0
0
0
0
1
2
1
2
0
0
0
0
1
4
2
0
1
0
1
2
1
0
0
0
0
1
0
1
2
0
0
1
0
6
2
0
1
0
1
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
2
2
0
0
1
1
2
0
0
0
0
0
1
1
0
0
0
0
0
2
2
2
2
1
0
0
1
1
0
0
1
0
0
2
2
0
1
0
0
0
2
1
0
1
0
0
2
0
0
0
0
1
0
2
0
2
1
0
2
2
2
2
0
1
0
0
0
0
2
4
0
2
2
2
0
0
1
0
1
1
0
1
2
0
1
1
2
0
0
2
1
0
1
0
2
0
0
0
0
2
1
0
1
1
0
0
0
0
1
0
2
0
0
0
0
1
1
2
1
0
0
3
0
0
0
1
0
3
1
0
1
0
1
0
2
1
2
0
0
0
0
1
0
1
1
1
0
0
0
2
1
0
0
0
1
0
0
2
1
2
0
0
2
0
0
0
0
2
1
0
1
0
0
0
2
0
2
0
0
1
3
2
0
0
0
0
0
0
1
0
0
2
0
4
1
0
0
2
0
0
2
0
0
1
3
2
0
0
0
0
1
0
1
0
2
0
0
1
1
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
2
1
0
1
0
0
2
1
2
1
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
1
0
1
0
2
0
1
0
0
2
0
1
0
1
0
0
0
2
0
2
0
0
0
1
2
0
0
2
1
0
1
0
2
2
0
1
1
0
0
1
2
2
0
0
0
1
1
2
1
0
0
0
0
2
1
1
2
0
0
0
1
1
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
2
2
0
1
1
0
3
0
0
1
0
0
0
1
1
2
1
0
0
0
0
0
0
1
1
0
0
2
0
2
0
1
0
0
1
2
0
2
2
0
1
0
0
0
0
2
1
1
1
0
2
0
1
3
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
2
0
0
1
2
1
1
0
0
1
2
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
3
0
3
1
2
0
0
2
0
1
0
1
0
1
2
0
0
0
2
1
1
1
0
2
0
0
0
0
2
3
0
0
0
1
0
1
0
2
1
1
2
1
0
1
0
1
0
1
1
1
0
1
0
2
0
2
2
3
2
2
1
0
0
0
2
2
2
1
1
2
0
0
4
0
3
0
0
1
0
0
0
0
1
0
1
0
0
2
2
2
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
1
2
0
0
0
1
1
2
3
2
0
0
2
0
2
0
1
0
2
0
0
2
0
3
0
0
1
1
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
2
0
0
3
0
1
0
0
0
0
1
0
0
0
0
2
0
1
1
0
1
0
0
0
0
1
1
0
0
2
0
0
2
0
0
0
0
0
1
3
0
0
0
1
0
0
4
2
2
1
0
0
2
0
0
0
0
2
0
0
2
0
0
0
1
0
1
0
0
2
1
0
1
0
0
0
0
0
0
0
0
1
0
2
1
0
0
1
1
1
0
1
0
0
0
0
0
1
0
0
0
1
2
2
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
1
0
1
2
2
0
0
3
0
2
0
0
2
2
0
2
1
2
1
0
0
0
0
0
0
0
0
0
1
3
2
0
0
0
1
0
3
0
0
1
4
2
0
0
1
2
0
1
0
0
0
0
1
2
2
0
0
0
2
0
0
1
0
1
2
3
1
0
2
0
2
1
1
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
1
2
0
3
2
0
0
1
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
1
3
2
0
1
2
0
0
0
0
0
1
0
1
0
0
2
1
2
2
0
1
0
0
1
0
2
0
0
3
3
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
3
0
2
2
1
1
2
2
0
0
0
0
0
2
4
0
0
0
1
0
0
2
0
0
2
1
2
0
0
2
2
1
0
1
2
2
0
1
0
0
0
0
1
1
0
0
0
2
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
2
1
2
1
0
2
2
0
0
0
0
0
0
2
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
2
1
0
0
0
4
0
0
1
0
0
0
3
0
0
1
1
0
1
2
1
0
0
2
0
0
2
2
0
0
2
2
0
0
0
0
3
0
0
1
0
0
2
2
1
1
0
0
2
0
2
0
0
0
0
0
0
2
2
1
1
0
0
1
0
2
0
0
1
1
0
0
1
0
0
0
1
0
1
2
1
0
2
0
2
0
0
0
0
0
0
0
4
0
0
1
0
0
2
0
0
0
0
0
3
0
1
1
2
0
1
0
0
2
1
0
0
0
0
2
0
0
0
0
2
2
2
1
0
2
2
0
1
0
0
0
1
0
1
1
0
1
0
2
0
0
0
0
2
2
2
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
1
2
0
0
0
0
1
0
0
2
1
1
0
0
2
0
2
1
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
2
1
1
0
2
0
0
0
0
2
1
0
1
0
0
0
0
0
0
2
0
0
3
0
0
1
1
2
0
0
0
0
1
2
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
4
0
0
1
2
1
1
1
0
2
4
2
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
1
0
1
0
0
0
2
3
0
0
0
0
1
0
1
2
0
0
2
0
2
0
0
0
1
0
0
0
0
1
3
1
0
5
2
2
2
2
0
2
0
2
0
0
0
0
0
0
0
2
2
0
2
2
2
0
0
1
1
0
0
0
1
0
0
0
3
2
1
0
2
0
1
0
1
0
0
0
1
1
0
0
2
0
0
0
0
0
1
2
1
0
0
2
2
0
1
0
0
0
1
3
0
0
0
1
2
2
0
1
0
2
1
2
1
0
0
1
1
0
2
0
0
0
2
0
0
0
0
2
0
1
2
1
0
0
0
0
1
0
2
0
1
0
2
0
0
0
0
1
2
2
0
0
0
0
3
0
2
1
2
0
0
0
0
0
2
0
0
1
1
0
1
1
2
0
1
2
0
2
0
1
1
0
2
0
0
0
1
1
1
0
2
0
1
0
0
1
1
2
0
1
0
1
0
0
2
0
2
0
0
1
2
2
1
1
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
2
1
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
2
0
3
0
1
0
2
2
0
1
0
0
0
0
2
1
0
0
2
0
1
0
3
0
1
2
0
0
1
0
0
1
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
1
0
3
2
2
0
0
0
3
0
0
2
2
0
0
0
3
0
0
0
0
0
2
1
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
2
2
1
1
1
2
1
1
0
0
1
2
0
1
0
3
2
2
0
2
0
0
2
2
0
0
0
0
0
1
0
0
0
2
1
1
0
2
2
0
0
0
0
0
0
1
0
2
0
2
0
2
0
0
0
2
2
1
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
1
1
0
0
1
0
0
3
0
0
1
1
1
0
0
1
0
0
6
0
0
0
1
0
0
1
1
1
0
2
0
0
1
0
0
0
0
0
1
1
0
1
1
0
0
0
2
0
2
1
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
1
3
0
2
0
0
0
0
1
0
0
0
2
0
0
2
1
0
1
0
1
1
1
0
2
1
0
0
0
1
0
4
1
3
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
1
1
2
1
0
1
0
1
1
0
0
1
1
1
5
0
1
1
2
2
0
2
2
3
0
0
0
1
0
0
1
1
0
0
0
2
0
3
0
0
0
0
2
0
0
1
1
0
0
0
1
0
1
0
2
0
0
2
1
0
0
1
0
1
0
0
1
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
2
1
2
0
1
2
2
2
0
2
4
0
2
0
2
1
0
0
0
0
0
2
0
2
0
0
1
0
0
2
2
1
1
0
0
2
0
1
2
1
2
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
2
1
1
3
0
1
1
1
0
0
2
1
0
0
0
1
2
0
0
0
1
0
0
4
0
0
0
0
2
0
2
0
0
0
0
0
1
1
3
0
0
0
1
1
1
0
1
1
0
0
0
0
1
0
1
1
2
0
1
0
0
0
1
0
1
1
1
0
0
0
0
2
1
1
0
0
1
0
0
0
0
0
0
1
0
0
2
0
1
1
0
0
0
0
2
0
0
0
2
0
1
1
1
1
0
0
1
2
2
1
0
0
0
0
0
0
0
0
0
1
2
1
2
0
0
1
1
1
0
0
1
2
0
2
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
2
1
0
0
2
2
0
0
0
0
0
2
0
1
0
3
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
3
2
1
0
0
0
2
0
0
2
0
1
2
0
0
0
0
0
0
0
1
2
0
0
1
0
1
0
2
1
0
0
1
0
2
1
0
1
3
2
1
0
0
2
2
0
0
2
0
0
0
1
1
0
0
2
0
2
0
0
2
1
0
2
2
1
0
1
1
0
1
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
2
1
0
2
0
0
3
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
3
0
2
0
0
0
0
2
1
0
1
2
2
0
2
1
0
1
1
0
0
0
0
0
1
0
1
2
0
0
0
2
0
1
0
0
0
0
0
1
1
1
0
2
0
1
0
1
0
0
1
2
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
2
1
0
0
0
0
1
1
0
2
0
0
1
1
0
0
0
3
0
0
3
0
2
0
2
0
0
0
1
0
1
2
0
1
0
1
0
2
0
0
0
2
0
0
1
2
0
2
0
1
0
1
0
1
0
0
2
0
0
0
1
0
3
0
1
0
2
0
0
0
0
2
0
0
1
0
0
2
2
0
2
1
0
0
0
2
0
2
0
1
1
1
0
0
3
0
0
0
0
0
1
0
0
2
1
0
0
0
2
0
0
1
2
2
2
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
2
0
0
0
0
2
0
2
0
0
1
2
1
1
0
1
0
2
1
0
0
0
0
1
0
1
1
0
2
2
0
0
0
1
2
1
0
2
0
0
2
2
0
0
0
0
0
0
0
0
6
2
2
0
1
1
2
0
2
0
0
0
1
0
1
1
0
2
0
2
0
1
2
0
2
3
3
1
2
1
4
1
1
1
0
1
0
0
2
2
0
2
2
0
2
2
0
1
2
0
0
1
2
0
1
0
0
2
1
0
0
2
1
1
0
0
0
0
1
0
0
0
1
0
0
0
1
2
0
2
0
1
2
0
0
0
0
1
0
0
2
0
4
0
0
1
0
0
0
2
1
0
0
1
2
2
1
0
1
0
0
0
0
1
0
1
0
2
1
2
1
0
0
0
0
1
2
1
0
0
0
0
0
0
0
2
1
1
0
0
1
2
0
1
0
2
0
0
0
0
1
0
0
2
0
0
1
3
1
7
0
0
0
1
0
1
0
1
0
0
1
1
1
0
0
2
1
7
2
3
1
1
0
0
2
2
0
2
1
0
1
0
0
1
2
0
1
2
2
0
2
0
2
0
1
0
1
2
0
0
0
5
0
0
0
0
0
2
0
1
2
3
0
0
0
0
1
1
0
1
2
0
0
0
0
0
2
0
0
2
0
1
1
0
0
1
0
2
0
1
2
0
2
0
1
2
1
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
1
0
0
1
0
0
1
0
1
0
0
0
0
2
0
0
1
0
2
1
0
1
2
0
0
0
2
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
1
0
0
1
0
2
0
0
0
1
1
1
0
2
1
0
1
2
0
0
2
0
0
1
0
0
0
3
0
1
0
0
2
1
0
1
0
0
1
1
1
1
1
0
2
0
1
0
0
0
0
0
1
0
0
2
1
0
1
3
1
1
0
2
0
2
1
2
1
3
1
0
1
1
2
1
2
1
0
0
1
0
0
0
2
2
0
1
1
1
0
0
1
0
0
0
2
0
1
1
2
0
2
2
1
0
2
0
2
1
1
0
0
0
0
2
0
1
1
1
2
0
0
1
0
0
1
0
2
0
0
0
0
2
0
1
1
1
1
2
0
0
0
0
0
0
0
3
0
0
4
1
0
0
0
2
0
2
1
0
0
0
1
0
0
0
3
0
0
0
2
0
2
1
2
0
0
2
1
2
1
0
0
0
1
2
0
2
1
0
1
2
1
2
0
2
2
0
0
0
1
0
0
1
11
0
2
2
2
0
1
0
0
2
2
1
0
2
1
2
0
0
0
0
1
1
0
1
0
0
1
2
0
2
0
3
0
2
0
1
2
1
0
0
0
0
1
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
1
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
3
1
1
0
1
2
1
2
0
0
2
2
0
0
2
0
0
0
1
0
0
2
1
0
2
1
1
1
1
1
0
0
0
1
2
1
2
2
0
1
1
2
1
0
1
0
0
1
1
1
1
0
0
1
0
0
0
3
0
0
0
1
2
0
0
1
0
2
0
0
1
1
0
0
0
0
0
2
0
3
1
0
0
2
0
1
2
0
2
0
3
1
0
0
0
0
0
0
2
0
0
0
3
0
1
1
1
0
0
0
0
2
0
0
0
0
1
1
0
0
0
1
1
0
0
2
2
0
0
0
0
0
1
0
2
0
0
1
0
1
0
2
0
0
1
2
1
1
0
0
1
2
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
1
0
2
2
0
2
0
0
0
1
1
1
0
1
1
0
1
0
0
0
1
2
0
0
0
0
0
0
1
1
0
2
0
2
0
2
0
2
2
0
1
2
0
0
0
2
4
2
0
0
0
2
0
0
0
0
1
0
0
1
0
2
0
0
1
0
0
2
0
2
1
0
0
2
0
1
0
2
1
2
1
0
1
0
0
0
0
1
1
0
0
0
0
2
2
0
1
0
2
1
1
1
2
0
0
1
1
0
2
0
0
0
4
0
0
2
1
0
1
0
1
0
0
1
0
0
2
0
0
1
0
1
0
2
0
2
0
0
1
2
0
1
1
0
2
1
0
2
0
0
0
0
1
0
0
1
1
1
3
0
0
0
1
0
0
0
2
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
2
0
0
0
0
2
0
0
1
1
2
0
0
0
2
0
1
1
2
2
0
0
0
1
0
1
1
0
1
2
1
0
1
0
0
2
0
0
2
1
0
2
0
1
0
2
0
1
0
0
1
0
3
0
0
2
1
1
0
2
0
2
1
0
0
0
2
0
2
1
2
0
0
1
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
1
0
0
2
2
2
0
0
2
3
1
0
1
0
0
0
0
2
2
0
3
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
2
2
0
0
1
0
1
1
2
0
1
0
2
1
0
0
0
2
0
2
1
1
0
0
0
1
6
1
0
1
0
1
0
1
1
0
2
2
1
2
0
2
0
0
0
0
1
0
1
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
2
2
2
1
2
0
0
1
0
1
0
0
0
0
1
1
0
0
0
2
1
1
0
1
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
3
0
1
2
1
2
0
0
0
1
0
0
0
0
0
1
2
1
0
0
0
0
2
1
0
1
1
1
0
0
2
0
0
2
0
1
1
2
0
1
1
0
1
0
1
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
1
0
0
1
0
1
2
0
0
0
0
0
1
0
1
1
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
2
2
1
0
0
2
0
0
1
1
1
0
1
0
0
1
2
2
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
2
0
2
0
2
0
0
0
1
0
1
2
2
0
0
3
0
2
0
1
1
1
0
0
2
2
0
1
0
0
0
0
0
0
1
1
2
0
0
0
2
1
2
2
2
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
2
3
2
1
0
0
0
2
0
0
0
2
1
0
1
0
0
0
0
2
2
1
1
0
1
1
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
1
0
1
0
1
2
0
2
0
1
0
0
0
1
0
1
0
3
1
2
0
0
0
1
0
2
0
0
0
0
0
0
1
0
2
0
1
0
1
0
0
1
0
0
2
0
0
2
0
1
0
0
0
1
0
0
2
0
2
2
0
0
0
0
0
3
1
1
0
2
1
0
1
0
1
2
1
0
1
0
0
0
0
2
0
1
0
0
0
1
1
1
2
0
0
3
0
1
0
2
0
0
0
0
1
0
0
2
0
0
2
0
0
2
0
1
1
0
0
2
0
1
0
1
0
1
1
0
1
0
2
0
0
0
2
1
0
0
0
0
1
2
4
0
1
2
1
1
1
2
0
0
1
2
0
0
2
2
0
0
0
2
0
0
0
1
0
2
1
0
0
0
0
2
0
1
1
0
0
1
1
0
1
0
0
0
0
0
0
0
2
1
0
1
0
0
2
2
0
0
1
1
1
0
1
1
1
0
2
0
0
2
0
0
0
1
0
2
1
1
0
0
2
0
0
0
0
2
2
0
0
1
0
0
0
0
0
1
3
0
0
1
1
0
0
0
0
1
2
0
1
0
0
1
2
0
1
1
0
0
0
0
0
0
0
0
0
2
1
0
2
0
1
0
0
2
1
1
0
0
1
0
0
2
0
0
2
0
2
0
2
0
1
0
0
0
0
0
0
1
0
0
0
2
3
0
1
0
1
0
0
0
2
1
1
0
2
0
0
0
2
1
2
2
0
2
1
0
7
2
1
1
1
0
0
0
1
1
0
0
1
0
0
0
0
0
1
3
0
0
1
0
0
1
0
0
0
2
1
0
1
0
0
0
0
2
0
0
0
2
1
0
1
2
0
0
0
1
0
2
0
1
1
0
0
0
0
0
2
0
1
0
0
2
0
1
1
0
0
1
1
0
0
1
1
2
1
0
2
0
1
2
2
2
0
2
0
1
0
1
0
0
0
0
0
2
1
0
0
0
4
2
0
0
0
0
2
0
1
0
2
0
0
1
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
2
1
1
0
1
1
2
0
0
2
0
1
0
0
0
0
0
0
2
0
0
1
0
2
2
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
2
1
1
0
1
2
0
2
0
1
1
0
0
0
0
0
1
0
0
2
1
0
2
0
0
0
2
0
2
0
0
2
2
0
1
1
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
1
0
0
2
0
2
0
1
1
0
0
1
0
0
1
2
0
1
1
0
0
0
0
2
0
2
0
0
2
0
0
2
0
0
0
0
1
0
0
1
0
1
0
2
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
2
2
2
0
2
2
0
0
0
0
1
0
0
1
0
1
0
1
1
1
0
0
1
0
2
0
0
1
0
0
1
0
0
0
1
1
1
0
2
0
0
2
0
0
0
2
2
1
3
1
2
0
1
0
3
2
0
0
1
5
0
2
1
2
0
1
0
0
2
0
0
1
0
0
0
0
1
0
0
1
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
2
2
0
2
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
1
0
2
0
1
0
1
2
2
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
1
1
0
0
0
0
2
1
0
0
0
0
0
0
1
0
1
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
1
2
2
0
0
0
0
2
0
3
0
2
2
2
1
0
0
1
0
0
1
1
0
2
1
2
2
2
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
1
2
0
2
0
0
1
2
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
2
2
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
2
1
2
1
5
0
0
0
0
2
0
2
0
0
0
0
0
1
0
1
1
2
0
0
0
0
0
2
0
0
0
0
3
0
0
1
0
1
0
2
0
0
0
1
2
1
3
1
2
0
1
0
0
0
0
0
0
0
1
0
1
0
2
0
2
0
0
0
1
0
2
0
0
1
1
1
2
0
0
0
1
0
1
2
2
1
0
0
1
1
1
0
0
0
1
2
0
0
1
0
1
0
0
0
0
1
0
2
0
0
1
0
2
0
2
0
0
2
1
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
1
2
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
2
2
0
0
1
1
0
0
0
0
3
2
1
2
0
0
2
2
0
1
2
1
1
0
0
2
1
2
1
2
2
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
1
1
2
0
0
1
1
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
2
1
1
0
1
3
0
1
0
0
1
2
2
1
0
0
2
1
0
0
0
0
1
2
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
1
0
0
2
2
2
0
0
0
0
2
1
0
0
2
0
2
2
1
0
2
1
0
0
1
2
0
2
0
0
0
0
0
2
1
0
0
2
2
3
0
0
0
0
2
1
0
0
0
0
1
0
0
1
1
2
0
0
0
1
1
1
1
0
1
0
0
1
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
1
0
1
0
2
0
1
1
2
0
0
0
0
0
1
0
0
1
0
1
0
0
0
2
1
5
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
2
3
2
0
0
0
0
0
2
0
2
1
2
2
0
1
0
1
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
1
0
2
2
0
1
1
2
0
0
0
0
1
0
0
0
0
0
0
0
2
1
2
1
2
2
1
0
1
0
0
0
0
1
0
0
2
2
0
4
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
1
0
1
2
2
0
2
2
0
0
1
1
0
1
0
0
0
1
2
0
2
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
1
0
0
0
2
0
0
0
1
0
1
0
0
0
0
2
2
0
1
0
1
0
0
0
1
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
1
2
1
1
1
0
0
1
0
0
0
0
0
0
1
0
2
2
0
0
1
0
0
0
2
0
0
0
1
0
1
0
1
0
0
2
1
0
0
0
0
2
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
2
0
0
2
2
0
0
1
0
0
2
1
0
0
4
0
0
2
2
2
0
1
0
1
0
0
0
0
1
2
0
1
0
1
0
0
0
0
2
0
0
0
0
2
0
1
0
0
2
1
1
2
0
2
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
2
2
1
0
0
1
0
0
0
0
2
0
0
0
2
2
0
2
1
0
1
0
1
1
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
1
1
0
1
1
0
3
1
1
0
0
1
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
2
1
0
0
0
0
2
1
0
0
0
1
2
0
0
0
0
0
0
1
1
0
2
0
1
0
1
1
1
0
0
0
2
0
2
1
1
2
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
1
1
0
1
0
0
2
2
0
1
1
2
0
0
1
0
1
0
0
0
2
0
2
0
1
2
1
3
0
0
2
0
0
0
1
0
0
1
0
1
2
0
0
2
1
0
0
0
0
0
1
2
1
0
0
2
0
1
1
1
0
1
0
3
2
0
0
0
2
1
1
0
3
0
1
0
0
0
1
1
1
0
0
0
0
4
2
0
0
0
0
1
0
0
0
1
1
2
0
0
0
1
1
2
0
0
1
0
3
0
1
1
0
2
0
1
1
0
0
0
2
0
2
2
1
1
0
2
1
2
2
0
0
0
1
2
1
0
0
1
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
2
1
3
0
0
0
0
1
1
1
0
1
1
0
1
0
0
0
1
1
0
0
0
2
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
4
1
0
0
1
0
2
2
0
2
1
0
0
2
0
0
0
1
0
1
0
2
0
0
0
2
2
0
0
0
2
0
0
0
0
1
0
0
1
1
0
1
2
0
1
0
0
0
1
1
0
1
1
0
2
0
0
0
1
0
6
0
0
0
0
0
0
0
2
0
0
3
0
2
2
0
0
0
0
0
0
0
0
0
3
0
1
0
1
0
0
0
2
0
1
0
0
0
0
0
0
1
0
1
1
2
0
0
2
0
1
0
0
1
1
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
3
1
2
0
0
0
0
0
0
0
0
0
1
2
2
0
1
2
0
0
0
0
2
1
2
1
0
0
0
2
2
2
0
0
1
1
2
0
0
0
0
0
2
0
0
0
0
1
2
0
0
1
0
0
1
0
0
0
0
2
4
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
1
0
0
1
2
0
0
2
2
0
1
1
0
0
0
0
2
0
0
0
2
0
0
4
0
0
0
0
1
1
7
0
0
0
0
0
0
0
2
0
1
2
3
2
1
0
0
1
0
0
0
1
0
2
1
2
1
0
0
1
2
0
0
1
0
0
0
1
1
0
2
2
0
1
0
1
0
3
1
0
0
0
0
0
0
0
2
0
1
0
2
1
0
1
2
1
1
0
0
0
0
2
1
0
0
0
0
1
0
0
0
2
2
2
0
1
0
0
0
0
0
1
1
0
2
0
0
0
2
2
2
0
1
0
1
1
2
3
0
0
0
1
0
1
0
3
1
2
0
1
0
0
2
0
0
0
0
0
0
1
0
1
0
0
1
0
2
2
0
0
0
0
0
0
0
1
0
2
1
1
0
0
0
0
0
0
1
0
2
0
1
0
0
1
1
1
0
0
0
1
2
0
2
1
0
1
0
2
5
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
1
0
0
0
0
0
1
1
2
1
0
2
2
0
0
0
0
3
1
1
1
2
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
3
0
1
2
0
1
2
0
2
1
0
0
0
5
0
2
1
1
0
0
1
3
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
3
2
0
0
0
1
1
3
0
1
0
0
0
0
0
1
0
0
0
2
0
3
0
0
0
0
1
2
0
0
0
0
1
0
2
2
2
2
2
0
1
0
1
0
0
1
0
0
0
1
0
14
0
0
1
1
0
2
0
0
0
2
0
2
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
3
0
1
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
2
2
2
1
2
0
2
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
1
3
1
0
2
1
0
2
0
1
0
1
0
0
1
0
0
0
2
0
0
0
1
0
1
2
2
0
3
1
1
0
0
0
2
0
1
2
0
0
1
0
1
1
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
2
1
2
2
1
1
2
1
0
0
0
1
0
2
0
0
1
1
0
0
2
0
0
0
2
2
1
1
0
0
0
4
1
0
0
0
0
1
2
0
0
0
1
1
0
1
6
0
0
0
0
1
0
0
0
2
0
1
0
1
2
0
0
1
1
0
0
1
2
0
0
0
1
0
0
0
1
1
0
1
1
2
2
2
0
1
0
1
0
0
0
0
0
1
0
2
1
1
0
1
0
0
0
0
0
1
0
0
1
0
2
2
0
1
0
0
0
2
2
0
0
2
2
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
2
0
2
1
0
2
2
0
1
1
0
1
0
2
0
0
1
0
0
0
0
2
2
0
1
0
0
0
1
2
2
1
2
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
2
0
0
0
1
0
0
1
0
0
0
0
1
0
0
2
1
0
0
0
3
0
1
0
0
1
1
0
0
1
0
2
0
1
0
0
0
1
0
2
0
0
0
2
0
0
1
1
1
0
1
2
2
2
1
2
2
1
1
2
1
0
0
0
0
0
1
0
0
0
0
2
0
2
0
1
2
0
1
0
0
0
0
1
0
2
1
2
0
1
1
1
0
1
0
2
0
0
2
0
0
0
2
3
0
0
1
0
1
0
0
0
0
1
1
0
0
0
1
0
2
1
0
0
0
0
1
0
0
1
2
0
1
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
1
2
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
1
0
1
2
0
3
0
0
0
0
3
0
2
0
0
6
0
1
2
0
1
0
0
0
2
2
2
1
0
1
0
0
0
1
1
0
1
5
2
2
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
2
1
2
0
0
2
2
0
2
1
1
0
0
0
0
2
0
0
1
1
0
1
1
0
0
1
0
0
0
0
0
1
1
2
0
1
0
1
0
1
1
1
0
0
2
0
0
2
2
3
0
0
0
1
1
0
0
1
2
0
2
2
0
0
0
0
0
0
3
0
2
1
1
0
0
0
0
0
0
2
0
0
0
1
0
2
1
0
0
0
0
0
0
2
1
0
0
1
0
0
2
2
0
0
1
0
0
2
0
1
0
0
0
0
0
8
0
0
2
0
2
0
0
1
0
1
0
0
1
0
0
2
0
2
2
2
1
0
1
0
0
2
0
2
0
0
0
0
0
3
0
0
0
0
0
0
1
2
2
0
0
0
2
1
1
0
0
0
0
0
0
2
2
1
0
1
2
0
1
1
2
1
1
0
0
0
0
2
1
2
1
0
0
0
0
0
0
0
0
0
2
0
1
2
1
0
0
0
2
0
0
0
1
1
0
0
2
0
0
1
1
0
1
2
0
2
2
0
0
0
0
2
2
0
0
0
2
1
0
0
0
2
0
1
2
0
0
0
2
0
0
2
0
0
0
0
1
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
1
2
1
0
2
0
0
0
0
0
1
1
1
1
1
2
0
1
0
1
3
0
0
2
2
1
0
1
1
1
2
1
0
0
0
0
1
1
2
0
0
2
1
0
0
0
0
0
2
2
0
0
2
1
0
2
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
3
2
1
0
0
0
0
0
0
0
0
1
0
1
1
0
3
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
2
0
2
0
0
0
0
1
2
0
0
0
2
2
0
0
2
0
0
0
0
1
2
0
0
0
0
2
1
1
3
0
0
0
0
1
2
0
0
0
1
1
0
0
2
3
1
0
0
0
1
0
0
0
0
2
0
2
0
2
3
0
0
0
1
2
2
0
1
3
0
0
0
0
0
0
0
0
1
0
0
0
2
2
1
1
2
0
0
2
3
0
2
1
2
1
0
0
1
2
0
0
1
1
0
2
0
1
1
0
0
0
0
0
2
2
1
0
0
1
0
0
0
0
1
0
0
1
1
1
1
0
0
1
2
0
0
2
0
1
2
0
0
1
1
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
2
2
0
1
0
0
0
0
0
1
0
2
1
0
0
2
2
0
5
2
1
0
2
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
2
0
1
0
0
0
2
0
0
0
1
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
2
2
0
0
1
0
2
0
2
1
1
0
2
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
1
0
3
1
0
2
1
2
2
2
0
1
0
2
0
1
5
2
0
2
1
0
2
0
0
0
1
0
1
0
0
0
2
0
0
0
1
3
0
0
0
1
0
2
0
0
1
0
1
0
0
0
0
0
1
1
1
0
0
2
1
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
1
1
2
0
5
2
0
0
0
1
0
0
0
2
1
0
0
2
2
0
2
0
0
1
2
0
1
0
0
0
1
0
0
0
0
2
0
2
2
0
0
1
0
0
1
1
0
0
0
0
0
0
0
2
2
2
3
0
2
0
1
3
0
1
1
0
0
1
0
0
0
1
1
1
2
0
0
0
0
0
0
2
0
0
0
1
1
1
0
0
0
2
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
3
1
0
2
0
1
0
0
1
1
0
0
1
0
1
0
2
1
0
0
1
1
0
1
2
0
0
0
2
0
1
0
1
0
0
0
4
1
2
1
0
0
0
0
0
2
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
2
1
0
0
0
0
0
0
0
2
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
2
0
0
1
1
0
0
2
0
0
0
0
1
0
2
0
0
2
0
1
2
0
1
0
1
5
1
0
2
1
0
0
0
2
2
0
2
0
0
1
0
0
0
1
1
1
0
2
2
0
0
0
1
2
0
0
0
2
1
0
1
0
1
0
0
0
0
0
0
1
1
2
2
0
0
0
0
0
2
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
1
1
0
0
1
1
2
0
1
0
1
2
1
0
1
0
0
0
1
2
2
0
1
2
0
1
0
0
2
0
0
1
2
0
0
2
0
0
0
0
0
1
2
1
1
1
1
0
1
0
0
1
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
2
0
0
1
1
3
1
1
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
1
1
1
1
1
1
2
2
0
1
2
0
0
2
0
0
0
2
1
0
0
0
1
1
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
1
2
0
1
0
2
0
0
0
0
0
1
1
1
0
2
0
0
0
0
0
1
1
0
1
0
0
1
2
1
2
0
0
0
0
0
1
0
2
1
0
1
1
0
0
0
0
0
1
1
2
0
0
1
2
0
1
1
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
2
2
1
1
1
1
0
0
2
0
1
2
0
0
0
0
0
0
0
1
1
0
2
2
0
0
0
0
0
1
0
0
2
0
2
1
0
0
0
1
0
0
2
0
1
0
2
0
0
2
2
0
1
2
0
0
2
1
1
0
1
0
2
0
0
0
0
0
0
0
0
2
2
0
1
0
1
0
3
1
0
0
0
0
0
0
0
1
0
2
1
2
0
1
5
0
2
0
3
0
0
0
0
0
3
1
0
0
0
1
0
1
0
2
0
0
0
2
2
0
1
0
1
1
0
0
1
0
1
1
2
0
0
2
2
1
2
0
0
2
2
2
4
0
0
0
2
4
1
0
0
0
1
2
0
0
4
0
0
0
1
0
0
0
1
0
3
2
0
1
2
2
0
0
0
0
2
1
0
0
0
0
0
1
2
1
1
0
1
1
1
0
0
1
2
2
0
0
2
2
0
0
1
1
0
0
0
2
0
2
1
2
0
0
0
1
1
3
0
0
0
1
1
0
1
2
0
0
0
1
0
0
2
0
0
0
3
1
1
1
0
0
2
0
0
0
0
2
1
0
2
0
0
0
0
2
2
0
2
0
2
0
1
0
0
0
0
0
2
1
1
3
0
2
2
0
1
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
2
0
0
0
2
2
0
1
2
0
1
2
0
2
0
1
0
0
1
0
1
0
1
0
1
2
0
0
0
0
0
2
0
0
0
1
0
0
3
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
2
1
0
0
0
0
2
0
1
3
3
0
1
1
0
0
2
2
1
0
0
0
0
0
0
0
0
1
2
2
1
2
0
2
0
1
0
2
0
1
0
0
1
1
0
0
2
1
2
0
1
0
0
2
2
0
0
0
0
0
1
0
1
0
2
1
1
2
1
0
1
1
2
2
1
2
0
0
0
0
0
0
1
0
2
2
5
2
0
1
0
1
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
2
1
0
0
0
0
2
0
1
2
0
4
0
2
1
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
3
0
0
0
0
0
0
0
1
0
0
2
0
0
3
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
1
4
2
1
1
0
0
0
1
0
3
0
2
0
1
0
0
0
0
1
1
0
0
2
0
1
1
1
1
0
0
1
0
2
1
2
0
0
0
2
0
0
0
1
0
0
2
0
1
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
1
0
0
1
1
1
0
0
0
0
0
0
0
2
0
2
1
2
1
1
2
2
0
0
0
1
3
0
0
1
0
0
1
1
0
0
0
2
1
0
0
0
1
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
1
2
0
0
0
0
2
0
2
0
0
0
1
0
1
0
0
2
1
1
1
1
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
1
2
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
2
0
0
0
1
2
0
0
2
0
2
2
2
1
0
0
0
0
1
0
0
0
2
0
1
1
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
2
1
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
3
0
2
3
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
2
5
1
0
2
1
0
0
0
2
0
0
2
0
0
0
2
0
0
2
0
1
2
0
0
0
1
2
0
4
0
1
0
0
0
2
1
0
5
2
0
0
0
2
3
0
0
0
1
0
1
0
0
1
1
2
0
0
1
2
0
1
1
0
0
0
0
0
0
1
2
0
1
0
1
0
0
1
0
0
0
1
0
0
3
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
2
0
1
1
2
0
0
2
0
0
0
0
0
1
0
1
0
1
1
2
0
0
0
2
0
1
0
2
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
2
0
0
1
2
0
0
0
2
0
1
0
0
0
2
1
0
2
2
0
2
1
1
0
2
0
2
1
0
1
1
1
1
0
0
1
1
1
1
1
1
0
0
1
2
0
0
5
1
1
0
0
0
0
0
0
2
2
2
0
1
1
1
1
0
0
2
0
1
0
0
2
0
2
0
0
2
0
0
0
2
1
0
0
2
1
0
2
0
1
2
0
0
0
3
0
0
0
2
0
0
1
1
2
0
0
2
0
0
2
1
2
0
0
1
3
2
0
0
1
0
2
0
0
0
2
0
1
1
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
1
1
1
1
1
1
2
0
0
0
0
0
0
1
1
0
1
0
1
0
1
0
1
0
1
0
2
0
2
2
1
2
0
1
0
0
1
0
0
1
0
1
0
0
1
0
0
0
1
1
1
0
0
0
0
0
2
0
2
0
0
1
2
2
0
2
1
2
0
1
0
0
2
0
0
0
0
0
1
0
1
1
0
1
0
1
0
2
0
0
0
0
2
0
1
0
3
1
0
0
1
4
2
0
0
0
1
0
0
0
0
2
1
1
0
0
1
0
0
0
1
0
0
1
0
0
0
1
1
2
0
2
1
0
0
0
0
0
0
0
2
1
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
3
1
0
0
0
0
0
1
0
2
0
0
0
1
0
0
2
2
0
3
2
3
0
2
0
0
1
2
0
0
1
2
0
1
0
1
0
0
2
1
1
0
2
1
1
0
1
0
0
0
0
0
0
0
1
2
0
2
0
0
1
0
0
0
2
0
1
0
1
1
0
0
2
0
1
1
1
1
0
0
0
0
0
2
0
2
0
0
0
2
0
1
0
2
2
2
2
0
2
0
2
0
1
0
0
2
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
4
0
0
0
1
0
0
0
2
1
0
2
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
1
0
1
2
0
0
2
0
0
1
0
1
0
1
1
0
2
0
0
2
0
0
0
1
1
0
0
0
1
0
2
0
0
0
1
0
0
0
1
2
0
0
0
2
2
1
2
2
0
0
0
0
1
2
1
0
1
2
1
0
0
0
0
0
0
1
0
3
1
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
1
0
2
0
0
2
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
1
1
1
5
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
3
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
4
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
3
0
0
4
1
0
2
0
0
0
1
2
3
4
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
2
1
0
2
0
2
0
0
1
0
1
0
2
1
0
2
3
0
0
1
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
2
1
0
0
0
1
0
1
1
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
2
1
4
0
2
0
1
1
2
1
0
1
2
1
0
0
0
0
0
0
0
0
0
0
1
18
2
0
0
0
0
2
0
0
0
2
2
3
1
0
0
0
1
0
1
2
0
1
1
2
0
0
0
1
0
0
0
0
0
0
0
0
3
0
1
0
2
0
0
1
0
2
2
0
0
2
2
0
0
1
3
0
1
0
0
1
1
1
1
0
0
0
2
3
2
0
0
1
2
1
0
2
2
0
0
1
0
1
2
1
2
0
1
0
2
1
0
0
0
1
0
1
2
0
0
2
0
2
1
1
0
0
2
2
0
1
2
0
2
0
0
0
0
2
1
0
1
1
2
0
0
1
0
1
2
2
1
3
0
0
0
0
0
2
0
2
0
0
0
1
1
0
0
0
0
1
0
3
0
0
0
1
0
0
1
0
0
0
2
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
3
0
1
1
0
2
2
0
0
0
1
0
0
0
0
0
0
2
0
2
1
0
0
1
0
0
0
1
2
1
0
0
2
1
0
2
0
0
1
0
1
2
1
3
2
0
0
1
0
0
1
1
1
0
2
0
0
0
0
0
1
0
2
0
2
0
2
1
0
7
2
0
0
0
2
0
1
1
0
2
0
0
1
0
2
2
0
2
1
0
0
1
2
0
0
0
2
0
1
0
0
1
0
0
1
1
1
3
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
2
0
2
0
0
0
2
0
0
1
0
0
1
0
2
1
0
0
0
0
2
2
1
0
1
1
0
0
0
1
0
2
0
2
2
1
0
0
0
3
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
2
1
2
0
1
0
0
2
1
0
0
0
0
2
1
1
2
1
2
0
0
0
0
0
2
0
2
1
0
1
0
0
0
1
1
2
0
0
0
0
1
1
1
0
1
1
0
0
0
0
3
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
2
2
0
0
1
2
2
0
1
1
2
1
0
0
2
0
1
1
2
0
0
1
0
1
2
1
1
2
0
2
0
2
0
1
1
0
2
0
0
1
0
0
2
0
0
2
1
2
0
0
0
0
1
0
2
0
0
1
0
0
1
0
2
3
2
2
0
2
2
0
0
0
1
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
1
0
0
1
2
0
2
1
0
0
0
1
1
0
0
0
0
2
2
2
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
2
2
0
2
0
0
0
0
1
1
0
1
0
0
1
0
2
1
2
0
0
0
1
0
0
0
0
1
0
0
2
0
0
1
0
3
0
2
1
2
1
0
0
0
1
0
0
2
1
0
1
0
2
0
1
2
1
0
0
0
1
0
0
0
0
0
0
2
2
0
0
1
1
0
0
0
1
4
0
0
0
0
0
1
3
0
2
0
0
2
1
1
0
0
0
1
0
2
0
2
2
2
0
2
0
0
0
1
0
0
1
2
0
0
2
1
1
0
0
1
1
0
0
0
0
1
1
2
2
0
1
2
2
2
3
0
0
1
0
1
2
0
1
0
0
2
0
1
1
1
0
0
0
0
2
1
0
0
0
2
1
0
0
2
0
1
0
0
2
0
0
3
1
1
1
0
2
0
0
0
2
2
0
0
0
1
0
0
3
0
0
0
0
0
0
2
1
0
1
0
0
0
0
2
1
0
0
1
0
2
0
1
0
2
0
0
0
0
0
1
0
2
0
0
0
0
2
0
2
0
2
3
0
2
0
0
1
1
0
0
0
1
0
2
2
0
1
1
0
0
0
0
2
0
0
1
0
2
0
1
2
0
1
0
0
0
0
0
1
0
0
0
0
3
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
3
1
0
0
1
0
3
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
1
2
1
2
0
0
0
0
0
0
1
0
0
1
1
1
0
1
1
2
0
2
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
1
0
0
0
2
1
2
2
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
2
0
1
1
1
2
0
0
0
0
2
1
2
0
2
0
0
0
2
0
2
0
0
1
1
0
0
2
0
0
1
0
0
3
0
0
2
1
2
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
2
0
0
0
2
2
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
1
1
0
1
1
0
3
0
0
0
0
0
1
2
0
1
1
1
0
0
0
2
1
0
0
2
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
1
0
2
1
1
0
1
0
2
0
2
0
0
2
0
0
1
0
0
0
0
1
1
0
2
0
2
0
2
0
1
2
1
1
0
0
0
0
2
2
0
0
1
0
0
0
1
1
0
1
0
0
0
1
0
2
1
0
2
0
0
0
2
0
0
2
1
0
0
0
1
1
1
0
0
2
1
0
1
0
0
0
0
0
0
0
2
2
1
0
1
1
2
0
0
0
1
0
2
0
1
1
0
0
1
2
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
2
1
2
2
2
0
0
1
1
1
0
2
0
2
2
0
1
0
1
2
0
1
0
2
0
0
1
2
0
1
0
0
2
0
0
0
1
0
0
1
0
0
2
0
0
0
0
1
0
1
1
1
0
0
2
0
0
0
0
1
0
0
0
2
0
1
2
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
2
1
1
2
1
0
2
0
0
1
2
0
0
0
0
0
0
0
2
1
0
0
1
1
0
0
1
0
0
0
1
1
1
1
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
1
1
0
9
1
0
1
0
1
1
1
2
0
0
0
0
1
0
2
1
2
1
2
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
1
1
1
0
4
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
2
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
1
0
3
0
1
2
1
3
0
1
0
1
0
0
0
0
1
1
1
2
0
2
0
2
0
0
0
2
0
1
1
0
2
0
2
2
0
0
1
0
0
0
0
0
0
1
1
0
1
1
1
0
1
0
0
0
1
0
0
0
3
2
0
0
1
0
2
0
1
1
0
0
0
1
1
0
0
0
0
0
1
2
1
1
0
0
0
1
1
1
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
1
0
0
1
0
2
0
2
0
2
0
1
0
1
2
1
1
0
0
0
2
0
2
2
2
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
2
0
2
0
0
1
0
0
2
0
0
2
2
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
1
2
0
2
0
3
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
2
0
0
2
0
3
1
0
0
2
0
1
0
1
1
4
0
1
0
1
1
0
2
2
0
0
0
0
2
6
0
0
1
2
0
0
2
0
2
0
1
1
0
2
0
1
1
1
0
1
0
0
0
2
2
0
0
1
1
0
2
2
0
1
0
0
0
0
3
0
0
0
0
0
2
0
2
0
1
0
0
0
2
2
0
0
2
0
0
2
0
0
0
1
0
2
2
1
0
0
2
0
0
2
2
0
0
1
0
2
0
0
0
0
1
0
0
3
0
0
0
0
0
0
2
0
0
0
2
0
0
1
1
1
1
1
0
0
1
0
0
0
0
0
0
7
2
0
0
0
1
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
2
2
1
1
2
0
0
2
0
0
1
0
1
2
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
3
2
2
0
0
1
0
1
2
0
0
0
1
3
1
2
2
2
1
0
0
1
2
0
0
0
2
1
1
0
0
0
2
0
2
0
1
2
0
0
1
0
0
0
0
0
0
1
1
0
0
2
0
0
0
2
2
0
0
1
0
0
0
2
0
0
0
1
0
2
1
0
2
0
0
1
2
0
0
0
3
0
0
0
2
2
0
0
0
0
2
0
2
0
0
1
0
1
2
0
2
0
0
0
4
2
0
2
0
2
1
0
1
1
2
0
1
0
0
2
1
0
0
2
0
0
0
0
1
0
2
2
2
2
1
0
1
0
0
0
0
1
1
0
0
2
0
1
0
1
0
0
0
1
0
0
2
0
0
0
1
2
0
1
0
0
1
2
1
0
0
1
0
1
0
0
0
2
1
1
0
0
0
1
0
2
0
0
0
0
0
1
2
1
3
0
2
0
3
1
0
0
0
0
2
1
0
1
0
0
2
2
0
1
1
0
0
1
0
0
0
0
0
1
0
1
2
0
1
2
0
2
0
0
0
1
0
1
0
0
0
1
1
2
0
1
0
2
0
0
0
0
0
1
0
0
1
0
0
1
0
2
2
1
0
1
0
0
0
1
1
2
0
0
1
1
1
0
0
0
0
0
1
1
1
1
0
2
1
3
2
0
2
0
0
1
1
0
0
1
0
2
0
2
0
1
0
0
0
1
0
0
1
1
2
0
0
1
2
0
0
2
2
0
2
0
0
0
1
2
0
0
0
1
1
0
0
0
0
0
2
1
2
1
2
0
1
3
0
2
0
0
1
0
0
0
0
2
1
0
0
0
2
1
0
0
0
0
0
2
1
1
0
1
0
0
2
2
2
2
1
1
1
1
1
1
0
0
1
2
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
2
3
2
0
0
2
2
2
2
0
2
0
0
1
1
3
1
0
2
2
0
0
0
0
0
0
1
2
0
0
0
1
0
1
2
2
1
2
0
0
2
1
0
0
1
0
1
0
0
2
0
0
0
1
0
1
0
8
4
0
0
0
0
0
0
0
0
0
0
2
2
1
0
2
2
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
1
0
0
1
0
0
0
1
1
0
2
0
0
0
2
0
0
0
0
0
1
2
2
0
1
2
1
0
1
2
0
0
1
1
0
0
0
0
1
1
1
1
0
0
2
1
1
2
0
0
1
1
1
3
1
0
0
2
0
0
0
2
0
1
1
0
0
1
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
3
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
1
0
1
1
0
2
2
2
0
0
2
1
1
0
1
0
0
1
1
0
1
1
0
0
0
1
2
2
0
2
1
0
0
1
0
0
0
0
1
1
0
0
1
1
0
0
1
1
2
0
2
0
0
0
0
0
0
2
1
0
1
1
2
2
1
0
2
1
0
0
1
2
0
0
0
1
0
0
2
2
0
2
0
2
0
2
0
0
0
0
2
2
0
2
0
1
0
1
0
0
2
2
0
0
1
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
1
0
0
2
0
1
3
0
0
0
0
1
2
2
1
1
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
2
1
1
0
0
0
1
1
0
0
0
0
3
0
2
0
3
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
2
0
0
0
2
2
0
3
0
0
2
0
2
0
2
5
1
0
0
0
3
2
0
0
0
0
0
0
0
0
1
0
0
3
2
4
1
1
2
0
0
0
1
1
2
0
0
1
2
3
1
1
1
3
0
0
0
0
0
1
2
0
0
1
0
0
2
1
0
0
1
0
0
2
0
0
0
0
0
1
0
1
0
1
0
1
0
1
0
0
0
2
0
2
0
0
1
1
2
0
1
0
1
1
2
3
0
1
0
0
1
1
0
2
0
1
1
2
2
1
0
0
0
0
1
0
2
0
1
1
0
2
0
0
1
1
2
1
0
1
2
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
2
1
0
2
2
0
0
0
0
0
1
0
3
0
0
3
1
0
1
0
0
0
0
2
3
1
1
0
1
2
0
1
0
0
1
0
0
0
0
1
0
0
2
0
0
0
1
1
2
0
1
1
0
0
0
0
0
0
0
2
1
0
0
1
0
1
1
0
1
0
1
1
0
1
0
0
0
1
0
0
2
0
2
1
2
0
0
0
1
0
2
0
1
0
0
2
0
0
0
0
1
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
2
0
0
1
1
0
0
1
2
0
0
0
0
0
0
2
0
1
1
0
2
0
0
2
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
2
1
0
0
0
1
0
3
0
0
3
0
2
1
1
2
0
0
0
0
0
2
0
0
0
0
1
1
0
1
2
1
0
0
1
0
1
4
1
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
1
0
2
1
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
2
2
1
0
2
0
1
0
0
0
0
1
2
2
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
1
2
1
0
1
1
0
0
0
1
0
0
1
0
2
0
0
2
1
2
0
3
0
0
0
1
0
0
0
2
1
0
1
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
1
0
2
2
0
0
0
1
1
1
0
0
2
1
0
0
0
0
1
0
0
1
2
0
0
0
2
0
2
0
1
1
0
1
0
0
0
2
1
2
0
0
9
0
0
2
0
1
0
0
0
0
1
0
0
0
0
2
0
1
0
0
2
1
0
0
0
1
1
0
2
2
0
0
2
0
1
0
0
1
1
1
0
0
1
0
1
0
1
0
2
0
0
0
2
2
0
2
0
2
0
2
0
2
0
3
0
2
2
2
0
0
0
0
2
0
0
1
0
2
0
0
1
0
2
1
0
0
1
0
1
2
1
0
1
1
0
0
0
1
0
0
0
2
2
1
1
0
0
1
1
0
1
0
1
1
2
0
0
0
0
0
2
1
0
0
1
0
0
2
0
1
0
0
1
0
1
2
2
0
0
0
0
0
1
2
0
1
2
2
1
1
0
0
1
0
0
1
1
2
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
1
0
2
1
0
2
1
0
3
3
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
2
1
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
1
1
2
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
2
5
0
3
2
0
0
0
2
1
0
0
2
3
0
2
0
2
2
2
1
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
1
1
0
2
0
0
1
1
2
0
0
0
2
0
0
0
2
0
0
1
1
1
2
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
2
1
1
0
0
0
3
0
1
0
1
1
0
0
0
1
0
0
2
1
0
2
0
2
0
2
0
0
2
0
0
3
0
0
2
1
0
1
0
0
2
0
0
2
0
0
2
1
0
0
1
2
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
1
3
1
0
2
0
0
0
1
1
2
0
3
0
0
0
0
0
1
0
0
2
2
1
0
0
0
1
0
0
0
1
2
2
1
1
1
0
0
0
0
2
1
0
2
1
2
0
1
0
1
1
0
0
0
0
2
1
1
0
0
2
0
0
1
0
0
3
1
0
0
0
1
0
2
0
0
0
0
2
0
1
2
0
1
2
0
1
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
2
2
2
1
1
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
1
1
0
0
2
0
2
0
2
1
2
0
0
0
1
3
0
0
0
2
1
2
0
0
1
2
0
2
1
0
1
0
2
0
2
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
2
2
1
0
0
1
1
0
0
2
2
1
2
0
2
2
0
0
1
0
0
0
1
0
0
1
1
0
1
1
2
1
0
0
1
0
2
2
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
1
1
0
1
0
1
0
0
0
2
0
0
0
1
2
0
1
2
0
2
1
0
1
1
0
0
0
0
0
1
2
0
0
2
1
2
2
0
0
3
0
2
0
0
1
0
0
0
1
0
0
0
1
1
1
2
2
2
0
0
0
1
0
0
2
0
0
0
2
0
2
0
1
1
0
0
2
2
0
0
2
2
0
0
1
4
1
0
1
1
1
0
2
0
1
2
0
1
2
1
2
1
0
0
2
0
0
0
0
0
0
2
2
1
0
0
0
0
0
2
0
1
2
1
0
1
0
1
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
1
0
1
0
0
1
1
0
1
0
0
0
1
0
0
2
0
0
2
1
0
1
2
2
0
3
1
0
1
0
1
0
1
1
0
0
0
0
0
1
1
0
0
1
0
1
0
2
1
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
1
1
2
0
1
0
0
0
2
1
0
0
0
0
0
0
1
0
7
1
0
2
2
2
2
0
2
1
0
0
0
0
2
1
0
1
0
2
2
2
2
0
2
0
0
1
0
0
1
2
2
2
0
1
0
1
1
2
0
0
0
0
2
0
0
2
0
0
4
2
0
3
0
2
1
0
1
0
0
0
0
0
0
0
0
3
0
0
2
1
0
1
0
2
0
0
0
0
4
2
2
2
0
2
0
1
0
2
0
0
0
0
1
2
0
0
0
0
0
1
1
0
2
1
0
1
2
1
0
0
0
0
2
0
0
0
2
0
0
2
2
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
1
1
1
0
2
0
2
0
0
0
0
0
1
1
2
2
2
3
0
0
0
1
2
0
2
0
0
2
4
0
0
2
1
0
2
2
1
0
2
0
0
0
1
1
0
1
0
2
0
0
2
1
0
2
0
2
2
0
0
0
1
0
0
0
4
0
2
1
0
0
0
0
1
1
0
2
0
0
2
0
1
0
0
0
3
2
0
0
2
0
0
0
1
0
2
3
0
0
2
0
2
2
1
0
0
0
1
1
2
0
1
0
0
0
0
0
0
0
0
0
1
0
1
2
1
0
1
1
1
1
0
1
2
2
0
2
0
0
3
0
0
0
1
1
0
0
1
0
1
2
2
1
0
1
0
0
0
0
2
0
0
0
0
0
2
1
1
0
0
1
2
1
0
0
0
0
0
1
1
0
2
0
2
0
1
0
0
1
0
0
0
0
2
2
0
0
0
0
2
1
0
2
0
0
2
2
0
1
0
2
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
1
0
0
0
3
0
0
0
1
0
0
1
0
0
2
0
0
1
0
1
3
2
0
0
2
0
1
0
1
0
0
1
1
0
5
0
1
0
0
0
0
0
0
2
1
2
2
0
0
2
2
1
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
2
0
0
2
0
0
1
0
2
0
0
0
1
1
0
1
0
1
1
0
0
0
2
1
2
0
0
2
2
0
1
1
1
0
0
2
1
0
1
1
0
1
0
0
1
1
0
0
0
0
2
0
2
0
0
0
1
1
0
2
1
1
2
0
0
1
2
0
0
0
1
0
0
0
1
2
2
0
1
0
1
0
0
1
0
0
2
0
1
1
1
0
1
2
2
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
4
2
1
1
1
2
1
1
2
0
0
0
0
1
2
0
0
0
0
2
0
0
1
1
0
1
0
1
0
1
2
0
2
1
0
0
0
2
0
0
2
0
0
0
0
2
1
1
0
1
0
1
1
2
0
0
0
1
2
0
0
0
2
1
0
1
0
0
1
0
0
0
1
0
0
0
2
1
0
2
2
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
2
2
1
0
1
2
0
2
0
0
0
1
0
0
0
2
3
2
0
1
0
1
1
3
0
1
0
0
1
2
1
0
0
0
1
0
0
0
0
0
0
3
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
2
0
0
0
0
0
0
0
1
0
3
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
1
2
1
2
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
1
0
0
0
2
2
0
1
0
2
0
0
1
0
1
1
0
1
1
0
1
0
1
1
1
0
1
0
0
1
0
4
1
1
1
2
1
1
0
0
2
0
2
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
1
0
1
0
1
1
0
1
0
2
1
0
1
1
0
0
0
1
2
0
0
2
1
0
0
0
0
0
2
3
0
0
0
0
1
0
1
0
2
4
0
0
0
2
0
0
0
0
1
0
0
0
0
1
1
0
2
0
1
0
0
1
0
1
2
0
2
1
0
2
0
0
0
2
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
2
1
0
1
2
2
0
0
0
0
0
2
0
0
0
1
0
0
1
2
0
0
1
0
0
0
2
2
1
1
0
0
1
3
0
0
0
0
0
6
0
1
2
0
1
0
1
1
0
2
0
0
2
2
0
1
2
2
1
2
1
2
0
0
2
1
0
0
0
2
0
0
1
0
0
1
0
1
0
1
1
2
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
3
0
1
1
1
2
0
0
0
0
1
0
0
0
1
0
0
2
0
2
1
1
2
0
0
2
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
2
1
2
0
1
2
2
0
0
0
0
0
0
0
1
1
1
2
0
0
0
1
0
1
0
3
1
0
1
2
2
0
0
0
0
2
2
1
0
2
0
1
0
0
0
0
2
0
1
0
2
0
0
2
0
0
0
2
1
0
1
1
0
0
1
3
0
0
0
1
0
2
0
1
1
1
0
0
0
1
2
0
0
0
2
0
1
0
1
0
2
2
2
1
2
0
0
0
0
1
0
1
0
0
1
1
0
2
0
0
0
1
0
6
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
1
0
0
2
0
0
0
0
4
2
0
2
2
0
0
1
0
0
0
2
0
1
1
2
2
1
0
0
0
2
0
0
1
0
1
2
2
2
2
3
0
0
0
1
0
0
2
0
4
0
0
2
0
1
3
0
0
0
1
5
0
2
2
0
2
1
0
1
0
1
1
5
1
0
1
0
2
1
0
2
0
0
0
0
0
0
1
1
1
0
0
0
1
1
0
2
0
0
0
0
2
1
0
2
0
1
0
0
1
0
0
1
1
1
1
1
2
4
0
0
0
1
0
0
0
0
1
0
3
0
2
1
0
0
1
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
2
0
0
0
0
0
2
2
0
2
0
1
0
1
0
2
1
0
2
0
2
1
0
2
4
0
2
0
0
1
0
0
2
0
1
0
0
0
0
1
0
0
0
2
0
0
1
0
0
2
0
0
0
0
2
1
0
1
0
0
0
0
0
1
0
1
2
1
0
1
1
1
2
2
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
1
0
2
0
2
0
0
2
0
0
0
0
2
0
1
0
0
0
1
0
2
1
0
0
2
0
2
0
0
0
0
1
0
0
2
0
0
2
0
0
2
0
2
0
0
0
2
1
2
2
0
0
3
2
2
1
1
1
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
2
4
1
1
1
0
0
0
0
0
0
2
0
2
0
0
0
2
2
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
2
0
3
2
1
0
0
0
0
0
1
1
0
1
2
0
0
2
0
1
2
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
1
2
1
0
0
1
2
0
1
0
2
0
0
5
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
2
0
2
2
2
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
1
2
0
0
2
0
3
0
3
1
2
0
2
0
0
0
1
0
0
2
2
0
1
0
1
0
0
2
0
1
0
0
0
1
0
2
0
1
1
0
0
0
0
0
1
1
1
2
0
0
0
1
1
1
1
2
0
2
0
2
4
0
0
0
0
1
0
0
1
0
0
2
1
2
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
2
1
0
1
1
0
0
0
0
1
0
3
2
0
1
0
0
0
2
2
0
0
0
0
1
0
1
1
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
1
1
0
1
1
1
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
3
0
0
0
0
2
0
0
0
0
0
1
0
1
0
3
0
0
0
1
2
2
2
0
1
1
0
0
2
1
0
1
2
2
1
0
0
0
1
0
2
1
0
2
1
0
1
1
0
1
2
1
1
2
0
0
0
2
1
0
1
3
0
0
1
0
0
1
0
0
1
1
2
0
0
3
2
1
0
1
1
0
2
2
0
2
1
0
0
0
1
2
2
2
2
0
1
0
0
4
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
2
0
0
0
1
2
0
1
0
3
1
2
3
2
1
0
3
1
0
0
2
1
1
2
0
1
2
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
1
1
2
1
0
0
1
0
0
0
1
1
1
1
1
0
0
1
1
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
1
1
2
1
2
1
2
0
0
2
1
0
1
2
0
0
0
0
2
1
0
0
1
2
1
0
1
1
1
0
0
1
0
0
0
1
0
2
0
2
2
0
0
0
0
1
2
1
1
1
0
0
2
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
3
1
2
0
0
1
0
1
0
0
0
0
0
0
2
3
2
0
1
1
0
0
2
1
1
1
2
0
2
0
3
0
0
0
0
0
1
1
0
0
0
0
2
0
1
0
0
0
2
2
0
1
2
3
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
2
0
0
2
0
2
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
2
1
0
1
0
1
2
0
1
0
1
0
0
0
0
4
1
1
2
0
0
2
0
0
2
0
1
0
2
2
2
2
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
1
1
3
1
0
0
0
0
0
0
0
1
0
1
3
2
0
0
0
0
0
2
0
0
2
0
2
0
0
0
1
0
0
2
0
0
7
0
1
0
1
3
2
0
0
0
0
2
1
0
0
0
2
1
1
1
0
1
0
0
1
0
1
0
0
0
0
1
2
2
0
0
1
0
1
2
0
0
1
0
0
0
1
1
1
0
1
0
2
1
0
0
2
0
0
2
1
0
2
1
0
0
0
2
0
2
0
0
2
0
2
0
1
2
2
0
2
1
1
1
1
0
0
2
1
0
2
0
1
0
0
2
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
2
2
1
2
0
0
2
0
0
0
1
0
0
6
0
1
0
2
0
2
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
2
2
0
1
0
0
2
2
0
2
0
1
2
2
0
1
0
2
2
0
0
0
2
0
0
0
0
1
0
1
0
2
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
4
2
0
0
1
0
2
0
1
2
2
2
1
0
0
1
0
0
0
0
1
0
0
0
5
2
2
2
3
1
0
2
0
0
0
3
0
0
2
2
2
0
2
1
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
1
0
2
0
0
1
0
1
0
0
1
0
0
0
0
0
1
2
0
0
0
0
2
1
1
0
0
0
2
0
1
0
0
0
2
0
0
2
0
0
0
1
0
1
0
2
1
2
0
2
2
1
0
2
0
0
0
0
1
2
0
1
1
2
2
0
0
1
2
1
0
0
2
0
0
2
0
1
0
0
0
0
1
0
0
2
1
0
2
0
1
2
0
0
0
0
2
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
2
2
2
2
0
0
0
0
0
0
0
2
0
0
3
0
2
2
1
0
1
1
0
1
0
0
0
0
0
0
1
2
0
1
1
1
0
0
0
2
2
0
0
0
3
0
2
0
2
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
1
0
0
2
4
0
2
0
1
2
0
0
0
1
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
2
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
1
0
2
1
0
0
1
1
1
0
2
1
0
1
1
0
2
0
0
0
0
0
0
1
1
0
0
2
0
0
1
1
0
0
0
0
0
2
2
0
0
0
2
0
0
1
2
0
2
1
2
1
2
0
1
1
1
1
0
1
1
1
1
2
2
1
0
1
0
0
0
1
0
0
0
0
4
0
0
1
2
0
0
0
2
0
1
1
1
1
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
2
0
2
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
2
0
0
1
1
1
0
2
0
0
1
0
1
0
0
0
0
1
0
1
1
0
3
0
0
2
0
1
2
0
2
4
0
3
0
0
2
4
0
2
0
0
1
0
2
0
0
1
2
3
0
0
2
1
1
0
1
0
0
2
0
0
2
3
0
0
2
0
0
2
2
0
0
2
0
0
1
2
1
0
0
0
1
0
0
0
1
0
3
0
0
0
2
0
1
0
0
0
0
1
0
0
2
0
1
1
2
2
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
3
0
0
1
1
2
2
0
0
2
0
0
6
0
1
1
2
0
2
1
0
0
1
1
0
1
2
2
2
0
0
0
0
0
0
0
0
1
0
2
0
0
2
1
1
1
0
1
1
0
0
0
1
0
0
1
2
0
1
0
2
1
0
0
2
2
0
0
3
1
3
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
2
0
1
0
1
0
0
1
2
0
0
0
1
0
0
2
3
0
0
1
1
0
1
2
0
1
0
0
0
0
1
1
0
0
1
0
2
3
0
0
0
0
2
0
2
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
3
0
1
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
3
1
0
0
2
2
2
0
3
1
0
1
1
1
0
1
1
1
1
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
3
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
1
3
1
2
0
0
0
0
2
0
1
0
0
1
1
0
2
0
1
0
2
0
0
0
4
0
1
2
0
0
2
0
0
0
2
2
1
2
2
0
0
2
2
2
0
0
0
0
1
1
0
2
0
0
0
1
0
0
1
2
0
3
6
0
0
0
0
2
1
0
0
0
0
0
1
2
0
1
1
0
0
0
0
3
1
0
0
2
0
0
0
0
2
2
0
0
0
3
0
0
1
2
2
0
0
0
1
2
2
1
0
0
1
0
0
1
0
0
0
1
1
1
2
0
0
1
0
0
2
2
2
2
0
0
0
1
0
0
0
1
0
0
2
0
1
1
2
0
0
3
2
0
0
2
0
0
0
0
1
1
0
0
0
2
0
2
1
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
1
0
2
2
0
0
0
0
1
0
1
2
2
1
1
0
0
2
2
1
0
1
2
2
0
2
0
1
0
1
0
1
0
1
2
1
0
0
2
1
0
0
0
1
1
1
2
1
2
3
3
0
0
0
2
0
2
1
1
0
0
1
1
0
0
0
0
1
2
0
0
1
1
2
0
0
0
1
0
0
0
2
2
1
1
1
0
0
1
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
2
0
1
3
2
0
0
1
1
1
2
0
2
0
2
0
0
0
1
1
0
0
4
1
0
2
0
2
0
0
2
1
0
0
3
0
0
2
0
1
1
0
0
0
2
2
0
0
0
0
1
0
2
0
0
2
1
0
0
0
0
0
0
0
1
2
0
0
2
0
0
2
0
0
0
1
2
0
1
0
0
0
1
1
1
2
2
1
0
1
1
0
1
0
2
2
2
0
0
0
2
0
0
0
0
1
1
0
6
1
0
1
0
0
1
0
2
0
1
0
0
0
0
2
0
2
1
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
3
0
0
0
0
0
0
1
2
1
0
1
0
1
0
2
0
0
2
1
0
0
0
2
0
0
1
0
0
0
0
1
2
1
0
0
0
0
0
0
1
1
0
2
2
2
0
1
4
0
0
0
0
3
0
0
0
3
0
2
0
1
2
0
0
0
2
1
1
0
2
0
0
0
2
1
0
0
2
0
2
1
0
0
2
2
0
0
1
0
0
2
0
2
0
0
0
0
1
0
1
2
0
1
0
1
1
2
1
1
0
0
0
1
2
0
2
0
0
0
0
2
1
0
0
0
0
0
1
0
0
1
0
0
3
0
0
0
2
0
0
1
0
0
0
0
2
1
2
1
0
1
0
2
1
0
1
0
1
1
1
0
0
2
0
0
0
2
0
1
2
2
2
0
0
2
1
0
3
0
0
0
0
1
0
0
1
0
0
0
1
2
0
1
0
1
1
0
1
2
0
0
0
2
3
2
0
2
0
0
0
0
0
0
1
0
2
1
0
2
0
0
0
1
0
2
2
2
0
2
0
0
1
0
0
0
0
1
0
0
2
0
0
2
2
1
1
1
0
0
0
3
0
0
0
1
0
1
0
0
2
0
1
1
0
4
1
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
3
0
0
0
2
1
0
1
0
0
2
0
1
0
1
2
0
0
0
2
1
1
2
0
0
0
0
2
0
0
1
0
0
2
2
1
0
1
1
0
2
2
0
0
0
0
0
2
0
0
1
0
0
2
0
1
1
1
0
0
0
2
0
1
1
0
3
1
2
1
0
0
0
0
0
0
0
1
1
1
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
2
3
0
2
0
0
3
0
0
0
0
0
2
1
0
2
1
3
0
3
0
0
0
0
0
1
0
0
0
2
2
2
1
0
1
0
1
2
0
2
1
2
2
0
0
0
3
0
0
1
0
0
1
1
0
1
1
1
3
0
0
0
4
2
2
0
0
0
1
1
2
1
1
1
2
1
0
0
0
0
0
3
1
0
3
0
1
2
3
0
0
2
0
1
0
1
0
0
2
0
1
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
1
2
2
0
0
1
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
1
0
1
0
2
0
0
1
0
0
1
2
0
2
2
1
0
0
0
0
0
2
0
2
0
0
1
2
2
1
2
0
0
2
0
3
0
0
1
4
2
0
0
1
0
0
2
2
0
2
2
3
0
0
0
0
4
1
1
2
0
2
2
0
0
0
0
1
0
0
0
2
3
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
2
0
1
1
2
0
2
2
0
1
0
0
0
0
1
0
0
1
1
0
2
0
0
1
1
0
0
2
2
0
0
1
1
0
0
1
0
0
1
3
0
1
1
1
0
0
1
2
2
0
0
2
0
0
1
3
0
0
0
0
1
0
2
1
2
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
2
2
1
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
1
2
0
2
0
0
0
2
0
0
0
0
0
2
1
0
3
1
0
1
1
0
2
0
0
0
0
1
0
0
0
2
1
0
2
0
0
2
0
0
1
1
1
0
0
0
0
0
0
0
0
2
1
1
0
2
1
0
2
1
0
2
1
0
1
0
0
0
2
0
2
0
0
0
0
3
2
0
0
2
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
3
3
2
0
0
1
1
0
0
1
0
0
2
0
0
2
2
2
0
1
0
0
2
1
0
0
0
1
2
0
2
1
0
0
1
0
2
1
0
0
0
0
2
2
0
0
1
0
1
0
2
1
5
0
1
0
1
0
1
0
0
3
2
2
1
0
0
0
2
0
0
0
0
0
0
2
0
2
2
1
1
0
1
2
0
0
0
0
4
0
1
0
2
1
0
1
0
3
0
3
2
0
2
0
2
0
1
0
1
0
0
0
0
0
1
0
1
0
0
2
0
0
1
0
0
0
2
0
2
0
2
0
1
0
0
1
0
0
0
0
0
0
1
0
2
1
3
0
2
0
1
0
0
0
0
2
1
0
2
0
0
0
1
0
0
1
0
0
1
0
1
0
0
1
1
1
0
1
0
2
0
0
0
0
2
0
2
0
3
0
0
2
0
1
1
0
0
2
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
1
1
2
0
2
0
2
2
0
0
1
1
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
1
0
1
0
0
0
1
1
0
0
0
1
1
0
0
2
2
1
1
2
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
2
0
0
1
0
0
0
0
2
0
0
1
0
1
0
0
0
0
1
1
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
1
0
1
0
0
0
1
0
0
0
2
0
0
0
2
1
1
0
1
1
0
0
0
2
0
1
0
0
0
2
2
2
2
0
0
2
0
0
0
0
0
2
0
0
0
1
0
2
1
0
1
0
2
1
0
0
0
1
2
2
0
1
2
0
1
2
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
1
0
1
1
1
0
0
2
2
1
0
1
0
1
0
2
2
0
1
0
0
0
0
1
0
1
0
3
0
2
0
2
0
5
0
2
0
0
2
1
0
2
2
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
2
0
0
1
0
1
1
2
0
2
0
2
0
1
2
3
2
2
2
0
0
2
0
2
0
0
0
2
0
0
1
2
2
0
0
1
2
2
0
0
0
0
0
2
0
0
0
2
1
1
0
0
1
2
0
0
0
0
2
1
0
1
2
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
1
1
1
1
0
0
0
0
0
2
1
2
0
0
0
1
0
0
0
0
2
0
0
2
0
2
3
2
0
0
0
1
1
0
0
2
0
2
0
0
2
2
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
2
0
0
0
2
0
2
0
1
0
1
2
0
0
0
0
1
0
0
1
0
0
0
1
0
1
2
1
2
0
1
0
1
0
0
2
2
0
0
3
2
2
1
0
0
0
0
0
0
0
0
2
1
0
2
0
0
1
0
3
0
1
1
0
0
0
0
0
0
0
0
0
1
2
0
1
1
0
1
1
3
1
1
0
0
1
2
1
1
2
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
1
0
0
0
0
1
2
0
0
1
0
0
2
0
1
0
0
1
2
0
0
2
0
0
2
2
2
0
0
0
0
3
0
0
0
0
0
1
0
2
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
1
1
1
0
1
1
1
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
3
1
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
1
0
0
1
1
0
2
2
2
1
0
1
1
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
4
0
0
0
0
0
1
0
0
0
0
0
2
1
2
0
0
0
2
2
2
2
0
1
1
1
1
1
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
2
1
0
0
0
0
1
2
2
0
1
0
0
1
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
2
0
2
3
0
0
0
0
0
0
0
0
0
2
0
1
0
1
1
0
0
2
0
0
0
2
0
0
1
3
0
0
2
0
2
1
2
1
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
1
0
1
1
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
2
2
0
0
2
0
0
0
0
0
0
1
0
1
2
0
0
0
0
1
0
2
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
1
1
0
1
0
0
1
2
0
0
1
0
0
2
1
0
0
1
0
0
0
0
0
0
2
1
1
2
0
2
0
0
0
0
2
0
1
1
0
0
2
1
0
1
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
2
1
0
0
0
1
2
0
0
1
3
2
0
1
2
3
1
0
2
2
1
1
1
0
0
0
0
1
3
0
0
0
0
1
0
1
2
0
0
1
0
0
0
1
1
0
2
0
2
0
0
2
0
1
1
2
0
0
0
1
0
0
0
0
0
1
2
2
1
1
0
0
0
0
2
0
3
0
1
0
1
2
0
2
0
0
0
1
0
3
0
1
2
0
2
0
1
0
1
2
0
0
0
0
1
0
2
0
2
2
4
1
0
1
2
0
0
1
0
1
0
0
0
0
0
0
0
0
3
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
2
0
0
2
0
1
0
1
0
2
1
0
1
2
2
2
0
0
0
0
0
0
2
1
2
1
0
0
1
0
1
0
0
0
1
1
0
0
0
0
1
0
1
3
2
0
1
1
2
0
0
0
0
0
1
0
0
0
2
1
0
0
0
1
0
2
0
2
0
2
1
1
0
0
2
0
0
0
0
1
1
2
1
0
0
0
0
0
0
1
2
2
0
1
0
1
1
2
1
1
1
0
1
0
0
2
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
3
1
2
0
0
1
2
0
0
2
0
0
2
1
2
0
3
0
0
1
0
0
2
2
0
2
1
0
0
3
2
1
2
3
0
0
2
1
2
0
1
0
1
1
0
2
1
0
0
0
1
0
1
1
1
2
0
0
1
0
0
0
1
0
1
1
0
2
1
2
1
1
0
1
2
0
0
0
1
1
0
2
0
0
1
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
1
1
2
0
0
0
2
0
2
1
2
2
1
0
0
1
1
0
0
0
2
0
2
0
0
0
0
0
0
2
0
2
1
2
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
2
0
0
2
1
0
2
1
0
0
0
2
0
2
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
3
0
2
0
0
1
0
2
0
0
0
0
0
1
0
0
1
1
1
0
2
1
1
0
0
0
0
1
0
2
0
0
0
0
1
2
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
2
2
0
0
1
0
1
0
2
0
0
0
1
0
0
0
0
0
2
0
2
1
2
0
2
0
0
1
2
0
0
0
0
1
0
1
0
0
0
3
6
0
0
2
0
0
0
0
0
0
2
1
0
2
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
1
1
0
1
2
2
1
1
1
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
3
0
0
0
1
0
0
1
0
0
2
0
2
0
0
0
0
0
0
1
0
1
4
0
2
0
1
0
0
2
0
0
1
1
1
1
4
1
0
0
0
1
0
0
0
0
0
2
2
1
0
0
0
0
1
2
0
1
0
1
1
0
1
2
0
0
2
0
0
0
2
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
2
0
0
2
0
1
1
0
2
0
1
0
1
0
0
0
1
1
2
0
2
0
3
0
2
1
0
0
0
0
0
0
2
0
0
1
0
2
3
0
1
0
2
2
0
0
0
3
0
0
0
0
1
1
2
0
0
0
1
0
0
2
0
1
0
0
0
0
0
2
1
1
0
1
2
1
0
1
2
0
1
0
1
2
0
0
0
2
0
1
1
0
0
0
1
0
2
2
2
1
0
2
0
1
0
0
1
0
0
0
0
2
3
1
0
0
0
0
0
0
1
1
0
1
0
3
2
2
1
1
0
0
2
3
3
1
0
0
0
2
1
0
0
2
0
0
2
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
2
0
1
1
0
1
1
0
0
0
0
1
0
1
0
0
0
0
1
3
1
0
1
2
2
2
1
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
2
0
0
1
1
0
2
2
1
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
1
2
1
0
1
1
0
2
0
0
1
2
3
0
1
0
2
1
1
0
0
2
1
2
0
0
2
2
2
0
0
1
0
2
1
1
1
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
2
2
2
2
0
0
2
0
2
0
1
2
0
2
0
0
2
2
0
1
2
3
0
0
0
0
0
0
0
2
0
0
0
1
3
1
2
1
0
1
0
0
1
0
0
1
2
0
3
1
0
0
2
0
0
1
1
0
1
1
2
2
0
0
1
0
1
0
0
0
0
3
0
1
1
0
0
0
1
2
1
0
0
1
2
2
0
2
0
0
0
0
0
0
0
0
0
2
2
0
2
3
0
2
0
1
0
0
0
1
2
0
2
1
0
2
0
0
2
0
2
0
0
0
0
0
0
2
2
1
1
1
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
2
0
1
2
0
2
2
0
1
0
0
0
1
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
2
1
2
2
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
2
2
1
0
0
2
1
1
0
2
0
1
2
1
0
1
0
2
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
4
0
1
2
0
0
1
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
2
1
2
1
0
1
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
1
0
1
1
0
3
0
1
2
0
1
0
0
1
0
2
1
1
0
0
2
0
0
0
1
2
0
0
3
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
1
0
1
1
1
0
0
0
1
0
0
1
0
1
0
2
0
1
1
1
0
0
1
0
0
0
0
1
0
1
1
1
2
2
0
0
2
0
0
0
0
2
1
0
0
0
0
0
2
2
0
0
0
0
0
0
3
2
0
0
0
0
0
1
2
0
0
2
0
0
2
3
3
1
1
0
0
1
0
2
0
0
1
0
0
0
0
1
1
0
1
1
2
3
3
0
6
0
0
0
0
0
1
0
2
2
0
0
0
2
0
0
2
0
2
0
5
0
0
1
1
0
0
0
2
2
0
0
1
0
0
0
2
0
0
0
1
0
2
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
1
0
0
2
0
0
2
2
0
0
0
0
0
0
1
1
1
1
1
0
0
0
2
2
0
1
2
1
1
1
0
0
1
0
2
1
0
1
0
0
0
1
0
0
1
0
0
1
2
0
1
0
1
1
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
2
2
0
0
1
0
0
0
2
1
2
2
1
2
0
0
0
2
0
2
2
2
1
0
2
0
1
1
1
1
2
0
3
1
2
0
0
1
0
0
2
0
0
1
0
1
0
0
2
0
2
0
1
2
0
2
1
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
1
0
1
0
0
2
0
0
2
0
2
2
1
2
0
0
0
1
1
1
0
0
1
0
1
1
0
1
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
2
1
0
0
0
1
0
0
2
0
1
0
0
2
0
0
2
0
0
2
0
0
1
1
2
0
0
0
0
2
0
1
2
0
1
0
2
0
1
0
0
1
0
1
1
0
1
1
0
0
0
0
0
2
0
1
0
3
0
2
0
0
0
0
0
0
1
2
0
0
0
2
0
1
0
2
0
0
0
0
0
1
0
2
8
2
0
1
0
1
0
2
0
0
0
4
3
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
2
0
1
0
0
2
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
1
0
0
1
2
1
1
0
0
0
0
0
0
2
0
0
0
2
0
4
0
1
1
0
2
0
1
0
0
1
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
1
0
0
1
2
0
0
1
0
1
1
1
2
0
0
0
0
1
0
0
2
0
0
0
0
0
2
2
1
0
0
1
0
0
1
1
0
0
3
0
0
1
0
0
0
1
0
0
0
0
0
0
2
2
3
0
0
2
1
0
3
0
0
2
2
1
0
0
0
2
2
0
0
0
0
1
0
2
0
0
0
1
0
1
0
5
0
2
2
2
0
0
1
0
0
0
1
0
0
1
2
0
1
1
1
1
2
0
0
0
1
0
0
2
0
0
0
0
0
2
1
0
0
1
0
0
1
0
0
2
0
1
1
0
0
0
2
1
1
1
0
0
0
0
0
1
0
0
1
0
2
3
0
0
0
0
0
0
0
1
2
2
0
2
1
0
2
0
0
3
0
1
0
0
0
0
0
0
0
0
0
2
1
1
0
2
0
0
1
1
0
0
0
0
0
1
2
1
1
0
0
0
0
0
1
3
2
0
0
1
1
0
2
2
0
0
0
1
2
0
1
0
1
0
0
0
1
0
0
0
1
1
2
0
1
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
2
1
0
0
2
0
0
2
0
2
1
0
3
0
0
0
0
0
0
2
2
5
0
1
2
0
0
0
0
0
1
0
0
1
0
1
0
0
2
0
1
0
2
2
0
2
0
0
2
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
2
1
0
0
1
2
0
1
0
0
0
1
0
0
0
0
5
0
0
0
2
1
1
0
0
0
0
1
1
2
1
1
2
1
1
0
0
0
2
0
2
1
0
0
2
2
0
0
0
1
0
0
1
0
0
1
2
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
3
0
1
1
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
4
2
0
0
2
0
2
2
0
0
0
1
1
2
1
0
0
0
0
1
0
2
1
0
0
0
0
0
0
1
0
0
0
0
1
2
1
0
1
0
0
1
1
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
2
1
2
0
0
1
0
1
0
0
0
0
0
0
0
0
6
0
0
0
2
2
0
0
2
2
0
2
0
0
3
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
1
2
2
0
1
2
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
2
0
2
0
0
1
0
2
2
1
0
0
0
2
2
0
2
0
2
0
0
1
0
0
3
0
1
0
0
2
0
0
0
0
1
2
0
0
0
2
2
0
1
0
0
0
0
0
1
0
0
2
1
0
1
1
0
0
0
0
0
2
0
1
0
0
0
0
2
0
2
2
0
0
2
0
0
0
2
1
0
1
0
1
2
1
0
0
0
0
0
0
3
0
0
2
3
0
0
0
1
0
0
0
1
0
0
3
0
2
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
2
0
1
0
0
0
0
1
1
1
0
0
1
3
0
0
4
2
0
1
0
2
2
1
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
1
0
0
0
2
0
0
0
0
2
0
2
0
1
2
0
1
0
1
2
2
0
0
1
2
0
0
0
2
0
2
2
2
0
0
1
1
0
5
0
0
0
1
1
0
0
1
0
0
0
1
3
0
2
0
0
1
2
1
0
0
0
2
0
1
2
0
3
2
0
0
2
2
0
2
0
0
1
1
1
0
0
2
2
2
2
1
2
0
0
2
1
0
1
1
1
0
0
2
0
1
0
0
2
0
0
0
0
3
0
2
0
0
2
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
2
2
0
0
0
2
1
3
0
0
2
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
2
0
2
1
2
1
2
1
0
0
0
0
0
2
2
0
3
0
1
0
2
0
0
1
0
0
2
1
0
0
1
0
2
0
2
2
0
0
0
0
0
2
1
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
1
1
2
0
0
2
0
0
3
0
2
2
0
0
0
2
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
2
2
1
0
1
2
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
1
1
0
2
0
0
3
0
2
2
0
2
0
1
1
1
2
2
0
0
1
0
0
2
0
2
0
0
1
0
0
0
2
1
2
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
2
2
0
1
1
0
0
1
0
0
2
0
0
1
2
0
0
0
0
3
0
0
0
3
0
1
0
1
1
1
0
0
2
0
0
1
0
0
0
2
0
0
0
2
0
0
1
0
0
2
2
1
2
0
1
0
0
0
1
3
1
2
1
1
2
0
0
0
0
0
1
0
0
2
3
2
0
2
2
0
1
2
2
0
0
0
1
0
0
0
1
0
1
2
2
0
1
2
2
0
2
0
0
0
2
0
0
0
0
2
3
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
1
0
2
0
0
2
0
2
1
0
2
2
0
1
1
0
0
0
2
0
0
1
2
0
2
1
0
2
0
2
0
2
0
1
0
0
2
0
1
0
2
1
1
1
3
1
0
0
0
2
2
0
0
0
0
1
0
0
0
2
2
1
0
0
0
4
0
0
1
1
0
0
0
0
0
3
2
0
0
1
1
0
0
2
0
1
0
0
0
0
1
0
1
0
4
0
0
1
3
0
1
0
0
2
0
1
0
0
0
0
0
0
1
2
0
1
0
0
0
0
2
0
0
1
2
0
2
0
2
1
0
1
0
0
0
1
2
0
0
0
0
2
2
0
0
0
0
1
0
0
1
0
2
0
3
1
0
0
0
1
2
2
0
2
6
0
1
0
1
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
2
0
2
0
0
0
1
0
0
0
2
2
1
0
0
1
0
1
0
1
1
0
3
0
0
2
0
0
0
2
0
1
1
0
0
2
0
0
0
0
0
2
0
0
2
2
0
0
1
0
0
0
3
0
0
2
0
0
0
2
0
1
0
1
0
1
0
0
2
0
2
2
0
0
0
1
0
1
0
2
0
1
3
0
2
0
2
0
0
0
2
2
2
0
1
0
1
1
1
0
0
2
1
3
2
0
1
0
2
5
0
0
0
2
2
0
1
0
0
3
2
0
2
0
9
2
0
0
2
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
2
0
0
0
0
4
0
2
0
1
0
0
0
2
2
1
1
1
0
0
0
0
2
2
0
0
0
0
0
2
0
1
2
2
0
0
1
0
0
1
1
3
0
1
2
0
2
0
1
0
1
1
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
1
2
0
0
1
0
2
0
2
0
2
0
0
2
0
2
0
0
2
0
2
0
1
3
0
0
0
2
0
0
0
0
0
0
1
4
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
1
1
2
0
0
0
0
3
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
2
0
2
2
2
0
4
1
1
0
0
0
0
2
0
1
0
2
0
2
0
0
0
2
1
0
2
0
0
0
2
0
3
0
0
0
2
0
0
0
0
1
1
0
0
0
0
2
1
0
0
0
3
0
2
1
0
1
2
0
1
0
0
2
2
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
1
0
1
1
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
2
1
2
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
1
0
0
0
0
0
0
1
2
2
1
0
0
0
0
0
1
2
1
0
0
1
1
1
2
6
3
2
0
1
2
0
0
2
0
0
1
0
0
0
0
0
0
2
2
0
0
0
4
0
2
0
0
0
2
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
1
3
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
2
0
0
2
0
0
1
1
3
1
1
1
1
2
2
0
2
0
0
1
1
0
0
0
1
2
0
0
0
0
0
1
2
0
0
0
1
0
1
0
3
0
0
2
1
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
2
2
0
1
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
2
1
1
2
0
3
0
0
2
2
0
0
0
0
1
1
0
1
0
2
1
0
0
2
1
1
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
2
0
1
2
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
2
0
1
2
0
0
0
0
0
1
0
1
0
7
2
3
0
0
0
1
1
0
2
1
2
1
1
1
0
2
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
2
0
0
2
2
0
0
2
3
1
4
0
0
0
1
2
0
0
0
2
1
4
0
2
0
0
2
1
0
0
0
1
0
0
0
0
1
0
0
2
1
2
1
1
0
0
1
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
2
2
1
2
0
2
1
1
2
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
2
0
0
1
0
0
2
1
0
0
0
0
0
1
1
0
0
2
0
1
0
1
2
1
0
2
0
0
3
1
0
3
0
0
1
0
0
0
0
1
0
1
0
3
1
1
0
0
0
0
1
0
3
0
0
1
0
0
1
0
0
0
0
2
2
2
0
1
1
0
1
2
2
2
0
0
0
0
0
0
0
0
0
0
2
1
0
1
2
1
3
3
0
1
1
1
2
2
0
2
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
4
0
0
0
0
0
2
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
2
2
0
1
1
2
0
0
3
0
0
0
1
0
2
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
1
2
0
3
1
0
0
0
2
1
0
0
0
1
5
0
2
1
2
0
0
0
0
0
0
1
0
1
2
0
1
1
2
1
0
1
0
0
1
1
1
0
1
2
0
2
1
0
0
0
0
0
1
2
0
1
0
2
2
0
0
0
2
0
1
0
0
2
3
0
0
0
2
0
0
1
0
1
0
0
0
0
2
0
2
2
1
1
2
0
0
0
0
1
0
1
2
1
1
0
0
0
0
2
0
0
1
1
0
1
0
3
0
0
2
0
1
0
0
2
1
0
0
2
0
0
0
2
2
2
2
0
0
3
0
1
0
1
1
0
0
0
0
0
2
0
2
0
0
2
0
2
0
0
1
0
0
0
1
0
0
0
1
2
1
0
1
0
0
0
2
0
0
1
5
0
0
1
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
3
0
0
2
1
1
0
1
1
0
0
2
0
1
1
0
0
1
0
0
0
0
0
0
2
2
0
0
2
1
0
3
1
0
0
0
1
0
0
2
0
0
0
0
0
2
0
1
0
2
1
0
0
2
0
0
0
1
0
1
3
0
0
1
0
0
0
1
0
1
2
2
0
1
0
0
0
0
2
1
2
0
2
1
0
0
3
0
1
1
0
0
0
1
0
1
0
0
1
0
1
0
2
0
0
1
0
0
0
0
2
2
2
1
1
0
1
0
1
0
0
0
2
1
1
2
0
1
0
0
1
2
0
1
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
1
2
2
2
0
0
0
1
0
0
2
0
0
0
0
1
0
0
1
1
1
1
0
0
0
0
0
0
0
0
2
3
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
1
0
0
1
1
0
0
2
0
0
1
0
0
1
0
0
0
0
2
2
2
1
1
0
0
1
2
0
0
0
0
0
0
2
2
2
1
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
2
2
0
0
0
3
0
0
1
2
0
1
0
2
0
0
0
2
0
1
0
1
1
0
0
0
2
2
0
0
0
0
0
1
2
0
0
2
2
0
1
2
0
1
0
0
1
0
0
1
1
0
0
0
0
1
0
0
2
3
1
0
0
0
0
0
2
0
1
0
0
0
1
1
2
0
1
1
1
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
1
2
1
2
0
0
2
0
0
0
1
1
0
0
2
0
0
1
1
0
0
0
1
2
0
0
3
2
1
0
1
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
4
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
2
3
0
1
2
1
2
2
0
2
0
0
0
0
2
1
0
1
0
0
0
1
2
3
2
0
0
0
0
0
0
0
2
2
0
2
0
1
2
0
1
0
2
0
2
0
2
0
2
0
1
2
0
2
1
0
3
1
2
0
1
0
0
1
3
0
1
0
1
0
0
0
0
2
0
0
0
1
1
0
1
0
1
0
0
1
0
0
0
2
0
2
0
0
2
2
1
0
0
2
0
0
0
0
1
0
0
0
2
2
0
0
2
2
0
1
0
1
0
0
1
0
0
2
2
1
1
0
1
1
1
0
2
1
0
1
0
2
1
0
0
0
1
0
0
2
2
2
1
0
2
0
0
2
0
1
2
0
1
0
0
0
1
0
2
1
1
0
0
1
0
0
0
0
1
2
0
0
1
0
2
1
0
0
2
0
2
0
0
2
3
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
1
1
0
0
0
0
1
2
0
0
1
2
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
1
1
0
1
1
0
0
0
0
0
0
0
1
1
1
2
0
1
0
1
2
0
0
0
2
0
2
0
1
0
0
0
0
0
2
1
2
0
0
0
2
2
0
1
2
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
4
0
0
0
2
0
1
0
0
0
1
0
2
0
2
0
0
0
0
3
0
2
0
0
0
2
0
1
3
0
0
2
0
1
0
0
0
1
1
2
0
1
2
0
1
0
1
1
2
2
0
1
1
0
0
0
1
2
0
0
0
0
0
0
2
1
1
0
0
2
0
4
0
1
1
1
1
0
0
2
2
1
2
0
0
0
0
2
0
0
0
2
2
2
0
2
0
0
0
0
0
1
0
2
0
2
2
0
0
1
2
2
2
2
4
0
0
0
0
1
0
1
0
1
1
1
2
0
0
3
2
1
2
0
2
0
2
0
2
0
0
1
1
1
0
2
2
2
2
0
0
3
1
0
0
0
2
0
0
2
0
0
0
3
1
0
2
0
2
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
1
2
2
0
0
0
2
0
0
1
0
1
1
0
0
0
0
0
2
0
0
1
1
1
2
0
2
3
0
1
1
3
1
1
1
0
1
1
0
2
0
0
0
0
1
0
0
0
2
0
0
0
1
0
2
0
1
0
0
2
1
1
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
2
1
0
1
0
1
0
0
0
2
0
0
1
1
0
2
0
0
1
0
0
2
2
0
0
0
1
1
1
0
0
2
1
0
0
1
0
0
2
0
1
0
0
1
1
0
1
0
1
0
0
2
0
0
2
0
2
0
0
0
2
0
1
0
0
1
0
3
1
0
4
0
0
0
0
3
0
0
0
2
0
0
0
0
2
0
0
1
0
2
1
2
0
2
0
1
0
0
0
0
1
1
2
1
0
2
0
0
0
0
0
0
0
2
0
2
1
0
2
2
1
0
2
0
0
0
0
1
3
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
3
1
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
2
2
2
1
0
0
1
2
1
0
0
0
0
2
0
1
1
0
2
0
0
0
0
0
2
1
2
2
0
1
1
0
0
0
0
0
0
0
1
2
0
1
0
0
3
0
0
0
0
2
0
2
1
0
0
0
0
2
2
2
0
1
0
0
0
1
1
1
0
0
0
0
0
2
2
0
0
0
0
0
0
2
2
2
0
1
0
0
2
0
0
0
2
0
0
1
0
0
2
0
0
1
0
1
1
0
0
1
2
0
1
1
2
0
1
0
0
0
2
0
2
2
0
2
1
0
0
2
0
0
0
0
2
0
3
0
1
0
0
1
1
0
0
2
0
0
0
0
0
1
0
0
0
0
1
2
2
1
0
0
0
0
1
0
0
0
2
1
0
0
0
2
0
1
0
0
1
2
2
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
1
2
0
0
0
0
1
0
2
0
0
1
2
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
2
0
0
2
0
1
0
0
2
2
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
1
0
1
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
1
0
0
0
0
0
1
1
2
0
0
0
2
0
0
5
0
0
1
0
0
2
0
0
0
0
1
1
2
0
1
2
1
0
1
0
0
2
2
0
2
0
2
1
3
1
0
0
0
0
0
0
0
1
0
3
0
1
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
1
1
0
0
2
3
0
0
2
0
0
0
2
0
0
2
0
0
0
3
1
2
3
0
1
0
1
0
0
2
0
1
0
1
4
0
0
1
0
0
0
0
0
2
1
0
0
2
0
2
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
3
4
0
0
0
0
0
1
0
0
4
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
2
1
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
1
0
0
0
0
1
0
0
1
0
0
0
2
1
0
0
0
1
0
2
0
0
1
2
2
2
0
0
2
0
2
1
0
2
0
0
1
2
0
1
1
0
0
1
2
4
0
0
1
1
2
0
2
2
0
3
1
0
0
2
0
0
0
1
0
2
0
0
2
1
0
1
1
0
3
1
0
0
0
0
2
1
0
1
2
1
0
2
2
1
0
1
0
0
2
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
1
0
0
1
2
2
0
0
0
1
0
2
1
0
1
0
0
2
0
2
0
2
1
0
1
0
0
0
0
0
2
0
1
0
0
1
2
0
0
2
0
1
0
0
0
0
0
0
0
1
2
2
0
1
0
0
1
0
0
2
2
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
2
1
1
0
0
0
0
2
1
0
0
1
0
2
0
1
0
0
2
0
0
0
0
2
0
0
1
0
2
1
0
0
0
0
0
2
0
1
0
0
2
1
2
2
0
1
0
0
0
1
0
2
1
0
0
0
0
1
0
0
0
0
2
1
2
2
0
0
2
2
1
0
0
0
2
0
1
0
0
0
0
1
1
1
1
0
0
1
1
0
0
2
0
1
0
0
0
1
2
0
0
1
0
1
1
1
0
3
1
0
2
0
0
0
0
0
1
0
1
2
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
1
3
0
2
0
1
2
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
2
2
0
2
1
1
1
1
2
1
0
1
0
0
0
1
1
0
0
2
0
2
2
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
1
0
2
0
2
0
2
1
1
0
1
1
2
1
0
0
0
0
0
0
0
1
1
0
0
2
0
2
1
0
0
2
0
2
0
1
0
0
0
0
1
0
0
0
0
2
2
2
0
2
0
0
0
2
0
1
0
0
0
2
2
0
1
1
0
2
0
0
2
0
3
2
2
1
0
0
0
0
2
0
1
1
0
0
0
1
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
1
0
2
0
2
0
0
0
0
2
0
0
1
0
0
1
0
6
2
1
0
1
0
0
2
0
2
2
0
0
0
0
1
0
1
0
2
0
1
0
0
0
0
1
0
1
0
0
0
2
1
0
0
0
2
2
1
2
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
2
0
0
1
2
2
1
3
0
0
0
1
0
1
0
0
0
0
0
0
0
2
2
0
1
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
3
0
1
2
0
0
0
2
2
2
2
1
1
0
6
0
0
1
0
2
0
1
0
0
2
0
1
1
2
0
1
0
2
1
0
0
1
2
0
1
0
0
2
0
0
3
0
0
0
0
1
2
0
2
0
2
0
2
1
0
0
0
0
0
1
2
2
1
2
2
0
0
0
0
0
0
4
0
2
0
0
0
1
0
0
0
0
1
2
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
2
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
2
0
1
0
0
0
2
0
1
2
0
1
0
0
0
0
2
1
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
2
1
1
1
1
1
0
1
1
0
2
2
2
0
0
0
2
0
0
2
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
1
2
0
2
2
0
1
0
6
0
0
2
0
3
1
3
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
1
1
2
1
0
0
0
0
0
0
2
0
0
1
0
1
2
0
0
0
2
1
2
0
1
2
1
1
0
0
2
0
1
0
0
1
2
0
1
1
0
2
2
1
2
2
0
0
2
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
2
1
1
2
2
1
0
0
0
2
0
2
0
1
1
0
0
0
0
3
1
1
1
0
0
0
0
2
2
2
0
2
0
0
1
2
2
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
2
0
1
0
0
0
0
0
1
1
1
1
0
0
2
1
0
0
0
0
2
0
1
0
1
2
1
0
0
0
0
1
0
2
0
0
0
0
0
0
2
2
2
0
0
1
2
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
1
1
2
2
0
0
0
0
1
5
0
1
0
0
0
4
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
3
0
0
2
2
0
0
0
1
3
0
0
1
0
1
0
2
0
0
1
0
1
1
0
0
1
0
0
2
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
1
0
2
2
2
2
2
0
0
2
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
3
0
1
2
1
1
0
0
0
0
1
0
0
0
2
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
1
3
1
0
1
1
2
0
0
0
0
2
0
2
0
0
0
0
0
2
2
1
2
0
0
1
1
0
0
2
1
3
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
1
1
0
0
0
0
0
1
2
2
0
1
1
1
0
0
1
1
0
2
1
1
0
1
1
1
2
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
2
2
2
0
1
0
1
0
1
2
0
0
0
2
2
3
0
2
0
2
0
0
2
0
2
0
1
0
3
0
1
0
1
0
0
0
0
1
2
0
2
0
2
0
0
2
1
0
0
0
0
0
2
1
1
2
0
0
1
0
0
0
1
0
0
2
1
1
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
1
0
1
0
2
1
0
1
2
0
2
0
2
0
0
0
0
0
0
0
0
0
1
1
1
2
4
2
0
6
2
0
0
0
0
0
1
0
0
0
1
0
1
0
1
4
1
2
0
2
1
0
0
1
1
2
0
0
1
2
2
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
2
0
1
2
1
0
0
0
0
1
0
0
2
1
1
2
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
3
0
0
1
0
2
0
2
1
0
0
2
1
1
0
1
1
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
1
1
0
1
0
2
0
0
0
1
2
1
0
1
4
0
2
0
1
1
0
0
5
0
2
0
1
0
0
1
0
0
2
0
0
0
0
0
0
1
2
0
0
2
0
0
1
0
0
1
2
0
0
0
0
2
1
1
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
1
0
2
1
2
0
0
0
0
0
0
2
1
2
1
1
0
1
1
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
1
0
0
0
2
2
0
1
1
2
0
1
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
3
0
0
0
2
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
2
0
1
0
0
0
2
0
0
1
2
2
1
0
1
0
0
0
0
1
2
2
2
0
1
0
0
0
1
0
0
0
0
0
0
0
2
2
2
0
1
0
2
1
1
3
0
1
1
0
2
0
0
0
0
0
0
2
1
2
1
0
2
2
0
0
1
0
0
1
0
0
0
2
0
1
0
0
0
0
2
2
0
0
2
2
1
0
1
0
0
1
1
0
1
1
0
0
0
2
0
0
0
0
1
0
0
0
0
2
1
1
0
0
1
0
0
2
2
0
0
2
2
0
1
0
1
2
1
0
2
0
0
0
0
0
0
1
0
2
1
0
0
2
0
1
0
0
1
0
0
1
1
2
0
1
0
1
0
2
1
0
2
0
2
0
2
0
1
2
0
2
0
0
3
0
1
0
0
0
0
2
2
2
0
0
0
2
0
1
0
2
1
0
0
0
3
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
2
0
0
1
1
0
2
2
0
0
1
2
2
2
0
0
1
2
0
1
1
0
2
1
0
0
0
0
1
2
0
0
2
0
0
0
0
0
1
0
0
2
0
0
1
2
0
1
0
2
0
1
0
1
0
0
1
0
0
1
2
0
2
0
0
1
0
1
1
0
0
1
0
0
1
0
1
1
1
1
1
0
0
0
0
1
0
0
1
2
1
0
2
0
0
1
0
2
0
1
0
0
2
0
0
2
0
0
0
0
2
2
0
0
2
3
1
1
0
2
2
2
0
0
2
0
1
2
0
0
0
2
0
0
1
1
1
0
0
1
0
0
1
2
2
0
0
0
2
2
1
2
0
2
1
0
2
0
0
2
0
0
1
0
0
0
1
0
1
1
0
0
0
0
2
1
2
0
2
1
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
1
0
0
2
0
1
1
1
1
2
0
0
0
2
0
1
0
0
0
0
3
0
2
0
0
0
1
2
2
0
2
0
1
1
0
1
1
1
2
2
2
0
0
0
0
0
2
0
2
3
1
0
0
0
1
2
0
0
3
0
0
0
1
0
1
0
0
0
0
2
1
0
2
0
1
2
2
0
0
0
0
2
0
2
0
0
0
0
1
0
2
0
1
0
1
1
0
1
1
1
2
0
1
2
1
1
1
2
0
0
1
1
2
0
0
0
2
1
2
0
0
2
2
1
0
2
0
2
1
0
1
0
1
0
0
1
2
0
1
0
0
2
0
1
1
0
0
1
1
0
0
0
0
0
1
2
0
0
1
0
0
0
0
2
1
0
2
0
0
2
0
1
0
1
2
1
1
0
1
2
1
2
0
0
1
1
0
0
1
1
1
3
2
2
0
0
0
1
0
2
1
0
0
0
0
2
0
2
0
2
1
0
0
0
1
2
0
0
0
0
1
0
3
0
0
0
0
0
0
1
2
0
0
3
0
0
2
0
2
0
2
0
0
1
0
2
0
0
0
1
0
0
0
1
1
0
0
0
0
0
2
2
0
2
0
0
1
0
0
0
0
1
1
0
2
1
0
1
1
0
0
2
2
0
0
2
0
0
0
2
1
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
1
2
0
1
0
0
2
0
0
0
1
0
0
0
0
2
2
0
2
0
0
0
0
0
1
2
0
2
2
2
2
0
0
0
0
1
1
0
1
0
1
1
0
1
1
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
2
1
0
1
0
1
0
2
3
0
1
0
0
2
0
0
0
0
0
2
1
2
0
1
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
1
0
0
0
2
1
1
2
1
1
0
0
3
1
2
0
0
0
0
1
4
2
1
0
0
1
0
0
0
1
1
1
1
0
1
0
1
2
0
2
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
3
2
1
1
0
1
0
1
0
0
0
2
0
0
1
0
2
0
2
0
2
0
2
0
1
0
0
0
0
0
1
0
0
0
0
1
0
2
2
2
1
2
2
0
0
1
1
2
1
1
2
1
0
0
1
0
0
0
2
0
0
1
2
0
0
0
1
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
5
0
0
0
0
0
1
2
0
2
0
0
0
0
2
2
0
0
0
1
1
0
2
2
2
0
0
1
0
1
0
1
2
1
0
8
1
0
0
1
2
2
2
0
2
0
0
0
0
1
0
1
0
2
0
2
1
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
1
3
1
0
1
2
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
2
1
0
2
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
2
2
2
2
0
2
1
0
2
2
0
0
1
1
0
0
0
0
1
0
1
1
0
0
0
2
0
0
0
4
0
1
2
0
0
2
0
2
0
0
0
2
0
0
0
0
1
0
1
2
0
1
0
0
1
0
0
0
0
2
0
2
1
0
0
0
0
1
0
0
0
2
1
0
0
0
2
0
1
0
2
2
0
0
1
2
0
2
1
0
0
4
0
0
0
2
2
1
0
1
0
1
1
0
2
2
2
0
0
0
0
0
2
0
2
2
0
1
0
0
2
0
0
2
1
2
0
2
0
0
0
0
2
1
2
0
0
0
1
0
0
0
1
0
1
0
0
3
2
0
0
2
0
1
0
0
3
0
0
0
0
1
0
0
0
2
2
0
1
0
0
1
0
0
0
2
0
0
1
1
0
0
3
2
0
1
2
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
1
0
0
0
2
1
3
0
0
1
0
0
0
0
1
2
2
1
2
1
0
0
2
0
0
2
1
2
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
2
2
0
0
2
1
0
0
0
0
1
0
1
0
0
2
2
0
1
1
1
0
1
1
0
0
0
0
1
2
1
0
0
0
0
0
0
1
2
0
2
0
1
0
0
0
0
1
2
0
2
3
0
0
0
0
0
4
1
0
0
1
1
0
0
0
2
0
0
0
0
2
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
2
2
0
0
0
0
1
0
0
1
0
0
2
1
0
0
2
0
1
0
0
0
0
1
0
0
0
2
2
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
1
0
0
0
1
0
2
0
2
0
0
0
0
0
2
0
0
0
1
1
0
0
1
0
2
0
0
0
0
0
0
1
1
2
0
2
0
0
0
0
2
2
1
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
4
0
2
0
0
0
2
2
0
2
1
2
0
0
1
0
0
0
1
1
2
2
2
1
0
0
0
1
1
0
0
2
0
2
0
0
3
0
2
2
0
0
0
0
2
0
0
1
2
0
1
3
1
0
0
0
0
0
0
0
1
0
0
0
1
2
1
1
2
0
0
2
0
2
0
2
0
0
0
2
0
2
0
0
0
2
1
1
0
0
0
1
1
0
2
0
3
0
0
0
1
1
1
5
0
1
0
2
0
2
1
0
15
0
2
0
0
0
0
2
1
0
2
1
0
0
0
0
1
0
0
1
0
0
0
0
2
0
1
0
1
0
2
1
0
0
1
0
1
0
1
2
0
2
0
1
2
1
2
2
2
0
0
0
0
5
0
0
1
3
1
0
0
2
0
0
2
1
0
0
0
0
0
0
1
2
0
2
0
3
0
0
0
0
2
0
1
0
4
0
1
0
2
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
1
0
1
3
0
0
0
0
0
1
0
0
0
1
0
2
0
1
1
2
1
1
0
0
0
0
0
1
0
0
0
0
0
1
1
1
1
0
1
0
0
2
2
0
0
3
2
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
1
0
1
0
1
2
1
2
1
0
0
0
1
0
2
1
0
1
0
2
0
2
0
1
4
1
1
0
1
0
2
0
2
0
0
2
0
2
0
0
2
1
0
0
1
0
1
0
3
1
0
2
0
0
0
1
1
0
0
1
0
0
0
0
2
1
0
1
1
0
0
1
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
3
2
1
1
1
2
1
0
0
0
0
1
2
0
1
0
0
0
1
0
2
0
0
1
1
0
0
0
0
0
0
1
1
3
1
0
1
0
0
6
0
1
0
1
2
0
0
0
2
1
2
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
2
0
2
0
0
1
0
0
1
0
0
0
0
1
0
0
1
2
0
1
1
1
2
0
0
0
2
1
0
2
1
0
0
0
1
0
0
0
2
0
2
1
2
1
1
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
2
0
1
1
0
0
1
1
1
0
2
2
0
1
0
0
0
0
2
1
0
1
3
2
2
2
0
0
1
1
0
1
2
1
1
0
0
1
1
1
0
3
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
2
0
1
1
0
0
0
2
0
0
0
0
1
0
2
2
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
1
2
1
2
0
2
2
0
1
1
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
2
1
1
0
0
2
1
1
2
0
1
0
0
0
0
0
0
0
2
2
1
7
0
1
0
0
0
0
0
0
0
0
0
0
3
1
0
1
2
2
0
0
0
0
1
0
2
0
0
0
0
2
0
1
0
2
1
1
2
0
0
1
0
1
0
0
0
0
2
2
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
2
1
0
2
0
0
0
1
0
0
0
0
0
2
1
1
0
0
1
0
1
0
2
0
1
2
0
2
1
0
1
2
0
1
1
0
1
2
0
1
1
1
2
2
0
4
0
0
2
0
4
0
1
0
0
0
0
0
0
1
2
0
0
2
1
0
2
1
2
1
0
0
0
1
0
0
1
2
0
1
1
2
1
2
1
0
1
1
0
2
2
0
0
0
1
0
2
0
0
0
0
2
0
0
0
1
0
0
1
1
2
2
3
0
0
0
1
2
0
0
2
1
0
0
0
2
0
1
0
0
0
0
2
0
1
2
0
0
0
2
1
2
2
2
1
0
0
1
0
0
2
1
1
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
2
2
0
0
1
0
0
0
0
1
0
1
2
0
2
0
0
2
2
1
0
0
0
0
2
0
1
1
0
2
0
2
1
1
0
0
0
0
0
0
0
0
2
1
0
0
0
2
1
0
0
0
0
2
1
1
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
1
2
0
1
0
1
0
2
0
1
1
2
1
2
0
0
3
2
0
0
0
0
0
0
0
2
2
0
0
1
1
0
1
0
0
2
0
0
0
0
0
4
1
1
0
1
2
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
2
0
3
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
1
1
1
0
0
0
1
2
0
0
1
1
0
1
1
0
0
2
1
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
2
2
1
1
1
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
1
2
0
1
1
1
0
0
0
0
3
1
0
0
1
0
1
0
0
2
1
0
1
1
0
0
1
0
0
1
1
0
1
2
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
2
1
0
2
1
0
2
0
1
2
1
0
0
1
0
0
1
1
2
0
0
0
0
1
0
0
0
2
0
0
3
1
1
0
0
0
0
1
2
0
2
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
1
1
0
2
0
1
1
0
0
0
0
0
1
2
1
2
1
0
2
1
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
1
1
2
0
0
2
0
2
1
1
0
0
1
0
0
1
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
1
0
2
1
0
0
0
0
3
1
0
0
0
0
0
1
0
1
1
0
0
1
0
0
2
1
1
0
1
0
0
2
1
1
1
0
3
1
0
0
4
0
0
0
0
2
0
0
0
1
1
0
0
1
2
2
1
0
1
0
0
0
1
0
0
0
1
2
3
1
0
2
0
0
2
0
0
1
0
1
0
2
0
0
2
0
0
1
2
0
0
0
1
0
2
1
2
1
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
2
0
1
0
0
1
0
0
1
2
0
2
0
1
1
0
0
0
1
0
2
0
0
1
0
0
0
1
0
0
1
1
3
1
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
2
0
1
0
0
1
0
1
0
2
0
1
0
1
1
0
1
0
0
0
1
1
0
1
2
2
1
0
0
2
2
0
1
3
0
0
0
2
1
1
0
0
2
2
0
0
0
3
0
2
0
0
0
0
0
0
1
2
3
0
1
3
1
0
0
0
0
0
1
0
0
1
1
0
2
0
1
0
0
0
2
1
0
0
0
2
0
0
0
0
2
1
2
2
0
2
2
0
0
0
0
1
0
1
0
3
2
0
0
0
0
0
0
1
0
2
0
0
1
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
3
2
0
1
1
1
0
1
0
0
2
1
2
0
0
0
1
0
1
1
1
0
1
2
0
2
0
2
0
0
1
1
0
1
0
1
0
1
1
2
0
0
1
0
1
2
0
1
0
1
0
0
0
1
2
0
1
2
0
1
0
0
0
0
1
2
2
1
2
1
0
0
0
2
0
0
2
0
0
0
2
0
0
3
0
0
0
2
1
0
2
0
0
0
1
2
0
0
0
0
0
0
2
0
0
3
1
0
3
0
0
1
0
0
0
0
1
0
0
1
0
2
0
0
1
1
0
0
0
2
1
0
0
1
2
2
1
0
1
0
2
2
0
0
2
0
2
1
0
0
1
1
0
0
0
0
0
0
1
0
0
1
1
1
2
0
3
0
1
0
0
1
1
0
0
3
0
0
0
4
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
1
0
0
0
0
1
0
1
0
2
1
1
0
0
0
2
0
2
0
0
1
0
0
0
0
2
0
1
1
0
0
1
2
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
2
0
0
1
0
0
0
2
3
2
0
1
3
0
2
1
1
0
0
0
0
3
1
0
1
0
0
2
0
2
1
0
2
1
0
1
0
0
0
0
0
0
0
1
1
2
0
1
1
0
2
0
0
2
1
1
0
2
1
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
2
0
0
0
0
0
0
1
0
2
2
0
2
2
0
2
0
0
0
1
0
2
0
0
2
1
0
0
0
0
1
0
0
1
1
0
0
1
0
0
2
0
2
1
1
1
2
0
1
0
2
1
0
0
3
0
0
1
0
1
0
0
2
0
1
2
0
0
0
0
0
2
1
0
0
2
1
0
1
2
2
1
0
0
1
0
0
0
0
0
0
4
0
1
1
2
0
2
0
2
1
0
0
0
0
0
0
2
2
2
0
0
0
0
0
1
1
1
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
3
0
0
2
0
0
0
2
2
0
0
0
3
2
1
1
0
0
2
1
1
1
0
0
1
0
2
0
1
0
0
0
1
1
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
2
2
1
1
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
2
1
1
1
0
0
0
0
0
0
0
0
3
0
1
0
4
0
0
0
0
2
1
2
0
0
0
0
1
2
0
0
0
1
1
0
0
1
0
1
0
0
1
1
0
2
0
2
1
0
0
2
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
5
2
0
0
0
0
0
0
0
1
1
1
2
0
4
0
0
1
0
0
2
2
0
0
0
0
1
2
0
0
1
1
0
2
0
0
0
1
0
1
2
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
2
0
0
0
3
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
2
0
0
1
1
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
2
2
0
0
0
2
0
2
1
2
1
0
1
2
1
2
0
0
2
2
1
0
0
0
1
1
2
0
1
2
2
1
0
1
1
0
0
1
1
1
0
0
0
2
2
1
0
1
1
1
2
0
0
1
0
0
0
0
1
0
2
0
1
0
1
0
1
0
3
0
0
1
0
2
0
1
0
2
0
1
1
0
0
3
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
2
2
2
0
0
2
0
0
1
0
3
0
1
1
2
0
0
1
1
2
1
1
0
2
2
0
0
2
1
0
0
2
0
0
0
1
1
2
2
1
0
1
0
0
0
1
2
0
0
2
1
1
0
0
1
2
1
0
1
2
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
1
0
3
0
2
1
1
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
1
1
1
0
0
2
1
1
0
2
0
2
0
0
0
1
0
1
0
0
0
1
2
0
0
1
0
2
0
1
0
0
0
1
1
1
0
1
3
0
2
0
2
0
0
0
0
0
0
0
1
1
0
1
1
0
2
0
0
1
0
0
2
0
0
0
1
1
0
0
1
1
2
0
1
0
3
0
1
0
0
2
1
0
1
0
0
0
1
1
2
0
0
0
2
0
0
0
0
2
0
1
3
0
1
1
0
0
2
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
1
1
8
1
0
0
2
1
0
1
0
1
2
0
0
2
1
0
0
0
1
3
1
0
1
2
0
2
0
2
0
2
2
0
0
1
0
0
1
1
0
2
0
1
0
2
0
0
0
2
0
1
2
0
0
0
0
1
0
0
6
0
1
1
2
0
2
1
0
9
0
0
1
0
0
0
0
0
3
1
0
2
0
0
2
2
0
0
1
1
0
0
2
0
0
0
2
0
1
0
0
0
0
0
1
1
0
0
0
0
0
2
0
1
1
1
1
0
2
2
1
0
1
2
0
0
0
1
2
0
0
2
0
0
2
0
0
2
1
2
0
0
1
0
0
2
1
2
0
0
0
0
1
1
0
0
0
2
1
0
0
0
0
0
3
0
0
0
2
1
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
2
1
1
0
1
0
0
0
1
2
0
0
0
1
1
0
1
0
0
0
2
0
0
0
0
0
5
2
2
2
1
2
2
1
0
0
2
0
2
0
1
0
2
0
0
1
1
0
0
0
1
0
0
0
0
1
0
2
0
2
0
2
2
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
2
0
1
0
1
0
0
0
1
0
0
2
0
2
0
0
1
0
0
2
0
1
0
0
0
1
1
0
0
0
1
2
1
0
1
2
0
1
0
0
0
0
0
0
2
1
2
1
0
0
2
2
1
0
2
1
0
0
0
0
0
2
2
1
1
2
0
0
1
0
0
1
4
1
1
0
2
0
2
0
0
0
0
3
2
0
0
1
1
0
2
1
0
0
2
1
0
1
0
1
1
0
2
1
0
1
0
0
1
0
0
1
2
0
1
1
0
0
2
0
2
2
1
1
0
1
1
0
1
0
0
0
1
2
1
0
0
2
1
0
0
0
1
0
1
0
1
1
2
2
2
0
1
0
0
2
0
0
2
0
0
2
1
0
2
0
1
0
1
0
3
0
2
1
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
2
0
0
2
0
2
2
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
1
2
0
0
2
2
0
1
0
0
2
0
0
0
1
1
1
0
1
1
2
0
2
0
0
1
1
1
2
0
0
0
2
1
0
2
0
0
2
0
0
1
0
0
0
2
0
0
1
1
0
2
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
2
2
1
2
0
2
1
0
0
0
0
0
0
0
0
0
3
2
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
2
1
1
0
1
1
1
1
0
1
0
2
0
1
0
2
1
0
0
1
0
3
0
1
0
1
2
2
0
0
3
2
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
2
2
0
2
2
0
0
0
1
2
1
0
0
0
1
0
1
0
1
0
0
2
0
0
1
2
0
0
1
0
1
2
1
1
0
2
1
0
0
1
3
1
0
1
0
1
1
1
2
0
0
0
0
2
0
0
0
0
1
2
0
1
1
2
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
2
1
0
2
0
0
0
1
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
2
0
1
0
2
1
2
0
0
0
2
0
0
0
0
0
0
0
1
1
0
1
0
2
0
1
1
2
1
0
1
2
1
0
2
0
0
0
1
0
0
2
0
0
0
1
1
2
0
1
0
0
0
0
0
0
2
2
2
0
1
2
0
0
2
2
0
0
1
2
2
0
0
1
2
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
2
0
1
0
0
2
2
0
0
0
0
0
0
1
0
1
3
1
0
1
0
0
0
0
0
2
1
0
1
0
0
2
0
1
0
3
1
1
0
1
2
0
0
1
1
0
2
0
1
0
1
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
1
0
0
2
0
0
1
0
1
0
0
0
0
0
1
1
0
1
0
0
0
2
1
2
1
1
0
0
1
0
0
0
1
0
1
1
0
0
2
2
0
0
0
0
0
2
2
0
0
0
0
2
0
0
1
0
0
1
0
1
2
1
2
0
0
0
1
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
3
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
2
2
1
2
0
2
0
2
0
1
2
0
2
1
0
0
1
0
1
1
2
0
3
0
0
0
0
2
0
0
2
0
1
2
3
0
2
2
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
4
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
2
0
0
0
1
0
2
0
1
2
0
1
0
0
0
1
0
0
0
1
0
2
2
1
2
0
3
0
1
4
0
0
2
1
6
1
0
1
0
0
0
1
2
0
0
2
1
0
2
2
0
1
2
2
0
3
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
1
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
3
0
1
1
0
0
1
0
0
2
0
2
4
0
1
3
0
2
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
1
0
0
1
0
0
0
1
2
0
0
2
0
0
0
1
0
0
0
1
2
0
0
2
2
0
1
0
0
1
2
0
0
0
9
0
1
0
2
0
0
1
2
0
0
1
1
1
1
0
0
0
2
0
0
0
0
0
1
0
0
1
0
2
1
2
2
1
0
1
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
1
0
0
2
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
2
0
2
0
0
1
1
0
0
0
2
0
2
0
0
0
1
1
0
1
0
0
0
0
0
0
2
1
3
2
2
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
1
0
0
2
1
0
0
1
0
2
0
0
0
1
0
0
1
0
0
1
4
0
0
0
0
2
2
1
2
1
0
1
1
0
0
1
2
0
2
1
0
1
0
0
0
0
0
0
0
1
1
1
0
0
1
2
0
0
1
0
0
1
0
0
0
0
1
1
2
0
1
1
1
0
0
1
1
1
2
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
2
0
0
2
0
0
1
0
0
3
0
1
1
1
2
0
0
1
2
0
0
0
2
0
2
0
1
0
0
0
0
0
4
3
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
4
0
1
0
0
0
2
0
0
2
0
0
1
0
1
1
0
1
0
0
2
0
0
0
2
2
0
1
0
0
2
1
0
0
1
0
0
1
0
3
0
0
0
0
0
0
2
0
2
1
0
0
0
0
1
0
0
2
1
0
2
3
1
1
0
3
1
2
0
0
2
0
3
0
1
0
0
0
1
1
0
0
0
0
1
1
2
0
0
1
2
2
1
3
1
0
1
2
0
1
0
0
2
1
2
0
1
1
1
2
0
2
0
0
0
0
0
2
2
2
0
0
1
2
2
0
0
1
0
0
2
0
0
0
0
1
0
1
3
0
0
1
0
0
0
1
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
2
0
0
0
3
2
0
2
0
0
0
0
0
0
0
2
0
0
2
0
2
0
1
1
0
0
0
1
0
2
1
1
0
0
1
0
2
1
0
1
0
0
0
0
2
0
0
2
0
0
2
0
0
1
0
1
2
0
2
0
2
2
1
10
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
2
0
1
2
1
1
1
1
0
0
0
1
0
1
0
2
0
4
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
1
1
1
0
3
0
0
2
0
1
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
2
2
3
0
0
2
0
0
0
1
0
2
2
0
2
2
0
0
1
0
0
1
1
0
0
0
2
2
1
0
1
0
0
1
1
0
2
2
0
2
2
0
1
0
1
0
0
0
0
2
0
1
0
2
0
0
0
2
0
0
2
1
2
1
1
2
0
0
2
2
2
1
1
2
0
1
0
2
1
0
1
0
0
0
2
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
2
0
2
1
2
0
0
0
0
0
0
1
0
2
0
3
0
0
1
0
1
0
0
1
0
1
2
1
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
1
2
0
2
1
0
0
1
0
0
1
0
0
2
0
1
0
0
0
2
1
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
3
1
0
1
0
2
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
3
0
0
1
1
0
0
0
0
1
1
0
0
0
0
1
0
0
2
0
0
0
1
1
1
0
0
0
1
0
1
2
0
0
0
0
1
0
0
2
1
2
2
1
1
0
1
2
0
0
2
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
2
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
1
0
1
3
0
2
0
1
0
0
0
1
0
0
0
2
0
2
0
0
1
2
1
2
0
0
0
0
0
1
0
2
1
2
2
0
0
2
0
0
2
0
0
0
0
1
1
1
0
0
2
0
1
0
1
2
1
0
2
1
0
1
1
2
0
0
0
0
1
2
0
0
0
0
0
1
1
0
1
1
0
0
0
1
2
1
0
0
0
4
1
0
0
0
0
1
1
0
0
0
2
2
0
2
0
1
0
0
0
0
0
2
2
0
0
0
2
0
0
3
0
1
1
1
3
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
4
0
0
0
0
1
0
0
0
2
0
0
0
0
2
1
0
0
2
0
1
0
2
0
0
1
1
1
1
1
2
0
2
0
3
1
1
1
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
2
0
0
2
1
0
0
2
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
2
0
0
0
1
2
0
0
0
0
2
2
0
0
0
0
0
0
0
1
1
1
2
1
1
1
2
2
2
0
0
1
0
1
0
0
2
1
1
0
2
0
0
2
0
0
0
0
1
3
2
0
0
0
0
1
0
2
0
0
2
0
2
0
1
0
2
0
0
0
1
0
0
0
0
3
0
0
0
1
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
3
0
0
0
0
0
0
2
2
0
0
0
1
0
0
1
0
1
1
0
0
0
6
0
2
0
0
2
1
2
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
5
0
1
2
0
0
0
0
0
0
1
1
1
1
1
0
3
1
2
0
1
1
3
1
0
1
2
1
0
0
0
0
1
1
2
2
1
0
1
2
1
0
1
0
1
0
1
1
0
3
0
0
1
1
2
0
0
0
0
0
2
1
2
0
0
0
1
1
1
1
0
0
0
3
0
2
0
0
0
0
0
0
0
0
1
1
1
0
1
0
1
0
0
0
2
2
0
2
2
0
2
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
2
1
0
2
4
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
1
0
0
0
2
1
2
0
1
1
1
2
0
1
1
0
0
1
0
1
0
2
0
0
2
0
0
0
1
2
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
2
0
0
0
0
2
2
2
0
0
2
2
0
0
2
1
1
2
0
2
2
0
0
1
0
0
1
1
1
4
0
0
0
0
0
2
2
0
0
2
1
0
0
0
1
0
0
2
0
1
1
0
0
2
0
0
1
0
1
2
0
1
1
0
0
1
0
2
2
2
2
1
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
2
1
0
2
0
4
0
1
1
1
0
0
0
1
0
1
0
1
3
0
0
0
0
1
0
2
0
0
1
0
0
0
2
0
1
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
2
0
0
1
0
2
2
0
0
0
2
1
1
0
2
0
4
2
0
2
1
0
0
0
1
0
0
0
2
2
6
2
0
1
0
1
2
0
3
1
2
1
0
2
0
0
0
2
1
1
0
0
0
0
1
1
1
0
0
0
0
2
0
2
1
1
0
0
1
0
1
3
0
0
2
0
1
0
0
0
1
0
1
0
2
1
2
1
3
2
0
1
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
1
0
1
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
2
0
0
1
0
2
0
1
0
0
2
0
0
0
1
1
1
0
1
0
1
2
1
1
2
0
0
0
1
0
0
1
2
2
0
2
0
0
2
0
0
1
2
0
2
0
0
1
0
2
0
1
1
0
0
0
1
0
1
0
0
2
0
0
2
1
1
0
0
2
2
0
2
1
0
1
0
2
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
2
0
0
2
0
0
0
1
3
0
1
0
2
0
0
2
2
0
0
1
0
2
2
2
2
0
2
2
0
1
0
0
0
2
0
0
0
0
0
3
2
0
0
2
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
2
0
1
0
3
0
0
0
2
1
0
0
1
1
0
2
1
0
0
0
1
0
0
0
0
1
1
0
0
0
2
0
0
3
2
2
0
0
4
0
0
0
2
0
0
2
1
1
0
0
0
1
0
2
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
2
0
0
0
2
2
0
0
0
1
0
0
0
0
0
2
1
0
0
1
2
0
0
0
0
2
0
0
0
0
1
1
0
0
1
0
1
0
1
0
0
0
2
2
0
0
2
1
0
3
1
2
0
0
0
1
1
0
0
0
1
1
0
3
1
0
2
0
0
0
1
0
2
2
0
0
0
3
0
0
2
0
0
0
1
0
0
0
0
1
0
1
1
2
0
0
0
0
1
0
0
1
1
0
2
0
0
2
0
0
0
1
1
1
0
2
1
0
0
0
0
0
1
1
0
0
0
0
1
1
2
6
0
1
2
0
0
0
2
0
1
1
0
0
2
0
3
2
0
1
0
1
0
1
0
1
1
0
0
2
0
0
0
0
4
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
1
1
0
0
0
2
2
0
0
0
0
1
1
0
2
1
0
1
0
1
1
1
0
1
1
1
0
0
0
0
1
1
0
0
0
0
3
2
0
0
0
3
0
1
0
2
0
0
0
1
0
0
1
0
1
2
0
0
1
1
1
0
2
1
0
0
0
0
0
2
0
0
0
1
2
1
0
0
1
0
0
0
2
1
0
0
2
0
0
0
0
0
1
2
0
0
2
0
1
0
2
0
0
0
2
0
0
2
0
0
0
1
0
0
0
1
0
0
0
1
0
0
2
0
0
0
2
2
1
0
0
0
0
0
0
1
0
2
2
1
2
0
0
0
1
2
0
2
0
0
0
2
0
1
0
0
0
2
2
1
2
1
0
3
2
0
0
1
0
2
0
1
0
1
1
0
2
0
0
0
1
1
0
1
0
1
0
0
0
0
1
2
0
0
0
1
0
1
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
4
0
0
0
2
0
1
0
2
1
0
2
0
0
2
0
0
1
0
2
1
0
1
0
2
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
1
0
3
2
0
0
0
0
2
0
2
0
1
0
2
1
3
0
0
0
2
0
0
0
0
1
2
0
0
0
0
2
2
0
0
0
2
0
0
0
2
2
0
0
2
2
0
0
0
0
2
0
0
0
2
0
0
0
1
1
0
1
0
1
1
0
2
2
0
2
0
2
0
1
0
0
0
2
0
1
2
2
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
1
1
1
1
0
0
0
1
2
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
1
0
1
1
1
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
3
0
0
1
2
1
1
0
0
0
0
0
0
0
0
1
2
0
1
0
1
0
2
1
0
2
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
5
0
0
0
1
0
1
0
1
2
0
1
0
0
2
0
1
2
2
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
1
2
0
1
0
1
2
1
1
2
0
0
0
0
2
0
2
1
0
0
2
0
2
1
2
0
2
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
1
1
1
0
1
0
2
1
1
1
1
0
2
1
1
0
0
0
2
0
0
0
2
0
0
1
0
1
2
0
2
0
0
2
1
0
2
0
0
0
2
0
0
1
0
0
0
1
0
0
0
1
0
0
0
2
0
1
0
0
0
0
2
0
0
0
1
1
2
2
2
0
0
0
2
0
0
0
0
0
2
1
2
2
0
0
0
2
0
0
1
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
2
1
0
0
2
0
0
0
0
1
2
1
1
0
0
0
0
1
2
0
1
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
2
1
1
1
1
0
0
0
1
1
2
1
1
0
1
0
0
3
1
0
0
0
2
2
1
2
2
0
0
1
2
2
1
0
0
0
0
3
0
2
1
0
1
0
2
1
0
0
0
0
0
0
2
2
0
1
0
0
1
0
2
0
2
0
0
1
1
0
0
2
1
1
1
1
0
0
0
0
0
0
0
1
1
3
0
2
0
0
0
0
0
2
2
2
0
3
0
0
1
0
0
0
0
2
1
0
1
2
0
0
0
0
1
1
0
0
2
0
0
1
0
0
1
0
1
0
2
0
0
0
0
1
0
0
0
0
1
3
0
1
0
0
0
5
2
1
1
2
0
0
2
0
0
0
0
2
1
0
1
1
0
2
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
1
0
1
0
0
1
0
1
1
0
1
1
1
0
1
0
2
0
2
1
0
0
2
2
0
2
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
1
0
0
0
2
0
1
0
0
0
2
0
1
2
1
1
3
1
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
2
0
1
1
0
0
0
2
0
0
1
2
1
0
1
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
2
1
0
0
0
1
2
2
0
0
0
0
0
0
1
2
2
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
1
1
2
0
3
1
0
0
0
2
0
0
1
0
1
0
0
0
1
0
2
1
1
2
1
0
1
0
1
2
1
1
0
0
1
1
0
0
0
0
0
0
0
1
1
0
2
0
0
2
0
0
1
1
2
0
0
1
0
2
0
0
0
0
1
2
0
1
0
2
1
0
0
0
0
1
2
0
0
0
0
1
1
2
1
2
1
0
0
2
0
0
0
0
2
0
2
1
1
0
2
1
1
1
0
0
0
0
2
0
1
0
0
0
1
0
3
0
1
1
0
0
0
0
0
0
0
1
2
0
0
0
2
2
1
0
0
0
0
0
0
0
0
1
0
2
2
0
0
2
2
0
0
3
1
0
2
0
2
0
0
3
0
0
4
0
0
1
0
2
1
0
3
0
0
0
1
2
0
0
3
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
1
0
0
1
2
0
0
0
1
2
2
1
4
2
0
0
1
0
1
2
2
0
0
0
2
2
0
0
0
0
0
1
3
0
1
2
1
2
1
0
0
0
0
1
0
1
2
3
0
0
0
0
2
0
2
1
0
0
2
1
0
0
2
0
0
0
1
0
1
0
1
0
0
0
0
0
0
2
0
0
2
2
0
2
0
5
0
0
2
0
0
0
1
1
0
0
0
1
1
1
1
0
0
0
2
2
0
1
3
0
2
2
0
0
2
0
1
1
2
1
0
0
0
2
2
1
0
0
0
0
0
0
2
0
0
1
1
2
0
1
0
1
2
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
2
2
0
0
2
2
0
2
1
0
1
0
2
1
2
0
2
0
0
1
0
0
1
1
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
3
0
2
0
0
2
3
0
0
0
2
0
0
1
1
0
0
2
1
1
2
1
0
0
0
0
0
1
2
2
0
0
0
1
6
1
0
1
1
0
2
2
1
2
1
2
0
0
3
0
2
0
0
1
0
2
2
1
2
2
2
1
2
2
1
0
0
0
0
1
0
2
1
1
0
0
1
0
0
0
1
0
0
1
0
2
0
2
0
0
0
0
1
1
0
0
1
0
0
1
0
2
0
0
0
3
0
1
2
2
1
1
2
1
1
0
0
2
0
1
0
0
0
2
0
1
1
0
0
0
2
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
5
0
2
1
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
1
2
0
2
0
0
1
0
0
0
0
1
0
2
0
2
0
0
0
0
2
0
0
0
3
0
1
0
2
0
0
1
0
0
0
1
0
1
0
2
1
0
0
2
4
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
1
0
0
0
1
0
0
1
0
1
0
2
3
1
0
0
1
0
1
0
0
0
1
0
2
0
1
3
0
0
1
2
2
2
0
2
2
0
0
0
0
0
2
0
0
2
1
0
1
0
0
0
9
1
2
3
2
0
2
0
0
1
0
0
0
2
1
1
2
2
0
1
1
0
0
0
0
1
1
0
0
2
0
1
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
1
2
1
1
0
0
1
1
2
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
1
0
2
1
0
1
0
0
0
0
0
2
0
2
0
0
4
1
1
0
3
2
0
0
1
1
0
2
0
2
1
1
1
0
0
0
0
0
1
2
2
0
0
2
0
4
2
1
0
0
0
0
0
2
0
2
1
2
0
0
0
0
0
0
1
1
0
0
2
0
4
0
0
1
0
1
0
0
1
0
0
2
1
0
0
0
1
1
1
1
0
0
2
0
2
1
1
2
0
0
1
2
0
0
0
0
1
2
2
0
0
1
0
1
1
0
1
2
0
0
0
0
3
1
2
1
0
1
0
2
0
2
0
1
0
1
1
0
0
1
2
1
1
0
0
0
2
0
0
1
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
2
0
1
1
1
0
0
0
2
0
0
2
1
0
0
0
0
0
1
0
0
1
1
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
1
0
1
0
2
0
0
0
0
0
0
0
2
1
0
4
1
0
0
0
2
0
1
0
0
0
0
0
1
5
0
0
2
1
2
1
0
0
1
0
0
0
1
8
0
2
0
0
2
0
1
2
2
0
3
1
3
0
1
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
1
2
1
1
2
0
2
2
3
1
0
2
1
2
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
1
2
2
0
0
0
0
2
0
0
0
0
3
0
1
0
0
1
1
1
2
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
1
0
0
0
2
2
2
1
0
3
1
0
2
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
2
0
0
0
0
0
0
1
2
0
2
0
1
2
0
0
0
1
1
0
2
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
1
1
0
1
2
0
0
2
0
0
2
0
2
1
1
0
0
0
0
0
0
2
0
1
1
0
1
1
4
0
1
2
2
2
0
0
1
0
1
0
2
2
1
2
4
2
2
1
2
0
1
2
1
0
1
1
0
0
2
0
0
1
1
0
2
1
1
1
0
1
1
0
0
2
0
0
0
0
0
0
2
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
1
7
2
1
0
0
0
0
2
2
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
1
0
1
0
1
0
1
2
2
0
0
0
0
1
0
0
1
0
1
1
2
0
0
2
1
2
0
0
0
1
0
0
0
0
1
2
1
2
1
2
2
3
0
0
2
0
5
0
0
2
0
0
2
0
2
0
0
0
1
1
2
0
0
1
1
0
1
0
0
0
0
2
1
0
1
0
2
0
1
1
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
2
0
1
0
0
1
1
0
0
0
0
1
0
1
1
0
2
1
2
4
2
5
0
2
0
1
2
0
1
2
2
1
2
0
2
0
0
0
1
1
0
1
0
0
0
0
2
3
0
1
2
0
3
0
3
2
0
0
0
1
1
3
3
1
0
0
0
0
2
0
2
2
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
2
3
0
0
0
0
2
2
2
1
0
0
2
1
1
0
1
0
0
1
0
0
0
1
1
2
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
1
0
0
2
0
2
2
0
0
1
0
0
2
1
0
1
2
0
0
2
0
1
0
0
0
0
0
0
2
2
0
1
2
0
0
2
1
2
2
0
1
0
0
0
8
0
1
1
0
0
0
1
0
3
0
2
1
1
2
0
2
1
0
0
2
2
0
2
10
0
0
0
1
0
0
2
0
0
2
2
2
2
2
0
2
0
1
0
3
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
1
0
2
1
0
0
2
2
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
2
0
0
1
0
2
0
0
0
0
0
2
2
5
1
0
0
3
2
0
2
2
1
1
1
1
0
0
1
0
2
0
5
0
0
1
0
1
2
0
0
1
0
0
1
2
2
2
1
0
2
1
0
1
1
1
2
1
2
1
1
0
0
0
0
1
1
0
0
0
0
0
0
1
2
1
0
0
4
0
2
1
0
0
1
0
1
0
0
0
1
0
0
0
0
2
0
0
0
3
0
0
0
2
0
0
0
0
1
1
0
2
0
2
0
1
1
2
0
0
0
0
0
0
0
0
0
2
2
0
0
2
1
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
1
8
2
1
1
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
1
1
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
1
2
2
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
2
0
0
0
0
1
0
0
0
0
1
2
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
1
1
0
5
0
0
1
1
0
0
1
0
1
0
1
2
0
0
0
1
0
2
3
0
0
1
0
1
0
1
1
1
0
0
2
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
1
0
2
2
0
2
2
0
0
2
0
0
1
0
1
0
0
0
0
2
0
1
1
1
0
0
2
1
1
0
2
0
0
1
2
1
0
0
0
1
1
2
0
0
2
0
1
0
0
0
1
0
0
0
0
2
1
0
0
1
0
1
0
0
2
1
1
1
0
1
0
2
0
2
0
0
0
1
1
0
0
2
2
1
1
0
0
0
0
0
0
0
0
1
3
2
2
0
2
0
0
2
1
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
2
0
2
1
1
1
2
1
1
0
0
2
0
0
1
2
0
2
0
2
0
0
0
0
0
0
1
0
0
0
2
0
2
0
1
1
2
0
0
0
0
0
0
4
0
1
2
1
0
0
0
0
0
0
2
1
0
1
0
2
1
0
0
2
3
2
2
2
0
2
0
2
0
2
0
1
0
0
0
0
0
2
2
0
1
0
0
2
0
0
1
2
0
1
0
0
1
0
0
0
2
2
0
0
0
2
0
0
0
2
0
1
3
1
0
2
0
0
0
0
0
2
0
0
1
0
1
2
2
1
1
0
0
2
3
1
0
0
0
0
0
1
0
1
0
2
0
2
0
0
0
2
0
0
0
4
1
0
0
0
1
0
2
0
0
2
0
0
0
0
0
2
0
0
0
2
1
0
0
1
2
0
0
2
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
2
0
1
0
0
0
0
0
2
2
1
0
0
0
0
1
1
2
2
2
0
0
1
0
2
0
2
1
1
0
0
3
0
0
2
0
0
0
0
2
0
1
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
1
2
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
2
1
1
2
1
0
0
0
0
0
0
2
0
1
1
0
1
0
1
0
0
0
0
1
0
0
1
2
0
0
2
3
1
0
0
2
3
1
0
1
3
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
1
0
0
0
1
1
0
0
1
2
0
0
1
1
3
1
1
0
0
0
1
0
3
2
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
1
1
0
0
1
0
0
0
0
1
0
3
2
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
2
1
1
1
1
1
1
0
0
0
0
0
2
2
0
0
1
1
0
2
0
0
0
1
0
2
4
0
2
0
2
5
0
1
1
0
0
0
0
0
0
0
2
0
0
2
1
2
0
2
0
1
0
0
0
0
0
0
2
0
0
2
0
0
2
2
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
1
1
1
2
0
0
1
2
0
1
1
2
1
3
0
0
0
0
3
2
1
0
0
1
2
0
0
0
1
0
0
2
0
0
0
0
2
2
1
2
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
2
1
0
1
0
1
0
1
2
0
0
0
1
0
2
1
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
1
1
1
0
0
2
1
0
0
1
0
0
0
1
0
0
1
0
2
0
2
0
1
0
0
2
2
2
1
0
3
0
2
0
0
0
0
0
2
0
2
0
0
1
0
0
1
0
0
0
1
0
2
1
0
2
0
3
1
1
1
0
1
0
1
0
1
0
0
0
0
0
0
2
0
0
1
0
1
2
0
2
0
0
0
2
0
2
0
1
3
0
0
0
2
1
0
2
2
0
1
0
0
0
0
2
0
0
0
2
0
0
1
1
0
0
2
1
1
0
0
0
0
1
0
0
2
0
0
0
2
1
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
2
2
0
2
0
0
2
1
0
0
0
0
1
0
1
0
2
2
0
0
1
2
2
0
0
2
0
2
2
1
2
1
1
1
1
2
2
2
0
1
0
0
2
0
2
0
1
2
0
1
0
0
0
1
1
0
2
0
2
1
0
1
0
0
2
2
1
2
0
0
0
2
2
0
0
2
2
0
0
2
2
0
0
1
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
1
2
1
0
0
2
1
3
1
0
0
0
1
0
0
1
1
0
0
0
0
2
0
1
0
0
1
0
2
0
0
1
1
0
2
0
0
0
0
2
1
1
2
1
0
0
0
2
0
0
2
1
1
0
0
2
0
4
1
2
0
1
2
1
0
0
2
0
0
0
0
5
2
0
0
2
0
3
0
2
2
0
0
0
1
0
0
0
0
1
2
1
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
2
1
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
2
0
2
1
0
0
1
0
0
1
1
2
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
3
0
0
1
1
0
0
0
0
1
0
1
0
1
2
0
0
0
2
2
0
0
0
0
0
0
2
1
1
0
0
1
0
0
0
0
0
0
1
0
3
0
2
3
2
1
1
0
2
1
0
0
0
1
2
0
0
0
0
1
2
1
2
2
0
0
0
2
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
1
4
0
0
1
0
0
0
3
0
0
0
1
0
0
0
0
0
2
2
2
2
2
0
0
0
0
0
2
1
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
2
0
0
0
1
1
0
0
2
0
1
1
1
0
2
0
2
0
0
1
0
0
0
4
0
0
2
0
0
0
2
0
1
1
0
0
0
2
0
1
0
2
2
0
0
0
2
0
2
1
0
2
2
0
0
2
1
0
0
1
2
2
1
0
0
0
0
2
0
1
0
0
1
0
0
0
0
1
1
0
0
2
2
1
2
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
2
3
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
3
1
0
5
0
2
2
0
1
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
2
1
2
0
0
1
0
0
1
0
0
0
2
0
0
0
0
1
2
0
1
1
0
0
2
1
0
2
0
1
0
2
0
2
0
0
0
0
0
1
0
0
2
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
2
2
1
2
0
0
0
3
0
0
1
2
0
0
0
2
0
0
0
1
0
0
1
0
2
0
2
0
2
1
0
2
0
0
2
3
0
2
1
1
1
1
1
1
1
2
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
1
0
3
0
2
0
0
0
0
3
1
1
2
0
1
0
0
2
0
1
1
0
1
0
0
0
2
0
0
0
1
0
0
3
0
2
0
1
0
0
0
1
2
0
0
1
1
0
0
0
1
1
0
1
0
0
0
1
2
0
2
0
0
0
2
1
0
0
0
2
2
0
2
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
2
2
1
0
1
2
2
1
2
0
0
2
0
0
0
0
0
1
0
1
0
0
1
0
1
1
2
0
0
0
0
0
0
2
2
0
0
2
1
1
0
0
1
2
0
0
3
1
1
0
0
2
0
0
3
0
0
0
0
0
0
2
3
0
0
1
0
0
0
0
2
1
2
1
1
0
0
0
2
2
2
0
1
2
2
1
0
0
2
0
1
0
1
0
1
0
2
0
2
0
2
0
0
0
2
0
0
1
1
2
0
0
0
2
1
2
0
0
0
0
0
0
0
0
2
1
1
2
0
0
1
0
2
2
1
2
1
1
0
0
3
1
1
3
0
0
2
2
0
3
2
0
0
1
0
1
0
1
0
0
0
2
1
2
0
0
2
1
0
2
0
0
2
1
0
1
0
1
0
0
3
2
0
0
0
2
2
1
0
0
0
0
0
1
2
1
0
0
2
0
0
0
0
0
1
3
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
1
1
2
1
0
2
1
0
1
1
2
1
0
2
0
1
0
1
1
0
0
0
1
0
0
0
1
0
0
1
0
0
2
0
1
2
0
0
2
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
1
1
0
0
1
1
1
1
0
0
1
1
1
0
0
2
2
2
0
0
0
0
0
2
0
0
0
2
0
0
0
3
0
1
2
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
2
0
0
0
0
2
0
0
2
2
1
1
1
1
1
1
0
0
1
2
1
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
1
0
0
1
1
2
2
1
2
0
1
1
0
0
0
0
0
2
0
0
0
1
0
0
3
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
1
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
1
0
0
1
1
0
0
1
0
0
2
0
1
0
2
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
1
0
3
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
2
1
1
1
0
0
1
0
0
1
0
2
0
0
0
0
1
0
2
0
0
2
1
0
0
0
0
0
0
0
0
1
2
0
2
1
1
0
2
0
0
0
0
0
0
0
0
0
2
1
2
0
0
2
1
0
0
0
1
0
1
1
3
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
2
2
1
2
2
2
0
0
1
0
0
0
0
0
2
0
1
2
8
0
0
2
1
1
2
0
0
2
0
0
0
0
1
0
0
1
2
0
2
1
0
0
0
2
0
2
2
1
1
0
1
1
0
0
1
0
0
1
1
2
0
0
0
0
0
0
2
2
1
0
2
1
0
0
0
0
1
1
2
0
1
2
0
1
1
0
0
0
0
1
1
2
0
0
0
1
1
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
1
0
0
1
1
0
0
0
1
3
2
0
1
0
0
0
0
1
0
4
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
2
2
2
2
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
2
0
2
0
0
1
0
2
1
2
1
2
0
0
0
2
2
0
2
0
0
3
2
0
2
0
0
0
0
0
0
1
2
2
0
0
2
1
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
1
2
0
0
0
0
2
2
1
1
1
0
0
3
0
1
1
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
2
2
0
1
0
4
0
0
0
0
0
0
1
0
1
0
0
0
2
2
0
1
0
1
2
0
0
2
2
2
1
0
0
0
1
1
0
1
1
1
0
0
0
0
2
1
1
0
0
0
0
2
0
0
2
0
0
2
0
0
2
2
0
0
2
0
0
2
1
0
0
3
2
0
0
1
1
1
2
1
0
0
2
0
0
1
1
3
1
0
2
0
1
0
0
0
2
1
0
0
0
1
0
2
1
0
0
0
0
2
1
0
1
0
1
0
2
0
1
0
0
2
0
0
0
2
0
0
0
1
0
2
0
1
2
0
0
1
2
0
2
0
0
1
0
1
1
0
2
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
3
0
1
2
2
2
0
1
2
0
0
1
0
0
3
0
2
0
0
0
0
1
1
0
1
0
1
0
1
1
0
1
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
1
2
0
1
0
0
2
0
1
0
0
1
2
0
0
1
2
2
2
0
0
1
1
1
1
0
1
0
1
1
1
0
0
0
0
0
0
1
0
0
1
0
1
1
0
2
0
0
0
1
1
1
1
1
1
0
2
2
1
1
0
0
2
2
0
1
2
0
0
0
0
0
0
1
1
2
0
0
2
1
0
0
0
2
0
2
1
1
2
0
1
0
0
2
1
1
0
1
0
0
0
0
2
0
0
1
2
0
2
0
2
0
0
1
0
0
1
0
0
2
0
2
2
0
1
0
1
0
0
2
1
0
2
0
4
0
1
1
2
0
0
0
0
0
4
0
0
0
2
0
2
0
0
0
2
0
1
0
2
0
2
1
0
0
0
0
1
1
0
0
2
0
0
0
2
1
1
0
0
0
1
0
1
0
0
0
2
0
3
2
0
0
2
1
0
0
0
0
2
1
0
0
0
0
0
0
1
1
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
1
2
0
0
0
1
1
2
1
0
1
0
2
2
0
0
0
0
1
1
0
1
2
0
0
0
1
0
2
2
1
1
0
1
0
0
2
1
0
0
0
2
0
1
0
1
1
0
2
0
0
0
0
2
0
0
0
0
1
0
1
1
1
2
0
0
0
1
0
1
0
2
0
0
0
0
0
1
0
1
0
0
2
0
0
1
2
2
2
0
0
1
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
1
0
0
1
2
1
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
1
0
2
2
0
0
1
0
1
0
0
0
1
0
0
0
1
0
1
1
1
0
0
2
0
0
3
0
0
2
0
1
1
1
0
0
0
0
1
0
0
0
0
1
2
0
0
0
1
0
2
0
0
0
1
0
0
0
0
2
0
1
0
2
0
2
1
0
0
0
0
0
1
0
0
1
1
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
2
2
2
2
2
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
2
0
0
2
0
3
1
0
1
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
1
0
4
0
0
0
1
2
0
1
2
2
0
0
0
0
2
0
0
0
2
0
0
0
1
1
0
0
1
0
3
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
1
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
2
2
0
1
1
0
0
0
0
3
0
0
0
0
2
0
1
0
1
1
2
0
2
0
1
2
0
4
2
0
2
0
0
1
0
0
0
0
0
1
1
0
1
0
2
0
3
1
2
0
2
1
0
2
1
0
1
0
0
0
2
0
0
1
1
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
2
0
1
1
0
2
0
1
0
0
1
0
0
1
0
0
2
0
0
1
0
0
3
0
0
2
0
0
0
0
1
0
2
0
2
0
0
0
1
0
0
0
0
2
1
1
0
0
0
0
1
1
1
1
1
1
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
1
0
0
1
0
0
0
2
0
1
1
0
0
2
0
2
0
2
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
2
1
2
2
0
0
0
0
0
0
2
0
1
0
1
1
1
3
0
0
0
0
2
0
0
2
2
0
0
1
0
0
1
0
0
0
0
2
2
0
0
0
1
1
0
1
0
3
2
0
1
2
2
0
0
0
2
2
0
0
0
1
0
2
4
0
0
0
0
2
3
2
0
0
0
2
1
0
0
1
0
0
1
0
0
0
0
2
0
0
2
1
0
2
2
0
0
0
0
0
0
1
0
0
2
0
0
2
1
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
4
0
1
2
2
0
2
2
1
1
1
1
0
0
1
0
0
1
2
1
0
2
2
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
2
1
2
2
0
1
0
1
1
1
3
0
0
0
0
2
2
0
1
0
2
0
0
1
1
1
1
0
0
0
0
0
2
0
0
2
0
0
1
0
2
0
1
3
1
0
0
0
1
1
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
1
4
0
1
0
0
1
0
2
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
2
2
0
2
2
3
2
0
0
0
1
1
0
0
2
0
2
1
0
2
0
1
1
1
2
0
1
0
2
0
1
0
0
2
0
0
2
1
1
0
0
2
0
2
0
0
1
2
0
0
0
0
0
0
1
2
2
2
2
0
0
2
2
1
0
1
0
0
1
1
0
0
0
1
0
2
0
0
0
1
0
0
2
0
2
0
1
0
0
0
0
0
1
0
2
1
0
0
1
0
1
1
0
0
0
0
1
1
2
3
0
0
1
0
1
0
0
0
0
2
0
3
0
0
0
0
1
2
0
0
0
0
2
1
0
1
1
1
0
1
1
0
0
0
1
0
1
3
2
0
0
0
0
2
1
0
1
1
0
0
1
1
2
2
0
1
0
0
0
1
0
0
0
0
2
0
1
2
0
1
0
2
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
4
2
0
0
2
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
2
0
0
0
2
1
0
2
0
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
2
0
1
0
0
0
0
1
0
3
0
0
1
0
2
0
2
1
0
0
1
0
0
0
0
0
0
1
0
0
0
3
0
1
0
0
1
0
2
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
1
0
1
0
2
0
2
2
0
0
2
0
2
1
1
2
0
2
0
0
0
1
1
0
0
1
0
0
0
0
1
2
0
1
0
2
1
0
0
2
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
2
0
1
1
1
1
1
1
0
0
0
0
1
0
2
1
1
0
3
0
3
1
2
0
0
2
0
1
1
2
0
0
0
0
0
1
2
1
0
0
0
0
1
1
0
0
1
2
0
0
3
1
0
2
1
2
0
2
2
1
0
0
1
1
2
0
1
0
3
1
0
2
0
2
0
1
0
1
0
0
1
0
0
0
3
0
2
0
0
1
0
1
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
1
2
1
0
1
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
1
0
0
0
0
1
0
0
0
0
2
0
1
1
0
1
1
0
0
3
1
1
2
2
0
2
2
0
1
1
1
1
0
0
0
0
2
0
0
2
2
0
0
1
1
2
0
1
1
0
0
0
0
4
0
0
1
0
0
1
1
1
0
0
0
2
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
2
2
0
0
1
0
1
2
0
0
0
0
0
0
1
0
0
1
0
0
2
1
2
2
0
0
0
2
0
0
0
0
0
0
2
1
0
1
0
0
0
1
0
2
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
2
0
1
0
0
0
0
0
1
2
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
3
0
2
0
3
2
2
0
0
1
2
0
0
2
0
1
1
1
0
0
2
1
0
0
0
0
1
0
0
2
0
0
1
1
2
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
1
1
1
0
1
0
1
1
3
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
2
1
1
2
0
1
2
0
0
0
1
0
2
0
0
1
0
0
0
1
1
2
2
1
0
0
1
0
3
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
1
0
1
0
0
0
1
2
2
0
3
0
0
2
0
0
0
0
0
1
0
0
0
1
1
2
1
0
0
1
0
0
0
0
0
0
1
1
2
0
2
0
0
0
0
0
0
0
1
0
1
0
2
1
2
0
0
0
2
0
0
0
2
2
0
0
1
1
0
1
0
1
1
0
0
0
0
0
1
0
0
1
5
2
0
0
1
0
0
2
0
1
4
0
0
0
9
0
0
0
2
1
0
1
0
1
0
2
2
0
0
0
1
1
0
2
0
0
0
1
0
0
1
0
0
0
1
1
1
0
1
0
0
1
0
2
0
2
1
0
0
1
0
2
2
0
1
0
0
0
1
0
1
1
2
0
0
0
1
0
0
0
0
0
0
1
2
0
1
0
1
0
0
1
0
2
0
1
3
2
0
0
2
0
1
2
0
2
1
0
0
0
1
1
2
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
1
1
0
0
0
1
0
0
0
1
0
1
2
2
0
2
0
3
0
2
0
0
0
0
0
2
2
0
0
2
0
1
2
2
0
0
0
0
0
0
0
2
2
0
1
2
1
1
2
0
1
0
0
1
0
0
2
0
0
0
2
2
0
0
0
2
2
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
1
1
3
2
0
1
1
0
0
0
0
0
0
2
1
0
2
0
0
2
2
1
0
1
1
0
0
0
1
0
1
4
1
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
2
1
2
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
8
1
0
1
0
0
0
0
0
1
1
1
0
0
1
1
0
2
1
0
0
1
2
0
1
1
0
0
0
0
1
0
2
0
0
2
0
0
0
2
0
1
1
1
2
1
0
2
0
0
0
3
0
0
2
0
0
0
1
0
0
0
1
2
0
2
0
0
0
2
0
0
1
2
0
2
1
0
0
1
1
0
1
0
0
0
0
0
2
0
2
2
0
2
2
2
0
0
2
0
0
0
0
0
2
1
2
2
0
0
0
1
0
0
1
0
2
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
1
0
0
2
2
1
1
0
1
0
0
0
2
0
0
2
0
2
0
0
2
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
1
2
3
1
0
1
0
0
0
1
1
0
0
0
0
1
2
1
0
2
1
1
0
0
0
2
0
2
0
0
1
0
0
1
1
0
2
0
0
0
0
3
0
1
0
1
0
2
1
1
1
0
0
0
2
1
0
0
1
1
0
0
1
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
2
1
0
1
0
0
0
2
1
12
0
0
2
0
1
2
0
2
1
1
3
0
0
1
2
0
0
2
0
0
1
0
0
0
1
2
0
0
1
1
1
0
1
0
2
0
2
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
1
0
0
0
0
3
0
0
2
0
1
0
2
0
0
1
0
2
2
0
3
0
0
2
0
2
0
0
0
2
0
0
3
0
1
0
1
1
4
1
0
1
0
2
0
0
0
2
0
2
0
0
2
0
0
2
0
0
0
1
1
1
2
0
1
1
1
0
2
1
0
1
0
1
1
0
1
0
0
0
0
1
1
2
2
2
0
0
2
0
0
0
0
0
0
0
1
0
2
2
1
0
3
0
0
0
0
2
0
0
1
1
0
0
0
0
0
1
0
2
3
0
0
0
0
2
0
2
2
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
2
2
0
0
0
1
2
0
0
1
0
1
0
0
2
2
0
2
0
0
3
0
2
0
0
0
0
0
0
3
1
0
0
0
2
2
0
0
0
1
0
1
2
0
0
2
2
0
0
0
0
0
1
0
2
0
1
0
0
0
2
1
0
0
1
0
0
0
0
1
1
1
0
0
1
2
0
1
1
1
1
0
0
2
0
2
0
0
0
0
1
2
2
0
2
2
0
0
2
2
2
1
0
0
2
2
0
2
1
0
0
1
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
2
1
0
1
0
0
0
0
1
0
2
0
1
0
0
1
1
0
2
0
0
0
0
0
2
2
0
0
1
0
2
0
1
0
2
2
1
2
0
0
0
0
0
1
0
1
1
1
1
2
0
0
0
2
2
1
0
2
0
0
0
2
0
0
3
1
1
2
0
1
0
0
0
1
0
1
0
0
1
2
0
0
1
2
3
0
2
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
3
1
0
1
1
0
1
0
1
1
2
1
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
2
1
2
0
0
0
0
0
1
0
1
0
0
0
2
0
2
2
0
0
0
0
1
0
0
2
0
0
1
0
1
1
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
1
0
1
0
1
0
1
1
0
2
2
3
1
0
1
2
0
0
1
1
0
0
0
0
0
1
0
0
5
0
0
0
0
2
1
2
0
1
1
2
0
3
1
0
0
0
0
2
1
0
2
0
0
2
2
2
1
0
0
0
1
0
0
1
3
1
0
1
0
1
0
3
2
0
1
1
0
0
0
1
0
0
2
1
0
2
2
1
1
1
0
1
2
2
0
0
2
0
0
5
0
0
2
0
0
2
0
2
0
1
1
2
0
0
0
0
2
1
3
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
2
1
2
1
1
1
0
1
2
1
0
1
2
1
0
1
0
0
1
0
0
0
0
0
1
2
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
2
1
1
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
1
1
0
0
0
1
1
2
0
0
2
0
0
0
1
0
0
0
2
0
1
0
0
0
1
0
0
0
1
0
0
0
1
1
1
2
0
1
0
0
0
1
0
2
0
0
2
0
1
0
0
1
1
0
0
2
2
1
0
0
0
0
0
1
0
1
2
2
0
0
0
0
1
1
1
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
2
0
1
4
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
3
0
0
0
1
0
0
1
1
2
0
0
0
0
0
0
1
2
2
2
1
0
0
2
1
0
0
2
2
1
0
1
2
1
0
2
0
0
1
3
2
0
0
0
0
1
1
0
0
2
0
0
2
1
0
0
0
0
0
1
2
1
0
0
0
0
2
2
0
1
1
0
0
2
0
0
3
1
0
0
0
0
0
3
0
1
2
0
1
0
0
0
0
1
1
0
1
2
0
0
0
0
0
2
2
0
0
0
2
0
0
2
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
1
4
0
1
0
2
2
1
0
2
1
0
1
0
0
0
0
0
2
0
0
2
2
0
1
0
0
0
0
0
0
0
1
3
0
1
1
2
3
2
0
0
0
1
1
0
0
0
0
0
2
2
0
0
0
0
2
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
2
2
0
0
1
0
1
0
1
0
0
0
0
1
2
0
0
2
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
2
1
0
0
2
2
0
1
0
0
0
2
0
1
0
2
2
0
2
0
0
0
1
0
3
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
2
2
0
1
2
1
2
1
0
0
0
0
0
1
2
0
2
1
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
2
1
0
0
0
3
0
0
1
1
0
0
1
0
1
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
2
2
0
0
0
1
2
2
1
1
1
1
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
2
2
0
1
0
0
0
2
0
1
0
1
0
2
1
0
3
2
0
0
0
2
0
0
1
0
2
1
2
3
0
0
0
0
2
2
2
0
0
2
0
0
1
0
0
0
1
1
0
2
1
0
1
0
2
0
0
0
1
1
1
0
1
1
0
2
0
0
0
0
1
0
1
0
2
1
2
1
0
2
0
0
3
0
0
0
2
2
0
0
0
0
2
0
1
1
1
1
1
1
0
2
0
0
2
0
1
0
0
0
0
0
2
0
1
2
0
2
1
2
0
0
0
2
0
0
0
0
2
0
2
1
0
0
0
0
2
0
0
0
1
0
1
1
0
0
0
0
1
0
0
2
3
0
1
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
2
1
2
0
0
0
0
0
2
0
0
1
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
2
2
0
2
0
1
0
0
1
0
2
0
0
1
0
0
1
0
0
1
1
2
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
1
0
1
0
1
2
0
1
0
0
0
1
0
0
0
0
2
0
2
0
0
0
1
0
3
2
1
2
0
0
2
0
1
0
0
2
0
1
2
0
0
0
0
1
0
0
4
0
0
3
1
0
1
0
1
0
0
2
0
0
2
0
0
1
1
0
0
1
2
1
0
2
0
0
3
0
1
2
0
1
0
0
0
1
0
0
1
0
0
0
1
0
1
1
0
2
2
1
1
0
0
0
0
1
2
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
2
0
0
0
2
1
0
2
1
0
2
2
1
1
1
0
0
2
2
1
0
0
0
0
0
0
2
0
0
0
2
0
2
1
0
1
0
0
0
0
1
2
2
2
0
0
0
1
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
2
2
2
0
0
2
0
0
1
1
1
1
0
0
0
0
1
1
0
0
1
1
3
0
2
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
1
1
1
1
0
2
0
0
0
0
0
3
0
3
0
1
0
0
0
2
0
0
0
1
1
0
1
0
1
0
2
1
0
0
1
0
0
0
0
1
0
2
0
0
0
0
3
0
2
0
0
2
1
0
1
0
0
0
0
0
1
2
0
0
0
3
2
0
1
0
2
0
1
2
0
0
0
0
1
1
0
0
1
0
0
0
0
2
0
2
2
2
0
0
0
0
0
0
4
1
0
0
0
0
0
0
1
0
3
0
0
2
1
0
0
0
0
1
1
0
0
0
1
1
1
0
0
2
0
0
0
0
0
1
0
2
2
2
0
0
1
1
1
0
1
1
2
17
0
0
2
0
0
1
0
0
0
0
0
0
3
1
1
0
1
1
2
1
1
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
2
2
0
0
2
2
0
2
0
0
0
2
0
0
2
1
0
0
0
0
0
0
2
2
0
2
2
1
0
2
1
1
0
0
1
1
2
1
0
1
0
0
1
0
0
0
2
0
0
0
1
1
0
1
0
1
0
1
0
1
0
1
1
0
0
0
2
0
0
0
0
1
0
2
2
0
2
0
1
0
0
0
0
0
0
2
0
2
0
2
2
0
2
0
0
1
0
0
1
0
2
0
2
0
1
1
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
2
2
0
0
0
2
1
0
0
2
0
1
0
0
0
2
0
1
0
2
0
1
2
4
1
0
2
1
0
0
0
0
0
0
1
0
1
3
1
2
0
0
1
2
0
2
1
1
1
1
0
0
0
0
2
0
0
0
2
2
2
1
0
1
0
1
0
0
0
1
2
0
0
0
0
0
0
1
1
0
0
0
1
1
2
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
1
2
0
2
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
1
1
2
1
0
2
0
0
1
0
2
0
2
0
0
0
0
0
2
0
1
0
2
0
0
0
1
1
2
1
0
0
0
0
2
0
1
1
0
0
0
0
1
0
1
0
3
0
1
3
0
2
0
0
0
2
0
0
0
0
0
0
1
3
0
0
2
1
1
1
2
3
0
1
0
0
0
2
0
0
2
0
0
0
2
1
2
0
0
0
0
2
0
0
1
2
0
2
0
0
2
0
1
0
1
1
2
0
1
2
1
2
0
0
2
1
0
2
0
0
1
4
0
2
1
1
0
1
0
0
2
0
1
2
0
1
2
1
2
0
0
0
3
0
1
1
0
0
0
2
0
0
2
0
2
0
0
0
1
2
0
0
1
2
0
0
0
1
0
0
1
1
0
2
0
1
0
0
0
2
2
2
0
0
2
1
1
0
1
2
1
0
0
2
1
1
1
0
0
0
0
2
7
2
0
2
1
2
0
0
0
0
2
0
0
0
1
0
1
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
2
0
0
2
1
0
3
1
0
0
1
0
1
0
0
2
0
0
0
2
0
2
0
2
1
0
0
2
0
1
1
0
1
1
1
1
1
1
0
0
1
1
0
0
0
0
1
0
0
2
0
0
0
8
0
2
1
0
2
0
0
1
2
2
0
1
2
0
0
0
2
1
1
1
1
0
1
2
2
1
1
0
0
1
0
0
0
2
0
0
0
0
0
1
1
1
1
1
0
0
0
0
0
2
0
0
1
2
0
1
2
1
2
0
0
1
1
0
1
1
0
1
2
0
0
2
1
0
0
0
1
1
1
0
1
4
1
0
0
1
0
0
2
0
2
0
1
2
0
2
0
1
0
2
1
2
0
1
0
0
0
2
1
2
0
3
0
0
0
1
1
0
0
2
0
0
3
0
3
1
0
2
2
0
0
0
1
1
1
2
2
1
0
0
2
0
1
0
0
0
1
2
0
1
0
1
1
2
0
0
1
0
0
0
0
0
2
2
0
1
0
2
1
0
1
0
4
0
1
1
0
1
1
2
2
2
2
0
1
1
1
0
0
2
0
0
2
9
0
0
2
0
0
2
0
0
2
0
2
1
1
0
0
0
0
0
2
0
3
0
0
0
0
2
1
0
0
0
1
1
1
0
0
3
0
2
0
1
1
0
1
2
0
0
2
1
0
2
3
1
0
0
0
2
0
1
0
1
0
0
0
0
2
0
2
0
2
0
2
1
0
0
2
0
0
2
0
0
2
0
0
0
2
0
0
0
2
2
1
0
1
1
1
0
1
2
2
0
0
0
0
0
2
1
0
0
0
0
0
1
2
0
1
2
2
1
1
0
0
0
0
2
0
0
0
1
0
0
2
1
2
2
0
0
0
0
1
1
0
0
1
0
0
0
0
2
0
0
0
2
2
0
1
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
1
0
1
1
1
0
0
2
2
2
1
2
0
1
0
1
0
0
0
2
0
0
4
1
0
1
0
0
0
0
1
1
2
2
0
2
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
2
4
5
1
0
1
0
1
1
0
0
0
0
1
1
3
2
2
2
1
0
0
2
0
2
0
0
0
1
0
1
2
0
1
0
1
0
1
0
2
0
0
0
2
1
3
1
1
0
0
0
2
1
0
0
0
0
1
0
2
3
2
0
0
0
0
0
0
2
0
0
2
0
0
3
1
3
1
0
0
2
0
1
0
1
2
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
1
0
2
2
0
1
0
0
2
1
2
0
0
0
0
0
0
0
2
0
2
1
0
0
2
0
0
0
0
1
1
0
1
0
0
1
1
0
0
0
0
1
0
0
2
1
0
2
0
2
0
0
0
0
0
1
0
0
1
2
1
1
0
1
1
1
0
0
1
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
1
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
2
2
0
0
0
1
2
0
1
0
1
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
2
0
2
1
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
4
0
1
0
0
0
0
2
0
0
0
0
0
0
2
1
2
1
0
1
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
1
2
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
2
2
2
0
0
0
0
0
2
0
2
2
1
1
2
0
0
1
2
1
0
0
2
0
0
1
0
1
2
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
1
2
0
3
0
2
0
0
2
2
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
3
2
0
0
1
2
1
0
0
2
2
0
1
0
1
2
0
0
1
0
2
2
0
1
0
0
3
0
0
0
0
2
1
0
1
1
0
0
2
1
2
2
1
0
2
1
1
1
1
2
0
3
1
0
1
1
0
2
0
0
1
1
0
2
2
0
1
0
1
0
1
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
1
0
1
1
0
1
0
2
2
0
2
1
0
1
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
1
0
0
1
2
1
0
0
1
2
0
0
0
0
1
1
1
1
0
0
0
0
2
0
1
2
0
0
0
1
0
2
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
4
1
0
0
0
1
0
1
0
0
0
1
0
0
0
1
2
1
1
2
0
0
1
0
0
0
0
0
2
0
1
1
2
1
0
0
0
0
2
2
0
0
1
0
0
1
0
0
1
2
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
2
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
2
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
3
1
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
2
0
0
1
0
2
0
0
1
1
2
0
0
0
2
0
1
1
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
2
0
3
1
3
0
1
0
2
1
1
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
2
3
0
0
2
0
0
0
0
2
0
1
0
2
0
0
0
1
0
0
0
2
0
0
1
2
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
3
0
1
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
1
1
0
0
0
0
0
0
0
2
1
0
0
2
0
0
2
0
1
2
0
2
1
0
0
2
0
0
0
1
0
2
1
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
2
0
2
1
2
1
0
1
0
0
1
0
0
1
2
0
2
1
0
0
2
0
0
0
0
2
2
0
0
0
0
1
1
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
2
2
1
2
1
0
0
0
2
0
3
0
0
3
0
0
1
1
0
0
2
2
1
0
1
2
0
1
0
0
1
0
0
0
0
0
0
2
1
2
0
0
0
0
1
0
0
0
0
1
0
0
1
1
3
0
0
1
0
0
0
2
1
0
2
1
1
1
1
2
0
0
0
2
0
0
2
2
0
1
6
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
4
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
2
0
0
0
0
1
1
0
0
1
0
2
1
0
0
0
2
1
2
1
0
1
1
0
0
0
0
2
0
0
0
0
0
0
4
1
0
2
2
2
1
0
2
0
0
0
2
1
2
0
2
0
0
0
1
2
0
2
0
2
0
0
0
0
0
1
0
2
2
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
2
1
2
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
2
2
0
1
0
2
0
1
0
2
0
0
2
0
0
0
0
0
1
0
1
1
0
0
0
1
2
1
1
1
0
0
0
0
2
0
0
2
2
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
1
0
0
2
1
0
1
0
0
0
0
1
1
0
0
2
2
2
0
0
2
0
0
1
0
1
0
0
0
0
1
1
0
0
0
1
0
2
1
0
0
0
3
0
0
0
0
2
0
1
1
0
1
1
1
0
0
0
0
0
0
2
1
2
1
0
1
0
2
1
0
2
0
1
0
0
0
1
0
2
1
2
0
0
0
1
0
0
0
0
0
1
1
0
1
0
2
2
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
9
0
0
1
1
2
0
0
0
0
0
1
1
2
2
0
0
0
0
2
0
2
2
2
0
0
2
0
2
0
1
0
1
0
0
1
0
0
0
2
0
0
1
1
2
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
3
0
0
0
2
2
0
1
2
0
1
0
0
3
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
3
0
2
0
2
1
0
0
0
0
0
0
1
0
0
0
0
1
1
2
1
3
0
1
0
0
0
1
1
2
4
2
0
2
2
1
0
0
0
2
0
0
1
0
1
0
0
0
1
0
2
0
0
2
0
1
2
2
2
0
0
0
2
2
1
0
0
1
2
0
1
0
0
1
1
0
3
0
0
0
0
1
1
0
0
1
0
2
0
0
0
1
1
2
2
0
0
2
0
0
1
0
0
0
0
0
1
0
0
2
2
1
1
0
0
1
2
2
1
0
0
0
1
0
0
1
0
1
1
0
2
3
2
2
0
0
0
0
2
0
2
0
0
0
0
0
2
2
2
0
1
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
2
1
0
0
0
0
2
0
0
2
0
3
1
0
0
0
0
0
0
2
3
2
4
0
2
0
0
0
2
0
2
0
2
0
0
1
0
2
0
0
0
0
0
0
0
2
1
1
0
1
1
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
2
0
3
2
0
0
1
1
0
0
2
3
2
2
0
0
0
0
2
0
1
0
1
0
0
0
1
1
0
0
0
0
2
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
1
0
2
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
2
0
0
1
0
2
1
0
1
2
0
2
0
0
0
0
0
1
0
0
1
0
2
0
2
0
2
1
0
1
0
0
0
0
0
0
0
1
0
0
2
3
0
0
2
2
1
0
1
0
0
0
0
2
0
2
2
1
2
0
0
0
0
1
1
0
1
0
0
1
1
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
3
0
1
0
1
2
2
0
2
2
2
0
0
2
0
1
0
0
1
1
0
0
2
0
0
1
0
2
1
0
2
0
2
0
2
0
0
0
2
1
0
2
2
1
0
1
2
0
2
2
2
0
0
0
0
2
0
2
0
0
1
0
0
2
0
0
0
0
2
1
0
2
0
1
1
1
0
0
1
3
0
1
1
0
1
0
0
0
2
0
0
0
0
0
7
0
0
0
3
0
0
3
2
2
1
0
0
1
0
0
0
0
2
2
1
2
0
0
2
2
1
0
0
0
0
0
0
0
0
1
2
0
0
1
1
0
0
1
0
0
2
0
0
2
0
2
1
1
2
0
1
0
1
2
0
0
1
0
0
1
2
0
1
0
0
2
2
1
0
0
1
1
1
0
0
0
1
1
2
1
0
0
0
0
0
0
2
0
1
1
0
2
0
1
0
0
0
0
0
1
2
2
1
0
1
2
0
0
1
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
2
1
1
0
0
2
0
1
0
0
0
2
0
0
0
2
1
1
0
0
0
0
2
0
0
1
1
2
0
2
0
1
1
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
1
13
0
0
1
0
0
1
1
2
0
0
1
0
1
0
0
2
1
1
0
1
0
2
1
0
0
0
0
2
2
0
0
1
1
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
2
1
0
0
0
0
0
0
1
3
1
0
2
0
0
0
3
2
0
0
0
0
0
0
0
0
1
0
2
1
0
1
0
0
0
1
0
0
0
0
2
0
0
0
2
2
0
0
1
2
0
1
0
1
2
0
0
1
0
0
2
0
2
0
1
2
3
1
1
0
2
0
1
0
0
0
1
0
0
1
2
0
0
1
0
2
0
0
2
1
2
0
0
0
0
0
1
0
0
0
2
1
0
0
0
1
0
0
0
0
2
0
0
1
1
0
1
1
0
2
0
0
2
0
0
1
2
1
0
0
1
1
0
1
5
0
1
1
1
0
2
2
0
1
0
2
2
1
0
0
1
0
0
2
1
1
2
1
0
1
0
2
0
1
1
0
1
1
0
0
1
0
1
0
0
1
1
1
0
0
1
0
0
0
0
0
2
0
1
0
2
2
0
0
2
1
0
2
1
1
1
2
2
0
1
2
1
0
0
0
1
1
0
0
1
0
1
0
1
3
1
2
0
0
1
2
0
1
0
0
1
1
3
0
0
0
0
0
0
2
1
2
2
1
0
2
1
0
3
0
1
0
1
1
0
0
0
2
1
0
1
0
0
0
0
0
3
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
2
0
0
2
1
0
0
2
0
1
0
0
0
0
0
0
1
1
0
3
0
0
0
0
1
0
1
0
2
2
1
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
3
0
0
1
2
0
2
0
0
0
2
0
0
2
2
1
0
0
0
2
0
1
1
0
1
0
0
0
0
1
0
0
1
0
2
1
0
1
0
0
2
0
1
0
0
0
0
0
1
0
1
1
1
0
0
0
0
2
0
2
0
0
9
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
2
2
0
2
1
0
0
1
0
0
2
6
2
0
1
0
1
1
0
0
0
2
0
0
0
1
0
0
1
0
0
0
4
1
1
1
2
0
0
0
3
2
1
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
1
1
2
2
0
1
1
4
1
1
2
2
0
0
3
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
2
0
0
0
1
0
2
2
0
0
2
0
2
0
1
0
2
0
2
0
0
1
0
1
1
2
1
0
1
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
2
4
6
1
0
0
0
1
2
1
2
1
1
2
0
1
0
1
1
0
2
0
0
1
1
1
0
0
0
3
0
0
0
0
0
0
0
0
0
2
2
1
0
2
0
0
2
0
1
1
1
1
0
1
0
1
0
0
0
0
0
1
0
0
3
3
0
1
1
2
0
0
0
1
0
1
0
1
0
3
0
0
2
0
0
0
0
0
1
2
2
0
2
1
1
0
2
1
1
2
0
0
0
2
0
0
0
2
2
0
0
2
0
0
0
0
2
0
0
2
1
1
0
1
0
0
2
1
0
0
0
0
0
1
1
1
0
0
0
0
0
1
1
0
0
0
1
2
0
0
0
1
0
2
1
1
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
1
0
0
1
0
1
0
2
1
0
1
1
1
0
1
1
3
3
1
2
1
0
0
1
0
2
2
3
2
1
2
0
4
0
1
1
2
2
0
0
0
1
0
2
1
2
2
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
2
1
2
1
1
0
0
0
0
1
1
2
1
0
0
2
0
0
1
0
1
0
1
0
2
0
1
0
1
0
1
2
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
2
1
0
3
0
0
0
2
0
0
0
2
0
0
0
1
0
1
0
0
0
1
1
0
8
2
2
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
2
0
0
1
1
1
1
1
0
1
1
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
1
1
1
1
0
1
1
1
0
2
0
2
0
1
0
0
0
0
0
0
1
0
0
1
0
2
1
2
1
1
2
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
2
0
1
1
1
1
0
2
0
1
0
0
0
0
2
1
1
2
1
2
1
0
1
1
0
0
1
0
0
0
0
2
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
2
1
0
0
0
1
2
2
2
0
0
2
0
2
1
0
3
0
2
1
1
0
2
0
0
0
0
2
0
1
1
0
1
1
2
0
2
0
0
1
0
2
0
2
2
2
0
1
1
0
1
2
0
0
0
2
1
0
0
1
0
0
2
1
0
0
0
2
0
2
0
0
2
0
2
0
0
0
1
4
1
0
0
1
2
0
1
2
1
0
1
2
0
0
1
1
1
0
0
0
2
0
0
0
1
0
2
1
1
1
2
2
0
1
1
2
0
0
2
0
0
2
0
2
1
3
2
0
0
3
0
0
2
0
1
2
0
1
1
2
1
0
1
3
0
0
0
0
1
0
0
0
2
1
2
1
0
0
0
1
0
0
2
0
1
0
0
2
2
0
3
0
0
1
0
1
0
0
2
1
0
0
0
0
0
0
2
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
1
3
0
1
2
0
2
1
0
2
0
0
0
0
2
0
2
2
0
0
1
0
0
1
1
2
0
0
2
0
2
0
0
1
0
0
0
0
0
2
1
0
0
0
1
0
1
0
0
1
1
1
0
0
0
1
0
0
0
2
0
1
0
1
1
0
0
2
1
0
2
2
1
0
0
2
0
1
0
2
2
0
2
0
2
1
1
2
1
0
1
1
3
1
2
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
1
0
2
1
1
0
2
0
0
0
0
1
1
0
0
2
0
1
1
1
0
2
0
0
0
0
1
2
0
0
0
1
2
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
1
2
0
1
2
3
2
0
1
1
5
2
1
1
0
3
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
1
1
0
0
0
0
0
0
2
0
2
2
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
2
2
0
2
0
2
0
2
0
0
0
0
0
1
1
2
0
1
2
1
0
0
0
0
0
0
0
2
0
1
0
1
0
2
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
2
2
0
0
0
2
0
0
0
1
0
0
2
0
1
0
1
1
2
2
0
0
1
2
0
1
1
2
0
0
1
0
0
0
1
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
1
1
0
1
1
0
0
0
0
1
0
6
0
1
2
1
0
4
2
0
0
0
2
0
1
0
0
0
0
0
0
0
4
0
1
0
0
1
2
0
0
0
0
2
2
1
1
0
0
0
0
1
0
0
2
2
0
0
0
0
0
1
0
0
1
2
1
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
4
1
2
0
0
0
2
0
0
0
0
0
2
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
2
2
2
0
0
1
2
0
0
3
0
0
0
0
0
0
2
0
2
0
0
1
1
0
2
0
0
0
2
1
0
0
0
1
3
1
2
0
0
0
0
0
2
0
2
0
0
1
0
0
0
2
2
2
0
0
0
0
0
2
0
1
0
0
0
0
1
1
2
0
0
0
0
0
1
0
2
2
0
1
0
0
1
2
2
1
0
0
2
0
1
0
0
2
0
1
0
2
0
1
0
2
1
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
2
0
0
1
0
0
1
0
1
0
0
0
2
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
2
1
1
0
1
0
3
0
1
0
0
0
0
2
0
1
1
3
0
0
1
0
0
0
0
2
1
0
0
2
0
0
2
0
1
1
1
2
2
0
2
0
0
1
1
1
0
1
0
0
0
2
0
0
1
2
0
2
0
2
2
0
0
0
0
0
2
0
1
1
0
1
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
2
0
0
1
0
1
0
0
1
0
1
2
0
0
0
2
0
0
0
1
1
0
0
1
0
0
1
0
2
0
0
0
0
0
0
1
1
0
2
2
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
2
1
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
1
0
1
1
1
0
0
0
2
0
0
0
0
0
2
2
0
1
1
1
0
0
1
2
1
0
1
0
1
1
0
1
0
1
2
0
1
0
0
0
2
0
1
1
0
2
1
2
0
0
1
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
5
1
1
2
0
0
1
1
2
1
1
0
1
2
0
2
0
0
0
0
2
0
2
5
0
0
0
1
0
0
0
0
1
0
0
0
2
2
0
1
1
0
2
0
0
1
0
0
1
0
0
0
0
1
0
3
0
2
1
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
2
1
2
1
2
1
0
1
0
2
2
0
1
0
0
0
0
0
2
0
0
0
0
1
2
2
1
1
0
0
0
0
2
2
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
1
2
0
2
1
1
0
0
2
0
2
1
0
0
1
0
0
0
0
0
1
0
0
1
2
0
0
0
1
2
0
0
0
0
0
0
0
0
2
1
0
1
0
1
2
1
1
1
1
0
1
0
2
1
0
0
0
2
0
1
0
0
2
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
2
1
0
0
1
0
2
0
0
0
3
1
2
0
0
2
0
0
0
0
0
3
1
1
0
0
1
0
0
0
0
5
1
1
0
0
1
0
0
3
0
0
0
1
1
0
0
0
2
1
2
0
0
0
1
0
0
0
0
1
0
1
0
2
0
0
2
1
0
0
2
0
0
1
0
0
0
0
2
0
1
1
0
0
0
2
0
1
0
1
0
0
0
1
2
2
2
1
0
1
2
0
1
0
0
1
0
0
0
1
1
0
1
0
0
0
2
1
0
1
0
0
1
0
0
0
2
0
0
1
0
0
2
0
1
2
0
2
0
1
0
1
0
0
0
0
0
0
2
0
0
1
1
1
0
1
0
0
2
3
2
1
0
1
1
2
1
0
0
0
1
0
0
1
1
3
1
1
2
0
0
0
0
0
1
1
1
0
0
1
1
1
0
0
0
3
0
2
1
0
0
1
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
2
0
0
0
1
0
1
0
0
0
0
0
4
0
2
1
0
0
0
1
0
2
1
1
1
0
0
0
0
1
0
1
1
1
0
1
2
2
0
0
0
0
1
0
0
2
0
1
0
0
2
0
1
0
2
0
0
0
0
0
1
0
0
2
0
0
0
2
0
1
0
0
0
0
0
2
0
2
0
0
0
2
0
0
2
2
0
2
1
1
0
2
0
1
2
0
0
0
0
0
1
1
2
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
1
4
0
1
0
1
0
0
1
0
0
2
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
1
1
0
2
1
1
1
2
1
0
2
1
2
1
1
0
1
1
2
1
0
2
0
0
1
1
0
0
2
0
0
7
0
0
2
1
2
2
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
2
1
2
0
2
0
0
1
0
0
2
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
1
0
1
0
2
1
0
0
2
0
0
3
1
1
0
1
1
2
0
2
0
0
0
0
3
1
2
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
2
2
0
0
1
0
0
0
0
3
1
0
1
0
0
1
2
0
1
0
0
1
0
3
0
4
0
0
0
1
0
3
2
2
2
0
0
2
0
1
2
0
0
1
0
2
0
1
1
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
1
0
0
0
0
2
0
0
1
0
0
2
0
1
2
0
1
2
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
2
0
0
0
0
1
2
0
2
0
0
2
0
1
0
0
0
0
0
1
2
1
0
2
1
0
0
1
2
0
0
1
0
0
1
0
2
0
2
0
1
2
0
2
0
0
2
0
1
1
1
0
0
1
1
1
0
0
0
2
0
0
0
1
2
0
0
2
1
0
0
4
0
1
0
0
1
1
1
0
0
4
0
1
0
0
1
1
0
1
0
0
0
1
0
0
1
3
1
1
1
2
1
1
0
0
0
0
1
0
0
0
0
1
1
0
5
1
0
0
2
0
0
2
0
0
0
0
3
0
1
0
0
1
0
0
0
2
1
1
0
0
0
2
2
2
1
0
2
0
2
1
2
0
2
1
0
1
0
0
1
0
0
1
0
0
0
2
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
2
0
2
0
1
2
2
0
0
2
2
0
1
0
1
4
0
0
2
0
0
0
1
0
0
1
0
2
1
0
0
0
1
0
0
0
0
0
1
0
1
2
0
2
2
0
1
1
0
2
0
1
2
2
0
0
0
0
0
1
2
0
1
1
0
2
0
1
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
2
0
0
1
2
2
0
0
0
0
0
2
1
0
0
0
2
0
0
2
1
1
2
0
0
0
0
0
0
0
0
0
1
2
1
2
0
1
0
1
5
0
2
0
2
0
0
2
1
4
0
0
1
1
2
0
0
0
0
0
2
2
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
2
2
0
2
0
1
1
1
2
1
1
0
2
2
1
0
0
0
2
0
0
0
0
0
3
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
1
0
1
0
2
0
0
1
0
3
2
0
1
1
2
0
0
0
0
2
0
2
2
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
1
0
1
1
1
0
0
2
2
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
2
1
0
1
0
1
2
1
2
0
1
2
0
2
1
0
0
2
0
0
0
4
0
0
0
1
0
1
0
1
0
0
0
2
2
2
0
0
0
2
2
7
2
3
0
1
2
0
0
0
0
0
1
0
2
1
0
0
0
1
0
2
0
0
0
2
0
2
0
0
1
0
1
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
1
0
0
2
0
0
2
0
0
2
0
0
0
1
1
0
1
2
0
0
0
0
0
0
1
0
0
1
2
0
0
1
0
1
0
0
1
0
2
2
2
0
0
0
0
2
1
2
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
3
2
0
0
0
2
0
0
0
0
0
2
2
1
0
2
0
1
0
1
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
2
0
0
1
0
1
0
0
3
1
1
0
0
0
1
1
1
2
0
1
0
0
0
0
0
0
0
0
1
0
1
3
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
1
0
1
0
0
0
3
2
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
1
0
0
2
0
0
0
2
0
1
0
1
4
0
0
1
1
0
1
0
2
2
2
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
1
1
0
0
1
0
1
0
4
0
2
0
1
0
2
0
1
2
0
1
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
2
1
0
1
2
0
1
0
2
0
1
0
0
0
0
0
2
0
2
0
0
3
0
0
0
0
0
0
0
2
0
0
1
2
2
0
1
0
0
1
0
0
0
2
0
1
0
0
1
0
2
0
3
0
2
2
0
0
2
0
1
0
3
0
0
1
0
0
0
0
0
0
2
1
0
0
0
2
1
0
2
0
0
0
0
2
0
1
0
0
0
2
0
0
1
2
0
0
0
0
1
2
0
0
2
0
1
0
0
1
0
2
0
0
2
1
0
4
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
2
0
0
0
2
0
1
4
0
0
1
2
0
1
2
2
1
0
0
0
2
2
0
0
0
0
2
0
0
2
2
0
0
0
1
2
0
0
1
0
1
0
0
2
1
2
0
2
3
0
2
1
0
2
1
0
2
0
0
1
0
0
0
0
1
0
3
0
2
0
0
0
1
0
2
0
1
0
0
2
2
2
2
1
2
0
1
1
0
0
1
0
1
0
0
0
1
1
2
0
1
0
1
1
0
0
2
2
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
2
4
0
0
2
1
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
1
1
0
0
1
1
2
0
0
0
1
0
0
0
1
2
2
2
0
2
0
1
1
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
2
0
0
0
1
2
2
0
4
1
0
0
0
0
0
0
1
0
1
2
0
0
2
1
0
0
0
0
0
0
0
2
0
0
1
0
0
7
1
0
5
0
1
0
4
0
2
1
0
0
0
1
3
0
1
2
0
0
0
0
2
0
2
0
0
0
0
1
0
0
1
2
1
0
0
1
0
0
1
1
1
1
2
0
0
1
0
1
0
0
2
2
0
0
0
0
2
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
2
1
0
2
0
0
0
0
2
0
2
0
1
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
1
1
5
0
0
2
1
2
2
0
1
0
1
0
0
0
1
1
0
1
3
0
0
0
2
0
2
0
0
2
0
0
2
0
0
0
0
1
0
2
0
1
1
0
0
2
0
2
2
0
1
0
0
0
0
0
2
0
1
0
2
0
0
2
1
0
2
0
2
0
1
2
0
0
0
0
0
0
2
2
0
2
2
1
2
0
1
1
3
0
0
1
0
0
2
2
0
2
0
0
1
0
0
2
1
2
1
0
0
0
1
1
0
3
0
2
0
3
1
2
0
1
0
0
0
0
2
1
2
0
0
2
2
0
1
0
0
1
0
1
0
0
1
0
2
0
0
2
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
2
3
1
2
0
0
0
1
1
0
2
0
0
1
2
0
2
1
0
0
1
0
0
2
0
2
0
1
0
1
0
0
0
0
0
0
1
0
0
2
0
2
1
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
1
0
0
0
1
0
0
1
1
0
0
0
1
1
0
0
1
2
0
1
1
0
2
0
2
1
0
0
3
1
1
1
2
0
0
0
0
0
0
1
1
1
4
0
0
0
1
2
2
0
3
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
2
0
0
0
2
0
0
0
1
0
1
1
1
0
2
1
0
0
0
0
0
1
1
0
0
0
2
1
0
0
0
1
1
0
1
2
0
4
1
1
0
0
1
0
0
0
0
0
1
0
2
1
2
1
0
2
2
0
0
1
0
0
1
1
0
0
0
2
0
1
0
0
1
0
0
0
4
0
3
2
0
0
0
0
0
2
1
0
0
1
0
0
2
1
0
3
0
0
2
3
0
3
1
1
0
0
0
1
2
0
1
0
0
0
0
0
2
0
1
2
0
1
0
1
0
2
0
0
0
2
0
2
0
0
1
2
0
1
2
0
0
1
0
1
0
2
2
2
0
0
0
0
0
2
2
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
3
1
0
0
1
1
0
1
0
2
0
2
0
0
5
2
0
1
0
0
0
2
1
2
2
0
0
0
1
0
0
0
0
0
1
2
2
2
0
1
1
1
2
1
0
0
0
1
2
0
0
2
1
0
3
0
0
2
1
0
5
0
0
1
0
0
1
0
0
0
1
2
2
0
0
0
2
0
0
0
0
1
0
0
0
0
1
2
1
0
0
2
1
0
0
2
1
0
1
1
0
2
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
6
1
1
1
0
0
0
0
0
2
0
0
0
2
0
3
0
0
0
1
0
0
0
2
0
0
0
0
1
0
2
0
2
0
0
0
0
2
1
1
2
0
0
0
0
1
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
1
1
0
0
0
0
0
1
0
0
2
0
0
0
0
2
1
0
2
0
1
2
0
1
2
0
0
0
0
0
2
2
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
1
0
2
0
1
0
0
0
1
0
0
0
0
3
2
0
0
0
1
2
1
1
2
1
0
0
1
0
1
0
0
0
1
0
1
0
1
0
1
0
0
0
0
1
1
0
0
1
0
0
2
1
0
2
2
0
3
1
1
1
2
1
1
1
2
2
0
2
1
1
0
1
1
3
1
0
0
0
1
2
4
1
0
0
0
0
0
1
1
1
0
0
0
0
1
1
1
1
0
2
1
1
0
0
2
1
0
2
1
0
0
1
1
1
0
1
1
2
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
2
0
0
0
1
0
0
2
0
2
0
2
0
0
0
1
0
0
0
3
0
0
1
0
2
0
0
2
0
1
2
2
0
0
0
2
0
1
1
0
0
0
0
2
0
0
1
0
1
1
0
2
1
0
2
1
2
2
0
0
0
1
0
0
0
2
0
0
1
0
1
0
1
1
2
1
1
3
1
0
0
2
0
0
0
0
0
2
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
1
0
1
2
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
2
0
3
1
0
0
1
0
1
2
0
0
1
1
0
0
0
0
1
0
2
0
0
1
1
0
0
2
0
0
1
0
1
0
0
0
1
1
0
0
0
2
2
1
1
2
0
1
0
1
0
0
3
0
0
2
2
0
0
0
0
0
0
0
0
2
0
1
0
1
1
0
1
0
0
1
0
2
2
0
2
1
0
0
0
0
0
1
1
2
1
0
5
2
2
0
2
0
0
0
0
1
1
0
1
1
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
3
2
0
0
1
1
0
0
0
0
0
0
2
0
0
2
0
0
0
4
1
0
0
2
2
0
0
0
0
0
2
0
0
0
1
1
1
0
0
2
0
1
1
1
0
0
1
2
0
0
2
0
3
1
3
0
0
0
0
2
0
0
0
2
0
0
1
0
2
0
0
1
1
1
3
1
1
3
0
0
0
0
0
0
1
0
3
0
0
1
1
2
1
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
1
1
1
0
0
0
0
3
2
0
1
0
0
2
3
2
0
0
0
3
2
0
2
1
1
1
2
1
0
0
0
0
0
0
0
1
2
0
0
2
0
1
0
1
0
2
0
2
0
2
1
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
3
1
1
0
0
0
0
0
0
0
1
1
1
0
0
1
1
0
2
0
1
1
0
0
0
1
1
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
2
0
0
1
0
2
2
0
0
2
1
1
2
0
0
0
0
0
1
0
1
0
2
0
0
0
0
1
0
3
1
0
2
0
0
0
2
1
0
0
1
2
1
0
0
1
0
1
0
0
0
1
0
2
1
3
0
0
0
2
0
0
1
1
0
1
2
0
2
1
2
0
2
0
0
0
0
0
0
0
0
2
0
0
1
2
1
2
0
1
1
1
0
0
0
0
0
1
0
1
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
1
0
0
1
0
0
0
0
0
0
0
0
2
1
0
2
0
1
1
0
0
0
0
0
0
1
2
0
0
2
0
0
0
1
1
0
1
0
0
1
2
2
0
0
0
1
0
0
1
2
0
0
0
3
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
2
0
2
2
1
0
0
0
0
0
2
1
0
1
2
0
1
0
0
0
0
1
0
1
3
0
2
1
1
0
2
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
4
2
0
0
0
0
0
2
1
0
0
0
2
3
0
0
0
1
0
0
0
0
2
0
1
0
2
0
0
1
2
0
0
1
0
0
2
0
0
4
2
2
0
1
2
3
2
0
1
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
2
1
0
2
0
1
0
0
1
3
5
0
0
0
2
0
1
2
1
0
0
2
0
0
0
0
0
0
0
1
1
2
0
1
1
1
0
1
2
0
1
2
3
0
0
0
2
2
2
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
1
3
2
0
2
2
1
0
1
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
1
1
2
1
0
1
0
1
0
2
0
0
2
0
1
0
1
0
0
4
2
0
0
0
0
0
0
0
0
2
0
1
1
0
0
2
0
2
0
0
1
1
2
4
0
1
2
0
1
0
0
0
1
0
0
3
2
0
2
0
1
0
0
0
2
1
0
2
0
2
0
2
0
1
2
2
1
0
2
1
0
1
2
0
0
0
1
0
2
0
0
1
0
0
0
4
0
0
0
0
0
2
1
0
0
0
2
0
1
0
0
0
0
1
0
0
0
1
1
1
0
0
1
1
2
2
0
0
3
0
0
2
0
1
0
0
0
0
2
1
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
1
2
2
2
2
0
0
0
2
0
0
3
2
1
0
1
0
0
4
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
3
2
0
1
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
3
0
1
1
0
0
1
0
0
2
1
1
0
0
0
1
0
0
2
0
2
0
0
1
1
0
1
0
2
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
1
2
2
0
3
1
1
0
0
1
1
1
2
5
2
0
2
1
1
1
3
0
2
0
2
1
0
0
0
0
0
0
0
2
1
0
0
1
1
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
1
0
1
2
1
0
0
1
1
0
0
2
1
0
0
1
0
1
0
0
1
0
0
0
0
0
2
1
0
0
0
2
0
1
1
0
0
1
0
0
1
0
0
0
0
1
0
2
1
2
2
2
1
0
2
0
2
0
2
1
0
0
0
0
1
1
0
1
1
0
1
2
1
2
0
2
0
0
0
0
0
1
0
0
2
2
2
2
1
0
0
0
4
0
0
2
2
0
2
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
2
2
0
0
2
0
0
0
0
1
0
1
3
1
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
1
2
2
1
0
1
0
0
0
1
1
0
0
0
2
0
0
2
0
2
2
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
1
0
1
1
1
0
6
1
0
1
0
2
0
0
0
0
1
1
1
0
3
1
2
2
0
1
2
2
0
1
0
0
0
2
2
0
0
1
0
0
2
0
6
0
2
2
0
1
2
2
0
1
1
0
0
1
2
2
1
2
0
0
0
1
1
0
0
0
0
2
0
2
0
1
0
1
2
1
0
0
1
0
1
0
0
1
0
0
2
0
0
2
0
0
0
0
0
1
2
1
0
0
0
1
1
0
0
0
2
0
0
1
1
2
0
2
0
1
0
2
0
1
1
0
0
0
0
0
1
2
2
3
2
1
0
0
2
0
2
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
1
0
1
0
1
1
0
0
0
0
0
1
2
0
1
1
0
0
0
0
1
0
0
0
0
2
0
3
0
1
0
1
1
1
1
0
1
0
1
2
0
0
1
2
0
1
0
0
0
0
0
0
1
0
0
0
2
0
1
0
2
0
0
0
1
0
1
0
0
1
1
2
1
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
1
3
2
0
0
0
0
0
1
2
1
0
1
2
1
0
0
2
1
0
3
0
1
0
0
1
0
0
0
1
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
3
0
1
0
0
2
2
1
3
0
0
0
2
2
0
0
0
0
1
0
1
1
0
1
0
0
1
0
0
1
2
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
2
0
1
0
0
1
1
0
2
1
0
0
4
1
1
0
0
0
2
0
1
2
0
2
0
2
0
1
0
1
1
1
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
14
0
1
1
1
0
1
0
0
2
0
1
0
0
2
0
2
2
0
0
0
1
1
0
0
0
0
2
0
1
0
0
0
2
0
1
1
0
0
0
1
0
0
0
0
0
1
2
2
0
1
2
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
2
0
1
0
0
1
0
0
1
0
1
0
0
2
0
0
0
0
0
3
2
1
0
0
2
0
0
0
1
2
2
0
0
3
0
0
0
1
0
0
0
1
1
0
1
2
0
0
0
0
0
0
0
2
0
1
1
0
0
0
2
0
0
0
1
0
1
0
0
0
0
1
0
0
2
3
0
0
0
0
0
0
0
0
0
2
0
2
2
2
3
0
2
3
1
1
0
0
0
1
1
1
1
0
0
1
0
2
0
10
2
0
1
1
2
0
2
2
0
0
0
1
0
0
0
2
0
0
2
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
2
2
2
1
0
0
0
0
1
0
0
2
0
0
1
2
0
0
1
0
0
0
2
0
3
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
2
0
1
1
0
0
2
0
1
1
0
0
0
1
1
0
0
2
0
1
0
0
1
0
0
0
0
3
1
0
2
0
0
0
0
0
0
1
0
1
1
1
1
1
0
0
0
2
0
0
0
1
0
1
2
3
0
1
1
0
0
1
0
2
0
0
1
2
2
0
0
0
0
1
0
0
2
0
0
1
1
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
2
3
0
2
1
1
0
2
0
1
0
1
0
2
0
0
0
1
0
0
0
0
0
4
1
0
0
0
0
0
1
1
2
2
0
2
0
0
1
1
2
1
0
0
0
0
1
1
0
2
2
0
0
0
0
1
3
2
1
2
0
0
0
2
1
2
0
0
2
1
0
1
1
0
5
1
0
0
0
1
0
0
1
0
1
0
0
0
3
2
0
0
1
1
0
2
0
0
0
0
0
1
1
0
0
0
0
1
1
2
0
2
0
2
2
0
0
0
0
2
2
0
0
0
2
0
0
2
1
0
3
2
0
0
1
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
1
2
3
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
2
0
2
1
3
0
1
0
1
4
0
0
0
2
0
1
1
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
2
1
0
1
2
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
2
0
0
1
2
2
0
0
0
0
1
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
1
0
0
0
1
2
0
2
2
1
0
0
2
0
0
0
0
0
0
0
1
1
1
2
2
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
1
0
1
2
0
0
0
0
1
1
0
0
3
1
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
6
0
0
1
2
2
0
1
0
0
0
0
0
2
0
0
2
1
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
2
2
1
1
0
0
0
0
1
0
1
0
2
0
0
0
0
0
2
1
1
0
2
0
0
0
0
0
1
1
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
4
0
1
0
2
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
2
0
0
2
1
0
0
2
0
0
1
1
0
2
0
1
1
0
1
0
1
0
0
1
0
2
0
2
0
2
0
1
2
0
0
2
0
1
0
0
2
2
0
2
0
2
0
2
1
0
0
2
0
1
0
0
2
2
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
2
0
0
1
1
1
2
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
1
0
2
0
1
0
1
0
0
0
1
0
0
2
2
1
0
0
2
2
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
1
2
0
0
1
1
2
2
1
0
1
0
1
0
2
1
1
2
2
2
5
2
2
0
0
0
1
1
1
0
0
0
0
1
1
1
0
0
2
0
2
0
2
1
0
0
2
0
1
0
0
0
2
1
0
2
0
0
0
1
1
1
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
2
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
2
0
0
0
0
0
0
1
0
0
3
2
0
1
0
1
2
0
0
1
2
2
0
0
0
0
1
0
2
1
0
5
1
1
0
1
1
0
0
0
0
2
0
0
1
1
0
2
2
0
0
0
0
0
0
0
2
0
0
1
1
0
2
2
1
1
1
0
1
0
0
1
0
0
0
2
0
1
1
2
0
2
0
2
0
0
0
0
0
1
0
1
0
0
1
0
0
2
0
0
0
2
1
2
0
0
2
0
3
0
2
0
2
0
0
0
0
0
0
0
1
0
0
2
1
1
0
0
0
0
0
0
2
0
0
1
0
3
1
0
0
0
5
1
1
0
2
3
1
0
0
0
0
1
1
2
0
1
0
1
0
1
0
0
2
0
1
2
0
0
0
0
0
0
0
0
3
2
0
2
0
2
0
0
0
1
0
0
0
2
0
3
0
0
2
2
0
1
0
0
2
0
0
2
0
1
0
1
0
0
1
0
1
2
0
0
1
0
0
1
2
2
0
0
0
1
0
0
1
0
0
2
0
0
1
1
0
1
2
0
2
1
1
2
2
0
0
0
0
0
0
1
2
1
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
1
1
4
0
0
0
0
1
1
0
0
0
2
1
0
2
2
0
0
0
2
2
0
1
0
1
1
2
0
0
2
2
0
0
3
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
1
2
1
0
0
0
2
0
0
1
1
2
0
0
0
0
0
1
0
2
1
0
0
0
9
0
0
0
0
0
0
0
2
1
1
2
0
2
1
0
1
1
0
0
0
2
2
0
1
1
0
0
1
0
0
0
2
0
0
1
0
1
2
1
0
1
0
0
0
1
0
0
1
0
1
1
3
1
0
0
1
0
0
0
1
0
0
2
0
0
0
1
0
1
0
0
0
2
0
1
0
0
0
0
0
2
1
0
2
0
0
0
0
1
0
2
3
0
1
0
0
0
0
0
2
0
0
0
0
2
1
1
0
0
0
0
0
0
0
3
0
0
0
0
2
2
0
0
1
0
0
0
0
1
1
0
0
0
2
1
0
1
0
0
2
0
1
0
2
0
0
1
0
0
2
1
2
0
1
0
1
0
2
0
1
2
0
0
1
1
0
2
1
0
0
0
2
0
1
0
1
2
0
0
1
2
2
1
0
0
0
2
2
0
2
0
2
0
0
1
1
0
0
0
2
0
1
0
0
1
1
1
1
2
0
0
0
0
1
2
2
2
2
2
6
1
0
1
2
0
0
1
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
2
1
0
1
0
0
1
2
0
0
3
0
0
0
0
2
0
1
0
2
0
1
0
0
0
0
0
0
0
3
0
1
0
1
3
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
1
0
0
1
1
0
1
1
1
0
1
4
0
0
0
2
1
0
0
0
2
1
0
0
0
0
0
1
0
0
2
2
0
0
1
0
0
2
0
0
0
0
2
0
0
1
1
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
3
0
0
0
0
6
0
0
0
0
0
2
0
0
2
1
1
0
2
0
0
0
0
0
0
2
0
0
0
1
1
1
1
0
0
0
1
2
1
0
0
0
2
0
2
0
0
0
1
0
0
2
1
0
0
1
0
2
1
1
1
0
0
0
2
1
0
1
1
1
0
0
2
0
0
1
0
0
2
2
1
1
2
0
0
2
0
3
0
0
0
0
0
0
1
0
0
1
3
0
0
1
0
0
0
2
0
2
2
0
2
1
0
3
0
2
0
0
0
0
0
2
3
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
2
0
0
0
5
2
0
0
0
1
2
1
0
1
0
0
0
2
2
1
0
1
0
0
0
1
1
0
2
2
4
2
0
0
2
2
0
1
0
1
2
2
1
1
1
1
0
0
0
2
2
0
4
1
2
0
2
1
0
2
1
0
0
0
0
0
1
2
0
0
0
2
0
0
1
0
2
0
0
0
0
2
0
0
1
1
0
3
1
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
2
0
0
0
1
1
1
0
1
0
0
0
2
1
0
1
0
2
0
0
1
0
1
0
2
0
0
3
0
0
0
2
0
1
1
0
0
1
0
0
0
2
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
1
1
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
1
1
0
2
0
1
0
0
0
0
2
2
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
2
0
0
0
2
0
2
0
5
2
0
0
0
1
0
0
0
0
2
0
1
1
0
0
0
0
0
0
2
2
1
2
0
0
2
0
0
2
2
1
0
0
0
0
0
0
2
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
2
0
3
0
1
1
1
0
1
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
1
1
0
2
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
8
0
0
0
0
0
0
2
0
0
2
0
1
2
1
1
2
0
0
2
2
0
0
0
4
1
2
3
2
0
2
0
0
0
0
2
0
1
0
0
0
4
1
0
0
2
2
2
0
0
1
1
1
0
0
1
2
0
2
2
2
0
1
0
0
2
0
1
2
0
0
0
1
0
0
1
0
0
1
1
0
0
2
1
0
0
1
0
1
0
3
2
0
0
2
0
0
1
0
0
0
1
0
0
0
1
1
0
1
1
3
1
0
1
1
0
1
0
0
0
0
2
0
1
0
1
0
0
0
0
0
3
2
0
0
0
0
0
0
0
2
0
0
0
2
2
1
0
2
1
0
0
2
0
1
2
2
0
0
0
0
0
2
0
3
0
0
0
0
1
0
0
1
0
0
0
2
1
0
0
0
1
0
1
0
0
1
3
0
0
0
0
0
2
2
2
1
0
0
0
0
0
1
5
2
0
1
2
1
1
0
1
0
2
1
2
0
0
0
0
1
0
0
2
2
0
0
1
0
0
1
1
2
1
2
1
1
0
2
1
1
1
1
1
0
0
0
2
1
0
0
0
0
0
2
0
2
0
0
2
2
0
0
0
0
0
0
2
1
1
0
2
0
2
1
0
0
0
0
1
0
0
2
0
0
0
2
0
2
0
0
4
1
0
0
1
0
0
2
1
1
2
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
3
0
0
0
1
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
2
0
0
0
0
0
2
1
2
0
1
1
0
2
1
1
2
0
1
1
0
0
2
0
2
1
0
2
0
1
0
0
2
0
1
2
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
5
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
1
0
2
0
2
1
0
1
2
2
0
1
1
0
1
0
1
0
2
0
0
0
1
0
0
0
1
0
2
1
2
2
2
0
0
1
3
0
0
2
1
1
0
1
1
0
0
2
2
0
1
0
0
1
0
0
0
0
2
3
2
0
2
0
2
0
1
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
1
1
0
0
0
2
2
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
2
1
0
0
0
1
0
2
0
0
0
0
0
0
1
0
1
1
0
1
1
1
0
0
2
0
2
2
0
0
2
0
1
0
1
0
0
1
1
1
1
0
0
2
0
0
1
0
2
1
0
1
0
1
0
0
0
0
0
0
1
3
0
0
6
1
0
0
2
3
1
1
2
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
6
0
1
0
0
0
0
0
0
0
2
0
0
1
2
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
1
0
0
0
1
1
2
0
0
0
2
0
1
0
0
1
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
1
0
2
0
0
1
1
0
0
0
1
0
2
0
0
2
0
2
1
0
0
0
0
0
2
1
0
2
2
0
0
0
1
1
1
1
0
0
0
4
2
0
2
0
0
2
0
0
1
1
1
0
1
1
1
2
0
0
0
0
0
1
0
0
2
0
0
1
0
1
2
0
0
1
0
1
1
0
0
0
1
2
1
1
2
0
0
0
0
1
1
0
0
1
1
0
0
0
2
1
0
0
0
0
0
0
0
1
2
0
1
0
0
2
0
0
0
0
0
2
0
3
1
3
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
1
0
1
0
1
0
5
0
1
1
1
0
0
2
2
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
1
0
4
0
0
0
2
0
1
0
0
0
0
0
1
2
0
1
1
1
0
1
0
0
0
0
1
1
0
2
0
0
1
0
0
1
0
0
0
2
0
0
0
2
1
0
0
2
2
1
0
0
1
2
0
0
0
0
1
1
2
1
2
0
2
0
0
1
2
0
0
1
2
0
2
0
1
0
0
1
0
0
0
0
2
0
1
0
2
0
0
2
0
0
0
0
0
1
0
1
2
0
0
0
0
0
1
0
2
0
2
0
1
0
0
0
2
0
0
0
1
0
0
0
2
1
0
0
2
1
0
0
0
0
0
0
2
2
3
1
3
1
0
0
0
2
1
0
0
0
0
1
0
2
0
1
0
0
0
0
2
1
0
0
1
1
0
0
0
4
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
1
2
0
1
1
1
0
0
0
3
0
2
0
1
0
3
2
2
2
0
0
1
1
0
0
0
2
0
1
0
0
1
1
0
0
0
0
2
0
0
2
1
0
0
0
2
0
1
1
0
1
1
3
2
0
2
0
0
2
0
2
1
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
2
1
0
2
1
0
0
2
2
0
0
2
1
0
1
0
1
0
0
0
1
0
0
1
1
4
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
1
2
0
0
2
0
2
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
3
0
0
0
0
3
0
0
1
2
0
0
0
2
2
5
1
2
1
1
0
1
0
0
1
0
0
2
0
1
2
2
2
3
0
0
0
1
1
0
0
1
1
0
1
2
0
1
0
0
2
1
2
2
0
0
0
0
1
0
0
3
0
0
0
2
0
0
0
0
0
1
1
1
2
0
0
2
0
0
4
0
1
0
1
0
0
0
2
0
0
0
1
2
1
0
0
0
0
0
0
0
2
2
0
0
0
1
1
0
0
0
2
1
2
1
1
0
2
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
1
2
1
1
0
0
0
1
1
0
0
2
0
0
1
0
0
0
0
0
2
1
2
0
0
0
2
0
2
2
0
0
0
2
1
3
2
2
0
2
0
3
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
1
1
0
0
0
1
2
0
0
0
1
2
0
2
1
0
0
2
0
0
0
2
0
0
0
0
5
1
0
1
1
0
0
2
0
0
0
0
0
0
4
0
1
1
0
2
0
1
1
0
0
0
2
1
0
0
2
2
0
2
3
2
0
2
0
0
0
0
0
2
0
0
1
1
0
1
1
0
0
1
0
0
0
0
1
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
1
1
0
0
0
0
0
0
1
0
0
2
0
0
1
0
2
0
0
1
1
0
0
2
0
1
0
0
0
0
3
0
0
0
1
0
0
0
2
0
1
2
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
1
0
2
2
0
3
0
1
1
1
0
0
1
0
1
0
0
0
0
1
0
2
1
0
1
0
0
1
1
1
0
1
0
1
0
1
0
0
0
0
0
1
2
0
0
2
0
0
3
0
0
2
2
0
1
0
0
2
0
0
0
2
0
2
0
0
0
1
0
1
0
0
1
0
0
0
2
2
0
0
0
0
1
2
0
0
0
2
2
0
0
0
2
1
1
0
1
1
0
1
2
0
1
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
3
1
0
2
2
2
0
0
1
2
1
1
0
2
2
0
2
0
2
1
0
2
2
0
0
3
2
0
2
0
2
0
1
0
0
0
0
2
0
0
0
1
0
3
0
0
0
0
0
0
1
0
0
1
1
0
0
0
2
1
0
1
2
2
0
0
1
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
2
0
4
0
0
0
1
3
0
1
0
0
2
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
1
2
1
1
1
2
3
2
2
0
0
0
2
1
0
0
0
2
1
0
0
0
2
1
0
0
0
2
0
1
2
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
1
0
2
2
1
0
0
1
2
2
0
0
2
0
7
0
0
2
0
0
0
0
1
0
1
2
0
0
1
1
1
1
0
0
2
0
0
0
0
1
1
2
2
1
0
0
0
2
0
2
1
2
2
2
0
0
0
2
4
1
0
0
0
1
0
1
1
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
2
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
1
0
0
0
0
1
0
0
1
0
1
2
0
0
2
2
1
2
0
2
0
2
1
2
2
0
0
2
0
0
1
1
0
2
0
1
2
0
0
3
2
2
0
2
0
0
0
3
0
2
0
1
0
0
0
0
1
1
0
1
2
1
1
0
0
1
0
2
1
0
0
3
2
1
0
0
0
0
0
0
1
1
2
1
1
0
1
1
0
1
0
1
1
0
0
1
0
0
1
0
3
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
2
2
1
1
0
1
0
0
2
2
0
1
0
1
2
1
0
0
0
0
1
0
0
0
0
0
5
0
0
1
2
0
0
0
0
2
1
0
0
0
0
1
2
0
2
0
2
2
0
0
0
1
0
0
0
1
0
2
1
0
0
2
0
0
2
1
0
0
1
0
0
0
0
1
2
3
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
2
2
2
0
0
1
1
0
0
0
0
2
0
1
0
1
2
2
1
0
3
0
1
0
1
1
1
1
0
1
0
0
0
2
0
2
2
0
0
1
1
2
0
0
0
0
0
0
1
0
0
0
4
1
0
1
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
2
1
0
2
0
2
0
1
0
0
1
0
2
1
0
0
2
1
1
1
2
1
2
1
0
1
1
0
0
1
1
1
2
2
0
0
2
2
1
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
3
2
0
0
2
0
0
2
0
0
0
1
0
2
1
0
0
0
1
0
0
1
0
3
0
0
0
0
0
0
0
0
2
0
2
1
0
0
2
1
1
0
1
1
1
3
0
1
1
0
2
1
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
1
0
1
2
2
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
2
2
2
0
2
1
0
2
0
1
1
0
0
0
2
1
0
0
0
1
0
1
0
2
0
3
0
0
0
1
1
2
1
1
0
1
1
0
0
1
0
0
1
0
0
3
0
0
1
3
1
2
0
0
1
0
2
2
0
2
2
0
0
0
0
2
0
2
0
0
1
0
0
0
1
0
0
0
1
0
0
2
0
1
0
0
2
0
1
0
2
0
0
1
2
0
2
0
2
1
0
1
0
1
3
2
0
0
0
2
1
0
1
2
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
2
0
1
2
3
0
0
1
0
0
0
2
3
2
4
0
0
4
0
0
2
2
0
0
0
1
0
0
0
0
0
0
1
1
0
3
0
0
2
2
1
2
1
0
2
0
1
2
1
0
2
1
0
0
0
0
2
0
0
0
2
0
1
0
1
0
0
2
1
0
1
2
0
2
1
1
0
2
0
1
3
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
1
0
2
2
0
1
0
0
0
0
0
0
2
0
0
1
1
3
2
0
0
0
0
2
0
0
2
2
0
0
0
0
0
2
0
1
0
0
1
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
2
0
1
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
2
2
0
0
1
0
0
2
0
0
0
0
0
1
1
0
1
0
0
0
0
4
2
2
0
2
0
0
1
2
0
2
0
1
0
0
1
2
2
3
0
0
0
1
0
1
0
0
0
0
2
0
1
1
0
0
0
0
1
0
0
1
0
0
0
1
2
0
0
2
0
0
0
0
0
1
0
1
2
1
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
1
0
0
0
0
1
0
2
0
2
0
2
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
1
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
1
5
3
1
0
2
1
1
1
1
0
0
2
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
2
0
1
2
2
0
2
0
0
1
0
0
2
2
1
1
1
0
0
2
0
0
1
2
2
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
1
0
0
0
1
2
1
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
1
2
1
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
2
1
4
0
2
0
0
2
0
0
3
0
0
1
2
0
0
0
0
0
1
1
0
0
1
0
0
0
3
2
0
0
0
1
0
0
0
0
0
2
0
1
0
2
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
2
1
0
0
2
0
1
0
1
2
0
1
0
3
3
0
1
0
2
0
0
0
0
0
0
2
2
2
0
1
0
2
0
2
3
1
1
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
1
0
0
2
0
2
1
2
2
2
0
0
0
0
1
0
0
2
0
1
2
0
1
0
0
0
1
0
0
0
2
1
2
0
0
0
0
0
0
0
2
0
2
2
0
0
0
2
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
2
1
0
0
0
1
0
1
1
0
0
1
0
1
2
0
1
0
1
1
1
0
0
2
2
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
1
2
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
1
0
2
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
2
0
0
0
0
1
1
2
0
2
1
0
1
1
0
0
0
0
0
2
1
0
1
1
0
0
2
0
1
1
0
0
0
0
1
1
2
0
1
1
1
4
0
1
2
1
0
0
0
2
0
0
0
0
0
2
2
1
2
0
2
1
0
0
1
0
0
0
0
2
0
3
1
1
0
0
1
0
1
2
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
2
0
0
2
1
0
1
0
0
1
3
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
1
0
1
0
1
1
0
0
1
2
2
0
2
0
0
0
0
0
1
0
0
1
0
2
0
0
0
1
2
0
0
0
0
0
2
0
2
1
1
0
0
0
0
3
0
0
0
0
1
0
0
1
1
1
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
2
0
0
1
1
1
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
2
0
0
2
0
0
0
1
0
0
0
0
1
1
0
2
2
1
0
0
2
1
2
2
3
0
0
0
1
2
0
1
1
0
1
2
0
2
0
1
1
0
1
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
2
0
0
2
0
0
0
0
2
0
0
1
0
0
0
2
0
0
1
0
1
2
0
0
0
1
2
1
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
3
2
0
0
0
2
1
0
0
1
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
1
0
1
1
0
0
1
0
0
2
0
1
0
2
0
0
2
1
0
0
0
2
0
2
0
2
1
0
0
1
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
1
3
0
1
0
0
2
0
3
1
0
0
2
1
1
1
1
0
0
0
1
0
0
0
2
1
1
2
0
0
0
0
1
0
0
2
1
1
0
0
0
1
0
1
0
0
0
0
0
0
2
0
1
2
0
1
1
0
0
0
0
1
0
0
2
2
0
0
0
2
0
2
0
0
1
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
2
0
2
0
2
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
1
1
1
0
0
2
0
1
0
0
0
1
2
1
1
0
1
0
1
0
1
0
0
4
1
2
0
0
0
2
1
2
0
0
0
2
1
1
2
0
1
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
2
0
1
1
0
1
0
0
1
0
0
0
0
1
0
0
0
1
2
0
2
0
2
0
0
2
3
1
0
1
1
0
0
2
0
0
2
0
0
0
1
0
2
0
0
1
2
0
2
2
1
2
1
0
1
0
1
0
1
0
1
1
0
0
1
1
0
1
0
0
0
0
2
0
0
1
2
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
2
0
0
0
2
1
0
0
2
1
0
1
0
0
1
1
0
1
0
0
1
0
0
2
1
0
1
0
0
0
0
0
1
1
0
0
2
0
0
1
1
0
0
0
0
1
2
0
1
0
0
0
0
1
1
0
1
0
1
1
0
1
2
0
0
2
1
1
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
2
0
2
0
0
1
1
0
0
1
0
0
2
0
0
0
4
0
0
0
6
1
0
0
0
2
0
1
1
0
0
0
1
0
0
0
1
0
0
1
0
0
2
2
0
0
0
0
0
1
1
0
2
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
1
2
2
0
2
0
1
1
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
1
1
2
0
1
2
1
0
1
1
0
1
1
0
0
1
0
2
1
0
0
0
0
0
1
1
0
0
0
0
2
0
0
2
1
0
0
1
0
1
0
0
0
2
0
2
2
3
0
0
0
1
1
0
2
0
1
0
0
2
0
0
2
0
0
1
0
0
1
0
1
0
0
2
1
0
0
1
2
1
1
0
2
1
0
0
0
0
0
0
1
0
0
0
1
1
0
2
2
1
4
0
1
2
2
1
7
0
2
1
0
1
0
2
0
1
2
0
0
0
0
0
2
1
0
2
0
0
2
1
1
1
0
2
0
0
0
0
2
1
0
2
0
1
1
2
0
1
1
0
0
0
1
0
0
0
1
0
5
0
0
1
1
0
0
1
0
1
2
2
1
3
0
2
1
6
1
1
0
2
0
0
2
1
0
1
2
2
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
1
1
0
0
0
1
3
4
3
1
2
3
0
0
0
1
2
0
0
1
0
1
2
1
0
1
0
2
0
0
3
2
2
0
3
0
2
0
0
1
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
2
0
2
0
0
2
2
0
0
3
0
1
1
2
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
2
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
1
2
1
0
0
0
1
1
3
2
0
0
1
0
0
0
1
0
0
2
0
0
2
1
0
0
2
0
3
0
1
2
0
0
0
0
2
0
0
0
2
1
0
1
0
0
1
1
2
0
2
0
0
1
0
1
1
0
0
3
0
0
0
0
0
0
3
0
1
0
0
0
0
0
2
0
0
0
1
1
0
0
2
0
2
0
0
0
0
1
1
0
0
0
0
0
0
2
1
0
0
0
1
1
0
0
0
0
1
0
0
1
1
1
1
0
0
1
1
0
2
0
2
0
3
0
1
0
1
0
1
1
2
1
0
4
1
1
0
1
2
0
0
0
0
1
1
1
1
1
1
0
2
1
2
0
0
0
1
0
2
3
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
2
2
2
0
1
0
2
2
2
2
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
2
2
2
2
0
0
0
2
4
0
1
1
1
1
1
0
0
0
0
2
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
2
4
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
2
1
2
0
0
0
2
0
0
0
2
0
1
0
0
0
0
1
2
0
2
0
1
2
0
1
0
1
2
1
0
0
1
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
1
1
0
2
1
2
2
2
0
2
3
0
0
1
1
0
3
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
2
0
1
0
0
0
0
2
0
1
0
0
0
0
0
2
2
0
1
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
3
2
0
2
0
0
3
0
3
0
0
0
1
0
1
0
1
0
0
1
0
6
0
1
2
2
1
1
0
0
0
1
0
0
0
0
0
2
0
0
0
1
1
2
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
2
0
0
0
1
0
1
0
0
0
2
1
0
1
0
3
0
0
0
0
0
0
1
0
1
0
1
0
1
1
1
1
2
0
0
1
0
0
1
2
2
2
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
2
2
0
0
1
0
0
2
2
1
0
1
0
0
0
0
3
0
1
1
1
0
0
1
1
1
1
2
1
1
4
0
0
2
0
0
0
0
1
1
2
0
1
0
2
0
2
0
0
0
0
1
0
0
1
1
1
2
2
1
0
0
2
1
0
1
0
0
0
0
2
1
0
1
0
3
1
1
2
0
1
3
2
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
1
0
1
1
2
1
0
0
1
1
0
2
0
0
2
0
0
1
0
2
0
0
3
0
0
0
0
2
0
0
0
1
1
2
0
0
0
0
1
0
0
0
3
0
2
0
1
2
0
0
1
0
0
0
0
0
0
0
1
1
1
1
0
2
0
0
0
1
2
0
2
0
0
2
2
1
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
1
1
1
0
1
0
0
0
1
1
2
0
0
2
1
0
2
2
0
0
1
3
2
2
0
0
3
0
0
3
0
0
0
1
0
0
0
3
0
2
1
1
2
0
0
1
0
2
0
0
2
2
0
0
0
0
0
0
0
1
0
2
0
1
0
0
1
1
0
1
1
0
1
0
1
0
1
0
2
0
0
0
1
2
1
0
2
0
2
1
1
2
2
0
2
1
2
0
0
0
1
0
1
0
0
0
1
0
0
0
0
2
0
1
0
3
1
0
2
2
0
0
1
1
0
0
0
0
1
1
1
0
0
0
0
0
0
2
0
0
0
2
0
1
1
0
1
2
0
0
2
0
0
0
0
0
2
0
0
1
0
2
2
0
0
1
1
2
0
1
1
0
0
0
3
0
1
0
1
2
0
0
0
0
0
0
0
0
0
1
2
4
3
1
1
2
0
1
0
0
2
2
1
1
0
2
0
0
0
2
0
0
0
0
1
0
0
1
1
0
0
4
0
0
0
1
0
0
0
2
0
2
0
2
0
1
0
1
0
1
0
4
2
1
0
0
0
2
0
2
0
0
2
0
1
1
0
0
1
0
1
0
3
1
1
1
2
2
1
0
2
0
0
2
2
0
0
0
0
0
0
1
2
0
0
1
0
1
1
0
1
0
1
1
3
0
0
1
0
0
0
2
0
1
0
2
1
0
0
1
0
2
0
0
0
0
0
0
1
0
0
1
2
2
2
2
0
0
0
0
0
0
0
2
2
1
2
2
0
0
2
1
2
0
0
0
1
2
0
3
0
2
2
0
0
1
0
2
0
0
0
0
1
1
2
0
1
0
0
1
0
0
0
0
0
2
0
2
0
1
1
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
1
0
0
2
0
2
0
0
0
0
0
1
0
1
2
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
2
0
1
2
0
2
1
0
0
0
0
0
1
0
1
0
0
0
1
2
0
0
2
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
1
0
2
1
0
2
0
2
0
0
0
0
0
1
2
0
0
0
0
0
1
1
2
0
0
0
0
0
2
0
0
1
0
0
0
2
2
2
0
0
1
0
0
1
2
0
0
0
0
0
1
0
3
2
0
0
0
1
1
0
0
0
0
0
0
2
2
0
0
0
0
1
1
0
0
0
2
2
1
4
0
1
1
2
0
0
0
0
1
0
0
0
2
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
2
2
0
2
0
3
0
0
3
0
1
1
1
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
3
0
1
1
1
0
2
2
0
1
0
0
0
0
0
0
0
2
0
0
0
1
3
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
2
0
2
2
1
0
1
2
1
0
1
2
0
1
1
0
0
5
1
2
0
0
0
3
1
0
2
1
1
2
0
0
0
1
1
0
2
1
0
0
1
1
0
9
2
2
1
0
0
1
2
2
1
0
0
0
0
1
0
0
1
0
2
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
1
0
1
0
2
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
2
1
1
0
2
1
1
2
1
0
0
2
0
0
0
0
0
1
3
0
0
0
0
0
3
0
0
1
0
2
0
1
2
0
0
1
0
1
0
2
2
2
0
1
0
0
1
0
0
0
2
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
2
0
0
0
0
0
1
0
0
3
0
2
2
0
0
2
0
1
0
0
1
0
0
1
0
0
2
1
0
0
0
1
1
0
1
2
2
2
2
2
0
2
3
1
0
0
1
0
0
1
0
2
1
2
0
0
2
0
0
2
2
0
0
2
0
2
0
0
0
0
0
1
0
0
2
0
2
1
0
0
1
1
0
0
1
0
0
2
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
4
1
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
2
1
0
3
0
0
2
0
0
1
1
0
0
2
0
0
1
0
3
0
1
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
2
2
0
2
1
1
0
0
0
0
0
2
0
0
1
1
2
1
2
0
0
2
0
0
1
0
0
1
0
0
0
0
3
0
2
0
0
0
0
0
0
1
0
0
3
0
2
2
0
3
0
0
1
0
2
1
1
0
3
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
2
1
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
1
1
0
2
2
0
1
2
0
0
1
0
1
1
0
0
0
2
1
0
0
0
1
1
0
0
2
1
0
0
1
1
1
0
2
1
0
0
2
1
0
1
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
1
0
2
5
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
2
2
0
0
0
2
0
1
2
0
0
0
0
4
0
0
0
2
0
0
2
1
0
0
0
2
1
1
0
0
1
0
0
0
0
1
0
2
0
0
0
0
2
0
2
0
0
0
2
1
0
0
0
1
0
0
0
2
1
1
1
2
0
1
0
2
0
0
0
2
2
2
1
0
2
0
0
0
0
0
0
2
1
1
2
2
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
2
2
0
0
1
1
0
0
0
0
0
0
1
2
2
1
0
0
0
0
2
5
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
1
2
0
0
2
0
1
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
2
0
1
1
1
2
0
0
1
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
2
0
2
1
0
0
1
1
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
2
1
0
0
0
0
1
0
0
0
1
3
0
2
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
1
2
1
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
1
1
0
2
0
1
0
2
0
2
1
1
1
0
0
0
2
0
1
2
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
2
0
2
1
0
0
0
1
0
0
2
1
0
0
0
1
1
0
0
3
0
1
0
0
0
0
1
1
1
1
0
1
2
2
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
1
0
2
1
1
6
0
1
0
2
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
2
1
0
1
2
0
1
0
1
0
1
0
0
0
0
0
0
1
2
0
2
2
2
0
0
0
0
2
0
0
0
0
0
2
2
1
0
0
1
0
1
0
0
0
2
0
0
2
1
1
0
0
2
1
2
1
2
2
0
0
0
0
1
0
0
2
0
0
1
0
2
0
0
0
0
2
2
0
0
0
3
0
1
0
0
1
0
1
1
2
2
2
0
0
0
0
1
0
0
0
0
2
0
2
1
0
0
0
1
0
1
1
0
0
0
0
0
3
1
1
1
0
0
2
0
0
2
2
2
0
0
2
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
1
1
0
1
1
2
0
1
2
0
0
3
0
1
0
2
3
2
2
1
1
1
0
2
0
2
0
0
0
0
0
2
1
0
2
0
0
0
2
2
0
0
0
0
0
2
0
0
2
1
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
2
2
0
0
0
1
0
1
0
1
0
0
0
1
1
1
1
0
1
1
3
2
2
0
0
2
1
0
0
0
0
2
0
2
0
1
0
2
0
0
0
0
0
1
2
0
0
0
1
0
2
1
0
1
1
1
0
1
0
2
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
2
0
0
2
0
0
1
0
1
0
3
2
1
1
1
0
0
2
0
2
1
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
3
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
1
0
0
0
3
0
0
0
0
2
2
0
2
0
2
0
0
0
0
0
0
1
0
0
0
1
3
0
0
0
0
1
0
0
0
0
0
3
0
0
1
1
0
0
1
0
0
2
1
1
1
0
0
0
0
0
1
0
2
2
0
0
0
0
2
0
1
0
0
0
0
2
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
1
0
0
1
2
0
2
0
0
0
2
0
0
0
0
0
2
0
2
0
1
3
1
0
2
2
0
2
2
1
1
0
0
0
1
2
1
0
1
2
0
2
1
1
0
0
0
0
2
0
1
0
2
0
1
1
0
0
0
2
1
0
5
0
2
0
2
0
0
1
0
0
1
0
0
2
0
1
1
0
0
0
0
0
0
0
3
2
0
0
0
1
1
0
0
1
1
2
0
0
1
0
1
0
0
0
0
1
2
1
1
0
0
0
1
1
0
1
0
0
0
2
0
0
2
0
1
0
1
2
0
0
2
1
0
0
0
0
1
0
2
1
0
0
3
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
2
0
2
0
0
2
0
0
1
0
0
2
0
1
0
1
1
1
3
0
1
0
1
0
0
0
1
0
1
1
0
0
0
1
1
1
1
0
0
0
0
0
0
2
0
2
1
0
2
0
2
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
2
1
0
0
2
0
0
0
1
2
1
3
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
1
0
0
0
2
1
0
2
0
0
2
0
0
2
0
2
1
0
0
0
0
0
1
1
2
1
0
0
2
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
2
1
0
0
2
1
0
1
1
0
0
2
2
0
1
0
0
2
0
1
0
0
0
1
0
0
1
2
1
2
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
2
2
0
2
7
2
0
2
1
2
0
2
1
0
0
1
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
3
0
0
0
1
0
1
2
0
0
0
2
2
0
0
2
0
1
2
0
2
0
1
3
2
0
0
0
0
3
0
1
3
0
0
0
2
2
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
3
0
2
0
1
0
0
0
0
0
1
0
2
0
1
2
0
0
1
1
0
1
1
1
0
0
0
0
0
0
2
0
3
3
0
0
1
2
1
1
3
2
0
0
2
0
2
2
0
1
0
0
0
2
0
0
0
0
0
0
1
2
2
0
1
0
0
1
0
0
1
2
1
1
1
2
0
2
0
0
2
1
2
1
0
0
0
1
0
1
0
0
0
0
0
0
1
2
0
1
0
1
2
2
0
0
0
1
4
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
1
0
2
2
0
0
0
1
1
0
0
1
2
1
2
1
0
1
0
0
2
2
0
0
0
0
0
0
0
1
0
1
0
0
2
0
2
1
0
0
0
1
0
2
0
2
2
0
0
3
1
1
1
0
0
1
0
0
0
0
2
1
1
0
2
0
3
0
0
1
0
1
2
2
3
0
1
0
2
0
0
1
0
0
1
0
0
2
0
0
1
0
0
1
0
1
2
2
2
0
1
0
0
2
0
0
4
2
0
0
0
0
2
0
2
0
2
0
2
0
0
1
2
0
3
1
2
2
0
2
0
0
0
1
0
0
2
0
2
1
0
0
2
1
0
0
0
2
0
0
1
0
0
0
2
0
0
2
1
0
0
0
1
2
0
0
0
0
0
1
3
0
2
1
0
2
1
0
0
0
0
2
0
2
1
1
0
0
0
1
0
1
2
1
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
2
1
0
0
2
1
2
0
3
1
0
3
0
2
1
0
0
2
2
0
2
0
0
2
0
0
0
0
0
0
0
1
1
3
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
2
2
0
2
0
0
2
1
0
2
0
0
2
0
0
0
2
2
0
2
2
0
2
1
0
0
0
1
1
2
0
2
1
0
0
0
0
2
1
0
0
0
2
0
0
0
3
0
2
0
1
0
0
2
0
0
0
0
1
0
2
1
3
0
0
0
0
1
0
0
0
2
0
0
2
1
1
1
0
0
0
0
0
0
2
0
2
0
2
0
2
2
0
0
0
0
1
0
1
0
0
0
2
2
2
2
0
0
0
0
0
0
1
2
0
2
1
2
0
2
1
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
1
0
1
0
0
0
2
0
0
2
0
0
1
0
0
1
2
1
1
0
2
0
0
2
2
1
3
0
0
0
0
0
0
2
1
2
0
0
0
0
1
1
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
3
0
1
0
0
0
1
1
1
1
0
0
1
2
0
1
0
1
0
0
0
0
0
2
2
0
0
0
1
1
0
0
0
0
3
0
0
0
1
0
2
1
0
0
1
0
1
2
0
0
0
1
1
0
2
2
2
1
0
1
1
0
0
1
2
0
0
1
2
1
0
0
2
0
1
2
0
0
3
1
0
2
1
1
0
0
0
1
1
0
0
2
0
0
1
0
2
0
2
0
1
0
0
2
0
0
0
0
2
0
1
0
4
2
0
1
0
0
0
0
1
0
0
2
0
0
0
2
5
0
0
1
0
0
1
0
2
0
0
0
0
1
0
1
1
0
1
1
2
0
4
2
0
0
0
1
0
0
0
1
0
2
2
0
0
1
1
2
0
1
2
3
0
0
1
0
1
0
0
0
0
0
1
0
2
2
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
3
0
1
0
2
0
2
0
0
0
0
0
0
2
0
2
1
0
1
0
2
0
1
2
0
2
1
2
0
0
0
0
1
0
0
3
1
1
1
0
0
2
1
1
0
1
0
0
2
0
1
1
2
0
1
1
0
2
0
0
0
1
2
1
0
3
1
0
0
0
0
2
1
0
0
0
0
1
1
2
0
0
0
1
4
0
0
0
1
1
0
0
0
0
0
0
2
1
0
0
0
0
0
2
2
0
0
1
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
1
3
2
1
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
1
1
1
0
0
0
0
2
0
0
0
2
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
2
0
3
0
0
1
1
1
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
1
0
2
2
0
0
2
0
1
0
0
0
0
0
1
2
2
0
0
0
0
1
0
0
3
1
1
0
0
1
1
0
2
2
0
0
0
1
2
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
1
0
1
1
2
2
2
0
2
0
1
2
3
0
2
0
0
0
0
1
0
0
0
1
1
0
0
2
1
0
0
1
0
1
0
2
0
0
1
0
1
0
2
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
2
0
2
0
0
2
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
1
2
3
2
0
2
0
0
0
2
0
0
0
1
0
2
0
2
2
0
0
1
1
0
1
2
0
0
0
0
0
0
1
0
0
2
2
2
1
0
0
1
1
0
0
0
3
0
0
0
1
0
2
0
3
0
0
0
0
5
3
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
2
2
0
0
1
1
0
2
1
0
0
1
1
0
2
0
1
0
1
0
0
1
0
0
1
1
1
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
1
0
0
0
0
0
2
1
1
0
0
0
0
0
0
1
0
0
2
0
2
0
0
2
0
0
1
2
0
0
2
0
3
0
1
2
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
1
2
1
0
1
0
0
2
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
2
1
0
0
0
2
0
0
2
1
0
0
1
1
0
0
0
0
0
1
1
0
0
2
0
0
0
1
0
2
2
2
0
3
2
0
0
0
1
0
0
2
2
1
0
0
1
0
1
1
1
0
2
3
0
0
1
0
1
0
1
0
2
0
1
2
1
0
0
0
2
0
0
0
0
0
0
1
2
1
0
0
1
1
1
1
0
2
2
0
0
1
2
0
2
1
0
0
0
0
0
0
0
3
0
0
0
1
0
1
0
2
2
1
0
3
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
2
2
2
1
0
0
1
2
0
0
0
2
0
0
0
0
0
1
2
0
1
0
0
0
1
0
0
0
1
0
1
0
0
2
2
0
0
1
0
0
0
0
2
0
1
0
2
1
0
0
1
2
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
2
0
0
2
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
2
1
2
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
3
0
1
1
1
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
2
0
3
2
2
2
1
0
0
0
2
2
0
0
0
0
0
1
0
1
1
1
0
2
0
1
2
1
4
0
0
0
1
1
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
1
0
2
2
1
0
1
0
0
0
0
1
2
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
5
1
0
2
0
1
0
2
0
1
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
1
1
0
0
0
0
0
0
0
0
0
2
2
2
1
8
2
1
0
1
0
2
0
0
2
0
1
2
0
0
2
2
5
0
0
0
0
1
0
0
0
2
1
0
0
2
1
1
0
0
2
1
0
1
0
0
1
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
1
1
0
0
0
2
1
2
3
0
0
0
0
1
0
0
1
1
0
0
2
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
2
0
2
0
0
0
2
0
1
2
0
0
2
2
1
0
0
0
2
1
0
0
0
0
0
0
1
0
0
1
1
0
1
0
2
0
2
0
0
0
2
1
1
0
0
1
1
0
1
1
0
1
1
0
0
2
0
1
3
1
0
1
2
2
0
2
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
2
2
1
1
2
2
0
1
0
0
2
4
1
0
1
1
2
0
0
0
1
0
1
0
0
1
1
0
0
0
2
1
1
2
0
0
1
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
2
0
2
2
2
0
0
0
1
0
1
0
0
2
1
1
0
0
0
2
1
0
1
1
1
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
2
0
1
1
0
1
0
0
0
1
1
0
0
2
0
0
0
1
2
0
1
0
2
0
2
0
2
0
2
0
3
0
0
1
1
1
0
0
1
1
0
0
0
0
0
2
1
0
1
2
0
0
0
0
1
0
1
0
0
0
2
0
0
0
1
2
0
0
1
0
0
1
1
1
0
0
0
0
1
2
0
0
0
1
2
0
0
0
2
1
0
0
1
2
2
1
0
0
2
0
1
2
2
3
1
0
2
0
2
1
0
2
0
0
2
0
0
0
0
0
2
0
1
1
0
1
0
0
1
2
0
0
0
0
0
2
0
0
2
0
0
2
0
1
0
1
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
1
2
2
0
0
0
0
1
1
1
0
0
0
1
0
0
1
0
1
0
1
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
1
1
0
0
0
2
1
0
0
1
0
0
1
0
1
1
0
1
0
6
0
1
1
0
0
2
1
1
1
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
1
1
1
2
2
0
2
0
2
2
1
0
0
0
1
2
1
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
1
0
1
0
0
0
0
2
2
3
0
2
2
0
2
0
0
1
0
1
1
0
1
2
0
2
2
0
0
0
0
0
0
2
0
0
2
0
2
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
1
0
0
1
2
0
1
2
2
2
0
1
0
2
0
1
0
0
2
1
2
0
0
1
2
0
0
2
0
1
1
0
0
1
1
0
1
2
1
0
0
1
0
2
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
2
2
0
2
1
1
1
0
3
0
0
1
0
2
0
1
0
0
0
3
1
0
0
0
1
0
0
0
2
0
0
1
0
0
1
0
1
2
0
0
1
0
0
1
2
1
0
0
1
0
0
0
1
1
1
1
0
0
0
0
0
1
3
0
1
0
1
2
1
0
0
1
0
0
2
1
1
2
0
0
2
1
1
0
0
0
0
0
2
0
0
0
0
1
1
1
1
0
0
1
0
0
0
2
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
1
1
1
0
0
2
1
1
1
3
0
1
0
0
1
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
1
0
0
0
1
0
1
1
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
1
0
4
0
1
1
0
0
0
1
0
0
0
1
1
0
1
0
1
0
0
0
0
0
2
1
2
0
1
1
0
0
1
2
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
2
0
0
0
0
1
0
0
0
0
2
2
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
4
0
5
0
1
1
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
1
2
0
0
0
0
0
0
0
1
0
0
1
4
0
2
0
0
0
0
1
2
2
2
0
2
0
1
4
1
1
13
1
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
1
0
2
0
2
0
0
0
0
1
1
0
1
0
0
2
1
0
1
1
0
1
0
0
0
0
0
0
3
0
1
1
0
1
0
2
1
0
2
1
0
2
1
2
0
0
1
0
0
1
0
0
2
1
0
0
1
0
1
1
0
0
0
0
0
3
0
1
2
1
0
1
0
1
0
0
0
2
0
2
2
2
0
2
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
1
0
0
2
2
0
0
0
2
2
0
0
0
0
1
1
1
1
1
0
1
2
0
0
0
0
1
2
2
1
0
1
1
0
0
0
1
2
0
4
0
0
0
2
0
1
2
4
1
0
0
0
2
0
0
4
0
0
0
1
0
0
1
1
2
0
0
1
0
2
3
2
1
2
0
0
0
0
0
2
0
2
1
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
5
0
0
0
1
0
1
0
1
0
0
2
1
0
2
0
1
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
3
1
0
2
0
2
1
1
0
2
2
0
0
1
0
6
0
1
1
1
0
1
0
0
2
2
0
0
0
0
0
1
2
1
2
1
0
0
2
2
1
0
0
0
1
0
2
0
0
0
0
1
0
1
0
2
1
0
0
0
0
1
0
0
2
2
0
0
2
2
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
3
0
0
1
0
2
0
1
0
1
2
2
0
0
2
0
1
1
3
1
0
1
2
0
1
1
1
0
0
1
0
1
0
1
0
0
0
1
1
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
1
1
2
0
1
0
0
1
2
0
1
1
0
0
0
0
0
0
0
0
2
0
1
0
0
1
1
0
1
0
0
0
0
2
0
0
0
0
2
0
0
1
0
2
0
0
3
0
2
0
0
1
1
3
0
1
0
2
1
1
2
0
0
0
2
2
0
0
2
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
3
1
3
1
1
1
2
0
0
2
0
2
0
0
2
2
0
1
0
0
1
0
0
0
2
2
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
3
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
1
2
0
0
1
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
1
2
2
1
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
4
2
1
0
0
0
0
1
0
3
0
0
1
1
1
0
0
0
2
0
0
1
0
0
0
0
1
1
0
2
2
2
1
0
0
1
0
0
1
0
0
1
3
0
2
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
3
0
1
0
2
0
0
0
0
0
0
1
1
2
1
0
0
2
0
0
0
0
0
0
1
1
0
0
1
0
0
2
0
1
0
2
0
0
1
0
1
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
1
2
0
1
0
0
0
0
0
0
1
0
0
0
2
0
1
0
2
0
0
2
1
0
0
2
0
0
1
0
0
2
0
0
0
1
0
0
0
0
1
1
1
1
0
1
1
2
1
1
2
0
0
0
1
1
2
0
0
1
0
1
0
0
0
0
1
0
2
0
0
0
0
0
2
0
2
0
2
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
2
0
2
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
2
0
0
0
2
0
0
1
0
1
0
0
1
0
2
0
0
2
0
2
1
2
2
0
0
0
0
0
1
0
0
0
0
6
0
1
1
0
0
0
2
2
0
1
0
2
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
1
0
2
0
1
1
0
0
0
0
0
1
1
0
1
0
0
1
2
1
0
1
0
1
2
1
0
0
0
2
0
1
2
1
0
0
2
2
1
2
1
0
0
2
2
2
0
2
0
0
2
2
0
0
0
2
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
1
1
2
2
0
0
0
0
2
0
0
1
1
3
2
0
0
2
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
2
2
1
1
0
2
0
1
0
2
2
0
0
3
0
0
1
1
1
0
0
0
1
0
0
1
0
0
0
1
0
1
0
2
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
6
0
1
0
1
0
2
1
0
0
0
1
1
0
1
0
0
0
2
0
0
0
0
0
1
2
0
0
0
1
2
0
1
0
0
1
2
0
2
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
3
2
0
2
1
1
1
0
0
1
0
1
0
2
3
2
0
2
0
2
0
2
0
1
0
0
2
0
2
2
0
1
2
2
1
2
2
0
1
0
3
0
2
2
0
0
0
2
2
2
0
1
0
0
0
2
0
0
0
0
1
0
1
0
0
1
0
0
1
0
2
0
0
1
0
0
0
0
1
1
0
2
0
1
2
0
0
1
2
2
0
2
0
0
0
1
0
0
0
1
1
2
2
0
0
0
0
1
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
1
2
2
0
0
1
1
1
0
0
0
0
0
1
1
0
2
1
2
0
0
0
0
0
0
3
0
1
0
1
0
0
0
0
0
1
2
0
0
0
1
0
0
1
0
1
0
0
2
0
0
0
0
0
2
0
0
0
2
2
1
2
1
0
0
2
0
2
1
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
2
0
2
0
1
4
1
1
0
1
0
2
0
1
1
0
0
0
0
0
0
1
1
0
1
2
0
2
2
1
0
0
0
0
2
1
0
1
2
2
0
2
1
2
0
2
0
0
0
1
4
0
0
0
0
0
2
0
0
1
0
3
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
2
0
1
2
0
1
1
0
0
4
0
1
0
0
0
2
2
0
0
0
1
1
0
1
0
0
1
0
0
3
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
2
2
0
0
0
0
0
2
7
2
2
0
2
0
0
2
1
0
0
0
2
0
2
0
1
1
1
1
2
0
0
2
0
1
0
2
0
2
1
0
0
0
0
1
1
0
0
2
2
0
1
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
1
2
2
0
0
2
0
1
1
2
0
0
0
2
0
0
0
1
2
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
2
0
2
1
0
2
1
0
0
0
0
0
0
0
1
1
0
0
7
0
0
0
1
1
1
0
3
0
2
1
0
1
0
3
0
0
2
0
1
2
0
2
1
0
2
0
0
2
1
0
1
0
1
1
2
0
0
0
1
0
2
0
0
1
0
0
0
2
2
1
2
2
2
2
0
0
0
2
1
1
0
0
0
0
1
2
1
0
1
0
1
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
1
1
1
1
0
1
1
0
0
0
2
1
0
2
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
2
0
2
0
2
0
2
0
0
1
0
0
2
0
1
0
0
0
2
0
0
1
0
0
1
1
2
0
0
0
0
0
0
1
0
2
0
0
1
2
2
0
2
0
2
1
0
0
0
0
3
0
1
1
0
2
0
1
1
1
0
1
0
0
0
1
0
2
2
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
1
0
2
1
0
2
0
0
1
0
0
0
0
0
2
0
0
0
2
1
0
0
2
1
2
2
0
0
0
0
1
0
0
2
0
1
1
1
0
2
0
1
0
0
2
0
2
0
1
2
0
0
1
2
2
1
1
0
0
0
2
1
2
2
0
0
2
3
0
0
0
0
0
1
0
5
0
0
0
2
1
0
2
0
0
0
2
1
0
0
0
1
1
0
0
1
0
0
0
0
1
1
1
1
2
2
1
1
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
1
1
0
2
2
1
1
1
0
0
0
1
0
2
2
0
0
0
1
0
1
2
0
1
0
1
0
1
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
1
0
1
0
0
1
0
0
0
0
0
0
2
1
2
0
0
1
1
1
0
0
0
0
2
2
1
0
2
0
2
0
2
0
0
1
2
2
0
1
0
2
1
1
1
0
0
0
1
0
1
1
0
0
3
1
3
0
0
0
2
2
0
0
2
0
1
1
0
2
2
0
1
1
2
0
0
1
1
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
2
0
2
1
0
0
1
1
0
0
2
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
2
1
1
2
0
0
2
1
3
0
1
4
0
2
1
0
0
0
3
0
2
1
2
0
1
0
0
1
0
1
0
3
0
0
0
0
1
0
2
2
3
0
2
2
2
2
0
2
1
0
0
1
1
2
0
0
1
2
4
0
0
0
0
1
1
1
0
2
0
2
1
0
0
2
0
2
1
0
2
0
0
1
1
1
2
0
2
1
2
0
2
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
1
1
3
1
1
0
1
2
0
0
1
0
1
1
2
2
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
1
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
2
0
0
1
0
1
0
0
1
1
2
0
0
2
0
0
0
1
0
0
0
2
3
2
2
0
2
1
0
0
0
1
0
0
0
0
1
0
0
0
1
2
0
0
1
0
0
3
0
1
0
1
0
0
1
0
1
1
0
0
1
0
0
2
3
0
1
0
2
0
0
2
0
2
0
0
2
0
0
0
1
0
2
0
2
0
1
2
1
0
0
1
0
2
2
1
0
0
1
0
1
0
0
2
0
1
1
0
0
0
2
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
3
1
1
0
1
0
2
0
1
0
2
1
1
0
1
2
3
2
1
3
0
1
0
0
2
2
0
1
1
0
2
0
0
0
0
0
0
1
0
1
1
2
1
0
0
0
0
2
1
0
0
0
1
1
0
0
0
0
1
0
0
2
0
1
0
0
1
0
0
2
0
1
0
1
0
3
0
0
1
0
0
0
0
2
0
0
2
3
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
1
1
0
0
0
0
0
2
1
0
2
0
1
0
2
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
2
0
0
0
0
0
2
0
1
2
0
0
1
0
1
1
1
0
0
2
1
0
4
0
2
0
0
0
3
1
0
0
0
0
0
1
0
0
2
2
1
0
3
2
0
2
2
0
0
2
0
1
2
1
2
0
0
1
1
2
1
1
0
0
1
0
0
1
0
0
0
0
3
0
2
0
2
2
0
1
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
3
2
0
0
2
0
0
0
0
0
0
1
0
0
7
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
2
0
0
0
1
1
0
0
0
0
2
2
0
0
2
0
1
2
0
1
0
0
1
1
0
0
0
2
0
0
3
0
2
0
2
1
2
1
0
1
0
0
2
0
0
0
0
0
0
0
2
2
0
0
1
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
2
0
1
1
2
0
0
0
1
0
2
2
2
1
0
2
0
2
0
2
0
2
1
0
0
0
2
1
2
0
0
0
1
3
0
0
0
0
0
2
2
2
2
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
1
1
2
2
6
2
0
0
0
0
0
0
0
0
1
0
2
0
2
0
1
1
1
1
1
0
0
0
0
1
0
1
0
3
1
1
0
0
0
0
0
0
0
0
1
1
1
3
1
0
2
2
1
3
2
1
0
3
1
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
4
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
1
0
3
0
0
0
0
2
0
0
2
0
0
0
4
4
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
1
2
0
2
0
1
1
1
0
0
1
0
0
0
1
2
0
2
0
1
0
2
0
0
0
0
0
1
0
2
1
0
2
0
0
0
2
2
0
0
2
0
2
0
1
0
1
1
0
2
1
0
0
1
1
0
0
1
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
3
2
2
1
0
0
0
0
1
0
2
0
2
2
0
3
0
0
0
1
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
2
0
0
0
0
0
1
1
0
2
4
3
0
0
1
2
0
0
2
0
0
0
0
1
0
0
0
0
1
2
0
0
1
2
0
0
2
2
2
2
0
0
2
0
0
0
2
0
1
1
0
0
0
0
0
0
0
2
1
0
0
1
1
0
0
0
0
1
2
0
0
0
1
0
2
1
0
1
0
0
0
0
2
0
1
1
1
0
1
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
2
0
1
1
0
1
2
0
0
0
0
0
0
1
2
0
0
2
0
0
2
1
0
0
1
1
2
0
0
2
0
1
2
0
0
0
0
1
3
1
0
1
0
2
1
0
0
0
2
2
0
0
2
0
1
0
2
0
0
1
1
0
0
1
0
1
2
1
2
0
0
2
0
1
0
0
2
0
3
0
0
0
0
1
0
0
1
2
0
0
0
2
1
0
2
0
0
0
1
0
0
0
0
1
0
0
1
2
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
3
0
2
1
0
2
1
1
2
0
0
1
0
2
2
1
0
0
0
0
1
2
4
1
0
0
1
2
0
1
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
1
1
2
0
1
0
0
0
1
0
0
0
2
1
0
1
1
2
0
2
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
1
1
2
0
2
0
0
0
0
2
0
1
0
0
2
2
0
1
0
0
0
0
1
0
0
2
0
2
0
1
2
1
0
0
0
1
2
1
0
2
0
2
1
0
0
2
1
1
1
1
1
2
0
0
1
1
1
2
2
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
1
0
0
1
0
2
0
1
2
2
0
1
1
1
0
0
0
2
0
1
0
2
0
1
0
1
0
0
2
0
0
0
0
1
2
0
0
0
0
2
0
2
1
2
1
0
2
0
1
0
2
0
0
0
0
0
1
2
0
0
1
2
0
2
2
0
0
1
1
0
0
2
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
3
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
1
0
0
1
3
0
0
0
0
2
0
1
0
1
0
0
0
2
0
0
0
1
2
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
2
0
0
2
1
1
0
2
2
2
2
0
0
0
1
2
1
0
1
0
0
1
0
0
1
0
0
2
0
1
2
1
0
1
0
2
0
0
0
0
1
0
0
0
2
0
0
1
3
2
0
0
0
6
0
0
0
1
0
0
1
2
0
0
0
0
1
0
2
0
2
0
1
1
0
2
0
0
0
2
0
2
0
0
0
2
1
0
0
0
1
2
0
0
0
2
1
1
0
1
2
0
0
1
3
0
1
1
0
1
0
2
2
0
0
0
0
2
2
2
0
2
3
1
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
1
2
2
0
0
0
2
0
0
0
0
1
1
2
1
0
0
0
0
2
0
0
2
2
0
0
0
1
1
0
0
2
0
0
0
0
3
0
0
0
1
0
2
0
1
0
0
0
1
0
0
0
0
2
0
0
3
0
0
0
0
1
3
0
1
0
0
0
0
0
0
3
2
2
0
0
0
0
0
0
0
1
0
0
1
2
2
0
0
0
0
0
0
1
0
1
0
1
0
0
0
2
0
0
0
0
0
0
14
3
0
0
0
0
2
0
0
0
1
0
0
1
0
2
0
1
0
2
2
2
1
2
2
1
1
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
1
2
2
1
0
0
0
1
0
3
1
1
1
0
0
0
0
1
0
0
1
0
1
2
0
0
0
2
0
0
1
0
0
0
0
0
1
2
0
0
1
0
1
0
0
4
1
1
0
0
3
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
1
0
0
0
1
0
1
0
1
0
0
0
1
1
2
2
0
2
1
2
0
0
0
0
0
1
1
1
0
1
0
0
2
0
3
0
2
0
0
0
2
1
1
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
2
2
2
0
0
0
2
0
0
0
0
1
1
2
0
0
0
2
0
4
0
0
0
0
0
2
0
2
2
1
0
0
2
1
0
1
0
0
0
1
0
0
0
0
0
0
1
2
2
0
1
2
1
0
2
2
0
3
2
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
1
0
0
0
0
2
0
0
0
0
1
1
1
2
1
0
0
0
1
0
0
1
0
0
0
2
1
0
1
0
0
2
1
1
2
1
0
2
0
0
0
1
0
2
0
0
2
0
0
0
0
1
2
1
0
2
2
0
3
2
0
1
3
2
0
3
0
0
2
0
0
0
0
0
0
2
2
1
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
2
2
0
0
2
2
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
1
0
0
1
0
1
2
1
0
1
1
0
1
0
0
1
0
0
1
0
1
2
0
2
0
0
1
0
2
2
0
2
0
1
0
0
0
3
0
0
0
2
0
0
3
0
0
0
2
0
0
2
2
1
0
0
0
2
0
1
0
0
0
2
0
1
2
0
0
0
2
0
0
2
0
2
1
0
0
1
1
2
2
0
0
0
0
0
0
0
1
2
2
0
0
0
2
1
0
0
0
0
0
0
2
2
0
0
0
2
2
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
5
0
1
2
1
0
0
1
1
1
0
0
2
0
0
1
0
1
0
2
0
1
1
1
2
0
2
0
0
1
0
2
1
0
0
0
0
2
0
1
0
0
1
1
0
0
2
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
2
1
1
0
0
0
1
1
2
2
0
0
0
2
0
2
1
2
0
0
1
1
0
2
0
0
1
1
0
0
0
0
1
0
1
1
1
1
0
1
0
1
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
1
0
2
1
0
2
0
0
2
0
0
0
2
0
0
0
2
0
0
0
1
0
0
2
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
2
1
0
2
1
2
2
1
0
1
0
0
1
0
2
0
0
0
0
0
0
0
2
2
0
0
2
1
0
1
0
0
0
2
1
0
0
0
2
0
0
0
1
0
0
0
0
3
2
0
0
2
0
0
0
0
0
3
0
0
0
1
1
0
0
1
0
2
0
0
4
0
1
2
0
2
2
0
0
2
2
1
0
0
4
1
0
0
2
0
0
0
0
2
0
2
1
3
1
0
2
0
1
2
0
0
2
0
0
1
0
0
1
1
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
2
0
0
2
2
2
0
1
0
0
1
2
0
0
1
1
0
2
2
0
2
0
0
0
0
1
2
0
2
2
0
2
0
0
0
0
0
2
1
1
1
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
4
0
1
0
0
1
1
0
0
1
1
0
2
1
0
1
1
0
0
2
1
0
1
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
4
1
0
0
2
0
0
2
0
0
0
2
2
1
1
0
2
0
1
1
2
0
2
0
2
0
1
1
1
0
0
0
2
1
0
1
0
1
0
0
1
1
0
3
1
2
0
0
1
0
0
2
0
0
0
2
0
0
1
1
0
0
1
0
0
0
2
2
2
0
0
0
0
0
2
2
0
1
1
0
1
0
4
0
0
0
1
2
0
0
0
2
2
1
1
0
3
1
2
2
1
1
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
2
2
1
0
0
0
2
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
3
0
0
0
2
0
0
1
2
0
0
0
0
1
0
2
0
1
0
2
0
0
2
0
0
0
0
1
2
1
0
2
0
0
0
0
1
2
1
1
0
1
1
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
1
0
1
0
1
0
0
2
0
2
1
2
0
0
0
2
1
0
0
2
1
0
0
2
1
0
1
0
1
1
2
0
0
0
0
0
2
2
2
0
0
0
0
0
0
1
0
0
0
2
0
0
1
2
0
1
2
2
0
0
0
2
1
1
2
1
0
1
1
2
2
0
2
0
1
0
0
1
0
0
2
0
0
0
0
1
2
0
1
2
1
1
0
0
0
0
0
0
2
1
0
0
0
0
1
1
0
0
1
2
0
0
0
1
0
0
0
1
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
1
1
0
1
0
0
0
1
0
0
1
0
0
1
0
0
2
0
2
2
0
0
1
2
1
0
2
0
2
0
2
1
0
0
2
1
0
1
1
1
1
0
0
0
1
0
0
0
1
0
1
0
2
2
0
0
0
0
0
2
0
5
0
1
0
1
2
0
2
1
2
0
0
0
1
2
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
1
1
2
1
0
1
0
0
2
1
0
0
2
2
0
0
0
0
0
3
0
2
1
0
2
1
4
1
0
0
1
2
0
1
0
0
2
1
2
1
2
0
0
3
2
0
3
1
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
3
0
0
0
0
0
0
0
1
0
0
1
2
2
0
3
0
0
2
2
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
2
2
2
0
0
1
0
2
0
1
0
0
0
0
2
0
1
2
1
0
1
0
2
0
1
0
0
1
2
0
0
0
1
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
2
1
1
2
2
0
0
1
1
0
0
0
0
0
0
0
1
2
0
1
1
1
0
2
1
0
0
1
1
2
0
1
0
2
0
0
0
0
0
1
1
0
0
2
0
0
1
0
0
0
2
0
1
0
1
0
2
6
0
0
0
1
1
1
2
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
1
1
2
0
0
1
0
0
0
2
0
0
0
1
0
0
0
2
1
0
1
1
0
0
0
0
2
1
2
0
2
3
2
0
0
0
2
1
2
1
0
0
1
0
0
2
0
0
0
0
1
1
2
0
0
2
0
1
2
2
2
1
1
0
1
2
0
0
0
2
2
0
0
1
0
0
1
1
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
1
0
2
2
0
0
2
0
0
0
2
0
2
2
2
1
2
0
1
0
1
2
0
0
0
0
1
2
0
1
2
0
3
2
0
2
0
0
1
0
0
0
1
1
0
2
0
0
0
0
0
1
1
2
0
2
0
2
0
2
2
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
1
1
0
1
0
0
1
0
1
2
0
1
0
2
0
2
1
3
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
1
0
0
2
0
0
0
0
2
2
1
0
0
1
0
2
0
0
2
0
1
0
0
0
1
0
0
2
1
0
1
0
0
0
1
1
1
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
2
1
2
0
0
3
0
1
1
1
0
0
1
0
0
0
0
2
1
0
0
1
2
0
1
0
1
0
0
0
0
3
0
2
0
0
2
0
0
0
2
1
2
0
0
1
0
0
0
2
0
0
1
1
2
0
2
0
0
1
1
0
2
0
1
0
1
0
0
1
2
0
0
1
0
0
1
0
1
1
2
0
2
2
2
1
0
2
2
2
2
0
0
1
0
1
1
2
1
0
1
1
2
0
2
2
1
0
1
0
1
0
0
0
0
2
0
1
1
2
0
0
3
2
0
1
0
0
2
2
1
0
0
0
1
2
0
1
0
0
0
2
2
1
0
0
0
0
0
1
2
0
1
0
0
3
1
0
0
1
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
1
2
0
2
0
0
0
1
1
0
0
0
2
1
0
0
0
0
0
2
0
1
0
0
0
0
2
0
1
0
2
0
0
1
2
2
1
0
2
0
0
0
1
2
0
1
1
0
1
0
1
1
0
0
3
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
1
0
0
0
1
0
3
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
1
0
2
2
0
0
2
4
1
2
0
0
2
0
2
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
2
2
1
2
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
1
0
6
1
1
1
1
2
1
1
1
0
0
1
0
0
1
0
0
0
0
1
1
2
0
0
0
0
1
2
0
0
2
2
0
1
0
0
0
2
0
2
0
0
0
0
0
0
1
0
2
1
0
0
2
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
2
1
2
0
0
0
1
0
1
1
1
2
1
0
1
0
2
1
2
1
2
1
0
2
0
0
2
1
0
1
0
0
0
0
0
0
1
1
1
1
0
0
1
0
0
0
2
2
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
2
1
0
0
0
0
2
0
1
1
2
2
1
0
2
0
0
2
0
0
1
0
0
2
1
1
0
0
0
1
2
0
0
0
1
0
1
0
0
0
0
0
1
1
1
2
2
2
2
1
1
2
0
0
2
3
0
0
2
2
0
1
2
0
2
0
1
0
2
1
1
0
1
0
0
0
1
2
0
0
2
0
0
1
2
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
1
0
0
1
0
2
1
0
1
0
0
0
2
2
0
0
2
1
2
0
1
0
1
2
1
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
2
2
1
1
0
0
2
0
1
0
0
0
2
0
0
0
0
1
0
2
1
0
0
0
0
0
1
1
3
0
0
0
0
2
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
2
0
0
0
2
0
0
1
0
0
2
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
1
2
2
2
0
1
0
2
0
0
1
0
2
1
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
3
2
0
1
1
0
0
0
0
1
0
2
0
1
1
2
0
0
0
0
0
1
2
0
2
0
1
1
2
1
0
0
1
2
0
0
2
1
0
0
1
0
0
1
1
1
0
1
1
0
2
2
0
0
1
0
0
1
0
0
0
0
0
3
0
1
2
3
0
1
2
2
0
0
5
1
0
2
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
1
0
1
0
0
1
0
3
2
0
0
0
0
0
2
0
0
2
0
1
2
0
0
2
2
1
2
2
0
2
0
1
2
0
0
1
0
1
0
0
2
1
0
0
1
1
1
0
0
2
2
0
2
2
1
3
1
2
0
1
0
1
1
0
0
0
0
2
0
2
0
0
0
0
0
1
2
0
2
0
0
2
1
0
0
0
2
3
0
2
1
0
1
0
1
0
0
1
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
1
2
0
0
0
1
0
1
1
0
0
2
0
1
0
0
0
1
0
0
0
0
2
0
0
3
1
0
0
2
0
2
2
0
0
1
2
0
0
0
0
1
0
0
0
1
2
1
1
0
0
0
0
2
3
0
0
3
1
0
0
1
1
0
2
0
0
2
2
1
0
2
2
1
0
0
1
2
0
1
1
0
0
1
0
2
0
0
0
0
3
2
0
0
0
0
0
1
2
1
0
1
0
1
1
0
0
7
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
1
0
2
0
1
0
0
1
0
2
0
1
0
2
1
2
2
0
0
1
3
0
0
3
1
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
2
0
0
2
0
1
1
0
2
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
2
1
1
1
2
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
2
0
0
0
0
0
1
2
2
1
0
0
0
0
0
2
1
2
0
2
2
0
2
0
0
2
0
2
2
0
0
0
0
0
0
0
2
0
1
1
1
0
0
2
0
0
0
0
1
0
1
2
0
0
0
1
1
2
0
0
1
2
0
0
2
0
0
0
1
2
2
0
0
0
2
2
0
1
0
0
0
1
2
0
0
1
1
0
1
0
0
2
2
0
0
0
0
2
0
1
2
1
0
0
1
0
0
0
2
0
0
0
1
1
0
0
0
1
0
2
1
0
1
1
0
0
1
0
2
1
2
0
0
0
1
0
0
0
2
2
3
2
2
0
0
0
2
0
2
3
0
0
1
0
0
2
0
0
0
1
0
2
0
1
0
2
2
1
1
0
1
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
3
2
1
0
0
1
3
1
1
1
2
2
0
3
1
0
0
0
0
1
0
0
0
0
2
3
0
0
0
0
0
0
1
1
0
0
1
0
2
0
2
0
3
2
0
0
0
1
1
1
0
1
0
0
0
0
0
0
3
0
1
2
1
1
0
0
0
1
2
1
1
0
2
1
1
0
1
0
1
0
2
0
2
0
1
0
3
1
0
0
0
0
0
0
0
0
1
2
2
1
0
0
1
2
0
0
0
3
2
1
1
1
0
0
2
0
0
2
1
1
1
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
1
0
1
1
1
0
0
2
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
1
0
1
0
2
0
2
1
2
2
1
1
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
1
0
0
0
0
1
2
2
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
2
2
1
2
0
0
0
0
0
0
1
2
1
2
1
2
0
0
0
2
1
0
0
0
0
1
0
0
2
0
0
2
0
0
0
1
0
2
0
0
0
0
0
3
0
0
0
5
0
0
2
0
2
0
0
1
0
2
0
1
0
0
0
2
1
2
0
0
1
0
0
0
2
0
0
2
0
1
0
2
1
0
0
3
1
2
1
0
0
1
0
0
0
0
2
0
2
2
1
0
1
0
0
0
1
0
1
1
0
0
0
2
0
0
0
1
0
0
1
0
3
2
3
0
0
0
2
0
2
0
1
0
0
1
0
0
1
0
1
0
1
0
1
0
0
0
2
2
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
2
1
2
2
2
0
0
0
0
2
0
2
0
1
1
2
1
0
0
0
0
1
0
0
0
2
0
1
2
2
2
2
2
0
2
0
0
0
3
0
0
2
2
0
2
0
1
0
2
0
0
0
0
0
0
1
0
1
1
2
0
2
0
0
3
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
3
1
0
0
0
0
0
0
0
1
0
1
0
0
1
2
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
2
2
0
0
1
0
1
0
2
1
0
0
1
0
1
0
0
1
0
3
1
0
2
0
0
1
2
0
6
0
0
2
0
1
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
1
0
2
1
2
1
1
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
4
0
0
1
1
1
2
0
0
1
0
0
1
0
1
2
1
1
2
0
1
1
0
0
0
2
0
0
0
1
0
0
2
3
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
1
1
0
0
0
1
0
1
0
0
2
2
0
0
0
1
0
3
1
0
1
0
0
0
2
3
1
0
1
0
0
2
1
1
0
0
0
1
1
0
1
0
2
2
1
1
0
2
0
2
0
0
2
0
0
0
0
1
0
1
1
2
1
0
0
0
0
1
0
0
3
2
2
0
0
0
1
0
1
0
1
0
0
1
0
0
0
2
2
1
2
2
0
0
2
0
0
2
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
1
1
3
0
0
2
0
0
2
1
0
0
2
0
2
0
0
1
0
0
1
1
0
0
2
1
2
0
2
0
0
2
2
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
2
1
2
0
6
1
2
0
2
0
0
0
1
0
0
0
0
0
2
3
0
0
0
2
0
2
2
0
1
1
1
1
0
2
0
1
3
1
2
1
0
0
1
0
0
0
0
2
1
2
0
0
0
0
0
0
1
0
0
0
2
1
0
0
2
0
1
0
1
2
2
0
2
0
1
1
1
0
0
0
0
0
4
0
1
1
1
0
0
1
0
0
1
0
0
1
2
0
2
0
0
1
0
2
0
0
2
1
1
0
0
0
0
0
2
0
3
0
0
2
0
0
0
1
0
2
1
1
1
1
1
1
0
0
5
0
3
0
0
0
2
0
1
1
0
1
0
0
1
0
0
0
4
2
0
0
2
0
2
0
0
1
0
1
2
1
0
0
2
2
1
0
0
0
2
0
1
0
0
0
1
0
2
0
0
0
2
1
2
0
0
1
1
0
0
0
2
1
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
3
0
0
2
2
2
0
0
0
1
2
0
0
0
0
0
0
1
0
2
0
2
0
1
0
2
1
1
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
1
1
0
2
0
0
5
0
2
1
0
2
1
0
1
0
0
0
0
0
1
1
0
2
0
1
2
2
2
0
1
2
0
0
4
0
0
1
1
0
2
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
4
0
0
0
1
1
1
0
0
0
1
1
2
0
0
0
1
2
0
0
0
0
3
2
3
1
0
0
0
0
0
2
1
0
2
0
0
0
1
0
0
2
0
1
0
1
1
0
1
0
2
0
0
0
0
0
1
0
1
0
0
1
0
0
3
0
2
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
1
2
0
0
2
0
2
0
2
0
0
1
2
0
2
1
0
1
1
0
0
1
0
2
0
0
2
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
1
0
3
2
0
1
0
0
1
0
0
0
0
0
0
1
0
2
0
1
1
0
0
0
1
0
3
0
2
2
2
0
1
0
2
1
0
0
1
0
1
2
2
0
0
2
0
0
1
2
0
0
1
0
2
2
0
0
2
0
1
0
0
1
0
0
0
1
1
3
0
2
0
0
0
0
0
2
0
1
0
0
1
0
2
1
0
0
0
2
0
0
0
0
0
4
1
0
0
3
0
0
0
0
1
0
3
0
0
0
1
0
2
2
0
3
0
0
1
0
0
0
0
1
0
0
2
0
2
0
1
2
0
0
0
0
0
0
1
0
2
0
2
0
0
0
2
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
1
1
0
1
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
4
2
1
0
0
0
1
1
0
1
2
0
0
0
0
1
1
2
1
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
2
2
0
2
0
1
0
0
2
1
0
1
2
0
0
1
0
1
0
2
1
1
2
0
2
0
2
3
2
0
0
0
0
0
1
0
0
0
2
2
1
0
0
2
0
0
1
0
1
2
0
1
0
0
0
1
1
2
1
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
3
2
0
1
0
0
0
0
0
0
0
0
1
1
2
0
0
0
1
0
0
0
2
2
0
0
0
0
2
1
0
2
6
2
0
0
2
0
1
1
0
0
2
3
0
2
0
2
5
0
1
0
2
2
0
0
1
0
0
0
1
1
2
0
1
2
1
0
0
2
0
0
0
1
2
0
0
0
0
0
2
2
0
2
1
0
0
0
0
1
2
0
0
0
3
0
1
1
1
0
1
0
0
1
0
2
2
0
2
4
1
1
4
2
0
0
0
2
0
0
1
1
0
0
2
1
1
0
0
0
0
0
0
0
0
2
0
2
1
0
1
0
0
2
0
0
1
0
1
1
1
0
1
1
2
1
0
1
0
2
0
2
1
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
1
8
2
0
2
0
1
0
1
0
0
2
0
1
0
0
0
2
1
0
2
2
0
3
1
1
2
0
2
0
0
0
0
1
2
2
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
2
1
0
2
0
1
0
1
3
0
0
0
0
2
0
1
2
1
0
0
0
1
0
0
0
0
1
1
0
2
0
2
1
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
2
0
0
0
0
2
0
2
1
0
0
0
1
0
0
0
0
0
0
0
3
0
1
0
1
0
1
1
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
2
2
1
2
1
0
1
1
0
1
0
1
2
1
1
2
1
0
0
0
0
0
0
0
0
0
1
1
2
0
1
0
1
0
0
1
0
0
1
0
2
2
2
0
4
0
0
2
0
0
0
0
0
1
0
0
2
0
0
3
2
2
0
0
2
0
0
0
0
0
0
2
2
0
1
0
1
0
2
0
0
1
0
0
1
0
1
1
0
2
0
0
2
3
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
2
0
2
0
1
2
0
2
0
0
0
0
0
0
0
0
4
2
0
0
1
0
1
0
0
3
0
0
0
0
1
2
2
0
0
0
0
0
0
2
1
0
2
0
0
1
1
0
1
1
0
2
0
2
2
0
0
0
0
0
2
2
0
0
0
2
1
0
2
1
1
0
0
0
0
1
0
0
0
2
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
2
1
1
1
1
0
2
0
0
0
1
0
2
2
0
0
0
0
1
0
0
0
0
2
0
3
2
0
0
0
0
0
2
0
0
0
0
1
2
1
0
0
0
0
0
0
1
0
0
2
0
0
1
2
0
2
0
1
0
0
2
1
2
1
0
0
0
2
2
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
1
1
1
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
1
1
0
0
2
0
0
0
0
2
0
3
0
0
2
0
3
0
0
0
2
0
2
0
0
2
0
1
2
0
0
0
0
0
1
0
0
1
2
0
3
0
0
0
1
0
0
0
1
0
0
2
0
0
2
0
0
2
0
1
0
0
1
0
1
2
0
0
2
2
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
2
1
0
2
0
0
0
0
2
2
0
2
0
1
0
2
0
0
0
0
1
0
2
1
0
2
0
1
0
1
0
0
0
0
0
1
2
0
1
0
0
0
0
0
3
0
0
0
0
0
0
1
1
2
1
1
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
2
1
0
0
1
1
0
0
2
1
1
0
1
0
0
0
0
1
1
2
0
1
0
2
0
2
1
0
0
0
1
3
1
0
0
0
0
2
0
1
2
0
0
1
0
1
1
1
2
2
0
2
2
1
2
0
0
1
2
0
1
0
1
0
2
0
1
2
2
0
2
0
2
2
0
0
1
0
0
3
0
1
0
2
1
0
0
1
1
0
2
0
1
0
0
2
1
2
0
1
0
0
0
0
0
0
0
2
1
1
2
0
2
2
3
0
0
2
0
2
0
2
0
1
0
1
0
2
0
1
2
0
0
0
0
1
2
0
2
0
1
0
0
0
0
2
0
2
2
1
0
0
2
1
0
0
2
0
0
0
0
0
2
0
0
2
2
2
0
0
1
1
1
2
1
0
0
2
2
1
1
0
2
2
1
0
1
0
1
0
1
0
4
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
3
0
0
2
1
2
0
1
0
0
1
2
0
0
0
0
1
2
0
0
0
0
2
0
1
2
0
0
0
1
1
0
1
0
1
0
0
1
1
0
2
0
1
0
2
0
0
2
0
1
0
2
0
0
1
0
5
3
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
1
0
2
0
0
0
0
0
2
2
1
0
0
0
2
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
2
1
0
1
0
0
1
1
1
0
2
0
0
0
0
1
2
2
2
0
0
0
1
1
2
0
2
0
1
2
0
0
0
0
0
1
1
2
1
1
0
2
0
0
1
2
0
0
0
1
0
0
0
2
0
0
1
0
0
2
1
0
0
0
0
2
2
0
0
1
0
0
0
1
0
2
1
0
0
2
0
1
1
2
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
2
1
0
2
1
0
2
0
0
1
2
2
0
1
0
1
1
0
0
0
0
0
0
1
0
1
0
2
2
2
0
0
0
0
2
1
2
0
1
1
0
2
2
2
0
0
1
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
2
2
0
0
0
0
2
1
1
2
0
2
0
1
0
2
0
1
1
1
2
2
0
0
0
2
1
0
0
0
0
2
0
1
0
2
0
0
0
0
3
0
1
0
0
0
2
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
2
1
2
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
1
4
0
1
2
2
0
1
0
1
4
2
0
1
0
0
2
1
0
0
0
1
2
0
0
2
2
0
2
0
0
0
0
0
0
1
1
2
2
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
2
0
0
2
1
1
0
0
0
0
2
0
2
3
2
0
1
0
0
0
0
3
0
0
1
1
0
1
0
0
2
1
0
0
0
2
0
0
1
0
0
0
2
0
0
0
1
0
1
0
0
2
0
1
0
0
0
2
0
2
2
0
0
1
0
2
1
0
0
0
0
2
0
0
0
1
0
1
0
2
2
0
0
0
0
0
0
0
2
1
0
0
2
0
0
2
0
0
1
1
0
2
2
2
3
0
1
0
0
1
1
0
1
0
0
0
0
1
2
1
0
2
1
0
2
0
0
0
1
0
2
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
1
2
2
0
2
2
1
0
0
3
0
0
0
1
1
1
0
0
0
0
0
0
3
0
0
0
1
0
0
2
2
0
0
2
2
0
1
2
0
0
1
0
0
0
0
1
1
2
2
1
0
0
0
2
0
0
1
0
0
0
2
0
0
0
1
0
2
0
2
3
4
0
2
0
0
2
0
1
3
1
2
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
2
0
0
1
2
0
0
0
1
0
0
1
2
0
2
0
0
1
2
2
2
2
0
0
2
0
2
1
1
0
0
0
2
0
1
1
0
0
1
2
0
0
2
0
2
0
0
2
0
0
0
0
0
1
1
1
0
2
0
0
2
1
0
1
0
0
1
2
0
0
0
0
0
0
1
3
0
0
2
2
1
2
0
1
0
1
1
0
1
0
0
0
0
2
0
0
3
0
1
1
0
0
0
1
0
1
0
0
1
0
0
1
0
2
0
1
2
2
1
2
0
1
0
1
0
0
0
1
1
0
1
2
0
2
0
1
0
0
0
1
0
1
2
0
3
0
0
0
1
1
0
1
0
1
0
1
0
2
0
2
2
0
7
1
0
0
0
2
0
2
2
0
1
2
0
0
0
0
2
1
0
0
1
0
2
2
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
1
1
2
0
0
1
0
2
2
2
2
0
1
0
1
0
2
1
0
1
0
0
3
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
2
0
2
1
1
2
0
0
2
2
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
9
0
0
5
0
1
0
2
1
0
1
1
0
2
0
0
0
0
0
0
0
0
1
1
0
1
0
1
1
1
1
2
0
0
0
2
1
0
1
0
1
2
0
0
2
0
0
1
0
1
1
1
0
0
0
0
0
2
3
1
1
0
3
0
1
0
0
0
0
1
0
2
2
0
2
0
0
0
0
2
1
2
2
0
1
0
2
0
0
0
1
3
0
0
0
0
0
1
2
2
0
1
0
2
0
1
0
0
2
0
2
1
2
0
2
2
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
1
0
2
0
0
1
0
0
1
1
0
2
0
0
0
0
1
1
2
1
0
2
0
1
1
2
1
0
0
1
0
0
1
0
3
1
0
0
1
0
2
0
0
0
0
1
2
1
0
0
2
0
0
0
0
0
0
0
1
0
2
0
3
0
0
1
0
1
0
1
0
1
2
0
2
1
0
0
0
0
0
0
0
1
0
0
0
2
0
7
0
0
0
0
1
0
1
2
0
0
0
0
1
0
0
0
0
1
0
1
1
1
3
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
3
0
0
2
0
0
2
0
1
1
1
0
1
0
0
2
0
0
3
2
0
0
0
0
0
0
0
1
7
1
1
0
1
1
1
1
0
1
0
0
0
0
2
0
0
0
2
2
1
0
0
0
2
0
0
0
0
1
1
2
0
2
0
1
0
2
0
1
2
0
2
0
0
2
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
2
0
0
0
2
0
0
1
0
1
0
2
2
2
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
2
2
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
1
0
2
1
0
2
0
1
0
2
2
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
1
1
1
1
0
0
1
0
4
0
2
2
0
1
0
2
2
0
2
0
2
0
0
3
0
0
0
1
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
2
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
2
0
0
0
2
1
0
0
1
0
1
0
1
0
0
1
0
0
0
0
1
1
0
0
3
1
0
0
0
0
0
0
0
2
4
1
1
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
5
3
0
1
1
0
2
1
0
0
0
0
0
0
0
1
0
1
2
1
0
2
0
0
1
0
1
1
0
0
0
0
0
1
0
0
2
1
2
1
2
1
0
0
0
0
0
0
2
0
0
1
0
0
0
2
2
0
1
0
0
0
0
0
0
0
1
1
2
0
2
2
3
1
0
0
0
0
1
2
0
2
0
2
1
2
1
2
0
0
0
2
0
0
1
2
3
0
2
0
1
0
0
0
0
0
0
0
1
3
0
0
2
0
0
0
1
0
0
2
0
0
1
0
1
0
0
0
1
0
2
0
0
1
0
0
0
0
1
1
2
0
0
0
4
2
0
2
0
0
0
0
0
0
2
0
0
0
3
0
1
0
0
0
0
0
0
1
1
1
2
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
2
3
0
0
0
0
1
0
2
0
0
1
1
2
0
2
0
1
1
0
2
1
2
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
2
0
1
2
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
1
2
0
2
2
1
2
0
1
0
0
0
2
0
1
0
3
0
1
2
1
0
0
5
0
0
2
2
1
0
0
2
0
0
0
0
0
0
0
2
0
0
3
0
1
0
0
0
1
0
1
2
1
0
2
0
1
0
0
1
1
1
0
0
0
0
0
0
0
1
1
1
1
0
2
0
1
0
0
0
0
1
0
0
2
0
2
2
0
0
0
2
0
1
1
0
2
1
0
2
7
0
0
1
1
2
1
0
3
1
1
1
0
0
0
1
2
0
0
0
0
0
2
0
1
2
0
0
2
1
2
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
2
0
0
2
0
1
3
0
0
0
1
0
1
1
0
0
5
1
0
0
0
0
0
0
0
0
0
1
0
0
2
3
4
2
0
0
0
0
2
1
0
0
0
0
0
2
0
0
2
0
0
0
2
2
0
1
0
2
1
0
0
0
0
1
0
0
2
2
0
0
0
2
0
0
0
4
6
0
1
0
0
0
1
0
0
2
0
0
0
0
0
1
2
0
0
1
0
3
0
1
0
0
1
2
0
0
0
1
0
0
3
0
0
0
0
2
0
0
2
1
0
0
0
2
2
2
0
1
0
1
0
1
1
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
2
0
1
1
0
0
0
0
2
0
1
1
0
1
0
0
0
0
0
0
0
0
1
2
1
0
2
2
0
1
1
0
2
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
2
2
0
1
1
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
1
1
1
0
0
0
0
1
2
0
1
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
1
0
1
1
1
0
0
0
0
0
2
0
0
1
0
0
1
1
1
0
1
2
0
0
0
1
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
2
0
0
2
0
0
2
0
3
0
2
1
0
0
3
0
2
0
2
0
3
0
2
1
0
0
0
0
0
0
0
1
0
1
1
1
1
1
3
1
0
2
0
0
0
0
1
0
1
2
0
0
0
0
1
0
0
0
2
2
0
0
1
0
2
0
1
2
2
0
2
0
1
2
0
0
0
0
0
2
0
2
0
0
0
2
1
2
0
2
0
0
0
2
0
0
1
0
0
0
0
2
2
0
0
1
2
0
2
0
0
0
2
1
1
0
1
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
1
2
1
0
2
0
0
0
0
0
2
0
2
0
0
2
0
0
2
1
0
1
1
1
2
0
0
0
0
2
1
0
0
0
0
0
0
2
2
2
0
0
1
1
2
2
0
0
1
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
1
0
1
2
0
0
0
0
0
2
0
0
2
1
0
2
0
1
0
2
1
1
0
2
0
0
2
0
0
0
0
0
1
0
0
0
1
1
1
1
0
2
0
0
2
0
0
0
0
0
0
2
0
1
0
1
1
0
0
0
2
0
0
1
0
3
0
1
0
0
1
1
2
0
1
0
1
1
2
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
2
0
0
0
1
1
0
0
3
2
0
2
0
0
2
1
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
2
0
2
0
0
0
2
0
2
0
0
0
5
0
1
2
0
1
0
0
1
1
0
0
2
2
1
0
2
0
2
2
0
0
0
2
2
0
0
0
1
0
1
0
2
2
0
0
0
2
2
0
1
0
0
1
0
0
0
0
0
2
0
1
0
1
0
0
1
1
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
2
0
2
0
1
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
1
0
0
0
2
0
1
0
1
0
1
0
0
0
0
1
0
2
1
0
0
0
2
2
2
0
0
1
1
0
1
0
3
2
0
0
0
1
0
1
0
0
0
0
1
1
1
2
0
0
0
0
0
2
0
0
0
2
0
0
2
2
3
0
0
4
0
0
1
0
4
0
2
0
0
0
0
2
2
0
1
0
2
0
0
1
0
0
0
0
1
1
0
1
2
0
4
1
0
0
1
0
1
1
2
3
0
1
0
0
1
1
1
2
0
0
1
0
2
0
1
1
1
0
2
0
1
0
0
0
0
1
0
0
0
1
0
2
1
0
0
0
2
0
2
1
0
2
0
1
0
0
0
3
0
1
0
0
1
2
0
0
2
0
0
0
0
0
0
2
1
0
2
0
0
0
1
0
3
0
0
0
0
0
0
2
0
0
1
1
0
0
0
1
0
0
0
2
0
0
0
0
1
0
2
1
0
1
0
0
0
1
1
0
0
0
0
0
1
1
0
2
0
4
2
1
0
0
1
0
0
0
1
0
0
3
1
1
1
1
0
0
1
0
0
0
0
1
2
1
0
1
0
0
0
0
0
1
0
0
1
0
4
0
0
0
0
0
0
2
3
0
0
2
0
0
0
2
0
2
4
5
1
2
0
4
0
1
1
2
3
4
2
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
1
0
3
0
0
2
2
3
0
0
0
0
0
2
1
1
2
0
0
0
1
1
0
1
0
0
1
2
2
0
0
0
1
1
2
0
0
0
1
0
2
2
2
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
3
0
1
2
1
1
2
3
0
0
1
1
2
0
0
0
0
1
0
1
1
1
0
1
0
0
0
1
0
1
1
0
1
2
0
0
2
0
2
3
2
0
1
0
0
1
0
0
0
0
1
1
0
1
1
2
0
2
0
1
0
0
0
0
0
2
0
0
1
0
0
1
0
1
1
0
0
0
0
0
2
0
0
2
1
0
0
1
2
0
1
2
0
1
1
2
0
0
2
2
1
0
3
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
2
0
0
2
1
0
2
1
0
0
3
2
0
0
0
1
0
1
0
2
1
2
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
2
0
1
0
0
2
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
2
1
1
1
0
0
0
0
2
1
0
0
0
1
0
0
0
0
1
1
0
1
0
0
1
1
0
0
0
2
1
2
0
0
0
1
0
1
2
0
2
1
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
3
0
1
2
1
0
2
0
1
0
2
0
0
2
0
1
0
0
0
1
0
1
0
2
2
5
0
0
0
2
2
2
3
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
2
0
1
0
1
1
1
2
2
0
0
0
1
1
0
0
0
0
0
0
3
0
0
1
0
12
0
0
0
0
0
0
0
2
1
0
1
1
2
0
0
0
0
0
2
0
0
0
2
0
0
1
0
4
0
0
1
0
1
2
0
0
1
0
1
0
0
1
1
0
3
0
0
2
0
2
0
4
0
4
1
1
0
0
0
0
0
0
2
0
1
2
2
0
0
2
1
0
0
1
0
0
0
4
2
0
3
2
0
0
0
1
0
0
2
1
1
0
2
0
0
2
0
0
0
1
3
0
2
0
0
1
0
0
2
0
0
0
0
1
0
1
2
2
2
1
1
0
1
0
1
1
0
2
1
1
1
0
2
0
2
0
0
0
0
2
0
2
0
0
1
2
0
5
2
0
2
0
2
1
0
0
0
2
0
1
2
2
2
3
1
0
0
0
0
0
0
2
0
2
1
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
1
0
0
2
0
2
0
2
2
0
1
0
0
1
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
1
1
0
1
0
0
0
0
0
0
1
2
0
2
0
0
0
2
0
2
1
0
1
3
0
0
2
0
0
1
1
0
2
0
3
0
1
0
2
0
1
1
0
0
0
1
0
1
0
0
0
1
0
0
2
0
2
0
0
1
2
0
0
2
0
0
0
1
1
0
3
1
0
0
0
2
0
0
2
2
0
0
0
1
0
1
0
1
0
1
1
0
0
0
2
0
0
0
1
2
0
2
0
0
0
0
2
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
1
0
2
0
0
2
0
1
0
1
2
0
0
0
0
0
1
1
1
0
0
0
2
0
2
1
0
0
0
0
0
1
1
1
1
1
0
0
2
0
1
0
1
0
2
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
2
0
0
2
2
0
0
0
0
2
2
1
0
3
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
1
0
0
0
2
0
1
0
1
0
0
1
2
0
0
1
0
3
0
0
0
0
3
0
0
1
0
2
1
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
1
0
0
0
1
1
2
2
2
0
1
0
1
0
0
2
0
0
2
2
0
0
1
1
0
0
1
3
2
0
0
0
1
1
2
1
0
2
0
1
0
1
0
0
0
1
2
0
2
0
1
1
0
0
0
2
2
0
2
0
1
1
1
0
2
0
0
0
0
0
2
0
1
0
0
0
1
2
0
0
0
0
1
2
0
1
0
1
0
0
0
1
2
2
0
0
0
1
2
0
0
0
0
2
0
2
0
2
0
1
1
0
0
0
0
1
0
1
0
0
0
1
1
1
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
2
2
1
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
1
2
0
0
0
0
0
1
0
1
2
0
2
1
0
0
4
2
1
0
2
1
0
0
0
0
2
0
2
0
0
0
1
0
2
1
0
0
0
0
2
0
0
0
1
1
0
0
1
1
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
1
0
2
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
4
0
1
3
1
0
0
2
1
0
2
0
0
0
0
0
2
1
0
2
0
2
0
0
0
2
0
1
1
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
1
0
1
2
1
0
3
1
0
2
0
0
0
0
1
1
0
0
1
0
2
0
2
0
0
0
2
2
2
0
0
0
0
0
0
0
2
0
0
2
0
1
0
1
0
0
0
0
0
2
0
0
0
1
1
0
1
2
2
1
0
1
0
0
2
0
2
1
0
1
1
1
2
1
2
0
2
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
1
1
0
2
0
0
1
0
2
0
1
2
1
2
1
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
2
1
0
2
1
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
1
0
0
2
1
0
0
0
2
2
2
0
2
0
0
0
0
0
0
2
0
0
1
0
0
1
1
0
0
2
0
0
2
0
0
2
0
0
0
0
2
0
1
0
0
0
2
0
0
1
1
3
3
0
0
1
0
1
0
0
2
0
0
0
1
0
2
2
2
0
2
0
0
0
0
1
0
0
0
0
2
0
1
1
1
2
0
2
0
0
0
1
1
2
0
1
1
1
1
2
0
0
1
0
0
2
0
0
2
1
0
2
0
2
1
0
0
0
2
0
0
2
0
2
2
0
0
0
2
0
0
1
1
0
3
2
0
3
1
2
2
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
2
0
0
0
0
0
0
2
0
1
0
0
0
5
2
1
1
0
0
0
2
1
1
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
2
0
1
0
0
0
0
0
1
0
5
2
0
0
0
1
1
0
0
2
0
0
2
1
2
1
0
2
2
0
1
0
2
2
2
2
0
2
0
2
0
1
2
0
1
0
2
0
2
0
1
2
1
1
0
1
0
0
0
10
0
0
0
2
0
0
0
1
0
0
1
0
2
0
2
0
2
1
0
0
0
0
3
0
0
2
0
0
0
0
2
1
2
0
0
0
2
1
0
1
0
0
1
0
0
1
0
0
1
0
0
0
2
1
0
0
2
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
2
1
0
3
2
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
1
0
1
1
0
0
1
2
0
1
2
0
1
0
0
0
0
0
0
0
2
1
0
1
0
0
1
2
0
0
2
0
0
2
0
2
2
0
0
0
0
1
0
0
1
1
1
0
2
0
0
0
2
1
0
0
0
0
1
0
1
0
1
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
2
0
2
0
2
1
1
0
0
0
2
2
0
1
0
0
1
2
0
1
1
0
0
2
1
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
2
0
1
2
0
0
0
0
0
1
2
2
0
1
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
2
0
1
0
0
0
0
0
1
2
2
2
0
0
0
0
0
2
2
2
2
0
1
0
0
0
1
8
0
1
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
2
1
0
0
0
0
0
2
2
0
2
1
0
0
0
0
1
0
0
1
2
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
2
0
2
1
1
1
0
1
2
0
0
0
0
2
1
2
2
0
0
0
0
0
2
1
2
0
1
1
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
2
0
0
2
2
2
1
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
2
0
2
0
2
0
0
0
0
0
0
2
0
0
2
2
0
0
2
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
2
1
1
0
0
0
2
1
1
0
1
0
1
0
2
0
0
0
0
1
0
0
0
2
0
1
0
1
0
1
2
0
1
0
0
0
0
0
3
1
0
0
0
1
2
0
2
0
0
0
1
0
2
0
0
0
1
0
1
0
0
1
0
0
0
0
2
0
0
2
2
0
0
2
0
0
0
2
0
1
2
0
0
1
0
0
2
2
1
0
1
4
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
1
0
2
1
1
0
2
5
1
2
2
1
0
0
0
0
0
1
0
1
1
0
2
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
2
0
2
1
1
1
0
2
1
1
0
0
0
0
1
0
1
0
1
2
0
2
2
1
0
1
0
0
2
2
0
2
2
1
0
1
0
1
0
1
0
2
0
1
0
4
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
2
0
2
0
0
0
0
2
1
1
0
0
0
0
0
0
1
0
0
2
0
2
2
0
0
0
1
0
2
0
1
0
0
1
0
2
2
0
0
0
3
0
0
0
1
0
0
0
0
2
1
0
0
0
0
1
2
2
0
2
1
1
0
1
0
0
0
1
0
0
2
0
2
0
1
2
0
0
0
0
1
2
0
0
0
1
0
0
0
1
0
2
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
1
0
2
0
0
0
0
2
4
1
0
2
1
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
1
3
0
0
0
0
1
2
0
0
1
0
0
0
0
2
1
2
2
1
0
1
2
2
3
0
1
0
0
1
1
1
1
0
0
2
0
0
0
0
0
1
1
0
0
1
0
1
2
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
2
2
1
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
1
0
2
0
2
0
0
0
1
1
2
0
0
0
1
2
0
1
0
0
0
0
0
0
0
2
2
0
0
2
2
0
2
2
0
1
0
0
0
0
0
0
2
2
0
0
0
1
0
2
0
1
1
0
1
2
1
1
1
0
2
3
0
3
2
0
0
2
1
2
0
5
0
0
0
0
1
1
0
1
0
1
0
0
1
0
0
1
2
2
0
1
0
0
1
2
2
1
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
2
0
1
0
0
0
0
1
2
0
0
0
1
2
2
1
0
0
0
0
0
0
1
2
0
0
2
0
3
2
0
2
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
1
1
0
0
0
0
0
0
0
2
0
1
0
1
0
1
2
1
1
0
0
0
0
0
0
2
0
0
0
0
3
0
2
0
1
0
0
3
2
0
0
2
2
0
0
1
2
0
2
0
2
2
2
0
0
0
1
2
0
1
0
0
1
0
1
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
1
2
0
0
1
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
1
0
0
0
2
0
0
2
0
0
0
1
0
0
2
2
2
0
2
1
0
0
0
0
0
0
0
0
0
1
1
1
2
0
1
1
0
2
0
2
0
0
0
1
0
0
2
2
1
0
0
1
0
1
0
2
1
0
0
1
1
1
0
0
0
0
1
0
1
0
1
2
0
0
0
0
2
1
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
1
2
2
0
0
0
0
0
0
0
1
0
0
0
2
2
1
0
1
0
0
0
0
0
1
1
0
0
1
0
2
0
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
2
2
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
4
1
1
0
1
0
0
0
1
0
1
0
2
1
0
0
0
0
0
0
0
0
0
1
2
2
2
0
2
0
0
0
3
1
1
0
0
0
1
0
1
0
1
0
2
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
2
2
1
0
0
0
0
2
0
2
0
2
2
0
0
0
0
0
0
2
0
3
1
0
0
2
2
3
0
1
1
0
0
0
0
0
0
0
1
2
0
0
0
0
1
2
0
2
0
0
2
2
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
1
0
1
0
1
2
1
0
0
2
1
0
1
0
2
2
2
0
1
0
0
0
1
1
0
0
1
1
2
0
0
0
1
0
1
0
0
2
1
0
2
2
1
0
1
2
1
2
1
0
0
2
0
0
1
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
2
2
0
3
0
0
0
2
1
0
0
0
0
1
0
4
1
1
0
1
2
0
0
0
0
2
2
0
0
1
1
0
0
2
0
1
0
1
1
2
4
0
0
0
0
1
0
0
2
2
0
1
2
0
0
2
0
0
0
0
0
0
1
0
0
2
2
2
2
1
1
0
0
1
1
1
1
2
0
0
0
2
0
2
1
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
1
2
0
0
1
0
0
0
0
0
1
2
2
0
0
0
0
1
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
2
0
0
0
4
1
2
0
1
2
2
0
2
1
0
0
0
2
1
0
0
3
0
0
0
2
0
0
0
2
0
0
1
1
1
1
0
0
2
0
0
0
0
1
0
0
2
1
1
1
0
2
0
1
0
0
4
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
2
2
0
0
1
1
0
0
0
0
1
0
0
2
2
1
0
0
2
1
0
0
0
0
1
1
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
2
1
2
2
2
0
2
0
1
0
1
0
0
0
2
1
0
0
0
0
0
1
0
3
0
1
3
0
2
2
0
0
0
2
4
1
0
0
1
0
2
2
1
2
0
0
2
2
0
2
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
2
0
0
1
0
0
2
0
0
3
3
0
1
0
0
0
2
1
0
0
0
0
0
1
2
0
0
1
2
2
0
0
0
1
1
0
2
0
2
1
2
0
2
0
1
0
1
0
2
1
0
0
1
2
1
0
0
2
0
0
1
2
2
1
0
0
2
0
0
0
2
0
0
1
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
2
1
0
0
0
0
2
2
2
1
0
0
0
0
0
1
0
3
0
0
1
0
2
0
0
2
1
0
0
0
0
0
0
0
0
1
0
2
3
2
0
0
0
0
0
0
0
7
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
2
0
0
1
2
0
0
1
1
0
2
2
1
0
0
0
0
0
0
1
1
0
0
0
0
1
1
2
0
2
1
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
2
0
0
0
0
3
0
1
0
0
1
0
0
0
1
2
1
0
0
0
1
0
0
0
0
2
0
2
3
0
0
1
0
1
1
0
0
0
0
1
2
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
2
1
0
2
3
2
0
0
0
2
0
0
4
1
0
0
0
0
1
2
0
0
1
2
0
0
0
0
0
0
0
2
1
1
0
1
0
1
0
1
2
0
1
1
2
1
0
0
0
1
0
2
2
0
0
2
2
2
1
1
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
2
2
1
1
3
0
0
2
0
2
1
0
2
2
2
0
0
1
0
0
2
0
0
1
2
1
0
0
0
2
2
1
2
0
1
3
0
0
0
2
1
1
0
1
1
1
0
0
0
2
0
1
2
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
4
0
1
2
0
0
0
0
2
1
0
0
1
0
0
1
0
0
1
0
1
0
0
1
1
0
1
1
0
0
0
0
0
3
0
0
0
0
2
1
0
0
0
2
0
2
0
2
0
0
0
1
0
1
0
1
1
0
0
1
0
0
2
0
0
1
0
1
0
2
0
0
0
0
0
1
0
2
1
0
0
1
0
0
1
0
0
0
2
0
0
0
0
1
0
0
3
4
0
0
0
0
0
0
0
1
0
1
1
0
0
1
2
0
2
1
0
0
0
2
0
0
1
0
0
2
1
0
1
1
2
0
0
1
2
2
0
0
0
0
2
0
0
1
0
0
1
1
2
2
0
2
0
0
2
0
2
0
0
2
0
1
1
2
2
0
3
0
0
2
0
1
1
0
0
1
1
0
1
0
1
0
0
2
1
1
0
0
0
2
0
1
0
0
0
1
0
0
0
0
3
1
0
0
0
3
1
1
0
1
0
1
0
1
0
1
1
0
0
0
0
0
1
0
2
0
0
0
2
2
0
1
0
0
0
0
0
1
1
0
0
1
1
0
0
0
2
0
0
0
1
0
1
1
0
1
2
0
0
2
1
0
0
1
2
2
0
3
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
2
2
0
1
2
0
2
0
2
1
1
3
0
0
1
2
1
0
0
0
0
1
0
2
0
0
2
1
1
0
0
0
0
2
0
0
0
2
2
0
2
1
0
1
2
0
0
0
2
1
0
0
0
2
2
0
1
1
1
0
2
2
0
0
0
0
1
1
0
0
1
0
1
0
2
1
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
1
0
1
0
2
0
0
0
2
2
0
0
0
2
0
2
1
1
0
0
0
0
1
0
0
2
0
2
0
0
2
0
0
1
1
1
1
1
0
1
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
2
1
0
1
0
3
0
1
1
0
1
0
0
0
2
0
5
2
0
2
2
2
2
0
0
1
1
0
0
0
0
0
0
2
1
2
0
0
1
0
2
0
0
0
0
0
2
1
1
2
0
1
0
2
0
0
0
2
0
2
0
1
0
1
0
0
0
1
0
0
0
0
0
1
1
2
1
2
1
1
0
0
0
0
0
1
0
1
0
0
0
2
0
0
1
2
0
0
0
2
1
0
0
0
1
0
0
3
0
0
0
1
0
1
0
0
1
0
0
2
1
0
1
0
0
2
0
0
1
0
0
0
2
0
1
1
2
0
1
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
1
0
0
1
0
1
1
2
0
0
0
0
2
1
0
2
0
0
1
0
2
2
2
0
0
2
3
0
0
0
2
0
1
0
1
0
2
0
0
0
0
0
1
0
0
2
1
0
2
0
0
1
0
0
0
1
2
1
1
1
2
0
2
2
0
2
0
0
2
3
0
0
0
1
2
0
2
0
0
0
1
0
0
3
0
1
2
1
1
0
0
1
2
0
0
0
2
0
2
0
0
1
1
1
2
2
0
0
0
0
0
2
0
0
2
0
1
1
0
0
0
0
1
0
0
0
2
0
1
0
0
2
4
0
0
0
0
0
0
1
0
0
1
4
1
0
0
0
0
0
0
0
0
1
0
2
0
0
2
1
2
0
0
0
0
0
0
0
0
2
0
0
2
0
1
2
2
0
1
0
1
2
0
1
0
2
0
1
0
1
1
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
1
1
2
0
0
1
1
6
0
3
0
2
0
0
1
2
0
0
0
1
1
0
0
1
2
1
1
0
1
1
2
2
0
2
0
0
2
0
1
0
0
0
0
1
1
2
1
2
0
1
0
1
0
0
2
0
2
0
1
1
1
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
1
0
1
0
5
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
4
0
0
0
0
1
0
1
0
0
1
0
2
1
2
2
0
2
2
0
0
2
2
2
1
0
2
2
1
1
2
0
0
0
1
0
0
0
1
0
3
0
0
0
0
2
0
0
0
1
0
0
2
3
2
0
1
1
2
0
0
0
1
2
1
0
0
0
0
0
0
0
1
1
2
1
2
0
0
0
1
0
1
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
1
2
1
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
2
0
2
3
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
1
1
0
0
0
1
1
0
1
0
0
0
1
1
0
0
0
1
0
0
0
2
3
1
2
1
1
0
0
0
0
0
2
1
0
2
0
0
1
2
0
0
3
0
0
0
1
0
0
0
1
0
0
0
2
0
0
2
0
2
0
3
1
2
2
0
0
1
0
1
2
0
1
0
3
2
2
0
0
0
2
0
0
1
0
0
0
2
1
2
2
1
0
1
2
0
0
0
2
0
0
0
0
0
1
2
0
2
0
0
0
0
0
1
0
0
2
0
2
0
1
0
0
1
2
1
2
0
0
2
4
2
0
1
0
1
0
2
0
0
0
0
0
1
1
0
0
1
0
3
0
0
1
5
0
0
1
0
0
1
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
1
0
2
2
1
0
3
2
1
1
0
0
1
1
2
0
2
0
2
0
1
1
0
0
2
2
1
0
1
0
0
0
0
4
1
0
4
2
2
2
0
1
0
0
0
0
1
3
2
0
2
0
2
0
2
1
2
1
0
0
1
0
2
0
0
2
1
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
1
0
1
0
0
4
0
1
0
0
2
0
1
1
1
0
0
1
0
0
0
0
0
1
1
0
2
0
2
0
1
1
0
2
0
2
0
1
0
0
0
1
0
2
0
0
0
2
0
1
1
1
0
1
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
1
1
1
1
7
0
1
1
0
1
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
1
0
0
0
2
1
1
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
2
1
1
2
1
0
1
1
2
2
0
1
2
1
0
3
1
0
2
0
0
1
1
1
0
0
0
2
1
0
1
2
0
1
2
2
2
0
2
1
0
0
2
2
0
0
2
1
0
0
0
0
3
2
0
1
0
0
1
1
1
1
1
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
1
2
2
2
0
2
2
2
0
0
0
2
0
2
0
2
0
0
0
0
2
1
1
0
2
1
0
0
0
1
1
1
1
0
0
2
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
1
0
1
0
0
0
0
0
2
1
1
1
1
3
0
1
2
1
0
0
1
0
0
1
0
0
0
2
0
0
0
0
1
2
1
0
0
2
2
0
1
0
0
0
2
2
0
0
0
0
2
0
0
2
2
0
0
2
1
1
0
0
0
1
1
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
3
2
0
0
1
0
0
1
2
2
2
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
2
0
2
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
1
2
0
1
0
0
3
2
2
0
0
2
0
0
0
0
0
0
1
1
0
1
0
1
0
1
0
0
0
1
0
0
0
0
2
2
3
0
0
0
0
0
1
0
0
0
0
0
1
3
0
0
2
1
0
0
3
0
0
1
0
1
0
0
0
0
2
0
0
2
0
0
0
1
2
2
2
0
0
0
0
0
1
2
5
0
2
0
0
0
0
1
0
0
3
0
0
0
0
0
1
0
0
0
0
1
0
0
2
2
1
1
0
2
0
1
0
1
0
1
0
1
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
2
1
3
0
1
1
0
0
0
0
3
0
0
0
3
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
2
2
0
0
1
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
2
0
0
2
0
3
0
0
0
2
2
2
2
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
1
1
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
1
1
2
4
0
0
1
0
0
0
0
1
2
1
0
2
0
0
1
0
1
1
0
0
0
2
1
0
0
2
1
1
0
0
0
0
1
0
3
0
0
2
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
2
2
1
1
0
1
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
3
3
0
2
3
0
2
0
2
0
0
1
0
2
1
0
0
2
0
1
0
1
0
0
1
2
2
0
2
0
0
0
1
0
0
2
0
1
0
2
0
2
1
0
2
1
0
0
1
2
2
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
3
0
0
1
0
0
0
2
1
0
1
0
3
0
0
2
0
0
0
0
0
2
1
2
1
1
0
0
0
2
0
1
2
1
2
0
2
1
1
2
0
2
0
0
0
1
2
0
3
0
0
2
1
0
0
5
0
0
0
2
0
1
1
0
1
0
2
0
1
2
2
0
0
0
0
0
0
0
1
0
2
2
0
0
1
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
2
0
1
4
2
0
0
0
2
1
1
0
0
0
0
0
1
2
0
0
1
1
1
0
0
0
2
0
0
2
2
0
1
0
2
0
2
0
0
1
0
2
0
0
0
4
0
0
0
0
0
1
2
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
2
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
2
2
2
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
2
1
2
2
0
0
0
1
1
0
2
0
0
1
0
0
0
0
2
1
2
1
2
0
2
2
0
0
0
2
1
1
0
2
0
0
2
0
0
1
1
0
0
0
1
1
0
0
1
0
0
1
0
0
2
1
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
1
2
0
2
0
0
1
1
0
0
1
0
1
0
1
2
0
0
1
0
0
2
0
0
2
0
1
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
1
1
0
0
0
0
0
1
2
2
1
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
1
2
0
0
2
0
2
1
1
2
0
2
0
0
1
2
0
2
0
2
0
2
0
1
2
0
0
1
1
0
2
1
0
0
0
0
0
2
0
0
0
0
2
0
0
2
1
0
2
1
0
0
2
1
2
0
0
0
2
1
0
2
0
0
0
0
0
0
0
2
0
1
0
1
0
2
0
1
1
0
3
0
0
2
1
1
1
0
1
0
0
1
0
0
0
1
2
0
0
2
0
0
0
3
0
2
0
2
0
0
0
0
1
0
0
0
1
1
0
0
0
0
2
0
0
0
2
0
1
0
3
1
2
0
0
1
1
0
1
1
1
2
0
0
0
2
2
1
2
0
0
0
2
1
0
0
4
1
0
0
0
2
0
0
2
0
2
1
0
1
0
2
0
0
0
1
1
1
0
0
2
1
1
2
0
0
0
0
1
0
0
1
0
2
0
0
1
2
1
1
1
0
0
1
2
3
1
0
2
0
2
1
0
1
0
1
0
0
0
0
2
3
0
0
2
2
0
0
0
0
0
0
0
2
1
0
0
0
0
1
2
0
1
0
0
0
0
1
1
0
2
2
2
1
2
2
1
0
0
2
0
1
0
1
0
0
0
0
0
0
2
1
2
2
1
1
1
2
0
0
1
0
0
2
1
0
1
0
1
0
2
0
0
0
0
2
0
0
2
2
1
2
1
0
2
1
0
0
0
1
1
0
0
1
1
2
2
0
0
0
0
0
0
0
0
1
0
2
1
1
0
2
0
2
1
0
1
1
2
0
0
0
0
0
0
2
2
2
0
1
1
0
0
0
0
0
0
0
0
1
1
0
3
1
0
1
2
0
2
2
0
0
0
0
2
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
2
2
0
0
1
2
1
0
0
0
2
0
0
0
0
1
0
1
0
0
1
3
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
1
2
0
1
1
2
0
2
0
0
1
2
0
0
2
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
2
2
1
0
2
2
0
2
1
1
0
2
0
1
4
0
0
1
2
1
2
0
2
0
0
0
0
1
1
2
1
2
0
1
0
0
0
1
7
0
0
2
2
2
0
1
1
1
0
0
0
1
1
0
1
0
6
0
2
0
0
2
2
0
1
0
1
0
0
0
1
0
0
0
0
3
2
0
0
0
0
2
0
1
0
4
1
0
1
1
1
0
1
2
0
1
0
0
2
0
1
1
0
0
2
1
1
1
0
2
0
0
1
0
0
0
2
0
0
2
0
0
1
0
0
1
1
0
1
0
2
0
0
1
1
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
3
2
2
0
2
0
0
1
0
2
1
1
1
0
2
1
0
0
0
2
0
0
1
1
1
2
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
2
1
1
0
1
1
0
0
0
1
0
1
1
0
0
0
2
1
2
0
0
2
0
2
0
0
0
1
2
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
2
1
0
1
1
0
0
1
1
1
0
0
1
0
0
0
0
0
0
2
1
0
0
0
2
0
0
2
0
3
0
2
0
1
0
2
1
2
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
2
0
1
0
0
0
0
0
2
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
6
0
0
0
2
2
0
2
0
1
0
2
0
0
0
0
1
0
0
0
1
0
1
0
0
1
1
2
2
0
1
0
0
0
1
0
0
0
2
0
0
3
0
0
0
1
0
2
0
0
1
0
0
1
1
2
2
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
1
2
1
0
0
0
0
0
0
0
0
0
1
0
2
0
2
2
0
0
0
0
1
1
0
0
2
0
2
2
0
2
0
2
2
2
0
0
0
0
6
2
0
2
1
1
0
1
2
2
1
0
0
0
3
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
1
0
0
0
1
0
0
2
0
1
1
0
1
0
1
0
2
1
0
0
0
1
0
1
0
1
0
0
2
0
0
0
1
0
0
0
0
3
1
0
0
2
1
2
0
1
0
0
2
0
0
0
0
1
2
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
1
0
0
1
0
2
0
2
0
0
0
2
1
0
0
0
1
3
10
1
0
1
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
1
0
1
2
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
1
1
0
0
2
1
2
0
2
1
2
1
0
2
0
1
2
1
0
2
0
3
0
0
0
2
2
0
0
0
0
0
2
0
1
0
2
3
1
0
0
0
1
1
0
1
1
2
1
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
2
2
0
0
2
2
0
1
0
0
0
2
0
2
1
0
0
0
0
2
0
1
2
2
0
0
1
2
2
1
1
0
2
1
0
0
0
2
0
1
0
0
0
4
1
2
0
0
0
2
1
0
0
2
0
0
0
2
2
0
2
1
2
0
1
0
2
0
0
0
1
1
0
0
1
0
1
2
1
1
0
2
0
0
0
1
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
2
2
1
1
0
0
0
0
2
0
0
0
2
0
0
0
1
1
0
1
0
1
2
0
0
0
2
0
2
0
0
2
0
0
2
0
0
0
1
2
0
1
1
0
2
0
0
2
0
2
0
0
0
0
0
1
0
2
0
0
2
3
0
5
2
2
0
0
0
2
0
0
3
0
0
2
1
0
1
0
0
0
2
0
0
1
2
0
2
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
1
0
2
3
0
1
0
1
0
1
0
2
2
1
0
1
0
0
2
1
0
1
0
3
0
0
1
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
2
1
1
0
0
2
0
0
3
2
1
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
1
1
0
0
0
0
1
0
1
1
0
2
1
2
2
0
0
1
0
2
1
0
0
2
0
0
2
0
0
0
0
0
1
2
2
2
1
0
0
1
1
0
2
1
2
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
1
0
1
1
0
2
0
0
0
1
1
2
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
2
2
2
1
0
0
1
0
0
0
0
0
0
0
1
2
1
2
1
0
0
1
1
0
0
2
1
1
0
0
0
0
2
0
0
1
0
2
0
0
1
2
2
2
2
0
0
0
0
3
0
0
0
0
1
1
0
1
1
1
0
0
0
2
1
0
2
2
0
1
1
0
0
0
0
0
2
0
0
0
2
0
1
1
0
0
2
1
1
0
2
0
0
0
0
0
0
2
2
1
0
0
1
0
1
2
3
0
0
1
2
0
0
2
5
1
0
2
1
0
1
1
0
2
2
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
2
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
4
1
0
0
0
0
0
2
2
0
0
0
0
0
2
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
2
0
0
2
0
0
1
2
0
0
0
0
0
0
1
0
4
1
0
0
2
0
2
0
1
2
0
1
1
0
0
0
1
0
1
0
0
0
1
2
0
0
0
0
2
0
2
1
1
0
2
0
2
0
0
1
0
0
0
0
2
0
0
1
0
0
0
1
1
0
0
1
0
0
0
1
0
0
2
1
2
1
1
0
0
2
0
0
0
2
1
0
0
0
1
1
2
2
0
2
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
2
0
0
2
0
0
1
1
1
1
0
0
0
0
1
1
0
2
0
2
0
1
1
0
0
0
0
0
0
1
0
0
2
0
2
1
0
0
0
1
0
1
1
1
0
0
0
0
0
2
0
0
1
2
0
1
0
0
0
0
1
0
0
2
0
1
2
0
0
0
1
2
0
1
1
1
2
1
0
2
1
0
0
0
1
0
2
2
0
0
3
1
1
0
0
1
0
0
2
1
1
1
0
0
0
0
1
0
0
0
0
2
1
0
0
2
0
1
0
1
0
0
0
2
0
0
0
0
0
1
0
1
0
0
1
1
2
0
0
0
0
0
2
2
0
0
1
0
1
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
1
0
1
2
1
1
0
0
0
0
1
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
4
0
1
1
1
1
2
0
0
0
0
2
0
2
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
1
0
2
1
0
0
0
0
2
1
0
1
0
0
0
0
2
0
0
1
2
0
0
0
0
2
1
0
3
3
0
0
1
0
0
2
1
2
1
0
2
0
1
1
0
0
0
2
2
1
1
0
0
0
0
0
0
1
1
0
2
0
1
2
0
0
0
1
0
2
0
0
0
0
1
1
0
1
1
2
0
1
0
2
2
0
0
1
3
0
0
2
1
0
0
1
0
3
0
0
2
2
0
0
0
0
1
1
0
0
0
2
0
0
0
2
0
0
0
2
1
2
0
2
0
0
2
0
0
0
0
0
1
2
2
2
0
2
2
0
2
0
1
0
0
0
2
1
0
0
0
2
0
0
0
1
0
0
1
0
0
0
1
1
0
0
2
2
0
0
2
2
2
1
2
0
0
0
1
0
0
0
0
0
0
2
1
0
2
0
0
0
1
0
0
0
0
0
2
0
0
1
0
1
1
1
0
2
0
1
0
0
0
1
2
2
0
0
2
2
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
3
0
0
2
0
1
0
1
1
5
0
0
0
2
0
2
1
0
0
0
0
0
2
1
1
2
1
2
2
0
1
2
0
0
1
2
0
1
2
0
0
1
0
0
1
2
0
0
2
1
0
0
2
2
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
1
2
0
0
0
1
1
0
0
1
0
0
0
0
1
1
0
0
0
2
0
0
2
1
1
1
3
0
4
0
2
0
2
0
1
0
0
0
1
1
0
0
0
0
0
1
1
0
0
2
0
0
0
0
1
0
1
0
0
1
0
1
2
2
0
3
2
1
0
0
2
0
0
0
0
0
2
2
0
2
0
2
1
2
0
0
0
2
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
1
2
0
0
0
0
2
1
0
0
2
0
0
2
0
2
0
1
0
1
2
0
0
2
0
0
0
0
0
1
0
0
0
0
2
1
2
1
0
0
2
0
2
0
0
0
0
0
0
0
3
2
1
0
0
1
0
0
1
0
2
1
0
4
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
2
0
3
2
0
1
2
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
2
0
1
2
0
0
0
2
0
0
0
1
2
0
1
1
0
0
0
0
0
2
2
0
2
0
2
0
1
2
4
0
1
0
1
0
0
2
2
0
0
0
0
3
0
0
0
0
1
1
0
1
1
0
0
0
0
1
2
0
0
0
1
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
2
4
2
0
0
1
2
2
0
1
0
3
1
0
0
1
0
0
0
3
0
2
0
2
0
2
2
0
2
2
0
0
0
0
0
2
0
0
2
0
0
3
1
1
0
2
0
0
0
0
2
1
2
2
1
2
1
1
1
1
0
0
0
2
0
0
0
0
2
1
2
0
1
2
0
0
0
1
2
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
2
2
0
2
0
1
0
0
2
1
2
2
0
1
0
0
0
0
2
0
1
0
1
0
0
0
1
0
0
1
2
1
0
0
2
0
2
1
0
0
0
2
3
0
0
0
0
0
0
0
0
1
1
0
0
0
3
0
1
0
1
0
0
1
1
0
0
0
0
1
1
2
1
1
1
3
1
2
0
0
2
1
0
0
0
0
1
0
1
2
1
1
0
0
2
0
0
2
0
1
0
1
1
0
0
2
0
1
0
0
0
0
0
0
3
0
0
0
0
2
1
1
0
0
1
1
0
2
4
0
0
0
2
0
0
1
0
0
0
3
0
1
1
2
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
3
1
0
0
0
1
0
0
0
0
1
1
3
0
0
0
0
0
2
1
0
0
0
3
0
0
2
2
0
0
0
1
2
1
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
2
1
1
1
1
1
3
2
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
2
1
2
0
1
0
2
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
2
0
0
0
3
2
2
1
1
0
3
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
2
2
0
0
2
0
1
1
1
0
0
0
2
0
0
0
0
0
0
2
2
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
1
2
5
1
4
0
0
0
2
2
0
0
0
1
0
1
0
0
0
0
2
0
1
1
0
0
0
0
1
0
0
1
2
1
2
0
0
0
1
0
2
0
0
0
2
0
0
2
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
2
0
0
2
0
0
1
2
0
2
0
0
0
1
2
0
1
0
1
1
0
2
0
1
0
0
2
1
0
0
2
1
0
1
1
0
3
0
1
1
1
0
0
0
1
0
1
6
2
0
0
3
2
0
2
1
0
1
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
1
2
0
1
1
2
2
1
2
1
0
2
2
0
0
0
2
0
1
0
0
0
0
2
3
2
1
0
0
1
3
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
1
2
0
1
0
0
1
2
0
1
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
1
0
0
2
0
0
1
0
2
0
2
0
2
1
0
0
0
0
1
0
0
2
0
1
2
2
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
1
0
2
0
1
0
1
0
0
1
1
1
0
1
0
2
0
0
0
0
1
0
3
0
0
0
0
0
3
0
1
0
0
0
0
0
0
2
0
2
3
0
0
2
0
0
1
2
0
1
0
1
2
1
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
1
0
0
0
0
0
0
0
4
0
1
0
0
0
1
1
2
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
2
0
1
0
0
1
2
0
4
0
2
2
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
1
0
1
2
1
2
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
1
0
0
2
0
0
0
1
2
1
0
1
0
0
0
0
0
1
3
2
2
0
2
2
1
0
2
1
0
0
1
2
0
0
0
2
0
1
0
1
1
0
0
2
2
0
0
0
1
0
0
1
0
0
0
1
0
0
0
2
0
2
0
0
1
0
0
0
1
2
0
0
0
2
2
0
2
0
1
2
0
0
1
3
0
0
0
1
2
0
0
0
0
1
0
2
0
2
0
0
1
0
1
0
0
0
0
0
1
0
0
2
0
1
1
0
0
0
1
0
0
1
0
0
0
0
2
0
1
1
0
4
0
1
1
0
1
1
0
0
0
2
1
0
0
3
0
0
0
0
0
1
2
0
2
0
0
2
1
0
0
1
1
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
1
0
0
0
0
1
1
0
0
2
0
1
1
1
0
0
1
2
1
1
0
2
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
1
1
9
0
1
0
0
1
2
2
0
0
0
0
0
0
0
1
1
2
0
2
0
0
0
3
0
0
2
1
1
0
0
0
1
1
2
1
2
0
0
1
1
0
1
0
2
0
0
1
0
0
0
1
1
1
0
0
0
0
0
2
0
0
2
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
1
0
2
0
0
2
3
0
1
1
1
0
0
0
2
1
1
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
1
1
0
0
0
2
2
0
0
0
0
0
0
0
1
2
0
0
0
2
0
2
0
1
0
0
1
1
0
0
0
2
1
1
2
0
0
2
1
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
1
0
0
0
0
2
0
2
0
2
1
0
4
0
2
0
0
0
0
0
0
2
1
0
0
1
0
1
0
0
1
0
0
0
0
2
1
0
0
0
0
1
0
1
0
2
0
1
2
0
1
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
1
1
0
2
2
0
0
2
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
1
1
0
1
0
0
0
2
0
0
2
0
2
0
0
0
2
0
1
1
0
0
0
2
0
2
1
1
2
0
0
0
2
1
1
1
0
1
1
0
1
0
0
1
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
3
0
0
0
1
2
0
0
2
1
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
1
1
2
0
2
0
0
0
1
2
1
0
0
1
0
1
0
3
0
0
1
1
0
2
0
0
1
0
0
0
1
0
2
0
1
2
0
1
0
0
0
0
1
0
1
2
0
0
1
3
0
0
0
1
0
1
0
0
0
0
0
1
2
0
1
1
0
0
0
0
0
2
0
1
0
0
0
2
1
2
0
0
1
0
0
0
0
4
0
0
0
2
0
1
0
2
0
2
0
0
1
0
1
0
2
1
1
1
0
0
0
0
2
0
1
1
0
1
1
2
0
0
2
1
0
2
0
2
2
0
0
1
1
0
0
2
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
2
0
2
0
1
0
2
0
0
2
2
2
0
0
1
0
2
2
0
1
0
1
0
2
2
1
0
0
2
0
0
1
0
1
0
0
0
2
0
0
1
2
2
0
0
1
0
0
2
0
0
0
0
0
0
0
1
1
1
0
0
0
2
1
2
0
2
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
1
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
2
1
2
0
0
0
2
0
0
0
0
0
1
0
0
1
1
2
0
0
1
0
0
2
0
0
0
1
2
0
0
2
0
2
1
0
0
0
1
0
2
0
0
1
0
2
0
0
3
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
2
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
1
0
1
0
2
0
1
1
0
0
1
3
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
1
4
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
8
0
0
0
0
1
0
0
0
3
0
2
0
0
3
0
0
2
0
0
0
1
0
0
2
2
0
0
2
1
0
1
0
0
0
2
2
1
0
0
1
2
0
1
1
1
2
0
0
0
0
0
0
0
0
2
1
0
0
0
1
2
0
0
0
2
3
1
0
1
0
0
2
3
0
0
0
1
4
2
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
1
2
1
1
0
3
2
0
0
2
2
1
0
0
1
0
0
0
0
3
3
0
2
1
2
0
0
0
1
0
2
0
2
0
0
2
0
2
1
4
0
0
0
0
1
2
2
0
0
1
1
2
0
0
0
2
2
2
0
0
2
0
0
0
0
0
1
0
1
1
0
0
2
1
0
3
0
0
0
2
0
1
2
2
0
0
0
4
1
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
2
0
0
1
0
1
0
3
1
0
0
2
0
0
2
3
0
1
0
1
2
1
1
2
0
0
0
0
0
0
0
1
0
1
0
1
2
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
2
1
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
1
1
0
0
0
1
2
0
0
2
1
2
0
0
0
0
1
2
0
2
0
0
1
0
0
0
1
0
0
1
0
0
0
2
0
0
2
1
0
0
2
0
1
0
2
0
0
2
2
0
0
0
0
1
0
1
0
0
1
2
2
0
0
0
0
0
0
5
2
1
0
0
0
0
2
0
1
1
0
0
0
3
0
0
0
1
0
2
0
1
0
0
1
0
0
0
0
1
2
1
0
1
0
1
1
0
0
0
1
2
0
0
0
2
0
2
1
2
0
0
0
0
0
6
0
0
0
0
1
1
0
0
0
2
0
0
1
0
1
1
2
0
0
0
0
1
1
0
0
0
2
3
2
0
0
1
1
0
1
0
1
0
0
0
0
2
0
0
0
1
0
2
1
0
0
0
0
1
0
1
2
0
2
0
1
0
0
1
1
2
1
1
0
0
1
0
2
1
2
0
0
1
0
0
0
0
2
2
3
2
2
0
3
1
1
1
0
0
2
0
2
0
0
0
1
1
0
1
1
0
1
1
0
0
0
0
1
0
2
2
0
2
0
0
1
1
0
1
0
1
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
2
1
0
1
2
0
0
0
1
0
0
0
0
0
1
0
2
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
2
2
0
1
0
2
2
0
0
1
0
3
1
0
0
0
0
0
0
1
2
1
2
0
1
2
1
0
2
1
0
2
0
2
1
0
1
0
0
1
0
0
0
2
3
0
0
0
0
0
0
1
2
0
0
0
0
2
1
0
1
2
0
1
0
0
0
0
0
0
0
1
0
0
0
2
2
0
1
0
3
0
0
2
0
1
1
0
1
0
0
0
0
0
0
0
2
2
1
1
0
1
1
2
0
0
2
0
1
0
0
1
0
1
1
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
1
0
1
0
1
0
0
2
2
0
1
1
0
0
2
0
0
0
0
1
1
0
0
2
0
0
2
1
2
0
1
0
2
0
1
1
0
0
1
0
0
2
0
0
2
1
2
0
0
2
0
1
0
0
1
2
0
2
1
2
0
2
0
0
0
3
0
0
0
0
1
0
0
0
4
0
0
1
0
0
0
2
0
0
1
0
2
2
0
0
1
1
2
0
1
0
1
0
1
0
0
1
1
2
0
0
0
1
0
2
2
1
0
0
0
0
0
0
0
0
0
0
3
1
1
0
3
0
0
0
2
0
2
1
0
0
2
0
0
0
0
0
1
2
0
0
1
2
1
0
0
1
0
0
2
0
0
0
2
0
0
2
1
0
0
1
0
0
0
1
0
1
0
2
1
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
2
2
2
0
0
0
0
1
0
1
0
0
0
1
0
2
0
0
1
0
0
1
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
1
2
0
0
0
0
1
0
1
0
0
1
2
1
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
2
1
0
0
1
0
2
2
0
1
2
2
0
1
2
0
2
0
0
2
0
2
0
0
2
0
0
0
2
2
0
0
1
2
1
0
2
0
2
0
1
0
1
0
0
1
0
1
1
0
0
2
1
2
0
0
2
1
1
0
2
0
1
2
0
0
2
1
2
0
0
0
1
0
0
0
0
1
2
0
0
1
2
0
1
0
1
2
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
1
2
1
0
0
0
0
2
0
2
0
0
1
2
0
1
0
2
1
0
3
0
0
1
0
2
2
0
2
0
1
0
2
1
1
0
2
0
0
2
2
0
2
0
1
1
0
1
0
0
2
2
0
1
2
0
0
0
1
2
1
2
1
0
1
0
0
0
1
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
4
0
0
1
1
1
0
1
2
0
0
0
2
2
1
3
1
0
0
0
1
0
1
0
2
0
0
2
0
2
0
2
0
2
0
0
1
2
0
0
0
2
0
1
2
0
0
0
0
2
0
0
1
3
2
0
1
0
0
2
0
0
0
2
1
2
1
0
3
0
0
1
0
1
0
0
0
0
0
0
1
0
2
0
2
2
0
0
1
0
0
0
0
0
0
2
0
1
1
1
2
2
1
0
0
1
0
2
0
1
2
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
2
1
1
2
0
1
2
0
1
0
0
0
0
0
2
0
1
0
0
3
1
1
0
1
0
0
0
2
1
1
0
3
1
1
2
0
0
0
0
2
0
0
1
1
1
0
0
0
2
2
2
1
1
0
1
1
2
0
0
0
2
0
0
1
0
3
2
1
0
2
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
3
0
1
0
3
1
0
0
0
1
0
1
1
0
0
0
2
0
1
0
0
2
1
2
0
2
0
3
1
2
0
0
0
0
0
0
3
0
1
0
2
0
0
1
1
1
0
0
2
0
0
2
0
2
1
1
0
0
0
1
0
0
1
2
1
1
1
0
0
1
0
1
0
0
0
2
0
0
1
0
1
0
0
0
1
0
0
0
2
1
1
0
1
1
0
1
0
0
0
0
0
0
0
0
2
1
1
0
0
0
3
1
0
0
0
2
0
0
4
1
3
3
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
1
1
0
1
0
0
0
2
2
1
0
1
2
0
0
0
0
1
1
1
1
1
0
1
0
0
1
2
0
1
2
2
0
0
0
2
0
0
2
4
0
1
0
0
0
2
0
0
2
0
2
0
2
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
3
0
0
2
0
1
1
2
0
3
2
0
0
1
0
0
0
1
2
0
0
2
1
0
1
1
2
2
2
2
0
0
0
0
1
2
2
0
0
0
1
0
3
0
0
2
1
1
2
2
2
0
0
2
0
0
0
0
0
1
0
2
1
0
0
0
2
0
0
1
2
2
1
1
0
1
1
0
1
3
0
0
1
0
1
1
0
1
1
2
0
1
3
0
2
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
2
0
2
1
0
0
0
0
0
2
0
0
0
2
0
2
0
0
1
0
4
1
0
1
0
0
2
0
0
0
2
0
2
2
1
0
2
1
2
0
1
0
1
1
1
0
0
1
2
1
0
1
0
0
0
1
0
0
0
2
2
0
3
1
1
2
0
0
2
0
1
2
0
1
0
0
0
0
1
1
0
0
0
0
1
1
0
2
3
1
0
2
2
0
2
1
0
2
1
2
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
1
0
0
2
1
0
0
0
0
2
0
0
1
1
0
0
2
0
2
0
0
0
1
2
0
2
0
0
1
0
0
0
1
0
1
0
0
0
2
0
0
1
2
2
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
2
2
0
0
2
2
1
0
0
1
0
1
2
2
1
0
0
0
0
0
1
0
0
0
1
0
2
2
0
0
2
2
2
1
2
0
0
0
0
2
0
0
2
0
0
1
2
0
0
2
0
1
1
0
0
0
5
0
0
2
0
2
0
2
0
1
1
2
2
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
3
1
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
1
2
0
0
2
1
0
0
2
0
0
0
0
0
1
0
2
0
0
2
0
1
0
0
0
2
2
1
1
0
0
0
0
0
0
1
2
0
0
0
0
1
1
1
0
0
0
0
6
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
1
0
0
0
0
1
0
1
0
2
2
2
0
3
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
1
0
0
1
1
0
0
0
0
1
0
2
0
2
3
2
0
0
2
0
0
1
0
0
0
2
0
5
0
0
2
0
2
2
2
0
2
2
2
0
1
2
0
0
1
0
0
2
1
1
0
0
1
0
0
1
2
1
1
0
1
1
0
2
2
0
1
0
2
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
1
2
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
1
2
0
0
1
0
0
2
1
0
1
0
1
2
1
1
0
0
0
0
1
0
0
1
1
1
0
1
0
1
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
1
1
5
0
0
0
1
0
0
1
4
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
2
0
0
0
0
2
0
0
1
0
0
2
2
1
1
1
0
2
0
0
0
0
0
2
0
0
1
4
0
0
1
3
0
1
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
1
2
1
1
0
2
0
0
2
0
0
0
2
0
2
0
0
1
0
1
1
1
2
1
0
0
2
0
2
1
0
2
0
2
0
0
0
1
0
0
0
0
1
0
2
1
2
0
0
0
2
0
0
0
0
2
2
0
0
0
1
1
0
0
0
2
1
0
0
0
0
0
0
1
1
0
2
1
1
0
2
0
0
1
1
0
0
0
0
0
2
1
2
1
1
0
1
1
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
1
0
0
1
1
1
1
0
1
0
1
0
0
0
0
2
0
0
1
0
0
1
3
0
0
1
0
0
2
0
2
2
0
1
1
0
0
0
0
1
0
2
1
3
0
0
1
1
1
1
1
2
0
0
1
1
0
0
0
0
0
2
0
1
0
1
0
1
2
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
1
0
0
3
0
0
2
2
0
1
0
0
0
0
0
0
0
1
0
1
1
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
2
1
0
1
1
2
1
0
0
0
0
0
1
1
0
1
0
0
1
1
0
0
0
0
1
2
1
1
0
2
0
0
1
1
1
2
1
0
1
1
1
1
0
0
1
0
0
0
2
0
1
1
1
0
1
0
0
2
1
0
2
1
1
2
0
0
0
2
1
1
0
0
2
0
3
3
2
0
0
1
1
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
1
2
0
0
1
0
5
0
0
1
0
1
0
1
0
0
0
0
1
0
0
2
0
1
0
0
0
0
2
0
0
1
2
0
1
0
0
2
0
1
0
0
2
0
0
0
0
3
1
0
0
1
2
1
0
0
0
2
1
0
1
0
0
2
1
1
0
0
0
0
1
0
0
2
1
0
0
1
2
0
0
0
0
1
0
0
0
0
0
2
0
0
2
1
0
0
1
0
0
0
2
1
0
0
1
1
3
0
1
0
0
0
0
0
1
0
2
2
0
0
0
2
0
0
0
0
1
1
1
0
2
1
0
2
0
0
0
1
2
1
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
1
2
0
0
0
0
1
0
1
0
0
0
2
0
2
0
2
0
0
0
0
2
0
0
0
2
2
2
2
0
0
1
2
0
1
0
0
2
0
0
3
1
0
0
0
1
2
0
0
0
0
1
0
1
2
0
0
3
0
0
0
0
0
1
0
1
2
0
0
0
1
0
2
0
0
0
3
0
0
2
2
1
0
2
0
0
1
0
0
0
1
1
0
2
1
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
1
1
2
0
2
0
0
1
0
2
0
2
0
2
0
0
1
0
0
0
0
0
0
1
1
1
1
0
0
1
0
0
2
0
2
2
0
2
0
0
2
0
1
0
0
0
1
1
1
2
0
0
2
1
1
0
0
2
0
0
2
2
2
1
1
0
0
0
0
0
1
2
0
0
1
2
0
1
1
0
2
0
0
1
1
0
0
1
0
0
0
0
0
2
1
1
0
0
0
1
1
0
0
1
2
1
2
0
1
2
2
0
0
0
2
0
0
1
1
2
1
1
2
1
2
0
0
1
0
2
1
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
1
0
0
2
0
1
2
0
0
1
0
0
2
1
0
0
2
1
1
0
0
1
0
0
2
0
1
2
5
0
0
0
0
0
0
0
0
2
0
4
0
2
0
2
3
0
1
0
3
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
2
1
1
0
4
0
1
0
2
0
0
1
0
1
0
0
0
1
2
0
0
0
0
2
1
0
1
1
2
0
2
0
0
1
0
0
1
0
0
2
0
0
2
1
2
3
0
2
0
0
0
0
0
2
0
1
1
1
0
2
0
2
0
0
1
0
0
3
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
2
0
1
3
0
1
0
2
2
0
0
0
2
0
0
0
1
1
0
1
2
1
0
0
2
0
2
0
2
0
0
0
0
1
0
3
0
2
1
0
0
2
1
0
0
1
2
0
1
1
6
1
0
1
2
1
0
0
0
0
0
1
0
0
1
0
2
0
1
0
1
2
0
1
0
0
0
1
2
2
2
1
1
0
0
2
0
0
2
1
2
0
0
0
1
2
1
0
1
0
0
1
0
0
0
2
1
0
2
5
1
2
0
1
0
0
0
0
0
0
1
0
1
0
0
2
2
0
2
2
1
0
3
0
0
2
0
0
0
0
0
0
2
0
2
0
0
2
1
0
1
1
1
0
0
1
2
1
0
0
0
0
0
2
1
0
0
0
0
1
2
0
0
0
0
1
1
0
2
0
0
2
0
0
1
0
2
1
2
0
0
0
0
1
0
1
1
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
4
0
0
2
0
2
0
0
0
0
1
0
1
2
1
0
3
0
3
0
0
2
0
0
1
0
0
0
0
0
0
1
1
0
1
9
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
2
0
0
2
2
1
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
1
1
0
0
1
2
0
0
0
0
1
0
0
2
0
0
0
0
0
1
1
1
1
0
0
0
2
2
0
2
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
2
0
1
3
0
0
0
2
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
1
0
2
0
0
1
0
0
0
0
0
2
0
2
0
0
1
0
0
2
1
0
0
0
0
0
1
0
0
0
2
1
0
1
0
0
2
0
0
0
0
2
2
0
0
2
0
2
0
1
0
0
2
1
2
1
0
2
2
1
0
1
0
0
0
0
0
1
0
0
2
0
0
2
0
2
0
1
0
0
1
1
0
1
0
2
1
1
1
1
1
0
0
0
3
0
1
2
1
0
0
0
2
0
2
0
0
2
0
0
1
0
0
0
0
0
2
3
0
2
0
2
1
0
0
0
1
1
0
0
1
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
2
0
1
1
2
1
2
2
0
0
0
1
1
1
2
0
0
0
2
2
2
0
0
1
0
2
0
0
0
2
1
1
1
1
2
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
1
0
0
2
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
1
0
0
2
0
0
2
0
1
0
2
0
0
0
0
2
0
1
2
0
1
0
2
0
0
0
2
0
0
0
1
0
1
0
2
2
0
0
1
1
3
0
2
2
0
1
0
2
0
1
0
0
0
0
0
0
1
2
0
0
0
3
0
0
0
2
1
1
1
0
0
0
0
0
0
0
0
0
0
3
0
1
1
1
2
0
0
0
0
0
0
0
0
1
1
1
2
0
2
0
1
0
1
2
0
0
0
0
0
3
0
1
1
2
0
0
2
1
0
0
2
0
0
0
0
1
0
1
1
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
2
1
1
0
0
0
1
0
0
0
1
0
6
3
1
1
0
2
2
0
0
0
0
0
2
0
0
1
2
1
0
1
0
2
0
2
0
0
1
2
2
2
2
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
2
0
1
1
0
0
0
1
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
1
0
1
1
0
1
2
1
2
0
0
0
0
0
0
0
0
0
2
1
1
1
0
0
2
0
0
1
0
1
2
0
1
0
0
0
1
1
0
1
2
1
0
0
0
2
2
0
0
0
1
0
0
0
1
0
0
0
2
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
3
0
0
1
0
2
1
0
0
0
2
0
0
0
0
0
1
0
1
2
1
2
3
1
1
0
0
0
0
0
2
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
3
2
0
0
0
1
0
0
0
1
0
0
0
1
2
0
0
1
1
0
0
0
0
1
1
0
1
1
2
2
0
0
1
0
1
1
0
0
1
1
0
2
1
2
1
1
1
0
0
0
2
6
0
0
0
0
0
0
0
1
0
2
0
1
0
1
0
0
0
0
0
0
1
4
1
1
0
0
0
0
0
2
0
0
0
1
0
2
1
0
0
0
0
0
0
0
2
1
0
1
2
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
2
2
0
0
0
0
1
2
0
2
0
0
0
1
0
1
0
1
2
1
2
2
1
0
1
1
0
0
1
1
0
0
2
2
0
1
0
0
0
1
0
0
3
1
0
1
0
1
0
0
0
2
0
0
0
0
0
1
0
2
0
1
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
1
1
2
0
1
4
3
2
1
0
0
2
0
0
0
0
0
0
1
4
1
2
0
2
1
0
2
1
2
1
0
0
0
1
0
1
0
0
0
1
1
0
0
2
0
1
0
2
0
0
0
1
0
0
1
0
0
0
0
2
0
2
2
0
0
0
1
1
1
0
0
0
2
3
0
1
1
0
0
3
0
2
2
2
0
2
0
0
0
1
0
2
0
0
2
1
3
0
0
1
0
1
2
0
0
0
0
0
0
2
0
3
2
0
0
0
0
2
1
1
0
0
0
0
0
2
2
1
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
1
0
0
1
0
0
0
1
2
1
1
0
0
2
0
0
0
1
1
0
1
1
1
2
1
0
0
0
0
0
2
1
2
1
1
1
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
2
0
0
2
3
0
0
2
0
1
0
0
0
0
2
0
1
0
1
2
1
1
0
1
0
0
0
1
1
0
2
2
0
1
1
1
0
2
2
2
1
2
1
1
2
2
0
1
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
2
0
0
0
0
0
1
1
0
0
0
2
1
0
0
0
0
1
1
1
0
2
0
1
1
2
0
0
0
0
1
2
0
0
1
1
0
0
2
0
1
2
1
2
0
0
2
0
2
0
2
0
0
0
0
0
1
0
0
1
1
2
0
1
0
0
1
2
1
0
1
0
0
0
2
1
0
1
1
0
0
0
0
0
1
1
2
0
0
2
1
0
2
0
0
0
0
1
0
1
1
0
0
1
2
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
2
1
4
1
0
0
0
0
4
0
0
0
0
2
1
2
1
1
2
2
0
0
2
0
0
0
2
0
0
0
0
2
0
2
0
1
3
1
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
1
1
2
0
2
3
0
2
1
1
0
0
0
2
1
3
0
1
0
0
3
1
0
2
2
2
0
1
0
2
0
0
1
0
0
1
0
0
0
0
1
3
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
1
0
2
0
0
1
0
2
0
0
1
0
0
2
2
1
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
2
0
0
1
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
2
0
3
0
1
0
0
1
0
3
2
1
0
1
0
0
1
1
0
2
1
0
0
0
0
1
2
0
3
0
1
0
2
1
0
0
0
0
1
0
0
0
2
0
2
0
1
0
0
0
2
0
2
1
1
1
1
2
0
0
0
0
0
0
2
0
0
2
2
0
0
2
0
2
1
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
2
0
0
2
2
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
1
0
1
1
1
1
1
0
1
0
0
2
0
0
1
0
0
2
2
2
1
0
0
3
0
1
0
1
0
1
0
0
1
1
0
1
0
2
0
0
2
0
0
0
1
1
3
0
2
0
4
2
0
0
1
0
0
0
2
0
0
2
1
0
2
0
0
0
3
1
2
0
2
0
0
1
0
0
0
0
3
0
2
0
0
2
0
2
0
2
2
2
0
0
2
0
0
0
0
1
1
1
0
0
1
0
0
1
1
1
0
0
0
0
0
2
0
2
0
1
2
0
2
0
2
3
0
0
2
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
2
0
0
2
2
0
1
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
1
0
1
0
0
0
0
0
1
0
2
0
0
1
2
0
0
1
0
5
0
0
0
0
1
1
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
1
2
0
1
4
0
0
1
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
2
1
0
0
1
0
2
1
0
0
0
2
1
2
0
0
0
1
1
2
0
0
0
1
0
0
3
2
0
0
0
0
2
1
1
0
0
0
1
0
0
0
0
1
0
0
3
1
0
0
0
0
0
2
1
1
2
0
0
0
1
0
1
0
1
0
0
1
2
0
1
2
0
1
1
1
2
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
5
0
2
0
0
1
2
0
0
0
0
0
1
0
2
0
2
1
2
0
0
0
0
2
0
2
0
1
2
0
0
0
0
0
1
2
0
0
0
0
3
1
0
0
2
1
1
0
0
1
1
0
0
0
0
2
2
0
0
2
1
0
2
2
2
1
0
2
0
0
0
0
2
1
0
0
2
1
1
2
0
2
1
0
1
2
2
0
1
2
0
0
2
2
2
1
0
0
0
2
2
0
1
0
0
0
0
0
1
0
1
0
1
1
2
0
2
0
4
2
0
2
1
0
1
0
2
1
0
0
1
0
2
0
0
1
0
0
0
0
0
2
0
0
1
0
2
2
1
0
0
2
0
2
0
0
0
0
0
0
2
2
0
1
0
1
0
2
1
0
3
0
0
2
1
0
0
2
0
0
2
2
2
2
0
0
0
0
0
0
1
0
1
1
0
2
2
0
0
0
2
6
2
0
2
1
0
0
0
0
1
1
0
0
2
2
0
0
0
2
0
2
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
2
0
2
0
1
0
0
1
0
2
0
0
0
1
1
0
0
0
0
1
0
0
2
0
0
1
0
3
1
0
0
0
0
2
2
2
2
2
1
0
2
2
0
1
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
1
0
1
1
0
0
1
0
0
0
0
0
3
0
0
2
1
1
0
0
0
1
1
0
0
0
3
1
0
0
11
0
2
0
0
1
0
0
2
1
0
0
1
2
0
0
0
1
0
0
0
0
0
0
2
0
2
1
1
2
0
3
0
2
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
1
2
0
2
1
0
1
2
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
2
0
0
0
1
1
0
2
0
0
0
0
0
1
0
0
1
1
0
2
1
0
1
1
2
1
0
0
0
0
1
2
0
2
0
1
2
0
2
2
1
2
0
1
2
1
1
0
0
0
3
2
0
0
0
2
0
1
1
0
1
0
2
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
2
0
2
0
1
1
0
0
0
0
1
1
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
2
0
0
0
0
1
0
3
2
1
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
1
1
0
0
0
2
0
0
1
0
0
2
0
1
0
0
0
0
1
2
0
1
1
0
1
2
0
2
2
0
1
0
1
1
0
2
1
0
0
0
0
0
1
0
0
2
1
0
0
2
0
0
0
1
2
0
3
0
1
0
0
0
1
0
0
0
1
1
0
0
1
1
1
0
0
1
1
1
1
1
0
0
2
0
1
1
0
0
1
1
1
1
1
0
0
0
0
0
2
0
1
0
0
1
0
1
0
0
0
1
0
1
2
2
0
5
0
0
0
0
0
0
0
1
0
2
1
0
0
1
0
0
2
0
1
1
2
0
0
1
1
3
3
0
0
2
0
0
1
0
1
0
0
0
0
1
1
0
1
1
0
1
0
0
2
0
2
1
2
2
1
3
0
0
0
1
3
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
2
0
1
0
3
0
1
0
0
1
0
2
0
0
2
0
2
0
1
0
1
0
2
0
0
0
2
0
1
3
0
0
1
2
0
0
0
0
0
2
0
3
0
0
2
0
0
0
8
0
0
0
0
0
2
1
2
1
1
0
0
0
1
0
1
0
2
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
2
2
2
0
1
2
0
0
0
0
1
1
0
0
0
2
2
1
0
0
1
0
1
3
0
2
1
0
0
0
1
0
0
1
0
2
4
0
0
2
0
2
0
2
0
0
0
0
1
0
0
1
0
0
2
1
0
0
0
4
0
2
1
1
1
0
1
0
2
0
1
3
0
0
1
0
2
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
1
0
0
0
0
0
0
0
3
2
1
0
2
0
0
0
0
0
0
2
2
1
0
1
1
1
0
0
0
1
0
1
0
0
0
1
1
0
0
2
2
0
0
2
2
0
0
2
0
1
0
2
0
0
2
0
0
1
0
0
0
0
1
0
0
1
2
2
2
0
1
2
1
1
1
0
0
0
0
0
1
0
2
0
1
1
2
0
0
0
0
0
0
0
0
2
0
0
5
0
1
0
0
2
0
0
1
0
2
2
1
1
2
2
0
0
0
0
0
0
0
1
0
1
1
1
0
0
1
0
1
2
0
0
0
1
1
0
2
1
1
0
2
1
1
2
0
2
1
0
1
1
1
1
0
2
0
1
1
2
0
0
0
0
1
1
1
0
0
1
2
0
2
3
2
2
0
1
1
1
1
1
2
0
2
0
0
2
1
0
1
0
1
0
2
0
0
0
0
0
2
1
2
4
0
0
0
2
1
2
2
2
0
0
2
0
1
1
2
0
0
1
0
0
0
0
2
2
2
0
1
0
0
2
1
5
0
0
3
2
0
0
1
0
2
0
0
2
2
1
0
1
0
0
0
2
7
0
1
0
0
0
0
0
1
1
0
0
0
1
2
0
1
1
0
1
2
0
0
1
2
1
2
0
0
2
2
0
2
0
1
0
1
0
0
2
0
0
0
2
1
1
2
2
0
0
0
0
1
2
2
0
2
1
0
0
0
1
0
2
2
3
0
1
0
0
2
0
1
0
0
1
2
0
0
0
0
0
0
0
0
1
0
2
3
1
0
1
1
2
0
0
0
0
2
2
0
2
2
2
0
2
2
2
1
2
1
0
1
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
1
1
1
2
1
1
0
2
0
0
0
0
0
0
1
0
0
1
1
2
0
0
0
1
2
0
0
0
0
0
0
0
0
2
1
0
2
1
2
0
0
0
0
0
1
2
3
0
0
0
2
0
0
0
0
1
1
1
2
2
0
0
7
1
0
2
2
0
0
1
0
2
2
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
2
3
1
0
1
0
0
0
1
0
0
0
0
0
2
2
0
2
1
0
0
1
0
0
3
1
0
0
1
1
0
0
0
2
0
0
2
0
1
0
0
1
1
0
1
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
4
2
0
1
1
2
0
0
0
1
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
2
1
1
0
0
0
0
0
2
0
1
1
2
0
1
0
2
0
0
1
0
0
0
0
2
0
0
0
0
2
1
2
0
1
2
0
0
0
0
1
2
0
0
0
1
0
0
2
0
1
0
1
1
1
0
0
0
2
2
1
1
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
1
0
0
0
2
0
1
1
1
0
0
0
1
2
0
1
0
1
0
0
2
0
0
0
0
0
0
0
2
0
1
2
0
1
2
0
2
1
1
1
0
0
0
1
1
0
1
1
0
0
0
1
1
0
1
0
1
0
0
0
1
0
0
0
2
0
0
0
1
0
1
0
0
2
1
0
0
1
0
0
0
1
0
1
0
0
1
0
0
4
0
0
0
0
2
1
0
2
1
1
2
2
1
2
0
0
0
1
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
2
0
0
0
2
0
0
2
2
0
0
0
0
2
0
1
0
1
0
0
0
1
1
0
2
0
3
0
2
1
1
1
1
0
2
2
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
2
2
0
0
1
0
0
1
1
0
0
1
0
0
0
1
0
1
0
1
1
0
0
1
0
2
2
0
0
2
0
0
2
0
0
0
0
2
0
0
0
1
1
0
1
0
1
2
2
0
2
0
0
0
0
3
2
1
0
2
0
0
1
0
2
4
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
2
0
4
1
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
2
2
0
2
0
1
2
2
0
0
0
0
7
1
0
2
2
0
1
2
0
0
0
0
2
0
0
1
0
0
0
2
0
2
2
0
0
1
2
0
0
2
0
1
0
1
0
1
0
0
0
1
7
0
2
0
1
1
2
1
0
0
0
0
1
2
1
1
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
1
1
0
0
1
3
0
2
1
0
0
0
0
0
0
0
1
0
1
1
0
0
2
2
1
0
0
2
0
0
1
0
2
3
2
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
1
2
0
0
1
0
0
0
1
1
2
1
2
0
0
0
0
0
0
0
3
3
0
0
1
2
1
0
1
0
0
0
0
2
1
2
0
0
0
1
0
1
2
1
1
0
0
0
1
0
2
0
1
0
0
0
1
0
0
2
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
2
0
2
2
2
0
0
2
2
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
1
0
0
2
1
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
1
0
1
0
0
0
1
0
1
0
1
0
4
0
1
2
0
2
0
4
1
1
2
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
1
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
4
0
0
0
0
1
0
0
0
2
1
0
2
2
0
0
0
0
0
0
2
2
0
1
0
1
0
1
0
0
0
0
2
1
0
0
1
2
1
0
0
0
0
0
1
0
0
2
0
1
2
1
2
0
0
0
0
2
0
1
0
0
1
0
1
0
0
0
0
0
1
1
2
2
0
0
0
2
0
0
1
2
2
0
1
1
2
1
1
0
0
2
0
2
0
0
1
0
0
0
1
2
1
0
0
1
1
0
0
0
0
2
2
0
1
0
1
0
0
0
0
0
0
3
1
1
2
2
0
1
0
0
1
0
1
0
0
0
1
2
0
1
1
1
2
0
0
0
0
2
0
1
0
0
0
1
0
0
2
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
1
3
2
0
2
0
0
2
2
1
0
0
0
2
0
1
1
0
0
1
2
0
1
2
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
1
2
0
3
1
1
0
1
1
2
0
0
2
2
1
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
3
1
0
0
2
2
0
0
2
0
0
0
2
0
0
1
1
1
1
1
0
2
0
0
2
0
0
0
0
2
0
0
0
2
2
1
0
1
2
0
0
0
0
1
1
0
0
0
2
3
0
0
2
0
2
0
0
2
2
0
0
0
1
0
0
1
0
0
1
1
2
2
0
2
1
0
1
1
1
0
1
0
0
0
2
0
0
0
0
1
1
2
1
1
1
0
0
0
1
0
0
2
2
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
1
0
2
0
1
2
5
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
1
0
1
0
0
0
2
0
0
1
0
2
1
0
1
0
2
0
0
0
1
0
0
2
0
0
1
2
0
0
2
1
2
1
0
0
2
0
0
1
1
0
2
0
0
1
0
0
1
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
3
0
0
1
1
1
0
0
0
0
0
2
4
2
0
1
1
0
2
0
0
2
1
0
0
0
0
0
0
1
0
1
1
0
1
0
0
1
1
0
0
2
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
1
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
1
0
0
1
0
2
0
0
2
0
0
1
0
1
2
1
0
2
1
0
0
1
2
0
1
0
1
0
3
0
0
2
2
0
2
2
1
2
0
0
0
1
2
0
1
0
0
2
1
0
0
0
0
0
4
2
0
0
0
0
2
1
0
1
0
0
0
1
0
1
0
0
1
1
0
1
0
1
1
0
0
1
1
1
2
0
0
1
0
0
1
0
2
2
2
0
3
1
0
0
2
0
1
2
2
1
1
0
3
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
2
0
0
0
1
1
2
0
1
2
2
0
0
2
3
2
1
1
1
0
2
1
1
0
0
2
0
0
0
1
2
2
2
0
1
0
0
0
0
2
0
1
0
1
0
0
2
3
0
2
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
2
2
1
2
2
0
0
0
0
2
0
0
0
0
2
0
2
1
1
1
1
1
1
0
0
0
0
0
2
0
2
1
0
0
0
2
2
1
2
0
1
1
2
0
1
1
0
0
0
3
2
1
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
2
2
2
0
0
1
1
0
0
0
1
1
0
1
0
1
0
1
0
1
2
0
1
0
1
1
0
0
0
0
2
0
2
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
2
0
0
0
0
1
0
0
0
2
0
2
0
1
2
0
4
0
0
0
2
0
1
1
0
1
1
0
0
1
0
1
1
0
0
2
0
0
0
1
0
0
0
0
0
2
0
1
1
0
2
1
0
0
0
0
2
1
0
1
0
0
1
1
0
2
1
0
1
0
1
0
1
1
0
0
0
0
1
2
0
0
0
0
2
2
3
0
0
2
2
1
2
0
2
2
0
0
0
0
1
0
2
0
9
1
0
2
0
0
2
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
2
2
0
2
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
2
0
2
0
1
0
0
0
0
2
0
0
0
0
1
1
1
0
2
2
2
0
1
0
0
0
0
1
2
0
0
0
0
1
0
2
2
2
4
0
0
0
0
2
0
0
0
3
1
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
1
1
0
2
0
0
1
1
0
0
0
0
0
2
0
0
0
2
0
0
1
0
1
2
0
2
1
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
2
0
2
0
0
0
2
2
0
1
1
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
3
2
0
5
0
0
1
0
1
0
0
4
2
1
0
0
2
0
0
2
1
0
0
0
0
1
2
0
0
2
0
0
0
1
0
6
1
2
0
2
0
0
0
0
0
0
1
0
1
0
2
0
2
2
2
0
0
0
2
0
1
0
0
0
0
1
2
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
1
0
1
1
1
2
0
2
0
1
0
0
0
0
0
2
2
2
2
0
0
1
0
0
1
1
2
0
0
0
1
0
3
0
1
0
2
0
1
1
1
1
0
1
2
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
2
0
2
0
0
2
0
1
1
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
1
1
0
1
0
1
0
0
2
0
0
0
2
0
0
0
0
1
5
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
2
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
2
1
0
0
6
0
2
2
0
0
3
2
0
0
0
0
1
0
0
0
0
2
1
0
0
0
1
1
0
0
0
1
0
2
0
2
2
0
1
1
0
0
0
0
2
2
0
0
1
0
0
0
2
2
0
1
2
1
1
1
0
0
0
1
0
0
1
0
1
2
0
0
2
0
1
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
1
2
0
0
0
1
0
1
2
2
1
1
1
0
1
2
0
2
0
2
2
2
0
1
2
1
0
0
0
0
1
2
2
0
1
0
2
0
1
3
0
1
0
0
0
2
0
0
2
0
4
0
3
0
1
1
1
0
1
1
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
2
3
0
0
0
1
1
0
2
1
0
2
0
0
1
0
0
2
1
0
0
0
1
0
0
1
0
1
2
0
0
0
0
2
2
0
0
2
1
0
2
2
2
0
0
1
0
0
0
0
0
2
0
2
0
0
2
1
0
0
0
2
2
0
1
0
2
1
2
0
0
1
3
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
1
2
1
0
0
2
0
1
1
1
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
1
1
1
1
1
1
0
0
1
0
1
1
0
0
2
1
0
0
2
0
0
0
2
0
1
0
2
2
2
2
1
0
0
0
0
0
1
1
0
1
0
0
0
2
2
0
0
1
1
0
2
1
1
0
1
1
1
0
2
0
2
0
0
0
0
0
0
0
1
2
1
1
1
0
0
0
2
2
0
0
2
0
0
0
0
0
0
1
1
0
1
1
0
1
0
0
0
1
0
0
0
0
2
0
2
0
0
0
1
0
0
1
1
1
0
1
0
1
2
0
0
0
1
1
2
0
0
1
2
0
0
0
0
1
0
1
0
0
0
2
0
2
1
2
0
2
0
0
2
1
1
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
2
0
0
0
0
1
2
1
0
2
0
1
0
0
1
0
1
0
0
1
0
0
4
2
0
1
0
2
1
0
1
1
2
1
3
0
0
2
0
0
0
0
0
0
1
2
2
0
0
0
0
0
2
0
2
1
0
0
0
2
0
2
0
2
2
1
2
1
1
2
0
0
2
3
0
0
2
0
2
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
3
3
0
0
0
0
0
0
0
0
0
0
0
2
1
2
2
1
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
1
0
1
0
0
2
0
0
2
0
0
4
0
0
1
1
0
0
0
0
0
1
2
0
0
2
0
0
1
1
1
0
0
2
3
0
0
2
0
0
2
2
1
0
2
2
2
0
1
1
1
2
0
0
0
0
1
1
2
0
0
2
0
0
1
1
0
0
0
2
1
0
2
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
1
2
1
2
0
2
0
0
2
0
0
0
1
2
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
1
2
0
0
1
1
2
2
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
2
0
1
1
2
2
0
0
0
0
0
1
1
2
2
0
0
0
0
0
0
1
1
1
1
2
0
1
1
0
2
0
1
0
1
0
1
0
0
0
0
0
1
0
1
0
0
2
0
3
0
0
0
1
1
2
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
1
1
2
0
1
0
0
0
1
0
0
0
0
0
2
1
0
0
1
0
0
2
1
0
0
0
2
0
0
0
2
2
0
0
0
1
0
0
0
2
0
2
2
0
0
1
2
1
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
2
0
0
0
0
2
1
3
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
2
1
2
2
0
0
2
1
0
1
1
0
1
0
1
2
0
0
1
0
4
2
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
1
0
1
0
2
0
2
0
0
0
0
0
2
2
1
1
0
0
2
2
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
1
2
0
0
0
2
0
0
0
1
0
0
2
0
1
2
0
0
2
0
0
0
4
0
0
0
2
0
0
3
0
1
2
1
0
0
1
0
0
0
0
1
0
0
0
2
1
0
2
1
0
0
0
2
1
1
2
2
1
0
2
0
1
0
1
0
1
2
1
2
1
2
0
0
0
0
3
1
0
1
0
2
0
0
0
0
1
1
0
0
0
1
0
0
2
4
0
0
0
0
2
2
0
1
2
0
1
2
1
1
0
1
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
3
0
2
2
0
2
1
2
1
0
1
2
2
2
0
0
0
2
0
2
2
0
3
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
1
2
0
1
2
2
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
1
2
3
0
0
0
1
0
2
0
2
1
0
1
0
0
0
0
0
1
0
1
1
0
1
1
0
1
0
2
0
0
0
0
0
1
0
1
2
0
1
0
1
0
0
0
1
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
2
0
2
0
0
0
1
2
1
0
1
2
2
0
2
0
1
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
2
0
1
1
0
0
0
2
0
2
1
2
0
0
0
0
2
1
2
0
0
0
3
0
0
1
0
0
0
0
0
0
0
1
1
1
0
1
1
0
0
0
0
2
1
1
0
0
0
0
2
2
0
2
1
0
2
0
1
1
0
0
0
2
2
0
0
0
0
0
0
0
2
0
9
2
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
2
0
0
1
0
1
0
1
0
0
0
0
2
0
0
2
1
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
2
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
1
0
0
2
1
2
1
0
1
2
0
0
0
2
1
0
2
1
0
0
0
0
0
2
2
2
1
0
0
0
1
1
0
2
2
1
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
2
0
1
3
0
0
0
0
2
1
1
1
1
1
0
0
0
1
0
0
1
0
2
1
1
0
0
1
0
0
0
0
0
0
1
0
2
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
1
2
1
1
0
0
2
1
0
1
2
1
3
0
2
1
1
0
1
1
0
0
0
0
0
2
0
0
0
1
1
0
1
0
1
2
0
0
0
2
0
2
0
1
0
2
0
0
0
1
2
0
0
1
0
1
1
0
1
0
0
1
0
1
0
0
0
0
2
0
0
0
0
1
0
1
1
0
1
2
1
1
0
1
0
0
0
1
1
0
0
1
0
0
0
0
1
0
2
0
0
0
0
3
0
2
0
0
0
1
0
4
0
0
0
2
0
2
0
0
0
0
0
1
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
2
0
2
0
0
0
0
0
1
2
0
0
1
0
0
0
0
1
0
2
0
1
0
0
1
2
0
2
0
0
0
1
2
0
2
1
2
1
0
0
2
0
0
0
0
1
1
2
0
1
0
0
1
0
0
1
0
0
2
0
0
0
3
0
1
0
0
1
1
0
0
1
0
2
2
0
0
1
1
0
1
1
0
1
0
1
0
0
0
2
1
1
1
0
0
0
0
1
0
0
0
0
2
0
1
0
1
1
0
1
1
1
0
0
0
2
0
2
2
2
0
0
0
2
2
0
0
0
1
1
0
1
2
1
0
2
0
2
0
2
1
2
2
1
0
0
0
2
1
0
2
1
0
0
2
1
0
1
0
0
2
2
0
1
0
0
0
0
0
1
0
1
2
0
0
0
2
0
2
0
0
0
3
0
0
0
1
2
1
0
1
2
0
1
2
1
2
0
1
3
0
1
1
0
1
0
0
0
2
1
0
0
0
1
2
3
0
0
0
1
2
0
0
3
2
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
1
0
0
0
0
2
0
3
0
1
0
0
2
2
0
0
0
0
0
0
2
0
1
2
0
0
0
2
0
2
0
1
0
2
0
0
2
1
0
0
3
1
0
2
1
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
2
0
2
0
0
2
1
0
2
0
2
0
0
1
1
0
0
0
0
3
0
0
1
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
2
0
2
0
0
0
1
0
0
0
2
2
2
2
1
1
0
0
0
0
1
0
1
0
0
2
1
2
2
0
0
2
0
0
1
0
0
2
0
2
0
0
0
5
1
2
1
1
1
1
0
0
2
2
0
0
0
1
2
0
1
2
0
0
0
1
0
2
1
0
0
0
0
0
0
3
1
0
0
0
0
2
0
0
1
0
1
0
0
1
2
0
2
0
0
0
2
3
2
0
0
0
0
0
0
0
0
2
5
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
1
1
2
0
0
3
1
2
0
0
0
1
0
2
0
0
2
0
2
0
0
0
2
5
1
1
2
1
0
2
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
2
1
0
2
0
0
0
2
0
0
2
2
0
0
0
0
3
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
2
1
0
0
1
0
0
2
2
0
0
0
0
2
0
0
1
0
2
3
0
0
0
0
0
2
0
2
2
2
2
0
0
1
0
1
3
0
1
0
0
1
1
3
1
1
1
2
1
0
0
0
2
0
0
2
1
2
0
0
1
0
1
0
0
0
0
0
0
1
1
1
0
2
0
1
0
0
1
0
0
0
1
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
1
2
0
0
0
2
2
0
0
1
1
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
1
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
2
1
0
0
0
0
1
1
0
1
1
1
1
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
2
2
3
2
2
1
2
2
3
0
4
0
0
0
1
1
0
4
0
0
0
0
0
0
1
1
0
2
0
1
0
0
1
0
1
0
0
0
0
1
0
0
1
1
0
0
0
4
1
1
1
0
1
1
3
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
3
0
0
1
0
1
0
0
2
2
1
0
4
1
0
1
0
0
0
0
1
0
0
0
0
0
1
1
3
1
0
0
0
0
1
2
1
0
1
0
2
2
1
0
1
1
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
2
1
1
0
1
0
0
2
0
2
0
2
2
1
0
0
1
0
0
2
2
0
0
4
0
0
0
1
2
0
0
0
0
0
2
0
2
1
0
0
0
1
2
0
0
1
0
2
0
3
0
0
0
1
2
0
0
1
2
4
0
0
0
1
2
2
1
0
0
0
2
2
0
1
0
2
2
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
1
0
2
1
0
2
2
1
0
0
4
0
1
0
0
1
1
0
1
1
2
0
0
0
0
0
2
1
0
1
1
0
0
0
0
1
2
0
0
3
1
1
1
2
0
1
0
1
1
1
0
0
1
0
0
0
2
2
1
1
1
0
0
0
1
1
2
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
1
2
2
1
2
0
1
0
2
2
1
1
3
0
1
1
1
0
2
0
0
1
0
0
0
0
2
1
0
0
1
1
0
0
0
1
0
1
0
1
0
2
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
1
0
0
0
3
0
3
0
0
0
1
0
1
1
0
0
1
1
1
0
1
0
2
1
0
0
0
1
2
2
1
0
0
0
0
1
0
0
1
1
0
0
0
1
2
0
1
0
2
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
2
0
0
1
0
1
2
0
1
0
0
0
0
0
1
2
0
0
0
1
0
1
1
0
2
0
0
0
2
0
2
0
0
3
2
1
2
1
2
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
2
0
1
1
0
0
1
1
0
0
0
2
1
0
2
0
0
0
0
1
2
0
0
0
1
1
2
0
0
0
0
0
0
2
0
2
0
0
1
2
2
2
1
0
2
0
1
0
0
0
0
1
0
0
0
4
0
0
0
1
1
1
0
2
2
0
0
0
0
0
0
1
1
2
0
0
0
0
1
0
0
3
0
2
0
0
0
1
0
2
2
0
2
0
0
1
1
2
2
0
2
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
2
1
0
2
0
1
0
0
0
1
0
5
0
1
0
2
2
0
2
0
1
0
0
0
9
0
2
0
1
1
2
0
0
2
0
2
1
2
1
2
3
1
0
2
0
0
0
0
0
0
2
1
0
0
1
2
0
2
0
0
0
1
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
3
2
0
2
2
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
2
1
0
2
0
1
1
2
1
2
0
8
1
0
0
1
1
0
3
0
0
2
0
0
1
1
2
0
1
2
1
0
0
0
0
0
0
1
0
2
1
1
0
0
0
3
2
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
1
0
1
0
1
0
2
0
0
0
2
0
0
0
0
0
0
1
1
2
1
2
0
2
1
2
0
0
0
0
0
0
0
2
1
0
0
1
2
0
1
0
0
0
0
0
0
0
0
1
1
1
2
0
0
0
2
0
1
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
1
2
0
0
5
1
0
0
0
1
1
1
0
2
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
2
0
2
0
0
0
2
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
1
0
0
2
0
1
1
0
2
0
0
0
0
1
2
0
0
0
1
0
0
2
2
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
2
2
1
2
0
1
0
0
0
1
1
1
0
2
0
0
0
0
1
0
0
2
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
4
2
0
0
0
0
2
0
0
1
0
0
1
2
4
1
2
0
0
0
0
0
0
0
2
1
2
0
0
2
1
1
1
0
0
0
1
0
2
2
1
1
0
1
0
1
0
0
1
2
1
1
0
1
0
0
0
1
2
0
0
0
0
2
0
2
0
0
0
0
2
2
1
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
1
2
0
0
2
0
0
0
4
0
1
0
1
0
1
0
0
0
2
0
1
0
0
1
0
1
0
2
2
1
2
2
1
0
1
0
0
2
0
0
0
0
0
1
0
2
1
0
0
2
0
0
0
0
0
0
0
0
1
2
0
2
1
2
0
2
0
0
0
2
0
1
1
0
1
1
2
0
0
0
0
0
0
0
0
1
0
0
2
2
1
2
0
0
1
0
0
2
1
0
0
4
1
1
2
2
0
0
0
1
0
0
2
0
3
1
0
0
0
0
1
0
0
1
0
9
0
1
2
0
2
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
3
2
2
0
0
7
2
0
1
0
0
3
0
0
1
2
0
1
1
1
1
0
0
1
0
0
0
0
1
1
0
1
2
2
0
1
0
0
0
0
0
0
0
1
0
0
6
0
0
0
0
0
1
1
3
2
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
1
2
0
0
2
2
0
0
0
0
0
0
1
0
0
1
1
2
0
2
0
0
0
1
0
0
1
1
0
2
0
3
0
2
0
1
0
0
1
1
3
1
0
0
4
0
0
1
2
2
2
0
0
0
2
0
0
2
0
0
0
0
2
0
0
1
0
2
1
2
0
0
0
0
4
0
0
0
2
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
2
0
0
0
0
0
0
2
2
0
0
1
0
0
0
1
0
2
2
0
2
5
0
0
2
0
2
0
0
2
0
0
0
0
1
0
1
0
0
2
2
0
2
0
1
1
1
0
1
0
0
2
2
1
0
0
1
2
1
0
1
0
2
0
0
1
0
0
2
0
0
0
0
0
1
0
1
0
4
0
0
0
2
0
1
0
0
0
0
2
2
0
0
0
0
0
0
1
2
0
0
0
2
1
0
0
0
0
2
0
2
0
1
2
2
2
0
0
0
0
1
1
0
0
0
0
2
0
2
0
0
0
0
0
0
1
2
0
2
0
0
0
2
1
2
0
0
0
0
0
0
0
1
1
0
0
0
2
0
1
0
1
0
0
0
2
1
0
2
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
1
1
0
2
0
0
2
0
5
0
0
0
0
2
0
1
0
0
2
0
0
0
0
1
1
3
2
0
0
0
1
2
0
0
0
1
0
0
1
0
2
0
2
1
0
0
2
0
0
0
1
0
3
2
2
0
1
0
0
1
0
1
0
0
0
2
2
0
0
2
1
0
0
0
2
1
2
0
0
0
0
0
0
1
1
0
2
0
0
2
2
0
1
1
0
1
0
2
0
1
1
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
3
0
0
1
0
0
3
1
2
0
1
0
0
0
1
0
2
0
1
0
0
1
0
2
0
0
0
4
1
0
0
2
1
0
0
0
2
2
1
2
0
0
1
0
0
0
1
2
1
0
0
0
1
1
0
0
0
1
2
1
2
2
0
0
0
2
0
2
0
6
1
0
0
1
0
2
0
2
0
2
1
0
0
0
0
0
1
2
0
0
0
0
4
1
2
0
0
2
0
0
0
0
1
0
0
0
2
1
2
0
2
1
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
1
2
0
2
0
1
1
0
0
1
2
1
0
0
0
2
1
2
0
0
3
0
0
3
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
2
0
2
0
0
0
1
0
2
3
2
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
1
1
2
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
2
1
0
0
2
0
1
0
0
2
2
0
1
1
0
0
1
0
0
2
1
0
1
2
0
0
0
1
0
0
0
2
3
0
2
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
2
0
2
2
0
0
0
0
0
0
2
0
2
2
2
0
1
2
2
0
0
2
0
0
0
0
0
1
0
2
0
0
0
2
2
2
0
0
2
0
1
1
1
0
0
2
0
0
0
0
0
0
1
2
0
2
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
1
2
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
1
0
0
1
0
0
0
0
2
2
2
0
1
0
2
1
0
0
3
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
2
2
0
2
2
0
0
0
0
3
0
1
0
0
0
0
0
0
1
0
1
0
0
0
2
0
2
0
1
1
1
0
1
2
0
0
0
1
0
0
0
0
0
0
2
0
0
1
2
2
2
0
2
1
0
0
0
0
0
0
0
2
0
1
0
1
0
2
1
2
1
1
1
1
0
0
0
0
0
1
0
0
1
1
1
0
0
2
1
1
0
2
0
2
2
0
0
0
0
0
2
0
0
2
1
0
0
0
0
1
0
2
0
0
1
1
0
1
1
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
3
1
2
2
2
0
2
2
1
2
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
3
0
2
0
0
0
0
1
0
0
1
0
2
0
0
0
1
0
1
1
2
0
1
1
2
2
0
2
0
0
0
0
0
2
0
0
1
0
0
0
2
0
1
0
2
0
1
0
0
1
0
0
1
0
0
2
0
2
1
3
0
0
0
0
0
2
0
0
1
1
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
1
0
0
2
2
0
0
0
0
1
0
2
0
0
0
2
0
2
1
1
0
1
0
2
1
0
0
1
0
0
2
2
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
3
0
0
1
3
0
0
1
2
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
2
1
0
0
0
2
0
0
0
1
0
1
0
0
0
1
2
0
0
0
1
0
0
0
2
1
0
0
1
0
1
0
2
2
0
0
0
0
1
1
0
0
2
2
0
1
0
1
2
0
0
0
0
0
0
0
0
0
1
1
2
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
2
1
0
2
0
0
0
0
0
1
1
0
0
0
0
0
2
0
2
0
0
2
2
2
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
2
1
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
2
5
1
0
0
1
2
1
0
1
0
0
0
2
1
0
0
1
4
0
1
0
0
0
2
0
0
0
2
0
1
0
0
0
2
1
1
1
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
2
1
1
0
2
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
2
2
1
1
1
0
0
1
0
0
0
0
2
2
0
0
2
0
0
0
0
2
2
0
0
0
1
2
1
0
2
1
0
2
1
0
0
0
0
0
1
1
0
0
1
2
1
1
0
2
0
0
0
0
2
0
0
0
0
1
2
0
1
0
0
0
1
0
5
0
0
0
2
0
0
2
2
2
0
1
0
1
0
0
1
0
0
0
0
0
0
2
1
0
1
0
0
2
2
0
2
0
0
0
3
0
1
2
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
1
1
0
1
1
0
2
0
1
2
0
2
0
0
2
2
0
1
2
0
2
2
2
1
1
2
0
1
1
3
1
0
0
0
1
1
3
0
1
1
0
0
0
0
0
1
0
2
1
1
0
0
1
0
1
0
0
0
0
1
2
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
2
1
0
0
0
3
2
0
0
0
2
0
0
2
0
0
0
1
0
0
0
2
0
0
1
0
2
0
0
0
1
2
0
1
0
1
0
2
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
2
2
0
0
2
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
2
0
0
2
1
1
0
1
4
2
2
1
0
2
0
1
0
0
0
2
0
1
0
1
0
0
0
4
1
0
2
1
1
2
0
1
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
4
1
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
4
2
2
1
2
2
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
1
0
0
2
0
0
0
2
0
0
0
1
2
0
1
1
2
0
2
2
0
0
0
0
2
0
0
0
1
2
1
2
1
2
0
0
1
2
0
1
0
0
1
2
0
0
1
1
2
0
0
0
0
0
0
0
2
0
2
2
1
0
0
1
0
0
2
0
0
0
0
1
2
2
0
0
1
2
2
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
2
0
0
2
2
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
3
0
0
1
2
0
2
1
2
0
0
0
1
1
1
0
1
0
1
3
0
0
0
0
0
0
0
2
2
0
1
0
1
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
1
2
1
2
0
2
2
0
0
0
1
1
1
0
0
1
1
0
2
2
0
2
1
3
2
2
0
0
5
0
0
1
2
1
0
4
1
1
1
0
2
0
0
0
0
2
0
0
1
2
1
1
2
0
0
1
0
0
2
0
0
2
1
0
0
1
0
0
2
2
0
0
0
2
0
0
0
0
0
0
2
3
0
0
2
0
0
1
0
0
0
0
4
1
0
1
1
0
0
0
2
1
1
0
0
2
0
1
0
2
1
2
1
0
0
1
0
0
0
0
1
1
0
0
0
0
2
2
2
2
2
2
0
1
0
0
0
0
0
0
1
0
2
1
0
1
0
0
2
2
0
0
0
1
0
3
2
0
0
0
2
0
2
0
4
0
1
0
0
0
2
0
0
0
0
0
1
0
2
1
2
2
0
0
1
0
0
2
2
1
1
0
0
1
0
2
1
0
0
1
2
1
0
0
2
0
2
2
0
0
0
0
0
0
0
1
2
1
1
0
1
0
0
0
0
0
0
0
0
2
2
0
0
2
2
1
1
0
2
2
1
0
0
0
2
1
2
0
1
0
0
1
1
0
2
0
0
0
2
0
0
0
1
1
0
0
0
0
1
0
2
1
0
0
2
0
2
2
1
0
1
0
2
0
1
0
0
0
0
1
2
1
2
2
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
2
0
1
2
0
0
0
0
0
1
0
0
0
2
0
2
1
1
0
0
1
0
2
1
2
0
2
0
2
1
0
1
0
1
2
0
2
0
0
0
0
1
0
1
1
2
2
0
2
2
0
0
1
1
0
0
1
2
0
2
2
0
0
0
0
1
1
2
0
1
1
0
0
0
2
2
0
2
1
1
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
1
1
0
3
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
2
1
0
0
2
0
0
0
0
0
1
1
0
0
1
0
1
0
0
2
1
0
2
0
2
0
1
3
2
1
0
2
0
0
0
2
0
1
0
2
0
2
1
6
0
0
1
0
0
0
0
0
0
2
2
1
0
2
1
0
0
0
0
1
0
1
1
2
0
0
0
2
1
1
0
2
2
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
2
0
1
0
0
0
2
2
0
2
1
0
1
1
0
0
1
1
2
2
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
2
0
0
2
2
0
1
0
0
2
0
0
0
2
0
1
0
0
2
0
0
0
0
0
4
0
0
0
0
0
2
2
1
0
0
0
2
2
1
2
1
0
0
0
2
3
0
2
0
0
2
1
4
0
2
0
0
0
0
0
0
1
2
0
0
1
1
0
0
0
0
0
0
2
1
1
1
0
0
1
0
0
1
1
0
1
2
1
0
1
2
1
1
0
0
3
0
0
3
0
1
0
0
1
0
0
2
1
0
0
0
2
0
1
0
0
1
2
0
2
1
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
2
0
2
0
0
1
0
0
2
0
0
1
0
0
1
0
0
0
1
0
0
0
2
0
0
0
2
3
1
2
0
0
1
0
2
1
0
0
1
0
1
0
0
0
0
1
1
0
1
0
2
0
0
0
0
1
0
2
2
2
1
1
0
1
2
0
0
1
2
1
1
0
0
0
0
0
1
1
0
0
1
0
1
1
0
0
0
1
2
0
0
2
0
2
1
1
0
0
1
1
2
1
0
0
0
1
0
3
2
0
0
2
1
0
2
0
0
1
3
1
0
0
2
0
2
2
1
2
1
0
0
0
0
1
1
0
0
0
0
0
2
0
2
0
1
2
0
0
0
0
0
0
0
0
1
1
2
0
0
4
0
0
0
0
2
0
3
0
2
1
2
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
1
0
2
0
0
3
1
2
0
1
0
0
1
0
0
1
1
0
0
0
0
2
1
2
0
0
0
1
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
1
3
2
1
2
2
0
0
1
1
0
1
0
0
2
1
0
0
0
0
1
0
0
0
0
3
1
0
0
0
1
0
2
0
0
2
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
1
1
0
0
0
1
2
0
0
0
0
0
1
0
0
0
1
1
0
2
0
3
0
0
1
1
2
4
0
0
0
2
1
0
1
1
1
0
0
0
2
2
1
1
0
0
2
0
0
2
0
0
0
0
0
3
0
1
2
0
1
2
0
0
0
2
0
0
0
1
2
0
0
0
2
1
0
0
2
1
3
0
1
0
0
1
0
1
2
0
0
2
0
0
1
1
0
0
0
2
2
1
2
0
0
1
0
0
1
2
0
0
2
0
0
0
2
2
0
2
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
2
2
0
2
0
0
0
3
0
0
0
2
1
0
1
1
0
0
0
0
0
0
0
2
0
0
2
1
0
0
2
0
0
0
0
1
1
0
0
0
0
2
1
0
0
2
0
0
2
0
0
0
1
0
2
1
1
0
0
1
3
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
1
1
0
0
1
1
0
2
0
2
0
0
0
0
0
1
2
0
1
0
2
0
0
0
0
0
0
1
1
2
0
0
0
2
0
0
2
0
2
0
0
0
0
0
1
1
0
0
2
1
0
0
1
3
0
0
0
1
2
0
2
0
1
1
0
1
0
2
2
1
2
1
1
0
1
2
0
2
0
0
0
0
2
0
0
0
0
1
2
0
2
0
2
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
5
0
2
0
1
2
0
0
1
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
2
0
1
0
1
1
0
1
1
0
1
2
1
1
0
1
1
2
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
2
0
0
2
0
2
1
0
3
1
1
1
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
1
0
2
0
2
0
1
0
0
0
0
0
0
2
1
0
0
2
1
2
0
0
0
1
1
2
0
0
1
1
0
0
0
1
2
0
0
0
0
0
0
1
1
0
2
2
0
1
0
0
1
0
2
0
0
0
1
2
0
2
0
1
0
1
0
1
0
0
1
0
1
0
0
2
1
1
0
0
2
0
0
2
1
0
1
1
0
0
0
0
0
0
5
1
1
0
0
0
2
1
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
14
0
1
0
0
1
0
2
0
1
1
2
1
0
0
0
0
0
0
0
2
1
0
2
2
1
1
0
1
0
1
2
0
0
0
0
1
0
0
2
0
0
2
2
0
0
0
0
1
1
3
2
0
0
0
0
2
2
2
0
1
0
1
1
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
3
1
0
0
1
0
0
0
1
0
1
0
0
0
1
2
0
0
1
0
2
1
1
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
1
0
0
1
0
0
0
3
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
1
2
0
0
2
0
0
0
1
0
0
2
2
0
1
0
0
2
1
0
2
0
0
0
0
0
0
3
0
0
0
1
1
0
1
0
2
1
0
1
0
4
0
0
0
2
0
1
2
1
0
1
0
2
0
0
0
0
1
0
1
0
0
1
0
0
2
2
0
1
2
2
1
1
0
0
1
0
1
1
0
2
0
0
1
0
0
2
0
0
0
0
0
2
1
1
0
0
0
0
0
1
2
1
0
0
0
2
2
0
2
0
0
0
2
0
1
0
0
0
0
0
1
2
0
1
0
0
1
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
1
1
0
2
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
1
1
0
2
1
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
1
1
0
0
0
1
1
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
2
0
2
1
0
0
2
1
2
0
0
0
1
1
1
0
0
0
0
0
1
2
2
0
1
2
2
1
0
2
0
0
0
4
0
0
2
1
2
1
1
0
0
0
0
0
2
0
2
1
3
0
4
0
1
2
2
1
0
0
2
0
0
2
0
0
1
1
2
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
1
0
1
0
0
1
0
0
1
0
2
1
0
1
0
0
2
0
0
0
2
0
0
0
0
0
1
0
2
2
0
0
0
1
2
0
0
1
0
1
0
1
0
3
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
1
2
0
0
0
0
0
0
0
2
0
2
0
2
2
1
0
0
0
0
2
2
0
1
2
0
0
0
1
1
0
0
0
1
2
0
0
0
0
0
2
0
1
2
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
2
0
0
2
0
2
2
0
0
2
1
0
0
1
2
0
1
0
0
2
1
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
3
1
2
1
0
0
0
0
0
0
1
2
1
0
0
3
1
3
2
0
0
0
0
15
0
3
2
0
0
2
0
1
2
0
0
0
0
2
1
1
2
0
1
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
1
0
2
1
2
1
1
0
1
0
1
1
2
1
0
0
0
2
0
0
0
1
2
0
2
0
1
2
0
0
3
1
0
0
0
1
1
0
0
0
0
0
2
1
0
2
1
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
2
3
0
4
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
2
1
0
0
0
1
0
0
0
1
0
0
0
3
0
2
0
1
3
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
1
0
2
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
1
2
2
1
0
2
0
2
0
1
0
0
0
1
2
1
1
0
1
2
1
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
1
1
0
0
4
2
0
3
0
1
0
1
1
0
2
1
0
0
0
1
3
0
0
0
0
0
0
1
0
0
0
2
0
2
0
1
0
0
0
0
2
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
3
2
0
1
0
2
0
0
1
0
2
1
0
1
2
1
1
0
0
2
0
1
0
0
1
0
2
1
0
1
0
0
0
0
1
0
0
0
0
1
0
2
0
0
1
0
0
2
1
0
2
1
1
0
1
0
1
0
0
0
0
0
0
0
2
1
2
0
0
0
0
1
0
1
0
0
1
0
0
0
0
2
0
0
0
1
1
1
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
2
1
0
0
2
0
0
0
0
2
0
0
2
0
0
2
0
1
0
0
2
1
0
1
0
0
0
0
0
0
0
0
1
0
2
2
2
0
0
0
0
0
0
2
2
2
2
2
1
0
0
2
0
2
0
3
0
2
0
1
0
1
2
0
0
2
0
0
0
0
1
0
1
1
2
0
0
2
0
0
1
0
2
3
0
0
0
1
1
2
1
0
2
0
0
0
2
1
1
2
1
1
0
0
0
0
3
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
2
0
2
0
1
0
1
1
0
1
0
2
2
1
0
0
1
0
0
2
0
1
0
2
0
0
1
3
0
0
1
0
2
1
2
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
2
2
0
1
0
0
0
1
2
1
0
1
0
0
0
1
0
1
0
0
0
0
2
1
0
2
0
0
1
0
0
0
4
0
2
0
0
0
0
0
0
0
2
3
0
0
0
0
0
1
0
2
0
0
0
0
0
2
2
1
0
0
1
0
0
2
0
0
0
3
2
2
0
0
1
1
0
0
0
0
2
2
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
1
0
2
0
0
0
0
1
0
0
0
2
0
2
1
0
1
0
0
1
1
0
1
0
0
2
0
2
0
1
0
1
0
0
0
0
0
2
3
1
0
0
1
0
1
1
0
1
0
0
0
0
1
0
0
0
0
1
0
2
3
1
1
0
0
0
0
0
1
1
0
0
0
0
3
2
2
0
2
0
2
1
2
1
0
0
2
1
1
3
0
2
0
0
1
4
1
2
2
0
0
0
1
0
1
0
2
1
2
0
0
2
0
0
0
2
1
0
0
2
0
0
0
1
0
0
0
0
0
1
0
3
2
0
2
0
0
0
0
0
0
0
0
2
2
0
2
0
1
3
2
0
2
2
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
1
3
0
0
0
0
0
0
0
1
2
2
1
1
0
0
2
3
0
0
0
0
1
0
2
1
0
1
0
2
0
0
0
0
0
0
2
2
0
1
1
0
0
0
0
1
0
0
0
2
1
0
7
0
2
0
2
0
2
0
1
0
0
1
1
1
0
1
0
0
0
1
1
1
0
0
0
0
1
0
1
1
3
2
2
1
1
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
1
0
0
0
1
0
0
1
0
0
2
0
1
0
2
0
0
0
0
2
2
0
0
0
1
0
0
0
1
0
0
0
0
2
1
1
0
1
0
0
1
0
0
1
0
0
0
0
1
2
0
1
3
0
2
0
1
2
0
2
0
2
0
1
0
0
1
0
0
1
0
2
0
0
2
0
1
0
0
0
0
0
1
0
0
2
1
0
0
1
0
0
0
1
1
0
0
2
1
0
0
2
2
0
1
0
2
1
2
1
1
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
2
0
0
1
0
0
0
1
1
0
0
1
1
0
0
1
0
2
3
1
0
2
0
0
1
1
0
0
2
0
1
0
1
0
0
0
0
1
0
2
3
1
2
1
0
0
1
4
1
0
1
2
1
2
0
2
1
2
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
2
0
0
0
2
1
0
0
2
3
1
1
1
1
0
0
0
2
0
0
0
2
0
2
0
0
0
0
2
1
0
0
2
2
1
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
2
2
2
3
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
2
1
0
0
0
0
1
0
1
1
0
0
0
1
2
1
1
0
0
0
0
1
2
1
0
0
2
0
1
2
0
1
0
2
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
2
0
1
2
1
0
0
0
0
1
0
0
0
0
0
2
1
2
2
1
1
1
0
1
0
0
1
0
0
1
1
1
0
1
0
0
0
0
0
1
2
0
1
2
0
0
1
1
1
3
2
0
2
0
0
2
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
1
1
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
2
2
2
0
3
1
0
0
2
0
1
3
0
0
1
0
0
0
0
2
1
2
0
0
2
0
0
1
0
1
0
2
0
0
2
1
0
0
2
0
0
0
0
1
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
1
0
0
0
0
0
2
2
0
1
1
0
0
0
1
0
0
0
1
0
0
0
2
0
2
0
0
0
0
2
0
0
0
2
0
1
2
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
1
1
0
0
2
0
0
2
2
0
2
0
0
0
1
1
0
0
0
2
2
1
0
0
2
0
0
2
2
0
1
2
1
0
2
1
1
1
0
0
1
0
1
1
1
0
1
0
2
2
1
0
2
1
2
2
0
0
0
0
0
0
1
13
0
1
0
0
0
0
0
0
2
2
2
1
0
0
0
0
0
1
0
0
2
2
1
0
0
2
0
0
0
2
1
0
1
0
2
1
2
1
1
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
3
2
0
0
0
0
0
2
0
0
0
1
7
1
1
0
1
1
0
2
1
0
0
1
0
2
1
2
0
0
2
0
0
1
2
0
3
1
0
0
0
3
0
0
0
1
0
1
1
0
1
2
0
0
0
4
0
0
2
0
0
0
1
0
0
0
0
0
2
1
0
1
0
0
2
0
1
0
0
2
2
0
0
0
0
2
2
0
0
0
1
0
1
2
2
0
0
0
0
0
0
2
0
1
0
2
0
2
0
3
0
0
0
0
0
0
0
1
2
2
1
0
0
1
0
0
0
1
3
0
0
0
0
2
0
0
1
1
2
0
0
1
0
0
2
0
1
1
0
0
2
1
1
1
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
1
0
1
0
0
2
1
0
0
0
3
0
0
1
0
0
2
2
0
1
0
0
2
0
1
0
2
0
1
0
1
0
0
2
0
0
0
1
1
1
2
0
0
0
0
1
2
1
1
0
2
0
2
2
0
2
2
0
0
1
0
0
0
4
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
1
0
2
1
3
2
2
0
0
2
0
2
1
0
1
0
0
0
2
1
0
0
1
0
2
0
2
1
1
0
0
0
0
0
0
0
0
1
1
0
2
0
1
0
0
1
0
0
0
0
0
0
0
2
0
1
1
0
1
0
0
0
2
1
0
2
0
0
2
0
2
0
0
0
2
3
0
0
1
0
1
2
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
3
0
1
1
0
2
1
0
0
2
3
0
0
0
0
2
2
1
0
0
2
2
1
2
3
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
2
0
0
1
0
0
0
2
0
0
0
2
1
0
1
0
0
1
0
0
1
2
0
0
2
4
1
1
1
0
2
1
2
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
2
0
1
0
0
1
0
0
1
7
0
1
1
0
0
0
1
0
1
0
0
0
0
1
1
2
0
0
2
0
0
0
1
0
0
1
0
3
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
2
1
3
2
1
0
0
0
0
0
0
1
0
1
1
1
1
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
2
1
0
3
0
2
0
0
1
2
0
0
1
0
1
0
2
2
1
0
0
0
2
0
0
0
0
0
0
0
2
3
0
0
1
4
0
1
0
0
1
0
0
0
1
0
0
0
2
1
0
0
0
0
0
1
1
0
0
0
1
0
3
0
2
0
3
0
2
0
0
1
2
0
2
0
0
1
0
0
2
0
2
0
0
0
2
0
0
5
0
0
1
0
0
0
0
1
1
0
0
0
2
0
2
2
0
0
0
0
1
0
2
0
0
1
1
0
0
1
0
2
0
2
0
0
0
2
0
0
0
0
1
2
1
2
1
0
2
0
0
4
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
5
1
0
1
0
4
0
1
2
0
0
0
2
0
1
2
0
0
0
2
1
2
0
1
0
0
0
1
1
0
1
2
2
1
2
2
1
2
0
2
1
0
1
0
0
2
0
2
0
2
0
1
2
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
2
2
2
2
1
0
2
0
2
0
2
1
1
2
0
1
1
2
0
2
1
3
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
1
0
0
1
0
0
0
1
0
2
0
0
1
0
0
2
0
0
2
2
0
1
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
2
1
0
0
0
2
2
0
1
2
0
1
2
1
0
0
1
0
0
1
1
0
0
1
0
2
2
0
0
0
2
1
0
2
0
2
1
0
3
1
2
2
0
0
0
1
1
0
1
0
2
0
0
0
1
0
0
0
2
2
0
2
2
2
0
1
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
1
3
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
2
1
1
0
0
0
2
1
1
0
0
0
0
0
0
0
2
2
1
0
0
2
0
0
3
0
0
1
0
0
1
0
2
0
2
1
0
2
2
0
0
2
1
0
0
1
2
0
0
1
2
0
0
0
1
0
2
0
0
2
0
2
0
0
0
0
1
2
1
1
0
1
0
0
4
0
0
0
1
2
0
0
0
2
1
1
0
0
1
0
2
0
2
0
1
0
0
2
0
0
1
0
0
0
3
0
0
0
0
0
0
0
2
0
0
1
1
1
0
2
2
0
0
0
0
0
0
1
1
0
0
0
0
2
0
3
0
2
1
0
0
1
0
2
0
2
3
1
1
2
0
1
1
2
0
1
0
0
1
0
0
1
1
1
1
1
0
0
0
0
1
1
2
2
0
0
0
0
0
1
0
2
2
0
1
3
0
2
0
0
2
1
0
1
0
1
0
2
1
2
0
1
0
2
2
2
0
1
1
0
0
0
0
0
0
2
0
2
1
1
0
0
0
2
1
0
1
1
1
0
0
2
2
0
1
1
0
1
2
0
2
0
0
1
0
0
0
2
0
1
0
1
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
2
0
0
0
1
2
2
0
0
1
0
0
0
0
1
1
0
1
0
0
0
2
2
1
2
1
0
2
0
0
0
0
2
2
0
0
0
1
1
0
0
0
2
1
0
1
0
2
0
0
1
0
2
0
0
1
0
0
1
1
0
0
0
1
0
0
0
1
1
1
1
0
2
0
1
1
1
0
1
0
0
2
0
0
0
0
2
0
0
1
2
0
1
2
0
0
1
2
0
1
0
0
0
0
0
3
2
0
0
1
0
1
0
2
1
0
0
2
0
0
0
0
0
0
2
1
1
0
1
1
2
0
0
1
1
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
2
0
2
0
0
0
0
0
1
1
0
0
2
0
2
1
0
0
0
0
0
0
2
0
2
1
0
0
0
1
1
0
1
0
0
2
2
0
0
1
2
1
2
2
1
2
0
0
0
0
0
0
0
0
0
2
0
2
1
0
1
1
0
1
1
1
2
0
0
1
1
2
0
2
0
1
1
2
0
0
2
0
0
0
0
0
1
1
0
0
0
0
1
2
0
2
2
0
2
0
0
1
0
0
1
1
0
0
0
1
1
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
1
2
0
2
0
0
2
0
0
0
0
0
0
0
2
1
0
0
2
0
2
1
0
0
0
2
2
1
0
1
1
0
2
1
0
0
0
1
0
0
0
0
0
1
1
1
2
0
0
0
0
0
1
0
0
2
2
0
1
3
1
0
0
0
1
0
0
2
0
0
0
2
1
1
0
0
0
0
0
0
1
2
0
0
2
2
0
2
0
1
0
0
2
0
0
0
0
1
1
0
0
2
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
1
2
0
2
2
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
4
2
2
2
0
0
1
0
2
0
0
0
2
0
0
0
0
0
1
0
1
0
2
1
2
0
0
2
1
0
0
0
0
0
0
4
1
0
0
2
2
1
0
3
0
0
0
0
0
0
0
0
1
1
2
1
0
1
1
0
1
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
1
0
1
2
1
1
0
2
0
0
0
1
0
2
2
0
2
0
1
2
0
1
0
1
0
0
0
2
1
1
0
0
0
0
1
2
0
2
0
0
1
1
0
0
0
0
1
1
0
0
1
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
1
2
2
0
0
0
1
1
0
0
0
2
0
0
1
2
1
0
0
0
0
2
0
1
0
1
0
0
2
1
2
0
1
0
2
0
0
1
0
0
2
0
1
0
2
0
1
2
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
1
0
0
0
2
0
2
0
0
0
0
0
2
0
0
2
1
0
1
1
0
0
0
0
0
0
1
1
0
0
1
2
0
2
0
0
2
0
0
0
0
4
1
2
0
0
0
2
0
0
1
5
1
2
1
0
2
1
2
0
0
0
1
1
1
0
0
0
0
2
0
1
0
1
3
0
2
1
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
2
0
0
1
0
1
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
3
0
0
5
1
1
2
1
2
0
0
3
1
1
0
0
2
0
0
0
2
0
0
2
2
1
1
1
1
0
0
0
0
2
0
0
0
1
2
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
1
0
0
2
0
0
2
0
0
1
0
1
2
0
0
0
0
2
0
1
2
0
0
0
0
0
0
3
1
1
1
1
2
1
2
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
2
2
2
3
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
1
0
1
0
0
0
2
0
1
0
0
1
0
1
0
1
1
1
0
2
2
2
0
0
0
0
0
0
0
2
2
0
0
1
0
0
2
0
1
0
0
1
0
0
0
2
1
0
3
0
0
3
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
2
0
2
1
1
1
0
0
2
0
0
2
1
0
0
0
3
0
1
0
2
0
0
0
0
0
2
0
0
1
2
2
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
3
1
4
0
1
1
2
0
0
0
2
2
0
0
0
0
0
0
0
0
1
1
0
2
0
0
1
0
0
1
0
0
0
1
0
0
0
3
0
1
1
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
1
2
1
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
2
0
0
0
0
2
0
1
0
0
0
0
1
0
2
0
0
0
1
0
1
0
0
0
2
1
0
0
2
0
1
1
0
0
0
0
2
1
0
2
1
0
3
1
0
0
1
2
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
2
1
1
0
2
1
3
1
0
1
1
2
0
2
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
1
0
0
2
0
0
2
1
0
2
2
0
2
1
0
1
0
0
1
0
1
0
1
2
0
0
2
2
0
0
0
0
2
1
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
2
0
0
0
0
1
0
0
0
1
0
1
0
1
0
1
0
0
0
1
1
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
1
2
1
0
1
0
2
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
1
2
0
2
2
0
0
0
1
0
1
0
2
0
0
2
2
0
2
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
1
1
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
2
0
0
0
3
0
1
0
0
0
0
0
0
0
2
0
1
1
0
1
0
0
0
0
0
0
1
1
2
0
0
1
2
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
1
1
0
0
0
0
2
1
0
1
1
1
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
1
0
0
2
0
1
1
1
0
2
1
0
0
1
1
0
0
1
3
0
0
0
1
0
0
0
0
1
0
2
0
0
2
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
2
0
1
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
1
2
1
1
0
2
0
0
0
1
0
1
0
0
2
0
2
0
0
2
1
0
1
0
0
1
2
0
0
0
0
0
0
1
0
2
1
0
0
0
2
1
1
0
0
0
0
1
1
2
0
2
2
0
0
0
2
1
0
1
0
0
1
1
0
0
0
1
2
1
1
0
2
1
0
0
1
1
0
0
0
0
1
0
2
0
0
0
0
0
3
2
0
2
1
1
1
0
0
0
0
1
0
0
2
0
0
1
2
2
0
0
0
1
0
1
0
0
0
0
3
0
0
0
0
2
0
0
0
0
1
1
1
1
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
2
3
0
0
1
1
1
0
1
1
0
1
2
0
1
0
0
0
0
2
0
0
0
2
1
0
0
0
1
0
0
0
0
0
1
0
0
2
0
2
2
0
0
0
3
1
0
0
0
1
0
2
0
2
3
1
1
1
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
1
0
0
2
0
0
0
0
1
0
0
2
1
2
1
2
0
1
2
2
2
2
0
0
2
0
0
2
0
0
0
0
1
1
0
2
1
0
0
0
0
0
1
0
0
1
0
0
0
2
2
0
1
0
1
1
0
0
0
0
0
3
0
1
1
0
1
1
2
2
1
2
0
0
3
2
1
1
1
0
2
0
0
0
1
0
0
2
1
0
2
0
2
2
2
2
1
0
2
0
0
1
1
0
1
0
2
0
0
0
2
0
0
0
0
1
0
1
3
0
2
0
1
1
0
2
0
2
0
0
0
0
1
2
1
0
0
0
0
2
0
2
2
2
0
0
2
0
0
1
1
1
0
1
1
0
2
0
0
0
2
0
0
0
2
2
0
2
3
0
3
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
2
0
1
0
0
1
1
0
1
0
0
0
1
2
0
0
2
0
2
0
1
4
0
0
1
2
0
1
0
1
1
0
0
0
0
2
2
0
2
0
0
1
0
2
3
0
1
2
0
0
0
0
1
0
2
0
0
1
0
2
0
1
0
1
0
0
0
0
0
1
0
1
0
3
0
0
2
2
0
2
0
0
0
1
1
2
2
0
1
1
2
1
1
1
0
3
0
0
1
0
0
0
0
0
0
1
2
0
0
1
1
3
1
1
0
0
0
0
2
2
1
0
0
0
0
0
1
1
1
2
0
0
0
1
0
2
0
1
0
0
2
2
2
0
0
0
2
0
2
2
3
0
2
0
2
0
1
2
2
0
2
0
1
0
4
0
0
0
1
1
0
1
0
0
0
0
0
2
0
0
0
1
2
0
0
0
2
0
0
0
2
2
0
0
2
0
1
2
0
0
0
1
0
0
0
1
1
2
0
0
0
0
0
1
0
2
2
0
1
0
1
3
0
1
0
2
1
0
0
0
0
0
0
0
2
0
0
0
2
2
0
1
0
1
0
1
1
0
1
0
0
0
0
1
1
0
0
1
2
0
1
0
2
0
0
0
1
1
0
2
1
0
0
2
0
1
1
0
0
1
1
0
0
0
0
4
2
0
0
0
1
3
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
2
2
1
1
0
1
0
0
0
0
0
2
0
2
2
1
1
0
2
0
1
0
2
0
2
2
1
0
1
2
0
0
0
2
0
1
0
0
0
2
1
0
0
2
0
1
0
0
2
0
1
1
0
0
0
0
3
0
2
0
0
0
0
1
1
0
0
0
4
2
0
2
1
1
2
0
1
0
1
0
2
0
0
0
2
3
1
0
0
2
0
1
0
3
0
0
1
0
2
0
0
0
0
1
1
1
1
0
2
1
0
0
0
0
0
0
1
2
1
1
0
0
0
0
0
0
1
0
0
0
2
1
1
0
1
2
0
0
0
1
0
0
2
3
2
2
0
1
0
0
2
0
1
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
1
2
0
0
0
0
1
1
1
1
0
0
0
2
2
0
2
2
0
1
1
1
3
0
2
2
0
0
1
0
0
0
0
2
0
1
1
0
3
0
1
1
2
0
0
2
2
0
0
0
0
0
0
1
0
1
2
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
2
0
1
1
0
0
0
3
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
1
1
0
0
1
1
0
2
0
0
1
0
0
1
0
2
2
1
1
1
1
1
0
1
1
2
0
2
0
1
1
0
0
0
0
0
0
2
0
0
1
2
0
0
2
0
2
1
1
2
1
1
0
0
0
2
0
0
2
0
0
2
1
0
1
3
2
0
0
2
0
2
0
0
0
2
0
0
2
0
0
0
1
1
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
3
0
1
2
0
0
0
2
1
0
2
1
1
0
2
2
0
0
1
0
0
0
0
0
2
1
0
0
1
0
1
1
2
0
2
0
0
3
1
0
0
0
4
0
3
2
2
0
2
0
1
1
1
1
0
0
0
0
0
0
1
0
1
2
2
1
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
1
2
2
0
2
1
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
3
0
0
0
0
0
1
1
0
1
0
1
0
0
1
0
0
0
0
0
2
0
2
0
1
2
0
0
1
0
2
0
1
0
0
0
1
1
2
1
3
3
0
1
1
2
0
0
2
1
0
0
1
2
2
0
0
0
0
1
2
0
2
0
1
1
0
1
0
0
2
0
0
0
1
1
0
2
0
0
0
1
0
1
0
2
0
0
0
1
0
2
0
0
0
0
3
2
1
2
2
0
0
2
1
0
0
1
2
0
0
1
3
0
0
0
0
1
1
1
0
2
2
0
1
0
0
1
0
0
0
1
0
0
0
0
2
0
1
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
3
2
0
2
1
1
0
0
0
0
2
2
0
1
0
0
2
0
1
0
1
1
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
1
0
0
1
0
2
0
1
0
3
0
0
0
2
2
1
0
0
2
0
1
0
1
1
1
3
1
1
1
0
0
0
0
1
0
0
1
2
0
0
1
0
0
0
1
1
0
1
0
2
0
2
0
0
2
2
0
1
0
0
0
0
1
0
1
0
2
0
2
0
3
0
2
1
0
0
0
0
0
2
1
0
0
1
1
0
0
0
2
1
0
2
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
1
2
1
0
0
3
2
0
2
0
1
2
2
1
1
0
1
2
2
1
2
2
1
1
0
0
0
2
0
1
1
1
0
0
0
0
0
0
3
2
1
0
1
0
0
0
0
0
2
0
0
1
2
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
2
0
0
1
1
2
0
0
1
0
1
1
1
0
0
1
1
1
0
1
0
2
0
0
0
0
1
0
0
1
0
0
0
3
0
2
1
0
0
2
0
0
2
1
2
0
1
0
2
0
3
2
1
0
1
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
2
1
0
0
0
2
0
0
0
0
2
0
1
0
0
1
0
0
2
0
0
0
2
0
1
0
0
2
0
0
0
0
1
2
1
0
0
0
0
0
0
2
1
0
2
1
1
0
5
2
0
0
0
0
0
1
0
0
1
2
1
0
0
2
0
2
0
0
2
1
0
0
0
2
1
3
1
0
0
0
2
0
1
0
0
0
0
0
0
1
1
0
0
1
4
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
2
0
0
3
0
1
1
0
0
0
0
0
2
1
0
1
0
1
0
0
0
2
0
0
1
1
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
1
3
2
0
1
0
1
2
1
0
0
0
0
0
0
2
2
1
0
0
3
0
1
2
0
0
1
0
0
0
0
1
0
4
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
1
0
1
1
1
1
0
0
0
0
0
0
0
0
1
1
2
0
1
2
0
0
2
1
0
2
1
0
1
0
0
2
2
1
2
0
0
0
0
3
1
0
1
0
0
1
0
0
0
4
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
2
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
2
2
0
0
0
0
0
1
2
0
0
2
0
0
0
0
2
1
1
1
0
1
0
0
0
1
0
0
0
1
0
0
0
2
0
3
0
1
1
0
0
0
1
0
1
0
2
2
2
1
0
0
1
2
0
0
0
0
0
1
0
2
1
0
0
0
0
1
0
1
0
2
0
2
1
0
1
0
1
0
0
1
0
1
0
1
0
0
0
2
1
0
0
3
1
4
1
0
1
0
0
0
4
0
1
0
2
0
1
1
1
5
1
0
0
0
0
0
2
0
1
0
0
0
1
0
1
0
0
0
1
2
0
0
0
2
0
0
0
3
1
0
0
0
1
0
0
0
2
2
2
0
0
1
0
2
2
1
0
0
0
1
2
0
0
1
2
1
0
0
0
0
3
1
2
0
0
0
2
0
0
0
1
0
0
0
10
0
0
0
0
0
0
0
1
0
2
0
2
0
1
1
0
0
0
1
1
1
0
0
1
0
2
0
2
1
1
1
1
0
0
0
0
2
0
0
0
0
3
1
2
1
0
0
0
0
2
0
1
0
1
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
2
2
0
0
1
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
1
0
0
2
2
0
0
2
1
2
5
0
0
1
0
0
0
0
0
1
0
1
0
1
2
0
0
0
0
0
1
3
0
2
0
0
1
2
0
0
1
0
3
1
0
2
0
0
0
2
1
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
3
0
0
2
1
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
2
0
1
0
0
0
2
4
0
0
1
1
1
0
0
0
1
0
2
0
1
1
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
2
1
0
2
0
0
1
0
2
0
1
1
1
0
1
0
0
2
0
0
0
1
1
0
0
0
0
0
1
0
0
2
0
1
0
0
0
2
2
3
1
2
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
1
2
1
2
0
0
1
0
2
3
0
0
1
0
0
1
2
4
0
1
0
2
2
0
0
1
0
0
0
0
0
1
2
0
1
0
0
0
0
0
1
3
0
0
1
0
0
0
0
0
0
0
1
1
0
0
2
1
0
0
0
1
0
2
0
0
0
2
0
0
0
2
2
0
0
2
1
1
0
0
0
2
0
2
2
0
1
0
0
2
1
2
0
0
1
0
1
1
1
0
0
0
0
1
1
0
0
1
2
0
0
2
0
0
0
0
0
1
1
0
1
0
1
0
1
0
3
1
0
0
1
0
0
1
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
1
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
2
0
2
0
0
0
1
0
2
0
0
2
0
0
2
2
0
0
1
0
0
1
2
1
0
0
0
1
2
0
1
1
0
1
2
0
1
0
0
0
0
3
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
1
0
1
0
2
1
1
0
1
0
2
2
0
0
1
2
0
0
0
1
0
1
0
2
0
2
1
1
3
0
0
0
0
2
2
0
0
0
1
3
0
2
2
0
2
0
0
0
1
2
0
0
0
0
1
0
1
2
0
1
2
1
2
0
0
0
0
2
0
2
1
1
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
2
1
0
0
1
0
2
0
0
0
2
0
2
0
2
0
2
0
0
0
0
0
0
0
0
1
2
0
2
1
2
3
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
3
1
1
0
0
0
1
0
2
2
2
0
1
1
2
0
0
2
2
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
1
1
0
0
1
1
0
0
0
0
2
0
2
1
4
2
0
0
0
1
1
3
0
1
0
1
0
1
0
0
1
0
0
1
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
4
2
1
0
0
1
0
1
0
0
0
0
2
0
0
3
2
2
0
2
2
0
0
0
0
0
2
2
1
2
0
0
1
0
0
0
1
0
2
1
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
2
0
4
2
2
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
1
0
1
1
0
1
2
1
0
2
0
1
2
0
0
2
0
0
1
0
1
0
0
0
0
0
2
2
0
1
2
1
0
0
2
1
0
0
0
2
2
2
0
0
0
0
0
2
1
1
0
0
2
1
0
2
2
0
0
0
0
0
1
0
1
0
1
2
0
2
1
0
1
1
1
0
0
0
1
2
1
2
2
1
2
1
1
0
0
0
1
2
0
2
0
0
0
2
3
0
0
0
0
0
0
0
0
2
1
2
1
0
0
0
0
0
0
0
0
2
2
0
0
1
1
0
1
0
0
1
2
1
1
0
0
0
1
2
0
0
0
0
0
0
0
0
3
0
0
1
0
0
2
0
0
0
2
1
0
1
2
2
1
0
2
0
2
0
1
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
2
2
2
0
0
1
0
1
0
1
1
0
1
1
2
2
0
1
2
0
0
1
1
0
0
0
1
0
0
2
1
1
3
0
2
0
2
1
0
0
0
0
0
0
2
0
2
0
2
0
2
0
0
0
0
0
2
0
0
0
2
0
0
1
1
0
0
1
1
0
1
1
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
1
0
2
2
2
0
1
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
1
0
1
2
1
0
1
1
0
0
0
2
1
0
0
1
1
2
1
0
0
0
0
0
2
1
1
2
0
2
0
1
0
0
0
0
2
0
2
1
0
0
0
1
2
0
0
0
0
2
2
0
0
0
0
1
0
1
0
1
1
0
1
2
0
2
0
0
2
0
0
0
0
0
0
2
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
1
0
0
0
2
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
1
0
1
3
0
0
0
0
0
0
2
1
0
2
0
2
0
0
0
0
1
2
1
0
0
3
0
0
1
0
2
0
1
0
0
2
0
0
0
0
1
0
0
0
0
2
2
0
0
1
1
0
2
1
1
2
0
0
1
0
0
0
0
0
2
2
0
0
0
0
1
1
0
2
1
0
0
1
0
0
0
0
1
0
1
0
0
0
2
0
0
0
1
2
2
1
0
0
0
4
0
0
1
1
0
1
1
0
0
0
0
0
5
0
1
0
0
0
2
0
1
0
1
1
2
0
2
1
0
2
0
0
1
0
0
0
2
0
0
0
1
2
0
0
2
0
0
0
1
2
0
1
0
0
0
0
1
1
0
0
2
0
0
2
1
0
0
0
0
0
0
2
0
1
0
0
2
0
0
6
2
2
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
9
0
1
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
2
2
1
1
0
0
2
0
0
0
0
2
1
0
0
2
0
4
0
0
0
0
1
0
1
1
0
1
2
0
0
0
1
0
0
0
0
2
0
1
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
1
1
0
0
1
0
2
1
0
0
1
0
1
2
0
0
1
0
0
0
3
0
3
2
0
2
0
0
0
2
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
2
0
3
0
1
1
0
2
0
1
0
1
2
0
0
0
2
0
1
0
0
0
0
3
0
0
0
0
1
0
1
1
0
1
0
0
1
0
2
2
1
0
1
1
0
0
2
0
1
1
0
0
0
0
2
0
2
0
0
1
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
1
0
1
2
1
1
0
0
3
0
0
0
0
1
0
0
0
0
7
0
3
0
0
0
0
1
0
0
1
0
1
0
0
0
0
2
1
1
1
0
0
0
0
2
2
2
0
2
0
2
2
0
0
0
0
0
0
1
1
0
0
0
2
0
0
1
2
0
0
0
1
0
0
1
0
1
0
0
1
0
2
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
2
1
2
2
0
1
0
2
0
2
2
0
1
1
0
2
2
0
2
0
1
1
1
0
0
0
0
3
0
5
0
2
0
3
2
0
0
0
1
0
1
1
0
0
2
0
0
1
1
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
2
0
1
0
0
1
0
2
0
5
1
1
2
0
0
0
1
0
0
0
0
1
0
2
1
0
0
0
1
0
1
0
0
2
0
0
2
1
0
0
2
1
0
1
0
0
0
0
1
0
2
0
0
0
1
1
2
1
1
0
1
0
0
0
0
0
2
4
0
2
0
0
3
0
0
0
1
1
1
0
0
1
2
0
0
0
1
1
0
1
0
0
0
0
1
0
1
0
0
1
0
0
1
2
1
0
2
0
0
2
2
0
0
2
0
0
0
3
0
0
1
1
0
0
1
0
0
0
1
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
1
0
0
0
2
0
2
3
0
0
0
0
0
2
0
2
3
1
2
1
2
0
0
1
0
2
0
0
0
0
2
1
0
0
0
1
1
3
2
1
0
1
3
0
1
0
0
0
1
0
0
2
0
2
2
0
1
2
1
2
2
0
0
2
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
3
1
0
0
2
0
0
0
1
1
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
1
0
2
1
1
2
1
0
0
0
0
1
0
0
0
1
2
0
0
1
0
0
2
1
2
0
0
0
1
0
0
0
0
1
0
0
0
2
2
2
0
0
0
0
2
2
1
0
1
0
0
2
0
0
0
2
3
2
1
3
2
0
0
0
2
1
1
2
0
1
2
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
1
2
0
1
0
0
1
2
3
0
1
0
1
0
0
2
0
1
0
0
1
1
1
0
2
0
0
2
1
1
0
0
0
1
0
0
0
0
2
2
0
1
4
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
3
2
1
0
1
0
2
0
1
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
1
2
1
0
0
1
1
0
1
2
0
0
1
5
0
1
2
0
1
0
0
0
0
0
0
0
1
0
2
4
1
2
0
1
0
2
2
0
1
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
1
1
1
0
0
1
1
1
1
0
2
2
2
1
2
1
2
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
1
1
0
2
0
2
0
0
0
1
2
1
0
1
0
1
2
0
1
0
1
0
1
4
0
1
0
1
0
2
0
0
1
1
1
0
0
0
0
0
3
0
1
1
2
1
0
2
3
0
1
0
1
0
1
0
0
1
2
2
0
1
1
0
0
0
0
0
2
1
1
0
0
1
2
2
1
0
1
2
1
0
0
0
2
1
1
0
0
2
1
0
1
0
1
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
1
1
1
0
0
1
0
4
2
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
1
0
2
2
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
2
0
2
1
0
1
0
1
0
0
1
1
0
3
2
1
1
0
2
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
2
1
1
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
2
0
0
0
2
0
1
0
0
4
2
1
0
1
0
0
0
1
0
2
2
2
0
0
0
0
2
1
0
2
2
2
1
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
3
2
0
2
1
1
2
0
0
6
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
2
2
1
0
0
1
0
0
0
0
0
1
0
0
2
0
2
0
1
2
1
1
0
1
0
2
0
1
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
1
0
0
1
2
2
3
0
0
2
1
2
1
0
0
0
5
2
2
0
0
1
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
1
2
0
2
2
0
1
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
3
1
1
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
1
1
0
3
1
2
0
0
1
1
0
0
2
1
1
0
1
0
1
1
1
0
2
0
0
0
1
0
3
0
0
2
1
0
2
0
0
1
0
2
0
1
0
0
2
0
0
1
0
2
0
2
0
0
1
0
0
0
2
0
1
0
1
1
0
1
2
0
0
1
2
0
0
0
0
8
0
2
2
0
1
1
0
0
1
0
0
1
0
7
0
0
2
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
1
0
2
1
2
2
1
0
0
0
1
0
0
0
0
0
3
0
1
0
0
0
2
2
1
0
1
2
0
0
0
0
0
1
0
1
0
0
0
0
3
0
2
0
1
2
0
0
0
1
0
0
0
1
0
0
0
0
1
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
1
3
1
1
1
2
1
0
0
0
0
0
0
0
1
0
1
1
0
0
3
2
1
2
1
2
0
1
0
1
2
0
0
2
0
0
0
0
2
2
0
0
1
1
0
1
0
0
1
1
0
0
0
0
0
0
1
0
2
2
1
2
0
2
0
0
0
2
0
2
1
2
0
0
1
0
0
0
0
1
2
3
0
2
0
0
0
0
2
1
1
0
2
1
1
0
0
3
0
1
0
2
1
1
0
0
1
0
2
2
1
2
0
1
0
2
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
2
2
2
0
0
0
0
0
3
2
0
0
2
2
0
0
1
1
0
1
0
2
0
2
0
0
0
0
0
2
0
2
4
2
0
1
2
0
1
1
0
0
1
2
0
1
2
0
0
2
0
0
2
1
0
0
0
1
0
1
3
1
0
0
0
0
1
0
1
0
0
2
1
2
1
0
0
1
0
0
1
2
2
2
0
0
0
0
1
1
0
0
2
1
1
0
1
0
0
0
0
1
1
2
1
2
0
0
2
1
0
0
0
0
0
1
0
0
1
0
1
0
0
2
2
0
0
0
0
1
0
0
0
2
2
2
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
3
0
0
1
2
2
0
0
1
1
0
1
2
0
0
0
2
1
0
0
0
1
0
0
0
3
0
0
0
0
1
0
1
2
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
1
0
2
0
0
0
0
2
1
1
1
2
0
2
0
1
0
0
0
0
2
1
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
2
0
1
0
0
1
0
0
0
0
1
0
1
0
1
0
0
1
0
3
0
2
0
2
1
0
0
0
1
0
1
0
2
0
2
2
1
1
0
0
1
0
0
0
0
0
0
3
1
1
0
0
0
2
0
0
2
1
2
0
0
0
1
1
0
2
1
1
0
0
0
0
1
3
0
0
0
2
0
2
1
1
0
0
0
1
0
2
1
0
0
0
1
2
0
0
0
2
1
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
2
2
0
0
0
0
0
0
0
1
0
3
2
1
0
0
0
0
0
0
2
2
1
0
4
0
0
2
1
2
1
0
0
2
0
3
0
0
0
3
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
4
0
1
0
1
0
2
0
0
0
0
0
0
0
1
5
0
1
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
2
2
0
2
1
0
2
0
0
0
1
2
0
2
0
2
1
0
3
2
2
0
0
0
0
1
0
1
0
0
1
1
0
0
0
1
1
0
1
0
0
1
1
0
1
0
1
0
4
0
2
0
0
2
0
1
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
2
0
1
0
1
0
0
1
1
0
0
1
0
0
0
2
0
1
0
0
1
0
1
0
1
0
0
0
0
1
0
2
0
0
1
0
0
0
3
0
0
3
2
0
1
0
1
0
0
1
0
0
0
0
1
0
1
0
0
1
0
1
1
2
0
0
0
1
2
1
1
0
0
2
1
0
0
2
0
3
0
1
1
0
0
1
0
1
0
2
0
0
1
0
2
0
1
0
0
0
0
1
0
1
1
1
1
0
2
1
0
0
2
0
0
0
0
2
1
1
1
2
0
0
1
0
1
0
1
1
2
0
0
2
0
2
3
0
0
1
1
1
1
0
2
0
0
2
2
0
0
2
0
2
0
0
0
0
2
2
1
1
1
0
0
0
2
1
0
1
0
2
0
0
0
0
1
3
1
1
0
0
2
1
0
0
0
2
0
1
1
1
0
0
0
0
0
0
3
0
2
1
0
0
1
0
0
0
1
0
1
0
0
0
3
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
1
0
3
1
0
0
1
0
0
2
0
0
0
1
0
0
1
0
1
1
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
1
0
2
0
1
1
2
0
2
2
0
1
0
0
0
2
2
1
0
2
2
0
1
0
0
0
0
2
0
0
2
0
2
0
0
2
0
0
0
0
0
0
2
0
2
0
0
2
2
1
0
2
0
0
0
0
3
0
1
0
1
2
0
1
1
0
1
0
2
0
0
0
3
1
2
0
2
0
0
2
0
2
2
0
0
0
0
0
0
0
0
1
2
0
3
0
0
0
2
3
0
1
0
0
2
2
1
1
0
4
0
1
1
0
0
0
2
0
2
0
2
0
0
1
1
1
1
0
0
0
1
1
1
2
1
1
0
1
0
1
0
0
0
1
0
2
0
0
0
0
2
0
0
1
2
1
2
0
0
1
1
0
0
0
0
0
1
0
0
1
1
0
0
1
0
2
2
0
0
3
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
1
2
0
0
0
1
0
2
1
0
2
0
0
0
1
2
0
0
0
2
0
2
0
2
2
0
0
0
0
0
2
0
1
3
2
1
0
0
1
2
0
0
2
0
0
2
1
0
0
0
0
0
2
2
0
0
0
0
1
2
0
2
2
0
2
0
1
1
2
2
1
1
0
0
1
0
0
0
2
0
0
1
0
1
0
0
0
2
0
0
0
2
0
0
1
0
0
0
1
0
1
0
0
1
0
0
2
0
0
2
1
1
0
2
0
0
0
1
0
0
0
0
2
0
1
2
0
1
0
0
1
1
0
0
0
0
2
3
0
0
1
0
0
2
0
2
0
0
0
0
0
1
0
0
0
2
1
1
0
0
0
0
0
1
2
0
1
1
0
0
1
2
2
0
2
2
1
2
0
0
0
1
0
0
0
0
0
0
0
2
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
2
0
0
0
0
1
0
1
0
1
2
0
0
1
2
2
1
0
0
1
0
1
1
0
0
1
0
1
2
1
0
1
0
0
0
0
0
0
1
2
1
0
2
1
1
2
0
0
0
2
0
0
2
1
1
0
0
1
2
0
2
0
1
0
2
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
2
2
2
0
0
1
1
1
0
0
0
0
0
1
0
4
1
1
2
0
4
0
2
1
0
0
1
0
0
0
0
2
1
2
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
2
0
0
0
0
1
1
0
0
0
0
0
1
0
2
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
1
0
0
0
2
0
0
1
1
1
1
1
0
0
0
0
0
1
0
0
1
0
0
1
0
1
1
0
1
0
0
0
0
1
0
0
4
0
0
0
0
3
0
1
0
0
4
1
0
0
5
0
1
2
0
1
1
1
0
1
1
1
0
0
0
1
0
0
0
2
0
2
0
0
1
3
1
0
0
0
1
0
0
2
1
2
2
0
0
2
1
0
0
0
0
0
0
0
0
1
0
2
6
1
0
4
0
1
0
0
0
1
1
1
1
0
2
2
0
0
2
0
1
1
2
2
2
1
1
2
0
1
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
1
1
0
0
1
0
1
0
1
0
0
0
2
0
0
0
0
0
2
0
0
2
1
0
0
1
0
0
2
1
0
0
1
0
2
2
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
2
0
1
0
0
0
2
1
0
1
2
0
1
2
1
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
1
0
3
0
0
0
0
0
0
2
1
0
0
0
0
0
1
1
0
0
0
0
1
1
2
1
2
0
2
0
0
0
0
2
2
0
0
2
1
0
1
0
0
1
1
0
0
2
0
0
0
1
1
0
0
1
2
0
0
1
0
1
0
0
1
2
2
2
0
1
1
1
2
1
0
2
3
2
0
0
0
2
2
0
0
2
0
0
2
1
0
0
0
2
0
0
2
2
0
1
0
1
2
2
1
0
0
0
2
0
1
1
0
0
0
0
1
0
1
2
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
1
0
1
0
0
0
0
0
0
1
2
0
2
2
0
1
0
0
1
1
3
0
2
0
1
0
0
1
2
2
0
0
2
1
2
0
2
2
0
2
1
0
0
0
0
0
0
1
0
2
1
1
0
0
0
1
0
2
0
2
1
2
0
2
0
0
1
0
0
0
0
0
1
1
2
1
0
2
0
0
0
1
0
2
0
5
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
2
1
0
1
2
0
0
2
0
0
0
0
0
0
0
2
1
1
0
0
1
2
2
0
0
1
2
1
0
0
0
2
0
0
0
1
4
1
0
0
2
0
0
2
0
0
1
1
2
1
0
1
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
2
0
0
2
0
1
0
0
0
1
0
0
0
1
0
2
0
0
0
0
2
2
1
0
0
1
1
1
0
1
1
2
0
3
0
2
0
0
0
0
0
1
0
0
2
0
0
0
2
1
0
1
1
0
2
2
0
1
0
0
1
1
1
0
0
2
1
1
1
0
0
2
0
0
0
1
0
0
2
0
0
0
1
0
0
2
1
0
0
1
1
0
2
0
1
3
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
2
1
0
1
1
0
0
0
0
0
0
1
5
1
1
2
1
0
1
1
2
2
0
0
2
1
2
0
0
2
1
0
0
0
0
1
1
0
0
0
1
0
2
0
1
0
1
2
2
0
2
0
0
0
4
0
1
0
2
0
0
0
2
0
0
1
1
0
1
2
0
0
0
0
2
0
0
1
0
0
2
1
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
1
0
0
1
0
0
1
0
0
0
1
2
0
1
3
1
0
2
1
0
0
0
0
2
0
0
1
0
0
0
0
1
2
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
3
2
0
0
0
0
1
0
2
2
1
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
4
1
1
2
0
0
0
0
2
0
3
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
2
2
2
0
0
1
0
3
0
0
2
1
0
1
0
0
1
0
0
0
1
2
1
2
0
0
1
0
1
0
1
1
1
1
0
2
1
1
0
0
1
0
3
0
0
0
1
2
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
4
2
0
3
0
2
0
1
1
1
0
1
0
1
0
3
2
0
0
1
1
2
1
0
0
2
2
0
0
0
0
3
1
1
0
2
0
0
3
2
2
0
0
0
2
4
1
0
0
0
0
0
0
2
0
0
0
1
1
0
2
2
0
1
0
0
0
2
0
0
0
0
0
1
0
0
2
2
0
0
1
0
0
1
1
0
0
0
2
1
0
0
2
1
0
1
1
0
0
0
2
0
0
0
0
0
0
3
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
2
0
2
0
2
2
0
1
1
0
1
0
0
0
0
0
0
0
2
0
2
4
0
0
1
1
2
1
0
0
1
0
0
0
2
3
0
1
0
2
0
0
3
0
2
2
0
0
0
2
0
0
0
2
0
0
0
1
0
1
0
1
0
1
0
0
1
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
2
0
1
0
1
0
0
0
2
0
2
0
1
0
0
0
1
1
0
0
0
2
0
0
1
0
0
0
2
1
0
1
1
0
1
0
2
2
1
0
2
0
2
2
0
0
0
0
0
1
2
0
0
2
0
0
0
0
1
2
2
0
1
0
1
1
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
1
1
1
1
0
0
2
0
0
1
1
0
0
2
2
0
0
2
1
0
0
2
0
2
2
0
1
0
0
0
2
0
0
0
0
0
0
3
2
0
1
0
1
2
2
1
1
0
1
0
0
0
0
0
1
1
0
1
0
0
3
1
0
0
1
0
1
0
2
1
1
0
1
0
2
0
1
0
1
0
0
1
1
2
1
2
0
0
0
13
0
0
2
1
0
0
0
2
2
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
1
0
0
2
0
3
1
1
0
0
0
2
0
0
0
2
0
4
0
1
0
0
1
0
0
0
2
1
0
0
1
0
0
0
0
1
1
0
1
2
1
0
1
1
1
0
1
2
0
1
0
0
1
2
1
0
0
0
0
2
0
0
0
2
2
0
0
0
2
0
1
0
0
1
0
0
2
0
2
0
1
2
0
0
0
0
2
0
0
0
0
0
1
1
0
2
0
2
1
0
0
3
0
1
0
0
0
1
0
0
0
0
0
0
3
2
1
1
0
0
0
5
2
0
1
0
0
1
0
0
2
0
0
2
0
0
3
2
0
1
1
0
0
2
0
0
0
0
2
0
1
0
0
0
2
0
1
0
0
0
1
0
2
0
0
0
0
0
0
2
1
0
0
0
1
1
3
0
0
1
2
0
2
0
2
0
0
0
0
0
3
0
0
2
0
2
1
0
0
0
0
4
0
2
1
2
2
2
2
0
0
0
2
0
2
0
1
0
1
0
0
0
2
1
0
1
0
0
0
1
0
0
0
1
0
2
0
0
2
0
0
1
0
1
1
0
1
2
0
0
2
0
2
1
0
1
0
0
3
2
0
0
2
0
0
0
2
0
0
0
2
1
0
0
0
1
2
1
0
2
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
2
1
0
0
0
0
0
0
3
0
1
0
0
2
0
0
0
0
0
2
1
2
0
1
0
0
1
0
0
1
1
0
1
0
2
0
2
2
1
0
1
0
1
0
2
1
0
0
0
0
0
0
6
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
2
0
1
1
0
0
1
2
2
0
0
1
0
0
0
2
1
0
0
2
0
0
0
0
0
0
2
1
0
0
0
2
0
1
0
2
0
0
3
1
2
3
4
0
2
1
2
0
1
1
0
0
0
2
0
1
0
0
1
2
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
2
2
0
0
0
0
0
1
0
0
1
0
1
0
1
4
1
1
0
0
0
0
2
0
0
0
1
0
0
2
2
1
0
0
0
1
0
1
2
0
0
1
2
0
0
0
0
0
1
2
2
0
1
2
1
0
0
1
1
0
0
0
0
0
0
0
2
1
0
1
1
2
0
2
0
0
1
2
0
0
2
1
0
0
1
1
0
0
1
0
2
0
1
0
2
0
0
0
0
0
0
0
2
1
2
0
1
2
2
2
0
0
1
0
0
0
2
2
0
0
1
2
0
0
1
0
0
0
2
2
1
2
1
0
2
0
0
2
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
2
1
0
0
0
1
2
0
1
0
2
0
1
0
2
0
1
0
0
1
3
0
0
0
2
2
0
0
1
0
0
0
2
0
0
2
2
3
0
0
0
0
0
0
0
0
1
2
0
0
2
1
1
5
0
0
3
0
0
2
0
2
0
0
0
0
0
1
0
0
2
0
2
0
0
2
1
0
0
1
0
0
1
0
0
2
1
0
0
2
2
1
0
0
0
2
2
1
2
0
2
0
0
1
0
0
0
2
0
0
0
0
2
0
1
0
1
2
0
1
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
4
0
0
2
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
2
1
1
2
0
0
6
2
1
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
2
0
1
0
0
1
2
1
0
1
0
1
2
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
1
0
1
0
1
0
0
0
2
0
2
0
2
2
0
0
1
0
0
1
0
2
0
0
2
0
2
0
0
2
1
0
0
0
2
0
1
0
0
0
0
0
1
1
2
1
0
1
0
0
0
0
0
0
2
1
0
0
2
0
1
0
0
0
0
2
2
2
0
1
0
1
0
2
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
1
2
0
2
0
3
3
0
0
0
2
2
0
0
2
1
2
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
2
2
0
1
0
1
1
0
0
0
2
1
0
0
0
3
0
0
2
2
0
0
0
2
0
0
0
0
1
2
0
2
0
1
0
0
0
0
1
0
1
0
1
0
2
0
0
0
0
1
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
1
0
1
0
0
3
1
0
0
1
0
0
0
0
1
0
0
0
0
1
2
1
1
2
1
1
1
0
2
0
0
0
2
0
2
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
2
2
1
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
2
0
2
0
0
0
1
2
0
0
1
1
2
1
1
1
0
2
0
1
2
2
0
0
0
0
0
0
0
0
2
0
0
1
1
1
0
0
1
1
2
1
1
0
0
0
0
1
0
1
2
0
0
2
0
0
1
0
0
1
1
0
0
0
0
1
1
0
2
0
0
1
0
1
1
0
1
0
2
2
1
0
0
1
1
2
1
2
0
1
0
0
2
0
2
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
3
0
0
0
2
1
0
0
0
3
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
2
1
0
2
0
1
2
0
0
1
1
2
0
4
2
0
2
0
0
1
0
1
0
0
2
0
0
0
0
2
0
4
0
0
0
0
2
0
0
0
0
0
0
1
2
0
1
2
0
1
2
0
0
1
0
0
0
0
2
0
0
0
0
0
3
0
1
1
1
0
0
0
3
0
0
1
0
0
1
2
0
0
0
0
1
1
0
2
0
3
0
0
2
1
0
0
0
1
0
0
0
0
0
2
0
2
0
0
2
1
0
2
0
1
0
0
1
0
1
1
0
0
2
0
0
1
1
0
0
1
1
0
0
0
2
0
2
1
0
2
0
0
0
0
0
0
1
0
0
0
0
1
2
0
1
0
2
0
0
0
0
0
0
0
0
2
2
1
1
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
2
1
0
1
0
0
0
0
0
1
2
0
2
0
2
2
0
0
0
1
0
2
0
0
0
0
1
1
2
0
1
0
1
0
0
0
2
0
0
0
0
1
0
1
0
0
0
2
1
1
0
0
1
2
1
0
0
0
0
2
1
1
0
2
0
2
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
1
0
1
1
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
3
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
1
1
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
2
2
2
0
0
0
0
1
0
2
2
0
0
1
0
0
0
2
2
1
2
0
1
0
0
2
0
0
2
0
1
1
1
2
0
0
2
0
1
0
0
0
0
0
0
0
2
0
1
2
0
0
1
1
1
0
0
2
1
1
2
2
1
0
0
1
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
2
0
0
0
0
1
1
0
0
2
2
2
0
2
1
1
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
1
0
0
0
0
0
0
2
0
1
0
2
2
0
0
1
0
0
0
2
2
0
2
0
0
0
1
1
1
1
0
1
1
2
0
0
1
0
0
2
0
1
0
0
1
0
0
0
1
0
0
2
2
1
0
0
0
2
2
0
1
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
1
0
0
2
1
2
0
2
1
0
0
0
2
1
0
0
0
1
0
0
0
0
1
0
1
3
0
0
0
1
1
2
0
2
0
1
0
2
0
2
0
1
2
0
0
0
0
2
0
2
1
0
0
0
0
2
0
0
2
2
1
0
0
0
0
0
2
2
0
1
2
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
2
1
1
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
1
1
1
2
0
1
0
2
1
1
0
0
0
1
1
0
0
0
1
0
0
0
1
2
0
1
0
0
1
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
1
0
2
2
2
0
0
2
1
0
1
2
0
0
1
0
2
0
1
2
2
2
0
0
1
2
0
1
0
0
3
0
0
1
1
1
0
0
0
0
1
1
1
0
2
0
0
2
2
0
0
0
2
2
0
0
0
1
1
0
0
0
2
0
0
3
1
1
3
0
2
2
2
0
1
0
0
2
0
2
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
1
0
1
0
0
0
0
0
1
0
0
2
2
0
2
0
1
2
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
2
0
0
0
0
0
1
2
2
2
0
0
2
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
1
2
0
1
0
0
1
1
1
0
0
0
1
0
0
1
0
0
2
0
0
0
0
1
0
2
2
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
2
0
0
0
1
0
1
0
1
2
1
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
1
0
1
0
2
0
1
0
2
1
0
2
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
1
0
0
1
0
0
0
2
0
1
2
2
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
1
2
0
0
0
0
1
1
0
0
2
2
0
2
0
0
0
0
0
0
1
2
1
1
0
0
0
0
0
2
0
0
1
1
1
2
0
2
0
0
2
0
0
0
2
0
2
1
1
0
0
0
3
1
1
0
0
2
0
0
0
0
1
0
0
0
0
1
1
2
0
2
1
0
1
2
1
0
1
7
0
0
0
0
0
1
1
0
0
0
1
0
2
2
1
0
2
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
1
2
0
2
2
0
0
0
0
1
6
0
1
1
3
2
0
2
0
2
1
0
1
2
2
2
0
0
0
0
1
0
0
1
1
0
3
0
0
0
2
1
2
0
1
0
0
1
1
0
2
0
0
3
0
1
2
0
1
0
0
0
3
0
0
0
0
0
3
0
0
0
0
2
0
2
1
2
2
0
0
2
2
0
0
1
0
1
1
0
0
2
2
0
0
2
0
0
1
0
0
1
2
0
0
0
0
0
0
1
2
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
1
0
1
1
1
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
1
0
0
0
0
0
0
2
0
0
0
0
2
1
2
0
0
0
0
1
2
0
0
1
0
0
2
1
2
0
1
1
0
0
2
1
0
0
0
2
2
1
0
1
0
0
0
0
2
0
1
1
0
1
0
2
1
0
1
1
0
0
1
0
0
1
2
0
0
2
2
2
0
1
0
2
0
1
0
0
0
0
0
2
3
2
0
1
1
0
0
2
0
0
1
0
0
0
2
1
0
2
0
0
0
0
2
1
0
0
1
2
1
0
0
0
0
1
0
0
2
0
0
0
0
2
2
0
0
2
0
2
1
0
2
1
1
0
0
0
2
0
2
0
0
0
0
2
1
0
1
2
2
1
0
0
0
0
1
4
0
2
0
0
0
0
0
1
1
1
1
1
2
3
0
0
0
1
0
0
2
1
1
0
0
0
0
0
0
1
0
2
2
2
0
2
0
0
0
1
1
0
1
5
0
0
0
2
1
0
0
0
0
0
2
1
2
0
0
2
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
2
0
0
0
0
2
1
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
1
0
0
1
0
0
0
1
0
2
0
0
0
0
1
1
1
1
0
2
1
1
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
2
0
1
2
1
2
2
1
1
0
0
0
2
0
2
0
0
0
1
0
0
2
0
2
2
1
0
1
0
0
0
1
2
0
2
0
2
1
1
0
0
2
1
0
0
0
2
1
2
2
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
1
0
0
0
0
1
0
2
2
0
0
0
2
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
1
2
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
2
1
0
1
2
1
2
0
0
0
2
0
1
0
0
0
0
1
1
1
0
1
2
2
2
0
0
1
0
0
2
1
0
2
0
2
2
0
0
1
0
2
0
2
2
2
0
0
0
2
2
0
0
3
0
1
1
0
2
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
1
0
2
1
0
0
1
1
2
1
0
1
0
0
0
2
1
0
2
0
0
1
0
0
0
1
0
4
1
0
1
0
2
1
1
2
0
0
0
0
1
0
2
0
0
1
2
1
0
1
2
0
0
1
0
0
0
1
1
2
3
0
0
0
1
1
2
1
1
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
2
1
0
0
0
0
0
0
2
0
0
2
0
0
0
1
2
0
0
0
0
1
2
0
0
2
1
1
1
0
0
0
0
0
0
1
0
1
0
2
0
1
0
0
0
0
0
0
0
1
0
1
2
0
0
1
1
0
1
0
1
0
0
0
0
0
2
1
1
0
0
1
1
0
0
0
2
0
1
0
1
0
2
0
0
0
2
0
0
2
0
0
1
1
0
0
0
0
1
0
0
2
1
2
0
0
0
2
1
0
0
1
0
0
1
0
1
1
2
1
0
0
0
0
0
2
1
1
1
0
0
0
2
0
1
1
3
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
5
0
1
1
0
2
0
0
0
1
0
2
1
0
2
0
2
2
0
0
0
0
0
2
1
0
0
0
2
1
0
0
0
0
3
0
2
2
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
1
1
1
2
0
1
3
0
2
0
1
1
0
0
0
1
0
0
1
0
0
2
1
1
0
0
0
0
0
1
0
1
0
2
0
0
1
2
2
0
0
1
1
2
0
0
0
0
1
0
2
1
2
0
0
0
1
0
2
0
0
1
0
2
0
0
0
1
1
1
0
1
0
0
0
1
1
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
1
0
2
0
0
1
1
2
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
1
0
0
2
0
1
0
0
1
1
2
2
1
0
1
0
0
0
1
0
0
0
1
0
0
0
2
0
1
1
0
0
0
0
1
0
0
0
1
2
2
3
0
2
0
0
1
0
0
1
0
0
0
5
2
0
0
1
1
0
1
0
0
0
0
1
2
0
0
0
1
3
1
1
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
1
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
2
1
0
0
1
2
0
1
1
2
0
0
0
0
3
1
0
0
0
1
0
0
0
1
0
2
0
1
0
3
0
2
0
1
2
2
1
2
0
0
0
2
1
2
0
1
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
1
2
0
0
1
1
2
0
1
0
0
0
0
1
0
0
2
0
2
0
0
1
0
0
0
0
2
1
0
2
1
2
1
2
0
0
1
0
2
1
0
0
2
0
2
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
2
0
1
1
0
0
2
0
1
0
1
0
0
1
0
0
0
1
0
0
2
2
2
0
0
0
0
0
0
0
2
0
3
0
0
1
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
1
0
1
0
0
2
1
0
0
2
0
1
1
0
0
0
0
2
2
0
2
0
0
2
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
2
1
0
1
2
0
1
2
0
0
1
1
2
2
1
2
0
0
2
2
0
0
0
2
0
0
2
2
2
0
2
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
1
1
0
0
1
0
1
5
1
0
0
0
0
2
1
0
1
1
0
0
0
0
2
2
0
0
0
0
1
0
1
0
0
2
0
0
2
0
0
1
0
0
0
2
0
0
0
1
1
1
0
0
0
0
1
0
1
0
0
2
2
0
0
0
1
0
0
0
0
1
0
2
2
1
0
0
1
0
0
2
0
2
1
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
1
0
2
0
0
2
0
0
0
0
2
0
2
0
0
0
2
1
0
2
0
1
0
0
0
0
1
3
2
2
0
0
0
2
0
0
1
0
2
1
0
0
0
1
0
0
0
2
2
0
0
0
0
1
0
2
1
2
0
1
0
0
0
0
1
0
0
1
1
0
0
2
0
1
0
0
2
0
1
2
0
1
0
0
1
0
0
1
0
0
0
1
0
1
1
0
0
0
2
0
1
0
1
1
2
0
0
2
2
1
1
0
1
0
1
0
0
0
0
2
2
0
2
1
0
2
0
1
0
0
1
0
0
3
2
2
0
0
1
0
2
0
0
3
2
1
0
1
2
0
1
0
1
0
0
0
1
2
0
1
2
0
0
0
0
2
1
2
0
0
0
1
1
0
0
0
1
2
0
0
0
2
0
0
1
2
1
0
0
0
0
1
0
0
1
2
0
0
0
1
1
0
0
2
1
0
1
1
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
1
4
0
0
0
0
2
0
0
0
0
0
1
1
0
0
1
0
0
0
2
1
0
1
0
0
0
1
1
2
1
1
2
1
1
0
0
2
0
1
1
2
2
3
0
0
0
1
0
0
0
0
0
2
0
2
1
0
1
0
0
2
0
0
0
2
0
0
0
1
0
1
0
0
2
1
0
1
0
0
0
1
0
1
0
0
0
0
1
2
0
0
2
1
0
1
2
0
0
2
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
1
1
1
0
0
0
1
2
0
1
0
0
0
1
1
0
1
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
1
0
1
2
2
0
0
0
0
0
2
1
1
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
1
0
1
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
4
1
1
0
0
0
0
1
0
1
0
0
1
0
0
1
2
1
0
0
0
0
0
0
0
1
0
0
1
2
2
0
0
1
0
0
0
2
0
0
0
2
0
1
2
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
2
1
0
1
0
0
0
1
0
1
0
0
2
0
0
2
0
0
0
2
2
0
0
0
2
0
2
0
2
0
2
1
1
0
2
0
2
1
0
0
1
0
1
0
1
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
1
2
0
1
3
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
2
0
0
1
1
0
0
1
0
2
0
0
0
0
0
0
0
1
0
2
2
1
2
0
0
2
2
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
1
1
1
0
0
0
2
2
0
2
0
0
3
0
0
2
1
1
0
0
1
0
2
3
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
1
0
1
2
1
0
0
2
0
1
0
1
0
1
1
2
1
0
1
0
0
0
2
2
2
0
0
2
2
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
1
0
1
2
2
0
2
2
2
0
0
1
0
1
0
1
1
0
0
1
2
0
0
1
1
1
0
0
0
0
2
1
0
0
1
1
2
0
0
0
0
2
2
0
2
0
1
2
0
0
0
1
0
1
1
0
0
1
0
0
2
0
0
2
0
2
1
2
0
0
2
0
0
0
1
0
0
1
2
2
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
2
2
2
0
1
0
0
0
2
1
2
0
0
0
2
2
0
2
0
2
1
1
0
0
0
1
1
0
1
3
0
1
0
1
0
2
1
0
0
0
1
0
0
1
0
2
0
0
0
1
0
0
1
2
0
3
0
0
2
0
0
0
1
0
1
0
1
1
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
2
0
2
0
0
0
0
0
0
2
4
0
2
0
1
0
0
0
0
2
0
1
0
3
1
0
0
0
0
2
2
0
0
0
2
2
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
2
1
0
0
0
0
1
0
0
0
0
0
2
0
2
1
0
0
1
0
0
1
0
0
0
2
2
0
1
1
0
0
1
0
2
1
0
0
0
2
0
0
0
1
0
0
2
0
0
0
1
1
0
0
0
1
0
3
2
0
0
0
1
0
2
1
0
2
0
0
2
1
1
1
0
0
1
0
2
0
0
2
2
0
0
0
0
2
0
2
0
0
0
0
0
0
3
1
1
0
1
1
0
2
1
2
0
2
1
0
0
1
0
2
2
1
0
1
1
0
0
0
0
1
0
0
1
0
2
0
1
1
0
0
0
0
0
0
0
2
0
0
3
1
0
0
2
1
0
0
0
2
2
2
2
1
1
0
0
0
0
1
0
1
1
2
2
0
1
0
2
1
1
2
1
0
0
2
3
0
1
0
2
0
0
0
0
2
2
0
1
0
0
1
2
3
0
1
2
1
0
2
1
0
1
1
1
2
2
0
0
4
2
0
1
0
0
1
2
0
0
0
1
1
2
0
2
0
0
0
0
2
1
2
0
0
2
1
1
0
1
0
1
0
1
2
2
0
0
1
0
2
2
2
0
1
0
0
0
0
1
2
0
1
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
2
0
1
2
1
0
0
0
0
2
0
1
1
0
0
1
2
0
2
0
0
1
0
1
0
0
1
0
1
0
0
3
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
3
1
0
2
0
0
2
1
0
0
1
0
2
0
1
1
0
0
0
2
4
2
0
3
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
1
1
1
0
2
0
0
0
0
1
0
1
2
0
1
0
2
0
1
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
2
0
0
1
0
1
0
0
0
1
1
0
1
1
1
0
0
0
2
0
2
1
1
2
0
0
0
3
1
0
0
2
0
1
0
2
1
0
0
0
1
0
0
2
1
1
0
0
2
0
0
0
0
2
0
1
2
2
0
0
1
2
0
0
0
0
2
0
0
1
2
0
0
0
1
1
0
1
1
1
0
1
1
0
0
0
0
0
0
0
0
1
1
0
1
0
1
3
1
1
0
1
1
0
0
2
0
1
0
3
1
2
0
0
0
2
0
2
0
0
1
2
0
0
0
0
1
0
0
0
1
1
0
1
0
0
2
1
2
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
2
0
0
1
0
3
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
1
1
0
1
1
1
1
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
1
0
1
0
1
0
2
2
2
0
0
0
1
0
3
1
1
1
0
0
0
0
2
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
2
0
2
1
0
0
3
1
0
2
0
0
2
0
0
0
0
1
3
0
0
0
2
0
0
0
0
1
1
2
0
1
4
0
0
0
1
0
0
0
0
0
0
0
1
0
1
2
0
0
0
1
0
0
2
0
0
2
0
2
1
1
1
0
2
0
0
1
0
0
2
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
2
1
2
0
0
0
1
0
0
1
0
2
0
0
0
2
0
2
0
0
2
1
1
1
0
0
0
1
1
0
0
0
0
2
2
0
0
0
0
0
1
0
1
0
1
0
0
1
1
2
1
0
4
1
0
2
0
1
1
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
1
2
1
1
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
1
2
0
0
1
0
0
0
2
1
1
0
0
1
0
0
2
1
2
0
3
1
0
1
4
0
0
2
2
2
0
1
0
1
0
0
1
1
1
0
0
0
0
2
0
0
2
1
0
2
1
2
0
2
0
1
1
2
0
0
0
0
0
2
1
0
1
0
1
0
0
1
0
2
0
0
0
0
3
0
0
0
0
2
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
1
0
1
1
2
0
0
0
0
0
2
0
0
2
0
0
3
0
1
1
0
1
0
0
1
0
2
0
2
2
0
0
1
0
0
2
0
2
2
1
0
0
1
0
1
0
3
0
0
0
2
3
0
0
0
0
1
0
1
2
0
0
0
1
1
1
2
0
0
0
2
2
0
2
1
0
0
1
0
1
1
0
0
0
0
1
0
0
2
1
0
1
2
0
1
0
1
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
2
1
0
0
0
1
0
0
2
1
0
0
0
2
0
0
2
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
1
1
0
0
1
0
0
0
0
0
2
0
1
1
0
2
2
2
0
0
1
2
0
0
0
1
0
0
0
0
1
2
1
0
0
1
1
1
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
1
1
2
1
2
0
1
0
2
2
2
0
2
0
2
0
0
0
0
2
0
2
2
1
0
2
1
1
2
0
0
1
0
1
0
1
0
0
2
1
0
0
0
0
0
1
0
1
0
0
0
0
2
2
1
0
1
1
1
1
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
2
2
0
2
0
0
0
2
0
0
0
0
2
0
0
6
1
0
0
1
0
1
2
1
0
1
1
0
2
0
0
1
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
4
2
2
2
2
1
0
0
0
0
2
0
0
1
1
0
0
1
0
1
0
0
1
1
0
2
1
0
1
2
1
0
2
2
0
3
0
0
0
1
0
0
1
0
0
2
0
2
0
0
1
1
0
0
1
0
2
0
0
1
0
0
2
1
1
0
0
1
0
2
0
0
2
0
0
1
2
0
0
0
2
0
0
0
0
0
0
1
1
2
1
1
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
1
1
0
0
0
1
0
2
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
2
0
0
1
0
5
0
0
0
0
0
3
1
0
0
1
0
0
0
0
0
0
1
2
2
2
1
0
1
1
0
2
0
0
0
0
0
1
3
2
0
0
0
0
1
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
1
2
2
2
0
0
1
0
0
3
2
2
0
0
2
0
2
1
0
0
0
2
0
0
0
2
1
2
1
2
2
2
0
1
0
1
0
0
1
0
1
0
0
1
0
2
0
0
2
0
1
0
0
0
1
0
0
2
2
0
0
1
0
0
1
2
0
1
2
1
2
1
2
0
0
0
1
0
3
2
0
0
2
0
0
0
0
1
1
0
0
0
1
4
0
0
2
1
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
3
1
0
0
1
0
2
0
2
0
1
1
2
1
0
2
0
0
0
0
0
0
2
0
2
0
1
0
2
0
0
1
2
0
1
0
0
3
0
0
0
1
0
2
1
1
1
0
3
0
0
2
0
2
0
0
0
0
2
0
0
1
0
2
0
0
1
0
0
1
0
1
1
0
1
1
2
1
0
2
0
1
0
0
0
0
2
1
5
1
0
0
0
0
0
1
3
0
2
2
0
0
0
2
0
2
0
2
2
2
1
0
0
2
0
0
1
0
0
1
2
2
0
0
0
1
2
0
1
0
0
1
0
2
2
0
1
1
0
0
2
2
2
0
0
0
0
1
3
2
2
2
2
0
2
0
0
0
0
0
0
1
0
2
2
0
1
2
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
2
0
2
1
1
1
1
0
0
2
2
0
0
0
0
0
1
0
0
3
0
1
0
0
1
2
1
0
0
2
0
1
0
0
2
1
2
0
1
0
2
1
1
2
1
1
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
1
4
0
0
0
0
0
0
1
3
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
2
2
1
0
1
1
0
0
0
1
0
1
1
0
1
2
1
0
0
0
1
0
0
0
2
0
0
1
0
0
0
1
0
0
1
0
0
0
2
2
0
1
0
0
0
1
0
0
0
1
0
2
0
0
2
2
1
0
1
0
3
1
0
2
3
0
0
1
0
0
0
1
2
0
2
2
0
0
0
0
2
0
1
2
2
0
0
0
1
0
1
3
0
0
4
0
0
2
2
0
0
0
0
0
0
2
0
1
0
0
2
2
3
0
2
1
1
0
0
0
0
1
1
2
1
2
1
2
1
0
0
0
0
0
0
1
0
0
0
0
1
0
2
1
2
0
0
0
0
2
0
2
0
0
0
5
1
0
0
1
0
0
1
0
2
2
0
2
0
1
1
2
1
1
0
0
2
2
2
0
0
1
2
0
2
0
2
2
0
1
0
2
1
2
0
2
0
0
0
2
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
3
1
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
2
2
0
1
1
0
0
3
2
1
0
0
1
0
0
1
0
0
1
0
1
1
0
1
1
0
0
2
0
0
0
0
0
0
1
0
0
2
0
2
0
0
1
1
1
1
0
0
0
1
0
0
2
3
0
0
0
0
1
0
0
2
1
1
1
1
0
0
0
0
2
2
1
0
1
1
0
0
0
1
2
1
1
0
1
0
2
2
1
0
1
1
0
0
0
1
0
0
2
0
0
2
0
0
0
1
2
2
0
3
1
0
1
2
2
0
0
0
1
1
0
0
0
0
2
0
0
1
0
0
0
0
2
1
3
0
2
0
2
0
2
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
2
0
2
0
0
2
0
2
1
0
2
0
0
1
0
0
2
0
1
0
0
1
3
0
1
2
0
0
2
1
0
0
0
0
0
0
0
2
1
1
0
2
0
0
2
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
3
1
1
1
1
1
0
0
0
0
0
0
2
3
1
0
2
1
0
2
0
0
0
0
0
0
0
2
2
2
0
1
0
1
1
0
0
0
0
0
0
3
0
1
1
0
2
1
0
0
1
0
0
0
1
0
2
0
2
0
0
0
2
0
0
0
0
0
2
2
0
1
1
0
1
1
0
0
0
0
2
0
1
0
0
0
0
2
0
0
2
0
0
0
2
0
1
0
0
1
1
1
2
0
3
0
0
0
2
2
2
1
0
0
2
1
0
0
2
0
0
2
2
2
2
0
0
0
1
0
2
1
0
0
0
0
1
0
0
2
0
0
0
0
0
2
1
1
1
2
1
0
0
1
0
0
0
0
2
0
0
0
2
0
1
2
1
0
1
2
1
0
1
1
1
0
1
0
0
0
2
0
0
2
0
0
2
0
0
1
3
1
0
0
2
1
0
0
2
5
0
0
1
2
0
0
0
0
2
2
0
0
0
2
1
0
1
0
2
0
1
1
0
0
2
0
1
0
0
0
0
0
0
2
2
2
2
1
0
0
0
1
0
1
0
1
2
0
0
0
0
1
0
3
1
0
1
0
0
0
0
0
0
1
0
1
1
0
1
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
2
0
0
2
1
0
0
0
2
0
0
2
2
0
1
1
2
0
0
0
2
1
2
0
0
1
0
0
0
0
1
0
0
2
0
1
1
0
2
0
0
0
0
0
2
2
0
0
1
2
1
0
0
1
0
0
0
0
0
0
2
0
0
2
2
0
0
2
2
0
2
2
0
1
0
1
1
0
1
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
1
2
2
0
0
0
2
1
0
0
0
1
0
0
1
0
2
0
0
2
1
1
0
1
2
0
0
0
1
0
0
1
0
0
1
2
0
0
0
1
0
2
2
0
2
1
1
0
2
1
0
0
3
2
2
0
0
0
0
1
0
1
1
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
2
2
0
0
2
0
0
0
2
2
2
0
0
1
0
0
0
0
0
2
0
0
1
2
1
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
1
0
4
0
0
0
0
0
2
0
0
1
0
2
2
2
1
2
0
0
1
1
2
0
3
2
1
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
2
0
0
0
1
0
1
0
0
0
0
2
2
0
0
1
2
2
0
3
2
0
0
2
0
0
1
1
0
0
0
1
1
0
2
0
0
0
0
0
1
1
1
0
0
0
1
2
1
1
1
0
2
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
2
0
2
0
2
0
3
2
0
5
1
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
1
0
1
0
2
2
0
2
0
0
1
2
0
1
0
2
2
0
1
0
0
0
0
0
0
0
1
2
0
0
0
1
0
2
1
2
1
0
0
3
0
0
0
1
1
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
3
0
0
0
0
2
2
2
0
0
2
0
0
2
2
0
0
0
0
3
1
0
0
0
2
0
0
1
0
2
1
2
0
0
0
0
0
0
0
2
1
0
0
1
0
1
2
0
0
0
0
1
0
2
0
2
0
0
0
1
2
0
1
0
1
0
5
2
1
0
1
0
2
1
0
1
0
0
1
0
0
2
0
0
0
4
0
0
2
1
0
3
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
1
1
1
1
0
0
0
0
0
2
0
2
0
2
0
1
1
1
1
0
0
2
1
2
2
1
1
0
0
0
0
0
1
2
0
0
2
2
0
0
0
0
2
3
1
0
2
1
0
0
5
2
0
0
0
0
0
0
0
1
1
1
2
2
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
2
1
2
0
3
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
1
0
0
1
0
0
1
2
2
0
0
0
0
0
1
1
0
0
3
0
0
1
0
0
1
2
0
0
0
2
0
0
2
0
1
2
1
1
0
0
0
0
1
0
0
0
1
0
2
0
0
0
2
1
0
0
0
1
1
0
0
0
0
0
2
0
0
2
0
0
1
2
0
1
0
0
0
1
0
2
1
0
0
0
0
2
2
0
0
2
0
2
0
0
1
0
1
2
0
0
0
0
1
0
0
1
0
1
2
0
1
1
1
2
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
3
2
1
0
0
2
0
0
2
0
1
2
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
1
2
0
0
1
2
0
0
0
0
1
2
2
0
0
0
0
3
0
0
0
0
0
2
0
0
2
1
0
2
2
0
0
1
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
1
2
0
0
0
0
0
2
0
1
2
2
0
0
0
1
0
0
0
2
0
1
2
0
4
1
0
0
0
2
3
2
5
0
2
0
1
2
0
0
0
0
0
1
0
0
1
0
2
0
0
1
0
0
1
0
0
1
2
0
0
0
2
0
2
0
2
0
2
0
0
0
1
0
0
0
1
1
2
0
0
0
1
0
1
0
0
1
0
1
1
2
0
1
0
1
0
2
1
0
2
0
0
0
1
2
0
0
0
1
1
0
0
0
0
2
2
0
0
0
6
0
0
1
2
1
1
1
2
1
0
0
0
0
0
0
0
0
0
1
2
0
0
2
1
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
1
2
2
0
1
0
0
0
0
2
2
0
0
1
2
0
2
0
0
0
0
1
0
2
0
0
0
2
0
1
0
2
10
2
4
0
2
0
0
2
0
0
1
0
0
0
0
0
1
0
0
4
0
0
1
2
1
0
1
0
0
0
0
1
1
2
1
2
0
1
1
0
2
2
0
1
2
3
0
0
2
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
1
0
0
1
0
0
0
2
0
2
0
0
0
2
0
0
2
0
3
0
2
0
0
2
2
0
0
0
2
1
0
3
0
0
0
0
1
1
0
1
1
0
1
0
0
0
2
0
0
0
0
0
1
3
0
0
0
0
1
1
2
0
1
0
0
2
1
1
0
0
1
1
2
0
3
2
0
0
1
2
0
0
0
0
1
2
0
0
2
2
0
0
1
0
3
0
0
0
0
3
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
2
1
2
0
0
0
0
2
0
0
0
1
1
0
0
0
0
1
1
1
1
1
0
2
1
0
0
1
0
0
2
1
0
0
2
1
2
0
2
2
0
1
0
2
0
0
0
1
0
0
0
1
1
0
2
0
1
2
0
0
0
1
0
1
1
1
2
2
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
2
2
1
1
0
1
1
0
0
0
0
1
0
2
2
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
5
0
1
0
2
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
1
0
1
0
0
0
5
0
0
0
1
0
2
1
1
1
1
0
1
1
0
1
2
0
1
0
0
0
0
0
1
0
0
2
0
5
4
1
1
1
0
2
0
0
0
0
0
0
0
0
2
0
2
0
2
9
1
6
1
1
1
2
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
2
1
0
0
2
0
1
1
1
1
0
0
1
1
1
0
0
0
2
0
0
0
0
1
0
0
3
0
1
0
1
2
0
0
1
2
0
2
0
0
0
0
2
1
0
2
0
2
0
0
0
0
0
1
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
3
0
0
0
1
0
0
0
1
0
1
0
1
1
0
0
1
0
1
3
2
2
1
2
0
0
2
0
0
0
3
0
1
0
1
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
2
0
2
2
2
0
0
0
2
0
3
0
1
1
0
0
0
0
2
0
0
1
0
0
0
1
2
1
1
1
0
2
0
0
2
0
2
0
0
0
2
0
1
0
0
2
0
0
2
0
1
0
0
0
0
1
0
0
1
2
1
1
0
0
0
3
0
0
0
0
0
0
1
0
1
0
0
1
1
1
0
0
1
0
0
2
0
0
1
1
0
2
0
0
3
0
2
0
1
1
0
0
2
0
3
2
0
1
2
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
3
0
0
0
0
0
3
0
1
0
0
0
0
1
0
1
2
0
1
0
0
0
1
2
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
1
0
1
4
0
1
0
1
0
0
0
0
0
0
1
2
0
1
0
0
2
0
0
1
1
1
1
1
1
2
2
1
2
2
2
0
0
0
2
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
3
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
1
1
2
1
0
0
0
1
1
0
3
2
0
0
1
0
2
0
0
1
2
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
1
1
0
0
1
2
0
2
1
0
0
0
0
0
0
2
2
0
1
2
0
1
0
2
0
1
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
1
0
1
2
0
2
0
0
1
0
0
0
0
0
2
1
0
0
2
0
2
0
2
0
1
1
0
0
0
0
1
1
1
0
1
0
1
1
0
0
2
1
1
0
0
2
0
0
2
0
2
0
0
0
0
1
2
1
2
0
0
0
2
1
0
0
3
0
1
0
0
2
0
1
0
1
1
2
2
1
0
0
1
1
0
0
0
2
0
0
0
0
0
2
0
0
0
5
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
1
0
1
2
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
2
0
1
0
1
0
1
0
1
0
0
1
0
0
2
0
2
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
4
1
0
1
0
0
0
0
1
0
1
0
1
1
0
0
1
1
1
5
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
2
2
0
0
0
0
3
0
0
0
0
3
0
0
0
0
1
1
0
2
2
0
0
0
0
1
0
1
2
2
3
2
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
2
0
0
0
1
2
1
0
0
1
0
0
0
1
0
0
1
1
0
0
0
2
2
1
0
0
1
2
0
0
0
2
0
2
1
2
0
0
1
0
1
0
0
0
0
0
2
0
2
0
0
1
0
0
1
1
0
2
1
0
0
2
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
1
0
0
1
0
2
2
0
0
1
1
0
1
0
1
1
0
0
0
0
0
2
0
0
2
0
1
1
0
0
1
0
0
0
2
1
0
0
2
0
3
2
1
1
1
0
0
0
3
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
2
2
0
0
2
1
1
0
1
0
0
0
0
1
0
0
3
0
1
0
0
2
0
0
1
0
0
0
2
0
0
2
0
1
0
0
2
0
1
2
0
0
0
1
1
0
2
2
2
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
2
2
1
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
2
2
0
0
0
0
0
0
2
4
0
0
0
0
1
0
2
0
0
1
2
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
2
0
0
2
2
0
0
0
0
1
1
0
1
0
2
0
1
1
0
0
0
2
2
1
0
0
0
1
2
1
2
1
1
0
3
0
0
1
0
2
0
2
1
0
0
0
1
1
0
0
1
1
0
0
0
0
1
0
0
2
1
1
2
0
1
1
1
0
0
0
2
1
0
2
2
0
1
2
1
0
0
1
0
1
2
0
2
1
0
2
1
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
1
0
1
5
0
0
2
0
2
2
2
2
0
0
2
1
0
0
0
0
0
2
0
0
0
2
2
0
0
0
2
1
0
1
0
3
0
0
0
0
0
0
0
1
0
0
0
2
2
0
2
0
0
0
2
0
0
3
0
1
0
1
0
2
1
0
2
0
0
0
2
0
0
0
1
0
0
0
1
0
0
1
0
0
2
0
0
0
1
2
0
0
0
0
2
1
0
0
0
0
0
2
0
2
1
2
2
0
0
0
1
1
0
2
1
0
0
0
0
0
0
2
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
1
0
2
1
0
3
2
0
2
1
0
0
0
0
0
3
2
0
1
1
2
0
0
0
0
2
0
0
0
2
0
1
0
1
0
1
0
2
1
0
1
0
0
2
0
2
0
0
2
2
0
1
0
1
2
1
2
0
0
2
1
0
0
1
0
0
0
0
2
0
0
0
1
2
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
1
0
0
2
0
0
0
0
0
2
2
0
1
0
0
2
0
2
3
0
0
1
0
1
1
1
1
1
0
1
0
1
0
0
2
1
0
2
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
1
2
0
2
1
0
0
1
0
0
0
0
0
1
0
2
0
0
1
0
0
1
0
1
2
1
2
1
0
2
0
0
0
1
0
4
2
1
0
0
1
0
0
2
1
2
1
2
0
0
1
0
2
0
1
0
0
4
0
1
1
0
0
2
1
0
2
0
0
2
0
0
0
1
1
2
0
1
2
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
2
0
0
2
0
1
2
0
0
0
0
0
1
0
0
0
1
1
1
1
0
2
0
1
2
3
0
0
0
1
1
0
2
1
0
3
0
1
2
1
0
4
0
1
1
6
0
0
1
3
0
1
0
0
0
0
2
0
0
2
0
2
0
2
0
0
1
1
0
2
0
2
0
1
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
1
4
0
0
0
1
1
1
0
0
1
1
0
0
0
1
2
0
1
0
1
0
0
2
0
0
1
0
0
0
0
2
0
2
0
3
1
1
1
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
1
2
1
2
0
2
0
1
2
3
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
1
0
2
0
0
2
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
1
0
1
2
1
2
0
0
0
0
0
1
0
1
0
0
0
2
0
0
1
1
0
0
0
0
1
2
0
0
0
0
2
0
0
3
0
1
0
1
0
3
0
0
0
0
0
1
2
0
2
0
2
0
0
0
1
2
1
0
0
1
0
1
2
0
0
0
0
2
2
0
2
0
2
0
0
0
1
0
1
0
0
0
0
2
0
0
0
1
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
2
1
0
0
0
2
0
0
0
0
2
2
2
0
5
1
2
0
0
0
0
0
1
0
0
2
1
0
1
1
1
0
0
0
3
0
0
2
0
2
0
2
1
1
0
0
0
1
1
1
0
0
0
0
1
1
1
1
1
0
0
0
2
0
0
2
0
1
0
0
2
2
1
0
0
0
0
0
2
3
0
0
1
0
0
0
0
0
1
0
2
0
0
2
0
1
2
4
0
1
0
0
0
0
0
0
0
0
6
2
1
1
0
0
0
0
0
0
0
1
3
0
2
1
0
0
0
1
2
1
2
0
0
2
0
0
0
0
0
1
4
0
0
0
0
2
0
1
0
1
1
0
1
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
2
0
1
1
1
0
3
2
0
0
1
0
1
0
0
2
2
0
2
0
0
0
2
0
2
3
0
0
1
0
0
2
0
0
0
2
0
2
2
2
0
2
0
0
0
0
1
1
2
0
2
2
0
1
2
0
2
1
2
1
0
0
0
1
0
0
0
1
0
0
0
2
1
9
1
1
2
0
0
0
2
0
2
0
1
2
0
1
1
1
2
1
0
0
2
2
1
0
0
1
2
0
0
0
0
2
0
2
3
1
0
0
2
0
1
0
0
1
0
3
0
1
1
1
0
0
0
4
1
0
0
0
0
2
0
5
0
0
2
0
0
1
1
2
1
0
0
2
2
0
0
2
0
0
1
2
1
2
2
0
0
0
1
1
2
0
0
0
2
2
0
2
1
0
0
0
0
0
1
0
0
2
1
1
0
0
1
0
0
1
1
1
1
0
2
0
1
0
1
0
2
0
0
0
0
0
0
0
2
0
1
1
0
0
2
0
2
0
0
0
1
2
2
0
0
0
0
0
0
0
2
0
0
2
2
0
1
0
1
2
0
2
0
1
0
1
0
3
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
1
2
0
0
2
1
1
0
1
0
0
0
0
2
0
2
0
1
2
0
2
2
1
0
2
0
1
0
1
2
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
2
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
2
1
1
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
3
0
0
0
2
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
1
0
2
0
0
1
0
0
1
0
0
1
0
0
2
0
1
1
0
0
2
1
0
0
0
1
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
3
0
3
0
0
0
2
2
2
0
0
1
0
1
0
0
0
0
1
0
2
0
0
0
0
1
0
2
0
0
2
1
0
0
0
0
0
1
2
0
0
0
2
0
0
2
2
2
1
0
2
0
1
0
2
0
2
2
1
0
0
0
0
0
0
0
0
0
2
0
2
1
2
1
0
0
2
0
0
0
2
1
0
0
0
0
1
0
0
2
1
0
0
1
0
0
2
1
0
2
2
0
0
0
0
2
0
1
0
0
1
2
0
0
1
0
3
0
1
0
1
0
0
4
0
0
0
0
0
0
0
0
2
2
2
0
1
2
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
1
2
0
2
0
0
0
1
0
1
1
0
0
2
0
1
1
0
1
0
1
0
0
1
1
3
1
2
0
2
0
2
0
1
1
2
0
0
0
1
2
0
0
2
2
1
1
2
1
2
0
0
2
1
0
1
0
0
0
0
2
1
0
0
1
1
0
0
0
0
1
3
0
1
2
0
1
0
0
1
0
4
0
2
1
0
6
0
0
2
1
0
2
2
1
0
0
1
1
0
0
2
1
1
0
2
0
2
1
2
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
1
0
0
2
1
0
0
0
0
1
1
1
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
1
2
0
1
1
1
1
0
1
1
2
0
0
0
0
0
0
0
2
0
1
0
0
2
0
2
0
1
0
1
0
3
1
1
0
0
0
0
0
1
0
2
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
2
0
2
1
0
1
0
0
0
0
0
2
0
0
1
0
1
0
0
0
2
0
0
0
0
1
0
0
1
0
1
0
2
0
0
0
1
0
0
2
0
2
0
1
1
0
0
0
0
1
2
2
1
0
0
0
0
0
0
0
0
1
1
0
0
1
2
1
0
1
1
0
0
0
3
2
0
1
0
0
2
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
3
1
1
2
2
2
0
1
0
1
2
2
0
1
0
2
0
0
1
0
1
0
2
0
0
0
0
0
2
0
1
1
1
1
1
1
0
0
2
1
0
0
0
1
0
0
0
1
0
2
0
0
2
0
2
0
0
2
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
3
0
1
0
0
0
2
0
0
1
1
0
0
0
0
0
0
1
1
0
0
2
0
3
0
1
2
0
0
2
0
0
1
2
1
0
0
1
0
0
0
3
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
2
0
1
1
0
2
0
0
2
0
2
1
0
1
0
0
1
3
1
0
1
0
0
2
1
0
1
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
2
0
1
1
0
0
1
0
1
2
0
0
0
1
0
0
1
0
2
2
0
0
0
2
0
1
1
1
0
1
0
0
0
2
0
1
0
1
2
1
0
0
0
0
0
0
1
0
2
1
1
0
0
1
2
0
0
1
0
1
0
0
0
0
2
1
2
2
2
0
2
0
0
0
1
2
0
0
1
0
0
0
0
2
1
2
2
1
0
0
1
0
2
2
0
0
0
0
2
2
4
0
0
0
0
0
2
0
0
1
2
2
1
0
1
0
0
1
0
2
0
2
0
0
0
0
2
0
0
0
1
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
2
1
0
0
1
0
2
4
0
0
0
0
0
1
0
0
3
0
0
0
0
2
0
1
1
0
1
0
0
0
0
3
0
0
0
0
0
1
1
0
1
2
2
0
0
0
1
0
0
0
1
1
0
1
1
2
0
1
1
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
2
1
1
0
0
0
0
0
0
0
1
0
1
0
0
1
1
1
0
0
0
0
0
1
0
0
2
0
2
2
1
0
2
1
0
0
0
2
1
1
0
0
2
2
0
2
1
1
1
0
3
1
0
0
2
2
0
0
1
0
0
0
1
1
2
1
1
0
0
2
2
0
0
0
0
1
4
0
2
2
0
0
2
2
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
1
1
0
2
0
0
0
3
0
0
1
1
2
0
0
0
1
0
0
0
1
1
1
0
0
0
0
6
1
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
1
0
0
1
0
2
0
0
0
0
1
0
0
0
1
0
0
1
0
4
0
0
0
2
0
0
1
1
0
0
0
3
0
0
0
2
1
1
0
1
0
2
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
3
0
3
2
2
0
2
2
0
0
0
1
2
1
1
2
0
0
2
2
2
0
0
0
0
2
1
0
2
0
0
0
1
1
2
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
2
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
3
0
1
1
0
2
0
0
0
0
1
0
0
2
0
0
2
0
1
1
2
2
0
0
4
0
0
0
0
1
0
0
2
1
0
0
0
1
2
2
1
1
0
0
0
2
2
1
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
4
0
2
0
0
0
0
1
3
0
2
2
0
2
2
1
0
2
0
1
0
0
0
0
0
1
2
2
0
1
1
0
1
0
0
1
2
0
0
2
0
0
0
1
0
0
0
0
0
2
2
3
4
0
0
0
0
2
2
0
0
1
0
0
1
0
0
0
0
2
0
2
0
0
0
0
1
0
1
1
0
1
0
0
2
0
0
2
0
0
0
0
0
2
2
0
0
1
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
1
1
0
0
2
2
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
2
2
1
2
2
0
2
2
0
0
0
0
2
1
0
2
0
2
0
0
2
0
2
2
4
0
2
3
0
0
0
0
2
0
2
1
2
1
1
0
1
0
2
2
0
2
3
1
0
0
0
1
1
0
0
2
2
0
1
0
1
1
1
2
2
0
0
0
0
0
0
0
1
1
0
0
2
1
0
0
0
0
0
0
1
2
1
2
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
3
0
0
3
0
0
0
1
0
1
0
1
0
0
1
0
0
1
0
1
2
0
1
0
1
0
0
0
2
0
0
1
3
2
1
0
2
3
0
1
0
0
0
0
0
2
2
1
0
1
1
0
0
0
0
0
0
0
1
1
2
2
0
1
0
1
0
0
3
0
2
0
0
0
0
1
0
0
0
1
2
0
0
2
1
0
2
2
0
0
0
2
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
2
1
2
2
0
0
0
1
0
0
0
1
0
0
2
1
2
0
0
0
0
1
0
0
0
0
2
1
0
0
1
0
0
0
1
0
0
2
0
0
1
2
0
0
1
0
1
0
0
2
1
2
0
2
2
1
0
0
2
0
0
1
1
2
0
0
2
2
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
2
0
0
2
2
0
0
1
1
2
1
0
2
0
0
0
1
0
1
0
1
0
0
1
1
1
1
1
0
0
0
1
0
0
1
0
1
0
0
0
1
2
1
1
0
0
0
0
0
2
1
0
0
1
1
0
0
1
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
3
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
2
0
2
1
0
1
2
2
1
3
2
0
1
0
0
3
0
2
0
0
0
0
0
1
0
0
1
0
0
2
0
0
1
0
2
0
0
2
0
0
1
2
1
0
2
2
0
0
1
0
0
1
1
0
0
0
1
0
2
0
0
0
1
1
0
0
2
2
1
0
0
1
2
0
2
0
2
0
0
4
1
0
0
0
0
0
2
1
1
0
1
3
1
0
2
2
2
0
0
1
0
0
0
1
0
2
0
1
0
0
0
0
0
0
2
1
0
0
0
2
1
1
0
1
0
2
0
0
0
0
0
1
0
0
2
0
1
0
1
0
0
1
1
0
0
2
2
2
2
2
0
1
0
0
0
0
2
0
0
2
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
1
1
1
2
1
0
0
1
1
0
0
0
1
1
1
1
1
0
1
2
1
1
1
0
3
1
0
0
0
0
0
0
4
1
0
0
0
1
0
0
0
1
0
0
2
2
0
0
0
0
2
2
2
1
0
0
2
0
0
2
2
0
2
0
0
2
1
1
0
2
2
0
0
2
1
3
3
0
1
0
0
2
0
0
0
1
1
0
0
0
1
0
0
1
0
1
1
1
1
1
0
0
0
2
1
0
1
0
0
0
2
0
0
0
2
0
0
0
2
5
0
0
0
2
1
0
1
1
2
2
0
0
1
2
1
2
0
0
1
0
0
0
2
0
2
0
0
1
0
6
0
1
4
0
0
0
2
1
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
1
2
0
2
0
0
0
0
2
3
0
1
1
1
1
1
0
0
0
0
0
0
0
0
0
1
2
1
1
1
2
0
2
0
0
1
1
0
0
0
0
0
1
1
1
0
0
0
1
2
0
0
0
3
2
0
0
0
0
2
0
2
0
2
0
0
0
0
0
3
2
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
1
2
1
2
0
0
1
2
0
2
2
0
0
1
0
2
1
0
0
0
0
2
0
1
0
1
0
1
0
0
0
0
0
1
2
2
1
1
0
0
0
0
2
0
0
0
0
0
0
0
1
1
2
1
0
0
4
1
0
2
0
0
0
0
2
2
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
1
1
1
0
2
0
1
0
0
2
1
0
2
0
1
1
0
0
0
2
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
3
0
0
0
1
0
0
0
1
2
0
0
1
2
0
0
0
0
0
0
3
0
2
0
2
0
2
0
3
0
0
0
1
0
0
2
2
0
0
0
0
2
0
0
0
2
2
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
2
1
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
2
0
0
0
0
2
0
1
0
0
1
2
0
0
0
0
1
0
2
0
1
2
0
0
0
0
0
2
0
0
2
2
0
0
0
2
1
0
0
0
2
3
0
0
1
0
0
0
0
0
1
2
0
2
2
0
0
1
0
0
0
2
0
0
1
0
0
0
2
1
0
0
0
1
2
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
1
0
0
2
0
1
0
0
0
0
1
0
2
0
2
0
0
0
2
0
0
0
0
1
0
0
1
1
0
0
0
1
0
2
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
2
0
1
0
1
0
0
0
2
1
0
2
1
0
1
1
0
1
2
0
0
0
0
0
1
2
2
1
0
1
2
3
1
0
0
0
2
1
0
1
0
2
0
0
0
0
2
0
0
0
0
0
1
2
1
0
0
0
2
1
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
2
0
2
0
1
0
0
1
2
1
2
0
2
0
1
0
0
1
2
1
0
1
0
1
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
2
1
0
1
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
1
2
0
0
0
0
0
0
0
1
1
2
0
0
2
0
2
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
3
0
0
4
2
0
0
0
1
0
0
1
0
2
0
0
1
0
0
0
2
0
0
0
0
2
0
1
2
0
0
0
0
1
2
0
1
1
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
2
0
0
1
2
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
1
1
1
0
2
0
1
0
0
2
0
1
2
0
0
0
0
0
0
0
0
2
0
3
0
2
2
2
1
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
1
1
2
0
2
0
0
0
0
1
1
0
0
0
0
0
0
1
1
2
0
1
0
0
3
1
1
0
2
1
2
0
0
1
2
3
2
0
1
0
0
1
2
0
2
2
0
1
1
0
1
0
0
0
1
0
0
1
2
0
2
0
1
0
0
0
1
0
3
1
0
1
0
0
0
4
0
0
0
1
3
0
0
0
2
1
0
2
0
1
0
0
0
1
2
1
0
0
0
1
0
2
0
0
0
2
0
2
0
0
2
0
0
0
0
0
2
0
2
0
0
0
1
0
3
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
4
2
0
2
0
2
2
0
0
0
1
0
0
0
0
0
1
1
0
3
0
0
1
1
2
2
2
1
0
0
1
0
0
0
2
0
1
1
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
1
0
0
0
0
0
2
2
1
2
0
0
0
0
1
0
0
2
1
1
0
0
0
2
4
2
0
0
0
0
1
0
1
1
0
0
0
1
2
0
0
0
1
1
1
0
0
0
0
0
0
1
0
1
2
2
0
0
2
0
1
1
0
1
2
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
1
0
1
2
0
2
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
2
2
1
0
4
0
2
2
0
0
0
0
0
0
0
0
0
0
1
2
0
1
2
2
0
0
1
0
1
1
0
0
0
1
1
0
1
2
0
0
0
1
0
0
1
0
1
2
0
1
0
1
1
1
0
2
0
0
0
0
0
2
1
0
0
0
1
0
0
2
0
2
0
2
1
2
1
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
4
0
2
0
1
0
0
1
0
2
2
0
2
1
0
1
1
2
0
2
1
0
0
0
2
2
0
0
1
0
0
0
0
0
1
2
2
1
1
3
1
2
1
1
0
1
0
1
4
0
1
0
1
0
0
1
0
0
0
1
2
0
2
4
0
0
0
0
0
1
1
2
1
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
1
0
1
0
1
0
1
0
0
0
0
0
2
1
5
0
2
1
0
0
1
2
0
0
0
0
3
2
0
1
0
2
0
1
1
1
0
1
0
0
2
1
0
0
0
0
1
0
0
0
0
2
1
2
0
1
0
1
0
0
0
2
1
0
2
0
0
0
2
0
2
0
0
2
2
0
0
0
1
1
3
0
0
0
2
1
0
2
0
0
2
3
1
0
2
1
0
0
0
2
1
0
0
1
0
0
0
1
1
0
1
0
1
2
2
0
0
0
2
1
0
0
0
2
1
0
1
2
0
1
0
1
0
2
0
0
0
0
2
1
1
1
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
2
1
2
2
0
0
0
1
1
0
0
1
2
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
2
1
0
2
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
1
2
0
1
0
2
0
0
2
0
0
0
0
1
0
0
0
1
0
2
1
0
0
1
2
0
1
0
0
1
0
0
0
1
2
1
2
0
0
1
1
0
1
2
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
1
0
3
0
0
0
1
0
1
0
1
2
0
0
1
0
1
0
0
1
0
0
0
2
0
0
0
0
1
1
0
2
0
1
0
2
1
0
1
0
2
0
1
0
0
0
0
1
0
2
1
0
0
2
1
0
2
0
0
2
0
3
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
2
1
0
1
0
1
1
2
0
2
0
0
0
1
0
0
0
0
1
0
2
2
0
1
2
0
1
0
0
0
2
0
1
2
0
0
3
0
0
0
0
2
1
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
1
1
3
2
2
0
1
0
2
2
0
2
0
0
2
0
2
1
0
1
0
1
0
0
2
0
2
2
0
0
2
2
0
0
0
1
1
0
0
0
0
0
2
2
2
0
0
1
2
2
0
0
2
2
1
2
0
0
0
1
1
1
3
0
0
0
0
1
0
1
2
1
1
1
1
0
0
0
0
0
2
2
0
1
2
0
0
0
0
0
0
1
2
2
1
1
0
0
2
0
2
0
0
0
0
2
0
1
2
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
2
2
0
1
0
0
1
2
0
1
0
0
0
2
0
1
1
0
1
0
0
1
0
0
0
0
0
0
2
0
1
1
1
0
0
0
2
0
0
0
2
0
0
1
2
0
2
0
2
2
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
1
1
0
0
1
1
0
1
0
0
1
0
3
1
0
1
0
0
1
1
0
2
0
2
0
0
0
0
0
2
1
0
0
2
0
0
1
0
3
1
2
0
0
0
0
0
0
0
0
1
0
1
0
2
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
2
0
0
2
0
0
2
1
2
0
0
0
0
0
1
2
2
0
0
2
0
0
0
0
0
1
1
0
1
2
0
1
1
0
0
0
1
1
2
1
1
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
2
1
1
0
0
0
0
0
1
2
0
0
2
3
0
0
1
0
0
0
1
1
2
0
0
1
0
2
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
2
1
1
0
0
0
0
0
1
0
0
0
0
0
2
1
0
2
2
0
2
1
1
2
0
1
0
0
3
1
0
0
1
0
1
0
0
2
0
2
3
0
0
0
1
0
1
0
0
0
0
1
0
2
0
0
0
2
0
1
1
0
1
0
3
1
0
0
0
2
2
0
1
0
0
0
0
1
1
1
0
1
0
0
0
1
1
1
0
0
2
2
0
0
0
0
2
0
2
0
0
2
1
2
1
2
0
1
2
0
1
2
1
1
0
2
1
2
0
1
0
0
1
1
0
1
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
2
1
0
0
0
1
0
0
1
0
1
0
2
1
0
0
0
2
0
1
0
0
1
0
0
2
2
0
2
0
0
1
0
0
2
0
0
1
0
0
0
0
3
1
0
0
1
3
0
0
0
1
1
0
0
0
0
0
2
1
0
0
0
2
0
0
2
1
0
1
1
0
0
0
0
0
1
2
0
0
0
1
0
1
0
2
1
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
2
0
0
2
1
0
2
1
0
1
2
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
2
0
2
1
0
2
2
0
0
1
0
2
0
0
0
0
3
0
0
1
2
0
0
0
0
0
2
0
1
1
0
1
0
0
1
1
2
0
0
2
0
1
0
2
2
0
0
0
0
2
1
1
1
1
0
0
1
0
0
2
0
1
2
2
1
1
2
0
0
0
1
0
1
1
0
0
1
0
0
0
2
0
2
0
9
0
0
0
0
0
2
1
2
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
1
0
0
1
1
0
1
1
0
0
0
0
1
1
0
2
0
1
0
0
0
1
2
0
2
0
2
2
0
1
0
2
0
2
2
0
2
0
1
0
0
2
1
0
0
2
0
2
0
0
0
0
0
3
1
0
0
2
0
2
2
0
0
1
2
1
0
2
0
2
0
0
1
0
0
1
2
1
0
0
0
0
1
1
2
0
0
0
0
2
0
4
0
0
2
2
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
1
0
0
2
1
0
0
0
2
1
0
1
1
1
0
1
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
2
1
1
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
2
2
1
1
0
0
1
4
2
0
0
0
0
1
0
1
0
0
2
2
0
0
0
0
0
2
2
1
1
0
0
0
1
2
1
0
0
1
0
1
1
0
1
0
2
0
0
1
2
0
1
2
0
0
0
1
0
1
2
1
0
0
0
0
4
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
1
0
2
0
1
2
2
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
2
1
2
2
0
2
0
0
0
2
0
1
0
0
2
2
2
2
1
0
0
0
0
1
1
1
0
0
0
0
1
1
2
2
0
0
1
0
2
2
0
0
0
0
0
2
2
0
2
2
1
1
1
1
0
1
1
2
0
0
1
0
0
1
0
1
0
2
0
0
2
1
0
2
0
0
2
0
0
2
2
0
2
0
0
1
0
0
0
2
0
2
0
2
0
0
3
1
0
2
1
0
0
4
3
0
0
0
0
1
0
0
1
1
0
0
2
0
0
2
1
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
1
1
0
0
0
0
2
1
0
1
2
0
0
0
0
1
2
3
1
1
0
0
0
1
0
0
1
2
0
0
0
0
0
1
3
2
0
0
0
0
1
2
2
0
0
0
0
1
1
1
1
1
1
1
0
2
0
0
2
1
0
1
0
0
0
0
1
0
0
1
0
2
0
0
0
1
1
1
0
3
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
1
0
0
2
0
0
0
0
2
1
0
2
1
0
0
0
1
0
0
1
2
0
0
0
2
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
6
0
1
2
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
2
0
0
0
2
0
2
1
1
0
0
0
2
0
0
0
1
1
2
0
4
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
2
0
0
0
0
0
2
0
2
0
0
0
2
0
2
0
0
0
1
0
0
2
1
0
2
0
0
0
0
1
2
0
1
0
0
1
2
1
0
0
0
1
0
0
1
1
2
2
1
0
0
2
2
0
1
0
2
0
0
2
1
0
1
0
0
0
0
0
2
2
0
2
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
2
2
0
0
0
2
2
1
1
0
0
0
1
0
0
0
2
1
0
0
1
0
1
0
2
3
0
1
1
0
1
1
1
2
1
2
0
1
0
0
3
0
1
0
0
1
1
1
2
1
0
0
1
1
1
0
0
1
0
0
1
0
0
0
2
0
0
0
1
2
0
2
2
0
0
0
2
0
1
1
2
1
0
0
1
1
0
0
1
0
0
2
0
1
0
1
0
1
2
0
1
0
2
1
0
1
1
1
2
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
2
0
1
0
1
2
2
0
1
1
1
0
0
3
2
0
1
1
0
2
0
1
1
1
1
1
0
2
0
2
2
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
2
0
0
1
1
2
2
1
2
1
1
2
2
0
0
2
2
2
0
0
0
2
0
0
0
0
0
0
2
1
2
0
0
0
0
1
2
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
1
0
0
2
0
1
1
0
1
0
0
0
2
2
0
0
1
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
3
1
0
5
0
0
0
2
2
0
1
0
1
2
0
1
0
1
1
3
0
1
2
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
2
1
0
0
2
2
0
0
1
2
3
0
4
1
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
1
1
1
1
0
1
0
0
2
0
3
0
0
0
0
2
0
1
0
2
0
1
1
0
2
0
0
2
1
2
1
1
0
0
0
0
3
0
0
1
0
0
0
0
0
0
2
2
0
2
0
0
0
2
2
2
0
1
1
0
1
2
2
0
1
0
0
0
0
1
2
0
0
2
0
1
1
0
0
0
0
1
0
1
2
1
0
0
0
2
0
0
0
1
0
0
0
0
2
1
1
0
0
0
0
1
0
2
0
0
2
0
1
1
0
0
0
2
1
0
0
0
0
1
0
1
0
0
0
1
1
1
0
0
0
2
0
0
1
0
2
2
3
1
2
1
2
0
1
0
0
0
1
0
0
1
2
1
3
3
2
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
2
0
1
1
2
0
2
0
1
0
3
1
0
2
1
0
0
1
0
2
0
0
0
0
0
1
1
0
0
1
0
2
2
1
3
1
1
0
1
0
0
3
1
0
1
0
1
2
0
1
2
1
1
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
1
0
6
0
0
0
0
0
2
1
1
0
0
0
1
0
0
0
1
0
0
0
2
2
0
0
1
0
0
0
0
1
0
2
0
0
1
1
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
2
1
1
0
0
0
1
2
0
1
0
1
0
0
0
2
0
0
0
0
4
2
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
1
1
0
2
0
1
0
0
2
0
0
1
2
0
0
1
0
0
1
0
0
2
1
2
2
0
2
0
3
2
0
1
0
0
0
0
1
0
2
1
0
0
0
1
4
0
1
2
0
1
1
1
0
0
1
2
2
0
0
0
0
0
0
1
3
0
0
0
0
0
1
1
0
0
0
2
1
1
1
2
2
0
0
0
0
0
2
0
1
0
0
0
2
1
1
0
0
0
0
0
0
0
3
0
0
2
2
1
3
0
2
1
2
0
0
0
0
0
0
0
0
0
2
0
1
1
0
1
0
2
1
0
0
0
1
0
0
1
0
2
2
1
0
0
0
0
0
1
2
0
0
2
0
3
0
1
0
1
2
0
2
0
0
0
1
0
0
0
1
2
2
0
1
3
2
2
1
1
1
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
1
1
0
1
0
1
2
1
0
1
1
0
0
1
2
2
0
1
0
0
0
1
2
2
0
0
0
1
0
0
0
1
0
1
0
0
2
0
0
1
0
0
13
2
2
3
0
0
0
2
1
2
1
0
0
0
0
0
1
0
2
2
2
1
0
0
0
0
0
0
9
1
0
0
2
2
2
0
0
1
1
0
0
2
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
2
2
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
3
1
0
0
0
0
0
2
1
0
1
0
0
2
0
0
0
0
1
1
1
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
1
2
0
0
0
2
2
1
0
0
0
2
1
0
0
1
0
0
1
0
0
2
2
0
1
2
0
0
0
1
0
0
1
2
0
0
1
0
1
2
2
0
0
1
0
0
2
0
0
2
1
2
0
2
2
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
1
2
0
0
2
0
0
2
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
1
0
0
2
0
2
0
1
0
0
2
0
0
1
0
1
1
1
2
1
0
0
1
0
0
0
0
0
1
1
0
2
1
0
0
2
0
2
0
1
1
0
0
0
0
0
2
3
0
0
2
0
0
1
0
2
0
0
0
0
0
0
1
1
2
2
0
1
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
1
2
0
0
0
2
1
1
0
0
4
2
0
1
1
0
1
0
0
0
2
1
0
1
2
1
0
0
0
1
0
1
0
0
1
0
1
0
0
1
0
1
2
2
0
1
0
0
0
2
2
2
0
1
0
2
2
0
2
0
1
0
0
0
0
0
0
0
0
4
1
0
2
0
0
1
0
1
2
0
0
0
0
2
1
0
1
2
0
2
1
1
0
1
2
0
2
0
2
3
0
0
0
0
1
0
0
0
1
0
0
0
0
1
3
0
0
0
0
0
0
0
1
0
0
1
3
0
0
2
0
2
1
1
2
0
0
0
0
1
0
2
0
2
0
1
0
0
0
0
0
1
2
2
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
1
1
2
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
1
3
2
0
0
0
0
0
1
1
3
1
2
1
2
0
1
0
1
6
0
1
1
0
1
3
2
2
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
2
1
1
0
0
1
0
0
0
0
2
0
0
2
2
0
0
2
4
0
0
1
0
0
0
1
0
0
2
0
0
0
1
0
0
0
2
0
0
0
2
2
1
1
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
2
0
1
1
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
1
1
0
1
0
1
0
1
2
2
1
0
4
0
2
0
0
0
0
0
6
2
0
0
0
0
1
0
1
2
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
2
0
0
2
0
2
2
0
0
0
0
0
0
0
0
1
2
0
0
1
0
1
2
2
1
0
2
1
0
1
2
1
0
1
2
2
0
2
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
2
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
1
2
0
1
1
1
0
2
1
0
2
0
2
1
0
2
0
0
1
0
0
0
2
0
2
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
1
1
0
1
2
0
1
2
0
1
0
2
1
0
0
1
1
0
0
0
0
0
1
0
1
1
3
0
0
1
0
0
1
2
2
0
0
0
0
0
1
0
3
2
0
1
0
0
0
0
0
1
0
0
3
0
1
0
0
2
0
0
0
0
0
0
0
0
1
1
1
3
1
0
0
0
2
2
0
0
0
2
0
1
0
2
2
0
0
0
0
0
2
0
0
0
0
0
3
2
0
0
0
0
2
1
2
1
2
0
0
2
1
0
2
0
1
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
2
2
1
2
0
1
0
0
2
0
1
0
0
0
1
0
2
0
1
2
0
0
2
0
0
0
2
1
0
2
1
1
0
0
0
2
2
2
2
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
2
0
0
0
0
1
1
0
0
1
1
0
0
0
1
2
2
0
0
0
2
0
1
0
1
1
1
0
0
0
3
0
0
1
0
0
0
1
0
0
2
0
2
0
0
3
0
0
0
3
0
0
0
0
2
0
0
1
0
0
1
0
1
0
1
2
0
1
0
1
0
1
0
0
0
0
2
1
0
0
0
0
0
0
2
2
2
1
0
1
2
2
0
1
0
0
0
1
0
0
1
2
2
0
1
2
1
3
0
1
2
0
1
0
1
0
0
1
0
2
3
0
0
2
2
3
0
2
1
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
2
0
0
0
0
1
2
0
1
1
0
0
1
0
0
0
0
0
5
0
1
2
1
0
0
0
0
0
2
0
0
2
1
0
0
0
2
5
0
2
2
2
2
0
1
0
0
0
0
0
0
0
1
1
0
0
0
2
2
1
2
1
4
0
0
0
0
0
0
1
0
1
0
2
1
0
2
2
0
0
0
0
1
1
0
1
0
0
2
1
1
1
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
2
2
0
0
1
3
0
1
2
2
1
1
1
0
2
0
0
0
2
1
1
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
1
0
1
1
0
0
1
1
1
2
0
0
0
0
2
2
0
0
0
3
1
0
0
0
1
2
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
1
1
0
3
1
0
0
1
1
2
0
0
0
0
0
2
0
0
1
1
0
0
4
1
1
0
0
0
2
1
0
0
2
1
2
2
0
7
1
0
1
2
0
1
0
0
0
0
0
0
1
0
2
0
0
2
3
0
0
0
3
1
1
0
1
1
0
0
2
0
1
0
0
0
0
2
0
1
0
3
1
0
1
0
1
5
0
0
0
1
0
0
0
2
0
0
0
2
1
0
1
1
0
0
0
0
1
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
2
2
0
0
2
0
0
0
1
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
2
1
1
0
2
1
0
0
0
2
0
2
1
0
0
0
2
0
2
1
0
1
0
0
0
0
2
0
1
1
0
0
0
1
0
0
0
0
1
1
0
0
2
1
0
0
0
0
1
3
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
2
1
0
1
2
0
0
0
0
1
0
0
3
0
5
2
0
0
0
2
2
0
2
1
0
2
2
0
3
0
0
0
3
0
0
0
0
3
1
2
0
0
1
2
3
2
2
2
0
1
1
1
0
1
0
0
0
1
0
2
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
3
2
0
5
1
2
1
0
1
0
0
0
0
1
0
0
2
0
0
1
0
0
2
1
2
2
2
2
1
0
0
1
0
0
2
0
2
0
0
1
1
2
2
0
2
2
0
1
0
0
0
0
1
0
0
0
0
0
0
1
3
0
0
0
2
0
1
0
1
0
0
0
1
0
1
0
0
1
0
0
2
0
1
2
0
0
2
1
0
0
1
0
1
1
2
1
2
0
0
0
1
0
0
1
0
0
0
0
1
1
0
1
0
0
2
3
0
0
2
0
0
2
0
1
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
2
1
0
1
1
1
2
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
3
0
0
2
0
0
2
0
1
2
0
0
1
2
0
2
0
1
0
0
2
1
0
1
0
1
0
0
2
2
0
0
0
2
0
0
0
2
1
0
1
0
0
0
0
2
2
1
0
1
1
1
0
0
0
0
0
1
0
2
0
0
2
2
3
2
0
0
1
0
0
0
0
0
0
0
0
1
8
2
0
0
2
0
2
2
2
0
0
2
0
0
2
0
1
0
2
1
0
0
2
0
1
0
2
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
1
0
0
1
1
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
2
1
0
1
0
2
0
0
0
2
2
1
2
1
0
0
0
0
0
3
0
1
2
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
1
0
1
0
0
0
0
2
0
2
0
0
3
0
0
2
1
0
1
4
1
1
0
0
0
0
0
1
1
2
0
0
0
0
2
2
1
1
2
1
0
0
0
0
1
0
0
1
1
0
2
0
0
0
1
0
2
1
1
0
1
0
1
2
0
0
0
1
0
0
2
0
0
0
1
0
0
0
3
0
1
0
1
1
0
2
2
1
1
1
2
1
1
0
2
1
3
3
2
2
1
0
1
0
3
1
2
2
0
0
0
0
1
2
2
0
2
1
0
2
0
0
2
0
2
2
0
6
2
0
0
2
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
2
1
0
0
0
1
2
1
0
2
2
1
2
2
0
1
0
2
0
2
2
0
0
0
2
0
1
0
2
0
0
2
0
1
2
0
1
4
2
2
1
0
0
0
0
1
2
0
0
0
0
1
0
0
1
1
0
4
0
2
0
0
1
0
0
0
1
1
0
2
2
2
0
1
1
0
1
1
0
1
0
0
0
0
0
0
2
1
0
2
0
1
2
1
2
2
0
0
2
0
0
1
0
0
0
0
2
1
1
0
0
1
1
2
0
1
0
0
0
0
0
0
1
0
0
0
1
2
0
1
0
0
0
0
1
1
0
0
1
2
0
0
0
1
2
1
1
2
0
1
1
0
1
2
0
0
0
0
0
0
0
1
2
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
1
0
1
0
0
0
0
0
1
0
3
0
0
1
0
0
0
1
0
0
0
1
0
2
1
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
1
2
0
0
2
0
0
1
0
0
2
0
0
1
0
0
3
0
0
0
2
1
0
2
1
2
2
2
0
0
1
0
1
1
0
1
1
1
1
2
0
0
0
2
1
2
2
0
1
0
0
2
0
0
0
3
0
2
0
0
2
0
3
0
1
1
0
0
1
0
3
0
0
2
1
0
1
2
2
0
0
1
2
1
2
0
1
0
1
0
2
0
0
1
0
0
0
3
1
2
2
1
1
0
0
1
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
1
1
0
1
2
2
0
1
1
0
1
0
0
0
0
0
3
1
0
0
0
0
1
0
0
0
0
1
1
1
1
2
0
0
0
0
1
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
2
0
0
0
2
0
0
1
1
0
2
0
0
1
2
1
0
0
0
0
0
1
0
1
0
1
0
1
0
1
0
0
0
1
2
3
1
0
0
0
0
0
1
2
1
0
1
0
0
0
0
2
1
1
0
2
0
1
1
1
0
0
1
1
0
2
0
1
2
2
0
0
0
0
0
2
0
0
0
0
2
3
0
2
2
0
2
0
0
2
0
0
0
1
2
0
0
1
2
2
0
1
0
1
4
0
0
0
0
1
1
0
2
0
2
0
0
0
0
1
0
0
0
1
2
1
2
0
0
1
0
0
0
2
1
0
0
2
2
0
1
0
0
0
2
2
2
2
0
1
0
2
0
2
0
0
0
2
2
2
1
1
0
0
0
0
1
1
0
0
0
2
0
2
0
2
1
1
1
2
0
0
0
2
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
2
3
0
1
0
0
2
0
0
0
0
0
2
2
0
1
0
1
0
2
2
0
1
0
2
0
0
0
1
1
2
0
1
0
0
0
2
2
0
1
0
0
2
0
2
0
0
2
0
1
1
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
1
0
0
0
0
2
0
2
0
2
0
0
2
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
2
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
2
2
2
2
2
0
1
0
2
0
0
1
0
1
0
0
1
0
2
0
1
1
0
0
1
0
1
2
1
1
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
2
1
0
0
2
1
0
2
0
0
0
1
1
0
2
0
0
2
0
2
0
0
0
2
1
0
1
0
0
0
2
2
0
0
0
0
0
0
1
2
0
1
1
1
2
0
0
0
0
0
0
1
1
0
2
1
2
1
0
0
1
0
1
0
0
1
2
1
0
0
0
2
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
1
0
1
2
0
0
0
2
2
0
0
2
0
4
0
2
0
2
0
0
0
0
2
1
0
0
0
0
1
0
1
1
0
0
2
1
3
0
0
2
1
0
1
0
1
0
0
0
1
0
1
0
0
0
2
0
2
0
0
0
0
0
2
0
0
1
0
2
1
0
1
0
1
1
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
2
0
1
0
1
2
1
1
2
0
1
0
0
0
1
0
0
0
2
1
1
1
2
0
2
0
0
0
1
0
0
0
2
2
0
1
0
0
0
0
2
0
0
0
0
1
0
1
0
1
0
2
0
1
2
3
1
0
0
1
0
1
0
2
0
1
1
1
2
2
2
0
0
0
0
2
1
0
0
0
2
0
1
0
4
1
0
2
2
0
1
0
0
0
2
0
0
0
1
3
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
2
3
0
1
2
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
2
1
0
1
2
0
0
4
0
0
1
0
0
2
0
0
0
0
1
1
2
1
2
0
0
1
2
0
0
0
0
0
2
0
2
0
2
0
0
0
2
2
0
1
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
2
1
5
0
2
2
2
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
1
1
0
2
1
0
0
0
0
1
2
0
2
1
1
2
0
0
0
0
1
2
2
0
0
2
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
2
0
1
1
0
1
0
0
0
1
1
2
0
1
0
0
1
0
2
0
0
2
1
0
3
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
1
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
1
1
0
0
3
0
0
0
0
0
0
2
0
1
2
2
0
0
0
0
1
2
2
1
0
2
2
1
1
0
2
0
0
0
0
0
1
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
2
0
0
0
0
0
2
2
1
0
2
1
2
1
1
0
0
0
2
2
0
0
0
1
2
2
0
1
1
1
2
3
2
0
0
0
0
0
1
1
3
0
1
1
1
0
0
1
0
2
0
4
0
0
2
0
1
1
0
2
1
0
1
0
1
0
0
2
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
2
2
0
0
0
0
0
0
2
0
0
3
1
0
2
0
2
2
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
1
0
2
2
0
2
0
0
2
0
0
1
2
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
1
1
0
0
0
0
2
2
0
0
0
2
0
2
0
2
0
3
0
0
2
2
0
0
0
0
2
0
2
0
1
2
1
0
0
2
2
0
0
0
2
0
2
0
0
2
0
0
0
1
2
0
0
0
0
0
0
1
0
2
0
1
1
0
0
0
1
2
0
1
0
1
0
0
1
1
0
0
1
0
1
0
0
2
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
2
0
0
0
1
2
1
1
2
1
2
2
0
1
1
0
0
1
2
0
1
2
0
1
0
1
0
1
0
0
0
0
0
0
0
2
2
0
1
0
0
0
1
0
0
0
0
0
1
0
12
1
0
1
2
0
0
1
2
0
2
0
0
1
1
0
2
1
0
2
0
2
0
1
0
0
0
0
2
0
0
1
1
0
2
0
2
2
0
0
0
0
2
0
1
0
1
0
0
2
0
2
2
0
0
1
0
0
0
0
0
3
1
2
1
2
3
2
0
0
0
2
2
0
0
0
0
2
2
0
0
0
0
1
0
0
1
2
0
1
1
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
2
1
1
1
0
0
0
1
2
0
0
2
0
0
0
1
1
0
1
1
0
1
1
0
0
1
1
1
1
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
2
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
2
1
0
2
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
2
0
0
0
1
0
0
2
0
1
0
0
1
0
2
0
0
0
0
1
1
1
0
2
0
0
0
0
0
1
0
1
2
3
2
0
1
0
3
2
0
0
1
0
3
2
0
0
1
0
1
1
2
2
0
2
0
0
0
1
0
0
2
0
2
1
2
0
2
0
0
2
2
2
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
2
0
0
2
0
2
0
0
0
2
0
3
1
0
1
0
0
1
0
0
2
1
0
1
2
2
1
0
1
1
1
1
0
2
1
0
2
0
0
2
0
2
0
0
2
2
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
1
2
0
0
2
0
0
0
2
1
0
2
0
1
2
4
0
2
1
0
1
2
2
1
1
1
0
0
0
1
1
0
0
2
0
0
0
0
0
1
0
1
0
2
2
0
3
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
2
0
0
0
0
1
1
0
1
1
0
0
0
0
2
2
0
0
0
0
0
2
1
0
0
2
2
1
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
1
0
1
2
2
0
2
1
0
2
0
2
0
2
0
1
0
2
1
1
0
0
0
2
0
0
0
0
2
2
0
2
0
0
0
0
0
1
0
0
0
2
1
2
2
0
0
1
0
0
0
2
0
1
2
0
0
0
1
1
1
0
0
2
3
0
2
3
0
0
0
1
0
0
0
2
0
2
3
2
2
1
2
0
1
1
1
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
2
2
0
1
1
1
0
0
0
0
1
0
1
1
0
0
0
2
0
1
0
0
0
2
0
2
2
1
0
3
0
0
0
0
1
2
1
0
0
0
1
1
0
1
0
0
0
0
0
2
1
2
1
0
0
0
0
0
1
3
0
0
1
0
0
0
0
0
2
1
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
1
1
0
2
0
1
0
1
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
2
2
0
0
0
0
0
0
2
0
7
0
1
0
1
0
2
0
5
1
0
2
0
0
0
2
0
2
2
0
0
0
2
0
2
0
2
2
0
1
4
2
0
1
0
1
0
0
1
1
2
0
0
1
1
0
1
0
1
2
1
2
0
0
0
1
0
0
0
0
0
1
0
0
0
1
3
2
0
0
1
0
0
1
0
0
2
0
0
0
2
2
0
0
1
0
0
1
0
0
1
3
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
4
1
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
1
0
2
0
1
2
0
1
0
0
1
0
0
0
0
2
0
0
0
3
1
1
2
2
2
0
2
0
2
0
0
0
0
0
1
2
0
0
0
1
0
0
0
1
0
0
1
0
2
0
1
0
0
0
2
1
0
2
0
1
0
0
0
0
0
0
3
0
1
1
1
1
0
2
1
0
1
1
0
1
0
0
1
0
3
0
0
2
1
0
2
0
1
1
0
2
0
0
0
1
1
1
0
2
0
0
2
0
0
0
2
0
0
0
0
1
0
2
0
1
0
1
0
0
0
0
0
0
1
3
2
0
0
2
2
1
0
1
0
0
0
0
0
1
0
2
0
2
0
0
0
2
1
0
1
0
2
0
1
0
0
0
0
0
0
0
1
2
2
1
2
0
0
0
0
0
1
2
0
0
1
2
2
1
2
0
0
0
0
0
2
1
0
2
1
2
2
0
1
2
0
2
1
2
0
0
1
0
1
0
1
2
2
0
1
0
0
0
0
2
1
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
1
1
1
2
0
1
0
0
0
0
0
1
0
0
2
0
0
0
1
1
0
2
2
0
0
1
0
1
2
1
0
0
0
0
1
1
0
2
0
0
0
0
1
0
1
0
0
0
1
0
0
1
1
1
2
2
2
0
2
0
2
0
0
4
2
2
0
2
1
1
0
1
0
0
0
0
0
0
1
0
0
3
1
0
1
0
0
0
1
2
0
0
2
2
1
2
0
2
2
3
0
0
0
1
1
0
1
2
0
0
2
1
0
3
0
0
0
0
1
2
0
1
1
0
1
0
1
1
0
2
0
1
0
0
0
1
1
1
0
1
0
0
1
2
2
0
1
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
2
0
2
3
0
0
0
1
1
1
0
0
0
0
0
1
2
0
0
0
0
0
2
1
0
0
0
2
0
0
1
0
0
2
3
0
0
8
2
1
1
2
0
0
1
0
1
1
1
0
0
0
1
1
1
2
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
2
1
0
0
1
0
0
2
0
3
0
0
0
1
0
0
2
2
0
1
2
0
0
2
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
2
1
0
0
1
1
0
2
2
0
0
2
0
2
0
2
0
1
2
0
0
1
3
0
1
2
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
4
0
0
0
1
2
0
0
0
0
1
2
0
1
0
0
2
1
1
0
0
2
0
0
0
2
0
0
0
0
2
0
1
0
0
0
1
0
0
0
2
0
2
0
1
0
0
1
0
0
2
2
0
0
0
1
2
1
0
1
0
3
2
0
2
0
0
2
4
3
0
0
2
0
0
2
0
0
0
0
0
1
0
0
3
0
1
2
0
1
1
0
0
0
2
0
1
1
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
3
0
2
1
0
0
1
0
0
0
3
1
0
3
1
1
0
0
0
0
0
0
2
0
1
2
3
0
0
0
2
0
0
3
1
0
0
0
0
0
0
1
2
0
1
0
0
1
2
1
0
2
2
1
1
2
2
0
0
0
1
0
1
0
2
0
0
2
0
2
0
0
0
0
1
0
0
0
2
0
0
1
0
2
0
0
0
0
2
2
0
4
1
3
1
1
0
0
2
1
0
0
0
1
0
0
1
1
2
0
1
0
0
0
1
0
2
3
0
0
1
1
1
0
0
0
0
0
0
2
3
2
0
0
0
2
0
0
0
3
1
0
0
2
2
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
2
1
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
2
0
2
0
0
0
0
0
1
1
1
1
0
0
1
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
3
0
2
1
0
0
0
0
0
0
1
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
1
0
2
1
1
1
0
0
1
0
0
0
0
1
2
1
0
2
0
0
1
1
0
2
0
0
1
1
0
1
0
0
0
0
0
0
1
0
2
2
2
3
0
1
1
1
1
1
0
0
0
0
2
1
0
2
0
0
1
3
0
2
0
0
0
3
1
0
2
2
0
0
0
1
1
2
1
0
0
1
0
0
1
2
0
0
0
2
1
0
1
6
0
2
0
2
1
1
0
2
0
2
2
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
2
0
2
2
1
2
1
2
0
0
0
0
0
2
0
3
2
1
0
2
0
2
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
3
1
0
2
0
0
0
1
0
0
0
1
0
0
0
0
1
1
1
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
2
0
2
2
0
0
1
1
0
1
0
1
0
3
3
0
0
1
0
2
1
2
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
1
2
0
0
0
2
0
1
1
3
0
0
0
0
1
2
1
0
0
4
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
3
0
2
2
1
0
1
0
0
0
0
0
1
0
0
0
0
3
1
0
2
0
4
0
1
2
2
0
1
1
2
0
0
0
0
1
0
0
0
1
4
0
0
0
2
0
0
1
1
2
1
0
0
1
1
0
2
0
0
0
0
1
0
0
0
2
2
2
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
2
2
1
2
0
0
1
0
0
2
0
0
2
0
0
0
2
0
2
0
0
2
0
0
3
2
0
0
1
1
2
3
2
2
0
1
1
0
0
1
0
2
2
0
1
1
3
2
2
0
2
0
2
0
0
0
0
3
0
0
0
0
0
1
0
0
1
0
2
0
0
1
0
1
0
0
1
0
2
0
1
1
0
0
1
0
2
1
0
0
0
0
0
1
2
1
0
0
1
1
0
1
0
0
1
2
0
0
0
3
2
2
2
1
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
2
0
2
0
0
1
2
0
0
2
0
1
0
0
1
1
1
2
1
1
0
0
1
0
0
1
0
0
2
1
2
0
0
1
0
0
2
2
0
0
0
0
0
2
0
1
1
2
0
2
0
2
1
0
0
0
2
0
1
0
1
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
2
0
0
0
2
0
0
1
2
0
0
0
0
0
1
2
2
2
0
0
0
0
1
0
3
0
0
2
1
0
0
1
2
1
0
0
2
1
0
1
2
0
0
2
0
1
1
0
0
0
2
2
2
1
0
3
1
1
1
0
1
0
0
2
0
0
4
0
0
0
0
0
0
0
1
0
1
0
1
2
0
0
0
2
0
0
2
0
4
0
0
0
0
0
1
0
0
0
0
0
2
1
2
1
0
0
0
1
0
2
1
0
0
1
1
0
0
1
2
1
1
0
0
0
0
1
1
2
2
0
2
1
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
1
0
1
1
0
2
2
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
1
0
0
1
2
1
0
0
0
1
3
0
0
0
0
0
0
0
2
2
1
0
0
0
0
2
0
0
0
0
0
1
2
0
0
1
1
2
2
2
0
0
0
0
2
0
1
0
0
1
0
0
2
0
2
2
0
0
0
1
0
2
0
2
0
0
0
0
1
1
1
0
0
0
2
0
1
2
2
1
0
2
1
0
0
0
2
1
0
2
0
2
1
0
2
0
0
1
1
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
5
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
5
1
2
0
0
1
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
2
3
1
0
0
0
2
0
0
0
1
0
0
1
0
0
2
2
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
1
1
1
0
1
0
0
2
0
1
0
0
2
2
0
0
0
2
2
3
1
2
0
0
0
0
2
0
2
0
2
1
0
0
0
0
0
1
2
2
0
0
2
0
0
1
1
2
0
1
0
1
1
2
0
2
2
0
0
3
0
0
1
0
0
2
0
0
0
2
1
1
0
0
1
0
2
1
0
0
1
0
0
0
0
1
0
2
0
1
1
0
3
2
0
0
0
5
0
1
0
0
1
2
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
2
0
0
2
0
0
0
4
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
1
2
0
2
0
0
0
0
2
0
0
2
0
0
0
2
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
2
1
0
2
4
2
0
2
0
2
2
0
0
1
0
1
1
2
0
0
1
1
0
3
2
2
0
0
1
0
0
2
0
0
0
0
0
0
1
2
0
3
0
0
2
0
0
0
2
0
3
0
2
1
0
0
1
0
0
1
1
0
0
0
1
0
2
0
2
1
0
0
0
0
2
1
0
0
1
0
1
0
0
0
2
1
1
1
0
0
1
0
0
1
2
0
0
4
0
1
0
2
0
0
1
1
0
1
0
0
0
0
0
0
0
1
2
1
2
2
0
0
0
0
2
1
2
0
1
0
2
0
2
0
0
2
3
0
1
1
1
0
0
0
0
0
1
1
2
0
0
1
0
0
0
0
0
1
1
0
1
0
1
2
2
0
2
0
2
2
0
2
2
2
2
2
2
0
0
0
2
0
2
0
0
2
0
1
3
2
0
0
0
1
1
0
0
0
1
0
2
0
0
2
0
1
0
2
1
1
0
1
2
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
1
1
1
0
1
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
1
2
0
2
1
0
0
1
0
2
1
0
1
1
1
1
0
0
0
1
1
0
2
0
1
2
0
0
0
0
0
2
0
0
0
0
1
2
2
0
0
0
1
0
1
0
0
0
0
0
1
0
1
1
0
0
1
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
2
2
1
0
0
0
1
0
0
0
0
0
0
2
0
2
1
0
0
0
2
0
0
0
1
0
1
0
1
1
2
0
0
0
2
1
0
0
0
0
0
0
0
3
0
1
0
2
0
0
0
0
2
1
0
1
0
0
1
0
0
2
2
0
0
1
2
0
2
0
0
2
0
0
0
2
2
0
1
1
2
3
0
0
0
0
2
2
0
0
1
2
0
0
0
0
1
1
0
1
1
0
2
2
1
1
0
0
0
2
0
0
0
1
0
1
1
2
0
1
3
0
0
0
1
2
0
2
0
0
2
0
1
0
1
0
1
2
0
1
0
0
1
0
2
0
0
0
0
0
2
2
0
0
1
1
0
1
1
0
0
2
0
0
0
0
2
0
0
0
0
2
1
0
0
2
1
1
0
0
0
1
1
2
0
2
0
0
0
2
0
0
1
0
1
0
1
0
1
1
2
0
2
0
0
0
1
0
0
1
0
1
0
1
2
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
3
0
2
1
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
1
1
1
0
2
2
0
2
2
1
0
3
0
2
0
0
1
0
2
0
0
3
2
0
1
0
2
0
2
0
0
2
1
3
0
1
2
2
0
0
0
2
0
0
0
0
0
0
2
1
0
0
2
2
0
0
0
0
0
2
1
1
2
1
0
0
0
2
2
0
1
0
0
0
1
0
4
0
0
0
0
0
0
2
2
3
1
0
0
0
0
0
1
1
0
2
0
0
4
2
2
2
0
0
0
1
1
0
0
0
0
0
2
2
0
1
0
0
2
0
0
0
1
2
0
2
0
0
2
0
0
0
2
0
2
1
0
1
0
1
0
0
0
2
0
0
2
2
1
0
0
1
0
0
1
0
0
1
0
0
1
0
1
0
1
2
0
1
0
0
0
0
0
2
2
0
0
2
0
2
0
0
0
2
0
0
0
0
1
1
2
2
1
0
1
2
0
1
1
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
2
0
1
0
2
0
0
0
0
0
1
1
2
0
0
0
2
0
2
0
1
0
1
0
1
0
0
0
2
1
0
3
0
2
1
0
0
1
5
2
0
0
1
0
2
2
0
0
0
0
1
0
0
1
0
1
0
0
0
0
2
2
2
3
1
1
0
0
0
1
3
0
0
2
0
2
0
2
0
1
0
0
0
0
0
0
0
2
0
0
1
1
2
0
0
0
1
2
0
0
1
0
1
0
0
1
2
0
0
1
0
2
0
1
0
2
2
2
0
0
0
1
0
2
2
1
2
0
1
0
0
4
0
1
0
1
4
1
2
0
0
2
0
2
2
1
0
2
0
0
0
1
0
2
1
0
1
2
2
0
1
0
0
0
2
0
0
2
0
0
0
0
2
1
1
2
0
2
4
4
0
0
0
1
1
0
1
0
2
2
0
0
0
1
1
2
1
0
0
1
1
0
0
0
2
1
0
0
0
0
0
0
0
2
0
2
1
2
0
1
1
0
0
2
0
0
0
0
0
1
0
0
1
1
0
1
2
0
1
2
0
0
1
0
0
1
0
2
0
2
0
2
0
1
3
1
0
0
2
2
0
1
0
2
0
2
2
1
0
0
0
0
0
0
0
1
0
2
0
0
0
1
1
1
0
0
0
0
2
2
0
2
1
0
0
0
0
2
0
0
2
0
2
2
0
2
2
3
1
2
2
0
0
2
0
1
0
0
0
0
1
0
1
2
2
2
2
2
2
0
0
2
1
0
1
0
2
0
2
2
0
0
0
0
3
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
1
2
1
1
0
1
0
0
0
1
1
1
0
2
0
0
1
0
1
1
0
0
0
0
0
2
1
0
1
0
0
2
0
0
1
1
0
0
0
1
0
2
0
0
1
1
1
0
1
0
1
0
2
0
1
0
0
1
0
0
1
1
0
0
2
0
0
2
0
0
0
0
0
0
2
2
0
0
0
2
0
2
2
0
0
1
5
0
0
0
1
1
0
0
0
3
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
1
2
0
0
2
0
0
1
0
1
0
1
1
0
0
0
0
0
0
1
0
2
1
0
0
0
1
0
0
1
1
1
0
0
0
1
1
0
2
2
2
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
2
0
1
1
0
0
0
0
0
0
1
3
2
0
0
0
1
0
0
2
0
0
1
0
2
0
5
1
0
0
0
0
1
2
1
1
0
2
1
0
1
0
1
1
1
1
0
1
0
0
0
2
0
1
0
0
2
0
0
0
2
0
0
1
1
0
0
0
1
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
2
2
1
2
2
2
2
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
1
0
1
0
0
2
1
2
2
0
2
2
2
1
1
2
1
2
1
0
2
1
0
1
1
1
0
0
2
0
0
1
2
0
0
0
1
0
0
0
1
0
2
2
0
2
0
2
0
0
0
0
0
0
0
2
1
0
2
0
0
2
2
1
1
0
1
1
0
2
1
1
2
0
1
0
2
0
0
0
0
2
2
2
2
0
2
2
0
1
0
0
0
0
1
0
0
2
0
0
0
2
0
1
0
0
0
0
0
1
1
2
0
4
0
0
0
1
1
1
0
1
2
1
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
1
2
0
0
2
0
3
0
0
0
2
0
0
2
1
2
0
0
0
2
0
1
0
1
2
1
2
1
0
0
0
2
1
2
0
1
2
1
2
3
0
2
2
0
0
1
0
2
2
0
0
0
0
0
0
0
0
2
2
0
3
2
0
0
0
1
0
0
1
1
0
0
0
0
3
0
2
1
1
2
0
2
0
1
0
0
1
0
1
1
0
1
2
0
1
2
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
3
2
0
0
2
0
2
0
0
1
0
0
0
0
0
3
1
0
2
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
3
0
1
1
0
0
0
0
2
0
2
1
1
1
0
1
0
0
1
0
0
0
0
2
1
0
1
1
0
0
1
2
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
3
2
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
1
2
1
1
0
2
0
0
1
1
0
0
1
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
1
0
2
0
0
0
3
0
0
0
0
2
0
0
0
0
1
1
1
0
2
0
0
2
1
0
0
0
0
0
2
0
6
1
1
0
2
1
0
0
0
0
1
0
0
1
0
0
0
2
0
0
1
1
0
0
0
1
0
0
1
0
0
1
1
0
0
0
1
1
1
1
1
1
0
0
2
1
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
2
0
1
0
6
0
2
2
2
2
2
0
0
0
0
0
2
2
0
2
1
0
1
0
0
1
1
1
0
0
1
0
0
1
0
0
0
0
0
2
0
0
2
1
0
1
0
0
0
0
1
1
0
2
2
1
2
0
0
2
2
0
0
0
0
1
3
0
0
0
0
2
1
0
1
2
0
1
0
0
0
0
2
0
0
0
2
1
0
0
0
2
0
1
1
1
1
0
0
1
0
2
0
0
0
0
0
1
0
1
1
0
0
2
1
2
0
0
0
0
1
1
2
0
0
2
0
1
0
0
2
0
1
0
2
1
0
8
1
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
1
0
1
0
1
2
1
0
1
0
0
0
2
0
1
2
0
2
0
0
0
1
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
2
0
0
0
2
1
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
1
1
2
0
1
0
2
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
2
2
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
1
0
2
0
0
2
1
1
0
2
0
2
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
1
0
0
3
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
2
2
1
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
2
2
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
2
0
1
0
1
0
1
0
1
0
2
0
0
2
0
0
1
0
0
1
1
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
3
0
1
0
0
1
0
1
2
1
1
1
0
0
2
0
0
0
0
0
2
0
0
1
2
2
0
0
0
0
0
2
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
2
0
3
0
0
0
1
1
1
0
3
0
1
2
1
0
0
2
0
1
0
0
2
1
1
1
1
2
0
0
2
0
1
2
0
0
2
0
0
2
0
2
0
1
0
3
2
1
2
2
1
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
1
0
1
2
1
0
1
0
0
0
2
2
0
0
0
0
2
1
0
0
2
1
0
1
0
0
1
3
1
2
0
0
2
0
2
1
1
0
0
0
0
0
2
1
1
2
3
2
0
2
0
0
5
0
1
0
0
1
1
0
2
0
1
0
0
0
0
0
0
0
0
1
2
1
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
1
0
2
0
2
0
4
0
2
1
1
0
2
2
0
2
1
0
1
0
0
0
0
0
1
0
1
0
1
2
0
2
0
0
1
1
1
2
1
4
0
2
0
1
0
0
0
0
2
1
1
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
1
0
1
1
0
0
1
1
0
2
0
0
1
0
0
0
0
2
0
0
0
0
1
2
0
2
0
1
0
0
2
2
2
0
1
2
0
0
0
1
0
2
0
0
2
1
0
0
2
0
2
1
1
0
0
0
0
0
0
0
0
3
2
1
2
0
3
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
3
2
0
2
0
0
0
1
0
0
0
2
0
0
0
2
2
1
3
1
1
0
0
0
0
0
0
1
0
0
1
2
2
0
1
3
1
0
0
0
2
0
0
1
0
0
2
0
1
0
0
5
0
0
0
2
0
0
1
0
0
0
5
0
0
2
1
0
0
0
1
0
1
1
1
0
0
1
1
0
0
2
0
1
4
0
0
0
0
0
0
1
1
1
0
1
0
0
0
1
0
2
0
0
0
2
1
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
1
2
0
1
0
0
0
1
0
0
1
0
0
3
0
0
0
1
0
0
1
2
0
0
1
0
1
0
1
1
0
2
7
2
0
1
0
0
2
0
0
0
2
0
0
0
1
2
0
0
1
2
1
0
0
0
0
0
2
2
0
1
2
2
0
3
1
1
1
2
0
0
2
0
1
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
3
1
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
1
0
1
0
0
1
1
2
0
1
2
0
1
1
1
1
0
0
0
0
0
0
2
1
1
2
1
2
0
2
0
1
1
0
1
2
0
0
2
0
0
1
2
1
0
1
1
1
0
0
0
0
0
2
2
0
1
1
1
2
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
2
1
0
1
0
0
1
0
0
0
2
0
3
1
0
1
0
0
0
2
0
1
1
1
0
0
1
0
0
0
0
0
0
0
2
2
1
2
0
0
2
2
0
0
0
1
2
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
1
1
2
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
2
0
2
3
0
0
2
2
1
0
0
2
0
0
2
1
0
0
0
0
1
0
0
1
1
0
1
0
0
0
1
0
0
2
0
1
1
0
0
0
1
2
2
0
2
1
1
0
0
0
1
0
2
0
2
0
2
2
0
0
0
0
0
1
0
1
0
0
0
2
2
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
1
1
0
3
0
0
0
0
1
0
0
0
0
0
3
0
2
1
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
1
1
0
2
0
2
0
2
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
1
1
0
1
0
0
2
0
0
0
2
0
3
1
3
3
1
2
0
1
0
0
0
0
0
1
1
1
1
0
0
0
0
0
2
2
0
0
2
1
0
2
0
0
0
0
0
0
1
1
2
0
0
0
0
1
2
0
0
1
2
0
1
0
1
0
0
2
0
2
1
1
0
0
1
2
2
0
2
0
1
0
1
0
1
0
0
0
2
0
0
0
1
0
2
0
0
2
0
0
1
2
1
0
0
0
0
0
0
0
0
1
0
1
1
2
2
1
0
3
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
1
2
0
2
2
0
0
1
2
1
2
0
1
0
2
0
3
0
2
3
0
0
0
2
0
0
0
2
1
0
1
2
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
2
0
2
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
4
0
2
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
2
0
0
2
0
2
0
2
0
1
0
5
1
0
0
0
0
0
1
0
0
1
0
0
1
0
2
0
1
0
4
0
1
2
0
2
0
0
1
0
2
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
2
1
0
0
4
0
1
0
0
0
1
4
0
0
0
2
2
0
2
0
0
0
0
0
2
0
0
1
2
2
0
0
0
0
0
1
0
0
2
1
0
1
0
0
0
2
0
2
0
4
0
0
0
0
1
0
2
2
0
1
0
0
0
0
2
1
1
0
0
2
0
0
1
0
0
1
0
2
1
0
0
1
0
0
1
0
0
0
0
2
1
2
2
0
1
0
2
0
1
0
0
1
2
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
2
0
0
2
0
0
2
0
1
1
14
0
0
0
1
0
0
1
0
2
0
1
0
0
0
2
0
1
0
0
0
0
2
1
0
1
0
2
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
2
0
1
0
0
0
1
0
1
0
0
0
1
2
0
2
0
0
2
1
0
2
0
1
0
0
0
0
0
2
0
0
2
1
0
0
0
1
0
1
1
0
0
0
1
0
1
1
0
0
0
0
2
2
1
2
1
0
1
0
0
1
1
0
0
0
2
0
0
0
0
0
1
2
0
3
0
0
0
0
2
2
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
1
0
2
0
0
3
0
0
0
0
0
0
1
0
1
1
2
1
0
0
0
1
1
1
1
0
2
0
2
2
0
1
1
0
0
0
0
0
0
0
2
2
2
0
0
2
0
1
0
2
0
0
2
0
0
2
0
1
1
1
0
1
0
0
0
0
0
0
1
0
1
2
1
0
1
2
0
1
1
2
0
1
0
0
2
0
1
0
0
0
0
1
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
4
2
0
0
2
2
0
0
0
0
0
1
0
1
0
0
2
0
1
1
0
2
0
0
0
0
1
1
0
0
1
0
0
1
1
0
0
0
0
2
2
1
2
0
0
1
0
0
0
0
1
0
0
0
2
1
0
1
0
0
0
0
1
1
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
1
0
0
0
0
2
0
1
2
0
0
0
0
0
0
2
0
1
0
0
2
2
0
2
0
1
1
0
1
1
0
0
0
1
0
0
0
0
2
2
0
2
0
0
0
1
2
0
0
3
1
1
1
0
0
0
0
1
2
1
0
0
3
1
1
2
2
1
0
0
0
2
0
1
1
0
0
1
0
2
0
1
0
0
1
3
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
1
0
2
2
0
2
0
1
0
2
2
1
0
1
1
1
0
0
1
0
0
0
1
0
1
0
0
1
0
0
1
1
2
0
0
0
0
2
0
0
0
0
3
0
2
5
2
0
0
0
0
1
0
2
0
2
0
0
1
0
1
0
0
0
2
1
1
2
2
0
0
0
0
0
0
2
1
0
0
1
0
1
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
1
0
1
0
1
0
1
0
0
0
1
1
0
0
1
0
3
0
2
1
2
0
0
2
0
0
2
1
2
2
2
1
3
0
0
0
1
0
0
0
0
0
2
1
2
1
1
0
2
2
0
1
0
2
0
1
0
0
2
1
0
0
0
0
1
2
1
2
0
0
2
3
1
2
2
1
0
0
0
0
0
0
0
0
3
0
0
0
0
2
1
1
0
2
1
1
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
2
1
0
1
0
1
1
2
0
0
0
2
0
0
2
0
0
0
0
0
2
2
0
0
2
0
0
0
0
2
0
1
0
0
1
2
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
2
0
0
2
1
1
2
0
0
1
0
1
0
0
1
1
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
2
4
0
0
0
2
0
0
1
2
2
2
0
0
2
2
0
2
0
2
1
1
0
0
2
0
0
1
0
0
0
1
0
0
0
3
0
1
2
2
0
1
1
0
0
1
0
0
1
0
3
1
0
0
0
1
1
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
2
2
1
0
2
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
1
1
0
2
2
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
2
1
2
0
0
0
1
0
0
0
0
2
0
1
0
2
2
0
2
0
1
2
0
1
0
2
0
0
1
0
2
2
0
2
0
0
1
2
2
0
0
0
0
0
0
0
0
1
1
0
2
0
1
0
0
0
0
1
0
0
2
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
6
0
0
0
2
2
0
1
0
0
1
2
0
2
0
1
1
2
0
1
0
0
0
0
0
1
0
1
1
0
2
0
0
2
1
1
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
1
2
2
1
1
0
3
2
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
1
0
1
1
0
1
0
2
2
0
0
1
2
1
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
1
1
0
0
1
2
0
1
2
0
0
0
1
1
0
3
0
2
0
0
0
0
1
0
2
1
0
0
1
0
2
0
1
1
0
1
0
0
1
1
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
1
1
2
0
0
0
1
1
1
3
1
2
2
1
0
2
0
0
2
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
1
3
0
0
1
0
1
1
0
0
1
0
0
2
1
0
2
2
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
4
0
2
0
0
1
1
1
1
0
1
0
2
0
0
0
0
2
0
0
2
1
0
1
0
0
0
2
0
0
0
1
0
1
2
0
1
1
0
3
0
0
0
1
2
2
0
0
0
0
0
0
1
0
1
0
0
1
0
1
1
0
1
1
1
0
1
0
0
0
2
1
0
2
1
2
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
3
0
0
0
0
2
2
2
1
0
2
2
1
1
1
0
0
2
0
2
0
0
0
1
2
0
0
1
0
0
0
0
0
1
0
0
2
1
1
0
0
1
0
1
0
0
0
0
2
0
1
2
0
1
0
0
0
2
0
1
1
2
2
1
1
0
1
1
2
1
0
3
0
0
1
0
2
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
1
2
0
0
1
2
0
1
0
0
0
0
0
1
0
1
0
0
0
4
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
2
0
0
0
1
1
2
0
0
2
0
2
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
2
1
0
0
0
1
0
0
0
2
0
0
1
0
2
0
3
0
0
2
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
1
1
2
0
1
2
0
1
0
1
1
0
0
0
1
2
1
2
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
2
0
2
0
0
1
0
0
0
2
0
3
0
0
0
1
2
1
0
0
0
1
2
1
2
0
0
0
1
0
0
0
2
2
0
0
0
0
0
2
0
1
2
0
0
0
2
2
0
2
0
1
0
0
1
0
0
0
2
0
2
1
0
2
0
0
0
3
2
1
2
0
0
0
0
0
0
1
1
0
0
3
2
0
0
0
1
2
1
0
2
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
1
2
2
2
0
1
2
0
0
0
0
0
0
0
0
1
1
0
2
1
0
0
2
0
2
1
2
1
1
0
0
0
2
0
0
2
1
1
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
2
0
0
0
0
1
0
0
1
1
2
2
1
0
0
0
0
0
1
0
1
0
0
2
0
0
0
2
0
2
0
2
1
0
0
1
0
2
5
0
3
0
0
0
2
0
2
0
1
4
0
0
0
4
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
2
1
1
0
0
1
0
2
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
2
1
0
1
0
0
0
1
2
0
0
2
2
0
0
2
2
1
0
0
1
3
0
0
0
2
0
0
0
0
2
0
0
1
2
0
2
1
0
0
0
1
2
0
0
0
0
2
0
0
1
0
1
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
2
1
1
0
1
0
0
0
2
2
0
0
1
1
1
1
0
0
0
1
0
1
0
0
5
2
0
0
0
1
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
2
1
0
0
0
0
1
1
1
0
0
0
2
2
0
0
3
0
0
3
5
0
0
1
0
0
0
2
1
1
0
2
1
0
1
2
1
0
0
0
0
0
1
1
0
2
2
1
1
1
1
2
1
0
1
2
3
2
0
0
0
0
0
0
0
0
1
1
0
0
2
1
3
0
0
0
0
1
1
2
2
0
0
1
2
1
0
0
0
0
1
0
0
0
0
0
0
1
1
2
1
1
0
0
0
2
2
0
1
0
0
2
0
2
0
0
1
2
0
0
2
2
0
2
0
1
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
1
0
0
0
0
0
2
3
1
0
0
1
2
1
1
0
0
0
0
2
3
0
1
0
0
1
0
1
2
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
2
1
2
2
2
0
0
2
2
0
0
2
0
0
2
0
2
2
0
0
1
0
2
1
0
2
0
0
0
0
0
2
1
2
0
4
0
1
0
2
0
0
2
2
1
0
0
0
0
2
0
0
2
1
0
0
0
0
0
2
1
0
2
0
1
2
0
0
1
1
0
0
0
0
1
0
2
0
2
1
1
0
0
1
1
0
0
0
0
2
0
0
0
2
0
0
2
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
1
1
1
1
1
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
2
0
1
0
0
3
1
0
0
2
0
0
0
2
0
0
0
2
0
0
0
1
0
1
0
1
0
0
0
0
2
3
0
1
2
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
1
1
1
2
0
0
2
0
0
2
0
0
1
0
0
1
0
2
2
0
0
1
1
0
0
0
0
1
2
1
1
0
1
1
2
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
3
0
2
2
1
1
0
2
0
1
0
1
1
0
1
2
0
0
1
2
1
0
0
0
2
1
0
1
0
1
2
0
2
0
0
0
0
0
1
2
0
2
0
0
2
2
2
0
1
0
4
0
0
0
1
1
0
0
0
0
0
0
1
2
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
1
0
1
0
0
0
0
2
2
1
0
1
1
1
1
0
0
0
1
0
0
0
1
1
2
2
0
0
0
1
0
2
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
2
1
0
0
1
0
0
1
0
0
0
1
2
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
1
0
0
2
1
0
0
2
0
1
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
2
0
1
2
0
2
0
2
0
0
0
0
1
2
2
0
0
0
0
0
0
0
2
0
1
2
2
0
0
0
1
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
2
1
0
2
0
0
1
0
0
3
0
0
0
1
0
2
0
2
0
4
0
1
0
0
0
2
0
1
0
0
0
2
0
1
1
0
0
1
0
2
0
0
2
0
0
3
2
0
0
0
0
0
0
2
0
1
1
0
1
2
0
0
3
0
0
1
0
1
2
1
2
0
1
0
0
0
0
1
0
2
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
2
1
1
0
2
1
2
2
2
0
0
0
1
0
1
0
1
0
0
0
1
1
2
1
0
0
0
2
2
0
1
0
1
0
2
2
0
1
1
4
0
0
0
0
1
0
0
0
0
0
2
0
2
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
3
0
0
1
1
0
0
2
1
0
0
1
0
2
1
0
0
1
1
0
0
0
2
0
2
0
0
1
0
1
1
0
0
0
0
0
1
2
0
0
1
2
1
1
1
0
2
0
0
1
3
0
1
2
1
0
0
0
1
1
2
2
0
0
0
0
0
2
0
0
0
0
1
0
1
0
1
0
0
1
2
0
2
2
0
0
0
0
1
0
0
0
0
0
1
1
3
0
1
2
2
2
2
4
1
0
2
0
0
0
3
2
0
2
0
0
3
0
0
0
1
0
0
1
0
0
2
1
1
2
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
1
1
0
2
0
0
1
0
1
0
0
2
0
2
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
2
1
2
0
2
0
3
2
0
0
0
0
3
0
0
0
2
2
4
0
0
3
1
1
1
0
1
1
0
4
2
2
0
0
0
2
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
2
1
0
0
0
0
2
2
1
1
0
2
1
0
1
1
0
1
1
0
0
2
2
0
0
0
2
0
0
1
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
1
0
1
0
2
2
2
0
0
0
0
0
1
2
2
2
0
1
0
0
0
0
0
2
1
1
0
0
3
2
2
0
1
0
0
0
1
1
0
2
1
2
0
1
0
0
3
1
0
0
0
2
1
0
0
0
0
0
0
0
2
1
3
0
3
1
0
0
1
0
2
0
0
0
0
2
1
1
0
1
0
0
1
0
2
0
0
0
1
1
0
0
2
1
2
0
0
0
0
0
0
1
0
1
0
1
2
0
1
1
0
1
0
0
0
1
0
2
0
1
3
0
0
0
0
0
4
0
0
1
0
2
0
0
2
0
2
1
1
0
1
0
2
3
0
0
1
1
0
0
0
1
2
1
0
0
0
1
0
0
1
1
1
0
1
0
2
0
2
0
2
2
2
2
0
0
1
2
0
2
0
0
0
1
2
1
2
0
1
0
0
2
0
0
0
0
1
0
0
2
2
0
0
1
1
0
2
1
0
0
0
0
0
0
1
0
2
1
1
0
0
0
1
0
2
4
1
0
0
0
0
1
2
0
3
0
0
0
0
0
1
1
0
2
0
0
0
0
0
1
2
1
0
1
0
2
0
0
1
2
0
2
0
1
2
0
0
2
2
0
0
2
2
2
0
0
0
0
0
0
0
2
1
0
0
1
1
2
0
0
0
0
2
0
0
0
1
2
0
3
2
0
0
1
1
0
0
2
0
1
2
2
0
1
2
0
2
2
0
2
0
0
0
0
1
0
2
0
0
2
2
1
2
0
1
2
0
1
1
0
0
0
2
2
1
1
1
1
0
0
0
0
0
1
0
2
0
2
1
1
0
0
1
0
0
0
0
1
2
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
1
0
1
2
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
1
2
0
0
2
0
0
2
0
0
0
1
0
1
2
1
0
0
0
2
3
1
0
2
0
0
2
3
1
1
0
0
0
2
2
0
1
0
0
1
0
1
1
1
2
0
2
0
0
0
1
0
0
0
1
0
2
0
0
0
0
6
0
0
3
0
1
0
0
2
0
1
2
0
1
2
0
0
0
1
2
0
0
1
0
2
2
0
2
0
0
1
2
1
0
0
2
0
0
0
0
0
0
0
2
0
1
2
2
0
2
0
0
1
0
2
0
0
0
0
1
2
0
0
0
0
2
0
0
2
0
2
3
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
1
2
0
0
2
0
0
2
1
3
0
1
1
0
0
1
2
0
0
0
1
2
0
0
0
0
2
2
0
2
0
1
2
1
1
0
0
2
2
0
0
0
1
0
0
2
2
0
1
0
3
0
3
0
1
0
0
0
2
0
0
0
0
1
0
0
1
1
1
2
0
2
4
1
0
1
0
0
0
2
0
0
0
0
0
0
0
1
2
2
0
0
0
0
1
0
0
1
1
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
2
2
0
0
2
2
0
0
0
2
3
1
0
2
1
0
1
0
0
0
2
0
2
1
2
1
0
2
0
2
0
0
2
0
1
2
0
3
2
1
0
1
1
0
2
0
0
0
0
3
0
0
0
0
2
0
0
2
0
2
0
2
2
2
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
2
2
2
2
0
2
1
0
0
2
0
0
2
0
0
0
0
0
2
1
1
1
1
1
0
1
1
0
0
1
2
2
1
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
1
1
0
0
2
2
1
2
2
0
7
0
0
1
0
2
0
0
2
0
0
0
0
0
0
1
2
1
0
1
0
1
0
0
2
0
0
0
2
1
0
0
1
0
0
2
0
1
1
2
1
0
2
0
0
0
0
0
0
0
2
1
0
0
2
0
1
1
1
2
1
1
2
0
1
1
2
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
1
2
2
0
0
1
2
1
0
0
1
0
0
2
1
0
1
0
1
0
1
1
0
0
1
2
1
0
0
0
0
2
0
0
1
0
1
1
0
0
1
2
0
0
0
0
1
1
0
1
1
0
0
0
0
2
5
0
0
0
1
0
1
2
1
2
0
0
0
0
2
0
2
1
1
2
0
2
0
1
0
0
3
0
0
2
1
1
2
0
1
2
0
0
1
0
0
0
0
1
0
0
2
0
3
0
0
1
2
0
2
0
0
0
1
0
0
2
1
0
0
0
0
0
0
2
0
3
2
2
1
1
0
2
1
1
0
1
0
0
0
0
1
2
1
0
2
1
1
0
0
2
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
1
0
0
2
0
0
2
1
2
1
0
0
2
0
0
2
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
2
2
2
0
0
0
2
2
0
2
1
2
2
1
0
0
0
0
2
0
0
1
2
0
0
0
2
2
0
0
1
0
0
1
2
0
2
0
2
0
0
0
0
1
1
2
0
0
4
1
0
0
1
0
1
0
1
0
2
0
1
0
1
0
1
2
0
0
0
0
1
2
0
2
1
1
0
0
2
0
0
1
0
1
1
0
1
2
1
0
0
0
1
0
0
1
1
0
0
0
0
0
2
0
0
0
1
0
0
1
0
1
0
0
2
0
2
1
0
0
1
0
0
2
0
0
1
2
3
0
1
0
1
2
0
2
0
0
1
0
0
0
1
1
1
2
0
0
0
0
1
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
2
0
0
0
0
0
0
1
1
0
0
4
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
2
0
0
1
1
0
2
0
0
0
0
1
0
0
3
0
1
0
0
0
0
0
0
1
0
2
2
0
0
1
0
0
2
2
1
0
0
0
1
1
2
0
0
0
0
2
1
1
0
1
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
2
0
0
1
0
2
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
2
1
0
0
0
2
0
0
0
0
1
1
0
0
0
2
0
2
1
0
1
0
2
0
0
1
2
2
0
1
0
0
0
1
0
0
0
2
0
0
1
1
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
5
0
0
2
0
0
2
0
1
0
0
0
2
0
0
1
0
2
0
1
0
2
0
0
0
1
0
0
0
0
1
0
1
1
0
0
3
0
1
2
0
0
0
2
0
0
1
2
0
2
0
0
0
2
0
0
1
2
1
0
0
0
0
0
0
0
2
1
0
2
15
1
1
1
0
1
1
0
2
0
0
0
2
2
1
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
1
1
0
2
1
2
0
2
0
1
1
0
0
1
2
0
1
1
0
0
0
0
2
0
0
2
0
1
1
1
1
0
0
1
1
0
0
0
0
1
0
3
2
0
0
0
1
1
1
1
2
2
0
0
1
1
0
0
0
0
1
0
1
2
0
0
1
2
1
0
1
3
1
1
0
1
0
0
2
1
3
0
2
1
0
0
1
1
0
1
0
0
3
2
1
0
2
1
0
0
0
1
1
1
0
0
0
0
1
0
1
1
0
1
2
0
0
0
0
2
0
1
0
1
2
2
1
0
0
0
0
1
0
0
0
0
1
1
0
1
2
0
0
0
4
0
2
0
3
0
0
2
0
0
1
0
0
0
2
0
1
2
0
1
0
0
0
0
2
2
0
0
0
1
0
0
0
2
1
0
0
0
1
2
0
0
0
1
2
0
2
0
0
2
0
0
1
1
2
0
0
1
1
2
0
3
1
0
0
0
0
1
0
0
2
2
0
0
2
0
0
1
1
0
2
2
0
1
1
1
0
2
2
0
0
2
0
2
0
0
1
0
0
0
1
2
0
0
0
4
0
2
0
0
0
2
0
0
0
3
1
0
0
2
3
1
0
3
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
1
2
2
3
0
0
3
0
0
1
0
0
0
0
2
0
0
0
1
0
1
0
0
0
1
1
1
0
0
0
0
2
3
0
1
2
0
0
0
1
0
0
0
1
1
0
0
2
0
0
2
1
0
1
0
0
2
2
2
0
0
4
0
3
2
0
0
2
0
2
0
3
2
0
2
2
0
1
0
1
0
0
1
0
2
1
1
0
0
1
2
1
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
2
0
0
2
0
1
1
0
0
3
2
0
0
0
0
2
0
2
2
2
2
1
0
3
0
1
3
1
2
0
0
0
0
0
0
1
1
1
1
1
0
2
1
0
2
0
0
0
0
0
0
1
1
1
3
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
1
0
0
0
0
1
2
2
0
1
2
0
2
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
1
0
0
2
1
2
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
2
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
2
1
0
1
2
0
1
0
0
1
2
0
0
2
0
0
0
0
0
0
1
0
2
2
0
1
0
1
1
0
0
2
2
0
0
1
3
1
0
0
1
0
1
1
0
1
0
0
2
0
0
0
5
0
1
1
1
0
0
0
0
1
0
2
1
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
2
0
0
0
2
0
0
0
3
0
1
0
0
2
0
0
0
0
0
0
0
2
2
2
1
1
0
0
2
0
2
0
1
1
1
1
0
0
0
0
1
2
0
2
2
2
4
0
0
1
0
1
2
0
0
1
1
0
0
0
1
2
0
1
1
0
1
0
2
0
0
0
0
0
2
2
0
1
1
0
0
0
0
1
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
2
0
0
1
2
0
0
0
2
0
0
0
0
0
1
2
0
0
1
0
2
0
2
0
4
0
2
1
0
0
3
0
1
1
0
0
1
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
1
2
1
0
0
1
2
0
0
0
1
0
0
0
0
0
1
2
2
0
0
0
1
0
0
0
2
2
1
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
1
0
1
0
2
0
1
0
2
0
0
2
0
0
0
0
0
0
0
2
0
1
0
1
2
0
0
0
1
0
2
2
1
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
1
0
2
1
1
0
0
1
2
0
1
1
1
1
2
0
0
2
2
2
0
2
2
2
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
1
2
0
1
0
0
0
0
5
0
0
0
0
2
1
0
1
0
2
0
1
0
1
0
2
0
1
2
2
0
0
2
0
0
0
1
0
2
0
2
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
1
0
1
1
2
2
0
0
0
0
0
1
0
0
0
0
1
1
1
0
1
0
0
0
0
0
1
0
0
2
0
0
3
0
0
0
0
2
0
0
0
2
0
2
0
1
0
1
0
2
0
0
0
0
2
0
1
2
0
0
0
2
1
0
0
3
0
1
0
0
1
0
0
1
1
0
2
0
0
0
0
2
0
1
0
0
1
0
1
1
0
0
2
2
2
0
2
0
0
0
2
1
0
1
0
2
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
2
2
0
2
0
0
0
3
1
10
2
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
2
1
0
0
0
0
1
1
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
2
0
2
0
1
0
4
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
2
0
0
1
0
0
1
0
2
3
2
0
0
2
1
0
1
0
0
0
1
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
1
2
0
0
0
0
0
1
1
0
1
1
0
1
2
0
1
3
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
2
4
0
2
0
0
0
1
2
0
0
0
2
0
2
1
0
0
0
1
0
0
0
0
1
1
1
0
1
0
0
2
1
2
0
0
0
1
0
0
1
0
0
1
0
0
1
0
1
1
0
0
1
0
2
0
0
0
0
2
0
0
2
0
0
0
1
0
2
2
1
1
0
2
0
0
1
0
0
0
0
2
0
1
0
0
0
2
0
0
1
0
1
2
0
1
1
0
0
1
0
2
0
2
2
2
0
2
0
2
0
1
0
0
0
0
1
2
2
1
2
1
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
5
0
1
0
0
0
0
2
0
1
0
0
0
1
1
2
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
2
1
0
1
3
1
2
0
0
1
0
1
2
1
0
1
2
0
1
0
2
1
2
0
1
2
0
1
4
0
2
1
2
0
0
0
0
2
1
0
0
0
0
2
1
2
0
0
0
2
1
0
2
1
0
2
1
2
0
0
1
1
0
0
2
0
0
1
0
0
2
0
0
2
0
0
2
1
0
0
0
0
0
2
0
2
0
2
2
0
0
1
1
1
0
1
2
0
2
2
2
0
0
0
0
3
1
0
1
2
0
3
0
0
1
0
2
0
0
0
0
2
2
0
0
0
3
0
0
0
0
1
0
1
0
0
0
2
0
1
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
2
0
0
1
6
0
3
0
0
3
2
1
0
0
0
0
0
2
1
1
0
1
2
0
1
0
0
2
0
1
0
2
0
2
2
0
1
0
0
2
0
0
0
0
1
1
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
2
0
0
0
2
1
2
1
0
0
0
0
1
1
0
0
0
2
0
1
0
1
2
0
0
0
0
0
0
0
1
3
0
0
1
3
2
1
0
0
2
2
0
2
1
2
0
0
0
0
0
0
1
0
0
3
0
0
0
0
2
1
0
1
0
1
1
1
0
4
0
0
0
2
0
0
0
1
0
0
0
1
0
2
1
0
0
2
0
2
0
2
0
1
0
0
0
0
2
0
1
1
0
1
1
1
2
2
2
1
0
0
0
2
0
1
2
1
2
0
0
0
0
0
0
0
0
0
0
1
1
0
2
2
0
0
0
1
1
0
0
0
0
2
1
0
2
0
0
2
0
0
0
1
0
0
0
2
1
2
0
0
2
0
0
0
1
0
0
0
0
0
2
0
3
2
1
0
0
0
0
1
1
0
2
0
1
0
2
0
1
0
0
0
0
2
0
0
0
1
0
2
0
2
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
2
0
2
0
1
0
0
1
1
2
2
0
1
2
3
1
0
1
2
1
0
0
0
0
1
0
0
0
2
0
0
3
0
0
2
4
0
2
0
2
0
0
1
1
0
1
2
3
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
1
0
0
1
1
1
0
0
0
1
0
0
0
0
0
1
2
0
2
0
0
1
0
1
0
3
2
1
2
1
1
6
0
0
1
4
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
2
0
2
1
0
0
2
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
2
0
5
0
0
0
0
0
2
0
0
0
0
1
1
0
2
0
0
1
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
2
3
0
2
1
0
1
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
2
0
0
1
0
1
0
0
2
0
1
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
2
0
0
2
0
0
0
2
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
3
0
0
0
0
1
2
1
0
2
0
0
0
1
1
0
2
2
0
0
1
2
0
1
1
2
0
0
0
1
1
0
1
0
0
0
0
1
2
0
0
1
1
2
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
1
2
0
0
1
2
0
1
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
1
0
0
1
1
1
2
0
0
2
2
1
1
1
1
0
0
1
0
0
0
2
2
0
0
0
0
2
1
0
0
0
0
1
1
0
1
2
0
0
1
0
2
0
0
0
0
2
1
2
0
0
1
1
0
2
2
2
1
1
0
0
1
0
0
0
0
1
2
0
0
3
0
0
5
0
0
2
1
0
0
0
0
1
0
1
0
2
2
0
1
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
3
1
1
0
2
0
2
1
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
2
1
0
2
1
1
2
2
2
1
0
2
1
1
0
1
0
0
0
0
1
0
0
2
0
0
0
0
2
0
1
1
2
0
1
0
3
0
2
0
0
0
1
3
0
0
2
2
0
1
0
1
2
0
1
1
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
2
0
2
2
1
0
2
0
2
0
0
0
1
0
0
1
1
0
0
2
0
0
0
1
2
1
2
2
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
2
0
2
2
0
2
2
1
0
0
0
0
0
3
1
0
0
3
3
1
0
0
0
0
2
0
1
0
0
0
1
1
1
1
0
1
0
1
1
1
1
0
0
2
2
0
0
1
2
0
1
0
0
1
0
0
0
0
1
1
2
1
1
3
0
2
2
2
0
0
1
0
0
2
0
1
0
1
1
3
0
1
1
0
1
0
2
0
2
2
2
1
0
3
0
0
0
2
2
1
0
1
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
2
3
0
1
1
2
0
2
0
0
0
0
1
0
0
1
0
0
1
2
1
0
2
1
0
1
1
0
2
3
1
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
1
2
0
0
1
0
0
1
0
0
0
2
0
1
2
0
0
1
1
1
0
2
0
2
0
0
2
0
0
0
2
0
1
6
0
0
2
0
0
2
2
0
2
2
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
2
0
0
6
1
0
0
2
0
0
1
0
2
2
0
0
1
1
1
0
0
1
1
0
0
0
0
1
2
0
3
0
1
1
2
1
0
1
2
0
2
0
0
0
1
0
2
0
0
0
0
0
0
2
1
1
0
1
0
0
1
2
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
1
2
0
1
1
0
0
1
0
0
0
1
1
2
0
0
0
0
1
1
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
1
2
0
2
2
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
7
2
2
1
0
1
3
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
2
1
0
2
1
1
0
0
0
1
1
0
1
1
0
0
1
2
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
2
0
1
2
0
1
0
2
0
0
0
0
1
0
0
0
0
0
1
2
2
8
2
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
2
0
2
1
1
0
0
0
2
0
1
0
0
0
2
1
0
0
1
1
0
1
2
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
2
2
1
0
2
0
2
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
1
0
1
1
0
1
0
0
1
2
2
1
0
0
0
0
0
2
2
1
0
1
0
1
2
0
0
11
1
0
2
0
0
0
0
0
0
2
2
1
3
0
2
2
1
2
0
0
0
0
1
2
1
0
1
0
1
2
0
0
1
2
1
0
1
2
1
0
0
0
2
1
0
0
0
0
0
0
1
0
2
1
1
0
2
2
2
0
1
0
0
0
3
2
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
2
0
2
0
2
1
0
1
0
0
0
1
2
2
0
0
0
0
0
1
2
3
1
2
6
1
0
0
0
0
0
0
1
1
0
2
4
1
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
3
1
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
1
0
2
0
2
1
1
1
3
0
0
2
1
1
1
1
1
0
2
0
2
0
1
2
0
2
2
2
0
1
4
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
1
0
0
2
1
1
0
2
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
1
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
2
1
0
2
0
0
0
0
0
0
0
1
2
0
4
0
0
1
0
0
1
0
0
0
0
0
0
1
0
2
0
2
3
0
0
0
0
0
1
0
1
2
0
0
2
1
0
0
0
0
0
1
1
2
0
0
0
0
2
0
0
0
2
2
1
0
0
2
0
0
1
0
0
1
0
0
0
0
1
0
0
1
1
2
2
1
2
0
0
1
1
0
0
2
0
0
0
1
2
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
2
0
2
2
0
0
1
1
2
0
2
1
0
1
0
0
2
0
1
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
2
0
0
0
1
0
0
0
4
0
0
0
1
0
2
0
1
0
2
0
1
0
1
1
0
0
2
1
3
1
0
2
0
2
0
2
0
0
0
1
1
2
0
1
0
0
1
1
0
1
1
1
0
0
0
0
3
0
0
0
0
2
0
0
0
3
0
0
1
1
0
0
0
1
0
0
2
2
1
0
4
0
2
0
1
1
0
0
1
0
0
2
1
2
0
0
0
0
0
1
0
0
0
0
2
2
0
0
2
2
0
0
0
0
0
0
0
0
1
0
2
2
1
1
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
1
2
1
0
0
2
0
1
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
1
0
2
0
0
0
2
0
0
1
1
0
1
0
0
2
0
1
0
1
0
0
1
0
2
0
0
1
0
0
0
2
0
0
0
3
2
2
0
0
0
0
0
1
0
2
0
1
0
0
0
0
2
2
0
2
2
2
0
0
0
0
1
1
0
0
0
0
0
2
0
2
1
2
1
3
2
0
0
2
2
0
1
2
0
2
0
0
0
0
1
0
2
0
0
1
0
1
0
1
0
2
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
6
0
0
0
2
0
1
1
0
0
2
2
0
1
4
0
0
1
0
0
1
1
2
2
0
1
2
1
0
2
0
0
1
2
1
0
2
0
0
6
2
2
0
0
0
0
0
2
0
0
1
0
2
0
1
0
1
0
2
2
0
2
0
0
0
0
0
0
2
2
1
0
1
1
1
0
1
2
3
0
0
2
0
1
0
1
0
1
0
0
0
1
2
4
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
2
0
0
1
1
4
1
0
0
0
0
0
0
2
1
1
0
0
0
0
2
0
0
1
0
0
0
2
2
3
2
2
7
2
0
0
1
2
1
0
0
0
0
1
3
1
0
0
1
0
2
0
0
1
1
1
0
1
1
0
0
2
1
0
1
1
0
0
0
0
1
0
0
1
0
0
1
1
0
1
2
1
0
3
0
2
0
2
0
2
1
3
0
0
0
0
0
0
2
1
0
1
1
0
0
2
0
3
0
0
1
0
0
2
0
2
1
0
0
2
0
0
2
0
0
1
2
0
0
0
1
0
1
2
0
0
1
2
0
1
0
0
0
0
0
3
0
1
2
2
1
0
0
0
0
2
2
0
2
1
1
0
3
0
0
2
0
1
1
2
2
0
0
1
2
3
0
1
0
0
1
1
2
0
0
1
1
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
3
1
0
0
0
0
0
2
0
2
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
1
0
0
0
0
1
1
2
2
1
3
0
0
0
0
1
2
1
0
0
1
0
2
2
0
3
1
0
1
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
1
2
0
0
0
2
1
0
1
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
5
0
0
0
0
0
0
2
1
2
0
0
2
1
0
0
0
1
0
1
2
0
2
0
1
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
2
2
0
0
1
2
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
1
2
1
0
3
0
2
0
1
1
0
0
0
1
0
1
0
0
1
1
0
0
2
0
0
1
0
0
0
2
1
0
2
0
0
0
1
0
1
0
0
1
0
1
0
0
3
0
1
0
3
1
2
0
1
1
2
2
0
0
0
0
0
0
1
2
0
0
0
0
2
2
1
1
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
1
0
0
1
0
2
2
0
0
0
0
2
2
0
0
2
2
1
0
0
0
0
0
0
0
3
0
0
0
2
1
1
2
1
0
0
0
0
0
2
0
1
2
0
2
0
2
0
0
2
2
1
0
0
0
0
1
2
0
0
0
2
2
0
0
0
1
1
0
0
0
0
0
0
0
2
1
0
0
1
1
0
1
2
0
0
0
2
0
1
2
0
0
0
0
3
2
0
2
0
0
2
1
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
2
0
0
1
2
0
1
0
2
0
2
1
0
0
2
0
0
0
0
3
2
0
2
0
1
0
0
2
1
0
1
1
0
2
1
0
0
0
0
2
1
0
1
2
1
0
3
1
0
2
1
2
0
0
1
0
1
0
0
0
0
2
2
1
0
0
1
0
0
0
0
2
0
0
1
0
2
0
2
0
2
1
0
0
2
1
2
0
1
2
0
0
0
0
0
2
2
2
1
0
0
0
0
1
2
2
1
0
0
0
0
2
0
0
1
0
2
0
0
0
0
1
2
2
0
0
2
0
2
0
0
1
0
2
2
0
0
0
1
0
2
0
0
1
1
1
0
0
0
0
4
0
2
0
0
0
1
0
1
0
0
0
0
0
0
1
2
3
0
0
0
0
0
2
0
0
1
1
0
1
1
3
0
1
1
2
1
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
1
1
0
1
0
3
2
3
1
1
2
0
0
0
0
2
0
2
0
0
1
0
0
1
0
2
1
0
1
0
1
1
2
0
1
3
0
0
0
0
0
1
0
1
1
0
0
2
2
0
4
0
2
0
0
2
1
0
0
1
2
0
0
0
1
2
0
1
2
1
0
1
0
1
0
2
2
1
1
1
0
0
0
1
1
2
0
0
2
1
0
1
0
2
1
0
2
2
2
1
0
0
2
2
0
2
0
0
1
2
0
0
0
0
2
2
0
1
1
3
0
0
0
2
1
0
0
2
0
2
0
0
0
2
1
3
1
0
1
2
0
0
0
0
0
0
1
0
0
0
2
3
0
4
0
0
1
0
0
0
3
0
0
0
2
0
0
2
0
0
0
2
1
0
0
1
1
2
1
0
0
2
2
0
1
2
1
0
1
0
0
0
0
0
2
0
2
2
1
0
2
1
2
0
1
0
2
3
1
2
0
0
2
0
0
1
0
2
0
2
0
0
3
2
1
1
0
0
0
1
0
0
0
1
2
2
0
0
2
0
1
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
2
0
0
2
0
1
0
1
0
0
0
1
0
1
0
2
0
2
0
1
0
0
0
1
2
0
0
0
0
2
0
5
2
0
0
0
1
1
0
0
0
1
0
0
1
1
1
1
1
0
1
2
0
2
0
0
0
0
1
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
1
1
0
0
2
0
0
0
0
0
3
0
0
0
1
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
2
1
2
0
0
0
0
0
0
0
1
2
0
0
2
1
0
1
1
0
2
0
2
0
1
1
1
0
0
2
2
0
0
0
1
2
0
2
0
0
0
2
1
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
1
1
0
1
0
0
0
0
3
0
0
0
0
0
1
0
2
1
0
0
1
2
0
0
0
0
1
0
0
2
1
0
2
2
0
0
0
0
0
0
0
0
0
2
2
0
0
3
3
2
0
0
5
0
1
0
1
0
2
0
1
0
0
0
2
0
0
0
1
0
3
0
2
0
0
2
0
2
2
1
1
0
0
1
0
0
1
0
0
0
1
1
0
0
0
1
0
0
2
0
0
0
1
0
2
0
0
1
0
0
0
1
0
0
2
1
0
0
1
0
1
0
0
1
0
2
1
2
0
0
2
1
1
0
0
1
2
2
0
2
1
0
2
0
0
2
1
0
2
0
0
1
2
0
0
0
1
2
0
1
0
0
2
0
1
0
0
2
1
0
1
0
0
1
0
0
0
1
2
0
0
0
4
0
0
0
0
2
1
0
0
2
0
1
0
0
0
1
0
0
2
1
0
0
0
1
0
2
0
0
1
0
2
0
0
1
2
2
2
4
0
1
0
1
0
2
0
2
2
0
1
0
1
0
0
2
0
0
0
0
2
1
2
0
0
0
0
0
2
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
2
3
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
1
0
2
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
2
3
0
2
0
1
2
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
1
0
0
1
0
0
0
0
1
0
0
4
0
1
1
1
0
2
1
2
0
1
0
0
0
1
2
1
0
2
0
0
0
2
2
0
2
0
2
0
0
1
1
2
0
1
2
1
0
2
0
0
0
0
3
0
0
0
0
0
2
0
0
0
2
0
1
0
3
0
0
0
0
0
0
0
0
0
1
2
2
2
2
1
1
0
0
0
1
1
0
5
0
0
0
0
0
0
0
3
2
0
0
0
1
1
0
0
0
1
0
1
0
10
0
2
1
2
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
1
0
1
0
2
0
2
0
0
0
4
0
0
0
0
1
4
0
0
0
0
0
2
0
1
2
2
2
4
1
0
0
0
2
2
2
2
0
0
1
0
0
0
2
1
1
0
0
0
0
1
0
0
0
0
2
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
2
1
0
0
0
0
0
0
1
2
0
0
1
1
0
0
2
0
0
2
0
1
1
0
2
0
0
0
1
0
2
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
1
0
1
0
1
0
0
2
2
0
0
1
0
3
0
2
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
1
2
0
0
1
2
1
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
2
0
0
0
4
1
1
0
0
0
0
0
1
2
0
0
2
0
0
0
1
0
1
4
1
1
0
1
0
1
0
0
0
2
0
1
0
2
0
0
0
0
2
1
0
0
0
0
1
2
0
0
1
1
0
0
2
1
0
2
0
0
3
2
0
0
0
1
0
0
0
0
1
1
1
2
1
1
0
0
0
1
0
0
0
0
2
0
0
0
1
1
2
1
0
0
1
2
0
1
2
0
2
0
0
2
0
0
0
2
2
1
0
0
2
1
0
1
0
0
0
1
0
0
0
1
0
1
1
0
2
0
1
0
0
0
2
0
0
2
2
2
0
1
0
1
0
0
0
1
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
2
0
0
2
1
0
2
0
3
2
1
1
0
0
0
1
0
2
0
2
2
0
1
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
1
1
0
0
0
0
1
0
0
1
0
2
0
1
0
0
0
2
0
1
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
1
0
1
0
0
0
0
2
0
0
2
0
1
1
0
0
1
0
2
0
0
0
5
0
0
1
0
1
0
1
0
5
0
0
2
2
1
2
1
1
0
1
0
1
0
1
1
0
2
2
0
0
0
0
0
0
0
2
1
0
2
0
0
0
1
0
0
2
2
1
0
0
1
0
0
2
1
0
2
0
1
1
2
0
0
0
1
2
0
2
1
0
0
1
0
0
2
0
0
0
0
0
0
0
2
2
2
1
0
0
0
0
2
0
6
2
2
1
0
0
3
2
0
2
0
1
2
0
0
0
0
1
1
0
0
0
0
1
0
2
0
2
0
0
3
0
0
1
0
2
1
0
0
1
2
1
1
0
0
2
2
2
2
0
0
1
2
1
1
0
0
0
1
1
1
1
0
2
1
0
0
0
0
1
0
2
1
0
2
0
0
2
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
2
0
1
0
1
0
3
2
0
2
0
0
0
0
1
2
2
0
0
2
2
0
0
0
2
2
3
0
1
0
2
2
2
0
0
2
2
2
0
2
2
0
0
2
0
0
0
1
0
0
0
0
0
2
1
0
0
2
2
0
0
0
0
2
0
0
1
0
2
0
0
2
0
3
0
1
0
1
0
1
2
0
0
2
1
0
0
0
0
1
1
2
0
0
0
2
1
2
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
1
0
2
1
1
2
0
0
1
0
1
0
0
0
0
0
0
2
0
0
1
0
1
0
1
0
0
0
2
0
1
2
0
2
1
0
2
1
2
0
0
1
1
1
10
2
0
1
1
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
2
1
0
4
2
0
0
1
0
1
0
3
0
0
1
0
0
2
0
0
2
1
1
0
1
0
0
2
0
0
0
0
0
0
1
2
1
0
2
0
0
0
0
0
2
0
1
0
0
0
2
2
1
0
0
3
0
3
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
1
0
1
0
0
0
2
0
0
0
1
1
0
0
0
0
0
2
0
0
0
1
0
1
1
0
0
2
0
1
2
0
0
0
2
1
1
0
0
0
0
0
2
2
0
0
0
1
1
0
0
0
0
0
0
2
0
0
1
1
1
0
0
4
0
0
1
1
1
0
0
0
1
1
2
2
2
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
2
1
1
0
0
0
1
2
0
1
0
2
2
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
1
1
2
1
0
1
3
0
0
0
0
2
0
2
0
0
0
0
2
0
0
1
1
0
2
0
0
0
0
2
1
0
0
0
0
0
3
0
0
1
0
1
1
1
0
0
0
0
0
2
2
2
0
0
0
0
0
1
0
1
0
2
2
0
0
1
1
0
2
0
0
1
1
0
0
1
0
1
2
0
0
2
0
1
3
0
2
1
0
2
0
2
0
0
3
1
0
2
1
0
2
2
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
1
1
1
2
2
0
0
2
0
2
2
0
1
1
2
2
0
0
0
0
0
0
3
0
1
0
1
0
0
1
0
1
1
0
0
1
0
0
1
2
0
0
2
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
2
2
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
2
2
1
1
3
0
0
1
0
0
2
2
2
0
0
0
2
2
0
0
1
0
0
1
0
0
1
0
0
1
0
2
1
0
2
0
1
2
1
0
0
2
0
0
0
3
0
0
1
0
1
2
0
1
2
0
0
0
0
0
0
2
1
0
1
0
0
2
0
0
0
2
0
2
1
0
1
0
2
0
0
0
2
0
0
0
0
0
1
2
0
1
0
0
3
0
0
1
2
1
0
0
2
0
0
0
0
0
1
1
5
0
0
0
1
0
3
2
0
0
0
0
0
0
1
0
0
2
1
2
1
0
0
1
1
2
0
2
2
1
0
2
1
1
0
1
0
3
0
2
0
0
0
0
2
0
2
2
1
0
0
0
1
2
0
0
0
0
2
0
0
1
1
1
0
0
0
0
2
1
1
0
1
1
0
0
0
2
2
2
0
2
0
0
0
0
1
2
1
2
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
2
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
1
0
4
0
2
0
0
2
0
2
2
2
0
0
0
0
6
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
2
3
1
2
2
0
2
0
0
4
0
1
0
0
0
1
0
0
1
2
1
0
0
2
0
0
0
0
0
1
0
1
0
2
0
2
1
5
2
0
1
0
0
3
0
1
0
1
0
0
0
2
1
0
0
0
2
2
0
1
0
1
1
0
0
2
2
1
0
0
0
0
0
2
2
0
0
0
0
4
2
1
0
2
1
0
0
2
0
0
0
0
0
1
0
0
1
0
2
1
0
0
0
0
1
2
1
0
0
0
1
0
0
2
1
0
0
1
0
0
0
0
1
0
0
1
0
1
1
1
1
0
0
0
0
2
4
0
0
3
2
2
0
0
0
2
2
0
0
0
2
2
0
0
0
0
0
2
1
1
2
1
0
0
0
0
1
2
1
1
0
0
1
1
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
3
0
2
0
2
1
0
0
1
0
0
0
1
0
0
0
1
0
2
0
2
2
0
0
0
4
0
1
2
0
2
0
1
0
0
0
0
0
0
2
0
0
2
2
0
1
2
0
1
0
2
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
1
3
1
0
0
0
1
0
1
0
1
1
2
0
0
0
1
0
1
2
0
0
0
1
0
0
1
0
0
2
1
2
1
0
0
0
2
0
0
1
1
2
2
0
0
0
1
2
1
1
0
0
0
0
0
1
0
2
0
0
1
1
0
0
1
2
0
3
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
3
2
1
0
1
0
0
0
2
0
0
0
0
2
2
0
0
0
2
1
0
0
2
0
0
0
0
1
2
0
0
1
0
0
0
1
2
0
2
0
1
0
0
0
1
1
1
2
0
0
1
0
0
0
0
0
1
2
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
2
0
0
0
2
1
2
0
0
0
0
0
1
3
0
2
0
0
1
1
0
2
1
0
2
0
0
0
2
0
1
2
2
2
0
0
0
0
2
0
0
0
0
0
0
1
2
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
1
2
1
2
2
0
2
0
1
1
0
1
0
2
1
1
1
0
0
0
1
0
2
2
0
1
0
0
2
2
2
1
2
2
1
4
2
0
2
1
0
0
1
0
1
2
0
1
1
1
1
0
0
1
2
0
0
1
0
1
3
0
0
0
0
0
1
2
0
0
2
0
2
0
0
1
0
2
0
1
1
0
2
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
2
0
0
0
2
0
0
1
0
0
2
0
1
1
1
0
2
0
1
1
1
0
0
0
0
0
2
2
0
1
2
0
1
0
2
2
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
1
0
0
0
1
2
0
0
0
1
0
0
0
0
0
2
3
2
1
0
0
0
2
0
1
0
1
0
1
0
0
0
0
1
1
0
1
0
1
0
1
0
2
2
0
1
1
0
0
0
0
2
1
0
0
2
2
1
1
3
1
0
0
0
0
1
0
2
2
3
1
0
0
1
2
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
3
0
0
0
0
2
0
2
1
0
0
0
1
0
1
0
0
0
0
2
1
0
0
0
0
1
0
0
1
2
0
0
0
1
0
1
0
0
2
0
0
1
0
0
0
1
0
2
0
0
2
2
0
0
0
2
0
0
0
0
2
0
0
1
0
0
2
0
2
0
0
0
2
1
2
1
0
0
1
0
0
0
0
1
2
0
0
0
0
1
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
2
2
2
2
2
0
1
0
1
1
0
1
0
0
1
0
0
0
1
1
0
2
1
0
1
0
1
0
2
1
0
1
0
1
0
6
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
1
1
2
0
1
1
0
1
2
0
1
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
2
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
6
0
1
0
0
1
0
0
0
2
2
2
1
0
0
2
2
0
0
0
1
2
0
0
0
0
1
0
3
0
1
0
0
1
2
1
0
0
1
0
1
0
0
0
1
1
0
0
1
0
0
7
0
0
0
0
0
0
1
6
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
1
2
0
0
0
0
0
1
0
0
1
0
0
0
1
2
0
0
0
0
1
1
1
0
0
0
0
0
1
2
1
1
1
0
2
1
0
2
1
0
0
0
0
0
1
0
0
1
3
1
1
1
1
0
0
0
2
0
0
0
0
1
0
0
0
3
0
0
1
1
0
0
0
2
0
0
1
1
2
0
0
0
1
0
2
3
2
2
0
0
2
0
2
0
0
1
0
1
0
0
0
3
1
0
2
0
0
2
3
0
0
1
1
0
1
0
1
0
2
0
0
0
2
1
0
2
2
0
1
0
0
0
0
2
2
0
0
2
0
1
0
0
2
0
0
0
0
1
0
1
0
0
0
1
2
0
2
0
2
2
0
0
2
2
2
6
0
0
2
1
0
0
0
0
1
0
0
0
0
0
2
3
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
2
0
2
2
3
0
4
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
3
4
0
1
0
2
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
2
0
2
0
0
2
0
2
0
2
1
1
0
2
2
1
0
2
2
0
0
0
2
1
0
0
0
0
0
2
0
1
2
0
0
1
2
0
7
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
2
2
2
6
2
0
0
2
1
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
3
1
0
0
1
0
0
0
0
0
0
0
2
1
1
0
0
2
0
0
2
1
0
0
2
0
0
2
0
0
0
0
0
0
0
2
1
0
1
0
0
1
2
1
0
0
0
1
0
0
1
0
0
0
1
1
0
2
2
0
0
2
0
0
2
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
1
1
0
2
4
0
1
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
1
2
0
1
0
1
0
1
0
2
0
0
0
0
1
1
0
1
1
0
0
0
1
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
1
0
0
2
0
0
0
1
0
0
0
0
2
2
3
1
1
0
1
0
0
2
2
2
0
2
0
0
1
2
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
1
1
0
0
0
0
2
0
0
2
0
1
0
0
0
1
0
2
0
0
0
0
2
2
0
1
0
0
2
1
1
1
0
2
0
0
0
0
2
0
2
0
0
0
0
1
1
1
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
3
0
1
0
0
1
2
0
0
0
2
1
0
3
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
2
0
1
0
0
1
0
1
0
1
0
0
0
1
2
0
1
0
0
0
0
1
0
2
1
2
1
2
1
0
0
0
0
2
1
0
1
1
0
0
0
2
0
0
2
1
0
2
0
2
0
0
1
1
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
2
4
0
1
1
1
0
1
0
1
0
2
0
0
0
1
0
2
0
1
1
0
2
0
0
0
0
1
2
2
0
2
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
2
5
1
0
0
2
2
0
0
2
0
0
0
0
2
1
1
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
1
3
1
0
2
0
0
0
1
0
0
2
0
1
2
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
2
0
0
3
2
0
2
0
2
0
0
2
0
0
0
0
1
1
1
0
0
0
2
1
0
0
1
0
0
0
2
0
1
2
0
0
0
2
0
0
2
0
0
2
1
0
0
0
0
0
0
1
2
1
0
1
0
1
0
0
0
1
0
2
0
1
1
0
0
0
2
0
0
2
1
2
2
1
0
0
0
1
2
0
0
2
3
0
1
0
0
1
0
1
0
1
0
0
0
2
1
0
2
0
0
1
0
2
0
0
0
1
1
2
0
2
0
0
0
2
2
0
1
1
1
0
2
0
2
0
0
1
0
0
0
0
0
0
2
1
1
3
0
1
0
0
2
0
0
2
1
1
1
2
3
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
1
1
2
0
2
0
3
0
2
2
2
0
0
0
2
0
0
0
0
2
1
0
1
1
2
1
0
2
1
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
1
2
0
2
1
2
0
2
0
0
0
1
2
1
0
0
0
0
2
1
1
0
1
0
0
2
0
1
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
1
2
2
1
2
0
0
1
0
0
0
0
2
1
0
2
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
1
0
1
2
2
1
0
0
1
0
0
2
0
1
0
1
0
0
0
0
0
2
0
2
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
1
2
0
0
2
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
2
0
2
0
0
1
0
0
2
2
0
0
0
2
0
0
0
0
0
0
1
0
2
0
2
0
2
0
1
0
1
3
0
0
0
0
2
1
0
2
0
1
2
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
2
1
0
0
3
1
0
2
1
0
0
2
1
0
2
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
2
2
2
0
0
1
1
0
1
0
1
0
0
0
2
2
0
0
0
0
2
0
0
1
0
0
0
0
2
0
2
0
2
0
2
2
0
0
0
0
0
1
2
0
1
1
0
0
2
0
0
2
0
0
2
2
0
1
1
0
0
1
1
0
0
2
2
0
0
1
0
0
2
1
5
2
0
2
0
3
0
2
0
0
2
0
0
0
2
0
2
0
0
1
0
1
2
1
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
2
0
0
1
2
0
1
2
0
1
0
1
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
2
2
0
1
1
0
0
0
1
1
1
0
1
2
0
0
0
0
2
0
0
0
2
0
0
0
2
1
1
0
0
0
2
2
0
1
1
0
0
0
2
1
0
2
0
0
2
1
2
1
1
2
0
0
0
0
0
1
0
0
0
0
2
1
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
3
0
0
2
1
2
2
2
0
0
0
0
1
0
0
0
2
0
0
0
0
2
2
0
1
2
4
2
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
1
1
0
7
0
2
0
0
2
0
0
0
0
1
0
0
0
0
1
2
0
2
0
2
0
2
0
1
2
1
2
1
3
0
1
0
0
0
0
2
0
0
0
1
0
0
0
2
2
0
0
0
1
1
1
0
0
0
2
0
0
0
1
0
0
0
2
0
2
0
0
0
2
0
1
0
1
1
2
0
1
0
0
0
0
1
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
2
0
1
1
0
1
0
0
0
0
0
2
0
0
0
2
0
1
0
0
1
0
1
0
0
1
0
1
0
0
0
1
1
1
0
2
0
0
2
0
1
1
0
1
0
2
0
2
1
1
0
2
1
0
1
2
0
2
0
0
2
1
0
0
0
0
1
3
1
1
0
0
1
0
0
0
1
0
2
1
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
2
2
0
1
0
2
2
0
0
2
1
0
0
0
0
0
1
0
1
0
1
1
0
2
0
2
2
1
2
2
0
2
0
0
0
0
0
1
0
0
2
1
0
2
0
1
0
1
1
0
2
1
0
0
0
0
2
1
2
2
0
0
0
0
0
1
2
0
2
0
0
0
0
2
0
0
0
1
1
0
0
2
2
1
2
3
0
0
0
0
0
1
0
1
1
1
3
1
0
1
1
0
0
1
0
1
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
2
0
0
1
0
0
2
0
0
1
0
0
0
2
0
2
1
0
0
1
2
1
0
2
0
1
0
3
3
1
0
1
0
1
1
1
2
0
1
0
0
0
2
0
0
1
0
2
0
0
0
0
1
0
0
2
2
0
1
2
0
1
0
1
2
0
0
0
0
1
0
1
0
0
0
0
2
2
0
0
0
2
1
0
1
0
0
0
2
0
2
2
0
0
0
0
2
2
2
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
2
2
0
0
0
1
0
0
0
4
1
1
1
3
0
0
2
0
1
2
0
1
0
1
0
2
0
2
2
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
3
1
0
0
1
1
0
0
0
0
1
0
2
1
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
4
0
0
0
0
0
1
2
1
1
1
1
0
1
1
1
0
0
0
0
2
0
2
1
0
0
1
2
0
1
0
0
0
0
1
0
0
0
2
1
0
0
2
0
0
1
1
2
0
0
0
0
0
2
0
2
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
3
0
0
2
0
1
0
0
0
0
3
0
0
2
0
3
2
0
0
0
0
3
1
0
0
0
1
0
1
0
2
0
0
0
2
2
0
2
0
2
2
1
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
4
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
2
1
1
0
2
0
0
1
0
0
1
0
2
0
2
0
0
1
1
1
0
1
0
0
1
1
0
0
2
2
0
0
1
1
0
2
0
1
1
0
0
1
0
0
0
2
2
0
0
0
1
0
1
2
1
3
0
0
2
0
0
0
1
0
0
1
0
7
0
0
0
0
0
0
0
0
2
0
0
2
3
0
3
1
2
2
0
0
0
1
2
1
0
1
0
3
2
2
1
0
0
1
0
1
0
0
0
0
2
2
0
0
1
2
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
1
0
2
0
2
2
2
1
2
2
2
1
1
1
0
1
0
0
2
0
0
0
0
3
0
0
0
1
1
0
2
1
1
0
2
2
0
0
0
1
0
1
2
2
0
3
0
0
0
2
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
2
0
0
0
2
2
0
3
1
0
0
2
0
0
2
0
0
0
0
0
0
2
1
0
1
0
2
0
1
1
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
1
0
0
2
2
2
0
1
0
1
0
0
0
1
1
2
0
1
2
1
0
0
0
0
1
0
2
0
2
0
1
0
0
0
0
0
3
0
0
0
0
0
2
1
0
2
0
0
0
1
1
0
0
2
1
2
0
1
1
0
3
0
0
0
0
1
1
0
0
0
2
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
1
0
0
1
1
2
2
0
1
1
0
1
1
0
1
2
0
0
0
0
1
1
1
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
1
0
0
1
0
0
1
1
1
0
1
0
0
0
2
0
1
2
0
2
0
0
0
0
2
0
0
1
0
0
0
6
0
0
0
1
0
2
2
2
0
0
0
0
0
0
1
0
2
0
1
1
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
2
2
0
0
0
1
0
0
0
1
0
2
0
0
2
0
2
1
0
0
0
0
0
3
0
0
2
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
2
0
0
2
1
1
0
1
0
0
2
0
0
0
0
3
0
1
0
1
0
2
2
0
2
0
0
0
0
2
2
0
0
0
1
2
0
2
2
0
0
1
0
2
0
0
2
1
2
2
0
1
0
1
0
0
0
1
1
1
0
0
2
0
0
0
0
2
0
0
3
0
0
0
2
0
2
2
0
0
2
1
1
0
2
1
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
1
1
0
1
0
0
0
1
4
1
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
2
1
1
2
0
1
0
0
0
1
0
0
2
1
0
1
2
2
1
0
0
0
0
2
0
0
0
0
2
2
1
0
1
0
0
2
0
0
0
1
0
0
0
0
2
2
1
0
0
0
0
0
2
2
1
0
1
0
0
6
0
1
2
0
0
0
0
0
0
2
0
0
2
0
0
1
0
2
2
0
0
0
2
0
1
0
0
2
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
1
0
1
1
1
0
1
0
0
1
4
2
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
1
0
0
2
0
0
0
0
0
0
1
2
0
2
3
2
0
1
0
0
0
0
2
0
2
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
2
2
1
1
0
0
1
1
0
0
0
0
2
1
0
0
0
2
1
0
1
0
1
2
0
1
0
1
0
4
2
0
1
0
0
0
1
1
0
2
0
0
1
0
1
0
0
2
0
0
0
0
2
0
0
1
2
0
0
2
0
0
0
1
0
2
1
0
0
0
1
0
2
0
0
0
1
0
0
1
1
0
0
0
0
1
1
2
0
1
0
0
2
0
1
0
0
1
0
0
2
0
1
0
3
0
0
0
2
0
0
0
2
1
0
0
0
2
1
0
0
0
0
0
2
0
0
0
2
2
0
2
1
0
0
2
0
0
0
1
0
2
0
0
0
2
0
0
0
2
2
0
0
1
0
1
0
0
0
7
0
0
0
0
1
0
1
2
1
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
2
1
1
1
1
2
1
0
0
0
0
0
0
3
0
2
0
0
2
1
1
0
1
0
0
0
0
3
0
1
0
0
2
1
0
0
0
2
0
0
0
0
0
0
2
1
3
1
0
1
2
0
2
0
0
1
2
0
2
0
0
0
0
0
0
2
1
0
0
0
2
3
0
1
0
2
0
0
2
2
1
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
1
3
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
2
0
2
0
0
0
0
0
1
0
2
1
0
0
0
0
1
0
2
1
0
0
1
0
0
2
1
2
0
0
0
0
2
0
1
0
0
1
2
2
0
0
0
1
0
0
0
0
0
1
2
1
0
0
0
0
1
4
2
1
3
2
0
2
2
0
0
0
0
0
0
0
0
0
1
0
1
2
1
1
0
0
3
2
0
3
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
1
0
2
1
0
0
1
0
2
0
1
0
0
1
0
1
1
2
2
2
1
2
0
0
0
2
0
0
0
1
1
0
1
0
0
2
0
2
2
0
0
0
1
0
0
1
1
0
0
0
2
1
1
0
1
2
1
1
0
0
0
2
0
1
0
0
0
1
2
2
2
0
0
0
1
0
0
0
0
1
1
2
0
1
2
0
2
0
0
0
1
0
1
2
0
0
0
3
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
2
2
0
2
0
0
2
0
1
1
0
1
0
3
1
0
1
0
0
1
1
1
0
1
1
2
2
0
1
2
0
0
0
0
0
0
1
2
1
0
2
1
2
0
0
3
0
0
1
1
0
0
0
0
1
0
2
2
1
1
0
1
0
0
0
1
0
0
2
0
0
0
0
1
0
0
1
1
1
0
0
2
1
2
2
2
0
0
1
1
0
1
1
1
1
0
1
0
0
1
0
1
1
0
0
1
0
0
0
1
1
2
0
0
1
1
0
0
0
0
0
0
0
0
1
0
2
0
0
2
2
2
1
0
1
1
1
0
0
0
0
0
0
2
0
0
0
2
0
1
2
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
2
1
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
1
2
0
3
0
0
0
0
2
0
0
2
2
2
0
2
0
0
0
0
2
0
0
0
1
1
0
1
0
0
0
0
0
2
0
1
0
1
1
0
0
0
0
1
0
0
3
1
0
0
0
0
1
0
0
0
2
1
1
2
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
1
1
2
0
1
0
0
0
2
0
2
2
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
1
0
1
0
4
2
0
1
0
0
0
0
1
0
0
2
0
0
0
1
0
2
0
0
0
1
0
0
0
0
1
0
2
2
1
0
0
0
0
0
0
0
0
1
1
0
2
0
1
0
1
2
0
0
2
2
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
1
0
1
3
0
2
0
0
0
0
0
0
0
1
3
0
1
1
0
0
2
2
0
1
3
2
0
2
0
0
0
0
1
0
2
0
0
3
1
0
0
0
0
1
0
2
1
1
0
1
0
1
1
1
0
1
2
0
0
0
5
0
0
1
0
1
1
0
0
2
1
0
0
0
0
2
3
0
1
0
2
1
0
1
0
0
0
0
1
2
1
1
0
0
0
1
0
0
0
1
0
1
0
0
1
2
0
1
0
2
0
3
1
1
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
1
5
1
2
0
0
3
0
0
0
0
1
1
0
0
0
0
2
0
1
0
0
0
1
0
1
0
0
0
1
0
1
2
0
1
1
2
0
2
2
0
2
0
2
0
0
1
0
0
0
1
1
0
0
0
1
0
2
1
2
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
1
1
0
0
0
1
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
1
1
2
0
3
0
1
1
0
0
1
0
0
0
0
0
2
0
2
0
1
0
1
0
0
0
0
0
0
0
2
0
2
1
1
0
0
0
1
0
1
0
0
1
0
0
1
1
1
0
1
0
0
0
2
0
0
1
2
0
0
1
0
0
0
2
1
0
0
2
2
1
0
1
0
0
0
1
0
1
0
2
2
0
0
1
0
0
1
0
0
0
2
0
0
0
1
0
3
0
0
2
0
1
0
0
2
1
0
2
0
2
0
0
1
0
0
1
0
2
1
2
1
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
1
0
0
0
2
0
0
2
1
0
2
0
2
0
2
1
0
1
0
0
1
1
0
2
0
0
0
0
2
0
0
0
0
0
1
1
1
0
0
0
0
0
0
2
1
1
0
1
1
0
2
1
0
2
1
0
1
1
1
1
1
3
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
6
0
0
3
2
2
1
2
0
0
0
0
1
0
2
2
0
0
1
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
2
0
1
0
2
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
1
0
2
0
0
0
0
0
2
0
2
1
0
0
0
1
0
1
0
1
0
2
0
3
1
0
2
1
1
1
0
1
0
0
1
2
2
2
3
0
2
0
1
0
0
2
3
2
1
2
1
0
2
0
2
0
1
0
0
2
1
1
1
1
2
2
1
0
0
0
1
1
0
2
1
0
0
0
0
0
3
1
0
1
1
0
0
2
0
3
2
0
6
2
1
1
2
3
0
0
2
0
1
2
1
0
0
2
1
0
0
1
0
2
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
1
2
2
0
0
0
2
0
2
1
1
0
1
2
1
0
0
0
3
0
0
0
0
2
0
0
0
0
1
2
0
0
1
0
0
2
1
0
1
0
1
0
0
0
0
2
0
0
0
0
0
3
1
0
0
0
3
1
0
1
2
0
1
1
1
1
0
1
0
1
0
0
0
1
2
0
3
0
0
0
1
3
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
2
0
0
1
0
2
2
0
1
0
1
2
1
0
1
1
1
0
0
0
0
0
0
3
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
3
0
1
2
0
0
0
2
1
0
1
1
0
0
0
1
0
0
2
0
2
0
0
3
0
1
1
0
1
0
1
0
1
1
1
1
0
1
0
2
2
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
2
0
2
1
0
0
0
0
0
2
0
0
0
1
1
0
1
2
0
0
0
2
0
2
0
1
0
1
1
0
0
0
0
0
0
2
1
0
3
0
2
0
0
3
0
2
0
1
0
1
1
0
2
2
0
2
1
4
0
2
1
1
1
0
2
1
0
0
0
2
0
0
0
0
0
2
0
0
1
1
2
0
0
0
1
2
1
0
0
0
0
0
0
1
1
1
0
0
0
0
2
2
0
0
0
3
0
0
0
0
2
0
0
0
0
1
2
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
1
0
3
0
2
0
2
2
0
2
0
1
0
0
2
2
0
1
3
0
0
1
0
2
2
2
0
0
0
2
0
0
0
2
0
1
0
2
0
2
0
3
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
2
0
1
0
2
2
2
2
0
0
0
0
0
1
1
2
0
0
0
2
0
0
0
1
0
0
0
2
2
0
0
0
0
1
0
2
1
0
0
1
0
0
2
0
1
1
1
0
0
0
0
0
2
0
0
2
0
2
2
0
0
0
2
0
2
0
0
0
1
0
1
1
1
0
0
1
1
2
2
0
0
0
0
0
0
0
1
1
0
0
0
1
2
2
0
1
2
0
0
0
0
2
0
0
0
0
0
2
0
1
3
0
1
1
0
0
1
0
0
2
3
2
2
1
0
0
0
2
1
1
0
0
0
0
0
1
0
1
1
1
0
0
0
0
1
1
0
1
2
2
0
0
2
0
0
1
0
1
0
0
0
0
2
0
0
0
3
0
1
0
2
0
0
0
3
0
1
0
0
1
0
0
2
0
0
0
0
0
2
0
2
0
0
0
2
0
0
2
0
0
0
1
0
1
0
2
2
1
0
1
0
1
0
1
2
0
1
0
0
1
0
0
0
0
0
1
3
0
0
0
0
0
0
1
1
1
0
0
2
0
0
2
0
0
0
1
2
0
2
0
1
1
0
2
1
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
1
2
0
2
2
2
0
1
0
0
1
2
1
2
0
0
0
0
0
0
0
0
1
0
0
3
1
0
3
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
1
0
2
0
2
0
0
0
1
2
0
2
0
0
0
0
3
1
0
0
0
2
0
0
0
2
4
1
0
0
0
0
0
1
2
0
0
0
2
1
0
0
0
1
2
0
1
1
0
0
0
0
0
0
3
0
2
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
1
0
1
0
0
1
0
2
0
0
1
0
0
1
0
0
0
0
1
1
0
1
2
0
2
0
0
0
2
0
0
2
0
0
0
0
2
0
1
1
0
0
0
0
0
0
1
2
2
0
0
0
2
1
0
0
1
1
2
2
1
2
0
0
0
0
2
0
0
1
0
2
0
1
2
2
0
1
0
0
0
1
0
1
0
2
0
0
0
0
1
0
1
0
2
0
1
2
0
1
0
0
0
1
0
1
0
2
0
0
0
1
0
0
0
2
2
1
0
0
0
2
0
0
1
2
2
1
1
0
0
1
0
2
2
1
0
0
0
2
0
0
0
2
2
1
2
0
0
0
0
1
2
0
0
2
1
1
0
0
0
0
3
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
2
0
1
1
2
0
0
0
2
0
2
1
2
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
1
1
2
2
2
1
1
0
0
0
1
0
1
2
0
0
1
1
1
0
0
0
0
2
0
0
0
2
0
0
1
2
0
0
0
1
0
0
2
0
0
0
0
0
2
1
0
0
0
0
2
0
1
0
2
0
0
1
3
0
0
0
0
0
0
2
0
0
1
2
1
1
0
0
0
4
0
0
0
0
0
2
1
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
1
1
0
1
2
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
2
0
2
0
0
4
0
0
0
2
1
1
0
2
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
2
0
2
0
0
0
0
2
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
1
2
1
0
0
0
0
0
3
0
0
0
0
0
1
0
1
0
0
0
3
0
1
1
2
0
0
0
0
0
2
1
0
0
1
1
2
1
2
0
0
2
0
0
0
0
0
2
0
1
1
0
0
1
0
1
0
1
0
3
1
0
0
2
0
0
0
1
0
1
3
1
1
0
0
0
1
0
0
0
2
0
0
1
0
0
2
3
1
1
0
2
0
2
0
2
1
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
3
0
0
0
2
0
0
1
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
2
0
1
0
0
2
2
1
0
2
0
1
3
0
1
0
0
0
0
0
2
2
0
0
0
0
2
1
2
0
0
0
0
2
1
0
0
1
2
0
0
2
0
2
1
0
1
1
0
0
2
1
0
0
2
0
2
0
0
2
1
0
0
0
2
0
1
0
0
0
0
0
0
2
0
3
0
2
1
0
0
3
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
1
1
0
0
2
2
0
1
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
3
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
3
2
1
0
1
1
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
2
0
0
1
1
1
11
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
1
1
0
1
3
0
0
0
0
0
0
1
0
2
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
1
1
0
0
2
0
1
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
2
0
0
3
0
2
2
0
0
0
2
0
0
2
0
0
1
0
1
0
0
1
3
0
2
0
1
1
0
2
0
0
0
0
2
1
0
2
0
0
2
2
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
2
0
0
1
0
1
1
0
1
3
0
0
1
0
1
0
1
1
0
0
0
0
1
3
0
0
1
1
2
0
0
0
0
1
0
0
0
3
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
2
0
0
2
0
0
0
0
0
0
1
0
2
2
0
0
2
0
0
0
1
0
1
1
0
2
0
1
2
2
2
2
0
0
1
1
1
0
0
0
2
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
2
0
1
0
1
0
1
0
2
0
0
2
1
2
0
1
0
1
0
0
0
4
0
0
0
3
2
3
2
0
0
0
0
0
0
2
0
2
0
0
2
0
0
2
0
1
0
0
2
0
0
1
0
0
0
1
0
2
1
0
2
3
0
0
0
2
1
2
1
0
2
0
0
2
0
1
1
0
0
0
0
1
1
0
2
0
0
1
0
1
2
2
0
0
0
0
1
2
0
2
1
1
2
0
1
1
1
1
0
0
0
1
1
0
1
0
0
0
0
0
2
0
1
2
0
0
2
1
1
2
0
0
0
0
0
1
0
2
0
0
2
2
1
2
2
0
0
0
2
0
0
0
2
0
0
0
1
0
1
1
0
0
1
0
2
0
0
0
0
1
0
2
0
0
0
0
0
2
0
1
0
1
1
0
0
0
0
1
1
0
0
0
0
0
2
0
3
0
0
2
0
0
1
2
1
2
1
1
0
0
2
0
0
3
0
0
0
3
0
0
3
0
1
1
0
0
3
1
0
0
2
2
1
4
0
2
0
0
0
2
0
0
0
1
0
2
1
1
0
2
0
0
0
0
0
1
2
0
1
0
2
0
0
2
1
2
0
0
0
0
0
0
1
2
4
0
0
1
2
0
2
0
0
0
0
0
1
1
0
0
0
2
1
1
1
1
2
2
2
0
2
0
0
1
1
1
0
2
2
0
0
0
0
0
0
2
1
1
0
3
0
0
1
0
1
2
2
0
2
1
0
1
0
2
0
0
2
1
2
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
2
1
0
0
2
1
0
2
0
0
1
2
1
0
1
1
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
2
0
0
2
2
0
1
0
0
2
0
1
2
0
0
0
1
0
1
0
1
0
1
1
2
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
1
0
2
0
1
1
2
1
0
1
0
2
2
0
0
0
0
1
0
2
0
0
0
2
1
0
0
0
1
2
0
0
1
0
1
0
1
1
1
3
0
0
0
0
0
2
0
0
1
1
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
3
0
0
0
0
0
1
2
0
0
0
0
0
0
2
2
3
1
1
2
0
0
0
1
2
0
0
2
0
0
2
1
1
2
0
1
0
0
1
0
0
0
0
0
0
1
1
3
2
2
1
1
0
0
1
0
2
2
1
0
1
0
1
1
2
0
1
0
0
1
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
1
2
0
2
2
0
0
1
0
0
1
1
0
2
1
0
2
0
0
1
0
1
0
1
1
0
0
1
0
0
2
0
2
0
1
0
1
0
0
0
0
0
0
0
2
1
1
4
2
4
0
0
0
0
0
0
0
0
1
3
0
0
2
1
0
0
0
0
1
0
2
1
0
1
1
0
1
0
0
2
1
1
0
1
0
0
2
2
0
2
1
4
0
0
0
1
0
1
0
0
0
2
0
0
0
0
1
0
0
1
0
2
0
0
0
1
0
0
1
0
0
0
0
0
2
0
1
0
1
1
3
0
0
0
0
0
1
1
0
3
0
0
0
2
2
1
0
0
0
0
0
0
1
1
0
0
0
2
1
0
0
2
0
1
0
1
0
1
0
1
1
1
1
1
3
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
4
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
1
2
0
2
0
1
2
1
1
0
0
0
0
2
0
1
0
1
0
0
2
0
0
1
0
1
1
0
0
1
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
2
0
4
1
2
2
0
0
0
1
0
0
2
0
0
2
2
1
0
2
0
2
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
2
0
1
2
0
1
2
0
0
0
0
2
1
2
1
0
0
0
0
0
0
2
0
0
0
0
2
2
2
1
1
0
0
2
1
0
0
0
0
1
0
2
5
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
2
0
0
0
1
1
0
0
0
0
2
0
0
0
2
0
0
0
1
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
2
0
0
0
0
1
2
0
0
0
1
0
0
0
0
1
1
0
0
0
1
3
2
0
2
0
0
0
1
0
0
0
1
0
2
2
0
1
2
1
0
0
0
0
2
0
1
0
0
0
0
2
0
3
0
1
1
2
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
1
1
1
0
2
0
2
2
2
0
0
0
0
0
2
0
2
1
2
2
1
0
1
1
0
0
1
1
0
0
2
1
2
1
0
0
0
0
2
0
2
0
0
0
1
0
2
0
1
0
0
1
0
0
0
0
0
2
2
0
1
0
0
2
0
0
1
0
2
0
2
0
3
0
0
2
0
0
0
0
0
1
0
0
1
2
0
0
2
2
0
0
0
0
0
2
0
1
1
0
1
2
0
0
2
0
0
0
2
0
1
2
0
0
0
2
0
1
0
1
1
0
2
0
0
2
2
0
2
0
0
0
0
0
0
1
2
1
0
0
0
0
0
2
1
2
0
0
1
0
4
1
0
0
1
0
0
2
1
3
2
0
2
0
5
0
0
2
2
1
1
1
0
0
0
0
2
0
1
2
1
1
0
2
1
0
0
2
2
0
1
0
0
0
2
0
2
0
0
0
2
0
2
0
1
0
1
0
0
2
0
0
0
0
0
0
1
0
2
2
0
0
0
0
3
0
0
0
0
0
0
0
1
0
3
0
2
1
2
0
1
1
2
0
0
0
0
0
2
0
0
2
2
1
0
2
0
1
0
0
0
4
0
2
0
0
1
0
1
2
0
0
1
1
0
2
0
2
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
4
0
0
2
0
0
2
0
0
2
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
2
0
0
1
1
0
2
1
0
2
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
1
2
2
0
0
0
1
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
1
2
1
1
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
1
0
0
1
2
0
0
1
0
1
2
0
2
0
2
2
0
0
0
2
0
0
0
0
0
2
1
2
1
0
1
0
0
0
2
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
2
2
1
0
1
1
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
3
0
1
0
0
0
2
1
1
2
0
1
0
0
0
2
0
2
0
0
0
1
0
1
1
0
0
0
2
0
0
0
0
0
0
2
0
1
2
3
0
0
1
0
2
1
3
0
0
2
0
2
0
0
0
1
0
0
0
2
0
0
1
2
0
0
1
0
2
1
1
0
1
0
1
0
0
0
0
1
2
2
1
0
2
1
0
0
0
1
0
0
0
1
0
0
2
0
0
1
1
0
0
0
2
1
1
0
0
0
0
1
0
0
0
2
1
2
2
0
0
0
0
0
2
0
1
0
0
0
0
2
0
2
0
1
2
1
0
0
1
2
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
2
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
2
0
0
0
3
0
2
0
0
0
0
2
2
0
0
3
2
2
2
1
2
1
1
1
0
1
2
0
0
0
1
0
2
0
0
1
2
2
0
0
0
0
1
1
2
0
1
2
1
2
2
0
1
0
1
0
1
1
1
0
1
0
0
1
0
1
0
2
1
0
0
2
0
1
0
0
0
0
2
3
1
0
0
1
1
0
0
0
0
2
1
0
0
0
1
0
1
0
1
2
0
1
0
3
0
0
0
0
1
0
1
2
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
1
2
0
0
1
1
0
0
1
1
1
0
0
2
0
0
1
0
2
0
0
2
0
0
0
1
1
0
1
0
1
1
2
0
0
0
2
1
0
0
0
2
1
2
3
2
0
1
0
0
0
1
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
4
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
2
1
0
1
0
0
1
2
0
3
0
2
2
1
1
1
0
1
1
1
0
0
2
0
0
0
0
0
2
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
1
1
1
1
0
4
0
0
1
0
0
0
0
0
2
0
2
2
0
0
0
0
1
0
2
1
1
0
1
0
2
1
0
0
0
0
0
1
0
2
0
2
2
2
0
0
0
0
3
1
0
0
1
1
2
2
1
0
0
0
0
2
0
1
1
0
0
0
0
1
0
0
2
0
0
1
2
0
0
2
1
2
1
0
0
0
2
1
2
0
1
2
2
0
0
1
0
1
0
71
0
0
0
0
1
0
2
0
0
2
2
1
1
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
2
3
0
0
0
2
2
0
0
2
0
2
0
2
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
1
2
2
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
1
2
0
0
1
2
0
0
0
2
0
1
0
0
1
0
2
0
2
0
0
1
0
1
1
0
0
0
0
2
1
1
0
11
2
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
1
1
1
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
1
0
0
2
2
0
0
0
1
0
0
0
0
1
2
2
0
0
1
0
1
0
1
1
0
0
0
1
0
3
0
0
0
2
0
0
0
0
1
0
0
1
2
0
2
0
0
2
0
1
1
0
1
0
1
0
1
0
2
0
1
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
2
1
2
0
0
0
0
0
0
2
0
1
0
1
0
0
2
1
2
0
2
0
2
0
0
0
2
2
0
0
0
0
0
3
0
2
0
0
0
1
0
0
0
1
1
1
0
1
1
0
0
0
0
2
1
1
0
1
0
2
1
1
1
0
3
0
1
2
2
0
2
0
0
2
0
0
2
2
2
2
0
1
2
0
0
2
1
1
1
2
1
2
0
0
0
0
1
0
4
2
1
0
2
0
1
0
0
1
0
1
0
0
0
0
1
2
1
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
2
2
2
2
1
0
1
0
2
2
0
0
1
0
0
1
2
0
0
2
1
2
0
0
0
0
2
1
1
2
0
0
1
6
0
0
0
0
0
0
2
1
0
0
2
1
1
0
1
0
3
1
2
2
0
0
1
1
0
2
0
1
0
1
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
1
0
2
1
0
0
2
1
1
0
2
2
0
0
2
0
0
2
2
0
1
0
1
1
3
0
1
0
0
0
2
2
2
0
0
0
1
0
2
2
0
0
0
0
3
0
1
1
0
1
2
2
1
1
2
0
1
2
0
2
1
0
0
0
0
1
0
2
0
1
1
0
0
1
2
0
2
0
2
0
0
0
0
0
0
2
1
1
0
2
1
0
0
0
0
2
1
1
0
0
1
2
1
0
0
0
1
1
1
0
0
0
0
2
0
0
0
0
0
0
0
1
2
1
1
0
0
0
2
2
0
1
0
1
0
2
0
1
1
0
1
1
0
2
2
0
0
0
0
0
0
1
2
0
1
0
2
2
0
0
1
2
0
1
1
0
0
1
0
0
0
0
1
0
0
1
2
2
0
3
0
0
0
0
0
0
1
1
1
1
0
0
2
0
0
1
0
1
1
0
1
0
2
1
1
1
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
2
0
2
0
2
1
0
3
1
0
1
1
0
0
0
0
1
0
0
0
0
1
1
0
0
2
0
1
0
0
0
0
0
2
0
1
0
0
0
1
0
3
1
0
2
0
1
2
1
0
2
2
2
0
1
0
1
2
0
0
2
1
1
1
1
0
1
0
0
0
0
0
1
0
2
0
2
0
1
0
0
0
0
1
1
1
0
2
0
2
0
2
1
0
0
0
1
2
2
3
0
0
0
0
2
0
4
0
0
1
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
2
1
0
0
1
0
0
1
0
1
2
2
0
2
0
0
0
2
0
0
1
0
1
0
0
0
0
2
2
0
1
0
0
0
0
1
3
0
2
2
0
0
0
0
1
0
0
0
1
0
2
0
0
1
0
1
2
0
0
0
0
0
0
0
2
0
0
2
1
2
0
0
0
0
0
2
0
2
0
2
0
0
1
0
1
1
0
0
0
0
0
0
1
0
2
0
0
2
0
1
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
1
3
0
1
0
0
1
0
0
0
1
2
0
1
2
2
0
0
0
0
0
2
1
1
0
5
0
0
2
1
0
1
0
0
0
0
1
0
2
0
1
0
0
0
0
1
0
4
1
0
0
0
0
0
0
0
1
2
1
2
1
1
2
0
2
2
0
1
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
2
0
2
0
1
0
0
0
0
0
1
3
2
0
0
0
2
0
3
0
0
2
3
0
1
0
0
4
0
0
1
0
2
0
0
2
0
0
0
0
2
0
1
0
0
1
0
1
0
0
0
0
0
0
0
2
2
2
1
0
0
1
0
0
0
1
2
1
0
0
0
2
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
2
1
0
2
1
0
0
4
0
2
0
0
2
1
0
0
2
0
1
2
1
2
0
0
2
1
0
0
1
0
0
0
1
0
1
1
1
1
1
0
2
0
1
1
0
1
1
0
0
0
1
2
0
1
1
2
0
0
0
0
0
0
1
0
0
2
0
1
1
0
0
2
1
2
0
0
0
0
1
0
0
0
1
1
1
1
1
0
2
1
1
0
0
1
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
1
0
0
2
0
1
0
0
1
1
0
0
1
1
0
0
2
2
0
0
2
1
0
1
2
0
5
0
0
1
2
0
0
0
1
0
0
2
1
0
0
0
1
0
0
0
1
1
0
3
0
0
0
0
0
1
0
0
2
0
1
1
2
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
1
0
0
2
1
1
0
0
4
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
1
0
0
2
0
0
1
0
2
1
0
1
2
0
2
1
1
0
0
0
0
0
0
0
0
1
2
0
2
1
4
0
0
0
0
1
0
0
0
2
1
0
2
2
2
0
2
0
0
0
0
0
2
1
0
0
1
0
0
0
0
2
0
0
1
1
0
1
0
0
2
0
2
2
0
1
2
0
0
2
1
2
1
1
0
0
1
2
0
0
0
2
2
5
0
0
4
0
0
0
0
1
0
0
0
1
2
0
1
0
1
0
1
1
3
0
0
0
0
0
0
0
2
2
0
2
1
0
0
2
0
0
0
2
2
0
2
4
0
1
0
0
2
0
0
0
0
1
0
1
0
1
0
0
0
2
0
0
1
1
0
0
0
0
0
10
1
1
1
2
0
0
2
2
0
0
2
0
2
2
0
9
2
0
0
2
2
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
2
1
0
1
0
0
0
0
1
2
0
2
0
1
1
0
0
3
0
2
0
2
0
0
0
0
0
2
3
0
1
0
1
1
0
0
0
0
0
0
1
0
1
1
2
0
3
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
2
0
0
3
2
0
0
0
0
0
2
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
2
2
1
2
1
0
0
0
2
0
1
0
0
1
2
2
0
1
0
0
1
0
0
0
1
0
0
2
0
1
0
0
0
0
1
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
1
0
0
2
2
0
0
0
2
2
0
1
2
0
0
1
0
0
1
2
0
0
1
0
1
2
0
2
2
0
0
2
0
2
2
2
0
0
2
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
1
2
0
0
2
0
2
1
0
1
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
2
2
0
2
0
0
0
0
1
2
0
0
0
1
0
2
2
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
1
1
1
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
2
1
1
0
1
1
2
2
0
1
2
1
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
1
0
1
1
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
2
1
2
2
0
1
2
0
0
2
1
3
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
1
2
0
1
0
0
0
1
0
0
2
0
0
0
0
0
1
1
1
0
0
2
0
1
2
0
0
0
0
1
2
2
2
1
0
1
0
0
2
0
0
0
2
0
2
0
2
2
0
0
0
1
0
2
0
1
0
0
0
0
2
1
2
2
0
1
2
0
2
2
0
0
0
0
0
0
1
0
2
2
0
3
1
1
0
0
1
1
0
3
0
2
2
0
0
0
1
0
0
1
0
0
2
0
0
0
0
1
3
0
2
0
2
0
1
1
0
2
0
1
0
0
2
0
1
0
0
6
1
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
1
2
0
0
0
0
2
0
1
0
1
1
2
2
5
0
0
1
0
2
2
1
0
1
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
1
0
0
1
3
0
1
0
0
1
3
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
3
0
0
2
0
2
0
0
0
0
0
2
0
2
0
0
0
4
1
0
3
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
1
2
0
1
2
0
2
0
0
0
2
1
0
0
0
2
1
1
0
0
0
2
1
2
1
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
1
0
1
0
2
0
0
1
2
2
1
2
0
0
0
0
1
0
0
2
1
0
2
0
0
0
0
0
1
4
2
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
1
1
0
0
1
1
1
0
2
0
4
2
2
0
2
2
0
1
3
3
0
0
0
1
3
0
1
2
0
1
0
0
0
3
0
0
2
0
0
0
0
1
0
0
0
2
0
0
2
2
0
1
1
0
3
0
0
0
1
0
0
0
1
0
2
1
0
0
0
0
0
0
4
0
0
0
1
0
1
2
0
2
0
2
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
3
1
0
0
0
0
0
1
0
0
0
2
1
0
0
1
1
0
2
3
2
2
1
0
0
0
0
1
2
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
2
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
2
2
1
2
0
0
0
1
1
1
0
0
2
0
0
2
3
0
0
0
0
2
0
0
0
2
0
2
0
2
0
0
0
2
0
2
1
2
0
1
0
0
1
0
1
0
5
0
1
0
0
0
0
1
2
0
0
0
1
0
0
0
2
0
1
2
3
1
0
0
0
0
0
0
0
2
1
0
1
0
0
0
3
0
0
1
0
0
1
0
1
0
0
0
0
2
0
0
1
4
0
0
0
0
1
2
0
2
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
2
1
3
2
0
2
0
2
1
3
2
0
0
1
0
0
1
1
0
0
0
0
2
0
1
0
0
2
1
2
0
2
0
1
1
2
1
2
1
0
1
3
0
1
1
0
0
1
0
1
2
0
2
0
0
0
1
2
1
0
0
0
1
0
0
0
0
2
0
0
1
2
0
0
2
0
0
1
2
2
0
0
0
1
0
0
0
1
0
0
0
1
2
0
0
0
1
0
1
0
1
1
0
1
1
0
0
0
1
0
1
0
2
1
1
1
0
0
2
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
1
1
0
0
0
0
0
1
1
0
0
0
1
2
2
0
1
0
0
0
0
0
0
2
0
0
1
1
2
1
0
0
0
1
0
0
1
1
3
1
0
0
0
2
0
0
1
2
0
0
1
1
2
0
1
0
0
1
2
0
0
1
0
0
1
0
2
0
0
0
2
0
2
1
0
3
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
1
1
3
0
0
1
0
2
1
2
0
0
1
1
0
1
0
0
1
1
1
1
0
2
0
0
0
0
0
0
1
0
0
0
1
2
0
1
0
2
0
1
2
2
0
1
0
2
1
1
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
1
0
1
0
1
0
2
0
0
0
0
1
0
0
0
2
2
1
2
0
2
1
0
2
1
0
0
1
1
0
3
1
1
0
0
0
2
0
2
0
0
0
0
0
2
1
0
0
0
0
2
2
0
0
1
0
0
0
1
2
0
0
2
1
0
1
1
1
0
0
2
0
2
0
3
2
0
0
0
2
2
0
1
0
2
2
0
2
0
1
0
0
0
0
0
2
2
1
2
0
3
1
5
0
1
0
0
1
0
0
1
0
0
0
0
1
0
2
1
0
0
0
0
0
2
0
0
5
2
0
0
1
2
0
2
0
0
1
2
2
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
2
2
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
4
0
2
0
0
0
0
0
1
1
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
2
0
1
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
1
1
1
2
2
1
1
2
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
2
1
0
2
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
2
1
0
0
0
1
1
0
0
0
0
0
1
1
1
1
2
0
0
1
0
0
0
0
3
2
0
0
2
1
1
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
2
2
1
0
2
0
0
2
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
1
2
1
2
1
1
0
0
0
2
0
1
2
0
2
0
0
1
2
0
2
0
0
3
0
2
0
2
2
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
2
1
0
0
1
2
0
1
1
0
0
1
2
0
0
2
0
0
0
1
1
1
3
0
1
0
1
1
1
2
0
1
0
2
0
2
0
0
0
4
0
2
0
0
1
0
0
2
0
1
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
2
2
1
2
0
1
1
2
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
2
1
1
0
0
0
1
0
0
0
2
1
0
0
2
1
0
0
0
5
0
0
0
0
0
0
0
1
2
0
0
2
0
0
1
0
0
2
0
0
0
2
0
2
0
0
0
2
1
0
0
4
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
2
2
0
2
0
2
2
0
0
0
1
0
2
1
0
0
1
1
0
1
0
0
0
1
0
2
0
1
2
4
0
0
0
0
0
1
2
1
0
1
1
3
0
1
0
0
0
2
0
2
1
1
0
1
0
0
0
1
1
1
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
1
0
1
0
0
0
2
0
1
0
2
2
0
0
2
1
2
0
0
1
2
2
2
0
0
2
0
2
1
2
1
0
0
0
2
0
2
2
1
0
0
0
0
0
1
1
0
0
2
0
2
0
2
1
1
1
0
2
0
1
2
0
1
0
0
2
0
2
0
0
1
0
3
1
2
0
0
0
3
0
0
0
0
0
2
0
2
0
1
1
2
0
2
2
1
0
0
0
0
2
0
1
0
2
0
2
0
0
0
0
0
0
2
0
0
1
1
1
0
0
1
0
1
0
0
0
0
0
1
1
0
0
2
1
0
0
0
1
1
0
0
1
0
0
0
0
0
1
3
2
0
0
1
0
0
2
0
0
0
1
1
2
1
0
0
0
1
0
2
0
0
2
0
0
0
1
0
1
1
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
1
1
0
0
0
0
0
2
1
0
1
1
0
2
0
0
0
0
0
0
0
2
0
0
1
0
1
1
1
0
0
1
1
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
1
0
1
1
1
0
2
0
0
0
6
1
0
2
0
0
0
0
0
0
1
2
1
3
1
1
1
0
0
1
0
1
1
1
0
0
1
0
2
0
0
1
1
0
0
0
1
0
0
3
0
0
0
0
4
0
0
0
0
0
6
2
0
1
0
0
0
1
2
2
1
1
1
0
0
2
0
0
1
0
1
3
1
1
1
4
3
1
1
1
0
0
2
4
0
0
0
0
2
0
1
0
0
1
1
0
0
0
3
2
0
6
1
0
0
2
0
2
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
3
2
0
0
2
0
3
0
0
0
0
0
3
2
2
0
0
3
1
0
2
2
1
1
0
0
0
2
1
0
0
0
0
0
2
0
1
2
0
0
0
0
3
0
2
0
0
0
0
0
0
2
1
1
0
0
2
2
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
2
0
0
0
0
2
2
2
0
0
0
3
0
0
1
1
2
1
1
0
1
1
0
0
0
0
0
3
1
0
0
1
0
1
5
0
0
0
0
0
1
1
0
1
1
0
0
0
0
1
0
1
3
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
1
0
0
2
0
0
0
0
0
0
0
0
3
0
0
1
0
2
0
2
0
3
0
1
2
2
2
0
0
1
1
0
1
1
0
2
2
0
2
0
0
1
1
1
0
0
1
0
0
0
3
0
0
0
2
2
0
1
0
1
0
0
2
1
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
2
1
0
0
1
0
2
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
2
1
1
0
0
0
2
1
0
0
0
0
1
0
0
1
2
2
1
1
1
1
0
2
1
0
1
2
1
0
1
0
0
0
0
0
2
0
0
1
0
0
4
1
0
0
1
2
1
1
1
0
0
0
2
0
1
0
2
1
0
2
0
0
2
0
0
0
0
2
0
2
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
1
0
2
2
0
0
2
0
0
2
1
0
1
0
2
0
1
1
2
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
2
0
0
0
1
2
0
1
0
0
0
0
2
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
3
1
2
0
0
1
0
0
3
0
2
0
1
0
1
0
2
0
0
1
2
0
2
0
1
1
0
2
0
0
0
0
2
0
0
0
2
0
0
2
1
0
0
0
1
0
1
1
2
0
2
0
0
2
0
0
0
1
0
0
0
0
1
1
1
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
2
1
0
0
1
3
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
2
1
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
3
0
2
1
0
0
0
0
1
1
0
2
2
2
2
1
1
1
0
0
2
1
0
2
0
0
0
2
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
2
1
2
0
0
2
1
0
0
0
0
0
0
1
0
1
0
2
2
2
0
2
2
2
0
0
0
0
1
0
0
0
0
1
2
1
0
0
1
0
1
0
0
0
1
2
0
0
0
0
0
2
1
1
2
0
0
0
2
0
1
1
0
1
0
1
0
0
0
0
0
1
1
2
0
0
0
2
0
0
0
0
1
0
2
0
1
2
2
0
1
0
0
1
0
0
0
0
1
1
0
0
2
1
0
0
2
0
1
1
1
0
0
0
2
0
0
0
2
2
0
2
0
0
2
0
0
2
0
0
2
2
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
2
0
1
2
0
0
2
0
0
1
0
0
1
0
2
1
0
0
0
1
0
0
0
0
1
0
2
1
0
2
1
0
0
0
1
0
1
2
0
1
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
2
0
0
0
0
1
0
0
1
0
2
0
2
0
0
1
0
0
1
0
0
0
1
2
0
2
0
0
2
1
0
0
2
1
0
0
1
0
2
1
1
0
0
1
1
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
2
0
0
2
2
0
2
0
0
0
2
1
2
0
0
2
0
0
2
1
0
0
2
0
0
0
0
2
2
2
0
1
0
0
0
1
0
1
0
0
0
0
2
1
1
1
0
1
0
0
1
0
0
0
0
2
0
1
2
0
3
1
2
2
1
1
0
0
1
1
2
0
0
2
1
0
2
2
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
2
0
1
0
0
0
1
2
2
2
0
1
0
0
3
0
1
0
2
1
2
0
0
1
0
2
2
0
0
0
2
0
0
0
1
0
2
0
2
2
3
0
1
2
1
2
0
0
1
0
0
2
2
0
0
0
0
2
0
0
0
2
0
0
0
1
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
1
2
0
0
0
1
0
2
0
2
0
0
2
0
0
0
0
0
3
0
0
2
2
0
0
0
0
3
0
0
2
0
0
1
1
0
0
0
0
1
0
0
0
0
1
2
1
1
0
2
0
0
0
0
3
2
0
0
0
2
2
2
0
1
2
0
2
0
0
0
2
0
2
2
0
0
2
0
1
0
0
0
0
2
1
0
1
2
1
2
0
0
0
0
0
1
1
1
0
2
0
2
1
0
0
2
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
2
0
2
1
0
1
0
0
1
2
0
0
0
0
0
0
2
5
2
0
0
1
0
0
0
0
0
1
0
1
1
1
0
0
2
2
1
2
1
1
0
0
2
0
1
1
1
1
1
1
0
0
2
0
1
0
0
0
0
0
2
0
0
0
1
1
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
1
0
2
0
0
1
0
2
0
0
0
0
1
0
0
0
3
0
0
3
0
0
0
0
1
0
0
0
0
2
0
1
1
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
1
0
2
0
0
2
0
2
0
0
0
2
0
1
1
2
0
1
0
1
0
0
2
2
1
0
2
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
1
0
2
1
1
0
0
1
1
0
0
1
1
0
0
0
2
0
0
0
0
0
1
1
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
1
2
1
0
0
0
1
0
0
2
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
1
2
0
1
0
0
0
1
0
0
0
0
0
0
2
1
1
0
2
0
0
0
0
0
0
2
1
1
1
0
2
0
1
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
1
0
0
1
0
1
1
1
0
0
2
2
0
2
2
0
0
0
2
0
0
1
2
1
0
3
0
1
0
0
0
3
1
1
0
1
2
0
1
0
0
2
0
0
0
2
0
1
2
3
0
1
1
3
1
0
2
2
0
1
0
0
0
2
0
1
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
3
0
2
2
0
1
1
0
1
0
0
2
1
2
0
2
0
1
1
0
0
0
1
0
0
0
0
0
0
2
2
2
1
2
2
1
0
0
1
2
4
2
1
1
0
0
0
2
0
1
0
2
1
0
1
0
1
0
2
1
0
2
0
0
0
0
0
0
2
0
0
1
2
0
2
1
2
2
0
0
0
1
0
1
0
0
0
1
1
1
1
1
0
0
2
1
0
2
0
0
0
0
0
2
0
1
0
0
1
0
1
0
0
3
0
2
1
0
0
0
2
2
1
0
0
0
2
0
0
0
1
2
0
1
0
0
0
0
4
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
1
2
0
2
1
0
2
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
1
0
0
4
5
0
0
0
0
0
2
0
1
2
0
1
1
0
2
3
1
0
0
0
2
0
1
0
0
0
0
0
1
0
0
2
0
1
1
1
2
0
0
1
0
1
0
0
0
2
1
0
2
0
1
1
0
1
0
0
1
1
0
2
0
0
0
1
2
2
0
1
2
1
1
1
1
0
1
0
0
0
2
1
0
1
0
1
0
2
0
0
1
6
0
0
2
0
1
0
0
0
0
0
0
1
0
1
0
1
2
0
3
0
0
0
2
0
0
0
4
0
0
0
1
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
2
1
0
0
1
1
1
1
2
0
1
2
2
0
2
1
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
2
0
0
1
1
0
2
1
1
0
0
0
0
0
0
1
1
1
0
1
0
2
0
2
2
1
0
0
0
2
0
2
2
0
0
1
0
3
0
1
1
2
0
0
2
1
0
0
1
0
0
0
0
0
0
1
0
3
1
1
1
2
2
2
1
2
0
1
0
0
1
0
0
2
0
1
0
0
0
0
2
1
0
1
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
1
0
0
0
0
1
2
0
0
0
0
1
0
1
0
0
0
1
2
1
0
2
0
0
0
1
0
0
0
0
0
1
0
0
2
0
1
0
1
1
0
0
2
0
0
0
1
2
0
0
0
0
1
0
1
0
0
1
0
0
0
1
1
0
0
4
1
1
1
0
2
1
0
0
0
0
2
0
0
0
0
0
2
0
0
2
1
2
0
2
1
0
0
2
0
0
1
1
0
0
1
1
1
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
2
0
0
2
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
1
2
0
1
5
0
1
2
2
1
0
0
0
0
0
0
0
0
2
0
0
3
2
2
0
0
3
0
0
1
1
1
0
1
2
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
2
0
0
2
1
0
1
2
2
0
0
0
0
2
2
0
0
2
1
0
5
0
2
1
1
0
1
0
0
3
1
1
1
2
0
2
1
1
0
0
1
1
0
2
1
0
0
2
0
1
0
0
0
1
1
4
1
1
0
2
0
2
0
2
0
1
0
0
0
0
1
2
0
0
0
0
2
0
0
2
1
0
0
0
1
2
2
1
1
0
2
2
0
0
0
1
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
1
1
1
0
0
0
3
2
0
1
1
1
0
2
0
2
0
0
0
0
2
0
0
0
2
0
2
2
1
2
0
1
1
1
1
0
0
0
2
2
0
0
1
2
1
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
1
2
2
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
3
1
0
2
0
2
0
0
0
0
1
2
1
0
1
3
2
0
0
1
1
0
0
0
0
2
0
0
0
0
2
1
1
4
2
0
0
1
0
2
0
0
0
0
0
2
0
1
2
0
0
0
2
1
0
2
1
1
0
0
0
0
2
1
1
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
1
0
2
0
1
0
2
2
0
0
0
0
0
0
1
2
1
0
0
2
0
0
1
0
0
0
1
1
1
0
0
1
1
0
0
1
0
0
0
0
0
0
2
0
0
0
1
2
0
2
2
4
2
1
1
0
0
0
0
1
2
0
0
2
0
2
0
0
0
1
2
1
0
2
2
1
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
3
0
0
0
2
0
0
0
2
0
1
1
0
0
2
2
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
2
0
0
1
0
0
1
0
1
1
0
0
1
1
0
2
0
0
0
1
0
0
2
2
0
1
1
0
0
0
0
0
0
0
1
2
2
1
2
0
0
2
1
1
0
1
0
2
0
0
0
4
0
0
0
2
0
0
0
1
2
1
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
1
0
2
0
2
0
0
0
0
1
1
0
0
0
1
1
1
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
4
0
1
0
1
1
2
2
0
0
0
1
0
1
0
0
2
2
0
2
2
0
0
0
1
1
1
0
1
0
0
0
0
1
3
1
1
0
0
0
1
2
1
1
0
1
0
0
2
1
1
2
1
0
2
0
1
0
1
2
0
0
0
0
2
1
2
2
1
0
2
1
0
0
0
1
0
0
1
0
2
0
0
2
2
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
2
0
1
0
1
0
2
0
1
0
1
0
0
2
0
1
0
0
0
0
1
0
2
0
2
0
0
3
0
2
1
0
0
0
2
1
1
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
2
0
0
1
2
3
0
0
0
2
1
1
0
4
1
2
1
1
0
2
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
2
1
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
1
1
0
1
2
0
0
0
0
0
0
2
0
1
1
2
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
2
3
1
0
0
0
2
0
0
2
2
0
0
0
0
0
1
0
1
0
0
0
0
0
1
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
1
2
2
0
0
1
1
1
0
0
0
0
0
0
1
0
1
2
1
0
2
2
1
2
0
0
0
0
0
0
0
1
1
0
2
2
2
0
0
0
0
0
0
0
2
0
0
0
1
0
1
1
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
2
0
2
2
0
0
0
1
0
1
0
0
0
1
1
0
0
0
1
2
2
0
2
1
1
0
1
0
0
0
0
0
0
1
2
1
2
1
0
3
2
0
0
2
2
0
0
0
0
2
1
0
0
0
1
0
0
2
2
0
1
4
1
2
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
2
2
0
0
1
0
1
0
0
2
2
1
0
2
0
0
1
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
2
2
2
0
1
0
1
0
2
1
0
0
1
2
1
0
2
0
0
0
2
0
0
0
0
2
1
0
2
0
0
1
0
0
2
2
1
0
0
1
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
2
0
2
0
0
1
2
1
2
2
1
0
0
0
1
0
1
0
0
0
0
2
1
0
2
2
0
0
2
2
1
0
0
1
0
0
1
1
0
0
0
0
1
1
0
0
0
2
0
0
0
0
1
1
1
0
0
0
0
1
1
0
1
0
0
1
0
2
0
2
1
2
0
1
0
0
1
1
0
0
0
3
0
1
0
0
0
2
0
0
0
0
2
2
1
0
0
0
1
0
0
0
2
0
3
0
1
2
0
1
0
3
0
0
0
1
2
0
0
2
0
0
1
1
0
1
0
1
2
0
1
0
0
0
1
1
2
1
0
2
0
0
0
1
0
2
0
0
0
2
2
0
2
0
0
1
1
1
0
2
0
1
0
1
0
1
2
0
1
1
2
2
2
0
2
1
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
1
1
2
7
2
0
0
1
1
2
0
0
0
0
2
0
3
0
2
0
2
0
2
0
1
1
2
0
2
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
2
0
0
0
1
2
0
2
0
0
0
0
0
0
2
0
1
0
2
0
0
3
0
0
1
0
1
2
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
1
2
0
1
2
1
0
0
3
1
0
2
0
0
0
0
1
0
0
1
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
1
0
0
0
1
0
4
0
0
0
2
0
1
0
0
1
0
2
0
0
0
0
0
0
1
1
0
0
1
2
1
0
0
0
0
0
1
0
2
0
0
1
2
1
0
0
0
2
0
2
0
0
1
0
0
0
1
0
1
0
1
0
2
1
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
1
0
2
1
2
1
0
0
0
1
0
0
0
0
1
1
0
2
0
0
1
0
2
2
1
2
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
2
0
2
0
0
0
1
0
2
1
1
0
2
2
1
1
0
0
0
1
1
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
1
0
2
0
1
0
1
0
0
2
2
0
0
0
1
0
1
0
0
3
0
0
0
1
2
2
1
1
0
0
0
0
3
2
0
1
2
2
0
1
2
3
0
0
2
2
2
0
2
0
0
0
0
0
0
2
0
4
0
2
0
1
1
2
0
0
2
0
4
0
0
1
0
1
1
0
2
0
1
2
2
2
0
0
0
0
0
0
0
1
0
0
0
5
0
1
0
0
0
0
5
0
7
0
0
0
2
1
2
2
0
3
0
1
0
2
0
1
0
2
2
2
0
0
0
1
0
0
2
1
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
1
0
1
0
0
2
2
1
0
2
2
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
1
1
0
1
1
2
0
0
0
0
0
1
1
0
0
0
0
2
2
2
0
0
0
0
2
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
1
1
0
2
0
0
0
0
2
0
1
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
1
0
1
0
2
2
0
2
0
0
0
2
0
0
0
3
1
2
2
1
0
0
0
0
0
0
1
0
2
0
1
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
5
0
0
0
2
0
0
0
2
0
1
0
2
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
1
2
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
1
0
0
0
0
1
2
0
0
0
0
1
1
2
1
0
0
0
0
0
4
2
0
0
2
1
1
0
0
1
0
0
0
0
2
0
1
0
0
2
0
1
2
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
6
2
0
1
0
0
2
0
0
0
1
1
2
3
1
0
1
2
0
0
0
3
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
1
1
1
2
2
1
0
0
0
2
1
0
2
0
1
1
0
0
0
0
0
0
1
0
2
1
0
2
2
0
0
0
0
0
1
0
0
1
2
2
0
0
0
0
0
1
1
0
0
0
1
0
2
1
0
0
3
0
0
2
1
0
0
2
0
0
0
0
2
0
2
2
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
2
1
0
0
0
3
2
0
2
2
0
0
0
1
0
0
1
0
0
0
0
1
0
1
1
0
2
2
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
2
1
1
2
0
1
0
1
0
3
1
2
1
2
2
0
2
2
0
1
1
1
0
0
1
2
1
0
0
0
0
0
2
2
2
0
0
2
0
0
2
0
0
0
2
2
0
0
0
0
2
1
0
1
0
0
1
0
1
0
0
1
2
2
0
0
2
0
1
0
0
0
0
0
1
1
1
2
1
0
1
2
1
0
1
0
1
3
0
0
0
1
2
0
3
0
1
0
0
1
0
2
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
1
1
2
2
1
0
1
2
0
0
0
0
2
1
0
1
0
0
2
1
1
0
0
0
0
1
0
0
1
2
1
1
0
2
2
0
0
0
0
0
1
2
1
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
1
0
1
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
2
0
0
0
2
2
0
0
1
0
1
0
2
0
0
0
0
1
0
0
0
2
1
0
0
0
1
0
3
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
1
0
0
2
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
2
0
0
2
0
2
0
0
2
0
0
1
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
2
1
0
2
0
2
1
1
0
0
2
0
0
0
2
1
0
1
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
3
0
0
2
2
3
1
0
0
1
0
2
0
1
4
0
1
0
0
0
2
0
1
1
0
0
3
0
1
0
0
1
2
0
0
1
0
0
0
0
0
0
0
1
2
1
0
0
0
2
0
0
1
2
2
2
1
1
0
0
0
2
1
0
0
0
2
1
3
0
2
2
1
1
0
0
0
0
0
2
0
0
0
1
0
1
2
0
1
0
0
1
2
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
2
2
0
2
0
0
0
2
0
0
1
0
1
0
2
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
2
1
0
1
2
1
2
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
2
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
1
0
2
0
2
2
0
0
1
2
0
0
2
1
0
1
3
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
2
0
1
3
0
0
0
0
1
0
2
0
2
0
0
1
2
0
0
1
2
0
0
2
0
0
1
2
0
1
0
2
2
0
1
0
0
0
0
0
0
2
0
0
1
0
0
2
2
0
2
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
2
0
0
0
0
1
1
1
2
0
1
0
2
1
2
0
0
1
2
1
2
1
3
1
0
0
0
0
1
1
0
2
1
3
0
0
2
0
0
4
0
0
0
2
1
3
0
0
0
0
1
2
2
0
0
2
2
0
1
0
0
2
0
0
2
0
2
1
2
1
0
1
1
1
0
0
0
0
0
2
0
0
1
1
1
2
6
0
0
2
0
0
0
0
2
1
0
0
2
0
0
0
0
0
1
0
1
2
0
2
0
0
3
1
2
2
0
0
1
1
0
0
2
1
0
0
0
2
0
0
2
0
1
0
0
0
0
0
1
0
1
1
0
0
0
1
2
1
1
1
1
1
0
0
1
2
0
0
0
1
2
2
1
0
1
1
0
0
0
3
0
1
0
0
0
1
0
1
2
2
0
0
1
0
0
0
0
1
0
0
1
1
2
0
0
0
0
0
2
0
0
0
1
1
2
2
0
1
3
1
2
1
0
1
1
0
0
0
0
1
0
0
2
2
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
1
2
0
0
0
0
0
1
2
2
0
0
2
0
0
0
1
0
0
0
0
0
0
1
1
1
1
2
1
0
0
1
3
0
1
0
0
3
0
1
1
0
2
0
0
2
1
0
0
0
0
1
0
0
0
1
0
1
0
1
0
1
0
0
1
0
0
0
0
2
1
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
4
0
2
0
0
0
0
0
2
0
1
0
4
0
2
1
0
0
2
1
0
0
0
2
2
0
0
0
0
0
1
0
0
0
1
1
2
0
0
0
1
1
1
1
1
0
1
0
0
0
0
0
1
2
2
0
2
2
1
1
0
0
0
2
2
2
0
0
1
0
1
1
0
0
0
0
2
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
3
2
1
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
2
0
2
2
1
1
1
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
2
0
2
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
3
1
0
0
0
1
0
1
0
1
0
1
0
2
0
0
0
1
2
0
0
0
0
0
0
2
0
2
1
0
1
1
1
0
0
0
0
2
0
0
1
2
0
1
0
2
1
1
1
2
2
1
0
0
1
0
2
1
2
0
0
0
1
0
1
0
0
1
0
0
2
1
0
0
1
0
0
2
0
0
0
1
0
2
0
0
1
0
1
2
0
1
0
0
0
0
1
0
0
1
2
0
1
0
0
0
0
2
2
0
0
0
0
2
1
2
0
2
0
1
0
0
1
0
2
0
0
0
1
0
0
0
1
0
0
2
0
0
1
0
0
1
0
1
2
0
0
2
2
0
1
1
0
2
0
0
1
0
0
0
0
0
0
0
2
1
0
1
0
1
0
0
1
1
1
0
1
0
0
0
0
0
0
2
2
2
1
0
2
0
0
1
1
0
1
0
0
1
2
1
0
0
1
0
0
2
0
0
2
0
0
0
2
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
2
0
1
1
0
0
0
0
2
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
1
0
2
2
0
0
0
1
2
0
0
0
0
0
2
0
0
1
0
2
0
0
0
2
1
0
1
3
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
1
2
0
1
0
1
1
0
1
1
1
0
1
0
0
0
0
1
1
0
0
2
0
2
0
0
0
2
2
0
1
0
2
0
2
0
1
1
0
1
0
0
0
0
0
2
1
0
0
1
1
0
0
1
1
0
0
1
0
0
0
1
0
0
1
0
0
0
1
1
1
0
2
3
1
0
0
0
2
1
0
0
0
0
2
0
0
1
1
0
1
0
2
0
3
0
1
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
1
0
2
2
1
2
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
1
1
2
1
1
1
1
1
0
1
0
0
1
0
0
2
2
0
0
2
0
0
1
1
0
2
0
0
0
2
2
2
0
2
2
0
1
0
0
2
0
0
0
2
0
0
1
1
0
0
6
1
0
1
0
0
0
0
0
2
0
0
2
1
0
1
0
2
1
0
0
0
0
2
0
1
1
1
1
1
0
0
0
2
0
0
2
0
1
2
0
0
0
2
0
1
2
0
0
3
2
0
1
0
2
0
0
2
0
1
0
0
0
0
2
2
2
0
0
1
0
0
1
2
2
0
3
0
0
0
2
4
2
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
3
2
1
0
1
1
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
1
0
1
0
1
0
1
0
1
2
1
3
2
0
2
1
0
0
0
0
1
2
0
0
0
0
0
1
2
0
2
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
2
1
0
1
0
0
0
0
0
0
0
1
1
0
3
0
0
0
0
1
0
0
0
1
0
0
2
0
0
2
1
2
0
0
0
0
1
1
0
1
0
2
0
1
0
1
0
2
0
1
1
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
10
1
2
1
0
3
2
0
0
0
2
0
1
0
1
0
0
0
0
2
0
1
2
0
2
1
0
0
1
0
1
0
1
0
0
1
0
1
0
1
1
1
2
0
1
3
0
0
2
2
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
2
0
0
2
2
1
1
0
2
0
0
2
0
1
1
1
1
0
1
2
2
2
1
1
0
2
0
0
2
2
0
0
0
2
0
1
2
3
0
3
0
0
3
0
0
0
0
3
0
0
2
0
0
0
1
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
2
2
0
1
0
0
3
0
0
1
0
0
0
0
0
1
0
1
0
1
0
2
1
0
0
2
0
1
1
0
0
0
0
0
0
0
2
0
1
0
0
1
0
3
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
1
1
2
1
0
2
2
0
2
0
0
0
0
0
0
0
1
0
1
2
0
1
0
0
0
0
2
0
0
2
0
0
0
2
1
0
2
1
1
0
0
0
0
0
0
0
0
0
1
2
2
2
0
1
0
0
1
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
1
0
0
0
2
0
1
1
0
1
1
0
3
0
0
0
1
0
1
0
1
1
1
0
2
3
2
2
1
1
3
1
0
2
0
0
0
0
0
2
0
0
2
0
0
2
0
2
1
0
1
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
2
2
0
0
2
2
2
0
1
0
4
1
0
2
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
2
1
0
0
0
1
0
1
0
1
0
4
0
1
2
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
2
1
0
1
0
0
2
0
2
0
0
0
0
3
0
0
1
3
1
3
0
2
0
0
3
0
2
0
1
2
1
0
2
1
0
0
2
0
2
0
2
0
1
0
1
0
0
2
2
0
0
1
0
0
2
0
1
0
0
2
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
3
0
0
1
0
0
0
1
0
0
0
0
1
0
2
2
2
2
2
1
0
0
0
0
0
0
0
0
2
0
2
0
2
2
0
0
0
0
0
0
0
2
1
0
1
1
0
0
0
0
0
3
2
0
0
1
0
2
1
2
0
0
0
1
0
0
0
2
0
3
2
1
3
2
2
0
2
0
0
1
2
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
2
0
1
0
0
4
0
2
0
0
2
0
2
1
0
2
4
1
4
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
2
0
2
2
0
2
2
0
0
1
0
0
0
1
1
0
0
0
0
0
1
1
2
0
2
2
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
6
1
2
1
1
1
0
0
2
0
1
0
1
0
0
1
0
0
2
0
0
0
0
0
2
0
0
2
1
0
2
0
1
0
2
0
0
0
1
0
2
0
1
2
2
1
0
0
2
1
1
0
0
1
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
2
2
2
0
2
0
0
0
0
0
2
1
1
0
0
0
0
2
0
0
1
0
0
0
0
0
1
1
2
0
1
0
0
2
1
0
0
1
2
2
1
1
1
0
2
2
0
0
0
0
0
0
0
0
0
2
0
3
0
0
2
1
0
0
0
1
0
0
1
0
0
1
1
0
2
0
0
1
1
1
0
0
0
0
0
1
2
0
0
0
1
0
2
0
0
1
0
0
0
1
0
0
0
1
2
1
0
0
0
1
0
0
3
0
0
3
0
0
2
0
2
0
1
0
1
0
0
2
0
0
0
2
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
3
1
1
0
2
0
4
0
0
0
1
1
0
0
1
0
1
0
1
1
2
2
0
0
2
0
2
1
0
0
0
2
2
0
0
1
1
0
1
0
1
1
0
0
2
0
0
0
0
2
2
0
1
2
0
0
0
1
0
1
1
1
0
0
0
2
0
0
2
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
2
1
0
0
0
0
0
2
2
1
0
1
0
0
0
0
1
0
2
0
0
1
1
5
0
0
2
2
0
0
0
2
0
1
1
0
0
0
2
1
0
2
0
2
0
0
1
0
0
2
0
0
0
0
0
2
2
2
1
0
0
0
2
0
1
0
1
0
2
2
0
0
0
1
1
2
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
2
1
0
2
2
0
0
2
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
1
1
0
1
1
0
0
0
1
0
1
1
0
0
0
1
9
1
0
0
0
0
0
1
0
1
1
0
2
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
6
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
6
0
1
1
0
0
0
1
0
3
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
1
0
3
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
1
1
2
0
0
0
2
1
1
0
3
1
0
0
0
1
0
0
0
0
0
0
0
2
1
2
2
0
0
1
1
2
0
0
2
0
0
0
0
0
0
0
1
1
0
2
0
1
2
2
1
0
1
0
0
1
0
2
1
0
0
1
3
2
1
0
0
0
1
2
1
0
0
0
0
0
2
0
2
0
2
0
0
0
0
1
2
2
0
2
0
1
0
1
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
1
2
2
0
0
2
0
0
0
2
2
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
2
1
0
2
2
2
0
0
0
1
0
0
2
0
2
1
1
0
1
0
1
1
2
0
0
0
2
0
0
0
2
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
2
2
2
0
3
0
0
1
2
1
0
0
1
0
0
0
0
0
2
0
0
1
0
2
0
0
2
2
0
0
0
0
1
1
1
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
1
2
1
3
0
2
0
0
0
0
2
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
1
2
0
0
1
2
0
2
1
0
1
1
0
1
0
0
2
0
0
0
0
1
0
0
0
1
0
2
0
2
0
0
0
0
1
2
0
0
2
2
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
1
0
2
1
0
0
0
0
0
0
0
2
1
3
1
0
1
3
0
0
0
1
0
0
1
0
0
0
0
0
0
2
1
0
2
1
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
2
2
0
0
1
0
0
0
0
0
2
4
0
0
0
1
1
2
0
1
2
1
2
0
0
2
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
2
0
1
2
0
0
0
1
0
0
0
0
1
5
0
0
0
0
0
1
13
0
1
2
0
1
0
1
1
0
2
0
0
0
0
0
3
0
0
0
1
0
0
0
0
2
0
2
1
2
2
0
1
0
0
1
0
0
1
2
1
0
0
2
0
0
0
2
0
2
1
1
0
1
2
1
0
0
2
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
2
1
0
0
0
0
0
1
0
2
0
1
2
8
2
0
0
2
0
1
0
0
0
2
0
0
0
1
0
0
2
2
1
0
1
0
1
1
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
3
1
0
1
0
0
0
1
3
0
0
1
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
1
1
0
0
0
2
0
0
1
0
0
0
2
0
0
2
0
0
1
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
2
0
0
2
2
0
0
0
2
0
0
0
1
1
0
0
0
1
2
0
0
2
1
0
1
1
0
2
0
0
0
2
0
0
0
0
0
1
0
1
0
1
0
2
0
0
0
0
0
0
0
2
1
0
2
2
2
1
2
0
2
6
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
1
2
0
0
1
2
0
0
0
1
2
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
1
0
0
2
2
0
2
0
2
0
0
0
0
1
0
1
0
2
0
0
4
0
0
2
0
1
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
2
1
1
2
1
2
0
0
0
1
2
0
0
0
0
0
2
1
2
0
2
0
2
0
1
1
0
0
0
2
0
2
1
0
1
0
0
1
1
0
2
0
0
0
0
0
1
0
0
0
2
0
0
2
1
0
0
0
1
0
0
0
0
0
0
2
1
0
1
0
0
0
2
0
2
0
2
0
1
0
2
0
2
0
1
0
0
1
1
1
2
2
0
1
2
0
0
0
1
2
0
1
2
0
0
2
0
0
1
0
0
2
0
0
2
0
0
0
0
2
2
1
1
1
0
0
0
2
0
0
1
0
2
1
2
0
1
0
0
1
2
0
0
2
2
0
1
1
2
0
1
0
2
1
0
1
0
0
0
5
0
0
1
0
4
0
1
0
0
0
0
2
0
0
1
0
5
0
1
0
0
0
3
0
0
2
2
2
0
1
1
0
2
0
0
2
0
0
0
0
2
1
0
1
2
0
0
0
5
1
0
2
0
1
1
1
1
2
0
0
0
0
1
1
2
0
1
2
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
1
0
0
0
1
1
2
0
0
0
0
0
0
2
0
0
2
2
1
0
0
0
0
0
1
0
1
0
1
0
1
0
2
0
0
0
3
0
0
2
1
0
0
2
0
1
1
1
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
1
0
2
2
0
1
0
0
0
2
0
0
1
1
0
2
0
1
2
0
1
0
0
2
3
1
0
0
2
0
1
1
1
0
0
2
0
2
0
2
2
1
0
1
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
2
2
0
0
1
2
1
0
0
0
0
2
0
0
2
0
1
0
2
0
2
2
1
0
0
3
0
1
0
0
3
2
0
2
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
2
0
0
5
2
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
1
0
0
0
0
1
0
0
1
0
2
1
0
0
0
0
2
2
1
0
2
0
2
2
0
1
0
0
0
0
1
0
0
1
2
2
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
2
0
1
0
0
0
0
2
0
2
0
0
0
1
1
1
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
2
1
0
0
0
0
1
1
0
1
2
0
1
1
1
2
0
2
0
4
0
1
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
4
1
2
1
1
0
0
0
0
2
0
0
0
2
0
2
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
1
0
1
0
0
0
6
1
0
0
0
0
0
1
0
0
0
0
0
2
1
2
2
0
0
0
1
2
1
0
0
0
0
0
0
0
0
3
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
2
0
0
2
0
0
0
0
1
1
0
0
2
1
0
0
0
1
1
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
1
0
0
0
0
2
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
4
1
2
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
1
1
1
8
0
0
2
1
0
1
1
2
1
0
0
1
0
0
1
1
0
0
2
0
1
1
2
0
0
1
0
1
0
0
0
0
2
0
2
2
0
0
2
2
2
1
1
0
0
2
0
0
2
0
1
0
0
1
0
1
0
2
0
0
0
0
2
0
2
2
0
0
0
0
2
5
1
0
0
0
1
0
0
2
1
2
0
0
0
0
2
1
0
0
1
0
2
2
1
0
0
1
1
0
0
0
0
0
0
2
1
0
1
0
2
1
2
0
3
0
0
1
2
3
0
1
1
0
0
2
0
0
0
1
0
1
1
2
0
0
2
0
0
1
2
0
1
2
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
6
2
0
1
0
1
0
0
0
0
0
1
1
1
2
0
0
1
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
2
1
0
0
1
2
0
0
0
1
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
2
1
2
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
1
2
0
0
0
1
2
0
0
1
0
0
0
0
1
0
2
1
0
3
0
0
1
0
0
1
0
0
0
2
0
0
0
1
0
0
2
0
1
0
0
0
2
0
0
0
1
2
1
1
0
2
0
0
1
0
0
0
0
2
1
0
0
0
2
0
1
2
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
2
2
0
0
0
0
0
3
2
0
0
0
1
0
0
1
1
1
2
0
2
0
1
1
0
0
0
0
1
2
1
0
0
0
0
0
2
0
0
0
0
0
2
0
10
0
2
0
1
0
0
0
0
2
2
0
2
0
0
0
1
0
1
0
1
1
0
2
2
0
0
2
0
0
0
1
2
1
0
0
0
0
0
0
0
4
0
0
0
1
2
2
0
0
0
1
0
0
2
0
0
2
1
1
6
0
0
0
2
2
0
0
0
0
0
0
0
6
1
2
2
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
1
0
2
0
0
0
1
0
2
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
2
1
0
3
1
0
1
0
2
0
1
1
0
2
2
0
1
0
0
0
2
1
0
0
0
1
0
0
2
0
0
2
2
0
0
1
2
0
0
0
0
2
0
1
3
0
0
1
1
0
0
1
0
1
2
1
0
2
2
0
0
0
0
2
0
0
1
3
0
1
2
0
0
0
1
0
1
0
0
0
0
1
0
1
0
1
1
1
0
1
2
0
0
0
0
0
0
0
1
3
0
0
3
0
0
0
0
0
0
0
2
0
2
1
0
1
0
1
2
2
0
1
0
0
2
1
0
0
0
2
1
0
2
0
1
0
1
2
2
1
0
0
1
0
0
2
2
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
2
1
0
1
0
2
0
2
1
0
0
1
0
0
0
0
0
2
1
0
0
0
1
1
0
2
0
2
0
0
1
0
0
0
0
0
3
0
0
2
1
0
1
0
0
1
1
0
0
2
0
2
0
0
0
1
0
2
0
1
0
0
2
0
1
1
2
0
0
1
1
1
1
0
1
0
0
0
0
1
0
2
0
0
0
1
1
2
0
0
0
1
2
0
0
0
0
0
2
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
1
1
0
2
0
0
1
2
0
0
2
1
2
0
1
0
0
0
2
0
1
1
1
2
0
0
0
0
1
0
1
2
1
0
0
2
1
0
0
0
0
1
0
1
0
0
2
1
0
2
1
0
0
0
2
1
0
1
0
1
2
0
0
2
0
0
0
2
2
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
3
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
2
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
1
1
0
2
2
0
2
0
1
0
0
0
0
1
0
0
1
0
0
1
2
2
1
1
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
1
0
2
0
1
0
0
0
0
0
2
2
0
2
0
1
0
4
0
2
3
0
0
1
0
0
0
2
2
0
1
0
0
2
2
1
1
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
1
2
2
0
1
1
0
2
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
3
1
0
0
2
1
0
1
0
1
0
1
1
0
0
1
2
0
0
0
1
1
1
0
0
0
0
0
1
0
0
1
1
1
0
2
0
0
0
2
1
0
2
1
0
0
1
0
0
0
0
0
2
3
2
0
2
1
0
0
2
1
0
1
0
0
0
2
2
0
2
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
5
2
2
0
0
0
0
0
1
2
0
0
1
0
2
2
0
2
1
0
1
1
0
1
6
1
0
0
0
0
2
4
1
2
0
0
0
2
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
1
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
2
0
1
2
3
0
1
1
0
0
2
1
0
0
1
1
0
1
0
2
2
0
0
0
0
1
1
0
0
1
0
2
0
0
0
0
0
2
1
0
0
0
0
0
1
4
1
0
0
0
1
1
0
0
0
0
1
0
0
1
1
0
0
0
0
1
2
2
0
0
2
0
1
0
1
0
0
0
0
2
0
0
0
0
3
0
1
0
1
2
0
1
2
0
2
0
0
0
2
0
2
2
1
0
1
0
0
1
1
1
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
1
1
1
1
0
0
2
0
1
2
0
1
1
0
2
0
0
0
0
1
1
3
2
0
1
0
0
0
0
2
2
1
1
2
0
0
0
1
0
0
0
1
0
2
1
0
2
0
1
1
0
2
1
0
0
1
0
0
1
0
2
0
2
0
3
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
2
1
0
0
0
1
2
0
0
2
0
1
0
0
0
2
2
0
2
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
1
0
2
2
1
2
0
0
0
0
2
0
0
0
1
1
0
3
2
0
0
1
1
0
0
2
2
0
0
0
1
0
2
0
3
2
0
1
2
0
0
0
0
1
1
0
0
0
0
2
2
2
0
0
0
0
2
0
2
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
2
1
2
2
1
2
1
0
1
0
0
1
0
0
0
2
0
0
0
1
0
1
0
2
2
0
1
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
2
0
0
0
2
0
2
2
1
2
2
0
0
0
2
0
0
0
2
1
0
2
0
0
0
0
1
0
0
0
2
1
0
2
0
1
1
2
2
1
2
0
0
0
3
0
2
0
1
1
0
0
0
2
0
0
1
1
1
0
1
0
0
1
0
0
1
0
2
1
1
0
2
2
0
0
0
0
0
2
0
1
0
2
0
2
1
0
2
0
0
3
0
1
0
2
1
0
0
1
0
2
0
1
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
1
0
0
0
0
5
0
1
0
2
3
0
2
1
1
0
0
1
0
0
0
1
1
0
0
1
0
0
0
1
0
2
0
0
1
0
1
0
1
1
0
2
2
1
0
0
2
0
0
2
2
0
1
0
1
1
0
0
1
2
0
1
1
1
0
0
1
2
0
2
0
0
0
1
0
2
0
0
0
0
1
0
2
2
1
1
1
1
0
2
0
0
0
1
0
1
1
0
1
0
0
2
2
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
2
0
2
1
0
0
0
0
0
0
0
2
1
0
0
2
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
1
0
0
2
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
1
0
1
0
1
0
0
2
1
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
2
0
1
0
0
0
2
0
0
1
1
0
0
1
1
0
0
2
0
2
1
0
1
0
2
0
2
0
2
1
2
1
0
0
2
2
2
2
0
1
0
1
0
2
2
2
0
0
0
3
0
2
0
3
1
0
2
0
0
0
0
2
0
2
0
2
2
2
1
0
2
0
0
0
2
0
0
3
0
0
0
1
1
0
0
0
2
0
0
1
1
1
0
0
0
2
0
0
2
0
0
2
1
1
2
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
2
1
0
0
0
0
1
0
1
0
1
2
2
0
0
0
0
0
1
1
0
2
1
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
3
0
0
0
1
1
0
0
1
1
0
0
0
2
0
4
1
1
0
1
0
2
2
0
0
0
0
2
1
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
1
2
0
1
2
1
0
1
0
2
0
0
0
0
1
0
1
2
1
2
0
0
0
0
1
2
2
0
1
1
2
0
1
0
0
0
2
0
0
2
0
3
1
3
0
0
0
2
0
0
0
2
4
2
1
2
2
1
0
0
2
1
1
1
0
2
0
0
1
2
1
2
2
0
0
0
1
1
2
2
0
1
0
1
1
2
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
2
0
1
2
0
0
0
3
1
4
0
1
1
0
2
0
1
0
2
0
2
1
2
0
0
1
0
2
1
0
2
0
0
0
2
1
0
1
0
0
2
0
0
1
0
1
1
2
0
2
1
0
0
0
2
2
0
1
0
2
1
0
0
0
1
0
2
0
0
0
2
0
0
2
2
2
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
1
1
1
0
2
0
0
0
1
0
1
2
2
2
1
0
2
0
2
0
0
0
0
0
0
0
0
1
2
2
1
0
0
0
0
0
2
1
3
0
0
0
0
2
0
2
0
1
0
0
0
1
2
1
0
0
1
2
0
0
0
0
2
1
1
1
0
2
0
0
0
2
0
0
0
0
0
0
1
0
2
2
0
1
1
0
0
0
0
0
1
2
0
2
1
1
1
0
0
0
0
1
1
0
0
0
2
0
0
1
0
0
0
1
1
1
0
0
2
3
1
0
0
1
0
1
2
0
0
2
0
0
0
0
0
3
0
2
1
0
0
0
0
1
1
0
2
0
0
1
1
2
0
0
0
0
1
0
0
0
4
0
0
0
3
0
1
0
1
2
0
0
1
0
0
0
1
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
2
1
2
0
0
1
0
0
0
0
0
2
0
0
0
1
4
0
2
1
0
0
0
2
0
0
0
0
1
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
2
1
1
0
0
0
2
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
2
1
2
0
0
0
2
0
0
0
0
0
0
0
1
1
2
4
0
0
0
0
2
0
0
0
2
0
2
0
3
2
2
0
0
0
0
0
2
0
2
2
1
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
1
0
0
1
0
0
0
1
4
0
2
0
0
0
3
1
0
0
0
1
2
0
0
1
1
0
0
0
2
2
2
0
0
2
1
0
0
2
0
0
1
3
0
1
4
2
2
2
0
0
0
0
0
0
0
5
1
0
0
0
0
0
0
1
3
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
1
2
1
0
1
0
1
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
2
0
0
0
1
1
1
0
1
0
1
2
1
0
0
0
0
2
0
0
0
0
0
2
0
1
2
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
1
1
2
0
2
1
1
2
0
0
0
0
0
0
2
1
0
1
2
0
1
0
0
0
0
0
1
1
2
3
1
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
2
0
0
4
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
2
1
0
0
2
0
1
0
2
1
1
0
2
0
1
0
0
0
0
0
2
0
2
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
1
1
0
4
0
1
1
2
2
1
0
1
0
0
2
0
0
0
1
0
0
0
0
2
1
0
0
1
0
2
0
1
2
2
0
0
0
0
0
1
2
1
2
1
2
0
2
0
0
2
0
0
0
2
0
2
0
2
2
0
2
0
2
0
0
0
0
2
1
0
3
1
0
0
2
0
0
0
1
0
2
0
0
3
1
1
2
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
1
0
1
1
0
0
0
2
2
0
0
1
2
0
2
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
2
1
0
1
2
0
0
1
2
1
1
0
1
1
1
1
2
1
2
0
2
3
0
0
2
0
0
2
0
1
3
2
0
0
0
0
2
3
0
2
1
1
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
1
0
0
0
2
1
0
0
0
2
0
1
2
1
0
0
1
2
1
0
1
1
1
2
0
0
1
0
0
0
0
1
0
1
0
4
4
2
1
2
0
0
2
0
1
0
1
0
0
2
2
0
1
0
0
2
2
0
2
2
0
0
0
0
0
0
0
0
2
0
1
3
2
0
0
1
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
1
0
0
0
1
1
1
0
2
0
0
2
1
0
0
0
0
0
1
0
1
3
0
0
0
2
1
1
0
2
0
2
0
0
1
0
2
3
0
0
1
0
0
1
2
0
12
1
3
0
2
1
3
1
0
0
1
2
2
0
0
0
2
0
0
2
0
1
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
1
0
0
0
0
0
0
3
0
0
0
0
2
0
0
1
1
0
0
0
1
1
1
0
0
0
0
3
2
0
0
0
0
2
0
0
0
2
0
1
0
2
0
0
0
0
2
1
1
1
0
0
2
2
2
2
0
0
0
1
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
1
0
0
1
1
0
2
0
0
0
2
2
1
0
1
0
0
0
2
0
0
1
0
1
0
0
1
0
2
0
2
2
2
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
6
0
0
0
0
0
1
2
0
1
0
1
2
2
1
2
3
1
0
2
0
0
0
0
3
1
0
0
0
0
0
0
0
1
1
0
2
0
1
1
0
1
0
2
2
0
2
1
0
0
0
0
1
0
1
0
0
2
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
2
0
0
0
0
2
1
1
0
0
1
0
0
0
4
0
0
0
0
0
0
2
0
0
1
1
0
1
1
1
1
0
0
0
1
2
0
0
1
0
0
1
0
1
2
0
1
0
0
0
1
1
0
0
1
1
0
2
0
1
0
2
0
0
0
2
0
0
1
2
0
1
2
2
0
0
0
1
0
2
2
0
0
1
0
0
4
1
0
2
0
0
0
0
0
2
3
0
0
0
0
1
0
0
1
0
1
0
0
0
2
0
0
1
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
2
2
1
2
2
4
1
2
0
0
0
2
1
0
3
0
2
0
1
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
1
1
1
1
0
0
0
0
0
1
0
2
1
2
3
0
0
0
0
0
0
0
1
0
0
0
5
1
2
0
0
2
1
0
2
0
2
0
2
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
1
0
0
2
1
0
0
1
3
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
1
0
1
0
1
2
0
0
2
1
0
0
0
0
1
0
1
0
0
0
2
0
1
0
1
0
0
0
0
1
0
0
2
2
2
0
0
0
2
4
0
2
0
2
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
1
1
2
2
1
1
0
2
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
2
1
0
0
2
0
0
2
0
1
3
0
2
0
0
0
0
1
0
2
0
2
0
0
0
2
0
0
3
0
0
0
0
1
0
0
0
0
0
2
7
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
2
2
0
0
0
2
0
1
0
0
0
0
1
2
0
0
2
2
2
2
0
0
0
3
0
2
2
0
0
1
0
0
0
1
1
2
1
0
1
0
2
1
0
0
1
1
2
1
0
1
2
0
0
0
0
2
2
0
2
0
1
1
0
2
0
2
0
2
1
2
0
0
1
2
0
0
0
1
0
2
2
1
0
2
0
0
0
0
0
1
2
2
2
0
0
0
1
0
0
2
0
0
0
0
2
0
1
0
1
0
2
0
1
0
0
0
0
1
0
1
0
1
2
2
0
2
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
2
0
1
0
1
2
0
1
0
0
1
3
4
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
1
0
0
2
1
1
3
0
0
2
2
2
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
2
1
1
0
2
2
0
0
0
1
0
0
0
0
1
0
1
0
1
2
0
1
1
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
1
0
1
0
3
0
0
0
0
1
0
1
0
2
1
1
0
0
1
0
3
0
2
2
1
2
2
2
1
0
3
1
1
2
1
0
1
0
0
2
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
2
3
0
0
0
2
0
0
0
0
2
0
0
1
2
0
0
1
1
2
1
2
0
1
1
0
0
0
1
3
0
1
1
0
0
0
2
0
2
1
0
2
0
1
0
0
0
1
1
0
2
0
2
0
0
2
0
0
0
1
2
0
0
1
0
1
2
2
0
0
6
1
0
0
0
1
1
0
1
2
0
0
0
2
0
0
0
0
1
1
1
1
0
0
2
0
0
2
1
0
0
2
0
0
2
2
0
0
0
2
1
2
0
1
2
0
0
0
0
0
0
1
0
0
5
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
1
0
2
0
0
1
2
1
0
0
0
2
0
1
0
0
1
2
0
0
0
0
1
1
2
1
0
2
2
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
2
0
0
2
0
2
0
0
0
0
0
0
1
1
1
2
0
1
1
0
0
0
1
3
4
0
1
0
0
2
0
0
0
1
0
0
0
0
1
2
1
0
1
1
0
0
0
1
1
0
0
0
0
1
0
1
0
0
1
0
1
0
0
2
0
0
0
0
2
0
1
0
1
2
2
0
0
1
1
1
1
0
2
0
0
0
0
0
0
0
1
1
0
0
0
2
1
2
0
0
0
1
0
0
2
0
0
0
0
0
2
2
2
0
1
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
3
0
0
2
0
0
1
0
1
2
1
2
0
0
0
0
1
1
2
0
0
0
0
0
0
2
0
0
2
2
1
0
0
0
0
0
0
0
2
0
0
0
0
2
1
1
2
0
0
1
2
2
0
0
0
2
0
0
0
0
1
1
0
0
2
0
0
0
0
2
2
0
0
0
1
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
1
2
2
0
1
0
0
2
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
1
0
1
2
0
0
0
0
2
0
0
0
1
2
2
0
0
0
1
0
0
2
1
1
1
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
1
0
2
1
2
0
0
1
0
0
0
0
0
1
1
0
0
0
0
2
1
0
0
2
2
1
2
0
2
0
1
0
3
0
0
0
2
1
0
0
1
2
0
0
4
1
0
1
0
1
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
2
0
1
0
0
0
2
0
0
0
0
0
1
0
2
0
1
0
0
0
2
1
0
2
1
2
0
1
1
1
0
1
1
0
0
0
0
2
0
0
0
0
2
0
0
2
1
2
0
0
0
2
0
0
0
1
2
1
1
1
0
5
0
0
1
0
0
1
0
0
1
0
1
1
0
0
0
2
0
0
1
0
1
5
0
0
0
1
0
0
0
1
2
0
0
0
1
2
0
0
1
1
1
0
1
0
0
1
0
0
1
2
0
0
0
1
0
0
0
1
0
4
0
1
0
0
0
1
0
2
0
2
1
0
0
4
0
0
0
0
1
2
0
0
0
2
1
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
2
1
2
2
2
1
0
1
0
1
0
1
0
1
1
0
4
2
1
0
0
0
1
0
2
0
0
2
0
0
0
2
0
1
0
0
0
1
0
0
0
0
1
2
0
0
2
1
0
0
2
0
0
0
1
2
2
7
2
0
1
2
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
3
0
0
1
0
0
0
1
1
1
0
1
0
1
0
0
0
0
2
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
2
1
2
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
2
2
0
0
0
0
6
0
0
0
0
1
2
0
0
0
0
0
0
2
0
3
2
1
0
1
0
2
0
2
0
2
1
0
1
2
0
0
0
0
1
0
0
1
1
0
2
2
0
0
0
2
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
2
0
1
2
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
3
1
0
0
0
1
0
2
0
1
2
1
0
0
0
1
0
0
0
0
0
2
0
2
0
2
2
2
1
0
0
0
2
2
1
0
0
2
0
0
2
1
0
3
2
0
0
0
0
0
0
1
2
2
2
1
0
2
0
0
0
0
1
2
1
3
0
0
2
0
1
0
0
1
0
1
1
0
2
1
0
0
1
0
0
0
2
1
2
1
1
0
0
0
0
0
2
3
0
0
0
0
2
2
1
0
1
2
0
0
1
2
0
0
0
0
1
1
2
0
0
0
1
2
1
2
0
0
0
0
0
2
1
1
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
1
2
0
0
0
4
2
0
0
1
2
4
0
2
0
0
3
0
1
1
2
0
0
0
0
1
0
0
1
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
1
1
0
0
2
1
1
2
1
1
1
2
0
0
1
2
2
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
1
0
0
0
1
1
0
0
1
0
2
0
0
1
0
0
0
0
2
0
1
1
2
0
1
2
1
2
0
2
0
0
0
0
0
0
0
2
0
1
1
0
1
2
0
1
1
0
1
0
2
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
1
0
1
2
0
0
1
1
1
0
2
0
2
0
0
0
0
1
0
1
0
1
0
0
0
0
1
2
2
0
0
0
0
2
1
1
0
0
3
0
0
0
0
2
1
0
2
1
0
1
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
2
1
2
0
0
1
1
0
1
3
0
0
2
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
2
2
2
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
1
0
1
1
1
0
0
0
0
1
0
0
2
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
2
2
0
0
1
2
0
0
0
0
2
2
0
0
0
0
0
1
2
2
0
2
2
2
0
0
2
0
0
1
1
2
1
0
1
0
1
2
0
2
0
0
1
1
0
2
2
0
0
1
0
1
0
0
0
0
1
0
2
2
0
0
2
0
0
0
0
0
1
2
2
0
0
1
0
1
0
1
1
0
0
0
2
1
0
1
0
0
0
0
1
1
2
0
1
3
0
1
2
0
1
0
0
0
0
0
2
0
2
0
1
0
2
1
0
0
0
0
0
0
0
1
2
1
0
0
1
0
0
0
1
0
2
0
1
0
0
2
0
0
2
0
2
0
0
0
2
1
0
1
1
2
2
1
0
0
2
2
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
2
0
1
0
0
2
1
0
0
0
0
1
1
2
0
0
1
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
1
0
1
0
0
2
2
1
0
0
1
0
0
2
2
0
0
0
0
2
0
0
0
1
2
2
0
1
0
2
1
1
2
1
1
0
0
2
1
0
0
2
2
0
0
2
0
0
0
0
1
1
1
2
1
0
0
0
2
0
0
0
1
1
2
0
0
0
1
0
0
0
1
0
2
2
0
1
0
1
2
1
0
2
2
2
0
1
2
0
0
1
0
1
0
2
1
1
0
0
2
2
2
1
0
2
0
0
1
1
0
2
2
0
2
0
0
1
1
1
0
0
1
2
2
2
0
2
1
0
2
0
0
0
0
1
2
0
0
1
1
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
1
1
1
2
0
0
0
2
1
1
1
0
2
0
0
2
2
0
3
0
1
2
2
2
2
2
1
0
0
0
1
2
0
0
0
0
2
0
1
1
0
1
1
0
0
1
2
1
0
2
1
2
3
0
0
1
0
1
0
1
1
3
1
0
1
1
2
1
2
0
5
1
3
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
1
0
0
2
2
1
1
2
0
0
1
1
1
0
0
1
0
0
1
0
1
2
1
0
0
0
1
0
2
1
1
0
0
1
0
0
1
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
2
4
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
1
2
0
2
0
0
2
1
0
2
2
0
0
0
0
2
1
2
0
1
1
2
2
1
0
1
0
0
2
7
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
2
2
1
2
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
2
0
0
0
1
0
0
1
0
0
1
2
1
0
0
0
0
1
1
0
0
1
2
0
0
0
0
0
0
1
0
0
0
1
0
0
2
1
0
0
1
2
0
2
2
1
0
0
0
1
0
0
2
0
3
1
0
1
2
1
1
2
0
1
0
0
0
1
1
0
1
0
2
1
2
2
2
0
1
0
0
0
0
0
0
1
2
2
0
0
2
1
2
0
2
0
1
0
0
0
1
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
1
1
0
1
0
0
0
0
0
2
2
0
1
1
0
0
2
1
1
2
0
0
0
2
0
1
2
0
0
2
0
0
2
0
1
0
2
1
0
0
1
0
1
0
0
0
0
2
2
0
1
3
0
0
1
1
0
0
0
0
1
0
1
0
1
0
2
1
2
0
0
0
1
1
1
2
2
0
0
1
0
0
0
2
0
2
0
2
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
1
3
0
0
0
2
1
0
2
1
0
0
1
0
0
1
0
0
0
1
0
2
1
1
0
0
0
0
2
2
2
0
0
1
0
0
1
0
1
2
2
0
0
1
0
0
0
0
0
2
2
0
2
1
1
0
0
2
0
1
1
2
1
0
1
1
1
0
2
0
0
0
0
2
0
1
2
0
5
1
1
1
2
2
0
2
0
2
0
2
0
1
0
1
0
0
0
0
0
0
2
0
1
5
0
2
0
2
0
2
0
0
1
0
0
0
1
1
2
0
1
0
0
0
2
2
0
0
0
2
1
3
1
2
2
2
0
0
2
0
0
2
0
1
0
0
2
0
0
1
0
0
1
0
0
0
0
0
1
0
0
3
1
0
4
0
0
0
1
1
2
0
2
0
0
2
0
0
0
0
0
1
2
0
1
0
0
1
2
1
2
0
1
2
0
0
0
4
0
3
1
0
2
0
0
0
1
0
0
1
1
0
1
0
1
1
1
0
1
1
2
0
0
0
2
0
0
0
0
0
0
0
1
1
1
0
2
0
1
0
2
0
0
0
2
1
0
1
2
0
1
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
2
0
1
0
0
0
0
0
0
2
1
0
0
0
1
0
1
2
1
0
0
0
1
2
0
0
1
0
0
2
2
0
0
0
0
0
1
0
0
1
1
5
2
0
2
2
2
3
0
2
2
1
0
0
2
0
0
1
2
2
4
0
0
1
0
1
2
1
2
2
0
0
0
1
0
0
1
2
0
0
0
0
0
1
2
1
1
0
0
0
0
0
2
2
1
0
0
0
0
2
3
0
1
0
0
1
2
0
0
0
0
0
3
0
2
0
0
0
2
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
3
0
0
1
1
2
0
0
0
1
0
0
0
1
2
2
0
2
0
2
0
1
0
1
0
1
0
0
2
0
1
0
0
0
0
2
0
0
0
1
0
0
0
2
2
2
0
2
0
0
2
1
0
2
2
0
2
1
2
0
0
2
0
0
2
3
0
0
0
1
2
0
1
1
1
2
0
0
0
1
0
1
2
0
2
0
0
1
2
0
1
0
0
0
2
0
0
0
2
0
0
1
0
0
1
0
2
1
0
1
0
2
0
0
2
0
1
0
2
0
0
0
0
0
2
0
0
1
1
0
0
0
1
2
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
1
1
0
0
0
0
0
1
0
2
2
0
0
0
1
1
0
0
0
2
0
0
1
3
0
0
2
0
0
0
1
2
0
0
0
2
2
0
0
0
1
0
1
0
0
0
1
2
0
0
0
0
0
1
2
1
0
0
0
1
0
0
1
1
0
0
0
3
1
1
2
0
1
2
0
2
1
0
0
2
0
0
0
0
0
2
0
2
3
2
0
3
1
0
2
0
0
1
0
4
0
0
0
1
0
1
2
1
2
2
2
0
0
0
0
0
0
3
1
2
0
0
0
0
0
0
0
1
1
2
0
1
0
2
0
0
0
0
1
1
0
2
0
1
0
2
0
2
1
1
0
0
0
1
0
0
1
1
2
0
0
0
0
1
0
1
2
0
1
0
0
0
0
1
1
1
0
3
0
1
0
2
0
1
0
0
0
1
1
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
2
0
0
0
0
2
3
0
0
0
5
0
2
0
0
0
0
2
0
2
0
0
0
0
1
0
0
1
0
1
0
0
2
0
2
1
0
0
1
1
0
2
0
1
1
1
1
1
0
0
3
0
0
1
0
2
0
3
0
0
2
0
0
1
1
0
0
1
2
0
0
0
0
0
0
2
0
1
2
1
0
0
0
2
2
0
0
0
1
0
4
0
0
0
2
0
1
0
0
2
1
0
0
2
1
0
2
1
2
1
2
0
3
0
0
1
0
0
0
0
1
0
1
1
0
0
2
0
0
0
0
1
0
1
0
0
0
0
2
0
0
1
1
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
2
0
2
0
0
1
0
0
0
0
2
1
2
0
1
0
0
0
1
0
1
0
2
0
2
0
0
2
0
0
0
1
1
0
0
0
2
0
0
1
0
0
2
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
3
0
0
2
1
2
1
1
1
0
0
0
1
1
2
2
4
3
0
1
1
1
0
3
0
2
2
0
1
0
0
1
1
2
1
0
0
0
0
1
0
0
0
0
2
0
1
1
0
1
0
0
1
1
0
0
1
0
3
0
2
2
0
3
1
1
2
0
2
0
2
0
3
2
2
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
3
0
2
2
2
2
1
1
0
1
0
0
0
0
2
0
1
0
1
0
0
2
0
0
0
1
0
0
0
0
0
1
3
0
2
0
2
0
0
2
0
2
1
0
2
0
1
0
2
1
2
1
1
1
2
0
0
1
0
0
0
1
1
1
0
2
0
0
0
2
0
3
2
1
1
1
2
1
0
2
0
0
2
1
0
0
0
1
1
0
0
0
0
2
1
0
0
0
2
1
0
2
0
1
0
0
1
0
0
2
0
0
2
0
1
0
0
0
0
0
0
1
1
0
0
2
0
0
0
1
0
0
2
1
0
0
1
1
1
3
0
0
0
2
2
0
0
0
1
1
0
0
1
2
0
2
1
1
0
0
0
0
0
2
1
0
0
2
0
1
1
2
2
0
3
0
1
0
0
0
0
0
0
1
2
0
2
0
0
1
3
2
0
0
0
2
1
1
0
3
3
0
0
0
0
1
1
2
1
0
1
0
0
2
0
2
0
2
0
2
1
1
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
3
0
1
0
1
0
2
0
0
0
0
2
2
0
1
0
0
0
0
2
1
2
1
0
0
0
3
0
0
0
0
0
0
2
1
1
0
1
1
1
2
2
0
0
0
0
0
1
1
0
0
0
1
0
2
0
1
1
2
0
2
0
1
0
2
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
1
1
0
2
2
1
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
2
0
0
1
0
2
1
0
3
0
0
1
2
0
0
1
3
2
0
0
0
0
3
2
0
3
0
1
0
0
0
2
0
0
0
0
0
0
3
0
0
2
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
3
1
1
1
0
1
2
0
1
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
2
1
2
2
0
2
2
1
2
0
0
0
0
3
0
1
1
1
0
0
0
1
0
0
0
0
0
0
2
2
2
2
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
10
0
0
0
0
0
1
1
2
0
2
0
0
0
0
0
0
0
0
0
1
3
0
0
0
2
2
1
0
1
0
1
2
1
1
0
1
1
0
1
0
0
2
0
2
1
1
1
0
0
0
0
0
1
2
2
0
1
2
2
2
0
2
0
0
1
1
0
1
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
2
0
0
1
0
2
2
0
1
0
2
0
2
0
2
0
0
7
0
1
0
1
0
0
0
0
0
2
2
2
0
0
0
0
0
0
1
0
0
1
3
0
0
0
1
1
0
1
0
2
0
2
0
0
0
0
0
2
2
1
0
0
0
0
2
0
0
0
0
2
0
2
0
0
2
0
0
2
0
2
1
0
0
1
0
0
2
1
0
0
0
2
0
0
1
1
1
0
0
1
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
2
1
2
0
1
1
0
0
0
0
1
0
0
2
0
0
0
1
2
0
0
2
1
1
0
0
0
0
2
2
1
0
0
2
0
0
0
2
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
2
2
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
7
0
1
2
1
0
1
2
1
3
0
4
0
0
0
0
0
0
1
2
0
2
1
1
2
2
0
2
0
0
0
0
2
1
1
0
0
0
0
2
0
1
0
1
0
1
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
1
1
0
2
0
2
0
1
0
0
0
1
1
1
1
1
1
0
1
0
0
2
2
0
0
0
0
2
0
3
2
1
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
2
1
1
2
0
0
0
0
0
0
1
1
0
1
2
2
2
1
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
2
2
12
1
0
0
0
1
1
1
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
2
0
0
0
1
1
0
0
0
0
2
1
2
1
2
0
0
0
0
0
0
1
2
2
2
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
2
2
1
1
0
2
2
1
0
2
0
1
1
0
1
2
0
0
0
0
2
0
0
2
0
1
1
2
0
2
0
1
0
2
1
0
0
0
1
1
1
0
0
2
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
2
0
2
5
0
1
0
1
4
1
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
1
0
0
0
1
1
0
2
1
0
3
1
0
1
1
0
1
1
2
0
0
0
2
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
1
0
4
0
0
2
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
2
1
1
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
1
2
2
2
2
0
0
0
1
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
1
1
1
0
0
0
0
2
1
0
0
0
1
1
1
0
0
0
0
1
1
1
0
1
0
1
0
0
2
0
0
0
0
0
0
1
1
2
1
1
1
0
1
0
0
1
1
2
0
0
1
2
0
2
1
2
0
0
2
1
2
0
0
0
0
1
2
0
0
2
0
0
1
3
0
1
0
1
2
0
0
2
0
0
0
0
2
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
3
0
2
0
0
0
0
0
0
2
0
1
2
0
0
2
0
2
0
2
0
0
2
0
2
0
0
1
3
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
2
1
0
1
1
0
0
0
2
0
0
1
0
0
0
0
0
1
2
0
2
0
1
2
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
2
0
2
0
1
2
3
0
0
0
4
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
2
1
0
0
0
1
0
0
0
0
0
2
2
0
0
0
1
0
2
0
1
1
0
0
2
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
1
2
4
0
0
1
0
0
4
0
2
3
0
0
1
0
1
1
0
0
2
0
2
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
4
1
2
0
0
2
0
2
1
0
1
0
0
1
0
0
2
0
0
1
0
0
1
2
0
1
2
2
2
0
2
0
0
0
1
1
2
0
3
2
0
0
2
0
0
2
3
0
2
0
1
0
2
0
0
0
0
0
0
0
1
0
1
1
1
0
0
1
0
0
0
8
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
2
0
0
0
0
0
1
1
0
2
1
0
2
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
1
0
3
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
1
1
2
0
0
0
0
2
1
0
1
0
0
0
0
1
1
0
1
2
0
1
1
1
2
0
2
0
0
0
1
0
1
0
1
0
0
0
0
0
1
2
0
2
2
1
2
0
0
0
0
0
0
0
7
3
2
0
1
2
0
0
0
3
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
2
1
1
0
0
1
2
0
0
0
1
0
0
1
1
1
0
1
0
1
1
0
0
1
0
1
0
0
2
1
0
0
0
1
0
0
1
0
0
0
0
1
0
1
1
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
2
0
2
2
2
1
0
1
0
0
2
1
2
2
0
0
0
0
0
2
2
1
2
1
2
0
0
0
0
2
1
0
0
1
0
1
0
1
1
0
0
0
0
2
1
0
0
0
0
0
0
2
1
2
4
1
0
0
2
2
0
0
0
0
0
0
0
0
1
0
2
1
2
1
2
0
2
2
2
0
0
0
0
9
0
0
1
0
0
0
2
0
2
0
2
0
0
1
1
2
1
0
1
1
0
0
0
1
1
0
1
0
2
0
0
0
1
2
0
0
0
2
2
1
1
2
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
9
1
0
0
1
1
0
0
1
1
1
1
0
0
3
1
0
0
1
1
0
0
0
0
2
1
2
0
1
1
0
1
0
0
0
0
0
0
3
1
0
0
0
1
0
0
0
0
3
1
0
1
2
1
0
0
7
0
0
2
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
1
1
0
1
0
1
2
0
2
0
1
1
1
1
0
0
2
0
2
0
1
2
0
0
2
0
4
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
2
2
1
0
0
0
0
0
1
1
0
0
0
0
0
1
3
0
1
0
0
0
1
2
0
0
2
0
0
1
1
1
1
0
0
0
1
3
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
2
0
0
0
1
0
0
1
8
0
1
0
1
2
0
0
0
0
0
2
1
2
0
2
1
1
2
2
2
1
1
2
0
0
0
2
2
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
2
0
0
0
1
0
0
2
0
0
0
0
2
0
2
0
0
2
0
3
0
0
0
0
2
3
2
0
0
0
0
1
1
1
0
0
0
0
2
2
0
0
2
0
2
0
0
0
0
1
0
1
2
0
0
0
0
0
0
2
0
0
1
0
1
0
1
0
1
0
2
1
0
2
0
0
2
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
1
2
2
1
0
2
0
0
2
0
1
0
2
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
3
1
0
0
0
0
1
2
0
0
2
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
2
0
2
0
2
2
2
0
0
2
0
0
0
0
0
0
0
2
1
0
0
2
0
1
0
1
0
0
0
0
0
2
0
1
0
2
0
2
1
0
2
0
0
0
1
2
2
0
0
1
0
2
0
0
0
1
0
0
2
0
0
0
1
2
0
2
0
1
2
0
2
1
2
0
0
0
0
1
0
0
3
0
2
1
0
1
0
1
1
1
0
0
3
0
2
0
2
0
1
1
0
1
0
0
0
0
2
1
0
0
0
2
2
0
3
1
0
2
1
1
0
1
0
2
2
2
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
2
0
2
1
0
0
1
1
2
0
0
0
1
0
0
2
2
0
0
1
0
1
1
0
2
0
1
1
1
0
0
0
0
0
1
0
2
0
0
1
0
0
0
1
0
0
4
0
0
1
1
0
2
0
0
0
2
0
1
1
0
1
1
1
0
0
2
0
0
0
0
0
0
1
2
0
2
2
0
1
2
0
2
0
1
2
0
0
0
2
2
0
2
1
0
1
2
0
1
2
0
1
2
0
0
0
1
0
1
0
2
0
1
2
3
0
1
1
0
0
0
1
0
1
1
0
1
0
1
0
0
2
0
0
0
1
2
0
0
0
1
1
0
2
1
0
0
1
4
2
0
2
0
0
0
2
0
0
2
2
0
0
1
1
2
0
1
0
1
0
0
0
0
2
0
0
2
1
0
1
0
0
0
1
0
0
2
2
0
2
1
0
0
2
0
1
0
0
1
2
0
0
1
2
1
1
1
1
0
0
0
0
1
0
0
0
2
2
2
2
0
0
2
1
0
1
1
0
1
2
0
0
0
0
1
0
0
0
1
1
0
0
2
0
1
0
0
0
0
2
1
0
0
2
2
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
2
0
0
0
1
0
0
1
0
2
1
1
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
2
0
1
1
0
0
0
0
2
0
1
0
1
0
2
1
2
0
2
2
2
1
0
1
2
3
0
0
0
3
0
0
2
0
0
1
2
0
0
1
0
2
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
1
1
0
1
1
0
0
0
1
1
1
0
0
0
1
1
1
2
0
1
2
1
0
1
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
2
0
1
2
1
0
0
0
3
1
2
0
0
0
0
0
0
1
0
0
2
0
0
1
2
0
0
0
0
2
1
3
0
0
0
0
1
0
0
0
0
0
0
2
3
0
0
0
0
0
0
2
0
0
1
1
3
1
0
0
0
0
0
1
2
1
0
0
2
0
1
2
0
0
0
2
0
1
0
1
0
3
1
0
2
4
2
0
0
0
2
4
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
2
0
0
0
1
2
2
0
0
0
0
1
0
0
1
5
0
0
0
0
0
0
0
1
2
2
0
0
0
2
2
2
1
1
2
2
1
0
0
1
2
0
0
1
1
1
0
0
2
0
0
0
0
0
2
0
2
0
1
0
1
0
0
1
2
1
0
0
1
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
3
2
0
2
1
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
1
1
0
0
0
0
3
2
1
1
1
0
0
1
2
0
0
3
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
1
2
0
0
2
0
2
0
1
0
1
2
1
0
0
1
1
1
0
3
2
0
0
3
2
0
0
0
1
0
1
2
1
0
0
0
1
1
0
0
0
0
1
0
2
0
2
0
0
0
0
2
0
0
0
1
0
0
1
0
1
1
1
0
0
0
0
1
2
0
0
2
0
0
0
0
0
2
1
0
2
1
0
1
1
0
0
0
1
1
2
0
0
1
0
0
0
0
0
1
1
2
1
2
2
0
2
2
0
0
0
1
1
1
0
2
2
0
0
2
0
0
0
0
1
2
0
0
0
0
1
1
0
1
1
0
1
2
2
0
0
1
0
0
0
0
0
1
2
1
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
2
1
1
0
2
2
0
0
2
1
1
2
1
2
0
1
0
0
0
0
3
0
2
1
0
0
0
0
1
0
0
1
0
2
2
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
2
0
0
0
0
1
1
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
1
2
0
0
0
0
1
2
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
2
0
2
0
0
0
0
2
2
2
0
0
0
2
2
0
2
1
0
0
0
2
0
0
2
2
0
1
1
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
1
0
0
0
2
0
1
0
3
1
2
1
1
1
0
0
2
0
0
1
1
0
0
0
2
0
1
0
2
1
1
0
0
0
0
1
2
0
1
2
2
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
2
1
0
1
0
0
1
1
0
1
1
2
0
0
0
0
0
1
2
0
3
0
0
1
0
0
1
0
0
0
2
2
0
1
0
2
0
0
2
0
2
1
1
2
1
0
0
0
2
0
0
4
0
0
1
0
1
0
0
1
0
1
3
2
0
3
0
0
1
1
1
0
1
0
1
0
2
0
1
0
0
0
0
1
0
0
1
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
4
1
1
1
0
2
0
1
2
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
2
1
0
2
1
2
0
2
2
0
2
0
0
1
2
1
0
2
2
0
1
0
0
1
0
2
1
3
0
1
0
0
0
1
0
0
0
0
1
3
0
0
0
1
2
2
0
0
0
0
1
0
2
0
0
2
2
1
1
0
1
0
2
0
0
0
0
0
0
1
1
0
0
0
0
1
0
2
2
0
0
0
2
1
1
0
1
2
0
2
2
0
1
0
0
0
2
0
1
1
0
1
0
1
0
0
3
0
0
1
0
0
0
0
1
1
2
2
2
1
0
0
0
0
0
0
1
2
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
3
0
0
2
0
2
3
0
1
0
2
0
2
0
0
0
1
0
1
0
2
0
0
0
0
1
0
0
0
1
2
2
1
0
2
1
0
0
0
2
0
2
2
2
1
0
0
2
1
0
0
0
0
0
1
0
2
1
0
1
1
0
0
0
1
2
0
2
0
0
0
0
1
1
0
1
1
1
0
0
2
2
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
2
1
0
0
0
2
1
0
2
1
0
2
0
0
0
0
0
1
0
2
2
2
1
1
2
1
0
2
0
2
0
0
2
2
1
2
1
0
0
0
1
1
1
2
0
0
1
0
0
2
0
2
0
2
0
0
1
2
0
1
1
0
0
1
0
0
1
0
0
2
0
0
0
1
0
1
0
2
2
0
0
2
1
1
0
0
0
0
0
0
8
1
0
2
0
0
2
0
0
0
0
0
0
2
2
2
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
2
2
0
0
2
0
2
0
2
2
1
0
1
0
0
0
0
0
1
0
1
1
1
1
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
1
2
0
0
0
2
0
0
0
0
1
1
0
0
0
1
2
0
1
0
1
0
1
2
1
0
2
0
0
0
3
2
0
0
0
0
1
1
2
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
2
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
1
2
2
0
2
0
4
2
1
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
2
0
3
1
1
0
0
1
0
0
3
1
0
0
0
2
1
0
2
0
1
0
0
0
0
0
0
0
1
1
2
0
2
1
1
1
0
0
2
0
0
0
0
0
0
1
6
0
0
2
2
3
1
4
1
2
0
0
1
0
0
0
0
1
0
1
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
1
1
0
1
1
0
0
1
0
1
0
2
0
1
2
2
0
1
0
0
3
0
3
1
0
0
1
1
1
1
0
0
1
3
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
4
0
2
0
0
1
0
0
0
1
0
0
0
1
0
2
0
0
2
1
0
1
0
1
0
2
2
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
2
0
3
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
1
0
0
0
2
2
2
1
1
1
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
1
2
2
1
2
0
1
1
2
0
1
1
0
2
1
0
1
1
0
0
2
3
1
0
1
2
0
0
0
0
0
0
0
0
6
2
2
1
1
0
0
0
1
0
2
1
2
1
2
0
0
2
0
0
0
0
0
2
0
2
0
3
0
2
0
2
0
0
1
2
2
0
0
0
0
1
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
2
0
2
1
0
0
1
1
0
0
2
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
3
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
1
0
2
0
2
1
1
0
0
0
0
0
0
0
3
0
0
2
1
1
1
1
0
1
0
0
0
0
1
0
0
1
0
0
0
1
2
0
2
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
1
2
2
0
0
0
0
1
0
1
0
0
0
0
0
3
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
2
0
0
3
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
2
0
3
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
2
0
0
2
0
0
1
2
0
0
0
2
0
1
0
1
0
0
2
0
2
2
0
0
0
2
2
2
1
2
0
0
2
0
0
0
0
2
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
1
0
0
2
0
1
2
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
2
2
0
0
1
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
2
1
1
1
2
0
2
2
0
1
1
0
1
0
2
0
0
0
0
1
0
0
2
2
0
2
0
1
1
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
1
2
1
1
1
0
2
0
0
0
0
2
0
4
0
0
0
0
2
0
0
1
0
0
0
2
2
1
0
2
1
0
1
0
0
0
0
0
2
1
0
0
0
0
0
2
2
0
0
0
0
0
1
1
1
2
0
0
1
1
2
0
1
2
1
0
8
0
0
0
0
2
0
2
0
2
1
1
0
1
2
0
0
0
1
0
1
0
0
2
0
0
0
1
0
0
1
2
1
0
1
1
0
0
0
1
2
0
0
2
2
0
0
0
0
0
1
0
2
0
0
0
3
2
0
2
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
2
2
0
0
0
0
2
1
0
1
1
0
1
0
0
0
0
0
2
0
2
1
2
0
0
0
0
0
2
1
2
0
1
0
1
0
1
0
1
1
2
1
0
0
0
2
2
2
0
1
0
0
1
0
1
0
0
1
1
0
0
2
1
0
1
0
1
0
0
0
2
0
2
0
1
1
0
2
0
0
0
4
0
0
2
0
0
0
0
0
1
0
2
2
0
0
2
0
0
1
0
0
0
1
0
2
0
0
0
2
0
1
0
0
0
1
0
0
2
0
0
0
1
0
2
0
1
2
0
1
0
2
0
0
0
1
0
1
0
0
0
0
0
0
2
1
1
0
2
1
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
2
3
2
0
0
0
1
0
1
0
1
0
2
0
2
0
0
2
1
0
2
1
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
2
0
0
0
0
2
0
0
0
1
4
2
0
0
0
0
0
2
0
2
0
0
1
1
1
1
1
2
0
0
2
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
3
1
1
0
2
0
0
0
0
2
0
2
0
2
2
0
0
0
0
1
1
0
0
2
0
0
0
0
0
1
0
2
0
2
0
2
1
1
1
2
2
0
0
0
2
2
0
0
2
2
2
0
0
0
1
1
0
0
1
0
2
0
1
2
0
1
0
0
9
0
2
0
2
1
0
1
0
1
0
1
0
0
0
0
2
0
0
0
1
3
2
1
1
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
3
0
0
1
0
0
0
3
0
0
1
0
0
2
0
0
1
0
0
0
2
0
2
0
1
0
0
2
1
0
0
0
0
2
3
0
1
2
0
1
0
0
1
0
2
0
1
0
0
0
0
5
0
0
0
0
1
0
1
2
2
0
2
2
0
2
0
0
0
0
0
0
0
1
2
1
1
0
1
0
0
3
0
0
0
1
2
1
0
0
0
0
0
1
0
0
0
1
0
0
2
1
0
2
2
2
2
1
0
0
0
2
2
0
0
0
2
1
1
2
2
0
0
1
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
2
0
0
1
2
0
2
2
0
1
2
0
0
0
2
0
0
1
1
0
0
0
1
0
0
1
0
2
0
3
2
1
1
1
0
0
1
2
2
2
0
0
0
1
1
2
0
0
0
1
0
0
1
0
2
0
2
2
1
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
1
0
2
1
1
0
1
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
2
1
2
0
0
1
0
2
1
0
0
2
2
0
0
1
0
0
0
1
2
2
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
3
0
2
2
3
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
2
0
0
2
0
0
2
0
2
0
0
1
1
0
0
0
2
1
2
0
0
0
0
0
2
2
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
1
2
0
0
1
0
2
0
1
0
0
0
0
1
1
0
2
0
1
3
2
0
2
2
0
0
0
0
0
0
0
0
1
0
0
2
1
0
1
0
3
2
2
1
1
0
1
1
2
0
1
0
2
0
0
1
0
1
0
1
0
1
2
0
0
0
0
1
2
1
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
2
1
0
0
0
0
3
0
0
0
0
3
4
1
1
2
0
0
0
0
3
0
0
1
1
0
0
2
0
2
2
2
2
1
0
1
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
2
0
2
3
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
1
2
0
0
0
2
1
1
3
2
0
5
0
2
0
1
0
2
0
2
2
0
1
1
0
2
1
2
0
0
0
0
2
0
0
0
0
0
0
0
1
5
0
0
1
1
0
0
0
2
0
0
2
1
0
0
0
1
1
0
4
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
2
1
0
0
0
0
0
0
0
4
2
1
0
1
0
0
0
0
0
0
0
0
0
2
0
2
2
2
0
0
2
2
2
0
1
1
0
1
0
0
0
1
2
2
0
0
0
2
0
0
2
2
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
2
0
1
2
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
1
0
0
0
1
2
1
0
0
1
0
2
1
1
0
0
1
2
2
1
0
2
2
1
0
1
2
2
1
2
0
0
1
0
2
1
0
1
0
2
2
0
1
0
0
0
0
0
1
0
0
3
2
2
2
0
0
2
0
0
0
3
1
1
5
1
1
0
0
2
0
0
1
0
0
1
2
3
0
2
0
1
0
0
0
2
0
1
1
0
2
1
0
0
2
0
0
0
1
1
0
2
0
0
1
0
0
2
0
2
2
0
2
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
1
0
2
0
1
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
1
2
0
2
2
0
0
2
0
0
0
0
2
1
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
2
1
0
0
0
0
0
0
4
0
1
1
1
2
0
0
0
1
2
1
0
2
0
0
0
0
0
1
0
0
2
0
1
2
0
3
0
0
0
1
0
2
0
1
0
0
0
0
0
2
0
0
0
2
1
1
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
2
0
3
0
2
1
0
1
0
1
0
0
3
0
0
0
0
1
0
0
2
1
0
1
1
0
0
0
0
0
1
0
1
2
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
3
0
1
0
0
2
0
0
0
0
1
1
2
1
0
0
2
1
1
0
0
0
0
1
0
1
0
0
1
0
0
0
2
2
2
2
2
1
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
1
2
0
2
7
2
0
0
1
0
2
1
2
0
1
0
2
2
0
0
0
0
2
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
1
1
0
3
0
0
0
0
2
0
2
0
1
2
2
2
0
0
0
2
2
0
0
2
1
0
0
1
2
1
2
2
0
2
1
0
2
0
0
1
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
2
1
2
0
0
0
0
2
1
0
0
0
0
0
1
0
0
2
0
2
1
0
0
0
1
1
2
0
0
2
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
2
0
0
0
1
1
2
1
0
0
3
0
0
0
1
1
2
1
1
0
0
0
0
1
0
1
1
0
0
0
2
2
0
0
0
1
0
3
0
1
1
2
1
2
0
0
0
0
0
2
0
2
2
1
0
2
4
0
0
0
0
2
0
1
0
2
0
0
0
2
0
2
0
0
2
0
1
0
0
0
2
0
0
2
0
0
0
1
1
0
3
1
0
1
0
0
0
0
4
0
1
0
1
0
0
0
1
0
0
0
2
0
0
2
0
0
1
0
2
1
1
0
2
1
2
0
2
0
1
0
0
0
0
1
0
0
2
1
0
3
0
0
0
0
0
2
1
2
2
1
0
2
1
0
1
2
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
4
0
0
0
2
2
0
0
1
3
1
1
1
0
1
0
0
2
3
0
0
0
0
0
0
0
0
0
2
5
0
1
0
0
0
0
2
0
0
0
1
0
1
0
1
0
0
0
0
2
0
1
0
0
2
1
0
1
2
0
2
0
0
2
0
0
0
0
0
0
0
0
2
2
1
0
0
2
1
0
0
0
0
0
0
1
0
2
0
2
0
1
1
0
1
0
0
0
0
0
1
0
0
1
1
1
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
1
2
2
0
0
0
0
0
0
1
0
2
0
0
0
1
1
1
1
0
0
1
0
0
0
0
0
1
1
0
0
0
2
1
0
2
1
0
2
2
2
0
2
0
0
2
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
1
2
0
0
0
0
1
1
2
0
2
0
1
0
0
4
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
2
2
0
3
0
0
1
1
2
0
1
1
0
0
0
3
1
0
1
1
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
2
0
1
1
0
0
0
2
0
3
2
0
1
0
1
2
0
1
0
0
2
0
4
0
0
0
3
2
0
0
0
0
0
2
0
0
2
2
0
0
1
2
0
0
0
0
1
0
0
0
2
1
2
0
2
0
0
0
0
0
1
0
0
0
1
0
2
1
0
0
0
0
1
1
0
0
0
0
2
0
0
2
0
6
1
0
0
2
0
0
0
3
0
1
0
1
1
1
2
1
0
0
0
0
0
0
2
0
1
0
0
0
2
1
1
0
0
0
0
1
1
1
0
0
0
2
2
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
2
1
0
0
0
1
1
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
1
1
2
0
1
2
2
0
0
2
0
2
1
2
0
0
0
1
1
0
1
0
0
0
0
2
0
1
0
0
1
3
0
2
0
2
1
0
1
1
0
0
1
1
0
1
0
2
1
3
0
1
0
0
0
0
1
3
0
0
0
1
2
2
0
2
0
0
0
1
0
0
2
1
1
0
0
1
0
0
1
0
2
0
2
0
0
0
2
0
1
0
1
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
1
2
0
1
0
2
0
1
2
1
2
1
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
2
2
0
2
2
1
0
0
2
2
0
2
0
0
0
0
2
0
0
2
0
2
1
2
3
0
2
0
0
0
1
1
0
2
0
0
0
2
0
0
0
1
0
4
1
0
0
2
0
2
2
1
4
0
2
0
0
1
0
0
0
0
3
0
0
0
0
3
0
0
0
0
2
2
0
2
0
0
0
0
1
0
0
0
1
2
2
0
2
2
0
0
2
0
0
2
0
0
0
0
0
0
1
1
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
1
2
0
0
2
1
0
0
2
0
4
2
0
0
2
0
0
0
0
0
1
0
0
2
1
4
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
1
0
2
0
0
0
2
2
0
2
2
0
1
1
0
2
0
0
0
0
2
2
2
0
0
1
0
0
0
2
2
0
0
0
2
0
1
2
1
0
1
0
0
0
1
3
1
0
0
2
0
0
1
0
1
0
0
0
1
1
2
0
1
0
0
0
0
1
2
2
1
2
1
0
0
1
0
0
0
1
0
0
2
0
0
0
1
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
1
1
0
0
2
0
1
0
0
2
1
1
2
0
0
1
1
0
1
1
0
0
0
1
4
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
2
0
1
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
1
1
0
0
0
0
0
0
1
1
4
1
0
1
1
2
0
0
0
1
1
0
1
0
0
2
0
0
0
0
2
2
0
0
1
1
1
6
2
0
0
0
2
1
2
2
0
0
0
0
0
3
0
1
1
3
0
0
0
0
0
3
0
2
0
1
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
2
0
0
0
0
2
1
0
2
0
2
0
0
0
2
0
0
1
0
0
2
1
2
1
1
2
2
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
2
1
0
1
0
2
0
0
0
2
3
0
0
0
2
2
0
2
0
2
2
0
0
2
0
0
0
0
1
0
0
2
2
2
2
1
0
0
0
2
0
0
0
2
0
0
1
0
1
2
0
0
0
0
0
1
1
0
2
2
2
1
1
0
0
0
1
0
1
1
1
2
0
3
2
0
2
1
2
1
0
0
4
0
2
0
0
0
0
0
2
2
0
2
2
0
0
2
0
2
0
1
2
0
0
1
1
1
0
0
0
0
0
2
2
1
0
0
2
0
2
0
0
0
0
2
1
1
2
3
2
0
0
0
1
0
0
0
1
1
0
0
0
2
0
1
2
2
3
0
1
0
2
0
2
2
1
2
0
0
2
1
2
0
2
1
0
1
0
0
0
0
0
2
1
1
0
2
1
0
0
0
0
2
1
2
0
0
0
0
2
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
1
1
0
2
0
0
1
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
1
2
0
1
0
1
0
0
2
0
3
0
2
2
2
0
0
1
1
1
0
1
0
0
0
0
2
1
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
1
1
1
2
5
0
2
0
1
0
1
0
0
1
2
2
0
0
0
0
0
0
0
2
0
0
0
2
1
0
1
0
2
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
1
2
0
0
1
0
2
0
0
2
0
0
0
0
1
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
2
1
2
1
2
0
1
0
0
2
1
0
0
1
0
0
0
0
2
2
2
0
1
2
0
0
3
2
0
1
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
1
1
4
1
0
2
0
2
0
0
0
0
0
2
2
2
0
0
1
1
0
0
0
0
1
1
2
0
0
2
0
2
1
0
0
0
0
0
2
1
1
1
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
2
2
1
0
2
1
1
0
0
0
0
0
1
0
0
2
0
2
0
3
1
0
1
0
2
0
0
0
0
2
1
0
0
2
1
0
0
0
2
1
0
0
0
2
2
1
2
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
2
2
0
0
0
2
0
0
1
1
0
0
0
2
1
3
0
0
1
0
1
1
0
0
2
2
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
1
2
0
0
2
0
0
0
1
0
4
3
0
1
0
0
0
2
0
0
1
0
1
1
2
2
2
0
0
2
1
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
2
1
2
1
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
3
1
1
0
0
0
1
0
0
0
2
1
1
0
1
0
0
2
0
0
1
0
0
2
2
1
2
1
0
2
0
2
0
1
0
2
0
0
0
0
0
1
0
1
1
0
0
1
0
1
1
0
1
2
0
0
0
2
1
0
2
1
0
2
0
0
0
0
0
0
0
0
0
2
1
0
3
0
0
1
0
0
0
2
0
0
0
0
1
1
0
0
2
0
0
1
0
2
2
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
1
1
2
0
0
0
1
1
2
0
0
0
0
2
1
0
0
0
0
1
1
2
0
1
2
2
1
0
0
2
1
2
0
0
0
0
0
1
2
2
0
1
1
7
0
0
0
1
2
0
0
2
2
1
0
0
1
0
0
0
2
0
1
0
3
2
0
0
0
1
0
0
2
1
1
1
0
2
0
0
0
1
1
2
1
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
2
2
0
2
0
0
2
2
0
0
0
1
0
1
0
0
0
1
0
0
1
1
1
2
0
1
0
2
1
2
1
2
0
0
0
0
1
0
0
0
2
0
0
0
1
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
1
2
0
0
1
0
2
0
1
0
2
0
1
1
0
0
2
3
2
2
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
2
0
0
0
0
1
2
1
1
0
2
2
2
2
2
0
0
0
2
0
0
2
0
1
1
0
0
0
1
0
0
0
2
0
2
2
2
0
0
0
1
1
1
2
0
1
0
0
0
0
0
0
2
0
2
1
0
1
2
2
2
2
1
1
0
2
1
2
0
1
0
1
2
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
1
0
1
0
1
2
1
0
0
0
0
1
3
0
2
0
0
1
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
2
1
1
2
1
0
2
0
2
0
0
0
1
2
2
0
0
0
1
0
2
2
2
0
0
0
0
0
2
2
2
2
0
0
2
1
1
0
0
1
2
0
0
1
1
0
0
0
0
2
0
0
1
0
1
0
0
1
0
0
3
0
1
0
0
0
2
0
1
0
2
0
0
0
0
1
1
0
2
0
0
2
1
1
0
0
0
3
0
2
0
0
1
2
0
0
0
0
0
0
0
1
1
2
0
2
0
0
0
0
1
1
3
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
1
0
0
1
2
0
0
0
1
2
2
2
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
1
2
0
4
0
0
2
0
1
0
0
0
1
1
0
0
0
3
0
0
2
0
2
0
0
0
0
2
2
0
0
1
0
0
1
1
0
0
1
0
1
2
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
1
1
0
1
0
0
2
0
1
2
0
0
0
2
5
2
0
0
0
0
0
4
0
1
0
0
0
0
1
1
0
0
1
2
0
1
0
0
1
0
0
2
0
1
1
2
0
0
0
2
0
1
0
0
0
0
1
1
0
0
2
1
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
1
2
0
0
2
0
0
1
0
0
2
0
2
0
0
2
0
2
0
1
0
1
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
1
2
0
0
0
0
0
0
0
0
2
1
0
1
0
2
0
0
1
0
1
3
1
0
2
0
0
0
1
1
0
0
1
0
2
3
0
0
2
0
0
2
1
0
0
0
0
0
0
0
1
0
1
1
2
2
1
1
0
2
0
1
0
0
2
1
2
4
0
1
0
0
0
0
1
0
0
0
3
1
0
2
0
0
2
0
0
2
0
1
0
0
1
2
0
0
1
2
2
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
2
0
0
1
0
0
2
0
0
3
0
3
2
0
0
0
1
0
2
0
1
1
1
0
1
0
0
1
0
0
1
0
0
3
0
2
0
2
0
3
0
4
1
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
2
2
1
1
0
0
1
0
0
0
0
0
0
1
2
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
1
1
3
0
0
1
1
0
0
1
0
0
1
1
0
0
2
1
2
0
0
0
1
2
0
0
0
1
1
0
0
1
0
0
1
1
2
0
2
1
1
0
2
1
0
0
0
0
1
0
0
2
0
0
0
1
1
0
0
0
0
0
2
0
1
0
2
2
1
1
0
1
2
0
1
1
0
2
0
0
1
2
2
0
1
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
5
1
2
0
0
1
0
1
1
2
0
1
1
0
0
1
0
0
1
0
0
0
1
1
1
3
1
1
2
1
0
0
0
1
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
1
2
0
1
2
0
0
1
0
0
0
1
0
2
0
0
0
0
2
0
0
2
0
1
0
0
1
1
1
0
0
2
0
0
2
1
0
2
0
0
0
1
0
1
6
0
0
0
0
0
0
1
0
1
1
2
0
0
1
0
0
1
1
2
1
1
0
0
0
1
0
0
2
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
2
1
0
0
0
0
3
0
0
0
0
2
0
0
0
0
2
0
0
0
1
2
0
0
0
1
2
4
1
0
1
0
0
2
0
1
0
0
0
0
2
0
0
2
0
2
0
0
0
1
0
0
2
0
2
0
0
0
0
2
0
0
0
1
1
0
0
0
2
0
0
2
0
2
0
0
0
0
0
1
0
0
1
0
2
1
1
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
2
0
0
2
2
0
0
0
1
0
0
1
0
2
1
0
0
0
2
1
1
2
0
2
0
0
0
0
0
1
0
0
0
2
2
0
1
0
0
2
1
0
2
0
0
0
0
2
0
0
1
1
1
3
0
0
1
0
0
0
0
2
1
1
1
0
2
0
0
0
2
0
0
0
2
0
0
1
1
0
0
1
2
0
0
1
0
1
0
2
2
0
1
2
0
1
0
0
0
0
0
3
1
0
0
1
0
0
1
2
0
3
1
0
1
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
2
1
0
3
0
2
0
0
0
0
1
3
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
2
1
0
0
0
1
0
1
0
2
0
1
1
2
0
0
0
1
0
1
0
0
0
0
1
0
2
1
0
0
0
1
0
0
1
0
1
2
0
0
0
0
2
0
1
0
0
2
4
0
0
0
1
2
0
0
0
2
0
3
0
1
2
2
0
0
0
0
2
2
2
2
0
0
2
0
1
0
0
1
2
1
2
1
1
0
1
0
0
1
0
1
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
1
0
2
0
2
1
0
0
0
0
0
1
1
2
2
0
0
0
1
1
0
2
0
1
0
1
3
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
2
1
3
0
0
0
1
2
0
0
0
2
2
1
0
0
0
2
0
1
0
0
2
0
1
0
1
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
2
1
0
1
2
0
1
1
1
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
1
0
1
0
2
0
2
0
0
2
1
0
0
0
0
0
0
0
0
3
2
1
0
0
1
0
0
0
1
3
2
1
0
1
0
2
0
0
2
1
1
0
2
0
2
2
1
0
2
0
2
0
0
2
0
1
0
1
0
1
0
0
0
1
0
0
0
0
1
2
1
0
0
1
0
0
1
0
2
0
0
2
1
0
0
2
0
1
0
1
1
0
2
0
1
0
0
2
0
2
0
0
0
0
0
2
0
0
2
0
2
0
0
0
2
2
2
0
0
0
0
0
4
0
0
1
0
0
1
0
1
2
1
0
0
2
0
1
1
2
0
0
0
1
2
2
0
0
0
2
0
0
0
3
2
2
0
1
0
0
0
2
0
0
0
0
1
0
1
0
0
2
0
2
2
2
1
2
0
0
0
0
0
0
0
1
2
2
0
1
2
0
1
0
0
1
1
2
1
3
0
2
1
2
1
1
2
0
2
0
0
3
0
1
2
0
2
0
2
1
1
0
0
2
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
1
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
1
0
2
0
1
0
0
0
2
1
0
0
2
0
0
1
2
0
0
1
1
3
0
0
1
2
0
1
0
1
0
0
1
0
2
0
1
1
0
1
0
2
1
0
0
1
0
0
2
1
0
0
0
0
0
0
1
2
0
0
1
0
2
2
1
1
1
1
0
0
1
0
0
0
1
0
0
1
0
1
2
0
0
0
1
1
2
0
1
0
0
0
0
0
1
0
1
2
0
0
1
0
0
2
0
1
1
1
0
1
0
0
2
0
0
1
0
3
1
0
2
2
0
0
0
0
0
0
2
1
0
0
0
1
0
2
0
0
0
1
1
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
1
0
0
1
0
0
0
0
1
2
1
1
0
1
0
0
0
0
1
2
0
1
0
1
0
1
1
0
1
1
0
2
0
1
0
0
2
0
0
2
2
1
1
3
2
2
1
0
0
0
0
0
0
0
0
1
1
0
2
0
1
0
2
2
0
2
0
2
0
1
0
1
0
1
3
0
2
0
1
1
2
0
1
3
0
0
0
2
2
0
2
1
1
1
0
0
0
0
2
0
2
0
2
0
0
1
0
0
0
0
2
3
2
0
1
0
0
2
1
2
0
0
0
0
0
2
0
2
0
0
0
0
2
1
0
0
0
1
0
0
2
0
0
0
2
0
0
1
0
0
1
0
0
0
2
1
2
3
2
2
2
0
0
1
1
0
2
2
0
0
1
2
2
1
0
2
0
0
0
3
0
0
3
0
0
2
0
2
0
0
0
1
0
1
0
2
0
2
0
1
1
1
0
2
1
0
0
0
0
1
0
0
1
0
1
2
0
0
0
0
2
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
2
0
1
0
1
0
0
0
2
2
0
1
0
3
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
1
1
0
0
0
0
0
1
1
1
0
0
1
0
0
0
1
0
0
4
2
0
1
1
1
0
2
3
0
0
0
0
0
0
0
1
2
0
0
2
2
1
1
0
0
0
0
2
0
1
2
0
0
0
0
2
0
0
0
7
0
0
0
2
0
1
1
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
1
0
2
0
0
0
2
0
1
3
0
2
2
2
1
0
0
2
0
0
1
2
1
1
1
0
1
1
1
2
0
0
1
0
4
0
0
2
0
0
2
0
0
2
1
0
2
2
0
1
0
1
2
0
1
2
0
0
1
0
0
0
0
0
1
3
0
2
0
0
0
0
2
0
1
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
1
0
1
1
0
0
0
2
0
0
2
0
0
0
0
1
0
0
2
2
0
0
1
1
2
0
1
0
0
2
1
1
0
2
0
1
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
1
1
1
0
0
1
1
1
1
0
2
0
7
0
0
0
1
0
0
3
0
0
2
0
1
0
2
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
1
1
0
1
2
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
1
0
2
2
0
0
2
2
0
0
1
2
0
1
0
0
3
1
0
0
0
0
0
2
1
0
0
0
0
0
0
2
1
1
0
2
2
0
1
1
0
0
0
1
0
0
1
1
0
1
0
0
1
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
1
0
1
1
0
2
0
0
2
2
0
1
0
0
2
0
1
0
1
0
2
0
0
1
0
0
2
2
1
3
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
1
0
2
0
1
0
1
0
2
2
0
0
0
1
1
0
2
2
2
0
0
1
0
0
1
2
2
0
0
0
1
0
2
1
2
2
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
1
0
0
0
0
2
0
1
1
1
0
1
2
1
0
1
0
2
0
0
2
2
0
0
0
5
0
2
0
0
2
2
0
2
0
0
1
0
0
0
0
3
2
1
0
2
2
0
0
2
0
0
0
0
0
1
0
2
0
2
0
2
3
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
2
0
1
1
1
0
0
0
1
2
0
0
0
2
0
1
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
1
2
0
0
2
0
2
0
0
1
0
1
0
0
0
2
0
0
0
0
2
0
0
1
0
0
1
9
1
1
0
2
0
1
1
1
1
0
0
0
2
2
0
1
0
0
0
0
0
0
1
0
1
2
1
0
0
0
0
2
0
1
0
1
0
1
0
0
1
0
0
1
0
0
0
2
1
0
4
0
0
2
0
2
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
2
0
2
0
0
2
0
0
0
1
0
1
1
1
0
0
2
1
0
0
1
2
2
0
0
0
0
0
2
0
2
0
0
1
1
0
0
0
0
2
2
0
0
2
0
1
2
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
2
1
2
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
1
1
0
1
1
2
1
0
0
2
3
1
0
2
0
1
0
0
6
0
0
2
0
0
0
1
1
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
1
1
0
2
2
2
2
2
1
0
2
0
0
1
0
0
0
1
0
0
0
2
1
1
0
0
2
0
0
0
0
2
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
1
2
0
1
0
0
0
0
0
0
0
0
2
0
0
2
2
1
2
0
0
0
1
2
1
2
0
6
1
0
0
0
0
0
1
0
3
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
1
1
0
0
0
1
1
0
1
0
1
1
0
1
0
0
0
1
1
0
0
0
2
0
0
0
1
0
1
0
0
0
0
2
0
1
2
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
2
1
1
3
2
0
0
0
2
0
0
0
2
1
0
0
2
1
0
1
3
1
0
2
2
1
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
2
0
1
1
2
0
2
0
2
0
1
0
0
2
0
1
1
4
2
0
0
2
0
0
0
1
0
0
0
2
2
1
3
0
0
1
1
1
0
0
0
0
0
0
0
2
1
0
2
1
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
2
2
2
1
0
0
0
2
2
1
0
2
0
0
1
2
0
0
3
0
2
0
1
2
0
2
0
0
0
1
0
0
0
2
0
2
1
0
0
0
1
2
0
0
2
0
0
1
0
1
1
0
0
0
1
1
1
2
0
0
0
2
2
0
0
0
0
2
0
1
0
2
0
0
2
2
1
2
0
0
0
3
0
0
0
1
2
0
0
0
2
2
2
1
0
1
1
0
0
1
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
1
0
2
2
0
2
0
0
0
2
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
1
2
1
0
0
0
2
0
0
1
0
0
1
2
0
1
2
0
0
0
2
0
1
0
2
0
0
2
1
0
0
0
1
1
0
2
2
0
0
0
2
0
0
1
1
0
0
0
1
2
0
2
0
0
2
1
0
0
0
1
0
0
0
1
0
0
0
2
3
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
1
4
1
2
1
0
1
0
2
0
0
1
1
0
0
0
0
1
1
0
0
3
0
0
1
0
1
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
1
0
2
2
0
1
0
1
0
0
0
0
0
0
1
0
4
0
2
2
0
1
3
0
0
0
1
1
2
2
1
1
4
0
1
0
0
0
0
0
1
1
0
0
1
2
0
0
1
1
2
0
0
0
0
0
0
2
2
1
0
1
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
1
1
1
0
0
0
0
0
0
2
0
0
1
1
0
2
1
0
1
2
0
0
0
2
0
0
0
0
1
2
0
2
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
1
0
2
1
1
0
0
2
0
0
0
0
1
2
0
0
0
1
0
0
0
0
1
0
0
0
2
2
0
0
1
0
2
0
1
1
0
2
0
1
0
0
1
0
1
0
0
2
2
0
0
0
2
0
0
0
2
2
1
1
0
1
0
2
0
0
3
1
0
2
0
0
0
0
0
1
2
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
1
0
0
2
0
2
0
0
2
0
0
0
0
0
1
0
1
2
0
0
0
0
1
1
1
0
0
1
1
0
0
0
0
2
1
0
1
2
0
0
2
0
0
1
1
0
1
0
1
1
2
1
0
0
0
0
1
0
0
0
2
0
0
5
0
0
2
0
0
1
0
2
2
1
0
0
1
1
2
4
1
0
0
1
0
1
2
0
0
0
0
1
0
0
0
0
2
2
1
0
1
2
1
0
0
0
0
1
0
1
3
1
1
0
1
1
2
0
0
2
2
2
0
3
1
0
0
0
1
2
2
1
0
1
2
0
0
2
2
2
0
2
0
0
1
0
0
2
0
0
3
0
1
2
2
6
0
1
0
0
0
2
1
1
0
1
0
2
1
2
1
0
2
1
0
1
0
0
0
0
0
1
0
1
2
0
1
0
0
0
0
1
0
0
2
0
1
0
0
1
0
1
1
0
2
1
2
0
2
1
0
1
0
0
3
0
0
0
0
0
0
1
2
0
0
0
1
1
2
2
2
1
0
2
0
0
0
2
0
0
2
0
0
0
2
1
1
2
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
1
1
0
0
0
2
1
0
1
1
0
0
1
3
1
0
0
0
0
1
0
4
2
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
1
2
1
0
0
0
0
1
0
0
0
0
2
0
1
1
0
0
2
2
1
0
1
2
2
1
0
1
1
0
3
0
0
0
2
0
0
0
0
1
1
2
2
0
0
0
0
1
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
1
1
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
2
1
2
2
1
7
0
0
0
1
0
0
1
1
0
0
1
0
1
0
0
0
0
2
0
2
1
0
1
2
0
0
2
0
0
1
1
1
0
1
2
0
0
1
0
2
2
0
2
1
2
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
1
2
1
0
0
1
0
0
2
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
1
0
0
2
3
0
0
2
1
4
0
0
0
0
2
0
1
1
0
0
0
2
3
1
0
0
1
1
0
0
2
0
2
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
2
0
2
2
2
1
2
1
1
2
0
1
1
1
2
0
0
0
1
1
0
0
0
0
0
0
2
0
1
3
1
1
1
0
0
2
0
0
0
0
0
0
2
2
0
0
2
0
0
1
2
0
2
0
0
0
0
0
2
2
0
2
2
0
0
1
0
2
0
0
0
3
0
1
0
0
0
2
1
2
0
0
1
1
1
2
1
0
0
1
2
2
0
0
0
0
0
0
0
1
1
1
2
0
1
1
2
0
0
2
2
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
1
1
0
0
0
3
0
0
1
1
0
0
0
2
1
0
2
1
0
2
0
0
0
0
2
1
0
0
0
0
0
1
4
1
2
1
0
0
0
0
2
1
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
1
1
0
1
0
2
4
0
0
1
1
0
0
0
0
1
1
1
1
0
0
0
0
0
0
1
3
0
0
0
0
0
1
0
0
0
1
1
5
2
0
1
1
1
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
2
1
1
0
3
0
1
0
0
0
0
1
1
0
1
0
0
0
1
2
1
0
1
0
0
1
1
0
2
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
1
1
3
0
0
4
1
0
0
2
1
0
0
0
1
1
0
0
0
0
0
1
1
0
0
1
1
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
1
2
1
1
1
1
0
2
0
0
3
0
0
2
0
0
2
2
0
0
0
1
0
2
0
1
2
2
1
0
1
0
4
0
0
3
0
0
3
1
0
0
1
1
0
1
0
2
0
2
0
0
2
2
2
2
1
1
1
0
0
2
0
0
2
0
0
0
0
0
1
0
2
2
0
2
1
0
2
0
2
0
0
0
1
0
1
0
2
0
2
1
2
0
0
0
0
0
1
0
0
2
0
0
2
0
2
0
0
0
3
0
0
1
0
0
1
0
0
0
3
1
2
1
0
0
2
2
2
0
1
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
1
0
2
0
0
1
1
0
2
0
2
2
0
0
0
0
0
0
0
1
0
2
2
2
0
0
1
2
1
1
0
1
0
2
0
2
0
0
0
1
0
1
0
3
1
1
0
0
2
1
1
2
0
1
1
0
1
1
1
2
2
1
0
0
3
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
2
1
2
1
2
1
0
0
0
1
2
0
0
0
0
7
0
0
0
0
1
0
4
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
2
0
1
0
1
0
0
2
1
2
0
0
2
0
0
2
1
0
0
1
0
2
0
0
0
0
2
2
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
3
1
0
0
0
0
0
0
0
3
2
0
0
0
0
1
0
2
0
0
2
0
0
0
2
1
0
2
0
0
1
0
2
0
0
0
1
0
2
0
1
0
1
0
0
0
1
1
0
0
0
2
0
0
0
0
0
2
2
0
2
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
1
0
1
1
0
0
0
0
2
0
0
0
2
0
2
2
0
2
0
0
0
0
1
1
2
1
0
2
0
0
0
0
0
0
1
0
1
0
0
2
2
0
0
0
1
2
2
0
0
0
0
1
2
1
1
0
2
0
0
2
0
0
2
2
0
1
2
1
0
0
0
0
1
2
2
0
0
0
1
2
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
2
0
0
0
0
0
2
2
0
3
0
1
0
0
0
0
0
2
2
0
1
0
0
0
0
1
1
0
0
0
0
0
0
2
2
1
0
1
0
0
0
0
0
0
1
0
1
1
1
1
0
3
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
4
0
0
0
2
0
0
2
2
2
0
4
0
0
1
0
0
0
1
1
1
1
0
0
0
3
2
2
0
0
0
1
0
0
1
1
2
0
0
0
0
0
0
2
2
0
4
2
0
0
0
1
2
2
3
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
2
1
2
3
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
2
0
1
0
1
0
2
0
0
0
2
1
0
0
0
0
1
1
1
0
1
0
0
1
0
1
2
1
0
0
0
2
1
1
0
1
1
1
0
0
0
0
0
2
0
0
0
2
0
0
2
2
0
0
1
0
2
0
1
0
0
1
0
0
0
1
0
0
1
2
1
0
0
2
0
0
0
0
2
0
0
0
0
0
4
0
1
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
2
0
0
2
0
0
2
1
0
0
0
1
1
1
2
0
1
0
0
1
0
0
1
2
0
0
1
0
0
1
0
2
2
0
0
0
1
0
2
1
0
0
0
0
2
2
2
0
0
2
0
0
0
0
2
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
1
0
0
1
0
0
2
1
0
3
0
2
0
0
0
0
1
1
1
0
0
3
0
0
2
0
0
0
0
0
1
2
0
5
1
0
0
0
3
1
1
0
0
1
1
2
0
0
1
0
1
0
0
0
2
1
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
1
1
1
1
0
2
1
0
0
1
0
1
0
1
1
4
2
0
0
0
0
1
1
2
0
0
1
1
0
0
0
0
1
2
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
2
1
2
1
0
0
2
0
0
0
0
2
0
0
1
2
1
0
0
0
0
1
2
1
0
0
3
1
1
2
0
0
0
2
0
0
0
1
0
0
1
0
0
1
3
3
4
0
0
0
0
2
2
2
1
0
1
1
2
1
0
0
0
2
0
0
0
0
2
0
0
2
0
2
0
2
1
2
0
2
0
0
0
1
2
1
1
0
1
0
0
1
0
1
0
0
2
1
2
0
0
7
2
0
0
1
0
1
0
0
0
0
1
0
1
2
0
0
0
1
0
0
0
1
0
0
1
1
0
0
2
1
2
0
0
1
0
0
1
2
0
0
2
0
0
0
1
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
1
0
2
2
0
0
0
0
2
0
0
0
0
1
0
1
0
2
0
0
0
1
1
1
0
0
3
0
0
0
0
2
0
0
0
2
0
0
0
1
0
2
1
1
0
0
0
1
1
0
1
1
0
0
0
0
1
0
0
0
3
0
0
1
1
1
1
0
0
0
1
0
2
0
1
1
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
1
2
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
1
2
1
2
2
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
3
0
1
0
1
2
0
0
1
2
2
1
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
2
0
0
1
1
0
0
0
2
2
2
0
2
1
0
0
0
0
2
0
0
0
2
0
2
0
0
2
0
2
2
0
2
0
0
0
0
0
3
2
0
0
0
0
0
0
0
2
0
0
1
2
2
0
0
0
1
1
0
1
0
0
0
0
2
0
1
1
0
0
0
0
1
2
2
0
0
1
2
1
2
2
0
2
0
0
2
1
0
0
0
0
0
1
0
0
0
2
2
0
0
1
0
1
0
1
1
0
0
0
0
0
1
2
0
0
1
1
2
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
2
0
1
0
1
2
2
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
1
0
1
0
2
0
0
1
0
0
0
0
0
0
1
0
0
2
0
1
1
0
0
2
0
1
0
2
1
2
0
2
1
0
0
0
0
0
0
1
0
3
1
0
2
3
0
0
1
2
0
0
1
0
0
0
2
1
0
0
0
0
0
0
1
0
0
4
1
2
0
1
1
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
3
0
2
0
1
0
1
0
0
0
1
0
0
1
1
1
0
0
2
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
2
0
2
2
0
0
0
1
2
0
0
0
0
1
0
1
0
0
0
0
2
2
0
0
0
0
2
0
1
0
0
0
2
1
2
0
0
0
0
0
0
1
1
0
0
0
0
0
2
2
0
0
2
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
1
2
0
1
0
0
2
0
2
0
0
2
0
0
0
1
2
0
1
1
2
1
0
0
1
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
2
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
2
0
0
3
2
0
0
1
2
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
2
0
2
0
0
0
0
0
1
0
1
3
0
0
0
0
2
2
0
1
0
0
0
1
0
0
1
0
0
0
2
0
0
0
1
1
1
0
0
0
0
0
1
1
0
1
0
0
2
0
0
0
0
1
0
2
0
0
1
0
0
1
0
0
1
2
0
3
1
2
1
1
1
2
0
0
0
2
0
3
0
0
0
0
0
1
0
1
2
1
0
2
0
0
1
1
0
0
0
1
0
1
1
2
1
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
1
0
1
0
1
2
0
0
2
1
0
0
0
1
0
0
0
2
0
8
0
0
0
0
0
0
0
2
0
2
2
2
1
0
0
1
0
4
4
2
0
0
0
2
3
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
2
2
0
0
1
0
1
0
1
2
0
1
0
1
0
2
2
0
2
0
0
0
2
0
0
1
0
0
0
2
2
1
0
1
1
0
2
0
2
0
0
0
0
0
2
0
2
0
0
0
1
2
2
0
2
0
0
2
3
1
0
0
1
0
1
0
1
0
1
0
0
1
4
0
0
5
0
0
0
0
2
0
0
5
1
1
2
2
0
2
1
3
0
0
2
1
2
0
0
1
0
0
1
2
0
0
1
2
1
2
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
5
0
0
1
0
0
0
1
0
2
2
1
1
0
0
2
0
0
0
1
1
0
0
0
0
0
0
1
2
0
0
1
1
1
1
0
0
2
0
0
1
0
0
3
0
0
2
0
2
2
0
0
0
0
0
2
0
0
2
2
0
0
2
2
3
1
2
0
2
0
1
2
2
2
1
0
2
0
0
1
3
2
0
2
0
1
0
0
2
0
1
1
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
2
0
0
1
0
1
1
1
0
2
2
3
0
1
2
3
1
2
2
0
0
0
0
1
2
0
1
0
0
2
0
0
1
0
0
0
2
0
0
5
1
0
0
1
1
0
2
0
0
0
0
0
0
0
1
0
1
0
9
0
0
0
1
0
0
0
0
1
2
0
1
0
1
2
1
2
0
0
2
1
1
1
2
1
1
3
0
1
3
0
0
1
0
0
0
2
1
0
1
0
0
0
0
0
2
0
3
0
0
0
1
0
0
0
0
0
1
0
0
2
5
0
0
0
1
1
0
0
0
2
2
1
2
0
2
1
2
0
2
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
3
0
0
0
0
2
1
0
2
2
0
1
2
1
0
0
0
1
2
3
0
2
0
0
1
0
0
0
0
3
5
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
2
0
1
2
1
0
0
2
0
0
1
1
2
0
0
0
0
0
1
1
1
3
1
2
2
0
0
0
3
1
1
1
2
1
1
1
2
0
2
1
3
1
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
1
0
0
1
0
0
1
1
0
1
2
0
1
1
0
1
1
1
2
0
0
1
0
1
0
0
0
1
2
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
2
1
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
1
2
0
2
0
1
1
2
0
0
1
0
0
0
0
1
1
0
0
0
5
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
4
2
2
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
1
0
2
0
1
1
1
1
3
0
0
0
0
0
0
2
2
0
2
0
0
2
2
2
0
1
2
0
0
0
0
0
0
0
2
0
0
2
2
2
0
2
0
0
0
2
1
1
0
0
2
0
0
0
1
0
1
0
1
0
0
1
1
2
0
0
1
0
1
0
0
0
0
1
0
1
1
2
0
0
1
2
1
1
0
0
0
3
0
1
0
0
1
2
1
0
2
1
3
1
0
0
0
1
1
1
0
2
0
1
1
0
0
0
0
1
1
3
0
2
0
0
2
0
0
1
2
2
0
0
0
1
2
0
1
0
0
1
1
0
0
0
3
2
0
0
1
0
0
0
1
2
0
7
1
0
1
0
2
0
0
0
0
0
2
0
0
0
0
2
2
1
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
2
2
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
1
1
0
0
0
0
0
2
3
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
2
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
2
0
0
1
1
3
1
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
1
1
2
0
0
1
0
1
2
0
2
2
0
1
1
0
0
1
0
1
2
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
2
1
2
0
0
1
0
4
2
2
1
2
0
0
4
1
2
0
0
0
1
0
0
2
0
0
0
2
0
0
1
2
0
1
0
0
1
3
0
2
0
0
0
1
0
0
3
0
0
1
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
1
0
1
1
0
1
0
1
0
0
1
2
0
0
0
0
1
1
0
0
2
2
0
1
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
2
2
2
0
0
1
0
0
0
0
0
3
3
2
3
0
1
1
2
3
0
2
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
2
4
0
2
1
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
2
2
3
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
2
4
0
0
0
1
0
0
1
2
0
0
0
0
0
0
2
0
2
0
1
0
0
0
1
1
0
1
0
2
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
2
1
0
0
2
0
0
2
1
1
0
1
2
0
0
0
0
1
2
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
2
0
3
2
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
1
2
0
2
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
2
0
0
0
1
6
1
1
1
1
0
0
0
1
0
1
0
1
0
0
0
0
0
1
2
0
0
0
0
2
0
0
3
0
0
1
0
1
1
0
0
0
0
0
0
1
1
0
2
2
0
1
2
1
0
1
0
0
0
0
0
2
0
1
0
0
0
1
0
2
0
2
0
0
0
2
0
2
0
0
0
7
1
0
0
2
0
0
0
2
0
2
2
0
0
0
0
2
1
0
0
0
0
0
2
1
2
3
0
0
0
2
1
0
0
0
0
0
0
2
2
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
1
1
0
2
0
2
0
0
2
0
2
0
1
0
0
2
0
3
1
2
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
1
1
0
2
0
3
0
0
0
0
0
1
1
0
1
0
0
0
2
0
2
2
0
2
0
1
0
0
0
0
0
0
0
2
0
2
1
2
1
1
0
1
1
0
1
1
0
0
0
0
0
1
2
0
1
0
0
0
1
0
1
0
0
0
2
0
2
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
2
1
0
0
0
1
0
1
0
0
0
2
1
0
2
2
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
2
0
2
2
0
2
0
2
0
0
1
0
0
1
0
0
1
1
1
1
0
0
2
2
1
2
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
1
1
0
2
0
0
0
0
0
2
0
0
0
2
0
1
0
1
0
2
0
0
0
0
0
0
1
0
0
1
1
0
1
0
1
0
0
0
0
0
0
1
1
1
0
2
1
0
2
0
1
0
1
0
0
0
1
0
2
0
2
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
2
0
2
2
0
0
0
0
0
2
3
3
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
2
0
2
0
0
1
1
2
2
0
0
1
0
0
2
2
0
2
2
2
0
2
0
0
1
0
0
2
1
3
0
0
0
0
0
0
2
2
1
2
2
0
2
0
0
0
1
0
0
1
2
2
0
0
1
1
0
0
2
0
2
2
1
2
2
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
2
2
2
0
0
1
1
0
1
1
0
0
1
0
1
0
0
0
1
0
0
1
1
3
0
0
0
2
2
1
0
1
0
1
0
0
1
1
0
0
0
1
4
0
0
1
0
1
2
0
1
4
0
1
1
0
0
0
1
2
0
0
1
3
2
2
1
0
1
2
1
0
0
2
0
0
2
0
0
1
1
0
2
0
2
1
0
1
0
0
2
1
0
0
3
2
1
2
2
0
0
0
0
0
1
1
0
1
0
4
0
0
0
2
0
0
0
0
0
0
2
0
0
1
1
0
1
0
1
2
1
1
0
1
0
1
0
1
2
1
0
2
0
0
0
0
1
0
1
1
1
0
0
0
0
2
0
0
2
2
0
0
2
1
0
2
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
1
2
0
0
1
0
2
0
0
1
0
0
0
3
0
2
0
0
1
0
2
0
1
1
0
0
0
1
2
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
2
1
0
0
0
2
0
0
0
0
2
0
0
0
0
1
2
0
1
2
1
0
1
0
0
1
1
0
1
3
1
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
1
0
2
0
0
2
1
0
1
2
0
1
0
0
0
0
0
0
0
3
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
2
0
0
1
0
0
0
0
3
1
0
0
3
0
1
0
0
1
0
4
0
2
0
0
0
0
0
0
0
2
0
1
2
0
0
0
1
0
2
0
3
1
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
1
2
1
0
0
7
0
1
0
0
0
0
0
2
2
0
0
1
2
0
0
0
0
1
1
0
1
0
1
0
0
1
0
1
2
0
0
0
0
1
0
1
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
3
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
2
2
0
0
0
0
0
2
0
2
0
2
2
2
0
0
0
0
0
2
0
2
1
0
2
0
0
2
1
2
0
0
1
0
0
1
0
0
0
1
0
1
1
0
0
0
0
2
0
0
0
0
2
0
2
3
1
0
0
0
0
0
0
0
1
2
1
2
0
0
0
0
0
0
1
1
0
0
1
0
0
2
2
2
0
1
0
1
0
0
0
2
0
0
2
0
3
2
0
1
1
0
0
0
2
0
0
2
2
0
0
0
0
2
0
0
0
0
2
2
2
1
0
1
2
1
2
1
0
1
0
2
1
1
0
0
0
1
0
2
0
1
1
1
0
0
4
0
0
2
0
2
2
0
0
0
3
2
0
1
2
0
0
0
0
2
1
0
0
2
0
2
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
1
0
1
0
0
2
0
0
1
0
2
0
0
0
0
1
1
1
0
1
0
0
0
1
0
0
2
0
0
1
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
2
1
1
0
0
2
2
0
2
0
1
1
0
0
2
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
2
2
1
0
0
0
0
0
0
0
1
0
0
3
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
1
2
0
1
0
0
0
2
2
0
0
1
1
0
1
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
3
0
0
0
2
2
0
0
1
2
0
0
0
2
0
1
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
2
0
0
2
2
1
2
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
2
0
1
0
4
0
0
0
3
1
0
0
0
0
0
2
1
1
0
0
0
1
4
0
1
1
0
0
0
0
4
0
1
1
0
0
0
2
0
2
0
1
1
0
1
1
1
1
0
0
2
0
0
1
2
1
1
1
1
0
0
0
0
2
3
1
2
0
1
0
1
0
0
0
0
2
1
0
2
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
2
0
1
2
1
0
0
0
0
0
1
2
1
3
2
2
2
0
0
2
0
0
0
0
2
0
0
2
2
2
2
0
0
0
0
7
2
0
0
0
0
0
1
1
1
0
0
0
0
2
1
2
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
1
0
2
0
1
0
2
2
0
0
0
0
1
0
0
0
1
0
2
1
2
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
2
0
2
3
0
0
1
0
0
0
0
0
3
0
0
1
0
0
0
0
6
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
1
1
0
2
2
1
0
2
0
2
2
0
0
0
0
0
0
2
2
0
0
0
3
0
0
0
2
1
0
0
0
0
1
0
0
2
2
0
0
1
1
0
0
2
2
0
0
1
2
0
2
2
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
1
1
0
1
0
0
0
3
0
1
0
2
0
0
0
1
0
1
0
2
0
1
0
0
3
0
0
0
2
0
0
0
1
1
1
2
0
0
0
0
0
0
0
0
0
2
2
2
0
2
0
0
1
2
1
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
2
1
0
1
1
0
1
2
2
0
2
0
1
0
2
1
0
0
0
0
1
2
4
0
1
0
0
0
0
0
1
0
0
0
2
2
2
0
0
0
1
0
0
0
0
2
1
2
2
0
0
2
0
0
1
1
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
1
1
1
0
1
0
1
0
1
0
2
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
1
3
0
0
1
0
1
0
1
0
0
2
2
1
0
0
2
0
1
2
1
0
0
1
0
0
2
1
0
1
1
0
0
0
0
2
0
1
0
4
0
0
0
2
1
3
0
0
0
0
0
1
0
1
0
1
0
0
1
1
0
2
0
1
0
1
0
3
2
2
2
0
0
1
1
0
0
1
0
0
2
1
0
1
0
1
0
1
0
3
0
2
0
0
1
0
3
0
0
0
1
0
0
0
0
0
1
2
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
2
2
0
1
0
0
1
1
2
0
0
1
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
2
1
1
1
0
0
0
0
1
3
2
0
1
1
0
0
0
1
2
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
2
0
2
2
1
1
1
0
2
0
0
0
1
2
0
3
0
0
0
0
0
2
3
1
0
0
0
1
0
0
2
0
0
0
0
1
0
0
1
2
1
2
0
1
0
1
0
0
0
1
2
2
1
0
0
0
1
2
2
0
1
0
1
0
0
0
0
1
0
2
0
1
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
2
0
0
0
0
1
0
2
2
2
3
2
0
0
0
0
2
2
0
0
1
0
2
1
2
1
1
0
0
0
0
0
1
1
2
0
0
0
1
0
1
0
1
0
2
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
2
0
0
0
1
1
1
0
0
0
0
1
0
0
1
2
0
0
1
0
0
1
1
0
2
0
0
0
0
0
2
2
0
1
0
0
0
0
1
0
2
0
0
1
1
1
0
0
0
2
0
4
0
0
2
0
0
1
0
2
0
3
0
0
0
1
1
0
2
1
2
0
0
2
1
2
0
0
0
1
1
0
1
0
0
0
2
0
0
0
0
1
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
3
1
0
2
0
0
2
0
0
0
0
1
2
0
0
2
0
2
1
2
0
2
0
0
2
1
0
0
1
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
2
2
1
0
1
0
0
2
0
0
1
0
1
1
2
0
2
0
0
0
0
1
0
0
0
0
1
4
0
2
0
1
1
0
2
0
0
1
0
1
2
0
1
2
2
0
1
0
0
0
1
4
2
2
0
3
0
0
2
0
1
2
0
0
0
2
0
0
0
0
1
1
2
0
0
1
2
1
2
0
2
0
0
0
0
2
1
1
0
1
1
0
2
3
0
0
0
1
1
3
0
1
0
2
2
1
2
2
0
1
1
1
0
0
1
2
2
1
0
0
2
0
0
1
2
0
0
0
2
2
0
4
0
1
1
2
0
0
1
1
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
2
2
0
0
0
2
2
0
1
0
0
2
0
1
1
0
0
0
1
0
0
1
1
1
1
0
0
0
2
1
0
0
0
1
0
0
1
0
0
0
0
0
1
1
1
2
2
0
0
0
0
0
1
0
0
1
2
1
2
0
1
1
0
2
0
2
1
0
0
0
1
0
0
3
2
0
0
0
1
0
0
0
1
1
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
1
1
0
0
1
1
0
0
1
1
2
0
1
1
0
2
0
2
0
0
0
0
0
0
1
1
1
0
0
0
0
2
0
2
2
2
1
0
0
2
1
0
1
0
0
2
1
0
0
1
0
0
2
0
3
0
0
0
1
3
0
1
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
1
0
1
1
2
0
0
2
0
1
1
2
2
2
0
0
3
1
0
2
0
0
2
0
1
1
0
0
1
0
2
1
2
1
1
0
0
0
0
1
0
0
0
1
0
0
2
1
0
2
1
0
1
1
1
1
2
1
0
0
0
1
0
1
0
0
2
0
0
0
0
0
2
0
0
2
2
2
1
0
0
0
0
0
0
1
0
2
1
0
0
0
2
2
0
0
0
2
2
0
2
0
0
2
0
0
0
0
2
2
0
3
1
0
1
2
0
1
3
0
0
0
1
0
0
0
1
2
2
0
0
0
0
0
1
1
0
0
0
2
1
1
0
2
0
1
0
2
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
1
0
1
1
2
0
0
0
0
2
1
0
2
0
0
0
0
2
0
3
0
0
0
0
3
1
1
0
0
0
1
0
1
1
0
0
1
1
0
0
2
1
0
2
1
0
2
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
2
0
0
3
2
1
1
0
0
1
2
2
1
0
0
2
2
0
0
0
0
0
2
2
0
0
1
0
2
0
0
1
0
0
1
0
0
0
2
1
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
3
0
2
2
0
0
0
0
1
2
0
0
0
0
1
1
0
0
0
0
0
0
1
0
3
0
0
2
0
1
0
0
0
0
1
2
0
0
0
0
1
2
0
2
0
2
2
0
0
1
0
1
4
2
0
0
2
1
0
0
1
0
1
1
0
2
0
0
0
1
0
0
1
2
0
2
0
1
3
0
0
1
0
0
0
0
0
2
0
2
0
1
1
0
2
2
0
0
0
5
0
0
0
0
0
2
2
0
2
2
0
0
0
0
1
0
2
0
2
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
2
2
0
1
0
0
0
0
1
1
0
2
5
1
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
1
1
0
2
0
0
0
0
0
1
1
0
1
1
0
2
0
1
0
0
1
0
2
1
0
1
1
1
1
0
1
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
1
0
0
0
2
1
0
2
1
0
2
3
2
0
0
0
2
2
0
3
0
1
0
0
1
0
0
0
0
2
0
0
1
1
0
0
1
1
0
0
0
2
0
2
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
1
0
0
2
0
2
0
2
0
3
1
0
2
1
1
0
0
0
0
2
0
1
2
0
0
2
0
0
1
0
1
2
3
1
1
0
0
1
1
0
0
0
1
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
1
1
0
1
1
0
0
0
0
2
1
2
0
0
0
0
2
0
0
0
0
1
0
0
0
3
0
1
1
1
2
1
2
0
0
0
0
0
0
1
1
2
0
2
0
2
1
0
1
0
2
1
0
2
1
1
2
0
1
0
1
0
2
0
1
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
3
0
0
0
1
0
0
0
2
0
0
3
1
0
1
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
1
0
1
1
0
2
0
0
0
0
1
0
0
0
1
0
1
8
0
2
1
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
1
0
0
0
2
1
1
0
1
0
1
2
0
2
2
0
2
0
2
0
1
2
0
0
0
2
0
1
1
0
0
0
1
0
0
0
0
1
1
0
2
0
0
1
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
1
1
0
0
0
0
2
0
0
2
2
5
0
0
0
0
1
0
0
1
0
0
1
0
1
2
0
0
0
0
2
0
0
0
1
2
0
0
2
1
0
1
0
1
0
0
1
1
1
1
0
1
0
0
0
0
0
1
0
0
2
1
2
1
2
0
0
1
0
0
1
1
2
1
3
2
0
2
0
0
0
0
0
0
0
1
0
0
0
1
2
1
2
0
0
2
0
2
0
0
0
0
0
2
0
2
1
0
0
1
0
0
4
3
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
2
0
1
0
1
1
1
0
1
1
0
2
0
0
0
0
1
2
2
1
1
1
2
0
0
1
0
0
0
2
0
3
2
2
0
2
0
0
0
2
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
1
0
1
1
3
0
1
0
1
2
0
1
1
1
0
1
2
0
0
0
1
0
0
0
0
0
2
0
0
3
0
0
1
0
0
0
2
1
0
0
1
0
1
0
0
2
0
0
1
3
2
0
0
1
2
0
1
0
1
0
0
0
1
2
1
0
2
0
1
0
0
4
2
0
2
1
0
2
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
2
1
0
0
0
2
4
1
0
1
1
1
3
0
1
0
2
0
0
0
2
0
4
0
0
0
0
0
2
3
1
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
1
0
0
0
2
1
2
1
0
0
0
2
1
0
0
0
2
1
0
1
2
0
2
1
0
0
2
2
1
1
0
0
0
0
2
1
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
2
0
0
1
1
2
0
0
0
2
2
1
0
2
3
0
1
1
0
0
1
2
0
0
1
0
3
0
0
3
0
0
1
0
0
3
0
1
2
0
0
0
0
1
0
1
0
0
0
0
2
0
1
1
0
0
1
0
3
0
0
0
0
0
3
2
8
1
0
2
1
0
0
0
1
0
0
0
0
0
2
0
0
0
2
1
1
0
0
2
2
3
2
0
2
0
2
0
0
0
0
1
1
0
0
0
1
0
0
2
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
1
0
0
0
2
2
2
0
1
0
2
1
0
0
0
0
2
0
2
0
0
0
0
3
0
1
2
1
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
1
0
0
1
0
2
3
2
0
0
0
0
0
0
1
2
0
0
0
2
1
2
0
2
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
2
0
0
1
0
0
1
0
0
0
2
0
2
0
1
1
0
1
0
1
0
0
0
1
0
0
1
0
2
2
0
2
1
0
0
0
0
1
0
0
0
0
0
2
2
0
1
1
0
1
0
0
0
2
0
0
3
0
0
4
0
1
1
0
0
0
3
0
2
0
0
1
3
0
0
0
0
2
0
2
1
1
2
1
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
1
0
1
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
2
2
0
0
2
0
0
1
0
0
0
2
0
0
1
0
0
0
2
2
2
0
0
0
0
0
1
2
2
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
1
2
0
2
0
0
0
1
4
0
1
2
2
0
0
0
1
2
0
0
0
1
2
2
0
1
0
0
2
0
0
0
1
0
0
2
0
0
0
2
1
0
0
0
1
0
1
0
0
2
0
3
0
0
2
0
0
0
0
0
0
1
2
2
0
1
3
0
0
0
0
0
2
1
2
0
0
0
0
2
0
0
1
0
0
1
0
2
0
0
2
1
0
0
1
1
1
2
0
1
2
0
2
1
2
2
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
3
0
0
1
3
0
1
0
1
0
0
0
0
1
0
0
1
1
2
2
0
0
1
0
0
0
0
0
0
2
0
0
1
0
2
1
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
1
0
2
2
2
1
2
1
0
2
0
2
1
2
0
2
0
0
0
0
1
2
1
0
2
0
0
1
0
1
0
1
1
2
0
1
0
2
0
0
1
0
0
2
0
1
1
2
2
0
1
0
0
5
0
0
2
0
1
0
0
0
0
0
1
1
2
0
0
1
2
0
1
2
0
1
0
0
2
1
0
0
0
0
2
0
0
2
2
0
0
0
1
1
0
1
0
0
0
1
1
2
0
0
0
1
0
0
0
0
2
0
0
0
8
0
3
0
2
0
2
3
2
0
1
2
0
2
2
0
2
1
1
0
0
0
2
2
0
2
0
0
0
2
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
2
1
2
0
1
0
0
0
0
0
3
0
1
1
1
0
0
1
0
0
2
2
0
2
1
0
0
0
1
0
0
0
0
2
0
0
2
2
0
0
2
0
0
0
0
0
1
1
2
0
0
1
0
0
0
0
2
1
0
2
0
2
0
0
2
2
2
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
1
1
0
1
2
2
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
1
1
1
2
0
2
1
0
2
0
2
1
0
1
1
1
0
0
0
1
2
0
0
0
1
0
2
0
0
2
0
1
0
2
0
2
2
0
0
0
0
0
0
0
2
0
2
0
1
0
2
2
0
2
2
2
0
2
2
0
2
2
0
1
1
3
0
0
2
0
0
2
0
0
0
0
0
2
1
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
2
1
0
0
0
0
1
0
0
0
0
0
1
0
1
2
1
0
0
1
2
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
3
0
1
1
0
1
0
0
0
2
1
0
0
1
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
2
1
0
0
2
3
0
0
2
1
0
0
2
2
0
0
2
0
2
1
0
0
0
1
2
1
0
2
0
0
1
1
0
1
2
1
1
2
0
2
1
0
0
1
0
0
2
0
0
0
1
0
1
0
2
1
0
0
0
0
2
0
0
0
1
0
2
0
0
2
0
2
0
0
2
0
0
1
0
0
1
4
0
0
1
3
2
1
0
1
2
0
0
2
0
0
0
0
1
0
0
2
2
0
0
2
0
2
0
1
0
0
0
2
2
1
0
2
2
1
0
4
0
0
1
2
2
0
2
2
0
1
1
1
0
2
0
1
2
2
1
2
2
0
0
4
1
0
0
0
1
0
2
0
1
0
0
0
0
0
0
2
1
3
0
0
1
0
1
2
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
2
0
2
0
1
2
0
0
2
1
1
0
0
2
1
1
0
1
0
1
0
0
2
2
0
0
2
1
0
1
0
0
1
0
0
0
0
0
2
0
0
2
2
0
0
0
2
0
2
0
0
0
2
2
0
1
0
0
0
0
0
0
0
2
0
0
0
1
5
1
0
0
0
0
0
1
1
2
0
1
0
2
2
2
0
0
1
0
0
2
2
0
1
2
0
2
0
2
0
0
0
2
0
0
0
0
0
2
1
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
3
0
1
5
0
2
0
6
0
2
0
47
1
0
1
0
1
2
0
2
0
0
3
0
0
1
1
0
1
2
0
1
3
1
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
2
0
1
1
2
0
1
0
1
1
1
4
0
0
0
2
0
1
0
1
1
1
2
0
2
0
0
1
0
1
1
0
0
0
0
0
0
0
0
5
0
0
0
1
0
1
2
2
1
0
2
0
0
0
0
0
1
0
2
3
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
1
0
4
2
0
0
2
0
0
1
0
0
2
2
0
1
3
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
1
1
0
0
0
2
0
2
0
0
1
1
0
1
2
3
2
1
1
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
6
3
2
0
0
1
1
0
3
0
1
2
2
0
1
0
0
0
0
0
0
2
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
2
1
0
2
3
0
1
0
0
4
0
0
2
0
0
2
1
3
0
4
0
1
2
0
2
3
0
0
1
1
0
0
3
0
2
2
0
2
0
0
1
2
0
1
1
0
0
1
1
0
0
0
0
0
0
1
0
0
1
2
2
2
1
0
2
0
0
0
0
1
0
0
0
0
1
1
1
0
1
0
1
1
0
0
2
0
0
2
2
0
2
2
0
0
1
2
2
1
2
1
2
0
0
0
2
0
2
0
0
1
0
0
0
0
2
0
0
0
0
2
0
1
0
1
0
0
0
1
0
0
0
0
3
0
0
0
1
0
2
2
4
0
1
1
1
0
0
1
2
0
2
2
0
0
0
2
0
0
0
0
1
2
1
1
0
1
0
0
3
2
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
2
2
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
1
0
1
0
1
0
0
0
2
0
1
0
0
0
3
0
1
0
0
1
1
0
0
0
2
2
1
1
2
1
0
0
2
0
0
3
0
1
2
2
0
0
0
2
0
0
0
2
2
0
0
0
0
0
1
0
2
0
0
2
0
2
0
0
2
1
0
2
2
1
1
0
0
0
2
0
2
2
0
2
0
0
1
1
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
2
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
2
0
2
0
1
2
0
0
1
1
4
0
0
0
1
0
3
0
0
2
0
1
0
0
1
1
1
1
2
2
0
2
0
1
0
0
0
0
0
0
2
1
2
0
2
0
2
1
2
1
0
0
0
0
1
0
0
1
0
0
2
2
0
0
0
0
0
0
3
1
0
0
0
2
0
0
0
1
1
0
0
1
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
2
1
0
2
0
2
1
1
0
1
0
0
0
1
0
0
2
2
0
0
2
0
2
0
2
0
2
2
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
2
1
0
0
2
0
2
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
2
0
1
0
2
0
0
4
0
2
0
0
0
0
1
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
1
2
1
1
1
2
2
0
1
1
0
1
0
3
0
0
0
2
0
0
0
2
0
2
0
3
0
0
0
0
1
1
1
1
2
1
0
0
0
1
0
0
0
2
0
1
0
0
0
0
1
0
2
1
0
2
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
1
1
2
2
0
2
2
0
2
0
0
3
0
0
2
0
2
0
2
2
0
0
0
0
1
1
0
0
0
0
1
0
1
1
0
0
0
1
0
1
0
0
2
0
0
0
0
0
1
0
1
2
0
0
1
0
1
0
0
0
0
0
2
0
0
2
5
0
2
2
1
3
2
0
0
0
0
1
0
1
2
0
0
0
1
0
1
0
0
2
1
1
1
0
2
3
0
0
1
0
2
0
0
0
0
0
0
2
2
0
0
1
0
0
0
2
0
2
1
2
1
2
3
1
2
0
0
2
0
2
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
2
1
0
2
0
0
2
0
0
0
0
0
0
0
1
1
0
2
2
1
3
1
0
0
2
0
0
0
0
2
0
1
0
1
2
2
1
4
0
2
0
0
0
7
0
0
1
0
2
0
1
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
2
0
0
0
1
0
0
0
1
0
0
0
2
0
1
0
0
0
1
1
2
0
2
1
1
0
0
1
0
1
1
0
0
0
1
0
1
2
2
0
0
0
2
2
0
0
1
1
0
1
1
1
1
1
2
0
2
0
2
1
2
1
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
2
0
0
0
0
1
2
0
1
0
2
2
2
1
0
0
1
0
0
1
1
0
2
6
1
0
0
3
0
1
1
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
1
1
0
0
2
0
0
1
1
2
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
1
0
0
3
2
2
0
1
1
2
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
2
0
3
1
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
2
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
3
0
1
0
0
0
0
1
0
0
1
0
0
3
0
0
0
1
0
0
1
1
0
0
3
0
1
2
2
0
2
0
0
1
0
2
3
0
0
2
0
0
0
0
1
0
2
0
0
0
1
0
1
0
0
0
1
0
0
0
2
0
0
0
0
1
1
2
0
0
0
0
0
2
0
0
0
1
1
2
0
0
1
2
1
1
1
1
3
0
2
1
0
1
2
2
2
1
0
1
0
0
0
0
0
0
1
0
2
1
2
2
0
0
1
0
0
1
1
1
0
0
0
2
0
2
1
0
0
0
0
0
1
2
0
0
1
1
3
2
1
0
1
0
0
2
2
0
0
1
1
0
0
1
2
1
2
0
2
0
5
0
0
0
1
0
0
2
0
0
1
0
0
1
1
0
0
1
0
1
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
1
0
2
0
0
2
3
2
0
0
0
2
0
2
0
2
0
1
0
0
1
0
2
0
1
2
0
2
0
0
2
1
2
0
2
0
1
2
0
1
1
0
0
2
0
0
2
0
0
0
0
2
0
2
0
0
1
2
0
0
0
0
0
2
1
1
0
2
1
0
2
0
2
1
0
1
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
2
1
1
0
0
0
0
1
0
0
0
0
1
2
1
0
1
2
0
0
0
1
2
0
1
1
0
0
0
1
2
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
2
1
2
1
0
2
3
0
3
0
2
0
1
2
1
2
0
0
1
0
1
0
0
1
1
0
2
0
2
1
0
0
0
0
0
2
0
0
2
0
2
0
0
2
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
1
0
2
1
0
2
2
0
0
1
0
2
1
2
0
0
2
0
1
2
2
1
1
0
1
0
1
0
1
2
0
2
1
1
0
0
0
0
0
0
2
2
2
2
0
0
0
0
2
0
0
0
1
0
2
1
0
0
0
0
0
2
0
0
2
1
0
0
1
1
2
0
2
0
0
0
1
0
0
0
1
1
2
0
0
0
0
0
0
4
0
1
0
0
0
0
2
1
0
0
0
0
0
1
0
0
1
0
0
0
0
3
2
2
0
0
0
0
0
2
2
3
0
0
0
2
0
0
0
2
2
0
0
3
0
2
0
3
0
1
1
0
2
0
0
1
1
0
1
0
0
0
0
0
2
0
0
2
0
1
0
0
2
3
0
1
0
2
2
3
0
1
2
1
0
1
0
0
0
1
2
0
0
2
0
2
1
0
2
1
1
0
1
2
2
0
2
3
0
0
0
0
2
0
0
2
0
1
0
0
0
2
0
0
2
0
0
0
2
0
0
0
1
2
0
1
1
1
0
2
0
1
2
0
0
2
0
0
0
1
0
0
0
1
1
2
2
1
0
0
0
0
0
0
2
0
0
0
0
1
2
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
2
2
0
0
2
0
1
1
1
0
2
1
1
1
1
0
0
2
0
2
1
1
0
2
0
2
3
2
0
1
0
0
3
0
0
1
0
1
0
0
1
0
0
0
1
4
0
2
0
0
1
1
0
0
0
0
0
0
1
0
4
0
0
1
0
0
1
0
0
0
0
1
2
0
1
0
2
2
0
3
2
2
0
0
0
0
0
0
0
0
0
2
0
0
2
1
1
0
2
0
1
0
1
0
2
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
2
0
0
0
3
0
1
0
1
1
0
0
1
1
0
1
0
0
1
0
1
0
2
0
1
2
2
3
1
2
1
1
1
2
2
0
0
2
0
1
0
0
1
0
2
0
0
1
0
0
1
2
0
0
0
0
0
2
0
0
0
0
2
0
1
0
1
1
0
0
0
0
0
0
1
0
0
2
1
0
1
0
0
1
2
1
0
2
1
1
0
0
0
2
0
0
0
1
2
0
0
1
0
1
0
1
1
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
1
1
3
0
0
1
0
0
0
0
0
1
1
0
0
3
0
1
0
0
1
0
1
0
0
0
1
0
1
2
0
0
0
0
0
4
0
0
2
2
1
0
1
1
2
2
0
3
0
1
0
0
2
0
0
1
0
0
0
1
0
0
1
0
2
0
0
0
1
1
0
0
2
2
0
0
1
0
1
1
2
1
0
0
2
1
2
0
0
0
1
0
0
2
0
2
0
2
0
0
0
0
0
2
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
2
0
0
2
0
0
0
1
0
2
0
0
3
0
1
1
0
0
0
1
2
0
0
0
2
2
2
0
2
0
0
2
2
0
1
0
0
1
1
0
0
0
0
0
1
0
1
2
0
0
2
2
0
0
0
0
0
1
3
0
0
0
1
1
2
0
0
2
2
1
2
1
0
0
0
0
0
1
0
0
1
0
0
0
3
1
0
2
2
1
1
0
0
0
2
1
0
0
1
0
2
0
0
1
10
0
0
2
0
2
0
0
1
0
0
0
1
0
1
0
2
1
1
0
0
0
1
0
1
0
2
0
0
0
0
0
0
1
2
0
0
0
1
0
1
0
1
0
2
0
0
2
0
0
0
1
0
0
0
1
2
1
0
0
0
0
0
0
0
3
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
3
2
1
0
0
1
2
0
0
0
0
0
0
0
1
2
2
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
2
1
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
1
2
1
2
4
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
1
2
0
2
2
0
1
0
2
2
0
2
0
0
2
2
0
1
0
0
1
0
0
0
1
0
1
1
0
0
1
1
1
1
1
0
0
0
1
0
0
2
0
2
1
2
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
3
2
1
0
0
1
2
2
1
0
1
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
1
2
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
1
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
3
2
0
0
0
0
0
2
0
2
0
0
2
0
2
3
0
0
2
0
0
0
2
0
0
1
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
2
0
2
0
0
0
0
0
0
1
1
1
0
1
0
0
2
0
0
2
2
0
2
1
2
0
2
0
0
0
0
2
0
0
0
1
0
2
0
0
4
2
2
0
2
0
1
1
0
0
2
0
1
0
0
2
0
0
0
1
2
0
0
2
0
0
0
1
2
0
0
0
2
0
0
2
1
0
0
1
2
2
1
2
0
0
0
0
0
1
3
0
1
0
3
0
0
0
1
0
0
0
2
0
1
2
0
0
0
1
2
0
3
0
2
1
2
0
0
0
1
0
0
0
2
0
0
2
0
1
0
0
1
0
1
0
0
0
0
2
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
2
1
2
1
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
1
0
0
2
2
2
0
0
0
1
0
0
0
0
0
1
1
1
1
1
2
0
0
0
1
1
0
2
0
0
0
0
0
1
0
0
1
0
0
1
0
3
1
1
2
0
0
1
0
0
2
0
0
2
2
1
2
0
2
1
0
0
0
1
0
0
0
0
1
2
0
1
2
1
1
0
0
1
0
0
1
2
0
1
3
0
0
0
1
2
0
0
2
0
2
0
1
0
2
1
0
0
2
0
0
1
0
1
0
0
0
0
1
0
0
0
0
2
1
2
0
0
1
1
1
1
0
0
1
1
0
0
0
0
1
0
0
3
1
0
0
0
0
0
2
1
2
1
0
0
1
0
1
2
0
1
0
0
2
0
0
2
0
2
1
1
0
0
2
2
2
2
2
2
2
2
0
0
0
2
0
2
1
2
0
0
2
0
0
0
1
0
0
0
2
1
0
0
0
0
0
2
0
0
0
3
1
2
2
1
1
2
2
0
2
1
1
2
2
8
2
1
1
0
2
0
2
0
0
1
1
3
2
2
0
0
0
2
0
0
0
2
0
0
1
0
2
1
0
1
1
1
0
0
0
0
2
1
0
0
1
2
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
2
0
2
0
0
0
0
1
0
2
2
0
3
0
0
0
1
0
0
0
1
1
0
0
2
0
2
1
0
2
0
0
0
0
0
2
0
2
4
1
0
0
2
0
0
1
0
0
1
1
2
0
1
0
1
1
0
2
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
2
0
2
0
0
1
0
1
2
0
2
1
0
0
1
0
1
2
0
1
0
1
0
1
3
1
0
0
0
2
1
0
0
2
0
0
0
0
0
0
2
2
0
2
0
1
1
0
0
0
0
2
2
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
1
0
0
1
2
0
0
1
0
0
1
0
1
1
2
0
2
0
0
2
0
2
0
0
1
2
0
0
1
0
1
0
0
1
4
0
0
2
2
0
0
0
2
0
1
2
0
0
3
1
1
1
0
0
0
0
2
0
2
0
0
0
1
0
0
0
2
3
1
1
0
1
0
1
1
1
0
0
0
1
0
0
1
3
0
2
0
0
0
1
1
0
1
0
2
0
0
0
0
1
1
0
2
0
2
2
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
1
0
0
3
0
2
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
1
0
0
2
1
1
0
0
0
0
0
1
1
1
2
0
2
0
2
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
1
0
2
0
2
0
1
0
0
1
2
0
0
1
0
0
0
1
0
0
1
1
1
2
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
1
0
1
0
0
0
0
0
2
2
2
2
1
0
0
0
2
1
1
0
1
2
1
0
0
3
2
1
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
1
0
1
1
0
1
0
0
0
0
1
2
0
0
0
1
0
0
1
2
0
0
2
2
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
1
2
2
0
0
0
0
0
1
1
1
0
1
1
3
0
2
0
1
2
2
2
1
2
0
2
1
0
0
2
0
0
0
0
0
0
1
0
3
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
1
2
2
2
2
0
1
0
2
0
0
1
0
0
1
0
1
3
1
0
0
0
1
0
1
1
0
0
0
2
1
0
0
1
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
2
2
0
0
0
4
1
0
2
0
2
0
0
0
2
0
0
0
0
0
3
0
0
0
1
1
1
0
2
0
1
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
1
0
1
0
2
3
0
0
0
2
0
0
2
0
0
1
1
0
1
0
2
0
0
0
0
2
0
2
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
1
0
0
0
0
0
2
2
1
0
2
3
2
0
1
0
0
2
0
0
2
2
0
3
0
2
1
0
1
0
2
0
2
0
0
2
0
2
1
0
0
0
1
0
0
1
0
0
2
0
2
1
1
0
0
0
2
1
1
0
0
0
1
0
1
1
1
0
0
2
0
3
2
2
2
0
0
1
0
0
0
3
2
0
0
0
0
0
1
1
0
1
0
1
0
1
0
2
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
2
0
2
1
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
2
1
0
0
0
0
2
1
0
1
0
1
0
0
1
3
0
0
1
0
0
0
0
0
2
0
2
1
0
2
0
1
0
2
2
0
0
0
1
0
2
0
1
0
0
1
0
1
1
2
0
0
1
0
0
0
4
1
1
0
1
0
0
2
0
1
0
0
0
0
1
0
2
0
0
0
2
1
0
1
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
1
0
2
1
0
1
2
0
2
0
2
0
1
0
0
1
0
1
0
2
0
2
2
1
0
0
0
5
0
1
1
0
2
0
0
2
1
0
0
2
0
0
0
0
0
1
0
0
0
7
2
0
1
0
0
1
0
2
0
0
2
0
2
0
1
2
1
0
0
0
0
0
0
2
2
0
0
2
0
0
0
2
0
2
2
0
0
1
1
0
1
0
0
2
0
0
0
0
1
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
1
2
0
1
0
2
0
0
0
2
0
0
0
0
1
3
0
0
1
1
0
0
2
0
0
0
1
0
0
0
2
2
0
1
1
0
2
3
0
0
0
2
2
1
1
1
0
1
0
0
0
2
1
0
1
1
0
1
1
0
1
0
0
0
0
0
0
1
2
2
1
1
2
0
0
1
1
1
1
0
2
0
2
0
2
1
0
2
2
0
1
1
1
0
2
1
0
0
1
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
2
0
2
0
0
2
1
1
0
0
0
0
1
2
0
0
0
2
3
0
1
1
2
1
0
3
0
0
1
0
2
0
0
0
0
2
0
1
2
0
0
2
1
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
1
1
2
1
2
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
1
1
1
1
1
0
0
0
0
0
1
0
0
1
2
0
1
1
0
0
0
2
0
4
0
0
0
1
0
3
0
0
0
1
1
1
2
0
0
2
1
0
1
0
1
2
0
0
0
0
0
0
0
1
1
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
1
1
2
1
2
0
0
0
1
0
0
0
0
1
1
1
0
2
0
0
0
2
0
2
1
2
0
0
2
1
0
1
2
0
0
3
2
2
0
2
1
0
1
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
1
0
0
2
1
0
1
0
0
2
1
2
0
1
0
0
1
0
2
0
1
2
0
0
0
2
2
2
0
1
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
1
0
0
0
1
1
0
0
2
0
0
2
0
0
0
2
1
0
0
2
2
0
3
0
1
0
0
2
0
2
0
0
0
0
2
2
3
0
0
0
2
4
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
1
1
1
1
0
2
1
0
0
0
0
1
0
1
2
0
0
2
1
2
1
0
1
0
4
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
2
0
0
0
0
1
2
0
1
0
0
1
1
3
0
0
0
0
0
1
2
0
1
2
3
0
1
0
1
1
2
0
2
0
3
1
3
0
0
3
0
0
0
2
0
0
0
2
2
2
0
0
0
0
0
2
0
0
1
0
0
2
0
2
0
0
0
0
2
2
1
0
0
0
0
1
0
0
2
0
3
0
4
1
0
0
1
1
0
0
0
0
1
3
0
0
1
0
0
2
2
2
0
1
2
0
0
2
0
0
0
2
0
2
1
2
2
0
0
2
1
1
2
1
2
0
1
2
2
0
0
0
0
1
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
1
1
1
1
1
0
1
0
0
0
0
2
0
0
0
1
1
0
2
0
0
1
1
0
0
0
0
0
0
0
0
2
2
0
0
1
2
0
0
0
0
2
1
0
2
0
0
0
2
1
0
0
0
0
1
1
0
0
0
2
0
1
1
0
1
2
0
0
3
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
1
2
0
0
0
1
0
0
1
0
0
2
2
1
1
1
1
0
0
0
0
1
0
0
0
0
2
0
1
0
2
0
0
0
0
0
2
2
0
1
4
2
1
0
0
0
0
0
2
0
0
0
2
2
2
0
0
1
0
0
2
0
0
0
0
0
0
1
1
0
1
0
0
3
2
2
2
1
0
0
2
2
1
1
0
2
0
0
2
0
1
0
0
0
1
3
0
0
0
2
2
2
2
1
0
2
0
0
0
1
1
1
0
2
1
1
0
3
1
0
0
1
1
0
2
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
2
0
2
2
0
1
0
0
0
1
0
0
1
2
0
4
0
2
0
0
2
0
0
0
0
1
1
0
0
0
2
1
0
0
0
0
0
2
1
2
0
0
2
1
0
1
0
0
0
0
1
0
1
0
2
2
0
1
0
0
1
3
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
1
6
0
0
0
0
2
0
0
1
0
2
1
3
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
1
2
0
0
1
0
0
0
1
0
0
0
2
0
2
2
2
0
0
0
2
0
2
0
0
0
0
2
0
2
0
0
1
0
1
0
1
2
0
0
2
3
0
1
0
2
0
0
0
2
1
0
2
1
0
2
0
1
1
1
1
0
1
0
0
0
0
0
4
0
2
0
0
0
1
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
2
1
0
1
3
0
2
0
1
0
1
0
0
2
2
2
0
0
1
1
0
0
0
2
0
3
2
1
0
0
0
0
0
0
0
1
2
1
0
0
2
0
0
0
0
2
2
1
1
0
0
2
0
0
1
0
1
0
0
0
0
0
0
1
0
2
2
0
2
0
0
1
1
0
1
2
1
0
0
0
2
0
2
1
0
0
0
1
0
1
0
0
1
0
0
0
0
2
2
0
1
1
0
2
0
2
0
2
1
0
2
0
0
1
3
0
1
1
3
0
2
1
0
1
0
0
2
0
0
0
3
0
0
2
4
2
0
1
0
1
0
1
2
0
0
0
0
0
0
2
2
0
1
0
0
4
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
5
0
1
0
1
2
1
2
0
2
0
0
1
1
2
1
1
0
0
0
0
1
1
0
0
2
1
2
1
2
1
2
0
0
0
2
2
0
0
0
0
0
0
2
2
2
0
1
0
0
0
0
0
0
2
2
0
2
2
0
0
0
0
0
0
0
0
0
3
0
2
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
2
2
2
0
1
1
0
1
0
0
2
0
1
3
0
0
2
2
0
0
2
1
0
2
1
2
2
2
1
0
0
0
1
0
2
2
0
0
1
0
0
0
2
0
2
0
2
2
1
0
0
0
1
1
0
0
0
2
1
0
0
1
0
0
2
2
2
0
0
1
1
0
2
0
0
0
2
0
0
0
0
2
0
1
0
1
1
0
0
0
0
0
1
0
3
0
0
2
0
0
1
0
0
0
2
1
0
0
0
2
0
0
0
2
0
0
1
2
0
1
0
0
1
0
2
1
2
0
0
1
2
1
0
2
1
0
1
0
1
0
0
2
0
1
0
1
0
0
0
1
2
2
1
2
0
0
0
0
2
0
1
1
0
0
2
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
2
0
2
2
0
1
1
0
0
0
0
2
0
0
0
1
0
0
0
2
0
2
0
0
0
0
1
0
0
1
0
0
0
1
0
1
2
0
0
2
0
1
2
1
0
1
2
0
0
1
1
0
1
2
0
0
0
1
0
0
0
2
0
2
0
2
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
2
2
0
0
6
2
2
0
0
1
0
0
2
0
0
0
1
2
0
1
0
0
0
1
0
0
1
0
0
0
0
0
7
1
0
0
0
0
0
0
1
0
1
0
0
1
0
1
1
2
0
0
1
0
0
1
1
2
3
1
0
0
0
1
2
0
3
2
1
0
0
1
0
0
0
2
2
1
1
0
0
0
0
1
0
2
2
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
2
1
0
0
1
2
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
2
0
2
2
1
0
0
2
1
2
1
0
2
0
1
1
0
2
0
1
0
0
1
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
1
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
2
0
0
0
2
0
2
0
1
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
1
0
3
2
0
0
2
0
0
0
0
1
1
1
0
0
0
0
2
2
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
2
1
2
0
0
1
1
0
2
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
2
1
0
1
0
0
0
3
0
0
0
0
1
0
3
0
2
0
0
0
3
2
4
0
1
1
0
0
0
4
3
0
0
1
0
0
0
0
2
0
0
0
0
1
2
0
1
0
0
0
1
2
1
0
1
3
1
0
0
0
1
1
0
2
0
0
2
1
1
0
0
0
0
0
2
2
0
2
0
2
1
0
1
0
4
4
0
1
2
3
2
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
1
2
0
2
0
2
0
0
2
0
0
0
0
1
0
0
0
0
2
2
1
0
1
0
0
0
1
1
0
1
0
0
0
0
1
0
1
1
0
1
0
2
0
0
1
0
0
2
1
0
0
0
0
2
0
0
1
2
1
0
0
0
1
0
0
1
0
1
0
0
0
2
2
0
0
2
0
1
0
1
2
1
0
2
1
0
0
0
1
1
2
0
2
1
0
0
2
0
2
3
0
0
0
2
0
0
1
0
0
1
3
1
0
2
0
0
1
0
1
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
2
0
2
2
2
1
0
1
0
0
0
1
0
0
1
1
0
0
4
0
0
0
5
0
2
0
1
2
1
0
4
3
0
1
0
1
0
1
0
0
0
0
0
0
2
9
0
0
2
1
1
1
0
0
2
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
2
0
2
2
1
0
1
0
2
0
0
1
1
0
0
0
1
0
0
2
2
2
0
1
0
0
0
0
2
0
0
1
0
0
0
0
1
2
1
1
0
0
1
0
1
0
2
1
0
0
0
2
0
1
2
0
0
0
0
0
1
1
1
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
1
0
3
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
2
0
2
1
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
2
1
0
0
2
0
0
0
2
3
0
2
2
2
0
0
0
1
1
0
2
1
0
0
2
0
1
0
0
3
4
0
2
0
0
0
1
2
1
0
0
2
0
0
2
1
0
1
1
0
0
1
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
2
1
2
0
0
0
2
0
0
1
0
1
0
2
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
2
0
1
1
0
2
1
0
0
0
1
2
0
4
0
2
0
1
1
0
0
0
2
0
0
0
0
2
0
1
2
0
0
1
0
0
1
0
0
1
0
2
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
2
0
1
0
0
2
0
0
1
0
0
3
0
0
0
0
0
2
1
0
1
0
0
3
0
0
0
0
0
0
0
2
0
1
2
2
1
0
1
0
0
1
0
1
2
0
0
0
2
2
0
1
1
0
2
0
0
0
0
0
2
4
0
1
2
0
0
0
0
0
1
2
0
0
0
2
2
0
2
1
1
0
2
1
0
0
0
0
1
1
1
0
0
0
2
0
1
0
0
2
0
1
0
0
0
0
0
0
2
2
2
0
2
0
2
0
1
0
0
0
0
0
1
0
0
2
0
1
0
1
2
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
1
0
1
1
1
0
1
2
1
0
3
0
1
0
0
2
0
1
2
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
1
0
0
0
0
4
0
1
0
0
1
0
1
0
0
0
3
1
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
2
0
0
0
1
1
0
0
0
0
2
2
0
2
2
0
1
0
0
2
0
1
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
1
0
0
1
0
2
2
0
1
0
2
3
0
1
0
1
0
0
0
2
0
1
0
0
1
2
2
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
2
2
0
2
1
1
0
1
1
0
1
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
2
1
0
0
0
0
2
1
0
0
0
2
1
0
1
0
0
0
0
1
1
1
0
1
1
1
1
0
0
0
0
0
2
1
2
0
0
0
3
2
0
1
0
3
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
1
1
1
1
0
0
0
0
1
0
0
1
0
0
2
0
0
0
2
0
0
3
0
1
0
1
2
0
0
0
0
0
0
0
2
0
1
2
1
1
1
0
1
0
0
1
1
2
0
2
0
1
1
2
0
1
0
0
0
2
1
0
2
0
1
0
2
3
0
0
1
0
0
0
0
0
0
3
1
1
2
0
0
0
0
0
2
2
0
0
0
1
1
0
2
0
0
0
1
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
1
1
2
1
0
0
1
1
0
1
0
1
0
0
1
2
2
2
0
0
2
1
0
2
0
0
0
1
0
0
1
0
0
0
1
0
2
0
1
0
0
0
0
0
1
0
2
1
0
2
0
0
0
0
0
0
0
1
0
6
0
0
2
1
0
1
0
1
2
0
2
0
1
0
0
0
1
2
0
1
2
0
2
2
0
0
1
2
3
0
0
1
0
1
1
0
0
0
0
1
0
1
0
0
1
1
2
0
0
1
0
0
1
1
0
2
1
1
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
2
2
0
1
1
0
0
0
2
0
1
0
0
1
0
1
0
1
0
2
0
0
0
2
0
0
1
0
0
0
0
1
1
2
1
0
1
0
0
1
0
0
0
1
0
1
2
0
0
0
0
2
2
0
1
0
1
0
2
0
1
1
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
1
1
0
0
2
0
2
0
0
0
0
0
1
3
0
0
1
0
0
0
2
2
0
0
1
1
0
0
0
1
1
0
0
2
0
0
0
2
1
1
1
0
2
1
0
0
0
1
2
0
0
0
0
0
0
1
4
2
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
3
1
1
0
0
0
3
0
0
1
0
0
1
0
0
0
1
0
2
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
2
0
0
1
0
1
0
1
2
0
5
0
2
0
0
0
2
0
2
0
0
0
1
0
1
0
0
2
3
0
0
1
0
1
2
0
0
6
0
0
1
0
0
0
0
0
0
0
0
1
0
2
1
1
0
1
0
0
0
0
0
0
0
1
1
2
0
0
1
1
1
0
1
1
0
2
3
2
0
0
0
0
1
0
0
0
0
0
2
0
3
0
1
6
0
0
0
1
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
2
1
1
1
1
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
3
2
0
0
0
2
1
0
2
0
2
2
1
2
1
1
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
2
0
2
0
0
0
1
1
1
0
3
0
2
2
1
0
2
0
1
0
0
0
0
1
3
0
1
1
2
0
1
2
2
0
0
0
0
0
1
0
0
2
0
0
1
2
0
0
2
0
0
0
2
0
2
0
2
2
0
0
2
0
1
1
1
0
1
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
2
2
2
1
0
0
0
1
0
1
1
0
0
2
2
0
0
1
2
2
0
0
4
0
0
0
1
2
1
0
0
0
0
2
0
0
2
0
0
2
2
1
1
0
0
0
1
0
0
1
3
1
0
1
2
2
0
1
0
0
0
0
0
3
0
0
2
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
1
0
0
0
2
0
1
1
0
0
1
0
0
0
0
1
1
2
0
0
0
2
0
0
0
0
1
0
1
2
0
0
0
2
0
1
0
0
2
0
2
0
0
0
2
0
2
0
1
0
0
1
0
0
0
0
2
0
1
0
2
2
0
0
0
0
2
0
0
1
7
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
1
0
2
0
0
1
1
1
1
2
0
0
4
0
1
0
0
2
1
0
0
0
0
0
1
0
2
0
1
0
0
1
0
0
0
1
2
0
0
0
0
0
0
2
0
0
1
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
2
1
0
2
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
3
1
0
0
2
0
0
0
2
2
0
0
0
0
1
0
2
1
2
2
0
2
0
0
0
2
1
0
2
0
2
0
0
2
0
0
2
0
0
2
2
0
0
1
0
3
2
0
0
0
0
0
0
2
2
2
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
1
1
0
0
0
0
1
0
0
2
1
0
0
0
0
1
2
0
1
0
0
0
2
0
1
0
0
2
0
0
0
1
0
0
2
0
0
1
0
1
0
0
0
0
2
2
1
0
1
2
2
0
0
0
1
0
1
0
0
0
0
0
0
0
1
3
1
1
1
2
1
0
0
1
2
2
0
0
0
0
0
0
2
0
0
2
2
0
0
2
0
0
0
0
0
0
1
2
0
1
0
1
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
2
0
0
0
0
0
2
1
0
0
2
0
0
1
0
1
0
0
2
0
2
0
0
0
0
0
1
2
2
0
0
1
2
0
0
0
0
0
0
0
0
1
1
1
1
1
0
0
2
2
0
1
1
0
1
1
0
0
0
0
0
1
1
0
1
0
0
1
1
0
0
2
2
1
0
1
0
0
0
0
0
1
0
0
2
2
0
0
0
2
0
0
0
1
0
0
0
2
2
1
0
1
0
2
0
0
0
0
3
0
0
3
0
0
0
0
2
0
0
0
0
2
0
0
1
2
0
2
1
0
2
0
1
1
0
0
0
0
1
0
0
1
2
1
0
0
0
0
2
1
0
1
2
3
1
0
0
0
0
0
1
0
0
0
2
1
0
1
2
0
1
0
0
2
1
0
1
0
0
0
0
1
0
2
0
0
0
2
1
0
0
2
1
1
0
2
1
2
0
0
0
0
2
0
0
1
1
0
1
2
1
1
1
0
0
0
0
2
1
1
2
1
0
2
0
0
0
2
0
0
1
0
1
2
2
0
2
0
1
0
0
0
1
2
2
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
1
1
1
0
0
2
2
0
1
0
1
0
0
4
0
0
1
0
1
0
0
0
0
0
2
1
0
1
0
2
0
2
0
0
0
0
1
0
0
1
0
1
0
0
2
0
1
5
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
2
1
0
0
0
1
0
0
0
0
3
2
0
1
0
0
0
0
0
0
3
0
0
2
1
1
0
0
0
0
1
2
0
2
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
2
0
0
0
1
0
1
0
1
0
1
0
0
0
1
1
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
1
1
0
2
1
2
1
1
1
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
1
0
1
0
2
0
0
0
0
2
0
1
0
1
0
0
1
0
0
0
1
0
1
0
0
1
1
0
0
2
2
0
0
1
0
2
2
0
2
0
1
0
1
1
0
0
1
1
1
2
2
1
0
2
0
1
1
0
0
0
0
0
2
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
1
1
2
1
1
2
0
0
1
0
1
0
0
2
0
2
0
1
0
3
0
0
1
1
1
0
0
0
3
0
0
1
1
1
0
2
0
2
1
0
1
1
0
0
1
0
0
4
1
1
0
0
0
0
0
2
0
1
1
0
0
0
1
0
0
0
1
1
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
1
0
0
0
2
0
0
0
0
0
2
1
2
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
1
1
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
2
1
0
1
0
0
0
2
0
0
2
1
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
1
2
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
4
2
0
0
1
1
1
0
2
1
2
0
1
0
0
0
1
1
1
1
2
2
0
0
5
0
2
0
0
4
2
2
0
0
0
0
1
0
2
0
1
1
0
1
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
1
2
0
0
2
2
0
1
0
2
2
1
1
0
2
0
0
0
0
1
2
0
1
0
2
0
2
2
0
0
2
2
1
1
3
1
0
1
0
0
0
1
0
2
1
2
0
0
0
0
1
1
3
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
2
0
1
0
1
0
0
2
0
2
2
0
3
0
2
0
2
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
2
0
1
2
1
2
0
0
0
0
4
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
1
0
2
0
0
2
0
0
0
2
2
0
0
0
1
0
0
2
2
0
0
0
1
0
0
0
0
0
0
1
1
1
2
0
0
0
1
0
0
0
1
0
0
0
1
2
0
2
0
0
0
0
1
0
0
1
1
2
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
3
0
2
2
2
0
0
2
0
0
1
2
0
1
0
2
0
2
2
1
1
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
2
0
0
0
0
0
2
1
1
0
2
0
1
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
2
1
0
1
0
2
0
0
2
0
3
2
0
0
0
0
2
0
2
0
2
0
2
0
1
0
0
1
0
1
0
0
0
1
2
0
0
2
1
1
0
0
0
0
2
3
1
0
0
2
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
1
1
3
2
1
0
0
2
0
2
1
0
0
0
0
1
0
0
0
1
1
0
0
1
1
0
2
0
1
2
2
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
2
0
2
0
2
2
0
1
0
0
0
0
2
0
1
1
0
0
0
1
2
0
0
1
2
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
1
4
2
0
0
0
1
0
0
1
1
2
0
0
2
1
0
2
1
1
1
0
1
0
0
2
2
2
2
2
1
0
0
2
0
1
2
0
1
2
0
0
2
2
0
2
2
0
0
0
0
1
1
1
0
1
0
0
1
0
0
1
0
1
0
0
0
2
0
0
2
0
0
1
0
3
0
0
0
0
2
1
0
0
3
2
0
0
0
1
0
0
0
0
2
0
2
0
0
2
2
2
0
1
0
0
1
0
0
2
3
0
0
2
0
2
0
0
2
0
0
0
1
0
0
0
0
0
1
0
2
2
0
2
0
0
0
0
0
3
1
0
0
3
0
0
0
2
0
0
0
1
2
0
0
1
0
0
0
0
2
0
0
0
0
1
1
0
0
2
0
2
0
0
0
1
1
1
1
3
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
1
0
2
0
0
1
0
0
1
1
0
0
0
0
3
2
2
0
1
0
0
0
0
1
2
0
0
1
0
0
1
2
1
0
0
0
0
1
1
0
1
1
0
2
2
1
0
1
1
0
4
0
0
0
0
0
0
0
2
2
2
0
0
1
0
2
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
5
0
2
1
1
1
0
1
0
0
0
1
1
0
2
0
0
2
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
1
2
0
1
0
2
2
0
2
0
2
2
0
0
1
0
2
2
0
1
0
0
0
1
2
0
1
1
0
1
1
2
1
0
0
1
1
1
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
1
1
1
0
0
2
1
0
1
0
0
2
0
1
0
0
2
0
0
0
0
2
2
2
1
0
0
2
2
0
0
0
0
0
2
2
0
0
2
1
0
0
2
1
0
1
0
1
1
0
2
0
0
1
0
0
2
1
6
2
0
1
0
2
1
1
7
0
1
0
2
2
0
0
1
2
4
0
1
2
2
0
2
1
0
0
0
3
0
3
1
0
0
1
0
1
0
0
1
0
0
0
2
0
1
1
0
0
2
2
0
0
1
0
2
0
1
2
0
2
2
0
1
0
0
0
1
0
2
0
0
0
1
1
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
2
2
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
1
0
1
2
0
0
0
0
0
2
1
1
0
2
0
1
0
0
3
0
0
7
0
0
0
3
1
0
0
2
0
3
0
0
0
0
0
0
2
1
2
1
3
0
0
0
2
1
0
0
0
0
1
0
0
1
2
0
0
0
1
2
0
0
0
4
0
0
0
0
2
0
0
3
1
0
0
0
0
0
1
1
2
0
0
2
3
0
0
0
0
0
1
0
0
0
0
1
1
0
0
2
0
1
0
2
0
0
3
0
3
0
1
0
0
0
1
3
1
0
1
0
2
0
2
1
0
0
2
0
0
2
0
0
2
2
0
0
0
0
1
0
0
2
0
0
2
0
2
3
2
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
2
2
0
0
0
1
0
2
2
1
0
0
0
0
0
0
2
0
2
0
2
0
1
0
2
1
0
2
0
0
0
0
0
1
0
0
0
1
0
0
2
0
1
0
1
0
0
0
0
2
3
0
1
1
0
0
0
1
2
0
1
1
0
0
1
0
0
0
1
0
1
4
0
0
0
1
0
2
1
2
3
2
1
0
6
0
0
2
0
0
0
2
0
1
2
0
0
0
0
1
0
0
0
1
1
0
1
2
0
0
0
0
0
1
0
0
0
0
2
0
1
0
1
2
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
3
2
1
0
2
0
0
0
2
2
2
0
0
0
1
2
1
1
0
4
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
2
0
3
0
1
1
0
3
1
1
0
0
0
0
2
0
1
1
0
0
0
0
2
2
0
0
2
2
0
0
0
0
2
0
0
4
0
0
1
0
3
0
0
0
1
2
1
2
2
0
2
0
1
0
0
1
1
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
1
1
0
1
1
0
0
0
2
1
0
0
0
0
2
0
2
0
1
1
2
0
0
2
2
0
0
1
0
1
0
0
1
0
0
2
0
0
3
0
1
2
2
0
1
0
0
0
2
1
2
0
0
0
2
0
0
1
2
0
0
0
0
2
1
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
1
0
0
1
0
1
2
0
0
1
1
1
1
0
1
0
1
1
0
0
0
1
0
2
0
0
0
0
1
1
1
1
1
0
0
0
1
0
2
0
0
0
0
2
2
0
1
0
1
0
0
3
0
0
2
0
0
1
0
1
0
0
0
1
1
1
0
0
0
0
0
0
1
1
2
2
1
0
0
0
0
1
0
0
0
3
0
0
2
0
0
2
0
3
0
0
0
1
3
0
1
0
1
0
0
0
0
0
0
1
2
3
0
3
0
0
0
0
3
0
0
2
0
2
1
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
2
2
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
2
4
0
0
0
2
0
0
0
1
0
2
0
0
0
0
2
0
1
2
2
0
0
0
1
3
0
2
1
0
0
0
1
2
2
1
2
0
0
0
0
0
2
1
1
2
0
0
0
0
0
2
0
0
2
0
2
2
0
0
0
0
0
0
0
1
0
0
2
0
2
1
0
2
0
1
0
1
0
1
0
0
0
2
0
1
1
0
2
1
0
0
0
0
1
2
0
1
0
0
2
0
0
2
0
0
2
0
1
0
0
0
1
0
0
0
2
0
2
0
0
2
1
1
0
1
0
0
3
0
0
0
0
0
0
2
0
3
1
0
0
1
1
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
1
2
1
0
2
0
0
0
0
1
0
0
0
0
2
0
2
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
2
0
2
1
0
2
0
1
0
0
1
0
0
0
0
0
2
0
0
1
0
1
1
1
0
0
1
1
1
0
1
0
0
1
0
2
0
2
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
2
1
0
0
0
0
1
0
1
0
0
2
0
0
0
1
2
0
1
0
1
0
2
0
0
0
2
0
2
1
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
4
0
1
0
0
0
0
0
2
1
0
0
0
2
2
2
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
2
2
0
0
1
0
1
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
3
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
2
1
0
0
0
0
1
0
1
1
1
2
0
0
0
0
2
0
1
1
2
0
2
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
2
0
1
0
0
1
1
1
1
0
1
1
0
2
2
1
0
1
3
0
0
0
0
0
0
1
0
0
2
1
0
1
0
0
2
0
2
0
0
2
0
0
1
0
3
0
2
2
0
2
0
2
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
1
3
0
1
1
0
0
2
1
0
2
1
0
0
1
0
2
0
0
0
2
0
2
0
2
0
0
2
0
1
2
0
0
0
2
0
1
1
0
1
0
0
2
2
0
2
1
0
0
0
1
0
0
6
0
0
0
1
0
0
3
2
2
0
0
2
1
1
0
2
2
0
0
0
0
0
0
2
0
1
0
0
0
1
0
2
0
2
1
2
0
0
2
5
0
0
0
0
0
1
0
0
0
0
3
1
1
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
2
3
0
0
2
1
1
0
2
1
0
2
0
2
1
0
1
1
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
2
0
1
2
3
0
1
0
2
2
1
2
0
1
0
0
1
0
0
0
1
0
1
4
0
1
0
1
0
0
0
1
0
0
1
2
2
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
2
1
0
0
0
0
0
1
1
0
2
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
2
1
0
0
0
1
0
0
1
4
1
1
1
1
1
1
0
2
0
2
0
1
0
0
3
1
0
0
2
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
2
1
0
1
2
3
1
0
1
1
1
0
2
3
0
1
2
2
1
1
1
0
0
0
0
2
1
0
7
2
2
0
0
0
0
0
2
1
0
0
0
0
0
2
1
1
1
0
1
0
0
0
1
1
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
1
0
3
0
0
2
0
1
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
2
0
0
1
3
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
2
0
0
0
0
2
0
1
3
2
0
2
2
2
1
0
0
4
2
1
0
1
0
1
1
1
2
1
0
2
0
0
2
0
3
2
0
0
0
1
1
0
1
3
1
0
2
0
2
1
2
0
2
0
2
2
1
0
1
0
0
2
0
0
0
1
0
2
0
0
0
0
2
0
0
1
1
0
0
1
0
0
0
1
0
2
2
0
2
1
0
2
1
1
0
1
0
2
0
1
0
1
2
1
0
0
0
0
1
1
0
0
2
0
0
0
0
0
1
1
0
2
0
0
2
0
0
0
1
1
0
0
0
0
1
0
0
0
3
2
1
1
0
2
1
1
1
2
0
1
0
0
1
0
0
2
0
0
0
0
1
2
2
0
2
0
1
0
0
1
0
0
0
0
1
0
0
0
1
2
0
0
0
1
0
0
0
0
1
1
1
0
0
0
1
0
0
2
2
1
0
0
1
1
1
0
2
1
0
1
0
1
0
0
0
0
0
1
0
0
3
0
1
1
0
1
0
0
0
1
0
2
2
0
0
0
1
0
1
0
2
0
1
1
4
0
2
0
0
0
1
0
0
0
0
1
0
3
1
1
0
1
0
2
0
1
2
0
0
1
0
0
1
0
0
0
0
0
0
1
2
1
0
0
0
0
1
0
0
2
1
0
1
1
0
0
13
0
2
0
0
0
2
0
0
1
0
1
1
2
0
0
0
0
0
0
2
0
1
0
2
1
0
0
0
2
2
0
0
1
0
0
0
0
2
1
1
0
1
0
0
0
1
0
1
2
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
2
4
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
1
0
1
0
0
0
2
1
1
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
4
0
2
1
2
0
0
0
2
0
2
4
0
2
1
1
0
2
0
1
2
0
0
0
0
1
1
1
1
2
0
0
1
0
2
0
0
0
1
2
1
0
0
0
0
0
2
0
3
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
2
0
2
0
2
0
0
2
2
2
0
2
2
1
2
0
0
2
0
0
0
1
0
1
0
0
0
0
2
1
0
3
3
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
1
1
2
2
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
2
0
0
2
1
0
0
0
3
2
0
1
0
0
1
0
0
2
2
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
1
3
0
1
1
1
0
2
2
0
2
0
0
1
0
2
0
0
2
5
1
1
0
0
1
1
2
0
0
1
0
1
0
0
0
0
2
2
0
1
0
1
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
2
1
0
1
0
1
0
0
0
0
0
0
3
0
0
0
2
0
1
0
1
1
2
2
2
0
1
2
0
0
1
0
2
0
2
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
2
5
0
0
2
0
1
1
1
1
0
0
2
1
1
2
1
1
0
0
0
5
2
2
2
0
0
1
1
0
1
0
0
2
0
0
1
1
4
1
0
1
0
2
2
0
0
0
0
2
1
0
1
1
1
0
0
0
2
0
2
0
0
0
0
0
2
0
2
0
0
0
2
2
3
0
2
0
0
0
1
0
0
1
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
1
0
0
0
2
0
0
0
1
1
1
0
2
0
0
1
2
2
0
0
0
1
0
0
1
2
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
2
0
1
1
0
0
0
0
2
0
1
1
0
0
1
2
1
0
2
0
0
1
0
0
0
1
0
2
1
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
1
0
2
0
0
0
2
0
0
2
1
1
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
1
0
0
0
0
0
0
0
1
0
2
3
0
0
0
0
2
1
2
0
1
0
0
0
1
0
0
0
2
1
2
0
0
0
2
0
0
0
3
2
0
2
1
1
2
2
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
2
2
1
0
1
1
2
0
0
1
0
0
0
0
0
0
1
0
0
3
3
1
0
0
1
0
2
1
2
1
0
0
2
2
1
0
0
0
0
0
2
0
2
6
0
0
2
0
2
10
0
2
2
2
0
1
2
0
0
0
1
1
3
1
2
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
2
2
0
1
0
1
0
1
1
0
0
0
0
2
1
4
2
0
0
1
0
0
0
0
1
3
2
0
0
0
0
0
2
1
0
1
2
0
1
0
2
1
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
2
1
2
0
2
1
0
1
0
1
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
3
0
2
2
1
0
0
0
1
1
1
0
0
2
0
0
2
1
0
0
0
0
0
1
1
0
0
0
0
2
2
0
0
2
0
0
0
0
2
1
0
0
2
0
0
2
0
0
1
0
0
1
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
1
1
0
2
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
2
1
0
0
0
1
0
0
0
1
2
0
0
0
1
0
1
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
2
0
1
0
1
0
1
0
2
0
1
1
0
2
0
2
1
1
1
0
0
0
0
2
0
3
2
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
2
0
1
0
0
2
1
0
0
0
1
2
0
2
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
2
2
0
1
0
1
0
2
1
0
1
1
0
0
3
0
0
0
0
0
1
1
0
0
0
3
2
1
10
0
0
0
2
0
2
0
0
3
1
0
0
1
0
1
1
1
1
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
2
3
0
0
0
2
0
4
0
0
0
1
0
2
0
0
1
0
0
0
0
0
4
0
0
0
1
0
0
0
0
2
2
1
0
1
0
2
0
0
0
1
2
0
1
1
1
0
0
0
0
0
1
2
0
3
0
1
2
2
0
0
0
0
4
1
5
2
1
2
1
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
2
0
1
2
0
0
0
0
1
0
0
1
2
2
1
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
0
0
2
3
2
0
0
2
0
1
1
0
0
0
0
1
0
0
3
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
2
0
1
0
2
0
1
0
0
0
1
0
2
0
2
0
5
0
2
2
2
2
2
0
1
0
1
0
0
2
0
2
0
0
2
0
0
2
0
1
0
0
2
0
0
0
1
0
0
0
1
2
2
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
1
2
1
1
2
0
0
0
1
0
0
0
3
1
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
2
0
1
0
0
2
0
0
2
1
0
0
1
1
0
0
0
1
1
0
1
1
0
2
0
0
0
0
0
2
0
1
1
0
0
2
0
1
0
2
0
2
1
2
2
2
0
0
1
0
0
0
1
0
0
1
0
1
0
0
1
0
1
0
2
2
0
1
1
1
1
0
2
0
1
0
0
1
1
0
2
2
2
1
0
0
1
0
1
0
0
2
0
0
0
1
0
1
0
2
0
0
1
0
0
0
0
1
0
0
2
2
0
1
2
1
0
0
0
1
1
0
0
0
3
0
3
0
1
0
1
0
1
0
1
0
1
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
1
1
2
2
2
0
1
0
0
2
2
0
0
0
0
0
0
0
1
1
2
0
0
1
0
0
0
1
0
0
1
0
0
0
4
2
0
0
2
1
6
2
0
1
0
0
4
0
0
2
2
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
2
1
0
0
1
0
1
0
0
2
0
2
0
2
0
0
2
1
0
0
0
0
0
1
1
1
1
0
0
3
0
1
2
1
1
0
2
0
1
0
2
0
2
1
0
2
0
0
2
0
0
0
1
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
1
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
1
1
0
0
0
3
2
0
4
0
2
0
2
0
1
3
0
0
1
0
0
0
0
1
0
1
1
0
0
0
1
2
1
0
1
2
1
0
1
2
0
1
0
0
0
2
0
0
2
0
0
1
5
1
0
2
0
2
1
1
2
1
1
0
2
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
1
0
2
0
3
0
0
0
0
0
3
2
2
0
1
1
0
2
0
0
0
1
0
2
1
0
0
2
2
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
2
0
2
0
0
2
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
2
0
1
1
2
2
1
0
0
1
2
0
0
1
0
0
1
0
0
0
1
0
0
0
2
1
1
0
0
2
0
0
1
2
0
1
0
3
0
0
2
2
0
0
2
0
0
0
0
0
0
0
1
0
1
0
2
1
2
2
2
0
0
1
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
1
2
0
1
0
0
2
0
2
2
1
0
0
2
0
2
0
2
0
0
4
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
2
1
2
0
1
0
2
1
1
2
0
1
2
0
1
0
2
0
0
1
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
2
0
1
1
2
0
0
1
2
0
0
0
1
1
0
2
1
1
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
2
0
1
0
0
0
2
1
2
1
0
0
0
2
0
0
0
0
1
0
1
1
0
1
2
1
1
2
1
0
1
1
2
2
0
0
0
1
0
1
1
0
0
0
0
1
0
1
2
0
0
1
1
1
0
0
0
0
2
0
0
0
0
1
2
0
0
1
2
2
0
0
0
2
1
1
0
2
0
1
0
0
2
0
0
2
1
2
0
1
0
2
0
1
0
2
0
0
0
0
0
0
0
0
1
1
3
0
1
0
3
0
4
0
0
2
0
2
2
0
4
1
0
1
0
0
0
2
0
0
0
2
1
1
1
0
1
0
0
0
1
0
1
0
1
0
0
0
0
1
1
0
0
2
0
0
1
1
1
2
2
0
1
0
0
0
0
0
0
3
0
2
1
0
0
0
0
3
1
2
0
0
3
0
1
3
0
0
0
0
0
0
2
0
0
2
2
0
1
1
1
1
3
1
2
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
2
1
2
1
2
1
0
0
0
0
1
0
0
1
0
0
0
0
0
2
2
2
0
0
1
0
1
1
0
1
0
0
0
2
0
1
1
0
1
0
1
0
1
2
0
0
1
1
2
1
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
1
0
0
0
0
1
1
1
2
2
0
1
1
0
0
0
3
0
0
1
1
0
0
0
1
1
2
0
2
1
1
0
0
0
2
2
0
2
0
2
1
3
1
0
0
1
0
0
1
2
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
1
2
2
0
2
2
0
0
0
0
0
2
0
0
0
1
1
1
0
0
0
0
0
0
2
2
2
2
1
2
0
0
2
0
3
0
1
1
0
2
1
0
0
0
0
0
3
0
0
2
1
0
1
0
0
1
1
1
0
2
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
1
1
1
0
0
0
0
2
1
2
2
1
1
0
0
2
0
0
1
2
1
0
0
0
0
2
0
1
2
1
1
2
0
0
0
0
0
2
0
0
0
1
0
1
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
1
1
2
0
0
0
2
0
0
1
0
0
1
0
0
1
1
0
0
2
2
0
0
1
1
0
0
2
0
0
0
1
0
0
1
0
1
2
0
0
0
1
0
0
1
0
0
0
0
1
2
0
0
2
2
0
1
3
0
0
2
1
1
0
1
0
0
0
0
2
1
1
0
2
0
2
0
2
0
0
0
0
1
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
2
0
1
0
5
1
2
0
2
0
2
0
0
0
1
0
1
1
0
0
0
1
0
2
0
0
1
0
0
0
1
0
0
2
0
0
1
1
1
0
0
1
2
0
2
2
2
1
0
0
0
0
0
0
2
2
0
2
0
0
0
1
0
0
0
2
2
0
1
1
2
2
0
0
1
0
0
0
3
0
0
0
0
1
0
0
0
2
2
0
1
0
0
0
1
0
0
2
0
2
0
1
1
0
0
2
0
1
0
0
0
0
1
0
1
0
1
0
0
2
2
3
0
1
1
0
3
2
1
0
1
2
1
1
2
1
0
0
0
0
0
0
0
1
2
0
1
0
2
0
0
1
0
0
0
2
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
2
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
1
1
0
0
0
0
2
1
0
2
1
0
0
0
0
0
0
0
2
1
0
0
1
0
0
1
1
0
0
0
2
0
0
2
0
0
1
2
0
0
2
1
0
1
0
2
0
2
1
0
1
1
0
0
1
1
0
0
0
0
1
2
0
4
0
0
1
0
3
0
2
0
0
0
3
0
0
0
2
1
0
2
2
3
0
0
0
1
2
0
0
1
0
4
1
1
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
2
2
2
0
0
0
2
1
0
1
2
2
0
0
0
0
1
0
0
2
1
1
0
0
1
0
0
0
2
0
2
2
0
0
0
2
0
0
1
0
2
0
0
0
3
0
2
0
4
0
0
1
2
0
0
1
2
0
1
1
0
2
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
2
2
1
1
0
0
3
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
2
1
1
0
3
1
1
0
2
0
0
0
0
0
0
2
0
0
1
0
2
0
2
0
1
0
0
1
5
0
1
0
2
0
0
0
1
1
1
0
2
2
0
0
0
0
1
1
0
0
0
1
0
0
2
1
0
1
0
2
1
1
0
0
1
0
0
0
0
0
1
0
5
0
2
0
0
2
0
2
1
0
2
0
0
2
0
0
0
1
1
0
0
0
0
1
1
0
2
0
2
0
1
0
1
2
0
0
0
0
0
0
0
0
2
2
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
2
3
0
0
0
0
0
1
0
0
2
1
0
1
0
0
0
1
7
1
4
1
0
2
0
0
2
0
0
0
2
0
1
2
0
0
1
0
0
2
2
0
1
0
2
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
1
0
0
1
0
0
0
1
2
0
2
0
0
2
0
0
0
1
2
1
0
2
0
0
0
2
1
0
0
2
0
1
0
0
1
2
0
0
0
0
0
3
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
2
1
1
1
1
0
0
0
1
1
0
0
2
2
0
1
0
2
2
0
1
0
2
2
3
1
1
0
1
0
3
1
0
0
0
1
0
0
0
0
1
2
0
2
1
1
1
1
0
1
0
1
1
1
0
1
0
0
0
0
0
1
0
1
0
2
0
0
0
2
0
1
2
0
0
1
0
0
0
1
1
1
0
2
0
1
1
1
0
0
2
0
0
2
0
1
0
2
0
2
2
0
2
0
0
2
0
0
2
2
2
0
0
0
0
0
0
0
0
3
2
0
0
0
1
0
1
3
0
0
0
0
1
0
2
1
1
1
0
1
0
0
0
0
0
2
3
2
0
1
0
0
1
0
0
2
0
0
0
0
0
0
1
2
0
0
2
0
0
0
1
1
1
0
0
1
1
0
0
0
0
2
2
0
2
0
1
1
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
2
0
2
2
2
2
1
0
0
0
0
0
2
0
3
2
1
0
0
1
1
2
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
1
0
2
0
2
1
2
0
0
0
0
0
0
1
0
1
3
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
2
0
0
1
0
3
2
0
0
1
0
0
0
0
0
0
0
4
0
0
1
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
1
1
0
0
0
1
1
0
0
1
0
0
1
1
1
0
0
0
0
0
4
0
0
0
0
1
0
0
2
0
0
1
1
0
0
2
0
0
0
1
0
0
0
2
0
2
1
0
1
1
0
0
0
0
1
1
1
0
2
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
1
2
0
0
0
1
1
0
1
0
0
0
2
1
1
1
0
0
2
0
2
0
0
0
0
0
1
1
1
0
2
0
0
0
1
0
1
0
0
1
0
1
2
0
0
0
0
5
0
0
2
0
2
1
0
1
0
0
2
2
0
0
0
0
1
2
0
2
2
0
1
1
2
0
2
2
0
3
0
0
0
2
1
0
2
0
0
0
0
1
2
1
0
0
2
2
0
2
0
0
1
0
2
0
0
0
0
1
0
1
0
0
0
2
0
2
2
2
1
0
0
2
1
0
1
1
0
0
0
1
0
0
1
1
0
0
1
1
0
0
0
0
1
1
0
0
2
0
0
1
2
0
0
2
0
2
0
1
1
0
0
2
0
0
2
0
0
2
0
1
2
0
0
1
0
0
0
2
2
3
2
0
0
1
0
1
0
0
2
1
0
2
2
0
0
0
2
1
0
2
0
0
2
2
3
0
0
0
0
1
0
2
1
0
1
0
0
0
0
1
0
1
1
2
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
1
2
0
0
0
0
0
1
2
0
0
0
2
2
0
1
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
2
1
0
0
0
2
1
3
1
0
0
0
0
4
0
0
0
0
2
2
0
0
1
1
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
2
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
1
2
2
0
2
0
0
2
1
2
0
2
1
2
3
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
1
0
0
0
0
2
1
1
0
0
0
0
1
1
2
0
0
2
0
0
0
0
1
0
0
0
2
0
0
2
2
1
0
1
1
1
0
1
1
2
0
1
0
0
2
0
0
0
1
1
1
0
2
0
0
0
0
3
0
1
0
0
1
1
0
0
1
0
1
0
0
0
0
0
1
1
0
0
2
0
1
1
0
2
1
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
1
2
0
0
1
2
0
2
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
2
2
1
2
2
0
2
0
0
2
0
0
0
1
0
1
0
0
0
1
1
0
0
1
2
0
0
1
1
0
0
2
1
2
0
0
2
0
0
1
0
0
1
0
0
1
0
0
2
1
0
0
1
2
0
2
0
0
0
1
2
0
1
0
0
2
0
1
0
2
0
3
2
0
0
0
0
0
2
0
2
0
0
0
1
1
0
0
0
0
0
1
2
0
3
0
0
0
2
0
0
2
0
0
1
0
1
1
1
1
0
0
0
2
0
0
2
0
0
2
1
0
1
2
0
0
1
2
0
1
0
0
0
0
0
0
2
2
0
1
2
1
2
0
2
0
1
0
1
0
1
2
0
0
2
0
0
0
1
0
0
1
2
0
0
0
0
2
2
0
0
0
0
0
1
0
0
2
0
0
3
0
0
2
2
2
1
0
2
0
2
1
2
1
1
2
0
1
0
0
0
0
2
2
0
2
0
0
1
0
0
1
0
2
1
1
0
1
0
0
0
2
2
0
0
0
0
1
0
0
0
2
0
0
1
2
0
1
2
0
0
1
0
0
0
1
2
1
0
0
1
0
0
2
2
0
2
0
2
0
2
1
2
0
1
2
0
2
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
2
1
0
1
0
1
2
0
0
0
0
0
0
1
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
3
2
0
0
2
1
0
0
0
1
0
0
0
0
0
0
1
2
1
1
0
0
0
0
0
1
0
1
1
0
0
2
0
3
0
2
0
1
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
3
0
1
0
2
2
0
0
2
2
0
1
1
0
0
0
1
0
0
2
1
1
0
0
0
1
1
1
0
2
0
2
1
0
0
0
3
2
1
0
0
2
0
0
0
0
0
0
1
2
1
0
2
2
1
0
2
4
0
0
0
2
1
1
2
0
0
3
0
2
0
0
1
0
0
0
0
1
0
0
2
1
2
0
0
0
1
0
1
0
1
0
0
1
1
0
1
1
0
0
0
1
1
1
1
0
0
0
0
2
0
0
0
2
0
0
2
0
1
0
2
2
0
0
2
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
1
0
0
1
1
2
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
1
0
0
1
2
1
1
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
3
0
0
0
0
0
0
1
0
0
1
0
2
1
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
3
0
0
0
2
0
0
2
1
1
1
0
0
0
0
0
2
1
0
1
0
2
2
2
0
0
0
2
0
0
0
1
0
0
1
2
0
0
2
0
0
0
2
0
2
0
2
0
1
0
0
0
0
0
0
0
0
2
0
2
0
1
2
2
3
0
1
0
1
0
0
0
2
0
0
0
1
2
0
1
2
2
1
0
0
0
0
0
0
1
0
2
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
1
2
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
2
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
3
1
2
0
1
0
2
2
0
1
0
1
1
0
0
0
0
0
1
2
0
1
2
1
2
0
1
0
0
2
1
0
0
2
0
0
1
0
0
1
0
2
0
2
1
0
2
1
2
1
0
0
0
0
0
1
0
3
0
1
2
2
1
1
1
1
0
1
0
0
0
1
0
2
1
6
1
0
0
2
0
2
0
0
0
2
0
3
0
2
1
3
1
0
0
1
1
2
0
0
0
2
0
2
0
0
2
0
1
0
0
0
0
0
1
2
1
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
2
0
1
0
1
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
1
0
1
1
0
0
2
0
1
0
0
0
1
1
0
1
0
1
2
0
1
0
0
1
1
0
1
0
0
0
1
0
2
0
0
2
0
3
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
2
2
0
2
0
1
2
0
1
0
1
0
0
1
1
0
0
0
0
1
1
0
0
0
1
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
2
1
0
1
1
0
0
1
1
2
0
0
0
0
1
1
0
0
0
3
0
0
1
2
1
2
2
0
1
0
0
2
0
0
0
0
0
1
1
0
1
1
0
0
1
0
1
1
2
0
0
0
2
2
0
0
0
0
2
2
0
2
2
1
2
2
0
0
0
0
0
0
5
0
0
0
0
1
1
0
0
1
1
0
1
0
0
0
1
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
3
3
0
1
1
1
0
2
0
0
0
0
0
2
0
0
0
2
0
2
0
2
0
1
2
0
1
0
0
2
2
0
2
0
2
1
0
1
0
0
2
1
0
0
0
0
0
0
2
1
2
1
2
0
0
1
0
2
0
0
0
0
2
2
0
1
0
0
2
1
0
0
0
1
1
0
0
0
1
0
1
1
2
0
0
2
0
0
1
0
0
1
1
2
1
2
2
2
0
0
1
0
2
1
0
1
0
1
0
1
3
1
0
0
1
1
1
0
2
0
0
0
0
1
0
0
3
1
0
0
2
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
2
2
1
0
0
1
0
0
0
1
1
0
1
0
0
0
1
2
0
2
2
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
3
0
1
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
2
0
0
0
0
0
1
0
1
2
0
0
0
0
1
1
0
1
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
1
2
0
0
0
0
0
1
0
0
1
2
0
0
2
2
0
0
0
0
0
0
1
0
1
1
2
1
0
0
0
0
0
0
0
0
0
2
3
0
0
2
0
0
0
1
0
0
1
2
3
0
0
0
1
2
2
1
3
0
0
0
0
0
0
0
1
0
0
0
2
0
5
1
0
0
2
0
0
0
0
0
1
1
2
0
0
0
1
1
0
1
2
0
1
1
1
0
1
0
0
1
1
0
0
0
0
0
0
0
2
2
0
0
0
1
0
1
0
0
0
2
0
0
1
0
2
0
0
1
0
0
0
2
0
1
0
2
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
3
0
0
1
0
1
1
2
0
2
0
0
0
0
1
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
2
1
0
0
1
1
2
0
0
0
0
0
1
1
0
0
1
0
0
0
1
2
0
2
0
1
0
0
0
4
0
0
2
1
0
1
2
1
1
0
0
2
1
0
0
1
0
2
0
1
0
0
0
0
0
1
0
2
0
1
0
0
2
0
2
0
1
0
0
0
0
0
0
0
1
0
1
0
2
1
1
2
0
2
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
2
0
0
0
0
0
1
1
0
2
2
2
0
0
2
2
0
0
2
2
0
0
1
1
2
1
0
0
1
0
0
2
0
2
0
1
0
1
0
2
2
0
0
0
2
3
1
0
0
0
0
1
0
0
1
0
2
1
0
0
0
0
1
0
0
0
2
2
0
0
0
3
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
1
1
2
1
0
0
3
1
0
0
2
0
0
0
0
0
0
1
1
0
1
0
2
0
1
0
0
0
2
2
0
2
0
0
0
0
0
0
0
2
0
1
2
1
0
1
2
0
1
4
2
2
2
2
1
0
2
0
0
0
2
0
0
0
2
0
2
0
0
1
0
0
1
3
1
1
0
2
0
0
0
1
0
2
1
1
0
1
1
3
1
0
0
0
0
0
0
0
0
0
2
2
2
5
0
0
2
0
0
0
0
1
0
0
1
1
2
0
0
0
1
0
0
0
1
0
1
2
0
0
0
0
0
2
0
0
2
0
3
1
0
1
0
0
1
0
0
0
1
1
0
2
0
0
0
0
0
0
0
2
1
2
2
0
2
0
0
1
0
1
1
0
2
0
1
2
0
0
0
0
2
0
2
1
1
0
0
1
0
1
0
2
0
0
2
2
0
2
0
0
0
1
1
0
1
0
0
2
0
0
2
1
0
3
0
0
0
3
2
0
0
1
0
0
0
0
2
0
1
0
1
0
0
2
1
2
0
0
0
1
2
0
1
0
2
0
0
0
0
0
2
1
0
1
0
1
0
1
2
1
0
0
1
2
0
0
1
2
0
2
0
2
4
0
1
0
0
0
0
0
2
2
0
1
1
0
0
0
0
0
1
2
2
2
2
0
2
0
0
0
0
0
2
2
0
2
1
2
0
0
0
3
1
2
0
0
0
1
1
0
0
2
0
0
1
0
0
0
1
1
0
0
2
2
1
0
0
0
0
1
1
2
0
0
0
0
0
0
2
1
0
0
1
0
2
2
0
0
0
0
1
0
0
2
0
0
2
0
1
0
0
0
1
1
2
1
0
0
1
1
2
1
0
0
0
0
0
2
0
0
0
0
2
2
1
0
0
0
0
0
0
0
2
0
3
0
1
0
0
1
2
0
1
1
0
1
0
0
0
0
2
0
1
0
0
0
1
1
0
0
2
0
2
0
0
2
0
0
1
0
0
2
0
0
0
2
0
2
2
0
0
1
0
0
4
0
0
0
0
0
0
1
1
0
2
0
2
0
0
0
0
0
1
2
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
2
2
2
0
0
1
0
0
0
0
1
1
0
2
1
0
0
0
0
3
1
0
0
2
0
0
0
0
2
0
1
2
2
1
1
0
0
2
0
0
1
1
1
0
1
1
0
1
0
1
0
0
1
0
1
0
0
0
1
2
1
0
2
0
2
0
3
0
0
0
0
0
0
0
1
2
0
2
1
1
0
0
2
3
1
0
2
0
0
1
0
1
0
1
0
0
2
5
1
0
0
0
0
2
1
0
1
2
0
0
0
0
0
0
0
0
1
0
0
1
1
2
0
1
0
2
0
0
2
0
2
0
1
0
2
0
0
2
1
2
0
0
2
0
0
0
1
1
0
1
2
0
0
0
0
1
0
0
1
0
2
1
0
2
0
2
0
0
0
2
0
2
1
0
0
3
1
1
1
0
1
0
2
0
2
0
0
1
0
2
0
0
0
1
2
2
1
0
0
0
1
0
2
0
1
0
1
0
0
0
0
1
2
2
0
2
1
0
2
0
0
0
0
2
1
2
1
2
1
0
0
0
2
3
0
0
0
2
2
0
0
1
0
0
0
2
0
0
1
1
0
2
1
0
0
1
2
0
0
3
0
0
1
0
0
2
1
1
0
1
2
1
0
1
1
2
0
0
0
0
0
0
1
0
1
2
1
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
2
2
0
2
0
2
0
0
0
0
0
0
0
0
2
2
0
2
2
1
0
2
1
1
0
2
2
0
1
0
0
0
0
0
1
1
0
0
0
2
0
1
2
1
2
0
5
0
2
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
2
1
0
0
1
0
2
0
0
0
2
1
0
0
1
1
0
3
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
1
1
0
0
2
0
1
1
1
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
1
0
0
4
0
0
1
0
0
0
2
0
0
3
1
0
0
0
0
4
2
0
0
2
1
1
2
0
2
0
0
2
0
1
0
2
2
0
1
2
0
2
0
0
0
0
0
2
0
0
1
0
0
0
2
1
0
0
0
0
0
1
0
0
0
2
1
2
0
1
0
1
1
1
0
0
1
0
1
0
1
0
0
0
1
0
2
0
2
1
2
2
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
2
1
0
2
0
1
1
1
0
0
0
2
1
0
1
3
0
0
0
1
0
0
0
4
1
0
0
0
0
1
2
0
0
0
2
2
0
0
0
1
1
2
2
0
0
2
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
2
1
1
0
0
0
0
0
2
0
2
0
1
1
2
0
2
0
0
0
1
0
0
1
1
1
0
1
0
1
0
0
3
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
1
0
0
0
2
0
0
2
1
0
3
1
2
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
1
0
0
3
1
0
1
0
0
0
0
0
1
0
1
2
0
2
0
0
0
0
0
1
1
2
0
0
0
1
0
2
0
0
0
0
1
1
1
0
2
0
0
0
1
0
0
2
0
3
0
2
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
2
1
0
1
2
2
2
1
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
2
0
2
0
1
0
0
0
1
3
0
0
1
1
0
0
0
1
2
0
0
0
1
5
5
2
0
0
1
0
0
1
2
0
2
1
0
2
2
0
1
0
2
0
1
1
0
1
1
1
0
0
0
0
2
0
0
1
0
2
2
0
0
2
0
0
2
1
0
1
0
1
2
0
2
0
2
0
0
2
1
2
1
0
1
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
2
1
0
0
4
1
0
0
0
0
0
2
1
0
0
0
0
0
2
1
2
0
2
1
0
2
1
0
0
0
2
0
1
2
0
2
0
1
2
2
0
0
1
0
0
1
0
0
0
0
2
1
2
0
0
0
2
0
0
0
0
0
0
1
0
1
2
0
0
0
1
0
2
0
1
2
1
0
2
1
0
1
0
0
1
3
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
1
2
2
1
0
1
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
1
0
0
0
0
0
1
3
1
0
0
0
0
0
0
0
0
2
0
1
1
7
0
0
1
2
1
0
0
0
1
0
2
1
0
0
1
1
0
0
2
0
1
2
1
0
0
1
1
0
2
0
1
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
1
0
0
1
0
0
1
0
2
0
0
2
0
0
0
1
1
2
0
1
2
0
0
2
1
0
0
1
0
1
1
0
1
1
0
0
0
2
0
0
0
0
1
1
0
2
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
3
3
0
0
0
0
2
0
2
0
2
1
2
0
0
0
0
0
2
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
2
0
0
1
0
1
0
2
1
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
2
0
0
0
0
0
0
0
3
2
2
2
0
0
0
1
0
0
1
3
0
0
1
2
0
0
1
1
0
0
2
0
1
0
1
0
0
2
0
0
0
1
0
1
0
2
0
2
2
2
0
1
0
0
0
0
1
2
0
2
0
3
0
0
0
1
0
0
0
3
4
0
1
2
2
2
0
2
0
1
2
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
1
2
0
0
1
0
0
0
1
0
2
0
0
0
0
1
0
0
0
1
1
0
0
0
0
2
0
0
2
0
2
1
0
0
2
1
0
2
0
2
2
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
1
2
1
0
0
0
1
0
0
3
1
2
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
1
1
0
0
2
0
0
0
1
0
2
2
2
1
2
2
0
0
0
1
0
0
2
0
2
0
0
1
0
0
0
2
0
0
0
1
2
2
0
0
0
1
2
0
3
0
0
1
0
2
0
0
0
1
0
1
1
0
1
2
0
2
0
0
1
1
1
0
0
0
1
1
2
0
0
1
0
0
2
2
0
0
1
1
1
1
0
0
0
0
0
2
1
0
2
0
0
0
0
1
0
2
0
1
0
1
2
1
1
0
0
0
0
0
2
1
0
2
0
0
0
0
0
1
0
0
1
2
0
1
0
0
2
2
1
1
2
2
0
0
0
2
2
1
0
0
0
0
0
2
2
0
0
1
0
1
0
0
0
1
2
2
0
0
0
0
0
0
2
0
0
1
2
0
3
1
0
1
0
0
1
0
0
0
0
0
1
0
0
2
0
1
2
0
1
2
0
1
0
0
1
1
0
0
1
0
0
2
1
1
0
0
0
0
0
2
3
1
2
0
2
0
0
1
0
1
2
0
1
0
0
1
0
0
0
2
1
0
0
0
0
4
0
0
0
0
0
0
1
0
2
1
1
0
0
1
0
0
2
0
1
2
2
1
4
1
0
0
0
2
0
1
1
2
2
0
1
1
0
1
2
1
0
2
0
0
3
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
2
4
2
2
1
0
0
2
0
2
0
0
0
0
1
0
2
0
2
1
1
0
1
0
1
2
3
0
0
0
1
1
0
0
1
3
0
2
0
0
0
1
0
0
4
3
0
0
2
0
0
1
0
0
2
0
2
0
1
0
0
0
0
0
1
1
0
2
0
0
3
2
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
1
0
1
4
0
1
1
0
0
2
2
0
0
0
2
1
0
1
0
0
0
0
0
0
2
0
0
0
0
3
2
0
0
0
1
0
1
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
2
0
0
1
1
1
1
0
0
0
0
1
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
3
2
1
0
0
0
1
2
0
0
2
2
1
0
1
1
0
0
1
2
0
2
1
1
0
1
2
0
0
2
0
0
1
2
0
1
0
0
1
0
0
0
2
2
2
0
0
1
2
1
0
0
1
2
0
3
1
0
0
0
0
0
1
4
0
1
0
0
0
0
0
2
1
2
0
2
1
0
0
0
2
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
1
2
0
1
2
0
0
0
1
0
0
2
0
0
2
1
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
2
2
1
0
0
0
2
0
0
0
1
0
0
2
0
2
0
2
0
0
0
1
2
0
0
0
1
0
0
0
2
0
0
3
2
0
0
0
2
0
1
0
0
0
0
1
1
1
0
1
2
1
0
0
0
0
2
0
0
0
3
0
1
0
1
1
2
0
0
1
0
1
0
0
1
1
1
0
0
1
2
2
0
1
2
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
2
1
1
1
2
1
1
0
1
0
2
0
0
1
2
0
0
1
0
0
0
2
0
2
0
4
1
0
1
0
2
1
0
0
0
1
0
2
1
0
0
1
0
2
0
0
2
3
0
0
0
2
1
0
2
0
0
0
2
0
0
2
2
0
2
0
0
0
0
0
0
2
1
2
1
1
0
2
0
2
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
1
0
1
1
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
2
0
1
4
2
0
1
2
0
0
2
2
0
2
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
1
1
2
2
2
0
0
0
0
0
0
1
2
1
1
1
0
0
2
2
0
0
0
2
0
1
1
0
0
0
2
1
0
1
1
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
2
1
1
2
1
1
2
0
0
1
2
0
1
2
0
1
0
2
0
2
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
2
0
0
0
0
1
0
1
2
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
2
2
0
2
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
1
0
2
0
0
2
0
2
0
0
0
0
4
0
2
1
0
0
0
1
0
0
0
1
0
0
1
0
1
2
0
0
2
0
0
0
1
1
0
0
0
0
0
0
2
1
0
1
0
2
0
1
1
1
0
0
0
2
0
0
0
1
0
0
0
0
1
2
2
0
1
0
2
0
0
2
1
0
0
0
2
0
0
0
0
2
0
2
2
0
2
0
2
1
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
2
0
0
0
2
3
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
2
0
0
2
0
2
1
0
0
0
1
0
0
0
1
0
1
3
1
0
1
0
2
0
2
1
0
0
0
1
1
0
0
0
0
0
2
0
1
0
4
1
1
0
1
1
0
0
0
0
1
0
0
2
0
1
0
1
0
0
1
0
0
0
0
0
2
0
0
2
0
0
3
2
0
0
1
1
2
0
0
0
2
1
1
3
1
0
2
1
0
1
0
0
0
0
0
0
1
0
0
4
0
0
0
0
2
0
2
1
0
0
0
2
0
0
0
0
1
0
1
2
0
0
0
0
0
1
0
0
0
1
0
0
3
1
1
2
0
0
0
0
0
1
0
1
0
0
3
0
0
0
0
2
2
0
0
0
0
0
0
0
0
4
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
1
1
1
1
1
0
0
3
0
2
0
2
1
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
1
0
0
0
2
1
0
1
2
0
1
0
0
0
0
1
0
0
3
0
0
1
2
2
1
1
0
0
0
0
1
0
0
0
0
0
1
2
0
2
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
2
1
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
2
1
1
1
0
0
1
0
1
2
1
0
2
2
1
1
2
2
1
1
0
0
0
1
0
0
0
0
0
2
0
2
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
4
0
0
0
2
0
1
0
0
0
0
1
2
0
0
3
0
3
1
1
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
1
2
0
0
2
0
0
0
2
0
1
0
2
0
1
0
2
0
1
2
1
2
1
0
0
1
1
3
0
0
1
2
0
0
0
0
0
1
1
0
1
1
0
0
0
1
0
2
0
2
2
0
0
2
0
2
0
0
1
0
0
0
1
2
3
2
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
1
2
1
1
1
0
1
2
0
0
0
0
1
0
2
2
0
1
1
0
0
0
0
0
0
0
2
0
2
0
0
0
2
1
0
2
2
0
0
0
0
0
1
6
0
0
0
0
2
0
0
0
3
2
0
0
0
0
0
0
0
1
0
0
1
0
0
1
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
2
0
1
0
2
0
2
0
2
0
0
0
0
1
0
0
0
2
1
2
0
0
2
0
0
0
0
0
1
1
2
0
2
2
0
1
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
1
1
3
0
0
0
1
0
0
1
2
1
0
0
2
3
1
0
0
0
0
2
0
3
0
0
2
0
0
0
0
0
0
1
2
0
0
1
2
2
2
0
2
0
0
0
2
0
0
2
1
2
0
2
1
2
2
0
2
1
1
1
2
0
2
1
1
2
1
0
0
1
1
4
1
0
0
0
0
0
0
0
2
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
2
1
2
0
0
0
0
0
0
0
0
2
1
0
0
1
1
2
4
0
1
2
0
0
2
1
1
1
0
0
0
2
1
2
0
0
0
2
0
0
0
0
0
0
1
3
2
0
1
0
0
0
0
0
2
0
0
1
1
0
2
0
2
0
0
1
0
0
1
0
1
0
1
0
1
0
1
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
2
3
0
0
0
1
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
2
2
2
0
1
1
0
1
0
0
0
0
0
0
3
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
1
0
0
1
2
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
1
0
4
0
1
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
1
1
0
1
1
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
2
2
0
0
2
1
1
0
0
0
2
0
1
0
1
1
0
2
0
2
0
0
1
0
1
0
0
0
1
0
0
1
0
0
1
0
0
1
1
0
0
0
0
1
1
0
1
2
0
1
0
1
0
1
1
1
0
0
0
1
0
0
2
1
0
2
1
0
1
1
2
0
0
0
0
2
2
2
0
1
0
1
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
1
0
2
1
7
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
1
0
0
0
1
0
3
0
2
2
0
0
0
0
2
0
2
0
1
0
0
1
0
2
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
2
1
6
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
2
0
1
0
1
0
0
1
4
1
0
0
2
1
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
1
2
0
0
0
1
0
2
1
2
0
0
2
0
1
0
0
0
3
0
1
1
0
0
0
0
2
0
0
0
0
0
2
0
0
1
1
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
1
1
2
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
2
3
0
0
0
1
0
2
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
1
0
2
0
1
0
1
0
2
1
1
1
0
0
0
0
0
2
0
2
1
0
1
0
0
1
2
0
0
0
2
1
1
2
1
2
0
1
0
0
0
0
0
0
2
2
2
0
1
0
2
0
1
2
1
2
0
2
0
0
0
1
1
0
0
0
1
2
0
1
3
0
0
0
2
0
1
0
1
1
1
1
0
2
0
0
0
0
2
1
2
0
0
2
2
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
2
0
0
2
0
1
0
1
0
0
0
0
0
0
0
3
3
2
0
2
1
2
0
1
0
0
1
0
2
1
0
1
0
0
1
0
0
0
0
1
0
1
2
1
1
0
0
0
2
2
1
0
0
0
0
2
2
0
0
1
0
3
0
1
1
3
1
0
0
1
2
0
1
0
0
0
0
0
0
2
2
0
0
0
1
2
0
1
0
2
0
0
0
1
1
1
0
1
0
0
0
0
1
1
2
2
0
0
2
0
3
1
1
0
0
1
2
2
0
0
2
1
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
3
0
0
2
0
2
0
0
0
1
0
1
0
1
0
3
0
0
0
3
0
0
0
1
0
2
0
4
1
2
1
2
0
2
0
2
0
0
0
1
0
0
1
0
0
2
0
0
3
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
1
0
1
1
0
3
0
0
0
0
1
1
0
0
1
1
2
2
0
1
2
1
0
1
0
1
1
0
1
0
2
1
0
1
0
2
0
0
0
0
0
0
1
2
0
0
0
2
0
0
2
2
1
2
0
1
0
0
0
0
1
3
3
0
0
1
2
0
0
1
0
2
0
2
1
0
2
3
1
0
1
0
2
0
2
0
1
0
2
1
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
2
1
2
0
1
0
2
1
2
0
2
0
1
0
0
0
2
2
1
1
0
1
3
0
1
0
0
2
0
2
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
1
0
0
1
2
0
0
0
2
1
0
1
0
1
1
0
2
0
0
2
0
2
0
0
1
2
2
0
0
0
0
0
1
2
0
3
0
9
0
0
2
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
2
1
1
0
0
0
0
0
2
1
1
0
0
0
0
1
2
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
2
2
0
1
0
2
2
0
0
0
2
2
2
2
0
0
1
4
0
0
1
1
0
3
0
0
2
2
0
0
0
0
0
0
0
2
0
2
1
2
0
2
1
0
2
0
2
0
0
0
0
2
1
0
0
2
2
3
0
0
3
0
0
0
0
2
1
0
1
2
2
0
0
2
0
0
2
0
0
0
0
0
1
0
0
3
0
0
0
2
1
0
2
0
0
0
1
0
1
1
1
0
2
2
2
1
2
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
3
2
0
0
1
0
0
0
2
2
0
0
2
2
0
0
2
0
0
0
1
1
0
1
2
0
0
1
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
2
0
1
0
2
0
0
0
2
0
0
1
0
0
2
0
0
0
0
2
2
1
0
2
0
0
0
0
0
0
2
0
0
0
2
1
0
2
0
2
1
2
1
1
0
2
2
0
0
1
0
2
0
1
1
2
1
0
0
2
0
1
0
0
0
2
2
0
2
3
0
1
0
2
0
0
0
2
0
0
1
0
0
1
0
2
0
0
2
3
0
0
2
0
2
0
0
0
1
2
2
0
0
2
0
0
3
0
1
0
1
2
0
0
0
0
1
0
2
0
2
1
1
1
0
1
2
1
0
0
1
4
0
2
1
1
0
0
0
1
0
0
0
0
1
0
0
2
0
1
0
2
0
0
1
0
0
0
2
0
2
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
1
2
2
0
0
1
2
0
2
1
0
1
1
0
0
0
0
0
0
2
1
1
2
0
0
3
0
0
3
1
0
0
0
0
0
0
1
2
0
0
1
0
0
1
0
0
0
1
0
0
2
0
0
0
1
0
1
0
0
0
0
5
0
0
1
0
1
0
2
2
1
0
4
2
0
2
0
0
0
0
1
0
2
0
0
0
0
0
1
1
0
1
0
2
1
1
0
1
0
0
1
0
2
1
0
2
2
1
1
2
1
3
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
2
0
0
0
2
0
0
0
2
1
0
1
1
1
0
2
2
0
1
0
0
0
0
0
1
5
0
0
2
0
2
3
4
0
0
2
2
1
2
1
2
2
0
0
0
1
0
0
1
1
0
2
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
1
0
1
2
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
5
0
0
0
0
0
0
0
1
1
0
2
0
0
1
0
0
2
2
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
3
0
3
2
0
2
1
0
0
0
0
0
4
0
1
1
0
3
1
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
2
2
2
1
2
0
0
1
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
2
1
0
1
0
0
0
2
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
2
1
1
1
1
1
0
0
2
0
5
2
2
0
1
2
0
0
0
0
1
0
0
0
2
0
0
0
2
0
1
2
1
0
0
0
2
0
0
0
0
0
2
2
1
2
2
2
0
2
0
0
2
2
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
1
0
2
2
0
2
3
0
0
2
0
0
1
2
0
2
1
0
0
0
2
1
0
0
1
1
0
0
0
0
2
1
1
1
1
0
1
2
1
0
0
0
1
1
0
0
0
1
0
0
0
1
2
0
1
0
0
0
0
0
1
0
0
0
3
1
2
0
0
1
0
1
0
0
0
0
0
1
0
2
0
0
0
2
0
2
1
0
0
2
0
0
1
0
0
2
1
2
0
0
0
1
0
0
2
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
2
0
1
0
2
0
2
2
0
0
0
1
0
1
1
1
0
2
1
1
2
0
0
2
2
0
2
0
0
0
0
0
0
0
2
2
1
0
0
0
1
0
0
1
2
0
2
0
0
0
0
0
0
0
2
1
1
0
0
0
1
0
1
0
0
0
1
0
0
0
2
1
0
0
1
0
1
0
4
2
0
0
0
2
1
0
2
0
1
2
2
0
0
0
0
0
0
1
1
0
0
2
0
0
1
2
0
0
0
1
0
1
1
1
0
1
2
2
0
2
2
0
2
1
0
1
0
0
0
2
1
1
1
1
1
1
1
0
0
0
2
0
0
0
1
0
1
3
2
0
0
1
0
3
0
0
0
0
0
0
1
2
0
0
2
0
0
1
0
0
1
1
0
1
0
1
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
3
1
0
2
1
0
0
4
0
0
0
1
1
0
0
0
0
1
2
1
0
0
0
0
2
0
1
0
0
1
0
0
0
3
3
2
0
0
2
0
1
0
2
0
1
2
5
1
0
2
0
0
0
0
0
0
1
1
2
0
2
0
0
0
1
2
0
0
0
1
5
1
0
0
1
1
0
0
2
0
1
2
0
0
3
0
3
0
1
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
2
1
2
3
0
1
0
0
0
2
0
0
0
0
1
1
0
0
1
1
0
0
2
0
0
2
1
0
2
0
0
0
1
0
0
0
2
2
0
0
0
1
0
0
1
0
2
1
1
1
3
2
1
0
2
0
1
1
0
1
0
2
0
0
0
1
0
1
1
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
2
0
2
1
0
0
2
1
0
0
0
1
0
0
0
2
0
1
0
0
0
0
3
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
2
0
1
1
0
1
0
0
1
1
0
1
0
0
0
2
0
3
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
1
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
2
3
2
1
0
2
1
0
0
0
0
1
1
0
0
2
0
1
2
2
0
0
1
3
1
2
0
1
1
0
1
0
2
1
0
1
1
0
2
1
0
0
1
0
0
1
0
0
0
1
0
0
2
1
1
0
0
0
0
1
1
0
0
0
0
1
2
0
2
0
0
0
0
1
1
0
2
0
0
0
0
2
1
1
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
1
2
0
0
0
3
0
0
0
2
0
1
0
0
0
1
2
0
0
3
0
0
0
2
0
0
2
1
0
1
0
0
0
0
1
2
0
0
0
0
2
0
1
1
0
2
0
1
0
0
2
0
2
2
2
0
0
2
0
1
1
0
0
0
0
3
0
2
0
2
0
0
0
0
2
0
2
1
0
1
0
0
1
2
0
1
1
3
1
2
2
2
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
1
0
2
2
1
2
1
0
0
1
2
4
3
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
2
0
2
1
0
0
1
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
3
2
1
1
0
2
0
1
2
1
0
0
2
0
0
0
1
0
0
1
0
1
0
0
2
1
2
0
0
1
1
0
0
0
0
2
0
0
2
0
2
0
2
0
0
0
2
0
0
2
0
2
1
2
0
1
2
1
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
4
0
1
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
1
2
1
0
0
0
1
1
0
1
2
1
0
2
0
3
2
0
1
1
0
2
1
2
2
2
2
0
1
2
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
2
0
0
1
0
1
1
2
0
0
0
0
2
0
2
1
0
0
0
0
3
1
1
0
0
0
0
2
0
0
0
2
2
0
1
2
0
1
0
1
1
1
1
0
1
0
2
2
1
1
2
2
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
1
1
6
0
0
0
1
0
0
0
0
1
2
1
0
0
2
0
0
0
1
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
3
0
0
1
3
0
0
1
2
1
0
0
0
1
0
0
0
0
0
0
0
2
1
0
1
0
0
1
0
0
0
0
0
0
2
2
0
1
0
0
2
0
1
0
0
0
0
1
0
3
0
0
0
0
0
3
2
0
0
0
1
2
2
0
1
2
0
0
0
1
0
2
2
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
2
1
1
0
0
0
0
1
1
0
2
1
0
1
0
0
0
0
0
0
0
2
1
0
0
0
2
2
1
0
0
0
0
0
0
1
0
0
1
1
1
2
4
1
0
0
0
2
0
1
1
1
0
0
0
2
3
1
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
1
2
1
2
3
0
0
0
2
0
0
3
1
1
1
0
1
2
1
1
0
0
2
0
0
0
0
0
1
0
1
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
2
2
2
1
0
0
2
3
0
0
2
0
0
2
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
2
1
0
0
2
4
0
0
0
0
1
2
4
0
0
0
0
1
0
0
1
0
1
3
2
0
0
1
0
0
0
1
0
0
0
2
0
0
2
0
0
2
0
1
2
0
0
1
0
0
1
1
1
0
1
0
2
2
0
2
0
1
1
2
0
0
0
1
8
1
0
0
0
2
0
0
1
0
0
0
0
0
0
2
1
1
0
1
0
1
1
1
0
2
0
0
0
2
0
2
0
2
0
3
0
0
0
0
1
2
0
0
2
0
2
2
0
1
1
2
0
1
0
2
1
1
0
2
0
2
0
0
0
1
1
1
1
0
0
1
2
0
2
2
2
0
1
1
0
2
0
0
1
2
1
2
0
0
0
0
1
0
0
0
1
0
0
0
0
2
1
0
1
0
0
0
0
0
3
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
2
0
0
1
3
0
0
0
0
3
2
1
1
0
0
2
0
0
1
0
0
0
0
3
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
2
0
1
0
2
0
1
2
0
2
0
1
0
0
0
3
2
0
2
1
0
0
0
0
0
0
1
0
2
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
2
1
0
1
1
0
1
2
0
2
0
0
1
2
0
3
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
3
0
0
2
0
0
0
0
1
2
0
0
1
2
1
0
2
0
1
1
1
0
2
1
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
2
1
1
3
1
2
0
0
0
0
0
0
0
0
0
0
0
0
5
1
0
1
0
0
0
0
0
2
2
1
1
1
0
2
2
0
0
2
3
0
0
2
0
2
0
2
2
1
1
1
2
0
0
0
0
2
0
0
0
4
0
0
1
0
1
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
2
0
0
0
0
1
0
2
0
0
1
2
0
1
1
0
0
0
0
1
0
0
0
0
2
0
1
0
0
1
0
0
2
0
0
3
0
3
0
0
1
0
0
0
1
1
0
1
0
1
0
0
1
0
0
0
0
0
1
1
1
2
0
0
0
2
0
0
0
2
2
0
2
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
1
2
2
1
0
0
0
0
0
0
1
0
2
0
0
2
1
0
1
0
1
1
1
1
1
0
2
0
0
0
1
0
1
2
0
1
0
0
1
0
0
0
2
0
0
0
2
1
0
0
0
2
1
0
0
0
1
2
0
0
0
0
2
2
0
0
1
1
0
2
0
2
0
2
1
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
1
1
2
0
2
0
1
0
0
0
1
0
0
1
0
0
1
1
0
2
0
0
0
0
2
0
0
3
0
0
0
1
2
3
0
2
0
2
0
0
2
1
2
0
0
2
2
0
2
0
0
3
0
2
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
1
2
0
0
0
2
1
0
0
0
1
2
2
0
2
0
0
1
2
0
2
1
3
0
2
0
0
1
0
0
2
2
1
2
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
4
1
0
0
0
0
0
1
0
2
0
0
0
1
2
1
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
1
1
0
0
1
0
1
2
2
2
2
2
2
0
0
0
1
2
3
0
0
0
2
2
2
1
0
1
0
2
0
1
0
0
0
1
0
3
0
1
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
2
1
1
0
3
1
0
1
0
2
0
1
1
1
0
2
0
0
0
0
1
0
0
0
0
2
0
1
2
1
1
2
0
2
2
0
1
1
1
2
1
0
0
2
2
0
0
2
2
0
0
0
0
2
1
0
0
0
0
1
0
2
2
2
1
0
0
1
2
2
4
0
0
0
0
1
0
2
2
0
0
0
2
3
1
1
2
1
1
0
2
2
1
0
0
1
1
0
1
0
1
1
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
2
0
2
0
0
1
0
0
0
0
0
1
0
0
0
1
2
0
2
0
0
2
0
0
1
0
2
0
0
0
2
0
1
0
0
1
0
1
1
0
0
0
0
2
1
2
0
1
0
1
0
1
0
1
2
1
3
1
0
0
2
0
1
0
0
2
3
0
0
0
1
0
2
0
0
2
0
1
1
1
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
1
2
0
0
2
0
0
2
2
0
0
2
1
0
1
0
1
1
0
0
0
1
0
0
2
0
0
0
1
1
0
0
2
0
1
2
0
0
2
1
2
1
1
2
0
1
0
1
0
0
0
0
0
1
2
0
0
2
0
0
1
0
1
0
0
0
1
3
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
3
1
0
0
0
0
0
1
0
0
0
1
0
2
0
0
4
1
1
0
2
0
0
0
1
1
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
1
1
0
1
0
0
3
1
1
1
0
0
1
0
2
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
2
2
0
2
2
2
0
1
0
2
0
2
0
0
0
2
2
0
1
1
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
4
1
1
0
2
0
0
0
0
1
1
1
1
0
0
2
2
0
0
1
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
1
1
3
0
0
0
1
1
0
0
2
1
2
2
0
1
1
0
0
1
0
0
0
2
0
0
0
1
2
0
0
1
1
1
2
0
0
1
0
1
0
2
0
2
2
0
0
0
2
1
1
2
0
0
0
0
0
0
4
0
3
1
0
1
0
1
0
1
2
1
0
0
0
0
2
1
1
0
0
1
0
0
0
0
1
2
2
1
0
0
2
0
2
0
0
0
0
0
0
0
1
1
0
1
0
0
2
6
1
0
0
0
0
0
2
1
1
1
2
1
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
1
1
0
0
0
2
0
0
0
2
1
1
0
0
0
0
0
0
0
0
1
1
1
1
1
3
0
2
0
1
1
0
1
1
1
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
2
1
2
0
0
2
2
2
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
2
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
4
2
1
1
1
2
2
3
0
1
0
2
1
1
0
0
0
1
2
0
0
2
0
0
0
2
3
2
0
2
6
1
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
2
1
1
0
0
0
0
1
1
0
0
2
2
2
0
0
0
1
0
1
0
0
0
0
0
0
0
3
0
2
0
0
2
0
0
0
0
1
1
0
2
2
0
0
0
0
2
2
1
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
1
0
2
0
0
1
9
0
1
0
0
1
0
0
0
2
0
1
0
0
0
0
1
1
0
2
2
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
1
3
0
0
2
0
4
0
1
3
2
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
2
0
2
1
0
2
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
2
0
0
0
1
0
0
1
0
1
0
0
0
0
1
2
2
0
1
1
0
0
0
1
2
1
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
2
1
1
2
3
0
1
2
0
1
1
1
1
1
0
0
0
0
0
1
0
0
0
0
0
2
2
0
1
2
1
0
0
2
1
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
1
2
2
0
2
1
4
0
0
3
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
11
0
2
0
2
1
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
1
0
0
1
0
0
1
1
2
1
0
0
0
0
0
3
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
1
1
1
2
1
0
0
1
0
2
2
0
0
0
3
0
2
1
0
2
2
0
0
0
1
2
0
0
0
1
0
1
0
1
0
1
0
1
0
0
1
1
2
0
0
1
0
1
1
0
0
0
2
2
1
0
0
0
0
1
0
0
0
1
2
0
0
2
1
0
1
3
0
0
2
2
1
0
1
2
1
0
3
1
0
2
0
0
1
0
1
2
0
0
0
1
0
2
0
0
2
2
0
0
1
2
0
0
1
2
0
2
0
0
0
1
1
0
0
0
1
1
1
1
1
0
1
0
2
0
1
1
0
0
0
0
0
0
2
2
1
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
2
2
0
0
2
0
0
0
0
2
2
0
2
0
0
0
0
1
0
2
1
0
1
0
2
0
0
0
0
0
0
3
0
0
2
0
0
2
0
1
2
0
0
0
0
0
3
0
0
0
2
1
0
1
1
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
1
0
1
1
0
0
1
0
0
2
2
0
2
2
2
0
1
2
1
0
0
0
0
1
0
2
0
0
2
0
0
0
1
1
0
2
0
0
1
0
1
0
0
0
1
0
0
1
0
2
0
1
1
1
1
0
2
0
0
2
0
1
1
0
0
1
0
0
2
0
0
0
0
2
0
0
0
2
2
2
0
0
0
0
0
2
1
1
0
2
0
0
0
0
0
0
0
0
1
0
2
1
0
1
1
0
0
1
0
0
1
2
1
2
6
0
0
0
0
0
3
0
0
0
4
0
2
3
0
1
0
2
0
2
0
2
0
1
0
1
1
0
0
2
1
0
0
3
0
2
0
0
2
0
1
0
0
1
0
0
0
2
2
0
0
2
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
1
2
0
2
0
0
0
1
2
0
0
1
2
2
0
0
0
1
0
0
2
0
1
1
3
1
0
0
1
0
0
0
1
2
0
2
2
0
0
2
1
2
0
0
0
1
4
2
0
0
0
1
2
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
1
0
1
2
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
1
0
0
2
0
0
1
1
0
0
1
1
0
0
0
1
0
8
0
1
0
0
1
1
0
1
2
0
0
0
0
1
1
0
0
2
4
0
2
0
0
0
0
0
2
0
1
2
0
1
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
1
0
2
0
1
1
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
2
0
1
0
2
1
0
2
0
0
0
0
2
0
0
2
0
1
0
2
1
0
0
0
1
3
0
1
2
0
0
0
0
1
0
1
0
2
2
0
2
0
0
1
0
1
0
0
0
0
0
0
1
0
0
2
2
0
0
0
1
0
1
1
0
1
0
0
1
2
0
0
0
0
0
0
0
1
2
0
0
0
2
2
0
0
2
2
0
2
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
2
2
1
2
0
0
0
0
1
1
0
1
1
1
0
0
0
2
0
2
0
1
1
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
1
1
2
0
2
0
0
1
0
0
1
0
2
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
1
0
0
0
0
2
0
1
1
1
0
1
1
2
0
0
2
1
2
0
0
0
0
0
1
0
3
1
0
1
0
2
3
0
0
1
0
3
0
0
0
0
2
1
1
0
0
1
3
2
1
2
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
2
0
2
2
0
0
0
2
0
3
0
0
1
0
0
0
0
1
0
0
0
0
1
0
2
1
0
0
2
0
0
0
1
1
2
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
1
0
1
0
1
0
1
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
2
1
0
0
1
1
0
0
2
0
2
2
0
2
1
1
0
0
0
0
0
0
0
1
0
2
5
0
2
0
1
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
2
0
1
1
0
0
2
0
2
0
0
2
0
2
0
2
2
0
0
0
0
1
0
1
1
2
0
0
0
0
1
0
0
0
0
1
0
2
0
2
3
0
0
0
0
0
0
2
0
1
0
1
2
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
2
6
1
1
0
0
1
2
0
0
3
2
1
1
1
0
0
0
1
0
0
0
3
0
2
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
2
0
0
3
1
0
0
0
0
1
2
0
1
2
0
0
0
0
2
1
0
0
1
0
1
0
0
0
0
0
0
0
2
0
1
0
0
1
2
0
0
0
1
0
0
1
1
0
0
1
1
0
2
1
1
0
0
0
0
0
2
0
1
2
0
0
2
0
0
0
1
0
1
2
0
2
0
2
1
2
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
2
1
2
2
0
2
0
2
0
0
4
0
1
1
2
0
0
0
1
3
2
0
0
0
1
0
0
3
0
0
2
0
1
0
0
1
0
1
0
1
0
0
0
0
2
0
0
0
1
2
0
0
0
0
1
1
1
1
2
0
1
0
1
0
0
2
2
1
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
2
0
0
0
1
0
0
2
0
2
0
1
0
2
0
0
0
0
0
1
1
1
0
1
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
3
1
0
2
2
1
0
2
1
0
0
1
0
0
0
1
3
1
0
1
0
0
0
1
0
0
0
2
0
0
0
2
0
0
3
0
0
0
0
1
0
0
0
0
2
0
0
0
0
3
0
1
2
0
0
0
0
0
0
2
0
0
1
1
2
0
0
0
2
2
0
1
0
0
2
0
1
1
0
0
0
0
0
0
1
0
2
0
2
0
2
1
0
1
2
2
2
1
0
0
3
0
0
1
0
0
0
2
1
2
3
0
1
0
2
1
0
0
1
0
0
0
0
2
0
1
0
0
0
0
2
0
0
2
1
1
0
0
0
1
0
0
0
1
0
0
2
0
0
1
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
2
1
0
0
1
1
0
4
0
0
0
2
0
0
0
1
0
0
1
1
0
1
0
2
0
0
2
1
0
2
0
0
0
0
1
0
0
0
0
2
2
0
0
2
0
2
1
0
3
0
1
2
2
0
1
0
0
1
1
1
2
0
0
0
0
1
2
0
2
0
0
0
0
2
2
0
0
0
0
0
1
0
0
1
2
1
1
0
2
0
0
2
0
0
2
2
0
1
2
0
0
0
1
1
2
1
0
0
0
0
5
0
2
1
1
1
0
0
2
2
2
1
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
1
0
0
2
2
0
1
0
0
2
1
1
2
0
0
0
0
0
0
0
4
1
0
0
1
6
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
2
2
0
0
0
2
0
0
1
0
0
1
0
2
0
1
0
5
0
0
0
0
0
0
0
0
0
2
2
1
0
1
0
0
0
2
0
0
0
2
0
0
0
1
2
0
0
0
2
1
1
0
0
2
0
1
2
0
2
0
0
1
2
0
0
2
1
3
1
0
0
1
0
0
0
2
0
2
1
0
0
0
2
2
0
1
2
1
0
0
0
0
1
0
1
1
0
0
0
2
0
0
0
0
2
0
1
3
1
0
0
1
5
4
0
0
0
0
1
1
1
1
1
0
0
0
0
0
3
0
0
2
0
0
2
0
0
1
1
0
0
0
0
2
0
0
0
2
0
2
1
2
0
1
1
1
0
1
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
3
1
1
0
0
0
0
0
2
1
0
2
0
2
0
0
0
1
0
0
1
2
2
0
0
2
0
0
0
2
0
2
2
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
2
0
1
0
0
1
0
0
0
1
1
0
0
0
2
0
0
1
1
0
2
1
1
2
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
2
2
0
0
1
0
0
0
4
1
0
0
0
2
2
0
2
0
2
0
1
0
0
0
0
1
0
0
0
0
1
1
0
1
2
0
0
0
1
3
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
1
0
2
0
1
1
1
2
2
1
1
1
1
0
0
0
0
0
0
2
0
1
1
2
1
1
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
2
2
0
3
0
0
0
0
1
0
1
2
2
0
0
0
0
0
0
1
0
0
0
0
0
1
1
2
2
0
0
1
2
0
0
0
2
2
0
1
0
1
0
0
0
2
0
1
0
0
0
0
0
2
2
1
1
0
2
0
0
1
0
0
0
0
1
1
1
2
3
2
0
0
0
1
0
0
0
1
2
0
0
1
0
0
1
0
1
1
0
1
0
1
0
1
0
0
2
1
3
2
0
0
0
2
0
2
2
0
0
0
1
0
0
2
0
1
1
0
2
2
0
0
0
2
0
1
0
0
0
1
0
0
2
0
0
1
0
0
1
0
0
2
1
0
0
1
0
2
1
0
0
0
0
3
0
1
1
0
1
4
2
0
0
0
3
0
2
0
1
0
0
2
0
0
0
3
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
2
1
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
1
0
0
1
0
0
0
3
2
2
0
0
2
0
2
1
0
2
0
0
1
0
1
0
0
0
1
0
1
0
0
0
1
0
0
2
0
1
1
0
0
0
0
0
1
1
1
0
1
0
0
2
0
0
0
1
0
0
0
0
1
0
2
0
2
1
1
1
0
1
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
2
0
0
2
2
1
0
0
2
0
0
1
1
2
0
1
1
0
2
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
2
1
0
1
1
0
0
0
0
2
0
1
0
0
0
0
0
1
1
0
0
0
1
1
0
2
0
0
1
0
2
0
1
2
1
1
0
1
0
2
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
1
2
1
2
0
1
0
2
0
1
0
2
0
1
2
0
0
0
1
0
1
1
2
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
2
1
0
2
2
1
1
2
1
1
0
0
0
0
2
0
1
1
1
0
0
1
2
0
0
1
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
1
0
0
2
2
0
0
0
1
0
0
1
0
3
0
1
0
0
0
1
0
0
0
0
0
3
1
0
0
0
0
1
1
0
2
1
0
0
2
0
2
0
2
2
0
0
1
0
1
0
1
0
0
2
0
0
1
1
0
1
0
1
2
0
0
1
1
0
1
0
0
2
0
1
0
2
2
1
0
0
0
0
0
1
1
1
2
0
1
1
0
1
0
2
2
0
1
0
1
0
2
1
1
1
0
0
0
2
1
2
1
0
1
0
0
0
1
0
0
1
2
0
1
1
0
0
1
0
1
1
0
0
0
0
2
0
2
0
0
1
1
0
0
3
1
2
0
2
0
2
1
1
1
1
0
1
0
2
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
1
1
0
0
3
0
0
2
0
0
0
0
0
0
1
2
2
0
0
2
3
4
2
2
0
2
0
0
1
0
1
0
2
0
3
0
0
1
1
0
0
0
2
1
0
2
0
0
2
0
2
2
0
0
0
1
0
2
0
2
0
2
0
0
2
3
0
1
0
0
1
2
0
2
0
0
1
0
2
2
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
2
1
1
0
0
0
3
2
0
0
0
0
0
0
0
0
0
2
2
1
0
1
2
0
0
1
0
2
0
0
0
2
2
2
0
0
1
0
0
0
2
0
2
0
0
2
1
0
2
1
1
3
1
0
4
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
2
1
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
1
2
1
0
2
0
0
0
0
0
2
0
0
1
0
2
1
0
0
1
0
0
0
2
0
0
1
1
0
2
0
0
0
0
0
2
0
0
1
0
0
0
2
0
2
0
0
1
1
0
1
1
1
0
2
0
0
1
0
2
2
0
0
2
2
2
4
0
0
0
1
1
0
0
0
0
0
1
2
2
0
2
0
1
0
0
0
0
2
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
2
0
1
0
0
2
0
0
0
0
5
1
1
0
1
0
2
2
2
1
0
2
0
0
1
0
0
0
0
1
0
2
0
3
1
0
0
4
0
0
1
0
0
1
1
1
0
0
1
2
1
1
0
1
0
0
0
1
0
2
2
0
0
0
0
0
0
1
0
0
2
0
2
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
1
3
0
0
0
2
0
2
0
0
0
0
1
0
0
1
1
0
1
1
0
0
2
0
1
0
1
1
2
0
0
0
0
0
0
1
1
0
0
0
2
0
3
2
0
2
3
2
0
0
2
0
0
0
0
2
0
1
0
3
0
1
0
1
0
2
0
0
1
0
2
1
0
0
2
2
0
0
0
1
2
1
1
0
0
2
1
2
1
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
1
2
0
0
3
2
0
0
0
0
2
0
0
1
0
1
0
0
0
1
0
1
2
0
2
2
2
0
0
0
0
0
2
0
0
0
2
0
2
0
2
0
0
0
2
2
0
2
0
2
0
0
0
1
2
0
0
0
0
0
2
0
0
2
0
2
2
1
2
0
0
0
1
0
0
2
1
1
2
2
0
2
0
0
1
0
0
2
0
0
0
1
0
0
0
0
1
1
0
0
2
0
1
1
1
2
3
2
1
2
1
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
1
1
1
0
0
2
0
2
0
2
0
1
0
2
2
2
0
0
1
0
0
0
0
3
0
1
0
2
0
0
1
0
0
1
0
0
0
0
0
2
0
1
0
2
0
0
1
1
2
2
2
1
1
0
0
2
2
0
0
2
0
0
0
0
0
0
2
0
0
2
0
2
2
2
2
2
0
1
0
0
2
1
2
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
2
1
1
1
1
1
0
0
0
0
2
0
5
2
0
1
0
0
0
1
1
1
2
0
0
0
2
0
3
0
0
1
0
2
0
0
0
0
0
1
1
2
2
0
0
0
1
0
0
0
0
1
0
0
0
4
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
1
0
1
0
0
0
1
1
1
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
1
3
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
1
2
0
2
0
0
1
0
0
0
0
0
0
2
1
2
1
0
3
1
0
0
0
1
0
1
0
0
0
2
0
0
1
0
0
2
2
1
2
1
0
1
2
1
0
2
2
2
0
1
1
0
0
1
2
1
2
1
0
0
1
0
1
1
0
0
2
0
1
1
0
0
1
0
0
1
2
0
0
0
2
1
0
0
1
0
0
0
1
1
1
0
0
0
2
2
2
1
1
2
0
0
0
1
0
1
0
0
1
0
2
2
1
0
0
0
1
1
0
0
2
0
1
1
2
1
1
1
0
0
2
0
0
0
0
0
0
2
0
1
3
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
2
0
1
0
2
0
2
0
0
3
0
1
0
1
0
0
0
0
0
1
0
1
1
1
1
0
1
1
2
2
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
1
0
2
2
0
1
2
1
0
0
0
0
0
1
0
0
0
2
1
0
1
0
0
0
0
1
1
2
0
2
4
1
1
0
2
1
0
1
1
0
0
2
1
0
0
0
0
0
1
2
1
0
2
1
2
0
0
0
1
0
2
0
0
0
2
1
0
0
1
2
0
2
1
0
1
0
0
0
1
1
0
0
1
0
0
2
2
2
0
1
0
0
0
0
1
0
3
0
4
0
0
0
1
1
0
2
0
0
0
1
0
0
1
2
0
1
0
2
1
1
0
0
0
1
0
0
0
2
1
2
2
1
0
0
1
0
0
2
0
1
0
0
0
3
0
2
0
2
0
0
2
0
0
0
0
0
2
1
2
1
1
0
0
2
0
0
2
1
0
2
0
0
0
3
1
0
0
1
0
0
2
0
0
2
2
1
0
0
0
0
0
0
2
2
0
0
1
1
0
0
0
0
0
1
0
0
1
2
0
0
1
1
2
0
2
1
1
1
1
2
0
0
1
0
2
1
2
0
0
0
1
0
1
0
0
0
0
2
0
1
0
0
0
0
2
0
2
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
1
1
0
2
0
0
0
0
0
0
0
0
2
0
1
2
0
0
1
0
0
1
0
1
0
2
9
1
4
1
1
0
0
0
0
1
0
2
1
0
0
0
0
1
0
0
0
2
2
1
0
2
0
1
0
0
0
0
1
2
1
0
0
0
2
1
1
2
1
0
0
0
1
1
2
0
2
0
2
2
0
3
1
2
1
0
0
1
4
1
1
2
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
1
0
2
0
0
0
0
0
2
1
0
1
2
0
0
0
1
2
0
2
0
0
1
0
2
0
0
1
0
0
3
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
1
0
3
1
0
2
1
0
2
0
1
2
0
0
0
0
1
0
0
0
1
1
0
0
0
0
2
1
0
0
0
1
2
0
0
5
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
2
0
3
2
1
1
0
0
0
0
6
0
2
1
0
1
0
1
2
2
0
2
1
0
0
0
1
0
0
0
1
0
0
2
0
1
1
0
0
1
0
0
2
0
0
2
2
0
0
1
0
0
2
2
2
0
1
0
0
0
0
0
0
1
0
2
0
0
2
1
2
3
0
0
1
2
0
0
0
0
2
0
0
1
1
1
0
0
0
1
0
0
0
0
1
3
1
0
2
0
0
2
1
0
0
0
2
1
0
0
1
2
1
0
0
1
3
2
1
1
1
0
0
0
1
2
0
2
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
2
1
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
2
1
0
0
0
0
0
1
0
0
2
0
1
1
0
2
3
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
2
1
2
0
2
1
4
0
1
2
2
0
0
0
0
0
0
2
1
0
0
1
0
1
0
1
0
0
0
2
1
0
2
0
0
2
1
2
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
1
2
1
0
0
0
2
0
0
1
0
1
0
0
0
0
1
0
0
2
0
0
0
2
2
2
0
0
0
0
1
0
2
0
1
0
0
2
1
0
0
0
0
0
4
0
0
1
0
0
0
1
0
0
2
0
0
1
0
0
1
0
1
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
2
0
0
0
0
2
0
1
2
2
0
0
1
0
0
2
0
1
1
2
0
1
0
1
0
0
3
0
2
2
1
1
0
2
2
0
1
1
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
2
1
0
0
0
1
0
2
1
1
0
1
0
0
0
2
0
0
0
0
1
0
2
0
0
0
3
0
0
1
3
0
0
2
0
0
0
2
0
1
0
2
0
2
0
0
0
2
1
1
0
0
0
1
0
2
0
0
0
3
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
2
1
0
0
1
1
2
1
0
0
1
2
1
0
0
1
0
0
2
0
1
0
0
0
2
0
0
2
0
0
0
0
1
2
2
2
1
0
1
0
0
0
0
2
0
1
2
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
2
1
0
1
1
0
0
0
1
0
2
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
2
1
0
2
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
7
0
0
0
2
1
0
0
1
0
0
1
2
2
2
0
0
0
2
0
1
2
0
0
0
2
2
2
1
1
0
0
2
0
0
0
1
0
1
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
1
1
0
0
0
1
0
1
0
1
0
1
0
0
2
0
1
0
10
0
0
0
1
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
1
0
0
0
2
1
0
2
0
0
0
0
2
0
2
0
0
0
1
2
2
1
2
0
1
0
0
1
0
2
2
1
0
0
0
0
0
0
2
0
1
0
0
3
0
1
0
0
0
2
0
1
0
1
2
1
0
0
0
3
0
0
0
0
0
2
0
0
2
1
1
1
0
0
2
0
0
2
1
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
2
1
0
0
3
1
1
0
2
2
0
2
0
2
1
0
0
2
2
2
0
1
0
1
0
3
1
0
0
0
0
0
0
0
0
1
2
1
0
2
4
2
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
1
2
2
0
1
2
2
0
0
0
1
0
3
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
1
0
1
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
1
0
7
0
0
0
0
1
0
2
0
0
1
2
1
0
0
0
0
8
0
1
1
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
1
0
0
1
2
0
0
2
3
0
1
1
0
1
2
0
1
2
1
0
2
1
1
2
0
2
0
2
0
0
1
0
0
0
2
2
1
2
0
2
0
2
2
0
0
0
1
1
0
2
2
1
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
1
0
2
2
3
0
1
0
0
0
1
0
0
0
2
2
0
0
2
0
0
2
0
1
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
1
0
2
0
1
1
0
0
1
0
1
2
1
0
1
2
4
1
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
1
4
0
1
2
0
0
0
1
0
0
0
0
1
1
0
1
1
0
2
0
0
2
1
3
0
0
2
2
2
0
0
0
0
1
0
0
0
2
2
1
0
2
2
0
1
2
0
1
1
2
1
0
0
1
2
1
0
0
0
0
1
0
0
2
0
1
0
0
0
1
0
0
0
2
0
0
1
0
2
1
0
0
0
2
0
1
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
3
0
0
1
0
0
3
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
3
0
2
0
0
0
2
0
0
1
0
0
0
1
1
1
0
1
1
0
0
2
0
0
2
0
0
0
2
0
0
0
2
1
0
1
0
3
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
2
0
0
0
2
0
2
1
1
0
0
1
2
0
0
2
1
1
0
0
2
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
3
0
0
2
0
1
0
2
1
0
0
0
0
0
1
1
1
1
1
0
1
2
0
0
1
1
0
1
0
1
0
1
2
2
2
0
0
2
0
0
0
2
0
0
0
2
3
0
3
1
1
2
1
0
0
1
0
0
0
2
0
0
1
1
2
0
0
0
1
0
0
2
0
1
0
4
0
0
0
0
0
0
0
1
0
0
2
4
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
1
0
0
2
0
2
0
2
0
0
0
2
1
0
0
0
1
0
0
0
2
0
2
0
0
0
3
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
4
0
2
1
2
0
1
2
1
0
0
0
0
0
1
2
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
5
1
0
0
1
1
0
0
0
1
2
2
3
2
0
0
2
1
1
0
0
0
0
1
1
0
0
1
1
0
0
0
1
2
0
1
0
0
2
0
2
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
2
0
2
0
0
0
2
2
2
0
0
0
0
1
2
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
1
0
0
1
0
2
0
2
0
0
2
2
2
0
2
0
0
0
0
1
2
1
0
0
2
0
0
1
0
0
2
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
1
0
1
0
0
2
0
2
1
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
2
0
0
1
1
1
0
2
2
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
1
1
0
2
0
0
0
3
0
2
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
2
2
0
0
0
0
0
1
2
0
0
1
2
1
0
0
1
2
3
0
0
2
1
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
2
1
2
1
0
2
0
1
0
0
0
1
3
1
1
2
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
1
2
0
0
1
0
1
1
0
0
3
0
0
0
0
0
1
2
1
0
1
0
1
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
1
2
2
1
0
0
2
0
1
3
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
1
0
0
0
0
0
0
2
2
0
2
0
0
1
0
0
0
2
1
0
1
1
2
2
0
2
0
0
0
1
1
0
0
1
0
2
0
1
0
2
0
1
0
0
0
0
1
0
0
1
0
0
0
0
2
2
1
2
1
2
0
0
0
0
0
0
0
1
0
0
2
2
1
0
0
1
2
0
1
2
0
2
0
1
0
0
0
1
0
1
0
2
1
1
0
1
0
2
1
1
0
0
1
0
2
0
0
0
0
1
0
3
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
1
2
0
0
0
2
0
1
4
0
0
2
0
1
1
0
0
1
1
0
0
0
1
0
2
0
0
0
2
0
2
2
1
0
0
0
0
0
1
0
0
0
2
1
0
0
1
0
1
0
1
0
1
0
0
1
1
1
1
1
0
0
0
0
0
1
1
0
1
1
0
2
2
1
1
0
2
0
0
1
2
0
2
0
2
0
0
0
0
1
1
2
0
0
0
0
1
0
0
0
1
0
2
0
1
1
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
1
0
0
0
1
1
0
2
2
2
0
2
0
0
0
4
0
3
2
2
0
0
2
2
0
0
2
1
2
0
0
1
0
1
0
2
4
1
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
2
0
0
2
1
1
0
1
1
0
1
0
0
0
1
1
0
2
2
0
1
0
2
4
0
2
3
0
1
0
0
0
2
2
0
0
2
0
2
2
0
0
0
0
0
0
1
2
2
0
1
1
1
2
0
0
0
0
0
1
2
2
0
0
1
0
0
0
3
2
1
2
0
0
2
2
0
0
2
0
0
0
2
0
1
0
2
1
0
0
0
0
0
0
1
1
0
0
2
1
2
0
1
1
0
2
0
0
0
0
3
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
2
0
0
1
2
1
0
0
0
1
0
0
2
0
1
2
0
3
0
0
0
1
1
0
2
1
1
0
2
1
1
0
0
0
0
1
2
2
2
0
0
0
0
0
2
0
2
1
0
0
0
1
1
0
2
1
0
1
0
2
0
1
0
0
0
0
2
0
1
1
0
0
0
0
5
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
1
1
0
1
2
0
1
1
0
0
1
0
0
2
1
0
1
0
3
0
1
0
0
0
0
1
1
0
1
0
0
0
1
2
0
2
2
2
2
2
2
0
2
0
0
0
0
2
0
0
1
1
1
0
0
3
0
0
0
0
1
3
2
0
2
0
0
0
2
1
0
1
0
2
0
0
2
1
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
4
1
1
1
0
0
0
0
0
0
2
1
0
1
0
0
1
0
0
0
0
1
2
1
1
0
2
0
2
8
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
2
0
2
0
1
0
2
0
0
0
0
0
0
1
0
1
0
1
2
1
0
1
0
2
0
2
0
2
1
2
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
1
0
1
0
4
0
0
0
0
0
0
0
2
1
3
1
0
2
1
0
0
1
0
2
0
0
0
2
2
0
0
0
1
0
0
0
0
1
1
0
0
0
2
0
1
2
0
0
3
0
0
0
1
1
0
0
2
0
0
2
1
1
0
0
0
0
1
0
0
0
2
0
1
0
2
0
1
1
0
0
0
1
0
0
0
0
1
1
0
0
0
2
0
0
2
3
0
2
2
0
2
0
0
2
5
2
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
1
1
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
3
0
0
0
0
0
0
2
1
1
1
2
1
1
0
0
0
1
2
0
0
2
0
2
1
0
1
3
1
0
1
0
0
1
1
1
0
2
5
1
0
2
0
1
0
2
0
1
0
1
0
2
1
0
0
3
0
0
2
2
0
1
0
0
2
0
0
1
0
0
2
0
0
1
0
0
0
2
0
2
1
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
1
1
0
1
1
0
1
0
0
1
0
0
0
1
0
0
0
1
1
0
0
1
0
0
2
1
1
0
0
2
0
2
0
0
2
0
2
0
1
0
0
2
0
3
0
0
0
2
0
0
2
0
2
2
1
2
2
0
0
0
0
1
0
0
0
2
2
0
0
1
2
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
3
1
2
2
0
0
1
0
0
2
0
2
1
2
0
1
0
0
1
0
0
0
0
0
0
0
1
2
0
0
2
0
0
2
1
2
0
0
0
2
0
0
2
2
2
0
0
2
0
2
0
0
0
2
1
2
0
0
0
0
1
0
1
1
1
0
0
2
0
0
0
1
0
1
2
0
0
1
0
0
0
2
3
1
2
0
1
1
2
0
6
0
2
0
0
2
2
0
0
1
0
0
1
0
0
2
1
1
0
0
2
2
0
0
1
2
2
0
2
0
0
1
1
0
0
1
0
1
2
0
0
3
0
0
1
0
0
1
0
0
2
2
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
2
3
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
5
0
0
0
1
1
1
0
0
0
1
2
0
2
0
2
0
0
2
0
2
2
0
0
0
2
0
0
1
0
0
0
1
0
0
0
4
0
0
0
2
2
2
0
0
0
0
0
2
1
0
0
0
0
1
2
0
0
0
0
0
0
0
2
2
1
2
0
2
1
0
0
0
0
0
0
0
0
3
1
0
0
1
0
2
0
1
1
0
0
0
0
0
1
0
1
0
1
0
0
0
1
1
1
0
2
0
0
2
0
0
0
0
0
0
2
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
1
0
0
2
1
0
0
0
2
2
0
0
2
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
8
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
2
1
1
2
0
0
0
2
1
1
0
2
0
0
1
0
0
0
1
2
0
0
2
0
0
0
1
0
0
0
2
0
1
2
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
1
1
0
0
0
0
1
1
2
2
1
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
3
0
1
0
0
0
0
0
2
2
0
2
0
0
0
0
2
0
1
0
0
0
0
3
1
0
0
2
0
1
0
0
0
1
1
2
0
0
2
1
2
0
1
0
0
0
1
1
1
1
2
0
0
1
2
0
0
0
0
2
1
0
0
1
2
1
2
0
1
1
2
1
0
0
0
0
0
0
1
1
1
0
0
0
0
2
0
1
0
0
2
3
0
2
1
0
0
0
1
2
0
0
1
0
0
0
1
1
0
2
3
0
1
0
1
0
0
1
2
1
0
0
1
1
0
0
0
2
0
2
1
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
3
0
0
2
0
2
0
1
2
0
1
0
2
0
0
0
0
1
1
0
2
0
0
1
0
2
2
0
0
0
1
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
11
0
2
0
1
0
2
0
0
0
0
1
1
2
1
2
0
1
0
1
0
0
1
0
1
1
2
0
0
2
0
0
0
0
1
0
2
2
3
1
0
1
3
0
2
1
2
1
0
2
2
0
1
0
0
0
0
2
1
2
0
2
0
0
1
1
0
0
4
1
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
1
0
0
0
2
2
2
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
2
0
2
2
1
0
2
1
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
1
1
0
0
0
2
1
0
0
0
0
0
2
2
0
1
0
1
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
1
2
0
2
1
2
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
1
0
0
0
1
1
1
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
2
1
0
2
0
0
0
0
2
0
0
2
0
2
0
0
0
2
0
0
0
0
1
1
1
0
1
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
2
1
0
0
1
1
0
2
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
2
1
1
0
1
0
1
0
0
1
1
1
2
0
0
0
2
0
4
1
0
0
2
0
2
1
2
0
2
0
0
2
0
1
0
0
1
6
0
0
0
2
0
0
0
0
0
0
0
0
2
0
3
0
1
1
0
0
1
0
0
1
0
1
0
0
0
4
2
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
5
1
2
0
0
2
2
0
0
2
0
0
1
2
0
0
0
2
1
0
2
2
0
0
1
0
0
1
1
0
0
0
0
0
1
2
0
0
1
2
0
0
0
1
0
1
1
2
0
0
0
0
0
2
2
0
2
0
2
2
0
0
0
2
2
1
1
0
0
0
0
0
0
1
0
1
0
0
1
0
2
1
0
0
0
0
2
2
0
1
1
0
1
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
1
1
1
0
0
0
0
2
0
2
0
0
0
2
1
1
3
2
1
2
0
1
0
0
0
2
0
0
1
1
0
0
2
0
1
3
1
0
0
0
1
2
2
0
0
0
0
0
2
0
0
0
0
2
1
2
0
0
0
2
0
0
2
0
1
0
0
0
4
0
1
0
0
2
0
0
0
0
1
2
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
1
2
0
0
0
0
1
2
2
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
2
2
1
1
2
0
1
2
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
1
1
1
0
4
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
1
0
0
1
0
2
0
0
0
1
2
0
1
1
0
0
4
1
0
2
3
2
0
1
1
2
1
2
1
0
0
0
0
2
0
2
1
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
1
1
1
1
0
1
0
0
0
0
1
4
0
1
0
0
0
0
4
1
0
0
0
1
1
0
0
0
1
0
2
2
0
0
0
0
2
0
1
0
0
0
0
0
1
0
2
0
2
0
1
0
0
1
0
0
0
0
2
0
1
2
2
1
1
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
2
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
2
0
2
2
0
0
1
0
2
0
0
1
0
0
0
1
0
2
0
0
2
0
2
0
0
1
0
0
0
1
0
0
1
2
0
0
0
0
1
0
1
1
2
0
2
1
2
1
1
0
0
1
1
1
0
3
0
2
0
0
2
0
2
0
1
0
2
0
2
1
2
0
0
0
2
2
2
2
2
2
1
0
1
0
0
1
0
0
1
0
0
2
2
1
0
2
0
2
0
0
0
1
0
0
0
1
0
1
0
0
2
0
0
1
2
1
0
0
0
2
1
0
0
0
1
0
1
0
1
0
2
0
1
0
0
0
0
1
4
0
0
0
0
0
3
0
0
1
0
2
2
1
0
0
1
0
0
0
0
0
1
0
1
0
1
1
0
1
0
2
0
1
4
0
0
0
0
0
2
1
3
1
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
2
0
0
0
1
1
0
2
0
1
1
2
2
2
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
1
0
2
1
0
0
0
2
0
0
0
0
0
2
1
0
0
1
0
1
3
0
1
0
0
1
0
2
0
1
2
0
2
0
2
2
0
1
1
0
0
2
2
0
0
0
0
1
0
1
1
2
0
0
0
0
0
0
3
0
2
1
1
0
0
0
0
2
0
1
0
0
0
2
1
0
0
0
0
2
0
0
1
2
1
2
0
0
1
0
2
0
0
0
0
1
2
2
0
0
0
0
2
3
0
1
1
0
2
0
0
1
0
2
2
3
0
0
0
0
1
0
0
0
3
2
0
1
2
0
1
0
0
0
0
0
1
2
0
2
0
2
1
0
1
0
0
2
0
1
0
0
1
0
2
0
0
5
0
2
2
0
0
0
0
1
0
2
0
1
0
0
1
0
0
0
1
1
1
0
2
1
1
0
1
0
0
1
1
0
1
0
0
1
0
0
0
0
1
0
2
0
0
0
1
1
0
0
2
0
0
1
0
0
0
1
1
0
1
3
1
2
2
2
0
1
0
2
1
0
1
1
0
2
0
1
2
0
2
0
2
0
2
1
1
2
0
2
0
0
0
1
0
1
0
0
2
0
0
0
0
1
1
0
0
0
1
0
2
1
0
1
0
2
0
0
2
0
1
0
1
0
0
3
2
0
2
1
0
0
0
0
3
1
0
0
2
1
0
2
1
0
0
2
2
1
1
2
1
0
2
2
0
2
2
0
0
0
0
2
0
1
0
2
1
0
1
1
0
0
1
0
1
0
1
2
1
0
2
0
1
1
1
0
1
0
1
1
0
1
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
1
1
2
0
1
1
6
0
0
2
0
0
2
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
1
1
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
2
0
1
0
0
1
0
0
0
0
0
0
1
0
2
0
1
0
0
2
2
0
4
1
0
0
1
2
0
1
0
0
0
0
2
0
0
1
0
0
2
0
2
0
1
1
0
1
1
0
3
0
0
0
0
1
0
2
0
1
0
0
1
1
0
0
0
0
1
1
1
0
2
0
0
1
0
2
0
0
2
0
2
2
1
3
2
0
0
0
1
0
2
0
1
0
0
0
0
0
1
2
0
1
1
2
1
0
2
0
0
1
0
2
0
0
1
1
4
2
2
0
2
1
1
0
0
2
0
1
0
0
1
0
0
0
2
0
0
0
0
1
0
1
0
0
2
1
2
2
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
1
2
1
0
0
0
0
0
2
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
1
2
0
1
0
0
0
1
1
0
1
0
0
0
0
0
1
0
3
2
0
2
2
1
1
0
1
0
3
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
1
0
2
0
2
2
2
1
0
0
1
0
0
0
1
1
0
0
0
0
2
0
2
2
0
2
0
0
2
1
0
0
3
2
3
0
0
0
1
1
0
0
2
0
0
2
0
1
1
1
1
2
2
0
0
3
1
1
0
0
1
1
2
1
0
2
2
0
3
0
1
1
3
3
0
0
2
0
2
0
0
2
2
0
1
1
0
0
0
1
1
0
0
0
0
1
2
0
0
0
1
1
0
1
0
1
1
2
0
0
1
0
0
0
0
0
2
1
2
2
0
0
2
0
2
2
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
2
1
1
0
1
2
0
0
1
1
1
1
0
2
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
1
2
0
1
1
0
0
0
0
0
1
2
0
3
0
0
0
9
1
0
2
2
0
1
0
1
1
0
0
0
2
0
1
2
0
0
0
2
0
0
0
0
0
1
0
1
1
2
0
2
0
0
1
0
1
1
0
0
0
8
0
1
2
0
0
0
1
0
2
0
0
0
1
0
2
1
0
2
1
2
0
0
0
0
2
0
1
0
1
2
0
1
0
0
0
1
1
0
1
0
1
0
0
2
0
0
2
1
1
0
0
0
2
0
2
2
0
1
1
0
1
1
0
0
2
0
0
0
0
0
2
0
0
2
0
0
1
0
2
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
2
0
1
2
1
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
1
0
2
1
0
0
2
0
0
1
0
0
0
1
1
0
0
0
2
2
0
2
0
0
0
1
0
0
0
0
1
0
1
0
1
1
0
0
1
0
0
1
0
0
0
0
0
3
0
0
0
0
1
0
1
3
0
0
0
1
2
0
2
0
2
0
0
2
0
0
0
2
1
1
1
0
0
1
0
1
0
0
2
1
1
0
2
0
1
0
0
0
0
0
0
1
0
0
1
1
2
1
0
1
0
0
0
0
2
0
0
3
0
0
0
0
1
2
0
2
0
1
0
0
1
0
0
1
1
0
1
1
3
0
0
0
0
0
0
0
0
0
1
0
2
2
0
1
2
1
1
2
0
0
0
1
0
1
0
5
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
1
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
2
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
3
1
2
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
2
0
0
2
1
2
2
1
2
2
1
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
1
0
2
1
1
0
0
0
0
0
2
0
0
1
0
1
2
0
2
1
0
1
1
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
1
0
2
2
0
0
0
0
1
2
0
0
1
0
0
1
0
0
0
0
0
2
0
1
0
0
2
1
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
2
0
1
5
0
0
2
2
0
2
1
0
0
0
0
0
2
0
0
1
1
2
0
1
2
0
0
2
1
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
3
0
0
0
1
0
2
0
0
1
1
0
2
0
0
0
2
0
0
1
0
0
2
0
1
1
1
0
0
1
0
2
2
1
0
1
0
1
2
0
0
0
1
0
2
1
2
0
0
1
2
1
0
0
0
1
0
1
2
0
1
0
2
2
0
0
0
0
1
1
0
1
0
1
1
0
1
0
0
3
0
1
1
2
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
2
2
2
3
0
0
0
0
0
0
1
0
0
0
1
0
1
0
2
0
0
0
0
1
0
0
2
0
0
1
2
1
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
3
1
2
0
0
2
0
0
0
1
1
3
1
1
0
0
0
0
1
1
0
0
2
1
0
1
1
0
2
2
0
1
2
0
0
0
1
2
2
1
1
0
0
2
0
0
1
0
0
1
0
2
0
0
1
1
1
0
2
0
0
0
1
0
2
1
0
1
1
0
2
0
1
1
0
1
1
2
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
2
0
0
0
0
0
0
2
1
1
0
0
1
0
2
0
0
1
0
0
0
0
2
1
1
2
2
0
1
1
2
0
1
0
0
0
1
1
1
2
1
0
0
2
0
2
0
2
1
1
0
0
1
1
0
1
0
0
3
0
1
0
0
0
0
0
0
2
2
2
1
0
1
0
1
1
0
0
2
0
1
2
1
0
1
2
0
0
1
2
1
0
0
1
0
0
0
0
0
0
2
1
2
2
0
2
0
0
1
0
0
0
1
0
2
3
0
0
2
1
1
0
0
0
0
0
1
4
0
1
2
0
0
0
0
1
0
3
1
0
0
2
0
0
0
0
2
2
0
0
0
2
1
2
0
0
0
1
0
0
1
0
2
2
0
1
2
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
2
0
0
1
0
1
1
2
2
1
0
0
0
3
0
0
1
0
0
0
0
1
0
1
2
0
0
0
2
2
1
0
4
0
1
1
0
0
0
0
2
1
2
0
0
0
0
0
2
2
1
1
1
1
0
0
1
1
1
2
0
0
0
0
1
2
2
1
2
0
0
2
1
1
0
3
1
4
1
1
0
3
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
3
1
0
0
0
0
1
0
0
2
2
0
2
0
0
0
0
0
0
2
0
1
1
0
2
0
0
0
2
0
1
0
2
1
0
1
0
0
2
2
0
1
0
2
2
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
1
0
1
0
0
0
1
2
2
0
2
2
2
1
0
0
0
2
0
3
0
1
0
0
0
0
0
1
0
0
1
0
1
0
1
2
0
1
0
2
0
0
1
1
2
1
0
0
2
1
0
0
0
0
1
0
0
1
0
2
2
0
0
0
2
1
0
2
0
0
2
2
0
1
0
0
4
2
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
1
2
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
2
1
1
2
0
0
0
1
2
1
0
0
2
1
0
1
1
2
0
0
1
0
2
0
0
2
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
5
1
0
1
1
0
2
1
2
0
0
0
0
0
1
1
0
0
0
0
0
2
1
0
0
1
0
0
1
0
0
0
2
0
0
1
1
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
1
0
0
1
2
0
0
0
0
0
0
1
0
6
0
0
1
0
1
3
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
7
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
2
0
0
1
0
0
2
0
2
0
0
0
0
2
1
1
2
0
1
0
2
0
0
1
0
0
3
0
0
0
0
2
0
0
0
1
2
2
0
2
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
2
2
0
0
1
1
1
0
1
2
0
0
0
0
0
0
1
0
0
0
0
1
1
1
1
0
1
0
0
2
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
2
0
0
0
1
0
0
1
0
1
1
1
0
1
2
0
0
4
0
1
2
1
1
1
0
0
0
2
0
2
2
0
0
0
1
0
0
0
1
0
0
0
0
0
2
4
0
0
2
0
0
2
2
0
0
0
0
0
0
2
1
1
0
1
1
1
0
1
0
0
0
1
0
0
0
2
0
0
0
2
0
1
0
0
0
2
3
0
0
2
4
1
1
0
1
0
1
2
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
2
2
2
1
0
0
1
0
2
0
0
1
0
1
2
0
0
2
1
2
2
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
2
1
0
1
0
0
0
2
0
2
0
0
1
1
0
2
0
0
0
1
2
0
2
0
2
2
0
0
0
0
0
4
2
0
0
0
0
2
2
0
0
0
0
0
2
0
0
2
1
0
0
0
2
0
2
0
0
0
0
0
2
0
2
2
0
0
0
0
2
1
0
1
0
2
0
0
2
1
0
0
0
0
0
1
0
2
2
0
2
1
0
1
0
0
2
0
1
0
2
1
0
0
2
0
0
0
1
0
1
0
1
0
0
0
1
1
0
1
0
0
1
0
1
0
1
0
0
2
0
2
2
0
0
0
0
0
0
1
0
1
0
0
1
3
0
1
0
0
0
0
0
0
0
1
2
0
2
1
1
2
0
0
0
1
2
1
1
0
0
0
0
0
0
0
1
1
0
1
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
2
0
0
1
2
0
0
1
0
2
0
0
0
1
2
2
0
2
0
2
0
1
0
0
0
0
0
1
0
0
3
0
0
1
0
0
0
0
0
1
0
1
1
0
0
2
1
0
0
0
1
3
0
0
1
0
2
0
1
0
0
0
0
0
1
2
2
0
0
0
2
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
1
1
1
2
1
2
1
0
0
2
1
2
0
1
1
0
0
3
2
2
2
0
1
0
0
0
2
0
1
4
0
1
0
1
1
2
2
0
0
1
0
0
1
2
0
2
1
2
0
1
0
0
1
0
2
0
1
1
1
1
1
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
2
2
2
0
2
2
2
2
2
0
0
2
0
0
1
0
2
0
0
2
0
0
1
2
0
1
2
1
1
1
1
1
0
0
0
0
1
0
0
0
0
3
0
0
0
2
0
0
1
0
0
1
0
2
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
3
3
0
1
2
2
0
0
1
0
1
0
0
0
0
0
1
2
0
2
0
2
0
0
2
0
0
0
1
1
0
2
0
2
2
2
0
0
2
1
0
1
0
1
1
4
0
1
2
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
2
0
0
0
1
2
0
1
1
0
2
0
0
0
0
2
0
0
2
2
0
0
0
0
2
0
0
0
1
2
0
0
1
2
2
5
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
2
1
2
0
0
1
0
3
1
0
1
0
0
1
1
1
2
0
0
0
0
2
2
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
2
2
0
0
1
0
1
0
0
0
1
0
2
2
4
1
2
0
1
3
0
0
1
0
0
0
0
0
2
0
0
0
2
3
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
3
0
3
2
0
1
1
0
0
0
1
0
1
0
0
0
2
2
2
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
1
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
2
0
2
0
1
0
0
1
1
1
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
2
2
0
0
0
1
2
2
0
1
0
0
0
1
0
2
0
0
0
0
0
1
1
1
2
1
1
2
0
1
2
0
0
1
1
0
5
2
0
0
2
0
2
0
1
0
1
0
2
1
0
1
0
0
0
0
0
0
1
0
0
1
3
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
2
0
0
0
2
1
1
0
1
2
0
0
0
0
0
2
0
2
3
1
0
1
1
0
0
0
0
0
0
1
0
1
0
0
2
0
1
0
0
2
1
1
0
0
0
0
2
0
1
0
0
1
2
0
0
1
0
1
1
0
1
0
0
0
1
1
1
0
1
0
1
1
1
0
2
0
1
0
0
1
2
2
0
0
0
0
2
1
1
0
0
1
0
0
0
1
1
0
0
2
1
1
1
2
1
0
0
2
0
0
1
0
2
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
1
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
2
2
2
0
2
1
0
0
2
0
0
1
0
1
0
1
0
0
1
2
0
0
0
1
0
1
1
2
0
0
0
0
2
0
0
0
0
0
2
0
1
2
1
0
0
1
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
1
0
1
2
0
3
0
0
2
0
0
0
1
0
2
0
2
0
0
1
0
0
0
1
0
1
2
0
1
0
1
0
1
1
0
0
0
1
0
0
0
0
3
0
0
0
0
0
1
0
0
2
0
0
2
2
1
0
0
1
1
1
0
0
2
1
0
0
3
2
0
0
2
2
0
5
0
0
0
0
2
0
2
1
0
0
0
0
2
1
1
0
2
0
0
0
0
0
0
3
2
1
1
2
0
0
0
0
1
0
1
2
0
2
1
0
0
0
2
0
1
1
1
1
0
0
0
0
3
0
1
1
1
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
1
0
0
2
0
0
1
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
2
0
2
2
0
1
0
0
0
0
1
1
1
0
1
2
2
0
2
2
0
0
0
0
1
0
2
2
2
0
0
1
0
0
2
0
0
3
1
1
2
0
2
0
0
0
0
2
0
0
1
1
2
0
0
1
0
1
2
0
0
0
1
1
3
0
0
0
1
1
0
0
1
0
0
0
0
0
2
0
2
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
2
1
1
1
0
1
0
1
0
1
0
2
0
0
0
0
4
1
1
1
0
0
0
2
0
0
0
2
0
0
1
1
1
0
0
2
0
0
0
0
0
2
1
0
0
1
2
0
2
0
4
4
0
0
0
2
1
2
0
0
0
0
1
3
2
0
2
0
0
0
2
2
0
1
1
0
0
0
0
0
1
0
0
0
2
1
0
2
0
1
1
0
1
0
1
1
0
1
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
1
1
2
2
0
0
0
0
2
1
0
0
1
0
1
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
2
0
1
1
0
1
0
0
0
1
4
2
1
0
0
0
2
0
0
0
0
1
0
2
1
1
0
1
0
0
0
0
0
2
1
0
0
0
4
0
1
1
1
2
0
1
0
0
2
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
2
0
1
0
0
1
1
0
2
0
1
2
2
0
1
2
2
0
1
1
0
0
1
0
0
0
0
0
1
0
2
0
0
2
0
1
1
0
0
0
1
1
0
1
0
0
0
1
0
2
0
1
0
1
0
0
0
0
1
2
0
2
2
1
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
1
0
0
0
0
1
1
1
1
2
0
1
0
2
0
1
1
0
1
1
2
1
1
1
0
0
1
0
0
0
0
0
1
0
0
0
1
2
1
2
0
1
6
2
0
2
1
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
2
0
2
1
2
3
2
2
2
0
0
0
1
0
0
0
0
1
0
3
0
2
0
0
1
0
2
2
0
1
0
0
2
0
1
13
2
0
0
1
2
0
0
0
2
0
0
0
0
0
0
2
1
0
0
5
0
2
0
0
0
1
0
2
0
2
0
0
0
2
0
1
2
0
1
1
0
0
1
0
0
0
1
2
0
0
0
0
0
1
0
2
1
0
1
0
0
1
0
0
0
0
0
1
2
0
2
2
0
2
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
1
1
3
0
2
1
0
0
1
0
1
1
2
0
0
1
2
0
4
1
1
0
0
0
0
2
0
2
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
3
0
1
0
0
2
1
0
1
0
1
2
1
0
0
3
2
2
0
0
2
0
1
0
0
2
1
2
0
2
0
0
0
0
0
0
0
0
0
1
0
1
2
1
1
2
1
0
0
2
2
0
0
0
0
0
1
1
2
0
0
2
0
1
0
2
1
0
2
0
1
0
2
2
1
0
1
2
1
1
0
1
1
1
0
1
1
0
2
1
0
0
0
2
0
0
0
1
2
0
0
0
2
0
0
2
0
2
0
2
0
2
0
0
0
1
0
2
0
2
0
0
0
0
2
0
0
0
0
1
0
2
0
1
1
0
0
0
0
0
0
1
0
1
2
2
0
2
0
0
1
0
0
0
1
0
1
0
2
0
0
0
0
1
2
0
0
2
2
0
0
0
0
1
0
1
0
2
2
0
1
0
0
1
0
0
2
2
2
1
1
1
0
2
0
1
0
2
0
0
0
0
2
1
0
0
0
0
0
2
1
1
2
0
0
0
0
1
0
0
2
1
0
0
0
2
2
1
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
1
0
0
0
0
2
0
1
2
2
0
2
1
1
1
0
0
2
2
0
0
0
0
0
1
1
1
0
0
0
1
2
1
2
1
2
0
2
1
0
1
2
0
1
2
1
1
0
0
1
0
2
0
1
0
0
0
1
1
1
0
0
0
0
2
1
2
0
2
0
0
0
0
0
0
0
1
0
1
1
0
2
3
0
2
1
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
1
0
0
1
0
1
1
0
0
0
0
2
0
0
0
0
1
0
2
1
0
3
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
2
0
0
0
0
3
1
0
5
0
1
0
0
4
2
2
1
2
1
0
0
0
2
1
0
0
1
1
0
1
0
0
1
2
1
2
0
0
0
0
0
1
1
1
0
1
0
0
0
2
0
2
0
0
1
0
4
0
2
0
0
2
0
2
1
0
0
1
1
0
0
0
2
0
0
0
0
0
2
1
0
1
0
2
1
1
0
0
13
0
1
1
3
1
3
0
0
0
0
0
2
0
2
0
0
0
1
6
1
0
0
0
0
1
0
0
0
2
1
2
2
1
1
1
0
0
1
0
1
0
2
0
3
0
1
0
0
0
0
2
0
1
0
0
0
4
0
2
0
0
0
2
0
0
0
2
0
2
2
1
0
1
0
1
0
0
2
0
1
1
1
0
0
0
0
0
2
0
2
0
0
0
1
0
0
1
0
0
0
0
2
1
1
1
0
4
0
0
2
1
1
0
1
0
1
0
0
1
2
0
0
0
0
2
2
0
1
2
0
0
0
0
1
0
2
1
2
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
1
1
1
2
1
2
0
0
1
5
0
0
2
1
2
0
2
0
1
2
2
0
0
0
0
2
2
1
1
0
2
0
1
0
1
0
2
1
0
0
1
2
0
0
2
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
1
0
2
1
1
2
1
0
0
2
2
0
2
0
1
0
1
1
2
0
1
0
0
1
1
0
0
2
1
0
2
2
0
2
0
0
0
0
2
1
0
0
0
0
0
1
0
0
1
0
1
0
2
0
0
0
2
0
0
1
0
2
0
0
2
2
1
2
0
1
0
2
1
0
2
0
0
0
2
0
0
0
2
2
1
2
0
1
1
2
0
1
1
0
0
1
0
0
1
1
1
0
1
0
0
1
0
2
1
2
0
1
0
1
0
0
0
2
0
1
0
0
2
0
2
1
1
0
2
2
1
0
0
1
0
1
0
2
1
1
2
0
2
1
0
0
1
2
0
0
2
0
0
2
2
0
2
0
1
2
0
0
0
0
1
1
2
1
1
2
0
2
3
0
0
2
0
0
1
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
1
4
0
0
1
0
0
2
0
0
0
0
0
0
0
2
2
0
2
1
0
0
0
1
0
1
0
1
2
0
0
0
0
2
2
2
1
1
1
0
2
0
1
2
0
1
2
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
1
1
0
1
0
2
2
0
1
0
0
1
0
2
1
0
0
1
2
2
0
0
0
0
0
4
2
2
0
0
2
0
0
0
0
1
0
0
1
0
2
1
2
4
2
0
0
0
1
0
1
2
0
0
0
2
0
1
2
0
0
1
0
0
0
0
0
2
1
2
0
2
0
0
0
3
1
1
1
2
2
0
2
1
1
1
0
0
0
0
0
2
1
0
0
1
0
2
2
0
1
2
0
0
0
0
0
0
2
1
2
1
2
0
0
0
1
0
0
3
1
2
0
1
2
1
0
1
1
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
1
2
0
1
1
3
2
0
0
1
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
1
0
0
0
3
1
1
0
0
0
0
0
2
0
0
2
0
0
3
0
0
0
0
1
1
0
0
0
1
2
0
0
0
2
1
1
2
2
0
0
1
0
0
1
0
2
0
1
0
2
2
0
0
0
1
1
1
2
0
2
1
0
0
0
0
3
1
2
1
0
0
0
0
1
2
0
1
1
2
1
0
0
3
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
1
0
1
0
0
0
2
0
1
0
0
0
2
0
0
0
0
1
0
0
1
0
0
2
2
4
2
2
0
0
0
0
0
2
0
0
1
0
1
0
0
1
0
1
0
3
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
1
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
1
2
0
0
1
2
0
0
0
0
0
2
0
0
1
1
0
0
0
2
0
0
0
0
1
1
1
1
0
0
0
2
0
0
3
0
1
1
0
2
2
2
3
1
0
2
0
0
0
0
2
0
2
0
2
1
1
3
0
2
1
2
0
1
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
2
0
3
0
0
0
0
0
0
0
0
1
0
2
1
1
0
0
0
0
1
2
0
2
1
0
0
0
0
0
0
0
0
1
2
0
2
0
0
11
0
0
0
0
0
0
2
0
0
0
1
0
1
2
2
1
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
2
0
0
1
0
0
1
1
1
1
0
0
0
0
0
0
0
0
2
1
0
0
1
2
0
0
2
2
0
1
0
1
0
0
0
0
2
0
0
2
1
0
0
2
1
0
2
2
0
0
1
1
1
0
4
2
2
0
2
0
1
0
4
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
1
0
1
1
0
2
0
0
0
1
0
1
2
2
1
2
2
1
0
1
0
0
2
1
1
0
1
1
0
0
0
1
0
0
2
2
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
1
0
1
0
4
1
1
0
0
1
0
2
0
0
1
0
1
0
0
2
1
1
0
1
2
0
0
0
0
0
0
1
1
1
0
2
0
0
1
1
0
1
0
0
2
0
0
1
1
1
0
0
1
0
0
0
0
1
0
0
2
2
2
1
1
1
2
2
0
1
0
0
0
0
0
1
0
1
0
0
0
2
2
2
0
0
0
0
0
0
2
1
0
2
1
2
0
0
0
0
0
2
2
0
0
0
0
2
0
1
0
0
0
2
0
0
2
0
0
0
0
0
3
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
1
2
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
2
2
0
0
0
1
1
0
1
0
0
2
0
0
0
2
1
2
0
0
0
0
3
2
2
2
0
2
0
1
1
2
0
0
0
1
0
1
1
1
0
1
0
2
0
0
2
2
0
1
1
0
0
0
2
0
0
0
0
0
1
0
0
1
2
1
2
0
2
0
1
2
0
0
1
2
0
0
0
2
2
2
2
0
1
0
2
2
1
0
0
0
0
2
0
2
0
0
1
1
0
1
0
3
1
3
1
2
0
0
0
0
0
0
2
2
0
0
0
2
0
0
1
2
0
0
0
0
1
0
1
1
1
1
1
0
0
2
0
0
0
1
2
0
2
2
0
0
0
2
1
0
0
0
1
0
0
1
1
0
0
1
0
0
1
0
0
1
2
1
0
0
0
0
0
4
2
0
0
5
0
2
0
2
1
0
0
5
0
0
2
0
1
0
0
1
0
1
1
0
0
2
0
0
2
2
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
3
0
1
1
0
1
1
0
1
0
0
2
0
1
1
0
2
0
1
2
0
0
0
0
0
0
2
1
1
2
0
0
1
1
0
1
2
0
2
1
1
1
0
0
0
0
0
1
2
1
0
0
2
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
2
1
0
0
1
0
0
4
1
0
4
2
0
0
0
0
0
0
0
0
0
1
3
0
0
2
2
0
0
1
0
0
0
2
0
0
8
1
0
0
0
4
0
2
1
2
3
2
0
2
1
0
1
2
0
4
0
2
2
0
1
1
0
5
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
2
2
0
0
0
2
1
0
0
0
2
0
2
2
1
0
0
1
0
0
0
0
0
0
0
0
8
0
1
0
3
0
0
0
0
0
0
0
2
1
0
0
0
2
2
0
0
0
0
1
2
0
0
2
1
0
0
0
0
2
1
1
2
0
2
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
2
0
1
0
2
0
1
0
0
0
1
2
2
2
0
0
0
0
0
0
2
0
3
2
0
2
1
0
0
0
2
0
2
2
2
2
0
0
0
0
0
2
1
2
0
0
0
0
0
0
1
0
0
1
2
1
0
0
0
0
0
2
2
0
0
0
2
0
5
2
0
0
0
2
2
0
1
0
0
0
1
1
1
1
0
0
0
1
0
0
1
0
2
0
0
0
0
1
2
0
1
1
0
1
0
1
1
0
2
0
0
1
1
0
2
0
0
0
5
2
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
1
0
0
0
2
0
0
2
2
0
1
0
0
0
1
0
2
0
2
1
4
1
0
0
0
0
0
2
0
2
0
0
0
1
0
0
1
0
1
0
0
2
2
0
0
2
0
2
0
0
0
1
1
0
0
0
1
0
0
0
1
1
0
0
1
0
0
1
1
0
2
2
2
0
3
0
0
0
0
1
0
0
1
0
2
0
0
2
1
1
2
1
2
0
1
0
0
0
0
0
1
0
0
4
1
1
0
2
0
0
0
2
0
2
2
0
1
7
1
1
1
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
1
1
1
0
1
2
0
1
0
1
0
2
0
0
0
1
0
1
0
0
2
0
1
2
3
1
0
0
2
1
1
0
0
0
2
1
2
1
3
1
2
0
2
0
0
0
0
0
1
2
0
0
0
0
1
0
0
1
2
2
0
1
0
2
0
1
1
2
0
2
2
2
1
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
1
0
0
0
0
0
1
0
2
2
1
2
0
0
0
3
0
0
0
2
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
2
2
0
1
1
0
0
0
0
3
0
2
2
0
0
1
0
2
0
1
0
3
0
1
2
1
0
0
0
0
0
2
0
0
0
0
1
0
0
2
5
0
0
2
2
1
0
1
0
0
0
0
1
0
0
1
0
0
0
5
0
1
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
1
2
0
2
2
2
0
0
0
0
0
0
0
1
0
0
1
2
1
0
2
0
3
2
0
0
1
0
0
0
0
1
0
2
1
0
0
1
0
0
0
2
1
0
1
0
0
2
1
2
0
0
1
1
2
0
0
0
0
0
2
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
1
1
0
0
1
1
0
2
1
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
1
2
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
3
0
0
1
1
0
1
2
0
0
0
1
0
0
2
0
0
2
2
1
2
1
1
1
1
0
0
0
0
0
0
2
0
0
2
1
2
0
0
2
0
0
0
2
2
0
0
1
0
2
1
0
0
5
1
0
0
0
1
0
2
0
1
0
2
1
1
0
0
0
1
0
1
1
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
2
0
1
0
2
2
3
3
3
2
1
0
0
2
1
0
2
0
0
2
0
0
0
0
0
1
3
0
1
0
1
0
0
0
2
1
0
0
2
0
0
0
0
0
1
1
1
0
1
1
0
1
1
0
1
0
2
0
0
0
1
2
0
0
2
2
2
0
0
0
0
0
0
1
1
0
0
1
0
0
2
0
0
0
2
0
0
0
1
1
1
0
2
2
0
2
2
2
0
0
0
2
0
2
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
2
0
2
0
0
1
2
1
2
0
0
0
2
0
0
0
1
0
1
0
1
0
0
2
1
0
1
2
0
0
0
0
1
0
0
1
0
1
0
0
2
0
0
0
0
2
0
0
1
0
1
0
3
0
1
1
0
0
2
1
2
1
1
0
1
0
0
0
1
2
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
3
0
2
1
0
2
2
0
0
2
0
2
5
2
1
0
0
0
2
1
0
0
0
1
0
0
2
2
1
0
0
0
2
0
0
2
0
1
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
1
1
1
1
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
1
1
2
1
0
1
0
0
2
2
1
1
0
1
0
0
0
1
1
1
0
0
0
0
2
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
1
0
2
0
1
0
2
2
1
1
1
0
0
0
1
0
0
2
0
0
1
0
0
0
1
0
0
1
0
0
2
2
2
0
3
1
0
2
0
1
0
0
2
1
0
0
0
0
2
0
1
2
1
0
2
1
0
0
0
3
1
2
1
1
0
0
0
0
0
2
1
0
2
2
0
0
0
0
1
0
0
5
2
1
0
0
1
0
3
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
3
2
1
0
0
0
0
0
1
0
1
0
0
1
2
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
2
2
0
2
0
0
0
0
1
0
0
1
0
1
1
0
3
0
2
0
1
0
0
0
1
1
0
0
2
2
1
0
0
0
2
1
1
0
0
0
0
0
1
0
0
0
0
3
2
0
2
0
0
0
2
1
0
0
0
1
0
0
2
0
1
0
2
0
2
0
1
1
1
0
0
1
0
2
1
0
0
2
1
2
0
2
2
2
2
1
2
2
0
2
0
0
0
1
0
2
0
2
0
0
2
2
0
2
0
0
1
1
2
0
0
1
2
0
1
2
4
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
1
1
0
1
0
2
2
0
0
1
0
0
0
0
0
0
1
1
1
0
1
0
2
1
0
2
2
1
2
0
1
0
0
0
1
0
0
0
1
2
0
1
2
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
1
1
0
1
0
0
0
0
0
2
0
1
2
1
0
1
2
0
0
0
2
2
0
1
0
2
0
1
0
0
0
0
0
0
1
0
3
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
1
0
3
0
1
2
0
0
0
0
1
1
1
0
0
0
0
0
0
0
2
2
0
2
1
1
0
0
0
1
0
0
1
2
0
1
2
0
0
0
0
0
2
1
1
0
2
0
0
0
0
0
2
1
0
0
1
0
1
0
1
1
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
1
1
0
1
2
0
0
0
0
1
2
1
2
2
0
3
1
2
0
0
2
0
0
2
0
0
2
2
0
1
1
2
1
2
0
1
0
1
0
2
0
2
0
0
2
0
0
0
0
1
0
0
1
2
0
0
0
0
2
0
0
1
0
0
2
0
0
1
0
1
1
0
0
0
1
0
0
3
2
2
0
0
2
0
0
0
0
1
0
0
1
0
0
1
0
2
0
0
0
0
2
0
1
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
1
1
0
0
1
0
2
0
0
0
2
2
0
1
1
0
1
2
0
0
0
0
0
0
2
1
1
2
0
0
0
0
0
0
0
0
1
0
1
1
0
2
1
1
0
0
0
1
1
0
1
0
0
0
0
0
0
1
1
0
1
0
0
2
0
2
2
2
3
0
1
0
0
2
0
0
0
1
1
0
0
1
0
0
0
0
0
5
4
0
0
0
1
2
0
1
0
0
2
0
0
0
0
0
1
0
2
0
2
0
0
2
0
0
2
0
0
1
1
0
2
0
0
0
0
0
0
0
1
2
2
0
0
3
2
1
1
2
0
2
0
1
0
4
0
0
0
1
0
0
2
1
0
0
1
0
1
2
0
1
0
1
1
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
2
2
2
0
2
0
1
0
0
2
0
0
0
2
0
1
2
2
1
1
0
1
0
0
1
0
0
0
0
1
0
1
0
1
0
1
2
0
1
2
1
0
0
2
0
0
2
0
0
1
0
0
0
0
2
0
0
0
1
0
1
2
0
0
0
0
0
0
2
0
4
0
0
1
0
1
0
0
0
1
0
0
2
0
0
0
0
2
0
1
1
0
1
0
0
1
1
1
0
2
2
2
0
0
0
2
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
2
2
1
0
0
0
1
0
2
0
0
0
1
2
1
2
0
2
2
0
0
2
0
1
1
1
0
1
0
0
0
0
0
2
0
0
0
1
0
2
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
2
0
2
1
1
0
0
2
0
0
2
2
0
1
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
2
0
0
3
2
0
0
1
0
1
0
0
0
0
1
1
0
0
0
1
1
0
0
0
2
0
0
1
0
0
2
0
2
5
0
2
2
1
2
1
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
2
0
0
0
2
0
1
0
5
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
2
0
0
2
0
0
1
0
0
1
0
0
6
0
1
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
2
2
0
1
0
0
0
1
1
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
2
0
3
2
2
0
2
0
0
1
0
0
0
0
0
2
2
0
0
0
1
1
0
0
0
0
0
2
0
2
1
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
1
0
2
1
1
0
0
0
2
0
0
1
0
2
0
0
0
0
1
0
0
0
2
2
0
1
1
0
0
0
1
0
0
1
0
0
1
0
2
0
0
0
0
0
0
1
3
2
1
0
2
0
0
0
0
0
1
1
2
2
0
0
0
0
4
0
0
0
2
0
0
1
7
1
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
1
0
2
0
0
0
0
0
0
0
0
2
3
2
3
0
0
1
0
1
0
0
1
0
0
0
0
2
2
0
0
1
1
0
0
2
0
3
1
0
0
0
0
1
1
0
2
0
0
0
1
2
0
0
0
0
0
1
0
0
0
1
0
0
1
1
1
0
1
0
2
0
1
0
2
2
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
2
2
1
1
0
0
1
2
0
4
1
0
1
1
0
0
0
1
0
0
2
0
2
2
2
0
2
0
0
0
0
1
0
0
0
2
2
1
0
0
0
0
0
1
0
0
1
0
1
2
0
2
0
0
1
0
2
1
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
2
0
2
0
0
0
2
0
1
0
2
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
2
2
1
0
0
1
1
0
0
1
0
0
2
0
0
0
0
0
0
1
2
1
1
1
0
2
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
2
1
0
0
0
2
2
0
0
0
0
1
0
0
2
1
0
1
0
1
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
2
2
0
1
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
1
1
0
0
2
2
1
0
0
1
0
0
0
1
1
2
2
1
1
1
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
1
1
1
0
2
0
0
0
0
2
3
2
0
0
0
4
1
0
0
0
0
1
0
0
0
0
0
2
1
1
0
0
0
1
2
2
0
0
0
0
0
3
1
0
0
3
0
0
0
2
0
1
0
1
2
0
2
3
0
1
0
0
0
0
0
0
2
1
0
1
0
1
1
2
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
1
1
0
1
1
0
0
0
0
2
0
1
2
1
0
0
0
1
0
0
0
0
2
0
1
1
0
0
0
1
0
1
2
0
2
0
0
2
0
1
2
0
0
0
1
1
2
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
1
1
0
1
1
2
0
1
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
2
1
1
2
2
2
1
2
1
1
0
0
0
0
0
0
2
0
2
2
0
0
0
2
0
1
0
0
0
1
0
0
0
0
2
1
3
2
0
0
2
1
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
1
1
2
1
0
0
0
0
2
1
1
1
0
1
0
2
2
1
0
0
0
2
1
2
2
0
2
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
1
0
2
1
1
2
1
0
1
2
0
1
0
0
1
0
0
2
2
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
4
2
0
0
0
0
0
0
1
0
0
1
0
2
2
2
1
3
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
2
1
1
0
0
1
0
0
2
0
1
0
1
2
2
2
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
2
1
1
0
0
1
2
0
1
0
1
0
0
1
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
1
2
0
0
0
3
0
1
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
1
0
2
0
1
0
1
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
1
0
2
0
1
0
0
0
0
0
0
1
1
2
0
0
2
0
0
2
2
0
0
0
0
1
0
2
0
0
2
0
2
0
0
0
2
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
2
2
0
1
1
0
1
0
2
0
0
0
1
2
0
0
1
0
0
2
1
0
0
0
0
1
1
0
0
1
2
0
0
2
1
0
0
0
2
0
0
2
1
1
0
0
0
2
0
1
0
1
0
1
0
1
1
1
0
1
1
1
1
1
0
0
1
0
0
0
0
0
1
0
0
0
2
1
1
0
0
1
1
2
1
0
0
0
1
0
0
1
1
0
0
1
1
1
2
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
1
1
2
0
1
0
0
0
0
0
0
2
0
0
2
2
0
2
0
1
0
2
0
0
1
0
4
0
1
0
2
2
0
2
0
1
1
1
0
0
0
2
1
1
0
0
0
2
0
1
2
0
0
0
0
0
1
0
0
0
0
1
0
2
1
0
0
1
0
0
0
0
1
1
3
0
0
0
0
0
0
0
2
1
0
0
0
1
2
0
2
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
3
0
0
2
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
1
0
0
2
2
2
2
0
0
0
2
1
0
0
1
1
0
0
2
2
0
0
1
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
3
2
0
0
2
2
0
0
0
2
0
0
1
1
1
2
1
0
0
0
0
0
2
0
1
0
0
3
0
2
0
2
0
0
0
3
0
1
0
0
0
0
1
0
4
0
0
0
2
0
1
0
0
1
2
0
0
0
0
0
0
0
2
0
1
0
1
0
1
2
0
1
2
2
0
0
1
4
0
1
2
0
1
2
0
0
2
1
1
0
2
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
2
0
0
1
1
1
0
2
1
1
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
2
2
1
1
0
0
0
0
1
1
0
0
0
2
0
0
1
0
0
2
0
0
0
1
0
1
1
0
2
2
0
1
0
2
0
0
0
1
1
2
0
2
1
2
1
0
1
2
1
2
0
0
0
0
2
1
0
0
0
0
0
1
0
1
1
0
1
0
0
2
2
0
0
0
0
1
0
0
1
2
0
0
0
0
2
5
0
0
3
0
0
0
0
0
1
0
0
1
2
0
2
0
1
0
0
0
1
0
0
1
0
0
2
2
0
0
0
1
0
0
0
0
1
3
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
1
0
0
2
0
3
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
1
2
0
0
0
0
2
2
3
0
1
0
2
0
2
0
0
1
0
0
0
1
2
0
0
0
0
1
2
0
1
4
2
0
0
0
0
0
0
0
2
0
1
0
0
1
0
2
2
2
0
2
0
0
1
1
0
2
2
0
0
0
0
0
2
1
0
2
0
2
0
0
1
2
1
0
1
2
0
0
0
0
0
0
1
2
0
0
2
2
0
0
2
1
0
1
0
2
1
0
1
0
0
0
0
0
0
1
0
2
1
2
2
2
1
0
0
2
0
1
1
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
2
0
1
0
2
1
0
0
2
2
0
0
0
1
0
2
0
1
0
2
0
1
0
0
0
1
1
2
0
2
0
0
0
2
0
0
0
2
0
2
2
0
2
2
0
1
0
0
0
0
0
0
1
0
1
0
0
2
0
0
5
1
0
1
1
1
2
2
0
1
1
0
1
0
1
0
0
1
3
3
0
1
0
1
1
1
1
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
2
0
1
0
1
0
1
0
2
1
0
2
0
1
1
0
3
2
0
2
0
0
0
0
0
0
4
0
2
2
1
0
0
0
2
0
1
2
0
0
2
0
2
0
0
0
1
1
0
2
2
0
0
0
2
1
0
0
0
0
2
2
0
0
0
3
0
0
0
0
0
0
0
2
0
1
0
0
0
1
1
2
0
1
0
2
0
3
0
1
0
0
1
0
0
0
1
0
2
0
0
2
1
0
0
2
1
0
0
2
1
2
2
1
1
0
1
0
2
0
1
0
1
1
1
0
0
0
0
2
2
1
0
0
0
0
0
0
0
1
1
1
0
0
2
0
2
1
0
0
2
0
0
1
0
0
0
1
0
0
2
0
1
0
0
0
0
2
1
0
2
2
0
0
0
0
1
0
0
0
0
2
1
2
0
2
2
0
0
0
3
0
0
0
1
0
2
2
2
0
0
2
2
0
0
0
1
0
0
3
0
2
2
0
0
2
1
0
0
0
0
1
2
2
1
2
0
0
2
1
1
0
2
1
0
0
2
0
0
0
0
3
0
0
0
4
0
1
2
0
3
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
6
0
0
0
0
2
1
0
0
0
2
0
1
0
0
1
0
0
1
0
0
2
0
2
2
0
4
0
4
0
0
0
0
0
0
0
0
1
0
1
2
2
0
0
0
2
0
0
0
0
3
0
1
2
0
0
2
1
2
0
1
1
0
2
0
0
1
0
1
0
2
2
0
0
0
0
2
0
1
0
0
2
2
0
0
0
0
0
1
1
0
3
0
1
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
2
0
2
0
3
1
2
1
1
0
0
0
0
1
1
1
0
2
0
1
1
0
0
0
0
2
0
0
1
2
0
1
2
0
2
0
1
0
0
1
1
0
1
2
3
0
0
0
0
1
0
0
1
0
2
0
2
0
0
2
2
0
2
2
2
0
2
0
0
1
1
0
2
1
1
1
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
2
0
2
0
2
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
1
1
0
0
0
0
0
2
0
2
0
0
0
1
0
2
0
2
0
0
1
1
0
0
0
0
3
2
0
2
2
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
1
1
0
0
0
0
0
0
0
1
0
0
2
0
1
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
1
0
0
11
1
0
1
0
2
0
2
0
1
3
0
0
0
0
0
1
0
0
0
3
2
0
0
2
0
2
2
0
3
1
0
0
1
1
0
0
1
0
0
1
1
1
0
0
0
2
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
2
0
0
0
0
1
4
0
0
2
0
1
1
2
0
0
0
0
1
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
1
1
0
1
0
2
0
0
1
1
0
1
1
0
0
2
2
0
1
2
1
1
1
2
0
2
0
2
2
2
0
0
0
0
0
0
0
2
3
1
0
2
0
0
0
0
0
3
0
0
1
2
0
0
1
2
0
0
0
0
0
0
1
2
2
0
2
0
2
0
0
0
0
2
0
1
0
0
0
0
0
2
2
1
1
0
0
0
3
0
0
2
0
1
2
0
1
0
0
0
3
0
2
2
2
0
0
0
1
1
2
2
0
0
2
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
1
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
1
0
1
2
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
2
1
0
7
2
0
0
0
0
0
0
2
0
2
0
0
2
2
1
1
2
0
0
3
0
1
0
2
2
0
0
0
0
1
2
0
0
0
0
2
0
6
2
0
0
0
1
0
0
1
0
0
0
0
2
2
0
0
1
1
1
2
1
0
1
0
2
0
0
0
0
0
0
0
1
2
0
0
2
2
0
0
0
0
0
2
1
0
1
0
0
1
0
1
0
0
0
0
0
1
2
1
3
0
0
0
1
0
0
2
1
0
3
0
2
2
0
0
1
0
1
2
1
2
1
0
1
3
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
2
2
0
0
1
0
1
2
1
2
0
1
0
0
0
1
0
2
1
0
0
1
0
2
0
2
0
0
0
0
0
2
0
2
2
0
1
0
0
0
0
0
0
3
6
0
0
1
0
0
0
1
0
1
1
2
2
2
0
1
0
0
0
4
2
3
2
1
2
0
2
2
0
1
0
0
0
1
0
2
0
2
0
0
0
0
1
0
2
1
0
0
0
0
0
1
0
0
1
1
1
0
1
0
0
2
1
0
0
0
1
0
0
0
0
0
1
1
1
0
1
1
0
1
0
2
1
1
0
0
0
1
0
0
2
1
0
0
0
0
2
2
0
2
2
1
0
1
2
0
0
0
2
4
1
0
0
0
1
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
1
2
2
0
2
0
0
0
0
0
0
1
2
1
0
1
8
0
0
1
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
3
2
1
0
0
1
0
0
1
2
2
0
1
0
0
2
1
0
0
2
0
0
1
2
0
2
2
2
0
0
0
0
2
0
0
0
2
2
3
0
0
1
0
0
0
0
2
0
0
0
0
2
1
2
0
1
2
1
1
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
2
0
2
1
0
1
0
1
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
2
1
3
0
0
0
0
3
1
0
0
0
1
1
0
2
0
2
1
1
0
0
0
2
0
1
0
0
1
2
0
0
0
1
0
0
1
1
0
0
2
2
0
0
0
0
2
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
1
0
2
0
0
0
0
1
0
2
1
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
1
2
1
2
0
0
2
2
0
0
2
2
4
3
0
2
0
1
0
0
1
2
0
0
0
1
0
1
0
0
0
1
0
0
0
2
2
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
1
3
0
0
0
1
0
2
0
1
6
2
0
0
1
1
0
0
0
0
2
0
1
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
5
0
2
0
1
2
0
0
0
2
2
1
0
0
0
0
0
0
1
0
0
2
0
1
0
0
1
0
1
2
0
1
1
0
0
0
0
0
0
0
2
2
0
0
3
0
2
0
0
0
0
0
1
2
2
0
14
0
0
2
0
1
2
2
1
1
0
0
2
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
1
0
1
1
1
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
3
1
0
1
0
0
0
1
3
0
1
1
1
0
1
1
2
0
1
0
2
0
2
0
0
0
1
0
0
3
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
1
0
0
1
0
2
0
2
1
0
0
0
2
0
0
0
0
0
2
1
0
1
0
1
0
1
0
1
0
0
0
2
2
0
1
0
1
1
0
0
0
1
0
5
1
0
1
0
2
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
1
2
0
0
1
1
0
2
0
0
2
1
0
0
2
0
2
1
0
1
0
2
0
0
2
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
2
0
2
1
0
10
0
1
0
0
0
0
0
1
0
0
0
2
0
2
0
2
2
0
0
2
1
1
0
2
3
0
0
0
2
0
2
0
0
0
0
2
0
0
2
0
0
2
0
0
1
0
0
2
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
2
1
1
0
1
2
2
0
2
0
2
0
1
0
0
0
0
0
3
0
1
0
1
0
0
0
0
0
0
2
1
0
1
3
0
0
2
0
0
0
2
2
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
1
4
0
0
0
0
0
0
0
4
2
0
2
0
0
0
1
0
0
0
0
0
1
0
2
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
2
4
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
2
2
1
0
0
0
0
0
2
6
0
0
0
0
0
3
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
3
0
0
0
2
3
0
0
2
1
0
0
0
0
0
2
2
0
0
0
0
2
1
0
0
0
2
2
1
1
0
2
0
1
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
1
0
0
0
0
2
0
0
2
1
5
0
0
1
1
0
0
0
0
0
0
0
2
0
0
1
3
2
0
1
0
0
2
7
0
1
2
1
0
1
0
1
2
1
0
2
0
5
2
2
0
0
1
0
1
2
1
1
2
1
0
1
0
2
1
1
2
1
2
0
0
0
1
0
0
3
0
0
1
2
1
0
2
0
1
0
1
0
0
0
0
1
0
0
2
0
0
1
1
0
0
0
0
0
0
0
2
3
0
1
2
0
0
1
0
0
2
1
1
0
1
0
2
0
1
0
2
0
0
3
0
2
2
0
1
1
2
1
1
2
0
2
1
0
0
0
1
0
0
1
1
0
0
0
1
0
0
2
1
0
0
0
0
2
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
2
0
0
0
0
0
1
0
2
0
0
0
2
1
0
0
0
0
2
1
1
2
0
2
0
1
0
0
0
0
3
0
0
0
0
3
1
2
2
0
0
2
0
0
1
1
1
1
2
0
3
2
2
0
1
0
1
0
1
1
2
1
0
2
0
0
2
0
1
0
1
0
2
0
0
1
0
0
2
1
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
2
0
1
1
0
3
0
3
0
0
0
2
1
1
1
2
2
0
0
1
2
2
2
0
2
2
0
0
1
2
4
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
2
1
0
0
0
0
0
0
0
0
2
1
2
0
0
1
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
2
1
0
0
1
1
0
0
2
0
0
1
0
2
2
2
1
0
2
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
2
2
0
1
0
0
0
1
1
0
0
2
1
0
1
0
0
1
1
1
2
1
0
2
1
0
1
1
1
3
2
0
0
0
2
1
2
2
1
1
0
0
1
0
0
1
0
0
0
0
1
2
1
0
1
0
0
2
0
1
0
0
2
0
0
2
0
0
2
2
4
2
0
1
0
0
0
0
2
2
2
2
1
0
2
0
0
1
0
0
0
0
1
0
2
2
1
0
2
1
0
0
0
0
1
2
0
2
1
0
0
2
1
0
1
1
2
0
0
1
0
1
3
0
1
2
1
1
0
2
2
0
1
1
0
0
1
0
0
1
2
0
0
2
0
0
1
1
0
0
0
0
0
1
0
2
2
1
1
0
2
0
0
1
0
0
0
0
0
2
1
1
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
2
0
0
0
1
0
2
2
2
0
0
0
1
0
1
0
0
2
0
0
0
0
1
0
2
0
0
0
0
1
1
1
0
0
0
0
0
0
2
0
0
0
2
1
0
1
0
1
2
0
1
0
1
3
0
1
0
0
0
2
0
1
0
0
2
0
0
2
0
1
2
0
1
0
0
0
3
0
0
1
2
1
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
2
0
0
1
1
0
0
0
0
0
0
1
0
0
0
3
2
2
1
0
1
0
0
0
2
0
1
0
0
0
0
0
1
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
1
0
1
0
0
1
1
2
1
1
0
0
2
2
2
1
0
2
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
2
1
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
3
0
1
1
1
0
2
0
0
3
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
1
1
0
1
0
1
0
1
3
1
0
1
0
0
1
0
0
0
1
1
0
0
1
0
2
0
1
2
0
0
0
0
2
0
0
0
1
3
0
0
2
1
0
0
1
1
0
0
1
0
1
1
2
0
1
0
0
0
1
1
2
1
0
0
0
0
0
0
1
0
1
0
2
2
0
2
0
1
2
0
1
2
2
0
0
1
0
2
0
1
0
2
0
0
2
1
1
0
0
2
2
0
0
2
1
2
1
0
0
1
0
0
0
2
1
0
0
0
0
1
5
0
2
2
0
0
0
2
0
1
0
0
1
0
2
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
2
0
1
1
1
2
0
0
3
0
2
1
0
1
0
0
0
0
0
0
2
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
2
1
1
0
1
0
0
0
0
1
0
0
0
1
0
0
1
1
0
2
0
1
3
1
0
0
0
7
0
0
0
2
0
2
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
2
0
2
0
0
1
1
1
2
0
0
1
1
0
0
0
0
1
1
0
2
2
1
4
0
0
0
4
0
0
0
0
1
2
0
0
0
0
0
2
0
2
2
0
0
0
0
0
2
2
1
1
1
0
0
0
0
0
0
2
0
0
0
1
0
2
1
1
2
0
0
1
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
3
2
0
0
0
1
0
0
0
1
0
0
2
1
0
0
0
0
1
1
0
1
0
0
1
0
2
1
1
1
1
2
1
0
0
0
0
0
3
0
0
0
2
0
1
0
1
2
0
1
0
2
3
1
2
2
2
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
2
1
0
2
0
0
2
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
1
3
0
0
0
2
0
2
2
2
1
0
0
2
0
0
0
1
0
0
0
0
0
2
1
0
2
0
0
0
1
0
1
1
0
0
2
1
0
0
1
0
1
0
1
1
0
0
2
0
0
0
0
0
2
3
0
0
1
1
0
0
1
0
0
0
2
2
0
1
1
1
0
1
0
1
0
0
0
1
0
1
0
0
0
0
1
1
0
1
0
0
1
1
0
2
2
0
2
0
0
2
0
0
1
0
0
1
0
1
0
0
1
2
2
0
0
3
0
0
0
0
2
1
1
0
0
0
2
2
1
0
2
2
0
3
0
2
0
0
2
0
0
0
2
2
1
2
0
0
3
0
0
0
0
2
2
0
0
1
0
1
0
0
0
1
0
0
1
1
0
1
2
2
0
0
0
0
2
2
0
2
1
0
0
0
0
1
2
1
2
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
3
0
0
1
0
0
2
1
0
0
2
0
0
0
0
0
2
1
0
1
0
0
0
1
1
1
0
1
0
1
2
0
1
0
2
0
2
0
1
2
2
0
1
1
0
0
0
0
0
0
2
2
0
1
0
0
1
0
0
2
2
0
1
4
0
0
2
0
1
0
0
0
1
3
0
0
0
1
0
1
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
3
0
0
1
0
2
3
2
0
2
2
2
0
0
2
0
2
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
1
2
2
0
0
0
0
1
0
0
1
0
0
1
0
0
2
0
2
2
1
0
0
0
1
0
0
0
0
0
0
6
1
1
0
2
3
1
0
0
0
1
1
0
0
0
2
0
1
0
0
2
0
1
2
0
0
2
0
0
0
0
1
2
0
1
0
1
0
2
2
1
0
0
1
2
0
0
1
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
1
0
1
0
0
0
0
2
1
0
2
0
1
0
0
2
0
0
1
0
0
0
1
0
0
0
0
2
0
2
1
1
0
2
0
0
0
2
1
4
2
0
2
0
0
0
1
0
2
0
0
0
0
0
0
1
3
0
2
0
0
2
2
0
0
0
2
1
1
0
2
0
0
1
0
1
0
0
1
0
2
1
0
0
0
0
1
0
0
0
1
1
1
0
0
0
2
1
1
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
4
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
4
1
1
1
0
1
2
0
1
0
0
2
0
3
0
0
1
2
1
0
0
0
0
0
2
1
0
1
0
1
1
0
2
0
0
0
0
2
0
1
0
0
0
1
0
0
1
1
0
0
3
1
0
0
2
2
0
1
0
2
0
0
1
2
1
1
2
0
1
2
0
0
0
1
1
0
1
1
3
0
4
2
0
0
0
1
2
0
2
1
1
2
0
0
0
0
0
0
0
2
0
1
2
0
0
0
1
2
1
0
0
1
0
1
0
0
0
1
2
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
2
1
0
0
0
2
2
2
3
1
0
0
0
0
2
0
0
0
2
0
2
0
2
0
2
0
0
2
1
2
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
2
0
1
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
1
2
0
1
1
2
0
2
1
0
1
0
0
1
0
0
0
0
1
0
0
1
1
1
0
0
2
0
0
1
9
3
2
0
0
0
1
2
1
0
1
0
3
2
0
1
0
0
0
0
0
0
0
2
1
1
1
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
1
2
3
2
2
0
0
0
1
0
1
1
1
1
0
0
2
0
0
0
0
0
0
2
0
2
1
0
0
2
1
0
0
1
0
0
0
0
0
0
1
1
0
2
2
0
0
0
0
0
0
2
0
0
0
1
1
1
0
0
0
0
0
1
0
1
0
1
1
0
0
1
0
0
0
0
0
1
0
2
0
1
0
1
1
1
2
2
0
0
0
0
0
0
0
0
0
0
0
2
1
2
1
2
0
0
2
1
0
2
0
0
0
1
0
0
0
2
0
0
3
0
0
0
0
0
0
1
0
0
0
1
0
1
2
0
0
0
0
0
1
0
0
2
0
2
2
0
0
2
1
0
0
1
2
0
2
0
0
2
1
0
0
1
0
2
2
1
1
1
0
0
0
0
0
1
0
2
2
1
0
1
3
2
1
2
0
0
2
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
2
0
0
2
0
0
3
0
0
1
1
2
0
2
0
1
0
0
2
0
0
2
0
0
1
0
2
0
0
0
0
2
1
0
0
0
1
0
0
1
2
2
1
0
2
0
0
1
0
2
0
1
0
1
0
2
0
0
1
1
0
2
0
0
1
1
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
1
2
1
0
1
0
2
0
0
0
0
1
1
0
0
1
0
2
0
0
2
1
0
0
0
2
0
0
3
1
0
2
0
0
2
0
1
1
1
0
1
0
0
1
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
2
0
1
1
0
3
3
0
0
2
1
0
2
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
1
1
0
2
0
1
0
2
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
2
1
0
0
2
0
0
0
1
2
0
2
1
0
2
2
0
0
2
0
0
0
1
0
0
2
0
0
0
0
1
0
1
2
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
1
2
0
0
0
2
1
0
0
2
0
0
3
0
0
0
0
1
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
1
0
3
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
3
0
0
0
0
0
0
1
1
0
1
2
0
1
1
0
0
3
1
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
1
0
2
0
2
0
0
0
2
2
0
1
0
0
2
2
0
0
1
1
2
0
0
0
1
0
0
5
2
0
2
0
0
0
0
0
1
0
0
0
0
2
0
1
0
1
0
3
0
2
2
1
0
0
0
0
0
1
0
0
2
0
1
1
2
0
0
1
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
2
0
3
2
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
1
0
2
1
1
1
0
0
0
0
1
2
0
3
0
0
0
0
0
3
1
2
0
0
0
0
0
2
0
0
0
0
2
0
2
2
0
0
1
2
0
0
2
0
0
2
1
0
3
0
2
0
0
2
0
1
0
0
0
0
1
1
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
2
0
1
2
0
0
0
1
5
0
0
0
0
0
1
2
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
1
1
1
1
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
2
0
0
1
4
1
1
0
0
0
0
1
0
0
0
0
2
0
2
0
0
4
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
2
0
1
2
3
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
1
0
0
0
1
1
0
0
2
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
1
2
0
2
1
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
1
2
1
0
4
0
2
0
4
0
1
0
0
0
0
2
1
4
0
1
2
0
1
2
1
0
0
2
1
0
1
0
0
0
2
2
1
0
0
0
1
0
0
1
0
2
0
0
0
2
0
0
0
1
1
4
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
1
2
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
3
0
0
0
1
0
0
1
2
2
0
1
1
0
0
0
0
2
0
0
2
0
2
0
0
1
0
0
0
1
0
0
0
0
0
1
1
2
0
0
0
1
2
1
4
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
1
0
1
0
2
2
1
2
1
2
2
2
2
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
2
2
1
0
0
2
0
2
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
4
2
0
2
1
0
0
0
0
0
3
0
1
1
0
1
0
0
0
1
0
1
2
0
0
1
0
1
2
0
0
0
0
2
0
0
1
0
2
0
0
1
2
1
1
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
1
2
0
1
0
2
3
0
1
1
0
0
1
0
0
0
0
2
0
1
1
1
2
0
0
0
0
2
0
0
0
0
2
0
3
2
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
2
0
1
1
1
0
0
0
0
1
0
0
3
0
0
0
2
1
1
2
0
0
0
0
1
0
0
1
0
0
1
0
2
1
2
0
0
2
1
1
0
0
2
2
0
0
1
0
0
0
0
3
2
0
1
2
1
2
0
0
2
0
0
1
1
0
0
1
0
0
0
0
0
1
0
1
0
2
0
0
0
2
2
0
0
3
1
1
2
0
0
1
0
0
0
1
0
0
2
1
0
0
0
0
2
1
0
0
3
0
3
3
1
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
2
1
0
0
1
0
1
0
2
1
1
1
0
0
0
1
1
1
2
0
0
0
1
0
0
0
0
2
3
0
1
0
0
2
0
3
2
0
0
0
2
1
0
0
0
0
0
1
0
0
2
0
2
0
0
1
0
2
0
0
1
0
0
2
0
0
0
0
1
1
0
0
2
0
1
0
2
2
0
1
0
0
0
0
2
1
2
1
0
0
2
0
0
1
0
0
0
0
2
0
0
0
1
0
2
1
1
2
0
2
0
0
7
0
4
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
1
0
2
1
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
1
0
0
8
0
2
0
0
1
0
0
2
1
0
0
1
0
0
0
1
2
0
2
0
0
0
0
1
0
2
2
0
0
0
2
1
1
0
0
0
2
2
2
0
1
0
1
0
1
1
0
0
1
0
1
0
0
2
2
0
3
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
1
1
5
0
1
1
1
1
0
2
0
0
0
0
2
0
2
1
1
1
5
3
0
0
0
0
0
2
0
0
2
0
0
0
1
2
0
1
0
0
2
0
0
0
1
0
1
0
0
0
0
2
0
0
0
1
0
1
0
2
0
0
0
2
0
2
0
1
1
0
0
2
0
0
0
0
0
0
2
1
0
2
0
2
0
1
0
1
0
1
0
1
0
0
3
0
0
0
0
0
0
2
0
0
2
2
0
2
0
0
0
2
0
0
2
0
0
1
0
2
0
1
0
0
0
0
0
2
0
0
0
0
2
2
0
5
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
3
2
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
1
1
0
0
1
0
0
2
0
2
0
2
2
0
0
0
1
2
0
0
0
0
0
0
0
0
2
3
0
1
0
0
1
0
0
1
2
0
1
0
0
2
0
2
1
1
2
2
1
0
0
0
0
0
2
1
2
1
3
0
0
1
0
0
1
0
2
0
1
0
0
1
0
0
1
0
1
1
0
2
0
2
2
0
2
1
0
0
2
3
1
0
0
0
0
0
0
2
1
2
1
0
0
0
0
0
2
2
2
0
1
0
1
1
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
2
0
0
0
1
2
0
0
1
0
0
0
1
0
0
1
1
0
0
1
2
0
3
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
1
1
1
1
1
0
0
0
2
0
0
1
2
0
2
1
0
1
0
1
2
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
1
0
1
0
0
1
0
0
2
2
2
0
0
0
0
0
1
0
0
2
0
0
0
0
3
0
1
1
0
1
0
0
1
1
0
1
0
0
0
0
0
2
1
1
1
2
1
1
0
2
0
0
0
0
0
1
1
0
0
5
1
0
0
0
1
3
0
0
0
2
0
0
2
0
3
2
0
0
0
2
3
1
0
0
0
0
0
0
0
1
0
1
0
0
3
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
1
1
2
0
0
1
3
2
0
2
2
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
4
2
2
0
0
0
0
1
0
2
1
1
1
1
1
0
0
1
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
1
1
1
0
0
0
0
2
0
0
1
2
0
0
0
0
1
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
2
2
2
2
1
1
1
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
1
0
2
1
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
2
0
2
0
1
0
2
0
1
0
0
1
0
1
2
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
2
1
6
0
1
1
0
0
2
2
0
0
6
0
0
2
2
0
0
1
0
1
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
2
2
1
0
4
0
1
0
0
1
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
3
2
0
0
2
0
1
1
1
2
1
0
2
0
2
0
2
0
1
0
0
2
2
0
0
0
0
0
2
3
0
0
0
1
1
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
2
0
2
0
0
0
0
2
1
2
0
2
0
0
0
0
0
2
2
0
0
0
0
0
3
1
0
0
0
1
0
0
1
0
2
0
2
1
0
1
1
1
1
0
0
0
0
2
1
0
2
0
0
0
1
0
1
1
1
1
1
0
0
0
2
1
0
1
2
0
0
0
0
0
1
0
2
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
1
0
0
2
1
2
0
0
0
0
0
0
2
0
2
0
1
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
2
1
0
0
0
2
1
0
0
0
1
0
1
2
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
1
2
0
0
2
0
3
0
1
1
0
0
1
0
0
0
1
0
0
0
0
1
1
1
0
2
2
1
0
0
3
0
0
0
1
0
0
2
1
0
1
1
0
0
1
0
0
1
0
0
1
0
0
0
3
2
2
0
0
0
0
1
1
0
2
1
0
2
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
3
1
4
0
0
1
2
0
0
0
0
2
0
0
2
0
1
0
1
1
0
1
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
2
0
3
0
0
1
1
0
2
1
0
2
0
0
0
0
0
1
0
0
2
0
2
1
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
2
0
1
0
0
0
2
0
2
2
0
0
0
1
0
0
0
2
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
1
1
0
0
0
0
2
2
1
1
0
1
1
0
3
0
2
0
0
0
0
0
2
0
1
0
1
1
0
2
0
2
0
2
0
2
1
2
0
1
1
0
3
0
0
0
0
0
0
0
1
0
0
1
0
2
0
2
0
0
2
2
0
1
2
2
0
3
0
1
2
0
1
0
0
0
0
1
0
1
0
0
1
2
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
2
1
0
2
3
0
0
1
1
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
1
2
0
3
0
0
2
0
0
1
0
0
3
2
0
0
1
0
0
1
0
1
0
2
0
0
1
1
1
0
0
2
1
0
1
0
1
1
0
1
0
1
0
2
2
2
1
1
0
0
0
1
1
1
0
3
0
2
0
0
0
0
0
3
1
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
2
1
2
0
0
0
2
1
0
1
0
0
1
0
0
0
1
0
1
0
1
1
2
3
0
1
0
2
4
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
3
1
2
0
0
0
0
1
1
0
0
0
0
0
0
2
3
0
1
0
1
2
0
1
0
0
0
0
0
1
2
0
0
0
1
2
0
1
1
0
0
2
0
0
0
0
1
0
1
2
0
0
2
0
0
1
2
2
0
0
4
0
1
2
0
1
1
0
2
2
0
0
0
0
0
2
0
0
0
1
1
2
2
0
0
1
0
0
2
1
1
0
0
2
2
1
0
0
2
0
2
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
2
1
1
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
1
2
1
0
1
0
2
1
1
2
1
0
0
1
0
0
2
0
0
0
0
1
2
1
0
0
0
2
0
1
0
0
2
1
0
1
1
1
2
2
0
2
2
2
0
0
2
0
0
1
2
1
0
2
0
0
0
0
0
2
0
0
0
2
0
2
0
2
0
2
1
0
0
1
1
0
1
1
0
0
1
0
0
1
0
0
1
2
2
0
0
0
2
0
0
0
2
4
0
0
1
0
2
2
1
0
1
2
0
0
2
2
2
2
0
3
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
3
2
2
0
1
0
0
0
0
2
4
1
0
1
1
2
2
2
0
0
0
1
0
1
0
2
2
0
0
2
0
0
0
1
0
1
2
0
1
0
0
1
0
1
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
2
0
1
0
2
0
0
1
1
0
1
1
0
1
0
1
0
1
1
0
0
0
0
1
0
2
0
2
1
0
0
0
0
2
0
0
1
0
1
0
0
0
0
2
3
1
2
0
0
1
2
0
1
0
2
1
0
1
0
0
2
0
1
3
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
1
2
0
0
0
0
0
1
2
0
1
1
2
1
3
0
1
0
1
0
0
0
4
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
2
1
2
1
0
1
0
0
0
1
0
0
1
0
1
0
1
0
0
2
0
2
0
0
0
1
2
0
2
0
1
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
1
2
0
2
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
2
0
2
0
0
0
2
0
1
2
1
1
2
1
1
0
0
4
0
3
0
1
0
0
0
0
2
1
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
1
0
1
3
1
0
0
2
0
2
0
1
1
0
1
0
0
2
0
0
0
2
0
0
1
0
0
2
2
0
0
2
2
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
1
2
1
1
0
2
0
0
0
0
1
1
1
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
1
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
1
0
2
0
1
1
0
0
1
2
0
0
0
0
0
1
0
0
1
0
1
1
2
0
0
0
0
0
0
3
0
2
1
1
4
0
0
1
0
1
0
1
1
0
0
1
2
1
2
1
0
0
1
0
1
1
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
2
2
1
0
1
2
0
2
0
0
0
1
0
0
1
1
0
2
4
0
1
0
0
0
0
0
0
0
0
2
0
2
0
2
0
1
0
0
0
0
0
2
0
0
0
1
0
1
0
2
0
0
0
1
1
2
0
1
0
0
4
0
2
0
0
2
2
2
0
1
0
0
0
0
0
0
1
0
0
2
4
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
1
2
1
2
0
2
2
1
0
2
1
0
1
1
1
1
1
0
0
0
0
2
0
0
0
1
0
1
1
2
1
2
0
0
0
0
0
0
1
3
0
3
1
0
2
2
0
0
0
2
1
0
0
0
1
0
0
2
2
2
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
2
0
0
2
2
1
0
0
0
2
1
0
0
0
0
0
1
1
0
2
0
0
2
0
2
0
1
0
0
1
0
1
0
2
0
0
0
0
1
2
0
0
0
1
2
0
0
2
1
0
2
0
0
1
0
0
2
0
1
0
2
0
0
0
1
1
0
1
2
0
0
1
0
0
1
1
1
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
1
0
0
0
2
0
0
0
0
1
0
2
0
1
0
0
2
0
0
1
0
0
0
0
1
0
3
0
0
2
0
0
0
0
9
1
0
1
0
0
0
0
2
2
1
0
0
0
1
0
0
0
0
0
2
0
0
2
0
1
1
0
0
0
0
1
2
1
0
1
0
0
0
2
0
0
0
0
0
1
0
0
2
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
1
1
2
2
2
2
2
1
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
2
1
2
1
1
1
2
1
0
0
0
2
0
0
0
4
2
0
0
0
0
1
0
0
2
0
1
1
3
0
0
1
2
2
2
0
2
0
1
0
2
0
0
2
0
1
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
1
5
0
2
0
0
0
0
0
0
3
0
2
0
0
1
1
0
0
1
0
2
0
0
1
0
2
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
1
2
2
0
2
2
1
0
0
0
2
1
0
1
0
0
3
0
0
0
0
1
1
0
1
0
0
0
0
2
0
1
2
0
0
1
0
2
0
2
0
0
2
0
1
2
0
1
0
1
2
0
2
0
0
0
0
0
1
0
2
1
0
0
1
1
1
0
0
0
1
2
2
0
0
2
0
1
3
1
0
2
0
1
0
0
0
0
2
2
0
1
0
0
1
1
0
7
1
0
0
0
1
1
0
0
0
0
0
0
2
0
0
1
0
0
1
1
0
3
0
0
1
0
1
1
0
0
3
1
0
0
0
0
0
0
0
1
0
0
1
1
2
0
0
2
0
0
1
3
2
0
1
0
0
0
0
1
2
1
1
2
0
0
2
0
0
1
0
2
2
0
0
2
0
1
0
1
2
1
1
2
0
2
2
0
2
0
0
2
2
1
0
2
0
4
2
3
0
2
0
0
0
0
1
1
1
0
0
2
1
0
1
0
2
2
0
1
1
1
1
1
0
0
2
0
0
0
0
3
0
1
0
0
2
1
0
1
0
0
0
0
3
0
1
0
2
1
2
0
0
2
1
2
2
0
1
2
0
3
0
0
1
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
3
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
2
0
1
2
0
1
0
0
2
0
0
1
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
4
0
0
0
0
1
0
0
0
1
1
1
2
0
1
0
0
0
1
2
0
0
0
0
2
0
0
2
2
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
3
2
1
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
1
0
0
2
0
0
0
0
0
0
1
1
0
1
1
3
0
1
0
2
1
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
1
0
2
2
1
1
0
2
0
0
1
0
2
0
0
0
0
0
1
0
2
0
0
0
0
1
0
1
0
1
0
2
1
0
0
3
0
0
0
1
1
0
0
3
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
2
0
0
2
0
0
2
1
1
0
2
0
1
3
0
1
4
2
0
0
0
0
1
0
1
1
2
2
1
0
1
2
1
1
0
1
2
2
0
1
0
1
0
1
2
0
0
2
1
0
4
0
3
1
1
1
0
0
4
0
0
0
1
0
1
1
0
0
0
2
2
0
0
2
0
2
0
2
0
1
0
1
1
0
0
1
3
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
2
0
0
1
0
0
0
0
0
2
0
0
0
2
0
1
0
1
1
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
3
1
0
1
0
0
0
0
0
0
2
2
0
0
0
2
0
0
2
1
1
0
1
0
1
1
1
0
0
0
0
0
1
2
0
0
0
1
2
0
0
2
0
0
0
0
0
1
2
0
0
3
1
0
1
0
2
1
0
1
2
0
0
0
2
0
3
0
0
0
1
0
0
0
1
0
0
1
0
0
2
0
0
0
2
0
2
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
1
3
1
0
0
0
1
0
0
1
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
2
1
0
0
2
1
0
2
1
2
0
1
1
1
0
1
0
2
1
0
0
0
0
0
1
0
0
2
2
3
1
0
0
1
0
0
1
0
0
0
2
2
3
0
0
0
2
1
0
1
0
0
6
0
0
2
0
2
0
0
0
0
1
0
2
3
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
2
2
0
2
0
1
0
2
0
0
0
2
0
2
0
2
0
0
0
1
0
0
1
2
0
0
0
2
1
0
1
1
3
0
0
1
1
0
2
0
1
2
2
2
0
0
2
1
0
2
0
1
0
3
0
0
0
0
0
0
0
2
1
0
1
1
1
0
3
1
0
1
0
0
2
0
1
1
1
0
0
0
1
2
1
0
1
0
0
0
1
0
1
0
1
1
0
3
0
0
2
1
1
2
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
2
2
1
2
2
0
1
3
0
3
2
1
2
0
0
0
1
0
0
2
0
2
2
0
0
1
0
0
0
1
1
1
0
1
3
1
1
0
1
0
2
1
0
0
0
0
0
0
0
1
2
0
0
1
1
0
0
1
0
1
3
0
0
0
0
2
2
0
1
1
0
2
0
0
0
2
0
2
0
3
0
0
0
0
1
1
0
0
0
0
0
2
2
0
0
2
0
3
1
0
0
1
0
0
0
0
0
0
0
0
3
2
0
0
3
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
1
8
1
0
0
2
0
0
2
0
1
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
2
1
2
0
2
0
0
2
0
0
1
0
2
2
0
0
0
0
1
1
0
0
4
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
1
1
0
0
2
1
0
0
0
2
2
2
1
2
0
0
0
0
1
0
0
0
0
0
1
0
0
1
2
0
0
0
2
0
0
1
0
1
1
0
1
0
0
2
0
0
0
0
2
0
0
0
0
2
0
1
0
1
0
2
0
0
1
0
2
0
0
0
0
2
2
0
0
0
2
1
0
2
1
1
0
0
0
0
0
0
2
0
2
0
0
1
4
0
1
0
0
1
1
3
0
0
0
2
0
0
0
2
1
0
1
1
2
0
2
0
0
1
0
0
1
2
0
0
0
0
1
0
0
2
0
0
0
1
2
2
0
0
0
0
1
1
0
0
2
0
0
0
0
1
1
1
1
0
0
1
0
2
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
1
2
1
0
0
0
2
0
0
1
2
1
0
0
0
0
2
1
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
2
0
2
0
0
0
0
2
2
1
3
0
1
0
0
1
1
1
1
1
0
0
0
0
2
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
1
2
2
0
1
0
1
0
1
0
0
0
0
1
1
0
1
0
0
0
0
3
1
0
0
0
1
0
2
1
2
0
0
4
0
1
0
0
2
0
1
2
0
0
0
0
0
0
3
0
0
0
0
2
0
0
2
1
2
0
0
0
0
1
0
0
1
1
1
2
1
1
0
1
0
0
0
2
0
0
1
0
1
1
0
0
0
0
2
0
2
0
2
0
1
0
0
2
1
1
0
0
2
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
2
1
0
0
0
1
1
2
0
0
0
0
0
0
0
2
0
1
2
0
0
2
0
2
0
1
0
0
5
0
0
0
1
0
0
0
2
0
2
0
0
4
2
0
0
0
1
0
0
0
1
0
1
0
0
2
1
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
3
1
0
0
1
0
0
2
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
1
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
8
3
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
2
2
0
2
2
1
2
0
0
0
0
1
0
0
0
1
1
2
0
1
0
0
0
2
2
0
0
0
0
0
0
0
1
4
3
0
0
1
0
0
0
0
0
2
0
0
2
1
1
1
0
0
0
0
2
2
0
0
0
0
0
2
0
1
2
0
0
0
0
0
1
2
1
2
0
0
0
0
0
1
0
0
0
2
1
1
0
0
0
2
0
2
2
1
0
1
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
2
1
2
2
0
2
0
2
0
2
0
0
0
1
2
6
0
0
0
2
0
0
2
0
0
2
0
0
1
2
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
4
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
3
0
1
1
1
0
0
0
0
0
0
0
1
0
4
0
2
2
0
1
1
0
0
0
1
2
2
2
1
0
0
2
0
1
2
0
2
0
2
0
2
1
1
0
0
0
0
2
1
0
2
0
1
0
0
1
0
0
2
1
0
1
1
2
0
1
0
0
0
4
2
0
1
0
2
0
1
1
2
0
0
0
2
2
2
0
2
0
0
0
0
1
1
1
0
2
1
0
0
3
2
0
1
0
2
2
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
5
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
1
0
1
1
0
0
0
0
2
0
0
1
1
0
0
1
0
0
1
0
1
0
0
1
2
0
0
8
1
0
1
0
0
1
0
0
0
1
0
0
0
0
3
2
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
1
0
2
0
1
1
2
0
0
2
0
0
1
2
0
0
0
0
0
0
1
2
0
0
1
0
1
1
3
0
0
1
0
2
1
2
2
0
1
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
3
1
0
0
0
1
0
4
0
0
0
2
1
1
0
2
1
0
0
1
2
0
1
2
0
0
1
0
1
0
0
0
5
0
2
0
0
2
1
2
0
0
1
0
1
1
1
0
2
1
1
0
0
2
0
0
0
0
0
0
0
0
1
0
1
2
1
0
0
0
2
2
0
0
1
2
0
0
0
0
0
0
0
0
1
0
1
0
0
1
2
0
0
3
2
0
0
1
0
1
0
0
1
2
1
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
2
2
1
1
0
0
0
1
1
1
0
1
1
0
0
3
1
2
1
2
0
0
2
0
0
0
0
0
0
2
0
0
1
0
1
0
1
0
1
0
0
0
0
0
2
0
0
2
0
0
1
2
0
0
1
0
0
1
0
4
0
0
0
0
1
1
0
0
0
2
0
0
2
0
2
2
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
1
0
0
4
0
2
0
0
1
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
1
2
0
0
2
0
0
1
2
2
0
0
0
0
0
0
1
2
1
1
1
0
0
0
0
1
2
0
0
2
1
4
0
1
0
0
0
0
0
2
0
1
0
0
1
1
2
0
0
0
3
1
0
2
1
0
0
0
1
0
0
2
0
0
0
2
0
1
2
0
0
1
0
1
0
2
2
1
1
0
0
1
2
2
0
2
0
1
0
0
0
0
0
0
0
0
2
1
2
0
0
1
0
0
1
1
2
0
1
1
0
2
0
1
0
2
0
0
2
0
2
1
1
0
0
0
0
1
7
0
2
1
1
0
0
0
0
1
0
2
0
0
2
0
2
2
1
1
3
1
0
0
1
2
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
3
2
1
0
1
2
0
0
0
3
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
1
0
0
2
0
0
1
2
0
2
1
0
2
0
0
0
1
2
0
0
2
0
2
1
1
0
2
2
0
0
0
0
0
0
0
2
2
0
0
1
0
1
1
0
0
0
2
0
1
0
0
1
1
2
0
1
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
2
2
0
1
0
0
2
0
0
1
1
0
0
1
0
0
2
1
1
0
0
0
0
1
2
2
2
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
2
2
0
0
1
1
0
2
0
1
2
1
1
0
2
2
0
0
1
0
1
0
0
0
2
0
0
1
2
0
1
2
0
0
0
0
0
1
0
2
1
0
0
0
1
1
2
0
0
0
1
1
0
1
3
0
0
0
2
0
0
1
1
2
1
1
0
2
0
0
4
0
0
0
0
0
1
2
2
0
0
0
1
0
0
2
0
2
0
0
0
2
2
0
3
0
0
0
1
1
0
2
1
1
0
2
0
0
2
0
0
1
0
0
0
2
0
2
0
0
0
1
1
0
0
0
0
0
1
2
1
1
0
1
0
0
1
2
1
0
1
0
2
1
0
0
1
0
1
2
0
0
1
0
1
0
0
1
2
3
0
2
0
1
0
0
0
0
0
1
2
2
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
1
1
0
0
0
1
0
0
1
0
1
0
1
1
0
0
0
2
0
1
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
1
0
2
2
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
1
1
1
2
0
0
0
0
1
1
1
0
0
0
3
0
2
2
1
0
0
2
2
0
2
0
0
2
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
1
1
1
0
2
0
0
0
1
0
1
2
0
0
1
2
1
0
0
1
2
0
0
1
3
2
1
0
0
2
0
0
1
0
2
2
2
0
0
2
0
0
1
0
0
1
0
0
1
0
0
1
1
0
0
3
0
0
2
1
2
1
0
0
0
1
0
0
1
0
1
1
1
0
0
1
0
0
1
0
2
1
0
0
1
0
0
2
2
0
1
0
0
2
2
2
0
0
0
0
0
0
1
0
1
1
0
0
2
1
0
2
0
0
2
2
0
0
1
1
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
1
2
1
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
2
0
1
1
0
0
0
1
0
0
0
0
0
1
0
2
2
0
0
0
0
0
2
2
0
1
0
0
1
0
2
0
0
0
0
1
2
1
1
2
0
2
0
0
2
0
0
2
0
2
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
2
0
0
1
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
3
1
2
0
0
1
0
0
0
0
0
1
0
2
1
2
0
1
0
1
0
0
1
0
0
0
0
2
2
1
0
0
0
0
0
0
2
1
0
0
2
0
0
2
0
0
0
0
0
0
0
2
2
0
0
2
0
2
1
0
1
0
1
0
2
0
0
1
1
0
2
0
0
1
0
1
0
1
0
1
0
1
0
0
0
0
0
0
1
2
0
3
0
5
0
2
1
1
0
0
0
0
0
0
0
0
4
1
0
2
0
1
0
0
1
1
0
0
1
0
0
0
0
1
0
2
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
3
0
0
0
0
2
0
1
1
0
2
0
0
2
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
1
1
0
0
2
0
2
2
0
0
0
2
0
1
2
0
0
0
0
0
0
0
1
0
1
0
2
1
0
2
0
1
0
0
0
0
0
1
0
1
0
2
1
1
1
0
1
0
0
2
0
0
0
0
0
0
1
0
2
0
2
0
1
1
0
0
1
0
0
0
0
1
0
1
2
0
0
0
1
0
2
0
0
0
1
0
1
0
1
1
1
1
2
1
1
1
0
0
0
3
1
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
2
1
0
1
2
2
0
0
2
0
2
1
0
0
0
2
1
1
1
1
0
0
0
0
0
0
1
1
5
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
2
0
0
2
0
1
0
0
0
0
2
2
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
3
0
0
1
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
2
1
1
0
1
2
0
1
1
0
0
0
0
0
1
1
0
0
1
1
2
2
0
0
4
2
0
0
3
0
0
1
0
0
1
2
1
0
0
1
0
1
1
0
0
1
0
0
0
1
0
0
3
1
1
0
3
0
0
0
0
3
2
1
0
0
1
0
1
0
8
1
0
0
0
1
0
0
0
1
0
2
0
1
2
0
1
1
2
0
0
1
1
0
2
0
0
0
0
0
0
0
2
0
1
1
1
0
0
0
0
1
0
0
0
0
1
0
2
0
1
0
0
0
0
0
2
2
1
0
0
0
1
0
0
5
0
0
0
2
1
2
1
0
0
0
0
0
4
1
0
2
1
2
0
0
0
0
0
2
0
2
0
0
1
1
0
1
1
0
0
0
2
0
2
0
0
1
0
1
0
0
0
1
1
0
0
0
1
3
1
0
5
2
0
2
2
0
0
2
1
0
0
2
0
0
0
2
0
2
1
0
0
0
0
0
2
0
1
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
3
0
3
0
0
0
1
2
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
1
2
1
0
2
0
1
0
0
0
0
0
0
0
0
1
2
1
0
0
1
2
0
1
0
0
0
2
0
1
0
2
2
0
0
1
2
0
0
0
1
0
0
1
0
0
0
1
1
4
0
0
0
1
0
0
2
2
2
0
2
0
1
0
0
0
2
0
0
2
3
0
0
0
0
2
1
2
0
1
0
0
0
0
1
2
0
2
2
0
2
0
2
0
0
0
0
0
0
0
0
2
1
1
0
2
0
1
2
2
0
2
1
0
0
2
0
0
0
2
0
1
0
1
1
0
2
1
2
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
2
2
0
2
0
0
0
2
0
0
0
1
2
0
0
0
0
1
2
2
0
0
1
0
0
0
1
0
2
2
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
2
0
0
1
0
0
2
0
2
1
0
4
1
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
4
2
0
0
0
2
0
0
1
0
2
1
0
0
0
0
1
0
2
0
0
0
2
2
0
2
2
0
2
0
1
0
0
2
0
2
0
0
0
0
1
0
0
0
2
0
1
0
0
1
2
0
1
0
0
0
1
2
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
2
1
0
1
0
1
2
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
2
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
2
1
4
0
1
2
2
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
2
1
0
0
1
0
0
1
2
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
1
2
0
0
1
0
0
1
2
0
0
0
2
0
0
0
0
2
1
0
1
2
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
1
2
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
1
0
1
0
0
0
0
1
0
2
0
0
1
0
0
2
2
2
2
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
1
0
1
0
1
2
1
1
1
1
0
2
0
0
0
0
0
1
1
1
0
0
2
1
0
7
0
2
0
0
0
3
2
0
2
0
0
1
1
0
2
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
4
0
0
0
0
0
1
0
0
2
2
0
0
0
0
2
1
2
0
0
0
0
1
1
0
0
2
1
0
0
2
0
1
1
0
0
1
0
1
0
0
0
1
0
0
3
2
0
0
1
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
2
0
0
0
0
1
0
0
0
1
1
0
0
4
0
1
0
0
1
1
0
1
2
0
0
1
0
0
0
0
1
1
0
0
0
2
1
0
0
0
1
0
0
0
0
1
2
0
0
0
1
0
0
0
1
0
0
0
1
0
0
2
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
1
2
0
2
0
2
4
0
0
1
0
0
0
3
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
2
0
0
1
1
2
0
1
0
1
1
0
1
0
0
0
0
0
0
0
2
0
0
2
2
0
0
2
1
0
1
2
0
0
0
1
2
0
1
0
0
0
1
0
2
0
0
0
0
2
0
1
0
7
0
0
1
2
0
2
0
2
0
2
2
1
2
3
2
0
1
2
1
1
0
0
0
0
0
0
0
0
3
0
1
0
0
2
0
0
0
0
0
0
0
0
1
1
1
2
2
0
0
1
0
1
1
0
0
1
1
2
2
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
3
0
1
0
0
2
0
0
2
0
0
1
0
2
0
1
2
3
2
2
0
0
0
0
2
2
2
1
2
2
0
0
0
0
0
0
1
0
2
0
1
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
2
1
1
0
2
0
0
0
0
1
2
1
0
0
0
0
0
2
1
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
2
0
1
0
1
0
0
2
0
0
0
0
0
1
2
2
0
0
0
0
1
0
0
0
0
0
0
1
1
3
0
3
0
0
4
0
2
1
0
0
2
2
0
0
0
0
1
0
1
0
2
0
0
0
2
0
2
0
2
0
2
4
2
0
0
3
1
2
0
2
0
2
0
0
0
0
0
0
2
1
0
0
0
0
4
2
1
0
2
0
0
0
0
0
1
1
0
1
1
1
1
0
1
0
1
0
0
1
0
0
0
2
1
0
2
0
2
1
2
0
2
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
2
1
0
1
1
2
0
1
0
0
0
0
0
0
0
1
0
2
1
0
1
0
0
2
0
2
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
1
1
1
0
0
0
0
0
2
0
1
2
0
2
1
0
0
0
0
0
2
0
0
2
0
1
0
0
2
1
1
0
0
0
1
0
0
1
3
1
1
0
0
0
0
0
0
0
1
0
1
2
0
2
2
0
0
2
0
2
0
2
0
0
2
0
1
0
0
1
1
0
2
0
2
0
0
0
1
2
0
2
1
0
2
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
2
1
0
0
1
1
3
1
5
1
0
0
0
1
2
2
1
0
0
0
0
0
0
2
0
1
0
0
0
0
2
2
1
1
0
1
1
0
5
0
0
1
0
0
0
1
1
0
2
0
1
2
0
2
1
0
0
0
0
0
0
2
1
0
1
1
1
1
7
0
0
0
0
0
1
1
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
1
2
0
0
2
1
0
2
0
1
0
1
1
0
2
0
1
0
0
1
2
0
0
0
0
1
0
0
0
0
6
0
0
1
2
0
0
0
1
0
0
0
0
0
3
1
1
0
0
1
0
0
0
1
1
0
0
0
2
1
0
0
2
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
1
0
5
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
2
2
2
1
1
0
0
0
0
2
0
0
0
1
0
0
1
2
0
1
1
2
0
0
0
0
2
0
1
0
0
0
1
0
1
0
0
0
2
1
1
0
0
2
0
0
2
2
2
0
0
0
0
1
0
1
0
0
2
0
1
1
0
1
2
0
0
1
0
0
0
2
0
0
2
2
0
0
0
1
0
1
2
1
1
0
0
0
0
0
0
1
2
0
0
0
3
0
0
0
1
2
0
0
0
0
1
1
0
0
1
1
0
0
0
2
2
2
0
0
0
2
0
2
1
0
1
0
0
1
0
0
0
0
1
2
0
2
0
2
0
3
2
2
0
0
4
2
2
0
2
0
1
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
1
1
0
1
0
2
0
0
0
0
0
2
0
0
0
1
0
1
1
0
2
0
0
0
1
0
2
1
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
2
0
1
1
2
0
0
2
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
3
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
2
0
0
2
3
2
2
0
0
1
0
0
2
0
1
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
1
0
1
0
0
1
0
2
0
0
0
1
2
1
0
1
0
0
2
1
1
0
0
0
0
0
2
2
2
1
0
0
2
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
1
2
0
1
0
2
0
0
0
0
0
0
0
1
1
0
2
0
0
0
1
0
0
0
0
3
0
2
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
3
0
0
0
2
0
0
0
0
2
0
0
2
1
0
1
1
0
1
2
0
0
0
2
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
1
0
2
0
0
1
1
1
3
2
0
0
0
0
1
2
1
2
2
0
0
2
0
1
0
0
0
1
0
0
2
2
0
0
0
0
1
0
1
0
0
0
1
0
0
0
2
2
1
0
2
0
1
1
0
0
2
0
2
0
1
1
2
0
1
0
0
0
0
0
2
0
0
1
1
0
0
0
5
1
2
3
0
1
0
0
0
0
0
3
0
0
1
0
0
1
1
2
1
0
0
0
0
2
0
0
0
1
2
1
0
0
0
2
0
1
1
0
0
0
0
2
0
0
1
0
0
1
0
0
2
1
3
0
1
0
0
1
0
1
0
1
1
0
0
1
0
2
2
0
0
2
0
2
0
0
0
2
0
2
2
0
0
0
1
1
0
2
1
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
2
0
1
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
1
2
0
2
0
1
0
2
0
0
0
0
0
1
1
0
2
0
2
1
1
0
1
0
0
0
0
0
1
0
1
0
0
0
2
2
0
2
0
3
2
0
1
0
0
1
0
0
0
1
0
0
0
2
2
1
0
0
0
0
4
0
2
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
2
2
0
0
0
0
0
1
0
0
0
0
0
2
1
0
1
0
0
0
2
0
2
0
0
0
0
3
0
1
0
0
1
1
2
2
0
1
0
0
3
1
0
2
1
0
0
1
1
1
0
0
0
2
0
0
0
1
1
2
2
1
0
0
2
2
0
2
0
2
2
0
0
0
0
5
0
0
0
2
1
2
0
0
0
0
1
0
0
2
2
1
2
3
0
0
1
2
0
2
2
0
0
0
0
1
0
2
0
0
0
0
2
2
1
0
0
1
2
2
1
0
0
2
1
0
0
3
1
0
0
1
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
2
2
0
0
0
0
1
0
2
0
1
1
0
0
2
0
1
0
0
0
2
2
1
0
1
0
2
0
1
1
0
1
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
2
0
1
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
3
0
2
0
1
0
0
0
1
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
3
2
0
0
1
0
1
2
1
0
0
0
0
0
1
1
0
4
1
3
0
0
2
0
0
0
0
2
1
1
0
0
0
2
0
2
2
0
0
0
0
1
0
2
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
1
1
2
2
1
0
1
2
0
0
0
1
1
0
0
0
1
0
0
0
0
2
0
2
1
1
0
0
0
1
0
0
0
0
1
2
0
0
0
2
0
0
0
1
0
2
0
2
1
0
1
2
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
2
0
0
1
1
0
0
2
0
2
0
0
0
0
0
2
1
0
0
0
4
0
3
2
1
0
0
3
0
2
0
0
0
1
2
0
2
0
0
1
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
1
2
0
0
0
0
3
0
0
0
1
0
0
0
0
0
2
2
1
0
0
0
0
0
1
1
0
2
1
2
1
0
1
0
0
0
0
2
0
0
2
0
0
0
0
1
1
0
0
1
0
0
1
0
1
0
0
1
1
0
0
0
0
2
0
0
0
0
0
1
1
1
3
0
0
1
0
1
7
1
1
2
2
0
2
0
1
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
1
2
1
0
2
0
0
2
2
0
0
0
2
2
0
0
0
0
2
0
2
2
0
0
2
1
0
0
0
2
2
0
0
0
2
0
2
0
1
2
0
2
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
1
3
3
1
0
0
1
0
0
1
0
0
0
0
2
1
1
0
0
1
1
0
2
2
1
0
2
0
0
0
1
2
0
0
0
0
0
1
2
0
0
2
1
0
0
0
1
0
2
0
1
0
1
0
0
0
0
0
0
0
2
0
2
4
1
0
0
0
3
0
1
0
2
0
0
2
0
1
0
0
0
0
1
0
0
2
1
1
1
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
1
0
2
1
1
0
0
0
0
2
0
0
3
0
1
0
1
0
0
1
0
0
1
1
0
1
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
2
0
0
0
0
1
0
1
0
1
2
1
1
2
0
2
0
0
1
2
0
1
0
1
0
0
2
1
0
1
1
1
0
0
0
2
1
0
0
0
0
0
2
0
0
2
0
0
2
0
1
0
0
2
1
2
0
0
2
0
0
1
3
1
1
0
2
2
2
1
2
0
0
0
0
0
0
0
2
1
1
0
1
2
2
0
0
1
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
1
0
0
0
1
0
2
3
1
1
0
0
0
1
2
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
1
0
0
1
2
0
0
0
0
0
0
2
0
0
0
1
1
2
1
0
0
2
0
2
1
0
2
2
0
1
3
0
2
1
0
1
0
0
0
0
0
0
0
0
1
0
1
4
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
1
2
0
0
0
0
2
0
1
2
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
3
0
2
0
0
1
0
0
2
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
2
2
0
0
2
1
0
0
0
0
0
2
2
0
0
1
0
0
1
1
1
1
0
0
0
2
0
0
0
0
2
1
0
1
0
0
0
1
1
4
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
1
0
0
1
1
2
0
0
1
0
2
0
0
1
0
0
2
0
0
1
2
1
2
0
1
0
2
0
2
0
0
0
2
0
0
0
0
2
1
0
1
1
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
2
0
0
4
0
2
0
0
0
0
0
2
0
1
1
0
0
0
2
0
0
1
0
1
0
1
2
1
2
0
0
2
0
0
1
2
0
2
1
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
1
2
0
0
0
2
0
2
0
1
2
2
0
0
0
0
1
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
1
0
0
0
1
4
0
1
0
2
0
0
0
0
0
0
0
0
1
2
1
0
0
2
0
2
0
0
2
0
1
5
0
2
0
0
1
0
1
0
0
0
1
1
2
0
1
1
1
0
0
0
0
1
0
0
1
2
4
0
0
2
1
1
0
2
0
1
2
0
1
0
2
2
0
1
0
0
0
0
2
1
0
0
2
3
2
3
2
0
1
0
0
0
0
0
0
0
0
4
2
2
0
1
2
2
0
1
0
0
0
0
0
0
0
2
3
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
1
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
1
0
1
2
1
0
1
0
2
1
0
0
1
0
2
1
0
2
0
0
1
2
0
1
1
0
0
0
2
0
0
2
0
0
0
1
0
0
3
0
0
0
1
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
3
0
0
1
0
1
0
0
2
0
0
2
2
0
1
0
0
0
0
2
0
1
1
1
2
2
1
0
0
2
1
0
1
0
0
0
2
0
1
0
0
0
0
1
3
0
0
1
4
1
0
0
1
2
0
2
0
0
0
1
0
0
0
1
0
1
0
0
0
1
2
1
1
0
0
0
2
0
1
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
3
3
0
0
0
0
0
0
2
0
3
0
2
0
2
0
2
1
2
1
2
0
2
1
2
2
0
0
1
2
0
0
0
0
1
0
2
0
0
0
2
1
1
0
1
0
0
1
1
1
0
0
0
1
0
1
1
0
1
0
1
2
0
0
0
1
0
2
0
2
2
2
1
1
0
0
0
0
0
0
0
1
0
1
0
0
2
1
0
0
1
1
1
0
0
1
0
0
2
2
0
0
0
0
2
0
1
0
1
0
0
1
2
2
0
0
0
0
0
1
0
0
0
0
0
0
1
1
3
1
1
2
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
2
2
0
0
2
0
0
0
0
0
2
2
1
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
2
0
1
2
0
0
2
2
1
1
1
0
0
1
0
1
1
0
0
1
1
2
0
0
0
2
2
0
0
1
0
0
1
1
0
1
0
2
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
1
0
0
0
5
1
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
5
2
0
0
1
2
0
0
0
1
0
1
0
0
0
2
0
2
0
2
0
0
1
0
1
0
0
2
0
0
0
0
0
1
0
0
0
1
0
2
1
0
0
0
0
0
0
2
2
0
0
0
1
2
0
2
0
0
1
0
0
0
0
2
0
1
1
0
0
0
0
0
2
0
0
1
2
0
1
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
2
2
1
1
0
1
0
0
1
1
0
2
0
0
0
1
1
2
1
0
0
0
2
0
0
2
0
2
3
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
2
0
1
1
0
2
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
2
0
3
0
0
0
0
2
1
1
2
1
0
0
1
0
0
4
3
1
0
1
0
0
0
0
3
1
0
2
0
0
2
2
0
2
0
1
1
0
2
0
4
0
0
0
0
2
1
0
0
0
0
2
2
0
0
0
1
0
1
3
3
1
6
0
0
0
2
2
1
1
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
2
0
0
0
0
1
0
0
0
2
0
2
0
0
2
0
1
1
0
2
2
2
0
0
0
0
0
0
0
0
0
1
0
0
2
2
2
0
0
1
1
0
1
0
0
0
0
2
0
0
0
1
1
1
0
0
1
0
0
0
1
0
2
0
0
2
2
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
2
2
2
0
0
2
0
0
0
0
0
0
0
0
0
1
2
1
0
0
2
0
3
2
0
1
0
0
1
1
0
0
0
0
0
0
0
1
2
0
0
3
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
2
0
0
2
1
0
0
0
0
2
0
0
0
0
3
2
0
2
0
0
0
0
0
0
1
1
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
2
2
1
0
1
1
1
2
1
2
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
1
2
0
0
0
1
1
0
1
0
0
0
0
0
1
2
0
2
0
0
0
1
0
0
2
1
1
0
0
2
0
1
0
0
0
2
0
0
3
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
1
1
2
1
0
0
1
0
1
0
3
0
1
0
0
2
0
0
1
0
4
0
0
1
0
1
0
2
0
2
1
0
2
0
0
0
1
1
0
2
0
2
0
0
1
0
2
2
1
0
0
1
0
2
0
0
2
3
1
0
0
0
3
0
1
0
0
0
0
0
0
0
0
2
2
1
0
1
0
1
0
1
1
2
0
0
0
1
0
0
0
0
2
2
0
0
0
0
3
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
3
0
0
1
0
2
0
0
1
0
0
1
0
0
2
1
2
0
2
0
3
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
1
0
1
0
0
0
0
2
2
2
2
1
2
1
0
0
2
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
2
1
1
2
0
0
0
3
0
0
1
2
1
0
0
0
0
0
0
0
2
2
1
0
1
1
1
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
2
2
0
0
0
1
0
1
0
0
2
3
0
0
0
1
1
1
2
1
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
2
0
1
1
0
2
0
0
0
1
0
0
1
1
0
0
1
3
0
2
3
0
0
0
2
1
0
1
0
1
0
0
2
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
2
0
2
1
0
0
0
0
2
3
2
1
0
0
1
0
0
3
0
0
4
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
2
0
1
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
2
1
1
0
0
2
2
0
0
0
0
2
2
0
0
1
0
2
0
0
1
1
2
1
0
0
0
1
0
0
1
1
1
0
2
0
0
1
0
3
0
0
0
0
0
0
0
2
1
0
2
1
0
2
0
2
2
2
2
2
0
0
2
1
1
0
1
2
0
0
0
2
0
0
1
1
0
0
1
0
1
1
0
0
1
0
1
0
5
0
0
0
0
2
0
1
2
1
2
1
1
1
0
0
0
1
3
0
0
0
0
3
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
2
2
0
0
0
1
1
2
0
0
0
1
0
0
2
1
0
0
2
2
0
2
0
0
2
1
0
0
1
2
0
2
1
0
0
0
0
0
1
0
1
3
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
1
0
1
0
2
0
0
0
0
0
2
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
3
0
0
2
2
0
0
2
0
3
1
0
0
0
0
2
0
1
0
0
0
0
2
0
2
2
0
2
2
0
2
1
1
1
1
0
1
1
1
0
0
3
0
2
0
1
3
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
1
1
0
2
0
0
2
0
0
0
0
2
2
1
0
2
1
0
1
1
0
0
1
0
0
1
0
0
0
0
0
2
1
0
0
2
0
2
0
2
0
0
2
0
1
0
1
1
0
2
1
1
0
0
0
2
0
0
0
1
1
0
0
0
1
0
4
1
0
0
1
2
1
2
2
0
0
2
0
0
0
0
0
2
0
0
1
0
1
4
0
2
0
0
2
0
1
0
0
2
0
1
1
2
0
0
0
1
1
0
2
0
0
0
1
0
0
0
0
0
0
1
0
2
2
1
2
0
0
0
0
0
1
0
1
0
0
0
2
0
0
2
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
2
0
2
0
2
1
0
1
2
2
0
2
2
2
0
0
2
1
2
2
0
0
2
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
2
2
2
0
1
2
2
0
1
1
0
0
0
0
0
1
0
0
1
0
1
0
0
2
2
1
0
2
0
0
5
3
0
0
2
1
0
1
1
0
0
0
1
1
2
1
0
0
1
0
2
1
2
3
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
5
0
2
0
0
1
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
1
0
2
1
0
1
0
1
1
1
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
2
1
0
0
2
0
0
0
0
2
0
0
0
1
1
0
0
0
0
1
0
0
0
0
2
1
1
0
2
0
1
0
0
0
1
2
1
0
0
1
2
0
1
1
1
1
0
1
0
1
1
0
0
0
0
2
1
0
1
0
1
2
0
2
0
0
0
2
0
1
2
0
2
0
2
3
0
1
1
2
0
0
1
1
1
2
2
0
0
0
0
0
1
2
2
2
0
1
0
2
2
1
0
0
3
0
0
0
0
0
0
2
1
1
1
0
1
0
0
1
2
0
1
0
3
0
0
0
0
1
0
0
1
0
2
0
1
2
0
0
0
0
3
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
2
0
0
0
2
0
2
0
0
2
2
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
2
1
2
0
2
1
0
0
2
0
0
0
0
0
2
2
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
1
2
1
0
0
2
0
0
2
1
1
0
0
1
0
0
0
2
0
0
0
2
1
0
1
0
3
1
0
2
0
2
1
0
1
2
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
1
0
0
2
1
2
0
0
0
0
1
2
0
0
0
1
1
2
1
0
2
0
0
1
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
1
0
1
0
3
0
1
0
2
0
2
0
1
2
0
0
0
0
2
1
1
0
0
0
0
0
2
0
1
0
0
0
2
0
4
2
0
1
1
0
1
1
0
0
0
0
0
0
0
4
2
2
1
0
1
0
0
2
0
0
2
0
1
0
3
2
0
1
0
0
1
1
0
3
1
0
0
0
1
0
2
1
0
1
0
0
1
1
2
0
0
1
2
0
1
0
1
0
2
0
0
2
2
1
2
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
1
1
1
0
2
0
2
2
3
4
2
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
1
1
1
0
2
1
2
0
0
2
1
2
0
0
2
1
0
0
1
2
0
0
0
2
0
0
1
0
0
0
0
3
0
2
2
0
2
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
2
2
0
0
1
0
0
1
0
1
2
1
0
0
2
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
2
0
0
2
0
2
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
2
2
2
0
0
1
0
0
1
1
0
0
0
3
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
4
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
2
3
0
1
1
2
2
1
1
1
0
1
3
2
0
2
0
0
1
1
0
2
0
0
2
1
0
0
0
2
0
0
0
2
1
0
3
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
3
0
1
0
0
0
0
2
0
2
0
2
0
2
0
1
0
0
0
0
0
1
2
2
1
2
0
1
0
1
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
1
1
2
2
1
0
0
0
2
0
0
1
0
0
1
1
2
0
1
0
0
0
0
0
0
1
1
0
2
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
2
1
0
2
1
1
0
0
2
1
0
2
2
0
2
0
2
2
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
2
0
1
0
1
0
0
0
0
0
2
2
1
1
2
2
0
0
1
2
0
0
0
0
0
0
0
2
3
0
1
2
1
0
0
0
0
0
0
0
0
2
1
1
4
1
0
0
0
2
0
0
2
0
0
1
0
1
3
1
1
0
0
0
0
2
2
0
1
2
0
0
2
0
0
2
2
2
0
1
0
2
0
0
0
1
0
0
0
2
2
2
1
1
0
0
0
0
0
1
0
1
2
0
0
1
2
1
0
0
0
0
0
0
0
1
0
1
2
0
1
2
2
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
4
0
1
1
5
0
0
0
0
0
0
0
2
0
0
0
5
0
0
0
0
2
0
0
2
0
0
1
2
1
0
0
2
2
0
1
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
2
0
2
2
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
2
0
2
3
0
1
0
0
2
0
1
0
0
0
0
0
2
2
0
2
0
1
0
0
0
2
2
1
0
0
0
0
0
0
0
3
0
0
2
0
2
0
1
2
1
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
2
1
0
1
0
0
0
0
3
0
0
0
2
2
2
2
0
1
0
2
0
0
0
0
2
0
0
0
2
0
1
2
2
0
2
0
0
0
2
1
2
0
0
0
2
1
1
0
2
0
0
2
0
0
2
0
0
0
0
3
1
0
1
1
0
0
0
0
0
1
0
0
2
0
0
1
1
2
0
1
2
2
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
2
0
0
2
6
0
0
1
0
0
0
1
2
1
1
2
1
0
0
0
2
1
0
0
2
2
0
1
0
1
0
2
0
0
0
2
0
0
0
0
0
1
2
1
2
0
0
1
0
0
2
2
3
0
0
2
1
0
2
1
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
3
0
0
0
2
0
0
1
0
2
2
0
1
0
0
0
1
0
0
2
0
0
0
2
0
0
0
1
1
0
0
1
0
0
1
1
0
1
0
0
1
1
0
0
0
2
3
1
0
0
0
1
1
0
0
0
1
2
0
1
0
0
0
0
0
2
0
2
0
2
0
0
0
0
2
0
1
1
1
0
0
1
0
0
1
3
1
2
2
0
0
0
1
0
2
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
2
0
0
1
0
1
0
1
0
0
1
0
0
0
0
2
1
2
0
1
0
0
0
1
2
0
0
2
0
0
2
0
0
0
0
1
0
2
0
2
0
0
0
2
2
0
0
2
0
1
0
0
1
0
0
0
0
1
0
2
1
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
3
0
1
0
1
1
0
0
1
2
0
1
0
2
2
0
0
2
0
2
2
0
0
0
0
1
2
0
2
2
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
1
1
1
0
1
0
0
1
0
1
0
0
0
1
0
1
0
0
2
2
0
2
0
0
2
0
2
1
2
0
0
1
1
0
0
0
2
0
2
0
0
1
0
0
2
0
2
2
2
0
0
2
0
0
1
2
1
0
3
0
1
0
1
0
0
0
2
1
0
0
2
1
1
2
1
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
2
0
0
1
6
1
2
0
1
0
2
1
0
0
0
2
2
0
1
0
0
2
1
1
0
0
0
1
0
0
0
2
0
2
1
1
0
1
0
0
0
1
0
0
1
0
0
2
2
0
0
1
2
0
1
0
0
2
5
0
0
0
0
1
0
0
0
0
0
2
1
1
3
0
1
0
0
0
1
0
0
2
2
0
0
0
1
1
1
0
0
0
4
0
2
1
2
1
4
1
2
0
0
0
0
1
0
2
1
0
2
1
0
0
0
0
0
0
0
2
2
0
2
2
2
0
2
0
1
0
0
2
0
0
0
0
1
1
1
1
1
1
1
1
1
1
0
0
1
0
2
1
0
0
2
2
0
1
0
0
0
2
1
0
0
0
0
0
2
0
1
1
0
0
0
0
0
2
0
0
0
0
2
2
1
0
0
0
0
1
0
2
1
0
1
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
2
2
0
0
0
2
0
2
0
2
0
0
3
2
0
1
0
1
0
0
0
0
0
0
0
0
2
0
1
0
2
0
2
0
0
0
1
3
2
0
0
0
0
1
0
0
0
6
1
0
8
3
0
1
2
0
0
0
2
2
0
0
1
1
2
0
0
0
0
0
4
0
0
0
0
0
0
0
1
1
1
2
0
0
0
3
0
0
0
1
2
1
0
0
0
0
0
2
2
0
2
0
0
0
1
0
0
2
1
1
0
0
1
0
0
0
1
0
2
1
2
0
0
1
0
0
0
1
1
1
1
2
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
2
0
0
2
0
0
1
2
1
1
1
2
2
0
1
0
0
0
0
0
0
0
0
1
1
1
2
0
0
0
1
0
0
0
0
0
0
2
1
0
0
2
1
0
0
0
1
0
1
0
0
0
0
0
3
0
0
0
0
0
0
1
1
1
0
0
2
0
0
1
0
0
1
11
1
1
1
0
0
2
2
0
0
2
2
0
2
0
2
0
1
2
0
0
1
4
0
0
1
2
2
0
0
0
0
0
0
1
1
0
0
2
1
0
1
1
0
3
0
2
0
0
1
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
2
1
1
0
0
2
0
0
0
0
1
0
2
0
3
0
0
0
1
0
1
1
0
2
1
2
1
0
1
0
0
1
0
2
0
0
2
1
2
0
0
2
0
1
0
0
2
0
1
0
1
1
2
0
1
1
1
0
2
1
0
0
0
0
0
0
1
2
0
1
2
0
2
0
1
0
0
1
2
0
2
0
0
2
0
0
4
0
0
0
0
1
0
2
2
0
1
0
2
1
1
0
0
0
0
0
0
2
0
1
0
1
3
0
3
0
0
0
1
1
0
0
0
2
0
3
0
1
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
1
1
0
0
2
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
2
1
0
0
0
0
0
1
6
0
1
2
2
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
2
0
0
1
0
1
2
0
0
0
0
0
1
1
2
2
0
0
0
2
1
1
0
1
0
1
1
1
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
3
0
2
1
1
2
0
4
0
0
0
0
1
0
1
0
1
1
0
0
0
1
0
2
0
1
0
0
2
0
0
0
0
0
1
1
0
2
0
0
0
2
0
0
0
0
1
1
0
5
0
1
2
2
2
0
1
0
2
0
1
2
0
1
0
0
1
0
2
1
2
0
0
1
0
0
2
0
2
2
1
4
2
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
2
0
1
1
0
2
0
0
0
0
0
0
1
0
1
0
0
2
0
0
2
0
0
0
1
2
1
0
0
0
1
1
2
0
0
1
0
0
0
1
2
0
0
0
1
2
0
0
2
0
0
1
0
0
0
0
0
2
1
0
2
1
0
0
0
0
0
2
1
1
0
0
0
0
2
0
0
1
1
1
0
0
0
1
0
0
0
0
2
1
1
2
0
0
0
0
1
1
1
0
0
0
0
1
1
1
0
0
2
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
2
0
2
1
0
0
2
2
0
0
2
0
0
0
0
1
0
3
0
0
2
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
2
2
1
2
2
2
0
2
0
2
0
1
2
0
0
0
0
1
0
1
0
1
0
1
0
0
3
0
0
1
0
0
2
0
0
0
2
0
1
0
0
1
2
0
2
1
0
0
2
0
0
0
2
0
2
1
1
0
0
1
0
0
2
0
0
1
4
0
1
0
1
0
0
0
0
0
1
1
1
0
0
0
1
0
1
0
2
0
1
0
0
2
1
2
1
0
1
1
1
1
0
0
1
0
1
1
0
0
1
0
2
3
0
2
0
2
3
1
1
1
2
0
0
0
1
3
0
1
0
0
1
2
0
2
1
0
1
1
0
1
2
0
1
0
0
1
0
0
1
0
1
0
0
0
0
1
0
2
0
0
0
5
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
1
0
1
0
2
0
0
0
2
0
1
1
0
0
1
0
1
0
0
2
0
0
1
1
1
0
0
0
0
1
0
0
6
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
4
2
0
0
0
0
0
0
0
2
1
3
0
1
0
0
0
1
1
0
2
0
1
1
2
3
0
1
0
2
0
0
0
1
1
1
0
0
2
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
1
2
0
0
1
2
0
2
2
1
1
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
2
0
0
0
0
1
0
0
2
0
2
2
1
0
1
2
2
1
1
0
1
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
2
2
1
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
1
0
4
1
0
0
0
2
2
0
0
0
0
2
1
1
0
0
0
0
2
2
0
0
0
0
0
1
2
0
0
0
1
2
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
1
0
2
0
1
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
1
4
0
1
0
2
2
1
0
0
0
0
1
0
0
0
0
0
3
2
0
0
2
0
1
1
0
0
2
1
0
0
0
2
2
2
0
0
1
1
0
1
0
0
1
0
0
0
1
1
0
0
0
1
0
1
0
2
0
2
2
0
1
0
0
0
0
0
0
1
0
0
0
0
4
0
1
1
1
0
0
1
0
0
0
0
2
1
0
0
6
2
2
2
2
1
2
0
0
2
0
2
0
0
1
0
0
2
0
0
1
0
0
1
0
0
0
1
0
6
1
0
0
1
0
2
2
1
0
0
1
0
2
0
0
0
1
0
0
0
2
3
1
2
0
0
0
0
0
2
0
0
2
2
1
2
2
2
2
0
0
0
0
1
1
2
1
0
1
1
2
0
3
0
0
1
1
2
2
1
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
1
2
0
1
2
0
0
2
0
1
2
0
1
1
0
0
1
0
0
0
4
1
0
1
0
2
2
0
0
0
0
2
1
2
0
2
0
0
0
3
0
2
2
2
1
2
1
2
0
0
2
1
0
0
2
1
0
0
1
0
0
0
0
0
2
1
0
0
0
2
2
0
0
0
0
0
2
1
2
1
0
1
0
0
0
0
3
0
1
0
0
1
0
0
0
0
0
0
2
2
1
0
0
0
0
1
0
1
0
4
2
0
0
2
0
0
0
1
2
0
0
0
0
0
0
1
2
0
1
1
1
0
0
1
0
1
0
0
1
0
1
0
2
0
2
0
0
0
0
0
2
1
0
3
0
0
0
1
2
0
0
0
0
0
0
2
1
1
1
0
3
0
2
2
0
2
2
0
2
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
2
2
0
2
1
2
2
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
2
0
0
1
0
1
2
0
0
0
0
0
0
0
2
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
1
1
0
0
1
2
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
1
1
0
0
1
1
1
0
0
1
1
1
0
0
0
1
0
0
0
1
1
2
2
0
2
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
1
0
0
1
0
0
0
3
0
1
1
0
0
0
2
0
0
0
1
7
0
2
2
1
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
2
0
2
1
1
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
1
2
1
0
4
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
2
1
0
2
0
2
1
0
2
2
0
0
0
0
0
0
0
1
2
3
0
0
0
0
0
0
2
0
2
0
0
0
3
0
2
1
1
0
2
2
2
0
1
1
2
0
0
0
1
0
2
0
1
1
1
0
0
0
3
0
0
0
1
0
2
3
1
0
0
0
0
2
0
2
1
6
1
0
0
3
2
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
3
0
0
2
0
1
1
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
1
0
2
0
1
0
1
0
0
0
2
2
0
2
0
0
0
0
0
1
0
2
0
2
1
0
2
0
0
2
0
0
0
2
0
0
2
2
0
0
1
0
0
2
1
1
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
2
0
0
1
2
0
0
0
0
1
2
0
0
0
1
0
1
1
1
0
1
2
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
3
0
1
0
0
0
2
0
2
2
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
2
2
0
1
0
0
1
0
0
0
1
0
0
2
0
0
2
0
0
4
2
1
1
0
0
2
0
0
0
2
1
0
0
0
2
0
0
0
0
2
0
0
2
1
2
0
0
0
0
0
0
1
0
1
1
2
1
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
1
0
2
1
0
0
2
1
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
4
0
0
1
0
1
0
0
0
0
0
0
0
1
2
1
0
0
3
1
0
0
0
3
0
1
0
0
0
2
1
2
1
1
1
0
2
2
0
0
1
0
0
2
0
2
1
0
2
1
1
2
0
2
0
2
0
1
1
2
0
0
0
1
0
2
0
0
0
0
0
0
1
1
0
2
0
0
0
2
0
0
0
2
0
1
0
0
2
0
0
2
0
1
0
0
1
0
0
0
2
0
1
2
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
2
4
0
0
1
1
0
1
0
1
0
2
3
2
1
0
1
0
1
2
1
1
2
0
0
0
0
2
0
0
0
2
0
0
0
1
0
3
0
0
0
1
0
0
0
0
1
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
2
2
2
0
1
0
0
0
0
2
1
1
2
2
1
0
2
0
0
1
2
1
0
2
1
0
1
2
1
1
2
0
0
2
2
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
1
1
0
0
1
0
0
0
2
1
0
0
2
0
0
0
2
1
2
2
0
0
1
0
2
3
0
0
0
0
2
0
0
0
1
0
2
1
1
4
0
0
0
0
0
0
0
2
0
0
0
1
2
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
1
2
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
1
2
2
0
0
0
0
0
1
1
0
2
2
0
0
1
1
0
2
1
2
1
1
2
0
0
0
1
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
3
0
1
1
2
1
1
0
0
0
0
0
1
0
1
0
2
0
1
2
0
0
1
0
2
0
0
0
0
0
0
1
0
1
1
0
1
1
0
0
1
0
0
2
0
1
2
0
0
0
2
0
0
0
0
1
0
1
0
0
1
2
0
0
0
0
0
1
0
0
2
0
2
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
2
1
0
0
2
1
0
0
2
0
1
0
1
0
0
4
0
0
1
0
0
2
0
0
0
0
0
2
0
0
2
2
1
0
0
0
0
2
2
0
1
2
0
3
1
1
0
0
0
1
0
1
2
1
1
0
0
1
2
1
1
0
0
2
1
0
0
3
1
1
0
2
0
0
1
0
1
1
2
1
1
1
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
1
0
1
0
2
2
0
0
1
0
0
0
1
0
2
2
0
0
4
1
0
0
0
2
0
1
1
1
0
1
0
0
0
2
2
2
2
0
0
0
1
0
0
1
1
2
2
0
0
0
0
2
1
0
0
0
0
0
1
0
7
2
1
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
2
1
2
1
0
2
0
2
0
0
0
0
4
1
0
0
1
0
2
0
0
2
2
0
4
3
1
1
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
2
0
0
2
1
0
1
0
0
1
1
0
2
1
0
0
1
0
2
1
2
1
0
1
0
1
0
3
0
1
0
2
0
2
0
1
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
2
0
1
0
2
2
0
0
0
0
1
0
0
0
1
0
0
1
1
2
0
0
1
2
0
0
1
0
0
1
1
2
1
0
1
1
2
0
1
0
1
1
0
0
1
0
0
1
0
1
0
1
0
1
1
0
2
1
2
1
1
0
0
0
0
0
0
0
0
3
2
0
0
1
0
1
0
0
0
0
0
1
0
1
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
1
0
0
1
1
0
2
2
2
1
0
0
1
0
1
1
0
0
0
1
2
1
0
1
2
0
1
0
0
0
0
0
2
0
2
6
0
1
0
1
1
0
0
2
0
0
0
0
1
0
2
0
1
2
0
2
2
0
0
2
1
0
0
0
1
1
1
1
2
0
2
0
1
2
1
2
0
2
2
1
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
7
0
0
1
2
0
1
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
1
2
0
1
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
1
0
0
0
2
0
2
2
1
0
0
0
0
0
0
2
1
0
0
2
1
0
1
0
0
2
0
2
0
0
0
1
0
0
1
0
2
2
1
2
2
0
1
1
1
1
2
1
3
1
0
0
2
2
2
2
0
0
0
0
1
0
4
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
2
0
0
0
0
2
2
3
1
0
0
2
1
2
0
2
2
2
1
0
1
0
1
1
0
0
0
2
2
1
0
2
1
0
0
0
0
0
1
2
0
0
1
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
1
2
0
0
0
1
0
1
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
1
1
2
1
2
1
0
1
0
0
0
2
0
0
0
2
0
0
0
1
1
1
1
1
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
2
0
2
0
0
0
1
1
0
0
1
0
0
2
0
0
0
0
1
0
0
1
0
1
0
2
0
0
2
0
1
0
0
0
6
0
0
1
4
1
1
0
0
0
0
0
0
1
0
1
0
2
1
3
0
3
0
1
0
0
2
0
1
0
1
2
2
1
0
0
0
0
0
2
0
1
1
1
0
0
1
1
0
0
3
0
1
0
0
1
5
0
1
0
0
0
0
0
1
2
0
1
0
1
0
0
2
0
0
1
0
1
1
0
1
1
0
1
1
1
0
0
1
0
3
2
0
0
2
0
1
1
0
2
2
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
1
2
0
0
1
2
2
0
1
2
2
0
1
2
2
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
2
0
0
0
2
1
5
0
0
0
0
6
0
0
0
0
1
0
2
0
0
1
0
0
0
1
0
0
0
0
1
2
0
2
0
2
2
0
1
2
0
2
0
0
1
0
2
2
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
2
0
2
0
2
0
2
2
0
2
0
0
2
0
0
0
1
2
0
0
1
2
0
2
2
2
1
0
1
0
0
1
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
1
0
2
0
0
6
3
0
1
2
1
0
1
0
0
0
2
1
3
2
2
0
0
1
0
0
0
1
1
0
2
0
1
1
1
0
0
0
2
0
0
0
2
1
0
0
0
0
1
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
1
1
0
0
0
1
2
1
2
2
0
0
0
0
0
2
0
2
0
0
1
0
0
0
2
1
2
0
1
2
0
1
0
0
3
2
0
1
0
1
1
0
0
0
0
1
0
1
0
2
0
0
0
1
0
1
2
0
2
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
3
0
1
0
0
0
0
2
0
1
0
2
1
0
2
2
1
0
0
3
0
0
0
0
2
0
0
0
1
0
0
1
0
2
1
0
0
0
0
1
2
0
2
1
2
0
2
0
0
0
2
2
0
0
2
0
0
0
2
0
0
1
0
2
1
0
0
0
0
2
2
1
0
1
2
0
0
0
1
0
0
0
1
0
0
1
0
0
3
1
0
1
2
0
0
0
1
0
0
0
0
0
1
0
2
0
0
1
1
1
0
0
0
0
2
0
0
1
0
0
2
1
1
3
0
3
0
2
0
1
0
0
1
1
0
2
0
1
0
0
1
1
0
0
1
0
2
2
2
0
0
2
0
1
0
1
1
0
0
0
1
0
0
2
0
1
1
1
0
0
0
2
0
1
0
0
0
1
0
0
1
0
1
0
2
0
0
0
0
0
1
0
0
1
0
2
0
2
2
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
2
0
0
2
0
0
0
4
0
2
1
1
2
0
0
0
0
2
2
2
0
0
1
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
1
1
0
0
0
1
0
0
2
0
0
0
2
3
0
0
1
0
2
2
1
0
1
0
4
0
1
0
0
0
1
2
0
0
0
0
0
0
3
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
1
1
0
0
0
2
0
2
2
1
0
4
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
2
2
1
0
0
0
0
0
0
0
1
0
0
3
2
0
0
0
0
0
0
0
1
0
2
1
2
0
1
0
1
0
0
2
1
1
2
2
0
1
0
1
0
2
0
0
0
0
2
3
0
0
1
0
0
1
1
0
0
0
0
1
2
1
0
0
2
1
1
2
1
0
0
1
2
0
0
0
0
1
0
0
2
1
0
1
1
2
2
0
1
0
2
1
2
1
0
0
1
2
1
1
0
1
1
4
0
0
0
0
0
2
0
1
2
0
0
2
2
1
0
2
0
0
0
0
0
0
1
0
1
0
2
0
0
0
1
0
2
0
0
0
0
1
0
0
2
1
1
2
0
1
2
2
0
0
1
0
0
2
3
0
0
2
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
2
0
2
0
0
0
0
1
0
0
0
1
0
4
1
0
0
1
0
1
1
0
0
0
0
2
1
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
2
0
2
0
0
0
1
0
1
0
0
1
0
0
0
2
0
0
2
0
1
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
1
1
1
2
0
0
2
1
1
1
0
1
0
0
0
1
1
0
0
3
1
1
0
2
0
0
2
1
0
0
0
2
0
0
1
0
0
1
0
0
1
2
1
3
0
1
2
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
1
0
0
3
0
0
1
0
1
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
1
2
2
1
0
0
0
1
0
0
0
0
0
2
0
0
1
0
1
2
0
1
0
2
0
0
0
1
0
0
1
2
2
0
1
1
2
1
1
1
0
1
0
0
0
0
2
0
1
3
0
0
0
2
1
1
0
0
1
0
0
0
2
1
0
0
0
1
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
1
0
3
2
0
0
0
0
0
1
0
0
2
1
1
0
0
0
0
0
0
0
0
2
0
0
1
0
2
1
0
2
0
1
0
2
0
2
1
3
2
1
0
0
0
0
1
1
1
0
0
2
1
1
0
1
0
2
0
2
0
2
1
0
0
0
0
0
2
1
1
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
3
2
2
1
0
2
0
2
1
0
0
1
2
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
2
2
1
2
0
0
0
0
0
0
0
2
0
2
0
0
0
2
1
0
1
0
0
0
1
0
2
0
0
1
1
1
3
0
0
1
1
1
0
0
0
1
0
0
0
2
1
0
0
1
0
1
0
2
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
2
1
1
0
0
2
0
0
2
0
2
2
1
3
1
2
2
1
1
1
1
0
0
2
0
1
0
0
0
4
0
1
2
0
0
0
0
0
0
0
0
0
0
2
1
0
3
0
2
2
1
0
1
0
2
3
0
0
1
1
0
0
1
2
0
1
0
2
0
0
2
0
2
5
1
0
0
2
0
1
2
1
0
0
0
1
0
0
1
0
1
1
0
2
0
2
0
1
1
0
1
0
1
3
2
1
1
0
2
2
0
0
4
0
0
0
0
0
2
2
0
2
0
0
0
0
2
0
1
1
0
0
2
2
0
1
0
1
0
0
1
2
1
0
0
2
3
1
1
0
0
1
2
0
0
1
0
2
0
3
0
0
0
0
0
0
0
1
0
2
0
2
0
1
2
0
0
0
0
1
0
1
1
0
3
2
0
1
0
0
0
0
0
1
2
0
2
0
0
2
0
2
0
1
1
2
0
0
0
0
0
0
1
0
0
2
1
1
1
0
0
1
0
0
2
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
2
0
2
1
0
2
0
0
1
0
1
1
1
0
0
0
0
0
0
8
0
0
1
1
0
2
1
0
2
0
2
0
0
1
1
2
1
0
2
0
0
2
0
2
0
0
1
1
0
1
0
0
0
1
0
0
0
1
0
1
0
2
0
0
3
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
3
2
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
2
2
0
0
0
2
2
0
2
3
1
2
0
0
0
3
0
1
3
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
2
2
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
2
1
1
0
1
0
0
0
1
2
2
8
1
0
0
0
6
2
1
0
0
1
2
0
2
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
3
0
0
0
3
1
0
0
0
0
4
2
1
0
3
0
1
1
0
0
0
2
0
0
0
0
1
0
1
0
1
1
1
0
2
0
0
0
2
2
2
0
2
0
0
0
2
1
2
1
2
0
0
0
0
0
0
1
0
0
0
0
4
0
2
0
0
0
0
1
0
1
0
0
2
1
2
1
0
2
1
0
0
3
0
1
0
3
0
0
1
1
0
0
0
1
0
1
0
2
0
2
1
0
2
2
0
0
0
0
2
0
1
1
1
2
0
0
1
2
0
2
1
2
0
0
0
0
0
1
1
2
0
0
0
0
0
1
2
0
0
2
1
2
2
0
0
1
0
2
0
0
0
1
2
0
2
1
1
0
0
1
0
2
2
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
4
0
0
1
0
0
0
1
1
1
2
0
0
0
0
2
1
1
0
1
1
0
0
4
0
0
0
0
2
0
2
0
2
2
1
2
0
0
2
0
0
0
0
0
2
0
0
0
0
2
1
1
2
1
0
2
0
1
1
0
0
0
0
0
2
0
0
0
0
0
3
0
1
1
0
0
0
2
0
2
2
0
2
2
0
2
0
2
0
0
0
1
0
0
0
2
0
1
0
0
0
2
1
1
1
0
2
0
0
0
0
1
2
2
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
1
0
3
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
1
1
1
1
0
1
0
0
0
0
0
1
2
0
0
1
0
0
2
0
1
1
0
0
0
0
1
0
0
0
0
0
1
1
0
2
0
0
0
2
1
1
0
0
0
0
1
0
0
0
0
0
0
1
1
2
0
3
3
2
0
1
0
0
0
1
0
1
0
1
1
0
0
2
2
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
1
1
0
1
2
1
0
2
1
1
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
2
3
0
2
1
1
0
0
0
0
0
2
0
2
0
2
2
0
0
0
2
1
0
0
1
0
2
0
1
0
2
0
0
0
0
2
2
1
0
0
0
1
0
0
3
0
2
1
1
0
2
1
0
1
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
1
0
2
2
0
0
0
0
2
1
0
0
0
0
0
0
0
1
1
0
2
0
2
0
1
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
1
2
0
1
0
2
0
0
2
0
0
2
0
0
0
0
0
2
0
2
1
0
2
1
1
1
0
1
1
0
0
0
1
0
0
0
0
1
0
2
0
2
1
1
0
2
0
2
0
2
2
0
2
2
2
2
0
0
1
0
0
0
2
0
0
0
1
0
0
1
1
1
0
0
0
0
1
0
2
0
0
0
0
1
1
2
1
0
1
1
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
4
2
0
2
0
2
1
0
2
0
0
2
0
2
1
1
0
1
0
2
1
1
0
3
0
1
0
0
2
1
1
0
2
0
0
1
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
1
0
0
0
2
1
2
2
0
2
0
0
2
1
0
0
0
2
0
2
0
3
6
0
0
2
0
0
0
0
0
1
0
1
1
0
1
2
1
0
2
0
0
2
0
0
0
0
3
0
0
0
0
2
2
0
2
3
2
0
0
1
3
0
0
0
1
0
0
0
1
1
1
0
0
0
2
1
1
1
0
2
0
0
0
1
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
2
4
1
0
0
0
0
1
0
0
0
1
2
2
0
0
0
1
0
0
0
0
0
0
0
2
1
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
2
3
0
1
0
0
3
1
0
2
0
1
0
2
0
1
0
0
1
0
0
1
0
1
0
1
1
1
2
0
1
0
0
2
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
1
2
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
2
0
2
2
0
0
0
0
1
1
2
1
0
0
0
0
2
0
2
0
3
2
2
2
2
1
1
0
1
0
1
0
1
1
1
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
1
0
1
0
0
0
0
1
0
0
2
2
1
0
0
2
2
2
0
1
2
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
2
0
2
1
1
2
0
0
0
1
0
0
2
2
2
0
0
2
1
1
2
0
2
0
0
2
1
1
2
0
2
0
0
2
1
0
0
0
2
2
2
0
0
2
0
0
0
0
3
1
0
0
2
0
2
1
2
0
1
0
2
1
0
1
0
0
1
0
1
2
1
2
2
2
1
2
0
0
1
1
0
1
1
1
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
2
0
2
0
0
2
0
0
2
0
0
0
0
2
2
0
1
2
0
0
0
2
1
2
0
0
0
2
0
0
1
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
2
1
0
0
0
0
0
1
2
2
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
1
3
1
1
0
1
0
2
0
0
2
1
0
1
2
0
1
0
2
0
0
0
0
1
0
2
1
2
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
2
1
0
0
0
3
2
2
2
0
4
2
1
1
1
0
2
2
1
0
0
0
0
2
0
1
0
0
0
1
2
2
0
0
0
1
0
0
0
0
2
1
0
0
0
1
0
1
2
1
2
0
1
0
2
0
1
1
0
2
2
0
0
2
0
2
1
0
0
1
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
1
2
8
0
0
0
2
0
3
0
2
1
1
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
1
2
0
0
0
2
0
2
0
0
0
2
2
0
0
0
1
1
0
0
0
2
0
2
1
0
0
2
0
0
0
0
0
1
1
1
0
1
0
0
2
1
2
2
0
0
0
1
0
1
0
0
0
2
0
0
1
0
0
0
1
0
0
0
1
1
2
1
0
3
0
2
2
0
3
1
2
2
3
0
1
4
0
0
2
1
0
0
2
0
2
0
0
1
0
0
3
0
0
0
0
0
3
0
1
1
1
0
2
0
1
0
0
0
0
2
1
1
0
1
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
1
1
1
2
0
2
0
0
0
0
0
1
1
0
0
2
0
0
0
1
0
2
1
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
1
0
2
0
1
0
1
2
0
0
1
1
0
1
0
1
0
0
0
0
0
1
1
0
1
1
0
0
0
0
2
0
2
3
0
0
2
2
1
0
0
2
2
0
0
0
0
4
0
0
2
0
2
0
0
2
0
0
2
0
1
0
0
0
1
0
2
2
0
0
2
0
0
2
0
0
0
0
1
0
0
0
2
0
0
2
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
2
0
2
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
2
1
0
0
0
0
1
0
0
2
0
1
0
0
0
1
0
2
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
1
1
2
0
0
3
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
4
1
0
2
0
0
0
1
0
0
0
2
1
0
0
0
0
2
0
1
2
0
0
0
1
0
1
0
1
0
0
0
0
0
0
2
0
1
0
1
3
0
0
0
0
1
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
1
1
0
2
0
1
1
2
2
0
1
0
2
0
0
0
0
0
1
0
2
0
0
1
0
0
1
0
0
0
2
1
0
0
0
0
0
1
0
0
0
2
0
0
5
1
2
0
3
1
1
0
0
0
0
0
1
0
0
0
1
0
2
0
1
0
1
2
0
0
1
0
0
0
0
0
0
0
0
4
0
2
0
2
1
2
1
2
0
1
0
0
0
2
0
0
2
0
1
2
1
0
0
0
0
0
1
1
0
0
0
1
0
1
1
1
0
2
0
0
2
1
0
0
0
0
0
0
1
0
2
2
2
0
0
2
1
2
1
0
0
1
1
2
0
0
1
1
0
2
0
1
0
0
0
0
1
1
2
0
2
1
1
2
2
0
2
1
0
2
0
0
2
0
2
2
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
2
0
0
2
0
0
2
2
1
2
2
1
0
1
0
2
0
0
0
1
0
1
1
0
1
0
0
0
0
1
1
1
0
1
0
0
1
0
1
0
1
0
0
0
0
7
2
0
0
2
0
0
2
1
0
0
1
0
0
0
0
0
0
0
3
0
0
2
0
1
0
0
0
0
0
1
2
1
1
0
0
0
0
3
0
1
2
0
0
0
0
0
0
0
0
0
2
0
2
1
1
2
1
0
0
0
0
4
0
0
0
2
1
2
1
0
0
1
0
0
2
1
0
0
0
0
0
2
2
0
0
0
0
2
1
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
2
0
0
1
0
2
2
1
2
2
2
2
0
0
0
2
1
2
0
0
0
0
0
0
1
0
1
1
0
0
1
2
2
2
1
3
0
2
0
1
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
1
0
0
1
1
0
2
0
0
2
0
2
0
1
0
0
0
1
0
0
0
0
2
0
2
2
2
0
1
0
0
2
0
1
0
0
0
0
0
1
1
0
1
0
2
0
0
1
2
1
0
0
0
0
0
0
0
1
0
2
0
1
1
1
1
2
0
1
1
0
2
1
1
0
0
3
0
1
0
2
0
2
0
0
0
1
0
0
2
2
0
0
0
0
1
0
0
2
1
0
0
0
0
1
2
0
0
0
0
0
0
2
1
0
3
0
1
1
0
0
1
1
0
1
0
0
1
0
0
0
2
2
0
1
0
2
1
0
1
3
2
1
1
1
0
0
1
0
1
0
2
0
0
1
1
1
2
2
0
0
1
0
1
0
0
0
2
2
0
2
1
0
0
2
0
2
0
1
0
0
0
1
1
0
0
2
0
1
0
1
2
0
0
0
1
1
0
1
1
0
1
2
0
2
2
2
0
0
1
1
0
0
1
1
0
3
0
0
1
2
1
2
0
0
0
2
0
0
0
2
2
0
3
1
1
2
2
1
1
0
0
1
2
0
0
0
1
0
0
0
0
0
1
2
0
0
0
2
0
1
0
0
0
1
0
0
1
0
0
2
0
0
2
0
1
0
0
2
0
2
0
1
0
0
0
0
0
2
0
1
0
1
1
1
1
1
6
0
0
0
0
0
1
2
1
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
1
1
0
1
2
0
0
0
0
0
0
1
2
0
0
2
0
2
2
0
0
1
0
0
0
0
1
2
2
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
1
2
0
0
0
0
2
2
2
0
0
0
1
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
1
2
3
1
0
2
0
0
0
0
0
1
0
2
0
0
1
2
1
2
0
2
2
0
0
1
0
1
0
0
2
1
1
1
1
0
2
0
0
0
0
2
1
2
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
1
0
0
0
0
0
0
0
1
0
2
3
0
0
2
1
0
2
0
1
0
3
1
0
0
2
2
0
0
0
0
2
0
0
0
2
2
0
0
0
0
2
1
2
2
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
2
2
0
2
0
2
0
7
0
0
1
0
0
0
1
0
1
1
2
0
0
0
0
1
0
0
0
13
1
1
1
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
6
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
1
0
0
2
0
1
0
1
0
1
2
0
0
0
0
0
1
0
0
1
0
1
0
0
2
2
5
1
1
1
0
0
0
2
2
0
0
0
0
1
0
0
2
0
0
0
0
1
0
2
0
2
0
2
1
1
1
0
0
0
3
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
2
2
0
1
2
1
0
1
2
0
2
1
0
0
0
0
1
1
0
2
0
2
1
0
1
1
0
1
3
0
0
0
0
0
0
1
0
0
2
0
2
1
1
2
0
0
1
0
0
0
0
0
0
2
0
1
1
0
2
0
2
0
0
0
1
0
0
0
2
0
1
0
2
0
1
0
0
0
1
2
0
0
0
0
2
2
1
2
1
0
0
0
1
0
0
0
1
1
1
1
0
0
2
0
0
0
2
1
1
0
0
1
0
1
2
2
0
0
1
0
3
1
1
1
0
2
0
2
0
1
0
0
1
0
2
1
0
0
0
0
0
2
0
0
1
0
0
1
1
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
4
0
2
2
1
1
0
0
1
0
0
2
0
1
0
0
0
0
2
0
0
2
0
1
0
2
2
0
2
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
1
1
1
2
2
0
1
0
0
1
3
0
0
0
0
0
0
0
0
1
1
1
0
1
2
0
0
2
2
0
0
2
0
0
1
2
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
2
0
2
0
0
2
0
1
0
1
0
0
0
0
1
0
2
0
0
0
1
1
0
1
1
0
0
2
0
2
0
0
3
2
1
0
0
1
0
0
0
1
1
2
0
2
0
2
0
1
2
2
0
0
0
0
2
2
3
0
1
1
0
0
0
0
0
0
0
1
0
2
0
3
0
0
0
2
2
1
0
1
0
1
0
0
0
2
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
3
2
0
0
0
0
1
0
0
1
0
0
0
1
2
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
1
2
0
0
0
2
0
0
0
1
0
2
0
0
1
0
0
1
2
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
1
1
0
0
0
1
2
0
0
0
0
1
1
1
1
0
1
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
2
1
0
2
2
0
0
0
0
1
1
1
2
1
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
1
2
2
2
0
1
1
0
0
0
2
0
0
0
1
0
0
2
0
0
1
0
2
0
0
3
0
0
1
0
2
0
0
3
0
1
0
0
0
0
0
2
2
0
0
0
0
0
2
0
1
1
1
1
0
3
3
0
0
2
0
1
0
0
1
2
0
1
2
9
0
0
0
1
2
1
0
0
2
0
1
0
2
0
1
0
0
1
0
2
2
2
0
1
2
2
1
0
1
3
0
0
2
0
1
2
0
3
0
0
0
1
1
1
2
0
0
0
0
0
0
0
2
0
2
0
1
2
0
1
2
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
1
1
2
0
0
0
1
0
0
0
0
0
0
2
2
4
1
0
0
0
0
1
0
2
1
0
0
2
1
1
0
0
0
1
0
0
1
0
0
2
1
1
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
2
0
2
1
2
0
0
1
2
0
1
1
0
2
1
2
3
0
2
1
0
0
3
2
0
1
1
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
1
1
0
1
3
0
1
1
0
0
1
1
0
2
3
1
0
0
0
0
1
1
0
0
1
0
0
0
1
2
0
2
0
0
1
1
0
0
1
0
0
1
0
0
0
1
2
0
3
0
2
0
0
2
0
0
0
0
0
0
1
3
0
0
3
0
1
1
0
0
0
0
1
3
0
0
0
0
0
0
0
0
2
2
0
4
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
2
0
2
0
0
1
0
1
1
2
0
0
0
1
2
2
2
0
0
1
0
2
0
0
0
0
1
0
2
1
0
1
0
0
0
0
2
10
1
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
1
2
0
2
0
0
0
0
0
1
1
1
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
2
0
0
3
0
0
1
0
1
1
0
1
1
0
1
0
0
1
1
2
2
0
0
4
2
0
2
1
2
2
1
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
2
0
1
0
2
1
0
1
0
2
1
0
0
0
0
0
0
0
1
2
1
2
0
3
1
2
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
2
2
0
0
0
1
0
2
0
2
0
2
0
0
0
0
2
0
2
1
0
1
0
0
2
3
1
1
0
0
2
0
1
2
1
1
1
2
0
0
2
0
2
2
1
0
0
2
1
0
0
2
0
0
0
0
2
4
0
0
0
2
1
2
0
0
0
0
0
0
2
0
0
0
2
2
0
0
1
0
0
1
0
0
0
0
0
3
0
1
1
0
0
0
1
0
4
1
1
1
1
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
1
1
0
0
0
0
0
0
2
2
1
0
1
0
0
0
0
0
0
0
1
0
0
1
1
1
2
0
0
0
3
2
1
2
0
0
1
0
1
1
1
0
2
2
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
2
0
0
1
2
2
0
0
0
1
1
0
1
2
0
0
2
0
1
0
2
0
1
2
0
0
2
2
1
2
0
2
0
1
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
1
0
2
0
0
0
2
1
2
0
1
0
0
0
1
0
0
2
2
2
0
0
0
1
0
1
0
1
0
0
0
1
3
0
0
2
0
1
0
1
2
3
0
0
1
1
0
0
0
2
1
2
0
0
1
2
2
2
0
0
0
1
0
0
2
1
0
1
0
2
1
1
0
1
2
2
0
0
1
0
0
0
1
0
1
1
2
4
0
0
0
2
0
0
0
3
0
2
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
2
1
1
2
0
1
2
0
0
0
2
0
0
0
4
0
2
1
0
0
0
0
2
1
2
0
0
0
1
0
0
0
0
1
1
1
1
1
1
1
0
0
0
1
0
1
0
3
1
2
0
1
0
0
0
0
2
3
0
0
1
0
0
0
0
1
0
1
0
0
1
2
1
2
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
1
1
2
2
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
2
2
0
2
3
2
0
0
2
2
0
0
0
2
1
0
0
1
0
6
0
0
1
1
0
1
0
0
0
2
0
0
0
0
0
2
2
0
0
0
1
2
0
0
0
0
1
0
1
2
2
0
2
2
0
2
1
0
0
2
0
0
0
0
1
2
1
0
0
0
3
1
0
1
0
0
0
0
0
1
1
0
0
2
0
2
1
0
0
0
1
0
2
0
1
0
0
0
0
1
0
0
0
6
0
0
2
0
1
1
1
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
2
1
0
0
1
0
0
0
2
1
0
0
2
1
2
1
0
0
0
0
0
0
0
0
0
2
1
0
0
2
1
1
1
1
0
0
0
2
0
0
0
1
0
0
1
2
1
5
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
1
2
0
0
2
1
1
0
0
1
0
0
2
2
4
0
0
1
0
0
0
0
0
0
0
3
0
1
0
0
2
1
2
0
0
0
0
1
1
1
1
0
0
2
0
2
0
2
0
1
0
0
2
0
0
1
1
0
0
2
1
0
0
0
1
1
0
0
1
0
0
2
2
0
0
1
1
0
10
2
2
2
0
0
0
4
2
0
1
0
0
0
2
0
0
0
1
2
2
2
0
1
1
2
1
1
1
0
0
0
0
0
0
0
1
0
2
2
0
0
2
0
1
0
0
0
0
0
0
2
1
0
0
3
0
1
2
0
1
0
0
1
2
0
0
2
1
0
0
2
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
1
1
1
0
0
1
0
2
0
1
0
0
0
2
1
0
1
0
3
0
0
0
0
1
1
1
1
0
0
0
1
0
0
1
0
2
0
2
0
1
3
1
0
0
0
2
3
0
0
1
0
0
1
0
0
0
0
1
0
0
0
2
0
0
2
0
0
2
2
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
3
0
1
1
0
0
0
2
1
1
2
0
2
0
0
2
1
1
1
2
0
3
1
0
0
0
0
0
0
0
0
1
0
0
1
2
2
2
0
1
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
1
0
2
0
2
0
0
0
1
0
0
1
0
0
1
0
0
2
1
0
1
0
1
2
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
2
1
5
1
0
0
0
1
0
0
2
1
0
0
1
0
0
0
0
0
3
0
0
1
2
0
0
2
0
0
2
0
0
0
0
1
0
1
0
0
0
0
2
0
1
2
1
2
2
0
0
2
0
2
1
0
1
1
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
5
0
2
0
2
0
2
1
1
2
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
3
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
2
0
1
0
1
1
1
0
0
0
1
1
1
0
0
1
2
0
0
2
2
0
1
2
0
1
1
9
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
1
3
2
0
12
0
1
2
2
0
0
0
0
0
0
2
2
1
1
0
0
0
0
0
1
1
2
0
0
0
2
0
0
0
0
0
0
0
0
8
0
2
2
0
1
1
0
2
2
0
0
0
3
0
2
2
0
0
0
1
2
1
1
0
0
0
2
3
0
0
1
1
0
1
0
2
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
1
0
1
0
2
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
1
2
0
0
1
2
0
2
0
3
2
1
0
2
2
1
2
0
3
0
2
0
0
0
1
1
0
0
0
1
0
0
2
0
0
0
1
2
0
0
0
0
1
0
0
1
0
0
0
2
0
1
0
0
0
2
2
0
2
1
2
0
2
0
0
0
0
0
0
1
0
2
3
0
0
0
1
0
0
0
2
0
2
0
0
0
1
0
0
0
3
0
0
1
0
2
1
0
0
1
0
2
0
0
0
2
0
0
2
4
0
0
0
1
0
0
0
0
1
2
0
3
1
1
0
1
2
0
0
2
3
0
1
0
1
0
0
0
2
0
0
0
3
0
0
0
1
1
0
0
1
1
0
1
0
1
2
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
1
0
1
0
2
1
0
0
1
0
2
2
0
3
0
0
0
1
0
1
0
0
0
1
2
0
0
0
0
2
2
2
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
3
2
1
0
0
0
0
2
2
1
1
1
1
1
1
0
1
2
1
0
0
1
0
4
0
2
1
0
0
1
2
0
0
3
0
0
0
1
0
0
1
0
0
2
0
0
2
2
0
2
0
2
0
2
0
0
0
1
1
0
0
2
0
1
1
1
0
0
1
0
2
2
2
0
0
1
0
0
0
2
0
0
1
2
0
0
0
6
1
0
1
1
0
0
1
2
0
0
0
0
3
1
1
0
0
0
0
1
2
2
1
0
0
0
0
0
1
0
2
0
0
2
0
0
0
1
0
2
0
5
0
2
0
0
2
1
1
2
2
1
2
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
1
2
0
0
2
1
0
0
1
0
0
7
0
0
2
1
0
0
0
2
0
0
0
0
2
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
2
0
2
0
1
1
0
1
0
0
0
2
1
0
0
2
3
1
1
1
0
0
2
0
0
0
1
0
2
1
2
0
0
2
0
0
0
2
1
9
2
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
3
0
0
0
0
1
0
1
0
1
0
0
1
2
0
2
0
0
0
0
0
2
1
2
2
0
0
2
1
0
2
0
1
0
0
2
1
0
0
1
0
0
2
0
0
0
2
0
1
0
1
0
2
0
1
0
2
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
2
1
0
0
0
0
1
1
1
0
1
2
0
0
5
0
2
0
1
0
2
2
2
0
0
1
2
0
0
0
0
0
1
0
0
2
1
0
2
2
0
2
0
1
0
2
0
0
3
1
0
0
0
0
0
1
0
1
1
0
3
1
2
2
0
1
0
0
2
0
0
2
0
0
0
1
1
2
2
0
2
0
1
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
1
1
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
1
0
2
0
1
0
1
1
0
0
0
0
0
1
0
0
2
2
0
0
0
0
1
0
2
1
1
0
2
0
1
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
1
0
2
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
1
0
0
0
0
0
2
0
1
1
1
0
0
2
0
1
1
0
2
0
2
2
2
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
2
0
0
0
0
0
1
0
0
0
0
1
0
1
2
0
0
2
0
0
0
1
3
0
0
1
0
5
1
0
2
2
0
0
2
2
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
2
0
1
2
1
0
0
2
2
1
0
0
0
0
0
0
0
1
0
0
0
2
0
1
2
1
1
2
3
0
3
0
0
0
1
0
1
0
1
0
0
0
0
2
1
1
2
1
0
2
0
0
3
2
1
0
3
0
4
0
1
1
1
2
2
0
2
0
0
1
1
0
4
0
0
1
0
1
1
1
0
0
2
0
0
0
0
2
1
0
2
5
0
1
0
0
1
0
0
0
2
0
0
0
0
0
2
1
0
0
1
0
0
2
3
0
0
0
0
0
2
0
0
0
3
1
0
0
1
1
2
1
2
2
0
0
1
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
2
2
0
1
0
1
1
0
0
2
1
1
1
0
1
1
0
2
0
2
3
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
2
1
0
0
2
2
2
0
2
0
0
1
0
0
2
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
2
1
0
0
0
1
0
1
0
0
1
0
2
1
2
1
0
1
0
0
2
0
1
3
1
1
0
2
1
0
0
1
0
1
1
0
0
2
0
1
0
0
0
0
0
2
2
0
0
0
0
0
1
3
0
0
0
0
2
1
1
1
0
0
0
0
0
0
1
2
0
2
0
0
2
1
0
0
0
2
0
1
0
0
0
0
1
0
2
0
3
0
0
2
2
2
1
0
1
0
0
2
0
0
0
1
0
0
0
1
2
2
2
0
0
0
2
2
0
0
2
1
0
0
0
2
1
0
0
1
2
1
0
0
0
2
2
3
0
0
1
1
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
4
0
0
0
2
0
2
0
1
1
0
0
2
0
3
2
0
1
1
2
1
0
0
0
0
0
0
0
2
0
1
0
1
2
2
2
0
1
1
0
0
0
2
1
1
2
3
2
0
0
0
2
1
1
0
0
0
0
0
2
0
0
2
1
0
2
1
2
2
0
0
0
0
0
2
0
1
1
0
1
2
1
0
0
0
0
3
0
0
1
1
0
1
2
1
3
0
2
0
0
2
0
0
2
0
0
0
1
1
0
0
0
1
2
0
0
2
1
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
1
0
3
0
1
0
0
2
7
1
0
0
1
2
1
1
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
2
2
0
0
1
3
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
2
0
2
0
0
2
1
2
0
1
0
0
1
0
1
0
1
12
1
1
0
0
0
0
0
1
0
0
1
0
2
0
1
1
0
2
0
0
0
1
1
2
2
1
1
0
3
0
0
0
0
0
2
2
0
1
0
2
0
0
0
1
2
0
0
0
2
2
0
0
1
0
0
0
1
0
0
0
4
3
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
2
1
0
0
0
0
1
1
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
2
2
1
0
1
1
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
1
2
0
0
0
2
0
2
1
0
0
0
2
0
1
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
1
2
1
0
1
1
2
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
1
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
1
1
1
0
0
2
1
1
2
2
2
0
0
4
0
1
0
1
1
1
2
0
0
0
0
0
1
1
0
0
1
1
2
0
2
0
0
0
0
0
0
1
1
1
0
0
0
0
1
1
1
1
1
0
0
0
2
2
0
1
0
0
0
0
0
0
2
0
1
3
0
0
1
0
2
2
1
0
0
1
0
0
0
1
1
0
2
0
1
0
0
1
0
0
1
0
0
0
2
1
0
2
0
0
0
1
0
1
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
1
0
0
1
0
2
1
0
0
2
1
1
0
1
1
0
2
0
0
0
0
0
0
1
2
2
0
0
0
1
0
0
2
1
2
0
1
0
0
0
0
0
0
1
1
1
0
2
2
0
1
2
2
1
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
1
1
0
2
1
0
1
1
1
1
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
2
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
2
2
0
1
2
0
1
0
2
1
2
0
2
0
1
1
0
2
0
2
1
1
0
0
1
0
0
0
1
2
0
0
1
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
1
0
0
1
0
0
1
2
0
0
3
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
2
0
2
1
0
0
0
0
0
1
2
2
2
0
0
5
2
3
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
3
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
2
0
0
2
0
0
1
1
0
1
2
1
2
0
2
0
2
0
0
0
1
0
3
0
0
0
0
0
0
1
1
1
0
2
0
5
0
0
1
1
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
2
1
1
3
0
0
8
0
0
1
1
0
2
1
2
1
2
2
0
0
0
0
0
1
1
2
0
0
1
0
0
0
0
0
0
1
0
0
0
1
2
3
1
2
3
1
0
0
1
1
4
0
1
1
0
0
2
0
1
0
0
2
0
1
0
2
1
0
0
0
0
0
0
0
0
3
1
2
2
0
0
2
2
0
0
2
2
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
1
1
0
2
6
0
0
0
0
1
1
0
0
1
0
0
0
0
1
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
2
0
0
1
1
0
2
0
0
0
0
2
2
0
1
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
1
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
1
1
0
0
1
2
2
3
0
1
0
2
0
2
2
0
1
0
2
0
1
0
0
2
0
0
0
0
1
3
0
3
0
0
1
3
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
2
2
1
1
2
0
0
2
0
1
2
1
0
0
0
2
0
0
0
0
0
0
0
2
1
0
1
0
1
3
2
1
0
0
0
0
1
0
0
3
1
1
0
0
1
0
1
0
0
0
1
0
0
2
1
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
1
2
0
0
1
2
0
1
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
3
0
0
2
0
0
0
2
0
0
2
0
0
0
0
2
3
0
0
2
0
1
1
0
0
2
0
1
0
1
2
1
0
1
0
1
0
1
1
2
0
0
2
2
0
0
0
3
1
0
1
0
0
1
2
1
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
1
0
1
1
0
1
2
0
2
0
0
1
0
2
0
0
2
0
3
0
0
1
2
1
1
1
0
2
1
2
0
0
0
0
1
1
2
0
2
2
4
0
0
0
2
2
0
0
0
2
0
2
0
0
1
0
0
0
1
2
0
2
0
0
0
1
0
0
0
1
0
0
2
1
0
0
0
0
0
2
0
0
0
1
1
2
0
0
2
0
1
0
0
0
0
0
0
0
0
3
1
0
2
0
1
0
0
0
0
1
0
0
0
2
0
0
2
1
2
1
2
0
0
0
0
2
1
0
0
0
0
2
0
2
0
0
1
0
0
1
2
0
1
0
0
2
1
0
1
1
0
0
2
1
0
2
2
0
0
1
0
1
0
0
0
0
0
1
0
0
2
0
2
2
0
0
0
0
0
0
0
2
2
0
1
0
1
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
2
0
2
2
0
1
2
3
1
1
0
0
1
0
2
0
0
2
1
1
0
1
1
0
0
2
0
1
0
0
0
0
0
2
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
2
1
0
2
2
2
0
0
0
3
0
1
0
0
0
0
1
0
1
1
0
2
0
0
1
0
0
0
2
1
1
1
1
1
0
0
2
2
2
2
0
2
0
1
1
5
1
2
0
1
0
0
1
0
0
1
0
2
2
0
0
0
1
0
1
3
2
0
0
0
0
1
0
1
0
0
1
1
0
2
0
2
0
0
0
1
0
1
1
0
0
1
1
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
1
0
1
0
2
0
0
0
2
0
0
1
0
0
0
0
1
0
0
1
1
0
2
0
0
2
1
0
0
0
0
1
0
0
1
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
6
1
2
0
2
0
0
1
2
0
2
1
1
0
1
0
0
1
2
2
2
2
2
0
0
0
0
1
1
0
1
0
0
0
1
2
0
0
1
1
0
1
1
0
2
1
0
5
0
2
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
1
1
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
1
1
0
0
1
2
1
0
0
7
1
0
1
0
0
1
0
2
1
0
2
0
0
2
0
0
0
0
0
0
2
0
0
2
0
1
1
1
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
2
0
0
1
2
0
2
0
1
0
0
0
1
0
2
3
1
3
0
0
1
2
0
0
1
0
0
2
1
0
0
0
0
2
0
0
1
0
0
1
2
0
2
0
1
0
2
0
0
0
2
2
0
2
0
3
0
1
1
2
1
3
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
6
0
0
1
2
2
2
1
0
0
0
2
1
0
0
0
0
2
1
0
0
0
0
0
1
1
1
0
0
0
1
3
0
0
2
1
0
0
0
1
0
0
0
0
0
2
0
1
2
0
1
0
0
1
1
0
0
0
0
1
1
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
2
1
2
0
0
0
0
1
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
2
2
2
1
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
2
1
0
0
0
1
3
0
0
0
1
0
0
0
2
0
3
0
0
1
0
0
0
0
2
0
1
1
0
0
2
0
0
2
0
1
1
0
1
0
2
1
1
1
2
1
2
2
3
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
5
1
2
1
0
2
1
0
0
0
0
0
2
0
0
0
0
0
2
2
2
0
2
0
0
0
0
0
0
0
0
1
0
2
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
2
0
2
1
1
0
2
2
2
0
0
1
2
1
0
0
0
2
0
1
0
0
0
0
1
0
0
0
2
0
0
0
2
0
1
1
2
0
1
2
0
3
2
2
2
0
2
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
1
0
0
2
0
0
2
2
0
3
1
1
1
2
2
0
2
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
2
1
0
0
1
0
0
0
0
4
1
0
0
0
1
0
0
2
1
2
1
0
1
0
1
2
0
0
1
0
0
1
0
0
0
0
2
0
1
0
0
1
1
0
0
0
0
0
0
0
2
0
0
1
0
0
2
2
0
0
0
0
0
2
2
1
0
0
0
0
2
0
0
1
1
0
0
0
0
1
1
0
1
0
0
0
1
1
1
0
0
1
2
0
1
0
0
0
0
1
3
0
1
1
2
0
0
1
0
2
0
1
0
1
1
1
3
0
0
1
1
1
0
0
1
0
2
0
0
0
0
0
1
2
0
0
0
0
0
3
2
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
2
1
0
2
2
1
2
0
0
1
0
1
3
0
2
0
0
2
1
0
0
0
0
0
2
0
0
0
1
0
3
0
2
0
1
2
0
0
2
0
0
0
1
0
0
0
1
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
2
1
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
2
0
3
0
0
2
2
1
0
1
0
1
1
1
1
1
0
1
1
1
0
0
2
0
2
0
1
1
0
0
0
0
0
2
0
0
2
0
0
0
1
0
1
2
2
0
0
1
1
1
0
0
1
0
0
1
0
1
2
0
0
1
1
0
0
0
2
0
2
0
4
0
0
0
0
1
0
0
0
1
2
0
2
2
0
1
0
0
0
2
0
0
0
2
1
1
0
0
0
1
0
3
0
0
1
2
0
0
1
2
0
1
0
1
1
0
2
0
0
0
1
1
3
0
0
2
0
0
0
0
0
0
1
0
2
0
1
0
2
0
1
0
0
1
0
2
0
1
0
2
1
0
2
0
1
0
0
0
1
3
0
0
0
1
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
3
1
0
1
2
2
0
0
2
0
0
0
1
1
0
0
2
1
0
0
1
1
0
0
0
2
2
0
2
1
1
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
1
2
0
0
0
0
0
1
1
0
0
1
0
0
2
0
2
4
1
1
0
0
1
0
0
0
0
0
1
1
0
0
0
2
0
1
0
0
0
1
0
0
0
1
0
0
0
0
2
1
0
0
1
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
1
0
1
0
1
2
2
2
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
2
2
0
2
2
0
0
0
0
1
0
1
1
1
2
2
0
2
0
1
1
0
0
2
2
1
1
0
0
0
0
0
0
2
1
1
3
1
2
0
1
0
0
1
0
2
0
0
0
0
1
0
0
1
0
0
0
1
1
1
1
1
0
0
0
1
1
1
0
1
2
1
1
2
1
0
1
0
0
3
0
0
0
0
0
4
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
2
0
1
0
1
0
2
0
1
0
4
1
1
0
2
0
0
1
0
0
2
1
0
0
0
1
2
1
0
0
0
1
0
2
0
1
2
0
1
0
1
2
0
0
1
1
0
2
0
0
0
1
0
1
2
2
0
0
2
2
0
0
2
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
2
1
0
2
1
0
2
0
0
2
0
0
0
0
2
2
0
2
0
1
0
1
0
1
2
1
0
2
1
0
1
0
0
1
2
0
0
0
2
2
0
0
0
0
0
0
0
2
0
2
1
0
0
1
0
1
0
0
1
0
0
1
1
0
0
1
2
3
1
1
1
2
0
0
0
1
1
0
0
2
0
1
1
1
0
0
0
0
2
0
0
0
0
1
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
2
1
2
0
0
2
0
0
0
1
2
0
0
0
0
2
0
0
0
0
2
1
1
2
0
0
0
0
0
2
1
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
1
1
2
0
1
1
1
0
1
2
1
1
0
2
0
0
0
0
0
0
0
0
2
1
0
2
2
0
0
0
2
0
1
0
0
0
0
1
1
1
0
0
0
0
0
1
2
2
0
0
0
2
0
0
0
0
0
1
2
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
1
0
1
2
0
1
1
1
0
0
3
0
0
2
1
0
1
0
1
1
0
1
0
0
1
0
0
0
3
2
0
1
2
0
0
0
0
0
1
2
1
2
0
1
0
0
0
2
1
0
2
0
1
1
0
0
0
0
5
0
0
0
1
0
0
0
0
0
1
2
1
2
0
0
1
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
2
2
0
1
0
2
2
0
0
0
1
0
1
1
0
2
2
0
0
2
0
2
0
0
1
0
1
2
2
0
1
0
2
0
1
2
0
0
0
1
0
2
1
0
1
1
0
0
1
1
1
0
0
2
0
0
4
0
2
0
1
1
0
1
2
0
0
1
0
1
0
0
2
0
0
1
0
2
2
1
2
0
0
1
2
0
0
0
1
1
0
1
1
0
0
0
0
1
0
0
0
2
2
1
0
0
0
0
1
0
2
0
1
0
2
0
1
0
2
0
0
1
0
0
0
0
0
1
0
0
1
0
2
1
2
0
0
2
0
0
2
0
0
1
2
3
0
0
1
0
2
0
0
2
2
0
1
0
0
1
0
2
3
1
2
0
0
0
0
2
0
0
0
2
1
0
0
1
0
0
1
0
0
0
0
0
1
2
3
2
0
1
0
2
0
0
1
1
2
1
0
1
1
2
0
0
0
2
2
1
0
3
0
0
0
3
0
0
2
0
2
0
0
1
2
0
0
0
2
0
1
2
1
0
1
1
0
2
2
0
0
0
0
1
0
0
2
0
0
0
0
2
2
0
1
3
0
0
2
0
0
0
0
0
0
1
1
0
9
1
1
0
1
0
0
0
0
2
2
0
0
0
0
0
1
0
2
0
0
2
0
0
0
2
2
0
2
0
2
1
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
3
0
1
0
0
0
0
1
2
2
1
0
0
0
2
0
0
0
0
0
0
1
0
2
4
1
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
3
1
0
1
1
0
0
2
0
0
2
0
0
0
0
0
2
1
0
0
0
1
0
2
1
0
0
0
2
0
0
0
0
0
2
0
2
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
2
1
1
0
0
1
0
0
2
0
1
0
1
0
1
1
1
1
2
0
0
2
0
0
0
1
1
0
0
0
2
0
1
0
0
2
2
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
2
0
2
1
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
1
1
1
1
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
2
1
1
2
0
0
0
2
2
2
0
2
2
1
1
0
2
1
2
1
0
0
1
0
1
2
0
0
2
2
0
0
0
0
0
0
0
0
2
0
2
2
0
2
0
1
1
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
1
2
0
0
1
0
2
1
0
2
0
0
0
0
1
0
0
0
2
1
2
1
0
1
0
0
1
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
2
0
0
0
1
2
1
2
2
2
0
0
1
0
0
0
2
0
0
3
0
1
0
1
0
0
0
2
0
1
0
0
0
0
2
2
0
0
0
1
0
0
0
2
3
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
2
0
0
0
1
5
3
1
0
3
0
0
0
0
0
4
0
0
1
2
0
1
0
0
0
2
0
0
2
0
1
1
0
2
2
0
0
1
1
1
0
0
0
1
1
0
0
1
2
0
2
0
0
1
1
0
1
5
3
1
1
1
0
3
0
0
0
0
0
0
0
2
2
0
0
1
1
0
0
0
0
0
0
1
0
0
0
2
2
0
1
0
0
2
1
1
0
2
0
0
1
2
2
2
1
2
0
0
1
2
0
0
2
0
2
3
0
2
2
0
0
1
2
0
0
0
0
2
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
2
5
0
0
0
1
0
0
2
0
2
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
2
0
2
0
0
2
0
0
1
0
1
0
0
1
0
0
1
2
1
2
2
0
2
1
0
0
0
0
3
0
0
0
0
0
1
0
1
1
2
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
2
2
1
0
2
0
0
2
0
0
1
0
0
1
1
0
0
0
0
0
0
2
1
2
1
0
2
1
2
1
1
0
1
0
0
0
2
0
3
0
0
0
0
0
2
1
0
2
1
0
0
2
0
2
0
0
0
3
0
0
0
0
0
2
0
0
1
3
0
0
0
2
0
0
1
2
0
0
0
2
0
2
0
0
0
2
0
1
1
0
1
0
0
0
0
1
0
0
1
2
0
1
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
2
1
1
1
0
1
2
0
1
2
0
0
1
1
0
0
0
2
1
1
2
0
0
0
0
0
1
2
0
0
0
0
1
0
2
0
0
2
0
2
0
0
0
0
2
2
0
3
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
2
0
2
1
0
0
0
2
2
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
2
2
1
0
0
0
0
1
0
1
1
1
0
0
1
0
0
0
0
2
2
0
0
1
0
1
0
0
0
0
2
2
0
0
2
1
0
0
1
0
0
0
2
1
0
0
2
0
2
1
0
1
1
0
2
1
0
0
0
0
2
0
0
0
0
0
2
0
2
1
1
1
0
0
0
2
0
2
2
2
3
1
0
0
1
0
1
0
0
2
1
0
1
0
2
2
0
1
0
0
0
0
1
0
0
2
0
0
2
2
0
0
0
1
0
0
1
0
0
2
0
1
1
0
0
0
2
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
2
2
0
0
0
0
1
0
2
0
2
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
1
0
1
0
2
1
0
2
2
0
0
0
0
0
2
0
0
0
0
1
0
0
2
1
0
2
0
0
0
0
1
1
1
0
1
0
1
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
2
2
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
3
0
1
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
1
2
0
1
0
2
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
1
1
1
0
3
0
0
1
0
1
0
2
0
0
0
0
0
1
2
0
0
1
1
0
0
1
0
0
2
0
1
1
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
1
0
2
2
1
2
0
2
0
1
0
0
1
0
0
2
0
0
0
2
0
0
1
2
0
1
1
0
0
1
0
0
2
1
0
2
3
0
0
0
1
0
2
0
0
3
0
0
2
0
1
0
1
0
1
0
2
0
0
0
0
2
1
1
1
0
1
5
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
3
2
3
0
2
1
0
0
0
2
2
0
2
0
2
1
0
1
1
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
1
1
1
0
2
1
1
1
0
0
0
0
2
0
0
2
0
0
0
2
0
1
0
2
1
0
0
1
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
2
0
1
1
0
2
0
0
2
1
0
2
2
0
0
1
1
0
0
2
0
2
0
1
0
0
0
1
2
1
0
3
1
0
0
2
2
1
1
0
1
1
0
0
2
2
0
0
1
0
3
1
0
1
0
1
1
1
1
0
0
0
1
0
2
1
1
1
1
0
2
3
0
0
0
1
0
0
1
0
2
0
0
1
2
2
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
3
2
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
1
1
0
0
0
1
0
2
0
1
0
1
1
2
0
0
0
0
0
0
0
0
0
2
3
0
1
0
0
0
2
0
0
1
1
1
0
0
0
0
1
2
0
2
0
2
1
2
2
0
0
0
0
2
0
0
2
0
0
0
2
0
0
1
7
0
1
2
0
0
0
0
2
0
0
2
2
0
2
0
1
2
1
1
0
0
1
0
1
1
1
0
0
0
0
2
0
2
1
1
0
0
0
0
0
0
2
0
1
2
1
2
0
2
0
1
1
0
0
0
2
1
2
1
0
2
2
0
0
2
2
0
1
0
0
0
1
1
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
3
0
0
0
2
1
3
0
0
0
2
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
2
0
2
2
0
0
1
2
0
2
0
6
0
0
1
0
0
0
1
2
1
0
2
0
0
1
0
0
1
0
2
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
2
1
0
1
1
1
3
0
0
0
1
2
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
1
1
1
0
0
1
1
2
0
2
0
0
3
0
0
0
0
0
2
2
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
1
2
4
0
1
0
0
0
0
2
0
0
1
1
0
2
2
0
1
1
0
0
1
1
2
2
1
1
1
0
0
0
1
1
2
2
0
0
2
1
0
0
0
2
0
2
0
0
0
2
2
0
2
0
0
0
0
4
1
0
0
0
1
0
0
1
1
0
0
2
0
0
1
0
0
1
2
1
0
0
0
0
1
2
0
0
1
0
0
1
0
2
2
2
1
2
0
0
2
0
0
0
2
1
0
0
1
0
0
2
0
0
1
0
0
0
2
1
0
0
0
0
2
0
0
1
1
1
0
0
1
0
0
0
2
0
1
1
3
0
0
0
0
13
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
1
0
0
0
1
0
0
0
0
2
0
0
0
2
0
2
1
0
0
3
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
1
0
0
1
2
2
0
0
0
0
1
0
0
3
1
0
0
2
0
2
1
0
0
0
0
0
0
0
1
0
1
2
2
0
1
0
1
0
0
0
0
0
1
0
0
0
2
5
1
1
0
0
1
2
0
0
2
1
1
0
0
0
0
1
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
2
0
2
1
2
0
2
1
0
0
1
0
2
1
1
0
1
1
0
3
0
1
0
0
0
1
2
2
0
0
2
0
1
2
0
0
0
1
0
0
1
1
1
0
0
2
0
0
0
1
2
3
0
0
0
1
3
2
2
1
0
3
0
1
2
0
1
0
2
0
2
0
2
1
1
2
0
1
0
0
2
0
0
1
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
1
0
1
1
0
0
0
2
0
0
0
1
0
2
0
2
1
0
1
1
0
0
1
0
0
0
1
2
2
0
2
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
1
3
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
2
2
0
0
2
1
0
0
0
1
1
0
1
0
1
2
0
0
2
4
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
1
2
0
2
0
0
0
0
1
2
2
0
0
1
0
0
0
2
0
0
2
2
0
2
0
1
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
2
2
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
2
0
1
2
2
0
2
1
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
2
2
0
0
1
0
0
1
2
0
1
0
0
0
0
0
1
1
1
0
3
1
0
1
0
1
0
0
1
0
2
0
0
0
0
1
4
2
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
3
0
0
2
1
1
0
2
0
0
0
1
0
0
0
2
1
3
2
1
2
0
1
2
0
1
0
2
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
1
3
1
0
0
1
2
0
0
1
2
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
1
2
2
3
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
3
0
0
1
0
1
0
2
1
2
1
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
1
0
0
0
0
1
1
0
0
0
0
2
1
0
1
0
0
0
0
2
0
0
1
0
0
0
0
4
0
0
1
0
2
1
2
1
0
2
3
0
0
0
0
1
2
2
0
1
0
0
1
0
2
0
0
0
2
1
0
0
2
0
0
0
0
0
1
1
2
1
0
1
0
1
0
1
0
2
0
0
1
2
0
2
2
2
1
4
0
1
0
0
0
1
0
2
1
2
2
0
0
0
2
2
0
8
0
0
0
0
2
1
0
1
0
0
1
1
0
0
1
1
1
0
0
0
2
2
0
0
0
0
2
2
0
0
2
1
2
1
0
1
2
0
1
0
1
1
0
0
0
0
0
1
0
2
0
1
1
2
2
1
2
0
0
2
1
1
0
1
1
2
0
1
2
0
0
0
0
0
0
2
0
1
0
6
0
0
0
0
0
0
0
0
0
2
2
0
0
3
2
0
0
0
2
0
0
1
0
1
0
0
1
0
4
0
0
1
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
1
0
2
0
1
0
0
1
0
0
0
0
1
2
1
2
1
1
0
0
1
0
0
2
0
0
0
2
0
0
2
1
0
0
2
2
0
0
0
0
1
0
1
0
0
0
0
0
0
2
1
0
0
0
0
2
0
2
0
0
2
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
2
1
0
1
0
1
0
0
0
0
1
0
1
0
0
1
0
0
2
2
1
1
0
0
0
0
2
0
0
0
0
2
0
1
1
0
0
0
0
1
0
0
2
0
0
0
0
2
2
2
0
0
1
2
1
0
2
1
1
1
0
0
0
0
0
0
0
0
0
0
2
1
3
0
0
0
0
0
0
2
0
1
0
0
0
2
2
0
0
1
2
0
1
1
1
0
0
0
1
0
0
1
0
0
2
0
0
0
0
2
2
1
2
0
0
0
1
1
0
1
1
0
0
2
0
0
0
0
0
0
2
2
0
2
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
2
2
0
6
3
0
0
2
0
2
2
2
0
2
1
0
0
0
0
1
0
1
1
0
0
0
1
1
0
1
0
0
2
0
1
0
3
0
0
1
2
3
1
1
1
0
0
0
0
1
1
0
1
0
0
2
0
1
0
0
2
0
0
3
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
1
1
2
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
2
0
1
0
0
1
0
0
1
2
1
2
1
1
0
2
0
1
1
3
0
0
0
0
0
1
1
0
2
3
0
0
1
1
0
0
0
0
2
0
2
1
3
2
0
1
0
3
0
0
0
0
1
1
0
2
0
0
0
0
0
0
5
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
2
0
2
1
0
1
0
1
0
3
1
0
0
0
0
0
0
2
2
1
0
0
0
0
2
0
1
2
0
0
0
1
2
0
2
4
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
3
0
0
0
0
0
2
0
2
0
1
1
2
0
2
1
0
0
0
2
0
2
0
1
1
0
1
1
0
2
0
0
1
0
0
0
1
0
0
2
2
2
0
5
2
0
0
0
0
0
0
1
1
0
2
0
1
0
0
0
0
2
2
1
0
0
1
0
0
0
0
0
1
1
1
0
0
0
1
0
2
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
1
2
1
2
0
0
0
0
2
0
0
0
0
1
0
0
1
2
1
0
1
0
0
0
0
1
2
2
0
2
0
0
0
0
0
0
1
0
1
0
0
0
3
0
0
1
0
2
0
0
0
0
1
2
2
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
1
2
1
1
0
0
1
1
2
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
2
2
0
0
2
2
0
0
2
1
1
0
0
1
1
0
0
0
0
0
0
1
2
1
0
0
2
0
0
2
0
0
0
1
1
0
2
2
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
2
1
0
2
0
0
1
1
2
1
1
2
0
0
2
0
0
0
1
0
1
1
0
0
0
0
0
0
1
2
0
2
0
0
2
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
1
0
0
2
2
2
2
0
1
0
2
0
0
0
0
1
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
5
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
2
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
4
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
1
0
2
2
0
0
0
0
2
1
0
2
0
0
0
0
1
1
0
0
2
0
0
0
0
2
0
1
0
0
0
2
0
0
1
1
1
0
1
2
2
2
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
1
0
2
0
0
0
0
2
1
0
0
2
0
0
1
0
3
1
0
2
0
2
0
0
0
0
1
1
2
0
1
0
0
2
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
2
1
0
1
0
0
2
0
0
2
0
0
0
0
0
0
9
0
0
0
1
0
0
2
0
0
0
2
1
2
0
0
0
2
1
0
0
1
1
0
0
0
2
0
1
0
2
0
3
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
2
0
0
3
0
1
0
1
1
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
1
1
0
1
2
2
0
0
2
2
1
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
2
0
2
0
0
0
1
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
2
1
1
0
0
0
0
0
0
2
1
2
2
1
0
0
0
0
0
1
0
2
0
1
0
2
1
0
2
2
1
2
1
0
0
0
0
1
0
0
0
0
1
0
1
0
1
1
0
2
1
0
0
0
0
0
2
0
1
2
0
0
0
1
0
2
2
0
1
1
0
0
0
1
2
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
2
0
0
2
0
0
0
1
0
1
0
2
0
2
1
2
2
0
0
1
0
0
0
2
0
2
0
0
0
1
1
0
1
0
2
0
0
2
0
0
0
1
0
0
0
0
0
2
1
0
2
2
2
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
2
1
0
1
0
0
2
2
2
0
0
0
0
0
2
0
1
0
0
1
2
0
0
0
1
0
2
0
2
2
2
0
2
0
0
0
2
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
1
2
2
1
0
0
0
0
0
0
0
0
2
1
2
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
1
0
0
1
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
2
0
1
1
2
0
2
2
2
0
2
0
0
0
2
0
1
1
3
0
1
1
1
0
0
0
2
1
0
0
0
1
3
2
0
0
1
0
2
0
2
0
0
1
2
2
2
0
0
0
0
0
0
3
0
1
2
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
2
0
1
0
2
0
1
0
0
0
1
0
2
1
1
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
2
2
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
4
0
0
2
3
0
0
0
0
2
0
2
0
0
1
2
0
2
2
0
1
2
0
2
2
2
0
0
1
1
0
0
2
0
0
2
0
1
1
2
0
0
2
1
0
1
0
1
2
0
3
0
0
1
0
0
0
0
1
0
1
1
0
2
0
2
0
0
1
0
0
2
1
0
0
1
0
1
0
0
0
1
1
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
2
0
0
2
0
0
0
0
1
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
2
1
3
1
0
0
2
2
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
1
2
1
0
0
2
0
2
1
1
0
0
1
0
0
1
0
0
0
2
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
1
0
2
0
1
0
1
1
1
0
0
0
2
0
2
1
0
0
0
0
0
2
2
0
1
0
1
0
2
2
2
3
1
2
0
0
3
0
0
0
0
0
2
2
0
0
0
0
1
0
0
1
0
0
1
1
1
1
2
0
2
0
0
0
1
0
1
0
0
0
1
0
0
0
0
2
0
0
2
0
2
0
2
0
2
0
0
0
0
1
0
1
0
0
0
2
0
0
1
0
2
0
2
2
2
1
2
2
0
2
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
2
1
0
0
2
1
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
2
0
1
0
0
2
1
2
2
2
1
0
0
1
0
1
0
0
1
0
1
1
0
2
0
1
0
0
0
1
1
1
0
0
1
0
1
2
0
0
2
0
0
0
2
2
0
1
0
2
0
0
1
0
0
0
0
0
4
0
3
0
1
1
2
0
0
1
0
0
0
2
0
0
0
0
2
0
1
4
0
2
1
3
0
0
1
0
2
0
0
0
2
0
0
0
2
0
0
0
0
2
0
1
2
2
0
0
1
1
0
0
1
0
2
1
1
1
3
0
0
0
2
1
0
0
0
2
0
0
0
2
1
0
0
1
0
2
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
1
3
0
1
0
3
0
0
0
5
0
0
0
3
1
2
0
1
1
0
2
0
1
2
1
0
1
0
1
0
0
2
0
0
1
1
2
0
0
1
1
0
0
1
2
1
0
0
0
0
1
0
0
5
0
2
2
0
1
1
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
1
0
1
0
0
0
0
0
1
2
0
0
1
0
2
1
2
1
0
0
0
3
1
0
0
0
0
0
2
0
1
0
0
1
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
2
0
2
2
2
0
2
0
0
0
0
0
0
2
0
2
0
2
0
0
0
1
0
0
1
0
2
0
2
2
0
0
1
0
0
0
0
0
2
0
0
1
2
0
1
1
0
2
0
0
0
1
0
0
1
0
2
0
2
1
1
1
1
0
1
0
0
0
1
1
0
0
0
1
0
0
2
0
2
0
2
0
0
0
1
1
0
0
1
1
0
0
0
0
0
2
2
0
2
0
0
0
0
2
0
1
0
1
0
2
0
0
0
0
0
1
1
1
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
2
1
1
0
0
1
2
0
0
1
0
0
1
1
2
2
0
0
1
0
1
1
0
0
0
0
0
1
2
0
2
0
0
1
1
1
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
2
3
1
0
2
2
0
0
0
2
3
0
1
0
0
0
2
1
2
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
1
3
0
2
0
0
2
0
0
1
2
0
0
1
3
2
0
0
0
0
1
2
1
0
0
0
0
1
0
1
2
2
0
2
1
0
2
1
1
2
0
2
2
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
1
0
1
0
1
1
1
1
1
0
0
0
2
0
1
0
0
0
1
0
1
0
0
1
0
2
0
1
1
0
1
2
0
1
1
0
2
1
0
0
0
0
1
2
0
8
0
2
2
3
0
0
0
0
2
2
1
0
1
0
0
0
2
0
3
0
1
1
0
0
1
0
0
0
1
2
2
2
0
2
0
0
2
0
1
1
0
2
2
1
1
2
2
0
0
0
2
1
1
0
0
0
0
0
0
2
2
0
0
1
0
1
1
0
0
0
1
0
2
0
1
2
2
1
1
0
2
2
0
0
2
0
1
1
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
2
1
0
2
1
1
0
2
1
0
0
1
0
0
2
1
0
2
0
0
2
0
0
2
0
2
1
0
0
0
0
2
0
0
0
2
0
0
0
0
2
1
0
0
1
0
0
2
0
2
0
0
2
1
2
1
0
0
0
0
0
0
1
1
2
0
1
0
0
4
0
0
2
2
0
1
2
2
0
0
1
1
0
1
2
1
0
0
0
1
1
2
0
0
0
1
1
0
1
0
2
5
0
0
0
0
2
0
1
0
0
0
0
1
0
2
2
0
0
0
1
0
1
0
0
0
2
1
1
0
0
0
0
1
1
0
0
0
0
1
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
2
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
1
1
0
0
2
0
0
0
0
0
1
0
2
0
1
0
1
0
0
2
3
2
1
0
0
1
0
0
0
0
1
0
0
1
0
0
1
2
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
1
0
1
2
0
0
0
0
0
1
1
0
0
0
2
1
2
0
0
0
2
2
0
0
0
0
0
0
0
2
0
2
0
3
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
1
0
1
1
1
0
0
0
0
3
1
3
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
1
1
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
3
1
1
0
0
0
0
0
0
0
0
0
2
3
0
2
1
0
0
2
1
0
0
2
2
0
0
0
1
2
2
0
2
0
0
0
0
0
0
2
1
0
0
1
0
0
2
0
0
2
2
0
0
0
0
2
0
1
0
0
0
0
1
0
2
2
2
0
1
0
1
0
0
0
0
1
2
0
0
2
1
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
1
1
0
0
2
1
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
3
2
1
0
2
0
0
0
0
0
3
2
3
2
0
1
0
1
2
0
0
0
1
0
1
0
6
0
0
0
2
0
0
2
0
0
2
0
0
2
1
1
0
0
1
2
0
1
0
2
2
1
1
1
0
0
1
0
0
0
2
0
2
0
0
3
0
0
0
1
1
0
0
0
0
3
0
0
0
0
1
3
1
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
1
0
2
2
0
0
0
0
0
0
0
4
0
1
2
0
0
0
0
0
0
1
0
0
0
1
2
0
3
0
2
0
2
0
0
0
2
0
0
2
0
2
1
0
0
0
0
1
1
0
0
0
2
0
2
0
2
0
0
0
1
1
0
0
0
0
0
2
0
1
0
0
0
2
0
0
2
1
1
0
0
0
0
0
2
1
0
1
0
1
0
2
0
0
1
1
1
1
1
0
0
1
5
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
1
0
0
2
1
1
0
0
1
0
2
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
2
2
2
0
0
1
1
0
0
0
0
1
1
0
1
2
2
0
0
1
1
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
3
0
0
3
0
4
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
1
0
0
1
0
0
0
1
1
0
0
0
1
1
0
1
0
1
0
1
0
2
2
0
0
0
0
0
0
1
0
2
2
0
2
0
1
2
2
0
0
1
0
0
0
2
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
2
1
0
0
0
0
2
0
0
0
3
1
0
1
2
1
0
2
0
0
2
0
0
2
0
13
0
0
1
1
0
0
1
2
0
0
0
0
0
2
1
2
1
1
1
0
1
2
1
0
2
0
1
0
0
1
1
0
0
0
1
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
1
0
0
0
2
2
3
0
2
0
0
0
0
1
0
2
0
1
0
0
2
0
2
0
0
1
0
0
0
0
0
2
1
0
0
1
0
0
0
0
2
2
0
2
3
0
0
1
0
1
1
1
1
1
0
0
2
2
0
0
0
0
0
0
0
2
1
0
0
0
2
1
0
0
0
2
0
0
1
0
2
0
2
1
2
0
2
1
0
1
0
0
2
1
1
1
1
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
2
2
0
0
0
2
0
2
2
0
0
1
1
1
0
2
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
3
2
0
1
0
0
0
0
2
0
2
0
2
0
0
0
0
2
0
0
0
0
2
2
0
2
2
0
2
1
0
1
0
2
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
2
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
2
0
0
2
0
0
1
0
3
2
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
1
1
1
0
2
0
0
0
2
0
0
0
0
0
0
1
3
0
0
1
0
0
0
1
0
0
2
0
0
0
2
0
0
2
0
0
1
1
0
2
0
0
0
0
0
0
0
0
2
0
4
4
2
0
2
0
2
2
2
0
2
2
0
0
1
0
1
0
1
0
0
3
2
0
0
1
0
0
1
1
0
2
0
0
1
0
0
2
0
1
3
2
3
0
0
0
0
2
0
0
1
0
0
0
1
0
0
2
1
0
3
0
0
0
0
1
0
0
0
0
0
0
1
0
1
2
2
1
0
0
0
2
0
1
1
0
0
0
1
2
0
2
2
0
0
2
0
1
0
2
0
0
1
0
0
0
0
1
1
0
1
1
1
0
1
3
0
1
0
1
0
0
2
0
0
0
0
2
0
0
0
0
1
1
1
2
0
1
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
2
1
2
1
1
0
1
1
1
2
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
2
1
2
0
0
1
0
1
2
0
0
0
1
0
1
0
0
0
0
1
1
0
0
3
1
0
0
0
0
0
0
2
1
1
1
1
2
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
1
3
1
0
0
0
1
0
0
1
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
3
1
1
2
0
2
3
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
2
0
2
1
0
0
2
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
1
1
0
2
0
0
1
1
0
2
0
2
0
0
0
1
0
0
0
0
2
0
2
2
0
2
1
0
2
1
2
0
0
0
1
0
1
0
1
2
0
2
2
0
0
0
2
3
0
0
1
0
2
1
0
0
0
2
0
0
1
1
0
2
1
1
0
0
1
0
1
0
0
0
1
1
1
1
0
0
1
2
1
4
0
1
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
3
1
0
0
1
0
0
1
0
1
0
1
2
2
1
1
0
0
2
2
1
0
1
0
0
0
2
0
0
3
0
2
2
0
0
0
0
0
0
0
0
3
3
0
1
1
0
0
2
0
0
0
2
0
0
1
2
0
0
2
0
0
0
2
0
0
1
2
0
0
0
2
0
0
1
0
0
0
2
0
1
0
0
0
0
3
2
1
1
0
2
0
1
0
0
1
0
2
0
0
0
0
0
4
0
2
0
0
0
3
0
0
0
0
0
2
3
0
2
2
1
0
2
1
0
1
2
2
2
1
0
1
1
0
0
3
0
1
0
0
2
0
0
0
2
0
0
1
2
0
1
2
0
0
1
0
0
1
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
2
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
3
0
2
0
0
1
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
1
1
0
0
2
0
0
4
0
0
1
0
3
0
0
1
0
0
0
0
0
1
1
0
3
2
1
0
0
2
1
0
0
1
0
2
1
0
2
0
0
1
0
0
0
1
1
1
1
1
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
3
0
2
0
1
0
0
0
1
1
2
2
2
4
0
0
2
0
1
0
0
0
0
0
2
0
1
2
0
0
2
1
0
1
0
0
0
0
0
1
0
1
1
2
0
0
0
2
0
1
2
1
0
1
0
0
0
0
3
2
1
0
0
0
0
0
2
0
2
0
1
0
0
1
1
0
2
0
0
1
2
0
0
0
1
2
1
2
0
0
1
1
0
0
0
2
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
3
2
0
0
2
2
0
0
2
0
0
1
0
0
1
0
0
1
0
1
2
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
2
0
2
1
0
2
0
1
1
0
2
1
0
1
0
3
0
0
1
0
2
2
0
0
0
0
1
2
1
0
0
0
0
1
2
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
2
2
1
0
2
1
0
2
0
1
2
0
1
0
2
0
0
2
2
0
0
0
0
0
0
0
2
2
0
0
1
0
1
0
0
0
0
1
0
1
0
3
0
3
0
2
1
2
0
1
3
1
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
1
0
1
3
0
1
1
2
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
2
7
0
2
0
1
2
2
0
0
0
2
2
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
2
0
0
3
0
0
0
2
0
0
0
0
1
0
0
0
1
2
0
1
0
5
0
0
0
1
0
3
1
0
0
0
2
2
0
0
0
1
0
2
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
1
1
1
0
1
1
0
0
0
1
0
1
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
2
1
1
0
0
0
6
1
0
0
1
1
1
2
0
0
2
0
1
2
1
0
0
0
0
1
2
0
0
0
0
0
2
0
0
3
1
2
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
1
0
1
0
0
0
1
2
1
0
0
2
0
2
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
2
1
1
0
0
0
2
2
0
2
0
2
1
0
0
1
2
2
0
0
0
2
1
0
2
2
0
0
1
1
0
1
0
1
1
0
1
2
0
0
2
0
0
0
0
0
2
0
2
2
2
0
0
1
2
0
2
1
0
0
2
4
0
2
2
0
0
1
0
2
2
0
1
1
0
0
0
0
0
2
0
0
0
1
0
0
0
1
2
0
0
1
0
1
2
2
1
2
3
0
2
0
0
0
3
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
1
0
1
0
0
2
0
0
1
1
1
0
0
0
0
0
0
1
0
0
2
1
2
1
0
1
1
0
0
0
1
2
2
1
1
1
1
0
0
0
0
0
0
0
0
0
2
2
0
1
0
2
1
0
1
1
0
0
1
0
2
0
0
0
0
2
2
0
0
0
0
0
1
2
2
3
0
0
1
0
0
0
0
0
2
0
1
0
1
2
0
0
1
2
0
2
0
0
0
0
0
0
1
0
1
1
0
0
1
1
0
0
0
1
1
1
0
1
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
1
2
1
0
0
0
0
0
0
2
1
0
1
0
0
2
0
0
0
0
0
2
0
2
0
0
0
1
1
0
2
1
0
0
2
2
0
1
1
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
10
4
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
2
0
2
2
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
1
0
2
0
3
2
0
1
1
0
0
0
0
0
1
0
0
1
2
0
1
0
0
2
2
2
1
1
2
0
0
0
0
1
2
2
0
1
1
0
0
1
1
0
0
0
1
0
1
0
2
0
1
0
0
0
0
0
0
1
1
2
2
1
0
0
0
0
2
0
0
1
0
2
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
3
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
2
1
3
1
0
1
0
0
0
1
2
0
2
2
0
0
0
0
0
0
2
3
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
3
0
1
0
0
2
2
0
0
1
0
0
1
2
2
2
2
0
1
0
0
2
2
0
0
0
0
1
0
1
0
2
0
0
2
0
0
0
0
0
1
0
2
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
1
0
0
0
0
0
0
2
0
2
8
1
2
2
1
1
0
0
0
1
1
0
0
0
2
0
1
0
0
1
1
0
1
1
1
1
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
2
1
1
2
0
0
1
0
0
0
2
0
0
0
0
2
0
1
0
2
2
1
0
0
0
0
0
2
2
0
2
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
1
2
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
1
0
0
0
0
0
1
1
3
0
0
0
0
0
1
0
1
1
0
0
1
1
0
0
0
1
0
1
2
0
0
2
1
0
1
1
0
0
1
0
2
2
2
2
0
2
1
0
0
1
1
0
0
1
0
0
0
2
0
0
1
0
2
5
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
1
0
1
3
0
0
0
5
1
0
0
0
0
2
0
1
0
1
0
0
2
0
2
0
0
0
0
0
1
0
1
2
0
0
0
0
2
0
1
0
2
0
0
0
2
1
0
0
1
2
2
0
0
5
0
0
0
0
0
0
2
0
1
0
0
0
0
1
2
1
2
2
0
0
2
1
3
0
1
2
0
0
0
0
0
1
0
0
1
0
0
2
1
0
0
0
0
1
0
2
5
0
0
0
0
2
1
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
2
2
1
0
0
1
2
1
0
0
0
1
0
0
0
2
0
1
7
1
1
2
0
0
0
0
0
1
0
0
2
2
0
0
0
1
0
2
0
0
0
0
0
1
0
1
0
1
1
4
0
1
0
2
0
0
1
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
3
2
0
1
0
1
0
2
0
0
0
0
2
1
0
0
1
2
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
1
2
1
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
1
1
1
1
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
2
0
0
1
1
0
2
0
0
1
2
2
1
0
0
1
1
0
0
0
0
1
1
0
1
0
0
0
2
2
0
2
0
0
0
2
0
2
1
0
0
0
1
0
1
1
0
0
2
0
2
1
0
1
0
2
1
1
1
1
0
0
6
2
1
0
1
0
1
0
2
0
0
0
1
2
1
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
1
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
2
0
0
0
0
0
0
0
2
0
0
0
1
3
1
0
1
0
2
1
0
0
1
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
2
0
1
0
0
0
1
2
0
0
0
2
0
1
1
0
2
0
0
0
0
0
0
1
0
2
2
0
2
2
0
2
0
2
2
2
1
0
0
0
0
0
2
0
0
2
1
0
0
1
0
0
0
2
2
0
0
0
0
0
1
2
0
1
2
0
0
1
1
0
1
0
0
0
0
0
1
1
0
0
1
0
2
0
1
1
0
0
0
1
0
0
1
2
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
1
2
1
0
0
0
0
1
0
1
1
1
0
0
0
0
1
0
2
1
0
0
0
0
0
0
2
0
0
1
0
0
1
1
1
1
1
0
0
1
0
0
0
0
2
1
0
1
2
1
2
2
2
0
2
1
0
0
0
0
1
2
2
1
0
1
0
1
0
2
0
0
0
1
1
0
0
0
2
0
2
0
2
1
1
0
0
0
1
0
0
1
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
2
0
0
0
1
1
0
0
0
0
2
1
0
2
0
1
2
0
2
0
1
0
0
1
1
1
0
0
1
1
0
0
2
0
2
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
2
0
2
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
3
0
0
1
1
0
1
0
1
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
1
1
0
1
0
0
1
0
0
1
0
1
0
0
2
2
0
0
0
2
0
0
1
0
0
1
0
0
1
0
0
2
0
0
0
0
1
0
3
0
0
0
1
1
0
0
2
0
0
0
0
1
0
3
0
0
0
1
0
2
0
2
2
1
0
0
1
0
0
0
0
0
0
0
2
2
0
2
2
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
1
2
1
2
0
1
0
2
2
0
0
2
2
0
2
1
1
2
1
0
4
2
0
0
1
0
0
0
0
1
2
2
1
2
0
0
0
2
0
1
1
0
0
2
1
1
0
0
0
3
0
1
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
1
1
0
0
3
1
0
0
0
0
2
1
1
0
3
0
2
2
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
2
1
2
0
1
0
0
3
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
1
0
0
1
0
0
0
2
0
1
0
1
0
0
3
0
0
0
0
0
0
1
1
2
1
0
1
2
0
0
1
1
0
2
2
0
1
2
2
0
0
2
1
1
0
0
0
0
2
4
0
2
0
0
0
2
2
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
2
0
0
2
0
0
0
2
0
0
0
1
1
1
0
2
2
1
0
0
1
2
0
2
0
0
0
0
2
0
1
2
0
0
0
0
2
0
0
0
2
2
0
0
4
0
2
0
1
2
0
0
0
0
0
1
2
1
0
1
0
0
0
0
0
0
1
2
1
5
0
2
0
0
1
0
0
0
0
1
3
2
2
1
0
0
0
0
1
1
2
0
1
3
0
0
0
2
0
2
1
1
0
1
0
2
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
2
0
0
0
1
1
1
1
2
0
3
2
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
2
0
0
1
0
2
0
1
1
0
0
0
0
0
0
1
0
2
1
2
0
0
2
2
0
1
0
1
2
0
0
3
1
0
1
0
0
2
0
1
0
0
2
0
1
0
0
0
1
1
0
0
0
0
0
2
1
0
1
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
2
1
6
2
0
0
1
1
0
0
0
1
0
1
0
1
0
2
2
0
0
0
0
0
0
5
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
2
2
1
2
0
2
0
0
0
0
0
1
0
1
2
2
2
1
0
0
2
1
0
0
0
1
2
0
0
2
0
0
0
1
1
0
1
2
0
1
2
1
1
0
0
0
0
1
2
0
1
1
2
1
1
0
0
0
0
2
3
2
1
2
0
0
0
0
1
1
1
0
2
1
1
0
1
2
0
2
0
0
2
0
0
2
0
0
1
1
1
2
0
0
0
0
1
0
1
0
1
0
0
0
0
2
0
0
2
0
0
0
2
1
0
0
0
0
0
0
1
0
0
3
0
1
0
0
0
0
1
0
0
0
2
0
1
0
0
2
0
0
1
0
0
0
0
2
2
0
0
0
1
0
2
1
0
0
0
1
1
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
3
0
0
1
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
2
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
2
2
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
2
2
1
0
1
0
0
0
0
0
1
2
1
1
0
0
0
1
1
0
0
0
1
0
0
1
0
0
1
0
0
1
1
0
1
0
0
3
1
0
2
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
3
0
0
0
0
1
0
1
2
0
0
1
1
0
2
0
0
0
1
0
0
1
3
3
0
0
2
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
3
2
0
0
1
0
0
3
0
3
1
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
2
1
0
0
0
0
2
0
3
1
0
0
2
0
0
0
0
0
2
2
0
0
1
2
2
0
0
1
2
0
1
2
0
2
2
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
2
2
0
0
2
2
2
2
0
0
0
0
0
3
0
1
2
0
1
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
1
0
2
1
1
2
1
1
0
0
3
0
2
0
1
0
1
1
0
0
0
2
0
2
0
1
1
2
0
0
1
1
1
1
0
1
1
2
2
1
0
0
0
0
0
1
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
1
0
2
2
2
1
0
0
0
1
0
0
0
0
1
0
0
0
3
0
0
1
0
2
0
1
0
0
1
0
1
0
0
0
2
0
3
1
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
2
2
1
1
0
2
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
2
0
0
2
1
1
1
0
1
0
0
0
0
0
1
2
0
0
0
0
2
1
0
0
1
2
1
1
0
2
1
0
2
0
0
0
0
0
2
0
2
0
0
1
0
0
3
2
1
0
2
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
2
1
1
2
0
0
0
0
0
1
0
0
1
0
2
0
0
2
0
0
0
0
1
0
5
0
0
0
0
1
0
0
0
2
0
1
2
2
0
0
0
0
1
0
1
0
0
2
1
0
2
0
1
0
0
2
2
0
1
0
2
2
0
0
0
0
2
1
0
2
0
0
2
1
0
1
1
0
0
1
0
1
0
1
7
0
1
0
0
0
2
0
0
2
1
1
1
2
0
1
1
0
0
0
1
0
0
0
0
2
0
0
1
0
2
0
2
0
1
1
0
0
0
2
0
0
0
2
0
1
2
2
0
1
0
0
0
0
0
0
0
0
0
1
2
2
0
1
0
1
2
2
0
1
0
0
2
0
2
0
0
2
0
2
0
2
2
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
2
0
0
2
0
0
0
1
1
0
1
0
2
0
2
2
2
2
0
0
2
1
0
2
1
0
0
0
0
2
0
2
2
0
0
2
0
1
0
4
0
1
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
1
0
1
2
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
1
2
1
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
1
2
2
0
2
0
1
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
4
2
1
2
0
0
0
1
0
1
1
2
0
1
1
0
0
0
2
0
1
2
0
0
1
1
0
0
0
0
2
0
1
2
0
0
0
0
2
0
0
0
0
1
1
2
1
2
1
2
0
0
0
2
0
2
2
0
2
0
1
2
1
2
1
0
0
2
0
0
1
2
0
0
3
0
2
0
1
1
0
0
1
0
1
0
0
3
2
0
0
0
0
1
1
0
0
1
0
0
0
1
0
2
1
0
0
0
2
2
2
1
0
1
0
0
0
0
1
0
0
0
2
2
1
1
2
2
0
1
0
1
1
0
2
0
2
2
0
0
0
0
1
0
1
2
1
0
0
0
0
0
0
2
0
1
3
0
2
1
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
1
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
1
3
0
0
0
1
0
0
0
1
0
0
0
0
2
1
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
3
0
2
0
0
2
2
0
1
2
2
2
0
1
0
2
0
0
0
1
0
1
2
1
0
0
3
2
0
1
2
1
1
0
0
1
0
0
2
0
0
0
1
1
0
0
2
3
2
1
0
0
0
1
2
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
2
2
2
0
0
0
2
1
0
1
0
0
0
2
0
0
0
0
1
0
0
1
0
1
0
1
1
0
1
0
2
1
1
2
0
0
0
0
0
0
0
0
0
2
2
0
2
0
1
2
0
0
0
1
3
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
3
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
1
2
0
0
1
2
0
0
2
1
1
2
0
0
0
2
0
0
1
1
1
0
0
2
2
0
0
0
2
0
0
0
3
0
0
1
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
2
0
0
0
0
1
2
0
2
1
0
2
0
0
0
0
0
0
2
0
2
0
0
1
0
0
1
2
0
0
1
0
1
2
0
2
0
1
1
0
0
3
1
1
1
0
2
2
2
0
2
0
1
2
1
0
0
0
2
0
2
0
1
0
0
0
2
1
0
0
2
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
1
3
1
0
0
2
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
1
2
1
0
0
0
0
0
0
1
0
0
0
1
0
0
2
2
0
0
0
2
0
0
0
0
2
0
0
0
2
1
0
1
0
2
2
2
0
0
0
1
1
0
2
0
0
0
2
0
1
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
2
2
2
2
2
0
0
0
0
0
2
0
2
0
0
3
0
2
2
0
1
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
2
0
0
1
0
1
1
0
1
0
0
1
0
1
1
1
0
2
0
0
0
2
1
0
0
0
0
2
0
2
0
0
0
0
0
0
3
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
2
0
2
1
0
0
2
0
3
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
2
0
0
0
1
0
0
1
0
0
2
0
0
0
1
0
0
1
0
1
0
1
0
0
1
0
1
13
1
0
0
1
0
0
2
2
0
0
1
0
1
0
2
2
0
0
1
0
0
0
2
2
0
0
0
2
2
2
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
1
1
2
1
0
0
1
1
1
1
0
1
1
0
0
1
1
0
0
2
1
0
1
1
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
2
0
0
0
0
1
0
2
0
2
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
3
0
1
1
0
0
0
0
0
0
3
0
0
0
3
2
0
1
0
2
2
1
0
1
0
1
0
0
0
1
1
2
0
1
0
0
0
1
6
0
3
0
0
0
0
0
0
0
0
2
1
2
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
2
0
0
2
1
0
1
1
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
1
3
1
2
1
2
1
0
1
2
0
0
1
0
0
2
0
0
0
0
2
2
1
0
0
1
0
0
0
0
0
1
0
0
1
1
0
2
2
0
2
0
1
2
1
0
1
2
0
0
1
0
2
0
0
1
1
1
3
0
0
0
0
2
0
2
0
1
0
0
1
2
0
0
1
0
0
0
0
2
0
0
1
1
1
0
0
2
1
2
0
2
0
2
1
1
1
2
0
0
2
0
0
0
2
0
0
0
0
0
1
2
1
1
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
4
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
2
0
1
0
0
0
2
1
0
0
1
0
2
0
0
0
2
0
0
0
0
2
0
2
1
2
0
2
0
0
0
2
1
1
0
0
1
1
1
0
2
0
0
2
1
0
0
0
0
2
1
0
0
0
0
2
2
1
0
0
0
0
0
1
2
0
0
0
0
0
1
2
1
2
1
0
0
0
2
1
0
0
0
0
0
3
2
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
1
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
1
0
3
0
1
0
2
0
0
0
1
0
0
2
0
2
1
1
0
2
0
0
1
0
2
0
0
0
2
0
0
2
1
0
0
2
7
2
0
1
2
2
2
1
2
0
2
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
1
0
2
1
2
0
0
2
0
0
0
2
0
2
2
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
2
0
1
1
0
0
1
2
0
1
2
1
0
0
0
2
0
1
1
2
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
2
2
0
0
2
1
0
0
2
1
0
1
0
2
0
2
0
0
2
2
0
2
0
1
0
1
1
2
0
0
0
1
0
1
0
0
0
1
2
0
1
1
0
0
0
1
0
0
2
0
0
1
0
2
1
0
1
0
0
1
0
0
0
0
2
0
2
0
0
2
0
0
2
0
1
2
0
0
1
2
0
0
2
0
0
1
0
0
0
2
0
0
1
0
1
0
1
2
0
0
0
0
2
0
0
1
2
2
1
1
0
0
0
2
2
0
0
1
2
3
1
1
4
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
3
0
1
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
1
0
0
1
0
1
0
3
0
0
0
0
2
2
0
1
1
1
0
0
2
0
0
0
0
1
1
0
2
0
3
0
0
0
1
0
0
0
0
0
1
0
0
1
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
1
2
2
0
0
2
0
0
1
1
0
0
0
0
1
1
0
1
0
0
1
0
0
0
2
0
0
1
0
2
0
1
0
2
0
0
0
2
1
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
1
1
1
5
2
0
0
0
1
0
0
1
0
2
0
0
0
0
2
1
0
0
1
2
1
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
3
2
1
2
0
0
1
2
0
2
0
0
0
0
0
0
0
0
1
1
0
0
1
2
0
0
1
0
8
0
0
1
0
0
0
0
1
0
0
2
1
0
1
1
3
0
0
0
0
0
1
0
1
0
0
0
2
0
2
2
1
0
1
0
1
0
0
2
0
2
1
3
2
0
0
0
0
2
0
1
0
0
1
0
0
2
0
1
0
0
1
0
0
1
0
1
0
2
0
0
0
2
0
2
1
0
0
0
0
0
0
1
0
2
1
0
0
2
0
0
1
5
0
0
0
0
0
1
0
0
1
0
1
0
1
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
3
0
0
1
2
1
1
1
2
1
0
0
0
1
1
1
1
1
0
0
0
1
0
3
1
2
1
1
2
0
1
0
0
2
1
0
0
1
0
0
0
0
2
1
0
2
1
1
1
0
2
0
0
1
0
0
2
0
1
0
2
0
2
0
0
2
0
0
1
0
0
1
0
1
0
2
0
1
0
1
0
2
0
0
0
0
2
2
0
0
0
5
0
0
1
0
0
2
1
2
1
0
0
0
0
0
0
2
1
1
0
0
1
0
0
0
0
2
0
0
0
0
2
3
0
1
0
1
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
1
0
0
1
0
3
0
0
2
1
0
0
0
0
0
2
0
0
1
0
2
0
0
1
2
2
0
0
1
0
0
0
0
1
0
0
1
2
0
0
2
1
0
1
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
2
0
1
0
2
0
3
0
2
0
0
0
0
0
2
0
1
0
0
1
0
2
1
0
1
2
0
1
1
0
0
0
0
1
1
1
2
0
2
1
1
1
2
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
1
2
2
0
1
0
0
0
2
2
0
2
0
4
0
0
0
2
0
2
3
2
0
1
2
0
0
0
0
2
2
1
0
1
0
5
0
4
0
0
0
1
0
2
0
1
0
2
0
0
0
0
2
0
0
0
0
0
2
1
2
0
1
0
0
0
2
0
0
0
1
2
0
0
0
0
3
0
0
0
3
1
0
0
11
0
0
0
0
0
2
0
1
0
2
0
0
1
0
0
2
0
1
1
0
1
0
0
2
0
0
2
0
0
0
2
0
0
1
2
0
0
0
1
0
2
0
1
1
0
0
1
0
0
0
0
2
0
2
2
0
0
0
0
1
0
0
0
0
1
1
0
1
1
0
0
2
0
1
0
1
1
1
2
0
0
0
0
1
1
0
2
0
0
1
0
0
0
2
0
1
0
0
2
0
0
0
0
2
1
0
0
1
1
0
1
0
1
0
1
0
0
0
0
0
2
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
1
0
3
1
0
2
0
2
2
0
0
0
0
0
0
2
1
0
1
2
0
0
0
0
0
0
0
0
0
1
3
0
2
0
0
0
2
2
2
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
1
1
0
0
0
0
1
2
2
1
0
2
0
0
0
2
1
0
0
0
0
0
1
2
0
1
1
0
0
0
0
0
0
0
2
1
1
0
1
1
0
1
0
5
0
1
0
0
0
2
2
0
0
0
0
0
2
3
0
1
3
2
2
0
2
1
0
6
0
0
0
0
1
1
0
0
2
2
0
1
1
0
2
1
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
2
2
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
2
1
0
1
1
0
0
2
0
0
2
0
0
2
1
0
2
0
0
2
0
0
1
0
0
1
0
1
1
2
0
0
1
0
4
2
0
0
0
0
0
0
0
1
0
0
0
2
2
0
2
2
1
2
0
2
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
1
0
0
2
0
1
0
0
2
0
1
2
2
5
0
2
0
1
0
0
0
0
2
2
1
0
2
2
0
2
0
2
0
0
1
0
1
0
0
2
0
0
1
1
0
2
0
1
2
2
1
0
0
1
0
0
0
2
0
1
1
0
0
2
1
1
0
1
0
0
0
2
2
2
1
0
0
0
0
1
1
0
1
0
2
1
1
0
0
0
0
1
0
1
1
0
1
0
0
1
0
1
0
0
1
2
0
0
2
0
0
2
0
0
0
0
0
0
2
3
2
0
0
2
0
1
0
0
2
2
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
1
0
0
1
0
1
0
0
2
1
2
2
0
3
1
0
0
0
1
1
0
1
0
2
0
0
5
0
1
2
0
1
0
1
2
1
0
0
0
0
1
3
2
2
0
0
2
1
0
0
0
2
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
1
1
0
1
1
0
0
2
0
0
1
2
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
2
2
0
0
0
0
0
1
0
2
0
0
0
2
0
1
2
2
1
1
2
0
0
0
0
0
1
0
0
2
0
2
0
1
0
1
0
0
0
0
2
1
2
1
2
0
0
1
0
0
0
0
0
0
2
0
1
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
1
2
2
3
0
0
0
0
0
3
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
1
3
0
1
1
0
0
2
1
0
0
2
0
0
0
2
0
0
0
1
0
0
0
2
1
0
0
2
0
1
0
2
0
2
2
1
1
2
2
0
0
0
1
0
0
0
2
0
2
0
2
2
1
0
2
0
1
2
0
3
0
0
2
0
2
1
0
2
0
1
0
1
0
1
0
0
1
1
0
1
1
1
0
0
0
0
2
2
2
1
1
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
1
2
1
0
1
2
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
1
1
0
0
0
0
0
1
1
0
1
8
1
0
0
0
0
1
0
0
1
0
1
0
3
0
0
0
2
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
3
0
2
0
0
2
1
0
1
2
0
0
1
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
1
1
0
0
2
1
0
0
0
0
0
1
3
0
0
2
1
0
0
2
3
2
0
0
1
1
0
2
0
0
1
0
0
0
0
2
0
0
0
2
0
0
2
0
0
2
1
0
2
2
1
2
1
0
1
0
1
0
0
1
2
0
0
0
0
1
0
1
2
0
0
0
1
0
0
0
0
0
2
2
0
1
1
0
2
0
0
1
0
1
0
0
3
2
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
2
2
1
2
0
0
0
0
0
0
1
1
0
2
0
0
0
2
0
2
0
0
0
2
0
0
2
1
2
2
0
0
1
2
0
1
0
1
0
2
0
2
2
1
0
1
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
1
3
3
0
0
2
2
0
1
2
0
0
0
0
0
0
2
0
0
2
1
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
2
0
0
1
0
0
1
0
0
0
0
1
0
0
1
1
0
0
1
0
1
0
1
2
0
0
2
2
1
0
0
2
3
0
1
0
3
0
0
0
3
2
0
0
0
0
0
0
0
3
2
0
2
0
0
2
3
1
0
0
0
0
2
1
1
2
0
0
1
0
3
0
0
1
0
1
2
2
1
0
1
0
1
0
0
2
2
0
0
0
2
1
0
0
0
2
2
1
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
1
0
1
0
0
2
2
1
0
2
0
0
1
1
0
0
0
0
2
2
1
1
0
0
0
0
0
1
0
0
1
0
0
0
2
0
1
1
0
0
0
0
1
1
2
0
0
2
0
1
1
0
0
0
1
1
0
3
0
0
0
0
0
0
2
1
0
2
0
1
0
0
2
0
2
0
0
0
1
1
0
0
0
1
2
2
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
1
2
0
2
0
1
0
1
0
0
2
1
0
3
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
1
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
1
0
1
0
0
1
2
2
2
0
0
0
1
0
2
1
0
0
0
0
0
1
0
1
0
1
1
0
0
2
0
0
2
0
0
1
1
0
0
1
2
2
1
1
0
1
0
2
0
0
0
1
1
0
2
2
2
1
0
0
0
0
0
2
4
1
1
0
0
1
0
0
1
1
2
0
0
0
0
0
0
1
2
0
2
2
0
2
1
1
1
2
1
2
1
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
1
0
2
2
0
0
0
0
2
1
2
0
1
0
2
1
0
1
2
0
0
0
0
3
1
1
1
2
0
0
0
0
0
1
1
0
0
0
3
2
1
0
0
0
0
0
0
2
0
1
0
2
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
2
0
2
0
0
1
0
1
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
2
0
0
0
1
2
0
0
2
0
0
2
0
1
0
2
2
0
2
0
0
0
0
0
0
2
1
0
2
0
2
2
1
0
0
1
0
0
3
2
2
1
1
2
1
0
2
1
0
1
1
0
1
0
0
2
0
0
0
1
2
0
0
1
0
0
2
0
0
1
0
2
0
1
0
0
0
2
2
0
0
1
2
1
0
1
0
1
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
4
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
1
0
1
0
0
0
0
2
2
5
2
1
1
0
1
0
0
2
1
0
0
1
2
0
0
0
1
0
0
0
1
0
0
0
2
0
0
2
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
1
2
0
0
0
1
0
3
2
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
1
0
1
2
2
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
2
2
0
1
0
1
0
0
0
1
0
2
0
0
2
0
2
0
0
0
2
1
0
2
1
0
1
0
2
0
1
0
1
2
0
2
1
0
0
1
0
2
0
0
0
0
2
0
0
2
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
3
1
2
2
0
0
1
0
2
1
0
1
0
1
1
0
2
2
2
0
0
2
2
0
0
2
0
3
0
2
1
0
1
0
1
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
2
2
1
0
2
0
0
1
2
2
0
1
0
0
0
1
0
0
3
0
1
0
1
2
0
0
0
0
0
1
0
2
2
0
1
0
0
0
1
0
2
2
4
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
2
0
0
1
0
0
0
2
2
1
0
2
2
2
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
1
0
0
2
0
0
0
0
0
1
1
0
0
0
1
2
0
2
2
1
1
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
3
0
2
1
1
0
0
0
1
0
0
3
0
0
2
0
0
1
1
0
2
0
0
1
0
1
1
0
1
0
0
0
1
2
0
0
0
1
1
0
2
0
0
0
1
0
1
0
0
0
0
2
0
1
1
1
0
0
0
1
0
0
0
0
0
1
0
2
2
2
0
0
0
1
0
0
0
2
2
0
0
1
2
2
1
2
0
1
0
2
0
0
1
0
0
2
0
0
1
1
0
0
0
0
2
1
0
1
0
0
2
1
0
1
1
0
2
0
0
0
0
0
0
0
0
0
3
1
1
0
1
0
0
0
1
2
1
0
1
1
2
1
0
1
1
1
0
1
0
0
4
1
0
2
0
0
0
0
0
0
0
0
2
3
0
0
0
2
2
6
0
0
0
1
0
0
1
2
1
0
0
0
1
1
0
0
0
1
1
2
0
0
0
1
0
0
0
0
1
0
0
0
0
2
1
2
0
1
0
0
1
1
0
0
2
0
1
0
0
1
2
1
0
2
2
0
0
0
0
0
5
0
0
0
2
2
1
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
2
1
0
0
0
0
1
0
0
3
2
0
0
0
0
0
0
0
2
1
0
2
0
0
0
1
0
0
0
1
1
0
4
0
0
1
2
0
0
0
0
0
2
0
0
2
2
0
0
1
2
0
0
0
0
0
0
0
2
3
0
2
0
0
0
1
0
2
0
2
0
0
0
0
0
3
0
0
1
0
0
0
0
1
0
0
1
1
1
0
3
0
0
3
1
0
2
0
1
0
0
1
0
0
0
2
3
0
0
0
1
2
0
1
1
0
0
1
1
1
1
1
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
1
0
2
1
1
0
1
0
0
1
0
1
2
0
2
3
0
0
2
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
1
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
2
2
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
3
3
1
1
0
0
0
2
1
1
2
1
0
0
2
0
0
1
0
2
1
2
0
0
1
0
0
0
1
0
1
1
2
1
0
0
1
0
0
0
0
2
0
2
0
2
0
1
2
1
1
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
1
2
0
1
1
0
1
0
4
2
1
1
2
1
0
3
1
0
1
1
0
0
2
0
0
0
0
0
0
1
2
0
0
0
1
2
2
0
1
1
2
1
0
1
1
0
0
0
0
0
0
0
1
1
0
1
1
2
0
0
1
0
2
1
1
0
0
0
0
1
0
0
2
0
2
1
0
2
0
0
2
2
0
1
0
2
2
1
2
0
2
0
1
0
0
0
0
1
0
0
1
1
2
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
1
2
0
0
0
0
2
0
2
0
0
2
1
0
2
0
0
2
0
1
2
0
0
0
2
2
2
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
1
0
1
0
0
0
0
0
0
2
0
0
2
0
1
0
1
0
0
0
1
0
2
0
0
2
0
1
0
0
2
3
0
1
1
0
0
4
0
1
2
0
2
0
0
0
0
1
0
1
0
0
0
2
0
0
2
2
0
0
0
0
2
0
2
1
2
2
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
2
2
1
1
0
0
4
0
0
0
0
0
0
0
0
1
0
2
0
2
1
2
1
0
0
0
3
0
0
0
1
1
2
0
0
0
0
0
0
1
3
0
1
1
1
0
1
2
0
3
0
0
0
1
0
0
0
2
1
2
0
0
1
2
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
2
2
1
0
0
0
0
1
2
1
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
1
1
0
0
1
1
2
0
1
1
0
1
0
1
0
0
0
0
3
1
0
1
0
0
2
0
0
0
2
2
0
1
0
0
1
0
2
0
1
0
2
0
1
0
0
0
0
2
1
2
1
1
0
0
0
0
0
0
0
0
1
2
1
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
2
2
0
0
0
3
1
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
2
3
1
0
1
1
2
0
1
0
1
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
2
1
1
0
0
0
2
1
1
1
0
0
0
0
2
0
1
0
1
2
1
0
0
0
0
0
2
1
0
0
0
0
0
2
0
1
0
0
2
3
2
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
2
1
0
1
0
1
0
0
1
0
0
2
0
0
0
0
0
0
2
0
1
0
1
0
1
0
0
0
2
0
0
0
0
2
0
2
0
1
0
1
1
0
0
0
0
0
2
0
1
1
1
0
1
0
1
0
0
0
0
0
2
0
2
0
0
2
1
2
1
1
0
1
2
1
2
2
3
1
1
0
1
0
1
1
0
0
0
0
2
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
1
0
0
0
0
0
2
1
1
0
0
0
2
1
1
0
0
2
4
0
3
0
2
0
0
0
0
0
0
1
1
0
2
0
1
2
0
0
0
0
0
2
1
0
0
0
1
0
1
1
4
0
1
1
0
1
2
1
0
2
1
0
0
2
1
0
1
1
2
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
3
0
0
0
0
0
0
0
0
1
0
0
1
0
1
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
2
1
0
0
2
0
0
1
0
1
0
0
1
2
1
0
1
0
0
0
0
0
1
2
2
1
0
1
1
2
1
0
2
0
0
1
0
0
2
0
0
0
2
0
1
0
2
0
1
2
2
0
1
2
0
0
2
0
2
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
1
0
1
2
0
0
1
2
0
0
1
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
1
2
0
0
0
0
0
1
0
0
3
2
0
0
1
2
1
0
0
0
0
1
1
0
1
1
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
1
0
1
0
2
0
0
0
0
0
0
0
0
1
1
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
1
0
2
0
1
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
2
0
0
1
0
2
0
2
0
2
1
0
0
0
2
1
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
2
1
2
1
0
1
2
1
2
0
0
0
0
2
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
2
0
0
0
0
2
0
0
0
3
0
0
0
0
0
1
2
0
1
1
0
0
2
0
3
1
0
0
0
0
0
2
1
0
0
0
1
1
0
2
2
2
1
0
1
1
0
0
2
1
2
0
2
0
4
0
0
0
3
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
3
0
1
0
0
0
0
0
0
0
0
2
1
1
0
0
0
2
0
1
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
2
1
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
3
0
1
1
1
2
2
0
1
3
0
1
0
1
1
0
1
0
1
1
1
1
0
2
1
0
0
0
1
1
1
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
1
2
0
0
0
2
0
0
1
0
0
0
0
3
0
1
1
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
1
0
0
1
0
2
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
1
1
2
0
0
0
1
0
1
0
1
0
0
0
0
0
2
0
1
0
1
0
0
0
0
2
0
1
0
0
0
0
1
0
2
0
2
1
0
0
0
0
0
0
0
1
1
0
0
0
0
2
2
0
1
0
0
0
0
0
0
2
2
0
0
1
1
0
1
0
1
2
0
0
0
1
0
1
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
2
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
1
0
0
0
0
1
2
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
1
0
0
2
0
1
0
1
1
2
0
2
0
0
2
0
1
0
1
1
0
0
1
0
1
0
2
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
1
2
0
1
0
0
0
2
0
0
0
1
2
0
0
0
0
1
1
2
0
0
1
0
0
1
0
1
2
0
0
0
0
1
0
0
1
1
0
2
0
0
1
2
0
1
0
0
0
1
2
0
0
0
1
0
0
0
2
0
0
2
1
0
1
0
0
0
1
1
2
0
2
0
1
0
0
2
0
1
0
1
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
1
0
0
1
0
1
1
2
2
1
2
0
1
0
0
2
0
2
0
1
1
2
0
2
2
0
2
0
1
1
2
3
1
0
1
0
2
0
1
1
0
0
0
0
1
0
1
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
1
1
0
1
1
2
0
2
0
0
0
0
2
0
0
1
0
2
1
0
0
1
0
0
2
2
0
2
1
0
0
2
0
0
1
2
2
0
0
0
2
1
0
0
1
1
0
0
1
0
2
1
0
1
1
2
0
0
2
0
1
2
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
3
0
1
2
1
0
0
1
0
0
1
1
0
0
2
0
0
1
0
0
2
0
0
0
1
2
1
0
0
0
1
0
0
0
1
2
2
0
2
1
0
2
0
0
0
2
1
1
0
1
4
2
2
1
0
2
1
1
0
0
1
1
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
1
1
0
1
2
1
1
0
0
0
1
0
2
2
0
1
0
2
1
1
0
2
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
1
2
1
0
0
0
1
1
0
0
0
0
1
0
2
2
1
0
2
2
0
4
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
1
2
1
0
0
4
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
1
0
2
1
1
1
1
0
1
2
2
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
2
0
1
0
0
0
2
1
0
0
0
0
1
0
1
0
1
2
2
0
0
3
0
2
2
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
4
0
2
0
0
2
0
0
0
2
1
0
1
0
0
5
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
1
1
0
1
0
2
0
2
1
0
0
0
2
1
1
0
2
0
0
0
0
1
0
1
0
1
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
2
0
3
2
1
0
2
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
1
1
2
0
0
0
2
0
0
0
2
0
1
0
1
2
0
0
0
2
2
0
0
2
0
0
0
0
1
0
1
0
0
0
0
1
2
0
0
0
2
0
2
0
1
2
0
0
0
2
0
0
1
0
1
1
1
0
0
1
1
0
1
0
0
1
2
0
2
0
1
0
2
0
4
0
2
0
0
2
1
0
2
0
0
0
1
0
0
0
1
1
0
0
2
1
2
0
0
2
0
0
0
1
2
1
0
0
0
0
1
1
0
2
0
0
2
2
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
1
1
0
1
0
0
2
0
0
2
1
2
0
0
0
0
0
0
0
2
0
0
0
1
1
1
2
0
0
0
0
1
1
0
0
2
0
2
0
0
0
2
0
0
2
1
2
0
1
0
2
2
1
0
1
0
1
1
0
1
0
2
0
0
1
2
1
0
0
0
0
1
1
2
0
0
2
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
1
0
1
0
1
0
2
2
2
0
1
0
0
1
1
0
0
0
1
0
1
0
1
0
1
0
0
3
0
0
0
2
0
0
1
0
2
0
3
0
0
1
0
0
1
3
0
0
1
1
1
0
1
0
1
0
2
1
2
0
2
2
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
1
1
0
1
2
0
0
1
0
0
2
0
0
0
0
0
1
1
2
0
0
0
0
0
2
0
1
2
2
0
0
1
2
0
1
0
2
0
0
2
0
1
2
1
0
0
0
0
1
0
0
2
0
0
2
0
0
0
1
0
2
1
0
0
1
0
0
0
0
0
0
0
2
2
2
1
1
2
0
0
1
0
0
0
0
0
0
1
2
1
0
1
1
0
0
1
1
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
1
2
0
1
2
0
0
0
2
0
2
2
5
2
0
2
0
2
2
2
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
1
0
0
1
1
2
1
0
1
0
1
0
0
0
0
0
0
2
0
1
0
2
0
0
2
0
1
0
0
0
0
1
2
0
1
0
0
0
0
1
0
0
0
1
2
2
0
0
2
2
1
4
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
2
0
1
0
1
0
1
1
0
1
0
0
0
2
0
0
0
2
1
0
2
0
1
1
2
2
0
0
2
0
0
1
0
0
0
2
0
2
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
1
2
0
1
1
1
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
2
1
2
1
2
3
2
0
0
1
2
0
0
0
0
0
1
0
4
1
1
2
0
0
0
1
0
0
0
0
1
0
2
1
0
0
2
0
0
0
1
1
3
0
2
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
1
0
3
0
2
0
2
1
0
2
0
0
2
4
2
0
0
0
1
0
1
1
3
0
0
0
0
0
0
0
0
2
2
1
0
0
2
1
0
0
3
1
1
0
0
0
0
2
0
0
1
0
0
2
0
1
1
0
1
0
1
1
0
1
1
0
2
2
0
0
0
1
0
0
0
0
2
2
1
0
0
0
0
1
0
0
0
2
1
0
0
1
0
1
0
1
0
0
1
2
0
3
0
0
2
1
0
1
0
0
2
0
0
1
0
1
4
0
0
1
0
2
0
0
1
1
0
2
1
1
2
0
2
0
0
0
0
0
0
0
1
0
0
3
1
2
0
1
0
0
0
1
1
1
0
0
0
0
2
2
0
0
2
1
2
0
2
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
1
0
2
1
2
0
1
0
3
1
0
0
0
1
0
0
0
2
0
1
1
0
0
0
0
2
0
1
1
0
1
1
1
1
0
1
0
4
0
0
0
2
1
0
2
1
0
3
2
2
0
0
2
0
4
1
0
1
0
0
0
0
0
1
2
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
1
0
1
0
0
2
0
2
0
2
2
0
0
1
0
0
0
0
0
2
1
1
1
1
1
0
0
0
0
1
0
2
0
0
1
1
0
2
2
3
2
0
0
2
0
0
2
1
0
0
2
1
1
1
0
1
1
2
2
2
2
2
0
1
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
2
1
1
2
0
2
0
1
0
1
1
3
0
2
4
1
2
1
0
0
2
0
1
0
0
0
0
0
1
1
1
0
0
2
0
0
1
0
0
0
2
0
2
0
0
0
2
2
0
3
0
6
0
1
1
0
0
0
0
2
2
1
0
0
0
2
0
0
2
0
2
2
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
4
0
2
3
0
2
0
0
0
2
1
0
0
0
0
2
0
1
0
2
0
0
0
0
1
1
1
3
0
1
1
2
1
0
0
0
0
0
1
0
0
1
0
2
0
0
2
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
1
1
0
3
0
0
0
4
0
1
0
0
1
0
1
0
0
0
1
0
1
3
0
1
0
2
0
0
0
1
0
0
0
0
0
0
2
1
2
1
0
0
1
0
0
0
3
3
0
1
0
0
2
0
0
1
0
0
1
2
0
2
1
0
1
0
0
0
3
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
2
1
2
1
0
1
0
0
0
1
0
0
0
2
1
0
1
0
0
1
0
1
0
0
0
0
1
1
2
0
2
2
0
0
2
0
0
2
0
1
0
1
0
0
0
1
0
1
2
1
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
1
1
0
0
0
2
0
0
2
0
0
0
0
0
2
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
2
0
7
0
0
0
0
0
0
7
0
1
0
0
3
0
1
0
0
0
2
0
0
1
1
0
0
0
3
0
2
0
0
1
0
0
2
0
0
0
0
1
0
2
2
2
2
3
0
0
0
0
0
0
1
1
0
1
0
1
0
0
1
0
0
0
2
0
0
1
1
2
0
0
2
3
0
1
0
0
0
0
0
0
1
0
2
0
0
0
2
1
0
1
0
0
0
11
0
0
2
0
2
0
1
0
2
0
0
1
2
2
0
0
1
1
0
1
0
0
0
2
0
2
1
0
0
0
1
1
1
0
0
0
0
0
0
1
6
5
1
0
0
1
0
0
2
0
0
0
2
0
1
0
0
2
1
0
0
0
0
2
0
1
0
0
0
0
2
0
0
7
0
1
0
0
1
0
0
0
0
0
1
0
2
0
1
0
0
0
1
0
1
0
0
0
0
2
0
0
1
0
1
1
1
2
0
0
1
0
0
2
3
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
1
0
1
0
0
2
0
1
1
1
0
0
2
1
0
1
2
3
0
0
0
0
0
2
2
0
1
0
1
1
1
1
0
2
0
1
0
0
0
0
2
1
0
0
2
2
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
2
1
0
0
0
0
1
2
1
0
1
0
0
0
1
3
0
0
1
0
0
2
0
0
1
1
1
1
1
2
1
1
3
0
1
0
7
0
0
0
1
0
0
0
2
1
2
0
0
0
0
2
0
0
2
0
2
0
0
0
1
0
2
0
1
2
0
2
0
3
0
0
1
0
2
3
2
1
3
1
0
2
2
2
2
0
0
0
0
0
1
1
1
2
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
2
0
1
2
0
1
4
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
3
0
2
1
2
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
2
1
0
0
1
1
1
0
0
2
2
2
0
0
0
1
1
1
2
1
0
0
0
0
1
0
1
0
0
1
0
2
0
0
2
0
1
0
0
1
2
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
1
1
0
0
0
0
0
0
2
3
0
0
1
0
0
0
0
2
0
0
1
0
0
2
1
1
0
2
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
2
1
2
1
0
0
0
2
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
1
0
2
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
2
2
0
0
0
1
0
0
1
1
0
1
0
1
0
0
1
0
1
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
1
2
1
2
1
1
1
4
0
1
2
0
0
0
2
0
3
0
0
2
1
2
1
1
0
0
2
1
4
0
1
2
1
2
1
1
1
0
0
1
0
0
0
1
0
1
0
1
0
0
3
1
0
5
0
2
2
2
0
0
0
1
0
0
0
0
2
1
3
1
0
0
1
0
2
1
0
0
1
0
0
0
2
2
1
0
0
0
1
0
0
1
0
1
0
0
2
2
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
2
0
1
0
0
1
1
2
3
0
0
0
1
0
1
0
0
2
0
0
0
0
1
1
0
0
2
0
0
1
0
2
0
1
0
2
2
0
0
0
0
1
2
2
3
2
0
1
0
1
1
0
1
0
0
0
2
1
2
0
0
0
6
0
1
0
0
0
0
4
0
0
0
0
0
2
1
2
1
0
0
1
0
0
0
1
0
0
2
0
2
0
0
0
1
1
0
2
0
0
1
0
0
0
1
0
0
6
0
0
2
2
0
0
0
0
0
2
1
0
0
0
2
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
1
1
0
1
2
0
2
1
4
0
3
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
3
0
0
2
0
1
0
1
2
0
1
0
0
0
1
0
0
1
0
2
0
0
1
0
0
0
2
0
2
0
0
2
0
2
0
0
0
0
1
0
0
1
0
0
0
1
2
0
1
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
2
2
2
0
0
0
0
1
1
0
0
0
1
0
1
0
0
2
1
0
1
2
0
2
0
2
0
2
0
0
0
1
0
1
0
1
1
0
1
1
1
0
0
0
0
2
1
0
0
0
0
0
2
0
1
0
2
2
0
0
0
0
0
0
2
1
0
0
1
2
2
0
0
0
0
0
0
0
1
3
1
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
2
1
0
0
1
0
2
0
0
0
2
0
0
0
0
1
2
2
2
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
2
0
0
1
0
1
0
1
0
2
0
1
0
2
0
0
0
0
1
2
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
2
0
1
1
0
0
0
1
0
1
0
1
0
1
2
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
1
0
0
0
2
2
3
0
0
2
1
0
2
2
0
2
0
0
3
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
1
1
2
1
2
1
0
0
0
0
0
0
0
5
0
1
0
0
0
1
0
2
2
1
2
1
0
0
0
1
0
0
0
2
3
2
0
1
0
0
0
0
0
0
0
0
2
6
0
0
1
1
0
1
3
0
0
2
1
0
0
0
1
1
0
0
2
2
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
1
0
0
0
1
2
1
0
0
0
0
1
0
0
0
0
1
0
0
1
3
0
0
0
1
1
1
3
2
2
1
0
0
0
2
0
0
1
0
1
0
0
1
0
2
0
1
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
2
1
2
1
0
1
0
0
0
2
0
0
0
0
0
1
0
0
1
1
1
0
2
1
1
2
0
0
0
0
1
2
1
0
1
0
0
1
1
0
0
1
0
1
2
1
0
1
2
1
0
0
2
1
0
3
0
2
0
1
0
0
2
0
0
0
2
1
2
0
0
0
1
0
1
0
1
1
0
0
0
2
0
0
0
1
1
2
0
0
1
0
0
1
0
0
1
1
1
0
2
0
1
0
1
0
1
1
0
0
1
2
0
2
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
1
2
1
0
0
0
0
0
0
0
0
2
0
0
1
0
1
2
0
2
0
0
0
4
1
0
0
2
1
0
0
1
2
0
0
3
1
0
2
0
2
0
0
2
0
0
0
0
3
0
1
1
0
2
1
1
2
1
1
1
0
1
1
2
0
0
1
0
0
4
0
0
2
2
0
0
0
0
1
1
0
1
2
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
2
0
0
3
1
0
0
2
2
0
0
1
0
2
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
2
1
2
2
0
1
1
0
0
4
1
0
2
2
1
3
0
1
2
0
0
2
0
2
2
1
1
2
1
1
1
0
1
1
0
0
0
1
0
2
0
0
1
0
2
0
0
2
0
0
0
2
1
1
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
2
1
1
1
2
0
2
1
0
0
1
0
0
0
0
3
0
3
2
1
2
0
0
0
1
0
0
2
3
0
2
0
0
1
1
0
2
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
1
0
1
0
0
0
0
0
1
2
0
0
2
2
0
0
0
1
0
0
0
0
1
0
0
6
0
0
2
0
3
0
1
0
0
0
0
1
0
0
0
0
2
2
0
1
2
0
0
0
0
0
0
1
0
2
1
0
2
1
0
1
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
3
0
0
1
0
0
2
0
0
2
1
1
1
1
0
1
0
1
1
0
0
2
0
0
0
0
1
0
2
0
0
1
1
1
0
0
2
0
1
0
2
0
4
0
0
1
1
0
0
0
2
0
1
1
2
0
0
0
0
0
2
1
0
2
0
0
0
1
0
0
0
0
1
0
2
0
1
0
1
0
1
0
1
2
0
0
0
0
1
2
0
0
1
0
2
1
0
1
0
0
0
1
0
0
2
1
2
1
2
0
0
1
0
0
0
0
3
0
0
4
0
2
0
0
1
0
0
0
2
0
0
0
0
1
0
2
1
2
0
0
1
1
2
0
0
2
0
1
2
1
0
1
0
0
0
2
2
0
0
0
2
0
1
0
2
0
2
0
1
2
0
1
0
0
0
2
0
1
2
0
0
0
0
0
3
1
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
1
2
0
2
0
2
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
2
0
0
1
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
5
2
0
0
3
0
0
0
0
0
0
2
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
2
1
0
2
3
0
0
2
0
0
2
0
1
1
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
2
0
3
0
2
0
0
0
0
0
0
0
0
0
5
0
0
1
0
0
2
0
0
9
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
2
1
0
1
0
0
1
0
0
2
0
3
1
0
0
0
0
1
0
0
0
1
0
2
0
1
2
2
2
1
0
0
1
1
0
0
0
0
0
5
0
0
1
0
0
0
2
1
0
1
1
0
0
3
0
0
0
0
1
1
1
1
0
0
1
0
0
1
0
0
0
1
0
0
2
0
0
2
0
0
2
0
2
0
1
0
1
1
0
3
1
0
2
2
0
0
2
2
2
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
1
1
2
1
0
0
0
0
0
2
0
1
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
2
1
3
2
4
0
1
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
1
0
1
0
2
1
0
0
0
0
0
0
0
0
2
1
0
1
2
5
1
2
2
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
1
0
1
0
0
2
1
0
1
0
0
0
2
0
0
0
0
0
2
0
0
1
3
0
0
2
1
1
0
1
0
2
0
0
2
2
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
1
0
2
0
1
2
1
0
0
1
1
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
2
0
0
0
0
1
2
0
1
0
2
3
0
2
0
1
0
2
0
0
2
0
0
3
0
0
1
0
0
2
0
0
0
0
1
0
0
2
1
0
1
0
0
1
2
2
2
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
1
0
1
2
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
1
1
0
0
0
0
1
0
0
1
1
4
0
0
0
0
1
2
3
0
1
0
2
3
2
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
2
1
0
0
0
2
2
1
0
2
0
0
0
1
0
2
0
1
0
0
1
0
0
0
0
2
0
0
2
1
1
1
1
0
0
0
2
1
2
0
2
0
0
0
0
0
1
0
2
0
2
0
0
0
2
0
1
0
1
0
0
2
4
0
2
0
1
2
0
1
0
0
3
2
0
0
1
0
0
0
3
0
1
0
1
1
1
0
1
0
3
2
0
0
0
1
1
1
0
0
1
0
0
0
0
2
1
0
0
0
2
0
1
2
0
0
0
1
0
2
0
0
0
0
0
3
1
0
0
0
0
0
2
2
0
0
0
2
3
0
0
0
0
2
0
0
1
1
0
2
1
0
0
0
0
1
1
0
0
0
4
0
1
0
2
1
0
1
0
0
0
0
0
2
0
0
1
0
0
1
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
2
2
0
0
1
0
0
2
2
0
1
1
2
0
0
2
0
0
1
0
2
0
0
1
0
0
1
0
0
1
0
0
0
0
2
0
0
2
0
3
0
0
0
1
0
1
3
0
0
0
0
2
0
1
0
0
0
1
1
2
3
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
1
1
0
0
0
0
1
2
0
2
2
1
0
0
1
0
0
0
1
0
1
1
2
0
1
1
1
0
0
0
5
0
2
0
0
0
0
0
1
0
1
0
1
2
0
1
0
2
1
0
1
0
1
0
1
1
0
0
0
1
1
1
2
0
1
1
0
0
0
0
2
1
2
2
0
1
2
0
1
0
2
0
2
1
0
1
0
0
1
0
0
1
0
2
1
0
0
1
0
0
2
0
0
0
0
0
0
2
2
0
0
2
1
2
0
2
0
2
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
3
0
0
1
0
1
0
0
1
0
0
0
0
6
2
0
0
0
0
1
1
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
1
2
2
2
2
0
0
1
0
0
0
0
1
1
0
1
0
0
2
2
2
0
0
1
2
0
0
0
1
1
0
2
2
0
1
0
0
1
1
2
2
1
0
1
2
2
0
1
0
0
0
2
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
1
3
0
0
0
2
0
0
0
1
0
2
2
0
3
1
0
0
0
0
0
1
1
0
0
2
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
2
0
0
0
0
0
1
0
1
2
0
2
1
2
0
0
1
0
2
0
0
0
1
0
2
4
0
0
0
2
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
1
0
1
0
0
0
0
0
1
0
1
1
1
0
0
0
1
1
1
0
2
0
2
0
2
2
0
1
4
0
2
0
2
0
0
2
0
0
2
0
1
2
1
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
1
2
0
4
0
0
1
0
2
1
0
0
0
0
2
0
0
0
0
0
1
2
0
2
0
2
0
1
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
2
0
2
0
1
2
1
1
1
0
1
0
1
0
1
2
1
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
3
0
0
0
0
1
0
0
1
2
1
0
0
1
0
2
0
2
1
0
0
1
5
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
1
2
1
0
2
0
0
0
0
0
1
1
1
1
1
0
0
0
0
2
0
0
1
2
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
2
0
2
0
0
6
0
1
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
2
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
3
0
0
2
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
2
1
0
2
0
0
1
1
0
2
2
0
0
1
0
0
1
1
0
0
0
0
0
0
1
2
1
0
1
0
2
3
3
5
0
1
2
0
0
0
2
0
0
0
1
0
0
1
0
0
0
1
0
0
2
0
0
0
0
2
0
2
2
0
0
0
0
1
0
0
2
0
2
0
1
4
0
1
1
4
0
0
0
0
0
0
1
3
0
0
1
2
2
0
2
1
0
2
2
0
0
1
0
0
1
2
0
2
0
1
0
0
0
0
0
1
0
0
0
2
2
0
2
0
0
0
1
0
1
1
1
1
1
0
0
2
0
2
2
0
0
0
1
2
0
0
1
0
0
0
0
2
0
1
0
2
0
2
1
1
0
1
0
2
3
0
1
0
2
1
1
0
0
0
0
2
0
1
0
2
0
3
0
0
0
1
1
0
0
0
1
1
1
0
0
0
2
1
0
1
0
0
1
0
0
0
1
1
1
0
3
1
1
2
1
0
0
1
0
0
1
1
0
0
1
1
1
0
0
0
0
0
0
0
1
2
1
1
0
0
1
1
0
0
0
1
1
0
2
0
1
1
0
1
0
0
1
3
1
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
2
1
0
2
2
0
2
0
0
0
0
2
2
0
1
1
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
2
0
1
1
0
0
1
0
0
0
0
0
1
0
2
0
1
2
0
1
3
0
0
0
0
2
0
1
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
1
2
0
0
0
0
0
0
2
4
2
0
0
1
0
2
1
1
0
0
2
1
3
0
1
0
0
5
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
2
1
1
1
0
1
2
1
0
1
0
0
1
0
0
1
0
0
2
0
0
1
2
0
0
1
0
1
1
0
1
2
0
0
0
0
2
0
0
2
0
0
0
0
2
2
0
4
0
0
0
2
0
0
0
0
1
2
0
0
0
0
1
0
1
1
0
0
1
1
0
2
0
0
0
1
2
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
2
0
0
0
1
1
2
0
0
1
0
0
1
2
0
0
0
0
2
1
0
3
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
1
0
3
2
1
1
2
0
0
0
0
2
1
0
0
0
2
3
2
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
1
1
0
0
3
1
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
1
0
0
2
0
2
1
0
0
0
0
2
1
0
1
0
0
1
1
1
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
2
2
0
2
1
3
0
2
1
0
2
0
0
2
0
0
1
0
0
0
0
1
4
0
0
1
2
1
0
0
0
2
0
1
2
1
0
0
0
0
0
2
1
1
2
1
2
1
2
0
2
1
0
0
0
0
1
2
2
0
2
0
0
0
7
0
0
1
2
1
0
0
0
1
2
0
0
2
1
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
1
1
0
2
1
0
2
0
2
1
0
0
0
1
2
0
1
0
1
0
0
2
1
0
2
1
0
1
0
0
2
2
2
0
1
1
1
0
1
1
2
0
0
0
0
0
1
3
0
1
1
2
2
1
0
0
0
0
2
2
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
3
2
1
0
1
0
0
0
0
1
2
0
1
1
1
2
1
0
1
0
1
0
1
1
0
0
0
0
3
0
0
1
2
3
1
2
0
0
0
1
0
1
0
2
0
0
1
0
0
2
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
1
2
0
0
2
0
0
0
0
1
0
0
0
2
0
2
1
2
0
0
0
0
0
2
0
2
0
0
0
0
2
1
0
2
0
0
0
2
0
0
0
1
0
0
2
0
0
0
1
2
0
0
0
1
0
0
1
0
2
1
2
1
1
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
2
0
0
1
1
0
0
2
0
0
0
3
0
3
0
0
1
0
0
0
1
1
0
1
3
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
3
1
1
0
2
0
0
3
2
0
0
2
0
0
2
2
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
2
2
0
2
0
0
0
3
2
0
2
0
0
1
3
2
0
0
0
1
2
2
2
0
0
0
4
0
0
0
1
1
0
0
1
0
2
1
1
0
1
2
0
1
0
0
0
0
2
0
0
0
1
0
2
0
1
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
1
1
2
0
1
0
0
1
2
1
0
0
1
2
0
2
0
0
1
1
1
0
2
1
0
2
0
0
1
2
1
0
0
0
1
0
0
0
4
0
0
2
0
0
2
1
0
0
0
4
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
1
1
0
2
1
2
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
2
5
0
2
0
1
0
0
2
1
0
2
0
0
0
1
2
1
0
2
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
2
2
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
2
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
2
1
2
2
0
2
0
0
0
2
0
0
0
0
2
1
0
0
0
1
1
0
2
0
0
0
2
4
0
0
1
0
1
0
1
0
2
0
1
0
0
0
0
1
2
0
0
0
0
1
2
1
2
0
0
0
2
2
0
0
0
0
0
1
0
0
1
0
1
0
2
1
2
0
1
0
1
0
1
1
0
0
1
1
0
0
0
0
1
1
0
0
2
0
0
0
0
2
2
0
1
2
0
0
0
0
2
0
1
0
0
1
0
0
1
0
0
2
0
1
0
3
0
2
0
0
1
0
1
0
0
0
1
2
0
2
0
1
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
1
0
2
3
0
0
0
0
1
2
0
0
0
0
0
2
2
0
0
1
2
0
1
0
0
1
0
2
0
2
1
0
2
1
0
0
0
2
0
3
0
2
0
1
0
0
2
0
1
2
1
0
0
1
0
0
1
0
0
1
0
1
0
0
0
2
1
0
1
0
0
4
0
0
0
1
1
0
0
1
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
6
1
0
2
0
1
0
2
0
0
0
1
1
0
0
5
0
0
0
3
1
0
0
2
0
2
0
0
1
2
1
0
2
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
2
0
0
0
0
0
1
1
1
0
3
1
0
0
1
0
0
0
0
0
3
0
2
0
2
0
0
0
0
0
2
0
0
2
1
0
0
2
0
0
0
0
0
0
0
2
1
0
1
2
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
1
0
1
0
2
0
0
2
0
2
0
0
3
2
0
2
1
2
1
1
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
1
0
1
2
0
1
3
0
0
0
0
1
1
2
0
3
2
0
0
0
2
0
0
0
1
0
0
0
2
1
0
1
0
0
0
0
1
1
1
0
0
0
0
1
1
0
0
1
2
0
1
1
0
1
1
1
0
2
0
1
2
0
0
0
1
1
0
0
2
0
0
0
1
2
0
1
1
1
2
0
0
0
0
1
0
1
1
0
2
0
0
0
0
2
0
0
0
0
0
0
1
2
0
4
0
0
1
2
1
0
0
2
2
0
0
0
0
0
1
0
0
1
0
2
0
0
0
2
0
1
1
1
0
0
2
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
2
1
1
1
2
2
0
0
0
1
0
1
1
0
0
1
0
0
2
0
0
1
2
0
0
0
0
2
1
0
3
0
2
1
0
0
2
0
0
3
0
0
0
0
0
0
0
1
0
2
0
0
2
1
0
1
0
0
0
1
0
2
1
0
2
0
0
0
0
1
2
0
0
3
0
0
2
1
0
0
2
0
0
0
1
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
2
0
1
1
0
0
0
0
1
1
1
1
0
0
1
0
1
0
1
0
1
0
1
0
1
0
2
2
1
0
1
1
0
0
2
1
2
2
0
2
0
1
1
0
0
0
0
2
0
0
0
0
1
0
1
0
3
1
0
2
0
1
0
3
0
2
0
0
0
1
1
0
0
1
1
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
3
0
2
2
0
0
0
1
0
0
0
2
0
0
1
0
1
1
0
2
0
0
2
1
0
0
0
0
0
2
2
0
0
1
0
1
0
4
1
1
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
2
2
0
1
0
2
0
0
0
0
1
0
0
1
2
1
0
0
0
2
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
2
0
1
2
0
2
1
0
0
0
1
1
1
2
0
2
0
0
1
0
0
0
0
0
0
2
1
0
2
0
0
0
1
2
1
0
0
0
0
1
1
1
0
2
2
0
1
1
1
0
0
1
2
1
0
1
2
0
0
1
0
0
0
0
3
0
0
0
0
0
0
2
2
0
0
0
2
2
0
1
2
2
0
2
0
0
1
0
1
1
0
2
2
0
2
0
2
0
2
0
0
2
0
0
2
1
0
0
0
3
0
0
1
2
0
0
1
0
1
0
0
0
2
0
1
0
1
0
0
0
0
0
0
1
0
0
2
1
0
2
5
0
0
0
2
0
1
0
0
2
2
1
0
0
0
0
1
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
2
2
0
2
1
2
0
2
1
2
0
2
0
2
2
1
0
4
2
2
2
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
1
1
0
2
1
0
0
1
0
0
1
0
2
2
0
2
0
1
0
5
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
1
2
1
0
3
0
1
0
1
0
0
2
1
0
0
1
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
2
4
0
5
0
2
2
1
1
1
1
0
0
0
0
1
0
3
0
1
3
0
0
1
0
2
0
0
1
6
1
0
0
1
0
0
1
2
1
2
0
1
2
1
0
1
0
2
1
0
5
0
0
0
0
2
0
1
1
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
2
2
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
2
2
0
0
0
1
0
4
0
0
2
0
0
1
5
1
0
1
1
0
2
0
2
0
1
0
1
0
2
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
2
3
1
0
0
0
2
0
0
0
1
0
1
2
0
0
0
1
0
0
0
1
3
2
0
1
0
0
0
0
1
0
1
0
1
0
5
0
0
2
1
0
1
1
0
0
0
1
2
0
1
0
0
0
2
2
1
0
1
1
0
0
2
1
0
0
0
0
0
0
0
1
0
2
1
2
1
0
0
2
0
1
0
1
0
1
0
0
2
0
2
1
1
0
0
2
0
0
0
0
1
0
1
1
1
1
0
2
1
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
2
2
2
0
0
0
0
2
2
0
1
1
1
0
2
0
0
0
1
0
0
0
0
2
2
1
5
0
0
0
1
1
1
0
1
0
4
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
2
0
0
0
2
0
1
0
1
0
0
0
1
2
0
1
0
2
1
0
2
1
0
1
2
0
1
0
0
2
1
0
0
0
0
1
1
0
1
1
2
4
2
0
0
2
0
1
0
0
0
2
2
2
0
0
2
1
2
0
0
0
2
0
0
2
2
0
2
2
0
0
2
2
1
2
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
3
0
2
0
2
0
0
1
0
0
0
2
3
0
0
0
0
2
2
0
0
0
1
0
2
0
1
0
0
1
1
1
0
0
2
0
1
0
0
1
0
2
0
0
0
2
0
2
0
0
0
0
0
2
0
4
2
0
0
0
1
1
1
2
1
0
1
0
0
2
0
2
0
0
0
2
0
3
1
1
2
0
0
2
0
0
0
2
0
0
2
0
0
2
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
8
2
2
0
1
0
2
0
2
0
3
2
0
1
0
2
2
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
2
0
2
0
0
2
0
0
1
0
0
2
0
0
0
1
3
1
0
0
0
0
1
1
1
0
1
1
1
0
0
0
2
1
0
1
0
0
1
0
2
0
2
0
0
0
1
0
1
1
0
0
0
0
0
0
0
2
2
0
2
0
3
0
0
3
2
2
0
0
0
0
0
0
0
0
2
0
0
1
0
2
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
2
4
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
1
0
2
0
0
2
1
0
0
0
1
0
1
0
1
0
0
1
2
1
0
2
1
0
0
4
0
1
0
0
0
1
1
0
0
0
0
0
0
0
2
1
0
0
1
2
2
1
1
0
0
0
1
2
0
1
0
1
2
0
1
0
1
1
0
1
1
1
1
0
0
0
0
0
1
1
0
0
0
0
0
1
2
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
2
2
2
0
1
2
0
0
0
0
0
2
2
0
2
1
1
1
0
0
2
0
1
0
0
0
0
3
0
1
1
0
0
1
0
0
0
2
0
0
0
2
0
1
0
0
0
2
0
2
0
1
0
1
0
2
0
0
0
0
1
1
1
2
0
1
1
1
0
1
0
0
0
0
1
1
1
0
0
0
0
2
0
1
0
0
1
1
2
0
0
2
0
0
0
0
2
2
2
0
0
0
2
0
0
3
0
0
1
0
0
3
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
2
0
0
0
0
3
0
1
2
0
0
0
0
1
0
2
1
0
0
2
0
0
0
1
0
1
2
0
0
1
0
0
0
1
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
2
1
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
1
1
0
1
0
0
2
2
0
1
0
0
1
2
1
0
0
0
0
2
1
0
1
0
0
2
0
2
1
1
0
1
0
4
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
1
0
2
1
2
3
0
0
0
0
0
2
0
0
0
1
1
1
0
0
0
2
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
2
1
1
0
0
0
1
0
0
2
0
1
0
0
0
5
1
2
1
0
1
2
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
2
2
0
0
0
2
2
4
0
0
0
0
0
2
2
2
0
1
2
0
0
0
1
2
3
0
0
0
0
1
0
4
2
0
0
2
0
0
1
0
0
0
3
0
1
2
0
0
0
0
0
1
1
0
0
3
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
1
0
1
2
2
0
3
1
1
1
0
2
0
0
0
0
2
1
2
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
2
0
1
1
0
1
0
1
0
0
2
3
0
2
2
0
2
0
0
0
4
1
1
0
0
2
2
1
0
0
1
1
0
2
0
2
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
2
1
2
0
2
0
0
0
0
0
0
2
1
0
0
2
2
0
1
0
0
0
2
1
0
1
2
0
0
2
0
2
1
1
0
0
0
0
1
0
2
0
2
0
2
0
1
0
0
0
0
0
2
2
0
1
0
1
2
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
2
2
0
0
0
0
1
2
0
2
1
0
0
0
0
1
2
0
1
1
1
0
0
0
0
0
0
2
0
0
0
0
1
2
1
0
2
2
0
2
2
2
1
0
3
0
0
2
0
1
0
1
0
0
0
1
0
0
4
1
1
0
0
0
1
0
0
0
0
2
2
0
2
0
1
0
1
1
2
1
2
1
1
1
1
0
2
1
1
0
0
1
0
1
1
0
0
2
2
0
0
1
0
0
2
0
2
1
0
2
0
0
0
2
0
2
0
1
0
1
0
0
2
0
2
0
0
1
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
1
3
0
1
0
0
0
0
0
0
2
2
0
1
0
2
0
0
0
0
1
0
0
2
2
0
2
0
1
1
0
0
1
0
0
0
1
0
2
2
0
2
2
0
1
0
0
0
1
0
2
0
2
1
2
1
0
0
1
0
0
1
0
0
0
1
1
0
2
0
1
0
1
0
0
1
2
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
2
1
2
2
0
0
1
0
1
1
0
0
2
0
0
0
1
2
2
0
0
0
0
2
0
1
2
0
0
0
0
0
1
0
2
0
0
1
0
1
1
0
0
2
0
0
0
0
0
2
2
0
1
28
1
1
1
1
0
1
0
0
0
0
0
0
0
0
2
2
2
0
0
2
0
2
1
1
0
1
1
0
1
0
0
2
0
0
0
0
0
1
1
2
1
0
0
1
1
2
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
2
0
0
0
2
2
2
1
1
0
0
2
0
0
2
2
0
0
0
0
0
0
3
1
0
0
1
0
0
0
1
1
0
0
0
0
0
3
0
0
0
1
2
2
0
2
2
0
0
2
0
2
0
1
0
1
0
1
0
0
1
0
1
0
0
0
0
2
2
0
0
0
2
0
1
0
0
2
0
1
1
1
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
1
3
1
0
0
0
1
0
0
0
1
0
0
1
0
1
2
0
0
0
2
0
1
0
2
2
1
0
2
0
0
0
0
0
0
2
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
2
0
1
1
2
0
2
1
0
0
0
1
2
3
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
2
3
4
0
0
0
1
0
2
2
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
2
0
1
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
2
0
3
2
0
1
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
1
3
2
0
0
2
0
1
2
0
2
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
1
1
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
1
0
0
1
0
0
0
1
2
0
0
2
0
0
1
0
0
0
0
2
3
1
0
0
0
0
1
0
0
2
1
0
0
1
1
2
0
2
0
0
0
0
1
0
0
0
0
2
1
0
1
0
3
0
0
2
2
0
0
1
0
1
0
2
0
1
0
0
0
0
0
3
1
1
0
0
2
0
0
2
0
0
1
0
3
2
0
2
0
0
2
0
1
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
2
0
0
1
2
1
1
0
2
2
2
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
2
2
0
0
3
0
0
2
0
0
0
2
0
0
0
1
2
3
0
0
2
2
0
0
2
2
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
2
2
0
0
0
0
0
1
1
1
1
0
2
2
0
0
0
1
0
2
1
0
0
0
0
0
2
0
2
0
0
0
1
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
2
1
0
1
1
2
1
2
0
0
0
2
0
0
0
0
0
1
0
3
0
0
0
0
0
2
2
2
1
1
0
1
2
0
1
1
1
2
1
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
2
0
2
0
2
0
1
0
0
0
2
0
2
1
6
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
3
1
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
1
0
1
0
3
0
2
0
0
2
2
0
0
0
2
0
0
2
3
2
2
0
0
1
1
2
1
0
0
0
2
0
0
0
1
8
1
0
2
0
0
2
0
0
0
0
1
2
0
2
0
1
0
2
0
0
2
0
1
0
1
1
0
1
1
0
1
0
1
3
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
2
0
1
0
1
0
2
0
0
0
0
0
0
0
3
1
0
0
2
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
1
3
0
3
2
0
1
0
0
0
0
3
0
0
1
2
0
1
0
0
0
0
0
0
0
0
2
0
1
0
2
2
0
2
4
1
0
1
0
1
0
0
0
1
0
2
2
3
0
0
2
1
4
1
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
3
1
2
0
0
3
3
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
1
0
1
0
0
0
0
0
0
3
0
2
0
0
2
0
0
0
0
1
0
2
2
1
0
2
0
1
0
1
0
0
2
1
0
2
0
0
0
0
0
1
0
5
0
0
0
0
1
0
0
1
0
2
2
1
2
0
0
0
2
0
0
0
0
1
1
2
0
2
0
0
1
0
1
0
0
0
0
1
2
0
1
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
1
0
1
1
1
0
0
1
0
0
0
2
0
0
0
2
0
0
2
2
0
2
0
2
0
2
0
1
1
0
0
2
0
1
0
2
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
2
1
0
0
0
2
2
0
0
0
0
0
3
0
1
0
0
2
0
0
0
0
2
2
2
0
2
0
0
1
0
2
0
2
1
1
0
1
0
2
2
3
2
0
0
1
0
0
0
0
0
1
0
0
2
0
0
1
2
0
0
0
0
2
1
2
0
0
0
0
0
0
0
1
0
0
2
2
0
0
1
0
1
2
0
0
1
0
0
0
0
0
0
1
0
2
0
1
2
1
1
0
0
1
0
0
1
0
0
1
0
1
0
1
0
0
1
0
0
0
1
0
0
0
4
2
1
0
0
1
1
1
0
1
0
3
0
0
1
0
1
0
0
0
0
1
2
1
0
0
0
0
2
3
1
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
2
0
5
0
0
0
0
0
0
0
1
0
2
0
1
2
0
0
2
2
0
2
1
0
2
0
2
2
0
0
3
0
2
2
0
2
2
0
2
0
0
0
0
0
0
0
1
0
0
2
1
1
0
0
3
2
0
0
3
0
0
1
0
1
0
2
0
0
0
1
0
1
2
0
2
2
0
0
0
1
0
0
1
1
0
0
1
1
0
0
1
2
0
1
0
0
0
1
0
0
0
2
0
0
2
1
0
1
0
2
0
0
1
1
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
1
2
0
0
0
1
0
0
0
0
3
0
3
1
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
1
0
2
0
0
1
1
0
1
2
1
3
0
0
1
2
0
2
0
1
1
1
2
1
2
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
2
2
1
0
0
1
0
0
0
6
0
3
0
0
0
2
0
1
0
0
0
1
1
0
2
0
0
1
1
0
1
2
0
0
1
0
1
0
2
0
0
0
0
0
0
2
1
0
0
0
0
1
0
2
0
1
2
2
0
0
0
0
0
0
0
0
2
0
2
0
0
2
1
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
2
2
0
2
0
0
0
2
0
0
1
0
1
2
0
0
0
1
2
1
0
1
0
0
2
2
2
2
1
0
0
1
0
0
0
2
0
0
1
2
0
0
2
0
0
0
0
0
2
0
1
2
0
0
0
2
2
1
1
0
0
2
0
0
2
0
0
1
0
1
2
0
0
0
0
2
2
1
0
0
1
0
0
1
0
2
0
0
0
1
2
0
0
0
0
0
0
1
0
2
1
0
0
2
0
2
0
0
1
3
0
2
1
0
2
1
1
0
0
0
2
3
1
0
0
2
0
0
1
2
0
0
2
0
0
0
2
0
1
7
0
0
0
0
0
0
0
3
0
0
1
1
1
0
1
0
2
1
0
0
2
0
0
2
0
0
3
0
0
0
0
5
0
3
1
1
1
0
1
0
0
1
0
1
0
0
1
0
0
1
1
3
0
2
2
0
0
2
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
1
1
0
0
0
0
0
0
1
1
0
0
3
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
2
2
0
0
0
0
0
1
0
1
0
0
1
3
0
0
2
0
0
0
0
1
0
2
0
1
0
2
0
0
0
0
2
0
0
1
3
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
7
0
3
1
1
0
0
1
1
2
0
0
2
0
0
2
0
1
0
0
2
1
2
2
0
0
2
1
1
2
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
1
0
2
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
1
2
0
0
2
0
2
0
0
1
1
0
1
1
0
4
0
0
2
0
0
0
2
1
2
1
1
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
2
1
0
1
3
0
2
0
0
0
0
2
0
1
2
0
2
3
0
1
2
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
1
1
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
2
0
1
0
1
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
3
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
2
2
0
1
0
2
0
0
2
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
3
1
0
0
1
0
2
2
3
0
1
0
2
3
0
0
0
1
3
0
2
0
1
0
0
1
0
1
0
2
0
0
0
1
0
0
2
2
1
0
2
0
0
0
0
0
0
0
2
1
0
2
1
0
1
1
0
1
1
2
0
0
1
1
0
0
0
0
1
0
0
2
1
0
0
1
2
0
0
2
0
0
0
0
1
1
1
0
2
0
0
0
0
0
0
1
0
2
0
0
2
0
0
1
0
0
3
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
1
1
0
1
2
2
0
2
0
0
1
1
0
0
2
0
0
2
0
2
0
0
1
1
0
2
0
0
0
0
1
0
0
0
0
2
1
2
0
2
2
1
2
2
2
2
1
0
0
2
1
1
0
1
1
2
1
0
2
0
0
0
1
0
2
0
1
0
0
1
0
0
0
3
0
1
1
2
2
1
0
0
2
2
0
0
0
2
0
0
2
0
2
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
1
2
0
1
0
0
1
0
1
1
0
0
0
2
1
0
0
1
1
0
1
3
0
1
0
2
0
0
0
2
1
2
0
1
1
2
0
0
2
1
0
0
0
1
0
1
0
1
2
1
0
1
0
0
0
0
0
0
0
1
1
2
1
0
2
0
0
0
1
1
2
0
0
1
0
2
2
0
0
0
1
0
1
0
1
2
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
1
0
0
0
0
0
2
0
2
1
0
1
0
1
1
1
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
2
2
2
2
3
0
0
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
2
0
2
1
0
3
0
1
1
0
1
2
0
2
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
2
0
2
0
0
2
0
0
0
2
2
0
2
0
0
0
2
0
2
1
0
0
2
0
1
0
0
0
1
0
0
0
2
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
2
0
0
0
2
1
0
0
1
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
1
0
0
1
0
2
1
0
0
0
2
0
1
0
0
1
0
0
0
0
0
1
0
0
1
1
1
1
0
0
0
0
1
0
0
1
0
1
1
1
0
0
2
1
0
0
1
0
2
1
0
1
0
0
2
0
1
0
2
2
2
1
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
1
2
0
0
0
2
1
0
1
1
0
0
0
0
2
0
1
2
0
0
0
1
0
0
2
0
1
0
0
2
1
2
1
0
0
2
0
2
2
0
0
1
0
0
1
0
1
0
1
0
1
0
0
1
0
0
0
1
0
1
2
0
2
0
0
1
0
0
0
1
0
1
2
0
2
1
0
0
2
0
2
0
0
1
4
0
2
0
0
3
0
1
0
0
0
1
2
1
1
0
2
0
2
1
2
14
0
1
2
1
0
0
2
0
0
1
1
0
2
0
1
0
0
2
0
0
2
2
0
0
1
0
0
2
0
0
0
0
1
0
1
1
2
0
0
2
0
0
1
0
0
0
2
0
0
0
0
1
1
0
0
0
2
0
1
0
2
1
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
1
0
1
1
0
0
1
1
0
2
0
1
0
0
1
0
1
0
2
0
0
2
0
0
2
0
0
1
1
0
0
0
0
1
2
1
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
2
2
2
0
0
0
3
1
0
1
1
0
0
0
1
0
0
1
2
0
0
1
1
2
2
0
3
0
0
0
0
0
0
1
1
4
0
1
0
0
0
0
0
1
1
0
0
0
3
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
2
0
0
0
2
0
1
1
0
0
0
0
1
1
0
1
2
0
1
0
1
2
2
0
0
1
0
0
0
0
0
1
2
2
0
0
3
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
2
1
0
2
0
0
0
0
2
0
2
0
0
2
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
2
1
0
0
0
1
0
0
0
0
2
1
0
0
1
3
2
1
1
2
0
0
2
1
2
0
0
1
0
0
0
0
1
0
0
0
2
0
1
0
2
0
0
1
1
0
1
0
0
0
1
2
0
0
0
0
0
1
3
0
0
0
1
2
0
0
1
1
0
0
2
0
2
0
0
1
2
0
0
1
1
0
1
0
0
1
2
4
0
0
3
0
2
1
1
2
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
1
2
2
2
0
0
0
0
0
0
2
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
1
0
2
1
2
0
0
0
1
0
0
1
0
0
0
3
1
0
0
0
1
0
0
2
3
1
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
2
0
0
1
2
0
0
1
0
1
0
0
0
0
0
1
1
2
0
0
2
0
1
0
1
1
0
0
2
0
0
0
0
1
1
3
1
1
0
2
2
2
0
1
0
0
2
0
0
0
0
0
1
1
1
0
0
0
2
1
0
2
0
2
1
0
2
0
1
2
0
1
0
1
2
0
2
0
0
1
0
1
0
0
2
0
2
2
1
0
0
0
0
0
0
2
1
2
0
1
0
1
1
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
1
0
0
0
0
0
0
2
0
0
1
1
0
0
3
0
0
0
2
2
0
2
1
2
2
0
0
7
2
0
0
3
1
2
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
1
2
1
2
0
2
0
0
0
2
0
0
2
0
0
2
0
0
1
1
2
0
0
2
3
0
0
0
0
0
0
0
1
0
2
0
2
3
1
0
1
0
0
0
0
2
0
1
0
0
2
2
0
0
2
0
0
1
1
0
1
0
0
3
1
0
1
2
0
1
1
1
2
1
2
0
0
0
0
2
2
0
3
2
1
0
0
0
0
0
0
1
0
3
1
0
0
0
2
0
1
0
1
0
2
0
2
0
2
0
1
1
1
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
1
0
0
0
0
1
1
1
0
1
1
0
0
1
2
0
0
1
2
0
0
0
1
0
0
1
1
1
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
1
0
0
1
3
2
0
2
0
0
1
1
2
0
0
1
1
0
3
1
1
2
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
3
0
0
2
2
0
2
1
3
0
0
0
2
2
2
0
0
3
0
0
2
0
0
2
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
2
2
0
0
2
1
0
0
2
0
0
0
1
2
0
1
0
1
1
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
2
2
0
2
2
0
1
0
0
1
0
2
0
0
1
1
0
1
1
0
2
0
0
2
0
0
0
3
0
0
1
0
0
0
0
0
0
1
0
0
2
0
1
2
0
0
0
0
3
1
1
0
2
2
1
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
1
0
0
0
3
1
0
0
1
0
0
0
2
0
2
0
1
0
0
0
0
0
0
1
0
0
1
1
1
0
0
2
2
2
0
2
0
0
1
1
1
0
2
6
0
2
0
0
0
2
2
0
0
0
0
0
1
2
0
2
1
1
0
2
2
2
0
0
0
0
1
0
1
2
3
0
0
2
0
2
0
1
0
2
0
0
0
0
2
0
1
2
1
0
0
0
1
2
0
1
1
1
0
1
2
0
0
1
0
0
1
0
2
0
1
0
2
0
0
2
1
2
2
0
0
1
0
1
1
0
0
1
1
1
2
0
1
0
1
0
0
0
0
0
2
0
0
3
0
1
0
0
0
3
0
1
0
0
0
0
1
0
0
0
0
1
2
0
1
0
1
0
0
0
0
2
2
0
0
1
1
1
0
0
0
0
0
1
2
2
0
2
2
0
0
2
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
2
2
2
0
2
0
2
2
0
1
2
0
0
2
0
0
0
0
2
0
0
2
1
0
0
1
0
2
1
0
0
0
0
0
0
1
4
1
0
2
0
0
0
0
1
2
1
2
1
0
0
2
0
2
0
1
0
0
2
2
0
0
0
1
0
5
1
1
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
2
0
1
0
3
1
0
0
0
0
1
0
1
2
0
1
0
0
0
1
0
0
0
1
2
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
2
1
2
0
2
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
3
1
0
0
0
0
0
1
0
2
0
1
0
3
2
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
2
3
2
0
0
0
2
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
1
5
1
1
0
0
0
0
2
0
2
0
2
2
0
0
0
0
1
1
2
0
0
0
0
0
2
0
0
0
0
2
1
1
2
0
0
0
2
0
0
0
0
1
2
0
2
0
1
1
1
0
0
0
0
1
2
0
2
2
1
1
1
0
2
2
0
0
2
2
1
1
0
0
0
0
0
3
0
3
4
0
2
0
0
1
2
0
0
2
0
0
1
2
1
0
0
0
1
1
0
1
0
0
0
1
1
0
0
0
0
0
2
1
0
2
1
0
0
2
2
0
0
0
2
1
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
2
1
2
1
2
0
1
1
0
2
0
0
0
0
0
1
1
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
3
2
1
2
0
0
0
0
1
0
1
0
2
1
0
1
1
2
1
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
2
0
0
2
0
2
0
3
0
0
0
0
0
2
0
0
2
0
1
1
0
2
1
0
1
0
0
0
1
2
0
0
0
0
0
1
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
1
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
1
0
0
0
2
1
0
0
2
0
1
1
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
3
0
2
0
2
0
0
1
0
0
2
2
1
0
0
4
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
2
2
0
1
0
2
1
0
0
0
0
0
1
0
0
0
0
2
0
2
0
3
2
0
0
1
1
0
0
1
1
0
0
0
0
3
0
2
2
2
0
0
1
0
0
0
0
2
0
2
0
0
2
0
1
0
0
1
0
0
1
2
0
0
0
0
1
2
0
0
2
0
1
2
0
0
0
1
0
1
0
0
0
0
1
1
0
0
1
1
2
0
1
1
0
0
2
2
0
2
0
1
0
1
0
0
2
0
0
1
0
0
1
1
1
0
1
2
0
0
0
0
1
0
0
1
0
0
3
0
2
0
2
1
0
1
0
1
0
1
1
0
0
0
2
0
2
0
0
0
0
2
2
2
0
2
0
0
0
1
2
0
0
0
3
0
0
2
1
0
0
0
0
0
2
2
3
0
2
1
1
0
0
1
0
2
2
0
0
1
1
0
1
0
0
1
0
0
0
2
0
0
0
0
0
2
1
0
2
2
3
0
0
0
2
2
2
0
0
0
1
3
1
0
0
0
2
0
0
0
1
1
2
2
2
0
0
0
1
2
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
1
0
0
0
0
1
0
0
0
1
1
1
0
2
0
0
0
1
0
1
0
1
0
0
2
3
0
2
1
0
3
0
2
0
0
0
0
1
2
2
2
0
0
0
0
0
0
2
1
0
0
0
2
3
2
0
0
1
0
2
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
2
0
0
0
2
0
1
2
2
1
0
0
2
0
2
5
1
2
0
2
0
2
2
1
2
2
0
0
0
0
0
0
1
1
0
1
0
1
2
0
0
0
1
0
1
2
2
1
2
2
0
1
0
0
2
2
2
2
0
0
0
0
0
2
2
0
0
1
1
2
0
2
1
0
0
0
1
2
0
1
0
1
2
2
0
0
0
0
0
0
1
2
0
0
0
1
0
3
1
3
1
1
1
0
2
0
0
2
0
0
0
1
0
2
2
0
2
1
0
2
2
0
0
2
0
0
1
0
0
0
0
1
0
0
0
2
0
0
1
0
2
0
1
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
3
0
0
0
1
0
1
0
1
1
0
1
2
0
0
0
2
2
1
2
0
1
0
0
2
0
2
0
2
0
0
2
1
0
0
2
0
4
0
0
0
1
0
0
0
0
0
2
2
1
0
0
0
0
0
2
0
0
2
0
2
1
0
0
0
0
2
0
1
1
2
0
1
0
0
0
0
0
1
3
2
1
0
0
1
2
1
0
1
1
2
2
0
0
0
2
0
0
0
0
0
3
3
0
0
1
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
2
0
2
2
2
0
4
2
1
2
0
0
0
0
0
0
2
0
0
0
1
2
0
0
2
0
0
0
2
1
0
0
1
2
2
0
2
0
0
0
2
0
0
0
0
1
0
2
1
0
2
1
0
0
0
0
0
0
1
0
2
0
0
4
0
0
0
0
0
2
0
0
0
0
0
1
0
2
2
2
0
0
0
0
0
0
2
0
0
1
2
2
1
0
0
0
1
2
0
0
1
0
0
0
1
0
0
0
0
2
1
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
2
1
0
0
1
0
2
2
1
0
0
2
0
0
1
5
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
2
0
0
2
2
0
0
0
1
0
0
0
0
2
0
0
0
1
2
0
1
0
1
0
2
2
0
0
2
0
0
2
1
0
2
3
2
0
0
0
2
1
0
0
0
1
0
0
0
2
0
0
0
2
0
1
0
2
2
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
2
1
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
2
2
0
1
1
0
0
0
1
1
1
1
0
2
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
3
0
2
0
2
0
1
0
1
1
0
0
0
0
1
0
2
1
2
0
1
0
0
2
1
0
0
1
2
1
0
2
1
0
0
2
0
0
0
0
0
0
0
2
0
0
5
2
0
2
0
1
0
0
0
1
1
0
0
1
0
1
2
0
0
0
0
1
0
1
1
0
0
0
0
0
1
2
1
0
2
0
0
0
1
2
0
1
1
1
1
0
1
0
0
0
2
0
2
1
2
0
0
0
0
1
1
0
0
0
0
0
1
2
0
1
0
1
0
0
1
0
0
1
0
1
2
2
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
2
1
2
0
0
1
0
1
0
2
0
1
2
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
2
1
0
0
2
0
1
0
1
0
4
2
2
0
0
2
0
0
2
3
0
0
0
0
1
0
0
0
0
0
2
2
0
1
0
0
0
4
1
0
0
0
0
0
1
0
0
2
0
1
0
2
0
1
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
2
2
2
0
0
0
2
0
2
2
0
2
2
0
1
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
1
1
0
2
0
0
0
0
2
0
1
0
0
0
2
1
1
0
0
0
0
2
1
2
0
0
0
0
0
1
2
2
0
0
0
1
2
0
2
1
1
2
0
1
1
0
0
0
4
2
1
1
0
2
0
0
1
1
3
0
2
1
0
0
1
0
0
0
1
1
0
0
2
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
2
0
0
2
2
0
0
1
0
0
0
0
2
1
0
1
0
1
0
0
0
0
0
0
2
0
1
0
1
0
4
0
0
0
2
2
0
1
1
0
0
0
0
1
1
0
2
0
2
2
0
2
0
0
1
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
3
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
2
0
2
2
0
0
1
0
0
0
0
0
0
2
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
1
0
2
0
2
0
2
1
2
0
2
0
0
1
0
0
2
0
0
0
0
1
0
2
1
0
0
0
2
0
1
0
0
0
3
0
0
1
0
1
0
0
1
0
0
0
0
1
0
2
1
1
0
0
0
0
0
0
0
0
11
0
0
0
2
0
2
0
0
1
2
2
0
3
0
0
1
3
0
1
0
2
1
1
4
1
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
1
2
1
0
0
0
1
0
1
0
2
2
0
0
2
1
1
0
1
0
1
2
0
2
0
0
2
3
1
0
0
1
0
3
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
2
2
0
1
2
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
1
2
1
3
1
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
2
1
0
2
0
2
0
0
0
2
0
2
0
0
1
0
0
0
0
0
3
1
2
0
1
2
2
0
1
0
0
0
1
0
0
0
0
1
0
1
1
2
0
2
0
1
0
0
1
1
0
1
0
0
1
0
1
2
0
0
0
1
1
2
0
0
0
0
1
0
2
0
1
0
0
1
0
0
1
1
1
0
0
0
0
1
2
0
1
0
0
0
0
0
1
0
2
0
0
1
1
0
0
1
0
0
1
3
1
0
1
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
2
1
0
0
2
0
0
0
2
0
1
0
2
0
0
2
2
1
0
1
2
2
0
1
0
0
0
2
0
0
0
2
0
2
0
0
2
1
3
1
0
0
0
2
0
0
1
2
2
0
2
1
0
6
2
2
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
2
1
0
0
1
3
1
0
0
0
0
1
1
2
0
0
2
0
1
0
0
0
0
1
1
0
0
0
1
1
0
2
1
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
2
0
0
0
0
0
2
1
0
0
1
0
1
0
0
0
0
0
0
2
0
2
0
3
1
0
0
0
2
1
0
0
0
0
0
0
0
0
1
1
1
0
0
2
0
2
0
0
0
0
0
2
2
0
1
0
0
0
1
2
1
1
0
0
1
0
0
0
0
0
1
1
0
0
0
2
0
0
1
0
2
1
0
3
0
0
0
0
0
0
1
0
0
0
0
2
0
2
1
0
0
1
2
0
1
0
2
2
0
0
0
0
0
0
1
0
0
0
3
0
0
1
0
0
0
0
0
0
1
2
2
0
0
1
1
0
1
2
1
1
0
0
0
0
0
2
1
0
1
0
0
2
1
2
1
0
0
1
2
0
0
0
0
0
0
0
1
1
0
0
2
0
2
0
0
1
2
0
1
0
0
0
1
0
0
1
2
1
1
2
1
0
0
0
0
1
1
2
0
2
1
1
2
2
0
0
1
2
0
2
0
2
0
2
1
0
0
2
1
1
0
0
1
0
1
1
0
0
0
3
0
0
0
0
1
2
0
2
3
1
1
1
0
2
0
2
2
1
0
0
2
2
2
0
0
0
4
2
0
2
0
1
1
2
2
1
1
0
1
0
0
0
0
1
2
0
2
1
1
0
0
0
0
0
0
0
1
1
0
2
0
1
0
0
0
0
0
0
0
0
1
1
0
1
1
2
0
2
0
0
0
0
2
0
2
0
1
1
0
1
1
1
0
0
0
0
3
1
0
1
1
0
0
1
2
0
0
0
1
2
0
2
0
0
2
1
0
2
2
0
0
2
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
1
0
1
0
1
0
0
0
0
0
2
0
2
0
1
2
1
0
2
0
2
0
0
0
0
1
0
0
2
0
0
1
0
0
0
2
2
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
4
0
2
0
2
0
0
0
0
1
0
0
1
0
2
0
0
0
2
0
1
0
0
1
0
0
0
1
0
0
0
0
2
0
2
0
3
0
0
0
2
2
0
3
0
0
1
2
3
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
2
2
0
0
1
0
0
1
1
2
0
0
1
2
2
3
2
2
0
2
0
1
1
0
1
0
0
0
2
0
2
0
0
0
2
2
1
0
0
0
0
0
0
0
2
0
2
2
2
0
2
0
0
1
0
0
1
3
0
2
0
0
0
2
0
0
1
2
1
2
2
2
0
2
0
2
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
2
0
1
2
2
0
2
0
0
0
0
2
0
0
1
0
0
2
0
0
3
1
0
0
0
1
1
0
0
0
1
1
2
0
2
0
1
0
1
0
0
0
0
2
3
0
0
3
0
0
0
0
1
0
0
0
0
0
0
1
0
2
2
0
2
1
2
0
0
1
0
0
0
2
1
0
0
0
0
1
0
1
1
0
0
0
6
0
0
1
0
2
1
0
0
2
1
0
0
0
0
2
2
1
0
0
0
0
0
2
0
2
0
1
1
0
0
1
0
0
3
1
0
1
0
0
0
2
0
1
0
0
0
1
1
0
1
0
0
0
1
2
0
1
1
1
2
2
0
1
0
0
1
0
0
1
0
2
0
1
2
0
2
0
0
0
2
0
0
0
0
0
0
2
0
3
1
2
1
1
0
2
1
0
2
0
0
1
1
0
0
0
1
0
0
0
0
0
2
0
0
3
0
0
1
0
0
2
0
2
1
1
0
1
0
0
0
1
2
2
2
0
0
0
0
0
0
2
1
0
0
0
0
2
0
2
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
1
3
0
1
0
0
2
0
0
0
0
1
0
0
2
1
1
2
0
0
0
1
2
0
0
2
1
0
0
0
1
2
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
6
0
1
0
0
0
2
0
2
2
0
0
0
0
0
0
1
2
0
1
0
0
0
1
0
2
0
0
2
1
0
0
0
0
0
0
0
2
0
1
0
2
0
0
1
0
0
0
0
1
1
0
2
1
0
2
0
0
0
0
0
2
2
1
2
1
1
0
0
0
1
0
0
0
2
1
1
1
0
1
0
0
0
1
2
0
1
0
2
1
1
0
0
1
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
1
1
2
1
0
0
0
0
2
0
1
1
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
3
0
0
0
2
0
2
2
0
2
1
0
1
2
0
0
0
0
0
0
1
1
0
0
1
1
0
1
2
0
1
0
0
1
0
0
5
0
0
0
2
3
2
2
1
0
0
0
0
0
1
0
1
1
0
1
1
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
1
1
2
1
0
2
2
0
0
0
1
0
0
1
2
0
2
1
0
0
3
2
2
1
2
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
3
0
1
0
2
1
0
1
1
1
0
2
0
0
1
0
0
2
1
1
0
2
2
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
2
4
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
2
0
1
2
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
4
2
0
1
1
1
0
2
1
0
0
2
2
2
0
0
2
0
2
0
0
0
0
0
1
0
1
0
0
3
0
1
1
0
0
0
0
2
0
0
1
0
2
2
0
0
0
1
0
0
0
1
0
2
0
1
0
0
0
0
0
2
1
1
0
2
0
0
1
0
0
0
2
0
1
1
1
0
0
1
0
0
2
0
1
0
0
0
0
2
1
0
2
0
2
0
0
0
0
0
0
0
1
1
0
0
1
2
1
2
0
3
1
0
0
0
3
1
2
0
1
0
0
1
0
0
1
0
1
1
0
1
2
0
0
2
0
1
0
0
0
0
1
0
2
1
0
2
2
0
2
0
0
1
2
0
1
0
0
1
0
1
0
0
2
0
0
0
1
0
3
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
2
2
0
1
0
0
0
1
0
0
1
0
0
2
0
1
0
3
2
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
3
0
1
1
0
0
0
1
2
0
0
1
0
0
1
0
1
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
2
0
1
0
0
0
0
1
1
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
2
0
0
0
0
2
0
0
0
2
0
0
1
2
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
3
0
1
1
2
0
0
0
2
0
1
0
2
0
2
0
0
0
0
1
2
2
0
0
0
0
0
2
2
0
0
2
3
0
0
4
0
0
2
0
0
0
0
0
0
2
0
1
3
0
0
1
0
1
0
0
1
0
2
2
0
2
0
1
1
1
0
1
0
0
0
3
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
2
0
2
0
1
2
0
0
0
2
0
2
0
0
0
0
1
1
1
1
1
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
1
5
2
1
1
0
2
2
0
0
1
1
1
2
0
1
1
0
1
0
0
1
0
0
2
1
0
0
2
0
2
0
0
0
0
1
0
2
1
1
0
0
0
0
1
0
0
2
0
0
0
1
2
0
0
0
1
1
1
1
3
1
1
0
1
0
0
0
0
1
0
0
0
1
3
0
2
0
2
0
1
0
0
1
2
1
0
1
0
0
3
0
1
0
0
0
2
0
0
0
0
3
0
1
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
2
0
0
0
1
0
2
2
2
0
0
0
1
0
2
1
2
0
0
0
0
2
0
0
2
0
1
1
4
0
3
0
0
0
0
0
2
0
0
1
0
0
3
0
0
1
1
0
0
2
0
0
0
0
0
2
0
0
1
0
2
0
2
1
0
0
0
0
1
1
4
2
0
1
0
0
2
2
0
0
0
2
1
1
0
1
0
4
1
2
1
0
0
0
0
2
0
2
0
0
1
2
1
0
0
0
1
0
0
0
0
0
13
1
0
2
0
1
0
2
2
0
2
3
0
0
0
2
1
0
1
0
0
0
0
0
0
1
0
0
0
2
2
1
0
0
1
0
0
1
0
2
0
0
2
0
2
2
0
3
0
2
0
0
0
0
2
0
1
0
0
1
0
0
0
1
1
0
0
0
0
2
0
1
1
1
0
0
1
0
1
0
0
0
0
2
3
2
4
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
2
0
1
0
1
0
0
1
0
2
1
0
3
2
0
0
0
0
1
0
3
0
0
0
1
0
1
0
2
1
0
1
2
2
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
1
2
0
0
1
0
0
0
1
0
0
0
1
2
0
0
0
0
0
2
0
1
1
0
2
2
2
2
0
0
0
0
2
0
0
2
1
1
0
3
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
2
1
0
3
0
0
0
1
1
0
0
2
0
1
0
0
2
0
1
0
0
0
0
0
1
0
0
2
2
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
2
2
2
1
0
0
0
0
2
0
1
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
2
0
1
1
0
0
2
0
1
3
0
0
2
1
1
0
2
0
0
1
0
1
0
0
0
1
1
2
1
0
2
0
1
1
2
0
0
0
1
0
0
1
1
1
1
0
0
0
1
0
0
0
1
0
0
0
2
2
0
0
2
0
0
0
1
2
0
1
1
1
0
1
1
0
1
0
2
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
1
2
0
0
1
1
1
0
2
0
1
1
1
2
1
2
0
0
0
0
2
0
1
1
0
2
1
0
0
1
1
0
1
1
2
1
0
2
0
2
0
2
0
1
3
0
1
0
0
0
0
1
4
1
0
0
2
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
1
2
1
0
0
0
0
1
0
2
2
0
0
1
0
3
1
1
0
1
1
1
2
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
2
0
0
0
2
0
0
0
2
2
0
2
0
1
0
2
1
0
0
3
2
0
0
0
0
0
1
0
1
2
0
0
0
0
1
0
0
2
0
0
1
2
0
0
0
1
2
2
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
1
2
0
1
0
6
0
1
0
0
3
1
2
2
0
2
2
0
1
1
0
0
0
0
0
0
2
0
0
1
0
0
1
0
2
1
0
0
1
0
0
1
1
5
1
0
1
0
2
0
2
0
1
0
1
0
0
1
1
1
0
0
1
0
0
3
0
2
1
0
0
0
2
0
4
3
2
0
0
0
1
0
2
0
2
2
0
2
2
0
1
0
0
0
2
0
0
1
2
1
1
0
0
1
0
0
2
0
1
1
0
0
0
3
0
2
0
0
0
0
0
0
2
2
0
1
0
2
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
2
1
1
1
0
0
2
0
0
1
1
0
0
0
2
2
0
1
0
2
0
2
1
1
0
0
0
0
2
0
0
1
0
0
0
3
2
0
0
0
2
0
1
0
1
0
0
2
0
1
0
0
1
0
0
0
3
0
0
2
0
0
2
1
0
1
0
3
3
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
4
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
1
0
0
0
0
2
0
0
3
1
1
0
0
2
1
0
0
0
2
0
1
0
0
1
0
0
2
2
0
0
1
2
0
0
0
2
0
0
1
2
0
0
1
0
2
1
2
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
3
1
0
2
2
1
0
0
2
2
2
0
2
1
2
0
0
1
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
2
2
1
1
1
0
0
0
1
2
2
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
2
2
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
3
1
0
2
0
0
1
2
0
0
0
0
0
2
1
2
0
0
0
0
0
2
2
2
2
0
0
0
1
0
0
0
0
0
1
2
1
0
1
1
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
1
1
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
1
1
2
0
0
0
1
2
1
0
0
0
1
0
1
0
2
0
1
0
0
1
1
2
1
2
0
0
0
2
0
1
1
2
1
0
1
0
0
0
0
0
0
1
2
1
0
0
1
0
0
2
0
0
0
3
0
0
0
0
0
1
0
1
1
1
1
0
0
0
1
0
0
1
1
2
0
1
1
0
0
0
5
0
3
0
2
1
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
4
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
1
0
1
0
1
0
0
0
1
2
0
0
0
0
1
2
1
2
0
0
0
0
0
2
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
2
0
1
1
0
1
1
2
5
2
0
1
0
0
0
1
0
0
0
1
0
0
0
1
2
0
0
0
2
3
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
2
0
1
0
0
0
2
2
0
2
0
0
0
0
2
0
0
1
0
2
1
0
2
0
0
1
1
2
1
1
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
1
0
0
2
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
2
0
0
2
2
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
2
0
1
0
0
1
0
2
0
0
0
1
1
0
0
3
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
2
0
1
3
0
1
2
2
2
1
2
0
1
0
1
2
0
2
2
1
1
0
0
0
0
0
0
1
0
1
1
0
2
1
1
2
0
0
0
2
0
0
1
1
0
0
0
0
0
1
0
0
2
0
1
0
1
2
1
1
0
0
2
2
1
0
0
0
0
0
1
0
0
2
0
0
1
0
0
1
0
0
2
2
0
0
1
1
3
2
0
0
0
2
0
0
4
0
0
1
0
1
1
2
3
2
0
0
0
1
0
2
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
1
0
0
0
0
0
0
1
2
0
1
1
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
2
2
0
0
0
1
0
1
3
1
0
0
0
0
0
0
2
0
0
1
2
0
3
4
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
1
2
3
0
2
1
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
1
0
0
3
1
0
1
0
0
0
1
0
2
0
0
0
2
1
1
1
2
2
1
2
0
0
1
0
0
0
2
0
0
0
0
0
2
1
0
1
1
0
0
2
1
1
0
4
0
0
4
1
0
2
0
0
1
0
0
0
0
2
0
2
1
1
0
1
0
0
0
1
2
0
1
0
0
2
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
3
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
1
1
0
1
1
0
0
2
2
0
1
0
0
0
1
1
0
0
0
0
0
2
3
3
1
1
0
2
0
0
0
0
2
0
0
1
0
2
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
2
3
0
0
0
0
1
0
0
2
0
0
2
2
1
0
0
1
0
1
0
1
1
1
1
3
0
1
0
2
0
0
2
0
0
0
2
0
2
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
1
1
0
0
0
1
0
1
2
0
4
1
1
0
0
0
1
0
2
0
1
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
3
2
0
2
0
0
0
1
0
1
2
2
0
1
0
0
0
0
2
1
0
0
0
0
1
0
2
1
1
2
0
3
0
0
1
0
0
2
0
0
0
2
0
1
0
0
1
0
1
1
1
0
0
2
0
1
2
0
2
0
0
0
2
0
5
1
0
1
0
2
2
1
0
2
0
0
0
1
0
0
0
0
0
0
1
1
0
1
3
0
0
0
0
2
1
0
1
0
1
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
2
1
2
0
1
1
0
0
2
0
2
0
0
2
0
0
1
0
2
0
0
0
0
0
2
0
1
0
0
1
0
1
0
0
2
0
0
0
0
0
0
2
2
0
0
2
0
1
0
2
2
0
2
0
0
1
1
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
1
1
0
0
0
0
0
2
0
1
2
0
1
1
0
3
0
0
1
0
0
1
0
1
1
0
1
1
0
1
0
0
1
0
1
0
2
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
3
0
0
0
1
0
0
2
1
2
0
1
0
2
1
2
0
0
0
0
0
2
0
0
3
0
2
4
0
0
1
2
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
2
0
2
0
0
0
0
1
1
0
2
2
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
1
1
0
1
2
0
0
0
0
1
0
1
0
0
0
1
0
1
2
0
0
1
1
1
1
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
1
0
2
0
0
0
1
2
0
0
1
0
0
0
0
2
2
0
2
0
0
1
0
1
2
1
0
0
2
1
1
2
1
0
2
0
1
2
0
1
0
0
0
0
0
0
0
0
0
1
2
3
0
3
1
0
1
0
0
0
0
0
0
0
2
0
1
0
2
0
0
2
2
0
0
0
0
0
2
0
0
1
2
0
0
1
2
0
2
0
0
0
0
0
1
0
0
2
1
0
0
2
1
1
1
0
0
0
2
0
0
0
0
1
2
1
0
1
0
0
1
0
0
2
0
2
2
0
4
0
1
0
0
2
0
1
0
0
0
2
0
0
0
1
1
0
3
0
0
1
1
1
1
3
0
2
2
0
0
0
2
0
0
0
0
7
0
0
1
2
0
0
0
0
2
2
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
4
0
1
1
0
0
1
1
0
0
2
1
2
0
2
0
2
1
1
0
1
3
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
2
0
3
2
2
0
0
0
0
0
0
0
0
2
0
3
0
0
0
2
0
1
1
0
0
0
0
2
2
5
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
2
3
0
0
0
1
1
0
0
2
1
2
1
0
0
0
0
0
1
1
0
2
0
1
0
1
2
0
0
2
1
0
1
1
0
0
0
1
1
0
0
0
0
2
0
0
0
1
0
1
0
0
0
2
2
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
2
2
0
0
0
0
2
1
0
0
0
0
2
0
1
0
2
1
0
1
0
0
0
0
2
0
0
1
2
1
0
0
1
0
1
1
0
2
0
1
1
1
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
2
1
0
0
0
0
1
0
2
4
0
2
1
0
2
2
0
3
0
0
1
1
1
0
1
1
0
0
0
2
2
0
0
1
0
0
0
1
0
0
1
1
1
2
1
0
0
1
0
2
1
0
0
0
0
0
1
0
0
0
1
1
1
2
0
1
1
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
2
0
0
0
1
2
0
0
1
1
0
3
0
0
0
2
1
1
1
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
2
2
1
2
0
0
0
0
0
2
0
1
1
1
0
0
2
0
2
0
2
0
0
0
1
0
0
2
0
0
0
2
3
0
0
0
0
1
0
0
0
1
2
3
2
0
2
0
1
0
0
2
0
0
0
2
0
0
2
0
1
2
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
1
1
0
0
1
0
1
0
1
0
2
0
0
0
1
2
2
2
2
0
2
0
2
0
0
1
2
0
1
0
0
1
2
0
2
1
0
2
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
3
0
2
0
0
0
2
1
0
1
2
0
2
1
1
0
0
0
0
2
0
1
0
3
1
2
0
0
2
0
2
2
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
2
2
0
1
0
0
0
1
0
2
0
0
0
1
1
1
1
0
0
0
0
1
1
0
2
1
0
7
0
0
0
0
0
0
0
2
2
0
0
2
0
0
2
0
0
2
0
2
0
0
2
0
0
0
2
0
1
2
1
1
1
1
0
0
0
0
1
0
1
1
1
2
0
0
1
0
1
1
0
0
0
0
1
0
2
0
2
0
1
0
0
0
0
5
0
0
0
0
0
0
2
2
2
2
1
0
0
1
0
0
0
2
1
0
1
0
0
2
1
2
0
0
1
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
1
1
2
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
2
0
0
0
0
0
0
2
1
0
1
2
0
3
2
1
0
0
0
0
1
0
0
0
5
0
2
0
0
1
1
0
0
0
0
1
0
0
2
0
0
1
2
1
2
0
0
0
0
2
0
1
2
0
0
0
3
1
3
0
0
2
0
0
0
1
0
0
0
2
0
1
0
0
1
0
0
1
1
2
0
0
0
0
0
2
1
2
0
0
0
0
3
0
0
2
0
0
0
1
2
1
0
1
0
1
0
0
1
0
0
0
1
2
0
0
0
0
2
0
0
1
1
0
1
0
3
0
2
0
0
0
0
2
0
0
0
2
0
0
0
2
0
2
0
0
0
3
1
0
1
1
0
2
2
0
0
0
2
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
3
0
1
0
0
0
0
0
0
0
1
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
2
1
0
0
1
0
1
0
1
1
0
0
1
0
1
0
1
0
1
2
0
1
0
0
1
2
1
0
1
0
0
0
0
0
1
0
0
0
1
0
2
2
0
0
2
0
0
0
0
1
3
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
2
2
0
0
1
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
1
0
0
2
0
0
0
2
0
2
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
2
2
2
0
1
0
0
1
1
1
0
1
0
0
0
1
1
0
0
0
0
0
0
2
0
0
1
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
1
1
1
1
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
1
2
2
0
3
0
1
0
0
7
0
1
0
0
0
0
0
2
2
0
0
1
0
0
1
0
0
0
1
1
1
0
0
0
0
2
0
1
0
1
0
0
0
2
1
1
0
0
0
1
2
0
0
2
0
0
2
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
1
0
2
0
2
0
1
0
0
2
2
0
0
2
1
2
0
2
3
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
2
0
0
1
0
0
1
1
0
0
1
1
0
0
2
1
0
0
2
1
0
2
0
0
2
2
0
0
0
2
0
4
2
2
0
0
1
0
0
1
0
0
0
0
0
1
2
0
2
0
2
0
0
1
1
1
1
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
2
0
0
1
1
1
1
2
0
2
0
0
2
1
0
2
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
1
0
0
0
0
0
3
0
0
0
2
1
1
1
1
0
0
0
1
0
0
0
1
1
2
0
1
2
1
1
0
2
0
0
0
6
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
3
2
0
1
3
1
0
2
1
0
1
0
1
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
3
2
0
0
0
2
2
0
2
0
0
0
0
2
0
1
2
4
0
0
1
0
2
1
0
0
0
0
0
0
0
0
2
0
0
2
0
1
1
0
2
0
2
0
0
0
0
0
0
2
2
0
1
0
1
2
0
0
2
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
2
1
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
1
1
1
0
0
0
0
0
2
1
0
2
0
0
0
1
0
2
0
0
0
1
6
2
0
0
0
1
0
2
0
0
0
2
2
1
0
0
2
0
1
0
0
0
0
0
0
0
1
1
0
1
0
1
0
1
1
1
0
1
0
0
1
0
0
0
5
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
1
0
0
1
0
2
0
0
1
0
1
2
0
0
0
0
2
1
2
2
1
0
0
0
0
0
2
0
1
1
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
1
2
0
1
0
0
0
6
1
1
0
0
0
1
1
0
0
0
0
2
1
0
2
2
2
0
0
0
0
1
0
0
0
1
1
0
1
2
0
2
1
0
2
0
1
0
0
2
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
2
0
1
1
0
2
0
2
0
0
1
0
0
1
2
2
1
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
1
0
2
1
2
1
0
2
0
4
0
0
0
0
1
0
0
0
1
2
1
1
0
2
0
0
2
0
0
0
0
2
0
2
0
1
0
1
0
0
2
1
0
2
0
0
0
0
0
0
2
3
2
0
0
0
0
0
1
1
0
0
0
0
1
0
0
2
0
0
0
1
0
1
0
2
2
0
0
0
0
0
0
5
0
2
1
1
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
3
0
0
0
0
0
0
0
0
0
2
1
2
1
0
0
2
0
0
1
2
0
0
2
0
0
0
2
0
0
0
0
0
6
0
0
0
0
0
0
2
0
0
0
1
1
0
1
2
0
0
0
0
0
0
0
2
2
0
0
1
0
1
3
1
1
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
1
1
0
2
0
0
0
0
1
4
1
0
0
0
0
0
1
1
1
0
2
0
0
0
0
0
2
1
2
1
0
0
0
2
2
1
0
0
3
2
0
0
0
0
2
0
0
0
0
0
2
2
0
1
0
2
0
2
0
0
0
0
0
2
0
1
7
0
0
0
0
0
0
0
1
1
0
0
0
0
2
1
0
0
2
0
0
0
0
1
1
0
0
1
1
2
4
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
2
1
2
0
0
0
0
0
1
0
3
0
0
0
0
0
0
1
0
0
1
0
2
1
0
0
1
2
0
0
1
0
2
1
0
0
0
0
2
0
0
0
1
2
0
5
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
2
0
0
2
1
0
0
0
4
1
0
0
0
0
2
0
1
2
0
1
2
1
0
0
1
1
4
0
0
1
2
1
0
0
1
0
2
1
0
2
1
1
1
0
0
0
0
0
1
0
1
1
1
1
0
1
0
0
0
0
0
1
2
1
1
1
1
0
0
2
0
2
2
1
2
1
0
2
0
2
0
2
0
0
0
0
1
2
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
1
1
2
0
1
0
0
2
0
1
0
0
0
1
0
0
0
0
1
0
1
1
1
0
0
2
0
0
1
0
2
0
0
0
0
1
2
0
0
0
1
0
0
0
1
1
1
1
2
1
1
0
1
0
0
0
0
0
2
1
1
1
2
0
0
0
0
0
1
2
2
1
0
0
1
0
1
0
1
3
1
0
0
0
2
2
2
0
0
0
0
1
0
0
0
0
1
1
0
1
1
0
2
2
0
2
0
0
0
0
1
0
1
2
2
0
1
0
1
2
0
0
0
0
2
0
1
0
1
1
0
0
0
0
2
0
0
0
2
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
1
1
0
1
0
1
0
0
0
2
0
0
0
1
1
0
0
0
0
1
1
2
2
1
0
1
1
1
1
2
1
0
0
1
0
0
2
1
0
1
2
0
1
0
0
1
0
1
0
1
0
0
1
1
2
0
2
0
1
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
2
0
1
0
0
0
1
2
0
1
0
0
2
0
0
1
1
1
1
0
2
0
0
0
0
2
1
0
0
0
1
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
2
0
1
1
0
2
0
1
0
0
1
0
0
3
3
2
0
0
0
2
0
0
0
2
0
0
2
0
0
1
1
0
0
2
0
1
0
0
1
0
0
1
0
2
0
0
0
2
0
0
0
1
0
0
0
2
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
4
0
0
0
3
0
0
2
0
0
0
0
1
0
0
2
0
1
1
0
0
2
2
0
2
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
1
1
0
2
3
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
2
1
0
1
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
2
0
0
1
0
2
2
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
1
0
3
0
0
0
0
0
0
2
0
0
2
0
0
5
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
1
0
2
0
2
2
0
0
0
0
2
3
0
0
0
1
2
0
0
0
0
1
0
1
1
2
0
4
0
0
1
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
1
0
0
2
2
0
2
0
1
3
1
0
2
0
3
0
0
0
0
0
0
0
0
3
0
0
0
1
3
1
2
0
0
0
0
1
2
2
0
4
3
1
1
0
0
0
3
1
0
0
0
0
0
1
2
1
0
0
2
0
1
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
3
0
0
1
0
0
2
0
2
0
1
0
0
1
2
0
0
0
1
0
1
1
0
0
0
0
0
0
2
0
0
2
1
0
1
2
2
0
0
0
0
2
0
1
0
0
0
0
0
0
1
1
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
2
0
0
0
1
0
2
0
2
1
0
0
0
0
0
3
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
1
1
2
0
1
0
0
0
0
0
0
0
0
1
2
0
4
0
0
0
0
0
0
0
2
3
2
0
0
2
0
0
1
1
1
0
1
1
1
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
1
0
1
0
0
1
2
2
0
0
0
0
0
0
1
0
1
1
1
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
1
0
4
1
1
1
0
0
1
0
1
0
3
0
0
0
0
0
0
2
0
0
2
0
0
2
2
2
1
1
0
0
0
0
0
0
0
0
3
2
0
0
0
2
0
0
0
0
0
0
2
2
1
0
2
0
2
0
0
1
0
0
0
1
1
0
2
0
0
0
0
0
0
2
1
0
3
0
1
1
1
0
0
1
1
0
0
2
0
0
0
3
0
0
0
2
0
0
2
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
2
1
2
0
0
1
2
0
1
1
0
0
2
0
1
0
1
0
1
0
0
0
2
2
2
1
0
0
0
2
1
0
0
0
0
2
0
0
0
2
2
0
0
0
0
2
0
0
1
2
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
3
2
0
2
0
2
2
1
0
0
0
1
0
0
0
1
0
0
0
1
2
1
0
0
0
0
1
1
1
0
0
0
2
0
1
1
0
0
0
0
1
0
0
0
0
2
1
0
1
0
2
0
0
0
0
1
1
1
1
2
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
1
2
0
0
2
0
0
1
1
0
0
0
0
1
2
0
0
0
2
0
1
0
0
0
0
1
1
0
2
0
2
0
0
0
0
2
0
0
0
0
1
0
2
1
2
0
0
1
2
1
0
0
0
0
1
0
0
0
0
0
2
1
0
0
2
2
1
1
2
0
0
0
3
1
1
0
2
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
1
0
0
1
0
2
0
1
0
1
0
0
0
0
2
1
2
0
3
0
1
0
1
0
0
2
0
0
0
3
2
2
3
0
0
0
0
0
0
1
2
0
1
0
2
0
2
0
2
1
0
2
0
2
2
0
2
0
2
2
0
1
0
0
0
0
1
1
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
1
1
0
0
0
0
0
0
0
2
2
3
0
1
0
1
0
1
0
2
0
0
1
0
0
0
2
1
2
0
0
0
1
0
2
1
0
1
0
1
0
0
2
2
0
0
2
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
2
1
0
1
2
0
2
3
1
0
2
1
0
0
0
0
1
2
0
0
2
1
1
2
0
2
0
0
1
0
2
1
0
0
0
0
1
2
2
0
2
0
2
0
0
2
0
0
0
0
0
2
2
0
2
0
1
0
0
1
0
0
0
0
0
2
0
0
1
0
2
1
0
0
2
1
2
0
0
0
1
0
0
2
2
0
1
2
2
0
0
1
0
0
0
1
0
2
1
1
0
0
0
1
1
0
1
1
0
0
1
2
2
1
0
0
1
2
1
2
0
2
1
2
0
1
1
2
2
1
0
0
0
2
1
0
0
0
0
1
0
0
2
1
0
0
0
2
0
0
0
0
2
2
4
1
0
2
2
0
0
1
0
0
2
2
0
2
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
2
1
0
1
0
1
2
1
2
0
1
1
0
0
1
0
0
0
1
0
1
0
2
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
1
2
0
0
0
0
0
0
0
4
0
2
0
0
0
1
0
1
0
0
1
0
1
2
0
0
1
0
0
1
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
2
0
7
1
2
0
0
0
2
1
1
2
0
1
0
2
0
0
0
0
0
0
1
2
2
0
2
0
1
2
0
1
0
0
2
2
2
1
1
0
0
0
2
1
0
0
2
1
0
2
0
0
0
2
2
2
0
0
0
0
1
0
2
0
0
0
2
0
0
0
1
0
0
0
2
0
0
2
3
1
1
1
0
2
0
2
0
2
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
2
0
1
0
0
0
1
2
0
0
1
0
0
0
0
1
3
2
2
0
1
2
0
1
0
0
0
0
2
1
0
1
0
0
0
1
1
0
0
0
2
2
0
0
0
1
2
0
0
0
0
1
0
3
0
0
2
1
1
2
0
1
0
2
1
0
0
1
1
0
3
2
0
1
0
0
0
2
0
1
0
0
2
0
1
5
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
1
0
1
2
0
1
1
2
1
0
0
0
0
1
0
0
2
0
1
0
0
2
0
1
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
1
0
1
0
0
2
1
0
0
0
0
0
0
0
3
2
2
0
1
0
0
2
0
1
2
1
0
0
0
0
0
1
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
3
3
0
1
1
0
0
0
0
0
1
2
1
1
0
0
1
0
2
1
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
1
2
2
1
3
1
0
0
1
1
0
2
0
0
0
3
1
0
0
1
1
0
0
0
2
0
0
2
0
2
2
0
0
0
0
2
1
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
2
0
0
1
0
0
0
1
1
0
2
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
2
3
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
2
1
2
2
0
0
0
0
4
2
0
1
2
0
0
0
1
0
0
0
2
1
0
0
2
0
0
0
0
1
0
1
1
0
2
0
0
2
3
2
2
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
2
2
0
0
0
0
0
0
0
1
0
2
2
2
0
0
4
2
1
0
3
0
2
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
2
0
0
0
0
1
0
0
1
2
2
0
4
2
2
0
0
0
3
0
0
1
0
2
0
0
0
6
0
0
2
0
0
0
0
2
0
2
1
0
0
0
0
2
0
0
1
0
2
0
0
0
2
0
1
1
0
1
2
0
0
0
1
0
0
0
2
0
0
0
0
0
2
2
0
2
0
1
0
1
1
1
0
1
0
2
0
1
2
0
0
2
0
0
0
0
2
0
2
0
2
2
0
2
1
0
1
0
0
1
0
2
0
1
0
0
2
0
2
0
1
0
0
1
2
0
2
2
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
1
0
1
0
2
0
0
1
0
0
0
0
0
1
0
1
0
1
1
0
1
0
2
1
0
0
0
0
1
0
0
2
0
1
0
1
3
0
2
2
2
1
0
0
0
2
0
0
0
1
0
1
2
1
1
1
0
0
2
0
0
1
0
0
2
0
0
1
1
0
5
2
0
1
0
1
0
0
1
0
2
1
0
0
0
1
2
0
1
1
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
1
0
0
0
1
0
0
0
2
1
2
0
0
0
1
0
0
0
3
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
2
2
1
0
0
3
0
2
1
0
0
0
0
3
0
0
0
1
1
2
0
1
0
0
2
0
0
1
2
0
2
0
0
1
1
2
0
7
0
2
1
0
0
2
0
1
2
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
3
1
4
0
1
1
2
0
0
2
1
0
0
0
0
0
0
2
0
0
0
2
1
0
0
2
2
0
2
0
0
0
0
0
1
0
0
4
2
0
0
1
0
0
1
0
0
1
0
0
2
1
2
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
2
1
2
0
0
0
1
2
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
2
0
1
0
0
1
0
0
1
0
0
0
0
0
2
0
0
2
1
0
0
1
0
2
0
1
2
4
0
1
0
0
0
1
1
0
1
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
4
0
1
0
2
0
0
0
3
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
2
0
1
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
1
2
0
0
1
1
1
0
0
0
0
2
0
1
3
0
2
0
0
0
1
1
0
0
0
2
2
1
0
1
1
0
0
2
0
0
0
2
0
0
0
1
2
0
0
0
1
1
0
0
2
0
0
2
2
0
0
0
0
2
1
0
0
0
0
2
0
2
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
2
1
0
0
2
0
0
0
0
1
3
2
0
0
0
0
0
2
0
1
1
0
0
1
0
2
0
0
1
1
1
0
0
0
0
2
0
0
0
2
1
0
2
0
0
3
1
5
0
0
1
0
0
0
1
1
2
2
0
0
0
0
0
2
0
1
1
0
0
0
4
2
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
1
3
0
2
0
2
0
0
1
2
1
0
0
0
0
0
2
0
1
0
0
1
4
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
1
0
0
0
3
0
0
1
0
3
0
0
0
0
1
3
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
2
1
1
0
2
0
0
0
0
2
0
0
0
2
2
1
0
0
0
0
1
0
2
2
1
2
2
0
0
0
2
0
1
3
0
1
0
0
0
0
1
0
0
0
0
0
0
2
2
2
0
2
2
1
0
0
1
0
0
7
0
0
0
0
0
0
2
0
2
1
1
0
0
0
0
0
2
0
1
1
0
2
0
0
0
0
0
1
0
2
0
0
0
0
1
0
2
2
2
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
2
0
0
0
2
2
2
4
0
1
3
0
3
1
2
0
2
1
0
0
1
0
0
0
1
0
0
1
0
2
0
0
3
0
0
2
2
0
0
0
2
2
2
2
0
0
0
0
0
1
0
0
1
3
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
1
0
2
2
2
1
0
0
1
0
0
0
0
2
0
2
2
0
0
2
2
2
0
0
2
0
0
1
1
0
0
0
1
1
1
0
1
1
0
1
1
0
0
2
1
1
1
1
0
0
0
0
2
1
0
0
0
1
2
2
1
0
1
1
1
2
0
0
2
0
1
0
2
0
1
1
0
0
1
0
1
0
1
0
0
0
1
1
0
1
0
1
0
1
0
0
0
1
0
0
0
1
0
2
0
0
0
2
0
2
0
1
0
2
1
0
0
1
2
2
0
0
0
2
0
2
3
2
0
2
0
1
2
0
2
2
2
2
2
0
0
0
1
3
0
0
0
1
0
0
0
1
1
1
5
0
2
1
0
0
2
0
0
0
0
0
2
0
1
2
2
1
0
0
0
0
0
0
1
1
2
0
0
0
2
0
0
2
1
0
0
1
0
0
1
0
0
2
1
1
1
0
0
0
2
0
0
0
0
2
1
0
0
1
0
0
0
0
2
0
0
2
2
0
0
2
0
0
0
0
0
2
0
1
2
0
2
1
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
1
0
0
0
0
1
0
1
1
1
0
1
1
0
0
0
0
0
1
0
2
0
0
2
0
3
1
1
0
0
1
0
0
0
0
0
0
1
0
1
2
0
0
1
0
0
2
0
0
0
0
1
0
1
0
1
0
2
1
2
2
0
0
0
0
0
0
2
0
1
0
2
1
1
0
0
0
0
2
5
0
1
1
0
0
0
0
0
0
4
0
0
1
1
0
0
2
0
0
2
2
0
0
0
0
0
1
2
1
3
0
1
0
0
0
0
2
0
1
2
0
0
1
0
0
1
0
1
3
2
0
1
0
0
0
2
0
0
0
0
0
0
2
0
1
2
1
0
0
0
0
0
0
0
0
0
1
1
1
2
0
0
0
0
1
2
0
0
0
0
1
0
2
0
0
0
1
0
3
1
0
0
1
0
0
1
0
2
4
2
0
0
0
0
0
2
0
0
0
0
1
0
1
2
0
2
0
0
2
1
0
2
0
1
1
4
2
0
2
0
3
1
0
0
0
1
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
6
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
2
1
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
2
1
5
0
1
1
0
0
0
2
0
0
0
0
2
0
0
0
0
1
1
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
2
2
0
0
2
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
2
2
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
2
0
0
0
2
2
0
1
0
3
0
0
0
0
1
0
0
2
2
2
0
2
0
2
0
2
2
0
1
0
2
0
6
0
2
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
2
2
2
0
0
1
0
0
1
0
1
1
0
2
0
0
0
0
1
0
1
0
0
2
0
2
0
0
0
0
2
0
0
0
1
1
2
0
1
0
0
1
0
0
1
2
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
2
2
0
1
0
0
1
0
0
0
0
2
0
1
2
0
2
0
0
0
0
4
0
0
0
1
0
1
0
0
1
3
0
0
0
2
1
0
1
0
0
0
1
0
0
1
1
1
0
0
0
2
1
2
0
2
0
0
0
0
0
1
0
2
1
0
0
1
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
4
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
4
1
2
1
0
0
2
0
0
3
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
3
1
2
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
2
1
0
0
2
0
0
0
1
1
1
0
2
1
0
0
1
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
1
6
0
1
1
0
0
1
2
0
2
1
1
0
0
2
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
2
0
2
0
2
0
0
0
0
1
0
0
2
2
2
0
0
2
0
1
0
0
3
0
0
0
0
1
0
0
2
0
0
0
1
0
0
2
1
1
0
0
0
0
2
0
0
0
0
1
1
1
1
0
1
2
1
0
0
0
0
2
0
2
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
2
0
0
3
0
0
0
0
2
2
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
4
1
1
0
0
0
0
2
2
1
1
1
1
0
0
0
1
0
4
1
1
0
0
0
0
2
4
3
1
0
0
0
0
0
0
0
1
0
0
1
0
0
2
1
0
1
6
0
2
0
1
0
1
3
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
2
0
0
1
0
0
0
0
0
0
2
1
0
0
0
3
0
0
0
0
1
0
1
0
1
3
0
2
1
1
0
2
0
1
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
2
2
2
1
1
0
0
0
0
1
0
0
0
0
2
0
4
1
0
0
0
2
0
0
0
2
2
0
2
0
3
1
0
0
3
2
0
1
0
2
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
1
1
1
0
1
0
6
2
2
0
1
1
1
0
0
2
2
0
1
2
0
0
0
1
2
1
2
2
0
4
1
0
1
1
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
1
2
2
0
1
0
1
0
0
1
0
2
2
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
2
1
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
2
2
0
0
0
1
0
2
1
0
1
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
1
2
2
3
0
0
0
2
0
1
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
2
0
1
0
0
0
0
0
1
2
0
0
2
0
1
1
0
0
0
0
1
0
2
0
2
1
2
0
0
1
2
0
0
2
1
0
1
0
0
3
0
0
1
2
0
1
2
0
0
2
0
0
0
0
0
1
2
2
0
1
0
0
0
0
0
1
1
0
1
2
0
2
0
0
0
2
0
1
2
2
0
0
0
0
1
1
1
2
0
0
0
1
2
0
0
0
2
1
0
0
0
2
0
1
1
2
0
0
0
1
0
0
0
2
1
0
1
2
0
0
0
0
0
0
1
2
0
0
0
0
1
0
1
1
0
0
0
1
0
1
0
0
2
0
4
1
1
0
1
1
2
1
1
0
0
1
1
0
0
0
2
6
2
0
0
0
2
0
0
1
0
0
2
0
0
1
1
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
2
2
0
1
2
0
0
3
0
0
0
0
3
0
1
1
0
0
1
0
1
0
2
0
0
2
0
0
0
0
1
0
1
0
2
0
0
0
1
0
1
2
1
0
0
0
0
2
0
0
1
2
0
0
2
0
0
1
1
0
0
1
0
0
0
1
0
1
2
2
0
1
0
1
2
0
0
0
0
1
0
1
0
0
2
0
0
0
0
1
1
0
0
0
0
1
0
1
2
0
0
1
0
0
0
0
1
0
2
1
2
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
2
0
0
0
2
0
0
1
0
3
6
0
1
1
2
2
1
1
0
0
0
0
0
0
0
0
2
0
4
0
0
2
0
0
1
2
0
0
0
6
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
2
0
0
0
0
1
1
0
0
0
1
0
0
0
2
4
0
0
2
2
1
1
0
0
1
1
0
1
0
2
0
0
0
0
2
0
3
2
0
0
2
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
2
0
2
1
0
0
0
3
2
0
2
1
0
0
1
1
0
2
0
1
0
0
0
0
0
0
2
1
0
0
1
2
2
0
0
1
0
0
0
0
0
0
1
0
2
1
0
0
0
0
1
1
0
0
0
1
0
1
2
1
2
1
0
0
2
1
0
0
0
2
2
0
2
0
1
1
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
1
0
3
0
2
1
1
0
0
3
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
1
0
1
0
0
1
9
2
0
2
2
2
1
0
0
0
0
0
2
1
1
0
0
0
2
0
2
0
0
0
0
0
0
1
2
1
0
1
0
1
1
0
1
0
0
0
2
0
1
0
1
0
2
2
2
1
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
2
2
0
0
0
0
2
2
1
2
1
2
2
0
0
2
0
0
0
0
0
0
0
2
2
0
1
0
0
2
0
0
1
1
2
0
0
0
3
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
2
2
1
0
0
0
0
0
0
0
0
1
1
3
1
1
2
0
2
0
2
0
0
0
1
0
0
0
0
0
3
2
0
1
2
0
0
0
0
0
1
3
0
0
1
1
1
0
3
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
2
2
1
2
0
0
0
1
1
0
0
1
1
1
0
2
0
2
6
0
0
2
2
1
1
0
0
0
2
2
0
0
0
1
0
0
0
0
0
2
0
0
0
1
2
0
2
0
2
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
1
1
4
0
0
1
2
0
1
0
2
0
0
1
0
2
1
1
2
0
2
0
1
1
1
1
0
0
0
0
0
2
0
0
2
1
2
0
1
0
0
2
0
0
0
0
0
2
1
0
0
2
0
0
2
2
1
0
0
0
2
0
0
2
2
1
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
1
1
2
0
2
0
1
0
1
0
0
2
0
1
3
0
1
7
0
0
0
0
0
0
1
0
0
1
2
1
1
0
0
0
0
2
2
0
0
2
1
0
2
0
0
0
2
2
1
0
0
3
1
0
2
0
0
1
2
2
0
2
0
1
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
2
2
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
1
1
0
0
0
2
0
3
0
0
2
1
0
0
1
0
3
1
1
0
0
0
0
0
2
0
1
2
0
0
2
0
0
0
0
0
2
2
0
2
1
0
0
0
2
2
0
0
0
1
2
1
0
1
1
0
2
0
0
0
2
0
2
0
2
0
2
0
0
0
2
0
1
1
2
2
2
1
0
0
0
2
2
0
2
0
0
0
1
3
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
1
1
1
1
1
0
0
1
0
0
2
2
0
0
0
2
0
0
1
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
1
0
2
0
0
2
2
0
0
0
1
3
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
2
0
3
1
0
0
0
0
0
0
1
0
1
0
0
1
1
1
0
0
0
0
1
0
0
2
0
1
0
1
0
0
1
1
4
0
0
0
2
0
1
2
1
1
0
0
0
0
2
2
1
2
2
0
0
1
1
3
2
1
0
0
2
1
0
2
0
2
0
2
4
1
0
0
0
2
0
0
2
1
0
0
3
0
2
0
2
0
2
1
2
0
0
2
2
0
0
0
0
2
0
1
0
0
0
0
2
1
0
2
0
0
0
1
0
2
2
0
0
2
0
2
0
0
0
2
2
2
0
0
1
0
1
0
1
0
0
1
1
2
0
0
0
0
1
0
1
0
0
1
1
2
1
1
0
0
0
0
0
1
0
2
3
1
2
0
2
0
0
0
1
0
0
0
0
2
0
0
0
1
0
2
0
0
2
0
0
1
2
0
0
0
0
1
0
2
0
0
0
0
2
1
1
1
0
2
2
2
0
1
2
0
0
0
2
0
0
0
0
0
0
1
1
1
1
1
0
0
2
0
1
2
0
0
1
0
0
0
0
2
1
0
1
0
0
2
0
0
0
0
2
0
0
2
0
3
0
0
2
0
1
3
0
0
0
0
0
0
0
1
2
0
0
0
0
4
2
0
0
0
1
2
4
0
0
2
0
6
1
1
0
2
0
0
0
0
2
0
0
0
1
1
0
0
0
0
2
0
0
2
0
2
0
0
2
0
2
1
1
2
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
3
2
1
1
0
0
1
0
0
0
0
0
0
2
1
1
0
0
0
0
0
1
0
1
0
0
0
1
0
1
2
0
0
2
0
0
1
0
1
1
2
0
1
1
0
0
0
0
0
0
0
1
2
1
0
2
2
2
0
0
0
0
0
0
0
0
3
0
0
1
2
1
2
0
0
0
2
1
1
0
0
0
0
2
1
0
0
1
0
2
2
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
1
0
0
2
2
0
0
0
1
1
0
2
0
2
0
1
2
1
0
0
0
0
1
0
2
0
0
0
0
2
0
1
0
1
0
1
0
0
2
0
0
0
1
1
2
0
0
0
0
1
0
2
0
0
0
3
1
1
0
0
0
0
2
0
0
0
1
1
0
1
0
0
0
4
0
0
1
1
2
0
1
0
2
2
0
0
0
0
2
1
1
0
0
0
1
0
2
3
0
1
0
1
0
1
0
0
0
0
0
2
2
2
1
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
2
1
0
0
2
0
0
0
0
1
0
1
0
1
1
0
0
2
1
0
0
0
0
1
0
1
0
0
0
0
4
0
0
0
2
0
0
1
0
0
0
0
2
1
0
0
1
1
0
0
0
0
0
0
2
1
2
0
0
2
1
0
4
0
0
0
0
1
1
0
0
0
0
3
0
0
0
0
1
1
1
1
0
1
1
1
0
1
1
0
0
0
0
1
3
0
0
0
0
2
0
2
0
2
3
1
0
0
0
2
0
0
2
0
0
0
0
0
1
0
2
0
4
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
1
0
1
2
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
1
0
1
0
2
0
1
0
0
0
2
0
0
0
0
0
0
1
1
2
2
2
2
0
0
2
3
0
0
1
2
2
0
1
0
0
0
0
0
0
2
2
1
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
2
0
1
1
0
2
2
0
0
3
0
1
0
0
0
0
0
1
0
0
0
0
2
1
2
0
1
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
2
0
0
0
3
1
0
0
0
0
0
0
0
0
2
2
0
0
2
1
0
0
2
2
0
0
1
0
0
2
0
0
1
0
0
2
0
0
1
2
0
0
0
0
0
0
2
1
2
1
1
0
0
4
0
1
0
0
1
1
1
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
2
0
0
0
1
0
0
0
2
0
0
1
1
2
1
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
1
0
1
2
0
0
0
2
0
2
0
2
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
2
2
4
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
2
0
2
0
0
0
1
2
0
0
2
0
0
0
0
1
2
0
0
2
0
2
0
2
2
2
1
0
0
1
1
0
0
1
2
2
0
0
1
0
0
0
1
2
1
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
2
0
2
1
0
0
1
0
1
0
0
0
0
0
2
0
0
0
1
0
1
0
1
0
0
0
1
0
0
1
0
1
2
0
0
0
0
1
0
1
0
0
2
1
0
0
0
0
2
1
1
0
0
0
1
0
0
0
3
0
0
0
0
0
2
2
1
1
1
2
0
2
0
0
0
0
0
1
0
0
1
0
0
0
3
0
0
1
1
1
2
2
0
2
2
0
0
0
3
0
0
0
0
1
1
2
0
0
0
0
0
2
2
0
0
2
0
0
0
0
2
1
0
2
0
0
0
0
2
0
0
2
1
0
0
0
0
2
1
0
0
0
0
0
0
2
0
1
0
0
0
1
0
2
1
0
2
1
0
0
2
0
2
1
0
0
0
0
2
1
0
0
2
0
1
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
4
0
2
0
2
0
0
0
0
0
0
0
1
1
0
1
2
1
0
2
2
2
1
0
1
1
0
1
4
2
1
0
0
0
2
0
0
0
1
2
2
1
0
0
1
0
2
0
0
0
1
0
0
0
0
0
2
0
2
2
2
0
2
0
2
1
1
2
0
0
2
1
0
0
0
0
0
0
1
0
2
0
0
1
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
2
0
2
1
0
0
0
2
1
2
0
2
1
2
1
2
0
0
1
2
2
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
1
0
2
0
0
1
0
2
1
0
0
2
0
0
0
0
3
0
1
0
1
0
0
0
0
0
0
0
0
0
2
1
0
1
1
0
1
0
0
2
3
0
0
0
0
1
2
2
0
0
0
0
1
0
0
0
0
0
1
1
0
2
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
2
1
2
0
0
0
1
2
0
0
0
0
1
2
0
3
0
0
2
2
0
1
0
1
0
1
2
2
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
1
1
1
0
0
0
0
1
2
2
2
1
2
2
1
0
2
1
0
1
0
2
0
1
0
0
2
0
0
3
1
0
1
0
0
1
1
0
0
2
1
0
0
2
0
0
0
0
0
2
0
0
0
0
2
2
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
2
0
1
0
0
2
2
0
0
0
0
0
0
0
1
0
1
0
1
0
2
2
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
2
0
1
0
0
0
0
2
1
0
1
1
0
0
0
3
0
2
0
1
0
0
0
0
2
2
0
0
0
2
2
2
0
0
1
1
0
0
1
0
0
0
0
0
1
0
2
0
1
1
0
0
2
0
0
0
1
2
0
2
0
0
0
2
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
2
0
2
2
2
1
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
1
0
2
0
2
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
2
0
1
0
0
0
0
0
2
2
0
0
0
2
0
0
0
2
1
0
0
0
1
2
1
1
1
0
2
0
0
1
1
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
1
1
2
0
1
2
2
1
2
0
2
0
7
1
0
0
0
1
1
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
5
1
0
0
2
1
0
1
2
1
0
2
2
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
2
1
0
1
0
0
0
2
0
2
0
1
0
0
0
0
1
2
0
0
0
2
0
1
1
0
2
0
1
0
0
1
0
2
0
0
1
3
3
1
1
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
2
2
2
0
2
3
0
2
0
2
3
0
1
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
2
0
2
0
1
0
0
2
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
2
0
0
1
2
0
0
0
1
0
0
2
0
0
0
0
1
1
1
0
1
0
2
0
1
0
1
0
0
0
0
0
1
2
1
0
2
1
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
1
0
0
1
0
0
2
0
1
1
1
0
0
0
0
0
2
0
0
0
0
2
1
2
1
1
2
0
0
0
0
0
0
1
0
2
0
0
1
0
2
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
2
0
2
0
0
0
0
0
2
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
4
0
0
0
2
1
0
0
2
0
0
0
0
2
0
1
0
0
2
0
0
2
1
1
2
1
0
0
1
1
0
0
0
0
2
0
0
0
0
2
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
1
0
2
2
2
2
0
2
0
2
1
0
0
0
0
1
1
0
0
0
0
3
4
0
1
0
6
0
1
0
1
0
1
0
0
1
1
1
0
0
2
0
0
2
2
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
2
0
3
0
0
1
1
1
0
1
0
1
1
1
0
0
2
0
0
0
0
0
0
0
1
1
0
2
1
0
0
2
1
0
2
0
0
0
1
0
1
1
0
2
2
0
0
0
1
0
2
1
0
2
1
0
1
0
3
0
0
0
2
0
0
1
0
0
0
0
0
1
2
0
0
2
0
0
0
0
2
0
1
2
1
2
2
0
1
0
1
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
1
0
1
4
2
0
1
0
0
0
0
0
0
0
1
0
0
0
3
1
0
2
0
2
0
2
0
0
0
2
0
0
2
0
1
2
1
0
0
0
3
0
1
1
0
1
2
1
2
0
0
2
0
0
0
0
0
0
0
1
0
0
1
2
0
2
0
1
2
0
0
0
2
0
0
1
1
1
0
1
0
0
0
0
0
0
1
2
1
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
2
0
0
0
1
2
1
0
1
1
0
1
0
0
1
2
2
0
0
1
1
0
0
0
1
2
0
1
0
0
2
0
2
0
0
1
1
1
0
0
0
1
3
0
0
1
2
0
0
1
0
0
0
0
1
1
1
0
0
0
2
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
2
0
2
0
0
0
0
1
0
2
0
0
0
0
2
0
1
0
2
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
1
0
1
0
0
1
0
0
1
1
3
0
0
1
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
1
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
2
0
0
0
1
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
1
0
1
2
1
1
0
0
1
1
0
4
0
1
0
2
1
0
0
1
0
0
0
2
0
2
0
0
3
0
0
2
1
0
0
0
2
1
0
0
0
0
0
0
0
2
0
2
1
0
0
0
1
0
0
0
0
2
1
0
1
0
0
2
0
1
0
0
2
2
2
2
1
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
2
0
0
1
1
0
2
0
1
0
1
2
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
3
0
2
2
0
0
0
0
2
0
2
0
0
0
1
0
1
0
1
0
0
2
0
0
0
0
1
0
1
2
0
0
0
0
1
0
1
1
0
0
2
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
2
0
0
2
0
0
2
2
1
1
1
0
2
0
0
0
2
1
0
0
0
0
1
0
0
0
1
2
0
0
0
0
1
0
1
0
0
1
0
0
0
2
0
1
2
0
2
2
0
0
0
0
2
2
0
0
0
1
1
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
2
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
2
1
0
0
0
1
0
2
0
0
0
2
1
1
0
0
1
1
0
1
1
0
0
0
0
0
1
2
0
0
0
1
1
0
3
1
2
0
1
1
4
1
0
0
2
0
0
1
0
2
2
0
2
0
1
0
0
2
2
0
1
0
0
2
0
2
0
1
2
1
1
0
1
0
2
0
0
2
0
0
2
0
1
2
1
2
0
1
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
2
0
1
0
0
0
1
1
2
0
2
1
1
0
1
0
1
0
0
1
0
1
0
0
0
2
0
1
1
1
0
2
0
0
0
0
2
1
1
0
0
0
2
1
2
1
0
0
0
0
0
0
1
0
0
0
1
1
2
0
0
2
3
0
0
2
0
0
2
2
0
0
1
1
0
0
2
1
2
0
0
0
0
2
0
0
0
0
1
1
1
1
1
0
2
1
0
0
0
0
0
1
2
0
0
0
1
2
1
0
0
0
0
1
1
0
2
0
4
1
1
0
0
0
3
0
0
0
1
0
0
0
1
1
1
0
0
1
0
0
0
1
0
1
0
0
0
2
2
0
1
0
0
0
2
1
0
1
2
0
0
0
2
0
0
0
1
3
0
1
2
1
2
0
0
0
2
0
1
1
2
0
0
0
0
1
2
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
1
1
2
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
2
2
0
0
0
0
4
0
0
2
0
0
0
0
0
0
2
1
3
0
0
0
0
2
1
2
0
3
2
0
1
0
2
0
0
3
2
0
0
0
1
0
1
1
0
1
0
1
0
1
1
1
0
1
2
2
1
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
0
0
1
1
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
1
0
2
1
1
0
0
0
3
0
0
0
1
2
2
1
0
0
2
0
0
0
1
0
0
2
1
2
0
0
0
0
2
0
0
1
2
1
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
2
0
0
1
0
0
0
2
0
0
2
1
0
3
0
0
0
2
1
0
0
0
0
2
1
1
0
1
0
1
0
0
0
1
0
0
0
1
1
2
1
0
2
0
2
0
0
0
1
0
0
0
0
0
1
0
0
2
0
2
0
4
1
0
0
0
0
1
2
0
1
0
0
0
2
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
2
1
1
1
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
2
0
1
2
0
2
3
0
0
2
0
0
1
2
0
2
0
1
2
1
2
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
2
0
1
0
1
1
0
0
1
0
1
2
1
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
2
0
2
0
0
0
0
0
1
2
0
1
2
2
0
0
0
0
1
0
0
1
0
1
0
0
1
2
2
0
0
0
0
0
2
0
0
1
1
1
2
0
0
1
1
0
0
0
0
2
2
0
2
0
0
0
0
0
0
1
1
0
0
2
0
1
0
0
0
2
1
0
0
0
0
0
3
0
1
2
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
1
0
1
2
0
0
2
1
0
3
0
0
0
0
0
0
0
2
2
0
0
0
2
0
2
0
2
0
1
1
1
0
1
1
0
2
1
1
0
1
1
2
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
2
1
0
0
0
1
0
0
0
0
0
1
0
2
0
0
1
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
2
2
2
0
0
1
0
1
2
2
1
1
0
1
1
0
2
0
0
0
0
1
0
1
0
2
0
0
2
0
0
1
0
0
0
1
0
2
0
0
2
0
2
0
2
2
0
0
1
0
0
1
2
0
0
1
0
0
0
4
0
0
0
0
1
2
0
2
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
1
1
2
6
2
0
0
0
0
1
2
0
1
2
1
1
2
2
2
2
0
2
0
2
0
1
1
2
0
0
0
0
1
0
0
1
2
0
0
0
1
0
1
0
0
0
0
0
0
3
0
0
0
3
0
1
1
3
0
0
1
0
0
0
0
0
1
1
0
1
1
1
0
0
0
2
0
0
0
0
1
0
0
1
0
2
1
0
2
0
2
0
2
0
0
1
2
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
4
2
2
0
0
0
2
0
2
3
3
0
0
0
0
1
0
0
0
0
0
1
1
2
0
1
0
0
0
0
0
1
1
0
1
0
2
0
0
2
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
2
0
2
1
0
0
0
0
0
4
1
0
0
23
0
1
1
0
0
4
0
0
0
0
0
1
10
0
1
2
1
1
0
0
0
0
1
2
0
2
1
0
0
0
0
2
1
1
1
0
0
2
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
1
0
1
0
0
2
0
0
0
1
1
3
0
1
1
1
1
0
2
1
0
0
1
0
0
0
1
0
3
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
1
0
2
1
0
1
0
0
0
0
2
0
0
1
1
2
0
0
2
0
2
0
0
2
0
2
2
1
3
2
0
0
3
2
0
0
0
0
1
0
0
2
2
0
0
2
1
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
3
1
1
0
1
0
0
2
0
0
0
1
0
0
0
2
1
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
1
2
2
0
1
0
1
1
2
4
2
0
0
2
2
0
1
0
0
1
0
1
1
0
0
1
0
0
2
0
0
0
0
1
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
2
1
1
2
0
0
0
2
0
0
0
0
1
2
5
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
2
2
0
0
0
1
1
0
0
0
2
2
0
0
0
2
2
0
0
0
1
0
2
1
1
0
1
1
1
0
0
0
2
0
0
0
1
0
0
1
2
1
0
2
0
1
0
0
0
0
0
0
2
0
1
1
0
0
2
2
0
1
0
1
1
1
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
2
1
0
1
1
0
1
1
1
0
2
1
0
0
1
0
1
0
2
1
2
0
2
0
2
1
2
0
0
1
0
0
0
2
0
0
0
1
1
0
1
0
0
0
0
2
0
0
1
0
2
0
1
0
0
0
2
0
0
2
2
0
0
0
5
2
0
3
1
0
0
0
0
0
2
0
1
1
2
1
0
0
2
0
0
2
0
1
2
0
0
0
1
0
0
0
0
0
3
2
2
0
1
0
0
0
2
1
0
2
0
1
0
0
1
1
3
0
0
0
0
0
0
0
1
0
2
0
1
0
2
2
0
0
0
0
2
0
1
2
0
0
0
3
0
1
0
1
0
0
0
1
2
0
0
0
1
0
0
2
0
0
0
1
0
0
1
1
0
0
0
2
0
0
0
2
2
1
1
1
2
0
4
2
0
0
0
0
0
1
2
1
0
0
0
1
3
0
1
0
0
0
2
2
3
0
0
2
0
2
2
1
1
0
1
2
1
1
0
2
0
2
0
0
3
0
0
0
0
0
0
1
1
1
0
1
0
0
1
6
0
0
0
1
2
0
2
0
0
0
0
1
0
0
2
1
0
1
0
0
1
0
2
0
3
0
0
0
1
0
1
2
0
0
0
0
0
1
1
2
1
0
0
0
2
0
0
1
1
0
2
1
1
0
0
0
0
0
0
0
1
2
1
0
0
2
0
0
0
2
2
0
1
2
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
3
0
0
0
6
3
0
3
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
2
2
2
0
0
0
2
0
1
0
0
2
1
0
2
2
0
1
2
0
0
2
0
0
0
0
3
2
1
2
1
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
1
2
2
0
0
8
0
2
1
0
0
1
0
1
1
1
1
0
0
0
0
1
0
1
0
0
0
1
1
1
1
0
0
3
0
0
0
1
0
0
0
2
2
1
0
0
0
1
0
0
2
0
0
2
0
1
0
1
1
1
0
1
0
1
1
1
0
0
1
0
0
0
0
1
2
1
0
0
0
1
2
1
0
2
2
0
0
1
2
0
0
1
1
0
2
0
1
0
1
0
0
0
1
1
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
1
1
0
2
1
0
0
2
1
0
1
0
2
0
0
0
0
0
1
2
0
1
2
0
1
0
0
0
2
0
0
0
0
1
2
0
2
0
0
0
0
0
0
1
1
0
0
2
0
0
1
0
0
1
0
2
0
0
0
0
0
0
2
2
0
0
0
2
2
1
1
1
0
2
0
0
1
0
2
1
0
1
2
3
0
2
5
0
2
0
0
0
0
0
2
0
0
1
0
1
0
1
0
0
0
0
2
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
2
0
0
1
1
0
0
1
0
1
0
2
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
2
0
1
0
0
1
0
0
0
0
0
0
1
1
3
1
2
0
0
1
0
2
0
0
0
0
1
2
1
0
0
0
1
0
0
1
0
0
2
1
1
0
1
0
0
4
0
1
1
5
0
0
2
0
3
1
0
1
2
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
1
0
1
2
0
0
0
2
0
0
0
1
1
0
1
2
0
0
0
0
0
1
0
0
0
0
1
0
2
0
1
0
1
1
0
2
0
0
0
0
0
1
2
0
2
0
1
0
0
0
0
1
0
0
1
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
2
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
1
1
0
1
0
2
0
0
1
0
0
2
0
2
0
0
1
0
0
0
2
0
0
1
1
0
0
0
1
1
1
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
2
0
2
0
0
0
3
0
2
2
2
0
0
2
2
2
0
0
0
3
1
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
1
0
0
3
2
1
0
2
3
1
0
0
2
1
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
2
1
2
0
0
1
0
1
0
1
0
2
0
0
2
1
0
0
2
0
0
1
1
0
0
2
1
0
0
0
0
0
2
0
0
0
0
1
2
0
0
1
0
0
2
1
2
2
0
0
2
3
1
2
2
0
1
1
1
1
0
1
1
2
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
2
0
0
0
1
2
1
0
0
5
0
0
1
1
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
2
0
2
0
0
1
0
1
1
0
0
1
1
2
0
1
0
2
0
1
0
0
0
2
0
2
1
1
0
0
1
0
1
0
2
2
0
0
0
2
0
2
0
0
0
1
1
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
1
1
0
1
1
2
0
0
0
0
2
0
2
1
0
0
3
0
0
0
2
2
0
0
0
1
6
0
2
3
1
1
3
0
0
2
4
0
0
0
0
2
0
0
2
1
2
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
3
0
2
0
0
0
0
0
0
1
2
2
2
1
3
0
0
0
0
0
0
0
1
1
2
0
0
1
0
1
0
0
1
0
2
0
2
2
1
0
1
0
0
0
0
1
0
2
1
2
1
0
0
0
0
2
0
2
2
0
2
0
0
1
0
0
0
0
0
2
0
0
0
2
1
2
0
0
0
0
0
0
1
0
0
2
0
1
2
1
2
2
0
0
0
0
0
1
0
0
0
2
0
1
2
0
0
0
0
0
2
1
0
0
0
2
0
0
2
0
2
0
0
0
0
2
0
3
0
0
0
1
0
2
0
0
0
0
2
0
1
1
0
2
1
1
0
0
0
0
0
0
0
0
2
1
0
0
2
2
1
0
1
0
1
0
0
1
2
0
1
0
1
1
0
2
1
0
0
0
0
2
1
2
1
2
0
2
1
0
2
2
1
0
1
2
0
2
2
0
2
0
0
0
2
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
2
2
0
2
2
0
1
0
2
0
0
0
1
0
1
0
1
0
0
1
2
1
1
0
2
3
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
2
2
0
0
1
0
0
0
0
0
1
0
0
0
2
0
1
0
3
1
0
0
0
2
0
0
3
0
1
2
1
0
2
0
0
0
0
0
0
1
0
0
1
1
0
0
6
1
0
3
2
0
0
0
0
1
0
0
1
0
1
0
0
0
2
1
0
1
0
0
0
0
1
1
2
0
0
0
0
2
2
0
1
1
0
0
1
0
0
1
1
0
2
0
0
0
2
0
1
2
0
0
0
0
6
0
1
0
0
2
2
2
0
0
2
1
0
2
2
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
2
0
0
0
2
0
0
2
1
0
0
2
1
1
0
2
0
0
0
0
0
1
2
0
1
0
2
0
0
1
0
1
0
0
0
2
0
0
0
2
2
1
1
0
0
0
0
2
2
0
1
0
0
0
0
0
0
1
2
1
7
0
2
0
0
0
1
2
1
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
1
0
3
0
1
1
0
1
0
2
2
1
0
0
1
1
1
0
1
1
0
1
0
2
2
0
2
0
1
2
5
2
2
1
0
2
1
0
0
0
2
1
0
0
0
0
1
0
0
2
0
0
0
2
0
0
2
0
2
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
2
4
0
2
3
0
0
0
0
1
2
2
0
1
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
2
1
1
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
2
0
2
0
1
1
0
0
0
1
0
1
0
0
0
1
0
2
1
0
0
0
3
0
1
2
1
0
1
2
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
2
1
2
0
0
1
1
0
1
0
0
1
0
0
0
1
2
1
1
2
0
0
0
0
2
1
2
0
0
0
1
0
0
1
0
0
0
3
1
0
0
0
1
0
1
2
2
2
0
0
0
2
2
2
1
2
3
2
0
0
2
0
0
0
1
1
0
0
2
0
2
0
0
0
1
2
1
0
0
0
0
0
0
0
2
2
0
0
1
1
0
0
0
1
0
0
0
1
2
0
2
1
1
0
0
0
0
1
0
0
1
2
0
1
0
1
0
1
0
0
0
0
0
2
0
0
1
0
2
0
1
0
2
0
0
1
2
0
0
0
2
2
0
4
0
0
1
1
0
0
0
1
0
1
0
0
1
1
0
0
0
0
2
0
0
2
0
0
1
4
1
2
1
0
1
2
2
0
1
1
3
0
0
0
0
1
0
2
2
0
0
1
0
2
2
0
0
1
0
0
2
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
4
1
0
0
0
2
0
3
0
2
0
1
0
0
1
0
0
0
0
0
0
2
1
0
0
1
0
0
0
2
0
0
1
0
0
0
1
0
0
0
2
1
0
0
0
3
0
0
0
0
3
0
2
0
0
0
0
0
1
0
0
2
1
0
1
0
0
2
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
2
1
0
1
1
0
2
4
0
0
0
0
0
1
1
0
0
0
2
1
0
0
2
2
2
1
0
1
0
0
0
2
0
0
0
1
0
0
0
0
2
0
1
2
1
0
0
0
1
2
0
0
2
2
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
2
0
0
1
0
0
1
0
0
2
2
0
0
0
0
2
0
0
2
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
2
2
0
0
1
0
1
2
1
0
2
0
1
3
0
0
0
0
0
2
1
0
2
0
1
1
1
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
1
3
1
0
1
0
1
0
0
0
1
1
0
1
0
2
0
1
0
0
0
2
0
2
1
2
0
1
0
0
2
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
1
0
2
2
0
0
2
0
0
0
2
0
0
1
0
2
1
0
3
1
0
2
0
2
2
0
0
0
0
0
0
2
0
0
0
1
1
1
0
0
0
0
1
0
0
0
1
2
0
0
0
1
0
0
0
1
0
0
0
0
1
2
0
0
2
0
1
0
1
0
2
0
1
0
0
0
0
2
0
1
0
0
1
0
0
0
1
0
0
0
0
2
2
0
0
0
0
1
0
0
2
0
2
0
0
0
0
3
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
2
1
0
0
0
0
1
0
0
0
1
3
0
2
0
0
2
1
2
0
0
0
1
0
0
2
2
0
2
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
2
0
0
2
0
2
0
0
4
0
1
2
0
1
0
3
0
0
2
1
0
2
0
0
1
0
1
2
0
0
2
0
1
0
0
1
0
0
3
0
0
0
0
0
0
1
0
1
1
0
3
2
2
0
0
1
0
0
1
0
0
0
0
0
0
0
2
2
0
1
0
2
0
2
0
0
2
0
0
0
0
1
2
1
1
0
1
0
3
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
1
2
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
2
1
1
0
0
0
1
0
0
0
0
1
1
2
2
0
0
0
0
1
0
0
2
4
0
0
1
2
0
0
0
1
0
0
1
0
3
0
0
0
1
0
1
0
1
0
2
2
1
1
0
0
1
1
0
1
1
0
0
1
1
1
0
0
0
2
9
1
0
1
0
1
0
1
1
0
0
0
0
0
0
1
1
0
2
1
0
0
0
2
1
1
0
0
0
0
0
1
1
0
2
1
1
6
1
4
0
1
0
0
0
1
2
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
2
1
2
1
0
2
2
0
0
1
0
1
0
6
0
2
1
0
0
0
0
2
0
0
2
0
2
0
2
2
0
2
1
0
0
0
1
0
1
0
0
1
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
2
0
1
0
2
2
2
1
2
1
2
0
0
0
0
2
1
2
0
0
2
2
0
1
2
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
2
0
1
0
0
0
1
2
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
4
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
1
0
2
1
1
0
0
0
2
0
2
1
2
0
0
0
0
0
1
1
2
1
0
0
2
1
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
1
0
0
0
4
0
0
0
1
0
1
0
2
5
0
2
1
0
2
0
0
1
0
0
0
0
2
2
0
1
2
0
0
1
0
0
0
0
1
1
1
2
0
2
1
0
1
0
2
1
0
0
0
2
0
2
0
0
0
1
2
0
0
2
0
0
0
1
0
0
1
3
1
2
1
0
1
1
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
4
2
0
0
1
0
1
0
0
0
0
0
1
2
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
1
0
2
0
0
0
0
1
0
0
2
0
1
1
1
0
0
0
0
0
0
0
1
0
2
3
2
1
0
1
0
0
0
1
0
1
1
0
1
2
1
0
1
2
0
1
0
0
2
0
2
0
0
1
2
0
0
0
0
2
0
1
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
1
2
0
1
1
2
3
0
0
2
0
0
2
1
0
1
2
0
0
2
0
0
0
1
0
0
1
1
1
0
0
2
1
0
2
2
1
0
3
1
0
0
2
0
2
0
1
2
0
0
0
1
0
0
3
0
0
0
0
0
0
5
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
2
1
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
1
1
0
2
3
0
0
0
0
1
2
1
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
2
0
0
0
0
2
0
2
0
1
1
0
2
0
3
0
0
0
0
0
2
0
0
1
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
3
2
0
0
0
0
0
1
2
1
0
0
0
0
0
1
2
1
1
0
0
1
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
3
0
1
0
1
0
0
2
2
0
0
2
1
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
2
1
1
2
0
1
1
0
0
1
0
0
0
1
0
0
0
1
0
2
1
1
0
1
1
0
0
2
1
0
1
0
2
0
0
0
0
0
2
0
1
1
2
0
0
2
0
0
0
0
0
1
2
0
0
1
0
1
0
1
0
0
2
0
1
0
0
0
0
0
1
0
2
0
0
0
0
2
0
1
3
0
0
0
0
1
2
0
1
0
0
0
0
0
0
1
2
0
0
0
2
0
3
0
0
0
0
1
1
0
0
1
0
0
2
1
1
0
0
0
1
1
2
1
0
0
1
1
0
0
2
0
0
2
0
1
0
2
1
0
1
1
2
2
0
2
2
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
2
1
1
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
2
0
0
0
0
1
0
3
0
1
0
1
0
1
0
0
2
0
0
0
0
1
0
1
2
1
1
0
0
1
1
2
2
2
0
2
1
1
2
0
0
0
0
2
0
2
1
0
0
2
1
0
0
0
2
0
0
1
0
1
1
2
0
0
1
0
1
1
0
2
0
2
0
0
1
0
1
0
0
1
0
0
1
0
1
1
2
0
1
0
0
0
2
0
0
1
0
2
1
0
0
1
1
1
2
0
1
0
1
0
1
0
0
0
0
2
0
0
1
0
0
1
0
1
0
2
2
0
1
0
0
0
1
1
2
1
2
0
2
0
0
0
0
0
0
0
1
2
1
0
1
3
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
1
1
0
0
0
2
0
1
1
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
2
2
0
2
2
0
0
0
0
7
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
2
1
0
0
0
2
0
0
1
0
0
0
1
1
1
0
2
0
0
1
1
0
0
1
2
1
0
0
0
1
1
0
1
0
2
0
0
1
0
0
1
0
1
0
2
0
0
0
1
2
1
0
0
0
0
0
2
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
1
1
0
1
0
1
0
1
0
0
2
0
2
2
3
0
1
0
0
0
0
1
0
2
1
0
0
0
0
1
1
1
1
0
2
1
1
0
0
0
0
0
1
0
0
1
1
1
0
0
2
0
0
0
0
0
0
2
0
1
1
0
2
1
0
0
0
1
0
0
2
2
0
0
0
0
1
0
0
3
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
1
0
1
0
2
2
1
0
0
0
1
2
2
0
0
2
0
1
0
0
2
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
2
0
0
2
0
2
0
0
1
0
0
1
2
0
0
0
0
1
2
0
0
0
2
0
3
0
0
0
0
0
0
2
0
2
1
1
0
0
0
0
0
0
0
2
0
2
0
1
1
1
0
0
1
0
1
0
2
0
0
0
1
0
0
1
1
1
0
1
2
0
0
0
0
2
0
2
0
0
2
1
2
0
0
1
0
1
0
1
0
2
1
0
1
1
0
0
0
0
2
1
1
0
1
2
0
0
2
0
2
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
3
0
0
2
0
0
2
0
2
0
2
0
2
0
0
0
0
0
0
1
1
0
1
0
4
1
0
2
1
0
0
4
2
0
0
0
1
1
1
0
0
0
0
0
0
2
2
3
0
0
0
2
2
0
0
0
0
2
1
2
2
2
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
1
2
0
2
0
0
1
1
1
0
2
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
1
2
1
0
0
0
1
1
0
0
1
2
2
2
2
0
0
0
0
0
0
0
2
2
1
0
2
2
0
0
3
1
0
0
1
0
0
1
1
0
0
2
0
2
0
1
0
0
2
0
0
0
1
1
1
0
0
2
0
0
0
1
2
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
1
1
2
1
0
0
0
1
0
3
0
2
2
0
2
0
0
1
0
0
0
1
0
0
2
1
0
2
0
0
2
0
1
3
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
1
0
0
2
0
1
1
3
4
0
2
0
0
2
0
2
0
2
0
0
0
1
1
0
0
0
0
0
1
1
2
0
1
1
0
3
1
2
1
0
0
2
1
0
0
0
2
0
0
0
0
2
1
0
0
0
1
0
0
0
9
2
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
2
1
2
0
0
0
0
0
1
0
0
2
0
0
2
0
0
2
0
0
0
0
1
0
2
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
2
2
0
0
0
0
2
1
1
2
2
0
0
0
2
1
0
0
1
0
2
1
0
1
0
2
0
0
0
0
1
0
0
1
0
2
0
2
0
1
2
0
0
2
2
2
0
2
0
0
2
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
1
1
0
1
0
1
0
1
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
1
2
0
0
1
0
0
2
0
0
4
0
0
0
0
0
0
0
2
2
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
2
0
0
0
0
2
0
2
0
2
0
0
0
0
1
2
2
0
0
1
2
1
1
1
0
2
2
2
2
0
0
2
0
0
3
0
3
1
2
2
0
0
1
0
1
0
0
2
2
2
0
1
0
0
2
0
0
1
1
1
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
2
2
0
1
2
0
2
0
0
2
0
3
0
0
0
0
2
0
0
1
2
2
0
0
0
1
0
0
0
2
0
1
2
2
0
0
0
0
2
0
1
0
0
2
0
0
0
1
0
2
0
0
1
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
2
0
0
2
0
1
1
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
1
2
0
0
1
0
1
0
2
1
1
0
2
1
0
0
2
0
2
0
2
1
1
0
1
0
0
1
3
0
1
2
0
0
3
1
0
0
0
1
0
0
0
0
0
2
3
0
2
1
2
0
3
1
1
0
2
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
1
0
0
2
0
1
2
0
0
0
0
0
1
0
0
2
0
0
0
1
1
0
0
0
3
0
2
0
0
0
1
1
0
0
2
0
1
1
2
0
0
0
1
0
0
1
2
2
0
0
0
1
2
0
0
2
0
1
1
2
2
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
1
1
0
0
0
1
1
0
0
1
0
0
0
0
0
1
2
0
0
0
0
2
2
0
2
0
0
0
0
2
0
2
2
0
1
0
0
1
0
0
0
0
0
1
0
0
1
2
3
0
0
0
2
1
0
1
0
1
0
2
0
0
0
0
2
0
1
0
1
1
1
0
2
1
2
0
0
2
0
2
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
2
0
1
0
2
0
0
1
1
0
0
2
0
0
1
0
0
0
1
1
2
2
1
1
0
0
2
1
0
0
2
1
0
0
0
1
0
3
1
2
1
0
0
2
0
0
0
2
1
2
2
0
1
0
2
0
0
2
0
0
1
0
2
2
0
0
0
0
2
2
0
0
3
1
1
0
0
0
0
0
2
0
1
0
0
3
0
0
0
1
0
1
0
0
2
0
0
0
2
0
0
3
2
1
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
3
2
0
0
0
0
1
1
0
0
0
0
2
1
0
2
1
1
2
0
2
0
0
0
0
0
0
3
1
0
1
0
0
1
2
0
0
0
1
2
0
0
1
0
0
0
1
0
0
2
1
0
3
0
2
2
0
0
0
0
1
0
0
0
2
0
0
1
0
1
0
0
1
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
2
0
0
1
0
0
2
0
1
0
0
0
0
2
0
0
2
0
1
0
1
2
1
0
1
1
0
0
0
1
1
1
1
0
0
0
2
1
0
0
2
1
2
0
0
0
0
0
1
0
1
0
1
0
0
0
1
1
0
0
2
2
0
2
0
1
3
0
1
0
0
2
2
0
0
0
1
2
0
1
0
1
1
0
1
0
0
0
1
2
0
2
2
1
2
2
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
2
0
2
4
3
2
1
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
1
0
2
0
0
2
2
1
0
0
1
1
1
1
1
0
0
0
1
1
1
1
2
0
0
0
0
0
2
0
0
0
0
2
1
1
1
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
2
1
2
0
2
2
0
1
0
0
1
1
0
0
0
2
0
0
2
0
0
2
2
1
0
2
0
2
0
0
2
1
2
0
1
1
0
2
1
3
0
0
0
0
0
0
0
0
0
5
0
2
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
2
1
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
1
1
2
0
2
0
0
0
1
1
2
0
0
0
0
1
1
1
0
0
1
1
0
0
0
0
0
1
2
1
2
0
0
0
0
1
0
0
0
0
1
1
0
2
0
0
0
0
0
0
2
0
0
0
1
0
2
0
1
0
0
0
1
0
0
0
1
2
0
0
1
0
2
0
1
0
2
0
1
1
0
2
2
0
0
0
0
2
1
0
0
0
0
0
2
2
0
1
1
2
2
0
1
1
0
0
0
0
0
0
0
1
2
2
0
1
0
2
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
1
0
0
0
1
4
2
0
1
0
0
0
1
0
0
0
0
0
2
1
2
1
0
1
0
0
0
0
0
0
1
1
0
1
1
1
0
0
0
2
0
0
2
0
0
0
2
2
1
1
0
0
0
0
1
0
2
0
2
1
0
0
0
0
1
2
0
1
1
2
0
0
0
2
0
0
1
1
2
1
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
2
2
1
0
2
0
0
0
0
1
2
0
2
2
0
0
0
0
0
6
0
0
1
0
2
1
0
1
1
0
0
0
3
0
1
0
2
0
1
2
0
0
0
2
0
0
1
0
2
3
0
2
0
3
1
0
1
1
0
2
0
1
2
0
0
1
0
0
2
2
0
1
0
1
2
2
6
0
0
2
0
1
0
0
2
0
0
0
1
0
3
0
0
0
0
0
1
0
0
0
0
2
1
1
0
0
2
0
3
0
1
1
1
1
1
0
0
1
0
2
2
1
2
0
1
5
0
0
1
2
0
1
0
2
0
2
0
0
0
0
2
0
0
0
0
2
1
1
0
1
2
1
2
0
1
1
2
2
0
0
1
1
1
1
1
0
2
1
0
0
0
0
0
0
0
2
0
0
1
1
0
0
1
0
0
1
0
0
1
2
2
0
1
1
1
0
0
0
0
1
1
0
3
1
0
0
1
0
1
2
0
1
2
3
1
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
1
2
1
0
1
1
0
0
0
2
0
1
4
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
2
0
2
1
2
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
2
0
0
2
0
2
0
0
2
1
0
0
1
2
0
0
1
0
2
0
0
1
1
0
2
0
1
0
2
0
1
2
2
0
1
0
0
0
1
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
1
2
5
0
0
1
0
1
0
0
0
0
0
0
2
0
1
0
0
2
2
1
0
0
1
3
0
1
2
0
0
2
0
0
0
0
0
2
0
1
1
0
2
1
0
1
2
0
1
0
1
0
0
0
0
0
0
0
2
0
1
0
0
1
2
1
1
2
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
2
0
0
0
1
0
0
0
2
1
0
0
0
0
3
0
0
1
0
1
0
1
0
0
0
0
0
2
2
1
3
0
2
1
0
0
0
0
0
0
2
1
1
0
0
0
2
2
1
2
0
0
2
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
2
2
0
2
0
1
0
0
0
0
0
1
1
1
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
1
2
0
1
2
0
0
1
0
0
1
0
2
1
1
1
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
2
0
0
0
1
0
1
1
0
0
0
0
1
2
1
2
0
0
2
3
0
0
1
0
1
0
0
1
1
0
2
0
1
0
0
7
0
0
0
1
3
0
0
0
0
0
1
0
2
2
1
1
0
0
0
0
0
2
0
2
0
0
0
2
1
0
1
2
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
2
1
0
0
2
1
0
1
0
1
1
2
0
0
0
0
3
0
0
1
0
0
2
1
0
2
1
0
0
0
0
1
0
0
1
0
0
0
0
3
0
0
2
1
1
0
1
0
0
2
0
0
0
3
0
1
0
4
1
1
2
0
2
0
1
1
1
2
0
0
1
0
0
0
2
1
0
0
1
0
0
2
1
0
0
0
2
2
0
0
2
0
0
0
0
1
0
1
0
1
1
2
0
1
0
0
2
2
0
0
0
1
1
0
0
0
2
0
0
1
0
0
0
1
0
0
2
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
2
1
2
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
6
1
0
0
0
0
2
2
2
1
1
0
2
0
0
0
1
0
0
2
0
0
0
0
0
2
0
2
0
1
2
0
2
0
0
0
2
0
1
3
0
0
0
0
2
3
1
0
2
1
1
0
2
1
0
2
0
3
0
0
1
0
0
2
5
0
2
0
1
1
1
4
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
4
1
0
0
1
0
0
1
0
2
1
0
0
0
0
1
2
0
2
0
2
0
1
0
1
0
2
0
1
1
1
0
0
0
2
2
0
1
0
2
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
2
1
1
2
2
1
1
2
2
0
0
0
2
1
0
0
0
0
0
0
3
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
1
2
0
2
0
1
0
0
1
0
1
0
2
0
0
0
1
0
0
0
0
0
0
3
0
0
2
2
1
2
0
0
0
0
0
2
0
1
1
0
0
0
2
0
0
2
3
0
0
1
0
0
1
0
0
1
0
2
0
0
1
1
1
0
2
1
1
0
1
3
0
1
0
2
0
1
1
1
1
0
0
1
0
0
1
0
1
0
0
0
1
0
2
0
2
1
0
0
0
0
1
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
1
1
3
0
0
0
0
0
0
0
0
0
0
1
2
0
1
2
0
2
0
0
1
1
0
0
0
1
0
0
2
0
2
0
1
0
0
0
0
0
2
0
0
0
2
0
1
2
0
2
1
0
2
0
0
0
0
0
1
0
1
0
0
0
2
0
0
1
2
0
1
0
0
0
0
2
0
1
2
2
1
2
0
0
0
0
0
1
3
0
0
0
3
0
1
0
0
0
0
1
2
0
0
0
0
2
2
0
0
2
1
0
0
3
0
2
0
0
1
2
1
2
2
0
0
1
0
2
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
1
2
2
0
0
0
0
0
0
1
1
2
0
0
2
0
2
0
0
0
1
2
0
0
0
0
0
0
1
0
3
1
1
1
1
0
0
1
0
0
0
2
2
0
0
0
0
0
0
2
2
1
0
0
1
0
1
0
0
1
1
2
0
0
0
2
0
0
0
1
3
2
1
1
1
1
2
1
1
2
0
0
1
1
1
0
3
1
0
1
2
0
0
0
0
1
1
0
0
2
1
0
0
0
2
0
3
2
0
0
2
1
0
0
0
0
4
1
0
1
2
0
0
0
1
0
2
0
1
1
2
2
0
0
2
0
0
1
0
2
1
0
1
0
0
1
0
0
1
0
0
0
1
2
0
2
0
2
2
1
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
2
2
1
0
2
0
0
0
0
1
1
2
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
1
2
0
2
0
1
0
0
0
3
0
2
0
1
1
0
0
1
0
0
2
0
0
2
0
0
0
0
0
1
0
2
1
2
0
0
1
1
0
0
2
2
2
0
1
0
2
2
1
0
3
0
1
0
1
0
1
0
2
2
0
0
0
1
0
2
0
2
0
0
0
1
1
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
1
2
0
4
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
2
1
0
0
1
0
0
1
0
2
0
2
1
0
2
0
1
1
0
1
0
1
2
3
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
1
0
2
0
0
2
0
1
0
2
0
0
0
0
1
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
1
0
1
1
2
0
1
2
1
0
0
0
0
0
0
0
5
0
0
0
0
2
0
1
0
1
1
1
4
0
0
2
0
1
2
1
0
0
0
0
1
0
1
1
0
0
1
1
0
2
0
0
0
1
0
0
0
1
2
1
0
0
0
0
0
0
0
2
2
0
0
0
1
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
2
2
0
0
0
0
1
1
0
0
0
0
2
0
3
0
0
1
2
0
1
0
1
0
0
0
0
0
2
1
2
0
0
1
2
0
0
0
0
2
0
1
1
0
0
0
1
0
2
1
0
1
0
2
0
0
2
2
2
2
0
0
0
3
0
0
0
0
2
0
1
0
0
2
0
0
2
0
1
1
0
1
2
1
0
1
0
0
2
0
1
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
3
0
0
2
0
0
0
0
0
0
0
0
1
0
2
2
1
0
2
0
0
2
0
0
2
0
3
0
0
1
2
2
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
1
4
2
0
0
0
0
0
0
0
0
0
3
0
0
1
0
1
0
0
1
0
0
1
1
0
2
0
1
0
2
1
0
0
3
2
1
0
3
1
2
0
0
1
0
0
0
1
1
0
1
0
1
1
0
0
2
0
2
0
0
0
1
0
0
0
1
1
1
0
0
0
1
2
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
2
0
0
0
0
1
2
2
0
2
3
0
0
0
3
0
0
0
2
2
0
0
0
0
2
0
1
0
2
0
0
0
2
0
0
0
0
1
1
3
1
2
2
1
0
1
0
0
0
2
0
0
2
5
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
1
2
1
0
0
0
3
0
2
0
0
2
1
1
0
2
0
1
2
2
2
0
0
0
0
1
1
0
2
3
0
0
0
2
0
1
0
2
2
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
1
1
2
0
1
0
0
2
1
0
2
0
0
0
0
0
0
2
0
0
0
1
1
2
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
2
0
2
0
0
2
2
1
1
0
0
2
1
2
1
2
2
0
0
1
0
0
2
1
1
0
1
1
1
1
2
0
0
3
2
1
0
0
2
0
0
1
2
1
3
0
1
0
0
1
0
0
0
2
1
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
1
0
0
0
2
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
2
1
0
2
0
1
0
0
2
1
2
0
2
0
0
1
0
0
0
0
1
0
0
2
0
1
0
1
1
2
0
0
2
0
0
0
1
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
1
1
2
0
1
0
0
0
2
2
0
0
2
0
2
1
3
2
2
0
0
1
1
0
1
2
0
0
1
1
1
0
1
0
0
0
0
1
2
2
1
3
0
0
0
0
0
0
1
0
0
11
0
2
2
0
0
2
0
2
0
1
0
1
0
0
1
0
2
0
1
0
1
0
0
1
2
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
2
0
1
2
1
0
0
2
1
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
2
0
0
0
1
1
1
0
0
0
3
0
1
2
1
0
0
0
1
2
0
0
2
0
2
0
2
0
0
0
0
0
0
1
2
0
1
1
1
5
0
0
0
0
1
0
0
0
2
0
1
0
0
0
1
0
1
2
1
0
0
0
2
0
0
0
0
1
1
0
1
1
0
0
2
1
0
0
1
0
0
0
2
0
1
0
0
0
0
2
0
0
1
0
0
0
1
1
1
0
1
0
0
2
1
0
0
0
1
0
1
1
0
2
0
0
0
0
1
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
2
1
0
0
2
0
0
0
1
0
1
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
1
1
1
1
0
1
1
3
0
0
0
2
0
1
0
5
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
2
0
1
2
1
0
0
1
0
0
0
0
0
1
2
0
2
0
0
1
0
0
1
0
1
0
0
0
2
0
1
0
0
0
0
0
3
0
1
2
0
0
0
0
1
2
1
0
0
1
1
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
1
0
2
2
0
3
0
0
0
0
1
1
0
1
0
2
0
1
0
0
0
0
0
2
0
0
2
1
0
0
2
1
0
0
1
1
0
0
1
1
0
0
0
0
0
0
1
1
0
2
2
0
0
0
2
0
2
0
0
1
2
0
1
1
0
0
0
1
0
0
0
2
2
2
1
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
1
0
3
1
0
0
0
0
2
0
5
0
1
3
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
3
0
2
0
1
1
1
0
1
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
1
1
1
1
0
0
2
0
1
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
1
0
2
0
1
0
0
0
0
0
0
2
1
0
0
3
1
1
0
0
2
2
0
0
0
0
1
0
0
0
1
1
1
0
2
1
0
0
0
1
0
1
1
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
1
2
1
1
1
2
2
0
2
1
0
0
1
2
0
0
0
0
1
2
1
1
0
1
1
2
0
0
0
0
0
0
0
1
4
0
0
2
0
0
2
0
0
2
0
0
0
2
4
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
2
1
0
0
0
1
1
2
2
0
0
0
1
0
1
1
0
0
0
2
0
2
1
1
0
0
3
0
0
0
0
0
1
0
4
2
0
1
0
1
0
0
1
0
0
0
0
0
1
0
2
0
1
2
1
0
2
0
0
0
1
0
2
0
0
1
0
1
2
2
3
0
1
1
1
0
0
1
1
0
0
0
2
1
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
2
2
1
0
1
1
0
4
0
1
0
1
0
2
0
0
1
0
1
0
2
2
2
0
0
0
1
2
1
0
1
0
2
1
2
0
0
1
0
1
1
1
0
2
0
1
3
0
0
2
0
1
2
1
1
1
0
0
3
0
1
2
0
0
0
0
0
2
4
2
0
0
0
0
0
1
2
2
0
0
2
0
1
1
2
2
0
1
0
2
1
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
2
0
0
2
0
1
0
0
0
1
0
0
2
1
0
1
1
0
0
0
2
2
1
2
0
0
0
0
13
1
0
0
0
2
0
0
2
3
2
0
0
0
0
0
0
0
0
3
0
0
0
2
2
2
1
2
2
7
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
1
2
0
0
2
3
0
2
3
0
0
1
0
0
0
0
0
2
2
0
0
1
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
1
0
2
0
0
0
2
0
0
0
0
1
0
0
2
0
1
1
0
0
0
0
1
2
1
0
0
0
2
3
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
2
0
0
0
0
0
5
0
1
2
1
2
0
0
1
2
2
0
2
1
0
0
0
1
2
0
3
1
1
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
1
0
1
2
1
0
1
0
0
0
0
1
0
0
0
0
2
1
0
3
0
0
0
2
1
0
2
1
2
0
1
1
0
0
0
1
0
0
0
1
1
1
0
0
1
0
0
0
0
1
1
0
0
0
1
1
0
1
0
1
1
0
0
0
0
1
0
0
2
0
2
2
0
2
0
0
0
0
0
1
0
3
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
1
1
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
2
0
2
0
0
1
3
1
0
0
1
0
1
0
0
0
1
0
0
0
2
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
1
1
2
0
0
0
1
0
1
0
0
0
0
1
2
0
0
0
2
0
0
0
1
1
2
2
0
0
1
0
1
0
0
1
0
2
0
0
2
0
0
1
0
0
0
0
2
1
1
0
0
0
0
0
1
0
1
3
1
1
0
1
2
0
1
0
0
1
0
1
2
0
0
0
2
2
0
0
0
3
0
2
0
0
1
0
2
0
2
0
1
2
1
0
2
2
0
3
0
0
0
0
0
1
1
0
2
2
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
1
0
2
0
0
2
1
1
0
2
2
2
0
2
1
1
0
2
1
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
1
0
0
2
0
0
1
0
0
0
0
0
1
0
2
2
0
0
0
1
0
2
0
2
1
0
1
0
0
1
0
0
2
0
1
0
0
1
0
0
0
0
3
0
0
3
0
1
0
0
0
0
1
0
2
0
1
0
0
1
0
0
2
0
1
0
1
0
2
2
0
2
0
0
0
0
0
0
0
0
8
2
1
0
0
0
1
1
0
0
2
0
1
0
1
2
2
0
2
0
0
0
0
1
0
0
0
0
2
1
2
2
0
0
1
0
0
1
2
0
0
1
0
1
1
1
2
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
2
1
2
0
2
0
0
0
2
0
1
0
1
1
0
0
2
1
0
1
1
0
1
2
2
2
1
1
1
0
0
2
3
0
0
0
1
1
0
1
0
0
1
0
2
1
1
0
1
0
0
1
2
0
0
1
0
0
1
2
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
2
0
0
0
0
1
2
0
0
1
1
0
0
0
0
2
0
0
3
0
0
2
0
0
0
0
2
0
0
0
1
0
2
0
1
0
0
1
3
0
0
0
0
0
1
2
0
0
0
2
0
1
1
0
1
1
0
0
0
2
2
0
0
1
0
1
2
1
0
0
2
0
0
0
0
0
1
0
2
1
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
1
0
1
0
0
0
2
2
2
0
1
2
2
1
3
0
0
0
0
2
0
0
0
1
2
0
0
1
1
0
0
1
2
1
1
1
0
0
1
0
0
0
0
0
2
1
0
0
1
0
0
0
2
0
0
1
0
1
0
0
0
0
2
0
0
5
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
2
1
1
0
0
0
0
0
1
0
0
1
1
0
1
1
2
0
3
1
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
1
2
1
0
0
0
0
1
1
0
0
2
1
0
0
2
2
0
0
0
0
1
0
0
1
0
0
0
2
0
4
0
1
0
0
1
0
0
0
2
1
0
2
0
0
2
1
0
1
0
0
2
2
0
0
1
2
0
0
3
0
2
4
0
0
1
0
1
2
2
3
0
1
0
0
1
1
0
0
1
3
1
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
1
1
1
0
2
0
1
2
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
1
0
1
1
0
2
0
0
2
2
3
1
1
0
0
2
0
1
2
0
1
0
1
1
2
1
0
0
1
2
0
1
0
1
0
0
1
0
0
1
0
0
0
0
1
2
0
0
0
0
1
2
0
0
0
0
1
0
0
0
1
2
3
2
2
2
0
0
0
0
0
2
0
0
1
2
3
1
0
0
1
0
1
1
0
0
0
1
0
0
1
0
1
0
0
2
0
1
0
0
0
1
2
0
1
0
4
0
0
0
0
0
1
0
1
0
2
0
2
1
0
1
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
2
1
0
1
0
0
0
2
0
0
4
0
0
0
3
1
0
1
0
1
0
0
2
1
0
0
1
0
0
0
2
0
2
0
1
0
0
0
0
2
0
2
2
2
0
2
0
1
1
0
0
0
0
0
0
0
0
1
2
2
0
2
0
1
0
0
0
2
0
0
2
2
0
0
1
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
3
1
1
0
0
1
0
1
0
1
0
1
0
1
0
2
1
0
0
1
0
1
1
0
0
0
2
2
0
2
0
0
1
0
2
1
2
1
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
1
2
1
0
2
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
4
0
0
0
0
1
2
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
1
0
0
0
0
1
1
0
0
1
1
0
1
4
1
1
0
0
1
0
0
0
0
0
1
0
1
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
1
1
1
0
1
2
1
0
0
1
0
2
3
0
1
3
2
1
1
2
0
0
0
0
1
0
0
0
0
0
2
0
0
1
2
0
2
2
1
0
2
0
2
0
0
2
3
0
0
0
0
0
1
0
1
0
1
1
3
1
1
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
2
1
0
1
0
0
1
0
0
4
2
1
0
1
1
2
0
2
0
0
0
0
0
0
0
0
1
0
2
0
1
0
1
0
2
1
0
1
0
0
1
0
1
0
0
0
1
4
1
0
0
0
0
2
2
0
1
0
2
0
0
5
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
2
0
1
2
0
0
1
0
0
0
0
0
0
2
1
1
1
0
1
0
0
0
0
0
1
0
0
0
1
1
1
0
1
0
0
1
2
1
1
0
2
0
1
2
0
5
1
0
0
3
2
0
1
0
1
1
0
1
2
0
1
2
0
0
0
0
1
0
0
0
2
0
0
1
1
2
0
1
0
2
1
0
0
0
1
0
2
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
2
2
2
2
0
1
0
1
3
1
0
1
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
3
0
0
0
0
0
1
0
1
1
1
0
0
1
0
1
0
0
2
0
0
0
0
2
0
0
1
2
0
1
2
0
1
0
0
0
0
1
0
0
0
1
1
1
2
1
1
1
2
1
0
1
2
0
0
1
0
2
0
2
0
1
0
2
0
0
2
1
0
0
2
0
1
0
0
1
0
2
2
0
0
0
0
2
2
0
0
0
1
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
2
0
1
0
0
2
0
0
0
2
0
1
0
0
1
1
1
1
2
0
1
0
0
0
1
2
1
0
2
0
0
1
0
0
1
2
0
2
0
0
0
1
0
0
0
2
0
2
0
0
1
2
2
0
2
0
0
0
0
0
1
0
0
0
2
1
0
0
1
1
0
1
0
1
1
0
0
0
2
1
0
0
0
2
0
0
0
0
1
1
0
0
0
2
0
0
0
1
2
2
0
2
1
1
3
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
2
1
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
1
0
1
1
2
0
0
0
0
0
1
2
1
0
3
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
2
0
0
1
0
2
2
2
0
2
0
1
0
0
0
2
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
1
2
2
0
3
1
0
0
1
0
0
0
3
1
2
0
0
2
2
0
0
0
0
0
0
0
1
2
0
0
2
0
4
0
1
1
0
2
1
0
0
1
0
0
0
2
0
1
2
0
0
0
0
2
3
0
2
1
2
0
0
1
2
0
1
0
0
0
0
2
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
2
2
0
0
0
0
0
2
0
2
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
2
1
0
0
0
1
2
2
1
0
0
3
1
0
1
0
0
0
0
3
0
0
2
0
2
0
0
1
2
0
0
0
2
0
0
1
0
1
0
0
7
0
0
0
0
0
0
1
1
0
1
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
2
1
0
0
0
0
1
2
0
0
0
2
0
0
1
3
0
1
1
0
1
0
0
0
0
0
1
2
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
2
0
1
2
0
0
2
1
2
1
0
1
0
0
0
1
1
1
0
0
1
0
1
0
1
0
1
0
1
2
2
1
1
0
0
1
0
0
1
0
2
0
1
2
1
0
1
1
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
2
1
0
0
0
0
1
2
0
2
0
0
0
0
0
0
1
0
0
1
1
0
0
2
0
1
2
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
2
0
1
2
0
0
3
1
0
2
1
5
0
0
2
2
3
1
0
0
1
0
0
1
1
0
2
1
2
0
0
0
2
0
0
0
0
0
2
1
0
3
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
4
1
0
2
0
0
0
0
6
0
0
0
0
0
0
0
1
0
1
1
0
0
2
2
0
2
0
2
0
0
1
1
1
1
0
0
0
1
1
2
2
0
0
1
0
0
1
1
1
0
0
1
3
1
0
0
2
0
0
0
0
0
0
1
1
1
0
1
1
2
1
0
2
0
0
0
1
2
3
0
1
0
0
2
2
2
0
1
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
1
0
0
0
1
0
0
1
1
0
0
0
2
2
0
0
0
1
1
0
1
1
1
1
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
1
1
2
1
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
2
0
1
0
0
1
3
1
0
2
0
2
0
0
1
0
1
0
0
0
0
2
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
1
0
1
1
0
0
0
0
2
1
2
0
0
2
1
2
1
0
0
1
1
2
0
1
0
1
0
1
1
0
2
0
1
2
2
0
0
2
2
0
1
0
0
0
1
2
0
0
0
0
0
0
2
0
1
2
2
2
0
0
0
2
1
0
2
2
0
0
0
2
2
2
1
2
0
1
2
0
0
0
0
1
0
0
0
2
0
0
1
0
3
0
0
0
0
3
1
0
1
2
0
2
2
0
0
2
0
0
1
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
2
0
1
0
0
2
0
0
0
1
0
0
1
2
0
1
2
0
0
0
0
0
2
1
0
0
1
2
0
0
2
1
1
0
0
2
2
2
3
0
2
0
0
1
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
2
1
0
0
2
0
0
0
0
0
1
2
1
1
0
1
0
0
0
2
0
0
0
0
1
1
0
0
1
2
2
1
1
2
0
0
0
2
0
0
0
0
2
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
3
1
0
1
2
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
3
0
0
0
2
2
2
0
2
0
0
0
1
0
0
2
0
0
0
2
0
1
0
2
0
0
2
0
0
0
0
0
0
0
3
0
1
1
0
0
1
0
0
2
1
2
0
0
0
2
0
2
0
1
1
1
1
0
3
0
2
2
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
1
3
0
0
2
0
2
0
0
0
0
3
2
0
1
0
2
2
0
0
3
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
1
2
0
0
0
2
0
0
0
1
1
0
2
0
0
1
0
0
1
2
2
0
0
0
0
2
0
2
2
2
0
0
1
2
0
1
1
0
0
0
0
0
0
0
2
1
0
2
0
1
0
0
0
1
0
0
0
2
0
0
3
0
2
0
0
0
2
0
1
0
2
0
0
0
1
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
1
0
0
0
5
1
3
2
1
0
0
0
0
0
0
0
0
1
0
0
2
0
2
1
1
0
0
0
0
2
2
2
0
0
1
0
1
1
2
0
0
0
2
0
0
0
0
2
0
0
2
2
2
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
2
1
0
2
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
2
0
1
1
1
1
0
0
0
1
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
2
1
0
0
0
2
0
0
0
4
0
0
2
1
0
0
2
0
0
0
1
1
0
0
1
1
1
0
0
3
0
2
3
2
1
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
2
0
2
0
1
2
0
0
0
2
0
2
0
3
1
0
0
0
1
2
0
1
0
0
1
1
1
0
2
0
0
2
1
0
0
0
2
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
2
2
1
1
2
0
0
1
2
0
1
0
0
2
1
2
0
2
2
0
0
1
0
1
0
1
0
3
0
1
0
0
0
2
0
0
0
1
0
0
1
0
1
0
1
0
0
1
0
1
2
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
1
2
0
0
1
0
2
2
0
0
0
0
1
0
2
2
0
2
0
1
0
0
1
0
1
0
3
2
0
0
0
1
0
3
0
1
0
1
2
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
2
0
1
2
0
2
0
0
1
0
0
2
2
1
0
0
3
1
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
3
1
2
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
2
0
0
0
1
0
0
0
0
1
2
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
3
0
2
0
1
0
1
0
2
2
0
0
0
3
0
1
1
2
0
0
2
0
1
2
0
0
0
1
1
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
2
0
3
0
0
1
1
0
0
2
1
1
2
0
0
2
2
1
0
0
2
0
0
2
2
0
0
0
2
0
0
0
1
0
0
0
3
2
0
0
0
2
0
1
0
0
0
0
2
2
0
0
0
1
1
2
0
0
0
1
1
2
2
4
1
0
0
2
0
0
2
0
0
0
1
0
0
0
2
0
2
1
0
0
0
2
0
0
1
0
1
0
0
0
0
0
1
1
2
0
0
3
0
0
0
0
1
1
2
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
1
0
0
1
0
3
0
0
1
2
0
0
0
1
0
0
1
0
0
0
0
2
2
2
0
2
0
1
2
0
1
1
0
0
0
0
1
1
2
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
1
2
0
0
2
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
2
1
1
0
0
0
2
3
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
1
1
0
4
0
1
0
0
0
2
2
0
0
0
0
2
0
0
0
0
1
2
1
0
1
0
0
2
1
0
0
0
0
0
1
0
0
0
2
1
1
0
2
1
0
0
0
2
0
3
2
1
0
1
0
0
0
0
0
0
2
0
0
0
0
2
2
1
1
3
0
0
1
1
1
0
1
0
1
0
0
1
0
1
0
0
0
0
0
2
0
2
0
1
2
0
2
1
0
0
2
0
0
0
0
0
2
0
1
1
2
2
2
0
1
1
1
1
0
2
2
0
0
3
1
1
0
0
2
0
1
0
0
2
0
0
0
0
0
0
1
0
1
1
0
2
0
1
0
0
0
2
2
2
2
2
0
0
0
0
0
1
1
0
1
1
0
0
2
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
2
0
1
0
0
0
0
0
0
1
0
0
0
1
0
2
1
0
0
0
0
1
0
1
0
1
2
0
3
0
0
0
0
0
2
0
0
1
1
0
2
2
1
0
0
0
0
0
3
0
0
0
2
1
1
0
1
1
0
0
2
0
0
0
0
0
0
1
4
2
0
3
0
2
0
1
2
2
0
2
1
0
0
0
0
0
0
2
2
2
0
2
0
1
0
0
2
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
2
3
0
1
0
0
1
1
0
0
1
0
2
2
0
0
2
0
0
1
2
0
1
1
0
0
0
2
0
0
0
1
1
1
0
0
1
0
1
0
0
0
0
2
0
0
2
1
0
0
0
0
2
2
1
2
2
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
2
0
1
0
0
0
1
1
0
0
0
0
0
2
0
0
2
2
2
2
0
0
0
0
0
1
1
1
3
0
2
1
2
0
1
0
0
1
0
0
2
2
0
2
1
0
0
0
1
3
1
0
2
1
0
2
0
0
0
0
2
1
0
1
0
1
0
0
0
0
0
0
2
1
1
1
1
2
0
0
2
0
1
4
0
0
0
0
1
1
0
2
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
5
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
2
1
0
1
1
0
0
2
0
2
0
1
0
2
0
1
0
1
2
2
2
0
1
0
2
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
3
0
0
1
1
2
0
0
0
1
2
0
0
6
1
0
1
0
0
0
0
0
0
0
1
2
2
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
2
0
0
0
0
0
0
2
2
1
0
0
0
0
0
2
0
0
0
1
0
1
2
1
1
0
1
1
0
3
1
1
0
0
1
1
1
0
0
0
0
0
2
1
1
0
1
1
3
2
0
1
2
1
0
0
0
1
0
0
0
2
0
2
2
1
1
0
0
0
0
0
1
0
1
0
1
0
0
0
2
2
1
1
1
0
0
0
2
0
2
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
2
0
2
0
1
0
1
0
2
0
0
0
2
2
2
2
0
0
0
0
0
2
1
2
1
2
0
0
0
0
0
0
2
1
1
0
2
0
1
0
0
0
1
0
1
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
1
0
2
0
0
0
2
1
0
2
2
0
0
1
0
2
0
0
1
1
0
0
0
1
0
0
0
0
1
2
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
2
3
0
0
0
0
0
1
1
0
0
0
1
1
2
0
0
2
0
0
0
1
0
0
0
0
2
1
2
0
0
1
0
4
0
0
0
0
1
1
0
0
2
0
0
1
0
0
2
4
0
2
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
1
0
1
2
0
0
2
0
1
0
0
2
3
0
2
4
0
0
0
0
0
2
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
2
0
0
2
3
0
0
0
0
0
0
2
0
2
0
0
0
2
2
2
2
0
2
0
0
1
0
0
0
1
0
1
0
2
0
2
1
0
2
0
1
0
0
2
0
0
0
3
2
2
0
3
0
0
2
0
0
0
0
0
0
2
1
1
0
1
0
1
2
0
0
0
2
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
1
0
2
0
0
1
0
0
0
0
3
1
0
0
0
0
1
2
2
0
0
2
0
0
0
2
0
1
1
2
0
0
1
1
2
2
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
4
0
0
2
0
0
2
1
2
2
0
2
0
2
1
3
2
0
0
0
0
1
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
1
1
1
0
1
0
0
0
1
0
0
1
1
0
2
0
0
1
0
1
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
2
1
0
0
1
0
2
0
1
0
0
0
0
2
0
0
0
0
0
2
3
0
0
0
0
0
0
2
1
0
0
3
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
2
2
2
0
2
0
0
1
0
0
1
2
2
0
1
0
1
2
0
1
0
0
1
1
0
2
1
1
0
0
0
2
2
1
1
2
0
1
0
1
0
2
0
0
0
0
0
0
1
2
1
0
0
0
2
1
2
0
0
0
0
0
2
2
2
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
2
0
0
1
2
0
0
0
0
1
0
2
1
2
0
0
0
0
2
2
1
2
2
1
2
1
0
0
0
0
2
2
0
0
0
0
0
2
0
1
1
0
0
0
2
0
0
0
2
1
0
2
0
0
0
2
0
0
1
0
0
0
0
1
2
0
1
0
2
0
2
2
2
0
1
0
2
2
0
0
1
0
0
0
0
1
0
2
0
0
0
0
2
1
2
1
0
0
0
0
2
0
2
0
2
0
0
1
2
1
0
1
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
2
0
2
0
0
0
0
1
3
1
1
0
1
1
2
1
2
1
1
2
0
0
0
0
1
0
0
2
1
0
1
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
1
2
2
0
0
1
2
2
0
1
2
0
0
0
2
1
2
0
2
0
0
0
0
0
0
0
0
2
1
2
0
0
0
2
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
3
0
2
2
0
1
0
0
0
0
2
1
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
2
0
0
1
2
1
0
0
0
0
0
0
0
2
0
1
2
0
1
1
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
2
0
2
1
0
0
2
0
0
0
0
7
0
2
0
0
0
0
3
2
0
1
0
0
2
0
1
2
0
1
1
2
0
0
0
2
0
1
1
0
0
0
2
1
0
0
1
0
0
0
0
2
1
0
1
1
0
1
0
0
1
0
0
0
0
3
0
0
0
0
1
0
0
0
2
1
0
1
1
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
2
2
0
1
1
0
1
2
1
0
0
0
0
0
2
1
0
2
2
2
0
2
0
0
1
1
2
2
1
0
0
0
0
0
1
0
1
1
0
0
2
0
0
0
0
0
2
0
1
2
0
1
3
0
0
2
0
0
2
0
1
1
1
0
0
1
0
0
0
0
0
2
0
1
0
0
0
2
0
0
2
0
1
0
0
1
0
0
0
1
1
1
3
0
0
0
1
2
1
0
0
0
2
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
2
3
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
1
1
1
0
0
1
1
0
1
1
0
0
1
0
0
0
0
0
1
1
0
0
1
2
0
0
2
2
0
0
1
1
0
0
0
7
0
0
1
0
1
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
2
2
0
1
0
1
1
0
2
0
0
0
2
0
0
0
0
0
0
1
2
1
0
0
1
2
0
0
0
1
0
1
2
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
1
0
0
3
0
0
0
0
1
1
3
0
0
0
0
0
1
0
1
2
0
1
0
0
1
0
0
0
0
0
0
2
2
2
1
1
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
3
0
2
1
2
2
0
0
2
0
1
0
0
0
0
1
2
2
0
0
1
0
0
1
0
2
0
0
2
2
0
0
0
0
0
1
2
2
0
2
0
0
0
0
1
1
0
0
0
1
2
0
0
0
1
0
2
1
1
1
1
0
0
0
3
2
0
0
2
0
0
0
0
0
3
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
1
2
0
0
0
1
2
1
0
2
2
2
3
1
0
2
0
0
2
0
2
1
1
0
0
2
1
0
1
1
1
0
2
0
0
2
0
0
0
0
1
2
0
1
0
2
0
0
0
1
0
0
1
0
1
1
0
0
1
0
0
0
2
0
0
0
0
0
0
1
3
0
2
1
0
1
0
0
0
2
2
0
0
1
1
1
0
0
0
1
0
0
1
0
1
0
0
0
3
1
1
1
0
2
6
0
1
0
0
0
2
0
1
0
0
3
0
1
1
2
0
0
2
0
0
1
0
0
0
1
0
0
0
2
1
0
0
1
1
1
2
1
1
0
0
2
2
1
0
1
2
0
0
1
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
1
0
2
0
0
6
0
0
2
1
0
1
0
2
0
0
0
2
0
0
1
0
0
3
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
2
1
0
0
0
2
0
2
1
0
1
0
2
2
0
1
0
0
0
1
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
1
0
1
0
0
2
0
1
1
1
0
2
1
0
0
0
0
2
0
0
0
2
0
0
0
0
1
3
0
0
2
0
3
0
0
1
1
0
2
1
1
0
0
0
2
0
2
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
2
0
2
0
3
0
0
0
1
1
2
0
0
1
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
1
2
0
0
0
2
0
0
0
2
0
1
0
0
2
2
0
0
0
0
2
0
0
0
0
2
1
0
2
0
1
2
0
2
0
0
0
0
0
2
1
0
1
0
0
2
0
2
0
2
0
1
0
0
1
0
1
2
1
0
0
0
0
2
0
2
2
0
0
0
1
1
0
1
0
0
2
0
1
1
0
1
1
0
0
0
2
2
1
0
2
0
0
0
2
0
2
0
0
0
2
0
2
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
2
0
0
1
0
0
1
1
2
1
0
1
0
1
2
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
1
0
1
1
0
0
2
1
0
1
1
0
0
0
0
1
1
0
1
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
2
1
0
0
0
2
0
0
0
2
0
0
1
0
1
1
1
2
2
0
2
2
0
0
0
3
0
2
0
0
1
0
0
1
0
0
2
0
2
0
0
2
2
1
0
0
0
1
0
0
0
2
1
2
2
1
3
1
0
0
0
1
1
1
0
0
2
0
0
0
0
2
0
0
0
2
2
2
0
1
3
2
0
0
0
0
0
0
0
3
7
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
1
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
2
1
0
1
1
2
0
0
1
2
2
2
1
2
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
2
1
1
2
1
0
1
2
0
2
0
0
1
2
0
2
0
3
0
0
2
0
0
2
1
0
0
0
0
1
2
1
0
0
0
0
0
1
2
2
0
0
1
0
2
0
0
0
1
2
1
1
0
0
2
0
0
1
0
2
0
0
2
1
0
0
2
0
0
0
1
1
0
4
2
0
0
0
0
0
4
0
1
0
2
0
1
1
0
0
0
1
0
1
1
0
0
1
1
0
0
1
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
2
0
0
2
0
1
2
1
1
0
0
2
0
0
0
0
2
2
0
2
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
1
0
0
1
3
0
0
0
2
2
1
2
0
0
0
0
0
0
0
2
2
0
1
0
2
0
0
2
0
1
1
2
1
1
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
1
0
0
1
1
2
0
0
0
0
0
0
0
2
0
4
0
0
0
0
3
0
0
0
0
1
1
1
0
2
1
0
0
0
1
2
0
2
0
0
0
0
1
0
0
0
0
1
1
2
0
1
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
3
0
0
0
0
1
0
0
0
1
0
2
0
0
0
2
3
0
0
0
1
2
0
0
0
0
0
2
0
2
0
1
0
1
0
0
3
2
0
0
0
0
1
0
0
2
1
1
0
0
1
1
0
2
0
0
2
0
1
0
3
0
0
1
0
0
2
0
1
2
0
1
0
0
0
0
0
1
1
0
0
0
2
1
0
0
2
0
0
1
2
0
1
0
0
2
0
0
0
0
0
1
2
1
1
0
0
0
0
2
0
0
3
2
0
2
0
0
1
2
0
0
0
0
0
0
0
2
2
0
3
1
2
0
2
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
1
0
2
0
2
0
2
0
0
1
0
1
0
2
0
0
1
0
0
0
0
1
0
0
0
1
2
2
2
0
0
1
0
2
0
2
0
0
0
0
0
0
2
1
0
0
2
2
0
3
1
0
1
0
0
2
0
1
2
1
1
3
0
1
0
0
0
0
1
0
0
2
2
0
0
2
1
2
1
0
1
4
3
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
4
2
1
0
2
0
0
0
0
0
1
1
0
2
0
0
0
1
0
1
2
0
0
0
0
0
2
2
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
2
1
0
1
1
1
0
5
0
0
0
0
0
0
2
0
0
2
0
0
2
0
1
3
0
2
2
0
0
0
0
2
0
2
0
0
0
1
0
8
0
0
0
1
0
0
0
0
0
3
0
0
1
0
0
0
0
0
2
1
2
2
1
0
1
0
2
0
0
0
2
2
1
1
1
0
1
1
0
0
0
1
0
0
0
1
0
1
2
0
0
2
1
0
0
1
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
2
1
1
1
1
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
2
0
0
0
1
1
2
0
0
0
0
0
0
0
2
2
2
0
0
2
0
2
0
0
3
0
0
1
0
1
0
2
1
1
0
0
0
0
1
1
1
0
0
0
6
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
2
0
4
1
0
0
0
2
0
1
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
2
1
2
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
2
0
0
0
2
3
0
2
2
0
1
0
2
0
0
0
1
0
0
0
2
0
0
1
0
1
0
1
0
1
2
0
0
0
1
2
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
3
0
1
0
0
4
2
1
0
0
2
1
0
2
0
0
0
1
0
0
0
1
0
2
0
0
2
1
0
0
0
1
2
0
2
2
1
0
0
3
0
0
1
1
0
0
0
0
0
1
0
2
0
1
1
0
0
0
0
2
0
0
0
1
1
0
1
0
2
1
1
0
0
0
0
0
0
0
2
1
0
0
1
0
1
0
2
0
0
0
0
3
0
0
1
0
0
0
1
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
3
0
0
1
2
1
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
2
0
0
1
0
2
1
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
3
0
1
1
1
0
2
2
0
0
0
0
1
0
0
0
0
1
1
0
0
2
1
16
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
1
2
0
0
0
1
0
1
1
1
2
0
0
0
0
2
3
0
2
0
0
0
2
0
5
1
0
1
0
0
2
0
1
2
3
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
2
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
2
1
0
3
0
0
2
0
2
0
1
1
0
2
0
2
1
0
2
0
0
0
1
0
0
0
0
1
2
1
2
0
0
0
2
0
1
0
2
2
1
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
1
2
1
2
2
2
0
0
2
0
0
1
2
0
1
2
0
0
2
1
1
0
0
0
1
2
1
2
0
2
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
2
0
2
0
0
2
0
2
0
0
0
0
0
0
0
4
0
0
0
1
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
1
2
1
2
2
0
0
1
2
0
0
4
0
0
0
2
2
1
0
2
0
0
2
0
0
0
0
2
0
2
0
0
1
2
0
2
1
0
1
0
0
0
0
0
0
0
0
1
1
0
2
2
2
0
0
0
0
2
2
0
0
0
1
0
1
2
2
0
1
0
2
0
0
0
0
0
0
0
4
1
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
1
1
0
0
0
2
0
1
0
0
2
2
0
0
0
0
1
0
0
1
1
0
0
0
0
1
1
1
0
0
1
0
2
0
0
0
0
1
0
0
3
1
0
3
1
2
1
0
1
3
0
0
0
0
2
1
0
0
2
1
1
0
2
2
2
0
4
2
0
0
0
0
1
0
2
1
1
0
1
0
2
1
0
0
3
1
0
0
2
2
2
2
1
0
0
6
0
0
0
4
0
0
0
2
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
3
2
0
0
0
0
3
0
0
2
2
2
1
0
1
1
0
1
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
5
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
2
0
0
0
0
0
0
1
0
1
1
1
0
3
0
0
0
0
0
1
0
1
1
1
1
2
1
1
2
0
0
0
0
0
1
0
2
1
0
0
0
0
0
1
0
2
2
0
0
2
0
0
2
1
0
1
0
2
0
0
0
0
0
2
1
0
0
0
0
0
1
1
2
0
2
2
0
1
1
0
0
2
0
2
2
1
1
0
1
0
0
0
2
0
0
0
0
0
0
0
2
2
1
1
1
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
2
0
2
0
0
1
2
1
1
0
2
0
0
0
1
0
2
0
1
2
0
0
1
0
1
1
2
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
3
4
0
2
1
0
0
2
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
2
1
2
0
0
0
0
1
0
2
2
2
0
0
0
0
1
0
0
2
0
0
2
1
1
2
0
2
1
0
0
0
3
1
0
0
1
0
1
2
0
0
0
0
0
0
0
1
2
2
1
0
1
2
2
0
2
0
0
0
0
2
0
0
0
0
1
0
1
0
2
1
2
1
0
0
0
2
0
1
0
1
1
0
0
0
0
2
0
0
0
1
0
0
0
2
2
2
2
2
1
0
0
0
2
0
1
1
1
0
0
1
0
1
0
2
2
0
0
0
1
0
0
1
0
0
2
0
1
1
1
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
2
0
0
0
1
1
2
0
1
0
0
1
0
1
0
0
1
0
0
0
1
0
1
1
0
2
2
2
0
0
2
0
0
1
2
2
0
1
0
0
0
2
2
0
5
1
2
0
0
3
1
0
1
2
0
1
0
0
0
0
1
0
2
2
0
2
2
2
2
0
0
2
0
2
0
1
0
2
0
0
4
2
0
1
0
1
0
1
0
0
0
3
1
2
1
0
1
0
1
1
0
0
1
0
1
0
0
0
0
2
2
0
0
1
0
0
2
0
0
0
0
1
2
0
2
0
1
0
1
0
1
1
0
1
0
0
2
0
0
0
1
0
0
0
1
0
0
0
1
2
0
2
1
0
0
1
0
1
0
0
0
1
0
1
1
0
0
0
1
0
0
1
0
0
2
0
2
0
0
9
1
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
1
2
1
0
0
2
1
0
0
1
3
1
0
1
0
0
2
1
2
0
0
1
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
5
0
0
0
0
1
0
2
2
0
0
0
2
0
0
0
4
0
0
0
2
1
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
2
1
0
0
0
2
1
4
1
0
0
0
0
1
1
0
1
1
0
0
2
0
0
0
0
0
1
2
1
0
1
0
0
2
8
2
1
0
0
0
0
0
0
0
2
1
1
1
0
2
0
0
1
2
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
1
1
1
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
2
2
1
2
0
2
0
0
0
0
0
0
1
1
2
0
1
0
1
2
0
3
0
0
0
0
0
2
0
3
0
1
0
0
0
2
1
0
0
0
1
0
0
0
1
2
0
0
2
1
0
2
0
0
0
0
1
0
2
0
1
0
1
0
0
0
0
2
2
1
0
1
1
0
0
2
1
1
0
1
0
1
3
0
0
1
0
0
1
0
0
1
1
2
0
0
0
1
0
0
0
0
0
1
0
1
2
2
0
1
0
0
0
2
0
0
0
2
0
0
2
1
0
1
0
1
0
1
0
0
2
2
1
0
0
0
0
2
0
1
0
2
1
0
3
0
0
0
0
0
4
1
0
0
0
0
0
2
0
0
2
0
0
2
2
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
1
0
2
0
0
0
0
0
1
3
0
4
0
0
0
2
0
0
2
1
0
1
1
2
0
0
0
3
0
1
2
0
0
0
0
0
1
0
2
1
2
0
0
1
2
2
3
2
0
0
2
2
0
0
0
2
2
1
0
0
1
0
1
0
0
0
1
1
2
0
2
2
1
0
0
2
1
0
0
1
0
2
1
1
2
0
0
0
0
0
2
1
2
0
2
0
0
0
1
0
1
0
0
0
0
2
2
1
1
0
0
1
0
0
0
1
0
0
2
0
1
0
0
1
0
0
0
1
2
0
2
2
2
2
1
0
0
0
1
0
1
0
0
1
2
0
1
0
2
0
0
0
3
1
0
0
0
1
1
0
2
0
2
1
2
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
2
1
2
0
0
0
0
0
1
0
1
1
0
1
0
0
3
1
0
1
2
0
0
1
1
2
0
1
0
0
1
1
2
0
1
3
0
1
2
0
2
0
0
0
0
2
3
2
1
1
0
0
0
0
1
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
6
1
0
1
0
0
0
1
0
1
1
2
1
0
0
2
0
2
0
0
0
1
0
3
0
0
0
1
0
0
0
0
2
1
1
0
1
0
1
1
0
2
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
2
0
1
1
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
1
1
0
2
0
0
0
0
1
0
0
2
0
0
2
2
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
1
0
0
0
0
2
2
0
0
1
0
1
1
0
0
0
1
6
2
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
2
1
2
0
2
1
1
0
0
0
0
0
2
2
1
0
0
1
0
2
0
2
2
1
4
0
0
0
0
2
0
2
0
1
1
0
2
1
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
1
2
2
1
1
0
0
1
0
1
0
1
0
0
0
1
0
2
1
0
1
0
1
0
0
0
0
0
1
0
1
3
0
1
0
3
0
2
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
1
1
0
2
2
0
0
2
1
1
2
2
4
0
0
0
0
1
1
0
0
0
2
2
0
0
1
0
2
0
1
0
2
0
1
0
0
2
1
2
0
1
1
0
0
0
0
0
2
0
2
0
0
0
2
0
1
2
0
2
2
0
2
0
0
0
0
1
2
1
1
1
0
0
0
1
1
0
0
0
2
1
1
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
1
0
0
0
0
0
2
1
1
1
1
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
2
2
0
0
0
0
0
2
2
0
0
0
0
2
2
0
2
0
0
0
1
1
0
0
1
0
1
0
0
1
0
1
0
0
1
0
0
2
0
0
1
0
2
1
0
0
3
0
0
3
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
1
1
0
1
1
1
0
0
0
0
0
1
0
2
0
0
1
1
0
0
0
0
0
0
0
2
0
1
2
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
2
2
0
0
0
0
2
0
2
0
2
1
3
3
0
0
1
0
0
0
1
1
0
0
1
0
2
0
2
1
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
1
0
2
1
2
0
0
0
0
0
0
2
0
0
2
2
2
1
1
1
2
0
0
0
0
0
2
1
1
0
2
0
1
0
2
0
0
0
1
0
1
0
0
0
0
1
0
0
2
1
3
0
0
0
0
2
2
1
0
2
1
2
0
0
0
1
0
0
0
0
2
2
0
0
1
0
0
1
2
1
0
3
0
0
2
1
0
1
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
1
0
0
0
2
0
0
4
2
2
0
2
2
0
2
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
1
0
2
0
0
0
0
2
0
0
0
0
1
1
0
0
0
1
0
0
2
0
0
1
0
2
3
2
0
0
2
0
0
1
0
0
4
1
1
0
0
0
1
0
2
0
1
1
0
0
1
0
0
0
2
1
0
0
2
0
1
0
0
2
0
1
0
2
2
2
0
1
0
0
2
0
0
0
0
0
2
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
1
0
2
0
2
1
1
2
1
0
1
0
0
1
1
1
1
1
2
1
0
0
0
2
1
0
0
2
0
1
0
0
0
0
2
0
0
2
1
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
2
0
1
0
1
0
0
0
1
2
0
2
1
1
0
2
2
3
0
1
0
2
0
0
0
0
0
0
1
0
3
0
2
0
2
0
0
0
2
0
2
0
0
2
0
0
1
0
0
0
0
2
0
1
1
2
0
1
0
2
0
2
0
0
0
0
2
1
0
0
0
3
0
0
1
0
1
0
2
0
0
1
2
1
2
2
2
1
0
1
2
2
1
1
1
1
1
0
0
0
0
0
2
1
3
2
0
0
0
0
2
1
0
1
1
0
2
0
0
1
0
1
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
2
2
0
0
0
0
1
1
0
0
0
0
2
0
0
1
0
0
0
0
1
0
1
2
2
1
1
0
2
1
1
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
1
2
0
0
2
1
1
1
0
0
2
2
1
0
3
1
1
1
2
2
0
4
2
1
0
1
1
0
0
0
0
6
0
0
0
0
0
0
0
2
3
0
0
0
1
2
0
0
1
0
0
1
0
1
0
0
0
0
1
2
2
2
2
0
0
0
1
0
2
2
0
0
1
0
0
1
2
1
1
0
2
1
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
2
0
1
2
0
0
0
0
1
0
0
0
0
0
1
2
1
0
0
1
1
0
0
2
2
1
1
0
0
0
1
0
0
2
2
0
1
2
0
0
0
5
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
1
2
0
2
2
0
0
0
0
0
1
0
0
3
0
1
0
1
1
1
2
0
1
0
0
2
0
0
3
1
2
2
0
1
1
2
1
0
1
1
0
0
0
0
0
2
8
0
1
0
0
0
0
0
2
0
2
0
2
0
0
0
1
1
0
0
2
1
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
2
0
1
0
1
0
2
1
0
1
0
0
1
1
0
1
0
0
1
2
1
1
0
0
0
0
0
0
1
1
1
0
0
0
1
2
1
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
2
2
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
1
1
0
0
0
2
1
0
1
1
0
0
0
0
0
0
1
0
2
0
3
0
3
0
0
0
0
1
0
1
0
0
0
2
1
0
0
0
2
1
2
0
0
1
0
2
0
1
0
1
0
3
0
0
0
0
1
0
0
0
0
0
0
1
1
0
2
0
0
0
0
2
1
0
1
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
2
0
0
2
1
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
2
0
4
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
2
0
0
1
1
0
0
0
2
1
0
0
1
0
0
1
0
2
3
0
2
0
0
0
1
0
1
1
0
0
1
2
3
0
1
0
0
1
0
2
0
1
1
0
0
0
0
1
0
0
0
1
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
1
2
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
1
2
0
1
0
0
1
1
1
0
3
1
0
1
1
2
0
0
2
2
2
0
0
1
0
0
2
0
0
0
0
1
0
0
1
1
0
0
0
4
1
2
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
1
2
0
0
0
1
1
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
2
2
0
0
0
2
2
0
1
0
1
2
0
0
0
5
1
3
1
0
0
2
1
0
0
0
1
0
0
2
2
2
1
0
2
0
1
2
0
2
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
2
0
0
0
1
1
1
2
1
1
2
0
0
2
1
0
0
2
1
3
1
1
1
1
1
0
0
0
0
0
2
0
2
0
0
0
2
0
2
2
0
0
0
2
0
1
0
0
2
2
0
1
0
0
0
0
0
2
1
0
0
1
0
2
0
1
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
2
0
2
2
3
0
0
0
5
2
2
0
0
1
1
1
1
0
1
1
0
0
0
0
1
0
1
0
0
2
0
0
1
0
0
2
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
1
0
2
3
0
0
2
0
1
0
1
0
0
3
1
0
2
0
2
0
1
0
2
0
0
1
0
0
1
1
0
2
0
1
1
0
3
2
2
1
1
1
0
0
1
1
0
1
1
1
0
0
0
2
0
0
1
0
0
0
0
0
1
1
0
0
0
2
1
0
2
0
0
1
0
0
0
0
1
0
2
0
5
0
1
1
0
0
0
0
0
0
2
0
1
0
4
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
2
0
0
2
0
0
0
4
0
1
1
0
0
0
0
2
1
0
0
0
0
0
2
0
0
1
1
0
0
0
1
0
0
1
2
2
0
2
0
2
0
2
0
0
0
0
0
1
2
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
1
0
0
0
2
3
0
1
2
0
1
1
0
0
0
1
0
0
0
1
1
0
1
0
0
0
2
0
0
2
0
1
0
1
0
0
0
0
0
0
0
1
3
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
1
0
2
2
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
2
1
0
2
0
0
0
0
0
2
1
0
0
2
2
6
0
0
2
0
2
0
0
2
0
0
0
2
0
0
1
0
0
1
0
0
2
1
0
0
0
2
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
2
0
0
2
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
1
2
0
0
0
0
1
0
0
0
0
0
1
2
0
0
1
0
1
1
0
1
0
0
1
0
0
0
2
5
1
2
0
0
0
2
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
2
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
1
2
0
0
0
1
0
0
0
0
1
2
0
0
1
0
0
1
2
0
2
0
0
2
0
0
0
0
2
1
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
1
2
0
2
0
1
0
0
2
1
0
0
3
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
2
0
0
2
1
0
0
1
0
0
0
1
0
2
0
1
0
0
2
0
2
0
1
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
2
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
1
0
2
0
4
1
0
2
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
2
1
0
0
0
0
1
0
0
0
3
0
0
0
1
0
2
2
0
1
4
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
2
0
1
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
2
0
2
0
1
1
1
0
1
2
0
3
0
0
0
0
2
0
3
0
1
0
2
0
0
0
1
0
2
0
1
1
0
0
0
2
2
1
2
2
0
0
2
2
1
0
0
2
2
0
2
0
0
3
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
1
0
1
1
0
0
0
2
0
1
2
1
2
0
3
0
2
2
0
0
1
1
0
0
0
0
0
0
1
2
0
0
1
0
0
2
0
0
2
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
1
1
2
0
1
0
1
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
1
2
1
0
0
2
0
0
0
0
0
0
2
0
2
1
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
1
2
0
0
2
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
2
2
0
0
1
1
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
2
0
2
1
1
2
2
1
0
0
0
1
0
2
0
1
0
0
2
0
3
2
0
0
0
2
2
0
0
0
0
0
1
1
0
1
0
0
0
1
2
2
0
0
1
0
0
0
0
1
0
0
0
2
0
0
1
1
0
0
1
1
0
0
1
0
2
0
0
1
0
1
2
0
0
0
1
2
2
1
1
2
1
1
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
1
0
0
0
1
0
0
1
2
0
0
0
1
1
1
0
2
0
2
0
2
0
0
0
0
2
0
3
0
2
0
0
0
0
0
0
1
0
0
2
0
2
2
0
0
2
1
0
2
0
0
2
0
1
0
0
0
0
0
0
0
1
2
0
0
2
2
0
0
0
2
1
0
0
2
0
0
2
0
0
0
2
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
1
1
1
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
2
2
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
2
1
1
0
1
0
0
0
0
0
0
0
2
3
0
2
0
2
0
1
0
2
1
2
0
1
0
0
0
0
2
1
2
1
1
2
0
0
2
1
1
1
1
0
0
1
0
0
0
0
2
0
1
0
2
2
0
0
1
1
2
0
0
1
0
0
0
0
1
2
0
2
0
1
1
0
1
1
1
0
1
2
1
2
0
0
2
2
0
1
0
2
0
0
2
0
0
0
1
1
0
0
0
1
0
0
0
0
1
1
0
0
1
2
0
0
2
0
0
0
1
1
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
1
1
0
1
0
0
3
3
0
1
0
0
1
1
0
0
0
1
1
0
2
0
0
2
2
2
0
3
0
0
1
0
1
0
0
0
0
1
1
2
2
0
0
1
2
0
0
2
2
0
0
2
0
2
4
0
0
0
2
1
0
1
0
2
0
1
1
0
0
0
1
2
2
2
0
0
0
0
0
1
2
0
2
0
1
2
1
0
0
0
0
1
0
2
0
0
0
2
3
2
1
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
2
0
2
0
0
1
0
0
2
0
0
4
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
3
2
0
1
0
0
2
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
2
0
0
0
0
0
2
0
0
0
2
0
2
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
1
2
2
0
2
0
2
1
0
0
2
1
1
0
2
1
0
1
0
1
1
2
0
2
2
1
0
0
0
1
2
1
1
0
0
0
0
0
0
0
0
2
1
1
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
1
2
3
4
0
1
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
2
0
1
0
2
0
0
0
0
2
0
0
0
0
2
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
1
0
0
1
0
2
2
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
2
1
2
0
0
0
0
0
0
0
1
0
2
1
1
2
0
0
2
0
0
2
3
0
2
0
2
3
2
0
1
0
1
2
0
2
2
2
1
0
0
2
0
2
2
0
6
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
2
0
1
0
2
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
1
1
2
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
1
0
0
0
1
0
0
1
0
0
2
1
1
0
1
1
0
1
1
2
1
0
2
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
3
2
0
0
0
0
0
0
0
2
1
1
0
1
0
0
2
1
2
0
0
2
0
0
0
4
0
0
1
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
3
0
0
1
2
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
2
0
1
1
2
2
0
0
1
0
0
10
1
0
3
0
1
0
0
4
0
0
1
2
1
0
0
0
0
1
2
2
0
2
1
2
0
0
0
1
0
2
2
0
0
2
1
0
0
3
0
0
0
3
0
0
2
1
0
0
0
0
0
0
0
0
2
2
0
0
5
2
0
1
0
1
1
0
0
3
0
1
0
3
2
2
0
1
0
1
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
2
0
0
0
0
1
0
2
2
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
4
0
0
2
1
1
2
0
0
0
1
0
0
3
0
2
0
0
2
0
0
0
2
0
0
1
1
0
0
1
0
1
0
0
0
2
1
0
0
2
0
0
0
1
0
0
0
2
0
2
0
0
0
2
1
0
1
0
0
2
0
0
0
1
0
3
0
1
0
0
1
0
1
2
2
0
2
0
1
0
0
0
0
1
0
1
0
0
2
1
1
0
0
0
0
0
0
2
0
1
0
0
2
1
0
0
0
2
1
0
0
0
0
0
1
1
0
0
2
2
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
2
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
2
0
0
0
0
0
0
1
3
0
1
0
0
1
0
2
0
0
0
0
1
1
0
1
2
1
0
0
0
2
0
1
2
0
0
0
2
2
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
2
2
0
1
3
0
0
0
0
0
2
0
1
0
2
0
0
0
2
0
2
1
0
0
0
0
0
1
2
3
2
0
1
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
3
2
0
3
1
0
1
0
2
2
0
0
0
0
1
1
0
2
0
0
1
1
0
0
0
2
0
2
2
0
0
0
0
1
1
0
0
0
2
0
0
2
1
1
1
0
1
0
0
2
0
0
0
2
2
0
2
0
2
0
0
0
0
0
2
1
1
0
0
0
0
1
2
1
1
1
0
1
1
2
0
2
0
2
0
0
1
0
1
0
1
0
0
1
0
0
0
2
0
0
1
1
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
2
1
0
0
0
2
2
0
0
1
0
0
0
1
0
2
0
0
0
3
2
0
1
0
0
0
2
0
2
0
2
1
0
2
0
2
2
0
0
2
0
1
0
1
2
0
2
3
2
1
0
0
0
1
0
0
2
0
0
1
4
1
0
0
0
2
0
1
0
1
3
1
0
0
0
2
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
2
2
2
1
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
1
1
0
2
0
1
2
2
1
2
1
2
1
0
1
1
0
2
0
0
2
1
0
0
1
0
0
2
1
0
1
0
2
0
0
1
1
1
2
0
0
1
0
0
1
0
1
1
0
0
2
1
0
0
0
0
2
1
0
2
1
0
2
1
0
0
0
0
0
2
0
1
5
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
1
0
3
0
0
0
0
0
0
2
0
1
1
1
2
0
0
2
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
2
1
1
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
2
0
2
1
1
0
0
1
0
0
0
2
0
2
0
1
2
0
0
2
0
2
2
0
1
1
0
4
0
0
0
0
2
0
0
2
1
2
1
2
1
2
1
0
0
0
0
0
0
0
1
0
1
0
1
2
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
2
0
1
2
0
2
2
3
0
2
0
1
1
1
0
4
0
1
0
0
1
0
0
3
0
0
0
0
2
1
0
0
0
2
1
0
0
1
2
2
0
0
0
2
0
0
3
0
1
1
0
1
0
0
1
2
0
0
2
3
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
2
0
1
0
0
0
0
0
1
1
0
0
0
0
2
0
0
2
0
1
1
0
1
0
2
1
1
0
0
0
0
0
2
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
1
1
1
0
2
0
0
0
0
2
0
0
1
0
3
0
2
2
0
0
0
0
0
2
0
0
0
0
1
1
0
0
1
1
0
0
0
2
0
0
1
0
0
1
0
1
2
1
1
0
0
1
3
3
2
0
1
0
0
0
0
0
2
1
0
1
0
2
0
0
1
0
1
0
0
1
2
0
0
3
0
0
2
0
0
0
2
0
1
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
1
2
0
2
1
0
0
0
0
2
0
0
1
1
0
5
0
0
0
0
1
0
0
0
2
0
0
0
0
2
1
1
2
2
0
2
0
2
0
2
2
0
0
0
0
1
0
0
0
0
0
2
1
0
1
0
0
0
0
2
0
2
0
0
1
0
0
1
0
0
0
0
1
0
2
1
1
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
2
1
0
2
1
0
0
0
0
1
2
0
0
0
1
0
0
0
1
1
1
2
1
1
0
2
0
1
3
0
1
0
0
0
0
1
0
0
2
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
7
0
0
2
2
0
1
0
0
1
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
4
2
0
2
0
0
0
0
0
0
0
2
1
1
1
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
2
0
0
2
2
0
1
1
0
0
1
1
1
0
0
0
0
1
3
0
0
0
0
0
0
2
1
4
3
0
0
0
2
0
0
1
0
0
0
3
0
1
1
0
2
0
1
0
0
0
0
1
1
0
0
0
2
2
0
0
0
1
0
1
0
1
0
0
0
2
1
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
2
2
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
2
2
1
0
2
0
0
1
0
2
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
9
0
0
0
0
0
0
0
0
0
0
1
0
3
0
1
0
1
0
0
0
2
0
0
1
2
0
2
1
0
0
0
0
2
2
1
0
0
0
2
0
0
0
0
1
0
1
0
2
0
1
0
2
1
0
0
1
0
1
2
0
2
1
0
2
0
2
0
1
0
0
1
2
1
0
0
0
0
0
0
4
0
0
0
0
0
0
3
1
0
0
1
1
2
2
1
2
1
0
1
1
0
1
0
0
2
0
0
1
0
0
0
1
2
1
0
1
0
0
0
1
0
0
1
1
1
0
0
2
1
0
1
0
1
2
0
1
0
0
2
0
2
0
0
0
1
2
0
0
0
0
0
2
1
0
2
2
1
0
4
0
0
2
0
0
1
0
0
0
0
2
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
1
0
2
2
1
0
0
0
0
1
1
0
0
2
0
2
3
0
0
0
1
1
2
1
0
0
2
0
2
0
0
1
1
0
1
0
1
0
0
3
1
0
1
0
0
2
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
1
2
0
0
2
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
2
0
3
2
0
2
6
0
0
2
0
0
1
0
1
0
3
0
0
0
1
0
1
0
2
1
0
0
1
2
0
0
1
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
2
2
1
0
2
0
1
0
0
1
2
0
0
1
0
1
0
1
0
0
1
0
0
2
0
2
0
3
0
1
1
0
1
0
0
2
1
1
2
1
2
0
0
1
0
0
0
0
0
2
2
0
0
2
2
0
1
1
1
0
0
0
0
2
0
0
3
3
0
0
0
3
0
0
2
0
1
0
0
1
0
0
0
0
0
3
0
1
0
1
0
2
0
1
0
1
1
0
0
0
2
1
2
2
0
0
0
0
0
2
0
2
0
2
0
0
1
1
2
1
1
0
0
0
2
0
0
0
0
2
0
2
0
2
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
2
2
0
1
3
0
1
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
2
0
0
2
0
0
1
0
1
0
2
0
2
0
0
1
0
0
0
1
0
1
1
0
1
0
0
0
0
1
0
2
1
0
0
0
2
0
0
2
0
0
0
0
1
0
1
0
0
1
0
0
0
3
2
0
2
2
0
0
0
2
1
2
0
0
0
0
0
2
2
0
0
1
0
0
2
0
0
0
1
1
0
3
0
2
0
0
0
0
0
0
0
2
0
0
0
1
2
0
2
0
3
0
0
2
2
0
0
0
0
0
8
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
1
1
0
0
1
0
2
2
0
1
0
0
2
1
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
2
1
0
2
0
0
0
0
2
2
0
2
2
0
0
0
0
4
0
0
0
1
2
0
2
1
0
0
0
3
0
2
2
0
2
0
2
2
0
2
0
0
2
0
0
2
0
0
1
1
0
0
2
0
2
0
0
1
0
1
0
0
0
0
3
0
1
1
0
2
1
1
0
0
2
1
0
1
0
0
0
0
0
0
0
2
2
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
2
0
0
0
0
0
1
0
1
0
0
2
0
0
0
1
0
2
2
0
3
0
0
0
0
0
1
0
1
1
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
2
0
0
0
1
1
0
1
0
2
0
0
2
2
0
0
1
1
1
1
0
1
0
0
1
0
0
2
2
0
0
0
0
0
0
1
0
7
0
1
0
0
5
0
2
0
0
0
1
0
2
0
1
0
2
0
0
0
2
1
1
0
1
2
0
1
0
1
2
0
1
0
0
0
0
0
2
0
1
0
0
1
2
0
0
0
2
0
2
0
0
0
0
0
0
0
2
2
0
1
2
1
0
1
1
2
0
1
0
1
0
2
0
0
0
0
2
2
1
1
0
0
0
2
1
0
0
1
0
2
0
3
0
1
1
0
2
0
1
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
1
0
0
2
0
1
2
0
0
2
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
1
0
3
0
0
1
0
0
1
0
1
0
0
1
0
3
1
0
0
2
1
0
0
0
0
1
0
2
0
0
2
0
0
1
0
0
1
2
0
4
0
0
0
1
0
0
0
2
0
0
0
0
0
1
1
3
0
0
1
1
0
0
0
0
2
0
0
1
2
3
0
1
2
0
2
0
2
0
1
3
0
1
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
3
0
0
0
0
2
0
0
1
0
2
1
0
0
1
2
0
0
0
1
0
2
1
2
0
2
0
2
0
2
0
0
1
2
1
1
0
0
0
2
1
2
2
0
0
1
0
0
0
2
5
0
0
2
0
0
0
1
1
0
0
1
1
0
3
1
0
1
0
0
1
0
0
2
1
1
0
0
0
0
0
3
2
0
1
0
6
0
0
2
1
0
0
0
2
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
1
2
0
1
0
0
0
3
0
2
0
0
1
0
2
1
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
2
0
1
2
0
0
2
0
0
2
0
1
1
0
2
1
0
2
0
0
0
0
1
1
0
2
1
0
1
0
0
0
1
1
0
1
0
0
1
0
2
0
1
0
0
0
0
1
0
0
2
0
0
2
0
1
0
0
2
1
0
0
0
0
0
2
2
2
0
2
0
2
1
0
0
1
0
0
1
0
0
0
1
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
5
0
0
1
0
0
0
0
0
2
0
1
1
1
1
1
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
2
1
1
0
1
0
0
0
0
2
0
1
0
1
0
0
0
0
0
2
0
1
0
0
0
0
2
1
0
2
2
0
0
0
0
0
0
0
0
2
0
0
1
1
0
1
2
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
1
0
2
1
0
2
0
0
0
3
2
2
0
0
0
1
0
2
0
0
0
0
2
3
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
2
2
1
0
1
0
0
0
2
2
2
0
0
1
1
0
0
1
0
0
0
1
1
2
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
2
2
0
2
0
0
2
0
2
0
0
0
0
0
0
0
1
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
2
2
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
1
0
0
2
0
0
3
2
2
0
0
0
0
2
1
0
1
2
0
0
3
0
1
1
0
0
2
0
0
1
2
0
2
2
1
1
0
0
0
0
0
0
3
0
0
4
1
0
0
2
1
1
3
0
0
1
0
2
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
2
0
0
1
0
2
1
2
0
2
2
1
0
2
0
0
0
1
1
0
0
2
0
0
0
0
0
6
1
1
1
2
0
2
0
0
1
2
0
2
2
0
2
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
2
0
1
2
0
0
0
2
0
1
1
0
0
2
0
2
2
3
0
2
0
0
1
0
2
0
0
0
3
0
2
0
0
1
0
0
1
0
0
2
0
0
0
2
0
2
0
0
0
1
1
0
2
0
0
2
2
2
0
2
0
2
0
0
0
2
1
2
1
0
0
0
2
0
1
0
0
0
0
0
2
2
0
0
1
2
0
1
0
0
1
0
0
0
0
0
0
0
3
2
0
0
0
2
1
1
0
0
0
2
0
0
1
2
0
0
0
1
2
0
0
2
0
0
2
0
0
0
0
0
1
5
0
0
1
1
0
0
3
0
0
1
1
2
0
0
1
1
1
1
1
1
0
2
1
3
2
1
1
1
0
0
2
2
1
0
0
0
1
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
1
0
1
1
1
2
1
2
1
3
0
0
1
2
0
0
0
0
0
0
1
1
2
0
0
0
1
2
0
1
2
0
0
0
2
1
0
0
1
0
0
0
2
0
2
1
2
0
2
1
0
1
1
2
1
2
0
1
0
0
0
0
2
0
0
0
2
2
0
2
0
1
1
0
2
0
2
0
0
0
2
0
1
0
2
0
0
0
0
0
2
3
1
0
0
0
0
0
2
0
2
1
1
0
0
2
2
1
0
0
1
0
0
0
0
1
1
0
2
2
0
0
0
0
1
2
1
0
2
2
2
0
0
0
0
0
0
0
0
2
1
2
1
0
3
0
2
0
0
1
2
0
0
0
0
1
0
0
2
0
0
1
2
0
0
0
2
1
1
0
0
2
1
0
2
1
1
0
1
2
2
2
2
0
1
0
3
0
0
2
1
2
0
2
2
0
0
2
0
0
1
1
2
1
0
0
0
5
0
1
0
1
2
0
0
1
0
0
0
2
1
2
2
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
1
1
0
2
0
0
0
0
0
0
1
0
1
0
1
0
0
2
0
0
0
0
0
0
0
2
1
0
3
1
3
2
2
1
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
2
0
0
2
2
0
1
1
1
1
0
1
0
0
1
0
0
1
0
1
0
2
0
1
2
1
2
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
1
0
1
1
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
2
1
2
2
0
0
0
2
2
0
0
0
0
3
2
0
0
1
3
2
0
0
2
0
0
0
2
0
0
0
0
4
0
0
0
2
0
0
2
0
0
0
1
2
0
0
0
0
0
1
3
0
0
0
0
1
1
0
1
2
1
1
2
0
0
2
0
0
0
1
3
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
2
1
0
0
0
0
0
0
0
3
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
2
0
0
1
0
0
0
1
0
1
0
2
0
0
0
1
0
0
0
2
0
0
2
0
0
0
2
0
1
0
0
0
0
1
0
1
2
0
2
0
0
0
0
2
1
0
1
0
1
2
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
2
2
0
0
0
2
2
0
2
1
3
1
1
0
0
0
0
1
0
0
4
0
0
0
0
0
1
0
0
0
2
0
2
2
0
1
0
1
0
0
0
2
1
1
0
2
2
2
1
0
2
0
0
0
0
0
2
2
2
1
1
0
0
0
0
1
1
1
2
0
0
0
2
0
0
2
0
0
1
1
1
2
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
1
2
0
0
1
0
0
0
1
1
1
0
1
1
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
2
2
1
3
0
4
1
0
0
2
0
0
2
1
1
0
0
0
1
0
0
0
1
1
0
1
1
0
1
1
0
1
0
2
0
0
0
0
0
3
0
2
0
0
1
0
0
0
2
2
3
0
0
0
0
2
2
1
2
2
0
2
1
2
1
2
0
0
0
0
0
0
0
0
0
2
1
1
2
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
1
1
0
2
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
6
0
0
0
0
1
0
0
0
0
1
0
0
1
3
0
0
2
0
1
2
0
0
0
0
2
0
0
1
0
2
0
2
2
0
1
4
1
3
0
1
0
2
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
1
3
0
0
0
0
0
0
1
2
0
0
1
2
3
0
1
0
0
0
2
2
1
2
1
0
0
1
1
0
0
1
0
3
0
0
0
1
0
1
2
0
1
2
0
0
0
0
0
0
0
0
2
0
6
0
0
0
1
0
0
0
0
0
1
1
1
3
2
0
0
0
0
0
1
2
1
2
0
0
2
0
1
1
0
2
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
2
2
2
0
0
0
2
1
0
0
0
1
0
0
1
2
1
1
0
0
2
0
0
2
0
1
1
2
0
2
2
2
0
0
1
0
3
0
2
0
0
0
5
1
0
0
0
0
1
2
1
1
0
0
1
1
0
0
1
1
0
0
0
4
2
0
0
0
2
2
2
2
0
2
2
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
2
2
0
1
0
0
1
1
1
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
2
1
0
1
0
0
2
1
0
2
2
1
0
0
1
1
0
1
1
0
0
0
2
1
0
1
0
0
2
0
0
2
1
1
0
1
0
1
0
2
1
1
1
0
2
0
2
0
0
0
1
1
0
0
1
1
0
0
0
2
0
2
1
2
0
0
1
0
0
0
1
0
0
1
0
1
2
0
1
0
2
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
2
0
1
0
0
1
0
0
2
1
0
2
0
0
0
0
0
0
3
2
0
2
1
0
2
2
0
1
0
1
0
0
0
0
0
2
0
0
0
1
1
0
1
0
3
2
2
0
2
0
0
0
0
0
0
1
0
1
1
2
1
2
0
3
0
0
0
2
0
0
0
1
0
0
0
2
1
1
2
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
4
0
0
0
0
0
0
1
2
0
1
2
1
2
1
0
2
1
0
0
0
0
0
1
0
0
0
0
2
0
1
0
2
0
0
2
2
0
2
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
5
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
3
0
0
0
1
0
0
2
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
2
0
2
1
1
0
2
0
2
2
0
2
2
0
0
2
2
1
0
0
2
0
2
0
2
2
1
0
2
2
2
0
1
0
1
2
2
0
1
0
1
2
0
0
3
2
0
1
0
0
1
0
2
0
0
0
1
2
0
0
2
0
0
1
1
1
1
2
2
1
2
0
0
2
0
1
1
0
0
0
0
0
3
0
2
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
1
0
0
1
0
0
0
0
0
1
2
0
1
0
0
0
2
1
1
1
0
0
0
2
1
1
3
1
2
2
1
2
0
2
0
0
0
0
0
0
0
2
2
0
1
2
1
0
0
1
0
0
2
3
0
0
0
3
0
0
0
0
0
2
2
1
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
1
0
0
2
2
0
0
0
1
1
2
0
1
0
1
1
2
0
1
1
0
0
2
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
2
1
2
2
1
0
2
1
2
0
0
0
0
1
0
0
2
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
4
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
1
2
2
0
1
1
1
2
0
1
2
0
2
0
0
0
0
0
1
1
0
0
0
2
2
0
0
0
1
0
2
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
2
0
0
1
1
1
2
2
0
2
1
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
2
1
0
0
2
0
1
0
1
0
0
2
2
0
1
2
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
1
2
0
0
0
0
2
1
0
2
2
0
4
0
1
4
0
0
0
2
1
1
0
1
0
1
1
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
3
1
1
0
2
0
0
0
0
0
2
1
0
0
0
1
0
0
0
3
2
0
1
0
1
0
1
0
1
0
1
1
4
0
1
0
0
0
0
1
2
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
2
0
0
2
2
0
0
0
0
0
0
1
1
2
0
1
0
0
1
0
0
0
0
1
2
0
0
0
0
3
1
0
0
0
0
1
2
0
2
0
2
0
0
2
1
3
0
0
1
2
0
0
2
0
2
0
2
1
0
1
0
1
0
0
1
2
0
1
2
1
0
0
1
2
1
1
0
2
1
0
0
2
2
0
0
0
2
0
0
1
1
0
0
0
0
0
1
1
2
1
2
2
0
3
1
2
0
0
0
0
0
0
0
0
3
1
0
0
0
1
2
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
1
0
2
0
1
0
2
0
0
2
0
2
0
2
0
1
0
0
0
2
0
0
1
1
1
0
1
0
1
1
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
2
0
0
2
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
1
1
1
0
2
0
3
0
0
0
1
0
0
0
0
0
1
0
0
1
1
1
2
0
0
2
0
0
0
0
0
2
0
0
0
2
0
1
0
0
2
2
2
0
0
0
0
0
1
0
0
2
2
0
0
2
0
2
0
0
1
1
0
0
1
0
0
0
1
0
2
1
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
2
0
2
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
2
0
2
2
0
0
1
0
2
0
2
1
0
2
1
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
2
2
0
0
1
1
0
0
4
1
1
0
1
0
0
1
0
1
2
2
0
0
0
1
0
1
0
1
1
0
1
0
1
1
0
0
0
0
2
0
0
3
3
2
0
0
0
1
0
1
0
9
0
2
1
0
0
1
0
0
0
0
0
1
2
0
1
1
0
2
0
2
1
0
0
0
1
2
0
0
0
1
0
0
1
1
0
3
1
1
0
0
2
0
1
2
2
0
2
2
0
0
1
1
0
0
0
0
0
0
0
3
0
2
1
1
1
0
1
1
2
5
2
0
0
2
1
0
1
0
2
2
1
0
0
1
0
2
0
0
1
0
1
1
0
0
0
0
1
0
2
1
2
1
0
1
0
2
2
0
1
2
1
2
0
0
0
2
0
2
0
0
0
1
1
2
0
0
0
2
2
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
2
1
1
2
1
0
0
0
0
0
0
2
0
1
1
0
1
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
2
0
2
2
2
1
1
0
1
2
0
1
0
0
1
0
0
1
0
0
2
0
1
0
0
2
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
2
0
1
0
2
2
0
1
0
2
1
2
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
3
0
1
1
0
0
1
0
2
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
2
2
0
0
2
0
2
1
2
1
0
1
0
0
0
2
1
2
0
0
0
0
0
0
1
0
0
0
1
0
0
1
2
2
2
0
0
2
2
0
1
0
0
0
0
2
2
1
2
1
0
0
1
0
2
1
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
2
2
0
0
0
2
0
1
1
1
3
0
0
0
0
0
0
1
1
1
0
1
0
0
0
1
0
0
1
1
1
0
0
0
0
1
0
0
1
1
0
0
1
0
2
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
2
1
2
1
3
1
0
2
4
0
0
0
1
0
1
3
0
3
0
0
2
1
2
0
0
0
3
0
2
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
4
0
0
2
2
0
2
0
1
2
0
1
1
2
0
0
1
1
0
0
0
0
0
2
0
0
2
0
3
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
1
0
0
1
0
2
2
0
2
2
0
0
1
0
0
1
0
1
0
0
2
0
2
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
2
2
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
2
0
2
0
2
0
1
0
0
1
0
0
1
1
0
3
0
0
0
0
0
0
0
0
0
2
0
3
0
0
2
0
0
2
1
2
0
3
2
0
0
0
0
1
0
2
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
2
0
2
0
0
2
3
0
0
0
0
2
0
0
3
0
1
3
1
0
0
1
0
0
2
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
1
0
0
1
2
2
1
0
0
6
2
2
0
0
0
0
1
3
1
0
0
0
2
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
2
2
0
1
0
1
2
2
0
0
1
0
1
0
2
1
0
2
0
1
0
1
0
0
0
0
2
2
0
2
2
0
1
2
2
0
0
0
0
0
0
0
3
0
0
2
0
2
1
1
0
2
1
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
7
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
1
2
0
0
0
2
0
2
2
0
2
0
2
1
0
0
2
0
0
1
2
1
1
0
1
0
1
0
3
2
0
1
0
0
0
2
0
2
0
1
1
1
0
3
1
0
1
0
0
0
1
3
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
2
1
0
2
2
3
0
1
0
0
0
0
1
1
0
0
7
0
0
0
0
1
0
2
0
0
1
0
0
0
0
1
0
2
0
1
1
0
0
0
1
0
0
0
2
0
0
2
1
0
0
0
0
1
2
0
0
1
0
2
0
1
1
0
0
2
0
0
0
1
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
2
2
0
0
2
2
2
0
2
2
0
1
0
1
2
2
0
0
0
2
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
2
0
2
0
0
0
0
1
1
0
0
0
3
1
0
3
2
0
0
0
3
0
1
0
2
3
0
0
2
2
2
0
2
2
0
4
2
0
3
1
1
0
2
2
0
2
2
0
2
0
0
2
1
0
0
0
0
0
0
2
2
0
0
0
0
2
0
1
1
2
0
1
0
0
1
0
0
1
0
0
0
1
0
0
1
0
1
0
1
0
3
0
0
0
2
0
2
0
0
0
2
2
0
1
0
0
0
1
0
2
1
2
0
3
0
0
0
2
0
0
1
2
0
0
0
2
0
1
2
2
2
0
0
2
1
1
0
1
0
2
0
2
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
1
0
2
0
1
0
0
0
1
1
0
0
1
0
0
0
0
1
2
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
1
2
0
2
0
0
1
0
0
0
1
0
2
1
0
1
0
2
1
1
2
0
2
1
1
0
0
2
0
1
0
2
0
1
0
1
0
0
0
0
1
1
0
0
0
0
2
0
2
1
2
0
0
1
0
0
2
1
1
0
1
2
2
1
0
0
0
1
1
2
0
0
1
1
1
3
2
0
2
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
2
0
1
0
0
0
2
0
2
2
1
0
0
0
0
0
1
3
0
1
2
1
0
0
3
0
1
0
2
0
0
2
2
0
0
2
1
0
0
0
1
0
0
0
0
2
0
0
2
1
1
2
0
0
0
1
2
1
2
0
0
2
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
2
1
2
0
3
1
2
0
0
1
1
0
1
3
0
0
1
1
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
1
1
2
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
2
2
1
0
2
0
0
1
0
0
0
0
2
0
0
0
1
2
0
0
0
2
2
2
6
1
1
0
2
0
0
0
0
0
0
0
0
1
0
1
1
2
2
0
0
0
0
1
1
1
0
2
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
3
1
0
0
1
0
1
1
0
1
3
3
1
0
0
0
2
2
0
2
0
0
0
0
1
2
0
2
0
0
0
0
0
2
0
2
6
0
0
1
0
0
2
0
0
1
0
0
0
0
1
2
1
1
1
2
0
1
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
1
2
0
2
0
2
0
0
0
0
0
5
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
3
2
0
0
1
0
0
1
0
1
1
0
1
0
2
0
0
1
2
0
0
0
1
0
1
0
1
1
2
1
1
0
0
0
4
0
0
0
1
0
1
0
0
1
2
0
0
0
0
3
0
0
0
0
1
0
0
2
0
0
1
0
1
2
1
0
2
1
3
1
0
1
1
0
1
1
1
1
0
0
1
0
0
2
0
2
2
0
0
1
0
0
1
1
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
2
2
0
1
0
0
1
0
1
1
0
0
0
0
0
1
1
1
2
0
1
1
0
0
0
0
0
1
0
0
0
2
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
1
3
0
0
1
1
1
0
2
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
2
1
2
2
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
1
0
2
1
0
0
0
1
2
0
2
1
0
0
2
0
2
0
0
0
2
0
0
0
2
3
1
0
0
0
0
0
2
0
0
0
1
1
1
0
0
0
0
2
1
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
2
1
0
0
0
0
0
0
1
1
0
1
0
2
1
0
0
1
3
1
0
0
1
0
1
0
1
1
1
2
0
0
2
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
2
0
0
0
0
0
1
0
1
0
0
2
0
1
0
1
0
1
0
0
0
2
0
0
0
2
0
3
2
0
2
2
1
2
1
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
1
0
1
1
0
1
1
0
2
0
1
1
1
1
0
2
1
2
3
2
2
1
2
0
0
1
1
0
2
0
2
0
0
0
1
2
0
2
0
0
0
2
0
2
2
0
2
0
0
0
0
0
0
0
0
2
2
2
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
1
2
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
2
0
1
0
2
2
0
0
1
0
0
2
0
1
0
0
0
2
2
2
0
0
2
0
1
2
1
0
1
0
2
0
1
0
4
0
0
2
4
2
0
0
1
0
0
0
0
0
0
0
1
0
2
0
1
0
1
0
0
1
1
1
2
2
1
1
1
0
2
0
2
2
1
2
1
0
0
0
2
2
0
0
2
0
2
2
0
0
2
0
0
2
2
1
0
1
0
2
0
0
3
0
0
0
0
0
0
1
0
2
1
0
0
0
1
0
1
0
0
0
2
0
0
2
0
0
0
0
0
1
2
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
1
2
0
2
0
0
0
0
1
1
0
0
0
0
1
2
0
1
0
0
0
0
0
2
2
0
0
0
0
0
2
1
1
0
2
1
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
2
0
0
0
1
2
1
2
1
1
0
0
2
0
0
2
1
1
0
0
0
7
2
0
0
1
0
2
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
2
0
2
0
0
0
1
2
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
1
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
2
1
2
3
2
1
0
0
2
1
0
0
1
0
0
0
0
0
0
2
0
0
0
2
2
0
0
2
0
1
0
1
0
0
0
0
0
1
1
0
5
2
0
1
0
0
1
2
2
0
2
0
1
0
0
0
0
0
0
0
1
1
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
1
2
4
0
2
1
2
1
0
2
0
2
2
1
0
0
1
1
1
0
2
2
1
2
0
0
0
2
0
0
0
0
0
0
2
1
0
0
2
1
0
2
1
2
2
0
1
2
0
2
0
2
1
0
0
2
0
1
1
1
0
0
0
2
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
2
2
2
1
0
0
1
2
0
1
0
2
0
0
1
1
0
0
0
0
1
1
2
1
1
3
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
2
1
2
1
0
0
2
1
0
0
0
1
2
0
0
0
1
1
1
0
1
0
1
2
0
0
0
2
0
1
0
0
1
0
2
0
0
0
1
1
0
1
0
0
2
1
2
0
0
1
2
0
0
0
1
0
0
0
1
1
0
0
0
1
2
0
1
1
2
0
0
0
0
1
0
0
0
0
0
0
0
1
2
1
2
0
1
0
0
1
1
1
0
0
1
1
1
2
2
0
0
3
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
1
1
1
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
2
2
0
2
2
0
1
2
0
1
0
0
2
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
2
3
2
0
0
2
2
0
2
2
0
0
0
0
0
0
1
2
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
1
1
0
2
0
1
0
0
1
1
1
0
0
2
0
0
0
1
0
0
0
1
2
2
0
1
1
1
2
0
0
0
0
1
1
0
2
1
1
0
2
0
0
0
0
0
0
2
3
0
0
0
0
0
1
1
1
0
0
2
0
0
0
1
0
1
0
2
1
1
2
1
1
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
2
0
1
1
0
0
1
0
0
0
1
0
0
1
0
4
1
0
0
0
1
2
0
0
0
2
2
0
2
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
1
0
2
1
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
1
0
0
0
2
1
1
0
1
1
0
0
2
1
1
2
0
0
1
1
0
6
0
0
0
0
0
0
0
2
1
0
0
0
1
0
2
2
2
1
2
0
0
1
0
0
0
0
0
1
1
0
1
0
0
1
0
0
1
1
0
0
0
2
0
0
2
2
1
1
2
0
2
0
0
0
0
0
2
0
1
0
2
0
2
0
0
2
2
3
2
0
0
2
0
1
1
0
0
0
0
1
0
0
0
0
2
1
2
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
1
2
0
0
1
1
0
1
1
0
0
2
0
1
0
0
0
2
1
0
0
2
1
2
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
1
2
0
0
0
1
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
2
1
0
0
2
0
0
0
1
0
2
0
3
2
0
0
0
2
2
0
0
0
2
0
1
0
0
0
1
0
1
2
2
1
0
1
0
0
0
0
0
0
1
0
4
0
0
0
1
0
0
0
3
2
0
0
0
1
0
0
1
0
2
3
0
0
0
3
0
1
1
0
1
0
1
0
0
2
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
2
0
0
2
4
0
0
1
1
0
0
0
2
1
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
1
1
0
2
0
1
1
0
0
0
0
2
2
0
0
1
0
1
2
1
0
1
0
0
0
2
0
0
0
0
1
2
0
1
1
0
2
0
0
1
0
1
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
6
0
0
2
2
0
2
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
1
1
1
0
2
0
0
0
0
0
0
1
0
0
2
1
0
2
1
0
2
0
0
0
0
0
1
2
0
2
2
1
1
0
2
0
0
0
2
2
0
2
1
1
0
1
1
0
0
3
0
0
1
0
1
0
1
2
0
1
0
1
0
1
2
0
0
0
0
0
1
2
1
2
0
0
0
1
2
2
0
0
1
2
0
0
1
2
0
0
0
0
0
3
0
0
0
1
0
1
2
0
0
2
2
0
2
0
1
0
2
3
0
0
1
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
4
0
2
0
0
2
2
0
2
0
0
2
0
0
0
0
0
0
0
3
0
0
0
1
0
2
2
0
0
1
2
0
1
0
2
0
1
0
0
0
0
2
1
2
0
0
0
1
0
2
3
0
3
2
1
0
0
3
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
2
0
2
0
1
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
2
2
0
2
0
2
1
0
1
0
2
1
2
0
1
1
0
0
1
2
0
3
2
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
3
0
0
0
0
0
0
0
1
0
0
1
1
0
1
1
0
0
0
1
0
2
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
2
0
1
1
0
2
0
1
0
0
2
0
2
0
0
0
1
1
1
0
3
3
1
2
0
0
0
0
0
0
1
0
0
0
0
1
2
1
0
3
2
0
2
0
0
1
2
1
1
1
2
1
0
2
0
0
2
0
0
0
2
0
0
1
1
2
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
2
2
7
0
1
0
0
1
0
0
0
0
0
1
2
1
1
1
2
1
3
0
0
1
2
2
1
1
2
2
0
2
1
0
0
0
1
0
0
2
2
0
1
1
1
0
0
1
0
0
0
1
0
2
1
0
0
3
0
0
0
0
1
0
0
1
1
0
0
1
0
0
1
1
0
1
2
1
0
1
0
2
0
0
0
0
0
1
0
2
0
1
2
1
4
0
1
2
0
1
2
2
0
2
0
0
2
2
2
0
4
0
0
0
0
0
0
1
0
2
0
1
0
1
2
0
0
0
0
1
0
0
0
0
0
3
0
1
2
1
0
0
1
0
2
1
2
2
2
0
1
0
0
0
0
0
2
0
1
0
0
2
1
0
0
2
1
0
1
0
1
3
0
1
0
0
2
0
2
1
1
0
0
1
0
0
2
0
0
0
0
2
1
2
0
2
0
0
0
2
0
0
1
0
0
0
3
0
2
2
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
1
1
1
0
0
2
0
0
1
0
1
1
2
0
1
1
0
1
0
2
1
1
0
0
1
2
0
0
1
0
1
1
1
2
0
3
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
1
1
0
0
2
1
0
0
1
2
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
2
0
2
0
2
1
1
1
2
0
0
0
0
0
0
2
0
1
1
1
0
0
1
1
1
1
2
0
0
1
2
2
1
0
0
2
0
1
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
2
1
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
2
0
0
2
0
1
0
0
2
1
0
2
0
0
2
0
1
2
2
0
1
1
1
0
0
2
1
2
1
0
0
1
0
0
1
1
1
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
2
0
1
0
1
0
0
3
1
1
0
1
0
0
1
1
1
1
2
1
2
3
0
1
0
0
1
2
0
0
0
1
0
0
0
2
0
2
0
0
2
1
0
0
3
1
0
0
0
0
0
1
2
2
0
2
2
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
1
2
2
1
1
0
0
0
3
0
2
0
3
0
2
0
3
0
0
0
3
0
0
0
2
1
0
0
0
1
1
0
1
0
0
2
0
0
0
0
2
0
0
1
2
0
0
0
0
1
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
1
1
0
0
0
2
2
1
1
0
2
2
0
2
0
0
3
0
0
0
0
0
0
0
0
0
1
2
0
0
2
2
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
1
1
3
1
2
0
0
0
2
1
2
0
1
2
0
0
2
1
0
0
2
0
2
1
2
1
0
0
0
0
2
2
1
2
2
0
0
0
0
1
1
0
0
2
0
0
1
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
2
3
0
0
2
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
1
0
1
1
0
2
1
2
1
2
0
1
2
0
2
2
0
1
0
0
0
0
0
1
0
2
0
2
1
0
0
0
2
0
4
2
0
0
0
0
2
2
1
1
0
0
3
1
0
2
0
0
2
0
1
2
1
2
0
0
2
2
0
0
3
0
0
0
0
1
0
0
1
0
2
0
1
1
0
0
0
0
0
3
0
0
1
0
0
1
0
0
0
0
0
0
2
2
0
1
0
1
0
0
1
0
1
2
0
2
0
1
0
0
0
1
0
0
0
1
0
1
0
2
1
0
2
0
2
0
0
0
2
0
2
0
1
0
1
0
2
0
0
0
1
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
2
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
2
0
0
1
2
0
0
1
0
1
1
0
0
2
1
0
0
0
1
1
1
2
0
1
1
2
0
0
2
1
0
0
2
0
0
0
0
1
0
0
0
0
2
2
1
1
0
2
0
0
1
0
2
1
2
0
0
0
0
0
0
0
0
0
1
1
1
0
1
1
2
0
1
0
0
0
1
2
1
1
2
1
0
0
2
1
0
0
2
0
0
0
0
5
1
0
0
0
0
1
0
0
2
0
0
2
1
0
0
2
0
0
1
1
2
0
1
0
0
2
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
2
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
2
1
1
0
1
0
0
0
0
0
0
1
2
0
0
0
0
1
1
1
0
0
1
0
0
0
2
2
0
0
0
0
0
2
0
0
2
0
2
0
1
0
1
0
1
0
1
2
2
0
0
0
1
0
0
0
0
2
1
3
2
2
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
1
0
0
0
0
3
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
4
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
2
3
0
0
2
0
1
1
0
1
0
0
0
2
0
0
0
2
0
0
2
2
0
0
0
2
1
2
0
2
2
0
0
0
5
1
0
2
1
2
0
1
2
2
0
2
0
1
0
1
0
0
0
1
0
2
0
0
0
0
0
2
0
1
1
0
0
0
2
1
0
0
0
0
1
1
2
1
0
0
1
0
1
0
2
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
1
2
2
2
1
0
0
1
1
0
0
2
0
0
1
2
0
2
0
0
1
0
1
1
0
0
2
0
1
1
0
2
0
0
0
0
1
2
0
0
0
2
1
0
1
1
0
0
1
1
1
1
0
0
2
0
1
0
0
0
1
1
0
1
3
1
0
0
0
0
0
2
1
0
2
0
0
0
2
1
1
0
1
2
2
1
0
0
0
0
2
2
0
1
1
2
0
3
0
0
0
4
2
0
0
3
1
1
3
0
0
2
0
0
0
2
0
0
0
1
0
2
1
0
1
1
0
0
2
2
0
2
0
0
2
0
0
0
1
0
2
0
2
0
0
0
2
1
1
0
0
1
3
1
1
1
0
0
0
2
2
1
0
2
2
0
0
2
0
0
2
2
0
0
1
3
2
0
0
1
0
1
0
0
3
0
2
0
0
0
0
0
1
2
1
1
1
0
1
1
0
0
5
0
0
0
2
1
1
0
0
0
0
0
0
1
0
0
2
2
0
0
0
1
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
2
2
0
0
2
1
1
0
1
2
0
2
0
0
1
2
0
1
1
0
2
0
0
2
0
1
1
1
0
0
2
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
1
1
1
0
1
0
1
0
2
0
0
0
2
0
0
1
1
2
2
0
2
2
0
0
0
0
2
4
0
0
0
0
1
1
0
2
0
0
2
1
0
0
2
1
1
0
0
0
3
1
0
1
2
0
1
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
1
0
1
1
1
0
0
1
1
0
1
0
1
0
2
2
1
2
1
0
0
0
0
0
1
2
1
0
1
2
0
0
0
0
0
0
0
0
2
2
0
4
0
2
1
2
0
1
0
1
0
0
0
1
0
0
2
0
0
2
2
2
1
2
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
1
2
1
2
0
0
0
2
0
2
0
0
2
0
0
2
2
1
0
2
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
1
0
0
0
0
1
2
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
2
1
2
1
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
2
2
0
1
0
0
2
2
0
0
1
1
1
1
2
0
0
0
2
3
3
0
0
0
0
0
1
0
0
2
0
2
2
0
0
0
0
0
0
2
0
0
1
2
2
1
0
2
1
1
1
0
0
0
0
1
2
0
1
0
0
0
1
0
0
0
0
2
0
0
1
2
1
0
2
2
0
0
0
0
0
1
1
2
0
2
1
0
2
0
2
0
0
2
0
1
1
0
0
0
1
0
1
0
1
3
1
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
1
5
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
1
0
2
0
0
0
0
2
0
1
1
0
2
0
2
3
1
0
2
2
1
0
0
0
0
0
2
2
2
0
0
0
2
2
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
1
0
1
2
2
0
0
0
0
2
0
0
0
2
0
0
2
0
0
3
0
1
0
0
2
0
0
2
0
0
0
0
2
2
4
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
1
0
0
1
0
1
0
0
1
0
0
0
0
3
2
3
1
0
1
0
1
0
0
0
2
0
0
0
0
1
0
2
2
0
2
0
0
2
0
1
0
0
0
0
0
2
2
1
0
0
0
2
1
1
0
0
2
0
1
0
0
0
1
2
2
0
0
0
2
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
1
1
1
2
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
2
2
2
3
0
0
2
0
0
0
4
0
1
2
1
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
2
0
1
0
0
0
1
1
0
2
0
0
1
1
0
2
0
0
2
0
0
0
0
0
2
0
2
1
0
1
2
0
3
1
0
0
0
2
0
0
0
1
0
0
0
2
0
1
1
2
0
2
0
4
0
0
0
1
2
2
2
0
0
2
0
0
0
2
2
1
2
1
1
0
0
0
0
1
1
1
1
1
2
0
0
2
2
0
1
0
0
0
1
0
0
2
0
0
2
2
0
2
0
0
0
1
0
0
0
2
1
0
0
1
1
0
0
0
0
2
0
0
2
0
0
1
0
1
0
0
2
0
2
0
1
0
0
0
2
0
1
0
0
0
0
0
1
0
1
2
2
2
0
0
2
0
1
2
0
0
0
1
0
0
0
1
0
0
1
1
1
2
0
6
0
2
2
0
2
2
0
0
2
0
1
0
1
1
2
1
1
0
1
0
0
0
0
1
0
2
2
0
2
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
1
2
1
1
0
0
2
1
2
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
1
1
2
0
0
1
0
0
1
2
1
0
0
0
0
0
0
2
0
2
1
0
0
0
2
1
0
3
0
0
2
0
0
0
1
2
1
0
1
0
0
0
0
5
0
0
0
0
2
1
2
0
2
0
2
0
0
0
0
0
1
0
0
1
0
2
1
1
2
1
0
0
0
0
0
1
0
1
0
1
0
0
2
0
0
2
0
2
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
2
2
1
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
2
2
0
1
2
0
0
0
0
2
1
1
0
0
0
0
0
0
0
1
2
2
1
0
0
0
1
2
0
0
2
1
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
3
2
0
2
2
0
0
0
2
0
0
3
2
0
0
2
0
0
2
0
0
1
0
2
0
2
0
3
1
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
1
3
0
0
0
1
0
0
1
0
0
0
0
2
0
3
4
0
1
2
0
2
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
1
1
0
1
2
0
0
1
2
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
1
1
0
1
3
0
0
0
1
2
2
0
0
0
2
0
0
0
1
1
0
0
3
1
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
1
2
0
0
0
1
0
2
0
2
0
1
2
0
1
0
0
0
0
0
0
0
0
1
0
3
0
0
2
1
0
0
2
0
0
0
2
2
0
0
0
0
0
0
1
0
0
5
0
2
0
1
0
3
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
1
0
2
0
0
1
0
0
0
2
0
1
0
0
1
0
1
2
2
1
0
0
4
1
0
0
0
0
0
0
1
0
0
2
0
2
2
0
2
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
2
1
0
0
2
0
0
1
0
2
1
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
2
0
2
1
2
0
0
2
0
1
0
0
2
0
2
2
0
0
2
0
2
1
1
0
2
0
0
0
1
0
0
2
2
1
1
0
0
0
0
0
0
0
1
0
0
0
2
2
0
1
1
0
2
1
0
0
1
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
1
2
1
1
1
1
0
2
0
1
1
0
0
0
0
0
2
0
0
1
2
0
5
0
0
0
1
0
0
2
1
2
2
3
1
0
0
2
1
1
0
4
0
1
0
0
0
1
0
0
0
0
0
1
2
2
0
0
0
1
2
0
0
1
1
0
2
0
2
2
0
0
0
0
2
1
1
0
0
0
1
2
0
2
0
1
0
2
0
0
1
1
0
0
2
1
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
2
2
0
2
0
0
1
2
0
0
0
0
0
0
2
1
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
2
0
0
1
0
2
0
2
0
1
2
0
0
0
2
1
0
2
0
0
2
2
0
0
1
0
0
2
0
0
1
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
1
1
1
1
0
3
0
1
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
1
0
0
0
0
2
1
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
1
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
4
0
0
3
0
2
1
2
1
1
0
0
1
0
1
2
1
0
0
0
0
0
0
1
1
1
0
1
0
1
0
0
2
0
0
2
0
0
2
0
0
0
1
2
0
1
0
1
2
0
1
0
0
0
1
2
2
0
0
0
0
1
0
2
0
2
2
0
0
0
1
0
0
0
0
1
0
0
2
1
2
0
2
1
1
1
0
1
0
0
2
2
2
0
2
0
0
2
2
0
2
1
0
0
1
0
1
0
0
1
0
2
1
0
1
1
0
0
1
1
0
2
0
0
0
1
0
0
2
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
1
0
0
0
1
1
1
0
0
1
1
2
2
0
0
0
0
1
0
1
0
0
1
0
0
1
0
1
1
2
1
0
2
0
2
1
0
2
0
3
2
3
0
0
0
2
0
0
1
0
0
2
0
1
0
0
2
0
1
2
1
0
2
0
0
0
2
1
1
0
0
0
2
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
2
1
0
0
1
1
0
0
0
1
0
0
0
2
0
0
0
0
2
0
1
0
2
0
0
2
0
0
0
2
0
1
0
2
1
1
2
0
1
0
0
0
0
2
2
1
1
1
2
0
0
0
0
0
0
1
3
0
1
0
0
2
0
0
0
0
0
0
1
0
2
0
3
0
1
2
0
1
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
1
5
0
1
0
0
1
1
0
0
0
0
1
0
2
0
0
0
2
1
0
0
1
0
0
0
0
2
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
2
0
1
0
2
1
1
0
1
2
0
3
0
0
0
1
0
0
0
0
0
0
2
0
3
0
2
0
0
2
0
0
0
0
1
0
4
0
1
0
0
0
0
1
4
0
1
0
1
1
2
1
0
0
2
2
2
1
2
2
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
2
6
0
0
0
0
2
2
2
1
0
0
2
0
2
0
0
0
0
0
1
2
2
3
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
1
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
2
0
0
1
1
0
2
3
1
1
3
1
0
2
0
2
0
0
0
0
2
0
2
0
0
2
0
2
1
0
0
0
1
0
0
1
2
0
0
1
1
0
3
0
5
3
2
0
1
2
0
2
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
2
1
3
0
0
0
0
1
0
0
0
0
2
0
0
2
1
1
1
0
0
2
2
0
5
0
2
0
2
2
0
0
1
0
2
0
0
0
0
0
1
0
3
2
0
1
0
2
0
2
0
2
0
0
0
0
0
1
0
2
0
0
2
1
4
0
0
4
0
0
2
2
0
2
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
2
1
0
0
0
0
2
0
0
1
1
1
0
0
2
0
0
2
0
1
0
0
1
0
0
2
0
0
0
1
2
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
1
0
0
0
2
0
0
2
2
2
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
1
2
0
2
2
2
2
0
1
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
3
0
0
0
2
2
0
0
0
0
1
1
0
0
1
0
0
2
2
0
0
1
2
2
0
0
1
1
3
1
2
0
2
0
0
1
1
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
2
2
2
2
0
0
2
1
2
0
0
1
2
0
0
0
0
0
0
1
1
0
3
0
1
0
1
3
0
2
0
1
2
2
0
0
0
0
2
2
2
2
0
0
1
2
2
1
0
1
0
0
0
2
0
2
0
1
0
0
0
2
0
1
2
0
1
0
2
1
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
2
0
2
6
0
1
2
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
2
1
2
1
0
0
2
1
1
2
1
2
0
0
1
1
1
0
2
0
1
0
1
1
0
0
0
0
1
1
2
0
0
0
1
0
1
1
0
0
0
2
0
0
0
1
1
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
2
0
0
0
0
0
0
3
0
0
0
2
1
1
0
1
0
0
0
0
1
0
0
0
2
0
1
2
0
0
0
1
5
0
0
2
1
0
0
0
1
0
0
2
1
0
0
0
2
1
0
0
1
1
0
2
0
0
2
4
1
0
0
3
1
2
1
1
0
0
0
0
0
0
0
1
2
0
2
0
2
0
2
0
0
1
1
0
2
1
0
0
0
2
0
0
1
0
2
0
1
2
0
0
0
0
0
3
1
0
1
1
2
1
1
2
0
2
1
5
0
0
0
1
2
1
1
0
1
0
0
0
1
4
0
0
1
0
0
1
1
0
1
0
2
1
0
0
0
0
1
0
3
2
2
1
0
0
0
2
0
1
0
0
1
0
0
0
1
1
1
1
2
1
0
1
2
0
2
0
2
0
1
0
2
1
0
0
2
2
0
0
1
0
2
0
0
0
2
0
0
1
0
0
0
1
3
2
0
3
1
0
0
1
0
0
0
2
0
0
0
0
1
0
0
1
0
2
0
2
0
0
0
1
3
0
0
0
0
0
1
4
0
0
0
0
0
0
2
2
0
0
2
2
0
0
0
0
0
1
2
1
1
0
2
2
0
4
0
2
0
2
0
2
0
0
0
1
0
0
3
3
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
2
0
0
0
0
0
0
0
1
0
1
2
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
2
4
0
1
0
2
1
0
1
2
0
2
0
0
1
1
2
0
0
0
4
0
0
2
0
2
0
3
2
0
1
1
0
1
0
0
0
0
0
1
0
3
1
0
0
1
0
0
1
0
3
1
0
2
0
0
0
2
0
0
2
0
1
0
2
1
2
1
0
1
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
1
0
0
0
2
1
1
0
0
2
0
0
2
1
1
0
3
1
0
3
0
0
0
0
0
1
2
1
2
1
0
0
0
2
1
1
1
2
0
0
2
1
0
0
0
2
0
4
2
1
1
0
1
0
2
0
0
0
0
0
0
1
2
3
2
0
2
0
0
2
2
0
1
1
0
2
0
2
0
1
0
1
1
0
1
2
0
0
0
1
0
0
0
0
1
0
0
0
3
3
0
0
0
1
0
1
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
2
0
3
2
2
0
0
1
1
0
0
0
0
0
0
0
0
1
2
2
0
0
2
0
2
0
2
0
0
1
0
5
0
1
1
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
6
0
0
1
1
1
1
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
1
2
2
2
0
0
1
1
0
1
1
0
1
0
0
0
1
4
0
2
0
0
0
0
2
1
1
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
2
0
0
2
1
0
1
1
1
0
0
0
2
2
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
1
2
1
0
1
0
1
0
0
0
0
2
1
2
2
0
1
0
0
2
0
1
0
0
0
0
2
2
0
0
1
2
2
0
0
0
1
0
0
1
0
0
1
0
0
0
0
2
0
0
0
2
1
0
2
0
0
0
2
2
1
0
2
0
0
1
0
0
0
0
2
3
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
1
1
0
0
0
1
0
0
0
0
1
0
0
2
1
1
3
1
2
2
0
2
2
0
2
2
1
0
0
2
0
1
0
1
2
0
0
2
2
2
0
0
0
0
0
1
2
0
1
1
1
0
2
0
1
2
2
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
1
1
2
0
0
1
1
0
0
2
0
0
1
1
0
0
2
1
0
1
2
0
2
0
1
0
1
0
1
1
0
0
4
0
0
0
2
0
0
0
0
2
0
0
2
1
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
2
0
0
1
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
2
1
0
2
1
1
0
0
1
0
1
0
0
2
0
0
0
0
0
3
2
2
3
0
2
0
1
2
2
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
2
0
2
2
0
0
0
1
1
2
0
2
1
0
1
0
1
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
2
0
0
2
2
2
0
1
0
1
0
0
0
0
2
0
0
0
2
0
0
1
0
2
2
2
2
0
0
0
0
1
0
0
2
2
1
2
1
0
0
1
0
0
1
2
0
1
2
2
1
2
0
0
1
0
2
0
0
0
0
0
0
0
2
1
0
2
2
0
0
0
0
2
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
3
0
0
2
0
0
0
1
1
1
1
1
0
0
0
0
0
0
2
0
2
2
1
0
0
0
1
0
0
1
0
0
1
2
0
3
1
1
1
0
0
2
0
0
0
1
0
3
0
2
2
0
1
1
0
2
0
0
0
2
1
1
1
0
1
1
1
2
0
0
0
0
1
0
0
2
1
0
1
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
3
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
1
3
0
0
1
0
0
0
0
0
2
2
3
0
0
0
1
0
1
0
2
1
0
0
0
2
0
0
2
1
2
0
0
1
0
2
0
1
0
2
0
0
6
0
1
2
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
2
2
2
1
0
0
0
1
1
0
2
0
0
0
0
0
0
1
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
2
0
0
2
2
0
0
0
0
1
2
1
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
1
0
0
1
0
1
0
0
0
1
0
1
1
2
0
1
0
0
0
0
0
0
0
2
0
1
0
1
0
2
0
0
0
0
0
0
3
2
0
0
1
0
2
3
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
2
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
2
1
0
0
0
2
0
0
1
2
1
1
1
0
1
1
0
0
0
2
0
2
0
1
0
2
1
2
0
0
0
1
0
1
0
2
0
0
0
2
2
1
2
1
0
0
1
2
4
1
1
0
1
2
2
2
1
0
0
0
0
0
2
1
0
0
2
0
2
0
0
0
0
1
0
0
0
2
2
2
0
0
3
1
1
0
0
0
1
1
1
2
0
2
0
2
0
1
1
0
0
0
0
0
0
0
0
1
0
3
3
1
0
0
0
0
1
1
0
0
0
0
1
0
1
1
1
1
0
0
0
3
0
2
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
2
0
1
0
1
2
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
3
0
2
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
1
1
2
1
0
0
2
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
1
2
0
0
0
0
2
0
0
1
1
1
0
0
0
2
0
1
0
0
2
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
2
1
0
1
1
2
0
0
2
0
0
0
0
1
0
2
0
2
0
0
0
2
1
1
2
0
1
0
2
0
0
0
1
0
0
1
1
0
0
1
0
2
0
1
2
0
0
2
0
2
0
2
2
0
2
1
0
2
0
2
0
2
1
1
0
0
0
0
2
0
0
3
2
0
0
1
1
6
1
0
2
2
1
0
0
1
0
1
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
2
0
2
0
0
0
2
2
0
0
0
0
2
0
1
0
0
2
1
0
0
0
2
1
0
1
0
0
0
0
0
1
0
0
1
0
0
3
1
0
0
0
2
0
0
1
2
0
0
1
2
2
2
2
0
1
0
0
1
0
1
0
0
0
3
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
2
1
2
0
0
2
0
2
0
0
0
0
0
1
0
1
0
1
0
0
1
0
2
0
3
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
1
0
0
1
1
1
0
1
2
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
1
0
1
2
0
0
1
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
1
0
0
0
3
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
2
1
0
1
0
1
0
2
1
0
5
0
0
0
2
0
0
2
0
2
0
2
0
0
2
0
0
0
0
1
0
0
0
1
1
2
0
0
0
0
0
0
1
3
0
0
1
0
1
0
0
0
0
1
2
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
1
2
0
1
0
1
0
2
2
0
2
1
1
1
0
0
0
0
2
0
1
0
0
0
2
0
1
0
1
1
1
0
2
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
2
1
1
1
0
0
0
0
0
0
0
2
1
0
2
0
0
1
1
2
0
1
2
0
1
2
1
0
1
0
1
1
0
5
0
0
0
2
0
2
0
0
0
2
0
2
2
0
2
0
0
1
1
0
0
0
2
0
2
0
1
0
0
0
1
0
2
1
2
1
1
2
0
0
0
1
0
2
0
0
4
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
2
2
1
1
0
0
0
0
0
0
1
0
2
0
0
0
0
1
2
2
0
0
1
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
1
0
2
0
3
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
1
0
1
0
1
0
1
2
2
1
0
5
0
1
1
0
2
0
0
0
2
0
0
0
0
0
1
0
0
2
0
3
1
0
0
2
1
0
0
0
1
0
2
3
0
2
1
1
1
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
2
0
2
2
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
2
1
0
0
2
1
0
0
2
1
0
2
3
0
1
2
0
1
3
1
0
1
0
3
1
2
1
1
1
5
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
1
2
0
0
0
1
0
0
0
2
2
1
1
2
1
2
0
0
2
0
0
0
0
2
0
1
2
0
0
0
1
1
0
0
0
0
0
1
1
0
0
1
0
0
2
0
0
0
0
1
2
0
0
0
0
0
1
0
0
2
2
1
0
2
2
0
1
2
0
0
0
0
1
1
0
0
2
1
0
1
1
0
2
0
2
0
1
2
0
1
1
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
3
0
0
0
0
2
1
1
0
1
0
0
1
1
0
0
0
0
0
0
2
1
0
0
0
0
2
1
0
2
0
0
0
0
1
0
0
0
2
2
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
2
0
2
0
0
2
2
1
0
0
0
0
0
0
1
0
0
2
2
2
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
2
2
1
0
0
0
0
0
0
1
0
1
1
1
0
2
2
0
0
0
2
0
1
2
0
2
2
1
1
0
0
0
0
0
1
1
1
1
0
2
0
0
0
0
0
1
3
0
0
2
0
3
1
0
0
0
0
2
4
0
0
0
1
2
2
0
1
0
0
0
0
2
0
2
0
0
0
0
1
0
2
2
0
0
0
1
1
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
2
2
0
0
0
1
2
0
0
0
3
2
0
0
1
1
0
0
0
3
2
4
0
0
0
0
1
0
2
1
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
1
1
0
0
1
0
1
0
0
4
2
1
1
0
0
1
1
0
0
0
0
1
0
2
0
0
0
1
0
2
0
0
3
0
1
0
0
0
2
0
0
0
0
2
1
0
2
2
0
0
0
0
2
0
2
2
0
0
2
0
1
0
2
1
1
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
2
2
0
0
0
1
2
0
0
0
1
1
0
0
0
1
1
1
0
0
0
0
1
1
2
1
0
1
1
2
2
2
1
1
0
0
0
0
2
0
0
0
2
0
2
0
0
1
0
0
0
2
0
0
1
3
1
0
0
0
2
0
0
1
0
2
0
1
1
0
1
0
3
0
0
0
0
0
2
0
0
0
0
0
2
1
0
2
0
1
0
0
0
5
0
0
0
0
1
0
1
0
1
0
0
2
0
2
0
0
0
2
0
0
0
2
0
0
1
1
2
0
0
0
1
1
0
1
0
1
1
0
1
0
2
1
2
1
0
1
0
0
0
1
0
1
1
0
2
0
1
0
0
0
0
0
0
2
0
0
2
2
0
2
0
0
0
2
2
0
2
0
1
2
2
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
2
0
1
0
1
0
2
0
1
0
1
1
1
0
1
0
0
1
0
1
1
2
1
2
0
0
1
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
1
0
2
2
0
2
2
1
1
0
0
0
0
2
1
0
2
1
0
0
1
0
0
0
5
0
3
0
1
2
1
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
4
1
0
0
1
0
1
0
1
0
0
0
0
0
2
0
2
0
2
2
2
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
2
0
1
0
0
0
0
0
2
0
0
1
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
1
1
0
2
0
0
1
0
3
0
0
0
0
0
0
0
0
1
2
0
1
2
1
0
0
0
0
2
0
1
0
0
0
0
0
2
2
0
0
2
2
4
1
0
0
1
2
0
1
1
2
0
2
0
0
3
2
1
0
2
1
0
1
0
2
0
0
0
2
0
0
0
0
2
0
0
2
0
0
2
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
3
2
0
0
1
0
1
0
2
0
1
1
0
0
0
0
2
2
0
2
0
0
0
2
0
0
0
0
0
1
1
0
0
2
0
0
0
2
2
0
2
0
1
0
0
0
0
1
0
1
1
2
2
0
1
2
2
2
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
2
0
0
1
2
0
0
0
2
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
1
1
0
0
2
0
1
0
1
1
0
1
1
1
1
1
0
1
0
1
1
2
1
0
1
0
0
0
1
1
2
0
2
1
0
0
2
0
2
4
1
0
1
0
0
0
0
0
0
0
0
2
2
0
1
0
1
2
0
1
1
0
2
2
0
0
0
1
6
15
0
1
0
0
1
2
0
1
1
0
0
1
2
2
0
0
0
0
0
1
1
0
0
2
0
0
2
0
0
1
3
1
2
2
1
3
0
0
0
0
0
2
1
0
0
0
1
0
0
3
0
1
1
2
1
1
3
2
0
0
1
0
2
0
0
0
0
1
0
0
1
0
0
2
0
1
0
0
0
2
0
1
1
0
0
0
0
1
0
2
0
2
0
2
1
0
1
0
0
0
0
2
2
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
1
0
2
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
2
0
1
0
0
2
0
0
0
0
1
1
2
0
2
1
2
0
0
1
1
0
3
0
1
1
0
0
2
0
0
0
1
0
3
1
0
1
2
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
9
2
1
0
0
0
0
1
0
1
0
0
2
0
2
0
0
0
1
2
0
0
0
0
2
2
0
0
2
1
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
1
2
2
2
1
0
0
0
0
1
1
2
2
0
0
1
0
1
1
5
0
0
1
0
0
0
0
1
2
2
1
2
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
2
2
2
1
0
2
2
2
0
1
2
1
0
0
0
1
0
1
0
0
0
0
1
1
1
0
2
0
0
0
2
2
1
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
4
2
2
0
0
0
0
1
0
2
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
1
0
0
1
1
0
2
4
2
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
2
0
1
0
1
0
0
0
0
0
1
2
0
0
0
0
1
0
1
2
0
3
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
2
0
2
2
0
2
0
2
2
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
2
0
0
0
0
0
2
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
1
2
1
0
2
0
0
0
2
1
0
0
0
0
0
2
0
1
2
2
0
2
2
0
1
0
0
0
0
0
1
1
0
2
1
0
0
0
1
2
1
1
0
0
0
0
1
1
2
0
0
1
0
2
0
1
2
1
0
0
0
1
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
3
0
2
0
0
4
2
1
1
1
0
1
1
0
4
0
0
0
0
0
1
1
0
0
2
2
2
0
0
0
1
0
0
0
1
0
0
0
0
1
2
1
0
0
1
2
1
0
0
2
2
0
0
0
0
0
2
2
2
1
0
2
0
1
0
2
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
1
0
2
1
2
1
1
0
3
1
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
2
2
2
0
1
2
0
1
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
2
0
0
0
2
0
0
2
2
0
0
0
2
0
1
1
1
2
0
2
0
2
0
0
0
0
1
0
0
0
3
0
1
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
1
0
0
2
0
0
2
1
1
2
0
2
3
0
2
5
0
1
2
0
0
1
0
1
0
0
0
0
0
0
1
1
2
0
1
0
0
0
0
3
0
1
0
1
1
0
0
0
0
0
0
0
2
3
0
1
0
0
0
1
0
1
1
0
2
1
2
1
2
0
0
3
2
1
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
1
0
2
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
2
0
2
0
0
0
0
0
1
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
3
0
1
0
0
3
2
0
0
2
3
1
1
0
0
0
0
0
1
1
0
0
0
0
1
2
1
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
2
0
0
2
0
0
0
0
1
0
4
0
0
0
3
0
1
8
1
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
3
0
0
0
2
1
0
1
0
2
0
0
2
2
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
2
0
1
2
0
0
0
0
2
0
1
0
0
1
3
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
1
2
0
0
1
0
1
0
2
0
0
0
0
0
2
2
2
2
0
2
0
0
2
1
0
0
0
2
3
0
1
0
1
2
1
1
2
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
1
2
0
0
0
0
0
1
0
2
2
1
2
1
1
0
2
2
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
2
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
3
2
0
0
2
1
0
0
0
0
0
1
0
2
2
0
3
2
0
1
0
2
2
0
1
0
1
2
2
2
0
0
2
0
0
1
1
0
1
0
0
2
2
0
1
0
0
1
0
0
1
0
1
0
1
1
3
2
1
0
0
2
0
2
0
0
0
0
2
0
0
0
0
1
3
2
0
1
1
0
1
1
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
1
0
0
0
3
2
0
2
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
1
1
0
1
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
1
1
5
0
0
0
1
0
0
4
0
1
3
2
2
0
2
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
1
3
2
0
0
1
0
0
0
0
2
0
1
1
0
2
1
0
1
0
0
1
0
1
1
2
0
0
2
2
1
0
1
1
0
0
2
0
2
0
0
0
0
3
0
0
0
0
1
0
0
0
0
2
0
0
1
0
2
0
0
0
1
3
0
2
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
1
0
0
3
0
1
0
2
0
2
1
1
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
4
1
0
1
0
0
0
2
0
0
2
1
1
0
2
0
0
0
0
1
0
1
1
1
0
0
2
0
0
2
0
2
2
1
0
0
0
0
0
1
0
1
1
0
2
2
0
0
0
2
0
2
2
1
2
0
0
2
2
2
0
2
2
2
1
0
2
0
0
0
2
3
2
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
2
1
0
0
0
0
1
2
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
1
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
2
1
2
2
0
1
1
0
0
0
2
0
0
0
0
1
0
4
1
1
1
0
0
0
0
0
0
0
0
1
1
1
0
1
1
1
0
2
0
2
0
2
1
1
0
1
0
0
0
0
0
0
2
0
2
2
1
2
1
0
0
2
1
0
1
1
0
2
0
2
2
2
0
0
1
0
1
2
0
0
0
0
0
2
2
0
0
4
0
0
2
0
0
0
0
1
2
0
1
2
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
1
3
1
2
2
0
0
0
1
1
0
0
0
0
2
2
0
0
0
4
2
0
0
0
0
0
0
2
1
1
0
1
0
0
0
0
1
0
0
1
3
3
1
0
0
0
0
0
2
2
2
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
1
2
2
3
2
0
0
1
2
0
0
2
0
0
0
1
0
2
0
2
0
0
0
2
0
1
1
1
0
2
0
0
0
0
1
0
1
1
2
0
1
2
0
0
0
0
0
1
3
0
0
0
2
0
1
2
0
1
1
1
0
1
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
2
0
1
1
0
1
1
1
0
0
0
0
1
0
0
0
1
2
0
1
1
2
0
1
1
2
2
1
0
0
2
0
0
1
2
0
4
2
2
0
0
3
0
2
0
1
0
0
0
1
2
2
0
0
0
0
2
2
0
0
0
1
1
0
0
1
1
2
0
1
0
0
2
1
0
2
0
2
0
0
0
0
0
0
0
1
2
0
0
0
2
0
1
1
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
2
0
0
2
0
2
1
0
0
0
2
0
1
2
1
1
2
2
0
2
1
1
0
0
0
0
0
0
2
1
1
0
3
2
2
2
0
1
2
0
0
0
0
0
0
0
2
0
0
2
1
1
0
0
0
0
0
2
1
1
2
0
1
1
2
0
0
0
1
2
0
0
2
2
0
1
0
1
0
1
1
2
0
0
0
1
0
0
1
1
0
1
1
0
0
1
0
0
0
0
0
0
0
2
2
0
3
0
1
0
2
0
0
0
2
0
2
0
0
2
1
0
1
1
0
1
0
3
2
2
1
0
0
1
0
1
0
0
0
2
2
4
0
0
0
1
0
0
2
1
2
1
2
1
0
0
1
1
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
2
0
2
0
1
2
0
0
0
0
2
1
0
0
1
0
0
0
2
0
0
0
2
1
1
0
0
1
0
0
0
2
2
0
0
2
0
0
0
0
0
1
2
0
1
2
1
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
1
0
1
1
1
1
1
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
1
1
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
1
2
0
0
2
1
0
1
2
1
0
0
0
0
0
3
0
2
0
2
0
5
1
1
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
2
0
0
0
0
2
1
0
0
0
0
1
0
0
0
2
0
1
0
0
0
1
1
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
1
0
1
1
0
1
0
0
1
2
0
1
0
0
1
0
0
0
2
0
0
0
1
0
0
2
2
0
0
2
1
0
0
1
0
2
0
0
4
0
0
1
2
0
0
1
0
0
2
0
1
2
0
0
0
0
0
1
0
0
2
0
1
0
1
0
1
2
0
0
0
0
0
2
0
1
1
4
0
0
1
1
0
0
4
0
1
0
0
0
0
2
0
0
4
2
0
2
1
1
1
0
1
2
0
1
1
0
0
0
0
0
2
2
0
0
0
0
1
1
0
0
0
1
2
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
2
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
1
1
2
1
0
1
0
0
0
2
2
0
1
1
0
1
0
1
0
0
0
0
1
1
2
2
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
2
0
2
0
1
1
0
0
1
0
0
2
2
0
1
0
1
0
1
1
2
0
1
1
2
0
0
1
0
0
1
0
0
0
2
0
0
1
2
0
0
1
1
1
0
1
0
0
1
0
0
0
0
0
1
1
2
2
2
2
1
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
1
0
0
1
0
2
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
2
0
2
0
0
0
0
2
1
1
1
1
0
0
0
0
0
0
0
1
1
2
0
1
2
0
1
0
0
0
0
0
1
0
0
0
0
1
1
1
0
2
1
0
0
2
0
1
2
1
0
1
1
0
0
1
0
1
0
0
0
2
2
1
0
0
0
0
0
0
1
2
0
0
2
0
2
0
1
1
0
0
2
0
0
0
0
1
2
0
3
0
0
0
2
0
0
0
0
1
0
0
2
0
0
1
0
1
1
0
0
0
1
0
0
0
3
0
1
1
1
1
2
0
0
0
0
0
0
1
2
0
2
0
0
2
0
3
0
0
1
2
1
1
1
0
0
0
2
0
1
0
0
2
0
1
2
1
0
0
1
0
2
0
2
0
1
2
0
1
1
0
1
0
0
1
1
0
0
0
1
0
0
2
2
0
0
1
0
2
0
1
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
2
1
1
0
0
0
0
0
1
1
0
0
0
2
2
0
0
2
1
0
1
1
0
3
0
0
0
0
0
1
1
0
2
0
2
1
1
0
0
0
0
0
0
3
0
2
0
0
1
1
0
0
2
0
0
0
0
1
2
0
1
0
0
0
1
0
0
2
0
2
0
1
0
0
0
0
0
0
2
1
0
0
0
0
1
1
2
0
2
0
0
1
0
0
0
1
1
2
0
0
1
1
0
1
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
1
1
0
0
0
1
0
2
0
0
0
1
0
0
0
0
2
2
0
2
1
0
2
0
1
0
1
0
0
1
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
2
0
0
0
0
0
0
1
1
0
0
0
2
1
0
2
1
0
1
0
0
0
2
0
0
2
0
2
0
0
2
0
2
2
1
0
1
0
0
0
1
0
0
2
1
0
1
0
0
2
0
0
2
2
2
0
0
0
0
0
3
1
3
0
0
2
0
1
1
1
0
0
2
0
2
1
1
0
2
1
0
1
0
0
2
0
0
0
4
0
0
1
1
1
2
2
0
0
2
3
0
0
1
1
0
0
1
0
0
0
1
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
1
1
2
0
0
0
0
0
0
0
2
0
0
2
0
2
0
1
0
0
1
0
1
0
0
2
1
0
0
2
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
1
2
2
0
1
0
0
2
0
2
2
0
2
4
2
0
1
1
0
2
0
0
2
0
0
0
0
0
0
2
2
0
0
0
2
1
1
0
1
0
1
0
0
0
4
0
0
1
0
2
0
1
0
0
0
4
2
0
1
0
0
0
0
0
0
0
0
2
0
6
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
1
0
0
1
0
2
2
0
0
0
0
2
1
2
1
1
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
1
2
0
0
0
2
0
2
0
1
1
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
1
1
2
0
1
1
0
0
0
1
0
0
4
0
3
2
1
0
2
1
0
0
1
0
0
0
0
1
0
0
2
2
2
2
0
0
1
2
2
0
0
2
0
0
0
0
0
1
0
1
1
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
1
1
2
2
0
0
0
1
1
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
2
0
0
1
1
2
1
2
0
0
2
1
1
0
0
0
1
0
0
2
0
0
3
0
2
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
2
0
0
0
2
0
2
0
0
2
0
1
0
0
2
2
0
0
0
2
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
3
0
0
1
0
0
0
1
0
1
2
0
0
0
2
0
1
2
2
0
0
0
1
0
1
1
0
1
0
1
0
2
1
0
1
0
0
0
0
0
1
2
0
0
1
2
0
0
0
1
0
1
0
2
1
1
1
2
2
0
0
0
0
1
0
0
0
2
0
1
0
2
0
1
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
1
1
1
0
2
2
1
2
0
0
2
0
1
2
0
0
0
0
0
0
6
0
3
0
0
0
0
0
0
0
0
0
1
2
2
0
2
2
0
2
2
2
1
1
2
0
0
0
0
0
0
0
1
2
0
2
0
0
0
1
2
0
0
1
0
0
1
1
1
0
2
0
2
0
0
1
0
0
0
1
0
1
0
0
0
0
2
2
0
0
0
0
0
2
0
4
2
0
1
2
2
1
0
1
1
2
0
1
0
2
0
2
0
1
0
2
0
0
1
0
0
1
0
1
0
1
0
2
1
1
0
1
0
0
0
3
1
8
1
2
1
0
4
0
1
0
0
0
0
1
0
2
1
1
0
0
1
0
2
0
0
2
0
1
0
0
0
0
1
1
0
1
2
0
0
3
0
2
0
0
1
0
0
0
2
0
2
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
2
0
2
0
1
1
0
0
0
1
2
0
0
0
2
0
0
2
0
0
1
1
0
1
0
1
2
0
0
0
1
0
1
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
1
1
1
1
0
0
2
0
0
0
1
0
0
0
2
1
0
1
0
0
0
1
0
2
2
0
2
2
0
1
0
1
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
1
0
0
0
0
3
0
1
0
0
1
1
1
1
2
0
1
2
1
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
1
0
0
2
0
0
0
0
2
0
2
0
1
0
1
0
2
0
2
0
1
0
2
0
0
2
0
1
1
2
1
0
1
0
2
2
1
0
2
2
0
0
0
1
0
0
2
0
0
2
0
2
2
2
1
0
0
1
1
0
2
0
0
3
0
2
2
0
0
0
0
2
2
0
1
1
0
0
0
0
0
1
1
0
0
1
2
0
1
0
0
0
2
0
0
0
0
0
0
0
3
1
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
1
2
0
1
0
1
2
0
2
0
0
2
0
0
0
0
0
1
2
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
1
2
0
2
0
0
1
2
2
0
0
0
1
0
0
0
0
1
1
0
1
2
0
0
1
2
2
2
0
0
1
2
2
2
1
0
0
1
0
1
0
1
1
2
0
0
0
2
2
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
1
2
2
3
0
0
1
0
1
2
2
1
1
1
0
0
0
1
2
0
2
0
0
2
0
0
3
1
0
0
0
1
0
0
1
0
1
0
0
2
0
0
1
0
0
0
0
2
2
0
0
1
0
2
2
0
0
0
1
0
2
2
0
0
1
0
0
0
0
2
2
1
0
2
0
0
0
0
0
0
0
1
0
2
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
1
0
1
0
2
0
0
1
1
0
2
1
0
0
1
1
1
0
0
2
2
1
2
2
2
2
0
0
0
0
0
0
2
0
1
0
1
1
0
0
0
1
0
1
0
0
0
2
2
1
0
2
1
1
2
0
2
2
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
1
0
2
1
0
0
2
0
0
0
0
2
2
0
0
2
1
1
0
0
1
2
0
0
1
1
1
0
3
1
0
0
0
0
0
2
0
0
0
1
2
1
0
0
1
0
0
2
1
0
0
1
2
1
0
0
2
0
0
1
2
1
0
0
0
0
1
0
0
0
0
0
1
2
1
2
1
1
1
0
1
0
0
1
1
2
2
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
2
2
0
0
0
8
0
0
0
3
0
1
0
0
0
0
2
0
2
0
1
0
0
2
0
1
1
0
3
0
1
0
0
0
0
0
2
0
1
0
0
1
0
2
2
7
0
0
0
2
0
1
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
1
1
0
2
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
1
1
0
1
4
1
1
0
1
0
0
0
0
1
0
1
0
1
0
3
1
1
1
0
1
0
0
0
0
2
2
2
0
0
0
0
0
0
1
0
0
0
1
2
1
0
2
1
0
0
1
2
0
0
2
0
1
0
1
0
0
2
2
0
1
2
0
0
0
0
0
0
1
0
0
1
2
0
1
2
1
1
0
0
2
2
1
1
0
0
0
1
0
0
0
0
3
1
2
0
2
0
0
0
2
0
0
0
0
4
2
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
2
0
0
2
0
0
1
2
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
3
1
0
0
0
0
2
2
1
0
1
2
0
1
2
0
0
0
2
1
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
2
3
0
0
0
0
2
2
1
0
0
2
1
0
2
0
1
0
2
0
2
0
0
1
1
1
1
0
1
0
1
1
1
0
0
0
0
3
0
1
0
1
1
0
0
2
0
0
1
1
0
1
0
1
0
0
0
1
0
1
11
1
1
1
0
0
2
2
0
1
0
2
0
0
1
1
1
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
2
0
2
0
2
2
1
0
0
1
1
0
1
0
2
0
0
0
0
2
0
0
1
1
0
2
0
0
1
0
0
0
0
2
1
0
1
0
0
0
1
1
0
2
0
2
1
2
0
2
0
0
0
0
0
0
0
2
1
2
0
1
0
0
0
2
0
0
0
2
0
1
0
1
0
0
2
0
0
0
2
2
0
1
0
1
0
1
0
0
0
0
0
1
1
2
0
0
1
0
2
0
2
1
1
0
0
0
0
1
2
0
1
2
0
0
5
0
0
0
1
1
0
2
0
0
0
0
0
1
1
0
0
1
1
1
0
0
2
1
2
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
2
1
0
1
0
0
1
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
1
0
2
0
2
0
0
2
0
0
1
0
1
2
0
0
0
0
2
0
0
3
0
1
0
2
0
0
0
2
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
3
0
0
0
1
1
0
0
1
2
0
0
0
1
0
0
0
1
1
0
2
0
2
0
0
0
2
0
0
1
0
1
0
0
1
2
3
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
2
0
2
0
2
0
2
0
0
0
2
0
1
1
1
0
0
0
0
1
3
0
0
2
2
1
0
2
2
0
0
0
1
0
0
0
1
1
3
0
1
1
1
2
0
1
1
0
0
0
1
0
0
2
0
0
0
1
1
0
0
1
1
0
6
0
2
1
1
2
2
0
0
1
1
0
0
0
0
0
0
0
3
0
1
2
0
2
0
0
0
2
0
0
0
0
1
0
0
1
0
0
1
0
1
1
1
0
0
0
0
1
0
1
0
1
3
2
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
1
1
2
3
0
1
1
2
0
0
2
0
0
0
1
0
0
0
0
0
0
1
1
4
0
0
2
2
0
0
0
2
0
2
0
0
0
0
0
0
2
0
1
2
0
1
1
0
0
0
0
0
0
0
0
2
2
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
1
2
0
0
2
0
0
0
1
0
2
0
0
0
0
0
1
2
0
0
0
0
0
1
1
1
2
1
0
2
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
2
0
2
3
2
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
1
1
1
2
0
2
1
0
0
2
0
0
1
1
0
0
0
2
1
0
1
0
2
0
0
0
0
0
1
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
2
1
0
1
2
0
2
0
1
0
0
0
0
0
0
2
0
0
0
1
1
1
0
2
1
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
1
0
0
2
0
2
0
1
0
0
2
2
0
2
2
0
0
0
0
0
3
0
1
0
2
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
2
1
0
1
0
0
2
1
0
0
0
0
0
0
0
0
1
2
2
0
1
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
2
2
0
0
0
1
0
3
2
0
0
2
0
0
0
1
2
0
0
0
0
1
0
1
0
0
4
2
0
0
0
0
2
0
1
0
0
1
0
0
0
0
3
0
0
0
0
0
0
1
1
0
0
2
2
0
1
0
2
2
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
1
4
0
0
1
0
1
0
0
0
1
6
1
0
0
2
2
0
0
1
2
0
0
0
0
2
0
0
3
0
1
2
2
2
0
0
1
0
2
0
0
2
0
2
0
1
0
1
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
2
0
2
0
1
1
1
1
2
0
0
0
0
2
2
0
1
0
0
0
1
0
2
2
2
1
0
4
3
0
1
0
0
1
2
0
0
0
1
0
2
0
2
0
2
1
2
2
0
2
0
0
0
0
0
0
0
0
2
1
0
1
0
2
1
1
1
1
0
0
1
1
0
2
1
0
0
0
0
0
0
0
2
2
0
0
1
4
0
1
0
0
1
0
2
0
0
1
0
0
0
0
2
0
0
0
1
4
0
0
0
0
0
1
1
2
0
0
1
0
1
2
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
2
1
1
0
0
1
0
0
2
1
0
2
0
1
1
0
0
0
0
1
0
1
0
1
1
2
2
1
0
1
0
0
0
0
2
0
2
0
2
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
1
2
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
1
1
0
1
2
1
1
2
0
3
1
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
1
0
0
0
0
2
3
0
0
1
1
0
0
0
2
0
0
1
0
2
0
0
2
2
0
0
0
0
1
0
2
1
1
0
2
0
0
0
0
1
0
2
0
0
0
1
0
0
2
0
2
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
2
1
2
1
0
0
0
1
1
1
0
2
2
1
0
1
2
0
0
2
0
2
0
1
0
0
0
1
0
0
1
0
1
0
0
1
0
0
11
0
0
1
0
0
1
0
0
0
1
1
1
0
1
2
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
2
0
0
1
1
0
0
2
0
1
0
2
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
2
0
0
1
0
0
0
1
0
1
2
0
1
1
2
1
1
0
0
0
0
1
1
0
0
0
0
0
1
2
2
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
2
0
2
0
2
2
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
2
0
0
0
1
0
0
0
0
1
0
1
0
2
1
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
2
2
1
0
0
2
1
0
2
0
1
2
0
1
0
2
4
2
1
2
0
0
0
0
2
0
2
0
1
0
1
2
2
0
0
2
0
0
0
1
0
0
1
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
1
1
0
0
1
1
2
2
0
2
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
2
1
2
2
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
1
0
0
2
0
0
1
2
0
0
2
0
1
0
2
2
0
0
0
1
1
0
2
2
0
0
5
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
2
0
0
0
0
0
0
0
1
2
1
0
0
2
1
0
0
1
0
0
0
0
0
2
0
1
1
0
2
1
2
1
0
2
1
0
0
0
0
0
0
2
0
1
2
0
2
1
0
0
0
0
1
1
0
0
1
0
3
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
1
1
0
0
2
0
0
0
1
2
1
2
0
0
0
0
0
1
0
0
0
1
1
1
1
0
0
0
0
0
0
2
0
0
1
1
1
0
0
0
0
0
0
3
1
0
1
2
0
1
0
1
0
0
0
0
0
2
0
2
2
0
2
0
2
0
1
0
3
0
0
0
0
0
1
0
0
0
4
1
0
0
0
0
0
0
0
0
2
0
2
0
2
0
2
0
0
0
1
0
1
2
2
0
1
1
0
1
0
0
0
0
0
2
3
1
2
0
1
0
0
2
0
1
0
2
3
0
1
0
0
0
2
1
0
0
1
0
1
2
1
2
0
2
0
2
0
0
0
0
0
0
2
1
1
0
0
0
0
2
2
0
2
1
0
1
2
1
1
0
3
2
0
1
0
1
1
2
2
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
1
0
3
3
0
3
2
1
0
0
2
0
0
3
0
0
0
0
0
0
0
2
0
0
0
2
0
5
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
1
1
2
1
0
0
0
0
0
3
0
0
2
0
1
0
0
2
1
0
0
0
0
0
2
1
0
1
2
0
1
0
0
0
1
1
2
0
0
1
2
0
2
0
1
0
0
0
0
0
0
0
2
3
1
1
2
2
0
0
2
4
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
1
0
2
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
1
0
0
3
1
0
0
2
2
2
1
0
0
1
1
0
2
2
0
1
1
0
0
0
0
0
2
2
0
1
0
0
2
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
1
2
2
0
1
0
1
0
2
0
1
2
0
1
2
1
2
0
1
0
1
2
0
1
1
2
0
0
0
0
0
0
0
1
0
0
2
0
2
2
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
3
1
1
0
5
2
0
0
2
0
0
0
2
0
0
0
1
3
0
0
0
0
0
0
0
1
1
3
2
0
0
1
0
0
0
2
0
0
2
0
0
1
0
1
0
0
0
0
1
1
2
0
0
1
3
1
0
0
2
0
1
0
0
1
2
1
2
1
1
0
0
0
0
1
1
3
0
2
0
2
1
3
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
2
0
2
0
2
0
0
1
0
0
1
0
0
0
0
0
2
0
0
1
2
0
1
2
1
0
1
0
1
2
0
0
0
0
0
1
0
0
0
0
0
3
0
1
1
2
3
1
0
1
1
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
2
2
0
0
2
0
0
1
0
0
0
0
1
1
0
2
2
2
2
0
2
0
0
0
0
0
0
0
2
2
1
0
0
0
1
2
0
0
0
0
0
0
0
3
0
2
0
0
1
1
2
0
1
0
1
0
0
1
0
0
1
1
1
0
2
2
0
2
2
0
2
0
0
0
0
2
0
1
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
2
1
2
2
0
2
2
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
4
0
1
0
0
2
0
0
1
0
0
0
0
1
2
2
0
2
1
0
1
3
1
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
2
1
1
1
0
1
0
0
1
2
1
2
1
0
0
0
0
2
1
0
2
2
0
0
3
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
3
0
0
0
0
3
2
1
1
2
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
2
2
0
0
1
1
0
4
0
0
0
0
0
0
1
0
0
1
0
2
0
0
2
2
1
0
0
0
0
3
0
1
1
0
1
2
1
1
0
0
1
0
1
1
0
0
1
1
1
0
0
1
0
2
2
0
1
3
0
0
0
1
0
0
1
1
0
0
2
0
0
1
0
0
1
2
0
2
2
0
3
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
1
2
0
0
0
1
0
0
3
0
0
1
0
0
1
0
2
0
0
0
0
0
0
2
1
0
1
0
0
0
1
0
2
1
1
0
0
0
0
0
2
0
0
0
2
1
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
2
0
2
2
0
0
0
2
0
0
2
0
1
2
0
0
2
0
0
0
1
0
0
1
0
1
0
1
2
0
0
0
0
0
1
0
2
1
0
1
0
0
0
0
0
2
0
0
0
1
1
0
3
0
0
0
0
0
2
0
0
1
0
2
0
2
2
0
0
1
1
0
0
0
0
1
0
1
1
2
2
0
2
2
1
0
0
0
0
1
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
1
2
4
0
1
0
1
2
1
0
1
1
2
0
2
0
1
1
0
0
0
2
0
1
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
1
0
1
0
1
0
2
0
0
0
0
0
1
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
2
1
1
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
1
2
0
2
0
2
1
1
3
0
0
0
1
0
0
0
0
1
0
0
1
2
0
0
0
0
1
2
2
0
0
1
1
2
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
4
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
1
0
0
2
1
0
2
0
0
0
0
0
0
0
2
2
0
2
0
2
2
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
1
0
2
1
0
0
0
1
0
0
0
2
1
2
0
1
0
1
2
0
1
1
2
0
1
0
2
1
0
1
0
0
0
0
0
0
0
2
2
0
0
2
1
1
1
0
0
2
1
0
0
0
0
0
0
0
1
0
1
0
2
1
0
0
0
0
2
2
0
2
1
0
0
0
2
2
1
0
0
1
0
0
2
0
1
2
1
1
0
0
0
1
1
0
2
1
0
1
1
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
2
0
0
0
1
0
0
2
0
1
0
2
2
0
2
2
1
1
1
1
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
2
2
2
2
1
2
1
1
1
0
0
4
2
1
0
2
0
0
1
0
0
0
0
0
0
0
0
3
0
1
2
3
0
0
0
0
2
0
0
1
0
1
0
2
0
2
0
1
1
2
0
2
0
0
0
0
0
2
1
1
1
0
0
1
0
2
0
0
0
2
1
3
0
1
0
0
1
0
0
1
1
0
1
2
0
0
2
1
2
0
0
2
0
0
2
0
0
2
0
0
2
0
0
0
1
2
0
0
2
2
0
0
0
1
0
0
1
0
2
2
1
0
1
2
0
0
0
0
0
0
0
0
1
0
6
0
2
0
0
1
0
2
0
0
1
2
0
1
0
0
0
0
0
0
0
0
1
1
2
0
0
1
0
0
0
1
2
0
0
1
0
0
1
0
0
0
1
1
0
0
1
2
1
4
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
2
0
2
1
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
3
2
2
2
1
0
1
2
1
2
2
0
0
1
1
0
1
0
0
1
0
0
0
0
1
1
0
2
0
1
0
0
0
0
1
2
0
2
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
2
0
1
0
1
0
0
2
1
0
1
2
2
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
2
3
1
0
0
0
0
2
0
2
0
0
2
2
0
2
2
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
1
0
2
1
0
2
2
0
2
2
0
0
1
1
0
1
2
0
1
0
2
0
0
0
0
0
0
0
0
0
2
2
2
0
0
2
2
0
0
0
1
0
0
0
1
1
1
0
0
0
1
0
0
1
0
0
0
1
2
1
1
0
0
1
1
0
1
0
0
0
0
0
0
2
2
2
0
3
1
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
3
2
0
0
2
0
1
1
0
0
0
1
0
0
2
0
1
0
2
0
0
0
0
0
1
2
0
2
1
2
0
1
0
1
0
0
0
0
0
1
1
0
0
0
2
0
2
0
0
2
0
1
2
0
2
0
0
0
0
0
2
1
0
0
2
2
0
0
1
0
0
0
0
0
2
1
1
1
1
0
0
1
2
1
5
0
0
0
0
1
0
0
0
1
1
0
2
0
1
0
2
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
1
1
0
0
0
2
1
0
1
0
2
0
0
1
1
0
1
0
2
0
2
2
2
0
0
0
0
2
1
2
2
1
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
1
1
0
0
0
0
0
1
1
1
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
1
0
1
0
2
1
0
0
0
0
1
1
0
0
0
2
2
1
0
0
0
0
0
2
0
2
1
0
0
2
0
0
0
1
2
0
0
0
0
0
0
1
2
3
0
0
2
0
5
1
2
0
1
0
0
2
1
0
2
1
0
2
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
1
2
0
2
2
0
0
0
0
1
2
0
1
0
3
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
2
1
0
0
0
1
0
0
0
0
0
4
2
0
0
0
2
2
1
1
0
0
0
0
2
1
0
0
1
0
0
1
1
2
0
0
0
5
0
0
0
2
2
2
0
1
0
0
2
2
0
0
2
2
2
0
1
0
0
0
0
0
0
1
0
1
1
0
1
0
1
1
1
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
1
0
2
0
2
0
1
0
0
2
0
2
1
1
0
0
1
1
1
0
2
0
1
0
2
0
1
0
0
0
0
0
2
0
1
0
0
3
0
0
2
0
0
0
2
0
2
2
2
0
2
0
0
0
1
2
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
2
1
1
0
0
0
1
1
0
2
2
0
1
1
1
1
1
1
0
2
0
0
3
2
1
0
2
1
0
0
2
1
3
0
0
0
2
3
0
0
0
0
1
1
0
0
0
0
1
2
1
0
0
1
2
0
1
2
2
1
1
0
0
0
0
0
0
2
0
2
1
1
2
0
0
2
0
1
2
2
1
0
1
1
0
0
1
2
0
2
2
4
0
0
0
0
0
3
0
2
0
0
0
2
2
0
0
0
0
0
4
0
0
0
2
1
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
1
1
2
2
2
2
2
0
0
0
1
2
1
0
0
1
0
0
0
0
2
1
0
1
0
0
1
2
0
0
2
0
1
0
0
0
1
1
1
0
0
2
0
0
0
0
2
0
0
9
0
1
0
0
1
0
0
1
0
2
2
0
0
0
1
0
0
0
2
1
0
0
0
0
2
1
2
0
0
3
2
1
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
1
2
0
1
2
0
0
0
0
0
0
3
2
0
1
0
1
1
0
0
0
0
1
1
0
0
1
0
1
0
1
1
2
1
1
0
0
0
1
0
0
0
0
0
0
5
1
2
2
0
0
1
0
2
0
0
3
0
0
0
2
0
1
0
0
0
1
0
0
1
0
0
4
0
0
1
0
1
0
2
0
0
2
2
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
1
0
0
0
0
2
0
4
0
0
2
0
0
0
2
0
0
2
0
1
0
0
0
0
2
2
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
1
1
2
0
1
0
0
0
2
0
4
0
2
0
2
0
2
1
1
1
0
0
0
1
2
0
0
1
0
0
2
1
0
0
0
1
0
0
0
0
0
1
2
1
0
1
2
0
1
0
0
0
0
1
2
2
0
0
0
2
1
2
3
1
0
0
0
1
1
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
2
2
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
2
1
1
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
1
2
0
0
1
2
1
1
1
1
0
0
1
2
2
1
3
0
0
0
2
0
0
0
0
1
1
1
0
0
2
1
0
0
0
2
0
0
2
2
0
0
0
0
0
0
1
1
0
0
0
0
1
2
1
1
0
2
0
0
1
0
0
1
1
2
3
0
0
0
0
1
1
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
2
1
2
1
0
0
0
0
0
0
4
2
2
1
0
1
0
1
1
0
0
0
1
0
1
0
0
0
1
3
0
3
0
0
0
1
2
2
0
0
0
2
2
0
2
0
0
0
0
1
0
0
0
2
0
1
0
1
0
2
0
0
2
0
1
0
1
2
0
1
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
2
3
0
0
1
2
0
0
3
0
0
0
1
0
1
0
2
0
0
2
0
2
4
2
2
1
0
2
0
1
1
1
0
1
0
0
0
1
1
2
0
0
0
0
1
1
0
0
0
2
2
0
0
0
0
0
0
0
2
1
2
0
0
2
0
1
1
2
2
0
1
2
0
0
0
4
2
0
1
0
2
0
0
2
0
2
1
1
1
0
0
1
0
2
0
1
0
0
0
1
0
0
0
0
1
0
0
4
0
2
1
0
1
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
2
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
2
0
2
1
0
1
1
2
0
1
0
0
0
2
0
0
0
2
0
0
0
1
1
2
1
2
2
2
0
2
0
2
1
2
1
0
0
1
0
2
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
1
0
0
4
0
2
0
0
0
2
1
0
0
0
0
0
0
2
0
0
1
1
0
1
0
0
1
2
0
0
2
0
1
0
2
0
2
0
0
0
0
2
0
0
0
1
1
0
0
0
2
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
2
2
1
3
0
0
0
5
0
7
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
2
0
2
0
1
0
0
0
2
0
1
0
0
0
2
3
1
1
2
1
0
1
2
2
2
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
1
0
0
1
0
1
1
0
0
0
0
2
2
1
0
0
1
2
0
0
2
0
0
1
1
0
0
0
1
0
2
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
2
2
2
1
2
2
0
1
0
0
0
0
2
1
0
0
1
1
2
0
0
0
1
0
0
2
0
0
0
0
1
2
1
0
0
2
2
0
0
0
1
2
0
1
0
0
2
2
0
0
0
1
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
1
0
2
1
0
0
0
0
0
2
0
2
1
0
1
1
0
0
0
0
1
0
2
0
0
2
1
0
2
0
0
0
1
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
2
0
0
0
0
1
1
0
0
0
0
2
0
0
2
0
0
4
0
3
0
1
0
0
0
0
2
0
0
0
0
0
0
1
1
2
2
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
1
1
0
0
3
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
2
1
0
0
0
1
2
2
0
1
1
1
0
0
0
0
0
0
0
1
2
0
0
2
1
0
1
1
0
2
1
2
0
0
0
2
0
4
1
0
0
1
0
0
2
0
0
2
0
0
0
0
2
3
2
0
0
0
0
0
0
2
2
0
0
2
1
0
1
0
0
0
0
1
2
2
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
2
2
1
1
1
1
2
0
2
0
1
2
0
1
0
0
0
0
2
0
3
0
0
4
2
2
0
2
2
0
0
2
0
1
0
1
1
0
0
1
0
2
0
1
1
0
0
0
0
2
2
0
0
0
0
0
0
2
0
1
1
0
1
0
4
0
0
0
2
1
1
2
2
0
2
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
1
1
1
0
1
1
0
0
0
0
0
2
2
0
1
2
0
0
1
2
2
0
0
0
1
0
0
0
0
2
0
0
1
0
1
0
2
0
0
0
2
0
1
7
2
2
0
2
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
1
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
1
2
0
1
0
2
0
0
0
0
2
0
0
0
2
0
1
1
2
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
1
0
2
0
1
0
2
1
3
0
2
2
2
0
0
3
1
0
1
0
0
0
0
0
1
0
2
0
0
3
0
1
0
0
2
0
0
0
0
0
1
0
0
1
0
0
2
1
0
0
0
2
0
2
2
1
1
1
1
3
2
2
2
0
1
1
1
1
3
0
0
2
2
4
0
1
2
0
1
2
1
1
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
2
2
1
0
0
0
0
0
1
2
2
2
1
0
0
0
1
1
0
1
0
0
1
1
0
0
0
1
2
2
2
0
2
0
0
2
0
1
1
0
2
0
0
2
0
0
0
0
1
0
2
3
0
0
0
0
1
3
2
0
0
0
0
0
2
2
4
0
1
0
0
0
1
1
0
0
0
0
1
0
0
1
0
1
0
2
0
0
2
0
1
1
2
2
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
2
1
2
0
2
0
0
0
0
0
1
0
1
0
0
1
1
1
2
1
0
1
0
0
0
0
0
0
2
1
1
0
0
2
0
0
0
2
2
1
2
1
0
1
0
0
2
0
0
0
0
0
1
0
0
0
1
0
1
0
3
0
0
0
0
0
3
0
3
5
0
0
0
0
2
1
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
2
2
0
0
0
0
1
1
2
1
0
0
1
0
1
2
0
1
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
1
0
1
0
2
2
0
1
1
0
0
1
0
0
1
0
0
1
0
2
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
3
1
0
1
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
2
2
0
1
2
0
2
0
1
2
2
2
0
0
1
2
0
1
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
1
0
1
0
2
2
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
1
0
0
1
0
0
0
0
0
1
2
0
0
3
2
0
2
1
1
1
0
2
1
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
2
1
1
1
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
2
2
0
2
2
0
0
2
0
1
0
0
0
0
1
0
1
0
1
0
0
2
2
1
0
0
0
1
0
0
2
1
0
2
0
2
2
1
0
1
0
1
0
1
2
1
1
2
2
0
1
0
0
0
2
2
0
2
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
1
1
1
1
1
1
1
0
0
0
0
2
0
0
0
1
1
0
0
2
0
2
2
1
1
0
1
0
0
0
2
1
0
0
0
2
2
0
0
0
0
0
0
0
1
2
0
1
2
2
0
1
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
2
2
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
1
0
3
0
0
4
0
0
2
0
0
0
1
2
1
0
2
2
0
1
0
0
2
2
0
0
0
2
1
0
0
2
1
0
1
0
0
0
1
0
0
0
2
0
2
1
0
0
1
6
2
2
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
2
2
2
1
2
2
0
1
2
1
0
0
1
1
0
0
2
0
0
0
0
0
1
1
0
0
2
0
2
1
1
1
3
2
0
0
0
2
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
2
0
1
1
1
1
0
0
2
2
2
2
2
1
0
1
0
0
0
0
2
0
0
0
0
1
1
2
0
0
2
1
0
0
0
0
1
2
0
1
1
4
0
7
0
2
0
0
0
1
2
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
2
1
1
2
2
0
1
1
0
1
0
2
0
2
0
0
0
1
0
0
2
0
0
1
2
1
1
2
0
2
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
1
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
2
2
1
4
0
0
1
2
3
1
0
0
1
2
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
2
0
0
0
0
0
1
0
0
1
1
0
2
3
0
1
2
0
0
2
0
0
0
0
0
0
1
0
0
1
0
2
1
0
1
0
1
0
0
2
0
0
0
0
2
2
1
0
2
0
0
2
1
4
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
3
0
0
1
0
1
2
0
1
0
2
0
0
1
2
2
0
1
0
4
0
0
0
1
0
2
1
0
0
1
2
0
0
2
0
2
2
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
3
1
0
0
0
0
0
0
0
0
2
0
1
2
0
1
1
1
0
2
1
2
0
1
0
2
0
0
0
0
0
0
0
0
1
0
2
1
2
0
0
0
0
0
0
2
1
0
0
4
2
0
0
0
0
1
0
0
0
1
1
0
2
2
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
5
2
3
2
0
0
1
0
0
8
0
0
0
0
0
0
1
3
0
2
0
0
2
0
0
0
0
1
2
0
1
0
0
0
0
0
0
1
0
2
0
2
2
0
0
0
1
2
0
1
0
0
1
2
2
1
0
1
2
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
2
2
1
1
0
1
0
0
1
0
2
2
0
0
2
0
0
1
0
0
0
2
2
2
0
1
2
0
1
0
0
0
2
0
0
0
1
1
0
1
0
1
1
2
0
0
1
0
0
1
0
0
0
0
0
1
1
0
2
0
2
0
1
0
1
0
2
1
0
2
1
1
2
0
0
2
2
0
0
0
7
0
2
0
0
2
0
1
0
2
0
0
0
2
1
2
1
0
2
0
2
1
0
0
1
1
2
1
1
0
0
0
0
1
0
0
0
0
2
0
7
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
1
2
1
2
0
0
0
0
1
2
0
0
4
0
0
0
1
1
1
1
2
1
3
0
3
0
0
0
2
2
2
2
0
0
7
0
0
0
0
0
0
2
1
2
1
1
0
2
0
1
0
0
0
0
0
1
1
0
0
2
2
0
1
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
2
0
1
1
0
2
0
2
0
1
0
0
0
0
1
0
1
1
0
0
1
0
2
0
0
1
0
1
0
0
2
1
0
0
1
0
2
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
1
0
0
0
2
2
0
0
0
1
0
0
2
1
0
0
0
1
0
2
0
0
2
1
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
2
1
0
1
0
3
0
2
0
1
2
0
0
0
2
0
0
0
0
1
0
0
0
2
3
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
1
3
0
0
0
0
2
0
1
0
0
1
0
0
1
1
0
2
0
0
2
1
0
0
1
0
0
1
2
0
0
0
2
0
0
0
0
3
1
0
0
2
2
2
1
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
2
1
0
0
0
0
2
0
0
0
2
2
0
1
2
0
0
0
0
1
2
0
0
1
1
2
1
0
0
0
0
0
0
1
2
0
1
0
0
2
1
0
0
0
1
0
0
0
2
2
2
1
1
0
0
0
1
0
0
2
0
4
0
1
0
2
0
0
0
0
1
2
0
2
0
0
2
2
2
1
0
0
0
0
0
3
0
2
0
0
0
0
2
1
2
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
1
0
0
2
0
0
0
0
0
2
0
1
0
2
0
0
0
0
1
3
0
1
0
1
2
2
1
0
1
1
0
0
0
1
0
1
2
1
0
0
0
1
0
0
0
0
0
1
0
2
0
0
2
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
2
0
1
1
2
1
0
1
0
2
1
2
0
0
1
1
0
2
3
1
0
2
4
0
0
2
1
1
0
0
0
1
0
0
0
0
0
2
0
1
4
0
3
0
0
0
1
0
0
1
0
0
0
0
1
1
1
0
2
2
2
0
0
0
0
0
2
0
0
0
3
1
1
1
0
2
0
1
0
2
1
0
0
0
1
0
0
0
2
1
0
0
1
0
1
2
2
0
0
0
0
0
0
1
1
0
0
0
1
1
4
2
0
0
0
0
0
2
0
2
0
0
0
1
1
0
1
0
0
1
0
1
0
0
2
0
0
0
1
1
0
0
1
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
2
0
0
1
0
1
1
0
1
0
0
2
1
0
0
1
1
2
0
0
0
0
1
1
0
1
0
1
0
0
1
0
1
0
1
4
0
2
0
0
1
1
1
0
0
1
0
1
0
0
1
0
2
1
0
0
0
0
1
2
2
4
0
0
2
0
0
1
0
4
1
0
0
1
0
2
1
2
0
0
2
0
0
0
1
3
1
1
2
2
0
1
0
0
0
0
0
0
1
0
2
0
0
0
2
2
1
1
0
0
1
0
0
0
0
0
2
1
0
0
2
1
3
1
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
2
0
0
0
1
0
0
0
0
2
2
0
0
2
1
0
0
0
0
3
0
1
2
1
1
0
1
2
0
2
2
2
2
0
1
2
0
0
2
1
0
0
2
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
3
1
1
0
0
1
2
0
0
1
1
0
1
0
0
0
2
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
1
1
1
0
0
2
2
0
0
0
0
1
2
1
1
0
0
0
2
1
0
0
1
0
1
0
0
0
1
0
0
0
1
1
2
0
1
0
0
1
0
0
0
0
1
0
1
2
0
1
0
1
2
1
0
0
2
1
0
0
1
0
2
2
0
0
1
1
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
2
0
2
2
0
0
0
3
0
1
0
0
0
0
0
0
0
1
1
1
1
2
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
1
1
1
1
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
2
0
0
2
0
1
0
0
0
0
1
1
0
1
1
0
1
0
2
0
2
0
0
3
0
2
0
0
0
0
2
0
0
1
0
1
0
0
3
1
0
2
2
0
1
1
0
0
0
0
2
2
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
3
2
1
1
0
0
1
1
0
0
0
2
0
0
0
1
0
0
1
1
0
0
1
0
0
0
1
0
2
1
0
0
0
0
0
2
2
1
2
2
1
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
3
0
2
0
0
0
2
2
0
1
1
0
0
2
0
0
1
0
2
0
1
1
0
3
2
1
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
2
1
0
3
0
0
0
2
0
1
1
1
1
0
0
0
2
1
0
0
2
0
0
0
0
2
0
1
3
0
0
2
0
0
0
0
1
2
0
0
0
1
0
1
0
0
0
1
2
0
2
0
0
1
1
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
1
0
1
0
2
1
0
3
0
0
0
0
0
0
0
2
1
1
2
0
2
1
2
1
1
1
0
0
2
2
0
1
0
0
0
1
0
0
1
0
0
0
0
2
1
0
1
1
0
0
0
2
0
0
2
0
0
0
2
2
1
1
1
0
2
0
2
0
0
1
0
0
2
0
0
2
1
0
0
0
0
1
0
0
3
2
2
4
0
1
2
2
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
1
0
2
0
1
0
1
1
0
0
0
1
0
0
1
0
0
0
0
1
3
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
3
0
0
0
1
1
1
1
1
0
0
0
0
1
1
2
1
0
0
0
1
0
0
2
1
2
1
0
0
1
1
0
0
0
1
1
0
2
1
0
0
0
2
0
0
2
1
1
1
1
2
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
2
0
1
0
0
0
0
0
0
1
0
2
0
1
0
2
0
1
1
1
0
0
1
1
4
1
2
0
1
1
2
2
1
2
0
0
0
1
0
0
1
1
0
1
1
2
2
0
0
0
2
0
2
1
2
2
0
0
0
0
0
1
2
4
0
0
1
1
0
0
0
2
0
2
0
2
0
1
1
2
2
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
2
2
2
0
0
0
1
0
2
0
0
2
0
0
0
1
0
0
0
0
2
2
0
1
0
0
0
0
0
0
2
2
1
1
2
2
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
2
0
2
0
1
0
0
0
0
2
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
2
0
2
0
1
0
2
0
1
1
0
2
1
0
1
0
0
0
1
2
0
1
2
0
0
2
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
2
0
0
2
0
2
1
0
1
0
0
1
0
0
0
2
1
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
2
0
2
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
6
0
0
0
2
0
1
0
0
2
0
1
0
0
0
1
0
1
0
0
0
0
2
0
2
1
2
2
0
0
0
0
0
0
0
0
2
0
1
2
0
0
1
0
2
0
0
0
1
2
1
0
1
2
2
2
0
1
0
0
0
1
2
0
2
0
0
0
0
0
1
1
2
0
0
2
6
0
0
0
2
0
0
0
0
1
0
1
0
2
0
2
0
0
0
0
2
0
0
0
0
1
0
2
1
1
1
2
0
2
0
0
0
0
1
2
0
0
1
0
1
1
0
2
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
2
1
0
2
0
1
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
2
1
0
0
0
0
1
0
0
1
4
0
2
0
1
1
0
3
1
0
2
0
1
0
2
1
0
0
0
0
0
0
1
0
0
1
1
0
1
3
2
2
0
0
0
0
0
0
0
0
1
3
0
1
0
0
3
0
2
0
0
0
1
1
2
1
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
2
1
2
0
1
1
2
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
1
2
0
0
1
0
0
0
1
1
0
0
2
0
2
1
0
0
0
0
0
0
1
1
0
1
2
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
2
2
0
2
1
0
0
0
0
0
1
0
0
0
1
2
0
0
1
2
1
0
2
0
2
2
2
0
1
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
2
0
2
0
1
0
0
1
0
2
1
0
2
2
1
2
0
1
2
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
1
0
0
1
1
2
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
2
1
1
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
2
2
2
2
2
1
3
0
0
1
0
1
0
0
0
0
0
2
1
1
0
0
0
0
0
3
0
0
0
0
2
1
0
0
0
1
0
2
2
0
0
0
1
0
0
0
2
1
1
1
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
2
0
1
0
0
0
1
2
2
0
0
0
1
2
1
3
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
1
0
0
2
0
0
0
1
0
2
1
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
1
2
1
2
1
0
1
2
1
0
0
1
0
2
0
2
0
0
0
2
0
0
2
1
0
1
1
2
0
0
0
0
0
2
1
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
1
2
1
0
0
0
1
0
1
1
1
0
0
0
2
1
0
2
0
0
2
0
1
1
0
2
2
2
2
1
4
0
1
1
0
1
0
0
2
0
0
1
0
0
2
0
4
0
2
0
1
2
1
1
2
0
0
1
0
0
1
0
0
6
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
2
2
0
0
0
2
2
3
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
1
1
1
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
2
0
1
2
0
0
1
1
1
0
0
2
0
0
0
0
2
2
0
1
0
0
1
0
0
1
1
1
2
2
5
0
2
1
1
0
2
1
0
1
2
1
2
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
1
0
0
1
1
0
0
0
0
0
0
0
2
4
2
1
0
4
0
0
0
2
3
0
0
0
1
1
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
2
0
0
0
2
2
0
0
1
0
2
2
2
0
0
3
0
1
2
0
1
0
1
0
1
1
0
2
0
0
1
0
0
0
2
0
4
0
0
0
1
1
2
0
0
1
5
0
2
0
0
1
0
2
1
2
0
2
2
0
1
0
1
2
0
0
0
0
0
1
2
0
0
1
0
0
2
1
1
0
0
0
2
0
0
0
0
1
0
0
0
0
1
1
1
0
2
0
0
0
0
2
2
2
0
2
0
0
2
2
2
0
0
3
1
1
0
0
0
2
0
0
0
0
2
0
1
1
0
0
0
1
0
1
0
1
1
0
1
0
2
0
2
2
2
0
1
1
1
0
0
0
1
0
1
0
0
0
0
1
0
1
1
0
0
1
2
0
0
2
0
0
1
2
0
0
0
0
0
0
0
1
2
0
1
0
0
2
0
2
0
0
1
2
0
0
0
0
0
0
0
1
0
1
0
1
0
0
2
0
2
0
3
0
0
1
0
2
3
1
1
0
2
0
0
0
0
0
2
2
1
1
0
0
2
1
1
0
1
1
0
0
0
0
0
0
1
1
0
2
0
1
1
0
1
0
0
1
1
0
5
1
0
0
2
0
0
0
1
0
2
0
1
0
2
0
2
0
0
0
0
2
0
1
0
0
0
0
0
2
0
2
0
0
0
3
0
0
0
1
0
3
0
1
0
1
0
1
2
2
1
1
0
2
0
1
0
0
0
0
0
2
0
0
2
2
0
1
1
0
0
1
0
2
2
1
1
2
2
0
0
0
0
0
0
0
0
3
0
0
2
0
0
2
2
2
1
1
2
2
0
3
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
9
0
0
1
0
2
0
0
0
0
0
2
1
0
1
0
2
2
0
4
1
0
0
0
0
0
0
0
2
1
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
5
0
1
2
0
0
0
1
2
1
0
0
0
1
1
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
2
0
0
4
0
0
2
0
0
0
0
0
1
0
0
0
0
0
5
0
0
0
0
0
1
0
0
1
0
0
3
0
1
0
0
2
2
1
0
0
0
1
1
2
0
0
1
2
0
2
3
0
1
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
1
2
1
0
1
0
0
0
0
0
2
2
0
2
2
0
0
0
1
0
0
0
0
2
1
1
0
1
0
1
1
0
0
0
0
0
2
0
1
1
0
1
0
0
0
0
2
1
1
1
2
1
1
0
2
0
0
1
2
2
2
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
1
1
0
0
0
0
0
2
1
0
2
0
2
0
2
0
0
1
2
1
0
0
0
0
2
1
0
0
2
0
0
1
0
0
0
3
0
4
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
3
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
3
1
0
2
0
0
0
0
0
1
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
2
0
2
1
2
1
2
0
1
0
1
1
1
1
0
0
0
0
0
2
2
0
1
0
2
0
0
0
0
2
2
2
0
0
0
0
2
0
1
0
2
0
0
0
1
2
0
0
0
1
0
0
0
1
1
1
2
0
2
0
0
2
1
0
2
0
0
1
0
2
0
0
2
0
2
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
1
0
1
0
1
0
4
2
0
1
0
0
0
0
2
1
2
1
1
2
1
2
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
1
0
2
0
1
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
1
0
2
0
0
1
0
2
1
0
0
0
1
0
0
0
1
1
0
2
2
0
1
1
0
1
1
0
1
1
0
0
1
1
0
2
2
0
1
0
0
0
1
2
0
0
2
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
2
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
2
2
1
2
0
1
1
0
1
0
0
0
0
0
1
0
0
2
2
2
1
0
0
0
0
0
1
0
3
1
1
0
0
2
0
1
1
1
1
0
0
2
0
0
0
0
0
0
2
0
0
1
4
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
2
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
6
1
2
0
0
2
0
0
3
0
0
1
0
2
0
0
2
0
0
2
0
1
2
0
0
0
0
2
0
0
3
0
2
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
1
1
1
0
3
0
2
0
2
0
0
0
2
2
0
1
0
2
0
2
0
0
0
0
1
0
3
1
2
0
0
0
1
0
1
2
0
0
0
1
0
0
1
2
1
1
0
0
2
0
0
3
1
0
0
0
0
2
0
1
2
0
0
0
0
2
0
2
3
1
0
0
0
2
1
3
0
0
0
0
1
2
1
0
2
0
0
0
0
1
0
2
2
1
0
1
0
0
0
0
0
2
1
0
1
2
0
0
1
1
2
0
0
0
1
0
1
0
2
2
2
0
0
0
0
2
3
0
2
0
0
0
0
2
2
0
0
0
2
0
0
0
2
1
0
0
0
0
2
0
0
1
0
1
0
0
1
2
0
2
0
0
1
1
0
0
2
0
0
0
0
2
3
0
0
2
0
0
0
0
0
1
1
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
1
0
1
0
1
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
2
0
3
2
0
0
0
0
0
1
0
2
0
1
1
0
0
2
0
2
2
0
2
1
0
2
0
2
0
5
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
4
0
0
0
0
0
0
1
0
2
2
0
2
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
2
2
0
0
0
1
0
2
0
0
0
0
1
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
1
1
0
0
0
0
0
0
1
0
2
1
0
0
1
0
2
0
1
0
1
0
1
0
1
1
2
0
0
1
0
0
1
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
2
1
0
0
0
2
0
2
0
0
0
0
0
2
0
2
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
2
2
0
2
1
0
2
0
0
0
1
2
2
0
0
0
0
2
1
0
4
1
0
2
0
2
2
1
0
0
2
0
0
2
0
0
2
0
0
2
1
2
1
1
0
0
0
0
2
1
0
2
0
0
0
1
0
1
2
0
0
0
0
2
1
0
0
2
1
0
0
1
0
0
0
0
2
0
1
1
1
2
0
0
0
0
3
0
1
0
0
1
0
2
0
2
0
0
1
0
1
2
1
0
0
0
0
2
2
0
1
0
0
2
1
0
0
0
1
1
0
2
1
2
1
0
0
0
0
0
1
0
0
0
0
1
1
2
0
1
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
1
0
1
0
1
1
0
2
1
1
0
0
0
0
1
2
0
2
1
0
1
1
1
0
1
0
1
0
0
2
0
0
1
1
0
1
1
0
0
2
0
0
2
0
0
0
2
0
0
1
0
1
1
0
2
0
0
0
1
0
1
0
1
1
0
0
0
0
0
1
0
2
1
1
0
2
0
1
0
1
0
2
0
0
1
1
0
0
0
0
2
2
0
1
1
0
0
0
1
5
0
1
1
0
2
0
0
0
0
1
0
2
2
2
0
1
1
1
0
1
0
1
0
0
0
0
1
1
2
2
0
0
1
0
0
0
1
0
0
2
0
0
2
2
0
0
1
2
1
1
0
2
2
0
0
0
0
0
0
1
0
1
2
2
0
1
1
0
0
1
0
0
1
1
0
2
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
1
2
0
2
0
2
2
2
0
2
2
1
2
0
0
0
0
2
2
0
0
1
2
0
1
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
1
0
0
0
2
2
2
1
1
0
0
0
0
1
2
2
2
2
0
0
0
1
0
0
0
1
0
0
0
2
0
1
0
1
0
1
0
2
0
2
0
0
2
0
2
1
0
0
0
0
0
1
0
0
0
1
1
2
0
0
1
0
0
0
2
1
3
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
2
0
0
0
2
0
1
0
1
0
0
0
0
4
0
1
2
2
0
0
0
1
1
0
2
0
0
0
0
0
0
2
0
2
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
1
0
2
1
0
0
2
1
0
2
0
0
2
0
0
0
1
2
1
0
0
2
2
0
0
0
1
2
0
1
2
1
0
0
0
1
0
0
2
1
1
0
0
1
2
1
1
0
0
0
2
2
0
2
0
3
0
0
1
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
1
2
2
0
0
0
1
0
2
0
1
0
0
1
2
0
2
0
0
0
0
0
1
0
2
2
2
1
0
2
2
0
0
0
2
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
2
0
0
2
2
0
2
0
2
0
0
1
0
0
0
0
0
3
2
0
1
1
0
0
0
1
0
0
0
0
0
3
2
0
2
1
2
3
3
0
1
1
1
1
0
0
1
1
2
1
1
0
2
0
1
0
1
1
1
1
0
1
0
2
2
0
0
0
1
0
0
0
1
0
2
0
3
0
0
0
2
0
0
1
1
1
0
0
2
0
0
0
0
2
0
0
1
2
2
0
2
1
2
0
2
0
0
0
0
0
0
1
0
4
0
1
0
0
2
0
0
0
1
1
0
0
0
1
2
0
0
1
0
0
2
1
2
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
4
0
2
3
0
0
2
0
0
0
1
0
0
0
0
2
2
1
2
0
0
0
0
1
1
0
0
0
0
0
0
6
0
0
1
0
1
0
2
1
1
0
0
0
0
2
1
2
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
2
0
0
0
0
0
1
2
0
1
1
0
2
0
0
1
2
0
0
0
0
0
2
2
0
0
1
0
2
4
0
2
1
0
0
0
0
2
0
2
0
0
1
5
2
0
2
1
0
1
2
0
1
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
3
0
0
0
0
1
1
0
0
0
1
0
0
0
0
2
2
1
0
0
0
0
2
0
1
0
0
2
2
2
0
0
0
0
0
1
0
0
2
0
1
0
1
0
0
0
0
0
0
1
0
2
2
1
1
1
0
0
0
0
0
2
2
2
1
0
2
0
1
1
0
0
0
0
0
0
2
2
2
0
2
2
0
0
2
2
0
0
0
0
0
0
0
0
2
0
1
1
0
0
1
2
0
0
1
2
0
0
2
0
0
0
1
0
1
0
0
1
1
0
1
0
1
0
0
1
2
0
0
0
2
0
3
0
0
2
0
0
0
1
0
0
0
0
0
2
2
0
1
2
2
1
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
1
0
1
1
0
1
0
0
1
0
1
0
0
0
0
1
1
1
0
1
0
0
4
0
0
1
2
0
1
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
3
0
1
0
1
2
0
1
0
0
2
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
2
1
1
0
2
1
0
2
0
2
0
2
0
1
0
0
1
1
0
0
0
0
2
1
0
2
0
2
0
5
0
0
0
1
0
2
2
0
0
1
0
0
0
2
0
0
0
1
1
0
2
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
1
1
1
0
1
0
2
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
3
0
1
2
0
0
1
1
2
1
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
2
0
1
0
0
0
2
1
0
0
2
0
0
0
0
0
0
1
1
0
3
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
1
0
1
1
2
0
2
0
2
0
0
1
0
0
1
0
0
0
1
2
0
1
2
2
2
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
2
0
0
1
0
2
1
2
0
1
1
0
2
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
2
0
0
1
0
2
0
0
0
0
1
1
1
2
2
2
0
0
0
1
0
0
2
1
0
2
0
0
0
0
0
2
1
1
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
1
0
2
0
0
3
0
1
0
0
2
2
0
1
2
1
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
2
0
0
1
1
2
0
0
2
1
0
1
1
2
0
0
0
1
2
0
1
0
0
1
2
0
2
0
0
0
0
0
0
2
1
0
1
2
0
2
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
3
0
2
1
0
0
0
0
0
0
1
0
1
1
0
2
0
0
0
2
0
0
2
0
0
0
2
1
0
0
0
1
2
0
2
0
2
0
0
1
0
1
0
0
0
1
0
0
2
2
0
1
2
0
0
1
0
1
0
0
0
1
0
3
0
0
2
0
0
0
1
1
2
0
0
0
0
1
0
0
2
0
1
0
2
0
0
2
1
0
0
2
0
0
2
0
2
1
0
2
0
2
0
0
0
2
0
0
0
0
1
1
0
0
0
1
2
0
1
0
0
0
1
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
1
1
5
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
2
0
2
1
0
0
0
1
0
0
0
0
1
2
0
2
2
0
0
0
2
1
0
0
1
0
1
0
0
0
1
2
0
0
1
2
2
0
0
0
1
0
3
1
0
0
0
2
0
0
0
2
0
3
0
0
2
0
0
1
0
2
0
0
0
1
2
2
0
1
0
2
2
2
1
0
2
4
2
0
0
1
1
0
0
0
1
2
0
0
0
1
0
0
0
2
0
1
0
0
0
0
2
2
0
1
1
1
1
0
0
0
0
2
0
2
0
2
0
0
1
0
0
2
0
0
2
0
0
3
0
1
1
1
0
3
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
2
1
0
1
0
0
0
0
0
0
2
1
0
0
2
0
0
0
2
2
0
0
0
0
1
0
0
0
1
2
2
0
1
0
1
1
0
0
0
0
0
0
0
1
2
0
1
0
0
0
1
0
0
1
0
0
1
2
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
3
0
0
1
2
2
0
0
0
0
1
2
2
1
0
0
0
3
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
1
2
2
1
2
1
0
2
0
0
1
0
1
1
0
2
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
1
1
0
1
0
2
2
0
0
0
0
1
1
1
0
0
2
0
2
1
0
0
1
1
0
1
0
0
0
1
0
0
1
0
1
0
1
0
1
0
0
0
1
0
2
0
2
0
0
0
3
0
2
0
1
1
0
1
0
2
1
0
0
0
1
0
0
2
0
0
1
1
2
0
2
0
1
0
0
0
0
2
0
0
1
0
0
3
0
1
1
0
0
0
0
0
1
2
0
0
0
2
2
0
2
0
2
0
0
1
0
1
1
2
0
0
2
0
0
1
0
2
0
1
0
0
1
1
3
1
0
0
0
0
1
0
0
0
4
0
0
0
0
2
2
1
0
1
0
0
0
0
3
0
0
0
2
1
0
0
1
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
4
0
2
1
0
0
1
2
1
0
0
0
0
0
0
0
0
0
2
0
0
2
2
2
1
0
0
0
1
0
0
1
0
0
0
3
0
0
2
0
2
3
2
0
0
1
0
1
0
0
0
2
0
0
2
0
0
2
1
3
0
0
0
1
0
1
0
2
1
1
0
0
0
2
1
0
0
0
0
0
1
2
2
0
0
0
1
2
2
0
1
1
0
1
2
1
0
0
1
2
0
0
0
0
1
1
0
2
0
0
1
0
0
0
2
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
1
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
2
0
0
1
3
0
2
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
1
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
1
1
0
1
2
0
0
0
0
2
1
0
0
0
0
0
1
1
0
2
0
0
0
2
0
1
2
0
2
4
0
0
0
0
0
0
1
0
2
0
2
2
0
0
0
0
0
0
1
0
0
2
1
2
1
0
0
0
0
0
2
0
0
0
1
2
1
0
1
0
0
1
2
2
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
1
1
0
0
0
0
2
0
1
2
0
2
0
0
0
0
2
2
0
0
1
3
3
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
1
0
1
0
1
0
0
2
0
2
0
0
0
2
1
0
2
0
1
2
2
1
2
0
1
0
2
0
1
2
0
1
1
0
0
2
2
0
0
1
0
0
1
1
2
0
0
1
0
2
2
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
4
2
1
0
0
0
0
0
0
2
0
1
2
0
3
0
0
0
1
0
0
2
0
0
2
0
2
0
0
0
1
1
2
0
2
2
1
2
0
2
0
0
1
1
1
0
0
0
0
1
0
0
1
1
0
0
0
2
1
0
2
1
2
1
0
0
1
0
0
0
0
2
0
2
0
1
1
0
2
1
0
0
1
2
2
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
1
0
1
1
1
0
0
1
0
2
0
0
0
0
3
1
0
0
0
2
0
2
0
0
0
0
1
0
2
0
1
0
2
1
2
1
0
0
2
2
0
0
1
2
1
2
0
1
0
0
0
1
0
0
0
0
0
1
0
2
2
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
2
2
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
1
1
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
2
1
1
0
1
0
0
0
0
0
1
0
1
1
1
1
2
0
1
2
0
0
3
1
0
0
0
2
0
0
0
2
0
1
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
2
0
0
0
1
1
2
1
1
1
0
0
2
1
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
4
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
4
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
2
0
1
0
3
1
0
0
1
2
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
4
0
0
1
1
2
1
1
0
0
0
0
0
1
3
0
0
1
0
0
0
1
1
0
0
1
0
0
1
0
1
0
0
0
0
2
0
0
0
0
2
2
1
2
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
2
2
1
0
0
2
0
0
2
2
0
0
3
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
1
0
2
1
0
2
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
2
2
0
0
2
1
2
2
1
0
1
0
0
2
0
2
0
2
2
0
0
0
0
0
0
1
0
0
2
0
0
1
1
1
2
1
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
1
0
1
2
0
0
0
2
1
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
1
1
0
0
2
0
0
0
0
0
0
1
1
0
1
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
3
0
0
1
2
2
1
3
1
2
0
2
0
2
2
0
0
0
2
2
0
2
0
0
2
0
1
0
2
0
2
0
0
2
0
2
0
0
1
0
0
0
2
1
0
0
2
0
0
0
0
0
1
1
0
0
2
0
0
0
1
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
2
0
2
1
0
0
0
0
1
0
0
0
0
1
0
1
0
2
2
2
0
2
0
1
2
0
0
0
1
0
2
1
0
2
0
2
0
0
1
1
2
0
0
2
0
3
0
1
1
1
0
0
1
1
0
1
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
1
1
0
0
0
1
2
0
0
0
1
0
0
0
2
0
0
1
1
0
1
1
1
1
0
0
0
0
1
0
2
0
1
2
1
0
3
0
1
2
1
0
0
0
0
2
0
0
0
0
0
0
1
0
2
1
0
0
0
0
1
0
0
0
0
1
0
2
1
0
1
1
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
2
2
1
0
1
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
2
0
2
0
2
0
0
0
0
1
0
1
1
2
0
0
0
2
0
0
1
0
0
0
2
0
0
0
1
2
1
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
2
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
1
1
1
1
0
3
0
0
0
0
0
0
0
1
0
0
0
2
2
0
1
2
0
0
1
0
2
1
0
0
0
0
0
2
0
0
0
0
0
2
0
1
2
1
0
2
1
2
1
0
0
0
2
0
0
2
0
0
0
1
2
0
1
2
0
0
1
0
1
1
1
1
1
2
0
1
0
0
1
2
0
2
2
2
0
1
2
2
0
2
0
0
2
1
0
3
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
2
0
2
2
0
0
0
1
0
1
0
1
0
0
1
1
2
0
2
2
0
1
1
0
2
0
0
1
0
0
1
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
3
0
0
2
0
3
0
0
0
1
0
1
0
0
2
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
2
1
2
0
0
1
1
0
1
0
0
2
1
2
0
2
0
0
1
0
0
1
0
2
0
0
0
2
1
0
0
1
1
0
0
1
0
0
0
2
0
1
2
0
0
1
0
2
0
0
0
2
0
2
0
0
1
2
0
0
2
0
3
0
2
0
0
1
0
1
0
0
0
1
0
2
0
0
2
1
2
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
2
0
0
1
3
2
0
1
0
2
0
0
0
1
0
0
4
0
1
1
0
0
0
0
3
1
0
1
0
0
2
0
0
2
0
1
0
0
2
0
0
0
2
1
1
2
1
0
1
0
1
0
1
0
0
1
0
0
2
0
0
0
0
0
1
0
1
0
2
0
0
0
2
0
2
0
2
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
1
1
3
0
0
2
1
0
0
0
0
0
0
1
0
3
2
0
1
0
0
0
0
1
0
0
3
0
3
0
0
0
2
2
0
2
0
0
1
0
2
2
2
0
1
2
0
2
0
1
0
2
2
0
0
1
1
2
1
0
0
2
0
0
1
2
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
1
1
0
0
1
1
2
0
1
0
1
1
0
0
1
2
0
1
1
2
1
0
1
0
2
2
0
1
2
0
0
0
2
1
0
2
1
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
2
0
2
1
0
0
0
0
0
1
0
0
2
1
0
0
2
1
1
1
1
0
0
0
0
0
2
1
0
2
1
2
2
0
1
1
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
1
1
0
0
1
2
0
1
1
0
0
8
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
2
1
0
0
0
0
0
0
0
0
2
0
1
2
1
0
1
0
1
0
2
2
0
1
2
0
0
0
1
2
0
1
2
0
1
0
0
1
0
1
0
0
1
2
0
0
2
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
2
0
0
0
0
1
0
0
1
1
2
0
1
0
0
2
0
2
2
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
2
0
0
0
1
1
0
0
2
1
0
2
0
2
1
0
0
0
1
2
2
1
0
0
0
2
0
0
2
2
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
2
2
0
2
0
2
0
2
1
0
0
2
0
0
2
0
0
0
2
1
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
1
2
0
0
2
2
0
1
0
0
0
0
0
0
2
1
0
0
1
0
0
1
2
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
1
3
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
1
0
2
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
1
0
0
0
0
0
0
1
2
0
1
0
0
1
0
0
0
0
2
0
0
1
0
1
0
1
0
0
0
2
0
1
0
0
1
0
1
1
1
0
4
1
0
0
0
1
0
2
0
2
3
2
2
2
1
0
2
1
0
0
0
0
0
3
1
0
0
0
0
0
2
2
0
0
2
0
0
0
0
2
3
0
1
1
1
1
0
1
2
2
1
1
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
2
0
1
0
0
0
2
1
0
0
0
2
1
0
1
1
0
0
0
0
1
0
1
0
0
2
0
0
2
0
0
1
1
2
0
1
0
0
0
0
0
0
0
0
0
2
0
1
3
2
0
1
2
2
2
0
2
0
1
0
0
0
2
2
2
0
0
0
9
0
0
1
0
2
0
0
0
1
0
1
0
0
0
0
2
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
5
0
2
0
2
2
2
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
2
2
1
2
1
1
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
2
2
0
0
0
0
0
2
2
0
2
2
2
1
0
1
4
1
1
1
0
0
0
0
1
0
0
0
1
0
0
0
1
2
1
2
2
0
1
0
1
1
0
0
1
0
0
0
1
0
1
1
1
1
2
2
1
0
0
0
2
1
0
0
1
0
0
0
0
1
0
2
0
0
1
2
0
3
0
1
2
2
2
0
1
0
0
0
1
1
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
1
1
2
2
2
0
1
1
0
0
0
2
0
0
0
0
1
0
1
2
0
1
0
0
0
0
0
1
0
0
1
0
1
0
1
1
0
0
3
1
0
0
1
0
0
2
2
0
0
1
2
1
1
0
0
0
0
2
1
0
1
0
0
2
1
2
0
0
0
2
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
2
0
1
0
0
0
0
0
2
0
1
2
0
0
0
0
0
4
0
0
1
0
1
0
0
2
2
0
0
0
2
0
1
0
0
0
0
1
2
0
0
0
1
1
0
0
0
1
1
0
0
0
1
0
1
0
0
2
1
0
1
0
0
0
2
0
0
0
0
1
2
0
0
0
0
2
1
2
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
2
0
0
2
0
1
1
0
1
2
0
1
0
2
0
0
0
0
0
1
1
0
0
1
1
0
0
1
1
2
2
2
2
1
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
1
1
2
0
0
0
0
2
0
0
2
1
2
0
0
1
0
1
2
0
0
2
0
0
0
0
0
0
0
0
1
1
2
1
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
2
0
0
2
0
1
1
0
0
0
1
0
1
0
1
2
0
1
0
2
0
0
0
1
1
0
0
0
0
1
0
2
0
0
0
2
0
3
0
3
1
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
2
2
0
1
1
2
3
0
2
1
3
1
1
0
0
0
2
0
0
0
2
1
0
1
1
1
0
2
2
0
1
3
1
0
0
1
0
0
0
0
2
0
0
2
2
0
0
0
1
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
2
1
2
0
0
1
2
0
0
0
2
2
2
1
2
0
2
0
3
0
0
0
0
0
2
3
1
1
0
0
2
2
2
0
0
0
2
0
2
0
1
0
1
0
0
1
1
1
0
1
0
2
0
2
1
0
0
0
0
0
1
1
0
1
0
0
0
0
2
1
0
0
0
0
1
0
2
2
2
0
0
2
0
2
1
1
2
0
1
0
0
2
0
0
0
1
0
2
1
2
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
1
0
1
1
0
0
0
1
2
0
0
1
0
0
2
2
1
0
0
2
0
0
1
2
0
0
1
0
1
0
1
0
0
2
0
0
1
0
0
0
0
0
4
0
0
1
0
0
2
0
0
2
0
1
0
0
0
0
1
0
0
0
0
1
2
2
0
0
1
2
0
2
0
0
0
0
0
0
0
2
0
1
0
0
1
1
2
1
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
2
1
1
6
0
0
0
0
0
0
2
2
2
1
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
2
0
2
0
2
1
2
0
3
0
0
0
1
2
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
2
2
3
1
0
0
2
0
1
0
2
1
0
2
2
0
2
1
2
0
1
2
1
0
2
0
0
0
2
1
0
2
2
0
0
0
0
0
0
0
0
1
1
0
2
2
0
0
2
0
0
0
1
1
0
0
3
0
0
1
2
0
0
0
0
0
1
0
2
2
0
0
1
0
1
0
0
0
1
0
0
0
1
2
1
0
3
0
0
0
2
0
0
0
0
1
2
0
1
0
0
0
0
0
1
2
1
0
0
0
2
2
0
2
1
0
0
1
4
0
1
1
0
0
0
1
1
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
1
1
2
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
2
2
3
3
0
0
0
0
1
1
0
0
0
1
3
0
1
0
1
0
0
0
1
0
0
0
1
1
0
0
2
1
0
0
3
0
0
1
0
0
3
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
2
0
0
0
0
0
0
0
2
0
2
1
2
2
0
0
0
0
1
0
0
0
0
1
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
1
1
1
1
1
0
2
1
2
0
2
0
0
1
2
0
0
1
1
0
1
2
0
0
1
2
1
0
0
2
0
1
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
1
2
0
2
0
0
2
0
1
1
0
0
2
2
2
1
0
2
0
0
0
1
0
0
0
0
2
0
0
0
2
0
1
2
1
0
1
0
0
0
2
1
0
0
0
1
0
0
2
0
0
0
1
2
0
0
0
1
0
0
2
0
0
0
1
0
2
2
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
2
0
1
2
7
0
1
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
2
1
2
0
0
0
1
0
2
0
0
0
0
2
0
2
0
0
2
0
0
0
0
1
1
5
1
1
0
0
0
1
1
0
1
0
2
1
1
0
1
0
0
1
1
0
1
1
1
0
3
0
2
2
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
1
2
0
2
0
0
0
2
0
0
0
0
0
0
1
1
0
1
0
2
1
0
0
2
0
2
0
0
1
0
1
1
0
1
0
0
0
2
1
2
2
0
1
1
0
1
1
0
2
1
0
0
3
0
0
0
0
0
1
1
3
0
1
2
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
2
1
0
0
1
2
0
1
0
0
0
1
0
0
0
0
2
0
1
0
0
0
2
0
1
1
2
1
2
1
0
1
0
0
0
1
1
0
0
2
2
2
2
1
1
2
0
0
1
2
1
0
1
1
3
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
2
0
2
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
3
1
0
0
0
0
2
2
1
0
4
1
1
1
1
0
0
0
0
1
1
1
2
2
0
0
0
0
2
0
2
0
0
2
1
0
1
0
0
0
1
0
1
0
2
0
0
0
2
0
0
0
0
1
0
0
0
1
0
1
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
1
1
0
0
2
0
0
0
2
0
2
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
1
0
0
0
2
0
0
0
2
0
1
2
0
1
0
3
0
0
2
1
1
2
0
0
1
0
1
2
0
0
0
0
1
0
2
2
0
0
2
0
2
0
0
0
0
2
1
0
1
0
1
0
0
1
2
0
1
0
1
1
0
0
0
2
0
0
2
1
0
2
0
0
2
0
0
0
0
1
0
0
2
0
0
1
0
1
1
1
1
1
1
0
1
1
1
1
3
13
0
0
0
1
0
2
0
3
0
1
2
0
1
0
0
0
0
0
0
0
0
0
4
2
1
2
0
0
0
0
0
2
2
2
1
0
2
1
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
2
1
1
0
1
0
1
2
0
1
0
0
3
0
2
2
0
1
2
1
3
0
0
0
1
0
2
0
1
2
0
0
0
2
0
0
0
0
0
5
1
0
0
2
2
0
2
1
1
1
0
0
1
1
0
0
0
0
1
2
1
0
0
0
0
0
1
0
1
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
1
0
2
1
0
1
0
0
2
0
1
1
2
1
1
0
1
0
0
2
2
2
0
0
0
0
0
0
0
2
0
1
1
1
0
0
1
0
3
1
0
0
1
1
1
1
1
0
2
0
0
0
2
2
2
1
0
1
0
0
0
1
1
2
2
2
0
0
0
0
0
0
1
0
0
0
2
0
0
1
5
0
0
1
0
0
0
0
2
0
0
0
0
0
3
1
0
0
1
0
0
2
0
0
0
2
0
0
0
2
1
0
4
0
2
1
1
0
0
1
2
0
0
0
0
2
0
0
0
0
0
1
2
0
0
2
1
2
1
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
1
0
0
0
1
2
1
1
2
2
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
2
0
0
1
2
0
1
1
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
1
1
3
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
1
2
0
1
0
1
0
2
0
2
1
0
0
0
0
0
1
0
1
0
2
0
2
2
0
0
0
0
0
2
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
1
1
1
0
0
0
2
2
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
2
0
1
0
0
0
1
0
2
0
1
1
0
2
0
0
0
0
1
0
0
0
0
1
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
2
1
0
0
2
1
0
2
0
0
0
0
0
0
2
0
2
0
1
1
0
2
0
0
1
0
0
0
0
0
0
0
6
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
1
0
1
0
1
0
2
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
1
0
2
1
0
2
2
1
0
2
1
1
0
0
1
0
0
2
0
1
1
0
2
0
0
2
1
0
0
0
1
1
1
3
2
0
2
0
0
0
0
1
2
3
0
0
0
2
4
0
0
1
0
1
0
0
0
0
0
2
0
1
1
2
2
0
0
0
0
0
2
0
0
0
0
1
0
2
0
1
0
0
2
0
4
2
1
0
3
0
1
0
0
0
0
1
0
2
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
2
0
0
2
1
1
0
2
0
0
0
0
0
1
0
2
1
1
2
0
0
3
0
0
1
0
0
0
0
2
1
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
1
0
1
0
0
0
1
0
0
2
0
2
0
2
0
2
2
0
2
0
0
1
0
0
0
0
0
2
1
0
1
1
0
0
0
0
2
0
2
2
0
0
0
0
1
0
0
1
0
1
0
2
1
1
0
1
2
3
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
1
0
0
1
0
1
1
2
0
0
2
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
2
0
1
0
0
2
2
0
0
0
0
0
1
0
0
0
2
1
1
0
0
1
0
1
0
1
0
0
0
0
0
1
2
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
2
1
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
2
0
1
1
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
2
2
2
0
0
0
0
0
0
0
0
1
1
1
1
0
0
3
0
1
0
1
0
2
0
0
1
0
0
2
0
0
2
2
0
0
1
0
1
0
0
0
2
3
2
1
0
0
3
2
2
0
7
0
0
2
1
0
2
0
2
0
0
0
1
0
2
1
1
1
0
0
0
0
0
1
0
0
2
2
2
2
0
0
0
1
3
1
2
0
0
1
1
4
0
2
1
1
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
2
1
1
0
0
0
2
1
0
1
0
1
0
0
0
0
0
1
0
0
1
2
1
0
2
0
0
1
0
0
2
1
0
0
0
0
1
2
0
0
0
1
1
0
1
3
0
0
0
2
0
0
0
2
0
0
1
1
2
2
1
0
1
0
0
0
0
0
0
0
0
1
3
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
1
0
3
0
1
1
0
0
0
0
0
0
0
1
2
0
3
0
3
2
0
1
0
2
0
0
1
0
0
0
0
1
0
1
0
1
2
1
0
0
2
1
1
1
0
0
0
0
1
0
0
2
2
1
0
0
1
0
0
0
0
0
0
1
2
2
0
1
0
1
1
5
0
0
0
0
0
2
0
0
0
2
0
2
2
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
1
2
0
0
1
0
0
1
0
2
0
1
0
0
0
0
2
0
0
2
0
0
2
0
0
0
2
1
0
2
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
2
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
2
0
2
0
0
2
1
0
3
1
2
0
2
0
2
0
1
0
1
0
2
0
0
1
0
1
0
2
0
1
1
1
0
0
1
2
2
2
0
2
1
1
0
5
0
0
3
0
0
0
0
0
0
1
0
2
3
0
0
1
1
0
0
0
2
0
2
2
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
2
0
1
0
2
0
1
1
2
0
1
0
1
0
0
2
2
0
2
2
1
0
0
0
1
1
0
1
0
1
0
2
0
0
1
0
0
0
2
0
0
0
0
1
2
2
0
0
0
1
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
2
4
0
2
1
0
0
0
4
0
0
1
3
0
0
0
1
1
2
1
0
2
0
0
1
0
0
1
2
0
0
0
0
2
1
0
0
1
1
0
0
4
0
2
2
0
1
0
2
1
0
0
0
1
2
0
1
1
1
0
2
0
1
0
0
0
2
3
0
0
0
2
3
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
2
2
1
0
0
0
0
2
1
2
0
1
1
0
0
2
2
2
2
1
1
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
2
1
0
1
0
0
0
2
0
0
0
0
1
2
2
2
0
2
2
0
0
1
0
0
0
2
2
0
1
1
0
0
0
0
2
1
0
0
1
0
0
1
1
0
0
5
0
0
2
2
1
4
0
0
1
0
2
1
0
2
0
0
0
1
0
0
1
2
1
0
0
1
0
1
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
3
1
0
1
0
2
0
0
1
0
0
1
0
0
1
0
0
1
1
2
2
0
0
3
0
0
1
0
1
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
2
0
0
1
0
2
0
0
1
0
1
0
0
1
0
0
0
1
2
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
3
0
2
0
1
0
1
0
1
1
2
2
0
3
2
0
0
0
0
0
0
1
1
2
1
2
1
0
0
1
0
4
1
0
0
0
0
0
1
1
1
0
0
2
2
1
0
1
1
1
1
1
2
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
1
2
0
0
0
1
0
1
0
0
1
0
0
2
0
0
1
0
2
0
1
0
2
2
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
1
2
0
0
1
1
0
0
0
1
0
0
0
1
1
0
1
1
1
0
0
2
0
2
0
1
0
0
2
0
0
0
3
1
2
0
1
0
0
1
0
0
0
2
0
1
0
0
1
0
0
2
0
2
0
0
0
1
0
2
0
0
1
0
0
0
0
1
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
2
1
0
0
1
2
0
2
0
0
0
1
1
2
0
2
0
0
0
4
0
0
0
0
0
0
2
0
1
0
1
0
1
0
2
0
0
1
1
0
2
2
2
2
0
0
0
1
1
0
0
0
0
0
2
0
0
0
1
1
0
2
1
2
1
0
0
2
0
0
0
0
0
2
1
1
1
0
2
0
2
2
0
1
2
2
0
0
0
2
0
1
0
0
0
2
0
2
2
0
0
0
2
0
2
1
1
1
0
0
2
0
1
0
3
0
0
0
2
0
2
1
0
0
2
1
0
2
2
2
0
0
0
0
0
0
0
2
0
1
0
0
2
0
2
0
2
0
0
0
1
0
0
0
3
2
0
2
0
0
0
0
0
0
0
3
0
0
0
1
1
1
0
1
0
2
1
4
0
0
3
3
2
0
0
0
1
0
2
1
0
1
2
0
2
0
0
0
0
1
2
0
1
0
3
3
0
0
0
0
0
1
1
1
3
0
1
0
2
0
1
0
0
0
0
0
0
0
3
0
5
0
1
0
0
1
0
0
1
0
0
1
0
1
0
0
1
0
1
0
1
0
2
0
1
0
0
0
1
1
0
0
1
3
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
1
0
2
2
0
2
1
1
0
2
2
0
0
0
0
1
0
1
2
0
0
0
1
1
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
2
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
1
2
0
0
1
0
0
2
0
0
2
0
0
0
1
0
4
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
2
1
0
1
0
0
2
1
0
0
0
0
1
0
0
0
0
2
2
0
1
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
1
1
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
1
2
0
2
0
0
2
1
0
2
1
0
0
0
0
0
0
1
1
0
0
0
1
0
2
2
2
1
2
0
0
0
0
0
0
1
0
2
1
0
0
2
2
0
2
1
0
0
1
2
0
1
2
0
0
1
0
1
1
2
2
0
2
0
1
0
0
1
0
0
0
0
1
1
0
1
2
3
0
0
0
2
0
2
0
0
4
0
1
0
0
1
0
0
2
0
0
1
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
3
1
2
0
0
0
2
0
1
0
2
2
0
0
1
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
2
2
2
2
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
2
0
0
1
0
0
3
0
2
0
0
0
0
2
2
1
0
0
2
0
3
0
1
2
0
0
1
0
1
0
0
1
2
0
0
0
1
0
1
0
0
2
0
0
2
1
0
0
2
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
2
1
0
2
1
0
0
1
0
0
1
0
3
1
0
0
0
1
0
0
0
0
2
0
2
1
0
1
0
0
1
0
0
0
0
1
0
2
0
0
1
0
0
0
1
0
1
0
2
1
2
2
1
2
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
2
1
0
2
0
1
2
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
1
1
0
2
2
0
0
0
0
2
0
0
0
0
1
0
2
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
1
2
0
0
2
0
2
1
0
1
0
2
0
2
0
0
0
0
0
0
0
1
1
0
0
3
1
2
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
2
3
0
0
0
0
2
0
0
0
2
0
0
0
2
0
2
1
2
0
2
0
0
0
0
0
2
0
0
2
1
0
0
0
2
0
0
0
0
0
2
2
0
2
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
2
0
0
0
2
1
1
0
2
0
2
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
2
1
0
1
0
2
1
0
0
2
2
1
0
0
4
2
1
0
1
0
1
0
2
0
0
2
1
0
2
0
0
1
3
1
2
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
1
1
1
0
0
2
0
1
0
0
0
0
2
0
2
0
2
0
1
1
1
2
1
2
1
2
0
1
0
2
1
3
1
0
0
1
1
0
0
0
0
2
1
1
0
2
1
0
1
0
0
0
1
2
0
2
2
1
1
0
0
2
0
1
1
1
0
0
0
1
1
0
1
0
0
0
0
2
0
0
1
0
2
1
0
1
1
1
0
2
1
0
0
0
0
0
0
2
2
0
2
2
2
0
0
2
0
1
0
0
0
2
0
1
0
0
0
0
0
2
0
0
1
0
1
2
2
0
2
2
1
0
2
0
0
0
0
2
2
2
0
1
1
0
0
0
2
0
0
0
0
3
2
1
3
0
0
1
0
0
2
0
1
0
0
0
2
0
0
0
1
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
1
2
0
0
0
1
0
0
1
0
0
0
2
0
2
0
1
2
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
5
0
0
0
2
0
0
1
0
1
1
1
0
0
1
0
2
1
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
2
1
2
2
2
2
1
2
0
0
0
2
0
0
0
2
0
0
0
1
1
0
2
0
0
0
0
0
1
2
2
0
2
2
0
2
0
0
3
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
3
0
0
0
0
1
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
3
0
2
0
1
0
0
0
1
1
1
1
1
1
0
0
1
2
0
0
0
4
0
0
0
4
0
0
0
0
0
0
0
1
1
0
2
0
0
0
1
1
1
0
3
1
1
0
0
0
0
0
1
0
2
1
0
2
1
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
2
0
1
0
1
0
1
0
0
2
1
0
2
2
2
0
0
2
0
1
0
0
2
2
0
0
2
0
2
2
1
1
0
1
1
1
2
0
2
2
1
0
0
1
2
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
2
2
1
0
0
0
0
2
0
2
0
2
0
0
0
0
0
2
0
0
0
2
1
2
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
2
1
0
0
0
1
0
0
2
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
2
0
1
0
2
0
1
1
2
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
1
0
2
2
1
1
0
2
0
0
1
0
0
0
0
0
2
0
2
0
2
2
1
0
0
2
1
2
2
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
2
2
0
0
2
1
1
0
1
0
0
0
0
0
1
2
2
2
0
1
0
0
0
0
1
0
0
1
0
1
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
2
1
0
0
2
0
0
0
0
0
0
2
0
1
1
0
1
0
0
0
1
1
1
0
3
0
0
0
0
0
2
1
0
2
0
0
0
0
0
2
2
0
2
1
0
1
1
0
2
4
0
1
0
0
1
2
0
0
0
0
0
2
0
1
0
0
2
1
2
0
2
0
2
1
0
0
0
0
0
0
0
0
0
2
1
0
2
1
2
0
0
0
0
1
2
0
2
0
1
1
0
2
0
1
0
0
1
0
2
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
2
0
1
0
1
1
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
2
2
0
1
1
0
0
1
0
1
0
0
0
0
0
1
0
2
1
2
1
0
1
1
1
0
0
0
1
0
1
0
2
2
0
0
4
1
1
0
0
2
0
2
1
0
2
1
0
2
0
4
0
4
2
0
0
1
1
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
2
3
1
0
0
1
0
0
0
1
2
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
1
2
1
5
0
1
0
2
0
0
2
0
0
0
1
0
0
0
2
0
0
3
0
1
0
1
2
0
1
1
2
0
0
0
0
0
1
2
3
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
2
2
2
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
2
0
1
2
0
0
1
0
1
0
1
0
1
1
2
0
0
0
1
1
0
1
1
2
1
0
0
1
0
2
0
0
2
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
1
1
0
0
0
0
0
3
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
2
1
2
0
0
0
2
0
0
0
0
0
2
0
1
2
0
1
0
0
0
0
1
2
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
3
2
0
0
0
0
1
0
2
0
1
1
0
0
2
0
0
0
1
0
0
0
0
0
2
1
1
2
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
5
0
1
0
0
0
1
1
0
2
0
0
0
2
0
1
2
0
0
2
0
3
0
2
0
0
0
0
4
1
1
1
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
3
2
1
0
0
0
2
2
1
4
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
1
0
0
2
0
2
0
0
5
0
0
2
2
4
2
2
2
3
0
0
0
2
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
2
0
0
2
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
1
0
0
2
2
2
0
0
0
0
1
0
1
0
2
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
2
1
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
1
0
3
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
2
0
0
1
0
0
0
0
2
1
2
2
2
0
0
0
0
0
2
1
2
3
1
0
0
0
2
0
0
1
2
1
0
0
0
0
1
0
1
0
0
0
0
0
3
2
0
3
1
0
4
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
1
2
1
2
0
0
2
2
0
0
0
0
0
0
0
1
1
0
2
0
1
0
0
0
0
1
1
2
0
2
0
0
0
0
0
2
3
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
1
0
2
1
1
0
2
1
2
0
0
1
0
1
0
0
0
2
0
2
0
0
0
0
0
1
2
2
0
0
1
1
0
0
0
0
0
1
1
2
0
3
1
0
0
1
3
1
0
2
1
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
2
0
2
0
1
0
0
0
2
1
0
0
1
0
1
1
1
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
2
0
0
1
0
4
0
2
0
0
1
0
0
1
0
0
0
0
0
1
2
2
0
2
0
2
1
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
1
0
1
0
0
0
0
1
0
3
3
0
0
1
0
1
0
0
2
0
1
0
0
0
1
1
2
2
2
1
0
1
5
1
0
0
1
0
2
0
0
2
0
1
0
2
1
0
0
0
0
1
2
0
0
0
0
2
0
1
2
1
0
2
0
1
0
1
2
1
0
0
0
0
1
0
0
0
0
1
0
2
1
0
1
0
0
0
1
0
2
0
0
0
1
0
0
2
0
0
0
1
0
1
2
0
0
0
2
0
0
0
0
0
0
1
1
2
0
0
0
0
0
2
0
0
1
1
1
0
2
0
0
0
1
1
0
1
0
3
2
1
0
0
0
1
0
2
0
0
2
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
1
1
2
0
0
0
1
0
1
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
2
0
0
2
0
2
0
2
1
2
0
0
2
1
1
0
2
0
2
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
1
0
0
1
0
2
1
1
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
1
1
2
1
0
0
0
0
1
0
0
2
0
1
0
1
1
1
3
0
2
2
2
0
0
2
0
0
1
0
0
0
0
2
2
0
2
2
0
0
0
0
0
1
2
2
1
0
2
1
0
0
1
0
1
1
0
0
2
2
0
2
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
2
1
1
2
0
0
0
0
1
0
3
1
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
1
2
1
0
0
1
0
0
0
0
2
0
2
0
0
2
0
0
2
0
0
0
2
2
0
1
0
0
1
0
0
1
2
0
0
0
2
1
0
0
2
0
0
0
2
0
0
1
0
0
0
1
1
0
0
2
2
2
1
1
0
0
0
2
2
0
0
0
1
0
3
0
1
2
2
0
0
1
0
2
2
1
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
5
2
0
1
2
0
0
0
3
0
0
0
0
0
0
0
0
1
0
1
3
0
1
0
0
0
2
0
1
0
3
1
0
1
0
0
0
0
0
0
1
1
1
2
0
0
0
0
0
0
1
1
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
2
0
1
1
0
1
2
2
2
0
0
0
0
1
2
0
0
0
1
0
0
1
0
0
0
0
0
2
2
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
2
0
1
0
0
2
0
1
0
1
1
0
1
1
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
1
1
0
1
1
0
0
0
0
1
2
0
1
2
0
2
0
0
0
0
1
0
0
1
1
2
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
2
1
0
0
0
0
2
2
0
2
0
1
1
1
0
1
0
1
1
0
0
2
2
1
0
2
1
0
2
0
2
0
0
1
1
0
1
2
0
1
0
0
2
1
0
2
0
1
2
0
2
1
2
0
0
2
0
5
1
0
1
1
2
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
1
1
2
0
0
0
0
2
0
1
2
0
2
0
1
2
0
2
0
1
0
0
0
0
1
2
0
1
0
1
1
2
0
0
1
0
1
0
0
0
0
0
2
0
2
2
0
1
0
0
1
1
0
0
2
0
1
0
1
2
0
2
0
2
0
0
0
0
0
1
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
2
0
2
0
1
1
1
0
0
0
0
0
0
0
3
0
1
0
2
0
0
1
0
0
1
0
0
2
0
2
0
2
0
1
0
2
1
0
2
0
1
0
0
0
0
2
2
0
0
0
1
0
0
1
1
0
2
2
2
2
1
0
0
0
0
0
0
2
1
2
0
2
1
1
0
0
0
2
0
0
0
0
0
0
2
4
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
2
0
0
1
0
0
1
1
0
0
0
1
1
2
2
1
0
0
0
0
0
5
1
0
0
0
0
0
2
0
1
0
0
2
0
0
1
2
1
0
1
2
1
1
2
1
0
0
0
2
0
1
0
0
0
2
2
0
0
0
0
0
0
0
2
1
1
0
7
0
0
0
0
0
0
1
0
2
0
2
0
2
0
2
0
2
0
1
0
0
0
1
1
2
2
0
0
1
2
1
0
0
0
0
0
1
2
1
0
2
0
0
0
0
1
1
0
0
0
1
1
1
0
0
2
0
0
0
0
1
0
2
0
0
2
0
1
0
0
1
1
0
0
0
0
0
0
0
2
1
0
0
2
2
2
0
1
0
0
0
0
1
2
1
0
0
0
0
0
1
0
0
0
2
0
2
0
1
0
0
2
0
0
0
0
2
1
0
0
0
0
1
0
2
0
0
1
0
0
0
2
2
2
0
0
0
2
0
0
1
0
1
2
0
0
2
0
2
0
2
0
2
2
0
0
0
3
0
0
0
0
0
0
1
0
1
0
0
3
0
1
1
0
2
0
0
2
2
0
1
0
1
1
0
2
0
2
0
0
1
0
0
1
2
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
2
2
2
0
0
2
1
0
0
0
0
0
0
0
2
0
0
2
1
0
2
0
3
1
0
0
1
2
0
1
0
2
0
1
0
3
2
0
3
0
0
1
2
2
0
0
0
2
0
0
0
0
1
0
0
1
0
0
1
1
0
1
0
0
2
3
0
2
1
1
1
1
0
0
0
0
2
0
2
2
1
0
1
0
0
1
3
0
0
0
0
1
0
2
0
0
0
2
1
0
1
0
1
0
0
0
0
0
0
0
2
0
0
2
2
0
1
2
0
1
0
1
0
0
0
0
0
2
0
0
1
1
2
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
3
0
0
0
0
0
1
0
0
1
1
0
0
2
0
2
0
0
0
2
2
2
1
2
2
1
0
1
0
0
0
1
2
2
2
0
0
0
1
0
2
0
1
0
0
2
0
0
0
3
0
2
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
1
2
1
1
1
0
0
2
1
1
0
1
3
2
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
2
0
2
1
1
0
0
0
2
1
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
1
3
0
0
0
2
1
0
0
0
2
0
1
0
1
0
0
2
0
0
0
2
0
0
1
0
1
0
0
2
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
2
2
0
2
0
0
0
1
1
0
0
1
1
1
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
1
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
1
1
2
2
0
0
2
1
2
0
0
0
0
2
1
0
0
1
2
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
1
1
0
2
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
3
0
0
0
0
0
0
3
1
0
0
0
1
0
2
2
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
3
2
2
0
2
2
1
5
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
3
2
0
0
0
2
0
1
0
0
2
1
0
1
0
0
2
2
0
2
0
0
0
0
0
0
0
1
2
0
1
0
0
0
2
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
7
1
1
0
0
0
3
2
0
0
0
0
0
0
2
0
1
0
1
0
0
0
2
0
0
0
2
2
2
0
1
0
0
0
0
0
2
0
1
1
0
0
0
0
1
1
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
2
2
2
2
2
0
0
1
0
0
2
0
0
1
0
1
0
0
0
0
0
2
0
0
3
1
0
0
0
0
0
1
2
1
0
0
0
0
1
0
1
0
2
0
0
0
0
0
1
0
0
0
1
0
1
1
2
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
2
2
2
3
1
0
3
0
1
2
1
0
0
0
2
0
0
0
1
1
1
1
0
0
0
1
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
3
2
1
0
2
2
2
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
2
2
1
0
0
2
0
0
0
2
1
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
2
1
0
2
0
0
0
2
0
0
0
1
2
0
2
0
0
2
0
2
0
1
0
0
0
0
0
1
0
1
1
2
0
0
0
0
0
0
0
0
3
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
1
2
2
0
0
0
0
0
2
0
1
2
0
0
0
5
1
0
0
1
1
1
2
0
2
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
2
2
0
0
2
2
1
0
0
0
1
0
0
0
0
0
0
2
2
1
1
0
1
2
0
0
0
0
0
1
0
0
2
0
0
2
0
2
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
1
0
0
1
3
0
2
0
1
0
2
1
0
0
0
0
1
1
4
1
0
0
0
0
1
0
2
0
0
0
0
1
0
0
2
2
0
1
0
0
0
0
0
1
1
0
0
0
1
0
2
0
0
0
0
1
1
0
1
0
2
0
0
2
0
2
0
4
0
2
0
0
0
3
1
2
1
0
1
1
1
0
1
1
0
1
2
0
0
2
1
2
1
0
2
2
2
0
0
1
0
0
0
0
0
0
0
1
4
0
0
0
1
2
0
0
1
2
0
1
0
1
1
2
0
0
0
0
0
0
1
0
0
1
0
0
2
2
0
1
1
0
0
2
2
2
2
0
2
0
1
0
0
0
0
1
0
2
2
2
2
0
0
0
2
0
0
2
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
2
2
2
0
1
0
0
0
1
0
1
0
2
2
0
0
1
0
0
0
2
3
2
1
1
1
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
1
1
4
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
9
0
2
0
1
0
1
0
1
0
0
0
2
0
1
0
0
1
2
0
0
2
0
1
0
0
0
0
1
0
0
2
0
2
0
0
0
4
1
2
2
0
0
0
0
4
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
1
2
1
0
1
0
0
2
0
1
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
3
1
2
0
0
1
1
2
1
2
2
0
2
2
1
0
1
2
0
1
0
1
2
0
0
0
1
0
0
2
2
2
0
1
2
2
1
1
0
0
0
2
0
2
2
0
2
0
0
0
0
1
2
2
1
2
1
0
0
2
0
0
0
1
2
0
0
0
0
2
0
2
0
1
0
0
2
1
0
2
1
0
2
0
1
0
0
1
0
2
0
1
0
1
1
0
0
0
2
1
0
0
1
1
0
0
0
2
0
0
0
1
0
2
0
1
2
0
0
0
0
1
0
1
0
2
0
1
0
0
0
2
0
4
0
0
0
0
0
2
0
1
3
3
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
2
1
1
0
0
2
0
1
2
5
2
0
0
0
0
0
0
0
0
0
0
2
0
2
2
2
0
1
0
0
0
2
0
0
2
0
0
0
0
0
16
1
0
2
0
2
0
0
0
0
2
1
0
0
2
0
1
0
1
1
2
2
2
1
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
1
2
0
0
0
2
0
2
0
1
0
1
1
0
1
0
0
2
1
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
2
1
0
1
1
2
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
3
0
0
0
2
0
0
1
2
0
2
2
2
1
0
1
0
0
1
0
1
0
3
1
0
2
0
0
0
0
0
0
0
2
3
0
0
0
0
0
1
0
0
1
1
0
2
0
1
0
0
0
2
3
1
0
0
0
0
0
0
0
1
1
3
2
1
0
0
0
2
2
3
0
1
0
0
1
0
2
3
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
1
1
0
0
1
2
2
0
0
2
2
2
0
0
1
2
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
1
2
2
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
1
1
0
1
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
13
0
1
2
0
1
2
2
0
2
0
2
2
1
1
2
5
0
2
0
0
0
2
1
1
1
1
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
1
0
2
0
0
0
2
0
0
1
1
0
0
2
1
1
1
0
0
2
0
0
2
0
0
0
2
0
1
0
2
0
1
1
0
0
0
2
0
1
0
4
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
1
0
0
2
1
2
0
3
0
3
0
0
0
0
0
1
2
4
1
2
2
0
2
2
2
2
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
1
1
1
1
2
0
0
0
2
0
0
2
3
2
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
2
0
1
0
1
2
1
0
0
1
2
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
3
1
0
0
1
0
2
0
0
2
2
1
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
2
3
1
0
2
2
2
0
0
0
0
0
1
0
1
1
1
1
0
0
1
0
0
0
0
0
1
0
2
1
0
0
1
1
1
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
2
0
0
1
0
0
0
2
0
0
0
2
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
3
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
1
1
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
1
2
0
2
1
1
2
0
3
0
0
0
1
2
1
0
0
1
0
0
0
1
0
0
1
1
0
2
1
1
2
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
1
2
0
0
1
1
0
0
3
2
0
0
1
0
0
3
1
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
2
1
0
0
2
0
1
1
0
1
0
0
0
0
2
0
0
0
2
1
0
0
1
1
2
1
0
0
0
3
0
0
0
0
0
0
0
0
3
1
0
2
2
2
3
1
0
2
1
0
0
1
2
0
0
0
2
0
0
0
2
0
0
0
0
1
1
0
0
0
0
2
0
0
1
0
0
0
1
0
1
0
0
0
0
2
1
0
1
0
2
0
0
2
2
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
1
2
2
1
0
2
1
0
0
0
1
0
0
1
2
1
0
0
0
1
2
2
1
1
0
2
0
0
1
0
1
1
1
0
0
1
0
0
0
1
2
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
2
2
2
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
2
0
2
1
2
0
0
0
2
0
1
0
0
1
0
3
2
0
1
0
2
0
2
0
0
2
2
2
1
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
1
0
0
1
2
0
1
2
2
0
0
0
2
2
1
0
2
0
1
2
1
1
1
0
0
2
1
0
0
1
1
0
1
2
0
0
0
2
0
0
1
0
0
2
0
0
0
1
2
3
1
0
0
0
0
2
2
0
0
0
1
0
1
0
1
2
0
0
1
1
0
2
2
0
1
1
0
1
0
0
1
0
1
0
1
0
2
2
0
2
0
0
1
0
0
2
1
5
2
2
0
0
1
0
0
3
0
0
0
1
0
0
1
2
1
2
0
0
1
2
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
2
2
0
2
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
1
1
0
0
0
0
1
2
2
0
1
0
0
0
1
1
1
0
0
0
0
1
0
1
0
0
0
0
1
2
0
1
0
2
0
0
0
1
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
1
2
2
0
1
1
1
2
0
1
1
0
0
0
1
2
2
0
0
2
1
0
1
0
0
2
2
1
2
2
0
1
2
1
1
3
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
2
1
0
1
2
2
2
1
1
0
0
0
0
0
0
0
2
2
0
0
1
1
1
0
0
0
0
0
2
2
2
0
2
0
0
2
0
0
0
0
1
0
2
0
2
0
0
4
2
0
0
0
2
1
5
0
0
1
0
1
0
0
0
0
1
1
0
0
1
3
0
1
0
0
0
1
0
0
0
1
0
0
0
1
1
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
1
1
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
2
2
2
0
1
4
0
2
1
0
1
0
0
0
1
0
0
1
1
0
1
1
0
3
0
0
0
2
0
1
1
0
0
2
0
1
1
1
0
0
0
1
1
1
0
1
2
1
2
1
0
2
2
1
1
1
0
0
2
1
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
1
0
1
0
2
2
2
2
0
0
1
1
0
0
0
2
2
0
2
0
2
0
0
2
0
0
1
0
0
0
2
0
0
0
2
0
1
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
4
3
0
1
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
2
2
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
4
0
0
0
0
0
0
0
2
0
2
1
0
0
0
2
0
0
0
0
1
0
1
2
0
2
1
0
0
0
3
2
0
0
0
0
0
0
2
2
0
1
1
1
0
1
1
0
0
0
0
0
2
1
0
2
0
0
1
0
0
1
2
1
1
2
0
2
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
2
2
0
1
2
6
0
2
2
2
0
1
0
0
0
1
0
2
0
1
0
1
2
0
2
0
1
1
0
0
0
0
0
1
1
3
0
0
0
2
0
0
0
0
1
2
0
1
0
0
0
0
0
2
0
0
2
1
0
2
0
0
0
3
0
0
0
0
1
2
2
2
2
2
0
1
0
0
0
0
2
0
0
0
1
2
0
0
0
2
2
3
2
1
0
0
0
0
0
0
0
2
1
0
2
1
1
1
0
0
0
0
0
1
0
1
2
2
0
2
0
1
2
0
0
0
0
1
0
0
0
2
0
2
2
2
0
1
1
0
4
1
1
0
0
0
0
0
2
3
1
1
1
0
2
0
1
0
1
1
0
0
1
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
1
0
0
1
0
0
0
0
0
1
2
0
0
1
2
2
0
1
1
0
1
0
0
0
2
0
0
0
0
1
0
0
2
1
2
0
0
0
0
1
0
0
0
2
1
0
3
0
0
1
0
1
0
0
1
0
0
2
0
0
0
1
1
0
0
0
1
1
1
0
0
1
2
0
2
1
0
0
2
1
0
2
2
2
0
0
0
2
0
0
0
1
0
2
0
1
0
0
1
0
0
1
0
0
0
1
2
0
1
1
1
3
0
0
1
1
1
0
1
0
0
0
0
0
1
0
0
0
1
0
2
0
0
1
1
0
1
2
0
2
1
0
1
0
0
2
2
0
2
1
0
1
2
1
0
1
2
0
0
0
1
0
0
0
2
2
0
3
2
0
0
1
2
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
1
4
1
0
0
0
2
0
0
0
2
2
0
1
0
1
1
0
0
0
4
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
3
0
1
0
0
1
0
1
0
0
2
0
1
0
0
1
0
2
0
1
0
2
0
2
0
2
0
0
0
0
3
0
0
2
0
0
0
0
0
0
2
2
1
0
0
0
2
0
2
1
0
0
2
0
1
1
1
1
0
0
0
0
0
2
2
0
2
2
2
0
0
0
0
0
0
0
1
0
2
2
0
2
0
0
2
0
0
0
2
0
0
2
1
0
0
1
0
1
0
0
2
0
1
0
0
0
0
0
1
0
0
0
1
0
0
3
2
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
2
1
1
2
3
0
0
0
2
1
0
1
0
3
0
2
0
0
2
0
0
0
0
1
0
2
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
1
2
2
1
0
2
0
0
2
0
0
1
2
1
0
0
0
1
1
2
0
0
0
1
0
2
1
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
2
1
2
1
1
1
2
1
0
3
0
2
0
0
0
0
1
0
0
0
0
0
2
2
3
0
0
0
0
2
1
0
0
1
0
0
0
0
1
1
0
3
0
0
0
0
0
0
2
0
0
1
0
2
0
0
1
0
0
0
2
0
0
0
0
1
2
3
0
0
0
2
2
2
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
2
0
0
1
0
0
1
2
0
2
0
1
2
0
0
0
1
0
0
0
2
0
1
0
0
2
1
0
2
1
0
2
0
0
1
2
1
0
1
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
1
0
0
1
0
1
0
1
1
0
0
0
0
0
0
2
1
1
3
0
0
1
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
1
1
0
0
0
1
0
0
2
2
0
2
1
0
0
1
1
1
0
0
0
1
2
1
2
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
2
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
1
2
1
0
0
0
0
0
9
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
1
1
1
0
1
2
2
2
1
0
0
1
1
1
2
0
1
0
0
0
2
2
2
0
0
0
0
3
1
2
1
1
1
0
2
0
1
0
1
2
0
2
0
2
2
0
2
0
0
0
0
0
2
1
0
2
0
2
2
0
0
0
1
0
0
0
2
0
0
0
0
1
2
2
0
2
0
0
0
0
0
2
0
0
0
2
2
0
0
1
2
0
4
2
2
0
0
1
1
0
0
4
2
1
0
0
0
0
1
0
0
1
0
2
1
1
0
2
2
1
2
2
1
0
2
0
2
1
1
2
0
0
1
0
0
1
2
0
1
0
1
0
1
1
1
0
0
0
0
1
0
0
2
0
0
0
1
2
0
2
1
2
2
2
1
0
1
0
0
1
0
1
1
0
0
0
0
0
2
0
1
0
0
1
0
0
0
1
0
0
1
1
2
0
1
2
0
0
2
0
0
0
0
0
2
0
2
0
1
2
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
1
2
0
0
0
2
2
0
0
1
1
0
0
0
1
2
0
0
1
2
0
0
0
1
0
0
2
0
0
0
1
2
1
2
1
1
0
2
2
0
1
0
0
2
0
0
2
0
0
1
0
1
0
1
0
0
0
0
0
0
2
0
2
3
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
1
0
1
1
2
1
0
2
2
4
0
0
0
0
0
1
2
0
2
1
0
0
0
0
2
2
0
0
0
0
1
0
0
2
0
3
0
0
1
0
0
0
0
2
2
0
1
2
1
2
2
0
1
0
3
0
1
0
0
0
0
1
0
0
0
1
0
2
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
1
1
2
0
3
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
2
1
0
2
0
3
0
1
1
0
1
0
0
1
2
0
1
1
0
0
0
0
2
0
0
2
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
2
2
1
1
0
1
0
1
2
0
0
0
2
2
0
1
0
0
0
0
2
0
1
0
0
0
0
0
2
0
1
2
0
2
1
0
0
0
0
1
1
0
0
2
2
0
1
0
0
2
2
0
0
2
1
0
0
0
0
0
2
2
0
2
1
1
0
0
0
0
0
1
0
0
0
0
0
0
4
0
1
0
1
0
0
0
0
0
0
2
0
0
1
2
2
0
0
0
0
1
2
1
0
0
0
0
0
0
0
8
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
1
1
0
2
1
0
2
0
0
1
0
0
1
2
0
0
0
0
2
1
1
0
2
0
0
1
0
0
0
2
0
0
0
2
0
2
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
1
0
1
0
0
0
1
2
0
1
0
0
0
1
0
0
0
1
0
1
1
0
0
2
0
0
0
2
1
0
0
2
0
0
2
1
2
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
1
0
1
0
0
2
0
2
0
0
1
0
2
0
1
0
0
0
2
0
2
1
2
0
2
2
0
0
2
1
1
0
0
0
1
2
0
1
0
2
0
0
1
0
0
1
0
2
0
0
0
3
0
2
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
1
1
0
1
0
1
0
0
0
0
0
0
2
0
0
0
1
1
0
1
2
0
1
0
2
0
2
2
0
0
0
0
2
0
1
0
4
0
0
0
0
1
0
2
0
1
2
0
0
0
6
2
0
0
1
1
3
2
0
1
0
0
0
1
4
1
0
2
0
0
3
0
0
0
0
1
1
2
0
3
2
0
1
0
1
1
0
0
0
2
0
0
0
0
0
0
0
1
3
1
0
0
0
1
0
0
0
1
2
0
1
0
1
1
0
0
0
0
1
2
5
3
0
2
0
2
0
1
1
2
2
1
0
0
0
0
0
2
1
0
1
1
1
0
0
4
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
2
1
0
0
0
1
0
0
2
1
0
0
0
1
0
0
0
0
0
2
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
3
0
2
0
0
0
0
2
1
2
2
2
0
0
1
0
0
1
2
0
0
1
0
2
0
0
0
1
1
0
1
1
0
0
2
1
0
1
1
1
1
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
3
2
0
0
2
2
3
2
0
0
0
1
0
0
0
1
0
2
1
0
0
0
0
0
0
1
0
0
0
1
2
1
0
0
1
0
0
0
0
0
0
2
0
0
2
2
2
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
2
2
2
1
0
1
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
2
2
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
5
0
1
1
1
0
1
0
1
1
1
0
0
0
1
2
0
0
0
0
0
1
1
0
0
0
0
1
1
1
2
0
0
0
2
0
0
0
1
0
0
0
0
2
0
1
0
2
0
0
0
3
0
0
0
2
0
0
2
0
0
1
0
2
0
1
0
2
0
0
0
1
2
2
0
2
0
0
2
2
0
2
0
2
0
1
0
0
0
1
0
2
1
1
0
1
2
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
1
0
1
2
0
0
1
0
0
0
0
1
1
2
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
2
1
0
0
1
4
2
2
1
0
2
0
1
1
0
2
2
0
0
0
0
1
1
1
5
0
0
3
1
0
2
0
0
0
0
0
0
2
0
1
2
0
0
2
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
1
1
2
0
0
0
0
2
1
0
1
1
0
0
0
2
0
0
0
2
2
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
2
0
2
1
0
0
0
1
0
0
0
0
0
0
3
2
0
0
1
2
0
0
2
0
0
1
2
0
2
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
3
0
0
2
1
0
1
0
1
0
1
2
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
2
0
2
0
1
0
0
2
2
0
2
0
1
0
1
0
0
0
0
0
2
0
0
0
0
3
0
1
0
2
0
0
1
0
2
1
1
0
0
1
0
0
0
1
0
0
0
2
0
0
0
1
0
0
3
0
2
0
0
0
2
2
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
2
2
3
1
0
2
0
0
1
1
1
2
1
0
2
1
2
1
2
0
0
0
1
0
1
1
0
0
0
0
0
0
2
0
1
0
0
0
2
2
0
2
2
0
1
0
2
2
0
1
0
1
0
0
0
0
2
0
3
0
0
1
0
0
1
0
0
1
0
0
0
2
1
1
2
0
0
0
0
2
2
0
1
0
0
0
2
0
0
2
4
0
1
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
2
0
0
0
2
0
0
0
0
2
1
1
1
2
0
1
2
1
2
1
2
1
0
1
1
0
0
1
0
0
0
0
3
0
0
1
2
0
0
1
0
0
0
0
1
0
2
0
1
0
0
1
0
0
0
0
0
1
0
1
2
0
0
0
2
1
1
0
2
0
0
0
2
0
1
0
0
1
0
0
0
2
2
0
0
1
0
1
0
0
2
0
1
2
2
0
0
0
0
2
1
2
0
1
0
2
1
1
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
2
0
0
0
0
1
2
0
2
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
1
1
0
0
0
0
0
0
0
1
0
1
1
5
1
0
0
1
0
3
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
2
1
0
1
0
0
0
0
1
0
0
0
1
1
1
0
1
0
0
1
0
0
3
0
0
0
0
1
3
2
0
2
0
0
0
3
1
0
0
2
0
1
0
0
1
2
0
0
0
0
0
0
2
0
0
1
2
0
1
0
0
0
2
0
0
1
1
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
1
0
0
1
2
0
1
0
0
0
0
0
1
0
2
1
0
3
0
1
1
0
0
0
0
1
2
1
1
0
2
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
6
1
1
2
1
0
0
0
1
2
0
0
1
0
1
1
2
0
0
2
0
0
0
1
1
1
0
2
2
0
0
1
6
1
0
0
0
3
1
0
2
1
1
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
2
1
1
0
2
0
0
0
0
0
0
0
2
0
0
2
0
1
0
1
0
0
1
0
0
2
3
0
1
1
2
1
0
1
0
0
0
0
2
1
0
0
2
2
0
1
0
1
2
0
1
2
0
0
2
1
0
1
1
0
3
1
1
1
1
0
0
2
2
2
2
0
0
0
0
4
1
2
0
0
1
0
1
0
0
2
1
0
1
0
2
1
0
0
0
0
0
0
0
2
1
1
0
0
0
2
0
0
2
0
0
0
1
0
0
0
1
0
1
0
2
1
7
0
0
0
0
0
1
0
2
0
0
0
1
0
2
0
0
1
0
0
0
1
0
0
2
0
1
0
2
2
2
0
0
0
0
1
0
0
1
1
1
0
2
2
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
2
0
1
0
0
2
1
0
0
0
2
0
1
0
0
0
0
1
1
1
1
0
1
0
0
0
2
2
1
1
0
0
0
1
2
2
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
1
0
0
0
1
0
1
0
2
1
0
0
2
1
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
1
0
0
1
0
0
0
2
0
2
2
0
1
0
0
0
0
0
0
2
2
1
2
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
4
0
1
0
2
0
2
2
0
1
2
0
3
0
2
0
0
0
2
1
2
0
0
0
1
0
2
3
1
0
1
1
2
1
2
1
2
0
2
1
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
1
1
0
0
2
2
0
0
0
0
1
0
0
0
4
0
1
0
0
0
2
0
1
1
0
0
1
1
0
0
0
0
0
1
0
1
1
2
0
0
2
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
1
0
0
2
0
1
0
0
2
0
0
0
2
1
0
0
0
1
2
0
0
0
2
2
1
0
0
0
0
1
2
0
1
2
2
0
2
2
0
0
1
0
0
1
0
0
0
2
0
0
0
1
2
2
0
0
0
0
0
2
0
1
2
1
2
1
2
0
0
1
0
2
0
1
0
1
1
0
0
1
2
1
0
2
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
1
1
1
1
2
1
0
1
1
0
0
0
0
0
2
0
0
2
1
2
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
3
1
0
0
1
0
2
1
1
0
0
0
2
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
2
0
1
0
2
1
0
0
0
0
1
2
2
0
2
0
0
0
0
0
0
0
2
0
0
2
0
1
0
2
2
0
2
0
0
0
0
1
0
0
1
0
0
1
0
2
0
1
0
1
1
2
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
2
2
2
0
0
0
0
0
1
3
2
0
0
0
1
0
0
0
0
0
2
0
2
1
0
0
2
2
0
2
0
0
0
1
1
1
0
1
0
1
0
0
0
0
0
2
0
0
5
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
1
2
0
0
0
0
0
1
0
0
0
2
2
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
2
0
1
2
1
0
0
2
0
1
2
0
0
1
2
2
0
0
0
0
0
1
1
0
0
1
1
1
0
2
2
1
0
2
0
0
0
0
3
0
1
0
0
0
2
0
2
0
0
0
1
2
0
0
0
5
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
2
0
0
0
1
1
0
0
0
2
3
4
0
1
2
0
2
1
0
0
0
3
4
0
0
1
1
0
0
0
2
0
0
0
0
3
0
1
1
0
0
2
1
0
0
0
0
2
0
0
0
0
1
2
2
0
0
3
0
0
1
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
3
0
0
1
1
0
0
1
0
0
0
2
0
0
1
0
1
0
1
1
0
0
0
0
5
1
0
0
0
2
0
1
3
2
0
0
0
1
5
2
0
1
0
0
0
0
2
1
0
0
0
0
0
1
0
1
2
0
0
3
0
2
1
1
0
0
1
0
0
0
0
1
0
0
1
0
3
1
0
1
0
0
2
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
2
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
2
0
0
1
2
0
0
1
0
0
0
0
2
3
3
0
2
0
0
0
0
1
2
0
0
0
1
0
0
2
0
0
2
2
1
1
0
1
4
0
0
1
1
0
1
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
2
1
0
1
0
0
1
2
3
2
0
2
0
0
2
0
0
1
1
2
0
0
2
0
0
0
0
0
2
3
1
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
2
0
0
2
1
2
1
1
1
0
2
2
0
0
0
2
0
0
1
0
0
0
1
0
1
2
1
1
0
2
0
0
1
2
2
0
0
1
0
0
0
0
3
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
1
0
1
2
0
0
1
0
2
0
0
2
0
1
2
0
0
1
0
0
0
1
0
2
0
0
1
2
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
2
0
1
0
0
0
2
0
0
0
2
0
0
0
2
0
1
0
0
2
0
0
2
2
0
1
0
3
0
0
1
3
1
1
0
1
0
0
0
1
0
0
0
0
1
1
1
1
0
0
0
1
0
1
0
0
0
0
2
0
2
2
1
0
0
3
1
0
0
1
0
0
0
0
2
0
1
0
1
0
2
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
1
1
0
2
3
0
0
0
0
0
0
2
2
0
0
2
0
2
0
0
2
0
2
0
0
2
2
2
1
0
0
9
1
0
1
0
0
0
0
2
0
0
1
0
3
0
0
0
0
1
0
1
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
2
1
2
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
1
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
1
1
0
2
1
0
1
0
0
0
2
2
0
1
0
2
1
1
0
0
0
1
2
1
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
1
2
2
0
0
3
2
0
0
1
2
2
1
0
1
0
0
0
2
0
1
1
0
0
2
0
0
0
1
0
1
0
0
0
0
1
2
0
0
0
0
2
0
0
0
1
0
2
3
2
0
0
0
0
0
3
0
0
1
0
3
1
1
0
2
0
0
0
1
0
0
0
0
1
0
0
1
2
0
0
1
1
0
0
0
2
0
0
2
0
0
2
1
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
1
1
0
0
0
0
1
1
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
2
2
1
2
1
0
0
1
0
1
0
1
0
0
0
0
0
2
0
2
0
0
2
0
0
1
2
0
0
1
0
1
0
0
2
2
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
1
1
0
2
1
0
1
0
0
1
1
0
0
0
2
2
1
2
1
0
2
1
0
0
1
0
1
2
1
1
1
0
3
1
1
0
0
0
0
0
1
0
0
2
1
0
2
1
3
0
0
0
2
1
2
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
2
2
1
2
0
2
0
0
1
0
2
1
0
1
0
0
0
0
0
0
0
0
0
3
2
2
0
2
0
0
1
0
0
2
0
2
1
0
0
2
0
0
1
0
0
0
0
2
0
2
1
1
2
0
2
0
0
0
1
0
0
0
0
0
1
1
0
0
0
2
0
0
2
0
0
2
2
0
0
2
1
0
0
7
1
0
0
0
0
1
0
1
1
0
0
2
5
0
0
0
2
0
1
0
0
3
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
6
0
0
2
3
0
0
0
1
0
1
1
2
1
1
0
0
0
0
0
0
0
0
2
0
0
2
1
0
2
0
0
0
0
0
0
1
2
1
0
0
0
2
0
1
0
2
2
2
0
0
0
1
0
1
2
0
0
1
0
0
0
0
0
0
1
0
1
2
0
1
0
0
1
0
3
1
0
0
0
1
1
0
0
2
0
2
0
1
0
2
0
1
0
0
0
0
1
2
1
0
0
0
1
0
6
2
0
1
1
0
2
0
0
0
1
1
1
1
0
2
2
0
1
2
0
0
2
3
1
0
0
0
0
0
1
1
0
1
2
0
0
0
2
0
0
1
0
0
0
1
0
2
0
0
1
1
1
0
1
0
2
0
0
2
2
2
0
2
1
1
0
0
0
0
0
1
2
0
0
0
1
0
1
0
0
2
1
0
0
1
0
0
0
0
2
1
0
1
1
2
1
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
2
1
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
2
2
0
1
0
0
0
2
1
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
2
1
0
1
0
1
0
0
0
1
0
0
0
2
1
0
2
2
0
1
1
0
1
0
2
0
0
1
0
0
0
1
1
0
1
4
1
0
0
0
0
1
1
0
2
0
0
0
0
1
0
0
2
0
0
0
0
2
1
2
2
2
0
1
0
1
0
1
0
2
0
0
0
2
2
3
0
2
0
2
0
0
0
1
1
2
0
0
2
0
0
1
0
0
1
0
1
1
1
2
2
2
0
0
0
2
1
2
0
2
1
0
0
0
2
0
2
0
0
2
0
0
1
2
0
3
2
0
0
2
0
0
1
0
0
0
1
3
0
0
0
2
0
5
1
0
2
2
0
1
2
0
1
0
2
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
1
2
0
0
1
0
0
1
2
1
0
0
2
1
2
0
0
1
0
0
1
1
1
0
0
1
0
0
1
2
0
2
0
1
0
2
0
0
0
1
1
0
0
0
2
0
0
1
1
2
1
0
0
2
0
0
0
0
1
0
2
1
0
0
0
0
2
1
1
0
2
2
0
0
1
0
2
1
0
2
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
5
0
2
1
2
0
0
0
0
0
0
2
0
0
0
3
0
2
0
2
2
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
1
0
1
0
2
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
1
1
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
1
0
2
1
1
0
0
0
1
0
0
0
2
2
2
1
2
1
0
0
1
2
0
0
0
0
0
0
1
0
0
0
1
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
1
1
1
0
0
2
1
0
0
0
0
2
0
1
0
2
1
0
1
2
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
2
1
0
1
0
0
1
0
0
1
1
1
0
0
2
0
0
4
2
0
0
0
1
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
1
2
0
2
0
1
0
0
0
2
0
0
0
1
0
0
1
0
0
0
1
0
0
2
0
2
0
0
0
2
0
0
1
0
0
2
0
2
0
0
0
0
1
0
2
1
2
0
0
0
0
0
0
0
2
2
0
1
2
1
1
0
0
2
0
0
2
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
1
1
1
0
0
1
0
0
1
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
2
2
0
0
0
2
0
0
1
0
2
0
0
1
0
1
2
0
0
1
0
0
0
2
0
1
0
0
2
2
0
0
0
0
0
2
0
0
0
1
0
2
0
1
2
0
0
0
0
1
1
2
2
0
0
0
0
2
1
0
1
0
0
0
1
1
0
0
0
1
3
2
0
0
1
0
0
1
0
1
0
0
2
1
0
0
1
2
1
0
1
0
0
2
0
0
0
0
0
1
0
0
2
1
0
0
2
2
0
1
0
2
1
1
0
0
2
1
0
2
0
0
0
3
2
2
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
1
0
2
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
2
0
1
0
0
0
0
0
0
2
1
1
2
2
0
1
0
0
0
0
2
1
0
0
1
0
2
0
0
2
0
1
0
2
1
0
2
1
1
2
0
0
0
1
0
2
2
0
1
1
0
1
1
0
1
0
2
0
0
2
1
1
3
1
1
2
1
1
0
0
2
0
2
0
2
1
0
0
0
0
1
1
0
0
2
2
0
0
0
3
0
0
0
0
0
0
2
1
2
1
0
2
0
1
2
0
1
1
2
2
0
0
2
0
0
0
1
0
1
0
1
0
0
0
5
2
0
0
2
0
0
2
2
1
1
0
0
1
0
1
0
1
0
2
1
0
1
0
0
0
0
0
1
0
0
2
0
0
4
0
1
0
0
1
0
0
0
0
0
0
3
2
2
0
0
0
0
2
1
1
2
0
1
0
0
0
2
0
0
0
0
0
2
2
0
1
0
1
2
3
0
0
0
1
0
0
0
2
1
2
0
0
1
1
0
0
0
1
0
0
0
0
1
2
1
0
0
0
1
0
0
0
0
0
2
0
0
1
1
1
0
0
0
1
0
0
1
0
2
0
1
1
0
0
0
0
0
1
2
1
0
0
1
1
1
0
0
2
0
2
0
0
0
0
1
1
4
0
0
2
0
0
0
2
0
0
0
10
0
0
1
0
1
0
0
0
0
2
1
2
2
0
0
0
2
1
1
1
0
2
3
2
0
1
0
0
0
0
1
0
0
0
0
1
1
0
1
0
1
0
2
0
0
1
0
0
1
2
0
0
5
0
0
0
0
0
1
1
1
1
0
2
0
0
2
0
0
0
0
0
2
1
0
0
3
0
2
0
0
0
0
0
0
0
0
2
0
2
0
3
0
2
2
0
0
2
0
0
3
1
0
1
2
1
0
0
0
3
0
0
1
0
0
2
0
2
2
1
0
1
0
0
1
0
0
1
3
0
2
2
1
0
1
0
0
0
2
0
0
2
2
0
1
0
0
0
0
1
0
0
0
1
1
0
1
2
0
0
0
1
0
0
0
1
2
1
0
0
1
0
0
0
0
0
2
2
1
0
0
0
0
2
0
2
1
0
0
1
1
0
1
0
0
0
0
1
0
0
2
1
0
0
0
4
2
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
1
0
1
2
0
0
0
2
1
0
1
2
0
1
1
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
1
1
5
0
2
1
1
0
1
0
1
1
0
0
2
2
0
0
0
0
0
0
0
1
1
0
0
2
0
1
0
0
2
2
0
1
0
3
2
0
0
2
2
0
0
2
1
1
1
1
0
3
1
2
0
1
0
0
0
1
0
0
0
0
2
0
1
1
1
2
0
0
0
2
1
0
1
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
3
0
0
1
0
0
0
1
1
0
1
0
1
1
0
1
1
3
1
0
0
0
0
0
2
0
1
0
1
1
0
1
2
4
1
0
0
0
2
0
1
0
2
2
0
0
2
0
1
0
0
0
1
2
0
0
0
0
0
1
0
0
0
1
1
1
2
0
1
1
0
0
0
0
2
1
1
0
1
1
2
0
1
0
0
0
2
0
0
2
0
3
0
1
0
0
0
0
1
1
3
0
1
2
1
2
2
0
2
0
2
0
2
0
0
2
0
0
2
1
0
0
0
1
0
1
2
1
0
0
0
2
1
3
0
1
0
0
1
1
0
0
0
0
0
1
2
2
2
1
1
0
1
0
1
1
0
2
0
2
0
1
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
2
1
1
0
0
0
2
0
0
1
0
1
0
0
1
0
0
0
2
0
2
0
0
1
0
2
1
0
0
0
0
2
0
2
0
0
1
0
0
2
0
1
0
2
0
1
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
1
0
0
2
1
0
2
1
0
1
2
1
0
0
3
0
0
0
0
0
0
0
0
1
1
2
1
2
0
0
0
1
0
1
0
0
0
1
2
0
1
0
0
2
0
0
1
1
1
1
0
0
0
2
1
2
0
0
1
0
1
2
1
0
2
2
0
0
1
0
0
0
1
0
0
0
1
2
2
0
2
1
2
0
1
2
2
0
0
0
1
0
0
0
0
2
0
1
2
1
2
0
1
0
1
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
2
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
2
1
0
2
0
0
0
2
2
2
1
0
0
2
0
0
0
1
0
1
0
0
0
0
2
1
1
0
10
0
0
2
0
0
0
0
2
0
1
2
2
0
1
0
0
0
0
0
0
2
1
1
0
0
0
2
0
1
1
0
0
0
0
0
0
0
2
0
0
1
2
1
0
7
0
0
1
0
1
2
1
2
1
0
4
0
0
2
0
1
0
0
3
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
3
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
2
0
0
0
3
0
2
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
2
2
1
3
0
0
1
2
0
0
0
0
1
2
1
1
2
0
0
1
2
0
0
2
1
0
0
1
0
3
2
0
0
0
0
0
0
0
1
1
0
1
0
0
1
2
0
0
2
3
0
0
0
0
0
1
0
1
1
1
1
3
2
2
0
1
0
0
0
1
1
0
0
0
2
0
2
0
0
0
0
0
4
1
0
0
0
0
0
0
1
0
0
1
0
0
2
2
1
0
0
2
1
0
1
0
1
1
0
2
0
0
2
0
0
3
2
0
2
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
1
0
0
0
1
0
1
0
0
1
2
0
1
0
0
0
1
1
0
0
0
0
1
1
0
0
1
2
0
0
0
1
1
0
1
0
1
0
1
0
0
1
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
4
2
1
0
1
0
0
2
1
0
1
0
1
1
0
0
1
2
2
1
0
1
0
2
0
2
1
1
0
0
1
2
0
2
3
1
1
1
0
0
1
0
2
2
1
0
0
0
1
1
0
3
0
0
0
0
2
0
1
2
2
0
0
0
0
1
0
2
0
0
2
0
0
1
0
2
0
3
0
0
0
0
1
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
2
1
0
3
0
1
3
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
2
0
2
1
1
0
1
0
0
1
0
0
0
2
2
2
1
2
0
1
0
0
2
0
2
2
2
0
2
0
0
0
0
1
1
0
1
3
0
0
0
0
1
0
0
0
1
0
0
2
2
0
0
0
1
1
0
0
2
0
0
0
2
0
2
0
2
0
1
1
2
0
0
1
1
0
0
0
0
2
0
0
1
0
1
1
1
0
0
4
1
0
0
2
2
0
0
0
3
0
1
2
2
3
0
1
2
2
0
0
0
2
1
0
0
2
0
2
0
1
3
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
2
1
1
0
0
0
2
3
0
1
2
2
0
0
0
0
0
0
2
0
1
2
0
1
0
0
0
0
2
2
2
0
0
0
1
0
1
0
3
1
2
0
4
0
0
1
2
0
0
2
0
1
0
1
0
0
0
5
1
0
0
2
0
1
0
0
0
0
0
0
1
0
0
1
0
0
2
1
0
1
0
2
0
3
0
0
0
2
0
1
1
1
0
0
0
0
1
2
0
2
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
2
2
0
0
0
2
1
2
0
2
0
2
2
0
1
1
0
2
1
2
0
0
1
0
2
1
0
0
0
1
1
0
0
0
0
0
1
2
0
2
0
2
2
1
1
0
0
0
2
0
0
6
2
0
0
0
0
2
0
0
0
0
0
0
2
1
0
3
2
0
1
0
0
0
1
0
0
0
2
1
0
1
1
1
0
2
1
0
1
0
0
1
0
1
0
2
1
1
0
0
1
3
1
1
2
1
0
0
0
1
1
0
0
0
0
0
1
0
0
2
0
0
0
2
1
2
1
0
0
0
0
0
1
2
1
0
2
0
0
1
0
0
1
2
0
1
3
1
1
0
1
0
1
0
0
1
5
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
1
2
0
0
1
1
0
0
1
1
0
2
0
0
0
2
0
0
0
1
0
2
0
2
0
0
0
0
1
3
0
0
0
1
0
0
0
1
2
1
0
0
1
0
0
2
0
1
1
0
0
0
4
0
0
0
0
0
2
0
2
0
1
1
1
2
0
2
0
0
0
1
2
0
0
0
2
0
2
0
0
2
0
0
0
0
0
1
1
0
0
0
1
2
1
0
0
0
0
0
1
1
0
1
4
0
0
0
1
1
0
2
1
0
0
2
0
0
0
0
0
0
1
0
2
0
3
0
0
1
0
2
0
0
5
0
0
0
0
0
1
1
2
1
0
0
0
0
2
0
0
0
1
2
0
0
0
0
1
0
0
2
0
0
0
2
5
0
2
0
1
0
0
0
2
0
2
0
0
6
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
1
0
0
0
1
2
1
1
0
0
2
0
0
0
0
1
0
0
2
0
3
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
1
1
3
0
0
2
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
2
0
0
0
2
0
0
0
0
2
1
1
1
0
0
0
2
1
0
0
1
0
1
0
2
1
0
1
1
2
0
1
0
0
1
0
0
0
0
0
1
0
3
0
0
0
1
0
2
0
0
2
1
0
0
0
2
3
2
1
0
1
0
0
0
2
1
0
0
0
1
2
0
0
0
0
1
2
0
0
2
1
0
2
1
0
1
0
0
0
0
0
0
0
1
2
2
0
2
1
2
0
2
1
1
0
0
5
0
2
0
0
0
2
0
0
1
2
0
0
2
0
2
0
0
0
1
0
0
0
0
0
2
2
0
0
2
0
0
1
0
0
1
0
1
0
1
0
1
1
0
2
0
0
0
0
0
4
1
2
1
0
0
0
0
2
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
2
0
2
0
1
0
1
0
1
0
0
1
1
1
1
3
0
0
2
0
0
2
0
0
1
1
0
0
0
1
0
0
1
1
0
2
0
2
3
0
1
0
0
0
0
0
2
0
1
0
0
0
1
1
0
0
1
0
1
0
1
0
2
0
0
0
2
0
2
2
0
0
1
0
1
2
0
0
0
0
1
0
0
1
0
0
2
0
0
2
0
3
1
0
2
0
1
2
0
2
0
0
0
0
2
0
0
1
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
2
0
0
2
0
1
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
2
2
1
3
0
1
0
1
0
0
2
0
0
0
2
1
0
0
1
0
0
2
0
0
0
1
0
0
0
2
3
1
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
4
0
0
0
0
1
1
0
2
2
0
0
0
0
0
1
5
1
0
2
2
3
0
2
2
0
1
0
1
0
2
1
0
2
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
1
2
0
0
0
0
0
0
1
0
0
0
2
0
1
1
0
0
0
0
1
0
0
1
0
0
1
2
1
0
0
0
1
0
1
1
1
0
2
2
0
0
0
0
1
0
0
0
0
2
0
1
2
0
1
1
0
2
1
1
2
0
0
3
0
2
3
2
1
2
0
2
1
1
0
0
1
1
0
0
4
1
0
0
0
0
2
0
2
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
5
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
2
0
0
0
1
0
1
0
0
0
1
1
0
0
0
2
0
1
0
0
0
0
1
1
0
1
2
0
0
1
1
0
0
0
0
0
2
2
0
0
0
0
0
4
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
2
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
1
10
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
2
0
1
2
2
1
0
0
3
0
0
0
1
0
0
2
2
1
1
2
0
0
0
1
0
1
0
1
0
2
0
0
1
1
1
0
2
1
0
0
2
2
0
0
0
2
1
0
0
2
0
0
1
0
3
0
0
2
2
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
2
1
0
2
1
0
1
2
1
2
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
3
0
0
1
0
1
0
0
1
1
0
0
0
2
0
0
0
3
0
2
0
1
0
0
1
1
1
0
0
0
2
0
0
1
0
1
0
0
2
3
2
0
1
1
1
1
0
2
0
1
0
0
3
0
0
1
0
0
0
0
0
1
2
1
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
1
2
0
0
0
1
1
1
0
2
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
1
0
0
0
1
0
0
3
2
1
0
0
1
0
1
0
2
0
1
0
0
1
0
1
0
2
1
0
0
0
2
0
0
2
1
1
2
1
0
0
0
2
0
3
0
1
2
0
1
0
0
2
2
2
0
2
1
2
1
0
0
0
1
0
0
0
0
0
1
0
0
1
2
1
0
0
2
0
1
2
0
0
0
0
3
2
0
1
1
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
3
1
1
0
0
1
0
1
2
1
0
2
1
2
0
2
2
1
0
0
0
0
0
2
0
2
0
2
0
1
0
0
1
0
1
1
0
2
0
0
4
0
0
0
0
0
0
0
1
1
0
2
1
2
2
0
0
3
0
0
0
2
0
0
1
1
0
0
1
0
2
1
2
1
0
2
0
0
2
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
2
1
2
2
1
0
0
0
2
1
2
1
2
1
2
2
3
0
2
0
0
0
0
2
1
0
2
1
0
0
0
0
0
0
1
2
0
1
1
0
0
0
0
1
0
1
0
0
0
2
0
2
2
0
0
0
1
2
1
2
0
2
0
2
0
1
0
0
0
0
1
3
0
2
0
2
0
0
0
1
0
0
0
0
0
1
0
2
0
1
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
1
2
0
2
2
0
1
4
2
2
0
0
1
1
1
0
0
1
0
0
0
0
2
0
0
3
0
0
0
1
0
2
0
0
1
0
1
1
0
0
2
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
1
2
0
2
0
1
2
0
0
1
2
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
1
0
1
0
0
2
0
2
1
2
1
0
1
1
1
0
0
2
3
0
2
0
1
0
0
0
0
0
2
1
0
0
2
0
2
0
0
2
2
0
0
0
0
2
0
0
0
2
1
0
2
0
0
4
0
2
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
7
2
0
2
2
1
1
2
2
2
2
0
3
0
0
0
1
0
1
1
1
2
0
1
0
0
0
0
0
1
2
1
1
1
0
1
1
0
1
0
0
1
0
2
0
0
0
0
0
0
3
0
0
1
0
2
2
2
2
5
0
1
2
0
4
0
1
0
2
2
0
2
0
2
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
2
1
1
0
3
0
0
0
0
0
1
3
0
0
0
2
1
0
0
1
0
1
0
0
2
1
0
2
0
2
0
1
0
1
0
0
3
0
0
0
0
0
0
2
2
1
0
2
2
3
1
1
1
0
2
0
0
0
2
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
1
0
4
2
0
1
1
0
0
0
2
0
1
0
5
2
0
0
0
0
0
1
2
0
2
2
0
1
0
0
0
0
0
0
3
0
4
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
1
1
2
0
0
2
0
0
0
0
0
0
2
2
0
2
0
0
1
0
1
2
1
0
0
1
0
0
1
0
1
2
0
0
0
0
2
0
0
0
0
1
2
1
0
0
0
2
1
0
0
0
1
3
0
0
0
0
0
2
0
8
0
2
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
2
0
2
1
0
1
0
2
0
1
0
0
1
0
1
1
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
1
0
0
0
0
2
1
0
2
0
1
1
2
0
0
1
1
0
2
4
0
0
1
1
1
0
1
2
0
0
0
2
3
0
0
0
0
0
0
2
2
0
0
0
0
1
0
2
0
0
0
1
0
0
0
1
0
1
0
1
1
1
2
0
1
0
2
0
5
0
2
1
3
1
1
0
0
1
0
1
1
0
0
1
0
1
0
1
0
0
0
1
1
0
1
2
1
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
1
0
2
1
0
0
0
0
2
2
0
0
1
1
2
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
2
1
2
1
0
0
2
0
1
1
1
0
2
0
0
0
0
3
2
0
2
0
2
0
1
1
1
2
0
0
0
3
1
0
0
0
2
0
1
1
1
1
1
3
0
0
0
0
0
1
2
0
0
0
2
0
0
0
2
2
2
3
0
0
0
0
3
1
2
0
1
1
0
0
2
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
2
2
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
2
0
0
2
0
3
1
0
1
1
0
1
0
0
0
1
1
0
0
1
1
0
2
1
1
1
0
0
0
0
0
1
0
0
0
2
0
0
2
2
0
0
2
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
2
2
0
2
1
0
0
2
0
0
1
0
2
0
0
0
0
2
1
0
0
0
0
0
0
1
1
0
2
0
1
0
0
0
0
0
0
0
1
1
0
0
0
2
0
2
0
0
0
1
2
2
2
0
2
0
0
1
0
0
3
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
1
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
1
1
0
1
2
1
0
0
0
9
0
2
1
0
0
0
1
0
2
0
1
2
2
0
2
1
0
0
2
1
0
0
2
0
0
0
0
1
3
1
2
0
1
2
2
0
0
1
1
0
1
2
2
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
1
1
0
0
0
1
0
0
0
0
3
0
2
0
0
0
0
2
0
0
2
1
1
1
1
0
2
1
0
0
0
0
2
0
2
0
1
0
1
0
0
0
0
0
0
0
2
0
1
0
2
1
2
0
1
0
0
0
2
2
0
0
4
2
1
0
0
0
0
1
1
2
2
0
0
0
0
0
0
1
2
0
2
0
2
0
0
0
1
1
0
4
0
0
2
0
1
1
0
0
2
1
1
0
0
0
0
3
2
1
1
1
1
0
2
0
2
0
0
0
1
0
0
0
0
2
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
2
2
1
0
1
2
2
0
1
0
0
2
0
1
0
0
1
0
0
0
0
1
0
1
2
0
1
0
0
1
0
2
2
1
0
1
0
0
2
0
3
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
2
0
1
0
0
1
0
2
0
0
0
0
1
1
1
0
2
0
0
0
1
2
0
0
0
2
4
0
0
0
0
2
0
1
0
0
2
1
0
0
2
0
2
0
0
1
0
2
0
0
1
2
2
0
0
0
0
2
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
2
1
2
0
0
0
0
3
1
0
0
0
1
2
2
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
1
0
1
2
0
0
0
2
0
0
0
0
2
0
2
2
0
1
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
1
0
0
2
0
0
2
2
1
2
0
0
1
0
2
2
0
0
0
0
1
1
0
2
2
0
2
0
0
0
0
0
0
1
0
8
0
1
0
0
0
2
2
0
0
0
2
1
0
0
0
1
0
0
1
0
2
1
1
2
2
1
0
0
1
0
0
2
0
0
2
0
0
2
1
0
1
2
1
0
1
0
0
0
2
0
0
2
0
1
0
0
2
1
0
0
2
1
1
2
0
1
0
2
2
0
1
0
2
0
0
2
0
0
0
2
1
0
0
0
0
1
0
2
1
0
1
1
1
0
0
0
0
2
1
2
2
0
1
0
1
0
1
0
0
0
0
0
0
1
0
1
0
1
0
1
1
0
0
3
0
0
1
0
0
1
3
0
0
0
0
3
2
0
2
0
2
1
0
0
2
0
1
1
2
0
0
1
0
0
0
0
0
0
0
0
4
0
2
0
1
0
0
0
0
0
0
0
1
0
2
1
0
0
1
0
0
2
2
0
1
0
2
1
0
0
0
0
0
2
0
0
0
2
1
0
1
2
0
1
0
0
0
1
0
0
1
2
0
1
0
0
4
0
0
0
0
1
0
1
0
0
0
4
1
1
0
2
2
2
1
1
0
0
2
2
1
2
0
1
0
1
0
0
0
0
2
0
0
0
2
2
2
1
0
0
0
1
0
2
0
0
1
1
0
0
0
0
0
0
2
0
2
1
2
2
2
0
3
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
3
1
2
0
1
1
2
0
5
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
2
0
2
0
0
1
0
2
1
0
1
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
2
0
2
2
0
0
0
0
0
0
0
1
1
0
1
0
2
1
2
0
2
0
0
0
0
0
1
1
0
2
0
2
0
1
1
0
0
2
0
2
1
0
1
2
0
0
0
0
1
0
0
2
1
0
0
2
0
0
0
2
1
0
0
0
0
0
2
2
1
0
0
1
0
0
0
2
0
0
0
1
0
1
0
2
0
1
1
0
2
0
1
0
1
0
1
0
0
1
0
0
0
0
2
2
1
0
0
0
2
0
0
1
2
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
2
1
1
0
0
0
0
0
1
0
2
1
0
0
0
2
0
1
0
2
0
0
0
2
1
1
2
0
1
0
0
1
1
2
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
2
0
0
1
0
0
0
0
0
1
1
0
0
2
0
0
0
2
1
0
0
0
0
0
2
1
1
0
2
1
0
0
0
1
0
0
1
1
1
0
2
2
0
0
0
2
1
2
1
0
1
2
0
1
0
2
1
0
0
0
0
0
0
1
0
0
0
1
0
1
2
0
0
2
2
0
2
0
0
2
2
2
2
1
1
0
0
3
0
0
0
1
2
0
1
2
0
1
2
1
1
0
0
0
1
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
1
0
2
9
0
1
2
0
0
0
2
4
0
0
0
2
0
2
2
3
2
0
0
0
1
0
0
0
0
0
1
0
1
2
0
1
2
1
2
0
0
0
2
0
2
0
0
1
0
1
0
0
1
1
2
0
1
2
2
1
1
2
1
2
1
0
0
1
1
2
2
0
0
0
1
0
0
1
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
2
2
2
0
1
1
1
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
1
2
0
0
2
3
0
0
0
0
1
0
0
0
1
0
2
2
0
0
0
0
1
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
1
2
0
1
0
1
0
0
0
0
0
0
2
0
1
0
1
2
1
0
2
1
1
0
0
2
0
0
2
0
3
2
1
1
1
0
0
0
0
0
0
3
2
0
2
0
0
0
0
1
2
0
1
0
0
1
0
0
0
0
0
2
0
0
2
1
0
0
0
0
2
2
0
2
0
2
0
0
2
0
1
2
2
0
1
0
2
0
2
0
0
0
0
0
2
1
0
0
0
0
1
1
1
1
2
1
0
1
0
0
0
0
0
0
2
2
0
0
1
0
0
3
1
0
0
1
0
0
0
0
2
0
0
0
2
2
0
0
0
0
1
0
0
0
0
1
0
0
1
2
2
1
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
1
0
0
2
0
0
1
1
1
0
0
0
1
2
2
2
1
0
1
1
0
0
2
0
6
0
0
0
2
2
0
0
2
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
1
1
0
0
1
0
0
0
2
1
2
1
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
2
1
2
0
2
0
0
2
0
2
1
0
0
2
1
1
0
0
1
0
1
0
0
0
4
0
1
0
2
2
0
2
0
0
0
1
2
1
1
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
1
0
0
0
0
1
1
0
1
1
2
1
0
0
2
0
0
2
0
1
0
1
3
0
0
1
0
0
2
0
0
0
0
2
0
0
2
0
0
1
0
0
1
1
1
1
0
0
0
1
0
1
1
1
1
2
1
0
0
2
1
1
0
2
0
1
0
0
0
1
2
0
1
0
0
0
0
2
0
2
0
1
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
2
2
0
0
2
2
2
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
2
2
0
2
1
0
0
0
0
0
1
0
0
2
3
0
0
0
0
0
0
3
2
2
1
1
0
3
0
0
2
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
2
0
1
0
2
0
0
2
0
1
0
0
2
0
2
2
2
0
0
0
0
0
0
1
0
0
1
2
0
1
0
1
0
0
0
0
0
2
1
3
0
0
1
1
1
0
1
1
0
2
0
0
1
0
0
0
1
1
2
2
2
0
0
0
2
3
2
2
0
3
0
2
0
2
1
1
1
2
0
0
1
0
1
0
0
0
2
0
0
0
1
1
1
0
2
0
0
2
2
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
2
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
2
2
2
0
0
0
1
0
0
0
0
0
2
1
2
0
0
2
0
2
0
0
0
0
0
0
2
2
0
1
0
1
2
0
0
2
2
0
1
0
0
2
1
0
2
0
0
6
0
0
2
0
0
2
0
1
0
0
0
0
2
1
2
1
1
0
1
0
1
0
2
0
0
0
0
0
0
2
1
0
0
1
1
1
3
0
1
1
0
2
0
2
0
0
1
0
2
1
0
0
1
0
0
0
0
4
0
0
1
0
0
0
0
1
1
2
2
0
0
1
0
0
1
3
0
0
0
0
2
0
2
0
2
1
0
0
0
2
0
1
1
1
1
0
0
0
0
1
1
1
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
2
6
0
2
2
1
1
2
2
0
1
1
0
2
2
0
1
0
1
1
0
1
0
0
0
1
0
0
0
0
0
1
0
2
0
2
0
0
2
0
0
2
1
1
0
0
0
0
2
0
0
2
1
0
2
1
0
0
2
0
0
1
1
0
0
1
1
0
0
0
3
1
0
0
2
3
2
0
0
0
2
0
0
0
0
3
0
3
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
1
1
2
0
0
2
0
0
0
0
0
2
0
2
1
0
0
1
0
1
0
3
2
0
0
0
0
2
0
0
2
1
1
0
0
0
4
0
0
0
0
0
0
0
0
2
1
0
0
2
0
1
2
2
1
0
2
0
1
2
0
0
2
0
2
2
1
0
1
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
1
0
0
0
0
2
0
2
2
1
0
4
5
0
0
1
0
0
2
0
0
1
0
1
0
1
1
0
1
1
0
2
0
0
0
1
0
0
2
1
0
0
1
0
0
1
0
0
0
1
2
1
0
1
2
0
1
2
0
1
0
2
2
2
0
0
0
0
1
2
1
2
2
0
1
0
1
1
0
0
2
2
0
2
0
0
0
0
0
0
0
0
2
1
0
2
0
1
0
0
0
0
0
1
2
0
1
0
0
0
1
0
0
3
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
1
0
1
0
0
2
0
0
0
2
0
1
1
0
2
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
1
2
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
1
1
0
0
0
1
0
2
0
0
0
1
2
2
1
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
1
1
0
1
2
1
1
0
0
2
2
1
0
2
0
2
0
2
0
0
2
0
0
1
0
2
1
2
0
1
0
1
0
0
0
1
0
0
0
0
2
0
0
2
2
3
0
1
0
0
0
1
2
0
0
2
2
1
0
0
0
2
1
1
0
0
0
0
1
1
0
0
0
0
0
3
0
1
2
0
1
2
0
0
1
0
1
1
1
0
2
0
2
0
2
0
0
1
2
2
2
2
1
0
0
1
0
0
2
1
0
1
0
0
0
1
0
0
0
2
1
0
0
1
0
0
1
2
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
2
0
1
2
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
1
1
0
0
1
0
2
0
0
0
0
2
0
1
0
0
2
0
0
0
2
1
2
1
3
0
0
0
1
0
1
0
0
2
0
0
0
2
0
0
3
0
0
2
2
1
0
0
2
2
0
0
0
1
0
1
1
0
0
2
2
2
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
1
1
0
0
2
0
0
1
0
1
0
0
0
1
0
1
0
2
2
0
0
0
1
0
0
2
0
0
0
0
0
3
1
1
1
0
0
0
0
0
1
0
2
1
0
0
0
0
0
1
2
0
2
1
0
0
2
1
0
0
1
0
1
0
1
0
1
0
0
0
0
1
2
2
3
0
2
2
0
2
0
1
0
0
0
0
0
0
0
0
0
1
2
0
1
2
0
1
2
0
0
0
2
2
1
0
0
0
0
1
0
2
0
0
2
0
1
1
0
0
0
0
0
0
2
0
0
1
2
0
0
3
0
0
0
2
0
0
0
2
2
0
0
2
1
0
1
2
2
0
2
1
0
2
0
1
3
2
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
1
0
2
0
1
2
2
0
0
2
2
1
0
0
0
0
1
0
0
1
1
0
0
0
0
1
2
2
0
1
0
2
0
0
0
2
0
0
0
0
0
2
2
0
0
0
1
1
0
0
0
1
2
2
0
1
2
0
0
0
2
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
4
2
1
1
0
4
1
0
0
2
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
1
0
2
1
0
0
0
0
2
0
0
0
2
2
2
2
0
0
1
0
0
0
4
0
2
0
0
0
0
0
1
0
0
3
2
0
2
2
0
0
0
0
0
2
2
3
1
0
0
1
0
0
2
0
0
10
0
2
0
0
0
1
0
2
2
2
0
0
0
1
2
0
1
0
0
0
2
1
0
0
1
3
0
6
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
1
0
0
1
0
0
0
0
0
2
0
0
2
2
1
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
2
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
2
0
0
1
1
2
8
0
0
1
0
0
0
1
2
0
2
1
0
2
0
0
0
0
0
2
1
2
0
0
1
1
0
0
2
0
1
0
0
2
2
0
1
1
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
2
2
0
0
1
0
3
0
0
0
1
0
2
0
0
0
0
0
0
1
2
0
0
2
0
0
2
0
0
2
0
2
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
2
2
0
0
1
0
1
0
1
0
0
1
2
0
0
0
0
1
0
1
2
0
0
0
0
0
0
1
0
1
0
0
0
2
0
1
1
2
0
0
0
0
0
1
2
1
0
2
0
0
0
0
0
0
0
2
0
0
0
4
0
1
1
0
0
1
0
0
2
1
0
0
2
0
0
0
2
2
0
0
0
0
0
1
2
0
0
0
0
2
0
1
0
0
2
0
0
0
1
0
1
0
2
0
0
0
0
1
1
1
0
1
2
0
2
0
0
0
2
0
0
0
0
1
0
0
2
0
1
0
0
2
1
0
0
0
0
1
0
0
2
1
2
0
1
0
0
0
0
0
0
5
0
1
1
0
0
0
1
0
0
0
1
1
0
2
2
0
2
0
0
0
0
0
2
0
2
0
2
0
1
1
0
0
2
0
0
0
2
0
2
0
1
0
0
3
0
0
6
0
2
2
2
1
0
0
0
0
0
1
1
0
1
0
0
0
1
0
2
2
0
0
0
0
0
1
0
1
1
0
2
0
0
0
0
0
1
0
2
2
0
0
1
1
1
1
0
0
1
0
1
0
4
0
3
2
1
0
0
1
0
0
0
0
3
0
0
0
0
1
0
2
2
2
1
2
1
0
1
0
2
3
0
0
1
0
0
0
0
2
0
0
0
3
1
0
6
0
1
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
2
1
0
0
0
2
1
0
0
0
1
0
1
2
2
1
1
0
1
0
0
0
2
0
0
1
0
0
0
1
2
0
3
1
0
0
0
2
0
1
1
0
1
0
0
0
2
0
2
0
0
0
2
1
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
2
19
2
0
0
1
0
0
0
0
2
3
1
0
0
0
0
1
0
2
1
2
0
0
0
1
0
0
2
1
0
0
0
0
1
2
2
0
1
0
0
0
1
0
0
2
0
2
1
0
0
1
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
1
2
2
0
0
0
0
2
0
1
0
0
3
0
0
0
0
0
1
0
1
0
0
2
0
0
2
0
0
1
0
2
1
0
0
0
0
0
1
2
0
0
2
0
0
1
2
2
2
0
2
1
0
0
0
1
1
0
1
2
0
0
0
2
2
1
0
0
0
0
3
2
0
2
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
2
0
0
1
1
1
0
0
0
0
0
0
2
0
1
0
0
0
1
2
1
0
4
2
3
0
0
0
0
0
0
0
0
2
1
1
0
2
0
1
0
2
2
0
0
0
2
1
0
0
0
0
3
0
0
4
0
0
1
0
0
0
0
1
0
0
0
0
0
2
2
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
3
2
1
1
0
0
1
3
1
0
0
3
7
3
0
0
0
4
0
0
0
2
1
2
0
2
0
0
0
1
0
0
0
0
1
2
2
1
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
2
0
2
2
0
2
0
1
0
0
0
1
0
0
2
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
1
0
4
0
1
0
1
0
0
3
2
1
0
1
0
0
2
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
3
0
1
2
0
0
0
0
0
0
1
0
1
2
0
2
0
0
1
1
2
0
3
0
0
1
1
1
0
1
0
2
1
0
0
0
1
2
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
3
2
1
2
2
0
0
1
3
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
1
2
2
0
1
0
2
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
1
0
1
0
0
2
2
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
1
1
0
1
0
2
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
2
1
1
2
0
0
1
1
1
0
2
0
0
1
0
0
0
1
2
0
0
0
0
0
2
2
1
0
0
0
0
1
0
0
0
1
0
2
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
2
0
0
1
0
0
2
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
2
1
2
0
2
0
0
2
1
0
0
0
0
2
0
0
0
1
0
0
0
2
0
2
0
0
2
1
1
1
0
1
1
1
0
2
0
0
2
1
2
2
0
1
0
1
2
0
0
0
0
0
2
0
0
1
0
2
0
2
2
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
2
1
0
1
0
0
0
2
0
0
1
0
2
1
0
0
1
2
0
0
0
0
2
0
0
0
2
0
0
0
2
1
0
0
1
0
0
0
0
1
0
7
1
2
0
0
2
0
0
0
0
0
3
2
2
0
1
1
2
0
1
0
1
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
2
2
2
0
0
2
0
3
0
0
2
1
0
1
1
0
2
0
2
0
2
1
3
0
0
0
0
0
1
2
2
0
0
3
2
2
2
0
0
1
0
1
0
1
0
0
0
2
2
2
0
2
0
0
1
1
0
2
2
1
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
3
1
1
0
0
0
0
3
0
1
2
2
0
2
0
0
0
0
1
2
0
0
1
0
0
2
2
0
0
1
1
0
0
0
1
2
2
1
0
0
1
1
2
0
2
2
0
3
0
0
0
2
1
0
1
0
2
2
0
1
0
1
1
0
3
0
1
0
0
0
1
0
1
0
0
0
0
4
0
0
0
0
1
0
3
1
0
6
1
0
0
0
0
0
1
1
0
2
6
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
3
0
2
0
2
0
1
0
0
0
0
0
2
1
0
2
1
0
2
1
0
0
0
1
0
2
0
2
3
0
1
2
0
0
0
1
0
0
1
0
0
0
1
1
0
0
1
2
0
1
0
1
0
2
0
0
1
0
0
1
0
0
0
0
1
2
1
2
0
1
0
0
2
2
1
0
1
1
1
0
0
2
0
0
0
0
2
0
3
2
0
0
0
0
0
0
2
2
2
0
2
0
0
0
0
0
2
0
2
1
2
0
2
1
0
0
0
0
0
3
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
1
2
1
0
0
1
0
0
0
1
0
0
2
2
2
0
1
1
0
0
0
0
0
0
2
2
0
2
0
1
0
1
0
1
2
1
1
2
0
1
0
0
0
0
0
2
0
1
1
1
0
1
0
0
1
0
0
0
2
1
2
0
0
0
0
2
1
0
0
0
0
2
0
0
1
1
1
0
0
0
2
0
2
0
2
2
1
0
0
1
0
0
1
1
0
0
2
0
0
0
1
0
0
2
2
0
0
0
3
2
1
1
0
3
0
0
1
1
0
4
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
2
0
3
0
0
5
1
3
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
1
0
1
0
3
0
0
0
0
2
1
1
1
0
0
0
0
2
1
0
0
1
0
0
0
1
1
1
1
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
3
0
1
2
0
0
0
0
0
0
1
2
0
1
0
2
1
0
0
0
2
1
0
0
1
0
0
0
3
0
0
0
0
1
0
0
2
2
0
1
1
1
0
0
2
0
2
0
1
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
2
0
1
0
0
2
0
0
0
0
1
0
1
0
0
2
2
0
0
0
2
2
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
2
2
1
1
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
1
2
2
0
1
0
0
0
0
0
0
2
2
1
0
1
0
0
0
1
1
2
0
1
0
0
1
0
0
1
0
1
2
0
0
2
0
1
0
2
0
1
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
1
0
0
1
1
0
0
0
0
2
0
0
0
0
0
1
0
0
1
2
0
1
0
0
0
2
0
0
2
0
1
0
1
1
0
0
0
2
1
0
0
1
0
1
0
2
2
2
1
1
0
1
1
0
0
0
0
1
0
1
2
0
0
0
0
2
0
0
0
2
1
1
0
0
2
0
0
0
0
0
0
1
3
0
0
0
0
2
0
0
2
1
0
0
1
0
6
2
0
1
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
2
0
1
0
6
1
1
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
2
0
2
1
0
2
0
2
1
0
1
2
1
0
0
0
0
1
2
1
1
1
0
0
2
2
0
0
1
0
2
1
0
0
1
0
0
1
1
1
2
2
2
0
0
2
0
0
1
1
0
0
1
1
2
1
0
0
0
2
1
1
0
0
0
0
0
2
0
2
0
1
2
0
0
2
0
0
2
1
1
0
2
0
0
2
0
1
1
0
1
7
0
0
0
0
0
0
1
0
0
1
2
2
1
0
0
2
0
0
1
1
2
0
0
2
0
1
3
2
0
1
0
2
2
2
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
1
2
2
0
1
2
2
0
2
0
0
1
1
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
1
1
2
2
0
0
0
0
2
2
0
0
2
0
0
0
0
0
1
0
2
0
1
0
3
0
0
0
4
1
2
0
0
1
2
0
1
2
0
1
1
2
0
0
0
0
0
0
2
0
0
0
0
1
0
2
1
0
1
0
0
2
0
0
0
0
2
1
1
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
3
2
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
4
0
0
1
0
0
0
0
0
0
2
2
0
0
0
2
1
0
0
2
0
1
0
0
1
0
0
0
2
0
1
2
0
0
0
1
0
1
1
2
0
0
0
2
0
1
2
0
0
0
0
2
2
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
1
1
2
0
0
2
0
0
2
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
2
0
3
0
2
1
1
2
0
0
0
2
1
0
0
0
0
1
0
1
0
0
1
1
2
1
0
0
1
1
0
1
1
0
0
0
0
0
2
0
0
0
0
1
2
0
2
0
0
1
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
2
2
1
2
0
0
0
0
2
1
0
0
0
0
1
1
0
0
2
0
0
0
0
2
0
0
0
2
2
2
1
0
0
0
1
0
0
0
1
0
2
1
0
1
1
0
1
0
0
1
0
0
1
2
1
0
1
1
1
1
0
2
0
0
0
1
0
1
0
0
0
2
1
4
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
2
1
0
1
0
1
0
1
0
0
3
0
3
0
2
0
1
0
2
0
0
2
1
0
0
1
0
1
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
2
0
2
0
0
1
0
0
0
0
2
0
0
2
1
0
1
0
1
1
2
0
0
0
0
0
0
0
3
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
2
0
1
1
0
0
1
0
1
2
0
0
1
0
3
0
2
0
0
1
1
0
2
0
1
2
0
1
0
0
1
0
0
3
0
1
2
1
0
0
0
1
0
1
2
2
2
0
0
0
2
2
1
3
0
0
0
0
2
2
2
2
2
0
0
0
0
0
1
1
0
2
1
1
0
1
0
1
0
0
0
2
0
2
1
0
0
1
0
0
0
1
0
0
2
0
1
0
2
0
3
1
2
0
0
0
2
2
0
0
0
3
2
3
0
0
0
1
2
3
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
2
2
1
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
2
1
1
2
1
1
0
0
1
0
1
0
0
1
1
1
0
0
0
2
0
2
2
0
2
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
2
0
1
1
0
3
0
0
0
1
0
0
0
2
3
0
1
0
0
0
0
6
0
0
0
2
0
0
2
2
1
1
0
1
0
2
0
0
0
1
0
0
2
1
1
2
2
0
0
0
0
0
2
2
3
2
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
1
0
1
0
0
0
0
0
2
0
0
2
0
0
1
0
2
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
1
2
1
0
2
2
1
0
2
0
0
1
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
1
0
0
3
0
0
2
0
0
1
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
1
2
1
2
0
0
0
1
0
0
2
1
2
0
0
0
0
0
2
0
3
0
0
0
0
1
0
0
1
0
0
0
4
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
2
0
0
0
0
0
4
0
2
1
1
2
0
2
2
0
0
0
0
3
2
0
0
0
2
1
2
2
1
0
0
1
0
1
2
0
1
0
1
0
0
0
0
3
0
0
0
1
0
1
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
1
1
0
2
0
0
0
0
2
0
2
0
0
1
3
1
0
1
0
0
0
0
0
0
2
1
0
0
0
0
2
1
0
0
0
2
0
2
1
0
0
2
0
2
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
1
2
1
0
2
0
1
0
0
2
3
0
0
1
1
0
1
0
0
1
1
2
0
0
1
1
0
0
2
0
2
2
0
0
0
0
2
0
0
2
0
0
0
0
1
2
1
0
2
2
0
1
2
3
0
2
0
0
3
0
2
1
0
0
0
0
1
4
0
2
2
0
0
2
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
1
0
2
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
1
1
2
0
0
0
0
0
1
1
0
0
0
0
1
2
1
0
0
0
0
0
1
1
0
1
0
2
0
0
0
1
0
1
0
0
0
1
0
2
3
0
2
0
0
1
0
0
0
0
0
0
0
0
3
0
2
1
2
0
3
2
0
0
0
2
0
1
0
0
1
2
1
0
0
1
0
0
0
2
0
1
0
0
0
1
0
0
0
1
2
1
0
2
0
0
2
1
2
2
1
0
0
2
1
0
0
0
1
2
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
1
2
0
1
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
1
2
0
1
2
0
1
0
1
0
1
0
1
1
0
1
0
1
0
0
0
0
1
2
0
4
1
0
2
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
1
1
2
0
2
0
1
1
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
1
2
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
1
0
0
1
0
2
2
0
0
2
0
2
2
0
0
0
0
0
1
2
1
1
1
1
2
0
0
0
2
0
0
0
2
0
1
0
1
0
0
1
2
1
0
1
0
2
0
0
1
1
1
1
0
0
0
1
0
2
2
0
2
0
2
2
0
0
0
0
0
2
0
0
0
0
0
1
0
2
1
1
0
0
0
0
0
0
0
2
1
1
1
0
2
3
0
0
1
0
0
0
2
0
0
2
2
2
2
0
2
2
0
2
0
2
0
1
2
1
2
1
0
0
2
2
0
0
1
0
0
1
2
0
1
0
0
1
2
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
2
0
0
0
2
0
0
0
0
2
1
1
0
2
4
2
1
0
0
0
1
1
1
0
0
3
0
1
0
0
0
0
0
1
2
1
0
0
0
1
0
1
0
1
0
0
3
1
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
1
2
0
0
0
1
1
0
0
1
0
1
2
1
0
1
1
0
0
0
2
0
0
2
0
1
0
0
0
2
0
0
0
1
0
2
1
0
0
0
2
0
0
0
1
2
0
0
0
0
0
5
0
1
0
2
0
2
0
0
0
5
0
0
2
1
0
0
1
0
2
1
0
0
0
0
1
3
0
0
1
0
1
0
0
1
0
0
0
2
2
0
0
0
0
0
2
0
2
0
1
2
0
1
0
1
0
2
0
0
0
1
1
0
0
1
0
0
0
2
2
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
2
2
1
0
0
0
4
0
2
2
1
0
2
2
2
0
1
0
1
0
0
1
2
1
0
0
2
2
1
0
0
0
1
0
0
2
3
0
2
0
1
0
2
1
1
2
0
2
0
2
0
0
0
2
1
0
0
1
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
1
3
2
1
0
0
0
2
2
0
0
0
1
1
1
0
1
2
1
1
0
1
2
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
2
0
0
2
4
0
0
2
0
3
0
1
1
0
2
0
1
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
2
0
0
0
2
0
1
0
0
1
1
1
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
2
1
2
0
0
0
1
0
0
1
0
0
2
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
35
1
0
2
0
0
0
1
0
0
1
1
0
1
0
0
0
0
2
2
0
0
2
0
0
1
0
0
2
2
0
0
0
2
2
0
0
0
0
2
0
2
0
0
1
0
0
0
3
0
2
1
2
0
0
2
0
2
2
0
2
1
1
2
2
0
0
0
0
2
2
0
0
2
0
2
0
0
2
2
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
2
2
0
1
2
0
0
0
0
1
6
0
0
2
1
1
0
0
0
2
0
0
0
0
3
0
1
0
0
0
1
0
1
0
0
2
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
1
0
0
0
0
2
0
0
2
0
0
0
1
2
0
0
2
0
0
2
3
1
0
0
0
0
1
0
2
1
0
0
2
1
3
1
0
0
1
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
2
0
1
1
1
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
1
0
4
0
0
3
0
1
1
2
0
1
0
0
0
1
0
1
2
0
0
1
0
0
0
2
3
0
1
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
2
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
2
0
5
0
1
0
1
1
2
0
0
2
0
0
0
6
0
0
0
2
2
2
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
2
1
0
1
0
0
0
0
0
0
0
2
2
0
1
0
1
0
0
2
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
2
0
0
0
1
1
0
0
0
1
0
8
2
1
0
1
1
0
0
0
2
0
0
1
0
2
0
0
2
0
2
0
2
1
0
0
0
0
2
2
0
0
0
0
1
1
2
2
0
2
0
1
3
1
2
0
0
0
0
1
0
0
0
3
0
2
1
2
0
0
1
2
1
2
1
0
0
0
2
0
1
0
0
1
1
0
1
2
0
0
2
1
0
0
0
1
0
0
0
2
0
2
2
0
2
0
1
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
2
3
0
0
2
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
1
1
0
2
2
0
2
2
1
0
0
0
1
2
0
1
0
0
0
0
1
0
3
1
1
2
0
0
1
0
2
2
2
2
0
2
0
0
2
0
0
0
1
2
2
2
0
0
2
0
0
1
1
2
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
1
2
0
0
0
1
0
0
0
0
2
1
1
1
0
0
2
0
0
2
0
1
0
0
2
0
1
0
0
1
0
0
0
2
1
0
1
2
0
0
1
0
1
0
1
2
0
0
0
0
2
1
0
3
0
0
0
1
0
2
0
0
1
0
0
1
0
0
2
0
1
0
0
2
0
1
0
0
2
0
0
2
0
0
1
1
0
2
0
0
0
2
2
4
0
2
0
0
0
1
8
0
0
1
1
2
0
0
0
0
0
3
2
2
0
2
1
0
0
0
1
0
1
1
0
0
0
2
6
0
1
0
0
0
1
0
0
0
2
2
0
0
0
0
1
0
2
0
0
2
0
0
2
1
1
1
2
1
2
1
0
0
2
1
0
0
0
2
0
2
0
0
1
2
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
2
0
0
2
1
0
0
0
0
0
2
1
0
2
2
0
3
0
2
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
2
2
0
0
2
0
0
0
0
3
1
2
1
0
1
1
1
0
0
0
0
2
0
2
1
0
1
1
0
0
1
2
0
0
0
2
0
0
2
2
0
1
0
0
2
0
0
0
1
0
2
1
1
0
0
1
2
1
2
3
2
1
0
1
0
0
0
0
2
1
0
1
0
1
0
2
0
1
0
0
2
0
1
1
1
0
2
2
1
1
1
0
0
0
1
0
1
0
0
0
0
2
0
1
1
2
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
1
0
0
1
2
0
0
1
1
0
3
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
1
2
1
0
0
1
1
2
1
3
0
1
0
0
0
2
0
0
0
0
0
0
0
1
2
3
0
1
1
0
2
6
2
0
0
1
2
0
2
0
0
1
2
0
0
2
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
2
0
3
0
1
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
2
2
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
2
1
0
0
2
0
0
0
0
0
0
1
0
0
3
0
2
0
0
1
0
2
0
0
0
1
0
1
2
0
0
0
1
0
0
0
0
0
1
0
1
0
5
2
1
0
0
0
1
0
0
1
0
0
0
1
2
2
2
0
0
0
0
0
0
0
0
1
0
2
3
0
1
0
0
0
0
1
0
0
0
2
0
0
2
2
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
2
1
2
1
0
1
0
0
0
0
0
1
1
0
0
0
1
3
1
0
0
1
0
2
1
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
1
3
0
1
1
1
0
0
2
0
0
2
0
0
0
2
0
0
0
1
0
2
2
0
3
0
0
2
1
1
0
0
0
0
1
2
0
0
0
0
0
0
1
0
2
1
2
2
0
1
0
1
3
1
2
2
0
0
0
1
0
0
2
0
0
0
0
0
2
0
1
0
1
0
0
1
1
0
0
0
1
2
0
0
1
0
0
2
1
0
0
0
1
2
0
0
1
0
2
1
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
1
0
2
0
1
2
1
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
2
1
0
1
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
2
2
1
1
2
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
2
1
1
0
0
0
0
0
1
0
2
1
1
0
0
1
0
0
2
2
2
0
0
0
0
0
1
3
0
0
0
1
0
2
0
2
1
0
0
1
2
2
0
0
1
1
2
0
2
1
0
0
0
0
0
0
0
0
1
1
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
1
0
2
0
0
0
0
0
1
2
0
1
0
0
1
1
0
0
0
0
0
1
0
1
1
2
0
0
1
0
0
2
0
0
0
0
0
0
0
2
1
0
2
1
0
5
2
1
0
0
1
2
1
0
0
2
0
2
0
2
0
0
0
1
0
0
0
1
0
1
2
0
2
0
0
0
2
2
0
0
1
0
0
0
0
1
1
3
3
1
0
0
2
2
0
0
0
0
4
0
0
0
1
0
2
0
2
0
0
3
0
0
0
2
1
0
0
1
0
0
0
0
0
2
0
0
2
2
1
2
0
0
0
0
2
2
1
0
2
1
0
2
1
2
2
0
3
0
0
2
0
0
0
0
0
2
0
3
0
2
0
1
1
0
2
0
2
1
4
0
0
3
0
0
1
1
0
0
0
0
0
0
0
0
2
0
2
1
0
0
2
0
0
0
0
0
0
1
2
0
0
0
1
0
0
2
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
3
0
0
0
1
2
0
0
0
0
2
0
1
1
2
0
1
0
0
1
0
0
0
0
2
0
0
1
1
0
0
0
0
2
2
0
0
3
2
1
0
0
2
1
2
0
0
2
0
1
2
1
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
3
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
1
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
2
0
3
2
0
2
3
0
1
0
0
0
0
0
2
0
1
0
2
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
1
2
2
1
0
0
3
0
0
0
2
0
0
1
0
0
2
0
0
1
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
2
0
2
1
1
3
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
1
2
1
2
6
0
0
0
2
1
0
0
0
1
3
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
2
0
1
0
0
0
1
0
1
0
1
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
1
0
0
0
2
0
1
0
1
0
2
3
0
0
1
0
0
2
2
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
1
0
0
1
0
0
1
2
1
2
0
0
0
0
0
0
0
0
2
0
1
0
1
0
2
2
1
0
1
0
0
0
2
0
0
7
2
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
2
1
1
0
0
0
0
0
0
1
2
0
3
1
1
0
1
0
0
0
0
0
1
1
0
2
0
0
2
0
1
0
0
0
0
1
1
0
1
0
1
0
0
0
3
0
0
1
0
1
1
0
0
0
1
0
2
1
1
0
0
0
2
0
1
0
0
0
1
0
0
2
1
0
0
0
0
1
2
2
0
0
2
0
0
0
1
0
0
1
0
1
1
1
1
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
2
2
0
0
1
4
0
1
0
0
2
1
0
1
0
2
2
0
0
0
0
2
1
1
0
2
0
2
0
1
2
2
0
0
0
0
0
2
0
2
0
0
1
0
0
0
1
1
2
0
0
1
1
3
2
0
2
1
0
1
0
0
1
0
1
0
0
2
0
0
2
0
0
1
2
3
0
1
1
0
2
0
0
0
2
0
2
1
2
0
1
1
1
0
0
3
0
2
0
0
2
0
0
1
0
1
1
0
2
0
1
2
0
0
0
0
1
2
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
2
0
0
1
0
2
3
0
2
0
2
1
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
1
3
0
0
0
0
1
0
0
0
0
2
0
1
0
1
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
3
1
0
0
0
0
2
1
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
2
1
2
0
2
0
2
0
1
0
2
1
0
0
0
0
0
0
1
0
0
3
2
0
1
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
1
0
1
0
0
2
1
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
1
0
2
0
0
2
2
0
0
0
1
3
0
1
0
1
1
2
0
1
2
0
2
1
0
0
2
1
0
2
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
2
0
1
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
2
0
2
0
1
2
1
1
7
2
0
1
0
0
1
1
2
1
0
1
1
0
0
2
1
0
0
1
1
0
0
0
0
0
0
0
0
2
2
0
2
2
2
0
2
0
0
0
0
0
0
2
1
0
1
2
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
1
0
0
2
2
0
0
0
1
0
0
0
0
0
2
1
0
0
0
1
1
0
1
0
1
0
2
0
0
0
0
2
1
0
2
1
1
1
1
2
0
0
0
0
0
0
0
0
0
2
2
0
0
1
1
1
0
0
2
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
1
1
0
0
0
2
1
0
2
0
0
0
3
0
0
0
0
0
2
2
0
0
0
0
0
0
0
3
0
0
2
0
1
1
1
1
0
0
0
0
0
1
0
0
2
1
1
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
1
2
2
1
2
2
0
2
0
0
1
1
0
1
0
0
1
1
2
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
2
1
0
0
1
0
1
0
1
1
0
0
0
0
0
0
1
0
1
0
1
0
1
3
2
0
0
0
0
0
1
0
0
0
0
2
1
2
0
0
0
0
0
1
1
2
2
2
1
0
1
0
0
0
1
0
0
0
2
1
1
0
1
1
0
0
1
0
0
1
1
0
0
0
0
0
0
3
0
2
0
0
2
1
1
0
0
1
1
1
0
0
0
1
0
2
0
0
0
0
0
1
1
1
0
0
1
0
0
2
0
2
0
1
4
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
2
2
2
0
0
2
0
0
0
0
0
2
0
0
1
0
1
0
0
1
1
0
0
2
0
0
0
0
1
2
0
1
1
1
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
1
0
2
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
2
1
0
0
1
0
0
0
0
0
1
2
0
1
2
1
2
0
1
1
0
0
0
1
2
1
2
0
0
0
0
0
1
0
0
1
2
1
2
0
0
0
0
0
2
0
0
0
1
0
0
2
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
2
2
2
0
0
1
0
1
0
1
0
2
0
0
1
1
1
0
1
0
0
1
0
0
1
1
2
2
0
2
0
0
0
0
1
2
1
0
1
1
0
5
0
0
0
0
2
0
2
0
0
1
0
1
0
1
1
0
2
0
0
0
1
0
1
0
0
2
0
0
0
2
0
0
0
1
0
0
1
1
0
5
2
3
0
0
1
0
0
2
0
2
0
0
0
1
2
0
0
1
0
0
0
1
0
0
3
0
0
1
0
2
3
3
0
0
1
0
0
0
2
1
0
0
2
0
2
2
0
0
0
0
2
0
2
0
0
2
0
1
0
0
0
1
0
0
0
0
3
2
2
0
0
1
0
1
2
3
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
3
1
0
1
1
0
0
0
0
0
0
3
1
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
1
0
1
0
0
0
1
0
1
1
0
0
2
1
1
3
1
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
1
1
1
1
1
0
0
2
0
0
2
2
3
0
1
0
0
2
1
1
0
0
1
2
3
2
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
3
1
0
0
0
3
1
0
0
0
0
1
1
1
0
2
1
1
0
0
1
1
0
2
0
3
0
0
0
0
0
0
0
2
0
1
2
0
0
0
1
0
0
0
2
2
0
0
2
0
2
0
2
0
0
2
0
0
0
1
0
2
1
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
2
2
1
1
2
0
0
0
0
0
0
0
1
2
0
2
1
0
0
1
0
0
0
0
0
1
2
0
0
2
1
0
2
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
2
2
0
0
0
1
2
2
2
1
0
1
0
2
0
0
0
0
0
1
1
0
6
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
1
1
2
0
2
0
0
1
0
0
0
2
1
1
1
0
0
0
0
0
2
0
2
1
0
0
0
1
1
3
3
2
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
3
1
0
1
0
2
0
3
1
3
2
0
1
0
2
0
0
0
2
2
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
3
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
3
0
1
0
1
0
1
1
0
0
0
0
2
2
0
1
0
0
0
0
0
0
3
0
2
0
0
0
0
2
2
2
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
2
0
0
0
0
0
3
0
0
1
2
1
2
0
0
0
0
1
2
0
0
0
0
0
4
0
0
1
1
0
2
0
0
0
1
0
0
0
0
2
0
1
1
0
0
0
2
2
1
2
1
1
0
0
1
0
0
1
0
2
1
0
1
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
1
0
5
0
2
0
2
0
0
0
0
0
2
1
0
1
1
1
1
0
0
0
1
0
0
0
0
2
0
0
1
0
0
1
3
0
1
2
0
2
1
0
0
13
0
2
0
0
2
0
1
1
0
0
0
0
1
0
0
2
2
0
2
1
0
0
3
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
2
1
0
0
2
0
0
2
0
0
1
1
0
2
0
0
1
0
1
0
0
1
1
1
1
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
2
1
0
1
1
0
1
7
1
2
2
0
2
0
0
2
1
0
0
2
0
0
1
4
0
0
0
0
2
0
0
0
0
0
0
2
4
1
1
2
0
0
1
0
0
2
2
2
0
1
0
0
0
2
1
0
0
0
0
1
0
3
2
0
0
0
2
0
0
1
0
0
2
0
0
0
2
0
2
2
1
0
0
1
0
1
1
1
0
0
1
0
0
2
0
1
3
0
0
2
0
0
0
2
0
2
2
0
2
1
2
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
2
1
0
1
0
1
0
2
0
0
0
0
0
0
2
0
0
2
2
2
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
2
2
2
1
0
0
2
2
0
0
0
0
0
2
0
0
1
0
1
3
0
1
0
1
1
1
1
0
2
0
0
2
0
0
0
1
3
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
2
0
2
1
0
0
0
0
1
2
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
1
1
2
0
0
0
0
2
1
2
0
0
2
1
1
0
0
0
2
0
0
0
0
0
2
2
0
2
2
0
1
0
2
1
1
0
0
0
0
0
3
0
0
1
0
0
1
0
1
0
0
2
0
0
1
1
1
0
1
2
2
1
2
1
3
0
1
2
1
0
0
0
0
2
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
3
0
1
0
1
2
0
2
0
2
1
0
2
0
1
0
0
1
1
0
0
1
0
2
0
2
0
0
2
0
0
2
1
0
0
0
0
0
0
2
0
2
2
1
0
1
7
0
2
0
0
2
0
0
1
0
2
1
0
0
1
0
0
2
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
2
1
0
0
0
1
2
0
0
0
1
2
0
1
0
0
1
0
0
1
0
1
0
1
2
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
2
0
0
0
1
2
0
1
0
0
0
0
0
1
0
1
0
1
2
2
0
2
2
0
2
0
1
0
0
0
1
0
0
2
0
0
0
1
0
0
0
1
0
0
2
1
1
0
0
0
0
0
0
2
0
2
0
0
1
1
1
0
1
0
1
0
2
0
0
2
0
2
0
2
2
1
0
0
1
3
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
2
0
2
0
1
0
0
0
2
0
1
1
0
0
0
0
0
1
2
1
0
0
0
1
0
0
2
3
1
0
0
1
0
2
0
0
1
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
2
1
2
1
0
0
0
0
1
2
1
2
0
2
0
1
0
0
1
0
0
0
1
1
0
1
0
2
0
0
0
0
1
2
2
0
1
0
0
2
2
2
0
0
0
1
0
0
0
0
1
1
0
0
2
1
0
2
0
0
0
2
1
0
1
1
1
1
0
1
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
1
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
3
1
0
0
1
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
4
2
0
0
2
0
2
1
0
4
0
0
0
0
1
0
1
1
1
0
2
0
0
1
2
0
0
0
0
1
2
0
0
0
2
0
0
1
0
1
0
0
1
0
0
0
0
1
1
2
2
2
2
0
2
0
2
2
0
0
2
2
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
2
0
2
1
0
0
0
1
0
0
1
3
0
0
0
0
0
0
0
0
0
1
1
0
2
1
0
0
1
2
2
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
1
2
0
0
0
2
2
2
2
0
0
0
1
0
0
1
2
0
2
2
0
2
2
0
1
2
3
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
3
2
2
0
0
2
0
1
2
2
3
0
0
0
0
0
2
0
0
1
0
0
4
0
0
1
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
1
0
0
1
0
0
2
0
1
1
1
0
1
0
0
1
0
0
2
0
1
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
1
0
0
2
1
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
2
2
2
0
0
1
1
1
0
0
0
2
0
0
0
0
1
0
0
0
2
2
2
2
0
0
0
2
0
0
1
0
0
0
2
0
1
1
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
1
2
0
3
0
2
0
1
0
0
1
0
2
0
2
0
1
0
0
0
0
1
0
0
2
0
0
0
2
0
2
1
2
0
0
1
0
0
1
1
0
2
0
1
2
0
1
0
2
0
0
0
0
0
1
0
0
1
0
0
4
1
0
0
1
0
0
0
0
0
1
0
0
1
2
0
0
2
0
0
1
1
0
1
0
0
0
0
3
1
0
0
0
1
0
0
2
0
2
0
1
0
0
1
1
0
0
2
0
0
1
0
0
1
2
0
0
2
0
0
1
0
0
1
2
0
0
0
0
1
1
1
0
0
3
0
0
1
0
2
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
1
1
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
1
1
0
0
3
2
1
0
0
0
2
0
0
0
1
0
1
1
2
0
0
0
0
0
0
0
0
2
0
0
1
2
2
2
0
0
1
2
0
0
2
3
0
1
0
2
1
0
0
2
2
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
2
1
0
2
0
0
0
0
1
0
0
2
1
0
1
0
0
2
0
0
0
0
1
0
1
0
1
0
2
0
1
0
1
0
0
1
2
2
0
9
1
0
2
0
0
1
1
2
0
0
1
0
0
2
0
0
0
0
0
4
0
0
0
1
0
0
1
0
0
2
0
0
2
2
2
0
1
2
0
0
0
1
0
1
1
0
1
0
0
0
0
1
3
0
0
0
2
0
0
0
0
2
1
0
2
0
0
0
0
0
2
0
1
0
0
0
1
0
1
0
4
2
0
1
2
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
2
1
0
2
1
0
1
0
0
1
1
0
1
2
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
2
0
1
0
2
2
0
1
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
2
0
1
0
0
0
0
2
0
1
0
0
2
0
0
0
0
2
1
1
1
0
0
2
0
2
0
0
1
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
1
2
0
2
1
1
0
1
0
1
1
2
0
0
0
2
0
0
2
2
0
0
2
0
0
0
0
2
1
0
1
0
0
2
0
0
0
0
2
0
2
0
1
1
1
0
1
2
2
2
1
0
0
1
4
2
0
1
2
0
0
4
0
1
6
0
1
0
0
0
1
0
0
2
0
0
3
0
2
0
2
2
2
0
0
0
0
0
0
0
1
0
0
1
1
1
3
2
0
0
1
2
1
1
0
0
0
2
2
0
0
0
0
0
2
1
6
0
0
2
0
0
0
0
0
0
2
0
2
0
0
1
0
5
1
0
0
0
0
1
1
0
0
0
0
2
0
2
0
4
1
0
0
0
1
0
0
0
2
1
0
0
1
4
2
0
1
1
1
1
0
2
2
2
2
2
0
2
0
1
0
0
0
1
3
2
0
1
0
0
0
1
0
1
0
2
0
0
1
0
0
1
0
2
0
1
0
2
1
2
0
0
0
0
2
1
0
2
0
0
0
2
0
0
1
0
2
2
0
2
2
1
3
0
0
0
0
0
0
0
0
0
2
2
1
2
2
2
2
1
0
0
2
0
0
0
3
0
0
0
2
0
2
0
0
1
0
0
1
0
1
0
0
0
2
0
2
1
1
1
0
0
0
0
0
1
0
0
2
1
0
0
0
1
0
1
4
1
0
1
1
0
1
1
0
0
0
1
1
0
0
1
0
0
2
2
0
0
0
0
2
1
0
2
0
0
1
2
2
1
0
2
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
2
3
1
0
1
1
1
2
1
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
2
0
0
0
2
1
0
1
0
1
0
1
1
1
0
2
0
0
0
1
0
0
2
1
0
1
1
0
0
0
2
0
0
0
0
0
1
0
2
6
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
2
0
0
1
1
1
1
0
2
0
1
1
1
0
2
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
2
1
2
0
2
1
2
0
1
0
0
1
0
0
0
0
0
0
2
2
2
0
0
0
0
1
0
0
2
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
1
0
2
0
0
0
5
1
0
0
0
1
1
2
0
2
0
2
2
0
0
0
1
0
1
0
2
0
1
0
0
0
0
2
1
2
0
2
1
1
0
0
2
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
3
2
0
1
0
1
0
0
2
2
0
0
1
0
1
0
0
2
1
1
9
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
2
0
0
1
0
2
3
1
2
0
1
0
1
0
0
1
2
0
1
0
0
0
1
0
0
0
2
0
0
0
0
1
1
0
2
3
0
1
1
1
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
1
1
0
0
0
0
0
2
2
0
0
3
0
1
2
0
1
1
2
0
0
0
0
0
1
0
0
2
2
0
0
0
0
1
0
0
1
2
0
0
2
2
2
0
0
0
0
2
2
0
0
2
0
0
1
2
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
2
2
0
2
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
1
1
0
0
0
0
1
0
0
2
0
1
2
0
1
0
0
0
0
0
0
0
0
0
1
2
1
2
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
1
2
0
0
2
2
2
2
2
0
2
1
1
0
2
0
0
0
0
0
0
0
0
2
2
1
0
2
1
0
2
2
1
0
0
0
0
0
0
0
2
0
2
1
1
0
2
0
2
0
0
0
1
2
0
0
0
1
0
1
1
2
2
1
0
1
1
1
1
0
0
0
1
0
0
0
0
1
0
0
0
1
1
2
1
0
1
1
1
0
2
0
0
0
2
0
2
1
0
1
0
3
0
0
0
2
1
0
0
0
2
0
0
1
2
0
0
1
2
0
3
0
0
0
0
1
1
0
0
0
1
0
0
2
2
0
0
1
2
2
0
0
0
1
0
1
1
0
0
0
0
2
2
3
0
0
1
1
1
0
2
3
0
0
1
0
0
1
2
0
2
2
0
1
1
0
1
0
3
0
0
0
0
1
0
1
2
0
0
0
1
0
0
0
0
0
2
1
0
4
2
0
0
0
0
0
3
0
2
1
0
1
0
0
0
2
2
0
2
0
0
6
0
0
1
1
0
0
1
1
0
0
2
0
0
1
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
1
2
1
2
0
1
0
1
0
0
1
1
0
1
2
0
2
0
1
0
0
0
1
2
0
0
0
1
2
0
1
0
1
0
0
2
0
1
0
2
0
2
0
1
0
0
0
2
0
0
0
0
1
0
2
0
0
0
1
2
0
0
0
0
0
0
1
1
2
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
2
0
1
0
1
1
0
0
2
1
1
0
0
2
0
1
0
0
0
2
1
0
0
2
2
0
0
2
1
0
0
0
2
0
0
1
0
0
4
2
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
4
0
0
0
0
0
0
2
0
0
2
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
2
0
0
1
0
2
0
1
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
1
0
0
1
0
2
2
2
2
2
2
0
1
0
0
1
0
0
1
0
0
0
0
2
0
1
2
0
0
0
0
0
0
1
2
0
1
1
2
0
2
0
0
0
0
0
1
1
2
0
2
0
3
0
0
0
1
0
1
0
3
0
0
0
0
0
2
0
1
0
1
0
2
0
2
0
0
0
0
1
0
0
4
2
2
1
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
1
1
1
0
0
0
0
2
0
3
2
1
0
2
2
0
1
0
1
1
2
0
0
0
1
0
0
2
0
1
0
1
1
0
0
2
0
0
1
2
0
2
1
3
0
0
0
0
3
0
1
0
0
1
0
1
0
1
2
1
0
2
0
1
0
1
0
2
2
0
1
2
0
0
0
2
2
0
0
0
0
0
0
2
2
0
0
0
0
1
4
4
2
1
1
0
0
0
2
0
2
0
0
0
2
2
1
0
0
0
1
1
0
0
0
0
2
3
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
1
1
0
0
1
0
1
0
0
1
1
0
0
0
2
0
2
1
0
2
0
2
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
3
0
3
2
2
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
1
0
0
2
2
0
0
0
2
0
0
0
0
2
0
3
2
0
0
0
1
0
2
1
0
0
2
3
0
2
0
0
0
0
0
0
0
2
2
0
2
0
1
2
0
0
0
0
0
1
0
0
0
2
2
2
0
0
0
1
2
0
0
0
0
4
1
0
1
1
1
2
0
0
0
1
0
1
0
0
2
4
0
1
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
1
1
0
0
0
0
1
1
0
0
0
0
0
1
2
0
3
0
0
6
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
2
0
0
0
2
0
2
1
0
2
2
1
0
1
2
2
1
0
0
0
1
0
0
1
0
0
3
1
0
0
0
0
0
0
2
1
2
1
2
1
1
0
2
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
3
0
2
0
2
2
0
0
1
0
4
0
1
2
0
1
1
0
1
0
0
1
0
1
0
1
0
1
2
2
0
1
1
0
0
1
0
0
0
2
0
0
0
0
1
1
0
0
1
0
1
0
1
0
1
0
0
2
1
0
1
0
2
1
2
0
0
1
2
1
0
0
0
2
0
1
0
0
0
0
2
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
1
2
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
2
0
1
1
0
1
2
0
0
1
2
0
0
1
1
2
0
1
0
0
1
0
1
0
0
0
0
0
2
2
0
2
1
2
1
1
0
0
0
0
0
0
1
0
0
0
2
1
0
0
1
1
4
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
2
0
2
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
2
0
0
1
0
1
0
1
0
0
0
0
1
2
0
1
4
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
1
2
0
0
0
0
0
1
1
0
0
6
1
0
0
0
0
1
1
0
0
1
1
0
0
1
2
1
0
2
1
1
0
0
2
0
0
0
1
0
1
0
0
0
1
2
0
0
1
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
2
0
3
0
0
0
1
0
2
0
1
0
2
2
0
0
2
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
1
4
2
0
0
0
1
0
0
0
2
1
0
2
0
1
0
1
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
1
2
1
0
0
2
2
2
0
2
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
2
0
0
0
0
2
0
0
0
2
1
1
0
0
0
0
2
3
1
1
0
1
0
0
0
2
1
0
0
0
0
0
0
0
3
0
0
2
1
3
4
1
0
1
0
0
1
0
0
0
0
0
0
0
2
2
0
0
1
0
1
0
0
1
2
0
0
0
2
0
1
1
1
2
0
1
0
0
2
2
0
0
0
2
0
0
2
2
2
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
2
1
0
4
0
0
0
0
0
2
0
0
0
3
1
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
2
2
1
0
0
1
1
0
2
2
0
0
0
0
0
0
0
1
2
1
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
1
1
0
3
0
0
0
1
0
0
0
2
0
0
0
2
1
2
1
0
2
0
0
1
0
1
2
0
0
1
0
1
0
1
1
0
0
0
2
0
0
2
2
0
0
1
0
1
0
0
0
1
0
1
0
0
1
0
0
0
3
1
2
0
0
0
0
2
1
0
0
1
2
1
0
4
0
2
0
2
1
0
0
0
3
0
0
2
2
0
0
0
0
1
0
1
0
0
2
0
0
2
1
2
2
0
1
2
3
0
0
0
0
1
1
2
0
0
0
0
0
0
0
2
2
0
2
2
2
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
1
1
0
0
1
1
0
2
1
0
1
0
0
1
0
0
1
1
3
1
0
2
0
2
3
0
1
2
1
0
0
1
0
0
2
2
0
1
2
0
0
0
0
1
0
0
0
2
1
0
0
0
1
0
1
0
0
0
0
0
2
1
0
3
0
2
1
0
0
2
2
0
2
1
0
1
0
0
2
0
0
1
2
1
0
2
1
0
0
0
1
3
0
1
2
1
2
0
1
1
2
2
0
4
1
2
2
0
1
0
0
0
0
0
0
2
1
1
0
0
0
0
1
0
0
0
0
1
0
0
1
1
2
2
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
1
2
3
0
0
1
0
1
0
1
3
0
0
0
2
0
1
0
0
0
0
0
0
0
3
0
1
0
0
2
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
1
1
0
0
1
1
0
2
0
0
1
0
1
1
2
2
0
2
0
1
2
0
2
2
0
1
0
1
2
1
0
0
1
1
1
0
1
0
2
0
0
2
0
0
0
0
0
2
0
2
0
3
0
2
0
0
0
0
2
0
0
0
0
0
2
0
2
1
0
1
0
1
1
0
1
0
1
0
0
0
1
0
1
0
0
0
0
2
0
3
0
0
0
0
1
1
2
0
0
1
1
0
1
0
0
1
0
0
0
1
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
1
2
1
0
0
0
0
1
2
1
3
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
2
0
0
2
0
0
0
0
0
2
0
0
0
1
0
1
0
2
0
0
0
0
0
0
2
1
1
0
0
0
0
1
0
2
0
0
1
1
0
0
3
0
0
0
0
2
2
0
1
0
0
1
0
0
2
0
2
2
0
0
1
0
2
0
0
2
0
0
0
2
2
0
0
1
0
0
0
2
0
0
0
0
1
4
0
0
1
0
0
0
0
0
0
1
2
2
2
0
0
0
1
1
0
0
3
0
0
1
1
0
0
0
2
0
0
2
2
0
2
0
0
2
2
0
0
0
1
0
3
0
0
0
0
0
0
1
0
0
0
2
1
3
0
0
1
0
0
1
2
1
0
0
1
1
0
0
0
1
0
0
0
0
0
1
2
1
0
0
0
0
4
0
0
2
0
0
1
0
2
2
1
3
0
0
0
2
2
1
0
2
0
0
1
1
0
2
0
1
0
2
0
0
1
0
0
0
0
3
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
2
1
0
0
0
2
0
0
1
1
0
0
0
1
2
0
0
0
0
2
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
2
1
0
0
0
0
0
1
0
1
0
1
1
1
0
2
2
0
0
1
0
0
0
0
3
0
0
0
1
0
1
2
2
0
0
1
1
2
1
0
0
0
0
2
2
1
1
0
0
0
2
1
0
0
0
2
0
2
0
1
0
0
1
1
0
0
0
0
0
0
0
0
2
2
2
2
0
0
0
0
2
0
3
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
2
2
3
1
1
1
2
0
0
0
0
0
1
1
0
1
0
0
1
0
2
0
0
0
0
0
2
2
2
2
0
2
0
0
1
0
2
1
1
1
0
0
0
0
0
1
0
2
1
2
2
0
1
1
0
1
2
0
0
0
1
0
0
0
3
6
1
1
0
1
2
2
0
1
0
2
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
1
0
0
0
2
0
1
0
2
1
0
0
0
1
3
0
0
0
1
0
4
1
0
0
0
2
0
4
0
0
0
0
0
1
1
0
0
0
0
2
1
0
1
0
0
0
0
2
0
0
2
2
0
1
0
0
1
0
0
0
2
0
2
2
2
1
0
0
0
1
0
2
2
0
1
0
2
1
0
2
0
2
0
2
2
0
1
1
1
0
1
1
0
0
0
2
2
2
1
2
3
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
2
0
0
0
0
1
0
2
0
2
1
2
0
0
0
3
0
0
1
0
0
0
2
2
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
2
0
0
1
1
0
2
0
0
1
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
2
0
2
0
1
0
0
1
0
2
2
1
1
0
1
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
3
2
0
2
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
1
1
1
0
0
0
1
2
1
0
0
1
0
1
0
1
0
0
0
0
0
2
2
0
6
1
3
0
1
0
0
0
0
2
3
1
0
1
0
2
0
1
2
1
0
0
0
1
0
0
0
0
0
6
1
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
1
2
1
0
2
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
2
3
0
2
1
0
0
0
1
1
0
0
0
2
0
1
0
1
0
0
0
2
2
0
0
0
2
0
0
2
0
1
0
3
0
0
1
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
1
0
0
0
1
0
0
0
1
2
2
0
0
0
2
1
0
1
2
2
1
2
0
1
0
0
0
0
0
1
0
1
0
1
0
2
0
2
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
3
1
2
1
1
0
0
1
2
4
0
0
0
2
1
0
0
0
1
2
0
0
1
0
0
1
0
0
2
0
0
0
0
1
2
0
0
1
2
0
0
1
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
1
0
0
4
1
0
0
2
3
0
0
0
1
2
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
2
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
1
1
0
1
1
1
0
0
0
0
1
1
0
1
0
1
0
0
0
0
1
1
0
0
2
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
1
0
3
0
0
0
2
0
0
2
0
0
1
0
2
2
2
2
0
0
2
0
2
0
0
0
2
0
0
3
0
1
0
2
0
0
0
0
0
2
0
0
2
2
0
1
0
0
0
0
2
1
3
0
2
1
3
2
2
0
2
0
2
0
0
0
0
0
3
0
2
0
0
0
2
0
0
0
2
0
2
0
0
1
0
0
0
0
1
2
0
2
0
1
0
0
0
0
2
1
0
2
0
2
0
3
3
0
0
0
0
2
0
0
0
2
0
0
2
1
1
0
0
0
2
0
0
0
3
0
1
0
1
0
1
0
1
0
2
0
1
0
2
0
0
0
2
1
0
0
0
0
1
2
1
0
1
1
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
1
0
2
0
2
1
0
1
0
0
0
0
1
1
1
1
1
2
0
2
0
0
0
0
1
0
0
0
2
2
0
0
0
0
2
0
0
0
2
0
2
0
0
2
0
0
0
0
0
1
0
1
1
0
0
0
0
2
2
1
1
2
0
0
1
0
0
1
1
0
2
0
0
0
0
0
1
2
0
2
0
0
1
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
1
0
1
0
0
0
0
1
0
0
0
2
0
0
0
4
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
2
0
2
0
0
2
0
1
1
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
1
0
0
2
0
0
0
0
1
0
1
2
1
2
0
0
0
0
2
2
2
1
0
0
0
1
0
0
0
0
1
0
1
1
1
1
1
1
2
0
0
0
0
2
0
1
1
0
0
0
0
1
2
1
0
0
2
1
2
0
1
1
0
0
2
2
0
0
0
0
0
0
1
0
1
2
1
0
0
0
0
1
2
2
0
1
0
0
0
2
2
1
0
1
1
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
2
0
1
0
1
2
0
0
2
2
0
0
1
1
0
0
3
1
1
0
2
1
0
0
1
1
2
1
0
5
0
2
0
1
0
0
1
1
1
0
2
0
0
0
1
3
0
1
1
1
4
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
2
0
2
0
1
0
0
2
0
2
0
0
2
0
0
1
0
0
0
1
0
0
0
0
1
2
0
0
2
2
0
1
1
0
2
2
1
2
0
0
0
2
0
1
3
0
0
1
2
0
2
1
0
1
0
0
0
1
1
0
1
0
1
0
2
0
2
0
0
0
0
0
0
1
0
0
0
1
2
0
1
3
0
1
0
1
2
0
0
0
1
2
0
3
1
0
0
0
2
0
1
0
0
0
2
1
0
0
1
0
2
0
1
0
0
0
0
4
1
0
1
0
1
0
0
0
0
2
2
2
0
0
1
0
1
1
1
0
0
0
1
1
1
1
0
0
2
0
0
0
0
1
0
0
0
1
1
2
0
0
0
0
0
0
0
0
1
0
2
1
1
0
1
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
1
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
1
1
1
1
0
0
2
1
0
0
0
2
0
0
0
1
1
2
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
1
0
1
0
2
1
1
0
2
1
0
2
0
0
2
0
1
0
0
2
1
0
1
0
0
0
0
1
0
0
0
2
0
1
0
0
0
1
1
1
1
2
0
1
0
0
0
0
0
1
2
1
2
1
0
0
2
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
2
1
1
2
0
0
0
1
0
0
0
0
1
1
0
1
2
0
1
1
1
0
0
1
0
0
0
0
0
0
1
0
2
0
0
1
0
1
1
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
1
0
0
0
0
2
2
0
0
1
0
0
0
3
0
1
0
0
0
0
1
0
0
2
2
0
0
1
0
0
1
0
1
0
0
1
2
0
0
0
0
2
0
0
0
1
2
2
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
2
2
2
0
0
0
0
1
0
1
2
0
0
2
0
2
2
0
0
0
0
2
1
0
0
0
1
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
1
2
0
1
0
0
0
2
2
0
1
2
2
2
1
1
0
2
0
1
1
0
1
2
0
1
0
1
2
2
1
1
0
2
0
0
2
2
0
1
1
0
0
2
0
3
2
2
1
2
0
2
1
0
2
1
1
0
0
0
11
1
0
0
2
0
2
0
1
0
1
0
0
0
1
0
2
1
1
0
0
1
1
0
1
0
0
2
1
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
3
2
8
2
1
1
0
2
1
0
1
0
0
0
2
0
0
0
0
0
0
1
1
0
0
2
1
0
1
0
0
1
5
1
2
2
0
0
2
1
2
0
2
2
0
1
0
0
2
0
1
1
2
1
0
1
0
2
0
0
1
0
2
1
0
0
1
2
0
1
0
1
0
2
0
0
2
2
1
0
0
1
0
0
2
1
0
2
0
1
0
0
0
0
1
0
2
1
2
1
0
0
2
2
2
0
2
0
1
3
0
2
0
0
0
0
0
1
1
1
0
2
1
2
0
0
1
0
0
1
2
0
3
0
0
0
0
0
0
1
0
0
2
0
0
0
2
2
0
2
0
0
0
0
0
0
2
0
3
0
0
0
2
2
1
0
0
1
0
0
0
0
0
2
0
0
1
5
2
0
0
0
3
0
1
0
2
0
0
1
0
0
0
0
0
0
1
4
0
0
2
0
2
0
0
2
0
3
0
0
0
0
2
1
0
0
1
0
0
0
0
1
0
0
2
1
0
1
0
1
0
0
1
1
0
0
0
0
2
0
1
0
1
0
0
2
0
0
0
0
1
2
2
2
0
0
0
2
0
1
0
0
2
0
0
2
2
1
0
0
1
1
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
3
2
0
2
2
1
0
0
0
1
2
0
0
0
0
0
0
2
0
1
2
1
0
1
2
2
1
0
0
1
0
0
1
2
0
1
0
1
4
1
2
0
1
2
0
1
0
0
0
1
1
0
2
0
0
1
0
0
0
0
2
1
2
0
0
0
1
1
1
0
0
0
0
2
2
1
0
0
0
0
2
0
0
0
0
2
2
1
2
1
0
0
0
1
2
0
2
0
0
0
0
0
0
0
2
0
1
1
1
0
1
1
0
1
1
0
0
0
0
1
2
1
2
2
0
0
0
0
0
2
0
1
0
1
0
0
0
0
2
0
0
4
0
0
1
1
0
1
0
1
2
1
1
0
0
0
0
1
0
2
0
0
0
2
1
0
1
1
3
0
0
0
0
1
1
2
2
2
0
0
0
0
1
1
2
0
0
2
0
0
1
1
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
2
2
2
2
1
0
0
1
0
2
0
0
0
2
0
1
2
1
2
2
1
0
0
1
0
0
0
0
0
0
2
2
0
2
0
1
0
0
1
0
2
0
0
0
2
2
0
0
1
1
0
0
1
1
0
0
0
0
2
0
0
0
0
4
0
3
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
1
1
0
2
2
0
1
2
1
0
1
0
0
0
1
0
0
1
1
0
0
0
0
1
0
2
0
0
0
0
2
1
0
2
1
1
0
0
0
0
0
0
3
0
2
0
0
1
0
1
0
0
3
1
0
0
2
0
1
1
1
1
0
0
0
0
0
1
1
0
0
1
2
2
2
0
0
0
0
1
0
1
1
2
1
2
0
5
2
0
0
0
0
1
0
2
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
1
1
0
2
2
0
0
0
0
0
0
1
0
2
2
0
0
1
0
0
4
1
2
2
0
0
0
1
0
2
2
2
0
0
2
0
1
1
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
2
1
2
0
0
0
2
0
0
1
1
0
1
0
1
0
0
0
1
2
0
0
0
2
0
0
1
1
1
0
2
0
0
0
0
0
0
1
2
1
0
2
0
0
0
1
2
0
0
0
1
2
0
0
2
0
1
1
0
1
1
0
0
0
2
0
1
0
1
0
1
1
0
0
0
0
0
2
0
0
0
0
2
1
2
2
0
0
0
0
1
0
0
0
1
0
2
2
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
2
1
1
0
0
0
0
2
0
0
0
1
0
0
0
2
3
0
0
2
0
0
0
0
1
1
2
2
1
0
1
1
1
0
0
1
0
1
1
0
0
0
3
0
2
2
2
0
0
0
0
1
0
2
0
0
1
0
0
0
0
2
0
0
0
0
1
0
3
0
0
2
0
0
0
0
0
1
1
0
0
0
0
2
2
1
0
1
2
2
0
0
2
0
1
0
0
2
0
2
2
0
0
0
2
0
0
1
0
0
1
1
0
1
0
0
2
0
2
1
0
0
0
0
0
0
2
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
1
1
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
2
2
2
0
0
1
2
0
2
0
0
1
0
0
0
1
2
0
0
2
0
0
1
0
0
2
0
2
0
1
0
0
0
1
1
0
1
0
2
0
0
2
2
0
1
0
0
2
0
1
0
0
0
0
0
0
1
1
1
0
0
0
2
1
0
1
0
0
0
0
0
3
0
0
0
3
1
0
2
0
2
1
0
0
0
9
1
2
0
0
2
1
0
0
0
1
0
0
0
1
1
2
0
0
1
0
0
0
2
0
2
1
1
1
2
1
0
0
1
0
2
0
0
2
0
1
2
0
0
1
0
0
0
0
6
0
2
1
0
1
0
0
2
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
2
1
2
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
2
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
2
1
1
1
0
0
0
0
0
1
0
0
0
2
1
1
0
0
0
0
1
0
0
2
0
2
0
0
2
1
0
0
2
1
0
2
1
0
0
0
0
2
0
0
2
0
1
0
0
0
2
0
0
2
0
0
2
1
1
0
0
0
0
0
0
1
1
0
2
0
0
0
1
2
2
0
0
0
1
0
0
1
0
2
0
0
0
0
2
2
1
0
0
0
2
2
0
0
2
1
1
1
0
0
2
0
0
0
2
3
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
3
2
0
2
2
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
2
1
1
1
1
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
1
0
0
1
0
0
1
0
0
1
0
2
0
0
1
0
3
3
0
0
1
2
0
1
0
0
0
0
1
0
2
1
1
0
0
1
1
0
1
2
2
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
4
1
0
0
2
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
5
1
0
1
0
0
0
0
0
0
4
2
0
0
1
0
1
0
0
0
0
2
3
0
0
1
3
0
0
0
0
1
0
0
1
2
0
1
0
0
0
2
0
0
1
2
0
0
1
2
0
0
0
0
2
4
0
0
0
0
1
0
0
2
0
0
0
0
1
0
2
0
1
0
2
0
2
0
1
0
1
0
2
2
0
0
2
4
0
2
2
2
0
0
2
0
0
0
0
2
0
0
1
0
0
2
0
2
0
2
2
2
1
0
2
1
1
2
0
0
1
0
0
0
0
0
0
1
4
0
0
0
0
1
1
0
0
0
0
1
1
0
1
0
0
1
2
0
1
0
0
0
0
0
0
0
1
0
0
0
3
0
0
1
0
2
0
0
0
1
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
1
0
0
2
0
0
0
0
0
2
1
1
1
0
0
0
0
0
0
1
0
2
2
2
3
0
0
2
0
1
0
0
2
0
0
0
0
0
0
1
2
1
1
0
0
3
1
0
2
1
0
0
2
1
0
3
3
0
0
3
4
1
0
0
0
2
2
0
1
1
0
2
0
0
0
0
1
1
0
0
0
1
0
3
1
0
1
0
1
1
0
0
0
0
1
0
0
2
1
10
2
0
0
2
0
1
0
2
0
2
2
0
0
2
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
2
2
0
1
0
0
0
1
0
0
0
1
0
2
3
0
0
0
2
2
0
2
0
1
0
0
0
0
0
0
0
2
3
0
3
1
1
1
2
0
0
0
1
0
0
0
0
0
1
1
0
1
0
1
0
3
1
0
1
0
0
2
0
0
0
2
0
2
0
1
9
1
0
1
0
0
1
1
0
0
2
0
2
2
0
1
0
1
1
0
0
2
0
0
1
0
0
0
1
2
0
4
1
1
2
0
2
0
0
0
0
1
1
1
0
2
2
0
2
0
0
1
1
0
1
2
1
1
0
1
0
0
0
0
4
2
1
0
0
0
0
0
0
1
0
1
2
1
1
1
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
2
1
0
0
1
0
0
2
2
0
0
1
1
0
1
0
2
1
2
0
1
0
0
0
0
2
1
0
1
1
0
0
2
0
0
2
0
0
2
0
1
0
1
0
1
1
1
0
0
1
0
1
1
0
1
0
3
0
0
2
0
0
3
0
1
1
0
2
0
1
0
0
2
0
0
0
0
2
0
2
2
0
0
0
1
2
6
1
0
1
0
1
0
1
0
0
0
2
1
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
2
0
0
1
0
1
1
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
1
0
0
1
0
1
0
0
1
2
0
1
0
0
2
0
0
2
2
1
1
0
0
0
2
2
0
2
2
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
3
0
3
1
1
0
0
2
2
0
0
0
2
0
1
0
0
2
1
2
0
0
0
2
2
0
0
1
0
0
2
0
0
0
2
2
1
2
0
0
0
0
2
2
0
0
0
2
0
1
0
2
2
3
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
3
3
0
0
0
0
1
1
0
0
1
0
0
1
0
1
2
2
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
1
0
0
3
0
1
0
1
1
0
2
1
0
2
1
0
3
1
0
0
0
0
2
1
1
2
0
0
2
2
0
2
0
1
0
0
2
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
2
0
1
2
0
1
0
1
0
2
0
2
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
2
2
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
2
2
0
0
0
2
1
2
0
1
2
1
1
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
2
0
1
0
0
0
0
1
0
0
2
0
0
1
2
1
0
0
0
2
0
0
2
0
0
0
1
0
0
2
0
1
3
0
0
1
1
0
0
0
1
0
0
2
0
1
1
0
1
0
0
0
0
3
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
1
2
0
1
2
0
0
0
2
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
2
0
1
0
0
0
2
2
2
1
0
0
2
0
0
1
0
0
1
0
0
0
1
0
2
0
1
0
2
0
0
1
0
0
0
0
1
0
0
2
0
1
3
0
0
0
0
2
0
0
0
2
0
2
0
0
2
2
1
3
0
1
0
0
2
3
0
0
0
2
0
2
0
1
1
2
1
1
0
1
1
0
1
0
0
0
0
0
4
1
0
0
2
0
0
0
0
0
0
0
1
0
1
1
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
2
1
1
0
1
0
0
0
0
0
0
2
2
1
0
1
2
0
0
3
0
0
1
2
0
0
0
1
0
0
0
1
0
1
0
0
2
4
0
2
0
2
0
2
0
2
1
0
2
4
0
0
0
2
4
2
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
1
0
0
0
2
1
1
0
0
0
0
0
0
0
2
0
2
1
0
0
0
2
0
0
0
1
0
2
0
0
0
1
0
0
2
1
0
0
0
0
2
0
0
0
0
1
1
0
2
0
2
0
1
0
2
2
0
2
2
5
1
2
0
0
0
2
1
0
0
0
0
2
3
0
0
0
1
2
2
0
0
0
0
2
2
0
2
1
2
1
0
0
1
0
2
0
2
2
0
0
2
1
1
0
0
0
1
1
0
1
0
0
0
2
0
0
1
0
2
0
0
0
0
0
2
0
2
0
0
0
2
2
0
2
1
0
1
0
1
1
0
1
1
0
0
0
2
1
1
0
2
0
0
0
1
1
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
1
1
1
0
0
0
2
0
0
0
2
0
2
1
2
0
0
0
0
2
0
0
0
0
0
2
0
2
2
0
0
1
0
0
0
0
0
0
1
0
1
1
2
0
0
0
0
0
1
2
0
2
1
1
0
0
0
0
1
1
0
1
0
0
2
0
0
0
0
2
0
2
2
0
0
1
0
0
1
2
0
0
0
0
0
0
1
0
2
0
2
0
1
1
0
2
2
1
2
0
0
1
1
0
0
0
0
1
1
0
1
0
0
1
1
0
0
1
0
2
1
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
2
1
0
6
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
2
0
0
2
0
0
0
1
0
0
0
1
1
1
0
2
0
1
1
0
0
0
0
1
1
1
1
2
1
0
1
0
0
1
0
0
2
0
2
0
2
0
0
1
0
0
0
0
0
2
0
1
0
0
0
1
5
1
2
1
0
1
0
2
0
0
0
0
2
0
1
2
0
0
0
0
0
2
2
0
0
0
1
0
1
0
3
0
0
0
1
2
0
1
2
1
0
0
0
0
0
2
2
0
2
3
0
0
2
0
2
0
0
0
2
0
2
0
1
0
2
0
0
0
0
1
1
0
1
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
2
1
2
1
2
0
0
0
0
0
1
1
0
0
2
1
0
0
0
0
0
2
2
2
7
0
1
1
1
0
1
0
0
1
2
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
2
0
2
0
0
0
1
0
3
0
1
0
2
2
1
0
0
0
1
1
0
2
2
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
3
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
2
1
1
1
1
2
0
0
1
1
1
0
0
0
0
1
3
0
2
2
0
0
2
0
2
0
0
0
2
0
1
0
0
0
0
1
1
0
1
0
0
0
0
2
0
0
2
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
2
0
0
2
0
2
0
2
0
0
0
0
1
0
2
1
0
0
2
1
0
0
0
2
1
3
0
0
0
0
0
1
0
0
1
0
0
1
0
3
1
0
0
2
0
1
2
0
0
4
1
0
0
0
0
1
0
1
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
2
0
0
0
2
1
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
1
0
1
2
0
1
1
1
0
3
0
0
0
0
3
1
1
2
0
0
0
0
2
2
0
0
0
1
2
0
1
0
0
0
5
0
0
0
2
0
0
0
1
0
1
0
0
0
0
1
2
1
2
2
0
0
0
0
1
2
1
1
0
0
2
0
1
1
0
1
2
2
2
1
0
1
1
1
0
2
0
0
0
1
0
1
0
0
2
2
1
1
1
2
0
0
2
2
0
10
0
0
0
0
3
0
1
1
0
0
0
2
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
2
0
1
1
0
0
0
1
0
0
0
0
0
0
4
0
0
0
1
0
0
1
0
0
0
1
0
0
1
1
0
2
0
3
2
0
0
0
6
0
0
0
0
2
0
0
0
0
0
1
3
1
0
1
0
0
0
1
0
0
1
0
1
0
0
2
0
1
0
3
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
1
0
0
0
1
1
0
0
1
2
1
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
1
1
0
2
0
1
0
1
1
0
0
0
0
0
0
0
2
0
3
0
1
1
0
0
0
0
0
0
0
1
0
0
0
2
2
0
1
1
2
0
0
0
0
0
2
0
0
0
0
1
2
1
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
3
0
1
0
2
1
2
3
0
2
0
2
1
0
0
2
4
0
0
1
0
0
0
1
0
0
0
0
0
0
1
2
2
1
2
0
0
2
2
2
3
0
0
0
2
0
0
0
1
0
0
0
0
0
1
2
2
1
0
0
1
0
0
2
3
3
0
0
3
2
0
3
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
2
0
2
1
1
0
1
1
0
0
0
0
4
0
0
0
2
0
1
0
0
1
0
2
0
1
0
2
1
1
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
1
0
2
0
0
2
2
2
1
0
2
1
0
2
0
0
1
0
2
1
2
1
0
0
0
0
0
1
1
0
0
0
0
1
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
1
1
0
2
2
1
0
0
0
0
0
2
0
1
0
0
0
1
0
1
0
0
0
1
1
0
0
2
0
0
2
2
0
1
0
1
0
0
0
2
4
2
0
0
0
1
1
1
0
0
0
2
2
1
0
1
1
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
1
1
0
0
2
0
1
2
0
0
0
1
0
2
0
0
2
0
1
2
0
0
1
1
0
0
0
2
0
2
0
2
2
0
2
0
0
0
0
0
2
2
1
0
0
0
1
0
0
0
3
0
0
0
0
0
4
1
1
0
0
0
0
0
2
0
0
0
0
2
1
1
1
2
1
0
0
0
0
0
2
1
0
0
0
0
2
1
1
0
0
1
0
0
0
1
0
1
0
0
0
1
0
1
1
0
0
0
0
1
0
1
0
0
0
0
1
2
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
3
0
1
0
0
1
0
2
0
0
2
0
2
0
0
1
0
1
3
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
1
1
1
2
2
3
0
1
0
0
0
0
1
2
0
3
1
0
2
0
0
0
0
0
1
1
0
1
0
1
1
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
2
0
0
2
2
2
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
1
2
5
2
2
1
0
0
2
0
0
0
1
0
0
1
2
0
0
2
2
0
0
0
1
1
0
0
0
0
2
2
0
1
1
0
1
0
0
2
2
2
0
2
0
0
0
0
2
0
0
1
2
3
0
0
0
0
0
1
0
0
2
0
1
1
1
2
0
0
0
0
0
0
2
1
2
0
1
0
0
0
0
0
0
1
1
0
3
0
0
2
0
0
0
0
2
1
1
1
1
0
0
0
0
2
0
0
5
0
0
0
0
0
1
1
0
0
1
1
0
0
1
0
0
1
1
0
2
3
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
3
2
3
2
0
0
0
2
0
0
0
2
0
1
1
2
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
2
1
0
1
0
0
2
2
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
2
0
0
1
2
2
0
0
0
2
0
0
1
0
0
0
0
2
0
0
2
1
1
1
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
1
0
0
0
0
1
0
1
2
0
0
0
0
0
1
1
0
0
0
2
0
1
1
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
2
2
0
2
0
2
0
0
1
1
1
0
2
0
2
0
1
0
1
0
1
0
3
1
0
1
0
0
1
0
2
1
0
0
2
0
0
2
0
2
0
1
0
2
0
2
0
2
2
2
0
1
3
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
3
2
0
0
0
2
2
1
2
0
0
0
0
0
0
0
1
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
2
0
1
0
1
0
1
0
0
0
3
0
1
0
0
0
0
1
2
0
1
3
0
0
0
0
0
1
0
0
2
0
0
1
2
0
2
1
1
0
0
2
1
2
0
0
1
0
0
0
0
1
0
2
0
0
2
1
0
2
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
1
1
2
0
1
1
0
1
0
0
0
2
1
1
0
2
0
0
0
0
0
1
0
2
0
0
1
0
1
2
2
0
0
1
0
2
0
0
2
2
0
0
0
0
0
0
2
1
0
2
2
2
0
3
0
2
2
1
2
0
0
1
0
0
0
0
2
2
0
1
0
3
0
0
0
1
0
0
1
0
0
1
1
1
0
1
2
1
0
0
1
0
1
0
1
2
0
0
1
3
1
0
0
0
2
0
0
0
2
0
1
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
1
1
0
0
2
0
1
1
2
0
2
0
0
1
0
0
0
3
2
2
2
1
1
0
0
0
2
2
0
0
2
0
0
0
0
0
0
1
2
0
1
0
0
0
0
2
0
0
0
1
0
0
0
1
0
1
0
2
0
1
1
2
0
0
0
0
0
0
0
0
0
1
2
1
0
2
0
0
2
0
0
1
0
0
1
0
0
2
0
1
0
0
0
0
0
0
2
1
0
0
1
0
0
0
1
2
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
3
2
1
0
0
0
2
1
0
0
0
2
2
0
1
0
2
0
2
0
1
1
0
1
0
2
0
0
2
1
0
0
0
2
0
0
2
0
0
0
0
0
2
0
1
1
2
2
2
2
0
2
0
1
0
0
1
0
0
0
0
6
1
0
0
0
0
0
0
0
2
1
0
2
1
0
1
2
2
0
2
0
0
0
1
0
1
0
2
0
1
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
1
2
2
0
0
2
0
1
1
0
1
0
2
1
1
2
0
0
2
0
2
1
0
1
0
2
2
0
0
2
0
0
1
0
0
0
0
0
2
1
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
2
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
7
2
1
0
1
0
0
0
0
1
2
0
2
2
2
5
0
1
0
0
2
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
1
1
2
1
2
0
0
2
2
2
0
0
0
0
0
2
1
0
0
7
2
2
1
1
2
0
1
0
0
0
1
0
1
1
4
1
1
1
0
2
2
1
0
2
0
0
0
2
3
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
1
2
0
2
0
1
1
0
1
0
0
0
0
0
0
0
0
0
2
2
1
0
1
3
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
2
0
4
0
2
0
0
2
1
0
1
0
0
2
0
0
3
2
0
0
0
0
1
0
0
0
2
4
1
1
0
2
0
1
2
0
0
0
0
0
0
2
2
0
0
0
0
2
0
2
1
0
0
0
0
0
2
1
0
0
3
0
0
2
0
0
0
2
0
0
2
0
0
2
0
1
3
0
2
1
2
1
2
1
0
1
0
2
1
0
1
1
0
0
1
2
0
0
0
1
1
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
2
0
1
2
0
0
0
0
0
1
1
0
0
0
0
0
1
2
0
2
0
2
3
2
1
0
2
1
2
0
0
2
2
0
0
2
0
1
2
4
2
0
1
2
1
2
1
0
0
0
1
0
0
2
0
0
0
0
1
1
0
0
0
1
1
0
1
0
0
0
0
0
0
2
1
1
1
0
3
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
4
0
1
0
0
0
0
4
0
1
1
0
1
0
0
0
0
1
0
2
0
1
1
2
0
0
1
1
0
0
1
2
1
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
3
0
2
1
0
0
0
0
0
1
0
1
1
0
0
1
0
0
1
0
1
0
2
1
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
3
2
2
0
0
0
2
0
2
0
0
1
1
0
0
0
1
1
2
0
3
2
2
0
0
0
2
2
0
0
0
0
0
1
0
0
2
2
1
0
0
2
0
1
0
0
3
0
0
0
1
1
0
3
2
0
0
2
1
0
0
0
0
0
1
2
0
0
2
2
0
0
0
2
0
1
0
0
0
1
1
0
0
1
0
0
1
0
0
2
1
2
2
0
0
2
0
1
0
2
0
0
2
1
0
0
1
0
1
0
0
2
1
1
0
0
2
0
0
0
0
0
2
1
1
0
1
0
2
2
0
0
0
0
0
2
0
0
1
0
1
1
2
0
1
1
0
2
1
2
1
0
0
0
0
2
0
2
0
2
0
0
1
1
2
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
2
0
1
1
1
0
0
1
0
1
1
1
0
0
2
1
2
0
0
0
3
0
0
0
3
2
1
0
0
1
2
0
2
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
2
0
0
0
2
1
0
0
0
0
0
1
0
1
0
1
2
0
2
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
1
0
0
2
2
1
0
0
1
0
2
2
0
1
0
1
0
0
0
0
0
0
0
0
1
0
2
2
2
0
0
2
0
1
1
2
1
0
0
2
0
0
0
2
4
0
0
1
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
1
0
0
1
0
1
0
2
1
0
0
2
2
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
1
0
1
0
0
1
0
0
1
0
0
0
0
2
0
2
0
1
0
0
2
0
0
0
0
0
1
0
2
1
1
2
0
0
1
0
1
0
0
0
0
0
0
0
2
0
2
0
1
1
0
0
0
0
0
0
1
1
0
1
0
0
1
1
0
0
1
2
2
0
3
0
0
0
2
0
0
1
0
0
0
1
2
0
0
2
2
3
0
1
1
0
0
2
0
3
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
1
1
0
0
4
1
0
2
0
2
0
1
1
0
0
0
0
0
1
2
0
0
0
2
0
2
0
2
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
1
2
1
0
0
0
1
0
1
0
0
0
2
3
0
2
1
0
0
3
2
2
2
1
2
1
0
2
1
0
0
0
1
1
5
2
0
0
0
0
0
0
2
0
1
1
0
0
1
1
0
2
0
1
0
3
1
0
0
0
1
0
0
1
0
0
0
1
1
1
0
1
0
0
3
2
0
0
2
0
2
0
1
1
0
0
2
2
2
0
2
0
0
0
0
2
0
0
2
2
0
1
2
1
0
2
0
0
0
2
2
0
0
1
0
1
4
0
0
0
3
1
0
1
0
0
2
2
2
0
0
1
0
1
0
0
1
0
1
0
1
0
0
0
2
0
1
0
2
1
0
1
0
0
0
1
0
1
1
0
0
0
0
2
0
2
3
1
0
0
1
1
1
0
0
0
0
0
1
0
2
2
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
1
0
2
0
2
0
2
0
0
0
2
2
2
0
0
0
0
0
2
2
1
2
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
1
2
0
2
1
0
0
2
0
0
1
2
1
1
1
2
2
0
0
2
1
0
2
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
3
2
1
0
2
0
0
1
0
0
1
0
1
0
0
0
2
0
0
2
0
2
0
0
0
0
2
2
2
0
0
2
0
0
2
1
0
1
1
3
0
2
0
0
1
4
2
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
2
1
0
0
1
1
0
0
0
0
2
2
1
0
1
0
2
0
0
0
0
0
1
2
0
0
0
0
0
1
0
1
0
0
1
0
0
0
2
0
0
2
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
1
1
2
0
0
0
0
2
0
0
0
0
0
1
0
0
1
1
0
2
0
0
0
0
1
0
1
2
2
2
1
1
0
1
0
0
1
1
2
1
1
2
0
0
0
0
0
0
0
0
1
0
0
2
3
1
0
2
2
0
1
2
0
1
2
0
1
1
1
0
0
0
2
0
0
1
2
2
1
0
1
0
1
1
1
2
0
1
0
0
0
0
3
0
4
2
0
0
1
0
2
0
1
0
2
0
0
1
0
0
0
0
4
0
0
1
1
1
2
5
0
2
4
0
7
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
2
0
0
0
0
1
0
4
0
0
0
2
0
0
2
0
2
2
0
0
2
0
0
0
1
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
1
2
2
3
1
0
1
2
0
1
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
1
0
0
0
2
2
1
0
1
1
0
1
1
0
0
0
1
2
1
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
1
0
1
0
0
2
1
0
0
0
1
0
2
1
0
0
1
0
2
2
0
0
1
0
1
0
2
0
0
0
1
0
0
1
0
1
0
1
0
0
3
2
1
0
0
2
1
0
1
0
0
0
0
2
0
0
1
1
0
1
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
1
0
1
1
0
1
0
0
1
0
0
2
0
0
0
1
1
0
0
0
2
0
0
2
2
0
1
0
2
0
2
0
1
0
0
0
2
0
1
1
0
0
0
2
0
0
0
0
0
0
1
2
3
0
0
0
0
0
2
0
1
2
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
1
0
1
1
0
0
2
0
1
1
2
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
4
1
0
0
0
2
0
0
0
0
0
1
1
0
1
0
1
0
2
0
0
1
0
1
0
0
0
0
0
0
2
2
0
1
2
0
0
3
2
0
0
1
0
0
1
2
0
1
2
0
2
0
2
0
0
0
0
0
2
2
2
1
1
0
0
1
0
3
1
0
0
0
0
0
1
0
0
0
0
2
3
0
0
0
0
0
1
1
1
0
1
1
0
0
0
1
1
0
1
1
2
0
0
0
2
1
0
1
0
0
0
0
0
1
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
1
0
0
0
0
2
1
0
0
0
1
2
0
0
0
1
0
0
0
3
2
1
2
1
1
0
2
0
0
0
1
0
0
2
1
1
2
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
1
0
2
0
0
1
1
1
2
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
1
3
0
2
2
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
2
0
1
1
1
0
0
1
1
0
0
0
0
0
0
0
2
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
2
0
1
2
1
1
2
2
2
3
0
1
2
0
2
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
1
0
0
0
0
0
1
0
0
2
1
0
2
0
0
1
0
2
0
0
0
0
0
0
3
0
0
0
2
2
0
1
0
2
0
1
3
0
0
2
0
0
1
1
0
2
4
1
0
0
0
1
2
0
1
2
1
0
3
2
0
0
0
1
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
1
0
2
0
1
2
2
1
0
2
0
0
0
1
0
0
0
0
0
1
0
0
2
2
0
0
2
1
0
0
0
0
1
2
0
1
1
0
0
0
0
8
1
1
2
1
3
1
0
0
0
0
1
1
0
2
2
2
2
1
0
1
2
1
0
0
0
1
2
1
0
0
1
0
2
0
2
2
0
0
0
0
0
0
1
0
2
1
0
1
2
2
0
0
1
0
0
2
0
2
2
0
0
0
1
1
1
0
1
1
0
0
0
2
0
0
0
0
0
1
0
1
0
0
1
1
2
1
1
1
0
0
0
0
0
1
0
1
0
1
1
0
0
0
2
1
2
2
0
0
0
0
1
0
0
0
1
0
1
1
0
0
2
2
2
0
1
0
1
1
0
1
1
0
0
2
2
0
2
1
2
0
1
1
0
1
1
1
0
2
0
0
1
0
0
0
0
0
0
0
1
2
2
0
0
0
2
1
2
2
0
0
0
0
2
2
2
0
0
2
0
0
1
2
2
2
1
0
0
1
0
0
1
2
0
2
0
2
0
0
0
0
1
3
0
0
0
1
0
2
1
0
2
0
0
0
0
0
0
0
3
0
1
0
1
0
0
0
1
0
0
0
2
0
2
1
1
1
2
0
0
3
0
0
2
1
1
2
0
1
0
0
0
0
0
1
2
1
0
0
2
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
4
0
1
2
1
0
0
0
0
0
0
0
2
1
0
0
2
1
0
1
1
1
0
0
0
0
1
0
0
0
2
0
2
0
1
2
2
2
0
0
0
0
0
1
0
2
0
0
0
2
1
0
0
0
2
0
1
0
0
1
0
0
0
2
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
2
0
1
0
0
0
0
0
3
2
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
1
1
1
0
0
0
1
0
0
0
0
1
1
1
0
1
0
2
0
0
0
0
2
1
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
3
0
2
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
2
0
2
0
1
0
0
2
2
1
0
0
0
0
2
0
0
3
2
0
0
0
0
0
0
2
0
1
2
2
0
0
0
0
0
1
0
2
0
0
5
0
0
2
2
1
1
0
0
2
0
1
0
1
0
1
1
0
1
1
0
0
0
1
0
2
0
2
2
1
1
0
0
0
2
0
1
0
0
0
0
0
0
0
2
1
1
1
0
2
1
2
7
0
0
0
0
1
0
1
0
2
2
0
0
2
0
0
0
0
0
2
0
0
2
1
1
0
0
0
0
0
2
0
0
2
0
1
1
2
2
0
2
0
2
1
2
1
0
0
1
1
0
0
0
1
0
0
0
0
0
1
1
1
1
1
0
0
0
0
2
0
0
0
0
0
0
0
1
2
2
0
2
0
0
1
2
0
0
0
1
0
1
0
2
1
0
2
5
1
2
0
0
0
1
1
0
2
0
0
1
0
0
2
0
0
0
0
0
0
1
2
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
1
1
1
0
2
0
3
3
1
0
0
1
1
2
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
2
0
1
0
0
0
1
0
2
0
2
0
0
0
1
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
1
1
1
2
1
0
0
1
0
1
0
0
2
0
2
1
0
0
0
0
1
1
0
0
0
2
1
6
1
0
2
0
1
0
2
4
0
1
0
0
1
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
2
0
0
1
0
0
0
3
0
1
1
0
0
0
0
1
1
1
1
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
1
0
0
0
0
4
0
0
0
0
1
2
0
1
0
0
0
2
1
0
0
0
0
0
0
0
2
3
3
1
0
1
1
1
0
1
0
0
0
0
0
1
2
1
0
2
0
2
1
0
0
0
0
1
0
0
0
0
0
3
0
0
1
0
1
0
2
1
0
0
0
0
1
1
2
0
2
0
1
1
1
1
1
0
1
1
1
0
0
2
0
0
1
1
3
1
0
1
3
2
0
0
0
0
2
0
0
0
2
1
1
0
0
1
1
0
0
2
1
2
0
0
1
1
2
1
2
2
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
2
0
2
0
2
0
0
1
0
2
1
0
0
0
2
0
0
1
0
0
0
0
2
0
1
2
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
2
1
0
1
2
2
1
0
0
1
0
2
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
1
0
0
2
3
0
1
2
2
2
2
0
3
2
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
1
2
0
0
0
0
0
2
0
1
2
1
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
1
1
0
0
0
2
0
0
2
0
0
1
0
1
3
0
2
1
0
0
0
1
2
2
1
2
0
0
2
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
2
2
0
0
1
2
0
0
0
0
2
0
0
1
0
1
2
0
1
0
2
2
0
1
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
2
0
1
1
0
0
0
0
0
0
0
1
0
1
1
0
1
2
2
0
1
1
0
0
0
0
0
1
0
1
2
1
0
0
2
0
0
0
2
2
0
0
0
1
1
0
0
2
0
2
1
0
0
0
0
0
1
1
1
0
0
0
0
2
1
0
2
0
2
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
2
0
5
0
1
0
2
0
2
0
0
0
0
1
0
0
0
2
0
2
1
0
0
0
2
2
0
0
1
2
1
1
0
0
2
1
2
0
0
1
0
0
0
2
0
0
1
1
0
0
1
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
1
2
2
0
0
0
0
1
2
0
0
1
1
0
1
0
1
2
2
0
2
0
0
4
2
0
1
1
0
1
0
1
0
1
0
0
1
1
1
0
0
0
0
0
1
1
1
2
0
3
0
0
0
1
2
0
2
0
0
0
1
1
1
0
0
0
0
0
0
0
2
0
0
1
0
0
2
2
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
2
0
0
0
0
1
1
0
0
0
0
1
1
2
0
1
0
2
0
1
0
0
0
1
0
2
0
1
0
0
2
0
0
0
0
2
0
2
0
1
0
0
2
3
0
0
0
0
0
0
0
1
0
2
1
0
1
0
3
0
0
1
2
0
0
2
1
0
0
0
1
0
2
2
0
2
1
0
1
2
0
2
0
2
0
0
1
0
0
0
2
2
0
2
0
0
0
3
0
1
0
2
1
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
1
0
2
0
0
0
0
2
0
0
1
0
0
0
1
0
1
2
0
0
0
0
0
2
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
2
2
3
0
2
2
0
0
2
0
0
2
0
1
0
1
0
1
2
0
2
0
0
0
0
0
0
2
0
0
0
1
2
0
0
2
0
0
0
1
0
0
0
1
1
1
2
2
3
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
3
2
0
2
0
0
0
0
1
2
0
0
0
0
1
0
0
0
2
1
0
1
0
0
2
1
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
2
0
3
0
2
0
0
0
3
2
2
2
0
3
0
0
0
1
0
0
3
2
0
1
0
2
0
0
2
0
1
0
1
0
1
2
0
0
1
0
0
1
1
2
0
0
3
0
1
0
1
0
0
2
0
0
1
0
1
0
0
0
0
0
2
0
0
0
3
0
0
0
2
1
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
1
2
0
1
0
2
1
0
0
2
0
2
1
0
1
0
0
1
1
0
2
1
2
0
0
0
0
0
1
0
0
1
0
1
0
2
0
3
0
0
4
1
0
0
0
0
2
1
0
1
3
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
1
2
0
1
0
0
1
1
2
0
0
0
0
2
0
0
2
0
1
0
2
0
4
1
1
1
0
1
2
2
1
0
0
1
0
0
2
0
0
0
0
1
0
0
1
0
2
2
1
0
0
0
1
0
0
1
0
2
0
0
0
2
2
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
2
0
0
0
1
2
0
2
0
1
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
1
2
2
0
0
0
0
1
0
0
0
1
2
0
1
0
4
1
0
2
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
3
0
0
4
0
5
0
0
0
0
0
2
0
0
1
0
2
1
2
0
2
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
2
0
1
2
3
1
0
1
3
0
0
2
0
3
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
2
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
2
3
0
2
0
0
4
0
0
0
0
2
1
1
0
3
2
0
0
0
0
0
0
0
2
2
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
1
1
2
2
0
0
1
2
0
1
0
2
0
0
0
2
2
2
2
1
0
0
0
2
2
0
0
2
0
0
1
1
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
1
1
3
1
0
1
1
0
0
0
0
2
0
0
0
0
0
1
0
0
2
1
2
2
0
0
0
2
0
1
0
2
1
2
0
0
0
2
0
3
0
1
1
0
1
0
0
0
1
1
0
0
0
1
3
0
1
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
1
1
0
0
1
2
2
0
1
2
0
2
0
0
0
0
1
0
1
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
4
0
1
0
0
0
0
1
0
0
1
0
2
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
1
3
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
2
0
0
1
2
0
1
1
0
0
0
0
0
0
0
2
0
0
0
2
2
3
0
0
0
0
2
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
3
1
3
0
0
2
1
1
0
0
2
0
2
4
0
4
0
1
0
2
0
0
2
1
2
0
0
2
1
1
1
2
1
3
0
0
2
1
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
2
2
2
0
0
0
0
0
1
0
0
2
1
0
0
0
0
1
0
0
1
0
0
2
1
0
1
1
0
0
2
0
0
1
0
2
0
0
0
1
2
0
0
2
3
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
1
0
1
0
1
0
0
0
1
0
1
0
3
0
0
1
0
0
0
0
0
0
2
1
0
0
2
0
1
0
0
0
0
0
0
1
0
2
0
2
2
0
0
0
0
1
0
2
0
1
0
2
0
0
2
0
0
0
0
1
0
2
1
0
2
0
0
0
0
2
2
2
2
0
0
0
0
1
2
2
0
0
0
1
0
0
0
3
1
2
0
0
0
0
2
0
0
2
2
2
0
1
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
1
0
0
1
0
1
1
0
0
1
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
1
2
0
2
0
0
2
2
0
1
0
0
0
0
2
2
1
0
2
0
0
2
1
2
1
0
2
0
0
1
0
1
1
0
0
1
1
0
0
2
2
0
0
0
0
1
0
0
6
1
0
0
0
2
1
0
2
0
0
0
1
0
0
1
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
1
0
1
0
2
0
1
2
2
0
0
0
3
0
0
0
0
0
0
0
0
2
1
2
1
0
0
0
0
1
0
0
0
2
0
2
0
0
1
2
2
1
0
2
0
2
0
0
0
2
0
1
0
0
2
0
0
0
0
1
0
0
1
0
0
1
2
2
3
0
0
0
0
0
0
2
0
0
1
0
2
0
0
1
0
1
0
0
1
1
0
0
1
2
0
0
0
2
1
1
1
2
0
1
6
0
0
1
0
2
2
0
0
0
0
0
0
2
0
1
3
1
1
2
0
0
0
2
2
0
0
1
0
0
0
0
0
1
1
0
0
1
2
1
0
0
0
0
0
2
1
0
0
1
1
0
0
0
2
0
0
0
3
1
1
0
0
0
0
2
0
0
0
2
0
2
0
0
1
0
1
2
0
0
1
0
1
0
0
2
0
0
1
1
0
1
0
1
1
0
0
0
0
0
2
2
0
0
2
0
2
0
2
0
0
0
2
0
5
1
2
0
1
1
0
0
1
0
0
1
0
1
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
3
0
0
2
0
1
1
0
0
1
2
2
2
0
1
0
2
0
2
0
2
0
1
0
1
0
0
0
0
0
0
0
0
1
2
2
0
2
2
1
2
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
2
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
2
2
1
0
0
1
0
0
1
1
0
2
0
1
1
1
0
1
0
2
0
2
1
2
0
2
0
1
1
0
0
0
1
0
0
2
0
1
0
2
1
2
0
1
2
0
2
2
1
2
0
0
0
1
2
0
1
0
2
0
1
2
2
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
2
0
1
1
3
0
2
0
1
0
0
0
0
0
1
0
1
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
1
0
0
0
0
0
5
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
2
0
0
1
0
0
0
2
0
0
0
0
2
0
1
2
0
0
0
1
0
1
2
1
0
2
1
1
2
2
2
1
2
2
1
1
0
0
2
1
0
2
0
0
0
1
0
0
2
2
1
0
0
0
2
0
0
2
0
1
1
0
2
1
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
1
3
0
0
2
1
0
0
2
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
2
0
1
2
1
0
0
0
0
1
1
0
0
0
2
0
0
1
0
0
1
0
2
1
0
2
0
0
0
2
2
0
0
1
1
0
0
0
1
2
2
0
2
1
1
1
0
2
2
0
2
5
0
1
0
1
0
2
1
1
2
3
0
0
1
0
0
0
2
0
0
1
2
1
2
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
2
0
1
0
0
1
1
1
0
2
0
0
0
1
0
1
1
0
4
1
0
0
1
0
0
0
0
2
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
2
0
0
2
0
2
0
2
0
0
0
0
1
4
1
0
0
1
0
0
2
2
1
2
1
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
4
1
0
2
0
3
0
0
2
0
0
0
1
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
2
0
0
0
1
2
1
0
1
0
0
0
1
2
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
2
0
2
1
2
0
2
0
1
0
0
1
0
0
0
2
0
2
2
2
0
0
2
2
0
0
0
0
0
0
0
1
0
1
0
1
0
1
2
0
0
2
2
2
0
1
2
0
0
0
0
3
0
0
1
0
0
0
6
0
2
0
0
0
0
1
1
0
1
1
0
0
3
1
2
0
1
3
0
0
0
0
0
1
0
0
0
0
0
8
1
0
0
1
0
0
1
0
0
0
3
1
1
2
2
0
1
2
0
0
0
0
2
1
2
2
0
1
2
0
0
1
0
0
0
0
2
0
2
2
1
2
1
1
2
0
1
1
0
0
0
0
1
0
0
2
2
2
0
0
0
0
0
0
0
2
1
1
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
1
2
2
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
2
0
2
0
0
0
2
0
0
0
0
1
2
2
2
0
0
0
0
2
0
1
1
1
2
0
3
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
1
0
1
0
2
1
3
0
2
0
1
0
2
0
2
3
1
0
0
1
0
0
1
0
2
0
2
0
0
0
1
0
1
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
1
0
2
2
0
0
1
2
0
1
0
0
0
0
1
1
0
2
2
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
1
0
2
0
0
2
0
0
2
0
1
0
0
0
0
2
0
0
2
0
0
0
1
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
1
0
1
2
0
0
2
0
1
0
0
0
0
2
1
0
0
0
1
2
1
0
1
0
0
2
2
1
2
0
0
0
0
2
0
0
2
0
0
3
1
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
2
1
1
1
0
1
0
1
0
2
1
0
1
0
0
1
0
3
0
2
1
1
1
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
2
1
1
0
0
2
0
0
0
0
1
2
0
0
1
2
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
1
0
0
1
0
2
0
3
0
2
2
0
1
0
1
1
0
0
1
2
1
0
0
2
0
1
0
0
0
0
2
1
0
0
0
1
0
1
3
2
0
2
0
0
1
2
0
2
0
0
0
0
0
2
2
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
2
0
2
1
1
1
0
0
2
0
0
0
0
2
1
1
2
2
0
0
0
0
0
3
0
2
0
2
3
2
0
2
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
1
0
0
2
3
0
2
0
1
1
0
1
0
0
0
0
1
0
2
1
2
0
0
1
0
0
2
1
2
0
0
1
2
0
2
2
2
0
2
2
0
0
0
2
1
0
1
3
0
0
1
1
2
1
1
0
0
0
0
0
0
0
0
1
1
2
0
1
0
3
0
0
10
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
1
2
2
0
1
0
0
2
0
0
0
2
0
1
0
0
0
2
1
1
1
0
0
2
2
2
1
0
0
2
2
0
0
0
2
0
1
0
2
0
1
0
0
0
2
1
1
0
0
0
1
2
4
1
1
1
0
0
0
0
0
1
0
0
1
0
2
1
1
0
1
0
0
2
1
1
0
1
3
2
2
2
0
1
0
0
0
0
2
0
0
0
1
1
2
0
2
0
2
1
0
0
1
0
0
2
1
1
0
0
2
2
1
1
1
1
1
0
0
2
0
0
0
0
0
2
2
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
2
1
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
2
1
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
1
0
0
0
0
1
0
0
1
0
2
0
0
0
1
0
2
2
0
0
0
0
0
0
0
2
7
2
0
1
0
0
0
1
0
1
0
2
0
1
0
0
0
2
0
0
0
0
0
4
1
0
0
1
0
2
2
0
1
0
2
2
1
2
0
1
1
0
0
0
0
0
0
1
1
2
0
0
2
0
2
0
0
0
1
0
0
1
0
2
2
1
0
2
1
2
0
0
0
1
1
0
0
0
1
2
0
2
0
2
2
3
0
1
0
0
0
0
0
1
1
2
1
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
2
0
2
0
0
1
0
1
0
0
0
1
2
0
0
3
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
1
0
0
3
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
3
1
0
1
0
0
2
0
0
0
1
0
0
2
1
1
0
0
1
0
1
0
0
0
1
0
0
0
1
0
3
2
0
1
1
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
3
1
0
0
2
0
0
0
2
0
0
0
1
0
0
0
1
1
5
1
2
0
0
1
0
1
0
0
0
0
3
1
0
4
1
0
0
0
0
0
0
2
0
0
0
2
0
0
2
2
1
0
3
1
3
0
0
0
0
0
1
1
3
1
0
0
0
1
1
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
2
0
2
1
0
3
1
0
0
0
1
2
1
0
0
0
0
0
0
1
0
0
0
1
1
0
1
1
2
1
0
2
1
0
0
0
0
3
0
1
1
0
1
0
2
1
2
0
1
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
2
0
0
0
1
1
0
2
2
0
2
0
0
2
0
0
0
0
1
1
0
2
1
0
1
0
0
0
0
0
0
2
2
0
0
1
1
2
1
0
0
0
1
0
1
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
1
0
0
0
2
0
0
0
0
0
1
0
0
3
0
0
0
1
0
1
1
0
2
0
0
2
2
0
0
0
1
0
1
0
3
0
0
1
0
0
0
1
1
0
0
0
1
2
0
0
2
0
0
1
2
1
0
2
0
0
1
1
2
0
0
2
1
2
0
1
0
0
0
0
0
0
2
0
2
0
1
0
1
0
0
0
1
0
2
0
0
0
0
0
1
0
3
0
1
0
2
0
0
1
1
0
0
1
1
0
2
1
0
0
0
1
2
0
0
3
2
2
1
0
0
0
0
0
0
0
1
1
0
1
0
2
0
1
0
0
0
0
0
0
0
2
1
1
0
0
2
0
2
0
0
0
0
1
0
0
1
0
1
1
1
0
0
0
0
0
0
3
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
2
1
3
0
0
0
2
0
1
1
0
0
1
0
1
0
0
0
1
1
1
0
0
0
1
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
1
2
1
0
2
0
0
2
1
0
0
0
2
0
3
1
0
0
0
3
0
1
0
0
0
0
1
0
0
0
0
0
4
0
0
0
2
0
0
0
1
2
2
0
0
2
1
1
1
1
0
1
1
0
1
0
2
0
2
2
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
1
0
2
1
2
0
2
0
1
1
2
1
0
0
0
0
0
2
1
0
0
1
0
0
0
0
1
1
1
0
0
0
0
1
1
2
0
1
3
0
0
0
0
2
0
0
0
2
0
2
0
0
0
2
2
0
0
2
0
1
0
2
1
0
2
3
2
0
1
0
0
0
0
0
0
0
2
1
1
0
0
0
1
0
0
1
1
2
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
3
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
1
1
1
2
1
2
0
0
0
0
0
1
2
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
2
1
0
1
0
0
0
1
3
0
0
0
0
0
2
0
1
3
0
0
1
0
0
0
2
3
0
0
0
2
2
0
0
0
0
2
0
0
1
1
0
1
0
2
0
0
0
0
1
0
0
1
2
0
2
0
0
2
0
1
1
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
2
1
1
0
0
1
1
0
1
0
1
0
0
1
0
1
0
0
0
0
1
2
2
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
1
2
0
2
0
2
0
3
0
0
0
0
0
2
0
1
0
1
2
0
0
0
3
0
1
2
2
1
1
4
0
0
0
1
0
1
0
0
2
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
1
3
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
1
0
0
0
2
2
0
0
0
2
2
1
1
1
0
1
2
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
1
2
0
0
0
0
0
1
0
2
0
0
0
0
6
2
1
0
0
1
0
2
0
0
0
4
0
1
1
0
0
11
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
1
0
0
0
0
0
2
0
1
2
1
1
0
2
0
0
0
0
2
0
2
0
2
0
2
1
2
2
2
0
0
2
2
0
0
0
3
3
0
2
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
1
0
1
1
0
1
0
1
1
0
1
1
0
1
0
0
0
2
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
1
0
0
2
2
0
0
1
0
1
0
2
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
1
1
0
1
0
0
0
0
2
0
0
0
2
1
1
0
0
2
0
0
0
0
2
0
0
1
0
0
1
0
2
1
1
0
1
1
1
0
0
2
1
0
0
0
2
1
1
0
0
1
1
1
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
1
1
1
0
2
0
1
1
2
0
0
0
2
0
0
0
0
2
0
0
0
2
2
2
2
0
0
0
3
1
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
2
3
2
0
2
1
0
0
2
0
2
2
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
3
0
0
2
0
1
2
1
1
0
1
0
2
0
1
1
0
0
1
2
0
0
1
0
0
0
2
2
0
2
0
1
1
0
2
0
1
0
1
1
0
0
1
0
0
0
4
1
2
0
0
0
1
0
0
1
2
2
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
1
1
0
0
2
0
0
1
1
0
1
0
2
0
1
2
0
0
0
3
2
0
0
1
0
2
0
0
0
2
2
1
1
0
1
0
2
0
2
0
2
0
1
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
2
0
2
0
0
2
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
1
0
2
1
0
0
0
0
1
0
0
3
1
0
2
0
2
5
0
2
1
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
1
0
0
2
0
1
2
1
0
0
2
4
0
0
0
0
0
0
0
0
1
0
0
0
2
2
3
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
1
1
0
0
2
2
0
0
1
0
0
0
0
2
0
0
2
0
2
0
0
2
1
0
0
2
0
0
0
1
0
0
2
0
2
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
1
1
0
2
0
2
1
2
2
0
1
2
2
0
2
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
1
0
0
0
1
0
0
0
3
1
4
0
0
0
0
0
0
1
1
0
2
2
0
1
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
1
2
0
1
0
0
2
0
0
0
2
0
1
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
2
0
0
2
5
1
0
0
2
2
2
0
0
1
2
0
0
0
0
2
0
0
0
1
0
0
0
1
2
0
0
0
1
1
2
0
0
0
0
1
0
3
0
2
0
0
0
0
2
0
0
2
0
0
0
2
0
1
0
1
0
1
0
0
0
0
0
0
2
0
0
7
0
0
0
0
0
1
1
0
0
0
2
1
1
1
0
1
0
0
0
0
0
1
2
1
0
0
2
5
2
0
0
0
6
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
1
0
0
1
2
1
1
0
0
0
0
2
2
1
0
2
1
2
1
0
0
1
1
0
1
1
2
1
0
1
2
0
0
0
0
0
0
0
0
0
2
0
1
1
1
0
1
1
0
0
1
1
2
0
0
1
1
1
0
0
2
2
0
0
2
0
0
0
0
0
2
1
0
0
0
1
0
2
1
0
2
0
1
1
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
2
1
3
0
2
0
0
0
0
0
0
0
0
0
0
2
1
2
2
1
0
1
0
0
1
1
0
2
2
0
0
1
0
1
2
0
0
0
2
0
7
1
0
0
2
1
0
1
8
0
0
0
2
0
0
0
1
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
1
2
0
2
0
1
0
0
0
1
0
0
0
0
0
0
1
2
0
2
1
0
0
0
0
3
0
0
0
2
1
0
0
3
1
2
0
0
0
1
2
4
0
1
0
0
0
2
0
0
2
1
0
1
0
0
2
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
2
0
0
4
0
2
0
0
0
1
1
1
2
0
0
0
0
2
0
4
0
2
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
2
0
0
0
1
0
0
2
1
2
0
0
1
0
1
2
3
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
1
2
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
2
1
2
0
0
0
2
3
0
0
0
1
0
0
0
1
1
0
1
0
2
0
1
0
2
0
1
0
0
0
0
3
0
2
1
1
0
0
2
2
0
1
1
1
2
2
0
0
2
0
1
0
1
0
3
0
0
2
2
1
0
0
2
2
0
3
2
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
2
0
0
1
0
0
2
0
1
2
0
1
0
0
0
0
2
1
2
1
0
0
1
0
1
0
0
0
2
0
1
0
1
1
2
0
0
0
0
2
0
2
0
0
0
2
0
1
1
2
0
0
0
0
0
1
0
2
2
1
0
1
1
0
0
1
1
2
1
0
0
2
0
0
0
2
1
2
0
0
0
1
1
1
0
0
0
0
0
1
1
1
0
2
0
0
0
0
1
0
1
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
1
0
0
0
2
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
1
0
0
0
0
0
1
2
1
0
1
0
0
2
0
1
0
0
1
0
0
2
1
0
0
0
1
0
0
0
0
0
0
2
2
0
0
1
0
0
2
0
0
1
0
3
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
1
1
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
2
0
2
2
0
1
1
0
0
2
2
0
1
1
2
0
2
2
0
4
0
2
1
0
2
0
1
1
0
0
1
2
2
2
0
0
2
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
2
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
2
0
0
2
1
1
1
0
2
0
2
0
0
1
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
2
0
1
1
0
2
0
0
1
0
0
1
0
0
2
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
2
1
1
1
0
0
1
0
1
0
0
2
0
2
0
0
2
1
2
0
0
1
0
0
0
1
1
1
2
0
0
2
0
0
0
1
1
0
2
1
0
2
0
2
0
2
0
0
0
0
0
0
0
1
0
1
2
1
0
0
3
1
0
0
0
0
0
0
1
0
1
0
1
0
1
0
2
0
0
0
0
1
0
0
1
2
0
0
1
0
0
0
1
1
2
1
0
0
3
0
0
0
1
0
1
2
0
0
2
0
2
0
2
2
1
1
0
0
0
1
0
2
0
2
1
1
1
1
1
0
0
1
2
2
1
0
0
0
2
0
0
1
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
1
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
3
1
0
2
0
4
2
0
0
0
0
0
2
0
0
0
0
2
1
1
1
0
1
0
0
1
0
0
1
2
1
0
0
0
0
2
0
0
3
1
0
2
0
0
1
1
1
0
0
0
3
0
0
1
0
1
2
2
0
0
0
0
0
3
0
0
5
0
1
0
0
0
0
0
2
2
2
0
0
0
1
1
1
2
0
3
1
0
1
0
0
0
0
0
2
2
2
1
10
2
0
0
2
0
3
2
0
0
2
0
0
2
0
1
2
0
0
0
0
0
0
1
0
2
0
0
0
0
2
1
0
0
1
2
2
0
2
2
0
0
0
0
2
0
2
0
0
0
2
0
2
0
0
0
1
1
3
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
1
1
1
2
0
0
0
0
0
0
1
1
0
1
0
0
2
1
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
2
1
0
1
0
1
1
0
1
0
2
1
0
0
2
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
2
1
2
0
0
2
0
0
0
0
0
0
2
1
2
2
0
1
0
0
0
1
0
0
0
2
0
0
0
0
3
2
0
0
0
0
0
0
1
0
2
0
1
1
2
0
0
1
0
2
0
0
2
2
2
0
0
1
0
0
0
1
0
0
1
0
0
1
1
0
1
0
2
2
2
0
2
0
0
1
2
0
0
2
0
2
0
1
0
1
0
0
2
1
2
2
2
0
0
0
1
2
0
1
0
1
0
0
2
0
1
2
0
1
0
1
0
1
1
1
1
1
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
2
6
0
2
0
2
2
0
0
0
0
0
2
1
2
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
1
0
2
1
2
0
0
0
1
1
2
0
1
1
0
0
0
1
1
1
0
1
0
1
0
0
3
0
0
2
2
1
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
3
1
1
0
0
2
0
1
0
0
2
0
0
1
1
2
0
1
1
0
0
0
0
2
2
0
2
0
0
2
0
0
1
0
2
0
2
1
1
0
0
1
0
2
1
0
0
2
1
0
0
0
0
0
0
2
2
0
1
0
2
0
1
0
0
0
2
0
1
2
0
0
2
2
0
0
0
0
1
0
0
0
2
0
1
3
2
0
0
0
2
0
0
1
0
0
1
1
0
0
0
2
0
1
0
1
2
0
1
0
1
2
1
1
4
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
3
0
0
2
0
0
0
1
0
0
1
1
0
0
1
0
1
0
0
0
0
2
1
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
1
0
0
1
1
0
0
3
0
1
0
2
0
0
0
0
0
2
1
2
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
1
1
0
2
1
1
0
0
2
0
0
2
1
0
0
0
2
0
0
0
0
8
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
2
0
2
0
0
0
0
0
2
2
1
2
0
1
0
2
0
0
0
1
1
0
0
0
0
0
1
2
2
0
2
0
0
1
0
2
1
0
2
0
0
0
0
0
0
2
0
1
0
1
1
0
2
0
0
2
1
0
0
2
0
1
1
0
0
0
0
0
1
0
0
1
2
0
1
0
1
1
0
1
1
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
2
2
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
1
2
0
0
0
2
1
0
1
1
0
2
2
1
0
2
0
2
0
0
0
0
0
0
3
1
2
1
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
1
2
2
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
2
1
1
0
0
0
2
0
2
0
1
1
0
0
0
0
2
0
0
0
0
1
0
1
0
1
0
0
1
0
2
0
0
2
1
2
1
0
2
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
1
2
0
0
1
0
0
0
0
0
0
1
1
2
0
0
2
0
0
1
0
0
2
0
0
0
0
0
1
1
0
1
0
1
2
1
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
3
0
0
1
2
1
1
2
0
0
2
0
2
2
0
0
0
0
2
0
1
1
2
0
1
0
1
1
0
2
1
0
0
1
2
0
1
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
4
0
4
0
1
0
0
2
2
0
2
2
0
0
1
2
0
1
0
0
0
0
2
0
1
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
1
0
2
1
0
2
0
0
0
2
0
0
1
1
0
0
2
0
2
1
2
0
0
0
1
1
0
0
0
0
0
0
2
2
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
2
0
0
1
0
0
0
2
0
0
2
2
0
2
0
1
0
0
2
0
2
1
0
2
0
1
1
1
1
2
0
1
1
0
0
1
0
2
2
1
0
0
0
0
0
0
0
2
2
1
0
4
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
1
0
2
2
0
1
1
2
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
1
2
0
0
0
0
0
0
0
2
0
1
2
1
2
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
2
1
0
0
0
1
1
0
1
0
0
0
5
0
2
1
0
1
0
0
1
0
0
2
0
0
0
0
1
1
1
1
0
0
0
0
3
0
0
1
1
0
0
0
0
0
1
0
0
2
0
1
1
0
0
1
0
2
0
0
0
2
2
0
0
0
0
0
0
0
1
1
0
0
1
1
0
4
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
1
0
0
0
0
2
0
0
0
2
0
0
0
2
2
1
2
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
1
1
1
0
2
0
1
0
1
0
0
0
0
1
0
0
0
0
0
2
1
1
2
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
2
0
0
0
0
0
2
0
2
0
2
0
0
2
0
2
0
0
0
0
0
2
2
3
1
0
2
0
0
0
0
1
0
2
0
1
0
0
0
0
0
1
0
0
1
0
1
1
1
0
0
5
1
0
0
0
0
1
1
0
1
0
0
0
2
0
0
2
0
0
0
2
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
2
1
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
1
1
0
4
0
1
1
2
1
0
0
0
2
0
0
0
2
1
0
2
0
0
1
2
0
2
0
0
0
0
0
0
0
1
3
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
1
3
0
2
0
0
0
0
0
0
2
2
2
0
1
0
0
0
0
0
0
2
0
1
0
0
1
0
0
3
0
0
0
3
0
0
2
1
0
0
2
1
1
0
1
0
0
2
0
3
1
3
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
2
1
0
2
1
0
1
0
2
0
2
0
0
0
0
2
0
2
1
2
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
1
0
0
0
1
2
0
0
0
0
0
0
4
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
1
0
0
2
2
2
2
0
0
2
0
2
0
0
0
0
0
2
1
2
1
0
0
0
2
1
1
0
2
2
0
3
0
1
1
1
2
0
3
2
0
2
0
1
0
0
2
0
2
0
0
4
0
0
0
1
0
2
0
2
0
2
0
0
1
1
0
3
0
0
1
2
2
0
0
0
2
0
1
0
0
1
1
0
0
0
2
0
0
0
1
0
2
0
3
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
1
0
2
0
0
1
2
1
2
2
0
2
0
0
2
1
0
0
0
0
0
2
0
1
0
0
0
0
0
1
2
1
0
2
0
0
0
0
2
2
0
0
0
1
0
1
0
0
0
2
2
2
0
0
2
1
1
0
0
0
1
0
4
1
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
1
1
5
1
0
0
3
0
2
1
1
0
0
3
1
0
1
1
2
2
2
0
1
1
1
2
0
2
2
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
1
2
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
3
2
2
0
1
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
2
1
1
1
3
0
4
0
0
2
0
0
4
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
1
0
1
1
0
0
1
0
0
2
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
1
0
0
0
1
1
0
2
0
0
0
1
2
0
0
0
1
0
0
0
1
0
1
1
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
2
0
2
0
0
0
1
2
0
1
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
1
1
1
0
0
0
1
2
1
0
2
1
0
0
1
0
1
0
0
3
2
1
2
3
2
2
1
1
0
0
0
1
1
0
0
0
0
3
0
0
0
0
0
1
2
0
1
0
0
1
1
4
0
0
1
0
0
1
1
3
0
0
1
0
1
1
1
1
1
1
0
1
2
0
1
3
0
1
0
2
0
0
0
2
2
1
0
0
0
2
2
0
0
0
0
0
1
0
0
1
0
2
0
1
0
2
1
2
2
1
0
0
0
0
1
1
0
2
3
2
0
0
1
0
0
2
1
0
0
0
2
0
1
0
1
1
0
1
0
0
0
0
0
2
0
1
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
2
0
1
1
0
1
0
0
2
0
0
1
1
0
1
2
1
0
0
0
0
0
0
0
0
1
2
1
1
1
1
0
1
0
0
1
0
0
0
0
2
0
1
1
2
0
0
0
2
0
0
0
1
1
1
0
0
1
2
0
1
0
1
1
0
1
1
2
2
1
1
2
0
0
0
0
0
0
0
1
0
0
2
1
1
1
1
0
0
0
2
0
1
1
0
1
2
0
0
0
0
1
0
0
0
1
0
7
1
0
0
0
0
1
1
0
2
0
1
0
1
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
1
1
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
2
1
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
1
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
3
1
0
2
1
1
1
1
0
7
0
0
2
0
2
0
2
2
0
1
4
0
0
1
0
0
1
0
1
0
2
1
0
0
2
0
0
0
2
2
1
0
2
0
0
0
2
0
1
0
0
0
0
1
0
0
2
0
0
0
1
0
1
0
0
0
0
2
0
2
0
0
0
0
2
3
0
1
0
1
0
1
0
0
0
1
0
0
1
0
2
0
2
0
2
0
1
0
0
2
2
0
0
1
0
0
0
2
1
0
0
2
1
0
2
0
1
0
2
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
1
0
0
2
2
0
0
0
0
0
2
0
0
0
1
1
0
0
0
1
0
0
0
2
2
2
0
0
1
0
1
0
0
0
0
1
2
2
0
0
0
1
0
2
0
0
0
1
1
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
3
2
0
0
2
0
0
0
0
0
1
0
2
1
0
0
0
0
1
0
0
2
0
0
0
1
0
3
2
0
1
0
2
0
1
1
0
8
2
1
0
0
2
0
0
2
0
0
0
1
2
1
1
0
1
0
2
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
6
1
0
0
3
0
0
1
0
0
2
0
2
1
1
0
2
1
0
0
2
0
0
0
1
0
4
0
0
1
1
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
2
2
1
1
0
1
1
1
0
0
1
0
1
0
2
1
0
1
1
0
2
2
1
0
0
2
2
1
0
0
0
0
0
1
2
0
0
3
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
1
1
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
1
2
1
2
1
0
2
0
0
2
1
0
1
1
0
0
1
0
0
0
2
0
2
0
0
0
2
1
0
1
1
2
1
1
0
0
0
0
0
1
0
0
1
0
0
2
1
1
0
0
2
0
0
1
0
0
0
2
1
0
0
2
2
0
1
0
1
0
0
0
0
2
0
0
1
1
0
0
2
0
1
0
2
2
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
1
2
2
1
0
2
0
0
0
0
0
0
1
0
1
1
0
0
0
2
0
0
0
1
0
1
0
3
0
2
0
0
1
0
0
1
0
2
0
0
0
1
0
0
2
0
2
1
0
2
0
0
0
1
0
0
1
1
1
0
0
0
1
0
0
0
0
5
0
1
0
2
0
2
0
1
1
2
0
0
0
2
0
0
1
2
2
2
0
1
2
0
0
0
0
0
2
2
1
0
0
2
0
0
2
2
0
0
1
2
2
0
0
0
0
1
2
0
0
1
0
0
1
0
1
2
0
0
0
0
1
0
1
0
0
2
0
0
0
0
2
0
0
2
2
0
0
1
1
0
0
3
0
1
0
2
0
0
0
0
3
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
1
1
2
0
0
0
0
0
0
0
0
2
1
2
0
1
0
1
0
0
0
2
1
1
2
0
1
3
2
1
1
0
0
2
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
1
4
2
2
0
1
0
0
0
0
0
2
1
0
0
1
1
0
0
1
0
0
1
0
2
0
1
0
0
0
0
0
2
1
1
0
0
1
0
0
2
0
2
1
1
2
2
2
0
1
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
3
1
1
2
2
1
1
0
0
0
1
0
0
1
0
2
2
0
0
0
0
1
3
0
0
0
0
4
1
1
0
0
0
2
1
0
0
1
1
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
2
1
0
0
0
0
0
1
1
1
0
2
2
0
0
2
0
0
1
0
1
0
1
0
2
1
2
0
0
1
1
0
2
0
0
1
0
0
1
0
2
0
0
0
0
0
0
1
2
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
2
0
2
0
0
2
0
0
0
2
1
0
0
0
2
2
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
1
1
1
1
0
0
1
0
1
0
1
0
0
2
0
0
0
2
2
2
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
2
1
1
0
2
0
0
0
2
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
2
0
0
2
2
0
2
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
1
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
2
0
0
0
0
0
0
0
2
2
2
0
1
0
0
0
0
0
0
2
0
0
0
0
2
2
2
1
0
0
0
0
0
2
0
2
0
0
2
1
2
0
0
1
0
1
0
0
2
0
2
2
2
2
1
0
0
1
1
0
0
2
0
0
3
0
0
2
1
0
0
0
0
2
1
1
1
0
0
1
0
0
0
1
2
0
0
0
1
1
0
1
0
2
0
0
2
2
0
0
0
0
0
7
0
0
2
0
0
2
0
2
0
1
0
0
0
0
0
0
1
0
0
1
1
0
1
2
1
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
2
0
0
1
0
0
2
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
1
1
0
2
2
2
0
0
0
1
0
2
0
0
3
2
0
2
0
0
0
1
0
2
1
0
0
1
2
0
1
1
1
1
0
2
0
0
1
0
0
3
2
0
0
0
2
0
0
2
0
2
0
1
2
2
0
0
0
1
1
0
1
1
1
0
0
0
4
0
0
0
2
2
0
0
0
0
1
1
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
2
2
1
0
0
1
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
2
0
2
1
0
0
2
0
1
0
0
1
1
0
2
0
0
0
0
0
0
1
1
1
0
2
1
2
0
0
1
0
2
0
0
0
1
1
0
1
2
0
0
0
0
0
1
2
0
4
0
1
2
0
0
2
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
2
2
2
0
2
1
0
1
0
2
1
1
0
2
1
0
1
0
0
0
0
2
0
3
1
2
0
0
0
0
1
1
2
0
0
1
2
0
2
0
0
2
3
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
1
1
1
0
1
1
0
1
0
0
0
2
2
0
1
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
1
2
2
2
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
1
0
2
0
2
0
0
1
0
0
1
0
0
0
0
0
0
3
1
1
0
0
3
2
1
1
0
1
0
0
1
1
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
1
0
1
2
2
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
3
0
0
0
1
0
1
0
1
0
1
0
0
1
1
0
0
2
0
1
0
2
2
0
0
0
0
0
0
2
1
1
2
1
0
0
0
1
0
0
1
0
0
2
0
0
2
1
1
1
0
0
1
0
2
0
1
0
1
0
0
0
2
2
0
0
0
0
1
0
1
0
1
0
1
1
2
0
0
0
2
0
2
0
3
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
1
1
0
0
0
0
1
1
0
2
3
0
3
0
0
2
0
0
2
0
0
1
0
0
0
0
0
2
2
0
2
0
0
0
1
1
1
0
2
2
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
2
1
0
2
1
1
0
0
0
0
1
0
0
2
1
0
0
1
0
1
0
0
1
0
0
0
2
0
0
1
2
0
1
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
1
1
1
1
3
0
0
1
0
3
0
2
2
1
0
1
0
2
2
0
0
2
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
2
0
0
0
1
1
0
0
1
0
0
0
0
10
0
1
2
0
2
0
0
0
2
0
0
0
0
0
2
1
2
0
0
0
1
2
1
0
0
0
1
0
0
0
1
0
0
5
0
0
0
0
0
0
1
0
2
2
0
2
0
0
0
2
1
1
0
0
2
0
0
0
0
0
2
2
0
2
0
1
0
0
0
1
0
1
0
1
0
0
1
0
0
1
0
2
0
2
0
0
0
1
2
0
2
0
1
0
1
0
0
1
0
2
0
0
2
0
1
2
1
1
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
2
1
0
1
0
1
0
2
2
1
1
2
0
0
2
1
0
0
0
1
0
0
0
2
1
2
0
0
1
0
2
1
0
2
2
1
1
0
0
0
1
0
0
2
2
2
0
1
2
1
1
1
1
2
1
2
0
0
0
2
0
2
0
1
1
0
0
0
0
1
1
0
0
4
0
0
1
0
2
0
0
0
0
0
1
1
0
0
2
0
0
0
3
0
2
0
1
0
0
1
2
2
0
0
1
0
0
1
0
1
0
0
1
1
1
2
0
0
0
1
1
0
1
0
2
0
0
0
1
0
1
1
0
2
0
4
0
2
0
1
0
0
1
0
0
1
2
0
0
1
0
0
0
0
2
5
0
0
1
0
0
1
0
0
1
2
1
2
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
1
1
0
0
0
2
0
1
1
0
1
2
0
1
0
0
0
0
2
2
0
3
2
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
2
2
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
2
0
0
2
0
0
1
2
0
0
1
0
2
0
3
0
2
1
0
0
0
0
2
0
2
1
1
1
0
0
0
0
0
0
0
0
1
0
0
1
1
1
1
4
0
0
1
0
0
2
1
2
0
0
0
2
2
0
0
0
0
0
2
0
1
2
0
0
1
0
0
1
0
0
0
1
1
0
0
1
2
0
0
1
0
0
1
0
0
0
1
0
1
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
2
0
0
2
1
1
0
2
0
3
0
2
0
0
0
0
0
1
2
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
2
0
3
1
0
2
0
0
0
0
0
2
2
2
0
0
0
1
0
0
2
0
1
2
0
0
2
0
0
0
2
1
2
0
0
0
1
0
0
0
0
0
0
2
0
1
0
1
1
1
0
0
0
0
0
0
0
1
0
0
3
0
0
1
2
0
0
0
0
0
0
0
2
0
0
1
0
1
1
0
0
0
0
1
2
0
2
1
0
0
2
0
0
0
1
0
0
0
3
2
6
1
2
0
1
0
2
1
0
0
2
0
1
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
1
0
0
1
0
1
0
3
1
1
2
2
2
0
0
0
0
1
0
0
2
1
0
0
0
3
2
0
2
0
0
0
0
2
0
0
0
2
1
0
2
1
1
0
1
1
0
2
0
0
0
0
0
0
2
0
2
3
1
0
2
2
1
0
0
0
3
2
1
0
1
0
0
2
2
0
2
0
2
0
0
1
0
1
3
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
1
5
0
0
0
1
0
2
0
1
2
0
1
0
1
3
0
0
0
1
0
0
0
0
4
0
2
0
8
0
0
2
1
0
0
0
0
0
2
2
0
2
1
2
0
2
0
2
2
1
0
0
1
1
0
2
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
1
1
0
1
0
2
0
0
0
1
2
0
0
0
2
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
1
2
1
0
0
0
1
1
2
1
0
2
0
0
1
4
0
0
0
0
0
1
2
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
1
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
1
0
2
2
1
0
2
0
2
1
0
2
0
0
0
1
2
0
2
0
2
0
0
0
3
0
0
2
2
1
0
0
0
0
1
0
1
1
2
0
2
0
2
2
1
0
2
0
0
2
0
0
1
0
2
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
2
0
0
2
2
2
0
0
0
2
1
0
2
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
1
2
1
0
1
2
0
1
1
1
0
1
0
0
2
0
2
0
0
1
0
0
0
2
1
2
0
2
0
0
1
0
1
0
2
1
4
0
1
2
0
0
0
1
1
0
0
0
0
1
2
2
0
1
2
1
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
1
2
2
0
0
0
0
0
0
2
1
0
0
2
0
0
2
2
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
1
1
1
0
4
2
0
0
0
0
2
0
2
1
0
1
0
0
0
1
0
0
0
2
2
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
1
1
0
1
0
0
3
1
0
0
0
0
2
1
0
0
2
0
0
0
2
1
0
0
1
1
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
1
0
1
1
0
3
0
0
0
1
0
1
0
0
0
1
0
0
2
0
0
0
0
2
1
0
1
2
0
0
1
1
0
0
0
0
0
0
0
0
2
1
1
2
0
2
4
2
1
2
0
0
0
0
0
0
1
0
1
1
2
0
0
0
0
0
2
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
2
2
0
0
0
0
0
2
2
0
0
1
1
1
0
2
1
0
1
0
0
0
0
1
0
1
0
0
1
2
0
0
1
0
1
0
0
2
0
2
0
0
0
1
0
1
2
0
0
2
2
2
0
0
0
0
2
1
1
0
2
2
1
0
0
2
0
1
0
0
0
2
2
0
2
2
2
7
1
0
0
0
0
0
0
0
2
1
1
1
0
1
0
2
2
0
0
1
0
2
0
0
0
0
2
0
0
0
1
1
0
1
2
2
0
0
0
1
0
1
1
1
0
0
0
0
0
1
2
0
0
0
2
0
2
0
2
1
0
0
0
3
2
0
0
1
2
2
0
2
3
0
2
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
3
3
0
2
1
0
1
1
0
0
2
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
2
1
2
0
3
0
0
0
0
2
0
0
0
0
0
1
1
1
0
1
0
0
1
0
0
0
0
1
0
0
0
2
0
0
1
1
1
1
1
0
2
1
2
0
0
0
1
0
0
0
0
0
1
1
0
0
3
0
2
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
2
0
3
0
0
1
0
0
0
0
3
0
0
2
2
3
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
1
0
0
0
0
0
1
0
2
0
0
1
0
0
2
1
0
1
1
1
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
2
2
0
0
0
3
1
0
3
0
0
2
2
1
0
0
1
0
1
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
2
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
1
2
0
0
0
0
0
0
0
0
6
0
0
0
0
0
1
2
2
1
0
0
0
0
0
2
0
0
1
2
2
1
0
1
0
0
0
0
0
1
0
0
2
0
0
2
2
0
0
2
0
1
2
3
0
0
0
2
2
2
0
1
1
3
2
0
1
0
0
0
1
0
1
0
0
1
1
1
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
1
2
0
0
0
0
0
0
0
0
2
2
2
1
0
0
1
0
0
0
1
0
0
0
0
2
3
0
2
0
0
2
0
2
0
2
2
0
2
1
0
0
0
1
0
0
0
0
3
0
2
1
0
2
0
0
0
1
2
0
2
1
1
1
1
1
0
1
1
2
0
0
0
2
1
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
2
2
1
1
3
0
1
1
0
2
0
0
0
0
0
3
0
0
0
2
1
1
0
1
0
0
0
0
2
1
0
2
0
0
1
0
0
0
0
0
2
0
0
0
3
0
0
2
0
3
0
0
0
0
0
2
0
2
0
1
0
0
4
1
0
0
0
1
1
0
1
4
0
0
0
0
0
0
0
0
0
3
0
0
0
2
2
2
2
0
0
3
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
1
0
2
0
0
0
0
2
2
0
2
3
0
1
2
2
1
0
0
0
0
0
0
1
0
0
0
1
4
0
0
2
0
0
0
1
2
1
0
4
0
1
1
1
2
2
2
0
2
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
2
0
2
0
0
0
1
3
0
0
0
2
0
2
2
0
1
2
0
0
2
0
1
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
2
2
2
2
0
0
2
0
0
0
2
1
0
0
0
3
1
0
0
1
1
0
2
0
1
0
1
2
0
0
7
0
2
0
2
2
0
0
0
2
2
0
0
2
0
1
0
2
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
2
1
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
2
0
0
1
0
2
0
2
2
0
0
0
0
1
0
0
0
0
1
1
2
0
2
1
0
0
0
2
1
1
0
2
0
0
1
2
0
2
0
2
0
2
0
1
0
2
0
2
1
0
0
2
0
0
2
0
1
2
0
1
0
2
0
0
0
2
0
2
1
0
2
0
0
0
2
1
3
0
0
0
0
0
1
0
0
0
1
0
1
2
2
0
2
0
0
0
1
0
0
2
1
0
0
2
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
2
3
0
1
1
0
2
1
0
3
0
0
1
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
1
0
2
2
0
2
2
3
3
0
2
2
0
0
1
1
1
1
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
2
2
0
0
1
0
0
0
0
2
3
1
0
0
1
2
1
0
0
0
0
1
0
2
1
2
2
2
2
1
0
0
2
2
0
1
2
0
1
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
1
0
1
1
0
0
1
0
0
2
3
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
1
0
2
0
1
0
1
0
0
0
0
4
2
2
0
1
0
1
0
0
0
1
2
0
1
0
2
0
0
2
0
0
0
0
0
1
0
2
1
0
2
0
0
0
1
0
2
2
2
0
3
0
2
0
1
2
0
1
0
2
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
2
1
0
0
2
3
0
1
0
1
0
0
2
0
1
1
0
2
0
0
0
0
2
1
4
0
0
0
1
4
0
0
2
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
2
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
3
0
0
2
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
1
1
1
0
0
2
0
1
0
0
0
0
3
1
0
1
0
1
0
3
0
0
0
0
0
0
2
1
2
2
0
1
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
1
0
0
0
2
0
2
2
2
1
0
0
0
1
0
0
0
0
2
0
2
0
0
2
0
0
0
1
1
1
2
0
0
0
1
2
0
0
0
0
0
3
0
2
0
0
0
1
1
1
0
0
2
0
0
1
1
0
2
1
0
2
0
0
2
0
2
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
4
1
2
1
1
2
2
0
1
2
0
0
1
0
2
0
0
0
0
0
1
0
0
0
2
0
1
1
1
0
0
0
0
2
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
2
1
0
2
2
0
0
2
0
2
1
1
0
1
0
0
0
2
0
0
4
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
2
1
2
0
0
0
1
2
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
1
0
0
0
3
0
0
0
2
0
0
2
1
0
0
0
0
0
1
2
0
0
3
0
0
2
2
0
0
0
0
1
1
0
0
0
1
0
2
1
0
0
2
2
0
0
1
0
0
0
1
0
1
0
0
0
0
0
2
2
2
2
0
1
2
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
1
0
1
0
0
0
0
3
2
2
0
0
1
1
0
0
0
0
2
1
0
1
0
2
1
0
0
0
0
0
0
2
0
2
0
0
3
0
2
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
1
2
1
0
1
2
0
2
2
1
5
0
0
0
0
2
3
1
1
2
0
0
1
0
0
0
0
0
2
0
1
0
1
0
0
1
0
0
2
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
1
1
0
0
2
0
0
0
2
0
0
0
0
1
0
0
2
1
1
0
2
1
1
0
0
0
0
0
0
1
1
1
0
1
0
1
2
0
2
0
0
0
1
0
0
0
1
0
0
0
1
3
1
1
0
2
0
1
2
0
0
2
2
0
2
0
0
0
1
2
0
1
0
2
1
0
0
2
0
0
0
0
2
0
0
2
0
2
0
2
0
2
0
0
0
0
2
2
1
2
1
0
0
1
1
3
0
1
0
0
2
0
1
2
0
0
0
0
0
0
2
0
0
1
1
0
1
1
0
1
0
0
0
2
1
1
0
1
1
0
2
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
1
1
1
0
0
1
1
0
0
2
0
0
0
1
2
0
0
0
0
0
1
2
1
0
1
2
0
1
1
0
1
1
0
0
0
1
2
0
0
0
2
1
0
0
2
0
0
1
0
2
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
2
1
1
1
0
2
1
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
2
2
0
2
2
2
1
1
0
0
0
0
2
0
2
1
1
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
1
2
1
0
0
0
1
2
1
0
2
0
1
1
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
1
3
0
2
1
0
2
1
1
0
0
1
0
2
0
2
1
0
2
0
0
0
0
1
0
0
1
0
2
0
0
2
1
2
0
0
0
1
0
0
0
0
2
0
0
1
1
2
1
1
1
0
0
0
3
1
0
0
0
0
0
2
1
0
0
0
0
0
2
1
0
0
0
1
1
0
0
0
2
1
0
0
0
3
0
0
0
0
1
3
1
0
0
2
0
1
0
0
0
0
1
1
2
0
0
0
0
0
1
1
2
0
2
0
2
1
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
1
1
1
2
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
2
1
0
1
2
1
0
0
1
0
0
1
0
3
0
0
1
0
2
0
0
2
2
0
1
2
1
0
0
0
1
1
0
3
2
1
0
0
1
0
0
0
1
3
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
4
0
0
2
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
3
0
2
0
2
2
0
0
1
1
0
1
2
0
0
1
0
0
0
1
1
1
1
0
0
3
0
2
1
0
1
0
0
0
0
0
0
1
1
1
2
0
0
2
0
1
1
2
0
0
1
0
0
2
1
2
0
1
0
0
3
0
2
1
0
0
0
0
0
0
2
1
0
1
1
0
1
0
2
0
1
0
1
2
0
0
1
2
0
1
0
2
2
0
0
1
0
2
2
1
1
0
0
0
0
0
1
1
2
2
6
2
0
2
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
5
0
2
0
0
1
0
0
2
0
0
0
1
1
1
0
0
2
1
0
0
1
0
0
0
5
0
0
0
0
1
0
0
2
0
0
1
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
2
1
0
0
0
2
0
1
0
0
0
1
2
6
0
0
0
1
0
0
3
1
0
2
0
0
0
0
2
0
0
2
0
1
1
0
2
1
1
1
0
0
0
0
2
1
0
0
0
1
0
0
0
1
1
0
0
0
0
2
2
0
0
0
4
0
0
1
0
0
0
0
0
1
0
4
0
0
0
0
0
3
2
0
0
2
2
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
2
0
0
0
0
1
0
0
1
1
1
2
2
0
2
0
1
0
0
0
2
1
1
2
0
1
0
1
0
1
0
0
0
2
0
0
0
0
1
1
0
0
2
0
0
0
2
2
0
0
0
1
1
2
0
1
1
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
4
0
0
2
0
0
0
1
0
0
2
1
1
1
0
1
0
0
0
1
0
2
0
2
2
0
0
0
2
0
0
2
2
0
0
1
0
2
2
0
0
0
0
0
2
0
0
0
1
2
1
0
0
0
1
0
2
0
0
0
0
0
5
1
2
1
0
0
0
0
2
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
1
2
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
1
1
0
2
0
0
0
2
0
0
2
0
2
2
3
1
2
0
0
0
0
0
2
2
1
0
1
2
0
0
0
0
0
1
0
1
0
0
0
2
0
0
1
0
1
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
2
2
0
1
0
0
0
2
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
2
0
2
0
0
0
1
1
0
3
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
1
2
0
0
1
0
0
1
2
1
0
0
0
0
2
1
0
3
0
1
0
0
0
0
0
0
0
1
2
2
1
0
0
0
1
0
0
0
0
0
0
2
0
1
0
2
1
0
0
0
0
1
0
5
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
2
0
4
1
2
1
0
0
0
0
0
0
1
0
0
1
1
0
2
2
0
0
0
2
0
1
0
0
1
0
2
0
0
1
2
0
0
2
2
0
0
1
1
2
1
1
1
0
1
0
0
2
0
0
0
1
0
1
0
1
0
0
1
0
2
0
0
2
0
0
2
1
0
1
1
1
1
0
2
0
0
0
0
0
0
2
0
1
0
1
0
1
0
3
2
2
0
0
1
0
2
0
1
2
2
0
0
0
0
0
0
1
1
0
0
2
0
2
0
0
0
2
0
0
4
2
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
2
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
1
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
1
7
0
0
0
2
0
0
1
0
1
0
0
0
0
2
0
0
0
2
0
0
2
0
2
1
2
2
0
1
2
2
2
1
2
0
0
0
1
1
0
2
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
1
2
1
2
0
0
0
2
2
1
1
0
0
1
0
0
0
1
0
0
0
0
0
2
2
0
0
0
1
0
2
0
0
1
1
0
1
1
1
0
0
0
0
1
0
1
0
1
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
1
1
0
0
2
0
0
0
0
2
1
1
0
0
1
0
3
1
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
3
1
0
2
2
1
3
0
3
0
0
2
2
0
2
0
0
2
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
2
2
1
2
0
0
1
1
0
0
0
1
0
0
0
3
0
0
2
2
0
2
0
0
0
0
0
2
0
0
2
1
2
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
1
0
1
0
1
0
0
1
0
0
2
0
1
0
0
0
2
0
0
0
2
0
2
1
0
1
0
4
0
1
1
0
3
0
1
1
0
1
5
1
0
0
1
0
0
2
0
0
2
0
0
0
2
0
0
1
0
0
0
0
2
2
0
0
1
1
0
0
0
0
2
2
0
0
0
0
0
1
1
1
1
1
1
0
3
2
2
0
0
0
2
2
2
0
2
0
2
1
0
0
1
0
1
2
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
1
1
0
1
0
0
0
1
1
1
0
0
0
0
1
0
0
2
0
0
0
1
2
0
2
2
0
0
0
2
1
0
0
0
0
2
3
0
0
0
1
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
2
1
0
0
0
0
1
0
0
1
0
2
1
0
2
2
0
2
1
0
1
1
0
0
1
0
0
1
2
1
1
0
2
0
0
0
2
0
0
0
0
3
4
0
0
0
0
0
0
0
0
2
0
2
1
1
1
0
0
1
1
2
2
2
0
0
1
2
0
0
1
1
0
1
2
1
2
0
0
0
2
1
0
0
0
1
0
2
3
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
1
2
1
0
0
0
0
0
0
0
0
1
1
1
0
1
2
0
1
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
2
3
0
1
0
0
2
0
0
0
0
2
0
2
0
1
2
1
1
0
0
0
2
0
0
1
0
0
0
0
0
2
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
1
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
2
0
2
0
0
0
0
0
0
0
0
1
1
2
1
3
4
2
0
0
2
0
2
3
0
2
0
0
2
0
0
1
1
1
0
0
0
0
0
0
1
0
0
2
1
1
0
1
3
2
1
0
0
2
0
2
3
0
0
2
2
0
0
1
0
0
0
0
0
0
1
0
0
0
2
1
0
2
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
1
1
1
1
0
1
0
1
0
1
0
3
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
2
0
0
2
3
0
1
2
1
1
0
1
0
1
2
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
2
0
1
1
0
0
2
2
2
0
0
0
0
0
2
0
0
1
1
0
2
0
2
2
0
0
1
2
1
1
1
1
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
1
0
0
0
2
1
2
0
0
0
0
1
0
0
2
0
0
1
1
0
0
2
1
0
0
2
0
3
0
1
0
0
0
0
0
1
1
0
0
2
0
0
0
0
1
0
0
2
0
1
1
2
2
0
0
0
0
0
0
0
1
2
3
2
1
0
2
0
0
1
2
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
1
1
0
2
2
1
2
0
0
2
0
0
0
1
1
0
1
1
1
1
0
0
0
0
1
1
0
0
1
0
0
0
1
2
1
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
1
0
2
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
1
1
0
1
0
0
0
2
0
0
0
0
2
0
0
2
1
0
2
0
2
0
0
0
0
1
0
0
0
0
1
2
0
2
1
2
0
0
1
0
0
0
0
0
1
4
0
0
1
1
0
2
0
0
2
0
0
2
0
0
2
3
1
0
0
0
1
0
0
2
0
0
0
1
2
2
1
0
1
0
0
0
0
2
0
2
0
2
2
1
0
0
1
0
0
0
2
0
1
0
2
0
0
0
0
2
0
0
0
0
0
1
2
1
0
0
0
0
0
1
0
1
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
1
0
0
2
0
4
1
2
0
1
0
0
1
2
0
1
4
0
1
1
1
0
0
0
1
0
0
0
2
1
1
1
0
0
0
2
0
0
0
1
0
0
2
0
1
0
1
0
0
0
0
0
2
2
0
0
0
0
1
1
0
3
0
1
0
0
0
1
0
0
0
0
1
2
0
0
0
2
0
2
2
0
0
0
2
11
0
0
2
1
0
2
2
1
1
1
2
0
0
0
0
0
0
2
2
1
0
2
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
2
2
0
1
0
1
2
0
0
1
1
0
2
3
2
1
0
2
0
3
2
0
0
0
1
2
2
0
0
0
1
0
0
1
2
0
0
0
1
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
1
1
0
1
2
1
0
0
0
0
0
0
0
3
0
2
1
0
0
2
0
0
2
2
0
0
0
2
2
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
2
0
2
0
3
0
0
0
1
0
1
0
0
0
2
0
1
0
0
1
0
0
1
2
0
1
0
1
0
0
2
1
0
2
0
2
0
0
1
0
3
0
0
0
0
2
1
1
0
0
0
2
0
0
0
0
0
0
0
2
2
1
0
2
1
0
0
0
1
0
1
0
0
0
0
0
1
2
1
2
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
2
0
1
1
0
0
0
0
0
1
0
0
0
2
1
1
1
0
0
0
1
1
1
0
0
1
1
0
3
0
0
1
0
1
0
2
0
0
0
0
1
0
0
3
3
0
1
2
0
2
0
1
0
0
0
0
2
1
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
1
1
0
0
0
0
0
0
1
2
3
1
0
2
0
0
0
0
2
0
1
2
2
2
0
1
2
0
1
0
1
0
0
0
1
2
0
0
0
0
1
0
1
2
1
0
0
1
0
1
1
0
0
0
0
3
0
0
2
0
1
2
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
2
1
1
0
0
1
1
1
0
1
2
3
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
1
1
1
0
1
0
0
2
0
0
1
2
0
2
2
2
1
1
0
0
1
0
2
1
2
0
0
1
3
2
0
0
0
1
0
0
0
1
1
0
1
1
0
3
1
0
0
0
1
0
0
2
0
0
0
1
0
0
0
1
1
1
0
0
2
0
0
0
0
2
0
0
0
1
0
2
3
3
0
1
0
3
0
0
0
0
2
0
1
1
2
0
1
0
0
2
2
0
0
3
0
0
0
0
2
1
1
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
2
0
0
0
0
0
2
0
0
1
2
1
1
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
3
0
3
0
2
0
2
0
0
0
1
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
1
1
0
2
1
1
0
2
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
1
1
0
1
0
1
0
0
1
0
0
0
1
0
0
2
0
2
0
0
0
0
1
1
0
0
0
0
1
0
2
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
3
0
0
0
0
0
1
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
1
2
0
0
0
1
0
2
0
0
0
1
0
0
0
0
3
0
0
0
0
0
2
2
0
0
0
0
0
2
7
1
0
0
1
3
0
2
2
0
1
0
0
0
0
1
0
2
0
0
0
2
1
1
0
0
1
0
2
0
1
0
2
0
0
1
0
0
1
0
0
0
2
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
1
1
0
1
0
0
0
2
0
0
0
0
1
1
1
1
1
2
1
1
1
2
0
0
1
2
0
1
0
0
2
0
0
0
2
0
0
1
0
2
0
1
0
0
0
0
2
1
0
0
1
0
0
0
0
0
1
0
1
0
2
0
2
1
0
0
0
0
0
0
0
0
2
2
2
0
2
2
0
0
0
0
0
2
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
2
2
0
1
0
2
0
0
2
0
1
0
0
0
0
2
1
0
0
0
2
1
0
0
1
0
2
0
1
1
0
0
0
0
0
2
1
2
1
0
0
2
0
0
0
0
2
0
0
2
0
0
2
0
0
0
1
0
0
0
4
0
1
1
0
0
0
1
2
0
1
0
0
1
0
1
1
1
2
1
1
1
0
1
2
0
0
2
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
2
0
4
0
0
1
0
0
0
1
0
1
0
2
0
0
0
0
0
0
4
0
1
0
1
0
0
0
0
0
0
1
1
0
2
2
1
1
2
0
2
0
0
2
2
0
0
0
0
1
2
0
0
0
1
3
0
1
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
0
2
0
0
2
2
1
2
0
0
0
0
2
0
0
2
1
0
1
0
2
0
0
0
1
0
0
1
0
0
2
0
0
1
0
2
3
2
0
0
0
0
0
1
1
2
0
0
0
2
2
2
1
0
1
1
1
0
2
4
0
0
0
0
2
1
2
0
0
0
2
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
1
0
0
2
0
2
0
0
3
2
1
0
2
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
2
0
0
0
0
0
0
1
3
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
2
0
2
0
0
0
2
0
2
2
0
0
4
0
2
0
0
2
0
0
0
2
0
0
0
1
1
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
3
0
2
2
0
0
1
1
0
0
0
2
0
0
0
2
0
2
0
0
1
0
0
1
1
0
0
2
0
0
1
1
2
0
0
2
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
1
0
0
1
2
2
0
0
0
0
0
0
0
0
2
0
1
0
1
0
1
2
2
2
0
2
0
0
0
0
1
0
1
0
1
1
0
0
2
2
0
0
0
0
2
0
1
0
1
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
1
1
1
0
1
2
0
0
0
0
0
0
0
2
0
2
1
0
0
1
1
4
0
0
0
0
2
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
2
0
0
0
0
0
0
1
0
1
2
0
0
1
0
0
0
0
3
0
0
1
0
2
1
0
3
0
1
0
0
0
1
0
1
2
0
1
0
0
1
1
0
2
2
0
0
2
2
0
2
0
0
1
0
0
1
0
0
0
0
2
0
2
2
0
2
2
2
1
0
0
2
0
1
2
1
0
0
2
1
0
0
0
0
1
0
0
1
0
0
0
1
1
1
0
0
1
1
3
0
1
0
3
1
0
0
0
0
0
1
0
2
0
2
0
1
1
0
1
1
0
1
0
0
2
0
0
1
2
1
1
0
1
0
0
0
0
2
0
1
2
0
1
2
0
0
0
1
1
0
2
1
2
1
0
0
2
2
2
0
3
1
2
0
0
1
0
2
0
1
0
1
0
0
1
0
3
0
2
1
0
0
2
0
0
2
1
0
0
0
1
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
3
0
0
2
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
2
0
2
3
0
0
0
0
1
1
2
0
2
0
2
0
1
2
0
0
2
1
1
1
0
0
0
0
0
0
2
2
0
2
0
0
3
0
0
2
0
2
2
2
2
0
0
0
2
0
0
2
2
2
1
0
2
0
0
0
1
0
2
1
1
0
1
0
2
2
1
2
2
2
0
0
1
2
2
0
1
0
0
1
0
0
2
2
2
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
1
0
2
0
1
0
1
2
0
1
0
1
1
1
0
0
1
0
0
2
0
0
0
0
2
3
0
0
1
1
0
0
1
0
0
0
2
1
2
1
0
0
0
1
0
0
0
0
0
0
2
0
0
1
2
1
1
2
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
1
1
1
0
2
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
1
2
2
0
0
1
2
0
0
1
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
3
1
0
1
0
0
2
0
0
2
0
0
2
2
5
1
1
0
1
0
0
1
1
0
1
0
0
0
0
2
2
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
2
0
0
0
1
0
2
0
1
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
6
0
1
0
0
0
2
0
1
0
0
0
1
0
1
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
1
4
2
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
3
0
2
0
0
2
0
1
0
0
0
0
0
0
0
1
2
2
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
2
0
1
0
0
0
0
0
0
2
2
0
0
0
1
0
1
0
1
2
0
0
2
1
0
0
2
1
2
0
2
0
1
0
0
0
0
0
1
2
0
0
0
5
2
0
0
2
0
0
2
0
0
0
1
2
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
1
0
1
1
2
0
2
0
2
0
0
1
1
0
0
0
0
0
1
2
1
2
0
0
0
2
1
1
1
0
2
1
2
2
0
0
1
0
0
0
2
0
0
1
1
0
0
0
1
2
0
0
1
0
2
0
1
0
0
2
0
1
0
0
0
0
3
2
2
2
2
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
2
1
0
0
1
2
2
1
0
2
0
0
0
2
0
0
3
2
0
0
0
4
0
0
1
0
1
0
0
0
0
2
1
0
0
2
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
1
1
0
1
0
1
2
0
0
0
0
0
0
0
2
2
1
1
0
0
0
0
1
2
1
1
0
2
1
0
1
1
0
0
1
0
1
1
1
1
0
3
0
0
2
0
0
0
1
0
0
0
0
0
2
0
2
0
1
2
0
0
1
0
0
0
0
0
2
0
1
0
5
2
1
0
0
1
3
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
1
0
0
2
0
0
1
3
1
0
0
2
1
0
2
0
0
0
0
1
0
0
1
0
1
0
2
0
0
0
0
2
1
1
0
1
1
2
0
1
0
0
2
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
1
0
2
2
0
0
1
0
0
0
0
1
2
0
0
0
0
2
2
0
1
0
0
0
2
1
0
2
1
0
0
2
2
0
1
0
1
0
0
0
1
2
2
0
0
0
0
0
2
0
2
0
2
0
0
0
1
1
2
0
0
0
1
0
2
1
0
0
0
1
1
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
1
2
2
0
0
0
1
1
0
1
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
4
0
0
2
0
0
1
0
0
2
0
0
1
0
2
0
0
0
0
0
3
0
1
0
1
0
1
2
0
2
0
1
1
0
0
2
2
1
1
0
0
2
0
2
0
0
1
0
0
2
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
2
0
1
2
0
2
0
2
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
1
1
1
2
0
0
0
2
5
0
0
0
0
2
0
0
0
2
1
0
3
1
1
0
2
0
1
0
0
0
2
2
2
0
0
1
0
1
2
0
0
0
3
1
0
0
0
0
0
0
1
1
0
2
0
0
1
0
0
0
0
2
0
1
1
0
0
2
2
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
2
2
2
0
0
2
2
0
2
1
0
0
0
1
0
0
0
0
2
0
2
2
0
2
0
2
0
0
2
0
2
1
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
1
0
3
2
0
3
2
2
0
1
0
0
1
0
1
0
1
0
2
0
0
0
1
0
0
3
0
0
0
0
1
1
2
2
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
2
0
0
0
0
1
1
1
2
0
2
0
2
0
1
1
2
0
1
1
0
1
0
2
2
2
0
0
1
0
0
1
0
1
2
1
2
0
0
1
0
1
2
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
2
1
0
1
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
1
0
3
1
1
0
2
0
2
0
0
0
6
0
1
0
1
0
0
2
1
0
1
0
0
2
0
1
1
1
1
0
1
1
0
0
0
0
2
1
0
0
1
4
0
0
2
0
0
1
2
0
0
0
2
0
0
2
0
0
2
2
0
1
1
2
0
1
1
2
1
2
0
0
0
0
0
0
2
1
0
0
0
1
1
0
0
0
1
1
0
0
2
1
0
0
1
2
0
0
0
2
1
2
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
2
1
0
0
0
0
0
1
0
0
1
1
0
2
0
0
1
1
2
1
1
0
0
0
1
0
1
2
0
0
1
0
0
0
1
0
0
0
2
0
1
2
1
0
0
0
1
0
1
0
2
0
1
0
0
0
2
0
0
2
0
0
0
2
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
1
0
2
2
2
0
0
0
0
2
2
1
1
2
1
0
1
0
2
1
0
0
2
0
0
0
2
2
2
0
0
0
1
1
0
0
0
0
1
2
2
0
2
0
0
1
0
0
1
0
0
0
3
0
2
0
0
1
2
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
1
1
1
1
1
0
0
0
1
1
0
1
1
1
0
0
0
0
2
2
1
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
4
0
1
0
0
2
2
3
0
0
2
0
1
2
2
2
2
0
2
0
0
0
0
0
2
2
1
2
0
1
0
1
0
0
0
0
0
5
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
1
2
0
2
2
2
0
0
0
1
0
1
3
0
0
0
0
0
2
2
0
0
0
1
0
0
0
3
0
1
1
2
2
0
0
2
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
2
1
2
0
0
1
1
2
1
0
0
2
0
1
1
1
2
0
0
3
0
3
0
2
0
0
1
0
1
0
4
0
0
2
0
0
1
0
0
0
0
2
0
1
1
0
0
2
1
1
0
0
0
1
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
1
1
1
1
0
0
2
1
0
0
0
1
2
0
1
0
0
1
2
0
1
0
1
2
0
0
0
0
2
0
2
1
3
1
0
0
2
1
0
0
0
0
4
1
0
1
0
1
2
0
1
0
0
0
2
1
1
2
1
1
3
1
1
0
0
0
3
1
2
0
0
1
1
0
2
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
2
0
1
0
2
0
1
0
0
2
0
2
0
2
0
2
0
2
3
0
1
0
1
0
1
4
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
1
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
1
2
0
0
0
2
0
2
1
0
0
1
0
0
0
0
1
0
2
2
1
0
3
0
0
1
0
0
0
0
1
2
0
0
0
0
1
0
0
1
0
2
0
0
0
2
0
0
1
0
0
1
0
0
0
2
2
1
1
0
1
0
2
0
0
2
2
2
0
2
3
0
0
2
2
2
2
0
0
0
2
0
2
2
0
1
2
1
0
0
0
0
2
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
1
0
1
2
0
2
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
2
0
1
1
0
0
0
2
0
0
0
0
0
3
2
2
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
2
0
0
1
0
0
0
0
0
0
2
0
1
2
1
0
2
1
2
0
1
0
1
1
0
0
0
2
0
0
1
0
0
1
2
0
0
0
0
2
0
0
1
2
0
1
1
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
1
0
0
2
1
0
0
1
0
0
0
1
0
0
2
0
0
1
0
0
2
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
4
0
0
0
0
1
0
1
2
1
0
0
0
0
0
0
2
0
1
3
0
1
0
0
0
1
0
2
0
0
1
0
0
2
3
0
1
0
0
0
0
2
0
0
0
0
2
0
0
1
0
2
1
2
0
1
1
1
2
3
2
1
1
2
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
2
2
0
0
1
0
0
2
4
1
0
0
1
0
0
0
0
1
0
0
0
0
4
0
1
0
2
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
1
0
0
0
0
0
2
1
2
2
1
3
0
0
1
0
0
1
1
0
0
2
0
2
2
0
1
1
0
0
0
5
0
2
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
2
1
2
1
0
0
2
2
0
0
5
0
0
2
0
0
1
0
1
1
0
2
0
0
0
0
0
0
0
1
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
1
0
0
0
1
2
0
0
1
2
0
0
1
0
2
0
2
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
2
0
0
1
0
0
0
1
2
0
0
2
0
0
0
1
0
2
1
0
1
2
0
0
0
1
1
0
0
0
0
2
2
0
1
2
2
2
0
2
1
0
0
0
2
0
1
0
0
0
1
0
1
0
2
0
0
0
2
0
0
0
0
0
0
1
1
1
1
2
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
3
0
0
0
0
0
1
2
0
1
1
1
0
1
0
1
2
0
1
0
2
0
0
1
1
1
2
1
0
0
0
0
0
1
2
0
0
2
0
3
0
1
0
0
1
1
1
0
0
0
0
0
0
2
0
0
1
2
0
0
0
2
1
0
0
0
3
0
2
0
3
2
0
0
0
0
0
0
0
1
0
0
2
1
1
0
1
0
0
2
0
0
0
0
0
0
2
0
0
2
0
1
0
1
0
0
2
0
0
1
0
1
2
2
1
2
1
0
0
1
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
2
1
0
0
1
0
2
0
0
0
0
0
0
1
3
2
1
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
2
1
1
0
0
1
2
0
5
2
0
0
0
2
1
2
0
0
0
1
0
0
0
0
2
2
0
1
1
0
3
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
1
0
0
1
0
0
2
0
2
1
0
0
1
1
0
2
2
2
0
0
2
0
1
0
2
0
0
0
0
2
0
0
1
1
2
1
0
0
0
2
0
3
1
0
0
2
0
0
1
1
1
0
2
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
2
2
2
2
0
1
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
1
0
0
2
3
2
0
0
0
2
0
0
0
0
2
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
2
2
1
0
2
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
1
2
0
0
0
3
0
2
1
0
2
2
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
3
0
2
2
0
2
0
0
0
0
2
1
0
0
2
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
1
2
0
2
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
1
1
0
2
0
0
1
0
1
2
2
0
0
0
1
0
1
0
0
0
1
0
0
1
0
1
0
2
1
0
0
0
0
1
1
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
2
0
1
1
0
1
1
0
0
1
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
1
0
3
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
1
1
0
2
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
1
0
2
2
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
2
2
1
0
0
0
1
0
0
2
0
0
1
1
0
2
0
0
2
0
0
0
1
1
0
0
2
0
0
2
1
2
2
0
0
1
2
2
1
0
2
0
2
0
0
0
1
0
1
0
0
0
0
1
0
2
0
0
0
1
0
1
0
2
0
2
0
0
1
0
2
1
0
2
0
0
1
0
2
0
1
0
0
1
0
0
2
2
1
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
2
0
0
2
1
1
1
0
2
1
1
2
0
0
1
0
0
0
0
0
2
2
2
4
0
0
0
0
0
2
0
2
0
0
2
0
1
0
1
1
0
4
0
2
0
2
0
1
0
0
0
0
0
0
1
2
2
0
0
2
0
0
2
2
0
3
0
1
0
1
0
0
0
0
3
2
0
2
0
3
1
2
2
0
2
2
0
0
0
0
0
1
2
1
0
2
0
0
0
1
0
1
0
1
0
0
1
0
1
0
0
0
2
1
3
0
1
0
0
0
3
0
2
0
1
1
0
1
0
0
3
0
1
2
0
0
2
0
0
0
2
0
0
1
0
1
1
0
0
0
0
0
0
2
2
0
2
2
0
2
1
0
0
1
0
1
0
0
1
0
2
1
0
2
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
1
2
1
2
2
2
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
1
0
1
0
1
0
2
0
0
0
0
1
0
0
2
2
2
0
0
0
2
1
1
0
1
2
0
0
1
0
0
2
2
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
16
1
0
1
1
0
0
1
2
2
0
0
0
0
0
0
0
2
1
0
1
0
1
0
1
0
0
0
0
3
0
0
0
0
0
2
2
2
2
0
1
0
0
0
0
0
0
0
1
1
0
0
2
1
1
0
2
0
0
0
0
1
1
0
0
2
2
0
0
1
0
0
1
0
0
1
2
0
2
1
0
0
0
0
1
0
0
0
0
2
0
1
2
0
0
0
0
0
3
0
0
0
0
0
2
1
2
3
1
0
0
1
0
0
1
0
1
1
1
0
1
2
0
0
0
0
0
0
0
2
1
1
2
1
0
1
1
1
1
2
1
0
0
0
0
2
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
1
2
2
0
2
0
0
0
0
1
0
0
1
3
0
1
1
0
0
0
2
1
0
0
0
1
1
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
2
0
2
0
0
2
1
0
2
0
0
0
0
4
0
1
1
0
0
0
1
0
0
1
0
0
2
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
3
1
1
0
0
0
0
2
2
0
0
0
0
0
0
0
2
2
1
2
0
1
0
0
2
0
0
0
0
0
0
1
0
0
3
1
2
3
0
2
0
2
3
2
0
0
1
1
1
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
1
0
0
1
0
1
0
0
0
0
1
0
1
1
0
2
1
0
0
0
0
1
0
2
0
0
1
0
0
0
0
1
0
2
2
0
0
0
0
2
0
0
1
1
2
0
0
0
1
1
1
1
0
0
1
0
4
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
1
0
0
2
1
1
0
1
0
0
2
0
0
0
2
1
0
1
0
1
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
1
2
0
0
2
0
0
1
0
0
0
0
1
5
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
2
0
1
0
2
1
0
0
0
0
0
1
0
3
0
0
0
0
2
0
0
0
0
3
0
0
0
0
2
1
0
0
1
1
0
1
0
1
1
2
0
0
0
0
1
0
2
0
0
0
0
0
0
3
2
0
2
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
3
0
1
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
2
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
6
0
0
4
1
0
0
0
0
0
2
0
0
0
2
1
0
0
0
3
0
0
0
0
0
2
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
1
2
2
1
0
1
1
0
1
2
0
0
0
4
0
0
0
0
1
0
1
0
0
0
1
2
2
0
0
0
0
3
3
1
2
4
0
0
2
0
0
0
1
0
0
2
0
1
0
0
1
0
2
0
2
0
0
1
1
2
0
2
0
0
0
0
2
0
0
0
0
2
3
1
1
0
0
2
1
0
0
0
0
2
0
1
1
1
0
0
0
0
0
0
0
0
2
0
0
2
1
2
0
0
3
1
0
2
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
4
0
0
4
0
0
2
0
0
0
0
0
0
2
0
0
0
1
1
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
2
0
2
1
0
0
0
0
1
0
2
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
1
1
0
0
1
1
0
0
0
0
0
0
2
1
1
0
2
1
0
0
2
1
2
2
0
0
1
0
2
0
2
0
0
2
1
0
0
0
0
4
0
0
0
0
0
0
1
0
2
0
2
0
0
1
0
1
3
0
0
3
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
2
3
2
0
0
0
1
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
3
1
0
2
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
1
0
1
0
0
1
0
1
0
0
0
0
1
0
0
1
2
2
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
1
1
1
0
1
0
3
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
1
0
1
0
0
0
1
0
1
0
0
0
2
0
1
2
1
1
0
0
0
2
2
0
0
1
2
2
1
0
0
2
0
0
0
0
0
0
0
2
3
0
1
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
2
2
2
0
1
0
0
0
0
0
7
0
0
2
1
0
2
11
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
2
0
1
2
2
0
0
0
2
1
2
2
4
1
0
0
0
2
0
0
0
1
0
0
2
0
0
1
0
0
0
1
1
0
0
1
2
0
0
0
0
1
0
2
0
1
0
1
1
0
0
0
2
0
0
1
0
1
2
0
1
0
0
0
1
1
1
0
2
2
1
0
2
0
1
0
0
2
1
2
1
0
1
0
2
2
0
0
0
1
0
0
1
0
1
0
7
0
1
0
0
0
1
2
2
0
1
1
0
0
0
0
2
0
0
1
0
1
1
1
0
1
2
2
2
1
1
0
0
0
2
0
2
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
2
2
0
2
0
2
1
1
0
1
0
0
0
1
2
1
1
2
1
0
0
0
0
2
1
0
0
0
1
2
0
1
2
0
0
2
0
0
0
0
0
0
4
0
2
3
1
1
0
0
0
1
0
0
1
0
0
1
0
0
2
0
0
1
0
0
1
0
0
2
0
0
0
0
1
0
0
0
3
0
1
0
1
1
1
0
0
0
1
2
0
0
1
0
2
1
0
1
0
0
0
0
1
0
3
2
1
0
2
0
2
1
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
2
1
0
0
0
1
2
1
1
0
1
1
2
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
1
0
1
0
0
1
1
0
1
0
0
0
0
0
0
1
1
0
1
0
1
0
0
2
0
0
0
1
0
0
0
0
0
1
2
0
0
0
2
0
2
2
0
0
2
0
0
0
0
0
0
0
0
2
1
2
0
0
2
1
0
0
2
0
0
0
1
2
0
0
0
0
2
2
0
0
1
0
2
1
1
0
0
0
1
1
0
0
2
1
2
0
0
0
0
0
0
1
3
1
0
0
0
2
0
0
0
2
0
0
1
0
1
1
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
2
0
0
1
4
0
0
2
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
1
0
2
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
1
2
0
1
1
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
1
0
2
0
1
1
0
0
0
0
0
0
0
0
2
2
2
0
0
1
0
0
0
0
0
0
1
1
0
0
0
2
0
0
1
0
2
0
0
0
1
2
2
2
0
2
0
0
3
3
0
0
0
1
1
2
0
1
2
0
2
1
1
1
1
1
0
1
0
0
2
3
0
2
2
2
0
0
0
2
1
0
0
1
1
0
1
0
0
0
0
0
4
0
1
0
1
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
2
0
2
0
0
0
0
2
0
1
0
2
0
0
2
2
0
3
0
2
0
0
0
2
0
2
0
0
0
1
2
1
0
0
1
1
1
0
0
0
0
0
0
1
0
0
3
0
2
0
0
0
1
0
3
1
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
2
2
2
0
3
0
1
0
0
2
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
2
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
2
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
2
1
1
1
0
3
0
0
0
0
2
1
1
0
0
0
1
0
1
0
1
2
1
0
0
1
0
0
2
0
0
0
1
1
2
1
1
1
0
1
1
0
1
0
0
0
2
2
0
0
0
0
0
1
0
0
0
1
1
0
0
1
2
0
0
0
1
1
2
2
1
1
0
1
0
1
0
2
0
0
1
0
0
2
0
0
2
1
0
0
0
1
0
3
2
0
0
0
0
2
2
2
0
1
2
0
0
1
0
2
1
2
2
0
0
1
0
0
2
1
0
4
0
0
0
1
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
1
4
2
0
0
0
2
0
1
0
0
0
1
2
0
0
0
0
1
0
1
0
1
1
0
1
0
1
0
2
2
0
1
0
2
0
1
2
0
0
0
1
3
1
1
1
0
1
2
2
0
0
0
0
0
0
0
0
0
1
0
2
2
1
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
2
0
2
1
2
0
1
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
1
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
1
1
2
1
0
0
2
0
0
1
0
4
1
1
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
1
0
1
3
0
0
2
1
0
1
0
1
0
0
0
0
0
0
1
1
0
0
1
2
0
2
0
0
1
1
0
0
2
0
0
0
2
2
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
1
0
2
0
1
1
1
0
0
2
3
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
9
0
0
2
0
0
0
3
0
0
1
1
2
0
0
0
2
0
0
2
1
2
1
0
1
2
0
0
0
0
1
0
0
0
2
2
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
1
1
1
1
5
1
7
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
2
2
1
3
0
0
0
0
0
0
0
2
2
0
1
2
0
2
0
0
4
0
1
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
3
0
2
2
1
0
0
0
0
1
1
2
2
1
0
0
1
0
0
1
0
0
1
0
1
1
0
1
0
0
0
0
1
0
0
2
1
1
0
2
0
0
0
1
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
1
0
1
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
2
2
1
0
1
2
1
2
0
1
1
2
1
0
2
2
0
0
2
1
0
0
0
0
2
0
1
0
0
0
2
1
0
0
0
2
0
0
0
2
0
2
2
0
0
0
0
0
2
0
1
1
1
0
0
0
2
0
0
0
0
0
1
0
2
0
0
1
1
0
6
2
0
1
0
1
1
1
0
1
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
1
1
0
1
1
0
0
0
2
0
0
0
1
0
0
0
0
2
1
0
0
2
0
0
2
0
0
1
0
1
0
0
0
0
0
0
1
0
2
1
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
5
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
3
0
0
1
1
1
0
1
3
2
1
1
0
1
0
0
0
1
0
1
0
1
0
2
2
1
2
2
0
0
2
0
1
2
1
0
2
0
0
1
0
0
1
0
0
0
1
1
0
1
0
0
0
2
1
0
0
0
1
2
3
1
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
1
1
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
1
0
0
0
1
1
0
1
0
2
0
0
2
0
1
0
1
0
1
0
0
0
0
2
0
1
0
0
0
2
0
1
0
0
2
1
0
0
1
0
0
2
0
0
0
3
2
0
0
2
0
1
0
0
0
0
0
0
2
0
0
1
0
0
1
0
2
0
0
0
2
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
1
0
0
0
2
4
0
0
0
1
0
2
0
1
1
1
2
1
2
0
2
2
0
1
3
0
1
2
1
2
0
1
0
3
2
0
2
2
1
0
0
0
0
1
2
1
0
1
0
0
0
0
0
0
0
1
2
1
0
1
1
2
1
2
0
1
0
0
1
0
2
0
0
2
1
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
1
0
1
1
2
2
0
1
0
2
2
0
0
1
5
0
2
0
0
0
0
1
1
2
1
0
3
0
0
1
0
0
1
0
2
2
0
1
0
2
0
0
2
0
0
0
1
0
0
2
2
0
1
2
1
0
1
1
0
2
4
2
2
0
1
1
2
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
1
0
0
0
1
2
0
0
0
0
1
2
0
0
2
1
3
2
4
0
0
0
0
0
0
0
2
0
2
1
1
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
2
2
2
0
2
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
2
0
1
0
0
2
0
1
0
0
1
0
0
2
0
0
1
2
0
2
1
0
2
1
0
0
2
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
2
0
0
0
0
2
1
4
0
0
1
1
1
0
0
1
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
2
1
1
1
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
1
2
0
0
0
0
0
1
2
0
0
0
0
0
3
2
0
0
2
1
0
2
1
1
2
1
0
0
1
0
0
5
0
2
2
0
2
0
0
0
0
0
0
0
1
0
1
0
1
3
1
2
0
0
1
0
0
2
0
0
0
0
0
0
2
2
0
1
1
2
3
0
0
0
0
2
0
1
0
0
2
1
1
0
1
2
0
0
0
3
0
0
0
0
0
2
3
1
0
0
0
2
0
0
1
0
1
0
2
0
0
0
2
0
0
0
0
1
2
0
2
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
2
0
2
0
0
2
0
0
2
0
0
1
0
0
0
0
2
0
0
3
2
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
1
1
0
0
1
0
1
0
2
0
0
1
2
0
0
0
0
1
0
2
2
0
1
2
0
0
0
2
2
0
1
1
3
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
2
0
0
0
1
2
0
2
1
2
1
0
0
0
0
0
1
1
1
1
0
0
2
2
0
2
0
0
1
1
1
0
0
1
0
0
2
0
0
1
0
2
2
0
1
1
0
0
0
0
0
2
2
1
0
4
2
2
0
2
2
2
2
2
0
0
0
0
0
0
0
0
2
1
0
1
1
0
2
0
1
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
2
0
0
0
2
0
0
1
0
0
1
0
0
0
2
0
0
2
0
0
1
0
3
2
2
1
0
0
1
0
0
0
0
2
0
0
0
1
1
0
0
0
1
0
1
0
0
0
2
2
0
0
0
0
1
3
0
1
1
0
0
0
0
3
0
2
0
1
0
0
0
2
0
0
0
0
0
1
0
2
0
1
0
0
0
0
1
0
3
0
1
0
1
3
0
0
2
0
0
1
0
2
1
0
0
0
1
0
0
0
1
1
0
2
0
1
2
0
3
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
2
1
0
2
0
0
0
2
1
0
2
1
0
0
0
0
1
0
0
0
0
0
2
0
0
4
2
0
0
0
0
1
1
2
1
0
1
0
0
0
0
0
1
0
0
0
0
2
0
1
2
1
0
0
0
2
1
0
0
0
0
0
1
2
0
0
1
0
1
1
2
1
1
1
0
1
0
1
0
0
0
1
0
0
0
1
2
2
0
0
2
0
0
0
0
2
0
2
0
1
0
0
2
0
0
0
0
3
0
0
1
2
2
2
2
1
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
1
2
0
0
2
1
0
0
0
0
2
1
1
1
2
2
2
1
0
0
0
0
0
4
0
1
0
1
0
1
0
0
0
1
0
0
0
2
0
1
2
1
2
0
0
0
0
0
0
0
0
2
1
0
0
2
0
2
1
0
0
0
2
2
2
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
1
0
2
0
0
0
0
1
0
0
0
1
0
2
1
0
0
2
2
0
2
2
0
1
0
0
2
0
0
1
1
0
0
0
0
0
0
2
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
2
1
2
0
1
0
1
2
1
2
0
0
0
1
1
1
1
0
0
0
0
0
0
0
2
0
3
1
0
1
0
0
0
1
1
1
0
0
0
2
2
2
0
0
2
0
2
0
0
1
2
0
0
0
0
0
2
1
1
0
2
1
2
1
2
0
0
1
0
2
1
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
2
1
1
2
2
0
0
0
0
0
1
0
0
1
2
0
0
0
0
2
0
0
0
2
0
1
0
0
1
2
2
0
0
0
2
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
2
0
0
0
0
0
0
1
2
0
0
1
0
2
0
2
2
1
0
0
0
5
0
0
0
1
0
1
0
2
0
0
1
0
0
0
1
1
0
1
0
0
1
1
3
0
0
1
0
2
0
0
0
0
1
2
0
5
0
0
1
2
0
0
1
1
0
0
0
0
0
1
0
1
2
0
1
2
0
1
0
0
1
0
1
0
0
0
0
1
2
0
1
0
1
1
0
0
2
2
0
2
0
0
2
0
0
1
1
0
0
2
2
2
0
2
0
0
1
0
0
2
2
1
2
0
0
2
1
0
0
0
2
2
5
2
0
0
2
1
0
0
1
2
0
2
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
1
0
0
0
1
2
0
0
0
1
0
0
1
0
2
0
2
0
0
0
0
0
0
1
0
0
1
0
1
0
3
1
0
0
0
0
1
2
0
0
2
1
1
1
3
2
1
2
0
1
0
1
1
0
1
0
2
0
1
1
3
2
1
1
1
0
2
0
0
2
0
0
2
0
2
0
2
0
0
6
0
0
0
1
0
2
0
0
2
2
0
2
0
1
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
2
1
0
1
0
0
1
0
0
0
0
0
0
2
0
1
1
0
0
0
1
1
1
0
0
0
0
0
0
0
1
1
0
2
1
0
0
0
0
0
2
1
3
0
0
0
2
0
1
1
0
1
0
0
1
0
0
0
2
0
0
2
0
3
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
1
2
2
0
0
0
3
0
0
2
0
0
1
1
0
0
2
2
0
0
2
0
0
2
0
1
4
1
0
0
0
0
0
0
0
2
1
0
2
1
0
0
1
0
0
2
2
0
0
2
0
2
2
0
0
0
1
7
0
0
0
0
0
1
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
4
0
2
0
1
0
2
1
0
0
0
0
0
0
2
0
2
2
0
1
3
0
0
0
1
0
2
2
0
0
2
2
0
0
1
0
0
2
0
1
1
2
0
0
2
0
3
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
1
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
3
0
0
1
0
1
2
0
0
0
0
0
1
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
3
2
1
1
1
1
1
0
2
1
1
0
0
2
0
0
2
0
2
1
0
0
1
0
1
0
2
0
0
1
1
0
1
0
2
0
0
2
0
0
2
0
0
2
0
0
2
0
0
1
0
0
0
1
0
1
0
0
1
0
1
2
0
0
0
2
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
6
0
1
0
0
0
0
1
1
1
5
0
1
0
0
1
1
2
0
2
2
2
0
0
1
1
3
1
1
0
0
2
2
1
0
0
0
0
0
1
2
1
1
0
0
1
1
4
2
1
0
2
0
0
1
0
1
2
0
2
0
0
0
2
0
0
0
2
2
0
0
1
2
1
1
0
2
2
2
1
1
1
0
0
0
6
0
1
0
0
1
0
0
1
0
0
0
1
2
0
2
0
0
0
6
0
0
1
2
0
1
0
1
1
0
0
0
0
0
0
2
0
0
0
0
2
0
1
1
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
1
2
0
2
0
2
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
1
3
0
0
0
0
2
0
2
0
2
1
2
0
4
1
0
0
2
1
1
0
1
0
0
1
0
0
0
2
2
1
0
0
1
0
1
0
0
0
2
0
2
0
0
0
0
1
1
0
0
2
0
2
2
0
0
0
0
3
0
0
0
0
0
0
0
1
2
2
0
0
2
2
0
0
1
0
1
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
2
1
0
0
0
0
1
2
0
2
0
0
1
0
0
0
0
1
2
1
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
1
0
2
0
2
0
0
0
0
0
0
2
1
0
0
1
0
0
1
0
0
0
2
0
0
1
0
2
0
1
0
0
0
0
0
0
0
1
0
2
1
0
1
0
2
0
1
0
0
2
1
0
0
0
3
2
1
0
2
0
0
1
2
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
1
1
0
0
0
0
0
0
2
1
0
0
2
0
2
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
2
0
1
2
0
2
0
0
2
1
0
1
1
0
0
1
0
0
1
1
1
2
1
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
1
2
0
1
0
2
1
2
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
2
2
0
0
1
1
0
0
1
2
1
2
1
0
0
1
2
6
0
0
0
0
0
0
0
0
0
1
0
0
2
1
1
0
1
1
1
2
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
1
2
0
1
2
0
0
0
0
0
1
0
0
0
2
0
1
0
1
0
0
0
0
2
0
1
0
0
0
1
0
2
1
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
1
0
1
0
1
2
2
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
2
0
2
1
0
2
0
0
1
0
2
0
0
2
2
0
0
0
0
0
1
0
0
0
1
2
1
0
0
2
0
0
2
2
0
0
1
0
0
0
1
3
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
1
0
1
1
5
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
2
0
0
0
1
1
0
2
0
0
1
1
0
0
1
1
0
2
0
2
0
2
0
1
0
0
0
0
0
2
2
2
0
0
2
0
0
0
2
0
2
1
2
1
0
1
2
1
0
2
0
0
0
0
1
0
1
1
1
1
0
0
1
3
0
0
1
0
2
0
2
0
0
0
0
1
0
0
0
0
0
1
2
1
0
0
2
0
0
0
0
1
2
0
1
0
0
0
1
0
1
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
2
2
0
1
2
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
1
0
1
2
0
0
2
1
0
1
0
1
2
0
0
0
0
1
1
2
0
0
2
2
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
5
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
1
0
0
0
0
1
0
0
0
2
1
0
0
0
0
2
2
2
2
0
1
0
0
0
0
0
2
1
0
2
2
0
0
0
1
1
1
0
0
2
1
0
0
1
0
1
3
0
0
0
0
1
0
0
1
3
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
1
0
2
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
1
0
0
1
2
0
2
0
0
0
3
0
2
1
2
0
1
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
1
0
2
0
0
1
0
0
0
2
1
2
1
0
0
0
0
0
1
3
0
0
0
0
0
0
1
1
2
0
0
1
0
4
0
1
0
1
0
0
2
0
0
0
0
0
1
2
1
0
1
3
2
0
0
0
0
0
0
2
2
0
0
2
0
0
0
2
0
1
1
0
0
0
2
1
0
0
2
1
1
0
0
0
2
1
0
0
1
1
2
0
0
1
0
0
0
0
0
0
0
2
0
0
2
1
0
1
0
0
0
1
0
2
2
1
0
0
1
2
2
0
0
0
0
0
0
0
2
0
2
1
0
2
0
2
1
3
1
1
1
0
1
1
0
2
0
0
0
1
0
1
0
0
1
1
2
0
0
0
1
0
1
0
1
2
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
2
0
0
0
1
0
2
0
1
2
0
1
0
0
5
1
0
2
0
0
1
0
0
2
1
0
0
0
0
1
0
0
1
0
0
0
1
2
0
1
2
2
1
0
0
1
0
2
0
0
5
1
2
2
1
1
0
1
0
0
0
1
1
0
1
0
0
0
2
0
0
0
1
0
0
0
2
0
1
2
2
0
2
2
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
1
1
0
2
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
2
2
1
0
0
0
1
2
1
1
4
1
0
2
0
0
0
0
0
0
2
0
0
2
0
0
2
2
0
1
0
0
0
1
0
1
0
0
0
0
1
0
1
0
1
1
0
0
2
1
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
2
0
2
0
1
0
0
1
1
1
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
1
0
0
2
1
0
2
0
1
2
1
1
1
0
0
0
2
2
0
1
0
1
0
3
0
0
1
0
0
2
0
0
2
0
0
0
1
2
0
0
0
2
0
1
1
0
1
1
1
0
2
0
0
2
0
0
1
0
0
2
0
0
0
0
2
2
0
2
0
0
0
1
1
2
1
0
0
1
2
0
0
0
0
0
1
0
0
0
3
0
0
0
0
1
1
0
1
0
0
2
0
0
2
0
1
2
0
2
0
2
0
2
1
0
0
2
0
0
2
2
1
1
1
1
2
0
0
1
1
1
2
2
0
0
0
0
0
0
4
0
0
2
1
0
2
2
0
2
0
0
0
2
0
2
0
2
0
0
1
1
5
1
1
0
0
1
0
0
1
1
0
0
0
0
1
2
2
2
0
0
0
0
1
2
0
0
0
0
2
0
0
1
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
2
1
0
0
0
2
0
1
0
1
0
0
0
0
0
0
1
2
1
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
3
2
0
1
1
0
0
2
0
2
0
1
1
2
0
0
1
0
2
0
0
0
0
0
0
2
0
1
0
1
1
0
0
0
1
1
2
1
0
0
2
0
0
2
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
1
0
1
4
0
0
0
0
0
1
0
0
2
0
1
0
0
1
0
2
1
0
0
0
1
0
1
0
0
0
2
0
0
0
1
0
2
0
0
4
0
0
0
1
0
0
2
3
2
0
0
0
0
2
0
0
0
0
0
1
4
1
1
1
2
0
0
0
1
1
0
0
1
2
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
2
1
0
1
0
2
1
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
3
0
0
1
1
0
0
1
1
0
0
2
0
2
0
0
0
2
0
0
0
0
0
2
6
0
2
0
0
1
0
0
1
0
1
0
0
0
0
2
0
2
2
0
0
2
0
0
0
1
0
0
1
0
0
2
1
0
0
0
0
2
0
1
2
0
0
1
0
0
0
0
1
0
0
1
2
0
2
0
0
2
0
2
0
0
1
0
0
1
3
1
1
1
0
0
2
1
0
1
1
0
0
1
0
0
0
1
0
0
2
2
2
0
2
0
0
0
1
2
0
0
0
2
0
0
0
0
1
2
0
0
1
1
4
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
1
1
1
0
1
2
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
2
0
2
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
1
3
0
0
0
0
2
0
0
1
1
1
2
2
0
1
0
2
0
3
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
2
2
0
1
0
0
2
1
0
1
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
2
0
1
0
2
0
0
1
0
0
0
1
1
2
2
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
4
0
0
0
2
2
2
0
0
0
1
2
0
0
1
1
0
0
0
1
2
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
1
0
0
0
0
2
0
0
0
1
0
0
1
2
1
0
1
1
0
0
2
0
1
0
1
0
0
0
0
4
1
1
2
0
0
2
1
1
2
1
0
0
0
0
1
0
0
1
0
0
1
1
1
0
0
0
2
0
1
3
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
1
0
0
1
0
0
1
2
0
0
0
0
2
0
0
0
2
0
2
0
1
0
1
0
0
3
1
0
1
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
2
0
2
2
0
0
2
0
2
1
0
1
0
0
0
0
2
0
1
0
0
0
0
1
2
2
0
1
0
2
1
3
0
0
0
0
0
0
2
3
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
2
2
1
2
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
2
2
0
0
1
1
0
0
2
2
0
0
2
2
0
0
0
0
1
4
1
0
4
0
6
2
0
2
0
1
0
0
3
0
1
1
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
2
0
0
2
0
1
0
0
2
0
1
1
0
2
0
2
0
1
1
0
0
2
0
2
0
2
2
0
0
1
0
1
0
0
0
0
2
0
2
1
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
1
2
4
4
2
0
2
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
2
0
0
0
1
0
0
4
1
0
2
1
0
0
0
1
0
1
3
2
1
0
0
1
0
1
0
0
2
0
1
0
0
2
0
0
0
3
1
0
2
1
1
0
0
0
1
2
0
0
2
0
0
0
0
1
0
2
3
0
2
0
2
0
0
0
1
1
0
0
0
0
1
0
0
0
0
2
2
0
0
2
0
0
0
0
2
0
2
0
2
0
1
4
0
0
1
0
2
0
0
0
1
1
0
0
1
0
0
1
2
1
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
2
0
1
0
2
1
2
0
2
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
1
0
2
4
2
0
0
0
0
1
2
1
0
2
0
0
1
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
2
1
0
1
3
2
0
0
2
1
2
0
1
0
0
0
1
0
2
2
0
0
1
0
0
1
0
1
1
0
2
0
2
0
0
0
0
0
0
0
0
1
1
0
1
0
0
2
0
0
1
0
0
0
0
3
0
0
0
2
0
1
2
2
2
2
0
2
0
1
0
4
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
2
1
0
0
2
2
0
1
1
0
0
0
1
2
0
0
0
1
0
1
0
1
0
0
0
0
4
1
0
1
0
1
2
2
0
0
0
0
2
2
0
0
0
1
2
0
2
0
0
0
0
0
0
1
1
0
0
1
1
2
0
0
0
0
2
2
0
2
2
2
2
2
0
1
0
0
1
3
0
2
0
0
0
1
1
0
0
6
1
0
0
4
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
1
1
0
0
0
0
0
0
0
2
0
1
1
2
2
1
0
2
2
0
0
0
0
2
0
1
0
1
3
0
1
0
1
1
1
0
0
0
0
2
2
0
0
2
0
1
2
0
1
2
2
1
0
0
2
0
3
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
2
1
0
0
1
2
2
0
1
1
0
0
2
2
2
1
0
1
1
0
1
0
0
2
2
3
0
2
0
0
0
1
0
0
0
2
1
0
1
0
1
1
0
2
1
3
1
2
1
0
1
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
1
0
0
1
2
2
2
1
1
1
2
1
1
0
0
0
0
0
0
0
2
0
2
2
0
0
0
2
1
0
1
2
2
2
0
0
0
2
1
0
0
0
2
1
0
1
0
0
0
1
0
1
0
0
0
2
1
0
0
0
0
0
0
1
0
1
2
0
0
0
0
1
1
0
8
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
1
0
0
2
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
1
0
0
0
2
2
0
0
0
1
0
1
1
1
3
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
1
3
0
0
2
2
0
1
0
2
0
0
0
1
0
2
0
0
3
0
3
2
0
2
0
0
0
1
0
2
0
2
0
1
0
0
0
0
0
0
0
1
1
0
2
0
0
2
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
1
0
0
0
2
0
2
0
2
1
2
6
2
1
0
1
1
0
2
1
1
0
0
1
2
0
0
2
0
2
0
1
2
1
0
2
0
0
1
0
1
1
2
0
0
1
2
0
0
0
0
0
1
0
2
0
0
2
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
1
1
0
0
0
2
0
2
0
0
2
0
2
0
0
1
0
0
2
0
0
0
0
1
0
2
1
2
1
0
2
0
1
2
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
2
2
1
0
0
0
1
1
0
0
4
0
2
2
2
1
1
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
3
1
0
0
0
0
2
0
0
0
0
1
0
0
0
2
2
2
0
0
0
1
0
0
0
2
0
2
0
1
0
0
0
0
1
0
1
2
1
0
0
1
0
0
1
0
0
0
1
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
3
0
1
0
0
0
2
0
1
1
1
0
2
0
2
0
2
1
0
0
0
3
2
0
3
2
1
0
0
1
0
0
1
0
0
0
0
0
1
4
0
0
0
0
4
2
2
0
2
1
0
0
0
0
2
2
0
0
2
0
0
2
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
1
1
2
2
0
1
0
0
0
0
0
2
0
1
0
0
2
1
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
1
0
0
0
0
1
4
2
0
2
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
2
2
0
0
2
0
2
2
0
2
2
1
0
0
1
0
1
0
0
1
0
1
0
2
0
0
0
0
1
1
2
0
0
0
0
0
1
1
1
0
0
1
0
1
0
2
2
0
0
1
2
0
0
0
1
0
0
0
0
0
0
2
0
2
0
1
1
2
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
2
2
0
2
1
0
0
0
2
1
2
0
0
0
0
0
0
2
2
0
0
0
2
0
2
0
0
0
0
1
2
1
0
2
2
1
1
1
2
1
0
2
2
2
1
0
0
0
2
1
0
0
0
1
0
0
0
0
0
1
1
5
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
3
0
1
0
0
1
0
0
0
1
2
2
0
1
0
0
2
0
3
0
1
0
0
1
0
0
0
1
3
2
0
0
2
1
1
0
0
0
0
1
0
1
0
0
0
1
2
0
0
1
0
0
1
0
0
3
0
0
0
0
0
6
0
0
0
0
0
0
0
0
2
0
1
1
0
1
1
0
1
2
2
1
4
0
0
2
0
0
0
0
2
2
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
1
2
1
0
1
1
1
1
0
0
1
2
0
0
0
1
2
2
2
0
0
0
2
2
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
1
0
0
0
2
2
0
2
0
0
3
0
0
0
2
2
0
2
0
1
2
1
0
0
0
2
0
1
0
1
1
1
0
1
1
0
0
1
0
0
4
0
0
0
2
0
2
0
1
1
0
3
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
2
0
2
0
2
2
2
3
0
0
0
0
1
1
1
0
2
0
1
2
0
3
2
0
0
2
0
0
1
2
0
1
0
0
0
1
2
0
0
2
0
2
0
1
3
2
1
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
2
3
0
1
2
0
0
0
0
1
0
0
0
1
1
0
2
2
0
0
1
0
2
1
0
1
0
1
0
0
0
0
0
0
0
2
1
2
0
0
0
1
0
1
2
2
2
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
2
0
0
3
0
1
0
0
0
2
0
1
0
0
2
0
1
0
2
2
1
0
0
0
0
0
3
0
1
0
0
0
1
0
0
2
1
1
2
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
1
1
1
0
2
2
3
1
1
0
1
0
0
1
0
2
1
2
3
0
1
0
0
0
0
1
1
0
1
0
1
2
2
0
2
2
2
2
0
1
1
2
1
1
0
0
0
0
2
1
7
0
1
0
1
0
1
2
0
0
2
2
7
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
1
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
1
2
0
0
2
0
0
1
1
0
0
0
0
1
0
0
2
0
0
1
0
0
2
0
2
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
2
1
1
2
1
0
0
2
2
0
0
2
0
2
2
0
3
0
0
0
0
1
0
3
1
0
0
3
0
1
0
1
2
0
0
2
0
0
0
1
2
0
0
0
1
1
2
0
0
0
1
0
0
0
1
0
1
3
1
0
0
0
0
0
1
0
2
1
1
0
2
2
0
1
0
0
1
0
1
0
0
0
3
2
1
0
2
1
0
0
0
2
0
0
0
2
0
1
0
0
0
2
2
1
0
1
1
0
0
1
2
1
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
2
0
0
1
0
2
0
1
1
0
0
0
1
1
2
1
2
1
0
1
0
0
0
2
0
0
1
0
1
2
2
0
2
2
2
0
0
0
0
1
2
3
0
2
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
2
1
2
1
0
0
0
0
2
0
1
1
3
2
1
0
0
2
0
0
1
0
1
0
3
0
0
1
1
0
0
0
0
0
0
1
1
1
2
1
0
1
0
0
1
0
0
2
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
3
1
1
0
0
0
0
2
1
1
0
2
0
0
0
1
2
0
0
0
0
1
0
2
0
0
0
2
0
1
0
0
2
0
2
1
0
1
0
2
1
1
2
0
1
0
0
0
1
2
1
0
0
1
1
1
0
0
1
0
0
1
1
1
0
2
2
1
0
0
0
0
0
2
3
2
0
2
0
1
1
2
1
1
2
2
0
1
0
0
0
3
0
0
0
2
0
3
0
0
0
0
0
0
0
0
2
0
0
0
2
2
2
2
0
0
0
1
1
0
0
2
2
1
0
2
1
0
0
1
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
2
1
2
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
2
0
2
0
1
3
2
0
0
0
0
0
0
1
0
0
2
5
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
3
2
0
0
0
0
1
1
0
2
0
0
0
1
2
1
0
1
0
0
1
6
0
0
2
2
2
0
0
0
2
0
0
0
1
1
0
2
0
1
0
2
1
2
1
2
2
0
1
0
2
2
0
0
2
0
0
2
2
2
0
1
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
2
2
0
2
0
0
0
0
1
0
2
0
0
0
1
0
4
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
2
0
2
2
1
1
0
2
0
0
0
1
0
2
0
1
0
0
1
1
0
2
0
2
1
2
0
0
2
0
0
1
0
1
2
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
2
2
0
0
0
0
0
1
1
1
0
1
2
1
0
0
0
2
0
0
0
0
1
0
1
0
0
0
2
0
1
2
1
0
2
0
0
0
0
0
1
0
1
0
0
3
1
1
0
1
0
0
1
1
0
1
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
2
2
2
0
0
0
0
0
1
1
0
0
2
0
2
0
1
2
0
0
2
0
2
0
0
1
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
2
0
0
1
1
1
2
0
0
0
2
0
0
0
0
0
1
0
1
1
3
0
0
0
1
2
0
2
0
1
0
0
0
0
0
1
2
0
0
2
0
2
0
0
0
0
0
0
2
0
0
2
0
0
1
1
0
0
0
0
0
1
1
1
0
0
1
1
0
0
0
1
2
0
0
1
2
1
0
0
0
0
1
2
0
0
1
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
1
0
1
0
0
1
0
0
0
0
2
1
0
1
0
0
0
0
0
0
2
0
2
0
2
0
2
1
0
2
0
0
1
0
0
2
0
1
0
0
2
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
1
2
0
0
0
0
0
1
1
0
2
0
0
1
0
0
2
1
2
0
0
0
0
0
0
0
1
0
23
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
1
0
0
0
0
0
1
2
2
0
4
3
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
2
1
0
1
2
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
2
0
2
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
2
1
1
0
2
1
0
0
2
0
0
2
0
0
0
2
0
0
0
0
2
2
2
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
1
1
1
0
1
0
0
0
0
1
1
1
0
2
0
0
0
0
0
2
0
1
2
0
0
0
1
2
1
1
0
0
2
0
2
1
0
0
2
0
0
0
2
0
2
0
0
0
0
1
0
2
0
3
1
1
2
1
1
0
1
0
2
1
1
0
0
2
0
0
2
0
0
0
0
1
1
0
0
0
2
1
1
3
2
0
1
2
0
0
0
1
0
0
0
1
0
1
0
0
0
1
1
0
2
0
0
0
1
0
0
0
3
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
2
2
0
0
1
1
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
2
3
2
0
1
0
2
2
0
0
0
1
1
3
1
0
2
0
0
0
0
1
0
0
1
0
2
0
0
0
3
2
0
1
1
1
0
0
1
0
0
2
1
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
1
1
2
2
2
0
0
0
0
0
0
3
1
0
0
1
1
1
0
1
0
0
2
0
0
1
0
0
0
0
1
1
1
0
2
0
0
0
0
2
2
0
0
0
1
0
0
1
0
0
1
1
0
0
2
0
0
0
2
0
1
2
0
1
0
2
0
0
2
0
2
0
0
0
0
0
0
0
2
1
2
1
5
1
1
0
0
0
0
3
1
0
0
1
0
0
1
0
3
1
2
0
0
0
0
2
0
3
1
1
0
2
2
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
2
1
2
0
0
3
0
1
1
0
0
0
0
1
0
0
0
0
2
0
2
1
1
1
1
0
1
0
2
0
0
2
0
0
1
2
0
1
0
1
3
0
2
2
2
0
0
0
0
0
0
0
1
1
1
0
0
2
0
0
2
0
3
2
2
1
0
0
1
0
0
0
0
1
0
0
0
2
2
1
0
1
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
1
0
1
0
0
0
0
1
2
2
0
2
1
2
0
0
2
0
0
0
2
1
2
0
0
3
1
3
2
0
0
1
1
2
0
0
2
1
0
2
0
2
0
2
0
0
1
0
2
2
0
1
2
0
0
2
0
0
1
0
0
0
2
0
0
2
3
2
0
0
2
1
1
0
0
2
0
0
1
0
0
0
0
1
0
2
0
1
0
0
0
2
0
0
2
0
0
1
2
0
0
2
0
1
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
1
2
1
1
2
0
0
0
2
2
0
0
1
2
1
1
0
0
0
0
2
1
0
1
0
3
1
1
2
0
1
1
0
0
0
0
0
0
1
1
0
2
1
0
0
0
0
0
0
0
0
1
2
0
0
1
2
0
0
0
0
1
1
2
0
2
1
2
1
0
0
0
1
2
1
0
3
0
2
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
2
2
0
1
0
0
1
2
0
0
2
0
0
2
0
2
2
1
0
2
0
0
0
0
0
0
0
2
0
0
0
5
2
0
0
0
0
0
2
0
3
0
1
0
2
0
0
0
0
2
0
2
1
1
0
0
0
0
0
1
2
0
1
2
2
0
4
0
0
0
0
1
0
1
0
0
2
1
2
0
0
1
0
0
2
1
0
1
0
0
0
2
1
0
1
1
0
0
2
1
1
0
0
0
0
0
0
0
2
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
2
1
0
1
2
1
4
0
2
0
0
1
0
2
0
0
0
0
1
1
0
1
1
0
0
0
0
1
2
1
0
0
0
0
1
1
0
1
1
2
0
1
1
0
1
0
2
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
1
0
1
2
2
0
1
0
0
0
0
0
0
1
0
1
0
1
0
1
0
2
0
0
0
0
0
0
1
0
0
1
2
0
1
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
2
1
0
0
2
0
0
0
0
0
2
2
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
3
1
1
0
0
0
1
1
2
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
2
0
0
1
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
2
0
2
0
0
1
1
0
0
2
2
0
0
0
1
2
0
2
0
2
1
0
0
1
1
1
1
0
0
0
0
2
1
2
2
1
1
0
1
0
1
0
0
2
3
2
0
1
0
0
2
0
0
7
0
0
2
2
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
2
0
2
1
0
0
1
0
0
0
0
2
0
0
0
1
1
0
1
0
1
2
2
0
2
1
0
0
2
2
0
1
0
0
2
0
0
0
0
2
2
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
1
2
0
0
0
0
2
2
0
1
0
0
0
0
0
1
2
0
0
2
5
1
4
2
0
0
0
2
2
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
1
2
0
0
0
1
1
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
5
0
1
0
0
0
1
2
2
0
1
0
0
2
0
2
0
0
1
0
1
0
0
1
0
1
0
0
0
4
1
0
0
1
1
1
0
0
0
0
2
0
0
2
2
0
0
0
1
2
0
0
1
0
0
2
2
0
1
2
0
2
0
0
1
2
2
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
1
1
0
1
2
0
2
1
0
2
1
1
2
2
0
1
0
0
0
2
0
0
1
0
0
0
0
1
0
1
1
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
1
1
0
0
0
2
0
0
1
1
0
3
0
2
0
0
0
0
0
1
2
0
0
0
1
0
1
1
1
0
0
0
1
1
0
0
2
2
1
1
2
0
0
0
1
0
1
1
0
0
2
1
0
1
0
1
1
0
0
0
0
1
0
2
0
0
2
0
0
2
0
1
0
2
2
1
0
0
0
1
0
4
0
1
0
1
2
0
0
0
0
1
1
2
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
1
0
2
2
1
1
0
0
0
0
4
0
0
0
2
0
0
1
0
0
0
2
0
0
2
0
0
2
0
0
1
2
0
0
0
2
0
4
0
0
0
2
1
2
2
0
0
2
0
1
0
0
0
1
2
0
1
2
5
0
0
0
0
1
0
0
1
2
1
0
0
0
1
1
0
2
2
0
0
0
0
1
2
1
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
4
0
1
1
2
0
1
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
1
2
0
0
0
1
0
0
1
0
2
0
0
3
0
0
0
2
1
3
1
0
2
0
0
0
1
0
1
0
0
0
2
0
0
0
2
1
0
0
0
0
2
1
0
2
2
0
0
1
0
0
0
0
0
0
1
3
1
0
0
0
2
0
1
0
1
0
0
2
1
2
0
1
0
2
0
1
0
0
0
1
0
1
0
3
2
3
0
0
0
5
3
0
0
2
0
0
1
2
0
0
2
2
0
0
1
0
2
1
1
2
2
0
0
0
4
0
0
0
2
0
1
0
2
0
1
0
0
0
0
1
0
0
0
3
0
0
0
0
2
0
2
0
0
0
1
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
1
0
1
0
2
2
0
0
0
0
2
5
0
0
0
1
1
0
0
1
1
0
3
0
1
0
1
1
0
1
2
0
2
2
0
2
1
0
0
0
0
2
0
0
2
1
0
0
1
0
0
0
2
1
0
1
2
0
0
1
1
0
0
2
0
1
1
2
1
1
0
0
0
2
1
1
2
0
2
2
2
2
0
10
2
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
3
1
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
2
0
0
1
2
0
3
1
1
1
2
0
2
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
3
1
0
0
1
0
1
1
1
0
2
1
1
1
0
0
1
0
1
0
1
0
0
0
0
1
1
0
0
0
1
0
1
0
0
1
2
3
0
0
2
0
0
0
0
0
1
2
2
0
2
0
0
0
2
2
1
0
1
0
1
1
0
0
2
0
0
2
0
0
0
2
0
1
0
0
0
2
0
2
1
1
0
0
1
0
2
0
1
0
0
1
0
0
0
0
2
0
1
0
0
0
0
1
0
0
2
2
0
0
0
1
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
1
2
2
0
0
0
0
0
2
1
1
0
1
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
2
0
0
0
2
1
0
1
0
1
0
0
0
3
0
0
2
1
0
0
0
1
1
2
3
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
3
0
0
0
0
1
2
0
0
0
0
2
0
1
2
0
2
2
0
0
1
0
1
2
0
1
0
1
0
1
0
0
2
0
1
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
2
1
2
2
0
0
0
0
2
1
2
0
1
2
0
0
1
1
1
0
1
2
2
1
0
0
0
0
0
0
0
0
0
2
2
0
0
2
2
0
0
2
0
1
2
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
2
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
1
0
0
1
0
0
0
0
0
0
2
1
0
0
1
0
1
0
0
0
1
0
2
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
1
0
0
2
0
0
2
0
0
2
0
0
0
0
0
1
0
0
1
0
2
0
2
0
0
0
1
1
2
1
2
2
0
0
0
0
0
0
0
2
0
0
1
0
1
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
2
0
1
2
2
0
1
0
2
0
0
2
0
1
1
1
0
0
0
0
1
2
0
0
1
1
0
0
1
0
1
3
2
0
0
0
2
1
0
0
0
1
0
0
1
0
0
1
2
1
1
0
0
4
1
0
0
0
0
0
1
3
0
0
0
2
2
0
0
0
1
2
1
0
0
0
0
1
2
2
0
0
1
0
0
2
2
2
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
2
0
1
1
2
0
2
2
0
2
0
2
2
0
2
2
1
0
0
0
0
0
2
0
1
0
0
0
1
0
1
0
1
1
0
0
1
3
0
0
0
0
1
0
2
1
1
0
0
1
2
0
0
0
1
0
2
0
0
1
2
0
0
0
0
1
0
0
2
1
2
0
0
2
2
0
2
0
0
0
0
2
0
0
0
0
0
0
1
3
0
1
1
1
0
0
2
1
1
0
0
0
0
1
1
0
0
0
2
2
1
2
0
1
0
0
0
1
0
0
0
0
0
1
0
2
0
2
0
0
0
2
2
0
0
0
3
2
1
0
0
0
1
0
2
2
2
2
0
0
1
0
0
1
0
1
0
3
0
0
2
0
2
0
0
1
2
1
0
3
1
0
0
1
0
2
0
0
11
1
0
0
0
1
0
1
0
0
2
0
3
0
0
0
2
1
0
1
1
7
1
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
3
0
2
0
1
0
1
1
2
2
0
0
0
0
0
0
0
0
6
1
1
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
5
0
0
0
0
1
2
0
2
0
0
1
1
0
0
0
1
0
0
1
0
0
1
0
0
1
1
0
0
1
0
0
1
0
2
0
0
0
0
1
0
0
2
2
2
0
0
1
2
1
2
0
0
0
1
2
2
0
2
0
0
0
1
0
1
2
0
0
1
0
0
0
0
0
1
0
2
0
2
0
2
2
2
1
0
0
0
0
2
1
0
0
1
0
0
1
0
0
0
0
2
0
2
0
2
2
0
3
0
1
0
3
1
1
0
0
2
1
2
2
0
1
0
0
1
0
0
0
2
0
2
0
1
0
0
0
0
1
0
0
1
1
0
2
0
0
0
0
0
0
1
2
0
0
0
2
0
0
2
2
1
0
1
0
0
1
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
2
0
1
2
1
2
0
2
1
0
0
0
1
0
1
0
1
1
2
1
0
0
0
0
0
0
2
0
1
2
1
0
0
1
2
2
1
0
2
1
0
1
0
1
0
0
0
0
0
0
2
2
2
0
1
0
2
1
0
2
0
0
0
1
0
0
0
2
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
2
0
1
1
0
0
2
1
0
0
3
0
0
2
0
2
2
1
2
2
0
0
1
2
0
0
3
1
1
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
2
1
0
0
1
2
0
1
0
0
1
1
1
0
0
0
2
0
0
0
2
0
0
0
2
1
1
0
0
0
0
1
0
1
0
2
2
2
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
1
2
2
0
1
0
1
0
0
2
1
2
1
0
1
0
0
0
0
2
0
0
1
0
2
0
2
0
0
1
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
2
0
0
1
1
0
0
0
2
2
2
1
0
1
0
3
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
2
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
2
0
0
2
0
1
1
1
0
0
0
1
0
0
2
0
0
0
0
1
1
0
1
0
1
1
2
0
1
2
2
1
0
2
1
0
0
2
0
0
1
0
0
1
0
0
0
2
3
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
1
2
0
2
0
1
1
0
0
2
2
0
1
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
3
2
0
0
1
1
1
0
0
0
0
0
2
0
0
2
2
1
1
0
0
0
2
0
0
0
2
0
2
2
0
2
0
0
3
0
0
2
2
0
0
0
2
0
2
0
0
0
0
2
0
0
1
0
1
2
0
0
2
1
0
0
1
0
0
1
1
0
0
2
0
0
2
0
0
2
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
5
0
0
1
2
1
0
0
2
0
0
0
0
2
0
1
0
1
1
0
0
1
0
1
0
2
1
0
0
0
0
1
0
3
0
2
0
0
0
0
1
1
1
1
0
2
1
0
2
0
0
3
0
0
0
0
3
1
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
2
0
0
2
0
2
2
0
2
0
1
0
0
0
2
2
0
1
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
2
2
0
0
1
2
0
4
0
1
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
1
0
0
0
1
0
0
0
0
2
2
2
1
0
0
0
0
0
0
0
0
0
0
0
1
2
2
2
2
0
2
2
4
1
2
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
2
0
1
0
3
2
1
0
0
0
0
0
1
1
2
0
1
0
0
0
3
1
0
2
2
0
2
0
3
0
0
0
0
1
2
0
0
1
0
0
2
0
1
0
0
0
1
0
2
0
0
1
2
1
0
2
1
2
2
0
0
0
0
2
1
1
0
1
0
0
0
1
2
0
0
1
1
1
0
0
0
2
1
2
1
0
1
0
2
1
0
0
0
0
1
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
4
0
2
1
1
2
2
0
0
2
0
2
2
2
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
2
0
1
0
1
1
0
0
1
0
0
0
0
2
0
0
2
0
1
0
0
0
0
2
1
1
0
1
0
3
0
0
0
2
2
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
2
1
1
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
1
2
1
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
1
3
1
0
0
0
0
0
0
1
1
1
0
0
0
2
0
0
0
1
1
0
0
0
1
1
0
0
0
1
1
0
0
0
1
1
1
2
1
0
0
0
0
2
0
0
2
0
2
1
0
0
0
0
0
0
0
3
0
0
0
0
2
2
2
1
0
0
0
2
1
0
0
0
1
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
3
0
1
0
1
1
1
0
0
0
2
1
1
0
1
0
0
0
1
0
1
2
0
0
0
0
0
2
0
0
1
0
2
0
0
2
0
0
1
0
0
1
2
0
0
1
0
0
2
0
0
2
2
1
0
0
0
1
0
2
0
2
0
0
1
3
0
1
3
1
0
2
2
0
1
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
1
0
0
2
1
2
1
1
0
2
1
0
0
1
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
2
1
0
3
0
1
1
1
0
0
0
2
1
1
0
1
1
0
1
0
0
2
2
0
0
0
0
0
2
0
4
0
1
0
0
2
0
0
0
0
1
0
2
0
1
1
0
0
2
1
1
0
0
1
0
0
2
2
3
2
1
0
1
0
2
0
1
2
0
0
0
2
1
0
0
0
0
0
1
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
2
1
0
0
0
0
0
2
0
2
1
0
2
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
2
2
1
0
2
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
2
0
2
0
1
0
2
1
1
0
0
2
0
2
0
0
0
1
2
0
0
0
0
0
0
0
1
0
4
3
0
1
2
0
0
2
0
0
1
0
0
1
0
0
3
0
0
2
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
2
0
0
1
2
0
2
1
1
1
0
0
2
0
2
0
0
1
0
3
2
2
0
0
2
0
2
0
0
2
0
2
1
0
0
0
0
1
0
1
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
2
1
2
0
0
0
0
1
0
2
1
0
0
0
0
2
0
0
0
2
0
0
2
1
0
1
0
0
1
0
2
0
0
2
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
1
1
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
2
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
2
0
0
0
0
9
1
0
1
1
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
1
0
0
3
0
0
0
2
2
1
0
0
1
0
0
0
1
1
0
2
0
0
0
0
0
0
1
0
1
0
0
2
0
3
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
1
0
1
1
0
0
0
0
2
2
1
0
0
0
2
0
2
1
0
1
0
0
0
3
0
0
0
0
0
1
1
0
0
2
0
0
0
1
0
0
1
2
1
0
0
0
0
0
2
1
1
0
0
1
0
1
0
0
0
1
1
2
2
0
0
0
0
1
0
0
1
0
2
0
0
1
1
2
1
0
0
3
1
1
1
0
0
1
0
0
1
0
2
0
0
0
2
0
0
0
2
0
0
2
1
2
0
1
0
0
0
2
0
1
0
0
1
2
1
1
0
0
1
0
0
0
0
1
1
0
2
0
2
1
2
1
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
1
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
1
0
0
0
1
0
0
1
0
0
2
0
2
0
0
1
0
2
1
0
2
2
2
1
0
2
1
0
0
2
0
1
2
0
0
0
0
2
0
1
2
1
0
2
1
1
2
0
0
0
0
0
0
0
0
2
1
1
2
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
1
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
3
0
0
1
0
0
1
0
2
0
2
0
0
0
1
0
1
2
0
0
0
1
0
2
0
1
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
2
1
0
1
1
1
3
0
1
1
0
0
0
1
0
2
0
2
1
1
0
2
0
3
0
0
0
0
2
1
2
0
0
2
1
0
0
0
0
1
0
0
1
0
2
2
0
0
1
0
1
2
0
0
0
1
0
0
0
2
0
0
1
0
3
0
0
1
0
0
1
0
0
0
3
2
2
2
2
0
0
0
4
2
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
1
0
2
1
1
1
2
0
0
3
1
0
1
2
2
0
2
1
1
0
0
0
0
0
0
2
0
0
1
2
2
0
0
0
2
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
2
1
0
1
1
2
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
1
2
2
0
0
0
1
0
0
2
0
0
1
1
0
0
1
0
0
0
0
2
1
2
1
0
1
0
0
2
0
0
1
0
0
2
1
0
0
0
1
1
0
0
2
2
0
1
1
0
0
0
0
1
1
0
0
2
1
0
0
0
0
0
0
1
0
1
0
0
1
1
0
2
0
0
1
1
1
1
1
0
2
0
2
2
0
2
0
2
0
2
0
0
0
0
1
1
1
0
0
0
0
0
0
1
2
0
0
2
0
0
0
2
0
0
2
1
0
0
0
0
2
0
0
1
1
0
0
2
0
1
1
2
0
0
0
1
1
0
0
1
1
0
0
0
0
1
0
3
0
0
0
0
2
0
2
2
0
2
0
0
1
1
2
1
0
0
1
1
2
2
0
0
2
1
0
0
0
0
3
2
0
0
0
0
2
0
2
2
0
0
0
2
0
1
0
0
0
1
0
2
1
0
0
0
1
0
1
2
1
1
0
0
2
1
0
0
0
0
0
0
1
0
0
0
2
0
4
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
1
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
1
2
2
0
0
0
2
2
0
2
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
2
2
0
0
1
0
0
2
0
0
1
0
0
0
0
0
1
1
1
0
0
3
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
1
1
2
0
2
1
0
0
1
0
0
0
2
1
0
0
1
0
0
1
0
0
0
2
0
1
1
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
3
0
1
0
0
0
0
2
0
2
0
2
0
0
1
0
0
1
0
0
0
0
1
2
0
1
2
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
1
2
1
0
1
1
1
0
0
0
1
2
0
1
0
1
1
1
0
0
0
1
0
2
0
0
0
1
0
1
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
2
2
0
1
0
0
2
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
1
0
0
0
0
2
1
1
0
1
0
2
0
0
1
0
1
1
2
0
1
0
0
1
0
0
1
0
1
0
0
0
0
1
0
2
0
0
0
1
0
2
0
0
1
1
7
1
0
2
2
0
3
2
0
3
3
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
2
0
0
0
1
0
3
0
2
0
1
0
1
0
2
1
0
1
1
2
2
0
2
1
2
0
0
0
1
1
0
0
0
0
0
1
2
1
0
0
1
0
0
0
0
2
0
0
1
2
0
3
2
0
0
0
0
2
0
0
2
2
2
0
0
1
3
1
0
2
0
3
2
1
0
1
2
0
0
2
2
0
1
0
1
0
0
2
0
0
0
0
2
0
1
3
0
0
1
0
0
1
0
1
0
0
1
2
0
0
0
0
0
0
2
2
0
1
1
1
0
1
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
1
2
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
2
0
1
0
2
2
0
0
2
0
0
2
0
2
2
0
2
0
0
2
0
1
0
0
0
1
2
0
1
0
1
0
1
0
2
0
0
0
0
2
0
0
1
0
0
0
1
0
0
3
0
0
0
2
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
1
1
1
0
1
2
2
1
0
1
1
0
0
2
0
2
1
2
0
0
0
2
0
1
1
2
1
0
0
0
0
2
2
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
2
1
2
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
2
0
0
1
0
2
0
1
0
1
1
0
2
2
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
1
1
0
1
0
0
1
0
2
0
0
0
0
2
0
1
1
0
1
0
0
1
0
0
0
0
0
0
4
2
1
2
0
0
1
0
2
0
0
2
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
1
0
0
0
1
0
1
1
0
4
0
0
2
0
0
1
3
0
0
0
1
3
2
3
1
2
0
1
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
2
0
0
1
2
0
0
0
0
2
0
0
0
1
0
0
1
0
1
1
1
0
0
2
2
6
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
2
2
2
1
2
2
0
0
2
1
0
0
0
0
1
0
1
0
1
2
0
0
0
0
2
1
2
1
0
0
0
0
0
1
0
0
0
0
0
2
2
0
2
2
3
0
0
0
0
0
4
0
0
2
0
0
0
6
0
2
0
2
2
0
2
0
2
1
0
0
0
0
2
1
0
0
1
0
0
2
2
0
0
2
2
0
1
0
0
1
0
0
1
0
0
3
0
0
2
0
2
0
0
0
0
1
1
0
1
0
2
2
2
0
0
0
0
2
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
2
0
0
0
1
0
1
0
0
1
1
2
0
0
2
0
0
1
0
0
1
0
0
1
0
0
2
0
1
0
0
2
0
2
0
1
0
2
2
0
0
0
3
2
0
0
2
1
0
0
1
0
1
1
2
1
2
1
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
2
0
2
3
1
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
1
3
0
0
1
0
1
2
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
2
0
0
2
0
0
3
0
1
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
1
1
0
0
0
2
2
0
0
1
2
0
1
0
1
0
0
0
2
0
0
0
1
1
1
0
2
3
0
0
0
0
0
0
2
0
0
0
0
2
1
2
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
2
1
1
0
0
1
2
3
0
0
0
1
3
1
2
0
0
1
0
0
0
0
0
0
2
0
2
1
0
2
0
0
0
1
1
1
0
2
0
0
2
2
0
1
0
0
0
0
2
1
0
0
0
0
0
0
2
0
1
0
0
1
2
0
0
1
2
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
2
0
0
2
1
0
0
0
1
1
3
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
2
0
2
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
2
2
2
2
0
1
2
0
1
0
0
2
0
0
0
0
0
2
0
1
1
1
0
0
0
1
0
0
0
2
0
0
3
2
2
2
0
0
0
0
0
0
1
2
0
2
0
2
2
2
0
0
1
0
2
2
10
0
2
2
2
1
0
0
1
0
1
0
0
1
0
0
0
1
0
2
2
7
0
1
0
1
1
1
0
2
1
0
2
0
0
0
0
0
0
0
0
0
1
1
1
0
4
2
0
0
0
0
0
1
0
0
0
0
0
0
4
0
2
2
0
0
0
0
1
3
1
0
0
0
0
0
1
0
0
1
0
0
3
0
0
1
0
0
0
2
2
1
1
1
0
0
0
0
0
1
0
0
2
0
1
0
3
0
2
0
0
1
1
2
1
0
0
1
0
0
0
2
0
0
2
0
0
1
1
0
0
2
0
0
0
1
0
0
0
2
0
2
0
2
0
0
2
0
2
0
0
0
2
0
1
1
2
0
2
0
1
2
1
0
1
1
0
1
2
2
1
2
0
0
0
0
1
2
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
2
2
1
0
1
0
2
1
1
0
0
0
0
1
2
2
0
1
1
0
0
0
0
2
0
1
0
2
2
0
0
0
0
1
2
1
1
0
0
0
0
0
2
0
0
0
0
0
3
0
2
2
0
0
2
2
0
0
0
0
1
0
1
2
2
2
0
0
2
2
0
1
0
0
0
0
0
0
3
0
0
0
1
1
3
1
0
0
2
1
0
1
0
0
0
1
2
2
0
0
2
2
2
0
1
0
0
1
0
0
0
2
1
1
1
0
0
1
2
1
0
0
0
3
0
1
0
0
1
1
0
0
0
2
1
0
0
0
2
0
1
0
0
1
0
1
0
2
2
0
1
1
1
0
0
0
0
1
1
0
0
0
0
1
0
0
2
1
0
0
0
1
1
1
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
2
0
2
0
1
0
2
2
0
0
0
0
1
0
1
1
0
2
0
0
2
0
0
1
0
0
1
1
0
0
2
0
2
2
0
1
2
0
1
2
2
1
2
0
0
2
1
0
1
1
2
0
1
0
0
1
2
1
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
1
0
1
0
1
0
0
0
1
0
0
0
0
2
0
2
0
1
2
0
2
1
1
2
1
0
0
1
2
0
2
1
3
0
0
0
2
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
3
2
2
2
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
1
2
1
2
0
0
1
1
0
0
0
0
1
0
2
0
2
0
1
1
0
0
0
0
2
0
0
0
1
2
2
0
0
0
0
1
0
0
1
0
1
0
2
0
0
0
0
0
4
1
0
0
1
0
0
2
3
0
0
0
0
0
0
0
0
1
0
2
1
1
0
0
2
2
0
1
0
0
0
2
2
2
0
0
2
0
2
2
0
1
0
0
1
0
0
0
0
2
0
0
0
1
0
1
0
0
2
2
0
1
1
0
2
0
0
1
0
2
2
0
2
1
0
0
1
2
0
0
0
0
0
2
1
1
0
1
0
0
1
0
0
0
2
1
0
0
0
1
0
0
0
2
2
1
2
0
1
2
1
1
0
1
1
0
0
0
4
1
0
2
3
0
1
0
0
0
0
2
0
0
0
0
0
0
5
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
8
0
0
2
3
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
2
1
3
1
2
2
0
0
1
0
2
0
1
2
0
0
0
2
0
1
1
0
0
1
1
1
0
0
1
1
2
2
1
1
1
1
1
0
1
0
0
2
0
2
0
0
0
1
2
0
2
0
2
0
0
2
1
2
0
2
0
0
1
1
0
0
0
2
0
0
2
0
1
0
2
0
0
0
0
2
0
1
0
0
0
2
2
0
0
0
1
0
0
1
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
2
0
1
0
0
0
0
0
0
1
0
1
1
0
1
1
0
0
0
2
2
2
0
2
0
0
2
1
0
2
2
1
1
2
0
0
2
1
0
0
0
1
2
2
2
1
2
0
0
1
0
0
1
2
0
0
0
2
0
1
4
2
2
0
0
0
2
0
2
0
0
0
0
2
1
0
1
0
0
2
0
2
0
1
1
0
2
2
2
0
0
2
1
0
1
1
0
0
0
1
1
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
2
0
0
0
2
0
3
1
1
0
1
2
0
2
0
4
1
1
0
0
2
0
0
3
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
1
0
0
0
0
1
2
0
0
2
1
0
0
1
1
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
1
0
1
1
0
0
0
0
0
0
1
0
1
0
0
1
0
4
0
0
0
1
1
2
0
1
0
0
2
1
1
1
0
2
1
0
0
0
2
1
0
0
1
1
0
1
0
2
0
2
0
0
2
0
0
0
2
2
2
0
0
0
2
1
0
1
1
0
2
0
2
0
0
1
0
2
2
0
0
0
1
3
2
0
1
0
0
2
0
0
0
2
2
1
0
0
0
0
1
2
1
0
0
0
0
0
0
2
0
2
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
2
1
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
1
6
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
10
0
1
1
0
0
0
0
0
0
0
1
1
2
2
0
2
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
1
2
0
0
1
0
1
0
0
0
0
0
2
0
2
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
3
0
0
1
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
2
0
2
0
2
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
2
0
2
0
0
0
0
1
0
1
0
0
0
0
0
2
1
0
1
0
0
1
1
0
1
0
0
0
2
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
1
1
0
0
2
0
0
2
0
2
0
0
2
0
0
3
1
0
0
0
1
5
0
2
0
0
2
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
2
2
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
3
0
2
0
0
0
1
0
1
0
0
0
1
0
0
2
1
0
0
1
0
1
0
2
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
1
0
0
1
1
1
1
0
0
0
3
0
0
1
0
0
0
1
1
0
2
0
1
0
0
1
1
0
0
0
0
2
0
0
1
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
2
1
2
0
1
1
1
1
0
3
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
2
1
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
2
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
4
2
0
0
0
0
0
2
5
0
0
3
0
0
2
0
2
1
1
0
0
0
0
0
2
2
0
0
0
1
2
0
0
0
2
0
3
1
0
0
0
1
2
2
0
1
0
0
2
2
1
0
0
1
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
2
2
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
13
0
0
0
1
0
1
0
3
0
0
0
0
1
1
0
0
0
0
1
2
0
0
2
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
2
1
3
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
2
0
0
1
1
0
2
2
0
0
0
0
1
3
0
0
0
1
0
0
3
0
0
0
1
1
1
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
1
1
1
1
0
0
0
2
1
0
1
2
0
0
0
0
2
0
2
2
1
0
0
2
0
0
1
1
1
0
1
0
0
2
1
0
0
0
0
1
1
1
1
0
0
2
1
1
0
0
4
0
0
2
1
1
0
0
0
2
0
0
0
0
1
0
2
0
0
0
2
0
0
2
0
1
0
2
0
2
0
0
0
1
1
0
0
2
0
0
0
0
0
0
3
0
1
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
2
0
0
1
1
1
0
1
0
2
0
3
2
0
0
0
0
2
0
1
0
0
0
2
0
2
0
2
1
0
0
0
0
2
3
0
0
0
0
2
0
0
1
1
0
2
0
1
2
0
1
0
1
0
0
0
1
0
0
0
0
0
1
1
0
1
0
1
2
2
0
2
0
0
0
1
2
1
0
0
2
0
0
0
0
1
0
0
0
1
0
1
0
2
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
2
1
0
0
1
2
0
0
2
2
0
1
0
0
1
1
2
0
1
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
14
0
0
2
0
2
2
1
1
1
0
0
0
2
0
0
0
2
0
0
0
2
2
0
0
0
2
0
2
2
0
0
0
2
0
0
0
0
1
0
2
2
0
1
1
2
2
0
0
0
0
1
0
1
1
2
2
2
1
1
0
2
0
0
0
4
0
0
1
2
1
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
1
2
0
1
0
5
0
0
0
0
2
0
0
1
0
1
2
0
3
0
0
0
2
0
2
1
0
0
0
0
1
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
3
2
1
0
1
1
2
0
0
0
1
0
0
1
1
0
0
0
0
0
2
0
0
1
3
0
1
2
1
1
0
2
0
2
0
0
0
0
2
2
1
1
2
1
0
1
2
0
1
2
1
0
0
1
0
0
2
0
0
0
0
0
1
0
1
0
0
0
1
2
1
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
2
2
2
0
0
1
0
0
0
0
1
0
1
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
2
0
1
0
1
1
0
0
0
0
2
1
0
0
0
0
0
0
2
1
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
1
1
0
2
1
1
0
0
0
2
1
2
0
3
2
0
0
0
0
1
0
0
1
2
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
2
0
2
2
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
2
0
2
2
2
0
0
0
0
2
1
1
2
0
1
0
0
0
1
0
2
1
0
1
0
0
1
1
0
0
2
1
0
0
1
0
0
0
2
0
0
2
0
0
1
1
1
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
2
2
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
2
0
2
0
1
0
1
0
0
0
2
1
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
1
0
1
0
0
1
1
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
3
0
0
0
0
2
0
2
0
0
0
0
1
2
1
1
2
2
0
2
0
0
0
1
1
1
2
0
1
2
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
4
0
0
0
0
1
1
1
0
0
0
0
0
2
1
1
0
2
2
2
0
0
0
0
3
0
0
0
0
0
1
0
0
0
1
2
1
0
0
0
0
2
0
0
0
0
0
1
0
1
1
3
0
2
0
0
0
2
2
3
0
0
1
0
0
2
0
2
1
0
1
0
2
0
2
1
0
0
0
0
0
1
1
0
1
0
4
0
0
1
0
0
0
3
2
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
2
0
3
2
0
0
0
2
0
2
0
2
1
0
0
0
0
0
3
2
0
2
1
2
2
1
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
2
1
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
3
2
0
0
0
1
0
0
2
0
1
1
0
0
2
0
2
2
0
2
2
0
0
0
0
2
0
1
0
0
0
1
2
1
1
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
1
1
0
3
0
0
0
1
0
0
0
0
0
3
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
3
1
1
0
3
0
0
0
0
0
1
0
0
2
0
0
2
1
1
0
2
1
0
0
2
1
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
1
0
1
0
0
0
0
1
0
0
0
0
1
2
3
0
0
0
0
2
0
0
1
1
0
0
2
0
1
0
0
0
2
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
2
1
0
0
0
0
0
0
2
2
0
1
0
2
0
0
0
0
0
2
1
0
0
1
0
0
1
2
3
0
2
2
0
0
0
1
2
0
2
0
2
0
0
2
4
0
2
0
2
2
0
0
2
2
0
2
2
0
0
0
2
0
2
0
1
2
1
0
2
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
2
2
1
1
2
2
0
0
0
1
0
1
2
0
0
0
0
0
1
2
0
1
2
2
0
0
0
0
1
1
2
2
1
2
2
1
0
2
1
0
2
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
2
2
0
0
2
0
1
0
2
1
1
2
0
1
0
0
1
0
2
0
1
1
4
0
2
0
0
0
0
0
2
0
0
2
2
1
3
0
0
0
1
0
1
0
0
2
0
0
0
1
1
2
0
0
0
0
1
0
0
2
0
0
2
1
2
0
1
0
0
0
0
1
0
2
2
0
0
0
1
0
0
0
1
1
1
0
0
1
2
0
2
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
4
12
1
2
1
0
0
1
1
0
0
0
0
1
1
1
1
1
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
1
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
2
0
1
0
0
2
1
0
0
2
3
0
1
0
2
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
1
1
0
1
0
0
1
0
0
2
0
1
0
0
0
1
0
0
0
1
2
0
2
0
1
2
2
1
0
0
0
2
1
4
0
2
0
0
1
0
0
2
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
2
1
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
2
2
2
2
2
0
2
2
0
0
2
0
0
2
3
1
1
1
0
2
1
1
2
0
0
0
3
2
0
0
2
2
0
0
0
0
0
0
0
1
1
0
0
0
0
2
1
0
0
2
0
2
0
0
0
0
0
0
0
0
1
1
2
2
0
1
0
3
0
0
0
0
0
1
0
2
0
0
2
2
0
1
0
2
0
0
0
0
0
0
1
0
0
2
2
0
0
0
1
0
0
1
3
0
1
1
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
2
1
0
1
0
0
0
1
0
1
0
3
1
1
3
3
7
1
1
2
1
2
1
0
1
2
0
0
2
2
0
0
0
0
1
0
1
1
0
0
1
0
0
0
2
0
1
0
1
0
0
0
0
0
2
0
2
1
0
1
0
1
0
0
2
0
0
0
1
1
1
1
0
0
2
0
1
0
0
0
0
0
1
0
0
0
2
2
1
0
0
2
1
1
0
0
0
0
0
0
0
0
1
0
1
2
0
2
0
0
1
0
0
0
1
2
1
1
0
0
0
0
1
2
0
1
0
2
0
1
2
0
2
0
1
1
0
0
0
3
2
2
0
1
2
1
3
0
1
3
0
0
2
2
1
0
0
0
1
2
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
3
1
1
0
1
2
3
0
2
0
1
1
0
0
2
0
2
0
0
1
2
1
0
1
1
0
0
0
0
2
0
0
0
1
0
0
1
1
1
1
6
1
0
0
1
0
0
0
0
1
0
2
0
3
0
1
0
0
1
0
0
1
0
0
0
4
1
0
2
1
0
1
2
0
0
0
0
0
3
0
0
0
2
0
1
0
2
2
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
2
1
0
1
0
1
0
0
0
1
1
0
0
2
2
0
0
0
1
0
0
2
0
1
0
0
1
0
1
2
1
2
0
2
0
2
0
0
0
0
0
0
0
2
0
1
0
2
0
1
1
1
0
0
0
0
1
2
0
1
1
0
2
1
1
0
2
2
1
1
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
1
3
2
1
0
1
0
1
1
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
4
0
1
0
1
0
0
0
1
0
1
0
0
0
0
2
2
0
0
0
0
0
2
1
1
0
0
0
2
0
0
1
0
0
2
0
2
1
1
0
0
0
0
0
0
2
0
3
0
1
2
2
0
1
1
0
0
2
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
2
1
0
0
0
0
0
0
1
2
1
2
0
0
0
0
0
3
0
0
0
0
0
2
0
1
2
1
0
0
0
0
2
2
0
1
0
1
0
2
1
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
1
1
2
0
4
0
0
1
0
0
0
0
1
0
2
1
0
1
0
2
2
0
1
2
0
0
2
0
0
2
2
0
0
1
0
2
1
2
1
2
1
0
2
0
0
0
2
0
0
0
0
0
0
2
1
2
2
0
0
2
1
1
0
2
0
0
1
0
1
0
0
2
0
0
0
0
2
0
1
2
1
0
0
0
1
0
2
2
0
0
0
2
0
0
0
1
2
2
0
0
0
0
0
1
0
0
1
1
0
0
2
1
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
1
0
2
1
0
0
0
0
0
4
1
1
1
2
0
1
1
0
0
0
1
0
0
0
2
1
0
0
1
1
0
2
0
1
2
0
2
0
1
2
0
2
0
2
2
0
1
0
0
1
0
1
1
2
0
2
0
2
0
2
1
0
0
0
1
0
0
0
1
1
1
2
0
0
1
2
2
0
0
0
1
2
0
0
3
0
0
1
2
1
1
1
1
1
0
1
0
0
0
2
0
0
1
1
0
0
0
2
1
0
0
0
0
2
0
2
0
1
0
0
2
0
1
1
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
2
0
0
0
0
2
0
1
2
0
1
2
2
0
0
1
2
1
0
1
0
2
0
0
1
0
1
1
2
0
0
2
1
0
1
1
0
0
0
1
2
1
0
0
0
2
2
1
0
0
1
0
0
0
1
1
2
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
1
0
2
0
0
0
2
0
0
0
0
1
0
0
1
1
0
1
2
1
0
0
1
0
0
1
1
0
1
3
1
2
2
0
0
0
2
1
0
0
1
0
0
0
0
2
1
0
0
0
2
1
2
1
0
0
0
1
2
0
0
0
0
1
0
0
0
1
1
3
1
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
1
1
1
1
0
0
0
1
0
5
0
0
0
0
0
1
1
1
2
2
1
1
0
1
0
0
2
0
0
0
1
1
0
0
0
0
1
0
1
0
0
1
0
0
1
1
0
0
0
1
1
0
0
0
2
0
0
0
3
0
1
0
0
2
0
0
2
1
1
2
0
0
1
2
1
0
0
1
0
0
0
0
1
1
0
0
2
0
2
0
1
0
0
0
0
0
2
0
2
1
0
0
0
4
0
0
0
5
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
1
4
0
1
3
2
4
0
0
0
2
1
0
0
3
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
2
0
0
0
1
2
0
3
0
2
0
0
2
0
1
1
0
0
0
0
1
0
1
0
0
0
0
2
1
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
1
0
0
0
2
0
0
2
1
2
0
0
0
0
2
0
1
0
0
1
0
0
2
2
0
0
0
0
0
2
0
0
0
2
0
1
1
2
0
1
0
0
0
0
1
2
1
1
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
1
2
0
0
2
2
0
0
0
0
1
0
1
0
0
0
1
0
2
0
1
1
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
3
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
3
0
0
0
0
1
2
0
1
0
1
0
1
0
0
0
0
0
1
3
1
0
0
0
1
0
1
0
2
1
2
0
0
0
0
1
2
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
1
1
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
1
1
1
2
1
0
0
0
1
0
0
1
0
0
1
0
2
2
0
2
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
2
1
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
1
2
1
0
0
0
1
2
0
1
2
2
0
1
0
1
0
0
0
2
1
0
2
0
1
0
1
2
2
0
0
1
0
0
2
0
0
0
2
2
0
1
2
1
2
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
2
0
2
3
3
0
0
3
2
3
0
0
2
6
2
3
0
2
2
0
3
2
0
0
1
2
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
3
1
0
0
2
2
0
0
0
1
0
1
1
3
2
0
1
0
0
0
0
0
0
1
1
0
2
0
0
0
1
2
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
1
0
1
2
0
1
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
1
2
0
0
0
1
0
0
1
0
0
3
0
2
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
2
0
1
1
0
2
0
2
1
0
0
0
2
0
0
1
0
2
0
0
1
0
2
1
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
2
0
0
1
2
0
0
3
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
2
2
0
1
1
0
2
0
0
2
2
1
2
0
0
0
0
0
0
0
1
0
0
1
2
1
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
1
0
0
1
2
0
2
2
0
0
1
0
2
0
0
0
1
0
0
0
1
1
1
0
2
0
2
0
0
0
2
1
1
0
2
2
4
0
2
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
1
0
1
0
4
1
0
0
0
1
0
0
4
0
0
2
0
2
2
0
1
2
1
0
0
1
2
1
1
0
0
1
0
0
0
1
0
0
2
0
0
2
0
0
1
1
2
2
3
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
4
2
1
0
0
0
0
1
0
3
0
0
2
2
0
1
0
1
1
0
0
0
3
0
0
0
0
0
1
0
0
2
0
1
0
2
0
0
0
0
2
0
0
2
2
0
0
0
0
1
0
2
0
0
1
0
1
1
0
2
4
0
1
1
2
0
0
0
0
0
1
0
0
0
0
1
1
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
1
1
0
0
1
3
0
0
0
3
0
1
2
0
0
2
0
0
2
0
1
0
0
1
0
0
0
2
1
2
0
1
1
0
0
2
0
0
1
2
0
1
2
0
0
0
0
1
0
0
0
1
0
2
0
2
0
0
0
0
0
0
1
1
3
1
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
2
0
2
1
2
2
0
0
0
1
0
2
0
0
1
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
2
0
2
0
2
1
1
1
0
0
2
0
2
0
2
2
2
0
1
2
1
2
2
0
1
3
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
2
0
1
0
0
0
0
2
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
2
0
0
0
0
1
2
0
0
1
1
0
0
0
0
0
0
1
1
2
0
0
4
2
0
1
0
0
2
1
0
3
0
0
1
0
0
0
1
1
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
2
0
2
2
0
0
1
1
2
2
1
0
1
7
0
2
2
1
0
0
1
2
0
0
2
1
0
1
2
0
0
0
0
1
0
0
0
0
0
0
1
2
1
1
0
2
0
2
2
1
0
2
1
2
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
1
0
2
0
1
2
2
2
0
0
1
2
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
1
0
1
0
1
1
0
0
0
0
1
0
1
0
1
2
1
2
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
2
0
0
1
1
1
0
0
0
0
0
2
0
0
0
1
0
1
1
0
1
1
0
4
0
1
0
0
2
0
0
2
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
4
1
0
0
2
0
0
2
0
0
1
1
1
0
1
0
0
1
0
0
1
3
0
1
2
2
0
2
2
0
0
0
1
2
0
1
1
1
2
0
0
1
0
0
2
2
0
0
0
2
0
0
1
0
0
0
0
2
2
0
0
0
0
0
2
2
0
0
1
1
0
0
0
0
0
2
2
1
1
2
0
3
2
0
0
0
0
0
0
3
0
2
2
1
1
0
1
0
0
1
0
0
2
3
0
1
1
1
0
0
1
0
2
1
2
2
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
2
2
1
0
1
0
0
2
1
0
1
2
0
2
0
0
1
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
1
0
1
0
1
0
1
1
1
1
0
1
0
2
0
0
0
0
0
1
0
1
1
1
1
0
7
0
1
0
1
0
0
1
1
0
1
0
4
0
0
0
0
1
0
1
1
0
0
0
2
1
0
3
1
1
1
0
1
0
0
1
0
1
0
0
0
2
1
1
0
2
0
0
0
0
1
1
0
0
2
2
0
0
0
1
0
1
0
0
0
1
0
2
0
0
0
0
1
0
2
0
0
0
2
5
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
1
0
1
2
0
0
0
0
2
0
0
2
2
1
2
0
0
2
2
0
0
0
0
1
0
1
1
0
2
2
0
0
0
0
0
2
0
3
2
2
5
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
1
1
0
0
0
0
0
1
1
1
0
0
0
2
0
0
0
0
1
0
2
1
2
0
2
2
0
1
0
3
1
1
1
0
2
0
0
2
1
0
0
1
0
2
4
0
2
0
0
0
1
1
0
1
0
0
1
0
0
1
2
2
0
2
1
0
0
0
1
0
0
1
1
0
3
0
0
1
2
0
0
0
0
0
1
1
0
0
0
0
1
1
1
1
2
0
0
0
0
8
0
2
0
1
1
2
0
0
0
0
1
0
1
3
3
0
0
0
1
1
0
0
1
0
0
0
1
0
1
0
0
1
0
2
0
0
0
2
0
0
0
1
0
0
2
0
0
2
1
0
2
1
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
3
0
0
0
2
1
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
1
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
1
3
1
0
1
4
0
0
2
2
0
0
0
2
0
0
0
0
1
1
2
0
2
2
1
2
2
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
1
0
2
2
2
1
0
0
1
0
2
0
2
0
0
2
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
5
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
2
0
3
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
3
0
1
0
1
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
2
0
2
0
0
2
0
2
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
1
0
0
2
2
1
0
1
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
2
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
7
1
0
0
2
1
2
0
0
0
1
0
0
1
0
2
2
0
0
2
1
1
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
1
0
1
0
0
0
0
1
0
0
0
1
0
2
1
0
0
1
1
0
0
0
0
0
0
0
2
0
2
0
2
1
0
2
2
2
4
0
0
0
1
2
1
0
0
0
0
1
0
2
0
2
0
2
0
0
0
2
0
1
0
4
0
2
2
2
0
1
0
1
0
2
2
0
1
2
0
0
2
1
0
2
0
2
0
2
1
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
3
0
0
0
1
0
0
1
0
2
0
2
0
1
0
0
0
1
2
0
0
0
0
1
0
0
1
0
1
0
2
0
1
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
1
1
2
0
0
2
0
0
0
0
0
4
0
0
0
0
1
3
0
0
0
0
2
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
2
2
1
2
1
0
0
1
2
3
1
0
0
1
1
2
0
2
0
4
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
2
0
2
3
0
0
0
1
2
0
0
0
0
3
0
2
1
0
2
2
0
0
2
0
0
0
0
1
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
2
0
0
0
0
2
2
1
0
1
2
0
2
0
0
0
0
0
0
0
1
0
1
2
0
0
0
1
0
1
0
1
0
0
0
0
0
2
0
0
0
1
1
2
0
0
0
0
2
1
0
0
0
2
0
0
1
0
0
4
1
0
0
1
0
0
1
2
2
0
1
2
0
0
2
0
0
0
0
0
2
0
0
0
2
1
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
3
0
1
0
0
0
2
0
2
0
2
1
0
1
0
0
1
0
0
0
1
2
0
1
0
2
0
1
2
0
2
1
0
2
0
0
0
0
0
0
3
1
2
0
2
0
0
1
2
1
0
1
2
0
7
0
1
0
0
0
1
0
1
2
0
1
0
1
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
1
1
0
0
0
0
2
0
0
0
0
2
0
1
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
1
1
0
0
2
0
2
1
1
2
0
0
0
1
2
1
1
0
1
0
0
0
0
0
0
0
1
0
1
1
1
2
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
1
0
1
2
1
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
1
0
0
0
0
0
0
1
0
2
0
0
1
2
0
1
1
1
0
0
0
0
0
0
0
2
1
0
2
0
2
0
0
0
2
0
0
0
2
2
0
0
0
1
2
0
0
1
0
2
1
0
0
0
0
0
0
2
2
0
0
1
0
0
2
1
3
0
2
0
2
0
2
0
0
0
0
1
0
1
0
0
0
0
1
0
2
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
2
1
1
0
0
2
0
1
0
2
0
0
0
0
0
0
0
2
0
0
2
3
0
0
0
2
0
0
0
1
0
0
0
1
2
0
0
2
1
0
0
0
0
0
2
0
0
2
0
0
0
2
0
2
0
3
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
1
0
1
0
0
0
2
1
1
0
2
0
1
0
1
0
0
0
2
0
0
0
1
1
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
1
1
0
2
1
0
1
0
2
1
2
0
0
4
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
2
0
3
0
2
0
2
0
2
1
1
0
2
0
2
1
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
1
0
2
0
4
1
0
2
2
0
2
0
0
0
2
0
0
1
0
1
0
0
1
0
1
2
0
0
0
2
0
0
0
2
0
0
0
2
1
0
1
0
0
2
0
2
0
1
1
0
1
0
0
0
2
0
0
1
0
0
1
2
2
2
0
0
0
0
0
0
0
1
2
1
0
1
0
0
0
0
1
0
0
1
1
0
0
2
0
0
0
0
2
1
0
2
2
4
1
1
2
0
2
4
2
0
0
2
2
0
2
1
0
2
0
0
0
1
0
0
2
6
0
1
0
0
0
0
0
0
0
0
2
0
1
2
2
0
0
2
0
0
1
2
1
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
2
1
0
0
0
1
0
0
0
0
1
4
0
2
2
1
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
1
1
1
1
1
3
0
2
0
2
3
0
0
2
0
0
0
2
0
0
1
2
2
1
0
1
1
1
0
0
0
1
0
2
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
2
0
2
1
0
0
0
0
1
0
0
0
2
0
1
1
1
1
0
2
0
0
0
1
0
2
1
0
1
0
0
0
0
2
0
2
0
0
0
3
0
0
1
3
1
0
1
2
2
0
0
2
0
0
0
0
0
1
2
0
0
0
1
1
0
1
2
2
0
2
2
0
1
2
2
1
1
0
0
0
0
3
4
0
0
2
2
0
0
0
0
0
0
0
0
1
0
5
0
0
0
0
0
0
0
2
2
0
0
0
2
4
0
1
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
2
1
0
3
0
2
0
0
1
1
0
3
0
0
0
0
1
1
0
0
1
1
0
0
0
0
2
0
0
0
1
1
0
1
0
2
0
1
0
0
0
1
3
1
0
2
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
1
2
0
1
2
0
0
0
2
1
0
1
0
0
0
0
0
0
1
1
2
1
0
0
1
2
0
1
0
0
0
2
1
0
6
0
0
2
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
4
0
0
0
2
1
1
0
2
0
3
2
1
2
0
0
1
0
2
0
0
0
0
2
2
1
2
0
1
0
0
0
0
1
1
1
2
1
0
0
0
1
1
0
0
2
0
0
1
0
0
0
1
0
2
1
0
0
1
2
0
0
0
0
0
1
1
2
0
0
0
1
0
1
1
0
1
3
1
0
2
0
1
2
0
2
0
1
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
2
0
2
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
2
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
2
0
0
0
0
1
0
0
2
1
1
0
1
2
0
0
0
1
0
2
0
0
1
1
0
0
2
2
4
0
0
0
0
1
2
0
2
1
1
1
0
1
0
0
3
2
0
1
1
0
1
0
0
0
1
1
1
1
1
2
0
0
0
0
0
2
0
0
0
0
1
1
2
0
2
0
1
2
1
1
0
1
0
0
2
1
0
0
0
1
1
0
0
2
2
0
0
1
0
0
0
1
1
0
2
2
0
1
0
0
1
0
0
0
1
0
0
2
1
0
1
0
0
3
0
0
0
2
2
0
3
3
0
0
0
0
0
0
2
0
1
0
1
0
3
1
2
0
1
2
2
1
2
0
1
0
2
2
0
0
3
0
1
0
0
0
2
0
0
0
1
2
0
0
1
0
1
0
0
2
2
0
0
1
1
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
1
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
2
0
0
0
0
1
1
0
0
2
2
0
0
2
0
2
1
1
2
1
0
0
3
2
1
0
0
1
0
0
0
2
1
2
0
0
0
1
0
0
0
0
0
3
1
0
1
0
0
0
1
0
0
1
0
0
0
1
3
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
2
2
0
1
1
2
0
0
2
0
0
2
2
0
1
0
1
2
0
0
0
0
3
2
0
2
0
0
0
2
1
0
0
1
0
0
0
0
2
0
0
2
0
2
2
0
1
1
2
2
3
0
2
1
0
0
2
0
1
1
2
2
0
0
0
0
0
2
2
0
1
2
0
0
0
0
0
2
1
0
1
1
3
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
2
2
0
1
0
2
0
0
0
2
1
1
0
0
0
0
1
3
1
0
0
1
0
2
1
0
0
0
0
0
1
2
0
1
1
2
0
2
3
0
1
1
0
0
0
0
1
1
0
0
0
2
2
0
0
1
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
3
0
0
2
0
2
0
0
0
0
0
2
2
0
0
1
2
0
2
0
0
0
2
2
1
0
0
1
0
3
0
1
2
1
1
1
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
2
1
0
2
0
0
0
1
1
0
1
0
1
0
0
0
2
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
2
0
0
2
1
0
0
0
1
0
0
1
2
0
2
0
0
2
0
2
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
1
0
2
0
2
1
0
2
0
2
0
2
1
0
0
5
0
0
0
1
0
0
3
0
0
0
0
1
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
1
0
1
0
1
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
2
1
0
0
2
0
0
0
0
0
1
1
0
1
0
2
2
0
0
0
2
0
0
1
1
0
2
0
0
0
2
2
0
0
0
0
2
1
0
2
0
0
0
0
1
1
1
2
1
0
4
1
0
2
0
0
0
0
0
1
0
0
0
0
1
1
0
1
1
1
1
1
0
1
1
1
0
0
2
0
0
0
2
1
2
2
0
0
0
0
0
2
0
2
0
2
0
0
6
0
0
0
0
0
2
1
1
0
0
0
1
1
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
4
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
1
1
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
1
1
0
1
0
1
2
0
0
0
0
3
3
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
2
0
0
0
2
0
0
3
1
2
0
0
2
0
0
0
0
0
0
3
0
0
0
0
3
1
0
0
0
2
0
0
0
3
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
6
0
0
1
2
2
1
0
0
0
1
0
0
2
0
2
0
0
0
0
1
0
0
2
1
1
0
1
2
2
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
2
0
2
0
0
2
0
0
2
1
2
0
0
0
0
0
0
0
0
1
0
1
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
2
0
0
2
1
0
0
1
1
0
1
0
1
1
1
0
0
0
0
1
0
2
1
0
0
0
0
0
2
0
0
0
0
1
0
1
1
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
3
1
0
0
1
0
0
0
2
0
1
2
0
2
2
0
2
0
2
1
0
1
2
1
0
0
1
1
2
3
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
2
1
1
0
0
2
2
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
2
0
0
0
0
1
0
3
0
0
4
0
1
1
0
0
1
3
0
0
2
0
1
0
0
0
1
1
2
0
0
0
2
0
0
1
0
2
0
3
0
0
0
0
0
3
0
0
0
0
2
0
2
0
0
2
1
2
1
1
2
0
0
0
2
0
0
0
1
0
0
1
0
2
0
2
0
0
0
0
2
1
2
0
0
0
0
1
0
1
1
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
2
1
0
2
0
0
0
0
0
1
0
1
0
0
1
0
2
0
0
0
0
0
3
2
0
0
0
2
0
0
0
1
1
0
1
0
0
1
0
0
2
0
1
0
6
0
0
0
0
2
2
2
0
0
0
0
1
1
0
0
0
0
2
0
0
2
2
0
1
1
1
0
1
0
0
0
0
1
2
2
1
0
1
0
1
1
0
0
0
0
0
2
0
0
1
1
2
0
0
5
1
2
0
0
1
2
2
2
1
1
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
2
1
0
0
0
1
0
0
0
0
1
0
0
2
0
0
2
2
0
0
0
2
0
2
0
0
2
1
1
1
0
0
1
2
0
0
1
2
0
0
0
0
0
1
1
0
0
0
2
2
0
2
1
0
2
0
0
2
0
0
0
0
0
2
0
2
0
1
1
0
0
0
2
0
0
1
2
0
0
0
1
1
0
0
0
0
2
1
0
1
0
0
1
1
0
2
0
0
2
0
0
0
2
1
0
0
0
0
0
1
1
1
5
0
0
0
0
3
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
1
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
2
0
2
2
0
0
0
2
0
1
4
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
1
0
2
0
2
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
1
2
0
2
1
0
0
0
2
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
2
1
0
1
2
1
0
0
1
0
1
2
0
0
0
0
0
0
1
1
1
0
0
2
2
0
2
0
3
2
1
2
2
0
0
0
1
0
1
0
0
0
0
0
3
0
0
0
0
0
1
2
2
0
0
1
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
1
2
1
0
1
2
2
0
0
0
0
2
1
1
0
0
1
1
1
0
0
2
1
1
0
0
0
0
0
2
2
3
1
2
0
0
1
0
3
0
1
2
0
2
0
0
0
0
0
0
2
0
2
1
1
2
1
0
0
2
1
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
2
1
0
0
1
0
1
2
1
2
0
0
2
0
0
0
0
0
0
0
0
1
1
1
0
0
0
2
2
1
1
0
1
0
0
2
0
0
0
1
0
1
0
1
1
0
0
0
0
1
2
0
1
0
0
2
0
2
0
0
2
1
0
0
1
0
1
3
1
0
0
0
0
0
0
0
3
0
2
1
0
2
1
2
1
0
0
2
2
2
2
2
0
0
2
0
2
2
1
2
0
2
0
0
0
0
0
2
0
2
0
1
2
2
2
1
1
0
3
3
0
0
0
1
1
2
0
2
0
1
0
1
0
5
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
2
0
0
0
0
0
2
1
0
0
0
1
0
0
2
0
0
0
0
1
0
1
0
0
1
0
0
2
0
1
2
0
0
0
0
0
2
0
0
1
0
2
2
1
0
1
1
0
0
0
0
1
2
0
0
2
0
2
1
0
0
2
0
0
0
0
3
2
0
0
0
0
1
0
2
1
0
1
1
0
0
2
0
2
0
0
0
1
0
0
0
0
1
0
0
2
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
2
0
5
1
2
0
0
1
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
2
0
3
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
7
1
0
2
0
0
2
1
0
2
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
1
1
0
2
0
0
1
0
0
1
0
1
0
0
2
1
0
0
2
2
1
0
2
0
0
2
0
0
1
1
1
0
1
1
0
1
1
0
0
0
0
0
0
0
5
0
0
1
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
1
0
1
1
0
0
0
0
2
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
2
0
0
1
0
0
0
0
0
2
0
0
2
1
2
3
0
0
0
0
0
1
1
0
2
0
0
0
1
0
2
1
2
3
1
0
0
0
2
0
0
0
2
0
2
1
0
0
0
0
0
3
1
0
0
1
0
0
0
2
0
2
1
1
1
0
0
0
0
0
0
1
0
0
1
2
0
0
1
1
0
0
0
0
0
1
0
2
1
0
0
2
6
1
0
0
0
0
0
2
0
2
0
1
0
0
1
0
1
1
0
1
1
0
2
0
0
0
1
1
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
2
0
2
1
1
0
1
0
0
0
2
0
0
2
0
0
1
0
0
2
1
0
0
1
2
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
2
1
0
1
0
1
0
1
2
0
2
1
0
2
1
2
1
0
2
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
1
2
0
0
2
0
2
0
0
0
0
1
2
0
0
0
1
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
1
2
1
0
2
0
0
1
0
0
0
0
0
2
0
1
0
1
2
0
1
1
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
2
0
0
0
0
3
0
0
1
0
0
2
0
1
0
1
1
0
0
2
1
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
2
0
2
0
0
2
1
1
0
0
0
0
2
0
0
0
1
2
2
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
2
1
0
0
0
1
0
0
0
2
0
0
1
0
1
0
1
0
2
2
1
0
2
0
0
0
0
0
1
0
0
2
0
3
0
0
3
0
2
0
2
2
0
0
0
0
2
0
0
0
1
1
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
1
0
0
3
0
0
1
0
0
0
1
0
0
4
0
0
0
2
0
2
1
0
1
3
0
0
2
1
1
0
2
0
0
0
0
0
0
2
0
0
0
2
1
0
2
0
0
1
0
0
0
0
0
0
1
1
1
0
0
2
0
0
1
1
0
0
0
2
0
0
0
0
2
0
0
0
6
0
0
0
1
2
0
0
2
0
2
0
0
1
0
0
3
1
0
0
2
0
1
1
0
1
0
2
0
0
0
1
1
0
0
0
1
1
2
0
1
0
2
0
0
0
0
0
0
1
1
0
1
0
1
0
2
0
0
1
0
0
3
1
2
0
0
0
0
0
0
3
1
1
0
0
0
0
2
0
0
2
1
2
0
0
0
0
2
0
0
2
0
1
1
2
0
2
0
3
0
0
1
0
0
0
0
0
1
1
0
0
0
2
2
2
0
1
0
0
0
1
0
2
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
2
0
1
2
2
0
1
0
1
0
0
0
0
2
2
0
0
1
0
1
0
0
2
2
0
1
3
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
1
1
2
0
0
1
0
0
0
2
2
0
0
2
1
0
0
0
0
0
3
2
1
2
0
1
0
0
1
0
0
0
1
1
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
1
2
2
0
1
2
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
3
1
0
0
0
1
2
0
0
0
0
3
1
1
0
0
0
0
3
1
1
1
2
1
2
2
0
2
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
2
2
0
1
0
0
0
2
2
1
1
0
0
0
0
0
0
2
2
1
0
0
1
1
0
0
2
2
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
3
0
2
0
1
0
1
0
0
2
0
2
0
0
0
0
0
0
2
2
2
2
1
0
1
0
0
1
0
2
0
2
1
0
2
0
0
1
2
1
0
0
2
0
0
0
2
2
0
1
0
0
0
0
0
0
0
3
0
1
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
2
1
1
1
1
0
3
0
1
1
0
1
0
0
0
0
2
2
0
1
2
1
2
0
0
0
0
2
1
2
0
0
1
1
2
2
0
2
1
0
0
2
0
1
1
0
0
0
0
0
0
2
1
2
1
2
0
0
3
2
0
0
2
2
1
0
0
0
0
1
2
0
2
1
0
1
2
0
2
0
1
0
0
2
0
1
1
0
1
2
0
0
0
1
0
1
2
0
0
0
2
0
0
0
1
1
0
0
0
1
0
0
0
3
0
1
2
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
2
0
2
0
2
2
0
0
2
0
0
1
0
1
0
2
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
1
0
0
2
0
0
3
2
2
2
0
0
0
1
0
2
3
1
0
0
0
1
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
2
0
2
0
2
0
2
1
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
1
3
0
0
1
2
0
1
2
0
2
2
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
2
0
1
2
0
1
2
0
2
2
0
0
1
0
0
1
0
0
1
4
0
1
1
2
0
0
1
0
1
2
2
1
0
1
0
0
1
4
0
0
0
0
1
0
1
2
1
0
1
1
0
2
0
0
2
1
0
1
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
2
0
1
0
0
1
0
0
1
1
1
0
0
0
0
2
0
1
0
0
2
2
0
1
0
0
0
1
0
0
0
0
2
0
1
2
0
0
0
0
2
1
0
0
0
3
1
0
0
2
0
0
0
0
0
1
1
0
0
0
2
1
0
2
0
0
0
4
2
0
0
0
2
1
0
2
0
3
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
1
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
1
1
0
2
1
0
0
0
1
0
2
0
2
0
0
2
0
2
0
2
2
0
0
0
2
1
1
0
1
0
0
0
0
2
0
0
0
0
0
0
2
1
0
1
2
0
0
0
2
1
2
1
2
0
0
0
1
1
0
0
0
0
0
2
1
1
0
0
1
2
0
2
1
2
2
0
1
0
0
1
2
0
0
1
0
1
0
0
2
0
1
1
0
1
0
0
0
2
0
0
1
2
0
0
2
2
0
0
0
2
2
0
2
0
0
0
1
2
0
1
0
1
1
2
1
2
0
2
1
0
0
0
0
0
0
2
2
0
2
1
1
1
0
0
1
0
0
0
1
2
1
0
0
1
1
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
2
2
2
0
1
0
0
2
0
0
0
2
0
2
2
0
1
0
1
2
0
2
2
0
2
1
0
0
0
0
1
1
0
2
0
2
0
2
1
0
0
1
0
0
0
3
0
2
0
1
2
0
0
2
0
1
2
0
2
0
0
0
0
0
0
1
0
0
0
0
2
1
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
2
0
0
1
0
0
1
2
1
3
1
0
1
3
0
3
1
0
2
0
1
2
0
2
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
2
0
0
0
1
1
0
2
0
2
0
3
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
3
2
0
0
2
0
2
1
1
0
1
0
1
0
0
1
0
0
0
0
1
0
0
2
4
1
0
0
0
1
0
0
0
2
0
0
0
2
2
0
2
1
1
2
0
0
1
0
0
1
1
0
0
2
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
2
3
0
0
0
0
0
0
1
1
1
3
1
2
1
2
0
0
0
1
1
0
0
0
2
0
0
0
0
1
1
0
0
0
0
2
2
0
1
0
0
0
0
1
0
0
2
0
2
1
0
2
0
0
0
0
2
0
0
0
4
0
0
0
0
2
0
2
1
0
0
1
0
0
0
0
1
2
0
2
2
1
0
0
0
1
1
0
1
0
0
2
0
0
2
0
2
0
0
2
0
0
0
0
2
1
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
1
0
2
0
1
0
2
0
0
0
0
1
0
1
0
0
0
2
0
1
0
0
0
1
0
2
2
0
0
0
0
0
1
0
0
2
1
1
0
0
0
0
2
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
1
0
2
0
0
0
2
0
0
0
1
1
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
2
3
1
2
1
0
0
2
1
0
2
0
0
0
0
0
0
1
2
0
1
3
1
0
0
1
0
1
2
0
1
2
0
0
0
0
0
0
0
0
3
0
3
0
2
0
1
0
1
0
1
0
0
1
0
0
0
1
0
0
2
0
2
1
2
0
1
0
0
0
0
2
0
0
1
1
1
0
0
1
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
3
1
3
0
1
0
0
0
0
2
2
2
0
0
1
1
2
0
1
0
0
1
2
0
1
0
2
0
0
0
0
0
0
1
0
0
0
3
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
1
3
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
1
2
0
1
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
2
2
1
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
1
0
0
1
2
0
2
0
0
1
0
1
0
2
0
1
0
0
0
0
0
2
0
0
1
0
3
2
0
0
0
4
0
0
0
0
1
2
0
0
3
0
0
0
2
0
1
1
1
0
0
0
0
0
0
0
0
1
3
0
0
0
2
0
1
2
1
1
2
2
0
0
0
2
0
5
0
3
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
2
1
1
2
0
0
1
1
1
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
2
0
2
0
1
2
0
2
0
0
0
0
0
2
0
2
1
0
0
1
0
0
1
0
0
1
0
2
0
1
0
0
2
1
0
0
0
2
2
4
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
2
0
0
0
1
2
0
1
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
3
0
0
2
3
0
0
0
0
0
0
0
2
1
0
0
1
2
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
1
0
0
1
1
0
2
1
0
0
2
0
0
0
1
1
0
0
2
0
0
0
1
0
0
1
0
0
0
0
2
1
2
3
0
1
2
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
1
1
1
1
0
1
1
0
2
0
0
2
1
0
0
0
0
0
0
0
1
1
1
0
1
0
0
2
2
0
0
1
0
2
1
0
2
1
0
2
2
0
0
0
2
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
1
2
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
1
0
0
0
0
1
0
0
0
1
2
1
0
1
0
3
0
1
0
0
1
0
1
1
5
1
0
2
3
2
1
1
0
1
1
0
1
2
3
0
1
0
0
0
1
0
1
0
0
0
0
3
2
0
0
0
1
0
0
0
0
1
3
0
5
0
2
0
0
1
0
1
0
2
0
1
0
0
2
0
0
0
0
0
2
0
2
1
0
0
2
0
0
0
2
0
0
0
1
0
0
1
0
0
0
2
2
0
0
0
1
0
2
1
0
0
2
2
0
2
1
0
1
0
2
0
0
1
2
0
0
2
1
1
0
2
2
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
1
1
1
2
0
0
2
1
2
0
0
2
2
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
1
0
0
4
0
2
0
0
2
1
0
0
1
2
2
1
0
0
0
0
0
0
0
1
2
0
0
1
2
0
0
1
0
0
0
1
1
1
0
0
0
1
0
0
0
1
1
1
0
0
1
0
2
0
0
0
0
2
0
0
0
2
2
1
0
0
0
0
2
0
0
0
0
0
2
1
5
0
2
0
0
1
0
0
2
1
0
0
0
1
0
1
0
1
0
0
1
0
0
1
1
2
3
0
0
0
2
2
0
0
1
0
0
3
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
1
1
2
2
2
0
2
1
0
0
0
0
2
0
2
0
0
0
1
2
0
0
0
0
0
3
0
0
2
0
1
2
2
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
1
0
1
0
2
2
2
2
0
2
0
2
0
2
2
2
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
2
2
0
0
2
0
0
2
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
1
0
0
1
2
0
1
0
0
0
2
0
0
0
0
2
1
0
0
0
2
0
0
0
0
1
0
1
0
0
1
2
0
0
0
0
0
0
2
1
0
0
0
1
0
2
2
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
3
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
1
1
0
1
0
2
1
1
0
0
0
0
0
2
1
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
2
1
1
2
3
0
0
0
1
0
4
0
1
0
0
1
0
0
0
0
1
2
0
1
0
0
1
0
0
1
2
0
0
0
1
1
0
2
0
0
4
2
0
1
0
0
1
0
1
1
2
0
1
0
3
0
2
0
2
0
0
0
0
0
0
1
0
0
1
0
2
0
0
3
0
0
0
1
0
2
2
0
0
0
0
1
2
1
0
0
2
0
1
2
0
0
0
2
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
3
0
1
0
1
2
0
0
2
0
0
3
1
0
0
1
0
0
1
0
0
2
0
0
0
3
2
2
0
0
1
1
0
0
0
0
2
1
0
0
0
1
1
0
2
0
1
0
0
0
1
0
7
2
2
2
1
0
0
0
3
1
0
0
3
0
2
0
0
1
1
0
0
1
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
2
2
0
0
2
1
2
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
1
0
0
2
0
2
0
1
2
0
0
0
0
2
0
1
0
2
0
0
1
0
0
0
2
1
0
1
1
0
0
0
0
0
1
0
1
0
1
2
0
0
1
0
2
1
0
3
0
0
2
0
0
1
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
3
0
0
0
0
0
3
2
1
2
0
0
0
1
0
0
0
0
0
2
1
0
0
0
1
0
0
1
0
0
2
0
0
0
1
2
1
1
2
0
0
0
0
1
1
0
0
0
2
1
1
0
1
2
0
1
2
2
0
2
0
0
2
0
0
1
2
0
0
2
0
0
2
2
2
0
0
0
1
0
0
1
0
1
3
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
2
0
1
0
0
0
0
1
2
2
0
2
0
0
1
0
1
0
0
2
0
1
0
0
2
2
0
2
0
2
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
2
0
2
2
2
0
1
0
0
0
1
0
0
0
2
1
2
1
3
0
0
0
1
3
0
0
2
2
2
0
0
2
2
1
1
1
0
0
0
1
1
1
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
1
0
0
1
2
0
0
1
0
0
0
1
0
2
0
0
0
1
0
0
1
0
0
0
0
1
2
0
1
0
0
2
2
1
0
0
0
2
0
1
0
3
0
2
1
1
0
0
0
2
0
1
1
1
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
2
0
0
1
0
0
0
0
1
1
0
0
0
2
0
1
2
0
1
0
1
0
0
0
2
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
4
1
0
0
0
2
0
0
1
0
0
3
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
2
0
0
2
3
0
1
0
1
2
2
2
1
0
2
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
6
0
1
0
0
0
1
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
1
0
1
0
2
1
0
2
2
0
0
0
0
1
1
0
0
2
0
2
0
0
2
0
2
1
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
2
1
2
2
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
3
2
0
1
0
0
2
0
0
5
0
0
0
0
0
2
0
0
4
0
0
0
0
2
1
0
1
0
1
0
0
0
0
0
1
2
1
0
0
0
3
0
1
0
1
0
0
0
3
0
0
2
0
2
0
2
0
0
0
0
1
2
1
0
1
2
2
0
1
2
0
0
1
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
2
1
0
2
0
1
0
0
1
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
1
1
1
1
1
2
0
0
2
0
0
1
0
0
1
0
0
0
0
0
1
0
2
2
0
0
2
0
2
0
0
1
0
3
0
0
0
0
1
1
2
1
0
1
0
0
1
1
2
1
0
0
0
2
2
0
0
0
0
0
1
0
0
0
1
0
0
2
2
0
2
1
2
0
0
0
0
1
0
2
0
2
0
3
0
2
0
1
0
0
1
0
1
1
1
1
0
0
3
0
0
0
0
0
0
2
0
0
1
1
0
2
0
0
1
0
2
1
0
1
1
1
0
0
0
2
1
0
2
1
0
0
0
0
0
0
0
0
2
0
2
0
3
0
0
0
2
2
0
0
1
0
4
0
0
0
2
1
0
0
0
4
1
1
0
2
0
2
0
3
0
0
2
0
0
2
0
0
0
0
0
1
0
0
4
1
2
4
0
0
0
1
2
0
2
0
1
0
0
0
0
0
0
0
1
0
2
0
1
1
0
2
0
1
2
5
1
2
0
1
1
0
0
2
0
3
0
2
0
3
0
0
0
3
1
0
1
0
1
0
0
0
2
0
0
0
1
0
0
0
0
2
2
2
0
0
0
2
0
0
0
0
1
0
1
2
0
0
0
0
0
0
2
0
0
0
1
0
2
0
1
0
2
1
0
2
0
2
0
0
0
0
0
0
3
0
2
2
2
1
0
1
0
2
1
0
0
1
0
0
0
2
0
0
0
0
1
1
1
1
2
0
0
0
0
3
0
2
0
0
2
2
0
0
0
0
2
2
1
1
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
2
1
0
0
0
2
1
0
1
3
0
2
0
0
1
0
2
0
1
3
0
0
0
0
1
1
0
0
0
2
0
0
0
2
1
0
0
0
2
1
0
2
2
0
0
2
0
2
1
1
0
2
0
1
0
1
2
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
4
2
0
0
1
0
0
2
0
0
0
2
0
1
0
0
1
1
1
2
2
0
1
0
3
2
0
2
0
0
0
0
1
0
0
0
2
0
0
0
1
1
0
2
1
0
0
0
2
0
0
0
0
0
1
0
1
0
0
1
1
1
1
1
2
0
2
0
1
0
0
0
0
1
0
1
0
1
0
0
2
0
1
0
1
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
1
2
0
1
0
0
0
0
2
0
0
2
0
2
1
2
2
1
0
1
1
0
0
4
0
0
1
1
0
1
0
1
1
0
1
0
2
0
1
0
0
0
2
0
2
2
3
0
0
4
0
0
0
0
0
1
0
2
0
0
2
0
1
1
2
0
2
0
1
0
1
0
1
0
0
2
0
1
1
0
2
0
0
0
0
0
0
1
0
3
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
2
1
1
0
0
2
0
1
1
0
0
2
1
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
2
1
3
1
0
0
1
2
0
1
0
2
0
0
0
0
2
2
0
2
1
0
0
0
2
1
0
0
0
0
2
0
0
0
1
2
0
0
0
2
0
0
0
1
1
0
1
1
0
0
1
1
0
0
1
0
0
0
0
0
1
2
1
1
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
3
0
0
1
3
0
2
1
2
0
0
2
2
2
0
2
0
0
1
0
2
0
1
0
0
0
2
0
0
0
2
0
2
0
1
0
1
1
1
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
2
1
0
0
0
0
0
0
1
0
1
0
0
2
0
2
0
0
0
0
1
0
0
2
0
2
1
0
0
0
0
0
0
0
0
1
2
0
2
0
1
0
0
0
1
0
1
0
1
1
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
1
0
1
1
0
0
0
0
1
0
2
2
2
0
0
1
2
0
2
0
0
0
2
0
0
1
1
2
2
3
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
2
2
0
0
0
2
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
3
0
2
2
0
0
0
0
0
0
0
1
4
0
2
0
0
0
1
0
2
1
0
0
0
0
0
2
2
0
2
0
0
0
2
2
0
0
0
3
0
2
0
0
0
1
0
0
0
0
2
0
0
2
1
0
0
2
2
0
1
1
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
1
1
0
4
0
0
1
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
1
0
0
0
1
0
2
1
2
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
1
2
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
1
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
1
3
2
0
0
1
0
0
0
0
0
0
6
0
0
0
0
0
1
1
0
0
2
0
0
0
2
1
0
2
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
1
2
0
0
1
2
0
1
1
0
2
2
0
0
0
0
1
1
2
0
0
0
0
1
0
0
0
0
0
1
2
1
0
0
0
0
2
0
1
0
0
0
0
0
2
1
0
0
2
1
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
1
0
0
0
0
1
0
0
1
1
2
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
2
2
1
2
0
0
1
0
1
0
2
2
0
0
2
0
0
3
2
1
2
1
0
0
0
9
0
0
0
1
2
1
0
2
0
0
2
0
1
0
2
0
0
1
0
0
2
0
2
1
0
0
1
0
2
0
1
0
0
1
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
1
0
0
0
1
0
0
2
0
0
1
0
2
0
2
0
2
0
0
1
0
2
2
1
1
0
0
2
0
0
2
0
0
0
2
0
0
0
1
2
1
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
2
2
2
1
2
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
2
0
1
0
0
0
4
0
2
0
1
0
0
1
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
1
5
0
0
0
2
0
0
1
2
0
0
0
1
0
1
1
0
1
1
0
1
2
2
1
0
0
1
0
0
2
0
1
0
0
0
1
2
0
2
1
1
0
0
0
1
2
0
1
0
0
2
0
2
1
0
0
4
0
2
2
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
3
0
1
0
0
2
0
0
0
2
2
1
0
2
0
2
0
0
1
1
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
1
1
0
0
0
0
0
2
0
1
0
0
0
0
2
2
0
0
1
2
0
0
2
0
0
0
0
1
0
2
0
1
1
1
0
0
1
0
1
1
0
1
0
2
0
2
0
0
0
0
0
0
0
1
0
0
1
0
3
0
1
0
1
2
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
1
1
2
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
1
3
0
1
0
1
0
1
1
0
1
0
1
0
0
0
2
2
3
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
4
0
1
2
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
1
0
4
0
2
0
1
2
0
2
2
1
0
0
1
0
2
0
0
0
0
0
5
0
7
1
0
1
1
0
1
1
1
0
1
1
0
0
0
0
2
1
0
1
2
0
0
2
1
0
0
1
2
0
0
0
0
0
1
1
2
0
0
1
3
0
0
0
1
0
1
2
0
0
1
1
1
0
0
2
0
0
0
0
2
0
0
1
0
0
1
2
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
4
0
1
1
2
0
0
0
0
1
1
1
0
0
1
0
4
1
0
0
0
0
0
0
2
5
0
2
3
0
0
0
0
0
1
0
1
1
2
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
2
1
1
0
0
6
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
2
2
0
0
0
0
0
2
1
5
0
0
0
0
0
1
0
0
0
1
1
2
1
0
1
0
0
0
3
2
2
1
0
0
0
1
0
0
0
0
2
0
0
1
0
2
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
1
1
2
0
0
0
1
1
4
0
0
0
2
1
1
0
2
2
0
0
0
0
0
0
0
0
1
2
1
0
2
0
1
2
1
0
0
2
0
2
0
2
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
3
0
1
0
0
2
0
0
0
0
3
0
2
0
2
2
2
0
0
0
2
0
4
1
0
2
2
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
1
1
1
2
3
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
10
2
2
0
0
2
2
1
2
0
2
0
0
0
0
0
0
0
1
0
1
0
1
0
2
2
0
1
2
0
0
1
2
0
0
0
0
1
1
0
0
1
0
0
0
0
0
4
0
0
1
2
1
1
0
2
0
0
0
0
0
2
1
1
0
0
0
2
0
0
2
0
0
0
0
2
0
2
2
0
0
1
2
2
2
0
1
1
2
0
0
0
0
1
0
0
2
0
2
0
1
2
0
0
2
0
0
1
0
0
1
0
0
0
0
1
1
2
0
0
2
0
2
1
1
0
1
2
0
1
0
1
0
1
0
2
1
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
2
2
0
0
0
0
0
0
0
0
3
1
0
0
0
2
0
1
0
0
0
2
1
1
1
0
0
0
0
2
1
1
4
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
2
0
4
0
2
0
0
3
1
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
1
0
2
1
1
2
1
1
1
1
1
0
1
0
0
0
0
2
0
0
2
2
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
2
1
1
2
0
0
0
2
0
1
1
0
0
0
2
1
0
2
0
0
2
0
1
0
0
0
0
0
0
0
2
0
3
3
3
0
0
0
0
0
1
3
0
0
0
0
0
0
0
2
1
0
3
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
2
2
0
2
0
1
0
0
2
0
0
1
0
0
2
2
2
1
0
0
1
1
0
1
0
2
0
2
0
0
1
2
0
2
3
0
1
0
0
0
0
0
0
6
0
0
0
3
0
2
0
0
0
0
1
0
3
0
1
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
1
1
2
0
2
0
0
1
2
0
2
1
1
0
1
0
2
0
0
0
2
0
0
0
0
2
0
1
0
1
0
0
0
0
2
2
0
0
1
0
0
1
2
0
3
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
4
0
0
2
2
0
2
1
0
0
0
0
0
2
0
0
1
1
1
0
0
1
0
0
1
1
0
0
2
2
2
1
1
2
2
0
1
0
0
0
0
1
0
0
0
1
2
1
2
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
2
1
0
2
0
6
0
1
0
0
0
2
2
0
1
0
0
3
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
2
1
0
1
0
0
0
1
0
1
1
3
0
0
2
2
0
0
2
2
2
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
2
2
1
2
1
0
0
2
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
1
1
2
2
1
0
1
3
0
0
0
1
0
0
1
0
0
1
1
2
2
2
0
0
0
0
0
0
0
5
0
1
0
1
0
1
1
0
1
0
0
0
0
0
0
1
1
2
1
1
0
2
0
2
0
1
2
0
0
0
2
0
0
2
0
1
0
0
0
1
0
0
2
2
2
1
0
0
2
0
1
0
2
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
2
2
0
0
1
0
0
0
0
1
2
0
1
0
0
1
0
1
0
1
0
0
0
0
1
1
0
0
0
1
3
0
0
0
2
0
0
1
0
0
1
1
1
0
2
1
1
2
0
1
0
0
0
1
2
3
0
1
1
1
0
0
1
1
0
2
2
0
0
1
0
0
0
0
0
0
0
1
0
3
0
2
0
0
0
2
0
2
0
0
2
0
3
2
0
1
0
0
0
1
0
2
0
0
2
0
1
1
0
0
0
0
0
1
0
0
1
1
0
1
0
0
2
1
0
0
0
1
0
0
1
2
0
2
0
0
0
1
0
1
0
0
0
1
1
0
2
1
0
0
0
0
0
1
0
2
0
2
0
1
0
2
2
1
0
0
0
0
1
0
1
1
0
0
2
0
1
0
0
2
1
0
0
2
0
1
0
1
3
0
1
2
0
1
1
1
2
2
0
2
1
0
0
1
0
0
1
0
0
0
0
0
2
2
0
0
1
0
1
2
0
0
0
0
1
2
1
0
1
0
1
0
0
0
0
1
2
0
0
1
2
1
1
1
0
2
2
1
0
0
0
1
1
0
0
1
0
1
0
2
1
1
2
1
0
2
0
0
1
0
0
0
0
0
0
1
0
0
2
1
1
0
2
1
2
0
0
1
1
1
0
1
0
0
2
0
1
0
1
0
0
0
2
0
0
0
2
2
1
2
0
0
3
0
0
0
2
0
2
0
0
1
1
0
0
0
1
2
0
1
0
1
0
1
0
0
1
0
1
0
0
0
2
0
1
0
0
1
0
0
2
0
0
1
0
0
1
2
0
0
0
0
1
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
1
1
0
2
0
0
0
0
2
2
0
0
0
0
0
1
1
2
2
1
0
2
2
0
0
0
0
1
2
2
1
0
0
2
2
1
0
2
1
1
0
1
0
0
2
0
0
1
0
1
0
2
1
0
1
1
0
0
0
0
2
0
0
2
2
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
1
1
0
0
2
1
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
1
1
0
1
0
0
1
2
1
2
1
0
0
1
0
1
2
0
0
0
1
0
0
2
2
2
1
0
0
2
0
0
0
2
0
2
2
0
2
1
0
1
0
3
3
1
0
2
0
2
2
0
0
0
1
2
1
0
0
0
0
0
2
4
0
4
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
1
0
2
0
0
1
0
0
0
2
1
1
0
2
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
2
1
0
1
0
0
0
1
0
1
0
1
3
0
0
1
2
0
1
2
0
0
0
0
2
2
0
0
0
1
0
0
0
2
1
2
2
2
0
0
0
0
1
0
1
0
0
0
0
0
2
0
2
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
1
0
1
2
2
0
1
1
1
0
0
1
1
2
2
2
0
2
0
2
1
2
0
1
0
0
1
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
2
0
2
0
1
1
0
0
2
0
0
0
1
0
3
2
1
1
2
0
0
1
0
0
0
2
1
1
0
0
0
0
1
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
1
1
0
2
0
0
1
1
2
0
1
0
1
0
2
0
0
0
0
2
1
0
0
0
1
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
1
2
0
2
1
2
0
0
0
2
1
0
0
2
0
0
0
0
0
0
2
0
1
2
0
0
0
1
1
0
1
0
0
1
0
2
0
1
0
0
0
2
1
1
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
2
0
0
0
0
1
2
0
1
0
0
2
2
0
0
0
2
0
0
0
0
1
5
3
0
0
2
0
0
2
2
0
0
1
1
0
2
0
2
0
2
2
0
0
0
1
0
2
0
1
2
2
0
0
0
0
0
0
1
2
2
1
0
0
0
2
0
2
0
2
0
2
1
1
2
2
0
0
1
0
0
2
2
1
1
0
0
0
0
2
0
2
1
0
2
0
0
0
2
0
4
2
0
0
0
1
0
1
0
0
1
0
2
0
3
2
0
2
0
2
1
0
2
2
0
0
1
0
0
0
2
0
4
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
2
2
0
1
0
3
0
0
0
0
2
2
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
2
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
2
0
2
0
2
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
2
0
2
0
3
3
1
2
0
0
0
0
2
3
0
0
0
1
1
0
1
0
0
1
3
2
0
3
0
1
0
0
0
2
1
0
1
1
2
0
0
0
2
1
0
0
0
0
0
0
2
0
1
2
0
0
2
2
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
3
0
1
0
0
0
2
2
0
0
0
1
0
1
0
1
0
0
2
1
0
2
0
1
3
0
0
1
1
2
2
0
0
0
0
0
0
1
0
2
0
0
0
1
0
2
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
2
0
0
1
2
1
1
3
0
0
1
2
1
0
1
1
1
0
0
0
1
0
0
1
0
0
0
0
1
0
2
2
0
1
0
0
1
0
2
0
1
0
0
0
1
0
1
0
0
2
0
1
0
2
1
0
1
0
1
0
1
0
1
0
0
0
1
0
0
2
0
1
1
0
0
0
1
1
0
2
2
0
1
0
1
0
3
0
1
2
0
0
1
0
0
3
0
2
0
0
2
0
1
0
0
1
0
0
0
1
0
2
0
2
0
0
0
2
0
0
0
1
1
0
0
0
1
0
0
2
2
0
2
0
2
0
0
0
0
2
1
0
3
0
0
0
1
1
0
0
0
0
0
1
0
1
0
1
0
0
2
3
2
0
0
0
0
1
1
0
2
2
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
1
2
1
0
1
1
0
0
1
0
0
0
0
0
1
0
1
2
0
2
1
0
1
0
0
1
0
2
2
2
1
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
2
3
0
0
1
1
0
0
0
0
0
2
0
0
2
1
0
1
0
0
0
0
0
2
0
2
0
1
2
0
0
0
0
3
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
1
3
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
2
0
1
0
2
1
1
0
1
0
0
0
1
2
0
2
0
2
0
0
2
1
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
2
2
2
1
0
0
1
0
0
1
0
0
0
1
2
0
1
0
2
0
0
1
0
0
4
0
0
1
3
0
0
0
0
0
0
2
0
2
0
0
1
2
1
0
0
0
2
1
0
2
1
0
0
1
1
2
0
1
0
0
1
2
0
1
1
2
0
0
2
3
0
2
1
1
0
0
0
0
0
0
2
0
1
0
0
1
1
2
2
0
1
0
0
0
1
0
0
0
1
2
0
1
2
0
2
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
3
0
0
1
0
1
0
0
2
2
0
0
2
0
0
3
1
0
3
3
2
0
0
2
0
0
0
0
1
1
2
0
1
2
0
2
1
0
2
0
0
2
0
2
1
0
1
0
0
0
0
0
1
0
1
0
2
3
0
2
0
8
0
0
0
1
0
1
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
1
1
1
2
0
0
0
0
0
2
0
0
0
1
2
2
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
2
0
2
0
0
2
0
2
2
0
2
0
2
2
0
0
2
0
0
1
0
0
0
0
0
0
1
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
2
0
2
0
2
0
0
1
1
0
0
0
0
1
0
0
1
0
2
0
0
4
0
2
0
0
1
2
0
0
1
0
0
0
0
1
2
0
0
0
0
2
0
0
0
1
0
1
2
0
0
0
1
0
2
2
0
0
0
0
0
1
0
0
0
2
0
0
1
2
1
0
0
0
0
0
1
0
2
0
0
2
2
0
0
0
0
2
0
1
0
0
0
1
0
0
1
2
0
1
0
1
0
1
2
2
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
1
2
2
1
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
2
0
1
1
0
2
0
1
2
1
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
2
0
0
1
1
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
1
0
2
2
0
0
0
0
0
1
2
2
1
0
0
2
0
0
0
0
2
0
0
1
1
1
0
0
1
0
0
0
0
0
0
2
0
2
0
0
2
1
1
1
1
1
2
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
3
0
1
0
0
3
0
0
0
0
0
2
0
1
1
0
0
0
2
0
0
2
0
1
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
2
0
0
0
2
0
0
2
2
0
0
0
3
1
1
0
0
1
0
0
0
0
0
0
0
2
2
1
1
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
1
1
2
0
0
0
1
0
0
1
0
1
1
0
1
0
0
0
0
0
1
2
0
0
1
0
0
0
0
1
0
1
0
1
0
0
2
0
0
0
0
0
2
0
0
0
2
0
1
0
2
2
0
0
0
1
2
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
2
0
0
1
0
1
0
0
1
1
0
0
1
0
0
0
0
1
0
1
1
2
1
0
2
0
2
0
0
0
0
0
0
2
0
0
1
0
1
0
2
3
2
0
0
2
2
1
1
1
0
1
2
0
0
0
0
2
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
1
1
0
0
1
0
0
2
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
2
0
3
2
0
2
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
2
1
1
0
1
1
0
2
2
0
1
1
0
1
2
1
0
0
0
1
0
0
0
2
0
0
1
1
0
0
0
2
0
1
0
2
1
1
1
0
2
0
0
0
1
2
2
0
1
4
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
2
0
2
0
0
0
1
0
1
0
0
2
2
1
0
0
0
0
0
2
0
2
1
0
0
0
0
1
2
3
0
1
2
0
0
0
0
0
0
1
1
0
1
0
2
0
0
1
1
0
2
0
1
0
1
0
0
0
1
3
0
1
1
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
1
2
0
0
0
2
0
0
2
2
2
2
0
2
0
0
1
0
2
0
0
1
0
0
0
1
2
0
0
2
0
2
0
0
1
2
1
0
0
0
0
0
0
0
0
0
2
2
2
0
0
2
1
2
0
2
0
2
1
0
1
1
1
0
0
2
1
2
2
1
1
1
2
0
0
0
2
2
0
0
0
0
1
0
0
2
0
1
0
5
0
0
0
0
0
2
0
1
2
1
1
0
0
0
0
2
0
1
1
0
1
0
1
0
2
0
1
1
0
1
1
1
1
1
0
0
0
0
0
0
1
0
1
2
0
0
0
1
1
2
0
0
2
0
0
1
2
1
0
0
1
1
2
0
2
0
2
3
0
0
0
2
0
1
0
1
1
0
0
0
0
1
0
0
0
0
2
0
0
2
2
1
0
1
1
0
3
1
2
0
0
1
0
0
1
2
0
3
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
2
1
0
0
1
2
0
3
1
1
1
0
0
0
0
2
0
2
0
3
0
0
0
0
2
1
0
0
0
1
1
0
1
0
0
1
1
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
2
1
3
1
0
0
0
0
0
1
2
1
0
1
2
0
0
2
0
0
1
0
0
1
2
2
2
6
0
0
0
0
0
2
1
2
0
2
2
0
0
0
1
0
0
1
0
0
0
0
0
2
0
1
1
0
1
0
0
0
4
0
0
0
0
0
2
0
0
0
1
2
0
1
1
1
0
0
1
0
0
2
0
0
0
0
2
0
0
1
0
1
1
0
0
2
3
0
2
0
1
1
0
0
2
0
1
0
2
0
2
0
1
2
2
0
1
0
0
0
2
0
0
0
2
2
0
1
1
0
0
0
2
0
2
0
2
0
0
0
1
0
0
0
0
0
0
1
0
2
1
1
0
0
0
0
1
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
1
2
0
2
2
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
2
1
0
1
0
0
0
2
0
2
0
0
0
1
0
0
0
0
1
0
0
1
1
0
1
2
0
0
0
0
0
0
0
1
0
0
1
1
1
2
1
2
0
2
0
2
0
3
0
0
0
0
1
1
1
0
2
1
0
0
0
2
0
0
2
3
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
1
0
2
1
2
2
0
0
1
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
3
0
1
0
0
2
0
2
0
5
0
1
0
0
0
2
0
1
0
0
0
2
0
1
1
0
0
0
1
0
1
0
0
0
0
2
2
2
0
0
1
1
1
0
0
0
0
0
0
1
0
1
2
2
2
1
1
1
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
2
1
0
0
0
1
0
1
0
0
1
0
2
0
0
0
1
1
3
0
1
0
0
1
0
0
0
0
0
0
2
1
2
0
2
2
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
1
3
0
2
0
0
0
0
0
0
3
0
1
0
4
2
0
0
0
0
2
1
1
0
0
0
1
1
0
0
0
1
0
0
0
3
0
1
0
0
0
0
0
1
0
0
2
0
1
0
2
0
1
2
0
0
0
1
0
0
2
1
0
0
0
2
0
2
0
1
1
2
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
2
0
1
0
0
2
3
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
2
2
1
0
0
1
1
2
0
2
1
0
0
0
0
2
1
0
2
0
0
0
1
0
0
0
3
0
0
0
0
1
1
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
2
0
2
1
0
3
0
0
0
1
0
0
0
2
1
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
1
2
2
0
2
0
2
0
0
0
1
2
0
0
1
2
0
1
2
0
0
1
2
0
0
1
0
2
3
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
2
0
1
1
0
0
0
0
0
0
2
1
0
2
0
1
2
0
0
2
0
0
2
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
1
0
1
0
0
0
1
0
1
0
0
0
2
0
0
0
1
2
0
0
5
2
0
0
2
0
2
0
2
0
2
0
2
0
2
2
0
1
1
0
1
4
1
3
1
0
0
1
2
0
2
1
0
0
0
0
3
0
1
2
1
0
0
0
0
1
0
0
0
0
1
1
0
2
2
0
0
0
2
3
3
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
1
0
0
0
0
0
0
1
0
5
0
4
0
0
0
1
1
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
2
1
0
0
0
1
0
1
0
1
0
0
1
2
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
2
0
0
1
2
0
1
2
2
0
1
1
0
0
0
0
2
0
0
0
1
1
2
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
1
1
2
0
0
0
0
1
0
2
1
1
2
0
2
1
1
0
2
0
1
1
2
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
2
1
0
0
2
1
0
0
0
0
1
2
0
1
0
0
0
0
0
0
1
1
3
0
1
0
2
2
0
0
1
2
0
0
0
1
0
0
2
1
0
0
1
0
2
2
0
0
0
0
1
0
0
0
0
1
2
1
2
0
0
1
2
0
0
0
0
0
1
0
1
0
1
0
0
0
1
1
1
0
1
2
0
1
1
1
2
0
2
1
1
2
1
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
2
1
2
0
1
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
2
2
1
0
1
1
0
2
0
0
0
0
1
10
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
4
0
0
0
1
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
1
0
5
0
2
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
1
2
0
1
2
0
2
1
0
2
0
0
0
0
1
0
2
0
0
0
1
0
2
1
0
0
0
0
0
0
1
2
0
1
0
1
2
0
2
0
0
1
0
0
0
0
1
3
1
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
1
0
0
1
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
1
1
0
0
0
2
0
2
0
1
1
1
3
1
2
1
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
2
2
0
0
0
1
0
1
2
0
0
1
0
1
0
0
0
0
1
1
3
1
0
0
0
2
0
0
0
0
3
0
0
0
0
0
2
0
2
2
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
2
0
0
2
0
2
0
0
0
1
1
0
0
0
0
0
0
1
2
0
1
0
1
0
0
1
2
0
0
1
0
2
0
1
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
3
0
0
2
3
0
2
0
0
0
2
0
2
0
0
0
0
0
2
1
0
1
2
0
0
0
2
1
0
0
5
0
0
2
1
0
0
0
2
0
1
0
1
0
2
0
1
0
1
0
0
1
2
2
1
2
0
0
0
0
1
1
1
0
1
1
0
2
0
3
0
0
2
0
2
0
0
2
0
2
2
2
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
2
0
2
0
2
1
0
1
0
0
0
2
2
0
0
1
0
2
2
0
0
3
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
1
2
3
0
0
0
2
0
0
0
2
2
2
1
0
0
2
0
2
0
2
1
0
0
2
0
0
2
0
0
2
0
0
1
0
1
0
2
2
1
1
0
0
1
0
0
0
0
1
0
0
2
0
0
2
1
0
0
2
0
0
0
2
0
1
0
2
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
1
2
0
0
0
0
0
0
2
1
2
0
2
0
0
0
0
0
2
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
1
1
0
0
0
2
0
0
0
0
2
2
1
0
0
3
0
1
0
2
0
0
1
1
1
0
1
0
0
0
1
0
0
2
2
0
0
0
0
0
2
0
0
0
1
1
2
0
0
2
0
0
1
3
0
0
2
0
2
2
2
0
0
0
2
2
0
0
2
1
0
0
2
1
2
0
1
1
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
2
0
0
0
2
0
2
2
0
1
0
1
0
0
1
2
2
0
0
0
2
1
0
0
0
0
0
2
0
1
1
0
1
1
1
0
0
0
2
1
0
0
2
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
1
0
0
1
0
0
0
1
1
2
0
1
0
0
2
0
0
1
2
0
1
0
0
0
0
2
1
1
0
0
0
0
0
0
0
2
0
2
1
0
0
1
0
2
2
0
1
1
1
0
2
0
0
1
1
2
0
0
0
0
0
2
0
0
1
0
0
0
0
3
1
1
0
0
2
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
1
2
0
2
1
1
0
0
0
2
0
2
1
0
0
0
2
0
2
1
2
0
2
0
2
0
1
0
1
1
0
2
0
1
1
1
4
0
0
1
2
0
2
0
0
1
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
2
2
0
2
0
1
0
1
0
1
0
0
0
2
0
0
2
1
1
2
0
2
0
1
1
0
2
0
0
0
2
0
0
0
0
3
0
0
1
1
1
1
0
0
0
0
0
2
1
1
0
0
0
2
2
0
0
0
0
0
2
2
0
0
2
0
2
0
1
0
6
0
0
0
0
2
0
0
0
0
0
0
2
2
2
0
1
1
0
0
0
0
2
0
2
0
0
1
0
0
2
0
0
1
0
0
0
0
2
0
0
2
0
0
0
1
1
0
0
1
0
1
1
0
1
0
0
0
1
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
2
2
2
0
0
2
1
0
1
0
0
0
1
0
1
0
1
0
3
1
2
0
0
0
1
0
0
1
0
0
4
0
2
0
2
2
1
0
0
2
0
3
0
0
1
1
1
2
0
0
0
0
0
0
0
2
1
3
0
2
2
0
0
0
1
0
0
1
2
1
2
2
2
1
0
0
0
2
0
2
0
0
2
1
0
2
0
0
2
0
1
0
2
0
1
1
0
0
0
2
0
0
0
1
0
0
2
0
1
0
0
1
0
0
1
2
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
3
2
0
1
0
2
0
0
1
0
0
2
2
1
2
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
3
0
2
1
0
3
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
3
1
0
0
0
0
0
2
2
0
0
0
0
2
2
0
0
0
0
0
1
1
0
1
0
7
2
0
2
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
2
0
1
1
3
0
0
0
0
0
2
0
0
3
0
0
2
1
0
0
0
1
0
2
0
0
0
1
0
0
0
0
2
2
1
0
1
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
2
0
1
2
2
0
1
1
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
1
0
1
0
0
0
1
0
0
0
2
2
1
2
3
0
0
1
0
2
2
3
1
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
2
2
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
1
2
1
0
0
1
1
0
2
2
0
0
1
0
1
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
2
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
2
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
2
2
2
0
0
1
0
2
0
0
2
2
0
0
0
0
0
0
0
1
0
0
1
1
2
2
0
1
0
0
3
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
2
0
0
0
0
0
2
0
0
0
1
2
1
0
0
0
0
0
1
0
2
0
0
0
0
2
1
0
1
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
1
0
1
0
0
2
2
1
0
0
0
0
1
0
0
0
0
1
1
0
1
1
0
2
2
1
0
1
1
1
0
1
0
0
0
2
0
0
1
2
0
0
0
9
0
0
1
2
0
0
0
0
0
2
3
0
0
0
0
2
0
0
0
0
0
1
2
11
0
0
0
1
0
2
1
0
0
3
0
0
1
0
0
2
0
0
1
0
2
0
0
0
1
2
0
1
0
0
1
0
0
0
2
1
0
1
0
2
2
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
2
1
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
1
0
1
2
0
0
2
2
0
0
0
0
1
0
1
0
0
1
0
0
1
2
1
1
0
2
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
1
0
1
0
0
2
0
5
2
0
3
0
0
1
0
0
0
0
2
0
1
0
2
0
0
1
1
0
0
1
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
2
2
1
1
0
1
3
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
2
0
0
0
1
3
0
0
0
1
0
0
0
0
1
1
2
0
2
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
1
0
0
0
1
2
2
0
0
0
2
0
0
2
2
1
0
0
0
0
2
2
1
3
1
0
1
1
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
1
0
2
2
0
2
1
0
0
1
0
2
1
0
1
0
0
1
0
1
0
0
0
2
1
0
0
0
2
2
0
0
1
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
2
3
0
2
2
0
0
0
0
0
1
0
2
1
0
0
1
1
2
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
2
1
2
1
0
1
0
0
1
0
1
1
0
2
0
0
2
0
0
1
1
0
1
1
0
0
0
1
0
0
1
0
2
0
2
2
1
0
0
2
1
0
0
2
0
2
0
0
2
0
1
2
0
0
2
2
1
3
1
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
1
0
0
0
4
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
1
2
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
1
1
0
1
0
2
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
2
0
0
0
0
2
0
0
0
5
0
1
0
0
0
0
1
0
0
1
0
0
0
0
2
0
2
0
1
0
2
0
2
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
3
2
2
0
0
2
1
1
0
3
0
0
0
2
1
0
0
2
0
0
1
0
0
0
2
2
1
0
3
0
1
1
0
0
0
2
0
0
0
0
1
0
1
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
1
0
0
0
1
2
1
2
0
2
0
0
2
0
1
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
2
0
0
0
1
3
0
0
0
0
0
0
4
0
1
0
0
0
0
0
3
0
1
1
0
1
2
1
1
0
1
2
0
1
2
0
3
0
1
0
1
0
2
0
0
1
2
0
0
0
3
1
0
1
0
2
0
0
0
2
0
2
1
2
1
1
0
2
2
0
2
0
2
0
0
0
8
0
0
0
2
2
1
0
0
0
1
1
0
0
0
0
0
2
0
0
0
1
0
1
1
0
1
0
0
0
1
0
0
0
1
0
0
2
0
0
3
0
1
2
2
0
2
0
0
0
3
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
2
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
2
0
2
2
0
2
0
0
0
2
0
2
3
1
0
0
0
0
0
2
0
0
0
1
0
0
2
0
1
4
2
2
1
0
2
0
0
2
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
2
0
0
1
2
0
0
1
0
0
0
0
0
1
2
1
0
0
0
1
2
1
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
2
1
1
0
0
1
0
2
3
1
2
0
0
2
1
0
0
0
0
3
0
0
0
1
0
1
0
1
1
0
2
0
0
0
0
0
1
1
1
0
0
2
0
2
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
4
0
0
0
0
0
0
0
2
2
1
3
0
0
2
0
1
0
0
0
0
0
0
0
1
0
2
2
0
0
0
1
2
0
1
0
0
0
0
0
2
1
0
1
2
2
1
1
2
0
2
0
0
0
2
2
1
1
0
2
0
0
0
0
0
0
2
0
0
0
2
2
0
1
0
0
0
2
0
0
1
0
2
0
2
0
0
0
2
1
0
0
0
0
1
1
0
0
1
0
1
0
0
2
0
0
0
3
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
2
0
0
0
0
2
0
2
0
0
2
0
2
0
0
1
0
0
2
0
0
0
0
0
2
0
0
2
0
0
2
2
0
0
0
0
0
2
0
1
1
1
0
0
0
0
1
1
0
1
0
0
2
2
0
0
1
2
1
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
2
2
2
0
3
0
0
0
1
0
2
0
0
1
0
0
2
2
0
2
2
1
0
0
0
0
2
0
2
0
3
0
2
0
2
0
0
1
1
0
0
0
4
0
2
0
0
2
0
0
2
1
0
0
0
0
0
1
1
0
0
1
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
1
1
2
0
2
0
0
0
0
1
1
0
0
2
0
0
0
1
0
2
1
0
2
2
1
0
2
0
0
0
1
0
0
0
2
2
0
2
0
0
1
0
0
5
1
0
0
2
1
0
1
0
2
0
0
0
1
0
0
2
0
2
0
1
0
1
1
0
1
1
0
1
0
0
0
3
0
1
1
0
0
0
1
0
0
0
0
1
0
0
2
0
3
1
0
0
1
0
0
0
0
0
1
0
1
0
2
0
2
0
0
0
0
1
1
1
2
0
1
0
3
0
1
0
0
2
0
0
2
0
0
0
0
0
0
3
1
0
2
2
0
1
1
0
2
0
3
2
0
0
0
2
2
0
1
2
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
1
1
1
0
0
0
0
2
0
0
1
2
0
3
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
1
0
0
0
2
0
3
0
0
0
0
0
0
2
0
0
2
0
0
2
1
0
2
2
0
0
0
0
0
2
0
0
0
0
0
1
0
2
2
2
0
2
1
1
1
2
2
2
0
0
0
0
0
1
2
2
2
0
0
0
0
2
1
4
1
1
0
0
1
3
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
2
1
1
0
2
0
0
0
0
1
0
2
1
3
2
0
0
0
2
0
1
0
0
0
2
1
0
2
1
0
0
0
1
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
2
0
0
1
2
2
0
0
2
0
0
2
1
1
3
1
2
0
0
0
0
0
0
0
0
0
0
1
0
1
2
2
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
2
0
0
2
1
2
0
0
1
0
3
1
0
1
1
1
0
1
0
1
2
0
0
0
1
0
0
1
0
1
3
1
0
2
0
1
0
0
1
3
2
0
0
0
0
1
2
1
0
1
0
2
0
0
0
1
1
0
0
0
0
1
2
0
0
1
1
1
0
1
0
0
0
2
0
1
1
3
2
2
2
0
0
2
1
0
0
1
1
0
1
0
0
0
0
1
2
0
3
1
0
0
0
0
0
0
0
2
2
0
1
1
0
0
2
0
2
0
0
2
0
1
2
0
0
0
0
4
0
0
0
1
1
1
2
0
3
0
1
0
0
0
0
0
1
0
2
2
0
1
0
0
2
1
0
1
2
0
1
1
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
3
0
2
0
1
2
1
0
2
0
0
3
0
2
2
2
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
1
2
0
1
1
0
0
1
2
0
0
0
0
1
1
0
0
0
1
0
0
2
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
4
0
0
1
2
0
1
0
2
1
0
3
2
1
2
2
0
0
4
0
0
0
0
0
1
2
1
0
1
0
0
2
0
2
0
0
0
2
0
1
1
0
2
2
2
0
0
2
1
0
1
1
0
0
0
0
0
2
2
0
0
1
0
0
1
1
0
2
0
1
2
0
1
0
1
0
0
1
1
0
1
1
0
0
0
2
0
0
2
1
3
0
0
0
2
2
0
2
0
2
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
2
0
1
1
2
2
0
0
2
0
1
0
0
3
0
1
2
0
3
0
0
1
1
0
0
1
0
2
0
0
0
2
0
2
0
0
1
0
1
0
0
0
0
1
2
0
0
1
0
0
0
2
0
1
0
2
0
1
0
0
0
0
0
1
0
0
2
1
0
0
1
0
0
2
1
0
0
1
2
0
2
0
0
0
1
0
0
0
3
0
2
0
2
2
0
0
1
0
0
0
0
0
1
2
0
2
1
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
2
1
1
0
1
0
0
1
0
2
0
0
0
1
0
0
0
0
1
0
1
2
2
2
0
0
1
1
2
0
1
0
2
0
0
0
0
0
2
1
2
1
0
1
2
2
0
0
0
0
0
1
1
0
1
0
0
2
0
0
0
1
0
0
0
2
0
2
2
0
0
2
0
1
2
2
0
2
0
2
0
0
0
0
0
0
1
0
0
2
0
1
0
0
2
0
2
0
0
0
2
2
1
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
1
1
0
0
0
0
2
1
1
1
2
0
1
0
0
0
2
0
1
0
2
0
1
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
3
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
2
1
1
0
2
0
1
1
0
0
0
0
0
0
3
0
1
0
1
0
1
2
0
0
2
0
0
2
2
0
1
0
0
0
0
0
2
1
1
0
2
0
0
0
0
3
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
1
0
0
0
2
0
1
0
1
3
1
0
2
0
2
0
0
0
2
2
1
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
3
0
0
0
2
2
2
0
0
0
2
2
0
0
0
3
2
2
0
0
0
3
0
1
0
0
2
0
1
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
2
1
1
3
0
1
1
0
0
2
1
2
0
1
2
0
0
1
0
0
1
1
0
0
0
2
1
0
2
0
1
0
1
1
1
0
1
1
0
1
0
0
0
2
0
2
0
2
0
1
2
1
1
1
2
0
0
2
2
0
0
1
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
9
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
1
1
1
0
0
0
0
0
1
1
0
1
2
0
0
0
2
0
2
0
1
2
0
2
1
0
2
0
0
0
0
2
0
0
0
0
0
1
1
1
0
0
1
0
2
1
0
1
0
0
1
0
2
0
0
0
0
0
1
0
0
2
1
0
0
0
0
2
2
0
0
2
0
0
2
1
0
0
1
1
0
2
1
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
1
0
5
0
0
0
0
0
0
2
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
2
0
1
2
0
0
0
1
0
0
1
0
0
1
0
0
0
0
2
0
2
2
0
0
2
2
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
1
1
0
1
0
1
0
1
2
0
0
0
2
2
0
0
0
0
1
1
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
2
0
1
0
2
0
0
0
0
1
0
2
1
3
0
0
0
0
2
0
2
2
1
1
2
1
0
0
0
0
0
5
2
0
0
0
0
1
2
1
0
0
0
2
0
0
2
0
2
2
2
0
1
0
0
0
0
0
0
1
1
1
1
2
0
2
1
1
0
2
1
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
2
0
0
0
1
0
0
1
0
0
2
2
0
0
1
0
0
2
0
1
0
2
2
0
0
0
0
1
0
2
1
0
2
0
1
1
0
0
0
2
1
0
1
0
0
0
0
0
1
1
2
0
2
2
0
2
0
1
0
0
0
1
2
0
0
0
1
0
2
0
0
0
1
0
1
3
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
1
2
0
0
0
0
0
0
0
2
0
1
1
2
1
0
0
2
0
5
0
0
1
0
0
0
2
2
1
1
0
0
3
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
2
1
0
1
0
0
2
2
1
0
0
0
0
0
0
2
0
0
1
2
2
2
0
0
0
2
0
0
2
0
0
0
1
0
1
1
0
0
2
1
1
1
0
0
2
1
0
1
0
1
0
0
0
0
0
1
2
0
1
0
1
0
2
0
2
0
0
1
0
3
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
1
1
0
3
0
2
1
1
2
1
1
1
0
0
0
0
0
0
0
1
3
2
0
2
0
1
0
0
0
2
0
0
1
2
0
0
1
0
0
0
0
0
1
2
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
2
2
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
2
1
1
1
0
1
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
4
0
0
0
1
1
0
0
0
0
0
0
0
1
2
0
0
1
0
2
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
1
1
1
0
0
0
2
1
0
0
2
0
0
1
0
0
0
2
0
0
1
0
1
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
4
0
0
2
0
0
0
4
0
0
1
1
1
0
0
0
1
0
0
1
0
0
0
0
1
1
0
1
0
2
1
0
0
0
0
1
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
1
1
0
0
1
0
1
0
0
0
0
3
0
0
0
1
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
2
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
1
2
0
0
1
0
1
0
0
0
1
0
0
1
3
0
0
0
1
0
1
2
2
0
1
2
0
0
0
0
1
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
1
2
1
0
0
0
0
1
0
1
0
0
0
2
1
0
2
2
0
2
0
0
0
0
1
0
0
3
0
0
1
0
1
0
0
1
1
0
1
0
0
0
0
2
2
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
2
0
0
0
1
1
1
0
0
2
0
1
1
0
1
3
2
1
0
2
1
1
0
2
0
0
2
0
1
0
0
2
1
2
2
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
2
2
1
2
0
0
2
2
2
0
0
1
0
0
0
2
2
2
0
0
1
0
2
0
0
0
1
0
0
1
2
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
6
0
0
0
3
1
2
0
1
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
1
0
0
2
2
0
1
0
0
0
0
0
2
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
2
1
2
1
2
0
2
0
1
0
1
2
0
2
1
2
0
0
0
0
2
0
2
0
3
2
4
0
0
0
1
0
0
2
2
0
0
1
0
0
0
0
0
1
2
0
0
0
1
1
0
1
2
3
0
1
0
0
0
0
0
0
1
0
0
2
0
1
2
0
1
0
1
2
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
2
1
2
0
2
0
0
0
2
0
1
2
1
0
0
0
0
1
0
0
1
1
0
0
0
0
1
1
0
0
1
1
0
1
0
0
0
0
0
0
0
1
2
0
3
1
0
0
0
2
2
0
0
0
1
0
0
1
0
0
0
2
0
0
1
2
0
1
1
2
1
0
1
0
0
2
4
1
0
0
0
0
2
0
1
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
3
0
1
0
0
0
2
2
0
1
1
0
0
0
1
2
0
0
0
0
0
0
0
1
2
2
0
1
0
0
0
0
0
0
1
1
2
0
0
1
2
1
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
2
0
0
0
0
4
2
0
1
1
0
0
0
1
0
0
0
2
0
0
1
1
0
2
2
0
2
0
1
2
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
1
0
0
2
0
1
1
0
0
2
1
0
0
0
2
0
0
1
0
0
0
2
0
0
1
1
0
0
2
0
0
1
0
0
0
0
1
0
0
2
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
2
0
2
0
0
0
1
4
1
0
0
2
0
1
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
2
0
2
0
0
0
0
1
0
2
0
2
0
1
0
0
0
0
0
1
1
0
1
1
0
2
0
0
0
0
0
3
1
0
1
0
0
0
0
1
0
2
0
0
0
0
0
1
0
3
1
0
2
0
0
0
3
0
1
0
0
1
1
0
1
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
2
1
2
0
2
2
2
0
1
0
1
0
0
0
0
1
0
2
0
0
0
2
1
0
0
0
1
2
1
0
0
0
0
0
0
0
3
1
1
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
2
0
0
0
0
1
1
0
0
0
1
2
1
0
0
2
0
0
1
1
0
1
0
2
2
3
0
0
0
2
1
0
0
2
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
7
0
2
0
0
0
1
0
0
1
0
0
2
0
0
2
0
0
2
1
1
1
2
1
0
1
0
0
1
1
0
1
1
1
1
1
0
2
0
0
0
0
0
0
2
2
2
3
0
0
1
0
0
0
1
0
2
0
2
0
1
0
1
1
0
0
2
0
1
0
0
0
0
0
2
0
0
1
2
2
0
2
0
0
0
0
2
0
0
0
1
1
2
2
3
0
0
0
2
1
0
0
1
0
1
0
0
3
1
0
0
1
0
2
0
5
0
0
1
1
1
0
1
2
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
2
0
1
1
0
2
0
2
0
0
0
3
1
0
0
2
1
0
0
2
0
0
0
0
1
0
1
2
0
0
0
0
0
0
1
0
2
0
1
2
2
0
0
2
1
2
0
1
0
0
0
1
1
0
1
0
0
2
0
0
1
0
0
2
0
1
2
0
3
0
0
0
0
0
0
0
2
2
0
2
0
0
1
0
2
0
0
2
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
4
2
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
2
2
0
0
0
0
1
2
1
0
2
0
0
3
0
0
1
0
1
0
2
1
0
1
1
1
1
0
1
0
1
0
0
0
0
0
0
2
1
0
0
1
1
2
1
1
1
0
2
0
0
0
0
1
0
0
0
1
0
0
2
2
0
0
0
0
2
0
1
0
2
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
2
1
0
1
0
0
0
3
2
0
0
1
0
1
0
0
0
0
3
0
0
1
0
7
1
1
0
0
0
0
2
0
1
1
0
2
2
0
0
0
0
2
0
1
2
0
0
1
0
2
0
0
0
0
3
1
2
0
1
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
1
2
2
2
0
3
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
2
1
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
1
0
3
2
2
0
0
0
0
0
0
2
1
2
2
1
0
1
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
2
3
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
3
1
0
0
2
2
0
0
1
0
1
0
0
0
0
0
0
1
1
1
0
2
1
0
2
0
0
0
1
0
0
2
0
0
0
0
0
2
0
1
1
0
0
2
0
0
2
0
1
0
0
0
1
0
1
0
0
0
1
1
1
0
1
1
1
1
0
1
0
0
0
1
0
0
0
2
2
0
1
0
1
0
0
0
2
2
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
1
2
2
0
0
1
1
1
2
0
2
0
0
0
1
1
0
0
1
3
1
0
0
0
2
1
0
0
0
1
2
0
2
0
0
2
0
1
2
0
2
0
0
1
1
0
0
2
0
2
0
1
0
2
0
0
2
2
0
0
0
1
1
0
1
0
1
0
1
0
1
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
2
2
1
0
0
1
0
0
1
0
1
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
4
2
2
2
0
0
1
1
1
2
0
0
1
2
1
1
0
1
0
2
0
0
0
0
1
0
0
0
1
0
0
2
0
0
1
1
1
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
1
1
1
3
1
1
0
0
0
0
2
1
1
5
2
1
0
0
0
2
0
0
0
0
0
1
2
0
0
2
0
0
0
0
2
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
1
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
1
1
0
0
0
1
0
1
0
1
0
0
0
0
2
0
1
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
2
1
0
0
0
2
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
2
1
0
2
0
1
0
0
0
0
1
2
2
1
1
2
1
0
0
0
0
1
0
0
0
0
0
1
1
1
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
1
0
0
0
1
2
2
0
0
0
0
2
4
0
0
0
0
0
0
2
3
0
0
0
0
2
0
8
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
1
0
0
2
0
0
0
2
0
1
1
0
0
1
0
0
2
0
1
2
0
0
0
4
0
0
0
2
2
2
0
0
0
0
0
0
0
2
1
0
1
0
2
1
0
1
1
0
0
1
0
0
0
0
2
0
0
1
1
0
0
2
1
2
0
1
0
0
0
1
1
2
0
1
5
2
0
0
1
0
0
2
0
1
0
0
2
1
0
0
3
0
0
0
1
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
3
2
2
1
0
2
0
1
1
0
0
0
0
0
0
1
0
2
2
2
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
2
0
2
0
1
1
1
0
0
0
0
0
0
0
0
0
0
3
1
2
1
0
1
2
1
2
0
1
0
0
0
1
0
2
0
0
0
2
0
1
0
0
0
1
0
0
0
1
1
0
1
0
0
0
2
0
0
0
0
0
1
0
1
1
0
2
0
1
0
0
0
0
2
1
1
1
0
0
0
0
1
0
1
0
0
1
0
1
1
0
0
2
0
2
0
0
0
0
0
1
0
1
0
0
0
1
1
2
0
0
2
2
1
0
0
2
2
0
0
0
2
1
1
0
2
0
2
0
0
0
0
0
0
0
1
0
1
0
0
1
2
0
2
3
0
0
0
1
1
0
0
0
2
0
0
0
2
2
3
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
1
1
2
1
1
1
2
0
1
0
2
0
1
0
1
0
0
0
0
0
0
0
1
0
1
1
1
4
0
0
2
0
0
0
0
1
0
2
0
0
0
5
0
0
0
0
0
0
1
0
1
2
0
0
2
3
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
1
0
2
2
0
0
0
0
0
1
2
0
1
0
0
2
2
0
0
1
0
3
1
0
0
2
0
1
0
1
1
1
5
4
1
3
0
2
1
0
0
0
0
1
0
2
2
0
0
1
1
0
0
0
2
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
1
0
0
1
0
0
1
0
2
3
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
1
1
0
1
0
1
0
0
1
1
2
0
0
0
0
0
0
1
0
0
0
3
0
1
0
2
0
0
0
1
1
0
0
1
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
2
2
1
0
0
0
0
4
0
3
3
0
0
0
1
0
0
1
0
0
0
0
2
1
0
2
1
0
0
0
1
0
2
0
0
0
1
1
7
0
3
0
0
0
2
0
2
0
0
1
0
2
1
0
1
0
0
0
0
0
0
2
2
1
1
0
0
0
0
2
0
0
0
0
1
0
0
1
1
0
2
2
0
0
1
0
0
0
2
1
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
1
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
2
1
0
3
0
2
2
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
1
0
1
2
0
0
0
0
0
2
0
0
0
0
0
1
1
1
0
0
1
0
0
0
2
2
0
0
0
1
0
0
0
1
0
1
1
1
2
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
2
0
0
0
0
1
2
1
0
1
1
0
1
12
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
2
2
0
0
0
0
1
0
1
1
0
0
0
2
1
2
0
0
0
0
0
0
2
1
1
1
1
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
2
1
2
0
2
2
0
0
1
1
0
2
0
0
2
3
1
7
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
1
2
1
0
2
0
0
0
0
1
0
2
0
1
0
2
0
2
0
0
0
0
1
0
2
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
1
1
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
2
1
3
0
0
0
0
1
0
2
0
1
0
0
1
0
0
2
0
2
1
0
1
1
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
2
1
0
2
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
3
0
0
0
1
0
0
0
0
1
2
0
2
0
1
1
0
2
0
0
2
3
2
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
2
2
3
2
0
3
0
2
0
0
0
1
0
0
0
0
2
2
0
1
1
0
1
1
0
0
0
1
2
0
0
0
1
0
2
2
2
0
0
0
2
1
0
0
2
0
1
0
0
0
1
0
0
2
1
0
2
1
0
0
3
1
0
1
0
2
0
0
0
0
1
0
1
1
0
1
0
0
1
0
0
2
2
0
0
2
1
2
0
2
0
2
0
0
0
0
0
2
2
0
2
0
0
2
0
1
0
2
0
0
0
0
2
0
0
2
0
0
1
0
1
0
1
1
1
2
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
1
1
1
0
0
0
2
0
0
0
0
2
2
1
1
1
1
0
2
2
0
0
3
1
1
0
1
0
0
0
3
1
0
0
0
0
1
1
3
0
0
0
3
0
0
2
1
1
0
0
2
0
2
2
0
0
2
1
1
0
0
1
1
2
0
0
0
2
1
2
1
1
2
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
2
0
2
2
1
6
0
1
2
0
0
1
0
1
0
0
0
0
0
2
2
1
0
0
2
0
2
0
0
1
0
0
1
0
0
0
1
0
0
2
0
2
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
2
2
0
0
0
2
2
2
0
2
1
0
2
0
4
1
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
2
2
0
1
0
1
0
0
0
1
3
0
0
1
1
0
1
0
0
0
0
2
0
1
1
0
0
0
2
0
0
0
0
2
0
2
0
0
0
1
2
2
0
1
2
1
2
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
2
1
0
1
0
0
0
0
0
2
0
2
1
0
0
2
0
0
0
0
2
0
1
0
0
0
1
2
0
0
0
0
0
0
2
2
2
0
1
1
1
0
2
0
2
0
2
0
0
0
0
0
0
2
0
1
2
1
2
2
0
0
2
0
1
0
2
0
0
0
2
2
0
0
2
0
2
1
0
0
2
0
0
2
0
2
0
1
1
1
0
1
0
3
1
0
2
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
2
1
1
0
2
0
0
0
0
0
1
0
0
1
0
0
2
1
0
0
0
1
0
1
2
0
0
1
2
2
0
0
0
1
0
1
1
0
0
1
1
1
0
0
0
2
1
2
0
0
0
0
1
1
0
2
0
0
2
0
0
0
0
0
0
1
1
1
2
0
0
0
0
1
1
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
2
1
0
1
1
0
0
0
2
0
1
2
1
0
1
1
2
1
0
0
1
1
1
1
0
0
0
2
1
0
1
0
0
3
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
1
3
0
0
0
0
1
2
0
2
0
0
0
0
2
2
1
0
0
2
1
1
0
1
0
0
2
1
2
1
0
1
0
2
0
0
0
0
1
2
4
0
0
1
1
2
1
1
0
0
1
0
0
0
3
2
2
0
0
1
1
0
0
0
0
0
1
2
0
1
1
1
0
0
2
2
0
0
1
0
0
0
0
0
0
1
1
1
2
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
1
0
0
2
0
0
1
1
0
0
0
0
0
0
3
0
2
1
0
2
0
0
1
0
2
0
0
0
2
2
2
1
0
0
0
0
0
1
0
0
2
4
0
1
0
2
2
0
0
0
2
4
0
0
1
0
1
2
2
2
1
2
1
2
1
0
0
1
0
0
0
0
0
1
0
0
0
1
2
2
2
0
2
3
1
1
2
0
2
1
0
2
1
0
0
0
2
3
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
1
2
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
2
0
0
2
0
2
1
1
0
0
0
0
2
1
0
0
1
2
0
0
1
0
0
0
2
0
0
0
0
0
1
0
1
2
1
0
0
0
0
0
0
0
0
0
2
1
0
2
2
0
0
0
0
0
1
2
0
1
0
0
0
0
4
0
7
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
1
1
1
2
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
3
0
4
1
2
0
1
0
0
2
2
2
0
2
0
0
2
1
2
0
0
0
0
0
0
1
2
2
1
0
0
0
2
0
2
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
2
1
0
2
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
1
0
0
1
4
0
0
2
0
0
1
1
0
0
0
2
0
0
1
0
0
0
1
3
1
2
0
0
0
0
2
0
2
1
2
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
1
0
0
1
1
0
0
0
0
3
1
0
0
0
0
0
0
0
0
2
0
1
1
0
0
2
3
3
0
0
5
0
0
0
0
0
0
0
0
0
0
0
2
0
5
0
0
1
1
0
0
2
1
0
0
0
1
1
0
1
0
0
0
2
0
1
0
0
0
0
0
0
2
1
0
2
0
0
0
3
1
1
2
0
0
0
0
0
0
3
0
2
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
2
0
2
2
0
4
0
0
0
0
0
1
1
0
0
2
2
2
0
1
0
0
0
2
1
3
0
3
0
0
0
0
0
2
0
1
1
0
0
3
0
1
0
1
0
0
2
0
0
0
3
0
0
1
0
1
0
2
0
1
0
0
2
0
2
0
1
1
2
0
0
0
0
0
2
0
0
0
1
0
1
0
0
2
0
1
2
1
0
3
0
2
1
2
0
0
0
0
0
0
1
0
0
1
1
3
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
2
1
0
0
0
2
0
0
2
2
0
2
2
2
0
0
0
2
14
0
5
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
1
2
2
0
0
0
1
0
2
1
1
0
0
0
2
0
2
1
0
0
1
0
1
0
1
0
0
1
0
2
0
1
0
1
0
0
0
2
0
0
1
0
0
2
0
0
1
0
0
1
2
3
0
1
2
0
2
0
0
0
0
0
2
1
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
2
2
0
1
2
0
1
0
2
3
2
0
0
0
2
0
0
2
0
0
1
2
0
2
2
0
1
0
0
1
1
3
3
0
1
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
1
0
1
0
0
1
1
2
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
1
2
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
3
0
0
0
0
0
1
0
0
0
2
0
2
1
1
2
2
0
1
2
1
0
0
1
0
0
0
0
0
0
2
0
1
1
1
0
0
0
1
2
1
0
0
0
0
1
0
0
1
2
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
2
0
1
0
0
2
2
1
3
0
1
4
0
0
1
1
0
0
2
0
3
0
0
2
0
0
0
1
0
0
0
0
1
0
2
0
0
2
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
2
2
0
3
2
0
2
2
1
0
2
1
0
1
1
1
0
1
0
4
0
1
1
0
0
0
2
1
1
0
0
0
0
0
1
0
0
0
2
1
2
1
0
0
2
1
1
0
1
1
0
0
0
0
2
0
2
1
3
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
2
0
0
0
0
1
0
0
1
0
2
0
1
0
1
0
0
1
0
0
1
0
1
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
1
0
1
2
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
1
0
0
2
0
0
10
0
0
1
2
2
2
0
1
0
2
0
0
1
0
0
0
1
1
1
2
0
1
0
2
0
0
2
0
0
2
0
0
0
1
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
2
0
1
0
0
0
1
1
0
0
2
0
0
1
0
1
0
1
0
0
2
1
0
2
0
0
0
0
0
0
1
0
1
0
0
1
2
1
1
1
0
0
0
0
1
1
1
1
0
0
0
1
1
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
2
0
1
2
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
2
1
0
0
0
0
0
0
2
0
2
0
0
0
2
0
2
3
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
3
2
0
1
2
0
0
0
0
0
0
0
3
2
0
1
0
0
1
1
0
1
2
2
2
2
1
1
0
0
0
0
2
2
0
0
3
1
0
2
0
0
0
0
1
1
1
1
11
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
3
0
0
1
1
0
1
0
0
2
0
0
0
3
4
0
0
2
0
2
1
3
1
0
0
0
0
2
0
0
1
2
0
0
1
1
0
0
2
1
1
0
2
0
1
0
0
2
2
0
0
2
0
0
0
0
0
2
2
0
0
0
2
0
6
0
2
0
1
1
0
2
0
3
2
0
2
3
0
0
2
0
1
2
1
2
1
0
0
0
0
1
0
2
0
0
0
2
0
0
2
2
0
2
0
1
0
0
0
1
0
1
2
0
1
0
2
2
2
1
0
0
0
2
0
0
0
1
0
0
0
2
1
0
1
0
0
0
0
0
2
0
0
2
1
0
0
0
1
0
0
2
2
1
0
0
0
0
1
2
0
2
0
2
1
2
2
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
1
0
2
0
0
0
0
0
0
1
0
0
2
0
1
1
2
0
2
1
0
0
0
0
1
0
0
1
1
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
1
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
1
0
1
2
2
0
1
3
0
0
0
2
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
1
4
1
1
0
2
1
1
0
2
0
0
2
1
0
0
1
0
0
0
0
2
0
4
0
1
0
0
1
0
1
2
2
0
0
1
1
2
0
2
0
0
0
0
1
1
0
2
2
0
2
0
1
1
2
0
0
0
1
0
0
0
2
0
0
0
0
2
1
1
3
1
2
1
0
1
0
0
0
0
0
2
0
1
0
1
2
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
2
0
0
0
0
2
2
0
0
2
0
0
0
1
1
2
0
0
0
0
0
0
2
0
1
0
0
1
0
0
2
2
0
2
1
0
0
0
2
0
0
1
0
0
1
1
0
0
0
1
2
0
2
3
1
0
1
0
1
0
1
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
1
0
4
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
3
1
0
2
2
0
2
1
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
2
2
0
0
0
3
0
0
0
1
0
0
1
2
0
0
0
2
0
0
2
0
3
0
1
2
0
1
0
0
0
0
0
2
0
0
1
0
1
1
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
1
2
0
0
2
0
2
0
0
2
0
0
0
0
0
0
2
0
0
1
1
0
0
0
2
0
0
0
0
0
0
1
1
2
1
1
0
0
0
2
1
2
0
0
0
0
0
0
0
1
2
2
1
0
0
0
1
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
1
1
0
0
3
1
2
3
0
0
0
0
0
1
2
0
0
2
0
0
0
0
2
1
0
0
0
0
0
2
0
0
2
1
1
0
4
0
0
0
1
0
0
1
0
0
1
2
0
0
0
1
0
1
1
0
2
0
1
1
0
2
0
2
2
0
2
0
8
0
0
0
0
2
0
0
1
0
0
1
1
1
0
1
0
1
0
0
2
0
0
1
1
0
0
0
1
0
0
0
0
4
0
0
1
1
1
2
1
1
1
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
2
0
2
1
0
2
0
0
2
0
1
0
2
0
0
2
0
0
0
2
2
0
2
0
0
2
0
0
1
2
1
2
0
4
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
1
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
2
2
0
2
2
2
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
1
3
2
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
1
0
0
0
3
1
2
0
0
0
2
0
0
0
1
0
0
0
0
3
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
1
0
0
1
0
3
0
0
1
1
1
1
0
1
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
3
2
0
0
0
2
1
0
1
0
0
0
0
7
2
2
2
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
2
2
0
2
0
0
2
1
1
0
0
0
1
1
2
0
0
0
1
0
0
1
0
1
0
0
0
0
2
2
0
1
0
0
0
2
0
0
1
0
0
0
0
2
0
2
0
1
0
1
0
0
0
1
0
0
1
2
2
0
0
0
1
2
1
0
0
0
2
1
0
0
0
0
3
2
0
1
0
3
0
0
0
1
0
2
2
0
0
0
0
2
0
0
0
2
0
2
0
1
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
1
1
0
1
0
0
0
0
0
0
2
0
1
0
1
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
3
0
2
0
1
1
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
1
1
0
1
2
1
0
0
2
0
1
0
1
1
3
1
0
0
0
1
1
3
2
2
0
0
3
2
0
0
0
0
0
0
1
2
0
0
1
0
2
2
0
0
0
1
0
2
0
1
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
2
0
0
0
1
0
1
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
2
4
0
0
0
0
0
0
0
0
0
0
1
1
1
2
1
0
0
0
0
1
0
0
2
1
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
1
1
0
1
0
2
0
0
0
2
0
1
3
2
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
3
1
0
0
0
0
0
3
0
1
0
0
1
0
0
0
3
0
0
0
1
2
0
1
0
0
0
2
1
0
0
0
1
0
2
0
0
1
0
0
2
2
1
1
1
3
0
0
2
0
0
2
0
0
0
0
2
1
0
1
0
0
0
0
0
0
1
0
2
0
3
0
2
1
2
1
1
1
1
2
0
0
0
0
0
1
1
0
1
0
1
2
1
0
0
0
0
0
0
0
0
2
2
2
0
1
0
0
1
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
1
1
0
0
1
1
2
1
0
2
0
0
0
0
1
1
0
0
1
0
2
0
0
0
1
2
1
2
0
2
3
0
0
2
0
0
0
0
0
0
0
0
0
0
1
3
2
0
1
0
0
2
1
0
0
0
4
2
0
2
2
1
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
1
1
0
0
0
0
0
0
3
0
0
2
2
0
2
2
1
1
1
1
2
1
1
0
0
0
0
0
1
0
0
0
0
2
1
1
0
0
0
2
2
2
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
1
1
0
2
0
1
0
0
1
0
0
2
0
0
1
0
0
0
0
2
1
1
0
0
2
0
1
0
0
0
0
0
1
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
2
2
0
1
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
1
0
2
0
0
0
0
0
0
2
1
0
2
1
2
0
1
1
0
2
0
0
1
0
2
2
0
0
0
1
2
0
1
0
0
2
0
1
1
1
5
2
0
0
1
0
2
0
0
0
1
2
0
0
3
0
0
1
0
0
0
2
0
1
0
4
1
0
0
0
2
0
0
0
1
1
2
0
2
2
1
0
1
2
0
0
2
1
0
0
0
1
1
1
0
0
1
0
0
4
1
2
0
1
3
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
3
2
0
0
1
1
1
0
0
0
0
1
0
0
0
0
3
0
0
1
0
0
0
2
0
0
0
3
0
0
0
0
0
2
0
0
0
2
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
2
0
1
0
2
0
0
0
2
0
0
0
0
2
1
0
0
0
2
0
1
2
0
0
2
2
0
2
0
0
2
3
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
2
0
0
0
2
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
3
0
3
1
2
0
0
0
1
0
2
1
2
0
0
2
2
2
1
0
0
0
2
2
0
1
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
5
0
1
0
1
0
0
2
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
2
3
0
0
0
0
0
0
2
0
2
1
0
2
0
3
0
0
0
2
0
0
1
0
0
5
0
0
0
0
0
0
2
1
1
2
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
1
0
2
0
0
0
0
1
0
2
2
1
1
2
1
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
1
0
1
0
1
1
1
0
0
1
0
1
2
2
0
0
3
0
1
1
0
0
0
0
0
1
2
2
0
0
2
2
0
1
0
0
0
0
0
2
1
1
0
1
0
0
0
0
2
0
1
1
1
2
1
0
0
2
2
2
1
1
0
1
0
0
3
1
1
1
2
0
3
0
1
2
0
4
1
0
0
0
1
0
0
1
0
0
0
2
0
0
1
4
0
0
2
2
0
0
0
1
2
0
1
1
0
0
0
0
0
2
1
1
0
1
2
3
0
0
0
2
0
0
1
0
0
2
1
0
0
0
2
1
0
0
1
0
0
0
2
1
1
2
0
0
0
1
1
0
0
0
2
0
1
0
0
2
1
1
0
0
1
3
1
1
0
2
0
1
0
0
1
0
2
2
0
0
0
0
0
0
0
2
0
0
0
2
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
2
0
0
0
2
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
2
3
4
0
0
0
2
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
1
2
1
2
1
0
1
0
0
0
1
1
1
2
1
2
0
1
2
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
2
1
1
0
0
2
0
0
0
0
0
1
0
1
1
1
0
2
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
3
3
1
0
0
0
3
2
0
0
0
0
0
0
1
1
0
1
1
0
2
0
1
0
2
0
1
0
0
1
0
0
0
0
1
0
2
1
2
0
3
2
1
0
0
1
1
0
1
1
0
1
0
0
1
0
2
2
0
0
1
2
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
1
0
0
1
1
0
0
0
2
1
0
0
1
1
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
7
0
0
2
1
1
0
0
2
2
0
0
1
2
0
0
2
0
1
2
0
0
1
0
0
0
3
1
2
0
0
2
2
0
0
3
1
0
0
2
0
0
2
0
1
0
2
3
0
0
0
1
0
0
0
0
0
1
1
1
0
1
0
1
0
0
1
0
0
1
0
1
0
0
1
1
0
5
0
2
0
1
2
2
0
0
0
0
0
1
0
0
0
0
0
0
2
1
2
1
0
2
0
0
0
1
0
0
2
2
0
2
0
2
0
2
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
2
0
0
0
1
1
0
1
0
0
2
1
0
0
0
0
0
2
0
0
0
2
3
0
0
1
0
0
0
0
2
1
2
1
2
0
0
1
0
0
1
1
1
2
0
2
0
0
0
0
0
0
1
0
1
1
0
0
1
0
1
0
0
0
0
2
0
1
1
1
0
0
1
2
0
0
2
1
0
0
1
2
2
0
0
1
1
0
0
0
0
2
3
0
2
0
1
0
0
0
2
0
0
1
0
0
2
2
1
1
0
0
1
1
1
2
1
1
0
2
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
1
1
0
0
0
2
3
0
0
0
1
9
2
2
3
0
3
0
0
0
0
1
0
0
1
0
0
2
0
0
2
2
0
0
2
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
1
0
1
3
1
0
0
1
2
0
0
1
0
2
0
0
2
0
2
2
0
0
0
0
0
1
0
0
2
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
3
0
0
0
0
0
0
0
1
1
0
0
2
1
1
1
2
0
5
0
2
2
0
1
2
0
1
0
0
0
0
0
0
1
0
0
1
0
2
1
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
1
2
1
0
0
0
2
0
0
1
1
0
2
1
1
2
0
1
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
1
1
0
2
0
0
1
1
1
1
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
2
0
1
0
2
0
0
2
0
0
0
0
0
1
1
0
1
0
2
0
0
0
0
1
0
1
0
0
4
0
2
0
1
0
0
0
2
2
2
0
1
0
2
0
0
2
2
0
0
2
0
1
0
2
1
0
0
0
0
0
0
1
0
0
0
1
2
0
1
0
0
0
1
2
0
1
0
1
2
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
2
2
0
0
1
0
0
0
0
0
1
0
0
1
2
1
1
0
0
0
0
2
0
2
0
0
0
0
0
2
0
2
0
2
0
2
0
1
0
1
3
0
0
2
0
2
0
3
2
2
1
0
0
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
0
2
1
1
0
0
0
0
2
1
2
0
1
0
2
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
3
0
0
2
0
0
2
1
0
0
0
0
2
0
1
0
0
1
3
0
1
0
0
0
0
2
0
0
2
4
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
1
0
0
1
0
1
1
1
2
1
0
0
2
0
0
1
0
0
2
0
2
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
1
1
1
2
0
1
0
2
2
0
0
0
0
2
2
0
0
0
1
0
1
1
2
0
2
0
0
0
1
0
1
0
2
1
0
0
0
0
2
1
0
1
1
1
0
1
1
0
2
1
1
0
0
0
0
1
0
2
0
1
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
2
2
0
0
1
0
0
1
0
2
0
0
0
2
2
2
0
1
0
0
1
1
0
0
2
0
0
0
0
2
0
0
0
1
1
1
4
2
2
0
2
0
0
1
0
0
0
1
0
0
0
0
0
3
2
0
0
0
1
0
0
2
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
2
1
2
2
0
0
0
0
0
1
2
4
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
2
1
2
1
1
0
0
0
0
1
0
2
0
2
2
2
0
0
0
0
0
0
2
1
0
0
1
0
0
1
1
0
0
0
0
2
1
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
1
1
2
1
0
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
0
5
1
0
1
0
0
0
0
0
0
0
1
2
1
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
1
1
2
2
0
1
0
2
0
2
1
0
1
1
2
0
0
0
0
0
0
0
2
2
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
2
1
0
2
1
0
0
0
0
0
0
2
1
0
0
1
4
0
1
0
0
1
0
7
0
0
0
0
4
1
0
1
0
1
0
2
0
0
2
0
1
0
0
0
1
0
0
0
1
3
1
0
1
2
1
0
0
2
2
2
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
2
1
0
2
1
0
2
0
0
2
0
2
0
0
0
2
0
0
0
0
2
1
0
1
0
0
2
0
2
0
0
2
0
2
0
0
0
1
0
0
0
1
0
0
1
0
2
0
2
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
1
1
1
0
0
0
2
0
0
0
1
1
0
0
1
0
2
0
2
0
1
0
0
0
1
2
2
0
1
2
0
0
2
1
0
0
1
0
1
0
1
0
0
1
0
0
2
2
0
0
1
0
2
0
0
1
0
0
2
0
2
0
2
1
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
2
0
2
0
2
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
2
0
2
1
0
0
0
2
0
0
0
1
3
0
0
1
0
4
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
3
1
1
0
0
1
0
0
2
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
2
0
1
1
1
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
1
1
0
0
0
0
0
2
1
2
0
1
0
1
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
2
2
0
0
1
1
2
2
1
0
0
2
3
0
1
0
0
1
2
2
2
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
2
2
0
0
0
0
1
0
2
0
0
0
0
0
0
2
2
0
1
1
0
5
1
0
1
1
2
4
1
0
0
1
0
1
2
0
0
0
0
3
1
1
0
1
0
0
0
0
1
0
0
0
1
4
0
0
1
0
2
0
2
0
0
0
0
3
0
1
0
1
1
1
0
0
0
0
0
3
0
1
2
0
0
1
4
1
0
1
2
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
2
1
1
1
1
1
1
0
0
1
1
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
2
1
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
1
2
4
1
0
1
0
1
2
0
0
2
2
2
0
0
0
2
1
0
0
0
0
0
1
0
2
2
2
0
0
0
2
1
0
0
1
0
0
1
0
0
0
2
0
0
0
1
0
0
2
2
1
0
0
1
2
2
1
0
0
2
0
0
0
1
0
0
1
0
1
0
2
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
2
0
2
2
0
0
1
0
0
0
1
0
0
0
2
0
3
0
0
0
0
0
0
2
1
0
0
0
0
1
1
0
1
0
1
0
0
0
1
1
0
2
0
0
0
2
1
2
1
0
2
0
0
0
2
0
1
0
4
0
0
0
0
1
1
1
0
0
0
3
0
0
0
0
0
2
2
15
1
0
2
1
0
0
0
2
0
0
1
0
1
1
0
0
1
1
0
0
0
0
0
0
1
0
0
1
2
2
0
0
2
2
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
1
0
1
0
2
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
2
0
3
0
2
3
0
3
0
1
0
0
1
2
1
0
1
1
2
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
1
3
1
0
1
0
0
1
2
1
0
0
0
1
0
1
2
0
0
0
2
1
1
0
1
0
1
0
0
0
0
2
0
0
2
0
0
0
1
1
1
1
1
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
1
0
2
0
1
0
0
0
0
1
1
2
0
2
3
1
0
0
0
2
2
1
0
0
1
1
0
0
0
1
0
1
2
0
2
1
0
0
1
2
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
1
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
2
0
0
0
2
0
1
1
0
0
2
0
1
1
1
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
1
1
0
1
0
0
0
0
0
2
0
0
1
1
0
3
2
0
0
2
1
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
1
2
2
2
0
0
0
1
1
1
1
0
1
2
0
2
0
0
2
0
0
0
1
0
0
1
0
0
2
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
2
1
1
1
0
0
0
0
2
1
0
0
2
0
1
0
0
0
1
0
0
0
0
1
1
0
0
2
1
0
1
4
0
0
0
0
1
1
1
0
0
0
2
1
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
7
2
0
0
2
0
0
0
1
0
2
0
2
0
0
0
0
1
1
1
2
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
2
0
0
1
3
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
1
2
0
0
0
2
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
4
2
0
0
0
0
1
0
0
0
0
1
0
2
0
2
0
0
0
1
0
0
0
2
2
2
0
0
3
2
2
1
0
1
0
0
0
0
2
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
2
1
0
0
0
0
0
8
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
1
1
2
0
1
1
1
1
0
1
1
0
2
0
0
0
1
1
2
0
1
2
0
2
2
0
1
0
0
0
1
0
1
1
0
2
0
2
2
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
5
0
2
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
1
0
1
0
0
0
2
1
0
2
3
1
0
4
0
0
0
0
2
1
1
0
0
1
1
2
2
2
2
2
0
2
0
0
0
1
0
0
0
1
0
2
0
0
0
1
0
0
2
2
2
2
0
0
1
0
0
0
1
3
0
0
0
1
1
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
3
1
0
0
1
2
0
2
1
1
1
2
0
0
0
0
0
2
0
0
2
0
1
0
1
0
0
1
2
0
0
0
0
2
1
0
0
0
1
0
1
2
0
0
1
0
3
2
1
0
0
0
0
1
0
2
0
2
0
0
1
0
0
0
1
0
0
2
1
1
0
0
0
1
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
2
1
0
3
0
0
2
0
2
2
0
2
0
1
0
1
0
0
2
0
1
0
0
0
1
0
0
1
0
0
3
0
0
1
0
3
1
2
2
0
0
0
0
0
1
1
0
0
0
0
0
3
0
0
0
0
0
0
1
1
0
1
0
1
2
0
0
2
0
0
0
0
2
2
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
1
2
1
1
0
0
2
0
1
0
2
2
0
2
0
0
2
1
0
1
0
2
1
2
2
0
0
1
0
0
1
1
1
0
1
0
0
2
0
2
0
0
1
0
1
0
2
1
1
1
0
2
2
0
1
2
0
0
0
0
0
0
2
0
0
0
0
2
0
1
1
0
1
1
1
0
0
1
0
0
0
0
0
0
1
0
2
1
1
0
2
2
1
0
0
0
0
0
0
0
1
0
3
1
0
0
0
0
1
1
0
0
2
0
2
2
1
2
0
0
0
0
3
3
3
0
2
0
2
1
3
0
0
2
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
2
2
2
0
2
2
2
0
0
0
0
1
2
0
0
0
0
0
3
0
0
0
0
0
1
0
1
0
0
0
0
2
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
1
2
1
0
1
0
0
0
2
0
0
0
0
0
2
1
0
1
4
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
2
1
0
0
0
2
0
2
1
0
0
0
1
2
2
0
1
0
2
0
0
0
1
2
0
0
0
0
0
0
0
2
2
2
0
0
1
1
1
0
1
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
1
0
1
2
0
0
0
2
0
0
0
1
0
0
2
0
1
0
0
0
2
0
0
1
2
0
2
0
2
0
3
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
1
0
1
0
0
0
2
1
1
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
2
0
2
1
2
2
0
0
0
0
4
0
1
0
2
2
0
0
0
1
0
2
1
1
1
0
0
2
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
3
2
0
0
0
0
2
0
0
0
1
0
2
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
1
0
2
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
1
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
2
0
0
1
0
0
1
1
2
2
2
1
1
0
0
2
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
2
1
1
2
2
1
0
0
0
0
1
1
2
2
0
2
1
1
0
1
1
2
2
0
0
0
1
0
1
2
2
2
1
2
0
1
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
1
2
0
1
0
0
1
0
0
0
0
2
0
1
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
1
0
1
0
2
1
0
0
0
0
0
1
0
2
0
0
2
0
2
0
2
0
0
2
0
0
0
1
0
2
0
0
1
0
1
0
0
2
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
1
1
1
0
0
0
0
1
0
0
0
0
1
1
0
0
1
2
0
0
1
2
0
1
0
1
0
4
0
2
2
0
0
0
2
0
2
0
0
1
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
2
1
1
0
2
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
1
1
0
0
2
1
0
0
1
0
0
2
5
2
0
0
1
0
0
0
0
1
2
0
0
0
0
1
1
0
0
1
2
0
1
0
0
0
1
2
0
0
2
1
0
0
0
0
2
0
2
1
2
0
1
0
0
3
0
0
0
1
1
2
0
2
0
0
1
0
1
2
0
0
0
2
1
0
1
0
2
0
0
1
2
2
1
0
0
0
0
0
2
2
0
0
0
0
0
0
2
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
2
1
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
1
2
1
0
1
0
0
1
0
0
1
0
2
0
1
2
2
0
0
0
2
2
0
0
1
0
0
0
2
4
3
1
2
2
0
0
1
0
0
1
0
0
0
0
0
0
2
2
0
0
0
2
0
0
1
0
2
0
1
1
0
0
0
0
2
0
0
0
2
2
0
1
0
0
0
2
1
0
0
1
0
2
0
0
2
0
1
0
0
1
0
1
0
1
0
2
0
1
2
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
1
0
2
2
0
0
0
0
1
0
1
1
1
2
0
0
0
0
2
0
0
2
6
0
0
0
0
2
0
0
0
1
2
0
0
0
0
1
1
2
1
0
0
2
0
1
0
0
2
0
1
0
2
1
0
0
0
0
1
0
0
0
0
0
1
1
0
1
1
1
0
0
2
0
1
1
0
0
2
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
2
2
1
0
0
0
0
0
0
0
0
0
2
0
2
3
0
0
0
0
0
0
0
0
3
0
1
0
0
1
0
0
0
1
2
0
0
1
0
0
2
0
1
1
0
2
0
2
1
0
0
0
1
0
1
1
3
0
0
0
2
0
2
0
0
1
0
1
2
0
0
2
0
0
4
2
0
1
1
2
0
1
2
0
0
2
1
0
0
1
0
0
0
0
0
2
0
4
0
0
0
0
0
1
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
2
0
2
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
1
0
0
2
2
1
0
0
0
2
1
0
0
0
1
0
0
0
0
1
4
0
1
1
0
2
0
1
1
0
0
2
0
0
1
3
0
0
0
1
2
0
0
2
2
0
0
1
2
0
0
2
0
0
0
0
3
0
0
1
0
0
0
0
0
1
1
2
0
0
0
0
0
0
1
2
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
2
0
2
2
0
1
1
1
0
2
2
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
2
0
0
2
0
0
2
0
1
0
0
0
2
2
2
0
0
0
1
0
0
0
0
2
1
0
0
2
0
1
1
2
0
0
0
2
0
0
1
0
0
2
0
0
1
1
0
2
3
1
0
1
1
2
0
2
2
1
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
3
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
2
0
0
1
0
0
3
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
1
1
0
0
0
0
0
3
0
2
0
0
1
2
2
1
1
0
0
0
1
2
0
2
2
0
1
1
0
0
0
2
1
0
2
0
1
0
0
1
0
1
0
0
0
0
0
2
1
1
1
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
3
0
1
0
3
1
1
2
1
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
1
0
2
1
0
2
2
0
1
2
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
2
0
1
2
1
0
0
0
0
0
0
0
0
2
0
0
0
1
2
1
2
0
0
1
0
0
0
0
1
2
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
1
1
2
2
1
1
2
1
1
0
0
0
0
1
0
2
0
1
0
0
0
0
1
2
1
0
0
0
2
0
1
4
0
0
0
1
0
0
0
2
2
0
2
0
0
0
1
0
0
0
0
0
0
2
0
2
0
2
0
2
0
0
0
2
2
0
1
0
1
2
0
1
0
1
0
0
3
1
0
0
0
1
2
1
0
0
0
1
0
2
5
1
1
0
1
2
0
0
1
0
2
3
0
0
0
0
0
0
2
1
0
1
0
0
0
2
0
1
0
0
2
2
0
3
1
0
2
0
0
1
3
0
0
0
0
0
2
1
0
0
0
3
1
0
0
0
0
0
0
0
1
1
0
2
2
0
0
1
0
2
0
0
1
0
0
0
1
2
0
0
0
0
0
1
0
2
2
0
0
0
3
0
0
0
0
2
2
1
0
0
4
0
2
7
1
0
0
2
1
1
0
0
0
1
1
1
0
0
0
0
1
0
2
0
0
0
3
2
2
2
0
0
0
2
0
2
1
0
0
0
0
0
1
0
2
1
0
0
0
0
0
4
2
0
1
0
0
0
0
0
0
2
4
0
0
1
0
0
2
0
0
1
2
1
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
2
1
3
2
0
0
0
0
0
2
1
0
1
0
1
1
1
0
2
2
0
1
2
2
2
0
0
1
1
1
2
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
9
1
0
0
0
2
1
0
0
0
0
0
1
0
0
1
0
1
0
0
2
0
2
1
4
1
1
0
0
2
0
0
2
2
0
0
0
0
2
0
1
1
2
1
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
2
2
0
0
0
1
0
2
0
2
1
0
0
0
0
0
0
1
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
1
0
1
2
1
1
2
0
0
0
0
0
0
0
0
2
2
1
2
0
0
1
1
2
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
2
0
0
4
0
1
0
2
0
0
1
1
0
1
0
0
0
0
0
1
0
1
1
2
0
0
0
0
0
1
3
1
0
1
0
1
1
2
0
1
0
1
0
2
0
0
2
1
0
2
2
2
2
2
1
0
2
2
2
1
1
0
0
1
0
0
0
2
1
1
0
1
2
2
0
0
0
0
0
0
1
0
1
2
2
0
2
2
1
0
1
0
0
2
2
1
0
0
0
0
0
0
0
0
2
3
2
0
0
0
0
0
2
1
0
1
0
0
0
0
1
0
0
1
2
1
1
2
2
0
0
0
0
1
2
0
0
0
0
0
1
2
0
1
1
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
1
0
2
0
0
0
0
2
1
2
0
0
0
0
2
2
0
0
0
1
1
2
0
2
0
0
2
1
2
1
0
1
0
0
0
0
0
1
1
0
1
1
2
0
0
0
1
0
0
2
0
1
1
0
1
2
0
0
0
2
4
0
0
0
1
1
0
0
2
1
0
0
2
0
0
0
2
0
1
1
0
0
0
0
2
0
0
0
1
0
1
1
1
2
0
1
1
0
1
0
1
1
1
0
0
1
0
0
0
0
0
1
2
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
2
1
1
2
2
1
1
0
0
0
0
0
0
0
2
0
1
0
0
2
3
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
2
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
3
1
0
0
0
2
2
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
2
0
2
2
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
2
1
0
1
0
0
0
2
2
1
2
2
0
2
0
1
0
1
0
0
0
0
1
0
0
2
0
0
1
0
0
1
1
0
0
0
0
0
0
2
1
3
0
0
0
0
1
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
1
0
1
3
1
1
0
1
0
0
2
0
0
1
0
1
0
0
0
3
0
0
1
2
0
3
0
0
0
2
0
0
0
0
1
0
1
1
0
2
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
1
2
3
0
2
1
0
1
0
0
0
1
2
0
0
0
1
0
0
0
0
0
2
0
1
2
0
0
0
1
0
1
1
1
0
1
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
1
2
1
1
0
1
1
2
1
2
0
2
0
0
0
0
0
1
1
1
1
2
2
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
2
0
2
1
0
0
1
1
1
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
1
0
1
0
1
2
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
2
0
0
2
1
1
0
0
0
0
2
0
0
2
0
2
1
0
2
0
0
1
0
1
1
0
0
0
0
2
0
0
2
0
0
2
2
2
2
0
0
0
1
0
0
0
2
0
0
2
1
1
0
1
0
0
1
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
1
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
2
1
0
0
0
2
2
0
2
0
1
1
2
0
0
0
1
0
0
2
1
0
2
3
0
0
1
3
0
2
3
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
2
2
0
0
0
0
0
1
1
1
0
0
3
2
3
0
2
0
2
1
2
0
2
0
0
0
1
1
1
0
4
2
0
0
0
0
1
0
1
0
2
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
1
2
0
1
0
1
0
0
1
0
1
0
0
1
0
1
0
1
2
0
1
2
2
0
0
0
0
1
2
1
1
2
0
0
2
2
0
0
0
0
0
0
2
1
1
1
1
1
0
1
0
1
0
0
0
0
2
1
1
0
3
0
0
0
0
0
2
0
0
0
1
1
0
0
0
1
2
0
0
0
1
0
0
5
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
2
1
2
1
0
0
1
2
1
1
2
0
1
0
0
0
1
1
0
0
0
0
3
3
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
2
1
0
0
0
3
1
2
0
0
0
1
2
0
1
2
1
2
0
0
2
0
1
2
0
1
0
0
0
1
0
0
0
1
0
0
2
0
0
1
0
2
0
0
0
0
1
3
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
2
2
1
0
1
0
0
0
0
0
3
0
1
1
1
0
1
0
0
0
1
1
0
0
1
2
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
2
2
0
0
1
0
1
0
0
1
0
1
0
2
2
0
1
0
1
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
1
0
0
0
1
2
0
0
1
2
0
0
1
0
2
0
0
0
1
0
1
2
0
1
1
1
1
2
0
0
2
1
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
2
0
0
3
0
2
1
2
0
1
0
0
1
0
0
0
0
0
0
2
0
0
3
0
1
2
0
0
1
0
0
0
0
2
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
1
2
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
1
2
2
2
4
0
0
0
3
0
0
1
1
1
3
2
2
2
0
1
0
0
0
2
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
2
0
1
0
0
0
1
1
1
1
0
1
0
2
2
0
0
2
0
1
0
0
0
2
1
0
2
2
2
0
1
0
0
0
0
0
1
0
1
1
1
0
1
1
0
0
1
1
0
1
0
0
1
0
0
0
0
2
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
2
0
1
1
0
2
0
2
1
1
0
1
0
0
2
1
0
0
1
0
0
1
0
0
0
0
0
0
1
2
0
0
2
0
0
2
0
0
1
0
0
1
0
2
3
1
1
1
0
0
0
1
0
0
1
0
0
0
0
0
2
0
1
0
1
1
2
0
0
0
1
0
2
0
0
0
1
0
0
0
0
2
0
2
0
0
0
1
0
2
0
2
0
0
0
0
1
1
1
1
0
0
0
1
0
0
2
0
0
1
0
2
1
0
0
0
2
2
0
1
2
0
0
0
2
1
0
0
0
1
0
0
2
0
0
2
0
2
1
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
2
1
0
0
0
2
0
2
0
0
1
1
0
0
0
0
2
0
1
1
1
0
1
2
2
0
0
2
0
2
0
0
1
0
0
1
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
2
1
1
0
1
0
0
1
0
0
1
0
0
2
0
1
1
0
2
1
0
0
0
0
0
1
2
0
2
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
1
2
1
0
0
1
0
0
1
1
0
1
0
2
0
0
1
0
1
0
0
0
0
2
2
0
0
2
0
0
0
1
0
2
2
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
12
0
0
1
2
0
2
2
2
0
0
2
0
0
0
0
0
1
0
0
2
0
1
1
0
0
1
0
2
0
0
0
1
0
1
1
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
1
0
2
0
0
1
1
0
1
0
0
0
1
0
0
2
1
0
1
0
1
0
0
0
0
1
1
2
2
0
2
2
0
0
0
0
1
0
0
0
0
0
2
0
0
4
0
2
0
2
0
0
0
2
1
1
0
0
1
1
0
1
2
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
4
0
0
2
0
1
0
1
2
1
1
1
1
0
2
1
0
0
2
0
0
0
2
1
0
0
0
1
0
0
0
1
0
1
0
0
2
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
2
2
0
0
0
0
1
0
0
1
2
0
1
0
2
0
1
0
0
2
0
0
2
0
1
0
0
0
0
1
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
1
0
2
2
1
0
2
0
2
1
1
1
0
0
0
0
2
1
0
2
1
0
0
0
0
0
2
0
1
2
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
2
1
1
0
0
2
0
0
0
0
1
2
0
0
1
2
0
0
0
0
1
1
0
1
0
0
0
0
2
0
1
0
0
0
0
0
1
2
0
1
0
1
0
1
2
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
5
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
2
1
0
1
3
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
1
1
0
0
1
2
1
0
1
0
0
0
0
1
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
2
1
0
0
2
1
0
2
1
1
1
2
2
0
2
1
0
1
2
0
0
0
1
2
1
0
2
1
1
0
1
1
2
1
3
0
0
0
0
2
0
1
2
0
0
0
1
0
0
2
2
0
2
0
0
1
2
0
0
2
0
1
0
0
1
0
0
2
0
2
0
1
1
1
0
0
0
0
2
0
0
0
0
1
1
0
0
0
2
1
1
2
1
0
0
0
0
2
1
0
1
1
0
0
0
1
0
0
0
2
1
0
0
2
0
2
0
1
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
2
2
0
4
0
1
0
0
1
0
1
0
0
0
0
0
1
0
1
1
1
0
2
0
1
0
2
0
0
0
1
0
0
2
0
1
2
0
3
0
0
2
0
0
2
0
0
0
1
0
0
1
0
1
0
2
2
0
1
0
1
0
1
0
0
1
1
0
0
0
2
0
1
0
1
0
1
0
0
2
1
1
2
1
1
2
1
0
2
0
0
0
0
2
0
2
2
0
0
0
1
2
0
3
2
1
0
0
0
0
1
0
3
2
0
0
0
0
1
2
0
2
0
0
0
0
1
1
0
0
0
1
1
0
2
0
1
0
1
0
1
0
0
2
0
0
2
2
1
0
6
2
0
1
0
2
0
2
2
0
0
0
2
0
3
0
3
1
0
0
0
5
2
1
0
0
0
1
0
0
0
0
0
1
0
0
0
2
1
2
0
0
0
0
0
0
1
0
2
0
0
0
0
2
1
0
1
0
2
2
0
1
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
2
0
2
0
0
0
1
0
1
2
0
0
2
2
2
2
0
1
1
0
0
2
0
2
0
0
1
1
0
0
0
2
0
1
0
0
3
0
0
0
0
0
1
2
0
0
2
2
1
3
0
6
0
2
0
0
0
0
0
0
1
0
0
0
0
1
2
2
0
2
0
2
2
1
0
1
0
0
1
0
0
1
0
1
0
0
0
1
1
0
1
2
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
1
1
0
2
2
1
0
1
0
0
0
0
2
0
0
0
1
0
0
1
0
1
2
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
1
2
2
1
0
2
2
0
0
2
0
0
0
1
0
0
0
1
0
0
2
2
0
0
0
5
0
1
0
2
0
0
0
0
0
0
0
1
1
0
0
1
1
0
3
0
0
0
0
0
0
0
1
1
0
3
0
1
0
1
0
1
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
1
1
0
2
2
0
1
2
0
0
3
0
1
0
0
1
0
0
2
0
0
0
2
0
0
2
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
2
0
1
1
0
0
2
2
0
0
0
2
0
1
1
0
0
0
1
1
1
1
0
1
2
2
0
0
0
0
0
1
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
2
1
0
2
2
0
2
1
2
1
1
0
0
0
2
1
1
0
0
0
0
1
1
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
2
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
2
0
2
2
2
1
0
2
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
2
2
1
1
1
1
0
1
2
0
0
1
2
0
1
1
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
2
2
1
0
0
1
1
0
0
0
0
0
0
1
1
2
0
1
2
2
0
0
1
0
2
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
1
2
1
0
0
1
0
1
2
1
0
2
1
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
2
2
0
1
8
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
2
0
0
1
1
0
1
0
0
0
0
2
0
0
2
0
1
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
6
0
2
0
2
0
0
0
1
0
0
0
0
1
0
0
2
1
0
2
0
0
0
0
0
1
0
2
0
0
1
0
1
0
0
0
1
0
0
2
0
1
0
0
1
2
0
1
0
1
0
0
2
1
0
0
0
2
0
2
0
1
0
1
0
0
1
0
1
1
1
0
2
2
1
3
3
2
0
0
0
0
2
2
2
0
1
0
0
1
2
1
1
0
2
0
0
6
1
2
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
2
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
1
1
0
0
0
2
0
0
0
1
1
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
2
2
2
0
0
1
2
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
2
1
0
0
1
1
1
3
0
2
0
0
0
1
0
2
2
0
0
0
2
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
1
0
2
0
1
0
2
2
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
1
0
0
0
2
0
0
0
1
1
0
0
0
2
0
0
0
0
2
1
1
2
1
0
2
1
0
0
3
1
0
0
0
0
1
0
0
1
3
0
1
1
0
1
2
0
0
0
3
0
2
0
0
0
0
1
0
0
1
0
2
0
0
1
0
0
0
1
1
0
0
16
0
0
0
0
0
2
0
0
0
1
2
0
1
0
0
2
0
0
1
1
2
1
0
0
1
0
0
0
0
0
1
0
0
2
0
0
1
2
0
0
3
0
0
2
0
1
0
0
0
0
2
0
1
0
2
1
0
0
0
0
1
0
0
1
0
0
0
2
0
1
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
1
0
2
1
2
2
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
1
1
0
0
0
0
0
1
0
2
1
0
1
0
0
0
0
0
0
2
0
1
1
0
1
1
2
0
0
0
0
2
2
2
0
2
1
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
1
1
1
1
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
1
2
0
0
2
3
0
0
1
2
0
2
0
0
1
0
0
1
1
2
0
0
1
1
1
1
1
0
1
0
0
0
0
2
0
1
0
1
1
2
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
2
2
0
1
0
1
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
2
1
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
2
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
2
0
0
2
2
2
1
4
1
0
0
0
2
0
0
1
0
0
0
2
0
0
0
2
2
0
2
0
2
2
0
0
0
2
1
2
1
0
2
1
0
2
1
2
0
1
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
2
1
1
0
2
0
1
0
2
0
0
0
1
0
2
0
2
0
0
0
0
0
2
2
0
0
2
1
0
0
2
0
2
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
1
0
1
1
1
0
0
1
2
0
1
0
0
0
0
0
0
0
1
2
1
1
2
0
0
1
0
2
0
0
2
1
2
0
0
1
0
2
2
1
0
1
1
0
0
0
1
2
0
0
2
0
0
0
0
0
2
1
1
0
0
2
0
0
2
0
2
0
0
0
1
0
1
1
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
1
0
0
2
1
1
1
3
0
0
1
0
1
0
0
1
1
2
0
0
0
0
1
0
1
0
2
2
1
1
0
1
2
0
1
0
2
1
0
2
0
0
0
1
1
2
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
2
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
2
0
1
0
0
2
1
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
2
0
0
2
1
0
0
0
2
0
2
0
0
0
0
3
0
0
1
0
2
2
1
0
2
0
0
1
0
2
0
1
2
1
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
2
0
2
0
0
0
2
0
1
1
1
0
2
0
0
2
0
0
0
1
0
0
0
2
2
0
2
0
0
0
3
0
1
0
3
0
0
0
0
0
1
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
2
2
1
2
1
0
0
2
0
2
2
0
2
0
2
2
0
0
2
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
3
0
0
0
0
1
0
2
2
0
0
0
1
0
0
6
0
1
2
2
1
0
1
1
0
0
1
0
0
1
2
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
2
0
0
0
0
0
0
0
1
1
3
2
1
2
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
1
0
0
0
1
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
2
2
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
2
0
1
1
0
2
0
0
0
0
0
1
0
3
0
1
0
0
0
0
1
1
1
0
1
1
0
2
2
0
0
0
1
0
2
0
0
3
0
2
0
0
0
2
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
3
0
0
0
0
2
2
1
0
1
0
2
0
1
0
2
0
2
0
1
0
0
0
0
0
1
1
3
0
0
0
0
0
2
0
0
0
0
0
2
0
1
2
0
0
1
2
1
0
0
1
0
0
0
1
0
2
0
1
0
2
0
0
1
1
0
0
0
2
0
0
1
0
0
0
2
2
2
0
2
0
2
0
1
0
0
2
0
1
2
1
1
0
0
0
1
2
2
0
1
1
0
0
1
0
0
0
2
0
0
0
0
2
0
1
0
1
2
0
0
2
0
0
2
0
0
1
1
2
0
1
0
0
0
1
1
2
1
2
0
1
3
1
1
0
2
0
0
0
0
2
1
0
1
0
0
2
2
0
0
0
0
1
2
0
2
0
0
3
1
0
1
1
0
1
1
1
2
0
2
1
2
2
0
2
0
3
0
0
0
0
0
0
0
2
1
0
0
2
0
0
1
2
1
0
0
1
0
0
1
0
1
0
0
0
2
0
1
0
0
5
0
0
2
2
0
1
1
0
0
1
0
1
2
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
3
0
1
0
2
0
1
1
1
0
0
3
0
0
0
0
0
1
2
0
0
1
0
2
1
0
1
1
0
2
0
2
0
2
1
1
0
2
0
0
0
0
0
0
0
2
1
0
1
1
1
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
3
1
2
1
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
1
2
1
0
2
0
0
1
0
1
1
2
1
0
0
0
1
0
0
1
0
0
1
0
0
1
1
1
2
0
0
0
0
0
0
2
0
2
0
0
2
1
0
1
0
0
0
1
0
2
0
1
0
2
2
0
0
0
0
1
4
1
0
0
0
0
0
0
0
0
5
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
2
1
1
0
1
1
0
2
0
0
1
0
0
1
0
2
2
0
3
3
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
1
0
1
0
1
0
3
0
0
3
0
0
2
0
2
0
0
0
0
2
2
0
1
0
0
2
1
0
0
0
3
0
1
0
0
0
0
2
0
0
1
0
2
0
0
0
3
0
0
0
1
0
0
2
0
1
1
0
1
0
3
0
2
0
2
2
0
0
0
0
0
1
0
1
0
0
3
2
0
0
0
0
1
0
0
0
0
1
0
0
2
0
1
1
0
0
0
0
0
2
2
0
0
1
0
0
0
1
0
0
0
1
4
0
0
2
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
1
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
2
2
0
0
0
2
0
0
0
1
0
1
0
1
0
2
0
0
0
2
0
0
0
0
0
0
1
1
0
0
1
6
0
1
0
0
0
0
0
0
0
2
0
0
1
0
2
0
1
0
0
0
0
0
5
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
1
2
0
0
1
1
2
2
0
0
0
0
1
0
0
1
0
0
2
0
0
3
2
2
2
0
0
0
1
0
0
0
0
2
0
1
0
1
1
0
0
0
0
1
2
0
2
2
2
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
2
1
1
0
2
0
0
1
0
2
2
0
0
0
0
0
0
3
2
0
0
0
2
0
0
2
1
0
0
0
0
2
1
1
1
0
0
1
0
2
0
0
1
2
1
1
0
2
1
0
0
0
0
0
0
0
1
0
2
1
0
0
0
2
1
0
0
3
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
1
1
2
0
0
0
0
0
0
0
1
1
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
1
0
4
2
1
2
0
0
2
3
3
1
3
0
1
1
2
0
0
1
1
0
0
0
0
1
2
0
2
1
2
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
2
0
1
0
1
0
0
2
2
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
1
4
0
2
1
3
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
1
3
0
0
2
1
0
0
1
0
2
0
1
0
0
2
0
0
0
0
1
1
2
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
2
1
1
0
1
0
0
1
0
1
0
0
1
1
0
0
2
0
0
0
0
2
1
0
0
0
0
0
1
2
0
2
0
0
0
2
1
0
0
0
1
2
2
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
2
1
0
0
1
1
2
0
0
0
2
1
1
1
1
1
0
0
2
2
1
1
0
2
0
1
0
0
0
1
0
0
0
1
2
0
1
1
0
0
2
0
1
0
3
4
0
0
1
0
1
0
0
0
0
2
2
2
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
2
1
1
1
0
0
1
0
0
1
0
5
0
1
2
0
0
2
2
0
0
2
0
0
0
0
0
1
1
2
1
1
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
4
0
2
1
0
0
0
0
2
0
0
1
0
0
0
2
1
0
0
1
0
0
0
0
0
2
2
0
1
0
2
0
0
0
0
0
1
0
0
2
0
2
0
1
1
0
1
0
1
1
0
0
0
0
0
0
3
0
2
2
0
2
0
1
1
0
0
0
0
0
0
0
2
1
0
2
2
2
1
1
0
2
0
0
0
1
1
0
2
0
0
0
1
0
1
0
0
1
1
0
2
2
2
0
1
1
0
0
0
0
2
0
2
0
1
0
1
0
0
1
0
2
0
1
1
0
2
1
2
0
0
0
0
2
2
2
1
0
2
0
0
1
2
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
2
2
0
3
0
0
0
0
1
0
1
0
1
0
1
0
4
0
1
1
1
0
0
0
1
0
1
0
0
1
2
2
0
1
0
0
0
0
0
0
1
0
2
2
1
0
0
0
1
0
0
0
2
0
0
0
1
2
0
0
2
2
2
3
1
2
1
2
1
1
0
0
0
0
2
1
0
0
0
0
0
0
3
1
2
0
2
0
0
0
0
0
2
0
2
1
2
0
0
1
1
0
2
1
0
2
1
1
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
1
2
0
0
1
0
1
0
1
0
0
0
1
1
2
4
1
2
2
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
2
3
0
2
2
1
1
2
1
0
2
2
0
2
0
2
0
2
0
1
0
1
1
0
0
1
1
1
1
0
2
0
0
0
2
0
1
2
0
0
0
0
1
0
0
1
0
0
2
2
0
0
2
2
0
1
0
0
0
1
2
0
2
0
2
0
0
2
0
0
0
0
2
0
5
0
0
0
2
0
1
2
2
0
3
1
0
0
2
0
0
1
8
0
2
2
0
0
2
2
0
0
0
0
0
2
0
0
0
1
2
0
1
2
2
0
0
0
2
2
0
0
1
0
0
2
2
0
0
0
0
1
0
0
2
1
1
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
1
1
0
0
1
2
2
2
1
0
1
0
2
0
0
1
0
0
0
0
1
1
2
0
1
0
1
0
2
1
0
0
3
0
1
0
0
1
1
0
2
0
0
0
2
0
0
3
2
1
2
0
1
2
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
1
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
2
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
2
2
1
1
0
0
0
1
2
1
2
0
2
2
0
1
3
0
0
0
1
1
0
0
2
2
1
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
1
0
0
2
0
3
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
1
1
0
1
1
1
0
0
0
1
0
1
2
2
2
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
1
2
0
1
2
0
0
2
2
0
0
2
2
0
0
0
0
1
0
0
0
1
0
0
0
1
2
0
1
0
1
1
0
2
1
0
1
1
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
2
0
0
1
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
2
1
0
5
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
1
2
0
2
2
1
1
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
1
2
1
0
0
0
3
0
0
0
1
0
1
0
0
3
1
1
0
2
0
0
0
0
2
2
0
0
0
2
0
0
1
1
0
1
0
0
0
2
2
1
0
2
0
1
0
0
1
2
0
0
1
2
1
0
0
2
2
0
0
1
0
0
0
1
0
0
2
2
0
0
0
0
0
2
0
0
2
0
2
0
0
2
0
0
0
0
0
0
2
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
2
2
0
0
0
2
1
1
1
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
2
3
0
1
3
0
0
2
0
1
0
0
1
2
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
1
0
1
0
1
0
1
0
0
0
0
0
2
0
2
0
1
2
2
0
0
0
1
0
0
2
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
3
0
1
1
0
2
0
0
0
2
0
0
2
2
1
1
1
2
2
0
1
0
1
1
0
0
3
0
0
0
1
0
0
0
1
3
0
0
0
1
0
2
0
1
0
0
1
1
0
1
1
1
2
0
2
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
2
1
0
1
2
2
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
2
0
0
0
1
2
1
2
0
2
0
0
0
0
0
0
2
0
1
0
2
2
0
0
1
2
0
0
0
2
0
2
1
0
0
0
0
1
1
0
1
1
1
0
2
0
2
1
0
0
0
0
0
1
1
0
0
2
1
1
0
1
2
0
0
0
0
1
0
2
2
0
2
2
0
2
0
0
0
1
0
0
3
0
1
2
0
0
0
0
0
0
1
0
0
2
1
0
2
0
3
0
1
1
2
0
0
2
0
1
2
0
0
0
0
0
0
0
0
2
0
1
4
1
0
2
1
0
0
1
0
2
7
1
0
3
0
0
2
2
0
2
0
0
0
0
0
2
1
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
1
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
1
0
2
1
1
0
0
0
1
0
2
1
1
2
0
0
1
2
0
0
0
3
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
3
0
2
0
1
0
0
1
0
0
0
0
0
2
0
1
5
2
0
0
1
1
0
0
1
3
2
1
2
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
1
0
3
2
0
0
1
0
2
1
0
0
1
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
1
0
2
0
0
2
0
0
1
1
0
0
0
0
2
0
2
0
2
1
1
3
1
0
0
0
1
0
0
0
0
0
1
0
0
2
2
0
2
1
0
0
1
1
0
10
1
0
0
0
3
2
1
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
3
0
1
0
0
0
2
0
0
0
0
1
0
2
0
0
1
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
2
2
1
1
1
0
0
0
0
2
0
0
1
0
3
2
0
2
2
0
0
1
1
0
0
2
0
2
2
0
0
2
0
0
0
2
0
0
0
1
0
1
0
2
1
2
2
0
1
0
0
3
1
0
0
2
3
2
0
0
0
0
0
2
1
0
0
0
2
0
4
0
2
2
1
3
0
0
1
1
0
0
0
0
0
0
0
2
1
0
0
2
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
2
2
0
0
0
0
1
1
0
0
0
0
0
2
2
4
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
2
0
1
1
0
0
1
0
1
1
0
0
2
0
1
0
1
0
2
0
0
1
2
0
0
1
2
2
2
0
1
0
0
0
2
1
0
0
0
0
1
0
0
0
0
2
2
0
2
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
2
2
2
2
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
3
1
2
0
1
0
2
1
0
3
1
0
1
2
0
1
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
3
0
0
0
1
0
0
0
2
0
0
0
0
2
1
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
2
0
0
1
1
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
1
1
0
0
0
0
0
2
2
1
2
1
0
0
0
1
0
0
2
0
0
0
1
2
1
2
0
0
1
2
1
1
0
2
1
0
0
2
2
1
1
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
1
1
1
0
1
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
2
0
0
0
0
0
0
2
2
0
1
0
0
0
0
1
0
0
2
1
0
2
2
0
0
0
2
0
2
0
0
0
1
1
0
3
1
1
0
2
0
0
0
1
2
0
0
2
2
3
0
0
0
0
1
1
1
0
0
2
0
0
0
1
0
0
0
1
1
0
0
0
1
2
0
0
1
0
0
2
1
2
0
1
2
0
0
2
1
2
1
0
1
2
0
2
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
2
2
2
0
0
1
0
0
2
0
0
0
1
0
0
0
2
0
0
2
4
0
0
1
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
2
2
2
0
0
0
0
0
3
2
1
0
2
0
0
0
0
0
0
0
1
0
0
1
2
2
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
1
2
1
0
0
1
0
1
0
2
0
2
0
0
2
2
0
1
2
1
0
1
0
0
0
2
0
0
0
0
2
8
1
0
0
1
0
1
0
0
0
0
0
1
2
1
1
1
1
1
0
0
0
0
2
2
0
1
0
0
0
0
2
2
3
5
2
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
1
0
1
1
0
0
0
0
0
0
0
2
1
0
0
2
2
1
0
0
2
0
1
1
1
0
0
0
0
1
0
0
1
0
2
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
1
1
1
4
0
1
0
3
0
1
0
2
0
2
2
1
0
0
5
0
0
1
0
2
2
0
0
0
1
0
2
0
2
0
0
0
0
0
2
0
0
0
0
2
1
0
2
0
0
2
0
1
0
2
2
2
1
0
1
0
2
1
2
0
0
1
0
0
2
1
0
1
1
1
1
0
0
1
2
0
0
0
1
1
0
0
0
2
2
2
0
0
2
1
0
0
0
0
0
0
0
2
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
1
0
2
2
0
1
2
0
1
0
0
0
0
0
0
0
1
0
2
1
0
0
2
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
2
0
2
1
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
2
1
2
0
1
0
0
0
2
0
0
0
0
1
0
2
0
3
0
0
0
0
0
1
2
1
1
2
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
1
1
0
0
0
0
0
1
1
0
1
2
1
1
1
0
0
1
4
1
0
2
0
0
0
1
1
1
1
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
3
1
1
0
0
2
0
0
1
2
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
2
2
2
2
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
2
0
0
0
2
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
1
0
2
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
2
1
0
0
0
2
2
0
2
2
1
0
0
1
2
0
0
0
0
0
1
0
0
0
2
0
1
2
1
0
0
2
0
0
2
0
1
0
4
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
2
2
0
0
0
2
2
0
0
0
0
1
1
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
1
2
1
2
2
1
0
3
0
0
2
1
1
2
0
0
0
0
0
1
0
0
0
0
2
0
0
2
2
1
0
0
2
2
1
0
1
0
1
0
2
0
0
0
0
1
0
0
1
0
1
0
2
1
0
0
0
2
2
0
1
0
0
0
1
1
1
1
0
0
0
0
2
1
0
0
0
0
1
0
0
2
3
1
0
0
0
1
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
2
2
0
0
2
2
0
0
0
2
0
1
2
0
2
0
1
0
0
0
0
1
1
0
1
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
1
2
1
0
0
0
0
0
0
2
0
0
0
0
0
2
2
2
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
1
2
0
2
2
1
0
3
0
1
1
0
0
1
0
2
0
2
1
1
0
0
1
1
0
0
0
2
2
0
0
0
1
1
0
2
2
0
1
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
1
2
0
0
0
2
1
0
0
0
0
0
4
0
0
0
3
0
0
1
2
0
0
0
1
0
0
2
0
0
0
0
1
2
0
0
5
0
0
0
2
0
0
2
1
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
1
1
0
0
2
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
1
0
2
1
2
1
1
2
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
1
1
1
2
0
0
0
2
1
0
0
0
0
0
0
1
0
0
1
0
2
0
1
0
0
1
0
1
1
0
0
0
2
0
2
1
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
1
0
2
0
0
0
0
0
0
0
2
0
1
0
1
1
0
0
0
0
1
0
0
0
0
1
2
0
0
2
2
0
0
1
1
0
0
0
0
0
2
2
0
0
0
1
1
0
0
1
0
0
0
0
0
0
2
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
1
0
0
2
1
1
1
3
3
0
0
0
2
0
2
0
0
0
0
2
0
0
1
1
1
1
3
0
1
0
2
1
3
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
2
0
0
1
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
9
0
0
1
0
0
0
0
0
2
2
0
2
0
1
0
0
0
2
1
0
0
0
2
0
0
1
0
1
0
2
0
1
2
1
0
1
2
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
2
3
2
1
1
2
0
1
0
3
0
1
0
0
2
0
2
0
3
0
1
0
1
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
3
0
1
1
1
1
2
0
0
1
2
2
0
2
1
0
2
0
0
0
0
2
1
0
0
2
0
0
3
2
0
1
1
1
0
0
2
0
2
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
1
2
1
1
2
1
0
0
0
0
1
0
0
0
0
0
2
2
1
0
0
1
0
1
1
1
0
1
1
0
0
1
0
1
1
0
1
2
0
1
0
2
1
2
0
0
4
0
0
1
1
2
1
0
1
0
0
0
0
1
1
0
2
0
0
1
1
2
0
0
0
0
1
1
0
1
1
0
2
2
2
1
0
2
0
3
0
0
2
1
2
0
0
2
1
2
2
0
0
0
0
0
0
2
0
1
0
1
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
1
1
0
2
2
2
1
0
1
1
0
0
0
0
0
0
1
0
2
0
2
2
0
0
1
1
0
0
1
3
1
1
0
0
1
0
0
0
2
0
2
0
2
2
2
2
0
0
1
0
0
0
0
2
0
1
1
2
1
0
0
0
0
0
0
0
0
0
2
0
1
2
2
2
0
2
2
2
0
2
0
0
0
1
3
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
2
1
2
0
0
0
1
1
2
0
1
0
0
1
0
2
0
0
2
2
1
0
2
0
0
2
2
2
0
0
0
0
1
0
1
0
0
2
8
0
0
0
2
0
2
1
0
0
0
1
1
1
0
0
2
0
1
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
1
1
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
2
2
0
1
0
0
0
0
1
0
6
2
0
0
0
3
0
1
2
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
3
0
2
2
2
0
0
0
0
3
0
0
0
0
0
0
0
0
1
1
1
2
0
0
3
1
0
0
0
0
0
0
1
0
1
2
1
1
0
1
2
1
0
0
1
1
1
0
0
2
1
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
2
0
3
0
2
0
0
0
2
0
2
1
2
0
0
4
0
0
0
1
0
1
0
1
1
0
3
0
0
0
0
1
0
2
1
0
2
0
0
0
0
0
0
0
2
0
1
0
2
0
0
2
1
1
0
0
2
0
2
0
0
1
3
0
1
0
1
0
0
0
0
2
1
2
0
0
0
1
1
0
0
0
0
1
1
0
1
0
0
1
0
3
2
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
1
2
0
3
2
2
0
2
2
3
0
1
2
0
0
0
0
0
0
0
1
0
0
2
2
0
0
2
1
0
2
0
0
2
0
0
0
1
2
1
0
2
1
0
0
1
0
1
0
0
0
8
0
1
1
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
1
1
2
0
1
0
0
2
0
0
2
1
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
3
0
0
0
1
1
1
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
2
0
1
2
0
2
0
1
0
0
0
2
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
1
2
0
0
0
1
0
2
0
0
2
0
0
1
0
0
1
0
0
0
0
0
1
0
3
0
0
0
0
2
0
2
0
0
2
0
2
0
0
1
0
0
2
1
0
1
0
0
0
2
0
2
2
0
0
0
1
0
2
0
2
0
0
0
1
2
0
0
0
0
2
0
2
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
1
0
0
1
0
1
2
0
0
2
0
0
0
0
0
0
1
2
0
0
1
0
0
0
2
2
2
0
1
4
0
0
2
2
2
0
2
2
0
0
0
4
2
1
0
0
0
2
0
0
1
0
2
5
2
1
0
0
3
0
3
2
0
3
0
0
1
0
0
1
0
0
0
2
0
0
0
1
0
0
0
4
2
0
0
1
0
1
0
0
0
0
1
0
1
0
2
0
1
2
0
0
0
0
2
0
0
0
0
1
2
1
0
4
0
0
2
0
0
1
2
1
3
0
1
1
0
0
0
1
0
1
1
0
1
0
0
2
0
0
0
2
2
3
2
2
1
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
2
1
0
0
2
2
1
2
0
1
1
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
2
1
0
2
1
0
0
1
2
2
0
0
1
0
0
0
2
0
0
2
0
1
0
2
0
0
1
0
0
1
0
2
0
0
0
0
0
1
1
0
0
2
0
3
0
2
1
0
2
0
0
0
1
3
0
0
0
1
1
2
2
0
0
0
1
2
0
1
0
1
0
0
1
0
0
1
1
0
0
1
2
0
1
0
0
0
1
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
1
1
2
2
1
1
2
1
0
2
2
1
0
2
0
0
0
0
0
2
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
2
3
1
0
2
0
2
0
1
0
0
1
1
0
0
0
0
0
1
1
1
2
0
1
0
0
0
2
0
1
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
2
1
0
0
2
0
0
0
1
3
2
2
0
1
0
0
1
1
2
0
0
1
0
0
2
0
0
2
1
1
1
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
1
3
2
1
0
2
0
0
0
0
1
2
3
1
1
0
0
0
1
0
2
0
1
1
1
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
2
0
2
2
0
3
0
1
1
0
2
1
0
0
0
2
0
0
0
0
0
2
0
0
3
2
0
2
3
2
1
0
0
0
0
1
0
2
2
1
0
0
0
1
2
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
1
0
0
0
1
2
1
0
0
2
0
0
2
1
0
0
0
2
0
1
1
0
0
1
2
1
0
1
0
3
0
2
0
1
1
2
0
2
0
0
0
0
0
1
0
0
0
0
1
1
2
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
2
1
0
0
1
2
0
2
0
1
1
0
1
0
0
0
1
0
0
0
2
0
0
2
1
0
1
2
0
0
1
0
0
1
0
0
0
2
1
1
0
0
0
3
0
0
0
0
1
0
1
0
0
2
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
2
2
0
0
0
0
1
0
0
2
0
0
2
1
0
0
1
0
0
0
2
1
2
0
0
1
2
0
0
0
1
3
1
0
0
1
1
0
0
1
2
2
0
0
3
0
0
1
0
1
4
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
1
1
1
0
0
0
2
2
0
1
0
1
0
0
2
0
1
0
2
0
2
0
0
2
0
1
0
0
0
0
1
0
2
3
1
1
0
2
0
1
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
3
1
0
1
1
1
1
0
1
2
0
2
1
2
0
2
0
0
0
1
0
1
0
2
0
1
0
1
0
0
0
0
0
0
0
1
0
1
2
0
2
0
2
4
1
1
1
1
0
1
3
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
3
0
0
1
0
3
0
0
1
0
0
0
0
0
1
2
2
0
1
2
2
0
1
2
0
1
2
0
1
1
0
2
0
0
1
1
0
2
0
0
0
1
0
0
0
1
2
2
2
0
0
0
2
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
1
2
2
0
2
0
1
0
0
0
0
0
0
1
1
2
0
0
0
1
0
1
0
0
3
1
1
2
0
1
1
2
0
0
0
2
1
0
0
0
0
0
1
1
0
0
1
2
2
2
2
2
1
1
0
2
3
1
2
0
1
0
1
0
2
0
0
0
6
1
1
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
2
2
1
0
0
0
2
2
0
0
0
0
3
2
0
1
2
1
0
2
0
2
2
0
0
2
1
0
0
1
0
0
0
2
0
0
1
0
0
0
2
0
2
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
1
1
0
0
0
2
0
1
0
0
0
0
2
1
0
0
1
0
0
0
2
0
2
0
1
0
2
1
0
2
0
2
1
3
0
0
1
0
1
1
0
0
0
0
0
2
0
0
0
2
1
0
0
0
2
0
0
1
1
0
0
1
1
1
0
1
1
0
0
1
0
2
1
0
1
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
2
2
0
2
0
2
0
0
0
1
0
0
1
0
0
0
1
0
0
1
2
0
2
0
1
2
0
0
0
1
2
0
0
0
1
0
0
2
0
0
2
0
0
0
0
2
0
1
1
1
0
1
0
0
0
1
0
0
1
2
2
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
2
2
0
2
2
2
0
0
0
1
0
3
0
0
0
1
1
2
0
0
4
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
1
2
0
0
1
1
2
0
0
0
0
1
4
0
2
0
0
0
1
0
0
2
2
0
0
0
1
0
0
2
0
0
0
1
0
0
2
0
2
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
1
0
3
1
0
1
3
2
0
0
1
2
0
1
1
0
0
1
0
2
2
3
0
0
0
1
0
0
6
1
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
2
1
2
2
0
1
0
0
0
0
0
0
1
1
0
2
0
0
3
1
0
2
0
2
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
2
2
0
1
2
1
0
0
0
0
0
2
1
2
0
0
2
0
0
1
2
1
0
1
0
0
0
0
0
0
0
0
2
2
1
0
1
1
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
1
0
0
1
1
2
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
1
0
2
1
0
0
0
2
0
4
0
0
0
2
0
0
0
1
2
1
0
0
1
0
1
1
0
0
2
1
1
1
1
0
0
0
2
0
1
0
0
0
0
0
2
1
0
0
0
1
1
2
0
2
0
0
0
0
1
0
1
1
0
0
1
1
1
0
2
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
1
1
3
1
0
0
1
1
1
1
0
0
1
0
2
1
0
4
1
1
2
1
1
2
0
1
1
2
1
1
2
1
0
0
1
2
1
0
1
0
0
1
0
2
0
3
0
1
2
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
1
0
1
1
0
2
1
4
0
2
2
0
1
0
1
0
0
0
0
2
2
0
4
1
0
1
2
0
1
2
0
1
0
3
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
1
1
1
1
0
1
0
1
0
2
0
0
1
0
3
0
1
2
0
0
1
0
0
0
0
1
0
0
1
0
2
1
0
0
2
0
0
1
2
0
2
0
0
0
2
1
2
0
0
0
0
1
0
0
2
1
0
1
2
1
1
0
0
3
1
0
3
0
0
0
3
0
0
2
0
2
2
0
2
1
0
0
2
1
0
1
1
0
0
0
1
0
0
1
2
0
0
0
0
0
2
0
0
0
1
2
0
0
1
1
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
2
0
2
0
1
2
2
0
0
0
0
0
0
0
1
0
3
1
0
0
2
2
0
0
0
2
0
0
0
2
0
0
2
2
0
1
0
0
0
2
1
1
0
3
1
0
2
0
1
0
0
1
0
0
2
2
0
0
2
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
1
0
0
0
1
1
0
2
0
0
2
0
0
2
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
2
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
1
0
0
0
1
0
1
1
0
2
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
2
3
0
0
2
0
0
0
0
0
2
1
2
2
2
1
1
2
1
0
0
0
0
0
0
1
0
0
1
0
0
2
2
0
0
2
2
4
0
0
0
0
2
1
0
1
0
0
1
1
0
0
0
0
1
1
0
0
2
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
2
1
2
0
0
1
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
1
0
0
0
2
0
0
0
4
0
0
0
0
2
0
2
1
3
0
0
7
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
3
0
2
0
0
0
0
2
2
0
0
1
2
0
0
3
0
0
2
2
0
0
3
1
0
0
1
0
1
1
1
0
0
0
0
1
1
0
0
2
1
0
0
3
1
3
2
2
0
0
1
0
2
2
1
2
0
0
3
2
0
0
0
1
1
1
0
0
0
0
1
2
0
1
0
0
0
0
0
2
2
2
1
0
0
2
0
2
0
2
1
1
0
0
1
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
1
0
0
5
0
0
0
0
0
0
0
0
2
0
1
1
1
0
0
0
2
0
0
0
1
0
0
0
1
1
1
3
0
0
0
2
2
0
2
0
1
1
0
0
1
1
1
2
1
1
0
0
0
3
1
0
0
0
0
0
2
1
0
0
0
2
1
0
1
0
0
0
0
1
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
3
0
2
2
1
0
2
1
1
1
1
0
0
0
1
0
1
0
1
2
0
1
2
1
0
0
0
1
1
0
0
2
0
0
2
0
2
3
0
0
0
3
0
1
1
0
0
2
1
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
2
0
0
1
3
0
1
0
1
1
0
0
2
2
1
3
1
1
0
0
0
0
0
0
1
0
0
0
0
0
3
0
2
0
0
0
2
1
1
2
1
2
2
0
1
1
0
0
0
3
2
0
0
1
1
1
2
0
2
0
0
2
0
2
0
1
2
0
0
0
1
0
1
2
0
0
0
1
0
2
0
0
0
1
0
2
0
1
0
0
0
1
1
0
0
0
0
0
1
1
0
0
2
0
2
0
2
2
0
1
1
0
0
1
2
0
0
0
2
2
2
0
0
2
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
1
0
0
0
0
0
2
0
1
0
2
0
0
2
1
1
0
0
1
0
0
2
0
0
0
0
2
0
1
1
2
0
0
0
0
1
1
1
0
0
0
1
0
0
2
0
0
1
0
0
0
1
0
2
3
0
1
0
6
0
1
0
0
0
0
0
0
0
2
0
0
0
1
2
1
0
2
1
1
1
0
2
0
0
0
0
0
1
1
2
0
0
1
0
2
0
0
1
0
2
5
0
1
0
0
1
0
1
3
0
0
2
0
0
2
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
1
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
3
1
1
0
0
1
1
0
0
0
0
0
3
0
0
2
0
2
0
0
0
0
1
0
1
0
5
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
2
0
2
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
3
0
0
0
0
1
0
0
0
2
1
0
0
0
2
0
0
2
1
0
2
0
0
0
0
0
2
0
2
1
1
2
4
1
2
2
0
0
0
0
0
0
0
2
1
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
2
2
1
0
0
1
1
1
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
1
0
0
1
0
0
0
2
1
0
1
0
0
0
2
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
1
0
2
0
0
0
0
1
1
1
1
2
0
2
0
1
0
0
2
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
1
0
1
1
0
1
0
0
1
1
0
1
0
1
0
2
0
1
1
0
0
0
1
0
1
0
2
0
0
0
0
2
1
0
1
2
1
0
1
0
0
2
0
1
1
2
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
1
0
0
1
0
2
2
0
2
2
0
0
1
0
0
0
1
0
1
2
0
0
2
1
0
2
1
0
1
2
1
0
0
0
3
2
0
0
0
0
1
0
0
2
1
0
0
0
0
1
0
1
1
1
0
2
2
1
2
3
1
1
0
0
1
2
0
0
2
1
0
0
2
0
2
1
0
0
0
0
1
2
1
0
0
0
0
0
0
0
2
0
0
5
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
2
0
1
2
0
3
2
1
0
0
1
2
0
1
0
0
1
1
0
0
0
0
2
0
2
1
0
0
2
1
2
0
0
1
0
2
1
1
0
1
0
3
0
3
1
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
1
0
0
2
1
0
0
1
1
0
0
0
4
0
0
2
0
2
0
2
0
0
0
0
2
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
2
2
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
3
2
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
2
0
1
0
0
2
1
1
1
0
0
0
4
2
1
2
0
1
2
0
1
3
0
0
2
3
0
2
0
1
0
1
1
0
0
1
0
0
0
0
0
2
2
1
0
2
0
0
2
0
0
0
4
1
3
0
0
0
0
1
0
0
1
0
2
0
1
0
0
1
0
2
0
2
0
2
0
1
1
2
1
0
2
0
1
0
0
0
0
1
1
0
0
0
0
1
3
1
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
2
0
0
1
1
1
1
0
0
0
1
0
0
0
1
0
0
0
1
2
1
0
2
0
0
0
2
2
0
2
0
0
2
2
2
0
0
0
2
0
1
1
1
2
2
1
0
0
0
0
1
0
1
1
3
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
2
1
0
0
0
0
0
0
0
2
2
0
0
2
2
0
1
0
0
0
0
1
0
0
2
1
1
0
0
0
1
1
2
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
1
0
2
1
0
2
0
0
0
2
0
2
0
0
0
1
1
1
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
1
0
2
2
0
0
0
0
1
0
0
2
2
0
0
1
0
0
0
0
2
4
0
1
2
1
1
0
0
0
0
2
0
0
0
0
0
3
0
0
0
1
2
0
0
0
0
0
0
0
0
1
3
1
1
0
1
0
0
0
0
2
2
0
0
1
0
0
2
0
2
0
0
0
2
0
3
0
0
1
2
0
0
0
0
0
0
1
0
0
1
2
3
0
0
0
0
2
0
1
2
0
0
0
1
0
0
0
1
2
0
1
2
2
2
0
2
0
1
0
0
0
0
2
0
2
0
0
0
0
2
2
0
1
0
0
2
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
1
0
0
1
0
1
2
1
0
1
1
2
0
0
1
2
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
2
2
0
0
0
0
0
1
1
0
0
2
2
0
1
0
0
1
2
1
0
0
2
0
0
9
2
2
1
0
0
1
1
0
0
2
0
0
0
1
1
2
0
0
3
2
0
0
1
2
0
3
1
0
0
1
0
0
0
1
0
0
2
0
1
0
0
2
0
0
1
3
2
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
2
0
0
1
0
2
0
2
0
0
1
0
0
0
1
2
0
1
0
1
0
1
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
2
2
0
0
0
0
0
1
1
2
2
1
0
2
1
1
0
2
1
0
0
0
0
0
0
1
0
2
2
1
0
1
1
0
0
1
1
1
1
2
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
2
2
0
2
2
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
1
0
1
0
0
0
0
0
1
2
2
0
0
0
0
2
0
0
1
2
2
1
2
0
1
0
0
0
0
3
0
0
0
0
0
1
0
2
1
0
0
0
0
2
1
0
2
1
1
2
1
2
0
0
0
0
0
3
0
2
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
2
2
2
0
0
0
0
0
0
1
2
0
2
1
0
0
0
1
0
0
0
2
0
0
1
0
2
1
1
0
0
2
0
0
2
0
0
0
1
1
0
0
1
0
0
0
0
1
0
1
0
0
0
2
1
0
0
0
1
0
2
2
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
1
0
2
0
2
0
2
0
1
0
0
0
0
0
0
0
1
1
2
1
0
0
0
0
0
0
1
0
1
0
2
0
2
3
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
2
1
2
2
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
1
1
2
0
0
2
4
2
0
1
0
3
1
0
1
0
0
2
0
0
0
3
2
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
3
1
0
1
0
0
0
0
0
1
0
0
0
1
2
1
1
0
0
2
1
2
1
0
0
1
2
0
0
0
0
0
0
0
0
0
5
0
0
1
1
1
2
2
0
0
0
1
0
1
0
1
2
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
2
1
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
1
0
1
1
0
0
2
0
1
0
0
0
0
0
2
0
0
0
2
1
0
0
1
0
2
1
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
3
2
0
2
2
0
1
7
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
2
1
2
2
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
1
1
2
0
2
0
0
0
0
0
0
2
0
0
2
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
2
1
0
1
0
0
2
0
1
0
0
0
0
0
0
1
2
0
0
2
0
0
1
1
1
2
0
0
2
0
0
4
2
1
0
2
2
1
0
2
3
1
1
0
0
0
0
0
2
0
3
0
0
0
1
0
0
1
0
0
0
1
0
0
0
2
0
1
0
0
1
0
1
0
0
0
2
0
0
2
0
0
2
0
2
1
2
4
0
0
0
0
0
2
0
0
0
1
0
0
0
1
1
0
0
1
0
0
2
1
0
0
2
0
1
0
0
2
2
0
4
0
1
1
0
0
1
0
0
0
0
2
0
0
0
2
0
1
1
2
1
2
2
0
1
0
1
0
0
0
0
0
2
5
0
1
0
0
0
0
0
2
0
1
1
1
0
0
1
0
0
0
0
2
0
0
1
1
2
0
0
0
0
0
0
2
0
1
0
0
2
0
0
1
2
0
1
0
3
0
1
0
1
0
2
0
0
2
3
1
0
0
2
1
2
2
0
0
1
2
1
0
0
2
0
0
3
0
0
3
2
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
1
0
0
3
0
0
0
1
0
0
0
0
4
0
0
0
1
2
0
0
0
0
2
0
2
1
0
0
2
1
0
0
0
1
2
0
1
0
0
1
2
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
3
0
1
0
0
0
2
0
0
0
1
0
0
0
0
1
0
2
0
2
3
0
0
1
0
0
0
0
0
1
2
2
2
0
0
0
0
2
0
0
2
2
0
1
0
0
0
2
2
0
0
1
0
2
0
0
0
0
0
0
2
1
1
1
2
2
0
2
0
0
1
0
0
0
0
2
0
2
1
1
2
1
1
0
1
0
0
1
0
0
0
0
0
2
5
2
1
0
0
0
0
3
0
0
1
1
0
0
2
0
1
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
2
2
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
1
1
0
0
0
1
1
0
0
2
0
0
0
2
0
1
0
1
0
1
0
0
1
1
1
0
0
1
0
0
0
0
2
1
1
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
1
2
0
0
0
1
0
0
0
1
2
0
2
0
2
2
0
0
2
0
1
2
0
1
0
1
0
2
1
2
0
3
1
2
0
0
0
1
0
2
0
0
0
2
0
0
2
0
1
2
1
0
0
0
2
2
0
2
0
1
0
0
0
1
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
1
1
1
0
1
6
1
1
1
0
0
0
0
0
0
0
1
1
2
1
0
0
0
2
0
0
2
1
2
1
2
0
2
2
3
1
0
2
0
2
2
0
0
1
0
2
2
0
1
0
0
0
2
1
0
1
2
1
0
1
0
1
0
1
0
0
2
0
1
0
1
0
0
0
1
1
1
0
0
2
0
0
0
2
0
2
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
2
0
2
3
1
2
0
2
1
0
0
1
0
2
0
3
2
0
2
0
0
0
0
0
2
0
0
1
1
0
0
1
1
1
0
1
3
2
2
0
2
1
0
0
1
1
1
1
3
1
2
2
0
0
0
2
0
1
0
0
1
2
0
0
1
0
0
2
4
1
0
1
3
0
0
0
2
0
2
1
2
0
0
0
2
2
0
3
0
0
0
2
0
2
0
1
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
1
0
2
2
1
2
1
1
0
3
1
0
0
0
0
1
3
0
2
0
0
0
2
0
1
0
2
2
1
2
0
2
0
1
0
0
3
0
0
1
0
2
0
2
1
0
0
1
1
0
0
0
0
0
1
0
1
1
0
0
1
0
0
2
0
0
0
0
2
1
2
0
0
1
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
1
3
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
1
1
1
2
1
0
0
0
0
0
2
2
1
1
0
1
0
0
0
1
1
2
0
2
0
5
0
0
1
0
2
0
1
0
0
0
0
2
0
2
0
0
0
0
0
2
0
2
1
0
2
0
1
0
1
0
1
0
1
0
0
2
0
0
1
2
0
1
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
2
0
0
2
1
0
0
0
0
2
0
1
4
4
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
3
1
1
0
1
0
0
0
0
1
1
3
5
0
0
0
0
1
2
1
1
1
0
0
0
0
0
1
0
0
0
1
1
0
2
0
0
0
0
0
0
0
1
2
0
2
0
0
2
1
0
1
2
0
0
1
1
2
0
0
1
0
4
1
0
0
1
0
0
1
0
0
0
0
0
0
2
2
0
1
1
0
0
2
2
2
0
0
0
0
0
2
0
2
3
0
4
0
0
3
2
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
2
0
0
1
0
2
0
0
0
0
0
1
0
3
2
0
0
0
0
1
0
1
0
0
0
0
0
2
0
2
0
5
0
0
0
2
1
2
0
0
2
1
4
0
1
0
1
0
0
2
1
1
0
0
2
0
1
0
1
2
0
2
0
0
1
1
1
2
0
2
1
0
0
0
0
0
0
1
3
1
0
0
0
1
0
0
1
0
2
0
2
1
2
2
1
0
0
0
0
2
3
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
3
0
0
0
0
2
1
0
0
0
1
0
2
1
1
1
2
0
2
2
0
0
2
0
0
0
1
1
0
0
0
0
0
0
1
2
1
1
0
0
0
0
1
0
0
0
0
3
0
0
1
0
0
0
0
0
0
1
2
0
1
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
2
0
0
2
1
0
1
1
2
4
0
0
2
5
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
2
1
2
0
1
0
2
0
1
2
1
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
1
1
0
1
1
2
0
1
2
1
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
2
0
2
0
1
1
0
1
0
1
0
2
1
4
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
2
0
0
0
1
0
0
0
1
1
0
0
0
1
0
2
2
0
2
2
0
0
3
0
2
0
0
0
3
0
2
0
0
0
0
0
0
0
2
2
0
1
0
1
0
1
0
2
0
0
0
0
0
1
1
1
1
2
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
3
0
0
0
0
2
1
0
2
0
1
0
0
0
0
2
0
3
4
2
2
1
0
0
0
2
2
0
0
1
1
2
1
0
0
0
0
1
1
2
0
0
2
1
1
0
1
0
0
0
2
2
0
1
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
3
1
0
0
0
0
0
0
2
0
1
1
0
1
2
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
1
2
0
0
1
0
1
0
5
0
0
1
1
2
0
0
1
0
0
0
0
0
0
0
2
0
1
0
1
1
2
0
0
0
1
0
0
2
0
0
0
0
2
1
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
3
0
1
0
0
2
0
2
0
1
0
2
2
3
1
1
2
0
1
3
3
1
0
0
1
2
1
0
0
0
0
1
0
2
0
2
2
1
2
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
2
1
1
0
0
0
0
0
2
0
1
1
2
0
2
0
2
2
0
0
1
0
2
0
0
0
0
0
1
0
0
0
2
0
0
3
1
1
1
0
1
2
0
0
1
0
2
0
0
0
0
1
0
2
0
2
2
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
2
0
1
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
2
1
0
3
0
1
0
0
0
1
0
0
1
2
0
0
0
0
2
0
2
1
1
0
1
0
0
0
0
2
3
0
1
1
0
0
2
0
0
0
0
1
0
1
0
0
1
1
2
1
0
1
0
2
0
0
0
2
0
0
0
2
0
0
0
2
1
0
0
0
1
2
2
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
1
1
0
1
0
5
1
0
0
1
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
1
2
0
1
2
0
2
1
1
0
0
0
0
1
2
0
1
0
2
0
0
0
2
0
1
2
0
0
0
0
1
0
0
1
0
0
2
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
2
1
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
2
0
0
1
2
2
1
0
0
0
0
0
1
0
0
1
1
1
2
0
0
3
0
1
0
1
2
1
0
2
1
0
0
1
2
0
2
1
0
0
1
1
0
1
0
2
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
4
0
0
2
1
0
0
0
0
1
0
0
0
1
1
1
0
1
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
4
0
1
0
1
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
2
1
0
1
1
2
0
3
2
1
1
0
0
0
0
1
1
0
1
3
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
2
3
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
1
2
1
0
0
0
0
1
0
0
2
0
2
0
1
0
0
1
0
1
2
1
1
1
0
2
1
0
4
2
2
0
0
1
1
2
1
2
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
4
1
2
2
0
1
2
2
0
1
0
2
2
0
2
0
3
2
0
0
0
0
0
1
0
1
1
0
2
0
1
0
0
0
0
2
0
1
1
0
1
0
0
0
0
0
0
1
7
1
2
0
0
1
0
0
0
0
1
0
0
1
2
2
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
1
1
0
1
0
0
2
2
0
0
1
0
2
2
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
1
0
1
0
0
1
0
0
1
5
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
2
1
0
2
0
0
0
1
0
2
0
2
0
0
0
0
1
0
0
1
1
1
4
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
2
2
0
1
2
0
1
0
1
1
0
3
0
0
0
1
1
3
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
2
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
1
1
0
2
2
0
0
0
0
0
0
0
0
1
0
2
0
3
0
2
1
2
1
0
2
0
1
0
2
1
2
0
1
1
0
0
3
0
0
0
0
0
0
1
0
2
0
0
0
0
2
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
1
2
0
1
0
0
0
1
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
1
2
0
2
0
0
0
0
0
1
0
1
0
2
0
1
2
2
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
2
0
1
2
2
0
2
1
2
0
0
1
1
1
0
0
0
0
1
0
1
0
0
2
0
0
0
1
0
0
1
1
0
0
0
2
2
3
1
0
0
0
0
0
1
3
0
0
0
3
2
0
0
2
0
0
1
2
2
0
0
1
1
0
0
0
2
1
1
2
0
0
0
0
2
0
0
2
0
2
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
2
0
3
0
0
1
1
2
1
0
1
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
2
2
1
0
0
0
4
0
0
0
1
0
1
2
0
2
0
0
2
0
1
0
0
0
0
0
2
0
1
0
0
0
2
0
0
2
1
0
0
2
2
1
0
0
1
2
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
4
0
0
0
2
0
0
1
2
1
0
2
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
1
3
0
1
2
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
2
1
3
0
0
2
1
2
0
1
0
2
0
0
0
0
0
1
0
0
0
1
2
0
0
1
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
2
1
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
1
2
1
0
0
0
2
0
0
0
0
0
1
1
0
0
2
0
0
0
0
1
0
0
1
0
0
1
0
0
1
2
0
2
0
2
0
0
2
0
1
0
1
0
1
0
2
1
1
2
0
0
0
0
2
0
0
3
0
0
1
1
0
1
1
2
1
0
0
0
1
0
1
1
0
2
0
0
0
0
3
0
0
1
2
2
2
1
2
0
0
0
2
2
0
1
1
2
0
0
2
2
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
2
1
2
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
1
1
3
0
0
1
0
2
0
0
1
0
2
0
0
5
2
0
0
0
1
0
2
1
0
1
0
2
0
0
2
1
2
0
0
0
3
2
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
2
1
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
2
1
0
3
0
0
0
0
0
1
1
0
0
2
1
0
1
0
0
0
2
0
2
2
0
2
0
0
0
1
0
2
1
0
2
1
0
0
2
1
0
0
1
2
2
0
0
2
1
0
1
2
0
0
0
1
0
1
0
0
0
1
0
0
1
0
2
2
0
2
1
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
2
0
3
1
2
0
1
0
1
1
2
2
0
2
0
2
1
0
2
0
0
2
0
0
2
1
0
1
0
0
2
0
1
2
0
0
0
1
2
0
0
0
0
0
1
0
0
2
1
0
0
1
2
1
1
0
0
1
0
1
0
3
0
0
0
0
0
3
2
2
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
2
1
1
0
2
0
0
1
2
1
0
0
0
1
2
2
0
2
2
1
1
0
0
0
2
2
0
0
1
0
0
0
0
2
0
0
1
0
0
0
1
1
0
0
1
2
0
0
1
0
0
0
0
1
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
2
0
1
0
2
0
2
2
2
4
0
1
0
0
1
0
0
1
1
2
2
0
0
1
0
0
2
0
0
0
0
1
1
0
2
0
0
1
0
0
2
0
2
0
0
0
0
2
0
1
1
0
2
1
0
0
0
0
1
2
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
2
2
0
0
1
1
0
0
3
0
0
0
0
0
3
0
1
2
1
0
0
0
2
1
0
0
0
2
0
1
0
0
0
0
1
0
1
0
0
2
0
0
2
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
2
0
1
2
1
0
0
0
1
2
0
0
0
2
0
0
3
0
1
0
2
2
2
0
0
1
2
0
1
0
0
0
0
0
0
1
0
0
0
2
0
1
2
2
0
0
2
1
1
0
2
1
1
1
1
0
0
0
0
0
1
0
0
1
2
0
1
0
1
0
1
1
0
1
0
1
0
1
1
1
0
0
2
2
0
0
0
1
0
1
0
0
2
0
0
2
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
2
0
0
0
2
1
0
0
1
0
0
0
2
6
0
1
0
2
1
0
0
1
0
0
2
0
0
0
0
0
0
0
2
1
0
0
2
0
1
2
0
1
0
2
1
1
0
0
1
0
0
0
1
2
2
2
2
0
0
2
0
2
1
0
0
0
0
1
0
0
1
0
1
0
2
0
0
0
2
1
1
0
2
2
2
0
0
1
1
0
0
2
0
0
1
2
0
2
0
0
0
0
0
0
1
2
0
2
0
2
1
2
2
1
0
0
2
2
0
0
0
0
0
0
1
0
0
0
2
1
2
0
1
0
0
0
0
2
0
1
2
0
1
1
0
0
0
1
0
1
0
1
2
2
0
0
0
0
0
2
0
0
1
2
0
0
0
0
1
3
2
2
0
1
0
0
2
0
2
1
0
1
0
2
0
1
0
0
1
0
2
3
0
2
0
0
0
0
2
0
0
2
2
2
2
0
1
2
1
0
1
0
1
0
0
1
0
0
2
1
0
2
1
2
0
1
1
0
0
1
1
0
0
0
1
0
1
0
0
1
0
1
0
1
0
0
1
1
2
0
1
0
0
1
0
0
0
1
0
0
2
0
0
1
0
0
2
1
0
0
1
0
0
0
0
1
1
0
2
2
0
0
0
2
2
0
0
1
2
0
2
1
1
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
2
0
3
0
1
0
4
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
2
0
0
2
2
1
0
0
0
1
1
0
0
0
0
1
2
0
2
1
0
2
1
0
1
0
0
0
0
2
1
0
0
1
1
0
2
1
0
2
0
0
0
0
1
2
0
2
0
0
0
2
0
0
3
0
2
1
1
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
1
0
1
0
2
0
2
0
0
0
0
0
1
6
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
2
2
0
0
0
1
1
2
2
0
0
1
0
0
0
2
0
2
0
0
0
0
0
1
1
1
0
5
0
2
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
2
0
2
0
2
0
0
0
0
2
0
0
0
1
1
0
1
0
2
0
2
1
0
2
1
0
0
2
1
2
0
2
0
0
0
0
2
0
0
0
0
2
0
0
2
2
2
2
2
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
1
1
1
0
2
0
2
1
0
0
0
0
0
1
1
0
0
0
0
1
1
1
0
1
0
0
0
0
0
2
0
1
0
0
3
0
1
2
0
0
0
0
0
0
1
0
2
1
1
0
0
2
2
0
1
0
1
1
1
0
0
0
0
0
1
4
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
1
1
0
0
0
1
0
0
1
1
1
1
0
1
0
0
0
0
0
0
0
0
3
3
2
1
0
2
0
1
0
1
2
0
1
2
2
0
0
1
0
0
0
2
0
0
2
3
0
0
0
0
1
0
1
0
0
0
1
0
2
0
1
2
0
0
2
0
0
2
0
0
0
0
0
1
1
0
0
3
1
1
2
0
0
0
0
0
0
1
0
2
3
1
1
0
1
0
2
0
0
0
1
0
2
0
2
0
0
2
0
2
0
1
2
1
0
0
1
0
2
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
1
1
2
1
0
0
2
0
2
0
2
0
0
0
0
0
0
1
0
0
3
1
1
0
0
0
3
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
1
1
2
0
0
0
0
2
2
2
0
1
1
0
0
0
1
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
2
0
1
0
0
2
0
2
1
0
1
0
0
0
1
2
0
0
4
0
0
2
0
2
0
0
0
1
2
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
2
0
2
1
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
2
1
3
1
1
0
2
0
0
0
4
2
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
2
1
0
0
1
0
0
0
0
1
0
2
0
0
1
0
0
0
1
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
2
0
2
0
1
0
0
2
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
2
2
1
0
1
0
1
0
1
0
0
2
0
1
1
1
0
2
0
2
0
0
2
0
0
0
1
1
0
0
0
0
0
0
2
2
0
1
0
0
2
0
3
0
0
0
0
0
0
2
0
0
0
1
0
0
2
3
0
0
2
0
0
0
0
0
2
0
2
1
0
2
0
0
2
0
2
0
0
2
0
2
1
0
0
1
0
2
2
0
1
1
0
0
2
1
2
0
2
1
0
0
0
0
0
1
0
0
0
0
1
2
1
2
0
0
1
0
0
2
0
2
0
0
0
1
2
0
2
1
0
0
0
0
0
1
0
2
1
2
0
1
1
0
0
0
1
0
0
0
1
0
1
2
0
0
2
2
0
1
2
0
1
0
1
0
2
0
1
0
0
0
0
2
4
0
0
0
1
0
0
0
1
0
2
0
2
2
2
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
2
0
0
1
0
0
1
0
0
1
0
0
1
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
1
0
0
0
0
1
0
0
2
0
1
2
2
2
2
0
1
0
0
0
1
0
0
0
0
1
0
2
1
0
0
0
0
2
0
0
0
3
0
2
2
0
0
0
0
2
2
0
0
0
0
2
1
2
0
1
0
2
0
1
0
1
0
1
2
1
2
0
1
0
2
1
0
0
0
0
2
0
1
2
2
0
1
0
0
0
1
1
0
1
2
1
0
1
2
4
0
3
0
0
2
2
0
0
2
0
1
2
0
2
0
1
0
0
0
0
2
7
0
0
0
1
2
1
2
2
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
3
2
2
2
0
0
2
0
0
1
0
0
2
0
1
1
2
0
0
1
0
0
2
1
2
2
0
2
0
1
0
2
0
1
0
0
1
0
0
3
0
0
0
2
2
0
0
0
0
1
2
1
0
0
2
0
0
0
2
0
1
0
0
2
2
2
0
0
2
0
0
0
0
2
0
0
1
0
0
0
1
0
2
2
0
1
0
0
0
0
2
1
0
1
0
0
0
0
2
0
2
3
1
1
0
0
0
0
2
0
2
0
1
0
2
0
2
0
0
0
2
0
0
2
1
0
2
0
1
2
1
0
1
1
0
0
0
0
2
0
1
3
0
2
1
1
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
1
1
0
2
0
0
1
1
0
0
2
0
2
0
0
1
0
0
1
0
0
0
0
2
1
0
0
1
0
0
1
1
0
0
1
0
3
0
0
3
1
2
1
0
0
0
2
0
1
0
1
0
0
2
1
0
2
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
2
2
0
0
0
0
0
2
1
1
0
0
0
0
1
0
0
3
0
2
0
1
1
2
1
1
0
0
0
1
1
0
2
0
0
0
1
1
0
0
2
0
0
0
0
0
1
0
0
0
1
2
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
1
1
1
0
2
1
2
0
0
3
0
2
0
0
0
5
1
0
2
0
3
0
3
0
3
2
2
0
0
1
0
0
2
0
1
0
1
0
0
1
0
1
0
1
0
0
0
1
1
0
0
6
2
2
1
0
0
1
2
0
2
2
0
1
1
0
1
2
1
1
0
0
0
0
0
0
1
0
2
0
0
2
1
2
2
0
1
0
0
0
0
0
0
1
1
2
0
0
0
2
0
0
0
0
0
0
1
2
0
0
1
0
0
0
2
2
3
2
0
0
0
2
0
1
0
1
2
0
0
0
2
0
0
0
0
0
0
2
0
0
2
1
0
1
0
1
0
0
0
0
2
2
0
3
0
0
0
1
0
0
0
2
4
1
0
0
3
0
0
2
1
0
2
2
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
2
0
0
2
2
2
2
1
0
2
0
1
0
0
0
2
2
0
1
0
1
0
1
0
0
1
0
0
2
6
2
0
2
0
1
0
0
1
1
0
1
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
2
0
1
0
0
0
0
0
1
0
1
0
0
0
0
2
1
2
0
0
0
1
2
1
0
0
0
0
2
0
2
0
0
2
2
2
0
1
0
1
1
0
0
0
1
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
2
0
1
1
1
2
1
0
3
2
0
0
0
1
1
1
0
2
1
0
2
0
1
0
1
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
1
0
1
0
0
2
1
1
2
0
0
0
0
0
0
0
0
0
0
2
1
0
1
2
3
1
0
0
2
0
2
0
2
0
1
1
0
1
1
0
0
2
0
0
2
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
1
0
2
1
0
1
0
0
1
1
0
2
0
0
0
0
1
0
1
1
0
0
2
0
2
0
0
0
0
0
0
2
0
3
0
0
0
1
0
0
1
0
2
0
2
0
2
0
0
0
2
1
0
0
1
2
2
0
2
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
3
0
0
0
2
0
1
0
2
0
0
1
0
0
0
2
2
2
0
0
0
2
0
0
0
2
0
1
1
0
0
1
3
2
0
0
0
0
0
2
0
3
1
0
0
0
1
1
1
0
0
2
0
0
0
2
0
1
1
1
0
0
0
2
0
0
0
2
0
0
0
4
0
0
1
1
2
2
0
2
2
2
0
0
0
0
0
0
2
0
1
0
0
2
0
2
0
0
0
0
1
1
0
0
2
0
1
2
0
1
3
0
2
1
1
0
0
1
3
0
0
2
0
2
2
0
0
0
0
0
1
1
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
3
0
0
0
0
0
1
0
3
0
0
1
1
0
0
1
1
0
0
1
1
2
0
2
0
2
2
1
0
2
0
0
1
0
0
2
1
2
1
0
2
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
2
1
1
2
0
0
0
2
1
2
0
3
2
0
0
0
1
0
0
0
0
1
0
0
2
1
0
2
0
0
0
2
0
0
0
5
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
3
0
0
1
1
0
0
0
2
0
0
2
1
0
2
0
2
0
2
2
1
0
0
0
2
2
0
0
1
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
1
0
0
2
0
2
0
1
1
0
2
2
0
1
0
2
0
0
0
0
2
1
1
0
2
2
1
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
4
1
0
0
0
1
2
1
0
0
0
2
0
0
0
1
1
0
3
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
1
0
1
0
3
0
0
1
1
2
0
0
0
2
2
1
0
0
2
0
2
1
0
1
0
1
1
2
0
0
0
1
2
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
1
2
0
1
1
3
0
0
2
0
2
0
1
1
0
0
0
0
1
0
2
0
2
0
5
0
0
1
2
0
0
0
1
2
2
0
0
0
1
1
0
1
0
0
0
0
0
2
0
2
0
1
2
0
1
0
2
0
1
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
2
0
0
1
1
0
0
0
1
0
0
0
1
3
0
0
0
1
3
2
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
1
0
0
1
1
0
1
0
2
0
0
0
0
2
0
1
2
0
3
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
3
0
0
4
0
0
2
2
0
6
0
0
0
0
1
0
1
1
2
0
1
2
0
0
0
0
1
0
1
1
1
0
0
0
0
2
0
0
2
1
0
2
0
1
2
0
0
0
1
0
0
0
0
2
0
2
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
2
0
1
0
3
1
0
3
0
0
0
0
0
1
0
1
0
0
1
0
2
1
2
0
1
0
0
2
0
2
1
0
1
0
2
0
0
2
0
0
1
0
2
1
0
0
1
0
1
2
1
0
0
2
0
1
1
0
0
0
0
1
0
0
2
0
0
2
8
0
0
0
2
0
0
0
0
2
1
1
0
1
0
0
1
0
1
1
0
1
2
2
0
0
0
0
3
1
2
0
1
0
0
0
0
1
0
1
0
1
1
0
2
0
3
1
0
0
0
1
1
0
2
2
0
2
0
0
0
1
0
5
0
0
0
1
0
0
1
0
0
0
2
0
1
0
0
0
1
2
1
0
0
0
0
0
0
1
0
1
0
2
1
1
1
0
0
1
0
0
2
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
4
1
0
0
2
0
0
1
1
0
0
0
2
0
0
0
0
2
1
0
3
0
0
2
0
0
0
0
5
2
0
0
2
1
0
0
0
0
0
2
1
0
3
0
0
2
0
0
0
0
2
1
1
2
2
0
0
0
0
1
1
0
0
2
1
0
0
0
1
2
0
0
0
0
1
2
1
0
0
0
0
2
0
0
1
0
0
2
0
3
0
0
0
0
1
0
1
1
2
0
0
0
2
1
0
1
0
1
0
0
1
0
0
0
0
1
0
0
2
0
2
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
1
2
0
2
0
0
0
0
0
0
2
1
1
2
0
0
2
0
0
0
0
2
2
0
2
0
0
0
0
1
1
3
0
1
0
0
1
0
2
1
0
0
2
1
4
3
0
2
1
0
2
0
0
2
1
0
1
0
2
0
0
0
1
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
1
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
1
0
0
0
2
0
1
2
0
0
0
2
1
2
0
0
2
1
0
0
0
2
0
1
0
1
0
0
0
0
1
1
0
1
2
0
0
2
0
0
3
0
0
2
2
1
0
0
0
2
2
0
0
1
2
1
1
0
0
0
0
0
1
2
2
0
0
2
1
2
0
0
0
2
0
2
0
2
1
2
0
2
0
0
0
0
3
1
2
0
1
0
0
0
0
0
0
0
1
0
2
2
1
0
1
3
2
1
1
0
1
0
2
0
1
0
2
1
0
2
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
2
5
1
0
0
0
1
1
2
2
0
2
0
0
0
2
0
0
1
2
0
0
1
0
0
1
1
0
1
2
0
0
1
0
0
0
0
0
0
1
2
1
2
0
2
0
0
0
2
0
0
2
0
1
0
1
2
2
2
0
0
2
0
3
0
0
0
1
0
1
0
0
0
1
0
3
2
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
1
0
7
0
0
0
2
0
0
1
0
1
0
0
0
0
1
0
0
2
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
2
1
0
0
1
1
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
2
0
1
0
2
1
2
1
0
0
0
1
0
2
0
0
0
1
0
0
0
1
0
0
1
0
0
2
1
0
0
1
0
0
0
0
2
0
1
0
0
0
0
1
3
0
1
0
0
0
0
0
0
2
0
0
1
2
0
1
0
0
0
0
1
1
0
0
0
2
0
0
2
2
0
1
1
0
0
1
0
0
2
0
0
0
0
0
0
1
0
2
0
1
0
2
0
0
0
0
0
0
0
0
1
0
1
0
2
0
2
2
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
2
2
0
0
0
0
0
2
0
2
1
0
0
0
1
0
2
2
0
0
1
2
2
1
0
1
5
0
0
1
2
0
0
0
0
2
0
0
1
0
0
1
1
0
1
0
0
0
0
3
1
1
0
1
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
1
0
0
1
0
0
2
1
2
2
1
1
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
1
0
2
1
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
2
10
0
0
0
4
0
1
2
0
2
0
0
0
2
0
0
1
0
0
2
2
0
0
2
0
0
2
1
0
0
0
1
0
0
0
2
0
0
2
0
0
1
0
0
2
2
0
0
0
0
2
0
0
0
0
1
1
0
0
2
0
1
1
1
0
2
0
2
0
2
0
2
0
0
1
2
0
1
1
1
0
0
0
2
0
0
0
0
1
0
2
0
1
2
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
1
0
1
0
0
1
0
1
0
2
0
2
0
1
0
0
0
0
0
2
1
0
0
2
0
1
0
0
0
0
2
2
0
0
0
2
0
0
3
0
0
2
0
0
0
0
0
1
0
3
2
0
1
0
2
1
0
0
0
0
0
1
0
2
0
2
0
0
0
0
2
1
1
2
0
6
0
2
0
2
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
2
0
1
0
8
1
0
0
0
0
2
0
0
0
3
0
2
0
0
2
0
0
0
1
2
0
1
2
1
0
2
0
0
1
0
0
2
2
0
1
0
1
2
0
0
0
1
0
0
0
0
0
1
0
3
0
0
0
0
0
2
0
0
3
0
0
0
0
1
0
2
1
0
0
1
0
1
3
0
6
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
9
0
0
1
0
3
1
2
0
2
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
2
0
0
1
1
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
1
0
2
1
0
0
0
1
2
0
2
0
0
1
0
0
2
0
2
0
0
0
3
0
0
0
4
1
2
0
0
0
0
1
2
1
0
0
0
1
0
0
0
0
0
1
4
0
1
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
1
1
0
2
2
0
0
0
1
0
0
1
0
0
2
0
2
0
2
2
0
0
0
2
0
2
0
0
0
0
1
2
0
0
0
0
1
0
2
1
1
0
1
0
0
2
1
0
0
0
0
0
0
0
0
3
2
2
1
0
0
0
3
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
1
1
2
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
3
0
1
2
0
0
2
0
0
1
1
1
0
1
0
0
0
2
2
2
0
0
2
2
2
0
0
1
0
1
0
2
1
2
0
1
1
0
1
0
1
0
0
0
1
2
1
0
2
8
0
0
1
0
0
0
0
2
2
1
1
1
0
2
0
0
0
1
0
1
0
0
2
0
0
0
0
1
0
0
0
1
0
0
1
2
0
0
0
2
0
1
0
2
0
1
0
0
0
0
0
0
1
3
1
0
0
2
1
0
3
2
2
2
0
2
2
1
0
0
1
1
1
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
1
2
0
0
1
2
0
0
1
0
0
1
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
1
0
0
0
0
1
3
0
0
1
0
0
2
0
2
1
2
1
1
0
2
2
5
0
0
2
0
0
3
0
1
0
1
0
2
1
0
2
1
0
1
3
0
0
0
1
0
1
0
1
2
0
0
2
1
0
0
2
0
0
0
0
0
2
0
2
0
0
0
1
0
0
1
1
0
0
2
0
1
1
2
0
3
0
0
2
0
1
1
2
1
0
0
3
0
1
2
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
3
0
0
2
1
0
0
0
0
2
1
2
0
0
0
0
2
0
0
0
2
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
2
0
0
0
1
1
0
0
2
0
0
2
1
0
2
0
0
10
0
2
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
3
3
0
1
1
2
0
0
1
0
1
2
2
0
0
0
0
2
1
0
2
0
0
0
2
1
2
1
0
0
0
0
0
1
0
0
2
1
2
0
0
1
0
2
1
1
2
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
2
0
4
0
1
0
2
0
0
1
0
1
0
1
0
0
2
2
2
0
0
1
0
0
0
3
1
2
0
1
0
1
1
1
0
0
1
0
0
0
4
0
2
0
1
1
1
0
0
0
0
0
2
1
0
1
1
0
0
0
0
0
0
2
1
1
0
0
0
0
1
0
0
2
0
2
0
2
0
0
3
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
5
2
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
2
0
1
0
0
1
2
1
1
0
2
0
2
2
0
1
1
1
0
0
0
0
2
0
1
2
1
1
2
0
0
0
0
2
0
1
2
1
0
1
2
0
0
1
0
0
1
0
0
0
0
1
0
1
1
0
1
2
1
1
2
0
2
0
1
0
1
1
0
1
0
0
1
0
0
0
2
0
0
0
0
2
1
2
0
2
2
0
1
1
1
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
2
1
0
0
0
0
1
0
0
1
0
2
0
0
1
0
0
1
0
0
0
0
1
1
2
0
0
0
0
0
0
1
0
1
1
0
2
0
1
2
0
0
0
1
2
1
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
2
0
0
1
1
1
0
0
1
0
0
0
2
0
0
2
0
1
0
0
0
2
1
0
0
0
1
1
0
0
0
0
3
2
0
0
0
0
0
1
0
2
0
0
0
1
2
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
2
0
2
0
1
0
1
0
0
2
0
0
2
0
2
0
0
3
0
0
0
2
2
1
1
0
2
0
0
0
0
2
1
1
1
0
0
2
2
0
0
1
1
0
1
0
0
0
0
0
1
0
1
0
0
0
2
0
0
1
0
0
0
0
1
1
1
0
2
0
0
0
0
0
0
1
0
0
2
1
1
0
0
0
0
2
1
3
0
0
1
1
2
1
1
0
0
0
0
0
0
1
2
0
1
2
0
1
1
1
0
2
2
0
0
1
1
2
1
0
1
2
0
0
0
2
0
0
1
0
0
0
2
1
1
1
0
0
0
0
2
1
0
0
1
0
0
0
2
1
0
1
0
1
1
0
0
0
0
0
2
1
2
2
0
0
2
1
0
0
1
1
0
2
0
0
2
0
0
0
2
0
1
0
1
1
1
1
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
1
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
1
0
0
0
0
0
0
1
1
0
0
0
2
0
3
0
1
3
5
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
1
1
0
1
2
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
2
0
1
0
2
0
2
0
2
0
3
0
0
0
0
1
2
0
0
1
0
0
0
2
2
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
1
1
0
1
2
0
0
3
0
2
2
3
0
2
1
0
2
1
1
1
0
1
2
0
0
0
1
0
0
0
1
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
1
0
2
2
0
0
0
0
0
0
3
0
2
0
2
0
0
0
1
0
0
0
1
2
0
0
0
1
2
0
0
1
2
0
1
0
0
0
0
0
0
1
2
2
2
1
1
0
0
2
0
3
0
1
0
0
0
0
2
1
0
0
1
1
0
0
0
3
2
0
1
0
2
1
2
0
0
1
0
0
0
2
1
2
0
0
0
1
0
0
4
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
1
2
1
0
1
2
0
0
0
0
0
0
1
0
0
0
4
1
0
2
1
2
0
2
0
0
2
0
0
1
1
3
0
0
0
0
0
1
0
0
1
2
0
0
2
1
2
2
2
1
0
0
3
0
1
0
0
0
0
1
1
0
1
0
0
2
0
1
1
2
0
0
0
0
1
0
0
2
0
1
0
0
2
0
2
0
2
1
0
0
1
0
2
0
0
0
0
0
0
2
2
0
2
1
1
1
0
0
0
0
2
2
0
0
2
0
0
1
0
0
2
0
0
0
0
2
2
0
0
1
2
0
0
0
2
2
0
0
0
0
0
0
1
0
0
2
1
3
0
0
0
0
1
1
0
0
2
0
2
1
0
1
2
0
0
2
1
0
0
4
1
1
0
1
0
0
0
0
1
0
1
1
0
0
0
0
1
0
2
2
0
0
0
1
0
0
1
0
0
2
1
0
1
0
0
0
0
0
1
2
0
0
2
0
2
0
2
1
0
2
0
1
0
2
1
2
0
1
0
0
1
0
1
2
0
0
6
0
2
0
2
0
0
1
1
0
0
0
1
0
1
2
3
0
1
0
0
0
1
0
2
1
0
1
0
0
2
0
2
0
0
0
0
2
1
1
0
0
0
0
1
0
0
0
2
1
1
3
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
2
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
2
2
0
0
2
0
3
0
0
0
0
0
0
0
0
0
1
2
2
0
2
0
0
3
2
2
0
0
0
0
0
0
2
0
4
0
0
0
0
1
2
0
2
2
0
0
0
1
0
0
0
0
2
0
1
3
0
0
0
0
5
1
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
1
0
2
0
2
0
0
2
0
2
2
0
1
1
3
3
0
1
1
0
1
2
2
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
2
1
0
1
2
2
2
0
0
1
0
1
0
0
1
0
0
0
1
2
0
2
0
0
0
0
0
0
0
1
0
2
0
1
0
1
1
0
1
0
2
0
0
0
0
1
2
1
1
0
0
0
1
3
0
1
0
0
0
0
2
0
2
1
0
2
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
1
1
1
1
2
0
2
5
0
1
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
2
3
1
0
0
1
0
0
1
1
2
2
1
0
2
0
2
2
0
0
0
0
1
0
2
1
0
0
0
1
1
0
0
3
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
4
2
0
0
0
0
0
2
1
0
1
1
0
2
2
0
0
0
2
0
1
2
1
0
0
1
0
1
2
0
0
0
1
0
2
0
1
1
0
1
2
0
0
0
0
0
0
2
0
2
0
2
1
0
2
0
0
0
0
0
2
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
1
0
0
1
2
0
2
0
0
2
0
2
0
0
2
1
0
0
0
1
0
0
0
0
1
1
0
0
1
1
0
0
1
1
0
0
4
0
2
0
0
1
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
1
0
2
0
2
2
0
0
2
2
0
0
3
2
0
1
2
1
0
0
0
0
2
0
0
2
0
2
1
0
1
0
0
0
0
2
0
0
1
0
1
0
2
0
2
0
0
2
0
0
0
0
1
1
1
2
1
0
2
0
1
0
0
0
0
1
0
0
1
1
0
0
1
1
0
2
3
1
0
1
1
0
0
0
0
0
0
0
3
1
4
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
1
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
1
1
2
1
2
0
2
4
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
2
0
0
2
2
2
0
0
1
0
12
0
2
0
1
0
0
1
0
0
2
0
0
1
1
0
2
1
1
0
2
0
0
1
0
0
1
0
1
0
0
1
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
1
0
0
2
0
2
0
0
0
2
0
1
0
0
1
1
2
1
0
0
0
1
1
0
0
0
0
0
0
1
1
2
2
0
0
0
1
1
2
2
2
1
0
1
0
0
2
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
1
0
1
3
0
1
0
1
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
1
1
1
0
0
0
0
1
1
0
2
0
0
1
0
2
0
0
1
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
1
0
2
1
0
0
0
1
1
1
2
4
2
0
2
0
0
0
2
1
1
0
0
1
2
1
0
0
0
0
1
0
2
0
1
1
0
0
0
2
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
2
0
0
0
1
0
1
0
0
1
1
2
0
1
1
1
1
2
0
0
1
0
0
1
1
2
0
1
0
0
1
0
1
1
2
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
2
0
0
1
2
0
0
0
0
0
1
1
0
0
0
2
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
4
2
2
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
1
0
2
0
0
0
2
1
0
0
0
0
0
0
0
2
0
1
1
0
0
1
1
0
0
0
2
1
2
0
0
1
0
0
2
1
0
0
1
1
0
1
0
0
0
2
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
2
2
1
0
1
0
0
0
1
0
0
0
0
0
0
2
0
2
0
2
0
0
1
0
0
0
1
0
0
0
1
0
0
2
0
3
0
0
1
0
0
2
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
1
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
2
0
0
1
0
2
1
0
1
0
1
2
3
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
1
0
2
0
0
0
0
0
0
0
0
2
1
1
2
0
0
3
0
0
0
1
0
1
0
2
2
0
0
0
0
0
0
1
2
2
1
0
1
2
1
0
1
0
0
2
0
0
0
0
0
0
1
2
0
1
1
1
0
2
1
1
1
0
0
0
2
0
0
2
0
0
0
2
1
1
0
0
0
0
0
1
3
1
0
0
1
0
0
0
0
2
0
0
0
0
2
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
1
1
0
0
1
0
0
0
0
1
1
0
0
0
2
0
1
0
2
0
3
0
0
0
2
0
0
0
12
0
0
0
0
0
3
0
0
0
0
1
0
0
0
2
0
0
1
1
2
0
1
0
0
1
1
0
3
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
2
1
3
0
2
1
1
2
0
0
0
1
1
1
2
0
0
0
0
1
0
2
0
1
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
2
0
1
2
1
1
0
0
0
0
6
0
0
0
0
1
2
1
1
0
0
2
0
0
0
0
0
1
2
1
2
1
2
2
0
3
0
3
0
0
0
0
0
0
0
0
2
1
1
0
1
0
2
0
0
2
0
0
2
0
2
0
2
0
1
0
0
1
1
0
0
0
0
1
0
0
0
2
1
1
0
0
2
0
0
1
9
0
1
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
1
1
2
0
0
1
0
0
5
0
0
0
2
1
0
0
2
0
1
2
0
0
3
0
1
0
0
2
2
0
0
0
1
1
2
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
2
0
0
1
0
2
0
2
0
2
0
2
0
0
0
5
1
1
0
2
0
0
0
1
0
1
0
2
1
0
1
0
0
3
0
0
0
0
1
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
1
1
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
1
0
1
0
0
1
2
0
1
0
0
0
0
0
0
0
0
1
1
0
0
2
2
0
0
0
1
1
2
0
2
0
1
0
2
0
0
2
0
2
1
1
1
0
1
1
0
2
1
0
0
0
0
2
0
0
0
0
2
0
2
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
2
1
0
1
0
1
2
0
0
0
1
2
2
1
3
0
1
0
2
0
2
0
2
1
0
1
0
0
0
1
0
0
0
2
0
0
2
0
2
1
1
1
0
0
1
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
1
0
0
0
2
0
0
0
0
2
2
0
2
0
0
2
0
0
0
0
0
1
1
0
0
2
1
1
1
0
0
4
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
2
4
0
0
2
0
3
0
0
3
0
0
2
2
1
0
0
2
1
1
0
0
0
0
1
0
1
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
2
2
0
1
0
1
0
0
2
1
2
1
0
0
0
1
0
0
0
2
2
0
0
0
2
1
3
0
0
2
2
1
0
0
1
0
0
2
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
4
0
2
0
3
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
1
2
0
1
1
2
0
0
0
1
0
0
0
1
0
0
0
2
0
4
0
1
2
0
2
2
0
0
0
2
0
1
0
0
0
0
1
1
0
2
0
1
1
0
0
1
2
0
0
2
0
0
0
1
0
0
0
0
0
2
1
0
0
0
1
0
4
0
0
2
0
2
1
1
0
0
0
0
1
0
1
0
2
0
2
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
1
0
2
1
1
0
0
0
1
0
0
0
0
1
1
0
0
0
1
1
0
0
2
1
0
0
0
0
2
0
0
1
0
0
1
0
0
0
1
1
1
0
1
0
0
0
0
1
0
0
1
0
1
2
0
0
1
2
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
1
0
2
0
0
0
1
0
1
0
0
1
0
2
3
0
1
2
2
2
0
2
1
1
0
0
2
0
0
0
1
0
0
1
0
0
2
0
1
0
1
0
0
0
0
2
0
0
0
3
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
3
0
2
1
0
2
0
0
1
0
1
1
1
1
0
2
0
2
0
1
1
1
3
1
0
1
0
0
0
0
0
0
1
2
0
1
0
1
1
0
0
2
0
0
1
2
0
0
1
2
0
1
0
2
2
0
0
0
0
0
0
2
0
1
2
1
0
0
0
0
1
0
1
2
2
1
0
2
1
1
2
1
1
0
1
1
0
0
0
0
0
0
2
2
2
2
1
0
1
0
2
0
0
1
2
0
3
0
0
0
0
0
0
1
0
1
0
0
3
1
1
0
0
0
2
0
2
0
0
0
2
2
0
0
2
0
0
0
0
0
1
0
2
2
1
0
0
0
0
1
0
0
0
0
2
2
0
1
0
0
2
0
1
0
0
2
0
2
0
1
2
0
1
1
0
0
2
0
0
0
0
1
3
1
2
2
4
0
0
2
3
0
0
0
1
0
1
2
0
1
2
0
2
0
0
0
1
2
0
0
0
1
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
1
1
2
0
0
0
1
1
1
1
2
0
0
1
0
1
0
0
1
0
2
0
0
0
0
1
2
0
1
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
1
0
1
2
1
2
0
0
0
1
0
0
0
0
0
2
3
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
5
0
0
0
0
1
2
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
2
2
0
0
0
2
0
0
2
0
0
0
2
0
2
0
0
1
1
2
0
0
2
0
1
1
1
0
1
0
0
0
1
0
0
0
3
0
2
0
0
0
1
2
4
1
5
1
0
0
0
2
2
0
0
0
1
0
0
2
0
0
1
1
0
1
1
0
0
2
0
0
1
2
1
0
0
0
0
1
0
2
1
2
2
1
0
2
0
0
0
0
0
1
0
1
1
3
1
1
0
2
0
2
0
2
0
0
0
1
1
1
0
0
1
0
0
0
1
1
0
0
1
0
0
3
0
0
0
1
2
2
1
3
0
1
1
1
0
1
0
0
1
2
0
0
0
2
2
1
1
0
0
2
0
0
0
0
0
2
0
2
0
1
1
1
0
0
0
0
0
1
1
0
0
0
2
1
0
0
2
0
1
0
1
0
1
0
1
1
1
1
0
0
2
1
0
0
1
0
0
0
1
0
2
0
0
0
2
0
1
2
0
1
2
1
0
0
0
0
1
1
2
0
0
2
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
2
2
0
2
0
1
1
0
0
2
0
0
0
1
2
0
0
1
0
0
1
2
0
0
0
0
1
2
1
1
1
0
0
0
2
2
0
7
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
1
0
2
0
0
2
0
0
1
0
1
1
0
0
0
1
2
0
2
1
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
2
2
0
0
2
0
2
3
2
0
0
0
1
1
1
0
2
0
0
0
0
1
1
0
0
3
0
0
1
0
2
1
1
0
2
0
0
0
0
0
1
0
0
1
2
0
2
0
0
0
2
0
0
1
0
0
0
0
1
0
1
1
0
0
1
0
0
2
2
0
0
0
0
0
0
2
0
1
0
2
0
1
2
0
0
0
0
2
0
0
1
0
2
0
2
2
1
1
2
2
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
2
0
0
1
2
0
0
3
1
0
0
2
0
0
7
2
0
2
0
2
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
1
2
2
0
0
1
0
0
6
0
0
1
0
0
2
1
0
0
0
2
0
0
0
1
0
1
1
0
2
2
2
1
0
1
2
2
0
2
0
1
1
1
1
0
2
0
2
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
1
0
0
0
1
0
2
0
1
0
0
2
0
1
2
2
0
0
1
0
0
0
0
0
2
2
0
1
0
1
0
0
1
0
2
1
0
0
1
1
2
0
1
0
1
2
0
1
0
0
1
0
0
1
0
0
0
2
1
1
0
1
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
2
0
1
0
1
0
2
1
1
0
0
0
1
1
2
1
0
0
2
0
0
0
2
1
0
0
0
1
1
1
0
0
0
0
0
0
2
1
0
0
3
1
0
0
1
0
0
0
2
1
0
0
1
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
2
0
2
2
0
2
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
1
0
0
5
0
1
0
0
0
1
2
0
1
1
1
0
1
0
1
3
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
2
0
0
0
0
2
2
2
0
1
0
0
3
0
2
0
0
0
0
4
1
0
1
0
1
2
0
0
0
2
4
1
0
2
0
1
0
0
1
0
0
0
0
0
0
1
1
1
1
1
0
0
1
2
1
0
16
0
0
1
1
0
0
0
0
0
0
0
4
0
0
2
0
2
0
0
1
0
0
0
2
2
0
2
0
0
1
1
2
0
2
0
0
0
2
0
1
0
1
1
1
1
0
0
1
0
0
0
2
0
0
2
0
0
0
0
2
1
0
0
1
3
0
0
4
1
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
1
0
1
1
1
1
0
1
1
1
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
1
2
0
2
0
0
2
0
0
0
0
1
0
1
2
1
0
2
0
1
0
0
0
2
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
7
0
1
2
0
0
1
1
3
1
0
0
0
0
0
0
3
2
0
1
0
0
0
1
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
2
2
0
1
0
1
0
5
0
1
1
0
0
1
0
1
0
0
0
0
0
4
0
0
2
0
0
1
2
0
1
0
3
1
0
1
0
1
0
0
2
0
0
0
0
0
1
0
1
0
0
1
0
2
1
1
0
0
0
0
2
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
2
2
3
0
0
1
0
0
1
0
0
1
0
0
0
0
2
2
0
0
2
0
3
1
0
0
0
2
1
2
0
0
2
1
0
0
1
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
3
0
0
2
1
0
2
2
0
0
0
1
0
0
0
0
1
0
1
0
2
0
1
0
1
0
2
1
0
0
1
1
0
2
2
0
0
0
2
0
0
1
1
2
0
1
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
2
2
0
0
1
1
0
0
0
0
1
0
1
1
0
1
0
0
2
2
1
0
2
1
2
0
0
1
0
0
0
2
0
0
0
4
2
2
0
2
2
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
1
0
0
0
0
3
0
2
0
0
0
0
0
0
3
3
1
0
0
0
0
0
0
2
0
0
2
2
0
1
2
0
0
0
2
0
0
0
2
0
0
0
1
1
0
0
0
1
0
2
0
0
0
0
2
0
2
0
0
0
2
2
2
0
2
2
1
0
0
1
2
1
2
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
3
0
0
1
1
3
1
2
0
0
1
0
0
0
0
1
0
1
1
1
0
0
0
0
0
2
0
1
0
1
1
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
6
1
0
0
0
0
2
2
2
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
1
2
0
0
2
1
0
0
0
2
1
0
0
1
0
0
2
0
0
2
0
1
0
0
2
0
2
0
0
0
2
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
1
1
0
3
0
2
0
0
1
1
0
2
0
0
1
0
0
1
0
0
2
0
0
0
2
1
0
0
0
0
2
2
0
2
0
0
0
1
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
1
1
1
0
1
0
0
0
0
2
0
1
1
2
0
0
0
1
1
1
2
0
1
0
0
0
0
2
0
0
1
2
0
0
0
0
2
0
0
0
0
2
2
0
2
1
0
0
1
0
2
0
1
5
0
0
0
5
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
1
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
1
1
0
0
0
1
2
0
0
1
0
1
2
0
0
0
1
0
0
0
0
0
0
2
1
0
1
0
1
0
1
4
0
2
0
0
0
0
2
1
0
2
2
0
0
0
3
0
0
1
0
1
0
0
0
0
0
0
2
0
0
1
0
0
2
1
2
0
0
0
0
0
1
1
2
0
0
0
0
0
1
0
0
1
0
2
0
0
1
0
0
0
2
0
0
0
2
0
0
0
2
1
0
2
2
1
1
2
0
0
1
0
0
1
0
0
1
1
2
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
2
2
1
2
1
0
2
2
0
1
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
2
1
0
0
0
1
1
0
1
2
2
0
1
0
0
0
1
1
2
1
0
0
1
0
0
0
1
1
0
1
2
0
0
0
1
0
0
0
0
0
2
1
0
2
0
1
0
0
0
0
2
0
1
1
0
0
0
1
1
1
0
3
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
1
0
0
1
0
0
0
0
0
2
0
2
0
0
0
1
4
2
1
0
0
2
0
0
1
0
0
2
0
2
0
0
2
0
2
2
0
0
0
0
1
0
2
1
0
0
2
1
1
1
0
0
0
0
1
0
0
0
1
0
0
1
3
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
2
0
2
0
3
0
1
0
1
0
0
0
2
1
0
2
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
1
0
2
0
0
0
1
0
0
1
0
0
0
2
0
0
1
0
1
2
0
2
0
0
2
1
0
0
1
0
0
0
2
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
1
0
1
0
0
0
2
0
0
1
1
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
2
2
0
0
0
1
0
3
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
3
0
2
1
1
2
0
1
2
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
1
2
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
1
0
1
0
0
1
2
2
2
0
1
0
1
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
6
2
0
0
0
1
0
0
0
2
2
0
1
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
3
0
1
0
1
0
0
0
1
0
1
1
1
0
0
0
0
1
0
0
0
0
1
1
0
1
0
2
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
1
2
2
3
2
1
0
0
0
1
0
0
0
1
0
0
2
0
1
1
1
0
2
0
1
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
1
1
2
0
1
0
2
0
2
0
0
0
0
2
0
2
1
1
2
2
0
1
2
0
2
0
0
0
0
0
0
1
1
0
1
2
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
1
0
0
2
0
2
0
2
0
0
0
1
0
1
0
0
2
0
0
0
2
0
0
0
1
1
1
0
2
1
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
3
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
1
1
1
0
2
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
2
2
1
0
0
1
1
0
0
0
1
3
0
0
0
1
0
3
0
0
2
0
0
1
1
0
0
0
0
1
0
0
0
0
0
2
2
0
0
2
2
2
2
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
3
3
0
0
1
1
0
2
0
0
1
2
0
0
1
0
0
1
0
2
0
1
0
1
2
1
0
3
1
0
0
0
2
1
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
1
1
0
2
0
1
2
0
0
0
0
1
1
2
1
0
1
2
0
0
2
2
1
0
1
2
0
0
2
0
0
0
1
0
0
1
0
1
0
1
1
0
2
0
0
0
1
1
1
0
1
0
1
2
1
0
1
0
0
1
0
1
0
2
0
0
0
0
0
1
0
0
2
2
1
0
0
1
0
2
0
0
0
0
0
2
0
0
0
1
1
6
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
1
2
1
0
0
0
0
0
0
0
2
1
0
1
0
1
3
0
2
0
2
0
0
0
3
0
1
0
0
0
0
0
0
1
0
1
0
0
0
2
1
0
2
0
3
1
0
2
1
0
0
2
0
4
1
0
1
0
2
0
1
1
3
2
2
0
1
1
0
0
0
2
2
0
0
0
0
2
0
1
0
2
0
0
0
1
0
1
1
0
2
2
2
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
1
3
0
0
0
0
3
1
2
1
0
2
2
0
0
1
2
0
0
0
0
1
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
1
1
2
0
5
0
1
1
2
0
0
0
1
2
0
1
0
0
0
3
0
0
0
1
1
0
0
2
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
1
0
1
0
2
0
2
0
0
2
2
0
0
1
4
0
2
0
0
0
0
1
2
1
0
3
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
2
0
0
0
0
1
0
1
1
1
0
0
0
0
2
0
0
2
2
0
1
0
2
0
0
0
1
2
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
1
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
1
0
4
0
0
0
0
6
1
1
1
0
1
0
0
2
0
0
0
0
3
2
0
1
2
2
0
0
2
0
0
0
1
0
2
1
0
1
2
0
0
1
0
2
0
1
0
0
0
0
2
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
2
1
0
0
4
1
0
0
2
2
1
0
2
1
1
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
2
1
0
2
1
0
2
0
0
0
0
1
0
0
2
2
0
0
1
0
1
2
1
0
0
0
4
0
1
1
2
0
2
2
1
0
0
0
0
0
0
0
0
0
2
2
1
1
0
0
0
1
2
2
0
0
1
2
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
2
0
0
2
1
1
1
1
0
0
0
0
2
0
0
2
0
0
0
0
1
2
0
2
0
3
0
0
1
0
2
0
1
0
0
0
1
0
2
1
0
2
1
0
1
0
2
1
0
0
0
0
1
0
2
3
0
1
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
2
0
1
0
1
0
1
0
5
0
2
1
2
0
1
0
0
0
2
1
0
2
2
1
0
0
2
0
1
0
0
2
0
0
0
1
0
2
0
0
2
1
0
1
1
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
2
1
0
2
0
0
0
2
2
2
1
0
0
0
0
0
0
2
0
0
1
1
0
0
1
0
2
0
0
1
1
0
0
0
2
1
0
3
3
2
1
1
2
3
0
0
2
0
2
2
1
2
0
0
2
0
1
1
2
0
0
0
0
3
0
0
2
0
1
0
1
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
2
0
0
1
0
1
1
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
3
0
2
0
0
0
0
1
7
2
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
2
1
1
2
1
0
0
0
1
1
0
0
2
0
0
1
0
0
0
1
0
2
0
1
0
2
0
2
0
1
1
0
2
0
0
2
0
2
0
2
2
0
0
0
1
2
2
1
2
0
0
1
0
0
0
0
2
0
4
1
0
1
0
0
0
0
0
1
0
5
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
3
2
0
1
1
0
2
0
1
1
0
0
0
0
0
0
1
1
0
0
2
0
0
0
1
1
2
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
1
0
0
0
1
0
2
0
0
0
0
2
0
1
0
2
0
0
1
0
0
2
0
0
0
0
0
1
1
0
0
1
2
4
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
1
0
2
2
0
0
0
0
0
1
2
0
0
0
0
0
2
0
1
0
0
1
1
0
0
1
1
1
0
0
0
1
0
0
2
2
2
1
0
0
2
2
0
2
1
0
2
0
2
2
1
0
0
0
1
0
0
0
1
0
3
0
0
2
3
0
0
0
0
1
2
0
2
1
0
0
1
0
0
0
1
1
0
2
1
1
1
0
1
0
2
0
1
2
2
0
2
1
0
1
2
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
2
0
2
1
2
0
2
0
2
1
1
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
1
0
0
2
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
2
1
3
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
1
0
1
1
0
2
0
0
0
2
2
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
2
2
0
0
2
0
1
2
1
0
0
0
2
1
0
2
0
0
0
2
0
0
0
2
0
1
0
2
1
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
1
4
1
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
1
1
1
1
2
0
0
1
0
0
0
2
0
0
2
2
0
2
0
0
1
0
0
0
0
0
0
2
2
1
2
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
2
0
0
0
1
2
0
2
0
0
0
0
0
2
1
0
2
0
1
2
0
0
0
1
0
1
1
0
2
0
1
2
0
0
3
0
1
0
0
0
2
1
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
2
0
1
0
0
1
0
1
0
0
0
1
0
0
0
1
1
2
0
0
2
0
0
0
2
0
2
0
0
0
0
2
1
2
2
1
0
0
1
0
0
0
1
3
0
2
2
0
2
1
0
0
0
3
1
0
0
0
0
0
0
0
1
0
2
1
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
2
0
2
0
2
2
1
0
2
0
0
2
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
1
0
2
0
0
1
1
1
1
0
0
0
2
0
0
1
0
0
0
2
2
1
2
0
0
2
0
0
0
0
0
2
0
0
1
1
1
1
0
0
1
0
0
0
0
0
1
1
0
2
2
0
0
1
1
0
2
2
0
0
0
0
0
0
1
5
0
0
2
2
0
2
1
1
2
0
2
0
0
0
1
0
0
0
3
0
0
0
0
0
1
0
2
0
1
0
4
2
2
3
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
1
0
1
0
0
0
0
2
0
0
1
1
1
0
0
0
0
0
0
0
0
4
1
1
0
0
1
2
1
1
0
0
0
0
0
1
2
0
0
0
0
0
3
0
0
1
2
0
0
2
0
0
2
0
0
0
0
2
0
1
0
0
0
0
1
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
2
1
2
0
0
2
0
0
0
0
0
3
0
2
0
0
1
1
2
3
0
0
0
1
2
0
0
2
0
0
0
0
1
1
1
1
1
0
0
2
2
2
0
0
1
0
2
0
2
0
0
2
0
1
0
0
0
0
1
0
2
0
0
0
0
2
1
0
2
0
0
2
1
1
2
1
0
0
0
0
0
1
0
0
0
2
2
0
2
0
0
0
2
0
1
0
1
0
2
0
0
0
2
0
0
1
0
4
1
0
2
2
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
1
1
0
0
1
1
2
0
0
0
0
0
0
1
0
3
2
1
2
2
2
0
2
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
1
0
2
0
0
0
0
2
0
1
1
0
0
2
0
0
0
0
0
0
2
2
1
0
0
0
1
0
2
0
0
0
0
0
0
1
1
2
0
1
0
0
0
0
0
2
0
0
0
2
1
1
1
1
1
0
0
0
1
2
0
1
0
0
0
0
5
2
0
1
0
0
0
0
0
3
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
2
1
0
0
0
2
0
1
0
2
0
2
0
0
2
2
0
1
0
0
0
2
0
0
0
0
2
1
5
0
0
0
1
1
0
1
0
0
0
2
1
3
0
1
0
1
0
0
2
0
2
4
1
2
2
1
0
0
0
0
0
1
0
2
1
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
2
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
1
2
1
0
0
0
0
0
1
1
0
2
2
0
1
1
0
2
1
0
0
0
0
1
2
0
2
1
1
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
1
1
0
0
0
2
0
1
0
2
1
0
1
0
0
1
0
2
0
2
0
0
0
2
0
1
0
0
0
2
0
1
0
1
0
0
1
0
0
0
5
1
0
0
0
0
0
0
0
0
2
0
1
0
1
1
0
0
2
0
0
0
0
1
0
0
0
0
2
2
1
0
2
2
0
0
0
1
0
2
2
1
2
2
0
2
0
0
1
0
1
0
0
0
0
3
1
0
0
3
1
2
0
0
0
0
0
1
0
0
1
1
2
1
2
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
1
1
0
2
0
0
1
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
2
0
0
1
1
0
0
0
0
1
1
2
0
2
0
0
0
1
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
2
0
2
1
1
0
0
2
0
1
0
0
2
0
0
0
0
0
2
2
1
0
2
0
2
2
2
1
1
1
0
0
0
0
0
1
0
0
0
2
1
0
1
0
1
2
0
0
2
2
0
2
0
0
1
0
2
2
1
2
2
0
0
2
2
0
1
0
0
0
0
0
0
0
0
2
0
2
1
1
0
2
0
0
1
0
0
0
0
0
2
0
2
4
0
1
1
1
0
1
0
0
2
2
0
0
1
0
0
0
2
0
0
1
0
0
3
1
2
0
1
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
1
2
0
2
2
0
0
2
0
0
2
1
0
2
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
1
1
0
0
0
2
1
0
0
0
2
1
0
0
2
0
0
1
2
0
0
0
2
2
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
2
2
1
0
2
0
0
0
1
0
0
1
0
0
0
0
0
3
2
1
2
2
2
0
0
0
0
1
0
0
0
1
0
1
1
0
0
2
0
1
2
0
0
0
1
0
0
1
0
1
1
0
1
1
0
0
0
2
1
0
0
1
0
0
0
3
2
0
0
0
0
1
0
0
0
0
1
0
2
1
1
0
1
1
0
2
0
2
2
0
0
1
0
0
2
2
0
0
2
1
2
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
1
1
0
2
2
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
1
0
1
0
2
0
2
0
0
0
2
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
2
0
2
0
0
0
2
0
0
2
0
2
0
1
0
2
0
0
1
0
2
1
0
0
0
0
0
2
3
0
3
1
2
4
1
0
0
2
0
1
2
1
0
0
0
0
0
0
0
4
2
0
0
0
0
1
1
1
1
1
0
0
2
0
1
0
0
2
1
1
2
0
0
0
2
0
2
0
1
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
2
3
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
2
0
1
1
3
2
2
0
0
2
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
4
2
0
1
1
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
1
2
0
2
0
0
0
0
1
0
0
1
0
1
0
3
0
1
0
0
0
1
0
2
0
0
5
0
2
0
1
0
3
2
0
0
1
2
1
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
1
0
0
1
0
0
1
0
2
0
0
6
0
0
2
0
0
2
2
0
0
0
2
0
2
0
2
0
3
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
1
3
0
1
0
0
0
2
0
2
0
0
1
1
2
2
2
0
0
4
2
0
0
2
1
0
0
0
0
1
0
1
0
2
2
0
0
2
1
0
1
2
0
0
0
0
1
2
0
1
2
0
0
0
0
1
2
2
0
2
0
2
0
0
0
1
1
0
1
0
0
0
0
1
0
1
1
0
3
0
0
0
1
0
0
0
0
0
0
0
1
0
2
2
1
1
0
1
0
2
0
0
0
0
0
0
0
0
0
1
1
1
1
0
2
0
0
1
1
0
3
1
0
0
2
3
1
1
1
0
0
1
0
3
2
3
2
1
0
1
2
0
0
1
2
2
0
2
2
0
0
0
2
0
1
2
0
1
0
0
1
0
0
0
0
1
1
1
0
1
0
0
0
0
1
2
0
1
1
0
1
0
2
1
0
2
0
0
2
0
0
0
1
1
1
0
1
0
2
3
0
1
0
1
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
1
0
0
1
2
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
1
1
2
0
1
1
0
1
0
2
0
1
0
0
2
0
0
2
2
0
0
1
2
1
0
1
0
1
0
2
0
0
2
0
0
2
0
0
0
2
0
1
0
2
2
0
0
0
2
0
0
1
0
0
0
0
2
1
0
2
2
0
1
2
0
2
0
1
0
1
0
0
1
1
0
2
0
8
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
2
1
0
1
0
1
0
1
2
0
0
1
2
1
0
0
1
0
2
0
0
0
1
0
1
0
0
2
0
1
0
4
0
2
0
0
0
0
0
0
2
0
0
0
1
2
1
0
0
1
1
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
1
2
0
1
0
0
0
0
1
1
1
0
1
0
1
0
0
0
0
0
2
0
1
2
0
2
0
0
0
0
0
1
2
0
0
0
1
2
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
1
0
1
1
0
0
1
1
0
0
0
2
0
2
1
0
0
1
1
1
0
1
0
0
0
2
1
2
0
0
7
2
0
1
0
2
0
0
0
2
0
0
0
1
0
0
0
2
0
0
1
2
2
0
0
2
0
0
0
0
0
0
0
2
1
2
0
2
2
0
2
2
1
0
0
1
0
5
0
1
0
0
0
0
2
2
1
0
2
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
2
0
1
1
0
0
0
2
0
0
0
2
0
2
1
0
0
2
2
0
1
0
0
2
1
0
0
0
1
0
0
1
1
0
0
0
2
0
0
0
1
0
0
1
1
0
1
0
0
0
1
0
0
2
0
0
1
0
0
0
0
5
2
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
2
0
1
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
2
0
0
2
0
0
1
2
0
0
1
3
1
3
0
0
0
0
2
0
1
2
1
0
2
1
1
1
1
1
0
0
0
2
0
0
0
2
1
1
0
1
0
0
0
2
0
0
0
2
1
1
0
2
2
0
0
0
0
0
2
1
0
2
0
0
2
0
1
1
0
0
1
0
0
0
0
2
1
0
2
0
0
2
1
1
0
0
2
0
1
0
2
0
0
1
2
1
2
0
0
0
0
0
0
0
2
2
4
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
1
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
2
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
2
0
2
0
2
1
0
0
4
0
2
0
0
0
0
0
2
0
0
0
2
1
0
1
0
0
0
0
0
0
0
2
0
2
0
1
1
0
0
1
0
0
0
0
0
0
0
2
1
1
0
2
2
0
0
0
3
0
0
2
0
2
0
0
0
0
2
0
0
0
2
1
0
1
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
4
0
0
1
0
0
1
0
2
0
0
2
0
0
1
0
0
1
0
0
1
0
0
1
0
1
0
0
2
1
2
1
0
1
0
0
0
0
0
0
0
1
0
0
2
2
2
0
0
2
0
0
1
1
1
0
1
0
2
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
2
0
0
0
2
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
3
0
3
0
0
0
0
2
0
0
0
2
0
0
2
0
2
0
1
0
1
0
0
0
1
1
0
0
1
0
0
2
2
0
0
0
1
0
0
1
0
0
2
2
0
0
1
0
0
0
2
0
0
2
2
0
3
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
1
2
1
0
0
2
1
0
0
2
0
0
0
1
0
2
1
2
2
2
1
0
2
0
1
0
0
0
0
0
4
0
0
0
2
2
1
2
1
2
0
0
2
0
0
1
0
0
0
1
0
0
1
0
1
0
2
0
2
2
0
1
0
0
0
1
0
0
0
0
0
0
0
2
2
1
0
2
0
0
1
0
1
1
2
0
1
1
0
2
1
1
2
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
1
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
2
1
0
0
1
0
0
0
2
0
1
1
0
1
1
0
0
3
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
1
1
2
0
0
1
0
1
0
0
1
2
1
0
3
0
2
0
0
1
0
1
1
0
1
0
0
0
0
0
2
0
1
1
0
0
0
2
0
0
0
2
0
2
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
1
2
0
0
0
0
0
1
1
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
1
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
1
0
2
0
0
1
0
2
0
1
1
0
0
2
0
0
1
0
2
1
0
2
0
1
1
0
0
1
2
1
0
0
0
2
0
0
0
0
1
2
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
2
0
1
2
2
0
0
0
0
0
0
0
2
1
0
0
1
0
1
1
0
0
1
0
2
0
0
1
0
2
0
0
2
0
2
2
0
0
0
0
0
2
0
0
2
0
1
2
0
0
0
0
0
0
0
0
2
0
1
1
0
0
1
0
0
2
0
0
2
0
1
0
0
2
0
0
0
2
0
2
1
2
2
0
0
0
1
1
0
2
0
1
1
1
0
0
1
1
0
0
0
0
0
0
1
0
2
1
0
0
1
0
0
1
0
1
0
1
0
0
1
0
0
3
0
0
0
4
0
0
0
0
2
2
2
0
1
0
0
2
0
0
1
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
3
0
0
0
0
1
2
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
1
0
2
7
0
0
1
2
0
0
0
0
0
0
0
1
1
1
2
0
2
1
2
0
0
0
1
1
0
2
2
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
1
0
0
2
0
0
0
0
1
1
0
2
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
2
0
0
3
2
0
0
1
0
0
2
0
2
2
4
1
0
2
0
2
0
1
1
1
1
0
2
2
0
1
0
0
2
0
2
2
0
1
0
0
1
0
0
0
3
0
0
1
1
1
0
3
0
0
0
0
0
0
2
0
2
8
0
2
1
0
2
6
1
3
1
1
0
1
1
0
2
1
0
0
0
1
0
1
0
2
0
2
2
0
0
0
2
0
0
1
3
2
0
0
2
2
1
0
1
1
2
2
0
0
0
0
0
0
0
0
2
1
1
2
0
1
0
0
2
2
0
0
1
2
0
0
0
2
2
0
3
2
0
2
2
0
0
0
1
0
2
2
0
1
0
0
2
1
0
1
0
1
0
0
1
0
0
1
1
1
0
0
0
0
0
0
2
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
1
2
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
1
0
0
1
2
2
0
2
0
0
0
2
1
2
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
5
1
0
0
0
0
1
0
1
0
0
0
1
0
0
2
2
1
0
1
0
0
0
0
0
1
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
1
0
2
1
0
0
0
1
0
0
1
1
0
0
0
2
1
0
0
0
0
1
0
0
0
1
1
1
0
0
1
2
0
2
0
0
0
0
0
0
0
2
1
1
1
0
1
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
2
0
1
2
1
0
2
1
0
0
1
1
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
1
1
2
0
0
0
1
2
0
0
0
3
3
0
1
1
0
0
0
0
0
0
0
2
2
0
1
2
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
3
2
2
0
0
1
0
1
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
3
2
0
2
0
0
0
0
1
0
0
2
0
0
0
2
0
0
2
1
0
0
0
0
0
2
0
0
2
0
2
0
0
0
2
1
1
0
2
0
2
0
0
4
2
2
0
1
0
2
0
2
1
1
0
1
0
2
2
0
0
1
0
2
0
2
0
1
2
0
0
0
1
0
0
0
0
0
1
0
2
0
2
0
1
1
0
0
2
2
1
0
0
1
0
0
2
0
3
0
0
0
2
1
0
0
0
0
0
2
0
0
0
2
1
2
0
0
2
2
0
1
0
0
0
0
1
4
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
2
1
0
0
2
0
1
1
0
0
0
0
0
0
2
0
1
1
1
0
4
0
0
1
2
0
0
0
2
0
0
0
2
1
2
0
0
1
0
2
0
0
1
1
0
0
0
1
2
0
0
0
1
1
0
1
0
0
0
1
0
2
0
2
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
2
1
1
0
0
0
0
0
0
0
2
1
0
0
1
0
3
0
2
1
1
0
0
0
0
0
0
1
2
1
1
1
0
0
0
0
0
3
1
0
0
0
0
1
1
0
4
2
0
1
0
1
1
2
1
0
1
0
3
0
1
0
0
2
0
0
2
0
1
0
2
1
0
0
2
0
3
0
0
2
0
1
0
0
0
2
0
0
0
5
1
0
2
1
2
1
0
0
1
0
0
1
1
0
0
2
0
0
3
2
1
0
1
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
3
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
2
0
0
0
1
2
2
2
0
2
1
1
0
1
0
0
6
2
0
3
0
1
1
0
1
0
0
0
2
0
2
1
0
2
1
2
0
2
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
2
1
0
2
0
0
2
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
2
0
0
0
0
0
2
0
2
0
0
2
1
0
0
1
2
2
2
0
0
1
0
0
0
0
0
2
0
2
0
3
0
1
0
0
0
0
0
0
1
0
2
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
1
0
0
0
1
0
0
1
0
2
2
2
0
0
0
2
1
1
1
2
1
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
2
1
0
2
2
0
0
0
0
0
1
2
3
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
1
0
1
1
0
0
0
0
2
1
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
2
1
1
0
0
0
0
0
0
0
1
1
2
1
0
0
0
0
0
1
1
0
2
3
1
0
0
0
0
0
2
3
2
1
0
2
2
2
1
0
1
1
0
0
0
0
0
1
2
1
0
1
0
1
0
0
1
0
2
1
1
2
0
1
0
0
0
2
0
0
1
0
2
0
0
0
1
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
2
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
2
2
2
2
0
2
0
0
0
1
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
2
2
0
2
2
2
1
0
0
1
1
1
1
0
0
0
0
2
0
1
2
0
0
5
0
0
2
2
1
1
0
0
0
2
0
2
2
0
0
0
0
5
0
1
2
0
0
2
1
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
2
0
3
1
0
0
0
0
0
0
1
0
1
2
2
3
1
0
0
2
0
0
4
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
1
0
0
0
2
2
1
0
3
1
0
1
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
2
0
2
2
0
0
1
1
2
3
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
2
0
0
0
2
1
2
0
1
1
0
0
0
0
1
2
0
2
1
0
2
0
2
0
2
2
2
4
0
0
1
0
0
0
0
2
0
1
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
2
2
0
0
1
0
0
0
0
0
2
0
0
0
0
3
3
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
3
0
0
0
0
1
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
3
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
3
1
1
0
2
0
2
1
0
1
1
0
2
3
0
0
1
6
0
0
1
0
2
1
0
0
1
1
2
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
1
2
1
1
3
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
3
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
1
1
2
2
0
0
2
2
2
2
0
2
1
1
0
0
2
1
0
0
0
2
0
1
0
3
0
1
2
2
0
0
1
1
0
3
0
0
1
0
0
0
0
0
0
0
3
2
0
2
0
3
0
2
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
2
1
0
1
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
2
0
2
0
0
2
2
0
0
0
2
2
0
0
0
0
2
2
2
1
0
0
1
0
0
0
0
0
1
0
0
1
0
2
1
1
1
2
0
0
1
0
0
0
0
0
1
0
2
0
1
1
0
2
0
0
0
1
2
1
0
1
0
0
0
3
0
1
0
0
2
1
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
3
0
0
0
2
0
0
1
1
2
0
1
0
1
2
0
0
2
1
0
2
0
2
0
0
0
0
1
0
1
0
0
0
2
2
0
0
0
0
0
1
2
1
0
0
0
1
1
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
2
2
0
0
0
2
1
2
0
0
0
0
0
2
1
0
2
1
0
0
0
1
0
0
0
0
3
0
0
1
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
2
0
2
0
0
2
1
2
2
1
2
0
0
2
0
1
0
1
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
3
1
0
1
0
0
0
0
3
1
1
1
0
0
1
2
4
0
2
2
0
2
0
2
0
0
0
1
1
0
0
0
0
1
0
0
0
4
0
1
0
1
0
1
0
0
2
0
0
3
0
0
0
0
0
2
1
0
1
0
0
1
0
0
0
0
2
0
0
2
1
0
0
0
0
2
0
2
1
3
1
0
1
0
1
0
0
0
0
0
2
2
5
0
0
0
3
1
1
0
1
0
0
1
0
0
0
0
2
2
1
0
0
2
0
2
0
0
0
2
1
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
1
0
0
1
0
0
1
1
1
0
0
0
1
2
1
0
0
1
2
3
0
0
0
3
0
0
0
2
0
2
0
0
0
0
2
0
0
0
1
0
0
2
0
5
0
0
0
0
1
1
0
0
0
1
4
0
1
1
0
0
0
1
2
2
0
2
0
0
0
1
1
2
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
2
0
1
2
0
1
0
1
2
0
0
0
0
0
1
3
0
0
2
0
1
2
0
0
0
2
0
1
1
0
0
1
0
0
1
0
1
0
2
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
1
0
1
1
0
0
0
1
1
0
2
0
0
1
0
0
0
0
1
0
2
0
2
0
2
0
3
0
2
2
1
2
3
0
2
1
2
1
0
0
0
0
1
2
0
0
0
0
0
2
2
1
2
0
2
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
4
3
0
0
0
2
0
0
0
0
0
2
2
0
0
2
0
0
0
2
0
0
0
2
1
0
2
0
0
0
0
0
0
1
1
2
0
0
0
2
0
0
2
0
0
0
0
1
1
0
0
2
2
0
0
0
3
0
0
2
1
2
0
0
0
0
1
3
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
2
1
0
1
0
3
0
2
1
0
1
0
1
0
0
1
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
4
0
0
1
2
0
1
0
0
0
2
2
0
1
0
0
2
0
0
0
1
1
1
1
0
0
0
0
1
0
0
1
0
2
0
1
2
0
0
0
0
2
1
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
2
1
2
0
0
0
0
0
0
0
2
2
1
2
0
0
0
0
2
1
0
0
3
0
0
0
2
0
0
1
0
2
1
1
0
2
0
0
0
1
2
0
1
2
1
1
0
0
0
1
0
2
0
0
0
0
0
2
0
0
1
2
0
0
1
1
0
0
0
0
2
1
0
0
1
1
1
0
0
1
3
2
1
0
0
0
0
2
0
0
0
0
0
2
0
0
2
1
0
2
0
0
2
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
2
0
1
0
1
0
1
2
0
2
1
0
2
2
0
0
1
0
0
2
1
2
1
2
0
0
0
2
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
2
5
1
0
0
2
2
0
1
1
0
0
1
1
0
0
0
0
0
2
0
0
1
1
0
0
0
1
0
0
2
2
0
1
0
0
0
0
0
0
1
0
4
0
0
0
1
0
0
2
0
0
2
0
2
1
2
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
1
0
0
0
2
1
0
0
0
2
0
0
2
0
2
0
0
2
0
2
1
0
2
0
2
0
2
0
0
0
0
0
1
2
2
0
2
1
0
5
1
2
2
0
0
0
0
2
1
2
0
0
2
0
4
1
0
0
0
0
1
0
0
1
0
1
2
1
0
1
2
0
0
0
2
2
0
0
0
2
0
0
0
0
1
1
0
0
2
0
0
0
2
0
2
1
0
1
2
0
0
1
1
2
0
0
0
2
0
0
0
0
0
0
1
0
1
0
1
2
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
2
2
1
0
0
1
2
2
0
1
0
0
0
0
0
1
1
0
2
0
2
0
1
0
0
0
2
0
2
0
0
2
0
0
0
1
0
3
0
2
0
0
1
0
2
0
0
0
1
0
1
0
0
0
2
0
1
0
2
0
0
0
2
0
0
0
2
0
0
2
1
0
2
2
0
1
2
0
1
2
0
0
1
0
0
0
0
0
2
2
0
2
1
0
0
1
2
2
0
0
2
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
2
6
1
5
0
1
2
1
0
1
0
0
2
1
0
1
0
2
0
1
0
0
1
0
0
0
2
1
0
0
0
0
0
1
1
0
1
1
1
1
1
1
0
0
1
2
0
2
1
1
1
0
0
2
0
2
0
0
2
0
0
2
2
0
0
1
0
0
0
0
0
1
0
2
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
1
2
1
0
2
1
0
0
0
1
0
0
0
1
2
1
0
0
0
0
0
0
2
0
0
0
0
2
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
1
0
0
0
2
0
0
0
0
2
0
0
2
0
0
2
1
0
1
3
0
2
0
0
2
1
0
1
0
0
2
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
2
0
0
1
0
0
1
2
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
1
2
1
0
0
0
0
1
0
1
0
0
2
3
2
0
0
0
1
0
0
0
0
0
1
1
1
3
0
0
2
2
0
1
0
0
1
2
0
1
0
0
0
0
2
2
0
2
0
1
0
0
0
1
0
2
0
0
1
0
0
1
1
0
1
1
2
0
0
0
0
0
0
0
1
0
0
0
0
2
2
1
1
1
1
8
0
1
0
2
2
0
1
0
0
0
0
0
0
0
0
1
2
0
0
1
0
3
0
0
0
3
2
0
0
0
0
0
0
2
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
2
2
0
0
0
0
0
1
1
2
2
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
2
2
2
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
5
0
1
0
0
2
1
2
2
2
0
1
0
0
1
0
0
0
2
2
1
2
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
1
0
0
2
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
2
2
0
0
0
2
1
1
0
2
2
0
0
0
0
0
0
0
1
1
0
2
0
0
1
0
1
0
2
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
2
0
1
4
0
2
0
0
0
2
3
0
0
2
2
0
0
2
0
0
1
0
2
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
3
0
0
0
0
0
0
0
0
1
0
0
2
2
2
0
0
1
2
0
1
0
0
0
2
0
1
0
0
2
0
0
2
2
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
2
0
0
2
0
0
0
0
0
1
1
3
0
0
1
0
0
0
0
0
0
0
0
1
3
0
4
1
0
0
1
1
0
0
0
1
2
0
0
0
0
0
0
2
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
2
2
0
2
0
0
0
0
1
0
1
0
0
1
0
0
2
2
0
0
0
0
0
1
0
0
0
0
1
0
2
1
0
0
0
2
0
0
0
0
0
2
1
0
2
0
0
1
1
0
0
0
1
0
0
0
1
2
0
2
1
0
1
0
0
1
0
0
0
0
0
0
2
0
1
0
2
0
2
0
1
2
0
1
2
0
1
0
0
0
2
1
2
1
0
0
0
1
0
0
3
0
1
0
1
0
0
1
1
1
1
0
1
0
0
0
0
1
0
1
2
0
0
2
2
1
2
0
1
0
2
1
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
2
1
2
0
0
2
2
2
0
0
0
0
0
0
2
3
2
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
1
1
1
0
2
0
2
0
0
0
0
0
0
0
0
2
0
2
0
2
0
2
1
0
0
0
1
0
0
2
0
0
0
0
1
1
0
0
0
2
0
1
0
1
0
0
1
1
2
0
1
0
0
0
0
0
0
0
0
2
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
1
0
3
0
0
0
0
0
0
0
3
0
2
1
1
0
0
3
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
4
0
0
0
0
0
0
0
2
0
0
2
1
2
0
2
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
3
2
0
0
0
0
2
0
0
2
0
0
0
1
3
0
0
0
2
0
0
0
1
0
1
0
1
1
1
0
0
1
2
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
2
0
1
0
0
0
2
3
0
6
0
0
2
1
0
0
1
8
0
0
0
0
2
0
1
0
0
1
0
0
0
0
1
0
0
0
1
4
2
0
1
1
1
0
1
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
2
0
2
2
0
1
2
0
0
1
1
0
0
0
0
2
0
0
0
2
3
2
1
1
0
0
1
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
2
1
2
0
1
0
3
1
0
0
2
2
0
2
0
2
1
2
1
2
0
0
0
2
2
0
0
2
0
2
0
5
0
4
0
0
4
2
1
0
2
0
1
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
1
1
1
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
1
0
0
2
1
0
1
0
0
0
1
1
1
2
1
1
0
0
2
1
0
0
0
0
0
1
0
0
1
1
0
8
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
1
0
2
1
0
1
2
2
1
2
0
0
0
0
1
2
0
0
1
0
2
2
1
0
0
0
1
0
0
0
1
1
0
2
0
0
0
0
1
0
0
2
2
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
2
0
0
1
2
0
0
2
0
0
1
1
0
0
1
1
0
2
1
0
0
0
0
0
0
0
0
1
0
0
1
2
2
2
0
7
0
0
0
2
0
1
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
2
1
0
0
0
0
2
2
1
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
1
0
1
1
1
1
0
2
0
1
0
0
0
2
2
1
1
0
0
2
0
1
0
0
0
0
0
4
1
0
2
1
0
2
0
0
1
2
1
1
2
2
0
0
1
1
1
0
1
0
0
4
0
0
1
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
2
2
0
1
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
1
0
0
2
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
2
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
6
0
2
3
0
1
1
0
0
0
0
0
2
2
0
0
1
0
1
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
2
1
0
0
0
0
2
0
0
1
1
2
0
0
2
2
2
0
0
2
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
2
0
0
1
1
2
2
1
0
0
2
0
0
2
0
0
2
0
0
1
0
1
1
0
0
2
0
0
0
0
0
2
2
3
1
0
0
2
0
0
2
0
0
2
0
0
0
3
5
0
0
0
0
3
0
0
0
0
0
0
9
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
6
1
0
1
2
0
0
0
0
1
1
2
2
1
0
0
1
2
0
0
0
1
1
0
0
2
0
1
3
0
2
0
0
2
2
2
0
2
1
0
1
0
0
0
0
2
1
2
0
0
3
0
1
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
1
0
0
3
2
0
2
1
0
2
0
0
0
0
2
0
0
1
1
0
2
0
0
0
2
0
0
0
0
2
1
0
0
2
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
3
2
2
0
3
0
2
0
0
0
1
0
0
0
2
0
0
0
1
0
2
1
3
0
1
3
2
2
0
0
1
1
0
2
0
0
2
2
0
0
0
0
0
1
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
2
1
0
0
1
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
2
2
2
3
1
0
1
0
0
0
0
0
1
2
0
1
2
2
0
0
4
0
0
0
0
1
0
0
1
0
0
2
0
0
0
1
0
2
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
1
2
0
0
0
2
2
0
2
0
0
2
2
0
1
1
0
2
2
2
0
0
1
0
1
1
0
1
0
1
2
2
0
0
0
2
1
1
1
0
0
1
1
0
2
0
1
0
0
1
2
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
2
2
0
2
2
0
2
2
0
2
1
1
0
0
0
0
3
0
1
0
1
0
1
0
1
2
0
1
2
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
2
1
2
0
2
1
2
2
0
0
1
2
0
2
0
1
1
0
2
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
1
0
2
2
0
0
0
1
1
1
0
1
0
1
0
1
1
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
2
0
2
2
1
0
2
2
0
0
0
0
2
0
0
2
0
0
2
2
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
5
0
0
0
3
3
2
1
0
0
1
0
1
0
0
1
0
0
1
0
2
0
0
0
2
0
1
0
0
1
0
0
0
0
1
3
0
0
0
2
0
1
0
0
0
0
1
0
1
1
0
2
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
2
0
0
0
0
3
2
2
2
0
1
0
2
0
11
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
1
1
1
0
3
2
2
2
0
0
2
0
1
0
0
0
1
0
2
0
0
2
2
0
0
2
0
0
2
0
2
1
0
0
1
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
2
0
0
0
1
2
0
0
0
2
1
1
1
2
0
0
0
0
0
0
0
1
3
0
2
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
1
3
0
0
1
0
2
2
0
0
1
0
0
0
1
0
1
2
0
0
0
1
2
0
3
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
1
0
0
0
1
0
0
1
0
1
1
0
1
0
2
0
0
0
0
0
0
0
0
0
1
1
0
2
1
0
0
0
5
0
0
0
0
3
1
2
2
0
2
0
0
2
0
0
3
0
0
1
0
1
0
1
2
0
3
0
0
0
0
2
2
2
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
1
0
2
1
0
1
1
0
0
0
0
0
1
2
1
2
1
1
0
0
0
0
0
2
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
1
0
2
1
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
1
2
0
0
0
0
1
2
0
0
0
0
0
3
0
2
0
0
1
1
0
2
0
0
0
0
2
0
0
0
2
1
0
0
1
2
4
0
0
0
1
0
2
3
1
2
0
0
2
1
2
3
2
1
0
0
0
0
0
2
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
3
0
1
0
2
0
2
0
0
0
0
0
1
2
1
1
0
1
2
0
0
2
0
0
1
0
2
1
2
1
0
0
1
0
2
0
1
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
6
0
0
0
0
1
0
2
0
0
1
0
2
0
2
1
0
3
0
2
2
1
0
0
2
1
0
0
2
4
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
2
0
1
0
3
0
0
2
0
3
0
0
2
0
0
0
0
1
0
0
2
0
0
1
0
1
0
0
2
0
0
0
0
1
0
2
2
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
2
1
1
0
0
0
0
2
1
2
2
0
0
0
0
2
1
1
0
2
1
0
2
2
0
0
0
1
0
1
2
0
2
0
0
1
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
2
1
0
0
0
0
1
0
0
3
0
0
0
0
2
0
1
1
0
0
1
0
2
0
0
0
0
0
0
1
1
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
2
0
2
1
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
1
0
1
0
2
0
1
0
0
0
0
1
0
1
3
0
0
2
0
2
1
2
0
0
0
0
0
1
0
0
1
0
0
3
0
2
0
0
1
1
0
0
2
0
0
0
0
1
0
0
1
0
2
1
1
0
1
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
2
2
2
0
0
0
0
1
0
1
1
0
2
1
0
0
0
2
2
0
1
0
0
1
0
0
0
0
2
0
0
0
1
2
0
1
1
1
0
1
3
0
3
0
2
0
0
1
0
4
0
0
0
0
0
2
1
2
0
0
1
0
0
2
1
0
1
1
0
0
0
1
0
2
0
1
0
3
2
1
1
0
1
0
1
2
0
2
0
0
0
0
2
1
0
0
0
1
0
2
2
0
1
0
1
2
0
0
2
2
3
0
1
1
1
2
2
2
0
0
2
0
1
0
2
0
0
0
0
0
2
0
0
0
2
1
1
0
1
2
0
1
1
0
0
0
0
1
1
0
2
1
0
0
2
2
1
1
0
0
0
0
1
0
1
1
0
0
0
0
0
2
3
0
2
0
0
0
0
1
0
0
2
0
2
1
1
0
1
2
0
0
0
0
0
1
0
0
1
1
0
0
0
2
1
7
0
0
0
3
1
1
0
0
0
0
2
0
0
0
3
0
2
0
0
3
2
0
2
2
2
0
0
0
0
0
9
0
0
0
0
0
0
2
1
2
0
2
0
1
0
2
0
2
0
0
1
0
0
2
0
0
0
0
0
1
2
0
0
0
0
2
1
1
0
1
0
0
0
0
2
0
1
2
0
0
1
0
0
0
1
0
0
1
0
3
1
2
0
2
0
0
0
4
3
1
1
0
0
0
1
0
0
0
0
1
0
0
0
2
1
0
0
0
0
1
1
0
0
0
2
2
0
0
1
2
0
0
0
0
0
2
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
3
1
0
0
2
3
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
1
1
2
0
1
0
0
1
0
2
0
3
1
0
0
1
0
0
2
2
0
2
1
4
0
0
0
1
2
0
0
0
2
0
0
0
0
2
2
0
0
0
2
1
2
0
0
0
0
0
0
0
1
1
2
0
0
0
0
1
2
2
0
0
1
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
3
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
2
1
0
1
3
0
0
1
0
1
2
0
0
1
1
1
1
0
0
0
1
0
2
0
0
0
2
0
0
0
0
2
2
0
0
1
0
0
1
1
0
0
0
1
0
2
2
2
0
0
0
2
1
1
0
2
0
0
0
0
0
0
2
1
0
3
0
0
0
0
2
0
2
2
1
0
2
1
2
0
0
0
2
1
0
0
1
0
1
0
0
0
2
1
0
0
1
2
0
0
0
2
0
0
1
0
2
1
0
2
0
1
1
1
2
0
0
0
0
2
0
0
2
1
0
2
0
0
1
0
2
2
0
2
0
1
1
1
1
0
0
0
1
0
0
0
0
3
1
0
1
0
2
1
1
2
0
6
0
1
2
0
0
0
0
1
0
0
1
0
2
1
0
1
0
2
1
0
0
0
1
1
0
0
0
2
2
0
0
2
2
0
1
2
0
0
1
1
0
0
2
1
0
1
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
2
1
2
2
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
2
1
0
0
1
1
0
1
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
1
1
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
2
0
0
0
1
1
0
1
0
0
0
0
0
2
0
0
2
0
0
2
1
2
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
2
0
0
1
0
2
0
0
0
1
0
0
2
0
2
0
0
0
2
1
0
0
0
0
1
2
0
1
0
0
0
2
0
0
0
0
2
1
1
2
0
3
0
0
2
1
0
0
1
0
0
0
1
0
2
3
2
0
0
1
1
0
1
0
0
0
0
0
1
0
0
3
0
0
0
2
1
0
0
0
2
0
0
2
3
2
0
0
0
0
0
0
2
1
3
2
1
0
2
0
0
0
1
0
2
0
2
1
1
0
0
0
0
0
1
0
0
0
0
0
2
1
1
1
1
2
2
0
2
0
2
0
2
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
2
1
2
0
2
0
2
1
0
0
2
0
1
0
2
1
1
1
0
0
2
0
0
1
1
0
0
1
0
1
0
0
2
2
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
2
0
1
0
2
0
0
0
0
0
2
1
0
0
0
0
1
0
2
1
2
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
2
0
0
1
2
2
2
0
0
0
3
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
2
0
1
1
2
1
0
0
0
1
2
1
0
0
0
1
2
0
0
0
0
1
0
0
0
1
0
2
1
1
0
0
0
1
0
0
2
2
1
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
1
1
0
2
1
0
2
1
0
0
0
2
1
0
1
2
0
0
0
1
1
0
2
1
1
0
0
0
0
0
0
0
0
2
0
0
1
2
1
2
0
1
1
1
0
0
0
0
0
0
0
1
3
2
0
0
0
1
0
1
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
2
1
1
2
0
0
2
0
1
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
2
2
0
1
0
0
3
3
1
2
2
0
2
0
0
2
0
0
0
0
2
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
2
1
2
3
2
0
0
0
3
0
0
2
0
1
2
0
0
0
0
0
1
1
1
0
0
2
1
0
0
2
0
0
0
1
1
1
0
1
0
2
0
1
2
1
0
0
1
0
1
3
0
0
0
0
0
1
0
0
0
3
0
0
0
0
1
0
1
1
0
0
2
0
0
0
0
0
1
0
0
1
1
1
1
2
0
0
0
0
0
0
2
0
0
0
0
1
1
1
2
0
1
1
0
2
2
1
0
0
0
1
0
0
0
1
0
2
0
0
0
0
2
1
0
2
0
0
1
1
0
0
2
1
0
0
1
0
1
0
0
0
0
2
0
2
0
2
2
2
0
3
2
0
0
1
0
0
0
1
2
1
0
1
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
2
0
2
1
0
0
0
0
3
2
2
1
0
1
1
1
1
2
2
0
0
0
0
0
0
2
2
0
0
0
0
0
2
2
2
1
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
1
0
1
0
1
2
1
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
3
2
1
0
0
1
0
1
0
0
0
2
1
0
0
0
3
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
1
0
0
2
2
1
1
0
1
0
1
3
2
0
1
0
0
2
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
3
1
0
1
0
2
2
0
0
0
1
1
0
0
0
0
0
3
1
1
1
2
2
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
3
0
1
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
3
1
1
1
0
1
3
1
0
2
0
0
2
0
1
0
0
1
1
0
0
2
2
0
0
2
0
0
0
1
0
0
1
2
0
0
2
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
2
0
2
0
0
1
1
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
2
0
0
2
0
0
0
0
5
2
0
1
0
1
3
0
0
0
0
2
0
0
0
1
1
2
0
0
0
0
0
1
2
0
0
2
2
0
0
0
1
0
2
2
2
0
1
2
0
1
0
1
2
0
2
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
2
1
0
0
1
3
2
0
1
2
0
0
2
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
1
0
2
0
1
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
2
2
0
2
2
0
0
0
0
0
1
0
1
0
0
1
1
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
3
0
1
0
1
1
2
0
1
0
0
0
0
0
1
2
2
1
0
0
0
0
0
1
2
0
2
2
0
1
0
0
2
0
0
2
0
0
0
1
0
1
1
0
0
2
1
0
0
1
2
1
0
0
2
0
1
2
0
1
1
0
0
2
0
2
0
1
2
1
1
0
0
2
0
0
1
0
2
2
0
0
2
1
0
0
0
0
0
1
0
2
0
1
0
0
1
0
1
2
2
1
2
0
2
0
2
3
0
1
2
2
0
2
0
0
1
0
0
0
1
0
0
0
2
0
2
0
1
0
0
0
0
1
0
1
4
0
0
0
1
0
0
1
3
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
1
2
0
0
0
0
2
0
1
2
2
0
0
0
1
0
1
0
0
2
0
1
0
1
0
3
1
1
0
2
1
0
0
0
0
2
1
0
0
0
0
2
1
2
1
1
0
1
1
0
0
0
3
1
0
0
0
2
0
2
0
0
0
0
2
2
1
0
0
0
0
0
0
2
0
0
1
1
0
0
1
0
0
0
0
0
2
1
2
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
2
1
0
0
1
0
2
1
0
0
1
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
1
1
0
0
0
2
1
0
0
1
1
0
2
0
0
0
5
0
1
0
0
0
0
0
0
0
0
2
2
4
0
0
0
4
1
2
0
0
1
0
0
1
0
0
1
0
1
0
0
2
0
1
2
0
0
2
0
0
0
1
1
0
1
0
2
0
2
1
0
0
0
0
1
1
0
0
0
0
0
2
2
2
0
2
2
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
1
0
0
0
3
0
0
0
1
1
2
0
4
2
0
0
0
0
0
0
0
0
1
3
2
0
1
0
3
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
2
1
1
1
0
0
0
0
2
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
1
0
0
1
0
2
0
2
0
0
1
0
2
0
1
0
0
0
2
0
0
2
2
1
0
1
0
1
0
0
0
0
0
0
2
0
0
1
2
0
0
1
1
0
0
2
2
0
0
2
0
1
2
2
1
0
0
0
0
1
0
0
2
3
2
1
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
2
0
2
1
0
0
0
1
0
0
0
0
1
0
3
2
0
0
0
0
2
0
0
1
1
0
0
0
2
0
2
0
2
2
0
1
0
0
2
0
0
0
1
0
0
0
0
2
1
2
0
0
0
0
0
1
2
1
2
0
2
0
0
0
1
0
0
0
2
2
0
1
0
0
0
0
1
2
0
0
0
2
0
0
1
1
0
0
0
1
0
1
3
0
0
1
0
0
0
1
0
1
0
0
2
0
0
1
0
1
0
2
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
1
0
1
1
0
0
2
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
2
0
2
0
0
1
0
1
0
2
0
0
0
1
0
0
0
0
0
0
2
0
1
2
1
1
0
2
0
0
0
2
1
0
1
2
2
0
1
1
0
0
1
1
0
3
0
1
0
0
0
2
0
0
0
0
0
2
0
2
2
1
1
1
0
0
0
0
0
0
4
0
0
1
0
1
0
1
0
1
1
3
1
2
1
0
0
0
1
0
0
1
0
2
0
1
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
1
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
2
0
1
0
0
2
2
0
0
1
0
1
1
1
1
0
0
1
0
0
0
0
2
0
0
0
0
1
3
3
0
2
2
0
0
0
0
0
1
0
2
0
1
0
1
1
0
2
1
2
0
0
1
1
1
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
1
1
0
1
1
1
0
2
1
0
0
0
1
0
0
1
0
0
2
0
1
0
0
2
0
2
0
0
0
0
0
2
1
1
2
0
0
0
0
0
0
0
2
2
2
0
0
0
0
1
2
0
1
0
0
2
2
1
0
0
0
0
0
0
0
2
0
0
0
2
2
2
1
0
2
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
3
1
0
0
2
0
1
0
1
1
1
0
0
0
0
0
0
0
1
0
1
0
2
0
0
2
1
0
0
0
0
1
0
0
2
0
0
1
2
1
0
1
0
1
0
2
2
0
2
2
1
0
0
2
2
2
0
0
0
0
0
1
2
0
2
0
1
2
0
2
2
0
0
0
0
0
0
1
0
1
0
0
0
2
1
1
2
1
0
0
0
0
0
0
0
3
2
0
0
2
0
2
0
0
0
0
2
0
0
0
0
1
0
0
1
0
1
0
2
2
0
2
0
2
0
0
0
2
0
2
2
2
2
0
0
0
0
0
1
0
0
0
2
1
0
2
2
0
0
0
0
2
0
1
0
1
1
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
2
0
1
0
1
0
0
0
0
1
1
0
0
0
1
0
0
1
0
2
0
0
0
2
2
0
0
0
0
0
0
2
0
3
0
0
2
0
0
1
0
0
0
0
0
0
1
1
2
0
0
0
0
0
1
0
0
2
1
0
2
0
0
0
0
1
0
1
1
2
0
3
2
1
0
2
0
0
0
2
0
0
0
2
0
2
2
0
0
1
0
0
0
0
3
0
2
1
1
0
2
2
0
0
2
1
0
0
1
2
0
0
0
1
0
0
0
0
2
0
0
0
0
2
2
0
2
0
0
4
0
2
1
0
0
0
1
2
0
1
0
0
0
2
0
0
0
0
0
2
0
2
0
2
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
1
4
1
0
0
1
1
0
0
1
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
2
0
3
0
0
2
1
0
0
0
0
0
0
2
1
0
2
2
2
0
0
1
0
0
0
0
0
0
0
0
1
0
2
3
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
1
1
1
0
0
0
1
1
0
0
0
2
0
2
0
2
0
2
0
1
0
2
1
1
0
2
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
1
0
2
1
0
0
2
0
0
0
0
1
0
1
2
0
0
1
1
0
0
0
0
0
2
0
2
0
0
1
0
0
1
0
1
0
0
2
0
0
0
1
0
0
1
0
0
0
0
3
0
0
1
0
0
0
2
1
3
0
1
0
2
0
0
0
1
2
0
0
0
2
3
2
0
0
1
0
2
0
2
0
1
0
0
0
0
1
0
0
2
0
0
6
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
1
0
0
1
0
0
0
1
3
2
1
0
0
3
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
2
3
0
0
0
1
0
0
0
1
2
1
0
1
0
1
1
0
1
0
0
0
0
0
0
2
0
0
3
0
2
0
2
0
0
0
0
0
0
0
1
0
2
0
0
2
1
1
0
0
1
2
1
0
2
0
0
0
0
0
1
2
0
0
1
1
0
0
0
1
2
1
1
2
3
0
0
0
0
0
0
0
4
1
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
2
2
0
1
0
0
1
0
0
2
1
0
0
0
0
0
1
0
1
0
0
2
0
1
0
0
0
3
1
0
0
0
0
0
0
0
1
0
2
0
2
0
0
1
0
0
2
2
2
0
2
1
0
1
0
3
0
2
3
0
2
0
2
0
1
0
0
0
2
2
2
0
0
2
0
2
0
1
0
0
0
0
1
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
1
0
2
3
1
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
3
0
0
0
2
0
0
1
0
2
0
0
1
0
0
2
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
2
0
0
1
0
1
0
2
0
2
0
1
0
0
0
2
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
1
1
0
2
0
0
0
1
2
1
1
0
0
0
2
2
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
2
2
0
1
0
1
1
0
2
0
0
0
0
1
1
0
0
0
1
1
0
0
2
1
1
0
2
0
1
2
0
0
2
1
2
0
0
2
0
2
0
0
1
0
2
1
0
2
1
2
0
3
0
0
0
0
2
0
2
0
2
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
1
2
1
3
0
2
0
0
1
2
2
0
0
0
0
0
2
0
1
1
0
0
0
1
1
0
1
0
0
0
0
2
0
0
0
2
0
0
1
0
0
1
1
0
0
1
1
0
2
1
1
1
0
0
0
3
1
0
1
0
0
0
0
0
3
2
0
1
0
3
2
0
0
0
0
0
0
0
1
2
0
0
0
2
1
2
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
2
0
0
1
1
0
2
2
0
0
0
0
2
1
0
0
0
0
2
0
0
2
0
0
0
0
2
2
0
2
1
0
0
1
0
0
0
0
1
0
0
2
0
1
0
0
0
1
0
0
1
0
2
0
0
0
0
0
1
0
2
2
1
2
3
0
0
2
1
0
0
1
1
1
0
0
2
1
0
1
0
2
0
1
1
0
2
0
0
1
0
0
2
0
0
0
1
1
1
0
2
0
0
0
0
1
2
0
0
2
1
1
0
1
0
2
0
0
0
0
0
0
0
1
1
0
0
2
1
2
1
1
0
2
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
3
2
0
0
0
0
2
0
0
1
0
1
2
1
0
2
0
0
1
0
2
0
1
0
2
1
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
3
0
1
0
0
0
1
0
2
2
1
1
3
2
1
0
0
0
0
0
0
1
1
0
0
2
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
2
1
2
2
0
0
2
0
3
2
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
1
3
1
2
0
0
1
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
1
5
2
1
0
2
0
5
0
0
0
0
2
2
2
0
1
2
1
0
0
0
0
0
0
1
2
0
2
0
0
0
0
1
0
2
1
2
0
0
0
1
0
1
0
1
0
0
2
0
1
0
0
2
0
0
0
2
0
0
2
0
0
2
0
2
0
0
0
0
0
2
1
2
0
1
0
2
0
0
1
0
1
0
1
4
0
1
0
2
0
0
2
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
2
0
0
0
0
0
2
1
1
0
0
0
1
0
0
1
2
2
0
0
1
2
0
0
1
0
0
0
2
0
2
0
0
0
0
0
1
2
0
0
0
0
0
1
2
0
0
0
2
1
1
1
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
1
0
2
1
0
0
0
0
1
0
2
0
0
0
3
0
2
2
1
0
2
0
0
1
1
0
0
0
2
1
2
2
0
0
1
0
0
1
2
2
3
0
2
2
1
1
1
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
1
1
0
0
0
0
2
0
1
2
1
2
0
0
2
2
0
1
2
0
0
0
0
0
1
1
1
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
4
0
1
0
0
0
2
0
1
0
2
0
0
2
2
0
0
0
0
2
0
0
1
0
1
1
1
0
0
2
1
1
0
0
1
0
0
0
2
2
0
0
2
0
1
0
1
0
1
2
0
0
2
2
0
0
1
2
1
1
0
0
0
0
0
0
1
0
0
1
1
1
0
0
2
2
0
0
0
2
1
2
1
0
0
0
0
0
2
0
2
1
1
0
0
0
3
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
2
0
1
0
0
0
1
0
0
0
1
0
2
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
1
1
0
0
0
0
0
0
0
2
0
1
1
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
1
2
0
2
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
1
0
2
2
0
1
2
0
1
0
2
0
0
0
2
0
0
0
0
1
0
0
0
1
2
2
0
2
0
0
2
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
1
1
0
0
3
0
0
0
1
0
0
2
0
0
0
0
2
0
1
2
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
2
1
0
0
1
1
0
0
2
1
0
0
1
2
0
0
0
0
0
1
1
0
0
0
0
0
2
0
1
1
1
0
0
3
1
2
2
0
2
1
0
0
0
1
0
0
2
0
1
2
0
2
2
3
0
2
0
0
0
1
0
0
4
0
0
0
0
0
1
1
1
0
1
2
3
0
1
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
2
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
2
0
3
1
1
0
2
1
0
0
1
1
2
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
3
0
0
0
2
1
0
0
0
0
0
3
0
1
0
2
1
2
0
0
0
2
0
1
1
0
0
0
2
0
0
0
0
2
0
0
0
1
3
1
0
0
0
0
0
0
0
1
0
0
0
2
2
0
4
0
0
0
0
0
0
1
1
2
0
1
1
0
1
0
1
0
0
0
1
0
2
1
0
1
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
1
1
0
0
0
0
0
0
2
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
2
0
2
1
0
1
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
2
0
0
0
1
3
0
0
2
2
0
0
0
0
2
1
1
0
0
0
1
3
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
3
0
0
0
0
2
2
0
0
0
6
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
2
1
1
2
0
0
1
2
0
2
1
1
0
0
0
0
1
1
1
0
0
0
2
0
0
2
0
0
2
0
0
0
2
0
0
0
3
0
1
1
0
1
0
2
3
2
2
1
1
0
0
0
2
2
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
1
0
2
1
2
1
0
0
1
0
1
0
0
1
4
0
0
4
2
1
0
0
3
0
0
0
0
0
2
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
1
0
0
0
0
1
1
2
1
0
0
0
0
0
2
1
0
1
0
0
0
1
0
2
0
2
0
0
1
0
2
1
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
1
2
0
0
2
2
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
1
1
1
1
2
1
0
2
2
0
0
0
0
0
2
1
0
2
0
0
1
0
2
0
1
0
2
2
0
1
0
2
0
0
2
0
0
0
2
0
0
0
3
1
0
2
0
0
1
0
2
0
0
0
0
2
1
3
1
0
2
0
0
0
0
0
1
0
1
0
1
1
1
1
4
0
0
0
0
0
0
0
2
2
0
2
0
1
2
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
1
4
0
0
2
1
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
2
1
0
0
2
2
0
2
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
3
2
1
0
1
0
3
2
0
2
3
2
1
0
0
1
0
0
0
0
0
0
0
0
2
2
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
2
0
0
0
0
1
0
0
1
1
0
0
0
0
0
2
1
0
0
2
1
2
0
1
0
2
0
0
1
2
0
2
0
0
0
1
2
2
1
1
2
0
2
1
2
0
3
0
0
0
0
1
0
1
0
0
2
0
2
1
1
0
0
2
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
2
0
1
0
2
0
2
0
2
0
1
1
2
2
0
1
1
0
0
2
0
2
0
2
2
2
2
0
1
1
0
0
0
1
0
2
0
1
2
0
0
2
0
2
1
0
0
2
1
0
0
0
0
2
1
0
0
0
0
0
0
1
0
2
3
0
0
1
0
0
0
4
0
1
0
0
0
3
0
0
1
0
0
0
2
1
1
0
0
0
1
0
0
0
1
2
0
0
0
3
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
2
1
1
0
0
1
0
0
0
1
2
1
0
0
0
0
1
2
0
1
2
1
3
0
1
2
2
3
3
0
2
2
0
0
0
1
1
0
5
0
0
2
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
3
0
0
1
2
0
0
0
0
0
1
0
1
1
0
0
1
1
0
2
0
0
2
0
0
0
0
0
0
1
1
0
1
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
1
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
2
10
0
0
3
2
2
1
1
0
0
1
0
0
0
1
0
2
0
0
1
0
2
0
0
2
0
1
1
2
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
2
0
0
2
0
0
0
0
0
1
0
2
0
2
0
0
0
1
3
0
0
0
2
2
3
0
0
1
0
0
2
0
0
0
0
0
0
0
1
1
0
2
1
2
2
0
0
2
0
0
1
0
0
0
0
2
1
1
1
2
0
1
0
2
1
0
0
2
0
0
0
2
0
2
0
2
2
0
0
0
1
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
1
2
3
0
1
0
0
2
0
1
2
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
2
0
2
0
0
0
0
2
0
0
0
0
1
2
2
0
1
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
1
0
1
0
0
2
2
0
1
0
0
1
0
2
0
0
0
0
0
0
1
2
1
0
3
0
0
0
1
0
1
1
0
1
0
0
1
0
0
0
1
2
0
0
1
0
0
1
0
0
0
1
2
1
0
2
0
2
1
0
0
0
0
0
0
0
1
0
2
1
1
2
0
0
0
0
1
1
0
2
0
1
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
2
1
0
0
1
0
0
0
0
5
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
1
1
2
1
0
0
0
0
1
1
1
1
0
2
2
2
1
2
0
2
0
1
1
2
0
1
0
0
0
0
2
0
1
1
0
0
0
0
0
2
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
1
0
2
0
1
1
0
2
0
2
2
2
0
0
0
1
0
0
0
0
2
2
1
0
2
0
2
2
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
2
2
1
1
0
2
2
0
0
0
2
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
2
0
0
1
1
0
0
0
0
0
0
3
0
3
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
2
2
0
2
0
1
0
1
0
0
1
1
0
1
0
0
0
2
0
0
0
0
0
1
0
3
0
2
0
0
2
0
1
1
0
0
2
0
0
0
2
0
0
2
0
0
1
0
2
2
0
1
0
1
0
0
2
1
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
1
0
2
2
0
0
2
0
0
2
1
0
0
0
0
0
3
0
0
0
1
0
2
0
0
0
1
1
2
2
1
0
2
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
1
1
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
1
0
1
3
0
0
0
0
0
0
2
1
0
0
0
0
1
2
1
0
2
9
2
0
2
0
0
0
0
0
1
2
2
1
0
1
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
1
2
2
0
1
1
0
0
1
0
0
0
2
0
1
1
1
0
1
1
0
0
0
0
0
1
0
3
0
0
2
1
1
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
2
2
1
1
0
0
2
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
3
2
2
3
0
2
2
0
0
1
2
0
1
0
1
0
0
0
2
1
0
2
1
0
1
0
1
0
1
1
0
0
1
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
2
2
2
0
0
0
0
0
1
0
1
0
2
0
0
0
1
2
0
0
1
0
0
0
0
2
0
2
2
1
0
0
0
0
2
2
0
0
0
1
0
0
0
1
0
0
0
2
0
2
0
0
0
1
0
3
0
0
0
1
0
2
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
4
1
0
3
2
0
2
2
0
0
2
0
0
0
0
0
0
1
2
2
0
2
2
0
0
0
0
0
0
2
0
2
0
2
0
0
2
0
2
0
0
0
0
0
1
1
0
2
0
1
2
0
0
2
1
0
0
0
2
0
0
1
1
0
0
0
0
1
2
0
0
0
0
2
2
0
0
1
2
2
1
0
2
2
0
0
3
0
2
5
0
0
1
1
0
0
1
2
1
2
0
0
0
2
0
2
1
1
1
0
0
1
0
1
2
0
0
0
4
2
0
0
1
0
0
2
1
2
0
1
0
2
1
0
0
0
0
0
0
0
0
0
2
1
2
0
0
2
0
0
1
1
0
0
2
2
0
1
0
0
1
0
0
0
0
0
0
2
1
0
2
0
2
0
0
0
2
1
0
1
0
0
0
1
1
2
1
0
0
0
0
1
0
2
0
0
1
0
0
0
2
2
0
0
0
0
2
0
0
0
2
1
1
1
0
2
0
0
0
0
0
1
0
0
2
1
0
0
1
0
2
0
0
0
1
3
3
0
1
0
2
2
0
0
1
0
0
2
1
1
0
0
0
1
1
2
0
0
0
0
0
1
1
1
0
0
3
0
0
0
1
0
0
0
2
0
1
0
0
1
0
1
0
0
0
2
1
0
0
0
3
3
1
1
0
2
1
1
1
2
1
0
0
0
0
2
2
1
0
0
0
0
2
0
0
2
0
0
0
0
3
1
0
1
0
0
1
0
0
1
2
0
2
1
0
0
2
0
2
2
2
3
0
0
0
2
1
0
2
0
3
0
0
1
0
0
0
2
2
0
0
1
2
0
0
1
2
2
0
0
1
1
0
1
1
0
1
0
0
1
0
1
2
0
0
5
1
0
1
1
0
0
0
0
2
1
1
0
2
0
0
0
0
1
0
2
0
0
0
0
1
2
1
0
0
2
0
0
1
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
2
2
0
1
0
2
0
2
0
1
0
0
1
0
0
0
0
1
1
0
1
2
1
1
1
0
1
2
0
2
0
0
2
1
2
2
1
2
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
1
2
0
2
1
0
0
0
0
0
1
1
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
1
1
1
1
0
1
0
1
0
0
0
3
2
0
2
0
2
0
0
1
0
0
0
0
2
0
2
0
1
0
0
0
1
1
0
1
0
1
0
1
0
1
0
0
2
1
0
0
2
1
2
0
1
0
2
0
0
0
1
1
0
3
0
0
1
2
1
0
0
0
0
1
1
2
0
2
0
0
0
0
0
0
1
1
2
0
2
2
0
2
0
0
0
1
0
2
1
2
0
0
0
0
0
0
0
0
0
1
1
0
0
2
1
1
1
0
0
0
0
0
2
0
0
2
0
2
1
0
2
0
1
0
0
0
0
2
1
0
0
0
0
0
0
1
2
0
2
1
1
2
1
2
0
0
0
1
0
2
0
0
0
1
1
0
1
0
0
0
0
0
2
0
2
0
0
1
0
0
1
2
2
1
0
0
0
0
0
0
0
1
1
0
1
1
0
0
2
0
0
1
0
0
0
0
2
0
0
1
1
1
1
2
0
0
3
1
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
2
0
0
2
2
1
0
0
0
2
1
0
2
0
1
1
0
2
0
0
0
1
0
0
0
2
0
0
0
0
3
0
0
2
0
1
1
2
2
0
2
1
0
0
2
0
0
0
0
1
2
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
2
0
0
2
0
0
0
2
0
1
1
1
2
0
0
0
2
0
2
0
0
2
0
0
0
0
0
1
2
0
1
0
0
1
0
0
0
3
2
2
2
2
1
2
1
2
0
0
0
0
0
0
2
0
0
0
2
2
0
0
2
1
0
0
0
1
0
0
2
0
1
0
0
0
0
5
2
0
0
0
1
2
2
0
2
2
2
2
1
2
0
0
0
2
0
2
1
0
2
1
0
0
0
0
1
0
0
1
0
2
1
0
2
0
1
0
1
2
0
1
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
1
0
1
1
0
1
2
0
4
0
0
0
0
0
1
2
1
0
0
0
1
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
1
3
0
2
0
0
0
1
0
0
1
1
0
0
0
7
0
0
2
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
2
0
2
2
0
0
0
0
0
1
2
0
3
3
0
0
0
0
0
0
0
0
0
2
1
3
1
0
0
1
2
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
2
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
1
0
2
2
0
0
0
1
0
0
0
0
1
0
0
1
0
0
2
1
0
0
0
0
0
3
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
1
2
2
2
1
0
0
0
0
0
0
0
0
2
0
0
1
0
1
2
0
0
0
1
0
2
0
0
0
2
0
0
1
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
2
2
2
1
0
1
0
0
0
0
0
0
0
2
2
3
1
0
1
2
0
1
2
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
1
0
0
0
2
1
0
1
0
0
2
0
0
2
2
2
0
1
0
0
0
1
1
0
0
0
0
0
0
1
1
2
0
1
1
2
0
0
1
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
2
2
0
2
0
0
0
3
0
0
1
0
2
0
0
1
2
0
0
0
1
2
0
1
0
1
0
2
0
0
2
0
1
0
0
1
0
0
0
1
1
0
0
0
0
1
2
0
0
3
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
1
1
1
0
2
0
0
0
3
0
2
0
0
1
6
2
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
1
2
2
0
0
0
0
0
0
2
0
0
0
0
6
1
0
1
0
2
0
0
0
1
0
0
0
2
0
1
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
1
2
0
1
0
2
0
2
0
0
0
2
2
0
0
2
2
0
0
0
0
0
0
0
0
1
0
2
2
1
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
2
1
1
3
0
2
2
2
0
0
2
0
3
1
0
1
0
2
0
0
3
0
1
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
2
0
0
0
2
2
0
1
2
1
2
0
4
2
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
3
1
2
1
3
0
0
0
2
0
0
0
1
0
0
1
1
0
0
2
2
1
0
0
0
1
2
0
0
2
0
2
0
0
0
1
1
0
0
0
1
0
1
1
0
2
2
0
1
2
1
2
0
1
3
0
0
0
0
0
0
0
2
2
1
0
0
0
0
1
0
2
0
0
0
0
1
1
2
0
1
2
1
2
0
0
1
0
1
0
4
2
1
0
0
0
0
0
0
0
0
3
2
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
1
2
0
1
1
0
0
2
2
0
1
0
2
0
0
0
0
1
0
2
0
1
2
2
1
0
1
0
1
0
0
2
2
0
0
0
0
1
2
0
0
1
1
1
0
2
1
2
1
3
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
1
0
0
1
3
1
3
0
2
0
1
0
0
0
1
0
0
2
0
3
0
0
1
0
0
2
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
1
1
0
0
1
2
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
2
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
2
0
2
0
0
2
0
0
0
0
0
1
0
0
0
1
0
2
1
1
2
0
0
0
0
2
1
0
1
0
0
0
0
1
6
2
0
0
0
0
2
0
0
0
0
3
2
0
2
0
0
0
0
2
1
0
0
0
0
2
1
1
0
0
1
0
3
0
0
2
0
0
2
1
0
2
1
2
0
1
0
1
0
1
1
1
0
2
0
0
0
0
0
2
0
1
0
0
1
1
0
4
3
1
0
0
2
0
0
2
0
2
2
2
1
1
0
0
2
2
0
0
0
0
0
1
2
1
1
1
3
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
1
2
0
1
1
1
1
2
0
1
0
2
0
2
1
2
0
2
0
0
3
0
0
1
2
0
0
1
2
0
2
0
0
0
0
0
1
1
1
0
2
0
1
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
2
3
0
0
1
0
0
0
0
0
0
0
1
2
1
0
0
0
1
0
2
0
0
1
1
0
0
0
2
0
2
0
2
0
0
0
1
1
0
3
0
2
0
0
1
2
1
0
0
2
0
0
2
0
2
0
2
0
0
2
0
0
0
1
2
1
2
3
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
2
1
0
2
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
2
0
2
0
1
1
0
1
0
0
0
1
2
2
3
1
0
2
0
0
1
1
1
0
1
2
1
0
1
0
2
1
2
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
1
1
2
2
0
0
0
0
1
0
0
2
0
2
0
0
0
2
3
0
1
2
0
0
0
3
0
2
0
2
0
3
0
1
0
2
0
0
0
2
0
0
0
0
0
0
1
0
1
2
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
1
0
0
2
6
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
1
2
1
2
0
0
0
0
2
0
2
0
2
0
2
0
0
1
3
1
0
0
2
0
2
1
4
0
0
1
3
0
1
1
0
0
2
2
0
0
2
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
2
0
0
1
0
0
0
1
1
1
0
1
0
0
2
0
0
0
0
2
1
1
0
0
0
1
0
1
0
0
0
0
0
2
0
1
2
0
0
1
0
2
0
0
0
0
0
0
0
2
3
0
2
0
1
1
0
0
1
1
0
1
0
1
2
0
0
0
1
1
2
0
0
1
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
2
1
0
1
2
0
1
0
2
0
2
2
2
1
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
1
0
0
2
1
1
1
1
0
0
3
1
1
1
2
0
0
0
2
0
0
1
0
0
0
0
0
0
2
1
1
0
0
1
1
0
0
0
2
1
0
0
0
0
2
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
5
0
2
3
1
2
2
0
2
0
0
1
1
0
1
0
0
0
1
0
1
0
0
0
6
2
0
0
0
0
0
1
4
2
0
0
0
2
0
0
2
2
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
3
1
0
0
0
2
1
0
0
0
1
0
1
0
0
0
0
0
2
1
0
0
0
2
0
1
0
1
2
2
0
1
0
1
0
0
0
1
0
0
1
2
2
0
1
0
0
1
0
1
0
0
0
2
0
0
0
1
0
2
0
0
0
0
2
3
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
2
0
1
1
0
2
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
2
1
0
0
0
1
1
0
0
1
0
0
2
0
0
0
2
1
0
1
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
5
1
0
1
0
0
0
1
0
0
0
0
2
0
0
2
1
1
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
2
0
2
2
0
0
0
2
0
0
1
0
0
4
0
1
2
1
0
0
0
1
0
0
1
0
0
1
2
0
1
2
0
0
0
0
0
1
0
0
2
0
1
1
0
1
1
0
2
3
0
0
0
2
0
1
0
1
0
1
0
0
0
0
0
0
1
1
1
0
0
1
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
2
0
4
0
0
1
0
0
0
0
0
0
1
1
0
2
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
1
0
0
0
0
1
2
1
2
0
2
0
0
2
0
1
0
0
2
0
1
0
0
3
0
0
0
0
0
0
1
1
0
2
0
2
1
4
1
2
0
0
2
0
0
0
0
0
2
0
0
3
0
0
0
3
2
0
1
2
1
3
2
0
2
0
2
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
1
0
2
2
0
0
0
0
0
1
0
0
0
0
3
0
0
1
0
0
0
3
0
0
0
0
0
0
0
1
1
0
1
2
0
0
2
1
0
0
0
0
0
4
2
1
2
0
0
1
1
0
1
3
1
0
0
1
0
1
0
11
0
0
1
2
1
1
0
1
0
0
0
0
2
2
0
1
3
1
0
0
1
2
1
0
0
0
0
0
1
3
2
2
0
1
0
1
0
2
0
0
1
0
2
1
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
2
1
0
0
0
3
2
0
1
0
2
0
0
0
1
0
0
0
2
0
0
0
2
0
0
2
0
0
1
0
1
2
0
0
0
2
1
0
0
0
0
1
2
6
0
0
0
0
1
2
0
2
2
0
0
1
2
0
0
0
0
1
0
1
2
2
1
2
1
0
0
1
0
2
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
1
0
2
0
1
0
1
0
2
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
2
0
1
3
0
0
0
0
0
1
0
2
1
0
0
0
1
1
1
0
2
2
0
1
0
0
0
1
1
0
0
1
0
0
2
2
2
0
0
1
0
2
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
2
1
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
2
0
1
3
0
2
0
2
0
0
0
0
0
0
2
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
2
1
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
1
1
2
0
1
0
0
1
0
0
0
0
1
0
0
0
2
1
0
0
2
2
0
1
0
2
0
2
1
0
0
0
0
1
2
0
0
0
1
0
0
0
0
2
2
0
0
0
0
2
0
1
0
0
0
0
1
1
1
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
2
0
3
1
1
0
0
0
0
0
1
2
2
0
0
0
0
1
2
2
0
0
0
0
0
1
0
0
1
1
0
0
0
0
2
2
0
0
0
1
2
0
0
2
0
1
2
0
0
2
0
0
0
0
1
2
0
1
0
1
2
0
2
0
1
1
0
2
0
0
0
1
0
2
0
0
2
0
0
0
0
2
0
1
0
0
0
2
0
0
4
0
0
2
1
2
0
0
1
0
2
1
0
2
0
1
2
0
2
0
2
0
0
0
2
2
2
0
0
0
0
2
0
2
1
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
1
1
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
1
2
0
0
1
0
0
0
0
2
0
1
1
1
0
0
0
2
0
1
0
0
0
1
1
2
0
0
1
0
0
0
0
2
1
1
2
2
0
0
0
2
0
0
4
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
3
1
1
0
2
0
0
2
0
1
0
0
0
2
1
0
1
1
2
0
0
0
1
1
0
0
1
0
1
0
1
1
1
0
0
0
0
0
1
0
0
1
0
0
1
2
0
0
2
0
0
0
0
0
2
1
0
1
0
2
0
0
2
0
0
0
1
0
2
1
2
0
2
0
1
0
0
1
2
0
0
2
0
0
0
0
2
2
0
0
0
0
1
2
0
0
2
0
0
0
0
0
2
0
1
1
0
0
0
2
0
1
0
1
0
1
0
0
2
0
0
0
2
0
0
2
1
2
2
5
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
1
0
1
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
2
2
0
2
0
0
2
0
1
0
0
0
0
2
1
0
0
1
2
2
1
0
0
0
2
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
1
2
0
1
0
0
0
0
0
0
2
0
2
0
0
2
0
0
1
0
0
0
1
0
0
0
2
0
0
1
0
0
0
1
0
1
1
0
1
0
1
0
0
1
0
1
0
0
0
2
0
2
0
1
0
0
1
0
1
0
0
1
0
0
1
1
0
2
0
2
0
2
1
0
1
0
1
0
0
0
1
0
1
0
0
0
3
0
0
0
0
0
0
3
0
0
0
0
1
0
0
3
0
0
1
0
0
1
0
0
2
1
0
2
1
1
0
0
1
0
2
0
0
1
0
0
2
4
0
0
2
1
0
0
2
0
0
0
0
0
2
0
1
2
2
0
1
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
1
0
2
1
2
1
0
0
2
0
0
2
1
0
0
0
2
2
0
1
0
0
3
0
0
0
0
0
0
1
0
0
2
2
0
0
2
3
1
2
3
0
1
1
0
1
0
1
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
2
0
2
3
2
0
0
0
0
2
0
0
1
2
0
0
0
0
0
2
1
0
0
0
2
2
2
0
1
0
1
0
0
0
1
2
2
2
0
0
1
1
1
0
0
0
0
1
1
0
0
0
0
2
0
1
0
2
1
1
0
0
1
0
0
0
0
2
0
0
0
0
1
2
2
2
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
2
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
2
1
0
1
0
0
0
1
1
0
0
2
0
0
0
2
0
0
1
0
0
1
0
3
0
0
0
1
0
2
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
2
0
0
0
1
1
0
0
0
4
2
0
2
1
2
0
2
2
0
0
2
2
0
0
0
3
0
1
1
0
0
1
0
0
0
2
0
0
0
2
0
1
0
1
0
0
2
0
2
2
0
1
0
0
0
0
0
1
0
2
0
1
0
0
0
0
1
1
0
2
2
2
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
1
1
0
0
1
2
0
0
0
1
0
2
0
2
0
0
1
0
0
0
1
0
2
0
0
2
0
0
0
2
1
2
0
5
0
1
0
0
1
0
0
0
2
0
0
0
0
0
2
0
2
1
1
1
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
1
0
0
2
2
0
0
1
0
1
0
1
0
2
0
0
0
0
0
2
1
1
0
0
1
0
0
3
1
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
2
0
0
1
0
0
2
0
1
0
2
0
1
0
1
0
1
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
1
2
1
0
1
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
3
1
0
0
0
1
0
0
1
2
0
0
0
0
2
0
0
1
2
2
0
0
0
0
0
3
1
0
0
1
1
0
1
0
0
1
5
0
0
0
1
1
0
2
0
0
0
2
0
2
0
0
0
0
2
2
0
0
0
0
1
2
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
3
0
1
0
2
1
0
0
2
4
0
1
0
0
2
0
2
0
0
0
0
0
0
2
1
0
2
0
1
0
0
1
0
1
2
0
0
1
0
0
2
1
0
0
0
0
0
2
0
0
1
0
0
1
1
0
2
0
0
2
0
0
1
0
0
1
0
0
2
0
1
0
0
2
0
2
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
2
0
0
1
1
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
1
0
1
2
0
1
0
0
0
0
2
0
1
0
2
0
0
1
2
0
0
4
2
2
1
0
2
0
0
0
1
1
0
0
2
0
1
0
0
0
0
0
1
0
1
0
2
0
1
2
1
0
0
1
1
1
0
0
0
0
2
0
0
1
4
0
1
0
0
1
0
0
0
0
0
1
2
0
3
0
0
0
0
0
0
2
0
0
2
0
1
2
1
0
0
0
1
2
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
2
0
1
0
0
5
1
0
1
2
0
0
1
0
1
1
1
2
0
2
0
0
2
0
0
0
0
2
0
1
0
0
1
1
0
2
0
0
2
0
1
0
0
2
1
0
0
0
0
1
2
2
0
2
0
0
1
2
0
0
1
0
0
2
0
1
0
0
2
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
1
0
2
0
0
2
0
2
1
2
2
0
0
0
3
2
0
0
0
0
0
2
0
2
1
0
1
0
0
1
2
0
1
0
2
2
2
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
2
2
0
1
0
1
0
0
1
1
5
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
2
1
1
2
0
0
1
0
2
0
0
0
0
2
4
0
1
2
0
0
0
0
1
0
0
3
3
0
0
2
0
0
0
2
2
0
1
0
0
1
3
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
1
2
0
1
0
2
2
0
1
0
0
1
1
0
1
0
0
0
2
2
3
0
0
0
0
0
1
0
0
1
0
2
2
0
2
2
0
1
2
4
0
1
1
1
1
2
0
1
0
0
1
0
0
0
0
1
1
1
0
1
2
2
0
0
2
2
0
2
0
2
0
3
1
0
0
2
3
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
1
1
2
0
0
0
0
2
0
1
0
2
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
3
0
0
0
2
3
2
0
0
3
0
0
1
0
0
1
0
0
0
0
2
1
1
2
1
2
0
0
0
1
0
0
2
1
0
0
0
0
2
4
0
1
0
2
0
0
1
0
1
0
2
0
1
0
1
0
1
0
0
1
0
1
1
1
2
2
0
0
1
0
1
0
1
1
0
0
2
3
0
0
0
0
0
0
0
2
2
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
4
1
0
2
0
0
0
2
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
2
0
2
1
0
0
2
0
2
0
2
1
0
2
0
1
2
0
1
1
0
0
1
0
2
0
0
1
0
0
0
2
2
0
0
1
0
1
0
1
0
0
0
0
0
2
0
1
0
1
0
0
0
0
1
0
0
0
2
1
1
0
0
0
0
0
1
0
0
2
0
2
1
0
0
1
1
1
1
0
1
2
0
0
0
0
0
1
0
2
0
0
1
1
0
1
1
0
1
0
4
0
1
1
1
0
5
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
3
0
0
0
2
0
2
0
3
0
1
2
1
0
3
1
0
1
0
0
2
5
1
0
0
0
1
0
2
0
0
2
2
0
0
1
0
0
2
0
2
1
0
0
0
4
2
1
0
0
0
0
1
0
3
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
1
2
0
0
0
0
0
2
0
2
0
0
0
0
1
1
0
1
0
0
0
0
3
0
0
2
1
1
2
1
1
0
0
1
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
2
2
0
2
1
0
0
2
0
0
1
0
0
0
0
2
1
0
1
2
0
0
1
0
0
0
0
2
0
0
2
0
2
2
4
1
1
0
0
0
3
0
0
0
0
0
0
3
1
0
2
2
2
1
3
1
2
1
0
2
0
0
0
0
2
0
0
0
3
0
0
2
2
0
0
0
1
0
1
0
1
0
1
0
2
0
0
2
0
0
0
0
2
0
0
1
0
2
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
2
5
0
0
0
1
2
0
0
2
1
0
2
5
2
0
0
1
0
1
1
0
0
0
0
0
0
0
1
1
1
0
2
1
1
2
0
1
0
2
1
2
0
0
2
0
2
2
1
0
0
1
0
0
2
0
1
0
3
0
0
2
0
0
2
0
0
2
2
2
0
1
1
0
0
0
0
2
0
0
0
2
0
0
1
0
0
1
2
0
0
1
2
0
1
0
4
0
0
0
0
0
3
0
0
0
0
3
0
2
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
2
2
0
0
0
0
1
2
2
0
0
0
0
0
1
1
1
0
2
0
2
0
1
2
2
1
2
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
1
0
0
2
2
2
1
2
1
1
2
1
0
2
0
2
1
0
0
2
2
0
1
2
1
1
0
0
1
1
1
0
1
0
0
0
0
2
0
0
1
2
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
3
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
1
0
0
2
2
2
0
1
0
0
2
1
2
0
2
1
0
0
2
0
0
0
2
1
3
0
2
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
4
0
0
0
0
0
2
2
2
2
0
0
2
0
0
0
0
2
1
2
1
1
0
2
0
0
2
0
0
2
2
1
0
0
0
0
0
0
1
0
3
2
1
2
0
0
0
2
4
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
1
1
1
0
1
2
1
1
0
0
2
0
2
0
0
0
0
1
2
2
1
1
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
2
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
1
0
0
2
0
1
0
2
1
0
0
0
0
0
3
1
0
5
0
2
1
2
0
2
0
1
1
6
1
0
2
0
0
0
0
0
2
0
0
2
0
1
0
2
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
3
0
0
0
0
0
0
0
2
0
0
9
0
0
0
1
0
0
2
0
1
0
0
2
1
0
2
2
1
2
2
2
0
0
0
0
0
0
1
1
0
1
1
0
3
2
0
0
1
1
1
0
2
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
1
0
0
1
1
1
4
2
1
0
0
0
0
0
1
1
1
2
0
1
2
0
2
0
0
1
1
2
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
2
0
0
1
0
0
3
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
2
1
1
0
2
1
2
0
0
1
0
2
0
0
2
0
0
1
0
3
1
1
2
0
1
1
0
1
0
0
0
1
2
1
0
2
0
0
1
0
0
0
2
0
1
1
0
0
0
1
0
0
2
1
0
0
0
1
0
2
0
1
1
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
2
0
1
0
0
0
0
0
1
1
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
1
2
0
1
0
1
0
1
2
1
0
1
1
0
2
2
1
1
1
0
1
0
2
0
0
0
0
0
0
0
1
1
0
1
1
1
1
0
1
0
0
2
2
1
3
1
0
0
0
1
1
0
0
2
2
2
0
0
0
2
2
0
1
1
0
2
0
1
0
0
0
0
0
2
1
0
0
0
0
1
0
1
0
0
0
1
0
2
0
1
1
3
0
0
0
2
0
0
1
0
1
0
1
0
1
0
2
2
3
0
0
1
0
0
0
0
0
2
1
1
2
0
0
2
0
0
2
1
0
2
2
0
0
0
0
0
0
2
0
0
2
1
1
0
0
1
0
0
2
1
0
2
3
0
1
1
0
0
0
0
2
1
0
2
1
2
2
0
0
2
1
0
1
0
1
2
1
0
1
2
0
0
1
1
2
0
0
3
0
0
1
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
2
0
1
1
2
0
0
0
1
0
1
0
2
0
0
0
0
1
0
1
2
3
0
1
0
0
1
0
1
2
0
0
2
1
2
2
0
0
2
1
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
2
2
0
0
0
0
2
0
0
1
0
0
2
0
0
1
0
1
0
3
1
0
0
2
1
1
2
0
2
0
10
1
2
0
2
2
0
1
2
0
0
0
0
0
1
1
2
0
1
1
0
0
0
0
0
0
0
0
2
2
2
2
0
5
2
0
0
0
0
0
0
0
1
2
0
1
1
0
0
0
1
0
1
0
0
0
2
2
0
1
1
1
0
2
2
1
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
2
0
0
2
0
0
2
0
0
0
0
3
1
5
2
0
1
0
0
0
2
0
0
0
0
0
0
5
0
0
2
0
0
2
1
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
2
0
0
1
0
0
0
2
0
2
1
0
1
2
0
0
0
1
2
0
2
1
0
0
0
1
2
1
0
0
2
0
1
0
0
2
1
2
0
1
1
0
2
0
1
0
0
2
0
0
1
0
0
0
2
0
1
0
0
0
0
0
1
0
2
0
0
0
1
2
0
0
0
0
4
2
1
0
0
0
0
2
2
1
1
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
2
2
1
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
1
0
0
0
0
3
1
1
0
0
2
0
2
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
1
0
0
0
3
0
1
0
1
0
0
0
0
0
1
0
2
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
2
1
0
2
0
1
1
0
1
2
0
0
0
0
0
0
2
1
0
0
1
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
1
2
3
2
0
0
0
2
0
2
2
1
0
0
2
1
0
0
0
2
2
2
1
0
1
2
0
0
0
0
0
1
0
1
0
1
0
0
5
0
1
0
1
1
0
1
1
0
2
1
1
2
1
0
0
0
0
2
0
0
2
1
0
0
0
0
2
0
2
2
0
0
1
0
0
1
1
1
1
1
2
0
0
2
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
1
2
2
0
1
2
0
0
0
3
0
0
0
1
2
0
0
0
0
0
1
2
0
0
0
1
0
1
0
0
1
1
0
0
0
2
2
0
1
2
0
0
0
2
1
2
0
0
2
1
0
0
0
5
0
0
1
0
1
0
0
0
2
2
2
1
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
2
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
1
0
0
1
6
0
0
0
2
0
1
0
1
1
2
1
0
0
0
0
2
0
1
4
2
2
0
4
2
2
0
0
0
0
0
0
1
0
1
0
0
2
0
0
1
1
2
0
0
2
0
0
0
1
0
1
0
2
0
0
1
1
0
0
0
1
0
0
1
0
1
1
0
1
0
0
0
0
2
2
1
0
1
0
1
1
0
0
0
0
0
2
0
0
2
1
0
0
0
1
1
0
2
1
1
0
0
2
1
1
1
0
0
1
2
0
0
1
0
2
0
0
0
2
0
0
0
0
1
2
0
2
0
0
0
0
1
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
1
2
0
1
2
0
0
2
0
0
2
1
0
0
1
0
0
2
0
0
0
0
1
0
2
1
0
1
0
0
0
0
1
0
2
1
1
0
1
1
0
0
0
2
0
0
0
2
2
0
0
0
1
0
1
0
0
0
0
0
2
0
0
1
2
0
1
0
0
3
0
0
2
2
1
1
1
2
0
0
1
0
2
1
0
0
1
1
0
1
2
2
0
0
0
2
1
1
2
0
2
1
0
0
1
0
0
1
0
0
2
0
0
0
0
2
1
1
0
0
1
0
0
2
1
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
3
0
1
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
1
2
2
0
2
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
2
1
3
2
2
0
2
0
1
0
0
2
2
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
1
1
2
2
0
0
1
0
0
0
0
2
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
1
0
2
0
1
1
2
0
0
2
0
1
1
1
0
0
0
0
0
1
2
0
0
1
0
2
2
0
0
2
1
0
1
0
1
0
3
0
1
0
0
0
0
2
0
0
1
1
0
2
0
1
2
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
2
0
2
0
0
0
2
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
2
1
2
0
6
1
1
0
1
1
0
2
1
0
0
0
1
1
0
2
1
1
0
1
0
0
2
0
3
0
0
2
1
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
2
1
1
0
0
0
0
0
1
0
0
0
1
1
2
0
0
1
2
0
1
1
0
1
0
1
0
2
0
0
0
0
2
1
1
0
1
0
0
3
1
2
0
0
2
0
1
0
0
1
0
0
1
0
2
2
1
0
0
2
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
1
0
0
0
2
1
0
0
2
0
0
0
1
2
0
0
2
0
0
1
0
0
0
2
1
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
1
1
0
1
0
0
0
0
1
0
2
0
1
1
0
2
0
0
3
3
0
0
0
0
0
2
0
0
0
2
1
0
0
0
1
2
0
0
2
1
0
0
1
0
0
0
2
2
1
2
2
2
0
2
0
1
2
0
0
1
1
0
0
0
0
1
2
0
2
2
1
0
2
0
0
0
2
0
1
1
0
0
0
0
0
0
1
0
1
2
1
2
1
0
1
0
0
1
2
0
0
0
0
1
1
2
1
0
1
1
0
0
0
1
0
1
0
0
1
0
0
0
1
0
2
2
0
1
0
1
0
0
0
0
0
1
0
2
0
0
0
2
1
1
0
0
1
2
0
0
0
2
0
1
2
0
0
0
1
1
0
0
0
0
2
0
0
1
0
2
2
0
6
0
2
1
1
1
0
1
0
0
1
1
0
2
2
0
0
1
2
0
0
0
0
0
2
0
0
0
1
2
0
1
2
0
1
0
0
2
0
0
0
0
0
0
3
1
0
1
1
0
1
0
0
0
2
0
3
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
3
0
0
2
2
0
1
0
0
0
0
0
2
1
0
0
0
1
1
0
0
0
1
1
0
2
0
1
1
0
0
0
0
0
1
0
2
0
0
1
0
0
2
1
1
0
0
0
0
1
0
0
0
1
1
0
0
2
0
2
0
0
0
0
2
1
0
0
2
0
2
0
1
1
0
0
0
0
0
0
2
0
0
0
1
1
2
0
0
2
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
2
0
2
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
3
2
0
2
2
2
0
2
2
0
1
0
0
0
2
1
0
2
0
0
1
2
0
0
0
0
0
1
0
0
2
1
0
0
2
2
2
0
2
0
1
2
0
0
0
1
0
0
0
0
2
0
0
1
2
0
0
2
1
0
0
0
2
0
0
1
0
1
0
0
1
1
0
1
1
0
0
2
0
0
0
0
1
2
0
0
0
0
0
2
1
1
2
0
0
1
0
0
0
0
0
0
1
0
1
1
1
0
0
0
2
0
0
0
2
0
0
1
0
0
2
1
0
0
0
2
0
0
1
1
2
0
0
0
1
1
0
2
0
0
0
2
0
0
0
0
2
1
1
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
1
1
0
0
2
1
1
0
1
0
0
2
0
1
0
1
0
1
0
0
2
1
0
1
1
0
2
0
1
2
0
0
2
0
1
1
0
0
0
1
0
0
2
2
0
2
0
3
0
0
2
1
0
0
0
2
2
0
1
2
1
0
4
0
2
0
0
2
1
0
0
2
0
0
0
0
0
0
0
1
0
4
0
2
0
0
1
0
2
1
0
2
2
2
2
2
0
0
0
2
0
2
0
0
2
0
2
1
0
0
0
1
0
2
0
0
2
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
1
3
2
2
1
0
3
0
2
1
0
0
0
0
2
1
0
1
0
0
0
1
0
3
0
0
0
2
0
0
0
1
2
0
0
1
0
3
1
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
2
1
0
1
0
2
2
0
2
0
0
2
2
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
2
2
0
2
0
0
0
0
0
1
1
2
1
1
2
0
0
0
0
2
0
7
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
3
0
0
0
0
0
3
0
0
1
0
0
1
0
1
0
1
0
2
0
2
0
1
2
0
1
0
2
0
2
0
2
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
1
1
2
0
0
0
0
1
0
0
0
1
0
0
2
1
2
0
0
0
0
0
0
0
0
1
0
2
2
0
1
0
2
2
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
3
0
0
1
0
0
0
0
0
0
1
0
0
2
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
1
2
1
2
1
0
1
0
0
1
0
2
0
0
0
0
2
0
2
0
0
2
1
0
0
0
0
3
2
0
0
1
0
0
0
1
0
2
0
0
3
0
0
1
0
0
0
1
2
0
0
0
0
2
0
1
0
1
1
0
2
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
2
0
1
0
0
0
0
1
0
3
1
2
0
1
1
0
2
0
1
5
0
0
0
0
0
0
0
0
4
0
1
1
3
0
1
2
3
0
1
0
0
0
0
1
0
2
0
2
1
2
0
0
0
2
0
1
0
1
0
2
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
1
1
2
1
0
2
0
0
2
0
3
0
0
2
2
1
0
1
0
2
1
0
0
0
2
0
0
2
2
0
0
0
0
2
0
1
2
2
0
0
0
2
1
0
1
0
0
2
0
1
2
0
0
0
0
0
2
0
0
1
9
0
0
0
2
2
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
6
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
1
0
2
0
1
0
1
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
1
0
2
0
3
0
0
0
0
0
0
0
4
1
0
0
0
0
1
1
0
0
1
0
0
0
0
2
0
1
2
0
2
0
0
1
2
1
2
2
1
1
0
0
1
2
0
0
0
1
0
0
0
0
1
1
0
0
1
2
0
0
2
0
0
0
1
0
1
2
0
0
0
0
2
0
2
1
0
0
2
0
0
2
0
0
0
1
0
0
0
1
0
1
0
1
1
2
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
3
0
0
1
1
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
2
0
1
2
3
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
1
1
2
2
1
0
2
0
0
0
2
0
0
2
0
0
0
0
0
2
0
2
0
0
1
0
0
0
1
0
2
1
0
0
0
1
1
2
0
0
2
0
0
1
0
0
0
1
3
2
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
1
0
0
1
2
0
0
1
0
1
2
0
0
0
0
3
0
0
0
0
1
0
1
0
2
0
0
0
0
2
2
3
2
2
0
1
0
3
0
6
0
0
0
1
0
2
0
0
4
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
1
0
0
2
0
1
0
2
0
0
0
1
1
0
2
0
0
0
2
0
1
1
0
1
1
2
0
0
2
0
0
0
0
0
0
1
2
0
1
1
0
1
2
0
0
2
1
0
1
0
0
0
1
1
2
0
2
0
0
0
1
1
2
0
0
2
1
1
0
0
0
0
2
4
0
0
2
0
0
0
0
1
0
0
0
1
0
0
1
1
0
1
0
0
0
1
4
1
0
1
0
1
0
0
0
0
1
2
2
0
0
1
0
0
0
0
0
0
2
2
0
0
1
2
0
0
0
0
1
0
0
1
0
1
1
0
0
0
1
0
1
1
1
0
3
1
0
1
0
0
1
1
2
0
1
4
1
0
0
0
0
1
1
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
2
0
1
1
1
2
1
1
1
3
1
1
2
0
0
1
0
0
1
0
0
1
2
0
1
0
1
0
0
0
0
0
0
0
3
0
0
2
0
0
0
1
0
0
2
2
2
0
0
0
0
1
0
2
0
0
2
0
1
1
0
3
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
3
2
1
0
4
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
2
1
0
2
0
0
2
1
1
1
0
1
0
0
0
1
2
0
1
0
0
1
1
2
1
0
0
1
0
2
0
0
3
0
0
2
0
2
1
0
0
1
0
0
2
1
0
0
2
0
0
0
0
2
0
1
0
0
0
2
0
0
0
2
0
3
2
0
0
0
1
2
1
0
1
2
0
0
0
1
0
1
0
2
0
2
0
0
1
0
2
2
2
0
1
0
1
1
1
2
0
2
0
1
0
0
0
2
0
0
1
1
2
1
2
0
2
0
0
0
2
1
0
1
2
2
0
0
0
0
2
2
0
1
1
0
0
0
0
1
0
0
0
0
0
2
0
1
0
2
2
0
2
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
2
0
2
2
0
0
0
0
0
1
2
2
2
0
1
0
0
2
0
1
1
0
0
0
1
0
0
1
0
0
2
1
2
1
0
1
0
1
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
1
0
0
0
2
1
1
1
0
1
2
1
0
0
0
0
3
0
0
2
2
0
0
1
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
1
1
2
0
1
1
1
2
2
1
1
1
2
0
0
1
2
0
0
0
0
0
0
0
2
0
2
1
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
2
0
2
0
0
0
2
1
0
1
0
2
0
2
0
1
2
2
0
0
0
1
2
2
0
0
2
2
0
0
1
2
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
2
1
0
0
2
0
0
0
0
1
0
2
0
0
1
3
0
0
1
3
1
0
0
1
2
0
0
0
0
0
0
0
0
2
1
2
0
0
0
2
0
1
0
3
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
2
2
0
1
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
2
3
1
1
2
3
0
0
1
0
1
0
0
0
1
0
2
0
0
0
2
2
0
0
0
0
0
0
1
0
0
1
0
0
0
2
1
1
2
0
1
0
0
0
1
0
0
2
0
0
1
0
2
1
0
0
2
0
0
1
1
3
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
2
2
1
0
0
2
0
2
1
1
0
1
1
0
0
0
1
2
0
0
0
2
0
0
2
0
0
0
1
0
0
0
1
0
0
0
1
2
0
0
0
2
0
1
0
0
0
1
0
8
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
1
1
1
1
0
1
2
3
4
1
0
1
0
0
0
2
0
0
0
2
0
2
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
1
2
0
1
2
0
1
1
2
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
2
1
0
1
1
0
2
2
3
0
4
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
1
1
0
0
2
0
0
0
0
1
2
0
0
1
0
0
4
3
0
0
0
2
1
0
1
0
2
0
2
0
2
0
1
3
3
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
1
0
0
0
1
1
0
2
0
1
0
0
1
3
2
2
0
0
1
0
0
0
2
0
0
0
2
0
0
0
1
0
1
0
0
1
1
0
0
0
0
1
0
0
1
1
0
0
0
2
0
0
3
0
0
0
0
0
0
0
2
1
2
1
0
0
1
2
0
2
1
0
0
2
0
0
0
0
1
1
0
0
0
1
0
2
1
0
0
0
2
1
0
0
2
2
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
2
1
0
1
0
0
0
0
2
0
0
0
0
1
0
0
1
0
3
3
0
0
0
2
0
0
0
0
1
0
0
1
0
2
2
0
0
0
1
0
1
0
0
2
2
0
1
1
2
0
1
0
2
1
2
2
0
2
0
1
0
0
1
0
1
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
2
0
1
0
1
0
1
0
0
0
0
2
0
1
2
0
0
0
0
2
1
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
2
2
2
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
1
0
0
2
0
0
1
0
2
2
0
1
0
0
0
0
2
2
2
0
0
0
1
0
2
0
2
0
0
0
2
0
0
0
0
0
1
1
0
0
0
1
2
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
1
0
1
2
0
1
0
0
8
0
0
2
1
0
0
0
0
0
0
0
1
2
3
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
1
0
1
2
0
0
0
0
0
1
2
0
0
2
0
0
1
0
2
2
0
0
0
2
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
1
2
0
0
2
0
2
0
1
0
0
2
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
2
0
1
5
0
0
2
0
2
2
0
2
1
0
2
1
0
1
0
1
0
0
0
1
0
2
0
2
1
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
1
0
1
0
0
0
0
2
0
1
1
0
0
0
1
2
0
1
0
2
2
0
1
0
0
3
0
1
0
1
0
2
0
0
1
0
2
0
0
2
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
2
0
2
2
2
0
2
0
0
1
0
0
1
1
0
3
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
2
0
2
0
0
1
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
3
0
0
0
0
2
2
0
2
0
0
0
1
0
0
2
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
3
2
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
1
2
2
1
1
2
2
0
2
0
1
0
0
0
2
2
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
3
2
0
2
0
2
0
0
0
0
1
0
3
0
0
0
0
1
2
0
0
3
0
0
2
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
2
1
0
2
0
2
0
0
1
0
0
0
2
0
0
1
0
1
0
2
0
1
0
1
0
2
0
0
0
1
0
0
2
2
1
0
1
0
1
1
1
0
0
0
0
0
2
0
1
0
0
1
1
0
0
2
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
1
0
2
2
0
0
0
2
2
0
0
0
1
1
0
1
0
0
0
0
2
0
1
1
0
0
0
0
1
2
3
3
0
0
0
0
1
0
1
2
0
0
0
1
0
2
0
1
0
0
1
0
1
0
0
1
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
2
0
2
0
0
0
0
2
2
2
0
0
0
0
1
1
0
0
1
0
2
1
2
2
0
0
0
0
2
2
1
0
1
1
0
0
0
0
1
2
0
1
2
0
0
2
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
2
0
2
0
0
0
1
2
0
2
0
0
0
0
0
1
1
0
2
0
3
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
3
1
1
0
0
2
2
0
0
0
2
1
0
0
1
2
0
0
1
0
0
1
0
1
2
0
0
0
0
0
1
0
1
0
0
0
2
1
1
0
1
1
2
1
0
1
0
0
1
0
0
0
0
0
2
0
1
3
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
2
0
1
1
0
0
1
0
0
1
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
2
0
0
0
2
0
0
3
2
1
0
1
0
0
0
0
1
0
2
2
1
2
0
0
0
1
0
0
1
1
0
1
2
1
0
1
3
3
0
0
0
0
1
0
0
1
0
0
1
2
0
1
2
0
0
0
5
1
0
2
0
0
0
0
0
0
0
1
1
2
0
0
0
0
2
1
0
0
2
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
1
0
1
0
0
2
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
2
0
1
1
0
0
0
0
0
2
0
1
2
2
1
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
1
0
2
0
2
2
0
0
1
0
1
0
1
3
2
2
3
2
0
0
1
0
2
0
0
2
1
0
2
2
0
0
0
2
0
2
0
0
0
0
1
0
1
1
0
2
0
0
1
0
0
2
0
3
0
0
2
0
1
3
0
0
2
0
1
2
1
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
1
0
0
0
2
0
3
1
0
2
0
2
0
2
2
1
0
3
0
0
1
0
0
0
0
0
1
0
3
1
2
0
0
0
1
0
0
2
0
0
0
0
1
1
2
0
1
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
1
2
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
1
1
0
2
1
2
0
0
0
1
0
0
0
2
0
0
0
0
3
2
1
0
0
1
0
1
0
1
2
0
1
2
0
1
2
0
0
1
1
2
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
2
0
2
0
0
3
0
2
2
0
0
0
0
1
0
0
2
0
1
0
1
1
0
3
1
0
0
1
0
2
0
0
0
0
2
2
0
0
2
0
1
2
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
2
0
1
0
2
1
0
1
0
1
0
0
2
0
2
2
0
3
0
0
1
0
0
0
0
2
0
0
2
0
0
1
0
0
2
0
0
2
0
2
0
0
0
0
0
1
0
0
1
0
0
2
3
0
0
0
2
0
2
1
1
0
0
0
1
0
2
0
0
1
0
1
2
0
0
0
0
0
1
0
2
0
0
2
0
1
0
1
0
0
0
1
0
0
2
1
1
2
1
0
0
0
2
2
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
2
2
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
1
2
0
0
1
1
0
0
0
0
2
1
2
1
0
0
0
1
3
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
3
2
0
1
0
0
0
0
2
2
2
2
1
0
0
0
1
1
0
0
0
0
1
0
0
1
1
0
0
2
0
0
2
0
1
0
0
1
0
2
0
1
2
0
2
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
2
0
1
0
2
1
1
0
0
0
0
2
2
0
0
0
0
1
1
0
0
1
0
2
2
0
1
1
1
0
0
0
0
2
0
3
0
1
0
2
1
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
2
0
0
0
1
0
0
0
1
0
2
1
0
1
0
0
1
0
0
0
1
0
0
0
3
0
0
2
0
1
1
0
0
1
2
0
0
1
0
0
2
1
0
2
0
2
3
1
1
1
0
0
0
0
1
1
0
2
4
0
1
1
1
0
0
1
2
0
0
0
1
2
1
1
0
0
1
1
1
2
0
0
0
0
0
2
0
2
1
1
0
2
0
0
1
2
0
0
2
0
0
0
0
1
0
1
2
2
1
0
0
0
1
1
0
0
0
0
0
2
1
0
0
3
0
2
0
0
2
2
0
0
0
2
0
0
0
1
1
0
0
0
0
2
2
0
0
1
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
1
1
0
1
0
0
1
0
1
1
1
0
2
1
0
0
1
0
0
2
0
0
0
2
0
2
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
2
2
2
1
0
0
1
0
1
0
0
2
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
1
2
0
0
0
1
0
0
2
1
0
0
0
2
2
0
0
0
1
1
0
0
0
0
0
2
0
0
0
2
2
0
1
0
2
0
0
0
0
0
0
0
2
5
0
0
1
0
0
0
0
0
1
0
0
2
1
3
2
1
0
1
2
3
1
1
0
0
0
0
0
1
2
0
2
2
0
1
0
2
0
0
2
0
3
0
2
0
2
2
0
0
1
0
2
1
0
0
1
2
0
0
2
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
1
1
0
0
1
0
0
2
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
1
0
2
0
0
1
0
0
2
0
1
1
2
0
0
1
0
0
1
0
1
0
0
0
2
0
0
0
0
0
1
0
0
2
2
0
0
1
1
0
0
2
0
0
1
0
0
2
2
1
0
1
0
0
2
0
1
1
2
2
1
0
0
2
1
2
0
0
0
0
1
0
2
0
0
0
2
0
1
1
1
0
1
0
0
1
0
2
2
0
3
0
0
0
1
0
1
0
1
1
1
1
0
0
1
0
2
0
0
0
1
2
0
0
0
1
0
1
0
0
0
1
1
1
2
0
1
0
0
0
0
2
1
0
1
2
2
2
0
0
1
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
1
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
1
1
0
0
1
1
1
0
0
1
0
1
0
0
0
0
0
0
1
0
2
1
2
0
1
0
3
0
0
2
0
1
2
0
1
0
2
0
2
1
1
2
0
0
0
0
2
0
0
1
1
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
2
1
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
2
0
0
0
2
2
0
1
0
1
0
1
0
1
2
0
0
0
1
0
0
1
0
1
0
0
0
1
1
1
2
2
0
1
0
1
1
1
2
2
2
2
0
1
3
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
3
2
0
0
0
0
0
3
0
0
1
1
0
0
0
0
0
0
1
2
1
0
1
0
0
2
0
0
0
1
0
0
0
1
0
0
0
2
0
2
2
1
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
2
1
0
1
0
1
0
0
1
0
0
1
0
0
0
0
1
1
0
1
2
0
1
1
2
0
0
2
2
1
0
0
1
0
0
0
1
2
0
0
0
1
0
0
2
2
0
2
0
0
2
1
0
1
0
0
1
2
0
0
1
0
1
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
2
0
0
0
0
2
2
2
1
2
1
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
1
1
1
1
2
2
2
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
1
1
0
2
3
2
0
1
2
0
1
0
1
1
1
3
3
0
2
0
1
2
2
2
1
1
2
3
1
0
0
0
1
0
2
2
1
0
0
3
1
0
0
0
1
0
2
0
0
0
1
0
1
0
1
2
0
0
1
0
0
0
2
1
1
1
1
2
0
0
0
0
1
0
2
5
0
3
0
0
2
0
1
0
1
0
0
2
0
1
2
0
0
0
0
0
2
2
0
0
2
0
3
2
2
2
1
0
0
0
0
0
0
1
0
0
0
0
1
0
2
2
2
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
2
1
0
2
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
1
0
2
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
2
1
0
3
0
0
3
0
1
2
2
0
0
2
0
0
0
0
1
2
1
2
0
0
2
1
0
0
0
0
0
0
2
1
1
2
0
0
0
0
0
1
2
2
0
0
0
0
0
3
0
2
0
2
1
2
2
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
2
0
1
0
0
0
0
2
1
0
1
2
1
2
0
0
0
1
0
0
1
2
1
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
1
2
2
1
2
2
2
1
0
1
0
0
0
1
0
0
2
2
0
0
0
1
1
1
0
1
2
1
2
0
0
2
1
0
1
2
0
2
3
2
1
0
0
2
0
0
0
2
0
1
0
0
1
2
1
0
1
2
0
0
0
1
1
0
0
1
0
2
0
1
1
2
2
0
2
0
2
0
2
1
1
2
0
0
1
1
0
0
0
0
0
1
2
0
0
2
0
0
0
1
0
0
3
1
0
1
0
1
0
0
2
0
0
3
0
0
2
0
0
1
0
0
1
0
1
0
0
0
0
0
1
1
1
0
1
2
2
0
0
2
2
1
0
2
2
0
2
0
0
0
0
1
1
0
1
1
1
1
0
3
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
1
0
2
2
0
0
0
2
1
5
0
0
2
2
0
0
4
0
0
0
1
0
2
2
1
0
1
1
0
0
0
1
0
0
1
0
0
1
1
1
1
0
2
2
0
1
0
0
1
2
2
2
0
0
0
0
1
1
2
0
1
0
0
0
2
0
0
0
0
1
0
1
1
0
2
1
1
1
0
1
0
0
0
0
0
2
0
0
1
2
0
0
0
2
1
0
0
0
2
2
0
0
0
2
0
0
0
0
1
2
0
2
0
3
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
3
2
1
0
0
0
0
0
0
5
1
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
2
0
1
0
1
1
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
5
0
0
1
0
0
0
0
0
2
0
1
1
2
0
0
0
0
2
1
0
3
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
2
0
0
1
0
0
0
2
4
0
0
1
0
0
0
1
1
0
0
0
1
0
0
1
1
0
0
0
0
3
0
0
0
1
0
0
2
0
0
1
0
0
1
0
2
2
0
0
0
0
2
2
1
0
0
2
1
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
2
0
0
1
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
3
2
0
0
1
0
0
0
0
2
0
0
0
0
1
1
0
1
0
2
1
0
0
2
0
0
2
0
0
1
1
0
1
2
2
0
0
0
0
0
1
2
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
3
1
1
1
0
2
3
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
2
1
0
2
0
7
0
0
2
0
2
0
1
2
3
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
2
0
2
1
0
0
1
1
0
0
0
0
0
0
1
1
2
0
1
0
0
1
0
0
0
1
2
0
0
0
0
1
0
0
0
1
0
0
0
2
2
2
0
1
1
0
0
1
0
2
0
0
0
0
0
2
0
1
0
0
0
3
2
1
0
0
0
0
1
0
2
2
0
1
0
1
1
1
0
2
0
0
2
1
0
2
0
0
0
0
0
2
3
0
0
2
0
0
0
0
0
1
0
1
2
1
0
1
2
3
0
1
0
0
1
1
1
0
0
0
0
1
1
0
0
2
0
1
2
0
0
0
1
0
0
0
0
1
0
2
0
0
2
2
0
0
2
0
2
1
0
0
1
0
0
1
0
0
2
0
1
0
2
0
0
0
0
2
0
1
1
0
0
2
2
0
1
0
0
1
2
0
0
0
1
2
2
0
4
2
2
2
0
1
0
2
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
1
1
0
2
2
0
0
0
0
1
2
2
0
0
0
0
8
3
1
1
0
2
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
2
1
0
0
1
0
0
1
2
0
1
3
2
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
1
0
0
2
0
2
0
0
0
2
0
0
2
0
2
1
0
2
1
0
1
1
0
2
0
0
0
2
1
0
1
2
2
0
1
2
0
0
2
2
2
0
1
2
0
0
2
0
1
0
0
0
1
0
0
0
0
3
0
0
0
1
0
0
2
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
3
0
0
1
0
0
0
0
0
3
0
0
1
2
0
0
1
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
2
1
0
0
0
0
2
1
2
1
2
0
1
1
0
0
2
2
3
0
0
1
0
0
3
2
0
0
1
0
0
2
3
0
0
1
0
1
3
0
1
0
1
0
1
0
1
0
2
1
0
0
1
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
1
1
0
0
0
1
0
2
2
0
0
0
1
0
0
2
1
0
2
4
0
0
0
2
0
2
0
0
0
0
3
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
4
0
0
0
2
0
0
3
0
1
0
0
1
0
0
0
0
0
1
1
0
1
0
1
0
0
1
0
1
7
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
2
4
0
2
1
2
0
0
0
0
1
0
1
0
0
1
0
2
0
2
2
1
0
0
0
2
0
1
0
0
1
0
0
0
1
0
2
0
2
0
0
1
2
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
6
0
0
1
0
0
0
0
0
0
1
1
2
0
0
1
2
0
1
1
2
1
0
0
0
1
0
0
2
2
2
0
2
0
0
0
5
0
2
1
2
0
4
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
2
0
2
0
0
2
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
2
0
0
2
0
0
0
1
2
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
4
1
1
2
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
1
1
0
2
4
2
0
0
0
2
1
0
0
0
0
0
1
1
0
2
3
1
0
1
0
1
0
0
1
0
1
0
2
2
2
0
1
0
2
1
0
1
0
1
0
0
0
2
0
2
0
0
2
2
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
1
2
1
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
1
0
0
1
3
1
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
3
0
0
0
1
2
1
0
0
0
1
0
0
2
0
1
0
2
0
2
0
0
1
0
0
2
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
3
1
2
2
0
1
0
3
0
0
0
0
0
2
2
0
0
0
0
0
2
0
1
0
0
2
0
2
0
1
0
0
2
0
2
0
0
2
0
2
0
2
1
2
1
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
2
1
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
1
0
0
2
1
2
0
1
0
0
0
0
0
2
0
1
2
0
0
0
1
2
0
2
0
1
1
1
0
1
0
1
0
1
1
0
2
1
1
0
0
1
2
0
4
0
0
1
2
0
0
1
0
2
0
3
0
0
0
0
2
0
1
0
0
0
0
2
0
0
1
0
2
2
0
2
0
0
1
2
0
0
0
0
1
0
2
1
0
0
0
1
0
1
0
1
0
2
0
0
0
0
0
0
2
1
1
1
1
1
0
2
1
1
0
0
3
0
0
2
1
0
0
0
0
0
0
2
0
0
3
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
2
2
0
2
0
0
0
0
1
0
0
1
3
0
2
1
0
2
1
2
1
2
0
0
2
3
0
0
1
0
0
0
0
1
3
0
0
0
1
1
2
0
1
0
2
0
3
2
0
2
3
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
1
2
1
0
2
1
0
0
0
2
0
0
0
0
2
1
1
0
1
0
2
0
1
0
3
2
0
2
2
2
0
0
2
1
1
0
0
1
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
1
2
0
1
0
2
1
1
0
0
0
1
2
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
1
0
1
1
0
0
1
1
0
0
0
0
0
1
2
0
0
0
1
1
1
0
0
2
1
0
0
0
0
0
0
0
2
1
0
1
0
1
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
1
0
2
1
1
0
0
0
0
2
0
0
0
1
0
0
1
0
2
1
1
0
0
0
0
2
0
1
0
0
0
0
6
0
0
0
0
1
2
0
0
1
0
0
1
1
0
0
2
2
0
0
1
1
0
1
2
1
2
1
2
0
1
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
2
0
0
1
0
0
1
0
0
2
0
0
0
2
1
1
0
0
1
0
2
0
0
0
0
0
0
1
2
0
0
0
2
0
0
1
2
0
1
0
0
0
0
0
2
0
0
3
0
1
0
0
0
0
2
0
0
2
0
1
0
0
0
2
0
0
2
2
1
0
0
3
1
0
1
4
0
0
1
2
0
1
0
0
0
0
2
0
2
0
2
2
0
0
1
0
1
0
0
2
0
1
0
0
0
0
2
0
0
0
1
0
2
1
0
0
1
0
1
0
0
1
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
2
2
2
0
0
1
0
0
0
0
0
0
0
1
1
0
1
2
2
0
7
2
0
0
1
1
0
0
0
1
0
1
1
1
0
0
2
0
0
0
2
0
0
0
1
0
2
1
1
0
2
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
2
0
1
0
2
0
0
0
0
0
1
0
0
1
0
0
2
0
0
1
1
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
2
1
1
0
1
0
1
0
0
2
0
0
0
1
0
2
0
0
0
3
2
0
0
0
0
3
0
0
2
0
4
2
0
1
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
2
1
0
1
0
2
0
0
0
1
1
1
1
1
0
0
1
2
0
0
1
0
2
0
0
2
1
1
1
1
1
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
1
2
1
0
0
1
1
1
1
0
2
0
0
0
0
0
0
0
1
2
0
0
1
2
0
0
0
0
2
2
0
1
1
1
0
3
0
2
2
2
0
0
2
2
0
0
0
0
2
0
1
0
1
1
0
0
1
0
2
1
0
0
2
0
0
1
2
0
0
2
2
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
1
0
4
1
2
0
1
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
1
1
0
0
0
0
1
2
0
0
2
1
0
1
0
0
0
1
4
0
0
0
0
0
0
1
0
2
0
0
1
2
0
1
0
0
2
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
1
2
0
2
1
0
0
0
2
0
3
0
3
1
2
0
1
0
0
0
1
2
0
1
0
2
0
0
0
1
0
1
0
0
0
1
2
0
0
0
0
0
2
0
2
1
0
2
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
5
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
2
0
0
0
2
6
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
1
0
0
0
2
1
1
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
2
2
0
1
0
1
0
1
1
0
0
2
0
1
2
0
0
0
0
2
1
0
0
2
1
1
0
0
0
0
0
0
0
0
2
0
1
1
0
1
0
1
0
0
1
0
0
0
0
0
2
1
0
1
2
0
1
0
1
1
1
2
0
2
1
1
1
0
2
0
0
1
0
0
0
0
0
0
0
1
1
2
0
0
1
0
1
0
0
1
0
0
1
2
0
0
0
0
0
0
2
1
0
0
1
0
3
1
1
1
1
1
0
0
1
1
0
0
0
1
0
0
0
1
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
1
2
0
0
0
0
0
0
0
1
2
2
1
1
0
0
0
0
1
2
0
2
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
1
0
1
2
0
0
0
0
0
0
0
3
1
0
0
0
1
0
0
0
1
0
2
0
2
0
0
0
1
2
1
2
1
1
0
2
0
1
2
0
0
0
0
2
0
0
0
0
0
1
0
1
0
2
0
0
0
1
0
1
11
0
2
1
1
0
0
2
0
1
0
0
0
1
0
2
0
0
1
0
3
0
0
0
0
0
0
1
0
2
0
2
0
0
0
2
1
0
2
2
2
0
2
0
0
0
0
2
2
2
0
0
1
0
0
2
0
2
1
0
0
0
0
1
0
3
1
1
0
0
0
3
1
2
0
0
1
1
1
0
0
0
0
1
1
0
1
2
1
0
1
1
0
2
1
1
2
0
2
0
2
1
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
1
0
2
2
1
2
0
1
0
2
0
0
0
2
0
1
1
0
1
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
1
1
2
0
0
0
0
1
0
0
2
0
1
2
0
0
0
0
0
1
0
0
1
1
2
3
0
0
0
0
0
1
2
0
2
0
0
0
0
1
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
2
1
1
0
2
2
1
1
1
2
0
1
2
0
1
0
1
1
0
1
0
2
0
1
0
0
1
0
1
0
0
0
2
1
1
2
1
0
0
2
3
1
1
0
0
2
1
0
0
0
0
0
0
0
0
2
0
2
1
0
0
1
2
1
2
1
3
2
1
0
1
0
0
2
0
0
1
0
0
0
1
0
1
2
0
1
1
2
0
0
1
0
1
1
0
0
0
0
0
1
2
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
1
0
1
2
0
0
0
2
0
1
0
1
0
2
0
0
0
2
1
0
0
0
1
0
1
0
1
2
0
0
1
1
0
0
0
0
2
0
2
0
1
2
0
1
0
0
0
0
0
2
2
0
2
2
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
2
1
0
0
3
0
1
0
0
0
2
1
0
0
0
0
0
0
2
1
0
1
0
2
2
1
1
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
1
0
2
1
1
2
0
2
0
1
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
1
0
0
0
2
1
0
0
0
1
0
0
2
2
0
0
1
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
1
2
4
0
0
1
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
1
1
0
1
1
0
0
0
1
2
2
1
0
0
0
1
0
3
0
0
0
0
0
0
0
0
1
0
1
4
1
2
0
1
2
0
0
0
3
0
2
0
0
1
0
0
0
2
0
0
0
1
2
0
0
0
1
0
0
0
1
0
0
0
0
0
2
1
2
1
0
0
1
0
0
2
0
0
0
1
2
0
1
0
0
0
0
0
1
0
0
0
2
0
0
2
0
1
0
0
1
2
2
2
0
1
1
0
0
0
0
1
0
0
0
1
0
1
1
0
0
2
0
0
2
2
1
0
2
0
0
1
0
0
0
2
1
1
0
0
0
1
1
0
0
0
1
0
2
0
1
2
2
0
0
1
0
0
2
0
0
1
1
2
0
0
0
0
1
2
3
0
0
0
0
3
1
2
1
1
0
0
0
2
0
0
0
2
0
0
4
2
0
0
0
0
1
1
2
1
0
0
0
0
1
0
0
0
2
2
0
1
6
0
0
0
0
1
2
0
0
1
1
0
1
1
0
0
1
0
1
0
1
1
0
0
0
1
0
0
0
5
0
0
2
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
2
0
0
2
0
1
0
0
0
0
0
0
1
0
1
1
2
0
2
0
2
0
0
1
1
2
0
0
2
0
1
0
0
0
0
1
0
1
1
1
0
2
2
0
0
0
2
1
0
2
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
1
2
1
0
2
0
0
0
0
1
0
2
0
2
0
2
0
0
1
1
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
2
0
3
0
1
1
2
2
1
0
0
2
1
2
0
0
2
0
0
0
0
2
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
1
0
0
2
1
0
2
3
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
2
0
0
2
2
2
0
0
3
0
0
0
2
0
0
0
0
1
0
1
0
0
2
0
0
1
0
0
0
0
0
1
3
0
1
0
2
0
1
0
1
0
1
1
0
1
0
3
0
1
0
0
1
1
0
0
0
0
0
1
3
1
1
2
0
0
2
0
1
2
0
0
2
0
0
0
0
1
2
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
1
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
2
1
0
0
2
0
2
0
2
0
1
0
0
0
1
0
1
0
0
0
0
0
1
1
0
1
1
1
0
0
0
0
0
0
2
0
0
0
0
1
0
2
2
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
2
2
2
2
0
2
1
1
0
0
0
0
2
0
1
0
1
1
1
0
0
1
2
1
0
1
0
0
1
0
2
0
0
0
3
0
2
2
1
1
0
0
2
0
0
0
1
0
1
0
2
0
1
0
1
2
1
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
1
0
2
2
0
0
2
0
0
2
0
0
0
2
2
0
2
1
0
0
3
0
0
0
0
2
1
0
1
0
0
0
1
0
0
2
2
4
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
2
1
0
2
0
0
3
0
2
1
2
0
2
0
1
0
1
0
3
1
2
2
0
0
3
1
2
0
2
0
3
4
0
0
1
0
0
0
0
3
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
2
2
0
2
0
0
0
0
3
0
0
0
2
0
2
0
0
0
0
1
0
0
3
1
1
0
0
0
2
0
1
0
1
1
1
1
0
0
0
1
0
0
0
0
1
0
2
0
0
0
1
0
2
0
2
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
2
2
0
1
0
0
0
2
0
1
0
2
1
0
0
2
0
0
0
1
1
1
1
0
0
2
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
1
1
0
0
2
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
2
0
1
0
0
0
0
2
0
1
0
1
1
0
0
3
0
2
0
0
0
0
2
3
1
0
0
1
0
0
0
1
2
1
1
0
0
1
0
1
0
0
0
0
2
2
1
0
2
0
2
2
0
0
0
0
0
2
2
0
1
0
0
0
2
1
0
2
1
2
1
1
0
0
0
0
1
1
2
0
0
0
0
2
3
0
1
2
2
0
2
2
0
1
1
0
0
0
2
0
0
0
0
0
1
3
3
1
0
0
0
0
2
2
1
1
0
2
0
2
2
0
0
0
0
2
1
0
0
2
1
2
0
0
0
0
1
1
1
2
2
0
0
1
1
1
0
2
0
0
1
3
1
2
0
0
0
0
0
2
1
1
0
1
0
0
0
0
0
1
0
1
0
1
0
2
2
1
0
1
0
1
1
0
0
2
2
0
2
0
0
1
0
3
0
2
2
0
2
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
2
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
2
2
2
1
0
0
1
2
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
1
2
0
0
0
1
1
2
0
0
0
0
2
1
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
1
0
1
0
2
0
0
1
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
1
0
3
0
0
0
0
2
0
0
2
1
2
0
0
0
1
2
0
0
0
1
0
0
0
1
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
2
1
0
1
0
0
0
1
1
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
1
0
0
1
0
0
1
0
0
1
1
0
1
1
2
1
0
1
2
0
0
0
1
0
1
0
1
2
0
0
0
2
0
0
0
0
1
0
1
2
1
1
2
0
0
0
0
0
0
0
1
1
4
2
0
0
0
2
0
3
1
2
0
1
0
0
0
0
0
0
1
2
0
0
0
2
0
2
0
0
0
2
1
0
0
1
0
0
1
0
0
0
3
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
1
2
0
0
0
1
1
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
2
1
2
0
2
2
0
2
0
0
1
4
1
1
0
0
0
0
1
0
3
0
0
0
0
1
3
0
0
0
1
0
0
1
2
0
2
1
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
2
2
1
0
0
0
0
0
0
0
1
1
0
0
0
3
2
0
2
0
0
1
2
1
1
1
0
2
0
0
0
0
0
2
2
2
0
0
1
1
2
0
2
1
0
0
0
0
2
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
1
2
2
0
0
0
0
2
0
0
0
1
2
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
1
2
0
0
0
0
0
1
9
2
2
1
2
2
0
0
2
0
0
1
0
2
0
0
2
0
2
2
0
2
2
0
0
2
0
0
0
2
0
0
2
1
0
0
1
2
0
2
0
0
1
0
0
0
1
2
2
0
0
0
0
2
0
0
1
0
2
1
0
0
0
0
0
2
1
2
1
0
1
0
0
0
0
2
0
0
0
0
1
2
0
1
0
0
1
0
1
1
1
2
1
1
2
0
1
2
0
1
2
0
0
2
2
0
0
3
0
0
0
0
2
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
1
2
2
2
0
0
0
3
1
0
0
2
0
1
0
2
0
1
0
2
0
0
0
0
0
0
2
2
2
0
0
0
0
2
0
1
0
0
1
3
2
0
0
0
0
1
0
0
2
0
2
0
0
1
0
0
0
1
2
0
1
2
0
1
0
1
2
2
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
2
0
2
1
2
0
0
1
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
3
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
2
1
1
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
1
0
1
0
0
0
0
0
0
0
2
1
2
2
1
0
1
0
1
0
0
0
2
0
0
0
1
1
3
1
2
0
0
0
0
1
2
2
0
0
1
0
0
2
0
2
1
0
1
0
2
0
0
0
3
2
2
2
2
0
0
0
0
2
2
0
1
0
0
0
0
0
0
2
2
1
0
1
0
0
0
2
2
0
2
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
3
1
1
2
1
0
0
0
0
0
1
2
0
0
1
1
1
0
1
0
2
1
2
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
1
1
1
0
0
2
0
1
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
2
0
0
2
0
2
0
0
0
0
1
1
0
0
0
0
4
0
0
0
0
1
1
0
0
0
1
1
0
0
3
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
1
2
1
1
0
0
0
0
0
1
0
0
0
2
0
2
2
1
2
2
0
0
0
0
0
0
0
3
3
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
2
0
1
2
0
0
0
1
14
0
0
0
2
2
0
0
0
2
2
0
0
0
2
2
0
0
0
0
2
0
0
0
3
0
0
1
0
2
0
0
0
0
0
0
0
1
0
1
1
1
1
0
1
0
1
1
0
0
0
0
0
0
4
0
0
0
0
1
1
2
0
1
0
1
5
1
2
0
2
0
0
3
0
2
0
2
1
1
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
1
0
1
2
0
0
0
2
0
1
0
0
1
0
1
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
2
0
1
0
2
0
0
1
0
0
1
1
0
0
0
0
3
1
0
1
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
2
2
2
0
1
0
2
2
0
0
3
0
0
1
2
0
0
1
0
1
0
1
2
0
1
2
1
0
0
0
1
2
0
0
0
2
0
0
0
1
2
1
0
0
1
2
1
2
1
0
1
0
0
1
0
0
1
0
1
1
0
2
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
2
1
3
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
2
2
0
2
0
0
0
2
1
0
0
0
2
0
1
0
0
0
2
0
1
2
0
0
0
0
0
2
1
0
0
0
2
0
2
1
0
2
1
1
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
6
0
1
0
0
0
0
0
0
0
1
2
0
1
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
1
2
1
0
0
0
0
0
0
1
0
2
0
0
0
1
0
2
0
1
1
0
0
0
2
0
0
1
1
1
2
0
1
0
0
0
0
0
2
2
0
0
1
0
1
1
2
2
0
2
0
0
0
1
1
0
1
0
2
0
0
0
1
1
1
2
2
1
2
1
0
0
1
1
0
0
2
1
1
1
0
2
1
0
0
1
0
1
0
1
2
1
1
2
1
0
2
0
0
0
1
0
0
0
1
2
1
1
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
3
2
0
1
2
0
0
0
0
3
1
0
0
0
0
2
2
0
2
0
0
1
1
1
2
1
1
0
0
1
2
1
0
1
0
1
2
1
2
2
1
3
0
0
0
0
1
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
2
0
0
1
0
0
1
2
2
1
0
0
0
1
3
2
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
2
1
0
1
0
0
0
0
0
2
2
2
2
0
2
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
2
2
0
2
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
2
1
0
0
2
2
0
2
2
0
5
1
3
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
1
1
0
0
0
1
0
2
1
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
1
0
1
4
0
0
0
0
0
2
0
0
0
1
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
2
3
3
2
2
1
2
1
1
0
1
1
0
2
0
2
0
1
1
1
2
0
0
0
0
2
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
2
0
1
0
2
2
2
2
0
0
1
0
1
1
0
1
0
0
2
2
1
1
2
0
0
1
2
2
1
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
2
0
1
0
0
1
2
1
0
0
1
1
1
1
1
2
0
0
1
1
0
0
0
3
0
2
0
0
1
2
0
1
0
1
0
0
0
4
0
0
2
0
1
0
0
0
0
0
1
1
0
0
0
2
0
2
0
2
0
2
0
2
1
2
0
1
1
0
0
0
1
0
2
0
0
0
2
0
0
1
0
0
0
2
0
0
0
1
1
0
1
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
1
2
0
0
0
0
0
0
0
2
0
1
2
0
0
2
0
0
0
0
2
0
2
0
0
0
1
0
0
0
1
0
2
1
0
0
1
0
1
0
1
0
0
0
1
0
0
1
0
2
2
2
2
2
0
2
1
1
0
0
2
0
1
2
0
0
2
1
0
1
3
0
1
0
0
0
2
1
0
0
1
0
0
0
0
2
2
0
2
0
2
0
0
0
2
1
0
3
2
0
0
0
0
0
0
2
2
3
1
0
0
1
0
0
2
2
0
0
0
0
0
0
0
2
1
0
0
2
0
2
0
1
1
0
0
0
2
0
0
1
0
0
1
2
2
0
0
0
0
0
2
0
0
0
0
1
1
2
2
0
0
0
2
0
0
0
0
1
1
0
2
2
0
0
0
0
2
1
0
0
0
0
1
0
0
2
0
0
0
3
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
4
0
0
2
0
0
0
2
0
2
0
1
3
0
0
0
1
1
2
0
0
1
0
0
0
2
2
0
0
0
1
2
1
0
0
1
0
0
0
0
0
0
1
0
2
1
0
0
2
0
0
0
0
0
1
1
0
2
0
1
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
2
2
2
0
0
0
2
0
0
2
1
1
0
3
2
0
0
0
2
1
0
1
0
0
0
1
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
1
4
0
0
2
0
1
0
0
4
0
2
2
0
0
0
0
2
0
0
1
0
0
1
2
2
0
4
0
1
0
0
2
0
0
0
0
0
1
0
0
1
0
1
1
0
1
2
0
0
1
0
7
1
0
1
1
0
2
0
1
0
0
4
0
0
2
0
3
2
2
0
1
0
0
0
0
1
2
1
1
0
0
1
1
0
1
1
0
0
0
0
0
0
0
1
3
0
2
0
0
0
0
0
0
1
0
1
0
1
1
0
1
2
0
2
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
1
0
6
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
2
0
2
1
0
0
0
0
1
2
1
0
2
0
0
0
1
0
0
0
0
0
2
0
2
1
2
0
0
0
1
3
2
0
0
1
0
0
0
0
0
1
0
0
1
2
0
2
2
2
1
0
2
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
1
0
1
1
0
2
2
0
0
1
0
0
0
2
0
0
1
0
1
0
0
1
0
1
1
0
0
0
0
0
0
1
3
1
1
0
1
2
2
0
2
1
0
0
1
0
0
3
0
1
0
0
0
1
2
1
1
0
1
1
0
0
0
2
0
0
0
0
1
0
1
0
2
1
0
0
0
1
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
2
0
0
1
0
3
1
2
0
2
0
0
0
0
0
0
1
3
2
1
2
2
0
2
0
0
0
1
0
0
0
1
2
0
0
0
2
0
0
0
2
2
1
0
2
1
1
2
2
0
1
0
1
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
2
0
0
3
3
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
2
0
2
1
0
1
0
2
0
0
1
2
0
1
0
0
2
1
2
2
0
1
2
0
0
2
1
1
1
0
2
1
0
1
2
0
2
2
0
2
0
1
0
0
2
0
0
7
0
4
0
1
0
0
2
0
0
1
2
2
1
0
2
0
7
3
1
1
0
0
0
0
1
0
1
0
0
0
0
0
2
0
1
1
0
0
0
0
0
3
1
2
0
2
0
3
0
0
0
2
0
2
0
0
0
0
0
0
1
1
2
0
1
0
0
1
0
3
1
0
1
0
2
0
1
2
0
1
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
2
0
2
0
2
0
3
0
0
0
4
0
0
0
1
0
0
0
0
2
0
0
2
1
1
2
0
1
1
2
0
0
1
1
0
0
0
0
2
2
2
1
1
0
0
0
1
0
1
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
1
0
1
0
1
1
0
2
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
1
2
0
1
0
1
0
2
1
0
0
1
1
0
1
0
2
1
2
1
0
0
0
0
1
0
2
0
2
0
2
0
2
0
0
2
0
2
0
0
2
0
0
0
2
0
0
1
0
1
2
0
1
3
0
0
1
2
0
0
0
0
0
0
0
0
1
2
0
0
2
0
1
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
2
1
0
2
0
2
0
2
1
0
1
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
3
0
2
0
0
2
2
2
0
0
0
1
1
1
1
1
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
4
1
2
0
2
0
2
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
3
0
0
0
2
0
1
1
1
1
1
1
1
0
2
0
0
2
0
0
0
0
3
0
0
0
0
1
0
3
1
0
1
0
0
0
2
2
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
2
2
1
2
0
1
3
1
0
0
0
0
2
2
0
1
2
1
0
0
0
3
0
0
0
0
0
0
0
0
5
0
2
0
1
2
2
0
0
0
1
0
0
0
2
2
0
0
0
0
2
0
0
2
1
0
1
0
1
1
0
0
1
1
3
1
0
0
0
1
0
1
1
0
0
4
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
2
2
0
0
1
1
0
2
0
2
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
2
2
0
0
4
1
0
2
0
0
2
0
0
0
2
0
0
0
0
0
1
1
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
2
0
1
2
0
1
2
0
0
0
2
1
0
1
1
1
0
1
1
0
0
0
3
1
0
0
0
0
0
0
0
2
0
0
1
0
0
2
1
1
1
0
0
0
1
1
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
1
1
0
2
0
0
0
0
0
2
0
0
0
0
1
2
0
2
0
0
0
1
0
0
0
0
1
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
3
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
2
1
1
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
1
0
1
0
0
0
0
1
0
0
0
2
1
0
0
2
0
2
0
0
0
2
0
0
0
1
1
0
2
2
2
0
0
0
0
1
1
0
0
2
4
1
3
2
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
2
2
2
1
0
0
2
0
1
1
0
0
1
0
1
0
2
0
1
2
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
2
0
2
0
1
1
1
2
2
0
0
1
0
2
2
0
0
0
1
0
1
1
0
2
1
0
2
0
0
0
1
2
0
2
1
1
2
1
0
0
0
1
0
1
0
1
0
0
0
0
2
0
0
1
0
0
1
1
0
0
2
2
0
0
0
2
0
1
0
2
0
1
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
1
1
0
0
2
1
1
2
0
0
1
1
4
0
1
0
1
2
0
0
3
0
1
0
0
0
0
2
1
1
0
0
0
2
1
3
2
0
2
0
2
0
2
2
1
1
0
0
0
1
0
0
1
0
0
2
0
2
0
1
1
2
0
0
0
1
0
1
2
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
2
1
1
3
2
0
1
1
0
0
0
0
0
0
2
1
0
2
1
0
1
0
0
0
2
1
1
0
2
1
0
1
0
0
1
2
0
0
0
1
2
0
0
0
2
3
0
2
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
2
1
0
0
1
0
2
0
2
0
2
0
0
2
1
2
0
0
2
0
1
0
0
2
0
2
0
0
1
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
1
3
0
2
0
1
2
2
0
2
0
2
1
2
1
0
1
0
0
2
2
0
0
0
1
0
0
3
0
0
0
0
0
0
7
0
1
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
2
2
1
0
2
1
1
1
0
0
0
0
2
1
1
0
0
2
1
4
0
0
0
2
0
0
0
0
0
2
2
0
2
1
0
1
0
1
1
1
2
0
0
0
2
0
2
2
1
2
0
0
0
0
2
0
2
0
0
0
0
0
2
2
2
2
4
0
2
0
7
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
1
1
0
1
0
2
0
0
2
0
1
1
0
0
0
0
2
1
0
0
0
1
1
2
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
2
0
0
0
2
2
1
2
1
0
0
0
0
0
1
0
0
2
0
2
0
1
0
1
1
0
1
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
2
1
0
0
0
0
3
1
0
1
1
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
1
0
0
0
1
2
1
0
1
0
0
2
2
1
0
0
0
0
0
0
0
0
0
1
1
0
0
2
4
0
1
1
1
0
0
0
0
1
1
0
0
0
1
0
0
3
0
1
0
1
3
1
0
0
0
1
0
1
1
0
0
0
0
0
1
2
0
0
2
0
1
0
0
0
2
0
0
1
1
2
0
0
1
2
0
0
0
0
1
0
0
2
0
3
0
2
0
2
0
0
0
0
0
2
2
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
2
0
2
0
0
2
0
1
0
1
0
0
1
0
3
0
0
0
1
0
1
0
0
6
0
1
0
2
0
1
0
0
0
2
0
0
1
5
0
0
0
0
0
0
2
0
0
0
1
1
0
0
2
2
0
2
1
0
1
1
2
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
1
2
0
2
0
2
0
2
0
2
2
1
1
0
0
0
2
0
2
0
1
0
0
3
2
0
1
0
0
2
0
1
0
1
0
0
0
0
0
0
2
0
0
1
1
0
3
2
0
2
1
0
0
2
4
0
0
0
2
2
0
0
0
1
1
1
0
0
0
2
1
0
0
3
0
0
1
1
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
2
1
0
0
0
2
2
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
1
1
1
2
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
1
1
1
0
0
1
2
2
0
0
1
0
4
0
1
0
1
0
1
2
0
0
2
1
0
1
0
0
2
1
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
1
0
0
0
1
1
0
1
1
2
2
0
0
1
0
2
0
0
0
0
2
2
0
0
0
0
1
0
0
2
2
0
1
0
2
1
2
0
0
3
0
0
0
1
0
0
0
2
1
0
2
0
0
3
0
1
0
2
1
0
1
0
0
2
0
1
0
0
2
1
2
1
0
0
0
0
0
0
2
2
2
0
0
0
0
0
2
2
1
0
0
0
0
1
0
0
0
2
0
0
3
0
1
1
0
0
0
0
3
1
2
3
0
1
0
2
2
1
0
1
0
0
0
0
0
0
3
0
2
0
0
0
0
3
0
1
1
0
2
0
2
0
0
0
1
1
0
0
0
0
0
2
2
1
0
0
0
0
0
0
1
0
2
1
1
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
1
0
0
0
2
0
1
1
0
1
2
2
0
0
0
1
0
0
2
1
1
2
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
2
0
0
0
0
1
0
0
0
2
2
0
1
0
3
1
1
0
0
0
2
1
0
1
2
2
0
0
0
0
0
2
0
0
0
2
0
1
2
0
0
0
2
0
0
0
1
0
4
0
0
0
1
0
2
0
0
0
1
0
0
0
0
2
0
2
1
0
2
3
2
1
0
2
1
0
1
0
1
0
0
0
0
5
1
0
0
0
0
3
0
0
0
1
0
2
0
0
2
0
0
1
0
1
1
2
0
1
0
1
2
1
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
1
0
0
2
1
0
0
2
0
2
2
2
2
0
1
0
1
0
0
2
0
0
1
0
2
2
0
0
2
0
0
1
0
0
0
0
0
0
2
1
1
2
0
0
2
3
0
1
0
2
0
0
1
0
0
0
2
0
0
2
0
3
0
0
0
0
2
1
1
0
1
2
0
1
1
1
0
2
0
0
2
2
0
1
0
3
2
2
0
0
0
2
0
0
1
2
2
0
0
2
0
0
1
0
1
0
1
0
0
0
0
0
3
0
0
1
1
0
0
0
1
2
0
0
2
0
3
0
0
0
2
2
1
0
1
0
0
0
2
0
2
0
0
0
2
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
2
0
1
0
1
2
0
1
0
0
0
0
0
1
3
1
0
0
0
0
2
0
0
1
0
0
0
0
2
2
2
0
0
0
0
0
2
0
2
0
0
0
2
0
1
2
0
0
0
2
2
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
9
0
2
0
2
1
0
0
3
1
2
0
1
0
0
0
0
0
1
0
0
1
1
0
1
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
2
0
0
0
0
1
0
0
0
3
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
2
2
1
0
1
0
1
0
0
1
0
0
2
0
0
0
1
0
1
2
0
0
0
0
2
0
1
2
0
0
1
1
0
0
0
0
0
2
0
2
1
1
0
1
0
1
0
0
0
0
1
0
2
1
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
2
0
0
1
0
0
0
1
0
1
1
0
0
0
1
0
0
0
2
0
2
1
0
1
1
0
2
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
1
0
2
0
1
2
2
0
0
2
0
1
0
2
0
0
0
1
0
0
1
0
0
1
1
0
2
0
1
2
0
1
2
0
0
2
1
0
3
0
0
0
1
0
0
2
0
2
0
2
0
0
1
1
0
0
1
0
2
2
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
2
0
0
3
2
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
1
0
2
1
3
0
1
0
1
0
3
0
0
0
0
0
0
1
0
1
1
2
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
2
0
0
3
0
0
1
2
2
0
2
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
1
0
0
0
0
2
0
0
1
1
1
0
0
1
0
0
0
2
0
0
1
0
0
0
1
0
1
1
1
1
0
0
0
1
0
0
0
2
0
0
0
1
1
0
2
2
1
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
2
0
1
1
0
0
0
1
0
0
0
1
0
2
0
1
0
1
2
1
1
1
1
2
0
0
0
0
0
1
2
2
1
0
1
2
0
0
0
0
2
0
0
0
0
0
0
2
3
0
0
0
1
0
1
1
0
0
0
2
0
1
0
3
1
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
1
0
0
1
2
0
2
0
2
0
0
0
0
2
1
2
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
1
1
1
2
0
0
2
0
1
0
2
0
2
0
0
0
0
2
0
0
2
0
0
2
1
0
0
0
0
0
2
6
0
0
0
2
0
0
0
0
1
1
0
1
0
1
0
2
0
0
1
0
0
2
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
2
0
0
0
2
1
2
0
2
2
0
2
1
0
3
0
0
0
1
2
1
0
2
0
2
1
0
2
0
0
0
0
0
1
0
0
0
1
1
0
0
2
0
0
0
0
1
1
3
0
0
2
0
0
0
0
2
0
1
0
1
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
1
1
2
0
0
0
0
1
1
2
0
2
0
1
0
0
1
0
1
0
1
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
2
2
1
0
0
1
0
2
2
0
2
2
1
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
1
2
2
2
0
1
0
1
2
0
0
2
0
0
2
0
1
2
0
0
0
2
2
0
0
1
3
0
0
0
1
0
0
0
2
1
1
0
0
0
2
0
0
1
2
0
1
2
1
0
0
2
2
0
0
2
1
2
2
0
0
2
0
4
2
0
0
0
2
1
0
0
1
0
1
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
2
2
0
0
1
1
0
0
0
0
0
1
2
2
0
1
0
0
2
0
1
0
0
0
0
0
0
2
0
1
2
1
0
1
0
2
0
1
0
1
0
0
0
0
1
1
0
0
1
0
2
0
1
0
0
1
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
1
0
2
0
1
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
2
1
1
1
0
2
0
0
4
2
0
1
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
1
0
2
0
0
0
1
3
0
0
0
0
1
3
1
0
0
0
1
1
1
1
2
0
2
0
2
1
0
0
4
0
1
0
0
0
0
3
0
0
1
3
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
1
2
0
1
2
0
0
0
1
0
0
2
0
2
1
2
1
0
0
0
0
1
2
0
0
0
0
1
0
2
1
0
2
1
0
0
0
0
0
0
0
1
0
1
0
0
2
0
4
0
0
0
0
0
2
0
0
0
0
0
3
0
0
1
0
0
0
1
0
0
1
0
2
1
1
0
0
2
0
0
0
0
3
0
0
0
0
0
2
0
0
0
3
0
3
2
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
2
2
2
2
1
0
2
0
0
0
1
0
1
2
0
2
2
0
0
1
2
2
2
1
1
0
0
0
0
0
0
0
0
0
4
0
0
1
2
0
1
1
2
1
1
0
2
0
1
1
2
0
0
0
0
0
0
2
1
0
0
1
0
0
0
1
0
2
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
3
2
0
2
2
0
2
1
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
2
0
0
0
2
0
1
0
0
1
0
0
0
0
0
3
0
1
2
1
0
0
0
2
1
0
0
1
2
0
2
0
0
2
2
2
0
2
0
1
1
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
1
0
0
0
2
0
0
1
0
1
0
1
0
2
0
1
2
1
2
0
2
0
1
1
1
1
0
1
0
0
0
2
0
1
0
0
0
1
0
0
0
1
1
1
0
0
2
0
0
0
0
0
0
0
0
2
2
2
1
0
1
0
0
2
2
1
1
0
0
1
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
1
1
0
2
2
0
0
2
0
0
1
1
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
1
0
2
0
1
0
2
1
0
0
0
0
2
1
0
0
1
0
0
2
0
0
2
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
1
1
0
2
1
0
2
0
0
0
1
1
0
0
0
1
0
0
2
1
0
0
0
0
1
0
2
2
2
0
2
0
1
2
0
1
0
0
0
0
2
2
0
0
0
4
2
2
3
0
0
0
0
1
0
0
4
0
0
1
1
0
0
1
0
2
1
0
0
1
1
0
0
0
1
1
2
0
2
1
0
2
2
0
0
1
0
1
0
0
0
0
1
0
0
1
1
1
0
0
3
0
0
0
3
0
0
0
0
0
0
1
0
2
0
2
0
0
0
2
1
0
1
0
0
0
3
0
0
0
0
0
0
1
1
2
1
0
0
3
0
2
2
0
0
0
0
2
0
2
1
2
1
0
0
1
2
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
2
0
1
0
1
0
2
0
0
1
1
0
0
1
2
1
0
1
0
0
1
0
0
0
2
2
2
0
0
0
0
1
0
0
0
1
2
0
1
1
0
1
2
0
2
2
0
3
0
0
1
0
0
0
0
1
1
2
0
0
1
0
1
0
2
0
1
0
0
0
2
4
0
0
2
0
0
0
0
0
1
0
0
2
0
1
0
2
0
0
0
0
0
0
0
2
2
0
1
0
0
1
1
1
1
0
1
0
0
0
2
1
2
0
0
0
0
2
0
2
0
2
0
1
0
0
2
0
0
1
0
0
1
0
0
1
0
0
0
1
0
2
0
0
0
2
0
0
1
0
0
0
1
0
0
1
1
0
0
2
0
0
2
0
0
1
1
2
0
0
2
1
2
1
0
0
0
0
0
0
1
0
2
0
0
0
1
0
1
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
1
0
0
1
1
3
0
0
0
0
0
1
1
1
0
0
2
0
0
0
0
2
0
0
0
1
0
0
1
2
0
1
0
0
1
1
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
2
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
2
1
2
0
1
1
0
0
2
1
0
1
0
0
2
1
1
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
2
0
0
0
0
0
1
0
1
1
0
0
0
0
0
2
0
2
3
0
0
2
0
2
0
0
0
2
0
0
3
0
0
2
2
0
0
0
2
0
0
2
2
0
0
2
0
0
0
2
2
0
1
0
0
0
0
0
2
0
1
1
0
2
2
0
0
0
0
0
0
1
0
0
1
0
0
2
0
1
1
0
1
0
1
0
3
2
2
0
1
2
0
0
0
0
0
3
0
3
1
1
0
1
0
1
1
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
1
2
2
2
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
2
1
1
0
0
0
0
0
2
0
0
0
3
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
1
0
0
1
0
0
2
1
1
0
2
0
0
0
0
1
1
0
0
2
1
1
0
0
1
1
0
1
0
0
1
0
2
0
0
2
0
0
0
2
0
2
0
2
0
0
0
2
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
4
5
0
0
0
0
0
0
1
0
2
0
0
1
0
2
0
1
2
0
0
0
0
2
0
0
0
0
1
2
0
1
0
1
0
1
0
2
0
2
0
0
5
2
0
2
0
1
2
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
1
0
1
0
1
0
2
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
1
1
0
3
0
1
1
0
1
0
0
2
1
1
2
0
0
1
1
2
0
0
1
0
0
2
0
0
2
0
1
0
1
0
0
0
0
0
0
3
2
0
1
0
0
0
0
2
0
2
0
1
2
0
1
0
3
0
1
2
2
0
2
0
0
1
2
2
0
2
0
0
0
0
2
0
0
0
2
2
0
1
2
1
0
0
2
0
0
0
5
2
0
2
2
2
0
0
0
0
1
1
2
0
0
2
0
2
0
1
0
1
0
2
0
0
1
2
0
1
0
0
2
0
0
1
2
2
0
0
5
3
0
0
1
1
0
0
0
0
2
0
3
1
2
2
2
1
0
0
1
0
2
1
0
2
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
2
2
1
1
1
0
1
3
1
0
0
0
0
2
0
1
2
2
0
0
1
0
0
2
1
2
2
1
1
2
1
0
0
0
0
1
4
2
1
0
4
0
0
0
1
0
0
1
2
0
0
2
1
3
0
1
0
2
1
0
1
1
0
2
0
0
0
0
3
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
1
0
1
0
0
0
2
0
2
1
1
0
1
2
1
1
0
2
2
1
2
0
0
2
1
0
2
1
0
0
0
0
1
1
0
2
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
1
0
1
1
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
2
1
0
0
0
1
1
0
0
0
0
2
1
0
0
2
0
0
1
1
0
0
25
0
0
0
0
2
2
1
0
4
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
1
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
2
0
2
0
0
1
1
1
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
2
0
2
1
0
1
2
0
3
0
0
1
2
0
0
0
0
0
0
0
3
1
0
0
0
0
0
4
0
0
5
0
1
0
0
2
0
0
0
2
0
0
1
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
2
1
0
1
2
1
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
1
1
0
3
2
0
2
1
2
0
0
0
0
2
1
0
0
2
1
0
0
0
2
1
2
0
0
1
0
0
0
0
0
1
1
0
2
0
0
2
0
0
0
1
0
0
2
1
2
0
1
1
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
2
0
0
1
2
2
0
1
0
0
0
0
2
2
1
0
0
1
1
0
0
0
0
0
1
1
0
2
0
2
0
0
0
0
0
0
2
1
4
0
0
0
0
1
0
0
2
0
0
1
0
0
0
2
2
0
1
1
0
2
0
0
0
1
1
0
1
0
0
0
1
3
0
0
1
2
0
2
0
0
2
1
0
2
2
2
0
0
0
1
0
0
1
0
0
0
0
0
1
2
1
1
0
0
2
0
0
0
0
0
0
0
0
0
1
2
2
1
1
0
1
2
0
1
0
0
0
2
0
2
1
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
2
2
0
0
0
1
2
1
0
0
1
0
0
2
0
0
1
0
1
0
2
2
0
2
1
0
0
1
1
1
0
1
0
0
1
0
0
0
0
0
0
2
1
2
0
1
0
0
0
0
0
1
1
0
2
0
1
0
1
2
1
2
1
0
0
2
0
2
0
2
5
3
1
2
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
2
0
2
2
0
1
0
2
0
0
0
0
0
2
0
1
2
3
0
0
0
0
2
0
2
0
0
0
2
0
0
2
0
0
0
2
2
1
2
0
0
2
2
2
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
2
2
0
2
0
0
0
3
0
1
3
0
2
0
0
1
1
0
3
1
1
0
2
1
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
2
2
2
3
0
0
0
2
0
0
2
0
0
0
0
4
0
1
2
1
0
0
1
2
0
0
0
1
0
0
1
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
1
0
0
0
2
0
0
0
2
1
2
0
0
2
0
1
0
1
1
0
0
0
2
0
0
0
0
2
2
1
1
0
0
1
0
1
0
0
1
1
1
1
1
2
0
0
0
0
2
0
2
0
1
1
0
0
0
2
1
0
0
1
0
1
0
0
1
0
0
0
2
2
0
1
2
0
0
0
0
0
0
2
1
1
0
0
0
0
3
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
3
0
0
0
4
0
0
1
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
1
2
1
0
1
1
0
1
0
0
0
0
1
2
0
1
1
0
2
1
0
0
0
0
1
0
0
2
2
0
0
0
1
0
1
2
2
1
0
0
2
2
0
1
1
0
0
2
0
0
0
0
1
1
1
1
1
0
0
0
2
1
1
2
2
2
0
0
2
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
2
2
0
0
3
0
2
0
0
0
0
1
1
0
0
1
0
0
1
2
0
0
1
0
1
1
1
0
2
2
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
1
0
0
0
0
2
1
2
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
3
1
0
0
0
1
1
0
0
1
0
0
0
4
1
0
0
2
0
2
0
0
2
0
0
1
0
0
0
1
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
3
0
2
0
0
0
0
2
2
0
2
2
0
0
0
1
1
3
0
0
0
0
2
0
0
1
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
2
0
0
0
0
2
1
0
2
1
0
2
0
0
1
0
0
2
0
1
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
3
0
0
2
0
1
0
0
0
0
0
2
0
1
1
1
2
0
0
0
2
0
1
0
0
0
0
0
1
0
0
2
1
0
1
0
2
0
0
3
0
2
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
1
2
2
2
1
1
0
2
1
0
0
1
0
1
0
0
0
1
6
1
1
2
1
2
0
0
0
2
2
0
0
0
0
0
0
0
1
0
2
0
3
0
2
0
1
0
0
0
0
0
0
1
0
2
0
2
0
3
2
0
1
1
0
2
5
2
1
2
0
0
0
0
2
0
1
0
1
1
0
1
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
1
1
2
1
0
1
2
2
0
0
1
2
2
0
1
0
0
0
2
0
0
1
0
1
0
0
1
0
1
0
1
1
0
0
2
2
0
0
0
0
0
0
0
2
0
0
1
2
2
0
1
0
0
2
0
1
0
0
0
0
1
1
0
0
0
0
2
0
2
0
1
0
0
1
2
1
1
2
0
1
0
1
0
2
1
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
2
4
2
1
0
0
2
0
0
0
0
0
0
2
0
0
1
1
0
1
2
2
0
0
0
0
1
1
0
0
0
2
5
0
2
2
0
0
2
0
2
0
0
1
0
1
0
2
3
0
0
2
1
0
3
1
0
0
2
1
2
3
1
0
1
1
0
0
2
0
2
2
1
0
0
0
0
0
1
0
3
2
2
0
1
2
0
1
0
2
0
0
2
0
0
0
0
2
1
2
0
0
0
0
0
3
0
0
0
1
0
0
2
1
2
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
2
0
0
0
1
1
2
1
1
0
1
0
1
0
1
1
0
2
1
0
0
1
1
1
2
0
1
0
2
1
0
1
1
0
0
0
0
2
2
2
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
3
2
0
0
2
2
0
0
0
2
0
2
2
0
1
2
0
0
0
1
0
0
0
1
2
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
2
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
2
2
0
0
2
0
2
1
0
0
0
3
0
1
1
2
0
0
0
2
1
0
2
2
1
0
0
0
0
1
2
1
0
0
1
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
1
1
0
1
4
0
0
0
0
1
0
1
0
1
0
1
0
2
0
0
0
0
0
0
2
1
1
2
2
2
0
2
0
0
0
2
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
2
0
0
1
0
1
3
1
0
1
0
0
0
0
2
0
1
1
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
2
1
1
1
0
0
0
0
0
0
2
0
0
1
0
0
1
0
1
0
0
0
0
0
1
1
0
2
0
0
0
2
1
0
0
0
0
0
0
0
2
0
1
1
1
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
2
1
1
2
0
0
1
1
3
0
0
0
1
0
1
2
1
0
0
0
1
1
2
1
0
0
0
2
0
1
1
0
0
1
1
0
0
0
0
0
0
3
0
0
1
2
1
1
0
0
1
2
1
1
3
2
1
0
4
2
2
1
1
2
0
1
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
1
1
2
0
1
1
0
0
0
0
0
0
0
2
0
2
0
0
1
1
1
0
0
0
2
2
0
0
0
1
0
2
0
1
0
0
0
0
0
1
0
1
0
1
0
0
2
2
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
2
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
1
0
5
0
0
2
1
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
2
0
2
2
0
1
0
2
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
1
1
0
0
0
0
1
2
0
0
0
3
0
1
0
2
2
1
0
0
0
1
0
0
3
0
0
1
0
2
2
0
0
0
0
0
0
2
2
0
3
0
0
2
0
2
1
1
1
1
0
0
2
0
0
0
1
0
0
1
1
0
2
0
1
2
1
0
1
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
2
0
0
1
0
1
0
1
0
1
2
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
1
2
1
0
0
2
2
0
2
0
2
0
0
1
1
0
0
0
2
1
0
0
1
1
0
0
0
1
0
1
0
0
0
1
0
3
3
2
0
1
1
0
2
0
0
1
0
0
0
0
0
0
2
2
0
1
0
0
0
0
2
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
2
0
2
0
0
2
0
0
2
2
0
2
0
0
1
2
0
0
0
1
0
2
2
1
0
0
0
0
4
1
1
0
2
1
1
0
2
1
0
0
2
2
0
0
0
0
2
0
2
1
1
2
0
0
0
0
2
1
1
1
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
2
0
2
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
2
0
1
0
0
1
0
2
0
2
1
1
2
1
1
1
1
0
0
1
1
2
0
0
1
0
2
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
3
1
0
0
1
2
2
2
0
0
0
2
1
0
0
1
0
2
0
0
1
2
0
1
0
0
0
2
0
0
1
0
1
0
0
2
0
1
0
2
0
0
1
0
0
0
2
0
0
3
0
2
1
2
0
2
0
0
0
1
1
0
0
2
1
1
2
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
1
1
2
0
0
0
2
0
0
1
0
0
1
0
0
2
0
0
0
0
0
2
1
0
0
0
1
0
0
4
1
1
1
0
0
0
0
0
1
0
0
2
1
0
0
2
1
2
0
0
1
0
0
3
0
2
2
0
2
2
1
0
0
0
1
0
1
1
0
1
3
0
0
3
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
1
0
0
2
1
0
1
0
0
0
0
0
2
2
0
0
3
1
0
0
2
2
2
1
0
0
1
0
0
0
0
2
2
1
2
0
0
0
0
3
2
0
0
1
0
0
1
0
0
0
2
0
2
1
0
0
0
0
1
1
1
1
3
1
0
0
0
0
0
0
1
0
0
0
3
1
0
0
0
1
0
0
0
1
1
0
2
0
0
1
0
2
0
0
0
2
0
0
0
0
0
4
0
2
0
1
0
0
1
2
0
2
0
1
3
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
2
1
0
0
0
1
1
0
0
0
2
0
3
0
0
0
0
0
1
1
2
2
0
0
2
2
1
0
0
0
0
2
0
0
0
0
1
0
1
0
0
1
2
0
1
1
0
0
2
0
2
2
1
2
2
0
0
0
1
0
1
0
1
0
0
2
0
0
0
2
0
0
0
0
1
0
1
1
1
0
2
0
1
0
0
2
2
0
1
0
1
0
0
1
0
0
0
0
2
2
0
0
0
1
0
2
1
1
0
1
0
0
0
1
0
3
0
2
0
0
0
0
0
0
1
0
0
1
0
5
7
0
0
2
2
0
0
0
1
0
2
0
0
1
0
2
1
0
0
0
1
0
0
4
2
1
0
0
0
0
0
0
1
2
1
1
0
2
0
3
0
2
0
0
0
2
1
0
0
0
2
0
0
1
1
0
2
2
0
0
0
1
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
2
2
1
1
0
0
2
1
0
0
1
0
0
1
0
2
0
0
0
1
0
2
0
2
2
1
0
0
0
2
1
1
1
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
1
0
2
0
3
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
3
0
0
0
0
0
1
2
1
1
1
0
0
0
3
0
0
1
2
0
1
0
0
0
1
0
0
1
0
1
1
0
0
0
2
0
1
1
1
0
0
0
1
0
0
3
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
1
0
1
1
0
0
0
2
1
0
2
0
0
2
2
0
0
2
1
1
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
1
2
2
0
2
1
1
3
1
0
0
0
2
1
0
0
0
2
0
0
0
0
0
1
1
1
0
2
0
0
0
0
0
0
2
0
2
0
0
2
0
0
1
0
1
0
0
1
0
0
0
0
1
1
2
0
2
0
0
0
2
1
1
0
1
0
1
1
0
1
1
1
2
0
0
3
0
2
0
0
2
0
0
2
0
0
1
2
2
2
1
2
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
2
2
1
0
2
0
1
0
2
0
0
2
0
2
0
1
0
2
1
1
0
0
0
0
3
1
2
0
0
0
3
1
1
0
1
2
1
0
2
0
0
0
0
0
0
1
0
2
2
0
2
0
1
0
0
1
0
0
0
1
1
1
0
0
0
0
1
0
2
0
0
0
2
1
3
0
2
0
0
2
0
0
0
3
0
1
3
0
0
1
2
1
2
0
0
1
0
0
0
2
2
0
0
0
1
1
2
3
2
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
1
0
1
2
1
0
0
2
0
1
2
0
0
0
0
0
2
4
0
0
0
1
1
0
0
0
4
2
2
0
0
2
1
0
0
0
0
0
0
2
0
2
0
2
4
0
0
0
1
0
0
1
1
2
0
0
2
0
1
1
1
2
0
0
0
0
0
1
0
0
2
2
0
0
2
0
1
0
0
3
0
1
0
0
0
0
2
0
2
1
0
0
0
1
2
0
0
0
1
0
0
0
1
1
0
0
0
2
0
1
1
2
0
2
0
1
0
0
0
0
0
0
3
0
1
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
2
3
0
0
1
5
0
0
0
2
0
0
0
2
0
0
0
0
0
3
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
2
2
0
2
0
0
0
0
0
0
2
0
0
2
2
0
2
0
0
1
0
0
2
2
0
1
2
1
0
0
0
1
3
0
1
0
0
0
1
2
1
0
2
0
3
1
0
2
1
0
2
0
0
0
1
2
0
1
0
0
2
1
1
1
0
0
1
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
2
0
0
0
1
1
0
0
0
1
0
0
0
1
1
2
0
2
1
0
0
0
2
0
0
2
0
0
0
2
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
3
1
2
0
1
0
0
0
0
0
1
1
0
1
1
2
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
2
0
0
1
0
1
2
1
0
1
2
0
1
1
0
0
0
0
0
2
1
0
2
0
1
1
0
0
2
2
2
0
2
0
0
1
0
0
0
2
0
0
0
0
1
2
0
0
0
2
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
5
1
0
0
0
1
2
1
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
1
2
1
2
0
0
0
2
1
0
0
1
2
1
0
0
0
2
0
0
0
1
0
0
0
0
0
1
4
0
0
1
0
0
0
0
0
0
0
0
2
0
1
2
1
0
0
0
0
0
0
2
2
2
0
0
2
0
0
0
2
2
0
2
0
0
2
0
1
0
0
0
0
2
0
1
0
0
0
1
0
0
1
0
1
1
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
1
0
0
0
1
0
0
0
0
0
1
2
0
0
1
0
0
1
0
0
0
1
2
0
0
0
0
1
0
1
1
0
0
1
0
0
3
2
1
0
2
0
1
0
0
0
0
1
0
2
1
0
0
4
0
1
0
1
1
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
1
2
0
0
0
2
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
2
0
2
0
0
0
0
1
1
0
1
2
0
0
0
0
0
0
0
0
1
0
1
1
2
2
0
1
0
0
1
0
0
1
1
2
2
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
1
2
3
0
0
0
1
2
0
1
2
1
1
3
2
0
0
2
0
0
1
0
0
2
1
0
0
0
1
0
0
0
0
1
2
0
0
0
0
1
0
0
2
0
0
0
1
3
1
0
0
1
2
0
0
1
0
1
1
1
0
2
0
0
0
0
0
2
1
0
0
0
0
0
1
2
0
1
0
0
2
0
1
0
2
2
1
1
0
4
0
2
2
2
0
0
1
0
4
0
1
0
0
0
0
0
2
2
0
1
0
0
0
0
2
2
2
0
0
0
1
0
0
0
1
2
2
0
0
0
0
2
0
2
2
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
2
2
1
3
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
8
9
0
0
2
0
0
2
3
0
1
2
1
1
1
0
0
0
0
1
0
1
0
0
0
2
0
1
2
1
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
3
2
0
1
1
1
1
0
1
0
1
2
0
1
0
1
0
0
3
2
0
0
2
0
2
0
0
0
2
0
0
1
0
1
0
0
1
0
2
0
0
0
0
4
3
0
1
0
2
2
0
1
1
1
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
1
0
0
1
0
1
0
1
1
0
2
0
0
0
2
0
4
0
1
2
0
2
0
0
0
0
0
1
1
1
0
0
1
0
2
0
0
1
0
1
0
0
1
0
0
0
1
2
2
2
0
2
2
0
0
0
0
0
0
0
1
0
1
1
1
0
1
0
0
0
2
1
1
0
0
2
0
0
0
0
0
0
0
0
1
0
1
1
1
0
2
0
1
1
0
2
0
0
0
0
1
2
0
0
2
1
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
2
1
0
0
1
0
0
1
2
2
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
1
1
2
0
0
2
2
0
0
0
0
1
2
0
0
1
0
0
0
0
1
0
1
1
2
0
3
0
1
0
2
2
0
0
0
0
2
2
0
0
1
0
0
0
1
2
0
0
0
2
0
0
1
0
1
2
2
0
1
0
0
1
0
0
0
2
0
0
0
1
0
1
0
0
0
1
2
0
1
0
1
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
3
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
1
1
0
1
0
0
2
0
1
0
0
1
0
0
0
2
2
0
0
1
1
1
0
1
0
0
2
1
1
1
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
2
1
1
0
2
0
0
0
5
2
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
2
1
1
0
1
2
0
0
1
0
0
2
1
2
2
1
1
1
1
1
1
0
0
0
0
0
2
0
0
1
1
0
1
0
0
2
0
1
1
1
0
0
0
0
0
1
0
1
1
1
0
0
1
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
2
0
0
0
2
1
0
2
0
2
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
2
0
0
0
0
0
1
0
0
2
1
0
1
0
2
1
1
0
0
0
0
0
0
1
0
4
1
0
2
2
2
0
2
3
0
1
0
0
2
2
1
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
2
2
1
0
1
1
1
2
1
0
0
0
2
1
0
1
1
0
0
0
1
0
0
1
0
1
1
0
1
0
1
1
4
2
0
2
0
0
1
0
0
2
1
0
0
2
0
2
2
0
1
2
1
0
0
2
0
0
0
2
0
1
0
2
1
0
0
2
0
1
0
0
1
1
1
1
1
0
0
0
0
2
0
2
0
0
0
0
0
0
1
2
1
2
0
1
0
1
0
0
0
0
0
1
1
0
2
2
1
1
0
0
1
2
0
5
0
1
3
0
0
0
0
0
1
2
0
1
2
1
0
2
2
1
2
2
0
0
2
0
1
0
2
0
0
0
0
2
1
1
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
1
3
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
2
0
0
0
2
0
0
0
1
0
0
0
2
1
0
0
0
0
1
0
1
3
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
2
1
0
0
0
0
0
1
2
0
1
0
1
0
1
1
0
2
1
1
0
2
2
2
0
0
2
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
1
2
0
0
0
1
0
1
1
0
2
1
0
2
2
2
2
0
0
0
0
1
0
0
0
2
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
1
0
1
1
2
1
1
1
3
0
0
0
1
1
1
0
1
0
0
0
3
0
1
1
0
0
0
4
0
0
0
2
1
0
2
0
2
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
1
0
2
0
0
1
0
0
1
0
0
0
2
0
2
2
0
0
0
0
2
2
1
0
1
0
3
1
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
2
0
0
0
0
1
2
2
0
0
0
3
0
2
0
0
0
0
3
0
1
2
0
0
2
2
1
0
0
1
0
0
0
0
2
1
3
0
2
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
1
0
2
2
2
0
0
0
2
1
0
0
1
0
0
2
2
0
1
0
3
0
0
0
0
2
0
0
1
0
0
1
1
2
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
2
1
0
0
2
0
1
1
1
1
0
2
0
0
1
0
2
0
1
0
1
0
2
0
0
2
2
0
0
3
2
2
0
0
1
0
1
0
0
0
2
0
0
2
1
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
2
0
0
0
0
1
1
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
1
2
1
1
0
0
1
0
0
0
0
0
0
2
0
8
2
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
1
1
0
0
0
0
12
0
1
2
0
0
0
0
1
0
0
3
0
0
2
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
1
0
2
3
0
2
1
3
0
1
0
0
1
0
2
2
0
1
0
0
1
2
4
0
0
0
1
0
2
0
1
1
0
0
0
2
0
0
0
1
0
0
0
0
2
2
2
1
1
0
0
1
2
2
0
0
1
2
0
0
0
0
0
0
2
2
0
2
0
1
0
1
0
0
0
3
0
0
0
0
0
2
1
0
0
2
0
0
1
0
2
0
2
0
1
0
1
1
0
1
2
0
2
1
1
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
1
0
2
2
0
2
0
0
0
0
2
1
1
0
0
1
3
1
1
0
0
0
1
0
2
1
2
0
0
0
0
0
1
1
0
0
0
2
0
0
0
2
0
1
0
0
0
2
2
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
6
0
2
1
0
0
2
0
1
0
0
2
0
0
0
2
1
0
1
0
0
1
0
0
0
1
0
1
0
0
5
0
1
0
0
1
2
0
0
0
2
0
0
0
1
0
0
2
0
0
0
1
1
1
1
0
1
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
3
1
1
0
0
0
1
1
0
0
0
0
2
1
0
0
2
0
0
1
2
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
2
0
1
0
0
2
2
2
1
2
0
1
2
1
1
0
0
1
0
0
1
0
2
2
0
1
0
0
0
2
2
0
0
2
0
0
2
1
1
1
2
0
2
0
0
0
1
0
2
1
0
0
2
1
0
0
0
6
2
1
0
0
1
4
0
2
2
2
0
2
2
0
0
2
1
0
2
0
1
0
2
0
0
0
0
2
0
2
0
0
0
1
0
1
0
0
0
0
0
2
0
1
1
1
2
1
3
0
0
0
0
1
0
0
0
0
0
0
1
2
0
1
0
2
2
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
1
0
1
2
0
2
1
0
0
2
0
0
0
0
0
1
0
2
2
0
0
1
0
0
0
0
1
2
0
0
0
2
2
0
2
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
2
1
2
0
0
0
0
1
2
1
0
0
0
2
1
2
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
1
2
1
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
3
2
2
0
0
1
0
1
0
0
0
2
0
0
0
2
0
0
0
1
0
0
2
0
2
0
0
0
2
2
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
1
2
1
1
0
1
0
0
1
0
2
0
0
1
1
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
1
2
0
1
1
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
1
0
0
2
0
0
2
0
0
0
2
2
1
1
2
2
1
1
5
0
0
1
0
1
1
2
0
1
2
2
1
0
3
0
0
1
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
1
0
2
0
1
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
2
0
0
0
2
0
1
0
2
0
0
2
0
0
0
0
1
0
0
0
0
1
1
0
1
2
0
2
0
0
0
1
0
0
0
2
0
0
0
1
1
0
0
0
1
0
2
1
1
1
2
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
2
0
2
0
1
0
1
0
0
0
2
1
0
2
0
0
0
3
1
0
0
1
3
0
1
0
2
2
1
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
2
1
0
0
1
1
0
1
2
0
0
0
0
0
1
2
0
1
0
1
0
3
1
0
1
0
2
0
0
0
2
1
1
0
0
1
0
0
2
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
1
2
1
1
0
0
1
1
2
0
0
0
2
2
1
2
0
1
1
1
5
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
3
0
0
2
0
0
0
0
2
0
2
1
0
1
5
0
2
1
0
0
1
1
0
0
0
0
0
2
0
0
1
2
0
0
1
2
0
0
0
1
0
0
0
0
2
2
0
1
0
0
2
0
2
1
0
0
0
0
2
1
0
0
0
1
0
2
0
2
2
0
1
2
2
1
3
0
1
2
0
1
0
0
2
0
2
0
0
1
0
1
0
0
0
2
1
0
1
0
0
0
2
0
0
0
1
2
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
1
0
0
0
0
2
2
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
2
1
0
2
2
2
1
0
0
0
0
0
0
0
0
1
0
2
0
0
2
2
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
2
0
2
1
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
1
1
1
2
0
0
0
1
1
0
0
0
0
0
0
0
2
1
2
1
0
0
1
0
0
3
0
0
0
1
0
2
2
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
1
1
2
0
1
0
0
0
0
0
0
0
2
1
2
1
2
0
1
0
0
0
0
0
0
1
2
0
1
0
0
0
1
0
1
2
1
1
0
2
0
0
0
0
0
0
1
0
0
2
0
2
0
2
0
0
0
2
0
1
0
2
0
0
2
0
0
2
0
0
2
1
3
3
0
1
0
2
4
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
2
1
1
0
0
0
0
2
3
0
1
0
0
0
0
1
0
0
0
0
1
2
0
0
2
0
0
0
0
0
2
0
0
0
3
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
1
2
0
0
0
0
1
1
0
2
0
0
1
1
0
0
1
0
0
0
0
1
0
0
2
0
1
2
0
0
2
0
0
2
0
2
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
2
1
1
1
0
0
1
0
0
0
0
0
0
1
0
2
1
0
2
0
1
2
2
0
3
1
0
1
0
0
0
0
0
1
0
2
0
0
1
2
2
4
1
0
2
0
0
1
2
2
0
0
0
0
1
0
2
0
1
2
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
2
1
2
1
0
0
0
0
0
0
0
0
1
2
0
0
0
1
2
1
1
2
1
2
0
0
0
0
2
0
0
2
0
1
1
0
2
1
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
2
0
2
0
0
1
1
3
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
1
1
1
0
1
2
0
0
0
0
0
2
0
0
2
1
2
0
2
0
0
1
2
0
0
0
0
1
2
0
0
2
0
1
0
0
0
0
2
1
0
1
1
3
0
0
2
0
1
1
0
0
1
0
0
0
0
2
1
1
0
0
0
1
1
0
2
0
0
1
0
2
2
2
0
0
0
0
1
0
1
0
0
2
0
1
0
0
2
0
0
0
1
0
0
0
0
2
0
0
1
0
1
0
0
0
2
1
0
0
1
0
0
0
1
2
0
0
0
0
2
1
0
2
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
2
2
2
0
2
1
1
2
0
0
0
0
0
0
2
2
0
2
3
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
1
1
1
0
1
0
1
0
0
0
0
1
0
1
0
2
0
0
1
2
2
0
2
0
1
0
2
2
2
2
0
0
2
0
1
0
0
0
1
0
0
2
1
2
1
1
0
0
1
0
2
0
0
0
1
0
0
0
1
1
1
2
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
1
0
1
2
2
0
0
0
2
1
0
0
0
2
0
2
0
0
0
0
0
0
1
3
2
2
1
0
0
2
1
1
2
0
0
2
0
0
0
0
0
0
2
0
0
1
0
2
0
0
2
1
1
0
0
0
0
0
1
2
0
0
2
0
1
0
4
1
0
0
0
1
0
2
0
0
1
0
1
2
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
2
0
0
1
0
0
2
0
2
0
0
0
0
2
0
1
0
0
0
1
2
0
1
2
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
2
2
0
0
0
4
1
2
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
3
0
0
1
0
1
1
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
2
2
0
0
0
0
6
0
2
1
0
2
0
0
0
1
3
0
1
0
2
1
2
2
0
3
2
0
0
0
0
0
0
1
0
0
1
1
2
0
0
1
1
0
2
1
1
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
1
0
2
2
0
0
0
0
1
1
0
2
0
0
2
2
0
0
2
0
0
0
4
1
0
1
3
0
0
4
0
2
0
1
2
2
0
0
1
0
1
2
0
1
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
1
0
2
1
0
1
0
1
0
0
1
0
1
0
1
1
0
0
0
2
0
2
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
2
0
2
2
0
2
2
0
2
0
3
2
3
2
0
0
2
0
2
0
0
0
2
1
2
1
0
0
0
0
1
2
0
2
0
0
0
0
0
0
1
0
0
2
2
0
0
1
0
0
1
0
0
1
0
0
0
0
0
2
0
0
2
0
1
1
0
0
0
3
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
1
1
2
2
1
2
0
0
1
2
1
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
3
0
2
0
1
1
2
3
0
0
0
1
0
0
2
0
0
2
0
1
4
2
0
0
0
2
0
0
1
0
1
0
1
0
0
2
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
2
0
1
0
0
0
0
2
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
2
2
0
1
1
0
2
2
0
0
0
0
2
0
2
0
0
0
1
1
0
1
0
0
0
2
1
0
0
2
0
2
0
1
0
0
0
1
0
0
2
0
0
0
2
1
2
0
1
2
0
0
1
0
2
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
2
1
0
1
0
1
0
0
2
0
0
0
0
0
2
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
1
0
1
0
3
2
0
0
0
1
0
0
0
1
0
2
1
0
0
0
2
1
2
0
0
0
0
0
0
0
0
2
2
2
0
0
1
0
2
2
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
3
0
2
3
1
0
1
0
1
1
0
1
0
1
1
0
0
1
1
0
2
0
0
2
0
2
0
0
1
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
4
1
1
0
2
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
3
0
1
1
0
0
0
0
0
2
0
1
2
1
1
1
0
0
0
0
0
0
0
0
2
4
0
0
0
2
0
1
0
0
0
0
0
1
0
2
2
1
1
0
0
0
1
0
1
1
0
0
2
1
0
0
2
0
0
0
2
1
0
1
2
0
2
0
0
2
0
0
2
0
0
2
0
0
0
0
1
0
2
1
0
0
0
1
0
1
2
2
0
0
1
0
0
0
3
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
2
1
0
1
2
0
3
2
0
4
0
0
0
2
1
0
0
0
2
0
2
1
0
0
0
0
2
0
0
2
0
2
0
0
2
0
0
0
0
2
0
0
0
2
2
0
0
0
1
0
0
0
0
2
1
0
0
0
2
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
2
1
0
3
0
1
0
0
0
0
1
2
6
0
0
0
0
0
1
0
0
1
1
0
1
2
0
0
0
1
0
0
0
2
0
0
2
0
0
0
2
3
1
0
2
1
0
3
0
0
0
0
0
2
0
2
0
0
3
0
0
2
0
2
0
0
1
0
0
1
0
2
0
0
3
1
1
0
1
0
1
0
1
0
2
2
0
3
1
2
0
0
0
0
2
1
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
1
0
1
0
0
0
0
0
2
0
1
0
0
0
1
2
0
0
0
1
1
0
2
1
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
2
1
0
1
2
0
1
2
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
2
0
0
1
0
0
0
2
1
1
0
0
2
2
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
2
1
0
0
1
0
1
0
0
0
1
0
1
0
1
1
1
1
0
0
1
0
0
0
0
0
2
2
0
0
0
2
2
0
0
0
0
1
0
0
2
0
2
0
0
0
0
1
1
0
2
0
1
0
1
0
0
0
1
1
0
2
0
2
1
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
2
2
1
0
0
0
0
1
0
0
2
5
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
2
0
0
1
0
0
0
2
3
1
0
1
1
0
0
0
2
1
0
0
0
0
0
0
1
0
0
3
0
0
1
0
0
2
0
1
0
0
2
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
3
0
2
0
2
1
1
0
0
0
0
0
2
0
1
2
0
1
0
0
0
0
2
1
0
3
0
0
1
2
3
0
1
1
0
1
0
0
2
0
0
2
0
0
0
1
1
3
0
0
0
1
0
0
0
0
7
2
0
0
0
1
0
0
0
1
0
0
0
1
0
2
0
0
0
1
1
0
2
0
0
1
3
1
0
0
0
0
0
2
1
0
2
2
1
0
2
0
2
0
1
0
0
0
1
1
1
1
0
2
0
0
6
0
2
0
0
0
1
0
1
0
2
2
0
1
1
0
2
0
1
0
2
0
2
0
1
0
2
0
1
0
0
1
1
0
0
2
4
0
0
2
0
0
1
1
0
0
2
1
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
1
0
0
0
2
1
0
1
0
1
0
0
1
0
1
0
0
0
2
0
2
2
1
1
0
2
1
0
0
1
4
2
0
2
0
1
2
0
0
0
1
0
0
0
0
2
0
2
1
1
2
2
0
0
0
0
2
2
0
2
0
0
0
0
0
1
0
0
8
0
0
0
0
2
1
0
0
0
0
1
1
0
0
0
1
1
2
0
0
1
2
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
2
2
1
0
0
0
1
0
1
0
2
1
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
1
1
2
2
0
1
1
0
1
2
0
0
0
0
0
2
0
1
0
0
1
0
3
0
0
0
0
0
2
1
1
0
0
1
1
2
1
2
1
0
0
0
0
0
3
1
0
2
0
0
0
0
1
0
0
1
0
1
2
2
1
1
2
0
0
1
2
0
0
1
0
0
0
1
1
2
2
1
0
3
0
0
0
0
0
1
0
2
1
2
2
2
0
2
1
0
0
0
2
0
0
0
0
0
2
0
1
0
2
1
0
0
1
0
2
2
2
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
2
0
2
0
0
1
0
0
0
1
0
1
0
0
0
0
0
2
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
1
0
1
1
0
1
0
1
0
0
1
1
0
1
1
1
1
0
0
0
1
0
0
1
2
0
1
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
2
0
1
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
2
1
2
0
2
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
3
0
3
2
0
0
2
2
0
2
1
2
0
1
0
0
0
0
2
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
2
0
0
0
1
0
0
0
0
0
0
1
2
0
0
6
0
0
0
0
1
0
0
0
2
0
1
0
0
1
0
3
0
0
1
1
0
0
0
0
0
0
2
1
0
0
1
0
0
1
1
1
0
0
3
0
0
1
0
0
0
0
1
0
2
0
0
1
0
0
1
1
0
0
0
0
0
0
2
1
3
0
2
1
0
2
0
2
0
2
0
2
0
0
2
0
0
2
0
2
2
0
2
0
0
0
2
0
0
0
2
0
1
2
0
2
2
0
0
0
0
0
1
0
0
1
0
2
0
0
1
2
0
0
0
1
0
1
2
0
1
1
0
0
0
1
1
0
0
2
0
0
0
0
0
2
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
1
0
2
1
3
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
2
0
1
0
0
0
1
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
5
1
0
0
2
0
0
2
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
1
2
1
2
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
2
0
0
2
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
2
0
0
0
0
2
1
1
0
2
0
1
0
1
1
1
0
0
0
1
0
0
0
0
0
1
0
1
0
1
2
1
0
2
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
5
0
0
0
2
0
0
2
0
4
2
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
2
0
0
1
3
0
0
1
1
1
0
0
0
0
1
0
1
1
2
0
0
0
0
1
1
1
0
0
1
2
1
0
2
0
0
2
0
3
0
2
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
4
1
1
1
0
0
2
1
0
0
0
0
0
0
1
2
0
1
2
0
0
0
0
0
0
2
0
1
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
3
0
0
1
1
0
2
0
0
2
0
0
0
1
0
1
2
0
0
5
0
0
0
0
2
1
0
0
0
2
1
1
0
1
1
4
0
0
0
0
1
2
0
1
2
0
0
0
2
0
2
0
0
1
2
2
0
0
0
0
1
0
2
1
0
0
2
0
0
1
0
0
3
0
0
3
0
0
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
2
0
1
1
0
1
0
0
0
0
2
1
0
3
0
0
0
0
2
2
0
2
0
2
1
0
1
0
0
2
0
0
0
0
1
1
2
0
0
0
1
0
0
0
0
2
1
1
1
0
0
0
1
0
0
0
0
1
0
2
2
0
0
0
0
1
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
1
1
0
2
2
0
0
0
0
0
0
0
0
1
0
2
2
3
0
0
0
0
1
2
0
1
0
0
2
1
0
1
0
0
0
0
1
0
2
0
0
0
0
0
2
0
1
0
0
1
1
0
1
2
0
3
0
2
0
0
1
1
1
1
3
0
0
0
2
0
1
0
0
0
1
2
0
2
2
1
2
0
1
2
0
0
0
0
2
0
0
2
2
0
0
1
2
0
1
1
0
0
0
3
0
0
0
0
0
0
1
2
2
0
0
0
0
2
1
2
2
0
0
2
0
2
0
2
0
0
3
1
0
0
3
0
0
2
2
0
0
0
1
0
0
0
0
2
0
1
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
2
1
2
1
0
0
2
1
0
1
2
2
0
0
1
0
0
1
0
1
1
2
2
1
2
0
1
0
2
3
0
2
1
1
0
1
1
0
0
1
0
1
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
1
1
0
0
2
0
2
0
0
0
0
1
2
0
0
2
0
1
0
0
0
2
0
0
0
1
1
0
2
3
0
2
0
1
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
1
1
0
0
0
4
0
0
2
1
0
1
0
0
0
1
0
0
2
0
1
0
2
1
0
0
1
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
2
0
3
0
2
1
1
0
2
2
3
1
0
0
0
5
1
0
0
0
1
2
0
1
0
0
2
1
2
0
1
0
0
0
2
2
2
1
2
0
0
1
3
2
1
1
0
0
1
0
1
0
0
0
2
1
0
2
1
0
0
1
0
2
0
0
1
2
0
0
0
0
0
2
2
0
0
0
0
2
1
1
0
1
0
0
0
2
0
1
0
0
1
0
0
0
0
0
2
1
0
0
1
0
0
0
1
0
0
2
1
1
2
0
2
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
2
0
2
0
0
0
1
0
0
2
1
0
2
0
0
0
0
0
1
1
1
0
0
2
0
1
0
0
1
0
1
0
0
1
0
0
0
1
0
0
1
3
0
2
1
2
1
0
0
0
1
1
0
2
1
1
0
1
0
2
0
0
0
0
1
0
1
0
0
0
2
1
2
0
2
0
1
0
1
1
1
0
0
0
0
0
6
2
0
0
0
0
2
0
1
1
0
1
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
1
2
0
0
0
1
1
2
1
0
0
0
2
0
0
0
2
1
0
1
0
0
0
0
2
2
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
2
0
2
2
0
1
3
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
1
0
0
2
0
1
0
1
1
0
1
1
0
0
0
1
0
1
0
1
0
2
0
0
2
0
1
0
0
0
1
1
0
1
1
2
1
0
1
1
0
0
0
4
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
1
2
2
0
0
0
0
0
1
0
1
0
2
0
2
1
0
1
0
0
1
0
0
1
2
0
2
0
0
0
0
0
0
4
1
0
1
0
0
2
0
1
0
0
2
0
1
0
0
0
2
0
1
1
0
5
0
0
0
1
1
0
4
0
0
0
1
2
0
0
0
0
1
1
0
0
0
1
1
0
2
0
1
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
1
3
0
1
0
0
1
0
0
0
0
0
0
0
4
0
2
0
2
0
0
0
0
0
0
0
0
0
1
1
1
0
0
2
0
1
0
0
1
0
1
0
0
0
0
1
1
0
0
1
1
1
0
2
1
0
0
1
0
0
2
0
0
1
2
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
1
3
1
1
0
0
2
1
1
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
2
0
0
0
0
0
2
1
1
2
0
2
0
1
1
0
1
2
0
0
0
0
2
0
0
1
0
0
0
2
0
1
0
1
1
1
0
0
1
0
0
2
1
0
0
0
2
0
0
1
4
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
2
0
3
2
1
1
0
0
0
0
0
1
1
0
3
1
2
0
1
0
0
0
0
0
2
1
2
0
0
0
0
1
1
1
1
0
0
2
1
1
2
3
0
0
0
2
0
0
0
1
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
1
2
1
1
0
0
0
0
2
0
0
0
2
1
0
2
1
0
0
0
0
0
0
0
2
0
2
0
1
0
1
1
0
0
0
2
0
0
2
0
2
0
2
0
2
0
0
1
3
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
2
2
1
0
0
1
2
0
2
2
0
0
0
0
0
1
0
2
0
1
0
0
1
0
1
2
0
0
0
0
0
0
1
2
2
0
1
0
1
2
1
1
0
0
2
0
0
1
0
0
0
3
0
1
0
0
2
0
1
1
1
2
1
1
0
1
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
1
0
1
1
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
1
1
0
2
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
1
2
0
0
0
0
0
2
0
0
1
2
1
0
0
1
0
0
1
0
0
1
0
0
0
2
0
0
1
0
6
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
2
0
0
2
0
0
1
0
1
0
0
0
0
0
2
0
2
2
2
0
0
1
2
0
0
0
0
0
1
0
1
2
2
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
2
0
0
0
0
0
1
0
0
1
0
0
0
1
2
1
0
0
0
2
0
0
2
0
0
2
0
0
2
0
0
2
0
0
2
0
0
2
0
0
0
0
0
1
0
2
1
0
2
2
0
2
0
0
1
2
1
2
3
0
0
1
0
0
1
0
0
1
1
2
2
1
0
0
1
0
0
0
1
0
1
2
0
0
0
2
1
0
0
2
0
0
0
1
1
2
0
1
0
0
2
0
0
4
0
0
1
2
6
0
2
2
0
0
0
0
0
0
2
0
0
1
2
1
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
3
0
0
1
2
1
3
0
0
0
2
0
1
1
2
1
0
1
0
1
0
0
0
0
0
0
1
0
1
0
2
3
0
1
0
0
0
0
3
2
0
0
1
0
0
2
0
0
2
0
0
1
0
0
0
0
3
1
1
0
1
0
0
0
0
0
1
0
0
2
2
0
0
4
1
0
0
0
0
0
1
0
0
2
0
0
5
2
3
0
1
2
0
0
0
3
0
2
0
1
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
1
2
0
1
0
0
0
0
1
2
1
1
0
0
0
0
1
2
1
1
0
0
2
0
1
1
2
0
0
0
0
0
0
2
0
3
1
1
2
0
0
0
0
0
0
0
0
2
1
0
2
0
1
1
0
1
0
2
0
0
0
2
0
1
2
2
0
1
2
0
1
0
2
0
0
0
0
2
2
5
0
2
0
0
0
0
0
2
1
0
0
0
0
1
1
0
0
0
0
2
1
0
1
0
1
0
1
0
0
1
2
1
2
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
1
0
2
0
0
0
1
1
2
0
2
2
0
0
0
1
0
0
2
2
1
0
2
1
2
0
0
0
0
1
1
2
0
2
1
0
2
2
0
0
0
1
0
2
0
2
2
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
2
0
2
0
2
0
0
0
1
1
0
1
0
0
0
0
0
1
1
0
0
1
0
0
1
1
0
0
0
0
1
1
0
0
0
1
2
0
2
0
0
0
0
0
0
0
2
0
2
0
1
1
1
0
1
0
0
1
1
0
1
0
0
0
2
2
1
0
0
0
2
0
2
2
0
0
2
3
0
0
0
0
0
2
0
1
1
0
2
2
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
2
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
1
1
0
0
0
1
1
2
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
2
2
1
1
0
2
0
1
0
0
2
0
1
1
0
0
0
0
1
1
0
0
0
2
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
2
2
0
2
0
0
0
2
0
0
0
1
0
0
1
0
0
1
0
1
2
1
0
0
0
5
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
1
0
1
3
0
0
0
0
0
1
0
2
0
2
2
1
0
0
0
2
0
1
1
0
0
0
0
1
0
1
2
2
0
0
0
0
2
0
2
2
1
1
0
2
1
1
0
2
0
0
0
2
0
0
0
1
0
2
2
0
0
1
1
0
2
2
0
0
0
0
1
1
2
2
0
2
0
0
3
0
0
0
0
0
1
2
0
1
1
2
0
0
1
2
2
0
0
0
1
1
1
1
1
0
0
0
0
0
0
1
1
1
1
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
4
2
2
0
1
0
1
0
0
0
0
1
2
2
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
3
1
0
0
1
0
0
0
0
0
0
0
2
3
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
1
4
1
0
2
0
0
0
0
0
0
2
3
2
0
0
1
0
0
2
0
1
0
2
0
2
0
0
1
0
0
1
0
1
0
0
1
1
0
0
0
0
3
0
0
0
0
0
0
1
0
2
0
2
0
1
1
0
2
0
2
0
0
2
0
0
0
0
3
1
2
1
0
0
2
1
0
2
0
0
1
1
0
0
0
0
1
2
0
0
0
0
2
2
0
3
0
1
0
3
0
1
0
0
2
1
1
2
2
0
1
1
0
0
1
0
1
0
2
0
2
0
0
1
0
0
1
2
0
2
3
0
0
1
2
2
0
0
2
0
1
0
0
2
0
2
4
0
0
1
0
2
0
1
1
0
1
0
0
0
1
2
4
0
0
1
1
0
1
1
2
0
1
0
0
0
1
0
0
0
0
0
1
0
1
2
3
0
0
0
1
0
0
0
2
1
1
0
0
2
0
0
2
4
0
0
0
2
1
0
0
2
0
0
0
2
1
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
1
2
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
1
0
0
2
1
0
0
0
1
1
4
0
0
1
0
0
0
2
2
1
2
0
0
0
1
0
2
0
1
1
2
1
0
2
0
0
0
0
0
2
0
0
0
1
2
0
0
1
0
1
0
1
1
1
3
0
1
0
0
2
0
2
0
2
0
1
0
0
1
2
0
0
0
1
1
2
3
1
0
1
0
0
1
0
0
0
1
0
0
0
0
1
1
1
0
1
0
0
0
0
2
0
4
2
0
1
0
0
1
1
1
0
0
2
0
3
0
0
0
0
1
0
0
2
0
0
3
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
1
1
1
1
0
0
0
2
0
0
0
1
1
0
0
0
1
0
0
0
0
0
4
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
1
0
1
0
0
0
0
2
1
0
1
2
0
1
0
1
0
0
0
0
2
0
1
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
1
0
0
0
1
0
1
1
0
3
2
1
0
1
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
2
2
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
2
1
2
0
1
2
2
0
2
0
0
2
2
0
0
1
2
2
0
0
0
0
0
2
0
0
0
2
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
2
2
2
0
1
1
2
0
0
0
0
2
0
2
1
1
0
1
1
2
1
0
0
1
2
2
0
1
0
2
0
0
2
0
2
2
1
2
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
1
0
1
0
0
0
0
2
0
0
1
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
2
1
2
0
0
0
0
0
0
2
1
1
1
3
0
0
0
0
0
0
1
0
0
2
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
2
1
1
1
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
3
1
1
0
2
0
1
0
0
0
0
1
0
2
0
0
1
1
1
0
2
2
0
0
0
1
0
1
0
0
0
0
0
0
1
2
1
2
0
1
0
0
0
2
2
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
2
0
2
1
0
0
0
7
0
2
0
0
0
2
0
0
0
1
2
0
0
0
1
1
0
0
0
0
2
0
0
1
0
2
0
1
3
0
0
0
1
2
1
0
0
2
0
1
0
0
1
0
1
0
0
1
1
0
2
0
1
0
3
0
1
2
0
0
0
1
0
0
0
2
0
0
1
1
1
0
2
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
2
1
0
1
2
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
2
0
1
0
1
1
1
2
0
0
0
0
1
2
0
0
1
0
0
1
1
0
1
0
0
2
0
0
1
2
0
1
0
2
0
0
2
0
0
0
3
2
0
2
0
1
1
0
1
2
2
3
1
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
2
1
0
0
0
0
0
0
0
1
0
1
0
2
0
3
0
2
2
2
0
1
0
2
0
0
0
0
1
0
2
2
0
0
0
0
2
0
0
2
2
2
2
0
1
2
0
0
0
0
0
2
0
0
0
2
2
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
2
1
2
1
0
0
1
1
3
1
0
0
2
0
0
0
1
1
0
0
0
0
2
0
0
2
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
2
1
0
0
0
0
2
0
0
0
2
0
0
0
2
2
0
2
0
0
0
1
1
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
3
0
0
2
0
3
1
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
2
2
0
0
0
0
0
2
1
0
2
0
0
1
0
0
1
0
0
0
3
0
1
2
0
0
2
0
0
0
0
0
0
0
1
0
1
2
0
0
0
1
0
1
0
0
0
2
0
2
0
1
0
0
1
2
2
0
2
2
0
0
0
0
3
0
1
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
2
1
1
0
1
2
0
1
0
1
2
0
0
0
2
0
0
0
2
0
1
0
0
2
0
0
0
2
0
0
0
2
1
1
0
0
0
0
0
2
0
2
0
1
0
0
3
3
0
0
1
0
2
0
0
5
0
0
1
0
1
0
0
1
0
2
2
2
0
0
0
2
0
0
2
3
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
2
7
0
1
0
2
0
0
0
1
1
0
2
0
0
1
1
0
3
0
2
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
2
2
0
0
1
0
0
0
0
2
0
2
0
0
0
1
0
1
1
2
0
1
0
0
0
1
2
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
1
2
0
0
1
0
0
2
8
0
3
1
0
2
0
2
0
0
4
0
2
2
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
2
1
0
1
1
0
0
0
2
0
0
1
1
0
0
0
3
1
1
2
0
2
0
0
0
2
0
2
1
0
2
1
0
1
2
1
0
0
1
0
0
0
2
0
0
0
0
0
0
2
2
1
1
0
0
2
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
2
0
0
1
3
0
0
2
2
0
0
0
2
2
2
1
0
2
0
3
2
0
2
1
0
0
0
0
1
1
1
0
0
0
0
0
2
0
0
2
0
0
2
2
1
0
0
0
0
2
0
2
0
0
2
1
0
0
4
0
0
3
0
2
1
0
0
2
2
0
0
1
2
0
1
2
2
0
0
2
0
2
0
1
0
2
2
1
0
0
0
0
0
0
2
0
1
0
1
2
0
0
2
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
2
1
1
1
0
1
1
0
1
0
1
1
0
1
2
1
0
0
2
0
1
0
1
0
0
0
3
0
2
0
0
0
0
1
0
0
0
2
1
2
0
0
0
0
2
0
2
1
0
0
0
1
0
1
1
0
1
0
1
0
0
0
0
0
1
1
0
0
0
1
3
0
1
1
2
0
0
0
1
0
0
1
1
0
0
2
0
1
3
0
1
0
0
0
0
0
1
0
0
0
2
2
0
0
1
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
2
0
2
0
0
0
0
2
2
1
1
1
0
0
0
1
1
0
0
0
2
2
0
1
2
0
0
0
0
0
0
2
0
1
0
0
0
0
2
1
2
0
0
0
0
1
0
2
0
0
2
1
0
1
1
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
2
1
2
0
0
0
0
2
2
0
0
0
0
0
0
1
2
1
0
0
2
0
1
1
0
1
0
0
0
9
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
1
3
1
0
0
2
2
1
0
2
2
0
0
1
0
2
0
0
1
1
2
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
3
2
0
0
0
2
1
2
2
0
0
1
0
0
1
0
0
0
3
0
1
0
0
2
1
0
0
1
0
0
1
2
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
3
0
2
0
0
0
0
0
0
2
1
2
2
1
0
0
0
0
0
0
0
2
0
3
1
0
0
2
1
2
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
4
0
0
2
1
0
0
2
2
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
3
1
0
0
0
0
1
2
0
0
0
2
0
0
0
2
2
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
2
0
2
1
0
0
1
0
0
1
0
0
1
1
0
0
0
1
1
0
0
2
0
2
0
2
0
0
1
0
0
0
0
0
0
2
2
0
3
2
0
0
1
1
1
2
1
0
1
0
1
0
0
2
0
3
0
1
0
0
0
2
1
1
0
2
2
0
0
0
0
2
3
0
0
2
1
1
0
1
0
0
2
1
1
1
0
0
0
2
1
2
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
3
0
1
3
2
0
0
0
2
2
0
2
1
0
2
0
3
2
1
1
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
2
0
0
0
1
0
0
2
0
0
2
0
0
0
2
2
0
0
0
0
0
0
2
0
0
1
2
0
2
2
1
0
1
0
2
1
0
0
0
0
0
0
0
0
0
2
0
2
2
2
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
2
2
0
1
0
1
1
2
0
0
0
1
0
1
0
0
2
0
0
0
1
0
3
0
0
0
0
1
0
1
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
2
2
0
0
1
0
0
0
3
3
2
0
0
0
0
0
0
1
2
0
2
0
0
1
0
2
0
1
0
0
0
0
0
0
1
1
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
2
1
0
1
1
0
1
0
0
1
0
0
0
0
0
0
1
0
1
2
0
0
1
0
1
0
0
1
1
1
0
1
2
1
0
0
0
2
0
0
1
0
0
0
3
1
0
0
2
0
0
0
1
1
0
2
1
1
2
0
2
0
2
1
3
0
0
0
2
0
1
0
1
0
0
0
1
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
1
0
1
2
0
0
0
0
0
2
1
0
0
0
0
2
1
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
1
0
1
0
0
1
2
0
1
1
2
0
2
2
1
1
3
2
0
0
0
2
0
0
1
2
0
0
2
0
0
0
1
6
2
1
2
0
2
0
1
0
0
1
0
2
0
0
0
0
1
0
1
0
1
0
0
1
2
0
0
0
0
2
2
0
0
0
3
2
0
1
0
0
0
1
1
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
1
1
0
0
0
1
1
2
2
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
2
2
0
1
2
1
2
0
1
1
0
0
0
0
1
1
0
0
0
0
3
0
1
1
0
1
1
1
3
2
0
0
0
2
2
2
2
2
0
4
1
0
0
2
1
0
1
1
1
2
2
0
0
0
0
1
1
1
0
0
0
2
0
0
0
1
4
2
0
1
0
0
0
1
2
2
0
1
3
0
0
1
3
0
2
0
2
0
0
0
1
0
1
0
4
2
0
0
1
1
2
0
2
4
1
2
2
1
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
4
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
1
1
5
2
4
1
1
2
1
0
0
0
2
5
1
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
3
2
2
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
2
3
0
1
1
1
0
0
0
0
4
0
2
1
0
0
0
0
0
0
1
0
1
0
2
1
0
5
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
1
0
0
1
1
0
1
2
0
2
0
0
1
1
1
0
1
1
1
0
0
0
1
0
0
2
1
0
0
0
1
1
0
0
3
1
0
4
1
0
1
0
2
2
0
0
0
2
1
0
0
0
0
0
0
2
1
1
1
0
1
0
0
1
0
0
1
2
2
0
0
0
0
2
0
2
0
0
0
2
0
0
2
0
1
0
4
2
0
0
1
0
0
0
0
0
3
0
0
0
4
0
1
2
0
0
1
0
2
1
0
0
1
0
1
0
0
0
2
0
0
2
2
0
1
0
2
0
1
0
1
0
0
0
0
2
0
0
0
2
0
1
1
2
0
0
2
2
2
2
0
2
1
1
0
0
2
0
0
4
2
0
0
1
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
2
0
0
0
1
2
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
2
0
0
1
0
1
0
0
1
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
5
1
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
2
2
1
0
0
0
2
2
1
1
0
1
1
1
2
3
0
1
0
2
2
0
0
0
0
2
2
4
1
0
2
0
0
0
0
0
1
2
1
0
0
1
2
1
0
0
0
0
2
0
0
1
2
0
0
1
0
2
1
0
0
0
1
2
0
0
2
0
0
2
0
0
0
0
2
0
1
0
0
1
0
0
0
0
1
0
0
0
2
2
1
0
0
0
0
0
2
1
1
1
0
3
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
1
0
1
0
2
1
0
0
0
0
1
0
0
1
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
2
2
1
1
0
0
1
0
0
0
2
2
0
0
1
0
0
1
2
2
0
1
0
1
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
3
1
1
0
0
0
1
1
0
0
0
0
0
2
2
2
0
1
1
0
0
0
1
2
2
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
2
0
1
1
0
0
1
0
0
0
1
1
0
0
0
0
2
2
0
0
1
1
0
0
0
1
2
0
0
1
0
1
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
2
1
2
1
1
2
0
1
0
1
1
0
0
0
0
1
0
2
1
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
2
2
2
0
0
0
0
1
0
0
1
0
1
0
0
2
0
2
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
2
0
1
1
0
0
2
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
4
0
1
0
1
2
0
3
0
2
1
1
0
0
0
0
0
0
1
2
0
1
0
1
0
0
1
0
0
0
1
3
0
1
0
0
0
0
0
1
0
2
0
2
0
0
2
0
1
3
0
0
0
2
1
0
2
0
5
2
1
0
1
0
0
0
0
1
0
0
2
1
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
2
2
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
1
0
0
9
2
1
0
0
0
0
0
0
2
0
0
2
2
1
1
0
0
0
0
2
0
0
0
0
1
2
0
1
2
0
2
0
0
0
0
0
0
1
1
0
0
0
2
0
1
0
2
1
0
0
0
1
0
2
1
2
0
4
0
0
2
2
1
0
0
1
1
4
1
0
0
1
0
4
0
0
2
0
2
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
2
2
1
0
0
0
1
2
0
0
1
0
0
1
0
2
0
0
0
1
0
2
2
0
0
0
1
0
2
0
0
0
0
0
0
0
1
1
0
0
5
2
2
2
0
0
0
0
0
0
0
2
0
1
2
0
1
0
0
1
1
1
2
0
0
0
0
0
0
0
1
0
2
0
1
0
2
0
0
0
0
0
0
2
2
1
2
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
1
1
1
0
1
0
0
0
0
1
0
1
1
0
2
1
1
1
1
0
0
1
0
1
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
2
0
2
0
0
2
0
1
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
3
0
2
0
0
1
0
1
1
0
2
2
0
0
0
0
2
2
1
2
0
0
0
0
2
0
1
0
0
0
0
0
1
3
1
2
3
0
1
2
0
0
6
2
0
0
0
1
0
1
2
3
1
2
0
0
0
0
2
0
1
0
0
1
2
2
1
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
3
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
3
0
0
2
0
0
1
2
0
0
2
1
2
2
2
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
1
1
0
0
1
0
0
1
2
0
1
1
0
0
2
1
0
0
2
0
0
2
0
1
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
2
0
0
2
0
2
1
0
0
0
1
1
0
1
1
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
2
0
1
1
2
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
2
0
0
0
1
0
0
1
1
0
1
0
2
0
2
0
2
0
1
1
2
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
1
1
2
1
0
0
0
2
1
1
0
2
1
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
3
0
0
0
1
1
1
0
0
1
0
0
1
0
0
1
2
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
1
2
0
0
2
0
0
1
2
0
0
0
0
0
0
1
1
0
0
1
0
0
3
1
0
2
0
1
1
0
0
0
2
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
1
2
2
2
0
0
0
1
1
0
2
0
0
1
1
2
0
0
2
0
0
2
0
2
0
0
0
2
2
0
0
0
1
2
0
0
2
0
2
2
0
0
5
2
0
2
0
0
1
2
0
3
0
0
0
2
0
1
0
0
0
2
0
0
0
1
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
2
2
0
0
1
0
0
0
0
2
0
0
0
0
1
1
1
2
3
0
1
0
0
0
2
2
1
0
0
2
1
1
0
1
2
0
2
0
0
1
0
1
2
1
1
0
1
0
0
2
2
0
2
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
2
0
0
0
0
0
2
0
0
2
0
1
2
0
1
1
0
0
0
0
0
1
0
0
1
2
0
1
0
1
3
0
0
1
1
0
1
0
0
0
0
0
0
1
0
2
0
0
0
1
0
2
1
0
0
0
2
0
0
0
3
0
0
0
2
2
0
0
0
1
1
0
2
2
0
1
0
0
1
0
2
0
1
0
1
2
0
2
0
1
2
0
2
0
0
0
0
0
0
0
1
0
0
2
2
0
1
0
2
0
0
0
1
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
1
8
0
0
5
2
0
0
1
0
0
0
0
2
2
0
2
2
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
2
0
1
0
0
2
0
0
0
2
1
1
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
1
2
0
0
0
1
0
0
1
0
0
2
0
2
0
2
0
0
1
2
0
1
0
2
2
1
0
3
0
2
0
0
0
0
0
2
0
2
2
2
0
1
3
0
0
1
0
0
1
2
0
0
0
1
2
2
0
1
0
2
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
2
1
1
0
1
0
1
2
1
0
0
0
2
1
1
0
0
0
0
0
0
2
1
0
0
0
0
0
2
1
0
0
0
2
2
0
0
0
2
0
0
0
2
1
1
0
1
2
0
0
2
1
1
2
0
1
0
0
2
0
0
0
2
1
0
1
0
0
2
1
0
2
2
1
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
1
1
0
0
2
0
0
1
6
0
1
0
1
0
1
2
0
1
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
7
0
2
0
1
0
0
3
2
2
0
2
0
1
2
0
0
0
1
1
0
1
0
0
0
0
0
2
2
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
1
0
1
1
0
2
0
1
2
0
0
1
0
2
1
1
2
1
0
0
0
0
5
2
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
2
0
0
2
1
2
0
3
0
1
0
2
0
0
0
2
1
1
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
1
0
2
0
0
1
2
1
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
2
0
1
0
0
0
0
0
0
1
0
1
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
2
0
1
0
1
3
0
2
0
1
0
0
1
0
0
1
0
2
1
2
1
1
0
0
1
0
2
2
1
0
2
3
1
1
1
0
0
0
1
3
1
0
0
2
0
1
0
0
1
2
0
1
0
0
2
2
2
1
0
1
0
2
2
0
0
3
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
2
0
2
1
0
0
0
0
1
0
1
2
0
0
2
0
3
0
0
0
0
2
0
1
0
0
1
0
0
3
1
0
0
0
2
2
0
1
2
1
0
0
2
0
0
0
0
2
1
0
2
2
0
1
0
0
2
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
3
2
0
2
0
1
2
1
0
0
0
1
0
2
0
0
0
1
0
0
1
1
1
0
0
0
2
0
0
0
0
2
1
0
0
0
1
3
0
0
0
0
0
0
0
0
2
1
0
0
1
1
0
0
0
1
1
2
0
2
0
1
1
0
0
0
1
0
1
0
0
2
1
0
0
0
0
0
0
0
0
1
0
1
1
2
2
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
2
0
2
1
1
0
0
0
0
0
0
0
0
0
1
2
0
2
1
0
0
0
0
0
1
0
0
3
2
2
0
0
1
0
0
1
1
2
2
0
1
0
0
1
2
2
0
0
0
0
0
0
2
1
0
1
0
0
0
1
2
0
0
0
1
2
0
0
1
0
0
0
0
1
0
1
0
0
1
1
0
2
1
0
0
0
0
0
1
2
0
0
0
0
0
0
1
2
0
2
1
3
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
1
0
1
2
2
0
0
2
2
0
0
2
0
0
0
1
1
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
3
0
0
0
2
0
1
0
0
0
0
2
0
0
0
1
0
2
1
1
0
1
0
0
1
0
0
2
0
0
0
0
0
1
2
0
0
2
0
1
0
2
0
0
0
1
0
2
1
0
0
0
0
0
2
0
1
1
0
0
0
1
2
0
0
1
0
1
2
0
2
0
0
2
2
2
1
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
5
0
0
2
0
2
1
0
0
0
0
0
0
0
2
2
1
3
0
0
2
0
1
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
3
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
1
2
0
0
1
2
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
2
0
0
0
2
1
0
0
1
0
0
0
0
2
0
1
0
1
2
0
0
0
0
1
0
0
1
0
1
0
2
0
0
1
0
0
0
0
0
0
2
1
0
1
0
2
1
1
2
0
0
1
0
0
3
0
2
6
2
0
0
0
0
1
0
0
0
0
0
1
1
1
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
2
0
1
2
0
0
2
0
0
0
3
0
2
0
0
1
0
0
0
1
3
2
0
0
1
0
3
0
3
2
0
0
0
0
0
0
2
2
0
0
0
0
1
1
0
2
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
1
2
0
1
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
2
0
0
0
1
1
0
2
0
0
1
1
0
2
0
0
0
2
0
1
0
0
0
2
0
0
1
2
0
1
0
0
0
1
2
2
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
2
0
2
2
1
0
0
1
0
2
1
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
1
1
1
0
2
0
0
1
0
2
1
0
0
2
0
2
1
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
2
2
0
1
0
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
1
2
0
2
2
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
1
0
0
1
2
1
0
0
0
1
0
1
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
1
2
0
0
0
0
0
2
0
0
2
0
1
0
1
1
0
0
2
0
0
1
2
0
0
0
2
0
1
0
0
0
0
0
1
0
2
0
0
2
2
1
0
2
0
1
0
2
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
3
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
2
0
1
0
2
0
1
0
0
0
0
0
1
2
2
0
0
0
0
1
3
2
0
3
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
3
0
0
0
1
2
1
1
0
0
0
0
0
0
0
2
0
1
1
0
1
2
3
2
1
0
0
0
0
2
1
1
1
0
1
0
1
1
0
0
0
1
2
2
1
0
2
2
0
0
0
0
0
0
0
2
1
0
0
1
0
1
0
1
0
2
1
0
2
1
0
0
0
0
2
1
0
0
0
0
0
0
0
1
3
0
2
0
0
1
1
2
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
1
0
0
4
3
1
0
0
3
1
1
0
2
0
0
0
0
2
1
2
0
0
2
0
1
1
2
2
2
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
2
2
0
0
2
2
0
0
2
0
2
0
0
1
1
1
2
0
1
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
2
0
0
0
1
0
1
0
0
0
0
2
2
1
3
2
2
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
1
2
1
0
2
1
0
0
2
0
0
0
0
2
2
1
0
2
1
0
0
0
0
0
1
2
2
1
0
2
0
2
0
0
1
3
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
1
0
1
0
0
0
0
0
2
1
0
1
0
0
1
0
0
1
0
0
0
0
1
0
1
0
1
2
0
0
0
0
1
0
0
0
1
4
0
0
0
0
1
2
0
2
1
1
2
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
2
2
0
2
0
1
0
1
0
1
0
0
0
0
0
1
0
1
0
2
0
1
1
2
0
2
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
3
0
0
1
0
0
1
0
0
3
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
4
0
0
1
2
4
2
1
0
1
0
0
0
1
0
0
2
0
2
1
0
1
0
2
0
0
1
0
0
0
0
0
1
1
0
0
0
0
3
0
0
0
0
0
1
0
0
1
2
0
0
0
0
1
2
0
0
1
0
0
0
0
2
0
0
0
2
2
0
2
0
0
1
0
1
2
0
1
1
0
0
2
0
0
1
0
1
0
0
0
0
1
2
0
0
0
0
1
0
2
0
0
2
2
2
0
2
2
0
1
3
1
0
1
0
0
0
0
2
1
0
1
0
1
2
2
0
1
2
2
0
2
0
1
1
0
2
2
0
0
1
2
2
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
1
0
1
2
0
0
0
0
0
2
0
0
0
2
2
2
2
0
1
0
0
0
0
0
2
1
0
3
1
0
0
2
0
0
0
0
0
4
0
2
0
1
0
1
0
3
0
2
2
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
1
1
0
0
1
0
1
0
0
0
1
0
1
2
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
2
0
2
1
0
0
2
0
0
0
0
0
1
0
0
0
3
0
1
2
2
2
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
3
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
2
0
0
0
1
0
2
0
2
1
1
2
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
3
1
0
1
3
0
0
2
0
0
0
1
0
0
1
0
0
0
2
0
0
1
1
0
0
4
0
0
0
2
1
0
0
0
0
0
1
0
3
0
1
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
2
0
2
2
0
0
0
2
0
0
1
0
0
0
2
0
0
1
0
1
2
2
0
1
0
0
1
0
1
0
2
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
2
0
1
2
0
0
0
2
0
0
0
0
2
2
2
0
0
0
0
0
0
0
1
2
0
0
0
2
0
3
0
0
1
0
1
1
2
1
0
0
0
0
2
0
1
0
0
2
3
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
1
0
2
1
0
1
0
0
0
0
2
0
0
1
0
2
0
2
2
0
0
0
1
0
0
1
0
0
2
0
2
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
3
0
2
0
2
1
0
1
0
0
0
0
0
2
1
2
1
0
0
0
0
2
1
0
1
0
2
0
2
0
0
0
2
0
1
1
0
0
0
0
0
0
0
1
2
1
0
0
0
1
0
3
2
0
2
0
2
3
1
0
1
0
1
1
2
0
1
0
1
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
1
0
0
2
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
1
0
3
1
0
0
0
1
1
2
2
1
1
2
1
0
2
1
2
1
2
0
2
2
0
1
0
0
0
0
0
1
0
1
1
2
0
2
0
1
2
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
1
1
0
0
0
0
0
5
0
0
0
0
0
2
0
1
0
2
2
0
1
0
1
1
0
0
1
0
2
3
2
0
1
2
4
0
1
1
1
1
0
2
0
0
1
2
0
2
0
0
2
0
0
2
2
1
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
2
0
0
2
1
2
0
1
1
1
0
0
1
0
2
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
2
0
1
1
1
0
0
1
2
0
2
0
0
2
0
0
1
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
2
1
0
2
0
0
2
0
2
3
0
3
0
0
0
2
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
1
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
1
2
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
2
1
2
0
0
0
1
1
0
1
0
0
0
3
0
0
1
1
0
1
0
0
0
1
0
2
0
0
1
2
0
0
0
0
2
0
1
0
2
1
0
2
0
0
0
0
1
0
0
0
1
0
0
1
2
0
0
1
0
1
0
0
0
0
6
0
0
3
2
0
1
0
0
0
1
0
0
1
0
1
0
0
2
2
0
0
2
2
0
2
1
1
0
0
0
0
0
0
0
1
2
1
0
1
2
2
1
0
3
0
1
0
2
0
0
0
0
2
0
1
0
0
2
0
4
1
0
1
0
0
0
1
0
0
2
0
2
0
2
0
2
0
0
0
0
0
1
1
0
2
0
0
0
1
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
2
1
0
1
0
2
0
1
0
0
2
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
2
2
0
1
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
3
0
0
0
0
2
0
2
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
2
2
2
0
0
1
3
2
0
0
0
0
2
0
2
0
0
0
0
0
0
1
2
1
0
3
0
0
0
3
2
0
2
0
1
1
4
0
0
0
0
0
1
0
1
0
0
1
0
0
0
2
1
4
1
1
1
0
0
0
1
1
2
0
2
0
0
0
0
1
2
1
0
0
0
0
1
0
0
2
1
0
0
0
0
1
0
2
1
2
1
0
0
0
1
0
1
2
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
2
1
0
0
2
0
0
0
2
0
2
1
2
0
1
1
0
1
0
1
1
0
0
0
1
0
1
0
2
0
0
0
1
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
2
2
1
0
0
2
1
1
1
1
1
0
0
0
0
0
0
1
2
0
0
1
2
2
2
1
2
0
0
0
0
2
0
0
0
1
0
2
0
0
2
0
2
2
0
2
0
1
0
2
0
0
0
1
0
1
1
0
0
0
0
2
1
1
1
0
2
1
1
0
0
0
0
1
0
2
0
0
3
0
0
2
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
1
0
1
2
0
1
0
0
1
0
1
1
0
2
0
2
0
0
1
2
1
0
1
0
1
0
0
0
0
0
0
1
0
2
0
0
0
2
0
2
0
2
0
2
0
0
0
2
1
0
1
1
1
2
1
0
1
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
1
0
2
0
0
5
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
1
0
2
1
2
0
1
0
1
0
1
0
0
1
0
1
0
0
0
0
0
1
0
1
2
0
1
0
1
1
0
0
1
0
0
0
0
0
2
1
0
1
0
0
0
0
1
0
0
2
0
0
2
2
0
0
0
1
0
3
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
2
0
2
1
1
2
0
2
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
2
1
0
1
0
0
0
0
2
2
0
0
2
2
2
0
0
0
1
1
2
0
0
2
0
0
0
1
2
3
1
1
0
3
0
2
3
0
0
2
1
0
0
3
1
1
0
1
0
0
2
2
0
0
0
0
2
2
1
2
0
2
0
1
2
0
1
1
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
2
0
0
0
0
1
0
2
1
1
0
1
0
0
0
1
2
2
1
0
0
0
0
1
0
0
3
1
0
0
2
1
2
0
2
0
2
2
1
2
0
0
0
0
0
0
0
2
2
2
0
0
0
1
0
1
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
1
0
0
0
0
1
0
0
2
1
0
0
0
0
1
1
0
2
0
0
0
3
0
0
2
0
0
1
1
2
1
0
1
1
0
0
0
0
2
0
1
1
0
2
0
0
0
2
1
2
1
0
1
0
0
2
1
2
0
0
2
0
0
0
2
0
0
0
0
0
2
2
1
0
0
0
0
0
2
0
1
0
2
0
0
1
1
2
1
0
1
0
0
0
1
0
0
2
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
2
2
2
0
0
0
0
0
1
0
1
0
1
0
1
0
2
1
0
2
0
0
0
1
0
2
2
3
1
0
0
0
0
0
1
0
0
2
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
2
3
0
0
0
0
4
0
0
0
0
2
0
0
2
1
0
0
0
1
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
1
3
0
2
1
1
0
0
0
0
0
0
2
0
0
0
0
8
1
1
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
1
0
1
1
0
0
2
0
0
1
0
0
1
1
2
0
0
1
0
0
1
1
1
2
0
0
0
0
0
1
0
0
1
0
0
0
0
1
2
1
0
0
2
2
0
0
0
2
0
2
0
1
2
1
0
0
0
2
0
0
0
0
1
0
0
0
3
2
0
1
0
0
0
0
0
1
0
1
1
2
0
0
1
0
0
0
0
0
0
0
0
0
2
2
2
0
0
2
0
2
0
1
0
0
0
0
0
0
1
0
1
1
0
1
0
1
1
2
0
0
1
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
2
0
1
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
4
2
0
0
0
0
1
0
0
0
0
2
0
0
0
2
2
3
0
2
1
0
0
2
0
0
0
0
0
1
1
0
0
0
2
0
1
0
0
0
0
0
0
0
1
2
0
2
0
0
0
1
0
0
1
1
0
1
2
0
2
0
0
1
0
1
1
0
1
0
2
0
1
0
1
0
0
0
0
0
1
0
1
0
1
2
2
1
0
2
0
1
0
2
0
1
0
1
0
0
1
0
0
0
5
2
0
0
2
0
0
1
2
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
2
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
2
0
4
0
1
0
0
0
0
0
1
0
2
0
0
2
0
0
0
1
2
0
1
1
0
0
0
0
1
2
1
2
0
0
0
0
1
0
1
0
1
0
0
2
0
1
0
0
2
0
1
0
2
1
0
0
2
2
1
1
1
0
2
0
2
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
2
0
4
2
1
2
1
0
2
0
2
2
0
0
3
0
3
0
0
0
0
3
0
0
0
2
1
0
0
0
0
0
0
0
0
1
2
2
1
0
0
2
0
1
2
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
2
0
0
0
0
0
0
0
0
2
1
8
0
1
0
0
2
0
2
2
2
0
2
0
0
2
0
1
0
0
2
1
2
0
2
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
1
2
0
0
0
0
1
2
0
0
0
2
2
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
3
0
0
2
1
1
0
0
0
3
0
0
1
0
1
0
0
0
0
3
0
0
2
2
0
0
0
1
0
0
0
1
2
0
1
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
1
2
0
1
1
0
2
0
2
0
0
0
1
3
3
2
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
1
4
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
2
0
2
1
0
0
0
0
2
0
1
2
0
0
2
0
0
1
0
3
0
0
0
0
1
0
0
0
1
0
0
0
0
3
0
0
1
1
0
0
1
0
0
2
1
0
2
0
1
1
0
2
0
0
0
3
0
0
2
0
0
0
0
1
1
0
0
0
0
1
0
3
0
0
0
0
1
0
0
0
1
1
0
0
1
2
2
0
2
0
2
0
1
0
0
0
1
1
0
0
0
1
1
0
1
0
0
0
0
2
0
0
0
1
2
2
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
1
0
1
2
0
2
0
0
0
0
0
1
0
2
1
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
2
0
0
2
1
1
0
0
0
1
2
0
0
0
0
1
0
1
2
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
2
3
0
1
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
1
1
2
0
1
2
0
1
0
1
0
0
1
1
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
2
1
1
0
2
0
0
1
1
2
1
1
0
2
1
0
0
1
2
0
0
2
0
0
0
2
2
2
0
0
0
0
0
0
0
2
0
0
0
1
9
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
1
0
1
3
0
1
0
0
0
0
0
0
1
2
0
1
0
0
0
2
2
0
0
0
0
0
1
1
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
1
0
2
0
0
0
0
0
2
0
0
0
1
1
0
1
1
0
0
0
1
0
0
0
1
1
0
0
4
0
2
2
0
2
0
1
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
2
1
0
0
0
1
2
0
2
2
0
1
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
1
2
0
2
0
0
2
2
0
5
0
2
0
0
0
2
0
2
1
0
0
2
0
1
0
1
0
0
1
1
0
1
2
1
1
1
1
0
1
2
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
2
0
0
0
0
2
2
0
2
1
0
0
0
1
1
1
2
1
0
0
2
0
3
0
0
0
0
0
1
0
1
0
0
2
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
1
0
2
2
0
2
1
1
0
1
0
2
2
1
2
0
0
2
0
0
1
0
0
3
0
1
0
0
0
0
0
0
0
0
1
1
2
1
2
4
1
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
3
1
0
2
0
0
1
0
0
0
1
0
2
0
1
1
0
0
0
0
1
0
0
2
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
2
0
0
0
1
1
3
3
1
0
0
0
0
0
1
0
0
0
2
3
0
2
1
0
0
0
1
1
0
0
0
2
1
1
2
0
1
0
0
2
0
0
0
0
5
2
1
0
0
1
0
2
0
0
0
0
0
0
2
0
0
3
0
2
2
0
3
2
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
1
0
2
0
2
2
1
0
0
1
0
1
1
0
0
0
0
2
0
0
0
1
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
1
2
0
0
1
0
0
2
1
0
0
2
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
2
1
0
0
0
1
0
3
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
1
2
0
0
0
0
0
0
0
2
2
1
2
0
0
2
0
1
0
2
1
0
1
0
0
0
2
0
0
0
2
0
1
1
0
2
2
0
0
0
1
0
2
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
2
1
1
0
1
0
1
0
2
0
0
0
0
1
1
2
0
0
0
0
0
0
1
1
0
0
2
1
0
0
0
0
1
1
0
1
0
0
1
0
0
1
0
0
0
2
2
0
0
1
0
0
0
2
1
0
0
0
0
0
0
1
3
1
0
2
2
1
0
1
2
1
0
0
1
1
1
0
1
2
1
1
0
1
1
0
0
0
0
1
0
3
2
1
1
0
1
0
0
0
0
0
2
0
0
0
1
0
1
0
1
2
0
2
0
0
0
0
1
0
0
0
1
0
2
0
0
1
0
0
2
0
0
2
1
1
1
0
3
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
2
0
0
0
0
1
1
2
0
0
2
1
0
2
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
2
0
2
0
2
0
1
1
0
1
1
1
1
1
0
2
1
1
1
0
0
1
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
2
4
2
0
1
1
1
0
2
1
0
1
0
0
0
0
0
0
1
0
2
0
3
0
1
0
2
2
1
0
1
1
2
1
2
0
0
1
2
0
0
0
0
0
2
1
0
0
0
2
1
1
2
0
0
0
0
1
0
0
0
1
1
4
0
0
0
0
2
1
1
0
0
1
0
2
2
2
0
7
0
0
0
1
0
0
0
2
1
0
0
2
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
2
0
1
0
0
0
1
0
1
1
2
0
0
0
2
0
2
1
0
2
3
1
0
1
0
1
2
0
2
0
0
0
0
2
1
0
0
1
0
0
1
2
2
1
0
0
2
0
1
0
2
0
0
0
0
1
2
0
2
1
0
0
2
2
0
0
1
0
2
2
2
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
1
0
0
0
0
0
1
0
1
0
1
2
0
0
0
1
1
0
0
2
0
0
0
0
0
1
0
1
0
1
1
3
2
1
1
2
0
0
2
1
1
2
0
0
1
0
0
2
2
1
0
0
1
1
0
0
2
0
1
2
1
1
1
1
0
1
0
2
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
2
0
2
0
1
3
0
0
0
0
0
2
0
0
2
2
1
1
0
2
2
0
1
0
0
0
1
2
2
1
2
2
1
0
1
0
1
0
0
0
6
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
1
2
0
0
1
0
2
0
0
1
0
0
0
1
0
0
1
0
4
0
0
2
0
0
0
0
0
0
0
2
2
1
1
0
0
1
0
1
0
0
0
0
2
0
3
0
0
0
0
1
0
1
0
1
2
2
0
0
1
0
1
0
2
0
0
0
0
2
2
1
1
0
0
0
0
0
3
0
0
0
1
2
0
0
1
0
0
0
4
0
2
0
3
0
0
0
0
0
1
0
0
2
0
1
1
0
0
0
0
0
1
0
2
0
0
0
0
0
2
2
0
0
0
1
1
0
0
0
2
1
0
0
2
0
2
1
0
0
0
0
2
2
1
2
2
0
0
2
0
0
0
0
0
0
3
0
1
0
1
0
2
0
3
0
0
1
2
0
1
0
1
1
0
1
0
0
0
1
2
2
0
0
0
1
1
0
0
0
2
1
0
2
0
0
1
0
1
2
0
2
0
0
0
0
0
1
2
2
0
1
1
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
1
0
2
0
1
1
1
0
2
2
0
0
0
0
2
3
0
0
0
0
0
0
2
0
0
0
2
0
1
0
1
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
2
0
1
0
0
0
1
1
1
0
0
2
0
0
1
2
0
0
0
1
0
0
0
0
2
2
0
0
0
1
0
0
2
0
0
1
2
0
1
0
0
2
2
0
0
0
2
2
0
0
0
0
1
0
0
0
1
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
1
0
1
1
0
0
0
0
2
0
1
0
1
1
1
1
1
2
0
0
0
1
2
1
0
0
0
1
2
0
2
0
0
0
4
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
2
1
1
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
4
0
0
0
0
0
0
0
2
0
0
3
2
1
1
0
2
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
2
1
1
0
1
2
0
0
2
2
0
0
0
0
2
1
0
0
2
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
1
0
1
1
1
0
0
1
1
1
0
0
0
0
0
0
2
2
1
2
0
2
0
0
0
0
0
0
0
0
2
2
3
0
0
2
1
0
0
2
2
2
0
0
0
1
0
0
0
0
0
1
1
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
2
0
0
1
0
2
1
0
0
0
0
0
0
0
2
1
0
0
0
2
2
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
1
1
0
1
0
1
2
2
0
0
0
0
0
1
2
1
0
2
1
0
0
1
0
2
2
1
0
0
3
0
2
2
1
0
0
0
3
0
0
0
0
2
0
0
2
0
0
2
1
0
1
0
0
0
0
0
0
2
0
0
0
0
1
2
1
1
2
2
1
0
0
1
0
0
2
1
0
1
0
0
1
0
2
2
0
2
0
0
0
2
0
0
0
0
0
2
2
0
4
1
1
0
0
0
2
0
2
0
0
0
0
0
1
3
0
0
0
1
0
2
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
3
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
2
2
0
0
0
0
0
2
1
0
2
0
0
0
0
1
0
0
0
1
0
1
2
0
0
0
0
1
1
2
0
0
1
2
1
0
0
2
0
0
0
0
1
0
0
1
0
1
1
0
2
2
2
0
0
2
0
1
0
0
0
2
0
0
13
0
0
0
1
0
0
0
2
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
1
0
0
0
0
1
0
0
0
3
0
0
1
0
1
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
2
1
0
2
0
0
0
0
0
0
1
1
0
2
2
0
1
1
0
0
0
1
1
0
0
2
1
0
0
0
2
0
2
0
0
0
0
0
0
2
1
0
1
1
0
2
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
2
0
2
0
1
0
0
0
0
1
0
0
2
0
1
0
0
0
1
0
1
0
0
1
2
0
1
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
3
0
0
2
1
1
0
0
0
1
2
0
1
0
2
0
0
2
2
0
1
1
2
0
0
0
0
1
0
1
1
0
0
1
2
0
0
1
0
0
2
2
0
0
0
1
0
1
0
2
2
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
1
0
1
0
0
0
2
2
0
0
0
0
1
0
2
0
2
0
0
0
1
0
1
0
0
0
2
2
0
3
2
0
0
1
2
0
0
0
0
0
0
0
2
1
0
0
1
0
1
0
3
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
3
1
0
1
2
0
1
0
0
0
0
0
2
2
0
1
1
3
0
0
0
0
2
4
2
0
0
0
0
0
1
0
2
0
1
4
1
1
0
1
0
0
1
1
2
0
2
0
0
2
0
2
0
0
1
2
0
0
0
1
0
1
1
1
0
0
0
11
2
0
2
0
1
0
0
0
1
1
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
2
0
0
0
1
0
2
0
0
2
2
0
0
0
3
1
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
1
1
0
0
0
0
0
2
0
0
1
1
0
2
2
2
0
1
0
0
0
0
0
1
0
1
2
0
1
1
0
0
2
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
1
0
2
2
1
0
0
0
0
0
1
1
0
0
2
0
0
0
1
0
0
0
0
2
0
1
0
2
0
2
0
1
0
0
0
0
0
0
1
0
2
0
0
1
2
0
2
1
2
0
0
2
4
0
0
0
0
0
0
2
0
1
1
1
0
0
0
1
0
1
1
0
2
1
0
2
0
1
0
2
1
0
0
1
0
2
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
1
1
0
2
1
2
2
0
1
0
0
0
2
0
3
0
0
3
0
2
0
2
1
0
0
0
1
0
0
0
2
1
0
2
0
0
2
0
0
2
2
0
0
0
2
0
0
1
0
0
0
1
2
0
0
1
3
0
0
0
0
0
0
0
0
2
2
0
1
5
1
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
1
2
0
0
0
0
1
0
0
1
2
0
2
0
2
4
0
2
0
0
1
1
0
0
2
0
0
0
2
0
0
1
0
0
1
0
1
0
0
0
0
0
2
0
2
1
0
0
2
0
0
0
0
2
0
2
0
0
0
2
0
2
2
1
0
0
0
0
2
2
1
0
2
0
3
1
0
0
0
0
2
0
1
1
0
2
0
2
0
0
0
0
2
1
2
0
0
2
0
2
0
0
0
2
0
0
2
2
0
2
0
1
1
0
0
1
2
0
0
2
2
0
0
0
1
0
2
1
0
1
1
1
0
0
0
0
0
2
0
1
0
5
0
0
1
2
2
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
1
0
2
2
0
0
0
0
0
0
4
1
1
1
0
1
0
0
0
1
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
2
2
0
0
0
0
2
0
2
0
0
0
2
1
0
0
0
1
1
0
1
0
2
0
1
0
1
2
2
2
2
0
2
3
0
0
0
0
1
0
2
2
0
1
0
0
0
1
1
3
0
1
2
0
0
0
0
2
0
5
0
0
2
0
0
1
0
0
1
2
1
1
2
1
0
2
1
1
0
0
1
0
2
0
1
0
0
2
1
2
0
0
0
2
0
0
0
1
5
0
0
0
0
2
0
0
0
1
0
1
2
0
0
0
2
2
0
0
0
0
0
0
1
1
0
2
4
0
2
0
0
0
1
0
1
6
0
0
0
0
0
2
0
0
0
0
3
0
1
0
0
2
0
0
0
1
2
0
0
2
0
1
2
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
2
1
2
1
2
1
0
1
1
2
0
0
0
2
3
1
0
0
2
0
0
1
4
2
0
2
1
0
0
0
1
0
0
0
1
0
2
0
0
0
1
1
1
2
0
0
2
0
2
0
2
0
1
0
1
0
0
0
0
0
0
2
0
0
0
1
0
2
0
1
0
2
0
1
0
1
0
0
1
1
0
0
0
1
1
2
1
2
0
2
0
0
0
1
0
2
0
1
0
1
1
0
0
2
0
0
0
1
1
0
0
0
0
3
0
0
0
1
3
2
0
0
0
0
0
1
2
0
0
2
0
2
0
0
1
1
0
1
2
0
0
2
2
2
0
0
3
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
1
0
0
1
0
0
0
0
2
0
1
2
0
1
0
0
1
0
0
1
0
0
2
0
2
0
0
2
0
0
0
0
1
0
1
0
2
0
1
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
2
2
1
0
0
1
0
1
1
0
0
0
2
0
0
0
1
0
1
0
0
1
0
0
0
3
0
1
0
0
0
1
1
0
1
0
0
1
2
2
0
0
1
2
0
0
0
0
1
0
0
1
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
1
0
2
0
0
0
1
1
1
2
0
0
1
0
0
2
0
0
1
2
0
3
0
0
1
1
0
0
2
0
2
0
0
0
0
0
1
2
0
0
1
0
0
1
0
3
1
0
0
0
1
3
0
0
0
1
0
1
0
0
0
0
0
2
0
2
1
1
1
2
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
1
0
1
0
0
1
0
2
0
0
1
0
0
0
0
2
0
0
1
2
2
1
2
0
0
0
0
0
1
2
0
2
0
0
0
1
2
2
0
0
2
0
1
2
0
0
2
0
2
1
0
0
2
1
1
0
1
0
0
1
0
1
0
2
0
0
0
1
0
0
2
2
2
1
1
2
1
1
2
0
5
0
1
0
2
0
0
0
0
3
2
0
0
0
0
2
0
0
1
0
0
2
0
0
1
0
1
1
0
2
1
2
1
0
0
0
0
0
1
0
1
2
1
0
0
0
0
1
0
0
0
1
0
0
2
0
1
0
0
0
2
0
0
0
1
1
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
3
2
0
0
0
2
0
0
0
0
0
1
1
2
1
1
0
1
1
0
1
1
1
1
3
0
0
0
1
0
0
0
2
1
2
0
0
1
2
0
1
0
2
2
1
1
2
1
0
1
3
0
0
1
0
1
1
1
0
0
2
0
0
1
0
2
0
0
0
0
0
0
1
2
0
0
2
0
1
0
0
0
2
0
1
1
0
0
1
0
0
0
0
0
0
2
0
1
2
1
0
2
0
1
2
0
1
2
3
0
1
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
7
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
1
1
0
1
0
1
0
0
1
2
0
0
0
2
0
3
1
0
1
0
4
1
0
0
0
2
1
6
1
1
2
0
1
0
2
0
0
2
2
0
2
0
0
0
2
0
1
1
1
2
2
1
0
0
0
0
1
1
0
3
0
1
0
0
0
2
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
2
1
1
1
0
2
0
2
0
1
0
0
0
3
0
0
0
0
1
1
0
3
0
0
2
2
3
2
1
0
0
0
0
0
1
0
0
2
1
2
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
1
2
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
2
0
2
0
0
0
0
2
0
0
0
0
1
2
2
1
1
0
1
0
0
0
5
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
2
0
0
1
0
0
2
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
2
0
0
2
0
2
0
2
2
2
1
1
0
0
0
1
2
0
2
2
0
3
0
0
0
1
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
2
2
0
0
0
1
0
0
3
1
2
2
0
1
0
4
0
0
2
4
0
0
0
2
0
0
0
1
2
0
0
2
0
0
0
0
2
0
0
0
1
2
0
1
2
1
0
1
0
2
1
2
0
0
0
0
0
0
0
1
2
2
0
0
1
2
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
2
0
0
0
1
0
0
1
0
1
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
2
0
2
0
0
0
1
2
1
0
1
0
1
0
0
0
1
2
1
0
0
0
2
0
1
0
2
0
1
2
0
0
1
2
0
2
0
1
0
0
0
0
4
0
2
0
0
0
3
2
0
0
0
0
3
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
1
0
0
3
0
0
0
1
2
1
0
0
0
0
0
1
1
1
2
1
0
1
0
2
0
2
2
2
0
0
0
0
0
0
1
1
0
0
1
1
3
1
2
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
1
0
0
1
2
0
1
0
1
2
0
0
1
2
0
0
1
2
0
0
3
2
0
0
0
0
0
0
4
0
1
0
1
0
0
0
0
2
1
0
1
0
0
0
0
0
4
0
0
1
0
2
0
0
0
0
3
2
1
0
0
1
0
0
0
3
2
2
2
0
1
0
3
0
0
2
1
1
0
0
1
0
0
0
0
0
0
0
2
0
0
2
2
0
0
2
1
1
0
0
2
1
2
0
2
2
0
0
0
0
0
3
2
2
0
1
0
1
0
1
1
2
0
1
1
0
2
0
1
0
1
0
1
0
0
1
1
1
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
1
1
1
4
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
2
0
0
2
0
1
0
2
1
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
2
1
2
2
1
0
0
2
2
2
0
0
1
0
0
0
2
1
2
0
0
2
0
4
1
2
2
0
2
0
0
1
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
2
1
0
0
1
0
0
1
1
1
0
2
1
0
0
2
1
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
2
1
0
0
0
1
0
0
0
1
1
3
1
0
1
1
0
3
0
0
0
1
1
4
0
0
0
0
2
0
2
0
0
0
0
1
1
0
0
4
0
0
2
0
0
1
0
2
0
0
0
3
0
0
0
0
1
0
2
0
0
0
1
0
2
0
1
1
0
2
1
0
0
0
0
0
0
0
2
0
0
0
1
3
0
1
2
0
2
0
0
0
1
1
1
0
0
0
0
1
0
4
1
0
0
2
0
0
2
2
5
0
1
0
0
0
0
0
2
0
0
0
0
2
2
1
2
0
1
0
0
0
0
2
0
0
2
2
0
0
0
0
1
0
1
0
3
1
1
2
1
0
0
2
0
0
0
0
1
0
1
3
2
0
0
0
0
1
2
0
0
2
2
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
2
0
0
2
1
0
0
0
2
0
1
1
2
1
0
2
1
0
2
0
0
0
1
0
0
1
0
0
0
0
0
2
0
3
0
0
0
0
1
2
0
0
1
0
0
0
2
2
0
0
0
0
1
0
1
0
2
2
2
1
2
0
0
1
1
0
0
3
1
1
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
2
0
0
0
0
2
2
1
1
0
2
0
0
1
0
0
1
1
2
0
0
0
2
1
2
0
1
2
0
2
2
0
1
0
0
0
0
2
0
0
1
0
0
0
2
2
0
0
1
0
0
0
1
0
0
1
0
2
0
0
0
1
0
2
2
0
0
1
0
1
1
0
2
0
0
0
1
0
2
1
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
1
1
0
3
0
0
2
0
0
0
0
0
1
0
0
0
1
2
1
0
1
1
0
0
2
2
2
0
2
0
2
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
3
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
1
1
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
1
0
1
1
0
1
2
0
0
1
2
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
1
0
0
0
0
2
0
0
1
0
2
2
0
2
0
0
0
1
2
0
0
0
2
2
1
0
1
1
0
0
1
0
0
1
1
2
2
0
2
1
0
0
1
0
0
2
0
3
0
1
0
0
0
1
2
0
0
0
0
1
0
0
2
1
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
1
2
2
0
0
0
0
0
0
1
2
0
0
2
2
0
0
0
0
1
2
2
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
1
0
1
4
1
2
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
3
2
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
3
1
0
0
0
0
0
0
0
1
0
3
1
0
1
2
1
0
0
0
0
0
1
0
1
1
1
1
1
0
1
1
0
2
0
0
2
0
0
0
0
1
0
0
4
2
0
1
1
0
0
0
0
0
0
2
0
1
1
0
2
2
1
0
0
1
0
1
0
0
2
3
1
0
1
0
1
1
0
0
1
0
2
1
0
0
0
0
0
0
1
2
0
0
0
1
2
0
0
2
2
0
0
2
0
0
2
0
1
0
1
0
1
0
1
0
0
1
0
2
1
1
1
1
0
0
0
1
0
0
2
3
3
0
1
2
2
0
0
0
0
1
0
0
0
0
2
1
1
0
0
2
1
1
0
0
1
0
2
1
2
1
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
2
0
0
1
0
1
0
0
0
0
0
2
2
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
3
0
0
0
1
1
1
0
0
0
0
0
1
0
2
0
0
0
1
1
0
1
0
1
0
0
2
1
1
0
0
2
1
1
0
0
0
0
0
1
1
0
2
1
2
0
0
0
2
1
1
1
0
0
3
2
0
0
1
0
0
1
0
0
1
0
0
0
2
0
1
2
0
0
0
0
0
0
1
1
0
2
1
2
0
2
2
0
2
0
0
0
0
0
1
1
2
1
1
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
1
0
1
0
0
0
0
2
2
0
2
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
2
3
4
0
0
0
2
0
0
2
2
0
1
0
0
0
3
0
2
0
2
2
2
0
1
0
0
2
0
1
0
0
2
3
0
0
2
0
0
0
0
0
2
1
0
0
1
0
1
0
0
2
2
1
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
2
1
0
2
5
1
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
1
2
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
2
1
2
0
0
0
2
1
2
0
0
2
0
0
2
0
1
0
2
0
0
2
2
1
3
0
0
0
0
0
0
0
1
4
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
3
0
0
0
1
0
2
0
0
1
1
0
2
0
0
2
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
2
0
1
2
0
0
0
2
0
0
2
0
0
0
0
2
0
2
3
0
0
2
0
2
1
0
1
0
1
0
1
1
1
1
2
0
0
2
0
4
0
0
0
0
1
2
0
0
2
0
0
0
0
0
1
0
2
1
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
2
2
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
1
2
0
1
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
1
0
0
1
2
0
1
0
0
0
1
2
0
0
0
2
1
0
2
1
1
0
2
0
0
3
2
0
1
0
1
2
0
0
0
0
0
0
0
0
0
1
2
0
1
0
1
0
2
6
0
0
0
1
1
1
2
0
2
2
0
2
0
2
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
1
2
0
0
2
0
3
0
0
2
0
0
0
1
2
2
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
2
0
0
0
2
1
0
1
1
0
0
2
0
0
1
0
0
1
0
1
0
0
3
0
0
2
2
0
2
2
2
0
2
2
0
0
1
0
0
0
1
2
1
0
0
0
0
1
1
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
5
1
0
0
0
0
0
2
0
1
0
0
1
0
0
2
0
1
1
0
2
0
0
0
2
0
0
0
0
2
0
0
0
2
3
1
0
0
0
0
1
1
1
1
2
0
0
0
0
0
0
0
0
1
0
2
1
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
1
1
0
2
1
1
0
0
0
1
0
2
0
1
0
0
0
0
0
2
1
2
0
0
1
0
0
0
1
2
3
0
0
0
1
0
0
0
3
2
2
0
1
0
2
0
2
0
1
2
0
1
0
0
1
2
0
1
2
0
0
0
0
0
2
0
1
0
0
2
1
0
2
0
0
0
2
0
4
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
1
3
0
1
1
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
2
0
1
0
0
1
2
0
0
1
2
2
0
0
2
0
0
0
1
2
0
0
1
1
1
2
0
0
0
0
0
2
0
0
0
0
1
0
0
2
2
2
0
0
1
0
1
3
3
1
1
3
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
1
2
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
1
1
0
1
0
1
0
0
1
2
1
0
0
0
2
0
0
1
0
2
2
0
2
0
3
2
0
0
0
0
1
0
0
0
2
1
0
1
1
0
2
2
2
0
1
2
0
1
0
0
0
1
0
0
0
1
0
1
0
0
1
0
2
1
1
0
0
1
0
0
1
0
1
1
2
0
2
2
1
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
2
1
2
0
0
0
0
0
0
0
1
1
2
2
2
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
2
0
0
0
0
0
0
1
0
2
2
1
2
0
0
1
0
0
0
2
0
2
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
3
0
1
0
2
1
2
0
6
0
0
0
0
1
2
1
0
1
0
0
1
0
0
0
1
1
0
1
0
0
2
0
0
0
0
0
1
0
0
0
1
1
0
0
1
2
2
1
0
0
0
0
1
2
2
2
0
0
0
0
0
1
1
2
1
0
0
1
1
1
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
4
1
0
2
2
0
1
0
0
2
0
0
0
1
1
0
2
1
1
2
1
0
0
1
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
1
0
0
1
0
2
1
1
1
2
0
0
0
0
0
0
1
0
1
2
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
2
0
1
0
0
2
2
0
0
2
0
1
0
0
0
2
0
0
0
1
0
2
0
3
2
2
0
2
0
0
2
0
0
0
0
1
2
1
1
1
0
0
0
0
0
1
1
0
2
0
0
0
2
2
0
0
0
2
0
0
0
2
1
0
2
1
0
2
0
1
1
0
0
2
1
1
0
0
0
2
0
1
2
0
0
0
0
0
0
2
0
1
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
4
0
0
2
0
1
2
0
0
0
2
0
0
7
1
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
3
0
0
1
0
0
3
0
0
0
0
0
0
2
0
0
2
0
0
2
3
1
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
2
0
1
0
0
1
0
0
1
2
0
0
0
1
0
2
0
0
1
0
0
0
1
0
1
1
0
2
1
0
0
2
1
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
1
2
0
0
0
1
2
0
2
0
0
0
1
1
1
1
0
3
0
2
0
0
1
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
3
2
0
2
1
2
0
0
2
0
1
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
2
3
1
2
0
2
1
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
2
2
1
0
4
0
0
2
2
2
1
0
1
0
0
1
1
0
0
0
1
2
0
0
0
1
1
0
0
0
0
0
2
0
1
0
2
1
0
2
0
1
0
0
2
1
1
0
0
0
0
0
1
0
0
0
0
2
0
1
0
1
0
0
2
2
0
0
1
1
0
2
0
1
1
1
0
0
0
1
1
0
3
0
1
0
0
1
2
2
0
1
2
2
0
0
1
0
8
2
0
0
0
3
2
0
0
0
0
2
0
0
2
1
0
2
1
1
0
2
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
2
0
0
2
0
2
2
0
0
0
0
0
1
0
2
0
0
1
0
0
0
1
1
1
1
0
0
0
2
0
0
1
0
0
0
2
1
0
0
1
2
0
0
0
0
0
0
3
2
1
0
1
1
0
0
0
1
1
0
0
0
0
0
1
2
1
0
0
0
1
0
0
0
2
1
0
0
2
0
1
1
0
0
1
0
0
1
1
0
0
0
0
4
2
0
2
0
0
0
0
0
1
1
0
1
2
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
2
0
0
4
0
0
0
0
0
0
0
2
1
0
1
0
0
2
0
0
0
0
0
2
0
3
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
1
2
0
0
2
0
0
1
1
2
0
1
1
2
0
0
1
5
0
0
1
0
0
0
3
2
2
0
1
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
3
0
2
0
0
2
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
4
1
0
2
0
0
5
0
1
1
0
1
0
0
0
0
0
1
0
0
1
0
0
1
2
0
0
0
2
1
1
0
5
0
0
2
0
0
2
2
1
1
0
0
1
1
0
1
0
0
0
1
1
2
0
0
0
2
0
1
1
0
6
0
0
0
2
3
0
2
0
1
0
1
0
2
2
0
0
1
0
1
0
0
1
2
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
2
0
0
2
0
1
0
1
0
1
2
0
1
0
0
1
0
0
0
0
0
1
2
0
2
0
1
0
1
0
3
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
2
0
1
0
0
0
1
2
2
0
1
0
2
0
0
2
1
1
1
1
0
0
0
0
0
0
0
2
1
0
0
1
0
1
0
0
1
1
3
0
0
0
0
1
1
0
2
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
1
2
0
0
1
2
0
0
0
1
0
0
0
2
1
0
1
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
2
0
0
1
1
0
0
0
0
1
3
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
2
1
1
1
0
0
2
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
1
2
0
0
1
1
1
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
1
2
0
0
0
1
1
1
0
2
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
1
1
0
0
0
0
2
0
2
1
0
1
0
0
0
2
0
1
2
0
1
0
0
0
0
0
0
1
0
0
0
1
1
3
0
1
0
1
0
0
0
1
0
0
0
0
2
0
0
0
1
0
1
0
0
2
1
1
1
1
0
2
1
0
0
0
1
0
0
2
1
0
0
0
0
0
0
2
0
0
0
1
0
2
0
2
0
4
0
3
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
1
1
2
2
0
0
0
1
1
0
1
1
2
0
0
0
0
0
0
1
1
0
0
4
0
0
0
2
0
0
0
0
0
1
2
1
0
0
0
2
0
1
2
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
1
0
1
2
2
0
2
0
0
0
1
0
0
0
0
2
2
0
0
1
0
1
0
1
1
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
2
1
2
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
2
2
0
1
2
1
0
2
2
0
2
0
0
0
0
0
0
1
0
2
3
0
0
0
0
0
0
3
1
2
0
0
2
0
0
2
0
0
0
0
2
0
0
2
0
0
0
3
1
0
2
0
2
0
0
0
0
0
1
1
2
0
2
0
0
0
1
1
1
2
0
0
1
1
0
0
0
0
2
0
2
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
1
0
1
0
0
0
1
1
4
1
0
0
1
0
0
2
0
0
1
0
2
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
1
1
2
2
0
0
2
2
0
1
1
2
1
0
1
0
0
0
0
2
0
0
0
2
2
1
0
0
0
1
1
1
1
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
2
2
2
0
0
2
1
1
0
2
1
0
1
0
0
1
1
0
0
2
1
0
0
0
0
0
1
0
0
0
0
1
0
2
0
1
0
2
0
0
2
0
0
1
1
1
0
0
0
1
1
2
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
1
2
0
3
1
0
2
1
0
1
2
2
0
1
0
0
1
0
0
2
2
0
2
0
1
0
0
0
0
0
0
0
1
1
0
2
1
0
0
2
0
0
0
0
0
0
0
1
0
4
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
1
1
0
2
0
1
4
0
0
1
1
0
1
1
0
0
0
0
0
3
0
0
0
1
1
0
2
0
0
0
0
2
0
0
3
0
2
0
0
2
0
0
1
1
1
1
0
0
1
0
0
2
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
1
0
0
1
1
1
0
0
1
0
0
1
0
0
1
0
1
0
2
0
1
0
0
0
1
0
0
0
2
0
2
1
2
0
0
1
0
2
0
1
2
0
0
0
0
0
0
1
0
1
0
0
1
1
2
0
0
1
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
2
0
1
0
0
1
2
0
0
0
2
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
2
1
2
1
0
0
2
0
3
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
1
2
0
2
0
0
2
1
0
1
1
0
0
0
0
0
1
0
2
0
0
0
0
1
1
0
0
2
3
2
1
1
0
0
0
0
0
0
0
0
2
0
0
2
2
0
1
1
1
0
0
0
0
0
2
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
1
0
2
0
0
0
0
0
0
2
0
0
7
2
2
2
1
2
1
0
0
1
0
0
2
0
2
0
1
0
2
0
0
2
1
0
0
3
2
0
2
0
0
1
6
0
2
0
0
3
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
1
0
2
0
1
2
0
2
2
0
0
0
0
2
1
0
0
3
0
0
0
2
2
0
0
2
0
1
0
1
1
2
2
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
3
0
1
2
0
1
0
2
0
0
1
2
0
1
0
0
0
0
0
0
2
1
0
0
6
1
0
0
1
0
2
0
2
0
0
2
0
2
1
0
0
0
2
0
0
2
2
0
1
2
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
2
0
0
1
1
0
2
0
1
0
2
1
1
0
0
0
0
1
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
2
1
1
0
2
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
2
0
0
2
1
0
1
0
1
0
2
0
2
0
1
0
0
0
2
1
0
2
0
0
0
0
3
0
0
0
0
0
0
1
1
2
0
0
0
0
1
1
0
1
0
0
2
0
2
0
2
0
2
1
0
0
2
0
2
0
0
0
0
1
0
1
0
2
1
2
0
0
0
0
0
0
0
0
3
0
4
0
2
2
1
0
2
1
0
0
0
1
0
1
1
0
0
0
0
0
0
2
0
1
0
1
0
0
0
2
1
0
1
0
0
0
3
0
1
2
2
0
0
1
1
3
0
0
1
0
2
2
0
0
1
0
0
1
0
1
2
0
0
2
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
2
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
1
0
1
0
0
0
2
0
0
1
3
0
0
0
0
0
1
2
0
0
1
0
1
1
0
2
0
0
0
0
0
0
0
0
0
3
2
0
3
0
1
0
0
0
0
0
2
0
0
2
1
0
1
1
0
1
0
1
1
0
0
0
5
0
0
0
1
0
0
0
0
0
0
1
0
1
2
0
0
2
3
0
0
2
0
2
1
2
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
2
1
2
1
0
0
1
1
0
0
0
0
2
1
0
0
0
1
0
5
0
1
0
1
0
0
0
0
1
0
0
0
1
2
0
0
0
2
2
0
0
2
0
0
0
1
2
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
2
0
2
0
0
1
0
0
1
3
0
0
0
2
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
1
0
1
0
0
0
0
0
1
0
1
2
0
0
1
0
1
0
2
1
2
3
0
0
0
0
0
2
1
0
0
0
1
0
2
0
1
0
0
0
0
2
2
3
0
0
1
0
0
0
0
0
0
0
2
2
0
0
2
0
2
2
0
1
0
0
0
2
0
0
0
2
0
0
2
0
0
0
2
2
0
0
0
0
4
0
0
2
1
1
1
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
2
2
2
0
0
0
1
2
0
1
0
0
0
2
0
2
4
0
0
0
0
2
2
0
0
1
1
2
0
0
0
1
2
0
0
0
2
1
2
2
1
0
1
1
0
0
0
0
1
0
0
0
0
0
1
1
1
2
2
0
2
0
0
0
0
0
0
1
2
0
2
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
2
0
1
1
1
0
3
0
3
2
0
1
2
0
1
0
0
1
0
0
0
0
0
1
1
0
1
4
0
0
0
0
0
0
2
2
0
1
2
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
2
1
0
1
0
0
0
0
0
2
2
0
0
1
2
0
2
0
2
3
1
2
1
1
0
0
0
0
1
2
0
2
2
2
1
1
2
0
2
0
0
0
0
0
0
1
0
0
0
1
2
0
1
1
2
0
0
1
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
1
2
0
0
2
2
2
1
0
1
2
1
0
1
0
0
0
0
2
0
2
0
0
1
2
0
0
0
0
0
1
0
0
0
0
1
1
1
0
1
0
0
0
2
1
0
1
1
2
0
0
1
0
0
2
1
0
1
0
0
1
0
0
1
1
3
0
1
2
0
0
2
1
0
2
1
2
0
0
2
2
0
1
0
1
1
1
1
0
1
1
0
0
0
2
2
1
0
1
0
2
2
1
0
2
2
0
0
0
1
0
0
1
2
0
1
0
2
0
2
1
0
5
0
0
1
0
2
0
2
0
9
0
1
0
0
2
1
0
0
0
0
1
0
2
0
0
2
1
0
2
0
0
1
0
2
1
1
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
1
0
0
2
2
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
2
0
2
0
2
2
0
0
0
0
0
0
0
2
0
0
1
1
2
2
0
0
0
4
1
0
2
1
0
0
2
0
0
0
0
1
2
1
0
2
0
2
0
0
0
2
0
1
0
0
0
1
2
0
0
1
0
0
0
1
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
1
0
1
0
0
1
2
0
0
0
0
0
3
1
0
0
2
2
0
0
0
2
0
2
2
4
3
1
0
1
0
0
0
2
1
1
1
0
1
1
1
0
2
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
2
0
1
2
0
2
2
0
2
3
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
1
2
0
1
0
2
0
2
2
0
2
3
0
0
0
2
2
0
1
1
2
0
0
0
0
2
0
0
0
0
2
0
0
0
2
1
1
0
1
0
0
0
0
0
1
1
1
2
0
2
0
0
0
1
0
1
0
2
2
0
0
0
0
0
2
0
1
2
1
0
2
1
0
0
0
0
2
0
2
0
0
1
0
1
0
0
0
0
0
1
0
2
0
0
0
1
0
3
0
2
1
1
0
0
0
0
0
0
0
0
2
0
0
0
2
3
0
0
2
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
2
1
1
0
0
0
2
0
2
0
3
2
0
0
0
0
0
0
1
0
1
1
1
2
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
3
0
0
0
0
2
1
0
0
4
0
1
0
0
1
0
2
0
0
0
0
1
0
2
2
1
1
1
0
0
2
2
1
0
1
0
1
1
0
0
0
1
0
2
1
1
2
0
0
0
0
0
1
1
2
0
0
0
0
1
0
2
2
0
0
0
0
0
0
2
0
1
0
0
2
4
0
0
2
1
0
3
0
0
0
0
0
0
0
0
0
2
1
0
2
0
1
0
1
2
2
0
0
2
0
1
5
0
1
0
2
2
0
0
1
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
1
2
0
2
0
0
1
2
2
1
0
0
0
0
0
1
1
2
1
0
0
0
0
0
1
4
0
0
0
2
0
2
0
1
1
2
0
1
0
1
0
3
0
0
0
0
1
0
0
2
0
0
0
0
1
1
2
2
1
0
0
0
0
1
1
0
0
0
1
3
0
1
0
1
0
4
2
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
1
1
2
2
1
1
2
0
0
1
0
2
0
0
1
0
0
2
0
0
0
4
0
0
0
0
2
0
0
0
0
1
0
0
1
1
0
0
0
1
2
1
0
0
2
2
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
1
5
0
1
1
0
0
0
2
0
0
0
1
0
4
1
0
0
1
0
2
0
2
0
0
0
1
2
0
0
0
0
3
2
0
0
0
0
1
0
0
0
2
1
2
0
2
2
0
0
0
2
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
1
0
2
1
0
0
2
0
1
0
0
1
0
2
2
0
0
1
2
0
0
2
0
2
1
1
0
0
2
2
0
2
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
2
0
1
0
2
0
0
0
1
1
0
0
0
0
1
0
1
1
3
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
2
2
2
1
0
0
1
2
0
0
2
1
0
0
2
2
0
0
1
0
0
2
1
0
1
0
0
0
0
0
2
2
1
1
1
2
1
0
2
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
2
2
1
0
0
4
0
0
2
0
0
0
0
0
0
0
0
1
0
2
2
3
1
2
1
0
2
0
0
0
1
1
0
0
0
0
0
1
2
1
0
1
0
1
0
3
1
0
2
2
1
1
0
1
0
0
0
0
0
1
0
0
0
1
1
0
2
1
1
0
2
0
1
2
0
0
0
0
1
2
1
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
2
1
1
2
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
4
0
0
2
0
0
0
0
0
2
2
2
0
2
0
2
2
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
1
0
0
1
0
2
1
0
0
1
0
0
0
0
2
0
2
1
1
0
0
0
0
0
1
4
0
2
1
0
0
0
1
2
0
0
1
0
1
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
2
0
0
0
0
0
1
1
0
2
1
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
2
1
0
2
1
1
1
0
2
0
2
2
0
2
2
0
1
0
0
0
0
1
1
0
0
0
1
2
1
0
2
2
0
0
1
0
0
2
0
0
1
0
0
0
0
1
2
1
0
0
0
2
0
1
10
1
2
1
0
0
2
2
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
1
2
0
1
2
2
0
1
0
0
2
0
2
1
0
0
2
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
4
0
1
1
1
1
0
0
1
0
0
0
0
0
1
0
1
0
2
0
2
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
1
0
1
0
2
2
0
0
1
0
0
0
0
0
2
1
0
2
1
0
1
4
2
0
0
0
4
0
1
0
2
1
2
0
0
0
2
2
0
0
0
0
0
0
1
0
1
0
0
2
0
1
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
1
2
2
1
0
1
1
1
0
0
1
0
0
1
0
0
1
2
1
0
0
0
0
0
3
1
0
0
1
1
1
0
0
0
0
0
3
1
0
0
0
2
1
0
2
1
1
2
0
0
1
0
1
2
1
1
3
0
0
1
0
2
0
0
2
0
0
3
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
4
0
2
0
1
1
0
1
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
2
0
2
1
0
0
2
0
1
0
0
6
0
0
0
2
0
0
2
0
0
2
1
0
0
2
0
1
1
0
0
0
0
1
2
1
1
2
0
0
1
1
1
2
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
2
2
1
0
0
0
0
0
0
0
1
0
2
1
0
0
0
1
0
0
2
2
0
0
2
2
0
0
0
1
0
0
0
0
2
0
2
0
1
0
3
0
1
0
0
0
2
0
1
0
1
0
0
0
2
2
0
0
0
1
2
3
3
0
1
1
0
1
0
2
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
1
2
0
0
0
0
2
1
1
1
2
1
0
2
2
0
1
0
0
2
0
0
0
2
1
0
1
2
2
2
1
0
2
0
0
0
0
0
0
0
0
0
1
0
2
1
0
1
0
3
0
0
0
2
2
0
1
0
0
1
0
2
0
1
2
0
1
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
1
1
1
1
3
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
1
0
2
0
0
1
0
1
0
0
0
0
1
0
0
2
0
1
1
0
0
0
2
1
0
2
0
2
2
0
0
0
0
0
0
0
0
1
2
0
0
2
2
1
0
0
1
0
0
2
0
0
0
1
0
0
1
0
0
1
0
1
1
1
1
2
0
0
0
0
0
0
0
0
1
1
0
1
2
2
0
0
0
0
0
2
5
0
0
1
0
1
0
0
0
0
0
1
0
2
2
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
1
1
2
0
2
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
4
0
0
0
0
1
2
1
1
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
1
0
1
0
2
0
2
0
0
0
2
0
0
0
2
2
1
0
1
0
0
0
2
0
0
0
0
0
2
2
1
2
1
0
0
1
0
2
0
3
2
0
0
2
0
0
1
0
1
1
0
7
0
0
0
0
2
2
0
0
1
1
1
0
0
0
2
0
0
0
0
2
0
0
0
2
2
1
0
0
0
1
3
0
0
0
1
1
0
0
1
2
0
0
0
0
1
1
0
2
0
0
0
1
2
2
1
4
0
2
1
0
2
0
1
1
0
0
1
0
0
2
0
0
1
1
0
5
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
2
0
0
3
1
2
0
0
0
0
1
1
0
0
2
2
1
2
2
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
1
2
1
1
0
2
1
2
0
2
1
0
0
0
1
0
2
0
0
1
1
0
0
1
0
0
0
1
3
1
1
1
1
0
1
0
0
0
2
0
0
0
0
1
0
0
2
2
0
0
1
0
0
4
0
3
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
2
0
0
0
3
1
1
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
1
1
2
0
0
0
0
1
0
1
0
0
2
0
2
0
0
0
0
0
0
1
1
0
0
2
1
0
0
1
0
0
0
1
2
2
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
2
0
1
0
0
2
0
0
0
0
1
0
1
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
3
2
1
0
1
1
0
1
2
1
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
1
0
1
0
1
2
0
0
0
1
0
1
0
2
0
2
1
0
1
3
1
2
0
0
0
1
7
1
0
0
1
0
2
1
0
0
0
0
1
2
1
0
0
1
0
2
0
1
0
0
0
1
1
0
2
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
7
1
2
1
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
2
2
0
0
0
0
2
1
2
0
2
0
3
0
0
0
1
0
2
1
0
1
1
0
0
1
0
0
0
0
0
2
2
2
1
0
0
0
1
0
0
2
0
0
0
1
0
0
0
1
0
1
0
3
0
0
1
0
1
2
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
2
0
0
2
2
0
1
1
1
0
1
1
0
1
1
1
1
2
0
0
0
2
2
0
0
2
1
0
2
0
0
0
2
0
2
0
1
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
2
2
0
2
0
0
2
2
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
2
1
1
0
0
0
0
0
0
2
1
0
1
0
1
2
0
1
1
1
0
0
2
0
2
0
1
2
0
0
0
0
0
0
1
0
2
0
0
3
1
0
0
1
0
2
1
0
1
0
0
0
1
0
3
2
0
0
0
1
0
0
0
2
0
0
0
1
2
0
1
0
0
0
0
2
2
0
0
1
2
1
0
0
0
1
0
2
0
0
0
0
0
0
0
4
2
0
2
1
2
0
0
2
0
2
0
1
0
0
0
0
0
2
2
2
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
1
0
1
2
0
2
0
2
0
0
0
0
1
0
0
0
1
0
2
0
2
0
1
0
1
1
0
0
1
0
1
1
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
1
0
0
0
2
1
0
2
0
1
0
0
0
0
2
0
2
5
2
2
0
0
0
0
0
1
0
0
0
0
2
2
0
0
1
0
0
0
0
2
0
2
2
0
1
1
1
2
2
10
1
0
0
1
0
1
0
0
2
2
1
1
0
0
2
1
0
0
0
2
0
0
0
0
1
1
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
2
1
0
0
2
0
1
2
0
1
0
1
0
1
0
0
2
1
1
1
0
0
0
3
0
0
1
0
2
0
0
2
2
0
0
0
2
1
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
1
0
0
2
1
1
0
0
0
1
0
0
0
0
1
3
0
2
0
0
0
2
0
2
1
0
0
1
1
0
0
2
1
0
1
0
1
0
0
0
0
2
0
0
0
2
1
0
0
0
1
1
2
0
1
0
2
2
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
2
2
1
0
1
2
0
0
0
2
0
0
2
1
0
0
0
2
0
0
0
0
0
1
0
0
1
1
2
1
0
1
0
0
1
0
0
1
0
0
2
0
0
0
0
2
1
0
2
2
0
0
0
0
0
2
2
0
0
4
0
0
0
0
2
0
2
0
1
2
3
0
0
0
2
1
0
0
0
1
0
0
0
1
0
0
0
2
0
1
0
0
1
0
0
1
0
0
2
0
0
0
2
3
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
2
2
2
2
0
0
1
0
2
1
0
0
2
1
4
1
1
2
0
0
0
0
1
0
2
5
2
1
2
1
0
0
2
1
0
0
0
0
1
1
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
2
0
1
0
0
2
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
1
0
2
0
3
0
0
0
1
0
2
1
1
0
0
2
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
2
0
2
2
2
0
0
0
0
1
0
3
0
0
2
0
1
0
0
0
1
0
0
0
0
2
1
0
0
0
0
1
1
0
2
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
1
0
0
2
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
2
0
1
2
0
1
1
2
0
1
0
0
1
2
2
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
2
2
0
0
0
0
0
2
0
2
0
1
1
0
1
0
1
2
0
2
0
1
2
0
0
0
0
0
2
2
0
2
0
1
0
0
2
0
0
0
1
0
0
1
2
0
0
1
1
1
0
1
2
0
2
0
2
1
0
0
1
0
2
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
1
0
0
2
0
2
1
0
0
0
0
1
2
2
0
0
0
1
1
0
0
1
0
1
0
2
0
0
1
0
0
0
0
1
0
1
0
0
2
0
0
2
0
1
0
2
0
0
3
1
0
1
0
1
2
0
2
0
0
1
2
1
0
1
0
0
0
1
3
2
3
0
0
2
1
0
0
0
0
0
0
0
0
4
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
1
0
0
1
1
0
0
1
0
1
1
0
1
0
0
0
0
1
0
0
2
0
0
1
0
0
0
2
0
0
2
1
0
0
0
0
2
0
0
1
2
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
2
1
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
2
0
0
2
0
0
1
2
1
0
0
0
3
0
2
0
1
2
3
0
0
0
0
2
2
0
2
0
1
0
1
0
0
7
0
0
0
1
1
2
0
0
0
0
1
2
2
0
0
0
1
0
1
1
1
0
2
0
1
0
0
2
0
2
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
1
0
1
0
0
0
0
2
0
0
0
0
1
0
0
2
1
3
0
0
0
2
2
1
1
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
3
0
0
0
2
0
0
2
1
0
1
0
0
3
0
2
1
2
0
0
1
0
2
0
0
2
0
0
0
0
0
3
0
0
0
2
1
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
2
1
0
2
0
0
0
1
0
0
0
1
2
0
0
0
1
0
0
0
1
0
0
0
1
2
0
0
1
1
0
0
0
1
2
1
0
0
3
0
0
0
0
1
2
0
0
3
1
1
0
0
1
0
2
1
1
0
0
0
0
1
0
0
1
0
2
0
0
0
2
2
1
2
0
1
2
0
0
1
2
0
0
0
0
2
0
0
1
0
2
0
0
2
0
1
0
3
0
3
0
0
0
2
0
0
0
1
0
0
1
1
0
1
2
0
0
1
0
1
0
2
2
2
2
0
2
1
0
2
1
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
2
0
0
1
0
0
0
0
1
0
2
0
0
2
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
1
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
2
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
2
1
0
0
0
1
1
0
0
0
0
0
2
3
0
0
1
2
0
0
1
0
1
1
1
0
1
2
1
2
0
0
2
0
0
2
2
1
2
1
0
0
0
0
0
1
2
2
2
0
0
0
0
1
0
0
0
0
1
0
1
2
0
0
1
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
2
0
0
1
0
1
0
1
0
0
0
0
2
0
1
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
2
1
0
0
0
1
2
0
1
1
0
2
0
0
0
0
2
0
0
0
1
2
0
0
0
2
0
0
2
0
0
2
2
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
2
0
2
0
0
2
0
1
1
2
0
0
2
2
0
1
1
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
2
0
1
0
1
3
0
0
2
2
4
2
2
2
0
2
1
0
1
1
2
2
0
0
0
2
2
0
1
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
1
2
2
1
0
2
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
1
0
2
2
0
0
2
0
0
1
1
2
0
0
2
1
0
1
1
1
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
1
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
2
1
2
1
0
0
0
0
0
1
1
2
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
3
0
0
2
0
1
0
2
0
0
1
1
1
0
2
0
1
1
0
0
2
0
0
0
1
5
2
1
0
2
0
0
1
0
0
3
0
0
2
0
0
2
2
0
0
0
2
2
0
0
0
2
0
1
2
0
0
0
0
1
1
2
0
0
2
1
0
2
0
3
1
1
0
0
0
0
0
0
0
2
0
2
2
0
1
1
2
0
0
1
0
0
0
2
0
5
0
1
2
0
0
0
0
1
4
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
2
0
0
1
2
0
0
1
0
2
2
0
0
2
1
1
0
0
1
0
2
0
0
0
2
1
0
2
1
2
0
1
1
2
1
0
1
1
0
0
0
1
0
0
0
0
1
0
2
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
1
0
0
2
3
0
0
2
2
2
0
0
5
1
0
3
1
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
2
1
0
2
0
0
1
1
1
2
0
1
0
0
3
1
0
2
2
0
0
1
0
3
0
0
2
0
0
2
1
1
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
2
0
2
0
0
0
0
1
3
0
0
2
0
0
2
0
2
2
0
1
0
0
2
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
1
0
0
0
1
0
1
0
0
2
1
0
0
0
0
2
0
2
0
0
3
2
0
1
1
0
1
1
2
1
0
0
2
2
0
2
2
0
2
0
2
0
1
0
0
0
3
2
1
0
0
2
0
1
0
0
0
0
2
0
0
1
2
0
1
0
2
0
1
0
1
2
0
0
0
0
0
0
1
0
1
0
1
1
1
0
1
0
0
2
0
3
2
1
0
1
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
2
0
1
0
0
0
0
0
0
3
0
2
0
0
3
3
0
1
0
3
1
0
0
1
1
0
0
0
0
0
0
2
2
0
0
0
1
2
2
2
2
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
1
0
0
1
2
0
0
0
1
2
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
2
1
0
1
1
0
0
0
0
0
1
3
2
1
0
0
1
0
0
1
0
0
1
1
2
1
0
2
2
0
1
2
2
0
1
0
0
2
0
0
0
0
0
2
0
0
0
1
0
1
2
1
1
2
0
1
0
0
0
1
1
0
0
2
0
1
0
1
2
0
2
0
0
2
1
0
1
1
2
0
0
2
2
1
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
2
1
0
1
0
1
0
0
0
0
0
1
5
1
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
2
1
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
3
1
0
1
0
1
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
1
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
1
1
0
1
2
0
2
1
1
1
1
1
0
2
0
0
1
2
0
0
0
0
1
0
2
0
0
1
0
0
3
0
1
0
0
0
0
0
1
0
0
0
1
2
0
0
0
2
0
0
1
2
0
0
2
2
2
2
0
0
1
0
0
0
1
0
2
0
1
0
1
1
1
2
1
0
1
2
1
1
0
2
0
2
0
2
0
0
1
1
3
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
4
0
0
0
1
0
1
2
0
0
1
1
2
2
3
2
1
0
1
0
2
0
0
0
2
0
2
0
2
0
2
0
1
0
0
0
1
0
0
0
0
2
1
0
0
0
1
1
0
2
0
0
0
0
2
0
0
0
2
1
2
0
0
2
0
0
0
1
0
2
0
2
0
1
0
0
0
0
1
0
1
0
0
2
0
0
0
2
0
0
0
2
3
1
0
0
1
2
2
0
0
2
0
0
0
0
2
1
0
0
0
0
1
2
1
2
0
0
2
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
1
2
0
0
0
0
2
0
0
0
4
1
2
1
0
0
2
0
0
0
1
2
0
2
0
0
0
0
0
2
1
0
1
0
0
0
0
0
1
0
0
2
0
0
0
2
1
0
0
3
1
0
0
0
0
0
0
0
2
1
0
3
0
0
1
0
2
2
0
0
0
0
2
0
0
3
0
1
11
0
1
2
0
2
0
1
0
0
1
1
0
1
0
0
0
0
1
1
1
0
1
0
0
2
0
2
1
2
0
3
2
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
1
0
0
1
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
2
1
2
0
1
2
0
0
1
1
0
0
2
2
0
2
0
2
1
0
2
0
0
1
10
0
0
2
0
2
3
1
0
0
0
1
0
0
0
0
0
0
1
0
2
1
0
1
0
0
0
0
0
1
2
2
0
0
0
0
2
0
2
1
0
0
2
2
1
0
1
0
0
0
0
2
0
1
0
1
1
2
0
2
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
2
0
0
0
0
2
0
0
2
1
0
1
0
0
2
0
1
3
2
1
0
0
0
0
0
0
2
1
0
0
0
0
2
2
0
0
1
0
2
1
0
1
0
0
0
2
0
0
0
1
0
0
2
2
0
0
1
2
1
0
2
0
2
1
0
0
3
0
0
1
1
0
0
2
0
1
0
0
2
0
0
1
0
2
0
0
1
0
2
1
0
1
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
3
0
1
1
0
0
2
0
0
2
1
0
1
0
0
1
1
0
0
0
0
1
2
0
0
0
2
0
0
0
2
0
1
0
0
0
1
1
1
2
0
1
1
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
1
0
1
2
0
0
0
0
0
4
1
0
2
2
0
2
2
0
0
0
0
0
0
0
1
0
0
1
1
0
2
0
2
0
0
0
0
2
2
0
0
0
0
1
0
2
0
0
1
0
0
0
2
0
1
0
0
1
0
3
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
3
0
0
0
1
1
0
0
0
0
0
2
1
0
0
0
1
2
0
1
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
2
1
2
0
0
2
2
3
1
0
0
0
0
2
0
0
2
3
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
4
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
2
0
0
0
0
2
3
0
0
0
2
1
1
2
0
0
2
0
0
0
0
0
0
2
0
0
1
3
1
0
1
0
0
0
2
0
2
0
3
0
2
1
1
0
1
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
1
1
0
0
0
0
1
2
0
0
0
1
0
2
1
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
1
0
1
0
2
0
1
5
1
0
2
0
0
0
0
0
1
1
0
0
2
0
0
1
0
1
0
0
1
0
1
0
0
0
1
0
0
2
0
0
0
0
1
2
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
2
1
0
2
0
1
1
0
0
2
0
1
3
0
0
0
0
0
2
0
1
0
0
0
2
2
0
0
0
0
0
1
2
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
1
0
2
0
0
0
0
1
0
0
0
2
0
0
1
2
2
2
1
2
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
1
2
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
1
2
0
2
0
2
0
2
1
0
0
1
0
0
0
0
1
2
0
2
2
0
1
0
0
0
2
1
0
2
0
0
0
1
1
2
2
1
1
1
0
2
2
0
0
1
2
2
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
2
0
0
0
1
0
0
0
0
1
2
0
0
1
1
1
0
0
1
0
0
0
0
0
2
0
0
0
1
2
0
0
0
2
0
0
0
0
3
2
0
0
0
2
2
1
1
0
1
0
4
0
0
2
0
2
1
1
2
0
0
0
1
1
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
1
1
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
2
2
2
0
1
3
0
0
0
3
0
0
0
2
0
1
0
1
2
0
1
2
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
1
2
0
1
0
0
0
0
1
0
0
0
0
0
0
1
2
0
2
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
3
0
2
1
0
1
3
0
1
2
1
0
1
0
3
0
0
1
2
0
2
3
1
2
2
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
1
0
1
0
1
0
2
0
2
0
2
0
2
1
0
1
2
2
0
0
0
2
0
0
0
2
1
0
0
1
1
1
0
4
1
0
2
1
0
0
2
0
2
2
0
1
2
1
2
0
0
2
2
0
0
0
0
0
0
2
0
2
0
0
2
0
2
0
0
1
2
2
2
1
0
1
0
0
3
0
0
1
4
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
2
2
1
0
0
0
0
1
1
2
2
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
1
0
2
1
2
0
0
2
0
2
0
0
0
0
0
0
0
0
2
1
1
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
1
0
2
1
1
1
0
0
0
2
1
0
0
0
0
3
0
0
0
0
2
0
0
0
0
2
0
2
0
2
2
0
0
1
1
1
1
0
1
1
2
0
1
1
1
0
2
0
0
2
2
0
0
0
0
1
2
0
0
0
0
1
0
2
0
2
0
4
2
0
0
3
2
0
0
0
2
0
0
2
0
0
2
1
1
0
0
0
2
2
0
0
0
0
0
0
0
1
0
2
2
2
1
1
1
1
0
2
2
0
0
0
0
2
0
0
0
1
2
0
1
4
0
1
1
0
0
0
2
2
1
2
0
1
2
2
0
2
0
2
0
0
0
1
1
0
2
1
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
2
0
2
0
0
0
0
2
2
1
1
1
0
0
2
0
0
0
0
0
1
0
1
0
0
1
1
0
0
1
1
1
2
0
2
1
0
2
0
0
2
0
2
1
0
0
1
0
0
2
0
0
1
2
0
1
0
2
0
0
0
1
0
0
3
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
1
0
2
0
1
2
0
2
0
0
0
0
0
1
2
1
0
1
0
2
2
0
0
4
1
0
0
0
2
0
0
0
0
1
2
0
0
0
0
2
2
0
0
2
0
2
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
2
2
2
0
0
0
2
0
1
1
1
2
0
1
1
0
0
1
0
1
0
0
1
0
0
0
0
3
0
2
0
2
0
0
0
0
0
1
0
0
1
0
0
1
0
1
2
0
0
0
1
2
2
0
0
0
0
0
1
0
2
0
2
0
1
1
2
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
3
0
0
2
0
0
2
0
0
1
0
0
0
0
0
1
0
2
0
1
1
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
2
0
1
0
1
0
0
1
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
1
0
0
2
1
0
0
1
0
2
0
0
0
2
0
1
0
0
0
1
1
0
0
0
0
2
0
0
1
1
0
2
0
0
0
1
0
0
1
1
0
2
2
0
3
0
0
0
1
0
0
0
0
0
2
0
1
1
2
2
2
0
0
2
0
0
2
1
1
0
0
0
0
0
0
2
0
2
0
1
0
0
0
2
2
2
0
1
1
4
0
0
2
0
2
0
0
2
0
2
0
0
0
0
0
3
0
1
0
2
1
0
2
2
0
0
0
0
0
2
2
0
0
2
0
1
0
1
0
2
0
0
0
0
1
0
0
0
0
0
1
2
2
0
0
2
0
0
2
1
1
0
0
0
0
2
0
2
1
0
1
0
0
1
1
0
2
0
0
0
0
0
2
0
1
0
2
0
1
2
0
1
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
2
2
1
0
0
0
2
1
4
0
0
0
0
0
2
0
0
0
0
0
0
1
1
2
1
2
0
2
0
0
0
0
0
0
2
0
0
2
1
0
0
1
0
0
0
1
1
0
0
0
0
2
2
1
0
0
2
1
0
1
0
1
0
2
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
1
0
2
0
0
1
2
1
1
1
2
0
0
1
2
0
0
0
0
0
1
0
1
0
1
2
0
0
0
12
0
0
0
2
2
0
0
2
0
0
2
3
0
0
0
0
1
0
2
2
0
2
1
1
1
1
0
2
2
0
0
2
0
0
1
0
0
2
2
0
0
1
0
1
0
0
1
0
0
2
2
0
3
2
0
0
1
2
0
2
0
0
1
2
2
0
0
2
0
2
0
0
0
0
2
0
0
0
1
0
1
0
2
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
1
0
2
0
0
0
2
0
0
1
0
2
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
3
0
0
0
1
0
1
0
0
0
8
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
1
2
0
0
2
2
2
0
0
2
1
0
1
0
2
0
1
0
1
0
0
2
0
3
2
2
0
2
1
2
8
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
1
0
0
0
2
0
2
0
0
0
1
1
0
2
1
0
1
1
1
2
0
0
0
1
0
2
1
0
0
0
0
1
1
1
0
0
0
0
0
0
2
2
0
1
0
1
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
1
1
1
0
0
1
0
2
0
0
2
1
1
1
1
0
1
1
2
0
1
0
0
0
0
2
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
5
0
0
1
2
0
0
1
0
1
0
0
2
2
2
1
0
2
0
0
0
1
0
0
1
2
0
1
2
1
0
0
0
2
2
2
0
0
2
0
0
1
1
0
2
0
0
1
0
0
1
1
2
1
0
0
0
0
2
2
2
0
0
2
2
0
0
0
0
2
1
0
0
2
0
0
0
2
3
3
0
1
2
0
0
0
0
2
0
0
1
0
0
2
1
0
1
0
0
0
1
1
2
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
1
1
0
0
0
0
0
1
1
0
1
0
0
1
1
0
0
0
1
1
1
0
1
0
0
1
0
0
0
2
2
2
0
1
0
0
1
2
1
0
0
0
0
0
0
0
0
1
0
2
2
2
0
0
0
0
0
1
0
2
0
1
0
2
0
0
0
1
0
0
0
2
0
2
0
0
1
1
1
4
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
4
1
0
0
2
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
2
0
1
2
2
0
0
1
2
1
0
1
1
2
0
2
0
1
0
2
0
0
0
0
0
0
2
0
1
2
1
0
1
0
0
2
0
2
0
2
0
0
0
0
1
0
0
0
0
6
0
0
0
1
0
0
2
1
0
2
2
0
0
0
2
2
3
2
0
0
1
0
0
0
0
0
2
0
1
1
2
0
0
0
2
3
0
0
2
0
1
0
0
0
2
2
0
1
2
0
1
0
0
0
0
1
0
0
0
2
2
0
1
0
1
1
0
0
2
1
2
2
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
1
1
3
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
2
0
2
0
0
0
0
0
4
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
2
1
0
2
0
0
0
2
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
2
2
0
0
0
0
0
1
0
0
1
1
0
2
0
0
1
2
2
1
1
0
0
0
0
1
1
3
0
1
1
1
0
0
4
2
0
1
2
2
3
1
0
0
0
1
5
0
0
2
0
1
0
2
0
2
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
2
2
0
0
1
1
0
1
0
0
0
3
1
0
0
0
0
1
0
2
2
0
0
1
2
0
0
0
0
0
0
1
2
0
1
2
0
0
2
0
1
0
0
1
0
1
0
0
1
1
0
0
0
0
2
0
1
1
1
0
1
0
0
0
2
2
0
0
1
2
1
0
1
1
0
2
2
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
1
1
0
1
0
0
0
0
2
2
0
0
0
1
1
0
0
0
1
0
0
0
2
0
1
2
0
1
0
1
0
2
0
2
0
0
0
0
0
0
0
0
2
2
0
0
1
2
1
0
1
2
2
0
1
0
0
1
0
1
0
0
0
0
0
2
0
0
2
0
2
1
2
0
0
0
0
1
1
2
0
0
2
0
2
2
1
2
1
1
1
0
0
0
1
0
0
2
0
0
0
1
0
0
2
2
3
3
0
0
0
1
0
0
0
1
1
2
0
0
2
0
0
0
2
2
1
0
0
0
1
0
1
2
0
1
0
1
2
0
0
1
2
1
0
0
0
1
0
1
2
1
0
0
2
1
0
0
2
0
0
0
0
0
0
1
1
0
2
0
2
1
0
1
0
2
0
1
1
2
0
2
0
0
1
0
1
2
0
0
1
1
1
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
1
1
0
1
2
0
0
0
0
2
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
2
0
0
0
2
1
0
2
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
1
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
3
1
2
0
0
0
0
0
2
1
0
4
0
2
3
1
0
0
1
0
0
1
2
0
0
1
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
1
2
1
0
1
1
0
0
0
0
0
0
1
0
0
0
2
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
2
0
0
1
0
0
1
1
0
1
0
0
1
0
2
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
2
1
0
2
3
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
2
0
0
1
0
1
0
1
2
1
0
0
2
0
0
2
2
1
0
0
0
0
3
2
2
1
0
0
0
0
1
1
0
0
0
0
0
0
1
2
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
2
2
0
1
0
0
1
0
0
3
1
0
0
1
1
2
1
2
0
2
0
0
0
2
0
2
0
2
2
0
2
2
0
1
2
2
0
1
1
1
0
0
1
1
1
0
0
0
2
0
0
1
3
0
0
0
0
2
1
1
0
2
2
0
1
1
0
0
3
2
2
2
0
2
0
0
2
2
1
0
0
2
0
0
0
0
0
2
1
0
0
2
0
2
2
3
2
1
0
0
0
0
2
1
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
2
1
2
0
0
0
0
0
2
1
0
0
0
0
1
1
1
2
0
0
0
1
0
1
2
0
0
2
0
0
1
1
0
2
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
1
0
1
2
2
0
0
0
0
0
0
1
2
2
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
2
3
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
1
0
1
1
0
1
0
2
1
0
1
0
1
0
0
2
2
0
2
4
2
0
0
0
2
2
0
2
0
0
0
0
0
0
1
0
2
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
1
0
2
1
0
1
1
0
1
0
0
1
0
2
0
0
1
2
0
1
0
0
2
2
2
1
1
0
2
0
0
1
0
0
1
1
2
0
1
2
2
2
0
1
0
1
0
0
0
2
1
2
0
0
0
2
0
0
0
1
2
0
0
0
1
0
2
0
1
1
1
0
0
0
1
0
1
0
1
0
0
0
0
2
0
2
0
1
2
0
1
1
0
1
1
1
1
0
0
0
0
0
0
3
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
2
2
0
3
2
2
1
1
1
2
0
0
2
0
2
0
0
1
0
0
0
0
0
1
0
0
1
0
2
0
1
0
2
0
1
2
0
2
1
0
0
1
1
2
2
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
2
2
1
1
1
0
1
0
0
0
0
2
0
0
0
2
0
2
0
1
1
1
0
0
1
0
0
0
0
1
2
0
0
0
0
1
0
0
0
1
1
1
0
1
0
0
0
0
1
2
2
0
0
2
0
2
0
0
0
0
1
1
0
2
0
0
1
0
0
2
0
0
1
0
0
1
0
0
0
2
0
2
2
0
1
0
2
1
0
0
1
0
0
0
1
1
1
1
0
0
0
0
0
1
0
0
0
0
2
1
0
0
2
0
2
0
0
0
0
0
2
1
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
3
0
0
3
0
2
1
1
0
0
1
0
0
0
2
0
1
0
0
0
1
1
2
0
1
0
0
0
0
0
2
1
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
1
2
0
4
0
1
0
0
0
0
0
0
1
1
0
0
2
0
1
0
0
0
0
1
1
0
0
2
0
2
4
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
1
0
1
2
0
0
1
0
1
0
2
1
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
1
0
0
3
0
0
0
2
1
0
0
1
0
0
2
1
0
0
2
1
1
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
2
0
0
0
0
0
2
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
3
0
1
0
2
1
2
1
1
0
0
2
2
0
0
2
2
1
0
0
0
0
1
0
1
3
0
0
2
0
0
0
0
0
0
5
0
1
0
0
0
0
0
0
1
0
0
2
0
1
0
1
0
1
0
0
2
2
0
0
2
0
2
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
1
0
2
0
0
0
2
0
0
0
1
1
0
0
2
0
1
0
2
0
2
2
0
1
0
1
0
2
1
1
0
2
1
0
0
1
0
1
0
2
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
2
0
0
1
2
0
0
0
1
0
2
0
2
0
1
0
0
2
0
0
0
0
3
0
0
1
0
1
0
0
0
1
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
2
1
0
4
1
1
2
0
0
0
2
1
0
0
1
2
1
1
0
0
3
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
2
1
0
1
0
0
1
1
1
2
2
1
0
0
1
0
0
0
2
0
1
0
0
0
1
0
0
0
1
0
0
0
0
2
0
1
0
0
0
2
0
2
0
2
0
1
1
1
0
0
0
0
3
2
0
1
1
0
1
2
1
2
0
1
1
0
0
0
0
2
1
1
0
0
0
0
0
1
1
3
4
2
0
1
0
2
1
2
1
0
2
0
2
1
1
0
1
0
1
2
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
1
0
1
2
3
0
1
2
0
1
0
0
2
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
1
0
0
0
2
1
0
0
2
1
0
0
0
0
0
1
1
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
1
2
1
0
0
1
0
0
2
0
6
3
2
1
0
1
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
2
2
2
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
1
0
0
0
3
0
0
0
0
1
2
2
0
0
0
0
2
0
1
0
0
2
0
1
1
0
1
0
1
1
0
0
0
0
2
1
2
1
0
1
2
1
0
0
2
2
0
0
0
0
1
0
0
1
0
1
0
0
1
0
1
0
1
0
1
3
0
1
2
0
0
0
0
1
2
0
0
0
1
0
1
2
0
2
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
2
0
0
1
0
0
0
0
1
2
2
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
2
1
0
0
0
0
1
1
1
0
2
2
2
0
0
2
0
0
1
0
0
1
0
2
1
0
0
0
0
0
0
1
1
1
4
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
2
2
0
0
0
2
1
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
1
2
1
1
0
2
0
0
0
1
1
2
1
1
1
1
0
2
2
0
0
1
0
1
0
2
0
0
1
0
0
0
1
2
0
1
0
0
2
1
0
0
1
1
0
0
3
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
3
0
1
0
0
0
0
2
0
1
1
0
0
2
0
2
0
1
0
1
2
0
0
1
2
0
2
0
0
0
1
1
2
0
0
0
0
0
2
5
0
2
0
1
1
0
1
0
0
0
4
2
1
0
1
0
0
2
0
0
0
0
0
1
0
1
3
1
2
0
0
0
0
0
1
1
0
1
2
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
3
1
0
1
2
0
1
0
3
0
0
2
1
1
0
1
2
1
0
0
0
0
1
1
1
0
1
0
3
1
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
1
2
2
2
2
2
1
0
1
2
1
0
2
2
0
0
0
0
1
0
0
2
1
2
0
0
0
1
2
0
0
0
0
0
1
0
0
0
2
2
2
2
0
2
0
2
0
0
2
1
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
5
2
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
3
0
2
0
2
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
2
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
2
1
1
2
2
0
1
0
0
0
1
0
0
2
1
0
0
0
0
1
5
0
2
0
0
0
2
3
0
0
0
1
0
0
0
1
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
2
2
0
0
0
2
0
0
2
0
2
3
0
0
0
2
0
0
3
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
1
0
1
0
0
0
0
0
0
1
0
0
2
1
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
1
0
2
2
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
1
0
2
1
0
0
2
0
0
0
0
0
0
0
1
1
0
0
2
0
1
0
1
0
0
1
0
5
0
0
0
0
2
1
0
0
1
0
2
0
0
0
2
0
0
1
3
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
1
0
0
0
2
0
1
1
1
0
0
0
1
2
2
1
2
1
0
2
0
1
1
0
0
1
0
1
0
2
0
0
0
0
0
0
0
2
0
2
2
0
1
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
2
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
1
1
0
0
0
2
0
0
2
0
0
2
0
2
0
0
2
0
1
1
0
0
0
0
2
0
0
2
0
0
1
0
2
1
1
0
0
0
2
0
0
1
0
1
2
1
1
0
0
4
0
2
2
3
1
0
0
0
2
1
1
2
0
1
0
2
0
0
0
0
2
1
0
0
1
0
0
1
0
0
0
2
0
0
2
1
0
0
2
1
0
0
0
1
0
0
0
0
0
0
2
0
2
0
2
1
0
0
0
0
1
0
0
0
2
0
0
0
0
3
0
0
0
0
0
2
1
2
2
1
2
0
0
0
0
0
0
2
0
1
1
0
1
0
0
0
0
1
0
0
0
1
2
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
2
1
0
1
0
0
0
0
0
2
0
0
2
0
1
0
1
0
4
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
2
2
0
0
0
2
0
0
0
1
0
0
1
0
2
2
1
3
0
0
0
0
1
0
2
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
1
3
2
0
2
2
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
1
0
2
1
0
0
1
0
0
0
2
0
2
0
2
0
0
1
0
0
0
1
2
1
2
1
0
0
0
0
0
0
2
0
1
2
1
1
0
0
0
2
0
0
3
0
1
2
0
2
2
0
3
2
0
1
2
0
0
0
1
0
1
0
1
3
0
0
0
0
0
0
0
1
0
0
0
2
1
9
0
0
0
1
0
0
2
0
1
1
0
1
0
1
2
0
1
0
0
2
2
0
1
1
1
0
0
1
2
0
0
3
2
0
0
0
0
1
0
0
0
0
2
1
1
1
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
2
1
2
0
0
1
2
1
0
1
0
0
0
0
1
1
0
2
0
2
0
1
0
1
1
0
0
0
0
1
0
0
2
0
1
2
1
1
3
0
4
0
2
1
0
0
0
1
1
0
0
2
0
0
0
1
1
0
2
0
0
0
1
0
0
0
0
2
2
0
1
0
0
1
0
1
0
0
1
2
0
0
0
0
0
0
0
3
0
2
1
0
0
0
0
0
0
0
1
2
0
0
0
0
1
1
0
2
0
2
1
2
1
0
0
1
0
1
0
0
2
0
0
2
0
1
0
0
0
3
0
0
2
1
0
0
1
0
2
2
2
1
0
0
0
0
1
1
2
0
1
0
0
0
2
0
0
0
0
2
1
2
0
0
0
0
1
0
0
0
0
0
0
0
3
0
1
0
1
2
0
0
2
2
1
3
2
2
1
0
0
1
0
2
1
0
2
5
0
2
0
1
1
0
2
2
2
2
1
0
0
0
1
1
0
1
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
1
0
3
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
3
0
0
0
2
1
0
1
0
1
0
0
0
0
0
0
1
2
2
0
0
0
2
0
0
0
1
3
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
2
0
1
0
1
1
0
3
0
1
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
2
2
0
1
0
1
0
0
3
0
0
0
2
0
0
1
0
0
0
1
1
0
0
0
1
1
0
1
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
2
0
2
0
0
1
0
0
2
0
0
0
0
1
0
0
0
2
1
0
1
1
0
2
1
0
1
0
0
2
1
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
2
6
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
1
0
1
0
0
2
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
1
0
0
0
2
2
3
0
0
0
1
0
0
0
1
3
0
2
0
0
0
1
0
0
0
1
0
1
0
2
0
0
0
0
1
1
3
0
0
0
2
0
2
1
2
0
0
0
1
1
1
0
0
0
2
0
2
0
2
1
0
0
0
0
0
0
1
1
0
0
1
1
1
1
1
2
1
1
2
2
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
3
0
0
0
2
1
1
0
0
0
0
2
2
2
2
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
1
2
1
2
0
0
0
0
0
0
0
0
1
1
1
3
0
0
0
0
1
0
0
2
0
0
0
0
3
2
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
2
0
0
1
0
4
1
1
0
1
2
0
0
1
0
0
0
0
0
0
2
2
0
0
0
1
2
2
2
0
2
0
0
0
1
0
2
0
0
1
0
1
1
0
0
2
0
2
1
0
0
2
1
1
2
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
2
2
2
0
1
0
3
1
2
1
0
2
0
1
2
0
1
0
0
0
0
0
1
2
2
0
0
2
0
0
3
0
0
2
0
0
2
0
0
2
0
0
1
2
2
2
0
0
0
0
0
0
0
0
0
3
1
1
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
1
0
0
2
2
0
0
0
2
0
2
2
0
3
1
0
0
1
0
2
3
0
1
1
0
0
0
0
0
1
0
4
0
0
0
0
0
2
1
1
1
2
0
0
0
0
0
1
0
2
2
0
2
1
1
2
0
0
0
2
0
1
1
2
0
1
0
0
1
1
0
1
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
2
3
0
0
0
3
0
0
0
0
0
1
0
0
2
0
0
2
0
1
2
0
1
0
2
0
2
0
0
1
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
1
2
4
0
0
0
1
0
1
0
0
0
2
0
0
2
1
0
0
2
0
0
1
2
0
2
0
0
1
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
2
2
0
1
0
0
2
0
2
0
0
0
0
2
0
1
0
0
0
1
1
0
2
2
2
0
0
0
2
0
3
0
1
2
0
1
0
1
1
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
1
1
0
0
0
0
2
1
0
5
0
1
0
0
1
2
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
4
1
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
1
1
0
2
0
2
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
3
2
2
1
0
1
0
2
0
0
0
0
1
0
0
0
0
1
0
0
2
0
2
1
0
0
2
0
0
0
0
0
2
0
2
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
3
0
0
1
1
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
1
2
1
0
0
2
1
0
0
2
0
0
1
2
2
1
0
1
0
0
0
0
0
0
0
2
0
1
2
2
1
2
0
0
0
0
0
0
0
1
0
0
2
1
0
0
1
0
0
3
2
0
2
2
0
0
0
2
0
2
2
0
2
0
2
1
2
1
0
0
0
0
0
0
0
0
1
0
0
1
1
2
1
0
1
0
0
0
0
3
0
0
0
0
1
1
0
0
0
2
1
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
3
0
2
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
2
0
0
1
0
0
0
0
2
7
0
2
2
0
0
1
1
0
2
0
2
0
1
0
0
0
0
0
0
1
1
0
2
2
0
2
0
0
2
0
0
1
2
0
0
0
0
0
0
0
2
1
1
0
0
2
0
0
2
0
0
2
0
0
2
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
2
1
0
2
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
1
7
0
1
2
0
2
1
0
2
1
0
2
0
1
0
0
3
0
0
0
0
1
2
1
2
0
0
0
1
2
0
2
2
0
2
7
1
1
0
0
1
0
0
2
2
0
3
0
0
7
3
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
3
0
2
2
0
1
2
1
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
2
0
0
0
2
0
2
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
2
0
0
0
2
2
2
0
1
0
0
0
0
1
1
0
0
0
0
1
2
1
2
3
2
0
0
1
0
2
2
1
2
2
0
0
0
1
1
2
0
2
0
0
1
0
1
2
1
0
0
0
0
1
2
0
0
0
0
1
0
1
0
3
0
0
1
2
0
0
2
0
2
1
1
2
0
0
1
2
0
1
2
0
0
0
0
1
0
0
2
0
0
0
1
1
3
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
2
1
1
1
1
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
2
2
1
0
2
0
0
0
0
1
0
1
1
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
1
2
0
2
0
1
0
1
0
0
0
0
0
2
0
1
0
0
1
3
1
1
1
0
0
0
0
0
1
2
0
2
2
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
1
0
2
2
0
2
0
0
0
0
0
2
1
1
0
0
0
0
2
3
0
1
1
1
1
0
0
1
0
0
1
0
0
0
2
0
0
1
0
1
1
0
2
1
0
1
4
1
0
0
2
0
0
1
0
0
1
0
4
2
0
0
1
2
1
1
0
0
0
1
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
2
2
0
2
2
0
2
0
2
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
3
1
0
1
0
1
0
0
0
0
2
3
1
1
2
1
0
0
0
0
0
0
0
0
2
1
0
1
0
1
0
2
0
0
0
0
0
1
2
0
4
0
0
0
0
0
3
0
0
2
1
0
2
2
0
0
0
2
0
0
0
0
1
1
0
0
2
1
0
2
2
0
2
0
0
0
0
0
1
0
0
0
0
2
1
0
1
3
0
1
3
1
2
4
0
0
0
2
0
2
0
2
0
0
0
1
0
0
0
1
2
2
0
0
0
0
0
0
1
2
1
0
0
0
1
0
0
0
2
1
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
1
2
0
1
0
1
0
0
0
2
0
2
0
2
0
1
0
3
0
1
1
0
0
0
0
0
0
2
1
0
2
2
0
0
0
1
0
1
1
0
0
1
1
0
0
0
2
0
0
2
0
1
0
1
0
0
0
2
1
0
0
0
2
0
0
0
0
2
0
1
1
0
2
0
1
0
1
0
1
0
0
0
0
0
2
0
0
0
0
2
4
0
2
0
1
0
0
0
2
0
2
0
0
1
0
2
0
0
1
0
0
0
1
3
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
2
1
1
0
0
2
0
1
0
2
0
0
0
2
0
1
0
1
0
0
0
0
1
1
0
2
0
2
1
1
3
0
0
0
0
0
0
2
0
4
0
0
5
1
0
0
1
1
0
2
0
0
0
2
0
2
0
2
2
0
2
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
1
2
0
1
1
0
0
0
1
2
1
2
0
2
0
1
1
0
0
2
1
0
0
0
0
0
0
1
0
2
0
0
2
2
0
0
2
2
0
0
0
1
2
1
0
0
0
0
1
0
0
0
2
2
1
0
0
0
0
2
0
0
2
3
2
1
0
0
0
0
2
1
0
2
3
0
1
2
0
0
0
1
2
2
2
0
0
0
1
0
2
2
0
0
0
1
2
1
0
0
2
0
0
0
0
1
2
1
1
1
0
0
1
0
2
1
1
1
2
1
0
0
1
0
1
2
0
1
1
0
1
0
3
0
3
0
0
0
1
0
2
0
1
0
1
0
2
0
0
0
0
2
0
2
1
2
0
0
0
0
0
2
0
0
2
0
2
1
1
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
2
0
0
0
0
1
2
1
0
0
3
0
0
1
2
0
0
0
0
2
2
0
0
0
1
1
2
0
2
1
0
0
0
0
0
1
1
1
1
1
0
0
0
0
1
0
3
2
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
1
1
0
0
0
1
0
0
1
0
1
0
0
2
0
0
0
1
1
1
0
0
0
0
0
2
0
2
2
0
0
2
2
1
0
0
0
0
1
0
0
1
0
0
0
1
0
2
0
1
0
2
1
0
1
1
0
0
1
0
1
0
2
0
0
0
2
2
2
0
0
0
1
0
1
0
2
0
0
0
1
0
2
2
2
0
0
2
1
0
0
1
2
0
0
2
0
0
0
1
0
0
0
1
0
0
3
0
1
1
0
0
0
0
2
1
2
1
0
2
0
1
2
2
1
1
0
2
0
1
0
0
0
1
0
0
0
0
1
2
0
0
0
0
2
1
0
0
0
0
0
0
3
0
0
3
1
2
1
0
1
0
0
0
0
2
0
1
0
1
0
0
1
2
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
2
1
0
0
1
0
0
2
2
1
0
0
0
4
0
0
1
0
0
0
0
0
0
2
1
0
0
2
0
1
1
2
0
0
2
1
1
0
0
2
0
1
2
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
2
0
2
0
2
0
0
2
0
0
0
0
0
1
0
1
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
2
0
2
2
1
0
0
0
0
0
1
0
1
0
0
0
1
1
1
0
1
0
0
0
0
2
0
0
0
2
0
0
2
0
0
1
1
0
1
0
0
2
0
0
0
0
1
3
0
0
0
2
0
0
1
0
2
0
1
2
1
0
0
0
0
0
2
0
1
0
2
1
2
0
0
1
0
0
0
1
1
2
1
2
0
0
0
0
1
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
1
2
1
0
0
2
0
0
1
0
0
1
2
1
0
0
0
0
0
0
2
0
2
1
0
0
0
2
0
0
0
0
0
0
2
3
6
3
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
2
0
0
0
0
0
1
2
0
3
0
1
0
2
2
0
0
2
1
0
2
2
0
0
0
1
0
1
1
1
1
2
0
0
0
0
2
0
2
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
2
0
1
0
2
0
1
0
0
0
0
0
0
0
1
1
1
0
2
0
1
0
1
1
0
0
0
1
0
0
0
1
3
0
2
1
0
1
0
0
0
0
0
0
0
1
6
1
0
0
2
1
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
2
1
1
0
0
1
0
1
0
0
0
0
0
2
2
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
1
1
1
0
0
2
2
0
0
0
1
1
0
1
2
0
0
0
1
0
0
0
1
1
2
0
0
2
0
2
0
0
1
2
0
2
2
0
1
0
0
0
1
0
0
0
1
2
0
0
1
0
0
0
2
0
0
1
0
6
0
1
0
1
0
4
3
2
0
1
0
2
0
0
1
0
0
3
3
2
2
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
2
0
1
0
0
2
1
0
0
1
0
2
0
1
0
0
2
0
0
2
0
2
1
1
2
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
2
1
0
1
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
4
0
2
0
0
0
2
0
0
3
2
1
0
2
0
0
0
0
0
0
0
2
2
0
2
0
0
0
1
0
3
0
1
2
0
2
0
0
1
2
0
0
1
2
0
2
2
0
2
0
1
0
2
2
0
0
2
1
0
1
0
0
0
2
2
0
0
0
0
2
0
1
1
0
1
1
0
2
0
0
0
0
1
2
2
2
2
0
0
0
0
0
2
2
0
0
0
3
0
1
1
0
1
0
1
1
2
1
0
0
0
0
2
0
2
0
1
0
2
3
3
0
0
0
3
0
0
2
1
0
1
0
2
1
0
0
1
1
3
0
1
0
0
1
0
0
0
1
0
2
1
0
2
0
1
1
2
0
0
0
1
0
0
2
0
1
1
1
0
0
0
1
0
3
0
1
0
0
0
0
0
0
0
1
1
1
2
0
0
1
0
1
0
0
0
2
2
0
1
0
2
2
0
0
2
0
0
0
0
3
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
1
0
0
0
2
2
0
0
1
0
0
1
1
0
0
2
0
2
2
0
0
0
2
0
0
1
0
0
0
2
1
1
2
1
0
1
1
0
1
0
0
1
0
0
2
1
2
0
0
0
1
0
0
0
1
0
2
0
0
0
1
1
0
2
0
4
0
0
0
0
1
1
0
0
1
0
1
1
1
1
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
2
2
0
2
1
1
0
3
1
0
0
0
2
1
2
0
0
1
1
0
2
0
0
0
0
2
0
1
0
1
1
0
0
2
0
0
0
0
1
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
2
2
0
0
0
0
0
1
1
2
0
0
2
0
2
0
0
0
0
0
1
0
2
2
0
2
1
0
0
4
0
1
2
0
2
1
2
0
0
0
0
1
0
1
0
0
0
2
2
0
1
2
1
0
1
0
0
1
2
2
1
0
0
0
0
0
0
2
0
0
0
1
0
1
1
0
0
2
1
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
2
2
2
2
0
0
1
2
0
4
0
1
0
0
0
0
2
0
0
1
1
0
1
0
1
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
3
1
1
0
0
0
0
0
0
0
2
1
1
1
0
0
2
0
0
0
1
0
0
0
2
2
2
0
2
0
1
0
1
2
0
0
1
0
0
0
0
0
1
0
2
1
2
1
2
0
0
1
0
1
0
0
0
0
2
0
0
0
0
2
1
2
0
2
0
0
1
0
0
2
0
0
0
4
2
2
1
0
0
0
0
2
0
0
0
1
2
2
2
0
0
1
0
0
1
0
0
0
0
1
1
0
0
2
0
0
3
0
0
1
0
0
2
1
0
1
2
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
1
2
0
0
2
0
0
2
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
4
2
0
0
0
0
0
1
0
0
0
2
2
1
0
0
0
0
1
2
2
2
2
0
1
1
0
0
0
0
1
2
2
1
1
0
2
2
0
0
1
0
0
3
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
4
1
0
0
0
2
0
0
0
2
0
1
1
0
1
1
0
2
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
2
2
2
0
0
2
0
0
0
0
1
1
0
1
1
2
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
1
0
1
3
1
0
2
0
1
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
2
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
1
2
0
2
0
0
1
0
1
1
0
0
2
2
0
0
0
1
0
0
0
0
2
0
2
2
2
0
0
1
0
3
2
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
2
0
0
0
0
1
1
0
0
1
2
0
2
1
0
0
0
0
1
0
2
0
0
0
0
3
2
0
0
0
0
0
0
1
0
2
1
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
2
1
0
0
0
0
0
3
1
0
2
1
1
0
0
0
1
0
0
0
0
1
2
0
1
2
1
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
1
0
1
1
1
0
2
1
0
0
1
0
0
2
2
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
2
1
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
1
2
0
1
0
0
1
0
0
0
0
2
2
0
1
0
2
1
1
0
0
0
0
0
0
0
2
2
0
0
1
0
1
0
0
2
0
0
0
0
2
1
1
2
2
0
0
0
0
2
1
0
0
0
0
0
0
1
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
1
0
0
0
1
0
2
0
0
0
1
1
0
2
1
0
0
0
0
0
0
3
0
0
1
0
1
1
0
0
1
2
1
2
0
1
1
1
0
0
2
2
0
0
1
0
0
1
0
0
0
1
2
2
1
1
2
0
0
0
2
2
0
0
1
0
0
0
1
1
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
3
1
0
0
2
2
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
2
0
0
0
2
2
0
1
2
0
0
0
0
2
1
1
1
0
0
0
1
0
1
1
0
0
1
0
1
0
0
1
2
0
0
0
0
2
0
2
3
3
2
1
2
0
2
0
2
0
0
0
0
2
2
0
0
0
2
0
1
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
1
0
2
0
0
2
1
0
0
0
0
0
0
1
2
0
0
0
0
1
1
3
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
1
2
2
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
2
0
2
0
1
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
1
0
2
1
0
1
0
0
0
0
1
0
1
0
0
2
2
0
0
1
0
2
0
1
0
0
0
0
1
1
1
0
0
0
3
0
2
2
0
0
0
0
0
1
0
2
1
0
0
0
0
0
4
0
1
0
2
1
0
2
0
2
0
1
1
1
2
0
0
1
0
0
1
0
1
0
0
1
1
2
0
0
1
2
0
2
1
1
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
1
0
2
2
0
0
1
2
0
0
2
2
1
1
2
0
1
2
1
0
2
0
0
2
0
0
1
1
0
2
0
0
2
2
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
1
1
0
0
0
1
1
1
1
0
2
0
0
0
2
0
1
0
1
1
0
1
0
1
1
0
2
1
1
0
0
0
2
1
0
0
0
0
1
0
1
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
2
0
2
0
2
1
0
0
0
2
0
1
1
1
0
0
0
0
2
0
0
0
0
0
2
2
0
0
1
1
0
0
0
1
2
1
0
0
0
2
1
0
1
1
0
2
0
0
2
1
2
0
0
2
1
0
2
0
0
0
0
0
2
0
1
0
0
1
0
1
0
0
0
0
0
2
0
2
2
1
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
2
2
2
2
2
0
0
0
0
0
0
0
2
3
1
1
0
1
0
1
1
2
1
1
2
0
0
1
1
1
0
0
1
0
0
1
1
3
2
2
1
0
0
2
0
1
0
0
0
0
0
0
0
0
1
2
1
1
0
0
0
0
0
1
0
0
1
0
0
1
2
0
1
0
1
0
0
2
2
2
0
0
1
0
0
0
5
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
1
0
0
0
0
0
0
2
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
2
2
0
2
0
0
1
1
2
2
0
1
0
1
2
2
0
0
0
2
2
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
1
0
2
2
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
3
0
0
0
2
1
0
0
0
0
3
0
0
2
0
2
0
1
0
1
0
0
2
2
0
0
1
0
2
0
0
2
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
2
0
1
0
2
0
2
2
2
1
0
0
0
1
2
1
0
2
0
0
0
0
0
0
1
1
2
1
1
0
0
0
2
0
0
0
1
1
0
2
0
0
1
0
2
0
2
0
1
2
1
0
2
0
0
0
1
0
0
1
0
0
2
1
2
0
0
0
0
0
0
0
3
0
2
2
2
0
0
0
0
1
2
0
0
2
0
0
0
0
0
4
0
1
0
0
1
0
1
0
0
0
2
1
2
0
0
1
1
1
1
2
0
1
0
0
0
0
1
0
2
0
2
0
2
0
0
0
1
1
0
0
0
2
0
2
0
0
1
2
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
1
0
0
3
0
0
0
0
0
1
1
0
0
1
1
0
1
2
0
0
0
1
0
0
0
1
2
1
0
0
1
0
0
0
0
0
1
2
0
0
0
2
0
1
0
2
1
2
1
0
0
0
0
0
0
0
0
2
1
2
0
0
2
0
1
0
2
0
0
1
0
1
2
0
0
0
2
0
1
0
0
1
0
1
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
2
1
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
1
0
4
0
2
1
1
2
0
2
0
0
2
0
1
0
0
2
1
0
0
0
2
0
2
2
0
0
3
0
1
0
0
1
1
0
0
1
1
0
1
0
0
1
1
0
0
2
0
0
0
2
0
0
0
0
1
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
1
0
1
2
0
1
0
0
0
0
0
2
0
0
1
0
3
0
0
0
2
0
0
1
0
0
0
0
0
1
0
2
1
0
0
0
1
2
0
0
2
0
0
0
1
0
2
2
0
0
3
0
1
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
3
0
0
0
0
2
0
1
1
0
1
0
0
0
1
1
1
2
2
0
0
0
1
0
2
0
1
0
0
0
0
1
0
0
1
0
0
1
0
1
2
1
1
1
0
0
0
2
1
1
1
1
0
0
2
0
3
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
2
0
0
0
0
0
0
0
1
0
0
2
2
1
2
0
1
1
0
0
4
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
2
0
0
1
0
0
1
0
2
0
0
0
1
2
2
0
2
2
2
1
0
0
0
0
1
1
1
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
2
0
4
2
1
1
0
1
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
3
0
1
2
1
2
1
0
0
0
0
0
0
0
0
0
1
0
0
3
1
2
0
1
0
1
0
0
2
1
0
0
0
1
1
0
0
2
2
3
1
0
0
0
0
0
0
1
0
2
1
1
0
1
3
2
0
0
0
0
0
0
0
2
0
0
1
0
1
1
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
2
1
0
0
0
1
0
2
0
4
0
0
1
0
0
0
1
0
0
1
2
0
0
0
1
0
1
0
2
2
0
0
0
0
0
1
2
1
0
0
1
0
1
0
1
0
1
0
0
1
1
2
0
0
1
0
1
0
2
0
2
1
1
2
0
0
0
0
1
1
0
2
0
2
0
1
0
0
0
0
0
0
0
1
2
0
1
1
2
0
4
1
0
0
0
0
0
1
1
0
2
0
1
2
0
0
1
2
0
0
1
2
0
0
0
0
1
0
1
0
1
0
0
2
0
0
2
0
0
2
0
0
0
0
1
2
2
0
2
0
0
0
0
0
2
2
0
2
0
0
0
2
0
1
0
0
1
0
0
0
0
0
2
2
0
5
0
3
0
2
2
2
0
0
3
2
1
0
0
0
0
0
0
0
2
3
1
1
0
1
1
0
0
1
0
0
0
0
2
0
2
2
0
0
1
1
2
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
2
1
2
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
1
0
0
0
2
0
1
0
3
0
1
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
2
0
0
1
3
0
0
0
3
1
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
2
0
0
2
0
0
2
2
0
0
1
0
1
2
0
0
1
0
0
1
1
1
0
0
2
1
0
0
0
2
2
0
1
0
1
0
0
0
2
2
0
0
1
0
0
1
1
0
0
2
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
1
2
2
0
2
0
0
2
0
2
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
1
1
0
3
2
0
1
0
0
1
0
0
0
2
2
0
0
1
2
2
1
2
0
0
2
0
0
0
0
2
2
1
0
0
1
1
0
0
0
0
0
2
1
0
2
0
0
0
0
0
2
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
2
2
0
0
0
3
0
0
0
0
0
2
3
0
1
0
0
1
1
0
0
0
0
1
0
0
2
1
0
2
4
1
0
0
0
1
0
0
0
2
1
0
1
0
0
0
0
0
1
1
0
1
0
2
0
2
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
2
3
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
2
2
0
1
0
1
0
0
0
0
1
24
0
0
0
1
1
1
0
1
2
0
1
0
0
5
2
0
1
0
0
2
0
1
2
0
0
2
0
0
0
2
0
0
2
0
0
0
2
0
1
1
2
0
1
0
0
0
1
0
0
0
0
0
0
2
2
1
0
1
2
2
0
0
0
0
1
1
0
0
0
0
0
3
0
0
0
0
0
2
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
3
1
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
2
0
1
2
0
1
1
0
0
0
0
0
2
5
0
2
0
1
0
0
1
0
0
2
1
0
0
0
2
0
0
0
2
2
0
0
2
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
2
0
2
0
2
0
2
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
2
0
0
2
2
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
1
1
0
0
1
0
1
0
0
0
0
0
2
0
1
0
4
1
0
1
0
2
0
0
1
0
0
1
0
0
0
0
2
1
0
5
1
1
0
1
2
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
2
2
0
1
2
0
0
3
1
1
1
0
0
0
0
2
0
0
2
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
2
0
0
2
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
2
2
0
1
0
0
1
1
2
0
2
0
0
0
0
0
2
0
0
0
2
0
0
1
1
0
0
0
0
0
0
2
0
1
1
0
0
3
0
0
2
0
0
0
0
1
0
1
1
0
0
0
0
0
0
2
2
0
0
0
1
1
0
2
0
2
1
1
1
2
0
0
0
1
0
1
0
0
0
1
0
0
0
1
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
1
0
1
2
0
0
1
0
2
2
0
1
0
1
1
0
2
1
0
2
2
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
1
0
0
2
2
0
0
2
0
0
2
0
0
2
0
0
0
0
1
2
0
0
1
0
0
0
2
2
0
2
2
1
0
1
0
0
0
0
0
1
2
1
0
2
1
0
2
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
1
0
0
0
2
0
0
2
0
0
0
2
0
1
1
0
0
1
0
2
0
0
0
0
1
2
0
0
0
0
1
0
0
0
2
0
1
1
0
0
0
0
0
1
1
0
0
2
1
2
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
1
0
0
0
2
1
2
0
0
1
3
2
1
0
0
1
0
2
0
1
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
3
0
1
3
1
0
2
0
0
0
0
0
0
0
1
3
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
1
2
1
2
0
1
0
2
0
1
0
1
1
2
0
1
0
1
2
0
2
0
0
2
0
0
0
2
0
0
0
0
1
1
2
0
2
2
0
0
1
0
1
2
0
0
1
1
2
1
0
1
0
0
1
0
0
1
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
2
0
0
1
1
0
0
1
0
0
0
0
0
2
0
1
1
2
0
1
0
2
0
2
0
0
0
2
0
0
0
0
0
0
1
0
1
2
0
2
0
0
0
0
2
0
0
0
2
0
0
1
1
0
0
0
3
1
3
2
2
0
0
0
0
1
3
0
0
0
3
0
0
0
2
2
1
0
1
0
1
2
1
0
0
0
2
3
0
1
2
0
0
2
1
1
0
0
1
0
1
0
0
2
0
0
0
0
1
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
2
0
0
0
0
1
0
0
1
0
2
0
0
0
1
0
0
0
0
1
1
0
0
0
1
1
0
0
0
1
4
0
0
0
2
0
1
0
3
0
1
2
3
2
0
1
2
2
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
2
0
0
0
2
2
2
0
2
2
1
1
0
1
1
0
1
0
0
2
1
1
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
1
0
1
2
0
0
0
0
0
2
0
2
0
0
1
0
1
1
1
0
2
0
0
1
0
0
0
2
2
0
0
2
0
0
0
1
1
0
0
2
0
2
1
0
1
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
2
0
0
2
0
3
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
1
0
2
1
1
0
0
2
0
0
1
0
0
0
0
0
1
1
3
0
0
2
0
2
0
2
2
0
1
2
0
0
0
2
2
2
0
1
0
1
0
0
0
2
0
0
1
0
1
1
0
0
0
0
0
0
0
0
3
0
2
0
0
2
0
0
2
0
1
0
0
1
0
0
2
0
0
1
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
2
1
1
0
0
0
2
0
2
0
0
0
0
1
1
0
0
0
0
1
2
0
0
0
0
1
0
0
0
1
2
0
1
0
0
1
0
1
0
1
3
2
0
0
0
0
2
1
0
0
0
2
1
2
0
2
0
0
0
2
0
0
0
1
0
0
0
1
0
0
1
0
1
0
1
2
0
0
1
2
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
3
0
1
3
2
0
0
0
0
2
0
0
1
0
0
0
2
0
1
2
2
1
0
0
1
0
2
0
0
0
0
0
2
0
1
0
1
4
2
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
2
1
2
2
0
0
0
0
0
1
0
1
1
0
1
0
2
2
0
0
1
0
0
0
2
0
1
0
0
0
0
0
1
0
2
0
1
0
2
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
2
1
1
0
2
2
0
0
0
2
0
0
1
0
2
1
2
0
2
0
0
0
0
0
2
2
2
0
2
0
1
1
0
0
2
0
2
2
2
2
0
0
0
2
2
1
2
0
0
3
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
2
1
0
1
0
0
2
0
0
2
0
1
0
2
0
0
1
2
0
0
2
2
2
0
0
1
0
0
0
1
0
2
0
0
4
0
2
2
1
2
2
0
0
2
0
0
0
2
0
1
2
2
0
1
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
2
0
3
0
1
1
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
1
0
0
1
0
0
2
1
0
0
1
0
0
0
0
2
0
0
1
1
0
0
1
0
2
0
2
0
0
1
2
0
0
0
2
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
1
0
1
0
2
0
0
1
0
0
2
1
0
0
2
0
1
0
0
0
0
1
2
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
1
2
1
0
1
0
2
0
1
1
0
0
0
2
0
0
0
0
1
0
0
1
0
0
1
2
0
2
0
0
2
1
1
1
1
2
0
0
1
0
2
2
1
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
1
0
0
2
1
2
1
0
0
2
0
0
1
1
2
0
0
2
1
0
0
2
1
0
0
2
2
0
3
1
0
0
2
0
0
2
1
1
1
0
2
2
2
0
0
0
0
0
0
2
0
0
0
1
2
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
1
2
0
0
0
0
1
2
0
0
2
2
1
0
0
0
0
0
0
1
0
0
0
0
0
1
2
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
2
1
0
2
0
2
0
0
1
0
1
0
1
0
0
1
2
1
0
0
1
1
1
0
1
2
2
0
1
0
0
0
2
0
0
1
0
0
1
2
2
2
0
4
3
1
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
2
2
1
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
3
1
2
0
0
0
3
0
0
2
0
0
0
3
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
3
0
0
0
1
0
2
1
2
2
1
0
1
0
2
0
0
1
2
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
1
0
1
0
1
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
2
1
1
0
1
0
0
0
0
1
0
0
1
0
0
0
2
1
1
0
3
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
2
0
1
2
2
0
2
0
0
0
0
0
1
0
2
0
1
0
4
0
0
0
0
2
0
1
1
0
1
1
0
3
0
1
0
2
1
0
1
2
0
0
1
0
1
0
2
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
3
0
2
1
0
0
1
0
0
0
0
0
0
2
0
1
0
2
0
0
2
0
0
2
2
0
1
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
3
0
1
0
0
0
0
2
0
0
0
0
0
1
0
2
1
2
2
0
1
0
0
0
2
0
2
1
0
1
2
3
1
0
0
1
0
0
2
2
0
1
2
3
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
3
1
0
2
1
2
0
2
0
0
0
0
0
1
2
1
1
0
0
0
0
1
0
1
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
1
0
1
1
1
0
1
0
1
0
1
0
1
0
0
0
1
1
0
1
1
0
2
0
1
1
0
1
0
0
0
2
0
0
1
0
1
1
1
0
1
0
0
0
1
0
2
2
0
2
2
0
0
1
0
0
0
0
1
0
0
2
1
2
0
0
2
1
0
0
2
0
0
0
0
0
0
0
1
2
2
2
2
0
0
0
0
0
0
2
0
2
0
0
2
0
1
0
1
2
0
1
1
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
1
1
0
0
0
1
2
0
0
2
3
2
1
0
0
0
2
0
2
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
1
2
0
1
0
0
0
0
2
2
0
1
2
0
0
0
1
1
2
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
3
0
1
0
3
1
0
1
0
2
1
0
0
0
1
0
2
1
0
0
1
0
2
0
0
2
2
0
2
2
1
1
0
0
1
2
0
0
1
0
0
0
1
0
1
2
0
1
0
0
0
2
0
0
0
0
0
1
1
1
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
2
0
1
2
0
0
0
2
1
0
0
0
2
5
1
1
2
0
0
0
1
0
2
0
0
0
0
1
1
0
0
1
1
0
1
1
2
0
0
1
2
3
0
0
0
0
1
0
2
2
1
1
0
0
0
0
2
1
2
0
0
0
1
0
0
0
0
3
0
0
1
1
1
0
2
1
0
0
0
0
2
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
2
2
0
0
2
0
0
0
0
2
2
1
0
0
2
0
0
0
2
0
2
1
0
1
2
0
2
2
1
2
1
0
0
2
0
0
0
0
2
2
0
0
0
1
0
0
0
2
0
0
3
2
0
2
4
0
0
1
0
2
0
1
0
0
2
0
0
0
0
0
0
0
1
1
0
0
1
0
1
2
0
2
2
0
1
0
0
3
0
0
0
1
0
0
1
2
0
1
0
0
2
0
1
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
1
2
0
0
1
1
0
3
0
0
2
0
0
0
0
0
1
2
1
1
0
1
2
0
0
1
1
1
0
2
0
0
0
1
0
0
0
0
2
0
3
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
2
1
0
2
0
0
1
1
2
2
0
1
1
0
0
2
0
0
0
0
0
0
2
4
0
1
1
0
0
0
2
9
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
2
0
4
0
3
2
0
1
0
0
0
2
0
0
2
0
1
0
0
0
1
0
1
0
2
0
0
0
0
1
2
1
0
0
0
2
1
2
0
0
0
0
2
1
2
0
2
0
0
0
0
1
0
0
1
2
1
0
1
0
0
1
1
2
1
0
0
0
1
0
1
0
3
1
0
0
0
1
0
2
0
2
0
0
1
0
2
2
1
0
0
1
2
2
0
1
0
0
2
2
0
0
0
0
1
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
3
0
0
0
0
1
1
0
2
1
0
0
2
2
1
0
2
1
0
2
0
0
0
3
0
2
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
3
2
0
0
1
0
0
1
0
0
0
0
0
0
0
2
3
1
3
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
3
0
0
1
2
1
2
1
2
0
0
0
2
0
0
2
1
2
0
2
0
1
1
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
1
1
1
0
0
2
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
1
12
2
0
0
0
0
1
0
0
0
1
2
0
0
0
1
4
1
1
2
2
0
2
1
0
0
2
0
2
0
0
0
0
0
2
2
1
0
1
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
1
2
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
2
1
0
0
0
3
2
0
1
0
1
0
2
0
2
0
1
0
2
0
0
1
0
0
2
1
0
0
0
0
0
1
2
2
0
0
0
1
0
1
1
2
0
0
0
0
0
1
0
0
0
0
1
0
1
2
2
0
0
1
0
0
0
2
1
0
0
0
2
1
0
0
0
1
3
2
2
3
0
1
2
2
0
0
0
0
2
1
0
1
1
0
1
0
1
0
0
1
1
0
2
2
2
1
1
0
0
2
4
0
0
1
0
0
0
0
0
1
2
1
1
0
1
2
0
2
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
2
0
1
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
1
2
2
0
3
0
0
2
0
0
0
0
1
1
0
2
0
1
0
0
0
1
0
1
0
0
0
2
0
0
2
0
2
0
0
1
1
1
0
0
0
0
0
1
0
0
1
1
2
0
0
0
1
0
0
2
0
1
2
0
0
0
0
1
4
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
2
0
0
0
1
0
2
0
0
1
0
1
0
1
2
0
0
1
1
0
1
1
0
2
1
0
1
0
0
0
0
0
0
1
2
1
0
3
0
0
0
0
1
2
1
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
2
2
2
0
1
0
1
2
0
2
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
8
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
3
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
4
2
2
0
0
0
0
0
1
0
0
1
2
1
1
0
3
0
0
0
0
0
1
0
0
3
1
2
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
1
0
2
1
0
0
1
0
0
2
1
1
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
2
0
0
1
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
1
2
0
0
0
2
2
0
1
1
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
4
0
0
1
0
0
0
1
0
2
1
0
0
0
2
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
2
1
1
1
1
0
1
0
1
0
0
0
0
0
1
0
4
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
1
1
0
3
3
1
0
1
1
0
1
0
1
0
0
0
0
0
3
1
0
1
0
1
2
0
2
0
3
2
0
0
2
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
3
0
1
0
0
1
0
0
0
0
1
1
0
0
1
2
0
1
0
0
0
1
0
0
0
0
0
0
0
6
0
0
0
3
0
2
0
0
0
2
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
1
3
0
0
0
0
1
0
0
2
0
0
1
2
1
1
2
0
2
0
2
0
1
0
0
1
0
1
0
1
1
0
2
1
2
0
1
2
0
0
0
1
0
0
0
0
0
3
1
0
0
0
0
1
0
0
0
1
2
0
0
0
0
1
0
0
0
2
3
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
1
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
1
0
2
2
2
2
2
0
1
0
1
0
0
0
0
1
0
0
2
2
3
0
0
0
0
0
0
0
1
2
0
7
0
0
0
0
1
2
1
2
0
3
0
0
2
2
1
1
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
1
0
0
0
0
0
3
1
0
1
0
0
0
1
2
0
0
0
0
2
2
1
1
0
2
2
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
1
0
1
2
0
2
0
1
1
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
2
2
1
0
0
1
2
0
0
0
0
2
0
0
0
1
1
2
1
0
2
0
2
0
2
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
2
1
2
0
0
0
2
0
2
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
2
2
0
0
0
2
0
1
0
0
1
1
0
0
2
0
2
0
1
0
0
2
0
0
1
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
1
2
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
1
0
0
2
0
0
1
0
0
0
1
2
0
1
1
2
1
2
2
1
0
0
0
0
1
3
0
2
1
1
1
2
0
4
1
2
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
2
0
0
2
0
0
1
0
0
1
0
0
0
0
1
1
0
2
0
1
2
0
0
2
2
0
0
0
0
0
1
0
0
0
3
2
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
2
2
0
1
0
0
2
0
0
0
1
0
1
0
0
0
1
2
0
1
0
1
0
2
0
0
1
1
0
1
0
0
1
0
1
0
0
0
0
3
1
1
0
0
0
0
0
2
0
0
0
1
0
0
1
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
1
0
0
0
0
2
0
0
0
3
1
0
3
0
0
2
0
0
0
0
0
0
0
2
2
3
0
0
1
0
2
0
0
1
0
1
0
1
2
0
1
0
2
0
0
1
0
0
0
0
1
0
1
1
0
0
0
3
0
0
0
0
2
0
0
1
0
1
1
0
1
5
1
0
1
0
2
2
0
2
0
0
0
0
1
0
2
3
0
2
0
1
2
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
2
1
2
1
0
0
2
0
0
0
2
0
2
0
1
0
0
2
1
0
0
0
1
0
2
0
0
0
1
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
1
1
1
0
2
2
0
0
1
2
0
7
2
0
0
2
1
0
0
0
2
0
0
0
0
0
2
0
2
0
0
2
2
1
1
0
2
0
0
0
2
0
1
1
0
0
1
0
0
0
0
0
2
3
0
0
1
0
0
2
0
0
0
3
2
0
0
0
1
0
2
1
0
1
1
1
0
2
1
0
0
0
2
0
2
0
0
0
1
2
1
0
0
2
2
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
2
0
2
1
3
2
0
2
0
0
0
2
1
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
1
0
1
2
1
0
0
0
0
1
1
1
2
0
0
0
1
0
0
2
0
1
1
0
0
1
1
3
0
0
1
1
2
0
0
0
0
1
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
2
0
0
1
0
0
0
2
1
1
0
0
1
0
2
0
2
1
0
0
0
3
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
1
0
2
0
0
2
0
0
1
1
0
1
0
3
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
1
0
0
1
0
2
0
0
0
2
0
0
0
0
0
2
0
1
2
0
0
0
0
1
0
2
1
2
1
0
1
1
0
0
0
0
2
2
0
2
2
0
0
0
1
0
1
1
0
1
1
0
0
0
2
0
1
2
0
0
0
0
2
1
0
0
0
0
1
0
0
0
1
0
1
0
2
2
0
1
0
0
4
1
0
1
0
1
1
0
0
0
1
0
1
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
3
0
1
11
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
2
0
2
0
0
1
7
1
2
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
1
0
0
3
0
1
3
1
1
2
0
1
0
2
1
0
0
1
2
0
3
1
3
0
0
2
2
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
1
2
2
0
2
0
2
0
0
2
0
0
0
2
1
1
1
0
0
1
0
1
0
0
0
0
1
2
0
2
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
3
0
1
1
1
0
0
0
2
1
0
0
0
1
2
2
0
0
0
2
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
2
1
0
2
0
0
0
1
0
0
0
0
0
0
2
0
1
2
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
1
2
1
0
0
1
1
1
0
0
1
2
1
2
0
2
1
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
2
2
0
0
0
1
0
2
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
2
1
1
0
0
0
0
0
2
1
0
0
0
0
0
2
0
3
0
1
0
0
0
1
2
0
1
0
1
0
2
1
0
0
1
2
1
0
2
0
1
1
1
0
0
0
1
2
0
0
0
1
0
1
2
0
0
0
1
0
0
1
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
5
0
1
0
0
2
0
0
0
0
0
0
2
2
0
0
0
1
6
0
0
1
1
3
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
3
0
0
0
0
0
2
2
1
2
0
2
0
0
1
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
4
2
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
3
0
2
1
1
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
2
2
1
0
0
2
1
0
0
0
0
1
0
0
2
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
2
1
2
0
2
2
1
0
0
0
2
0
0
1
1
2
0
2
0
0
0
0
0
2
0
2
1
0
0
1
2
2
0
0
2
1
0
0
1
0
1
1
1
0
0
1
0
2
0
1
0
0
2
0
0
1
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
2
0
0
1
1
2
0
2
0
0
1
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
1
0
0
2
0
2
0
0
1
3
2
0
2
0
0
0
0
1
0
2
0
0
0
0
0
2
1
1
0
0
0
1
0
1
1
0
2
0
2
2
0
1
0
1
2
1
0
0
0
2
0
0
1
0
1
2
0
2
0
0
2
0
0
0
1
0
0
0
0
0
2
2
0
1
0
0
0
1
1
0
0
0
1
0
2
1
2
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
1
1
1
0
0
0
0
1
0
0
0
1
0
3
0
0
1
0
0
2
1
1
2
0
0
1
1
2
2
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
1
1
0
2
0
0
0
2
0
1
0
2
2
0
2
0
0
0
0
1
2
1
0
0
0
0
1
0
2
1
0
2
2
0
0
0
0
0
2
0
0
1
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
3
0
1
1
0
0
0
0
0
0
0
1
0
2
0
0
1
0
2
0
3
0
2
0
0
2
2
1
1
2
4
2
0
1
1
1
0
0
1
1
3
0
0
1
1
1
0
0
0
2
1
0
0
0
0
0
0
2
0
0
1
1
0
3
2
0
1
0
2
1
0
2
0
0
2
1
2
1
0
1
0
0
2
2
1
0
1
0
0
0
1
0
2
1
2
0
0
0
0
0
0
1
0
1
2
2
1
0
0
1
0
1
2
1
1
1
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
1
0
2
0
1
1
0
2
2
0
0
0
1
0
0
1
0
0
0
0
1
2
1
0
0
0
2
0
2
0
0
0
0
0
2
1
0
0
0
0
2
0
1
0
0
1
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
1
0
1
2
1
0
0
0
0
0
2
0
2
2
0
0
0
0
1
8
2
0
0
1
0
2
2
1
0
0
0
0
0
2
0
0
0
2
1
0
0
0
1
0
2
0
0
0
0
0
0
2
2
2
0
2
3
0
2
0
2
2
2
1
0
0
0
0
2
1
0
0
1
0
1
1
0
1
0
0
1
0
3
1
2
0
1
0
0
0
0
2
0
0
0
0
0
1
1
2
1
0
0
2
0
2
0
0
0
0
2
0
1
1
0
0
0
0
0
0
2
0
2
0
2
1
0
3
0
0
0
0
0
0
1
0
0
2
1
1
0
0
1
0
0
1
0
1
0
0
0
2
1
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
1
0
1
1
1
1
0
1
1
3
4
3
2
0
1
0
0
2
3
0
0
0
4
0
0
1
0
0
2
1
0
1
1
0
2
0
0
0
0
0
0
0
1
2
1
2
1
0
0
0
2
0
1
0
0
0
0
0
0
0
1
4
1
2
2
0
1
1
0
0
0
0
0
0
2
0
0
3
0
1
0
2
2
0
1
0
1
3
0
2
0
1
0
1
0
2
1
1
0
1
1
0
0
0
1
2
0
1
0
2
1
0
0
0
1
1
1
0
1
2
0
1
0
0
0
1
1
0
0
0
0
1
0
2
3
0
0
0
0
2
1
0
0
0
1
0
3
1
1
1
0
0
0
0
0
0
0
0
0
0
1
1
2
0
2
1
2
1
1
0
0
1
2
0
0
0
2
0
0
2
1
0
0
0
1
3
1
3
2
0
0
2
2
0
0
0
0
2
0
1
1
2
0
2
0
0
0
2
0
0
1
2
0
0
0
1
2
2
0
1
2
1
1
1
0
0
1
0
2
0
0
2
2
1
0
2
0
0
1
1
4
0
2
2
0
0
0
2
2
1
0
1
0
0
1
1
2
2
1
1
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
2
0
0
2
0
0
0
2
0
1
0
0
0
2
1
1
1
1
2
1
0
1
0
1
1
0
0
0
2
0
0
0
1
1
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
1
2
0
0
0
1
2
0
2
1
1
0
0
1
0
0
0
0
2
1
0
1
1
0
0
2
1
0
1
0
1
2
0
1
1
0
0
0
0
0
2
2
0
0
0
0
2
0
0
1
1
0
1
0
0
0
0
0
0
5
0
1
0
0
0
1
1
0
0
0
0
0
3
1
0
0
0
0
0
3
0
0
0
0
2
2
0
2
0
0
1
1
2
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
6
1
0
0
1
0
0
0
0
0
2
0
0
1
1
0
0
0
0
2
0
0
2
0
1
0
0
0
0
2
0
1
0
0
2
1
0
2
1
2
2
0
0
0
0
0
0
0
1
0
0
2
1
1
1
1
0
0
0
0
0
0
1
1
1
1
0
1
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
3
2
2
2
0
0
0
3
4
2
2
0
1
0
1
0
0
2
0
0
1
1
0
2
0
1
0
0
2
2
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
2
3
4
0
0
2
2
0
0
0
1
2
1
0
0
0
0
0
0
0
2
1
0
0
1
1
3
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
1
2
1
0
1
0
2
5
2
2
0
2
1
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
2
2
0
0
2
2
0
0
0
0
0
1
2
1
0
0
1
2
0
2
1
0
0
0
2
0
0
0
4
2
0
2
0
0
0
1
0
2
0
2
0
0
2
1
2
2
0
0
1
1
0
0
1
0
1
0
1
1
2
2
0
0
0
1
2
1
0
0
2
0
0
1
0
0
0
1
4
0
0
1
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
2
2
0
0
1
0
0
0
2
0
0
1
0
0
2
0
1
0
2
0
0
0
0
0
2
2
0
1
0
0
0
0
2
2
0
9
0
0
1
0
0
0
0
0
1
0
2
0
2
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
1
2
0
0
0
2
1
0
2
0
0
0
0
0
3
1
0
0
0
0
0
1
1
2
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
1
0
1
0
0
2
0
0
4
1
0
0
2
0
0
0
0
1
0
1
0
2
0
6
0
0
2
0
1
1
0
0
0
0
0
0
0
0
1
1
2
0
0
0
3
0
1
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
2
0
0
2
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
1
0
1
0
1
2
0
2
1
0
1
0
0
2
0
0
0
0
2
2
0
2
1
0
0
0
3
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
1
2
0
0
2
0
0
2
0
0
0
0
1
0
2
0
0
1
0
1
2
1
0
1
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
2
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
1
0
1
1
0
0
0
2
0
0
0
2
1
1
1
1
0
0
0
2
0
0
0
0
0
2
0
2
3
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
3
0
0
1
8
2
2
0
0
1
0
0
0
0
0
0
2
1
0
1
1
2
0
3
0
0
0
3
2
0
0
0
1
2
0
0
0
2
2
0
0
0
0
1
0
0
0
2
0
1
2
1
0
1
0
0
2
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
4
1
0
1
2
2
0
0
0
1
0
2
1
0
2
0
2
0
2
0
3
0
0
2
0
0
1
0
1
2
0
0
0
0
0
2
0
2
0
0
2
0
2
1
1
0
2
0
1
0
0
2
0
1
1
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
1
0
0
1
0
2
0
2
0
0
0
0
0
1
1
0
1
0
1
0
2
0
0
0
2
0
1
0
0
1
0
2
1
2
0
2
3
0
0
0
0
1
2
2
2
0
2
0
0
0
1
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
1
3
1
0
2
1
0
0
1
0
1
1
0
7
0
1
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
2
0
0
1
2
0
2
0
0
2
0
0
1
0
0
0
1
1
0
1
2
0
2
1
0
0
2
0
0
2
0
0
1
2
0
0
2
0
0
0
1
0
5
0
0
0
0
1
2
2
0
0
0
0
1
1
1
0
3
1
0
0
0
1
0
0
0
0
2
0
0
1
0
2
2
2
0
0
0
0
0
2
0
0
2
0
0
0
0
1
2
2
0
0
0
0
1
2
0
0
1
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
1
2
1
2
0
0
1
0
0
0
0
0
4
2
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
2
2
0
1
2
0
2
0
0
2
2
1
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
1
0
1
0
1
1
2
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
2
2
1
3
3
1
1
2
0
1
0
0
0
2
2
0
0
1
0
0
0
0
0
0
1
1
0
2
0
0
0
0
1
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
2
2
1
0
0
2
0
1
0
0
0
0
0
0
1
1
1
2
2
1
2
1
0
0
1
0
0
1
0
0
0
0
2
0
0
0
1
0
1
2
0
0
1
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
1
0
0
0
1
2
1
0
0
0
0
0
2
0
2
3
0
2
2
0
2
2
0
2
2
0
0
0
0
0
0
0
2
1
0
2
2
1
0
0
0
1
0
0
0
0
2
0
0
0
0
2
1
0
1
2
0
0
0
0
0
0
0
1
1
2
1
0
0
1
2
0
2
3
0
1
1
0
1
6
0
0
0
2
0
1
2
0
2
0
1
1
0
2
0
1
0
2
0
0
0
2
0
0
1
0
0
1
0
2
0
0
0
0
1
1
0
0
0
1
2
1
0
0
2
0
0
0
1
1
2
0
0
0
0
2
1
0
0
0
0
3
0
0
1
3
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
1
1
0
2
2
2
2
0
0
0
2
0
2
0
0
2
0
2
0
0
0
2
0
2
0
2
1
0
0
0
3
1
0
1
0
0
3
0
2
1
0
1
2
0
0
0
1
1
1
1
0
0
0
2
0
0
2
0
2
0
1
1
0
0
2
0
1
0
0
0
0
0
0
1
1
1
1
1
0
0
0
1
2
1
2
0
0
0
2
1
1
0
0
1
1
0
1
4
1
2
0
0
1
0
0
0
2
0
2
0
1
0
1
1
0
0
0
1
0
0
1
1
1
2
1
2
0
0
0
1
0
0
0
0
1
1
0
0
0
2
0
2
2
2
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
1
2
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
3
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
1
2
1
1
0
0
1
0
2
1
2
1
0
0
0
0
2
0
0
2
0
3
0
1
2
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
4
2
2
0
1
0
0
0
0
0
1
0
0
0
0
2
2
1
1
0
2
0
0
0
0
1
0
1
1
0
2
0
0
0
0
0
0
1
2
0
0
0
0
1
2
1
0
1
1
0
1
2
2
0
2
2
0
1
0
1
2
1
0
1
0
0
0
5
2
0
0
0
1
0
5
0
0
0
0
2
1
0
0
2
0
2
2
0
1
0
1
0
0
2
2
0
0
0
0
0
0
0
2
2
1
0
2
2
2
1
1
0
2
0
0
1
0
0
0
0
0
2
1
0
0
1
1
1
0
0
0
1
2
0
0
0
0
0
0
2
2
0
0
2
0
0
0
3
1
0
0
0
0
0
0
0
2
0
2
2
2
0
2
0
1
1
1
1
2
1
0
3
2
0
1
0
2
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
2
1
0
0
0
1
0
3
2
2
0
0
4
0
0
0
0
0
0
0
0
0
0
1
2
0
0
4
0
0
0
2
2
0
0
0
0
1
2
0
0
0
2
0
0
0
2
0
0
0
1
0
0
1
0
0
1
1
0
1
2
0
1
2
0
2
0
0
1
0
0
0
4
1
0
0
0
1
2
1
0
1
0
0
2
0
1
0
0
1
0
1
1
1
0
0
2
0
0
0
1
2
2
1
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
2
2
0
2
0
0
0
2
3
1
2
0
2
1
2
1
2
0
2
1
0
0
0
1
0
2
1
0
0
0
0
3
0
0
0
0
1
1
2
0
0
2
0
0
1
0
2
2
1
0
0
2
0
1
1
2
1
1
0
0
1
1
2
2
0
1
0
0
1
0
0
1
1
5
2
2
1
0
2
0
0
0
0
0
2
2
0
0
0
0
0
1
0
1
0
1
0
0
0
0
3
0
0
3
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
2
2
0
2
1
2
1
0
2
2
0
0
0
2
2
0
1
0
0
0
0
0
2
0
2
0
0
2
0
1
0
2
2
0
1
1
1
0
2
0
0
0
1
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
2
2
0
0
1
1
1
0
0
0
1
0
0
0
0
0
1
2
2
2
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
2
2
0
0
0
0
0
0
2
0
1
2
1
1
0
1
1
0
0
2
0
0
1
1
0
3
1
1
0
0
0
2
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
1
3
2
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
1
2
0
0
0
0
2
0
0
1
0
0
1
0
2
0
0
0
0
2
0
1
2
0
0
2
0
2
0
0
1
0
0
0
0
2
1
0
1
0
0
1
0
0
2
0
0
2
2
0
3
0
1
1
0
0
0
0
0
0
0
0
0
2
1
1
2
1
2
0
0
0
0
0
0
0
2
0
0
2
1
0
1
0
0
0
1
0
0
0
1
1
1
0
0
2
0
2
1
0
1
0
0
1
0
2
0
0
2
0
2
0
0
0
0
0
2
0
2
1
0
0
0
1
0
0
1
2
2
0
0
0
0
2
0
0
0
2
1
2
0
1
0
1
0
0
2
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
1
0
0
2
0
1
1
2
0
0
0
1
0
0
0
1
0
0
0
0
3
0
2
0
1
0
2
1
0
2
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
3
3
0
0
1
2
0
0
0
1
0
3
0
0
0
0
0
0
1
2
2
1
0
0
1
2
0
0
0
1
1
0
0
0
0
2
0
1
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
2
1
0
2
0
2
1
0
0
0
2
1
0
0
0
2
2
2
2
1
0
1
0
0
0
1
3
0
2
4
0
0
1
1
0
2
0
0
0
1
0
0
0
0
1
1
0
0
0
2
2
0
0
0
1
0
0
2
3
2
0
0
0
0
0
0
0
0
0
2
0
0
5
0
0
1
0
0
0
1
0
0
1
0
0
2
1
0
0
0
1
1
0
0
2
0
0
0
0
2
1
1
0
0
1
2
0
0
0
0
2
0
0
1
0
2
1
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
2
2
0
2
2
0
0
2
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
2
1
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
2
1
0
0
0
2
0
0
0
1
1
0
0
0
0
0
2
2
0
1
1
1
0
0
0
0
0
0
1
0
2
0
1
0
2
0
2
0
0
3
0
0
2
1
0
0
0
0
2
1
0
1
0
1
1
1
2
2
0
0
0
0
0
0
0
1
0
2
0
0
1
2
0
0
0
2
2
1
0
0
2
0
0
0
0
0
1
0
1
0
3
0
0
0
0
1
1
2
0
0
0
0
0
0
2
1
1
0
1
1
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
2
0
0
0
1
2
0
0
0
4
2
0
0
0
0
0
0
0
0
1
2
0
0
4
0
0
1
2
0
0
0
2
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
9
0
0
0
0
0
0
0
2
1
0
0
1
2
2
0
0
0
0
0
0
2
0
3
0
0
0
1
2
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
1
0
1
0
0
0
2
1
2
0
0
0
0
2
2
1
0
2
1
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
1
2
0
0
3
1
0
0
0
0
0
0
0
2
2
2
2
0
0
0
1
1
0
0
0
0
1
2
0
0
0
0
2
0
2
0
0
1
0
0
0
2
0
0
1
0
0
0
1
0
0
1
0
0
1
0
1
1
0
0
1
0
1
1
2
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
2
2
0
0
0
2
2
3
1
0
0
2
0
0
1
0
0
1
2
2
0
0
1
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
2
0
2
0
2
0
1
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
2
1
2
0
2
1
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
2
1
2
1
0
0
2
0
0
0
2
1
0
1
0
1
0
0
2
1
0
0
0
0
3
0
0
2
0
2
0
0
1
0
0
2
1
0
1
1
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
1
3
0
0
0
2
2
2
2
1
0
0
0
1
0
1
2
0
2
3
0
2
0
1
0
1
1
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
1
0
1
2
0
0
0
0
1
1
0
0
0
1
0
2
0
1
0
0
0
0
3
0
2
0
0
0
1
0
0
1
0
0
0
0
0
2
2
2
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
1
0
0
2
0
1
0
0
1
0
0
1
0
0
1
1
0
0
0
2
2
0
0
1
0
1
0
0
0
0
0
1
0
1
0
2
1
0
0
0
0
0
1
2
0
1
1
0
0
0
0
0
0
3
2
1
2
0
0
2
1
2
1
0
0
2
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
1
0
0
0
1
0
2
0
0
1
0
0
0
1
1
0
2
0
0
1
1
1
1
0
0
1
1
0
1
0
1
0
0
1
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
1
7
0
2
0
0
0
1
0
0
1
0
1
0
1
1
0
0
0
2
0
1
0
1
1
1
0
0
0
2
3
0
1
1
0
0
0
0
0
0
2
2
0
0
0
2
1
0
1
0
4
0
1
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
2
0
0
1
0
2
0
0
0
1
0
2
0
0
1
2
0
0
1
0
29
0
0
1
2
0
0
0
1
1
0
0
0
0
0
1
0
0
0
2
2
2
0
1
0
0
0
0
2
2
0
0
1
0
0
0
2
0
0
1
1
2
1
0
0
0
0
0
0
2
0
2
1
0
0
2
1
1
0
0
0
0
1
0
0
0
2
2
1
0
0
1
1
2
2
0
0
0
0
0
0
2
0
2
2
0
1
0
0
2
0
2
0
0
0
0
0
1
0
1
0
0
2
5
0
0
0
0
0
0
0
0
2
0
0
3
0
2
0
0
1
1
0
1
0
0
1
0
2
0
1
0
0
0
0
1
0
0
1
1
1
0
0
1
3
1
0
2
0
2
0
1
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
3
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
2
2
0
1
0
0
0
3
2
0
3
3
0
0
2
0
0
2
1
0
1
0
0
0
0
0
1
0
4
1
1
1
0
0
0
0
1
2
0
2
0
0
0
1
1
0
0
2
2
1
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
1
0
2
0
0
2
0
0
0
1
0
0
1
0
0
3
0
0
0
1
0
1
1
0
0
1
0
1
1
0
0
0
0
2
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
2
0
0
1
0
2
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
1
1
2
2
6
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
2
1
2
0
0
1
0
0
1
1
0
2
0
0
2
0
1
0
0
1
0
1
0
2
1
0
0
3
2
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
1
1
0
0
0
1
1
0
0
2
0
0
1
0
0
2
0
2
1
0
0
2
1
0
2
0
1
1
2
0
0
0
2
0
2
0
0
0
0
0
0
2
1
1
0
0
0
0
0
1
0
2
0
0
0
1
0
2
0
0
0
0
2
0
0
1
1
0
0
1
2
1
0
0
0
1
0
1
0
1
0
1
0
2
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
1
0
1
2
1
2
1
2
0
1
0
2
1
0
1
2
0
0
2
2
1
0
0
1
0
1
0
0
1
0
3
2
0
1
1
0
1
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
1
0
0
4
0
1
0
1
0
1
0
0
2
2
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
1
0
1
2
0
0
0
2
0
0
0
0
2
0
0
2
2
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
1
0
2
1
0
2
1
0
0
0
0
2
1
0
1
0
2
0
0
0
1
0
1
1
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
1
0
0
0
0
0
2
0
0
2
1
0
2
2
0
1
0
0
0
0
0
0
2
1
0
0
0
2
0
0
1
0
0
4
1
0
0
1
0
1
0
0
2
0
0
1
0
0
0
0
2
1
0
0
2
0
0
0
2
1
0
1
3
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
2
1
0
0
1
1
0
1
1
0
1
0
2
0
0
1
1
0
0
0
0
0
1
1
0
1
0
2
0
2
1
0
1
7
1
0
0
0
1
0
0
0
2
1
0
0
0
0
1
0
0
1
0
3
0
0
2
1
0
1
0
1
1
2
0
1
0
2
1
0
2
2
0
0
3
2
1
0
0
2
0
0
0
2
0
0
2
1
0
2
0
2
2
2
1
0
0
0
0
1
0
0
0
0
2
0
1
0
1
0
2
2
0
0
1
1
0
0
0
0
0
3
0
2
0
1
2
0
2
0
1
0
0
1
1
0
2
1
0
0
2
1
0
2
0
0
1
0
0
1
2
1
1
0
0
1
0
0
0
1
2
2
0
0
1
1
0
0
0
0
0
0
1
2
1
0
2
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
3
0
0
1
0
0
1
0
0
0
2
2
2
1
0
2
0
1
1
0
0
0
0
1
0
0
0
4
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
2
1
0
2
2
2
1
0
2
0
0
0
1
0
0
2
2
1
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
3
0
0
2
0
0
0
1
0
0
1
0
0
0
2
0
0
1
0
1
0
2
1
0
2
1
1
0
0
0
0
0
3
1
0
0
0
2
0
0
1
0
1
2
0
2
1
2
3
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
2
0
2
1
0
0
0
1
0
0
1
1
0
0
0
0
0
1
1
1
0
1
0
0
0
1
2
2
1
0
0
0
1
0
0
0
0
0
0
2
1
1
1
2
2
1
0
2
3
0
2
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
1
0
2
2
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
2
0
0
2
0
2
0
0
2
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
2
1
1
1
2
2
2
0
0
1
0
0
1
1
1
1
3
1
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
1
0
2
0
1
0
2
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
2
1
1
1
0
0
0
0
0
0
0
1
2
0
0
0
0
1
1
1
0
0
2
0
0
0
0
0
2
0
1
0
0
1
2
2
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
2
0
0
0
4
1
0
0
2
0
0
0
0
2
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
1
0
1
1
0
0
3
0
0
2
0
0
0
1
0
1
0
0
1
1
0
0
2
0
0
1
0
1
2
2
0
1
0
2
0
0
0
0
0
2
1
0
0
2
0
1
0
0
0
0
0
0
0
0
4
2
0
0
0
2
2
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
3
0
0
1
0
0
2
2
0
1
0
0
1
2
0
2
0
0
1
0
0
3
1
3
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
2
1
2
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
1
2
2
1
0
3
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
2
1
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
4
0
1
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
1
2
0
0
0
0
0
2
0
2
3
1
0
1
0
0
2
0
0
0
0
0
0
0
2
1
1
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
2
3
0
1
0
0
2
0
0
0
0
0
1
1
1
0
0
2
0
1
2
1
1
2
0
2
3
0
0
1
0
0
3
0
1
0
0
0
0
1
0
1
2
2
0
3
0
0
0
1
2
0
2
0
1
2
2
1
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
5
0
0
1
0
2
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
2
0
0
2
1
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
2
1
0
1
0
1
1
1
0
1
0
0
3
0
0
0
0
0
0
0
1
0
0
1
0
2
1
0
1
0
2
0
0
0
0
3
1
0
0
0
1
2
1
1
0
0
2
1
0
0
2
0
0
0
1
2
0
0
0
0
0
2
2
1
0
0
1
0
0
0
0
1
1
0
2
0
1
0
2
2
2
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
1
2
0
0
1
2
1
0
1
0
0
1
0
0
0
0
1
0
0
2
0
1
0
2
2
0
1
2
0
0
1
2
0
1
2
1
0
2
0
1
0
0
0
0
0
0
0
0
0
1
1
1
1
2
1
0
1
0
0
1
2
2
2
0
1
0
0
2
0
2
0
2
0
2
0
0
0
0
2
0
0
0
1
0
7
0
0
0
0
3
0
1
0
0
0
0
0
1
0
2
1
0
0
1
0
1
1
0
0
0
0
0
1
0
1
2
0
2
2
1
1
0
0
3
0
0
1
0
0
1
0
0
3
0
0
0
1
0
0
0
2
1
2
2
0
3
3
2
2
0
1
2
0
0
2
0
0
2
0
0
0
2
2
1
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
1
1
0
0
0
2
0
1
0
0
1
0
0
0
1
0
0
0
0
2
0
1
1
1
0
0
0
0
0
0
2
0
0
0
2
0
0
3
1
0
1
2
0
0
0
2
0
2
0
0
0
0
0
3
0
0
0
2
0
2
3
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
1
0
1
2
0
0
0
5
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
1
0
1
2
2
0
1
2
0
0
0
2
1
2
3
2
3
0
0
0
0
2
1
0
0
2
2
0
2
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
2
0
0
2
0
1
2
2
2
5
0
1
1
2
0
2
1
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
2
0
2
1
0
2
0
0
2
0
0
2
0
2
2
2
0
0
0
0
2
0
2
0
0
1
0
0
0
1
0
2
0
2
1
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
1
0
3
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
2
0
0
2
0
0
1
0
0
1
1
0
0
1
2
1
0
1
2
0
1
0
0
0
1
0
1
0
0
1
0
0
0
1
1
2
1
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
7
0
0
2
2
0
1
3
0
1
0
0
1
0
2
0
3
0
0
0
1
1
0
1
0
1
2
1
1
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
1
1
0
3
0
1
0
0
2
0
2
0
0
0
0
1
0
0
0
2
0
1
1
2
1
2
0
0
2
2
0
0
1
1
1
1
0
2
0
0
0
2
2
0
2
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
2
0
0
0
2
1
1
1
2
0
0
0
0
0
0
0
0
2
2
1
1
2
2
0
1
0
1
0
0
1
2
1
1
0
2
2
0
0
0
0
0
2
0
2
0
0
1
2
0
0
0
0
2
0
0
0
2
0
2
0
2
2
1
1
1
0
1
2
0
3
1
0
2
0
2
0
0
1
1
0
2
1
2
0
1
2
2
0
4
1
2
0
0
0
0
0
0
1
0
0
1
0
2
0
2
1
1
0
0
0
1
0
0
2
2
1
0
1
0
0
1
0
0
0
0
2
1
2
2
1
0
1
0
1
0
0
2
0
0
0
0
1
0
0
0
1
1
2
1
2
0
0
0
0
1
0
0
0
0
1
2
3
1
1
2
1
1
0
0
1
0
0
0
1
0
2
1
1
2
0
2
2
1
2
0
0
0
0
0
2
0
1
1
0
0
1
0
1
0
0
2
0
0
2
0
0
0
0
0
1
0
3
0
1
0
2
0
0
1
0
0
0
0
0
0
1
0
1
1
2
0
0
0
0
0
2
2
0
3
0
0
0
1
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
1
0
0
2
0
1
1
2
1
0
0
0
2
0
2
0
0
2
0
0
1
3
1
2
1
0
2
0
2
1
2
0
1
2
0
1
0
0
0
0
0
1
2
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
1
1
0
1
0
0
0
2
0
0
2
0
5
0
0
2
1
0
2
1
1
2
0
0
2
2
0
1
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
1
0
2
0
2
0
2
0
1
1
1
0
1
1
0
0
0
0
0
1
1
1
1
1
1
0
0
0
0
0
2
0
1
0
1
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
1
0
2
0
1
0
2
0
0
1
0
1
0
2
0
1
1
3
0
1
0
0
0
0
2
0
0
1
1
1
0
2
0
0
0
0
0
2
0
2
0
2
0
3
1
1
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
2
1
2
0
1
0
0
0
0
0
1
2
0
0
1
1
2
1
1
2
1
0
1
1
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
1
1
2
0
0
1
0
0
3
0
2
2
3
0
0
1
1
1
0
1
0
0
1
2
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
2
0
1
0
0
1
0
0
0
1
0
2
0
0
1
2
2
2
0
0
0
1
0
3
1
0
1
0
2
1
0
0
0
1
0
0
1
0
0
0
0
2
0
1
0
1
0
0
0
0
0
1
0
0
0
0
2
0
2
0
1
1
0
0
0
2
0
1
0
1
0
1
0
0
2
1
0
1
1
4
0
0
0
1
0
0
0
0
1
0
2
0
1
0
0
1
0
0
1
1
1
0
1
2
1
0
0
0
0
2
0
4
0
0
0
0
2
0
0
1
1
0
0
1
0
2
0
0
7
0
1
0
0
0
0
0
1
2
0
0
1
0
0
0
1
0
0
2
0
2
0
0
0
0
0
1
0
0
0
1
0
2
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
2
1
2
0
2
0
1
0
0
0
1
2
0
0
0
0
0
2
2
2
1
0
1
2
0
2
0
0
0
0
0
0
1
0
0
1
1
0
1
1
2
0
0
0
1
0
0
0
0
0
0
2
2
0
2
0
0
2
0
0
0
2
2
0
0
0
1
0
0
1
1
0
2
0
0
0
1
0
0
0
0
1
2
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
2
0
0
0
2
0
1
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
1
0
1
0
1
2
1
0
2
0
2
1
0
2
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
2
0
1
0
0
0
0
5
2
0
2
2
0
0
0
1
0
1
1
2
0
0
0
3
0
0
0
0
0
0
0
2
2
1
0
0
0
0
2
2
2
0
2
2
0
2
1
0
1
2
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
2
1
0
0
2
0
0
0
0
0
0
0
2
0
1
0
2
0
0
2
0
0
1
0
5
0
2
0
0
0
0
0
0
2
0
1
1
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
2
2
0
1
0
0
0
1
0
0
0
1
2
2
1
1
1
0
0
0
0
2
2
0
1
2
0
0
1
1
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
2
0
1
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
2
1
1
0
1
0
0
1
0
0
1
0
0
2
0
1
0
1
1
2
1
0
0
0
0
0
0
1
0
0
2
0
1
1
0
2
2
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
1
0
0
1
0
0
0
0
1
0
0
0
0
2
1
2
0
0
1
1
1
1
0
3
2
1
0
0
1
0
0
0
1
0
0
0
1
1
0
0
1
0
1
0
1
0
2
0
0
0
0
1
2
0
0
0
3
2
1
1
0
0
0
1
2
0
1
1
0
1
2
2
2
0
0
3
0
0
0
2
0
2
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
2
1
1
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
4
2
2
0
0
0
0
1
2
0
0
2
1
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
2
0
2
0
2
1
0
1
2
0
0
0
0
2
2
0
2
0
1
0
0
0
0
1
0
1
2
2
3
0
0
2
0
0
2
5
2
0
2
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
2
0
0
1
2
0
3
0
0
2
0
0
0
0
0
2
0
2
0
0
0
1
0
2
1
1
0
1
0
0
1
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
1
2
1
0
0
0
0
1
0
2
0
2
0
0
0
0
2
1
2
0
2
0
2
0
0
0
0
2
0
1
0
2
2
1
0
1
0
1
1
0
0
2
0
2
0
2
0
1
2
0
1
0
0
0
2
0
2
0
0
0
1
0
0
1
2
2
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
1
3
1
3
2
0
0
0
1
1
0
0
0
0
1
0
1
2
0
0
0
1
1
2
1
2
0
1
2
1
0
0
0
0
2
1
0
0
2
0
2
0
2
1
0
2
0
0
0
1
0
0
0
1
2
1
2
1
0
2
1
0
0
0
0
1
1
1
0
0
0
1
2
0
0
1
0
0
1
0
2
0
0
0
0
0
0
1
1
1
2
2
2
0
0
0
0
0
0
0
1
0
0
1
2
0
0
2
0
1
2
0
0
1
0
2
0
0
0
1
0
2
0
0
1
0
0
0
0
2
0
0
0
1
2
0
0
0
1
0
2
2
2
0
0
2
0
0
0
0
0
1
1
1
0
2
0
0
2
0
0
0
0
0
1
1
1
0
1
0
6
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
3
2
0
0
4
2
0
2
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
2
0
1
1
1
0
2
0
0
1
0
0
2
0
2
0
0
0
2
0
1
2
1
0
0
0
0
2
0
0
2
2
1
0
0
1
2
0
0
1
0
0
1
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
1
0
0
2
2
2
0
0
0
1
1
0
0
2
0
1
0
3
0
2
1
0
0
0
0
2
0
0
1
0
0
1
0
1
3
0
0
0
0
1
0
0
2
0
2
0
0
1
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
2
2
0
1
1
0
0
2
2
0
2
0
1
0
0
2
1
2
1
0
0
0
0
1
1
0
2
1
0
0
1
0
1
1
0
2
1
1
0
0
0
0
2
2
0
2
2
0
0
0
0
0
0
1
0
0
0
0
2
0
2
2
0
1
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
2
2
1
2
0
0
2
2
0
0
1
0
0
2
0
0
2
0
0
4
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
1
4
0
2
0
0
0
0
0
0
0
1
0
0
0
2
2
0
1
0
2
2
2
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
1
0
2
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
2
0
1
0
0
0
2
0
1
0
1
2
0
0
0
1
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
2
2
0
1
0
0
0
0
2
0
0
1
2
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
2
1
0
1
0
1
0
2
0
0
0
0
2
0
2
1
2
0
0
1
2
0
0
3
1
1
0
1
0
0
0
2
0
0
0
1
2
1
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
6
0
0
0
0
0
2
0
0
1
2
0
0
0
2
2
0
0
2
2
0
0
0
1
3
0
0
0
1
2
2
0
2
2
0
2
2
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
1
0
1
2
1
2
0
2
2
0
1
0
0
0
1
0
0
0
2
0
0
0
2
1
1
0
2
0
1
0
2
0
1
0
0
0
2
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
1
0
1
1
0
2
0
2
0
0
2
1
1
8
2
0
2
0
2
0
0
1
0
0
0
0
2
0
1
0
0
2
2
0
1
0
2
2
0
0
0
0
0
0
1
0
0
1
0
0
1
2
0
0
0
1
0
1
0
2
1
0
0
0
2
2
1
1
0
0
0
2
2
0
0
2
0
1
1
0
1
3
2
1
0
0
1
0
0
1
0
0
0
2
2
0
0
0
2
1
0
0
1
1
3
2
0
0
0
0
2
0
0
0
0
0
1
2
2
0
2
0
0
0
0
1
1
0
0
0
1
0
2
2
1
1
3
6
2
0
0
0
1
0
1
2
1
0
0
0
2
2
0
0
2
2
0
2
1
2
0
0
1
0
1
0
0
2
1
0
1
0
0
1
0
2
1
1
1
2
1
1
1
0
0
1
2
4
0
0
2
0
0
0
0
1
2
0
2
0
1
5
0
1
1
2
0
1
2
0
0
0
2
0
0
1
0
0
0
1
1
1
0
0
1
0
0
1
1
0
0
1
1
0
0
0
1
1
0
1
1
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
2
2
0
1
1
0
1
1
0
0
2
0
0
1
0
0
0
0
0
2
0
1
1
0
0
1
0
0
0
1
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
1
0
1
2
0
0
3
0
0
0
0
0
2
3
1
0
2
0
1
0
0
2
1
1
0
0
0
0
0
0
1
1
0
1
0
1
0
2
0
0
1
0
1
2
0
0
1
2
1
2
0
1
0
2
0
0
0
2
2
2
0
1
1
0
1
0
0
1
0
1
2
1
0
1
0
0
1
0
0
0
1
2
0
0
1
0
0
0
0
0
2
1
2
1
1
0
0
2
0
3
0
2
0
1
0
2
2
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
2
1
0
3
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
2
1
0
0
0
1
2
2
0
0
0
0
2
2
1
1
2
0
1
1
0
0
1
0
0
0
0
0
1
2
0
0
2
1
0
2
0
0
0
1
2
0
2
2
2
0
0
0
0
0
0
2
1
0
0
2
0
2
0
2
0
0
0
0
0
1
0
0
0
1
0
3
0
1
0
2
1
1
0
2
1
0
2
1
1
0
0
2
0
0
2
0
0
0
0
0
0
2
1
2
0
0
3
0
2
0
0
3
0
0
1
0
1
0
0
0
1
0
2
0
1
2
2
0
0
2
0
1
2
0
0
0
0
0
3
2
0
0
0
0
2
0
1
1
0
0
0
0
0
2
1
2
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
1
0
0
2
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
2
0
1
0
0
0
0
0
1
0
1
0
1
1
1
2
4
2
0
0
0
0
0
0
0
2
1
0
0
1
0
2
0
1
0
0
0
1
0
1
2
1
2
0
2
0
1
1
1
1
0
0
2
0
0
0
2
0
0
2
2
1
0
1
0
0
1
2
0
1
1
1
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
2
1
2
0
1
0
0
0
2
0
2
0
2
0
2
2
0
0
0
2
0
1
1
1
0
1
0
2
0
2
0
2
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
2
0
0
1
0
0
0
1
1
0
0
4
0
0
1
1
1
0
1
0
0
0
0
0
3
0
1
2
0
0
1
0
0
0
1
0
0
0
0
1
0
2
2
0
0
2
0
1
0
0
1
0
0
0
0
2
0
1
0
1
0
0
0
0
4
0
0
1
2
2
0
0
1
1
0
1
0
1
1
1
0
5
0
2
1
1
1
1
1
0
0
0
2
0
0
2
0
2
1
0
2
0
2
0
1
1
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
1
0
0
0
0
1
0
1
0
0
1
0
1
2
2
0
1
0
4
1
2
0
0
0
2
0
0
0
1
0
0
1
2
0
0
0
0
0
0
1
2
0
2
1
0
1
0
3
4
0
0
0
0
0
2
2
0
0
0
2
1
0
1
0
0
0
1
1
3
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
2
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
1
0
0
0
1
0
2
2
1
2
0
0
0
0
1
1
0
1
0
0
1
1
2
1
0
0
0
0
1
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
1
2
0
1
1
0
0
1
1
2
1
0
0
0
1
0
0
1
0
0
0
0
1
0
2
1
1
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
1
1
0
2
4
0
0
0
0
2
1
2
0
0
0
0
0
1
0
1
0
0
2
2
1
0
1
0
0
0
0
1
2
0
1
0
0
0
0
1
1
1
0
2
0
2
0
0
2
0
2
5
0
3
0
0
2
1
0
0
1
0
2
1
0
1
0
2
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
2
1
0
0
0
2
0
2
0
0
0
0
1
0
0
2
2
0
1
0
0
0
0
3
0
0
0
0
0
1
2
0
0
4
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
1
1
0
0
1
0
1
0
0
0
0
2
0
0
1
2
2
0
0
0
0
0
0
0
0
0
2
0
2
0
1
2
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
3
2
1
0
2
0
0
0
1
1
0
0
0
2
0
0
1
0
0
2
0
1
3
1
2
0
1
0
1
0
0
0
2
0
0
0
1
0
2
1
1
1
2
0
0
0
0
2
0
0
1
1
2
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
2
1
2
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
1
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
1
0
1
0
1
2
2
0
0
2
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
1
0
2
1
1
0
1
0
1
1
1
0
1
0
0
1
1
1
0
0
0
0
1
1
0
1
0
0
1
2
2
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
3
1
1
1
0
2
0
0
1
0
0
0
1
1
0
0
0
0
0
1
1
2
0
0
0
2
2
0
0
0
0
1
0
2
0
0
0
4
0
2
1
0
0
0
0
1
4
0
0
4
0
2
1
0
0
0
0
0
0
1
0
2
0
0
0
1
0
2
0
0
0
0
0
0
2
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
2
0
2
0
1
1
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
1
2
2
0
0
2
2
0
0
1
0
0
0
1
0
0
1
0
2
2
0
0
0
1
1
1
4
0
0
1
0
0
1
0
0
0
2
3
0
0
2
1
1
0
1
0
2
1
3
2
1
4
0
0
0
2
1
0
6
0
0
0
0
2
0
3
0
0
3
0
0
1
7
0
1
0
0
0
0
0
1
0
0
0
0
2
2
2
1
2
0
1
0
2
0
0
1
1
0
2
0
0
1
2
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
2
1
0
0
0
0
2
2
0
1
0
0
0
2
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
2
0
1
1
0
0
1
0
1
0
2
2
0
0
2
0
1
1
1
0
0
0
0
2
1
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
1
0
1
0
0
0
0
2
0
0
2
2
0
1
0
0
0
1
2
1
0
0
0
0
2
0
1
1
1
0
1
0
0
0
1
0
0
0
0
1
0
0
3
1
0
0
0
0
0
0
0
1
0
3
0
2
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
1
0
0
2
0
0
0
2
0
0
0
1
0
3
2
0
0
0
1
0
0
0
1
0
0
2
0
0
2
0
2
1
5
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
1
0
0
0
2
0
1
0
2
2
0
0
0
0
0
2
1
0
3
1
1
0
2
1
0
0
0
0
3
2
2
0
1
0
1
0
1
1
0
0
0
0
2
3
0
1
0
0
1
0
0
1
1
1
0
0
2
0
0
2
0
5
0
2
0
1
0
2
0
0
2
0
0
2
0
0
2
0
0
1
0
1
0
0
0
1
0
1
1
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
2
0
1
0
2
1
0
0
2
0
0
0
1
0
0
0
0
1
0
2
0
0
1
2
0
0
1
1
0
0
1
2
0
1
0
1
0
1
0
0
1
2
2
1
0
0
0
1
1
0
1
1
0
1
0
0
3
0
0
0
0
1
1
2
0
0
0
2
0
0
0
0
2
0
1
0
2
2
0
0
0
2
1
0
0
0
0
3
0
1
3
0
1
2
0
2
0
0
1
1
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
2
1
1
3
0
0
0
0
2
0
0
0
1
0
2
0
2
0
0
0
1
0
0
1
1
0
0
0
0
0
5
0
0
0
2
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
1
1
0
1
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
2
1
2
0
1
2
0
0
0
1
1
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
7
2
0
1
1
0
2
0
0
1
2
0
0
1
2
2
0
1
4
0
0
0
1
0
0
0
0
0
0
1
0
2
1
0
0
0
0
2
2
2
0
1
0
0
0
0
1
1
1
0
1
1
0
1
0
2
0
1
2
0
0
2
0
0
3
0
0
0
0
1
2
2
0
0
3
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
1
2
1
0
0
1
0
0
4
0
0
2
0
2
1
1
2
0
0
0
2
1
0
0
2
1
1
0
0
0
1
2
0
0
0
0
0
1
0
1
2
1
0
0
0
0
2
0
0
0
1
1
1
1
0
0
0
1
0
0
2
1
1
0
0
0
0
0
0
2
0
0
3
0
0
0
0
2
0
1
0
2
1
1
1
0
1
0
0
0
1
1
0
1
1
0
0
0
0
2
0
0
0
0
2
5
0
0
0
0
2
0
1
0
0
0
0
1
2
0
0
0
0
1
0
3
0
1
2
2
0
0
0
0
0
0
0
0
0
0
2
0
2
1
1
0
0
1
2
1
0
0
0
1
0
0
0
0
0
2
0
0
1
1
0
1
0
0
0
0
1
2
1
3
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
3
0
0
0
1
2
0
0
2
0
3
0
0
1
0
2
3
0
2
0
0
0
2
1
0
0
0
1
2
0
0
0
0
2
0
2
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
1
0
0
0
1
0
2
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
2
0
0
0
0
1
5
0
2
0
0
0
0
0
0
2
1
2
2
0
0
0
0
0
1
0
3
0
0
0
1
0
0
0
0
0
2
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
2
1
2
1
0
0
0
0
1
0
1
2
1
1
1
1
6
1
0
0
0
0
0
1
0
2
2
0
2
2
1
0
0
0
2
0
0
0
0
1
0
2
0
0
2
0
2
1
0
2
1
0
0
1
0
1
2
0
1
1
1
0
1
1
0
2
0
0
0
0
1
3
2
0
1
2
0
1
1
2
0
0
0
0
3
0
2
1
0
0
2
0
0
0
2
2
1
0
2
2
0
0
2
1
1
0
1
0
0
0
2
1
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
1
2
1
0
2
2
2
0
0
2
0
2
0
2
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
2
0
0
2
0
1
0
3
0
0
0
1
0
0
0
0
0
1
0
2
1
0
0
2
3
2
0
0
1
1
0
2
0
2
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
2
0
0
1
2
1
0
0
1
0
1
0
0
0
2
1
0
1
1
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
2
0
2
0
1
0
1
0
2
0
2
0
0
0
2
1
0
2
1
0
0
0
1
0
2
1
0
0
0
1
0
0
0
0
0
1
1
2
2
0
1
0
0
0
0
1
0
1
0
0
0
2
2
0
0
1
0
1
1
0
0
0
1
0
1
2
1
2
2
0
0
0
0
2
1
0
2
1
0
3
1
0
1
0
0
0
0
1
0
0
0
0
1
1
2
0
0
2
0
2
0
0
0
0
0
0
2
0
1
0
1
0
1
1
0
0
1
2
1
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
1
2
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
2
1
0
2
0
1
0
2
0
0
0
2
1
0
0
2
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
2
0
0
0
1
1
1
1
2
0
1
2
0
0
2
1
1
0
2
0
2
2
0
2
0
3
0
2
3
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
1
1
0
2
0
0
0
1
0
0
2
1
0
0
0
2
0
0
1
0
0
0
0
0
2
3
1
0
0
0
2
1
3
1
1
2
0
1
1
0
1
0
2
0
0
1
0
0
0
2
1
0
0
2
2
0
0
1
2
0
0
1
0
0
1
0
2
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
2
2
0
0
1
2
0
0
2
0
1
0
0
0
1
0
0
0
1
0
0
0
2
2
1
0
0
1
0
0
2
1
0
0
1
2
0
0
0
0
1
0
0
2
2
0
0
1
1
0
0
0
2
0
0
1
2
0
0
0
0
2
2
0
0
1
0
1
1
2
0
0
1
0
0
0
0
0
0
0
1
0
0
2
1
1
0
1
0
1
0
0
2
0
2
1
2
0
0
3
0
0
1
0
1
2
0
3
1
2
0
1
0
2
1
1
0
0
2
1
0
1
0
2
1
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
2
0
2
0
0
2
1
2
0
2
0
2
1
0
0
0
0
1
0
0
0
4
0
1
1
0
1
0
2
0
2
1
0
0
2
0
1
0
0
0
0
1
1
0
2
1
2
3
0
0
1
0
1
0
1
2
0
1
1
0
0
0
0
0
2
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
2
1
0
0
1
0
0
0
0
3
0
2
0
2
1
0
4
0
1
0
0
2
1
0
2
2
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
2
1
0
0
1
1
0
1
0
0
2
0
3
1
2
0
1
0
0
0
0
2
0
1
1
0
1
2
0
0
1
0
0
0
0
2
1
1
2
0
2
1
0
1
3
0
1
2
1
0
0
0
1
2
0
1
0
3
0
0
2
0
2
0
1
1
2
0
0
0
0
4
0
1
1
2
2
1
2
2
2
2
0
0
1
0
1
1
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
2
0
2
0
1
0
1
0
0
0
2
0
0
0
0
3
0
0
2
1
1
0
0
2
0
0
0
0
1
0
2
0
3
0
2
0
1
2
0
0
1
0
2
2
0
0
0
0
2
2
2
0
1
0
1
0
1
0
1
1
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
1
0
0
0
2
0
0
1
0
4
0
0
1
0
2
0
0
0
0
0
0
0
5
2
2
0
0
0
1
0
2
2
2
2
1
1
0
1
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
1
0
0
2
0
2
0
0
2
2
2
0
2
0
0
2
2
0
0
0
0
2
1
0
0
1
1
2
2
1
0
0
2
0
0
1
0
0
0
3
0
0
0
0
1
1
0
2
2
2
0
0
0
2
0
0
0
0
1
2
1
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
2
0
0
1
1
0
2
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
2
2
0
0
1
2
2
0
1
0
2
2
2
0
1
1
2
1
0
0
0
0
0
2
0
0
0
2
0
2
2
1
0
0
0
0
1
0
1
1
2
0
4
2
0
0
2
0
0
2
0
1
0
0
0
0
0
2
0
0
1
2
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
2
2
0
2
0
0
0
0
2
0
2
2
0
0
1
0
1
2
0
1
1
0
2
0
2
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
2
0
2
0
2
0
1
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
1
0
0
1
0
0
1
1
0
1
0
0
0
3
1
0
2
1
0
0
2
0
1
0
1
2
0
0
3
0
0
0
0
0
0
0
0
0
1
3
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
1
0
0
2
0
1
0
2
0
0
0
0
2
0
2
1
0
2
0
1
2
0
0
2
0
1
0
1
0
1
0
0
0
3
1
0
1
2
0
1
0
2
1
0
0
0
1
2
0
0
0
1
0
1
2
0
0
0
1
0
1
1
0
2
0
2
0
2
2
0
0
2
0
0
3
0
2
1
0
1
0
0
0
0
0
0
0
2
0
0
2
0
2
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
4
3
0
1
0
3
0
1
0
0
0
2
2
0
1
1
1
1
0
2
0
0
0
3
1
0
0
0
0
2
1
2
2
2
1
0
2
0
0
0
0
1
2
0
2
1
0
1
0
0
0
2
0
2
0
0
0
0
1
2
0
1
1
0
0
0
0
0
2
0
1
0
1
0
0
2
0
2
0
0
0
0
0
0
1
2
0
2
1
0
1
2
1
0
0
0
0
2
0
2
2
0
2
0
1
0
0
2
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
4
0
0
2
0
1
0
1
0
3
2
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
2
0
2
0
1
2
2
1
2
0
0
1
0
0
0
0
3
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
1
1
2
3
2
0
1
0
1
1
0
0
0
0
0
0
1
1
2
2
0
0
1
0
1
2
0
0
1
0
0
0
1
0
0
1
2
1
1
0
2
2
1
0
2
2
0
0
0
2
0
0
0
2
0
2
2
2
0
2
0
0
2
1
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
2
2
0
1
1
2
2
0
2
1
0
0
1
0
3
0
1
0
1
0
3
2
1
0
2
0
0
1
2
0
0
0
1
0
1
0
0
3
1
0
0
0
0
1
0
1
0
1
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
1
1
0
0
2
0
0
0
0
2
0
1
2
0
1
0
0
0
1
2
0
0
0
0
0
1
2
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
1
0
2
2
1
0
2
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
2
2
0
0
0
0
2
1
2
2
0
0
1
0
1
0
1
1
2
0
0
0
2
1
1
0
2
0
0
0
1
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
2
2
0
1
0
1
0
2
0
0
1
0
1
0
0
1
0
2
0
0
2
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
1
0
1
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
2
0
0
1
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
1
0
0
4
2
1
1
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
3
0
0
3
1
1
0
1
2
0
0
0
2
0
0
0
0
0
1
1
1
1
1
0
2
1
0
3
2
0
2
0
0
0
0
0
1
0
1
1
2
0
0
0
2
1
0
0
0
0
2
0
2
1
1
0
2
2
0
0
0
0
1
2
2
0
0
1
0
2
2
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
1
2
0
1
0
0
2
0
2
1
1
0
0
1
0
2
1
0
2
0
1
0
0
0
1
0
0
1
0
0
2
2
0
1
0
0
0
1
0
0
0
0
0
0
0
4
0
0
2
0
1
2
0
1
2
0
0
0
2
0
1
1
2
2
0
0
1
0
1
0
1
0
2
0
0
0
0
1
3
2
0
2
0
1
3
2
1
0
0
0
0
2
0
1
0
2
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
1
0
3
0
0
0
0
2
0
1
0
2
0
1
1
1
2
0
1
0
1
0
2
0
2
2
0
0
1
0
0
1
1
0
0
0
0
0
1
1
0
0
1
0
1
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
5
1
0
1
1
2
2
0
0
0
2
0
0
1
0
1
0
0
2
0
0
2
0
2
1
0
0
1
0
0
0
1
0
2
1
0
0
0
1
1
1
0
0
1
1
0
0
0
0
0
2
1
2
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
2
1
1
0
0
2
0
0
1
0
0
0
1
0
0
0
0
2
3
2
0
2
0
1
0
0
0
0
0
1
0
1
2
2
0
0
3
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
1
3
0
0
1
1
2
0
1
0
0
0
0
0
1
0
2
0
1
2
1
0
0
1
1
0
0
0
0
1
1
0
0
2
1
2
1
1
2
0
0
0
0
1
0
3
1
0
1
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
1
1
2
0
0
1
0
2
1
2
0
0
2
0
0
0
0
0
0
0
0
3
0
0
1
1
0
0
1
0
1
1
1
0
0
0
0
1
0
2
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
4
2
2
0
0
0
0
1
0
1
0
0
0
0
0
2
1
1
0
0
0
2
0
2
2
0
0
2
0
0
0
0
0
7
0
2
0
0
0
2
1
1
0
0
1
2
0
0
0
0
0
2
0
2
2
2
0
0
0
4
2
0
2
0
4
0
1
0
0
0
2
0
1
0
2
0
0
0
2
0
0
2
0
1
1
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
1
0
0
2
0
0
0
2
0
2
0
3
0
0
0
1
1
2
0
0
0
0
0
2
1
0
0
1
2
3
1
0
1
0
0
0
0
2
0
1
0
0
2
0
1
0
0
0
0
2
0
1
0
0
0
1
1
0
1
0
2
1
0
1
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
1
0
0
2
0
0
1
1
0
0
0
1
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
1
2
1
0
1
2
0
1
0
0
0
1
0
1
2
2
0
0
0
0
0
1
2
0
1
3
2
0
1
0
0
0
2
0
1
0
4
0
0
0
2
1
1
0
1
1
2
1
0
0
0
1
0
0
0
1
1
2
0
1
0
1
2
0
2
2
1
1
2
0
0
1
0
2
1
1
0
1
0
0
0
1
0
0
1
2
0
2
2
0
2
1
3
0
3
0
2
0
0
0
0
1
0
0
0
0
2
2
2
1
0
1
0
0
1
0
0
2
0
3
1
0
2
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
1
1
0
0
0
1
2
2
0
3
0
0
1
1
2
2
0
0
2
0
0
0
0
0
0
2
0
0
2
2
0
2
0
2
1
0
1
0
2
1
2
0
2
0
1
0
2
0
0
2
1
0
0
1
0
0
2
0
2
0
0
0
0
1
0
1
2
0
0
1
0
1
0
2
2
0
0
1
1
0
2
0
0
2
0
0
1
0
0
1
2
1
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
2
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
2
2
0
0
0
2
2
0
0
1
0
0
0
0
1
2
0
1
0
2
0
0
0
1
0
0
0
4
0
2
0
0
2
0
0
1
1
0
0
0
2
0
0
1
1
1
0
0
0
0
0
0
2
0
2
0
1
4
0
0
0
0
0
0
1
0
0
2
0
2
1
0
0
3
0
0
0
0
0
0
3
2
2
0
1
1
0
1
2
0
1
2
1
0
0
0
0
0
2
2
0
2
0
1
1
0
0
0
1
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
1
1
0
0
0
2
2
1
0
0
0
0
2
2
2
1
0
0
0
1
2
1
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
2
0
0
1
0
0
0
2
0
1
0
1
0
2
0
1
1
0
1
0
0
2
2
0
0
0
1
2
0
1
0
0
0
2
0
0
2
0
0
0
0
0
1
2
0
2
0
2
0
2
0
3
1
2
0
0
0
0
0
0
0
0
0
2
1
1
0
2
1
0
0
2
0
2
0
0
0
0
0
0
0
2
0
2
1
0
2
0
3
0
1
2
1
0
1
1
1
1
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
1
0
2
0
2
2
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
1
0
0
0
1
0
1
0
1
2
0
1
0
0
0
0
0
0
0
0
2
3
2
2
2
0
0
0
0
0
2
0
1
0
2
0
2
0
1
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
1
3
0
0
0
0
0
0
0
0
0
0
0
1
0
1
6
0
1
0
1
0
0
0
0
1
1
0
0
0
2
0
0
2
0
1
2
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
2
0
0
2
2
0
1
0
0
0
0
0
0
2
1
0
0
2
0
0
0
3
0
1
1
0
1
0
1
0
0
0
0
1
1
2
0
0
0
0
0
2
0
0
0
2
0
1
2
1
0
0
1
0
0
0
1
0
1
2
0
0
0
2
2
0
0
1
0
0
2
0
2
1
3
0
1
2
0
1
0
1
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
2
0
2
0
0
3
2
1
0
0
0
1
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
2
1
1
0
0
1
0
0
0
1
2
2
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
2
2
1
2
0
2
0
0
2
0
0
0
1
0
0
3
2
0
1
2
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
2
1
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
2
2
0
2
0
0
1
1
2
0
0
2
0
3
0
0
2
0
2
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
2
0
0
1
2
0
0
0
1
2
0
0
0
2
4
2
1
1
0
0
1
0
0
2
1
2
0
1
0
2
2
0
0
0
2
0
0
2
1
2
0
0
0
0
0
2
0
0
0
0
1
2
0
0
2
4
0
2
4
0
1
2
1
1
1
2
1
2
0
0
0
0
0
1
0
0
1
2
0
2
2
1
0
2
0
0
2
2
0
0
1
2
0
0
0
0
0
0
0
3
2
0
0
0
0
1
2
0
0
0
0
3
1
0
2
1
0
2
5
0
0
0
0
2
2
3
0
1
0
0
2
0
0
1
0
1
2
0
1
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
1
1
0
2
2
0
1
2
1
1
0
0
0
0
2
0
0
1
0
0
0
1
0
3
0
2
2
0
0
1
0
2
2
1
0
1
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
3
0
1
0
0
0
0
2
2
0
2
0
0
1
0
1
2
1
1
2
1
2
1
2
0
0
0
1
2
0
0
0
0
2
0
0
0
2
0
2
2
0
2
1
0
2
0
0
0
1
1
2
5
1
0
0
1
0
0
0
0
1
0
0
0
0
2
1
0
2
1
1
0
2
0
3
2
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
2
1
0
0
1
2
1
0
0
0
0
1
0
0
0
2
0
0
1
2
0
0
0
0
1
1
0
0
0
0
2
0
2
0
0
0
2
1
0
0
0
1
0
2
0
2
2
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
2
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
2
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
3
1
0
2
0
0
1
2
0
0
24
1
2
0
0
0
0
1
0
0
1
0
1
0
2
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
1
0
0
0
0
2
1
0
2
0
0
1
1
2
1
0
1
0
1
1
1
2
1
1
0
2
0
3
0
0
0
2
1
2
0
0
0
2
1
0
0
0
1
0
2
0
2
0
0
0
2
1
0
1
1
2
0
0
0
0
0
1
0
0
0
2
2
0
0
1
0
0
2
2
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
1
0
1
0
0
0
2
0
2
0
0
0
2
0
3
1
1
2
1
1
1
1
0
3
0
1
0
0
0
3
0
2
2
1
0
1
4
0
2
0
1
0
0
2
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
1
0
1
2
0
0
0
0
0
2
0
0
0
2
1
2
0
0
0
13
1
0
2
0
0
3
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
4
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
1
1
0
0
1
0
2
0
0
1
0
2
0
0
1
0
4
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
1
1
0
2
2
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
2
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
2
1
0
2
1
1
2
2
1
2
1
2
0
3
0
2
1
0
0
0
1
0
1
1
2
0
0
0
3
1
0
1
0
2
0
0
0
0
2
0
0
0
0
0
2
0
1
1
3
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
2
0
0
0
0
2
0
0
1
0
0
2
2
0
0
0
2
1
0
0
1
0
0
1
2
0
2
2
0
0
2
2
1
0
1
0
1
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
1
1
0
0
1
0
2
2
0
2
0
0
1
1
0
1
0
1
0
2
0
2
0
2
1
1
0
1
0
0
1
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
2
0
0
2
2
0
1
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
4
1
0
0
0
0
0
3
0
1
0
2
0
0
2
0
2
2
0
2
0
2
0
2
0
0
1
0
1
0
0
0
0
0
2
0
0
2
1
0
0
0
1
0
0
0
1
1
1
2
0
0
2
1
1
0
0
0
2
1
2
0
0
2
0
1
0
0
1
0
0
0
0
1
1
1
1
0
0
0
0
0
1
0
0
0
0
2
3
0
1
2
0
2
0
0
0
1
2
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
2
0
0
0
1
0
1
0
2
0
0
0
1
1
0
0
1
2
2
0
0
1
1
0
0
0
0
2
1
0
2
0
0
0
2
1
0
0
0
2
2
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
2
0
2
0
1
0
0
0
0
3
2
2
0
0
2
0
0
1
0
0
0
2
1
0
0
1
2
0
0
2
0
1
0
0
0
1
0
1
1
0
0
0
1
2
1
0
0
1
0
0
1
0
2
2
0
0
0
0
0
1
0
1
2
2
2
0
2
0
0
1
4
0
0
2
0
2
2
1
0
0
2
0
0
1
0
1
0
0
1
0
2
3
1
2
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
1
2
3
0
0
0
0
0
1
0
0
2
0
1
2
0
0
0
0
0
0
0
1
2
0
0
0
1
0
1
0
0
2
0
0
4
2
0
2
1
1
0
2
0
1
0
0
0
0
2
0
2
0
0
1
0
0
1
0
0
0
2
1
0
0
1
2
1
0
2
0
0
3
1
2
2
1
1
0
2
2
0
1
2
2
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
2
1
0
0
0
0
1
0
0
0
2
0
2
1
1
3
0
2
0
2
2
0
0
0
0
0
2
0
0
1
2
0
0
0
0
2
0
3
0
0
1
0
0
1
1
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
1
1
0
0
2
0
1
1
0
0
0
0
0
2
0
0
0
0
1
0
2
2
2
2
0
1
0
1
0
2
0
0
0
0
2
0
1
1
0
2
0
1
0
0
0
0
0
0
2
0
1
0
2
0
0
1
0
0
2
0
2
1
0
0
0
2
2
1
2
1
0
1
1
0
1
0
2
0
0
2
0
2
2
2
0
1
1
2
0
2
2
0
0
1
0
2
1
0
0
0
0
2
2
0
2
4
0
1
1
1
0
0
1
0
0
1
0
1
2
0
0
1
2
0
0
0
2
0
0
2
1
1
1
0
0
3
1
1
0
1
0
1
0
0
2
0
0
0
0
2
0
0
3
0
0
1
0
0
2
0
0
2
1
2
0
2
1
2
0
0
0
2
0
0
3
1
0
1
2
1
0
2
2
0
0
2
0
2
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
1
1
0
0
0
2
2
1
1
0
6
2
0
0
0
0
0
0
0
0
2
2
1
2
0
0
0
0
0
1
0
0
3
2
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
1
1
1
3
4
0
0
2
0
0
2
0
2
2
0
0
0
3
0
0
0
0
0
0
2
2
1
2
1
0
1
0
2
1
0
0
0
0
2
0
0
1
2
0
0
0
0
0
1
1
1
1
0
0
2
1
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
1
0
2
0
0
0
0
2
0
2
1
0
0
1
0
0
0
0
1
1
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
2
2
0
0
1
0
0
0
0
0
0
2
2
1
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
3
0
0
0
1
0
0
1
2
0
0
0
1
0
0
0
1
0
0
1
0
0
1
2
0
0
0
0
2
0
0
2
1
0
2
1
0
1
1
0
0
0
1
2
0
0
0
0
0
0
3
0
1
1
0
0
0
0
0
1
0
1
0
2
0
2
0
0
0
0
0
1
0
5
0
2
0
0
1
1
0
0
2
0
0
2
2
0
0
0
0
2
0
0
0
0
3
0
0
1
0
0
0
0
0
1
1
1
2
0
2
0
0
1
1
0
0
2
0
0
0
1
0
0
1
0
0
0
1
2
0
0
2
0
0
1
2
1
0
1
1
0
3
1
0
2
2
0
0
0
2
0
2
1
0
0
0
0
1
0
0
1
2
0
3
0
0
0
0
1
0
0
0
0
3
2
0
3
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
1
0
1
2
1
0
2
0
0
0
0
0
2
3
1
5
2
0
0
0
0
1
0
0
1
0
2
0
1
0
1
0
0
2
0
0
0
0
0
2
0
1
0
1
3
0
0
0
0
2
1
0
0
0
0
0
1
0
1
0
1
0
0
2
1
0
0
1
0
0
0
0
0
0
0
1
2
1
0
1
2
2
0
0
2
0
0
2
0
0
1
1
2
0
0
0
0
2
0
0
0
0
0
2
0
0
3
1
1
2
0
0
0
0
2
2
2
0
0
0
0
0
0
1
0
2
2
3
2
1
0
1
4
1
0
0
0
0
1
0
0
0
0
0
0
0
0
3
1
0
0
0
0
2
0
2
0
0
0
0
4
0
1
0
0
2
2
0
2
2
2
1
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
3
3
0
0
0
2
0
0
2
0
0
0
0
1
2
0
1
0
0
0
0
0
1
0
0
2
0
2
1
0
0
0
0
1
2
2
2
1
2
0
0
0
0
1
0
2
0
1
0
0
0
3
0
1
0
1
0
1
1
3
1
1
0
0
2
3
2
2
1
0
0
1
2
0
0
0
0
1
0
4
0
2
0
2
2
0
0
1
2
0
0
0
0
0
0
0
0
1
0
3
0
1
0
2
2
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
2
0
0
2
0
2
0
0
0
1
1
0
2
2
0
0
2
1
2
0
0
0
0
1
0
0
3
3
0
0
2
0
0
1
0
0
0
2
2
2
1
0
2
0
2
0
2
0
2
0
0
0
2
2
0
2
0
2
0
0
0
0
2
0
1
0
0
2
0
1
0
0
2
1
0
0
2
0
1
0
0
2
0
1
0
0
1
1
0
2
2
0
0
0
0
0
1
0
0
2
1
0
0
0
1
1
0
0
0
1
0
2
0
1
0
0
0
0
1
2
2
1
2
1
0
1
0
0
1
0
0
1
0
1
1
0
1
0
2
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
2
1
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
1
2
0
0
0
0
4
0
0
0
0
0
0
0
3
0
1
2
0
1
0
0
0
0
4
0
0
2
2
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
2
1
1
0
0
0
0
0
0
1
1
2
2
1
0
2
0
2
2
1
0
2
1
0
0
1
0
1
0
0
0
2
2
0
1
0
1
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
2
1
2
0
2
1
2
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
2
0
2
0
0
0
1
0
0
1
2
0
0
0
0
0
1
0
0
3
1
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
1
0
2
0
0
0
1
0
0
0
2
0
1
0
1
1
0
0
0
0
2
1
0
0
0
1
1
2
3
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
2
0
0
2
6
0
0
2
0
0
1
1
1
2
1
1
0
0
1
0
0
0
0
0
0
0
1
2
0
2
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
1
0
2
0
0
1
1
0
2
2
2
0
1
0
0
2
0
0
0
0
1
2
1
0
2
0
0
1
1
0
2
0
0
2
1
1
2
0
1
3
2
0
0
0
0
0
0
0
1
0
2
0
2
0
2
0
0
0
1
0
0
0
5
1
0
2
0
2
0
0
0
1
0
2
0
2
2
1
1
0
2
2
0
0
0
4
0
3
0
0
0
0
0
1
1
0
1
0
0
0
2
0
0
0
2
1
0
0
1
1
0
0
0
0
2
0
0
2
0
1
0
4
0
0
0
0
0
1
0
0
0
2
1
2
0
0
0
0
2
0
0
0
1
0
0
0
1
0
1
1
0
2
0
0
2
1
0
0
0
0
0
0
2
3
0
0
0
1
2
2
0
0
1
0
1
1
0
0
0
1
2
0
0
0
0
1
0
2
2
1
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
4
0
0
2
1
0
1
0
2
0
1
2
0
2
1
0
0
0
0
0
0
5
0
0
0
3
0
0
2
0
1
0
0
0
1
2
0
2
0
0
0
0
2
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
2
2
0
2
0
0
0
0
0
0
0
0
0
1
1
1
0
0
2
2
0
3
0
0
1
2
0
1
1
2
2
0
2
0
0
0
1
2
0
0
0
1
0
0
0
0
1
0
2
0
0
2
1
0
0
2
2
0
1
0
1
1
0
2
0
0
0
2
0
0
1
0
0
0
0
1
0
0
3
0
1
0
0
0
1
0
0
0
0
2
1
1
1
2
2
2
0
1
0
0
2
1
2
0
0
0
2
2
0
1
2
0
2
0
0
0
0
2
1
2
1
0
0
0
0
1
17
0
0
1
1
0
0
0
0
0
0
0
0
0
1
7
1
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
1
2
0
0
0
1
2
1
2
0
0
0
0
2
1
0
0
0
1
3
1
0
0
1
2
0
1
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
1
0
2
1
1
0
0
0
0
1
0
0
0
2
0
1
2
1
0
0
1
0
0
1
2
2
1
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
2
0
0
1
1
0
3
0
1
1
0
1
0
0
1
2
0
0
2
1
2
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
1
0
2
0
0
0
2
0
0
1
0
2
1
0
0
0
2
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
1
0
0
0
0
2
2
0
0
0
1
0
0
2
0
1
0
2
0
0
0
3
1
1
1
0
1
1
0
2
3
1
1
0
1
0
2
0
0
0
0
0
2
1
0
0
0
0
1
0
0
2
1
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
1
1
2
2
0
1
0
2
0
1
2
0
0
1
0
2
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
1
0
1
2
0
1
2
1
2
1
0
0
0
0
2
0
0
0
1
0
1
1
0
3
0
1
0
0
0
1
0
0
0
4
0
0
0
0
0
2
0
0
0
0
1
0
1
2
2
0
0
0
0
0
0
1
0
0
0
0
2
1
1
2
0
0
0
0
1
1
0
1
0
2
1
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
2
0
0
0
0
1
0
3
0
1
0
0
1
1
1
0
0
0
1
0
0
2
1
0
0
0
1
0
2
0
1
0
0
0
2
0
2
2
2
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
1
2
1
0
1
0
1
0
0
0
0
0
3
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
1
0
1
2
1
0
0
1
1
2
0
1
0
2
0
3
2
0
0
1
0
2
0
2
0
2
3
0
2
0
2
2
0
0
0
3
2
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
2
0
2
2
1
0
1
1
0
0
1
1
0
0
2
0
1
0
1
0
0
0
1
4
0
0
1
0
0
0
0
1
0
1
2
0
0
1
3
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
3
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
1
0
1
1
0
2
0
0
0
0
0
1
0
1
0
0
2
1
0
0
0
0
0
2
0
2
0
0
0
0
1
2
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
1
0
2
0
1
1
0
3
1
0
0
0
2
3
0
0
0
0
4
0
0
0
2
0
0
0
0
0
1
1
1
0
2
0
1
3
2
3
1
0
2
0
0
2
0
1
0
0
2
0
0
0
0
0
1
2
0
2
2
0
2
0
2
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
4
0
1
0
1
0
0
0
2
0
0
0
2
0
0
0
1
1
1
0
2
0
0
2
0
0
0
0
0
0
0
2
0
1
2
0
0
1
0
0
2
0
1
1
2
0
0
0
0
2
0
1
1
0
2
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
2
1
2
0
1
1
0
1
0
1
0
1
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
1
2
1
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
3
0
0
0
0
0
0
1
0
1
2
0
0
2
0
0
1
0
2
0
2
1
1
0
0
2
0
5
1
0
0
0
2
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
3
2
0
1
0
0
1
0
1
2
0
0
0
0
1
2
0
1
1
0
0
1
1
1
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
2
1
11
0
0
3
0
1
1
0
0
0
0
2
0
1
0
2
0
2
0
0
0
0
1
0
1
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
1
0
2
0
0
2
1
0
0
0
0
0
1
0
2
1
1
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
1
1
0
0
2
0
1
0
1
0
0
0
0
0
2
1
0
2
0
1
0
1
1
0
0
1
0
0
1
0
0
1
0
2
0
2
0
2
1
1
1
0
2
1
0
0
1
0
0
0
2
0
1
0
2
0
0
1
0
0
0
0
1
0
2
0
0
1
0
4
0
1
1
0
2
2
0
0
1
0
0
1
0
2
1
2
0
0
1
0
1
1
0
0
1
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
1
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
3
0
0
0
1
0
0
0
2
1
0
0
0
1
1
0
0
0
1
2
2
0
0
2
2
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
1
1
0
0
2
0
0
0
0
0
2
0
0
2
1
1
0
2
1
0
0
0
2
0
0
0
0
0
2
2
0
2
2
0
1
1
1
1
0
0
0
3
0
1
0
1
1
0
2
1
0
2
0
2
0
1
2
0
0
2
1
0
0
0
0
2
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
1
0
0
2
2
2
0
0
2
0
0
4
0
0
0
0
2
0
0
0
0
1
1
2
0
0
0
2
0
1
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
2
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
2
1
2
0
1
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
2
0
0
2
0
0
0
0
1
2
2
2
0
2
1
1
0
0
0
0
3
1
0
1
0
0
0
0
1
1
0
0
0
2
0
1
0
0
0
0
0
1
0
1
0
1
2
1
1
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
1
0
0
0
0
2
0
0
0
1
1
4
0
1
0
0
0
2
2
0
0
0
0
0
2
1
0
2
3
0
0
0
0
0
0
0
0
0
3
0
0
1
2
2
1
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
2
0
2
0
1
1
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
2
0
1
1
2
2
0
0
0
0
0
0
0
1
0
0
0
1
0
3
0
0
0
0
0
2
2
0
2
0
0
1
0
0
0
0
0
0
2
3
0
3
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
3
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
1
0
1
2
0
0
2
2
1
2
0
0
2
0
0
0
0
0
1
1
0
1
0
0
1
0
2
1
0
1
0
0
2
0
1
0
0
1
0
0
0
2
2
1
1
0
0
0
0
2
1
2
2
1
0
0
1
1
0
0
0
2
1
2
0
0
1
0
0
0
0
0
0
2
3
0
2
1
0
0
0
0
1
1
1
0
2
1
0
1
0
2
0
0
2
0
2
0
2
0
2
0
0
1
0
0
0
0
2
1
1
0
0
2
2
2
2
0
0
0
0
0
0
2
0
0
0
1
2
0
1
3
0
0
1
0
0
9
3
0
2
0
1
0
0
0
1
0
0
0
1
0
2
1
1
0
3
1
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
1
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
2
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
1
1
0
2
2
0
0
2
0
0
3
0
2
0
2
0
2
2
0
0
2
0
0
1
2
2
0
1
2
2
2
0
1
1
0
2
0
1
0
0
2
0
1
3
0
0
1
1
0
0
0
0
1
2
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
1
2
1
0
1
2
0
0
0
2
2
2
0
0
1
1
2
0
0
1
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
2
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
2
0
4
0
2
1
1
0
0
0
0
2
1
2
0
1
0
1
2
2
0
0
0
0
0
0
2
1
0
0
0
2
2
0
0
0
1
1
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
1
1
1
0
0
1
2
2
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
1
3
0
2
0
1
1
0
1
0
0
2
0
0
2
0
0
0
0
2
1
3
2
0
0
0
1
0
1
0
2
0
0
0
0
1
0
0
0
0
2
1
1
0
0
0
0
0
1
2
1
0
0
2
0
2
1
0
0
0
0
1
1
3
1
2
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
1
1
0
0
0
0
1
1
2
0
1
0
2
3
0
0
0
0
2
2
0
1
0
0
0
0
0
3
0
1
1
0
1
3
0
0
0
1
2
3
2
1
0
0
0
0
0
1
0
0
0
1
0
2
2
1
0
1
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
3
1
0
2
1
0
2
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
1
2
0
1
2
3
1
2
0
2
0
0
2
0
0
0
0
0
0
2
2
2
0
1
1
2
1
0
0
1
1
0
0
2
0
0
0
1
1
0
0
1
1
4
0
1
2
0
0
0
1
2
0
0
1
0
1
0
0
2
0
0
1
0
2
3
2
1
0
0
2
0
1
0
2
0
1
1
1
2
3
0
0
0
0
0
1
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
1
2
1
1
0
0
2
0
1
0
2
1
2
0
0
1
1
2
4
0
0
1
3
0
0
0
1
0
0
1
1
1
0
0
1
0
2
1
0
1
6
0
0
0
0
2
0
1
0
2
2
0
1
3
1
0
0
0
0
0
2
0
1
0
0
2
0
1
2
1
2
0
2
2
0
3
0
0
2
0
0
2
1
0
2
0
0
0
2
1
0
0
2
0
0
2
1
2
0
0
0
2
2
0
1
2
0
1
0
0
0
2
0
1
3
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
2
2
0
0
2
0
0
0
0
0
1
1
1
0
0
0
1
2
1
1
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
2
2
2
0
0
2
0
0
2
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
1
0
1
2
0
0
0
0
1
0
2
0
0
0
0
2
1
0
0
0
0
2
0
0
2
0
2
0
1
0
0
0
0
2
0
0
2
2
1
0
1
2
0
0
0
0
0
2
1
1
0
0
1
0
1
0
2
0
1
1
1
1
0
0
3
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
1
2
0
1
0
1
1
0
0
0
1
0
0
1
2
2
0
2
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
2
0
1
0
1
2
0
0
1
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
1
2
1
0
0
2
1
0
0
3
0
2
0
0
0
0
2
1
0
1
2
0
0
1
0
0
2
2
0
1
1
1
2
0
0
0
0
2
0
0
1
2
0
2
0
0
1
0
1
0
1
0
0
1
1
0
0
0
0
1
0
0
0
1
0
1
3
0
0
2
2
0
0
0
1
0
2
0
0
0
0
0
2
1
0
0
0
2
0
1
2
0
0
0
0
1
0
0
0
0
0
1
0
0
3
1
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
2
1
1
0
0
0
0
1
3
0
0
0
0
1
0
2
0
0
0
1
2
2
2
0
0
2
2
2
0
0
1
1
1
1
0
0
2
2
0
0
0
0
0
0
0
1
2
1
0
0
0
2
0
1
0
0
0
2
1
1
0
2
0
0
1
1
0
2
1
1
0
1
0
2
2
0
0
1
0
0
0
1
0
2
2
1
0
0
0
0
1
0
0
0
1
2
0
1
1
0
0
0
2
1
0
0
0
0
0
1
1
0
1
1
0
0
0
0
1
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
2
1
0
1
1
0
2
2
1
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
2
1
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
2
0
1
0
0
0
1
0
0
0
1
0
2
1
1
0
0
0
0
1
0
0
0
0
0
2
1
0
0
1
1
0
1
2
0
0
0
2
0
1
1
0
0
0
2
0
0
0
0
0
3
2
3
1
2
1
1
0
1
1
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
2
0
0
2
1
1
2
0
0
1
0
0
0
4
0
0
1
0
2
1
2
1
2
1
0
2
0
0
0
0
3
2
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
3
0
0
0
1
2
3
4
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
6
0
1
0
0
0
0
0
1
1
0
0
1
0
1
0
1
2
0
0
0
0
2
0
0
2
0
2
0
0
2
0
1
0
0
4
0
2
0
0
0
1
0
1
0
0
0
1
0
3
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
1
2
1
0
0
0
2
0
2
0
2
0
0
1
1
1
0
2
2
2
0
0
1
1
0
0
0
0
1
0
0
2
2
2
0
2
1
2
0
1
0
0
2
0
1
1
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
1
0
0
2
2
0
0
1
2
0
0
2
1
0
0
2
1
1
0
1
0
0
0
0
1
1
1
1
1
2
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
2
1
1
1
2
0
0
0
2
0
2
0
0
1
2
1
0
2
1
0
1
0
0
0
1
0
1
0
2
2
1
0
0
0
0
2
2
0
0
1
1
1
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
2
1
0
1
0
1
0
2
0
0
0
0
1
0
0
4
0
3
0
2
2
0
0
0
2
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
1
0
1
2
0
1
1
0
0
0
0
2
1
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
2
1
1
0
0
2
0
0
0
0
0
0
1
0
2
0
1
0
0
1
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
3
0
0
0
2
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
4
1
0
0
0
0
0
0
0
1
0
0
1
0
2
1
1
0
0
1
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
2
0
1
1
1
1
0
0
0
1
4
0
2
0
1
0
0
3
0
0
1
0
1
0
0
0
0
1
2
0
1
0
0
0
2
0
0
1
0
1
0
0
3
0
3
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
1
2
2
0
2
1
0
0
0
0
0
2
2
1
0
0
2
2
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
1
0
0
0
2
0
2
0
0
1
0
2
1
0
2
0
1
2
2
2
0
0
0
0
1
0
0
1
0
0
0
1
0
1
1
1
0
0
1
0
2
0
2
2
1
1
0
0
0
2
0
1
0
0
1
1
0
0
1
1
0
1
0
1
2
2
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
2
0
1
0
1
1
0
2
0
0
0
1
0
0
0
0
0
2
1
0
2
1
2
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
2
0
0
2
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
1
2
1
1
0
1
0
0
0
3
0
0
0
0
0
0
1
0
0
0
1
2
2
0
0
0
0
0
0
0
0
1
2
0
2
1
0
0
0
0
0
0
0
0
0
1
0
2
0
1
2
0
0
0
2
1
2
1
1
0
0
0
0
0
1
0
0
0
0
1
2
0
2
0
1
0
0
0
1
0
0
0
1
2
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
1
0
2
0
2
0
0
0
1
0
0
1
0
0
0
0
2
0
0
2
0
0
0
1
0
2
1
0
0
2
0
1
0
0
0
1
0
2
0
1
2
0
2
0
0
0
2
1
2
0
0
0
1
1
0
0
0
2
1
0
1
0
1
0
0
2
0
2
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
2
0
1
0
1
2
0
0
0
1
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
3
2
1
0
1
2
4
0
0
2
0
0
1
0
0
0
0
2
0
0
3
1
1
1
0
0
1
0
0
0
1
1
1
0
0
0
0
1
1
1
3
0
2
0
2
3
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
1
0
1
0
0
0
0
2
0
0
0
1
1
0
1
1
0
0
0
0
0
1
2
0
2
0
3
0
0
1
0
1
0
0
1
2
2
2
0
2
0
0
1
2
0
0
0
2
0
3
2
0
2
1
1
0
0
0
1
0
0
0
0
2
0
0
1
0
0
1
0
1
0
4
0
0
0
0
1
0
0
2
0
1
0
0
0
1
0
1
1
0
2
0
0
0
1
0
0
2
0
0
0
0
0
2
1
0
0
0
2
0
0
1
0
0
2
1
2
0
0
0
1
0
2
0
1
2
2
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
2
0
1
1
2
2
1
1
0
1
0
0
2
1
0
0
2
1
2
1
0
4
0
1
1
2
1
0
1
0
0
0
2
0
0
0
0
1
0
0
2
2
1
0
1
1
0
1
0
0
2
0
0
2
0
1
0
0
2
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
1
2
1
0
0
2
3
2
0
1
1
0
0
1
0
0
0
2
1
2
0
0
0
0
2
2
0
0
2
0
0
1
0
1
1
2
1
1
0
2
1
0
2
2
0
0
1
0
2
0
0
0
0
1
1
3
0
1
0
0
0
2
0
0
1
1
0
0
3
0
1
0
0
2
0
1
0
2
0
0
2
1
0
0
0
0
0
0
0
1
1
1
2
0
0
0
0
0
0
1
0
1
0
1
0
1
1
2
1
2
0
1
0
0
0
0
1
1
2
0
0
0
1
0
1
3
0
0
1
0
0
2
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
1
0
0
0
1
1
0
2
0
0
1
1
0
0
0
2
3
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
3
1
0
0
0
0
1
1
0
2
0
2
2
0
0
2
1
1
0
0
2
0
0
2
2
1
0
0
0
2
0
0
0
2
2
0
1
0
2
0
2
0
0
1
0
0
2
1
2
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
1
0
0
2
1
0
0
1
0
1
2
2
0
1
0
2
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
4
0
3
1
0
0
0
0
0
0
0
0
2
0
0
0
1
2
1
0
0
2
0
0
0
1
1
1
0
0
1
1
0
0
0
0
0
2
0
0
0
1
3
1
1
0
0
0
0
2
2
0
3
0
0
2
0
6
0
0
1
0
1
0
1
1
2
0
0
0
0
2
2
2
0
0
1
2
0
0
0
0
1
1
0
0
0
2
2
0
0
0
2
0
0
2
0
0
1
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
2
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
1
1
1
1
0
2
1
0
1
1
2
0
2
0
2
0
0
0
1
1
1
1
2
1
1
0
1
2
0
0
0
0
0
0
0
0
2
0
0
1
1
0
1
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
1
0
0
0
5
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
2
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
1
2
1
0
0
0
0
0
0
9
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
2
0
1
0
2
0
0
0
1
2
1
0
2
0
0
1
0
0
0
0
1
0
2
3
0
1
0
0
0
3
0
0
1
2
2
0
0
2
2
2
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
2
0
1
0
2
1
0
0
1
1
0
2
0
1
0
0
0
0
0
2
0
2
0
0
1
0
0
0
1
1
0
0
0
0
2
2
0
1
1
1
0
0
2
0
1
1
0
0
0
0
1
0
2
0
0
0
6
2
0
0
2
1
0
2
0
2
0
0
2
0
2
0
2
0
0
2
0
0
0
0
2
3
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
2
0
0
0
1
0
2
2
2
0
2
3
2
0
1
0
0
0
0
0
1
2
0
0
0
0
2
1
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
2
0
1
1
1
0
1
0
0
0
1
4
2
2
1
0
1
1
1
0
0
0
1
0
0
1
0
0
0
1
2
1
2
0
0
0
3
0
2
0
0
0
0
2
2
0
0
2
0
0
1
1
2
1
0
0
0
0
0
0
0
0
0
2
2
1
2
0
0
0
1
1
0
0
0
0
1
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
1
0
0
0
2
2
0
0
1
0
0
2
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
1
1
0
1
1
1
2
1
0
0
2
0
0
0
1
2
4
2
0
2
0
2
0
0
0
2
0
1
1
2
0
1
0
0
2
0
0
0
0
0
1
0
0
2
0
2
0
0
2
1
0
0
0
1
0
0
0
0
2
0
2
0
2
0
0
0
1
2
1
0
0
3
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
2
0
1
1
0
0
1
3
0
1
0
0
2
2
0
0
0
1
0
2
0
0
1
0
1
0
0
2
0
0
1
1
0
0
0
0
1
0
0
1
0
1
2
0
1
6
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
2
0
0
2
2
2
1
0
1
2
0
0
0
0
1
1
0
1
0
0
0
0
1
2
2
0
1
0
0
0
1
0
0
0
1
0
0
1
2
2
2
0
0
0
0
2
1
0
0
0
0
1
0
0
0
1
3
1
1
0
2
0
1
2
0
0
0
0
2
0
2
0
0
1
1
2
1
0
0
1
0
2
0
2
0
1
0
0
0
0
0
0
3
1
0
0
0
0
1
1
0
0
2
1
0
2
1
1
0
2
0
0
2
2
0
2
1
1
2
0
0
1
0
1
0
1
2
1
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
1
2
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
2
0
5
1
1
0
1
0
0
1
0
0
1
1
0
0
0
2
2
0
0
2
0
0
1
2
0
0
1
1
0
0
0
2
0
0
2
0
1
2
1
2
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
2
0
2
4
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
1
0
0
1
0
1
0
0
5
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
1
1
0
0
0
0
0
1
3
0
1
3
0
1
0
2
2
1
0
0
0
2
2
1
0
0
0
2
2
0
2
0
0
1
0
1
2
0
3
0
2
1
0
1
2
0
2
1
0
1
0
1
1
1
6
0
1
0
0
1
0
0
0
1
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
2
0
1
0
1
1
1
0
2
0
0
0
1
0
1
0
2
0
0
2
0
0
0
1
0
0
2
1
1
0
4
0
2
2
1
2
0
1
2
0
0
0
1
2
2
0
1
0
1
0
2
2
0
0
2
1
1
0
4
0
1
0
2
0
0
2
0
5
0
0
1
0
0
0
0
0
1
1
1
0
0
2
1
1
1
0
0
1
0
1
1
3
1
0
1
0
0
0
0
0
2
2
0
0
0
0
0
1
0
1
2
0
2
1
0
0
1
2
2
0
0
0
3
3
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
3
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
1
2
0
1
2
2
2
0
0
1
1
0
0
1
2
2
0
0
0
0
0
0
0
1
0
0
1
1
0
3
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
2
0
1
0
0
0
0
1
0
1
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
2
2
2
0
1
0
0
1
0
0
0
1
1
1
2
0
0
0
2
0
0
0
1
1
0
1
2
0
3
0
0
1
1
0
0
0
0
0
0
0
1
1
2
0
0
0
0
1
0
0
0
1
0
0
2
1
1
0
1
0
2
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
4
2
1
0
1
1
0
0
0
0
2
1
1
0
1
0
0
0
1
2
2
0
0
0
2
0
1
0
1
2
0
1
0
0
0
0
2
2
2
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
1
2
0
2
4
0
2
0
0
0
1
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
1
1
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
3
0
0
1
0
2
0
0
2
1
2
1
0
2
1
0
3
0
0
1
0
0
0
0
2
0
0
1
0
2
2
0
2
0
1
0
0
2
1
1
0
0
0
0
0
0
0
2
2
0
2
1
0
1
2
2
0
1
2
2
1
1
0
1
0
0
0
0
2
1
2
0
1
0
1
0
2
2
1
2
0
1
0
1
0
1
0
0
1
0
1
0
2
0
0
1
1
0
1
0
0
0
1
1
1
1
0
0
3
0
0
1
0
2
2
1
3
0
0
1
0
2
2
1
0
0
2
0
0
0
1
0
1
0
0
0
2
2
0
0
0
2
0
2
0
1
2
0
0
0
0
0
0
2
2
0
0
2
0
2
2
2
0
2
2
0
0
1
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
3
1
0
1
0
0
0
0
0
0
0
2
0
0
2
0
1
2
0
0
0
0
2
0
0
1
0
2
0
1
0
0
0
0
1
0
0
1
0
0
1
3
0
2
0
0
2
1
2
0
0
0
0
0
2
2
1
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
1
1
0
2
0
2
0
0
0
0
1
2
1
1
0
1
2
0
1
1
5
1
0
2
0
2
1
0
0
1
2
2
1
2
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
3
2
0
0
0
0
1
2
0
2
0
1
0
0
0
0
2
2
0
0
0
1
0
2
1
4
0
1
2
0
0
0
1
2
0
1
0
1
0
2
0
2
2
0
1
2
0
2
0
0
0
0
0
1
0
0
0
0
0
1
2
1
0
0
2
0
2
2
0
2
0
0
0
2
1
2
0
0
0
1
0
0
1
1
1
1
2
0
1
2
2
0
1
2
1
1
2
1
1
0
5
2
2
0
2
1
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
3
0
0
0
2
1
0
0
1
2
0
1
1
3
1
1
0
0
0
2
0
0
0
1
0
0
2
0
1
1
1
1
0
2
0
2
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
2
0
0
1
0
0
2
0
0
2
2
0
0
0
0
1
0
4
2
1
2
1
0
1
2
0
0
0
1
0
0
0
0
2
1
2
1
0
0
0
0
1
3
0
0
0
0
0
1
1
1
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
2
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
2
0
1
1
0
0
1
1
1
0
1
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
1
1
0
0
0
0
2
0
1
1
2
2
2
1
1
0
0
1
1
2
2
0
0
1
2
1
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
2
0
1
0
1
0
0
0
0
0
1
0
0
0
4
1
2
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
2
0
0
2
0
2
2
1
0
0
0
0
1
1
2
0
0
2
0
1
0
0
0
0
2
0
0
2
1
0
1
2
0
2
0
0
0
0
2
1
2
2
2
1
0
0
1
0
3
0
0
0
0
1
0
2
0
0
0
2
0
0
0
2
0
2
0
1
0
2
1
0
1
2
1
0
0
0
0
1
0
0
1
0
2
0
1
0
0
1
1
1
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
3
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
1
0
2
0
0
0
1
0
2
0
0
1
0
3
1
1
0
2
0
0
1
3
0
0
0
0
1
2
0
0
1
0
0
0
2
0
1
0
3
0
0
0
0
0
2
0
0
1
1
2
1
0
0
1
0
0
0
1
2
1
0
1
0
0
2
1
0
2
0
0
1
0
0
0
0
0
0
0
0
1
2
1
0
1
0
0
0
0
3
0
0
0
0
0
0
4
1
0
1
0
1
2
1
0
1
3
1
1
0
1
0
1
0
0
0
1
0
0
1
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
1
2
1
1
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
1
0
1
0
1
0
0
0
2
0
1
0
0
0
1
2
4
0
2
1
1
0
0
0
0
1
0
0
2
0
2
0
0
2
0
2
2
3
0
1
2
2
2
1
1
0
3
0
0
0
2
2
0
2
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
1
2
0
0
0
0
0
1
1
0
1
0
0
2
0
0
2
2
0
2
0
0
2
1
0
2
0
2
0
2
1
1
0
2
1
0
0
0
0
0
1
2
1
2
0
1
1
0
1
2
0
0
0
0
0
0
2
0
0
2
2
1
0
0
3
0
0
1
0
0
1
1
0
0
0
2
1
1
0
0
2
0
0
0
2
0
0
7
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
2
1
0
0
1
2
2
1
2
2
3
2
3
0
0
0
0
0
0
0
0
2
1
1
1
3
2
0
0
0
2
1
0
0
0
1
2
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
1
3
0
0
0
1
0
0
0
1
1
1
0
0
1
1
0
0
1
1
2
0
0
0
0
0
0
0
2
1
2
0
0
0
1
2
2
0
1
0
2
4
0
2
2
0
0
2
0
0
2
0
2
1
0
2
2
1
2
0
1
1
1
0
2
1
2
0
2
2
1
1
0
0
0
0
0
1
3
0
0
0
0
1
1
0
0
0
1
0
0
1
0
2
2
1
0
0
2
0
0
0
2
2
1
2
0
2
2
1
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
2
0
2
1
0
0
0
2
1
0
2
0
0
0
2
0
1
1
0
0
0
0
1
1
1
2
0
0
1
0
0
2
0
0
1
2
1
0
0
0
1
0
1
0
0
0
1
0
2
1
0
2
2
0
2
0
1
0
1
2
0
1
3
0
0
1
0
2
1
0
0
0
0
2
2
0
2
2
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
2
1
0
0
1
1
0
0
1
0
2
0
0
0
2
0
0
0
1
1
4
0
2
0
0
0
2
1
2
0
0
0
2
1
1
0
0
1
0
2
1
2
1
2
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
1
2
2
1
0
3
2
0
2
1
0
1
0
0
0
2
0
0
0
0
0
1
1
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
2
0
0
1
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
1
2
2
0
1
0
0
0
2
0
0
0
2
0
0
1
2
0
0
0
2
0
1
2
0
0
0
2
0
0
1
0
1
0
0
1
1
0
0
0
0
0
1
1
0
0
0
2
0
0
0
2
0
2
2
2
0
1
2
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
1
1
1
1
1
1
0
0
1
1
1
0
2
0
0
2
0
3
2
1
0
0
2
1
2
0
2
2
2
2
1
0
2
2
2
3
0
2
0
0
0
0
3
0
0
0
0
2
1
0
0
0
0
2
0
0
1
0
0
3
1
1
2
2
2
0
0
0
0
0
1
0
2
1
1
1
0
1
2
0
2
0
1
0
0
2
2
1
1
0
2
0
1
1
2
0
0
0
2
1
0
2
0
0
0
0
1
0
0
2
0
0
0
1
1
1
0
0
0
1
2
0
0
0
1
2
2
1
0
0
1
0
2
0
0
0
1
1
1
2
0
2
1
0
0
0
0
0
1
0
1
0
2
0
0
0
1
0
2
1
0
0
2
1
0
2
0
1
0
0
0
1
0
1
2
0
0
0
2
0
0
0
2
0
1
0
0
0
2
2
0
2
1
2
0
0
1
0
0
0
1
0
1
2
0
1
0
0
1
0
0
0
1
0
1
0
2
1
0
0
1
0
1
0
2
1
0
0
1
2
0
2
2
1
2
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
1
2
0
0
0
1
1
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
1
2
1
1
0
0
2
0
2
2
0
0
2
1
2
0
0
1
0
0
1
0
0
3
0
0
1
1
1
0
0
0
1
0
2
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
2
0
2
0
0
2
0
2
1
5
0
1
0
0
2
0
0
0
2
1
0
2
2
0
0
0
0
0
2
0
1
0
0
1
1
2
0
0
0
0
0
1
2
0
2
3
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
1
0
1
0
2
0
2
1
2
0
3
0
1
1
0
5
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
3
2
2
0
1
1
0
0
2
1
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
2
1
1
0
0
0
0
0
2
1
1
1
3
2
2
0
0
1
0
0
1
0
0
0
1
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
1
1
0
0
0
1
1
1
0
0
2
0
0
2
1
2
1
2
0
1
1
0
0
2
2
0
0
0
2
0
2
0
0
0
1
2
1
0
0
2
0
0
2
0
2
0
1
0
2
0
1
2
0
0
0
0
0
0
0
2
2
0
0
3
1
0
0
0
2
0
0
0
1
0
1
0
0
2
0
1
0
0
0
1
6
0
0
0
0
0
2
0
0
0
2
1
0
2
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
3
0
1
2
0
0
1
3
2
0
0
0
2
0
0
0
0
1
1
0
0
2
2
1
0
1
2
0
2
0
0
0
1
0
0
0
2
1
1
0
2
0
2
2
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
2
2
1
0
0
0
0
0
1
0
1
0
0
0
2
0
2
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
2
2
0
1
2
2
0
1
1
0
0
3
5
0
0
1
1
0
1
0
1
0
0
0
1
2
0
0
0
0
1
0
1
1
0
1
0
0
1
0
0
0
2
0
1
0
0
1
0
0
0
1
2
0
0
0
2
0
2
1
0
1
2
0
2
1
0
0
0
0
2
0
0
0
0
1
0
1
0
0
1
1
1
0
0
0
0
4
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
2
0
2
1
2
2
0
4
1
1
0
0
0
0
0
1
0
1
0
2
0
0
0
5
1
0
0
1
0
1
1
0
2
1
1
0
0
0
0
0
0
1
0
2
0
1
0
1
2
2
0
0
0
2
2
0
2
2
2
1
0
1
0
0
0
0
2
1
0
0
2
0
2
1
0
0
0
0
1
0
1
0
0
0
1
2
0
0
0
3
2
0
1
0
1
1
0
0
0
0
2
1
0
2
2
0
1
0
1
0
1
1
0
1
2
0
0
2
2
1
2
1
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
2
1
2
6
0
0
0
2
1
0
0
0
0
0
1
1
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
1
2
1
2
0
2
2
1
0
1
1
0
2
0
0
1
1
2
2
0
0
0
2
1
1
1
1
0
0
1
0
0
0
0
0
2
0
2
0
1
1
2
1
2
2
0
0
0
4
0
0
0
0
0
1
2
1
8
0
0
0
0
2
1
2
0
0
0
0
0
1
1
0
0
0
2
1
0
1
0
1
0
1
0
0
0
0
0
0
1
0
1
2
0
0
1
0
0
0
2
0
0
1
0
1
0
1
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
2
0
1
0
0
0
1
0
0
0
1
2
0
2
0
0
0
0
2
6
2
1
0
0
0
0
0
0
2
2
0
2
1
0
1
0
1
0
1
0
0
1
0
1
1
0
2
0
2
2
0
1
0
0
0
3
0
0
1
1
0
2
0
0
0
0
1
0
0
3
0
1
2
0
1
0
0
1
0
2
0
0
1
8
2
2
0
2
2
0
1
0
1
0
1
1
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
5
0
0
0
0
3
0
0
2
0
0
0
0
1
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
2
3
0
1
2
1
0
0
1
2
1
2
1
0
0
0
1
10
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
2
1
2
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
1
0
1
0
0
0
2
1
2
0
1
3
2
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
2
0
1
2
0
1
1
0
0
2
0
0
0
1
0
0
0
3
1
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
2
1
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
2
0
0
2
0
0
2
1
0
0
0
0
0
1
0
0
1
1
0
0
1
1
1
2
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
2
0
2
0
4
0
0
2
0
1
1
0
2
0
0
1
1
2
2
1
0
1
0
0
0
2
0
0
0
2
0
1
0
0
1
2
0
0
1
2
0
2
0
2
1
1
3
0
3
0
1
0
2
0
1
0
0
0
0
2
0
0
1
0
3
0
2
2
0
0
0
2
0
2
0
0
1
1
0
1
0
0
2
2
2
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
4
0
0
0
0
1
0
2
2
0
1
1
2
1
0
0
0
0
1
0
2
2
1
0
2
2
2
0
1
2
1
2
1
1
0
1
0
2
0
1
0
0
1
0
0
0
0
1
0
0
0
2
0
0
1
0
2
0
0
0
1
2
1
0
1
1
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
2
0
0
0
1
0
1
3
2
0
0
0
2
0
2
1
1
0
2
0
0
1
1
0
1
1
0
0
0
2
1
0
0
0
0
1
2
0
0
0
0
2
3
0
0
2
0
0
0
1
0
0
3
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
2
1
1
0
2
1
0
0
0
1
0
0
5
0
2
0
0
0
1
0
0
0
0
0
0
1
2
1
0
0
1
1
2
0
1
1
0
1
0
0
1
1
3
0
0
0
2
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
2
2
0
2
2
1
0
0
0
0
1
0
1
0
0
0
0
1
1
2
0
2
0
2
0
2
2
0
0
0
2
0
2
0
3
0
0
2
0
0
2
0
2
0
4
1
2
0
0
0
1
2
1
0
0
0
0
2
2
0
0
2
0
0
0
1
0
2
0
2
0
0
1
2
2
1
2
0
1
0
0
0
2
1
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
2
0
0
0
1
0
0
2
1
0
0
0
0
0
0
1
0
0
0
2
2
0
0
2
0
1
0
0
0
2
2
0
0
1
0
2
1
0
2
2
0
0
0
1
2
1
0
0
0
1
0
0
2
0
0
1
0
2
0
1
0
1
2
2
1
0
0
0
0
0
0
0
0
3
0
0
2
0
0
1
0
1
0
2
0
0
0
0
0
0
1
0
5
1
0
0
0
2
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
3
0
0
3
0
0
1
2
0
0
0
0
2
2
1
0
0
0
0
0
1
1
0
2
1
0
0
0
2
2
0
0
0
1
1
2
0
0
0
2
0
0
0
2
1
0
2
2
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
1
1
0
0
0
0
2
1
1
2
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
1
0
2
1
2
0
3
2
1
2
1
0
2
0
0
3
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
3
0
1
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
2
0
0
2
0
1
3
1
2
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
1
3
1
0
0
0
3
0
0
0
0
2
2
1
1
0
0
0
0
2
0
0
0
0
0
0
1
2
3
0
0
0
2
2
0
0
2
0
0
1
0
0
0
0
0
0
0
2
2
1
0
0
2
0
0
1
1
2
0
0
0
0
0
0
1
1
1
1
1
0
1
2
0
2
0
1
0
0
0
0
1
0
0
2
0
0
3
1
0
0
1
0
0
0
1
1
2
0
0
2
0
2
0
0
1
1
0
1
5
1
0
0
1
0
0
3
0
1
1
0
0
0
0
1
0
2
1
0
1
2
2
1
2
2
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
3
2
0
1
0
0
1
3
0
3
0
1
2
0
2
2
3
2
1
0
0
0
1
0
0
0
2
2
2
0
0
0
2
0
0
2
0
1
0
2
0
0
1
0
2
0
0
1
0
0
1
3
1
1
1
0
1
0
0
0
1
1
1
0
1
0
0
0
0
0
0
1
0
1
0
2
1
0
1
0
0
0
0
0
0
2
0
1
0
2
0
0
4
2
0
1
0
0
0
0
0
0
0
4
0
1
0
0
0
1
0
0
0
1
0
0
0
2
0
1
1
1
2
0
1
1
0
0
0
2
0
1
1
0
2
0
0
0
1
0
1
1
0
0
2
0
0
0
1
0
0
1
1
0
1
2
0
0
0
3
2
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
1
0
2
0
2
1
1
2
1
0
1
0
0
1
0
1
0
1
0
0
0
0
2
0
0
0
1
0
1
0
1
1
0
0
0
1
2
0
0
0
2
0
0
2
1
0
2
0
0
0
0
0
0
0
0
1
0
2
2
0
2
0
0
0
2
1
0
1
1
2
1
0
0
0
0
0
1
0
0
2
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
2
2
0
2
1
2
0
0
2
5
0
2
2
0
0
0
1
0
0
0
2
0
0
0
0
0
3
0
1
0
2
0
0
1
2
0
0
0
2
0
0
3
1
0
1
0
1
2
0
0
2
0
0
1
0
1
2
0
1
0
0
2
0
0
1
0
2
1
0
0
0
0
1
0
1
0
2
2
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
1
0
0
2
0
4
0
1
0
0
2
1
2
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
1
0
2
1
2
0
2
3
0
0
0
2
0
1
1
2
0
2
0
0
2
1
0
0
0
0
0
0
1
1
1
1
2
0
0
2
0
2
1
0
0
2
2
0
0
0
0
0
0
0
2
2
0
2
2
0
1
1
3
0
2
0
2
0
0
1
0
1
1
0
0
0
1
1
0
0
2
0
0
2
0
3
0
0
2
2
0
1
1
0
0
0
0
0
0
0
0
2
0
1
2
1
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
1
2
2
1
0
0
0
0
1
0
1
1
0
1
1
0
1
0
0
2
2
3
0
0
0
2
0
1
0
0
0
0
2
0
0
0
1
2
0
0
0
1
2
0
1
0
0
2
0
3
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
2
1
1
1
3
1
0
0
0
2
0
0
0
1
0
0
0
1
0
3
0
2
0
0
1
0
1
2
1
1
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
1
2
2
0
2
2
1
1
1
2
2
3
0
1
1
0
1
3
1
0
0
2
1
1
2
0
2
0
0
0
2
2
0
0
0
0
0
0
2
2
0
1
2
0
0
2
1
3
0
1
0
2
0
1
0
0
2
0
2
0
0
0
0
0
0
2
1
0
0
2
0
1
2
1
1
0
0
0
0
1
0
0
2
1
0
0
2
0
1
2
1
4
0
0
2
0
0
1
1
0
2
1
1
0
1
0
2
0
1
0
2
0
0
0
0
0
1
1
2
0
0
1
0
2
0
0
0
1
0
0
0
0
0
1
2
0
3
0
0
0
0
0
0
2
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
2
1
1
2
1
0
0
0
0
1
0
2
1
1
2
1
1
0
2
0
1
1
0
0
0
2
2
0
0
0
0
0
1
0
2
0
3
0
2
0
0
0
0
0
1
2
0
0
4
0
0
0
0
0
0
0
0
2
1
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
2
1
0
0
0
1
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
2
2
0
1
0
0
0
0
1
0
2
0
4
0
2
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
2
0
1
0
1
2
1
0
1
1
0
0
0
1
1
0
0
0
0
1
1
0
0
0
3
0
2
0
0
0
2
1
0
0
0
1
2
2
2
0
4
1
1
0
0
2
1
1
0
2
2
2
0
1
0
1
1
2
0
4
0
0
0
2
0
0
0
0
0
0
0
2
2
1
0
0
1
1
2
0
0
0
1
1
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
4
0
1
0
3
1
0
1
0
0
1
0
0
0
0
2
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
2
0
1
0
1
2
0
0
0
0
0
1
2
1
1
0
2
0
1
0
2
0
1
1
0
0
0
0
0
2
1
1
0
0
2
0
1
1
0
0
2
0
0
0
0
0
0
0
3
0
0
2
0
0
0
2
0
0
0
1
5
0
1
0
0
1
0
2
2
1
1
2
1
0
0
0
0
0
0
0
2
1
2
1
1
1
2
2
0
0
0
0
0
1
0
0
0
1
2
0
0
0
2
0
0
1
0
0
1
2
2
0
0
1
0
1
0
2
0
0
2
0
0
0
0
2
0
0
2
2
2
0
2
0
0
2
0
2
0
2
2
2
2
1
2
1
0
0
0
2
1
0
0
6
1
0
0
0
2
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
2
1
2
0
1
0
0
0
1
1
0
0
0
0
1
6
0
4
0
2
3
0
1
2
1
2
0
2
2
0
3
0
0
0
0
2
0
1
1
2
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
4
2
4
0
1
0
0
1
1
2
0
1
0
0
2
0
0
0
0
1
2
0
1
0
2
0
2
2
0
1
2
0
0
1
1
0
1
0
1
0
1
0
0
0
2
1
0
0
1
1
0
1
0
0
0
1
0
2
2
0
1
0
0
0
0
0
0
3
2
1
0
0
1
2
0
0
0
0
2
1
0
0
0
0
0
0
2
0
2
0
1
0
2
1
0
1
0
2
0
0
2
3
0
2
1
1
0
0
1
1
0
2
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
1
2
2
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
2
1
1
1
0
1
2
0
3
0
3
0
0
0
1
1
0
1
2
0
0
0
2
0
2
0
2
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
2
2
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
3
2
0
0
0
0
1
0
0
0
2
0
2
2
2
1
0
0
0
0
2
1
0
0
1
0
2
0
0
1
0
0
0
1
0
1
2
0
0
0
0
1
0
1
2
1
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
4
0
0
1
0
1
2
1
2
0
0
5
0
1
1
0
0
2
3
0
1
0
2
0
0
0
2
0
0
1
2
1
0
1
0
2
1
0
0
1
0
2
0
0
0
0
1
1
0
0
2
2
0
1
0
1
1
0
0
1
1
2
0
0
2
0
0
0
2
2
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
2
0
0
2
0
0
0
1
0
2
2
2
0
0
2
1
2
0
0
0
0
0
2
0
1
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
1
0
1
0
0
3
0
1
0
0
0
0
0
1
1
2
0
0
3
0
2
0
0
2
1
0
0
0
0
0
2
2
3
0
2
1
0
0
1
4
1
0
0
0
2
0
1
0
0
1
0
0
1
3
0
2
2
0
0
0
2
0
1
1
3
2
0
0
1
1
2
2
0
0
0
0
2
0
0
1
1
1
0
0
2
0
2
0
0
0
1
0
0
2
0
1
0
0
1
0
2
1
0
0
2
1
0
0
0
0
0
0
2
0
0
2
0
0
2
2
2
1
1
0
1
0
1
2
0
0
1
0
0
0
1
0
1
0
2
2
1
1
0
0
2
1
0
0
0
0
0
0
0
0
1
1
2
0
0
1
1
0
1
2
0
0
0
0
0
0
2
0
0
0
2
0
3
1
1
0
0
0
1
0
0
2
1
0
1
1
0
0
2
2
2
4
0
0
3
2
0
2
0
0
1
0
0
2
0
0
0
0
0
2
0
2
0
0
1
0
0
1
2
1
2
1
0
0
2
0
0
2
1
0
1
1
2
1
0
0
2
2
1
0
0
0
0
0
0
1
0
1
0
2
0
0
1
0
0
0
0
1
2
1
1
0
2
0
1
0
0
2
1
0
0
0
0
0
1
0
2
0
0
1
2
4
2
0
1
1
0
3
1
1
0
0
0
0
2
2
2
0
0
0
0
0
0
1
0
1
0
2
0
0
0
2
1
0
0
0
0
0
2
1
0
0
0
0
0
3
0
0
0
0
0
2
2
1
0
0
2
0
0
0
0
2
0
1
0
2
0
2
1
0
0
2
0
0
1
1
0
0
1
0
1
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
1
1
2
0
0
2
2
0
1
0
2
0
0
0
1
0
1
0
0
1
2
1
2
0
0
0
1
0
0
2
1
0
0
0
2
0
0
0
1
0
2
0
1
0
0
0
2
2
0
1
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
3
0
0
0
0
0
1
1
0
0
0
0
2
1
1
0
1
0
2
0
2
0
0
0
0
0
1
1
2
1
0
0
0
0
2
0
4
0
0
0
0
0
2
0
0
2
0
0
2
1
0
0
1
1
0
0
1
1
0
3
0
2
0
0
0
0
2
0
0
0
0
1
2
0
1
0
0
1
0
0
2
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
2
2
0
0
1
0
0
1
1
0
0
0
0
0
1
0
1
0
0
2
0
0
2
0
1
1
1
1
0
0
0
0
0
0
1
1
0
1
2
1
2
1
0
0
0
0
0
2
1
0
0
0
1
0
1
0
0
2
1
5
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
2
3
0
0
1
0
1
1
0
1
1
0
1
0
2
0
0
0
0
0
2
0
0
0
0
2
1
0
2
0
0
0
0
0
1
0
0
1
1
0
1
1
1
0
0
2
0
0
0
0
0
2
0
0
2
0
0
2
0
2
0
2
3
0
0
1
0
1
2
0
2
0
0
0
0
0
0
0
1
2
0
0
0
1
2
0
2
0
1
0
1
1
0
2
0
0
0
0
0
0
0
4
2
0
2
0
2
0
0
1
0
2
1
0
0
2
0
0
0
0
1
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
2
3
0
1
0
3
0
0
0
3
0
0
0
0
1
0
0
0
0
2
1
0
2
0
2
0
0
0
1
1
0
0
1
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
2
2
3
1
0
0
0
0
1
0
2
2
0
1
0
1
0
0
0
0
0
1
1
0
0
1
0
3
2
0
1
2
0
1
1
1
0
0
0
1
3
2
0
0
1
0
0
0
0
0
1
0
1
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
2
2
0
0
0
2
1
0
1
1
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
2
0
3
1
0
1
0
2
0
0
2
0
2
0
2
2
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
2
2
0
0
1
1
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
2
1
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
1
2
0
0
0
1
2
0
0
2
1
0
2
1
2
0
0
3
0
0
0
0
0
2
0
1
2
1
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
2
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
2
0
0
1
0
0
2
0
0
0
1
1
0
0
1
1
1
0
1
0
0
0
0
0
0
0
2
0
0
0
3
0
2
0
2
0
0
0
0
1
2
0
1
0
0
0
0
0
0
2
0
0
2
1
2
0
0
0
0
0
0
0
0
2
0
4
0
0
2
0
0
0
1
1
0
0
0
0
2
0
0
0
0
1
1
2
0
0
1
0
0
0
1
1
2
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
2
1
1
3
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
1
1
1
0
0
0
0
0
0
0
1
2
2
1
1
0
2
1
1
0
0
0
2
0
0
2
1
0
0
0
0
2
0
0
2
0
0
1
0
0
1
0
1
0
1
0
0
2
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
2
2
4
0
0
0
0
1
0
2
2
0
0
0
0
2
1
0
3
2
0
0
2
0
0
0
1
0
1
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
1
2
0
1
1
0
0
1
1
0
0
1
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
2
1
2
0
1
0
0
0
0
1
0
0
0
1
0
1
2
0
1
0
2
0
0
0
0
1
1
2
0
0
0
2
0
1
4
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
1
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
2
0
1
0
1
0
2
1
2
0
0
2
1
1
1
0
2
2
2
0
1
0
0
0
1
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
3
1
2
2
1
4
0
0
0
0
1
4
0
2
2
0
0
2
2
1
2
1
1
2
2
0
2
1
0
0
2
0
0
2
3
0
0
0
1
1
1
0
2
0
2
0
0
0
2
1
0
2
2
0
0
0
3
1
1
1
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
1
1
1
1
1
1
0
1
0
0
0
0
2
2
0
0
0
0
2
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
1
0
2
0
3
0
0
1
1
2
2
1
2
0
2
0
3
0
3
0
0
2
0
0
0
2
0
0
0
1
0
2
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
1
1
2
1
0
0
1
0
0
2
1
1
0
0
1
0
1
0
2
0
1
0
1
0
0
0
1
0
2
1
0
1
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
2
0
2
1
0
1
0
0
1
0
0
2
2
0
2
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
2
0
0
3
2
0
3
2
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
2
2
0
0
0
1
0
0
2
1
2
0
1
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
1
2
4
0
0
0
0
2
0
1
2
3
2
1
6
0
0
0
0
0
0
2
2
1
0
0
2
0
0
1
0
0
1
0
3
0
0
0
0
0
1
1
0
2
0
0
2
0
0
0
0
0
2
0
0
4
2
0
0
1
2
1
0
0
0
0
1
1
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
1
0
0
0
1
4
0
0
2
1
0
2
0
0
0
0
0
0
1
0
0
2
0
1
2
2
0
2
0
3
0
0
1
0
0
1
2
0
1
0
0
1
0
0
0
0
2
1
0
0
2
0
0
0
0
2
2
0
0
0
2
2
0
3
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
2
0
1
1
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
1
2
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
2
0
2
0
0
1
0
0
1
1
0
0
0
0
0
0
1
1
0
0
2
2
0
0
0
0
3
2
0
0
0
0
0
0
2
0
1
0
2
0
2
0
0
1
0
2
1
0
0
2
1
0
0
0
0
0
0
0
1
1
2
0
0
1
1
1
0
0
1
1
2
0
2
1
0
0
1
0
0
0
2
0
0
0
2
1
3
0
0
1
2
0
1
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
1
1
1
1
3
2
2
0
0
1
0
0
0
1
2
0
0
0
0
0
0
2
2
2
0
0
1
0
2
0
0
0
0
1
2
0
0
1
0
0
0
3
0
0
0
2
0
0
0
1
1
2
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
2
4
1
2
0
0
2
0
1
1
0
0
0
2
0
0
2
2
3
0
1
0
0
1
0
1
2
1
0
0
0
2
1
1
0
0
0
0
0
1
0
0
0
0
2
2
2
2
2
0
1
2
2
0
0
0
1
2
0
2
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
1
1
2
0
0
1
0
0
0
1
2
0
0
2
0
0
2
0
0
2
0
0
0
0
1
0
0
1
0
2
1
1
0
0
2
2
0
0
0
0
0
0
0
1
0
1
2
1
1
0
1
0
1
0
2
2
0
1
1
1
1
1
0
0
2
0
1
0
0
0
2
0
0
0
1
0
0
0
0
1
0
1
1
1
2
0
2
0
0
1
0
1
0
0
0
0
2
0
0
1
0
2
0
0
2
0
0
2
2
2
0
0
4
0
0
0
0
1
0
0
1
0
1
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
1
2
2
0
2
0
1
1
3
1
2
0
1
0
0
1
2
1
0
0
1
1
0
0
1
2
0
0
0
0
0
0
1
0
0
1
0
0
1
2
1
0
0
1
2
0
0
1
3
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
1
1
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
3
1
0
0
0
0
0
3
0
1
1
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
1
0
0
0
1
3
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
1
0
0
1
0
0
1
0
0
0
2
0
2
0
1
0
1
0
0
0
0
1
1
1
0
1
0
0
0
1
0
0
1
0
1
2
0
1
0
1
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
4
0
0
1
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
2
0
0
1
2
2
1
0
1
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
2
0
2
2
0
0
0
1
0
0
0
0
1
2
2
1
0
1
0
0
0
2
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
1
1
1
0
0
2
0
0
0
0
0
0
1
2
2
0
0
2
1
0
0
1
2
2
2
1
0
0
1
2
0
0
0
2
2
1
2
0
1
2
2
0
1
1
0
0
0
1
2
0
0
0
0
0
0
0
2
0
1
1
0
2
0
0
0
0
1
0
3
1
1
0
2
0
2
0
2
0
1
0
0
0
2
1
0
0
2
0
0
0
2
2
2
0
1
0
0
0
0
2
0
1
2
1
0
0
1
0
0
0
0
2
0
1
2
0
1
2
3
0
0
0
0
1
1
2
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
2
0
0
0
2
0
1
1
0
0
0
0
0
0
3
0
2
0
0
0
0
0
2
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
2
2
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
1
0
3
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
1
1
0
1
0
0
2
7
7
0
0
0
0
0
0
0
2
0
0
0
2
4
1
0
0
0
1
0
0
0
2
1
1
0
0
0
1
0
1
0
0
1
0
0
1
0
2
2
0
2
0
0
0
2
1
1
1
1
2
1
2
0
0
0
2
0
2
2
0
0
0
0
2
0
1
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
1
0
1
0
4
2
0
0
3
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
2
2
1
0
0
0
0
1
3
1
0
0
1
0
4
1
2
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
1
1
1
2
2
1
0
0
0
0
0
2
2
0
2
0
0
1
0
1
2
4
0
0
0
0
3
0
0
1
0
0
0
3
2
0
0
0
0
0
1
0
1
2
0
0
1
0
0
0
2
0
0
0
1
4
2
0
0
0
0
1
0
0
0
1
0
2
0
0
1
0
0
2
0
0
2
2
0
1
2
0
0
2
2
0
0
1
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
1
2
0
0
0
0
1
0
1
0
0
0
0
1
2
0
2
0
0
2
0
2
0
2
2
0
0
0
0
1
1
1
0
0
0
0
1
0
2
1
0
0
0
0
4
2
0
0
0
0
1
0
1
2
1
0
2
2
0
0
0
0
0
1
0
2
1
0
3
0
0
0
2
1
0
0
1
0
0
0
0
0
0
1
0
2
0
0
3
0
0
1
1
1
0
0
0
0
0
1
0
1
1
1
0
0
0
2
2
0
0
1
0
1
0
0
1
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
2
1
0
1
2
2
1
0
1
2
2
2
1
0
0
1
0
1
0
1
0
0
0
1
1
0
0
0
1
1
3
0
1
1
0
0
0
2
0
0
2
0
0
0
0
0
0
1
2
2
1
0
0
0
0
0
0
0
2
0
1
1
0
1
0
2
1
0
2
1
0
3
2
0
0
0
1
0
1
0
2
0
0
1
0
1
1
1
0
2
1
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
1
0
2
0
0
2
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
2
1
0
1
0
0
0
0
2
0
1
2
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
1
1
0
3
2
1
0
0
2
0
0
0
0
0
0
1
1
1
0
0
2
2
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
1
0
0
1
2
0
0
0
2
0
0
0
0
2
0
1
0
0
0
2
1
0
0
1
1
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
1
0
1
0
3
0
1
0
0
2
0
0
0
1
3
0
0
2
0
0
0
0
0
1
2
0
0
0
0
2
2
1
2
0
0
2
0
0
1
2
0
0
1
1
0
1
0
1
2
2
0
0
0
0
1
0
0
0
2
2
1
2
0
2
1
0
0
2
0
0
0
0
0
1
0
1
0
3
1
1
3
0
1
2
2
0
0
0
1
0
0
0
0
0
1
0
2
0
1
0
0
0
1
1
2
1
2
1
0
0
2
0
0
2
1
1
2
0
2
1
2
0
0
0
1
0
0
0
2
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
1
1
0
0
2
0
0
0
0
4
1
1
0
0
0
1
0
0
2
1
2
0
1
2
2
2
0
2
0
0
0
2
0
0
0
1
0
0
3
2
0
0
1
2
0
1
0
0
0
0
1
0
1
0
2
0
0
2
0
0
0
1
0
2
0
0
1
0
1
2
2
1
0
0
2
0
1
0
2
0
1
1
0
0
1
2
0
2
1
0
2
0
0
0
0
0
0
0
1
0
0
1
2
1
1
0
0
0
2
2
0
0
0
0
0
1
0
0
0
2
0
0
0
2
1
2
0
0
1
0
1
2
0
2
0
0
3
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
3
4
0
0
2
0
0
0
0
0
0
0
0
0
1
2
1
1
3
0
0
0
0
1
0
0
0
0
0
1
1
0
0
2
0
0
2
0
1
0
0
2
0
0
0
1
1
0
0
0
2
2
1
4
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
2
0
1
2
0
0
0
2
0
2
0
0
0
0
1
0
0
0
2
2
0
0
2
2
0
1
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
1
2
0
0
0
1
2
0
0
0
0
3
0
4
2
1
0
0
0
1
2
2
2
0
0
0
1
1
2
0
0
0
0
0
1
2
0
1
0
1
1
0
0
1
0
0
3
2
0
1
3
0
0
2
0
0
1
0
2
0
0
2
0
0
0
2
0
2
0
0
0
0
0
2
0
1
1
2
0
0
0
1
1
0
2
2
0
0
0
0
1
2
0
2
0
0
2
0
0
1
0
2
1
1
0
0
0
0
0
1
2
0
0
1
0
0
3
0
0
0
0
0
0
1
0
0
1
0
1
1
1
0
0
0
0
2
0
0
3
0
1
0
0
0
0
1
0
2
0
0
2
0
0
3
1
0
0
0
2
0
0
0
1
2
0
0
1
1
0
2
1
2
0
0
0
1
0
0
0
1
0
0
0
2
2
2
1
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
1
0
0
1
0
0
1
1
0
2
0
2
0
0
0
0
2
0
1
1
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
3
0
0
0
0
0
0
0
2
3
0
1
2
1
1
1
1
1
1
2
0
1
2
0
0
1
0
0
0
2
2
0
0
1
0
0
1
0
0
0
0
0
0
0
2
2
1
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
2
0
1
1
2
2
0
0
2
0
2
1
1
1
0
0
0
0
0
0
0
0
0
4
2
0
1
2
0
2
0
0
1
0
0
2
0
1
3
0
2
0
1
1
0
3
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
2
2
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
1
1
1
0
1
2
1
1
1
0
0
0
0
3
0
3
0
2
0
0
1
0
0
0
0
1
0
0
1
1
0
2
0
0
1
2
2
0
0
3
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
2
0
0
1
1
0
0
2
0
0
2
2
0
0
1
0
0
0
2
1
0
0
0
1
0
0
0
0
2
0
1
0
1
1
0
0
1
2
1
1
2
0
0
1
0
0
0
2
2
5
1
0
2
0
0
0
1
2
0
2
0
0
0
0
1
0
0
1
0
1
0
1
2
1
0
0
2
0
1
0
0
0
0
0
0
1
1
2
0
2
0
1
0
2
1
0
2
1
0
0
0
1
0
0
1
1
0
1
2
2
0
2
0
1
0
0
2
1
0
0
0
2
0
2
0
1
0
0
0
0
0
0
1
0
0
0
3
0
3
0
1
1
1
0
0
2
2
2
0
1
1
0
2
0
0
0
3
0
0
1
0
0
1
1
1
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
2
2
2
0
1
0
1
2
0
0
0
0
0
2
0
1
0
0
0
3
0
0
1
0
7
0
2
0
0
3
0
2
1
0
0
0
0
0
2
1
2
1
0
1
2
0
0
0
0
1
1
2
0
0
0
0
1
2
0
1
0
1
2
0
0
1
0
0
0
0
0
2
0
0
1
0
0
2
2
0
0
2
3
0
0
0
0
2
0
1
1
0
2
0
1
2
1
0
0
2
0
1
2
1
1
0
0
0
2
0
0
0
2
0
1
1
1
0
2
0
0
1
0
1
0
0
0
0
2
0
2
0
1
1
0
2
1
2
0
0
2
0
0
0
0
1
0
0
0
2
2
1
0
0
0
2
0
1
0
0
0
1
2
0
0
0
1
0
0
1
0
0
1
0
0
2
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
2
0
0
1
0
1
1
0
0
0
0
2
0
1
0
2
0
0
0
0
0
2
0
2
0
2
0
0
0
0
1
2
1
0
0
1
0
2
0
0
1
1
1
0
1
2
0
0
0
0
2
1
0
1
2
2
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
2
0
1
0
2
0
3
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
1
0
0
1
1
1
1
2
1
2
0
2
0
0
0
0
0
1
1
0
0
0
0
1
0
0
2
0
2
1
2
1
0
0
1
0
0
0
0
0
0
0
2
0
0
1
2
0
0
1
2
2
2
2
1
0
1
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
1
0
1
2
1
1
2
0
0
0
0
0
2
0
0
0
1
2
1
3
2
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
1
2
2
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
1
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
1
0
1
2
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
1
0
0
0
2
2
0
1
0
1
0
0
0
2
0
2
0
0
0
1
2
1
0
0
1
1
0
1
0
0
2
3
0
0
1
0
0
0
0
0
0
0
0
0
1
3
2
1
0
0
0
2
0
0
3
0
1
2
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
2
0
0
0
0
2
2
0
0
0
2
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
2
0
1
0
1
2
0
1
0
2
0
0
0
0
0
1
0
2
0
1
3
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
1
1
0
2
1
0
0
2
0
0
0
1
1
0
1
0
0
0
0
0
0
2
0
0
1
3
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
2
1
1
0
2
1
0
0
1
0
2
1
2
0
0
2
1
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
2
2
1
0
1
0
0
2
0
1
2
0
2
0
0
1
2
0
1
0
0
2
0
2
2
0
0
0
0
2
1
2
2
0
0
0
0
0
1
0
3
0
0
0
2
1
0
2
0
1
1
1
1
0
2
0
0
0
0
2
0
1
2
0
0
0
0
1
0
1
2
0
0
2
1
2
0
0
0
0
1
0
0
1
1
1
0
0
0
2
0
1
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
2
0
2
0
0
2
0
3
0
1
2
0
2
0
0
2
0
0
1
2
0
0
3
2
1
0
1
1
2
0
0
0
2
0
2
0
0
0
2
0
0
2
2
0
2
0
0
0
0
0
2
2
1
1
2
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
1
0
2
1
2
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
2
0
0
1
2
2
0
0
3
0
1
0
0
1
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
1
3
0
0
0
1
0
0
0
1
0
1
0
2
0
2
1
0
0
0
0
1
1
2
5
0
0
0
5
1
0
0
1
0
2
1
0
0
0
0
1
0
0
2
0
4
0
0
0
0
2
2
0
1
0
1
0
0
2
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
1
0
0
2
0
0
0
1
0
1
2
0
0
2
0
0
2
2
1
0
1
4
1
0
0
0
1
2
2
0
2
2
1
0
0
5
0
2
1
0
0
1
0
0
0
2
0
2
1
0
0
0
0
1
2
0
2
0
0
0
0
0
1
0
4
1
0
0
1
0
0
0
1
1
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
1
1
1
1
3
3
0
2
0
0
0
0
0
1
1
0
1
0
1
0
0
0
2
2
1
0
1
1
0
2
2
2
1
0
2
5
1
0
5
0
1
0
2
0
0
0
0
1
1
0
1
0
2
2
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
4
0
2
0
1
1
0
0
3
0
0
0
0
0
0
0
2
0
0
0
2
2
1
0
1
0
0
0
0
1
2
0
1
2
0
1
0
0
4
0
0
2
1
0
0
0
0
0
2
1
0
0
0
1
0
0
0
2
0
0
0
2
1
2
0
0
0
0
3
0
0
1
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
1
1
2
1
0
0
1
1
0
1
0
0
1
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
3
0
2
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
2
1
2
0
0
2
0
0
2
0
1
0
0
1
0
3
1
0
0
0
0
0
0
2
0
0
0
0
2
2
1
0
0
1
2
0
0
1
2
0
2
0
1
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
2
0
1
0
0
1
3
0
0
1
0
0
2
0
0
0
2
0
0
0
0
1
0
1
1
0
0
0
0
2
0
0
1
0
0
1
0
0
1
0
0
1
0
0
1
0
0
1
1
0
0
0
0
5
0
0
0
3
0
1
0
2
1
0
0
1
2
0
0
0
0
0
2
1
1
0
2
2
0
0
0
0
1
1
2
1
0
0
0
0
1
2
0
0
2
1
0
0
0
1
1
1
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
2
0
1
0
1
2
0
0
0
0
0
0
2
1
2
2
0
0
1
0
0
2
2
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
2
3
0
0
1
0
0
2
0
0
0
0
0
0
2
0
2
0
2
2
0
0
0
2
0
2
1
1
0
0
0
0
0
2
3
1
0
1
0
3
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
2
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
1
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
2
0
0
2
2
0
0
0
0
2
1
0
1
0
2
0
0
1
0
0
2
0
2
0
2
0
0
0
0
0
2
1
0
3
0
0
0
2
0
0
1
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
1
4
1
0
0
0
0
2
0
0
2
0
2
0
2
1
1
0
2
2
0
0
4
1
0
0
1
2
0
0
5
0
0
1
2
0
3
0
0
0
1
0
0
2
0
0
0
0
2
0
1
0
2
0
0
0
2
1
0
0
2
0
0
0
0
1
2
0
0
0
0
2
2
0
0
0
2
1
0
0
0
0
0
1
0
2
0
0
0
2
0
0
1
0
1
0
1
1
0
0
0
0
2
1
0
2
0
2
0
0
2
1
2
0
2
1
1
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
2
1
0
0
0
1
0
0
0
2
1
0
2
2
0
0
2
1
2
0
2
0
1
0
1
2
0
0
0
0
0
0
2
0
0
2
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
1
2
1
1
1
0
2
1
0
0
2
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
2
1
0
0
0
2
0
0
0
0
1
0
2
5
2
0
2
0
0
1
2
2
1
1
0
0
3
3
0
0
0
0
3
1
0
0
1
0
0
0
0
1
1
1
0
0
2
1
0
0
0
1
0
0
0
0
0
2
0
0
2
0
2
1
2
2
2
0
2
0
1
2
0
2
0
0
0
0
1
0
1
2
0
0
0
0
1
1
1
0
0
0
0
1
2
0
0
1
0
0
0
0
2
1
0
1
0
1
2
1
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
1
0
1
0
1
0
0
0
2
3
0
0
0
2
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
2
1
2
1
2
0
0
0
0
1
1
0
1
1
0
0
0
2
0
1
0
1
0
2
1
6
0
0
1
1
0
0
1
2
0
0
2
0
1
0
0
0
0
0
2
1
0
0
0
0
1
0
0
2
1
2
0
0
0
0
2
0
0
0
0
0
4
2
0
2
0
0
2
1
0
1
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
2
1
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
1
2
0
1
1
0
2
0
0
0
1
1
0
2
2
2
1
4
0
1
1
0
0
0
0
0
2
2
2
2
0
0
4
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
2
1
0
1
0
0
1
0
1
3
1
2
1
0
0
1
0
0
0
2
2
2
0
0
2
0
2
2
1
2
0
0
2
0
0
0
1
0
0
1
0
0
1
0
0
2
0
0
2
1
0
0
0
0
3
1
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
1
0
0
2
0
2
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
2
3
2
2
2
0
2
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
2
0
3
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
2
2
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
1
1
5
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
2
1
0
0
0
2
0
0
2
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
2
0
1
3
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
1
0
1
0
1
1
3
2
1
1
1
0
1
0
1
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
1
1
1
2
0
0
1
0
1
2
0
0
0
2
0
2
0
0
0
1
1
1
2
2
0
0
2
1
1
2
1
2
0
2
0
0
4
2
0
2
0
0
0
0
0
0
0
0
1
2
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
2
0
0
2
0
0
0
0
3
0
1
0
0
3
0
5
0
2
1
2
0
0
0
1
2
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
3
1
0
0
0
0
0
2
0
0
0
0
0
0
4
0
1
2
0
1
0
1
0
0
0
2
0
1
1
0
0
1
2
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
2
0
1
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
1
0
1
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
1
1
1
0
0
1
0
0
1
2
1
1
0
0
0
0
0
2
1
1
2
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
3
0
0
1
1
0
0
0
1
1
0
2
0
0
0
1
0
2
0
1
0
0
0
2
0
1
0
2
1
1
1
0
0
2
1
1
0
0
3
0
0
2
1
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
1
1
0
0
1
0
1
0
0
0
0
1
2
0
0
0
0
1
0
0
2
0
0
0
2
0
2
0
0
0
2
2
2
0
0
0
1
1
0
0
0
2
0
0
0
1
0
1
2
1
3
0
1
0
0
2
0
0
2
0
3
0
0
0
0
2
2
0
0
0
2
3
1
2
0
0
2
0
1
1
0
0
0
2
0
0
0
1
0
2
0
1
0
0
0
2
1
0
0
0
2
1
0
0
0
0
2
1
0
1
2
0
1
1
0
0
0
2
0
0
1
0
0
0
0
2
1
0
0
1
0
1
0
0
0
0
4
0
1
0
1
2
2
0
3
0
3
0
2
0
1
0
2
2
4
2
0
2
0
0
0
0
0
1
0
1
2
0
0
0
2
0
0
2
0
0
0
0
1
1
0
0
3
0
1
1
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
2
0
0
1
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
1
0
0
2
0
0
2
1
3
2
1
1
0
0
2
0
1
0
0
0
2
3
0
2
2
1
0
0
0
2
2
2
0
0
0
0
0
1
0
1
0
2
0
0
0
1
0
0
2
1
0
0
0
0
0
1
0
0
0
0
1
0
3
0
1
0
0
1
0
2
1
0
1
1
2
1
0
0
1
0
0
0
0
0
1
3
1
0
0
2
0
0
3
1
1
0
0
2
0
0
0
0
0
0
1
2
1
0
1
0
1
2
2
0
1
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
2
0
1
0
1
1
0
0
0
0
0
0
2
0
0
0
0
3
0
1
0
0
1
0
2
0
0
0
1
0
0
0
2
0
3
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
1
2
2
0
0
0
0
0
0
0
2
1
1
0
0
1
16
3
0
0
0
0
0
2
1
0
0
0
1
0
1
0
0
0
0
2
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
1
1
1
1
2
0
2
1
0
4
0
0
0
2
0
0
2
0
0
2
0
1
2
0
0
0
0
0
0
2
2
0
0
3
0
1
1
0
1
1
1
2
8
2
4
0
2
0
0
1
0
0
0
0
3
0
2
2
3
2
1
0
0
0
2
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
3
3
2
0
0
0
0
1
2
0
2
2
0
1
0
1
0
1
0
0
1
0
1
0
1
0
1
2
0
0
1
2
1
0
1
1
2
1
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
1
1
2
1
2
0
0
1
0
0
2
0
0
0
2
1
1
0
0
1
0
0
0
2
1
0
2
1
1
0
2
0
0
0
0
0
0
0
0
2
1
1
2
0
3
2
0
0
0
1
0
1
0
0
0
2
0
1
1
0
2
1
0
2
0
1
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
2
0
0
0
0
1
1
2
0
0
2
0
0
2
1
1
2
0
1
0
2
0
0
2
0
0
0
0
0
0
2
2
1
0
2
0
0
0
2
1
2
1
2
0
0
0
0
0
2
0
1
2
0
0
0
0
0
1
1
0
0
2
0
0
0
0
1
1
0
0
5
1
0
1
0
0
2
0
1
1
2
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
1
0
2
1
2
0
1
0
0
2
0
1
1
3
0
0
0
2
1
1
2
0
0
2
1
2
0
0
2
0
0
6
0
0
1
0
0
0
0
0
1
0
0
2
1
2
0
1
0
0
0
0
1
1
0
1
0
1
0
0
0
1
0
0
0
0
3
0
0
0
0
1
0
2
0
0
2
0
2
0
0
0
2
0
0
2
0
0
0
0
0
2
1
0
1
1
0
1
0
0
1
2
1
0
4
0
0
0
0
2
0
0
1
0
0
0
0
2
2
0
2
0
0
0
1
1
1
2
0
1
1
1
1
0
0
0
2
2
0
2
0
0
2
0
0
2
0
0
0
0
2
0
0
0
1
0
0
1
0
1
0
0
0
1
1
1
0
0
0
1
0
1
0
1
0
0
0
3
0
0
2
0
0
0
0
0
0
1
1
2
2
3
1
0
1
2
1
0
1
0
1
1
1
1
1
1
1
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
1
2
2
0
0
0
0
1
0
0
0
0
1
0
2
0
1
2
2
0
0
0
3
0
1
0
0
1
0
0
1
0
0
1
0
1
1
0
1
0
1
2
0
1
0
0
0
0
0
2
2
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
1
2
0
2
0
0
0
0
2
0
0
2
2
0
0
1
0
0
0
0
2
0
2
1
0
1
0
2
0
0
0
1
0
1
2
2
1
0
1
2
2
0
0
0
2
0
3
0
2
2
0
0
0
0
0
1
0
1
1
1
0
0
0
0
1
2
1
1
1
1
0
1
0
0
0
0
1
0
2
2
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
1
2
0
2
0
1
2
0
0
1
2
0
0
1
2
2
0
1
0
0
1
0
0
0
2
0
0
2
2
0
0
0
3
2
0
1
1
1
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
1
1
0
1
0
0
2
0
2
0
0
2
0
0
0
3
0
2
0
1
1
2
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
1
2
1
0
1
0
0
1
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
1
0
3
0
0
0
2
0
0
1
2
1
0
1
0
0
0
0
2
2
0
0
2
2
2
0
1
2
0
0
0
0
0
1
2
0
0
1
2
2
0
1
2
3
0
0
1
0
0
0
2
2
1
2
0
2
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
2
0
0
0
1
1
1
0
0
0
0
1
0
0
4
1
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
2
0
0
2
2
0
0
0
0
0
0
2
2
2
2
2
2
0
1
0
0
1
0
1
1
0
0
0
1
0
2
1
0
0
0
1
3
0
0
0
0
0
1
2
0
0
0
0
2
0
2
1
0
0
0
0
1
0
0
2
1
0
2
0
0
0
0
0
0
0
0
2
0
1
0
1
0
2
0
2
0
1
0
0
0
1
0
2
2
0
0
0
0
3
1
0
0
0
1
1
0
0
1
1
2
0
1
1
3
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
1
0
0
0
0
2
2
2
1
0
0
0
0
0
2
3
0
0
0
1
0
1
1
2
1
0
0
1
1
2
4
1
1
1
0
2
2
1
1
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
4
0
0
0
2
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
1
2
1
2
0
0
0
0
0
1
1
1
0
0
0
1
2
0
0
0
0
0
1
0
0
3
0
0
0
2
0
0
0
1
0
1
0
2
1
1
2
3
0
0
0
1
1
0
0
1
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
2
2
0
0
2
0
0
0
0
0
1
0
0
0
3
1
2
0
0
2
0
0
0
0
1
0
0
1
0
3
0
0
1
0
0
0
0
2
2
1
0
1
0
0
0
1
3
0
0
3
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
1
1
0
1
2
2
0
1
2
0
1
0
1
0
0
0
0
0
3
1
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
1
1
0
1
0
1
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
2
2
0
1
0
1
0
0
3
0
3
2
0
0
0
0
0
0
1
2
0
2
2
0
0
0
0
0
1
1
0
0
3
1
0
0
0
0
0
2
3
1
0
0
0
1
1
0
1
2
0
0
0
1
2
0
0
0
2
2
0
0
1
0
0
3
0
1
0
1
4
1
1
1
0
0
1
0
1
0
1
0
3
0
0
0
2
2
2
2
0
0
1
0
0
0
2
0
0
0
0
2
2
0
1
0
6
2
0
2
2
1
1
0
0
0
0
1
1
2
0
2
0
1
0
0
0
1
1
0
0
4
1
1
1
0
0
1
0
0
0
3
0
3
0
0
1
1
0
0
0
0
2
0
2
1
0
1
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
2
1
0
0
0
0
3
0
1
0
0
0
2
2
0
2
0
1
0
0
0
0
0
0
1
1
0
0
0
2
2
0
0
1
1
0
0
0
0
0
0
0
1
2
0
0
2
0
0
2
0
2
0
0
0
0
1
0
0
2
1
0
0
0
0
0
2
0
0
0
0
2
0
2
1
1
0
1
0
0
0
0
0
1
1
2
0
1
0
0
2
0
2
2
0
0
2
0
0
0
2
0
0
1
0
0
2
2
2
2
2
1
2
0
0
1
0
0
3
0
1
0
2
0
0
0
1
0
0
0
1
1
3
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
2
2
1
0
0
2
0
0
1
1
1
0
0
2
0
1
1
0
0
1
2
0
0
0
0
1
0
0
1
1
3
0
0
0
0
4
0
1
1
0
0
0
2
1
0
1
0
0
0
0
1
1
2
0
0
1
0
2
2
0
0
0
1
1
0
0
0
1
0
2
0
2
1
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
2
0
1
0
0
2
0
2
0
0
0
0
0
1
2
0
0
0
1
0
0
0
2
2
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
2
1
4
0
1
2
0
0
0
0
1
0
2
2
0
1
0
0
0
2
1
0
2
0
0
2
2
0
0
0
2
0
0
1
1
1
3
0
1
0
0
1
0
0
0
0
1
0
3
0
0
0
0
2
1
2
0
0
0
0
0
1
0
0
1
1
0
2
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
2
0
2
0
2
0
0
1
2
0
0
1
1
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
3
1
0
0
0
2
2
0
0
0
0
0
2
2
0
1
2
1
1
2
2
1
0
1
0
0
2
2
0
2
0
0
1
0
0
0
0
0
1
0
1
0
2
0
0
0
0
2
2
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
1
2
0
0
1
0
2
1
1
0
2
1
0
2
2
1
2
0
0
1
0
2
0
2
2
2
0
0
0
0
0
1
3
0
1
0
1
0
1
0
1
2
0
2
2
0
0
0
1
2
1
0
2
0
2
2
0
1
0
0
3
0
2
1
0
2
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
2
2
0
0
0
0
0
0
2
0
0
2
0
1
1
0
0
0
2
2
0
2
0
0
0
0
0
0
1
1
1
1
1
0
0
1
0
0
0
0
1
1
2
2
2
2
0
2
0
2
2
0
2
0
0
0
0
3
0
0
0
0
1
0
0
0
2
0
2
0
4
0
0
0
0
1
1
0
0
1
0
0
2
0
0
1
2
0
1
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
2
0
2
0
1
0
2
0
0
1
2
0
0
0
0
2
0
0
0
2
1
2
1
2
0
2
0
0
1
1
0
1
0
2
1
0
1
2
1
0
1
0
1
1
2
0
0
1
0
0
0
0
3
0
0
0
1
3
0
0
0
0
0
1
1
0
0
0
0
2
1
0
2
0
0
1
0
2
0
0
1
1
0
0
0
1
2
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
2
0
0
2
0
0
0
0
1
2
1
0
0
1
0
1
1
0
0
0
0
0
0
0
1
2
2
0
0
1
0
2
0
1
2
2
1
1
0
0
0
1
1
0
0
0
1
2
0
1
0
0
0
0
1
1
0
1
0
0
0
0
1
0
1
2
1
2
0
2
2
1
2
1
0
2
0
0
0
2
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
2
0
0
2
2
0
2
0
0
0
0
0
0
3
1
0
1
0
2
0
1
0
0
0
0
0
0
1
1
1
2
1
2
1
1
0
1
0
0
0
2
0
0
0
0
0
0
1
2
1
0
0
0
1
0
0
1
1
0
1
0
2
2
0
0
0
2
2
1
0
1
0
1
0
1
0
0
1
0
0
0
3
0
0
0
1
2
2
0
2
0
2
0
2
0
0
0
0
2
2
1
2
0
2
1
2
0
1
0
0
0
2
0
0
0
1
0
1
0
0
1
0
2
0
0
1
0
0
3
1
1
0
0
0
0
1
0
0
2
0
1
0
2
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
3
2
3
0
0
0
0
1
0
1
0
0
2
0
1
0
0
0
1
1
0
0
1
1
0
2
1
0
1
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
2
0
0
1
0
1
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
1
0
2
2
0
2
2
0
3
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
1
0
0
1
2
0
0
0
0
1
2
0
0
0
1
0
1
0
1
2
0
1
0
2
1
0
1
0
0
1
1
0
0
1
0
0
3
1
0
2
0
0
2
0
0
0
0
0
0
2
0
2
1
1
0
1
2
2
0
0
2
0
0
0
1
1
1
1
0
1
1
0
0
2
0
1
2
0
0
2
2
1
1
1
0
0
0
1
0
0
1
2
0
1
2
0
0
1
1
0
0
0
0
0
0
0
0
2
0
1
2
3
2
1
0
0
1
0
1
1
0
0
0
0
0
0
3
1
0
0
0
0
0
3
0
2
0
0
2
0
1
0
0
0
2
0
0
0
3
2
0
0
0
3
2
5
0
2
0
2
2
0
2
0
2
1
1
2
0
0
0
0
0
2
1
0
0
0
0
1
0
0
1
1
0
0
2
0
0
0
0
0
0
0
1
1
1
0
0
0
0
2
0
1
2
1
0
0
0
0
0
2
2
0
0
2
2
1
0
0
0
0
0
0
0
0
2
0
0
3
1
0
0
0
0
0
0
1
2
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
2
0
1
2
1
0
0
0
0
2
0
2
0
0
1
1
0
0
2
0
1
0
2
0
2
2
0
0
0
1
0
0
0
1
0
1
1
0
1
2
1
0
0
0
0
2
0
1
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
2
1
2
1
0
0
0
2
0
0
0
2
0
0
0
2
0
0
2
0
0
0
1
1
0
2
0
0
1
2
2
0
2
0
1
0
4
0
0
0
1
0
0
2
0
1
0
0
1
0
0
0
0
0
1
3
2
0
0
0
0
0
0
1
0
1
1
2
2
0
0
0
1
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
1
2
0
1
0
2
2
0
0
0
0
1
0
1
0
1
2
0
0
0
2
1
1
1
1
0
0
0
0
0
0
1
0
0
1
2
0
0
1
0
2
0
0
0
0
1
1
0
2
1
0
1
0
0
0
2
0
0
1
0
0
2
0
1
0
0
0
2
1
0
0
0
0
1
0
2
0
2
2
2
2
2
1
0
2
0
0
1
0
3
0
1
0
2
1
0
1
0
2
1
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
1
0
0
0
0
2
1
1
1
2
1
1
0
0
3
0
1
0
0
0
0
0
1
1
2
0
0
0
0
0
1
0
2
1
1
1
0
0
2
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
2
2
0
2
0
0
0
2
2
0
2
2
0
0
1
1
2
0
0
2
0
1
0
0
1
2
0
1
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
2
0
2
1
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
1
2
0
0
0
0
0
2
1
0
0
2
1
3
0
1
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
2
2
0
0
1
1
0
0
0
3
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
2
1
0
0
0
2
1
1
2
2
1
0
0
0
0
2
4
2
0
0
0
0
0
3
1
0
0
2
0
0
0
0
0
5
0
1
1
0
0
1
0
0
1
0
0
0
2
1
1
0
0
2
2
0
0
1
0
0
0
2
2
1
0
0
0
0
2
0
1
1
2
0
2
0
0
2
1
0
0
1
2
0
0
0
0
1
2
0
0
2
2
0
0
0
1
0
0
3
1
0
0
1
1
2
1
2
1
0
0
2
0
2
1
0
0
0
0
0
2
1
1
2
2
0
2
1
0
0
0
2
1
3
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
1
2
1
1
0
0
5
1
0
0
0
0
2
0
3
1
0
0
0
1
0
1
0
0
0
2
1
0
0
0
2
0
2
0
0
1
0
0
0
0
1
0
1
2
0
0
0
1
0
2
0
0
0
2
2
1
0
0
0
2
0
2
0
2
0
0
2
0
0
1
2
1
0
2
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
2
3
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
2
0
2
0
0
1
0
0
0
1
0
0
0
2
1
0
1
0
1
0
0
1
2
0
2
0
2
1
1
0
0
0
0
2
0
2
2
0
0
0
0
1
0
1
1
0
0
0
0
2
1
0
0
1
0
0
0
0
2
1
0
2
0
0
0
2
0
3
0
1
0
0
0
3
2
2
1
1
2
1
0
2
4
2
2
0
2
2
0
0
1
0
0
0
1
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
3
2
0
0
0
2
0
0
2
0
0
0
2
0
2
1
0
0
0
0
0
1
0
0
0
0
0
3
0
1
2
0
0
1
2
1
0
0
0
2
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
1
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
2
0
0
2
2
1
0
0
2
0
0
2
0
0
0
0
0
1
0
1
0
2
0
2
0
0
0
0
2
0
0
1
0
2
0
0
2
0
0
0
1
0
0
0
0
0
2
2
0
1
0
0
2
0
0
0
2
0
1
0
1
0
0
0
2
1
0
0
0
1
0
0
2
0
0
1
0
1
0
0
1
1
1
0
0
1
0
0
0
2
2
0
0
0
3
1
0
0
0
1
0
0
0
1
1
0
0
1
2
0
1
0
0
0
0
0
0
1
0
0
2
1
0
1
0
0
2
2
0
0
0
2
1
0
0
2
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
2
0
0
2
1
0
1
1
0
0
0
1
0
2
1
0
0
1
0
2
1
0
0
1
0
0
1
0
2
1
2
0
0
0
1
2
0
1
1
0
0
0
0
0
2
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
3
0
0
0
1
0
0
0
0
0
2
0
1
1
0
0
0
0
1
2
0
0
0
0
0
0
2
0
2
0
2
1
0
0
2
0
1
0
0
0
0
1
3
0
0
0
0
0
2
1
1
2
0
0
0
0
1
1
2
1
2
0
0
1
1
1
0
0
0
0
0
3
0
1
0
2
0
2
2
2
0
0
0
0
0
0
1
0
2
0
0
3
2
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
2
0
0
1
0
0
0
0
0
0
0
0
2
0
1
2
2
0
2
0
0
2
2
0
2
2
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
2
0
1
0
0
0
3
1
0
0
0
1
0
1
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
3
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
1
0
2
0
1
2
0
0
0
0
1
2
0
0
0
1
1
0
1
1
0
0
0
2
1
3
0
1
0
0
2
0
0
0
0
1
2
0
2
1
0
0
1
0
1
1
0
2
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
2
0
0
0
0
2
2
0
0
1
1
0
1
0
2
2
2
0
0
1
0
0
1
1
0
0
0
1
0
2
1
1
1
0
0
0
0
0
1
1
0
2
0
0
1
0
0
2
1
1
0
1
2
2
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
2
0
2
1
0
1
0
1
2
1
1
0
0
0
1
0
0
0
0
0
0
2
0
2
1
0
0
0
2
0
1
1
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
2
0
0
3
0
0
0
2
1
0
0
0
0
0
0
4
0
1
0
0
0
0
2
1
0
0
0
0
0
0
1
1
0
1
2
0
0
0
2
0
2
0
1
2
0
0
2
1
3
1
1
2
0
0
0
0
2
1
0
2
2
3
0
0
0
0
1
0
1
0
0
2
0
4
0
1
0
0
0
1
0
2
1
0
1
1
2
0
1
0
0
0
2
0
0
0
3
3
1
1
0
1
2
0
2
0
0
2
0
0
0
0
0
0
0
0
1
3
0
1
0
2
0
1
1
0
0
0
0
0
2
0
0
2
0
0
1
0
0
2
2
0
2
0
0
1
2
2
2
2
2
2
1
0
0
2
1
0
0
0
0
0
0
0
1
0
2
2
0
1
1
1
2
2
0
0
0
0
0
1
2
0
1
0
1
0
1
1
0
2
0
0
2
0
0
0
0
0
3
0
2
0
0
1
2
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
2
0
1
2
0
0
0
0
1
0
0
0
2
1
0
1
0
2
0
0
0
1
2
0
2
2
0
0
0
1
0
0
1
0
2
0
0
1
2
0
2
1
0
0
0
0
2
0
0
0
0
0
0
2
1
2
0
0
0
0
1
1
2
2
0
1
1
0
0
0
0
0
1
2
1
1
0
1
1
0
2
1
1
0
0
0
1
0
0
0
0
0
0
0
0
2
1
1
2
0
2
2
0
0
1
1
0
3
1
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
2
1
0
2
0
0
2
2
0
3
1
1
2
0
0
1
1
1
0
2
0
1
3
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
2
0
0
2
2
0
0
0
1
0
0
0
0
0
1
2
0
2
0
2
0
2
1
1
2
2
0
1
0
0
2
0
2
0
1
2
0
2
2
0
2
0
0
1
0
1
2
1
0
0
0
0
0
2
0
0
0
5
0
0
1
0
0
0
2
0
2
0
0
1
2
1
0
0
1
2
0
2
0
2
0
2
0
0
1
2
0
0
1
0
1
0
1
0
2
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
1
0
1
0
0
2
0
1
2
2
1
1
0
0
1
1
2
0
0
2
1
0
0
0
1
0
1
0
0
0
1
0
1
0
0
2
0
0
2
1
2
0
2
0
0
2
0
1
0
1
0
1
1
2
0
1
0
0
2
0
0
0
1
2
0
1
0
0
2
4
2
1
0
1
2
2
1
0
0
0
0
0
0
1
2
1
0
0
0
2
0
4
0
0
0
1
1
2
0
0
0
2
0
0
3
1
0
2
0
0
0
0
2
1
1
0
0
1
1
0
3
0
0
2
0
0
1
2
0
0
0
0
2
2
2
0
1
0
0
1
0
2
0
1
0
0
1
0
2
1
1
0
0
2
0
0
1
2
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
2
2
0
3
0
1
2
0
2
0
2
0
1
0
2
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
4
1
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
3
0
2
1
2
0
1
2
0
1
2
0
1
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
2
1
0
0
1
0
0
0
1
0
0
1
1
2
2
0
2
0
0
2
0
2
0
1
0
2
1
0
0
0
2
2
2
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
1
0
0
0
1
0
4
0
0
0
0
2
1
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
2
0
2
5
1
1
0
0
0
1
0
0
2
0
2
0
2
1
0
0
0
0
0
1
1
0
1
2
0
1
0
0
0
2
2
0
3
1
1
1
0
0
0
2
0
0
0
0
1
0
1
2
1
2
0
0
2
0
0
0
2
0
1
0
0
0
2
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
1
1
2
1
3
0
0
2
0
0
0
0
0
0
0
0
0
2
3
0
0
0
2
0
0
2
4
0
1
0
0
0
0
0
2
1
1
1
1
2
1
0
2
0
2
0
0
0
0
1
1
2
3
1
0
2
0
2
0
0
1
0
3
2
1
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
1
0
0
0
0
0
2
2
2
2
0
0
0
2
2
4
0
0
1
0
0
2
1
0
0
0
1
0
0
2
0
0
1
1
0
0
0
1
1
2
2
0
1
1
2
0
0
1
2
0
0
0
0
1
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
1
0
4
2
1
1
0
2
0
0
0
0
0
2
0
0
2
3
1
0
0
1
2
2
0
2
2
2
0
2
0
0
2
0
0
1
1
2
0
1
0
2
0
2
0
4
0
2
1
1
0
0
0
0
0
0
0
2
1
0
2
2
1
0
0
1
0
0
1
0
0
0
1
0
2
1
0
1
1
1
0
1
1
1
0
1
0
0
0
0
0
1
2
1
1
1
0
0
0
1
0
0
0
0
1
2
1
0
0
2
0
1
0
1
0
0
1
1
2
1
0
2
2
2
2
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
3
2
0
0
2
0
0
0
1
0
0
0
0
2
2
2
0
1
0
1
1
1
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
2
0
2
2
0
0
1
0
1
0
0
2
1
0
0
0
0
0
2
0
1
3
0
1
0
0
0
2
1
0
0
0
0
2
0
0
2
1
2
2
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
2
2
0
1
1
1
0
0
0
0
0
0
0
0
1
0
3
1
2
0
2
1
0
0
1
2
0
0
1
0
2
0
0
0
1
0
0
1
0
2
2
1
3
0
2
0
0
1
0
1
0
1
0
0
1
0
1
1
1
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
1
0
0
0
4
1
2
0
2
0
0
0
1
0
0
1
1
0
0
2
1
1
0
0
0
0
7
1
1
2
1
1
0
1
1
1
2
2
1
0
0
1
0
0
0
1
0
1
2
1
0
0
1
0
1
0
1
2
0
0
0
1
1
0
1
2
2
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
2
2
1
1
0
0
0
0
0
0
0
1
2
2
0
0
0
1
2
0
0
0
0
1
0
0
0
2
2
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
1
0
0
1
1
0
2
1
0
2
0
0
1
0
2
0
0
1
0
0
1
0
2
2
0
1
2
0
1
1
1
2
0
0
2
1
0
2
0
0
1
0
0
1
0
0
1
1
1
2
0
0
1
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
1
2
0
2
2
1
0
0
0
0
0
0
0
1
2
0
1
2
1
0
1
0
1
1
0
1
0
1
0
2
0
1
2
2
0
1
1
5
0
0
0
1
2
1
0
0
0
0
0
0
0
2
0
2
0
1
3
0
1
2
0
1
0
2
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
1
2
2
0
1
2
0
0
2
2
0
2
0
0
0
0
0
0
2
0
1
0
0
2
1
1
0
0
0
0
2
1
0
1
0
1
0
1
2
0
2
2
0
0
0
1
2
2
0
0
0
1
0
0
1
0
1
0
0
0
2
0
0
1
2
0
1
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
3
0
0
0
0
0
0
1
1
3
2
0
2
0
1
1
0
0
3
3
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
2
4
0
4
0
1
0
0
0
0
0
4
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
2
2
0
1
1
0
1
1
0
0
0
0
0
0
1
0
1
2
2
0
3
2
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
3
0
1
1
0
0
1
2
2
0
0
0
0
0
0
2
0
2
1
0
0
1
0
0
0
0
1
0
0
1
2
0
0
1
0
1
2
1
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
1
0
0
2
0
2
1
0
3
2
1
1
0
1
0
2
1
0
1
0
2
2
0
1
1
2
1
0
0
2
0
1
1
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
1
1
0
0
0
0
0
2
0
1
0
1
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
2
1
0
0
2
2
0
1
0
1
0
0
3
1
2
2
0
0
0
0
1
2
3
0
0
0
0
1
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
3
0
0
1
0
0
0
2
0
4
0
0
2
2
1
0
0
0
2
0
0
0
0
1
2
2
0
2
1
0
2
0
0
2
0
0
0
0
0
0
1
0
3
1
2
0
0
4
0
1
0
0
2
0
0
1
0
0
0
2
0
2
0
0
0
2
2
1
1
0
0
0
2
0
1
2
2
0
0
0
1
1
3
0
0
0
2
3
0
3
0
0
0
1
0
2
1
0
0
2
0
0
0
2
2
1
1
0
0
0
2
0
2
1
2
0
2
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
2
0
1
1
2
0
0
0
0
0
0
0
2
0
0
0
0
1
2
2
0
1
2
0
0
2
0
0
1
6
4
1
0
0
7
0
2
0
0
1
0
0
0
0
6
0
0
2
0
0
2
2
0
1
0
1
1
0
0
2
2
0
0
0
0
0
0
1
0
0
0
1
0
1
1
2
2
0
2
0
0
0
1
0
0
0
0
0
1
2
2
0
0
0
0
0
0
2
1
0
0
1
0
0
0
2
2
0
0
0
2
0
2
2
0
0
0
0
0
1
0
0
0
2
1
0
0
0
2
2
0
0
1
0
0
0
0
0
1
1
0
0
0
0
2
0
0
6
2
3
2
1
0
0
1
0
0
0
1
2
2
0
0
0
0
2
1
2
1
0
0
0
0
1
3
2
0
2
2
0
1
2
0
2
2
0
1
0
2
0
1
1
2
1
1
2
1
0
0
0
0
0
1
2
0
0
0
0
2
0
2
2
1
1
2
1
0
0
1
0
1
0
0
0
0
1
2
2
2
0
1
0
2
3
0
2
2
0
0
0
1
0
0
0
0
0
0
2
0
2
1
2
0
0
0
1
1
1
0
2
2
0
2
2
0
2
0
0
0
0
1
2
0
0
1
0
1
1
2
0
2
1
0
2
1
1
2
0
1
0
1
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
1
0
0
1
0
3
0
2
0
0
0
0
0
0
1
2
0
0
0
1
1
1
0
1
0
0
0
0
3
2
1
0
1
0
2
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
1
1
2
0
0
1
2
0
0
2
0
2
0
1
0
1
2
1
0
2
2
0
0
1
0
0
1
0
0
0
0
2
2
0
2
2
2
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
2
0
1
0
0
0
1
0
1
2
0
0
2
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
2
1
0
0
2
2
0
2
0
1
0
1
0
0
0
2
0
1
2
0
1
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
2
2
2
0
0
0
2
0
2
0
1
0
2
0
0
0
2
1
0
0
0
0
0
0
2
0
0
2
2
0
2
0
0
0
1
0
2
0
0
2
0
2
2
0
0
2
1
1
1
0
0
0
0
0
1
2
0
2
0
1
1
1
1
0
0
0
0
0
0
1
1
0
1
0
1
1
0
0
0
1
0
1
0
0
2
0
2
0
1
0
0
2
1
0
0
0
0
0
0
0
1
1
0
0
2
1
0
0
0
2
2
0
2
0
0
0
0
1
0
1
1
0
0
0
1
0
1
0
0
0
0
1
0
1
0
1
0
2
0
0
0
0
0
0
0
0
1
1
3
1
1
0
1
0
2
0
0
0
2
2
0
1
0
1
2
1
0
0
0
0
0
1
2
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
4
1
2
0
1
0
2
2
1
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
1
0
0
1
0
2
1
2
0
0
0
0
0
3
0
1
0
1
1
0
0
0
1
0
0
0
1
0
0
1
1
0
0
2
3
1
0
2
0
2
2
0
0
0
1
1
0
2
1
2
0
1
1
0
1
2
0
1
2
0
0
0
2
2
0
0
1
0
0
0
1
1
2
0
0
0
0
1
2
0
0
1
2
0
0
0
0
0
0
1
2
0
2
2
0
3
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
2
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
1
0
2
2
1
0
0
2
0
1
1
0
0
0
1
2
0
1
2
1
2
0
2
0
2
0
0
1
2
0
1
0
0
2
0
0
1
1
1
3
2
0
2
0
0
0
0
2
0
0
1
0
2
1
3
0
0
0
1
1
0
2
0
0
0
0
4
0
0
0
0
0
0
0
1
2
2
0
1
0
1
2
0
2
0
0
0
2
0
0
2
3
0
0
0
2
0
0
1
1
1
0
2
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
2
2
0
0
1
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
1
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
1
2
1
1
1
0
0
0
1
1
0
0
0
0
0
2
0
0
1
3
2
1
0
0
0
0
0
1
2
2
2
0
1
2
0
2
1
2
0
0
0
2
0
0
0
1
1
1
1
1
1
2
1
2
1
1
0
2
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
1
0
2
0
0
0
0
0
0
0
2
1
0
0
1
0
2
2
0
0
0
0
2
1
0
0
0
0
0
1
0
2
2
0
0
1
1
2
0
1
0
1
0
0
1
2
0
0
0
1
0
1
1
0
2
0
1
0
0
2
0
0
1
0
0
0
2
1
0
0
2
0
2
2
0
3
2
2
0
0
0
0
0
2
0
0
0
1
0
0
2
1
0
1
1
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
2
0
0
2
0
0
0
0
0
2
1
0
2
1
0
2
4
0
0
0
0
0
0
0
2
3
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
1
2
1
0
0
1
0
0
1
2
0
2
0
2
1
2
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
2
0
2
1
1
0
0
0
1
0
0
1
0
0
2
0
1
0
0
2
0
1
0
2
3
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
3
2
0
1
1
1
0
0
2
0
0
1
0
2
0
1
0
0
0
1
0
0
3
0
2
1
0
1
1
0
1
0
0
2
0
0
0
2
0
0
2
0
1
0
0
0
0
2
1
0
1
0
1
0
0
0
0
2
2
1
1
0
0
0
0
2
0
0
0
0
2
2
1
1
0
0
0
2
2
0
2
1
0
0
0
3
0
0
0
0
0
0
0
2
1
1
2
0
0
2
0
1
0
0
1
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
1
0
1
0
0
2
0
1
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
1
0
2
2
0
0
0
0
0
0
0
0
2
2
1
1
2
2
0
0
1
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
2
0
0
1
0
0
0
1
0
1
0
2
0
0
0
0
5
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
1
1
0
0
1
0
2
1
0
1
0
0
0
1
0
0
0
1
1
1
0
0
0
0
1
0
0
1
0
0
2
0
3
0
0
0
2
1
0
0
2
1
0
0
0
4
0
0
0
0
0
0
0
1
2
0
0
5
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
2
1
1
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
2
0
0
0
0
0
1
0
2
0
2
0
0
2
1
5
0
3
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
2
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
2
0
0
1
2
2
0
0
1
0
0
0
0
0
2
0
0
1
1
0
2
0
0
0
2
1
0
1
2
2
0
2
0
1
0
0
0
0
0
0
1
2
0
0
0
1
2
2
0
0
0
0
1
0
0
1
1
0
0
2
0
1
0
1
1
0
0
0
0
2
1
1
0
0
3
0
0
0
4
0
2
0
1
2
0
0
1
0
2
0
0
1
0
1
1
0
0
0
1
0
0
0
0
2
2
2
0
1
2
1
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
1
1
0
0
0
2
0
0
1
1
0
0
2
2
0
0
1
0
2
1
1
0
0
0
2
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
3
2
1
1
1
0
0
0
1
0
0
0
0
1
3
0
0
2
0
2
0
0
0
3
0
2
0
0
0
1
1
0
1
0
0
0
0
0
2
0
0
2
1
2
0
0
0
1
0
0
0
1
0
2
2
0
0
1
1
0
0
1
0
0
2
0
1
0
0
0
0
0
2
0
1
3
1
0
0
0
2
0
0
0
0
1
2
0
1
0
0
2
1
3
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
2
1
1
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
3
1
0
0
0
0
0
1
0
1
0
0
2
0
1
1
0
1
2
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
2
2
0
2
2
2
1
2
0
1
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
1
0
0
0
2
0
2
2
0
3
0
1
0
0
0
0
3
0
0
0
1
2
2
0
0
2
2
0
1
2
0
1
1
0
0
1
0
1
0
0
2
1
0
0
0
0
1
2
0
1
0
0
2
0
1
1
1
2
1
1
0
0
0
0
0
1
1
1
0
0
1
1
0
0
0
1
1
0
2
1
0
0
0
1
0
2
1
1
0
2
0
0
0
0
0
0
0
7
3
2
1
1
3
0
1
0
0
0
0
0
1
2
0
0
2
1
2
1
0
0
1
0
1
1
0
0
1
0
1
1
1
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
2
1
0
0
0
0
0
1
2
0
0
0
1
1
3
0
0
2
2
2
0
0
1
4
0
0
2
0
0
0
1
0
0
2
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
2
1
0
0
1
0
0
2
0
1
0
0
0
1
0
0
2
0
1
0
0
0
0
2
1
1
0
0
0
0
0
1
2
0
1
0
1
0
0
0
0
0
1
2
0
1
0
2
2
2
0
0
2
0
1
0
0
1
1
0
0
3
0
0
2
0
0
0
2
2
0
0
0
0
0
0
19
2
0
0
2
0
0
2
0
1
5
1
1
0
0
2
0
0
0
0
0
1
0
0
0
1
2
0
0
0
1
0
2
0
2
3
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
2
3
0
0
0
0
0
0
0
3
0
0
0
2
0
1
4
0
0
2
0
0
3
1
1
3
1
0
0
0
0
2
2
0
0
0
0
2
0
0
1
4
2
0
0
0
0
0
2
0
0
0
0
1
0
0
2
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
3
1
1
0
1
0
0
0
2
0
2
0
0
0
0
2
0
0
0
2
1
1
0
2
0
0
0
0
0
2
0
0
2
1
0
1
0
0
0
1
0
0
1
2
1
1
0
0
0
2
1
1
0
1
0
1
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
2
1
0
1
2
0
0
0
2
2
0
0
1
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
5
2
0
2
2
0
1
1
0
0
0
0
2
1
1
1
1
3
0
0
0
0
0
1
0
0
1
4
0
2
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
1
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
1
1
1
0
0
1
1
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
1
0
1
2
1
1
0
3
0
0
1
0
0
1
0
0
3
0
0
0
2
0
1
0
0
1
0
2
1
2
0
0
0
0
2
0
2
1
0
2
0
0
0
1
0
0
0
1
0
0
1
1
0
0
2
0
3
0
0
0
0
0
0
0
2
0
1
0
1
2
0
0
0
0
0
0
0
1
1
1
2
1
1
1
1
0
0
7
1
0
0
2
0
0
1
0
0
0
1
0
1
0
2
2
0
2
0
1
0
1
0
0
0
0
0
1
3
0
0
0
0
1
3
0
2
0
2
1
0
0
0
2
0
6
1
0
2
0
1
1
0
0
0
0
2
2
0
0
1
1
1
1
2
0
0
0
0
5
2
1
0
0
0
2
1
0
1
4
2
2
1
0
0
0
0
1
0
2
0
0
1
0
0
1
0
0
0
0
2
1
0
1
2
0
1
0
0
0
0
0
2
0
0
2
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
3
1
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
1
0
3
0
2
0
0
0
0
0
0
0
0
2
1
0
2
1
0
0
0
2
0
0
1
1
0
1
0
0
3
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
2
0
0
0
1
0
0
2
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
1
2
0
0
2
0
2
1
0
2
0
0
0
0
2
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
1
0
0
0
0
0
2
0
3
2
3
2
2
0
1
0
0
0
0
1
0
0
1
0
1
0
2
0
0
0
0
0
1
0
0
2
1
0
0
1
0
2
1
0
0
0
0
2
0
2
2
0
0
0
1
1
1
0
0
0
0
0
0
0
0
2
0
0
0
1
1
1
1
0
0
0
1
0
0
0
2
2
0
2
0
0
1
0
0
0
2
1
0
2
0
0
1
1
1
0
2
2
0
0
2
2
0
2
0
0
1
0
0
0
0
1
0
0
2
0
1
4
0
2
0
0
0
1
1
1
0
0
2
0
2
0
0
0
0
0
2
2
0
0
2
0
1
1
0
2
2
0
0
0
1
0
0
1
0
1
2
2
0
0
0
0
0
1
2
0
0
2
1
2
2
2
1
0
0
2
2
2
2
0
0
0
2
1
0
0
1
1
1
2
2
2
0
2
1
0
0
0
4
0
2
4
2
2
0
0
0
1
0
0
1
1
1
0
0
1
0
0
0
0
0
1
0
0
0
1
3
0
0
0
1
2
1
1
2
2
1
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
2
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
3
0
1
1
0
0
1
1
0
0
0
0
0
2
0
2
2
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
3
0
0
2
0
2
2
0
0
0
1
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
2
0
0
0
0
0
2
2
1
2
1
0
0
1
0
0
1
0
0
1
1
1
2
0
1
0
1
2
1
0
0
0
1
0
1
0
1
0
1
0
0
0
1
0
2
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
1
1
0
0
2
1
0
0
1
0
2
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
3
0
1
3
0
0
2
0
0
0
0
1
0
0
0
0
2
0
2
1
0
0
2
1
0
1
0
0
2
0
0
0
0
0
0
1
0
2
0
3
1
0
0
2
1
0
0
2
3
5
1
0
5
1
0
0
1
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
1
0
0
0
3
0
0
1
1
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
2
0
0
0
0
0
0
2
2
1
0
2
0
0
0
0
0
2
2
0
0
0
0
0
2
2
0
1
0
0
2
0
1
2
0
0
0
0
0
0
2
0
0
0
2
0
2
2
2
1
0
0
2
0
2
3
0
0
2
3
0
0
0
0
2
0
0
0
1
0
1
0
2
0
3
1
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
3
0
2
0
0
2
0
0
0
2
0
2
0
2
0
1
0
0
0
2
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
2
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
2
1
1
1
0
0
1
1
0
0
0
2
1
0
0
0
0
0
2
2
0
1
0
0
0
0
2
1
0
0
0
1
0
2
0
0
2
1
0
0
2
0
1
0
2
1
2
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
2
0
0
0
2
1
1
1
0
0
2
0
0
0
1
1
1
2
2
2
0
1
0
0
0
0
1
1
0
2
2
0
2
1
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
3
3
2
0
0
0
1
1
2
2
0
2
0
0
1
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
2
0
0
0
0
0
2
2
0
1
0
0
0
1
0
0
0
0
2
1
0
1
1
1
1
2
0
0
0
1
2
1
0
1
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
3
0
0
0
2
0
1
0
0
2
0
1
1
0
2
1
1
0
0
0
0
0
1
1
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
4
2
1
2
0
0
2
1
0
1
0
0
0
1
2
0
3
0
1
1
0
0
2
0
0
0
0
2
0
0
0
2
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
3
0
0
0
2
0
2
0
1
0
1
2
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
2
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
1
1
2
0
0
1
1
1
0
1
0
1
3
1
1
0
0
0
3
1
0
1
0
0
0
2
0
0
0
0
0
2
1
0
0
2
0
2
0
0
2
0
0
3
2
0
0
0
1
0
0
0
0
2
0
1
0
0
0
2
2
0
0
0
1
0
1
1
0
0
1
0
1
0
0
0
2
0
0
1
2
1
0
0
0
0
1
2
0
1
1
0
0
0
1
0
3
0
0
0
0
0
0
0
2
2
0
1
0
1
0
0
2
1
1
1
0
0
2
0
0
0
1
2
2
0
0
0
0
0
2
2
3
0
0
2
1
0
0
0
2
0
0
0
0
1
0
0
2
1
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
2
0
0
2
0
2
0
0
2
0
2
0
0
0
1
2
0
0
0
1
1
2
0
2
0
0
0
0
2
0
2
2
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
4
0
1
0
1
0
0
0
2
2
0
0
1
2
0
1
0
0
2
0
0
0
1
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
1
0
2
2
2
1
0
2
0
1
0
0
0
0
1
2
1
2
1
0
0
3
0
0
1
0
2
0
0
0
0
1
0
2
1
5
2
2
1
0
0
2
1
0
2
0
2
0
2
1
0
0
2
2
1
1
0
0
2
0
2
0
0
1
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
2
2
0
1
0
1
1
0
2
0
0
1
1
0
1
2
2
1
0
0
0
2
0
1
1
1
0
0
0
0
0
0
2
1
0
0
1
0
0
0
1
0
0
1
2
1
2
0
3
0
0
0
0
0
1
0
1
2
0
0
0
2
0
1
0
1
0
0
0
0
0
0
1
0
2
0
2
2
0
0
3
0
0
1
1
1
1
1
2
2
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
1
0
2
1
0
0
2
1
1
0
0
1
0
0
1
0
0
0
0
0
1
1
2
0
0
1
0
2
2
0
2
1
0
0
2
0
1
2
1
0
1
0
0
0
0
2
1
0
1
3
2
1
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
1
1
1
1
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
2
0
0
0
1
3
0
0
1
0
0
0
0
2
1
0
0
0
0
2
2
2
0
0
0
1
0
0
1
1
0
2
0
0
0
0
0
1
0
1
0
2
0
2
1
0
1
2
0
0
0
2
0
0
0
0
0
1
1
1
0
0
2
1
1
0
0
2
2
2
0
1
1
3
1
0
0
1
1
0
0
0
2
2
2
0
0
0
1
0
0
0
0
0
2
1
0
0
1
0
0
0
1
0
0
0
0
2
0
0
1
1
0
2
1
0
0
0
2
1
2
2
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
1
1
0
4
0
2
0
1
0
0
2
0
2
1
0
0
2
0
2
2
0
0
0
1
1
0
0
0
0
2
0
2
2
0
0
0
1
0
0
2
2
0
0
0
0
1
1
1
0
0
1
2
2
0
0
0
0
0
0
2
1
0
0
1
0
2
0
1
0
1
1
0
0
0
0
0
0
0
0
2
0
2
1
1
0
2
1
0
2
2
0
0
0
0
1
0
2
1
1
0
0
0
2
0
0
0
1
2
0
0
1
0
0
2
0
0
0
2
2
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
4
0
1
1
0
0
1
0
0
0
0
3
0
1
0
0
0
0
2
0
1
2
1
0
0
2
0
2
1
1
2
1
0
0
2
0
2
1
0
0
0
0
1
2
0
0
0
1
0
1
0
2
0
2
1
0
0
0
1
2
1
2
0
0
1
0
1
1
2
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
2
0
1
0
0
2
0
0
0
1
0
0
2
2
2
0
1
1
0
2
2
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
2
1
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
2
1
0
2
2
2
1
2
1
1
0
0
1
0
1
0
2
0
1
2
1
0
0
0
0
2
0
1
0
0
2
0
2
0
0
0
0
2
2
1
0
2
2
0
0
0
0
2
0
1
0
2
0
0
0
0
2
2
1
0
0
2
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
2
1
0
0
0
1
0
2
1
0
0
0
0
1
0
0
0
0
0
4
2
2
0
0
2
0
0
0
2
1
0
0
0
1
0
0
0
4
0
1
0
0
0
0
0
1
0
0
1
0
0
3
0
2
1
1
0
0
2
2
0
0
0
2
1
0
0
0
0
1
0
1
0
0
0
1
0
0
2
0
0
2
0
0
0
1
0
0
0
1
1
0
0
0
0
2
0
1
2
0
0
1
1
0
0
0
0
2
0
1
0
1
0
0
0
1
0
1
0
0
0
2
0
1
0
0
0
2
0
1
0
1
1
0
1
1
0
0
0
0
0
2
1
2
1
0
2
0
3
0
0
0
2
1
0
0
1
1
0
1
0
0
2
0
0
0
0
0
2
1
0
0
0
2
0
2
0
1
3
0
2
0
0
0
2
0
1
1
0
0
1
1
1
5
0
1
0
0
2
0
2
0
1
0
1
2
1
0
0
0
0
0
1
0
0
0
2
1
0
3
2
1
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
3
0
0
2
0
0
0
1
2
0
1
2
0
2
1
0
0
0
0
1
2
1
2
0
1
2
1
0
0
0
0
0
0
1
0
0
2
0
1
2
0
0
2
0
0
0
0
1
1
0
2
2
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
9
0
0
0
0
0
0
0
0
3
0
0
3
0
0
1
0
2
1
0
2
2
0
0
0
1
1
4
0
0
0
0
1
1
0
0
0
0
0
1
1
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
4
1
0
0
1
0
1
1
2
2
2
0
2
1
0
1
1
0
0
0
2
0
0
1
0
0
1
0
0
1
0
1
1
0
1
0
0
0
2
0
1
0
1
0
0
0
0
0
2
0
3
2
0
2
0
3
0
0
0
1
2
0
0
1
0
0
0
0
0
0
1
0
0
2
0
1
0
2
0
0
0
0
0
0
0
10
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
6
0
0
0
2
1
0
2
0
1
0
0
0
2
1
0
5
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
2
0
1
0
0
2
0
2
1
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
1
0
0
1
2
0
0
0
0
3
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
1
2
1
0
1
0
2
2
1
0
0
1
0
0
0
3
0
0
0
0
0
1
0
2
0
0
0
0
1
0
2
0
2
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
3
0
0
2
2
1
0
0
0
0
0
1
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
1
1
0
1
0
0
0
0
0
2
1
1
0
0
1
0
2
2
2
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
2
0
0
0
1
0
1
0
0
2
0
2
0
2
0
3
1
0
0
0
1
0
0
2
0
0
1
0
1
0
0
0
0
3
0
0
1
0
2
2
0
1
0
1
0
0
0
0
2
2
0
1
2
2
2
0
2
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
2
0
1
0
0
0
0
0
3
0
0
2
0
1
0
0
3
0
0
1
2
2
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
2
0
1
0
1
0
0
0
0
4
2
0
1
0
0
2
1
0
2
0
1
0
2
0
2
1
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
1
0
0
1
0
0
0
0
1
0
2
1
3
0
2
0
2
2
1
2
2
0
0
1
2
0
0
0
0
2
1
0
0
0
0
1
0
0
1
0
0
2
0
1
1
0
0
1
2
0
2
1
1
0
2
0
1
0
0
0
0
0
0
0
2
0
1
0
1
1
0
0
0
2
0
0
0
0
2
2
2
0
0
2
0
2
0
0
0
0
0
0
2
0
2
0
0
1
0
1
0
0
0
0
0
5
0
0
0
1
0
0
1
2
1
0
0
1
0
2
0
0
0
0
0
1
0
0
0
1
1
1
6
0
1
0
0
1
0
1
0
0
0
0
0
1
2
0
0
0
0
0
4
0
2
2
2
0
0
0
0
2
2
2
0
2
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
1
0
2
0
2
0
2
0
0
1
2
2
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
1
2
0
0
0
1
2
2
1
0
0
1
0
1
2
2
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
3
0
0
2
0
2
0
1
1
0
2
0
0
0
2
0
0
1
2
2
2
0
0
0
1
0
2
1
0
2
0
1
1
0
0
0
0
0
0
2
0
4
1
0
3
1
6
1
0
0
2
1
0
1
0
0
0
1
0
1
0
1
2
0
2
1
4
2
2
0
2
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
2
0
0
1
2
0
2
0
2
2
1
2
2
2
0
0
0
1
0
0
0
1
0
0
2
0
1
1
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
1
0
1
1
2
2
2
1
1
0
0
0
0
0
0
2
0
0
0
1
2
0
0
1
1
0
0
2
0
3
2
2
1
0
0
2
0
0
3
0
1
0
0
1
0
3
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
2
2
1
2
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
2
3
2
0
0
0
0
2
0
1
0
2
0
0
0
2
0
0
0
0
6
1
1
0
0
1
0
0
0
1
0
0
0
2
0
0
0
1
0
0
1
0
0
0
1
1
1
0
0
1
1
0
4
0
0
0
1
0
0
0
0
2
2
1
0
0
0
0
0
0
1
0
2
2
0
0
0
1
0
1
0
0
1
2
0
0
0
1
0
2
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
4
0
0
0
2
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
2
0
1
2
0
0
0
0
1
2
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
1
0
4
2
2
0
3
0
0
0
0
2
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
4
1
2
2
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
1
1
0
0
0
0
0
0
1
0
1
1
0
1
2
1
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
2
0
1
0
0
0
3
0
3
0
0
1
0
0
0
2
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
4
0
0
0
1
2
0
0
2
1
0
0
0
2
0
2
0
0
0
1
0
0
2
2
0
0
0
2
0
0
0
0
0
1
1
0
0
1
0
0
0
1
3
0
0
1
1
2
0
0
2
0
2
0
0
0
2
0
0
2
2
0
0
0
1
1
0
0
0
2
0
0
2
0
2
0
0
0
0
3
1
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
2
2
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
3
2
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
2
1
0
0
0
0
0
1
2
0
0
0
2
1
0
0
0
0
0
0
0
0
2
2
0
1
1
0
0
0
1
0
0
1
2
1
2
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
2
0
1
1
0
0
2
2
0
0
0
2
2
0
0
1
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
2
1
2
1
1
1
0
0
0
0
2
0
1
1
0
0
0
1
1
0
1
0
0
2
0
0
0
0
0
2
0
2
0
2
1
0
6
0
0
2
1
0
2
2
2
5
0
2
0
2
1
1
0
0
2
0
0
5
1
0
0
2
0
1
1
0
1
0
0
1
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
2
0
0
2
2
0
0
0
0
2
1
0
0
0
2
2
1
1
2
0
2
1
0
0
2
0
0
1
0
2
0
0
0
0
0
0
2
2
1
0
0
0
0
0
1
1
0
0
1
1
2
2
0
0
1
0
1
0
1
0
1
1
0
2
3
0
0
1
1
0
2
4
1
0
0
2
0
0
0
0
0
1
0
1
1
0
1
1
2
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
2
0
2
0
2
0
0
0
1
2
0
0
1
0
3
0
1
0
0
0
0
2
0
0
2
1
0
0
0
0
0
1
1
0
0
2
0
0
0
4
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
4
0
0
1
0
0
0
0
1
2
0
0
0
2
1
0
1
1
1
0
2
0
0
1
0
2
0
1
0
1
1
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
2
0
1
0
0
2
2
0
0
0
2
0
0
1
0
0
2
1
0
0
3
1
0
2
0
0
1
0
3
0
1
0
0
2
0
0
0
1
1
0
2
0
0
0
3
0
1
2
0
0
0
1
0
0
0
3
0
2
2
0
0
0
0
0
0
0
2
0
1
1
0
0
1
2
0
0
2
0
0
0
0
2
0
0
0
1
1
1
0
0
0
1
0
2
2
0
0
0
1
0
1
0
0
0
1
0
0
0
0
3
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
2
0
1
0
0
1
0
2
0
1
2
0
0
0
2
0
1
0
2
0
1
0
1
2
2
0
0
0
2
0
2
1
0
1
2
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
4
0
0
0
0
2
0
1
0
0
2
3
0
3
0
2
2
0
0
0
0
1
0
0
0
1
0
2
0
0
0
2
1
2
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
1
0
2
1
0
0
0
2
0
0
1
0
0
0
1
1
0
2
1
2
0
1
0
0
0
0
0
0
0
1
2
2
0
1
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
4
1
0
1
0
0
2
4
0
0
0
2
0
2
1
0
0
0
0
1
0
0
0
0
3
0
0
0
0
2
1
0
0
1
1
0
0
0
1
0
1
0
0
0
1
1
0
2
0
0
0
0
0
0
1
0
0
1
0
3
0
0
2
0
0
2
0
0
2
2
0
0
0
0
0
0
1
0
0
1
1
2
0
0
1
0
0
0
1
2
1
0
0
1
2
1
2
0
0
0
0
0
0
1
1
0
0
2
0
1
0
2
0
0
3
2
1
0
0
1
0
0
1
2
0
0
0
0
0
0
1
2
4
1
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
3
1
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
1
0
0
1
0
0
3
0
1
1
1
1
0
0
0
1
0
2
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
1
1
1
0
3
1
0
0
2
2
1
2
2
2
0
2
1
0
0
1
0
0
0
2
1
0
2
2
0
2
0
1
0
5
0
3
0
0
2
1
2
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
2
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
2
0
2
0
0
0
2
0
0
0
1
2
1
0
1
0
0
0
0
0
0
2
2
0
2
1
0
0
1
1
2
6
0
0
1
0
0
0
0
1
1
0
2
1
0
2
1
1
1
1
2
1
3
0
0
2
1
0
0
1
2
0
0
1
0
0
0
2
0
2
0
1
0
1
1
1
0
2
0
2
0
0
0
0
0
2
0
0
0
1
0
2
0
1
0
0
0
0
1
0
0
2
1
0
0
0
1
2
2
1
1
1
0
0
1
2
1
0
0
0
2
0
1
1
1
0
2
2
0
0
2
0
1
0
2
2
0
0
0
1
0
0
1
2
1
0
0
2
2
0
1
0
0
3
1
0
0
0
3
2
0
0
0
0
4
1
0
1
0
3
0
1
0
0
0
2
1
0
0
0
1
0
1
0
0
0
1
2
0
0
2
0
0
1
1
0
0
0
2
1
0
0
0
0
0
1
0
2
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
2
3
0
2
0
0
2
1
3
0
3
0
1
0
0
0
0
0
0
4
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
3
2
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
2
0
1
0
0
0
1
2
0
0
2
1
1
0
0
1
0
2
0
0
0
0
1
2
1
0
2
1
2
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
3
1
3
0
0
1
2
0
0
0
2
0
0
1
0
0
2
1
0
1
0
1
0
0
0
2
1
0
0
1
0
0
0
1
0
0
0
0
1
0
3
2
0
0
0
0
0
3
2
1
0
0
1
0
0
1
0
0
2
2
0
0
1
2
0
0
0
0
0
1
0
0
0
2
1
0
2
2
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
1
1
0
0
1
1
0
0
1
0
1
0
0
0
0
0
2
3
1
0
0
0
0
0
1
0
2
1
0
0
1
0
1
2
0
0
1
1
0
0
0
0
2
0
0
0
1
1
1
0
0
2
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
3
2
0
0
0
3
0
0
0
3
0
0
0
2
2
2
1
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
2
1
0
3
2
1
2
1
0
0
3
0
0
2
0
0
1
1
0
2
0
0
1
3
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
1
2
0
0
0
2
0
2
0
0
2
1
0
1
0
0
1
0
1
0
0
2
0
1
1
1
0
0
2
0
0
0
0
0
1
1
0
2
0
0
1
2
1
1
2
0
2
1
0
2
0
0
1
2
0
2
1
0
0
1
1
0
0
0
1
2
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
2
2
2
0
0
0
0
1
0
0
0
1
0
0
1
1
2
0
1
2
2
0
0
0
1
2
1
1
0
2
0
0
0
2
0
0
1
0
1
1
0
0
0
3
0
0
0
2
2
2
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
1
1
0
1
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
3
0
2
1
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
2
1
2
0
0
1
0
0
0
0
0
0
0
2
1
2
2
0
1
0
0
0
0
0
0
2
2
0
3
0
0
0
0
0
0
1
0
0
0
1
1
1
0
2
0
0
0
0
0
0
0
0
0
1
0
2
1
0
2
0
1
0
0
1
0
0
1
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
1
0
2
0
1
0
1
2
0
0
0
1
0
1
0
0
0
0
0
2
0
0
1
0
2
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
2
1
1
0
0
0
0
4
0
2
2
0
0
0
0
2
0
1
2
0
1
0
1
2
2
0
0
0
1
0
0
1
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
2
0
0
2
1
0
0
2
0
1
0
0
1
0
0
0
0
0
0
1
1
0
2
0
0
1
0
2
0
0
0
0
2
1
0
1
2
1
1
1
2
2
0
1
1
0
2
0
0
6
0
1
1
0
2
0
0
0
1
0
3
0
0
2
2
0
0
1
0
0
2
0
1
1
0
0
0
0
1
2
1
0
3
0
1
2
3
2
0
0
0
2
0
2
0
0
0
1
0
0
2
1
1
1
0
0
2
0
0
2
2
2
0
0
3
0
0
1
0
1
0
2
0
0
0
2
1
1
1
1
1
2
0
2
0
0
0
0
2
0
0
0
0
2
2
0
2
0
1
0
2
0
0
0
0
0
0
2
0
0
0
1
0
1
0
2
2
0
0
2
0
0
0
0
1
1
1
0
1
1
0
2
0
2
0
0
0
0
1
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
2
2
2
1
2
1
1
0
0
0
1
0
0
0
0
0
2
0
2
0
2
1
5
1
0
2
2
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
2
2
0
3
0
1
0
2
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
1
2
1
0
3
0
1
0
0
0
0
0
2
2
2
0
2
0
0
0
0
0
0
1
0
2
2
0
0
2
0
1
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
2
0
0
1
0
0
0
1
2
0
1
0
2
0
1
0
0
1
0
1
0
0
0
0
0
0
2
2
0
0
2
1
0
1
1
0
2
1
0
0
2
0
0
1
0
4
0
2
0
0
1
0
1
0
0
1
2
0
2
3
0
0
2
0
1
1
0
0
2
0
2
0
2
0
0
0
2
2
2
1
0
0
0
0
0
2
2
0
1
0
1
0
0
0
2
0
0
2
0
0
1
0
1
0
0
0
0
0
0
2
0
1
0
1
2
2
2
2
0
0
0
0
0
2
0
2
0
0
1
5
0
1
3
0
1
0
0
0
0
0
2
0
0
0
2
1
0
0
2
0
2
2
2
0
1
0
0
0
2
1
0
0
1
1
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
1
0
1
0
0
0
0
2
1
2
0
0
1
1
1
0
0
0
0
0
1
1
2
2
2
0
2
0
0
0
0
2
0
0
0
0
1
2
0
0
1
2
0
0
2
0
0
0
1
2
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
1
1
2
0
0
0
1
0
0
0
0
2
0
1
2
0
2
0
0
0
0
1
0
0
0
2
0
0
1
1
1
0
0
1
1
0
0
0
0
2
0
0
0
0
1
1
2
2
0
0
0
2
0
0
0
0
2
0
2
1
0
1
0
0
2
1
0
0
0
0
0
2
0
1
1
1
0
0
1
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
1
0
2
0
0
2
0
0
0
1
1
0
1
2
0
1
0
0
0
2
0
1
0
2
3
0
0
2
0
0
1
0
2
1
0
0
0
1
3
1
0
0
0
3
0
0
0
0
0
1
0
1
0
0
0
2
1
0
0
1
0
0
0
2
0
0
1
0
0
1
0
1
1
1
0
0
0
1
0
0
0
2
0
1
1
2
0
2
1
2
2
0
0
0
0
1
0
1
2
2
2
1
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
1
0
3
2
0
0
0
2
1
0
1
0
1
1
0
0
1
0
1
1
1
1
0
2
1
0
1
0
0
0
2
0
2
0
2
2
0
1
0
0
0
2
1
0
2
0
0
0
0
0
2
0
1
1
0
2
0
0
0
0
0
2
2
0
0
0
0
1
1
1
0
3
0
0
1
2
2
1
0
0
1
0
1
0
0
2
2
0
1
1
0
0
0
2
0
0
2
0
0
1
0
0
0
0
3
0
0
2
0
1
1
0
0
2
0
0
0
2
0
3
0
4
0
1
2
2
2
1
1
0
3
0
1
1
0
2
2
0
3
0
0
1
1
0
2
0
0
1
0
0
3
2
2
0
0
0
1
0
0
2
0
2
0
0
1
1
2
0
1
0
0
1
1
0
0
1
0
0
0
0
2
0
0
3
0
4
0
0
1
1
0
2
0
0
1
1
0
0
0
0
3
1
0
1
0
2
0
2
2
0
0
0
0
0
2
2
1
0
0
0
0
0
1
0
0
0
1
0
0
2
1
0
1
0
0
0
0
1
0
0
0
1
2
0
1
0
1
0
2
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
3
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
2
1
0
0
0
2
2
0
1
0
2
0
0
0
0
0
0
0
4
1
2
0
0
1
1
1
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
2
1
0
1
0
3
1
0
2
0
2
0
1
0
2
2
0
0
1
0
1
0
0
0
1
0
0
1
1
0
0
1
1
0
1
0
2
0
0
1
0
0
1
0
0
1
0
0
1
1
0
2
1
1
0
6
0
0
0
2
0
0
0
1
1
0
1
0
0
3
2
0
0
0
2
2
1
0
0
0
0
1
0
0
0
0
0
2
1
0
0
1
1
1
0
2
2
2
1
6
2
0
0
0
2
1
1
0
0
0
1
1
1
0
0
0
2
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
1
1
0
1
1
2
2
0
2
0
1
2
2
0
2
2
0
2
2
0
1
0
0
0
0
2
0
2
0
0
0
2
0
2
1
2
0
0
0
3
0
2
0
2
1
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
1
1
1
0
2
2
2
1
2
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
3
0
0
3
0
0
0
0
2
0
2
0
0
2
1
0
2
0
0
0
1
0
1
0
1
0
1
1
0
0
0
0
1
0
0
2
0
0
0
0
2
0
2
1
1
0
1
2
0
0
0
0
2
0
1
0
0
0
1
0
0
1
0
0
0
2
2
0
1
0
1
1
2
0
1
0
0
0
1
0
2
1
0
0
3
0
0
0
0
0
1
1
0
1
0
0
0
2
1
0
0
2
0
1
0
0
1
0
1
1
0
0
2
1
1
0
0
0
2
0
3
0
2
0
3
1
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
1
2
1
0
0
0
0
1
1
0
0
2
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
3
2
0
0
0
0
2
0
0
2
0
2
0
1
0
1
2
0
2
0
1
2
1
0
2
3
0
0
2
0
0
1
0
1
0
0
1
0
0
0
0
2
2
1
0
2
0
2
2
0
0
0
0
2
1
1
0
1
0
0
0
0
0
0
0
0
2
0
1
0
1
1
0
1
0
2
1
0
0
0
0
1
0
1
4
0
0
0
0
0
2
0
1
0
2
0
0
0
1
0
3
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
1
0
1
0
1
0
2
0
1
1
0
0
0
1
2
0
0
2
0
0
1
0
1
1
0
1
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
2
1
2
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
2
1
2
1
1
0
0
2
0
0
2
0
0
1
0
1
0
1
2
1
1
2
0
0
2
0
0
1
1
2
0
0
0
2
0
2
1
0
0
2
0
5
0
0
1
1
0
0
0
1
0
2
0
0
0
1
0
2
0
0
0
0
1
2
0
2
2
0
0
0
0
1
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
1
0
0
3
1
3
2
0
4
1
1
0
0
0
1
0
0
2
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
2
2
1
0
0
2
0
2
2
0
2
0
2
0
2
0
0
0
0
1
0
0
0
0
1
0
1
0
1
1
0
0
1
0
0
0
0
1
0
1
0
2
2
0
4
2
0
0
1
2
0
0
0
1
1
0
0
0
0
1
2
0
1
0
0
5
0
0
2
1
2
0
0
1
2
0
0
0
0
0
1
2
2
0
1
2
0
0
0
0
0
2
0
0
1
0
0
1
1
2
0
1
0
2
1
0
0
0
1
0
0
1
1
0
0
3
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
1
0
0
0
1
2
0
2
0
0
0
2
0
1
0
3
0
2
0
0
0
0
1
0
0
0
3
0
2
0
1
1
0
0
2
2
2
0
0
0
1
0
1
0
0
0
3
1
0
0
0
2
0
2
1
2
0
0
0
2
2
0
0
0
0
2
0
0
2
0
0
2
2
0
1
1
0
1
0
0
2
2
2
0
0
0
1
0
0
0
2
0
0
3
2
2
0
1
0
1
1
2
1
0
0
1
0
2
1
1
1
1
1
0
1
0
0
0
1
0
2
2
2
2
1
0
1
0
0
2
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
2
0
1
0
0
1
2
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
3
1
0
0
0
1
1
0
0
2
1
2
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
1
0
2
0
0
0
0
1
0
1
0
0
1
0
2
0
2
0
0
2
2
4
0
0
0
1
2
0
1
0
0
2
0
0
0
1
1
2
2
0
1
0
2
0
2
0
4
1
0
0
0
0
0
0
1
2
2
0
1
2
2
2
0
3
2
1
1
1
1
0
0
1
2
0
2
0
0
0
0
0
0
1
2
0
0
1
0
2
0
0
0
1
1
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
2
1
0
3
0
0
0
2
0
2
0
2
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
2
1
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
2
2
1
0
2
0
0
0
0
2
2
0
0
2
0
0
2
2
0
2
6
0
0
0
0
0
0
0
3
0
0
0
0
1
0
2
1
2
0
2
0
0
3
0
0
0
0
2
0
0
2
0
0
0
0
2
2
1
0
0
0
0
2
2
0
0
1
2
0
0
1
0
3
1
0
0
0
1
1
2
1
0
2
2
1
0
0
0
2
1
0
1
0
0
0
0
0
1
0
0
0
1
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
1
1
0
1
0
1
2
0
0
0
2
0
4
0
0
1
0
2
1
3
2
0
1
0
0
2
0
1
1
0
0
1
0
2
2
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
2
0
0
1
1
0
1
0
0
1
0
0
0
0
0
2
1
0
0
0
0
1
1
2
0
1
2
0
1
1
0
1
0
1
0
2
0
0
2
0
0
2
2
2
0
1
1
0
0
0
0
0
3
0
0
2
0
1
2
0
1
0
0
2
0
0
0
0
0
0
0
0
2
2
1
1
0
2
2
1
2
0
0
0
1
0
0
1
2
1
0
0
0
2
1
0
0
1
1
0
0
0
3
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
1
0
0
0
2
1
0
0
0
0
0
2
1
2
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
2
2
1
0
1
0
0
1
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
2
0
0
0
0
0
0
1
0
2
1
1
3
0
0
0
1
1
1
0
0
2
2
0
1
1
0
0
1
2
0
0
0
0
2
0
2
1
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
2
3
0
1
1
1
0
2
1
0
0
2
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
3
0
2
0
0
0
0
1
2
1
0
2
0
0
0
0
2
2
0
0
0
1
0
2
0
0
1
0
0
0
2
0
3
1
0
1
1
0
0
1
0
2
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
1
4
0
1
0
0
0
1
1
0
0
2
0
2
0
2
1
0
0
0
1
4
4
1
1
2
0
0
0
1
0
0
1
2
2
2
1
0
0
2
0
0
0
0
1
1
0
2
1
0
0
1
0
0
3
0
0
1
0
1
0
0
0
0
1
0
1
0
2
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
1
1
0
0
0
1
1
1
1
2
3
2
1
1
0
1
0
2
0
1
0
1
1
0
1
1
1
2
0
0
1
1
0
2
0
1
1
1
2
2
0
2
0
0
2
0
0
1
2
0
0
0
0
0
0
2
0
0
0
2
0
2
0
2
2
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
2
1
0
0
1
1
0
1
0
0
2
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
3
0
1
1
1
0
0
1
1
2
0
1
1
1
0
0
1
1
0
2
0
1
0
0
6
1
0
0
2
0
0
0
3
1
1
2
0
2
2
0
0
0
2
1
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
2
2
0
0
1
1
1
1
0
0
0
0
4
2
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
2
2
0
2
2
0
0
4
2
1
2
0
1
0
0
0
2
0
1
0
0
1
0
0
1
0
0
2
2
0
2
0
0
0
0
0
0
1
0
0
0
2
1
0
0
1
1
0
2
2
2
2
1
0
2
0
0
0
0
4
1
1
1
0
0
2
0
0
0
0
0
2
0
0
1
2
0
2
1
0
0
2
0
0
1
0
2
2
0
0
2
1
2
0
1
2
1
0
0
2
0
2
1
0
2
0
0
0
0
2
0
1
0
2
2
1
1
0
0
0
0
0
0
2
2
0
1
0
0
2
0
1
0
0
2
0
0
1
0
2
4
2
2
0
2
1
1
0
0
1
0
2
2
1
0
0
0
0
0
0
0
1
2
0
0
1
0
3
0
0
0
1
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
2
0
1
0
0
0
0
2
0
0
1
1
0
1
0
0
2
0
0
0
0
2
3
0
2
2
0
0
1
0
0
0
1
0
2
0
3
2
1
0
0
2
0
0
0
2
2
1
1
0
2
0
2
0
3
0
0
1
0
0
0
0
2
0
0
0
1
2
2
0
0
2
2
0
0
0
1
1
1
0
0
3
2
1
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
3
2
0
0
3
0
0
1
0
0
1
2
0
0
1
1
0
0
0
1
0
2
0
2
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
1
0
1
2
0
2
0
0
0
0
1
0
3
0
0
0
1
0
0
6
1
0
0
3
2
0
2
0
2
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
2
1
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
2
1
0
1
0
0
2
0
0
2
0
0
1
0
0
0
3
0
1
0
1
2
0
1
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
2
0
2
0
0
0
1
1
0
2
0
0
0
1
0
1
1
0
0
1
2
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
2
1
0
0
0
0
1
0
1
0
2
1
2
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
1
0
1
2
0
0
1
0
0
2
1
0
2
1
0
2
1
2
0
0
2
2
0
0
2
0
1
0
0
0
2
2
0
0
0
0
0
1
0
1
0
1
0
0
0
1
2
0
0
2
0
0
0
3
2
0
1
0
0
0
2
0
0
0
0
1
0
1
0
1
1
3
0
0
0
2
0
2
2
2
2
0
0
1
2
0
0
0
2
0
1
0
0
1
0
0
1
0
2
0
0
0
0
2
1
0
0
1
0
0
0
0
0
2
1
0
0
0
2
0
1
2
1
0
9
2
0
0
0
0
2
0
0
1
0
1
0
2
0
2
0
3
2
0
0
0
1
0
0
2
1
0
0
0
3
0
4
0
0
0
1
1
0
1
0
0
0
0
0
2
2
0
1
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
2
0
3
0
0
1
1
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
0
2
0
2
1
0
1
0
0
0
0
2
1
1
0
0
1
1
0
0
1
2
2
2
0
1
2
1
0
0
0
0
1
1
0
1
0
2
1
2
1
3
2
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
1
2
0
0
2
0
1
2
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
1
0
2
1
0
0
0
0
2
1
0
0
0
2
0
2
2
0
0
2
0
0
2
0
0
1
0
3
0
2
0
0
1
0
0
2
0
0
1
0
0
0
0
0
1
1
0
0
2
0
0
0
0
1
0
1
0
2
0
3
1
0
0
2
0
0
0
0
0
0
1
1
1
0
0
0
0
1
1
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
1
0
0
0
2
1
0
2
0
1
1
1
0
2
0
0
2
0
0
0
0
1
0
0
2
2
1
2
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
2
0
2
2
1
0
0
0
0
0
0
0
1
2
0
0
1
0
1
2
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
1
0
0
1
2
1
2
0
2
0
0
0
1
1
0
2
0
0
1
0
1
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
2
1
0
0
0
0
1
0
0
0
2
2
0
1
1
1
2
0
0
0
3
0
3
0
0
0
2
0
0
0
2
1
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
2
0
2
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
2
0
0
0
2
0
0
0
0
0
1
2
0
2
1
2
0
2
1
0
1
2
0
0
1
0
0
0
0
2
2
2
0
0
2
0
2
0
0
1
0
1
1
1
1
2
0
2
2
0
0
1
1
1
2
1
2
2
0
0
2
0
0
0
1
2
1
2
1
2
1
0
0
2
1
2
2
0
1
1
0
0
0
0
2
0
0
2
4
0
0
0
1
0
0
1
3
0
0
0
1
1
0
2
1
0
1
0
0
0
0
1
1
1
0
0
0
0
0
1
1
2
0
0
0
1
1
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
2
1
3
1
2
1
0
0
1
1
0
0
0
2
2
1
0
0
2
1
0
0
0
1
3
0
2
2
0
0
1
0
0
0
2
1
0
0
1
2
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
4
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
1
0
2
0
2
1
0
1
2
0
0
2
0
2
0
1
0
0
2
0
0
1
0
0
0
1
0
0
0
0
1
0
2
0
2
1
1
0
0
1
1
1
0
0
0
0
0
0
4
1
0
0
1
0
1
2
0
0
0
0
0
2
1
0
0
1
1
0
0
0
0
1
2
0
0
1
0
0
2
2
0
2
0
0
1
0
0
2
2
0
0
1
0
0
0
0
2
2
2
1
0
0
0
0
0
0
1
0
2
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
2
1
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
2
0
2
2
0
0
1
0
1
0
0
1
0
1
1
1
0
1
4
1
1
0
0
0
1
0
2
0
0
1
1
2
1
2
1
1
1
0
1
0
0
1
1
0
0
0
1
0
0
1
1
1
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
2
0
0
0
7
0
1
0
1
0
3
1
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
1
2
0
0
1
0
0
2
2
0
0
1
0
1
0
0
0
1
1
0
0
1
0
1
1
1
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
1
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
5
3
2
0
0
0
1
0
4
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
3
2
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
1
1
2
1
0
0
0
0
0
0
1
1
0
0
0
19
0
0
1
2
0
0
0
0
1
0
6
1
0
0
2
3
1
0
0
2
0
1
0
0
0
0
2
1
2
2
1
0
0
0
0
1
0
2
1
0
0
3
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
3
0
0
1
0
2
3
2
0
2
0
1
0
0
1
0
0
1
1
0
0
1
1
0
1
0
0
0
0
2
1
2
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
2
0
1
1
0
0
0
0
2
0
0
0
1
2
0
0
0
1
2
0
0
0
2
1
2
1
0
0
0
0
2
1
0
0
0
2
3
2
1
0
2
0
0
0
0
1
1
2
0
1
2
0
1
2
1
1
2
0
0
0
1
0
0
0
0
0
0
0
1
0
2
2
1
0
2
0
2
0
2
0
0
0
2
0
0
0
0
1
0
2
2
0
0
3
1
0
0
0
3
0
1
0
0
2
1
0
0
2
0
0
0
1
0
0
1
0
2
0
1
2
1
0
0
1
0
0
0
0
1
1
0
1
0
0
2
2
0
0
1
0
0
0
0
1
1
1
0
1
0
2
0
0
6
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
1
0
0
0
2
1
1
0
2
0
0
1
0
0
0
0
2
2
2
0
3
3
1
2
1
1
0
0
0
1
0
2
2
0
0
0
0
0
2
1
4
0
0
0
0
1
2
0
0
0
0
1
0
0
1
2
4
0
0
0
1
0
2
1
0
1
1
0
0
1
1
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
2
0
1
0
0
2
0
0
2
1
0
0
2
0
0
2
0
0
0
2
0
3
0
0
0
0
0
1
1
0
2
0
0
0
0
1
2
0
2
0
0
2
1
0
0
0
1
0
0
1
2
1
0
0
0
0
0
0
2
0
2
0
1
0
2
2
2
2
1
2
0
2
0
0
1
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
3
0
0
0
1
0
0
2
1
0
0
1
0
0
0
2
0
3
0
1
0
0
2
3
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
1
1
2
2
0
1
0
2
1
2
2
0
0
1
0
0
0
1
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
1
1
1
0
0
5
0
1
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
2
1
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
1
1
1
0
0
1
0
0
0
0
0
1
0
2
0
0
3
0
2
1
0
2
0
0
1
1
0
1
0
0
2
1
0
1
0
0
0
1
0
1
0
2
1
0
1
0
1
2
2
2
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
1
0
0
0
0
4
2
1
0
0
2
1
1
2
0
1
2
0
2
0
0
2
0
0
2
2
0
0
0
0
1
0
2
1
3
0
1
2
0
0
0
2
0
1
0
0
0
1
4
2
0
0
0
2
0
0
0
1
2
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
2
1
0
0
0
2
0
0
0
2
0
0
2
1
2
0
0
1
0
2
0
1
0
1
3
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
1
0
0
2
0
0
0
1
0
2
0
0
1
1
2
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
1
0
0
1
0
1
2
0
0
0
2
2
0
3
0
0
0
0
0
1
1
0
1
0
0
0
1
2
1
0
2
0
0
1
0
1
0
3
2
1
0
0
0
0
0
2
0
1
2
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
1
2
0
2
0
1
0
1
0
2
1
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
1
2
0
2
1
0
0
2
1
2
0
1
0
0
2
0
0
0
0
0
1
1
0
2
0
0
0
1
0
2
0
2
3
2
0
0
0
0
0
1
3
3
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
1
0
1
2
2
0
0
2
1
0
0
1
9
0
1
2
2
0
2
0
0
0
0
0
2
1
0
1
1
1
2
2
2
0
3
0
0
1
1
1
0
0
1
1
2
1
1
0
1
0
1
2
0
0
2
0
0
0
0
2
0
0
0
1
0
2
2
0
0
1
0
1
0
2
1
0
1
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
1
0
0
0
1
2
1
1
0
0
2
0
2
2
0
1
2
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
1
1
0
0
0
1
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
1
1
0
0
0
0
1
0
2
0
0
3
0
1
2
0
0
3
0
0
2
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
4
1
0
0
1
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
2
1
1
0
2
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
1
2
2
0
2
1
0
0
0
3
0
0
0
1
1
0
0
0
0
0
2
0
2
2
2
0
0
1
1
0
2
0
0
1
0
0
0
0
0
1
1
0
2
1
1
4
1
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
2
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
1
2
1
0
0
0
0
0
2
0
0
2
1
1
0
1
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
2
0
0
2
0
0
0
2
0
0
1
0
2
0
0
2
1
1
2
0
2
0
0
0
1
2
1
0
1
0
2
0
0
1
0
2
1
2
2
0
2
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
1
1
1
1
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
1
2
1
2
0
0
2
1
0
0
2
1
2
1
1
1
1
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
2
0
2
0
2
2
0
1
0
2
1
2
2
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
1
0
3
0
1
0
0
2
0
1
0
0
3
1
2
0
1
0
2
0
0
2
0
0
0
3
1
0
0
1
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
1
1
0
2
1
2
0
0
1
2
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
2
0
2
1
1
2
2
0
0
0
2
2
1
0
0
2
0
0
0
1
2
1
2
2
1
2
0
0
1
0
0
1
0
4
1
2
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
1
1
0
0
0
2
1
1
0
0
1
0
1
1
0
2
0
0
1
0
0
2
0
1
1
0
1
0
0
0
0
0
0
1
2
2
0
1
0
0
0
0
1
1
0
0
2
0
0
1
0
0
0
3
0
0
5
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
2
1
0
0
0
0
1
0
0
1
1
1
0
0
0
1
0
0
0
1
2
1
1
0
1
2
0
0
1
2
0
0
0
0
0
0
1
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
2
2
0
0
0
0
0
1
0
1
0
0
1
1
0
0
6
3
0
2
0
4
0
0
2
0
2
0
1
0
0
0
0
1
0
2
0
0
1
1
1
1
1
1
1
0
0
0
1
0
0
0
2
2
2
2
1
0
0
0
1
1
2
2
0
1
1
2
2
0
2
1
3
0
2
2
0
0
0
2
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
3
0
0
1
4
0
2
1
0
0
1
3
0
0
0
0
0
1
0
0
3
2
0
1
0
2
0
0
0
2
0
2
0
0
1
0
0
0
0
2
2
1
0
1
1
2
0
1
0
1
1
0
2
0
1
3
2
1
0
2
1
1
2
0
0
0
0
0
1
0
0
0
0
1
1
0
2
0
0
3
0
0
0
2
1
1
2
1
1
2
0
0
0
0
1
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
5
2
1
0
0
1
2
0
0
1
0
3
0
0
1
1
2
2
0
0
0
0
1
2
1
0
1
0
1
1
1
0
1
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
1
0
2
2
2
2
0
0
0
0
0
0
1
1
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
3
2
0
2
0
0
0
1
1
1
0
0
0
0
2
0
0
3
0
2
1
0
1
2
2
2
0
0
0
0
0
0
2
0
0
0
2
0
1
0
1
1
0
1
0
0
1
0
0
2
1
0
0
3
0
0
0
0
0
0
0
0
2
1
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
1
3
0
0
0
0
1
0
1
0
1
0
0
0
0
3
1
2
1
0
0
2
0
0
0
0
3
0
2
2
0
1
0
0
0
0
0
0
1
0
1
2
2
1
0
1
1
2
2
0
0
1
1
0
2
0
0
1
1
1
1
3
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
3
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
3
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
1
2
1
2
0
2
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
1
3
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
2
0
1
0
2
0
0
0
1
2
0
1
2
1
0
0
0
0
1
0
0
1
0
2
0
0
1
1
0
0
1
2
0
0
0
0
2
1
2
1
0
0
1
0
1
1
0
2
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
2
0
0
2
1
2
0
2
0
2
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
2
1
0
0
2
1
0
1
1
0
2
2
2
0
0
0
0
1
1
1
1
0
2
0
1
2
0
2
0
0
0
0
0
1
0
2
0
1
0
0
0
0
2
0
1
0
1
0
0
2
1
0
0
0
0
0
2
0
0
1
2
0
1
2
5
0
0
0
2
0
0
0
0
0
2
1
0
1
1
1
0
0
0
1
2
0
0
0
0
3
2
1
0
0
0
0
0
0
0
0
0
0
3
1
1
0
0
1
0
2
1
1
2
2
0
2
1
0
2
0
1
1
0
2
1
0
0
0
1
0
0
0
0
0
2
1
0
0
2
2
0
0
2
1
0
0
0
0
0
0
3
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
2
2
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
1
1
0
0
0
0
0
0
2
0
0
1
0
0
2
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
2
0
0
1
1
2
0
0
1
1
0
2
0
0
0
0
1
0
0
0
1
2
0
1
0
0
0
0
0
1
0
0
0
2
0
1
1
0
0
0
0
2
0
0
2
3
3
2
2
0
1
2
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
1
2
0
0
0
1
0
1
1
0
0
0
0
0
1
2
2
1
0
0
2
0
0
0
0
0
0
2
0
0
0
1
2
2
0
2
1
0
0
0
0
2
2
0
0
2
2
0
0
0
0
0
0
1
0
0
2
3
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
2
1
2
1
0
0
0
0
0
0
1
0
0
2
0
0
0
3
0
3
0
0
0
1
0
0
0
0
1
0
1
1
0
2
0
0
1
1
0
0
1
0
2
2
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
2
0
0
1
1
0
1
0
0
0
0
1
0
0
0
1
1
0
2
2
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
1
0
1
3
2
0
0
0
0
2
1
0
1
0
0
0
0
0
0
1
0
0
0
2
0
1
1
1
0
0
1
0
1
0
1
0
0
0
2
0
2
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
2
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
2
0
1
0
1
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
1
1
1
0
0
0
0
2
0
2
1
1
1
0
0
2
2
0
0
1
2
0
2
0
0
0
0
0
1
1
0
0
0
0
1
3
0
1
0
0
3
2
0
0
0
2
0
0
2
1
2
2
0
0
1
0
1
3
3
2
0
0
0
1
0
2
0
1
0
1
1
1
0
0
0
2
1
0
0
2
1
0
2
0
2
0
1
1
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
2
1
3
0
1
0
2
0
0
1
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
2
0
1
2
0
1
2
1
1
0
2
0
1
2
0
0
0
0
1
0
1
0
0
1
0
0
0
2
0
0
1
0
2
1
0
1
0
2
0
0
2
1
0
0
2
2
2
2
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
2
0
2
0
0
0
0
2
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
1
5
0
0
0
0
0
0
0
0
0
3
0
2
0
0
4
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
4
0
0
2
1
0
0
0
1
4
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
2
0
2
0
0
2
0
2
2
0
0
0
0
1
0
0
0
2
0
0
1
1
0
0
2
2
1
0
0
0
0
2
1
0
3
2
0
0
1
1
0
0
0
0
0
1
0
1
1
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
1
0
0
2
0
0
0
2
0
2
0
1
2
0
0
0
0
1
1
0
2
0
2
2
0
0
0
0
1
0
1
1
0
0
0
0
0
1
1
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
1
0
0
0
2
0
1
2
0
0
0
1
1
0
0
0
2
2
1
0
2
1
0
1
1
1
1
1
0
0
2
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
2
1
0
0
2
0
0
0
1
0
0
0
0
1
0
0
2
0
1
1
0
1
2
1
1
0
2
1
1
0
0
0
1
2
2
0
0
0
1
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
1
2
2
0
2
0
2
0
0
0
0
0
0
3
0
0
0
0
0
1
2
0
3
0
2
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
1
1
1
2
0
0
0
0
1
0
1
0
0
2
0
2
0
0
0
2
0
1
2
2
0
0
1
0
0
0
2
0
0
0
2
2
0
0
0
1
0
1
0
0
0
0
1
0
0
0
2
0
0
1
0
1
3
1
2
0
2
2
0
0
2
1
1
1
0
0
0
0
0
1
2
0
0
1
3
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
1
3
0
1
1
0
0
0
0
1
0
2
1
1
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
1
0
0
2
1
0
0
0
0
2
1
1
0
1
2
0
0
2
2
2
0
1
1
1
2
0
0
2
0
1
0
0
0
2
0
0
0
0
2
0
0
2
1
1
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
1
1
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
1
0
0
0
2
0
1
0
0
0
2
0
0
2
0
1
2
0
0
0
1
1
0
1
4
1
1
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
3
1
0
0
0
0
0
0
1
0
1
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
3
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
2
0
1
4
1
0
0
0
0
2
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
1
1
1
0
2
0
0
2
1
1
0
1
1
0
1
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
2
0
1
0
0
2
0
2
2
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
3
1
2
2
1
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
2
2
0
0
0
0
0
0
0
3
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
1
0
3
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
1
0
0
2
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
2
0
0
1
1
0
2
1
1
2
2
2
0
0
1
0
0
0
2
2
0
0
0
0
2
2
0
0
0
2
1
0
1
0
0
0
1
0
0
1
1
1
1
1
2
2
1
1
0
0
0
0
2
0
1
0
0
0
0
0
2
2
0
1
0
2
1
2
2
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
1
0
4
0
3
1
1
1
2
0
0
1
0
0
1
2
0
2
0
0
0
0
2
2
0
0
1
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
2
0
2
0
1
0
0
2
0
0
0
1
1
2
1
2
0
0
0
0
1
0
1
2
1
0
2
1
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
2
2
3
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
2
0
0
0
2
0
0
0
0
0
1
1
0
0
2
1
2
2
0
0
2
2
0
1
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
1
0
4
0
0
0
0
0
0
1
2
0
0
0
1
2
2
2
0
0
2
0
1
0
2
0
0
0
0
1
0
0
0
1
1
1
0
1
1
0
0
0
0
2
2
3
0
2
1
2
0
7
0
2
0
0
0
0
2
0
1
0
0
0
0
2
0
1
0
1
2
0
0
0
1
2
2
1
0
0
0
0
0
1
0
1
2
0
0
1
3
0
0
2
1
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
5
0
2
0
1
1
0
1
1
2
0
0
2
0
2
1
3
1
0
2
1
4
0
2
1
0
0
0
0
2
0
0
0
0
2
1
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
1
1
0
0
1
0
2
0
0
2
1
2
0
1
2
2
0
0
0
0
0
0
1
0
0
2
2
0
0
1
0
0
0
0
2
2
0
0
0
1
0
1
0
0
1
0
0
1
0
0
3
0
0
1
2
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
1
1
1
0
1
0
0
0
0
0
2
0
0
1
0
2
0
0
2
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
5
0
1
2
1
0
2
1
1
1
0
0
1
0
0
0
1
2
0
1
2
0
0
0
2
0
0
0
0
0
0
0
1
2
1
0
0
0
1
0
1
0
0
0
0
1
0
1
2
2
0
1
0
0
0
0
2
1
0
0
1
0
1
0
1
3
2
2
0
0
2
1
1
1
0
0
2
0
0
0
0
0
0
2
0
2
2
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
1
1
0
0
2
0
1
0
0
1
0
1
0
0
1
1
1
1
0
0
2
1
0
9
0
1
0
0
2
1
0
0
0
2
0
0
0
2
0
0
2
0
0
2
2
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
1
0
2
0
0
2
0
0
3
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
1
0
0
0
1
0
0
1
0
2
0
1
2
1
1
0
0
1
1
1
0
1
1
2
1
3
1
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
2
0
1
0
0
2
0
0
0
1
0
1
0
0
0
0
2
0
1
0
0
0
0
1
0
0
2
0
0
0
0
2
2
1
1
2
1
0
2
0
0
0
0
1
1
0
1
0
0
1
0
0
1
1
0
1
0
0
0
2
0
1
0
0
0
0
3
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
2
0
1
0
2
0
0
1
0
0
0
0
1
0
0
0
1
0
1
3
2
0
0
0
0
6
1
0
1
0
2
0
1
0
1
1
0
0
1
1
0
0
0
0
0
0
0
2
0
0
2
2
0
0
1
0
0
1
2
1
0
2
0
0
0
1
0
0
2
2
1
1
0
0
1
1
1
1
0
0
2
2
1
0
0
0
2
2
0
0
1
0
2
1
0
0
0
0
0
1
0
0
0
1
3
1
0
1
1
0
0
0
2
2
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
2
0
0
0
0
2
1
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
1
0
1
1
1
0
2
2
0
2
2
0
0
2
1
3
0
0
0
0
0
0
1
0
0
0
2
1
1
0
0
0
0
1
1
0
0
2
1
0
0
1
0
1
0
0
1
1
0
1
0
0
2
1
0
10
0
1
0
1
0
1
0
0
0
0
2
0
0
0
2
1
0
2
1
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
2
0
0
0
0
1
2
5
2
2
0
0
1
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
1
0
2
1
2
0
4
2
0
0
2
1
0
1
2
0
2
0
2
0
1
0
1
4
0
1
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
2
0
0
2
1
0
1
0
0
1
1
1
2
0
3
2
0
0
0
0
0
0
1
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
2
0
0
1
0
0
0
0
1
1
0
0
0
2
0
0
2
2
1
2
0
1
3
0
0
0
0
0
0
2
0
0
0
0
2
0
3
0
0
0
2
1
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
1
4
1
0
0
2
0
0
0
5
0
0
0
0
1
0
0
0
0
1
2
1
0
0
0
1
0
0
0
2
1
1
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
1
1
2
2
0
0
2
0
0
2
1
0
2
0
0
0
2
0
2
1
2
0
0
0
2
2
0
1
0
1
1
0
0
0
0
2
0
2
0
2
0
1
0
2
0
0
2
0
1
0
1
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
2
0
3
0
1
0
3
2
0
1
0
0
3
0
0
2
0
1
2
2
0
0
0
1
0
0
2
0
0
0
0
0
2
4
0
1
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
1
0
0
2
2
1
0
0
2
0
1
0
0
2
0
1
1
0
0
0
0
0
0
2
3
2
0
2
1
1
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
2
0
0
2
2
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
2
0
3
2
1
2
0
0
2
0
1
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
2
1
0
2
1
0
1
0
0
0
1
1
3
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
2
0
2
0
1
0
2
1
0
0
0
0
0
0
0
2
0
0
2
0
3
0
0
0
1
1
0
0
0
4
3
1
0
0
0
3
0
0
0
1
0
1
0
0
2
0
0
0
0
1
2
2
0
0
1
0
0
1
0
0
1
0
0
0
2
0
0
1
1
4
1
1
0
0
0
0
0
0
2
0
2
0
0
0
2
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
3
1
4
0
0
0
1
2
0
1
1
2
0
3
2
0
2
1
1
0
0
2
0
1
1
0
1
1
0
0
1
0
0
0
0
0
1
2
2
2
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
2
1
1
0
0
0
0
0
0
0
1
0
0
1
1
0
1
2
1
0
1
1
1
0
0
0
0
0
0
3
0
1
2
0
2
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
2
2
2
2
2
0
0
0
0
2
2
1
0
0
0
0
0
0
1
0
1
0
0
1
0
2
0
2
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
1
0
0
0
3
2
1
0
0
1
0
0
0
0
0
3
0
1
0
0
0
3
0
0
2
1
0
1
0
3
0
0
0
0
1
2
2
0
0
0
2
2
1
2
0
0
0
2
0
1
1
0
0
2
0
0
1
0
0
1
0
0
0
0
0
2
2
1
2
0
0
3
0
0
1
0
0
2
0
1
2
2
0
1
0
0
5
2
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
2
2
3
2
0
0
0
0
0
0
0
0
0
0
1
0
3
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
3
0
2
0
2
1
1
0
0
0
2
0
1
1
0
0
0
0
0
1
0
1
0
0
2
1
0
0
0
1
2
0
1
0
1
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
1
5
0
0
0
2
0
1
0
0
0
3
0
0
2
0
2
0
1
1
2
0
0
0
2
0
0
1
2
0
2
0
1
2
0
0
0
5
0
1
2
1
0
0
0
1
2
0
2
0
0
0
0
3
0
0
0
1
0
2
2
1
0
0
0
0
0
0
2
0
2
0
0
2
1
1
0
0
1
0
1
1
2
3
0
1
1
0
0
0
0
0
0
2
2
0
0
0
1
1
0
2
0
0
0
2
0
1
0
0
0
1
0
2
2
0
0
0
0
0
0
1
1
2
2
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
1
1
0
3
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
1
1
0
0
1
0
1
0
1
0
2
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
2
1
0
0
0
1
2
2
0
1
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
1
0
1
1
0
1
0
1
1
0
0
0
0
0
0
0
1
1
1
0
0
1
0
2
1
2
0
0
0
0
0
2
2
0
0
1
2
0
0
0
1
1
0
1
3
0
0
0
0
2
1
0
0
2
0
1
1
2
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
1
0
0
2
0
0
0
2
0
0
0
0
1
1
1
0
0
3
1
0
2
0
0
0
1
2
0
2
2
0
3
0
2
0
0
2
1
1
1
0
2
0
2
0
1
0
0
0
2
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
2
1
0
0
0
0
2
1
0
2
0
1
0
0
1
3
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
2
1
2
0
0
0
2
1
0
0
0
0
2
0
2
1
1
0
0
2
0
1
0
0
0
2
0
0
0
0
2
4
0
1
0
1
2
0
1
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
2
0
2
0
1
1
0
2
0
1
0
1
0
2
0
0
0
0
0
0
1
2
0
0
1
0
1
2
1
2
0
0
0
0
0
2
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
4
0
2
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
1
0
1
2
1
0
1
1
2
0
0
2
0
1
1
2
0
0
0
2
2
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
2
0
0
2
0
0
1
0
1
2
7
0
1
0
1
1
1
0
1
0
3
0
0
1
1
0
0
1
2
0
0
0
0
0
0
2
2
2
2
0
1
0
0
0
1
0
0
0
0
0
0
2
1
2
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
1
0
0
1
1
2
1
0
0
0
0
0
0
1
0
0
0
0
0
2
9
0
2
1
3
0
0
0
1
1
1
0
1
0
0
0
0
1
0
0
1
0
0
1
0
1
0
2
2
1
1
0
0
0
0
0
0
0
2
0
0
1
0
1
0
1
2
0
0
2
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
2
0
0
1
1
0
0
0
0
1
0
1
0
0
1
0
0
0
2
0
1
1
0
1
1
0
3
0
2
2
0
2
0
0
1
0
1
0
0
2
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
2
0
1
0
1
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
2
1
2
0
2
2
0
1
1
1
0
0
1
1
0
0
1
0
1
2
0
0
0
0
0
0
2
1
0
0
0
2
2
0
0
0
2
0
0
0
2
0
1
0
0
2
0
0
4
0
0
0
0
1
0
0
0
0
2
1
0
1
2
0
0
0
1
1
0
0
0
0
3
0
1
2
0
0
0
0
2
1
2
1
0
0
1
1
2
0
2
0
0
0
1
1
0
0
2
0
2
0
0
2
1
0
0
3
2
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
2
1
1
1
0
0
0
0
0
1
0
0
1
2
1
1
0
0
1
1
2
0
2
1
2
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
2
4
3
0
1
0
2
1
0
2
0
1
0
0
0
0
1
0
2
1
0
1
2
1
0
0
1
0
2
0
1
0
2
1
0
2
1
0
1
0
2
0
2
0
2
1
2
0
0
1
0
0
1
0
0
0
1
0
0
2
0
2
1
1
1
3
1
0
0
2
0
2
2
1
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
1
0
0
1
0
0
1
1
0
1
0
0
0
1
1
0
1
0
0
0
0
0
1
0
1
1
0
1
1
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
1
1
0
2
1
2
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
2
0
2
0
1
0
1
0
2
0
1
0
0
0
0
2
0
1
0
0
2
2
0
1
0
0
1
0
2
0
0
1
1
1
0
0
1
0
1
1
0
0
0
1
0
0
0
2
1
2
1
0
1
0
2
1
1
0
1
0
1
2
0
0
2
1
1
0
1
0
0
1
0
0
0
0
0
0
0
1
1
1
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
2
2
2
0
0
2
3
0
0
0
1
1
0
1
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
1
3
2
0
0
2
0
0
0
2
1
0
0
0
0
0
2
0
0
3
0
0
2
2
0
0
0
0
0
2
0
1
1
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
2
2
1
0
0
1
0
0
1
2
0
1
0
0
0
0
2
2
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
2
0
1
0
2
0
0
0
1
1
1
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
2
1
2
0
0
0
0
0
0
0
1
0
2
1
0
0
2
1
0
3
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
1
2
2
0
0
0
4
2
0
0
0
2
0
0
1
0
1
3
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
1
0
2
2
0
0
2
0
2
0
1
0
1
1
1
1
13
0
0
0
0
0
2
1
2
3
0
1
0
0
0
0
0
0
2
1
2
0
0
2
1
0
1
0
1
0
0
1
1
1
0
0
1
0
0
0
0
0
1
1
0
0
1
0
1
0
0
1
2
0
0
0
0
0
0
2
0
1
0
1
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
1
2
2
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
3
0
0
0
0
0
1
2
0
1
2
1
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
2
2
1
2
0
0
2
0
0
2
0
1
1
1
2
1
1
1
0
0
0
0
2
0
1
0
1
0
2
0
0
0
2
0
0
0
1
0
0
1
0
1
2
0
2
0
0
1
2
1
0
0
2
1
0
1
1
0
0
2
1
1
2
0
0
3
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
1
1
0
0
2
1
0
0
0
2
0
0
0
4
0
1
2
0
0
4
2
1
0
0
0
2
0
0
1
0
0
0
0
0
4
2
2
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
2
0
2
0
2
2
0
0
0
2
0
1
1
0
0
3
0
0
2
0
0
1
8
0
1
1
2
2
1
0
2
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
2
1
0
0
0
0
1
1
2
0
0
0
0
0
2
0
0
1
0
0
0
2
1
1
0
0
0
4
0
0
0
2
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
6
2
0
1
1
0
2
2
2
1
2
0
0
0
1
0
3
0
0
0
0
0
0
1
2
0
0
1
0
2
0
0
1
0
0
1
2
0
0
0
0
2
0
1
0
1
1
1
1
1
2
0
0
0
3
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
1
0
1
0
1
0
1
0
1
0
2
0
1
2
0
0
0
2
0
1
1
0
1
0
1
1
1
3
0
0
0
0
1
0
2
2
0
2
1
0
0
7
2
0
0
1
2
1
2
0
1
0
1
0
0
0
2
0
0
1
0
0
1
1
0
0
1
2
0
0
1
0
2
0
0
1
1
2
2
0
0
1
0
1
0
3
0
2
0
2
0
0
1
1
2
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
1
1
0
0
0
2
1
1
1
1
0
0
0
2
2
1
0
0
0
3
0
0
1
0
0
0
2
2
0
0
2
0
0
1
0
0
2
0
0
0
1
1
2
0
1
2
2
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
2
1
1
0
0
0
0
1
0
2
0
2
0
2
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
3
1
1
2
0
2
0
0
0
0
2
0
2
0
0
0
2
0
3
0
0
0
0
1
0
2
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
1
0
2
2
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
3
0
1
2
0
0
0
0
0
2
1
0
0
1
0
0
0
2
0
0
1
0
0
1
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
2
2
1
1
2
0
2
0
0
0
3
1
0
1
2
0
0
2
0
0
2
2
1
0
0
0
0
1
0
0
0
0
0
0
0
2
1
2
0
0
2
3
0
0
0
1
0
1
0
2
2
1
0
1
1
1
0
2
1
2
0
1
1
0
0
0
1
0
0
1
0
0
2
0
2
1
1
1
1
1
0
2
0
1
1
0
0
0
2
0
0
1
0
0
1
1
1
2
3
0
1
0
0
0
0
2
0
1
3
0
0
0
0
1
2
2
0
2
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
3
0
0
0
0
2
2
0
0
0
2
2
0
2
0
1
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
4
0
1
0
0
1
0
0
1
0
2
1
0
1
0
0
0
0
1
0
0
2
0
0
0
2
1
0
1
2
0
0
0
0
0
0
0
1
1
1
0
1
2
1
0
1
2
1
2
0
0
0
0
0
0
2
0
1
2
3
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
1
0
0
1
1
2
0
0
0
2
0
1
1
0
2
2
0
0
0
1
0
0
0
0
0
1
0
0
0
2
2
2
0
0
0
0
2
0
2
1
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
1
0
0
1
1
1
0
2
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
2
2
2
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
1
0
2
2
0
2
0
0
0
0
0
0
0
2
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
2
0
1
2
2
0
0
0
1
0
0
2
1
0
0
2
0
1
1
0
0
0
0
0
1
1
1
1
1
1
2
0
0
2
2
0
0
0
0
1
2
0
2
0
1
3
0
0
0
0
0
0
0
2
0
1
0
0
0
1
1
2
0
1
0
1
1
4
0
2
1
0
0
2
0
1
0
0
1
0
0
2
2
1
0
0
1
0
3
2
0
1
0
1
2
2
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
1
0
0
1
0
1
0
2
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
1
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
2
0
1
1
2
0
0
2
0
1
1
0
2
0
1
1
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
1
1
0
1
0
0
2
0
0
0
0
0
2
0
1
0
1
0
0
2
0
2
0
1
1
1
1
2
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
2
1
2
0
0
0
0
0
1
2
1
1
0
0
0
0
0
1
2
0
0
0
2
2
3
0
0
0
0
2
1
1
0
0
3
0
2
2
0
0
2
0
0
1
0
2
1
0
2
1
0
0
0
0
1
0
1
1
0
1
2
0
1
0
1
0
0
2
2
0
0
0
1
0
0
0
1
0
0
2
0
1
0
2
2
0
1
1
1
3
0
0
2
0
1
1
2
1
0
1
0
2
0
0
1
1
0
0
2
3
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
2
2
0
0
0
2
0
2
2
0
0
0
1
2
0
3
3
0
0
2
2
0
1
0
0
0
1
0
0
1
2
1
0
1
1
2
2
0
1
3
0
0
0
0
0
0
2
0
2
2
0
0
1
1
0
0
0
0
1
0
0
2
0
0
3
0
1
2
1
0
2
0
0
2
0
0
0
1
1
1
0
0
1
0
1
1
2
0
2
0
0
2
1
0
0
2
0
0
1
0
0
0
1
2
0
0
0
1
3
0
2
1
0
0
0
0
0
1
1
1
0
4
2
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
1
2
1
0
1
1
0
0
0
2
2
0
2
0
0
1
0
2
9
0
1
1
0
0
0
1
0
1
2
0
0
0
1
0
3
2
2
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
3
0
1
0
1
0
1
0
0
2
1
1
0
3
0
0
0
2
0
0
2
0
0
0
0
0
2
1
0
0
0
1
1
2
0
1
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
3
2
0
0
2
1
0
3
0
0
1
1
1
0
0
0
0
1
1
0
0
0
2
1
1
0
1
0
0
1
1
0
0
0
0
0
0
2
0
1
0
0
1
0
0
1
2
1
0
2
0
2
1
0
0
0
0
4
0
1
2
0
0
2
2
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
2
0
1
2
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
1
0
1
1
0
0
0
0
2
2
0
1
0
0
1
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
1
0
0
1
0
1
0
1
2
1
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
2
3
2
0
0
1
0
0
1
2
0
0
0
0
2
0
1
1
2
0
0
1
1
1
0
0
2
0
0
3
2
0
0
1
0
0
0
0
0
0
0
2
2
0
0
1
0
3
0
0
4
0
0
2
2
0
1
0
0
1
1
0
0
0
2
0
0
0
1
0
1
0
2
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
3
0
0
0
2
0
0
2
0
1
0
1
2
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
1
2
1
0
1
0
1
0
1
0
2
2
2
0
0
1
2
0
0
2
0
0
0
0
1
0
0
0
1
0
0
1
2
0
1
2
0
0
0
0
2
1
0
0
1
4
2
1
1
2
1
0
0
0
1
2
0
0
0
0
1
0
0
1
0
1
2
1
0
0
1
0
1
0
0
1
0
0
1
2
2
1
0
1
0
0
2
0
0
0
2
0
0
2
0
0
1
0
0
0
2
0
1
1
2
0
2
2
0
2
3
0
0
2
0
0
0
0
0
2
0
0
2
0
1
0
3
1
0
0
0
2
0
0
0
2
0
1
0
2
2
0
0
2
0
0
1
0
0
0
0
0
0
1
0
1
2
0
0
1
0
0
0
3
1
0
0
0
0
0
2
2
0
0
0
0
0
0
2
2
0
1
2
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
3
0
0
2
0
0
0
2
1
2
0
1
0
0
1
6
0
2
0
0
2
0
0
0
1
0
0
0
2
2
0
2
0
2
0
2
2
0
0
0
1
0
0
0
0
3
1
2
0
0
2
0
0
2
0
0
0
1
0
2
0
1
0
0
1
0
1
0
0
1
0
0
0
2
0
2
0
0
2
0
0
0
0
2
0
2
0
0
1
0
0
3
0
1
0
0
0
0
0
0
2
3
0
0
0
1
0
1
0
0
0
1
2
0
2
0
2
0
0
2
1
1
0
0
1
0
3
1
0
0
0
2
0
1
0
2
0
0
1
1
0
0
1
1
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
1
2
1
2
2
2
2
0
1
0
0
1
1
2
0
0
6
1
2
0
1
2
2
0
0
1
0
2
1
0
0
0
0
0
0
0
1
3
1
0
1
0
0
2
1
0
3
1
0
0
1
0
0
2
0
2
1
1
0
1
0
2
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
6
2
1
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
2
2
3
0
2
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
1
1
0
0
0
1
2
0
0
1
1
0
0
0
0
0
0
0
1
0
1
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
2
3
0
1
2
2
0
1
0
2
0
1
0
0
3
1
2
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
4
0
0
0
2
1
2
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
2
0
3
1
0
1
2
0
0
0
2
0
0
4
3
2
1
0
0
2
1
0
0
1
0
0
1
1
0
0
2
0
0
0
2
0
1
0
0
2
1
0
1
1
0
2
0
0
1
2
0
0
1
1
0
1
0
0
2
1
0
0
2
0
0
0
1
0
2
0
2
0
2
2
1
1
1
0
0
1
0
1
2
0
0
2
0
0
2
0
0
0
0
1
1
0
0
0
0
0
1
0
1
1
0
2
0
2
0
0
0
0
0
0
0
2
1
0
1
2
1
0
0
0
0
3
1
0
3
0
0
2
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
1
1
0
2
1
0
0
1
0
0
0
2
0
2
1
0
0
0
2
1
0
1
1
0
2
1
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
2
2
0
1
2
0
0
0
0
0
1
0
2
0
2
0
2
0
0
2
0
0
1
0
0
1
1
0
1
0
2
0
0
0
0
0
0
1
0
0
2
0
3
0
8
0
2
0
0
2
0
2
0
0
0
0
2
0
0
2
1
0
0
0
1
0
1
2
0
0
1
1
2
0
0
2
0
0
0
0
0
2
2
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
1
0
0
0
1
1
1
0
2
0
0
1
0
1
0
0
2
0
4
2
0
2
2
0
1
0
0
0
0
1
1
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
2
2
0
2
2
1
0
1
0
0
0
0
0
1
2
2
0
0
2
0
0
1
2
0
0
1
1
0
0
1
0
1
0
2
0
0
0
2
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
1
0
1
0
0
2
0
3
0
1
0
0
1
0
1
2
0
0
0
2
0
1
3
0
2
1
1
1
0
0
0
1
6
0
2
0
2
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
1
0
2
0
0
0
2
0
1
0
1
0
0
1
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
1
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
1
0
0
0
1
1
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
1
0
0
1
0
0
0
1
0
0
0
0
2
2
2
1
1
1
0
1
4
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
2
1
0
0
0
0
0
2
0
0
0
2
1
0
0
0
1
2
2
2
2
0
2
1
1
0
0
0
1
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
2
1
2
1
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
2
2
0
0
2
2
0
2
0
1
0
0
0
0
3
0
2
1
1
0
2
0
0
1
0
4
1
0
0
0
0
4
0
1
0
2
0
0
0
2
1
2
2
1
1
2
1
0
0
0
0
0
2
1
0
1
2
0
0
2
0
0
1
0
0
0
0
0
0
1
2
1
1
2
1
1
0
0
0
0
2
1
3
0
1
2
3
0
1
1
0
1
0
0
1
2
1
0
0
0
3
1
2
1
0
1
0
1
0
0
0
2
2
0
0
0
0
2
1
0
0
2
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
1
2
1
0
0
0
0
0
1
2
0
2
0
0
2
1
2
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
2
2
5
2
0
0
0
0
0
0
2
0
0
2
0
0
2
1
1
0
0
0
0
0
2
0
2
0
2
0
0
1
0
0
0
1
0
2
0
1
0
2
0
1
0
1
0
0
1
3
0
2
0
0
3
0
0
0
0
1
0
1
0
1
0
1
2
0
2
0
0
1
1
0
1
0
1
0
0
3
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
1
0
1
0
0
1
0
0
1
1
1
0
0
0
1
0
2
2
2
0
0
0
0
2
2
2
0
2
0
0
1
2
0
1
1
0
0
0
1
1
0
0
2
1
0
0
0
1
0
0
0
3
0
0
1
1
0
0
0
1
0
1
1
0
0
1
0
2
1
1
0
2
1
2
0
0
1
2
0
0
0
0
1
0
0
0
0
1
1
1
1
1
0
0
0
0
0
0
2
1
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
2
1
0
0
1
2
1
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
2
0
1
0
0
0
0
0
0
0
2
0
0
2
0
2
0
1
1
0
0
2
1
0
0
0
0
1
0
0
0
1
0
0
2
2
2
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
1
0
0
1
0
1
1
0
2
0
0
0
2
1
2
1
0
2
0
0
0
0
1
1
1
0
0
2
0
0
0
2
0
0
0
0
1
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
2
0
1
2
2
0
1
0
2
1
1
1
2
2
2
0
0
2
2
0
2
1
0
2
0
0
0
0
0
1
1
1
2
0
0
0
1
1
1
2
0
2
0
0
0
0
2
1
1
2
1
1
0
0
0
0
0
0
0
2
2
2
0
0
0
0
1
1
0
2
2
1
0
0
2
2
4
0
0
1
0
0
0
0
0
1
0
0
2
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
2
0
0
2
1
2
0
1
1
0
1
2
1
2
0
3
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
2
0
5
0
0
0
2
0
0
0
2
0
1
2
0
1
0
0
0
0
0
2
2
2
0
0
0
0
1
0
2
0
0
0
0
1
0
3
1
1
3
0
1
2
0
5
0
1
1
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
3
0
2
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
2
0
0
2
0
0
2
2
0
0
0
1
1
1
0
0
0
0
0
1
1
2
0
0
1
1
0
2
0
0
0
0
1
0
0
0
0
0
4
1
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
1
1
2
0
1
1
0
1
1
0
1
0
0
2
1
0
0
1
2
2
2
0
0
1
0
0
0
2
0
1
2
0
1
0
0
0
0
0
2
0
0
1
1
2
1
0
1
0
1
2
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
2
1
0
0
2
0
1
2
0
1
1
0
1
0
0
0
0
0
6
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
2
0
1
0
1
0
0
1
0
0
0
1
0
2
1
2
0
1
3
1
0
0
0
1
0
0
0
1
2
2
0
0
0
0
0
0
0
3
2
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
2
0
0
1
0
1
0
2
1
0
0
0
0
0
0
0
1
0
0
2
2
0
2
0
1
1
1
1
1
2
0
0
0
0
0
0
2
1
0
1
0
0
2
0
0
0
2
1
1
1
0
2
0
1
1
0
1
0
0
0
0
2
0
0
1
1
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
2
2
0
0
2
0
0
0
0
1
2
0
0
0
0
1
0
0
1
2
1
0
2
0
3
2
0
0
2
0
0
2
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
1
0
0
1
2
0
2
1
1
0
0
2
0
1
1
0
1
1
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
1
2
0
0
0
2
0
0
0
0
0
1
0
1
2
0
0
1
1
2
0
0
0
1
2
2
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
1
1
2
1
0
3
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
3
0
0
2
0
1
0
0
0
0
2
0
6
2
1
2
0
6
2
0
0
0
1
0
1
2
0
2
1
0
1
0
2
1
0
0
1
3
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
2
0
1
0
2
1
0
0
2
0
0
4
1
0
2
0
1
0
0
0
1
1
1
0
1
1
0
0
2
2
0
2
0
0
0
2
1
1
0
0
0
0
1
0
2
0
2
0
0
1
0
0
0
0
2
1
0
0
0
0
0
2
0
1
0
1
3
2
2
1
1
0
0
0
0
1
0
6
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
2
0
0
0
0
0
0
2
1
0
3
1
1
1
0
0
0
1
1
0
2
0
0
0
0
1
0
1
0
0
1
0
2
0
1
0
0
0
2
0
0
0
1
1
0
0
0
0
0
1
1
0
2
2
0
3
1
0
0
0
0
2
0
0
1
0
0
1
0
2
0
0
1
2
0
0
0
0
2
1
2
0
0
1
0
1
0
2
2
0
0
1
2
0
0
5
0
2
0
0
0
0
8
1
0
2
0
2
1
0
0
0
2
0
0
1
0
2
0
0
3
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
2
1
1
0
2
0
3
2
0
1
0
0
0
1
1
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
2
1
0
2
0
0
1
2
0
1
1
0
2
2
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
1
2
2
2
1
3
0
0
2
0
0
2
2
1
2
2
0
1
0
2
0
0
2
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
1
0
2
0
0
1
0
1
1
2
1
0
0
1
0
0
0
2
1
0
0
2
2
0
0
0
1
0
1
0
0
2
0
0
0
0
1
0
1
1
3
0
1
2
0
1
0
1
3
0
0
2
0
0
0
0
0
0
1
0
2
1
0
2
2
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
2
0
0
1
1
1
0
0
1
2
2
0
1
0
2
2
1
0
1
0
0
1
1
0
0
1
0
0
0
6
0
0
0
0
0
0
1
1
0
0
3
0
0
2
0
0
0
0
0
2
2
0
0
0
2
0
0
0
2
0
2
2
2
2
2
0
2
0
2
0
0
0
0
0
2
0
2
0
2
1
2
1
0
0
0
3
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
2
0
1
0
0
1
0
1
0
1
2
1
1
0
2
0
0
0
2
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
2
1
0
2
0
0
0
2
0
0
0
2
2
0
0
0
0
1
0
0
0
2
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
2
0
0
0
1
0
0
2
0
2
0
0
0
2
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
3
0
0
2
0
2
0
0
2
0
1
0
2
1
0
0
1
1
0
2
1
0
0
1
0
1
0
2
1
0
1
0
0
0
0
0
2
0
0
3
0
2
0
0
0
2
1
0
0
0
0
2
1
0
0
0
1
2
0
1
0
0
2
1
0
0
0
1
0
0
0
2
0
0
1
0
1
0
0
0
2
0
0
0
0
2
0
0
1
1
0
0
1
0
4
0
1
0
1
2
0
0
1
0
0
0
2
0
1
1
0
0
0
1
2
0
2
2
1
0
0
0
2
0
0
2
0
2
1
2
2
2
0
1
1
2
2
1
0
0
2
0
0
0
0
0
0
0
1
1
1
2
0
0
0
0
2
0
0
1
0
0
0
0
0
2
2
0
5
0
2
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
2
0
0
2
0
0
0
2
0
2
0
2
0
2
0
2
0
0
0
0
0
0
2
2
0
1
0
0
0
1
1
2
0
1
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
2
2
0
0
0
0
0
0
1
2
0
0
2
2
1
0
0
2
0
0
1
1
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
1
1
0
1
2
2
0
2
0
1
0
1
2
1
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
3
0
0
2
0
2
1
0
5
0
1
0
0
0
0
0
1
0
0
1
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
2
0
0
0
0
0
1
0
1
0
2
0
2
3
2
0
0
0
0
1
2
0
0
2
0
0
2
1
0
0
2
1
0
0
0
1
1
2
0
0
2
2
0
0
1
0
0
0
1
2
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
2
0
0
1
1
0
1
0
0
2
0
0
1
1
2
2
0
0
0
0
3
0
0
2
0
0
0
1
0
0
1
1
0
2
0
1
0
1
2
0
0
0
2
1
0
0
0
0
2
0
2
0
3
1
1
0
1
0
0
2
0
2
2
1
0
1
0
0
0
1
2
0
0
0
1
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
4
0
2
0
2
1
0
0
1
2
0
0
0
0
0
0
0
0
0
1
1
0
0
2
2
0
0
0
2
0
0
0
0
2
1
0
0
0
1
0
0
0
2
1
1
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
2
1
2
1
0
0
1
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
2
2
3
2
0
0
0
2
0
3
1
2
1
0
1
0
0
0
0
0
1
0
1
2
0
0
0
1
0
0
0
1
1
0
1
1
0
0
0
1
0
0
1
0
0
4
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
2
2
0
1
1
2
0
0
2
0
1
0
0
0
0
0
1
3
0
0
2
0
2
0
0
0
2
0
0
2
0
0
1
2
0
2
0
0
0
0
3
0
1
0
0
2
0
1
3
0
1
0
2
1
0
0
0
0
3
2
0
2
0
0
0
0
3
0
0
0
1
0
0
1
2
3
0
1
0
0
0
0
1
0
0
0
0
1
0
2
0
0
2
0
2
2
2
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
2
0
1
0
0
3
0
0
0
0
0
2
0
2
2
2
0
0
1
2
0
0
0
0
2
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
1
2
0
2
0
1
2
2
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
1
1
0
0
0
3
2
2
0
0
1
0
0
0
1
0
0
1
1
0
2
1
0
2
0
0
1
0
0
0
0
2
2
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
1
0
0
0
1
0
0
0
2
0
1
2
2
0
2
2
0
0
0
0
0
0
0
3
0
0
0
1
0
1
0
0
2
0
0
0
0
1
0
1
1
0
2
1
2
1
0
0
0
1
0
0
0
0
0
2
0
0
2
1
2
1
0
2
0
0
1
0
2
0
0
1
1
0
1
2
0
0
2
1
2
1
1
0
1
1
1
0
1
0
0
0
2
0
1
0
0
1
1
0
2
1
1
1
0
2
0
0
0
1
0
2
0
0
1
0
0
0
0
0
2
0
2
0
0
0
2
0
1
0
0
0
0
0
1
0
0
2
0
0
0
1
2
1
0
0
2
0
0
2
0
1
0
0
0
0
2
0
1
2
1
1
4
0
2
2
1
0
1
1
1
1
0
2
0
3
1
0
0
4
0
1
2
0
1
2
1
2
0
2
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
2
0
1
0
0
0
0
0
2
0
2
0
0
1
2
1
1
1
1
1
1
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
1
1
0
0
1
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
3
0
1
2
0
1
0
0
2
2
0
1
1
0
2
0
0
0
2
0
2
1
0
2
0
0
1
4
0
0
1
0
4
2
0
0
0
0
1
3
0
0
2
1
0
2
0
0
1
0
0
0
1
2
0
1
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
2
0
2
0
0
1
0
0
0
1
0
1
0
2
0
0
0
0
0
1
0
3
2
0
0
0
0
1
2
0
0
1
2
0
2
0
0
0
0
2
0
0
2
0
0
2
2
2
1
1
0
0
2
0
0
2
0
1
3
1
0
1
1
1
0
0
1
0
0
1
0
0
0
1
1
2
0
1
1
2
0
0
0
1
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
1
0
0
2
2
1
1
0
2
0
2
0
0
1
1
2
1
1
2
2
0
2
0
0
1
0
2
1
2
0
0
0
0
0
0
0
0
0
2
3
2
2
0
1
0
0
0
0
1
1
1
1
0
0
0
0
1
0
0
0
2
1
0
0
0
1
0
2
0
1
0
0
0
0
2
2
0
2
1
1
1
2
0
1
2
1
1
4
0
0
1
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
1
1
2
0
0
1
0
0
0
0
0
0
2
2
0
0
1
0
0
1
0
1
1
2
0
1
1
0
0
0
0
2
1
0
0
1
2
0
1
0
2
0
1
1
0
2
1
1
0
0
0
0
0
1
1
0
1
1
1
0
0
2
0
1
2
1
1
1
0
0
0
1
0
0
0
0
0
1
0
1
3
1
1
0
0
0
0
0
2
0
0
1
1
0
0
0
0
2
0
0
0
0
0
1
2
0
0
3
0
2
2
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
2
0
1
1
0
2
0
0
0
1
0
0
0
1
1
0
0
0
2
0
0
1
1
0
0
1
1
0
1
0
0
0
0
1
2
0
0
1
0
1
0
0
0
0
2
0
2
1
1
2
0
1
0
0
0
0
2
1
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
1
1
2
0
1
0
0
0
1
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
1
1
1
0
1
0
0
2
1
0
0
0
0
0
3
0
0
0
1
3
0
2
1
0
0
1
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
1
0
0
2
0
1
0
2
0
1
1
0
2
2
2
1
0
2
1
1
1
1
0
0
0
0
2
2
0
0
0
0
1
1
2
0
0
1
2
1
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
1
0
0
1
0
0
2
0
0
1
0
0
0
2
0
0
0
0
1
2
2
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
2
2
0
0
1
0
2
0
0
0
0
0
0
1
2
2
1
0
0
0
0
0
0
1
0
2
1
1
1
2
2
0
1
11
0
0
2
2
0
0
0
0
1
0
1
0
0
0
0
2
1
0
1
2
0
0
2
1
1
0
0
0
2
1
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
1
2
0
0
0
0
0
1
1
1
1
0
0
0
2
1
2
2
1
0
1
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
3
0
1
2
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
1
0
0
1
0
0
1
1
0
0
1
1
0
0
2
1
1
0
1
0
0
2
0
0
0
0
1
1
0
2
2
0
0
0
1
0
0
2
0
0
2
2
0
2
0
0
1
1
0
0
0
1
0
0
1
0
2
1
0
0
0
0
0
1
0
0
0
1
1
1
0
1
0
0
1
0
1
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
2
0
0
0
2
0
1
0
1
1
0
0
1
0
0
2
0
2
0
1
0
0
1
0
1
0
2
1
0
0
0
0
0
0
1
3
2
0
3
2
0
1
0
0
0
0
0
0
0
1
1
0
1
1
0
0
1
0
1
0
0
1
0
1
2
2
0
0
0
0
0
0
2
3
0
0
0
1
2
2
0
0
0
0
0
0
3
0
3
0
0
2
0
3
0
0
1
0
1
2
2
0
0
0
0
0
0
2
0
2
0
0
0
2
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
1
0
2
2
0
1
0
1
1
1
0
2
0
0
0
1
0
0
0
2
1
1
2
0
0
1
0
0
3
1
1
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
1
0
2
1
1
0
1
0
0
0
0
4
0
0
0
1
0
2
0
1
0
1
0
0
0
1
0
0
1
0
2
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
2
2
0
0
0
2
0
0
0
0
2
2
1
2
2
1
0
2
0
0
1
1
1
0
0
1
2
0
2
1
0
0
0
1
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
1
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
1
2
0
0
1
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
1
2
1
0
1
2
1
0
0
0
0
1
2
0
0
0
0
2
1
0
0
2
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
1
3
0
0
1
1
1
0
0
1
1
0
0
0
0
0
2
1
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
2
0
2
0
2
1
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
1
0
0
0
3
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
2
6
2
2
0
0
0
2
2
2
1
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
2
1
2
0
1
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
1
0
0
1
2
0
1
1
0
1
0
1
0
2
2
2
0
0
5
0
2
2
0
2
2
0
0
1
0
0
0
2
0
0
2
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
1
0
2
1
1
0
2
2
1
2
1
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
2
2
2
1
0
0
0
0
1
1
1
0
0
1
1
0
2
0
0
1
0
0
0
0
0
2
0
0
2
0
0
1
1
0
1
2
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
3
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
2
0
0
3
6
1
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
1
2
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
1
1
1
0
0
1
0
3
0
4
2
0
1
1
0
0
0
0
1
0
0
2
0
0
2
0
1
1
0
0
0
1
0
2
0
1
0
0
0
0
2
1
2
0
1
0
2
0
0
0
0
2
2
0
0
0
0
0
0
1
2
0
0
2
1
0
0
1
0
2
0
0
0
1
0
0
0
3
0
0
2
0
0
0
0
0
0
0
1
0
0
2
1
2
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
2
2
2
1
0
0
0
2
1
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
1
1
1
0
0
3
1
0
0
2
0
2
2
0
0
1
0
2
0
1
1
1
1
2
0
0
1
0
1
0
7
2
0
0
1
0
2
0
0
0
0
2
2
2
1
2
0
0
2
0
2
1
1
0
0
0
1
2
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
1
1
1
1
0
1
0
0
0
1
0
0
2
0
0
0
1
1
1
0
1
0
2
2
0
0
1
0
1
0
0
1
2
0
0
1
0
0
0
2
1
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
1
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
2
0
0
0
1
2
0
2
1
0
0
3
2
1
0
0
1
0
0
2
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
2
1
0
2
1
0
1
0
0
2
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
1
0
2
0
2
0
0
2
2
0
0
1
1
0
1
1
0
2
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
2
2
0
0
5
0
0
2
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
1
2
0
2
0
2
0
0
1
2
0
0
0
2
1
0
0
0
5
2
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
2
0
0
0
2
1
0
2
0
1
0
0
1
0
0
1
2
0
0
0
0
0
0
2
0
0
1
0
0
2
1
0
1
0
0
1
0
1
0
0
3
2
0
1
0
0
1
1
0
0
2
0
0
0
2
2
1
0
2
0
0
0
0
0
0
1
2
1
2
0
2
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
2
0
0
1
1
0
1
1
0
1
2
0
3
1
0
2
0
0
0
0
0
0
2
1
0
0
0
0
2
2
0
0
0
0
1
1
1
1
0
1
0
0
1
2
2
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
1
1
0
0
1
2
0
0
0
0
0
0
0
2
2
1
0
0
0
0
1
0
0
0
0
1
2
2
0
0
2
0
0
0
1
0
1
1
0
0
2
0
0
0
2
0
0
0
0
2
1
0
1
0
1
1
0
0
0
2
2
2
0
0
2
0
0
0
2
0
2
1
0
0
2
0
0
0
1
2
0
0
1
0
0
1
2
0
0
1
2
2
2
1
1
1
0
0
0
2
2
0
2
2
0
0
0
0
1
0
0
1
1
0
0
2
3
0
0
0
0
0
0
1
3
0
0
0
1
0
0
0
0
1
1
0
0
3
0
0
0
2
2
2
0
1
1
2
2
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
1
0
0
0
0
2
2
0
0
1
1
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
1
0
0
1
0
0
1
0
2
0
0
2
0
0
2
1
0
0
0
0
0
0
5
2
2
0
2
0
0
1
0
0
0
0
2
0
2
1
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
1
1
2
1
0
0
5
1
2
2
0
0
2
0
0
0
0
2
0
0
1
2
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
1
2
2
0
0
2
1
1
0
0
0
2
2
0
2
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
2
0
0
0
2
1
0
0
2
1
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
2
0
1
0
1
1
0
0
0
2
0
1
0
0
0
2
0
0
0
2
0
0
0
2
2
0
0
7
3
2
1
0
0
0
0
1
0
0
1
0
1
0
0
1
1
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
3
2
1
2
0
2
0
0
0
1
0
0
1
2
1
0
1
0
0
0
0
2
2
0
0
0
2
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
1
2
2
2
2
1
0
0
0
1
1
0
0
0
2
1
0
0
0
0
0
1
0
1
1
1
0
0
0
2
0
0
0
0
2
0
0
0
3
0
1
0
1
4
0
1
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
3
1
1
2
0
1
2
1
0
0
0
0
2
1
0
2
1
2
2
0
0
0
0
0
0
2
2
0
0
1
1
0
0
1
0
2
0
0
0
2
1
0
1
0
2
0
0
1
1
0
0
2
0
1
1
0
2
0
0
0
0
0
2
0
0
2
0
2
1
0
1
1
2
3
2
0
0
0
0
0
0
1
0
2
2
2
0
2
0
0
2
2
0
1
0
0
0
1
2
2
1
1
1
0
0
2
1
0
2
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
1
0
0
0
2
0
0
2
2
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
2
0
0
1
0
0
0
4
0
4
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
7
2
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
2
2
2
2
0
2
0
2
0
0
1
1
2
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
1
1
0
2
0
0
0
1
0
0
1
0
0
0
2
0
1
0
0
0
0
3
2
1
2
0
0
0
0
1
1
0
1
2
1
0
1
1
2
1
2
0
1
0
0
1
0
0
2
1
0
0
0
0
0
1
0
0
0
2
0
0
4
0
1
1
1
1
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
2
2
0
1
1
0
1
1
0
1
0
1
0
1
0
0
0
1
0
0
2
0
1
0
0
2
0
2
0
1
0
0
0
0
1
2
2
0
0
0
0
2
0
0
2
0
1
0
0
3
1
0
2
1
0
0
0
0
1
2
0
0
1
0
1
1
1
0
2
0
0
3
1
2
0
0
0
1
2
1
0
0
0
2
2
2
1
0
2
0
0
1
0
0
1
0
0
0
0
2
2
0
0
1
0
0
1
0
0
0
4
1
0
1
0
0
1
2
0
0
0
0
0
0
0
0
1
0
1
0
1
2
1
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
3
0
1
2
0
2
0
2
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
2
0
0
0
1
0
1
0
0
0
1
1
0
2
0
0
0
0
1
0
1
0
0
0
1
0
1
1
1
0
0
0
0
1
1
0
2
2
0
0
2
1
2
2
0
0
1
0
0
0
0
0
1
1
0
0
1
0
1
0
0
3
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
5
0
1
0
1
0
0
0
0
0
0
0
0
1
0
2
2
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
1
2
0
0
0
1
0
3
0
2
2
0
1
0
0
1
0
0
1
2
0
0
0
0
2
2
2
1
2
0
1
2
2
1
0
0
0
0
0
2
0
0
1
1
0
0
0
0
2
0
0
1
0
0
1
3
0
0
2
0
0
0
1
0
1
2
0
0
1
2
2
0
2
0
0
3
0
0
2
0
1
0
1
1
0
1
0
1
0
1
0
2
2
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
2
2
0
0
1
0
0
0
0
1
1
1
1
0
2
1
0
0
0
0
0
2
0
1
0
2
0
0
1
2
0
0
0
2
2
0
3
2
2
0
1
1
0
2
0
1
1
0
2
1
1
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
1
2
0
0
0
0
0
2
0
2
0
2
1
0
4
0
0
2
0
2
2
0
2
0
0
0
0
2
2
0
0
1
1
2
2
0
0
0
1
0
0
2
0
0
2
1
2
2
0
0
3
0
2
0
2
1
0
1
0
2
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
2
2
1
1
2
0
0
0
2
0
1
0
1
0
2
0
1
0
0
0
0
2
0
0
3
1
2
0
0
0
1
0
0
1
0
0
0
2
0
0
1
0
1
1
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
1
0
0
2
0
0
2
0
1
0
0
1
0
0
0
1
0
0
2
2
0
1
0
1
0
2
0
0
0
1
0
2
2
0
2
0
0
0
1
0
2
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
1
1
2
2
0
0
1
1
0
1
1
1
0
0
0
2
0
1
0
1
1
1
0
1
2
1
0
2
0
1
0
0
0
0
1
0
2
2
0
1
0
0
0
0
1
1
3
1
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
2
0
2
0
0
0
0
3
2
0
0
0
3
1
0
2
0
0
1
1
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
2
0
1
0
0
0
4
0
0
3
0
3
2
1
0
0
2
0
0
0
0
0
0
0
2
1
0
3
2
2
1
0
1
0
0
0
0
1
0
1
1
2
1
0
0
1
2
0
2
0
1
2
1
0
2
1
1
0
0
1
2
0
0
0
0
1
1
1
0
2
0
0
2
1
0
0
0
0
2
0
1
0
2
0
0
2
0
0
2
0
2
0
1
1
1
2
0
3
0
2
0
1
0
0
2
0
1
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
2
2
1
0
1
1
0
2
1
1
0
0
2
1
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
3
0
1
2
0
0
1
1
0
1
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
2
0
2
1
0
1
0
0
0
2
0
1
0
0
0
2
0
0
1
0
1
1
0
1
0
2
0
1
0
0
0
2
1
0
0
0
2
1
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
2
1
0
0
0
1
0
0
1
1
0
2
0
0
0
2
2
0
0
2
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
2
2
0
0
2
2
0
0
2
0
0
3
1
1
0
2
1
0
2
2
0
0
1
1
3
2
0
0
0
0
2
0
2
0
2
0
0
3
0
0
0
0
0
0
1
0
1
0
0
0
4
1
1
0
2
2
2
0
4
0
0
0
0
1
0
0
0
1
0
2
0
2
2
1
0
1
0
0
1
1
1
2
2
2
0
0
0
1
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
2
2
0
0
2
1
0
1
1
0
2
1
2
1
0
0
2
0
0
2
0
1
2
1
1
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
1
0
1
0
1
0
0
0
2
0
1
1
0
1
1
2
0
0
2
1
0
0
0
0
0
0
0
0
1
1
2
0
0
0
2
2
0
1
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
2
2
2
0
1
0
0
1
0
0
0
3
1
1
0
1
2
1
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
1
0
1
0
1
1
2
0
2
0
2
2
1
0
0
0
0
0
2
1
0
0
0
2
0
1
0
2
1
0
2
0
0
0
0
1
2
1
2
2
0
2
1
2
2
0
0
0
0
2
0
0
0
0
0
1
2
0
2
1
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
1
0
0
1
1
1
0
0
0
1
1
2
1
0
0
2
2
0
0
0
0
1
1
0
1
1
0
0
1
0
0
3
2
1
0
0
6
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
1
2
0
0
0
1
2
0
0
0
0
0
0
2
0
0
1
2
0
2
2
1
0
0
1
2
0
1
0
0
4
0
2
1
0
0
1
0
0
1
0
0
0
1
0
0
2
0
1
0
2
0
0
0
3
0
1
3
1
0
0
0
0
2
2
2
0
0
2
0
0
0
0
1
0
0
0
2
0
1
1
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
2
0
1
2
1
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
4
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
1
1
0
0
1
2
0
0
1
1
0
0
2
2
0
1
0
2
0
0
0
1
0
0
0
1
0
2
2
0
0
0
0
1
1
3
2
1
0
1
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
2
1
1
1
0
0
0
0
0
1
2
1
0
0
1
0
1
0
3
3
1
2
0
0
1
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
2
0
0
1
1
0
3
1
0
2
0
0
0
0
3
2
0
0
2
1
2
1
0
0
0
0
1
0
1
0
0
0
1
0
1
2
0
1
1
0
0
0
0
2
2
0
2
0
1
3
2
0
0
0
1
0
4
0
0
1
0
2
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
1
0
1
2
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
5
0
1
0
1
1
0
0
0
2
1
2
0
1
1
0
1
0
2
0
0
0
2
2
0
0
2
0
0
2
0
2
0
1
0
0
2
1
0
0
0
0
2
0
0
1
2
0
0
0
0
0
1
3
0
0
1
0
1
0
0
0
1
2
0
2
0
1
1
0
0
1
1
2
2
1
1
0
0
1
0
0
1
0
0
0
1
0
0
4
2
0
1
1
0
0
0
1
0
1
0
1
0
1
0
0
1
0
0
2
2
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
2
2
0
1
0
0
0
0
0
0
2
0
1
2
0
0
1
0
0
0
2
0
4
2
0
2
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
1
2
2
0
0
1
0
0
0
0
0
0
3
1
1
1
3
1
0
0
2
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
2
1
0
0
0
1
0
2
2
2
0
0
2
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
1
0
0
0
3
0
2
0
1
0
0
0
0
1
0
1
2
1
0
2
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
2
0
2
0
0
2
2
0
0
0
1
0
0
1
1
0
1
0
0
0
0
3
1
0
2
2
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
1
0
2
0
2
0
1
0
0
0
0
0
2
0
2
1
0
0
1
0
0
1
1
0
2
2
0
2
0
0
2
1
0
0
1
0
0
0
1
0
2
0
1
3
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
1
0
2
0
2
1
2
0
0
0
0
0
1
2
2
0
2
0
2
0
2
0
0
1
0
1
2
0
0
2
3
1
0
1
0
1
2
2
0
1
0
2
0
1
0
0
0
0
0
1
1
0
0
0
0
0
2
2
1
1
0
0
2
1
0
0
0
2
0
0
0
0
0
2
1
0
2
0
2
0
2
6
0
0
1
0
0
2
0
1
3
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
1
1
0
0
0
0
4
0
0
0
2
1
0
0
0
1
0
1
1
0
2
2
1
1
1
1
1
1
0
2
2
0
0
0
2
0
0
0
0
0
3
0
1
2
1
0
0
1
1
1
0
1
0
0
1
0
1
0
0
1
0
2
0
0
2
0
2
1
2
0
1
0
2
0
0
0
0
1
0
2
1
0
0
0
1
1
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
3
0
0
0
0
2
0
0
1
0
0
1
0
2
0
0
2
1
0
1
0
0
2
2
0
1
1
1
0
2
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
3
1
0
1
1
0
2
0
2
0
0
0
0
2
0
0
1
0
2
0
2
2
0
1
2
1
0
0
2
0
0
0
0
2
0
0
1
1
1
0
0
1
0
0
0
2
0
0
0
1
0
1
1
1
0
2
0
1
4
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
2
0
0
0
1
3
2
0
0
3
2
0
0
0
0
2
2
0
1
1
0
2
2
2
1
0
0
0
0
0
1
2
2
0
0
2
0
2
0
2
0
2
0
0
0
0
2
0
0
0
1
0
0
3
1
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
2
2
0
3
1
0
1
0
0
1
0
0
0
2
0
0
2
0
0
0
0
1
1
0
2
0
0
0
3
0
4
0
0
2
0
0
0
5
0
0
0
2
1
0
1
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
2
0
0
0
0
2
0
1
0
1
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
1
0
0
1
2
0
2
0
1
0
1
1
2
0
0
0
0
0
1
2
0
0
1
1
0
2
2
0
2
0
1
1
1
2
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
1
0
0
0
0
0
2
0
1
0
1
0
1
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
2
0
4
0
1
2
2
0
0
0
2
0
2
1
0
0
0
2
1
0
0
0
5
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
2
1
0
0
2
1
2
2
0
0
0
0
0
0
0
2
4
0
0
1
1
0
1
2
0
2
0
0
0
2
1
0
0
0
0
0
2
2
0
2
1
1
1
0
0
0
0
0
1
0
4
1
0
0
0
2
1
0
0
3
0
2
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
1
1
2
1
2
2
2
0
0
0
0
0
0
1
0
0
0
1
0
2
1
0
1
0
0
0
2
0
2
0
1
1
1
0
1
2
0
1
2
2
1
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
1
1
0
0
0
1
0
1
0
1
1
2
1
0
0
1
0
2
1
0
0
0
1
0
0
2
2
1
0
0
1
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
3
0
1
0
1
0
0
0
0
0
1
0
2
1
0
2
0
0
0
0
0
0
2
0
0
2
1
1
2
1
2
0
1
0
0
0
1
0
2
0
1
0
0
0
3
2
1
1
2
1
1
0
2
2
2
0
1
1
2
0
0
0
1
1
1
0
1
1
0
2
2
1
0
0
3
2
0
0
0
1
0
0
0
2
4
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
2
0
7
0
2
1
0
0
0
1
3
0
0
1
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
1
2
1
1
0
0
0
2
0
0
2
0
0
1
0
2
1
2
2
1
0
0
0
0
2
0
0
0
0
1
0
0
2
0
3
0
11
2
2
0
1
1
2
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
1
0
4
1
0
2
0
2
1
1
0
0
0
0
1
0
0
0
0
1
0
0
1
2
0
2
0
2
2
0
0
2
2
2
0
0
2
2
2
1
1
1
1
0
1
0
1
2
2
1
1
2
1
0
0
0
2
2
1
1
2
1
0
1
2
0
0
0
0
0
0
0
0
2
0
2
1
0
1
0
0
1
0
2
0
2
1
0
0
0
1
0
0
0
2
0
0
0
1
0
0
1
1
0
0
0
0
0
1
1
0
0
2
1
2
0
4
0
0
0
0
0
1
2
0
2
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
1
2
1
0
0
0
2
0
1
0
0
1
1
0
1
0
2
1
0
0
0
0
0
0
0
2
1
0
0
2
3
0
1
2
1
0
0
0
0
2
0
2
0
0
0
0
0
1
1
1
1
1
0
2
0
1
0
1
0
1
2
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
1
0
0
0
0
1
1
2
0
0
0
2
1
0
2
2
1
0
0
2
0
0
0
2
1
2
1
0
0
1
0
1
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
4
0
0
0
0
0
0
1
2
0
2
1
0
0
1
1
0
1
1
2
1
0
2
2
0
1
0
0
1
2
0
0
0
0
0
1
0
0
2
0
0
1
0
2
1
1
2
0
0
0
3
0
0
0
0
1
0
1
2
1
1
0
1
0
0
2
0
0
0
0
1
0
1
0
0
0
2
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
2
1
2
1
2
0
0
0
0
1
0
1
0
2
1
0
1
0
0
0
0
1
1
0
2
0
0
1
2
0
1
2
0
0
2
1
0
0
1
1
0
0
0
2
1
0
0
0
1
1
0
0
0
1
2
0
1
1
0
2
0
0
1
0
5
0
0
1
1
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
1
3
2
1
0
2
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
3
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
1
0
0
0
2
2
1
1
1
0
0
0
1
2
3
2
0
2
0
0
0
0
0
3
2
0
0
2
0
1
3
0
2
0
3
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
2
0
1
0
0
0
0
2
1
0
0
0
0
1
1
1
0
0
1
0
2
0
1
0
0
1
2
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
2
0
0
0
2
2
0
2
0
0
1
0
2
0
2
0
1
1
0
1
1
2
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
1
0
0
0
0
1
0
1
2
0
1
0
0
2
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
2
0
0
0
1
2
0
0
1
2
0
1
2
1
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
2
0
1
0
2
0
0
0
1
2
1
0
1
0
0
0
0
0
1
0
4
1
0
0
2
1
0
2
0
0
1
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
2
2
2
1
0
0
0
0
2
0
2
0
0
0
2
1
2
0
0
2
0
0
0
2
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
1
0
0
2
2
0
0
0
2
0
1
2
1
1
0
1
1
1
0
1
0
0
0
1
0
0
0
0
2
2
0
2
0
4
1
1
1
0
4
0
2
0
1
0
0
1
0
0
1
0
2
2
0
1
0
0
2
0
0
0
0
0
0
1
0
0
1
1
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
1
2
0
0
1
1
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
2
1
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
1
1
0
0
1
2
2
0
2
1
0
0
0
0
1
0
0
0
0
1
2
0
0
2
1
0
2
0
0
0
1
0
3
1
0
2
3
0
0
0
1
0
2
0
0
0
0
1
0
0
0
2
1
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
2
0
0
3
1
0
0
0
0
0
2
0
2
0
1
2
2
1
0
1
0
2
0
0
0
0
2
2
1
2
0
0
0
1
0
1
0
0
0
2
0
3
1
0
0
0
0
1
0
3
1
0
0
1
0
0
0
0
0
0
0
4
0
0
1
1
0
1
0
0
0
0
3
0
1
0
1
0
2
1
0
0
2
1
1
0
2
3
1
2
0
2
1
0
2
1
0
1
1
2
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
2
1
0
0
0
2
1
0
0
1
2
2
0
0
0
2
0
0
2
0
0
0
0
1
1
2
2
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
3
1
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
2
0
2
0
0
0
1
2
0
2
0
0
0
0
2
0
0
1
2
3
0
3
0
2
2
0
0
1
0
0
0
0
1
1
1
0
0
0
2
2
0
0
0
0
0
0
0
0
2
2
1
2
1
0
0
1
0
0
0
2
0
2
0
0
0
0
1
2
2
1
1
0
0
0
1
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
2
2
0
5
0
2
0
0
0
1
0
1
0
0
0
0
2
0
3
1
0
2
0
0
0
2
0
0
0
0
0
0
2
0
2
0
2
1
0
1
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
2
1
0
1
0
2
2
0
1
0
0
2
0
2
0
0
0
0
1
0
0
0
1
2
0
2
0
2
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
1
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
1
0
1
0
2
0
0
0
0
2
0
2
0
1
0
0
6
1
0
0
0
0
0
3
0
0
0
1
0
2
1
0
0
1
0
0
2
0
0
2
0
0
0
0
2
0
2
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
2
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
1
3
0
0
0
1
0
0
0
0
1
2
3
1
1
1
0
0
2
0
0
0
2
1
0
0
1
2
0
2
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
2
2
0
0
1
0
0
0
0
0
0
0
2
0
0
2
1
2
0
0
0
0
2
2
0
0
0
0
0
0
1
2
0
2
0
0
2
1
0
0
0
1
1
2
0
0
0
2
0
2
3
1
1
0
0
0
2
0
0
1
2
1
2
0
2
3
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
1
1
1
2
0
2
1
0
1
0
2
0
0
0
0
1
0
0
0
1
4
1
0
0
0
0
1
1
0
0
0
0
0
2
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
1
0
1
1
2
0
0
0
0
2
4
1
1
1
0
1
0
1
0
0
2
0
2
0
1
2
0
0
0
1
0
0
0
1
0
7
2
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
2
1
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
2
1
2
1
0
1
1
2
2
1
0
1
0
0
0
1
1
1
0
0
2
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
3
0
2
0
0
1
2
1
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
3
0
0
1
0
0
0
2
0
1
0
1
0
1
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
2
1
0
0
0
2
0
0
0
1
1
1
0
0
2
0
2
0
0
1
0
2
1
0
0
2
2
2
3
2
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
2
1
0
0
0
2
0
0
0
3
2
0
0
0
2
1
2
2
1
2
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
1
0
0
2
0
2
0
0
0
0
3
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
2
1
2
0
0
0
0
0
1
1
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
1
1
0
1
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
3
0
0
0
2
0
1
0
0
0
1
1
0
0
2
1
2
0
1
1
0
0
1
1
0
2
0
0
0
0
0
1
0
0
0
0
3
0
0
2
2
1
1
2
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
2
2
1
0
1
0
0
0
0
1
2
6
2
0
2
0
0
0
0
2
1
1
0
0
0
2
0
1
0
0
2
2
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
1
0
0
1
2
0
1
0
0
0
1
0
1
0
0
1
0
0
1
0
2
1
4
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
4
0
0
0
0
1
0
0
0
2
0
0
2
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
1
2
1
0
0
0
4
1
0
1
1
0
0
2
0
2
2
0
0
1
0
1
3
2
0
0
0
1
0
2
2
2
0
0
0
2
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
1
1
1
0
0
0
0
2
2
0
0
0
2
0
0
1
0
0
2
1
4
0
0
2
0
0
2
1
0
0
0
0
0
1
1
0
0
0
1
0
2
0
0
0
1
0
0
1
0
0
0
1
1
1
0
0
0
0
1
1
0
7
1
0
2
1
2
1
0
0
1
0
1
0
0
0
0
0
0
1
1
1
4
0
0
0
1
0
0
0
0
2
0
1
1
0
1
2
2
1
0
1
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
3
0
0
4
2
1
0
1
2
0
0
0
2
1
1
0
0
0
0
0
7
0
2
0
3
0
2
2
2
0
0
1
1
1
1
0
2
0
0
0
2
1
0
0
2
0
0
0
1
0
0
2
1
0
0
0
0
3
0
1
0
0
0
0
0
0
0
1
0
0
2
0
1
2
3
0
0
2
0
1
0
0
1
0
2
1
2
1
0
0
0
0
0
2
0
0
0
2
1
0
0
1
0
0
1
2
0
2
0
2
0
2
0
0
0
0
0
1
3
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
2
0
0
2
0
2
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
2
0
1
0
0
3
1
1
0
1
0
2
1
0
2
1
0
0
0
0
0
0
0
1
6
2
2
0
2
1
2
0
0
0
0
0
1
4
0
0
1
0
1
0
0
0
1
0
1
2
0
1
1
2
0
4
1
1
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
2
0
0
0
1
1
1
0
0
0
0
0
1
0
0
10
1
0
0
0
0
1
2
0
2
1
1
0
0
1
1
0
0
3
0
1
0
2
2
0
2
0
0
0
1
1
0
2
1
1
0
0
0
1
0
0
1
0
2
0
1
3
0
0
0
0
0
0
1
0
0
1
4
2
0
0
2
1
0
1
2
1
0
2
0
2
0
0
1
0
0
4
0
0
3
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
1
0
2
0
0
0
0
1
2
0
1
2
3
0
2
1
1
1
1
1
0
1
0
0
0
0
0
1
0
1
2
0
0
0
0
1
2
1
0
0
2
0
0
2
3
0
2
0
0
0
0
1
2
0
0
0
0
0
0
2
2
1
1
1
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
1
1
1
1
1
1
0
0
0
1
0
1
0
0
2
0
0
4
0
2
0
2
0
2
0
0
0
3
0
2
2
0
2
0
2
0
0
0
0
1
0
2
1
1
1
2
0
0
0
2
1
2
1
0
1
0
0
1
0
0
0
0
1
3
2
1
1
0
0
1
0
0
0
0
0
0
2
1
1
0
0
1
0
0
4
0
1
0
2
0
0
0
0
0
1
0
1
1
2
1
0
1
1
2
1
0
0
0
0
0
2
0
0
0
1
1
2
2
2
0
1
2
0
1
0
0
3
0
2
0
0
0
0
0
2
0
0
2
1
2
3
3
0
0
0
1
0
0
0
0
0
0
0
1
2
0
1
2
2
0
0
0
0
0
0
1
2
0
0
1
1
0
1
0
0
0
0
0
0
2
0
2
0
0
1
0
0
2
0
0
2
0
0
1
0
2
0
0
1
2
0
0
1
2
0
1
2
3
2
0
0
1
2
0
0
0
0
2
0
0
0
2
1
0
0
0
3
1
1
0
0
2
0
1
2
0
0
0
2
0
0
0
0
2
2
1
0
0
2
0
1
0
1
0
2
1
2
2
0
2
0
0
0
0
0
0
1
2
2
1
0
0
2
0
0
0
2
2
0
0
1
0
2
0
0
2
3
0
0
0
1
1
0
0
0
0
0
0
0
1
1
2
1
2
2
0
0
1
0
0
2
1
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
2
2
1
2
1
0
0
0
1
1
0
2
1
0
0
3
0
0
0
0
0
1
1
0
0
2
0
1
0
1
2
0
1
1
0
1
0
2
0
2
0
0
0
1
1
1
0
2
0
0
0
0
1
0
0
1
1
0
2
1
0
0
1
1
2
0
0
2
2
1
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
2
2
0
0
2
1
0
1
0
0
2
0
2
2
0
1
1
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
3
2
0
0
0
0
0
2
2
0
2
0
1
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
2
2
2
1
2
0
0
0
0
0
0
0
1
1
2
1
0
0
0
2
1
0
0
1
0
1
0
0
2
2
2
0
0
2
1
0
0
1
0
2
0
0
0
0
2
0
0
2
0
0
0
1
0
2
0
1
2
0
0
0
1
0
1
0
2
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
1
0
1
0
0
1
0
0
2
0
0
2
0
0
0
0
0
2
0
0
1
2
0
1
0
1
1
1
1
0
0
2
1
1
0
2
0
2
0
0
0
0
0
0
0
0
0
1
1
2
2
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
1
2
0
2
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
2
2
0
1
0
2
0
0
1
0
0
3
0
0
0
1
1
0
1
0
0
0
2
3
0
0
2
2
2
0
0
3
0
1
0
3
0
0
0
0
0
2
4
0
1
0
1
0
0
2
0
1
1
0
0
1
1
0
0
0
0
2
0
2
0
1
1
0
0
0
0
1
0
2
2
1
0
0
0
0
1
0
1
0
0
0
2
0
0
1
3
0
2
0
0
2
0
0
0
0
1
0
3
0
1
0
0
1
1
1
0
0
0
1
0
0
0
1
1
0
0
1
2
1
2
1
0
0
2
1
0
0
2
2
2
1
0
0
2
0
2
0
0
1
0
0
1
3
0
1
2
0
0
0
0
0
1
0
1
2
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
3
1
1
0
0
0
5
1
0
1
1
0
0
2
0
0
1
2
1
0
1
1
1
2
0
0
2
0
0
0
0
0
0
1
0
0
1
0
2
1
1
1
1
0
0
2
0
0
3
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
3
0
0
0
0
0
1
0
1
2
0
0
0
2
3
0
1
1
0
2
0
0
0
0
1
2
1
0
1
0
0
0
0
4
0
0
0
2
0
1
2
1
0
0
0
3
0
0
1
0
0
0
1
0
0
0
1
2
0
3
1
0
0
2
2
0
0
3
2
1
0
0
0
2
2
0
1
0
1
0
0
2
0
1
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
2
3
0
2
1
0
0
2
0
0
2
0
0
1
0
1
0
0
0
0
0
1
2
0
0
0
0
2
2
0
1
0
0
2
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
1
1
0
0
1
0
1
2
2
2
0
1
2
2
2
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
1
1
1
0
0
0
0
0
1
1
0
0
0
1
0
1
1
0
0
1
2
0
0
0
0
0
0
0
0
2
1
2
1
0
2
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
2
0
2
0
0
1
0
0
0
0
0
2
0
3
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
1
0
0
1
0
0
1
2
0
2
0
2
1
0
0
0
0
1
2
0
0
0
1
0
1
0
0
0
0
1
0
0
1
1
3
0
0
0
1
1
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
1
0
1
0
0
0
2
2
0
0
0
1
1
0
0
2
0
0
1
0
0
3
0
0
1
3
0
3
0
0
2
0
5
1
1
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
8
1
0
0
2
0
1
0
3
0
2
1
1
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
1
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
1
2
1
2
1
1
0
1
0
0
1
1
1
0
2
2
1
0
0
0
1
1
0
0
1
0
2
0
1
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
2
0
1
1
0
0
1
1
0
0
0
0
2
1
0
0
0
0
1
0
2
2
2
0
1
0
0
1
0
0
1
0
1
0
0
0
2
0
0
0
2
1
0
2
2
2
0
1
0
1
2
1
0
0
0
1
0
0
1
1
0
0
0
1
1
1
2
1
0
0
2
2
0
2
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
2
0
1
1
0
0
0
1
0
1
1
2
0
2
0
1
2
1
2
0
1
1
0
1
0
1
0
1
2
0
0
0
1
0
1
0
0
1
3
1
0
0
1
2
0
0
0
0
2
0
2
0
1
2
1
2
1
0
0
1
0
0
0
2
0
0
0
2
1
0
0
0
1
2
0
0
0
1
0
0
1
0
1
0
1
2
1
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
1
2
0
1
1
0
2
0
0
0
1
0
0
0
0
0
0
2
1
0
0
2
1
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
2
0
1
0
2
0
0
0
1
0
0
3
2
0
0
0
0
1
2
0
0
0
1
0
0
0
1
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
2
0
0
1
5
0
0
0
1
0
2
2
0
0
0
1
0
0
1
0
0
0
0
1
2
0
3
0
0
1
1
0
0
0
2
0
2
0
2
7
0
0
1
2
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
1
2
1
1
3
1
1
1
0
1
2
1
0
2
0
0
1
0
2
1
2
0
0
2
1
0
0
1
0
1
0
1
1
0
2
2
1
0
0
1
0
0
0
1
2
0
0
2
0
0
0
4
0
0
2
0
2
0
0
1
2
0
0
1
1
2
2
0
1
3
0
0
0
1
3
0
0
2
1
0
0
0
2
1
0
0
0
1
0
0
0
2
0
2
0
1
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
1
1
0
0
0
1
2
0
1
0
2
2
0
2
0
2
0
0
0
0
3
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
1
3
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
1
2
0
2
2
2
2
3
0
0
2
1
0
0
2
1
0
1
0
0
0
0
0
0
3
1
0
2
0
0
1
0
1
2
1
0
0
1
0
1
1
1
1
0
0
0
0
2
0
1
0
0
0
1
0
0
0
2
0
0
0
2
2
2
0
2
0
1
0
1
0
0
1
0
0
0
1
2
0
0
2
2
0
0
1
0
0
1
2
0
0
0
1
4
0
2
2
1
0
1
2
2
0
2
0
1
0
0
2
1
2
0
0
0
0
1
3
3
0
1
2
0
0
0
1
0
0
0
1
0
0
0
2
2
0
2
2
2
2
0
2
0
3
0
1
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
2
0
2
0
0
0
2
0
1
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
3
0
0
0
0
1
0
1
2
2
0
0
2
0
0
2
2
0
0
0
0
2
0
2
0
0
0
0
1
0
2
2
2
2
1
1
2
0
1
0
2
0
0
2
0
2
1
0
2
2
0
0
1
0
0
0
0
1
4
0
0
2
1
1
1
0
1
0
0
1
0
0
2
2
2
3
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
4
2
1
1
2
1
1
2
1
0
1
0
0
0
0
0
0
2
1
0
2
1
0
0
0
0
1
0
4
0
2
0
3
1
1
0
1
1
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
2
1
2
0
0
0
1
0
0
0
0
1
0
3
0
3
3
0
2
1
0
0
1
0
0
0
0
1
0
0
0
1
1
0
1
0
1
0
0
3
2
0
0
0
2
0
0
0
0
2
0
0
2
0
0
1
1
1
0
0
0
1
1
2
0
0
1
3
0
0
0
2
0
2
2
2
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
2
1
0
0
2
1
1
0
0
0
0
0
2
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
1
1
0
0
2
1
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
2
0
1
1
0
2
0
0
0
2
0
2
0
2
0
0
2
0
2
2
0
1
0
1
1
0
0
2
1
2
0
1
0
0
3
0
0
2
0
1
0
0
2
2
0
0
0
0
0
0
1
0
0
2
0
0
1
0
2
1
0
0
2
0
1
1
1
2
1
0
0
0
2
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
2
1
2
0
0
1
0
2
2
0
2
0
1
0
0
1
0
0
0
1
1
3
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
2
2
0
7
0
0
0
2
2
0
1
0
2
3
1
0
0
2
0
0
2
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
2
1
1
1
0
0
1
0
0
1
0
3
2
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
1
2
2
2
1
0
1
1
0
0
0
0
0
0
0
3
0
1
0
0
2
0
0
1
1
0
2
0
0
2
1
2
0
2
0
0
0
0
2
0
0
0
0
1
1
0
0
1
0
0
1
0
1
1
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
1
2
3
2
1
1
0
6
1
2
0
2
2
0
3
2
1
0
2
1
0
0
0
1
3
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
1
1
3
0
0
2
0
1
0
0
0
0
0
0
1
1
2
1
0
0
0
1
2
2
0
0
2
0
1
0
0
0
2
0
1
2
0
1
2
1
2
0
0
0
0
0
4
2
0
1
1
0
0
1
0
0
0
2
0
2
1
0
0
2
0
0
2
1
0
0
2
2
2
1
0
2
0
1
2
0
0
1
0
0
0
2
2
0
1
0
2
0
2
0
0
1
0
0
2
0
0
0
0
2
0
0
1
1
1
0
2
1
1
0
2
0
0
2
0
0
1
0
2
0
2
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
1
1
2
1
2
0
0
1
2
0
0
0
0
0
0
2
2
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
2
1
0
0
0
2
0
2
0
0
4
0
1
0
1
0
0
1
3
0
3
0
0
0
1
1
2
2
0
0
0
0
0
2
0
2
0
1
2
0
0
1
1
0
0
2
0
1
0
1
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
2
2
2
0
2
2
1
1
2
0
1
0
0
0
3
1
2
2
2
0
5
0
0
1
1
0
0
0
0
1
2
4
1
0
2
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
2
2
0
2
0
3
0
0
0
0
0
0
2
0
0
2
2
2
0
2
2
0
0
0
0
0
0
0
0
2
2
2
2
0
0
0
4
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
1
2
0
0
2
0
0
0
2
0
0
0
0
0
2
1
0
0
1
0
2
0
0
1
0
0
0
3
2
0
2
2
0
0
2
0
1
0
0
0
0
2
0
0
0
1
2
3
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
1
1
0
0
0
2
0
0
1
0
0
1
1
2
2
0
0
2
0
0
0
0
0
1
2
1
0
0
0
0
0
1
0
0
4
1
0
0
2
1
2
1
1
1
1
0
2
0
0
1
0
2
0
0
0
0
1
1
1
2
0
1
1
0
2
1
1
1
2
2
0
2
2
1
0
0
1
0
2
0
0
2
0
0
0
0
1
0
1
2
0
0
1
0
2
0
2
0
0
0
0
0
0
0
1
2
0
0
1
1
0
3
0
3
0
2
1
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
1
4
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
2
2
0
0
0
0
0
0
2
0
2
11
0
2
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
2
0
0
2
2
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
1
1
2
0
0
2
2
0
0
0
0
0
0
0
0
1
2
2
1
0
0
2
0
1
2
0
0
3
2
0
0
0
1
0
0
2
1
0
2
0
0
1
0
1
0
2
0
0
0
0
0
1
0
2
0
0
4
0
0
0
0
0
1
1
0
0
2
0
0
1
0
0
1
2
0
0
0
2
2
0
1
0
0
2
0
0
0
1
0
0
0
2
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
1
0
1
0
0
1
0
0
0
2
1
0
0
0
2
2
0
0
1
1
0
1
0
0
1
0
2
0
0
2
0
0
0
0
0
1
0
2
0
1
0
0
1
2
2
0
0
0
2
1
0
0
2
0
0
1
2
0
0
0
0
2
0
0
0
0
4
0
0
0
0
2
0
1
2
0
0
0
0
1
0
2
1
0
0
4
0
0
0
0
2
2
2
1
2
2
1
0
1
2
0
0
1
0
0
4
2
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
1
6
1
0
0
2
2
3
0
0
0
0
0
0
0
0
0
1
2
0
1
2
2
1
0
2
3
0
0
1
1
0
0
1
0
1
1
1
0
0
0
0
2
0
0
1
1
0
0
2
0
0
0
1
1
0
0
0
2
2
0
2
0
0
0
3
0
0
0
1
0
2
0
1
1
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
1
1
2
2
0
0
0
0
2
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
1
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
2
0
0
2
2
0
0
1
0
2
0
0
1
0
0
1
0
0
3
1
0
3
0
0
2
2
0
2
2
1
2
1
0
1
0
1
0
0
2
0
0
0
0
0
1
0
2
0
0
2
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
2
0
0
0
2
0
0
2
2
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
2
1
2
0
0
0
0
0
1
0
0
1
2
0
1
0
0
0
0
0
1
1
1
0
2
0
0
2
0
1
0
0
0
0
0
0
1
0
0
2
2
0
2
0
0
0
0
0
2
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
2
1
0
1
0
0
0
2
3
0
0
0
0
0
2
0
2
0
1
4
0
1
2
0
1
2
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
2
1
1
0
0
0
2
0
0
1
2
3
0
0
1
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
2
2
1
0
1
2
2
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
1
0
0
0
2
0
0
2
0
1
0
0
0
3
0
0
0
1
0
0
0
1
2
2
2
1
2
1
0
2
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
2
0
0
1
1
1
1
0
0
0
1
1
0
0
0
0
1
1
2
0
1
0
2
0
0
2
0
0
0
0
2
2
0
1
2
0
0
0
1
0
2
0
2
0
0
0
0
0
2
0
0
2
0
0
2
1
0
0
1
0
0
1
0
1
0
2
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
1
1
3
2
0
1
0
2
1
0
1
2
0
0
0
0
1
0
0
2
0
0
2
2
0
0
0
0
0
0
4
0
0
1
0
1
1
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
1
2
0
0
0
0
0
0
3
2
0
2
1
0
1
0
0
2
0
1
0
3
1
2
0
2
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
1
2
0
0
2
0
2
1
0
1
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
1
0
0
3
0
1
0
0
0
2
1
0
0
0
0
1
2
1
1
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
1
2
0
0
1
0
0
0
2
0
2
0
0
0
1
0
4
2
0
1
0
2
0
2
3
0
2
0
0
0
0
1
1
0
0
1
2
0
0
0
2
1
2
3
1
0
0
0
2
1
1
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
1
2
0
0
0
1
0
0
0
0
0
2
0
0
1
2
0
3
0
2
0
0
1
1
1
2
0
0
0
3
4
0
0
0
1
1
0
1
2
2
1
1
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
1
0
2
1
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
2
0
0
0
1
2
0
0
2
0
0
0
0
1
1
0
1
0
3
0
0
0
0
1
0
0
1
0
2
1
0
0
0
1
1
0
1
2
0
1
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
1
0
0
0
2
0
1
2
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
3
2
4
1
0
3
3
0
0
1
0
0
0
0
2
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
3
1
0
0
0
0
2
2
0
2
2
0
1
0
0
2
0
0
0
1
0
0
1
0
2
0
1
2
0
0
1
1
2
0
0
0
2
0
0
2
0
0
0
0
0
0
1
2
2
4
0
0
2
0
2
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
1
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
1
0
1
2
0
0
0
1
1
0
0
2
0
0
2
0
2
0
2
0
0
1
0
0
0
1
0
2
1
1
0
2
2
1
0
0
0
1
1
2
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
1
1
0
0
0
2
0
0
1
3
0
2
0
0
0
0
1
0
0
1
0
0
1
2
0
0
1
1
0
2
2
0
0
0
0
0
2
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
2
2
1
2
0
0
0
0
0
0
0
2
0
2
1
0
0
0
2
0
0
0
0
0
0
0
2
0
2
1
0
0
1
0
2
0
1
0
1
0
1
2
0
0
1
0
0
1
0
0
0
1
2
4
0
0
0
0
0
1
0
0
2
0
0
1
0
2
1
0
1
2
0
1
1
0
0
2
0
2
3
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
5
1
0
2
1
1
0
4
0
0
2
1
0
2
1
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
2
2
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
2
2
1
1
0
0
0
2
0
0
2
2
0
0
0
2
0
0
0
0
0
2
0
2
2
1
1
0
2
2
0
0
1
1
1
1
1
1
0
0
0
0
0
0
2
0
2
0
2
1
0
1
0
0
0
0
2
0
0
0
0
0
1
1
0
0
1
0
2
0
0
1
0
2
1
1
0
1
0
0
0
0
0
0
2
1
0
0
1
1
0
1
1
0
2
0
2
0
1
3
0
0
2
2
0
1
1
2
0
2
1
0
1
2
2
2
2
0
0
3
0
0
0
1
0
2
1
0
0
0
0
0
2
0
2
0
1
1
0
1
1
0
0
0
0
0
1
1
2
0
0
0
0
1
0
0
0
1
0
0
2
1
0
1
0
2
0
0
0
0
2
0
1
2
0
0
0
1
1
0
2
0
0
1
1
1
0
1
0
2
0
0
0
0
0
2
2
0
2
0
2
1
2
0
0
2
0
2
2
0
0
0
0
1
0
0
1
0
0
0
2
1
0
1
1
0
0
0
0
0
0
2
0
0
0
1
1
1
2
0
2
0
0
0
0
0
0
0
2
1
0
0
2
0
2
2
0
0
3
0
0
1
0
1
1
0
0
2
1
0
2
0
1
0
2
1
0
1
1
1
0
2
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
2
6
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
2
0
0
0
1
2
2
0
0
1
1
2
0
1
2
1
0
1
1
2
3
0
0
0
0
0
0
1
0
0
1
1
2
4
1
0
1
0
0
0
0
0
1
1
2
0
0
1
1
2
2
1
2
0
0
0
1
0
0
2
0
1
1
0
0
0
1
1
1
0
0
0
0
0
1
1
0
1
1
0
0
0
3
1
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
1
1
0
0
0
1
2
2
0
0
3
0
2
1
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
2
1
0
2
0
1
0
2
0
0
0
1
0
0
1
0
0
2
0
2
0
1
2
2
0
0
0
2
0
2
1
1
0
1
0
0
0
2
0
0
0
1
1
0
2
0
0
1
2
0
2
2
0
0
0
2
0
0
0
0
0
2
1
0
5
0
1
2
0
2
1
2
0
0
0
2
0
0
0
0
0
2
0
0
2
0
1
1
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
2
2
0
2
0
1
0
2
0
0
0
0
0
0
1
0
0
3
2
0
0
1
0
2
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
1
0
0
0
0
0
0
2
2
0
0
4
1
2
0
0
2
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
2
2
1
0
0
1
0
0
0
0
1
2
4
0
0
2
2
1
2
1
1
1
2
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
1
1
0
1
0
0
0
0
0
0
0
1
1
0
1
0
1
0
2
2
1
1
1
0
0
0
1
0
1
0
0
0
0
0
0
2
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
2
0
2
0
0
0
0
0
1
0
2
0
2
1
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
3
1
0
0
0
0
0
0
0
0
7
0
0
4
0
0
0
0
2
2
0
2
2
1
2
0
1
3
0
2
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
1
0
1
0
1
2
0
0
1
0
3
0
1
1
0
1
2
0
1
1
0
0
0
0
0
0
1
0
0
1
2
0
0
1
0
1
0
2
0
0
0
2
2
2
1
0
0
1
2
1
2
1
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
2
1
0
2
1
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
2
0
1
0
0
0
0
1
1
0
0
0
2
2
0
2
0
0
0
2
0
1
0
2
1
2
2
0
2
1
1
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
4
0
1
1
0
1
2
0
1
0
0
0
0
1
2
0
0
1
2
0
0
0
0
2
1
0
0
2
0
0
0
0
0
1
1
0
4
0
2
0
0
0
0
0
0
0
0
1
5
0
0
0
1
0
1
0
0
1
2
2
0
2
1
0
1
0
0
1
0
0
2
0
0
0
2
0
0
0
0
2
0
0
2
1
1
0
0
2
0
2
0
1
0
1
1
3
0
0
2
1
0
0
1
2
0
0
0
1
0
2
1
0
0
0
0
2
0
1
0
1
0
0
2
0
0
0
2
0
1
0
1
0
2
0
2
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
1
2
2
1
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
1
2
0
2
3
0
2
2
0
1
1
2
0
2
2
0
0
2
0
1
0
0
0
1
0
1
2
0
3
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
2
0
0
0
0
1
0
2
0
1
0
2
0
0
0
2
0
0
2
2
1
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
2
1
1
0
0
0
2
0
0
0
0
2
1
0
0
0
0
1
0
0
1
0
2
0
0
1
1
1
1
2
0
2
0
2
0
0
0
1
0
2
2
0
1
0
0
0
0
0
0
1
3
2
2
0
0
0
0
2
2
2
0
0
0
0
2
0
2
0
1
3
0
0
0
0
1
0
2
0
2
0
0
2
1
2
1
0
0
0
0
0
0
0
0
2
0
2
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
2
0
2
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
2
1
1
2
2
1
0
2
2
0
2
0
0
2
0
0
1
0
1
0
7
0
0
1
2
0
0
0
2
0
0
0
1
2
0
2
0
2
2
2
0
0
1
0
0
2
3
1
0
2
0
1
0
2
0
1
2
2
2
0
0
0
1
1
0
2
0
0
2
0
0
1
3
0
0
0
0
3
0
0
0
0
0
1
1
1
1
1
1
0
1
0
0
2
0
0
1
0
0
0
1
0
0
0
1
1
2
1
2
0
1
1
0
0
1
1
0
0
2
0
1
2
1
0
0
2
0
2
0
0
1
0
0
0
2
2
0
2
2
0
0
1
0
0
1
0
0
2
0
1
0
1
1
2
0
0
2
0
4
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
2
1
0
5
0
1
1
0
0
2
0
1
0
0
0
1
1
3
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
2
2
0
6
0
1
0
2
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
2
0
1
1
1
0
0
0
0
1
0
0
1
0
2
0
0
0
0
1
0
1
0
0
1
2
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
2
2
0
1
0
0
0
2
0
0
0
0
0
2
2
0
1
1
0
2
0
0
2
0
0
0
2
0
2
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
1
0
4
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
2
0
0
0
0
2
1
0
1
0
1
0
0
0
0
1
0
0
0
1
1
0
2
0
0
0
2
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
2
2
1
0
0
0
0
2
1
1
0
0
0
1
1
0
0
2
0
0
0
1
0
0
1
0
0
1
1
0
0
2
0
1
0
0
0
2
0
0
1
1
1
0
1
0
2
2
0
4
1
0
0
2
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
2
0
0
0
3
2
0
1
1
0
0
3
0
0
1
0
2
1
0
0
1
0
0
0
4
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
2
0
0
0
0
0
5
1
0
2
2
2
0
0
0
0
3
0
2
0
0
1
2
0
4
0
2
0
0
0
0
0
0
0
1
0
2
1
1
1
2
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
2
1
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
2
0
2
0
0
0
0
0
1
1
2
0
1
1
0
2
0
1
2
2
0
1
0
0
0
2
2
1
1
1
0
2
0
0
0
1
1
2
0
4
0
0
1
2
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
2
0
1
0
2
0
0
0
0
1
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
4
1
0
2
1
2
0
0
0
0
0
0
0
2
0
2
2
2
0
0
0
0
1
0
1
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
1
0
2
1
0
0
0
1
1
2
1
0
0
1
0
2
0
1
1
0
0
1
2
2
0
0
0
2
0
1
2
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
1
0
1
2
0
0
0
2
0
0
1
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
2
2
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
2
1
0
2
3
0
2
1
0
1
0
0
5
0
0
0
0
0
0
2
3
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
1
1
2
0
1
0
0
1
2
1
0
0
0
0
0
2
0
0
2
0
2
0
1
2
0
0
0
2
0
0
0
0
0
0
2
0
1
2
2
1
1
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
1
0
2
2
0
1
2
0
0
0
0
0
0
1
3
1
0
0
0
1
0
0
1
1
0
0
0
0
2
0
0
2
2
0
2
2
0
0
0
0
0
0
0
1
1
2
2
0
0
1
0
0
0
0
0
0
0
2
1
0
0
4
1
0
0
0
1
1
0
3
0
0
0
0
1
0
2
0
1
0
1
1
1
0
0
0
1
0
1
0
0
0
0
1
0
2
0
0
0
0
1
0
9
0
0
2
1
2
0
1
0
0
2
1
0
0
0
0
2
2
0
0
2
0
1
2
0
0
1
0
0
0
2
2
0
0
0
0
0
1
0
0
2
1
0
2
2
1
0
4
2
2
0
0
0
0
1
1
0
1
1
0
1
0
0
0
4
3
2
0
0
1
0
1
0
1
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
1
0
5
2
0
0
0
1
0
0
0
0
1
0
2
1
1
1
0
0
0
0
0
0
0
1
6
1
0
0
2
2
0
0
0
0
0
0
0
1
0
0
2
0
0
1
1
0
0
0
0
1
1
2
2
0
0
0
3
2
0
0
0
0
0
2
0
2
2
0
0
0
0
1
2
0
3
3
0
2
0
0
0
0
2
3
0
0
1
2
0
1
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
2
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
1
0
2
0
0
1
0
1
0
4
2
0
1
0
2
0
0
3
2
0
0
1
0
0
0
0
2
2
0
2
0
0
2
0
1
1
1
2
0
0
1
0
0
2
0
2
3
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
2
2
0
0
0
1
1
0
2
1
0
1
1
1
0
1
0
0
0
1
0
0
1
2
0
0
0
1
1
3
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
1
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
2
0
0
2
2
0
1
0
2
0
0
2
1
0
0
0
1
2
1
0
0
0
0
2
1
1
2
0
0
1
0
2
1
0
0
2
1
2
2
0
0
2
2
0
0
3
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
1
0
0
2
1
2
0
0
2
0
2
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
1
0
0
0
2
0
1
1
1
0
1
0
0
0
2
0
2
0
2
0
2
3
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
3
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
2
2
2
1
0
1
1
0
1
0
1
2
1
0
1
0
1
2
0
2
0
1
1
1
0
0
0
0
0
1
0
1
2
0
2
0
1
2
1
0
0
2
2
2
0
3
1
2
0
0
0
0
0
0
0
4
1
0
0
2
2
0
0
0
1
0
1
0
2
0
0
1
0
2
0
1
0
1
2
1
0
0
0
0
5
0
2
2
0
0
0
1
0
1
0
0
0
1
1
0
0
0
1
2
0
3
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
3
1
0
0
1
0
0
0
0
0
0
1
2
1
0
1
2
0
0
0
2
1
1
0
0
1
0
1
0
0
1
0
0
0
0
1
2
0
1
0
1
0
0
0
2
0
0
0
2
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
1
2
0
2
1
3
3
0
0
1
2
0
1
2
1
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
2
2
0
1
0
1
2
0
2
2
0
0
1
0
2
0
0
2
0
0
0
2
0
0
2
0
2
1
2
0
0
0
0
1
0
1
0
1
0
0
2
1
1
2
2
1
1
0
0
2
0
0
0
0
0
2
0
2
2
0
0
1
0
0
0
0
0
1
0
1
1
2
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
1
0
0
2
0
0
1
1
1
0
0
2
0
0
0
0
1
1
1
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
2
0
0
0
3
1
1
0
1
0
0
3
0
0
1
0
0
1
0
0
1
0
2
1
0
2
0
2
1
0
0
0
1
0
0
1
1
0
0
2
2
2
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
2
3
0
0
0
0
1
2
0
2
0
0
3
0
6
0
0
1
0
0
0
2
1
0
2
0
0
1
0
1
0
0
0
0
0
0
0
1
3
0
2
1
0
0
0
0
0
0
1
2
0
0
0
2
1
0
0
0
0
1
0
2
0
0
2
0
0
1
0
2
0
2
0
1
0
3
1
0
1
1
0
0
0
0
0
1
0
0
2
1
3
5
0
0
0
1
0
0
0
1
0
1
0
0
0
2
1
0
0
0
1
0
0
0
1
0
0
0
0
2
2
1
0
0
0
2
0
0
2
2
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
1
2
2
2
1
1
0
0
2
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
1
0
0
1
2
0
0
0
2
0
1
1
0
0
2
0
0
0
0
0
2
0
0
0
2
0
1
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
1
3
1
2
1
3
0
0
1
1
0
1
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
2
0
0
1
1
0
2
0
1
0
1
0
0
0
2
0
0
1
0
1
0
0
0
0
0
4
0
0
2
1
1
2
0
1
0
0
4
1
2
0
0
0
1
1
0
1
2
0
0
0
0
2
2
2
1
0
1
1
0
2
1
0
0
0
0
4
0
0
0
0
0
0
1
1
2
0
1
0
0
0
1
0
1
0
0
4
0
3
0
0
1
2
0
0
0
0
0
2
0
0
0
4
1
0
0
0
0
0
1
1
0
0
3
0
1
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
2
1
0
0
0
1
0
0
2
0
0
0
0
1
2
2
1
2
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
1
1
1
0
0
0
0
1
3
2
0
1
0
5
0
0
0
0
0
1
0
2
1
0
0
0
0
2
0
0
2
2
0
0
0
2
3
1
0
1
0
2
1
0
1
0
2
0
1
0
0
2
0
0
2
0
1
1
0
0
0
0
0
1
2
0
3
0
2
1
1
0
0
1
0
0
1
1
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
3
0
0
2
0
1
0
0
1
0
0
2
0
0
0
1
0
1
0
2
0
0
1
4
1
0
0
0
0
0
0
0
2
0
1
0
0
1
2
0
1
0
0
0
0
2
0
0
0
0
1
0
0
2
0
2
1
0
0
1
2
0
3
1
2
0
0
2
3
0
2
1
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
3
0
1
0
0
2
2
2
1
0
0
0
1
1
0
0
1
2
0
0
0
0
1
2
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
1
0
0
1
0
2
0
0
1
2
0
0
0
2
0
0
2
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
2
0
1
1
0
1
2
2
0
2
0
1
0
4
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
2
0
2
0
2
2
2
1
0
1
0
0
2
0
1
1
0
1
0
0
0
0
0
1
0
1
0
0
0
2
1
1
0
0
1
1
1
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
3
0
0
1
0
1
0
0
1
0
3
0
2
0
0
0
2
1
0
1
0
0
0
0
0
1
2
1
0
0
1
0
0
0
0
1
2
1
0
0
0
3
0
1
0
0
1
2
0
1
0
0
0
0
0
2
0
0
0
0
4
1
0
1
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
2
0
2
0
1
0
1
0
8
0
0
2
0
0
2
9
1
0
1
2
0
2
0
1
0
0
1
2
0
0
2
0
0
0
1
0
2
0
2
0
0
2
0
0
0
1
0
0
1
1
0
0
0
2
1
2
0
1
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
1
0
0
0
0
2
0
0
3
2
0
2
0
1
0
2
0
2
0
3
2
0
0
0
2
1
0
0
1
0
0
0
0
0
0
1
2
0
2
1
0
2
1
2
0
2
0
1
0
0
1
0
1
2
0
0
2
2
2
1
0
0
0
0
0
1
0
2
1
1
0
2
2
0
2
0
0
2
0
3
0
0
0
3
1
1
2
2
0
0
0
1
0
2
2
0
0
2
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
1
0
1
0
1
1
0
0
2
0
0
0
0
1
0
1
0
0
1
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
1
0
0
1
2
1
0
0
0
2
0
1
1
0
3
0
2
0
2
0
0
1
0
1
0
0
2
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
1
0
0
2
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
2
0
2
0
2
1
1
1
0
0
0
1
0
0
2
1
0
0
1
0
2
0
0
0
0
3
0
0
2
0
0
1
1
0
2
0
0
0
0
2
0
1
0
2
0
0
2
0
0
0
0
1
2
0
2
1
0
2
1
1
0
0
0
2
3
0
0
0
0
1
1
0
0
0
0
0
0
3
0
1
1
1
0
2
2
0
0
3
3
0
3
1
1
0
2
2
0
0
0
0
1
1
2
1
1
1
0
1
0
2
0
0
0
0
2
0
4
1
0
1
0
3
0
0
0
1
1
1
2
2
0
0
1
0
0
0
0
0
0
2
0
0
3
0
1
1
0
1
0
0
0
1
2
0
1
2
0
0
1
1
0
1
0
0
0
4
0
0
1
0
0
1
0
1
1
0
0
0
1
2
0
1
2
0
2
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
1
3
0
0
0
0
0
1
0
0
0
2
1
0
1
0
0
0
0
0
0
0
2
2
1
0
1
0
1
0
2
0
0
1
2
0
0
0
0
0
1
0
2
0
1
0
0
1
2
2
0
2
0
0
0
0
0
0
0
2
0
0
0
2
2
1
2
0
2
0
1
2
0
2
1
2
0
2
0
0
0
1
0
2
1
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
1
1
2
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
2
1
2
0
0
0
0
3
0
1
0
0
0
2
1
1
2
0
3
0
0
1
2
2
0
1
0
0
0
2
0
2
2
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
2
1
2
1
0
0
0
1
2
2
0
2
0
1
2
0
2
1
4
3
0
0
1
0
0
1
0
0
0
0
2
1
1
2
1
0
1
1
0
1
2
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
1
2
0
0
1
0
0
0
0
0
2
3
0
2
1
0
0
0
1
0
0
0
0
0
0
2
0
0
2
1
2
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
2
2
3
3
0
2
0
0
0
1
2
1
0
0
1
2
0
1
2
2
3
0
0
2
0
0
0
1
1
2
0
0
0
0
1
0
0
1
2
0
0
1
2
2
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
1
0
2
0
0
1
2
2
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
2
2
0
0
0
0
0
1
3
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
2
3
0
0
0
0
0
0
0
1
1
2
2
0
2
0
0
0
1
1
0
2
2
0
1
0
0
2
0
0
1
1
0
0
2
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
2
0
2
0
0
2
0
0
0
2
0
2
0
0
0
0
2
0
0
2
1
1
0
0
0
0
1
0
1
2
1
0
0
0
1
2
0
0
0
1
2
0
1
2
0
2
0
0
1
1
1
2
1
0
1
1
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
1
0
0
0
0
2
1
0
0
0
2
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
2
1
0
1
2
0
2
0
2
0
0
2
0
0
2
1
0
1
2
1
0
1
4
1
2
0
0
0
0
1
1
0
0
0
0
0
0
1
0
2
0
0
0
0
1
1
0
0
1
1
0
0
1
4
0
2
2
0
2
1
2
1
0
1
0
0
1
0
1
2
0
0
2
1
0
0
0
0
1
1
0
2
1
0
2
0
2
0
0
0
0
1
0
1
3
0
2
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
1
2
1
2
0
0
0
0
0
0
0
2
0
2
1
0
0
3
0
0
0
0
0
2
0
0
3
0
0
0
0
2
3
0
1
0
2
1
1
3
0
0
1
0
0
0
0
2
1
0
1
2
2
1
0
0
0
0
0
0
1
0
0
0
2
0
1
0
1
0
0
0
1
0
0
0
0
0
2
1
0
3
1
2
0
0
1
1
0
0
1
2
1
0
3
1
0
2
0
0
0
0
0
0
0
1
0
2
2
2
0
2
1
0
0
3
0
0
1
0
1
0
0
0
1
0
1
0
3
2
0
2
1
1
0
2
0
0
2
2
0
2
2
1
0
0
0
2
0
1
2
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
1
1
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
4
0
1
1
1
1
1
0
0
0
0
2
0
0
3
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
2
1
0
2
1
0
1
1
0
1
1
0
2
0
2
1
2
2
1
0
0
0
0
1
0
0
0
0
1
0
1
0
1
1
1
0
1
0
2
2
0
0
2
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
1
0
2
0
1
0
0
2
1
0
0
1
0
1
0
0
1
0
1
2
1
0
2
2
1
0
0
1
0
0
0
0
1
0
0
0
0
0
3
0
1
0
0
0
1
0
0
0
0
0
2
2
2
1
0
0
2
0
0
2
0
0
1
0
2
1
1
0
0
0
0
1
0
2
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
2
2
0
1
2
2
0
0
0
0
0
0
0
0
0
0
7
0
0
2
1
0
1
0
1
2
1
1
0
2
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
2
1
0
1
2
0
2
0
0
0
1
0
0
2
0
0
0
2
0
0
2
1
0
2
1
0
0
0
0
0
2
0
1
0
2
0
0
0
1
2
2
0
0
1
1
0
3
2
0
0
0
0
2
2
1
1
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
2
0
2
0
2
1
2
0
0
3
2
2
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
1
0
0
2
0
5
0
0
1
0
0
1
0
2
0
0
0
5
0
2
2
0
1
1
0
0
0
2
0
0
3
0
1
0
0
0
2
0
1
4
0
0
2
0
2
1
0
2
0
0
0
0
2
0
1
0
2
0
0
1
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
1
2
1
1
0
0
1
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
1
1
0
0
1
1
0
1
0
0
0
0
1
0
0
1
1
0
0
0
1
2
0
0
2
0
1
0
1
0
0
0
0
0
2
2
0
0
2
0
0
1
1
1
0
0
0
0
0
0
0
1
1
0
2
0
0
0
1
0
0
1
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
1
0
1
1
0
2
0
2
1
0
0
2
1
3
0
2
2
2
1
0
0
0
0
1
1
1
1
0
0
1
1
1
0
0
2
0
0
1
1
1
0
0
0
0
0
0
2
1
1
0
2
0
1
1
0
0
0
0
0
2
1
0
0
0
2
0
1
1
0
0
2
0
0
2
0
2
1
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
2
0
0
1
0
0
0
2
0
0
1
0
0
0
3
0
0
2
1
1
2
1
2
0
0
0
0
1
0
0
0
0
3
2
0
2
1
2
1
2
0
1
1
2
0
0
1
0
0
1
0
2
0
1
2
2
0
1
0
0
1
0
2
0
2
0
0
1
0
0
0
1
2
0
2
0
0
0
0
0
2
1
2
1
0
0
0
2
1
0
0
0
2
0
0
6
0
2
0
1
0
0
0
0
0
2
2
0
0
0
0
1
1
0
0
2
0
0
0
2
0
1
0
3
2
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
2
1
1
0
0
3
0
0
0
0
5
0
0
0
0
0
1
0
0
2
0
1
0
1
0
2
0
2
0
2
1
0
2
0
2
2
0
0
0
1
2
0
1
0
1
2
0
0
0
0
1
0
2
0
2
0
0
1
0
0
1
3
2
0
1
0
1
1
0
1
0
0
0
0
0
0
0
1
1
2
0
0
0
2
3
4
1
0
0
0
0
0
2
0
0
2
1
1
0
2
1
0
0
0
0
3
2
0
2
0
0
0
1
0
0
1
1
1
1
2
0
1
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
1
0
1
2
0
1
0
0
0
0
0
3
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
1
2
1
1
0
0
1
0
2
0
0
1
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
2
0
2
1
2
0
0
1
1
0
0
0
0
0
0
0
2
1
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
3
1
0
2
1
2
0
2
0
0
1
0
0
3
0
0
5
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
1
0
2
0
1
0
0
0
0
0
0
2
0
2
0
0
2
0
0
2
0
0
2
1
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
1
2
1
0
0
1
0
1
0
1
2
2
0
0
2
2
1
0
0
2
1
0
2
0
2
1
0
0
2
1
0
0
2
2
0
0
3
0
0
1
1
0
1
0
0
0
0
1
0
1
1
0
2
0
0
0
1
1
0
2
1
0
0
0
3
1
1
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
2
0
0
2
0
2
1
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
2
0
0
2
1
1
1
1
0
1
0
0
0
0
0
0
0
0
2
2
0
0
1
1
1
0
0
0
2
0
0
1
0
0
2
5
0
0
0
1
1
0
1
1
2
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
2
0
1
1
1
2
1
0
0
1
2
2
1
0
2
0
0
0
0
0
1
2
0
1
1
2
0
0
0
2
0
1
1
2
1
0
1
1
2
0
0
0
2
0
0
0
0
0
0
1
3
0
2
1
1
0
1
2
0
0
2
0
0
0
0
1
0
0
0
0
1
2
2
2
2
2
1
0
0
1
0
0
0
0
0
0
1
0
1
2
0
1
1
0
0
0
0
0
0
2
2
2
1
2
2
0
0
1
0
1
0
1
0
0
0
0
0
2
0
0
0
0
1
2
0
1
1
0
0
1
1
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
1
0
2
0
2
0
4
0
0
0
0
1
2
0
0
1
0
2
0
3
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
2
0
2
0
2
1
2
1
2
3
0
0
0
0
0
2
0
0
0
1
0
0
2
0
2
0
2
1
0
0
1
0
0
1
0
2
0
0
1
1
0
3
2
0
0
1
0
2
1
0
0
2
1
1
0
0
1
1
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
1
2
0
0
0
0
0
1
0
2
0
1
1
0
0
1
1
1
0
1
0
2
2
0
2
1
0
1
0
0
0
0
1
0
1
1
0
0
0
1
1
1
2
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
1
1
1
2
0
0
2
2
0
0
2
0
3
2
0
0
0
0
0
0
0
1
2
0
0
1
1
2
0
4
0
0
0
0
0
2
0
0
3
0
2
0
2
0
0
2
0
0
0
0
0
0
2
1
0
0
1
0
2
2
0
0
1
0
0
0
0
3
2
0
1
2
2
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
2
2
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
1
0
0
0
1
2
1
2
0
0
0
2
0
2
0
0
1
0
0
2
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
2
2
0
0
0
0
1
2
0
1
1
0
0
0
0
0
1
2
0
0
2
0
0
1
0
0
0
0
0
2
0
1
1
1
1
1
0
0
0
2
2
0
2
0
1
0
2
0
0
0
0
2
0
2
2
0
1
1
0
1
0
0
0
1
0
0
0
1
2
2
2
0
0
3
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
2
0
1
1
2
2
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
2
0
0
0
2
4
0
2
1
2
4
0
2
3
0
0
1
2
1
0
0
0
1
2
0
0
2
0
1
0
0
0
0
0
0
2
0
1
0
0
1
0
0
1
0
0
1
0
1
0
0
2
0
1
0
0
0
1
1
2
0
0
0
0
0
2
0
1
1
0
0
2
3
0
0
0
0
0
0
1
0
1
1
2
1
0
0
0
2
1
1
2
1
0
0
1
2
0
0
2
0
1
0
2
0
0
0
0
0
0
0
2
2
1
1
0
2
1
0
0
0
1
1
2
0
0
0
2
2
0
2
1
1
2
1
0
0
0
0
0
0
2
1
0
0
0
1
0
0
1
0
2
0
0
0
0
0
2
0
0
2
0
1
0
1
0
0
3
2
1
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
1
0
0
1
1
0
2
0
0
0
0
0
0
2
1
1
0
0
0
2
0
0
2
0
0
2
0
0
2
2
0
0
1
0
2
1
0
0
1
2
1
0
2
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
2
1
2
2
1
0
4
0
3
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
1
1
2
0
0
0
2
0
0
2
0
1
2
2
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
2
1
0
0
1
0
2
1
0
0
0
0
1
5
2
0
1
0
1
1
0
0
1
1
1
2
0
1
1
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
1
4
0
3
1
0
0
0
2
2
1
1
0
3
2
2
1
2
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
2
1
1
1
0
0
2
0
0
1
0
0
0
0
1
0
2
2
0
0
1
0
0
1
0
2
0
0
1
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
1
0
2
0
0
0
2
0
0
1
0
1
0
2
2
0
0
0
2
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
2
0
2
2
2
0
0
1
0
2
2
0
2
1
1
0
0
3
1
1
0
0
1
0
0
0
1
1
0
0
0
2
0
0
2
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
1
0
0
1
0
1
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
1
0
0
1
2
0
0
2
1
0
2
0
1
0
2
2
0
0
2
1
0
1
0
2
0
0
0
1
0
0
2
1
0
2
0
0
1
0
0
2
0
1
0
2
2
0
1
1
0
1
0
0
0
0
0
0
0
0
2
0
1
0
2
1
1
0
0
1
0
3
2
0
2
2
0
2
2
0
0
0
2
0
0
1
0
1
1
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
2
0
0
1
0
1
2
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
3
0
0
1
2
0
1
0
3
0
1
2
0
1
0
2
1
1
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
4
0
2
0
0
2
0
0
1
0
0
2
0
1
0
0
0
0
0
1
1
0
0
2
0
0
0
2
2
0
1
3
2
0
0
2
2
0
0
0
0
0
2
1
1
0
0
0
0
1
1
0
0
1
0
2
1
2
0
1
0
1
0
0
0
0
0
2
0
0
0
0
1
1
0
0
2
2
0
2
0
0
0
1
1
1
1
1
0
0
0
1
1
2
1
0
2
2
0
1
0
2
0
0
0
0
0
0
0
2
1
1
0
0
0
1
0
0
0
2
0
2
3
0
2
1
0
0
0
0
1
0
1
0
1
2
0
2
2
0
0
0
0
2
6
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
1
0
0
1
1
0
1
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
1
0
0
0
0
0
1
0
0
0
0
2
0
0
2
2
2
1
0
0
2
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
2
2
2
0
0
2
0
1
0
1
1
2
0
0
0
0
0
0
1
1
0
1
0
0
3
0
0
0
2
0
0
0
0
0
3
1
2
0
2
2
2
0
2
0
0
0
1
0
0
1
0
1
1
0
3
0
0
0
0
2
0
0
0
0
1
0
0
0
2
1
1
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
1
2
1
2
1
0
0
1
2
0
0
2
1
0
1
0
2
0
0
2
1
2
0
0
0
0
2
0
1
2
2
1
1
2
2
1
1
0
1
1
0
2
0
0
2
2
0
2
1
1
0
1
1
1
1
2
0
0
0
0
0
0
0
0
2
3
2
0
0
0
0
2
1
1
0
0
0
3
0
2
0
0
0
2
0
5
1
1
0
2
1
4
0
0
4
0
0
1
2
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
2
0
2
1
0
1
0
0
0
0
1
2
0
0
2
0
0
1
1
0
3
0
0
2
0
0
2
1
2
0
0
2
0
0
1
1
0
1
0
0
1
0
0
0
1
2
1
0
1
0
0
2
0
0
0
2
0
0
2
0
0
1
1
2
0
0
0
2
0
2
1
2
1
8
2
0
2
0
0
0
0
1
1
1
0
0
0
1
0
0
1
0
1
2
0
1
0
0
2
0
2
1
1
0
2
0
1
1
0
0
2
1
0
0
1
0
2
0
2
0
1
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
2
0
1
0
2
1
1
0
0
0
1
0
1
1
2
0
0
2
1
2
0
0
0
0
0
1
0
0
0
0
2
1
2
1
0
0
0
1
0
0
0
0
0
2
2
0
0
2
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
2
0
2
1
0
0
0
0
0
1
2
0
2
1
1
0
2
4
1
2
0
0
0
0
0
1
1
0
0
2
0
0
0
1
0
2
1
1
0
0
0
0
1
0
2
0
1
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
1
2
1
0
2
1
0
3
0
1
1
2
1
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
1
0
2
0
2
1
1
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
2
1
1
4
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
2
0
0
1
0
1
0
0
1
0
1
1
0
0
0
1
0
0
0
0
2
0
2
0
0
1
0
0
0
1
0
0
0
1
0
0
2
0
0
1
1
0
2
2
0
0
0
1
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
1
4
0
2
0
0
1
1
0
0
0
0
2
0
1
0
1
1
0
1
2
0
2
0
2
2
0
0
1
2
1
2
0
2
2
0
0
0
2
0
0
2
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
1
1
0
0
2
1
0
0
2
2
0
3
0
0
2
1
0
1
0
1
0
0
0
0
0
0
1
0
2
0
1
2
0
0
4
0
0
1
0
0
0
0
1
1
2
2
0
0
2
2
0
0
1
0
2
1
0
0
1
2
0
0
1
0
0
0
0
0
0
1
2
0
1
1
1
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
1
1
2
0
0
0
0
0
0
0
0
2
0
0
1
1
1
1
0
1
2
1
0
0
1
0
0
3
0
0
0
0
0
2
1
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
2
0
1
0
1
0
0
0
2
2
0
0
0
0
0
0
0
3
1
1
0
0
1
1
0
2
1
0
1
2
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
2
2
2
0
0
1
0
0
0
0
2
1
1
0
1
0
0
0
1
1
1
1
0
0
0
0
1
2
0
0
0
0
1
2
0
1
1
1
0
0
0
4
2
2
0
0
0
0
0
0
1
2
0
2
0
1
0
0
0
0
1
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
4
2
0
0
0
0
0
2
1
0
2
0
0
1
2
1
0
0
0
0
2
2
2
1
1
2
0
0
0
1
0
0
1
0
1
0
2
0
0
1
0
0
1
2
1
0
0
0
0
0
0
4
0
0
0
2
0
2
0
2
2
0
0
0
0
0
3
2
0
0
0
0
2
2
1
1
1
0
2
0
1
2
2
2
1
0
0
0
0
0
2
0
0
2
0
0
0
0
3
2
2
0
2
0
0
2
0
0
1
0
1
0
2
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
1
1
0
0
0
0
0
3
1
0
1
1
0
2
2
0
0
0
1
1
1
4
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
1
1
2
2
0
0
0
0
2
0
2
1
1
1
0
0
0
0
0
1
0
0
1
0
1
2
1
1
0
0
1
0
2
0
0
2
0
2
0
0
0
0
0
0
1
2
1
0
1
0
1
0
1
0
1
0
0
2
2
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
2
0
0
2
1
0
2
0
0
0
2
0
0
0
2
2
0
1
1
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
2
1
2
0
1
2
0
0
0
0
0
1
0
0
3
0
0
1
0
1
2
0
0
0
1
0
0
0
0
1
1
0
2
0
0
0
0
1
0
0
0
0
3
3
0
3
0
0
0
0
0
1
2
0
0
1
0
0
0
0
2
1
1
0
0
2
0
0
0
0
0
0
3
0
0
0
1
0
2
0
1
0
2
0
1
0
0
1
0
0
2
2
1
2
1
0
0
0
0
2
0
1
3
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
1
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
1
0
0
2
1
0
0
2
0
0
1
0
2
1
0
0
2
2
0
0
1
2
1
0
2
1
0
1
0
2
0
0
0
1
0
0
0
0
1
0
1
1
0
0
1
1
1
0
1
0
0
0
0
0
1
2
0
2
1
0
0
1
4
0
0
0
2
2
0
0
0
1
0
0
1
2
2
0
3
1
0
0
0
4
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
3
0
1
0
0
2
2
0
2
1
1
0
0
0
0
0
0
2
0
0
0
0
0
2
12
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
2
1
1
1
0
0
1
0
0
2
0
2
0
0
2
0
2
0
2
0
0
0
0
2
0
1
0
0
0
1
1
0
0
0
0
0
2
1
2
1
0
0
0
0
2
2
1
2
3
0
1
0
1
3
2
0
2
1
0
0
0
0
2
2
0
0
1
2
0
0
2
0
1
0
1
0
2
1
2
0
1
3
0
0
1
0
2
1
0
0
0
0
5
0
0
2
0
0
1
0
0
2
0
0
0
2
2
0
0
0
3
2
1
0
0
2
0
2
2
0
2
0
2
0
0
0
0
1
1
1
0
0
1
1
0
1
0
1
1
0
0
0
2
2
0
0
0
1
1
0
0
0
0
2
0
1
1
0
0
0
2
2
2
0
0
2
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
1
2
0
1
0
2
0
0
1
1
2
1
2
1
1
2
1
0
1
0
0
0
0
0
0
3
0
0
1
0
1
0
0
1
0
0
1
0
0
0
1
1
1
1
0
0
0
2
0
0
1
2
0
0
0
2
0
0
0
0
0
0
1
2
0
2
0
0
0
0
2
0
0
2
0
1
0
1
2
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
1
2
2
3
0
0
0
0
0
0
2
0
0
0
1
1
2
1
0
1
0
0
0
3
0
0
2
0
1
2
0
1
0
0
0
1
2
0
2
0
1
0
1
0
0
3
0
0
1
0
1
0
0
0
1
2
2
2
0
0
1
1
1
2
2
0
1
1
0
1
1
1
0
0
0
2
1
0
0
0
2
2
0
0
1
0
0
1
1
1
0
0
0
0
1
2
2
0
3
0
1
0
0
2
1
0
0
0
1
0
0
1
0
0
0
0
1
1
0
1
2
0
0
0
0
0
1
0
0
0
0
3
0
0
3
0
1
2
0
0
2
0
1
1
0
0
0
0
2
2
0
2
0
0
0
0
0
2
2
0
1
1
2
0
0
3
0
0
0
2
0
2
1
0
0
2
1
2
1
0
0
0
0
0
0
0
3
0
0
1
0
0
1
0
1
1
0
0
0
1
0
1
2
0
2
2
0
3
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
2
1
0
0
0
2
0
0
1
0
0
0
1
0
0
0
1
0
0
2
0
1
0
0
1
0
1
2
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
1
0
3
2
0
0
0
0
1
2
2
1
0
0
2
0
0
0
0
0
0
2
0
1
0
5
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
2
2
0
0
1
0
0
0
2
0
0
0
0
0
2
3
1
0
0
0
1
2
0
0
0
0
0
0
2
0
1
0
0
0
1
0
2
3
0
2
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
2
0
1
1
1
0
1
0
0
1
2
0
4
0
0
0
0
0
1
0
0
2
0
1
0
0
2
2
0
0
1
0
4
0
0
1
1
0
0
1
0
1
0
1
1
0
0
2
1
2
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
2
2
0
0
0
0
0
0
2
0
2
0
0
0
4
2
0
0
0
3
0
0
0
0
2
1
2
0
2
1
2
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
1
1
0
2
1
0
0
1
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
1
2
0
1
0
0
1
1
0
2
0
4
1
0
2
2
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
1
1
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
3
2
1
1
0
0
2
0
1
0
0
1
1
0
0
3
0
1
0
0
0
1
0
0
0
1
0
1
4
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
1
0
2
0
2
0
0
0
0
1
0
2
2
0
0
1
0
2
1
0
4
0
1
0
0
0
0
0
0
0
0
0
2
0
1
2
0
1
1
0
0
0
0
0
2
0
2
2
0
3
0
2
0
0
0
2
0
0
1
1
0
0
1
0
1
2
2
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
1
0
0
2
0
3
0
2
0
2
0
0
1
0
0
2
1
0
4
0
0
1
1
0
1
0
0
1
0
0
0
0
0
1
2
0
0
1
0
0
2
2
0
0
2
0
0
1
0
2
0
0
2
0
2
0
3
2
0
0
0
0
0
0
3
2
1
0
1
1
0
0
2
0
2
2
0
0
0
0
1
2
0
1
1
2
2
1
2
0
2
0
0
0
1
0
2
0
0
1
0
0
0
2
3
2
0
2
1
1
0
2
1
0
0
0
2
0
0
0
0
0
2
1
0
1
2
0
0
0
2
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
2
1
0
0
0
1
0
1
0
0
0
0
0
0
2
2
0
2
0
1
0
2
2
1
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
2
1
0
0
0
0
2
1
0
0
0
2
1
0
2
0
0
0
0
1
1
3
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
2
2
2
0
1
0
1
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
3
1
1
0
0
1
0
2
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
1
0
1
0
0
1
2
0
0
1
1
1
0
1
0
1
0
1
1
0
0
3
0
0
1
0
0
1
1
0
1
1
2
0
0
2
0
0
0
0
0
0
1
0
1
0
1
0
2
0
0
0
0
1
0
2
0
0
1
1
0
0
0
2
3
0
0
0
2
0
0
2
0
0
2
2
0
0
0
1
0
0
1
0
0
0
0
1
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
3
3
0
0
0
0
0
1
0
0
1
0
0
5
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
2
0
2
0
0
0
2
0
0
1
2
1
1
0
2
0
2
1
0
2
0
2
2
3
1
0
0
0
0
1
0
0
0
0
4
0
0
0
0
2
1
0
0
2
0
0
0
0
2
0
2
1
2
0
4
0
0
0
1
0
2
0
0
0
1
0
2
0
0
0
0
1
0
0
1
0
0
0
1
2
0
0
0
2
2
0
0
1
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
2
0
1
0
0
1
2
0
0
0
1
0
0
2
0
2
0
2
1
0
0
0
4
0
0
2
2
2
0
1
1
0
1
0
0
0
2
0
0
0
1
1
0
1
0
1
3
0
0
1
0
0
0
2
0
1
0
2
0
3
1
0
0
0
0
0
1
3
0
1
0
0
0
1
0
0
2
0
0
1
2
0
0
0
0
5
0
0
2
2
0
2
0
2
0
0
1
0
2
2
3
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
2
0
0
1
1
0
0
0
2
0
0
0
0
0
4
0
0
1
1
0
1
0
0
0
2
0
0
1
0
0
0
0
1
1
1
1
0
1
0
2
0
2
2
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
2
0
0
1
0
1
0
0
0
0
2
1
1
0
0
0
1
0
0
1
0
1
0
2
1
0
0
0
2
0
0
0
0
2
1
2
2
0
0
0
0
1
0
1
2
0
1
1
0
0
2
0
0
0
2
2
0
0
0
0
3
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
3
2
0
2
5
0
0
0
0
0
2
2
0
0
0
0
0
0
0
4
2
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
1
1
2
0
1
0
0
0
1
0
1
0
1
0
0
1
1
0
0
1
2
1
0
0
0
2
0
0
1
0
0
0
0
1
0
2
0
0
2
0
0
0
1
0
1
3
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
2
0
3
0
1
1
2
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
1
0
0
2
0
1
0
0
0
0
2
0
0
2
2
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
1
2
1
0
0
2
1
2
0
0
2
0
2
0
1
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
4
5
0
2
0
0
2
1
1
2
1
1
1
0
1
0
0
1
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
1
0
0
0
1
0
2
0
2
0
1
2
2
0
0
0
0
0
1
0
1
0
0
2
0
0
1
0
0
0
0
0
0
1
1
0
1
1
1
0
1
1
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
1
0
0
2
2
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
1
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
1
0
0
0
2
0
0
0
0
2
0
0
2
1
1
0
1
1
2
0
0
2
0
1
0
1
2
0
1
0
2
0
1
2
0
0
1
0
0
1
0
4
0
3
0
0
0
0
0
0
0
1
2
1
0
0
3
0
0
2
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
2
0
0
0
0
0
2
0
2
0
2
2
0
0
0
1
0
1
0
0
0
3
0
0
2
2
2
1
0
1
0
0
0
0
2
2
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
2
1
2
1
1
0
0
0
1
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
1
0
1
2
0
1
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
2
0
0
2
0
0
0
1
0
2
0
0
0
2
0
2
1
0
2
2
0
0
0
0
0
3
2
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
1
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
2
2
2
0
1
0
0
1
0
2
0
0
0
0
0
0
1
1
0
0
0
0
2
1
1
3
2
2
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
3
0
2
1
0
2
0
1
0
0
1
1
2
0
2
3
0
2
3
1
1
0
2
0
2
2
0
2
0
2
0
0
0
0
0
2
0
2
0
0
0
2
1
0
0
0
0
0
7
0
3
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
1
2
2
0
0
1
0
0
2
0
0
0
1
0
1
0
1
2
2
0
0
0
0
0
0
2
0
2
1
1
2
1
0
2
0
2
1
0
1
1
1
1
0
0
0
2
0
1
0
0
1
0
0
0
0
0
2
2
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
2
0
3
1
2
1
0
2
2
0
0
1
0
1
0
0
1
0
0
2
1
2
1
1
0
2
0
2
0
0
0
0
1
0
0
1
2
0
0
0
3
1
0
0
0
0
2
2
0
1
2
0
0
1
0
0
0
0
0
0
0
2
0
1
1
2
1
2
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
1
0
1
2
0
0
0
2
2
0
0
0
3
0
1
1
0
2
2
2
0
1
2
0
0
0
0
0
0
1
0
1
2
0
2
0
2
0
0
0
0
0
0
0
3
2
2
2
0
2
0
1
0
0
2
0
0
0
1
2
0
0
0
2
0
0
0
1
0
2
0
2
0
0
1
1
1
1
3
0
1
1
0
0
0
2
0
1
0
0
0
0
2
0
0
1
3
0
1
0
1
1
0
2
0
0
0
0
0
0
1
0
0
0
0
1
2
2
0
0
0
0
1
0
2
0
2
2
0
0
0
0
0
0
0
1
0
2
0
0
3
1
0
1
0
0
0
0
0
0
2
0
1
2
1
0
0
0
0
0
0
0
0
0
1
2
0
2
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
1
2
2
0
0
1
2
2
1
2
0
0
2
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
1
0
2
0
3
1
0
2
2
0
0
0
2
0
0
0
2
2
0
0
0
2
0
0
0
2
0
0
0
2
0
0
1
0
0
0
2
0
0
0
2
0
0
4
0
2
0
0
0
1
1
0
0
0
3
2
0
0
0
0
2
1
0
1
0
1
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
1
2
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
2
1
2
0
0
1
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
1
2
0
0
0
0
1
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
2
1
0
1
2
1
0
2
0
0
0
0
0
1
0
0
0
2
1
0
0
1
0
0
1
0
0
0
0
2
0
0
2
1
1
0
0
2
2
0
1
1
0
1
0
0
0
2
1
1
1
1
0
0
2
0
0
3
0
1
0
0
0
0
1
1
2
0
0
1
2
0
2
0
0
0
1
2
0
1
0
0
1
0
0
1
0
0
0
2
1
1
0
0
1
0
0
1
0
0
0
0
1
0
0
2
1
2
1
0
0
0
0
2
1
1
0
0
0
0
2
0
0
2
0
0
2
0
2
0
1
0
0
1
1
0
1
0
0
1
2
0
0
0
1
1
2
1
0
0
1
1
1
0
0
0
1
0
0
1
1
3
1
5
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
1
0
0
2
3
1
2
0
0
0
0
0
1
0
0
0
0
1
1
0
2
0
2
1
0
0
0
0
0
1
0
0
0
2
0
0
1
2
0
0
0
0
0
2
0
0
2
0
0
0
0
1
2
0
2
2
1
0
1
0
0
0
1
0
1
1
2
0
2
0
0
1
0
0
0
0
1
2
1
0
0
1
2
1
1
0
0
2
0
2
1
2
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
1
0
1
2
2
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
2
1
2
0
0
0
2
0
1
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
3
1
2
0
0
2
0
1
2
1
1
0
0
0
1
0
4
0
2
0
0
2
0
0
1
0
0
1
1
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
2
1
0
1
1
0
0
1
1
2
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
1
0
1
1
1
1
0
0
1
0
0
2
0
1
1
1
0
0
2
0
0
0
2
2
0
0
2
1
0
0
1
0
0
5
0
1
1
0
0
0
1
2
0
0
0
1
0
1
0
0
0
1
2
2
1
1
2
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
2
1
1
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
2
2
0
3
1
1
0
1
2
0
0
0
0
0
2
0
3
0
1
1
0
0
1
2
0
2
1
1
0
0
2
1
1
0
0
1
0
2
0
1
0
0
1
1
2
0
0
2
2
2
0
2
0
0
1
2
1
1
1
4
1
0
0
0
0
0
1
1
1
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
2
2
1
1
1
1
2
0
2
1
1
0
0
0
2
0
0
0
0
0
0
0
1
2
1
0
0
2
0
0
0
1
0
0
0
0
2
1
0
1
0
0
0
0
1
0
2
1
1
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
2
0
1
1
2
1
0
0
0
2
1
0
2
0
0
2
0
0
2
0
0
0
1
0
1
0
0
2
1
0
0
1
2
0
0
0
0
0
1
2
4
0
2
0
1
0
0
0
0
3
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
3
2
0
1
0
0
2
0
2
0
0
2
0
0
2
0
0
1
0
3
2
0
0
2
1
1
1
0
0
1
0
4
0
0
0
0
0
1
1
0
0
0
2
1
5
2
0
0
0
0
3
0
1
0
0
1
2
0
1
0
0
0
1
2
0
3
2
2
0
1
1
0
0
1
0
0
0
0
1
0
0
0
2
0
1
2
0
0
0
1
1
1
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
2
0
1
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
2
0
0
1
0
1
0
1
1
0
0
2
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
4
1
0
1
2
2
1
1
0
2
2
0
0
3
1
0
1
1
2
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
6
0
0
0
0
1
1
2
0
1
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
1
1
1
2
2
0
0
0
2
1
0
2
0
2
2
2
0
0
1
2
1
2
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
1
0
0
2
0
1
2
0
0
1
0
1
1
0
2
2
0
0
0
0
2
0
0
0
1
2
0
0
0
0
2
0
0
0
1
1
0
0
2
1
1
0
0
2
0
1
2
0
2
0
2
1
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
2
0
0
0
0
2
1
0
0
2
0
0
0
0
0
2
2
1
0
0
0
1
0
0
0
0
0
0
3
0
0
1
0
1
1
2
0
0
0
0
0
2
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
1
1
0
0
0
2
0
0
0
1
1
0
0
0
1
0
0
0
0
2
0
0
1
2
0
0
0
0
1
1
0
0
0
0
0
0
2
1
0
1
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
1
1
1
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
1
0
0
0
2
0
3
2
0
0
2
1
0
1
0
0
0
1
0
0
1
6
0
0
1
0
2
1
0
1
0
0
0
1
1
0
1
0
1
1
0
0
0
0
0
0
1
1
0
1
0
2
0
0
0
0
2
0
0
0
1
0
1
1
2
2
2
0
4
0
3
2
2
0
1
0
2
3
0
0
3
0
0
0
0
0
0
2
1
0
1
3
1
1
0
0
1
0
0
2
0
0
2
0
2
1
2
2
2
1
1
0
0
0
1
2
3
0
2
0
0
0
2
0
0
2
2
0
0
0
1
0
0
1
0
0
1
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
1
1
0
0
0
1
2
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
2
2
3
1
0
0
1
0
1
1
1
1
2
0
0
0
2
2
1
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
1
0
2
2
0
2
2
0
1
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
1
1
1
0
2
2
0
0
0
0
0
0
2
0
1
3
0
2
0
0
0
0
0
1
0
1
0
0
0
0
2
1
2
2
0
2
0
0
0
0
1
0
2
0
1
1
2
0
2
0
0
3
1
0
1
0
1
2
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
2
0
0
0
1
0
1
2
0
0
0
1
1
0
0
2
0
0
0
0
0
0
2
1
1
0
0
3
0
0
2
0
0
0
0
1
1
0
0
3
0
0
0
0
2
1
0
0
1
0
0
2
0
0
0
0
1
1
1
0
0
0
2
0
2
0
1
0
0
0
1
0
0
0
0
0
1
1
1
2
0
0
0
0
2
0
1
0
1
0
1
0
0
0
0
0
0
1
1
2
0
0
0
2
0
1
0
0
0
1
1
0
1
0
1
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
3
1
2
0
0
0
0
2
2
1
2
0
3
2
0
2
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
1
0
0
0
1
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
2
0
0
0
2
1
2
0
0
0
1
0
2
2
0
2
0
0
2
1
0
0
1
1
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
1
0
2
2
1
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
1
1
0
2
3
0
0
0
0
0
1
0
0
0
1
1
7
0
0
2
1
0
0
0
0
0
1
2
2
1
0
0
0
0
0
1
1
1
0
0
0
0
1
2
1
1
0
0
0
0
2
2
2
0
0
0
1
0
0
0
0
1
3
0
1
1
3
1
0
0
1
1
0
1
0
2
1
0
0
2
2
0
1
1
1
0
0
2
2
2
0
2
0
2
1
0
1
1
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
1
0
2
1
1
1
0
0
2
0
1
0
1
1
0
0
0
0
2
0
1
2
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
1
2
0
5
5
1
2
1
0
0
0
0
1
0
0
1
0
1
0
0
1
2
0
2
2
1
0
0
0
2
1
0
0
0
2
2
2
0
0
1
0
0
1
1
0
0
1
0
1
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
4
0
0
2
3
0
0
2
0
0
0
0
3
2
2
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
1
0
0
0
2
0
1
1
3
0
0
1
0
0
2
0
0
0
2
0
1
0
0
2
2
0
0
1
1
0
2
2
0
0
0
0
1
0
1
0
2
1
2
0
0
0
2
0
1
1
0
0
2
2
1
2
0
1
0
1
0
1
1
2
0
0
0
0
0
0
0
0
0
0
1
2
0
2
1
0
0
1
2
2
0
1
0
0
0
0
1
0
0
1
1
1
0
0
0
0
2
2
2
0
0
0
0
0
1
2
0
0
0
0
2
0
0
1
0
2
2
1
1
0
0
0
1
0
0
0
0
0
1
2
2
0
0
2
3
0
1
1
0
5
2
1
1
2
0
2
1
2
0
1
2
0
1
0
0
0
2
3
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
2
2
0
1
0
0
0
0
0
1
1
3
1
2
0
0
0
2
1
0
0
0
0
0
0
0
3
0
0
1
0
1
2
0
2
0
0
0
2
2
0
2
0
0
2
0
0
1
2
2
0
2
0
0
0
2
1
0
2
0
0
0
1
1
2
2
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
2
1
2
0
4
2
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
2
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
1
2
0
0
3
1
1
1
0
2
2
1
0
1
0
2
0
0
0
1
2
7
1
0
0
0
0
1
0
0
0
1
0
2
2
0
0
0
0
3
0
1
0
2
0
2
2
0
0
0
0
0
0
1
0
0
1
0
2
1
1
0
0
0
2
0
0
1
0
1
1
0
0
1
1
2
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
1
0
0
1
0
1
1
0
1
0
0
2
0
0
1
2
0
0
0
0
0
0
2
1
2
0
0
1
1
0
0
0
0
3
1
2
0
0
0
0
1
1
4
2
0
0
1
0
0
0
2
0
1
2
0
0
0
0
0
2
1
1
0
0
2
1
1
0
2
0
0
0
1
0
2
0
0
1
2
0
1
0
0
2
0
2
2
1
0
0
2
2
0
2
2
2
2
0
0
0
0
0
0
0
1
1
0
2
0
0
2
1
1
0
0
0
2
1
0
0
0
0
0
0
1
1
0
0
0
1
1
0
1
0
0
1
2
4
1
0
0
0
0
0
1
2
2
0
0
0
0
0
2
1
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
2
3
2
2
4
1
0
0
1
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
2
2
1
0
0
0
1
2
0
2
1
0
2
1
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
4
2
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
2
1
1
0
2
2
0
1
0
0
2
0
0
2
0
1
0
0
0
1
1
0
2
2
0
2
2
0
0
0
0
1
0
1
0
2
0
1
0
0
2
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
1
0
0
0
2
0
1
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
1
0
2
0
0
1
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
2
1
2
3
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
2
1
2
0
0
0
0
0
1
0
0
2
0
2
0
2
2
0
0
1
0
1
0
0
0
1
3
0
2
0
0
1
2
0
0
0
2
0
0
0
1
0
3
0
0
1
2
0
1
2
0
0
0
1
0
0
1
0
0
2
2
1
0
0
0
2
2
2
0
1
0
1
0
0
0
2
0
0
0
0
2
0
1
2
0
1
0
0
2
1
2
0
0
1
0
0
0
4
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
2
0
1
0
7
0
3
0
1
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
2
0
1
2
0
1
1
0
1
0
0
2
0
0
0
0
2
0
0
2
0
0
0
1
1
2
1
0
0
0
0
0
1
1
2
0
3
0
0
0
1
0
0
0
1
2
0
1
0
2
1
0
0
0
1
0
0
0
2
0
2
1
0
0
0
2
1
1
1
0
0
0
0
0
2
0
2
1
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
2
0
2
0
2
2
2
1
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
1
1
1
1
0
1
0
0
0
0
0
0
2
0
3
1
1
0
2
1
3
2
0
1
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
1
0
0
2
1
1
0
0
2
0
3
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
2
1
2
0
0
1
2
0
1
2
0
2
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
1
0
0
1
0
0
2
0
1
2
0
0
0
0
1
0
2
0
0
2
2
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
1
0
0
1
0
2
2
0
4
0
0
0
0
1
0
2
0
0
2
1
0
4
0
2
0
0
1
0
1
0
1
1
0
0
0
0
1
1
0
1
1
2
2
0
0
0
1
0
0
0
2
0
0
0
0
0
2
2
2
0
0
2
0
0
1
0
0
2
2
1
0
1
0
1
2
0
1
2
1
0
1
0
1
0
1
2
0
1
1
1
0
0
0
0
0
2
0
0
0
2
1
0
1
0
0
0
0
0
0
3
0
0
0
0
0
1
2
0
0
1
1
0
1
2
0
1
1
2
1
2
0
0
0
0
0
0
1
0
1
1
0
0
2
0
0
0
2
0
1
0
2
0
0
0
2
0
1
0
0
0
0
0
1
2
3
1
0
0
0
0
1
1
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
3
0
1
0
0
0
2
1
4
0
2
1
2
2
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
2
2
0
2
1
1
2
0
0
0
1
2
0
2
2
5
3
5
2
2
1
0
0
2
0
2
3
1
2
1
0
0
0
0
1
0
2
0
1
0
0
0
2
0
0
0
0
3
2
0
0
2
0
0
0
1
0
0
0
2
1
0
0
0
1
0
1
0
2
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
3
1
1
2
0
0
0
0
0
1
0
0
0
3
2
0
0
0
0
0
0
2
1
0
0
2
0
0
0
1
0
0
2
2
1
1
0
0
0
2
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
1
1
0
0
3
1
0
2
2
0
0
2
2
0
1
1
0
0
0
0
0
0
0
1
2
1
0
0
0
0
1
2
0
0
0
0
0
3
0
1
0
0
0
0
1
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
2
0
0
1
0
1
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
2
0
0
2
1
2
1
0
1
1
2
3
0
0
2
1
2
0
1
2
0
1
1
0
0
0
0
0
0
0
2
0
1
1
2
1
2
0
2
2
1
0
0
0
2
0
0
0
0
1
0
0
2
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
1
0
1
0
0
0
1
0
0
0
0
2
1
0
2
1
2
2
0
0
1
0
1
0
0
0
0
2
1
2
0
0
0
0
0
1
0
2
1
0
1
2
0
0
1
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
2
1
0
1
0
0
2
0
0
0
1
1
1
2
0
0
0
2
0
0
0
0
0
1
0
0
2
2
1
0
0
0
2
0
0
1
0
2
0
0
0
0
1
0
0
0
1
0
0
2
0
1
1
1
1
3
0
0
1
0
0
1
2
1
0
0
1
0
0
1
2
0
0
0
0
0
0
0
2
0
1
1
0
1
0
0
0
0
0
3
0
1
0
0
1
0
0
0
0
0
2
0
2
0
0
1
0
0
1
1
0
0
0
2
0
0
0
0
3
0
2
0
0
2
1
0
2
1
2
0
1
0
2
0
0
0
0
0
3
0
3
5
2
0
3
0
1
0
0
0
0
2
4
1
0
0
0
0
2
0
2
0
2
0
1
0
0
2
2
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
1
0
2
0
0
3
0
0
0
0
0
0
0
1
0
0
1
1
3
2
1
1
0
2
0
2
0
2
1
0
1
2
0
2
0
0
0
0
0
0
1
2
1
0
0
0
1
0
0
1
0
2
0
0
0
0
0
2
0
0
0
3
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
1
2
2
1
2
0
3
5
0
0
0
0
0
1
1
0
2
2
1
1
0
0
0
2
0
0
2
0
2
0
0
0
1
0
0
5
0
1
0
0
0
0
1
0
0
0
2
1
0
2
0
1
0
0
0
0
2
0
0
0
0
2
0
0
1
2
0
1
0
0
0
0
0
1
0
2
2
1
1
0
0
0
1
0
0
0
2
0
2
1
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
1
0
0
1
2
0
2
0
0
1
0
0
0
0
0
1
1
2
0
0
2
2
3
0
0
1
0
2
0
0
0
2
2
2
0
0
0
0
0
2
0
0
2
2
1
1
2
2
0
1
0
0
3
0
0
1
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
2
2
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
2
2
2
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
2
2
0
0
2
0
1
0
0
2
1
1
0
0
2
0
1
0
1
1
0
0
3
1
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
4
0
1
2
0
1
0
1
0
0
0
0
0
1
1
0
1
2
0
2
0
1
0
0
0
0
0
0
1
2
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
2
1
0
0
0
0
2
2
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
3
2
0
0
2
0
0
2
0
0
2
0
0
0
0
2
1
1
1
0
0
1
1
0
0
1
0
0
0
1
0
0
1
1
0
0
1
2
0
0
0
1
0
0
1
1
1
0
0
1
1
0
2
0
0
1
1
0
0
0
0
2
2
2
0
1
0
2
2
1
0
2
0
1
2
1
0
0
0
1
0
0
2
1
1
0
0
0
1
0
0
0
1
2
1
2
0
0
1
0
1
2
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
2
0
0
1
0
1
0
0
0
0
3
0
0
0
0
0
0
2
0
0
1
2
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
2
1
0
1
0
0
1
0
0
2
1
1
3
0
0
2
0
0
1
0
0
2
0
0
1
0
0
3
1
0
1
1
0
1
1
1
2
0
0
0
1
0
0
0
2
2
1
1
0
0
0
0
0
1
3
0
0
0
1
2
0
2
0
1
0
0
2
0
0
0
1
1
0
0
0
0
2
0
0
2
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
2
2
0
0
0
0
0
0
0
1
0
2
2
0
0
2
2
5
0
0
0
0
3
0
0
0
0
1
0
0
1
0
1
2
0
0
2
1
0
1
1
1
2
0
0
0
0
1
0
1
0
0
1
2
0
1
2
1
1
1
0
0
0
2
2
0
3
0
0
0
0
0
0
2
0
1
0
0
1
0
0
2
0
0
0
1
0
1
1
0
2
0
1
0
2
0
0
2
1
0
0
0
3
2
0
0
0
0
0
0
1
0
0
0
2
2
0
0
1
0
0
0
0
2
0
0
0
0
0
1
2
0
1
1
0
0
1
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
3
1
0
0
2
2
0
0
0
0
0
1
2
1
0
0
0
1
0
0
1
2
0
2
0
3
0
0
0
0
0
1
1
0
0
3
2
1
2
0
1
1
2
2
0
2
0
0
0
2
0
0
1
0
2
0
0
0
2
4
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
1
2
0
2
2
0
2
2
2
0
0
0
1
1
2
1
0
0
0
0
1
1
2
1
0
2
1
0
0
0
3
2
0
0
1
0
2
1
0
1
0
0
0
1
1
0
1
0
1
0
2
1
0
1
0
2
0
1
0
0
1
2
1
2
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
1
0
0
1
2
0
0
2
2
0
0
1
2
0
0
0
0
0
0
1
0
4
0
2
5
0
0
0
2
0
0
1
2
2
0
0
0
1
1
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
2
0
0
2
1
1
0
0
2
1
1
2
0
0
0
2
0
0
0
0
2
1
0
2
1
0
0
1
0
0
2
0
0
0
0
1
2
2
0
0
1
0
0
1
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
2
0
2
2
3
0
0
2
0
0
0
0
0
0
1
1
3
3
0
2
1
0
2
0
0
0
1
0
0
0
1
0
1
0
2
0
2
0
1
1
0
3
0
0
1
0
1
0
0
1
0
0
2
0
0
1
3
0
0
1
1
0
2
2
0
1
0
1
1
1
0
1
2
1
0
2
0
1
1
1
1
0
0
1
1
0
0
0
1
0
1
1
0
1
0
0
2
2
1
0
0
0
0
2
0
0
0
0
2
0
0
0
1
1
0
0
0
1
0
0
2
3
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
2
2
2
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
1
2
0
1
0
1
1
0
1
0
0
0
1
3
0
0
0
0
2
2
0
1
1
0
3
2
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
2
0
3
2
1
0
4
2
2
0
0
0
2
0
0
2
0
2
0
1
0
0
2
2
0
0
0
0
1
4
0
0
2
0
0
0
1
0
0
0
1
3
2
0
0
0
0
0
0
1
0
1
1
2
1
0
0
1
4
0
0
2
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
2
2
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
3
0
1
1
0
0
2
2
2
0
4
0
2
0
0
0
0
2
0
2
1
0
1
1
1
0
0
0
1
0
3
2
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
1
1
0
2
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
2
1
1
0
0
0
1
0
0
0
0
2
0
0
2
1
0
0
0
1
0
0
1
2
0
1
1
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
1
0
0
2
0
0
0
0
0
2
0
0
0
2
0
1
2
0
0
0
1
0
2
0
1
2
2
1
2
0
1
0
0
0
0
1
2
1
0
0
0
0
2
0
0
2
2
0
0
1
1
1
1
0
1
0
0
0
0
0
2
2
2
1
1
0
0
0
0
5
3
0
0
0
0
1
0
0
0
0
2
2
0
1
0
1
1
2
0
0
0
0
2
0
0
0
0
2
0
2
0
1
2
0
0
1
1
0
2
0
1
0
0
0
0
0
0
2
1
0
1
0
2
1
0
2
1
3
1
0
2
0
0
0
0
2
0
0
0
2
2
0
0
0
1
2
2
2
4
1
0
0
3
0
0
2
2
2
0
2
1
0
0
2
0
0
2
0
0
0
0
0
0
0
1
1
0
0
2
1
0
0
1
0
0
0
2
1
0
1
0
0
1
0
0
2
2
2
0
2
0
0
2
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
1
0
1
1
0
0
1
0
1
2
0
0
2
0
0
1
0
0
1
0
0
1
2
0
0
1
1
2
2
1
2
0
0
0
0
2
0
1
0
2
3
0
0
4
0
0
2
0
2
1
0
2
0
0
1
0
1
0
0
2
3
0
2
0
0
0
1
0
0
0
0
1
0
1
0
1
2
2
1
0
1
0
0
0
2
0
0
1
0
0
2
0
1
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
1
1
0
0
0
1
2
0
1
2
0
0
1
2
2
1
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
2
2
0
0
0
1
0
1
1
0
0
0
1
1
1
1
1
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
2
2
0
1
1
1
0
0
2
2
2
2
0
0
3
0
2
0
0
0
1
0
2
2
0
0
0
0
0
1
0
1
0
0
2
1
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
2
0
2
0
2
1
1
2
0
0
0
1
2
0
2
0
2
0
2
0
0
0
0
1
1
0
3
0
0
0
1
0
0
1
0
2
1
0
0
1
0
0
0
0
3
1
0
0
0
0
0
1
0
0
2
0
1
0
0
0
2
0
0
0
2
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
1
0
1
1
1
2
0
0
0
2
0
1
0
1
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
2
1
1
1
0
2
1
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
2
0
1
1
0
0
2
0
2
0
0
1
0
1
0
1
0
1
0
0
1
2
0
1
1
2
0
1
0
2
2
0
1
1
1
0
2
2
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
1
0
0
2
0
0
0
0
2
1
0
0
1
0
1
2
0
1
0
0
0
0
2
0
1
2
0
0
0
0
1
2
0
0
2
1
0
0
0
2
1
1
2
1
0
0
1
0
0
1
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
1
3
2
2
2
0
0
2
1
0
1
2
0
1
0
1
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
2
0
2
0
1
0
5
1
5
1
0
0
2
0
0
2
0
0
0
0
0
1
1
2
0
1
0
2
1
0
2
0
0
0
1
2
0
2
0
1
0
2
0
0
1
1
2
1
0
2
0
0
2
0
0
1
0
2
0
0
0
0
0
2
1
1
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
2
0
0
0
1
0
0
0
1
0
0
0
2
1
0
2
0
2
0
1
1
2
0
0
0
0
2
1
0
3
3
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
2
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
2
0
2
2
0
0
3
1
0
2
1
0
1
2
1
1
0
1
0
2
0
0
2
0
3
0
0
0
0
0
1
5
0
0
1
0
0
0
0
2
1
0
1
1
0
1
0
0
1
2
0
0
1
2
0
0
2
0
0
1
5
0
1
0
2
0
2
2
0
2
0
0
1
0
2
0
1
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
4
0
0
1
0
0
3
0
0
1
0
0
0
0
0
0
2
2
0
0
0
1
1
0
2
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
3
2
1
0
3
1
0
0
0
0
0
2
1
0
0
1
2
1
1
0
0
0
0
0
0
1
1
0
0
2
0
0
1
0
2
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
1
0
0
0
2
2
0
3
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
2
0
0
0
1
1
1
0
2
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
2
1
0
0
1
0
0
0
0
0
3
0
2
0
2
0
0
0
0
2
1
1
0
1
0
0
1
0
0
3
2
0
0
2
0
0
0
3
0
2
1
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
1
0
3
0
1
1
0
0
0
0
0
0
2
2
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
3
1
1
0
1
1
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
2
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
2
0
0
0
0
3
1
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
2
2
0
0
0
0
1
0
0
0
0
1
2
0
0
0
1
1
0
0
1
1
0
0
0
0
1
2
0
0
1
0
0
2
2
0
0
1
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
0
1
1
2
2
1
0
2
1
0
2
0
0
0
0
2
0
0
0
1
2
0
2
0
0
1
0
0
0
0
0
0
2
0
0
2
1
0
2
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
2
0
2
0
1
1
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
2
0
0
2
0
0
1
1
0
1
0
1
2
2
1
1
2
2
0
0
0
0
1
0
0
0
0
0
0
3
0
1
0
1
0
0
1
0
0
0
2
0
0
4
0
0
1
1
0
2
2
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
3
2
0
0
1
0
0
0
2
0
1
0
0
2
0
2
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
3
0
2
2
0
1
0
1
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
1
1
1
0
0
2
0
2
1
0
1
2
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
2
1
0
0
3
0
1
0
0
0
2
2
1
1
0
0
0
0
0
0
0
0
2
0
2
0
1
0
2
0
0
0
0
2
0
0
2
2
0
1
1
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
1
0
1
2
1
0
0
0
0
1
1
0
0
0
2
2
0
0
0
1
1
0
0
0
0
1
1
0
0
2
1
0
2
0
0
0
0
2
0
0
2
4
0
2
0
0
1
1
1
0
1
0
0
0
2
1
2
2
0
0
0
0
0
1
2
2
0
4
1
1
0
2
0
1
0
1
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
1
1
0
2
0
2
0
2
1
1
0
0
1
0
1
0
0
0
0
1
0
0
2
0
1
0
0
2
1
0
2
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
1
0
1
0
1
2
2
1
1
0
0
0
2
2
0
0
2
0
0
0
0
1
2
1
1
0
2
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
1
3
2
1
0
2
0
0
0
0
0
0
1
0
1
0
0
1
3
0
0
1
0
0
0
1
3
2
0
2
0
2
2
0
0
0
0
0
1
0
0
2
0
2
1
0
0
1
1
2
0
0
0
0
0
1
2
0
0
2
1
3
0
0
2
1
3
0
0
2
2
2
0
2
2
1
2
0
0
0
0
0
0
0
2
0
1
0
1
1
0
0
2
2
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
1
0
0
0
1
0
1
0
1
0
0
0
0
1
1
2
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
2
1
1
1
2
1
0
3
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
2
0
0
2
0
2
2
1
2
0
0
0
2
0
1
0
0
0
0
2
1
2
0
2
0
0
1
0
0
1
2
1
2
2
0
0
1
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
2
2
1
0
0
2
1
2
0
2
2
1
1
2
0
0
1
0
0
1
0
0
0
2
0
3
0
0
2
0
1
0
0
0
1
0
0
0
2
5
0
0
0
0
0
0
0
0
1
1
0
0
0
3
0
0
0
0
0
1
1
0
0
0
2
1
1
1
2
0
2
1
1
1
0
0
1
0
0
0
1
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
2
1
0
0
1
0
0
2
0
1
1
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
2
2
0
1
0
1
2
0
2
1
2
0
1
1
0
0
2
0
0
3
0
1
0
0
0
1
4
0
0
1
0
2
0
1
0
0
0
0
0
0
0
1
1
1
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
1
0
0
0
2
0
0
0
0
0
0
2
0
2
0
1
0
0
1
0
2
2
0
0
0
1
1
0
2
1
0
0
1
0
0
0
0
1
2
3
0
1
0
0
1
0
0
2
0
0
0
2
0
0
1
0
1
0
1
2
1
0
0
3
0
0
1
0
0
1
0
3
0
0
3
0
0
0
2
0
1
0
0
0
1
2
2
0
0
1
0
0
0
1
1
0
0
0
0
1
0
2
0
0
0
1
1
1
2
2
1
1
1
0
1
0
1
2
1
0
0
0
1
1
0
0
0
0
2
0
2
0
0
0
2
0
1
0
0
1
0
0
0
1
0
1
0
0
2
0
0
2
1
0
1
0
2
2
0
0
1
0
1
0
3
1
1
1
0
0
0
1
0
0
2
0
0
0
2
0
2
0
0
1
0
0
1
0
0
2
1
0
0
1
0
1
1
1
0
0
2
1
1
2
0
1
0
1
0
0
1
5
5
2
1
0
2
1
0
2
0
0
0
3
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
1
1
1
0
2
0
1
0
1
1
0
1
0
2
2
2
0
0
0
0
1
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
1
3
0
0
0
2
0
0
0
1
0
1
2
1
2
1
0
0
1
0
1
0
0
1
1
0
0
0
2
2
0
0
0
0
0
2
0
1
0
1
0
0
5
2
2
0
0
0
0
1
0
2
0
0
0
3
0
2
0
0
0
2
2
0
0
0
0
1
0
0
2
0
0
0
0
1
3
2
0
2
2
0
1
0
1
2
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
1
0
1
0
2
3
0
4
0
0
2
0
0
1
0
2
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
1
2
1
0
0
4
0
1
2
0
1
0
0
1
1
0
0
2
0
0
0
1
2
0
1
1
0
0
0
2
1
0
0
2
1
3
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
2
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
3
0
1
0
0
0
2
0
0
0
3
0
1
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
2
1
2
1
0
2
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
2
0
0
0
2
0
1
0
0
1
0
1
2
0
0
0
1
1
0
1
0
0
0
2
2
0
1
0
0
1
0
0
1
2
1
0
0
1
0
0
1
0
0
2
2
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
2
0
0
0
1
1
0
0
0
0
2
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
3
0
2
0
4
2
2
0
0
0
0
0
1
0
1
2
0
2
1
0
0
0
1
1
3
0
0
0
0
0
0
2
0
1
0
1
0
1
1
0
2
0
0
1
0
0
0
0
1
2
0
1
1
0
2
1
0
0
0
0
1
1
0
1
0
0
1
0
0
1
1
1
0
1
2
0
0
0
2
2
0
2
0
0
0
4
0
1
0
0
0
0
2
4
1
2
0
1
0
1
0
0
0
0
1
0
1
2
0
0
0
0
1
0
2
0
2
1
0
0
0
2
1
0
0
0
0
2
1
4
0
2
0
1
2
3
0
0
0
0
0
0
1
1
2
1
0
0
0
1
0
0
1
0
0
1
1
1
0
0
0
0
2
1
0
0
0
0
1
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
1
6
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
2
1
0
1
0
2
0
0
2
2
0
1
0
0
0
0
1
0
0
2
1
0
0
0
1
0
0
0
2
0
0
1
1
0
1
1
1
1
0
0
1
0
0
0
3
2
2
2
2
0
0
2
2
1
0
1
0
0
0
0
0
0
7
0
1
0
1
2
0
0
1
0
0
0
2
0
1
0
0
0
0
2
0
2
0
1
0
0
0
2
0
0
0
2
1
0
0
0
2
2
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
2
0
0
0
2
0
1
2
1
2
1
0
0
2
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
2
0
0
1
1
0
0
0
0
0
0
0
2
1
0
0
1
1
0
0
1
2
2
2
2
0
0
0
1
1
2
0
0
2
5
0
0
0
2
0
1
0
5
1
0
1
0
0
2
0
1
2
1
0
1
2
0
1
2
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
2
0
0
1
1
2
2
0
0
0
2
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
1
2
0
1
2
0
1
2
0
2
0
2
0
2
0
1
0
0
2
0
1
0
0
1
2
0
0
1
0
1
3
1
4
0
0
0
0
2
2
0
0
2
0
0
2
0
2
1
2
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
2
1
0
0
0
0
2
0
2
0
1
0
2
0
0
0
2
0
0
0
1
2
2
0
1
0
1
2
1
0
0
0
0
1
0
1
0
1
0
1
2
0
0
2
0
0
1
0
0
1
2
0
1
0
0
1
2
0
2
2
1
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
3
2
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
2
0
2
0
0
0
0
2
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
2
0
0
2
2
2
0
0
1
2
0
1
0
0
0
1
1
1
2
0
1
2
0
1
0
1
1
0
0
0
1
0
1
0
0
2
0
2
2
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
1
1
0
1
0
0
1
1
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
2
1
0
0
1
0
1
2
0
0
0
0
0
2
2
0
0
2
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
1
0
2
1
0
0
2
0
0
0
0
1
0
1
2
3
1
2
0
2
1
0
0
2
1
2
0
0
1
0
0
0
8
1
1
1
0
1
0
0
0
0
0
1
0
0
1
2
0
1
0
0
3
1
0
0
1
0
0
3
1
0
0
0
0
0
0
0
1
0
2
1
0
2
0
0
1
1
1
2
0
2
0
0
1
0
0
1
3
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
2
1
0
0
0
0
0
0
2
1
1
3
0
1
1
0
2
1
0
2
0
0
0
0
0
1
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
1
0
0
2
1
0
1
1
0
2
0
2
0
0
0
1
0
0
2
0
0
1
0
0
0
0
2
0
0
1
0
1
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
2
1
0
2
0
0
0
0
5
1
1
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
1
0
1
2
1
0
0
0
0
0
0
2
2
1
0
0
2
1
0
1
1
0
0
0
0
2
2
1
0
0
1
0
2
0
0
0
0
0
1
0
0
0
1
2
0
0
0
2
1
1
0
1
0
0
0
0
3
0
0
0
0
1
0
1
0
1
0
2
0
1
0
0
0
0
0
1
0
1
1
1
2
4
0
0
1
0
0
2
0
0
1
0
2
0
0
0
0
1
0
0
1
0
0
0
0
1
2
1
0
1
0
0
2
1
0
0
2
1
0
2
1
0
0
0
0
0
2
1
0
0
2
0
0
1
0
0
0
0
0
2
0
0
2
2
0
0
0
3
0
0
2
2
0
1
0
2
0
0
0
1
2
0
1
0
0
1
0
2
1
0
0
1
0
1
0
0
0
0
0
3
2
1
0
1
0
0
2
1
0
1
0
0
0
0
1
3
0
0
1
0
0
0
2
2
0
0
3
0
2
0
2
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
2
2
0
0
2
3
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
2
1
0
0
1
0
2
0
0
0
1
2
0
0
2
2
2
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
2
0
0
2
4
0
0
1
1
0
0
0
0
3
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
4
1
0
0
0
2
0
0
1
0
0
0
0
2
1
1
1
1
0
0
1
0
0
1
1
1
1
0
2
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
1
0
0
2
0
0
2
0
0
0
0
1
0
0
1
0
1
2
2
1
0
0
0
2
4
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
2
0
4
1
0
1
0
0
0
0
0
0
2
3
1
0
0
0
2
2
0
0
1
2
0
0
0
1
3
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
1
0
1
0
0
2
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
2
1
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
1
2
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
1
1
0
1
0
0
0
2
0
0
0
0
2
3
1
2
0
0
2
1
2
6
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
2
2
0
0
2
0
1
0
2
0
0
2
0
1
5
0
2
0
0
2
2
1
1
1
2
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
1
0
1
0
1
0
0
0
2
0
2
0
0
0
3
1
0
0
0
0
2
1
1
0
1
0
0
1
0
0
1
0
0
2
0
0
0
0
6
1
2
2
0
0
1
0
2
0
1
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
1
0
0
2
0
0
0
2
2
2
0
5
0
0
0
3
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
2
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
8
1
0
1
0
0
0
0
1
0
0
0
0
1
0
2
2
0
0
0
1
0
1
2
1
1
0
0
2
0
0
0
0
0
1
2
0
1
0
0
0
0
2
0
0
1
1
1
0
0
0
1
0
0
0
0
1
1
0
0
0
2
1
0
0
0
2
2
0
0
0
0
0
1
0
1
0
1
0
1
1
0
0
0
0
2
1
0
0
2
2
0
0
0
2
2
0
0
0
0
0
0
0
1
0
1
0
1
1
0
2
0
0
2
1
0
1
0
0
0
0
0
1
0
5
1
1
0
0
0
2
0
0
0
1
0
0
1
1
0
0
2
0
0
0
0
4
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
2
1
0
0
0
1
0
2
2
0
2
3
1
2
2
0
2
0
1
1
2
0
3
0
1
2
0
0
0
0
2
0
0
3
1
2
1
0
0
2
0
0
1
0
0
0
0
1
0
0
2
1
0
1
1
1
1
0
1
0
0
1
2
1
0
0
0
0
2
0
2
0
0
0
0
0
1
0
1
1
0
2
2
3
0
0
0
2
1
0
2
0
0
0
1
0
0
2
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
3
2
1
0
0
1
0
0
3
0
1
0
0
1
0
2
0
0
2
0
1
2
1
1
0
2
0
2
0
0
2
1
2
0
2
0
0
0
1
3
1
1
2
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
2
1
0
0
2
2
0
0
0
0
1
1
1
0
0
0
1
0
2
0
2
2
2
1
1
0
0
1
0
1
1
0
2
2
0
1
0
0
0
1
0
2
0
0
1
0
1
0
0
1
0
2
1
1
0
0
0
2
0
1
0
0
2
2
1
2
1
1
0
0
1
2
0
2
1
1
1
2
0
0
2
0
2
0
2
1
0
0
0
0
0
1
0
1
0
1
0
0
2
1
0
0
1
2
2
1
1
0
0
0
1
2
0
1
0
2
1
2
0
3
0
0
0
0
0
0
0
0
1
2
2
0
2
0
0
2
1
0
0
0
1
2
0
0
2
2
0
0
0
0
0
2
2
2
1
0
0
1
1
0
3
0
3
1
0
0
0
1
0
0
1
2
1
0
0
2
2
1
2
0
0
0
0
2
0
0
1
2
0
0
1
0
0
1
0
0
2
0
0
1
0
1
0
0
1
1
0
2
0
0
2
1
0
2
2
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
2
0
0
0
0
2
0
1
0
2
0
2
0
0
0
0
0
0
3
0
1
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
2
2
0
1
0
0
2
2
2
0
2
0
1
2
2
1
3
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
2
0
0
2
1
0
0
0
1
0
0
2
0
0
0
2
0
2
0
0
1
0
2
0
2
0
2
0
0
0
2
0
1
0
1
0
0
2
0
1
1
0
2
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
1
1
1
0
1
1
0
0
0
0
2
2
0
0
1
3
0
0
0
0
0
2
0
0
0
0
2
0
0
1
1
0
0
0
2
1
0
1
0
0
0
0
1
4
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
2
1
0
2
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
2
0
0
1
0
0
0
1
3
0
0
1
1
0
2
2
2
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
2
0
1
0
1
1
0
0
1
0
3
1
0
0
0
3
1
2
0
2
1
0
0
0
0
1
0
2
0
0
1
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
2
1
1
0
1
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
2
0
1
1
0
1
1
1
0
0
1
0
0
0
0
0
1
1
0
3
0
0
0
0
0
2
1
2
1
0
0
2
1
1
0
2
0
2
0
0
0
1
0
0
0
2
1
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
1
0
1
0
0
2
2
1
0
2
0
2
0
1
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
2
3
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
4
1
2
0
0
1
1
0
3
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
2
0
2
1
2
0
0
0
0
1
3
2
1
1
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
2
0
0
0
1
0
2
2
2
0
2
0
2
1
2
2
0
0
0
0
0
0
0
1
1
2
2
0
0
2
0
1
1
1
0
0
1
0
0
0
0
0
1
2
0
0
1
0
0
0
1
1
1
0
0
0
2
2
2
0
3
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
2
2
0
1
0
0
1
0
1
0
0
0
0
0
0
1
1
0
1
0
2
0
2
0
0
0
1
2
0
2
0
1
0
1
1
0
0
0
0
1
1
0
0
0
2
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
3
0
2
2
0
0
0
0
2
0
0
0
1
0
2
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
2
1
2
0
2
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
11
0
0
0
0
3
0
0
0
1
0
0
1
0
1
1
2
0
2
1
3
3
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
2
2
4
3
1
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
3
0
1
0
0
1
0
0
0
1
2
0
0
0
0
1
1
2
0
0
2
1
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
1
0
1
0
1
0
1
0
0
0
0
0
2
0
2
0
2
1
0
0
1
0
1
1
0
4
0
0
1
1
0
0
0
0
0
1
3
1
0
2
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
2
1
0
0
0
2
2
0
2
1
0
0
1
0
1
3
0
1
0
0
1
2
0
5
1
0
1
0
0
0
0
0
0
0
0
2
1
0
2
0
0
1
0
0
0
0
0
0
0
0
1
2
3
1
0
2
1
0
0
0
0
0
0
0
0
2
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
2
0
0
0
1
2
0
2
1
0
0
0
2
0
0
0
2
1
2
0
0
0
2
0
0
0
3
2
2
1
0
1
0
0
1
2
0
1
0
0
0
3
0
0
0
2
1
1
2
0
4
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
2
0
0
2
0
0
0
0
2
0
0
0
2
1
0
2
1
2
0
2
2
0
0
2
0
0
1
1
0
0
2
0
0
0
1
2
0
0
0
0
0
1
1
2
0
3
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
2
2
0
0
0
1
1
0
2
0
2
1
2
0
0
1
0
0
1
0
2
0
2
1
0
0
0
0
1
2
2
1
2
0
2
0
0
0
0
0
2
3
0
0
0
1
1
0
1
0
1
0
0
2
2
2
0
1
0
0
2
1
0
3
2
0
1
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
2
0
0
1
0
0
0
0
2
1
0
1
0
0
0
1
1
0
2
0
0
2
0
2
0
1
0
0
1
0
2
1
0
0
0
2
0
0
1
0
2
1
1
0
4
0
0
0
0
0
2
0
1
0
0
2
2
1
1
0
0
2
1
0
2
2
0
0
3
1
0
2
0
2
0
2
2
0
0
2
0
0
0
2
0
0
0
0
1
2
2
2
2
2
0
0
1
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
1
0
0
2
1
0
1
1
0
0
2
0
0
0
0
0
0
0
2
2
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
4
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
2
1
0
2
4
0
0
2
0
0
0
1
0
0
3
2
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
1
0
1
0
0
2
2
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
1
0
0
1
0
2
2
1
1
0
10
0
0
0
0
0
1
1
0
1
0
0
0
0
1
2
4
2
2
1
0
0
1
0
0
0
2
0
0
0
1
0
2
0
1
1
0
1
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
1
1
2
2
1
2
2
0
0
2
2
0
0
0
0
0
1
0
0
1
2
0
0
0
0
1
1
1
0
0
0
2
0
0
2
7
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
2
0
0
2
2
0
1
0
0
0
0
0
1
0
0
1
1
2
0
0
0
2
1
1
1
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
1
2
1
0
0
1
0
1
1
0
1
1
0
0
0
0
0
0
1
0
2
0
0
1
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
1
1
0
0
0
1
0
1
0
4
0
0
0
2
0
0
0
0
2
2
1
0
0
0
0
0
1
0
0
0
2
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
2
2
2
0
0
0
0
0
0
2
1
0
1
0
0
0
1
1
0
0
0
2
2
0
2
0
0
0
2
1
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
1
2
2
3
1
0
0
1
0
2
0
1
1
4
2
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
2
0
0
0
2
0
1
0
0
0
0
0
0
1
2
2
2
0
0
0
0
0
0
0
0
7
0
1
0
0
2
1
0
2
0
2
0
0
0
0
0
1
2
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
1
1
1
0
2
2
0
2
2
0
1
0
0
2
0
0
0
0
0
2
0
0
0
1
2
0
0
2
1
0
1
1
1
0
2
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
2
1
0
0
0
1
2
1
0
0
0
2
2
0
2
2
0
0
0
0
0
0
2
1
0
0
0
0
4
0
0
2
2
2
0
2
0
0
0
2
0
0
0
1
0
2
0
0
2
0
1
0
0
0
0
0
1
2
0
2
0
2
0
0
1
3
1
0
0
0
1
0
1
0
0
0
1
0
1
1
0
0
3
0
0
1
1
1
0
1
0
2
0
2
0
1
2
1
2
1
0
0
0
0
0
0
1
1
0
1
0
2
0
0
0
0
0
1
0
0
0
0
2
1
3
2
0
0
0
2
1
0
0
1
2
0
1
1
0
0
3
2
1
1
0
0
0
0
1
0
0
0
0
0
2
0
0
1
2
0
0
2
0
0
1
2
0
0
0
2
0
2
1
0
1
0
2
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
2
1
2
1
1
0
0
0
0
0
0
0
1
1
0
2
0
0
3
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
4
1
0
1
0
0
1
3
0
2
0
1
0
0
0
0
0
1
0
0
1
2
0
0
2
0
0
0
0
0
0
1
0
0
1
0
2
1
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
2
1
1
1
2
2
1
1
0
2
0
0
0
0
0
2
0
2
0
2
0
1
0
0
0
1
0
2
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
2
2
0
1
1
0
0
0
2
1
1
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
2
0
0
2
0
1
0
0
2
1
0
0
0
2
0
0
2
0
0
1
0
0
2
0
0
0
2
0
1
0
0
0
1
0
0
0
2
2
0
0
0
2
0
0
0
0
1
2
1
0
0
1
1
0
0
2
0
0
0
2
2
0
3
0
0
2
1
0
1
0
0
2
1
0
2
0
0
0
2
0
0
0
0
0
2
0
2
2
0
1
2
0
0
1
0
2
0
0
1
0
0
0
2
1
2
0
1
4
0
1
1
2
0
0
0
2
0
0
0
2
4
0
2
0
0
0
0
0
2
2
1
0
0
0
0
0
1
0
0
1
2
0
2
0
0
1
2
0
0
0
0
0
1
2
0
0
1
0
1
1
0
0
1
0
0
0
1
0
0
0
2
0
2
0
2
2
2
0
1
2
0
0
0
0
1
0
2
0
1
1
2
0
1
0
2
0
2
0
3
0
0
4
0
0
3
0
1
2
1
0
1
2
0
2
0
0
0
1
0
2
0
0
0
2
0
0
0
2
0
0
0
1
2
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
2
1
0
0
1
0
2
1
0
0
0
2
0
0
1
3
0
3
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
1
1
1
2
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
1
1
2
1
2
0
0
2
0
0
1
2
0
0
2
0
0
0
0
0
2
0
0
3
0
1
1
0
0
0
1
1
1
0
0
1
1
0
0
1
4
2
0
2
0
1
0
1
0
0
0
0
0
0
0
1
1
1
2
0
0
0
0
1
0
0
0
0
1
1
0
1
0
2
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
1
0
1
0
2
0
2
1
1
1
0
2
0
0
0
0
1
2
0
0
2
1
1
1
0
1
0
0
2
0
1
0
1
1
1
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
2
2
0
0
2
6
0
1
2
1
2
1
0
1
0
4
0
1
0
2
0
0
0
0
0
1
1
4
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
3
2
1
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
3
0
1
0
2
3
0
0
0
2
0
0
0
0
0
2
1
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
2
0
0
1
0
0
0
0
0
0
1
1
1
0
1
0
1
0
1
0
1
0
0
0
0
0
0
3
2
1
0
0
1
0
0
1
0
0
0
2
2
2
1
3
1
0
2
0
1
0
2
0
2
3
2
0
1
2
1
0
0
1
0
3
2
1
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
5
0
1
1
0
0
0
0
0
1
0
2
0
0
1
1
2
0
1
0
0
0
0
0
2
1
0
0
0
0
0
2
0
1
0
0
0
2
0
0
2
1
1
0
0
0
0
0
0
1
2
1
0
0
1
0
2
0
2
0
0
0
0
0
1
0
2
1
0
2
1
0
0
0
0
0
0
0
0
3
0
1
0
1
1
0
2
1
0
1
2
0
1
0
2
1
0
0
2
0
0
0
2
0
0
2
1
0
0
6
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
3
1
0
0
1
1
3
1
0
5
3
0
1
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
3
1
0
0
2
2
2
0
0
0
0
1
1
1
0
2
1
0
0
2
0
0
0
0
2
0
1
0
0
2
2
2
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
2
2
1
0
1
0
0
0
0
5
2
0
2
0
2
1
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
2
0
2
1
0
0
0
0
0
2
0
0
0
2
2
0
0
1
0
1
0
0
0
2
0
0
2
1
0
0
0
0
1
0
1
0
0
1
0
1
2
0
0
1
2
0
0
0
0
1
1
0
1
0
0
0
0
1
0
2
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
2
1
0
0
0
0
1
0
1
2
0
2
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
3
0
0
1
0
1
3
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
1
2
0
1
1
0
0
1
0
0
0
0
2
0
0
1
0
0
1
0
1
0
2
2
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
2
1
1
0
2
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
1
0
2
1
1
1
0
0
0
0
1
0
0
2
0
2
1
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
2
0
0
0
2
0
2
1
0
1
2
0
0
0
3
0
0
0
0
0
1
0
0
0
1
0
0
3
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
1
0
1
2
0
0
1
0
1
2
0
1
0
0
0
1
0
1
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
2
2
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
2
2
1
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
7
1
0
1
0
2
0
0
0
0
2
0
0
0
1
0
0
1
2
0
1
1
0
2
0
0
1
0
0
0
0
2
0
1
2
0
1
0
1
0
2
0
1
1
0
3
0
0
1
1
1
1
2
0
2
0
1
2
1
0
0
0
1
0
0
0
1
0
0
1
0
0
2
2
1
0
0
0
0
0
0
2
2
0
0
1
0
1
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
2
0
0
1
2
2
2
0
1
0
0
1
0
2
0
0
1
0
1
1
2
0
2
1
0
0
0
0
1
0
0
1
1
0
1
0
2
2
1
1
0
0
2
0
0
1
0
1
0
0
0
0
1
2
0
0
0
0
1
2
0
0
2
0
1
0
0
3
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
2
0
1
4
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
1
1
1
2
0
1
0
1
0
0
0
2
0
0
0
1
1
0
1
2
2
0
0
2
0
0
1
0
2
0
1
0
2
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
3
1
0
0
0
0
0
0
0
1
0
0
1
0
1
1
1
0
1
0
0
0
2
0
0
3
0
1
2
1
0
0
1
0
0
1
0
0
0
0
1
0
0
1
1
1
0
1
2
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
2
0
0
0
0
1
1
2
3
1
0
0
0
0
1
1
1
1
0
0
0
0
1
0
1
0
0
1
0
0
2
0
2
0
3
2
2
3
0
0
2
0
1
0
0
2
0
2
0
0
0
2
2
3
0
2
0
2
1
1
2
2
0
0
0
2
2
2
1
0
0
0
1
0
0
0
2
2
0
0
0
1
0
0
0
1
1
0
0
0
2
0
0
0
2
0
0
0
2
1
0
2
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
1
0
0
0
3
2
0
2
0
0
1
0
0
2
1
1
1
2
0
0
2
1
1
0
0
0
1
2
2
1
1
0
1
0
0
0
2
0
0
2
1
2
3
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
3
0
2
1
0
0
1
1
0
2
1
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
2
2
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
1
1
1
1
0
1
1
0
0
0
0
0
2
3
0
0
1
2
2
0
0
1
0
0
0
0
1
0
2
0
1
0
2
0
0
0
0
2
0
1
3
0
0
0
2
0
1
2
0
2
2
0
0
0
1
0
0
0
1
0
0
1
0
1
2
1
0
2
0
2
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
1
0
0
2
1
0
2
0
2
2
0
1
0
0
2
2
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
1
0
0
0
0
0
3
1
2
0
0
0
0
0
1
0
2
1
2
0
1
0
0
0
0
1
0
0
1
1
0
2
3
0
1
2
0
0
0
0
1
0
0
2
2
2
2
0
0
1
0
2
0
2
0
7
0
2
0
1
0
0
0
0
0
0
2
2
0
2
0
0
0
1
1
2
0
0
0
2
0
2
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
2
1
0
0
0
1
0
0
2
1
2
0
0
0
0
0
2
0
0
2
1
1
0
1
1
0
0
1
0
1
1
1
0
0
0
0
0
0
5
1
2
1
0
0
2
2
0
0
2
0
0
0
0
0
4
0
0
0
1
0
0
1
0
0
0
2
1
0
0
0
2
0
1
1
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
1
1
0
0
2
1
0
2
1
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
2
1
0
0
2
0
1
2
1
0
0
2
1
1
1
0
0
0
0
0
0
0
1
3
1
0
0
0
0
0
0
0
0
0
3
2
0
1
0
1
1
0
0
0
0
1
3
1
0
0
0
1
1
0
1
0
1
0
0
0
1
0
0
0
2
0
0
2
0
0
3
0
0
0
0
0
0
2
0
0
0
1
0
2
0
2
1
0
0
0
2
4
0
0
0
0
0
0
2
2
1
0
0
0
1
0
2
0
0
0
2
2
0
1
0
0
0
1
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
3
0
0
2
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
2
0
3
0
2
2
0
0
2
1
0
0
0
1
0
0
0
0
2
0
0
0
1
0
1
2
0
0
0
0
0
3
2
0
0
3
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
2
0
0
0
1
0
2
0
0
1
0
0
0
0
1
0
0
0
2
0
1
2
0
3
0
1
0
0
3
1
0
0
0
4
0
0
0
0
0
1
0
2
2
0
0
0
0
1
1
1
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
1
2
0
1
0
2
2
0
0
2
2
0
3
1
0
0
0
1
0
1
0
0
1
0
0
2
0
2
1
0
0
0
0
2
0
0
1
1
2
2
0
2
2
1
1
1
1
0
0
1
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
2
1
1
1
1
2
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
1
1
0
0
0
2
2
1
2
2
0
0
0
2
2
1
3
1
0
0
2
0
1
0
1
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
1
2
1
1
1
0
1
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
1
2
1
0
0
1
0
0
2
0
0
1
0
1
0
0
1
1
0
1
0
1
0
0
2
0
0
0
0
0
0
0
2
1
2
2
0
0
1
0
0
1
0
1
0
3
1
0
0
0
1
0
1
1
1
0
0
2
0
2
0
0
1
0
2
0
0
0
0
2
2
0
0
0
2
0
2
0
0
0
0
0
0
1
2
1
1
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
1
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
1
0
0
0
0
0
0
1
0
0
2
0
0
1
0
1
3
1
0
0
0
0
0
2
0
2
2
0
0
0
4
2
0
2
0
0
0
6
1
1
2
0
0
3
1
0
1
2
2
0
0
0
0
1
1
0
1
2
0
0
1
0
0
1
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
1
2
2
0
2
0
1
0
0
0
2
0
0
1
0
1
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
2
2
1
0
0
2
0
0
0
2
1
2
2
0
2
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
2
0
1
0
0
2
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
1
1
0
1
0
1
0
2
2
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
1
0
1
2
0
0
0
2
0
2
0
0
2
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
2
2
2
0
1
1
0
0
1
2
0
0
1
1
0
0
0
2
0
5
1
0
5
0
0
2
0
0
2
0
0
0
0
0
1
0
1
0
0
0
1
2
0
0
1
0
1
0
1
1
0
2
2
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
2
1
0
2
2
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
2
1
0
0
0
2
0
0
1
1
1
0
1
0
0
0
0
2
2
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
1
2
0
1
0
0
1
0
1
0
0
2
0
1
2
0
0
0
0
1
0
0
0
2
2
0
2
0
0
1
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
2
0
4
0
1
2
0
1
2
0
1
0
0
0
0
0
5
1
0
0
2
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
3
2
1
0
1
1
2
0
1
0
3
0
0
2
1
0
0
2
0
1
1
0
1
2
0
0
0
0
0
0
1
1
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
5
0
0
0
3
1
0
0
2
0
0
0
0
1
1
2
0
1
1
1
1
0
2
2
1
2
2
2
0
0
0
2
0
2
0
0
0
0
3
0
0
0
2
0
0
1
2
0
3
0
0
2
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
2
0
0
1
0
2
1
2
1
0
0
0
0
0
2
1
0
0
1
1
3
1
2
1
3
0
0
2
0
0
0
3
1
0
0
1
1
0
0
2
2
3
1
2
1
1
2
0
0
0
0
2
0
1
0
2
0
2
1
1
0
0
0
0
1
0
1
0
2
0
2
0
0
2
0
2
0
0
0
0
2
1
0
1
0
1
0
2
0
1
1
0
1
2
0
3
0
0
4
0
0
1
1
2
2
0
2
0
0
0
0
2
0
0
1
0
0
0
0
2
2
0
0
0
0
0
1
2
0
0
0
1
0
2
0
0
2
0
0
0
0
3
1
1
0
3
0
1
0
2
0
2
2
0
0
0
3
0
1
0
0
1
0
2
0
1
0
0
0
0
0
0
2
0
0
0
2
0
1
0
1
0
0
1
0
0
0
1
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
3
1
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
2
1
0
2
1
1
0
0
0
2
2
1
0
0
1
2
1
2
0
2
1
2
0
3
0
2
0
1
2
1
0
0
0
1
0
0
1
0
0
0
2
0
0
0
2
0
2
2
0
0
1
0
0
1
2
0
0
0
0
2
0
0
0
0
1
2
2
1
1
0
0
1
2
0
0
0
0
0
0
0
2
1
0
1
0
0
2
1
2
1
0
0
1
1
0
1
0
0
1
0
0
1
0
1
2
2
0
0
0
1
0
2
2
0
2
0
0
0
0
0
1
0
1
0
1
0
1
2
0
1
2
0
1
0
0
0
1
2
3
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
2
0
0
2
0
1
2
0
1
0
0
0
0
0
1
0
2
1
1
7
0
0
0
1
0
0
1
0
1
0
0
3
0
0
0
2
0
0
2
0
0
1
1
0
0
7
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
2
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
1
0
0
2
0
0
2
0
0
0
2
1
0
1
1
0
1
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
2
1
2
0
2
1
1
0
1
0
1
0
0
0
3
1
2
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
5
2
2
0
1
0
2
0
1
1
0
2
1
0
1
0
1
0
0
0
1
0
0
0
0
0
2
2
1
2
0
0
0
0
2
0
0
2
1
0
2
2
1
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
2
1
0
2
1
0
0
0
0
1
0
0
2
0
1
1
0
0
1
0
0
0
1
0
2
0
0
6
1
2
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
1
0
0
0
2
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
2
0
0
2
0
2
2
0
0
0
1
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
2
0
1
0
0
2
2
0
1
0
1
0
0
0
0
2
0
0
2
0
1
0
1
1
0
0
2
0
0
0
2
0
1
2
0
1
2
0
1
0
0
0
1
1
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
1
1
1
2
0
0
0
1
0
2
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
3
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
1
0
2
1
0
0
3
1
1
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
1
0
0
1
0
2
8
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
1
0
2
1
1
2
0
0
0
1
2
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
1
0
0
2
0
0
0
1
1
0
0
1
1
1
0
0
2
3
1
0
0
0
1
0
0
0
2
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
2
1
0
1
0
0
2
0
1
0
4
0
2
0
0
2
0
0
1
0
2
0
0
2
0
0
0
0
0
1
0
2
2
2
2
2
2
1
0
1
0
2
0
2
0
0
0
1
0
2
1
0
0
1
0
0
2
2
2
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
1
2
0
0
0
0
2
1
0
0
0
0
1
2
0
0
2
2
0
0
3
0
2
0
0
0
1
0
1
2
0
1
0
1
0
2
0
0
1
0
0
1
1
2
1
0
0
2
0
2
0
0
2
0
0
2
0
0
2
1
0
3
0
1
0
0
3
1
0
0
0
2
0
0
0
0
2
0
1
0
1
0
2
1
1
0
0
0
0
2
0
0
2
4
0
0
1
0
1
0
0
0
0
0
1
0
0
2
0
2
0
1
0
0
0
2
1
0
0
0
0
2
0
0
0
1
0
1
0
0
2
0
1
0
1
0
1
1
2
0
2
1
3
0
1
2
0
0
0
0
2
0
0
1
0
0
2
1
0
0
0
2
1
1
1
2
2
0
1
1
0
1
0
0
0
0
2
1
0
1
0
0
0
0
0
2
0
1
1
0
2
1
0
1
0
1
1
0
0
2
0
0
2
1
0
0
0
1
1
0
0
0
1
1
1
0
0
0
0
1
1
1
0
0
0
1
1
1
0
0
1
0
1
0
2
2
0
2
2
0
0
1
0
9
0
1
1
0
1
2
0
0
2
3
1
2
2
0
2
0
0
0
1
0
0
1
1
0
0
0
1
2
0
0
2
1
2
0
1
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
1
1
2
0
1
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
2
2
2
0
0
1
2
3
0
0
2
0
2
0
0
2
0
1
2
0
0
2
1
0
2
0
0
1
1
2
0
0
0
0
2
2
0
0
0
0
3
1
0
3
0
0
2
0
0
3
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
3
1
0
1
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
1
0
2
1
0
0
2
0
0
0
1
0
0
0
2
1
0
0
2
2
2
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
1
0
0
2
16
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
1
0
0
0
1
2
0
1
0
0
0
1
0
0
0
0
2
2
0
0
2
1
0
1
0
0
0
0
0
0
3
0
0
2
0
1
1
0
0
2
0
0
0
2
2
0
0
0
1
1
0
2
0
0
0
0
0
3
0
0
1
1
2
0
1
0
0
0
0
2
1
0
0
1
0
2
0
0
2
1
0
0
0
1
0
0
2
0
0
1
0
0
0
0
1
0
1
0
0
0
1
2
0
0
0
0
0
2
1
0
2
2
0
2
1
0
4
0
0
0
0
2
0
0
1
0
2
1
0
0
0
0
2
1
0
2
1
0
1
0
2
2
0
0
2
0
0
1
0
2
0
2
0
2
0
1
0
2
1
0
0
1
0
0
0
0
1
1
0
1
0
1
0
0
2
0
0
0
0
0
0
0
1
3
0
0
0
2
2
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
2
0
2
0
1
0
0
3
0
2
2
0
4
2
0
0
0
0
0
1
1
1
0
0
0
1
0
2
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
2
1
0
2
3
1
0
0
2
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
1
0
0
0
0
2
1
0
0
0
1
0
0
2
0
0
2
0
1
0
2
0
0
0
0
0
3
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
2
0
1
0
0
2
1
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
1
0
0
2
0
0
0
0
1
3
0
1
0
0
2
0
1
0
1
1
0
0
0
2
0
0
1
3
2
4
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
1
2
0
1
0
0
2
1
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
2
1
3
0
0
0
2
0
2
0
0
0
0
1
0
0
4
0
2
0
0
2
0
0
2
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
1
0
2
0
0
0
1
0
0
1
0
1
2
0
2
0
0
0
0
2
0
2
0
3
0
1
1
0
0
1
0
0
2
0
0
2
0
2
0
0
0
1
0
2
0
0
0
1
1
0
2
0
0
0
0
0
0
1
0
0
0
2
3
0
1
2
0
0
0
0
1
1
0
0
1
0
0
0
1
0
2
0
0
1
0
1
0
0
1
0
1
2
2
1
1
1
2
3
2
2
0
1
1
0
1
0
1
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
2
0
3
0
0
0
0
0
2
2
0
1
0
1
0
1
0
2
1
0
0
0
2
0
1
0
0
0
0
0
1
1
1
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
2
0
2
0
1
2
0
2
1
5
2
0
2
2
0
0
1
0
0
2
0
0
0
0
1
0
0
1
0
2
2
0
0
0
1
2
1
0
0
0
0
0
2
0
1
0
1
0
1
0
0
0
1
2
1
1
1
2
1
0
2
1
2
0
0
1
2
0
3
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
1
0
0
0
2
0
1
1
1
2
0
1
0
2
0
0
0
0
0
1
2
0
0
1
1
0
0
0
0
1
0
1
1
0
2
1
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
1
1
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
1
2
0
0
2
0
1
0
0
1
1
1
2
2
1
0
2
0
1
2
1
0
2
1
1
0
0
2
2
0
1
0
1
0
0
0
0
1
1
1
0
0
2
0
0
0
0
0
0
2
2
2
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
1
2
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
2
0
0
0
0
0
0
0
0
0
2
1
1
0
1
0
0
1
0
2
0
0
0
0
1
6
2
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
2
0
2
0
0
2
1
0
1
0
2
0
2
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
1
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
1
2
0
2
2
1
0
1
0
0
0
0
1
0
1
0
0
0
2
0
0
0
1
0
4
0
0
0
0
0
0
1
0
1
0
1
1
0
3
0
1
0
0
0
0
0
0
0
2
1
0
2
0
2
1
2
0
1
2
2
0
0
1
0
0
2
0
0
0
1
1
0
1
1
1
0
1
1
0
1
0
0
0
1
0
2
0
0
2
0
0
1
1
0
0
1
0
0
0
1
0
2
1
2
0
0
0
0
0
0
0
0
0
1
0
1
2
1
0
2
2
0
0
2
0
0
0
0
0
0
0
1
0
1
0
2
2
2
1
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
1
0
2
3
0
0
2
0
1
0
0
0
1
0
1
1
1
2
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
2
2
0
2
2
1
1
1
2
1
0
0
2
1
0
2
0
0
0
0
0
1
1
0
2
0
2
1
0
2
1
0
0
1
0
1
0
0
0
0
0
1
0
0
2
3
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
1
0
0
1
1
1
1
0
1
0
0
0
1
0
0
1
0
0
0
1
2
0
1
0
2
0
1
0
1
0
0
0
1
1
0
0
0
0
1
3
0
0
0
0
1
0
0
0
0
1
0
1
2
2
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
2
1
2
5
1
1
0
1
1
0
0
2
0
1
1
0
0
1
0
0
0
7
0
0
2
2
1
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
2
1
2
0
1
0
3
0
0
0
0
0
0
2
2
0
2
1
1
0
2
0
0
2
0
0
0
0
1
1
6
1
1
0
1
0
0
0
0
2
0
1
0
3
1
2
0
0
0
0
0
1
0
0
0
0
1
0
2
0
2
0
2
0
1
0
2
0
0
1
0
0
0
0
1
2
0
1
2
0
0
0
1
1
0
1
0
0
0
1
0
2
1
0
1
0
0
2
0
2
0
0
0
2
2
0
1
0
2
0
0
2
0
2
1
1
0
0
0
0
0
0
0
0
2
0
4
1
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
1
0
3
0
2
0
0
1
0
0
1
2
0
2
0
2
0
1
0
0
1
2
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
1
0
0
2
0
0
0
2
0
0
0
0
0
3
1
0
0
0
0
2
2
0
0
0
0
2
1
0
0
0
2
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
2
0
0
1
0
0
0
0
0
0
1
1
0
3
0
0
2
1
0
0
0
0
0
0
0
2
1
0
1
0
0
0
1
1
0
0
0
2
0
1
0
1
0
0
0
0
0
1
0
0
0
0
5
2
0
0
1
0
0
2
0
0
2
0
2
1
0
0
1
0
3
0
0
0
2
0
1
0
0
0
0
1
2
2
2
0
1
0
1
2
0
1
0
0
2
0
0
0
0
0
1
3
0
1
1
0
0
0
3
0
1
2
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
2
2
2
0
2
1
0
2
1
0
1
0
1
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
4
0
0
0
1
0
0
0
2
0
0
1
1
1
0
0
1
2
0
0
1
2
0
0
0
1
0
2
0
1
0
0
0
1
0
0
0
1
0
0
0
2
0
0
2
1
1
0
0
0
0
0
0
1
0
4
1
1
0
0
2
2
0
0
0
0
1
1
2
4
2
1
0
0
2
2
0
2
0
1
1
0
0
2
2
0
0
0
1
1
0
0
2
0
2
2
0
0
0
1
1
0
0
0
0
0
2
0
2
0
1
0
2
0
0
1
0
1
0
3
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
1
0
2
0
0
2
2
0
1
0
0
0
0
2
1
0
1
0
1
0
0
0
0
0
2
0
0
0
0
2
2
2
0
1
2
0
1
2
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
6
2
0
0
0
0
0
1
0
3
0
1
1
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
1
2
2
0
0
0
0
0
2
0
0
0
0
1
3
0
0
0
1
2
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
2
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
2
1
0
1
0
0
0
2
0
1
1
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
1
0
1
0
3
2
0
0
0
0
0
0
0
0
0
0
1
2
0
2
2
0
2
1
1
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
1
0
0
0
2
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
3
2
0
1
0
0
0
1
2
0
0
2
1
3
1
1
1
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
1
2
2
2
1
2
1
0
1
0
1
0
0
0
0
1
0
1
0
1
1
0
0
0
2
0
2
0
0
0
0
0
0
1
1
0
1
2
0
0
2
1
2
0
1
0
0
2
0
1
0
0
1
0
1
1
2
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
2
2
1
2
0
1
0
1
0
0
0
0
0
0
2
0
1
0
2
0
1
2
0
1
3
1
0
0
0
0
0
1
1
0
0
0
0
0
2
1
2
0
0
0
0
1
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
2
0
1
2
0
0
0
3
0
0
0
0
1
0
0
0
1
0
0
2
0
0
2
0
0
0
0
2
1
0
0
1
0
0
0
2
1
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
2
1
0
0
0
0
2
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
1
0
2
0
1
0
0
1
1
0
1
0
0
1
1
1
0
0
2
0
2
2
0
0
0
0
1
0
2
2
0
0
1
2
0
1
0
2
0
0
0
2
0
0
2
2
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
1
1
0
1
1
0
1
0
1
1
0
1
0
0
1
0
0
0
3
0
0
0
1
0
1
0
3
2
2
1
0
1
2
0
0
3
2
0
0
0
0
1
0
2
2
0
2
1
0
0
0
2
0
1
2
0
0
2
0
0
1
0
0
0
1
0
1
2
0
2
0
0
0
1
1
4
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
1
2
2
0
1
1
0
3
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
1
2
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
1
0
0
2
0
0
1
0
0
1
0
1
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
2
0
0
3
0
1
0
2
1
1
0
1
0
1
0
2
0
1
0
1
2
0
1
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
2
0
1
2
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
2
2
0
1
0
0
0
2
2
0
0
2
0
0
2
0
2
3
2
1
0
2
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
2
1
1
0
2
1
0
0
0
0
0
2
2
1
0
1
2
3
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
1
2
0
0
4
1
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
3
2
0
0
1
1
0
0
3
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
1
0
2
0
0
1
5
0
0
0
0
1
1
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
2
0
1
2
0
0
2
0
1
0
0
0
0
2
0
0
1
0
0
0
1
0
2
2
3
0
0
0
1
0
2
0
1
0
0
0
0
2
2
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
1
2
0
0
2
0
1
0
2
2
0
0
1
0
0
0
0
0
0
1
3
1
1
2
0
0
6
0
0
0
0
0
0
0
0
2
1
0
1
1
0
0
0
0
0
2
2
1
1
0
0
1
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
2
0
1
0
0
1
1
0
0
0
0
0
0
0
1
2
1
1
0
0
0
2
2
0
0
1
2
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
3
1
0
0
1
2
0
1
0
0
0
0
0
2
0
1
2
0
3
3
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
2
2
2
0
2
2
0
1
2
0
0
0
1
2
0
2
0
1
0
0
2
0
2
0
0
2
0
0
0
6
0
0
0
2
1
0
0
2
0
0
3
0
1
0
0
1
0
0
0
1
2
1
0
0
2
0
1
1
0
2
1
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
1
0
2
0
1
0
2
2
1
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
3
0
1
2
0
0
1
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
9
1
0
2
0
1
1
2
0
0
0
1
1
0
0
0
0
0
0
2
0
2
2
2
0
3
0
2
1
1
1
0
0
2
0
0
0
0
1
2
1
0
1
0
0
0
0
0
0
0
3
0
0
0
2
2
2
0
0
0
2
2
1
0
0
0
0
2
2
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
3
0
0
0
2
0
1
0
1
0
0
0
1
0
0
1
0
0
0
2
2
1
2
0
2
0
0
0
0
0
5
0
0
2
0
0
1
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
2
1
1
1
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
1
2
1
0
1
2
6
1
2
0
1
2
0
2
2
2
0
0
0
1
0
0
2
1
2
1
0
8
3
0
0
0
0
1
0
1
2
1
2
2
0
2
2
0
0
0
0
0
0
0
3
0
2
0
1
0
2
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
2
0
1
0
0
5
0
0
2
1
0
1
0
0
0
0
0
0
0
1
5
1
0
0
1
0
0
0
0
0
1
0
0
0
2
3
1
2
0
2
0
0
2
0
1
4
0
0
0
0
3
0
0
0
0
0
1
1
1
0
0
1
0
1
0
0
2
1
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
2
0
3
1
0
0
0
0
2
0
1
0
0
2
2
3
1
1
3
2
0
1
0
2
0
0
2
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
2
1
0
0
0
0
2
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
2
1
2
0
0
0
2
2
1
0
2
1
1
0
0
2
0
0
0
1
1
2
0
2
0
0
1
0
0
1
0
0
2
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
4
0
0
0
1
1
0
0
2
2
1
0
0
0
0
1
0
0
2
0
0
1
0
1
1
0
0
1
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
7
0
2
1
0
0
0
0
2
1
0
1
2
4
0
0
2
0
0
0
0
0
0
0
1
1
1
0
0
1
0
1
1
0
1
0
0
1
1
0
0
0
2
0
2
0
0
1
0
1
0
0
0
0
1
1
1
0
0
0
1
0
2
0
1
0
1
1
0
2
0
0
1
0
1
0
0
1
0
2
0
2
0
0
0
0
2
2
1
0
0
0
0
1
0
0
0
0
0
2
0
1
5
1
1
0
0
2
0
0
2
1
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
1
2
1
0
0
2
1
0
3
0
2
2
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
1
2
1
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
1
0
0
0
0
2
0
1
1
0
1
0
2
1
1
0
2
0
0
2
0
0
1
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
1
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
8
0
0
2
0
2
0
0
1
1
1
0
2
0
2
2
2
0
0
2
0
0
1
0
0
0
1
2
0
2
2
0
1
1
0
0
3
0
0
1
0
0
0
0
1
1
1
0
1
0
0
0
2
0
1
0
1
0
0
0
2
1
0
1
0
2
0
2
2
2
0
0
0
0
1
0
2
0
0
0
0
3
0
0
4
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
2
1
1
1
0
3
2
2
0
2
0
2
2
0
1
0
0
2
0
0
2
0
0
0
3
0
0
0
0
1
0
2
2
2
0
1
0
2
1
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
3
2
0
0
0
0
1
0
0
1
0
0
1
0
0
0
2
2
0
1
0
0
2
0
0
0
2
0
0
0
1
0
0
0
2
2
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
1
0
1
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
1
1
2
1
1
2
0
0
2
0
0
2
0
2
2
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
2
0
0
0
0
2
0
4
1
0
0
1
0
0
0
0
2
0
2
0
1
0
0
2
0
0
0
14
0
0
1
0
0
2
1
0
3
0
0
1
2
0
0
0
2
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
2
2
0
0
2
1
0
0
0
0
0
1
0
3
0
1
0
3
1
0
1
1
2
1
0
4
0
0
0
0
0
1
0
0
1
1
0
2
0
1
0
0
2
0
2
0
0
0
0
2
1
1
2
1
1
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
2
0
0
1
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
2
0
0
1
0
1
2
1
1
1
0
0
0
3
0
0
0
2
0
1
1
0
0
2
0
0
0
0
0
0
0
0
1
0
2
1
0
2
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
1
1
1
0
0
2
0
0
2
1
2
1
0
2
0
2
0
0
0
0
0
0
2
1
0
4
0
0
0
2
1
1
1
0
0
0
2
2
0
2
2
0
1
1
1
1
0
0
0
1
2
0
0
1
1
1
0
2
0
0
2
0
2
0
1
0
0
0
1
2
1
1
0
0
0
0
0
1
0
0
3
0
0
0
2
0
0
0
0
2
0
3
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
1
0
0
2
0
2
0
0
0
2
2
1
0
2
0
1
1
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
2
0
0
1
2
0
0
2
0
0
0
1
2
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
1
0
5
0
2
0
0
0
2
2
1
0
0
0
1
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
5
1
0
0
0
0
0
0
0
0
1
2
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
2
0
1
2
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
1
1
0
2
2
0
0
0
0
0
3
0
2
2
2
2
0
0
0
2
1
0
0
0
1
0
1
0
2
0
0
0
0
2
1
0
0
2
0
1
0
0
0
0
2
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
2
0
2
0
0
0
3
1
1
0
0
0
2
0
4
0
0
6
1
0
1
1
0
0
0
2
1
0
0
1
0
1
0
2
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
2
2
2
2
0
2
0
2
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
1
2
2
0
0
0
0
0
0
2
0
1
2
0
1
0
2
0
0
0
0
0
0
1
0
2
0
0
0
1
0
1
2
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
2
0
1
1
0
2
0
1
0
2
0
0
0
0
0
1
0
2
2
1
0
0
0
0
0
0
0
0
0
0
3
0
0
1
1
2
2
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
1
3
1
2
2
0
0
0
1
0
0
3
0
1
2
0
0
2
0
2
0
0
1
0
2
2
0
2
0
1
2
0
0
0
0
2
2
0
1
0
1
1
0
0
1
0
0
0
0
1
4
1
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
1
0
0
2
0
0
0
1
1
0
2
0
0
0
0
0
2
2
0
2
2
3
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
2
0
2
0
0
2
0
1
2
1
0
0
0
0
1
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
3
0
1
0
1
2
0
0
0
0
2
1
0
2
0
0
0
0
1
0
3
0
1
0
0
0
0
2
0
0
1
2
0
0
0
2
0
0
2
1
0
0
0
2
2
1
0
2
0
2
0
0
0
3
1
1
0
0
1
0
0
0
0
1
0
0
2
2
0
1
2
0
0
1
2
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
1
2
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
1
1
0
0
2
1
3
1
0
0
0
0
1
0
0
1
0
1
1
2
0
1
2
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
1
2
2
0
1
0
0
3
0
1
1
2
3
0
0
0
2
2
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
3
0
0
1
2
0
0
1
0
2
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
1
0
0
0
1
0
2
2
0
2
0
0
0
0
1
0
2
5
0
0
0
2
0
0
0
2
1
2
0
1
0
0
0
2
2
2
0
0
0
1
0
0
1
0
1
1
1
0
0
1
3
2
0
0
0
5
0
0
2
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
2
1
0
0
0
1
0
1
2
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
2
0
0
0
1
0
2
1
1
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
1
1
0
0
0
0
2
0
0
1
1
2
2
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
2
0
2
0
0
1
0
2
2
0
0
0
2
2
1
2
1
0
0
1
0
1
0
2
0
0
0
1
2
0
0
2
2
0
0
0
0
0
2
0
2
0
0
2
0
0
1
0
0
1
1
0
1
0
0
0
0
2
1
0
0
1
1
1
0
0
0
0
0
2
0
1
0
2
0
0
0
0
2
0
2
0
2
2
1
2
2
2
2
0
0
1
0
2
0
1
0
0
0
1
1
1
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
2
2
0
0
1
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
1
0
0
1
1
1
1
0
0
1
0
0
0
0
1
0
0
2
1
0
0
0
0
3
2
0
1
0
1
0
0
1
0
1
0
1
2
2
0
0
0
2
3
0
2
2
2
2
2
0
0
0
0
2
0
0
1
0
0
0
2
0
1
2
1
0
0
1
1
2
0
0
0
0
0
2
0
0
0
2
1
1
1
0
0
0
0
0
2
2
0
0
0
1
2
2
1
0
0
0
0
2
0
0
0
2
1
0
0
1
2
0
0
0
0
1
0
0
0
0
1
0
2
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
2
1
0
1
0
0
0
2
1
4
0
0
0
0
0
2
0
2
2
0
0
0
4
0
0
2
2
1
0
0
2
0
0
3
0
2
0
1
0
0
2
0
0
0
0
2
0
0
0
4
1
0
2
1
2
2
2
1
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
2
0
0
0
0
2
0
2
1
0
2
0
2
0
2
0
0
2
1
2
0
1
0
1
2
0
0
0
1
1
0
1
2
0
0
0
0
2
0
1
0
0
2
0
0
1
1
2
0
1
1
0
1
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
2
1
0
0
2
0
0
2
0
0
0
1
0
2
2
0
0
3
0
0
1
2
1
0
0
0
1
3
0
1
0
0
1
1
1
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
1
1
0
1
0
1
0
0
0
1
2
0
0
0
0
1
0
0
0
0
1
1
0
0
0
2
0
2
1
0
2
0
0
0
1
0
2
3
0
0
0
2
0
0
0
1
0
0
1
0
1
1
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
1
0
2
2
2
0
0
0
0
0
0
0
1
0
1
0
1
0
0
2
0
0
0
0
1
2
0
2
0
0
0
1
1
2
1
0
0
0
0
0
0
0
0
2
1
1
0
0
0
2
0
2
0
0
1
0
3
0
0
2
1
0
0
2
1
0
2
0
0
0
2
0
0
1
1
0
0
0
0
0
2
1
0
0
1
1
0
0
0
2
1
0
0
0
2
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
2
2
1
2
0
3
0
0
0
1
2
0
1
2
0
0
0
2
0
0
0
0
0
2
0
1
0
0
2
0
0
2
2
0
2
0
1
0
0
0
0
0
0
3
0
0
0
2
1
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
1
2
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
2
0
1
0
1
0
0
0
0
1
1
1
0
1
2
1
1
1
0
0
3
0
0
2
0
0
2
0
0
2
0
0
1
2
0
1
0
0
4
0
2
1
1
1
0
2
1
1
0
0
0
0
1
0
0
0
2
1
0
1
0
0
2
0
0
7
0
0
0
0
0
0
0
2
0
2
0
0
2
1
1
3
2
3
0
0
0
1
1
0
0
4
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
2
0
3
0
2
0
2
2
0
2
0
1
0
1
1
0
1
0
0
0
2
2
0
0
1
1
0
0
0
0
0
1
1
0
1
0
2
0
0
0
0
0
1
0
2
0
0
2
1
0
0
0
2
0
2
0
0
0
0
2
2
3
1
4
1
0
0
0
1
1
1
0
0
0
2
1
0
0
1
1
0
1
2
0
0
1
2
2
0
0
2
1
2
0
0
0
0
2
0
0
0
2
1
0
0
1
0
0
0
1
1
0
0
3
0
0
0
2
1
0
2
2
0
2
1
2
0
1
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
2
0
0
0
4
1
2
0
2
0
3
0
0
2
0
0
2
1
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
1
1
1
0
0
0
0
1
0
2
1
0
1
2
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
3
0
0
0
0
1
1
0
0
1
0
1
0
2
0
0
0
0
2
0
2
0
1
0
1
0
1
0
0
0
2
0
2
0
2
0
0
0
0
2
0
0
0
10
0
2
2
2
2
2
2
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
1
0
0
1
2
1
2
0
0
0
0
0
0
0
0
1
1
2
0
0
2
0
1
0
0
0
0
2
2
2
0
0
0
0
0
1
0
1
0
1
0
1
1
2
1
2
0
2
1
2
2
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
2
1
1
0
2
2
0
0
3
0
0
2
1
0
0
0
2
0
0
0
0
2
2
0
0
2
1
1
1
2
0
0
0
0
0
0
0
2
0
2
0
2
0
1
0
0
2
0
1
0
0
0
2
1
1
0
1
0
1
0
1
2
1
1
0
2
0
2
0
2
0
2
2
0
1
0
0
2
2
0
2
2
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
2
0
0
0
2
0
2
0
1
2
0
0
1
0
0
2
0
1
0
1
0
2
0
2
0
1
0
1
1
0
0
0
0
1
4
0
0
0
0
1
0
0
0
0
1
2
2
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
7
0
1
2
0
0
0
2
1
0
2
1
0
0
0
1
1
1
0
2
2
2
0
0
0
0
0
2
2
0
3
1
0
0
2
3
1
1
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
2
0
1
0
0
1
0
1
1
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
3
0
0
2
0
1
0
0
0
2
0
2
2
1
0
1
2
0
0
0
1
0
1
2
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
2
0
1
2
0
0
0
0
1
0
1
0
0
0
0
0
1
2
1
2
1
0
1
0
2
2
0
2
2
0
0
0
2
0
0
0
0
0
2
1
0
0
2
0
0
2
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
2
1
0
0
1
0
2
0
0
0
1
0
0
0
0
0
2
0
3
2
0
0
0
1
0
0
0
2
0
2
1
0
0
2
2
0
0
0
0
0
0
2
0
0
1
1
2
2
0
2
1
0
0
1
0
2
0
0
0
2
2
0
2
9
2
0
0
0
1
0
0
1
2
2
0
2
1
0
2
0
0
0
1
0
0
2
0
0
2
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
2
3
2
0
0
2
0
2
0
0
1
1
0
0
0
0
0
3
0
0
0
2
1
0
0
1
0
0
0
1
1
0
0
0
1
0
0
2
0
2
0
0
0
0
0
3
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
2
2
0
11
0
1
0
0
0
2
0
2
1
0
0
2
2
0
1
6
2
2
0
0
1
1
0
1
0
0
0
0
1
0
1
4
2
1
0
0
2
1
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
2
2
0
0
0
0
0
2
2
1
1
1
0
0
0
0
1
3
1
0
0
0
0
0
1
2
2
0
0
3
2
2
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
2
2
0
0
0
1
0
0
1
1
1
1
0
0
2
2
0
2
0
2
1
1
0
0
0
0
1
0
0
0
2
0
2
2
2
0
0
1
2
1
0
1
0
2
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
1
4
0
0
0
0
0
1
0
0
2
0
1
0
1
2
2
0
0
0
0
0
1
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
2
1
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
1
2
0
2
0
2
2
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
1
1
0
0
0
1
1
1
0
0
0
2
0
2
0
0
1
1
0
0
0
0
0
0
1
0
2
0
0
0
1
3
0
0
0
2
1
0
0
0
2
0
0
0
1
0
1
0
0
0
2
0
0
0
2
0
0
1
0
2
3
1
0
1
1
0
0
0
1
0
1
0
0
1
1
2
0
2
0
0
1
0
0
0
1
2
0
0
1
1
0
1
1
2
0
0
1
1
2
0
1
2
1
0
1
2
0
1
1
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
1
1
0
2
2
0
1
0
1
0
0
0
0
1
0
1
2
1
0
0
0
0
2
0
0
0
0
2
0
2
0
2
2
0
2
0
0
0
1
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
3
1
0
0
0
0
2
1
2
1
1
0
0
2
0
1
1
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
2
1
0
2
0
0
0
0
1
2
0
0
1
2
0
2
0
0
0
0
0
0
0
2
2
0
3
1
2
0
0
0
0
0
0
0
0
2
1
1
0
1
0
0
2
0
2
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
2
1
0
1
2
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
2
0
0
2
0
1
1
0
2
0
0
0
2
0
1
0
0
0
0
0
0
1
1
0
0
1
1
1
2
0
2
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
2
2
0
2
0
0
0
1
2
0
0
1
0
0
2
1
2
0
0
0
0
0
0
0
1
1
3
0
0
1
0
3
0
0
0
0
0
1
1
0
0
0
0
0
0
2
1
1
0
5
0
0
2
0
0
0
0
1
1
2
1
0
0
0
0
2
0
2
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
1
0
2
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
4
2
0
1
1
0
1
0
2
0
0
1
0
2
0
1
2
1
1
1
0
1
0
2
0
0
1
0
1
0
4
2
0
1
0
2
0
1
2
0
0
0
0
0
0
1
0
0
0
1
2
0
1
0
2
2
1
2
1
0
0
0
2
0
0
2
2
2
1
0
0
0
2
0
2
2
0
2
15
0
0
0
1
0
1
0
2
1
5
1
0
0
1
0
1
0
2
4
0
0
0
2
0
1
1
1
0
0
1
2
2
2
0
0
1
0
2
0
3
2
1
1
0
1
2
2
0
0
1
0
2
0
2
0
0
0
2
0
2
0
0
0
1
0
0
1
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
1
2
2
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
2
1
0
0
0
0
0
1
0
0
0
2
1
1
14
1
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
3
0
0
0
1
2
0
2
2
1
0
2
0
2
0
0
2
0
0
2
1
1
2
1
0
1
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
2
1
0
0
0
0
1
0
2
0
0
2
0
0
1
1
0
0
0
0
2
0
2
1
2
0
1
0
1
0
0
1
0
0
1
2
0
1
1
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
3
2
2
2
1
0
0
0
0
1
4
1
2
0
2
0
1
0
2
0
0
0
0
0
0
1
1
0
0
0
0
2
0
1
1
0
0
1
2
0
0
0
3
0
1
0
1
0
1
0
3
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
1
0
1
1
0
0
2
3
0
0
0
0
2
2
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
1
0
0
2
2
0
1
2
0
0
0
0
1
0
0
0
2
1
0
2
2
0
2
3
2
0
0
0
1
1
0
3
1
0
0
0
2
3
1
2
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
2
1
2
0
0
0
0
0
1
0
0
0
0
2
1
0
1
0
0
0
2
0
0
0
1
0
0
1
4
0
0
2
1
1
2
0
0
0
0
0
0
0
2
0
1
0
1
0
1
0
1
2
2
0
0
1
0
2
0
0
0
7
0
0
0
0
2
0
0
0
2
1
0
0
2
0
1
0
1
0
1
2
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
1
0
0
0
0
0
3
1
0
0
0
2
2
0
0
0
1
0
2
0
1
1
0
1
1
1
2
0
0
0
1
0
3
0
0
0
0
0
3
0
0
0
0
1
0
2
0
0
0
2
0
0
0
5
0
1
0
3
0
0
0
0
0
0
0
0
4
1
0
0
1
2
0
0
0
0
0
0
0
1
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
2
2
0
3
3
1
1
2
1
1
2
2
2
2
0
1
1
0
0
2
0
0
0
0
1
0
1
0
1
0
1
0
1
1
2
0
0
0
0
1
1
0
0
0
1
0
2
0
2
0
0
0
2
0
0
0
0
0
1
1
0
1
0
0
0
0
0
2
1
0
0
0
0
2
0
2
0
2
0
0
1
0
2
0
1
1
0
1
1
1
0
1
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
2
0
0
1
2
0
0
0
0
2
5
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
1
0
1
0
0
0
0
0
3
0
1
2
0
0
0
0
0
0
0
0
1
0
1
1
0
0
2
1
2
0
0
0
3
1
1
0
1
1
0
1
0
1
1
0
2
0
0
0
0
0
2
1
0
2
2
2
2
0
0
1
0
1
2
0
0
0
3
0
0
0
0
1
0
2
0
0
0
0
2
2
0
0
1
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
2
2
0
1
1
0
0
0
0
1
0
0
1
0
0
1
0
1
2
2
0
2
2
0
2
1
0
0
2
0
0
0
1
0
2
0
0
2
0
2
0
0
1
0
1
2
0
0
0
2
0
2
2
1
1
0
1
2
0
2
2
1
2
0
1
0
2
0
0
2
0
2
0
3
0
0
0
2
0
0
1
1
1
1
4
0
1
0
0
0
0
2
1
1
0
0
2
1
2
0
0
0
0
1
0
0
1
0
1
0
0
3
0
2
2
0
0
0
0
0
0
2
0
1
1
0
3
0
2
0
0
2
0
1
0
1
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
2
0
1
1
0
0
0
2
1
0
2
0
1
0
0
0
0
1
0
0
0
0
0
1
2
0
0
3
0
1
0
1
0
1
0
1
2
2
1
2
0
2
0
0
1
3
0
0
0
2
2
2
0
1
0
0
2
3
0
0
0
1
0
0
0
0
0
0
3
0
1
0
0
2
0
0
0
0
0
0
1
1
0
0
2
1
2
2
1
0
4
0
1
0
0
0
0
0
0
0
2
2
2
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
2
0
2
0
2
0
2
1
0
0
0
0
0
1
0
0
0
2
0
2
1
2
0
0
0
0
0
2
0
2
1
0
1
0
0
0
1
0
0
1
2
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
7
1
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
2
2
0
0
2
0
1
2
0
0
1
0
0
2
1
2
0
0
0
1
0
1
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
1
2
0
0
0
0
0
0
1
1
0
0
0
2
1
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
1
0
2
2
0
0
0
0
0
4
1
2
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
1
3
1
2
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
2
1
3
1
1
0
2
1
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
1
1
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
2
0
2
1
1
2
2
0
1
0
0
2
0
2
1
1
1
0
1
0
2
1
1
2
1
0
0
2
3
1
2
2
0
1
0
0
1
0
0
2
2
0
0
0
1
0
0
1
1
1
0
0
3
3
2
0
1
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
2
1
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
1
1
0
0
0
2
0
2
0
1
2
0
1
0
0
2
1
0
2
2
1
0
0
0
0
0
0
0
1
1
0
0
2
0
0
2
0
1
0
2
0
0
0
1
2
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
1
1
0
2
3
3
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
2
0
1
2
0
1
0
0
0
0
0
0
1
10
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
1
1
0
2
0
2
0
1
0
1
0
1
1
2
0
0
2
2
1
2
0
1
1
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
2
2
3
0
0
0
0
2
0
1
2
0
1
1
1
0
0
1
0
0
1
0
0
1
0
2
1
1
1
2
0
1
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
3
0
0
1
0
0
2
1
0
0
2
0
2
1
3
0
0
2
2
0
0
1
3
2
1
1
1
0
0
0
0
2
0
0
0
0
0
2
1
0
1
0
0
3
0
0
2
0
0
2
0
0
0
1
1
0
0
2
1
2
2
1
0
2
2
2
1
0
3
0
0
0
2
3
0
0
0
1
2
1
2
0
0
0
0
0
2
0
1
0
0
1
1
2
3
2
0
1
0
0
2
0
0
0
2
2
0
0
0
2
1
0
1
0
0
0
0
0
0
2
0
0
0
2
0
1
1
1
0
0
1
1
0
0
2
2
0
1
3
0
0
0
2
0
0
2
0
0
0
0
2
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
2
0
0
2
1
0
0
0
2
0
0
0
0
2
2
0
0
0
0
1
0
4
0
0
0
0
0
1
2
0
0
1
0
2
0
2
0
0
1
1
0
0
1
0
3
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
1
0
0
0
0
3
0
1
0
0
0
0
2
1
0
1
0
0
0
1
2
2
0
0
0
2
0
0
0
1
0
0
0
2
0
1
0
0
2
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
3
1
0
0
0
0
2
3
0
0
2
2
0
0
1
0
0
2
2
0
0
0
0
1
2
0
1
0
1
0
0
1
0
1
1
1
0
0
1
0
0
0
6
2
0
2
0
0
0
2
0
1
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
1
0
1
2
2
0
0
1
0
1
1
0
0
2
0
0
0
0
1
1
0
1
0
2
1
1
0
0
0
0
2
0
1
0
0
1
0
0
2
3
0
1
1
0
0
0
0
0
0
2
1
2
1
0
0
0
0
1
0
0
1
1
0
0
0
1
1
1
0
0
0
2
0
0
4
0
0
0
1
0
2
0
0
0
0
0
0
1
2
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
2
1
0
0
0
0
0
1
0
1
2
0
1
0
0
2
0
0
1
1
0
1
0
2
1
2
1
0
2
0
0
2
0
2
0
1
0
1
2
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
3
0
2
0
0
0
1
0
0
1
2
0
2
0
0
0
0
0
0
0
1
3
0
2
2
2
0
0
0
1
0
0
1
0
0
2
1
2
0
0
1
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
1
1
2
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
1
1
0
0
1
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
1
0
2
0
2
0
0
1
0
2
0
0
2
1
0
1
0
2
0
1
0
0
0
0
1
3
0
0
2
0
1
0
0
4
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
2
3
0
2
1
0
0
0
1
0
0
2
1
0
0
0
2
2
5
0
2
0
0
0
0
1
0
0
0
0
0
1
3
0
2
0
1
0
0
1
0
0
0
1
0
2
2
0
1
0
2
0
1
0
1
2
0
0
0
0
1
2
0
0
0
0
0
0
0
2
2
0
2
1
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
1
4
0
0
2
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
1
2
0
0
2
0
1
2
0
0
2
0
0
2
1
0
0
3
0
0
1
1
0
1
0
0
1
1
0
1
2
0
0
0
0
1
0
2
2
1
0
0
0
0
0
1
0
0
0
2
3
1
0
3
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
1
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
2
0
1
2
1
0
2
2
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
2
1
2
0
2
0
0
0
0
0
0
0
2
0
2
0
2
0
0
2
0
2
0
0
2
3
1
1
2
0
0
0
0
0
1
1
1
0
0
0
2
0
0
2
0
2
0
1
0
1
0
2
0
3
2
0
1
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
2
0
1
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
3
0
1
0
0
0
1
2
0
0
0
0
0
0
2
2
3
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
2
2
0
0
0
2
1
0
2
1
2
0
0
0
2
1
2
0
0
1
0
0
0
0
1
2
0
0
0
0
3
0
2
0
0
0
0
0
0
4
0
0
0
2
0
0
0
0
1
0
1
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
1
0
1
0
1
0
0
1
0
1
0
1
0
0
2
0
2
0
0
0
2
0
0
0
4
0
0
2
1
0
1
0
0
0
0
0
1
0
0
3
0
1
2
1
0
0
2
0
0
0
0
0
0
1
0
2
1
1
0
1
0
0
1
0
0
0
0
0
2
0
2
2
1
0
2
0
0
0
0
0
1
0
0
2
3
2
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
3
2
2
0
0
0
0
0
2
0
0
2
0
0
1
0
1
0
0
1
0
0
0
0
2
0
1
0
0
1
2
0
1
4
2
0
0
1
2
0
1
2
0
1
2
0
2
2
0
1
2
0
0
1
0
2
0
1
1
1
1
1
0
0
2
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
2
1
2
2
1
0
0
0
2
2
0
2
0
1
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
2
2
0
0
1
0
0
2
2
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
2
2
2
2
1
2
1
1
2
0
0
0
1
1
0
2
0
0
0
3
0
0
0
0
1
1
1
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
2
2
0
0
1
0
2
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
2
4
1
2
0
0
0
0
0
0
1
0
2
2
0
0
0
2
1
1
0
1
0
1
0
0
2
0
3
3
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
2
0
0
2
1
2
0
0
0
0
0
0
1
2
0
1
1
2
0
0
1
0
2
0
0
0
0
1
0
2
2
1
0
0
0
0
1
0
0
0
0
2
0
2
1
0
0
2
0
1
1
0
0
0
0
0
2
2
2
2
0
0
2
2
0
0
0
0
0
1
1
0
1
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
2
0
0
2
0
0
0
1
0
0
1
1
0
0
0
1
0
1
0
0
2
0
0
2
0
0
0
2
1
0
0
0
1
0
1
0
0
1
1
0
2
0
1
0
0
1
1
1
3
2
0
0
0
1
0
1
2
0
1
0
1
1
0
2
0
1
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
2
1
0
0
0
0
3
1
1
0
0
0
0
0
0
2
0
2
0
1
0
1
1
0
0
2
2
0
2
2
1
0
0
1
0
1
2
2
0
0
1
2
0
2
0
1
0
1
0
0
0
0
2
0
2
1
1
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
1
0
0
0
2
0
3
0
2
0
0
0
0
0
1
2
0
0
1
1
1
0
0
0
0
0
0
0
2
2
0
0
2
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
3
2
1
0
0
0
0
2
1
0
0
2
0
0
0
1
0
0
0
1
0
1
0
0
0
0
2
0
1
0
2
0
0
1
0
2
2
0
2
1
0
0
1
0
0
1
0
2
0
2
2
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
2
0
0
0
0
2
0
1
0
2
0
2
0
2
0
1
1
1
0
3
1
1
2
0
1
0
1
2
0
0
0
0
0
2
0
0
2
2
0
1
0
0
0
0
0
1
0
0
2
2
0
1
1
1
1
0
0
1
0
0
2
0
0
1
2
2
2
0
0
2
1
0
0
0
0
0
2
0
0
1
0
1
0
0
2
2
0
0
0
2
1
2
0
0
0
0
0
1
0
0
0
2
1
0
0
1
1
0
0
0
0
0
2
1
0
0
0
2
0
0
0
2
0
2
1
2
1
1
2
2
0
0
0
0
0
3
2
2
0
1
0
0
0
0
2
0
0
1
0
0
0
0
1
1
5
0
0
1
0
2
3
0
1
1
1
0
2
2
1
0
1
1
2
1
0
1
1
0
0
2
2
0
2
0
1
0
0
1
0
0
0
0
1
0
2
0
1
1
0
0
2
1
2
1
0
2
0
1
1
0
0
0
2
0
1
0
0
2
1
0
0
0
0
2
0
0
2
0
0
1
2
2
0
1
1
0
2
0
0
0
0
2
2
0
0
2
0
0
0
1
1
2
0
0
0
0
2
2
2
0
2
1
0
1
1
0
1
0
0
0
3
0
1
0
0
0
0
0
1
0
2
2
2
0
0
1
0
0
0
0
2
1
0
0
1
0
3
1
0
1
1
2
0
0
0
2
2
0
2
1
1
2
0
0
0
0
1
0
0
0
1
0
0
3
2
0
2
2
3
2
1
0
0
0
1
0
2
0
0
0
0
1
0
0
0
1
2
0
0
1
2
1
1
0
0
0
0
0
0
2
1
0
2
0
2
1
0
0
0
1
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
1
0
2
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
2
2
1
0
0
0
0
1
1
3
0
0
1
0
0
0
2
0
1
1
0
0
1
1
0
0
0
2
0
1
1
0
1
0
0
1
0
0
1
0
0
1
0
0
1
0
1
1
2
2
2
2
0
0
0
0
1
0
0
2
0
0
2
0
0
0
1
1
3
0
2
0
1
1
2
0
0
0
0
1
0
0
0
2
0
2
0
0
0
2
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
2
0
2
0
1
0
0
0
0
3
2
0
3
0
0
1
3
0
2
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
3
0
0
1
0
0
0
0
2
1
0
0
1
0
0
0
0
0
2
2
1
0
0
0
0
0
1
0
0
1
0
0
0
0
3
2
1
0
0
3
0
0
0
2
1
1
0
1
0
0
1
1
0
0
0
0
1
2
0
1
0
0
1
0
1
0
0
1
2
0
0
2
1
0
2
2
0
0
0
2
0
0
0
2
0
0
2
0
0
1
2
0
2
0
1
2
0
0
2
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
2
1
6
0
0
0
1
14
2
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
2
2
0
0
0
5
0
1
2
0
1
0
2
0
1
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
1
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
1
2
0
2
2
0
0
0
0
0
0
0
2
0
0
0
2
0
1
1
0
0
0
2
0
0
1
0
1
0
1
1
2
2
0
0
0
0
0
0
0
0
2
0
0
2
1
2
2
0
0
0
0
1
0
0
0
9
0
0
2
2
2
0
1
1
2
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
1
3
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
1
0
1
2
0
1
2
0
0
2
0
1
2
0
3
0
0
2
1
0
0
0
0
2
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
2
2
1
1
2
2
0
0
2
1
0
1
0
1
0
0
0
2
0
1
0
0
0
0
2
1
2
0
0
0
0
1
1
0
1
2
0
2
0
0
2
1
0
0
1
2
1
1
0
2
0
2
2
3
0
0
0
0
1
0
0
4
0
0
0
1
0
0
0
1
1
0
0
0
1
0
3
1
0
0
0
0
0
0
0
0
2
2
0
0
1
1
0
2
0
2
0
2
1
0
0
0
0
0
0
3
0
0
1
0
1
0
2
3
0
1
0
0
4
2
0
1
0
2
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
2
0
0
0
0
2
0
1
0
2
0
0
1
0
0
0
1
2
3
0
0
2
0
0
0
0
2
0
0
0
0
2
0
1
2
0
1
4
0
0
2
2
0
1
2
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
3
0
1
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
2
0
1
0
0
1
0
0
2
0
0
0
0
1
2
0
2
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
1
3
1
0
2
0
1
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
3
2
0
0
0
1
2
2
0
0
0
0
1
1
0
2
0
0
0
1
0
0
0
1
0
1
1
0
4
2
1
0
1
0
2
0
1
0
1
0
0
1
1
0
0
0
2
1
1
0
0
1
1
0
0
0
1
3
1
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
2
1
1
1
2
0
0
1
2
0
1
1
0
0
0
2
2
2
2
2
2
0
1
1
1
0
1
0
0
1
0
0
0
0
0
0
2
0
0
1
0
2
0
2
2
3
0
0
0
2
1
0
0
1
1
1
0
0
2
0
1
0
2
0
1
2
2
0
0
2
1
2
0
0
0
0
0
1
1
1
0
0
0
1
0
1
0
2
1
0
0
0
1
0
0
0
0
1
1
0
1
0
2
0
0
0
2
0
0
1
2
0
0
0
0
0
0
2
4
0
0
0
0
0
0
2
2
0
0
0
0
2
0
1
2
1
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
2
0
1
1
0
0
0
1
2
1
0
1
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
4
0
0
0
1
0
0
2
1
2
0
4
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
1
2
0
2
2
1
0
0
0
1
2
0
0
0
0
0
0
1
2
0
1
0
0
0
2
2
0
0
0
0
1
0
1
1
0
0
1
1
1
1
1
0
1
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
1
0
2
1
1
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
2
2
0
0
1
1
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
2
0
1
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
1
2
0
0
2
2
0
0
0
0
0
0
0
1
2
0
0
0
0
2
2
0
0
2
0
2
1
0
0
0
0
1
1
1
0
2
0
0
0
0
0
1
0
1
1
0
0
1
1
1
0
0
2
1
0
0
0
0
0
0
1
1
1
0
0
0
2
0
0
0
2
0
2
0
0
2
0
0
0
1
0
1
0
0
1
2
0
0
1
0
2
1
2
0
2
2
0
4
0
0
1
3
0
1
1
3
2
2
0
1
0
1
0
0
1
0
0
0
0
3
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
2
1
0
0
0
0
1
0
2
2
1
0
0
1
1
0
0
0
0
0
4
0
1
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
2
2
2
2
0
2
0
2
1
2
0
0
0
0
0
0
0
1
0
1
2
2
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
1
2
0
0
0
2
0
0
1
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
2
2
1
1
0
0
1
0
0
2
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
1
1
1
2
0
0
0
0
0
2
1
2
0
0
0
0
0
0
1
2
0
0
2
0
0
2
1
1
0
1
1
1
0
1
0
0
2
0
0
1
0
0
0
0
0
2
0
0
2
1
0
1
1
0
0
2
0
2
1
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
1
2
0
0
0
0
2
0
1
0
1
0
0
2
0
0
0
1
2
0
0
0
1
2
0
0
1
0
0
0
0
0
2
4
2
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
1
2
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
1
0
2
1
0
0
0
0
2
0
1
0
2
2
2
0
1
0
1
0
0
2
0
0
0
0
2
0
1
0
2
1
0
1
2
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
1
0
0
1
1
1
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
1
2
0
0
0
2
0
0
2
2
0
0
1
0
0
2
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
2
0
2
2
0
2
0
0
0
0
2
1
2
0
0
0
1
0
1
1
2
0
0
0
0
0
1
1
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
1
3
0
1
1
1
0
1
2
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
1
0
1
2
1
0
0
0
0
1
2
0
1
0
2
0
0
1
1
2
2
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
1
0
2
0
2
1
0
2
0
1
2
2
0
2
1
0
1
0
1
1
2
1
0
1
1
0
0
0
0
0
0
0
0
0
0
2
1
1
2
3
2
0
0
2
0
0
0
1
0
2
0
1
1
0
1
0
0
2
0
0
2
2
0
1
2
0
0
0
0
0
3
0
0
3
1
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
3
1
1
0
1
2
2
0
0
0
0
1
1
1
0
1
2
1
2
1
1
1
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
1
0
0
4
0
0
1
0
2
0
0
1
0
1
1
1
1
0
0
1
0
2
0
1
0
1
1
0
0
0
0
2
0
2
0
0
1
0
2
0
0
0
0
0
1
1
1
0
0
0
0
2
0
1
0
1
0
0
0
2
1
1
0
0
0
2
2
0
0
0
0
0
0
0
1
2
0
0
2
0
1
0
3
0
0
3
2
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
3
0
2
2
0
1
0
0
0
0
0
1
0
0
2
0
2
2
1
0
0
0
0
0
0
1
0
0
2
0
0
1
2
2
0
0
1
0
1
0
1
0
2
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
2
1
2
0
2
2
0
0
2
0
1
0
4
0
0
0
0
3
0
1
0
0
0
1
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
1
1
1
0
1
2
0
0
1
0
0
0
1
0
2
0
0
1
0
2
0
1
0
0
2
2
0
0
0
2
0
0
0
1
1
0
0
0
1
1
0
2
4
0
0
0
1
2
0
0
0
1
2
0
0
0
1
0
1
0
2
1
0
0
0
0
2
1
0
2
0
0
0
1
1
0
0
2
0
0
0
0
0
1
1
0
2
2
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
2
1
0
0
0
2
0
0
1
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
2
0
2
0
3
1
1
1
0
0
0
0
0
0
0
0
0
0
0
2
1
3
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
1
1
0
0
0
0
0
0
1
1
0
0
2
0
0
1
1
0
1
0
1
0
0
2
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
1
0
2
2
0
1
0
1
0
2
0
1
0
2
2
0
0
0
2
0
2
2
1
0
0
0
0
0
0
1
0
1
0
0
0
0
2
1
0
1
0
1
0
0
0
0
1
0
4
1
2
0
2
1
0
0
0
0
1
1
2
0
1
1
0
2
2
1
2
2
3
0
0
0
1
0
0
2
0
0
0
0
0
1
2
2
0
0
0
0
0
0
3
2
1
1
0
0
0
0
0
0
0
0
0
0
2
1
2
0
2
0
1
2
1
1
1
3
1
0
0
0
0
2
0
1
1
0
0
0
0
1
3
0
0
0
0
0
2
1
0
1
0
2
1
0
0
2
1
1
2
0
2
0
0
0
2
1
0
2
0
2
0
0
0
2
2
0
0
0
0
2
0
0
0
0
2
0
2
0
0
3
0
0
0
2
0
2
0
1
1
2
1
0
2
0
2
0
0
0
0
2
2
0
0
0
2
0
1
2
2
2
0
2
2
0
0
1
2
0
5
1
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
1
1
0
0
2
0
1
2
0
0
6
0
1
0
0
2
0
2
1
2
0
0
1
0
2
0
0
0
0
0
0
1
2
0
1
1
2
0
1
0
0
0
0
0
2
2
0
1
0
0
1
1
0
2
0
0
1
0
0
2
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
2
2
0
2
1
0
2
0
0
0
1
0
0
1
0
0
0
5
0
0
0
0
1
0
0
2
0
1
2
0
0
0
0
1
0
0
0
0
0
2
0
0
2
1
0
1
2
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
1
0
2
1
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
2
0
2
0
0
0
1
2
0
2
0
1
2
1
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
1
2
0
1
0
0
0
2
0
1
0
0
0
0
2
1
0
0
1
0
0
3
2
0
1
1
0
0
2
2
0
1
0
0
0
0
0
1
2
0
0
0
0
1
1
0
0
0
0
0
0
0
1
2
0
1
0
4
0
0
3
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
1
2
1
0
0
0
3
1
0
2
0
2
1
0
1
1
1
0
1
1
0
0
0
1
1
1
0
2
2
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
2
1
0
2
0
0
0
0
2
0
1
0
2
0
0
1
0
0
1
1
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
1
1
0
0
0
1
1
0
0
2
0
0
2
0
2
2
0
1
2
2
1
0
0
0
0
0
0
1
0
0
0
1
2
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
1
2
1
5
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
2
0
1
2
0
0
0
1
2
3
0
1
0
0
1
0
0
0
0
0
1
0
0
3
0
2
0
1
0
1
0
0
0
0
0
0
1
2
2
0
1
0
1
0
1
1
2
0
0
2
1
0
0
0
0
0
0
0
0
0
2
1
0
2
1
1
0
0
0
0
1
1
1
1
1
1
0
0
0
0
0
1
1
0
1
0
0
0
0
2
0
0
0
1
0
0
2
0
0
1
0
3
3
0
0
1
0
1
0
1
0
1
0
1
2
1
0
0
0
1
1
1
2
0
0
0
0
0
2
1
0
1
3
0
0
1
1
1
0
2
0
0
1
0
1
1
0
0
2
0
2
0
0
0
0
1
0
0
2
1
3
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
1
0
0
0
1
2
0
2
1
2
2
1
0
0
0
0
0
0
1
2
1
0
1
2
1
0
0
0
0
2
1
0
1
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
1
0
2
2
2
0
1
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
2
1
2
2
0
0
0
2
2
2
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
2
3
0
0
0
0
1
0
0
1
0
0
0
2
0
0
1
2
0
1
3
0
0
0
0
1
2
1
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
2
0
1
1
0
1
0
2
1
1
2
0
0
1
0
0
1
2
0
2
2
1
0
1
1
2
0
0
0
0
0
2
2
0
0
1
0
0
0
1
1
0
2
0
0
0
2
2
1
0
0
0
0
0
1
2
2
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
1
1
0
1
0
0
1
0
1
0
3
0
1
0
0
0
0
2
1
0
0
0
0
2
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
2
0
1
0
1
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
3
0
0
0
0
0
1
0
1
0
2
0
1
0
0
1
0
0
2
0
0
2
1
0
1
2
1
0
2
0
0
2
0
2
0
0
1
2
1
0
0
0
0
0
0
1
1
0
1
0
1
2
0
0
0
0
1
0
2
0
1
0
0
2
2
0
0
1
0
1
0
0
1
1
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
2
0
0
1
0
2
0
0
0
0
1
0
1
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
2
0
1
0
0
0
4
0
1
0
1
0
0
0
2
0
0
1
1
0
0
1
0
0
2
0
0
2
0
1
0
0
0
0
0
1
0
1
2
0
0
0
1
0
0
0
0
2
0
0
2
0
2
0
0
1
2
1
0
1
0
1
0
2
0
0
2
0
2
0
0
0
1
1
0
0
0
0
3
0
0
0
1
2
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
2
2
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
2
0
2
2
0
0
0
0
0
0
0
1
0
1
1
0
0
2
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
1
0
0
0
0
0
2
0
0
3
0
0
0
0
2
2
1
0
1
0
2
0
0
0
2
3
0
0
1
0
0
1
2
0
0
0
0
2
1
1
1
2
1
0
0
0
0
1
0
0
2
2
0
0
1
2
0
2
2
0
1
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
1
2
0
1
1
0
0
0
0
1
1
1
0
2
0
2
1
0
1
0
0
1
2
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
2
3
2
0
0
0
0
0
0
0
2
1
1
1
1
0
0
0
0
0
2
2
1
2
1
2
2
3
0
2
0
1
0
0
0
2
0
2
0
1
1
0
0
0
0
1
0
2
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
2
0
1
1
0
0
0
2
2
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
2
0
1
2
3
2
1
0
4
2
0
0
0
0
0
1
0
1
1
0
0
0
0
0
2
0
3
0
2
0
1
2
0
0
1
0
0
2
0
2
0
1
2
1
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
1
1
1
0
0
1
0
1
2
0
2
1
0
0
0
2
0
0
0
0
0
4
0
2
2
2
1
1
2
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
2
0
0
0
0
0
2
0
1
0
2
1
0
2
0
1
0
2
0
0
0
0
0
0
0
1
2
0
2
1
0
0
0
0
0
2
1
1
1
0
2
0
1
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
1
2
1
0
0
0
2
1
0
0
0
1
0
0
1
2
0
2
0
0
0
0
0
1
1
0
0
0
2
4
0
1
2
1
0
0
1
1
0
0
1
0
0
6
1
0
0
2
0
1
0
0
2
0
0
0
1
2
4
0
0
0
1
2
1
0
2
0
0
1
2
2
4
0
0
0
2
2
3
1
0
1
0
0
1
0
2
2
1
2
2
2
0
0
2
2
1
2
0
1
2
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
1
0
0
2
0
0
1
2
0
0
0
1
2
0
0
0
0
0
2
0
1
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
2
2
0
1
0
0
0
0
2
0
0
1
1
2
2
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
1
1
0
2
0
2
0
2
0
0
0
1
2
0
1
0
0
0
1
2
0
0
2
0
0
2
1
2
0
0
0
0
2
0
0
1
1
0
0
0
1
0
1
0
1
0
2
0
0
0
1
2
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
1
2
0
1
0
1
0
0
1
0
0
0
2
2
2
2
0
1
0
1
0
2
2
0
2
0
0
3
0
1
0
0
0
2
2
0
0
0
0
0
0
1
2
0
0
1
1
1
0
2
1
0
0
0
0
0
2
0
0
1
0
0
1
0
0
2
0
0
1
1
2
0
0
0
0
0
1
0
2
0
0
0
0
2
1
0
0
2
0
1
0
1
0
2
1
1
0
0
3
2
0
0
1
0
0
0
0
1
0
0
3
0
0
0
0
1
0
1
1
0
2
0
3
0
0
0
0
2
2
2
3
0
3
2
0
0
0
3
0
2
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
2
0
0
0
0
0
2
2
0
1
0
2
0
2
2
0
0
1
1
0
0
1
1
0
0
0
0
2
2
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
2
1
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
1
0
0
1
0
0
0
2
1
0
1
1
1
1
0
0
3
2
1
1
1
0
1
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
2
0
0
0
0
0
0
0
2
2
1
0
0
1
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
1
1
1
1
0
1
0
1
0
2
1
1
0
0
1
2
0
0
0
3
0
0
1
1
2
0
0
1
0
2
0
2
0
0
3
0
1
1
3
1
1
0
0
0
0
7
0
1
0
0
0
1
2
0
0
2
0
0
0
0
0
1
0
1
1
0
1
1
0
2
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
4
0
3
0
0
0
0
2
0
2
0
1
0
0
2
0
2
0
2
0
0
1
1
0
0
0
0
1
0
2
0
2
1
0
2
0
0
1
2
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
3
1
0
0
2
0
0
0
0
0
0
2
0
1
1
0
0
2
2
2
0
0
0
0
0
2
2
0
0
1
0
1
0
0
0
0
1
0
0
1
0
5
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
3
2
0
0
0
1
0
1
0
1
0
0
1
0
4
0
0
1
2
0
2
0
0
2
0
1
1
0
0
1
0
1
0
2
0
1
0
1
0
0
0
0
1
1
0
0
1
1
0
2
0
2
2
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
1
1
0
1
1
0
3
0
2
0
1
0
0
0
1
2
0
1
0
0
0
1
0
1
0
0
1
0
0
1
1
0
3
0
0
0
0
1
0
1
0
1
1
1
1
3
0
0
2
2
0
0
1
0
2
2
0
0
1
1
2
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
2
0
1
0
0
0
0
2
1
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
1
1
2
0
0
1
0
0
0
0
0
0
1
2
0
0
0
1
4
1
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
1
1
0
0
1
0
3
1
1
0
1
1
0
0
0
2
0
1
0
0
6
2
1
0
2
1
0
1
0
0
0
0
0
1
0
0
0
2
2
0
0
0
2
0
2
0
2
0
1
2
0
0
1
0
2
0
0
0
1
0
2
0
1
0
2
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
3
0
2
0
1
0
1
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
4
0
1
1
0
1
0
2
1
1
0
0
2
2
3
1
0
2
0
0
0
0
2
1
0
0
0
2
1
1
0
0
0
2
0
1
1
2
1
1
2
0
0
1
0
0
2
0
0
2
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
1
0
0
2
0
1
0
0
2
0
0
1
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
1
0
2
0
0
2
0
2
0
1
0
0
1
2
2
0
0
2
0
2
1
2
0
0
0
1
1
0
1
2
1
2
0
0
1
0
0
2
0
0
4
0
0
0
2
0
0
2
0
0
0
0
2
2
1
0
0
1
1
0
0
1
0
0
5
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
2
2
0
1
0
0
0
1
0
0
1
1
0
1
1
0
2
0
1
0
0
3
2
2
0
0
2
0
0
1
0
0
0
2
0
2
0
1
0
1
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
2
0
2
0
0
0
0
1
1
0
0
1
0
0
0
0
2
3
1
0
4
0
2
0
0
0
0
0
1
2
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
1
0
0
1
2
0
0
2
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
1
2
0
3
0
0
0
2
0
0
0
2
2
2
1
1
0
1
0
1
0
1
1
0
0
1
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
3
0
0
0
0
2
1
0
1
0
0
0
0
0
1
1
2
2
0
2
0
0
1
0
1
0
0
2
1
0
0
0
1
0
1
1
2
0
0
0
1
1
0
3
0
0
2
0
0
0
0
0
1
1
1
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
2
0
2
0
2
0
1
0
0
0
2
2
0
2
0
1
2
0
2
2
2
0
0
1
1
1
0
2
1
2
0
0
2
0
0
0
0
0
3
0
0
1
0
0
2
0
0
0
2
0
2
3
2
0
1
0
0
0
0
4
0
2
0
0
0
0
1
0
1
0
0
0
0
0
1
2
0
1
5
0
0
0
1
1
0
0
2
0
0
0
0
0
2
1
1
1
0
0
0
0
2
0
1
0
2
0
1
0
1
0
1
0
1
2
2
0
0
0
0
0
0
0
0
0
1
0
4
0
3
0
1
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
1
1
0
0
0
1
1
0
1
3
0
0
2
0
4
0
0
1
2
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
3
0
2
0
2
0
0
1
0
0
0
1
3
2
0
0
0
2
2
0
1
0
4
2
1
0
1
2
0
1
0
0
0
0
1
0
1
0
0
0
0
0
2
1
0
1
3
2
1
2
0
0
3
0
2
2
0
1
0
2
0
0
0
2
0
2
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
2
0
0
2
4
0
2
1
2
0
1
0
1
1
1
0
1
0
1
4
0
2
1
0
0
0
0
0
0
9
0
0
0
2
0
2
0
1
0
0
1
0
0
1
1
2
2
0
0
0
0
1
0
1
0
0
0
0
2
2
2
1
1
1
0
2
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
2
0
2
0
0
0
0
0
0
1
0
2
0
1
0
2
1
2
2
1
1
0
0
1
0
0
0
0
2
0
1
0
1
2
2
1
2
2
1
0
0
0
2
1
2
0
0
0
2
0
0
1
1
0
0
0
0
0
2
0
5
1
0
0
0
1
2
2
0
0
0
0
0
0
2
0
1
0
2
0
0
1
1
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
2
1
2
0
0
1
1
1
1
0
0
0
2
1
0
0
0
0
0
2
2
0
0
0
3
0
0
0
2
2
2
0
0
1
2
0
0
1
0
0
0
1
0
1
1
1
0
0
0
0
1
2
2
0
0
0
0
1
1
0
0
1
2
1
0
2
0
2
0
2
0
1
0
1
0
0
1
2
2
2
0
1
0
3
0
2
1
0
2
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
1
0
1
0
0
0
0
1
1
0
2
2
0
0
0
0
0
1
0
1
1
1
1
0
0
2
2
0
0
2
0
1
0
0
0
0
2
1
1
0
0
0
0
0
0
2
0
0
1
0
1
0
1
2
0
0
2
0
0
0
0
2
0
0
2
1
0
0
0
1
1
0
0
0
2
1
0
2
0
2
1
4
0
0
0
0
0
1
0
0
1
0
0
2
2
0
2
0
0
1
0
1
1
0
0
0
0
1
1
0
0
0
0
1
0
2
1
0
0
0
2
1
1
2
1
0
2
0
0
1
0
3
0
0
0
1
0
2
0
0
0
0
2
1
1
1
0
0
0
0
2
1
2
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
1
0
1
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
2
1
2
0
2
0
0
0
1
2
0
0
2
0
2
0
0
2
0
0
1
2
2
0
0
2
0
2
0
1
4
0
0
0
2
1
0
0
2
3
0
0
2
0
0
0
0
1
0
0
0
2
0
0
2
1
0
0
0
0
0
0
2
0
0
1
0
0
1
1
0
1
0
0
1
1
0
0
1
0
0
1
1
0
2
0
0
2
1
0
1
0
0
0
0
0
0
0
0
2
2
0
1
0
0
1
1
0
1
0
1
0
1
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
1
1
0
2
2
0
0
1
0
4
0
2
0
0
0
1
1
1
2
1
0
0
0
0
1
1
0
2
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
2
1
2
0
0
0
0
1
1
0
2
0
0
0
2
0
2
1
2
2
0
0
0
0
2
0
1
2
0
1
0
0
1
0
0
1
2
3
2
0
1
1
0
1
2
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
2
1
0
2
0
0
2
0
1
0
1
0
0
0
1
0
0
0
2
0
2
1
0
0
0
0
1
1
2
0
0
0
2
1
2
0
2
0
2
0
2
0
0
0
1
1
1
1
0
2
0
2
0
0
0
2
0
0
0
0
2
0
0
1
0
1
1
1
0
1
1
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
1
1
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
2
2
0
0
1
2
1
0
0
0
0
0
0
0
0
1
0
0
1
0
3
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
1
1
2
0
2
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
1
0
2
0
0
2
1
0
1
0
0
0
0
0
0
1
2
0
0
1
0
0
2
0
2
0
0
1
0
1
0
0
1
1
0
0
2
0
2
1
1
1
1
2
2
1
0
0
0
0
0
0
1
2
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
1
0
3
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
2
0
2
0
0
1
0
1
2
0
2
0
2
0
2
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
1
1
0
0
0
0
0
0
0
2
1
0
0
0
0
2
1
0
2
0
2
0
0
0
0
0
1
1
0
0
0
0
2
0
4
1
0
0
1
2
0
0
0
2
0
0
0
1
0
0
0
2
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
1
1
0
0
2
0
2
2
0
2
0
1
0
0
0
1
0
0
0
0
2
0
2
0
0
0
3
1
3
2
0
0
1
0
2
2
0
0
2
2
0
0
1
0
0
1
0
0
0
0
2
0
2
1
0
0
0
0
0
2
0
2
0
1
0
1
1
1
0
2
1
0
0
1
1
0
1
2
0
0
1
1
2
0
0
0
0
2
0
2
0
0
2
1
0
0
2
2
0
0
0
0
1
0
0
1
1
0
0
0
1
0
2
5
0
0
0
2
1
0
0
1
0
1
1
0
1
1
1
0
1
1
0
0
0
2
1
0
2
0
1
2
0
0
0
1
1
1
0
1
0
0
1
0
0
0
3
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
2
0
1
0
0
2
0
2
0
0
0
2
0
0
1
3
0
0
0
1
0
0
2
1
1
0
0
0
2
0
0
1
1
2
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
2
2
1
0
0
0
0
1
0
1
2
0
1
1
0
2
0
0
1
0
1
0
1
0
0
1
0
2
0
0
0
0
2
0
0
0
2
2
0
1
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
1
1
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
2
0
1
0
0
0
0
0
1
0
0
0
2
1
1
0
0
0
2
1
0
1
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
1
0
0
2
0
2
1
0
0
0
0
0
0
0
1
0
0
2
2
1
1
0
0
1
1
1
0
2
2
0
0
0
1
1
2
3
0
0
0
0
0
0
0
2
2
0
2
0
0
1
0
2
0
0
2
0
0
0
0
2
0
0
2
2
0
0
1
0
2
1
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
2
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
3
0
2
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
3
0
0
1
0
2
2
0
0
1
0
2
0
1
0
0
0
0
1
0
0
1
1
0
1
0
0
2
1
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
1
0
1
0
0
0
0
2
3
0
0
3
0
0
3
0
2
1
0
0
2
0
1
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
1
1
0
0
0
0
0
0
2
3
1
2
1
0
0
0
0
2
1
2
0
0
0
1
1
0
1
0
3
0
2
0
2
0
1
2
1
0
0
1
0
2
1
1
1
2
0
2
2
0
0
0
4
0
2
0
0
1
0
0
0
0
0
2
0
0
1
1
0
2
0
0
0
2
1
1
0
3
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
2
0
0
2
0
0
1
0
0
0
1
1
2
0
1
0
0
0
1
0
0
0
2
1
0
0
2
0
0
2
1
0
0
1
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
2
1
0
1
3
3
1
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
3
0
1
0
1
0
2
2
1
0
0
1
2
0
0
2
2
0
2
2
0
0
0
2
0
3
1
1
0
0
1
2
0
1
0
0
0
0
0
2
0
0
1
18
1
1
0
0
0
0
0
0
2
1
1
0
1
2
1
1
0
1
1
1
1
0
0
0
0
2
0
3
2
0
0
0
0
0
2
2
0
1
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
1
2
1
1
2
2
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
2
0
1
2
0
2
0
0
0
1
1
0
0
2
0
0
0
0
1
2
0
0
0
2
0
0
2
0
1
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
2
0
4
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
2
0
0
0
0
1
0
1
1
0
1
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
1
2
0
0
0
1
1
0
0
0
0
1
0
2
0
3
0
0
0
0
2
0
2
0
1
0
1
0
0
0
0
3
0
0
1
0
0
2
0
0
2
0
1
0
0
1
0
0
1
3
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
2
0
0
0
0
0
1
0
0
2
0
2
2
3
1
2
1
0
0
0
1
1
0
4
0
0
1
2
0
0
0
0
0
0
2
1
0
0
2
0
0
0
3
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
3
1
0
0
1
0
0
0
0
0
2
0
0
0
1
1
0
2
0
0
1
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
1
1
0
0
1
1
1
0
0
0
1
1
0
0
0
2
0
0
0
1
2
0
1
1
0
0
2
0
0
2
0
0
0
0
2
2
1
0
0
0
2
2
0
0
0
0
2
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
1
0
2
0
0
1
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
2
0
0
0
0
2
0
0
2
0
2
0
3
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
2
1
1
2
0
2
1
0
0
1
0
0
0
2
2
1
0
2
0
2
3
0
2
1
1
0
0
1
0
2
0
1
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
1
2
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
2
0
1
3
1
2
0
0
1
0
2
2
1
2
2
0
0
0
1
1
1
2
1
2
2
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
2
0
0
1
0
1
0
0
1
0
2
0
0
1
2
1
0
1
0
0
2
0
1
0
0
1
3
0
2
0
0
1
0
0
0
0
0
0
1
1
0
5
0
0
0
0
0
0
1
1
0
0
0
2
0
2
0
0
0
2
1
1
2
0
2
2
0
1
0
0
0
2
1
0
1
1
0
0
0
0
1
2
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
2
0
0
0
0
0
2
0
2
0
0
1
2
0
0
0
0
1
0
3
0
0
1
2
0
0
1
1
2
1
0
0
0
0
0
2
0
2
0
0
1
0
2
0
0
0
0
0
0
1
2
2
0
0
2
0
0
0
1
1
0
0
2
0
0
0
2
2
0
0
1
2
1
0
1
2
0
0
0
0
1
0
0
1
0
0
0
2
2
0
2
0
0
0
0
0
1
1
0
0
0
0
2
1
0
0
1
0
1
0
0
0
3
1
1
1
0
0
2
0
2
0
2
2
1
0
0
0
4
1
0
0
0
0
2
1
0
0
0
1
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
2
0
1
1
2
0
1
2
0
0
0
1
0
2
0
0
0
2
0
1
2
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
1
3
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
2
2
0
1
1
3
2
0
2
0
0
2
0
0
1
0
0
0
0
0
2
0
2
0
0
3
0
0
1
1
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
2
2
3
0
2
2
0
0
2
0
1
2
0
0
2
1
0
0
0
2
2
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
2
2
1
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
4
0
0
0
2
1
0
0
2
0
4
0
0
0
1
4
0
1
2
1
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
3
0
0
0
0
0
0
2
2
0
0
2
1
0
2
1
1
1
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
2
2
4
1
0
0
1
0
1
0
0
2
0
0
0
0
0
1
2
1
0
0
0
0
0
1
0
2
0
0
1
6
0
0
1
0
1
0
0
1
0
0
0
4
2
0
0
0
0
0
2
0
1
0
0
0
0
1
2
0
0
0
0
0
0
2
0
1
0
1
0
0
1
0
1
1
1
0
0
1
2
1
1
1
0
0
0
0
2
1
0
0
2
0
0
2
0
2
0
0
1
0
0
0
2
0
1
0
2
1
2
1
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
2
0
2
0
0
0
0
1
2
0
0
1
0
1
0
0
2
0
0
1
0
2
2
0
0
1
0
0
2
0
2
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
1
0
2
2
0
0
1
0
1
0
0
1
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
3
0
2
1
0
0
0
1
0
0
0
0
2
1
0
0
2
0
1
1
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
3
0
0
2
1
0
1
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
1
0
1
2
0
0
0
0
3
0
0
0
2
0
0
0
1
1
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
1
1
0
0
2
0
1
0
1
0
2
2
0
0
1
1
1
0
0
0
0
0
1
1
0
0
2
1
0
0
0
0
0
2
0
0
0
0
4
0
0
0
2
2
0
0
0
1
0
2
2
0
0
0
0
0
1
0
0
0
0
1
0
2
0
1
0
0
0
1
0
1
1
0
1
1
0
1
2
0
0
0
0
0
0
2
0
2
0
0
2
0
1
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
2
0
3
0
0
1
0
0
2
0
0
0
4
0
1
0
0
1
0
1
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
2
1
0
1
1
0
1
0
2
2
0
0
2
0
1
1
1
1
2
0
2
0
0
1
2
1
0
0
0
0
2
1
2
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
1
0
0
1
0
0
0
2
2
1
0
0
1
0
2
2
0
2
0
0
1
3
1
0
0
2
0
0
0
1
0
0
2
2
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
3
1
2
0
0
2
3
0
0
2
0
1
0
0
0
0
0
0
1
2
1
2
0
0
0
1
3
0
1
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
3
1
1
0
1
0
0
1
0
1
1
2
3
0
2
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
1
1
1
2
2
0
2
0
1
0
0
0
2
1
1
2
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
2
1
0
2
1
1
2
0
2
0
4
0
0
0
0
0
2
0
0
0
2
0
2
0
0
1
0
0
0
0
2
1
0
1
2
2
0
0
2
0
0
0
1
0
0
0
0
0
1
1
0
0
0
2
2
0
1
0
0
1
0
0
0
0
1
0
2
0
1
0
0
0
1
0
0
0
0
2
0
3
0
1
2
0
0
1
2
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
1
0
2
0
2
0
0
0
0
1
0
2
3
0
0
2
17
0
0
0
2
0
0
0
3
2
2
0
0
1
1
0
0
2
0
2
0
0
2
1
0
0
0
0
3
1
1
0
1
1
2
0
2
0
0
1
1
0
0
1
0
1
1
0
0
0
0
2
1
0
0
2
0
2
0
0
0
0
1
0
0
2
0
0
6
0
0
0
0
4
1
1
0
0
0
1
0
0
0
0
0
0
0
1
2
0
3
0
0
1
2
0
0
1
0
0
0
1
0
2
0
0
0
0
2
1
2
0
1
1
0
0
0
3
0
0
0
0
2
0
0
0
0
2
0
0
2
0
3
0
1
1
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
2
0
1
0
0
0
0
0
1
3
2
0
1
1
0
2
1
1
0
1
1
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
2
0
1
2
1
0
2
2
0
1
1
0
0
2
1
0
0
1
2
1
2
0
0
2
0
2
1
2
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
2
2
0
0
2
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
4
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
2
0
0
1
0
2
1
2
0
2
0
0
1
0
2
3
1
0
0
0
2
0
1
0
0
0
2
2
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
1
1
1
1
1
1
2
0
3
1
0
0
2
2
0
2
1
0
1
0
1
0
0
0
2
0
1
0
1
1
0
0
2
0
1
0
0
2
0
0
0
1
2
1
3
0
0
0
1
0
0
2
0
2
0
0
1
1
1
0
0
2
0
0
1
1
2
2
1
2
3
0
0
0
0
0
1
1
0
0
2
0
1
3
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
3
0
2
2
0
2
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
1
0
0
1
0
0
2
2
1
1
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
6
1
0
1
0
0
0
2
2
0
1
0
14
0
0
1
2
0
0
0
1
0
0
1
1
1
2
0
1
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
1
0
0
0
1
1
1
0
1
0
0
0
2
0
3
3
0
0
1
0
0
0
2
2
2
2
0
0
0
2
0
0
0
5
3
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
1
0
2
0
0
2
0
0
2
1
0
0
3
1
1
0
0
0
0
0
0
2
1
1
1
1
0
0
2
0
0
0
0
2
0
0
2
0
2
1
0
1
0
0
0
1
0
0
0
1
1
0
0
0
1
0
1
1
0
2
0
0
0
0
1
0
1
0
0
0
3
0
0
0
0
2
1
2
1
2
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
1
1
0
1
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
3
0
0
0
0
0
1
0
0
1
0
2
0
1
0
0
0
0
2
1
0
0
1
1
0
0
1
0
0
1
1
0
0
0
3
1
1
1
0
0
0
0
3
0
1
1
0
0
0
1
2
6
0
1
0
0
0
0
1
0
2
0
2
0
2
0
0
1
0
0
4
3
1
0
0
2
0
2
0
0
0
0
1
1
1
2
2
2
1
0
0
0
0
0
0
0
0
0
0
1
1
2
2
0
1
1
1
2
0
1
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
3
0
1
0
0
0
0
0
2
0
1
1
2
0
0
1
0
0
1
0
0
0
0
2
1
1
2
1
0
0
1
0
2
1
0
2
0
0
0
0
1
2
0
0
1
2
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
1
0
0
0
4
0
1
0
0
1
1
0
0
0
0
0
1
2
0
0
1
1
1
1
2
0
0
1
1
0
0
1
1
0
0
0
1
0
2
2
0
2
0
1
0
1
1
0
0
0
2
1
0
1
0
1
2
0
1
0
0
1
0
2
0
0
0
1
0
3
0
0
0
0
1
0
2
0
0
0
0
0
2
1
0
0
1
1
1
0
1
3
0
3
2
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
2
0
0
1
1
2
0
2
0
0
0
0
1
1
0
0
0
0
2
1
0
1
2
1
2
0
0
0
0
0
2
0
0
0
0
1
1
1
1
1
0
2
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
2
2
0
0
0
2
2
2
0
0
0
0
1
0
0
2
0
2
0
0
2
2
4
0
1
2
0
0
0
2
0
0
1
1
1
2
0
2
2
0
2
2
0
0
0
1
0
0
0
0
0
2
0
1
0
0
2
0
0
2
0
0
0
2
4
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
2
0
3
1
0
1
0
0
0
0
1
0
0
0
2
0
0
2
2
0
0
0
1
0
1
0
1
0
0
0
2
2
0
1
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
2
5
1
1
0
2
1
0
0
0
0
2
0
0
0
0
2
2
0
2
2
0
3
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
1
1
0
0
2
0
0
1
1
1
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
1
1
0
2
2
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
1
0
2
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
1
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
2
0
2
2
0
0
0
1
0
0
1
2
1
0
1
2
0
0
0
2
1
0
1
0
2
0
0
1
2
1
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
3
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
1
0
0
0
1
2
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
2
0
0
0
1
0
1
1
0
0
1
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
3
0
0
2
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
2
1
0
2
2
3
0
0
2
0
1
2
0
0
2
2
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
1
0
1
0
2
1
2
0
2
0
0
0
0
0
0
0
2
2
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
3
3
3
2
1
0
0
0
0
2
0
0
0
0
0
0
2
2
0
2
1
0
1
0
2
2
1
2
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
1
0
1
0
1
0
2
0
2
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
5
0
3
0
1
1
1
2
2
1
0
0
0
2
0
3
1
2
0
0
0
2
2
0
0
1
0
0
0
0
2
0
3
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
1
1
2
0
0
0
0
1
2
2
0
0
0
2
0
0
0
0
0
1
2
0
0
1
2
0
2
0
0
0
1
0
1
0
0
2
0
2
0
0
0
1
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
1
0
0
2
0
0
0
1
0
1
0
0
0
1
1
2
2
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
1
0
0
0
0
2
0
2
0
1
2
0
0
0
4
2
1
1
4
0
0
1
0
0
1
9
0
0
2
1
0
0
1
0
0
2
0
0
2
3
0
0
2
0
0
0
1
0
1
3
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
2
2
0
0
0
1
0
0
1
1
0
0
1
1
5
0
0
2
1
1
0
0
2
3
0
0
0
1
2
2
0
1
0
0
0
1
0
0
1
1
0
0
0
2
1
2
0
0
0
0
0
0
0
0
1
1
2
1
2
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
4
2
1
1
2
0
0
2
1
1
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
1
1
0
0
0
0
0
0
2
0
0
1
1
0
0
2
0
0
0
0
0
0
2
2
0
0
0
1
0
0
2
1
0
0
0
0
0
0
1
2
0
2
0
0
1
0
0
1
0
2
0
0
0
1
1
0
1
2
0
2
0
0
1
1
0
2
0
2
0
0
0
0
2
0
0
1
0
0
3
1
0
2
2
0
1
2
0
0
0
2
1
0
1
0
0
0
2
1
2
1
0
0
0
1
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
1
0
2
0
2
0
0
0
1
2
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
2
0
2
0
2
0
0
2
0
0
0
0
0
0
1
0
2
2
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
3
0
0
0
1
0
0
0
1
0
0
0
0
2
0
1
0
0
1
0
1
0
0
0
1
0
0
2
0
2
1
0
2
1
2
0
2
2
0
0
0
0
2
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
2
2
1
2
2
0
2
1
0
0
0
0
2
0
2
1
2
0
0
0
1
2
0
0
6
1
0
0
0
0
1
0
0
0
0
0
2
0
3
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
1
2
2
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
2
2
1
1
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
1
2
2
0
3
0
0
0
2
0
0
0
0
0
1
1
0
1
0
0
2
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
4
1
0
1
0
1
0
0
0
0
0
0
0
0
3
0
0
1
2
2
2
0
1
0
2
0
0
1
0
0
0
2
6
0
0
1
0
1
1
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
2
0
1
0
0
1
0
0
0
1
1
2
0
1
1
0
0
0
2
0
0
0
0
1
0
0
2
0
0
1
0
1
2
0
1
0
0
2
0
0
3
0
0
0
0
1
0
0
2
2
0
0
1
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
7
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
3
2
0
1
0
1
0
1
0
0
0
0
0
2
0
0
2
1
0
2
2
0
1
1
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
2
0
0
0
0
2
1
2
0
0
0
1
2
0
2
0
0
0
0
3
0
2
0
1
0
0
0
1
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
3
0
2
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
2
1
0
0
1
0
2
0
0
0
2
0
0
0
2
0
0
2
0
2
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
1
0
0
0
2
0
1
1
1
1
0
2
0
2
1
0
1
0
0
0
1
2
0
2
1
0
0
1
2
0
0
0
2
0
0
2
2
0
0
2
0
2
2
2
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
1
1
2
1
0
0
0
1
2
0
0
1
0
0
0
0
0
1
0
2
0
0
1
0
1
0
0
2
0
0
0
0
1
0
0
0
1
0
1
2
0
0
0
1
2
0
0
2
1
0
0
1
2
0
0
0
0
0
0
0
0
2
0
1
0
0
1
2
3
0
0
1
0
0
1
0
0
2
2
0
0
1
2
1
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
2
0
0
0
0
2
1
2
0
0
1
0
1
0
1
0
0
3
0
1
0
2
0
0
0
0
1
1
0
0
1
0
2
0
0
1
0
0
0
0
2
2
0
0
2
2
0
2
1
0
1
0
0
1
0
0
0
0
0
0
0
2
2
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
1
0
2
0
3
0
0
2
1
1
0
0
1
0
0
0
1
0
0
0
1
0
1
2
0
0
2
0
0
0
0
0
0
2
2
0
0
3
0
0
2
0
1
0
0
0
0
1
1
0
2
0
1
2
0
0
0
0
1
2
0
2
0
0
0
1
0
0
0
0
2
1
1
0
2
0
0
0
0
3
1
2
1
2
0
0
0
0
1
2
0
0
0
0
0
1
0
6
1
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
2
2
0
0
0
3
0
0
2
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
4
0
0
0
0
0
2
0
2
1
1
0
0
0
0
0
1
0
0
1
1
0
2
2
0
0
2
2
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
1
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
2
1
1
1
0
1
0
2
0
0
0
1
1
2
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
2
0
1
0
1
2
0
0
0
1
0
1
0
0
0
1
2
2
2
2
0
0
1
0
1
0
0
0
0
0
1
2
2
0
0
2
0
0
0
0
1
2
0
1
2
0
1
2
0
0
1
0
0
1
1
1
0
0
2
0
2
0
0
0
1
0
2
0
1
0
0
0
0
0
1
0
0
1
2
0
0
4
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
2
0
0
1
1
2
0
0
1
1
0
0
1
1
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
1
1
2
0
0
0
2
1
0
2
0
2
0
1
1
0
0
0
1
1
3
2
0
0
0
2
0
0
0
0
1
2
2
0
0
0
2
0
1
2
0
1
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
2
0
2
2
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
3
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
1
3
0
4
0
0
0
0
0
2
1
0
1
2
1
2
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
2
2
2
2
0
1
0
0
0
1
0
0
0
0
0
2
2
0
0
2
0
3
1
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
2
1
2
1
2
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
2
0
2
0
0
2
0
1
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
1
0
3
0
0
0
1
0
0
1
2
1
1
2
1
0
0
0
2
1
1
1
0
2
0
0
0
2
2
2
0
2
0
1
0
0
0
2
0
1
0
1
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
1
1
0
0
0
0
1
0
1
0
0
0
2
1
1
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
1
0
0
1
0
2
0
0
0
0
1
1
1
6
0
0
1
0
2
0
2
0
0
0
0
1
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
2
2
2
0
0
0
0
0
0
1
2
1
1
0
0
0
0
1
1
0
0
2
0
0
0
2
2
0
0
0
0
1
2
2
0
1
1
0
0
0
1
1
1
0
1
0
1
0
0
2
0
0
0
2
1
0
0
0
0
2
1
0
0
0
1
0
0
0
3
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
1
0
6
0
0
1
1
0
1
0
1
0
1
3
0
1
0
0
0
0
0
0
1
2
0
0
3
2
0
1
0
0
0
0
0
1
0
0
0
2
0
0
1
2
0
1
1
1
1
0
0
0
1
0
1
0
0
0
1
0
0
2
0
0
3
1
1
0
2
0
0
0
2
0
1
0
0
2
0
1
0
1
6
1
1
2
2
0
0
2
0
0
0
0
2
2
2
0
0
1
0
0
1
0
0
0
0
0
1
5
0
2
0
0
0
1
1
0
0
0
0
0
2
0
1
0
0
0
0
1
1
1
0
0
0
2
0
1
0
0
0
2
2
0
0
0
0
0
2
2
1
0
0
0
0
2
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
2
2
3
1
2
0
0
1
0
2
2
0
0
0
0
0
2
0
2
5
0
0
1
1
6
0
2
2
0
1
1
0
0
0
1
0
0
0
0
1
1
2
2
2
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
2
0
2
1
0
0
0
4
1
0
0
0
0
2
4
0
1
0
0
0
0
1
0
1
0
1
0
2
1
0
0
0
2
2
0
0
0
2
0
2
0
0
0
1
0
1
0
0
2
0
2
1
2
0
0
0
0
1
2
0
0
0
1
1
0
1
1
0
2
0
4
0
1
1
1
0
2
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
3
1
0
1
1
0
0
0
0
1
0
2
1
0
0
0
0
1
0
0
1
0
1
2
0
0
2
0
0
0
1
0
1
1
0
0
0
0
1
0
2
0
1
1
2
1
0
1
0
1
0
0
0
0
0
0
1
0
1
0
2
2
0
0
1
2
0
0
0
0
2
1
0
0
2
0
0
7
1
0
0
0
0
2
0
1
2
0
0
2
1
1
0
1
2
0
0
0
1
0
0
0
1
0
2
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
5
2
2
0
0
1
0
0
0
0
0
1
2
0
1
2
0
2
1
0
2
1
0
0
0
2
1
0
2
0
0
2
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
2
1
0
0
3
0
0
0
0
2
0
1
2
0
0
1
3
1
0
2
1
0
0
0
0
0
0
0
1
4
0
1
0
0
2
1
0
2
0
0
0
0
0
2
2
0
0
1
2
0
2
0
0
1
0
1
0
0
1
1
0
2
1
1
2
0
0
1
0
0
1
1
0
2
0
1
1
0
2
0
1
1
0
1
2
0
2
0
0
1
0
3
0
0
2
0
0
1
0
0
2
1
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
2
1
1
2
3
0
1
2
0
0
1
0
3
0
0
0
1
2
0
0
0
1
1
0
1
0
1
1
1
0
0
0
1
2
0
1
1
0
1
0
4
2
0
0
0
1
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
2
2
1
2
0
0
0
2
0
0
0
0
1
0
0
0
1
1
2
0
0
2
0
3
0
0
0
0
0
2
2
1
0
0
0
0
0
0
1
1
0
0
1
0
2
0
0
2
0
0
0
1
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
2
1
1
0
1
3
0
0
1
2
2
0
0
0
2
0
0
0
1
1
0
0
0
2
0
0
2
0
0
2
1
0
1
0
2
1
2
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
3
0
0
3
1
2
1
1
0
2
1
0
0
2
0
0
1
1
0
0
0
0
1
0
0
0
1
1
0
1
1
1
3
0
0
0
0
2
1
0
0
2
0
0
3
0
2
0
2
1
2
2
1
0
0
0
1
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
1
0
1
1
2
2
0
0
0
0
1
1
1
2
0
0
1
0
2
0
0
0
2
0
0
1
4
0
0
4
0
1
0
1
0
2
2
2
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
2
1
1
0
1
0
1
0
1
0
0
1
0
0
0
0
0
1
0
2
0
2
2
0
0
1
1
2
0
0
1
0
0
1
0
2
0
0
0
3
1
3
0
0
0
1
1
0
2
0
2
0
0
0
0
2
0
0
1
4
0
1
0
1
2
2
0
3
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
2
1
0
0
0
0
0
0
1
0
2
0
1
0
2
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
1
0
0
1
0
2
2
0
1
2
0
1
0
1
1
2
0
0
2
0
0
0
2
2
0
1
1
0
0
0
1
2
0
0
2
2
1
4
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
4
0
2
0
0
1
1
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
2
1
0
1
0
0
2
4
0
0
0
1
2
0
2
0
2
0
0
0
2
0
0
2
2
2
0
0
0
0
0
0
1
2
0
1
1
1
2
2
0
1
1
2
2
0
0
1
2
1
0
1
0
3
0
1
1
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
1
2
0
0
1
0
0
0
1
1
0
0
0
0
2
0
1
0
0
0
1
0
0
0
3
0
2
2
2
0
0
0
0
2
0
0
0
0
0
1
3
0
0
2
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
1
1
1
0
2
1
1
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
1
0
0
2
0
1
1
0
0
1
0
0
0
2
1
1
0
0
0
1
2
2
0
0
1
0
2
2
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
2
1
0
0
1
0
0
0
2
2
1
0
1
0
2
0
1
0
0
0
0
1
1
2
0
4
0
0
0
1
0
0
0
2
0
3
0
0
2
0
0
2
0
0
0
0
1
2
0
0
0
2
0
0
0
0
1
0
1
1
0
2
0
0
0
1
0
0
1
0
0
0
1
0
1
1
0
0
0
0
1
0
1
0
0
1
1
2
0
2
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
2
0
0
1
0
1
2
0
0
1
0
0
0
0
1
0
0
1
0
2
0
2
1
0
1
0
0
0
0
2
0
0
0
2
1
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
5
1
2
0
0
0
0
0
0
0
0
2
0
1
1
1
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
2
0
0
2
0
2
0
1
0
2
0
1
1
0
1
2
2
2
0
0
1
0
1
1
0
1
0
6
0
2
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
2
1
1
0
1
1
0
2
0
1
0
1
2
1
0
0
1
0
2
1
0
2
0
2
0
0
0
0
1
0
1
0
0
0
0
2
0
1
0
2
0
2
1
4
3
0
0
2
1
0
0
2
0
1
0
0
0
0
0
1
0
0
0
1
2
0
0
1
1
0
0
0
0
1
3
0
0
0
1
0
1
2
0
0
2
2
0
0
0
0
0
0
0
2
1
2
3
1
0
0
0
0
0
0
1
2
2
0
1
0
1
1
2
1
0
1
2
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
2
0
1
0
0
1
0
0
2
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
1
3
2
0
2
2
2
0
1
0
0
0
0
0
0
2
0
2
1
0
0
0
1
0
0
0
0
1
0
1
0
3
0
2
0
1
1
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
1
0
0
1
1
2
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
1
2
1
0
0
3
0
0
2
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
2
1
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
3
0
1
2
1
2
1
2
0
1
0
1
0
0
1
1
2
2
2
0
1
0
0
0
0
2
0
2
0
0
2
0
1
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
4
2
2
0
0
0
0
1
1
1
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
1
1
1
0
0
2
0
0
0
1
1
1
5
3
0
1
1
1
2
2
0
0
0
3
1
2
0
0
2
0
0
3
0
1
2
1
0
2
0
2
0
0
0
0
2
2
0
0
0
2
0
0
0
1
1
1
2
0
2
0
0
0
0
0
0
2
3
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
2
0
0
2
0
0
2
0
0
1
0
2
0
1
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
2
0
2
0
0
0
1
2
0
1
1
0
0
1
0
0
1
1
0
0
1
1
2
0
0
0
2
0
0
0
1
1
0
2
0
0
0
0
0
0
0
1
2
0
0
4
0
0
0
0
1
2
0
0
2
0
0
0
1
3
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
3
0
2
0
0
2
1
0
2
0
1
0
2
0
0
1
0
0
2
2
0
2
0
2
0
1
0
1
0
0
1
2
2
2
3
1
0
0
0
2
2
2
1
0
0
2
2
0
0
0
0
2
0
1
0
0
1
0
0
2
0
2
0
1
2
0
1
0
1
0
10
0
0
2
0
2
4
2
0
0
2
0
2
2
1
1
2
2
0
2
1
2
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
1
2
1
1
0
2
0
1
0
0
0
0
2
2
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
2
6
0
2
2
2
0
2
0
0
1
0
2
0
0
0
2
0
1
2
0
0
1
1
0
0
0
0
1
0
0
0
2
1
2
0
1
0
0
2
0
0
0
2
1
0
2
1
1
0
1
0
0
0
1
0
0
0
3
0
0
1
1
1
0
0
5
0
0
0
1
0
0
1
0
1
0
0
0
0
0
2
0
2
0
1
0
0
1
1
0
0
1
1
0
0
0
2
2
1
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
2
2
0
0
1
0
0
0
2
0
0
2
1
1
1
0
0
2
0
0
0
0
0
0
0
1
0
1
3
1
2
2
0
1
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
1
0
1
2
1
1
1
0
0
0
0
2
1
1
1
0
0
1
0
0
0
1
2
1
0
0
0
1
0
0
1
0
0
1
2
2
0
0
0
1
0
1
1
0
2
0
0
1
2
1
0
0
0
1
0
1
0
0
0
0
0
0
2
0
1
0
0
1
0
2
0
0
2
2
0
0
0
0
2
0
0
0
4
0
0
0
0
2
1
0
0
0
0
0
1
0
0
2
3
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
2
1
0
2
1
1
0
0
0
1
3
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
2
1
1
2
2
1
1
0
0
1
0
1
0
0
1
0
0
0
2
0
2
2
2
0
0
2
0
0
0
1
2
0
0
2
1
1
0
0
0
0
2
0
0
0
0
2
1
0
1
0
0
0
2
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
1
1
2
0
0
0
2
1
1
1
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
2
2
0
0
2
0
0
1
2
1
0
0
1
0
1
0
0
0
2
1
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
9
0
0
1
0
0
4
0
2
0
0
0
0
0
1
1
3
1
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
1
1
0
0
0
0
0
2
0
0
2
0
0
5
1
2
0
0
0
0
0
0
0
1
0
1
2
0
2
0
0
0
2
0
0
1
2
0
2
0
0
1
2
0
0
0
1
2
0
0
1
0
0
0
1
2
0
0
0
0
3
0
0
2
2
0
0
0
1
0
1
1
0
0
0
6
0
0
0
1
0
1
1
0
1
0
2
2
2
2
2
0
0
0
0
0
1
1
1
0
0
2
0
2
0
0
0
2
1
0
1
2
0
1
0
0
2
0
2
1
2
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
1
0
3
2
1
2
2
1
0
0
0
0
0
1
1
1
1
0
0
0
1
0
1
2
1
0
0
1
1
0
0
0
0
0
0
2
0
2
3
1
1
0
0
0
0
1
0
2
0
2
0
0
0
2
0
2
0
0
1
0
0
1
1
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
2
1
2
2
0
0
0
0
2
2
0
3
2
1
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
2
2
0
0
0
0
1
0
1
0
0
2
0
0
2
0
1
2
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
2
2
0
0
0
0
2
2
0
2
0
0
0
0
0
1
1
1
0
1
0
0
2
0
2
1
1
0
0
0
2
0
1
1
0
2
1
0
0
1
0
0
0
0
0
1
1
2
0
2
1
0
1
0
0
1
0
0
3
0
0
0
0
0
0
0
2
0
1
0
2
1
0
1
0
0
3
0
1
3
0
0
1
0
2
2
1
2
2
0
0
0
1
0
0
0
1
2
1
0
0
2
0
1
1
0
0
0
2
0
1
0
1
1
1
0
1
0
1
0
1
0
0
0
0
0
0
2
2
0
1
2
2
2
1
1
0
0
1
2
1
0
2
0
0
0
2
1
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
2
0
0
1
0
2
2
0
0
1
2
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
3
2
1
0
1
1
0
0
2
2
0
1
2
0
2
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
4
1
0
0
1
2
2
0
0
0
0
2
0
0
1
0
3
0
0
2
2
0
1
0
2
3
1
0
2
2
1
2
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
2
0
1
0
2
0
1
0
0
2
0
1
1
3
0
0
2
0
0
0
2
0
2
0
0
0
0
1
0
2
2
0
0
2
0
0
2
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
1
2
0
0
1
2
0
0
2
0
1
3
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
1
2
3
0
2
1
0
0
0
0
0
0
0
1
0
0
0
1
2
0
2
0
1
0
0
2
0
1
1
2
1
0
0
0
2
0
2
0
2
0
1
2
0
0
2
0
2
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
1
0
0
0
0
3
1
0
0
0
1
2
0
1
1
0
1
0
0
0
1
2
1
0
0
0
1
4
0
1
0
1
2
0
0
0
1
2
0
0
0
0
2
2
1
0
0
4
2
2
2
0
2
0
1
3
0
2
2
0
0
3
0
2
0
1
0
0
0
0
1
0
4
2
0
0
0
0
1
0
4
2
0
1
0
0
0
0
0
0
0
2
1
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
2
0
1
1
0
2
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
1
2
0
0
1
2
0
1
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
2
0
2
0
0
0
0
1
1
0
0
0
1
0
1
0
1
0
2
0
0
1
1
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
1
2
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
1
0
0
0
2
0
0
2
0
0
0
1
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
1
2
0
0
2
2
2
1
0
0
1
0
0
2
1
2
0
2
0
0
0
0
3
0
0
0
1
1
1
2
2
0
0
0
0
0
0
0
2
2
0
0
2
2
0
1
1
0
0
0
0
3
0
1
1
2
1
0
0
0
1
0
0
0
1
1
2
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
2
1
2
0
0
0
0
0
0
3
0
0
2
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
2
0
0
0
0
0
2
0
2
0
0
1
0
0
1
0
0
1
1
1
2
0
0
2
0
2
2
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
2
0
1
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
1
1
0
0
0
0
0
0
0
0
0
1
0
2
1
1
0
3
0
1
0
1
0
1
1
0
0
1
0
0
0
0
0
0
3
1
0
0
0
1
0
3
1
1
2
1
0
0
0
1
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
3
1
0
2
0
1
2
0
0
2
1
2
2
1
1
0
1
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
5
0
0
1
0
0
0
0
2
0
0
0
0
0
3
3
0
0
1
0
0
1
0
2
0
0
2
0
0
0
1
0
0
1
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
2
0
2
0
3
0
0
0
2
0
2
0
2
6
2
0
0
2
1
2
1
1
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
1
2
1
2
0
0
0
2
0
1
2
0
0
0
0
1
0
0
0
0
1
1
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
3
0
1
0
2
0
1
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
1
0
2
2
1
0
0
0
2
0
0
1
0
2
2
0
0
0
0
1
2
2
0
0
0
0
0
1
4
0
0
0
0
0
0
1
1
0
0
2
0
2
0
0
1
0
2
2
1
2
2
1
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
1
0
2
0
0
0
0
0
1
2
2
1
2
1
0
1
1
0
0
2
0
3
0
0
0
0
0
2
0
0
1
0
1
2
0
0
0
0
0
0
0
1
1
2
2
0
0
0
1
2
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
2
0
0
0
2
1
0
1
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
2
0
0
1
1
0
2
0
2
0
0
0
0
0
1
0
2
0
0
2
0
0
1
3
1
0
1
1
3
0
0
0
0
0
1
1
0
0
2
0
2
0
0
2
1
0
0
0
4
0
0
0
0
0
0
0
0
0
5
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
2
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
1
0
2
0
0
1
0
0
1
1
0
0
0
0
0
2
1
1
0
0
1
0
0
0
0
0
2
1
0
6
0
0
0
1
0
0
1
1
0
0
0
1
0
2
0
2
0
1
0
0
0
0
1
0
0
0
2
0
0
1
1
0
2
1
0
1
0
3
0
1
0
0
0
1
1
0
2
0
2
1
0
0
0
0
2
0
0
1
2
2
0
2
0
0
0
1
0
0
0
3
0
0
0
0
0
2
0
1
0
1
0
1
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
2
1
2
0
2
0
0
0
0
0
1
0
3
0
2
1
1
1
0
0
1
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
1
0
1
0
0
0
0
1
1
0
1
0
0
2
0
1
1
0
0
1
0
2
0
1
0
0
2
0
0
0
2
0
2
1
1
0
0
0
1
0
0
0
0
2
0
2
0
1
0
0
0
2
0
1
0
0
0
2
2
2
1
1
1
2
2
0
1
0
0
0
0
1
0
0
0
2
0
0
2
0
2
0
0
0
1
0
0
0
2
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
1
0
0
2
2
0
0
0
0
2
0
2
0
1
0
0
2
1
2
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
1
0
1
2
0
1
0
0
0
1
2
0
2
1
0
0
0
2
0
0
2
0
1
1
0
0
0
2
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
1
1
2
2
0
0
0
2
1
2
0
0
2
0
3
1
0
0
0
0
0
1
1
0
0
1
0
1
2
0
0
0
1
0
1
0
2
13
0
0
1
0
1
2
0
1
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
1
2
7
0
2
1
3
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
2
0
2
0
1
0
0
0
1
0
0
0
1
0
1
0
0
2
2
3
1
0
1
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
2
0
0
1
0
1
1
0
2
0
0
1
1
1
1
0
0
2
0
1
1
1
0
2
2
0
1
0
0
2
0
0
0
1
2
1
0
0
1
1
2
0
0
2
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
2
2
0
0
0
2
0
0
2
2
0
0
0
2
2
0
1
0
2
1
0
0
0
0
0
2
0
0
0
0
1
0
2
0
2
0
0
0
2
0
0
0
1
2
1
1
0
1
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
2
0
0
3
1
2
0
0
0
0
0
0
0
0
2
0
1
0
0
2
1
0
1
0
3
0
0
0
1
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
2
0
1
0
0
2
0
0
0
3
5
3
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
1
0
1
2
0
1
0
2
0
0
1
1
0
0
0
0
0
0
0
2
3
1
1
0
3
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
2
0
2
0
0
2
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
1
1
0
0
0
1
1
0
0
0
2
0
0
2
2
0
0
2
2
3
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
1
2
0
0
1
0
2
0
1
2
0
0
2
1
0
0
2
2
0
0
0
1
1
0
0
0
0
2
1
1
0
2
0
1
1
0
0
0
1
0
0
1
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
1
0
0
1
0
0
1
0
0
0
1
3
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
3
0
2
2
0
3
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
2
0
0
1
1
1
2
2
0
2
1
2
1
2
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
1
0
0
2
0
2
1
0
0
0
2
0
0
0
0
2
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
2
0
3
0
0
0
0
1
0
0
0
0
1
1
2
0
1
2
1
0
0
0
0
2
2
2
1
0
1
1
0
2
0
0
1
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
2
2
0
0
1
2
1
1
1
1
1
0
0
0
0
0
2
0
1
0
0
0
1
1
1
0
2
1
1
0
0
0
0
4
1
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
6
1
0
0
0
2
0
0
0
0
0
0
0
2
2
0
1
1
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
1
1
2
0
1
3
2
2
1
2
0
0
1
0
1
0
1
2
1
0
1
0
1
0
3
2
2
2
0
2
0
0
0
2
2
0
2
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
1
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
4
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
1
0
1
0
0
2
0
0
0
0
2
1
0
2
2
2
0
0
0
2
0
1
0
0
1
0
1
0
1
2
0
0
0
2
0
1
0
1
0
2
0
0
1
0
1
2
0
0
0
0
1
0
0
0
0
2
1
0
0
1
0
0
0
0
0
2
2
0
0
2
0
2
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
2
0
0
2
0
1
2
0
1
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
2
1
1
1
1
0
2
0
0
1
1
2
2
0
2
0
2
1
0
1
0
0
2
0
2
1
0
0
4
0
0
1
0
0
2
0
4
0
0
0
2
0
2
0
1
0
2
0
0
1
1
0
0
4
1
1
0
0
2
1
2
0
0
0
0
1
0
1
1
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
3
0
1
0
2
0
0
0
1
2
0
1
2
0
0
0
1
0
0
2
0
0
0
1
2
0
1
0
0
0
2
1
0
0
0
0
1
0
1
0
0
0
0
1
2
2
0
0
1
2
0
0
0
0
3
0
2
0
2
0
1
0
2
2
0
0
0
0
3
0
0
1
0
0
0
0
0
1
0
0
1
3
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
1
1
0
0
0
0
0
2
0
0
1
0
0
1
0
0
2
0
0
0
0
2
3
1
1
0
1
0
0
4
0
3
0
1
0
0
0
0
0
0
1
2
0
1
1
1
2
2
0
0
2
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
2
0
2
0
0
2
1
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
2
1
0
1
2
0
0
1
0
0
0
0
0
1
1
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
2
1
2
1
2
0
0
1
0
2
2
1
0
0
1
2
0
2
0
0
0
1
0
2
0
0
2
1
0
0
0
1
0
0
2
0
1
0
0
1
2
0
1
0
0
0
1
0
0
0
0
0
0
1
0
2
0
1
0
0
0
2
0
0
1
0
0
0
2
2
1
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
1
2
1
0
4
0
0
0
2
1
0
1
0
0
0
0
0
1
2
1
0
0
2
0
0
1
0
1
0
0
0
0
1
2
0
0
3
0
2
0
0
0
0
2
0
0
0
1
0
1
0
2
0
0
0
0
0
1
0
2
0
0
1
0
1
0
0
1
0
0
1
0
2
0
0
3
0
1
0
0
2
1
0
0
1
1
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
1
0
2
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
1
0
1
2
2
0
0
1
1
1
0
0
0
2
1
0
0
0
0
0
0
0
1
0
1
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
1
0
1
2
2
1
1
0
1
1
0
0
0
0
2
0
0
0
0
0
1
1
2
0
0
0
0
2
1
0
0
0
1
0
0
3
1
0
0
0
0
0
0
1
1
2
0
0
1
2
0
1
1
1
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
2
2
1
0
0
0
2
0
0
0
0
0
2
0
0
1
2
0
0
0
1
0
0
0
2
1
0
1
1
0
1
1
1
0
1
3
2
0
3
1
2
0
0
1
0
0
2
0
0
1
2
0
0
0
0
1
0
2
0
0
1
0
0
0
2
1
0
0
2
0
1
0
0
2
2
0
2
1
0
0
0
2
0
0
2
1
0
1
2
2
3
0
0
0
0
0
2
0
1
0
0
1
0
0
0
1
0
1
3
0
1
0
1
0
0
0
0
1
0
1
1
0
0
1
1
0
0
0
0
2
0
2
0
0
1
2
2
2
0
0
0
0
2
0
0
1
0
0
0
3
2
0
2
0
1
0
0
3
2
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
2
0
1
2
0
0
1
2
0
2
1
1
0
0
2
2
0
0
0
0
2
0
0
0
1
0
0
3
1
0
2
0
1
0
1
1
1
2
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
1
2
1
1
0
0
1
2
1
0
0
0
1
1
0
1
0
3
2
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
2
0
1
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
1
1
0
0
2
2
0
0
1
1
0
0
0
1
0
0
0
2
2
0
2
0
4
4
0
0
2
1
1
2
3
1
0
0
0
0
0
0
0
1
0
1
1
1
2
2
0
2
0
4
0
2
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
2
1
1
0
2
0
3
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
1
0
0
0
0
0
0
2
0
0
1
0
0
2
2
1
0
1
0
2
0
2
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
1
1
0
2
0
0
2
1
0
2
2
1
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
2
0
0
2
0
0
0
0
0
1
0
0
2
0
1
0
0
5
0
2
0
3
0
2
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
1
0
3
1
1
1
0
0
1
1
0
0
1
0
0
1
2
0
0
0
0
1
0
2
0
0
0
2
2
0
0
0
0
2
0
0
0
0
1
0
1
0
1
1
0
7
1
2
0
0
0
1
0
0
0
0
2
0
2
0
2
0
1
1
0
2
3
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
3
1
0
2
0
1
0
1
1
0
0
0
1
0
0
3
0
0
0
0
0
1
1
2
6
0
0
2
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
1
0
1
1
0
2
2
1
2
0
4
2
0
0
0
1
2
3
2
0
0
3
0
0
3
1
0
2
1
2
0
1
0
1
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
1
0
2
0
2
0
6
0
1
0
0
0
0
2
0
0
2
0
0
2
1
1
2
3
2
0
0
0
0
0
1
0
0
3
1
0
0
2
0
0
1
0
0
0
2
0
2
0
3
0
0
1
0
4
0
2
0
2
0
1
0
0
0
0
0
0
0
1
2
0
2
0
0
2
2
3
0
1
0
0
0
0
0
0
0
0
3
0
0
2
2
1
0
0
0
0
2
2
1
0
1
0
2
1
0
0
1
0
0
0
0
0
0
2
0
0
2
2
0
1
1
0
0
0
0
1
0
0
2
2
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
2
2
0
0
0
0
2
0
0
0
0
0
1
1
0
2
0
3
1
0
1
0
2
1
2
1
0
2
1
0
0
2
0
2
2
1
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
2
2
2
1
0
1
0
0
1
0
0
0
0
2
0
0
0
0
1
1
3
0
0
1
0
0
1
0
0
0
1
2
0
0
0
1
0
0
1
0
0
1
1
0
1
1
0
1
1
1
1
0
0
2
0
0
0
0
0
1
0
1
2
0
1
0
0
0
0
0
3
2
0
0
0
2
0
0
0
0
1
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
1
2
0
1
0
1
0
0
1
2
0
0
0
0
2
0
1
2
2
1
1
0
2
0
0
1
0
0
0
0
0
2
2
0
0
0
2
0
1
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
3
2
0
1
1
2
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
1
2
0
0
1
0
2
0
2
1
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
1
0
1
0
1
0
3
2
0
0
0
0
1
0
0
1
0
0
1
0
1
2
0
0
0
1
1
0
0
0
2
0
0
1
0
0
2
0
0
2
0
0
2
3
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
3
0
2
0
2
0
0
0
0
0
0
0
0
1
1
0
1
0
0
2
1
2
0
0
0
0
0
0
0
1
2
1
0
1
2
2
2
0
0
0
2
2
1
0
0
0
0
2
1
0
0
1
0
0
2
0
1
0
1
0
0
0
0
2
0
2
1
1
0
1
0
3
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
2
1
0
0
0
1
3
2
0
0
1
0
2
2
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
3
0
0
2
1
0
2
0
0
0
0
0
0
1
1
1
0
1
0
2
2
0
0
2
0
0
0
3
1
1
0
0
0
2
0
1
1
0
0
2
2
0
1
2
0
3
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
1
0
1
0
0
2
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
2
0
1
1
2
0
0
1
3
0
0
3
2
2
0
2
0
2
2
1
0
1
1
2
0
3
0
2
0
2
0
1
0
0
2
1
0
0
1
2
0
2
0
0
0
1
2
2
0
2
0
2
4
0
1
0
0
2
0
0
0
0
3
0
0
0
0
2
1
0
1
0
1
0
1
1
2
0
0
1
0
1
0
0
0
2
0
2
1
0
0
0
1
2
4
2
0
0
1
0
1
2
1
1
0
2
0
1
1
0
0
0
0
0
0
0
0
6
0
0
2
0
2
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
2
0
1
4
0
0
0
0
0
0
0
1
0
2
2
0
0
1
0
2
0
1
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
3
0
0
0
1
1
1
1
1
0
1
0
1
2
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
2
1
2
0
0
1
0
0
0
0
1
2
0
2
0
1
0
1
2
0
1
0
2
0
0
1
1
2
3
0
2
1
1
1
0
0
0
1
1
0
3
2
2
0
0
0
0
2
2
0
0
2
0
1
0
3
0
0
0
0
2
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
1
0
1
1
1
0
0
0
2
2
0
0
0
1
2
0
2
2
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
2
0
0
0
0
1
1
1
2
0
1
2
0
2
0
0
0
2
2
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
2
0
0
0
1
0
0
0
1
2
0
0
1
0
2
1
2
0
0
0
1
1
0
2
0
0
1
2
3
0
0
1
1
0
0
0
1
0
0
0
2
0
0
1
2
0
0
1
3
0
2
2
1
0
0
0
3
2
0
0
3
2
0
1
0
2
0
0
0
0
0
1
0
2
0
2
0
0
2
1
0
2
0
0
0
0
2
2
1
2
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
1
0
2
0
0
0
2
0
2
0
0
1
0
1
1
2
0
2
0
0
1
0
0
1
0
1
0
0
0
1
0
0
1
1
0
0
2
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
1
0
2
0
0
0
1
0
2
0
1
0
0
0
1
0
0
2
0
0
0
0
0
2
1
0
2
0
0
1
1
2
2
0
0
0
2
0
0
0
1
1
0
2
0
2
0
1
2
0
2
0
1
0
1
0
0
0
1
1
0
0
3
0
1
0
0
2
1
2
0
0
0
0
1
3
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
1
2
0
1
0
0
0
1
0
0
1
0
1
0
0
1
0
2
0
1
0
1
0
0
2
0
0
2
2
0
0
0
0
0
1
2
0
0
0
0
0
0
1
2
3
2
1
0
1
2
0
0
0
0
1
2
1
0
0
0
0
1
2
0
0
1
0
0
2
0
0
1
2
1
3
0
3
0
1
2
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
2
0
0
1
1
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
1
0
0
2
0
2
1
0
0
0
0
2
2
0
0
0
2
2
0
0
0
2
1
1
0
1
1
0
0
2
0
1
1
1
1
1
0
1
0
2
1
0
2
1
1
2
0
0
0
0
0
2
2
0
1
0
1
2
0
0
2
1
1
0
1
1
2
0
0
1
0
1
1
2
0
2
0
1
0
0
0
0
1
2
0
0
2
0
1
0
2
0
1
1
1
2
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
1
0
0
2
7
0
0
2
0
0
0
0
0
0
0
2
1
0
1
2
0
0
1
0
0
0
0
2
1
1
0
1
2
0
0
0
0
1
2
0
0
1
1
0
1
2
1
0
0
0
1
0
0
0
0
0
2
2
1
2
0
1
1
1
1
0
1
2
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
2
2
2
0
0
0
0
0
1
0
2
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
1
0
2
0
1
2
0
0
0
2
0
1
2
0
1
2
0
2
0
1
0
0
0
0
0
0
0
2
0
0
2
2
0
2
0
2
0
0
1
0
0
0
0
0
2
0
0
1
0
1
0
0
1
0
1
1
0
0
1
0
1
0
0
1
2
1
2
0
0
1
2
0
1
2
0
0
0
2
0
0
1
0
0
2
0
0
2
0
2
2
0
1
0
1
1
2
0
0
2
2
2
1
0
2
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
1
0
0
2
1
1
1
0
0
3
0
0
0
2
1
2
1
0
3
0
2
1
1
0
0
0
0
0
0
1
0
0
0
0
2
0
1
1
0
0
0
2
0
1
0
2
2
4
0
0
0
2
2
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
2
0
2
0
0
1
0
1
1
0
0
0
0
0
0
2
1
2
2
2
0
1
1
0
0
0
0
2
0
3
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
1
3
1
0
2
0
5
0
1
2
1
1
1
0
0
0
0
1
0
2
2
0
1
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
11
0
0
0
1
2
0
0
2
0
0
0
6
0
0
0
2
0
1
2
0
2
2
0
0
2
1
1
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
2
2
0
1
0
2
0
0
1
0
2
0
2
2
1
0
0
2
0
0
0
1
2
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
2
0
2
0
3
1
0
0
0
1
1
1
1
3
0
0
0
0
1
0
3
0
0
1
0
3
0
0
3
0
0
0
1
0
8
0
0
1
0
3
0
0
0
0
0
0
2
0
0
1
0
0
1
0
2
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
1
0
0
2
0
1
0
2
1
1
0
0
0
0
3
0
0
1
0
0
1
1
0
0
0
0
0
2
0
0
1
0
0
1
1
0
0
1
1
0
2
0
0
2
0
0
1
0
0
1
0
0
0
1
0
0
1
2
0
0
0
0
1
0
2
0
0
2
1
0
0
0
0
0
2
0
0
2
0
0
1
1
0
1
1
0
0
0
0
0
2
0
0
0
1
1
0
0
1
1
0
1
0
2
0
0
0
1
1
1
0
0
0
2
0
0
0
0
1
1
0
0
1
1
0
1
0
0
0
0
0
3
2
0
0
2
3
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
2
1
0
3
0
0
0
0
1
2
0
0
2
2
0
0
2
3
0
2
0
0
2
0
2
0
0
0
2
2
2
0
0
0
2
1
0
1
2
0
3
1
0
1
0
0
0
2
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
2
0
2
1
0
2
0
1
2
0
0
2
2
1
1
1
1
1
0
0
1
1
0
0
1
0
1
0
2
2
0
2
0
0
0
0
0
0
3
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
4
0
2
0
0
0
2
0
0
1
0
0
0
2
2
0
1
2
0
2
0
0
0
0
0
2
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
1
0
2
3
0
0
0
0
2
0
0
1
0
1
0
0
0
1
0
2
1
0
0
0
2
0
1
0
1
2
0
2
2
0
0
2
0
0
1
0
0
0
2
2
3
2
0
1
0
0
0
1
2
0
2
1
0
0
0
0
1
0
0
1
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
3
0
2
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
3
4
0
2
0
2
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
1
0
0
2
1
0
2
0
0
0
1
0
1
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
2
6
1
1
0
2
0
0
0
2
2
0
4
0
2
0
1
2
2
1
0
1
1
1
0
0
1
0
0
0
1
0
2
0
2
0
0
0
2
0
2
0
0
0
0
0
1
0
1
0
0
0
2
2
1
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
4
4
0
0
1
0
0
0
2
0
0
2
0
0
1
1
0
1
0
2
2
0
1
0
0
0
0
1
0
1
0
0
1
0
2
0
1
0
0
2
1
0
1
0
0
1
2
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
1
2
0
1
1
2
0
2
2
0
0
0
1
0
1
0
1
0
0
0
0
0
4
0
0
0
0
3
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
1
1
0
2
1
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
3
0
5
0
0
0
1
1
0
0
1
2
0
0
2
2
1
2
2
1
1
1
1
0
0
0
0
1
0
0
2
0
2
0
2
0
0
1
0
0
0
0
0
1
0
1
3
0
2
2
0
2
2
0
1
1
1
2
1
1
0
3
0
0
0
0
0
3
2
1
0
2
0
0
0
0
2
1
0
0
0
0
0
1
0
2
0
2
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
2
0
0
1
2
2
1
0
2
1
0
2
2
0
1
1
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
2
0
0
0
3
0
1
0
0
0
2
1
0
3
2
0
2
1
0
2
0
0
2
1
1
0
1
1
2
0
0
0
0
2
2
1
0
0
0
0
0
2
0
0
0
0
0
3
1
0
0
0
0
0
1
0
0
0
1
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
2
1
0
0
1
2
2
1
0
0
1
0
0
1
0
2
0
2
0
0
0
2
2
0
0
0
0
2
2
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
2
2
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
1
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
1
6
0
0
4
0
0
5
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
1
0
1
1
0
0
0
2
2
2
0
1
0
1
0
0
0
1
5
0
1
0
0
0
2
0
0
0
0
0
1
0
0
1
2
0
0
0
1
0
0
2
1
1
0
0
0
3
3
0
0
2
0
1
0
1
2
2
0
1
1
1
0
0
0
0
0
2
0
1
7
2
2
0
0
1
2
0
0
0
2
2
1
0
2
0
3
0
1
1
0
2
2
0
5
0
1
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
1
1
0
2
2
1
1
2
0
0
3
3
1
2
0
0
2
2
0
0
0
0
0
0
3
2
1
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
2
0
2
0
0
0
1
3
0
1
0
0
1
0
1
0
0
0
0
0
2
1
1
0
0
0
0
2
4
0
0
1
1
0
0
1
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
1
0
2
2
1
0
0
0
0
11
0
1
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
2
0
0
2
0
0
1
1
0
2
2
2
1
1
3
0
1
0
2
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
1
1
2
1
0
3
0
1
0
0
1
2
0
0
1
0
1
1
1
0
0
0
0
0
1
0
0
1
0
0
2
0
0
1
0
0
0
2
0
4
2
0
0
1
0
0
3
0
1
0
0
1
0
2
0
2
0
1
0
0
0
0
2
1
1
2
0
0
0
0
0
1
1
2
0
0
0
1
1
1
0
1
3
3
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
1
0
1
2
2
3
2
0
2
0
0
1
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
1
0
0
2
0
0
1
1
1
2
2
0
2
0
0
0
2
2
1
0
1
2
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
2
2
5
0
0
0
0
1
2
0
0
0
0
0
2
1
0
0
1
0
7
0
0
1
0
2
1
0
0
0
0
0
0
1
0
0
1
2
0
2
0
1
0
0
0
0
0
1
2
0
0
0
1
0
1
2
0
0
2
0
1
0
2
0
0
1
2
0
1
0
1
1
2
0
1
1
0
1
2
1
0
0
1
0
0
1
0
0
0
0
0
2
0
0
2
0
0
1
4
2
0
0
1
2
1
2
1
0
3
0
1
1
0
0
0
0
0
0
0
1
2
0
0
1
0
0
1
0
1
1
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
1
2
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
2
0
0
0
0
2
0
0
0
2
1
0
0
0
2
0
0
0
0
1
0
0
2
1
1
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
1
2
1
0
0
0
0
1
1
2
0
0
2
2
2
1
1
1
1
2
0
2
1
0
1
0
0
0
0
1
1
0
1
0
0
1
3
2
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
1
1
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
1
0
2
1
0
0
0
2
1
2
2
0
1
0
0
0
0
2
1
2
2
0
0
2
0
0
2
2
2
1
0
0
0
0
0
0
0
1
2
0
0
2
2
0
2
0
2
0
0
2
0
0
1
2
2
0
2
0
0
0
1
0
1
0
0
1
1
0
1
2
0
0
0
0
3
0
0
2
0
2
1
0
0
1
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
2
2
1
0
1
0
1
0
0
0
0
0
0
0
1
3
1
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
3
0
0
1
0
0
0
2
0
0
2
0
0
0
0
1
0
2
1
0
0
1
2
0
0
0
0
0
2
0
0
1
1
0
0
0
1
0
0
0
0
3
1
2
0
0
0
7
1
1
2
1
1
0
2
0
0
0
0
0
0
0
2
2
3
3
1
0
2
0
0
0
0
0
2
0
2
0
0
2
3
1
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
1
1
0
0
0
0
1
0
2
2
0
0
0
2
1
1
0
0
0
0
0
2
0
0
1
0
0
0
1
0
1
2
1
0
1
1
2
0
0
2
0
0
0
0
0
0
1
2
1
1
1
0
0
0
0
0
0
0
0
1
0
1
2
2
0
0
0
0
0
1
2
2
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
2
0
1
0
0
2
1
2
1
0
2
3
0
0
0
0
1
0
2
0
0
0
1
1
1
0
0
1
0
0
0
1
0
0
0
1
0
0
1
3
1
0
0
0
1
0
0
1
1
0
2
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
1
0
0
1
1
2
0
0
2
2
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
2
1
2
3
1
0
1
2
0
0
0
1
2
2
0
0
0
0
0
0
0
2
0
1
0
0
2
1
2
0
0
2
1
0
2
0
0
0
0
0
0
2
2
0
0
0
2
2
1
1
0
0
0
2
0
0
0
2
1
2
0
3
0
0
2
1
0
0
1
0
1
1
1
1
0
0
0
1
1
0
1
3
2
0
0
0
0
0
0
0
2
1
0
0
0
0
1
1
0
4
0
2
2
0
9
0
1
2
1
2
0
0
0
2
0
0
0
2
0
0
2
0
2
0
2
1
0
2
0
2
1
2
2
0
1
0
1
0
0
2
2
2
0
3
0
2
0
0
2
2
2
0
2
4
2
0
2
1
0
0
1
0
2
0
0
0
0
2
2
1
1
0
1
1
0
1
0
0
0
0
1
2
2
0
0
0
0
0
0
1
3
1
1
0
0
0
2
0
0
2
0
0
0
0
0
1
2
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
5
0
2
0
1
0
0
0
1
0
1
0
0
0
0
11
0
0
0
1
0
2
1
0
2
1
2
1
1
2
0
1
1
1
1
0
0
2
1
0
2
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
2
0
2
2
2
1
1
0
2
1
2
0
1
0
0
1
0
1
0
1
0
2
1
0
0
0
0
1
2
0
1
0
1
1
0
2
2
1
1
1
0
2
1
0
1
0
1
2
1
1
0
0
2
0
2
1
0
0
1
0
1
0
0
0
0
1
0
0
0
2
0
2
0
0
1
2
0
2
1
2
1
0
0
2
1
0
2
0
0
1
4
0
0
0
2
0
0
0
0
0
0
2
2
0
0
1
0
2
1
0
0
2
0
2
2
0
0
1
0
1
1
0
0
1
0
0
0
0
1
2
0
2
0
1
0
1
2
1
0
0
2
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
2
2
0
0
1
1
2
0
2
0
1
0
2
0
1
2
1
0
0
2
0
0
1
0
1
0
0
0
0
0
0
5
2
0
0
0
1
0
0
0
0
0
1
0
1
1
0
2
2
1
1
0
0
0
1
3
1
1
2
2
1
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
1
1
0
1
2
2
0
1
0
0
2
1
1
0
2
1
3
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
1
0
2
0
1
0
1
0
0
0
2
1
0
1
0
1
0
0
2
0
2
1
0
0
2
1
2
0
0
2
0
2
0
0
0
2
1
0
0
0
0
2
0
0
0
2
0
0
2
0
0
1
0
0
2
0
0
1
1
1
0
1
1
0
0
2
1
0
1
0
2
2
0
0
0
0
0
0
0
1
1
0
0
0
0
1
2
0
1
1
0
0
0
2
0
0
1
0
0
2
0
0
0
1
0
10
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
1
0
1
0
0
2
1
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
2
0
0
2
0
2
1
2
2
2
0
1
0
0
0
0
1
2
1
0
0
0
2
0
2
0
2
1
0
0
0
4
0
0
1
2
0
3
2
0
1
2
1
0
3
0
1
2
2
0
0
0
0
0
1
2
0
0
0
0
0
1
1
1
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
1
1
1
0
0
0
0
0
1
0
0
1
1
0
5
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
1
0
1
0
0
3
0
0
0
2
1
0
0
0
0
0
0
3
0
0
0
2
0
0
0
1
0
1
2
2
1
1
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
1
0
1
0
2
0
0
0
1
0
0
0
1
0
0
1
0
0
2
0
0
1
0
0
0
0
1
1
1
2
0
0
1
2
2
1
2
0
1
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
1
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
3
1
0
1
0
2
0
0
0
0
0
2
0
2
2
1
1
1
0
0
2
0
2
0
0
2
1
1
1
1
1
0
0
2
1
0
0
0
0
0
0
2
0
2
2
0
0
1
0
0
2
0
0
0
0
0
1
0
1
0
0
2
0
1
0
2
0
0
0
2
0
0
0
1
0
0
0
2
0
3
1
1
0
0
0
2
1
2
0
0
2
0
0
1
1
0
0
4
0
0
1
1
0
0
1
0
2
0
1
1
0
1
1
0
0
0
0
0
2
0
1
0
1
1
1
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
2
0
1
1
1
2
0
1
0
2
0
2
0
1
1
0
0
0
1
1
0
2
1
1
0
0
1
0
0
1
0
0
0
0
2
1
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
1
2
0
1
1
0
0
1
1
1
1
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
1
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
2
1
0
0
0
1
1
0
0
1
0
0
1
2
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
2
0
0
2
2
0
0
0
0
0
2
0
0
0
1
0
2
2
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
2
1
0
2
0
1
0
0
0
0
1
3
2
0
2
0
2
0
0
1
0
0
0
1
2
0
0
2
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
2
2
0
2
0
0
0
2
2
0
1
0
0
0
0
0
0
1
1
0
2
2
0
0
1
2
2
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
1
0
2
0
0
2
1
0
0
0
1
2
0
0
0
0
2
0
0
0
2
0
0
1
0
0
2
2
0
1
0
2
1
0
0
0
0
2
2
0
1
0
0
1
2
2
2
1
2
0
1
0
0
0
1
0
0
2
0
2
0
2
0
0
1
0
0
1
1
0
0
1
0
0
2
0
2
0
1
2
0
0
0
1
0
2
2
1
0
0
1
1
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
1
0
1
2
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
2
2
1
0
2
0
0
1
0
3
1
1
0
1
0
1
0
0
0
0
1
0
0
2
1
2
1
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
2
2
0
0
0
1
1
0
0
0
0
0
0
1
2
1
2
0
1
1
1
0
0
0
0
2
2
0
0
1
2
1
1
1
0
0
0
0
0
0
1
3
1
0
1
1
0
2
3
3
0
0
2
2
0
1
0
3
0
0
0
0
0
0
2
0
0
0
0
1
3
1
1
0
0
2
0
0
2
1
1
0
1
0
0
1
2
0
3
0
0
1
0
1
2
0
3
1
0
2
0
2
3
2
2
0
0
2
0
0
2
0
2
1
1
0
3
0
0
2
1
0
0
0
0
1
0
0
2
2
0
0
0
1
0
1
1
2
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
6
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
2
2
0
0
0
0
1
0
0
2
2
0
0
0
0
1
2
2
0
2
2
0
0
2
1
3
0
0
1
0
0
1
1
2
1
2
0
0
1
0
0
0
0
0
2
1
1
1
0
2
0
1
0
2
1
0
1
1
0
0
2
1
2
0
1
0
2
0
0
1
1
2
2
2
1
1
1
0
3
1
3
1
1
0
0
0
1
1
1
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
2
0
0
0
0
2
0
0
2
0
2
0
1
0
3
2
0
0
0
0
0
2
0
0
0
2
2
2
0
0
0
1
0
2
3
0
2
0
0
0
0
1
0
0
1
1
1
2
0
1
0
1
1
0
0
0
2
0
0
0
2
0
0
2
0
2
0
2
0
1
1
0
1
0
2
1
1
0
2
0
0
0
1
0
0
0
1
0
0
5
0
0
0
2
0
1
1
0
0
0
0
0
1
2
0
0
1
0
1
0
2
1
1
0
2
2
0
0
3
0
1
0
2
0
0
0
0
0
0
2
1
0
3
1
0
0
1
1
0
0
1
1
0
0
0
0
1
0
0
2
0
0
2
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
2
1
1
0
1
2
2
1
2
0
0
0
2
1
0
0
0
1
1
0
2
0
0
0
0
0
2
1
0
1
0
0
2
0
0
0
0
0
0
0
1
0
2
1
1
0
1
1
0
0
0
1
1
3
1
1
1
1
0
2
0
2
0
0
1
2
0
2
0
1
0
1
0
0
0
2
0
0
1
2
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
2
1
2
0
0
0
0
2
2
1
0
0
1
1
2
2
0
0
0
1
0
0
0
0
2
2
0
0
2
0
2
0
0
1
0
0
1
0
1
1
0
0
3
1
0
1
0
0
0
0
0
0
2
0
2
0
2
1
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
1
0
0
1
5
0
0
2
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
2
1
1
0
0
1
0
1
0
0
2
2
2
0
1
0
0
3
3
0
1
2
0
0
3
0
2
0
1
1
1
0
0
0
1
0
2
2
1
1
0
0
0
0
0
2
0
1
1
1
0
0
2
2
1
0
2
2
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
3
2
2
2
1
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
2
3
0
0
0
0
1
2
1
0
0
1
0
1
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
2
0
1
2
1
2
0
2
0
2
1
0
2
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
1
0
2
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
5
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
1
0
0
2
1
0
0
0
0
2
0
0
0
0
0
1
1
1
0
0
0
1
0
0
2
2
0
1
0
0
2
1
0
0
0
0
2
0
0
0
1
0
0
0
0
1
1
0
2
0
0
1
2
0
2
0
2
1
1
0
1
1
0
2
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
3
0
0
0
0
0
3
1
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
2
2
0
0
0
1
0
0
0
0
2
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
2
0
0
0
0
1
2
0
0
2
0
0
1
2
0
0
0
0
1
2
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
1
2
1
0
1
0
0
2
0
0
1
0
1
0
0
2
0
0
0
2
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
3
2
0
2
1
2
0
1
0
1
0
2
0
1
0
2
0
1
2
0
0
0
0
0
0
2
0
1
1
2
2
2
0
0
0
1
0
1
0
2
0
1
1
0
0
1
0
0
0
0
0
1
1
3
0
0
2
0
0
0
1
0
0
0
0
2
0
0
2
0
1
0
2
0
0
0
2
1
0
0
0
2
1
0
3
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
2
1
1
2
0
0
0
1
0
0
0
0
0
0
1
2
0
1
0
1
0
2
0
0
2
1
0
2
1
1
2
1
0
0
1
0
2
2
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
2
3
0
0
0
1
0
0
1
1
0
0
1
0
0
1
0
0
2
1
2
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
1
0
1
0
2
0
3
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
3
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
1
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
2
2
0
1
0
1
0
1
2
2
0
0
2
1
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
1
2
0
2
1
1
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
2
3
2
0
0
1
2
2
0
0
0
0
1
0
0
2
2
0
2
0
0
1
2
0
0
2
0
0
2
1
1
0
0
0
0
0
1
0
0
2
1
0
0
0
0
1
0
0
2
1
0
1
2
0
1
0
0
2
1
0
0
0
0
0
0
4
0
0
1
0
2
0
1
2
1
1
0
1
0
1
0
0
0
1
0
0
0
0
1
0
1
0
1
2
0
1
0
0
2
2
0
2
0
0
0
0
0
1
2
0
1
0
1
1
1
1
0
1
0
0
3
0
0
1
0
2
2
0
2
0
1
4
0
0
0
2
1
0
0
5
2
0
0
0
1
0
0
1
1
0
0
2
0
2
0
0
7
2
2
0
1
0
0
2
0
0
2
1
3
3
0
0
0
0
0
2
0
0
1
0
0
2
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
2
0
0
1
1
1
0
0
0
2
0
0
1
1
0
0
2
0
1
0
0
1
0
0
1
1
0
0
0
0
1
0
0
1
0
4
0
2
0
0
0
2
0
1
2
3
1
0
2
0
0
0
0
0
0
0
0
2
0
1
0
2
2
1
0
0
0
0
0
0
1
2
1
0
0
2
2
0
0
0
2
2
0
0
0
0
0
2
0
2
2
1
2
0
0
0
0
0
2
1
0
2
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
1
1
0
2
0
0
1
0
0
2
0
1
0
2
2
2
2
1
0
0
0
0
1
2
0
1
1
0
0
1
0
0
0
1
2
2
0
2
1
2
2
0
3
0
2
0
2
0
0
1
0
0
1
0
1
0
0
2
0
0
1
0
1
0
0
1
1
4
0
0
2
2
2
7
0
0
0
0
2
0
0
0
0
5
0
2
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
2
3
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
1
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
1
0
2
1
0
0
1
1
0
1
0
0
1
1
2
0
0
2
1
0
2
0
1
2
0
2
0
0
0
0
0
2
0
2
2
1
0
0
0
2
1
2
2
1
1
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
2
0
2
1
0
1
0
0
0
0
0
0
1
0
0
0
2
2
1
0
0
1
2
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
1
2
0
0
0
1
0
4
0
0
0
0
0
1
1
1
1
1
0
0
0
0
2
1
2
0
0
0
1
0
2
0
0
0
1
0
0
2
2
0
1
1
0
0
0
0
0
2
0
2
0
0
0
1
0
0
2
0
0
0
1
1
1
2
0
0
1
1
0
0
2
1
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
1
0
1
0
1
0
0
1
0
0
2
1
1
0
1
0
3
0
2
0
0
0
0
0
1
0
2
0
2
0
0
2
0
1
1
1
2
0
4
0
0
1
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
1
1
1
2
0
0
0
0
1
1
0
2
1
0
0
0
0
0
2
0
0
2
0
5
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
2
0
0
2
0
2
1
0
0
0
0
0
1
1
0
2
0
1
0
0
0
0
3
1
1
0
0
1
0
0
4
2
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
2
0
0
1
0
0
1
1
0
1
0
2
0
0
3
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
1
0
5
0
1
0
0
2
1
0
1
0
0
1
0
2
1
2
0
0
1
1
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
2
0
1
0
0
1
4
0
0
3
0
0
0
0
0
0
0
0
0
1
0
2
1
2
1
0
2
1
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
1
0
0
2
1
0
0
2
0
0
0
0
0
3
0
1
2
2
0
1
0
1
1
0
1
1
0
0
2
2
1
0
1
0
0
0
0
2
0
1
0
0
1
1
0
0
0
2
0
0
0
9
0
0
0
0
0
1
2
1
2
0
1
0
0
2
0
0
0
0
1
1
1
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
1
1
0
0
0
0
2
0
2
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
2
0
2
0
0
0
1
0
2
0
2
2
0
1
0
1
0
1
0
2
0
0
0
0
2
0
0
0
0
2
1
2
0
1
0
0
3
2
0
0
1
0
1
0
0
0
1
1
1
0
2
0
0
0
0
0
2
1
3
0
1
0
0
1
2
0
0
0
1
0
2
0
1
2
0
0
1
1
0
0
0
2
0
0
0
4
0
1
0
0
2
0
0
1
2
2
1
0
2
0
0
0
1
0
0
0
1
1
0
0
2
0
1
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
2
0
2
0
1
1
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
1
2
0
0
0
1
0
0
0
0
0
1
0
3
0
2
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
1
0
1
0
0
0
0
2
0
0
0
2
0
1
0
0
0
3
3
1
2
0
0
2
2
1
0
0
2
2
0
2
2
3
2
0
2
0
2
0
1
2
1
0
0
0
1
0
0
2
1
0
0
2
0
0
2
0
2
1
1
0
0
0
0
0
2
0
0
0
0
1
1
1
0
0
1
0
10
1
1
0
1
0
1
1
1
0
0
0
1
2
0
1
1
2
0
1
0
1
0
2
0
1
0
2
0
0
0
0
3
2
0
0
0
0
0
3
0
1
2
0
0
1
0
0
1
0
1
0
0
1
0
0
1
0
2
1
0
2
1
0
1
0
0
2
0
1
0
0
1
0
2
0
0
0
2
1
2
1
1
1
0
0
0
0
0
1
0
2
2
1
2
0
1
1
1
0
0
2
1
0
1
2
0
2
0
0
0
1
0
1
1
1
1
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
1
0
2
1
3
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
2
0
3
2
2
0
0
0
0
5
0
0
0
0
2
1
0
0
0
2
2
0
0
1
0
0
0
1
0
0
1
1
2
1
1
1
0
2
0
2
1
0
0
0
1
2
1
2
2
0
0
0
0
2
0
1
1
0
2
1
0
0
0
0
0
2
0
0
0
0
1
0
0
1
2
3
0
0
0
2
2
0
2
6
0
2
0
1
0
1
2
0
0
0
0
1
0
1
2
2
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
2
0
1
0
0
0
1
0
0
2
2
0
2
0
1
0
0
1
0
1
0
0
0
1
2
1
1
0
0
0
4
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
5
1
0
0
1
1
0
0
0
1
0
0
0
2
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
1
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
3
0
1
2
0
0
1
0
2
2
1
0
2
0
0
0
0
1
0
0
0
0
0
2
1
2
0
2
2
2
0
0
0
2
0
2
1
0
2
0
0
2
1
0
0
2
0
0
0
2
2
3
1
1
0
2
0
1
2
1
0
0
1
0
1
0
2
0
0
0
2
0
1
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
1
2
4
0
0
2
0
1
0
0
0
2
3
0
1
1
2
0
1
0
0
0
2
0
0
0
2
6
0
1
0
0
1
0
0
2
2
2
0
0
2
0
2
0
0
2
0
1
0
0
0
0
0
2
1
1
2
0
0
0
0
0
1
7
1
1
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
3
2
1
2
0
0
0
0
0
2
2
0
0
1
0
0
0
2
2
1
2
0
0
1
1
0
0
0
1
0
0
1
1
2
2
1
0
0
0
2
1
0
2
0
2
0
2
3
0
1
0
0
1
0
0
0
0
0
1
0
0
2
0
0
2
1
3
1
0
3
0
1
0
0
0
2
0
0
1
1
1
1
2
0
0
0
0
0
2
0
5
1
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
2
1
0
0
0
1
0
2
0
1
0
6
0
0
2
2
0
0
2
0
0
0
2
1
0
2
2
0
3
0
1
2
0
0
0
1
0
1
0
0
0
1
0
0
2
0
0
0
1
0
1
0
1
2
1
0
0
1
1
0
2
0
0
0
0
2
2
0
1
1
0
1
2
1
0
1
0
1
0
1
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
1
2
0
0
0
0
0
0
2
0
0
0
1
0
2
1
0
0
1
0
0
1
2
0
1
2
1
1
1
0
2
2
1
2
0
0
1
2
3
0
2
0
1
0
1
2
1
0
0
0
1
2
0
1
0
2
0
2
2
2
0
0
0
1
1
2
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
1
2
1
0
1
1
0
1
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
1
0
0
0
0
3
0
3
0
0
0
0
2
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
2
1
0
0
0
2
2
2
0
1
2
0
2
2
0
1
2
0
1
1
2
0
2
0
2
2
0
0
1
2
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
1
1
0
2
1
0
0
0
0
4
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
2
1
0
0
1
2
0
0
1
1
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
2
0
0
0
1
0
1
2
0
1
0
0
2
0
0
1
0
0
0
2
0
2
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
2
0
2
0
0
2
0
0
1
0
0
0
2
0
0
0
0
1
1
0
0
2
1
0
0
0
0
1
2
0
0
2
0
1
0
1
2
0
2
1
2
1
2
0
0
3
0
2
2
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
1
0
0
2
2
0
0
3
2
0
2
0
0
1
0
0
1
0
0
0
2
2
0
1
2
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
1
0
2
2
0
2
0
1
1
0
0
2
1
0
1
2
0
2
3
1
0
0
0
1
0
1
0
2
0
1
0
0
0
1
0
2
1
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
2
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
3
1
0
1
2
0
0
0
2
2
0
2
2
0
1
0
0
0
0
2
2
2
1
0
0
1
0
0
0
0
2
0
2
1
2
0
0
0
2
1
0
0
0
0
0
1
2
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
3
1
2
2
0
0
0
0
2
2
1
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
2
1
0
2
1
1
0
0
0
0
1
1
1
0
0
0
1
0
2
1
0
2
0
1
0
0
0
1
2
0
2
0
1
0
0
0
5
0
1
0
0
1
0
0
0
2
0
0
2
1
0
2
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
1
2
0
0
0
2
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
2
2
0
2
2
0
2
1
2
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
2
1
2
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
2
1
1
0
0
2
0
2
0
1
0
1
1
0
0
0
0
2
0
0
0
0
1
0
2
0
1
1
0
0
1
1
1
1
0
2
0
1
2
0
0
0
0
0
2
0
1
1
2
0
2
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
2
0
1
0
1
2
0
0
1
0
0
0
1
0
1
0
1
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
1
2
0
2
1
0
0
0
1
1
1
1
4
2
1
0
0
1
1
1
0
0
2
2
1
0
0
0
2
1
1
0
2
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
1
1
0
0
0
2
0
1
1
0
0
0
2
0
1
1
1
4
1
2
0
1
0
0
0
0
0
0
1
0
1
0
1
0
1
0
1
1
1
0
0
2
0
1
2
1
0
0
1
2
0
0
1
0
0
0
0
0
0
2
1
0
0
2
2
0
3
0
2
2
0
0
1
0
0
1
2
1
2
0
1
0
2
0
0
0
0
0
0
1
0
1
1
0
0
1
0
1
2
1
0
0
2
0
0
0
0
0
2
2
3
1
0
2
2
0
0
1
0
0
0
1
0
0
2
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
2
3
0
0
1
2
0
0
1
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
2
2
0
1
1
1
0
0
2
0
1
0
0
0
2
0
2
2
1
3
0
0
1
1
0
0
0
0
0
1
0
0
0
1
1
0
2
2
2
1
2
2
2
0
0
0
0
2
0
1
0
0
0
0
2
0
2
1
0
0
0
0
2
1
1
0
1
1
6
1
1
0
0
2
0
1
2
0
0
0
0
2
1
0
0
2
0
0
0
1
1
0
1
0
0
0
1
1
1
0
0
0
2
0
1
1
0
0
0
2
1
0
0
0
0
2
1
2
1
0
0
2
0
1
0
1
1
0
0
2
0
0
0
0
1
0
2
0
1
2
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
1
1
0
0
0
0
2
0
1
2
0
1
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
1
2
0
2
3
0
0
0
0
2
2
0
0
0
1
0
0
1
0
2
1
0
2
1
0
0
0
1
1
3
0
0
1
0
0
0
1
0
5
2
2
1
0
0
1
2
0
1
2
0
2
1
0
5
0
1
0
0
0
0
0
0
0
0
1
0
2
1
0
0
1
1
0
0
0
1
0
2
0
2
0
0
0
0
0
1
0
0
1
0
2
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
3
0
2
1
0
0
2
2
0
1
5
0
0
1
0
1
1
0
2
0
0
0
1
0
0
0
0
2
0
0
1
0
1
0
0
0
1
1
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
1
0
1
0
0
0
1
1
0
1
0
0
0
2
0
0
0
0
1
2
0
3
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
2
1
1
0
0
1
2
0
0
0
0
1
0
0
0
0
1
0
2
2
0
0
0
1
0
0
1
2
0
2
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
3
1
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
1
0
2
1
0
0
0
0
2
0
0
0
0
1
1
2
1
0
0
2
1
0
0
1
0
0
0
0
2
2
0
0
0
0
0
1
2
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
3
4
2
0
0
0
0
2
0
2
3
0
0
0
0
0
0
2
1
0
0
0
2
0
1
0
0
1
0
0
1
1
0
0
1
2
0
1
0
0
3
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
2
0
2
2
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
1
2
0
0
0
1
2
0
0
1
0
1
3
0
1
0
1
2
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
2
1
2
0
8
0
3
1
0
0
0
2
0
2
2
0
2
1
1
0
2
0
0
2
0
0
0
0
2
0
2
0
0
2
0
1
0
0
0
1
0
1
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
3
2
1
0
0
3
2
2
0
1
0
0
0
2
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
2
1
0
1
2
2
0
0
1
1
1
0
0
0
1
0
0
0
0
0
2
0
1
0
0
2
1
0
2
0
2
2
1
0
0
0
0
2
2
0
0
1
1
1
1
0
0
0
1
2
0
0
0
3
1
0
0
0
1
0
1
0
0
2
2
0
0
0
0
0
2
0
0
1
0
1
0
1
1
0
0
2
0
1
0
2
1
1
2
1
1
0
2
0
0
1
0
0
1
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
2
0
0
2
0
0
0
2
1
1
1
0
0
0
1
0
1
0
2
1
3
2
1
0
1
0
0
2
0
0
0
0
2
1
2
0
2
0
2
1
1
0
0
0
1
1
0
2
1
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
2
0
1
1
1
0
0
2
0
0
0
0
1
0
2
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
1
2
1
2
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
2
1
0
0
1
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
1
2
1
0
1
0
2
0
0
7
0
2
0
0
1
2
0
2
1
2
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
1
0
0
0
3
1
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
1
0
2
0
0
3
0
0
0
2
0
2
0
0
0
0
0
2
1
0
0
1
0
0
2
0
0
0
0
1
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
1
2
0
1
0
1
0
0
0
0
0
0
0
0
1
0
2
2
2
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
1
0
0
1
1
0
0
0
0
0
0
1
2
0
0
1
0
0
1
2
0
0
1
0
0
2
0
0
0
3
0
3
1
0
2
0
0
1
1
1
3
0
0
2
0
0
1
0
1
0
1
2
0
3
0
0
2
2
0
0
1
2
1
0
0
0
1
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
1
2
2
2
0
1
2
1
0
0
1
0
2
0
2
0
2
0
0
0
0
0
0
2
0
0
1
1
0
0
0
1
0
0
0
1
1
3
1
0
0
1
1
0
0
0
0
2
0
0
1
1
0
0
0
1
2
0
0
0
0
2
0
0
0
0
1
0
0
2
1
2
2
2
2
0
1
2
1
1
1
0
0
2
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
1
0
2
2
0
1
2
0
0
0
0
0
0
1
1
0
2
2
0
0
0
1
2
1
0
0
2
2
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
3
0
1
2
0
1
0
0
0
1
0
2
0
0
0
0
0
0
1
0
2
1
0
0
2
2
0
1
0
0
0
0
0
0
0
3
2
0
0
0
2
3
1
0
0
3
2
0
0
0
0
0
3
0
2
0
0
0
1
0
0
2
0
2
2
0
0
2
1
1
0
1
2
0
0
1
0
3
0
0
0
0
1
2
0
0
1
2
2
0
1
2
1
0
2
0
0
0
0
0
0
0
1
2
0
0
0
1
2
0
1
0
1
0
2
0
0
1
0
0
0
1
1
2
1
0
2
1
0
2
1
2
0
1
0
0
0
2
0
0
0
0
0
2
0
0
2
0
1
0
1
0
0
0
0
2
2
0
0
0
0
0
1
2
0
1
0
2
1
1
1
2
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
2
0
1
2
0
2
0
0
2
2
1
0
0
1
1
1
0
0
0
1
3
2
0
1
1
1
2
2
0
2
0
1
0
0
0
2
1
0
0
0
0
3
1
1
1
1
2
0
0
0
0
0
1
0
0
0
0
2
0
2
2
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
3
0
0
0
0
1
1
0
0
0
4
0
1
0
1
0
0
0
2
0
2
0
1
1
0
0
1
0
0
2
0
1
1
0
0
0
2
1
2
0
0
0
0
1
2
0
0
0
2
0
1
2
0
2
0
2
0
2
1
0
0
0
0
0
1
0
2
2
0
0
2
1
1
2
0
1
0
0
0
1
2
1
0
2
0
1
2
1
0
0
2
0
1
0
0
2
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
1
1
0
1
1
0
0
2
2
1
0
0
1
1
1
3
0
0
2
0
0
2
0
0
2
0
0
0
2
1
0
0
2
0
0
2
2
2
0
0
2
1
1
2
0
0
0
1
0
0
0
2
1
1
1
1
1
0
0
1
0
0
1
0
0
1
0
0
1
1
0
3
0
0
0
2
1
0
0
5
0
0
0
2
1
1
0
0
1
0
2
1
0
0
0
0
3
0
0
0
0
1
1
0
5
0
0
0
0
0
2
0
0
0
0
0
2
2
1
1
2
0
0
0
0
3
0
0
0
0
0
0
1
0
3
1
0
1
2
0
1
0
0
2
0
1
1
0
1
1
2
0
0
0
3
2
0
1
4
0
0
2
0
0
0
1
0
0
0
2
0
1
1
1
0
1
0
0
2
0
0
0
2
0
1
2
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
2
3
2
2
2
0
0
0
8
2
2
1
2
2
0
0
0
1
1
0
0
1
2
0
1
0
0
2
0
0
0
0
0
1
0
2
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
1
0
0
2
0
2
0
1
0
0
0
0
3
0
1
1
0
0
2
2
0
1
2
0
0
7
0
0
0
0
0
2
1
0
0
0
1
0
0
2
1
1
0
0
0
0
1
0
1
1
2
0
2
0
0
0
1
0
2
1
1
1
0
0
0
0
2
0
3
0
1
0
3
1
1
0
1
0
2
1
0
1
1
0
1
0
2
0
1
0
1
0
0
1
1
2
0
0
0
0
0
0
0
0
1
0
1
0
2
2
0
1
0
1
0
2
0
0
0
0
1
0
2
0
0
0
1
1
0
0
1
1
0
2
0
0
1
0
0
2
0
2
0
1
2
0
0
1
0
0
2
0
0
2
0
1
2
0
2
0
2
0
2
0
0
0
1
1
1
0
0
0
1
1
0
2
0
3
0
0
2
2
3
2
0
2
0
0
2
2
3
2
0
0
2
0
0
1
0
3
0
0
0
2
0
0
1
0
0
0
0
0
1
0
2
1
0
0
1
0
2
0
0
0
0
0
2
1
2
1
0
0
1
0
0
0
1
0
1
0
0
0
1
1
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
2
1
2
1
2
0
2
0
1
0
1
0
1
1
0
1
0
1
0
3
1
0
0
0
0
0
0
0
0
0
0
3
3
0
2
0
0
1
1
1
3
0
0
1
1
1
1
2
0
2
0
1
0
0
0
2
2
2
1
2
0
0
0
0
0
2
0
2
2
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
2
1
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
2
1
0
1
0
0
0
3
0
1
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
2
0
0
1
0
2
0
2
0
0
1
0
1
0
2
0
0
1
2
0
0
2
1
0
0
0
2
0
3
0
1
2
0
2
0
0
1
1
0
2
0
0
0
1
0
0
0
2
1
0
1
1
0
0
2
0
0
0
4
1
1
0
0
0
0
0
0
2
0
0
3
0
0
0
0
1
0
0
1
2
0
1
2
0
0
0
0
2
0
1
0
0
2
0
2
1
3
0
0
1
0
0
1
0
2
2
2
1
2
5
0
0
0
0
2
1
0
0
1
2
0
0
2
2
2
1
2
0
0
0
2
1
0
0
2
0
0
2
0
0
0
1
0
1
2
1
0
1
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
1
2
0
0
0
0
1
0
1
0
0
1
0
0
2
0
1
2
0
1
3
1
1
0
0
0
0
0
0
2
2
1
0
1
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
3
0
0
0
1
0
0
0
2
2
1
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
2
2
0
0
0
0
2
0
0
2
0
0
2
0
1
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
2
0
0
0
1
0
0
0
0
2
0
0
2
0
1
2
0
2
0
1
0
0
0
6
0
0
1
0
0
1
0
2
0
1
0
1
0
0
2
2
0
1
2
1
0
0
0
2
2
1
0
1
0
0
0
1
4
0
1
1
2
0
0
0
2
0
0
2
1
0
0
0
0
0
0
1
2
0
0
0
2
0
2
1
1
0
2
1
0
0
0
2
1
1
0
0
0
0
0
0
2
0
1
1
0
0
1
0
1
1
1
0
0
0
0
0
0
1
0
0
0
1
3
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
3
1
0
0
2
0
0
1
1
0
0
1
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
1
0
1
1
0
2
0
1
0
1
0
2
1
0
2
1
3
2
1
0
0
2
0
0
0
0
0
0
1
2
2
2
0
2
0
0
0
0
0
2
0
3
1
2
1
0
1
2
1
1
0
0
0
0
0
2
0
0
0
2
0
1
0
1
1
0
0
0
2
0
0
2
0
0
0
2
0
2
0
0
0
0
0
2
0
0
2
1
0
0
2
2
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
3
3
0
2
0
0
0
0
0
2
0
1
0
2
2
0
0
0
1
2
0
0
0
0
1
0
0
1
1
0
0
2
0
1
1
0
0
2
0
0
0
9
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
2
1
0
0
0
2
0
0
0
0
0
0
1
2
0
2
0
2
2
0
1
0
0
1
0
1
2
0
0
0
1
1
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
1
0
2
0
0
0
1
0
0
0
1
2
0
3
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
1
0
0
0
4
0
0
0
0
0
0
1
0
2
2
2
2
1
2
0
0
3
0
0
0
2
0
0
0
1
0
2
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
2
0
2
1
2
2
0
1
0
0
2
0
4
1
0
2
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
1
3
0
0
0
1
0
1
1
2
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
6
1
2
2
0
2
0
0
0
1
0
2
2
0
2
2
1
0
0
0
2
0
0
0
2
2
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
4
0
1
5
2
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
1
0
0
0
1
0
1
0
0
0
2
0
1
0
0
0
0
0
0
2
2
1
0
1
2
0
0
2
0
2
0
0
0
0
1
0
2
1
0
1
1
1
1
2
0
0
0
0
0
0
2
0
3
0
0
0
1
2
1
0
0
0
0
2
1
0
0
1
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
4
1
0
2
0
0
0
0
0
2
0
3
1
0
0
0
0
2
0
0
2
1
0
1
2
0
1
0
0
0
0
0
0
0
0
2
0
0
1
2
1
0
0
1
0
2
0
2
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
2
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
2
0
0
1
0
0
1
1
0
1
1
0
0
0
1
0
0
0
0
2
1
1
0
2
0
2
3
1
0
1
0
0
0
1
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
3
2
2
0
2
2
1
0
0
0
0
0
0
0
0
2
0
0
2
2
1
0
0
2
0
0
0
0
0
0
0
1
1
2
0
2
0
0
0
2
1
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
2
2
2
2
1
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
2
0
0
2
2
1
0
0
2
1
1
0
1
0
2
0
0
1
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
2
2
0
1
0
1
0
1
0
1
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
1
0
0
2
0
0
2
0
1
2
2
0
1
0
1
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
1
0
2
0
0
0
1
0
0
2
0
0
2
0
1
2
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
2
0
1
0
0
1
2
1
2
0
0
2
2
0
0
0
2
0
2
1
0
1
0
0
1
2
0
0
2
0
1
0
0
2
0
1
0
0
0
0
2
0
1
1
0
0
0
0
1
0
1
2
0
0
1
0
0
0
0
0
2
0
1
2
2
0
2
0
0
2
0
2
0
0
0
1
2
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
1
3
0
0
2
0
0
1
0
0
1
0
1
2
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
1
2
0
0
2
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
1
0
1
0
2
2
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
1
3
0
1
0
1
0
0
1
0
1
0
0
1
0
0
6
2
2
1
2
0
0
2
1
0
1
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
2
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
2
0
1
0
2
0
0
2
0
2
0
0
0
0
0
0
1
2
1
0
1
2
1
0
0
1
1
0
2
0
1
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
3
3
0
1
0
0
1
0
0
2
1
1
0
2
1
0
0
0
0
2
2
2
0
0
0
0
0
1
0
1
0
1
1
2
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
1
1
3
2
0
0
2
0
1
0
1
0
0
0
0
4
0
0
2
0
3
2
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
2
0
1
0
0
1
0
2
0
0
0
0
0
2
1
2
1
0
0
2
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
2
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
1
1
1
0
0
3
0
0
2
0
0
1
2
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
2
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
1
2
0
0
0
0
0
0
0
0
1
1
0
1
0
0
2
0
0
2
1
0
0
0
0
0
1
2
0
0
0
2
0
0
2
1
1
0
1
1
2
0
0
2
1
0
0
0
2
2
0
0
1
1
1
0
1
1
0
1
0
1
2
0
0
0
0
1
0
0
1
0
0
0
1
1
1
1
0
0
0
0
0
1
1
0
2
1
0
0
0
0
0
2
2
1
0
0
0
2
0
0
1
0
0
1
0
2
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
2
2
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
2
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
2
1
2
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
1
0
0
2
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
2
2
1
0
0
2
1
0
0
1
2
1
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
2
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
2
2
1
0
0
0
1
0
1
0
0
2
1
0
0
0
0
0
2
0
1
0
0
1
1
0
0
0
1
0
0
1
0
0
1
0
2
0
0
0
0
0
0
1
0
1
0
0
3
1
1
0
1
0
0
0
0
1
2
0
0
2
0
0
0
0
0
1
0
4
2
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
3
0
0
0
1
2
2
3
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
1
2
1
1
2
0
1
0
0
0
0
2
4
0
1
4
0
0
0
0
0
0
0
0
0
2
6
0
0
1
0
3
1
0
1
0
0
2
2
2
0
0
0
0
2
2
0
2
0
1
0
0
0
0
0
0
2
1
1
0
0
0
1
1
2
2
1
2
1
0
0
2
0
0
1
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
2
2
1
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
1
0
2
1
2
2
0
0
2
0
0
0
2
0
1
0
1
1
0
1
0
0
0
1
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
3
3
0
1
2
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
3
3
2
1
0
2
0
1
0
0
0
0
0
1
2
2
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
3
0
2
0
0
2
2
2
0
0
2
0
1
1
1
2
2
0
0
0
0
1
0
4
0
0
2
1
2
0
0
0
0
0
0
0
2
2
0
0
0
0
1
1
2
0
2
0
0
1
0
0
1
0
0
0
2
1
1
0
1
0
0
0
0
6
0
0
0
2
2
2
2
0
0
1
0
0
0
0
2
0
0
2
2
0
0
2
0
0
0
2
1
2
0
2
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
3
2
2
1
0
1
0
2
0
1
2
1
0
1
1
2
1
0
0
0
0
0
1
0
1
0
0
2
0
0
0
2
2
1
1
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
1
1
0
0
2
2
2
2
1
0
0
2
2
0
0
2
1
2
0
0
1
2
0
1
0
0
0
1
1
1
0
2
1
0
0
1
3
1
0
2
1
0
0
1
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
1
2
0
3
0
0
0
0
0
0
0
0
1
0
2
0
0
1
2
1
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
6
1
0
2
0
0
1
0
2
0
0
0
2
1
0
0
3
0
0
0
0
2
0
0
0
2
0
2
2
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
1
1
0
3
0
0
0
1
0
0
0
0
1
0
0
1
0
2
1
1
0
1
0
1
1
2
0
2
0
0
0
2
1
0
1
1
0
0
0
0
0
0
0
2
0
0
3
0
0
0
1
0
0
2
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
4
0
1
0
2
0
0
0
0
0
0
1
1
2
2
0
0
0
3
0
1
1
0
2
1
0
0
0
0
0
2
1
0
2
0
1
2
0
0
0
0
0
2
0
2
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
1
0
3
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
1
1
0
2
0
2
0
2
0
0
0
0
1
1
3
0
0
3
0
1
0
0
0
1
1
2
0
0
2
1
0
2
0
0
0
0
0
5
2
0
2
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
1
0
0
0
2
2
0
2
0
0
0
1
2
0
1
1
0
0
1
0
0
1
0
1
1
0
1
0
0
0
1
0
1
0
1
1
0
2
0
1
1
0
1
3
1
1
0
0
0
0
0
2
1
2
0
0
2
2
0
2
0
2
0
0
0
0
2
2
0
1
3
0
3
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
3
1
2
0
0
1
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
1
3
0
0
0
0
0
1
0
0
0
0
0
0
1
1
2
0
1
1
1
0
2
0
0
0
0
0
0
0
0
0
2
1
1
0
2
0
0
0
2
2
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
2
1
1
0
1
2
1
0
2
0
0
0
1
0
0
0
0
1
0
2
0
3
1
2
0
0
0
0
0
2
0
2
0
0
0
1
1
1
0
2
2
2
2
0
0
1
2
0
0
0
1
0
1
0
0
0
0
0
2
1
0
1
0
1
0
1
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
2
0
2
0
1
2
0
0
0
2
0
3
0
0
1
0
1
0
0
0
2
0
0
0
0
2
0
2
1
2
3
0
0
2
1
2
0
2
0
0
1
0
0
1
0
0
4
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
1
1
1
0
2
1
1
1
0
0
3
0
1
0
0
0
2
0
0
0
2
0
0
0
0
1
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
2
1
1
0
0
0
1
0
0
0
1
1
0
1
2
2
2
0
1
0
0
0
0
0
1
0
2
0
0
2
0
0
2
1
1
1
0
1
0
2
0
0
0
1
0
0
1
0
2
2
2
0
0
0
2
0
0
0
0
2
0
2
0
0
0
1
0
1
0
0
2
0
1
0
1
1
1
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
2
1
0
0
0
0
2
1
0
0
2
0
0
0
2
2
1
1
0
0
1
2
0
0
0
1
1
0
3
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
2
2
0
1
1
0
0
1
0
0
0
0
0
0
2
1
1
1
0
2
0
0
0
2
4
2
0
1
0
2
0
0
1
1
0
0
0
0
1
1
0
1
0
1
0
0
0
2
2
0
0
0
1
0
0
3
0
0
1
0
1
0
2
1
1
2
3
0
2
3
0
0
1
0
0
1
0
0
1
2
0
1
0
2
1
2
0
2
0
0
0
0
1
2
0
6
0
0
2
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
10
2
2
0
0
0
2
0
2
0
1
0
0
1
0
2
0
3
0
0
2
0
1
0
0
2
2
0
0
0
1
0
1
1
0
2
2
0
0
0
2
2
0
2
0
0
0
1
2
1
1
2
0
5
0
1
0
0
1
0
2
2
0
1
2
0
1
0
0
0
0
2
0
1
0
0
2
1
2
2
0
0
4
2
3
2
2
0
0
1
1
1
1
0
2
0
0
0
1
3
1
0
0
1
1
1
1
0
1
0
0
0
1
2
2
0
1
1
2
0
0
2
2
2
0
0
2
2
1
1
0
1
1
0
0
0
0
0
0
0
2
2
2
1
0
0
1
0
1
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
2
1
2
2
0
0
2
0
1
2
0
0
0
0
2
1
0
0
1
1
2
1
0
1
0
0
0
2
0
0
1
0
0
0
2
0
0
0
2
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
1
0
1
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
2
0
2
0
0
0
0
0
0
3
0
0
1
0
2
0
0
0
0
3
0
2
0
1
0
0
0
0
0
1
2
0
0
0
1
4
2
2
3
2
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
2
2
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
2
0
0
1
0
4
0
0
2
0
2
0
0
2
1
2
1
0
2
0
0
0
0
1
1
0
1
0
0
0
1
1
1
0
0
0
0
0
0
2
1
0
2
0
0
1
0
0
1
0
0
1
1
0
0
0
0
2
1
0
0
1
2
2
1
1
0
0
2
0
0
0
0
0
0
2
1
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
1
1
0
0
0
0
1
2
0
0
2
0
1
0
0
2
0
2
0
0
0
0
0
1
0
1
2
0
2
0
1
1
0
0
0
2
0
0
0
0
4
0
0
0
0
2
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
5
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
1
1
0
2
2
0
0
1
2
1
0
1
0
0
1
0
2
0
2
1
0
1
0
0
1
0
0
0
1
1
1
0
1
0
1
1
1
0
2
0
0
0
0
1
0
2
0
0
2
0
1
0
0
0
2
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
1
3
0
2
0
2
2
0
3
0
0
0
0
2
0
0
0
0
1
2
1
1
0
1
0
0
1
0
1
0
1
2
1
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
2
0
0
0
0
1
0
2
2
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
1
0
0
2
0
1
2
2
0
2
1
0
0
0
0
1
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
1
2
0
0
0
1
2
2
0
0
0
1
0
1
1
1
0
0
0
1
0
1
0
1
0
0
0
2
0
1
0
3
2
2
3
0
0
0
0
0
0
1
2
2
2
0
0
0
0
0
0
1
0
2
1
0
0
2
2
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
2
0
1
0
0
0
0
2
2
1
2
0
0
0
0
2
2
0
2
0
0
3
4
0
1
0
0
0
0
1
0
0
2
0
0
4
2
0
1
0
1
0
0
0
0
0
1
0
0
0
2
0
2
2
0
0
0
0
4
2
0
1
0
1
2
0
0
0
2
0
2
1
0
1
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
2
1
0
2
1
0
0
0
1
0
3
0
2
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
2
0
0
0
0
0
2
1
0
0
2
0
1
5
1
0
0
1
2
1
0
1
5
1
2
0
1
0
0
2
2
0
1
0
0
1
0
0
0
1
0
2
0
0
1
2
0
2
1
0
2
0
0
0
2
0
1
2
1
0
0
0
0
0
1
2
1
0
2
0
2
1
0
0
0
0
0
0
1
1
0
0
0
2
1
0
2
1
0
2
0
1
0
0
2
0
0
4
0
0
0
0
1
0
0
0
0
0
1
0
1
2
0
0
1
0
2
2
0
2
0
1
1
0
0
2
1
0
0
0
0
0
1
0
0
3
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
1
2
2
0
1
0
0
2
2
0
0
0
0
2
0
0
1
0
1
1
2
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
1
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
1
2
0
0
1
0
0
0
0
1
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
1
0
0
0
2
1
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
2
0
1
0
2
1
0
2
0
0
0
1
2
1
2
2
0
1
0
0
1
0
0
1
1
0
0
1
0
0
2
2
0
1
0
1
1
2
0
2
0
0
0
2
1
0
0
0
0
0
0
1
0
1
2
0
2
0
1
0
1
0
0
1
0
3
1
0
2
1
0
0
0
0
0
0
1
0
0
0
2
0
0
2
2
2
2
0
0
1
0
1
1
0
2
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
6
0
0
0
2
3
3
0
2
0
0
0
1
0
2
0
2
1
0
1
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
3
0
0
1
1
1
0
0
0
2
2
0
2
2
0
0
0
0
1
1
0
0
2
0
2
2
3
0
0
0
0
0
1
2
0
0
2
1
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
4
0
1
0
0
2
2
2
2
0
0
0
0
1
1
2
0
1
2
0
0
0
0
1
1
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
2
1
0
0
1
0
0
0
0
1
0
0
0
2
0
1
0
2
0
0
1
0
1
1
0
0
1
0
1
0
2
0
1
0
0
0
1
2
1
2
0
0
1
2
2
0
0
1
1
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
2
1
2
0
3
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
2
0
0
4
0
0
2
0
1
0
0
2
0
0
0
0
1
1
0
2
0
0
2
0
1
0
1
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
2
0
1
0
2
0
0
0
0
1
1
1
0
0
1
0
2
1
0
1
0
0
1
1
1
0
0
0
0
0
1
1
1
2
2
0
0
0
2
3
0
1
0
0
0
0
0
2
0
1
0
2
0
0
2
2
0
0
1
2
2
0
0
0
1
2
1
2
0
0
0
0
1
0
2
0
0
1
2
1
0
0
0
0
2
2
0
0
2
2
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
1
2
0
0
0
1
1
0
2
0
0
1
2
1
2
3
0
1
0
0
0
0
2
1
0
1
1
0
1
0
0
2
0
0
0
0
1
0
1
0
1
0
1
0
0
2
1
0
1
0
2
0
1
0
0
0
1
0
0
2
2
0
2
1
2
0
1
2
0
0
1
0
2
0
2
2
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
2
2
1
0
1
2
0
0
1
1
1
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
2
2
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
2
0
1
0
2
0
2
0
0
2
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
2
2
0
1
2
0
2
2
1
0
0
0
0
0
1
0
1
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
1
2
1
1
0
2
2
0
2
0
2
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
3
1
1
0
0
0
0
0
1
0
0
0
1
0
3
2
0
0
0
0
1
0
1
2
2
0
0
2
1
1
0
0
2
0
0
0
0
0
1
0
0
0
5
0
0
0
0
0
0
0
2
1
1
2
0
2
0
0
0
2
0
0
1
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
3
1
1
0
0
0
2
0
2
0
0
0
0
1
1
0
0
0
1
1
1
0
0
0
2
0
0
0
0
0
1
0
2
1
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
1
0
0
2
3
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
1
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
2
3
0
0
0
0
2
0
1
0
0
0
0
0
1
1
0
0
1
2
2
2
1
0
2
2
1
2
2
1
0
1
1
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
2
1
1
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
2
0
0
1
0
2
2
0
1
0
0
1
0
0
0
0
1
0
1
0
0
3
2
3
0
0
0
1
2
1
0
2
0
1
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
2
0
1
0
0
2
1
0
0
0
0
1
1
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
1
0
2
0
2
1
0
2
1
0
2
0
1
0
0
0
1
0
0
0
2
0
1
2
2
0
2
1
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
3
0
0
0
0
1
1
0
1
1
0
1
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
1
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
2
0
0
0
1
2
0
2
0
2
0
0
1
0
1
2
0
0
2
1
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
2
0
0
0
0
2
1
0
0
1
1
0
0
2
0
0
2
0
2
0
0
0
1
2
0
0
0
1
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
1
0
0
0
0
1
2
0
0
3
0
0
0
1
0
0
0
1
0
0
2
0
0
2
1
1
2
1
0
3
2
2
0
2
1
0
0
1
2
0
1
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
4
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
2
0
1
0
0
0
1
1
0
0
1
1
0
1
0
0
1
1
1
0
0
1
0
0
0
0
2
2
0
0
2
0
0
0
0
0
1
0
1
0
2
0
0
2
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
1
1
0
1
0
2
0
1
0
0
0
1
1
2
2
0
2
0
0
2
1
0
0
1
1
2
0
2
0
1
3
0
2
2
0
0
0
2
0
0
0
0
0
0
1
2
0
0
1
1
1
0
1
0
0
1
0
0
0
0
1
0
0
2
2
0
0
0
1
1
1
1
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
2
0
0
2
0
1
1
0
1
2
2
0
1
0
0
2
0
0
3
0
2
0
0
1
1
0
0
0
0
0
1
0
2
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
2
2
0
0
2
1
0
0
1
2
2
2
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
3
0
2
0
0
0
1
0
0
0
0
0
2
1
0
1
1
0
0
0
1
0
2
1
0
2
2
2
0
0
1
0
1
2
0
2
0
0
2
1
0
0
0
0
2
0
0
1
2
1
1
0
2
2
0
2
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
2
0
0
2
0
0
2
2
2
2
0
0
1
0
2
2
0
0
1
0
0
1
0
0
1
3
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
1
2
0
0
1
1
1
0
2
0
0
2
0
0
0
2
1
2
0
1
1
0
0
0
2
0
0
1
0
2
2
1
0
0
1
0
0
0
1
0
2
1
0
1
1
1
2
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
1
2
0
0
0
0
1
1
0
3
0
1
1
0
2
0
0
1
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
3
1
2
0
0
2
0
1
0
0
0
1
2
0
0
1
0
0
0
2
0
0
2
1
2
0
0
0
3
0
0
1
0
0
0
1
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
2
2
2
0
1
0
0
0
0
3
1
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
2
1
0
2
1
2
1
0
0
1
0
2
0
0
0
2
0
0
0
3
5
0
1
0
0
0
0
2
0
0
0
0
2
0
0
1
1
0
0
2
1
0
0
0
0
2
0
3
0
2
1
1
1
1
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
3
2
2
0
2
2
0
2
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
3
1
1
0
1
1
0
0
0
0
2
0
0
0
2
1
0
3
1
0
1
0
1
1
0
1
1
0
1
0
0
1
0
0
1
2
0
1
0
0
0
0
1
1
0
0
0
1
0
1
1
0
2
0
0
0
0
2
2
0
1
2
2
2
0
0
0
0
0
0
1
0
0
2
0
2
0
0
3
2
0
2
0
0
0
0
3
2
0
0
2
2
2
1
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
2
1
0
0
1
0
0
3
0
0
0
1
1
0
2
2
0
1
0
0
1
2
0
0
1
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
1
0
2
0
1
2
2
1
0
1
5
0
2
0
0
2
1
0
0
0
0
0
1
3
2
0
1
3
1
0
0
0
0
2
0
2
0
0
1
2
0
0
0
2
0
0
2
0
1
1
0
2
0
0
1
0
0
1
0
1
0
0
1
2
2
0
1
1
1
0
0
1
0
0
0
2
2
0
0
0
0
2
0
0
0
2
0
1
2
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
2
0
0
1
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
2
2
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
2
0
1
2
0
0
1
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
2
1
1
0
2
0
0
0
3
0
0
0
2
0
1
0
0
2
0
0
1
0
0
0
2
0
1
2
0
0
0
1
0
1
3
2
0
0
0
0
1
1
2
0
0
0
0
1
0
1
1
1
0
2
0
2
0
0
2
0
0
0
0
0
0
0
1
2
0
2
2
2
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
2
0
0
2
0
1
1
0
3
0
1
3
0
1
0
0
1
0
0
1
0
0
1
2
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
2
2
0
0
1
1
0
2
0
0
0
0
2
0
2
0
5
0
1
1
0
0
1
1
0
1
0
1
2
1
1
0
0
0
0
3
0
1
0
2
2
0
0
0
0
1
0
0
3
0
2
2
1
0
2
1
2
0
0
2
0
0
2
0
0
2
1
1
0
0
0
1
1
0
1
0
0
1
0
2
0
0
3
2
1
0
4
0
0
0
2
1
1
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
1
2
0
3
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
3
0
1
0
0
2
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
2
1
0
0
1
0
1
0
5
1
1
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
1
1
0
0
2
0
0
0
0
0
0
2
0
0
0
1
1
1
2
0
1
0
0
0
2
0
2
2
0
0
2
2
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
2
1
0
2
0
0
0
0
1
0
0
2
1
0
2
1
2
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
2
0
1
0
0
2
0
1
1
2
2
0
0
0
0
0
2
2
1
0
2
0
0
0
2
2
1
2
5
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
2
0
3
2
0
2
2
2
1
1
0
1
0
1
2
0
0
0
0
0
2
0
0
1
0
1
0
0
1
0
1
2
0
2
0
1
1
0
0
0
0
0
0
0
2
1
2
0
0
0
2
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
2
2
0
0
0
0
0
0
0
1
4
1
1
2
0
0
1
1
1
0
0
2
0
0
0
0
0
0
0
2
2
2
0
0
2
0
4
0
0
1
0
1
2
0
2
1
0
0
0
1
1
1
0
0
0
1
1
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
1
0
0
3
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
1
0
0
1
0
3
1
0
0
0
0
0
1
2
1
0
1
1
1
0
2
0
2
0
2
1
2
0
2
0
2
1
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
2
1
2
0
0
0
1
1
2
0
1
1
0
0
0
1
1
0
2
0
2
0
0
2
0
1
0
1
2
1
2
0
0
1
0
2
2
0
1
1
0
1
2
0
0
2
0
2
0
2
0
0
1
0
0
0
1
1
1
0
0
0
2
0
0
1
0
0
0
2
2
0
0
1
0
0
4
1
0
0
2
0
1
1
0
1
0
1
1
0
0
2
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
2
0
1
2
0
3
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
2
1
0
1
0
0
0
1
0
0
0
1
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
6
1
0
2
0
0
1
7
2
0
0
1
2
0
2
0
0
0
2
0
1
2
0
0
1
2
0
0
0
0
0
0
2
1
1
0
0
1
1
1
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
3
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
2
0
2
0
2
2
0
0
0
1
0
0
0
1
1
1
1
1
0
3
0
2
0
0
1
2
0
0
2
0
1
2
0
0
0
2
1
0
2
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
1
1
1
1
2
1
1
0
0
0
0
0
1
2
1
0
2
0
0
3
2
0
0
0
2
0
2
0
0
0
1
2
0
0
2
0
0
1
1
0
0
0
0
2
1
1
0
0
0
0
2
0
0
0
0
4
0
1
1
0
0
0
1
0
0
0
0
1
0
0
3
1
0
1
2
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
2
0
0
0
2
0
0
1
2
0
0
1
2
0
0
2
0
0
1
0
0
0
0
0
0
0
2
1
0
2
0
0
2
0
0
1
2
0
0
0
0
0
2
0
1
2
0
0
2
0
0
0
0
0
0
0
1
1
2
0
0
0
1
0
1
1
0
2
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
1
1
0
0
2
0
1
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
1
0
0
2
1
1
2
2
0
0
0
0
2
2
2
1
0
0
0
2
0
1
0
3
0
0
2
0
0
0
0
0
0
2
0
1
2
0
2
2
0
1
0
2
0
0
0
2
1
0
2
2
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
2
2
0
0
0
0
0
2
2
1
1
0
0
0
2
0
0
0
1
2
2
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
2
0
1
0
2
0
0
1
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
2
0
1
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
1
0
0
2
0
2
0
0
0
0
1
1
0
2
1
1
2
2
2
0
0
0
1
0
2
0
0
1
0
0
1
2
0
2
0
0
0
0
1
2
1
2
2
0
1
0
0
2
0
0
0
0
1
0
0
1
0
0
0
1
2
0
1
1
0
0
0
2
0
0
1
1
0
1
1
0
0
2
2
1
1
1
0
0
0
0
1
0
1
2
1
3
1
2
0
0
2
0
0
2
0
1
0
0
0
0
2
0
0
0
2
0
0
0
2
2
0
5
0
0
0
1
2
0
3
0
2
1
2
0
1
2
0
0
2
0
1
1
0
0
0
2
0
0
0
1
0
0
1
0
0
0
2
0
2
0
0
2
1
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
1
0
2
1
2
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
1
0
1
0
1
1
0
1
2
1
0
2
0
1
0
1
0
0
0
0
1
3
0
0
0
0
0
1
0
0
0
2
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
3
0
1
0
1
0
0
2
0
0
1
0
2
0
0
7
0
1
1
3
0
2
0
0
0
2
0
0
2
2
1
0
0
0
0
0
3
2
0
2
0
0
0
0
0
0
2
0
0
2
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
1
2
1
1
2
0
1
0
2
0
2
1
1
0
0
0
0
2
1
0
1
0
2
2
2
0
0
0
0
0
0
0
0
2
0
0
2
2
1
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
2
2
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
1
0
1
2
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
3
0
1
0
0
1
1
0
0
0
0
0
2
2
0
0
0
2
0
1
0
0
0
0
1
0
0
1
0
1
0
0
2
0
0
0
1
0
0
0
3
1
1
0
0
0
1
0
0
0
0
2
0
1
2
1
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
1
0
0
0
1
3
0
0
0
0
2
0
2
0
0
1
0
0
2
0
0
1
0
2
0
0
1
0
0
0
2
0
2
0
2
0
1
0
0
0
1
0
2
0
2
0
0
0
0
1
0
0
1
2
1
1
2
0
2
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
2
1
0
2
0
0
0
0
1
2
2
1
2
1
0
1
0
0
0
0
0
2
2
2
0
1
2
1
0
1
0
0
2
0
0
0
0
1
2
2
1
0
0
1
1
0
0
0
2
1
0
0
0
1
1
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
1
1
2
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
1
1
0
0
0
0
2
1
1
0
0
0
1
1
0
0
1
0
1
2
3
1
0
0
0
0
0
1
0
0
0
0
0
2
0
1
1
0
0
0
0
3
6
0
0
0
0
0
0
0
0
1
0
0
1
0
1
2
0
2
2
2
1
0
0
2
0
0
0
2
0
1
2
1
2
0
0
0
6
0
2
0
0
0
0
0
0
1
1
0
0
1
2
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
2
2
0
0
1
0
0
0
0
2
0
1
0
0
1
0
0
2
1
0
1
1
0
0
0
0
1
1
1
2
0
2
2
0
0
1
0
0
3
0
1
0
0
0
5
0
0
2
0
0
0
4
3
0
0
2
1
1
0
0
3
1
0
2
0
1
0
0
0
0
0
1
2
0
0
0
1
1
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
1
0
2
0
0
2
0
0
0
3
0
0
0
0
1
0
2
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
1
2
1
0
0
0
0
1
2
0
0
2
0
1
0
1
0
2
0
0
0
0
1
0
0
0
1
2
0
1
0
0
0
1
1
2
0
5
1
0
0
0
0
0
1
0
0
1
0
1
0
2
0
1
0
0
0
2
0
0
0
1
1
0
1
1
1
0
0
1
0
0
1
0
1
0
0
0
1
5
0
0
1
0
2
2
0
0
2
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
1
0
0
2
2
2
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
1
1
0
0
0
1
1
2
0
0
1
0
2
0
2
0
1
0
2
0
0
1
1
0
0
0
3
1
1
1
1
0
0
0
2
0
1
0
0
0
0
0
1
0
1
0
2
0
1
1
0
0
0
0
0
1
1
0
0
0
2
1
2
0
0
2
0
0
0
0
2
2
2
1
2
0
0
0
0
0
0
0
0
0
1
3
0
0
3
0
2
1
0
1
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
1
0
2
1
0
0
2
0
0
0
0
0
0
1
1
1
2
1
0
0
0
3
0
1
1
1
0
0
0
1
0
0
1
2
0
0
0
2
1
0
2
0
1
0
0
2
1
1
1
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
1
1
0
0
1
0
2
0
0
2
0
1
0
0
2
3
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
2
1
0
0
2
0
1
0
0
0
0
0
1
2
0
2
2
0
2
2
0
3
0
1
0
3
0
1
0
0
2
0
0
0
0
1
0
0
2
1
1
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
1
0
0
1
2
1
2
0
0
0
1
1
0
0
1
2
0
0
1
0
0
1
0
0
1
4
0
0
2
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
1
0
0
2
0
1
0
0
0
1
0
0
6
1
2
0
2
0
0
0
2
0
2
0
1
0
4
2
1
0
0
1
2
0
1
0
1
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
2
2
2
0
2
0
0
0
0
1
2
0
2
0
0
0
2
1
0
0
2
2
1
0
0
2
2
0
2
0
1
2
0
0
0
2
0
1
1
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
2
0
0
1
0
0
2
1
1
0
0
2
2
0
0
2
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
2
0
1
2
0
0
0
2
0
0
0
0
0
3
2
0
1
0
1
0
0
0
1
1
0
0
0
0
1
0
1
0
2
1
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
5
0
2
0
2
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
3
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
2
2
2
0
0
0
0
0
2
0
0
1
0
3
0
0
0
0
2
0
1
0
0
1
0
1
2
0
0
4
1
0
0
0
2
0
0
0
0
1
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
2
1
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
2
0
2
0
0
0
0
0
1
0
0
2
0
0
8
0
0
0
0
3
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
1
0
0
1
1
2
2
2
0
2
1
0
0
0
2
0
0
1
0
1
0
2
0
0
1
0
0
1
1
0
0
0
2
0
2
1
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
2
1
1
2
1
0
1
0
0
1
1
1
1
1
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
1
0
0
0
0
2
2
0
0
0
2
0
2
1
0
0
3
0
1
0
0
0
2
0
1
1
0
0
1
0
2
1
1
0
1
0
0
0
1
1
0
1
1
2
1
0
0
1
0
0
2
0
1
0
0
1
0
0
1
2
0
1
0
0
0
2
1
0
0
0
1
0
3
0
2
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
4
0
3
0
0
0
2
0
0
0
0
0
0
0
5
1
1
0
0
0
0
0
0
2
1
2
0
0
0
0
2
2
0
0
1
2
0
2
0
1
0
0
0
0
0
1
1
0
0
0
1
1
0
0
1
0
0
1
0
0
2
2
0
2
1
0
1
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
2
0
1
2
2
0
0
3
1
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
6
0
0
2
0
1
2
0
0
2
0
0
1
0
0
0
7
0
1
1
1
0
1
2
3
1
1
0
0
0
1
1
3
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
2
0
2
0
2
0
0
0
0
3
2
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
1
1
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
3
0
0
1
1
2
0
2
2
0
0
0
2
0
0
0
0
0
1
1
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
1
0
0
1
2
0
0
2
0
0
0
1
0
0
0
2
0
1
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
1
0
1
0
0
1
1
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
1
2
3
0
1
2
4
1
0
1
1
0
1
0
0
0
7
3
1
0
0
0
2
0
0
0
0
0
0
1
0
0
2
2
1
0
0
0
0
0
0
0
1
2
0
1
0
0
0
2
1
0
2
1
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
1
0
2
2
1
0
0
1
1
0
0
0
1
2
0
0
2
1
2
1
0
0
0
0
0
3
0
0
0
1
0
0
0
1
0
2
0
1
2
1
2
1
2
0
0
0
0
1
0
1
0
5
0
0
2
1
1
0
2
0
0
0
0
0
0
0
2
0
2
1
0
2
1
1
3
0
0
0
0
0
0
1
2
0
0
0
2
1
0
0
0
2
2
2
0
2
0
0
0
2
0
2
0
2
1
0
0
0
1
1
0
0
1
0
3
0
0
0
0
0
0
2
1
0
0
0
1
0
1
2
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
1
0
2
0
0
0
0
0
1
1
2
0
0
0
2
0
1
0
0
0
2
0
0
3
1
0
1
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
2
0
1
1
1
2
0
0
1
1
0
0
0
0
2
1
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
2
1
0
0
0
2
2
1
0
0
0
0
1
2
1
0
0
1
0
0
0
1
2
1
0
1
0
4
0
2
1
0
0
0
3
1
1
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
3
0
0
0
0
0
1
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
2
0
2
0
1
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
2
1
0
0
0
0
1
1
0
2
0
0
0
0
1
2
1
0
0
1
2
1
0
0
0
2
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
1
2
0
1
2
1
0
2
0
0
0
0
1
1
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
1
1
2
2
0
0
0
1
1
0
0
1
0
1
0
0
0
2
1
2
2
1
0
0
2
0
2
1
1
1
1
2
0
1
1
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
2
1
0
1
0
2
1
1
2
0
0
0
0
2
1
0
1
0
1
11
0
0
2
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
1
2
0
1
0
2
1
2
0
2
0
3
0
1
2
1
0
0
3
0
1
0
0
0
1
2
0
2
0
0
2
1
0
0
0
0
2
0
0
0
0
0
1
0
0
3
2
0
0
0
0
1
0
0
0
2
2
0
0
1
1
1
3
0
1
2
2
0
2
0
0
0
0
1
0
2
2
0
0
0
2
0
0
2
0
0
1
1
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
2
0
0
2
1
1
1
0
0
1
2
1
0
0
0
0
0
2
0
0
2
1
2
0
0
0
0
2
0
1
0
3
1
0
3
0
0
0
0
2
0
2
1
0
1
0
1
1
1
0
0
0
0
1
1
1
0
2
1
0
0
0
0
0
0
1
1
0
0
0
0
1
2
1
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
2
0
0
2
0
2
0
1
0
2
0
0
0
0
2
0
1
0
0
1
0
0
0
0
1
2
0
1
0
0
0
3
0
2
0
2
0
0
0
0
0
1
0
2
1
1
2
0
2
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
4
0
1
0
1
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
3
2
0
0
0
3
2
0
0
0
2
1
0
1
0
2
0
0
0
1
2
0
0
0
2
0
0
2
1
0
0
2
0
2
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
1
0
0
0
2
2
0
0
0
0
1
1
1
0
2
2
1
0
1
1
0
2
0
1
2
0
0
0
0
0
0
0
2
0
1
0
2
0
1
2
0
0
0
0
0
0
0
0
1
1
2
3
5
0
4
1
1
0
2
0
2
0
0
2
0
1
2
0
0
0
2
0
1
0
0
0
0
0
1
1
2
0
1
2
2
0
1
2
2
2
2
1
1
0
0
1
0
0
1
2
1
2
2
0
0
1
2
1
2
0
3
0
0
2
2
1
0
0
1
1
2
0
3
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
1
2
1
0
0
2
1
2
2
1
0
1
0
1
0
0
0
2
0
1
0
0
0
1
0
0
2
0
1
0
2
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
3
1
0
0
2
3
2
2
1
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
2
1
2
0
1
3
0
2
0
0
0
0
0
1
1
2
2
1
1
0
2
1
0
1
0
0
0
2
0
1
0
0
1
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
2
1
1
1
0
0
0
0
0
2
2
0
1
0
0
2
1
0
0
0
0
1
0
0
0
0
0
1
1
1
1
0
2
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
4
0
0
2
2
2
0
3
2
1
0
0
1
0
0
1
0
2
0
0
0
3
0
2
0
3
0
0
1
0
1
0
2
2
2
2
0
0
2
1
0
0
0
1
1
1
2
0
0
0
0
0
2
0
0
1
0
0
0
2
0
2
0
2
0
0
0
0
0
1
2
1
2
0
0
0
1
0
0
1
1
0
2
1
0
0
2
0
1
0
0
0
1
0
0
1
0
1
0
2
1
0
0
1
0
0
1
0
0
0
0
0
2
1
0
2
0
0
0
4
0
0
1
0
0
0
0
1
0
0
0
2
0
0
2
1
0
0
2
1
1
0
0
2
2
0
0
0
0
0
0
1
0
2
0
1
0
0
1
0
0
8
2
2
0
1
0
1
1
0
0
0
0
0
0
1
0
1
2
0
0
1
0
2
0
0
0
1
0
1
0
0
2
0
0
1
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
1
1
0
0
0
1
1
0
1
0
0
0
0
2
0
2
0
2
0
1
0
1
1
0
0
0
1
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
2
3
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
1
0
1
0
2
0
0
3
1
1
0
0
0
1
0
1
2
0
0
1
0
0
0
0
2
0
0
0
0
1
0
1
1
0
0
0
2
0
0
2
0
1
2
1
0
0
0
2
0
2
1
1
0
2
0
3
0
2
0
1
0
0
0
1
2
0
1
2
0
0
0
0
0
2
1
0
0
0
3
2
1
0
0
0
0
0
0
1
0
0
0
2
0
2
2
0
0
0
1
1
0
0
0
1
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
6
0
0
1
2
0
2
1
0
0
0
0
0
1
1
1
0
2
1
0
0
0
0
2
3
0
1
0
0
1
2
2
0
1
0
0
0
0
0
1
0
1
1
0
0
2
0
0
0
1
2
2
2
0
0
0
2
0
0
2
2
2
2
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
4
0
3
1
2
0
1
2
0
1
2
3
0
0
0
1
1
0
0
0
2
0
0
1
2
0
0
2
2
1
2
0
0
0
1
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
2
0
1
0
2
0
0
0
0
0
1
3
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
3
1
0
0
2
1
0
0
2
0
2
1
0
0
0
1
1
0
0
0
2
2
0
0
1
0
0
1
0
0
0
0
2
0
1
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
3
0
2
0
0
0
0
0
0
0
0
1
1
2
0
2
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
2
0
0
0
0
0
1
2
1
0
0
0
2
2
0
2
2
0
2
2
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
2
0
2
0
0
0
2
0
1
2
0
1
1
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
7
0
1
0
0
2
0
1
2
1
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
1
0
1
0
0
0
1
0
1
0
0
0
2
2
1
0
0
0
0
2
2
0
1
0
1
1
1
0
0
0
0
2
2
0
0
1
0
2
0
0
1
2
2
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
1
2
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
1
2
0
0
0
3
0
0
1
0
0
0
2
2
1
0
0
0
0
0
0
0
2
0
0
0
1
0
2
1
0
0
0
0
1
2
1
0
1
0
0
0
1
2
0
0
0
0
1
3
0
0
2
2
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
2
0
0
2
0
0
1
1
0
2
2
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
2
0
1
0
0
1
2
1
0
0
0
6
0
0
0
2
2
1
0
0
0
1
0
1
0
0
2
0
0
0
0
2
0
1
0
2
1
1
0
2
1
2
0
1
0
1
1
0
0
2
0
0
0
0
0
0
1
1
0
0
2
1
2
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
1
2
0
2
2
0
2
2
0
1
0
1
2
3
0
0
2
0
0
0
0
0
1
1
0
3
1
2
0
0
2
0
0
0
1
1
0
1
2
0
2
0
2
0
1
1
1
2
2
2
0
1
0
2
0
1
2
0
0
0
0
0
0
1
0
2
1
0
1
1
0
1
2
2
0
0
4
0
0
0
2
0
1
0
2
1
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
2
2
1
0
0
1
0
2
2
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
1
1
0
2
0
1
0
0
0
0
1
0
1
0
3
0
0
0
1
0
0
0
0
3
3
0
2
0
0
0
1
2
2
0
0
0
1
1
2
0
1
2
0
0
2
0
0
0
0
1
2
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
2
0
2
1
1
0
0
0
2
2
1
0
0
1
0
2
2
0
1
0
1
0
2
0
0
0
1
0
2
0
2
1
0
1
0
1
3
0
2
1
1
0
0
0
0
0
1
0
0
1
1
2
2
0
0
0
0
1
1
1
0
1
0
1
1
0
0
1
0
0
0
1
4
0
2
0
1
0
3
2
0
2
0
2
1
2
2
1
0
1
1
0
0
0
0
0
0
25
0
0
1
0
0
0
2
0
0
1
3
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
2
0
1
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
2
0
0
1
0
1
0
2
3
0
0
0
0
1
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
1
1
1
0
0
3
1
0
0
0
2
1
3
0
1
1
0
0
0
0
1
0
1
0
0
2
0
1
0
1
2
1
1
0
0
2
1
1
2
1
0
2
1
1
0
0
1
0
3
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
1
0
0
3
2
1
2
1
2
0
0
0
0
0
6
1
0
2
0
0
1
2
2
0
0
0
2
2
2
0
0
0
0
0
1
2
1
1
2
2
0
2
0
0
0
1
1
0
0
2
0
1
2
2
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
2
0
2
1
2
0
0
0
1
0
1
0
2
2
0
0
1
0
0
0
2
2
1
0
2
1
2
1
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
1
0
1
2
0
1
3
0
1
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
2
0
0
1
0
1
2
1
2
1
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
2
2
0
0
0
0
0
1
1
0
2
0
2
2
1
0
0
0
0
0
1
2
2
2
2
1
0
0
0
0
2
0
1
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
2
1
0
0
2
0
2
0
1
1
0
0
0
0
1
2
0
0
0
0
0
1
2
0
0
0
2
0
2
0
0
0
1
0
1
2
0
0
1
0
1
1
0
0
2
0
0
0
3
0
0
3
0
0
0
0
3
0
2
2
1
0
0
2
1
0
0
0
2
0
0
0
0
2
2
0
0
0
2
1
0
2
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
2
0
0
2
1
2
0
0
0
1
2
1
2
1
0
0
0
0
0
1
1
1
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
2
0
0
0
2
0
1
0
0
2
2
0
2
1
1
0
2
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
2
2
1
1
0
0
0
0
1
0
0
4
1
2
0
1
0
0
0
0
2
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
3
1
2
0
0
0
0
1
3
1
0
1
0
0
0
0
0
0
0
2
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
2
0
6
2
1
1
0
0
0
2
1
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
3
0
1
1
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
1
0
2
2
3
0
1
0
2
2
0
0
0
0
0
2
1
0
0
1
0
0
0
2
0
0
0
1
2
0
0
0
1
0
0
2
0
2
3
1
1
2
1
0
0
2
1
2
2
0
1
0
0
1
0
0
0
3
0
0
0
1
0
1
2
0
0
0
0
0
0
2
0
1
0
1
2
2
0
0
1
0
0
1
0
0
0
0
0
2
3
1
3
0
0
1
0
0
1
2
2
3
0
1
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
2
0
1
0
0
1
2
1
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
3
1
0
0
0
0
2
1
2
1
1
0
0
2
2
2
0
1
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
1
0
1
0
0
1
0
1
1
0
0
0
1
0
1
0
0
2
0
0
0
3
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
2
1
1
1
3
0
0
2
2
2
1
0
0
0
0
2
0
0
0
0
2
2
0
1
1
0
0
0
1
3
0
0
0
0
0
2
0
0
2
1
1
2
0
0
2
0
3
0
3
0
2
2
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
2
0
1
0
2
0
0
0
0
2
0
0
2
2
5
0
0
0
1
1
0
0
0
2
2
0
2
0
0
0
0
0
0
2
2
0
0
0
1
2
1
0
1
0
2
3
0
1
0
1
0
2
0
0
0
0
1
1
1
1
0
0
2
2
0
0
0
2
0
3
0
1
0
1
0
0
0
1
0
0
3
1
1
0
0
0
0
2
0
1
0
1
2
1
0
0
1
0
0
1
0
0
0
2
4
0
0
1
1
0
1
2
0
0
1
3
0
0
3
0
0
0
2
0
2
2
2
0
0
2
0
0
0
0
0
0
0
3
0
0
0
1
1
0
0
0
2
0
1
0
1
1
0
0
1
0
1
0
1
1
0
0
1
2
2
0
3
0
0
0
0
0
0
2
0
0
0
2
2
0
0
2
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
4
1
1
0
0
2
1
0
1
2
0
0
0
1
0
1
1
0
0
0
0
2
2
0
1
2
1
0
1
0
0
0
1
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
1
0
0
0
0
0
1
1
0
0
1
1
2
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
1
1
0
0
0
0
0
4
2
0
0
2
0
0
0
1
1
0
1
0
0
2
1
1
0
2
0
0
0
0
0
0
1
0
2
0
2
2
0
0
2
0
0
0
0
0
1
2
0
0
0
0
2
0
0
1
0
0
0
2
0
3
0
2
2
0
2
0
0
0
0
2
0
0
0
0
2
0
1
2
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
10
0
0
2
0
0
0
0
2
1
2
1
0
0
2
0
1
0
0
1
0
2
0
0
0
2
0
0
1
0
0
1
0
2
0
1
0
1
0
0
3
0
2
0
0
0
2
0
1
0
0
2
2
0
2
0
0
0
2
0
0
0
0
0
2
2
1
1
0
0
1
0
0
2
0
1
0
3
1
0
0
0
2
2
1
1
1
0
0
1
0
0
0
3
0
0
0
0
0
0
2
0
0
0
1
2
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
1
1
0
0
0
0
1
2
0
2
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
2
2
1
0
3
0
0
0
2
1
0
0
0
0
1
0
1
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
1
1
2
1
1
0
0
0
0
1
0
0
2
0
1
1
0
0
1
0
0
0
1
4
0
0
0
1
4
1
0
0
0
0
1
0
1
0
0
0
0
1
1
1
1
0
0
0
0
2
0
1
2
1
0
1
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
3
0
1
1
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
1
0
2
0
0
2
0
0
0
0
0
1
0
0
0
1
0
1
2
0
0
0
0
1
1
0
0
1
1
2
3
2
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
2
0
0
0
0
0
0
2
0
1
0
1
0
0
0
2
0
2
1
0
2
0
0
0
1
0
0
0
0
0
1
2
0
0
2
3
0
1
0
0
0
0
0
1
0
1
2
0
0
0
0
0
1
0
0
1
1
0
4
0
0
0
1
3
0
0
0
0
2
0
0
0
1
0
3
0
0
0
1
1
2
0
0
1
1
0
0
0
0
2
2
0
0
2
1
2
1
0
0
1
2
2
0
0
1
0
0
0
0
0
1
2
1
0
0
0
1
0
0
1
0
0
0
1
1
0
3
0
3
0
0
4
0
2
0
0
0
0
3
2
0
0
0
1
0
0
1
0
1
0
0
0
1
2
1
1
0
0
0
0
0
0
1
0
0
1
4
0
0
3
0
0
0
1
2
0
0
0
0
1
0
0
2
4
0
0
0
0
0
0
0
1
0
2
0
1
0
2
0
1
0
0
2
0
2
1
0
0
0
1
0
0
0
0
1
0
1
1
2
0
3
0
0
0
0
0
1
0
0
2
1
1
0
0
0
1
0
2
2
0
2
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
2
0
0
0
0
1
1
1
1
0
0
0
0
2
7
3
0
0
0
2
0
1
1
1
0
2
0
0
0
0
2
1
0
2
1
3
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
2
2
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
2
0
0
1
0
2
2
1
1
1
0
0
0
1
0
1
2
0
1
0
0
1
0
1
1
1
0
0
3
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
1
2
1
2
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
1
0
0
3
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
1
0
0
1
0
0
0
0
0
0
0
1
0
1
2
0
4
1
0
0
0
1
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
1
3
0
0
0
0
0
1
2
0
1
0
0
3
2
0
2
0
1
0
0
1
1
0
2
0
1
0
2
0
1
0
0
2
0
1
0
0
0
0
1
1
1
2
2
1
0
1
1
0
0
2
2
1
2
2
0
0
0
2
1
2
0
2
0
1
2
0
0
0
0
0
0
2
2
1
2
0
0
2
0
0
0
0
0
0
2
0
0
2
2
1
0
2
0
0
0
1
0
0
0
0
1
0
2
0
7
0
0
1
1
0
0
2
0
0
0
1
1
0
0
2
0
0
0
2
0
0
3
3
0
0
0
0
1
0
0
0
0
2
3
0
0
0
0
0
2
0
0
0
0
0
1
0
0
3
1
0
1
1
4
1
0
1
1
1
0
0
0
0
0
1
0
0
2
1
0
1
0
1
0
2
2
0
0
0
0
0
0
1
1
0
0
1
2
0
1
0
0
0
0
0
0
0
2
0
1
2
1
0
0
0
1
1
0
1
2
2
1
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
2
1
1
0
1
1
0
0
0
1
1
2
1
1
2
0
0
0
1
2
0
0
2
0
0
0
2
2
0
0
1
2
0
1
0
0
0
0
0
0
2
1
0
0
0
0
1
1
0
0
1
0
1
1
3
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
2
4
0
0
0
2
1
0
0
1
0
0
0
1
1
2
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
2
0
2
1
0
0
2
0
2
0
0
1
0
0
1
0
0
1
1
2
0
0
1
0
0
0
2
0
0
2
0
2
0
0
0
2
0
0
0
0
2
0
2
1
0
1
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
3
0
0
0
0
1
0
1
2
1
1
0
2
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
1
2
0
0
2
1
0
0
2
0
1
2
1
0
0
2
0
0
0
0
1
0
0
2
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
4
0
0
2
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
3
0
2
2
0
1
1
1
3
0
0
0
0
0
0
2
1
0
1
0
0
0
1
2
1
0
0
2
0
0
0
0
2
0
1
0
0
0
2
0
0
0
1
1
1
0
0
1
0
2
1
0
0
0
0
1
2
1
2
1
0
2
0
0
0
0
2
0
0
1
0
1
3
3
0
1
0
1
2
0
2
3
2
0
0
0
1
2
0
2
0
1
2
2
0
0
2
1
0
0
2
0
1
0
1
0
0
0
0
2
1
0
0
1
0
0
0
0
1
0
2
0
0
1
0
0
2
0
0
1
0
0
2
3
0
0
0
4
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
1
0
0
2
2
0
0
2
2
0
2
0
0
1
0
1
0
2
2
2
0
0
2
0
0
0
1
2
0
2
0
0
0
2
1
0
0
0
1
2
2
1
2
0
0
0
1
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
1
0
0
0
2
0
2
1
2
0
0
0
3
1
2
0
0
0
0
2
0
2
2
0
0
1
0
1
1
1
0
0
0
5
0
0
0
0
0
0
2
0
2
0
2
1
0
0
2
1
0
2
0
1
2
0
0
2
0
1
0
2
0
1
0
0
3
0
2
0
0
0
1
1
2
1
0
2
0
0
0
1
0
2
0
0
0
0
1
0
2
0
0
4
0
0
0
0
1
0
0
0
0
0
2
1
0
3
0
1
0
0
2
0
0
0
0
1
3
0
0
2
0
1
2
1
0
1
0
2
0
0
1
1
0
1
2
0
1
0
1
0
0
0
0
1
0
0
0
1
2
2
0
0
2
0
0
0
2
0
2
0
0
1
3
1
1
1
2
2
0
0
1
0
0
5
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
2
0
0
0
1
0
0
3
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
4
0
0
0
1
1
1
0
1
1
0
1
2
0
1
0
0
0
0
2
0
1
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
1
0
2
1
2
0
1
2
0
0
0
1
0
1
1
1
0
1
1
0
1
0
0
0
0
0
2
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
1
1
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
2
1
1
0
0
0
0
0
0
2
0
0
0
1
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
2
0
0
0
2
3
0
4
0
0
1
1
0
1
1
0
0
0
0
0
2
0
0
1
0
1
1
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
1
1
0
3
2
1
0
0
0
2
0
0
2
3
0
2
0
1
0
2
0
1
0
1
0
0
0
3
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
1
2
0
0
0
0
2
2
2
0
0
2
1
0
0
1
0
0
0
0
0
2
2
2
0
1
1
0
0
0
0
2
0
0
0
0
1
1
1
1
0
0
2
0
0
0
2
0
0
1
0
1
1
1
0
0
0
2
0
0
0
1
2
1
0
0
2
0
1
0
0
0
1
0
1
2
2
2
0
2
1
2
2
1
0
0
0
2
1
0
0
0
0
2
0
1
0
0
0
0
0
2
0
1
0
0
0
0
2
3
0
0
0
0
0
2
0
1
2
0
3
0
0
2
0
1
0
2
0
1
0
3
0
0
1
0
0
0
1
0
0
2
0
0
2
2
0
2
0
0
0
0
2
0
1
0
1
1
0
0
0
0
1
0
0
1
0
0
2
0
0
0
1
4
0
0
2
2
0
0
0
1
1
1
0
2
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
1
2
0
4
0
0
0
5
0
1
0
0
0
0
0
1
0
0
3
0
1
0
2
1
0
0
2
0
0
0
1
1
0
1
0
0
2
2
1
2
1
1
1
0
0
0
1
0
0
0
1
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
3
2
0
2
0
0
1
0
0
2
0
0
1
0
0
0
3
3
0
2
0
0
0
1
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
2
0
2
2
2
2
1
0
0
0
0
1
1
0
0
0
0
2
1
2
1
0
0
1
0
1
2
0
0
0
2
0
1
0
0
0
1
0
0
4
5
1
0
3
1
0
0
0
0
1
1
0
0
0
2
0
0
0
2
2
0
0
1
1
1
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
2
0
0
2
1
3
0
0
1
0
0
0
0
1
1
1
0
2
1
1
2
2
1
0
0
0
0
3
0
1
1
2
0
1
0
1
0
0
1
0
1
1
0
2
1
0
0
0
0
0
2
2
2
0
2
1
2
0
0
2
2
2
0
0
1
0
0
0
0
0
2
0
1
1
0
0
0
1
2
1
0
0
2
0
0
0
1
1
0
0
2
0
1
0
0
1
0
0
1
0
2
1
1
0
0
2
0
0
0
0
2
1
1
0
0
0
0
0
0
0
1
2
1
0
1
1
0
0
1
2
0
1
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
2
2
1
0
1
0
1
0
0
0
1
0
2
2
1
2
0
0
2
0
2
0
0
0
2
1
0
0
1
0
0
0
0
1
1
2
0
0
0
0
0
0
0
1
0
1
2
0
0
0
1
0
0
0
2
0
0
0
1
1
2
0
2
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
1
2
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
2
0
2
1
2
0
0
2
2
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
2
1
2
0
0
0
2
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
2
2
0
2
1
0
0
2
0
1
0
1
1
0
2
0
0
1
2
0
0
0
0
2
2
1
0
2
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
3
1
2
1
1
0
0
0
0
2
0
1
2
1
1
2
0
2
0
0
0
1
7
0
0
0
2
0
0
1
0
0
1
0
2
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
1
0
2
0
0
2
0
0
0
0
0
3
3
0
0
0
0
0
1
1
1
1
3
1
0
0
0
0
0
0
2
0
0
0
2
1
0
1
2
1
2
1
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
1
1
1
0
1
0
1
0
1
1
0
1
0
2
0
0
0
0
2
0
0
0
1
1
0
1
0
0
0
0
0
0
1
3
1
0
1
1
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
2
0
1
1
0
0
1
0
0
0
2
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
2
2
0
0
0
2
2
0
1
0
1
0
1
0
2
0
0
0
2
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
1
0
0
0
2
1
0
2
1
0
0
2
0
1
0
1
0
1
0
0
1
2
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
2
2
2
0
0
0
2
0
0
0
1
2
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
2
2
0
0
1
2
0
0
0
0
0
0
0
1
1
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
2
0
0
2
0
3
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
2
1
0
0
0
1
0
0
0
0
1
2
1
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
1
3
2
1
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
1
0
1
2
0
2
0
0
0
0
0
0
2
1
0
1
0
0
1
1
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
2
2
0
0
0
0
0
0
0
2
3
0
0
1
2
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
2
1
1
0
0
0
1
2
0
0
0
2
0
2
0
1
0
0
1
1
1
0
0
0
0
1
0
2
0
0
0
1
3
0
0
0
1
1
0
0
1
0
1
2
3
0
0
0
0
2
2
0
0
0
0
1
2
0
1
2
0
0
0
0
1
2
0
1
0
1
0
0
0
0
4
1
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
2
0
0
0
6
0
2
0
0
0
2
0
0
0
1
1
2
1
0
0
0
1
1
2
0
1
0
1
0
1
0
0
2
0
0
0
0
1
1
1
1
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
1
0
0
1
0
1
1
2
0
0
0
1
0
1
2
2
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
2
1
0
1
0
2
0
1
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
1
2
0
0
0
0
0
1
0
2
0
0
3
0
2
0
0
0
1
0
0
0
2
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
2
1
0
0
3
1
0
0
2
1
1
0
1
1
0
0
0
4
1
2
1
0
0
0
0
1
2
0
0
1
1
2
0
2
0
0
0
0
0
1
0
2
2
0
1
2
2
2
1
1
0
1
0
0
1
2
0
0
2
1
0
2
1
0
0
3
2
1
2
0
1
0
0
0
0
3
0
2
0
1
1
0
0
0
0
0
0
0
1
1
2
0
0
0
2
0
2
0
0
0
1
1
2
1
2
2
0
0
0
0
2
0
0
0
1
0
0
0
1
0
1
1
0
1
2
4
2
0
0
0
2
1
0
1
0
0
2
0
0
2
2
1
3
0
0
2
0
1
0
2
1
0
2
1
0
0
0
1
0
1
0
2
2
0
0
2
0
2
1
0
2
1
2
0
2
0
0
1
0
2
0
0
2
0
1
0
0
1
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
2
0
0
2
0
0
0
0
1
2
0
2
2
0
0
0
2
0
2
2
0
0
1
1
0
1
2
0
2
1
2
0
0
2
0
2
4
0
0
0
1
0
1
0
0
1
1
2
0
0
2
3
0
2
0
0
2
0
1
1
2
1
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
2
1
2
0
2
0
2
0
0
1
0
2
2
0
0
0
0
1
0
0
0
0
0
3
2
1
1
0
2
0
1
2
0
2
0
1
1
0
0
2
0
0
0
1
0
0
1
2
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
3
2
2
0
1
0
0
0
0
2
1
0
0
1
0
1
1
2
0
0
1
0
0
2
1
0
0
1
0
0
2
0
2
0
1
0
2
0
1
1
1
3
1
0
2
3
2
1
0
2
0
0
0
2
2
0
1
2
1
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
2
0
1
0
0
0
1
2
0
1
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
2
0
1
2
0
1
3
0
0
0
0
1
1
0
0
0
0
1
0
2
2
2
1
2
0
0
1
0
2
0
0
2
0
2
0
0
0
0
2
0
0
2
2
0
0
0
2
0
3
0
2
3
0
2
2
0
0
2
0
2
2
0
0
1
0
0
0
2
0
0
1
2
0
2
4
2
2
0
0
0
1
2
0
1
3
0
1
0
0
0
1
2
1
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
3
0
0
2
1
0
2
0
2
0
1
0
0
0
2
2
0
0
2
2
1
0
0
2
0
2
2
2
0
0
1
0
1
1
1
3
0
0
0
0
2
1
2
1
0
0
0
1
0
2
0
0
0
0
1
2
0
1
0
2
0
0
1
0
0
0
0
1
0
1
0
0
0
0
2
1
2
1
0
2
1
0
2
0
0
0
0
1
2
0
0
1
0
0
0
1
2
0
1
3
0
0
1
0
0
0
0
0
0
2
0
1
1
2
2
9
1
0
0
2
0
1
1
2
0
2
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
1
0
2
1
0
0
2
0
1
0
0
0
2
2
0
1
1
1
1
0
3
0
2
3
2
1
0
0
1
2
0
2
0
1
0
1
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
2
2
1
4
1
0
0
0
0
0
0
0
0
0
0
2
0
1
3
1
2
0
0
0
0
2
0
0
5
0
1
0
0
0
0
0
0
2
2
1
0
2
1
0
2
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
2
2
1
0
0
0
0
1
0
0
0
2
0
3
0
0
0
2
1
0
0
0
2
0
0
0
0
2
0
1
1
0
2
3
0
1
0
3
1
0
1
2
2
2
1
7
3
0
0
1
0
0
2
1
0
1
0
0
0
2
0
0
0
1
0
1
1
2
0
0
0
1
0
2
1
0
0
2
0
1
2
0
0
2
1
0
1
0
1
0
0
2
0
0
2
2
0
0
0
2
1
1
0
0
0
0
1
4
2
0
1
1
1
2
2
0
0
0
1
1
1
2
1
2
0
0
0
3
0
2
0
2
2
1
3
2
1
0
0
1
2
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
1
2
2
0
2
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
2
0
0
1
1
0
2
2
0
1
0
1
0
2
0
0
0
0
1
2
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
1
0
0
1
0
0
0
0
2
0
0
1
0
0
0
2
0
2
0
2
0
0
0
0
0
0
1
1
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
2
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
2
0
3
1
0
0
0
1
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
2
0
0
2
2
0
0
0
1
0
2
2
0
2
0
0
2
2
0
2
0
0
2
0
0
0
0
0
0
1
1
1
2
0
0
0
0
2
0
1
0
0
5
1
0
0
0
1
1
2
0
2
0
1
0
0
0
0
0
1
0
0
0
0
1
2
0
2
1
0
3
1
0
2
0
0
0
0
0
0
1
1
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
1
0
0
0
2
0
2
0
0
2
2
1
0
2
1
0
0
1
0
0
0
1
0
2
0
1
1
1
0
0
0
2
0
0
1
2
1
0
0
1
2
0
0
1
0
1
0
2
0
0
2
0
2
1
0
2
2
3
2
2
1
0
0
0
0
0
1
1
0
2
3
0
0
0
1
0
1
0
1
1
0
0
2
1
3
0
0
1
0
1
0
0
1
1
1
1
2
1
1
0
1
0
1
0
5
2
0
0
0
0
6
0
0
0
1
1
0
2
0
2
0
2
0
2
0
0
0
1
0
0
2
1
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
2
2
1
1
4
0
0
0
0
0
2
0
0
0
2
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
1
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
4
1
0
0
0
1
0
0
0
2
0
0
0
0
2
1
0
2
1
0
1
0
0
0
1
1
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
2
2
0
0
2
0
0
1
0
0
1
0
0
0
0
1
2
1
0
0
2
1
0
2
2
0
1
1
2
0
0
2
0
0
1
0
1
0
0
0
0
0
0
2
4
9
2
0
1
0
0
1
3
2
2
0
2
0
0
0
0
0
1
0
1
0
0
2
0
1
1
0
0
3
0
0
0
0
0
0
1
1
1
3
1
0
2
0
1
0
0
0
0
2
2
0
0
0
1
0
0
1
0
2
0
0
1
0
1
2
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
1
0
0
0
2
2
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
2
2
1
0
0
0
2
0
0
1
0
2
1
0
0
0
0
0
0
0
2
1
0
2
0
0
0
1
1
0
2
0
1
0
0
0
0
0
1
2
0
0
0
2
1
1
0
0
1
1
0
0
0
0
1
0
2
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
2
0
0
2
2
2
0
1
2
0
0
0
0
1
0
1
1
0
0
0
2
0
0
0
0
0
1
0
0
1
0
1
0
1
0
1
2
0
0
2
0
0
0
0
2
0
2
2
0
0
0
1
0
0
1
2
0
2
0
3
0
0
0
1
0
0
3
0
0
1
2
0
1
0
0
2
0
1
0
1
0
0
1
2
2
0
2
0
0
0
0
2
0
2
0
2
1
0
2
0
0
2
1
0
0
1
1
0
0
0
0
0
0
0
2
1
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
1
0
2
0
0
0
0
0
0
2
0
0
0
3
1
3
1
0
0
0
0
0
0
0
0
0
2
0
0
1
1
2
0
0
0
1
1
1
0
2
0
0
0
0
0
0
2
2
1
1
0
0
1
0
1
1
2
0
4
1
2
0
0
6
0
2
0
1
0
0
2
1
0
0
0
2
0
0
2
0
0
1
2
1
0
2
0
0
1
1
0
2
1
1
0
0
1
1
4
0
2
1
0
1
1
2
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
2
1
0
1
0
2
0
0
0
2
1
0
2
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
3
2
2
2
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
2
2
0
1
0
0
0
1
0
0
0
1
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
1
1
0
0
1
3
0
2
0
0
0
0
0
0
2
0
0
0
1
0
1
0
1
2
0
0
0
0
0
2
1
0
3
3
0
0
2
0
1
2
0
0
0
1
0
0
0
0
0
2
0
0
1
1
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
3
0
1
0
2
0
1
1
1
2
1
1
2
0
0
1
0
1
3
0
2
0
0
1
1
0
0
0
0
2
0
0
0
1
0
0
2
1
0
0
1
2
0
0
0
0
1
0
0
3
2
0
1
0
1
1
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
3
1
0
1
0
2
0
1
0
0
0
1
2
0
0
0
0
0
1
0
2
0
0
1
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
3
2
0
0
0
1
0
0
0
2
3
0
0
2
0
0
2
0
1
2
1
2
0
0
0
1
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
2
1
0
0
0
2
0
1
0
0
0
0
0
1
4
2
0
2
0
0
2
0
2
2
0
0
0
0
0
0
2
0
2
0
2
0
0
0
1
0
1
1
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
1
0
1
0
2
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
4
0
0
0
0
0
1
3
0
0
0
0
0
0
0
1
1
0
0
2
1
0
0
0
0
1
2
0
2
0
1
0
1
0
0
0
4
0
1
1
2
2
1
0
0
0
1
1
0
0
0
0
0
2
1
2
2
0
2
1
0
0
1
0
0
2
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
2
0
1
0
1
0
0
1
0
3
0
1
1
2
0
0
2
2
0
2
0
0
0
2
0
1
2
2
2
0
0
0
1
0
0
2
0
2
0
0
0
1
1
1
0
0
2
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
2
0
0
1
1
0
2
0
0
1
0
4
0
0
2
2
4
0
0
0
3
1
2
2
1
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
2
2
0
2
0
0
0
0
0
1
1
0
3
0
0
1
0
2
1
0
0
0
2
0
0
1
0
0
0
1
0
0
1
3
2
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
1
0
0
2
0
1
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
1
3
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
2
0
0
3
0
0
2
0
1
0
2
0
1
2
0
0
1
0
1
0
2
0
2
0
0
2
0
1
0
1
4
0
2
0
1
0
2
1
0
1
0
0
0
0
0
0
2
1
0
2
0
1
0
2
0
2
0
0
0
0
0
4
1
1
2
0
0
1
1
0
0
0
0
0
0
2
0
1
0
0
1
2
1
0
0
0
2
0
0
0
0
0
0
2
0
5
0
0
0
1
0
1
1
0
2
1
0
0
2
2
0
0
2
2
2
1
0
1
0
0
1
2
0
1
2
0
2
2
0
0
0
0
2
0
0
0
1
3
0
2
0
0
0
0
1
2
0
0
2
0
0
2
0
1
0
0
0
0
0
1
2
1
1
0
0
0
0
1
2
0
0
2
0
0
3
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
2
0
0
0
0
2
1
0
1
1
1
0
2
0
0
0
0
0
1
1
1
1
0
0
1
0
0
2
1
0
0
0
1
0
0
0
1
0
0
3
1
1
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
2
2
1
0
0
0
2
0
0
1
1
2
0
2
1
1
1
2
0
0
2
0
0
0
0
0
0
1
2
1
1
1
0
2
1
2
0
0
2
1
3
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
3
2
1
1
2
0
2
0
0
0
0
1
0
0
2
1
0
0
0
2
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
1
2
0
1
2
2
1
0
0
0
0
0
1
2
2
1
0
2
1
1
0
0
0
0
1
0
2
1
1
1
0
4
0
1
0
2
0
0
1
0
0
0
0
0
0
2
2
0
0
1
0
1
2
0
1
0
1
1
0
0
0
2
0
0
0
2
1
1
0
0
2
1
2
0
2
0
0
0
1
0
0
3
4
0
0
1
2
1
1
1
0
0
0
1
3
0
0
0
0
1
1
0
0
1
0
1
2
1
0
0
1
0
0
2
0
0
1
1
0
2
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
3
0
0
0
2
1
2
0
0
0
1
0
0
0
1
0
0
2
0
0
0
1
0
2
0
1
1
0
0
1
1
0
0
0
0
0
1
0
0
0
2
0
1
0
1
1
2
2
0
1
0
0
0
0
0
2
0
0
0
1
0
1
2
0
2
1
0
0
1
0
2
2
1
1
1
0
0
0
2
2
1
0
0
1
0
3
0
1
1
0
0
1
0
2
1
1
0
0
0
0
1
1
0
0
0
0
1
0
0
1
2
0
3
0
0
2
0
0
0
1
0
2
0
0
1
0
0
0
2
0
1
0
1
0
1
2
0
2
0
1
0
0
1
2
1
2
2
2
1
1
0
0
0
0
2
0
0
0
3
2
0
4
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
1
0
0
1
0
1
1
0
0
0
2
0
0
0
2
0
0
0
0
0
1
2
0
0
0
2
2
0
1
2
2
2
0
2
0
0
1
0
5
0
3
0
1
0
2
0
0
1
0
1
0
0
2
0
1
0
1
0
0
0
1
0
0
0
2
2
1
2
0
0
0
0
0
0
2
0
0
0
1
1
1
3
0
0
0
0
0
0
0
1
0
0
0
1
1
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
2
3
2
0
0
1
0
3
0
0
1
0
0
1
0
6
2
0
0
0
0
0
0
1
0
0
0
3
0
0
1
1
0
0
0
1
2
0
0
2
2
1
2
0
1
0
1
2
0
0
0
0
0
2
1
0
0
0
2
1
0
0
2
0
1
1
1
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
2
0
2
1
1
1
0
0
6
0
0
0
2
0
0
0
2
2
1
1
2
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
2
0
2
1
0
0
0
0
1
0
2
0
2
0
2
2
0
2
1
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
1
0
3
1
0
0
0
0
1
1
1
2
0
0
0
0
3
2
0
0
2
0
1
0
0
0
0
2
1
0
0
0
0
0
2
0
2
0
0
0
1
1
0
1
0
0
2
2
0
0
0
0
1
0
1
1
0
2
0
0
0
0
0
0
0
0
0
4
0
2
0
0
0
0
1
0
0
2
0
2
1
0
0
1
2
0
0
1
0
0
1
1
1
0
0
0
1
0
0
1
2
0
1
0
0
0
1
0
1
1
0
4
0
0
4
0
2
1
0
0
0
1
1
2
0
1
2
0
0
2
0
0
0
1
0
0
2
3
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
2
2
1
2
0
0
0
10
0
1
0
0
0
0
2
3
2
0
0
1
2
0
0
0
0
1
1
0
2
2
0
1
0
0
1
0
1
2
0
0
0
0
1
0
0
0
1
0
0
1
2
0
0
1
2
1
0
3
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
2
1
1
1
0
0
0
2
3
0
0
1
1
1
0
1
0
0
1
0
2
0
1
1
0
0
1
0
1
0
0
1
0
0
1
1
0
1
0
0
2
0
1
0
0
0
0
1
0
0
0
1
0
2
0
0
1
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
1
0
1
0
0
2
1
0
0
1
0
0
1
0
0
0
0
2
0
0
2
0
0
1
0
0
2
0
0
0
0
1
1
0
1
2
0
0
0
0
2
0
2
6
0
1
0
1
0
0
0
0
0
1
2
0
0
0
1
2
1
0
2
0
0
1
0
0
2
1
1
2
1
1
2
2
1
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
2
1
0
2
1
0
2
0
0
0
0
3
2
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
1
2
1
0
0
0
1
2
2
0
0
0
0
1
1
2
0
0
0
0
0
0
1
0
0
2
1
0
1
1
2
0
0
0
2
2
0
0
2
1
2
0
0
2
2
0
0
0
1
0
2
1
0
2
0
2
0
0
0
0
0
0
2
1
0
0
1
1
1
0
2
0
0
1
0
3
2
0
5
1
4
0
0
0
2
0
2
1
0
0
1
1
0
1
3
2
0
0
0
1
0
0
0
0
2
0
0
2
0
2
2
2
0
2
2
0
3
2
0
2
0
0
1
0
0
1
2
0
2
1
0
2
0
0
2
0
0
1
1
2
0
1
0
1
0
1
0
0
2
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
2
1
0
0
0
0
2
0
2
2
0
1
0
0
2
0
0
1
0
0
1
0
0
0
2
0
2
2
0
0
0
1
1
0
0
0
0
0
2
0
0
1
0
2
0
0
2
0
0
1
0
0
0
2
2
1
0
2
0
0
0
4
2
2
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
1
1
1
0
1
2
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
1
2
0
1
1
0
0
1
0
0
0
0
0
1
1
0
0
1
0
1
1
0
0
1
0
0
1
1
0
2
0
0
2
0
1
2
1
2
0
0
1
0
0
0
2
0
0
0
2
1
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
1
2
2
0
1
0
0
0
0
0
12
0
0
1
1
1
0
0
1
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
4
0
3
0
1
0
1
0
0
2
0
2
0
2
0
0
1
1
2
2
2
0
0
1
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
3
0
0
1
0
0
1
0
1
0
0
2
0
0
1
0
4
1
0
1
1
0
2
2
0
0
0
0
0
3
2
0
0
2
2
1
3
0
0
1
0
0
3
3
0
0
0
0
2
0
0
1
0
0
2
0
1
0
0
0
0
1
8
0
0
2
2
1
2
0
1
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
6
0
1
1
1
0
1
3
0
0
0
0
0
2
3
2
2
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
1
0
1
0
0
0
0
0
2
0
1
0
0
2
1
0
1
2
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
2
0
1
1
2
2
0
0
2
0
0
0
0
0
1
0
0
0
2
1
2
0
0
0
2
0
0
0
0
2
0
2
2
1
3
2
0
0
0
0
0
0
1
0
1
1
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
3
0
0
2
0
1
0
0
1
0
1
0
3
0
0
1
0
1
0
0
0
1
1
2
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
2
0
0
0
1
0
1
1
3
0
1
0
0
1
1
0
1
0
0
0
1
0
2
0
1
0
0
1
0
2
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
1
2
0
2
1
2
0
0
0
0
0
0
0
2
0
1
2
2
2
0
0
0
0
2
1
0
1
0
1
0
2
0
1
0
0
0
0
1
0
1
1
0
0
0
1
1
3
0
0
6
0
2
0
2
0
0
1
1
1
0
0
1
0
2
0
2
0
0
0
0
2
2
0
2
0
0
2
2
1
0
0
1
0
0
0
0
2
3
1
1
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
1
2
0
2
0
0
0
1
0
2
1
3
1
0
0
3
0
2
1
0
0
0
1
0
0
0
0
1
0
0
2
1
1
1
0
2
0
0
0
0
1
1
3
0
1
0
0
0
1
3
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
2
0
0
0
1
0
2
0
1
1
0
0
0
0
1
0
0
2
1
1
0
0
0
1
0
1
0
1
0
0
0
2
1
1
0
0
0
0
0
0
0
0
1
2
0
0
1
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
2
2
1
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
6
1
0
2
0
0
2
0
0
0
2
0
2
0
1
1
0
0
0
0
2
0
0
0
2
0
0
2
2
0
0
1
3
0
0
1
1
2
2
2
0
2
1
3
0
3
0
0
0
1
1
0
0
0
0
1
0
0
0
3
0
3
2
0
1
2
0
0
0
0
0
0
0
0
1
1
0
0
0
1
2
1
0
0
0
0
2
1
2
1
0
6
1
0
2
0
1
0
3
0
0
0
2
2
0
1
1
1
0
0
0
0
1
0
2
0
0
0
0
0
0
4
5
0
0
2
2
0
0
0
2
2
0
0
0
2
0
0
0
2
2
2
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
1
2
0
1
2
0
1
0
0
0
0
1
2
2
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
1
0
0
0
0
0
2
1
1
0
1
2
0
3
1
1
2
0
1
0
0
1
0
0
5
0
0
0
2
1
2
0
0
0
2
0
0
0
0
0
2
0
1
0
3
0
1
0
0
1
0
0
0
0
0
2
0
2
1
1
0
2
2
0
0
2
2
2
0
0
0
1
1
1
1
0
1
1
0
2
0
1
0
1
1
0
1
0
0
1
0
2
0
0
2
1
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
3
2
1
0
0
0
0
0
1
0
2
2
0
0
0
2
0
0
0
0
0
1
1
0
0
1
1
2
2
0
0
2
0
0
2
0
0
2
0
0
1
0
0
0
0
1
0
4
2
0
0
0
0
1
0
0
0
2
0
2
0
0
1
2
0
1
2
0
1
0
0
2
0
1
2
0
0
0
2
1
0
0
0
0
1
0
0
0
2
0
1
0
4
3
0
1
2
1
1
0
0
0
0
2
1
0
2
2
1
0
0
0
0
0
1
0
2
0
0
1
2
2
0
0
0
2
0
0
2
2
2
0
0
0
2
0
0
0
0
0
0
2
2
2
0
1
1
0
1
2
0
0
0
0
0
0
0
0
1
2
1
0
0
1
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
1
1
0
0
0
2
1
1
0
0
2
0
1
1
0
0
0
2
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
2
1
2
2
0
0
1
0
0
0
1
0
0
0
2
0
0
0
1
1
0
1
0
0
2
0
2
2
0
2
0
2
0
1
0
2
1
1
0
0
2
2
0
2
0
0
0
0
0
0
1
2
1
0
2
0
0
0
0
0
0
0
1
0
1
0
1
1
2
2
2
0
1
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
1
0
2
0
0
0
1
2
2
0
1
1
2
0
2
0
0
0
0
0
0
1
0
0
0
2
0
1
2
0
2
1
0
2
2
0
0
0
1
0
0
2
0
2
2
1
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
2
0
0
0
0
0
4
0
0
0
0
1
0
1
0
0
0
0
1
1
1
2
0
0
0
0
0
0
1
0
0
1
2
0
2
1
1
0
1
0
2
0
0
0
0
0
0
2
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
1
2
0
1
0
0
1
0
0
0
1
1
0
0
2
0
0
0
0
2
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
2
0
1
0
4
1
0
0
0
1
0
0
0
2
1
0
0
0
1
0
2
0
2
0
0
3
0
1
1
0
0
0
0
0
0
2
3
1
1
0
1
0
2
0
0
0
1
2
0
0
2
0
2
0
0
0
0
0
2
2
2
2
1
1
2
2
2
0
1
0
2
2
0
1
2
2
0
0
1
2
0
3
1
0
2
2
1
0
0
1
1
0
1
0
1
0
1
2
0
1
0
2
0
0
0
1
0
0
0
0
1
0
0
2
1
2
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
1
1
0
0
2
1
2
0
0
0
2
1
0
0
0
0
0
1
2
1
0
0
0
1
0
2
0
0
1
1
0
0
1
0
0
2
0
0
1
0
1
0
0
0
0
0
1
2
1
0
0
0
0
0
0
2
0
1
1
2
0
3
1
0
0
2
0
0
0
2
0
0
1
0
0
1
2
1
1
0
2
1
0
2
0
2
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
4
1
0
0
13
0
1
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
2
1
0
0
2
0
2
0
0
0
0
1
0
0
3
0
0
0
1
0
2
1
0
0
0
0
0
1
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
1
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
0
0
1
0
0
2
1
0
0
0
2
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
2
1
1
0
0
1
0
2
0
1
0
2
0
2
2
0
0
0
1
1
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
1
2
0
2
0
0
0
2
0
1
0
0
0
1
0
0
1
0
1
0
0
0
2
0
0
1
0
3
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
2
0
3
2
0
1
0
0
1
0
1
1
0
1
0
0
0
2
0
0
0
0
1
0
2
0
0
2
0
1
0
4
1
1
1
0
2
0
0
0
1
2
0
0
1
1
0
0
0
1
0
0
2
2
0
2
0
1
0
2
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
2
2
2
0
0
1
0
0
0
1
2
0
2
1
0
1
3
2
1
0
0
2
1
0
0
1
2
0
0
1
1
2
0
0
2
0
2
1
2
0
0
0
0
0
0
0
3
0
1
0
0
0
0
2
0
2
0
1
0
0
0
2
0
0
0
0
2
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
2
2
1
3
0
0
0
1
0
0
0
2
0
1
2
2
0
0
2
2
0
0
0
2
0
0
2
0
2
2
1
2
0
0
1
1
0
0
0
0
3
0
1
2
0
1
0
0
1
0
2
2
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
1
2
2
0
0
1
0
1
0
0
2
1
1
0
2
0
0
0
0
0
3
0
0
3
0
0
0
0
2
0
0
0
2
0
3
0
0
0
2
0
1
2
1
1
0
2
0
2
0
0
3
1
0
5
0
1
0
0
0
0
0
1
0
0
2
0
0
2
0
0
1
1
0
0
1
2
0
0
0
1
2
0
0
1
0
1
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
3
1
0
3
0
0
1
0
1
0
1
0
0
0
2
1
0
0
2
1
0
1
0
0
0
0
0
0
2
1
2
0
2
0
0
0
0
0
0
0
2
0
1
0
1
1
0
2
2
0
0
0
0
1
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
4
2
0
2
0
2
3
1
2
2
0
2
0
0
0
0
0
2
1
0
0
0
3
0
0
2
0
0
0
0
0
1
0
1
1
0
4
0
0
0
0
1
2
2
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
2
2
0
1
1
0
0
2
1
2
2
0
1
0
2
0
2
2
2
1
2
2
0
1
2
0
0
2
3
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
5
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
2
1
2
2
5
0
0
0
0
0
0
1
0
0
3
0
0
0
1
3
1
1
1
2
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
1
2
2
0
2
0
2
0
3
0
0
0
0
0
2
1
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
2
0
1
0
0
1
0
0
0
0
0
1
1
0
2
1
0
2
1
2
0
1
2
0
1
1
0
0
0
0
1
2
0
0
0
1
1
0
0
0
0
0
0
1
2
1
1
0
0
2
0
1
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
2
0
0
1
0
0
2
0
0
2
1
0
2
1
0
1
0
0
6
1
0
1
0
0
1
2
0
0
0
2
0
0
0
0
1
1
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
1
0
1
0
0
0
1
0
0
2
1
0
1
2
3
2
0
3
1
0
0
2
0
0
0
0
0
2
1
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
2
2
0
2
0
0
3
2
0
0
0
2
0
0
0
2
0
1
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
1
0
0
1
1
0
0
0
0
2
0
1
3
2
1
1
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
1
13
0
0
2
0
0
0
0
0
1
0
2
1
0
2
2
0
0
1
0
0
0
0
0
2
0
0
0
0
1
2
1
0
1
2
0
0
1
1
0
1
2
0
0
0
0
0
0
0
2
0
0
0
3
0
1
0
0
3
0
1
0
0
2
0
2
0
2
0
0
0
2
0
0
0
2
2
1
0
1
1
0
0
0
2
0
2
0
2
1
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
2
2
1
0
1
0
0
1
1
1
1
1
0
0
0
1
0
3
0
1
0
0
0
1
1
2
0
0
0
0
1
1
1
0
0
0
0
0
0
0
3
0
1
0
2
0
1
0
2
0
0
0
0
0
0
2
0
1
0
3
0
1
2
0
0
0
0
2
1
0
0
2
1
2
0
0
0
0
0
0
1
0
0
1
2
2
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
1
1
1
1
0
0
0
0
1
2
0
0
0
0
0
2
0
1
0
0
1
0
1
0
1
2
0
1
1
1
0
0
0
0
0
1
0
0
2
0
2
1
4
4
1
1
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
2
0
0
2
0
0
1
0
1
0
2
2
1
1
0
2
0
0
0
1
1
3
1
0
0
0
0
1
1
2
2
2
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
2
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
2
2
0
2
1
0
1
2
0
0
2
1
0
0
2
2
0
1
2
0
0
1
2
0
0
2
0
1
0
2
2
1
2
0
2
2
0
0
0
1
0
0
0
0
0
2
1
0
0
0
1
3
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
2
0
0
2
0
1
2
0
2
0
0
0
2
0
0
0
2
6
1
1
1
1
0
1
0
0
1
0
0
0
2
0
1
0
3
0
2
0
4
0
0
1
1
2
0
2
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
2
2
1
3
2
0
2
0
0
2
0
0
0
2
2
0
3
0
0
2
2
0
0
0
0
2
0
0
1
0
4
3
2
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
3
1
0
0
1
0
0
2
1
0
0
0
1
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
2
1
0
1
0
0
0
0
0
1
0
0
0
0
2
1
0
0
1
0
1
2
1
0
0
0
2
0
0
0
0
0
1
1
1
0
1
1
1
1
2
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
1
1
2
0
1
1
2
0
0
0
0
1
0
0
0
0
1
1
1
2
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
1
0
1
1
0
3
2
3
0
2
0
0
2
2
0
1
2
1
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
2
0
0
0
1
0
0
1
2
0
0
1
0
0
0
3
2
0
2
0
0
2
0
0
0
0
1
1
0
1
1
1
0
0
2
2
0
0
0
0
1
0
0
0
0
0
2
2
0
1
0
2
1
1
0
0
0
2
0
0
0
0
0
1
2
0
2
0
0
0
0
0
2
1
0
2
1
0
0
2
1
0
2
0
2
2
0
0
1
2
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
1
0
2
4
0
0
3
1
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
2
0
2
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
1
2
3
0
0
0
2
2
0
0
0
0
0
1
1
0
1
0
2
0
1
3
0
3
2
0
0
0
2
0
0
3
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
1
3
1
0
2
1
0
0
0
1
0
0
0
1
1
0
0
1
1
2
0
1
0
0
0
1
0
2
2
0
1
1
0
2
0
0
2
0
0
1
0
2
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
1
2
1
2
2
2
1
0
0
0
0
1
0
1
2
0
0
0
0
2
0
0
1
0
2
2
1
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
1
1
1
0
0
0
0
0
0
0
0
2
1
2
2
0
2
2
0
0
1
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
1
1
2
2
0
0
0
0
2
0
0
0
1
0
1
2
2
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
2
1
0
1
0
0
0
1
2
0
2
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
1
0
1
0
0
0
2
1
0
1
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
2
1
1
0
0
2
0
2
0
0
0
2
0
1
0
1
0
2
2
1
0
1
0
0
2
2
1
1
2
3
0
2
2
0
1
0
0
2
0
1
1
2
0
0
0
1
0
2
2
0
0
0
0
0
2
0
0
0
2
2
1
0
0
1
0
1
1
0
2
0
0
2
1
0
0
0
2
0
0
2
0
1
0
0
2
0
0
0
0
1
2
2
0
0
1
5
0
0
0
1
1
0
2
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
6
1
1
0
3
0
0
2
2
1
0
0
0
1
0
0
0
1
1
1
0
2
2
1
1
0
0
1
1
0
0
3
0
2
0
0
0
0
0
0
1
2
2
0
0
1
1
1
0
0
2
1
0
1
0
0
1
1
0
0
1
2
1
0
2
1
2
0
0
0
1
0
2
2
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
2
1
2
0
0
0
0
1
2
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
2
1
1
0
0
2
0
0
0
3
0
0
0
1
1
2
0
2
0
0
2
0
0
0
0
2
1
0
0
0
1
4
0
0
0
2
1
1
0
0
0
0
0
2
1
0
0
2
4
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
1
0
1
2
0
2
0
1
0
1
0
0
0
1
1
0
1
2
0
2
0
1
0
1
1
2
2
0
0
2
0
0
0
2
2
0
1
1
0
1
2
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
1
0
1
0
1
0
2
0
0
1
2
2
0
1
1
0
0
2
0
1
0
2
1
0
1
0
2
2
1
1
1
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
1
2
0
0
0
3
0
0
2
1
1
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
1
1
0
2
3
2
1
0
0
0
0
0
7
0
0
2
0
0
0
0
1
0
2
0
0
2
3
0
0
2
0
2
1
2
1
0
1
2
0
2
0
0
1
1
0
0
0
1
1
0
2
0
0
0
0
0
1
0
0
0
0
1
0
2
0
1
0
0
2
0
0
0
0
1
0
1
1
0
0
0
2
1
0
0
0
0
0
2
2
0
0
0
0
1
0
3
2
0
0
6
0
1
0
0
1
0
0
0
1
1
1
0
0
1
0
0
0
0
0
2
2
2
1
0
2
2
0
0
1
1
1
0
0
1
2
0
2
0
0
0
0
1
0
1
1
3
0
2
0
0
0
1
0
1
2
2
0
2
0
0
0
2
0
2
1
1
0
0
0
0
0
0
1
2
3
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
1
1
1
2
1
1
1
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
2
0
1
1
0
0
0
0
4
1
1
1
0
0
3
0
0
2
1
0
0
1
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
2
0
0
0
2
2
1
0
0
0
1
0
0
0
2
2
0
2
1
1
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
1
2
0
2
2
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
3
2
1
0
1
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
2
2
1
0
2
0
3
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
2
2
0
1
0
1
0
0
1
0
0
2
0
2
0
0
0
2
0
0
0
2
0
2
0
0
0
0
2
0
2
0
1
1
0
2
1
0
0
3
0
0
2
0
0
2
1
2
1
1
0
0
0
0
0
0
1
0
0
0
1
2
0
0
3
1
2
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
3
1
0
0
2
2
0
0
3
2
0
0
2
0
0
0
2
1
0
0
0
2
0
0
1
3
1
0
0
0
0
0
0
0
2
1
1
2
0
0
0
1
1
0
3
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
2
0
2
0
0
2
2
0
1
0
1
0
0
1
0
0
0
2
1
1
0
0
0
0
2
2
2
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
1
0
0
2
0
3
2
1
0
0
1
2
0
0
2
1
1
1
0
0
1
0
2
2
0
0
1
1
0
1
1
2
1
0
0
0
0
0
0
1
0
0
0
1
2
0
1
2
1
0
0
1
1
0
1
2
0
0
1
2
0
1
0
1
1
0
0
0
0
0
2
0
0
3
0
2
2
0
0
2
0
0
1
0
2
0
0
2
0
0
1
2
2
2
0
0
2
0
0
0
1
2
4
1
0
1
0
0
1
0
0
0
0
0
2
1
0
0
2
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
2
0
2
0
1
1
0
0
0
1
0
0
0
2
2
2
1
0
0
0
0
0
2
0
0
0
2
0
1
0
2
0
2
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
2
1
0
0
0
2
1
0
2
2
2
0
1
0
0
1
0
1
2
0
0
1
0
0
0
0
0
2
0
3
0
0
3
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
3
4
0
0
0
0
1
0
0
2
0
1
1
0
0
1
2
0
0
1
1
0
0
0
0
1
1
0
3
0
1
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
1
0
0
1
0
2
0
0
0
2
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
2
0
1
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
2
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
2
1
2
0
1
0
0
2
0
1
0
1
0
1
0
2
0
0
1
1
1
0
0
0
2
2
0
2
0
2
0
1
0
1
0
0
3
2
1
2
0
0
1
0
0
1
1
0
0
2
0
2
1
2
0
1
0
1
0
1
0
0
1
0
0
0
2
0
1
1
2
0
2
1
0
2
0
0
1
0
1
1
0
2
0
0
1
1
0
0
0
2
0
0
0
0
2
0
2
0
0
1
0
0
0
0
1
0
1
0
1
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
1
3
2
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
2
0
0
0
1
1
0
2
0
0
0
2
1
1
0
0
1
1
0
2
0
1
0
1
0
1
1
0
2
2
0
1
0
0
2
0
0
1
0
0
0
2
0
0
0
2
3
0
0
0
0
2
1
1
0
1
0
0
0
1
1
0
0
1
0
1
1
1
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
3
0
0
0
1
0
0
8
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
3
2
0
1
0
0
0
2
0
0
1
0
1
0
0
5
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
2
0
2
2
2
0
0
0
3
0
0
0
0
0
1
1
0
0
0
1
3
0
0
2
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
2
2
0
0
0
0
2
0
1
1
0
0
1
1
0
0
0
0
1
0
0
0
2
1
2
0
1
1
0
3
2
2
0
0
2
0
0
1
0
0
0
0
1
0
0
2
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
2
0
0
1
3
0
0
0
4
2
0
2
0
0
0
0
0
1
0
0
0
0
4
0
5
0
0
0
1
0
0
0
0
0
0
1
0
1
2
0
0
1
0
1
2
1
1
0
0
1
0
0
0
0
0
0
2
1
1
0
0
0
2
0
0
0
0
2
1
0
0
0
5
0
1
0
1
0
0
0
0
0
1
2
0
0
2
1
0
0
2
2
0
0
1
0
1
1
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
1
1
0
0
0
0
1
1
1
2
0
0
1
1
0
1
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
2
0
0
1
2
2
0
0
0
2
1
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
3
4
0
2
2
2
2
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
2
1
1
0
0
0
2
2
1
0
0
0
2
1
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
1
0
1
0
0
2
0
3
0
0
0
0
1
0
0
2
0
0
2
0
1
2
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
1
0
2
2
0
0
2
0
0
1
1
1
2
2
0
1
0
0
1
0
2
1
0
0
0
2
0
1
1
2
0
0
0
0
0
0
0
3
0
0
1
0
9
2
0
0
0
2
0
0
1
0
0
2
0
0
0
3
0
0
0
2
0
3
0
0
1
1
0
4
2
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
1
0
0
1
2
1
2
1
1
0
0
3
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
1
0
0
1
0
0
0
0
0
0
2
2
1
2
0
0
0
0
0
0
1
3
0
1
1
0
2
2
0
0
1
0
0
0
2
1
2
1
0
0
0
2
1
1
1
0
1
2
0
2
1
2
0
0
1
0
1
0
0
2
0
1
0
0
1
2
2
0
2
0
0
0
0
0
2
0
2
0
0
0
0
4
0
0
0
0
2
0
2
0
0
0
2
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
1
2
3
2
0
0
2
0
0
2
0
0
1
0
2
1
0
0
0
0
0
0
0
4
2
1
1
0
1
0
0
0
0
0
0
2
0
0
0
2
1
0
2
2
1
0
2
2
0
2
2
0
0
1
0
1
0
1
1
2
0
2
0
0
0
0
1
0
0
0
2
1
0
0
1
2
0
0
1
2
0
1
1
1
0
0
0
2
0
0
0
1
1
0
0
0
0
5
0
2
1
1
0
0
0
0
8
0
0
1
0
0
1
0
0
3
0
0
2
1
0
2
2
0
0
0
2
0
1
0
0
1
1
0
1
0
3
0
0
0
0
0
1
2
0
1
2
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
1
2
1
1
0
0
2
1
0
0
0
0
0
2
2
0
0
0
0
0
2
0
1
1
0
0
1
2
0
0
2
1
0
0
0
2
2
1
0
2
0
0
1
0
0
1
1
2
0
0
0
0
0
0
2
0
0
2
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
3
0
0
2
0
0
0
2
0
2
2
0
0
1
2
0
0
0
0
1
1
0
0
1
1
1
1
1
0
1
0
4
1
0
0
2
0
0
0
1
0
2
2
0
0
2
2
0
2
0
1
1
0
0
0
1
0
2
1
1
1
0
0
2
0
0
0
1
0
1
0
0
0
1
0
1
0
3
5
0
2
0
0
0
0
0
2
2
0
0
2
0
1
0
0
0
2
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
4
0
0
2
2
0
0
2
0
1
0
0
2
2
0
2
0
0
0
0
0
3
1
0
0
0
2
2
0
0
0
1
0
2
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
3
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
2
1
0
2
0
2
2
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
1
0
0
1
1
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
1
0
0
0
0
1
1
1
0
2
1
0
0
0
0
1
0
0
1
2
2
2
1
0
0
0
0
0
1
1
2
0
1
0
1
2
1
0
0
0
2
2
0
0
0
1
1
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
1
2
0
0
0
2
3
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
1
2
1
0
0
1
4
0
0
2
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
1
0
0
1
2
1
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
2
0
4
1
0
0
0
0
1
1
2
4
0
1
2
2
0
0
0
2
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
2
1
0
4
2
0
2
0
2
0
0
0
1
0
0
0
2
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
2
2
1
2
1
0
0
3
0
0
0
0
2
1
1
5
0
0
2
2
0
2
0
1
0
0
2
1
0
0
1
0
2
0
2
2
1
0
0
1
0
2
1
0
0
2
0
0
0
2
0
2
2
0
2
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
1
0
3
0
2
1
0
1
0
1
2
0
0
1
0
1
2
2
0
1
0
0
0
1
1
0
1
2
0
1
0
1
1
0
1
0
0
0
0
2
1
0
1
0
0
0
0
0
1
2
1
0
0
2
0
0
1
0
2
1
2
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
1
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
2
1
0
0
0
0
2
0
1
2
2
1
0
0
0
0
0
0
3
0
0
2
1
0
0
1
2
0
0
0
0
2
0
1
2
0
0
0
0
0
2
2
0
1
0
0
0
2
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
2
1
0
0
2
0
2
0
0
0
2
0
0
2
1
1
1
0
1
0
1
1
0
0
0
0
1
0
1
1
0
1
0
1
1
1
2
0
0
0
0
2
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
2
0
2
0
1
0
0
2
0
0
1
0
1
1
8
0
2
0
0
0
0
1
1
0
0
0
2
0
1
2
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
1
1
1
0
2
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
2
0
1
1
0
0
0
0
0
0
0
2
2
1
2
0
0
0
0
0
0
0
0
3
1
1
0
0
1
0
0
2
1
1
0
0
2
0
2
0
1
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
2
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
1
0
0
0
1
2
0
2
0
0
4
1
1
1
2
1
0
0
1
2
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
1
2
1
1
2
0
2
0
0
0
1
2
0
0
0
0
0
2
1
1
0
0
1
1
0
1
0
1
0
0
0
0
0
0
4
2
1
1
0
1
0
0
2
0
0
0
2
1
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
1
2
0
0
2
0
0
0
1
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
1
2
0
2
0
2
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
2
1
2
0
1
1
3
0
0
0
1
2
1
0
2
0
2
2
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
3
1
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
2
1
1
0
0
0
1
1
0
2
0
2
0
0
0
1
0
0
2
0
0
2
1
0
1
0
2
0
0
0
0
1
3
2
0
0
0
0
0
1
1
2
0
3
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
2
0
0
0
2
1
0
3
0
0
0
0
0
2
0
2
2
0
0
0
2
0
2
0
0
1
1
0
0
1
2
0
2
0
0
0
0
0
2
0
0
0
2
1
0
0
0
1
0
0
2
0
0
0
0
0
2
1
2
0
1
2
0
0
0
1
0
2
0
1
2
2
0
2
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
3
0
2
0
2
0
0
1
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
1
0
2
0
0
1
2
0
1
0
0
1
0
2
0
0
0
2
1
0
1
2
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
1
0
2
0
1
0
1
1
0
1
0
0
1
0
0
0
1
2
1
0
2
0
0
2
1
0
1
0
0
2
0
1
0
0
1
1
0
0
1
0
0
1
0
1
0
0
0
0
4
1
2
1
2
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
2
0
0
1
0
2
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
2
0
0
3
2
0
2
0
0
1
0
0
0
0
0
0
1
2
0
1
2
2
0
0
1
0
0
0
2
1
2
1
1
0
1
0
0
0
1
1
1
0
0
2
0
0
1
1
2
1
0
2
0
2
2
0
0
0
1
2
0
0
0
0
0
1
0
3
1
0
0
0
2
2
1
2
0
0
0
2
1
0
0
2
2
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
4
0
0
0
4
0
0
1
1
0
1
2
0
0
1
0
0
1
0
2
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
1
2
1
0
0
1
0
0
0
0
0
1
0
0
2
0
1
0
1
0
1
0
0
0
2
0
0
2
0
2
0
0
2
2
0
0
1
1
1
1
0
0
0
0
1
0
0
1
0
0
1
1
1
3
1
0
2
0
0
0
0
0
1
2
2
0
0
1
0
1
1
0
1
0
0
2
0
2
0
0
2
1
0
3
2
0
0
0
1
2
1
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
1
1
0
1
1
2
0
1
0
0
2
0
0
1
0
2
1
1
3
1
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
1
1
0
1
0
2
0
1
2
2
0
0
0
0
0
0
1
0
2
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
1
2
0
1
2
0
0
0
2
0
0
0
5
0
1
1
1
2
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
2
2
1
0
1
2
1
1
3
1
0
0
0
0
1
0
2
1
0
2
4
0
1
0
0
0
1
1
0
0
2
0
0
2
4
1
0
0
0
0
0
1
1
0
2
2
0
0
0
1
1
0
0
0
0
1
1
0
0
1
0
1
2
0
0
0
2
0
1
2
0
1
0
1
0
0
0
0
0
2
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
1
1
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
2
0
1
0
0
0
2
0
0
1
0
2
1
2
0
0
2
0
0
0
1
1
2
0
1
0
0
0
0
0
2
0
1
0
2
0
1
0
0
0
0
0
0
0
2
0
2
1
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
2
0
0
3
0
0
1
0
1
0
2
2
0
0
2
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
1
3
1
0
0
0
1
0
0
1
0
0
4
1
0
0
2
0
0
0
0
2
0
2
2
2
2
10
0
0
0
1
2
0
0
0
1
1
0
0
0
0
1
0
1
1
0
2
0
1
1
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
2
1
0
1
2
0
2
1
2
1
0
2
2
1
2
3
2
0
0
1
0
1
2
0
0
0
0
3
0
2
0
0
0
2
3
1
2
1
0
0
1
1
0
0
0
1
0
1
1
0
1
0
1
2
0
2
0
0
0
2
0
0
1
0
0
3
1
1
1
2
0
0
0
0
0
2
0
0
0
2
1
2
0
1
1
0
3
0
0
2
0
1
3
2
0
0
1
1
1
0
0
0
2
1
0
1
1
0
0
1
0
0
0
0
0
2
0
0
1
1
2
0
0
0
0
1
1
2
0
1
1
0
2
3
0
0
0
0
0
2
0
0
0
0
2
0
0
2
2
2
0
0
0
2
0
0
1
2
0
0
0
0
2
0
2
0
1
0
1
0
0
0
0
0
0
2
2
0
0
2
0
0
0
1
0
0
0
0
2
0
0
2
0
1
0
0
2
1
0
0
0
1
0
0
0
1
0
2
0
0
2
0
2
1
0
0
2
0
2
0
0
2
0
0
0
2
1
2
0
1
2
0
0
0
2
0
2
2
1
0
0
0
0
1
0
1
2
1
0
2
1
0
0
0
0
0
0
2
1
2
0
2
0
0
0
0
1
0
0
1
0
1
0
0
0
0
2
1
0
1
1
1
0
2
0
2
2
0
0
0
0
0
2
0
1
0
0
0
1
2
0
0
1
0
2
2
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
2
1
0
1
2
0
1
1
0
0
0
0
2
1
3
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
3
0
1
2
1
0
0
0
0
2
0
1
0
0
0
0
2
0
2
1
0
0
0
0
2
0
0
2
1
0
1
2
2
0
2
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
1
0
0
0
2
0
0
2
0
0
2
2
0
2
0
0
0
0
2
2
0
3
1
2
0
1
0
2
0
0
1
0
2
1
2
1
0
2
0
1
0
1
0
2
2
0
1
0
2
0
0
1
0
0
0
0
0
1
1
2
0
2
2
2
0
0
0
0
0
3
0
1
0
0
0
0
0
1
0
1
2
1
0
0
0
1
0
2
0
0
0
0
2
0
1
0
1
0
1
2
2
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
2
3
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
2
0
0
2
0
0
0
2
1
2
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
1
0
0
2
0
2
0
1
0
2
0
0
3
0
2
0
0
2
1
0
1
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
2
0
2
0
0
0
2
0
0
2
0
1
0
5
1
2
0
0
2
0
0
1
0
0
1
0
0
1
2
0
0
1
0
0
0
0
2
2
1
1
0
0
0
2
0
1
2
0
4
0
1
0
0
0
0
0
0
2
2
0
0
1
0
1
0
1
2
0
0
0
2
0
0
2
0
2
1
2
0
1
0
0
0
0
1
1
0
1
0
2
0
0
2
0
2
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
1
0
2
1
1
2
0
1
3
1
0
3
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
2
1
0
0
0
0
0
0
2
0
1
2
1
0
2
0
0
0
0
2
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
1
1
0
2
1
0
0
0
0
0
1
2
2
1
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
3
0
2
0
0
0
0
3
2
0
1
1
0
1
0
0
1
0
0
0
0
0
1
2
2
1
2
2
0
0
1
0
0
0
2
2
0
12
0
0
0
0
0
1
1
0
2
0
0
1
0
0
2
1
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
1
0
2
0
2
1
1
1
0
0
2
2
2
0
0
2
1
0
0
2
1
0
0
0
2
1
0
0
0
1
0
0
0
2
3
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
1
2
0
0
0
1
0
3
0
1
1
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
1
1
0
0
0
0
2
1
0
0
0
4
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
2
0
0
0
0
1
0
0
2
0
1
2
1
0
0
0
2
1
0
0
0
1
1
1
1
0
2
0
0
1
1
1
0
2
1
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
1
1
0
2
0
1
4
0
0
2
2
0
0
0
0
2
0
0
1
0
1
2
0
1
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
1
1
3
2
0
0
0
2
0
1
3
0
0
1
0
1
0
1
0
0
3
0
1
0
2
2
2
2
2
0
0
0
3
0
2
0
0
2
1
0
0
0
0
1
1
1
0
1
0
1
0
0
0
4
0
0
2
2
1
1
2
0
2
0
1
0
0
0
0
2
0
0
1
0
1
0
1
1
0
1
1
0
2
0
2
0
2
1
0
0
0
1
3
0
1
0
0
1
0
0
2
0
0
0
0
0
0
2
1
1
0
1
0
0
0
0
5
0
1
0
0
2
0
0
0
0
0
1
0
1
0
0
0
1
2
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
1
0
3
0
0
0
0
2
0
1
0
0
3
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
1
0
1
1
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
1
0
1
2
0
1
0
1
0
1
1
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
2
1
0
0
4
0
0
1
2
2
0
1
0
0
2
1
0
0
2
2
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
3
0
0
2
1
0
2
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
1
2
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
2
0
5
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
2
1
1
2
1
1
0
0
0
0
2
0
1
2
2
0
0
0
0
0
0
2
1
0
1
0
1
2
1
2
0
0
3
0
1
0
0
0
0
0
4
0
0
1
0
1
0
0
0
1
0
0
1
0
1
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
1
0
0
2
0
0
3
0
1
2
1
1
2
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
1
0
2
2
1
1
0
0
0
0
1
0
0
0
1
0
0
1
2
0
0
2
0
2
2
0
0
0
1
0
0
0
0
1
5
2
0
1
1
0
0
0
0
0
2
0
1
0
0
0
1
0
0
2
1
0
0
0
1
0
1
2
0
0
0
0
0
0
3
0
0
1
0
1
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
1
1
0
0
0
3
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
1
0
0
1
0
2
1
2
0
0
0
0
2
1
0
1
0
1
0
2
1
0
1
0
1
0
2
2
1
2
0
1
0
0
0
0
1
2
2
0
0
0
0
2
1
0
2
0
1
3
0
2
0
3
1
2
0
0
2
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
3
0
2
0
0
1
0
2
0
2
2
0
0
0
1
3
0
0
2
0
0
2
1
2
1
0
0
1
0
2
0
0
2
1
2
1
0
0
0
0
0
0
1
2
1
1
0
0
0
0
2
0
2
0
0
1
0
1
1
0
0
1
2
1
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
1
0
1
0
0
0
0
0
0
2
0
2
1
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
2
0
0
0
2
0
0
2
0
0
1
0
1
2
0
0
1
2
0
2
2
0
1
0
0
0
0
0
1
8
0
1
0
2
1
0
0
0
0
1
0
2
0
2
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
1
0
1
0
0
0
1
0
1
1
0
0
0
1
0
2
1
0
2
0
2
0
0
0
0
2
0
1
2
1
0
1
1
1
0
0
0
1
0
0
2
0
0
0
2
1
0
0
0
0
0
0
2
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
2
0
0
0
0
1
2
1
0
0
1
2
0
2
0
0
0
0
1
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
2
1
0
0
0
0
1
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
2
1
0
1
0
0
0
0
0
0
2
0
0
1
0
1
2
0
0
0
0
0
2
0
1
0
2
0
4
0
0
0
0
2
0
2
1
0
0
0
0
1
1
0
3
1
2
1
2
2
0
0
1
1
0
1
0
2
0
0
1
2
2
2
1
3
0
0
0
2
1
0
2
0
1
0
0
1
0
1
1
0
2
0
0
0
0
0
2
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
1
0
2
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
2
2
1
0
0
0
2
0
0
0
1
3
0
0
1
0
2
0
1
0
1
1
0
2
0
0
0
2
2
2
1
0
0
1
0
2
0
0
0
0
1
5
0
0
0
0
1
0
0
0
2
1
1
1
1
2
0
0
1
1
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
3
0
0
0
0
3
0
0
0
0
0
2
0
0
1
0
4
0
0
3
5
0
2
2
4
0
0
0
0
1
2
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
2
2
1
0
2
0
1
0
2
0
0
0
0
1
2
2
0
1
0
0
2
0
0
2
2
0
0
0
0
1
0
0
2
2
0
2
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
2
0
2
0
2
0
0
1
1
0
1
1
0
2
0
3
1
0
1
1
0
3
0
1
2
0
0
1
0
0
0
1
0
2
1
1
0
1
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
2
0
0
1
0
1
0
0
0
0
2
1
1
0
2
0
1
0
2
1
2
0
1
0
1
0
0
0
0
1
0
1
0
0
2
0
0
2
0
0
2
0
0
1
0
0
0
2
0
1
1
1
0
0
0
2
1
2
0
0
0
0
1
2
0
0
0
0
0
0
0
1
1
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
1
0
0
0
0
0
1
0
0
2
0
0
1
0
2
2
0
0
0
0
0
0
1
0
0
0
2
0
0
1
1
1
0
0
0
0
0
0
2
0
0
0
1
3
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
2
0
0
0
2
0
0
2
0
1
0
2
1
2
0
0
0
0
0
0
0
1
2
0
0
1
1
1
0
0
0
2
0
2
0
2
0
2
0
0
1
1
1
0
3
0
2
0
0
0
1
3
0
2
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
2
1
1
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
1
0
1
1
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
1
1
0
1
0
2
0
0
0
0
1
2
0
0
0
1
0
0
0
0
1
0
0
1
2
0
0
0
3
0
0
1
0
0
2
2
0
2
0
0
0
1
1
2
4
1
0
0
0
0
2
0
1
2
0
1
2
1
0
0
2
0
1
0
1
0
0
0
0
2
2
2
0
2
0
0
1
0
1
2
0
1
1
2
0
0
2
0
0
0
3
1
1
2
0
0
0
0
0
2
0
0
2
1
0
0
0
2
0
0
0
0
0
0
1
0
3
2
4
2
0
0
1
1
0
0
0
0
6
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
2
0
1
0
1
1
0
0
0
0
0
0
1
0
1
2
0
1
1
0
0
0
0
1
2
0
2
1
0
0
2
0
2
1
2
0
0
0
0
0
2
0
3
1
0
2
0
2
0
1
0
0
0
0
0
1
3
0
2
0
0
0
1
0
0
0
1
0
2
1
1
0
1
3
1
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
1
0
2
0
0
0
1
0
0
0
0
0
0
3
0
1
0
1
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
1
2
0
1
1
0
1
0
0
0
2
1
0
0
0
0
1
0
2
1
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
3
0
1
0
0
1
3
0
1
0
0
0
2
0
0
2
2
0
1
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
1
1
0
2
0
0
0
0
2
0
2
0
0
3
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
2
0
0
3
1
0
1
3
0
0
2
3
0
0
0
0
0
4
2
2
1
2
0
2
0
2
1
0
1
0
0
0
0
0
3
1
0
0
2
0
0
1
0
2
1
0
0
2
2
0
0
1
2
0
0
0
1
0
0
2
0
1
3
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
4
0
4
2
0
1
2
0
0
2
2
0
1
0
0
0
1
4
0
2
2
0
0
2
1
0
0
2
0
0
1
0
1
0
0
0
3
1
1
0
2
1
1
2
0
1
0
1
0
0
1
0
0
1
7
0
1
0
0
1
0
4
2
0
1
1
0
0
0
2
0
1
1
1
0
2
0
1
0
0
0
0
0
0
0
2
0
4
1
1
2
0
0
2
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
1
0
1
0
0
0
2
0
0
2
0
0
0
0
0
3
0
3
0
1
0
0
0
1
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
3
0
1
0
0
1
1
0
3
0
5
0
0
1
7
0
0
2
0
0
0
1
4
2
0
1
0
1
1
1
0
0
0
0
3
0
2
0
0
2
1
0
0
3
0
0
0
0
0
0
0
0
0
1
4
1
0
0
0
3
2
2
0
0
3
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
1
1
0
1
3
1
0
0
1
3
0
0
2
0
0
1
1
1
0
1
0
0
1
2
2
0
0
2
0
0
1
0
1
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
2
0
1
1
0
0
0
0
0
0
2
1
0
0
1
0
0
1
2
0
1
0
0
2
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
1
3
0
0
0
0
0
2
1
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
3
1
0
0
2
0
0
0
1
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
1
0
3
3
0
2
2
4
1
2
0
1
2
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
2
0
2
2
0
2
0
0
0
0
0
2
2
1
0
0
2
0
2
2
1
0
0
0
0
1
0
0
0
0
0
2
2
0
1
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
2
0
3
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
1
2
2
0
0
0
0
0
1
2
1
0
0
0
0
0
0
2
1
0
0
1
0
2
1
2
2
0
1
0
0
2
0
2
0
0
1
1
0
0
1
2
1
0
1
1
1
2
1
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
2
1
2
2
4
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
1
0
2
0
0
0
0
1
2
2
0
0
2
1
0
0
2
1
0
0
1
1
2
2
1
0
0
0
1
0
2
2
0
0
0
0
2
0
1
0
0
2
1
1
0
1
1
0
2
2
0
1
0
0
0
0
0
2
1
2
0
2
6
2
0
2
0
2
0
0
2
0
0
0
2
0
1
0
2
1
0
0
2
2
0
1
2
0
2
2
0
0
0
0
0
3
2
1
0
0
0
0
1
1
2
2
3
0
0
1
0
0
0
1
1
2
1
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
4
0
0
1
0
0
0
0
0
0
1
2
0
0
0
2
2
1
0
1
1
0
0
0
0
0
0
0
1
0
0
3
1
1
0
2
0
1
1
0
0
0
1
1
3
0
0
2
0
0
0
1
0
0
2
0
0
2
2
0
0
4
0
1
2
0
1
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
3
2
2
0
0
0
0
1
0
0
1
0
0
2
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
3
0
0
0
1
2
0
2
2
0
2
0
0
1
2
0
0
1
3
2
0
0
0
0
1
1
0
0
0
1
2
0
0
0
0
2
1
0
1
0
0
0
0
2
0
2
2
0
0
0
3
1
0
0
0
0
0
0
1
0
2
1
1
0
0
0
0
0
4
1
0
1
0
0
1
0
0
3
0
0
0
2
0
1
0
0
0
2
2
0
0
1
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
4
0
1
1
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
2
0
0
2
0
2
0
2
0
1
0
2
0
0
0
0
1
0
2
2
0
0
2
0
0
2
0
0
0
0
0
0
0
2
2
0
1
2
0
2
1
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
2
1
2
0
0
0
0
0
0
0
0
0
0
2
0
1
1
2
0
1
0
2
0
0
1
0
0
0
1
1
1
2
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
2
2
0
2
1
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
1
1
0
1
2
0
2
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
1
0
0
1
1
1
0
1
1
0
1
0
0
1
1
1
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
4
2
2
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
1
2
0
0
0
2
2
2
1
1
2
3
0
0
0
0
1
1
0
0
0
0
0
1
0
2
0
0
0
2
2
0
0
1
0
0
0
2
2
0
0
0
1
2
0
0
0
2
2
0
0
2
2
2
1
0
2
1
0
0
3
1
0
1
0
1
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
1
0
2
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
1
3
0
1
0
0
2
2
0
0
2
0
1
1
0
0
1
0
0
0
1
0
1
1
2
0
2
0
1
0
0
2
0
2
2
2
0
1
0
2
2
0
0
0
0
0
2
0
1
0
1
1
4
0
0
0
0
0
1
0
0
2
0
0
2
0
1
0
2
1
0
0
0
0
1
1
0
0
0
1
2
0
0
0
1
1
0
0
0
0
0
2
1
2
0
2
1
0
0
2
2
2
0
0
0
2
0
0
1
0
2
1
2
2
0
0
2
0
0
0
2
0
0
0
0
1
5
0
2
0
0
0
0
0
0
1
1
1
0
0
1
0
1
0
2
0
0
2
0
0
2
0
0
2
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
2
2
2
1
0
0
0
0
0
0
1
0
0
3
1
0
1
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
4
0
1
0
2
2
0
1
1
2
0
0
1
2
2
0
0
2
2
1
2
0
0
0
2
0
0
0
1
1
0
0
0
2
0
0
0
1
0
0
0
1
2
2
1
2
0
1
0
2
0
0
0
0
2
0
0
1
0
0
0
2
0
2
0
0
0
2
0
0
0
0
2
1
0
1
0
0
2
0
0
2
0
0
2
0
1
2
1
0
1
0
1
2
0
1
2
0
0
1
0
0
2
0
2
1
0
0
1
0
1
0
2
1
0
0
0
0
0
0
2
0
0
0
2
3
1
0
0
2
2
1
0
2
1
0
1
0
1
0
2
2
0
1
0
0
0
0
2
0
1
0
0
0
2
0
1
0
2
0
2
2
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
1
0
1
2
0
0
1
0
0
0
0
1
0
0
2
0
2
0
0
2
0
0
2
0
0
2
2
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
2
0
0
1
2
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
2
0
1
0
2
0
0
0
0
1
0
0
0
0
1
1
1
2
0
0
0
1
2
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
3
0
0
0
2
0
0
0
0
2
0
2
0
1
0
0
0
1
0
1
0
0
2
2
0
1
0
1
2
0
3
1
0
0
0
0
2
1
2
0
1
0
0
1
0
2
2
4
1
1
1
2
0
0
0
0
0
0
0
2
2
0
1
1
1
0
0
0
0
1
0
0
0
0
1
1
2
0
1
0
3
0
0
1
0
0
0
1
2
0
1
0
0
2
0
0
1
0
0
0
0
1
0
1
0
1
1
0
0
2
0
0
0
2
0
0
0
1
0
0
0
1
1
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
1
3
1
0
1
2
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
2
1
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
3
1
2
0
1
0
2
1
1
0
1
2
0
0
1
2
0
0
0
2
0
2
0
2
0
0
0
0
0
1
0
0
2
0
1
1
2
0
0
0
2
0
0
2
0
0
2
1
3
2
0
1
3
0
0
0
0
1
1
1
1
0
0
0
1
0
0
0
0
0
3
1
0
2
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
2
0
2
0
0
2
0
1
0
0
0
4
1
1
2
1
2
0
1
0
1
0
0
1
0
0
0
0
0
1
0
2
2
0
1
0
0
0
0
0
0
0
0
1
1
2
1
0
0
0
1
0
1
1
1
0
2
0
1
0
0
1
0
2
0
1
1
1
0
2
0
0
0
2
0
0
1
0
0
1
2
0
0
2
0
2
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
3
0
2
0
1
2
0
0
2
0
1
0
2
0
0
1
2
0
2
1
1
2
3
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
1
0
2
0
7
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
2
0
1
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
3
2
2
0
4
0
2
0
2
0
0
2
0
0
0
0
0
1
0
0
2
0
0
2
0
0
1
0
1
0
1
0
1
0
0
2
0
2
2
1
0
0
0
3
2
0
2
1
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
2
0
0
1
0
0
0
2
0
1
1
2
0
0
0
0
2
0
0
1
1
0
0
0
2
0
0
1
0
1
0
1
0
0
1
0
0
1
1
1
1
0
0
1
2
1
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
1
2
2
0
2
0
0
0
0
0
3
2
0
2
0
0
1
0
0
1
0
0
1
0
1
2
0
0
0
2
4
0
0
0
0
0
2
2
2
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
4
1
2
0
1
1
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
1
1
1
2
0
2
2
1
0
0
2
0
0
1
2
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
3
1
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
1
0
1
0
1
5
0
1
1
0
1
2
0
1
1
0
2
1
0
0
0
0
0
1
0
1
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
1
0
0
4
1
0
0
1
0
0
6
0
1
2
1
0
2
1
0
0
0
0
1
1
2
0
2
1
0
0
0
3
0
0
1
0
1
0
2
2
0
1
3
2
0
0
2
2
0
1
1
0
0
0
0
0
0
1
0
0
2
0
0
1
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
1
0
1
1
0
0
0
0
2
0
0
0
2
0
0
2
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
1
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
2
0
2
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
1
0
1
0
1
0
0
2
2
0
2
1
0
0
0
1
0
0
1
0
0
0
2
0
1
1
1
1
0
0
0
1
0
2
2
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
1
0
2
0
1
2
0
2
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
1
2
0
1
0
1
0
0
0
2
1
2
0
2
0
0
0
0
0
0
1
1
1
0
3
0
0
2
0
0
0
0
0
1
1
2
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
1
2
0
0
0
1
2
0
2
0
0
0
11
1
1
0
1
2
0
0
2
3
0
1
0
1
1
0
2
1
1
2
0
0
8
0
2
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
4
1
0
0
1
0
0
0
0
0
0
0
1
2
0
0
1
0
0
2
0
0
0
0
0
2
0
0
3
0
1
1
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
3
0
1
0
1
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
4
1
0
0
0
0
0
0
0
3
0
0
0
0
2
0
1
0
2
2
2
2
1
1
1
0
2
1
0
2
0
0
1
0
0
0
2
2
1
1
1
2
1
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
2
0
1
1
0
1
2
2
0
1
1
0
0
0
1
0
1
0
1
1
0
0
2
0
1
0
0
2
0
1
0
0
0
1
1
0
0
0
1
2
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
2
0
2
0
0
1
2
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
1
1
1
0
2
1
0
0
0
2
0
0
0
1
1
0
1
0
0
2
0
0
0
1
0
2
0
0
2
0
0
0
2
0
1
1
0
0
0
1
1
0
3
0
0
0
1
1
1
0
0
0
0
2
2
0
1
1
0
2
0
2
1
1
0
1
0
0
1
0
1
0
1
0
2
0
0
1
0
10
1
0
1
0
2
0
5
0
0
2
0
0
0
2
0
0
1
0
2
0
0
1
2
1
1
0
1
0
0
1
2
0
1
1
2
2
0
0
0
0
0
0
0
0
1
1
2
0
2
2
1
0
0
1
2
0
2
3
2
0
0
0
0
0
0
0
0
1
3
1
0
0
0
0
2
0
0
0
1
0
0
1
0
2
0
1
1
0
2
0
0
2
0
0
2
2
0
1
1
2
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
1
2
1
0
3
0
1
2
1
0
0
3
0
0
0
0
0
1
3
0
0
0
2
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
3
0
0
0
0
0
0
2
0
2
2
0
2
0
2
0
0
2
0
3
0
0
1
2
0
0
2
0
2
0
4
0
2
1
0
0
2
0
0
0
0
0
0
1
0
0
2
0
1
0
1
1
0
0
0
0
2
0
1
1
0
1
0
1
1
0
1
2
0
1
0
0
2
0
0
2
0
0
2
2
0
2
0
0
1
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
1
2
2
0
0
0
1
0
0
2
1
0
1
0
1
0
0
0
2
2
0
0
0
0
1
0
1
0
0
0
3
0
0
1
2
0
0
0
2
2
0
0
0
1
0
0
2
0
0
0
0
0
1
2
0
1
0
1
0
0
1
2
2
0
0
0
2
0
2
2
1
0
3
0
0
0
2
0
2
1
0
1
0
1
0
2
0
2
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
2
1
0
0
0
1
1
2
0
1
0
0
2
3
0
1
0
1
0
0
1
1
0
2
0
1
0
2
2
2
1
2
0
1
2
0
0
4
1
0
0
1
0
2
1
0
0
1
0
0
2
0
2
0
1
0
0
1
1
0
0
2
1
0
2
0
2
0
1
1
0
0
0
0
0
0
1
0
0
0
0
2
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
1
0
2
2
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
1
0
2
1
1
0
0
0
0
0
0
0
3
2
0
0
0
0
1
1
1
0
0
0
0
0
0
1
1
0
4
1
0
1
0
0
0
2
2
0
0
1
5
1
0
0
0
0
0
0
2
0
2
2
0
0
1
1
2
1
0
0
2
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
2
0
0
1
2
0
1
0
1
0
1
2
0
1
0
0
2
0
1
2
0
1
0
0
1
0
0
0
0
1
1
2
0
0
1
0
0
1
2
1
1
0
2
0
0
0
1
1
0
0
0
2
1
1
0
0
1
0
4
1
1
1
0
0
1
0
1
0
0
0
0
1
2
2
0
2
0
0
0
0
1
1
1
0
0
1
2
0
0
0
2
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
2
1
2
3
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
2
1
0
3
2
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
2
0
0
2
0
0
3
3
0
0
2
0
1
0
0
1
0
0
0
6
0
2
0
1
2
1
1
2
0
0
0
2
2
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
2
1
0
1
1
2
2
0
0
0
0
0
0
0
2
2
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
1
2
0
2
0
0
0
0
1
0
1
1
0
2
1
0
0
3
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
2
0
0
1
0
0
0
0
0
2
0
2
1
2
2
2
0
0
0
2
1
0
1
3
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
2
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
2
0
0
2
0
3
0
0
2
0
0
1
0
4
0
0
0
0
0
3
0
2
0
1
2
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
1
0
0
1
0
2
0
2
1
0
2
0
0
0
4
0
2
1
0
2
1
0
1
2
2
0
0
0
1
0
2
2
0
0
2
0
1
0
0
2
1
3
5
1
0
1
0
1
0
1
2
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
1
0
1
0
1
1
0
0
2
0
1
0
1
3
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
1
0
1
0
0
0
0
0
2
0
0
3
2
0
2
2
0
0
1
0
2
0
1
0
0
0
0
1
2
0
0
2
2
2
0
0
0
0
2
0
0
1
0
1
2
1
2
0
0
0
0
0
0
1
1
2
3
0
0
0
1
0
0
0
0
1
0
0
0
0
2
1
2
0
0
1
0
1
0
1
2
0
0
0
1
0
0
2
1
2
1
2
2
0
0
0
0
0
2
0
0
0
1
0
0
1
2
0
0
0
0
2
0
1
2
0
1
1
1
0
0
1
0
0
2
0
1
0
0
0
0
1
0
2
0
1
0
0
1
1
0
0
0
1
2
1
1
0
0
2
0
0
0
1
1
0
0
0
1
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
3
0
0
2
2
1
2
0
3
0
2
1
0
0
0
1
1
1
0
2
0
0
0
0
1
0
2
2
0
0
0
1
0
0
1
2
1
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
2
0
2
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
2
1
2
1
0
0
2
0
1
2
0
1
2
0
1
3
1
0
1
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
2
4
3
1
1
2
2
3
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
1
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
2
2
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
2
1
2
1
2
0
0
0
0
1
0
0
1
1
0
2
2
2
0
1
1
0
2
2
0
2
0
7
3
2
0
0
0
0
0
0
1
0
2
0
2
1
0
1
2
2
0
0
0
2
0
0
3
0
1
0
0
1
0
2
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
2
0
0
2
2
1
2
1
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
1
2
0
2
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
2
0
0
2
2
1
0
0
0
0
0
0
0
1
0
0
2
2
0
1
0
0
0
1
0
1
2
0
0
1
0
0
1
1
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
2
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
2
0
1
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
1
2
0
3
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
2
2
2
0
2
0
1
0
0
1
0
0
2
0
0
0
2
2
0
0
1
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
1
0
6
0
0
0
1
0
2
0
1
0
0
0
1
2
0
0
0
0
0
2
2
0
3
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
2
2
1
0
1
0
0
0
2
0
0
3
2
0
1
0
2
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
6
0
2
2
0
0
0
2
3
1
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
1
2
0
2
1
0
0
0
0
0
1
0
0
0
1
2
0
0
0
1
1
0
3
1
2
0
0
0
2
0
0
2
0
0
2
2
0
0
1
0
1
4
3
0
0
0
0
0
1
0
0
0
2
3
2
0
0
1
0
3
0
0
0
0
1
2
0
0
0
3
1
2
0
1
0
0
3
0
0
0
0
0
2
0
0
2
0
0
2
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
1
0
0
0
1
0
0
0
3
0
0
0
1
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
2
2
3
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
1
1
4
1
0
0
5
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
2
2
1
1
0
2
1
1
0
0
0
0
2
0
2
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
1
0
2
0
0
1
0
1
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
3
0
1
1
2
0
1
0
0
0
2
0
0
0
0
0
1
4
0
2
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
4
4
0
0
2
2
0
2
1
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
1
0
0
0
0
2
0
2
0
0
2
0
0
1
0
2
0
0
2
0
0
1
0
0
2
2
1
0
1
0
2
0
0
0
1
3
2
1
0
1
0
0
0
0
1
1
0
0
0
0
1
1
0
3
0
1
1
0
5
2
0
0
0
1
0
1
2
2
1
0
0
1
0
0
0
1
1
0
0
2
0
2
2
0
0
1
2
0
0
0
0
0
1
0
0
2
1
2
0
0
0
0
0
1
0
0
2
2
2
1
0
0
0
0
0
1
1
2
0
0
1
1
1
1
2
0
1
0
0
1
0
0
0
1
0
1
2
0
1
1
0
2
0
0
0
1
1
2
1
0
0
0
0
0
3
1
2
0
0
2
0
2
0
0
2
0
0
0
1
1
0
0
0
0
1
0
2
2
0
0
2
0
0
1
2
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
2
0
0
0
0
0
1
0
0
0
0
1
2
4
2
1
3
1
1
2
0
0
0
0
0
1
3
2
2
1
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
1
3
1
0
2
1
3
0
0
0
1
2
0
0
0
2
0
0
2
0
0
0
1
2
0
2
2
0
1
0
1
0
2
0
3
0
2
0
0
0
0
0
0
0
1
0
0
3
0
0
0
2
0
2
0
0
2
1
0
0
3
3
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
1
0
0
0
1
0
0
1
2
1
0
1
1
0
0
0
0
0
0
0
1
0
0
2
1
0
0
1
1
2
2
0
0
2
0
0
0
2
0
1
0
2
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
5
0
0
0
2
1
2
0
0
1
2
2
0
0
0
0
2
1
2
2
0
0
4
4
2
1
0
0
0
0
1
0
1
0
1
2
0
0
1
0
3
0
0
0
2
0
0
0
1
0
2
0
0
0
1
2
0
0
0
0
0
2
0
0
1
2
0
0
2
0
0
0
0
1
2
1
1
0
1
3
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
1
0
1
1
0
1
2
1
1
0
0
0
0
0
1
0
1
1
0
1
0
0
0
1
2
0
0
0
0
1
0
1
1
0
0
0
1
0
2
0
2
0
2
0
0
2
0
1
1
1
0
0
0
0
1
0
0
0
0
0
2
0
1
0
2
1
0
2
0
0
1
1
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
2
0
0
0
2
0
0
0
0
1
0
1
1
0
1
0
0
0
0
2
1
1
0
0
0
2
2
0
0
0
1
0
0
1
0
0
1
0
0
2
2
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
2
0
0
2
0
1
1
0
0
1
0
1
0
1
1
0
0
2
3
1
3
1
2
0
0
0
2
2
0
0
1
0
1
0
0
0
0
1
1
0
0
0
1
0
0
2
0
0
1
2
0
0
0
0
0
3
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
1
1
1
2
0
1
2
0
0
0
2
0
2
0
0
0
1
4
0
0
0
2
0
1
0
0
1
1
0
0
2
1
0
0
2
0
1
0
2
0
1
1
0
0
0
1
0
2
1
0
0
0
2
1
0
0
0
2
0
2
1
0
1
0
1
0
1
0
0
0
1
0
3
0
0
0
0
0
2
2
0
0
1
1
0
1
2
2
1
1
0
0
1
2
0
1
0
1
1
0
0
0
1
3
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
2
1
0
0
0
0
0
3
1
1
1
1
0
1
1
0
1
2
1
0
1
2
1
0
2
2
0
0
0
0
2
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
3
1
1
0
0
0
0
2
0
0
1
0
1
2
0
0
2
0
3
0
2
2
0
2
0
1
0
0
1
2
2
2
1
0
0
0
1
2
0
3
0
0
0
0
0
0
0
1
0
1
0
2
0
0
3
1
0
0
0
0
1
0
0
4
0
0
2
0
1
1
2
0
4
0
0
1
0
1
1
0
0
1
0
1
2
0
1
0
0
1
0
1
0
0
0
2
2
0
3
1
0
0
2
0
0
0
1
0
0
2
1
0
1
0
0
0
0
0
0
0
1
6
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
2
1
0
0
0
0
0
1
0
1
0
0
1
0
0
2
0
0
2
1
0
2
0
2
0
2
0
6
0
0
1
2
0
0
1
0
0
0
2
2
0
1
0
0
1
1
0
1
2
0
0
0
0
0
0
0
0
0
2
0
2
2
2
0
1
3
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
2
0
2
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
1
0
0
0
1
0
0
1
0
2
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
2
4
0
2
0
0
1
2
1
0
0
3
0
0
1
1
0
0
0
0
1
3
0
0
2
1
2
2
1
0
0
0
1
2
1
2
0
0
0
2
0
1
2
1
0
2
1
1
0
0
1
1
0
0
0
0
1
2
3
1
0
1
1
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
2
0
2
2
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
3
1
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
1
0
2
1
0
0
0
0
0
0
2
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
3
0
1
2
0
2
0
0
2
0
0
0
1
0
2
0
0
2
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
1
0
2
0
1
0
1
1
2
0
2
0
0
2
2
1
0
0
2
2
1
1
0
0
0
0
0
0
2
2
1
1
0
0
1
0
1
0
0
0
0
2
1
2
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
2
0
1
0
1
0
3
1
0
0
0
2
3
0
0
2
0
0
2
0
0
0
1
0
3
2
0
1
0
0
2
1
1
1
0
0
2
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
1
1
0
1
0
0
1
1
0
1
0
0
0
0
2
0
1
1
4
2
0
0
0
2
2
2
0
1
0
0
0
0
1
0
3
0
0
2
1
2
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
2
1
1
1
2
0
0
0
0
1
0
2
1
0
0
0
0
1
0
1
0
0
2
0
2
2
1
0
0
2
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
1
0
0
2
2
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
2
2
0
0
1
2
0
0
0
1
2
0
0
1
2
0
0
0
0
0
0
2
0
1
2
0
0
1
0
0
3
2
0
0
1
1
0
0
1
0
0
0
0
2
0
0
2
2
0
3
0
2
0
1
0
0
0
2
2
2
2
0
0
0
3
0
0
2
1
1
1
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
1
1
3
0
0
0
0
2
2
0
2
0
0
1
0
0
0
0
2
0
0
1
1
2
2
0
0
1
0
1
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
1
2
2
0
0
1
0
1
1
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
1
2
2
1
2
0
0
0
2
1
0
0
0
0
1
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
2
0
2
0
0
0
2
0
0
0
0
0
1
0
3
0
0
1
1
0
1
0
1
0
0
2
0
0
1
0
0
0
2
1
0
4
1
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
5
0
1
1
0
0
0
1
1
0
0
2
0
2
1
1
2
1
0
2
0
0
0
1
3
2
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
2
1
1
0
1
0
2
2
0
1
0
0
0
0
0
1
2
2
0
0
0
0
1
1
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
2
1
1
0
2
2
0
0
0
1
0
0
0
1
0
5
1
1
0
0
0
0
0
1
1
0
0
0
0
2
1
0
1
0
2
0
1
1
1
0
0
1
0
0
1
2
0
0
0
2
0
2
2
2
0
2
0
1
2
1
1
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
1
1
1
0
2
0
0
2
2
0
0
5
1
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
3
2
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
2
0
0
0
1
0
0
0
0
1
1
2
1
1
0
1
0
1
1
0
0
0
0
0
1
0
1
2
0
2
0
1
0
0
0
0
1
0
1
2
0
0
0
0
2
0
2
0
0
0
2
0
0
1
0
0
1
1
0
0
0
1
1
0
0
1
0
0
0
3
0
0
0
0
1
1
0
0
3
2
0
2
0
0
2
1
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
2
1
0
0
0
3
0
0
1
0
0
1
0
0
2
0
1
0
1
0
0
3
0
0
0
2
0
0
0
0
1
0
0
1
1
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
2
1
0
0
9
0
0
0
3
0
1
1
0
0
0
1
2
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
2
0
2
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
2
1
0
0
1
0
3
0
0
1
2
2
0
0
0
0
0
2
1
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
3
1
0
2
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
1
0
2
0
2
0
0
2
0
0
2
0
0
1
2
1
2
0
0
0
0
0
2
0
0
2
0
1
0
0
2
1
0
3
0
0
0
0
0
0
1
2
0
0
1
1
0
0
0
2
0
0
0
0
8
0
0
3
0
1
0
2
1
1
0
0
0
0
1
1
1
1
0
2
0
0
1
0
0
1
2
0
0
0
0
2
2
2
0
0
0
0
2
0
0
1
0
1
0
3
0
0
2
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
2
0
2
1
0
1
0
0
1
1
0
0
3
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
1
1
1
0
0
1
0
1
1
0
0
1
1
1
3
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
3
0
0
0
1
0
0
1
0
3
0
2
0
0
0
1
0
0
0
0
1
2
1
2
0
2
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
3
0
2
2
0
0
1
0
1
1
1
1
0
0
1
2
0
2
0
0
0
0
0
1
0
0
0
1
0
2
1
1
1
0
0
1
2
1
0
0
2
0
2
0
0
0
3
0
0
0
2
1
0
0
0
2
0
1
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
1
2
2
0
1
2
0
0
0
0
0
0
1
1
0
3
0
0
0
0
2
0
0
1
0
0
0
0
2
1
1
2
1
0
2
0
0
0
1
1
1
2
0
0
0
2
1
0
0
0
0
0
0
0
3
2
0
1
0
0
1
1
1
0
0
0
1
0
0
0
1
0
3
0
0
0
2
0
0
0
0
0
1
2
0
0
1
0
2
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
2
0
0
2
1
2
0
0
0
1
0
0
1
0
0
1
0
2
0
2
3
1
0
0
2
0
0
0
0
0
2
1
0
1
2
0
0
0
0
1
2
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
1
0
6
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
2
2
0
2
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
5
1
0
1
0
0
0
0
0
0
0
0
0
2
0
1
1
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
1
1
0
0
1
0
0
0
0
2
0
0
2
0
0
0
2
0
1
2
1
0
0
0
2
2
2
0
0
0
0
0
0
0
2
2
0
0
1
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
2
2
2
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
2
0
1
1
1
1
0
0
0
0
2
0
0
2
1
0
0
2
0
0
1
1
0
1
0
0
0
1
0
1
0
0
0
3
1
1
1
2
2
0
0
0
0
2
0
2
2
0
0
0
0
1
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
2
0
2
0
0
0
1
0
0
3
0
0
1
0
1
2
1
0
2
1
1
2
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
4
1
0
1
0
3
0
2
0
0
0
0
0
0
2
0
0
2
0
2
0
0
1
0
0
0
0
2
1
0
0
0
1
1
0
0
2
0
2
1
1
2
1
1
0
0
0
0
0
1
0
1
2
1
1
0
0
0
0
2
0
0
0
0
1
1
2
2
2
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
4
1
0
4
0
3
0
0
1
1
0
0
0
0
0
1
0
0
2
2
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
2
0
0
2
0
0
0
0
1
2
2
0
0
0
0
0
0
2
2
2
0
1
0
0
0
2
2
1
1
0
0
0
1
1
0
0
0
0
0
0
3
0
0
1
0
1
0
0
0
0
2
0
0
0
0
2
1
2
2
0
1
0
0
3
0
0
0
1
1
0
0
0
0
0
0
1
2
0
0
2
2
0
2
2
0
0
0
0
0
2
2
0
1
1
0
0
0
0
0
0
0
0
1
2
2
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
1
1
0
0
2
0
0
0
1
2
0
2
0
1
0
0
2
0
0
0
0
1
0
0
1
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
1
1
1
1
0
1
1
1
1
0
1
0
2
0
3
0
0
0
0
0
4
2
1
2
0
2
1
1
0
0
0
1
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
1
4
0
0
1
0
0
1
2
1
1
0
0
2
0
0
1
1
2
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
1
2
0
0
0
2
0
0
1
2
0
0
1
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
1
1
0
2
0
1
0
1
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
1
2
2
1
2
2
0
1
2
0
2
2
0
0
0
4
0
1
0
1
2
0
4
0
1
0
0
1
1
1
1
0
0
0
0
0
2
0
0
0
1
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
1
2
0
0
0
0
3
2
2
2
0
0
1
0
2
0
0
2
0
0
0
0
1
2
0
1
1
1
2
2
2
0
0
2
0
0
0
0
0
0
0
0
1
0
2
2
0
0
2
2
2
0
0
0
0
0
1
0
1
2
0
1
1
1
1
0
0
2
0
0
0
3
1
0
0
0
2
1
2
0
0
1
2
2
1
0
0
0
0
1
0
0
0
0
0
2
0
3
1
2
0
0
0
1
0
0
0
0
1
0
0
1
1
0
1
0
0
2
0
0
2
2
0
2
0
0
0
2
2
12
1
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
1
0
2
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
2
1
1
2
0
0
2
2
0
0
0
0
0
2
0
0
2
0
1
1
0
1
0
0
3
3
0
0
0
2
1
0
0
2
0
1
1
1
2
0
0
0
0
0
1
1
0
0
2
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
2
1
2
0
0
0
0
2
0
0
1
4
2
0
2
4
2
0
0
0
2
2
1
1
0
0
3
2
1
2
0
1
2
2
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
2
0
1
0
1
0
1
2
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
4
0
0
1
0
1
0
1
0
0
1
2
0
0
0
1
0
0
0
0
1
1
0
0
0
2
1
0
0
1
0
2
0
0
0
0
1
1
0
0
1
2
0
0
2
0
1
0
1
2
0
0
1
1
0
0
0
1
0
0
0
0
2
0
1
0
1
2
0
1
1
1
2
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
2
0
1
1
1
0
1
0
0
4
1
2
2
0
0
4
2
2
0
1
1
1
0
0
0
1
0
2
1
0
0
0
1
0
4
1
0
2
0
0
1
1
0
0
1
0
0
2
0
0
0
2
0
0
1
2
0
0
1
0
0
0
0
0
0
2
0
1
0
0
1
0
2
2
1
0
1
0
0
2
2
2
0
2
0
0
2
0
2
0
0
0
0
0
0
1
0
0
1
2
2
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
1
2
3
0
0
3
0
0
0
0
2
1
2
0
0
0
1
2
0
2
1
0
3
2
0
0
0
0
2
0
1
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
4
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
2
0
3
1
0
0
1
0
0
2
1
1
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
2
2
0
0
0
0
2
0
2
3
0
0
0
0
2
1
0
2
0
0
0
1
2
2
0
1
0
0
0
0
0
0
0
3
0
0
0
2
1
0
0
0
0
0
0
0
5
0
1
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
2
0
2
2
0
0
0
0
1
0
3
0
1
1
0
0
2
0
2
0
0
1
0
1
0
0
2
1
0
5
0
0
0
1
2
0
1
1
0
1
0
1
1
1
1
0
1
0
0
0
2
1
0
0
1
0
0
0
1
1
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
2
3
0
1
0
0
0
0
1
0
0
1
1
0
2
2
2
1
0
0
0
0
2
2
0
0
1
0
0
2
0
2
0
0
3
2
2
0
0
2
0
0
0
0
2
0
0
1
0
1
2
0
1
0
0
0
1
0
0
1
3
2
0
2
2
0
1
1
4
1
3
0
1
6
2
0
0
0
0
2
0
2
0
0
1
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
3
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
1
3
0
2
1
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
2
0
1
1
0
0
0
1
0
0
0
1
1
1
0
0
1
0
2
0
0
0
1
0
0
1
1
1
1
0
1
2
0
0
2
1
0
0
0
0
0
0
0
2
0
1
2
2
0
2
1
1
1
2
0
0
0
1
0
1
0
2
0
1
1
2
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
2
1
1
0
0
0
1
0
1
2
0
0
0
1
2
0
0
0
2
0
1
0
0
2
1
0
1
0
1
0
0
0
2
0
0
0
0
0
2
2
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
1
2
2
3
0
0
1
2
0
0
0
1
2
0
2
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
1
0
0
0
2
0
0
1
0
0
2
0
0
0
3
0
0
0
0
2
0
0
2
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
2
0
0
0
2
1
0
1
0
1
0
0
2
0
0
2
1
2
1
0
0
0
2
0
0
0
2
0
2
1
0
3
0
2
1
1
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
5
4
2
0
0
1
0
1
0
0
0
0
0
2
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
4
0
1
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
1
0
2
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
3
2
1
1
0
2
0
0
0
0
1
1
1
0
1
1
0
0
0
2
0
1
0
0
0
0
0
0
1
1
0
2
0
0
0
2
0
1
2
0
0
0
1
0
0
0
0
0
1
1
1
0
2
3
1
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
4
0
1
0
1
1
0
1
0
0
2
0
0
2
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
3
0
0
0
0
6
2
2
0
0
2
2
1
0
0
0
1
0
0
3
1
0
0
2
0
2
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
2
0
0
2
1
0
0
0
0
0
0
4
0
1
0
0
0
0
2
1
0
2
0
0
1
2
0
0
0
1
0
4
0
2
2
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
1
0
1
1
0
0
1
2
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
2
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
2
1
0
0
1
2
0
3
0
0
0
1
0
1
2
2
0
0
1
0
0
0
2
1
0
0
0
0
2
0
0
0
2
1
0
0
0
1
0
0
2
1
1
2
0
0
0
2
0
0
0
1
0
0
0
1
0
2
0
0
3
0
0
0
0
2
3
0
0
0
1
2
2
0
0
0
0
0
0
1
0
0
0
1
3
0
0
0
0
1
1
2
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
2
1
0
1
0
1
0
0
0
0
1
1
8
2
0
1
1
2
0
0
0
0
2
0
0
0
1
1
1
0
0
2
0
1
1
0
1
2
0
1
0
1
0
0
2
0
2
0
1
0
2
1
0
0
0
3
0
1
3
0
0
0
0
2
1
0
0
0
1
0
0
3
0
0
2
0
1
0
2
0
1
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
1
0
1
1
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
2
0
0
0
2
1
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
4
0
2
1
0
0
0
2
1
0
2
0
2
1
0
0
0
0
1
2
0
1
2
0
2
0
0
0
0
1
0
2
2
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
2
2
1
0
0
1
0
0
1
3
0
1
1
0
0
0
2
0
2
0
0
1
1
1
0
2
0
0
2
0
0
0
0
0
1
0
1
2
2
1
0
0
2
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
1
1
0
1
1
0
0
0
1
3
0
0
0
1
0
1
1
1
0
1
0
0
1
0
0
1
1
2
0
1
0
0
0
1
0
0
0
2
0
0
0
2
1
0
0
0
2
0
0
1
2
0
1
0
0
1
2
0
0
0
0
0
2
0
0
2
0
0
1
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
1
0
1
2
1
1
2
0
0
0
0
1
1
0
0
0
1
0
1
0
4
0
2
1
2
0
0
1
0
0
3
1
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
5
2
2
0
1
0
2
1
0
3
0
0
2
0
0
2
1
0
0
0
1
2
1
0
0
0
2
0
0
0
1
2
0
2
2
0
2
0
0
2
0
0
0
0
1
1
1
1
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
2
2
0
0
2
0
0
3
0
1
0
2
6
0
1
0
0
2
0
1
0
0
2
0
1
2
0
1
0
0
0
0
1
1
0
2
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
2
2
0
0
1
0
1
1
0
0
2
1
0
1
0
0
0
0
2
0
0
1
1
1
0
3
0
0
0
0
0
0
0
1
0
0
1
0
1
5
1
2
2
0
0
1
0
0
0
1
0
1
0
0
2
0
1
1
1
1
1
0
0
0
1
1
2
0
2
0
0
0
1
1
0
0
2
1
2
0
1
2
0
1
2
2
0
0
0
0
1
0
0
2
1
0
1
2
0
0
0
0
1
2
0
2
3
2
1
0
0
0
0
2
0
2
0
2
1
0
2
0
0
0
2
0
0
0
0
1
0
0
1
1
0
2
0
0
1
0
2
0
0
0
1
0
0
0
0
1
2
0
0
0
2
2
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
3
0
3
0
0
2
0
0
1
0
0
2
2
0
0
0
1
0
2
3
0
0
0
3
0
0
4
0
0
1
0
0
0
1
2
0
0
0
1
0
0
2
2
0
0
0
0
1
0
2
1
1
0
2
0
2
0
0
0
2
1
2
4
2
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
6
1
0
1
2
3
2
1
0
0
1
1
0
2
0
0
1
2
0
0
0
1
1
2
0
0
0
0
1
0
2
0
0
2
0
0
1
0
1
0
0
2
0
1
1
1
0
0
3
0
0
7
0
0
2
2
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
3
0
1
0
1
1
0
0
0
2
0
0
2
2
0
2
0
1
0
0
2
1
0
0
0
0
0
0
0
1
1
0
3
0
0
2
1
0
0
0
0
0
1
0
0
2
1
0
0
0
1
0
1
0
0
3
0
0
0
1
3
1
0
0
0
1
2
0
0
2
1
0
1
0
1
0
0
1
1
0
1
0
2
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
2
0
2
0
3
0
0
1
2
0
0
2
2
0
0
0
2
0
1
1
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
3
0
0
1
0
1
0
0
2
2
1
0
0
0
0
2
0
0
0
0
1
1
0
1
1
0
0
3
2
0
2
1
0
2
0
2
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
1
2
0
0
2
0
1
0
0
0
0
0
1
2
0
1
0
0
2
0
0
2
0
0
0
0
0
0
2
2
0
0
0
3
1
0
1
1
0
0
0
0
0
1
2
1
0
0
1
2
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
2
0
0
0
0
0
0
0
2
0
2
2
2
0
0
0
0
2
1
0
1
0
0
0
1
0
2
0
1
2
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
3
2
0
0
1
0
2
0
0
0
0
1
0
2
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
3
0
1
0
0
1
2
2
0
0
0
0
0
0
0
2
0
0
0
0
1
2
1
0
0
1
0
0
0
2
0
0
1
0
0
0
2
1
0
0
0
0
2
0
2
0
0
0
1
2
1
2
0
0
2
1
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
2
0
0
0
0
0
3
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
2
2
2
0
0
0
1
0
2
2
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
1
1
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
2
0
0
2
0
0
2
0
0
0
1
0
2
0
0
2
0
1
0
0
0
0
2
0
0
0
0
1
2
0
1
0
1
2
0
0
2
0
2
1
0
2
0
0
0
2
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
2
0
2
1
1
0
1
0
0
0
2
2
0
0
0
0
0
0
1
0
2
0
0
0
0
1
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
2
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
1
2
0
0
0
1
1
1
0
0
1
0
1
1
0
0
0
1
0
0
0
0
2
0
2
0
0
1
1
1
0
1
2
0
0
1
0
0
1
1
0
1
0
0
1
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
2
2
0
0
1
0
0
2
2
0
1
0
0
0
0
0
0
0
0
2
0
2
1
0
1
2
1
0
0
0
0
0
2
0
0
0
0
1
0
1
1
0
1
1
1
0
0
1
0
2
1
0
0
1
1
0
0
1
0
0
0
1
0
2
0
1
1
0
0
2
0
2
1
0
0
2
0
1
0
1
2
0
0
1
0
0
0
2
0
0
2
1
0
0
0
1
0
0
0
2
2
0
2
1
0
0
0
1
1
2
0
2
0
1
0
1
0
0
2
0
1
0
0
2
0
0
0
1
0
2
0
1
0
2
0
0
1
0
1
2
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
1
0
0
0
0
0
0
2
2
0
0
1
1
2
2
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
1
0
1
0
0
2
1
2
0
0
0
0
0
1
1
0
0
0
3
1
0
2
1
1
0
0
2
0
1
1
0
0
0
0
0
1
2
0
1
0
1
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
1
0
0
0
0
0
1
0
1
0
2
0
0
0
1
0
0
1
1
2
0
2
2
2
0
0
1
0
2
0
0
1
0
1
1
0
1
0
0
0
1
0
0
0
1
0
2
2
2
0
0
1
3
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
3
1
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
1
0
0
0
1
2
1
0
0
0
1
0
2
2
2
2
0
0
1
0
0
0
0
0
0
3
0
1
0
0
0
0
2
0
0
0
0
2
0
3
2
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
1
2
0
0
1
0
1
0
1
2
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
2
2
0
2
0
1
2
0
0
0
2
0
1
0
2
0
0
1
0
0
1
1
0
1
0
1
0
2
3
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
1
0
0
0
2
0
1
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
2
0
1
1
2
0
2
0
0
0
0
1
0
0
1
2
0
0
1
2
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
3
2
2
0
0
1
2
0
2
0
2
0
0
0
2
1
0
0
0
0
0
0
2
0
2
2
0
0
0
0
2
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
1
0
4
0
0
0
1
1
0
0
2
0
0
1
1
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
1
1
0
0
0
1
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
1
0
0
0
2
0
1
0
0
1
0
1
0
0
0
0
2
1
0
1
0
0
1
2
0
2
0
0
0
1
0
2
1
1
0
0
0
2
0
1
1
0
0
0
0
8
0
0
0
2
2
2
0
1
0
0
2
1
0
0
0
1
1
2
0
2
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
2
0
2
2
1
0
2
1
0
0
0
2
0
0
0
1
1
1
1
1
0
0
1
0
3
0
0
2
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
2
0
2
1
0
0
2
2
2
1
0
0
0
2
2
0
1
0
0
0
2
0
0
0
0
0
0
3
0
0
0
2
2
0
2
2
0
2
2
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
8
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
1
0
2
1
1
3
0
2
2
2
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
1
2
2
1
0
1
1
2
1
0
2
1
0
1
0
0
1
0
1
2
0
0
2
7
0
0
0
0
2
0
0
0
1
1
0
0
0
1
0
2
0
2
2
0
2
1
1
0
4
1
0
1
1
2
0
2
0
0
0
2
0
1
1
1
0
0
0
0
1
2
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
1
0
2
0
1
1
1
0
0
0
1
2
0
0
2
1
0
0
0
0
1
0
2
0
0
0
0
0
2
1
2
0
0
0
2
0
0
2
0
2
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
2
2
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
1
0
0
2
0
3
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
1
2
0
0
2
0
0
1
2
1
2
0
0
0
0
0
1
1
2
0
1
0
1
0
0
0
1
0
0
1
0
2
0
2
1
0
1
0
0
0
0
0
0
1
0
2
1
1
0
1
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
2
1
0
0
0
1
1
0
2
0
0
0
3
0
0
0
0
0
2
0
1
0
0
1
0
0
2
0
0
2
1
0
2
1
2
0
1
0
2
0
0
0
1
0
0
1
0
2
0
1
0
2
2
0
1
1
0
0
0
0
1
0
0
2
0
0
0
1
0
1
0
0
2
2
0
0
0
2
3
1
0
2
0
2
2
1
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
2
0
0
0
1
0
1
0
3
0
0
0
0
1
2
0
2
0
0
0
0
1
2
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
14
2
0
0
0
0
0
0
0
0
1
0
0
1
0
5
0
0
0
2
1
0
0
0
2
1
0
1
1
1
0
2
0
2
0
0
1
0
2
0
1
1
0
0
0
1
1
0
1
1
0
0
2
0
3
0
2
0
2
0
0
0
0
2
0
2
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
1
1
2
1
0
2
2
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
2
0
0
1
2
0
0
0
0
0
0
1
0
1
1
0
1
2
0
0
0
0
0
0
1
1
1
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
1
1
0
0
2
0
0
0
1
2
0
0
1
1
3
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
2
2
2
2
4
2
2
0
1
0
0
3
2
0
1
1
0
0
0
1
0
0
0
1
1
0
2
0
0
0
0
5
2
0
0
0
0
0
0
0
1
1
2
0
2
0
0
0
0
3
0
0
1
0
0
0
2
2
1
0
0
0
1
1
0
0
0
0
0
0
0
0
2
2
1
2
0
0
1
0
0
0
0
2
0
0
2
0
0
0
2
1
0
0
2
0
2
2
0
0
1
0
1
1
2
0
0
1
2
0
2
0
1
0
0
0
2
2
0
0
0
0
0
2
0
0
0
1
0
1
0
1
0
1
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
2
2
0
0
0
2
0
0
1
0
0
1
1
0
0
0
2
0
0
0
2
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
1
0
0
1
2
0
0
1
0
0
0
2
2
2
1
0
0
0
1
0
1
0
0
2
2
0
0
0
0
2
0
0
2
0
2
0
1
0
0
2
0
0
2
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
3
2
0
0
0
0
1
0
0
2
2
0
0
0
0
1
0
1
0
0
1
1
0
0
0
1
0
0
1
0
1
0
0
2
0
1
2
2
0
0
0
2
2
0
0
1
0
0
0
2
2
2
0
0
0
2
2
2
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
2
1
2
0
1
1
0
2
0
1
1
0
1
0
0
1
0
0
1
0
0
0
0
1
1
0
1
2
2
0
1
0
0
2
0
2
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
8
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
1
0
1
0
2
0
0
0
1
0
1
1
0
2
0
0
1
0
0
0
2
0
2
1
0
0
0
0
0
2
1
2
0
2
0
0
0
0
2
2
2
0
1
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
1
0
0
3
0
0
0
3
1
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
1
0
0
0
1
1
2
3
0
0
0
2
1
0
2
2
0
2
1
0
0
0
1
0
0
2
2
0
0
0
1
0
2
0
0
0
1
2
0
0
1
0
1
1
2
0
0
1
0
0
4
2
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
1
1
0
1
2
3
0
1
0
2
0
1
0
0
0
0
2
0
0
0
0
2
0
2
0
1
2
2
2
1
0
0
0
0
2
0
0
1
2
0
0
1
0
0
2
0
0
2
0
0
0
1
2
0
1
2
0
1
2
1
0
0
2
1
1
0
1
0
0
0
1
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
3
1
0
1
0
1
0
1
0
0
0
1
0
2
0
0
0
1
2
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
3
0
0
1
0
0
2
3
0
0
0
1
0
0
1
1
1
1
0
1
0
0
1
0
0
0
0
1
0
1
0
1
0
1
0
0
1
0
0
3
1
2
0
1
0
2
2
0
0
1
0
0
1
0
0
1
1
1
0
0
0
0
0
2
0
0
2
2
2
0
0
0
0
1
2
0
1
0
1
0
3
2
2
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
3
1
0
0
0
0
0
2
2
5
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
1
1
0
0
1
0
0
1
0
2
1
0
0
0
0
1
0
2
0
0
0
2
0
1
1
0
2
0
0
0
0
0
1
0
2
0
0
0
0
1
0
2
0
0
0
1
2
0
2
0
1
1
0
0
0
0
0
0
0
2
0
2
0
1
0
3
0
0
0
1
0
1
0
2
1
0
1
0
0
0
1
0
1
0
1
0
1
1
0
0
0
1
0
0
0
2
2
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
2
1
0
1
0
2
0
2
2
1
2
1
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
2
1
1
1
0
0
1
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
1
2
0
2
2
2
1
0
0
2
6
0
0
0
0
0
2
2
1
0
0
0
0
0
0
1
0
0
2
0
1
0
1
1
0
0
0
0
0
2
0
0
1
2
0
2
0
0
0
2
0
3
0
0
1
0
2
0
0
0
1
1
2
0
2
0
0
0
0
0
0
0
1
2
2
0
0
0
0
2
1
0
0
2
0
2
1
1
1
1
2
0
0
0
0
1
2
0
2
0
2
1
0
1
0
2
1
0
0
0
2
0
2
0
2
1
0
0
1
0
1
1
0
1
2
1
0
1
0
1
0
0
1
2
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
6
0
4
0
0
0
2
2
1
0
0
0
0
2
3
0
0
1
1
1
0
2
0
2
0
2
1
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
2
1
0
0
1
0
0
0
0
2
0
1
2
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
1
1
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
2
1
0
0
0
0
2
1
1
1
2
0
0
1
1
1
0
1
2
0
0
0
0
2
1
2
0
0
0
0
1
0
0
1
2
2
2
2
2
0
0
0
0
0
0
2
0
0
2
3
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
3
0
2
0
1
1
0
2
0
0
2
3
0
0
2
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
3
0
0
0
2
1
0
2
1
2
0
0
1
0
0
0
2
1
2
1
0
2
0
1
0
2
0
1
2
0
0
0
0
0
0
2
0
0
2
1
2
0
0
2
0
1
0
2
0
0
2
0
0
0
1
0
2
0
1
0
0
1
0
0
3
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
1
0
0
2
0
0
0
0
0
3
0
0
0
1
0
1
0
1
0
2
1
0
2
0
0
1
2
2
0
0
1
0
1
0
1
0
2
0
0
1
1
0
0
0
1
0
1
0
1
0
2
1
1
0
0
1
0
0
0
0
0
1
0
1
0
0
2
1
0
1
2
1
0
0
0
0
0
0
0
1
0
0
1
2
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
1
0
0
1
0
0
2
0
0
1
1
0
0
1
0
1
2
0
1
1
0
0
0
2
2
0
1
0
0
1
0
1
1
0
0
0
0
0
2
0
2
2
0
1
2
1
0
0
2
2
0
0
0
0
0
1
1
2
0
2
1
1
2
1
0
0
0
2
3
0
0
0
0
0
2
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
2
0
0
0
1
2
1
0
1
0
1
2
1
1
2
0
0
0
2
1
1
1
0
0
0
3
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
1
0
0
2
0
2
0
0
0
0
2
0
1
0
0
1
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
2
0
3
0
2
0
0
2
2
1
1
1
0
1
0
4
2
0
0
2
2
0
1
0
0
0
0
0
0
0
2
0
0
2
2
0
2
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
2
0
0
2
0
0
1
2
0
0
0
0
0
1
2
1
0
4
0
0
0
2
0
0
0
0
0
2
0
2
0
2
0
2
0
0
0
1
1
2
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
3
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
1
2
0
0
1
7
1
0
2
0
0
1
1
0
3
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
3
0
3
2
2
1
0
1
1
2
0
1
0
0
1
1
0
2
2
0
0
2
0
0
0
1
0
0
0
2
0
0
2
3
0
0
0
0
2
2
0
2
0
0
1
0
1
0
0
0
0
0
0
0
2
1
0
0
0
1
2
0
0
0
0
0
2
0
1
1
0
0
0
2
0
0
0
0
0
0
2
0
2
0
2
0
0
2
0
3
1
1
0
2
0
2
0
0
1
0
0
2
0
2
0
0
0
2
3
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
2
1
0
0
0
0
0
2
1
6
0
0
2
0
2
0
1
0
0
1
1
2
0
0
2
1
0
0
2
0
0
1
0
0
0
0
2
0
3
0
0
0
0
2
0
2
0
3
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
1
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
1
2
1
0
0
2
0
0
0
0
0
0
2
0
0
1
2
0
1
2
0
0
0
2
0
0
0
2
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
1
0
1
2
3
2
0
0
0
1
0
1
0
1
2
0
2
1
2
0
0
0
0
1
1
2
0
0
1
2
0
1
0
2
1
1
2
1
0
2
0
2
0
1
0
0
0
2
1
0
3
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
1
2
2
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
1
2
0
0
0
0
0
0
1
0
0
1
0
1
1
1
0
0
1
1
0
0
2
0
0
2
1
1
0
2
0
0
0
0
0
1
2
2
0
0
0
2
0
1
0
0
0
0
0
0
0
2
1
0
3
1
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
7
2
1
1
1
0
0
1
0
0
1
1
0
0
1
1
5
0
0
0
1
0
0
2
1
0
0
1
1
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
1
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
1
2
0
0
1
0
2
1
0
1
1
0
2
0
0
1
1
1
1
2
1
1
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
1
2
0
0
2
1
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
2
2
2
2
0
2
2
0
0
1
0
2
0
3
1
0
2
2
2
1
1
0
0
1
0
1
0
1
0
0
3
2
3
0
0
0
2
2
1
0
2
0
0
2
0
0
2
2
1
0
0
0
0
2
1
0
0
0
0
3
1
0
0
0
0
1
0
2
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
1
1
0
1
1
0
0
0
0
0
1
1
0
0
0
0
3
2
2
0
1
0
1
0
0
0
0
1
3
0
1
0
0
0
0
0
0
1
1
2
0
0
1
1
2
3
0
0
1
3
2
0
0
1
0
1
0
0
0
3
0
0
1
0
2
1
2
2
0
2
0
1
0
1
0
1
0
0
1
2
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
3
0
0
2
0
0
1
0
0
0
3
2
0
1
2
2
1
0
0
0
0
0
2
0
0
0
1
0
0
1
3
1
2
0
0
0
2
2
0
1
0
0
0
0
2
0
1
1
2
0
1
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
2
0
2
0
0
0
0
0
0
0
2
2
1
2
0
0
0
2
0
0
2
1
0
3
0
0
1
0
0
0
0
1
0
1
2
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
2
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
1
0
2
0
0
0
0
3
0
0
0
2
1
0
1
0
2
1
0
2
0
2
2
0
2
0
0
0
0
0
0
0
3
0
0
2
0
2
2
0
0
0
1
2
2
2
1
0
0
0
0
1
0
0
2
0
0
2
1
0
0
1
0
1
2
2
3
2
1
1
0
2
0
0
2
1
1
0
0
1
0
0
2
0
0
0
0
2
0
1
0
0
0
0
1
3
1
0
2
2
0
0
2
0
2
2
0
2
1
0
2
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
2
1
0
1
0
0
0
0
2
0
2
2
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
2
1
2
1
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
2
0
1
2
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
1
2
0
0
1
2
0
1
0
0
0
0
0
2
2
0
0
1
1
0
0
1
0
0
2
0
0
1
0
0
0
0
1
0
0
1
1
2
2
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
1
0
2
2
0
0
0
0
2
0
0
0
1
0
0
0
0
2
2
0
0
0
0
1
0
3
1
2
0
0
2
0
0
1
0
2
0
1
0
0
0
0
0
0
2
0
2
0
1
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
2
1
1
2
3
0
0
2
0
0
1
1
0
0
0
0
1
4
0
0
0
0
0
0
2
0
1
0
2
1
0
0
0
1
0
1
2
1
0
0
0
2
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
2
2
1
1
0
3
0
2
2
1
0
2
0
0
0
0
1
0
0
0
1
0
0
0
2
0
2
1
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
1
0
0
1
0
0
0
1
0
3
1
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
2
0
0
0
1
0
2
0
0
0
1
1
0
2
0
0
0
0
1
2
0
0
0
2
2
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
1
1
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
2
2
2
0
2
2
1
1
2
0
2
0
0
0
2
5
1
1
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
1
1
2
1
0
0
2
0
0
0
0
2
0
2
0
0
0
0
1
1
0
1
0
0
1
0
0
1
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
1
2
2
0
0
1
0
0
0
0
1
0
1
2
2
0
0
0
0
2
0
0
0
2
0
1
1
0
2
1
1
1
0
1
0
0
2
2
0
1
0
0
0
0
0
0
2
2
1
0
0
2
0
1
0
2
1
0
2
0
0
1
0
3
0
2
1
1
2
0
0
1
2
0
2
0
0
0
1
0
0
3
2
1
0
1
0
0
3
0
0
1
0
1
0
2
0
0
2
2
1
0
0
0
2
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
2
0
2
0
1
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
1
3
0
2
1
1
0
0
0
0
0
1
2
0
0
0
0
1
1
2
0
0
2
0
1
0
0
2
0
0
0
1
0
0
0
0
1
2
1
2
1
0
0
2
0
2
2
0
0
0
0
1
0
0
1
1
1
1
0
2
0
2
3
2
0
1
2
0
0
0
1
1
2
0
2
1
0
0
1
2
0
0
1
0
1
1
1
1
0
2
2
1
0
0
0
0
2
0
0
0
0
1
0
2
1
0
2
1
2
1
2
0
0
0
0
2
1
1
0
2
0
1
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
6
0
3
1
0
0
0
2
2
4
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
2
1
0
1
2
0
0
1
0
2
0
0
3
1
0
2
0
0
0
1
2
0
2
0
1
0
0
0
3
0
1
0
0
2
0
0
0
2
2
0
0
2
1
0
0
0
1
0
0
3
0
1
0
0
0
5
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
2
0
2
0
2
0
0
0
2
0
1
0
1
2
2
2
0
0
1
8
0
0
0
0
0
0
1
0
2
1
1
2
0
2
0
2
0
1
0
2
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
2
0
0
0
3
0
0
1
0
0
1
2
2
1
0
2
0
0
0
0
0
0
0
1
3
0
2
1
0
2
0
0
2
0
0
0
1
1
0
0
0
3
2
1
2
0
1
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
2
1
1
2
0
2
1
0
0
1
0
1
1
0
0
0
0
1
0
2
0
1
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
1
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
1
1
1
2
2
0
1
2
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
2
0
1
1
0
2
1
2
1
0
0
0
0
0
0
0
0
2
0
0
1
2
0
1
0
1
0
0
2
1
0
0
1
1
1
0
0
1
0
1
0
0
1
1
1
0
1
2
0
0
2
0
0
1
0
0
3
1
0
2
1
0
0
0
1
0
1
1
0
3
1
1
2
2
0
0
2
0
2
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
2
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
2
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
2
2
1
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
3
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
1
0
0
0
0
0
0
1
1
0
2
2
0
0
0
2
0
1
3
0
1
2
3
2
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
2
2
0
0
0
0
1
1
2
1
2
0
0
0
0
0
2
0
1
1
1
3
0
2
0
0
1
0
0
0
0
1
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
1
0
2
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
1
1
2
1
0
0
0
1
0
0
2
1
2
2
2
2
2
0
0
0
0
0
0
0
0
0
1
1
1
2
1
2
0
0
0
0
1
2
1
0
0
1
0
0
0
0
0
1
0
3
0
0
0
0
1
1
0
2
0
0
0
0
0
0
2
4
0
0
0
1
1
0
0
0
1
4
0
0
3
1
0
1
2
1
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
1
0
1
0
2
0
1
0
4
0
0
1
0
0
1
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
2
0
0
2
0
0
1
0
3
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
1
0
1
0
3
2
0
1
3
0
1
1
2
1
2
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
2
1
0
1
1
0
1
0
0
1
2
0
0
0
2
2
0
2
2
0
2
0
5
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
1
1
2
0
0
0
0
2
0
0
0
0
0
0
1
2
1
0
0
0
2
0
0
2
0
0
0
2
2
0
2
1
0
1
0
0
1
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
1
0
0
1
0
2
1
1
0
0
2
0
1
1
2
0
1
2
0
1
2
0
0
1
1
1
2
0
2
2
2
0
1
1
0
2
0
1
1
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
1
0
1
1
0
0
0
2
1
1
2
0
1
0
1
0
0
0
1
1
0
1
0
0
1
0
6
0
0
0
0
1
0
0
0
3
1
1
2
0
2
0
2
0
0
0
2
0
1
1
1
0
0
0
0
0
2
2
1
2
0
0
1
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
1
2
0
0
2
1
2
4
0
1
0
2
0
0
0
0
2
0
2
0
2
4
0
0
1
0
0
0
1
0
0
3
0
1
2
0
0
0
0
0
1
0
0
0
1
0
1
0
1
2
0
0
1
0
0
2
1
1
0
0
0
0
0
1
1
1
1
2
0
0
0
2
0
0
1
2
0
0
0
0
2
0
0
0
0
1
0
0
1
2
0
0
0
0
0
1
1
2
1
0
0
2
0
0
0
2
1
0
0
0
1
2
1
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
1
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
4
2
0
0
2
0
0
2
1
0
0
0
0
0
1
0
0
0
0
1
0
1
1
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
1
0
0
1
0
1
0
3
0
0
0
3
0
4
2
0
1
1
2
0
2
0
1
1
0
0
2
1
0
0
1
0
0
0
2
0
0
0
0
0
4
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
2
0
2
1
1
0
0
1
0
1
0
1
1
1
0
0
0
1
0
2
1
0
0
0
0
0
0
1
2
1
0
1
0
0
2
0
1
0
0
4
1
0
0
1
0
1
0
0
2
0
1
0
1
1
1
0
2
2
3
1
0
2
2
0
2
0
0
0
2
2
2
2
0
2
0
1
2
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
2
2
0
0
2
0
0
3
2
1
2
0
0
0
2
0
0
0
1
0
2
2
0
1
0
0
1
1
0
0
0
0
2
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
3
1
0
1
0
0
2
0
1
0
1
0
3
0
1
0
2
2
0
0
2
0
0
2
0
0
1
2
0
0
0
0
2
0
3
0
1
0
0
0
1
0
0
1
1
2
0
0
1
0
0
0
1
0
0
0
0
1
1
0
1
0
0
1
0
2
0
2
0
0
0
2
1
0
0
2
1
0
0
0
0
0
1
1
0
0
2
0
1
0
1
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
1
0
1
1
0
0
1
0
0
0
0
1
1
1
2
2
0
0
0
0
1
0
1
0
2
0
0
0
0
2
0
1
1
0
2
1
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
1
0
2
0
0
1
1
0
3
0
2
0
0
1
0
0
2
0
0
1
1
0
0
0
0
0
4
1
1
1
0
0
0
3
0
0
0
0
0
1
2
1
0
1
2
0
0
2
0
0
0
1
2
0
0
1
1
0
0
0
0
0
0
0
2
0
2
0
1
1
0
1
2
0
2
0
0
1
0
2
2
3
0
0
1
0
0
0
0
0
0
2
2
1
1
2
0
0
2
0
0
0
1
0
0
0
2
0
2
0
0
0
0
1
0
3
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
2
2
0
0
1
1
1
1
2
0
0
0
0
0
0
0
0
1
2
0
0
0
1
1
1
0
0
1
1
2
0
0
0
1
0
2
0
0
0
1
0
2
1
2
0
0
1
1
0
0
1
1
0
0
2
2
0
1
2
4
0
1
1
0
0
1
1
0
0
1
0
1
1
0
1
0
0
0
0
0
0
1
0
0
1
1
0
2
1
1
0
0
0
0
0
1
3
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
2
0
0
2
4
1
1
1
2
0
0
2
1
1
1
0
0
0
0
0
0
2
1
0
2
0
1
2
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
2
1
1
0
0
0
4
1
2
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
1
0
1
0
3
2
1
0
1
0
0
0
0
2
0
2
1
2
1
1
0
0
0
2
0
0
0
0
0
5
0
1
2
0
1
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
1
2
0
0
0
0
0
2
0
0
1
1
0
2
1
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
2
1
0
0
0
0
1
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
1
2
0
0
1
2
1
0
0
0
5
0
1
0
1
1
1
0
0
0
1
1
0
0
1
0
0
0
2
1
0
0
0
3
1
2
0
0
0
2
2
0
0
0
0
1
1
2
2
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
2
0
2
0
1
2
2
1
1
0
0
0
1
2
0
0
1
1
2
2
1
0
1
0
0
2
2
0
0
2
0
2
0
1
1
0
0
0
2
0
1
0
2
2
2
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
1
0
1
0
0
0
1
1
0
0
1
0
0
0
1
0
0
1
2
2
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
1
0
2
1
0
0
2
1
1
0
2
0
2
0
0
0
2
0
0
0
1
1
0
0
2
4
2
0
2
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
2
2
2
0
2
2
2
0
0
0
1
0
0
0
1
2
0
0
0
0
1
0
0
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
1
1
0
0
0
0
2
0
1
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
1
0
0
2
0
1
3
0
2
0
0
1
0
1
0
2
0
1
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
2
2
0
0
0
0
2
2
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
1
2
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
3
2
0
2
0
0
0
0
0
0
3
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
1
0
2
0
0
2
2
2
0
1
0
0
0
1
0
1
2
2
0
0
0
0
1
1
1
2
0
0
1
0
0
0
2
2
0
0
1
2
2
0
4
0
1
1
0
2
0
2
0
2
0
1
0
0
0
0
0
2
1
1
2
2
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
1
0
2
0
1
2
0
0
2
0
1
0
0
0
0
0
0
0
2
0
2
2
0
0
1
0
1
2
1
2
0
1
2
0
1
0
1
0
2
2
2
0
1
1
0
0
0
2
2
0
0
0
0
2
2
2
0
0
0
2
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
1
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
2
1
3
2
0
2
0
0
0
1
2
0
2
0
0
0
0
2
0
2
2
0
0
1
1
1
1
0
2
2
2
1
0
1
0
1
2
0
1
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
2
0
0
0
3
2
1
0
2
0
1
0
1
0
2
2
2
0
0
0
0
0
2
0
0
0
0
0
0
2
7
0
0
2
1
4
0
2
0
0
0
3
0
0
0
1
0
1
1
0
1
0
2
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
2
0
2
1
0
2
2
0
0
0
0
0
0
2
1
0
0
1
2
0
2
0
0
2
1
0
0
0
0
0
0
2
2
3
1
0
1
0
0
0
0
2
0
0
0
0
4
0
3
0
2
4
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
2
1
0
1
0
2
0
0
1
1
0
0
0
4
1
0
1
0
0
0
2
0
0
0
1
0
1
0
0
3
2
0
1
0
0
0
1
0
2
0
1
0
3
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
1
2
0
0
0
0
0
1
2
1
1
0
0
0
1
2
0
0
2
0
1
0
0
0
2
0
1
0
1
2
1
0
0
1
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
2
1
0
0
0
2
0
0
1
1
0
2
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
1
2
0
2
0
0
0
0
2
1
0
0
2
1
0
4
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
1
1
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
1
1
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
1
2
0
2
0
1
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
2
0
0
1
0
1
0
0
1
2
0
0
0
1
0
0
0
1
2
0
2
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
4
1
1
1
0
1
1
12
0
0
0
0
2
0
0
0
0
4
0
1
0
3
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
3
1
1
0
0
0
0
2
2
2
2
0
0
5
0
3
2
0
0
0
2
0
0
0
0
2
1
2
1
0
0
1
0
1
2
0
0
2
1
1
0
0
2
0
0
0
0
1
0
2
0
0
0
4
1
0
0
0
4
1
0
0
0
1
1
2
0
0
1
1
0
0
0
0
1
2
0
0
1
2
1
0
1
1
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
2
1
0
2
0
2
0
1
1
0
2
1
0
1
2
1
2
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
2
0
2
1
2
0
0
0
2
1
3
0
0
2
1
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
4
1
2
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
2
2
2
3
0
0
2
0
0
0
0
0
0
0
2
2
1
2
0
0
2
0
2
2
2
0
0
0
2
3
0
0
2
1
1
4
1
0
0
1
0
2
1
0
0
1
0
0
2
0
2
0
2
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
3
0
1
1
0
0
2
0
0
0
1
2
2
2
0
1
0
0
0
2
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
1
2
1
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
2
1
0
0
2
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
2
0
0
4
2
0
2
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
2
0
1
0
1
1
0
0
0
0
1
0
1
0
1
12
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
1
0
0
2
2
1
3
0
1
0
0
0
3
0
0
0
2
0
1
0
2
3
1
0
0
2
2
1
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
1
1
0
1
0
0
0
2
1
0
0
1
1
2
1
0
0
0
0
0
0
2
2
0
0
0
1
1
0
0
1
1
2
2
0
0
0
2
0
2
0
1
0
2
0
0
0
0
0
2
0
3
0
1
2
0
0
1
2
0
0
0
2
2
1
2
0
1
1
0
0
0
0
1
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
2
1
1
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
3
2
2
8
0
1
0
0
1
1
0
0
0
1
0
0
2
0
0
0
3
1
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
1
0
0
0
2
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
2
2
2
0
2
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
1
1
0
1
1
0
0
2
0
1
2
0
0
0
1
2
0
2
0
1
0
0
2
2
1
0
0
0
3
0
0
0
0
0
1
0
2
0
0
0
2
2
1
2
0
0
1
2
1
2
0
0
2
2
1
1
0
1
0
0
0
0
0
1
0
2
2
1
0
0
0
0
0
0
2
0
2
1
0
0
1
2
1
0
0
1
0
1
1
0
0
1
4
1
0
2
0
2
1
0
0
0
0
0
0
1
1
1
0
0
0
2
3
0
0
0
1
1
0
1
1
2
0
0
1
0
1
2
1
2
1
1
0
0
0
0
4
0
2
0
2
0
0
0
1
0
0
0
0
2
0
2
0
0
0
2
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
2
0
0
0
0
0
0
3
0
0
2
2
0
0
0
1
0
0
1
0
2
0
2
2
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
1
0
0
0
0
1
0
2
0
0
0
0
2
1
2
0
2
0
0
0
0
1
0
2
0
0
2
0
1
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
1
0
2
0
2
1
1
1
1
0
1
0
0
2
1
1
2
0
1
0
1
0
1
2
0
0
2
0
4
2
0
3
1
0
0
1
0
0
0
2
0
1
2
1
0
1
2
0
1
0
0
1
0
1
2
0
1
0
2
0
0
0
2
2
0
2
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
8
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
1
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
1
0
0
1
0
0
2
2
0
0
3
0
1
0
0
1
0
2
0
2
0
0
1
1
0
0
0
0
0
0
3
1
0
2
1
2
1
0
0
0
1
2
0
0
0
0
1
1
0
0
1
0
0
0
0
2
0
0
1
0
0
1
0
2
0
1
1
0
2
0
0
1
2
1
1
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
3
1
0
0
0
1
0
0
2
0
0
1
0
0
1
1
0
0
0
0
1
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
2
1
0
0
1
0
0
0
0
1
2
0
2
1
1
2
0
0
0
0
0
0
2
2
0
2
0
2
2
0
0
1
0
0
1
0
2
1
2
0
1
1
0
1
0
1
0
0
2
0
2
0
0
0
0
7
0
0
1
0
0
0
0
0
0
2
1
0
3
2
0
1
1
2
1
2
0
0
0
1
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
1
1
0
1
0
1
0
2
0
0
0
0
0
3
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
4
3
0
2
2
2
0
1
0
0
1
0
0
1
0
2
0
2
1
1
2
0
2
1
2
0
0
1
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
2
2
0
2
2
2
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
2
2
2
0
2
2
0
0
0
2
0
3
2
0
1
0
0
0
0
0
2
1
0
0
0
0
1
0
2
0
2
1
0
2
0
0
2
0
0
0
0
0
1
2
1
0
0
1
0
0
0
0
2
2
0
0
0
0
2
2
0
2
2
0
0
1
0
0
0
1
1
1
0
0
0
6
7
0
0
1
0
0
0
2
0
1
1
3
0
0
0
0
0
1
2
1
2
0
0
1
0
0
1
0
1
0
0
0
0
0
1
2
0
2
0
0
2
2
0
0
0
0
2
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
3
0
2
1
0
0
0
0
0
2
1
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
1
1
0
0
2
0
0
0
2
0
0
2
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
3
0
0
0
0
1
0
1
0
2
2
0
0
2
0
0
0
0
0
0
2
0
0
0
1
2
0
1
0
1
1
0
0
1
2
2
0
0
0
2
1
1
0
2
1
0
0
0
0
0
2
0
1
0
0
0
0
1
3
2
0
0
0
0
0
1
0
1
1
0
0
1
0
2
0
0
0
1
0
1
3
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
1
1
0
0
2
0
0
1
2
0
0
2
3
0
0
0
4
2
0
2
0
0
0
0
0
1
0
0
2
0
0
2
0
1
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
1
0
1
5
0
1
0
0
1
0
0
0
0
0
1
1
0
0
2
0
1
1
3
0
2
0
2
0
0
0
2
1
0
2
0
0
0
0
0
0
1
0
3
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
1
0
1
0
0
0
0
2
0
0
0
0
0
0
2
1
1
2
0
0
1
0
1
0
1
2
0
0
0
5
1
0
0
0
1
0
0
1
1
2
2
2
0
1
0
0
1
2
0
2
1
0
0
1
0
1
0
0
0
2
0
1
1
0
1
2
0
0
1
1
0
2
2
2
0
2
0
1
1
1
0
1
2
0
0
0
2
4
2
0
1
0
0
1
0
0
0
2
1
0
2
0
2
0
0
2
0
0
2
0
0
1
0
2
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
2
1
0
0
0
0
2
1
0
3
0
2
0
0
0
0
0
0
1
0
1
2
1
0
0
0
2
0
0
2
0
2
1
0
0
0
2
0
2
0
1
1
2
0
0
0
2
0
3
0
0
0
0
0
0
0
0
2
2
2
0
1
0
1
2
2
2
0
0
1
2
0
2
0
0
2
2
0
0
0
2
0
2
1
0
0
0
0
0
0
0
1
0
1
0
3
2
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
2
2
1
1
1
2
2
2
0
0
1
0
0
1
2
0
0
2
0
0
1
1
1
1
0
2
0
0
0
0
0
2
1
0
1
1
0
0
2
0
0
3
1
0
1
0
1
0
0
1
1
1
0
0
0
0
0
0
1
1
0
0
0
2
0
1
0
0
0
0
3
0
0
0
0
1
0
0
1
2
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
1
2
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
2
0
2
1
1
0
1
2
0
0
2
0
1
0
0
0
0
1
1
0
1
0
1
1
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
1
2
0
0
2
2
0
1
1
0
0
0
2
0
1
0
1
1
0
0
0
1
0
3
0
0
2
0
1
2
0
0
0
0
2
0
0
0
1
0
1
0
0
1
0
0
0
2
1
1
2
0
0
3
1
1
2
1
0
0
0
0
0
2
0
2
1
0
1
0
0
0
0
1
0
0
2
3
2
2
1
0
0
0
1
2
1
4
2
2
2
0
1
0
1
1
2
1
2
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
1
2
0
0
2
1
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
1
2
0
0
0
1
0
0
0
0
1
1
0
0
1
0
1
1
2
0
0
2
1
0
0
2
0
2
0
1
0
1
0
1
1
2
2
0
0
1
1
0
2
0
1
0
0
0
0
0
0
1
3
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
1
0
0
0
0
1
1
0
1
1
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
2
1
1
0
0
0
1
3
1
1
0
0
0
0
4
0
2
0
0
0
2
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
2
3
1
0
0
0
1
0
1
1
0
1
0
0
3
2
2
0
2
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
2
4
1
0
0
2
1
0
2
4
0
0
2
0
2
0
1
1
0
0
1
0
0
0
0
3
1
0
0
2
0
0
0
0
0
0
1
0
1
1
0
0
0
0
2
0
0
1
0
0
0
0
2
2
0
0
1
0
0
2
0
0
0
0
0
2
0
1
2
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
3
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
2
0
1
0
0
0
0
0
0
2
3
0
1
0
3
0
1
0
0
2
2
0
1
2
1
0
2
0
2
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
2
2
0
4
1
1
1
2
0
0
0
0
0
0
1
0
0
0
1
0
1
0
2
2
0
2
1
0
0
2
0
2
2
1
2
0
2
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
5
0
2
1
0
0
0
0
2
0
1
0
0
2
0
0
0
1
1
1
2
1
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
4
0
0
4
0
0
0
1
2
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
2
2
0
1
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
2
4
1
0
2
0
1
1
0
0
0
0
0
0
1
0
0
1
1
1
0
2
1
2
2
0
3
1
2
2
0
0
1
0
0
1
5
0
0
2
0
1
1
1
0
1
0
0
0
1
1
1
1
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
1
0
2
1
6
0
0
2
1
0
0
2
0
3
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
2
2
0
0
0
1
0
0
0
0
1
2
0
0
0
3
1
0
0
1
0
0
1
0
0
0
2
0
0
2
0
1
1
0
1
0
0
2
2
2
0
0
2
0
1
0
0
0
1
2
0
1
0
0
1
4
0
2
1
0
0
0
2
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
1
0
2
2
0
0
1
2
0
0
0
0
1
1
2
0
0
0
0
1
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
1
0
0
0
2
0
2
2
2
0
0
0
0
2
0
0
2
1
2
1
2
0
3
1
0
0
0
0
0
2
2
1
2
0
0
0
1
2
1
2
1
1
0
0
0
0
0
0
2
0
6
2
1
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
1
1
0
1
0
0
1
2
0
1
0
1
2
1
0
0
2
1
0
1
0
0
4
0
1
0
0
0
2
0
0
1
1
0
0
0
3
0
0
1
0
1
0
0
0
0
0
0
2
1
0
1
0
0
0
2
0
0
0
1
4
1
0
0
0
0
4
1
0
0
6
3
1
0
0
2
0
2
2
0
0
3
0
1
1
2
0
0
0
0
1
0
1
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
1
0
9
0
0
1
0
2
3
1
0
1
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
4
0
0
0
0
2
1
0
0
2
0
0
0
0
1
0
1
2
2
0
0
0
1
2
1
0
0
0
0
2
5
0
0
2
0
0
1
0
0
0
0
0
0
0
2
2
1
2
2
0
0
0
2
2
0
0
1
0
3
2
0
0
2
1
1
2
2
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
1
0
1
0
1
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
3
0
1
1
0
1
0
1
1
0
0
0
0
1
0
1
1
0
0
3
0
0
2
0
0
1
1
0
0
0
0
0
1
2
2
0
0
0
0
2
0
0
3
2
0
0
1
0
1
0
0
0
0
0
2
0
0
0
5
2
0
1
0
0
2
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
1
0
2
0
0
0
1
2
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
2
0
2
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
2
2
1
0
1
1
2
0
2
0
0
0
0
1
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
1
0
3
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
2
1
5
1
0
1
0
0
0
0
1
0
2
2
1
0
0
0
0
0
0
3
2
0
0
2
1
1
0
2
0
0
0
2
2
0
0
0
0
1
1
2
0
0
0
1
0
0
0
0
2
0
0
0
1
2
2
0
0
0
0
2
0
0
0
0
0
2
1
2
0
1
0
2
0
1
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
2
0
0
2
0
2
1
0
1
1
1
1
0
2
0
1
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
5
0
0
2
2
0
1
2
0
0
1
0
2
0
1
1
1
1
0
0
0
3
0
0
1
0
0
1
0
1
2
0
1
0
1
0
0
0
0
0
2
0
0
2
0
0
0
2
2
2
0
0
1
1
3
0
2
0
0
1
0
2
0
0
0
1
2
1
0
0
0
1
2
0
0
0
2
1
0
0
1
0
0
3
0
0
0
1
3
0
1
1
0
0
0
0
0
2
0
0
1
0
1
0
2
2
0
0
0
0
0
0
1
0
0
0
2
0
0
1
2
1
0
2
1
1
0
1
1
0
0
1
1
1
0
0
2
1
0
0
0
1
1
1
0
0
0
0
2
0
0
2
0
0
0
0
1
0
2
0
1
0
0
1
0
0
0
0
1
0
1
2
0
2
1
3
2
0
0
0
1
0
2
1
1
0
6
0
1
0
0
1
0
0
0
0
2
0
1
3
0
1
1
0
0
0
2
0
4
3
0
1
1
2
1
0
0
1
0
0
3
0
0
2
0
0
0
0
1
0
0
1
0
1
1
0
0
0
1
0
1
1
2
0
0
0
0
0
3
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
2
2
1
2
1
0
0
0
3
0
2
1
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
4
0
0
0
2
0
2
1
1
0
0
2
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
2
1
1
1
2
0
0
2
2
0
2
1
2
0
0
2
1
0
1
0
0
0
0
0
1
0
2
2
1
1
2
0
0
1
0
2
0
1
0
2
2
0
0
0
0
0
2
0
2
1
2
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
2
0
1
0
0
0
1
2
2
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
3
0
0
0
1
0
0
0
0
0
1
0
0
0
1
2
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
2
0
1
0
0
2
0
1
0
0
0
2
0
1
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
1
2
0
0
0
2
0
0
2
0
0
0
0
0
0
2
1
0
1
0
0
0
2
1
0
0
0
1
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
2
0
0
0
1
0
1
0
0
2
0
1
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
1
0
0
2
1
1
0
2
1
1
0
0
1
1
0
2
1
0
3
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
3
0
1
0
0
0
0
2
0
1
1
0
2
2
2
0
0
0
1
0
1
2
0
2
0
2
0
1
1
2
0
1
0
2
2
0
0
1
4
2
1
0
2
5
2
4
0
0
2
0
3
0
1
0
0
2
1
1
0
0
0
1
1
1
3
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
2
0
1
0
2
0
0
0
1
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
2
0
0
1
2
0
1
0
3
0
2
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
2
2
2
1
0
0
0
1
0
0
0
0
3
0
0
2
0
0
0
0
0
2
2
0
1
2
0
0
1
0
2
2
2
0
0
1
0
1
0
0
0
2
0
0
0
2
0
0
2
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
2
1
0
2
0
2
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
1
1
2
0
1
0
2
2
0
0
1
0
2
0
2
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
1
1
0
0
1
0
0
5
2
0
0
0
0
1
0
2
2
2
2
0
0
2
1
0
0
0
2
0
1
0
0
1
0
0
1
0
0
0
2
1
1
2
0
0
2
2
0
0
0
0
2
0
3
0
1
0
2
3
0
1
2
2
0
0
0
0
0
0
2
0
0
2
0
0
3
0
2
0
0
0
0
1
1
0
0
2
0
1
1
0
2
2
0
0
1
1
0
2
0
1
0
1
0
0
0
0
2
1
0
0
0
3
0
0
0
0
1
1
0
0
2
1
3
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
2
0
0
0
2
2
2
0
0
0
0
0
0
0
1
0
1
0
0
0
1
2
0
1
0
0
0
0
0
0
0
1
0
2
1
0
0
2
2
1
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
4
2
2
1
2
0
1
1
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
1
2
2
0
0
0
0
0
1
0
2
2
0
0
0
1
0
2
0
1
0
0
0
2
2
0
1
1
0
0
0
0
0
2
2
0
0
5
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
2
0
1
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
2
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
3
0
0
2
0
1
0
2
1
0
0
0
1
0
0
0
1
0
0
1
1
2
2
0
0
0
0
2
1
0
1
0
0
2
0
1
0
2
2
0
2
0
2
1
0
0
1
2
0
1
2
1
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
2
0
0
2
1
0
0
0
2
0
1
0
0
0
0
0
2
1
0
1
2
0
0
0
1
1
0
1
2
1
2
1
0
0
0
0
1
1
0
0
1
0
0
0
0
1
2
0
0
2
0
1
0
1
0
0
3
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
1
2
1
0
1
0
2
1
0
0
0
0
0
0
2
0
0
1
0
1
0
1
0
2
0
0
2
0
0
1
0
1
0
1
0
0
2
0
0
0
0
4
0
0
0
1
0
2
1
0
0
0
0
0
1
0
0
0
2
0
0
1
1
0
1
0
0
1
2
1
0
1
3
0
0
0
1
3
2
0
0
1
0
1
2
0
1
0
2
0
0
2
0
2
0
2
2
0
2
0
0
0
0
0
0
0
1
0
0
2
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
2
2
2
0
1
0
0
0
2
0
0
2
0
0
0
1
0
1
0
2
1
1
2
1
0
0
0
2
0
2
0
1
0
0
1
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
1
2
2
2
0
0
0
1
0
0
0
0
0
0
2
0
0
1
1
1
0
2
0
1
0
0
0
2
0
0
0
1
1
0
0
0
2
2
1
0
2
1
1
0
1
2
0
0
0
0
1
0
1
0
0
0
0
0
2
2
0
0
0
0
2
0
0
1
1
1
2
0
0
2
1
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
1
0
1
0
2
0
1
2
0
0
0
1
0
0
2
0
0
2
1
0
0
1
2
0
0
0
1
1
0
1
0
2
0
2
0
0
0
1
0
2
0
0
0
2
2
0
2
1
0
2
1
1
2
0
1
1
0
0
0
2
0
0
0
2
0
2
0
2
0
2
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
2
3
2
0
0
2
2
2
0
0
2
0
1
0
1
1
1
1
0
0
0
6
0
0
2
0
1
2
0
0
0
2
0
0
2
0
0
7
1
0
0
0
2
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
3
0
0
2
2
0
0
0
0
0
0
1
2
1
2
0
1
2
0
0
1
0
0
0
2
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
1
1
1
0
2
0
0
0
1
1
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
2
0
2
1
2
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
4
0
1
0
0
0
0
1
1
0
2
0
0
0
0
1
1
0
0
1
4
2
0
0
0
0
1
0
1
0
2
1
0
1
0
3
0
1
0
2
2
0
0
2
0
0
1
0
3
0
0
2
0
1
0
0
1
0
0
1
0
0
5
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
1
0
0
0
0
2
0
0
0
0
0
1
1
0
1
0
0
0
0
0
2
2
2
0
1
1
0
2
0
2
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
1
2
0
0
2
0
0
0
0
0
0
2
0
2
2
0
1
0
0
1
0
0
0
1
2
1
0
1
0
1
0
0
2
0
0
0
2
1
2
2
0
0
2
2
0
0
0
0
1
0
0
0
1
1
0
0
0
0
2
0
0
0
2
1
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
2
0
1
1
2
0
0
0
0
1
2
1
3
2
1
0
1
0
0
0
2
0
1
0
5
1
0
2
2
0
2
0
2
1
0
0
1
1
0
0
0
1
0
0
2
0
1
2
2
0
0
1
6
1
2
0
2
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
1
2
1
0
0
0
0
0
1
0
0
1
0
1
2
0
1
0
3
1
0
0
0
0
0
0
0
0
1
0
3
1
0
2
0
0
0
1
0
2
1
1
2
0
2
2
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
3
2
0
2
0
0
2
0
0
0
2
1
0
2
2
0
2
0
0
1
2
0
0
2
0
2
0
0
0
2
2
2
1
0
2
1
0
1
1
0
0
3
1
2
2
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
2
0
1
0
0
0
0
0
0
0
0
0
2
2
2
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
2
1
1
2
0
0
1
0
0
0
0
1
0
2
1
0
0
0
1
0
2
2
0
0
2
2
3
2
2
0
2
0
1
0
0
0
1
0
2
1
0
1
2
2
2
0
0
0
2
2
0
2
1
0
0
1
0
1
0
0
2
0
0
0
0
0
2
0
2
1
0
1
2
0
0
3
1
0
2
1
0
0
2
0
0
1
0
1
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
1
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
2
0
3
0
2
0
0
2
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
2
2
1
1
0
1
1
1
0
2
0
0
0
3
0
1
0
1
1
0
2
0
0
0
0
0
0
2
2
2
0
2
0
2
2
0
0
2
0
0
1
0
0
2
0
0
2
0
0
1
0
0
1
0
0
1
0
0
2
0
1
2
2
3
1
2
2
2
0
3
0
0
1
1
1
2
2
1
0
2
1
0
2
0
0
1
0
1
0
0
0
3
2
0
0
1
0
0
0
2
1
1
0
1
2
0
0
0
1
0
2
2
0
0
0
0
2
0
0
0
1
0
1
2
1
0
2
1
0
0
0
0
0
0
0
2
0
1
0
1
4
0
1
0
0
0
0
0
1
3
0
0
0
0
1
1
1
0
2
2
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
2
0
0
1
1
1
0
1
0
2
0
1
2
0
0
2
0
1
0
2
1
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
2
0
2
0
0
0
0
0
2
0
2
0
0
2
0
0
2
0
1
0
0
1
0
1
2
0
1
0
0
2
0
0
0
0
0
1
0
2
0
1
2
0
2
0
2
0
1
3
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
6
2
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
1
1
0
1
3
0
1
2
0
3
0
2
0
0
1
0
0
0
2
0
1
1
0
0
0
0
0
0
3
1
1
0
1
0
0
1
2
0
0
0
0
0
0
1
0
0
0
1
0
2
1
0
0
1
1
1
0
1
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
2
0
1
0
0
1
1
0
0
1
0
0
2
0
0
0
1
0
0
0
2
3
2
1
0
0
0
0
2
0
0
2
2
0
1
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
2
0
0
1
1
1
1
0
0
2
2
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
3
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
1
0
1
0
1
1
2
2
1
0
0
1
0
1
0
0
0
1
0
0
0
2
0
1
0
2
0
0
0
0
2
0
1
0
0
1
0
0
1
2
0
2
0
0
1
0
2
1
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
7
0
1
1
1
0
2
0
1
0
1
2
1
1
1
2
0
3
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
4
0
2
0
0
0
0
0
1
0
1
2
1
2
0
1
0
2
0
0
0
2
0
1
2
0
1
1
0
2
0
0
1
0
1
4
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
3
0
0
0
1
0
1
0
1
0
0
0
1
0
1
0
2
1
2
2
0
0
1
3
0
0
3
0
0
2
0
0
1
0
2
0
2
0
0
1
2
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
1
1
2
2
0
2
0
0
1
0
4
0
1
0
0
1
0
0
1
2
2
1
0
2
2
0
1
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
1
0
1
0
1
1
0
0
0
0
0
3
0
0
0
0
0
0
2
0
2
0
0
0
0
0
3
0
0
2
0
1
2
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
2
2
0
0
0
2
0
0
0
2
1
0
0
2
0
0
1
2
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
1
0
2
2
0
2
0
0
2
0
0
2
0
0
2
0
1
0
0
0
0
1
1
2
1
0
0
0
2
2
0
0
0
0
0
2
1
0
0
6
0
2
0
0
0
2
0
0
2
0
0
2
8
2
0
0
2
0
2
2
3
0
0
0
2
1
0
2
0
0
1
0
0
2
0
0
0
2
2
2
0
1
0
0
0
0
0
0
0
1
0
0
2
2
2
2
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
2
1
0
0
1
0
1
2
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
1
0
0
2
0
0
0
0
1
0
0
1
2
1
0
0
0
1
1
0
0
1
0
2
0
0
0
0
1
0
1
3
1
2
1
1
0
0
0
0
2
0
2
0
1
2
2
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
1
0
2
1
0
0
0
0
1
2
0
0
0
2
0
1
0
0
0
2
0
1
1
1
0
0
1
0
1
0
0
2
0
0
1
1
2
0
0
0
0
1
0
0
0
0
2
0
0
0
1
1
0
0
0
1
3
1
2
0
2
0
1
0
0
2
2
1
1
1
0
0
2
0
0
2
0
2
1
0
0
0
2
1
0
0
1
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
1
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
1
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
2
1
1
2
0
5
1
0
0
0
0
0
0
1
0
2
0
0
1
1
2
2
1
1
0
1
0
1
2
2
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
1
0
0
0
1
2
2
0
0
1
1
2
0
0
0
0
0
1
0
0
0
0
2
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
3
2
0
0
0
1
1
0
2
0
0
1
1
0
0
2
2
0
0
1
2
1
0
0
0
0
0
0
0
0
1
3
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
2
1
3
0
0
2
1
0
1
2
2
2
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
1
0
2
0
1
2
0
1
0
2
0
0
0
0
0
1
0
2
0
1
0
1
0
0
0
0
2
0
2
0
0
0
1
0
2
0
2
0
2
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
3
1
0
0
0
1
0
0
2
0
1
0
1
0
0
0
2
0
0
0
2
2
0
0
0
0
0
2
0
0
0
1
0
0
2
3
0
2
2
2
0
0
2
1
0
0
3
2
1
2
0
1
0
2
0
0
1
0
0
0
0
0
1
0
2
1
0
0
0
1
0
0
0
2
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
1
0
0
2
1
0
2
8
0
0
0
0
0
0
0
0
0
2
0
2
0
1
1
0
0
0
0
0
2
0
1
0
1
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
1
0
6
0
1
1
0
0
2
1
2
0
0
1
0
2
0
2
1
0
4
0
2
2
0
0
0
1
2
0
0
1
0
0
0
0
0
0
2
1
0
0
1
1
0
0
0
3
0
0
0
0
2
0
0
0
0
1
0
0
1
1
1
0
0
3
1
0
1
0
0
3
1
2
0
0
1
0
0
2
0
0
1
0
0
0
1
1
0
3
1
0
0
0
0
1
2
0
2
0
0
1
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
1
1
1
0
2
1
1
0
1
0
2
1
0
2
0
0
2
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
2
1
0
0
1
2
1
2
2
0
2
0
0
2
1
0
0
0
2
2
0
0
0
0
2
0
2
2
0
0
1
2
1
1
0
0
2
0
1
1
0
0
0
2
0
1
0
0
0
1
0
1
1
0
0
2
1
0
1
1
0
1
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
3
0
2
1
1
0
0
0
2
2
2
0
2
0
0
0
2
0
2
0
0
0
0
0
1
1
2
2
1
0
0
0
0
0
0
0
0
2
0
0
1
1
2
1
0
2
1
0
0
1
1
0
0
0
1
1
0
1
0
2
0
2
1
0
2
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
2
0
2
1
0
0
0
3
1
1
0
0
1
0
0
10
0
0
2
1
2
1
0
0
1
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
2
0
2
1
0
1
0
0
0
0
0
2
0
1
1
1
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
1
0
0
5
0
2
0
0
0
1
0
0
0
3
2
0
2
0
0
2
1
0
2
1
0
0
0
0
0
2
0
0
2
0
0
2
2
2
0
2
1
1
2
0
0
0
1
1
0
1
0
0
0
2
2
0
1
2
0
0
1
3
0
0
0
1
2
0
0
1
0
0
1
2
0
0
0
0
0
1
0
1
0
0
2
2
0
1
0
1
0
0
0
0
1
0
1
0
0
3
1
4
0
0
1
0
0
0
0
2
0
0
2
0
1
1
1
0
0
0
1
0
0
0
0
0
7
1
0
2
0
0
0
1
0
0
1
1
0
1
1
0
1
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
2
0
0
2
0
0
2
1
0
0
0
0
0
1
0
1
3
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
2
1
0
0
0
0
2
2
2
1
0
2
0
0
0
0
0
0
0
2
0
0
0
2
3
0
1
0
2
0
1
2
0
0
1
0
0
0
2
0
1
1
0
0
1
1
2
0
0
0
2
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
2
1
0
1
2
1
1
0
2
1
0
2
3
2
0
0
2
0
1
0
0
0
2
0
1
2
0
0
0
0
4
0
0
2
0
2
2
1
0
0
2
2
1
0
2
1
0
0
0
1
0
2
1
0
2
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
3
0
1
0
2
0
0
0
0
0
2
2
1
0
0
0
3
2
2
0
1
0
0
2
1
0
0
0
2
0
1
0
0
0
0
1
0
0
1
0
3
0
0
0
0
0
0
1
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
2
1
1
0
0
1
2
0
0
1
0
0
1
2
1
0
2
0
0
1
0
0
0
0
1
2
0
2
1
0
0
0
0
2
0
0
2
1
1
0
1
0
0
0
0
0
1
0
1
2
2
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
3
0
0
0
0
1
2
0
0
0
0
1
0
3
0
0
0
0
0
0
3
3
0
1
0
5
2
0
2
2
1
2
0
0
0
1
0
2
0
2
2
0
2
0
1
0
0
1
1
1
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
2
1
2
1
0
2
0
2
0
0
0
0
0
0
2
0
0
1
1
0
0
3
2
0
0
0
0
1
0
1
1
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
1
2
1
0
0
0
0
0
1
0
2
2
1
1
0
0
0
2
2
2
1
0
1
1
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
1
1
2
0
0
2
1
0
0
0
0
3
0
0
2
0
0
0
2
0
0
0
0
0
2
0
2
0
0
1
0
0
1
2
0
0
1
0
1
0
1
0
2
0
0
0
0
1
0
2
1
0
0
0
2
0
0
2
2
1
0
0
0
0
0
2
2
1
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
2
0
2
2
3
1
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
2
1
1
0
2
0
0
1
0
2
1
2
2
1
0
0
1
1
0
1
0
0
0
0
1
0
1
1
0
0
0
0
1
1
0
0
0
2
0
1
0
0
1
3
3
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
2
2
2
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
2
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
2
2
2
1
0
0
0
0
2
1
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
1
0
1
0
0
2
0
0
2
0
0
0
2
1
0
1
1
0
0
1
2
1
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
1
0
0
1
1
0
0
0
2
0
1
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
2
1
0
2
0
3
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
1
3
0
0
2
1
0
0
0
0
3
0
0
0
0
1
0
0
0
1
1
2
3
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
5
1
0
2
2
0
0
0
0
1
2
1
0
0
0
1
2
1
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
2
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
2
0
0
3
0
0
1
0
0
3
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
2
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
1
0
1
1
0
0
2
0
2
0
1
0
2
0
2
2
3
1
0
0
0
2
0
0
0
0
0
1
0
1
0
0
1
0
2
1
0
0
0
2
0
0
1
2
1
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
1
2
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
1
2
0
2
0
0
0
0
0
0
1
0
0
0
2
2
0
1
0
2
0
0
0
1
2
1
0
1
0
0
1
0
2
2
0
0
0
0
0
1
0
0
0
1
1
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
1
0
0
1
2
0
0
0
0
2
2
2
0
2
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
2
1
0
2
1
0
0
1
1
0
1
2
0
0
0
1
0
0
0
0
0
0
3
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
2
0
2
0
2
2
0
0
0
0
1
0
1
1
1
1
1
0
0
0
0
0
0
0
1
0
1
0
2
0
2
0
1
0
2
0
0
0
2
0
0
0
1
2
0
0
1
2
0
0
1
2
1
0
2
0
0
0
0
2
0
1
1
1
0
1
1
0
0
2
0
2
0
0
0
0
2
1
0
0
2
0
1
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
2
0
0
0
0
2
1
1
0
2
1
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
1
0
0
0
0
2
1
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
2
2
0
1
0
0
0
0
0
1
0
2
1
2
0
0
0
2
0
0
1
0
1
1
0
0
0
0
0
0
1
2
0
0
0
0
1
0
1
2
0
0
0
0
2
2
0
0
1
0
0
0
0
0
2
0
0
2
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
2
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
1
0
0
2
1
1
0
0
0
0
0
0
0
0
0
1
2
0
1
2
2
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
1
0
0
2
1
0
1
0
0
0
0
2
0
1
2
2
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
1
2
1
1
2
1
0
1
1
0
0
1
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
3
2
1
0
1
0
0
1
0
0
1
0
1
0
0
1
0
2
1
0
3
2
5
0
0
0
2
0
0
0
1
2
2
0
2
1
0
1
2
2
0
1
1
2
0
2
0
2
1
0
0
0
0
0
0
0
1
0
0
1
0
1
2
0
0
2
0
0
0
3
0
0
0
0
0
1
0
0
0
1
0
5
0
0
0
0
0
1
0
0
0
0
0
3
0
2
0
0
3
0
0
0
0
1
1
0
1
1
0
0
0
1
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
1
3
2
0
2
0
1
2
0
0
0
0
0
0
2
0
2
2
0
2
0
0
0
0
2
0
3
0
0
0
0
0
0
0
1
2
0
1
1
0
2
0
0
1
0
2
0
0
0
0
2
2
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
2
0
2
1
1
0
0
0
0
1
2
1
1
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
1
0
0
0
1
2
1
1
0
0
0
0
0
2
1
1
0
1
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
2
1
2
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
2
0
0
0
0
0
0
2
1
2
2
2
0
0
0
2
2
0
0
0
1
0
2
0
2
1
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
2
0
3
0
1
0
0
0
1
1
0
2
0
0
1
0
0
1
0
1
0
1
0
0
1
0
2
2
0
0
0
1
0
1
0
2
2
2
0
0
0
0
2
0
0
3
1
0
0
0
0
2
0
2
0
0
1
1
0
0
1
0
0
2
0
0
0
0
0
0
0
1
2
1
0
0
1
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
3
0
1
0
0
2
0
0
1
0
0
0
0
3
0
4
0
0
0
0
0
1
2
2
0
2
0
0
1
1
0
0
2
0
0
0
0
2
1
0
0
0
1
0
2
1
1
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
1
1
2
0
0
0
1
0
0
1
0
1
0
0
1
0
0
3
0
1
0
0
0
0
5
1
0
2
1
0
0
1
2
0
0
2
2
2
0
0
0
0
2
0
0
2
1
2
2
1
0
0
0
0
2
0
0
1
0
1
0
1
0
0
2
1
0
2
1
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
2
0
0
1
0
2
0
0
0
2
1
2
0
0
0
0
0
2
1
0
0
0
1
1
0
1
0
0
0
1
0
1
0
8
1
0
0
0
2
2
2
0
2
1
6
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
1
0
0
1
2
0
0
6
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
2
2
0
0
0
1
2
2
0
2
1
0
1
0
0
0
0
2
0
0
1
1
0
1
0
2
2
1
1
0
0
0
1
0
1
0
0
2
0
0
1
1
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
2
1
0
0
0
1
0
1
0
0
0
0
1
1
0
0
1
1
2
2
2
1
1
0
3
0
0
0
1
0
1
2
0
0
0
0
2
1
0
0
1
0
0
2
0
1
0
1
0
2
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
2
1
1
2
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
2
2
1
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
2
0
1
0
1
2
2
2
0
0
0
0
0
0
0
0
0
2
0
1
0
1
1
0
0
0
0
3
0
2
0
0
1
1
2
0
0
0
0
1
0
0
1
0
2
0
0
1
2
0
0
0
2
1
0
0
0
0
1
2
2
0
2
0
2
0
0
0
0
0
2
0
0
1
1
0
0
0
1
0
0
0
0
1
2
0
0
0
2
2
0
0
0
0
0
1
2
0
2
2
0
2
3
4
1
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
1
0
2
0
2
0
0
2
0
1
0
0
1
3
1
2
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
2
2
0
0
0
1
0
2
0
0
1
0
1
2
0
1
1
1
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
2
0
1
1
1
0
2
0
0
0
0
2
0
2
0
0
0
0
2
1
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
3
0
1
0
2
0
0
1
1
0
1
0
1
0
0
0
1
1
0
0
1
0
0
0
1
0
2
1
1
3
2
1
1
1
1
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
1
0
0
2
1
0
0
1
3
0
0
0
0
0
0
0
1
2
3
0
2
0
0
2
0
0
1
1
1
0
0
0
0
1
2
2
0
0
0
0
0
0
1
3
1
0
0
0
0
2
2
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
3
0
0
7
0
0
2
2
1
0
0
2
0
1
0
0
0
0
1
0
2
1
1
1
0
0
0
0
2
0
2
2
0
0
1
2
2
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
2
0
2
1
0
1
0
2
2
2
0
0
1
0
0
2
1
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
2
0
0
0
0
2
0
0
1
1
0
0
0
2
0
1
1
3
1
0
0
0
0
1
0
0
0
1
2
0
2
1
0
0
1
0
0
0
1
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
5
0
2
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
2
0
0
0
0
3
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
2
2
0
1
2
1
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
3
2
1
0
0
1
0
2
0
0
2
0
0
2
1
1
4
0
1
0
0
1
0
0
0
2
1
0
0
2
0
0
2
0
1
0
0
0
1
2
0
2
2
0
0
0
0
0
2
2
0
0
0
2
2
0
0
0
1
1
0
0
0
0
0
0
0
0
1
2
0
1
1
1
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
1
0
0
0
0
2
2
1
0
0
1
0
0
1
1
0
0
0
1
1
1
0
2
0
0
0
0
2
0
0
0
0
0
1
5
0
0
0
0
2
2
0
0
0
1
0
2
0
0
2
2
1
0
1
1
0
1
0
1
0
0
0
1
1
0
0
2
0
0
2
1
1
0
1
1
0
1
0
0
0
0
0
0
0
0
2
2
0
0
1
0
1
0
0
0
0
0
3
0
0
0
1
1
0
2
1
0
1
0
1
1
0
2
0
1
2
1
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
2
1
0
0
0
0
1
0
2
0
0
0
0
0
3
0
0
2
1
2
0
4
0
0
0
2
0
0
0
2
2
0
0
0
0
2
1
1
2
0
1
2
2
2
0
0
0
0
1
0
4
0
0
0
0
2
1
0
0
0
0
2
1
0
0
1
2
0
0
1
2
0
0
1
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
2
0
2
0
0
0
2
0
0
2
2
0
4
0
0
0
0
1
1
2
1
0
0
0
0
1
2
2
2
0
0
2
1
0
0
0
0
0
1
3
2
0
2
2
0
2
0
0
0
3
0
0
2
2
0
0
0
0
0
0
3
0
1
1
0
1
0
0
0
1
0
2
1
0
2
0
1
0
2
0
0
3
0
0
1
0
1
2
1
0
0
2
0
1
1
2
2
0
0
1
1
3
1
0
2
0
2
1
7
0
1
4
0
1
0
0
0
1
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
1
1
0
0
1
2
1
1
2
0
0
2
2
1
1
0
0
2
1
1
3
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
2
0
0
2
0
1
0
1
1
0
0
1
2
2
0
0
0
2
0
0
1
0
0
0
0
0
2
2
0
0
0
2
0
1
2
2
0
1
1
0
0
0
0
2
0
0
5
2
2
0
1
1
2
0
2
2
1
0
2
0
0
1
0
2
0
0
0
1
0
0
2
2
1
0
0
0
0
0
2
0
0
2
2
0
1
4
0
2
1
1
0
0
0
1
0
0
2
1
0
0
0
3
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
2
2
2
0
3
0
0
0
2
2
1
1
2
3
1
0
0
0
0
0
0
1
2
2
2
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
5
0
0
3
5
2
0
1
1
0
0
0
1
1
1
0
0
1
0
3
1
1
0
0
0
0
2
2
0
1
0
0
0
1
0
0
0
1
0
0
0
2
1
2
1
0
0
2
0
0
0
2
2
2
0
2
0
0
0
0
1
1
0
0
1
0
2
0
0
4
2
0
0
1
1
0
2
0
2
0
1
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
11
2
0
0
0
0
0
2
0
0
0
1
0
0
2
0
2
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
2
0
0
0
2
2
2
2
3
3
0
3
0
1
0
2
0
0
0
1
0
0
2
1
0
0
0
1
2
1
2
1
0
2
0
1
0
0
0
2
0
2
0
0
1
2
2
0
0
0
1
0
1
0
0
2
1
0
0
2
0
0
1
1
0
0
1
0
2
0
0
2
0
1
0
1
1
0
0
1
1
1
0
0
0
3
0
1
0
2
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
1
0
0
0
1
0
0
0
1
0
1
3
0
0
0
1
0
1
0
1
5
1
1
1
0
1
0
2
0
2
0
0
0
0
0
2
1
0
0
0
2
0
0
2
3
0
1
0
1
0
0
2
0
2
1
0
1
1
0
0
3
0
0
1
0
0
1
2
3
0
0
3
2
0
0
2
0
2
0
0
0
2
0
0
1
0
0
0
0
1
2
1
1
0
0
2
2
1
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
2
1
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
1
1
0
0
0
2
2
2
0
1
0
1
2
0
0
0
0
1
0
2
1
2
0
0
0
4
0
2
1
1
2
0
0
2
1
1
0
2
0
0
2
2
0
1
0
0
1
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
2
1
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
1
1
0
0
0
2
2
0
0
0
2
1
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
3
0
1
0
0
0
2
0
0
1
1
2
2
2
4
2
1
0
0
1
1
2
0
0
0
2
0
6
0
0
2
2
1
2
2
1
0
0
1
0
0
0
1
1
2
0
0
0
1
0
0
1
0
1
1
0
0
0
0
2
0
1
0
1
0
0
0
3
3
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
2
0
1
0
0
2
0
2
0
1
2
0
1
2
1
0
0
2
1
0
0
0
1
1
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
1
4
0
0
1
0
7
1
1
1
1
0
0
0
1
1
1
1
0
0
1
2
0
0
0
0
0
0
2
0
0
0
1
1
2
2
1
0
2
2
0
0
0
3
0
2
2
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
3
0
2
1
2
2
0
0
1
1
0
0
0
0
1
2
0
0
2
0
0
0
1
1
0
3
1
0
0
0
1
0
0
2
0
0
1
0
0
0
1
0
0
0
2
0
2
0
0
0
2
2
0
0
0
0
0
1
2
1
2
1
0
0
0
0
0
1
0
1
2
1
0
0
1
0
0
1
0
1
0
1
0
1
0
0
0
0
0
2
0
1
0
1
1
0
0
2
2
0
2
0
0
1
0
0
0
1
0
0
0
0
0
2
1
0
1
0
0
1
2
1
0
0
0
0
0
0
0
2
0
1
1
0
1
0
2
0
0
0
0
1
0
0
1
0
2
2
0
0
0
0
2
0
0
0
0
2
0
2
4
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
3
0
0
0
2
1
1
1
0
0
1
2
0
2
0
0
0
4
0
0
0
1
1
0
0
0
1
0
2
0
0
2
2
0
1
2
1
2
0
2
0
2
0
0
0
0
3
0
1
0
2
0
0
0
1
2
0
0
2
1
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
2
1
0
2
2
0
2
1
1
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
1
3
0
0
2
0
0
2
0
0
1
2
0
0
0
0
0
0
0
1
2
0
0
1
1
0
1
0
0
1
2
1
0
0
0
1
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
1
1
1
0
0
0
0
1
1
1
0
1
0
0
0
2
2
0
1
1
1
0
0
2
0
0
0
4
0
0
0
2
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
2
2
0
0
0
0
2
2
2
0
0
0
2
2
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
1
3
0
0
1
0
0
0
0
2
2
0
0
0
6
0
0
0
1
0
0
0
1
2
1
0
1
1
0
1
0
0
0
0
1
0
0
0
0
1
0
2
0
1
1
0
2
0
4
1
1
0
1
0
0
0
1
2
0
0
0
2
0
0
2
0
1
0
0
0
0
1
2
4
0
0
0
0
1
1
1
0
2
0
0
0
1
0
0
0
0
2
2
0
1
0
0
0
1
0
1
1
2
0
2
0
0
2
0
0
1
0
1
0
0
2
0
0
2
0
0
1
0
1
2
2
0
2
0
0
0
2
0
3
0
1
2
0
0
1
0
0
2
0
0
0
0
0
0
1
0
1
1
0
0
0
2
0
2
0
1
1
0
0
0
2
1
1
1
0
0
0
0
5
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
3
1
1
1
0
0
0
0
0
3
1
0
0
0
0
2
0
0
0
1
0
0
2
0
1
0
0
2
2
0
0
0
0
0
0
2
0
1
0
1
0
0
1
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
1
2
1
0
2
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
1
1
2
0
3
1
0
0
4
2
2
1
2
0
0
0
1
2
0
1
1
1
2
0
0
2
2
1
0
0
2
0
1
0
0
0
0
0
3
0
0
0
0
0
0
1
0
1
1
0
0
0
2
2
0
2
0
0
2
0
0
0
0
0
2
0
0
0
1
4
1
0
1
2
1
0
1
0
0
0
0
2
1
1
0
0
0
1
1
0
1
0
0
0
0
0
1
2
0
0
1
0
2
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
2
0
1
0
2
2
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
2
2
1
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
2
1
1
0
0
0
0
1
0
0
3
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
3
2
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
2
1
1
0
0
0
0
0
2
0
0
5
0
0
0
0
1
0
1
1
1
0
2
0
2
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
1
2
0
1
2
1
0
0
1
4
0
1
0
0
0
0
1
1
0
2
0
0
1
0
0
0
0
3
0
1
2
0
1
1
0
0
2
0
0
0
2
1
1
0
2
0
0
1
0
1
0
1
2
0
0
0
0
2
0
2
0
1
2
2
1
2
1
2
0
1
2
0
0
2
0
2
0
1
0
0
1
0
2
1
1
2
1
2
2
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
2
2
0
0
0
1
0
2
0
0
1
2
0
2
0
0
0
0
1
2
1
0
2
0
1
0
0
1
0
0
2
0
0
2
2
0
2
0
0
0
1
1
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
2
3
1
1
1
1
2
0
1
0
2
1
0
2
0
2
1
0
0
1
2
0
1
0
1
0
0
0
0
0
0
0
0
0
2
1
0
1
1
1
2
0
2
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
1
1
2
2
0
0
0
0
0
1
0
2
0
1
0
0
2
0
0
0
1
0
0
0
1
0
1
1
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
3
2
1
2
0
0
0
0
1
0
0
2
1
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
2
1
1
0
0
0
0
0
0
0
1
1
0
1
1
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
4
2
0
1
0
0
1
0
2
0
0
2
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
2
1
0
2
2
1
0
1
0
0
1
0
3
0
0
0
2
1
0
0
2
0
2
2
0
0
2
0
0
1
1
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
1
0
0
0
2
2
2
0
0
2
0
0
1
0
0
0
0
2
1
0
0
0
2
0
0
1
3
1
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
2
0
0
1
1
1
0
0
0
0
2
0
0
0
0
2
2
2
0
0
1
0
0
0
1
3
1
0
0
0
0
0
1
0
4
2
0
0
1
1
0
0
0
0
0
0
0
0
2
1
0
1
1
1
0
0
0
1
1
0
2
1
0
2
3
0
0
0
0
0
1
0
0
2
3
0
1
2
0
1
1
3
0
0
2
2
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
2
2
0
1
0
0
1
1
0
2
0
0
0
1
1
0
0
0
1
0
0
2
2
0
2
1
1
3
0
2
1
2
1
1
0
2
0
0
1
0
0
0
1
2
0
1
0
1
0
1
0
0
0
0
0
2
0
0
0
1
1
2
0
0
1
2
0
0
2
0
2
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
1
0
8
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
1
1
2
0
1
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
4
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
4
0
0
1
2
3
1
0
0
2
0
0
0
0
0
0
1
0
0
0
3
1
1
0
0
2
0
0
0
0
1
2
0
1
0
1
0
0
0
1
1
1
0
0
0
0
2
0
2
1
2
0
1
3
0
0
1
1
0
0
0
1
1
0
2
0
0
0
1
0
0
0
0
2
0
2
0
2
1
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
1
1
0
2
2
0
2
1
0
0
0
1
1
0
0
0
0
0
2
2
2
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
2
2
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
1
1
0
0
0
0
2
1
0
0
2
0
1
1
0
0
1
0
0
1
0
0
0
1
2
1
0
1
0
0
0
0
1
1
0
0
1
1
1
0
0
1
0
1
0
0
2
2
0
1
1
0
0
0
0
0
1
0
0
0
1
0
1
1
0
2
1
2
2
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
3
0
0
0
0
1
0
0
1
1
1
2
2
0
0
2
1
2
2
2
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
3
1
1
0
0
0
0
2
0
0
0
0
2
0
1
2
1
0
1
2
0
0
1
0
1
0
0
2
0
0
0
0
0
1
0
1
1
0
0
2
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
4
1
0
0
0
0
0
0
0
0
2
2
0
1
3
0
1
0
0
1
0
2
2
2
0
0
0
0
0
0
0
2
0
1
0
0
2
2
3
2
0
1
0
1
0
0
1
0
0
0
0
0
2
0
0
2
2
0
0
0
1
0
1
1
0
0
0
0
0
2
1
0
0
2
1
0
0
0
0
1
2
0
0
2
1
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
2
1
0
0
1
0
2
2
0
1
1
1
0
1
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
1
1
0
0
0
0
2
1
1
0
0
1
0
2
0
1
0
0
4
0
2
1
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
3
0
1
2
0
0
1
0
0
2
0
0
2
1
0
0
0
1
0
0
0
2
0
0
1
1
0
1
2
0
2
3
2
4
1
0
0
2
0
1
0
0
3
0
2
0
0
0
0
0
0
0
0
0
2
1
1
0
0
1
0
0
0
0
0
0
1
0
0
2
0
2
2
0
1
0
0
0
2
6
1
2
2
0
0
1
1
1
0
0
0
0
0
0
2
1
1
0
1
2
0
1
0
2
2
0
0
0
0
0
0
0
0
1
4
0
0
0
2
0
1
1
1
1
2
0
0
0
0
2
0
0
0
0
2
0
1
0
2
1
0
1
0
2
2
1
0
0
1
0
0
0
0
1
2
0
1
0
0
0
0
1
1
2
2
0
2
4
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
2
0
3
0
1
2
0
0
0
0
0
2
1
0
3
2
2
0
0
1
0
0
0
2
1
0
2
1
1
2
2
0
0
2
0
0
0
0
2
0
0
0
3
1
0
1
0
4
0
2
0
0
0
0
0
0
0
0
1
0
0
1
2
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
2
1
1
0
0
4
0
0
0
0
1
0
1
1
2
0
0
2
0
2
0
1
0
0
2
1
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
1
0
1
0
2
0
0
0
1
0
0
0
0
1
2
2
2
1
0
0
0
0
2
1
0
1
1
0
2
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
2
0
2
0
2
0
1
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
1
2
4
0
0
0
2
0
2
0
0
0
1
0
0
2
0
1
0
1
0
2
1
0
0
0
0
2
1
0
0
2
1
0
0
0
1
0
0
1
1
2
0
2
0
0
2
1
0
0
0
2
0
1
0
0
2
2
2
1
0
0
2
0
1
0
0
2
2
0
1
1
0
3
0
2
2
0
0
2
2
0
0
0
1
0
1
0
0
0
0
1
0
0
2
2
1
0
0
1
5
2
0
0
0
0
2
2
0
0
2
1
1
0
0
0
0
1
0
1
1
0
0
1
0
2
2
2
1
1
1
0
0
0
0
1
3
0
0
0
0
0
0
0
0
1
1
0
0
2
0
1
3
0
0
0
2
0
3
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
2
0
2
1
0
0
1
1
2
0
0
2
1
2
2
0
2
1
1
0
0
1
1
1
2
0
0
0
0
0
0
2
0
1
0
1
1
1
0
4
0
1
0
1
2
0
0
0
2
0
0
0
0
2
0
0
2
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
2
1
0
0
0
0
2
1
1
0
0
2
0
0
1
2
1
2
1
2
2
1
1
0
0
1
0
1
0
0
2
1
0
2
0
0
0
2
0
2
3
0
0
0
0
2
0
0
0
0
2
0
0
0
3
1
0
0
0
0
1
0
0
1
1
0
1
2
2
0
2
0
0
0
0
0
0
0
0
0
1
1
0
1
0
2
2
2
0
0
0
0
0
0
1
1
1
0
2
1
1
0
0
0
1
0
2
0
2
0
0
0
0
2
2
1
2
0
2
0
1
1
0
0
1
1
0
0
1
0
1
1
0
0
0
2
0
0
0
2
3
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
1
0
2
2
0
1
2
1
0
0
0
0
0
2
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
2
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
2
2
2
0
1
1
1
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
2
0
0
2
0
2
0
0
1
0
1
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
2
1
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
2
1
0
1
0
0
0
2
0
0
2
0
0
3
0
0
0
0
0
0
3
0
0
1
2
1
0
8
2
1
0
0
2
0
0
0
1
1
1
1
2
2
0
0
1
0
0
0
0
2
0
0
2
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
2
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
3
1
1
2
0
0
0
1
0
0
1
0
1
0
0
1
2
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
1
2
0
0
0
2
0
1
0
0
1
0
0
2
1
0
0
0
0
2
2
0
0
2
0
2
0
0
0
0
0
0
2
1
0
2
1
0
7
2
0
0
0
0
0
1
2
0
1
0
2
1
3
1
0
1
2
2
0
0
2
2
0
0
1
2
0
0
0
2
1
8
0
2
1
1
2
0
0
0
0
1
0
0
0
0
0
1
0
0
4
0
0
0
0
2
0
0
0
0
0
0
0
1
1
2
2
2
2
0
0
0
0
0
1
1
0
0
0
2
0
0
0
1
0
1
1
2
2
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
1
0
2
0
0
0
0
0
1
0
1
0
0
0
2
1
2
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
1
2
1
0
0
0
2
0
0
0
0
1
1
0
0
0
1
0
2
1
0
0
0
0
0
0
2
1
0
3
1
1
0
0
0
1
0
0
0
0
0
2
1
2
0
0
2
0
0
0
0
0
0
2
0
1
1
0
2
0
1
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
1
2
0
1
0
2
3
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
1
1
0
0
1
0
0
2
0
0
0
0
2
2
0
0
0
0
0
1
1
2
2
0
1
0
1
2
1
1
1
0
0
0
0
0
0
0
1
1
0
0
0
1
1
2
1
0
2
0
1
1
0
2
1
0
1
1
2
1
2
2
0
0
0
0
0
0
1
0
0
1
0
2
3
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
2
0
1
1
0
0
0
2
1
0
2
0
0
0
0
1
0
1
2
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
2
2
0
0
3
2
0
1
0
0
3
0
0
0
0
1
0
1
0
0
2
2
0
0
0
0
2
1
0
4
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
2
1
0
0
1
0
0
0
2
0
0
1
2
0
1
0
2
0
0
0
0
3
1
2
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
3
0
0
0
0
0
1
2
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
2
1
1
0
0
0
0
3
0
1
0
0
0
1
1
1
1
2
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
2
1
0
0
2
2
0
0
2
0
0
0
0
4
2
3
2
1
1
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
2
0
0
0
1
2
2
2
0
0
1
0
0
2
0
0
2
0
1
1
0
1
0
0
2
0
1
0
0
0
0
0
0
0
1
3
0
1
0
0
1
0
0
0
0
1
2
0
2
0
1
0
0
0
0
5
0
0
0
2
0
0
1
2
2
1
0
1
0
1
2
2
1
0
2
0
0
1
0
0
2
2
0
0
0
2
0
2
0
1
0
2
1
0
0
2
1
0
0
0
1
0
0
2
0
1
0
0
0
0
0
1
0
2
0
0
0
1
0
1
0
0
0
0
0
1
2
0
2
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
1
2
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
1
2
1
0
1
0
0
0
0
2
1
0
0
0
2
0
0
0
0
1
0
2
0
1
0
2
0
0
0
1
0
2
2
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
1
1
2
0
3
0
0
0
1
0
0
1
0
0
0
0
0
4
0
1
0
0
0
4
0
0
2
0
0
0
0
0
2
5
0
0
1
0
0
0
1
1
0
2
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
2
3
0
1
1
1
0
0
0
1
0
0
1
3
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
1
2
0
2
0
2
0
2
1
2
1
0
0
2
1
1
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
2
5
1
0
0
3
0
0
0
2
0
0
0
0
0
1
0
0
2
2
1
0
1
0
1
0
1
0
0
1
2
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
1
0
0
0
0
0
1
1
1
0
0
2
0
0
2
1
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
1
2
0
1
2
1
0
0
0
0
1
1
1
0
0
1
0
0
0
0
3
0
0
0
0
1
0
0
0
2
0
1
0
2
0
4
0
2
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
2
1
0
0
2
0
1
3
1
0
1
0
0
0
0
0
1
0
0
0
1
2
2
1
0
0
0
0
1
2
3
2
0
0
2
1
1
0
0
0
0
1
0
0
0
0
1
2
0
2
0
0
0
2
1
0
0
0
0
2
1
0
2
1
0
3
0
0
0
1
0
0
0
2
2
0
1
0
1
1
1
0
0
0
0
1
2
0
2
0
2
0
2
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
4
2
0
0
0
0
0
1
0
1
2
0
0
1
0
2
2
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
6
0
2
0
1
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
3
0
0
1
2
2
1
0
1
0
1
0
0
1
1
1
2
2
0
0
2
0
0
3
1
0
0
2
2
0
0
1
2
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
4
0
2
2
2
0
2
0
1
0
2
0
0
0
1
2
0
1
2
0
0
0
0
0
0
2
0
1
0
13
0
0
1
0
0
2
0
0
0
0
1
2
2
1
1
0
0
0
0
0
2
0
0
2
1
2
1
1
1
1
0
1
0
0
0
0
1
0
2
2
0
4
0
0
0
1
0
1
1
0
0
2
2
0
1
0
1
0
1
0
0
0
0
0
5
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
2
0
0
2
4
2
0
0
0
0
1
2
2
0
0
0
1
1
0
0
2
1
0
1
0
2
1
0
0
0
0
2
0
0
1
2
1
1
0
0
0
0
0
2
0
0
0
0
1
0
1
0
1
0
3
0
0
0
0
0
0
0
1
0
1
1
4
2
1
0
0
0
1
0
0
2
2
2
0
0
0
0
0
2
0
1
1
1
0
2
0
0
0
0
0
0
0
0
3
0
1
1
0
0
2
0
0
0
0
0
1
2
1
1
0
0
0
2
0
0
0
3
1
0
2
0
0
0
2
1
0
1
1
0
0
0
0
0
0
0
2
1
0
2
1
0
1
0
0
0
0
2
0
0
1
0
0
0
0
2
0
1
1
0
0
0
2
1
2
0
0
0
0
2
2
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
1
1
2
1
0
1
1
1
0
1
0
0
2
2
0
0
0
2
1
0
1
1
0
0
0
0
1
2
2
1
1
2
0
0
0
0
0
0
1
0
2
0
2
0
1
1
0
1
1
0
0
1
1
0
2
0
0
0
1
2
2
0
0
0
1
1
2
2
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
1
0
0
1
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
2
0
2
2
0
0
0
0
0
1
0
1
0
2
0
0
2
2
2
0
0
2
0
0
2
1
1
0
1
3
1
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
2
1
4
2
1
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
2
2
1
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
1
0
1
2
0
4
0
1
1
1
2
0
0
3
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
2
0
2
0
1
0
0
1
0
0
0
1
3
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
1
1
0
2
1
1
0
0
1
0
0
0
0
0
1
0
0
2
0
2
2
1
0
2
1
0
1
0
0
1
1
0
2
0
0
1
1
0
0
0
2
0
0
1
1
2
2
4
0
0
0
0
0
2
0
1
0
0
1
2
1
2
1
0
0
0
3
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
4
0
0
0
0
0
0
0
2
0
1
0
1
2
0
2
0
0
1
0
0
0
0
2
0
0
1
2
2
4
1
0
0
0
0
0
0
0
1
0
1
0
0
2
0
2
0
1
0
1
1
0
1
2
0
0
0
1
0
0
0
1
0
0
2
0
2
1
0
2
1
1
1
2
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
2
1
0
2
1
2
0
1
0
0
1
1
2
0
1
3
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
1
0
1
0
0
0
1
1
3
0
0
1
2
0
1
0
0
0
0
0
0
0
3
0
2
2
1
0
0
0
0
1
1
1
0
1
0
2
2
0
0
1
0
0
1
0
2
1
0
0
1
2
0
2
1
1
2
0
0
0
0
4
0
0
0
0
1
0
1
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
2
0
2
1
4
0
1
2
2
0
0
0
1
1
2
1
0
0
3
0
1
2
0
0
0
0
2
0
0
0
0
1
0
1
2
0
1
0
0
0
1
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
1
0
0
0
1
2
0
0
1
0
0
0
1
0
0
0
1
2
0
0
1
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
2
2
1
2
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
1
0
2
0
2
0
0
0
0
3
0
1
0
0
1
1
2
0
0
0
2
0
0
0
1
1
0
1
0
0
1
0
0
0
0
2
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
2
1
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
1
3
0
1
2
2
0
0
0
2
0
0
0
0
1
1
0
2
1
0
0
0
2
0
1
3
3
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
2
0
0
1
1
0
1
0
0
1
0
0
0
1
2
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
6
1
0
0
1
1
2
2
0
0
2
2
1
0
0
0
1
2
0
0
0
0
2
0
2
2
2
0
0
0
1
0
0
2
0
0
0
0
0
2
0
2
2
1
1
0
1
0
0
2
0
0
0
0
0
0
2
0
2
1
0
1
1
0
1
0
0
0
1
1
0
0
2
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
2
0
0
0
1
0
2
0
0
2
0
0
0
0
3
0
0
0
1
0
0
0
2
1
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
2
0
0
1
0
2
0
1
1
0
0
0
0
2
0
0
1
1
1
0
0
0
2
2
2
0
0
0
0
1
0
2
0
0
0
1
0
0
3
0
3
0
2
1
0
1
1
1
1
0
1
1
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
2
0
2
0
2
2
2
2
2
1
1
1
0
0
0
1
0
0
0
0
0
0
1
2
1
0
1
0
0
0
0
0
2
0
2
1
0
1
0
0
0
2
1
2
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
2
0
3
0
0
0
0
0
1
1
0
1
0
2
0
0
0
0
2
0
1
0
1
0
1
1
0
0
2
0
4
0
0
1
0
2
2
0
1
0
0
0
0
0
2
0
3
0
0
0
5
0
1
0
2
0
3
2
2
2
1
1
2
0
0
2
3
0
3
2
0
2
1
0
0
1
0
0
0
0
0
1
2
0
0
2
1
0
0
0
0
2
0
0
0
1
0
4
0
0
2
0
0
0
2
1
0
1
0
0
1
0
0
1
0
0
1
1
2
2
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
2
3
0
0
0
0
1
0
0
2
1
3
2
0
2
0
1
1
2
0
0
0
1
0
2
2
1
0
0
0
0
0
0
0
5
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
2
0
1
0
2
0
2
2
3
0
0
1
0
2
0
2
1
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
2
4
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
1
1
0
1
2
2
2
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
2
0
2
0
0
0
0
1
0
0
2
0
0
2
0
2
2
1
0
1
0
0
2
0
0
0
0
1
0
0
1
0
0
0
2
2
2
1
0
2
2
0
1
0
1
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
2
0
0
0
2
2
1
0
0
0
0
1
0
0
0
1
0
1
0
0
2
0
1
0
0
0
1
1
0
1
0
2
3
2
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
3
0
0
4
2
0
1
2
0
0
1
0
0
1
2
0
0
0
0
0
1
1
2
0
0
0
2
0
0
0
0
3
0
0
1
1
0
0
2
0
0
1
2
0
2
0
1
0
3
0
1
0
2
0
0
0
1
0
1
0
2
0
2
0
2
0
0
1
0
3
2
1
1
0
0
0
0
2
0
1
1
1
0
1
2
0
0
1
0
0
0
0
0
2
0
2
0
1
1
0
1
0
2
1
0
2
1
0
1
0
1
0
1
2
0
0
0
2
0
2
2
0
0
2
0
0
0
0
0
0
0
1
2
2
0
1
1
0
2
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
2
1
0
0
0
0
6
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
1
0
2
0
1
0
0
2
0
2
0
0
0
1
0
1
2
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
1
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
2
0
2
0
0
0
0
0
1
0
2
0
1
1
1
1
0
0
0
2
0
0
0
1
1
0
0
0
0
0
1
1
0
1
0
1
1
2
0
0
0
0
2
0
0
0
0
2
2
0
1
0
2
0
1
2
0
0
0
1
0
0
0
0
2
0
0
2
1
2
0
1
1
0
0
0
2
2
0
3
0
0
0
1
0
1
0
2
1
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
2
2
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
3
1
2
0
2
0
0
0
2
2
0
1
0
0
2
0
0
0
2
0
1
0
1
0
0
0
0
5
0
2
0
0
0
0
0
0
3
0
0
0
2
1
0
0
0
0
2
0
1
0
0
1
0
2
2
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
2
1
2
0
0
1
0
0
2
1
0
2
0
0
1
1
1
0
0
0
0
2
0
0
0
0
2
2
0
2
0
1
0
0
0
1
2
0
0
0
2
0
0
0
0
1
1
0
1
0
2
0
1
1
0
2
0
0
0
0
0
0
1
1
2
0
2
2
3
1
0
1
0
0
1
0
1
1
0
0
0
2
0
0
0
1
1
0
1
0
0
0
0
1
1
0
0
0
0
2
0
0
0
2
0
0
0
1
1
4
2
1
2
0
0
0
2
2
1
2
0
0
0
1
1
2
0
0
0
1
0
2
4
0
1
0
0
0
0
1
0
1
2
0
0
0
0
0
0
2
2
0
0
0
0
2
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
2
2
0
0
0
1
3
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
1
1
0
0
1
1
0
0
0
0
0
1
0
0
1
2
1
1
0
0
2
0
1
0
1
1
1
0
1
0
0
1
0
2
0
1
0
2
0
0
0
1
0
0
0
0
1
0
1
2
0
2
0
2
1
1
0
0
1
0
0
2
2
0
2
0
0
0
0
1
2
0
0
0
1
3
0
1
0
0
0
0
1
2
2
0
1
0
0
1
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
2
2
1
1
2
0
2
0
0
0
0
0
0
0
2
0
2
2
0
2
0
1
1
0
0
2
2
2
0
2
0
2
3
0
0
0
0
1
2
0
0
2
0
0
0
0
0
2
0
0
2
2
0
0
0
0
2
0
1
0
0
1
0
0
0
1
3
1
0
0
1
1
0
0
2
0
0
1
0
0
0
0
2
5
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
2
2
0
2
1
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
1
0
2
0
1
1
1
1
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
2
2
0
0
0
0
1
1
0
1
1
0
0
1
0
3
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
3
2
0
1
0
0
1
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
4
0
1
1
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
1
0
0
1
1
1
0
1
0
0
0
0
1
0
1
0
2
1
2
2
0
0
0
1
0
1
0
1
1
0
0
2
0
0
0
0
2
2
0
0
0
2
0
0
1
0
2
1
2
1
0
0
0
0
1
1
2
0
1
0
0
0
1
0
3
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
1
1
0
2
1
0
0
0
4
0
1
0
0
0
0
2
0
1
1
0
0
0
2
0
0
0
1
0
0
2
2
1
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
1
0
3
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
1
1
0
2
1
1
1
3
1
0
0
0
1
1
0
0
0
2
0
0
0
0
2
0
1
0
2
0
0
0
0
0
1
0
1
2
2
0
0
1
1
1
2
1
0
0
0
0
1
2
2
0
0
0
2
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
1
2
2
0
0
0
0
0
0
1
0
0
0
2
0
0
1
2
0
0
0
0
1
0
0
2
0
2
0
0
0
0
2
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
2
0
1
2
1
0
0
0
1
1
2
0
0
1
1
0
0
2
0
0
0
2
0
0
1
0
2
1
0
0
1
2
0
0
0
2
1
0
2
2
0
0
0
0
2
0
0
0
2
0
0
2
2
0
0
1
1
1
0
2
0
2
2
2
0
0
0
2
0
2
0
2
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
1
0
0
0
2
1
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
1
0
2
0
0
0
4
1
0
0
0
0
2
0
0
0
2
2
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
2
0
1
0
0
0
0
3
0
2
2
2
1
0
2
0
2
0
1
1
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
2
0
2
1
0
0
2
0
0
0
2
1
0
0
2
2
0
0
0
2
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
2
1
1
2
0
0
0
0
0
2
1
0
0
0
1
0
1
1
0
1
1
0
2
0
0
2
0
3
0
2
5
2
2
0
0
1
2
1
0
2
2
2
0
1
1
0
1
1
0
0
0
1
1
0
0
0
0
0
2
4
2
1
0
1
0
0
0
1
2
0
0
1
1
1
2
0
1
0
0
0
2
0
0
2
0
0
2
1
0
1
1
2
0
2
2
0
0
0
0
0
0
0
0
0
0
1
2
2
1
0
2
0
2
1
0
0
0
0
2
1
1
1
0
1
1
2
2
1
2
0
0
0
0
1
0
0
0
1
1
0
1
0
1
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
2
1
1
0
0
0
0
0
0
1
0
0
2
2
1
2
0
0
0
1
3
0
0
0
0
2
0
0
2
0
0
0
2
0
1
0
1
2
1
1
1
2
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
1
0
1
2
2
2
0
0
0
1
0
2
0
0
1
2
0
0
2
0
0
0
0
2
0
0
2
0
1
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
1
0
0
1
1
0
0
0
0
2
0
1
0
2
0
1
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
2
2
0
0
0
0
0
0
0
3
0
0
0
0
1
1
0
0
3
0
2
0
0
0
0
0
0
2
0
2
0
2
0
0
2
1
0
2
0
0
2
4
0
0
2
0
0
0
0
0
2
1
0
0
0
0
2
0
2
0
1
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
1
0
0
3
2
0
1
2
0
3
1
1
0
2
1
0
1
0
0
2
2
0
2
0
2
0
2
1
2
0
0
0
0
0
0
2
2
1
0
2
0
0
2
2
0
1
0
0
0
1
0
1
2
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
1
3
0
2
1
0
0
1
1
0
0
1
2
1
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
2
0
0
3
0
1
0
0
0
0
0
0
0
3
2
3
0
0
1
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
1
0
1
1
0
1
0
0
1
0
2
1
1
2
0
1
1
2
0
2
2
0
0
2
0
0
1
0
2
2
0
0
0
1
2
1
1
1
2
0
0
0
1
0
2
0
0
0
2
0
1
0
0
2
1
0
1
1
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
2
0
1
0
2
2
1
2
1
1
0
2
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
1
0
1
1
2
0
1
0
2
1
0
0
2
1
0
0
0
0
0
2
1
2
3
0
0
0
0
0
1
2
0
0
1
0
0
1
0
1
0
0
0
1
0
1
0
1
0
0
1
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
2
0
0
0
0
0
2
3
2
2
0
0
0
0
0
1
0
2
2
0
1
0
0
0
1
0
0
0
2
1
2
0
0
1
0
2
0
0
0
0
0
1
0
0
2
0
0
0
1
0
2
0
0
1
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
1
2
2
0
0
2
0
1
0
0
0
0
0
1
0
0
2
0
2
1
1
2
0
0
2
0
0
0
1
0
0
1
0
0
1
0
0
1
2
0
2
0
0
0
0
0
2
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
2
0
1
3
2
1
0
0
0
0
5
2
2
1
0
0
2
2
0
2
0
0
0
0
0
1
1
0
0
0
1
0
2
2
0
0
2
0
0
2
2
0
2
0
2
2
0
1
0
0
0
2
0
0
3
1
0
1
0
0
2
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
1
1
2
1
1
3
1
0
0
0
2
0
2
0
0
0
2
0
3
2
2
0
0
0
2
0
0
2
0
0
0
0
1
2
2
2
0
2
0
0
0
0
5
1
0
0
0
0
1
2
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
3
0
0
0
0
2
0
2
0
2
0
0
0
1
0
2
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
2
0
3
1
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
4
0
0
2
0
1
0
1
0
0
0
0
2
0
2
0
2
4
0
1
0
0
0
1
1
1
2
0
0
0
2
0
2
2
0
0
0
0
0
1
0
0
2
1
0
2
0
0
2
0
0
0
0
1
0
1
0
2
0
0
0
1
2
2
2
0
0
2
0
0
1
5
0
1
0
1
0
1
0
0
0
2
0
0
1
0
0
2
2
0
0
0
2
1
1
0
1
0
0
0
1
0
0
0
1
0
2
0
3
1
0
0
0
2
0
1
0
1
2
0
0
1
0
2
2
0
1
0
1
1
0
1
0
3
0
1
0
0
1
1
0
0
0
2
0
2
2
0
1
0
0
2
1
0
1
2
0
0
1
0
1
1
0
0
1
1
0
0
0
2
0
0
2
3
0
0
0
1
0
2
0
1
0
0
0
3
1
0
0
0
2
0
1
0
1
2
0
0
1
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
1
0
0
0
1
0
0
1
2
0
1
0
2
0
2
0
3
1
1
1
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
1
1
1
0
2
2
0
2
0
1
2
0
0
0
1
0
2
0
1
0
0
0
1
1
2
0
3
0
0
2
2
0
1
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
2
3
0
2
0
1
0
2
0
0
0
0
1
0
0
0
1
0
0
0
2
1
0
0
0
0
0
1
1
0
1
1
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
2
2
0
0
1
0
0
0
2
0
0
0
0
1
0
0
2
0
1
0
1
2
0
0
2
1
0
0
1
0
0
1
2
1
2
0
0
0
2
0
0
0
0
0
1
12
0
0
2
0
1
0
0
1
2
0
2
3
1
0
0
0
2
0
3
2
0
1
0
0
0
1
0
2
0
0
0
2
0
1
0
1
0
1
0
0
2
0
5
0
0
0
2
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
2
1
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
2
0
2
0
0
2
0
0
0
0
0
2
0
1
4
0
0
0
0
0
2
0
2
0
0
4
0
0
1
0
0
2
0
3
2
0
1
2
0
2
1
2
0
0
0
2
0
1
0
0
0
2
2
0
0
0
1
0
0
0
0
1
0
2
0
1
2
0
1
1
0
0
1
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
2
2
1
0
0
0
0
3
1
0
0
0
2
2
1
0
0
0
2
1
1
0
0
2
0
2
0
0
1
1
3
0
1
2
1
0
1
0
0
0
0
1
1
0
1
2
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
3
0
0
0
1
0
0
0
0
2
0
0
0
1
2
3
1
1
4
2
2
0
0
0
0
2
0
0
0
0
2
1
0
0
2
1
0
0
0
2
0
0
0
0
0
2
0
2
0
2
0
0
2
2
0
0
1
0
0
0
0
2
1
2
0
0
0
0
0
0
0
7
0
1
0
3
0
2
0
1
0
0
0
0
0
0
0
2
1
1
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
2
0
0
0
2
0
1
2
0
1
0
0
0
2
1
0
1
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
2
0
1
2
2
2
2
0
1
2
0
0
1
0
2
0
0
2
1
0
0
0
1
0
0
2
1
1
2
0
0
0
0
0
1
6
3
0
0
0
1
0
0
0
2
0
2
2
0
0
2
1
2
0
0
0
0
1
0
1
0
1
0
0
1
0
0
2
0
0
0
0
1
0
2
0
2
2
1
2
2
0
2
0
1
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
2
0
0
2
2
1
2
1
0
0
0
0
0
0
10
2
0
0
0
0
0
1
0
0
1
0
2
0
0
1
0
0
0
0
2
0
2
0
0
0
1
0
0
1
2
1
0
0
0
0
1
0
1
2
0
3
0
0
0
0
0
0
0
0
2
0
0
1
0
0
3
0
0
1
0
0
0
0
0
0
1
0
0
2
0
1
0
0
2
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
3
0
0
0
0
0
1
8
0
2
0
1
0
0
2
0
0
1
2
2
1
0
2
1
0
0
0
2
2
2
0
1
2
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
0
1
0
0
0
1
2
2
0
0
2
3
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
2
0
0
2
0
2
0
0
0
0
1
2
2
1
0
2
0
0
1
0
0
2
0
0
1
1
0
1
0
2
2
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
1
0
1
0
0
2
1
2
2
0
0
0
0
0
1
6
0
1
1
0
1
0
0
1
2
1
1
0
1
0
0
1
0
0
0
0
0
2
2
1
1
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
1
1
1
2
0
2
0
0
0
0
0
1
2
1
0
1
0
2
0
0
1
1
0
0
2
2
1
0
0
0
2
0
0
2
3
1
0
0
1
0
0
2
3
2
2
0
2
1
3
0
0
0
2
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
3
2
0
0
1
0
2
0
2
0
2
0
0
1
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
1
1
2
0
0
2
2
0
0
0
0
2
0
1
0
0
0
0
0
1
0
1
1
0
2
0
2
0
0
0
0
0
0
2
0
1
0
2
2
1
3
0
2
0
1
2
0
0
0
0
1
0
0
0
1
2
0
2
0
1
0
0
0
2
2
1
2
1
1
0
0
1
1
0
0
0
0
0
2
0
0
0
2
2
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
2
0
0
1
2
0
2
1
0
2
2
1
1
0
0
2
1
0
1
0
0
0
0
0
0
1
0
0
3
1
3
0
0
2
3
2
0
0
2
1
0
0
0
0
3
0
1
0
1
0
1
0
0
0
1
0
0
1
3
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
2
0
3
1
1
0
1
0
0
0
0
0
0
1
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
2
0
0
2
1
2
0
0
0
0
0
2
0
0
2
0
2
1
0
1
0
2
0
0
1
0
0
0
0
2
2
0
0
0
0
0
1
1
2
0
0
0
0
1
0
0
2
2
4
0
2
1
1
1
0
0
1
1
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
1
1
0
1
4
0
1
0
0
2
0
0
2
1
0
1
0
1
2
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
1
1
0
0
1
0
0
1
1
0
2
3
2
1
0
0
0
0
2
1
0
1
1
0
2
2
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
2
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
1
2
2
0
2
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
2
0
0
1
1
0
2
0
0
0
0
1
1
0
0
0
0
1
1
1
1
1
0
0
2
1
0
1
0
0
0
1
0
0
2
2
1
1
0
0
2
0
0
0
2
2
2
3
0
3
0
2
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
2
2
0
2
0
0
1
1
0
2
1
0
0
0
0
1
0
0
0
2
0
3
0
1
1
1
0
3
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
1
0
2
1
1
1
2
0
1
0
0
0
3
0
2
1
0
0
1
2
0
0
0
4
0
0
2
0
0
0
0
1
1
0
0
2
0
1
2
0
1
1
0
1
1
0
0
1
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
1
2
1
0
0
2
0
2
0
0
3
0
0
0
1
1
0
0
0
1
1
0
0
1
0
1
2
0
0
2
0
0
0
2
0
2
0
1
1
0
0
2
0
0
0
0
1
0
0
0
0
2
1
0
0
1
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
4
2
0
2
0
2
1
1
0
1
0
1
1
0
0
1
0
2
0
0
1
2
0
1
2
2
1
1
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
1
0
2
0
0
0
0
2
1
0
0
3
0
0
0
3
0
2
1
0
0
0
1
0
2
0
2
0
0
0
2
0
0
4
3
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
2
0
0
0
2
2
0
0
0
0
2
0
0
2
0
0
0
0
3
0
1
0
1
1
1
0
1
0
1
2
0
0
4
0
2
0
1
0
2
2
2
0
2
1
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
1
0
0
0
0
0
1
1
1
1
1
1
2
0
2
1
0
1
0
0
0
0
0
0
1
2
0
0
3
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
1
0
1
0
1
2
0
0
3
0
2
1
2
1
0
0
1
0
0
0
1
0
0
0
0
1
1
1
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
1
0
1
0
0
1
0
0
0
0
0
2
1
0
0
2
0
0
1
1
0
0
2
0
0
0
1
1
0
2
0
2
1
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
2
2
1
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
1
0
0
0
0
0
2
0
2
1
0
1
0
2
3
2
1
1
0
2
2
1
0
0
2
0
0
0
1
2
2
0
0
1
0
0
1
1
0
0
0
0
0
2
1
1
0
2
0
1
3
0
0
2
0
2
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
2
2
0
3
0
0
2
0
1
0
0
2
2
1
2
1
0
2
1
0
2
0
0
3
0
1
2
0
0
0
2
2
0
0
0
0
1
3
1
0
0
0
0
1
0
0
1
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
2
1
0
0
0
0
0
2
0
0
0
0
0
1
1
1
2
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
1
0
0
2
2
0
0
0
2
1
2
1
1
2
0
1
0
0
1
0
1
0
0
1
1
0
2
0
1
0
0
2
1
1
2
0
0
1
0
0
1
0
0
0
0
2
0
1
0
0
4
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
2
0
0
1
1
2
2
0
2
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
2
0
0
0
0
2
0
0
1
3
1
0
1
0
2
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
2
1
0
2
2
0
0
1
2
2
0
0
1
0
2
0
1
0
2
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
7
0
0
1
0
1
1
1
0
1
1
2
0
2
2
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
2
3
0
2
0
2
1
1
2
0
0
2
1
0
0
0
1
1
2
0
0
0
1
0
0
0
0
0
2
2
0
1
2
0
0
1
1
1
2
0
2
0
0
0
1
0
1
1
1
1
0
1
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
1
0
0
2
1
1
0
0
0
0
2
0
0
0
2
1
2
0
0
0
0
0
0
0
3
1
1
0
0
2
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
2
0
0
0
0
0
1
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
2
0
2
1
0
0
0
0
1
3
2
0
1
0
0
2
0
0
0
2
0
0
0
1
2
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
2
2
1
0
3
2
2
2
1
0
0
0
0
0
1
0
1
0
0
0
2
2
3
1
0
0
2
1
2
2
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
1
0
2
0
0
1
0
0
0
0
0
1
0
2
0
0
1
0
0
0
2
1
0
2
0
1
0
0
2
0
0
0
1
4
0
2
2
0
0
0
2
1
0
0
0
1
2
0
0
2
1
3
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
1
1
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
2
0
2
0
1
0
1
0
0
0
1
0
1
1
0
0
2
2
0
0
0
1
3
0
0
1
1
0
0
1
0
1
2
0
2
2
2
0
0
0
0
2
0
0
2
0
1
1
0
2
2
1
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
2
2
1
2
1
0
0
2
0
0
0
0
0
2
0
0
1
2
0
1
0
1
5
1
0
0
0
0
0
0
0
2
0
3
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
2
1
0
3
0
0
2
0
0
0
2
2
0
0
1
1
0
0
0
1
0
2
0
0
1
1
0
0
0
1
2
0
0
0
1
2
1
0
2
1
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
2
1
0
1
0
1
0
1
0
1
2
1
2
1
2
1
2
0
0
0
0
2
0
0
0
1
1
0
2
1
0
0
1
0
0
0
0
1
1
0
2
0
0
0
2
0
2
0
0
0
1
0
2
2
0
1
1
2
2
1
0
0
0
2
2
0
1
2
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
3
0
0
0
0
0
2
0
1
0
5
2
0
0
2
0
0
1
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
1
2
2
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
1
3
0
0
0
0
0
1
1
0
0
2
2
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
5
0
0
1
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
1
4
0
0
0
0
0
0
0
1
0
1
2
1
0
1
3
2
1
0
0
0
0
1
0
2
0
2
2
0
0
2
1
0
2
2
0
0
1
0
0
2
0
1
0
0
0
0
0
0
2
0
2
4
0
0
0
0
0
1
0
1
1
0
2
1
1
0
3
2
1
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
2
3
2
2
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
2
1
0
0
1
0
0
0
0
2
1
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
2
0
2
0
1
1
0
1
0
0
0
1
1
0
1
2
1
3
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
2
0
1
0
0
1
1
2
2
2
0
0
0
0
0
2
0
2
2
0
0
1
1
1
1
0
0
0
0
2
0
0
3
0
2
0
2
0
0
1
0
0
0
2
0
0
2
1
0
0
0
0
2
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
1
2
0
2
2
0
0
0
1
0
1
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
1
0
2
2
0
0
1
0
2
0
0
0
0
0
0
0
1
2
2
0
0
0
1
1
1
2
0
1
0
1
0
0
0
1
2
1
1
1
1
0
0
0
2
1
0
0
0
0
0
2
1
0
0
2
0
0
1
0
2
1
0
0
2
1
1
1
2
0
0
0
0
1
0
0
0
2
0
0
0
2
2
0
1
2
1
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
3
0
0
0
0
0
0
1
0
1
2
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
2
0
0
0
2
0
0
2
0
0
2
0
0
0
2
2
0
1
0
3
1
0
1
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
2
0
0
2
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
1
1
0
0
1
2
0
0
1
2
0
0
0
2
2
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
4
0
0
2
0
3
0
0
2
0
0
0
2
1
1
0
2
0
2
2
0
0
1
1
1
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
1
2
1
5
0
2
0
0
2
0
0
1
0
0
0
0
0
3
0
0
1
1
0
1
1
0
0
0
0
0
0
2
0
1
0
2
1
0
0
0
0
1
2
1
0
2
1
0
0
2
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
1
2
1
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
3
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
1
2
0
0
2
0
1
0
2
0
1
1
1
0
1
0
3
1
0
0
0
1
0
2
0
1
0
0
0
0
0
0
2
0
1
0
0
1
0
0
1
2
0
1
0
2
0
2
0
1
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
1
2
0
0
0
0
2
1
0
2
0
0
2
0
1
3
0
0
0
0
0
4
0
0
0
0
0
0
1
0
2
1
2
0
0
0
1
0
0
2
0
3
0
2
0
2
0
0
0
1
2
0
0
1
0
0
1
2
0
2
0
0
0
0
0
0
1
2
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
2
0
0
0
1
0
0
2
0
2
0
1
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
1
1
1
1
0
0
2
1
1
0
0
0
0
3
2
0
1
2
0
0
2
2
0
0
0
0
0
0
0
1
0
4
1
0
0
0
4
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
2
2
0
2
0
2
0
1
0
2
1
2
2
2
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
1
0
0
1
0
1
0
0
0
0
0
0
0
2
2
0
2
0
3
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
1
3
0
0
0
0
0
0
1
0
2
0
0
0
2
2
2
0
0
0
0
0
2
0
0
2
0
1
0
0
1
0
0
1
0
1
2
2
0
0
1
0
2
0
2
0
0
2
0
2
0
1
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
4
2
1
0
0
1
0
2
0
0
1
0
1
0
0
2
0
0
3
0
0
2
1
0
0
0
2
1
0
0
0
0
2
0
0
2
0
0
0
1
0
0
2
1
0
1
0
0
0
1
3
2
2
0
0
1
1
0
0
2
0
0
2
1
2
0
0
0
0
0
1
0
4
3
1
0
2
0
2
0
2
1
0
0
0
0
1
0
0
3
0
0
0
0
0
1
2
0
0
2
1
1
2
1
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
1
0
0
1
1
1
0
1
0
2
0
0
0
0
2
1
0
0
0
2
0
0
3
0
2
0
1
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
1
1
0
2
2
2
0
0
0
0
1
0
2
2
0
0
2
0
0
0
1
0
1
0
0
1
0
1
0
0
2
0
2
2
0
2
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
3
2
2
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
1
2
0
0
0
1
0
2
2
2
2
0
1
0
0
1
0
2
0
2
2
1
1
0
1
1
0
2
0
0
0
0
3
0
2
0
2
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
1
0
3
0
0
2
0
0
1
2
0
1
0
2
0
1
0
2
1
0
0
0
0
1
0
0
0
2
1
0
0
1
0
1
8
1
2
5
0
1
0
1
0
0
1
1
0
0
0
0
3
0
0
0
0
2
2
0
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
0
2
2
1
0
0
2
0
0
2
0
1
0
0
0
2
0
0
0
1
2
1
0
0
0
1
0
0
0
0
0
0
1
2
0
0
1
0
2
1
0
0
2
0
0
0
2
0
2
0
0
1
0
0
0
2
0
1
0
0
2
0
2
0
1
1
0
0
0
1
0
0
1
0
1
2
1
2
2
1
2
0
2
1
0
2
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
2
1
0
0
2
0
0
2
0
0
1
1
1
1
0
2
0
1
0
0
0
0
0
0
0
1
1
0
2
0
1
0
0
1
1
0
0
0
2
0
0
0
1
2
1
0
2
0
0
2
0
1
2
0
1
0
0
0
0
0
1
0
0
1
0
1
0
1
1
0
2
1
1
2
0
0
0
0
2
1
0
0
1
2
0
0
1
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
8
1
0
0
0
0
1
0
1
0
0
0
0
0
2
1
2
0
1
0
1
2
0
0
2
0
0
1
0
1
2
0
1
1
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
1
0
0
1
2
0
1
0
0
2
0
1
1
1
0
2
0
0
0
1
1
1
0
0
0
1
0
0
0
2
1
0
1
0
0
1
2
1
1
1
0
1
0
2
0
0
0
0
0
0
0
1
2
1
0
0
2
0
2
0
0
0
0
2
2
0
2
2
0
0
1
0
0
0
0
0
0
0
1
0
0
1
4
0
2
1
1
1
2
2
2
0
2
1
1
0
0
1
0
0
2
0
1
0
0
0
0
0
2
1
0
0
0
0
3
0
0
2
1
2
0
2
0
0
2
0
1
2
0
0
1
0
0
2
0
0
1
1
0
0
0
0
0
0
0
1
0
2
1
2
0
0
0
3
0
2
0
1
0
1
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
2
1
2
0
1
4
1
1
0
0
2
0
2
0
2
0
1
1
0
0
0
1
3
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
2
0
1
1
0
2
0
2
0
1
1
2
0
0
0
0
0
0
0
2
3
0
0
0
1
1
0
0
2
0
1
0
2
1
1
1
1
0
1
1
0
0
1
0
0
0
0
2
0
0
0
1
3
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
2
0
1
1
2
2
1
0
2
0
0
0
0
0
0
3
0
0
0
0
1
0
2
1
0
2
1
0
0
1
0
2
0
1
1
0
2
1
0
1
0
0
1
1
0
0
0
0
0
1
3
0
0
0
1
1
0
2
1
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
2
1
2
0
2
2
1
0
0
0
1
2
2
0
2
0
0
0
0
1
2
0
2
0
1
0
0
2
1
0
2
0
0
0
0
2
1
0
0
0
2
2
2
0
0
2
2
0
1
1
1
0
4
2
0
0
1
3
2
2
0
0
0
0
0
5
2
2
0
5
1
0
0
0
0
2
1
1
0
0
0
0
2
0
0
4
0
1
0
2
2
1
0
1
1
3
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
1
1
0
3
0
0
3
2
0
1
0
2
2
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
1
2
0
0
0
2
0
0
0
1
0
2
0
0
0
0
1
0
0
0
4
0
0
0
1
1
0
0
0
0
2
0
0
0
2
3
0
2
0
0
2
2
0
1
0
2
1
1
1
0
0
0
2
1
0
0
2
2
2
0
1
1
0
0
0
2
0
0
0
0
0
0
1
1
0
0
1
1
1
3
0
0
0
0
0
0
2
0
1
1
0
1
0
0
0
2
0
1
2
0
0
0
0
0
2
1
0
2
0
0
2
0
0
0
1
0
2
0
1
0
1
0
2
1
0
0
1
0
1
0
1
1
2
0
0
0
0
0
1
1
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
3
0
1
0
4
0
1
0
1
0
0
1
0
1
2
0
0
0
0
0
2
0
1
0
0
2
2
0
0
2
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
2
2
0
0
1
0
0
1
0
1
0
2
0
0
0
0
1
2
0
0
0
2
0
0
1
0
1
1
0
3
0
2
0
0
4
2
2
1
0
1
2
0
1
2
0
1
1
0
1
1
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
1
1
0
0
0
1
0
2
0
0
0
2
0
1
0
0
4
0
4
0
1
0
0
2
1
2
0
2
0
0
0
0
1
0
0
2
1
0
0
0
0
0
1
2
0
0
0
0
1
0
2
0
0
0
1
0
0
0
1
0
1
2
2
0
1
0
1
0
1
0
0
1
0
1
1
1
0
0
1
1
1
0
1
0
1
0
0
1
2
1
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
2
1
0
2
2
1
0
2
0
0
0
1
1
2
0
1
0
0
0
0
1
0
0
2
2
2
1
2
0
1
0
1
0
0
0
1
0
0
0
0
0
0
2
0
1
2
0
2
2
1
2
0
0
0
0
2
0
0
0
2
3
1
2
0
0
0
0
1
0
1
0
0
0
0
0
2
0
2
1
1
0
1
1
2
0
0
0
0
1
0
0
0
0
0
2
0
0
1
3
1
1
0
0
2
0
0
2
0
0
0
3
1
0
0
1
0
1
2
0
0
0
0
1
0
0
0
2
2
0
1
1
2
0
2
1
0
0
0
0
0
0
2
0
1
3
2
2
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
1
1
1
1
1
1
1
2
0
0
0
0
0
0
0
1
0
2
1
0
0
0
1
0
2
0
0
0
1
0
0
1
0
1
0
1
2
0
1
1
0
0
1
0
0
0
2
0
2
0
2
0
0
0
1
1
2
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
1
1
1
2
0
0
2
2
0
2
1
1
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
2
2
0
2
2
2
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
2
0
0
0
1
2
1
0
1
1
0
0
0
2
0
1
2
0
0
0
0
1
2
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
2
1
1
1
0
0
3
1
0
0
0
1
0
2
2
0
0
3
0
0
3
0
0
1
0
0
3
2
0
1
1
0
0
0
0
1
1
0
1
0
0
0
0
1
2
0
1
1
1
2
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
2
0
0
0
3
3
0
1
0
2
0
0
0
1
0
0
1
0
1
2
0
0
0
0
2
0
1
2
0
2
0
1
0
1
0
2
1
1
2
0
0
1
0
0
2
0
0
2
0
1
0
2
0
0
0
1
1
0
1
0
2
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
1
1
0
3
0
0
2
2
1
1
0
0
1
0
1
0
0
1
0
0
2
2
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
2
2
2
2
2
0
0
1
2
1
1
2
0
0
0
1
1
0
2
0
1
0
0
1
0
0
2
0
0
2
0
0
2
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
2
0
1
2
0
0
0
1
0
1
0
0
1
2
1
0
0
0
1
0
1
2
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
2
0
0
2
0
0
2
0
0
0
2
1
1
1
1
0
2
0
1
0
2
2
3
0
1
0
2
0
2
0
1
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
1
1
0
2
0
0
0
0
0
2
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
1
0
1
1
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
2
1
2
0
1
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
2
3
0
0
0
2
4
0
2
1
0
0
3
2
0
1
0
0
0
0
0
1
1
0
2
0
1
1
0
0
0
1
1
0
0
0
2
0
1
0
0
0
1
2
1
1
2
0
2
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
1
2
2
2
1
0
0
0
0
2
2
0
0
1
0
0
0
0
0
1
0
2
2
1
2
3
0
1
0
2
1
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
1
2
0
0
0
0
1
2
0
0
0
0
2
1
0
0
1
1
2
0
0
2
2
1
1
0
2
0
2
0
0
1
0
1
2
2
0
0
0
1
1
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
2
1
0
1
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
1
2
1
0
1
0
2
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
2
0
0
1
1
0
0
2
2
0
1
2
0
0
0
0
1
2
2
0
1
0
0
1
0
0
2
0
0
1
3
1
2
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
3
0
1
2
0
0
0
2
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
2
3
0
0
1
0
0
0
1
0
0
0
0
1
0
1
2
0
0
1
1
2
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
3
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
1
2
0
0
0
1
0
2
0
0
1
0
1
2
0
0
0
0
0
2
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
1
0
2
1
0
1
3
0
2
0
0
2
0
1
0
1
0
2
0
2
0
0
2
0
2
1
0
2
0
1
3
0
0
0
0
1
2
0
2
0
0
0
1
0
0
4
0
0
0
0
0
0
0
1
0
0
0
2
2
0
1
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
1
0
0
1
0
0
2
0
0
1
0
0
2
0
0
1
0
0
2
2
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
2
2
0
0
0
0
2
0
1
1
0
0
0
0
0
0
1
0
0
2
0
0
5
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
2
1
0
0
1
0
1
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
1
0
2
1
2
1
0
2
0
0
0
0
0
0
0
0
3
0
2
1
0
0
0
0
1
0
0
0
0
0
1
2
0
0
1
0
0
0
2
0
0
2
0
1
0
2
2
2
3
1
0
0
2
0
0
0
0
3
1
0
0
2
1
0
0
2
2
0
0
2
2
2
0
0
2
0
0
0
1
1
0
0
0
0
1
3
2
1
1
0
0
0
2
1
0
2
0
1
2
0
0
0
0
0
1
1
0
2
1
2
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
1
0
0
1
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
2
0
2
1
0
2
0
1
3
1
1
1
2
0
0
2
0
3
0
0
1
0
0
2
0
0
0
0
0
1
1
0
1
0
0
3
0
2
0
0
1
0
1
1
1
0
0
2
0
2
0
0
2
0
0
0
1
0
0
0
2
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
1
2
0
0
1
0
0
0
2
1
1
0
2
0
2
1
0
1
0
0
0
2
2
2
0
0
0
0
0
0
0
0
1
1
0
1
5
0
1
2
0
1
2
1
0
0
0
0
1
0
1
0
0
2
1
2
1
1
0
0
0
0
1
0
0
2
1
0
1
0
1
0
2
0
0
0
2
1
0
0
2
0
0
0
0
2
0
0
2
0
1
0
0
0
0
3
0
0
0
0
2
1
2
0
0
0
1
0
0
0
0
5
1
0
1
1
0
0
0
0
1
0
2
0
0
0
0
2
0
0
1
1
2
2
0
0
0
0
2
1
0
0
1
0
2
0
1
0
0
0
0
2
1
3
0
0
1
1
0
1
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
1
1
1
0
0
0
0
0
1
0
3
1
2
0
2
1
1
0
0
0
2
0
1
1
1
0
0
0
1
0
0
0
0
0
1
2
0
2
1
1
1
2
0
2
1
0
2
0
0
0
2
0
1
0
2
1
0
0
1
0
1
2
0
1
4
0
0
0
0
0
0
0
0
1
3
2
2
2
0
0
0
2
3
3
0
0
1
0
0
0
0
2
0
2
0
0
2
1
0
0
0
1
1
0
1
0
2
0
1
0
1
2
0
0
1
1
2
0
0
0
0
0
2
0
0
2
1
0
0
0
0
1
1
1
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
1
0
0
2
0
3
3
1
1
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
3
1
0
0
2
2
0
3
0
2
1
0
2
2
2
0
5
2
2
1
1
0
1
0
1
3
0
2
0
1
0
0
2
2
0
0
1
2
0
1
0
0
2
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
2
2
0
0
2
2
2
1
0
0
2
3
0
0
0
0
1
2
0
0
1
0
1
0
0
0
2
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
1
3
0
0
0
0
0
1
0
1
0
1
0
0
0
0
2
0
1
0
0
1
2
0
0
0
0
0
1
0
1
2
0
0
0
1
2
2
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
2
0
0
0
4
0
0
0
1
0
0
1
4
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
2
2
0
5
0
0
1
0
0
2
1
1
1
1
0
2
0
0
0
0
1
1
1
2
2
1
2
1
1
0
2
1
0
0
0
0
0
1
3
0
1
0
2
0
1
0
2
0
0
2
0
0
0
0
0
1
0
0
2
0
0
1
2
0
0
0
1
0
0
0
1
0
4
2
0
0
0
1
1
0
2
0
1
0
0
2
1
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
2
0
0
2
0
0
2
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
2
0
0
0
1
0
0
0
0
2
1
0
1
0
0
1
1
2
0
2
1
0
0
0
3
1
1
0
2
3
2
1
0
2
1
2
1
0
0
1
0
0
0
0
2
0
0
1
2
2
0
0
0
0
2
1
0
0
3
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
1
0
1
2
2
1
0
0
0
0
0
2
1
1
3
0
0
0
0
0
0
0
1
0
2
0
1
1
0
2
0
0
1
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
2
0
2
2
1
2
0
0
0
0
0
0
0
0
1
0
0
3
0
2
1
2
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
3
1
0
0
0
2
0
2
1
0
0
0
0
2
0
0
1
0
1
0
1
0
0
0
2
1
2
0
0
1
0
2
1
2
0
0
2
0
0
1
2
2
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
3
4
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
2
2
0
0
0
0
0
2
2
1
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
1
3
2
2
0
1
2
2
0
2
0
2
0
0
0
1
1
0
1
1
0
0
4
2
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
2
1
1
0
0
2
0
1
0
0
11
0
2
0
1
0
5
1
2
0
0
0
0
0
1
1
0
1
0
0
0
2
0
0
3
0
0
1
0
1
0
0
0
0
0
1
0
1
1
2
0
0
1
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
1
0
2
2
0
0
0
0
0
2
0
1
0
2
1
0
0
0
0
2
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
1
2
1
0
0
2
0
3
0
0
0
3
0
2
1
1
0
1
2
0
0
0
0
0
0
0
0
2
2
2
1
1
2
0
0
2
0
0
2
0
0
0
1
1
0
1
0
0
2
0
2
0
0
1
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
1
1
0
0
1
0
0
1
1
0
2
1
1
1
0
1
0
0
2
1
0
2
0
2
1
1
0
0
1
1
0
3
1
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
1
1
0
2
0
2
1
0
0
2
2
1
4
0
0
2
0
1
0
1
1
1
0
0
0
0
2
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
2
0
0
0
0
0
2
1
2
0
0
1
1
0
0
0
2
0
0
0
0
0
1
0
0
0
2
1
0
1
0
1
1
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
2
1
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
2
2
1
0
2
0
2
2
0
0
2
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
2
2
0
1
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
1
1
0
1
1
0
1
2
1
0
0
0
0
0
0
0
0
1
0
2
2
0
2
1
0
1
0
2
2
0
0
1
1
0
0
2
0
1
0
0
0
1
0
2
0
1
0
2
0
0
0
2
0
0
0
2
2
0
0
1
0
0
0
4
0
0
2
1
0
1
0
0
0
0
2
0
0
2
0
5
2
0
0
0
1
0
1
0
0
2
0
2
0
0
0
0
0
0
1
0
0
2
2
0
0
0
1
0
0
0
2
0
1
2
0
1
2
0
3
0
0
2
1
0
2
2
0
1
0
1
1
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
3
0
0
2
0
0
0
1
1
0
0
0
0
1
1
0
1
1
0
0
1
0
2
0
1
0
0
1
0
2
3
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
1
2
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
1
0
4
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
1
1
2
0
0
1
0
0
0
1
1
0
2
0
0
1
0
0
1
1
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
1
2
0
0
1
3
0
1
0
0
0
2
1
0
2
0
0
1
0
1
0
1
2
0
1
2
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
2
0
2
1
0
0
0
0
2
1
0
1
0
0
1
0
1
0
2
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
1
1
1
0
0
1
2
0
0
0
0
0
0
0
1
0
2
0
0
2
0
2
0
1
0
2
1
0
2
1
0
2
0
0
0
1
1
0
0
0
1
0
0
2
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
1
1
0
2
0
1
1
0
0
0
0
1
0
0
0
2
2
0
0
2
0
1
0
2
2
2
0
2
0
0
0
0
2
1
0
2
2
0
2
1
1
0
0
1
1
0
1
1
0
0
3
1
0
0
2
0
0
0
2
5
0
2
0
2
1
0
1
1
2
0
0
0
0
0
2
0
0
0
1
0
3
0
0
2
2
0
0
0
2
0
1
0
0
0
3
1
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
2
2
0
0
1
0
0
0
1
0
0
1
1
2
0
0
0
0
0
0
1
2
2
0
4
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
2
0
1
0
1
0
0
1
0
0
0
0
1
0
1
0
3
2
1
0
2
1
0
2
0
1
2
0
0
4
2
2
0
0
0
2
0
1
0
1
3
1
2
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
1
0
1
0
0
1
2
2
1
0
2
3
3
0
2
2
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
2
0
2
1
0
6
0
2
0
2
0
2
0
3
2
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
1
1
5
0
0
0
0
0
2
0
0
0
1
4
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
2
0
2
0
0
0
1
1
0
2
0
0
0
0
0
0
0
1
0
0
2
0
2
2
0
0
1
0
1
2
2
0
0
1
2
1
0
1
0
0
1
2
0
0
0
0
2
1
0
2
0
0
2
1
3
2
1
0
1
0
0
0
0
0
0
1
0
0
1
2
4
0
2
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
1
0
2
2
0
3
0
0
1
0
0
0
2
2
0
0
1
0
0
2
0
1
0
1
0
0
1
0
0
0
0
1
1
0
0
1
2
0
0
0
0
1
0
0
2
1
0
0
0
2
1
2
1
0
0
2
0
2
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
1
0
1
0
0
0
0
0
2
2
0
0
0
0
0
2
3
0
1
0
0
0
0
1
1
1
0
1
0
2
0
1
2
1
0
0
0
0
1
2
0
0
0
1
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
2
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
1
0
2
1
0
0
2
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
3
2
0
1
0
0
0
0
0
2
1
0
2
0
1
0
0
0
0
1
0
2
0
0
2
1
0
1
0
0
0
0
0
2
0
3
1
1
0
0
0
0
0
0
3
0
1
0
0
1
0
0
1
0
0
2
2
0
1
1
0
1
1
1
2
0
2
0
0
0
1
1
0
0
1
0
2
2
2
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
3
2
0
0
2
2
0
0
0
0
3
1
0
0
0
2
0
0
1
1
0
0
0
1
0
0
0
2
0
2
0
0
0
2
2
1
0
0
0
2
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
3
2
0
0
0
0
1
0
0
0
1
1
2
0
0
0
1
2
1
0
1
0
1
0
0
1
2
0
0
0
1
1
1
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
1
2
1
2
2
3
0
1
0
1
2
0
0
2
0
0
1
0
0
1
0
0
0
0
1
0
2
1
1
0
0
0
2
0
0
1
2
0
1
2
1
0
0
0
1
0
0
0
1
0
0
0
1
0
2
2
2
1
0
0
2
0
1
2
2
2
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
1
1
0
1
0
2
0
1
1
1
0
3
0
1
2
0
2
0
0
3
0
2
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
2
1
0
0
0
1
0
1
0
2
0
0
0
0
0
2
0
3
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
1
0
1
1
0
0
0
1
3
0
0
1
0
1
0
1
0
2
2
0
0
1
1
0
0
1
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
3
3
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
1
1
0
1
0
0
0
1
2
2
0
2
0
0
2
1
0
0
0
0
2
1
1
3
0
2
0
0
0
1
1
0
2
0
1
0
0
0
0
0
0
0
1
1
0
0
2
2
0
2
3
2
0
0
0
6
2
2
0
0
2
0
3
0
2
0
0
1
1
0
0
1
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
1
3
1
1
2
1
0
0
0
0
2
0
0
0
0
0
0
2
1
0
3
0
0
0
0
0
0
0
2
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
2
0
0
1
0
0
2
0
1
1
0
0
0
2
0
0
0
0
1
3
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
2
0
2
1
2
1
2
0
1
0
0
2
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
2
2
0
0
1
0
0
0
0
2
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
1
0
1
1
0
0
1
0
0
0
0
0
1
1
1
0
0
1
2
2
0
0
0
1
0
1
0
2
0
0
1
0
0
0
1
0
1
0
3
0
1
2
0
1
1
1
0
1
2
0
0
1
1
3
0
1
1
0
2
0
0
2
0
0
0
0
2
2
0
0
0
2
0
1
0
1
2
1
2
0
0
0
0
1
1
1
0
0
5
0
0
1
1
0
1
0
1
0
4
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
1
0
0
0
2
1
2
1
2
1
0
0
0
3
2
0
0
0
0
0
3
0
2
0
0
0
0
2
2
2
0
0
0
0
2
1
1
0
0
2
0
0
0
0
0
0
0
0
1
1
2
2
0
0
0
8
1
1
0
0
2
0
0
0
0
0
3
0
2
0
1
2
1
1
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
3
0
0
1
0
2
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
1
2
1
0
1
1
0
1
0
0
1
0
1
0
0
0
1
1
1
0
0
0
1
0
1
1
0
1
0
0
0
1
0
0
0
2
0
2
0
0
0
2
0
2
1
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
1
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
2
0
2
0
1
0
2
0
0
0
0
1
0
0
0
0
1
2
0
1
2
3
0
2
0
0
0
1
1
0
0
2
0
0
0
0
1
1
0
2
0
1
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
3
0
0
1
0
0
2
0
0
1
0
0
0
0
2
2
0
0
1
0
0
2
2
0
0
1
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
2
2
1
1
0
0
0
0
0
0
0
2
1
1
0
1
0
0
0
0
3
0
1
0
0
2
0
1
0
0
0
0
0
2
3
0
0
2
0
1
1
0
0
0
2
1
1
0
1
0
0
0
0
1
0
2
1
0
0
2
2
0
0
1
0
1
0
0
2
1
0
2
0
0
2
2
3
1
2
0
0
1
0
0
1
0
1
0
2
0
0
0
0
0
2
1
1
3
0
0
1
0
0
2
0
1
0
1
1
2
0
0
0
1
1
0
0
0
0
0
3
0
0
1
0
1
1
0
0
0
2
1
2
3
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
2
0
0
0
2
1
1
0
0
1
1
0
2
0
2
2
1
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
1
0
0
2
0
0
0
0
2
1
2
0
1
0
0
1
0
0
0
2
2
2
0
0
2
0
1
0
0
0
0
0
0
1
0
2
0
0
3
0
1
0
1
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
1
2
1
2
2
0
0
0
2
0
0
1
0
0
0
0
0
2
2
1
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
1
2
0
0
1
0
2
4
1
2
2
0
0
0
0
0
0
2
2
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
1
2
0
0
2
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
2
0
1
0
0
2
0
2
2
0
0
2
2
2
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
1
0
0
2
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
1
0
2
1
0
2
2
2
0
0
2
0
0
0
2
2
0
2
0
0
0
0
0
0
2
0
0
2
0
2
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
1
2
1
0
2
0
0
0
1
0
0
0
1
1
1
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
2
1
2
0
2
0
2
0
0
1
1
0
1
2
0
1
1
0
2
0
2
0
2
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
2
0
1
0
0
1
1
1
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
1
0
2
2
1
0
1
2
0
1
1
1
0
0
0
2
0
0
2
0
1
0
1
2
0
0
0
0
2
4
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
2
0
4
0
1
2
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
1
0
1
0
0
0
1
2
0
1
0
1
0
2
0
0
0
2
0
0
2
1
2
2
0
0
0
0
2
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
1
2
0
2
0
0
0
0
0
1
0
0
1
1
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
2
1
0
2
0
1
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
1
1
5
0
1
2
2
1
0
0
2
1
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
1
0
3
0
0
2
0
1
0
0
2
0
2
0
0
1
0
4
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
2
1
0
0
0
2
2
0
0
1
0
0
2
2
1
0
2
1
1
2
0
1
0
2
2
0
1
0
0
0
1
0
0
0
0
1
2
0
0
0
2
0
0
0
2
0
0
0
0
0
3
0
0
2
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
1
2
1
0
1
0
0
0
1
1
0
0
0
1
4
0
1
0
0
1
2
1
0
1
0
0
1
0
2
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
2
2
0
0
1
0
1
0
0
0
1
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
2
3
2
0
0
1
2
0
0
0
0
2
0
1
0
0
0
1
0
0
0
1
2
0
3
0
1
0
2
0
1
1
0
0
0
1
0
2
0
0
0
0
2
2
2
1
0
0
0
0
1
2
0
0
0
2
1
2
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
1
2
0
1
0
0
1
0
0
1
0
0
0
1
2
3
0
0
3
1
2
0
0
0
0
1
2
0
2
2
0
0
1
0
0
2
0
0
1
1
0
2
0
2
3
0
0
0
10
0
2
1
0
0
1
2
0
0
0
0
1
2
0
2
1
0
0
1
0
1
1
0
0
0
2
1
0
2
1
1
0
0
0
0
1
2
2
0
0
0
0
0
0
0
2
0
1
0
0
0
2
1
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
2
0
2
0
1
0
0
2
0
2
2
0
0
2
0
0
3
1
0
0
2
0
0
0
0
0
0
3
0
0
0
2
0
2
0
1
0
0
0
0
0
1
0
3
0
0
0
0
0
2
0
0
0
0
0
2
0
2
2
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
3
2
0
0
1
0
1
1
2
2
0
0
0
0
0
2
1
2
0
0
0
0
0
1
0
0
2
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
2
1
0
1
0
0
0
0
0
0
0
1
0
0
1
2
2
0
0
0
2
0
1
1
3
0
2
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
2
0
1
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
1
2
0
1
1
2
0
2
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
1
2
2
0
0
2
0
2
1
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
1
2
0
2
0
0
1
0
1
0
2
0
0
0
1
1
0
2
0
0
0
3
1
0
0
1
0
2
1
0
0
0
1
0
0
2
0
2
0
1
2
2
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
1
0
2
0
2
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
1
0
0
2
0
0
0
0
1
1
2
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
2
1
0
0
0
0
2
0
0
0
2
2
0
0
1
0
1
0
1
0
1
0
0
0
0
0
2
0
0
0
2
3
1
0
0
0
0
2
1
2
0
2
0
2
0
0
2
0
2
0
0
0
1
0
0
0
0
0
1
0
0
1
2
0
0
3
2
0
2
0
0
0
0
0
0
0
1
0
1
2
0
0
1
0
0
3
1
2
0
0
1
0
0
2
0
2
0
0
1
2
2
1
2
0
0
1
2
4
0
0
3
2
0
0
0
0
0
2
1
0
2
1
0
0
2
0
0
0
1
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
1
2
3
1
0
1
0
0
0
0
0
4
2
1
2
0
0
1
1
1
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
1
2
0
2
2
0
0
2
0
0
2
0
2
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
1
3
0
0
0
1
2
0
3
0
2
1
0
0
0
2
2
1
0
2
1
3
2
2
0
0
0
2
0
2
2
0
0
1
0
0
0
0
0
2
2
0
0
0
2
3
1
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
2
1
0
0
1
3
0
2
1
0
1
0
0
0
0
0
3
0
0
0
0
1
0
3
0
1
0
0
2
1
0
1
1
1
0
0
1
1
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
1
0
0
1
2
0
0
0
1
1
0
0
0
0
0
2
0
1
0
1
0
0
0
0
1
1
3
0
0
1
0
0
0
0
0
1
0
0
0
12
0
1
1
0
2
0
0
0
1
0
0
2
1
1
0
1
0
1
2
1
2
1
0
0
1
2
0
2
1
0
0
1
0
4
1
1
0
0
0
1
1
0
1
0
0
0
1
0
0
2
1
0
0
0
4
2
0
0
0
0
0
0
0
2
1
2
0
0
0
2
0
1
0
1
0
1
0
0
0
0
2
0
2
0
0
0
1
0
1
2
0
0
1
0
0
0
1
0
1
0
0
1
1
2
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
1
1
0
2
0
3
2
0
2
2
2
1
0
0
1
1
1
1
0
2
1
1
0
0
2
1
2
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
1
2
1
1
2
2
0
0
2
0
1
1
1
0
0
0
3
0
0
2
4
2
0
0
2
3
0
1
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
2
3
0
0
0
1
0
1
1
0
1
0
1
0
0
0
0
2
0
1
1
0
0
0
0
1
1
2
2
0
0
0
0
0
2
0
3
0
0
3
1
0
2
2
0
0
0
3
1
0
1
0
0
0
0
0
1
0
0
0
11
0
1
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
2
0
0
2
0
2
0
1
0
0
0
2
0
0
0
0
0
2
0
0
2
1
2
1
0
1
0
0
0
1
0
0
0
2
0
2
0
6
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
2
0
0
3
1
0
0
0
0
1
2
0
0
0
2
0
1
0
2
3
1
0
0
0
4
0
0
0
1
0
0
0
0
0
1
1
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
2
0
1
5
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
2
0
0
0
1
0
0
0
1
0
0
0
1
0
0
2
0
1
0
1
1
1
1
0
0
0
2
0
0
0
1
0
0
0
0
2
0
2
2
0
1
0
0
1
0
2
0
0
0
1
2
0
0
0
0
2
2
0
2
2
0
0
0
0
0
0
2
2
0
0
0
1
1
2
0
2
2
0
0
0
2
0
0
0
2
3
0
0
0
0
1
2
2
1
2
0
0
0
2
0
0
2
0
0
2
0
1
0
0
2
0
0
0
2
0
0
1
2
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
1
0
1
0
0
0
0
0
0
2
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
1
1
0
2
0
0
2
2
0
1
0
2
2
0
0
1
0
1
0
0
0
0
2
2
0
0
2
0
0
1
0
2
2
0
0
0
2
0
0
0
0
0
0
1
2
2
0
1
0
2
0
1
0
0
0
1
2
0
0
1
0
2
2
0
0
1
0
0
0
2
0
1
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
2
2
2
1
2
0
0
0
0
0
0
1
1
0
0
0
2
3
0
0
0
2
0
2
2
0
0
0
1
0
0
3
2
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
1
0
2
3
0
0
3
0
0
1
0
0
1
2
0
0
0
0
5
1
4
0
1
0
2
2
0
0
1
1
0
1
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
2
0
3
1
2
0
2
0
1
0
1
0
0
0
0
3
1
1
1
1
0
0
2
2
0
2
0
2
1
0
0
0
7
0
0
0
0
2
1
1
0
4
3
2
2
2
2
3
0
0
0
2
0
0
1
1
0
0
1
0
0
2
0
0
4
2
0
0
0
1
1
0
3
1
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
1
0
2
0
0
2
2
0
0
0
0
2
0
1
3
0
1
1
0
2
0
0
1
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
4
0
2
1
1
0
0
0
2
0
0
0
0
0
0
1
1
3
0
0
1
0
0
0
0
1
0
2
0
1
2
2
11
2
0
0
1
0
0
0
0
0
1
0
0
1
0
1
1
2
0
0
0
1
0
0
2
0
0
1
0
0
1
1
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
3
1
0
1
0
0
1
0
1
2
1
0
0
0
0
0
0
0
1
1
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
1
1
0
0
1
0
0
0
0
2
0
1
0
0
0
0
2
0
0
1
2
3
0
2
0
1
1
0
2
1
2
0
0
0
0
1
0
0
2
3
0
0
0
2
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
2
2
1
2
0
0
0
0
2
0
0
0
1
0
0
0
2
1
0
0
0
0
3
1
0
0
0
1
0
0
1
2
1
3
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
1
0
1
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
1
2
0
1
0
3
0
0
0
1
2
1
0
0
2
0
0
1
0
2
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
2
0
2
0
0
0
0
1
2
1
0
1
0
0
1
0
0
1
2
1
2
0
0
0
0
0
1
0
3
2
2
1
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
1
2
1
1
2
0
0
1
0
0
0
0
0
1
1
0
0
0
2
1
2
0
0
0
1
0
0
0
0
0
0
1
0
3
0
1
2
0
0
0
0
2
0
2
0
0
3
0
1
1
0
0
0
2
1
1
0
1
1
0
1
3
1
2
0
1
1
0
0
0
1
0
6
1
0
1
0
0
0
0
1
0
1
1
0
2
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
1
1
1
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
2
1
0
2
2
2
0
0
0
2
0
1
0
0
2
0
1
1
0
2
2
0
2
2
0
3
0
0
0
2
2
0
0
0
0
2
0
0
1
0
0
1
2
1
0
1
2
0
2
2
1
2
2
1
0
2
2
0
1
0
0
2
0
1
2
0
0
1
2
0
1
2
2
0
0
1
2
2
0
0
4
0
2
2
0
0
0
0
1
0
2
0
1
0
0
0
2
2
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
1
0
1
2
2
0
0
2
0
1
1
0
2
0
0
0
0
0
2
0
2
0
1
0
1
0
0
0
0
3
0
0
1
0
2
1
1
0
1
0
2
0
1
3
1
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
1
0
1
0
0
0
0
0
2
2
0
1
1
0
1
0
0
0
0
0
0
2
0
0
0
1
1
0
2
1
1
1
0
0
1
2
0
0
1
0
1
0
0
1
1
0
0
0
0
1
0
4
0
2
2
1
0
0
0
2
2
1
0
1
0
0
1
2
0
0
1
2
0
1
0
0
2
0
0
0
1
0
0
2
0
0
2
1
0
2
2
2
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
1
0
0
0
0
0
0
2
1
2
0
2
2
3
2
1
0
1
1
0
2
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
2
1
2
0
0
0
2
2
0
0
2
0
0
2
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
2
2
0
0
0
1
0
0
0
2
0
0
0
0
2
0
1
1
1
0
0
0
2
0
0
0
1
0
1
0
1
1
0
0
2
0
0
1
2
2
0
2
0
0
0
1
0
0
0
0
1
0
2
0
2
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
2
1
2
0
2
2
0
0
0
1
0
0
2
1
2
1
0
0
0
2
0
0
0
0
1
1
0
2
2
0
2
2
0
0
0
2
0
0
0
1
0
2
0
2
0
2
2
2
0
2
0
0
0
1
0
0
2
0
0
3
1
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
1
2
1
0
1
0
0
0
1
1
0
0
1
1
0
4
0
1
0
0
1
2
1
3
2
0
0
0
2
0
1
2
0
0
1
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
3
2
0
0
0
0
1
1
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
2
0
1
1
0
0
0
0
0
0
0
2
2
2
0
0
0
1
2
2
2
2
3
2
1
4
0
1
0
0
0
0
2
1
2
0
0
0
0
1
2
0
1
1
2
0
1
1
0
1
2
1
0
0
2
0
1
1
0
3
0
0
2
0
0
0
2
2
2
2
0
1
1
3
2
0
0
2
2
1
0
0
1
2
0
1
2
2
0
1
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
3
0
0
1
0
0
1
1
1
0
2
1
0
0
2
1
1
0
2
1
0
0
0
1
0
0
1
1
1
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
3
0
0
0
1
2
0
1
4
0
0
0
0
2
0
1
0
2
0
1
2
0
0
2
0
0
2
1
2
0
0
0
0
2
0
1
0
1
0
1
1
0
2
0
1
0
1
0
2
2
0
7
1
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
1
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
2
2
1
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
1
0
0
0
1
2
0
2
0
0
1
0
1
0
0
2
2
1
3
0
1
0
0
0
0
1
2
2
2
2
0
0
0
0
1
0
2
0
0
0
0
0
1
0
2
0
0
0
3
0
1
2
0
0
0
1
0
0
0
2
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
1
0
0
3
0
2
0
1
2
2
0
0
0
2
0
0
0
2
0
0
2
2
0
0
1
0
2
2
2
0
0
2
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
2
0
0
1
0
1
2
0
0
2
1
1
0
0
2
0
0
0
1
0
0
0
0
0
1
2
0
0
0
3
2
0
1
2
0
0
0
1
1
0
0
0
0
0
1
0
2
0
1
2
0
0
1
0
0
2
1
0
0
0
2
2
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
2
1
2
0
0
0
1
2
1
0
0
0
2
0
0
1
2
0
0
0
0
1
2
0
0
0
1
0
0
0
0
2
0
0
0
1
1
0
0
0
2
2
0
0
0
0
2
2
1
0
2
1
1
2
2
1
0
1
0
1
2
0
0
1
1
0
2
0
0
0
0
0
1
0
0
0
0
0
2
2
2
0
2
1
0
0
8
0
0
2
1
0
0
0
0
1
0
0
1
0
0
0
0
1
4
0
1
0
0
0
2
0
2
0
1
0
3
0
0
0
1
0
2
0
1
0
3
0
0
0
2
1
0
1
0
0
1
1
0
0
0
0
3
0
0
1
0
0
2
0
2
2
0
0
1
0
4
0
0
0
2
2
1
0
0
0
2
0
1
0
2
1
0
2
0
2
0
3
0
1
2
0
1
3
1
0
1
0
0
2
0
0
0
0
2
3
0
3
0
0
0
0
0
1
1
1
2
4
1
1
2
0
0
0
1
2
2
0
0
0
2
3
1
2
0
1
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
3
1
0
2
0
0
1
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
3
0
0
0
0
2
0
0
0
1
2
0
1
1
0
1
0
0
1
1
2
0
2
0
0
0
2
0
3
0
0
2
1
0
1
0
1
1
0
0
0
2
0
0
3
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
2
0
1
0
2
2
0
2
0
2
1
0
1
0
0
2
0
0
0
1
0
2
2
0
0
0
0
0
2
1
0
2
0
2
1
0
0
2
0
0
0
0
2
1
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
1
1
0
0
0
0
2
1
0
2
0
2
3
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
2
2
0
0
2
0
0
2
0
0
0
0
0
2
2
0
2
0
0
1
0
0
0
0
0
1
0
1
0
0
0
2
2
0
0
0
0
1
0
2
0
0
2
0
3
0
0
0
2
1
0
2
0
0
0
2
0
0
2
2
2
1
0
0
0
0
1
1
2
0
2
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
2
4
0
1
0
0
0
0
3
0
0
0
0
0
1
0
1
0
2
1
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
2
0
0
0
0
1
0
0
0
0
0
1
1
2
0
0
0
0
0
2
0
0
1
0
2
0
0
0
3
0
0
1
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
2
1
1
1
0
0
0
0
0
1
1
0
0
2
2
0
0
0
2
2
0
1
0
0
0
0
3
0
1
0
0
0
0
0
2
1
1
0
0
0
2
3
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
1
0
0
2
1
0
0
0
0
1
0
1
2
1
0
2
0
0
0
2
0
2
2
0
1
0
2
0
2
0
2
0
2
0
0
2
0
0
2
0
1
2
0
0
1
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
2
1
0
0
0
0
0
0
1
0
1
0
3
0
0
1
0
0
1
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
2
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
2
0
0
1
0
2
0
0
1
0
0
0
0
2
2
1
0
0
7
0
0
1
2
2
2
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
2
1
2
0
0
2
1
0
0
1
0
0
2
0
0
0
2
2
1
1
0
2
0
0
0
1
0
0
0
0
0
0
1
0
2
1
2
0
4
0
2
0
0
0
2
0
0
1
0
2
1
2
2
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
2
0
0
1
0
1
0
2
0
0
0
0
1
1
1
0
0
2
0
0
0
1
1
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
2
1
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
2
0
0
0
1
0
1
0
0
0
1
1
2
0
1
1
5
0
0
0
0
0
2
0
2
2
0
0
1
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
1
0
0
1
0
0
0
0
1
1
0
0
1
1
2
0
2
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
2
0
1
0
0
0
1
0
2
3
0
1
2
0
0
0
0
2
2
1
0
0
0
0
0
2
1
1
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
1
0
1
1
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
2
0
0
1
0
0
1
0
0
0
3
3
2
2
2
0
1
0
1
0
0
0
1
1
0
0
0
0
1
1
0
1
0
0
1
2
0
0
0
0
2
0
0
0
0
0
1
0
0
5
0
2
0
0
0
0
0
0
0
0
2
1
1
1
0
0
0
0
2
0
0
0
0
2
0
0
2
0
1
1
0
0
0
2
0
0
0
0
1
1
0
0
1
0
2
0
3
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
1
0
0
1
0
0
0
0
2
0
1
0
0
0
0
2
0
1
0
2
0
0
1
0
0
1
0
0
2
2
0
0
0
0
0
2
4
0
0
0
2
1
2
0
0
1
0
1
1
2
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
2
0
3
0
2
0
0
2
0
3
0
0
1
2
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
1
0
0
0
1
0
1
1
0
1
0
0
0
0
1
2
2
2
0
0
0
0
0
1
0
3
0
0
0
1
0
0
0
2
0
1
0
3
2
1
0
0
0
0
1
0
0
1
0
0
2
2
2
2
0
0
0
2
0
0
1
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
3
2
0
0
2
0
0
0
1
1
0
0
2
0
0
0
0
2
2
0
2
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
3
0
2
0
0
2
2
2
0
1
1
0
2
0
0
0
1
0
2
0
6
0
0
0
2
0
0
2
0
0
2
1
0
0
1
0
0
2
0
0
2
0
0
2
1
1
2
2
0
2
2
0
1
2
0
0
0
2
0
3
0
1
0
0
0
0
1
0
0
0
1
0
4
0
0
0
2
2
0
1
0
2
2
2
1
2
1
2
0
0
0
0
0
1
0
1
1
0
3
1
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
1
0
0
0
2
0
1
0
0
0
1
0
0
0
0
1
2
0
0
1
2
0
2
0
0
5
2
1
0
0
1
0
0
1
0
0
0
2
2
0
2
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
2
2
0
0
3
0
0
0
0
0
0
2
0
2
1
2
1
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
3
0
0
0
1
0
1
2
0
0
0
2
0
0
1
0
2
2
0
1
0
0
0
2
0
0
2
2
2
0
0
0
0
1
0
0
0
1
1
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
1
2
1
1
0
2
0
0
0
0
0
1
0
3
0
0
2
1
2
1
5
0
2
0
0
0
0
0
0
2
0
0
0
2
1
0
0
1
0
1
0
0
1
0
2
0
0
1
1
1
0
2
1
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
2
1
3
1
0
0
0
1
0
0
2
1
0
0
0
0
0
0
1
0
2
1
0
0
1
0
0
0
0
0
2
0
2
2
0
0
0
1
0
2
0
0
1
0
1
0
0
1
0
2
1
0
1
0
0
0
0
0
0
0
1
0
2
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
1
2
0
2
2
0
0
1
1
0
0
0
0
1
1
0
1
0
2
1
1
0
0
1
0
0
1
0
1
0
0
2
1
2
2
0
0
0
1
0
0
0
0
2
2
0
2
0
0
0
0
0
2
2
1
0
0
1
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
2
0
1
0
2
2
0
0
0
0
0
0
2
0
0
2
1
0
0
2
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
2
2
0
0
0
2
0
0
0
0
0
1
2
1
0
0
1
1
2
0
1
0
1
0
2
2
0
0
1
2
1
0
1
0
0
2
0
1
0
2
0
2
2
0
2
1
0
0
1
0
0
0
1
1
0
1
1
0
0
1
0
0
0
1
2
0
1
2
1
0
1
0
1
0
2
0
0
0
0
0
0
2
1
0
1
0
3
2
0
0
1
0
1
0
2
0
0
1
0
2
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
4
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
2
1
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
1
1
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
1
0
0
0
1
1
2
0
0
0
1
0
0
1
0
0
0
0
0
1
2
0
2
1
0
0
0
2
0
0
0
0
0
1
0
0
2
0
3
0
3
0
0
0
0
3
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
4
0
2
0
0
0
2
0
0
0
0
3
2
0
0
0
3
0
2
0
1
0
0
0
1
1
0
0
0
1
2
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
2
2
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
2
1
2
0
1
0
1
0
0
0
1
2
1
1
0
3
1
1
1
1
0
1
0
1
0
0
1
0
0
1
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
1
0
0
1
2
0
0
0
0
2
2
0
0
0
0
0
1
1
1
0
0
0
1
1
0
2
0
0
1
0
0
0
1
0
0
0
0
0
1
0
2
1
0
1
1
1
1
0
2
1
2
0
1
1
0
0
0
2
0
0
2
2
0
1
0
0
1
1
1
2
1
0
0
1
2
1
0
0
2
1
2
0
0
1
2
1
1
2
0
1
2
1
2
0
2
0
0
0
0
2
1
0
0
0
0
0
1
0
1
1
0
0
1
2
0
0
2
1
0
1
0
2
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
2
0
1
1
1
0
0
0
1
2
0
0
0
1
1
2
4
2
1
2
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
2
2
0
0
0
1
0
0
0
0
0
1
1
2
0
0
0
0
1
0
1
0
1
0
0
1
2
0
2
0
0
0
0
1
0
0
0
1
0
0
2
2
0
0
2
0
0
0
0
0
3
2
0
2
0
2
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
1
0
1
0
1
0
2
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
1
1
2
0
0
2
0
5
0
1
0
1
0
0
0
0
0
1
2
2
1
2
1
2
0
0
0
0
3
0
2
1
0
0
0
0
1
0
0
2
3
0
0
2
1
0
0
3
0
0
1
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
1
1
0
1
2
0
2
0
0
5
0
0
1
1
0
2
0
0
0
2
0
0
2
2
1
2
1
2
0
1
1
0
0
0
3
0
0
1
2
2
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
5
0
3
2
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
2
1
0
0
0
2
2
0
0
2
0
1
2
2
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
2
1
0
1
0
0
0
2
2
2
2
2
0
0
0
1
0
0
0
0
8
0
0
0
0
1
0
0
1
1
0
0
0
2
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
2
0
2
0
2
0
1
0
0
2
1
1
0
2
1
0
0
0
1
1
0
1
0
1
1
0
0
0
0
1
2
0
0
2
2
3
0
0
1
0
0
0
0
2
2
1
2
0
0
0
1
0
2
0
2
1
0
2
0
0
2
0
0
3
0
0
0
2
0
2
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
3
0
1
0
0
0
2
0
0
0
0
1
0
0
0
1
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
3
2
1
0
2
0
0
0
0
0
0
0
2
1
0
1
0
2
0
0
0
1
1
0
0
1
2
0
4
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
2
0
0
0
1
0
3
0
1
1
0
2
1
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
1
0
2
1
1
0
0
0
0
4
3
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
2
1
2
1
2
2
1
0
0
2
0
0
3
0
0
0
0
1
0
1
2
0
0
3
2
0
0
0
0
0
2
1
0
0
2
0
0
4
0
0
0
0
0
0
0
3
2
1
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
1
1
1
0
0
0
2
0
2
0
1
1
0
0
0
0
0
1
2
0
0
0
0
0
2
0
2
0
0
2
2
2
1
0
0
1
0
0
0
2
0
0
0
1
2
2
0
1
2
0
0
0
2
0
1
0
0
0
0
1
0
0
0
1
2
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
2
1
1
0
1
0
0
2
1
2
0
0
2
0
0
0
0
0
1
4
1
0
0
0
1
0
0
2
0
2
0
0
0
2
1
0
0
0
1
0
1
1
1
1
0
0
0
0
2
0
0
0
0
1
1
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
1
1
1
1
2
2
0
2
1
0
0
0
1
2
1
1
1
0
0
0
2
0
3
0
0
0
0
0
0
0
2
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
2
2
0
2
0
0
0
1
0
2
0
0
0
0
0
0
3
0
2
2
2
2
0
1
0
0
2
0
1
0
0
0
0
0
0
0
3
0
1
2
0
0
1
2
0
1
0
0
0
1
4
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
2
0
0
0
1
0
0
3
0
0
1
1
0
0
0
2
0
0
0
0
0
3
1
1
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
1
0
0
1
0
1
0
2
3
0
2
2
0
0
0
2
0
0
1
2
0
0
0
0
0
1
0
0
0
2
0
0
2
0
1
2
0
0
2
1
1
1
0
0
0
0
0
0
2
1
0
1
2
2
0
0
0
1
1
2
2
0
2
1
2
1
2
0
0
1
0
2
0
0
1
1
0
1
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
2
0
1
0
0
0
3
0
1
2
0
2
0
0
2
1
2
0
0
1
0
2
1
2
0
0
2
0
0
0
3
0
0
2
0
1
1
1
0
0
0
1
2
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
3
0
2
0
1
0
0
3
0
2
0
1
1
0
0
1
1
0
0
0
0
0
6
1
0
1
2
0
1
0
0
0
0
2
2
0
0
2
0
1
0
1
0
1
0
1
2
1
0
0
0
1
0
0
4
0
0
0
0
1
0
3
0
1
2
2
0
0
0
0
0
2
2
0
1
1
0
0
0
0
1
2
2
2
0
0
0
0
2
0
1
2
0
0
0
0
0
0
2
1
3
0
3
0
2
0
1
2
1
0
0
1
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
1
1
0
0
0
0
1
0
2
0
0
1
0
0
0
0
2
2
2
1
0
0
0
2
0
0
2
0
0
2
2
0
0
1
0
0
1
0
0
1
0
1
0
0
1
0
0
2
2
1
0
0
1
0
0
1
0
0
2
0
1
0
0
2
0
0
1
1
0
0
2
0
1
2
3
0
0
0
1
0
2
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
2
4
1
1
1
0
0
1
0
0
0
0
2
0
0
2
1
0
0
3
1
1
2
2
0
0
0
0
0
1
0
6
2
2
1
2
0
0
2
2
0
0
0
1
2
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
2
1
0
0
1
0
2
0
3
0
0
1
3
0
0
0
0
0
0
0
2
0
2
0
0
1
1
0
0
0
0
2
0
0
1
2
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
1
1
2
2
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
2
1
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
1
1
2
0
0
3
1
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
3
0
0
0
2
2
0
1
0
0
0
0
0
4
0
0
2
0
0
1
0
0
1
0
1
0
0
1
1
0
0
0
1
0
1
2
0
2
0
0
0
0
0
1
1
0
2
0
0
2
1
0
0
2
2
2
0
0
0
0
2
0
2
0
0
4
3
0
1
0
0
1
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
2
0
0
0
0
0
0
3
2
0
0
0
0
0
0
2
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
1
3
2
1
0
0
2
1
0
2
1
2
0
1
1
0
2
0
0
0
0
0
0
0
0
2
2
2
1
2
0
0
0
2
0
1
2
0
2
0
0
2
2
0
1
0
0
0
1
0
0
0
0
2
1
2
0
0
1
3
2
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
1
2
3
1
0
0
2
1
0
0
0
0
0
0
2
0
0
1
2
2
2
0
0
0
0
1
1
1
0
0
0
1
0
0
0
2
2
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
2
0
1
2
0
1
0
2
0
1
0
0
2
1
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
2
1
1
1
0
0
0
0
0
0
0
1
2
2
0
3
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
1
1
0
1
3
0
0
0
0
1
2
1
0
0
2
0
0
0
2
0
0
0
2
0
0
2
2
0
0
2
1
0
0
2
0
2
0
3
0
0
0
2
1
0
0
0
2
0
3
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
1
0
1
1
0
2
0
1
1
2
3
0
0
0
0
0
1
0
0
1
2
0
0
0
0
2
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
1
1
2
0
1
0
1
0
2
1
0
1
2
0
0
2
0
1
0
1
0
1
0
0
2
2
0
0
0
0
0
0
1
0
0
0
1
4
0
0
1
1
0
0
0
2
2
1
0
0
0
0
0
0
2
2
0
0
0
0
2
2
2
1
0
0
4
0
0
0
1
0
1
0
1
0
1
0
0
2
2
0
1
0
0
1
0
1
0
2
0
0
0
0
2
2
0
1
0
0
1
1
0
2
1
0
1
0
1
0
2
2
0
0
0
0
2
0
0
2
1
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
1
1
0
1
1
1
1
0
0
0
1
2
1
2
2
0
0
0
1
0
2
0
2
3
0
0
1
0
0
2
0
0
0
2
1
1
0
0
0
0
1
1
1
2
1
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
1
0
2
0
0
0
2
0
2
0
2
3
1
1
1
0
2
1
2
0
1
0
1
1
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
2
0
2
2
0
0
0
0
1
0
0
0
3
0
0
1
0
1
3
0
1
1
1
1
0
0
1
0
0
1
0
1
0
0
0
0
2
0
0
2
0
2
2
0
2
0
1
2
1
0
2
1
0
1
3
1
0
0
2
0
0
0
0
3
0
0
0
3
0
1
0
1
0
0
0
1
0
1
1
0
0
0
0
1
0
1
0
3
1
0
2
2
0
0
0
1
0
0
2
4
0
3
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
1
0
1
1
0
1
0
0
0
0
0
0
2
1
1
0
0
0
1
0
2
0
0
1
1
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
2
0
0
1
0
2
1
2
1
2
1
0
1
0
0
1
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
2
2
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
2
0
3
0
0
0
0
0
2
0
2
0
1
1
0
0
0
2
0
1
1
0
0
2
0
0
0
0
0
0
1
1
2
0
1
0
0
0
0
0
0
1
2
0
0
1
0
0
1
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
3
0
2
0
1
2
0
1
0
0
0
0
0
0
2
2
2
2
0
3
0
0
2
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
2
2
0
0
0
0
0
0
0
2
2
2
1
0
3
0
0
0
1
2
1
2
0
1
2
0
2
0
0
2
0
0
0
0
0
2
0
1
2
0
2
0
0
0
1
2
0
2
0
1
1
2
1
0
0
1
2
2
1
0
1
0
0
0
0
2
0
0
1
0
0
1
2
0
0
0
0
0
2
2
0
0
0
2
1
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
2
1
2
2
0
0
0
2
1
1
2
0
0
0
0
0
1
0
0
2
0
3
2
0
0
2
1
0
1
0
0
0
0
1
0
2
0
0
1
1
0
1
2
1
2
2
0
3
0
1
2
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
1
0
0
1
1
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
2
0
0
1
0
1
0
2
1
3
0
2
0
2
0
0
1
1
0
0
1
0
0
1
0
0
0
2
0
0
5
0
2
1
0
2
0
0
2
1
0
0
2
0
0
3
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
2
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
3
1
2
2
0
2
0
0
0
0
0
1
0
0
2
1
1
3
1
0
1
0
1
3
0
1
0
2
0
0
0
11
0
1
0
0
0
0
0
1
1
0
1
1
2
0
0
1
0
1
0
2
2
0
0
1
2
0
0
0
0
2
1
2
0
0
0
0
2
0
0
0
0
2
0
1
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
3
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
3
0
2
2
0
1
0
0
3
2
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
4
1
0
0
2
0
0
0
1
0
1
0
1
1
1
1
1
1
1
0
0
0
2
0
1
0
2
0
0
2
2
0
0
0
3
2
0
4
1
0
0
0
1
0
0
1
2
1
0
0
1
1
1
0
2
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
3
2
1
0
1
2
1
0
0
2
0
0
2
0
2
1
1
0
0
0
0
0
1
1
0
1
0
0
0
2
0
1
0
0
0
0
2
2
2
1
1
0
1
2
0
0
0
0
0
3
0
1
0
0
0
2
2
2
0
0
0
0
1
2
0
0
0
2
1
2
0
2
0
0
1
2
3
4
0
0
0
2
0
0
0
0
0
0
0
2
1
2
0
1
0
0
2
0
0
0
0
0
0
0
1
1
2
0
0
1
0
0
0
0
0
0
2
2
0
2
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
2
1
0
2
0
1
0
0
0
0
0
1
0
0
0
1
0
4
1
0
0
0
0
4
0
0
0
1
1
0
1
0
0
1
2
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
1
1
0
7
0
2
0
0
0
0
1
2
1
0
0
0
2
2
0
1
0
0
1
2
2
1
1
0
0
0
1
0
1
0
5
2
1
0
0
0
0
1
0
0
0
0
1
0
1
1
2
0
1
0
0
0
2
0
1
0
1
0
2
0
1
0
0
0
3
2
0
1
3
1
0
0
0
0
1
3
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
1
0
1
1
0
0
0
1
0
0
1
0
1
0
0
1
0
1
1
2
0
0
0
0
4
0
0
1
0
0
1
2
0
0
0
2
0
0
1
0
0
1
0
0
0
1
0
0
1
2
2
1
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
6
0
0
0
0
1
2
2
0
0
1
2
0
3
0
2
0
0
0
0
0
1
2
1
2
2
2
0
0
0
0
0
0
0
0
0
1
0
4
0
1
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
2
0
0
0
0
2
0
0
0
0
2
2
0
0
1
1
2
0
0
0
1
2
1
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
5
1
0
0
2
0
1
1
0
3
2
2
0
0
1
0
4
0
0
2
0
0
2
1
0
0
1
2
1
1
0
0
0
0
1
0
0
0
0
1
1
0
1
0
1
1
0
0
0
0
0
3
0
1
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
1
1
1
0
3
0
0
0
0
1
0
0
0
2
2
0
0
0
0
1
0
0
0
0
1
0
0
0
1
2
0
0
0
2
0
0
0
0
1
1
0
0
2
2
0
2
0
0
0
2
1
0
3
2
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
2
1
0
0
0
1
2
2
0
2
0
1
0
0
0
0
1
0
1
2
0
1
2
0
0
0
0
0
1
0
2
2
1
0
0
0
0
1
2
0
0
0
2
0
2
2
0
0
3
0
0
2
1
2
0
0
0
0
0
2
0
1
2
0
1
0
2
0
0
0
1
3
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
1
0
1
0
2
1
2
0
4
1
1
2
1
0
1
0
0
1
3
0
3
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
2
0
2
0
0
0
1
0
0
1
1
0
0
1
0
3
0
2
0
0
1
2
2
2
0
0
0
2
0
1
2
0
0
3
0
2
1
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
2
1
1
0
2
0
1
0
0
0
1
2
2
0
1
2
1
0
2
0
0
0
1
1
1
2
0
0
0
0
0
2
2
8
2
0
1
0
0
0
0
0
1
0
0
1
0
3
0
0
0
1
0
0
0
1
0
2
0
0
1
1
0
0
1
0
1
0
0
0
0
2
2
2
0
1
0
0
0
2
1
0
1
1
1
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
2
2
0
0
1
0
2
1
3
0
0
2
2
0
2
0
1
0
2
0
0
0
0
0
0
2
1
0
0
2
0
0
1
0
0
2
2
0
1
0
1
0
0
0
0
0
0
1
0
2
0
0
1
0
0
3
0
1
0
2
0
0
0
0
0
0
0
2
4
2
0
1
2
2
0
0
0
2
0
0
2
0
0
2
0
3
0
1
1
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
1
1
3
2
0
0
0
0
0
0
0
1
1
0
1
2
0
0
1
1
0
0
1
0
0
1
0
0
0
1
3
0
0
2
0
1
0
1
0
0
0
2
0
2
1
0
0
0
0
2
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
1
0
0
0
2
2
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
2
0
0
1
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
2
2
1
0
0
0
3
0
0
0
0
2
1
5
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
1
1
2
1
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
2
2
0
6
1
3
0
1
0
0
2
0
0
0
1
2
0
2
0
2
0
1
0
0
0
1
0
2
1
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
2
1
0
0
2
0
1
1
1
0
0
1
2
0
0
0
1
0
1
1
1
0
0
0
0
2
1
2
2
1
0
0
0
1
0
2
0
1
0
0
0
0
0
1
1
0
1
1
1
1
0
0
2
0
0
0
3
2
2
0
0
0
6
0
0
0
0
0
0
1
0
2
0
1
0
0
2
0
1
0
0
0
2
0
0
1
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
2
1
0
1
2
0
2
1
0
1
0
1
2
0
0
0
2
0
1
0
1
2
1
1
0
1
3
0
2
2
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
1
0
1
0
1
2
1
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
2
2
0
0
2
0
1
2
0
2
0
1
0
0
1
2
0
0
2
1
0
0
0
0
2
0
0
0
2
0
1
2
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
3
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
2
0
0
1
0
1
0
0
0
2
0
1
0
0
2
0
1
0
0
2
0
1
0
8
0
0
1
4
2
1
0
0
1
0
1
0
0
2
0
0
1
0
2
2
2
2
1
2
1
0
1
1
0
0
0
0
0
2
2
2
1
0
0
0
1
1
0
1
2
2
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
1
2
0
2
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
1
1
0
2
0
0
0
2
0
0
0
0
0
0
1
2
2
0
2
0
0
0
2
2
0
1
1
0
2
0
2
0
0
0
0
0
0
1
2
0
0
0
3
1
0
0
2
2
0
0
1
13
1
0
0
0
0
0
1
0
0
0
0
2
1
2
0
2
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
2
0
0
0
2
1
0
2
0
0
1
0
0
0
1
0
1
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
1
0
0
2
0
2
0
0
0
1
0
0
5
1
0
2
2
0
2
0
0
1
0
0
1
1
0
1
0
1
0
0
3
4
1
0
0
0
1
0
0
0
0
1
0
1
1
0
1
3
1
0
0
0
2
2
1
1
0
1
0
0
1
0
1
2
0
0
1
1
0
0
0
0
1
1
0
0
0
1
2
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
2
0
2
0
0
1
0
0
0
2
0
0
1
1
0
0
0
0
0
2
1
0
1
1
0
2
0
1
0
0
0
0
0
0
2
2
2
0
0
1
0
0
1
0
1
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
1
0
1
1
0
0
0
2
1
0
0
1
4
0
1
1
0
0
0
2
1
0
0
1
1
0
0
0
1
2
0
0
0
0
0
1
1
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
2
0
0
0
2
2
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
3
2
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
1
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
2
0
1
0
0
0
0
2
0
2
2
0
1
1
2
0
1
1
0
1
1
0
1
0
0
1
0
0
1
0
1
1
0
0
0
1
0
0
2
1
1
2
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
1
1
3
0
0
0
2
0
1
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
2
0
1
0
0
2
1
0
1
0
1
1
0
1
2
0
0
2
2
0
2
0
2
1
0
0
2
0
2
0
0
0
3
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
2
2
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
2
0
2
0
1
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
2
1
0
0
0
1
0
2
2
0
0
1
1
0
2
0
1
0
0
0
1
0
2
0
2
3
2
0
2
1
2
0
1
2
0
0
0
1
1
2
0
1
1
0
0
0
0
0
2
1
0
2
1
0
0
1
1
0
0
6
0
1
0
0
0
2
0
1
0
0
0
2
0
0
1
2
0
1
2
1
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
2
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
3
0
0
3
0
2
1
1
1
0
0
0
0
0
0
1
0
1
1
2
0
1
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
2
1
1
3
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
2
1
1
0
2
2
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
1
0
0
2
0
1
0
2
0
0
0
2
0
0
1
0
0
1
2
0
0
2
0
2
0
0
0
0
1
0
0
0
0
2
0
1
2
1
0
2
0
0
2
0
2
0
0
2
1
1
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
2
1
1
0
0
1
0
0
0
1
0
0
0
0
2
0
0
2
0
1
0
0
0
0
1
0
0
0
1
1
3
2
0
4
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
2
0
2
0
1
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
2
0
1
0
0
0
2
2
1
0
0
0
0
0
0
0
0
1
1
2
2
0
0
0
0
1
0
0
1
0
0
1
0
0
0
4
2
2
0
0
0
1
0
5
0
2
0
0
0
1
0
0
3
2
0
0
0
0
1
2
0
1
1
0
1
1
2
0
0
2
0
2
0
4
0
0
1
2
1
0
0
0
2
1
0
0
0
0
1
2
0
0
0
0
0
0
1
0
3
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
2
0
0
0
3
5
0
2
1
0
0
1
0
0
0
2
0
2
2
0
0
2
0
3
0
0
3
0
0
3
0
2
1
1
2
1
0
5
0
2
1
1
1
0
0
0
2
0
2
1
2
3
0
0
1
0
1
0
0
0
1
1
1
0
0
0
0
0
2
0
0
1
0
0
1
1
1
1
2
1
1
0
0
0
0
4
0
0
0
0
0
2
1
1
0
3
0
0
0
0
0
0
0
0
0
0
1
2
0
0
3
2
0
2
0
0
0
1
0
0
2
3
1
1
0
0
2
0
0
0
0
2
2
0
2
0
0
0
2
2
1
0
0
0
0
2
0
1
0
1
0
2
0
1
0
2
1
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
1
0
3
0
2
0
0
0
0
0
1
3
0
1
1
2
2
0
0
0
1
0
2
0
2
0
3
3
1
0
0
0
1
0
0
2
0
0
1
1
0
2
0
1
0
2
0
0
0
0
0
2
1
0
1
1
0
0
0
2
0
0
0
0
1
0
2
1
2
0
1
0
1
0
3
1
1
0
1
1
0
0
0
2
0
1
1
0
0
0
0
2
0
1
1
0
0
1
2
0
0
2
0
0
0
1
0
1
0
2
0
0
0
1
0
0
0
2
0
0
2
0
0
1
1
3
0
1
0
0
0
0
1
0
1
0
1
0
2
2
0
0
2
0
0
0
0
2
0
0
2
0
3
0
0
2
4
3
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
3
1
0
0
0
0
1
2
0
1
1
0
0
3
0
2
1
0
2
0
2
0
0
0
1
0
2
0
0
0
0
0
1
0
2
2
2
1
0
0
2
1
0
1
2
0
3
0
0
0
0
1
2
2
1
0
0
0
0
2
0
0
0
1
1
2
0
2
1
1
2
1
0
0
0
1
0
0
1
1
3
0
1
2
2
2
1
1
0
0
0
2
1
0
1
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
2
2
0
0
2
0
1
1
0
1
2
2
0
1
2
0
2
0
0
0
0
0
2
0
0
0
2
1
0
2
0
0
0
2
0
1
0
3
0
0
0
5
1
1
2
1
1
0
2
0
0
2
1
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
2
0
0
0
0
0
0
2
2
1
0
0
0
2
2
0
0
0
1
2
1
0
0
1
0
1
1
0
1
0
0
0
0
1
0
0
2
2
0
0
0
1
0
1
0
1
2
2
1
2
0
0
0
2
0
2
0
2
0
0
2
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
1
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
1
1
0
2
0
1
0
2
1
2
0
1
0
0
0
0
2
0
2
2
0
0
1
0
1
1
2
0
0
3
0
1
0
0
3
0
0
1
0
2
1
0
0
2
1
2
0
2
0
0
0
1
0
0
0
0
0
0
2
2
0
3
11
0
1
0
1
2
0
0
2
0
1
0
0
0
0
0
0
0
4
0
3
0
1
0
0
0
0
1
2
0
0
0
1
0
2
0
0
0
0
0
0
2
0
1
0
1
1
2
0
0
4
1
0
2
2
2
0
1
2
0
0
0
2
0
0
1
0
2
0
0
0
1
0
0
2
0
3
0
0
0
0
0
0
0
0
3
0
0
1
0
2
2
1
0
1
0
0
0
0
2
0
2
0
0
0
2
0
2
1
2
1
1
2
0
2
1
1
2
0
0
0
0
1
0
1
2
1
0
0
0
0
0
0
3
0
0
0
0
0
2
3
0
1
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
1
2
0
0
2
2
2
0
1
0
0
1
2
1
0
0
0
1
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
2
0
1
0
1
0
1
1
0
1
1
1
2
0
3
2
0
2
0
0
0
0
0
1
0
1
0
0
0
0
2
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
1
1
1
0
0
1
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
2
0
3
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
1
2
0
1
0
1
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
2
1
0
0
1
0
0
0
2
0
2
0
1
0
1
1
0
0
0
2
2
0
0
2
0
1
0
2
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
2
0
0
0
2
0
0
0
0
0
0
2
0
1
2
0
0
0
0
1
0
0
0
0
1
1
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
1
2
2
0
0
0
0
1
0
1
0
1
0
1
0
2
0
0
2
2
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
2
0
0
1
1
0
0
2
1
0
0
0
0
0
0
0
2
0
1
2
0
0
2
2
1
0
2
1
2
1
2
0
2
0
0
2
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
2
0
1
0
0
0
2
1
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
2
2
0
1
0
1
0
0
0
0
0
1
0
1
0
0
1
2
0
0
2
0
0
1
0
0
3
0
0
0
1
0
2
0
0
0
1
0
2
1
0
0
2
0
1
0
1
0
0
2
0
4
0
1
0
0
1
2
1
0
2
0
1
1
1
0
0
1
1
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
1
0
0
0
0
3
1
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
2
0
1
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
1
0
0
1
0
1
2
0
0
0
3
0
0
0
1
1
0
0
0
0
3
0
1
0
0
0
0
1
0
2
2
0
0
0
0
0
0
1
0
2
0
0
4
1
0
3
0
0
1
0
0
0
0
0
3
1
0
2
0
1
2
0
4
2
3
0
0
2
0
0
0
0
0
1
0
1
0
0
1
1
0
0
1
0
0
0
2
1
0
0
0
2
1
2
1
2
0
1
0
0
1
1
0
1
0
1
0
0
0
0
0
1
0
0
2
2
0
2
0
0
0
0
1
2
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
1
0
0
0
2
2
0
2
0
0
0
0
2
2
2
1
1
1
0
2
2
1
1
1
0
0
1
0
0
2
0
1
0
2
0
1
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
1
0
1
1
0
0
0
1
0
0
0
2
1
0
2
1
0
1
0
2
2
0
0
2
0
2
0
0
2
2
0
1
1
0
0
2
2
0
3
0
0
0
0
0
1
1
0
0
0
2
0
2
0
0
2
0
1
2
2
2
1
0
0
2
0
2
0
0
2
0
0
0
0
1
2
1
0
1
0
0
0
0
2
0
0
1
0
0
0
1
2
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
1
5
1
0
0
1
0
0
0
0
0
2
1
0
1
0
0
1
0
12
0
1
0
0
0
0
2
1
0
0
2
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
4
1
0
0
0
0
2
0
1
0
0
1
3
1
2
0
2
0
0
1
2
0
0
0
1
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
3
1
2
0
1
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
1
0
0
0
1
0
2
0
0
0
0
2
2
0
1
0
0
2
1
0
0
0
0
1
0
1
5
0
2
0
6
0
2
0
3
1
1
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
1
2
0
0
2
2
0
0
0
0
0
0
0
3
0
3
0
2
0
0
1
1
0
0
0
3
0
2
0
2
0
0
0
2
2
0
0
0
1
2
0
1
3
2
1
1
1
2
0
1
0
0
2
0
0
2
0
0
0
0
0
1
0
0
2
0
2
0
1
0
1
0
0
2
0
2
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
3
0
2
2
0
0
2
0
0
1
0
1
2
0
3
0
0
0
0
1
2
0
1
2
0
2
0
0
0
1
0
4
0
0
0
0
0
0
0
0
2
1
0
2
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
2
0
1
0
0
0
2
0
0
2
2
0
0
0
1
0
0
1
3
0
0
3
0
1
2
2
0
0
2
0
0
2
0
0
1
2
0
0
0
0
3
3
0
3
0
1
1
2
1
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
2
1
1
0
0
2
1
0
1
0
2
2
0
0
1
1
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
2
1
0
1
1
0
1
2
1
2
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
3
0
2
1
2
0
2
0
2
2
5
0
1
2
0
0
0
0
0
1
1
1
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
2
0
1
0
0
1
2
0
0
0
0
7
2
1
2
2
0
0
0
0
0
0
0
0
0
2
0
3
0
0
1
1
0
2
0
0
0
2
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
1
0
0
0
3
2
4
0
2
2
1
0
0
1
0
0
0
1
0
1
0
1
2
0
0
1
1
0
1
0
2
0
0
0
0
0
1
0
1
0
0
0
0
1
2
0
0
0
0
1
1
0
1
1
0
0
4
0
0
0
1
0
2
2
0
0
0
2
0
0
0
0
2
1
0
0
0
0
1
1
2
0
0
0
0
2
0
0
0
1
0
2
0
2
0
0
1
1
0
0
1
0
0
0
1
1
0
4
0
3
2
1
3
1
2
0
0
1
0
0
0
1
2
2
0
0
0
5
0
0
0
1
1
0
0
3
0
0
3
0
0
0
0
0
0
2
0
1
1
0
0
0
0
1
0
0
0
0
2
0
1
2
2
1
1
0
0
0
0
0
2
0
1
0
0
2
3
0
0
0
0
0
1
0
0
1
1
2
0
2
0
0
3
0
2
0
2
0
2
2
0
1
0
0
0
1
2
2
1
1
0
0
1
0
0
1
2
0
2
0
0
0
1
0
0
3
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
2
1
0
0
0
0
1
2
0
0
0
0
2
0
1
1
2
0
0
0
1
1
0
2
2
0
0
2
0
0
1
2
0
0
2
3
2
0
1
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
2
1
2
0
1
4
2
0
0
0
0
1
0
1
0
0
2
0
0
1
0
2
1
0
0
2
1
2
0
0
0
2
1
2
3
0
0
2
0
1
1
2
0
0
1
1
1
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
2
0
2
2
0
0
1
3
2
0
2
2
0
0
0
0
2
1
2
1
3
0
0
1
1
0
0
2
1
0
2
0
0
0
0
2
0
1
0
0
2
2
0
1
0
1
0
0
2
1
0
1
1
0
0
0
2
0
2
0
0
2
2
0
0
1
2
0
0
2
0
0
1
0
1
0
2
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
1
1
0
0
0
0
0
1
2
2
0
1
0
1
1
1
0
1
0
2
0
1
0
1
0
0
0
0
0
1
1
0
2
0
2
0
2
0
0
0
1
0
1
2
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
2
0
2
0
2
0
0
1
2
0
0
1
0
0
0
1
1
1
0
3
2
0
2
0
2
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
1
1
0
1
0
0
0
0
2
2
1
0
2
2
0
0
1
0
0
0
0
0
2
1
0
1
0
0
0
0
1
0
1
0
0
1
1
2
0
2
0
0
2
0
1
1
1
1
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
2
1
3
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
2
0
0
1
2
0
0
0
1
1
2
0
2
0
1
0
0
0
1
0
0
2
2
0
2
0
1
0
0
0
1
0
2
1
0
0
1
0
1
0
1
0
0
1
1
1
1
0
2
1
2
1
0
0
2
2
2
1
0
0
0
0
2
2
1
1
0
0
0
1
0
0
2
0
0
0
0
0
0
1
1
0
2
1
0
0
0
0
2
2
2
2
1
2
1
0
2
0
0
0
1
0
1
0
3
0
1
0
0
2
0
1
0
1
0
1
0
2
0
1
0
0
1
0
0
1
2
1
2
0
0
0
2
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
1
2
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
3
0
1
0
2
0
2
0
0
1
0
0
1
2
1
0
1
1
1
0
1
0
1
0
1
2
0
1
2
1
2
1
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
1
1
2
2
0
0
2
1
1
0
0
0
0
0
1
2
2
2
1
1
0
0
1
2
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
3
0
0
2
0
0
2
0
1
3
0
0
0
0
0
2
1
0
2
0
0
0
1
0
0
0
0
0
2
0
1
1
1
0
0
0
0
0
0
2
0
0
0
2
0
2
3
0
2
0
1
0
0
0
0
2
2
0
1
0
2
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
2
0
0
1
4
1
0
0
0
0
0
0
2
0
2
1
0
0
2
2
0
2
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
2
0
0
1
0
2
2
2
1
0
2
0
0
0
0
0
0
4
0
0
0
0
1
1
0
1
0
2
0
1
0
0
0
0
0
0
2
1
1
0
2
2
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
1
0
1
0
0
0
0
1
0
1
0
1
0
2
0
0
1
0
0
1
0
1
2
0
2
0
0
0
0
0
4
1
7
1
0
0
1
0
0
0
3
0
0
0
0
1
0
2
1
0
0
2
0
0
0
0
0
1
2
0
0
1
0
0
1
1
1
0
2
2
1
0
0
0
0
2
0
2
0
2
2
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
2
3
0
0
0
2
0
1
2
0
0
1
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
1
1
2
1
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
1
0
0
2
0
0
0
1
0
0
1
0
0
1
0
2
0
2
2
0
2
0
0
0
0
2
0
0
0
0
0
2
1
0
2
1
0
0
1
2
2
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
2
1
2
0
1
1
1
1
0
0
0
0
0
1
2
0
0
1
0
0
0
2
1
0
0
1
0
3
0
2
1
0
2
2
1
2
0
2
2
0
2
1
1
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
1
0
0
1
1
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
2
2
2
1
0
0
0
1
0
0
0
0
0
0
0
3
2
0
0
1
0
1
0
0
0
2
0
0
1
0
0
0
0
2
2
0
0
1
2
0
1
1
2
0
1
0
2
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
1
2
2
0
1
0
0
1
0
0
0
0
1
0
0
2
0
2
3
0
0
0
1
1
0
1
1
3
0
0
0
0
0
0
1
0
0
0
2
0
2
1
0
0
0
0
1
0
0
1
0
2
0
0
0
2
0
0
0
1
2
0
0
2
0
0
1
0
0
1
0
0
1
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
2
2
0
0
2
1
3
0
1
2
2
0
2
0
1
0
0
0
2
0
0
2
2
1
1
0
0
0
1
3
2
2
3
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
2
0
0
0
2
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
2
1
1
2
0
0
1
0
0
1
0
2
0
1
2
1
1
1
0
2
0
0
2
2
2
0
0
2
0
0
1
2
0
0
2
0
0
1
2
0
0
1
1
0
0
0
0
2
0
0
1
0
1
0
2
1
2
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
4
0
2
0
1
1
0
0
2
2
0
0
0
1
1
1
1
3
1
0
1
0
0
0
0
1
1
2
2
0
2
0
1
1
1
0
5
0
0
2
0
0
0
0
0
2
1
0
0
1
0
0
0
0
1
2
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
1
2
2
0
2
0
1
0
0
1
0
0
0
0
0
1
0
2
2
0
2
1
0
2
0
0
1
2
0
0
1
1
0
0
0
0
0
0
0
0
0
2
1
1
0
0
2
2
1
0
0
0
1
2
0
2
0
2
0
0
0
0
0
1
0
0
2
2
2
1
0
2
2
0
1
1
1
1
2
0
2
0
1
0
0
0
1
0
0
0
0
1
2
0
1
0
0
2
0
1
0
1
0
1
2
0
0
0
2
2
0
0
0
0
0
0
0
0
2
2
1
2
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
2
0
1
0
0
2
0
0
1
0
2
1
2
2
1
0
0
0
0
2
1
0
1
1
0
0
0
1
1
2
0
2
0
0
1
0
1
1
1
1
0
0
5
0
1
1
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
3
0
1
1
1
5
2
1
0
1
0
2
1
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
1
0
1
0
0
1
0
0
0
1
1
1
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
1
7
0
1
0
1
0
2
0
0
0
0
0
0
0
2
1
0
0
1
1
2
0
1
0
0
1
0
0
0
0
1
0
0
0
2
0
1
0
0
1
0
0
0
0
1
2
0
2
1
0
0
0
0
0
0
0
2
1
0
0
2
0
0
2
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
2
1
1
2
0
0
0
2
2
0
0
0
0
3
1
0
0
1
2
0
0
0
2
0
0
0
2
0
0
0
1
0
2
0
0
0
1
1
0
0
1
0
1
2
1
4
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
1
1
0
0
0
0
2
1
1
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
1
1
0
1
1
1
1
0
1
0
2
0
0
0
1
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
1
0
0
1
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
2
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
1
0
0
2
0
0
1
2
2
1
0
2
0
0
0
1
0
0
1
3
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
1
0
1
2
0
0
1
0
0
1
0
0
0
0
2
3
0
0
1
1
0
0
0
0
0
1
2
0
0
0
0
0
2
1
0
0
0
2
0
1
0
2
0
0
0
0
0
1
3
0
2
0
0
0
0
0
1
2
0
0
1
0
1
1
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
2
0
1
0
0
1
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
2
1
1
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
1
2
0
1
1
1
1
1
0
0
2
0
0
1
0
0
1
2
0
0
0
0
0
0
2
0
0
0
3
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
2
2
0
0
0
1
2
0
3
0
1
1
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
1
0
0
0
0
1
0
0
0
3
2
0
0
0
0
0
1
0
0
2
2
2
2
1
3
1
0
1
2
0
0
0
1
1
0
0
2
0
0
1
2
0
0
0
0
0
2
0
0
1
0
0
0
2
0
3
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
2
0
0
3
1
0
0
0
0
0
1
0
0
1
2
2
0
0
1
1
0
2
0
2
0
0
0
0
1
1
2
0
0
3
2
0
0
2
2
0
0
1
2
1
1
1
2
0
1
0
0
0
2
0
0
2
0
0
1
1
1
0
2
0
0
1
0
0
2
1
0
1
2
0
1
0
0
0
0
0
2
0
0
0
0
0
3
0
0
1
2
1
0
0
2
1
0
0
0
1
9
0
1
0
0
1
0
0
0
0
1
0
1
0
3
0
0
0
0
0
1
0
0
1
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
1
0
0
2
0
0
1
0
0
0
0
1
0
0
0
2
2
0
0
2
0
0
2
0
0
0
0
0
0
0
2
1
1
0
0
2
2
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
2
2
2
0
0
1
1
2
0
0
2
0
0
1
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
2
1
3
1
1
2
0
0
2
0
0
0
0
3
1
1
2
0
0
1
0
0
2
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
1
1
1
0
2
0
0
0
0
0
0
0
2
2
2
1
0
0
1
0
0
2
0
1
2
2
0
2
0
2
0
1
0
0
1
1
1
0
2
0
0
0
0
0
0
1
0
1
1
0
0
0
2
0
1
0
0
0
1
0
2
0
0
0
3
0
1
0
0
2
2
2
1
1
0
0
1
0
0
0
2
1
0
0
0
2
0
0
2
3
2
2
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
1
2
0
2
0
3
0
0
2
0
2
1
0
0
0
0
3
0
0
1
0
1
2
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
5
1
1
0
5
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
2
0
0
0
0
1
0
0
2
0
1
0
2
0
2
2
0
1
0
0
0
1
1
0
0
0
0
0
1
1
0
1
1
1
1
0
1
0
0
0
0
1
1
0
0
0
1
0
1
0
1
2
0
0
0
0
1
0
2
0
0
0
2
0
1
0
2
0
0
1
0
1
0
2
0
0
2
0
0
0
0
1
0
0
0
2
0
0
2
0
1
0
1
0
0
1
0
0
1
1
3
0
2
0
2
1
0
0
2
0
2
0
0
1
1
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
3
2
1
0
0
2
0
2
0
1
0
0
0
2
0
0
0
0
2
2
2
1
1
0
0
0
0
0
1
0
2
1
1
0
0
2
0
2
0
0
0
0
2
2
0
1
0
0
0
0
3
0
1
2
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
2
1
2
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
1
1
2
0
0
0
0
0
1
0
0
2
1
0
0
1
1
1
0
0
0
1
0
0
0
1
1
1
2
0
2
0
0
0
0
1
1
0
2
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
1
1
0
0
2
1
0
0
0
1
1
2
2
0
3
1
0
1
0
1
0
0
0
1
2
0
2
2
0
1
0
0
0
0
0
0
0
0
0
3
3
0
0
0
0
0
0
0
1
2
2
0
0
0
0
1
2
0
1
1
0
0
0
2
0
1
0
1
2
1
0
1
0
0
0
0
1
2
0
1
0
0
1
1
0
0
0
0
0
0
2
0
0
0
1
0
2
0
2
0
3
2
0
0
0
0
2
1
0
0
0
0
0
2
0
0
1
0
0
0
2
0
1
2
0
2
2
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
2
4
0
0
2
0
0
1
0
0
0
0
1
1
0
2
0
0
0
0
1
2
2
0
2
0
0
2
0
0
0
0
2
0
0
1
0
0
2
0
2
3
0
1
0
0
1
0
0
1
1
0
0
0
0
2
2
0
0
0
1
1
0
1
6
0
0
1
2
1
2
2
0
0
0
0
0
3
0
0
2
0
0
0
0
0
1
2
1
0
0
0
2
0
0
0
0
1
2
0
0
0
0
1
2
0
1
0
2
0
0
1
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
1
0
2
1
1
0
2
0
0
1
0
0
1
0
1
0
2
7
0
0
0
0
0
0
0
2
0
1
2
0
0
2
0
1
1
2
2
2
1
0
0
1
0
1
0
0
2
0
2
0
2
0
1
0
0
2
1
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
1
0
0
1
1
0
0
2
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
3
1
0
0
0
1
0
0
2
0
1
0
2
2
2
2
0
1
0
1
2
0
0
3
1
0
2
0
0
3
0
0
0
0
2
0
0
1
0
0
0
2
1
0
0
4
2
1
3
0
0
1
0
0
1
0
0
0
2
0
1
0
0
0
2
2
4
0
0
3
0
1
2
0
0
1
1
1
2
1
0
0
0
0
1
0
0
2
0
1
2
0
1
0
0
1
0
2
1
0
2
1
0
0
2
0
3
1
0
0
0
0
0
1
3
0
0
0
0
0
0
2
2
1
1
0
1
2
0
0
0
0
0
2
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
2
0
1
0
1
0
0
1
0
0
0
2
2
0
0
0
2
0
1
1
0
0
0
0
1
1
0
2
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
1
0
1
0
1
0
1
2
2
0
1
0
0
0
0
1
0
1
0
0
2
1
2
2
0
0
2
2
0
0
2
1
2
0
0
0
2
1
0
0
0
0
1
2
1
0
0
0
0
0
0
2
2
1
1
0
0
0
1
0
0
0
0
1
0
0
0
2
0
1
1
0
0
1
2
0
0
0
5
0
1
2
2
0
2
2
0
0
0
2
0
0
2
0
0
3
0
0
0
0
0
0
0
0
1
1
1
1
0
0
2
1
1
0
1
0
0
1
0
1
1
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
2
2
1
1
0
0
2
1
0
0
1
2
0
0
0
1
0
0
1
2
1
0
0
0
0
0
1
0
0
2
0
0
0
1
1
1
0
0
0
1
0
2
3
1
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
3
0
0
0
2
0
2
2
0
0
0
0
0
0
1
1
1
0
0
0
0
0
2
1
0
0
2
0
1
0
0
0
0
0
2
0
1
1
0
0
2
0
2
0
2
0
0
0
1
1
0
0
1
0
1
0
1
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
2
0
2
2
2
1
0
0
2
0
0
0
2
0
1
0
0
1
0
1
0
2
2
1
2
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
3
1
0
1
0
1
0
0
0
0
0
0
0
0
2
1
2
0
0
1
0
1
2
0
0
3
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
1
1
2
2
0
0
2
0
0
0
1
0
0
1
2
0
0
0
0
0
1
0
2
2
0
1
0
1
2
0
1
2
1
0
0
0
2
0
0
0
1
0
0
2
1
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
3
2
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
3
2
2
2
0
4
0
0
2
0
1
2
0
0
1
0
0
0
0
0
0
2
0
0
0
1
2
1
0
1
2
0
1
1
1
0
0
1
1
1
1
1
1
0
0
0
0
2
0
7
0
0
1
1
0
0
0
0
0
0
2
1
1
0
1
0
0
0
0
0
0
2
0
2
1
2
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
8
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
2
2
1
0
2
0
0
5
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
2
2
2
2
1
0
0
0
0
1
0
0
0
1
0
0
0
2
0
1
0
0
2
0
2
1
0
0
0
2
0
0
0
1
0
1
6
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
1
0
2
0
0
1
1
0
1
2
1
0
1
2
0
2
0
0
0
0
0
0
0
2
0
2
1
1
0
0
1
1
0
0
0
0
0
0
0
2
0
0
1
1
0
2
2
0
0
0
0
2
1
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
2
2
0
0
2
0
1
1
1
1
0
1
1
1
0
2
0
2
0
0
0
2
2
2
0
0
2
1
2
0
0
0
0
2
1
0
0
0
0
1
1
0
3
3
1
0
0
0
0
0
1
2
1
0
0
0
0
0
2
2
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
1
0
3
2
2
0
2
1
1
0
0
1
1
1
1
1
4
2
2
0
2
1
2
0
2
0
0
0
0
0
0
2
0
0
1
0
2
3
0
0
1
0
0
0
1
1
0
1
0
0
0
1
0
0
2
0
3
0
1
0
2
0
0
1
2
0
0
0
0
1
0
3
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
2
1
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
1
2
1
0
2
0
1
0
0
1
0
2
0
2
0
0
0
0
0
1
0
1
2
0
0
1
0
1
2
1
0
0
1
0
0
2
2
2
0
2
0
0
0
3
1
0
0
1
0
1
1
0
2
0
0
0
2
0
0
2
5
2
1
3
0
0
0
0
1
0
0
0
1
1
1
1
2
0
0
0
1
0
0
0
1
2
1
0
2
2
0
1
1
0
1
1
0
2
0
2
0
0
1
2
2
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
2
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
2
0
1
1
2
0
2
0
1
2
0
0
0
0
0
0
3
2
2
0
0
1
2
0
0
0
1
0
0
2
1
0
0
0
0
0
0
3
2
0
0
1
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
1
1
0
1
0
0
1
0
0
0
2
3
1
0
0
0
2
0
1
1
0
0
1
1
1
0
0
1
1
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
2
0
1
2
0
0
0
0
1
0
2
1
0
2
0
0
2
0
0
0
2
0
1
0
0
0
1
3
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
2
0
1
0
0
1
0
0
1
0
0
2
1
0
2
0
0
3
0
2
0
0
1
0
0
0
0
0
1
1
0
2
0
0
2
0
0
2
2
2
1
0
0
1
0
0
0
0
1
2
3
0
2
0
1
0
0
1
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
2
0
0
0
2
1
0
1
2
0
2
0
2
0
0
0
0
0
1
0
0
2
2
0
1
1
0
0
2
0
0
0
1
0
1
0
0
0
0
1
2
1
0
5
2
2
0
0
2
0
1
5
0
0
0
2
2
0
1
2
2
0
0
0
0
2
0
0
2
0
0
0
0
1
2
0
2
0
2
0
1
0
1
4
0
0
0
1
1
0
1
1
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
3
0
0
2
0
2
0
5
0
0
1
0
2
0
0
2
0
0
0
1
0
1
0
1
2
0
1
0
0
0
0
1
1
0
1
0
0
1
0
0
0
2
1
1
0
0
1
0
0
0
0
4
1
2
1
1
2
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
2
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
2
1
0
0
0
1
2
0
2
0
0
0
0
1
0
2
0
0
0
0
0
2
1
2
2
0
0
2
0
1
1
0
1
0
2
0
1
0
1
3
0
0
0
0
0
0
0
0
2
1
0
3
2
0
0
0
3
0
0
0
1
0
1
0
0
2
0
0
0
2
0
0
1
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
3
0
0
1
0
0
1
0
1
2
0
0
0
1
2
0
1
2
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
1
0
1
8
0
0
1
3
2
0
0
3
0
0
0
1
2
2
1
0
0
1
0
1
0
0
3
0
3
0
0
0
1
1
0
2
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
1
1
2
0
1
0
0
2
2
0
0
0
0
1
0
2
0
0
2
0
1
1
2
1
1
0
1
0
0
0
2
2
2
0
0
0
0
0
0
1
0
2
0
1
2
0
0
0
1
0
1
0
2
0
0
0
4
0
2
1
0
2
0
0
0
0
1
1
0
2
0
2
2
0
0
0
0
0
0
0
2
2
0
0
0
1
2
0
0
0
1
0
2
2
0
0
0
0
2
0
1
0
0
1
0
0
0
0
1
0
1
1
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
2
2
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
2
1
1
1
1
0
1
0
0
1
0
2
2
0
0
0
2
2
0
0
1
0
2
1
1
0
0
0
0
0
0
2
0
0
2
0
3
0
1
0
1
2
0
2
0
0
1
2
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
5
2
0
0
0
0
2
0
1
1
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
1
4
0
0
2
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
3
2
2
2
1
1
0
1
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
1
0
2
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
2
2
2
0
0
0
1
0
2
2
2
2
2
0
1
1
0
1
2
0
2
1
0
1
0
0
2
0
0
2
0
0
0
0
2
2
1
1
2
0
0
0
2
2
0
1
2
0
2
2
0
1
1
2
2
0
0
1
1
2
1
0
0
1
0
0
0
1
1
0
0
2
0
1
2
0
1
0
2
1
2
0
1
0
0
2
0
0
0
1
0
0
2
0
0
1
0
0
1
2
0
0
0
1
0
1
2
0
0
2
0
0
2
1
1
2
0
0
0
1
1
1
1
0
1
3
0
0
0
2
2
2
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
2
1
1
1
2
1
2
0
0
0
0
0
0
1
0
0
1
2
2
1
0
0
2
1
0
2
1
0
0
0
0
1
1
1
2
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
5
0
1
1
1
0
0
1
0
0
1
1
2
0
0
0
0
0
0
0
0
0
2
2
1
2
0
0
1
2
0
0
1
0
1
2
0
0
1
0
1
0
1
3
2
0
2
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
1
0
0
1
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
1
1
0
1
1
0
1
1
1
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
3
0
0
1
0
0
2
2
1
0
1
1
2
0
0
0
2
0
1
1
1
0
0
0
0
0
1
0
0
0
4
2
0
2
0
0
1
2
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
2
1
1
0
0
0
0
1
0
0
2
2
1
0
1
0
2
2
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
2
0
0
2
0
2
3
0
0
3
1
2
2
0
0
2
2
2
2
0
0
2
0
0
0
0
1
0
0
0
2
0
0
2
1
0
0
0
1
0
2
2
1
2
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
5
1
0
1
0
5
0
0
2
2
1
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
2
1
0
0
1
2
0
0
0
0
0
2
1
0
0
1
0
3
0
2
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
1
2
0
0
2
2
1
0
0
0
0
0
0
2
0
1
1
0
1
0
2
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
1
0
0
0
0
1
0
2
2
2
0
0
0
0
2
0
0
1
1
0
0
0
1
0
0
2
0
0
0
1
2
2
0
1
0
0
2
1
2
1
1
1
0
2
0
0
0
0
0
0
0
1
2
2
0
2
0
0
0
4
1
2
2
0
0
0
0
1
0
0
1
1
3
0
1
2
0
0
1
0
0
0
0
3
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
1
0
0
0
3
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
1
1
2
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
1
0
1
0
0
0
3
2
2
2
2
0
2
0
0
0
0
0
0
1
1
0
2
1
1
0
0
0
1
1
1
1
0
2
1
0
2
1
2
2
0
0
0
0
0
2
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
1
0
2
0
0
0
0
0
2
0
0
1
1
0
0
1
0
0
2
2
0
0
0
2
1
0
0
0
2
0
2
0
2
2
0
0
1
0
2
0
0
2
0
0
2
0
0
2
0
2
0
0
0
2
0
1
0
0
1
0
2
2
0
1
0
0
0
1
0
0
0
2
1
0
0
1
2
0
1
0
0
0
0
1
2
0
1
0
1
0
0
0
2
2
1
0
0
0
0
0
2
1
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
2
1
0
1
0
0
2
0
2
0
0
1
0
1
0
0
0
3
0
1
0
3
0
0
0
1
0
3
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
1
1
0
0
0
0
1
0
0
1
1
2
0
0
1
1
0
0
1
0
0
1
0
2
1
1
0
0
0
0
0
0
0
1
2
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
2
0
1
1
2
0
0
0
0
2
0
0
1
2
0
0
0
0
0
2
0
4
0
0
0
0
0
1
2
3
0
0
5
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
2
2
2
0
0
4
0
0
0
1
1
0
2
0
2
0
0
0
0
2
0
1
2
2
1
2
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
3
2
2
0
0
1
0
1
1
2
2
1
0
0
2
0
1
2
1
0
0
0
0
0
2
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
2
1
0
0
0
0
0
1
0
0
2
1
0
1
0
0
0
0
0
0
2
0
0
0
1
2
0
1
0
2
1
2
0
2
0
0
1
0
0
1
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
1
2
0
1
2
0
0
2
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
3
2
0
0
0
0
1
0
1
3
0
0
0
1
2
0
1
1
1
2
0
0
0
0
1
0
1
0
2
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
3
0
2
1
0
0
2
1
2
1
1
0
0
0
0
1
0
0
1
2
1
0
4
0
2
0
1
2
0
0
0
2
0
0
2
3
0
2
0
1
0
0
1
0
1
0
0
0
0
1
0
0
2
1
1
0
0
1
0
0
2
0
0
0
0
0
0
1
0
1
1
0
0
3
0
0
2
2
1
3
1
0
2
0
0
0
0
0
1
1
0
0
1
0
0
0
2
0
0
1
2
1
0
0
0
0
0
1
1
2
0
0
0
2
1
1
2
0
2
0
1
0
0
1
2
1
2
0
2
0
2
0
0
1
1
0
1
0
0
2
0
1
0
1
0
0
0
3
2
0
0
1
1
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
1
0
2
2
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
1
2
0
1
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
3
1
1
0
0
0
0
0
0
2
1
0
0
0
2
1
1
1
1
3
0
2
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
1
0
0
1
0
0
2
0
0
0
0
2
1
0
1
1
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
2
1
2
2
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
2
1
0
0
0
2
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
2
1
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
2
2
0
2
0
0
2
1
4
0
1
0
0
1
0
1
1
0
0
2
0
0
0
0
0
1
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
1
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
2
2
0
2
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
6
0
1
1
0
2
0
0
0
2
1
0
0
1
0
2
0
0
1
0
0
2
2
0
1
0
2
0
0
0
2
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
2
2
0
0
2
0
0
0
2
1
1
0
2
1
2
1
1
0
0
1
1
0
2
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
2
2
0
0
0
0
1
0
0
0
0
1
0
1
2
2
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
2
0
1
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
2
2
0
0
2
0
1
1
0
2
0
0
2
0
0
0
0
0
2
2
1
0
0
0
1
0
0
2
0
1
1
0
0
1
0
0
1
1
0
1
0
0
0
1
1
1
0
0
0
2
2
0
0
0
2
1
0
0
2
0
0
2
0
2
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
1
1
0
0
0
1
0
1
1
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
1
0
1
2
1
0
2
0
0
0
2
0
0
2
1
0
1
2
0
2
1
2
0
2
0
0
0
2
0
0
0
1
0
1
0
1
0
1
0
1
2
0
2
1
0
0
0
1
2
1
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
2
1
0
0
0
1
1
2
0
0
0
0
1
0
3
1
0
1
0
0
0
2
0
0
0
0
0
2
0
1
0
1
2
1
2
0
1
0
4
0
0
0
0
0
1
0
2
0
0
1
0
1
1
0
0
1
2
0
0
1
1
0
0
2
0
0
0
1
0
1
1
0
2
0
1
0
0
3
2
2
0
0
2
0
1
2
0
0
2
0
0
0
0
0
0
2
0
0
1
2
0
0
2
0
2
1
1
0
1
2
3
0
1
1
1
0
0
2
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
4
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
1
0
2
2
1
0
3
2
0
0
1
0
0
2
2
0
2
0
1
2
0
0
0
0
0
2
0
1
1
0
3
0
2
2
0
0
0
0
2
2
0
0
0
1
0
0
1
0
1
0
1
1
1
1
0
1
3
0
0
1
0
0
0
0
0
2
0
2
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
2
0
1
1
0
0
0
0
0
0
4
6
0
0
0
0
2
1
1
0
0
2
1
0
0
2
2
0
0
0
1
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
2
0
1
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
3
1
0
0
0
2
1
0
0
1
0
2
0
0
4
0
0
2
0
1
2
1
0
1
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
1
0
2
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
1
1
4
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
1
2
0
2
0
0
3
2
1
0
1
0
0
0
0
0
1
0
0
2
0
0
0
2
0
1
0
0
1
0
0
0
3
0
2
0
0
0
1
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
2
0
1
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
1
0
3
0
0
0
0
2
1
0
0
0
0
2
2
1
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
2
0
2
1
1
0
2
1
0
1
2
0
2
2
0
1
0
0
0
1
1
0
1
2
0
0
0
2
0
0
2
1
2
0
2
0
2
0
2
0
2
0
2
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
1
0
0
1
0
0
0
0
1
2
0
0
1
0
0
0
2
0
0
0
0
2
5
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
1
0
3
0
1
0
0
0
2
0
0
2
0
1
2
2
1
0
1
0
1
1
0
1
0
0
0
0
2
0
0
0
1
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
2
0
0
0
0
0
0
1
1
0
1
1
0
0
0
1
2
2
3
0
2
0
1
0
0
2
0
3
1
0
1
0
1
0
1
0
0
0
1
0
1
2
0
0
1
4
1
1
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
1
0
0
0
2
0
1
2
0
1
0
1
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
2
0
0
1
0
2
0
0
2
1
0
0
2
0
0
0
0
0
0
2
2
0
0
0
1
0
2
0
0
1
1
0
0
0
0
2
0
0
2
2
1
0
0
1
0
2
0
1
1
0
2
5
1
0
0
1
0
0
0
2
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
2
0
0
1
0
2
0
0
0
0
0
0
1
0
2
2
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
1
1
0
0
0
0
7
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
1
0
0
1
0
1
0
2
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
7
2
0
1
0
2
0
0
2
0
0
0
0
0
2
1
0
0
0
1
0
1
0
0
0
0
1
1
0
2
1
2
0
1
0
0
2
0
1
0
0
0
0
4
0
0
2
0
0
2
0
0
0
0
3
1
0
1
0
1
0
1
0
0
0
0
1
1
1
1
2
1
0
1
2
1
2
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
2
0
2
0
1
0
2
1
1
0
0
1
0
1
0
1
0
0
0
1
0
0
1
1
0
0
1
1
1
5
1
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
2
0
1
4
2
1
0
0
1
0
1
2
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
1
0
1
3
2
0
0
0
0
0
2
1
1
0
0
0
1
0
0
1
2
2
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
2
0
1
2
0
2
0
1
1
2
1
0
0
0
2
2
0
0
0
1
2
0
2
0
0
1
2
0
0
1
1
0
0
2
0
0
0
0
2
1
0
3
0
0
0
2
1
4
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
1
0
2
2
0
1
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
2
1
2
0
0
1
1
0
2
0
1
0
0
0
2
0
0
0
1
0
0
1
2
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
2
2
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
1
0
0
2
1
0
1
0
0
1
0
1
2
1
3
1
0
2
0
0
0
0
1
2
2
1
0
0
0
1
1
1
0
0
1
0
0
0
1
0
3
2
0
2
0
0
0
3
1
0
1
0
0
0
0
0
1
0
0
0
0
2
0
1
3
0
0
0
1
1
0
0
0
1
0
0
0
0
2
0
2
0
1
0
0
0
1
0
3
2
2
2
1
0
0
0
0
2
2
0
0
4
0
0
0
0
2
3
1
4
0
2
1
1
0
2
4
0
0
0
0
0
0
0
1
1
0
2
0
3
2
1
0
0
1
2
3
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
2
0
2
0
1
0
1
0
1
0
1
1
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
4
0
2
2
0
2
1
2
0
0
3
0
1
1
0
0
2
1
0
0
0
0
1
0
0
2
0
1
0
0
1
0
2
0
2
0
0
1
0
1
0
0
0
0
2
2
0
0
2
0
0
1
2
0
1
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
2
1
1
0
0
0
1
2
1
0
2
1
0
2
2
0
1
1
1
0
2
0
2
0
0
1
0
0
0
0
2
2
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
2
1
0
0
2
0
2
2
1
1
0
0
1
0
0
0
2
0
0
0
2
0
0
2
2
0
0
0
1
0
0
0
0
1
0
1
0
1
0
1
0
2
1
1
0
2
1
0
3
0
0
0
0
0
2
1
0
0
0
0
1
1
0
0
0
0
3
2
2
0
2
0
0
0
0
1
0
1
0
1
0
0
2
2
0
1
0
2
1
0
4
0
3
0
0
1
2
1
3
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
1
1
0
2
0
2
0
2
0
0
0
0
2
0
0
1
2
1
1
0
0
0
0
0
0
7
0
0
2
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
2
1
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
1
2
0
0
1
0
1
0
0
2
0
2
0
3
1
0
0
1
0
1
1
0
0
0
2
0
0
0
0
4
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
1
0
0
0
0
2
2
1
0
0
0
2
0
2
0
0
0
3
0
0
1
2
0
1
1
0
0
1
0
0
0
0
2
1
2
2
2
0
2
1
2
0
0
0
1
0
0
0
0
0
2
1
0
1
0
0
0
2
0
0
0
2
2
0
0
0
2
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
2
1
1
1
1
0
2
0
0
0
1
2
0
0
1
2
1
1
0
1
2
0
0
1
1
0
2
1
0
0
0
3
0
1
0
2
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
2
1
2
2
0
2
0
0
0
1
0
0
0
3
0
2
0
0
1
0
1
0
0
0
1
0
1
0
2
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
1
2
0
0
2
0
1
0
0
0
0
0
0
0
0
2
1
2
0
1
0
0
1
2
0
0
0
0
0
0
1
1
0
1
0
0
5
1
0
2
1
1
0
2
0
0
0
2
2
0
2
0
2
2
0
0
2
0
2
2
0
0
0
0
0
0
1
0
0
1
2
0
1
0
0
0
0
0
0
1
2
0
0
2
0
0
0
2
2
0
0
0
2
1
0
0
2
1
0
0
0
0
0
1
2
0
0
0
2
0
2
0
0
2
0
0
2
0
2
0
0
2
0
0
0
0
0
0
2
0
0
1
4
2
2
1
0
1
0
2
0
0
0
0
0
0
0
3
1
2
1
2
2
2
2
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
1
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
1
1
1
0
0
0
2
2
0
2
0
0
6
0
1
1
0
0
3
0
2
2
2
1
0
0
2
0
0
0
1
0
1
0
0
0
2
0
1
0
1
0
0
0
0
1
0
0
2
0
0
1
1
0
0
0
0
1
1
0
0
2
1
0
2
0
0
0
0
0
0
0
1
2
2
0
0
0
2
0
0
0
0
1
0
0
2
1
0
2
1
0
2
0
0
0
2
2
1
3
0
0
0
1
0
0
0
3
1
2
0
1
1
0
0
0
1
0
0
1
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
2
1
0
1
1
2
0
0
2
0
2
0
1
1
0
0
1
1
1
2
0
2
0
0
2
2
0
0
0
0
2
1
3
0
0
2
0
1
0
0
0
1
0
0
0
0
1
0
0
3
2
0
0
1
0
0
0
0
1
2
1
0
0
0
1
0
2
2
0
1
2
0
0
0
1
0
0
0
0
0
1
2
2
2
0
4
2
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
2
1
0
2
0
1
2
1
0
0
1
0
0
2
0
1
1
0
0
0
0
2
2
1
0
1
0
8
0
0
0
0
0
1
0
1
3
0
0
1
0
0
0
2
0
1
0
1
0
0
0
0
2
1
3
0
0
2
4
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
5
0
3
0
2
0
2
0
0
1
2
1
2
1
0
1
0
0
1
0
0
2
2
1
0
1
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
2
1
2
0
0
1
0
2
0
0
2
1
0
0
0
0
0
0
2
2
2
1
0
0
1
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
1
0
1
2
0
1
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
1
1
0
2
2
0
0
0
0
1
0
0
0
4
1
0
1
0
1
1
0
0
0
0
0
1
2
1
1
0
0
0
1
1
0
0
0
3
1
0
0
0
1
0
1
0
1
0
0
1
0
0
0
1
0
2
0
1
1
2
0
0
1
3
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
2
2
0
0
0
0
0
0
2
2
0
2
0
2
1
2
0
2
0
1
1
2
0
2
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
1
0
3
2
0
0
1
0
0
0
1
0
2
4
0
2
1
0
1
2
0
0
1
0
1
0
3
0
0
0
1
2
2
0
0
2
1
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
1
1
0
2
0
0
0
0
1
2
2
1
0
0
0
0
0
0
1
2
0
0
0
0
1
0
1
1
0
0
0
0
0
2
0
2
0
0
2
2
0
0
1
0
0
1
1
0
0
1
0
1
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
2
2
2
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
1
0
0
3
0
0
0
0
0
0
0
0
2
0
0
2
1
1
0
0
2
0
2
0
0
0
0
2
0
0
2
0
0
1
2
0
0
0
0
1
0
1
0
0
3
0
0
1
0
1
2
0
1
0
0
1
0
0
1
2
1
0
0
0
0
0
2
0
0
0
0
1
1
1
0
2
2
1
2
0
0
3
2
1
0
0
0
0
0
0
0
0
1
2
1
1
1
0
0
0
2
2
2
0
1
0
2
3
0
0
2
1
0
0
1
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
2
0
1
0
2
1
0
0
0
0
0
0
0
2
2
0
0
0
0
1
2
0
0
0
0
2
0
1
1
2
0
2
1
0
2
1
0
0
0
0
0
2
0
0
0
0
0
2
0
1
2
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
2
0
1
0
1
0
0
0
1
0
1
0
0
0
1
2
0
1
0
1
0
0
2
2
1
0
0
0
0
2
2
2
1
0
0
0
2
0
0
6
0
1
2
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
3
1
0
0
0
3
0
0
1
0
3
1
0
0
1
1
0
1
2
1
0
1
1
0
1
0
1
1
0
1
0
2
2
0
0
1
2
3
2
0
1
0
2
0
0
0
1
1
0
2
0
2
2
0
0
1
0
0
1
2
2
0
2
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
1
0
0
0
2
0
1
1
2
2
2
0
0
1
2
0
0
2
0
0
2
0
2
0
1
0
0
0
0
0
1
0
2
0
2
2
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
2
0
0
0
1
0
1
0
0
2
0
2
0
1
0
1
2
0
0
0
0
3
0
0
1
1
0
0
1
2
0
0
2
0
1
0
0
2
2
0
1
1
0
1
1
0
0
2
0
2
0
2
0
0
3
3
0
0
2
2
2
2
0
3
0
0
0
1
1
0
0
0
0
2
2
0
0
1
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
1
2
0
0
0
0
1
0
0
0
2
0
0
0
3
0
2
0
0
0
1
0
1
0
0
1
0
2
1
0
2
0
2
0
2
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
2
1
2
1
0
0
1
1
0
0
0
0
0
4
0
2
0
0
2
0
0
0
1
0
0
0
2
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
1
2
0
0
2
0
0
0
1
4
0
0
0
0
0
0
1
0
0
0
1
2
1
0
0
0
0
1
0
2
2
2
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
1
1
2
0
1
0
1
0
0
2
0
1
0
1
0
0
1
1
0
0
3
1
0
0
0
0
0
0
1
2
1
0
0
2
0
1
0
2
2
1
1
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
1
1
1
2
0
0
0
0
1
1
2
3
0
2
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
2
1
0
0
2
0
1
0
0
0
0
0
1
2
1
0
0
0
0
0
2
0
1
3
0
0
0
2
0
2
1
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
3
0
2
1
1
0
2
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
2
0
2
2
1
1
2
0
2
0
1
0
0
0
1
2
0
0
1
0
2
0
2
0
2
0
1
0
1
0
0
0
2
1
0
1
0
0
0
0
1
0
0
0
2
1
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
3
1
0
3
2
0
0
0
0
0
0
2
0
0
1
2
0
2
0
0
0
0
0
3
3
1
0
1
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
1
0
0
1
2
0
0
0
0
1
2
0
0
2
0
0
2
0
1
0
0
1
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
3
1
0
0
2
2
0
1
0
1
1
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
1
2
0
0
1
0
3
2
0
0
0
0
2
0
1
1
0
2
2
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
2
2
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
1
2
1
2
2
2
0
0
1
1
0
0
2
0
0
2
0
0
1
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
1
2
1
0
2
0
1
0
0
0
0
0
0
1
0
0
3
0
0
1
0
0
1
0
1
1
0
1
1
0
0
0
1
0
0
0
0
1
0
3
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
1
1
0
0
0
0
2
1
0
0
3
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
2
2
0
0
1
0
1
0
0
0
0
2
1
0
0
1
0
1
1
2
0
2
1
1
0
0
1
1
0
0
2
1
1
1
2
2
0
0
0
0
0
1
0
1
0
1
0
0
0
2
0
0
0
3
0
0
0
0
1
2
1
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
2
1
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
2
1
0
6
0
4
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
1
0
2
0
2
0
1
0
0
0
2
0
2
1
1
0
0
1
1
0
0
0
1
0
2
1
0
0
4
2
1
0
0
0
1
1
0
1
0
2
0
2
0
0
2
2
1
0
2
0
0
1
0
0
0
1
0
0
2
0
2
2
2
0
2
0
0
0
0
0
2
2
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
2
2
2
1
0
0
0
2
2
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
2
3
0
0
0
0
0
0
0
0
1
0
1
2
0
0
3
0
0
0
2
0
0
1
0
1
0
0
0
0
0
1
2
1
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
2
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
2
2
2
2
0
0
2
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
2
1
0
0
1
1
0
0
2
0
0
2
2
0
0
1
0
0
1
0
0
0
5
0
0
2
2
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
4
0
0
0
0
0
1
0
1
0
4
0
0
0
2
2
2
0
0
1
0
3
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
1
2
1
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
2
0
1
0
2
1
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
2
0
0
1
0
0
0
1
2
1
2
2
2
0
3
1
1
2
1
2
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
2
1
2
0
3
0
2
0
2
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
2
0
1
1
0
0
0
1
0
2
1
0
1
1
0
0
3
0
0
0
2
0
2
0
3
1
1
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
2
1
0
0
1
0
2
1
0
0
0
0
1
1
0
1
0
0
1
0
1
0
0
0
0
1
1
0
0
0
2
0
1
2
1
0
2
1
0
0
1
2
1
1
1
0
2
0
3
1
0
0
1
1
0
2
2
0
0
0
0
0
1
0
0
0
0
0
2
1
4
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
2
0
0
2
0
0
0
1
2
0
0
1
0
0
2
0
1
0
1
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
2
0
2
0
0
0
0
0
0
1
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
2
2
0
1
0
0
0
0
0
0
0
2
2
2
0
2
0
0
2
2
2
0
0
0
1
0
0
0
2
0
0
2
0
1
0
2
2
1
0
2
1
3
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
1
0
0
2
2
0
2
1
2
0
0
0
1
0
0
0
1
0
0
0
2
1
2
1
0
0
1
0
4
0
0
1
1
1
1
1
0
1
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
2
1
3
2
1
0
2
2
1
1
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
2
1
0
0
0
2
0
0
1
0
0
0
0
0
0
3
1
1
0
0
1
0
0
2
1
0
0
2
0
1
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
1
0
1
0
1
0
1
0
0
0
2
1
0
0
2
0
1
1
0
2
0
0
0
2
0
2
0
0
0
0
2
1
2
0
0
1
0
0
2
0
1
0
0
0
1
0
0
7
1
2
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
5
0
0
1
0
1
0
0
1
1
1
0
0
0
1
0
0
0
0
3
0
1
0
0
0
0
0
2
0
0
2
0
2
1
0
2
2
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
2
1
0
0
0
2
2
1
0
0
0
0
0
0
0
2
1
1
3
0
2
2
1
1
1
2
0
1
0
0
1
0
1
0
0
0
0
0
0
1
1
0
1
1
1
0
0
2
0
0
0
1
2
0
0
3
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
3
0
0
0
1
1
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
2
2
1
0
2
1
1
0
0
1
0
0
2
2
0
2
0
0
0
2
0
0
2
1
0
1
0
0
2
0
2
1
0
0
1
0
0
0
1
2
2
1
0
1
2
2
0
0
0
2
0
1
1
0
1
0
0
0
2
2
0
1
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
2
1
1
0
0
0
0
0
0
0
0
0
0
1
3
3
0
0
1
2
0
0
3
2
2
1
1
0
2
0
0
0
0
0
1
1
1
2
0
0
0
2
2
1
2
0
0
0
0
0
2
1
0
2
0
0
2
2
0
1
1
2
0
4
2
2
0
1
0
0
1
0
0
1
0
1
1
0
0
2
2
0
0
1
0
0
0
0
1
2
1
1
1
0
2
2
2
0
1
1
2
1
1
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
2
2
0
0
2
1
2
2
5
0
3
2
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
3
2
0
0
0
0
1
2
0
0
2
2
0
2
1
1
0
0
0
0
0
0
0
2
2
1
2
1
2
0
0
0
0
0
0
0
0
2
2
0
0
0
1
1
0
2
0
0
3
3
0
2
0
1
2
1
0
2
3
0
0
0
0
0
0
2
0
1
1
0
2
0
2
0
0
0
0
0
0
1
1
1
1
0
2
0
0
3
0
2
0
2
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
6
1
0
0
0
2
1
0
1
0
0
2
1
0
2
1
0
0
1
1
0
0
0
0
2
0
0
2
1
1
2
0
0
1
0
0
2
0
1
1
0
0
1
1
1
1
0
0
0
0
1
0
0
0
0
1
2
0
1
1
0
2
2
0
1
2
1
0
2
0
1
0
3
0
0
0
0
1
0
0
0
1
2
0
1
1
1
0
1
2
0
0
2
1
0
1
1
0
2
1
0
0
0
2
1
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
1
0
1
1
0
2
1
0
0
0
0
0
0
0
1
1
0
1
1
2
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
1
0
1
0
0
0
2
0
0
1
0
1
0
0
1
2
1
1
2
2
0
0
0
2
0
3
3
1
0
0
0
2
1
2
2
2
2
0
1
1
0
0
1
0
0
1
0
2
1
0
0
2
2
2
0
0
0
1
0
1
0
1
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
1
2
0
0
1
0
0
0
2
0
0
2
0
0
0
2
1
2
0
2
1
3
1
1
1
1
0
2
2
0
0
0
0
1
1
0
2
0
0
1
2
0
1
1
1
0
0
2
0
0
1
0
0
0
2
0
1
1
1
1
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
1
0
1
2
1
0
0
0
1
1
0
0
0
0
0
0
3
1
1
0
2
0
1
1
0
0
0
0
0
0
2
2
0
2
1
0
2
0
0
1
0
0
0
0
2
1
0
0
0
0
2
0
2
1
3
0
2
2
0
0
0
1
2
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
3
2
0
2
1
0
0
0
0
1
0
0
0
0
2
1
0
1
0
2
0
0
1
2
0
0
1
0
2
0
0
1
4
0
2
0
0
1
0
0
0
1
1
0
1
0
2
0
0
0
1
0
0
1
0
1
0
0
0
0
1
1
1
0
1
0
0
1
0
5
0
2
2
0
2
0
0
0
0
0
2
0
0
0
0
2
0
1
1
0
0
0
2
0
2
2
0
0
1
0
0
1
0
0
0
0
2
1
0
0
2
1
2
1
0
2
0
0
0
0
0
3
0
0
0
1
0
0
1
3
0
2
2
0
0
0
0
0
0
1
2
0
0
2
1
1
2
0
0
0
0
0
0
2
0
0
1
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
1
0
0
1
1
2
0
0
0
1
0
0
2
1
2
0
1
0
2
0
1
0
0
0
2
0
2
2
0
2
0
0
0
0
0
2
0
0
0
0
0
1
2
1
1
2
0
0
2
1
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
1
1
0
0
0
1
1
2
0
0
0
2
0
0
2
0
0
0
0
3
0
0
1
0
1
0
1
0
1
2
0
1
1
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
3
0
0
2
0
0
0
2
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
1
0
0
0
0
1
0
2
0
0
1
1
0
0
2
2
0
0
0
2
0
0
0
0
0
0
2
0
2
0
2
1
0
0
0
0
2
1
0
2
0
1
1
0
0
2
0
0
0
0
0
0
2
1
1
0
0
2
0
0
2
0
0
1
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
2
1
1
0
0
0
2
0
0
1
0
0
1
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
1
1
0
0
0
2
0
1
0
0
0
2
1
0
0
0
1
1
0
0
0
2
0
2
0
0
0
3
1
0
0
1
0
0
1
1
2
0
0
0
1
0
1
0
0
1
1
0
0
2
2
0
0
0
0
2
0
0
0
0
1
0
1
2
0
2
0
3
2
0
2
1
2
3
0
0
2
2
2
2
2
0
0
0
0
1
0
1
3
0
0
0
0
2
1
0
2
0
0
0
0
1
1
0
0
0
2
0
0
0
1
0
1
0
2
2
2
0
0
0
0
0
1
1
1
0
0
1
0
1
2
2
0
0
0
0
3
0
0
0
2
0
0
0
0
1
0
0
1
2
0
0
0
0
1
2
0
2
0
0
0
0
2
0
0
1
1
2
0
1
2
1
0
2
2
0
0
0
1
1
1
1
1
0
0
0
2
0
0
0
2
1
1
0
0
0
1
1
0
0
0
0
0
1
2
2
0
0
2
2
0
0
1
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
1
1
0
0
0
2
0
1
0
0
1
0
0
0
0
1
0
0
2
1
0
0
0
1
0
0
0
1
2
2
2
0
2
2
0
0
1
0
2
0
2
0
2
1
2
0
0
0
0
0
0
0
1
2
3
2
2
2
1
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
3
0
1
2
0
0
0
1
1
1
1
0
0
0
2
0
0
0
0
1
0
0
2
2
0
0
1
0
0
2
0
0
1
2
0
0
0
2
2
0
0
1
0
2
2
1
1
0
2
0
0
2
1
0
2
0
0
0
0
0
0
0
1
1
1
1
1
0
0
2
0
0
0
0
0
0
0
1
2
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
2
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
1
0
1
0
0
2
0
0
0
1
0
0
2
0
0
0
2
2
0
0
2
1
0
0
2
1
0
0
0
1
0
0
0
0
1
2
0
3
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
1
0
1
1
0
1
0
3
1
0
0
0
1
2
0
0
0
0
1
2
2
3
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
2
0
0
2
2
0
0
1
0
0
0
0
2
1
1
0
2
1
2
0
0
0
0
0
2
0
0
0
0
1
0
2
1
1
0
0
1
0
3
0
0
0
1
1
0
0
0
0
1
0
0
0
1
1
0
2
1
0
0
2
0
1
0
0
0
3
0
0
0
1
0
0
0
0
0
0
1
2
0
2
0
2
0
0
0
0
0
2
0
2
1
0
0
3
0
0
0
0
0
0
0
0
0
1
2
1
1
1
1
0
0
1
0
0
0
1
2
0
1
0
0
0
2
0
0
2
0
0
1
0
0
0
0
1
0
1
2
1
0
2
0
1
0
0
0
2
2
1
0
0
0
0
2
2
2
3
1
0
0
1
0
1
0
2
0
1
2
1
2
0
0
2
0
0
1
1
2
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
2
2
2
0
0
1
0
0
0
2
2
1
0
5
1
0
2
0
0
1
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
2
2
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
3
0
0
2
2
0
0
0
0
0
1
0
3
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
2
1
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
1
0
1
2
0
0
2
0
0
0
0
1
2
0
1
1
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
3
0
2
2
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
1
1
2
2
0
1
0
0
0
1
0
1
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
1
0
0
2
0
1
0
1
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
1
0
0
1
1
1
1
1
1
0
0
0
0
0
0
2
2
0
0
1
1
0
1
0
0
0
0
0
1
1
0
0
0
1
1
2
0
2
0
2
2
0
0
0
0
2
0
0
2
2
0
1
1
0
0
1
0
1
1
0
0
0
1
0
1
1
1
0
0
1
1
0
2
0
0
2
2
0
2
1
0
0
2
1
0
2
0
0
1
0
0
0
0
1
1
0
1
0
0
2
0
5
0
1
1
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
1
1
1
2
0
0
0
0
0
2
2
0
2
0
0
1
4
1
0
0
1
1
0
0
1
2
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
2
1
0
0
0
0
2
0
0
0
1
2
0
0
2
0
2
1
1
0
2
1
1
0
0
1
0
2
2
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
2
1
0
0
2
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
3
0
0
2
1
2
0
0
0
2
0
0
0
0
1
0
1
0
2
0
1
2
0
2
0
2
0
0
0
0
2
0
0
0
0
3
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
3
1
0
0
0
0
0
0
0
0
3
1
1
1
0
0
2
0
2
0
2
0
2
0
0
2
0
1
0
0
2
0
1
1
0
0
1
0
0
0
1
0
1
0
1
2
0
3
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
2
2
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
3
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
3
2
2
0
1
0
0
0
1
0
1
0
0
0
2
2
2
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
1
0
2
2
0
2
2
1
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
1
0
1
1
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
1
0
0
0
0
1
0
2
2
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
2
1
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
3
0
0
0
1
2
0
0
1
0
0
0
2
0
0
0
1
0
1
1
2
2
0
1
1
2
1
1
2
0
0
0
0
2
0
1
0
1
1
1
2
0
0
0
0
0
2
0
2
4
0
0
1
2
0
0
4
0
0
2
1
1
0
2
0
1
0
0
0
2
1
0
0
0
0
0
2
1
0
0
1
1
0
0
2
0
2
1
0
0
2
0
0
0
0
0
1
1
0
0
1
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
1
2
2
0
0
2
0
0
0
2
1
0
0
0
2
0
0
1
2
2
0
2
1
0
0
2
0
4
1
1
1
3
0
2
0
1
0
0
0
0
0
0
0
2
1
0
1
0
2
2
0
0
1
1
0
2
2
0
0
0
1
4
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
1
3
0
1
2
0
0
0
1
1
1
0
0
0
1
0
2
0
0
3
1
1
0
2
0
0
2
0
1
0
2
0
1
0
3
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
2
2
0
1
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
1
1
0
1
1
0
0
1
2
4
2
0
2
0
0
0
0
0
0
2
0
2
0
1
0
2
1
0
0
1
1
1
0
0
0
1
0
0
2
0
0
0
1
2
0
0
0
0
0
2
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
1
0
1
0
0
0
0
1
2
2
2
0
1
1
0
1
2
0
0
0
0
0
6
2
0
2
0
0
0
1
0
1
0
1
0
1
2
0
0
1
0
0
1
0
0
1
2
2
1
1
0
0
1
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
2
2
0
2
1
1
0
1
0
2
0
1
0
0
2
0
0
0
0
0
0
4
2
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
2
0
2
2
1
0
2
0
0
2
0
1
0
0
1
0
2
2
0
0
0
0
1
0
1
1
0
2
0
0
0
4
2
0
0
1
0
0
2
2
2
1
2
0
2
0
0
0
1
1
0
2
0
1
1
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
1
0
0
3
2
0
2
0
0
0
0
3
0
2
0
0
0
0
0
2
2
0
2
2
0
2
1
1
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
1
1
0
0
0
0
2
0
1
0
2
0
0
4
1
0
0
0
0
0
0
1
0
0
0
2
0
1
0
1
0
0
0
3
0
0
0
0
0
1
0
1
1
0
2
0
0
0
0
0
1
1
0
0
2
3
0
1
1
0
1
0
0
1
0
0
0
0
2
2
0
0
4
2
1
0
2
2
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
2
1
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
2
0
1
0
0
0
0
0
2
0
2
0
0
0
2
1
0
1
1
0
1
0
1
1
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
1
0
1
0
1
0
0
2
1
0
0
0
0
1
2
0
2
3
2
0
1
0
2
2
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
1
2
2
2
0
0
0
0
0
0
0
2
0
2
2
1
0
2
0
0
0
1
2
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
1
0
0
0
2
1
0
2
2
0
2
2
1
3
2
0
1
0
2
2
0
1
0
0
0
0
1
2
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
2
1
0
0
0
1
2
1
2
0
0
1
0
2
0
0
1
1
0
0
1
0
2
0
0
2
2
0
2
2
0
0
0
1
0
2
0
2
0
2
0
0
0
1
0
0
0
1
3
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
3
0
1
1
0
0
0
1
0
2
2
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
2
1
0
0
3
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
5
0
0
1
2
0
0
0
1
1
0
2
0
0
1
0
2
0
2
0
0
1
0
0
0
1
0
0
0
2
3
2
0
0
0
0
0
1
0
4
0
0
2
0
0
1
2
1
0
0
0
0
0
0
0
2
1
0
0
0
3
0
2
3
0
0
0
0
2
0
0
0
0
2
2
2
0
0
2
0
0
0
2
0
0
2
1
2
2
0
0
0
0
0
0
1
1
2
0
1
0
2
1
0
0
0
2
1
1
1
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
2
0
3
2
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
2
0
0
0
0
2
7
1
1
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
2
1
1
0
2
0
1
1
0
0
0
0
0
1
1
1
0
0
3
0
2
0
0
0
0
2
0
0
0
1
0
0
0
1
1
1
0
0
0
1
1
1
0
1
2
0
1
1
2
0
2
1
0
2
0
0
0
1
1
1
0
0
0
0
2
0
1
0
0
0
0
1
0
0
5
0
2
1
0
1
2
0
2
0
0
0
0
1
0
0
1
1
1
0
1
0
1
1
0
0
0
0
2
0
0
2
0
1
2
0
0
0
0
0
0
1
2
1
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
1
2
0
1
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
4
1
1
0
0
1
1
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
1
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
1
0
2
1
1
0
0
1
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
1
2
0
0
0
0
2
0
1
0
1
1
2
3
3
0
2
0
0
0
2
0
2
0
0
1
1
0
0
0
2
1
2
0
0
0
1
0
0
0
0
2
2
1
0
0
1
0
1
0
0
0
3
0
2
0
0
0
1
2
1
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
1
0
0
0
1
0
2
0
2
0
0
2
0
0
1
1
0
2
1
1
1
0
1
0
0
2
0
0
1
0
2
0
0
2
0
1
0
0
0
2
0
1
0
0
0
2
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
2
0
1
0
1
1
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
2
1
0
0
0
2
0
0
0
2
1
0
2
3
2
0
2
1
0
0
1
0
0
0
0
0
2
0
0
0
2
2
0
1
0
3
3
1
0
0
2
2
2
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
2
0
1
0
0
0
0
0
1
1
0
0
0
1
0
2
0
0
1
0
2
2
2
2
2
3
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
1
0
3
0
0
0
4
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
2
1
1
2
1
1
0
0
1
2
0
1
0
1
0
2
0
0
2
0
0
0
2
0
0
3
0
0
0
1
1
2
0
1
1
1
2
0
0
0
0
2
0
0
0
0
0
0
2
1
1
0
0
1
0
0
0
1
0
1
1
9
0
0
0
2
1
0
6
0
1
0
0
0
3
0
0
0
2
1
2
0
2
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
3
2
0
1
0
1
0
1
0
0
0
1
0
0
0
1
2
0
2
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
2
0
0
1
0
0
1
1
0
0
1
2
0
2
2
0
1
0
2
2
0
0
3
0
0
1
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
2
1
0
1
0
2
0
0
2
0
2
2
0
0
0
0
2
1
0
0
1
2
0
0
0
1
4
0
1
0
0
2
0
2
0
0
1
0
0
1
0
0
1
2
0
0
0
5
1
0
2
1
0
0
0
0
0
2
2
0
2
0
0
0
1
0
1
1
0
2
0
0
0
0
0
1
0
1
2
2
0
0
2
0
0
1
0
0
0
0
0
0
0
2
1
0
0
2
2
1
0
0
2
0
1
1
1
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
1
0
0
0
2
0
1
1
1
0
0
1
0
0
0
2
0
0
2
1
1
0
0
0
2
2
0
0
1
2
0
0
0
2
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
1
2
0
0
0
0
1
2
0
2
1
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
2
0
0
0
2
0
2
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
2
0
3
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
2
0
1
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
1
0
2
1
1
0
0
0
1
2
1
0
0
1
0
0
0
0
3
0
0
0
2
0
0
0
3
0
3
0
0
1
0
1
0
0
0
2
0
1
0
1
1
2
0
0
0
0
0
0
1
0
2
0
1
2
0
0
2
0
2
0
2
0
0
3
0
0
2
0
0
0
0
1
1
0
2
1
0
2
0
0
1
2
0
2
0
0
1
0
0
0
0
0
1
0
1
2
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
3
0
2
0
1
1
0
2
2
0
1
0
0
0
0
2
1
0
1
0
3
0
2
0
0
0
1
0
0
0
0
2
0
1
2
0
1
2
0
0
0
2
1
0
1
3
2
3
0
1
1
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
2
0
0
0
2
0
2
0
0
1
0
1
2
0
0
2
2
0
0
0
1
1
0
1
0
0
0
0
0
2
1
1
0
2
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
3
1
1
0
1
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
2
0
0
0
2
0
2
0
2
0
0
0
0
0
1
0
0
0
0
1
3
0
2
2
2
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
2
1
2
0
0
0
0
2
0
0
2
1
0
1
2
1
0
1
0
0
0
2
1
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
1
0
0
2
1
2
2
0
0
0
0
1
0
0
2
0
3
0
0
0
1
0
0
2
2
1
0
1
4
0
0
0
1
0
0
0
0
0
0
0
2
1
2
2
0
0
0
0
2
0
2
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
3
0
0
4
2
1
1
0
0
0
2
0
0
0
1
1
2
2
2
0
0
0
1
2
0
2
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
2
0
1
2
0
1
0
4
1
1
2
0
0
0
0
0
2
1
0
0
0
2
0
1
0
0
0
0
1
2
0
1
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
2
2
1
1
1
0
0
0
1
0
1
1
0
1
1
0
0
0
1
0
2
0
0
3
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
2
0
1
0
1
0
0
0
0
1
4
0
0
0
1
0
1
0
0
0
2
0
0
2
2
0
0
0
2
0
1
0
0
2
2
1
0
1
0
0
0
0
0
0
0
1
1
2
0
0
1
2
1
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
1
0
0
2
0
1
0
0
0
0
0
2
1
2
1
0
0
0
0
1
1
0
1
0
0
2
0
2
0
0
0
0
0
0
0
3
1
2
1
0
2
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
1
0
0
2
1
0
0
0
1
0
0
0
0
0
0
1
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
2
3
0
1
2
0
0
1
0
0
0
1
0
0
1
1
0
2
0
1
0
1
0
2
0
1
2
1
0
1
2
2
1
0
0
0
2
2
0
0
1
0
0
0
0
1
2
0
0
1
2
1
2
0
1
0
0
1
0
0
0
0
0
2
5
1
0
2
1
1
0
0
0
0
3
0
1
0
0
0
0
0
0
2
0
1
2
0
1
1
1
0
0
0
3
0
1
0
0
2
0
0
1
0
0
2
0
1
0
0
1
1
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
2
0
0
0
1
5
0
0
2
2
0
2
1
0
0
0
0
2
0
2
1
0
2
0
2
0
0
0
0
1
2
1
1
0
0
3
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
1
0
0
1
2
2
2
0
2
0
0
1
0
0
0
0
2
0
1
2
0
0
0
1
3
0
1
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
1
2
0
0
3
3
0
0
0
1
0
1
2
0
0
1
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
2
0
0
0
0
1
0
1
0
0
1
2
2
0
1
0
0
0
0
2
0
0
1
0
1
0
1
1
2
3
0
2
0
1
2
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
1
2
1
0
1
2
1
0
0
1
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
4
0
3
0
0
3
0
1
0
2
0
0
0
0
0
0
0
0
13
2
0
0
0
0
1
1
1
0
0
1
1
0
0
1
2
0
1
2
1
2
0
0
2
0
0
0
1
1
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
2
3
0
0
2
0
0
1
1
2
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
1
0
0
0
1
2
2
0
0
0
3
0
0
0
1
0
0
0
0
0
1
0
0
2
2
0
1
0
0
0
0
0
0
0
1
1
2
0
0
1
1
1
1
0
2
1
2
0
0
0
2
3
1
2
0
0
0
1
2
0
0
0
0
2
0
2
0
0
0
3
0
2
0
0
1
0
1
0
1
1
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
2
1
0
0
0
1
0
0
1
0
3
1
0
2
3
2
0
0
1
3
1
0
0
0
1
0
1
0
1
0
0
2
0
2
1
0
0
0
0
1
0
0
1
0
0
0
0
2
0
1
0
0
1
0
1
0
2
1
0
0
0
2
1
1
0
0
0
0
0
1
0
1
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
2
2
2
0
2
2
2
0
0
1
2
0
0
1
0
0
0
3
0
2
0
0
0
1
1
2
1
0
0
1
0
0
2
0
2
2
0
4
1
2
1
0
1
1
0
2
0
3
0
2
1
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
1
1
1
1
2
0
2
1
1
1
1
0
0
2
0
0
0
2
0
0
2
2
0
2
1
0
2
0
0
0
2
0
1
2
0
0
1
1
1
0
0
1
1
0
0
0
1
0
0
0
0
2
1
0
0
0
0
2
2
0
1
0
2
0
2
0
0
0
1
2
0
1
0
0
2
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
1
0
2
2
0
0
0
0
0
0
2
2
5
0
0
0
0
0
2
0
1
1
1
0
0
0
1
0
0
0
1
0
0
1
1
0
1
1
0
0
0
1
1
0
0
0
0
0
2
1
0
0
0
0
0
0
2
2
0
0
2
0
1
2
1
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
1
0
1
0
1
0
2
0
0
2
0
2
0
2
2
1
0
1
0
0
1
1
0
0
0
2
2
3
0
1
0
0
2
1
0
0
0
1
1
0
2
0
0
0
0
0
0
1
1
2
0
0
2
0
0
2
2
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
0
2
0
1
1
1
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
2
0
1
0
0
1
0
1
0
0
0
0
0
2
1
0
1
0
1
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
2
0
3
0
1
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
3
0
1
2
2
1
0
0
0
0
1
1
0
0
0
1
4
2
0
0
1
1
0
1
0
1
0
2
2
1
0
0
0
3
1
0
0
0
0
0
0
0
1
1
4
0
0
0
0
0
1
2
0
2
0
0
0
0
2
2
2
0
1
0
1
2
0
0
2
0
0
1
2
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
1
2
2
1
0
0
2
0
0
0
0
0
0
2
0
1
4
0
0
3
2
2
0
0
1
0
1
1
0
0
0
1
2
1
2
0
1
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
2
0
0
2
1
0
2
2
1
0
0
0
2
1
1
1
2
1
1
1
0
1
1
1
0
1
0
0
2
0
0
0
1
2
0
1
2
0
0
0
0
2
1
2
0
2
0
2
1
0
0
0
0
2
1
0
0
0
0
0
1
1
1
0
2
0
2
2
1
1
0
0
2
0
0
0
1
0
1
0
0
0
0
2
1
0
0
0
0
1
0
0
1
0
0
1
1
0
0
3
1
2
0
2
0
0
2
0
0
2
1
0
2
0
0
0
0
3
2
0
0
1
1
2
0
1
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
3
0
1
0
0
1
1
0
1
0
0
0
0
0
0
1
0
3
0
2
0
1
1
1
0
0
0
1
0
0
1
0
2
0
0
1
3
0
0
0
2
2
0
0
1
0
1
0
2
0
1
0
0
0
0
0
0
0
0
2
0
1
1
2
1
1
0
0
1
1
0
0
1
0
0
1
2
2
0
0
3
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
1
2
0
0
1
0
0
1
0
2
0
1
0
2
0
0
0
1
2
0
0
0
0
2
2
1
1
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
2
0
1
0
0
2
1
2
0
2
2
2
0
0
1
0
0
0
0
1
0
0
0
1
0
1
1
1
0
0
3
0
0
0
0
0
2
2
2
2
1
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
1
1
0
1
0
0
0
2
0
0
2
0
1
2
1
0
2
0
2
0
0
0
0
0
2
0
2
0
1
1
1
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
2
1
0
1
0
2
1
1
2
0
0
2
0
0
2
2
0
0
1
0
1
1
3
1
0
0
0
1
0
0
1
0
0
0
3
0
0
0
2
0
0
0
0
0
2
0
0
1
1
0
0
0
2
1
0
0
0
1
1
0
0
1
0
0
1
0
0
2
1
0
1
2
0
2
2
2
0
0
3
1
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
3
0
1
1
0
0
1
0
3
0
1
0
0
1
0
1
2
1
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
1
1
2
2
0
1
2
2
0
0
2
2
0
0
0
3
0
0
0
2
2
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
1
2
0
2
0
1
6
0
0
0
0
2
2
0
0
2
0
0
2
0
3
1
0
1
0
1
0
0
0
2
0
0
1
0
3
0
2
0
2
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
1
1
2
1
0
0
0
2
0
0
1
1
1
1
0
0
0
1
0
0
0
1
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
2
2
0
2
0
0
0
0
0
0
1
0
1
0
1
0
1
1
1
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
1
0
2
0
0
2
0
0
1
0
0
0
1
2
0
1
2
1
2
4
0
0
0
1
0
1
0
0
2
0
1
0
1
1
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
2
1
1
0
0
1
0
0
3
2
0
0
0
1
1
2
0
3
2
0
0
0
0
0
0
0
1
0
1
0
1
2
0
0
1
0
0
1
0
0
0
1
1
0
0
0
1
2
2
2
2
0
1
0
0
0
2
1
0
0
0
2
0
0
0
0
1
1
0
0
2
0
0
0
1
2
0
0
2
0
0
2
0
0
1
0
0
0
3
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
1
3
0
0
2
0
0
7
0
0
0
0
3
1
3
0
0
0
0
2
0
2
1
0
0
0
2
1
2
1
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
2
1
1
0
0
1
0
0
0
0
0
0
5
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
2
2
1
1
1
0
4
2
2
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
1
2
0
0
0
0
1
1
0
0
1
2
2
2
1
2
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
2
0
0
4
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
1
0
1
2
0
0
1
1
0
2
1
0
0
0
0
2
1
1
0
0
0
2
1
2
1
0
0
0
0
2
0
0
0
0
0
0
1
1
0
1
2
0
0
0
0
0
0
1
0
2
0
2
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
1
1
1
0
0
0
0
1
0
2
0
0
0
1
0
2
2
0
1
0
0
0
0
2
1
0
1
2
2
2
2
0
0
0
2
0
0
0
0
1
0
0
0
1
2
1
0
1
0
0
0
2
2
1
0
1
0
0
0
2
0
0
0
5
0
0
2
1
1
2
0
2
2
1
0
2
0
2
1
0
0
2
0
2
0
0
2
0
1
0
1
2
1
0
0
2
1
3
1
2
0
0
0
0
0
1
1
0
1
0
0
0
1
2
0
1
0
0
0
0
2
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
2
1
2
2
1
0
0
2
0
1
0
2
2
0
2
2
0
0
0
0
2
0
1
0
0
0
0
1
0
4
1
0
0
3
0
0
0
1
0
0
2
0
1
0
0
0
0
3
2
2
1
0
0
2
0
0
2
0
7
0
0
0
2
0
0
2
0
2
0
1
0
0
0
0
1
0
0
0
0
0
1
2
2
1
0
2
0
0
0
0
2
2
0
2
0
2
3
2
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
1
2
1
1
1
2
1
0
0
0
0
1
0
0
1
1
2
0
0
2
2
1
2
0
0
0
2
1
2
0
0
0
1
0
0
4
2
1
1
2
1
0
1
1
1
0
0
0
0
2
0
0
1
0
0
1
0
2
0
2
1
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
1
0
0
0
0
2
1
1
2
2
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
2
2
0
0
0
0
0
0
1
0
0
2
2
0
1
0
0
2
0
1
0
0
2
2
0
1
0
0
2
1
1
1
0
0
2
1
0
0
1
2
0
0
1
0
0
2
0
1
0
3
0
1
0
0
1
2
1
1
2
0
1
0
0
0
1
0
2
1
2
0
0
1
1
1
0
0
1
0
3
0
1
2
0
1
2
1
1
3
0
1
1
0
0
1
2
2
0
0
0
1
2
0
0
1
9
0
0
1
0
1
2
1
0
2
0
2
0
0
2
0
0
1
0
0
1
0
0
0
2
0
0
0
1
0
1
1
1
0
2
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
1
1
0
0
0
0
0
0
2
1
1
2
1
0
1
2
0
1
0
1
0
2
0
0
0
0
0
1
0
0
2
2
0
0
1
2
1
1
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
2
0
1
1
0
0
2
0
1
1
0
0
2
0
0
2
1
0
1
2
0
4
2
2
0
0
0
2
1
0
2
0
0
0
0
1
0
0
0
1
0
2
0
1
0
0
1
0
0
1
0
0
2
0
2
0
0
0
0
1
1
0
1
1
2
2
2
0
1
2
1
1
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
2
2
0
2
1
0
2
0
0
0
1
1
3
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
1
0
0
0
1
0
1
2
0
1
3
0
2
0
0
0
2
0
4
1
2
0
2
2
1
0
0
1
0
1
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
3
0
0
1
0
0
0
1
0
1
2
0
0
2
0
1
1
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
2
1
2
1
1
0
0
0
0
0
0
0
0
2
1
2
0
0
2
0
0
2
1
1
0
0
1
0
2
0
0
0
0
0
0
0
2
3
0
2
2
0
1
0
2
1
0
2
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
2
2
0
0
2
1
0
2
0
0
0
0
1
2
1
0
1
0
0
0
0
0
0
3
2
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
1
0
2
0
0
1
0
0
0
1
1
0
0
0
0
1
1
0
2
1
0
0
1
2
1
0
0
0
2
1
0
0
2
0
1
0
1
2
0
2
1
2
1
2
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
1
0
0
0
0
2
3
0
0
1
0
3
0
2
0
0
0
0
3
2
2
2
2
1
1
0
0
2
1
0
0
1
0
2
0
2
1
2
2
1
1
1
0
0
0
1
0
1
0
2
0
1
2
0
2
0
2
1
0
0
0
0
2
3
0
1
1
0
0
0
0
0
3
1
0
2
2
1
0
0
0
1
1
0
2
0
2
1
0
2
1
1
0
2
1
0
0
1
0
0
0
0
0
0
0
1
6
0
0
2
1
0
0
0
0
2
2
1
3
7
0
0
0
0
3
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
3
2
0
0
2
0
2
1
2
0
0
0
2
2
0
0
0
2
1
1
1
1
0
0
1
2
0
0
0
2
5
0
0
0
0
0
0
1
0
0
0
0
4
0
2
0
2
1
0
2
1
0
1
0
1
2
0
0
0
0
1
0
0
0
0
0
4
0
0
0
2
2
0
0
0
2
1
1
0
0
0
1
1
0
2
1
1
0
2
0
0
0
0
2
2
1
1
0
1
1
0
1
0
0
1
0
2
2
0
0
0
1
2
0
1
0
0
2
2
0
1
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
1
1
0
2
6
0
0
1
0
0
2
0
0
1
2
0
0
1
0
0
1
2
1
1
0
1
0
1
0
1
0
0
3
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
3
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
2
2
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
2
1
2
0
1
3
0
1
0
0
2
2
0
2
0
0
1
2
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
9
1
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
4
2
0
0
2
0
0
0
3
0
0
0
2
0
1
0
0
0
2
2
0
0
0
2
0
1
0
2
0
0
2
0
0
0
0
0
0
0
3
0
0
5
2
0
0
1
2
0
0
0
0
1
0
1
2
1
0
0
0
0
1
0
1
0
0
1
2
2
0
3
0
0
0
1
0
0
0
3
0
0
1
0
0
0
0
3
0
0
2
1
2
1
0
0
2
1
0
0
0
2
3
1
0
0
0
0
0
0
2
0
1
0
0
0
1
0
2
6
0
0
1
2
2
2
0
2
1
0
0
2
1
2
0
0
1
2
0
0
1
0
3
0
1
1
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
4
0
0
2
3
1
0
0
0
1
0
0
0
0
0
0
0
2
2
0
1
0
0
2
1
0
0
2
0
0
2
1
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
3
0
1
0
0
1
0
1
0
1
0
0
0
3
0
0
0
2
0
1
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
1
0
1
1
0
0
2
1
3
0
0
0
1
0
1
2
0
5
2
2
0
0
2
0
0
0
0
1
0
1
0
0
1
0
0
0
2
0
0
0
1
1
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
3
0
0
0
0
1
0
0
0
2
1
1
0
0
1
0
0
0
0
2
0
1
0
0
2
0
0
2
0
2
1
2
0
0
1
1
0
1
0
1
0
1
0
0
0
2
1
0
1
2
0
0
0
0
0
0
0
2
1
2
2
2
1
0
0
1
1
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
1
0
2
1
0
2
0
2
4
3
0
0
1
2
0
0
0
0
0
1
2
2
2
6
2
0
0
0
0
0
2
2
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
3
0
1
0
0
2
0
0
0
0
0
0
1
0
2
1
2
0
0
1
0
0
1
0
0
0
2
0
0
0
0
2
1
1
0
2
0
1
1
1
1
0
0
0
1
2
1
0
0
2
0
1
0
2
0
0
0
1
1
1
0
2
0
2
1
0
0
0
0
0
0
2
0
0
2
1
0
0
0
1
0
1
1
0
0
2
0
0
0
0
4
0
0
1
0
0
0
0
3
0
1
0
2
0
0
0
1
0
0
1
2
0
0
1
0
0
2
0
0
2
0
0
1
0
0
0
1
0
0
0
3
0
0
0
2
0
0
0
1
1
0
1
2
0
2
0
0
0
1
1
0
1
3
0
0
0
0
0
1
0
1
0
0
6
0
0
3
0
0
0
1
2
2
0
1
2
1
2
0
0
2
0
2
0
1
1
2
0
1
3
1
2
0
0
1
0
0
1
0
0
0
3
0
0
0
2
2
0
0
0
0
0
1
1
0
0
0
0
2
1
2
1
0
0
2
0
2
2
3
0
2
0
0
0
2
2
0
0
1
2
0
0
2
0
2
1
0
2
2
0
0
2
0
0
1
1
1
0
0
1
1
2
0
0
1
1
1
0
2
0
2
0
2
1
1
0
1
0
0
2
2
0
1
0
1
0
0
2
2
1
1
3
0
0
0
2
2
1
0
1
0
0
0
0
0
1
0
0
1
2
2
1
0
1
0
0
1
0
1
0
0
1
0
4
0
1
0
1
0
0
0
0
0
1
1
2
1
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
1
0
2
1
0
0
1
0
0
0
0
0
0
0
0
4
1
0
1
0
0
0
0
5
0
0
0
0
1
0
0
2
0
0
0
2
3
1
0
0
1
0
0
2
0
1
2
1
0
0
0
0
1
0
2
0
0
1
0
2
0
1
3
1
1
2
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
2
1
2
0
0
1
0
0
2
0
0
1
0
0
1
0
0
0
0
2
0
2
2
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
1
5
0
0
0
0
2
0
1
0
0
0
0
0
2
0
1
2
0
2
0
0
0
0
0
2
2
0
0
2
2
0
1
0
2
0
1
0
2
0
2
0
0
1
0
0
1
1
0
0
0
0
1
2
0
1
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
2
0
1
0
0
2
2
2
1
1
0
0
0
0
2
0
1
0
0
2
0
0
2
0
0
0
1
1
0
0
2
1
0
0
0
1
1
0
0
0
0
2
1
0
0
2
2
2
1
0
1
0
1
0
1
0
0
0
0
1
0
0
0
1
0
2
0
0
2
1
0
1
0
2
0
4
1
0
2
0
2
0
0
0
0
0
1
1
2
0
1
0
0
0
0
0
2
0
0
1
1
1
1
1
0
0
0
0
0
0
3
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
1
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
2
0
1
1
0
0
2
2
1
2
0
1
0
0
0
1
0
2
1
1
0
2
0
0
1
2
2
0
3
1
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
2
0
0
0
0
1
1
0
0
2
2
1
0
0
1
0
2
0
0
2
2
1
0
0
1
5
0
0
0
1
0
2
2
1
1
2
1
1
3
2
2
0
0
0
0
2
2
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
2
0
2
0
1
0
1
0
2
0
0
0
1
0
2
0
3
2
2
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
1
1
1
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
2
2
0
1
1
0
2
0
1
1
1
1
1
0
0
1
0
0
2
3
2
1
0
0
0
0
1
0
0
2
0
1
1
1
2
1
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
7
1
2
0
2
0
2
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
2
0
1
2
1
0
0
1
0
0
0
2
0
0
2
0
1
0
1
0
1
2
2
0
0
2
0
0
0
1
0
0
1
0
3
0
0
2
2
2
2
0
1
1
0
0
0
2
2
0
0
0
0
0
0
2
0
0
2
1
0
0
2
9
0
0
0
0
0
0
1
0
0
0
2
1
1
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
3
0
0
0
1
0
2
0
0
2
0
1
0
0
0
0
1
0
0
2
0
0
1
1
0
0
0
0
0
0
0
1
0
0
2
0
1
0
1
0
0
0
1
2
0
0
0
1
0
1
1
0
2
1
2
1
2
1
0
0
6
0
1
2
1
1
0
2
0
0
0
2
0
0
0
0
0
0
2
1
0
0
2
0
0
0
1
1
0
0
2
2
2
1
0
2
0
0
0
1
0
0
0
0
0
2
0
0
1
0
2
0
3
0
0
2
0
0
1
1
0
0
0
1
0
0
1
0
0
0
1
1
2
2
0
1
1
1
1
0
0
2
2
0
0
1
0
0
0
2
1
0
1
0
1
0
0
0
0
0
1
0
0
0
3
0
2
1
0
0
2
1
0
0
1
1
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
1
2
0
0
1
2
0
0
2
0
0
2
0
2
0
1
0
0
0
2
0
0
3
0
1
2
1
1
0
1
0
0
1
0
2
2
0
1
3
0
3
0
0
1
0
0
2
1
0
0
0
0
0
1
2
0
0
2
0
2
2
2
1
0
0
0
1
1
0
4
0
0
2
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
2
1
1
2
0
0
1
2
2
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
1
1
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
2
1
0
1
0
1
0
0
0
0
2
2
1
2
0
0
0
0
0
0
0
1
0
1
2
1
0
0
0
2
0
1
1
0
0
0
0
0
0
2
1
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
1
2
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
1
1
1
0
2
0
0
0
0
2
0
2
1
0
2
0
1
0
1
1
2
0
0
2
2
2
0
0
8
0
0
1
0
0
0
0
0
0
1
0
0
2
0
1
2
0
0
0
0
0
2
1
2
0
1
0
0
2
2
1
2
1
0
1
0
2
0
0
1
0
2
0
0
0
1
0
0
0
1
2
1
0
0
2
1
4
0
0
0
0
0
1
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
1
2
0
0
2
0
2
1
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
6
0
0
0
0
0
0
0
2
2
0
0
2
1
2
0
2
0
1
0
2
0
0
2
0
1
0
0
0
0
1
0
0
2
0
2
2
0
4
0
0
2
2
2
3
0
2
2
1
0
0
2
1
0
3
0
0
1
0
2
2
2
1
0
0
1
1
0
0
4
1
0
2
2
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
1
0
2
1
0
0
0
1
2
0
2
2
0
1
0
1
2
0
1
1
0
0
0
0
1
0
2
0
2
2
1
0
0
2
0
0
0
1
0
2
2
0
0
0
2
0
0
1
1
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
2
0
0
2
2
1
3
1
0
0
1
2
0
1
0
0
0
5
0
1
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
2
1
0
1
1
0
0
0
2
0
0
0
3
0
0
0
1
0
0
1
2
2
0
2
3
0
0
1
2
0
0
1
0
0
0
0
2
0
0
0
2
0
1
0
1
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
3
1
2
1
0
0
2
0
0
0
0
1
1
1
0
0
0
0
2
1
0
0
2
1
0
0
0
2
0
0
0
0
0
2
2
0
1
1
0
0
2
0
1
0
0
2
1
0
0
1
0
0
1
5
0
1
0
0
2
1
1
2
0
1
0
1
0
0
1
2
1
0
0
2
0
1
2
0
0
0
0
0
0
1
0
0
1
0
0
2
2
1
0
2
0
0
2
2
0
1
0
2
1
0
0
0
1
2
0
0
0
2
0
0
0
2
0
0
2
0
0
0
1
3
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
2
0
1
1
0
0
2
1
1
2
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
2
2
1
0
2
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
1
0
0
1
0
2
1
0
0
1
2
2
0
2
1
0
0
1
1
2
0
2
0
2
0
2
1
0
0
2
2
1
0
0
2
1
2
0
2
2
0
0
2
0
0
1
2
0
2
2
0
2
0
0
1
1
1
0
2
1
2
0
0
0
1
1
0
2
0
0
0
0
2
2
1
1
0
0
1
0
0
0
2
1
2
0
0
0
0
0
0
1
1
0
0
2
2
2
2
0
0
0
0
0
2
2
1
1
0
1
3
0
0
0
0
1
0
1
1
2
2
0
0
0
1
0
2
2
0
0
0
2
0
2
0
0
2
1
4
0
1
0
2
2
2
0
0
0
2
0
0
0
4
2
0
0
1
0
2
1
0
0
1
0
1
1
0
0
0
2
2
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
1
1
0
1
0
0
1
0
0
1
2
1
1
0
0
2
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
1
2
0
2
1
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
1
0
2
3
0
0
0
0
1
1
0
2
0
0
0
0
2
2
2
0
1
0
0
0
0
1
2
1
0
2
0
0
1
2
2
2
2
0
0
1
0
0
0
0
0
0
2
0
0
2
2
2
0
0
3
2
1
0
0
2
0
1
2
0
0
1
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
2
0
0
2
1
0
0
1
0
0
0
0
1
0
0
0
0
10
1
0
2
1
1
0
2
0
0
0
0
0
0
0
2
0
2
0
1
0
4
0
0
0
1
0
0
0
0
0
0
2
0
1
2
0
0
2
1
0
0
0
0
2
3
1
2
0
0
1
0
0
2
0
0
1
0
3
1
2
1
0
2
0
1
0
1
0
2
1
1
1
1
2
0
0
1
0
0
0
2
0
1
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
2
0
0
0
1
2
0
2
0
3
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
2
2
0
2
2
1
0
0
0
0
0
1
0
2
0
2
0
2
0
0
2
2
0
0
0
1
2
2
2
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
2
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
2
0
0
4
1
0
0
0
0
2
0
2
0
2
1
2
0
2
1
2
0
1
2
0
1
2
0
1
0
0
0
1
0
2
0
0
0
0
0
0
1
3
2
0
0
2
2
1
0
0
1
2
3
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
2
0
0
1
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
2
0
1
0
0
1
0
1
0
0
2
2
0
0
0
0
0
0
1
4
0
0
0
2
0
1
1
2
0
2
0
2
0
0
2
0
0
2
0
0
0
0
0
1
1
0
0
0
3
1
0
2
0
0
0
2
2
0
1
0
0
3
0
1
0
0
3
0
0
0
0
1
0
2
2
0
0
0
1
3
0
0
0
1
1
2
0
1
2
1
0
2
0
0
0
1
1
1
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
2
1
1
0
2
0
0
0
2
0
2
0
0
0
2
0
1
0
1
1
0
0
0
2
0
1
0
0
1
2
0
0
0
0
2
3
0
0
0
0
2
2
1
2
0
0
0
0
0
2
0
0
0
1
0
2
0
1
3
0
2
0
0
0
0
0
1
0
1
0
2
0
2
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
1
1
0
0
0
1
2
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
2
0
0
0
0
3
0
1
0
1
0
0
0
1
1
2
0
0
0
0
2
3
0
3
0
1
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
1
0
0
0
1
1
2
1
1
0
1
0
0
0
0
1
2
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
3
3
2
0
1
1
0
0
0
2
0
0
0
0
2
2
2
2
0
2
0
0
2
0
2
1
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
5
1
1
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
1
0
0
0
1
0
0
1
0
2
0
0
2
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
1
0
1
2
1
0
1
1
0
2
0
0
0
3
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
2
0
0
2
2
0
1
2
2
1
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
3
0
0
2
1
1
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
4
1
0
0
0
2
2
0
2
2
0
0
0
2
0
0
0
1
0
2
0
0
3
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
2
2
0
0
1
0
2
1
2
2
1
0
0
2
0
1
1
1
0
2
0
2
0
0
3
1
0
0
0
1
2
3
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
1
2
3
1
0
0
1
0
0
1
2
0
0
0
0
0
0
0
2
2
0
0
2
1
0
0
1
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
3
1
2
0
0
1
0
0
0
1
0
0
0
2
0
0
1
0
0
1
0
0
1
1
0
1
0
0
0
0
2
1
0
0
0
0
1
0
0
1
2
1
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
1
2
0
2
0
5
1
2
1
0
0
1
1
0
0
1
0
0
3
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
2
0
0
0
0
0
1
1
0
2
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
1
2
0
0
0
0
0
1
0
0
2
0
1
0
1
0
0
0
0
0
0
1
0
2
0
0
2
1
0
0
3
0
0
1
1
0
1
0
1
0
0
0
2
0
0
0
2
0
0
2
0
0
2
0
0
2
0
2
0
0
0
2
2
0
0
0
1
0
0
2
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
2
0
2
2
0
0
2
0
0
0
0
2
3
0
2
0
0
0
2
0
1
0
0
0
0
0
1
1
0
1
1
2
3
1
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
1
2
0
0
0
1
0
0
2
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
1
0
0
0
0
0
1
0
0
0
0
0
2
0
1
2
0
0
0
3
0
0
0
1
0
2
2
0
0
0
2
0
0
0
0
0
1
0
1
0
1
0
2
0
0
1
1
0
2
0
1
0
0
0
0
2
1
1
1
4
0
0
0
0
0
5
0
1
1
0
2
0
1
0
0
2
0
0
0
2
2
0
2
1
0
2
2
3
1
0
2
1
2
2
0
2
2
2
0
0
0
1
0
0
1
0
0
1
1
1
2
0
0
2
1
0
0
0
0
0
1
1
0
2
1
1
1
2
1
0
2
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
2
0
0
0
0
0
0
0
1
2
0
2
1
0
1
2
0
0
2
0
0
0
0
1
0
1
0
2
1
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
5
2
1
0
0
0
0
1
0
0
2
2
0
0
0
2
0
2
0
1
2
3
0
3
0
2
0
2
1
2
0
0
0
0
0
3
0
0
0
1
0
1
2
0
0
1
0
2
0
0
0
0
3
1
0
0
0
0
0
0
2
1
0
0
0
1
2
0
2
0
2
1
0
0
0
0
0
0
2
0
2
0
1
0
2
1
0
0
0
0
2
0
0
0
0
2
3
1
1
0
1
0
0
1
0
1
0
0
0
2
0
0
2
1
0
1
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
4
0
2
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
2
1
0
0
0
0
0
1
0
0
0
0
2
1
2
0
0
2
0
0
0
1
2
0
1
2
0
2
2
0
0
3
0
0
0
0
0
0
2
3
0
0
0
2
0
0
3
2
0
2
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
2
0
0
1
0
1
1
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
1
0
1
0
0
0
2
3
2
0
2
0
1
0
2
0
0
0
0
1
0
0
1
0
2
1
0
4
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
3
0
0
2
1
0
0
0
0
0
0
0
0
0
1
1
2
1
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
2
4
0
1
3
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
1
1
4
0
0
2
2
0
1
1
0
2
0
0
5
0
0
0
0
1
0
0
1
0
0
2
0
2
0
1
0
2
0
0
0
0
0
3
0
0
0
0
0
0
1
0
2
0
0
2
0
1
0
1
1
0
0
0
0
0
2
0
0
0
0
1
1
0
2
0
1
1
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
2
0
0
0
1
0
0
0
1
0
2
0
0
0
0
1
0
1
0
1
1
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
5
0
0
0
0
0
0
0
0
0
1
2
2
1
0
2
0
2
2
0
0
1
0
0
0
2
1
0
0
2
1
0
1
0
1
2
1
2
0
4
0
2
1
0
0
1
2
2
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
2
0
1
2
1
2
0
2
0
2
0
2
0
0
0
0
0
0
0
2
0
0
2
1
2
2
1
0
0
0
1
0
0
0
0
0
0
2
2
0
1
3
2
0
0
1
0
2
0
0
0
0
0
1
2
1
0
0
0
2
0
2
1
0
0
2
0
0
2
1
2
0
2
1
0
1
0
0
0
0
2
1
1
1
0
1
0
2
2
0
0
2
0
0
1
0
1
0
0
0
0
0
0
1
0
0
2
0
0
3
0
0
0
2
1
0
1
3
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
1
1
0
0
1
0
2
0
1
0
1
0
0
0
2
0
0
0
1
0
0
2
0
0
0
2
0
0
0
1
0
1
0
0
0
2
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
4
0
2
0
1
0
3
3
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
2
2
1
0
0
0
0
2
0
0
2
0
0
0
2
1
0
1
0
0
0
0
2
0
2
1
1
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
3
0
0
0
2
0
0
1
1
0
0
0
0
0
1
0
1
2
0
0
0
0
1
1
1
2
2
1
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
2
0
0
2
1
1
0
1
0
2
1
0
0
1
0
0
2
2
0
1
0
0
0
0
0
0
5
0
2
0
0
2
1
0
2
2
0
1
0
2
0
0
0
0
0
2
0
1
1
0
0
0
0
3
0
0
0
0
2
2
0
0
0
0
0
0
2
0
3
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
2
1
0
0
0
1
0
0
0
2
0
0
0
0
2
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
1
2
0
1
1
0
2
2
0
0
1
2
0
1
4
0
0
0
1
0
0
0
0
1
0
0
0
0
1
2
0
1
0
0
2
0
0
0
0
0
3
2
0
0
0
1
0
0
0
2
0
0
2
2
0
0
1
0
0
1
2
1
0
1
0
2
2
2
2
0
0
0
3
0
0
0
0
2
0
4
0
0
0
1
0
0
2
0
1
0
0
0
2
0
0
0
3
1
0
0
0
0
0
0
0
0
1
2
4
0
0
0
0
0
0
2
0
1
0
2
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
2
0
2
1
2
2
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
2
0
1
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
1
2
1
0
0
1
2
1
0
0
0
1
0
1
0
1
0
0
0
2
1
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
2
0
0
0
3
2
2
0
0
0
0
0
0
1
3
1
0
0
1
0
0
0
1
0
1
2
1
2
0
0
1
0
0
0
0
0
2
2
0
0
1
0
1
1
2
0
0
0
0
1
0
2
2
2
0
0
0
2
2
1
2
0
0
2
0
0
0
1
0
0
2
0
2
0
2
0
2
2
0
1
0
0
1
0
0
0
0
0
2
1
0
2
0
0
0
0
0
1
0
0
0
0
1
2
0
0
1
2
0
1
0
0
2
0
0
0
0
1
0
0
1
1
0
2
0
0
0
3
1
0
2
1
2
0
0
1
2
2
2
0
0
1
0
2
2
0
1
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
1
0
0
1
0
2
0
0
0
0
0
0
1
0
0
2
1
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
1
1
0
2
1
2
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
2
1
0
0
3
0
0
1
1
0
0
0
2
0
0
1
0
3
0
0
0
3
2
0
1
0
1
0
0
0
1
0
2
0
1
2
0
0
0
0
2
2
2
2
0
1
0
0
1
0
0
1
0
0
0
3
0
1
0
0
0
2
2
2
0
0
1
2
0
0
0
1
0
1
0
0
0
0
1
0
1
0
2
0
0
0
0
1
2
0
0
2
0
2
2
0
0
1
0
0
1
0
2
0
0
1
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
2
0
0
11
0
1
2
0
0
2
2
0
1
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
2
0
0
1
1
0
0
0
0
1
2
2
1
0
0
0
1
4
1
0
2
0
0
1
1
0
1
2
0
0
0
0
0
3
2
2
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
3
0
0
0
5
0
2
0
0
0
0
0
1
0
1
2
0
1
0
0
2
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
4
2
2
0
0
0
0
0
0
0
1
1
1
1
2
0
0
1
0
0
0
0
0
0
1
0
2
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
1
0
2
0
0
2
1
1
0
2
0
0
0
0
4
1
2
0
2
2
0
1
0
0
0
1
1
0
0
0
2
1
1
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
1
0
1
0
0
0
0
2
1
0
1
1
0
0
0
0
0
1
0
0
2
1
0
0
0
0
1
2
0
0
1
2
0
2
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
1
0
1
2
0
0
0
0
0
2
1
1
0
0
2
0
2
1
1
0
0
0
0
0
0
0
2
4
2
1
0
1
0
1
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
1
2
1
0
0
1
0
2
0
0
0
1
2
0
0
0
0
2
1
1
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
2
0
1
2
2
0
0
0
0
0
0
2
1
0
1
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
1
1
0
2
2
1
0
0
0
2
1
2
0
2
1
1
0
0
0
0
1
1
0
1
2
0
0
0
2
0
0
1
1
0
1
0
0
0
0
2
0
0
1
1
0
0
0
2
0
0
0
0
0
2
0
0
1
2
1
1
1
0
1
2
0
0
2
0
0
0
1
0
2
1
1
0
3
2
1
0
2
0
1
1
0
1
1
0
0
0
0
0
0
0
0
2
2
2
0
1
1
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
2
0
1
0
1
1
1
1
0
1
0
1
1
0
1
2
1
0
0
2
0
0
0
1
3
1
0
1
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
2
1
0
0
1
1
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
1
2
2
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
1
0
2
0
2
1
1
0
0
0
2
2
0
4
0
0
2
0
2
0
0
0
0
0
0
1
1
1
0
0
1
0
2
0
0
1
1
0
0
0
0
0
0
1
2
1
2
0
0
0
0
0
0
1
0
0
0
2
2
0
1
0
1
1
2
0
0
2
0
1
0
0
1
0
2
2
0
0
1
0
1
0
1
0
1
0
0
0
0
1
2
0
1
1
0
0
2
0
0
2
0
1
0
0
0
0
1
2
0
0
0
2
0
1
0
0
0
0
0
2
1
1
0
2
1
0
0
0
0
0
0
0
2
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
2
0
1
0
0
2
0
0
0
0
1
0
1
0
0
0
0
2
2
2
2
0
0
0
0
2
0
0
2
1
0
0
0
2
0
0
2
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
1
2
2
1
3
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
1
0
1
2
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
1
3
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
1
1
1
0
0
1
0
0
1
2
1
0
1
0
0
0
0
0
0
2
2
1
0
0
1
1
2
2
3
0
1
0
0
2
1
2
0
0
0
0
0
0
2
1
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
2
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
1
0
0
0
0
2
1
0
0
1
0
0
0
0
0
1
0
1
0
2
0
0
1
1
0
0
0
2
2
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
2
0
2
1
0
0
1
1
0
2
1
0
0
0
0
4
0
0
0
0
0
0
0
0
1
2
1
2
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
2
1
0
0
0
0
0
2
0
1
2
0
0
0
0
1
1
1
0
1
0
2
0
1
0
0
0
3
0
3
0
0
2
1
1
1
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
1
0
0
0
0
0
1
1
0
0
1
2
0
0
1
1
1
1
0
0
3
0
0
0
1
2
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
2
2
1
1
1
0
0
1
1
0
1
0
0
0
1
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
1
2
0
0
0
1
0
0
0
0
0
2
2
0
1
0
0
0
1
0
3
1
0
0
1
0
0
0
0
0
0
1
2
0
2
2
0
0
0
0
0
2
0
3
2
0
2
0
0
1
0
1
0
0
2
0
2
2
1
2
2
0
0
2
0
1
2
2
0
4
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
3
2
0
1
1
0
0
0
0
2
1
0
0
1
0
0
0
0
0
1
1
0
1
0
0
1
0
1
2
0
1
0
0
1
0
0
2
0
0
0
0
2
0
2
1
0
2
0
0
0
0
0
5
2
0
0
1
2
0
2
0
0
0
0
0
2
2
0
0
1
1
2
0
0
0
0
0
2
1
1
0
0
2
2
0
0
2
0
1
0
0
0
0
0
0
2
2
0
1
1
1
0
2
0
0
0
0
0
0
0
2
2
0
0
2
0
2
2
1
0
0
2
2
1
0
0
2
0
0
2
0
0
0
0
1
1
1
2
0
2
0
1
0
0
1
0
1
1
0
1
2
0
1
2
1
0
0
2
0
0
0
1
0
1
1
0
0
1
0
0
2
0
0
0
2
2
1
0
0
0
0
0
0
0
5
0
0
0
0
1
0
6
0
2
0
0
1
2
2
1
2
2
0
2
2
0
0
0
0
2
1
0
0
1
2
0
0
1
2
0
0
0
0
0
0
1
2
0
1
2
1
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
2
2
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
1
0
2
0
0
3
0
1
0
0
0
0
2
2
0
0
0
0
0
0
1
0
2
0
2
2
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
3
0
0
0
0
0
2
1
1
0
0
0
0
2
1
1
0
3
0
2
0
0
1
2
2
2
0
0
0
2
1
1
0
1
0
0
1
0
0
3
0
1
2
1
0
0
1
2
3
0
0
1
2
1
2
0
0
0
0
2
0
0
1
2
0
0
0
1
2
0
0
1
0
2
0
0
0
2
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
1
2
2
0
0
2
0
0
0
0
2
2
2
0
0
0
0
2
2
0
0
0
0
1
2
0
0
1
1
1
0
0
0
1
0
0
2
0
0
0
0
0
3
0
0
0
2
2
1
2
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
1
1
0
0
2
0
2
2
3
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
2
0
1
2
0
0
2
0
2
0
2
0
1
0
0
1
0
2
0
0
0
1
0
0
1
0
2
2
0
0
1
2
0
0
0
0
0
0
0
1
2
0
0
2
1
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
2
1
2
2
0
0
0
0
0
0
0
0
2
1
1
1
0
2
0
2
0
0
2
1
1
1
0
1
1
1
2
1
0
2
0
1
2
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
2
0
2
0
1
0
0
0
2
0
0
0
0
2
1
2
0
0
2
2
1
2
1
1
0
2
0
0
0
0
1
0
0
0
1
2
0
1
0
1
0
0
0
0
0
1
1
0
0
1
0
0
1
1
0
1
0
0
2
0
0
0
4
0
1
0
0
0
0
0
1
2
0
2
0
1
0
0
0
2
0
0
1
1
0
2
1
0
2
0
0
0
0
0
0
1
0
1
2
2
2
2
0
0
2
0
0
0
0
1
0
3
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
1
0
0
0
1
0
0
2
2
0
0
2
0
0
1
0
2
0
0
2
4
1
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
2
0
0
0
0
7
1
1
0
0
0
0
0
2
0
1
2
0
3
0
0
0
0
0
1
7
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
2
0
0
2
0
0
1
0
0
1
0
1
1
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
1
1
0
0
0
0
0
4
1
0
0
2
0
2
0
0
0
0
4
0
0
2
0
0
0
0
0
0
2
2
0
1
1
0
1
2
0
0
0
2
2
1
0
0
2
0
0
0
5
0
0
2
1
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
1
0
0
1
2
0
0
2
0
2
0
0
1
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
1
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
2
0
1
0
0
2
1
1
1
0
1
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
1
2
0
0
2
2
0
0
0
0
0
0
2
2
0
1
0
1
2
2
3
2
0
0
0
0
1
0
0
0
0
0
2
0
1
1
1
0
0
0
2
0
0
0
0
0
0
0
0
1
1
1
2
2
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
2
1
0
0
1
0
2
1
0
0
1
0
0
0
2
0
0
1
0
0
0
1
0
1
0
0
0
0
5
2
0
1
0
0
0
2
2
0
1
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
1
0
1
2
0
0
0
0
0
0
0
0
2
0
0
1
1
2
0
0
0
0
0
0
0
3
1
0
0
2
1
2
0
0
0
1
1
0
1
0
0
0
2
0
0
0
0
2
0
0
0
2
0
2
1
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
5
0
1
1
2
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
1
2
0
0
0
0
2
1
1
2
2
1
1
3
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
2
0
0
1
1
0
3
0
3
2
0
0
2
0
2
1
1
1
2
0
0
4
1
2
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
2
0
0
1
0
1
2
2
0
0
0
0
0
0
2
0
2
1
1
1
1
0
0
0
1
1
1
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
2
1
5
1
0
0
0
0
1
0
2
0
0
3
0
0
2
0
0
2
0
0
0
2
0
1
0
0
1
1
1
1
1
0
0
0
0
0
0
0
2
1
0
0
0
1
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
2
0
2
0
3
1
1
1
1
1
0
0
0
1
0
2
0
0
2
3
0
2
2
0
1
0
1
1
0
0
0
1
0
0
0
2
0
2
1
0
1
1
1
0
0
6
0
1
0
0
0
0
0
1
1
1
0
1
0
1
1
0
0
0
0
0
3
4
0
2
1
1
0
0
0
0
0
1
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
2
1
0
3
1
0
2
0
0
0
0
2
0
0
1
2
2
0
0
1
2
1
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
1
0
2
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
1
0
0
0
0
0
0
5
0
0
1
2
2
0
1
0
0
0
2
0
1
0
0
0
0
2
0
1
0
0
0
0
2
1
0
1
0
2
3
0
0
0
1
2
3
0
0
0
0
2
0
1
0
0
0
2
0
1
0
1
0
0
3
0
0
2
0
0
0
0
2
1
0
2
0
1
0
0
2
0
2
1
1
0
2
2
0
1
2
0
2
0
2
0
1
2
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
1
2
0
1
2
0
0
2
0
0
1
0
0
0
0
0
2
0
1
1
0
0
0
0
2
1
0
0
1
1
1
1
0
0
2
2
2
0
0
0
0
1
0
4
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
2
1
0
0
2
0
2
0
0
0
0
0
0
0
1
0
3
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
2
1
0
0
0
1
2
2
2
0
0
2
0
1
1
0
0
2
0
2
2
0
1
2
0
0
1
0
0
0
2
0
0
0
0
0
2
2
0
3
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
1
0
1
0
1
0
2
2
0
1
0
2
1
1
0
1
0
0
0
0
1
0
0
1
1
1
0
0
0
2
0
0
2
1
0
1
1
2
0
2
2
1
0
1
3
1
0
1
0
0
1
2
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
2
0
2
0
0
0
1
0
0
0
0
0
2
1
0
0
0
1
0
3
3
2
1
0
1
1
0
0
2
0
0
1
0
0
0
0
0
0
1
2
2
1
0
1
0
0
0
1
0
0
2
1
0
0
1
0
2
0
1
0
0
0
0
0
0
1
0
0
0
1
0
2
1
0
0
1
0
0
0
0
0
0
1
1
2
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
2
0
2
1
0
0
2
0
0
0
1
0
0
2
0
0
3
0
0
0
0
0
3
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
2
0
1
0
0
2
1
0
0
0
1
2
1
0
0
0
1
0
2
0
4
0
2
0
0
2
2
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
2
0
0
0
1
0
2
1
0
0
0
1
1
0
0
0
2
2
3
1
2
0
1
0
0
1
0
0
0
0
0
2
0
0
2
0
1
0
0
1
0
2
2
1
0
2
0
0
2
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
1
0
2
0
0
0
0
1
1
0
1
0
2
2
1
0
2
3
0
0
1
1
0
0
0
2
0
2
1
0
0
2
0
0
0
1
1
0
1
0
0
1
0
2
1
1
0
0
0
0
0
0
1
0
0
2
2
3
1
2
1
1
2
2
2
0
0
0
1
0
4
2
2
0
2
1
0
2
2
0
0
2
0
0
0
0
1
2
1
0
0
1
0
1
0
2
0
0
0
1
0
0
0
0
0
1
3
0
2
0
0
2
0
1
0
0
1
1
1
0
0
0
2
2
0
1
0
2
0
2
2
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
1
2
0
0
7
0
0
0
1
0
1
1
0
0
2
0
0
1
0
1
2
2
1
2
1
1
0
2
1
2
0
0
1
2
0
1
3
0
0
2
1
0
0
0
0
1
0
0
0
2
1
0
2
0
1
2
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
2
2
0
0
2
0
2
0
1
1
0
0
0
0
2
0
0
2
0
1
1
0
0
1
0
0
0
2
0
0
0
1
0
1
0
1
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
3
0
0
0
0
0
0
1
0
1
2
0
2
2
2
1
0
0
2
2
0
0
1
0
2
0
0
0
0
1
0
2
0
0
0
0
0
1
1
0
1
2
1
4
2
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
2
2
0
0
0
0
1
0
0
0
0
0
2
2
0
1
2
0
0
2
0
1
0
1
0
0
1
0
0
0
1
1
0
0
1
2
2
0
0
1
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
1
1
2
0
0
0
2
0
0
1
0
0
1
0
0
1
2
0
0
0
0
2
1
1
0
0
0
2
0
0
3
1
2
4
2
1
0
0
1
1
0
1
0
3
1
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
2
1
2
0
2
1
2
0
0
0
0
0
1
1
0
0
0
2
1
0
1
0
1
2
0
0
3
2
0
0
0
2
1
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
4
1
0
0
0
0
0
1
0
0
1
2
0
0
0
0
1
0
2
0
2
2
0
0
1
2
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
1
2
0
4
0
0
0
0
0
1
1
2
0
0
0
2
1
0
1
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
1
0
2
2
1
0
0
0
0
1
0
1
0
0
0
2
0
2
1
1
0
2
2
0
0
1
0
0
0
0
0
0
2
2
0
0
1
0
2
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
2
1
0
0
0
2
0
2
0
1
0
0
0
0
4
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
3
2
0
1
0
1
0
0
0
2
1
2
2
0
0
0
0
0
0
0
1
1
1
0
1
2
0
0
0
2
1
1
1
1
0
0
0
0
0
0
0
2
1
1
0
0
1
0
0
0
0
0
0
0
0
2
1
1
2
1
0
0
0
0
1
0
2
1
0
0
0
1
2
0
0
2
1
0
1
1
0
0
0
1
1
1
0
0
0
0
0
0
1
1
2
0
2
0
1
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
2
1
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
2
1
1
0
0
0
0
1
0
1
0
1
1
0
1
0
0
2
3
0
0
0
0
1
1
0
0
2
1
1
0
0
1
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
1
0
2
2
0
1
2
1
0
1
1
2
1
3
1
0
0
2
0
1
0
0
1
0
2
1
0
2
2
0
2
2
0
2
1
1
0
1
0
0
1
0
0
1
0
0
1
1
2
0
2
1
0
1
0
0
2
0
0
2
2
0
1
0
0
0
2
0
0
0
1
0
1
1
0
0
0
1
2
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
3
3
1
0
1
0
1
0
2
0
2
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
2
2
1
0
1
2
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
2
1
1
2
1
0
1
0
0
1
0
0
2
1
1
0
2
1
2
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
2
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
1
0
0
1
0
0
2
0
1
0
1
2
0
1
0
0
0
0
2
0
0
0
0
0
6
2
1
1
2
0
0
1
4
0
0
0
1
1
0
0
2
0
1
0
0
0
2
0
2
0
1
0
3
3
1
0
1
1
0
0
1
0
0
2
1
0
0
0
0
0
1
0
0
1
1
2
2
0
0
0
2
2
0
2
1
1
0
0
3
3
0
0
2
0
0
1
0
1
0
0
0
1
0
0
0
2
0
1
0
0
0
1
0
2
0
2
0
1
1
0
1
1
0
2
0
0
0
0
0
0
0
1
1
0
2
0
1
2
1
0
0
0
1
0
1
0
0
2
0
0
1
0
2
0
4
0
1
0
2
2
2
0
0
0
3
1
0
0
0
0
0
0
0
0
2
3
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
2
1
2
0
1
0
1
0
1
0
0
0
2
0
2
0
0
0
0
1
2
1
0
0
0
0
0
1
0
2
0
0
0
1
2
0
2
0
2
0
0
0
0
0
1
2
2
0
2
2
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
2
0
2
1
1
0
2
3
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
1
2
0
0
0
0
0
1
0
2
2
1
0
0
1
1
0
0
1
0
1
2
1
0
0
0
0
2
0
0
1
0
1
1
0
0
0
0
0
0
0
0
2
2
1
0
2
0
2
0
0
2
2
3
0
0
0
1
0
0
1
2
0
0
0
1
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
2
2
1
0
0
0
1
0
0
2
1
1
0
0
0
2
1
2
2
1
0
0
0
0
0
3
2
0
1
0
0
0
0
0
0
0
1
1
0
2
1
0
0
0
0
1
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
2
0
2
0
2
2
2
4
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
1
1
0
0
1
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
1
2
0
3
0
0
0
0
1
3
1
3
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
1
2
0
0
0
1
2
0
0
0
0
1
0
0
0
2
0
0
0
2
0
2
0
1
2
0
2
0
2
0
1
1
2
2
1
0
0
1
3
9
2
0
0
0
0
1
0
0
0
1
0
0
2
0
2
0
0
0
0
2
0
1
0
0
1
1
1
0
3
0
0
0
0
0
2
0
0
0
2
0
0
1
2
0
0
2
1
3
1
1
0
1
0
0
0
2
0
1
0
0
0
0
2
1
0
2
0
0
2
0
0
0
0
1
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
3
0
0
0
0
0
2
0
0
0
0
2
0
1
1
0
0
1
0
0
2
0
0
1
2
0
0
0
1
2
0
1
0
0
2
0
2
2
0
1
2
1
2
2
0
2
1
0
1
0
0
0
0
0
0
2
0
2
0
3
0
1
0
0
0
0
0
0
0
1
0
0
2
1
3
0
0
1
0
2
0
1
0
2
2
1
0
0
1
0
1
1
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
1
2
1
0
1
2
1
1
2
2
0
2
0
2
0
1
0
0
0
2
0
0
0
0
3
1
0
0
0
1
1
0
0
2
1
1
2
0
2
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
3
1
0
0
0
3
2
1
0
1
0
2
0
2
0
0
0
0
0
0
1
0
0
0
2
2
1
0
0
0
2
0
2
0
0
1
0
2
0
1
0
1
0
2
0
3
2
2
0
0
0
0
2
1
0
0
2
2
2
2
0
1
0
2
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
2
1
2
0
1
0
0
0
1
0
4
0
0
0
0
1
0
0
2
0
0
1
0
0
0
1
0
1
1
0
0
2
1
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
2
2
0
1
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
1
0
0
2
2
1
0
0
3
0
0
0
0
2
1
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
1
1
0
2
0
0
0
0
0
0
0
1
2
2
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
1
3
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
1
0
2
2
0
0
2
2
1
0
0
0
0
2
0
0
0
4
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
2
1
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
2
0
2
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
2
0
0
0
2
0
0
1
0
1
1
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
1
1
1
0
1
3
0
3
2
0
0
1
0
1
0
0
1
3
1
2
0
2
0
1
0
0
0
0
3
0
0
2
2
1
1
1
0
0
0
5
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
3
0
1
0
1
2
2
0
0
0
1
1
0
0
0
1
2
1
0
0
0
0
2
0
0
0
2
0
0
0
2
1
2
4
1
0
2
2
0
0
1
0
0
0
2
0
2
2
1
2
0
0
0
1
2
2
0
2
1
0
0
0
1
2
0
0
0
0
1
1
0
0
2
1
0
2
1
0
1
1
1
2
2
0
1
2
0
0
1
0
0
0
0
0
0
0
1
1
1
2
2
1
0
0
0
0
0
0
1
0
1
2
0
1
2
1
0
2
2
1
0
0
0
1
1
2
0
0
3
2
0
0
1
0
0
1
0
0
2
0
2
2
2
1
0
0
2
1
2
1
0
0
1
0
1
0
0
0
0
2
1
0
0
0
1
1
0
0
0
1
0
2
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
3
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
2
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
2
0
6
1
0
0
0
2
0
1
0
3
1
2
0
0
0
0
2
0
2
1
0
2
0
1
0
0
0
0
0
0
0
1
2
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
2
1
2
0
0
0
2
0
0
0
0
1
0
1
0
0
0
1
0
1
0
1
0
2
0
2
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
1
2
0
1
0
1
0
0
1
0
2
1
0
1
1
1
1
0
0
1
0
2
0
0
1
0
0
2
2
0
0
1
1
2
1
0
2
0
2
1
0
0
0
0
1
0
0
0
0
1
0
2
1
0
1
4
0
2
2
1
0
2
0
0
0
2
0
0
0
2
2
1
2
0
0
0
0
2
0
0
2
0
1
0
2
0
1
0
1
0
1
0
1
1
0
0
0
1
0
1
0
0
0
0
3
0
1
0
0
0
1
1
2
0
0
0
0
1
0
0
2
0
1
1
0
0
1
0
2
0
0
0
1
2
2
0
0
0
0
2
5
0
0
0
10
0
0
1
0
3
0
0
0
0
2
0
2
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
1
1
0
0
0
0
1
2
0
0
0
1
0
1
0
0
0
1
0
0
0
2
0
4
0
1
5
0
0
0
0
2
1
0
0
2
0
0
2
0
2
0
1
1
0
1
1
2
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
2
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
2
0
0
2
1
0
0
0
2
1
0
1
2
0
0
0
0
2
0
0
0
0
0
2
0
1
1
0
0
0
0
0
2
1
0
2
0
2
0
0
0
1
1
0
1
0
0
0
0
1
3
0
0
1
0
1
0
3
0
1
0
5
0
0
2
0
1
0
2
2
0
0
2
1
0
0
0
0
0
1
0
0
0
0
2
0
2
1
0
1
0
0
0
1
0
0
0
3
0
0
0
0
2
0
1
3
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
1
0
1
1
0
0
3
1
0
1
0
1
2
0
0
0
2
0
0
2
0
0
0
2
1
0
0
0
0
2
0
2
0
0
0
0
3
0
1
0
0
0
1
0
0
1
1
0
1
2
1
1
0
0
0
0
0
1
0
1
1
2
1
2
2
0
0
1
2
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
1
0
0
2
0
0
2
1
6
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
1
0
0
1
1
0
0
1
2
1
0
0
0
0
1
1
0
0
0
2
0
0
1
1
2
3
0
0
2
2
2
0
0
2
0
0
1
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
1
2
0
0
2
1
0
1
0
1
0
0
0
1
1
0
0
2
1
2
0
2
0
2
0
0
1
1
1
3
0
2
0
0
0
0
2
0
0
2
0
1
0
2
0
2
0
2
1
0
1
0
1
4
0
0
0
2
2
2
0
0
0
0
1
0
0
0
0
0
0
1
2
2
0
2
0
0
0
0
0
1
0
1
0
0
0
0
3
0
1
0
0
0
2
0
0
0
1
0
0
0
0
2
5
0
1
1
2
0
0
0
0
0
0
1
0
0
0
4
0
0
6
0
2
0
2
1
0
2
0
1
2
0
0
1
0
0
0
1
0
0
0
0
3
2
2
1
2
0
0
0
0
1
0
2
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
1
1
0
1
0
0
1
0
0
2
0
0
1
0
0
2
0
0
1
1
0
1
0
2
2
2
0
0
2
2
2
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
1
1
0
0
0
2
0
1
2
2
0
0
1
1
2
0
0
0
0
0
0
0
4
0
0
0
13
0
1
0
0
2
0
1
2
1
0
0
0
0
1
1
0
0
1
0
0
4
2
0
0
1
0
0
0
0
0
1
2
0
0
0
1
0
1
1
2
0
0
0
2
2
2
2
0
0
0
0
0
2
0
0
0
1
0
1
2
1
1
0
0
1
0
1
2
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
2
2
0
2
0
0
0
0
0
1
1
1
2
0
3
2
0
2
1
1
2
0
0
0
1
2
1
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
2
1
0
1
0
0
1
1
0
2
3
1
2
1
2
0
0
0
0
1
0
7
0
2
2
0
0
2
0
0
2
0
0
0
2
0
0
0
1
2
0
0
0
2
0
1
0
1
0
0
0
0
1
1
1
2
0
0
0
0
4
0
0
0
0
0
2
1
0
0
0
1
0
0
0
1
0
2
1
1
0
0
1
3
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
2
1
0
0
0
0
2
2
0
2
1
0
1
0
0
0
0
0
0
1
3
1
1
2
1
0
3
1
0
0
0
2
0
0
0
0
2
1
3
2
1
0
0
0
0
0
0
2
0
1
1
1
2
3
2
0
1
1
0
0
0
2
2
0
0
0
0
2
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
1
7
0
0
2
0
1
2
1
0
2
0
0
2
2
2
0
0
2
1
1
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
2
0
2
0
0
1
1
0
0
2
0
0
7
0
0
2
0
0
0
2
0
1
2
1
0
0
1
0
0
1
1
1
2
0
0
0
0
5
1
0
2
2
1
0
2
0
2
0
0
0
2
0
1
2
2
0
2
0
0
0
0
1
0
2
1
0
0
0
0
0
0
1
0
0
1
0
1
2
0
0
1
2
2
0
0
0
0
1
1
0
2
0
0
0
1
0
0
2
1
0
0
0
2
0
0
2
0
1
3
2
0
0
0
1
0
2
0
1
0
0
1
2
1
1
0
0
0
0
0
0
0
2
0
1
0
1
1
0
0
0
2
1
1
2
0
0
0
2
0
0
2
0
0
0
0
2
2
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
1
2
2
0
0
0
1
0
0
0
1
0
0
2
2
0
2
3
0
2
1
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
1
0
1
0
1
1
0
0
0
0
0
1
0
0
2
0
1
0
2
0
0
2
0
2
0
0
0
2
1
0
2
1
1
1
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
1
0
0
2
0
1
0
0
0
2
2
0
0
0
1
0
1
3
0
0
2
0
0
0
0
0
1
0
0
0
1
4
0
0
0
1
0
0
1
1
1
0
0
0
1
0
0
2
0
0
0
2
0
2
0
0
0
0
2
1
1
0
0
1
0
1
0
1
2
1
0
0
0
0
0
2
0
0
0
0
0
3
1
2
0
0
0
2
0
2
0
1
0
2
2
0
0
0
2
0
0
1
0
1
1
1
2
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
2
1
0
0
1
3
0
2
1
0
1
2
0
0
1
0
0
0
0
1
2
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
1
0
0
2
10
2
0
2
0
1
1
2
0
0
0
1
1
0
0
0
2
0
0
1
1
1
0
0
1
2
1
1
1
0
0
2
0
2
0
0
1
1
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
2
0
3
0
0
0
2
0
0
1
0
0
1
0
0
2
0
0
3
0
2
0
1
0
2
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
3
0
2
1
2
1
0
0
1
0
0
0
0
0
0
2
2
0
2
0
0
0
2
1
0
2
0
0
0
0
1
1
0
1
1
0
1
1
0
0
2
1
0
0
0
1
0
2
1
3
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
2
0
0
2
0
2
0
0
0
0
1
0
1
0
1
0
2
0
2
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
1
1
0
0
0
1
0
0
0
2
0
1
1
0
2
1
0
0
0
2
2
0
1
0
1
0
1
0
0
1
0
3
1
0
0
0
2
2
3
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
2
2
2
0
1
0
1
2
0
0
0
0
0
0
0
1
2
0
2
0
1
0
2
2
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
1
0
2
0
0
0
1
2
0
2
0
0
0
1
0
0
0
0
1
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
2
0
0
0
1
0
1
0
0
1
1
0
2
1
1
1
1
2
1
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
2
0
2
0
0
0
1
0
3
2
2
1
0
2
1
2
0
0
0
2
0
0
0
0
0
0
1
1
2
0
0
0
0
1
0
1
1
0
1
1
0
1
1
0
2
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
3
2
1
2
1
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
3
0
2
0
0
0
1
1
2
0
1
1
0
0
3
0
0
0
0
2
0
0
5
0
2
0
0
0
1
2
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
1
0
1
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
2
0
0
0
0
1
0
3
0
0
0
2
0
1
0
0
0
2
2
0
1
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
2
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
1
1
0
0
0
0
2
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
2
2
1
0
0
0
0
2
2
2
0
0
0
2
0
2
0
0
0
2
2
2
0
0
0
2
1
0
0
1
0
0
0
0
1
0
0
0
1
0
2
0
0
1
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
2
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
2
1
0
0
0
0
0
2
2
2
2
1
2
2
0
0
0
1
4
1
0
1
1
0
0
3
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
2
0
2
2
0
0
2
2
0
0
2
2
1
0
0
0
0
0
0
0
1
1
0
0
3
0
0
0
0
0
3
0
3
0
2
3
0
2
2
1
0
1
1
0
1
1
0
0
2
2
0
2
1
2
0
0
1
0
0
0
1
1
0
0
1
2
0
2
0
0
1
1
2
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
1
0
0
1
0
0
0
0
1
0
2
1
0
2
0
0
5
0
0
0
0
0
0
0
1
1
0
0
0
2
1
0
1
0
0
0
1
0
0
1
2
2
0
0
0
0
0
0
2
0
1
1
0
0
0
1
1
1
2
2
2
1
0
0
0
2
0
0
0
0
2
0
1
0
2
2
0
0
0
0
2
1
0
1
0
0
0
0
0
0
2
0
3
1
0
2
0
1
1
0
2
0
0
0
1
0
0
1
1
0
2
1
0
0
2
0
1
2
0
0
0
1
3
0
0
0
0
1
0
0
2
0
0
0
1
0
0
2
0
0
2
0
2
1
0
2
0
1
2
0
2
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
1
1
0
0
2
2
1
1
0
0
0
1
1
0
0
0
0
2
0
0
0
0
1
0
1
0
0
2
0
1
1
0
3
0
0
0
0
0
0
0
0
0
1
1
2
1
2
0
0
0
1
1
2
0
0
0
0
0
0
1
1
1
3
0
0
1
0
1
0
0
0
0
3
0
0
0
0
0
0
2
0
2
1
2
0
0
0
0
0
0
0
0
3
2
0
0
2
2
0
0
2
0
0
2
0
1
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
2
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
2
1
0
2
1
0
2
0
0
0
2
0
2
0
0
2
1
0
0
1
1
2
0
0
0
1
3
1
0
0
1
2
0
0
1
1
0
0
0
0
1
0
0
1
0
1
0
2
0
2
1
0
1
2
0
0
3
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
2
0
0
2
0
1
2
0
0
0
0
1
0
0
0
0
0
2
0
3
0
0
2
0
0
0
1
0
1
1
2
0
0
0
0
0
2
0
0
0
1
2
0
2
0
0
0
2
2
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
2
1
1
0
0
0
2
0
4
0
1
3
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
1
1
0
1
0
0
1
0
0
1
1
2
0
1
0
2
2
1
1
0
1
0
3
0
0
1
0
0
0
2
0
0
2
0
2
3
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
1
0
1
1
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
5
0
1
0
0
0
0
0
2
2
2
2
2
0
2
0
0
1
2
0
1
0
0
0
1
3
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
1
0
0
0
2
1
0
0
0
0
1
0
1
0
0
0
0
0
2
0
1
0
2
0
0
1
0
0
0
2
2
0
0
0
2
1
2
0
2
0
1
1
1
0
0
2
0
0
0
0
0
0
0
1
1
0
1
3
0
0
0
1
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
3
0
0
0
0
1
5
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
2
0
0
0
2
0
0
1
2
0
0
0
0
0
0
1
0
0
2
4
2
0
0
2
1
0
0
0
0
1
0
2
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
1
0
0
0
0
1
0
2
2
0
0
2
0
1
0
2
0
1
1
0
2
0
1
0
2
0
1
1
1
0
1
0
1
2
2
0
1
0
2
2
0
0
0
0
1
0
0
0
3
0
0
2
1
0
2
0
0
0
2
0
0
0
0
0
2
1
1
0
0
2
0
0
0
1
2
0
0
2
1
1
1
1
0
2
0
2
0
3
0
0
0
1
1
0
0
0
0
0
2
0
0
2
0
0
0
1
1
2
0
1
0
2
0
0
2
0
1
0
0
2
1
2
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
1
1
1
0
0
0
0
0
0
0
2
1
1
1
0
1
1
0
0
1
3
1
2
2
0
1
0
0
0
1
2
0
0
0
2
1
0
1
0
0
1
0
0
1
0
2
2
0
0
1
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
2
0
2
3
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
3
2
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
2
1
0
2
1
0
0
1
0
0
0
1
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
1
0
2
0
3
0
0
1
0
2
2
7
0
2
0
0
2
1
2
0
1
2
0
2
1
0
0
0
1
0
1
0
1
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
1
0
1
0
2
2
0
0
0
4
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
2
3
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
2
2
0
0
0
2
0
2
0
0
0
0
0
2
0
1
1
1
1
0
0
0
0
0
0
2
0
0
0
4
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
2
1
0
1
0
0
1
1
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
2
1
1
0
0
0
0
1
0
2
1
1
0
0
0
0
0
1
1
2
0
1
0
0
0
0
1
1
0
2
2
1
1
0
0
0
1
2
0
1
2
2
0
3
2
1
1
1
0
0
2
2
0
0
0
0
0
0
2
0
1
0
1
0
1
0
2
0
0
1
1
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
1
2
0
1
0
0
1
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
1
1
2
0
1
0
0
0
2
0
1
2
1
0
1
0
0
0
2
2
0
2
0
0
0
1
0
0
0
0
0
2
1
1
2
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
2
0
2
1
0
1
0
0
0
1
0
2
0
0
0
0
1
2
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
1
1
1
0
0
2
1
0
2
0
2
0
0
0
0
0
2
0
0
1
1
0
1
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
1
1
2
1
0
0
0
0
2
0
2
0
0
1
2
2
0
2
2
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
5
0
2
1
1
0
1
0
0
0
0
0
1
0
1
1
0
0
0
2
0
0
0
1
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
1
0
0
0
1
2
0
2
1
3
1
0
1
0
1
0
0
1
0
1
0
2
0
1
1
2
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
2
0
0
2
0
1
2
0
1
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
2
0
0
0
0
0
1
2
1
0
1
0
0
2
1
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
1
2
0
2
0
1
1
0
0
0
0
2
1
2
0
0
2
0
0
0
1
0
0
1
1
0
2
1
0
0
0
0
0
0
2
2
4
0
0
0
2
0
0
0
1
0
0
0
0
1
1
0
2
1
0
1
1
0
2
2
1
0
1
0
2
2
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
1
1
2
0
2
0
2
0
0
3
2
1
4
2
0
0
0
2
2
0
0
0
0
1
2
0
1
0
2
1
0
0
2
0
0
0
0
0
0
1
0
1
0
2
0
0
2
0
1
0
0
0
2
2
0
0
0
0
1
1
1
2
0
0
1
1
1
0
0
0
1
1
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
3
0
2
0
0
0
2
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
1
2
0
0
1
1
2
0
0
2
0
0
2
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
1
0
2
0
0
1
1
2
0
2
0
0
1
0
1
1
0
2
0
1
0
0
0
2
0
1
2
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
2
1
0
0
1
0
2
0
1
1
1
2
0
0
1
1
1
2
2
0
1
1
3
3
0
0
0
0
0
0
2
1
0
1
0
0
1
2
0
1
0
0
0
1
0
0
0
2
1
0
0
2
0
1
1
0
0
0
0
1
5
0
0
0
0
0
0
2
2
0
3
0
0
1
0
0
0
0
0
2
0
0
2
0
1
1
0
0
0
0
0
0
0
1
0
1
2
0
0
1
0
1
2
0
0
0
0
0
0
0
1
3
0
0
0
1
2
0
2
0
2
0
0
0
0
1
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
1
2
2
0
0
0
0
0
1
0
0
1
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
1
0
3
0
0
0
1
0
2
0
0
1
0
2
2
0
0
0
2
3
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
1
1
0
0
0
0
0
2
2
0
1
0
0
0
1
2
1
2
0
0
2
0
1
0
0
1
0
1
0
3
0
7
2
0
2
1
0
1
2
0
0
0
0
1
0
0
1
0
0
0
4
3
1
0
1
0
0
0
0
0
0
2
0
0
0
0
2
2
0
2
1
0
2
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
2
2
2
1
0
0
3
2
1
1
0
2
0
0
1
0
2
0
2
1
0
1
2
0
0
0
2
0
0
3
2
1
0
0
0
3
3
1
1
1
0
0
2
1
2
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
1
0
2
0
0
1
0
1
0
0
2
2
0
1
0
1
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
2
2
1
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
2
0
3
0
0
1
2
2
0
2
1
1
0
2
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
1
2
0
0
0
0
1
2
0
2
0
3
0
1
1
1
0
2
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
2
0
3
2
0
0
0
0
0
0
2
0
0
0
0
1
2
0
2
2
0
0
1
0
0
3
1
2
0
0
0
0
0
0
1
0
2
0
0
2
0
0
2
2
0
2
1
4
0
1
0
0
1
0
0
1
2
0
2
1
1
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
1
0
1
0
0
6
1
0
1
0
2
0
2
0
0
2
0
0
1
1
1
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
1
0
2
0
2
0
2
0
0
0
0
3
2
0
1
0
0
1
1
0
0
1
2
1
0
0
0
1
0
0
2
0
0
1
2
2
0
1
0
0
0
0
2
0
0
1
2
0
1
0
2
1
0
2
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
1
2
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
1
0
2
1
1
1
0
1
0
0
0
0
1
0
2
0
0
0
1
0
0
1
2
1
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
1
0
0
0
2
0
0
1
0
0
1
0
0
0
1
0
0
2
0
1
1
1
0
0
1
2
0
2
0
0
1
0
1
0
0
2
1
2
0
0
1
0
1
0
0
2
2
1
0
2
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
1
1
1
0
0
1
2
0
0
1
0
1
0
1
0
0
2
0
1
0
1
0
2
0
0
1
0
1
0
0
0
1
0
0
2
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
2
0
0
0
2
2
0
0
1
0
3
0
1
0
0
1
0
0
2
1
0
0
1
0
0
1
0
1
1
0
0
1
1
0
0
0
0
0
2
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
3
3
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
2
0
0
3
2
0
2
1
0
0
0
0
0
1
0
1
0
0
0
1
2
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
2
0
2
0
0
2
0
0
2
0
3
0
1
0
0
1
0
0
0
0
0
2
0
1
2
1
0
0
0
0
0
0
0
1
2
1
0
0
0
0
1
0
0
2
1
2
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
1
2
0
0
0
2
1
0
0
2
0
0
2
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
2
0
2
1
0
0
0
1
0
0
0
0
2
0
2
2
0
1
0
0
0
0
0
2
2
1
0
0
1
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
1
2
4
0
0
0
0
1
0
1
0
0
0
0
0
2
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
2
0
2
1
0
4
1
0
0
0
0
0
2
0
0
1
0
0
0
0
1
2
2
2
2
1
1
0
1
0
1
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
1
0
0
0
2
1
2
0
0
1
0
0
1
2
3
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
1
0
0
1
0
1
0
1
0
1
1
2
3
0
0
2
2
0
0
2
0
0
0
0
0
1
0
1
1
2
0
1
0
0
0
0
0
4
0
2
2
0
3
2
2
2
0
2
1
0
2
2
0
0
1
0
1
1
0
0
2
2
2
2
0
0
0
1
0
1
0
0
0
2
2
0
1
0
1
0
1
0
2
1
0
0
2
0
2
0
0
2
3
0
0
2
0
1
5
1
0
3
0
0
2
0
0
0
1
1
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
2
0
0
2
2
2
2
2
0
1
1
0
2
0
0
0
0
0
0
1
0
6
2
0
0
2
0
0
0
2
0
1
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
1
2
0
1
0
0
2
2
1
0
0
0
0
0
1
2
0
0
0
2
2
0
0
0
1
3
2
2
0
0
0
0
0
0
0
2
0
1
0
2
1
1
0
0
0
2
1
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
1
2
2
1
0
0
1
0
1
0
0
0
5
1
0
1
0
1
0
0
1
0
0
0
2
1
0
0
2
1
1
0
0
1
2
2
1
0
1
2
3
0
0
1
2
2
0
0
0
1
0
3
0
0
1
2
0
0
1
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
2
1
0
0
0
0
0
0
2
0
2
0
1
0
3
2
2
0
0
2
1
0
0
2
0
2
1
1
3
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
1
2
1
2
1
2
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
2
0
0
1
0
0
0
1
1
1
2
2
0
1
0
0
0
0
1
0
0
0
1
0
0
0
3
0
1
1
2
0
0
0
0
0
0
0
0
2
0
1
1
1
0
0
1
0
2
3
0
0
3
1
0
0
0
1
2
3
0
2
0
0
0
0
0
0
2
0
3
0
0
1
1
1
0
0
0
1
0
0
2
0
0
0
0
0
3
1
0
3
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
1
1
1
0
1
1
2
0
2
2
0
0
1
2
0
0
1
1
2
0
1
1
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
3
6
1
0
0
0
2
1
0
0
2
1
0
0
1
0
0
0
2
2
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
2
1
2
0
0
2
0
2
0
1
0
0
0
2
0
0
1
1
0
0
0
2
0
2
0
1
0
2
2
4
2
1
0
2
1
1
2
0
0
0
2
2
1
1
0
0
0
0
0
1
2
0
0
0
2
0
2
0
0
0
2
0
0
0
0
2
1
1
2
1
0
2
1
0
2
0
0
0
0
3
0
1
0
2
2
0
0
0
0
0
0
2
2
2
2
2
0
1
0
2
1
2
2
0
2
0
0
1
1
1
2
2
0
0
2
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
2
1
2
0
1
0
1
0
2
0
2
0
1
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
1
0
0
0
0
2
2
1
0
0
0
2
0
1
1
1
0
2
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
1
2
2
0
2
0
1
0
0
0
0
2
2
0
2
0
0
0
0
1
0
0
1
0
0
1
0
0
2
3
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
1
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
2
0
2
0
0
0
3
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
6
0
1
0
0
0
1
0
2
0
0
0
0
0
1
2
0
0
0
1
1
2
2
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
2
2
1
2
2
0
3
1
2
2
2
0
0
0
0
0
2
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
2
2
1
0
3
0
2
2
1
1
2
2
0
2
0
0
1
0
0
1
0
0
2
0
0
2
0
1
2
0
0
1
0
0
1
1
1
1
0
1
2
0
0
2
1
0
0
1
2
1
0
0
3
0
0
0
0
0
2
0
0
2
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
2
0
2
0
0
3
1
0
1
1
1
0
0
2
0
1
0
1
2
0
2
0
0
0
1
1
0
1
0
2
1
2
1
0
0
2
1
1
0
0
0
1
0
1
1
0
0
2
0
2
0
0
1
2
0
0
0
0
0
2
1
0
0
0
3
0
0
2
2
0
0
0
2
0
0
2
0
2
2
1
0
0
0
1
2
0
2
0
0
2
0
3
1
0
2
1
0
0
1
1
0
0
1
0
0
2
0
2
0
0
1
0
0
2
2
1
0
0
1
0
0
1
4
1
0
0
1
0
0
1
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
2
0
3
2
0
2
0
0
2
0
0
2
1
0
0
0
0
2
1
1
1
0
1
1
1
0
0
2
1
1
1
2
0
2
0
0
0
0
1
0
0
1
0
0
0
0
2
0
1
0
0
0
0
1
0
1
0
2
0
0
0
2
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
2
1
2
1
3
0
1
0
1
0
0
1
0
1
0
0
2
0
0
0
2
1
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
2
2
2
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
1
1
2
2
2
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
1
2
2
0
0
0
0
2
2
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
2
3
0
0
0
0
1
0
0
0
0
0
2
1
0
1
1
0
1
1
1
2
1
0
0
0
2
2
0
2
0
2
0
1
0
0
0
1
0
2
1
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
2
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
3
0
2
2
2
0
1
1
0
2
0
0
0
0
0
2
0
0
0
2
1
2
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
1
2
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
2
1
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
7
0
1
0
2
0
0
2
2
0
0
0
0
2
0
0
0
0
1
4
2
1
0
1
2
0
1
0
0
2
2
0
0
0
0
1
0
0
0
2
0
2
0
0
2
1
0
1
0
1
0
0
0
0
0
0
0
2
2
2
0
0
0
1
0
4
0
9
3
0
1
2
2
1
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
2
0
1
3
1
0
2
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
1
0
2
0
0
0
2
1
0
2
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
2
1
0
0
1
1
1
1
0
0
0
2
0
1
2
0
0
0
2
2
0
0
2
1
0
0
0
0
0
2
0
0
2
1
0
2
0
1
2
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
1
1
0
0
1
0
1
2
1
0
2
1
2
2
1
1
2
0
0
0
1
2
0
1
0
0
1
0
0
1
2
0
0
0
1
0
2
2
1
2
1
1
0
1
0
1
1
0
0
2
0
2
2
0
2
0
3
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
1
0
1
2
3
1
1
0
0
1
0
2
0
0
0
0
1
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
1
0
0
1
2
0
1
2
1
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
1
0
2
0
0
1
0
1
2
2
0
1
0
1
0
2
1
0
3
1
0
3
2
2
0
1
0
0
0
0
2
3
0
1
0
2
4
2
1
1
2
3
0
0
2
0
1
0
0
0
2
0
2
2
2
0
1
0
0
2
2
3
2
2
0
0
0
2
2
0
0
1
1
0
1
1
2
0
0
0
0
0
0
2
0
0
3
0
0
0
1
0
1
1
0
0
1
0
0
2
0
0
2
0
0
0
0
1
1
3
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
2
0
0
0
1
2
0
1
1
3
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
2
1
1
0
0
0
1
0
0
0
0
0
0
1
1
2
2
1
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
2
1
2
0
1
0
0
0
2
1
1
2
1
0
3
1
1
0
3
0
0
0
0
0
1
0
0
2
0
1
0
0
2
1
1
2
0
0
2
1
0
2
1
0
0
0
0
2
0
1
0
0
0
0
0
1
3
2
0
0
0
0
1
1
0
2
0
0
2
1
0
0
0
0
2
2
0
0
0
2
0
0
0
1
0
0
2
2
0
1
0
0
2
0
2
0
0
1
0
1
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
1
3
0
0
2
1
0
0
1
0
2
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
2
1
1
0
0
1
1
2
2
2
1
0
0
1
0
4
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
2
1
0
0
0
1
1
0
1
2
2
2
0
2
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
1
0
1
0
0
1
0
1
1
0
1
0
1
0
0
0
2
0
0
1
2
0
0
0
2
0
0
1
0
1
2
0
0
1
0
2
3
0
0
1
1
0
0
2
0
0
2
0
0
1
0
2
1
0
2
1
0
1
1
0
0
0
0
0
1
0
0
0
0
2
1
1
0
0
1
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
2
2
0
0
0
0
0
0
9
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
2
1
0
2
4
2
2
0
0
1
0
0
1
2
2
0
1
0
2
2
0
0
1
0
0
0
0
1
0
2
0
0
2
1
3
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
2
0
0
1
0
1
0
2
0
2
1
0
2
0
0
0
1
0
0
0
3
0
0
0
1
0
0
1
0
0
2
2
2
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
3
0
1
0
0
1
0
0
1
2
1
2
0
0
0
0
0
0
2
1
0
2
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
1
2
0
0
2
1
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
2
0
1
0
1
0
0
0
0
2
1
0
0
0
0
3
2
1
0
0
0
4
1
0
1
0
1
1
2
0
1
1
1
0
2
1
2
0
0
0
0
1
0
0
0
0
0
0
2
1
1
0
0
0
0
2
0
0
0
2
1
2
0
0
0
0
0
2
2
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
1
0
0
0
0
0
0
1
0
0
2
2
2
0
1
0
1
2
1
0
0
0
1
0
0
0
0
2
0
2
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
1
0
2
0
0
2
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
1
2
1
0
1
0
1
1
1
0
0
1
0
1
1
0
2
1
2
0
2
0
1
0
0
0
0
1
0
0
0
0
1
0
2
0
2
1
2
2
0
1
0
1
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
1
0
2
0
0
0
0
3
1
0
0
0
2
0
0
0
2
0
1
2
0
1
8
0
2
0
2
0
3
0
2
1
0
0
2
2
1
2
1
2
0
0
1
1
0
0
4
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
2
0
0
0
0
1
0
2
0
0
0
1
2
2
0
1
0
2
1
1
0
2
0
1
1
0
1
1
0
1
0
0
1
1
1
0
2
2
0
0
0
2
0
2
0
0
0
1
1
0
2
1
1
0
0
0
1
0
2
0
0
1
0
2
0
1
2
0
0
0
0
1
2
2
0
1
1
0
0
2
2
0
0
2
2
0
0
0
3
0
0
1
0
1
0
1
0
1
1
2
0
0
1
0
0
1
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
1
2
2
0
2
0
0
0
0
0
0
0
0
1
1
1
2
2
3
1
1
0
0
1
0
1
0
0
2
2
0
0
1
0
0
0
2
0
0
0
0
2
2
0
0
0
0
1
0
1
1
2
0
2
0
2
0
0
0
2
0
0
3
0
0
1
2
0
0
1
0
0
1
0
2
1
1
1
0
0
2
1
0
0
0
3
0
2
0
0
0
0
0
1
0
0
2
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
1
0
0
2
0
0
2
0
0
0
2
1
0
1
1
0
0
1
1
2
0
0
0
1
2
1
2
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
2
1
0
0
1
1
0
2
1
2
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
1
0
0
0
0
2
0
0
2
0
1
2
0
2
0
0
1
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
2
2
2
0
0
0
0
2
0
3
0
0
0
0
1
0
2
0
1
2
0
0
0
0
0
0
0
0
2
1
0
3
0
1
1
1
0
2
1
0
1
1
0
0
0
0
0
0
0
2
2
0
0
1
0
0
2
0
2
1
1
1
0
3
0
2
0
2
1
0
2
1
2
2
0
0
0
1
0
0
0
1
0
0
0
2
0
1
0
0
0
0
2
0
0
2
0
3
0
0
0
0
1
0
0
0
2
0
0
2
1
0
2
0
0
2
2
0
0
0
0
0
2
0
0
0
2
0
1
0
3
0
0
0
0
2
0
1
0
0
2
3
0
1
2
1
1
1
1
0
0
1
0
0
0
0
0
0
0
1
3
1
0
1
0
2
2
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
1
1
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
3
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
2
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
3
1
0
2
0
0
0
0
1
0
0
2
2
0
2
0
0
1
0
0
0
0
1
0
0
1
2
0
0
1
2
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
3
0
1
1
0
3
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
1
0
0
0
0
1
2
0
0
2
0
2
0
0
1
2
0
0
0
1
0
0
0
1
2
2
0
0
0
0
0
2
0
1
0
3
3
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
2
2
0
0
0
2
0
0
0
0
0
1
0
1
0
3
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
1
2
2
1
1
0
2
2
3
1
1
0
0
0
0
0
1
0
2
2
0
0
1
0
0
0
0
2
0
1
1
1
2
0
0
0
0
1
1
1
1
1
1
0
0
0
0
0
1
2
0
0
0
0
0
4
0
0
1
2
0
2
2
0
0
2
3
1
0
2
0
0
1
2
0
1
0
0
0
0
0
2
0
1
2
1
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
2
0
2
1
2
0
0
0
0
2
2
1
0
1
0
0
1
2
0
0
1
0
0
1
1
0
1
2
1
0
0
0
2
2
0
0
0
0
1
0
0
1
0
2
0
0
2
0
0
0
0
1
2
1
2
0
0
0
0
1
4
3
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
1
1
0
0
0
3
1
0
0
0
1
0
2
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
3
0
1
0
1
2
0
1
1
1
0
3
0
0
1
2
0
0
0
1
0
1
0
2
2
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
13
0
1
1
0
1
0
1
2
0
0
0
0
0
1
0
0
0
1
0
1
1
0
2
0
0
0
0
0
1
1
2
1
3
0
0
0
0
0
2
0
1
1
0
0
2
2
0
0
2
1
0
1
0
1
1
0
0
1
0
0
2
0
0
0
0
0
1
0
0
2
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
2
0
0
3
2
0
0
0
2
0
1
0
0
1
0
2
0
0
5
1
0
0
2
1
0
2
0
1
2
0
0
0
1
0
1
1
0
0
0
0
2
0
0
0
0
1
1
1
1
1
1
0
0
2
0
1
0
2
0
1
1
0
1
0
1
0
1
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
5
1
0
0
0
0
0
0
0
0
2
1
1
0
2
1
0
0
2
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
1
2
2
1
0
1
2
0
0
2
0
1
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
2
0
1
0
1
0
1
0
0
2
0
0
1
0
1
0
0
3
2
2
0
1
0
0
0
0
1
1
0
2
2
0
2
0
0
1
0
0
0
1
2
0
0
0
0
0
1
2
0
0
0
2
0
4
0
1
1
0
0
0
2
0
1
0
0
0
0
1
0
2
1
0
2
1
0
0
0
0
1
1
0
1
0
0
3
2
0
0
0
2
0
0
0
1
0
0
0
1
3
0
2
0
1
0
0
0
2
2
0
2
1
1
1
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
2
2
2
0
0
1
0
0
0
2
0
0
0
3
1
0
0
0
3
0
1
2
0
1
2
1
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
2
3
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
3
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
1
1
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
1
2
1
0
0
0
0
1
1
0
1
0
0
0
0
2
0
1
2
0
2
0
0
0
0
1
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
2
0
2
1
0
2
1
0
0
0
0
0
0
0
1
0
1
2
1
2
0
0
0
1
2
0
0
2
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
1
0
0
0
2
0
0
1
1
0
2
2
1
0
1
0
0
3
0
0
2
1
0
0
0
0
1
0
0
1
0
2
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
1
0
1
3
0
1
0
2
0
1
1
2
1
1
1
0
0
0
0
1
2
0
0
0
1
0
0
1
1
2
2
0
0
0
2
0
1
0
0
2
0
1
1
2
0
0
0
1
2
0
1
0
0
0
0
1
1
0
0
1
0
0
3
1
0
0
3
1
1
0
0
2
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
1
2
0
0
0
2
2
0
0
1
0
2
0
0
2
1
2
2
1
0
1
0
0
1
0
2
0
0
0
2
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
3
0
0
1
1
4
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
3
0
2
0
1
2
0
0
1
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
4
0
0
0
2
0
0
1
1
0
2
2
1
0
0
0
2
2
0
0
2
0
2
0
1
1
0
0
0
0
0
1
0
0
0
1
2
0
1
0
0
0
0
2
0
0
0
0
0
3
0
1
2
2
0
0
6
0
0
0
0
1
0
2
1
0
2
1
2
3
0
1
1
2
0
0
1
2
2
1
0
1
0
0
0
1
2
0
2
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
2
0
0
2
1
0
1
2
0
0
0
0
2
2
0
1
1
0
1
0
1
5
0
0
1
0
1
1
0
6
0
0
1
0
1
0
0
0
1
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
3
1
1
0
2
1
2
1
1
0
1
1
1
3
0
0
0
1
1
2
0
0
0
0
2
3
0
1
0
0
1
0
2
0
0
2
1
0
0
0
0
2
1
2
0
0
0
2
1
1
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
2
1
1
2
0
0
4
0
0
1
2
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
1
1
2
2
0
1
0
0
2
2
0
1
0
0
2
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
1
2
1
0
0
1
0
0
3
0
0
1
0
0
0
0
1
2
0
0
1
0
2
1
0
0
0
1
0
2
0
1
0
0
0
0
1
2
0
0
0
0
1
0
1
1
2
0
0
0
0
0
0
0
0
1
1
0
0
1
1
1
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
1
2
0
0
1
1
0
0
1
0
0
1
1
1
1
0
0
0
0
0
0
0
1
0
5
1
1
0
0
0
0
0
0
1
0
0
0
0
2
1
0
1
1
1
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
3
2
2
2
0
0
1
0
2
0
2
0
1
0
2
1
0
1
2
0
1
0
2
0
1
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
2
2
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
1
0
1
2
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
2
0
1
0
0
0
1
2
0
0
0
1
2
0
0
1
0
0
1
0
1
1
1
1
0
2
0
1
2
0
1
0
0
0
1
0
2
0
0
0
4
3
1
0
2
2
0
3
0
2
0
2
0
2
2
0
1
2
1
0
2
2
1
0
0
1
4
0
1
0
0
0
1
0
1
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
1
1
1
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
1
2
0
0
0
0
0
2
2
1
1
0
0
0
0
2
1
0
0
1
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
1
2
0
0
2
2
2
0
1
0
0
0
2
1
1
1
0
2
3
0
2
0
0
1
0
1
0
1
0
0
2
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
1
1
1
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
2
0
0
1
1
0
1
0
2
0
0
0
0
2
3
0
0
0
1
0
0
0
1
0
0
1
1
0
2
2
1
0
0
1
0
0
0
0
1
1
2
0
1
0
0
0
0
1
2
0
0
1
1
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
2
1
1
0
0
0
1
1
0
2
0
0
0
0
2
2
2
0
0
0
0
2
0
1
1
1
0
0
0
0
0
1
1
0
2
1
2
1
0
0
1
2
0
1
0
0
0
2
0
0
3
0
0
2
1
0
1
0
2
0
0
0
3
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
2
3
0
1
0
3
2
0
2
2
0
0
0
2
0
0
0
2
4
0
0
2
0
0
2
2
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
3
0
1
0
2
0
0
0
0
1
1
0
2
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
2
0
0
1
2
0
0
0
0
0
0
1
2
1
0
0
0
2
1
1
2
1
0
1
0
0
1
0
1
1
0
1
0
2
2
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
3
1
0
2
1
1
0
1
0
0
0
1
1
0
1
0
0
1
0
1
0
1
3
0
0
0
2
0
0
1
2
0
0
2
0
0
0
0
2
0
1
1
0
2
0
0
0
0
0
0
0
2
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
2
2
1
0
1
1
1
2
0
0
0
0
0
1
2
0
0
1
0
1
0
3
0
2
1
0
0
2
2
0
0
0
2
0
0
0
2
0
2
0
1
0
0
0
0
1
2
0
0
0
0
0
2
0
2
0
2
1
1
0
0
0
0
0
0
0
2
3
0
1
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
4
2
0
0
2
0
2
0
0
0
0
1
0
2
0
0
1
0
0
0
0
1
1
0
1
2
0
0
1
0
1
2
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
1
0
1
1
0
0
0
1
1
0
2
0
0
1
2
0
0
2
0
1
0
1
0
3
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
1
2
0
1
0
0
3
0
0
0
1
1
1
0
1
0
0
0
0
0
0
2
0
2
1
1
0
0
0
0
0
0
0
1
1
2
0
0
0
0
1
0
0
2
0
0
0
1
0
1
0
0
0
0
0
2
0
1
0
1
1
0
0
1
0
0
1
0
0
2
2
2
0
2
2
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
1
2
1
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
1
0
0
0
1
6
0
1
0
2
1
0
0
0
0
0
0
0
0
2
1
0
0
1
1
1
0
0
1
0
0
0
2
0
1
2
0
1
0
2
0
0
0
1
3
0
0
2
0
1
1
1
0
2
0
0
1
0
3
0
2
1
0
0
0
0
0
0
1
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
1
2
1
0
0
0
2
0
0
1
3
0
2
0
1
1
1
0
0
2
2
0
0
0
2
0
0
0
0
0
2
1
1
1
0
0
1
0
0
0
2
0
2
0
0
0
2
0
1
0
0
0
1
0
0
2
0
0
2
0
1
0
1
2
0
0
1
0
0
0
0
1
1
2
0
2
0
0
3
0
0
0
0
2
1
2
1
0
0
0
0
2
2
0
1
2
0
1
0
1
2
0
0
0
0
0
1
2
0
0
0
0
2
0
0
2
0
2
2
0
0
0
1
1
0
1
1
0
0
2
0
0
0
1
0
1
0
2
0
2
0
0
0
0
0
1
0
1
0
2
0
0
0
0
2
0
0
2
1
0
0
1
1
0
0
2
1
1
1
0
0
0
0
2
0
0
1
0
2
1
0
2
2
0
0
2
0
2
0
0
3
1
0
0
1
0
0
1
2
0
1
0
0
2
0
2
0
0
1
2
0
0
2
0
0
0
1
1
1
0
0
0
0
0
0
0
3
0
0
2
2
1
2
1
0
0
9
2
3
0
0
0
0
0
1
1
1
0
0
0
0
0
1
2
0
0
0
0
1
2
0
0
0
0
1
1
2
0
1
0
0
1
2
0
3
0
2
1
1
2
0
2
0
0
0
0
0
2
1
0
0
0
2
1
0
0
2
1
0
1
0
1
0
2
1
0
1
0
0
0
0
1
0
2
0
1
2
1
0
1
0
2
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
1
3
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
1
0
2
2
2
2
1
0
0
0
2
0
1
0
0
2
1
2
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
2
1
2
0
0
0
0
1
0
0
0
0
2
0
0
3
1
2
0
2
0
0
2
1
2
0
0
1
1
1
0
0
1
0
2
2
0
1
0
0
1
2
4
0
0
2
0
0
0
0
1
2
0
2
1
1
0
0
2
1
1
0
1
0
1
0
0
3
1
0
0
0
2
1
0
0
1
1
1
2
1
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
1
0
1
0
3
0
9
0
0
0
0
2
1
1
0
2
2
2
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
1
2
1
2
1
0
2
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
1
2
0
1
0
0
0
1
0
0
0
1
0
3
2
0
2
0
0
2
2
1
0
0
2
0
0
0
0
1
2
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
2
2
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
6
0
0
1
1
1
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
1
0
3
0
0
2
0
1
0
1
0
1
0
0
0
1
0
0
2
0
3
0
0
1
0
0
0
1
0
0
2
2
0
0
2
1
0
0
1
0
2
0
0
1
2
0
3
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
1
1
1
2
1
0
0
2
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
2
2
0
0
1
0
1
0
0
2
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
1
0
5
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
1
2
2
2
2
2
5
1
0
1
0
2
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
2
3
2
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
1
1
0
0
0
1
1
2
0
0
0
1
0
0
0
2
2
0
2
0
0
2
0
0
1
0
0
1
1
1
2
0
1
0
0
1
0
1
0
0
1
3
0
0
0
0
1
0
1
0
2
0
0
0
0
2
0
1
0
0
3
0
0
0
2
1
1
0
0
1
0
0
0
1
0
0
2
2
0
0
0
0
0
2
1
0
1
0
0
0
0
2
0
0
1
1
1
1
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
2
0
2
0
2
2
0
0
1
0
0
2
2
0
2
1
0
1
1
0
0
0
0
0
0
0
2
1
1
0
0
2
0
0
0
0
2
2
1
2
0
2
0
1
2
1
0
2
0
2
2
2
1
1
0
2
7
0
2
0
1
0
1
0
0
0
0
0
1
1
1
2
1
0
0
2
0
0
0
2
0
0
2
1
1
0
0
0
0
1
1
0
0
0
1
0
0
0
2
0
1
2
0
1
0
0
0
0
2
0
3
1
1
0
0
0
0
0
0
1
0
0
1
2
2
2
2
2
2
0
0
0
0
2
0
0
1
0
0
2
0
2
0
0
0
0
0
0
3
2
0
1
2
1
0
1
1
0
0
2
0
0
0
0
2
0
0
2
2
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
2
2
0
1
1
0
1
0
0
2
3
2
1
0
2
0
0
2
2
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
2
1
0
0
2
0
0
2
0
1
2
1
0
1
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
2
1
0
1
2
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
2
1
0
1
0
2
0
0
0
0
0
0
1
1
0
1
1
0
1
0
0
0
0
0
0
0
0
2
0
2
2
0
1
0
0
0
0
2
0
2
0
0
0
0
0
1
2
1
0
0
0
0
1
1
1
0
0
0
2
0
0
2
0
2
2
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
2
3
1
0
0
0
1
0
0
0
0
0
0
0
0
1
3
2
1
0
0
2
0
0
0
2
1
0
0
0
2
0
1
0
3
1
1
0
0
0
0
1
0
0
0
4
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
1
2
0
0
1
0
0
0
3
0
2
2
1
0
1
1
3
0
2
0
0
0
0
0
0
1
3
0
0
0
3
0
1
0
0
0
0
0
0
3
1
8
0
1
0
0
0
0
0
0
1
1
1
0
3
0
0
0
1
2
1
0
0
1
2
2
0
0
1
0
2
0
0
0
0
0
0
1
0
0
2
0
1
1
1
0
0
2
2
0
1
0
0
0
1
0
0
0
2
1
1
0
0
1
0
1
1
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
2
2
0
0
0
1
2
1
0
0
2
0
2
0
2
0
2
0
1
2
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
1
1
0
4
2
0
0
0
0
2
0
3
1
0
0
1
0
2
1
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
1
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
2
1
0
2
0
1
0
1
0
0
1
0
2
0
0
1
1
0
0
1
0
3
0
0
0
0
2
2
1
0
2
0
1
0
1
2
1
0
0
0
1
0
0
0
0
2
2
0
0
0
1
0
0
1
0
2
2
1
1
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
1
2
0
0
1
0
2
0
1
1
0
0
0
1
2
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
2
2
2
1
2
0
0
1
1
0
0
0
1
1
0
0
0
0
1
0
0
0
2
2
2
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
3
2
1
0
0
1
3
0
0
3
0
0
1
0
2
0
0
1
2
0
0
0
2
1
1
1
2
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
1
0
2
1
1
0
1
2
3
1
2
0
1
2
1
2
1
5
0
2
2
2
0
0
0
0
1
0
0
0
0
1
0
1
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
1
0
1
2
2
1
0
2
0
1
1
0
7
0
2
0
0
2
2
1
0
0
0
0
1
0
2
0
0
0
2
0
3
0
0
0
2
1
0
0
0
1
0
0
0
1
2
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
5
0
1
0
0
0
2
0
1
2
2
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
1
0
0
0
2
0
2
0
0
2
0
0
1
0
0
1
0
2
0
1
0
0
0
0
0
1
0
1
0
0
1
0
2
3
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
1
0
0
3
1
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
2
0
0
0
1
0
0
1
0
1
2
0
7
1
2
0
0
1
1
0
0
1
2
2
0
1
0
1
0
0
0
2
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
2
1
0
0
0
0
1
0
0
1
0
2
0
0
2
0
0
2
0
1
1
1
2
0
0
0
3
0
1
0
0
0
2
1
0
0
0
0
0
0
0
3
1
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
1
2
1
1
0
2
2
1
1
0
0
1
0
0
0
0
0
0
0
2
1
2
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
3
0
0
0
1
0
0
0
2
0
0
1
1
2
1
0
1
0
0
0
0
0
2
0
0
0
1
0
2
1
0
0
0
2
1
0
2
0
0
1
1
2
0
0
0
0
1
0
0
1
1
0
2
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
1
2
0
0
1
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
2
0
0
0
1
2
0
0
0
1
1
0
0
0
2
2
1
1
0
0
2
0
0
0
0
0
3
2
1
0
0
1
0
2
0
1
0
0
0
2
2
0
2
0
2
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
2
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
2
0
0
3
0
2
1
0
0
2
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
1
0
1
2
0
0
0
0
1
0
2
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
2
1
0
2
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
1
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
2
2
0
1
0
2
0
1
1
1
1
0
0
1
1
0
1
0
0
0
1
1
0
0
0
0
0
2
5
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
1
1
0
1
1
1
1
1
1
0
2
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
2
0
0
0
0
3
0
0
0
0
0
0
2
1
1
0
1
1
0
1
0
1
2
2
1
1
2
0
2
2
3
1
0
0
1
0
1
0
0
0
1
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
2
1
2
3
1
1
0
0
0
0
3
2
0
1
0
0
1
0
1
3
1
0
0
0
0
2
0
1
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
1
1
0
0
2
1
0
2
2
0
1
0
0
2
1
0
0
2
0
0
1
2
2
1
1
2
0
0
0
2
1
0
2
0
0
0
1
0
0
2
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
1
2
0
2
2
0
2
0
2
0
0
1
0
1
0
2
0
2
0
0
0
0
2
2
0
1
1
0
0
0
0
1
0
0
4
1
0
0
0
0
0
0
0
1
1
1
2
2
2
1
0
1
0
0
2
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
1
2
0
0
0
0
1
2
0
0
2
0
0
2
0
0
0
2
0
2
1
0
0
1
0
0
0
1
2
0
1
0
1
0
1
1
0
0
0
1
1
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
4
0
0
0
0
1
0
2
0
0
0
2
1
0
0
0
1
0
1
0
1
0
1
0
0
1
0
0
2
1
0
1
1
0
2
0
0
0
1
0
2
0
2
0
0
2
0
1
0
0
1
1
0
2
0
1
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
2
3
1
0
0
2
0
1
0
2
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
2
0
3
0
0
2
0
0
2
0
0
0
0
1
0
0
1
0
2
2
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
2
0
1
2
0
1
0
0
2
1
0
2
1
2
1
0
1
0
2
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
2
0
0
2
0
0
1
0
0
0
0
1
1
0
0
1
2
0
0
0
1
2
1
0
2
0
0
0
0
2
0
2
0
0
1
0
0
0
1
2
2
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
2
2
0
2
0
2
1
1
0
2
0
1
0
1
2
1
0
4
0
0
2
0
0
0
0
0
1
2
0
1
0
2
0
0
3
3
2
2
2
0
1
0
0
1
0
2
2
1
0
0
2
1
2
0
0
1
0
0
2
0
0
2
0
1
0
0
0
0
1
0
2
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
5
1
2
2
0
0
0
1
0
0
0
1
1
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
1
0
2
0
2
0
0
0
0
1
1
2
0
2
1
1
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
2
2
0
0
1
0
0
1
2
1
2
2
0
0
0
2
2
0
2
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
2
0
0
2
0
4
2
0
1
0
1
1
0
0
1
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
1
0
0
0
1
2
1
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
3
0
1
1
1
0
2
1
0
1
0
2
1
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
2
0
1
0
0
0
1
0
0
3
2
0
2
3
0
0
0
0
0
2
2
0
1
0
1
0
1
0
1
1
0
0
2
0
1
2
0
0
1
0
2
0
2
0
2
0
1
2
2
2
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
2
0
3
1
1
2
0
2
1
0
0
0
1
0
0
0
2
1
2
2
0
0
1
0
1
0
0
2
1
0
0
1
1
0
0
1
1
0
0
0
0
1
0
1
2
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
1
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
1
2
0
0
2
0
2
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
2
1
0
2
2
0
0
0
0
0
1
14
0
1
0
4
2
1
1
0
0
0
2
2
0
0
0
0
1
0
3
0
0
0
0
0
0
0
2
0
0
0
1
2
0
1
0
2
0
0
0
0
1
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
1
0
0
2
2
2
5
0
0
0
1
0
0
0
0
0
2
2
2
0
3
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
1
2
0
0
2
0
2
0
1
0
1
0
0
0
0
2
1
2
2
0
0
1
0
1
0
0
1
0
3
0
0
3
0
0
0
0
0
2
0
1
2
2
1
0
0
2
0
0
0
2
1
0
0
2
0
1
0
0
1
0
0
0
0
1
0
0
0
2
0
0
1
0
0
1
0
0
1
1
0
1
2
0
3
2
1
2
0
0
2
1
0
2
1
0
2
1
0
1
1
0
4
0
0
2
0
2
0
0
0
2
0
2
1
0
0
0
2
0
1
1
0
1
0
1
0
0
2
1
0
3
1
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
2
0
0
0
1
2
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
1
1
1
0
0
2
3
1
1
0
3
0
1
0
0
2
0
0
0
2
2
0
0
1
0
0
1
0
2
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
1
2
1
0
1
0
0
0
0
0
2
0
2
0
0
1
0
0
0
2
1
0
0
2
0
0
2
0
0
0
0
2
0
0
0
1
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
2
2
0
0
0
2
2
0
2
2
2
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
3
1
1
0
2
0
0
1
0
2
0
2
2
1
0
1
0
0
2
2
1
0
1
0
0
0
2
0
1
1
2
0
2
0
0
1
0
0
0
0
0
2
0
1
1
2
0
1
1
1
2
1
0
1
2
2
0
0
0
2
2
0
3
2
0
2
2
2
0
0
0
0
1
0
1
2
0
1
0
1
0
1
0
1
0
0
0
1
0
0
0
2
2
0
0
0
1
2
0
0
1
0
1
1
0
0
1
0
0
0
2
0
1
0
0
0
0
2
0
2
1
0
0
1
1
1
2
1
3
1
0
0
1
13
0
0
0
0
2
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
2
1
0
0
0
0
1
1
2
0
0
2
1
2
0
0
0
0
1
0
0
0
0
0
2
2
2
0
0
1
1
1
0
2
0
0
0
1
0
0
2
1
0
1
2
0
1
0
0
1
2
0
0
1
0
2
0
0
0
0
1
2
2
0
0
2
0
0
2
2
0
2
1
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
2
0
1
0
0
2
0
2
0
1
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
2
0
0
0
1
1
0
2
1
1
0
0
0
0
4
1
0
0
0
0
0
0
1
0
0
1
2
0
0
0
1
0
0
1
0
1
0
0
4
0
0
0
1
1
0
2
0
0
1
1
2
0
2
0
2
2
0
2
0
0
0
1
1
1
0
0
0
1
2
1
2
2
0
2
2
1
0
5
0
1
2
1
0
0
2
1
0
0
0
2
0
2
0
1
2
2
0
0
1
0
0
0
1
1
1
2
2
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
2
0
0
3
0
0
1
0
2
0
1
0
0
0
2
0
0
1
1
2
2
0
0
0
0
1
2
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
4
0
2
2
0
1
0
1
0
0
2
0
0
0
0
0
5
0
0
1
0
0
0
0
2
1
0
2
0
0
0
1
0
0
1
0
0
0
0
1
0
2
0
0
0
0
1
1
0
0
2
0
0
1
0
1
1
0
2
1
0
1
0
0
1
1
2
1
0
0
0
0
0
0
0
2
0
10
0
2
6
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
2
2
1
0
0
1
0
2
4
1
1
0
0
0
1
0
2
2
0
0
0
2
0
0
0
4
0
0
2
0
2
0
2
0
2
0
0
0
2
0
0
0
0
0
1
0
0
1
2
0
0
2
0
2
0
0
0
2
0
3
2
2
2
2
1
2
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
1
1
2
0
1
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
2
0
0
2
1
0
2
2
0
0
0
1
0
0
0
0
0
1
0
4
0
0
0
2
2
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
2
0
0
0
0
0
2
0
0
0
2
2
0
2
2
0
2
0
0
0
1
0
0
1
2
1
0
0
0
1
1
2
2
1
2
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
2
1
2
0
0
2
0
2
1
2
1
0
0
1
0
2
3
1
0
2
2
0
1
0
1
2
1
1
0
1
1
2
0
2
0
1
0
0
3
3
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
1
1
2
0
0
0
0
0
0
0
2
3
2
2
1
0
0
0
0
0
0
0
1
2
1
2
1
0
0
0
2
1
0
0
1
0
2
2
0
0
0
2
5
2
1
2
3
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
1
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
3
0
1
0
2
0
2
1
0
0
0
0
0
2
0
0
1
2
0
2
1
0
0
0
0
0
0
2
0
0
0
2
1
1
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
1
0
0
0
0
2
0
2
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
3
1
0
0
1
1
2
1
0
1
0
0
1
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
3
0
0
0
0
0
0
1
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
1
1
0
0
0
2
0
1
0
1
0
0
2
0
1
0
0
0
2
1
1
0
1
0
1
1
0
0
1
0
1
0
0
1
0
0
1
2
1
0
0
1
1
0
0
0
0
0
0
2
0
1
0
1
0
0
2
1
2
2
2
0
0
1
0
0
0
1
0
2
1
0
0
0
0
7
0
0
1
0
0
0
0
0
0
0
0
5
1
1
0
1
1
0
0
2
2
2
0
2
0
0
2
0
1
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
3
0
1
1
0
0
7
1
0
2
0
0
1
0
0
2
0
0
0
0
0
0
1
0
2
2
0
0
0
0
1
2
2
1
0
0
2
0
2
2
0
0
3
0
0
2
2
0
0
2
0
1
0
0
1
0
0
1
2
1
0
1
2
0
1
3
0
1
1
2
0
1
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
1
2
1
1
0
0
1
1
0
0
0
1
0
1
1
0
2
0
0
1
1
0
2
0
0
0
1
1
0
2
2
1
1
1
1
0
0
2
0
1
0
0
2
1
3
1
0
0
2
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
4
0
1
0
2
1
1
1
1
0
0
2
0
0
1
2
4
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
3
1
0
0
1
1
0
0
2
1
0
0
0
0
0
1
0
0
2
0
0
1
0
2
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
2
0
0
0
2
0
0
0
0
1
0
1
1
1
1
0
1
1
2
0
2
0
0
0
2
3
0
0
0
2
0
0
2
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
2
0
0
0
2
2
4
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
1
0
2
0
0
1
1
0
2
0
2
1
2
2
2
0
0
3
1
1
0
0
0
0
0
0
2
1
0
0
0
2
0
2
0
2
0
2
1
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
7
1
0
0
0
0
0
0
2
0
0
1
2
0
0
2
2
0
2
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
1
2
0
1
1
0
1
1
2
0
0
1
0
2
1
0
0
0
1
0
0
0
0
1
0
3
3
1
2
0
0
1
2
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
2
0
1
2
0
0
0
0
0
0
1
1
1
0
1
0
0
0
4
1
0
0
1
0
2
0
0
1
1
0
1
0
2
2
0
1
0
0
2
0
1
1
2
0
2
0
0
1
1
1
0
0
2
0
0
0
2
1
2
0
2
0
0
0
2
1
2
2
2
1
0
1
1
0
0
0
1
0
0
0
1
1
0
0
3
1
1
0
0
2
0
1
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
1
0
1
0
1
0
0
3
1
0
1
0
0
0
0
2
0
1
0
0
3
0
0
0
0
2
0
0
1
2
0
0
0
2
0
0
0
2
1
0
1
0
1
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
1
0
0
1
2
0
2
0
2
0
0
0
0
2
6
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
2
2
0
0
1
0
2
0
0
0
0
0
0
2
0
1
1
1
2
0
0
0
2
1
0
0
3
1
2
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
2
0
0
0
0
0
1
0
0
1
0
2
0
3
0
1
0
0
2
0
0
2
2
0
0
0
3
0
2
2
0
0
0
0
3
0
0
0
1
0
0
0
0
2
1
2
0
0
0
0
0
0
1
1
0
0
0
1
2
0
0
0
0
1
0
0
0
2
0
1
2
0
0
2
0
0
2
1
2
0
1
0
0
0
4
0
0
0
1
0
1
0
2
0
2
0
0
0
0
4
2
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
2
0
0
1
0
3
0
1
0
1
2
0
0
0
2
0
0
0
0
0
0
1
1
2
0
0
0
1
2
1
0
1
4
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
2
1
1
0
1
0
0
2
0
0
1
2
2
0
1
0
1
0
0
0
0
1
1
0
0
0
1
2
1
1
0
0
0
2
3
0
0
0
0
0
0
0
3
1
1
2
0
2
0
1
1
0
1
2
1
0
1
0
3
1
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
1
0
0
2
2
0
1
0
1
0
0
0
0
2
1
0
0
0
1
2
0
0
0
1
1
0
0
1
0
0
0
0
0
2
0
0
2
2
2
0
1
0
1
2
2
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
2
0
0
2
0
0
0
1
0
1
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
2
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
2
1
0
1
0
0
0
1
0
2
0
1
0
0
1
1
0
0
2
1
2
0
1
2
2
1
0
2
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
1
0
2
0
2
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
4
0
0
3
1
0
5
0
4
0
0
0
0
0
1
0
1
2
1
0
2
0
1
0
1
0
0
0
0
0
2
0
1
1
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
1
1
0
2
2
0
0
0
2
0
0
2
0
0
0
0
0
2
1
0
0
1
2
0
0
1
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
2
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
2
2
0
0
3
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
2
1
1
0
0
0
0
6
1
1
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
1
0
0
0
2
1
0
2
0
0
0
1
0
0
0
0
0
2
1
0
2
0
0
0
0
0
2
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
2
0
0
1
0
1
2
0
2
0
2
2
0
0
0
0
1
0
0
0
2
0
2
0
0
5
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
1
1
0
2
2
1
1
0
0
1
2
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
2
0
1
1
0
0
0
2
0
0
0
0
0
0
0
4
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
1
0
1
0
2
0
1
0
0
0
0
2
2
0
2
2
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
2
0
0
2
0
5
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
2
2
0
2
2
0
2
0
4
2
0
2
1
0
2
0
0
0
2
0
0
1
0
0
2
1
0
0
0
0
2
3
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
2
1
0
0
4
0
1
1
1
2
2
0
2
2
1
2
2
1
1
0
1
0
0
0
1
2
0
0
1
2
0
0
1
2
2
2
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
2
2
2
2
2
0
0
1
2
0
1
1
0
0
0
0
0
0
0
1
0
0
2
2
0
2
0
1
0
0
0
2
2
0
0
0
2
1
2
0
2
0
0
1
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
1
2
3
0
0
2
0
0
1
0
0
0
0
1
0
2
1
0
0
0
0
3
1
0
0
2
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
1
0
0
2
0
2
0
1
0
0
1
0
0
0
0
1
1
2
0
0
1
1
2
1
0
0
2
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
1
0
0
2
0
0
2
0
0
0
0
1
1
1
0
0
1
1
0
0
1
2
1
0
0
2
0
2
1
0
1
0
0
0
0
0
0
2
0
2
2
1
0
0
0
0
0
0
2
4
0
0
0
0
1
0
2
2
0
1
2
2
0
0
0
0
1
2
0
0
2
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
1
1
0
0
1
1
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
4
0
2
1
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
2
0
1
0
0
0
1
3
0
1
3
1
0
0
0
0
3
2
2
0
2
0
0
0
0
1
1
0
0
0
0
1
0
0
2
2
1
0
0
2
0
0
2
2
2
0
2
2
0
0
4
1
0
0
1
0
0
0
0
2
0
0
0
0
4
0
2
2
0
0
1
0
0
0
0
0
3
0
0
0
5
0
2
0
0
0
0
0
0
2
1
0
1
0
2
0
0
0
3
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
2
0
0
1
0
2
0
0
0
0
0
2
0
2
2
2
2
2
0
1
0
0
1
2
1
0
0
0
0
0
1
2
0
0
1
1
2
2
1
1
0
0
0
0
0
1
0
1
2
0
3
2
0
1
0
0
1
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
2
1
0
1
0
2
0
0
2
0
1
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
2
1
0
3
0
0
0
0
1
1
0
0
0
0
0
0
2
2
0
1
2
4
3
0
1
0
0
1
0
2
2
1
0
0
3
2
0
2
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
1
0
0
0
2
0
0
0
0
2
1
2
0
2
0
1
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
1
0
2
0
1
0
0
0
0
0
2
0
0
0
0
2
0
1
1
1
2
0
0
1
2
0
0
0
1
0
2
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
3
0
0
1
0
0
0
1
1
0
0
0
0
0
0
2
0
0
1
1
0
1
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
3
0
0
0
0
2
2
0
0
0
0
0
0
2
2
5
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
5
0
0
2
0
0
0
0
0
0
0
3
0
0
2
2
2
2
0
0
2
0
0
1
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
2
2
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
2
2
0
2
2
0
0
0
0
2
0
0
1
0
0
0
0
0
1
1
0
0
0
2
0
0
2
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
2
1
0
1
0
0
2
0
0
0
0
0
0
1
0
0
1
0
1
0
2
1
2
2
1
0
0
1
0
2
0
2
2
1
1
0
1
0
0
2
1
0
0
2
0
2
0
0
0
0
1
1
0
0
0
1
1
0
2
5
0
0
0
1
1
0
0
2
0
0
0
0
0
0
1
0
7
1
0
0
0
0
0
1
2
0
0
0
0
1
2
1
2
0
2
2
0
2
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
1
0
2
1
0
0
0
2
0
0
2
2
2
0
1
2
2
2
0
1
2
1
2
1
0
0
0
1
0
1
1
0
0
0
0
2
0
1
2
0
0
1
1
0
2
1
1
0
1
1
0
0
0
0
0
2
0
1
0
0
0
1
0
1
0
0
2
0
0
0
0
0
2
0
0
1
2
0
0
2
2
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
3
1
0
0
5
0
0
0
0
3
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
2
0
0
0
0
0
0
2
0
2
5
1
0
0
0
1
0
0
0
1
0
1
2
0
0
1
2
0
3
0
0
0
0
0
0
2
0
2
2
1
0
0
0
1
1
0
0
1
0
0
0
2
0
4
2
0
0
3
2
0
0
0
0
0
0
1
1
1
0
1
0
0
1
0
0
2
0
3
0
0
0
0
2
0
1
0
2
1
1
0
0
0
4
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
1
0
0
2
0
1
0
0
0
1
2
0
2
0
0
0
0
0
1
0
1
0
1
2
0
0
0
0
0
3
1
2
1
1
1
0
0
0
3
0
1
0
0
2
0
0
2
1
1
0
2
1
2
0
0
0
0
0
1
2
0
2
0
0
0
2
1
0
1
0
0
0
0
1
0
2
0
0
0
1
1
3
2
0
0
0
0
0
3
0
2
1
0
1
0
0
1
0
1
2
2
2
0
0
0
1
2
3
1
0
0
0
0
0
0
1
1
0
0
0
2
0
0
1
2
1
0
1
0
1
0
0
2
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
1
0
1
0
0
0
0
2
1
2
2
2
1
1
0
0
0
1
0
1
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
1
0
1
0
0
0
0
1
0
0
1
0
5
0
1
0
2
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
2
1
0
2
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
2
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
2
3
0
0
2
1
0
3
0
0
0
1
3
2
0
2
0
1
2
0
0
1
0
3
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
2
0
0
0
1
0
1
1
1
0
1
0
0
1
2
0
1
0
1
0
1
0
0
0
0
0
0
2
1
2
1
0
0
0
0
2
1
1
1
0
2
0
1
1
2
1
0
0
0
3
0
2
2
0
0
2
0
0
0
0
1
0
0
2
0
1
0
2
1
0
0
1
0
1
0
1
0
1
0
0
0
4
0
1
0
1
0
0
0
1
0
1
0
3
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
1
1
1
0
0
0
0
0
2
0
0
0
2
3
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
3
1
2
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
2
1
1
1
0
0
1
1
0
0
0
2
0
2
0
0
0
0
1
0
0
1
1
0
0
3
0
0
0
0
0
2
0
0
2
0
0
0
0
2
3
1
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
2
2
3
0
0
0
0
0
0
1
0
2
0
0
2
2
0
0
1
0
2
0
1
0
0
0
1
0
2
0
2
0
1
1
1
0
2
1
1
0
0
0
3
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
2
0
0
0
0
0
1
0
0
2
1
0
1
0
0
0
0
0
0
3
1
2
0
0
0
0
0
1
0
1
4
0
0
0
1
2
1
0
2
0
0
0
0
6
0
0
2
1
0
1
2
0
1
0
1
0
0
0
0
0
2
2
1
0
0
0
0
0
2
2
1
0
2
4
0
0
0
0
0
0
0
0
3
0
2
2
1
0
2
0
1
1
0
0
0
0
2
2
0
2
0
2
1
0
0
2
1
0
0
1
0
0
0
1
0
0
2
1
0
0
0
3
1
0
0
0
0
0
0
0
0
2
2
0
0
5
0
1
0
1
1
0
0
0
0
1
1
0
0
0
0
1
1
0
1
0
0
0
2
0
2
0
1
0
0
0
0
0
1
2
2
0
1
2
0
1
0
0
2
0
2
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
3
1
0
0
1
0
1
1
2
0
2
1
4
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
2
1
0
0
1
0
1
0
2
0
0
2
1
1
0
0
0
1
1
1
2
0
2
2
1
0
0
2
2
0
1
0
0
0
1
1
0
0
0
2
1
0
1
2
0
0
0
2
2
0
0
2
0
0
0
0
1
1
0
0
0
0
2
0
0
0
2
2
1
0
0
0
5
0
0
1
1
0
2
2
0
0
2
2
0
2
0
0
0
0
0
0
0
2
0
0
0
2
1
0
1
1
0
1
0
2
0
0
1
0
2
0
2
0
0
0
1
2
2
0
2
0
0
2
0
0
2
2
2
0
0
1
4
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
2
0
0
1
0
1
1
0
0
0
0
2
2
2
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
1
0
1
0
6
1
0
0
2
0
2
0
0
1
1
0
0
0
1
1
2
0
1
2
0
0
0
1
4
0
1
1
0
1
2
2
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
2
2
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
1
0
0
0
3
2
2
0
1
2
1
2
0
1
1
2
0
1
1
0
0
0
2
0
1
0
0
5
0
0
1
2
0
0
0
1
0
0
0
0
0
0
1
2
0
0
2
3
1
1
1
1
0
0
0
3
1
2
1
0
2
3
0
1
1
0
0
2
0
0
0
2
0
0
0
0
0
2
1
2
2
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
2
0
1
0
1
0
0
0
1
1
2
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
3
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
1
0
0
1
2
2
0
0
0
0
0
0
0
0
1
2
2
0
1
1
2
1
0
2
0
0
0
1
2
0
2
0
1
1
1
0
2
5
0
2
1
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
2
1
0
0
0
1
1
0
1
0
0
0
1
1
3
1
1
0
0
1
0
1
0
1
0
2
1
0
1
0
0
0
2
2
0
1
2
2
1
2
1
0
0
0
0
1
0
2
0
2
1
0
1
0
0
0
0
1
0
1
0
1
0
0
2
0
2
0
1
0
2
2
0
0
0
0
0
0
1
0
2
0
1
0
1
1
0
1
1
0
3
2
2
0
0
1
0
2
0
0
0
0
0
2
1
0
0
0
0
2
1
3
0
0
2
2
5
0
0
3
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
2
3
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
2
0
1
0
1
2
0
0
2
0
0
2
0
2
0
2
2
1
1
0
0
0
0
0
2
0
0
0
1
1
0
1
0
0
0
0
2
0
2
2
2
0
0
0
0
0
0
0
1
0
0
2
0
0
2
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
5
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
2
1
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
2
2
1
0
2
2
0
0
1
2
0
2
1
0
0
0
0
1
0
0
0
0
0
1
4
1
0
2
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
2
1
2
0
2
2
2
1
1
0
2
0
0
0
1
0
0
2
0
0
0
0
2
0
2
0
1
2
0
0
7
0
0
0
0
1
0
0
1
0
0
2
1
0
0
1
1
0
0
1
2
0
1
2
0
0
1
0
0
2
0
4
0
0
1
0
0
0
0
1
2
0
0
0
2
1
0
1
2
0
0
1
0
0
0
2
2
0
0
0
0
1
1
0
0
2
1
0
1
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
2
1
0
1
1
0
1
0
0
0
2
0
0
0
1
1
0
2
0
0
0
0
0
1
2
0
0
1
0
2
0
0
0
2
0
0
0
3
0
1
1
0
2
0
0
0
0
0
1
2
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
1
0
0
0
2
1
3
1
0
0
0
1
1
2
1
0
1
2
0
2
2
0
1
0
0
0
3
0
2
0
2
1
0
0
0
0
0
2
0
0
1
1
3
1
2
0
1
1
0
2
0
1
2
1
0
1
0
0
0
0
1
0
1
0
2
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
1
2
2
0
0
0
0
0
1
2
0
0
2
0
2
6
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
2
0
2
0
0
1
1
0
2
0
0
0
0
0
0
2
1
2
0
0
3
2
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
2
0
2
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
1
2
0
0
1
2
0
0
0
0
0
1
1
0
2
0
1
0
0
0
0
0
2
1
0
0
1
0
0
0
2
0
0
2
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
1
0
2
1
0
0
0
0
0
0
0
1
3
1
0
0
0
0
0
0
2
2
1
2
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
1
2
0
0
0
0
1
2
0
0
1
0
0
2
0
0
1
1
2
0
2
2
0
0
1
1
0
0
1
1
2
1
0
1
0
0
0
0
0
2
0
1
2
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
1
1
0
1
1
0
1
0
1
0
1
2
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
2
2
0
0
0
1
0
2
0
0
1
1
0
0
0
1
0
0
2
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
2
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
3
2
0
2
2
0
1
0
0
0
2
1
0
2
0
0
0
3
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
2
0
1
2
0
0
3
0
0
0
0
2
1
2
1
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
1
5
0
0
0
2
1
2
2
0
2
0
0
2
2
0
2
0
0
0
1
2
0
0
0
2
3
1
0
1
0
1
0
1
0
1
2
3
2
0
0
0
0
0
0
2
1
2
1
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
1
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
2
2
2
0
0
1
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
1
1
2
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
2
1
0
0
0
1
0
0
0
0
1
1
2
2
0
1
0
2
0
0
0
0
0
1
2
2
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
1
3
0
0
0
0
3
0
2
0
2
2
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
3
1
0
3
1
0
0
2
0
0
0
2
0
0
2
1
1
0
0
1
0
2
0
1
1
0
0
1
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
2
0
0
0
0
1
0
2
1
2
0
0
0
1
0
0
0
2
2
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
1
0
1
2
1
1
0
1
2
1
1
0
0
0
0
0
0
2
1
0
1
0
0
0
2
0
6
2
2
2
2
0
0
2
0
0
0
0
1
0
1
1
0
2
1
0
1
1
0
0
1
2
0
0
0
2
1
1
0
0
1
0
0
0
0
0
0
3
0
1
0
2
0
2
0
1
2
0
0
1
1
0
2
0
0
2
0
0
1
2
0
0
0
1
2
0
1
2
0
0
2
0
0
0
2
0
0
0
0
0
1
2
1
0
0
2
0
0
2
0
0
0
1
0
1
0
0
2
0
0
0
1
2
2
0
1
0
0
1
0
1
1
1
0
0
0
0
3
0
0
2
2
0
0
1
0
1
2
0
0
0
2
0
2
1
0
1
1
4
2
1
0
1
2
0
0
3
2
1
0
0
0
0
0
2
2
1
0
0
0
1
0
0
1
0
2
1
1
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
2
2
0
1
1
1
1
0
0
0
2
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
1
2
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
3
0
1
2
1
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
2
3
0
0
0
1
2
1
2
0
0
0
0
0
1
0
2
1
0
2
1
0
0
0
0
1
1
0
0
0
0
0
0
0
3
0
0
0
2
1
1
1
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
2
2
0
0
1
0
2
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
1
2
0
2
0
0
1
0
0
2
2
0
0
0
0
0
1
0
2
0
3
1
1
1
0
0
2
0
2
0
0
1
0
1
0
0
0
1
0
0
1
0
0
2
0
1
0
0
0
0
0
2
2
0
1
1
2
0
0
1
2
1
0
1
1
0
2
0
1
3
0
0
0
1
2
0
3
1
0
0
0
0
0
2
0
0
0
3
0
0
2
0
2
1
0
0
2
0
0
2
0
0
1
2
1
0
0
0
0
0
0
1
2
2
0
2
0
0
0
1
0
2
0
0
0
1
2
0
3
0
0
0
2
0
0
0
0
0
2
2
1
1
0
0
0
2
0
0
0
1
2
2
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
3
2
0
0
0
1
0
0
3
0
0
0
1
0
2
0
0
0
0
0
1
2
1
0
2
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
1
2
2
0
1
0
0
1
2
1
2
0
0
3
2
1
1
0
3
0
3
0
0
2
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
2
0
2
0
0
1
1
1
0
0
1
0
2
0
0
0
0
0
1
0
1
1
0
0
1
0
0
1
0
0
0
2
0
0
0
1
2
0
0
0
2
1
1
0
0
0
0
1
0
0
1
0
1
0
0
2
0
1
2
3
0
0
3
1
0
0
0
0
1
0
2
0
0
0
2
1
2
0
0
0
0
2
1
0
1
0
1
0
2
0
1
0
0
2
2
1
0
0
1
1
0
2
1
1
0
1
0
0
2
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
2
1
1
0
0
1
3
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
1
1
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
1
2
1
0
0
0
0
2
0
0
0
0
0
0
2
0
1
1
0
1
0
0
1
0
0
2
1
0
1
0
1
0
0
0
1
3
0
0
0
0
1
0
0
0
0
1
0
0
1
0
2
1
3
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
2
0
1
0
2
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
1
1
0
2
0
1
2
1
3
0
0
0
0
1
0
2
0
1
2
2
0
0
0
1
1
0
2
0
0
0
1
3
0
1
0
0
0
0
1
0
0
1
0
4
1
0
0
0
0
1
1
2
2
0
0
0
2
0
2
0
0
2
2
2
0
2
2
2
0
2
1
0
1
0
1
0
1
1
0
2
1
0
2
1
0
0
0
0
0
2
0
0
1
0
1
1
1
1
0
1
0
0
2
0
1
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
2
2
0
0
2
1
0
1
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
1
2
0
0
1
2
0
0
0
0
1
2
0
0
2
0
1
4
1
0
0
0
1
2
0
0
0
2
1
1
0
1
1
0
0
0
3
0
0
0
1
0
1
0
1
0
1
2
1
1
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
3
0
2
3
1
0
0
2
1
0
0
0
0
2
0
1
0
1
2
0
2
1
0
1
0
1
1
1
0
0
0
0
0
4
0
1
0
4
0
0
1
0
2
0
0
0
0
2
0
0
0
1
0
3
1
1
2
0
2
1
1
1
0
2
0
1
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
3
0
0
1
2
0
0
0
0
1
0
0
0
1
1
0
0
2
1
0
2
2
2
2
0
2
0
1
2
2
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
1
2
0
1
0
3
0
0
0
0
1
0
1
0
1
0
0
0
2
0
2
1
0
1
0
0
0
1
0
0
1
0
0
0
0
1
2
0
2
1
2
0
2
0
0
1
0
0
0
1
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
1
0
0
3
0
1
2
0
1
1
0
0
0
0
1
2
1
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
2
0
2
0
1
0
0
0
0
2
1
1
2
1
0
0
0
2
0
0
0
0
0
1
1
2
2
0
0
3
0
0
1
0
0
2
2
0
0
2
2
0
0
1
2
0
0
0
0
1
1
1
0
1
1
0
0
0
0
1
1
1
2
0
0
0
2
1
0
0
2
0
0
2
0
0
0
0
2
0
0
1
0
2
0
0
2
1
0
1
2
0
0
0
2
1
2
0
1
1
2
0
0
0
0
1
0
0
0
2
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
2
0
1
0
1
0
3
4
0
1
2
0
1
0
0
0
3
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
1
0
1
1
0
0
0
1
1
0
0
2
0
1
3
2
0
0
0
6
0
0
2
0
0
0
2
0
1
1
1
2
0
1
5
0
2
0
0
0
0
0
2
0
0
1
0
0
1
2
0
0
0
0
2
0
2
1
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
3
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
2
3
0
1
0
2
2
0
0
1
0
0
0
0
2
2
0
2
0
1
0
0
0
0
2
2
2
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
2
2
0
1
0
0
0
0
1
2
0
1
0
0
1
0
1
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
2
2
1
3
2
2
0
2
0
0
2
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
3
1
2
1
2
2
0
0
1
0
1
7
1
0
1
0
0
0
1
0
0
0
0
1
2
0
1
0
0
0
0
0
2
2
1
2
2
0
2
0
0
2
0
0
0
1
1
1
0
1
1
0
0
3
1
0
2
3
0
0
0
0
2
3
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
1
2
0
1
0
0
2
0
0
0
2
2
0
0
0
0
0
0
3
2
2
0
0
0
0
2
0
0
0
0
1
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
2
2
0
3
2
1
1
0
0
2
0
0
0
1
2
1
0
2
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
1
0
1
1
0
1
1
0
0
0
2
0
1
0
2
2
0
1
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
2
2
0
0
2
0
3
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
3
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
1
3
0
1
0
1
0
0
1
0
1
2
2
1
0
0
0
0
3
0
0
2
0
0
0
1
0
0
2
0
2
0
2
0
1
1
0
2
2
2
3
1
0
0
1
2
2
0
0
0
0
0
1
1
0
1
1
2
0
2
0
0
1
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
1
0
0
0
0
2
2
1
3
0
2
0
0
1
2
0
0
0
0
0
0
2
0
1
2
0
0
0
2
0
0
2
2
0
3
0
0
0
1
1
2
0
0
1
0
2
1
1
0
1
0
0
1
0
1
1
0
0
0
0
0
2
1
2
0
1
0
0
2
2
3
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
1
0
0
2
2
1
0
1
0
1
0
0
1
1
1
1
0
1
1
1
0
0
0
0
0
0
2
1
0
1
0
2
0
0
1
0
0
0
1
0
1
0
4
2
2
0
0
2
0
2
0
0
0
0
0
0
2
0
0
2
1
1
0
1
0
0
0
2
1
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
2
0
2
2
0
0
1
0
0
1
0
0
0
0
0
0
1
2
1
0
0
2
0
0
1
2
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
2
0
0
2
2
0
2
0
0
0
1
1
1
1
0
0
1
2
2
0
0
5
0
4
0
0
0
2
1
0
0
0
1
1
2
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
3
2
0
0
1
0
2
1
0
0
0
0
1
0
1
1
0
0
1
1
0
0
2
0
1
2
2
0
0
0
2
0
0
0
0
0
1
0
0
2
1
0
2
1
0
2
0
0
2
1
0
2
1
0
1
0
1
1
0
0
2
2
0
0
0
0
0
0
0
2
0
2
1
2
0
0
0
0
0
0
0
2
2
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
5
1
2
0
0
1
0
0
0
1
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
1
2
0
1
0
0
0
1
0
2
1
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
1
0
0
0
1
0
2
0
0
2
2
0
0
0
1
0
0
0
0
0
2
3
2
0
0
0
0
0
1
0
1
1
4
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
1
0
1
0
0
1
0
0
0
0
1
0
0
1
1
0
1
0
1
6
0
0
0
0
0
0
0
0
0
0
3
2
3
0
1
0
1
0
0
0
1
0
1
2
0
2
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
2
0
1
0
0
0
2
0
0
0
1
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
2
2
2
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
1
0
0
0
4
2
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
2
0
3
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
2
0
0
2
0
3
1
1
0
2
0
1
2
0
2
0
1
2
0
1
4
0
0
1
0
2
0
0
0
2
2
2
2
0
1
1
0
0
0
2
0
1
0
0
0
1
0
0
1
1
0
2
0
1
0
0
1
0
0
0
1
0
0
0
1
2
0
0
3
0
2
0
1
3
0
0
0
1
2
0
0
2
1
2
2
2
1
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
1
0
2
2
0
1
0
0
0
0
1
0
0
0
2
0
1
0
2
2
0
1
0
1
0
2
0
1
0
0
1
0
1
2
2
0
0
2
0
1
0
0
2
0
1
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
2
0
1
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
2
0
0
1
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
1
0
2
0
0
1
3
2
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
2
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
3
2
1
2
1
0
0
0
2
0
2
1
1
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
3
2
0
0
0
0
0
1
1
2
0
0
0
0
2
0
1
0
2
1
2
0
2
0
0
2
0
0
0
2
0
0
2
1
0
0
0
1
1
1
0
1
0
0
2
1
0
0
0
1
0
0
1
0
0
1
0
0
2
2
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
2
0
2
0
2
2
0
1
0
2
0
0
0
0
0
0
0
0
0
3
0
0
3
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
1
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
2
0
0
0
0
2
2
1
0
0
0
1
0
0
1
0
1
0
2
2
0
1
3
0
0
1
2
1
0
0
0
2
0
1
0
0
0
0
0
0
1
0
2
0
0
1
0
1
0
0
0
0
0
0
2
0
0
1
0
0
1
0
1
0
2
3
0
0
2
0
0
0
0
2
0
0
1
0
3
0
1
0
1
1
1
2
1
0
0
0
0
0
0
0
0
1
2
1
5
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
1
0
2
2
2
2
0
0
0
2
0
0
3
4
0
1
0
3
1
0
2
1
0
1
0
1
0
0
2
0
1
4
0
0
0
0
0
0
0
1
1
0
1
0
1
1
0
1
0
3
2
0
1
0
0
0
0
1
2
0
0
1
2
1
0
0
1
1
2
0
0
2
0
2
0
0
1
0
0
0
2
0
0
0
0
1
1
0
1
0
2
0
0
1
2
0
0
0
0
2
0
1
0
2
0
2
0
0
0
0
1
0
0
0
1
1
1
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
2
0
2
0
0
2
0
0
0
0
1
0
2
1
0
1
1
0
1
0
2
0
0
0
1
0
0
2
0
1
0
1
0
0
1
2
0
0
0
0
0
1
0
2
0
1
1
0
0
2
0
0
0
0
1
0
0
0
2
1
2
1
0
0
0
2
1
0
0
0
0
0
0
0
9
0
0
0
2
2
1
0
0
7
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
2
0
1
0
2
0
0
0
2
0
0
1
0
1
2
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
2
1
3
1
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
1
0
0
2
0
0
0
2
2
1
0
0
0
0
0
0
2
0
1
0
0
1
1
0
0
0
2
1
2
1
0
0
0
2
0
0
0
0
2
0
1
0
1
2
0
0
0
1
2
0
0
0
0
3
1
0
2
7
0
1
1
0
0
1
0
0
2
1
0
0
1
0
0
2
0
1
1
1
2
0
0
0
0
0
0
2
2
0
0
1
1
0
0
1
0
1
0
0
2
0
0
0
0
2
1
0
1
0
2
0
2
0
0
0
0
0
1
0
1
0
1
0
1
0
1
0
1
1
0
0
2
0
0
0
0
0
1
0
0
1
2
0
2
0
1
1
0
2
2
0
0
1
1
1
0
1
0
0
0
0
1
2
1
0
0
2
0
2
0
2
0
0
0
0
1
0
2
2
0
1
0
0
0
0
0
2
0
0
2
0
0
3
1
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
1
1
0
0
2
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
1
2
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
3
0
0
0
0
0
0
0
2
0
2
0
2
0
0
4
2
0
0
2
0
1
0
0
2
0
0
1
0
0
0
0
0
1
0
0
2
0
3
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
2
1
0
1
0
0
0
0
0
1
0
0
2
0
0
2
1
0
2
1
0
0
2
0
2
0
2
0
2
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
2
1
2
2
0
0
0
1
0
2
0
0
3
1
1
0
1
1
2
1
0
0
2
1
0
1
4
2
2
0
0
0
1
2
0
2
1
1
0
1
0
0
0
0
0
2
0
3
0
0
1
0
0
0
2
0
0
1
2
0
1
0
2
1
2
0
3
1
3
0
0
1
1
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
2
2
0
2
0
0
0
1
0
0
0
0
0
1
1
0
0
0
3
0
2
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
1
0
1
0
2
0
0
0
4
2
1
4
0
0
2
0
4
0
1
0
0
0
1
0
2
2
0
0
1
0
0
2
0
0
1
2
1
1
1
2
2
0
0
2
0
0
0
0
0
2
2
1
1
0
2
0
0
0
2
2
1
0
0
1
0
0
2
3
0
1
0
0
0
0
0
2
0
0
0
2
0
1
1
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
1
0
1
2
0
0
1
0
0
1
0
0
1
0
0
2
1
0
0
1
1
0
2
0
0
1
1
0
0
2
0
2
0
1
0
0
0
1
0
2
2
0
0
2
2
0
1
2
0
0
0
0
2
0
0
0
0
0
2
1
1
0
0
2
0
1
0
0
2
2
2
0
0
0
0
1
0
0
1
0
1
1
1
2
0
0
1
0
0
0
0
0
0
1
3
2
3
2
0
2
3
3
0
0
0
1
0
1
0
0
0
1
0
0
0
2
0
0
1
1
2
0
0
0
0
2
0
0
0
2
1
0
1
0
0
1
0
0
0
1
2
1
1
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
2
0
0
0
3
0
1
1
0
0
1
0
0
2
2
2
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
2
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
1
0
2
0
0
0
0
2
0
0
0
0
0
2
0
2
2
1
2
2
0
0
2
0
0
1
0
0
1
0
1
1
0
1
0
0
0
0
1
3
2
0
0
0
0
0
1
0
0
1
0
0
0
1
2
0
0
1
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
3
1
1
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
2
1
1
1
0
2
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
2
2
0
0
1
1
0
1
0
0
0
6
1
0
3
2
1
0
0
2
0
0
0
0
1
0
0
0
1
1
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
6
1
2
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
2
0
0
2
0
2
2
9
0
0
0
0
1
1
2
2
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
2
1
1
1
0
3
0
1
0
0
0
0
0
2
1
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
2
0
0
2
0
0
0
1
0
2
2
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
2
1
2
2
0
2
0
0
0
2
0
0
1
0
1
0
1
0
1
0
2
1
0
2
2
0
2
2
0
1
0
0
0
0
0
0
0
1
1
2
0
0
2
2
0
1
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
4
2
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
1
2
2
1
1
0
0
0
0
1
0
0
0
0
0
1
1
0
2
0
1
1
0
0
0
1
1
0
1
1
1
0
2
0
0
1
0
2
0
1
1
0
2
2
1
0
0
0
1
0
2
0
0
0
2
3
0
1
0
0
0
0
2
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
2
1
2
1
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
1
0
2
2
1
0
0
1
0
0
0
1
1
0
1
0
0
1
1
1
0
2
0
0
0
1
0
0
1
2
0
0
2
0
2
0
1
0
2
1
0
0
3
1
0
0
0
0
2
0
0
1
1
0
1
0
0
2
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
2
4
0
0
1
1
0
3
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
3
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
1
0
0
2
0
0
2
0
0
0
0
1
2
1
1
2
0
1
0
2
0
2
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
2
1
0
0
0
1
0
0
0
0
1
0
0
2
0
1
0
0
0
1
0
0
2
0
0
0
0
0
2
1
2
0
1
0
0
0
2
1
1
2
1
0
0
0
0
2
2
0
0
0
0
0
1
0
1
0
2
0
2
0
0
0
0
1
2
0
2
1
0
3
0
0
1
0
2
0
1
0
2
0
2
0
0
0
0
1
2
0
0
1
0
0
0
1
2
0
2
0
0
0
0
0
0
1
0
1
2
1
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
1
2
1
0
0
1
2
0
0
2
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
1
0
1
0
3
0
0
0
1
0
2
2
0
0
0
2
0
1
1
0
0
2
2
2
2
1
0
0
1
0
1
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
1
2
1
1
0
2
0
2
0
0
0
0
0
1
1
0
0
1
1
1
0
1
0
0
0
0
0
0
0
1
0
1
2
1
0
0
0
0
0
2
0
3
0
0
1
0
0
2
0
0
2
0
1
0
0
1
2
0
0
0
0
0
6
2
0
0
0
1
0
0
0
0
0
0
4
1
0
3
1
0
0
1
0
2
2
2
0
2
0
0
0
0
1
1
0
1
1
0
0
2
0
0
2
0
2
1
0
0
1
2
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
2
1
1
0
1
0
0
0
2
0
2
0
0
0
0
0
0
1
1
0
0
2
2
2
2
2
2
2
0
1
0
2
2
0
0
0
0
0
1
4
0
2
2
0
0
4
2
0
0
1
0
0
0
0
2
0
2
0
3
0
0
0
1
0
0
0
1
0
3
0
0
1
4
0
5
0
0
3
1
2
0
2
0
1
0
0
2
2
1
0
0
0
2
1
2
0
0
1
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
2
2
0
1
0
1
0
1
2
0
2
0
1
3
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
2
1
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
2
0
2
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
2
1
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
1
0
0
0
1
0
0
3
0
0
0
0
0
0
1
1
0
0
2
1
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
2
1
0
0
1
0
0
0
0
0
2
1
1
0
0
3
1
2
1
0
0
2
0
2
0
0
0
1
0
2
1
1
0
1
2
0
0
0
1
1
0
0
2
0
0
0
0
0
1
0
0
0
0
1
2
0
1
0
0
2
2
0
0
0
1
0
0
2
0
1
1
1
0
0
0
1
0
0
0
1
0
2
2
0
0
2
0
0
0
2
1
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
1
2
0
0
2
1
0
0
0
2
2
0
1
2
0
0
1
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
2
2
0
0
1
0
1
1
0
0
2
0
2
0
2
0
2
0
2
0
0
0
0
1
0
0
0
0
0
2
3
0
1
0
0
0
1
0
0
1
1
0
0
2
2
3
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
2
2
2
1
2
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
1
2
0
1
0
1
0
1
3
0
1
2
1
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
2
0
1
1
2
0
2
2
2
0
0
2
0
0
2
1
0
2
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
2
2
0
0
0
2
0
2
0
0
0
0
0
2
0
1
2
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
2
3
0
0
1
0
1
0
1
1
0
6
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
2
0
0
0
0
0
0
1
2
0
1
0
1
3
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
1
0
0
0
0
2
1
0
0
0
0
0
3
0
0
1
0
0
2
1
2
1
0
0
2
2
1
1
1
1
0
1
0
0
0
1
1
0
0
0
0
4
0
0
0
0
1
0
0
0
1
2
0
1
2
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
2
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
2
0
0
0
2
2
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
2
1
1
0
2
0
0
0
2
0
2
1
0
0
2
2
2
0
0
2
0
0
1
0
0
1
0
0
2
2
2
2
1
0
2
0
0
1
0
0
0
1
1
1
0
0
2
0
2
0
0
2
2
2
0
1
0
2
2
0
1
2
0
0
0
2
0
0
0
2
0
1
0
0
2
2
0
0
3
1
0
2
0
1
0
0
0
0
0
0
0
0
1
2
0
0
5
2
1
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
1
0
1
1
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
1
1
2
0
0
2
0
0
1
0
1
0
0
2
1
0
0
0
1
1
0
0
0
1
0
2
0
0
0
2
2
0
1
1
0
0
0
0
0
3
1
2
0
0
0
2
2
1
0
0
0
1
0
0
0
2
1
0
2
0
1
0
0
0
0
0
0
1
2
0
0
0
2
0
2
0
0
0
2
0
2
2
0
2
0
0
0
0
0
4
0
2
2
0
1
0
0
0
0
7
0
0
1
0
2
0
2
1
0
0
2
1
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
3
1
0
2
0
2
0
0
0
0
2
2
0
2
0
2
0
0
0
0
2
1
1
3
2
0
0
1
0
2
0
1
0
0
1
2
0
1
2
0
1
0
0
3
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
1
0
0
0
1
0
1
3
2
1
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
3
0
0
2
0
0
2
1
0
1
1
0
0
0
0
1
1
0
1
2
0
3
0
2
0
1
0
2
0
2
1
0
0
2
0
2
0
0
3
0
2
1
0
1
3
0
0
0
1
0
0
2
0
0
2
2
0
0
2
0
1
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
1
1
1
0
1
0
1
2
0
0
0
0
0
1
0
0
0
1
2
0
2
0
0
0
2
0
0
3
0
0
0
0
2
0
2
0
0
1
1
0
0
0
0
0
0
2
0
1
2
0
2
1
0
0
0
0
2
4
1
0
1
0
0
0
0
0
0
1
2
0
1
2
0
0
1
0
0
1
0
1
0
2
2
0
0
0
1
1
0
1
0
2
2
0
0
2
0
0
0
1
0
2
0
0
0
1
0
0
2
0
0
1
0
0
2
1
1
0
0
1
1
3
0
0
0
0
0
0
0
0
0
1
1
0
2
0
1
0
1
0
0
1
0
0
0
0
0
0
2
0
2
0
0
1
1
2
1
0
0
1
1
0
0
0
0
1
1
1
0
0
2
0
0
2
0
0
3
1
1
0
0
0
1
0
0
0
1
0
0
0
4
0
2
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
2
0
2
0
0
0
1
0
0
0
1
0
0
0
1
0
2
0
0
0
0
2
2
0
0
4
0
0
0
1
0
0
0
2
0
0
0
0
2
0
2
0
2
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
1
2
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
1
2
0
1
0
0
2
1
0
1
0
0
0
0
2
1
2
3
2
1
0
0
1
0
0
0
2
0
2
2
1
0
2
0
2
2
0
0
0
2
0
0
0
0
2
1
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
1
1
0
1
2
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
2
0
0
1
2
0
2
0
0
0
0
0
2
0
2
0
2
2
1
1
0
2
0
2
0
2
2
0
3
0
1
0
2
0
1
0
0
1
2
1
1
0
0
0
0
0
2
2
0
0
2
4
1
2
1
0
0
2
0
0
1
1
0
1
0
0
0
0
1
0
0
2
0
0
1
1
0
1
0
0
0
3
3
2
1
0
1
0
1
0
0
0
0
0
0
1
0
0
2
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
1
0
1
0
0
1
1
2
0
0
1
0
0
1
1
0
0
0
1
0
1
2
0
0
0
1
1
1
0
0
1
1
0
0
2
0
2
0
0
2
1
0
0
0
2
0
1
2
0
0
1
0
0
2
0
0
2
0
0
0
0
0
1
1
0
0
2
0
2
0
1
0
0
2
1
0
0
0
1
1
0
1
1
0
0
4
0
0
2
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
1
0
0
0
0
0
0
3
0
2
0
1
2
2
2
1
0
2
0
0
0
2
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
1
0
0
0
2
1
0
2
0
0
0
0
0
2
0
0
2
0
0
0
2
0
2
3
2
0
0
1
0
1
0
0
0
2
0
0
1
0
2
0
0
0
0
1
1
2
0
0
0
2
0
2
2
3
1
1
1
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
3
0
1
0
0
2
0
1
0
1
0
0
0
0
2
2
0
0
2
0
1
0
0
0
1
1
0
0
1
1
3
0
2
1
1
1
2
1
0
1
0
1
0
0
0
0
1
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
1
0
1
0
0
0
0
0
2
3
2
0
0
1
1
0
1
2
0
0
0
0
1
2
0
2
0
0
2
2
0
0
0
2
0
2
1
0
1
0
2
2
3
1
1
0
2
0
0
0
0
0
2
0
2
0
2
1
0
0
0
1
0
1
0
0
0
1
2
7
1
1
0
1
1
0
2
1
0
0
3
0
1
1
0
2
0
0
1
0
0
0
0
0
1
0
2
1
0
0
0
0
2
2
0
0
1
0
0
0
0
0
1
0
0
2
2
0
0
0
2
0
0
0
8
2
0
0
0
4
1
0
0
0
2
0
0
2
1
1
2
1
0
0
2
0
0
2
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
2
0
1
0
1
2
2
2
2
0
0
0
0
1
0
1
1
0
0
1
0
1
0
0
0
2
2
2
2
0
1
0
0
0
1
0
2
0
1
0
2
0
1
0
0
1
2
0
1
2
1
4
0
2
0
0
0
0
1
0
1
1
1
0
0
0
1
2
0
1
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
2
1
1
2
0
0
0
0
0
2
0
0
1
2
0
0
1
0
1
0
3
0
2
0
1
0
0
2
0
0
1
0
0
0
1
1
0
1
2
1
2
0
0
2
1
3
1
0
0
1
0
0
1
0
0
1
0
0
0
2
0
1
0
0
0
0
3
0
1
2
0
1
1
0
0
0
1
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
1
2
0
1
0
2
0
0
0
0
1
0
2
0
0
0
1
1
0
1
0
2
1
2
0
0
0
0
0
1
1
1
0
0
1
0
0
1
3
0
1
0
1
0
0
2
0
0
0
0
2
2
0
0
2
0
0
0
2
1
0
0
0
1
0
0
0
0
6
0
2
0
2
2
0
0
1
2
1
0
1
0
2
0
1
0
0
0
2
2
0
0
0
0
1
0
1
2
0
2
0
0
0
0
0
0
1
3
2
2
0
0
0
2
0
2
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
6
0
3
0
1
2
2
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
1
1
0
1
0
2
0
0
1
2
2
0
2
0
0
2
0
1
2
0
1
1
0
1
0
1
0
1
1
2
1
1
1
0
2
0
1
1
0
1
0
1
0
1
1
0
0
0
0
0
0
2
0
3
2
2
0
2
0
0
0
0
0
2
0
2
1
1
1
0
0
0
0
0
0
1
2
0
2
1
1
0
0
0
0
0
0
2
0
0
1
1
0
0
2
0
0
0
0
1
1
1
0
0
0
0
0
2
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
4
1
0
1
0
0
0
0
0
1
0
0
0
2
2
0
0
3
0
1
0
0
0
0
0
0
0
0
2
0
1
1
1
2
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
2
0
2
0
1
0
0
0
1
0
2
0
1
0
1
0
0
2
0
0
0
2
0
2
2
0
0
0
0
1
2
1
1
2
1
0
0
5
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
2
1
0
0
1
0
0
1
0
1
2
0
2
0
0
0
0
0
2
0
0
0
0
1
1
1
2
2
1
0
0
0
2
0
2
0
0
0
0
0
0
1
2
0
0
0
1
0
0
2
0
1
1
1
0
0
2
0
2
0
0
1
2
0
1
2
0
0
1
0
0
0
0
1
0
1
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
2
0
0
1
2
0
0
0
0
0
1
0
0
0
1
2
1
1
0
2
1
0
1
0
0
0
2
0
0
2
0
1
0
0
3
7
1
2
1
2
2
0
0
0
0
2
0
0
0
3
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
2
0
3
1
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
2
0
0
2
0
0
0
0
1
3
0
2
0
0
0
0
2
2
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
1
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
1
2
1
0
0
0
0
1
1
0
1
0
0
0
1
0
2
11
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
2
2
3
0
0
1
0
0
3
1
0
0
0
0
0
1
0
1
1
0
0
5
0
1
0
0
0
0
2
1
0
2
0
2
0
0
0
1
0
0
2
0
0
1
0
0
1
0
2
1
0
2
2
0
1
1
0
0
0
0
2
0
0
0
2
0
1
0
0
1
0
1
1
0
0
0
0
0
2
0
0
1
0
1
0
0
2
0
2
0
0
0
2
0
0
1
2
2
1
0
0
0
0
0
0
2
0
0
0
0
0
4
0
2
1
2
0
2
2
0
1
2
1
1
0
0
0
0
2
0
0
2
0
0
1
0
3
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
2
1
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
1
0
1
1
3
2
1
0
0
2
2
0
0
0
2
0
0
0
0
2
3
1
1
0
0
2
0
0
1
2
0
1
1
0
0
0
0
0
0
1
0
1
0
1
2
1
1
0
1
2
0
1
1
0
0
1
0
0
0
2
0
0
0
0
2
0
1
1
2
1
0
2
0
0
0
0
0
0
0
0
4
1
0
0
2
0
2
0
1
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
2
1
1
2
3
0
0
1
0
0
0
2
2
0
0
0
0
2
1
0
2
0
1
3
0
1
0
0
0
0
0
1
0
0
1
2
0
0
1
0
0
2
2
0
0
0
0
1
1
2
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
1
2
2
1
0
2
1
0
0
0
2
0
0
1
0
1
0
1
0
0
2
0
0
0
0
1
1
0
2
2
0
0
1
1
0
0
0
0
0
2
1
2
2
0
0
0
3
0
1
0
0
0
0
1
0
2
0
1
1
0
0
0
1
2
0
0
1
0
0
0
1
3
1
0
2
2
0
0
2
0
2
2
0
0
0
1
0
0
1
0
0
0
0
0
2
1
0
1
0
1
2
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
4
0
0
0
1
2
0
0
1
0
0
2
1
2
0
1
2
0
1
0
0
1
0
0
0
2
4
1
0
1
0
0
2
0
0
0
2
0
2
0
3
1
0
1
0
0
0
0
2
0
0
0
2
0
0
4
3
0
0
2
0
0
0
1
0
1
0
1
2
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
1
1
0
2
3
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
6
0
2
2
1
0
0
0
0
0
0
0
0
0
1
2
1
0
0
4
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
2
0
0
1
0
0
0
2
0
4
1
0
0
0
1
0
0
0
0
1
0
1
0
1
0
2
2
0
0
2
2
0
1
1
2
0
0
1
0
0
1
0
0
1
0
0
1
0
1
0
0
0
1
1
0
2
0
2
0
0
0
0
0
2
0
0
0
2
2
1
1
0
0
0
1
0
0
0
0
0
2
2
2
1
2
0
0
0
1
0
0
0
0
2
0
2
0
1
0
1
0
2
0
1
0
0
0
0
0
1
2
2
2
0
0
1
2
0
0
1
0
2
0
1
2
0
1
0
2
0
1
0
1
0
2
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
1
0
1
1
2
0
0
2
0
0
0
1
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
2
0
0
1
0
1
0
0
2
1
1
1
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
2
0
0
0
0
3
0
2
0
2
2
0
0
2
0
0
0
4
0
0
1
0
2
2
0
2
3
1
0
0
1
0
3
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
2
3
0
0
1
2
0
8
0
1
0
0
2
0
2
2
1
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
2
2
0
0
2
2
0
0
0
0
0
1
0
3
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
1
2
0
2
1
0
0
0
2
0
2
2
0
0
0
0
0
0
0
2
0
1
0
0
2
1
0
0
1
1
0
1
0
5
0
0
0
1
2
0
1
0
2
0
1
0
0
0
0
0
2
0
0
1
0
3
0
1
1
2
2
0
0
0
1
0
1
1
0
0
0
0
2
0
1
4
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
5
0
0
1
0
0
2
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
2
1
0
0
1
0
1
0
0
2
1
1
0
0
1
0
1
0
0
0
0
1
2
0
1
1
1
0
0
0
2
2
0
0
0
0
2
2
0
2
0
1
1
2
0
1
0
0
0
0
0
0
0
0
1
0
2
1
0
2
2
0
0
0
1
0
2
1
1
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
4
2
0
0
2
0
0
0
2
0
0
0
0
0
5
2
1
0
0
0
0
0
2
0
0
2
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
2
1
2
0
0
1
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
1
0
0
1
0
0
0
0
3
1
0
0
1
0
0
0
0
0
4
0
0
0
1
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
1
2
0
0
0
2
0
0
2
4
1
1
0
1
1
0
0
1
0
1
1
0
0
1
0
2
0
0
0
0
2
0
1
0
2
2
2
1
0
0
0
2
0
0
1
2
0
0
0
2
2
1
1
0
0
0
0
0
0
0
6
1
1
1
0
0
1
2
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
2
1
0
0
0
2
0
1
1
0
0
0
1
0
2
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
1
0
0
1
2
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
3
0
0
0
0
0
2
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
1
1
0
3
1
0
1
1
0
1
0
0
1
2
1
0
0
1
0
0
0
0
1
0
1
1
0
0
0
2
0
0
0
0
0
0
1
2
0
1
0
1
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
2
0
0
2
2
0
0
0
0
2
3
1
2
0
0
2
0
1
2
1
1
0
1
2
0
2
0
1
0
1
0
2
2
0
2
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
1
0
1
1
0
2
0
0
0
1
1
0
2
2
2
0
0
1
0
0
0
0
0
2
1
1
0
0
0
0
0
0
2
1
2
0
2
1
2
2
1
2
1
0
1
0
0
2
0
0
2
0
1
2
0
0
0
0
2
0
0
0
0
0
1
1
0
1
2
0
0
1
0
0
0
0
0
0
0
0
3
0
0
2
0
0
1
0
2
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
5
0
0
0
1
0
0
0
2
0
0
2
7
1
0
2
0
0
0
1
0
0
0
0
3
0
1
1
1
0
0
2
1
0
1
0
0
0
0
2
0
3
0
0
1
0
0
1
0
1
0
0
0
2
0
2
1
0
2
0
2
2
1
0
2
0
0
0
0
2
0
1
1
0
0
2
0
2
0
0
0
0
0
1
2
2
0
0
2
0
0
2
0
6
1
0
0
2
2
2
0
0
1
0
2
0
0
1
1
2
0
0
1
2
0
0
0
2
2
2
0
2
0
0
0
1
1
0
0
0
0
1
2
0
0
4
1
0
0
0
1
1
2
0
0
0
0
1
1
0
2
1
0
2
0
2
1
0
1
2
0
1
0
0
0
0
1
2
2
2
0
0
2
5
0
2
1
0
0
0
1
0
0
0
2
1
0
6
0
0
1
0
2
3
1
0
0
0
0
0
0
0
0
0
1
0
1
3
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
2
0
2
0
1
2
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
1
0
1
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
1
2
0
0
0
2
0
0
2
0
0
0
2
2
2
0
1
0
1
0
2
0
0
1
1
0
1
0
0
0
0
0
0
0
3
0
0
0
4
0
3
0
0
1
0
4
0
0
0
1
1
1
2
1
0
0
0
1
0
1
0
0
0
1
1
1
0
2
0
0
2
2
1
0
0
2
2
0
1
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
4
0
0
0
2
4
0
0
0
0
0
0
0
2
0
0
0
0
0
4
0
0
0
0
0
1
1
0
0
2
0
0
0
0
2
0
1
1
0
1
2
2
1
0
0
2
0
2
1
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
2
0
0
0
0
1
0
0
0
1
1
0
1
1
1
2
0
2
0
0
1
0
0
0
2
2
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
2
0
1
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
1
1
0
0
1
0
2
1
0
1
0
0
2
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
2
2
0
0
0
0
3
2
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
1
0
0
0
1
1
0
0
1
0
1
1
1
1
0
2
2
3
1
0
0
2
0
2
0
0
0
1
2
0
2
1
2
1
0
0
0
0
0
3
0
0
1
1
2
0
0
0
0
0
0
1
0
0
0
2
1
1
2
0
1
0
2
0
1
0
1
6
0
0
3
0
0
2
0
0
2
0
1
0
0
2
0
1
0
0
0
0
0
0
0
2
3
1
0
0
2
1
0
0
1
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
1
2
2
0
0
0
0
2
0
0
2
0
1
0
0
1
1
1
0
0
0
0
1
0
0
0
2
1
0
1
0
0
1
0
0
0
1
0
0
2
0
0
1
1
1
0
0
2
1
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
2
0
1
2
0
2
0
0
0
0
0
1
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
1
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
2
2
1
0
0
0
3
0
2
0
1
0
2
0
0
0
0
1
1
0
1
2
2
0
1
1
0
0
0
0
2
1
2
0
2
0
1
0
0
0
2
1
0
1
0
1
4
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
2
2
2
0
0
0
0
0
2
2
0
0
3
0
2
2
0
0
0
0
0
0
1
0
2
0
0
2
1
1
1
0
1
2
0
0
0
0
2
0
1
2
0
0
1
2
0
1
0
0
0
0
1
0
1
1
2
0
0
1
0
0
0
2
1
3
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
2
0
3
1
0
2
0
0
1
0
0
2
4
1
4
0
2
1
0
0
2
1
0
0
0
3
0
4
0
1
0
0
0
0
0
0
0
1
2
1
0
2
1
2
0
1
0
0
0
0
2
2
0
1
0
0
0
0
0
2
2
0
0
2
0
2
0
0
0
0
3
1
1
0
1
2
0
0
2
1
2
0
1
0
0
0
1
0
1
0
2
1
1
4
1
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
1
0
1
1
0
1
1
1
0
1
0
0
1
1
2
3
0
0
2
2
1
1
3
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
1
0
2
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
3
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
2
2
0
0
2
0
0
0
2
2
0
4
0
1
0
1
0
0
1
2
1
1
0
1
0
0
1
2
2
0
0
3
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
1
1
1
0
2
0
1
0
0
2
2
1
1
0
0
0
0
0
1
0
0
2
0
0
0
0
2
2
0
1
2
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
1
1
0
0
0
1
0
0
1
0
0
0
0
2
0
2
0
1
0
2
0
1
1
1
0
2
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
2
1
0
2
3
1
2
1
0
0
2
0
1
0
0
0
0
1
2
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
3
1
0
0
1
2
0
0
0
2
2
1
0
0
0
0
1
0
0
0
1
1
0
0
0
2
2
0
1
0
2
0
0
0
0
0
0
1
2
1
0
0
0
2
0
2
2
0
2
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
3
2
0
0
0
2
0
2
0
0
0
0
2
0
1
2
1
2
2
1
0
2
0
2
0
0
0
0
2
0
1
0
2
0
0
0
1
2
0
0
1
2
0
3
0
1
2
0
5
0
2
1
0
1
0
0
0
0
1
2
1
2
0
0
0
0
0
2
0
0
1
0
0
2
0
1
0
2
0
2
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
2
0
1
0
2
0
0
1
0
0
0
2
0
3
0
2
0
0
0
1
0
1
0
0
0
1
6
0
1
0
1
0
2
1
0
0
0
4
0
0
0
1
1
1
0
0
2
0
0
0
0
0
0
0
2
2
3
2
1
1
2
1
0
0
1
0
0
1
2
2
0
1
0
1
0
0
0
1
0
2
0
0
2
0
0
1
0
0
0
0
1
2
1
0
0
0
0
2
0
4
0
0
0
2
1
0
0
2
0
1
0
0
0
1
0
1
2
0
2
0
2
1
0
1
2
0
0
0
2
2
2
1
2
2
0
1
1
0
0
0
0
1
0
1
1
0
1
0
0
0
1
1
1
0
1
0
2
0
0
2
0
2
0
1
2
0
0
1
0
0
0
1
0
2
2
0
0
0
0
1
0
2
1
0
0
2
0
0
1
0
0
0
0
1
1
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
2
0
0
1
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
1
0
2
3
0
4
2
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
2
1
0
1
1
0
0
0
2
2
0
0
3
0
0
0
0
1
1
0
1
2
0
0
1
0
0
1
1
0
2
0
0
0
3
2
0
0
0
0
0
2
1
0
1
2
0
0
0
0
1
2
0
2
0
0
0
1
2
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
1
0
0
2
0
2
1
1
0
1
0
0
1
1
0
1
0
3
0
0
0
0
0
0
0
1
2
0
0
0
0
1
1
0
2
0
2
0
0
2
0
0
0
0
0
0
1
1
3
0
0
0
0
1
0
0
0
0
0
2
1
0
0
1
0
0
2
0
0
3
0
0
1
0
0
0
2
1
0
2
2
0
2
1
0
1
0
2
1
1
0
2
0
1
2
0
1
0
2
1
0
0
0
0
0
0
0
0
2
1
1
0
0
2
2
0
0
0
0
0
3
0
0
0
0
0
1
0
0
2
0
3
0
1
0
1
2
1
1
0
0
0
0
0
0
1
0
0
0
2
0
0
3
0
1
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
2
1
2
0
0
1
2
0
0
1
0
0
0
2
2
2
3
0
0
0
3
1
1
1
1
1
1
2
0
1
0
2
2
1
2
0
2
4
2
2
0
1
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
2
2
0
2
0
0
2
1
0
1
0
0
2
0
0
0
1
0
0
2
0
1
1
1
0
0
0
0
0
2
0
0
2
0
1
0
2
1
0
2
0
2
0
0
0
0
2
0
0
0
0
1
0
2
1
0
1
1
0
2
2
0
0
0
0
1
2
0
0
0
2
1
0
0
2
2
1
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
1
3
2
0
3
2
0
0
0
0
1
2
0
0
0
0
1
0
2
0
1
2
2
0
2
2
0
2
0
0
0
0
0
2
0
1
0
1
2
2
0
2
2
0
3
0
0
0
0
0
1
0
0
1
0
2
2
0
0
0
0
0
0
0
1
1
2
2
0
1
0
1
0
0
0
0
0
0
0
2
3
0
1
2
0
0
0
0
2
0
0
2
0
1
2
0
0
0
2
0
2
0
1
0
1
0
0
1
2
0
0
0
2
1
2
0
0
0
2
2
2
1
0
2
0
0
0
3
0
0
0
0
2
0
1
0
0
0
2
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
1
0
1
0
1
1
1
1
2
0
2
2
1
2
1
1
2
0
2
0
0
0
1
0
1
0
0
2
1
0
0
0
2
0
0
0
1
0
0
0
2
0
0
1
0
1
1
0
0
2
0
2
3
2
1
1
0
2
2
0
1
0
1
2
0
0
3
0
1
2
2
2
0
0
2
0
0
0
1
1
0
0
2
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
3
0
1
2
0
2
2
2
2
1
2
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
2
1
0
2
0
0
0
2
0
2
0
2
2
0
0
0
2
0
0
0
1
0
0
1
1
5
2
3
1
2
3
1
1
0
0
1
0
2
1
0
0
3
1
1
0
0
0
1
2
1
0
4
0
0
0
1
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
1
0
0
2
0
2
0
0
0
0
0
2
0
2
4
1
0
3
2
0
1
0
2
0
0
2
0
0
0
0
2
1
0
0
0
2
2
0
1
0
0
2
0
0
0
2
0
1
2
0
2
0
1
1
0
2
0
0
0
2
1
0
0
0
1
2
1
1
2
1
1
1
0
0
2
2
0
1
0
0
0
1
0
0
2
1
1
1
2
5
0
1
1
1
0
0
0
1
1
2
2
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
2
0
1
2
1
1
0
0
0
0
0
2
0
1
0
0
0
1
2
3
2
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
2
2
2
0
2
0
0
0
0
2
1
1
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
3
0
0
0
0
0
1
0
4
1
0
0
2
0
0
2
1
0
0
0
2
1
0
0
0
2
0
0
1
1
0
0
2
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
1
0
1
2
0
0
0
0
0
2
1
1
0
0
0
0
1
3
0
1
1
1
0
0
0
0
0
0
2
1
0
1
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
1
1
0
2
0
0
0
0
2
2
0
0
0
0
0
2
1
1
1
0
0
1
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
1
2
0
1
2
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
2
0
0
0
2
1
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
2
0
0
2
1
0
2
0
0
2
2
0
1
0
1
1
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
1
0
1
1
0
2
1
0
0
1
0
0
3
0
0
0
0
2
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
3
2
0
4
3
0
2
1
3
1
0
0
0
3
3
0
0
2
1
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
1
3
0
0
0
0
0
2
0
1
0
0
3
1
1
0
0
2
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
2
0
2
2
0
0
0
2
2
0
0
2
1
2
0
0
0
2
1
0
0
0
2
1
0
1
0
0
0
1
0
0
1
1
1
0
0
1
0
0
0
0
3
1
0
2
2
2
0
0
0
1
0
1
0
0
0
0
1
0
2
0
0
2
0
0
0
0
1
1
1
0
0
0
2
0
2
0
0
1
0
2
0
2
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
3
1
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
4
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
2
0
1
2
1
2
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
2
0
0
0
2
0
1
0
1
0
2
0
1
0
2
0
0
1
0
2
0
2
0
0
0
0
1
0
0
0
4
0
0
0
2
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
1
0
1
2
0
0
0
0
2
0
2
0
3
0
0
0
0
1
2
2
0
1
0
2
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
1
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
6
0
0
1
0
2
4
2
2
1
1
1
0
1
0
2
1
2
1
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
2
0
0
1
2
2
0
0
0
1
2
6
0
0
0
0
0
0
0
0
2
0
0
2
0
4
1
0
2
0
2
0
0
2
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
2
1
0
0
2
2
2
0
0
0
0
0
1
0
2
0
1
2
2
0
0
0
3
0
2
0
0
1
0
0
0
2
1
0
0
0
2
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
3
0
0
3
0
0
0
2
0
0
0
0
0
0
1
1
0
2
0
2
0
0
0
2
2
1
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
1
2
2
2
0
0
1
0
0
0
1
1
1
0
0
2
2
2
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
1
0
0
0
1
0
0
2
0
0
3
0
0
0
0
1
0
0
2
1
0
0
1
0
1
0
2
2
1
0
0
2
2
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
1
1
2
2
2
3
1
2
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
1
0
0
2
0
0
0
2
0
0
0
0
0
2
0
1
2
1
0
2
1
0
2
0
0
1
0
2
2
0
0
2
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
1
0
1
0
0
1
0
0
0
2
1
0
3
1
0
0
0
1
1
1
0
0
2
0
1
2
2
0
2
0
1
0
2
0
2
0
1
0
0
0
0
1
0
3
0
0
0
0
1
0
2
1
0
0
0
1
1
0
0
2
0
0
0
2
0
1
2
2
2
0
0
1
1
0
2
0
0
0
1
0
0
0
0
0
0
2
0
2
0
2
0
1
1
0
0
0
0
0
1
0
0
0
4
2
2
2
0
2
3
0
3
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
7
2
0
3
2
0
0
2
2
1
1
2
0
1
0
0
0
2
0
0
0
1
2
0
2
2
2
0
0
0
1
0
0
0
0
1
0
0
2
2
3
0
1
0
0
1
0
0
0
0
0
2
0
1
2
2
2
0
0
0
2
0
1
1
0
0
1
1
0
1
2
2
2
1
0
2
0
0
0
0
0
2
0
0
2
0
1
2
0
2
0
0
0
0
6
0
0
2
1
0
0
0
0
0
0
0
1
1
2
0
2
0
0
1
0
0
2
0
2
0
0
0
1
2
1
2
0
0
2
0
0
0
0
0
2
1
2
0
0
2
3
2
1
0
0
2
0
0
1
1
1
0
2
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
2
1
2
0
0
2
0
2
2
5
0
0
0
2
0
1
0
0
3
4
0
0
1
0
0
2
0
0
2
3
2
0
1
1
0
3
0
0
0
1
1
0
2
1
2
0
0
1
1
0
0
0
0
0
1
0
2
0
2
0
2
0
0
2
0
1
0
0
1
2
0
0
1
0
2
0
0
0
0
0
0
2
4
0
0
1
0
0
0
0
2
0
0
0
0
2
0
2
2
1
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
2
2
0
0
1
1
0
2
1
0
0
1
0
0
1
2
0
1
2
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
2
3
0
2
0
1
1
0
0
0
0
0
2
0
2
0
1
1
0
0
0
2
0
1
0
0
0
0
2
0
2
1
2
0
1
4
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
1
1
0
0
0
0
0
2
1
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
2
2
0
1
0
0
0
0
1
0
1
1
0
0
3
1
2
2
0
0
2
0
0
1
1
0
1
0
0
0
4
0
0
0
0
0
0
0
1
0
2
1
1
0
0
2
0
0
0
0
1
2
2
0
0
0
0
2
0
0
1
2
0
3
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
2
0
1
0
0
2
0
0
0
0
1
1
0
0
0
2
0
1
0
0
0
0
2
1
0
2
0
1
0
0
0
2
0
0
0
2
0
1
0
1
1
2
1
0
0
0
0
2
1
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
1
1
0
1
0
0
2
0
2
0
2
0
0
0
3
0
0
2
0
3
1
0
2
0
0
1
0
0
1
0
5
0
0
0
0
0
0
1
0
1
2
2
0
0
1
0
0
0
1
0
1
0
1
1
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
2
0
2
0
2
0
0
1
0
0
0
0
0
4
2
1
2
0
0
1
0
0
2
0
0
1
2
0
0
0
0
1
0
0
1
0
0
0
1
1
0
2
0
0
0
0
1
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
1
2
0
2
0
0
2
2
1
1
0
2
0
0
0
0
1
0
2
0
0
1
1
0
0
2
2
0
0
2
1
0
0
0
2
0
1
1
0
0
0
2
0
0
1
0
0
2
0
0
0
0
3
2
0
1
1
0
0
1
0
1
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
1
2
0
1
0
1
0
0
0
0
1
2
0
0
0
0
0
2
0
2
2
0
1
1
0
0
0
3
1
2
0
3
0
0
2
2
0
0
0
2
0
1
1
2
0
0
0
1
0
2
0
0
1
0
0
0
0
2
1
0
0
10
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
2
0
1
0
0
1
0
0
0
0
0
1
2
0
0
1
0
0
0
2
2
0
3
2
1
2
0
2
0
0
0
0
0
2
2
1
3
0
3
0
2
1
0
0
0
1
2
0
0
0
0
0
0
0
2
1
2
1
0
0
0
1
0
0
0
1
0
0
1
1
2
2
1
1
0
0
1
0
3
2
2
1
0
2
1
1
0
1
0
2
0
0
1
1
0
0
0
0
0
2
1
1
1
0
0
1
0
0
0
2
1
0
2
0
0
4
0
2
0
0
0
0
0
1
2
1
0
4
2
0
0
0
0
2
0
1
0
2
3
0
0
1
1
0
1
0
0
0
0
0
1
0
0
1
2
0
2
2
0
1
0
0
1
0
0
0
1
2
3
1
1
0
0
0
1
0
1
2
0
0
0
1
2
2
0
0
1
2
4
0
2
0
0
0
0
1
0
2
0
0
0
0
2
1
2
0
0
0
2
0
0
0
3
2
1
1
1
0
0
0
0
2
0
0
2
0
2
0
1
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
2
0
0
1
0
2
0
0
0
2
2
0
0
0
1
1
1
0
0
0
0
2
0
0
0
2
2
0
0
0
0
2
0
0
0
0
2
3
0
1
0
0
0
1
0
2
0
0
1
0
2
1
1
2
2
0
2
0
0
0
0
1
0
0
2
0
0
1
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
3
1
0
0
0
0
2
6
0
0
1
0
2
2
0
0
0
0
0
0
2
0
1
1
0
0
1
1
0
0
0
0
1
1
0
0
2
1
0
0
2
1
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
2
1
0
1
1
0
0
0
3
0
2
0
2
0
0
0
2
1
2
0
1
0
0
0
1
2
1
1
0
0
0
0
0
2
0
1
0
0
0
2
0
0
2
0
0
0
0
1
1
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
2
1
2
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
2
0
2
1
1
1
0
0
0
0
0
0
0
1
1
2
0
1
2
0
1
2
1
0
0
2
1
0
2
2
0
2
4
0
0
1
0
1
0
2
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
1
2
2
2
0
2
0
2
0
0
2
2
2
0
1
0
1
1
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
1
0
1
2
0
0
0
1
0
0
2
2
2
0
1
0
9
0
0
0
0
0
0
2
2
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
2
0
2
0
1
1
1
2
1
0
0
1
0
2
2
0
2
0
0
0
0
4
1
0
1
0
0
0
0
0
0
0
0
2
1
4
0
0
0
1
0
0
1
0
0
1
0
2
0
2
3
2
0
1
0
2
1
2
0
2
1
0
1
2
0
0
1
1
2
0
0
0
1
1
1
0
0
2
0
0
1
0
1
0
1
0
0
1
0
1
1
1
0
0
1
0
2
1
0
0
2
0
1
0
0
2
0
0
0
2
0
2
1
0
2
1
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
2
1
0
1
0
0
2
1
0
1
1
0
2
0
0
0
0
0
0
2
2
0
0
2
0
2
2
0
0
0
1
0
5
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
2
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
5
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
4
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
1
1
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
2
1
2
1
0
0
0
0
1
1
1
0
1
0
0
2
0
2
1
2
2
1
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
2
1
1
2
2
0
0
1
1
0
0
0
2
1
1
1
0
0
0
0
3
0
0
0
0
2
2
1
0
0
0
0
0
2
1
0
2
0
0
1
1
2
2
2
0
0
1
0
0
1
0
0
0
1
2
0
2
0
0
0
1
0
0
0
1
2
2
0
0
1
0
2
0
0
1
1
0
1
2
1
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
1
2
0
0
0
1
2
1
2
0
0
0
0
1
0
2
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
1
2
2
1
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
3
1
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
3
1
0
2
0
2
0
0
1
1
0
0
0
0
2
0
0
1
2
2
0
0
1
0
0
1
1
0
2
0
0
1
2
0
0
2
0
2
0
0
1
0
0
0
1
0
2
0
0
0
0
1
0
0
2
0
0
0
1
2
1
3
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
2
2
0
0
1
0
0
0
2
0
0
2
0
0
0
2
2
0
2
0
0
0
2
0
0
1
1
0
0
0
0
0
1
2
2
3
0
1
0
0
0
1
2
0
0
0
0
0
2
0
1
1
0
0
0
1
0
2
0
2
2
0
2
2
2
0
1
2
0
1
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
1
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
2
0
1
2
1
0
0
0
0
0
0
0
1
0
1
0
2
0
0
2
2
0
2
0
2
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
2
2
1
0
0
2
0
1
2
0
1
0
0
1
0
2
0
0
1
0
0
0
3
2
0
0
1
0
2
0
1
0
0
0
1
0
1
0
0
2
0
1
1
2
0
0
1
0
0
0
0
2
1
4
1
0
2
0
1
0
2
3
1
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
1
0
1
0
0
0
0
0
0
2
2
2
0
0
2
0
1
0
0
0
3
2
0
3
0
1
2
3
0
0
0
0
0
2
0
0
0
0
2
1
0
0
2
0
0
1
0
0
2
1
1
0
2
0
0
0
4
0
3
0
0
0
0
2
1
0
0
1
0
1
1
2
0
2
1
0
0
0
0
0
1
4
0
2
4
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
2
0
0
0
0
1
0
1
0
0
4
2
2
0
0
0
0
1
1
0
2
2
1
0
1
1
1
0
0
1
0
0
1
2
0
2
0
0
2
0
0
0
0
0
1
0
0
0
2
2
0
0
0
2
2
0
0
0
2
1
2
0
0
0
0
0
2
1
1
1
0
0
1
0
2
0
0
0
0
2
0
0
0
0
1
2
2
0
0
2
2
1
0
0
0
0
0
2
1
0
1
0
1
2
0
0
1
0
0
2
0
0
1
1
2
0
0
0
2
0
1
0
0
0
1
1
2
2
1
0
0
2
0
0
0
0
2
0
0
0
1
0
1
0
2
0
0
0
2
0
1
1
0
0
0
0
2
2
0
1
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
2
2
1
2
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
1
0
1
0
0
2
0
2
1
1
0
0
0
3
0
0
0
1
0
1
0
2
0
0
0
1
0
2
2
2
2
0
0
0
0
0
2
2
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
3
2
0
2
0
1
0
4
2
0
2
1
2
0
0
1
1
0
4
0
0
0
1
0
0
2
1
0
0
0
0
2
2
0
0
0
2
1
0
2
0
2
0
0
2
0
2
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
1
0
2
0
0
1
2
0
1
2
2
0
1
0
0
2
0
2
0
1
0
1
0
2
1
3
0
0
0
1
3
0
0
1
2
0
2
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
1
2
0
1
0
1
4
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
2
1
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
1
2
1
1
0
2
1
0
2
0
1
0
0
0
1
0
1
0
0
2
2
3
2
0
1
2
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
2
2
0
2
2
1
2
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
1
0
1
3
0
1
2
0
0
2
0
0
0
0
0
0
1
1
1
0
1
1
2
0
2
2
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
1
1
0
2
0
0
0
0
0
1
2
0
0
2
2
1
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
4
2
0
0
0
1
0
0
1
0
2
0
1
0
2
0
0
2
0
0
0
0
3
2
1
0
0
0
0
1
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
1
2
2
0
1
0
0
0
2
1
2
1
0
0
0
1
1
2
0
0
2
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
2
1
1
0
3
0
0
0
0
0
2
2
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
2
1
0
0
0
0
0
0
2
0
1
2
0
1
2
1
0
1
4
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
3
0
2
0
0
1
1
2
0
1
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
2
0
0
0
1
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
2
2
0
1
3
0
0
0
0
1
0
2
3
0
0
0
0
0
1
2
0
0
1
0
2
2
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
3
0
1
1
2
9
0
1
0
0
2
0
0
2
3
0
0
0
0
1
0
2
2
0
1
0
3
0
0
0
0
0
0
2
1
0
1
0
0
0
2
0
0
2
0
2
0
0
0
0
1
1
0
0
0
1
2
6
0
0
0
1
0
1
1
1
1
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
2
0
0
2
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
1
0
0
0
0
0
0
1
2
1
0
0
1
0
0
0
1
2
1
0
0
0
0
0
0
0
1
0
0
2
1
0
2
0
0
1
0
2
1
2
1
2
0
0
0
0
1
0
1
1
0
1
1
1
0
0
1
0
2
0
4
0
2
0
1
1
2
0
1
1
0
2
0
0
0
2
1
2
0
1
0
2
1
0
0
0
0
0
0
0
0
1
0
2
2
1
2
0
1
0
0
0
1
0
0
1
0
0
0
0
2
2
1
1
0
1
1
2
0
3
0
0
1
1
0
0
2
1
0
0
0
0
0
1
2
0
0
1
1
2
1
0
1
2
0
0
2
1
1
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
4
1
0
1
0
0
1
0
1
0
0
1
0
2
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
2
2
1
0
0
1
0
0
2
1
0
0
1
0
0
2
0
0
1
2
0
0
0
2
0
2
1
0
3
1
0
1
0
0
0
2
0
1
0
2
0
0
3
2
0
0
0
2
1
0
0
0
3
1
2
0
0
3
0
1
0
1
0
2
0
0
1
0
2
0
2
0
0
0
0
0
0
1
2
0
2
1
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
1
0
1
2
2
0
2
1
0
0
2
4
0
0
1
0
0
1
0
1
3
0
0
2
0
2
0
0
0
2
1
2
0
0
0
1
1
1
0
0
1
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
5
0
0
0
0
2
0
1
0
1
0
0
0
0
2
0
1
0
0
1
1
0
0
1
0
0
2
0
0
0
0
0
0
1
0
2
0
2
2
1
2
0
0
0
0
2
3
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
1
0
0
0
2
2
2
0
2
0
2
0
1
1
0
2
0
0
0
0
0
0
2
0
1
1
2
1
0
2
2
1
0
0
1
1
0
1
1
2
2
0
0
2
0
2
0
1
1
2
0
0
0
2
0
0
2
0
0
1
0
0
2
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
2
0
0
2
0
2
3
0
2
1
2
2
0
1
2
0
0
0
1
0
1
1
2
0
0
0
2
0
2
0
2
2
0
0
0
0
0
0
1
2
0
1
2
0
0
0
2
0
1
2
0
0
0
1
0
2
0
0
0
2
0
1
0
2
0
1
0
1
0
2
1
0
2
1
1
0
0
2
1
0
5
2
0
1
0
0
0
1
0
2
2
0
1
0
1
0
1
0
1
0
0
3
0
0
0
1
1
2
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
2
2
0
0
1
0
0
0
0
1
1
2
0
0
0
0
0
0
2
0
0
3
0
2
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
2
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
1
1
0
2
0
1
0
1
0
2
0
0
1
0
0
0
0
2
2
0
1
0
1
0
0
0
0
0
0
2
0
1
0
0
3
1
0
1
1
0
0
1
2
0
0
2
0
2
2
4
0
1
0
0
1
0
2
2
0
0
0
0
2
0
0
0
0
0
2
0
0
1
2
0
1
0
2
0
0
1
0
0
0
0
0
1
2
0
0
2
2
0
2
0
0
0
2
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
2
0
3
1
0
0
0
0
0
0
2
0
0
3
4
0
0
0
0
0
0
0
1
0
2
1
0
0
0
1
0
0
2
0
2
0
2
2
3
2
1
4
1
0
0
0
0
0
0
0
0
2
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
2
0
0
2
0
0
0
2
0
0
1
2
1
1
0
0
0
0
1
1
2
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
12
1
2
0
2
1
0
2
0
0
2
0
0
0
0
0
1
2
0
1
2
2
1
0
2
0
1
1
0
0
0
0
2
2
0
2
2
1
3
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
2
1
1
0
1
2
1
0
2
0
0
0
0
1
2
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
3
1
0
2
0
0
1
1
0
1
2
0
0
2
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
2
2
2
0
0
1
0
0
1
0
1
0
0
1
0
0
0
1
0
1
0
0
0
1
0
2
2
0
0
2
0
3
0
0
0
1
2
0
0
0
0
0
0
2
0
0
1
0
1
1
0
2
0
2
0
0
0
0
0
0
1
1
0
1
1
0
1
0
1
0
1
0
0
0
0
0
0
1
1
1
0
0
0
1
3
0
0
0
2
2
1
1
0
2
0
0
2
0
0
0
1
1
1
1
2
1
1
1
0
2
1
0
0
0
0
0
0
0
0
2
2
0
2
1
0
1
1
1
0
0
2
0
0
0
0
0
2
2
1
2
1
2
1
2
1
0
0
1
0
2
0
2
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
1
0
0
1
0
2
0
0
2
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
1
2
0
0
0
0
0
3
0
0
0
1
0
1
0
0
1
0
1
0
1
1
3
2
0
2
0
0
0
2
0
0
0
1
0
0
2
0
0
0
3
0
0
2
0
0
0
2
1
0
1
0
0
2
2
0
0
2
1
0
0
0
3
0
0
0
2
0
0
0
2
0
1
0
2
1
1
1
0
2
2
0
1
0
2
0
2
0
2
0
0
0
0
1
0
1
0
2
0
3
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
2
0
0
0
0
2
3
0
0
2
0
0
0
2
0
0
2
1
1
0
0
0
0
0
2
0
2
0
0
1
1
0
0
0
0
2
1
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
1
0
1
1
1
1
1
0
2
0
0
2
2
0
0
1
1
0
1
2
0
0
0
1
1
2
3
2
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
1
0
2
0
0
0
2
2
0
0
2
1
0
0
0
2
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
2
0
1
0
0
0
1
2
2
0
0
0
0
0
0
0
2
2
1
0
1
2
0
0
0
1
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
1
0
1
0
0
1
0
0
2
1
0
0
2
0
0
2
1
1
0
0
1
1
1
0
0
0
0
1
1
0
0
2
2
0
0
0
0
0
1
1
2
4
1
0
1
0
0
0
2
1
1
1
2
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
1
0
0
2
0
0
2
0
1
0
2
0
0
1
0
1
0
0
0
0
2
0
1
1
0
0
2
3
1
0
0
2
0
0
0
0
0
0
0
1
1
2
0
1
1
0
0
0
1
0
0
0
0
0
0
2
0
1
1
0
0
0
2
0
1
2
0
1
2
0
0
0
3
2
0
3
2
0
0
1
0
1
0
1
0
0
0
2
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
2
0
2
1
1
1
0
1
2
0
1
1
0
3
2
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
2
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
1
2
1
1
2
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
2
0
4
0
2
0
0
1
2
0
0
0
1
2
0
2
0
0
0
2
0
0
0
0
1
2
0
1
2
0
0
2
0
0
0
0
1
0
2
0
0
0
1
0
0
0
1
2
1
0
1
0
0
1
0
1
1
0
1
2
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
1
0
0
2
1
0
1
2
0
0
0
1
0
1
0
0
0
1
3
0
2
0
1
2
0
2
2
3
0
1
0
0
0
0
1
0
2
0
2
2
2
0
0
0
0
0
0
2
0
1
1
0
0
0
2
0
0
0
0
0
3
0
0
0
3
0
0
0
0
2
0
1
0
0
2
0
0
0
0
1
0
2
0
2
1
0
0
2
0
0
0
0
8
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
4
1
1
2
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
2
2
0
0
0
1
0
2
0
1
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
1
2
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
3
2
2
0
0
2
3
3
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
2
2
1
0
0
0
0
0
1
0
0
0
0
0
0
2
1
1
0
0
0
2
1
2
2
0
1
0
0
0
0
5
2
0
0
0
0
0
4
0
0
0
0
0
0
0
1
4
0
1
2
0
0
0
0
0
0
2
0
1
0
3
1
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
2
2
1
1
0
0
0
0
0
1
1
1
0
0
1
0
2
1
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
8
1
2
0
2
1
1
2
0
0
0
1
2
0
0
0
0
2
1
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
2
0
2
0
0
4
2
0
1
1
0
0
2
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
2
0
0
2
0
1
0
0
2
1
0
0
0
1
4
0
0
1
2
0
1
0
0
0
1
0
2
1
0
0
0
0
2
1
2
0
0
1
1
2
0
2
2
0
0
1
0
0
0
2
1
0
0
1
0
1
2
2
0
0
1
2
0
1
0
1
0
0
2
0
1
1
0
1
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
2
0
0
0
0
0
0
2
1
0
0
1
0
0
0
1
2
0
2
0
0
0
0
0
1
2
2
1
1
0
1
3
2
0
0
0
0
1
0
0
0
0
0
3
1
0
2
0
0
2
2
0
1
1
0
0
0
0
0
1
0
2
0
0
0
0
0
1
2
2
1
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
1
2
2
0
0
0
0
0
0
1
1
0
2
0
0
0
0
2
1
1
2
1
0
0
0
2
1
2
1
0
1
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
5
1
0
0
2
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
4
0
0
2
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
1
2
0
0
1
0
2
2
2
1
1
2
1
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
2
2
0
0
0
2
8
0
11
1
1
1
0
0
0
2
0
0
1
2
0
1
1
0
1
0
0
0
2
0
0
0
1
0
0
2
0
0
0
1
1
0
0
0
1
2
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
2
0
1
2
0
2
0
1
2
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
2
1
0
0
0
2
2
0
1
1
0
0
0
0
0
0
0
1
3
0
2
0
1
0
1
0
1
0
2
0
2
0
0
1
1
1
1
2
0
0
0
0
2
2
0
0
0
0
2
0
0
0
2
1
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
4
0
0
0
1
0
0
1
0
0
0
3
0
1
0
0
2
2
1
3
2
0
0
0
1
2
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
1
0
0
1
2
1
0
0
1
1
0
0
0
4
2
0
2
0
1
2
0
0
0
0
0
2
1
1
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
1
0
0
0
3
3
0
0
0
0
0
2
2
1
0
0
2
0
2
0
0
0
0
1
0
0
0
2
0
4
0
0
0
0
2
2
2
0
0
0
0
0
1
1
0
0
1
2
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
1
0
0
2
0
0
0
0
2
1
0
2
0
0
0
0
0
0
1
0
1
1
0
0
1
1
1
0
2
0
0
0
1
0
0
3
2
1
0
0
2
1
2
2
1
2
2
0
0
1
0
2
3
0
0
0
0
0
0
0
1
2
1
0
2
2
0
1
0
2
0
0
1
0
0
2
1
1
0
0
2
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
2
2
1
1
0
0
0
1
2
1
0
0
0
0
0
2
0
1
0
0
0
1
0
2
0
1
0
0
1
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
2
2
1
0
2
0
0
0
0
0
0
0
3
2
1
0
1
1
1
2
2
1
1
0
0
0
2
2
2
0
0
0
3
0
0
2
0
0
1
0
2
1
1
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
1
0
3
0
2
0
0
0
0
3
0
1
2
0
0
0
0
0
0
0
0
1
0
0
2
1
1
3
1
0
0
0
0
1
0
2
2
0
0
0
0
2
0
2
0
0
2
0
2
0
2
0
0
0
0
1
0
0
1
2
0
0
0
0
2
2
0
0
1
0
0
0
1
0
0
0
3
0
1
0
0
0
2
5
2
0
0
0
0
0
1
0
0
1
1
0
0
0
0
2
0
2
0
0
1
0
1
2
1
1
0
0
0
0
0
2
0
0
0
1
3
1
2
0
1
0
0
1
3
1
0
0
0
3
0
0
1
0
0
0
0
0
2
2
0
2
2
1
0
0
2
0
3
0
0
2
0
1
0
2
0
1
0
1
0
0
1
0
0
0
0
2
2
0
0
0
1
0
0
2
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
1
1
0
1
1
0
0
0
1
2
1
0
0
0
2
2
1
0
0
2
0
0
0
1
0
1
0
0
1
2
1
0
0
2
2
1
2
0
1
2
2
0
0
0
2
0
2
2
1
0
0
0
1
0
0
0
0
0
3
0
2
0
0
1
0
2
3
0
1
1
1
3
0
2
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
1
2
1
1
0
0
0
1
0
1
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
4
0
0
0
1
0
2
2
0
0
2
2
2
1
0
0
0
2
0
1
0
2
0
0
0
0
4
0
0
2
0
0
0
0
1
1
0
2
0
2
0
0
0
0
0
0
0
0
1
1
0
1
0
1
2
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
2
0
1
2
0
1
1
1
2
1
0
3
0
0
2
0
2
1
0
0
0
1
2
2
1
1
0
2
0
0
0
1
1
0
0
0
0
1
0
1
1
0
1
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
2
0
0
1
0
1
0
0
1
0
0
0
2
1
0
2
2
0
3
0
0
0
0
0
0
1
1
2
0
0
2
0
0
1
4
0
0
0
2
3
0
0
0
0
0
0
0
0
0
1
3
2
0
0
0
1
2
0
0
0
0
0
0
0
0
1
2
2
2
2
2
0
0
0
1
0
2
0
1
2
1
0
1
2
3
0
0
3
0
0
4
0
1
0
0
0
1
0
0
0
0
0
0
3
1
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
2
2
0
1
1
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
4
0
2
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
1
1
1
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
1
1
2
0
0
0
0
0
0
0
1
0
2
2
0
0
3
0
2
1
0
1
0
0
4
0
1
1
0
1
1
0
0
2
2
0
0
1
0
0
2
0
0
1
0
0
1
0
0
1
1
0
2
0
0
0
0
2
0
2
0
0
0
6
0
1
0
2
0
0
0
1
4
0
0
1
0
0
2
1
0
1
0
0
0
0
2
0
0
0
0
0
2
1
2
2
2
2
0
0
1
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
2
2
0
0
0
1
1
0
0
2
0
0
2
1
0
3
0
0
3
2
0
2
1
0
2
0
2
0
0
0
0
2
2
0
1
0
0
0
0
1
1
1
0
1
2
0
0
0
2
0
1
0
2
1
0
0
0
0
2
0
2
0
0
0
0
0
3
2
3
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
2
0
2
0
0
1
2
0
0
1
2
0
2
0
0
1
0
2
0
0
0
0
0
0
2
0
1
2
0
1
0
0
0
0
2
2
1
1
0
0
2
2
0
3
1
1
0
1
2
2
0
1
1
0
0
1
0
0
2
0
1
0
0
0
2
0
0
1
2
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
1
0
0
1
2
1
0
0
6
0
0
0
0
2
1
0
0
2
0
0
1
2
0
1
0
0
0
0
0
1
2
1
2
0
0
0
1
0
0
0
4
0
1
0
0
0
0
1
0
1
1
0
1
1
0
0
0
0
0
1
0
1
1
0
0
2
2
1
2
0
0
0
2
2
0
1
3
0
1
1
1
0
0
2
1
0
1
0
0
0
0
0
2
0
2
0
3
1
2
2
0
0
2
0
0
0
1
1
0
2
0
0
1
0
0
2
0
0
0
0
3
0
0
0
1
0
2
0
0
1
2
0
1
1
2
0
0
0
1
1
1
0
1
0
0
0
1
1
0
2
0
1
1
1
0
0
0
0
0
2
0
0
0
3
0
2
0
0
1
1
0
2
0
0
0
0
0
2
2
0
0
0
2
2
2
1
0
1
1
0
1
1
1
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
1
0
1
2
0
1
1
0
2
0
1
1
0
2
0
1
0
0
0
2
0
0
0
2
0
1
0
0
0
1
2
2
0
0
1
1
1
3
0
0
1
0
0
0
0
0
2
0
1
0
2
0
0
0
2
0
0
1
0
0
2
2
0
1
0
2
1
3
0
0
1
0
0
0
0
1
0
2
2
2
0
1
0
3
1
1
1
3
2
0
0
2
2
0
1
1
0
1
0
0
0
0
0
0
0
0
1
2
1
0
2
0
1
2
0
0
2
0
1
0
1
0
0
0
0
0
0
2
1
0
1
2
0
0
0
1
1
0
1
0
1
2
1
0
0
0
2
2
0
2
2
0
0
0
1
1
0
0
2
0
0
0
0
3
2
1
3
0
0
0
3
1
2
0
0
3
1
0
0
2
1
0
0
2
0
1
0
2
0
0
2
1
2
2
2
0
0
0
0
0
1
1
0
0
0
0
2
1
0
1
0
0
0
0
2
0
2
0
0
1
0
0
1
0
0
0
0
2
2
0
1
0
2
0
0
2
0
0
0
2
1
0
1
0
0
0
0
1
1
0
2
0
2
1
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
3
2
1
0
1
0
0
0
0
0
0
1
0
1
0
2
0
1
2
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
1
2
0
0
0
1
1
1
0
0
0
0
2
1
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
1
1
0
1
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
3
0
2
0
2
0
1
0
0
0
0
0
1
1
0
2
2
0
0
0
0
0
0
0
0
1
1
0
2
0
1
0
2
0
0
0
0
2
0
3
0
3
0
1
0
2
0
0
2
0
1
5
1
0
2
3
0
0
2
0
1
0
0
0
0
0
0
0
0
2
2
0
0
1
2
0
0
0
1
0
0
0
0
0
1
0
1
2
0
2
0
1
0
0
0
0
0
0
2
1
2
0
0
0
3
1
0
0
0
0
2
0
2
3
1
0
1
0
2
1
0
4
0
0
0
2
2
1
0
2
0
0
1
2
0
2
0
0
0
2
1
1
0
0
1
4
0
0
0
1
0
0
0
1
0
0
0
1
0
0
2
0
0
0
1
0
1
0
0
0
0
2
1
2
0
0
0
0
2
2
2
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
4
1
0
0
0
0
1
0
2
0
0
0
0
0
2
1
0
3
2
0
1
2
2
1
0
0
0
0
0
0
0
1
2
0
0
0
1
1
0
2
1
1
0
1
1
0
1
0
0
2
2
1
0
1
0
1
0
2
1
0
0
1
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
2
3
2
1
0
2
1
1
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
1
0
0
1
1
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
2
0
0
0
0
0
0
1
1
0
1
0
2
2
2
0
1
0
2
0
0
0
1
0
0
2
0
2
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
2
0
0
1
1
0
0
2
0
0
0
1
0
2
2
0
1
0
2
0
2
2
0
0
1
0
0
0
2
1
1
2
0
0
3
1
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
1
0
2
0
1
1
0
0
2
0
0
2
0
0
0
0
2
2
0
0
1
0
0
2
1
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
2
0
0
1
0
3
0
3
0
0
2
0
0
1
1
2
0
0
2
0
0
0
0
0
0
0
0
2
2
0
1
1
3
2
0
2
1
0
0
0
0
0
1
2
0
2
0
0
1
1
0
0
0
1
0
2
0
2
0
0
0
1
0
0
0
2
1
0
1
0
2
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
2
0
1
0
2
0
0
0
1
0
3
1
0
1
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
1
1
1
0
3
0
0
0
0
0
0
3
0
2
1
0
0
0
2
0
3
0
3
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
1
1
0
2
0
0
0
0
1
2
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
2
1
2
0
0
2
0
1
1
0
0
0
0
1
1
1
2
1
0
2
0
0
2
0
0
1
0
0
0
0
3
0
1
0
2
1
0
0
0
0
1
0
0
1
0
0
1
2
0
0
1
0
1
1
0
2
0
2
0
0
1
1
1
0
2
0
0
1
2
0
1
1
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
2
1
2
0
1
0
1
0
0
0
0
0
2
0
1
2
0
2
1
0
1
3
0
1
0
0
0
3
1
0
0
0
0
0
1
0
0
0
0
2
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
2
1
0
1
0
3
0
0
0
0
0
0
1
1
2
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
1
0
0
2
1
2
2
0
1
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
2
1
0
2
0
1
0
0
1
0
1
0
0
0
0
0
1
2
0
2
1
0
0
0
2
0
2
0
0
0
0
0
0
3
0
0
0
0
0
2
0
2
2
2
0
1
0
2
1
0
1
2
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
2
2
0
2
0
1
0
0
0
2
0
0
1
0
0
1
0
0
2
1
1
0
2
0
0
0
5
0
0
1
0
2
0
0
0
0
1
0
1
1
0
2
1
2
0
1
2
0
2
1
2
0
1
1
1
2
0
0
0
0
2
0
0
0
0
2
0
2
0
0
1
0
0
2
0
0
2
3
1
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
1
1
2
1
1
1
0
2
0
0
0
0
2
1
0
2
0
0
1
0
0
1
1
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
1
0
0
2
0
0
2
0
1
0
0
3
2
0
0
0
0
0
0
0
2
2
0
0
1
0
0
1
0
2
4
0
2
0
1
1
0
0
0
0
0
2
2
0
0
2
0
2
0
2
1
0
0
0
0
2
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
2
0
0
2
0
1
0
0
1
1
0
1
0
0
1
2
0
0
2
0
0
0
2
2
1
0
1
0
1
0
0
2
1
0
0
0
3
1
2
0
2
0
0
0
2
0
0
2
0
2
1
0
1
1
0
0
0
0
1
2
1
1
1
2
0
0
0
0
2
0
2
1
0
1
0
1
1
0
0
0
2
0
0
0
0
0
1
1
1
2
0
2
0
0
0
0
0
0
0
0
0
1
0
5
1
2
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
1
1
0
2
1
0
2
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
2
0
2
0
2
2
1
2
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
2
1
0
2
0
0
0
2
0
0
0
0
1
0
0
1
0
2
1
0
0
2
1
2
0
0
1
0
0
2
0
1
0
0
1
1
0
1
0
0
1
2
2
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
2
0
1
2
2
0
0
0
0
7
0
0
3
1
0
0
2
1
2
0
2
0
1
1
0
0
0
0
1
2
0
1
0
0
1
0
0
0
3
0
2
2
0
2
0
0
0
0
0
0
0
2
0
1
0
1
2
0
0
3
0
0
0
0
1
1
1
0
2
2
0
2
1
0
0
2
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
2
0
2
1
1
0
0
0
0
0
2
0
0
2
2
0
0
0
2
0
2
0
0
2
0
0
3
0
0
0
2
0
1
2
1
4
1
0
0
0
0
0
2
0
0
0
2
0
0
0
1
1
0
2
0
2
1
3
0
0
0
0
0
0
0
1
2
1
0
1
1
0
4
2
0
0
2
1
1
1
2
2
2
0
1
0
0
1
0
0
0
1
0
0
2
0
2
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
1
1
1
1
0
0
0
0
2
1
1
0
0
0
2
0
0
0
1
1
0
0
1
0
0
2
0
2
1
0
0
3
0
0
0
2
1
1
1
0
2
0
0
0
0
0
0
0
2
0
2
2
1
0
1
0
1
2
2
0
2
1
0
0
1
0
0
1
0
0
0
3
0
0
0
1
2
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
2
2
0
1
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
4
0
0
0
1
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
1
1
0
2
1
3
0
0
0
1
2
0
2
2
0
0
0
1
0
1
0
0
1
0
2
0
0
1
0
0
0
2
0
0
0
1
0
0
0
1
2
0
0
0
1
2
4
2
3
0
2
1
1
0
1
0
0
0
0
2
1
0
1
0
0
0
1
0
1
0
3
0
0
0
0
3
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
3
0
0
0
1
1
0
0
1
1
0
0
2
2
0
0
0
2
0
0
0
2
0
0
2
0
1
2
0
0
1
2
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
1
0
2
3
0
0
2
0
0
1
0
1
0
0
0
1
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
2
0
0
0
1
2
0
1
2
0
0
1
0
0
0
1
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
1
1
0
0
0
1
2
0
0
2
0
2
2
1
1
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
2
0
1
0
0
1
0
0
2
0
1
2
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
1
0
1
0
2
0
0
1
0
0
0
0
0
0
3
0
3
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
1
0
0
1
0
2
0
0
2
2
0
1
1
0
0
0
1
1
2
0
2
0
1
1
0
2
1
1
0
1
1
0
0
0
0
0
1
0
0
0
2
1
2
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
2
0
1
1
0
0
0
2
0
1
1
0
0
0
0
1
0
1
2
0
0
0
0
1
2
0
1
0
0
0
0
0
1
0
2
0
0
0
1
1
2
0
1
0
0
0
0
0
1
0
1
0
2
0
0
1
0
1
0
1
0
0
0
2
1
1
1
0
0
2
0
0
0
0
0
0
0
2
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
2
0
2
2
1
0
1
1
0
0
0
4
2
2
0
0
2
0
0
2
0
0
0
2
0
2
2
3
1
0
2
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
2
0
0
2
2
0
0
2
0
2
0
0
0
1
1
0
0
0
0
1
2
0
2
2
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
3
1
1
1
0
3
0
2
4
0
1
0
2
3
0
0
0
3
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
1
0
2
0
2
0
0
0
0
2
0
0
1
0
1
2
2
0
1
0
0
2
0
0
0
0
2
0
0
1
1
0
0
1
1
0
0
1
2
0
0
0
1
0
0
0
1
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
4
0
2
2
0
0
0
2
0
0
2
0
0
0
2
0
0
2
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
2
4
3
1
0
2
2
2
0
2
0
0
1
1
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
2
0
0
2
1
0
1
0
0
0
0
0
1
0
0
1
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
1
2
0
0
0
0
0
0
0
1
1
0
2
2
0
3
0
0
1
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
2
1
0
1
0
0
0
0
1
1
2
0
0
0
2
2
0
1
0
1
0
2
0
0
1
0
1
0
0
0
2
1
0
0
2
0
2
0
0
0
0
1
0
0
1
1
1
1
0
2
0
0
2
0
1
1
1
0
0
0
0
0
1
0
2
0
0
0
0
0
1
1
0
0
0
0
0
2
0
1
1
1
0
0
0
1
1
3
2
0
0
1
0
0
0
0
0
0
1
1
0
0
2
2
1
0
1
0
1
0
1
0
0
1
0
2
0
0
2
0
2
2
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
2
6
0
2
0
2
1
0
0
0
0
1
0
0
0
1
2
2
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
1
0
1
2
0
0
1
1
0
0
0
0
2
0
0
2
1
3
2
0
0
1
1
2
2
0
3
0
2
0
0
1
0
0
1
1
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
1
0
0
0
2
4
0
0
0
1
0
0
0
2
1
0
1
0
2
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
2
2
0
0
2
1
0
2
1
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
1
0
1
0
2
0
2
2
1
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
2
0
1
1
0
2
0
0
0
0
0
0
2
0
2
0
0
2
0
0
2
0
2
0
0
0
0
2
0
0
1
0
0
0
2
0
0
2
0
2
0
2
3
2
0
0
0
0
2
2
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
1
2
2
2
0
0
0
1
0
10
1
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
2
0
0
0
0
3
2
0
2
0
1
0
1
0
0
1
1
0
0
2
1
0
2
3
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
2
1
1
0
2
2
0
2
0
0
0
2
1
2
2
0
2
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
2
1
1
0
0
1
0
2
0
0
0
1
0
0
2
0
0
1
1
0
1
0
0
0
2
0
0
0
0
0
1
4
2
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
4
0
0
0
3
2
0
0
2
1
0
0
0
0
2
2
0
0
0
4
1
0
1
0
3
0
0
0
0
0
2
0
1
0
0
1
0
1
2
0
0
0
0
0
1
0
0
0
1
2
1
0
0
0
0
0
0
1
1
0
1
1
1
0
0
0
0
0
2
0
1
2
0
0
2
0
0
2
0
1
2
2
2
0
0
1
0
0
0
2
0
0
0
0
0
1
2
0
1
0
2
1
0
1
0
0
0
1
0
0
0
2
1
0
0
1
0
0
0
2
0
1
0
1
0
2
1
0
0
1
2
0
0
1
0
0
2
1
1
1
2
0
1
0
2
0
0
2
2
0
0
0
2
2
2
0
2
0
1
1
0
0
2
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
2
0
2
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
2
0
2
1
0
0
0
1
1
0
0
2
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
3
2
1
2
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
1
1
0
1
1
1
1
0
1
0
0
0
0
0
0
1
1
0
0
0
3
0
3
0
2
1
0
2
0
0
0
1
0
0
0
2
2
0
2
2
0
2
1
0
0
2
0
0
0
0
0
0
0
1
1
2
0
0
0
2
2
0
2
1
1
0
0
0
0
3
0
2
1
0
0
1
0
2
2
0
1
0
1
0
0
2
0
0
0
1
2
0
0
0
2
0
1
1
2
0
1
0
0
0
0
0
2
0
0
1
1
0
1
0
1
2
0
0
2
1
0
0
0
0
0
1
0
3
1
0
0
0
1
0
0
0
0
0
2
0
2
0
2
2
0
2
0
0
0
2
1
0
2
0
1
1
0
1
1
0
1
2
0
0
1
0
0
0
2
0
0
2
2
0
0
0
0
1
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
1
1
1
0
1
0
0
0
0
1
0
2
1
0
0
0
1
2
0
1
0
2
0
1
0
0
0
0
0
0
0
0
3
0
2
1
0
0
0
4
0
1
0
0
2
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
2
2
0
2
0
0
1
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
1
2
0
0
2
0
3
0
1
0
0
0
0
2
2
1
3
0
0
2
2
0
2
0
1
0
0
1
0
0
1
0
1
0
1
2
1
2
0
2
2
0
3
0
1
0
1
0
0
2
1
0
2
1
2
1
0
1
0
2
2
2
2
1
0
2
3
2
2
1
0
0
2
1
0
0
0
1
0
2
2
0
0
3
0
0
1
2
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
2
2
0
0
1
0
1
2
0
0
0
0
1
2
1
0
0
0
3
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
3
0
0
0
0
1
0
1
2
0
0
1
0
0
1
2
0
0
2
0
1
0
0
0
1
1
0
2
0
0
0
3
1
1
0
0
0
0
2
2
0
0
2
0
0
3
2
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
7
0
0
0
0
0
1
0
0
1
2
0
0
0
0
2
1
2
1
2
0
1
2
0
0
0
0
0
2
0
0
1
0
4
2
1
0
1
0
0
1
0
0
1
0
0
1
0
0
2
2
0
1
0
2
0
0
2
1
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
1
0
2
0
1
0
2
0
0
0
0
0
0
3
1
0
0
0
0
0
0
1
1
0
1
3
0
4
0
0
1
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
2
0
0
2
0
2
0
0
0
0
1
3
0
0
0
0
0
0
1
2
0
0
2
0
2
1
0
0
2
2
1
0
0
1
0
2
0
2
0
0
1
3
0
0
0
2
1
2
1
2
0
0
0
1
0
2
2
0
0
3
1
0
0
0
3
0
2
0
2
0
2
1
0
0
0
0
0
2
0
0
2
0
1
1
15
0
0
0
1
2
2
1
0
0
0
0
1
0
0
0
0
1
4
0
2
0
0
2
3
1
1
0
1
2
1
0
3
0
1
2
1
0
0
0
0
1
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
1
0
0
1
1
0
2
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
1
1
1
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
1
2
1
0
0
0
0
2
0
2
1
0
2
0
0
1
0
2
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
2
2
0
2
0
0
0
3
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
1
2
1
2
0
0
2
4
0
1
0
0
1
0
0
0
1
0
2
0
0
2
2
0
0
1
1
0
1
1
0
2
1
3
0
0
0
1
0
0
3
1
0
0
2
0
0
0
0
1
1
0
0
0
2
0
2
0
2
2
0
0
0
0
0
0
2
0
4
2
0
0
0
1
2
0
0
0
0
2
2
0
1
0
0
0
0
1
2
0
0
0
0
0
1
0
3
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
1
0
2
1
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
1
2
0
2
0
0
2
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
2
1
0
0
0
0
2
1
0
0
3
1
2
1
0
2
2
0
0
2
2
0
1
0
0
1
0
1
0
1
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
1
1
0
1
0
0
0
0
2
2
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
2
1
0
1
2
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
2
0
0
2
0
0
1
0
2
3
0
0
0
0
2
4
4
0
2
0
0
1
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
1
0
0
0
1
0
2
2
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
2
0
0
0
0
0
0
0
0
2
3
0
0
2
0
0
0
4
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
1
2
0
2
0
0
2
0
0
1
0
0
1
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
3
1
0
2
0
3
0
0
0
0
0
2
1
0
3
0
2
2
0
2
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
1
3
0
0
0
2
0
1
0
1
2
0
1
0
0
0
2
0
1
1
0
0
0
2
1
0
0
1
0
2
0
1
0
0
2
0
1
0
1
0
2
2
1
0
0
0
0
0
0
0
0
2
0
0
1
1
1
0
1
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
2
0
1
0
2
2
5
0
0
0
2
0
0
0
1
0
0
1
0
0
1
0
2
2
0
0
2
0
0
1
0
0
2
2
0
0
0
0
0
0
1
0
0
1
2
2
0
2
0
0
1
2
0
1
0
0
1
3
0
0
0
0
1
2
0
0
2
2
0
0
0
1
1
0
0
1
0
0
1
0
0
1
0
0
0
1
3
0
0
2
2
0
0
2
1
2
1
0
2
1
2
0
1
0
1
2
0
1
1
1
0
2
0
0
1
0
0
0
2
2
2
1
2
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
2
0
1
0
0
0
1
0
2
0
0
0
0
1
2
0
0
0
1
0
0
0
0
2
0
0
1
1
1
0
1
1
0
1
0
0
2
0
0
0
0
0
0
3
0
0
0
2
0
1
2
0
0
2
0
1
0
0
0
0
2
0
0
0
1
1
2
1
0
1
0
0
1
1
0
0
0
2
1
0
0
1
0
2
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
2
0
2
0
1
0
1
0
0
0
1
0
1
0
0
0
1
1
0
2
0
1
3
0
1
0
1
2
0
0
0
0
1
2
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
2
2
2
0
2
0
0
0
1
0
0
1
1
0
0
0
2
0
1
1
0
0
2
1
0
0
2
2
0
1
0
1
0
1
2
1
0
0
0
0
0
0
0
1
2
1
0
1
1
0
2
0
0
3
1
0
1
0
0
2
1
1
0
0
1
0
2
2
0
1
0
0
1
1
2
0
2
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
3
1
0
0
2
0
1
0
0
0
3
0
2
0
1
0
0
0
1
0
1
0
2
0
0
0
0
1
2
3
1
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
1
2
0
2
0
0
1
3
2
0
0
0
2
0
1
1
0
0
2
0
1
1
1
1
0
2
1
4
0
0
2
0
1
2
0
1
2
0
0
1
0
2
0
1
1
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
1
1
3
2
1
0
0
0
0
0
2
2
0
2
2
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
2
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
3
0
2
0
2
0
2
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
2
2
0
1
2
1
0
0
0
1
0
0
0
0
3
2
1
0
0
2
0
2
0
0
0
1
1
0
0
1
0
0
0
1
0
0
2
3
1
1
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
1
1
2
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
2
0
0
0
2
4
0
1
1
0
2
0
0
1
0
1
2
0
0
0
1
0
1
2
1
1
0
1
0
0
2
0
0
0
1
2
0
0
0
0
2
0
0
0
0
2
2
1
1
0
0
2
0
0
2
0
0
2
0
1
2
0
2
0
1
0
0
1
0
0
0
2
0
2
1
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
1
0
0
2
0
0
0
0
2
2
0
2
0
0
0
1
0
0
2
0
0
0
2
1
2
0
0
0
0
1
0
2
0
1
1
0
2
2
0
1
0
0
0
0
0
0
2
1
2
0
0
2
2
1
3
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
2
2
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
2
2
3
0
0
0
2
0
0
0
1
2
0
6
0
1
12
1
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
2
0
0
0
0
0
0
1
0
0
2
1
2
0
0
0
0
2
2
1
0
1
2
0
0
3
0
0
0
1
2
0
0
0
2
0
2
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
2
0
0
2
0
0
0
0
1
2
2
1
4
2
1
0
1
2
1
0
0
0
0
0
0
0
0
0
1
2
0
1
2
0
0
1
0
0
2
1
1
1
2
0
1
1
0
0
0
0
0
1
0
1
1
0
2
0
0
2
0
0
0
0
0
1
1
0
2
0
0
0
0
0
1
0
0
0
0
2
3
0
0
2
0
0
0
0
0
2
0
0
1
1
0
2
3
0
0
2
4
0
0
2
0
0
0
0
1
0
1
0
2
0
1
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
2
0
1
0
0
0
0
1
0
0
0
1
0
0
0
2
0
1
0
3
2
1
2
1
0
0
0
0
0
0
2
0
0
2
2
0
2
1
1
1
0
0
0
0
0
1
0
2
0
0
1
0
0
0
3
0
2
1
1
1
0
2
0
0
0
0
0
2
1
0
2
1
0
0
2
1
0
1
2
3
0
0
1
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
2
3
1
0
0
0
2
0
2
2
0
0
0
0
2
1
0
1
0
2
0
1
0
0
0
0
0
0
0
1
2
0
2
0
0
2
2
0
2
2
0
1
1
0
0
0
0
1
0
0
1
2
1
1
2
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
1
0
2
1
0
0
0
0
0
2
1
2
0
0
0
2
2
0
0
2
2
1
0
1
0
1
2
0
0
0
2
1
1
0
2
0
0
0
1
1
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
2
1
1
1
0
0
0
1
0
0
0
2
1
0
0
0
0
2
1
0
2
2
1
0
0
0
0
0
0
0
1
0
0
2
0
0
1
1
0
0
1
0
1
0
0
2
1
2
0
0
0
1
2
0
2
2
2
0
1
0
1
1
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
2
0
1
0
0
0
4
0
0
0
0
0
0
1
3
0
0
0
0
0
2
0
1
0
2
1
0
0
1
2
7
5
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
1
1
0
4
2
0
1
1
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
3
1
0
1
2
0
0
1
3
0
0
0
0
3
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
1
1
1
0
1
0
1
0
0
0
0
0
1
0
0
0
1
2
0
2
0
1
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
3
1
0
0
2
0
1
0
0
0
0
1
2
0
1
0
0
1
0
0
2
0
0
0
0
0
1
1
0
0
0
1
0
0
1
3
0
0
0
3
0
0
2
0
1
1
0
0
0
2
0
0
0
0
0
1
2
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
2
1
2
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
3
2
0
0
0
0
2
0
0
0
1
0
0
1
2
3
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
1
0
0
1
0
2
2
1
1
0
2
1
0
0
0
1
1
1
0
1
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
1
0
1
0
1
0
0
1
0
0
1
2
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
7
0
0
0
0
2
0
0
0
0
0
0
1
2
3
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
3
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
2
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
2
1
1
1
0
2
0
2
0
0
1
1
2
2
2
1
1
0
0
1
0
0
3
2
2
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
3
0
2
0
0
0
0
0
1
0
2
0
0
2
1
1
0
2
0
0
0
0
1
0
0
2
0
0
0
0
1
2
0
0
2
1
0
0
4
0
0
0
0
0
0
1
0
2
2
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
1
2
2
2
0
0
0
1
0
0
0
2
0
1
1
1
0
0
0
0
0
2
2
0
0
0
1
2
2
2
3
0
2
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
2
2
2
2
2
2
1
0
2
1
1
0
0
2
2
0
1
1
0
0
1
1
1
0
0
2
0
1
1
0
0
0
1
4
1
1
0
0
2
0
0
1
0
2
0
2
2
1
0
0
0
0
0
1
0
0
2
0
0
2
0
0
1
2
0
1
2
1
0
1
0
0
2
0
0
0
1
1
3
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
1
1
2
0
2
2
0
1
1
0
0
0
0
0
2
2
0
1
1
1
0
2
0
1
0
0
1
2
0
0
0
1
1
2
1
0
0
0
2
1
1
1
2
2
0
3
0
4
0
0
1
1
0
0
0
0
0
0
1
2
0
2
0
0
1
1
0
1
0
0
1
0
1
0
2
2
2
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
1
0
2
1
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
1
0
1
2
0
2
0
0
0
0
2
0
2
0
2
2
0
0
0
0
0
0
1
0
1
1
1
0
1
0
0
2
1
0
0
0
0
1
0
2
1
1
0
0
1
2
0
0
0
0
1
0
0
0
2
0
0
2
1
0
1
1
2
0
0
1
0
2
0
0
0
0
0
0
1
1
2
1
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
1
0
0
0
0
1
3
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
1
0
2
1
2
0
2
0
0
1
0
4
1
1
2
2
0
0
0
0
1
1
0
0
0
1
0
2
0
2
0
0
0
0
2
0
1
2
0
0
2
1
1
0
2
0
1
2
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
1
1
0
2
0
0
1
0
0
0
0
2
1
0
0
0
1
0
2
0
0
1
2
0
0
2
1
0
0
2
0
0
1
0
0
0
2
0
0
1
0
4
0
0
0
0
0
2
0
0
2
1
1
0
2
0
0
0
0
0
0
0
2
2
1
0
1
2
2
0
1
1
2
0
0
0
2
0
1
2
0
0
2
0
0
2
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
2
0
1
2
2
2
0
0
0
0
2
1
0
0
0
0
2
0
1
1
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
2
0
2
2
0
1
0
1
0
0
0
0
0
1
2
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
3
0
0
0
1
2
0
2
2
0
1
0
0
1
0
1
1
0
0
0
0
0
2
0
1
2
2
0
2
2
0
0
2
2
1
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
3
0
1
0
0
1
0
0
1
0
0
1
3
1
2
0
0
0
1
0
0
2
2
0
0
2
1
2
0
0
0
0
0
2
0
0
1
1
0
0
3
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
3
0
1
0
0
1
2
0
2
1
0
1
2
0
0
1
0
0
0
0
2
1
0
0
1
0
3
1
2
0
2
0
2
0
0
1
3
0
2
0
0
0
0
0
1
0
1
1
1
0
0
0
2
2
3
2
2
0
2
0
5
2
3
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
5
1
0
0
2
0
3
1
0
0
0
0
0
2
0
0
0
1
0
0
2
2
0
0
2
2
0
0
0
1
0
2
2
0
1
0
0
0
0
0
0
1
2
0
0
1
2
0
0
0
0
2
0
0
2
2
0
0
1
0
1
2
1
0
0
0
0
2
1
0
1
2
2
0
0
0
0
1
0
1
2
1
0
0
0
0
0
1
0
1
1
0
0
1
2
1
1
2
1
0
0
0
1
1
0
1
0
1
0
1
0
2
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
2
1
2
2
0
0
1
2
0
2
0
1
1
0
0
0
0
0
1
0
1
0
0
2
2
2
2
0
1
1
2
2
0
2
2
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
1
2
1
1
0
2
0
2
1
1
1
2
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
2
1
1
0
1
1
0
0
0
2
2
2
2
2
0
1
0
2
0
0
0
0
2
1
0
0
2
1
2
0
0
0
2
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
2
0
0
1
0
2
1
1
0
0
1
1
0
1
0
0
1
2
0
1
3
0
1
1
0
0
2
2
2
0
3
2
0
0
2
1
0
2
2
2
1
0
0
1
0
2
0
0
0
0
2
3
0
1
1
0
0
0
4
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
1
0
0
2
2
0
1
1
0
1
0
0
0
1
0
1
5
1
1
0
0
0
0
2
0
2
1
0
0
0
2
1
1
2
0
0
2
0
1
1
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
1
2
0
0
0
1
0
0
0
0
0
2
0
0
1
0
2
0
1
0
2
2
0
0
0
0
0
2
1
0
0
0
2
0
1
0
2
0
1
1
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
3
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
3
0
0
2
0
7
1
1
1
0
0
1
0
3
0
0
0
0
4
0
0
0
0
0
0
3
0
0
0
1
2
0
0
0
4
1
0
1
2
0
0
5
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
3
2
0
1
2
1
1
0
2
1
0
0
0
0
0
2
0
0
0
0
0
2
1
0
3
0
1
2
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
1
0
0
1
0
1
0
0
0
0
2
1
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
1
2
0
2
2
0
1
0
2
0
0
0
0
0
2
2
1
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
2
2
1
0
0
0
0
2
1
1
1
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
1
0
0
1
2
0
2
0
0
0
0
1
0
0
2
0
3
0
2
2
0
2
2
0
1
1
0
0
0
1
2
3
0
0
1
0
0
0
2
0
0
1
0
0
1
0
0
0
2
1
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
5
2
1
0
0
1
0
2
0
0
0
0
1
0
0
1
1
1
0
2
0
0
2
0
2
2
0
2
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
2
2
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
1
1
1
0
2
0
2
1
0
0
1
0
0
1
0
0
1
0
0
2
0
0
2
0
0
0
2
0
0
1
1
0
0
0
2
0
0
0
2
1
0
0
0
0
0
1
3
5
1
0
0
0
0
1
1
1
1
2
2
0
0
0
0
0
1
0
1
0
0
3
0
1
0
0
0
1
0
1
0
0
0
1
0
2
0
0
0
1
2
0
1
0
0
2
0
1
0
0
0
0
1
0
0
0
2
2
0
2
0
1
1
0
0
1
0
1
0
0
0
0
0
0
1
2
2
0
0
0
0
1
1
0
1
0
2
0
1
0
0
0
5
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
2
2
0
0
2
0
0
2
1
0
0
0
2
1
1
3
0
0
3
0
0
1
4
0
1
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
1
0
1
1
0
0
1
1
0
0
2
1
0
1
2
0
0
1
0
0
1
2
0
0
0
0
0
0
1
2
0
2
0
2
2
2
1
0
1
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
3
0
0
0
0
0
2
1
1
1
1
0
0
0
0
1
0
0
0
0
2
2
1
0
0
0
3
0
0
0
0
1
2
1
0
4
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
1
0
0
0
2
0
0
0
2
1
0
0
2
1
1
1
0
1
0
0
2
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
2
3
0
1
2
2
2
0
0
3
2
2
0
0
2
3
2
2
2
0
0
0
2
0
0
0
0
1
0
2
1
1
2
1
0
0
1
0
0
1
0
1
1
0
3
2
1
0
0
0
0
0
0
0
2
0
3
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
2
2
2
0
0
0
2
1
0
0
1
0
0
1
0
2
3
1
0
0
0
3
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
1
0
0
1
3
0
1
2
0
2
1
0
2
1
1
2
0
1
0
0
0
0
1
0
1
0
1
1
0
0
0
0
1
2
1
3
2
0
0
0
0
1
0
0
0
0
1
0
2
0
0
3
0
0
0
1
2
1
0
0
1
2
1
0
0
2
2
0
1
2
1
4
0
2
0
0
1
0
1
0
0
1
1
0
0
0
2
0
0
1
1
0
0
2
1
1
1
1
0
0
0
1
0
2
1
2
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
1
2
0
1
0
0
2
0
2
0
2
0
3
2
1
2
0
0
3
0
0
1
2
2
1
0
0
0
0
0
1
0
0
0
1
1
2
2
0
0
0
0
1
2
2
2
0
0
0
0
0
0
0
1
2
0
2
0
1
0
0
2
0
0
0
0
0
0
0
2
0
1
1
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
1
2
0
0
0
2
1
0
1
0
1
0
2
0
0
1
0
3
0
2
0
0
1
0
1
1
0
0
1
2
0
0
0
0
2
0
2
0
3
0
0
0
0
0
0
0
2
2
2
2
0
0
0
2
0
0
0
2
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
1
0
0
0
0
1
0
0
2
2
2
2
0
0
2
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
1
1
2
0
2
2
1
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
2
1
0
0
3
0
0
1
1
0
2
0
0
0
2
2
1
0
0
0
2
0
0
0
0
0
0
2
0
0
1
2
0
0
0
1
1
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
1
0
2
2
0
0
0
1
0
0
1
0
0
0
0
2
3
0
0
0
0
4
4
0
2
0
0
1
2
0
0
0
0
1
1
1
0
0
0
0
0
2
2
0
2
1
0
1
0
0
0
0
0
2
1
0
2
0
0
0
2
2
0
3
0
0
0
1
0
2
0
0
1
1
2
0
0
2
0
0
0
2
2
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
2
0
1
0
0
0
2
2
0
0
1
0
0
0
0
1
0
2
2
0
0
0
1
1
0
0
0
1
0
0
3
0
0
0
2
1
0
0
1
0
0
1
0
0
0
1
0
1
2
0
0
0
0
0
0
2
1
0
2
1
0
1
1
0
0
0
0
0
0
1
2
2
3
2
1
0
1
0
1
0
0
0
0
0
2
1
0
0
3
2
1
0
0
0
0
0
2
0
0
0
1
0
2
0
1
2
2
1
0
2
1
0
1
1
2
2
2
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
4
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
2
2
0
0
0
2
2
0
0
0
0
1
2
0
0
1
0
1
0
0
0
1
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
1
0
1
2
0
0
2
0
0
1
0
0
0
0
0
0
1
0
1
0
2
1
0
2
0
2
0
0
0
0
0
1
0
0
2
0
0
0
1
2
2
0
0
0
2
0
2
0
0
0
2
0
1
0
0
1
0
1
0
0
0
1
0
1
0
2
0
2
2
0
0
0
0
0
0
0
0
3
2
0
1
2
2
1
0
0
3
0
0
0
0
1
0
0
0
2
0
0
1
0
1
0
2
2
0
0
0
0
2
0
0
0
0
0
0
2
1
0
2
2
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
2
0
0
0
1
0
1
1
3
1
0
0
2
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
1
0
1
2
0
0
2
1
0
0
0
0
1
1
0
2
0
0
2
0
0
1
1
0
0
2
1
2
0
0
0
0
2
1
0
1
1
0
0
1
0
1
2
0
1
2
0
1
2
0
0
0
0
2
0
1
2
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
2
1
0
0
0
1
2
0
1
0
0
0
0
10
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
2
1
0
2
2
0
0
0
3
0
0
0
0
0
0
0
2
0
2
0
1
2
0
0
0
0
2
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
1
2
0
1
0
0
0
1
0
0
0
2
0
0
1
2
2
0
2
0
2
0
1
0
0
2
0
1
1
1
0
2
0
0
0
2
2
2
0
1
0
1
0
0
1
2
1
0
0
0
0
0
0
0
2
0
0
1
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
2
2
1
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
2
1
2
2
0
0
0
0
1
0
0
2
0
2
1
0
0
2
0
0
0
0
0
1
0
1
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
1
3
1
2
0
0
0
1
0
0
0
0
2
2
0
0
1
0
0
0
2
0
2
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
2
2
0
1
1
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
1
0
0
0
2
2
1
0
0
1
0
0
0
1
0
0
0
2
1
0
1
0
0
0
2
1
0
0
0
0
1
0
0
0
1
0
0
0
2
0
3
1
0
0
0
0
0
0
0
1
1
0
2
1
1
2
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
2
0
2
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
1
2
0
0
1
0
0
0
0
1
1
0
1
1
2
0
0
2
2
2
0
0
2
1
0
1
0
0
0
0
0
1
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
1
0
1
1
2
0
2
2
0
0
0
0
2
0
0
0
2
2
0
0
1
0
2
0
0
1
0
0
3
0
1
0
2
0
0
2
0
0
1
1
0
1
0
1
0
0
0
0
2
1
2
0
2
3
0
0
0
0
1
0
0
0
0
0
0
0
1
2
2
2
0
0
0
2
1
0
0
0
0
2
0
0
2
0
2
2
1
2
1
1
0
1
0
3
0
0
0
1
2
0
0
0
0
2
0
0
2
0
0
0
6
0
2
0
0
2
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
1
0
0
0
2
1
0
0
1
1
1
0
0
0
2
0
1
2
0
0
1
2
2
0
0
0
0
0
1
2
2
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
2
2
2
0
0
2
3
1
2
1
0
0
0
1
2
0
0
1
1
3
0
1
1
0
0
0
1
2
0
0
1
0
0
0
2
1
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
1
1
2
0
0
0
0
2
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
2
0
0
2
1
0
2
0
0
0
1
2
0
0
0
1
0
0
1
1
2
0
0
1
1
1
0
2
0
0
0
1
0
1
0
0
1
1
1
0
1
0
3
1
1
0
0
1
2
2
0
0
1
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
2
0
2
1
0
1
0
1
0
0
0
1
0
0
2
0
0
1
0
0
2
0
0
1
0
1
0
2
0
2
0
0
0
0
0
1
0
1
0
0
0
1
2
1
1
0
0
0
0
0
1
0
0
0
0
2
0
0
1
2
0
1
0
0
1
0
1
0
0
2
0
2
1
1
1
0
1
0
0
3
0
0
1
0
0
0
2
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
1
0
0
2
0
0
0
2
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
1
1
0
0
2
2
0
0
1
0
0
2
1
2
0
0
0
0
0
0
1
0
0
7
0
0
0
0
2
0
0
0
0
2
2
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
4
0
0
1
0
1
0
0
0
1
0
1
0
1
1
2
1
0
1
1
0
1
1
0
0
0
0
0
1
0
1
2
2
0
0
0
2
0
0
1
1
0
1
0
1
1
1
0
0
2
0
0
0
0
1
1
2
0
2
0
0
0
0
2
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
2
1
0
0
1
1
1
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
2
0
5
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
2
1
0
0
0
0
2
0
1
3
0
1
0
1
1
0
0
0
0
2
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
2
2
0
0
0
1
3
1
1
0
0
2
0
0
1
1
1
0
1
1
0
0
2
1
0
2
1
2
1
0
2
0
0
1
2
1
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
2
0
2
0
0
0
1
0
0
0
4
1
2
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
1
1
0
1
0
0
0
0
0
0
1
0
1
0
2
0
1
1
0
3
1
0
2
0
0
0
0
1
0
2
0
0
0
0
0
1
2
2
0
0
0
0
2
1
1
0
0
1
1
2
0
0
2
0
1
1
2
0
1
0
0
2
0
0
0
0
0
0
2
1
2
0
0
1
0
8
2
2
0
2
0
1
0
0
0
0
0
0
2
1
1
0
0
0
0
1
0
0
1
0
1
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
1
0
0
3
1
0
1
0
0
0
0
0
0
0
1
0
2
0
0
1
0
2
0
0
1
1
2
0
0
1
0
0
1
0
1
0
0
0
1
1
0
0
1
0
2
0
2
3
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
1
5
0
0
0
0
0
0
1
2
0
0
0
1
1
1
1
0
0
0
1
0
1
3
1
1
0
1
0
0
2
0
2
0
1
0
0
2
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
1
1
2
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
1
2
2
1
1
0
1
0
2
0
2
2
2
2
1
1
0
0
0
0
0
1
3
0
2
0
0
0
0
0
3
0
1
1
2
0
3
0
1
0
0
1
0
0
0
0
0
1
2
1
0
0
0
3
0
0
1
0
0
2
0
0
0
0
1
1
2
2
0
1
0
0
0
0
3
0
0
0
2
2
0
1
1
0
1
2
0
1
0
0
1
1
1
0
0
0
2
0
0
0
0
0
3
1
2
1
2
2
0
1
1
0
1
0
0
2
0
1
1
0
0
0
0
0
0
2
1
0
2
1
1
0
0
0
2
1
2
1
0
0
0
1
1
0
0
0
2
0
2
0
1
0
0
1
0
0
0
1
0
0
0
0
2
0
2
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
1
0
0
2
0
0
1
0
1
0
0
1
2
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
2
3
0
1
0
0
1
1
0
2
0
2
0
0
1
2
0
3
0
1
1
1
0
0
1
0
0
0
0
0
0
0
1
1
1
2
0
0
0
2
0
1
3
2
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
1
1
1
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
2
1
0
1
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
1
0
0
2
0
0
1
0
4
1
0
1
0
0
1
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
1
2
1
2
0
0
1
0
0
0
1
0
0
1
0
0
0
2
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
3
0
0
1
0
2
0
2
1
0
0
3
1
0
0
1
2
0
1
2
0
0
0
0
0
0
1
0
0
1
0
2
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
2
0
2
1
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
1
2
1
0
0
2
0
0
0
2
0
0
1
0
2
1
0
0
0
1
2
0
1
0
1
2
0
0
1
0
0
1
0
4
0
0
0
0
1
0
1
0
0
1
0
0
1
1
1
2
1
0
1
0
1
0
1
0
0
0
1
1
0
1
2
1
1
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
1
2
0
2
0
0
0
0
0
2
0
0
0
1
0
1
2
1
2
0
0
0
0
2
1
2
0
0
2
2
2
2
1
0
0
0
2
0
2
0
1
2
1
0
2
2
0
0
1
0
0
1
0
0
0
2
0
0
0
0
2
0
2
0
2
0
0
1
0
2
0
0
0
0
3
0
1
0
1
0
0
0
3
2
1
0
0
0
0
0
0
2
3
2
0
2
1
2
2
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
3
0
1
2
0
1
0
0
0
0
0
1
2
0
2
1
0
1
0
2
2
2
0
0
0
0
0
0
0
2
0
0
2
1
1
0
0
0
2
0
0
0
0
0
1
0
0
1
1
1
0
0
1
0
1
0
3
1
2
0
0
1
2
1
0
2
1
0
2
0
0
2
1
2
0
0
0
0
0
2
0
4
0
0
2
0
2
2
1
0
0
2
0
0
2
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
2
1
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
1
0
2
0
0
3
0
1
0
1
0
0
1
0
0
2
2
0
0
0
1
0
1
2
0
0
1
2
1
0
0
0
3
2
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
1
3
0
0
0
2
0
1
3
1
2
3
0
0
2
0
4
0
1
3
2
2
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
2
1
0
0
1
0
1
0
0
0
0
0
1
2
0
1
1
0
0
1
1
0
2
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
3
2
0
4
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
2
2
0
0
2
0
0
1
2
0
0
0
0
2
1
3
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
3
1
0
0
1
1
0
0
0
1
0
0
0
3
0
2
0
0
0
1
0
1
0
1
1
0
0
0
0
1
0
1
0
0
2
2
0
1
2
1
0
2
0
1
2
2
1
1
1
0
3
0
0
1
0
0
0
0
1
0
2
0
2
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
2
0
0
2
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
1
0
0
0
2
0
2
0
2
0
1
0
0
0
0
2
0
0
1
0
2
0
1
0
2
0
0
0
0
2
1
0
0
0
1
0
0
2
1
1
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
1
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
5
2
0
0
0
0
1
1
2
2
0
0
0
2
0
0
2
0
2
0
2
2
0
2
0
0
0
0
0
2
0
0
2
0
5
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
1
1
2
0
0
0
2
0
0
1
1
0
3
0
0
3
0
3
2
0
0
0
0
0
0
1
0
0
0
0
2
1
0
2
0
0
8
0
3
0
0
0
1
1
0
1
0
0
1
3
2
0
2
2
0
3
1
2
0
0
1
0
0
2
0
0
0
2
2
0
0
0
0
0
0
2
1
0
0
0
0
2
1
3
2
0
0
3
0
0
0
0
0
1
2
0
0
2
0
3
0
0
0
1
0
2
0
2
0
0
0
2
0
0
0
2
0
0
0
1
2
0
0
2
2
0
0
1
1
0
0
0
0
0
0
1
0
2
0
0
1
0
0
1
0
0
0
2
1
1
2
0
0
0
0
0
1
1
0
0
0
2
0
0
1
2
2
0
0
1
1
0
1
1
0
1
1
0
0
0
0
0
0
1
3
2
2
0
0
3
0
3
2
0
2
2
0
1
0
0
0
0
1
0
1
0
0
1
0
0
1
0
2
0
0
0
2
4
2
1
0
1
0
1
0
1
0
0
2
1
1
0
0
2
0
2
2
0
0
1
2
2
0
0
0
2
3
0
0
0
2
2
0
0
0
0
0
0
0
2
0
2
1
0
2
1
0
2
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
2
1
0
2
0
0
1
0
2
1
0
0
1
0
1
2
0
0
1
0
0
2
3
0
0
0
1
2
0
0
1
0
0
0
0
2
0
2
0
1
0
2
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
2
0
0
0
2
2
0
2
0
0
2
2
0
0
0
0
0
0
2
1
0
2
2
1
0
0
0
0
2
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
1
0
0
2
1
0
0
0
1
1
2
1
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
1
0
1
0
2
0
0
0
0
0
2
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
2
1
1
1
0
0
0
0
0
0
0
0
2
0
1
2
6
2
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
1
2
0
2
0
0
0
1
0
2
0
2
1
0
1
1
0
0
1
2
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
1
3
0
0
2
0
0
0
0
0
1
1
1
2
2
0
2
0
0
2
0
0
0
2
2
0
0
1
0
0
2
0
2
0
0
2
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
1
1
1
0
2
0
0
0
0
0
1
1
0
0
1
0
2
0
1
0
2
0
0
0
1
0
1
0
0
0
0
0
1
0
2
0
0
0
0
1
0
2
1
1
0
0
0
0
0
0
2
1
0
1
2
0
0
0
2
0
0
1
2
0
0
2
0
2
0
2
1
0
2
2
0
1
2
0
0
0
2
0
2
0
1
0
0
2
1
0
0
2
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
1
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
2
2
0
1
1
2
0
2
2
1
0
0
0
0
2
0
0
0
0
0
2
0
2
2
2
0
0
0
2
2
2
6
2
0
1
0
0
2
0
0
0
1
0
0
1
3
0
0
0
1
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
3
2
0
0
0
2
0
0
2
2
0
1
2
0
0
2
1
0
0
0
0
0
0
2
3
0
1
2
2
1
0
2
0
2
1
0
2
0
1
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
1
0
0
0
1
0
0
0
0
2
0
1
2
0
0
0
0
0
2
1
1
0
0
2
3
0
0
0
1
0
0
1
0
0
0
2
0
0
1
0
0
0
1
0
1
0
0
0
0
0
2
2
0
1
2
0
0
0
1
0
1
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
2
0
1
0
1
0
0
0
1
2
0
0
0
0
0
0
3
0
0
0
0
2
0
2
1
0
0
0
3
2
0
0
0
0
0
1
1
0
1
0
0
0
3
0
1
2
2
0
2
1
0
0
1
2
0
1
0
0
1
0
0
0
0
0
1
2
0
2
0
2
1
0
0
0
0
0
2
1
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
2
1
0
1
0
0
2
0
0
0
3
2
5
2
0
1
0
0
3
0
0
0
1
0
0
0
0
0
0
2
0
0
1
2
0
0
0
2
0
5
0
0
0
0
2
0
0
0
0
1
0
0
1
0
1
0
0
1
2
0
1
0
0
0
0
1
0
1
0
0
1
2
1
2
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
1
1
0
0
0
0
0
1
1
0
0
3
3
1
0
1
0
1
0
0
0
1
0
1
0
0
0
1
1
2
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
2
1
2
1
4
1
0
0
2
1
0
2
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
2
1
0
1
0
2
2
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
2
0
0
0
0
0
3
0
1
0
0
2
2
0
2
0
0
0
2
0
1
2
1
1
1
1
0
2
2
0
0
0
0
1
0
0
0
1
0
0
0
2
2
0
2
2
0
0
0
0
2
1
0
0
2
0
1
1
0
0
1
0
0
0
0
1
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
3
0
0
2
1
0
0
0
1
0
0
0
0
0
3
1
0
1
2
2
1
1
1
2
2
0
1
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
2
2
0
0
0
3
1
0
0
0
0
2
0
0
0
1
0
0
0
2
2
1
0
0
0
5
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
1
1
0
0
0
0
1
2
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
2
0
1
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
2
2
0
1
2
2
0
0
1
1
2
2
0
2
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
1
2
0
2
2
2
1
1
1
0
0
0
0
0
0
0
1
0
0
4
0
0
1
0
0
1
0
0
0
2
0
0
2
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
2
0
1
2
2
0
2
0
2
0
0
0
2
1
2
0
0
0
1
0
0
1
1
3
2
0
0
0
0
0
0
0
2
0
0
0
1
2
2
2
1
1
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
2
1
0
2
2
0
2
1
0
2
1
0
0
1
0
0
1
0
1
0
1
1
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
2
0
1
2
0
0
2
0
0
2
2
0
1
1
0
0
0
1
0
0
0
2
2
0
0
0
2
3
0
0
0
0
0
2
1
1
0
0
0
1
2
0
0
0
0
2
2
0
3
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
2
1
0
2
2
0
2
0
1
2
2
0
2
2
1
0
0
0
0
0
0
2
0
2
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
2
1
0
0
2
0
0
2
1
0
2
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
1
0
0
0
1
2
0
0
0
1
1
1
0
2
0
0
1
0
1
0
0
0
0
1
1
1
0
0
2
1
0
0
0
0
0
0
0
2
2
0
4
0
0
1
2
1
0
2
0
1
0
0
0
0
0
0
2
0
0
0
1
0
1
2
2
0
1
0
1
0
0
0
1
2
2
2
0
0
0
0
0
2
2
0
2
0
0
1
0
0
0
0
1
0
0
0
0
1
0
2
0
0
1
0
1
0
2
1
2
2
2
0
0
0
0
0
0
0
2
1
2
1
1
1
0
0
1
2
0
2
2
0
0
2
1
0
1
0
2
0
2
0
2
0
3
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
2
1
1
1
1
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
2
2
2
0
2
0
1
0
0
1
0
0
0
2
0
1
0
0
0
1
0
0
1
1
1
0
0
0
0
0
2
1
2
1
0
0
0
0
2
1
0
0
0
3
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
1
0
0
0
2
0
1
1
0
2
1
0
0
1
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
1
0
2
0
11
0
0
0
0
2
2
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
2
1
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
2
0
0
4
3
2
0
0
1
2
0
1
0
0
1
0
0
1
0
0
0
0
3
1
0
1
0
2
0
2
0
0
1
0
0
0
0
0
1
0
0
2
1
0
2
0
0
0
2
0
0
0
2
1
0
2
2
2
0
2
0
0
1
1
0
1
1
0
0
0
0
1
1
0
2
0
0
0
1
0
0
0
0
0
1
0
2
1
1
2
1
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
2
9
0
2
2
0
0
0
2
2
0
0
0
0
1
3
2
1
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
1
2
0
3
0
2
0
0
0
3
1
1
0
1
0
0
0
0
2
0
2
0
0
0
0
1
1
1
2
1
0
1
0
2
0
0
0
1
1
0
2
0
2
0
0
0
2
0
0
2
0
0
2
0
0
0
0
1
0
2
1
2
0
0
0
0
2
0
0
1
0
0
1
0
1
1
0
2
0
0
0
1
0
2
0
0
2
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
2
3
1
0
2
1
0
6
0
1
0
0
2
0
0
1
2
0
0
0
2
0
0
1
0
0
0
0
0
2
0
1
1
0
0
3
0
0
1
0
0
0
1
0
1
2
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
2
0
2
0
2
2
0
0
4
0
0
0
0
7
0
2
1
0
0
0
0
0
0
0
2
1
2
0
0
0
2
0
0
2
0
0
2
2
0
0
0
0
0
0
0
2
2
2
0
0
6
0
0
0
0
2
1
0
5
2
1
2
0
1
0
0
0
2
1
0
2
0
0
1
2
1
1
0
0
1
0
0
2
0
1
0
0
2
1
0
0
0
0
1
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
1
1
1
0
0
0
2
0
2
0
0
1
0
2
0
0
0
1
4
0
0
1
2
0
0
0
2
1
1
0
0
0
2
1
1
0
0
0
0
0
0
1
1
1
0
1
0
0
0
2
1
0
2
2
2
3
0
2
0
1
0
0
0
1
1
0
0
2
2
0
1
0
0
1
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
2
0
2
2
2
0
0
0
2
0
2
0
0
1
0
1
0
0
0
3
0
1
2
2
0
1
2
0
1
1
0
0
1
2
1
0
2
1
0
0
0
0
0
0
0
1
2
0
1
0
1
1
0
0
0
0
2
0
0
1
0
2
0
1
2
2
2
0
0
1
1
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
2
0
0
2
1
2
9
2
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
1
2
1
2
0
0
0
2
1
0
2
0
0
0
1
1
0
0
1
0
2
0
1
0
0
0
0
0
1
2
0
1
1
0
0
0
2
2
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
1
0
0
0
1
2
1
0
0
1
1
1
2
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
1
0
2
1
0
0
2
0
0
2
0
0
1
1
1
1
1
1
1
2
1
0
0
0
0
0
0
0
0
0
0
0
2
1
1
1
2
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
2
0
0
0
2
1
2
0
0
0
0
0
2
0
1
0
0
2
0
1
2
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
2
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
2
0
0
0
0
1
1
2
0
3
2
0
0
1
0
0
2
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
4
0
0
2
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
1
2
0
0
0
2
0
0
0
1
0
1
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
2
2
2
2
2
0
1
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
4
2
1
0
2
1
1
1
0
0
2
0
1
1
0
3
2
0
0
0
2
0
0
1
1
0
2
0
0
2
0
0
2
1
2
2
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
1
0
2
1
1
1
2
0
0
0
2
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
2
0
2
0
1
0
0
0
2
0
2
1
1
0
0
0
1
0
0
0
1
2
1
0
1
1
0
0
2
0
0
0
1
0
0
1
4
2
1
0
0
0
0
1
0
1
2
0
2
0
0
2
1
0
0
1
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
1
0
2
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
1
0
1
0
0
0
2
1
0
0
1
2
0
0
1
0
1
0
0
1
1
1
0
0
0
0
0
2
0
0
1
0
2
0
0
0
2
0
0
1
0
0
1
2
2
0
0
1
2
0
1
0
0
0
1
0
2
0
2
1
1
0
0
1
0
0
2
4
2
1
0
2
0
0
2
1
1
0
2
2
0
2
1
1
1
0
2
0
2
0
0
0
0
1
2
2
0
1
1
0
2
0
0
0
2
0
0
0
2
0
0
0
0
1
0
2
0
0
0
4
0
0
0
0
0
2
2
0
0
1
2
2
0
1
0
0
2
2
0
0
3
1
0
1
2
0
2
1
0
0
2
2
0
0
0
0
0
0
0
2
0
0
2
2
0
1
2
0
0
1
0
0
0
0
2
0
0
0
1
0
0
5
0
1
0
2
0
0
1
2
1
0
1
2
0
0
0
0
0
2
0
0
0
2
2
2
0
0
0
2
2
0
2
0
1
3
1
2
0
0
1
1
0
0
0
0
0
2
0
1
0
0
1
0
0
0
2
2
0
0
2
0
0
0
0
1
0
0
2
1
1
1
0
0
0
2
0
0
2
0
0
1
2
0
1
1
1
0
0
2
0
0
1
1
2
0
0
0
0
0
1
1
2
1
2
2
0
3
1
0
2
0
0
0
0
0
2
0
2
0
2
2
1
1
0
2
2
0
0
0
0
1
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
1
1
0
0
1
1
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
1
1
1
0
0
1
0
0
1
2
0
1
0
0
1
0
0
0
0
0
0
1
1
4
0
1
2
1
0
0
0
0
3
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
1
0
2
0
2
0
2
0
0
1
0
0
0
1
1
2
2
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
2
2
2
0
1
0
1
0
1
1
0
3
0
1
0
0
1
0
0
0
1
0
1
0
2
1
0
1
1
1
1
2
1
0
1
2
0
0
1
2
0
0
0
0
1
1
0
0
1
2
0
2
0
0
0
3
0
0
0
0
1
0
1
1
1
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
3
2
0
0
1
2
0
0
3
1
2
1
0
0
0
0
0
1
1
0
1
0
1
0
2
0
0
1
1
1
0
0
0
0
0
0
2
2
0
0
0
1
2
0
0
2
0
0
2
2
2
1
0
1
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
2
2
0
0
0
2
0
0
1
1
0
0
1
0
0
2
0
0
0
0
2
1
2
0
0
0
0
2
0
0
0
0
0
0
2
2
1
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
3
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
1
1
0
0
5
1
1
0
1
0
0
0
0
1
2
0
0
0
0
2
0
2
1
2
0
0
0
0
0
0
0
0
2
1
0
3
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
2
1
3
0
0
0
0
0
1
2
0
0
2
1
1
0
2
2
1
0
0
0
2
0
1
0
0
0
1
0
0
1
0
0
2
1
0
0
2
0
1
0
0
0
0
2
0
0
0
2
0
0
1
1
0
1
0
0
0
0
2
2
0
2
0
1
2
2
0
0
0
0
0
0
0
0
0
0
6
1
0
0
0
2
2
1
0
1
1
0
1
0
2
0
0
0
1
2
1
2
3
1
0
2
0
1
0
0
0
0
2
0
0
0
2
0
0
2
1
2
0
0
2
0
0
2
2
1
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
2
2
1
0
0
0
2
2
0
1
0
0
0
0
0
3
0
2
2
0
0
0
3
0
1
1
1
2
0
0
1
0
3
2
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
2
0
1
1
0
1
5
0
1
0
0
1
1
0
1
0
1
0
2
0
0
1
0
0
0
1
0
2
0
0
0
0
0
2
2
4
2
0
0
1
0
1
2
1
0
1
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
1
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
2
0
1
0
1
2
1
2
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
1
0
0
0
4
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
3
2
0
2
1
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
9
0
0
0
2
1
0
2
2
0
2
0
0
0
2
0
0
2
1
0
1
0
1
0
0
0
0
1
0
0
1
2
1
0
2
2
1
0
1
0
0
2
0
2
0
3
0
1
0
0
0
1
1
1
1
0
1
0
2
0
0
1
1
1
1
2
1
1
0
0
0
2
0
0
0
0
0
1
0
0
1
0
2
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
1
0
1
0
0
2
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
2
1
4
0
0
1
2
1
0
0
0
0
2
3
1
0
0
1
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
2
1
2
0
2
0
1
1
1
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
2
3
0
0
0
1
0
0
1
0
0
2
2
2
0
3
3
0
0
2
0
0
0
4
2
0
1
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
1
1
2
2
1
0
0
0
1
0
2
0
0
1
0
0
1
0
2
5
0
2
0
0
1
0
3
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
1
1
1
0
0
1
1
1
1
0
0
0
0
0
0
1
1
1
1
3
0
0
0
0
0
1
1
1
2
0
1
0
0
0
2
1
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
1
0
0
1
0
2
0
0
2
0
1
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
2
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
2
2
0
0
0
0
2
1
0
0
1
0
0
4
0
0
0
0
2
0
0
2
1
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
3
1
2
1
1
0
0
0
0
0
0
2
2
0
1
1
0
0
1
0
0
1
0
0
0
0
0
2
2
2
0
2
0
2
2
1
2
0
1
1
0
0
0
1
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
1
1
1
0
0
0
0
1
2
0
0
1
0
0
0
1
0
2
1
0
1
0
0
0
2
0
0
2
2
2
0
0
2
0
0
0
1
0
0
0
0
2
3
2
0
0
2
3
1
0
2
1
0
2
0
0
2
0
0
0
2
1
1
0
0
0
0
0
0
0
2
0
0
1
0
1
2
0
0
0
0
0
0
0
2
0
0
2
0
3
0
0
0
1
1
2
0
1
0
0
1
0
2
0
1
2
0
1
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
3
0
2
1
2
1
2
0
0
0
0
4
0
0
1
1
1
0
1
0
0
2
0
1
0
0
0
2
0
0
0
3
2
1
0
0
0
0
0
0
1
1
4
0
0
0
0
2
0
1
0
1
0
0
0
3
0
0
0
0
1
0
1
0
0
1
1
0
1
0
0
0
0
0
0
1
0
1
1
0
1
0
1
2
3
0
2
0
0
1
2
1
2
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
2
1
0
0
0
1
0
0
1
0
1
0
0
0
1
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
1
0
2
1
2
2
0
1
0
2
0
0
2
0
0
1
0
2
5
0
1
0
2
0
0
0
2
0
0
0
0
2
0
1
0
0
3
1
0
2
1
0
0
2
0
0
2
0
0
0
2
1
0
0
0
0
1
0
1
0
0
3
0
0
0
0
1
1
0
0
2
1
0
0
0
0
1
0
0
2
0
0
1
1
2
0
1
0
0
0
0
0
2
0
3
2
4
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
2
0
3
2
0
0
0
1
2
2
1
0
0
2
0
2
2
2
0
0
0
0
0
0
0
0
0
0
3
0
0
1
1
2
0
0
2
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
3
0
2
3
2
0
2
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
1
0
1
0
1
2
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
1
0
1
2
0
1
0
1
0
0
0
0
2
0
1
1
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
1
0
1
0
1
3
0
1
0
1
0
0
0
0
1
0
2
0
2
0
0
2
0
1
0
1
0
0
3
1
1
1
0
0
2
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
4
0
2
0
0
1
2
0
0
0
2
0
0
0
0
0
0
2
1
2
1
2
1
0
1
0
1
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
2
1
0
2
0
0
0
0
2
1
2
1
0
3
0
0
1
2
0
1
1
2
0
0
0
2
0
0
0
0
0
0
2
2
2
1
2
2
2
1
0
0
0
0
1
0
0
2
0
2
2
2
0
4
2
1
1
0
0
2
0
1
0
0
0
0
1
1
0
2
0
0
0
0
0
1
1
0
2
2
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
2
3
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
2
1
2
0
0
0
3
0
0
0
2
2
2
1
1
0
0
0
2
0
0
0
0
1
0
3
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
2
0
0
0
1
0
0
0
0
1
0
1
0
2
0
0
2
0
0
1
0
2
0
1
2
1
0
0
1
0
2
0
0
0
1
1
0
0
0
0
2
0
0
2
1
2
0
0
2
0
1
0
1
0
2
2
0
0
2
0
1
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
3
1
2
1
0
0
1
0
0
0
2
0
0
0
0
1
1
1
0
0
1
2
0
1
2
1
0
0
0
0
2
0
0
1
0
1
0
4
1
0
1
1
0
0
1
0
0
1
2
0
1
5
2
1
0
0
0
0
0
0
0
0
0
0
0
0
3
1
1
0
2
0
0
2
1
0
1
0
0
1
0
0
3
0
2
0
0
0
0
0
2
2
3
2
0
0
0
1
1
0
2
1
0
0
0
0
1
1
2
0
1
0
1
1
1
0
0
0
0
0
2
0
1
10
1
1
0
1
1
0
0
2
0
1
0
0
1
0
0
2
2
1
1
0
0
0
0
0
1
0
0
0
0
0
0
2
1
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
1
0
0
2
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
2
1
0
0
0
0
3
2
2
1
2
0
0
0
0
0
0
2
2
0
1
2
0
0
1
1
1
2
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
2
0
1
1
0
2
0
0
1
1
2
0
0
0
0
0
0
0
2
0
2
2
0
0
2
1
0
0
0
0
2
2
1
0
2
0
2
1
1
0
2
0
0
2
0
0
0
0
3
0
1
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
1
0
0
1
0
1
0
0
1
0
0
0
0
1
2
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
2
1
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
1
2
1
2
0
0
0
0
1
2
1
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
1
0
0
1
1
0
0
0
1
1
0
2
2
0
1
0
0
0
0
2
1
0
0
0
1
0
0
0
2
0
1
0
3
2
0
0
0
0
1
1
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
1
2
0
1
0
1
0
0
0
2
0
0
2
0
0
0
0
0
1
0
1
2
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
1
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
2
2
0
1
1
0
2
0
1
0
0
0
0
0
0
1
0
2
0
0
0
1
0
1
1
1
2
0
2
2
1
0
2
2
0
2
2
0
0
0
2
0
0
2
1
2
0
0
0
0
2
2
0
2
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
2
0
1
0
0
0
0
1
0
0
2
0
1
1
0
0
0
0
0
0
1
1
0
0
0
3
0
0
2
0
0
2
2
2
0
2
1
1
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
1
1
1
0
2
0
2
0
1
2
2
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
1
0
0
2
0
0
1
1
2
0
0
0
1
0
0
1
2
0
2
2
2
1
1
0
0
1
0
2
0
0
1
0
1
1
1
0
2
0
0
0
2
1
0
0
0
0
1
0
0
2
0
0
1
2
0
0
0
0
4
0
0
2
1
0
0
0
1
0
2
0
1
1
2
1
2
0
1
0
0
0
0
0
2
2
0
2
3
0
1
1
0
0
1
2
0
0
0
0
2
1
0
0
0
0
0
0
2
1
1
0
1
0
0
0
0
0
0
0
0
0
3
0
0
2
3
0
1
0
0
0
1
0
2
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
1
2
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
2
0
0
2
0
2
2
0
2
2
0
1
1
0
1
1
0
1
0
1
0
2
0
1
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
1
0
2
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
1
0
2
0
1
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
2
0
0
2
1
0
2
1
0
1
1
1
0
1
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
2
0
1
0
1
1
0
0
0
2
0
1
0
0
0
0
0
2
2
1
0
0
0
2
2
2
0
2
0
0
0
0
4
0
1
0
2
2
1
0
0
2
0
1
1
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
2
0
1
0
0
1
0
0
2
2
0
2
0
0
0
0
0
0
2
0
1
0
2
0
0
0
1
0
0
2
0
3
0
7
1
0
0
1
2
0
2
0
2
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
2
1
0
0
0
0
0
1
0
1
1
2
1
0
0
1
2
0
0
0
0
0
1
1
2
0
1
0
0
2
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
5
0
0
2
2
2
0
1
0
0
0
0
2
1
0
2
1
0
0
0
0
0
1
3
1
0
0
2
2
1
0
0
0
2
1
2
1
1
0
0
2
0
0
4
0
0
0
0
0
0
0
1
0
2
0
0
2
2
0
1
0
1
1
0
0
0
0
1
0
2
0
0
0
2
1
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
2
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
2
6
0
0
1
2
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
2
0
0
1
2
1
2
2
1
0
0
0
0
4
1
0
0
0
0
0
2
0
0
1
0
1
0
2
0
0
0
0
0
0
1
0
1
1
3
2
0
0
0
0
1
2
1
1
0
0
1
0
1
1
2
0
2
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
1
2
1
3
0
1
0
0
0
2
0
0
0
0
0
3
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
3
1
0
2
1
3
2
0
1
1
0
2
0
2
0
2
0
1
2
0
0
0
1
1
1
0
1
0
2
1
0
2
0
1
0
1
0
1
0
0
0
0
0
0
2
0
2
0
2
3
0
0
0
0
1
2
2
0
2
0
1
1
0
0
0
0
2
0
0
2
1
0
1
1
0
2
0
0
0
0
0
2
1
0
1
1
2
3
0
2
0
1
0
0
0
0
0
0
0
1
2
0
0
2
0
3
0
2
0
0
1
1
3
0
0
0
0
1
1
1
0
1
0
0
2
0
0
0
0
0
0
0
2
2
2
1
0
1
1
0
1
0
0
0
2
0
0
0
2
2
1
0
0
2
0
0
2
0
1
1
1
0
1
0
4
2
0
0
0
0
0
1
3
2
1
0
0
0
0
0
0
2
0
2
0
1
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
2
0
0
1
2
0
0
0
0
0
1
1
0
1
2
2
2
1
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
2
1
0
0
0
0
0
1
0
0
0
2
1
1
0
0
0
0
0
0
1
2
0
2
0
0
0
2
3
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
1
0
1
1
1
0
2
0
1
0
0
0
0
2
1
2
1
2
0
0
0
0
0
0
1
1
0
1
2
0
0
1
0
0
1
0
0
1
0
0
2
0
0
1
2
0
0
0
0
0
0
2
0
0
2
0
2
0
2
3
2
0
2
1
3
0
1
0
1
0
0
1
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
2
2
0
2
2
0
1
1
0
0
0
0
1
1
3
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
2
0
2
0
0
0
0
1
0
1
0
2
2
4
1
0
2
2
1
0
1
1
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
1
2
1
0
0
2
2
2
0
0
0
2
0
1
0
0
1
1
0
0
0
0
7
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
1
1
2
2
0
0
1
1
0
0
0
0
2
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
1
0
2
0
0
0
0
2
0
1
1
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
1
1
0
0
0
0
1
3
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
1
3
1
0
2
2
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
2
2
0
0
0
1
0
1
0
1
1
0
2
0
1
0
0
0
0
1
1
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
4
1
0
0
0
0
1
2
0
0
0
2
2
0
1
0
0
2
0
0
0
0
0
0
1
2
0
2
0
1
0
0
0
0
0
2
0
0
0
2
0
3
0
1
0
0
4
0
2
1
2
0
0
0
0
0
0
2
1
0
0
2
2
0
1
1
1
2
2
0
7
1
0
1
0
3
1
2
0
1
0
2
2
1
0
3
0
0
0
1
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
2
0
0
2
0
0
0
1
0
1
0
0
0
2
2
2
2
1
0
0
1
1
0
0
0
1
2
2
0
2
2
1
0
0
0
1
2
0
0
1
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
1
2
0
1
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
3
2
1
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
1
4
0
0
0
5
0
1
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
1
1
0
0
0
2
1
0
0
0
1
0
0
2
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
1
0
1
0
0
2
0
1
2
1
0
0
0
1
2
1
1
2
2
2
2
1
0
3
0
0
1
0
2
2
2
0
1
0
0
1
0
0
0
0
0
2
1
1
2
1
0
2
0
1
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
1
0
2
0
0
1
0
2
0
1
0
2
0
0
0
0
3
0
0
2
0
0
0
0
1
0
8
0
2
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
2
2
1
0
0
0
0
0
1
2
2
2
0
0
0
2
2
0
0
0
3
0
0
0
1
0
0
0
2
0
0
0
1
0
0
1
0
2
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
1
1
2
0
0
0
1
1
0
0
2
0
2
0
2
2
1
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
2
0
0
2
2
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
2
1
0
0
0
2
0
0
1
0
0
0
2
2
0
0
2
0
2
0
1
2
0
0
2
0
0
0
1
0
0
0
0
1
2
0
0
0
0
1
0
0
0
1
2
2
0
2
0
0
0
0
0
2
0
2
0
2
0
1
2
1
0
2
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
2
0
0
3
0
1
1
0
0
0
0
0
3
2
0
0
0
0
1
0
2
1
2
0
2
3
1
0
0
1
0
0
2
0
0
0
1
0
0
2
2
0
0
0
0
0
1
0
2
3
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
6
1
2
0
0
2
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
2
4
0
0
0
0
2
0
1
0
1
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
1
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
2
3
2
0
0
1
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
1
2
0
0
2
1
0
0
5
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
2
0
1
1
1
2
1
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
2
2
0
2
2
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
2
2
0
0
0
0
2
0
2
0
1
1
2
1
2
0
0
2
1
0
0
1
0
0
2
2
2
0
1
0
0
0
0
1
0
0
2
3
2
1
0
0
0
0
2
0
1
2
3
2
0
0
2
0
2
1
0
0
1
0
0
0
0
1
0
2
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
1
1
2
0
0
0
1
1
0
1
4
0
2
9
0
0
0
0
0
0
0
0
1
2
2
0
2
0
0
0
0
2
1
0
1
1
1
0
0
1
0
0
0
0
0
1
0
3
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
1
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
1
0
1
3
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
3
1
0
2
1
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
2
0
2
0
1
0
0
3
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
1
0
1
1
0
0
0
1
1
0
2
2
0
0
0
0
0
0
1
0
2
3
0
1
0
1
0
2
0
1
1
2
0
0
0
2
2
0
2
0
0
0
1
0
1
0
0
2
2
0
0
0
1
0
1
2
1
0
0
2
0
0
0
2
0
1
1
0
0
0
2
2
2
0
1
1
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
1
0
0
0
0
1
0
2
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
1
0
2
0
2
2
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
2
3
1
1
0
2
0
1
0
0
0
0
1
1
2
1
0
1
3
0
0
2
0
0
0
0
3
0
2
0
1
2
1
0
0
2
2
0
1
1
1
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
1
0
0
3
2
1
0
0
0
1
3
1
0
0
0
2
1
0
0
3
1
0
0
0
1
2
0
0
0
2
2
2
0
0
0
0
0
2
0
0
2
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
2
1
0
2
0
1
0
0
0
2
1
0
0
2
1
0
0
2
0
0
0
2
0
2
0
1
0
0
0
1
0
2
0
0
0
0
0
1
0
1
0
2
0
2
0
0
0
1
0
2
2
0
2
2
0
0
0
0
0
0
1
0
1
0
1
2
1
2
1
2
0
0
2
0
0
1
0
2
0
0
0
5
0
0
0
2
0
0
0
0
2
0
1
1
0
0
0
1
2
0
1
1
0
1
0
0
0
0
1
2
0
0
0
1
0
0
1
1
2
1
0
0
0
0
2
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
7
0
0
0
2
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
1
7
1
2
0
0
0
0
0
1
0
1
0
1
0
2
2
0
1
0
3
0
0
1
2
0
0
0
0
2
0
1
1
0
0
0
0
0
1
2
1
0
0
2
0
0
0
1
2
0
2
0
0
0
0
2
0
2
2
1
0
0
0
0
1
0
2
0
2
0
2
0
0
2
2
1
1
2
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
4
0
2
0
1
1
0
0
0
1
0
2
1
2
6
0
0
1
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
2
0
0
2
3
0
2
0
0
0
0
0
1
1
1
2
0
0
3
1
0
2
0
0
2
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
1
2
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
2
1
0
2
0
0
1
0
0
0
1
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
3
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
2
1
0
0
0
0
0
0
3
0
2
0
0
1
0
0
0
0
0
1
1
2
0
1
1
2
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
1
0
1
0
2
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
2
0
4
0
1
1
0
0
1
0
2
2
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
2
0
0
0
1
1
0
0
0
2
1
0
0
2
0
0
1
0
1
0
1
0
0
0
0
1
0
2
0
0
0
1
0
0
0
1
1
0
4
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
2
1
0
2
0
0
1
0
1
0
2
0
0
1
0
2
0
1
0
2
0
1
0
0
1
0
0
0
0
2
1
0
1
0
0
0
0
0
0
1
1
0
2
0
2
0
2
0
0
0
0
1
0
0
1
1
1
1
3
2
1
0
1
2
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
1
0
0
0
2
2
0
1
1
0
2
0
2
2
0
1
2
0
1
2
0
0
0
0
2
0
2
0
2
2
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
2
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
3
0
0
0
0
1
0
2
2
1
1
2
0
2
2
0
0
3
0
2
2
1
0
0
1
1
0
0
0
0
1
0
2
0
2
0
0
1
2
0
2
2
1
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
2
2
1
1
1
0
2
0
0
0
0
0
0
0
3
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
5
0
0
2
0
0
2
1
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
1
0
1
0
0
0
0
0
1
1
0
2
2
1
1
0
1
4
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
2
0
0
0
0
0
5
1
0
0
0
1
0
0
0
0
0
0
2
1
1
0
1
1
0
4
0
0
0
1
0
1
2
1
0
2
2
0
0
0
2
1
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
2
0
1
0
1
1
0
2
0
0
0
0
0
0
0
0
0
2
1
2
1
0
0
2
2
0
0
2
2
0
2
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
2
2
1
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
2
0
1
0
1
0
1
1
0
0
0
0
0
1
1
1
1
0
0
0
1
0
0
0
0
0
0
1
0
2
0
2
1
0
0
0
1
1
1
0
0
0
1
0
0
4
1
1
2
2
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
2
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
1
2
0
0
0
0
0
0
1
0
1
1
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
2
1
1
0
0
0
0
1
1
1
0
3
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
1
1
2
0
0
1
0
1
0
2
1
2
0
1
0
0
3
1
1
0
0
0
2
1
0
1
0
2
2
0
0
1
2
0
0
1
0
0
1
0
1
0
0
0
1
0
2
0
2
0
0
1
0
0
0
0
1
0
4
0
1
2
0
0
2
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
1
1
1
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
2
3
0
1
0
0
2
0
0
0
1
2
0
0
1
0
0
2
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
1
0
3
0
0
0
1
2
0
0
0
0
0
2
1
0
2
3
0
0
0
0
0
1
2
0
0
0
1
2
1
0
2
0
0
0
2
0
0
1
0
2
1
0
1
1
0
2
0
0
2
0
1
1
0
0
0
0
0
0
0
2
3
2
0
0
1
0
0
0
0
0
0
2
2
1
0
4
0
0
0
1
2
0
2
0
2
2
2
2
1
0
1
2
0
1
0
2
1
1
0
1
0
1
0
0
2
1
0
0
1
0
2
0
1
0
2
2
1
0
0
0
0
0
0
0
0
1
0
0
1
3
0
2
0
0
0
1
1
0
2
0
0
0
0
0
0
2
0
1
2
0
0
0
0
2
0
1
2
0
0
2
2
0
0
2
0
0
0
0
2
1
1
2
0
1
2
1
0
2
0
1
0
0
1
0
0
0
2
2
3
1
3
0
0
0
0
3
0
0
0
0
3
0
0
1
0
0
1
2
0
0
0
0
1
1
0
0
0
1
2
0
1
2
1
2
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
2
2
2
2
1
2
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
1
1
0
1
0
2
0
0
0
1
0
0
2
1
2
0
0
0
0
0
1
0
2
2
1
0
0
2
0
0
0
0
0
0
0
0
2
2
1
0
2
0
2
1
0
1
1
3
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
2
0
0
1
0
2
1
2
1
0
1
0
2
0
0
1
0
2
3
1
1
0
0
0
0
0
1
0
0
0
0
2
1
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
1
0
0
0
2
0
1
2
0
1
2
0
0
0
1
0
0
0
0
0
1
2
2
0
1
0
2
4
1
2
0
1
2
0
0
0
0
0
1
0
2
0
0
2
3
0
1
0
0
0
0
1
2
0
0
0
0
2
0
1
0
1
3
2
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
3
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
1
1
1
1
2
2
1
0
2
0
0
0
0
2
1
0
0
0
0
1
0
0
0
1
0
0
2
1
0
0
0
1
0
3
0
1
0
0
1
0
0
0
1
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
1
1
1
0
2
0
1
0
0
0
1
0
1
2
4
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
4
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
1
2
2
3
0
2
1
1
0
0
1
0
0
0
0
0
3
0
0
1
0
0
0
1
2
2
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
2
1
0
0
0
0
0
1
1
0
0
0
3
0
2
2
2
0
2
0
1
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
2
0
2
0
0
0
0
1
1
2
2
0
0
1
0
2
0
0
0
0
0
2
2
1
1
0
1
0
2
0
0
1
0
1
2
0
2
0
2
2
0
0
3
0
0
3
0
0
0
0
0
2
0
1
1
0
1
2
0
0
2
0
1
2
1
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
2
1
0
0
0
2
2
0
2
0
0
0
1
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
2
1
0
1
0
0
1
1
0
2
0
0
0
0
0
1
2
0
0
0
0
2
3
0
0
2
2
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
2
0
1
0
0
0
2
0
1
0
0
2
0
0
2
0
0
0
1
2
0
0
2
0
0
0
0
0
2
1
1
0
0
0
0
0
0
1
2
0
0
0
1
2
0
1
2
0
0
0
2
2
0
1
3
0
0
0
0
0
1
0
2
0
0
0
1
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
1
2
0
2
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
3
0
0
0
6
1
0
2
2
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
1
0
1
0
0
3
2
0
0
4
1
0
0
0
0
1
0
1
0
0
0
0
0
2
1
0
1
0
0
0
0
1
0
0
1
1
0
0
0
1
0
1
1
2
2
0
0
0
0
0
0
0
1
2
6
0
0
1
0
1
0
0
1
0
2
1
1
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
2
2
0
0
1
0
1
1
0
0
0
0
2
2
2
2
0
0
1
0
2
2
1
0
0
1
0
0
1
0
0
2
0
2
1
2
1
0
1
0
0
0
1
1
0
2
0
0
0
1
1
1
0
0
2
0
2
0
0
0
1
0
0
1
3
2
0
2
2
1
0
0
1
2
1
0
2
0
0
0
0
1
2
2
1
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
2
0
1
2
0
0
0
0
2
1
1
1
1
0
0
1
1
0
0
0
1
0
2
0
1
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
2
0
1
2
0
1
0
0
0
1
2
0
1
0
2
0
3
1
1
0
0
1
0
0
2
2
1
1
0
0
0
0
2
0
2
1
2
2
0
2
0
0
1
0
0
2
0
1
0
0
0
0
2
0
1
2
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
1
0
0
0
1
0
2
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
6
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
2
1
0
1
0
0
0
0
0
0
2
0
0
0
2
0
2
0
1
1
0
1
0
0
1
0
4
2
0
1
0
0
2
0
1
1
0
2
2
0
0
0
0
0
0
0
2
0
0
1
3
0
0
1
1
0
0
2
0
0
0
0
0
1
2
0
1
1
0
0
1
1
0
1
0
0
0
2
1
2
2
0
2
0
3
0
1
1
0
0
0
1
3
0
0
0
0
3
0
1
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
2
1
0
0
0
0
0
0
1
0
0
3
0
0
0
1
0
0
2
0
0
2
1
1
1
0
0
0
2
0
0
1
0
0
0
0
2
1
2
0
3
1
1
1
1
0
0
1
1
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
2
0
0
0
1
2
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
2
1
0
0
2
0
1
0
1
1
0
1
0
3
0
0
0
0
1
0
0
1
1
0
0
0
0
2
0
1
0
0
0
2
1
2
0
0
0
0
1
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
1
0
0
0
2
0
1
0
0
0
3
0
2
1
0
1
0
2
0
2
2
1
0
0
0
0
4
0
2
2
1
0
1
0
0
1
0
0
0
0
0
0
0
1
2
0
2
1
0
0
0
2
0
1
0
0
1
1
2
0
0
0
0
2
0
2
2
2
1
0
3
0
1
2
1
1
0
0
0
2
0
0
0
0
1
1
2
0
2
2
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
1
0
2
0
0
1
2
1
2
1
0
0
0
1
0
0
0
3
2
1
1
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
1
0
0
2
0
1
0
0
0
0
0
2
2
1
1
0
2
2
0
0
0
4
0
0
0
0
0
1
0
0
1
1
1
1
0
0
1
1
0
0
2
0
0
0
0
2
2
0
2
0
0
0
1
0
0
0
0
1
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
4
0
2
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
1
0
2
1
0
0
1
0
0
0
0
2
0
0
0
1
2
0
1
2
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
2
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
2
1
0
2
0
3
1
1
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
1
1
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
1
0
1
0
0
2
0
0
1
0
0
0
2
0
3
0
0
0
0
2
1
1
0
0
1
0
0
0
4
0
0
1
1
0
0
1
0
0
2
0
0
0
3
0
1
2
0
0
0
0
2
0
0
0
2
1
1
0
1
0
0
0
0
0
3
0
0
0
1
2
2
1
0
4
0
0
0
0
0
0
1
1
0
0
2
2
2
0
0
0
0
2
0
0
0
1
1
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
2
0
1
0
1
0
1
0
0
2
0
2
0
2
1
0
2
0
1
1
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
1
1
0
0
0
1
0
0
0
1
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
2
2
0
0
0
1
0
0
0
1
0
0
1
0
0
0
3
0
2
0
2
0
0
0
0
1
0
0
0
0
2
2
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
2
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
2
0
0
1
0
0
0
2
0
0
1
1
1
0
4
0
1
1
0
2
2
2
0
0
0
1
2
0
2
0
0
1
0
1
0
3
2
0
0
0
0
0
1
0
1
0
0
0
2
0
0
1
0
0
1
0
0
0
0
1
0
1
1
0
2
0
2
0
0
0
0
2
4
0
3
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
2
0
0
2
2
0
0
0
2
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
1
0
4
0
0
0
0
1
0
0
0
2
0
0
0
2
0
2
0
2
0
0
2
1
1
2
2
2
0
0
8
0
0
0
1
0
0
0
0
0
0
2
2
1
0
0
0
0
2
1
1
0
0
0
3
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
1
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
1
0
2
1
0
0
0
1
0
0
0
0
1
1
2
2
0
0
2
1
2
1
1
3
0
0
0
1
0
1
1
0
0
0
2
2
0
0
0
2
0
2
0
0
0
0
2
0
2
0
5
2
1
1
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
1
0
0
3
1
0
2
2
0
1
0
1
1
2
1
0
0
0
0
0
0
0
0
0
0
2
0
1
1
1
1
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
1
0
0
2
0
1
2
0
0
2
1
0
0
0
2
2
0
0
0
0
0
1
1
1
0
0
0
2
0
0
0
0
1
0
0
1
1
2
0
0
2
1
1
0
0
0
1
2
1
1
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
2
0
2
0
0
1
1
1
1
0
1
0
2
0
2
0
1
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
1
2
0
0
2
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
1
0
0
2
1
0
0
0
0
2
0
1
0
2
2
0
0
2
1
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
5
1
2
1
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
2
1
0
1
0
0
1
1
2
0
0
0
0
0
0
0
1
2
2
0
0
0
2
1
0
1
1
0
0
0
2
2
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
1
1
1
1
0
1
3
0
0
1
0
3
0
0
0
2
0
0
0
0
0
0
1
1
2
0
0
1
1
0
4
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
3
1
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
1
0
1
0
0
2
0
1
2
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
1
2
0
0
1
0
1
0
0
0
0
1
2
2
2
1
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
1
2
2
0
0
0
0
0
3
0
0
0
1
1
0
2
2
0
2
1
0
0
0
6
2
0
2
0
2
0
2
0
0
2
0
0
0
0
2
0
1
3
2
0
0
0
0
2
0
1
2
0
0
1
0
0
0
2
0
4
0
0
0
0
0
1
0
2
0
0
0
4
0
2
0
1
0
1
0
0
2
0
0
2
2
2
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
2
2
1
0
0
0
2
0
0
0
0
1
0
1
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
2
0
1
0
0
3
2
0
1
0
1
0
0
1
1
0
0
0
0
0
2
0
2
1
0
1
0
0
0
0
2
0
1
0
1
1
2
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
1
0
0
0
2
0
1
1
1
0
0
0
1
0
0
0
2
0
0
2
2
1
0
0
1
0
0
0
0
0
1
0
0
2
0
2
0
0
1
0
0
2
1
0
1
0
0
0
0
0
1
0
1
1
0
1
0
2
1
2
0
0
2
1
1
0
0
0
0
0
0
0
0
1
1
2
1
0
0
0
1
2
0
1
0
0
0
1
1
0
2
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
2
2
5
0
0
1
0
2
1
0
0
0
2
0
0
0
0
0
0
0
2
1
1
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
2
2
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
5
2
1
0
0
1
0
2
0
0
0
2
0
0
0
2
1
0
1
1
2
0
0
0
0
2
0
0
2
2
0
2
2
0
2
0
0
1
1
2
2
0
0
1
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
4
0
2
0
0
0
0
1
0
2
1
2
2
0
0
0
1
0
0
0
0
1
0
2
1
0
0
0
0
0
0
2
2
0
0
1
1
0
0
0
2
0
1
0
0
0
0
1
2
0
1
0
1
0
0
0
1
0
0
0
2
0
0
1
0
0
2
0
0
0
1
2
0
0
0
6
2
1
0
2
1
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
2
0
1
1
1
2
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
2
0
2
1
1
0
2
0
1
0
1
0
0
0
0
1
0
0
1
0
2
2
0
0
0
0
1
0
2
1
0
0
0
1
3
1
4
0
2
2
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
4
0
1
0
1
1
0
0
0
2
2
0
0
0
2
0
0
0
1
2
0
1
0
0
0
0
0
0
2
0
0
2
1
0
0
0
1
0
2
1
2
1
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
2
0
1
0
1
0
0
1
2
0
2
1
0
0
2
0
0
1
1
0
0
2
0
0
0
2
0
0
0
0
0
1
2
1
2
0
1
0
0
0
0
1
0
0
0
0
2
1
1
2
0
0
2
0
0
0
0
0
1
0
1
0
0
1
0
0
0
2
1
2
0
0
1
0
0
1
2
0
0
3
5
1
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
2
0
0
2
2
0
0
0
1
1
2
0
0
0
1
2
3
0
0
2
0
1
1
0
2
3
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
1
0
0
0
0
0
1
1
0
2
1
1
0
2
0
2
0
0
1
0
0
0
0
2
0
1
0
1
2
1
1
0
0
2
2
0
0
0
0
0
2
0
2
4
1
0
1
2
2
0
0
2
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
1
0
3
1
1
0
0
1
0
1
0
1
0
0
2
1
0
0
2
1
0
1
1
0
0
1
0
0
0
0
0
1
0
0
2
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
2
1
0
0
1
0
1
0
2
2
0
3
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
2
0
1
1
1
0
1
0
1
0
1
0
0
0
0
1
0
0
3
0
1
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
4
0
0
0
0
0
0
2
0
2
0
0
0
1
1
0
0
0
2
5
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
2
4
0
2
0
0
0
1
1
0
0
1
2
0
0
2
0
0
0
0
0
2
1
0
2
0
0
0
1
0
0
0
0
2
0
1
0
1
0
0
1
1
1
0
2
0
2
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
1
0
1
0
1
0
1
1
0
4
0
0
2
2
0
0
1
0
1
1
2
2
1
0
0
0
0
0
2
1
0
0
1
0
0
0
1
0
1
2
2
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
2
0
0
0
2
0
1
1
2
0
0
0
1
1
0
1
1
0
0
0
1
0
0
0
0
0
2
1
0
0
2
0
0
2
0
2
0
1
0
0
0
0
1
0
1
2
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
2
0
2
0
0
2
0
2
0
1
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
2
2
0
0
0
0
2
0
2
0
1
1
2
1
0
0
2
0
1
2
0
2
2
0
0
0
0
1
1
0
0
2
1
0
3
1
0
2
1
2
0
0
1
2
0
0
0
2
1
3
1
0
2
1
2
0
0
2
0
2
0
2
1
0
0
2
0
2
2
0
1
0
0
0
2
1
0
0
1
0
0
1
1
0
1
0
0
0
0
0
2
1
0
2
0
0
0
2
2
0
0
2
0
0
0
1
2
0
0
0
0
6
0
2
2
0
0
0
0
0
1
2
0
0
0
0
2
2
0
1
1
0
4
2
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
3
1
0
1
1
0
0
1
1
0
0
0
3
0
0
1
0
0
2
3
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
1
0
3
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
1
0
3
2
0
0
2
0
0
0
0
0
0
1
1
0
1
0
1
0
2
0
0
1
0
0
2
0
0
2
1
1
0
0
1
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
2
0
0
1
0
3
0
0
0
2
2
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
1
1
1
2
0
0
0
0
0
0
1
0
0
1
2
0
2
0
1
0
0
2
2
0
1
2
1
0
2
0
1
1
0
1
0
0
1
0
0
0
0
0
2
2
0
0
0
0
1
2
0
0
0
0
0
0
4
0
2
0
2
0
0
0
0
0
0
0
1
0
5
0
1
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
3
0
1
2
1
0
0
2
0
1
0
1
0
2
0
1
0
2
1
0
0
1
2
0
2
1
2
0
1
0
0
0
2
1
0
0
0
0
0
2
0
1
2
0
0
2
1
1
1
0
0
5
0
1
1
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
1
0
6
0
0
0
0
1
0
1
0
2
0
0
0
2
0
1
0
1
0
1
0
2
0
1
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
2
1
0
0
0
0
0
2
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
1
2
0
0
0
2
2
1
0
0
0
1
2
0
0
1
0
0
0
0
2
0
0
1
1
2
2
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
2
2
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
1
1
0
0
0
0
2
0
2
2
0
1
0
1
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
2
2
0
2
0
0
0
0
1
0
0
0
1
0
2
0
0
2
1
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
1
2
0
0
2
0
0
1
0
0
0
0
2
2
6
0
0
0
0
0
0
1
0
1
1
1
1
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
4
1
0
0
0
0
0
2
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
1
1
1
0
2
1
0
0
0
2
0
2
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
1
0
0
0
0
2
0
0
1
1
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
1
0
2
2
0
0
3
0
0
0
0
0
0
0
0
0
3
1
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
2
0
1
0
0
2
1
0
0
0
1
0
0
0
2
1
1
2
0
0
0
0
0
0
0
0
1
2
0
1
0
2
2
2
0
0
0
1
9
1
0
0
0
2
0
0
0
1
1
0
2
0
0
0
1
1
0
0
2
0
0
1
0
0
1
0
1
1
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
1
0
2
1
0
1
0
0
0
0
0
2
2
1
0
1
0
0
1
0
2
0
0
0
2
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
1
0
0
1
3
1
2
0
0
2
1
1
1
0
3
1
0
0
0
0
0
2
2
0
2
0
0
0
0
0
4
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
1
0
2
0
0
0
0
1
0
0
2
1
0
1
0
0
0
0
0
0
0
2
0
0
2
0
1
0
1
0
0
2
0
2
0
0
0
0
5
0
0
0
1
2
2
2
2
0
1
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
2
1
0
0
0
1
2
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
1
0
0
2
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
2
1
0
2
1
0
0
0
0
0
2
0
0
1
1
0
0
1
1
3
3
0
1
0
0
0
0
0
2
0
0
1
2
2
1
0
0
2
0
0
0
0
2
0
1
1
0
0
0
0
0
0
2
0
0
1
3
0
0
2
0
2
0
1
0
0
0
1
1
2
0
2
0
2
1
0
0
1
0
0
2
1
0
0
0
1
2
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
2
1
0
0
0
2
0
2
0
1
0
2
0
2
1
0
0
1
0
2
0
0
0
3
0
0
2
1
0
3
0
4
2
1
0
0
0
0
3
0
0
0
0
1
0
1
2
2
0
0
2
2
0
0
0
2
0
0
0
2
2
2
2
0
0
0
0
0
2
0
2
2
2
0
1
0
1
2
1
2
2
0
0
0
0
2
0
2
0
1
2
1
1
2
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
3
1
0
1
2
0
0
2
2
0
0
0
0
1
0
2
1
1
0
0
3
0
0
0
0
1
0
0
2
1
0
2
0
0
0
0
1
0
2
0
1
2
3
0
3
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
1
0
2
1
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
2
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
1
0
0
1
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
1
2
1
2
2
0
1
2
2
0
2
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
2
2
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
3
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
2
0
1
0
0
0
0
1
0
1
0
1
0
0
2
1
0
2
0
1
0
0
1
2
0
0
0
0
0
0
0
0
2
0
1
1
0
1
0
0
1
0
0
0
0
0
0
2
2
1
1
0
0
0
0
1
0
2
2
0
0
0
1
0
1
2
0
0
1
0
0
0
0
2
0
3
0
0
0
0
0
0
1
0
0
0
1
3
0
0
2
0
2
1
1
1
0
1
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
2
1
1
2
4
1
1
0
0
2
1
0
2
1
0
0
0
0
0
0
0
0
1
0
0
2
1
0
2
0
1
0
2
0
2
0
1
0
0
0
0
0
0
0
0
2
0
3
2
0
0
0
0
1
1
0
0
1
2
2
4
0
1
0
3
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
2
2
0
1
0
0
1
2
0
1
0
1
0
2
0
0
0
1
0
2
2
1
1
2
0
0
2
1
0
2
0
0
0
0
3
1
1
0
1
1
0
2
0
0
0
0
1
1
2
0
2
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
3
1
2
1
0
0
0
0
2
1
1
0
0
0
1
0
0
2
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
1
2
0
0
1
0
0
2
5
0
0
0
0
1
1
0
1
0
3
1
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
1
0
1
2
0
0
2
2
2
2
0
1
5
0
0
2
0
1
0
1
0
0
0
2
3
2
1
0
1
0
2
1
2
0
2
1
0
0
0
0
0
0
1
0
0
0
1
2
1
0
2
2
1
0
2
0
1
0
2
2
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
1
1
0
0
0
0
2
1
0
2
2
1
0
0
0
2
0
1
0
0
0
0
1
2
2
1
1
0
0
1
2
2
2
2
1
0
1
0
1
0
0
0
2
0
3
0
0
2
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
1
2
1
0
0
0
0
0
3
0
1
0
1
1
0
0
1
0
2
2
2
0
0
1
0
3
0
0
0
2
0
0
3
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
2
2
0
0
0
1
0
2
1
1
0
0
1
1
0
0
2
1
0
0
0
2
0
0
2
2
0
0
0
1
2
0
0
3
0
1
0
1
2
0
0
0
0
0
0
0
0
0
2
1
0
4
0
2
2
0
0
2
3
0
0
0
0
1
0
1
0
1
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
1
0
2
4
0
0
2
2
0
4
1
0
0
0
1
2
2
0
0
1
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
4
2
0
2
3
0
0
0
0
0
1
2
0
0
1
0
2
2
0
1
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
1
1
0
0
2
0
1
0
2
1
0
0
2
1
0
0
0
0
2
0
2
3
0
0
1
3
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
5
1
2
1
2
2
0
0
0
2
0
0
0
2
2
0
0
1
2
0
1
0
1
0
1
0
0
0
0
1
0
1
1
0
0
0
1
1
2
1
1
0
3
0
0
2
0
0
1
0
0
0
0
2
0
1
0
2
0
1
1
2
0
0
0
2
1
1
1
0
2
1
0
2
0
0
2
0
1
0
0
2
0
2
1
0
2
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
1
0
0
6
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
2
1
2
0
0
0
1
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
2
1
0
0
4
1
1
1
0
0
2
0
1
2
0
0
0
2
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
1
2
0
0
0
0
2
1
0
0
0
0
0
3
1
1
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
1
0
2
2
0
1
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
2
1
1
1
0
1
0
2
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
1
0
1
1
0
1
0
3
0
0
2
0
0
0
1
0
2
0
1
2
2
0
2
0
1
0
0
1
0
1
0
2
0
0
0
2
0
5
1
0
1
2
0
2
0
0
2
2
0
0
1
0
0
0
0
1
2
0
0
2
0
0
2
0
1
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
3
1
2
2
2
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
4
0
0
1
0
0
1
0
0
0
2
0
2
0
0
0
3
0
1
2
2
0
0
0
2
2
2
0
0
1
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
1
2
1
0
0
0
1
4
2
0
1
1
0
0
0
0
1
1
0
2
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
1
1
2
1
2
0
0
2
0
0
1
1
0
0
2
0
3
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
1
2
0
0
2
1
0
1
0
2
0
2
0
0
0
0
0
0
2
0
0
1
0
1
1
0
5
0
0
0
2
2
0
1
2
1
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
2
2
0
2
2
2
1
0
0
0
0
1
2
0
0
1
0
0
0
0
4
0
1
1
1
1
0
0
0
0
2
0
0
3
1
1
1
1
0
1
0
2
7
1
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
1
4
1
0
0
2
0
0
0
0
0
0
2
2
0
2
0
2
0
2
0
0
0
0
2
1
0
2
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
2
1
1
0
1
0
2
2
2
0
1
0
0
7
0
0
0
0
0
2
0
1
2
0
0
0
0
0
2
2
0
2
0
1
1
1
2
1
2
0
2
1
0
1
0
2
1
1
0
1
0
0
0
0
1
1
0
0
0
1
0
2
0
2
2
1
2
1
1
0
2
1
0
0
2
2
3
0
5
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
13
0
1
2
2
2
1
1
0
0
2
0
2
0
1
0
0
0
0
0
0
0
2
0
1
2
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
1
1
0
0
0
1
2
1
0
0
2
1
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
1
2
1
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
2
2
1
0
0
0
1
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
2
1
1
0
2
0
0
0
3
0
2
2
0
1
1
2
0
1
0
3
1
0
1
0
0
0
0
2
1
0
0
2
0
0
3
0
0
0
0
0
0
1
2
2
2
0
2
0
2
1
0
0
0
1
0
0
2
0
0
2
2
2
0
0
2
0
0
2
0
0
1
0
0
0
0
1
1
0
0
2
2
0
1
0
1
2
2
2
0
0
0
0
0
2
1
1
0
2
0
2
2
3
1
0
0
0
0
2
0
0
2
0
1
0
0
0
0
1
2
0
2
2
0
0
0
1
0
0
0
2
2
0
0
2
1
0
1
1
0
1
2
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
1
1
0
1
2
0
2
0
2
1
0
1
0
1
0
1
2
0
0
0
0
0
2
0
2
1
0
0
2
0
3
0
0
0
2
0
0
0
0
1
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
5
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
2
0
2
0
2
1
0
1
0
0
0
1
0
0
2
2
1
0
1
0
0
0
2
0
1
0
4
0
0
0
0
1
0
1
0
2
1
0
0
0
0
0
1
2
0
0
0
1
1
0
0
0
2
0
1
2
0
0
0
0
0
3
2
0
1
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
1
0
0
2
1
0
0
1
0
0
0
2
2
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
2
1
0
1
2
1
2
1
2
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
2
2
0
1
0
0
0
1
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
4
2
0
2
0
2
0
0
1
0
0
2
2
1
2
0
0
0
0
0
1
1
2
1
0
2
1
0
0
1
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
3
0
2
1
0
4
0
0
0
1
2
2
2
4
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
3
0
0
0
2
0
0
2
0
0
1
0
4
2
0
0
2
2
0
1
2
1
0
0
0
4
1
1
1
0
0
2
2
2
1
2
0
0
1
1
0
1
0
0
0
1
0
0
0
1
1
0
1
0
2
0
1
2
1
2
0
0
0
2
0
2
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
1
1
2
3
0
0
0
3
2
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
1
0
0
1
2
0
2
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
1
0
2
2
3
1
0
1
1
2
2
0
2
0
0
0
1
0
1
1
0
2
2
0
0
0
1
2
2
2
0
2
0
0
2
0
1
0
0
0
0
2
0
1
1
0
1
1
1
0
0
2
2
1
0
4
0
0
0
0
0
0
0
0
1
0
0
0
3
0
1
1
0
0
0
1
0
0
0
1
1
2
0
0
0
3
1
0
0
0
0
0
0
2
0
1
0
2
2
1
0
0
0
0
0
2
0
0
0
1
0
2
0
1
1
0
0
0
0
0
2
0
0
0
0
1
0
2
1
2
2
0
0
1
0
0
0
0
2
3
3
1
1
0
0
2
0
2
1
1
1
1
0
0
0
0
1
0
0
0
0
2
0
0
1
0
2
0
1
0
0
1
0
0
1
2
0
0
0
0
0
0
2
1
0
0
0
0
2
2
2
0
0
0
0
0
0
0
2
0
1
0
2
2
2
0
0
0
0
0
0
0
1
1
0
0
3
1
1
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
2
0
1
1
0
0
1
0
2
0
2
0
0
2
0
0
0
0
1
0
1
0
0
1
0
2
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
1
0
1
0
0
2
0
2
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
1
0
2
5
0
0
0
0
2
1
2
1
1
0
0
0
2
0
2
1
0
1
0
1
0
2
2
3
0
0
1
0
2
0
2
0
0
0
1
0
1
1
1
0
2
0
1
2
0
1
0
0
0
0
1
0
2
1
0
0
2
1
0
0
0
0
0
2
2
2
0
2
0
0
1
0
1
0
0
2
0
1
0
0
0
1
2
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
1
2
1
1
0
0
2
1
0
0
0
0
0
1
0
0
3
0
2
0
0
0
0
2
0
1
0
0
0
1
0
3
1
2
2
0
1
1
2
0
0
0
0
0
0
1
1
0
1
1
0
1
0
0
0
0
0
2
0
2
0
0
0
2
0
1
1
0
1
0
2
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
2
0
1
1
2
1
2
2
0
2
2
0
0
2
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
2
1
1
0
2
0
0
0
0
0
0
2
0
0
1
2
0
0
0
3
0
2
0
0
0
4
0
0
0
1
2
2
0
1
0
2
0
4
0
0
0
0
0
2
0
2
2
0
1
0
0
0
0
2
2
1
0
0
2
0
0
0
0
2
1
2
0
0
0
0
0
0
0
2
1
2
0
0
2
0
2
2
2
0
1
0
1
0
0
0
0
2
1
0
0
0
0
2
0
0
0
6
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
2
0
2
1
2
0
0
1
0
0
0
1
0
0
1
0
0
1
1
1
1
1
2
0
0
1
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
1
2
0
0
2
1
0
1
0
0
0
1
0
0
0
0
4
1
0
2
0
0
0
0
3
1
0
0
1
0
1
1
2
0
0
0
0
1
1
0
0
1
1
1
0
0
0
1
0
0
0
0
1
0
0
1
2
0
1
2
0
0
2
2
1
1
0
0
2
2
4
0
2
0
1
0
2
0
1
2
2
0
0
2
1
0
2
0
0
0
0
1
2
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
2
1
1
0
0
1
2
2
0
0
0
1
1
1
4
1
0
2
2
0
1
1
0
0
0
2
2
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
1
1
1
0
1
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
1
2
0
0
2
0
1
1
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
1
0
0
0
0
1
2
2
0
0
1
0
1
1
0
1
3
0
0
1
0
0
2
1
1
3
1
2
2
1
2
0
1
0
0
0
0
1
0
1
1
0
0
0
0
2
0
1
2
0
0
0
0
0
2
0
4
1
1
2
2
0
1
0
2
0
0
1
2
0
0
0
0
0
0
1
2
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
2
2
0
2
1
1
1
0
1
0
0
1
1
0
1
2
0
2
0
1
2
0
0
1
1
0
1
0
0
0
2
1
0
0
0
0
0
1
0
0
1
2
1
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
1
0
0
0
0
1
2
0
1
0
0
0
0
0
2
0
0
0
2
2
1
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
2
0
0
0
0
1
2
0
1
0
0
0
0
2
1
0
0
0
1
6
1
0
0
1
0
0
0
2
0
0
0
1
0
0
1
2
2
1
0
0
0
1
3
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
2
0
2
0
2
0
0
2
3
0
0
0
1
0
0
0
1
0
0
0
2
0
2
2
0
0
2
1
0
0
0
2
0
2
4
0
0
1
0
2
0
1
0
1
1
0
2
1
1
2
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
1
2
0
0
0
2
3
0
0
0
0
1
0
0
1
0
1
0
0
1
2
0
1
2
0
1
1
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
2
0
0
0
1
2
1
0
2
0
2
1
2
1
2
1
2
0
1
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
1
0
2
0
1
0
1
2
0
0
1
0
0
0
2
0
0
0
2
2
0
0
1
0
0
0
0
0
1
0
0
2
0
0
2
0
0
2
0
1
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
1
1
1
1
0
1
0
0
0
0
2
0
1
0
2
1
0
0
0
0
4
0
0
2
0
0
0
0
0
2
0
0
1
0
0
3
0
1
2
1
0
0
0
0
2
1
0
1
0
0
0
0
2
0
0
0
0
2
1
1
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
3
2
1
0
0
0
0
0
2
1
1
0
0
0
2
0
2
0
2
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
2
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
1
0
3
1
0
0
0
1
0
0
2
1
1
0
0
0
0
2
1
0
3
2
0
2
0
1
0
0
2
1
2
0
1
0
0
2
0
0
2
2
2
0
0
1
0
0
0
1
1
0
1
1
0
1
2
2
1
2
0
0
0
2
0
0
0
0
2
2
2
0
1
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
3
1
0
0
0
0
2
0
1
1
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
2
2
0
1
1
0
2
1
0
0
2
2
0
3
1
0
1
2
1
2
0
0
0
0
0
0
0
0
3
0
2
0
0
2
0
0
1
0
0
0
0
0
0
1
1
0
2
0
0
2
2
1
0
0
0
2
0
2
0
2
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
2
1
2
2
1
0
2
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
1
1
1
0
0
0
1
0
0
1
0
0
3
0
0
0
0
2
3
2
1
2
0
0
0
0
0
1
1
1
0
1
0
0
3
0
0
0
0
0
0
2
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
2
1
1
3
0
1
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
1
0
0
1
0
2
0
0
0
0
0
1
1
2
0
2
1
1
2
0
2
0
4
1
1
0
0
1
0
0
1
0
0
1
2
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
2
0
0
1
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
1
1
0
1
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
6
2
3
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
2
0
0
1
2
1
1
2
0
1
0
0
0
3
2
0
1
0
2
0
2
0
2
0
2
2
1
0
0
0
0
0
0
1
0
2
0
0
0
1
1
1
0
0
0
0
0
0
0
2
1
0
2
1
3
0
0
0
1
0
1
0
1
1
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
2
0
0
2
2
0
1
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
1
4
1
0
0
4
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
1
0
0
0
1
1
0
0
2
0
2
3
2
0
0
2
0
0
2
0
1
0
0
0
0
2
1
1
1
1
0
0
0
2
0
0
1
0
0
0
1
1
1
0
0
2
2
1
0
0
0
0
0
2
1
1
0
1
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
2
2
1
2
0
0
0
2
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
2
0
1
2
0
0
1
0
0
0
0
5
0
1
0
0
3
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
2
1
0
1
0
0
0
3
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
1
0
0
0
1
1
4
0
0
1
0
0
0
0
2
0
1
1
2
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
2
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
1
1
2
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
1
1
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
2
1
2
0
0
2
0
2
0
1
0
0
0
0
1
1
0
0
1
0
5
0
4
0
0
0
0
1
0
0
0
0
2
0
2
2
0
1
0
0
1
0
0
2
1
0
0
2
0
0
0
1
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
3
0
0
0
1
0
2
0
0
0
1
2
0
1
1
1
0
0
2
0
1
0
0
0
4
1
1
0
2
0
2
0
0
1
1
2
0
2
2
0
1
0
0
1
0
0
1
0
0
2
0
2
0
0
1
0
2
0
0
0
2
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
2
1
0
0
2
0
0
1
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
2
0
2
1
1
1
1
0
1
1
0
0
2
2
0
0
0
0
1
0
0
0
2
1
0
1
1
0
2
1
0
1
0
0
0
1
0
0
0
0
1
0
0
2
1
1
1
0
0
1
0
0
0
0
0
0
1
1
0
2
2
0
0
0
0
0
0
0
2
0
1
1
2
0
0
2
0
0
0
0
1
2
1
0
0
0
1
0
0
2
1
0
0
0
1
0
0
1
0
0
3
0
1
0
0
1
0
1
0
0
0
2
0
0
2
0
0
0
0
2
1
1
0
0
1
1
0
1
0
2
0
2
0
0
0
0
2
1
0
0
0
0
0
2
2
0
0
2
0
0
2
0
1
0
1
2
0
0
0
0
0
1
0
0
0
1
0
0
2
2
0
1
2
0
2
1
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
2
3
0
0
0
0
2
0
0
0
0
1
0
0
5
1
0
0
0
4
0
0
0
0
0
0
0
1
2
1
0
0
0
0
1
0
3
2
0
2
1
0
1
1
0
1
2
2
0
1
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
1
0
0
1
0
0
0
2
1
1
0
3
0
0
0
0
2
0
3
0
0
0
0
0
0
2
1
0
2
2
0
2
0
0
0
1
1
0
0
1
0
1
0
0
2
0
0
2
1
0
0
2
0
0
0
2
0
0
0
1
0
0
2
1
2
0
0
1
1
1
2
1
2
0
0
0
0
1
0
1
0
1
0
0
0
1
0
2
0
0
0
0
2
0
0
2
0
0
1
1
2
1
0
0
0
1
0
2
1
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
2
2
0
0
2
1
0
0
0
0
0
1
2
2
0
0
3
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
3
1
1
0
0
0
0
0
0
0
0
2
0
0
0
3
2
0
1
1
0
0
0
2
1
0
0
0
0
1
0
0
0
0
1
0
0
0
3
0
0
1
0
2
1
2
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
1
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
2
1
0
0
0
4
2
0
0
0
5
1
0
0
0
0
1
1
0
0
2
1
0
0
2
6
2
3
1
1
0
0
1
0
1
2
3
3
1
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
3
2
0
3
0
1
0
0
0
0
1
1
1
0
0
0
1
0
2
1
0
0
2
0
2
0
2
1
1
0
0
0
0
2
3
0
0
0
0
2
1
2
0
0
1
0
0
0
0
0
0
1
1
2
2
0
0
0
0
4
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
3
0
0
1
0
0
0
1
0
1
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
1
0
1
0
0
2
2
0
0
0
0
1
0
2
0
2
2
1
0
2
0
2
2
5
1
1
0
0
0
1
2
1
0
0
1
3
0
1
0
0
0
2
1
0
0
0
2
2
0
0
2
4
2
0
0
1
0
0
1
0
0
0
1
1
2
0
1
0
0
2
0
0
0
0
2
1
0
0
0
0
2
1
1
0
4
1
0
1
0
1
0
0
0
0
1
0
0
0
0
1
2
2
1
1
0
0
0
2
1
0
1
3
0
0
0
2
0
1
2
0
0
0
0
0
0
1
2
0
0
1
2
0
1
2
0
1
2
0
0
0
1
0
0
0
2
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
8
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
2
0
0
0
2
1
0
1
2
0
0
2
0
2
2
0
9
2
0
0
2
0
0
1
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
1
1
0
2
2
2
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
1
0
0
0
2
0
0
0
1
2
1
0
1
0
2
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
2
1
1
0
1
1
0
2
0
2
1
0
0
0
3
1
0
0
0
0
1
1
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
2
1
0
1
1
0
1
0
1
2
0
1
0
2
0
0
0
2
0
1
0
1
3
1
0
1
0
3
1
0
2
0
0
0
0
0
0
0
0
0
1
0
1
12
0
1
0
0
2
0
2
0
0
1
0
0
0
0
2
1
0
1
0
1
0
2
0
0
0
0
2
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
1
1
1
0
0
0
0
1
0
1
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
1
0
0
0
0
2
0
0
0
7
0
0
2
0
2
2
1
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
3
0
0
3
0
0
0
0
0
0
3
0
0
0
0
1
3
1
2
2
1
0
1
0
1
0
1
1
0
0
2
0
1
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
2
0
1
1
0
2
0
0
0
2
2
0
0
0
2
0
0
0
0
1
1
0
0
0
2
0
2
0
1
1
0
1
1
0
1
0
0
2
1
1
2
0
0
5
0
0
0
0
1
1
0
2
0
0
5
1
1
1
0
0
1
0
0
1
0
0
0
2
2
1
0
0
1
0
2
1
0
0
0
2
0
2
2
1
0
0
0
1
2
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
1
0
0
0
0
1
3
1
2
1
0
0
0
2
0
0
0
0
2
0
0
0
3
2
2
1
1
0
0
0
0
0
0
2
2
2
2
0
0
0
2
0
0
0
0
1
2
2
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
2
2
2
0
0
0
0
1
0
2
1
0
0
2
0
0
0
0
1
0
2
1
2
0
2
1
0
1
0
0
0
1
0
0
2
1
0
0
0
0
0
3
0
0
6
3
0
2
0
1
1
0
0
0
1
1
2
0
2
0
0
0
3
0
1
0
0
2
0
1
0
2
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
1
0
2
0
2
1
0
2
1
0
0
0
1
2
0
2
0
0
0
0
0
3
0
0
0
1
0
2
2
1
1
1
0
0
0
1
0
0
6
0
2
0
0
2
0
0
1
0
0
1
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
3
4
2
2
0
0
0
0
0
2
0
2
0
0
1
0
0
0
1
0
2
1
0
1
0
0
0
0
0
1
3
0
0
0
0
0
1
2
0
0
2
0
1
2
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
2
0
2
1
0
1
0
0
0
0
0
0
1
0
0
1
1
1
0
0
1
1
1
0
1
0
0
2
2
0
0
0
2
0
0
2
1
0
1
0
0
0
0
0
1
2
1
2
2
1
1
0
2
0
1
0
0
1
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
2
2
0
2
2
0
0
0
0
0
1
0
2
2
2
0
0
1
1
1
0
1
3
1
3
0
2
1
1
0
0
1
0
0
0
0
0
0
2
1
1
0
0
2
0
0
1
1
0
1
0
0
2
0
0
0
1
1
0
0
0
1
1
0
0
1
1
3
0
0
0
0
1
2
0
0
2
0
1
1
0
2
0
0
1
0
1
0
2
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
1
0
1
1
1
1
0
1
0
2
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
3
0
3
0
0
1
0
0
0
0
0
2
0
0
0
1
2
0
1
0
2
0
0
0
1
3
1
1
0
1
2
2
0
0
0
1
0
0
0
2
0
1
0
0
3
0
0
0
0
2
0
1
0
0
1
0
0
0
1
0
0
0
1
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
4
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
1
1
0
0
2
0
0
0
0
0
0
1
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
1
2
1
3
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
3
0
1
0
0
0
0
1
0
1
0
1
0
0
2
0
1
2
0
0
0
2
0
2
0
0
1
2
0
0
0
0
0
1
0
0
1
3
1
0
0
0
3
0
0
0
0
0
0
3
1
2
2
1
2
0
0
2
1
0
0
0
0
1
0
1
1
0
1
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
1
0
0
0
0
0
0
6
3
0
0
0
0
1
0
0
0
2
2
1
0
1
0
0
0
0
2
0
0
0
1
2
0
2
2
3
0
3
2
0
2
0
2
1
2
0
1
1
0
0
0
0
0
2
2
0
2
0
2
1
0
1
2
0
1
1
1
3
1
2
0
0
0
1
0
2
0
0
1
1
2
2
1
0
1
0
0
1
0
1
1
0
2
0
0
0
2
3
0
2
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
2
0
0
1
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
2
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
1
2
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
1
1
2
0
0
0
0
1
3
1
0
0
0
0
1
2
1
0
5
1
2
0
0
1
0
1
2
1
1
1
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
2
0
0
1
1
1
2
0
2
1
1
2
2
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
2
0
0
1
1
1
2
0
0
2
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
2
0
1
4
0
0
2
0
0
1
0
0
0
2
0
1
0
0
2
0
0
0
1
0
0
1
0
1
2
1
1
0
0
0
2
1
0
0
0
0
0
1
0
0
0
2
0
0
2
0
1
0
0
0
2
0
0
0
1
1
0
2
0
2
0
0
0
0
1
2
1
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
2
0
1
1
2
0
0
0
2
0
0
2
0
0
0
1
0
0
1
0
0
2
2
0
0
0
3
0
0
0
1
0
2
0
2
2
0
0
0
0
0
0
0
1
1
2
1
0
2
2
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
2
2
1
2
2
0
0
0
0
2
2
0
0
0
0
0
0
1
0
2
1
2
0
2
0
0
0
2
1
1
0
0
2
0
0
0
0
1
0
0
1
2
0
0
0
2
1
1
0
0
0
0
2
0
0
1
2
0
2
0
0
0
3
0
1
0
0
0
1
0
0
0
1
0
0
0
0
2
2
0
0
2
2
0
0
0
0
2
2
0
1
2
1
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
1
0
2
2
0
0
0
0
0
0
1
4
1
0
1
0
2
2
0
1
1
0
0
0
0
2
1
0
0
0
2
1
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
2
0
0
0
0
0
0
2
0
0
1
2
2
2
2
0
0
0
0
2
0
0
0
0
2
0
0
0
2
1
0
0
1
2
0
1
1
1
1
2
1
0
0
0
0
2
0
2
0
0
2
2
2
0
0
2
1
0
0
0
0
1
1
0
2
0
0
2
0
2
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
1
0
0
2
0
0
0
1
2
1
0
0
0
0
0
0
1
0
0
2
7
1
0
1
1
1
0
2
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
5
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
1
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
4
0
0
2
0
0
0
2
2
0
2
0
0
2
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
4
0
1
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
2
2
1
1
0
1
0
0
0
1
1
2
1
0
1
0
0
0
0
0
1
2
1
0
0
0
0
1
0
1
0
2
2
0
0
1
0
0
1
0
0
2
2
0
0
1
1
2
2
0
0
0
2
0
2
0
2
0
1
0
0
0
0
0
0
1
0
2
0
0
0
1
0
2
0
1
0
0
0
0
0
0
2
1
0
2
0
1
1
0
0
2
1
1
2
2
1
1
0
0
0
1
1
0
1
2
1
0
0
0
0
0
2
1
1
0
0
0
2
1
0
2
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
2
2
0
0
1
0
1
2
2
1
2
0
0
2
0
0
0
0
0
2
0
1
3
2
1
0
0
0
0
1
1
0
2
1
1
1
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
2
2
2
1
0
0
0
2
2
0
2
2
0
1
0
0
0
2
1
0
1
0
0
2
1
2
0
1
0
0
0
1
4
0
0
0
0
0
0
4
0
0
0
0
0
0
3
0
0
0
0
0
2
0
1
2
1
2
0
1
3
0
5
2
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
2
1
2
0
1
0
1
0
1
0
0
0
0
2
0
2
1
0
0
0
0
2
1
1
1
0
0
3
0
1
0
0
1
1
0
3
0
0
1
0
0
0
1
1
2
0
0
0
1
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
2
0
0
0
0
0
0
0
2
1
2
1
1
1
0
2
2
2
0
0
0
0
0
1
0
1
1
2
0
0
0
0
0
0
4
2
2
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
4
2
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
1
2
1
2
0
0
0
0
2
1
0
1
0
0
0
1
0
2
0
0
1
0
0
0
0
2
0
0
1
0
0
2
2
1
0
1
0
0
1
0
0
0
0
1
0
0
0
2
1
0
0
0
0
1
0
1
0
2
2
0
0
0
3
0
2
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
4
2
1
1
2
0
2
1
0
0
2
2
0
1
0
0
0
1
2
0
0
2
1
1
1
0
0
0
0
1
0
0
4
0
0
2
0
0
0
5
0
0
0
1
0
2
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
2
0
1
3
0
0
1
1
0
2
1
2
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
2
1
0
1
2
4
1
0
0
0
0
1
0
2
0
0
1
1
2
0
2
0
2
0
1
0
0
0
0
0
2
0
0
1
1
0
0
0
2
0
0
0
2
2
2
0
2
0
0
0
0
0
1
0
3
0
2
0
0
2
2
0
0
2
1
2
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
5
1
0
0
1
0
0
2
0
0
1
2
0
0
1
0
1
0
0
0
1
0
2
1
1
0
0
3
0
1
0
0
0
0
0
0
0
0
2
1
2
2
0
2
0
0
0
1
0
2
1
0
0
0
2
0
0
0
2
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
2
0
2
0
1
0
0
2
1
0
1
0
0
0
0
0
2
1
0
0
1
1
1
0
0
1
0
0
0
0
0
0
1
0
1
1
1
0
0
4
0
2
2
0
0
2
0
0
0
0
0
0
1
2
0
0
0
1
0
2
2
0
2
0
1
0
0
2
1
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
2
1
1
0
1
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
1
2
3
0
0
0
0
0
1
0
1
2
1
0
0
2
0
0
0
0
2
0
2
2
0
0
1
0
0
0
1
3
0
5
1
0
0
0
2
0
0
2
2
0
2
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
3
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
1
2
2
0
2
0
0
1
2
1
2
1
1
1
0
0
0
0
0
4
0
1
1
3
0
0
0
1
2
0
3
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
2
1
1
0
1
0
0
0
0
0
1
2
0
0
2
0
1
0
0
0
0
2
0
2
0
0
1
0
0
2
1
0
0
0
0
2
0
1
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
2
1
0
2
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
2
0
0
0
2
0
0
2
0
0
1
0
1
0
0
1
0
0
0
0
2
0
1
1
0
2
1
0
1
0
0
0
2
0
0
0
0
0
2
1
1
1
0
1
0
0
0
2
0
2
2
0
0
1
0
0
1
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
2
2
0
0
0
1
1
0
0
2
1
1
0
2
0
0
0
0
0
0
0
2
0
1
2
1
0
2
2
0
0
2
0
1
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
2
0
0
2
2
0
2
2
0
1
0
0
2
1
1
0
0
0
0
1
0
1
0
2
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
2
0
0
0
1
1
0
2
0
1
0
0
1
0
2
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
3
0
2
0
0
0
3
0
1
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
3
1
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
2
0
1
0
0
0
1
2
0
0
1
1
2
1
1
1
0
0
0
2
0
1
4
0
0
1
1
0
0
2
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
2
0
1
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
1
0
1
2
1
0
0
2
0
0
1
1
1
1
0
0
0
0
0
0
0
1
2
0
1
2
1
0
1
0
0
1
0
5
0
3
1
0
0
0
1
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
1
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
1
0
0
2
0
2
0
3
0
2
1
4
0
0
2
1
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
1
0
1
0
1
1
0
0
0
1
0
0
2
2
0
0
0
2
0
0
0
0
0
1
3
2
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
2
0
0
1
0
0
1
0
0
2
0
2
0
0
0
1
0
1
0
0
1
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
2
0
0
1
1
2
0
2
1
0
0
0
0
0
0
0
1
0
0
1
0
2
0
1
1
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
3
2
0
0
0
0
0
0
0
2
0
0
2
2
0
0
2
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
1
0
1
0
2
0
0
0
0
0
0
0
1
0
0
2
2
0
2
2
0
0
1
1
0
1
1
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
1
2
0
0
0
0
0
1
0
1
1
1
1
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
1
0
2
0
2
1
1
0
1
1
0
0
0
0
2
1
2
0
0
3
2
2
2
0
2
1
0
0
1
0
1
1
0
1
1
1
3
0
0
0
2
1
1
0
0
0
0
0
0
0
2
2
0
2
0
1
1
0
0
0
0
0
0
0
3
0
2
3
0
0
0
0
0
2
0
0
0
1
0
2
0
1
0
0
1
0
0
1
1
1
0
0
1
2
0
0
0
1
0
1
2
0
0
0
0
0
1
2
2
0
0
3
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
2
0
2
1
0
2
0
2
0
2
2
1
2
2
0
0
1
2
0
0
1
0
0
3
0
0
0
0
1
4
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
2
1
0
1
2
2
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
2
1
0
0
2
3
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
2
0
0
0
0
0
0
1
0
1
0
1
0
2
2
1
0
0
0
3
2
2
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
3
1
2
0
0
1
3
0
2
0
0
1
2
0
0
0
2
0
0
2
0
0
1
1
0
0
1
1
0
1
2
0
2
0
2
1
1
0
0
0
0
0
0
0
1
2
0
1
1
0
0
1
1
1
0
3
0
2
0
0
3
0
0
1
0
2
1
0
0
3
0
1
1
0
2
0
0
0
0
0
0
1
1
1
0
0
0
2
1
2
0
0
1
0
0
2
0
0
0
1
0
2
2
4
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
1
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
2
0
0
2
1
2
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
2
0
0
10
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
2
1
0
0
0
0
0
0
2
0
0
1
1
1
0
0
0
1
0
0
0
1
0
1
0
0
3
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
3
2
0
2
0
0
2
0
0
0
1
0
2
2
0
0
2
0
0
0
0
0
0
0
0
1
1
0
1
0
2
2
0
0
1
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
2
1
0
0
0
1
1
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
1
0
7
0
2
1
1
0
1
2
2
2
0
0
0
0
0
0
0
2
1
0
0
1
2
0
0
0
0
0
0
0
0
1
2
1
1
2
0
2
2
2
0
0
0
0
0
1
2
1
0
1
0
1
0
2
0
0
2
0
0
0
0
1
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
2
2
0
0
0
0
2
2
2
0
0
0
4
0
1
0
4
1
2
0
1
0
2
0
0
0
2
2
0
1
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
1
2
0
0
2
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
2
0
2
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
1
3
1
1
2
1
2
2
0
2
0
0
0
2
2
0
0
3
0
2
0
0
0
1
0
2
0
0
0
1
2
0
0
0
0
1
1
0
0
0
2
3
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
2
0
1
0
0
0
0
0
2
0
0
0
1
1
0
0
1
0
1
0
0
0
0
2
2
0
1
2
0
1
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
1
1
0
0
1
0
0
0
2
1
1
2
0
2
2
0
0
0
0
1
0
2
0
0
1
0
3
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
2
0
1
2
4
2
0
2
3
1
0
0
0
2
1
1
1
0
0
0
0
2
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
2
0
1
2
0
1
0
2
0
3
1
0
2
2
0
3
0
0
0
1
2
0
2
2
2
0
0
1
1
2
2
0
0
1
2
0
0
0
2
0
0
2
2
0
0
0
1
0
1
2
0
0
0
1
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
1
0
0
2
2
0
0
1
1
0
1
2
1
0
0
2
0
0
0
0
0
0
0
1
0
3
0
0
1
1
0
1
0
0
2
0
0
2
0
1
0
0
0
0
0
0
2
0
1
0
2
0
0
2
1
0
2
1
2
0
0
0
1
2
0
0
0
2
0
0
1
1
1
0
1
0
1
2
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
2
0
0
0
0
0
1
0
0
2
0
1
1
0
2
0
0
2
0
0
0
0
2
0
1
3
0
1
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
1
1
2
2
0
1
2
0
0
0
3
0
2
1
0
1
0
1
0
0
0
0
0
1
0
2
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
1
1
1
1
3
1
0
0
1
0
2
0
0
1
3
2
0
1
0
2
0
3
0
2
0
1
2
3
2
1
0
0
1
0
0
0
0
0
0
1
2
2
0
2
2
0
2
0
1
0
0
1
0
0
0
1
1
1
0
1
1
0
0
1
0
0
0
3
0
1
1
0
0
2
2
1
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
1
1
0
1
2
2
0
1
1
0
0
1
1
0
0
1
0
0
1
0
2
0
0
3
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
1
0
1
0
4
1
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
2
2
0
2
0
2
0
2
0
0
0
0
0
2
2
1
0
1
2
0
0
1
0
1
0
0
0
0
2
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
2
1
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
2
1
0
0
2
2
2
0
0
0
1
0
0
0
0
0
0
2
0
2
2
0
0
2
0
1
0
0
0
1
1
0
1
1
0
1
0
0
2
0
4
2
2
0
0
0
0
0
0
1
0
2
0
2
2
2
1
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
2
0
0
1
0
0
1
0
1
0
0
2
0
2
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
2
2
0
1
0
1
0
2
0
1
0
0
1
3
1
0
1
1
0
2
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
3
0
0
2
0
0
0
0
0
0
1
1
2
1
0
2
0
0
1
1
0
1
3
1
0
3
0
1
1
0
1
0
2
0
0
2
1
0
0
0
0
2
2
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
2
1
2
1
0
0
0
2
0
1
0
1
0
2
0
0
2
1
2
0
0
0
2
2
0
1
0
3
2
0
0
0
0
0
1
1
0
0
2
0
2
2
0
0
2
1
0
0
1
0
3
0
3
0
2
0
0
0
0
1
1
1
0
2
0
0
0
2
0
0
2
2
2
1
2
2
0
0
0
0
1
0
1
0
0
2
2
0
0
0
0
1
0
0
0
1
1
0
0
2
2
2
1
0
0
0
0
0
0
2
0
0
0
1
0
0
3
3
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
1
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
1
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
3
0
3
0
1
0
1
0
0
0
0
2
0
2
0
0
2
2
0
1
0
2
0
1
0
1
0
1
1
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
3
0
0
1
0
0
2
2
1
0
0
0
1
0
0
0
2
0
0
0
1
1
1
0
0
0
1
0
1
0
0
0
1
0
2
1
0
0
0
1
0
0
1
1
2
1
0
1
1
2
1
0
1
0
2
0
0
0
0
0
2
1
2
1
0
0
0
0
2
2
2
1
0
0
0
1
0
1
1
0
2
1
0
3
0
1
1
0
2
1
0
1
0
0
1
1
1
2
2
0
0
0
0
0
2
0
2
2
0
0
0
0
0
1
0
1
2
0
3
1
0
2
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
1
2
0
0
0
2
0
2
2
1
2
2
2
0
0
0
0
0
7
0
1
0
0
0
0
1
0
2
2
1
0
0
0
0
0
1
0
0
0
1
2
0
2
2
0
0
1
0
2
1
1
0
0
2
0
0
1
0
1
0
0
0
2
0
2
2
0
0
1
0
1
0
1
0
2
3
0
1
2
1
0
0
0
0
0
0
2
0
1
0
2
0
2
0
0
1
0
0
0
0
3
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
5
0
0
1
0
2
0
2
0
0
2
5
0
0
0
3
0
0
0
0
2
2
0
0
0
3
2
2
0
2
0
0
1
0
0
0
0
0
2
2
3
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
1
2
1
0
1
1
0
0
0
2
0
2
1
1
1
2
0
1
0
1
2
1
0
0
1
0
1
0
1
0
2
2
2
0
1
0
0
2
0
2
0
2
0
0
1
2
0
0
0
0
0
1
0
0
0
0
2
1
0
2
1
0
4
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
2
2
1
2
0
0
0
0
2
0
3
1
0
2
2
3
0
0
1
0
0
0
0
1
0
1
2
1
1
0
3
0
0
0
0
0
0
0
1
0
0
0
1
0
2
3
1
1
0
2
0
0
2
2
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
2
0
0
0
0
0
0
0
2
1
1
3
2
0
3
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
2
0
0
0
1
2
0
1
0
2
0
2
0
0
1
0
1
2
0
1
0
0
1
0
1
2
0
0
0
2
0
0
2
2
0
0
1
0
0
0
2
0
0
0
0
2
0
1
0
1
1
0
0
0
0
2
0
0
1
2
0
0
2
0
0
1
0
2
0
2
0
0
1
0
2
2
0
0
0
1
0
0
0
0
0
2
0
0
2
2
2
0
0
0
0
0
0
0
1
1
0
0
1
0
1
1
0
1
0
2
0
2
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
2
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
1
1
1
1
1
0
0
0
3
0
0
0
2
1
0
1
0
0
2
0
2
2
0
3
0
1
0
0
0
3
0
0
0
3
2
0
1
1
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
2
0
1
0
4
0
0
0
0
0
1
0
1
0
1
1
0
0
1
6
0
0
0
0
0
1
0
0
0
2
1
8
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
3
2
0
1
0
0
0
2
1
0
0
4
2
0
1
0
0
1
0
0
0
1
1
0
1
0
0
0
2
3
0
1
0
0
1
0
0
2
0
2
0
0
0
0
0
1
0
0
1
1
3
0
2
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
3
2
0
0
5
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
2
2
0
2
0
0
0
0
0
0
1
1
2
0
0
2
0
0
0
2
0
0
1
2
2
0
2
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
2
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
2
0
0
3
0
2
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
1
3
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
2
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
2
1
0
0
0
2
1
0
0
2
1
1
2
0
0
1
1
0
0
0
4
0
1
1
0
1
0
0
1
2
1
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
2
0
2
2
0
0
1
2
0
0
1
2
1
0
0
1
0
0
0
0
1
0
1
0
2
1
0
0
2
2
0
1
0
0
1
0
0
1
2
0
2
1
0
1
0
0
0
0
0
0
1
0
0
1
2
0
2
0
1
0
0
3
0
0
0
1
0
0
0
0
1
2
0
0
3
1
2
0
0
1
2
1
2
0
0
3
2
2
0
0
1
2
1
0
0
1
0
1
0
1
2
0
0
2
0
0
2
2
2
0
0
1
0
2
1
0
3
1
0
0
2
0
0
0
2
0
2
1
0
0
0
0
2
0
1
1
0
1
2
1
2
0
1
0
2
0
2
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
4
0
0
0
1
0
0
2
1
3
0
0
1
0
0
0
2
1
1
0
0
0
1
2
3
1
2
0
0
0
0
2
2
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
1
2
0
2
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
4
0
0
1
0
2
0
0
2
0
0
1
0
0
1
0
0
0
0
1
0
1
2
0
1
0
0
0
0
2
1
2
0
2
1
3
2
0
1
0
1
0
3
0
0
0
0
3
2
0
2
2
0
0
0
0
0
2
0
0
0
1
0
0
0
6
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
1
0
0
1
1
1
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
3
3
0
2
0
0
0
0
0
3
0
0
0
2
2
2
2
0
0
0
0
0
1
1
0
1
0
0
0
2
2
0
0
0
0
0
1
0
0
2
0
0
1
2
0
0
1
0
0
1
0
1
0
1
2
0
1
1
0
0
1
0
0
0
1
2
0
0
0
3
0
0
0
0
0
2
0
0
0
2
2
1
0
0
0
2
0
1
0
2
3
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
4
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
2
2
2
0
0
0
2
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
1
1
0
0
2
1
1
0
1
0
2
2
2
0
1
0
2
1
0
0
0
2
0
1
1
0
2
1
2
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
2
0
0
2
0
3
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
1
2
1
0
0
0
4
2
0
0
2
1
2
2
0
2
1
0
0
0
0
0
0
1
1
0
2
0
1
0
1
3
1
2
1
0
0
0
0
2
0
0
0
0
0
2
0
1
0
1
1
0
0
0
2
0
0
2
0
0
2
1
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
1
2
0
0
2
1
1
1
0
0
2
0
0
1
2
1
0
1
1
0
2
0
0
2
1
1
1
2
1
2
0
1
0
2
0
1
0
2
0
0
0
2
0
0
0
1
2
1
0
1
0
1
1
2
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
1
2
0
0
1
0
0
1
1
0
0
1
1
1
0
0
1
0
1
0
0
1
1
0
1
0
1
0
0
0
0
0
0
1
2
1
0
2
0
2
0
1
0
0
1
1
2
2
0
0
3
1
0
0
0
0
2
0
1
0
3
0
0
0
1
0
0
0
3
1
0
2
1
7
0
0
1
0
0
0
1
2
4
2
1
1
1
0
0
0
1
0
0
0
0
1
1
0
0
0
2
2
0
0
1
2
0
0
1
2
1
2
2
0
0
0
1
1
1
0
0
0
1
2
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
2
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
1
0
0
0
1
2
1
0
2
1
0
0
1
2
1
0
0
0
0
1
0
2
0
0
1
0
1
3
2
2
1
1
0
1
0
0
0
2
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
1
1
2
0
2
0
0
1
2
2
0
0
1
0
0
2
0
1
0
0
3
0
0
0
1
0
1
0
2
0
1
0
0
1
0
2
1
0
1
0
0
0
1
0
0
0
1
1
1
0
1
0
0
0
2
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
2
2
1
0
0
1
0
0
0
2
0
0
0
1
2
2
5
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
2
2
0
0
2
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
1
2
1
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
1
0
1
1
2
0
0
1
0
0
3
0
0
1
0
0
0
2
0
3
1
0
1
0
1
0
0
0
2
3
1
2
0
0
0
2
3
2
1
0
0
0
0
1
0
0
0
0
0
1
2
2
1
0
2
2
0
1
1
0
0
0
2
2
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
2
0
2
2
0
2
2
1
1
0
0
1
2
1
0
1
0
0
0
0
0
0
2
0
2
0
1
2
1
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
3
0
0
0
0
1
0
2
0
2
1
1
0
0
1
0
1
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
2
1
0
0
1
0
2
2
0
2
2
0
2
0
2
0
3
0
0
2
2
0
2
0
1
1
0
0
0
0
2
0
0
1
0
0
1
1
1
1
0
0
0
0
1
0
1
0
1
3
0
2
2
1
0
2
0
3
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
2
0
0
2
0
0
1
0
0
2
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
1
0
2
0
0
0
2
0
1
0
2
0
0
1
0
2
2
1
0
6
1
1
1
1
0
0
2
0
0
2
0
0
0
1
2
1
0
0
0
1
0
0
1
1
0
1
1
0
0
2
1
2
0
0
2
0
0
1
0
0
0
1
0
3
0
2
4
4
1
2
2
0
1
2
0
0
0
0
0
1
0
0
0
1
1
0
0
2
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
1
0
0
0
2
1
1
1
2
0
1
0
0
1
0
2
3
2
0
0
1
0
0
0
0
0
0
1
2
1
0
0
0
2
0
2
0
2
0
0
0
2
4
4
0
2
0
0
0
0
0
0
2
2
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
2
0
0
1
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
2
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
2
1
1
0
0
0
0
1
1
2
0
0
2
0
0
0
2
1
0
0
2
0
0
0
0
3
1
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
1
0
0
0
2
0
0
4
0
0
0
2
0
1
0
0
0
0
2
1
0
0
2
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
2
1
1
0
1
0
0
1
0
1
0
0
1
1
1
2
1
0
0
1
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
1
0
0
1
0
0
1
1
0
2
0
0
1
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
1
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
1
0
0
0
0
1
1
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
1
2
2
1
0
1
0
0
0
2
0
0
0
2
0
0
0
2
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
1
0
2
1
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
2
0
1
1
0
2
3
0
0
1
0
1
2
0
0
0
0
0
0
2
1
2
0
0
1
1
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
2
0
1
3
0
0
1
0
0
2
0
1
0
0
2
0
0
0
1
0
2
1
0
0
0
0
0
0
2
0
0
2
0
0
0
2
1
0
0
0
0
1
0
0
1
0
1
0
0
0
5
1
2
0
3
0
1
1
2
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
4
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
1
1
2
0
1
0
0
0
0
1
0
1
2
0
0
0
3
0
1
1
0
0
0
1
0
0
2
1
1
1
1
0
0
0
2
0
3
0
0
2
0
0
1
0
0
1
0
2
0
0
2
0
0
2
5
2
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
2
3
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
1
1
2
0
2
1
0
0
0
0
2
0
0
0
0
2
1
1
0
0
0
2
2
0
3
0
2
0
0
0
1
4
0
0
0
0
0
0
0
0
2
2
0
2
0
1
1
1
0
0
2
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
3
1
0
0
0
2
0
2
0
1
0
0
0
0
2
1
2
0
1
0
0
1
2
0
1
1
0
2
1
2
0
3
0
0
1
0
1
0
0
1
1
0
2
0
0
0
0
1
1
0
2
2
0
2
0
0
0
0
1
3
2
0
0
0
0
0
0
1
2
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
2
0
1
0
0
1
2
0
2
0
1
2
2
0
1
0
1
2
2
0
0
0
0
0
0
0
2
0
0
1
0
0
2
1
0
0
0
0
0
2
1
2
1
1
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
2
0
1
2
1
0
1
0
1
1
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
1
0
0
2
2
0
0
0
1
0
0
0
0
2
1
1
0
1
1
0
1
0
0
0
0
0
4
0
0
0
2
0
0
0
1
0
2
0
0
3
0
3
0
2
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
2
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
2
1
0
0
2
0
1
0
1
1
0
0
2
0
2
0
0
2
2
1
3
1
0
0
0
0
2
2
0
0
0
1
1
0
0
1
0
2
1
0
0
0
0
0
0
2
2
0
0
1
1
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
2
0
0
3
0
2
2
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
1
0
2
0
0
1
1
1
1
1
1
0
0
0
0
2
0
0
0
1
0
1
0
0
0
2
0
2
0
1
0
0
0
0
0
0
1
2
0
1
3
0
0
0
2
0
2
0
0
2
0
0
0
4
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
1
2
0
2
1
2
0
0
0
0
0
1
0
4
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
2
0
1
1
2
0
0
0
2
1
0
0
2
0
2
0
0
0
0
0
1
0
0
3
2
0
0
1
0
1
0
0
0
0
0
0
2
2
2
0
1
0
3
0
0
0
0
2
0
2
0
1
1
0
1
0
0
0
0
0
0
1
0
0
1
0
3
1
2
0
2
0
0
4
2
0
1
0
2
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
1
0
0
0
2
0
0
2
0
2
0
1
0
0
0
0
2
3
3
5
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
3
1
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
1
0
2
2
1
0
2
0
2
2
1
0
2
2
0
2
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
4
0
0
0
0
2
1
2
0
1
0
1
0
3
0
0
1
0
0
1
0
0
0
0
3
0
1
0
2
2
2
1
0
2
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
4
0
0
2
0
0
0
0
2
0
0
1
0
0
0
1
0
0
1
2
0
0
2
0
0
0
1
1
0
2
0
0
0
1
0
1
0
1
1
1
0
3
1
0
0
0
0
0
2
0
5
0
2
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
2
1
2
3
0
0
0
0
2
0
0
1
0
1
1
1
0
1
0
2
0
2
0
0
1
1
2
0
0
0
0
1
0
0
0
0
3
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
1
0
0
1
0
1
1
0
0
0
1
1
0
0
1
0
0
2
2
0
1
0
2
2
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
3
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
9
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
2
1
0
0
1
0
0
1
2
0
0
0
0
0
2
2
0
3
1
0
2
1
1
0
0
0
0
1
0
0
1
0
0
1
0
1
2
0
1
1
1
1
0
0
2
0
0
2
0
0
2
0
0
0
1
0
1
0
0
0
1
1
0
0
1
0
0
2
0
0
2
0
0
1
0
2
0
1
2
2
0
2
1
0
0
0
0
0
0
0
1
1
1
2
0
0
1
0
0
0
0
3
0
0
0
0
2
0
1
1
0
0
2
0
0
0
0
0
1
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
1
0
0
0
2
0
1
0
0
0
3
1
0
2
1
0
3
0
0
3
2
1
2
0
1
2
0
1
2
0
2
0
0
2
1
0
2
2
2
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
2
2
3
0
1
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
1
3
0
0
0
0
2
0
0
0
1
0
4
2
0
1
0
0
2
0
2
0
2
2
0
2
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
1
1
1
0
0
2
0
1
0
2
2
0
1
0
1
2
1
1
2
2
0
0
0
0
0
0
2
1
1
1
1
2
1
0
3
2
1
1
2
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
2
0
1
0
0
0
1
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
3
0
0
0
0
2
12
0
0
1
1
0
1
2
1
0
0
2
0
0
0
0
0
4
0
1
1
1
0
0
0
1
0
0
0
1
2
4
0
1
0
1
0
1
0
0
1
2
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
2
1
2
0
0
0
0
0
0
0
2
0
2
1
0
0
0
1
1
1
0
0
1
3
0
1
2
1
1
0
3
2
3
0
0
1
1
0
0
0
2
2
0
0
0
2
0
0
1
0
0
2
0
0
0
1
0
1
1
0
1
2
0
2
2
0
0
1
2
1
0
2
0
2
2
0
0
0
2
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
2
2
2
0
0
0
2
0
0
0
0
2
0
0
1
4
0
0
0
0
0
2
0
0
3
1
2
0
0
0
1
1
1
0
2
0
0
0
0
0
0
0
0
0
3
0
2
0
1
2
0
0
0
1
0
0
2
0
3
0
0
1
2
0
1
0
0
0
0
0
0
0
2
0
0
2
1
0
0
1
2
0
3
1
0
0
1
0
6
2
0
0
1
0
0
0
0
2
0
0
1
0
0
0
2
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
1
2
0
1
0
0
1
4
0
1
1
0
2
0
0
0
0
0
0
3
0
1
0
1
0
1
7
0
0
0
0
0
2
2
0
0
3
0
1
2
0
0
0
2
0
0
0
0
0
0
2
0
3
0
0
0
2
1
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
1
0
1
0
2
0
0
0
0
0
1
0
0
0
1
1
0
0
4
0
2
0
0
0
0
0
1
0
1
0
1
2
0
0
3
0
0
0
0
1
0
0
0
0
0
0
1
0
2
2
0
0
0
0
2
0
1
1
1
0
0
2
2
0
0
2
0
1
0
0
1
0
0
4
0
1
1
0
0
1
0
0
2
1
0
0
0
2
1
0
1
0
0
0
0
0
0
2
0
1
2
0
0
1
0
1
0
2
1
0
0
2
0
2
2
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
1
1
0
1
0
0
0
0
2
0
2
2
0
0
0
0
2
2
3
0
0
1
0
0
0
1
0
3
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
2
2
2
1
0
0
2
1
3
0
0
0
0
0
4
1
0
2
0
1
0
0
2
0
0
0
1
1
0
0
0
1
0
0
2
7
1
1
1
2
1
0
2
1
0
1
0
0
0
1
0
0
0
0
2
1
0
1
0
0
0
1
0
2
2
3
1
0
0
0
2
0
1
0
0
0
1
2
0
14
0
2
2
0
0
2
1
0
0
0
0
1
1
0
1
0
0
0
0
2
0
1
0
0
0
1
0
1
0
0
2
2
0
0
0
0
0
0
2
0
1
0
1
0
2
1
0
0
2
0
0
1
2
0
0
3
3
0
0
0
2
0
1
0
2
3
0
1
2
0
1
0
0
1
0
0
0
4
0
1
4
1
0
0
1
0
0
0
1
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
1
0
1
0
2
1
0
0
0
1
1
0
0
0
1
1
0
2
0
1
0
0
0
0
0
2
1
0
1
2
0
2
0
0
2
2
0
0
1
2
0
2
0
2
0
0
0
2
0
0
0
1
0
0
0
4
0
0
0
0
0
2
0
1
2
0
0
1
0
0
1
0
2
0
2
0
2
0
2
1
4
0
0
0
1
0
0
6
1
0
0
1
0
0
0
0
2
2
0
0
0
0
2
2
2
1
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
1
0
0
0
2
3
0
0
0
1
1
1
0
1
0
0
0
0
0
2
0
0
1
1
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
3
1
1
0
0
0
0
2
0
0
5
0
0
0
3
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
1
2
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
1
0
0
2
0
1
0
2
0
1
2
0
0
0
0
0
0
2
1
0
1
2
0
0
0
1
1
0
3
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
2
0
0
0
1
1
0
0
1
0
0
0
0
3
1
0
0
0
0
0
1
0
0
0
1
0
0
2
0
1
0
2
1
1
0
2
2
0
0
0
0
0
1
2
0
0
0
0
1
0
3
0
1
1
0
7
0
0
2
1
2
0
2
0
0
0
1
2
0
0
0
1
2
3
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
2
3
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
1
0
0
2
2
0
0
2
0
0
0
0
0
2
1
1
0
0
1
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
2
2
0
0
3
0
1
0
0
0
0
0
2
0
0
2
0
1
0
1
0
0
0
0
0
0
0
4
0
0
2
0
2
0
0
0
1
2
1
0
0
2
0
1
1
1
0
1
0
0
1
0
2
3
1
0
2
0
0
0
0
0
2
0
0
1
0
0
0
2
2
2
1
2
1
2
1
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
3
0
2
0
5
1
0
1
0
0
1
0
2
0
1
0
2
1
2
2
0
0
0
0
0
2
0
0
0
1
0
0
0
2
1
2
3
2
0
2
0
2
0
0
0
1
0
0
1
2
0
2
0
0
0
0
1
0
0
1
0
0
0
0
1
1
2
2
2
0
0
1
0
0
0
0
2
0
1
0
0
2
1
0
0
2
0
2
0
0
1
1
1
0
0
0
0
1
0
0
2
1
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
1
0
1
1
0
0
7
2
2
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
3
0
1
0
4
0
0
0
0
0
0
1
0
3
0
0
0
1
1
0
0
0
1
1
0
1
0
0
2
0
3
0
0
0
0
0
0
1
1
1
0
1
1
0
0
0
2
1
0
2
0
0
0
0
2
0
1
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
1
2
2
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
2
2
1
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
1
0
0
2
1
0
2
0
1
0
1
0
1
0
0
1
2
0
1
0
1
2
0
0
0
0
0
1
0
0
0
2
0
0
0
2
2
1
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
2
0
0
0
0
1
2
2
0
0
2
0
0
0
3
3
1
2
0
0
2
1
2
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
2
1
2
2
1
1
1
0
0
0
1
0
2
0
0
2
1
1
0
0
1
0
0
2
0
0
0
0
1
1
1
1
0
0
0
0
0
0
2
0
0
3
0
0
0
0
1
1
1
2
0
0
0
0
1
0
1
0
0
1
2
0
0
0
1
1
0
0
0
0
2
0
0
2
2
0
2
0
0
0
0
1
0
0
0
1
1
0
0
1
1
1
0
1
0
0
0
2
0
0
1
2
1
1
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
1
0
0
0
2
2
1
2
0
0
0
0
2
0
0
0
2
0
1
1
1
0
0
1
3
2
3
2
0
2
0
1
0
0
0
0
0
2
2
0
1
0
0
0
0
2
2
0
0
0
0
1
0
2
1
1
1
1
0
1
0
0
2
0
0
2
1
0
3
4
0
0
1
0
0
0
0
0
0
0
1
2
2
2
2
0
4
0
0
0
0
3
0
2
0
0
0
2
0
0
0
1
0
2
2
1
0
0
0
0
2
2
0
0
0
2
0
0
0
1
1
0
1
1
0
0
0
0
0
1
0
2
1
2
0
0
3
2
0
0
0
2
1
1
2
2
0
3
0
1
0
0
3
1
0
1
1
0
0
0
2
2
1
2
0
0
0
0
0
0
0
2
0
1
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
2
1
2
1
0
0
1
0
1
1
1
2
0
0
0
0
0
0
1
1
0
1
2
2
0
0
0
1
2
0
1
0
0
0
0
0
1
2
0
0
2
0
0
2
2
0
0
2
0
0
0
2
0
0
1
1
0
1
0
0
1
1
3
2
2
1
0
0
0
0
0
0
2
0
1
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
2
0
1
2
0
1
2
0
0
0
2
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
1
2
0
0
2
0
0
0
3
1
2
2
0
2
1
0
0
0
2
0
0
3
1
2
2
1
2
0
2
2
0
0
0
0
0
2
2
1
1
0
1
0
0
0
0
3
1
1
0
0
0
2
1
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
3
0
0
2
1
0
0
0
2
0
0
2
3
1
0
0
2
0
1
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
2
0
0
0
2
0
1
0
0
0
0
2
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
2
0
2
0
0
2
0
0
0
2
6
0
3
0
2
1
2
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
1
1
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
2
0
1
2
0
2
0
0
1
0
1
0
0
0
0
1
0
2
1
1
0
1
0
0
2
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
1
0
0
1
3
1
0
1
0
0
0
0
0
0
0
2
0
1
0
0
2
0
1
3
0
1
2
1
0
0
0
0
0
0
0
0
0
0
1
2
2
2
2
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
3
0
1
0
0
0
0
2
0
3
1
0
2
1
1
0
1
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
2
2
0
0
2
0
2
2
0
0
0
2
0
2
0
0
3
0
0
2
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
1
0
0
0
2
1
2
2
0
0
0
0
0
0
1
0
1
2
0
0
1
0
0
0
0
0
0
0
2
0
1
0
2
0
0
2
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
2
5
1
1
0
1
1
1
1
1
2
0
0
2
0
0
2
0
1
0
1
3
0
1
2
0
0
1
1
1
1
1
2
0
1
0
1
0
0
0
2
2
2
1
1
2
0
2
0
0
0
1
1
1
0
0
0
0
0
0
1
2
0
1
0
0
0
2
0
0
0
1
1
0
0
0
1
0
0
2
0
0
1
2
1
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
1
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
2
1
0
0
0
2
2
2
2
0
0
1
1
0
0
0
1
0
1
0
0
0
0
2
2
1
0
0
0
0
2
0
1
1
1
0
1
0
1
2
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
2
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
1
0
0
0
0
1
1
1
2
0
2
0
0
0
1
1
0
0
2
0
0
0
3
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
2
0
1
1
1
0
1
2
0
1
1
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
1
0
1
0
1
0
0
0
0
2
0
0
2
3
0
0
0
0
0
1
0
2
2
0
2
1
2
0
1
4
0
0
0
1
1
0
0
0
0
0
1
2
1
2
0
2
1
0
2
2
0
1
0
0
0
0
0
0
2
2
1
0
1
0
1
0
0
2
0
0
0
0
0
1
2
0
0
1
0
0
0
0
1
0
0
0
2
2
3
0
0
0
0
1
2
1
0
2
0
2
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
2
0
1
1
0
0
2
2
1
1
2
0
2
0
0
0
0
0
0
0
1
2
0
0
0
2
1
0
0
1
0
0
1
2
0
1
0
2
2
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
2
2
0
0
1
2
2
0
0
0
0
2
2
2
0
2
1
0
1
0
3
0
0
0
2
1
0
2
1
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
2
0
1
0
2
0
0
1
0
0
2
0
0
0
0
0
0
2
2
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
1
3
0
0
0
1
0
0
0
1
2
1
3
1
1
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
2
0
2
1
1
1
0
1
2
0
0
0
0
0
1
0
0
2
1
0
2
1
0
0
0
1
0
2
1
0
2
1
0
0
1
1
0
1
0
0
0
0
2
0
1
0
0
0
2
1
2
0
0
0
1
1
0
2
1
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
2
1
2
1
0
1
0
0
1
1
1
0
0
0
1
3
0
0
2
0
1
1
1
0
0
0
2
0
2
0
0
0
0
2
0
1
2
0
0
1
0
0
0
0
2
0
0
0
2
1
1
0
1
1
0
0
0
0
2
2
2
0
3
0
0
0
0
1
0
3
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
1
2
2
1
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
1
2
0
1
1
0
3
0
1
0
2
0
2
2
0
0
0
0
2
1
1
0
0
2
0
0
1
1
1
1
0
1
2
2
0
1
2
2
1
3
0
0
1
0
0
2
0
1
2
0
1
0
0
1
2
0
0
2
0
2
0
0
0
1
0
1
0
0
0
0
0
2
1
0
1
0
0
1
2
0
0
0
0
1
0
0
1
2
1
2
0
0
0
0
0
1
2
1
0
0
2
1
1
1
2
0
0
0
0
1
0
0
0
0
1
0
4
1
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
1
0
2
1
0
2
2
0
0
6
0
2
0
0
0
0
0
0
0
0
0
0
0
8
0
0
0
4
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
2
2
1
1
0
1
0
2
0
0
1
0
1
1
0
1
1
0
0
1
0
0
0
3
1
1
1
0
0
0
1
1
2
0
1
1
1
0
1
0
0
1
1
0
0
0
0
0
2
2
3
0
1
2
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
1
1
0
1
2
0
2
0
0
0
0
0
0
0
2
1
3
2
0
0
1
0
0
0
0
4
1
2
0
2
2
1
3
0
2
0
0
1
0
0
0
2
0
2
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
1
1
0
2
0
0
3
0
2
0
0
0
0
1
0
0
0
0
1
1
0
0
2
1
0
0
0
0
0
2
0
2
1
0
0
1
0
0
1
2
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
1
2
2
1
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
1
2
0
1
0
0
1
0
0
0
1
0
0
2
2
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
6
1
0
2
0
1
2
0
2
0
0
0
0
4
0
2
0
0
0
0
0
0
0
1
0
0
2
2
0
0
2
0
1
0
0
1
0
1
0
0
0
1
1
0
0
2
2
0
2
0
1
0
0
1
0
1
1
0
1
0
0
0
1
1
1
1
0
2
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
1
2
2
0
2
0
0
3
0
0
0
0
2
0
0
2
0
2
1
0
0
2
1
0
0
0
0
2
0
0
1
0
2
0
0
1
1
1
0
0
0
3
0
0
1
0
2
1
0
2
1
0
0
0
2
0
0
0
1
5
0
0
0
0
0
0
1
0
2
0
0
0
2
0
1
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
1
2
1
2
3
0
0
3
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
1
1
0
1
1
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
3
0
2
2
0
0
2
0
0
0
0
1
2
1
0
1
0
1
2
1
0
0
0
2
0
1
1
0
1
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
1
2
0
0
1
1
0
1
0
0
1
0
0
2
0
0
0
0
0
2
2
2
1
1
0
0
0
2
0
2
0
0
0
0
3
0
1
1
1
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
1
3
2
0
0
2
0
0
0
1
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
2
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
5
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
1
1
0
0
2
0
1
1
0
2
2
0
2
0
1
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
2
0
1
4
0
0
0
0
0
0
0
2
2
1
0
2
2
0
0
0
0
2
2
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
1
0
2
0
1
0
0
1
2
0
3
0
0
0
0
0
0
2
0
0
1
0
0
2
0
1
2
2
1
2
0
0
0
0
1
0
0
1
0
1
1
0
2
1
0
0
2
0
0
2
0
0
1
0
1
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
2
1
0
0
1
1
0
0
2
0
0
1
0
1
2
1
0
1
0
1
0
3
2
0
0
2
0
0
1
2
0
0
0
0
0
2
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
1
2
4
0
2
2
0
0
0
0
1
0
0
1
0
2
0
2
0
0
0
0
2
3
0
1
0
0
0
3
1
0
1
1
0
0
2
0
1
2
3
0
0
0
0
0
1
0
2
0
0
2
0
1
1
0
3
2
0
0
1
2
0
0
0
0
0
2
2
2
2
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
1
0
0
2
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
3
0
1
0
0
2
0
1
1
0
0
0
1
0
2
0
0
2
2
0
0
0
2
0
0
2
1
2
1
0
0
0
1
0
1
0
2
1
0
1
0
0
0
0
0
2
1
0
0
1
2
1
1
0
0
2
0
0
2
2
0
1
0
0
0
2
1
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
2
0
0
1
0
0
0
0
1
0
0
0
2
2
0
2
0
0
0
2
0
2
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
6
2
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
2
3
0
0
0
0
1
2
0
0
1
1
1
0
0
0
2
0
0
1
1
2
0
0
1
0
0
2
3
0
0
1
1
1
2
0
0
2
2
0
0
2
1
0
2
1
1
0
0
1
0
2
1
1
1
0
1
1
0
1
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
2
2
0
0
0
1
0
2
0
0
2
0
1
0
0
1
3
0
0
2
1
1
0
0
1
0
0
2
0
2
2
0
1
1
0
3
1
0
0
1
0
0
0
0
0
1
0
3
0
1
0
0
0
0
0
0
0
2
0
2
1
0
2
2
2
0
1
0
1
0
2
0
0
0
0
4
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
2
3
1
2
0
2
0
0
0
0
1
0
0
2
0
0
0
2
0
0
2
0
0
0
1
0
1
1
2
2
0
1
2
1
2
1
0
0
1
1
0
0
2
2
0
2
0
1
0
1
0
0
0
0
0
2
0
0
0
1
2
0
0
0
1
2
0
0
0
2
1
1
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
1
0
4
1
1
0
0
0
0
0
2
2
0
2
0
0
0
0
1
0
0
5
0
1
2
0
0
0
0
1
0
0
0
1
0
0
1
0
1
3
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
1
0
1
2
0
0
2
2
2
1
0
0
1
2
2
0
0
1
0
0
2
0
0
1
1
1
0
0
1
0
0
1
2
0
0
3
1
0
1
1
1
0
1
1
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
1
0
0
1
2
0
0
0
1
1
0
0
1
0
0
1
0
1
0
0
0
1
1
2
1
0
2
2
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
1
1
2
2
0
0
0
0
0
0
0
0
0
0
1
0
2
4
1
0
2
1
0
0
0
0
2
0
0
0
2
2
0
1
0
0
0
2
0
1
1
2
0
3
1
2
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
3
2
0
1
0
0
0
0
3
0
2
0
0
2
3
2
0
0
0
0
0
0
1
1
0
2
0
0
0
1
1
1
1
0
0
0
0
1
0
0
0
3
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
1
0
1
2
0
0
0
0
2
0
2
1
0
0
1
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
2
2
0
0
0
0
1
0
5
0
0
3
0
1
0
2
0
0
0
1
1
0
1
1
0
0
1
0
0
0
2
0
2
2
2
0
1
3
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
2
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
2
0
1
0
0
0
2
0
1
1
2
1
0
0
0
0
0
0
1
2
0
1
1
1
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
1
0
2
0
0
1
0
2
0
2
0
2
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
1
0
1
1
1
2
2
0
0
0
0
0
0
0
1
0
2
0
2
0
1
0
0
0
1
0
0
0
0
2
2
0
0
0
0
1
0
1
0
0
1
0
2
0
0
1
1
2
0
0
1
0
2
0
1
2
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
2
0
0
1
0
0
0
0
2
0
0
2
1
2
0
0
0
4
0
0
2
1
2
0
0
0
0
0
0
1
0
1
0
0
1
2
0
0
0
0
0
0
1
0
1
2
2
2
0
1
0
2
0
1
0
0
0
0
2
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
2
2
1
2
0
1
2
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
2
1
1
0
0
0
0
2
1
0
0
0
0
0
0
1
2
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
1
2
0
1
0
1
0
0
0
1
0
2
1
1
0
1
1
1
2
1
0
2
0
1
2
0
2
0
1
0
0
0
0
0
1
2
0
0
2
1
2
0
0
0
0
0
2
0
1
0
2
0
2
1
0
0
2
0
3
1
0
0
0
0
2
0
0
0
0
0
0
0
2
1
1
0
2
1
0
0
0
2
0
0
2
1
1
0
0
0
0
2
1
2
0
0
1
0
0
0
1
0
1
2
0
2
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
1
0
2
0
0
0
0
1
1
2
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
1
2
1
0
0
0
1
1
2
3
0
0
0
0
0
0
2
0
1
0
1
1
0
2
0
0
1
1
2
0
2
0
1
0
1
2
0
0
0
0
0
0
0
0
0
2
2
1
0
2
5
2
2
2
0
2
1
1
0
0
0
0
0
0
2
1
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
2
2
0
1
0
0
0
0
0
1
1
2
0
2
2
0
1
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
1
2
1
1
2
1
2
0
0
3
1
0
0
1
3
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
1
0
2
0
0
0
2
3
1
2
0
1
2
2
0
2
0
1
2
0
0
0
0
0
0
0
3
2
2
2
2
0
0
1
0
1
0
0
0
0
0
2
0
0
2
0
1
0
1
2
2
0
2
1
0
2
0
0
0
0
0
1
0
0
0
1
1
1
1
0
1
1
1
0
0
0
3
2
0
0
6
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
4
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
1
2
0
1
0
1
0
0
4
0
0
2
1
0
0
0
0
2
2
0
0
0
0
1
0
1
0
0
0
1
1
0
2
2
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
2
0
1
0
0
1
2
0
0
0
2
0
1
0
1
3
2
0
0
0
0
0
0
2
0
0
1
0
1
0
2
0
0
1
0
0
0
0
0
0
2
0
2
1
0
0
0
1
1
0
1
0
0
1
0
0
4
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
2
0
2
1
0
0
0
2
1
0
0
1
0
0
1
0
2
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
1
0
0
2
1
0
1
2
1
0
1
0
2
0
1
1
0
0
0
0
2
0
0
0
2
0
1
0
1
2
0
1
0
0
0
0
0
0
2
0
0
0
4
1
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
1
0
2
2
1
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
1
2
0
0
0
2
0
0
0
2
1
0
0
0
0
2
0
0
0
0
1
1
0
1
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
1
1
2
0
1
0
2
1
0
0
0
0
0
0
0
1
3
1
0
0
0
3
0
1
0
0
2
0
1
0
0
3
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
3
6
1
1
0
0
0
1
0
2
1
0
0
0
2
0
0
0
0
2
1
2
0
0
0
0
0
0
2
2
0
0
0
0
1
1
2
0
0
0
1
0
0
1
0
0
1
0
1
0
0
1
3
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
2
2
0
0
1
0
0
3
1
0
1
0
2
0
0
0
0
1
2
0
0
0
1
0
1
0
0
2
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
1
0
0
0
2
2
0
1
0
0
7
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
3
0
2
0
0
0
0
2
0
0
2
0
0
0
0
2
0
3
0
2
1
0
1
2
0
1
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
1
1
0
0
0
2
0
1
2
0
0
2
0
0
3
2
2
2
2
2
0
0
1
1
2
2
2
1
0
0
2
0
0
1
0
1
0
0
2
0
0
0
0
2
0
1
0
1
1
0
1
0
2
3
0
1
0
0
0
1
0
1
0
0
2
1
0
2
0
1
2
2
1
0
0
1
0
0
0
1
1
2
2
0
1
2
1
1
0
1
0
1
2
0
0
0
3
1
2
2
0
0
0
0
0
0
0
3
1
0
1
0
0
0
0
2
0
0
0
1
0
2
1
1
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
2
0
0
1
0
0
0
0
3
0
0
0
0
0
0
3
1
0
1
1
2
1
0
1
0
2
2
1
2
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
2
2
2
0
1
0
0
0
0
0
0
0
1
0
0
2
0
2
2
3
1
1
2
1
2
0
0
0
1
0
0
1
4
0
1
0
1
1
2
0
2
2
1
0
0
0
0
0
0
2
1
0
0
0
1
0
2
2
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
1
1
0
2
2
2
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
2
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
3
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
1
0
0
2
2
0
0
0
1
0
2
1
1
0
2
0
0
2
0
0
0
1
0
0
0
0
1
0
1
1
2
0
0
0
0
0
0
0
2
1
0
0
2
2
0
0
0
0
0
1
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
2
0
0
1
0
2
0
1
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
1
2
1
0
0
0
1
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
2
2
0
1
0
0
0
4
1
0
3
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
1
6
0
0
1
0
0
0
2
0
0
0
0
1
1
2
1
0
0
0
0
0
1
0
0
0
0
2
1
0
0
2
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
1
1
0
2
1
0
1
1
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
1
0
0
1
2
4
1
0
2
0
0
1
0
0
1
0
1
0
0
0
1
0
0
1
1
2
0
0
2
1
0
1
2
2
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
1
1
0
0
0
1
0
2
0
1
2
0
2
2
1
0
1
0
2
0
0
2
4
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
2
1
1
3
2
0
1
2
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
2
0
1
2
1
0
0
2
1
0
0
1
0
2
0
0
0
2
1
0
0
0
0
0
0
1
1
0
0
0
2
0
0
2
0
1
0
1
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
2
1
0
2
0
1
2
2
1
0
2
2
0
2
0
0
2
0
0
0
0
2
2
0
1
2
2
1
0
0
0
2
1
0
2
2
0
0
0
0
0
0
0
1
0
0
2
1
0
1
2
2
0
0
2
2
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
2
0
0
2
0
1
0
2
0
0
0
0
0
2
0
1
1
0
4
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
2
0
1
0
0
0
1
0
1
0
2
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
1
2
2
0
0
2
0
0
0
1
0
0
2
2
0
1
0
1
1
0
1
0
0
0
0
1
0
0
0
0
2
1
1
2
0
0
0
0
0
0
2
0
2
3
1
0
0
0
2
0
2
1
0
0
0
0
0
3
0
1
0
0
2
0
2
0
0
1
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
1
0
0
0
2
1
1
0
0
1
2
0
0
0
0
2
1
2
1
0
2
1
0
0
0
0
2
1
1
0
0
0
0
0
0
0
3
1
0
0
1
2
0
1
0
0
2
2
0
1
0
1
1
2
1
1
1
0
0
0
2
0
0
0
1
0
2
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
1
0
0
1
0
0
2
0
0
0
2
0
1
0
0
0
0
2
1
0
0
2
0
0
0
0
1
3
0
1
0
1
3
1
0
0
1
1
2
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
2
2
0
0
0
1
2
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
1
2
0
0
0
1
0
0
2
0
0
0
1
2
1
1
0
0
0
0
0
0
0
3
2
1
0
0
1
0
1
1
2
0
3
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
1
0
1
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
2
0
2
0
0
1
0
0
0
0
0
2
2
2
0
2
1
2
2
0
3
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
1
0
2
2
4
0
3
0
0
0
0
0
1
2
0
1
0
1
2
0
0
0
0
0
0
0
0
0
2
2
1
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
3
0
1
1
2
1
0
0
1
0
0
0
2
0
0
1
2
0
0
1
0
0
0
1
2
0
0
1
0
0
0
0
2
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
1
1
1
0
0
2
0
2
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
3
2
0
0
0
1
0
0
0
0
2
0
1
0
1
0
1
0
2
0
0
0
1
0
0
2
0
0
0
1
2
0
0
0
1
0
2
0
2
1
0
0
2
1
1
0
0
2
2
1
0
0
0
2
0
0
0
0
0
0
0
2
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
2
2
0
0
0
0
1
2
0
2
9
2
0
0
0
3
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
2
2
0
0
0
0
0
2
0
1
0
1
1
0
1
2
0
0
0
0
0
0
0
2
1
2
0
2
0
0
1
3
1
2
2
0
1
0
2
0
0
1
0
0
2
1
0
0
4
0
2
2
0
0
0
0
1
0
0
0
0
3
0
0
2
0
4
0
0
0
2
2
0
0
0
0
3
1
2
1
0
0
0
1
0
0
1
0
1
4
0
0
0
0
0
0
1
0
2
1
0
0
2
2
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
1
2
1
1
1
0
2
1
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
1
1
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
1
2
0
1
1
1
0
1
1
0
0
0
2
2
0
0
0
0
1
1
1
0
2
1
0
1
0
0
2
0
0
1
0
0
2
0
0
0
0
0
1
0
0
2
3
2
0
1
2
0
1
0
2
1
0
3
1
0
0
0
0
2
0
1
0
0
1
2
1
2
0
1
0
0
0
0
2
0
0
0
1
0
2
0
1
0
1
0
0
1
0
0
0
1
1
0
0
1
0
0
1
0
1
0
0
0
0
1
0
1
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
2
0
0
0
0
0
0
0
0
2
2
0
1
0
3
0
2
0
0
2
2
0
2
0
2
0
0
0
0
1
2
1
0
0
1
0
2
1
0
3
0
0
0
1
0
2
2
0
1
0
1
0
1
0
2
0
0
0
0
1
0
0
1
1
0
1
0
2
0
2
0
1
0
0
0
1
1
1
0
0
0
0
0
1
0
2
0
1
0
0
0
0
2
0
1
0
0
0
0
1
1
0
2
0
1
0
2
1
0
0
0
0
1
0
0
0
0
2
0
3
1
2
2
1
2
0
2
0
0
0
0
2
0
0
0
2
0
1
2
2
0
1
0
1
1
0
0
0
0
1
1
0
0
0
2
0
1
0
0
0
0
2
2
1
0
1
1
0
1
0
0
2
1
1
0
0
0
1
0
0
0
0
0
0
1
1
1
0
2
0
0
3
2
1
2
1
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
2
1
0
2
1
0
0
0
2
0
0
0
0
0
2
1
0
0
0
1
2
0
0
2
2
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
5
1
0
1
1
2
2
0
1
0
0
2
0
0
0
1
2
0
0
1
2
0
0
0
0
1
2
0
1
0
0
1
0
1
2
0
2
0
0
2
2
1
1
0
1
0
0
2
0
0
2
1
0
2
1
0
1
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
4
0
0
1
0
0
2
0
0
0
1
1
0
0
0
0
0
2
2
2
6
0
0
0
0
0
0
0
0
0
0
0
0
1
1
4
0
1
2
0
2
0
0
2
1
1
0
0
0
2
0
1
0
2
0
2
0
2
0
1
2
1
1
0
0
1
1
1
2
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
2
0
1
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
2
0
1
1
0
4
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
2
1
2
0
1
0
0
0
0
1
2
0
0
1
1
0
0
0
0
0
0
1
0
2
1
2
1
0
0
1
0
0
0
0
0
1
2
1
2
0
0
2
1
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
1
0
0
0
0
0
1
0
1
1
2
0
0
0
2
0
0
1
1
1
0
0
0
0
0
2
0
1
1
2
2
0
0
0
0
3
0
0
0
3
0
0
3
1
0
2
0
2
0
0
0
1
1
0
2
0
2
0
0
2
0
2
0
0
0
0
0
0
1
1
0
0
0
1
1
0
1
0
1
1
0
0
2
0
1
2
0
2
0
2
1
0
1
0
1
0
2
1
0
0
0
0
2
0
0
0
1
2
1
0
0
2
3
0
1
2
0
1
0
0
0
2
2
0
0
0
3
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
1
1
0
0
2
3
0
0
0
2
0
0
0
0
0
1
0
2
1
2
1
0
0
0
0
0
1
0
0
0
0
2
3
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
2
2
2
0
0
1
0
1
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
1
2
2
0
0
0
2
0
2
1
0
0
0
0
0
0
2
0
2
1
1
1
0
2
1
2
0
1
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
4
0
0
2
1
1
0
0
2
0
0
0
0
2
2
0
2
0
0
0
2
1
0
2
0
1
0
0
2
2
0
0
1
0
0
0
0
2
0
0
2
0
2
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
2
2
0
0
0
0
0
0
0
2
1
2
1
1
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
1
1
1
2
0
1
0
1
1
0
2
4
0
0
0
0
3
0
0
2
0
0
2
0
0
0
0
1
0
0
1
0
0
2
2
0
0
3
0
0
1
0
0
0
0
0
2
2
1
0
0
0
1
0
1
1
0
0
0
1
0
0
1
0
1
0
0
2
0
2
0
2
1
0
0
0
0
1
0
1
1
0
0
0
2
0
1
0
1
0
1
3
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
2
0
1
0
0
1
0
0
2
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
2
2
0
0
0
1
2
0
0
1
0
0
0
1
1
0
1
0
1
3
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
2
2
2
0
0
0
0
2
0
2
0
0
0
1
0
2
0
2
0
2
0
6
1
0
0
2
0
2
0
0
2
0
2
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
2
0
1
1
0
0
2
1
0
2
0
4
0
0
0
1
0
0
0
0
4
1
1
0
1
2
2
1
1
1
0
0
2
1
0
0
0
0
1
1
0
1
0
4
2
1
0
0
0
0
1
2
0
1
0
0
1
2
0
1
0
0
2
0
0
0
2
0
2
0
1
1
0
1
0
0
1
0
1
0
0
0
1
3
0
1
0
0
1
1
0
0
0
0
0
0
0
2
1
0
2
1
2
0
2
0
0
1
0
0
0
0
1
0
1
0
0
2
1
1
0
0
1
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
2
2
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
2
2
1
0
0
0
0
0
0
1
2
2
2
0
1
0
0
0
0
0
2
2
1
1
2
0
0
4
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
2
1
1
1
0
1
0
0
1
0
2
0
0
4
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
2
2
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
2
2
0
0
0
0
5
0
1
0
1
0
2
0
0
2
1
2
1
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
3
0
8
1
2
0
0
2
2
0
0
0
0
0
0
1
0
1
0
2
2
1
0
0
2
0
1
2
6
1
0
2
0
0
0
2
2
1
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
5
0
1
0
0
2
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
2
0
0
1
0
1
0
0
1
0
0
0
0
1
1
2
2
2
0
2
0
1
0
0
0
0
0
2
0
0
2
2
2
0
0
2
0
2
0
0
1
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
1
1
1
1
1
1
0
0
1
0
0
0
0
0
0
2
1
1
0
1
1
2
2
0
0
0
0
2
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
2
2
4
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
1
1
0
0
1
2
0
0
2
1
1
0
0
0
2
0
1
2
1
0
1
2
0
0
1
0
0
2
0
2
0
0
2
2
0
2
0
1
2
1
2
0
0
2
1
0
1
1
0
2
0
0
1
2
0
0
2
0
0
1
0
2
0
0
0
1
2
0
0
0
1
1
0
2
0
0
1
0
3
1
0
0
2
0
0
2
0
0
0
0
2
0
2
0
1
0
0
2
0
0
0
2
0
2
4
0
0
2
0
0
3
0
0
0
2
0
0
1
0
1
0
0
1
0
0
2
0
0
0
1
1
0
0
0
6
2
0
1
0
0
0
1
1
2
0
0
0
0
2
1
2
0
2
0
2
2
0
0
0
1
0
0
1
0
0
1
1
1
1
0
1
0
0
0
0
0
2
1
2
2
1
0
2
0
1
0
0
2
0
0
3
0
0
0
0
0
3
1
0
6
0
1
0
0
0
2
2
0
0
2
0
0
0
2
0
0
1
0
0
0
2
0
0
2
0
1
0
1
0
0
0
0
2
2
2
0
0
3
0
2
1
2
2
0
1
0
0
1
0
0
0
2
0
0
1
2
0
0
0
1
0
1
2
0
0
2
0
1
0
1
0
0
0
1
2
0
1
2
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
2
0
1
0
0
0
1
2
1
2
1
0
1
1
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
1
2
2
0
1
0
0
0
0
1
0
2
0
0
2
1
2
0
2
0
0
0
0
0
2
1
3
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
2
0
2
0
0
1
1
1
0
0
0
0
0
2
1
0
0
1
0
0
2
1
0
0
2
0
4
2
0
0
0
0
1
0
0
0
0
2
2
1
1
0
0
0
0
2
0
0
1
0
0
2
2
0
4
0
2
0
1
0
3
0
1
0
3
0
0
0
3
0
1
0
1
0
0
0
0
1
0
2
1
1
0
1
3
0
2
0
0
2
0
2
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
1
2
0
2
0
0
1
0
2
0
0
0
0
1
1
2
0
0
0
0
1
0
0
0
2
2
0
0
1
0
1
0
0
1
2
0
1
0
0
0
1
1
0
0
1
0
1
0
0
0
2
0
1
0
0
0
0
0
1
0
0
2
2
2
1
0
0
2
0
1
4
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
1
1
0
2
0
0
1
0
0
0
0
0
0
3
1
0
0
1
0
0
0
0
0
0
2
1
0
0
2
0
2
0
0
1
0
0
1
0
0
1
0
0
3
1
1
0
0
0
0
0
4
0
2
2
1
2
0
0
1
0
2
1
2
0
0
1
0
0
0
2
2
0
2
0
0
0
0
3
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
3
0
0
0
0
0
0
1
0
2
0
0
1
1
0
1
0
2
0
1
0
0
1
0
2
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
3
0
1
0
1
0
0
3
0
1
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
2
0
2
0
2
2
1
2
0
2
0
0
2
0
0
0
1
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
1
1
5
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
3
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
2
0
1
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
2
1
3
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
1
0
0
1
0
0
1
0
2
0
1
2
1
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
2
3
0
2
0
0
0
1
1
0
2
0
0
0
2
0
1
0
2
0
0
3
0
0
0
0
0
1
0
0
1
1
0
1
0
2
0
0
0
0
1
0
0
1
0
2
2
0
1
1
0
2
2
0
0
2
2
0
2
0
0
0
1
2
2
0
2
1
0
0
0
0
1
2
1
2
1
0
0
0
0
1
0
0
1
0
2
1
3
0
0
1
2
0
1
2
1
1
0
0
0
0
1
0
0
0
1
2
2
0
0
2
2
0
0
0
0
0
0
0
1
2
1
1
0
0
0
0
1
0
0
1
0
2
0
1
0
0
0
3
0
0
2
0
0
1
0
0
3
0
7
0
2
0
1
0
3
0
2
1
0
0
2
0
0
0
1
0
0
0
0
1
1
1
1
0
0
0
2
1
2
1
0
2
2
1
0
0
1
2
0
0
0
0
2
0
1
2
0
0
0
0
0
1
1
2
0
3
0
0
0
0
1
0
0
0
3
0
0
0
0
0
2
0
0
2
0
0
1
2
1
3
0
0
0
0
2
0
3
0
0
0
0
0
0
4
1
0
0
0
0
0
1
0
2
0
3
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
2
2
0
1
0
1
0
2
1
0
2
0
4
0
2
1
0
2
2
0
0
1
0
0
0
0
0
1
1
1
0
1
0
0
0
1
0
0
0
1
2
0
0
1
0
0
0
2
0
0
1
1
0
0
3
0
0
3
3
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
2
0
2
0
9
0
2
2
2
0
0
1
0
0
3
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
4
1
0
2
1
1
1
0
0
0
0
0
1
0
1
0
0
0
0
3
0
0
0
2
2
0
0
0
0
0
1
1
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
2
2
2
0
0
0
0
2
0
1
0
2
1
1
2
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
2
1
0
4
0
0
0
0
0
0
0
1
1
0
2
2
1
1
0
1
1
0
0
0
0
1
0
0
0
0
2
0
1
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
2
2
1
0
0
0
1
2
0
1
2
0
0
0
0
2
0
0
2
1
0
1
0
2
0
1
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
4
0
2
0
0
1
2
0
1
0
2
2
1
1
0
1
1
0
2
0
3
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
1
0
2
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
1
1
0
2
0
1
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
1
0
2
0
0
1
0
0
1
0
1
1
0
1
1
1
0
2
0
0
2
0
0
0
0
1
1
0
1
2
1
0
0
3
0
0
2
0
1
0
0
1
2
0
1
1
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
1
0
0
1
2
0
1
1
1
0
1
1
2
0
1
0
0
0
2
0
0
0
0
0
2
0
2
1
2
2
0
0
0
0
2
0
1
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
2
2
1
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
2
0
1
0
0
3
0
0
0
0
0
4
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
2
2
1
1
0
0
0
1
0
1
2
0
0
0
0
0
5
0
0
0
2
0
2
0
1
0
1
0
2
2
0
0
1
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
1
1
0
0
0
2
0
0
0
2
0
1
0
0
0
0
4
0
1
0
0
1
0
0
1
0
2
2
1
0
0
0
0
2
0
2
2
0
0
2
1
1
0
0
0
3
0
2
0
1
0
2
1
0
0
1
0
0
0
0
2
1
0
1
0
1
2
0
1
0
0
0
2
0
0
2
0
0
0
2
0
2
1
2
1
0
1
0
0
0
0
1
1
0
0
1
1
1
0
0
2
0
0
1
1
2
1
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
1
2
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
2
2
2
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
1
2
0
1
0
3
1
2
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
2
1
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
1
1
0
1
0
0
0
0
1
4
0
0
1
0
0
2
0
0
2
0
2
1
0
2
2
0
1
2
2
0
0
0
0
2
0
0
0
2
0
2
1
0
2
0
0
1
0
2
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
2
2
0
0
2
0
3
2
0
1
2
0
0
1
2
0
0
0
0
1
2
0
1
1
1
0
0
0
1
0
0
0
0
0
0
2
0
1
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
1
0
1
0
0
0
1
0
0
2
0
0
2
2
1
1
0
0
0
1
0
0
0
2
1
1
0
0
2
0
0
1
1
0
0
0
0
0
0
1
2
0
0
0
2
2
1
0
1
1
0
2
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
2
1
0
0
0
2
2
0
1
2
1
0
0
1
0
0
0
2
0
0
0
0
2
0
0
2
2
0
0
2
0
0
0
0
0
0
2
4
6
1
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
2
2
0
2
2
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
1
2
2
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
1
0
1
0
0
0
2
0
0
0
0
2
2
1
0
1
1
0
2
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
1
0
2
1
0
0
3
1
1
0
2
0
4
2
0
0
2
0
0
0
0
0
0
0
1
0
2
1
0
2
0
1
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
1
2
0
1
0
0
0
0
1
0
0
0
0
0
0
2
2
1
0
0
2
2
0
0
1
0
2
0
2
0
2
0
1
0
0
0
0
2
0
1
2
2
0
2
0
0
2
0
0
1
1
2
0
1
2
0
0
0
0
2
2
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
2
1
0
0
0
0
0
1
1
1
1
6
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
1
2
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
2
2
1
0
1
0
0
1
0
2
0
0
0
0
1
1
2
0
5
0
0
0
0
0
0
0
0
1
1
0
2
1
1
0
2
0
2
0
0
0
0
5
0
2
1
3
2
0
0
0
0
1
0
1
2
0
1
0
0
2
2
0
1
1
0
0
1
2
0
2
0
0
0
2
0
0
0
2
0
1
1
1
0
0
1
0
6
0
0
0
0
3
3
2
3
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
2
1
1
0
0
0
1
0
0
2
2
2
0
0
0
2
1
0
0
2
0
0
0
0
2
0
0
0
2
0
0
1
0
0
1
2
0
0
2
0
0
2
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
3
1
0
0
0
2
1
0
0
1
0
1
2
0
1
5
0
2
0
0
0
1
1
0
0
0
2
0
0
2
0
0
2
2
2
0
2
0
1
2
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
1
2
0
3
0
0
0
1
0
2
0
2
2
2
0
2
0
2
1
0
0
0
1
0
1
1
0
1
0
2
1
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
2
2
3
0
1
2
2
4
1
1
0
0
1
0
2
0
1
0
2
0
1
0
0
0
2
0
1
2
0
0
0
0
0
1
2
2
0
1
0
1
0
0
0
1
0
0
1
0
1
0
2
1
0
1
0
0
0
0
0
0
1
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
1
0
0
2
1
1
0
0
0
2
0
0
0
0
0
2
0
2
0
2
1
0
0
0
1
0
1
0
0
2
0
1
1
2
1
1
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
1
0
1
2
0
0
1
0
0
0
0
1
1
1
0
0
1
3
1
0
0
1
0
2
0
0
0
0
2
0
4
2
0
2
0
0
1
1
0
2
0
1
2
2
2
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
2
1
0
0
1
0
0
0
0
2
2
0
0
2
0
0
3
0
0
1
0
2
2
2
0
2
0
0
1
2
0
0
1
0
0
1
0
0
0
0
2
0
0
2
1
0
0
2
0
0
0
0
0
1
0
2
2
0
0
1
0
2
0
0
0
3
1
2
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
2
0
0
2
1
0
2
2
0
0
0
2
0
2
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
2
0
2
1
0
0
2
1
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
2
0
1
0
0
0
0
1
2
0
2
0
0
0
1
0
2
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
1
0
0
2
0
1
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
2
1
1
0
0
0
2
1
0
0
0
1
2
0
0
0
0
0
2
0
0
1
0
2
0
1
0
2
0
0
0
0
0
2
0
3
1
0
0
1
1
0
0
0
0
0
0
2
1
1
1
0
1
0
3
2
1
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
3
1
2
0
0
0
0
2
1
2
0
0
4
1
1
0
1
0
0
0
0
0
1
0
0
1
1
0
0
2
1
0
1
0
2
0
0
0
2
0
0
1
1
0
0
0
2
2
0
2
2
0
1
0
0
0
0
1
4
0
0
1
1
0
0
0
0
0
0
2
2
0
2
2
0
0
0
0
1
2
1
0
0
0
2
0
2
1
0
2
0
0
0
0
0
0
0
0
1
2
0
0
1
1
2
0
1
1
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
1
2
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
1
2
0
1
2
0
2
0
0
1
1
0
0
0
1
2
0
0
0
0
0
2
1
0
0
0
1
0
0
0
2
1
1
1
0
8
0
0
0
2
0
2
0
1
2
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
2
0
0
0
0
1
2
1
0
0
0
0
0
0
2
0
1
1
0
0
0
1
0
3
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
3
2
1
0
0
0
2
0
0
1
0
2
0
1
0
0
1
0
1
0
2
1
4
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
2
2
0
2
0
0
2
0
1
0
0
0
0
0
0
0
2
1
0
0
1
1
0
0
0
1
0
0
1
2
1
2
0
0
1
0
1
0
0
3
2
0
1
0
0
2
0
1
0
0
1
0
0
0
0
2
2
1
0
0
1
0
0
3
0
2
2
1
0
0
0
2
0
1
1
2
2
0
2
2
1
1
1
0
0
2
1
1
0
0
0
2
0
0
1
0
0
4
0
1
2
1
1
0
0
2
0
0
2
0
2
0
0
0
0
2
0
1
1
0
0
0
1
1
0
4
0
2
0
0
0
1
0
2
0
1
0
0
0
1
1
1
0
0
0
0
0
2
0
0
3
0
0
0
0
2
0
0
1
0
4
0
1
1
0
0
2
0
0
3
2
2
0
0
1
0
0
0
0
1
0
0
0
0
1
2
2
0
1
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
2
0
2
1
0
1
0
2
0
2
0
0
0
1
0
0
2
1
1
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
2
0
2
2
2
2
1
1
1
0
0
1
0
2
2
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
1
1
0
2
2
0
1
0
0
0
0
1
1
2
0
2
0
0
0
2
0
0
1
0
0
2
3
0
1
0
0
0
0
0
2
0
3
1
0
0
2
1
0
1
0
1
0
0
1
1
14
1
0
2
0
1
2
2
0
1
0
0
0
0
0
2
0
1
1
0
1
0
0
0
0
1
0
2
0
2
0
0
0
2
0
2
0
0
0
1
1
0
1
0
2
0
1
0
0
0
0
0
0
1
0
0
0
2
1
2
3
2
0
5
1
0
0
2
0
0
1
0
0
1
0
0
2
0
1
0
0
0
0
1
0
0
0
1
0
1
2
1
1
0
0
2
0
1
4
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
2
1
1
1
0
1
2
0
2
0
2
1
1
2
1
0
0
1
3
0
0
0
0
0
2
2
1
2
2
0
0
0
0
0
0
2
0
0
0
3
0
1
1
3
2
0
0
0
0
3
0
0
0
1
1
0
1
2
0
2
6
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
2
1
0
1
1
2
2
0
1
1
0
0
0
2
2
0
1
0
0
0
0
2
0
0
0
0
0
2
2
0
1
0
0
1
1
0
0
0
0
0
3
2
0
0
0
0
2
1
0
2
0
0
0
2
0
2
1
0
2
0
0
1
1
0
2
0
1
0
2
2
0
0
0
1
0
0
0
2
2
2
0
0
1
2
0
0
0
2
0
0
2
0
0
0
2
1
0
0
0
0
2
2
0
1
0
1
2
0
2
1
2
0
1
0
0
0
1
2
3
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
2
0
0
0
0
2
0
0
1
0
0
2
0
0
0
2
0
1
1
0
0
1
0
0
0
4
2
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
1
0
2
2
0
0
2
0
0
0
0
0
2
0
2
1
0
0
0
0
0
2
0
0
0
0
0
1
0
1
1
1
2
0
0
0
2
0
0
0
0
0
2
0
2
1
1
3
0
0
2
0
0
0
2
0
1
1
0
0
2
2
0
2
0
0
1
1
0
0
0
0
2
1
2
1
2
0
0
2
2
0
0
0
0
2
0
0
0
0
0
3
0
4
0
0
0
0
0
0
0
2
2
1
0
0
0
0
2
0
1
0
0
0
0
2
0
0
2
0
1
0
0
5
0
2
0
0
1
0
1
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
2
0
2
2
0
0
0
0
0
2
3
0
1
0
0
1
2
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
1
0
1
0
0
0
2
2
0
0
0
0
2
0
0
2
1
1
0
0
1
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
1
0
0
0
2
0
0
1
0
0
0
2
1
2
1
0
3
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
2
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
2
0
0
0
0
3
2
0
2
0
1
0
1
0
0
1
0
2
1
0
2
2
1
0
0
7
0
1
2
3
1
0
0
0
2
1
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
1
1
1
2
1
0
0
0
0
0
0
0
1
0
2
1
0
2
1
0
2
1
2
0
2
0
0
0
0
2
0
0
0
3
0
0
2
0
2
3
0
0
0
1
0
2
1
0
1
2
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
2
0
2
0
1
1
0
1
0
2
6
0
0
2
0
2
1
0
0
0
0
0
0
4
2
0
0
1
1
0
0
2
0
0
0
1
0
0
0
3
0
2
0
1
0
0
0
0
0
2
0
2
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
1
0
0
1
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
2
1
2
0
1
0
1
1
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
3
0
0
0
0
1
3
2
0
1
1
0
2
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
2
0
1
1
1
0
1
2
2
0
2
0
1
0
1
0
1
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
4
0
0
0
0
0
1
0
1
0
1
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
1
1
1
1
2
0
0
0
0
0
7
0
0
0
1
2
2
1
2
1
0
0
0
0
2
2
0
0
2
1
1
0
1
2
1
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
1
2
1
0
2
1
2
1
0
2
2
0
1
1
0
0
0
0
0
0
3
1
0
0
1
0
2
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
1
0
1
0
1
1
2
0
0
0
1
0
0
0
0
0
2
1
1
0
1
0
1
0
0
0
3
0
2
1
2
1
0
1
1
2
0
0
0
1
0
2
0
0
0
0
2
0
1
0
1
0
1
1
1
0
2
0
2
0
0
1
1
0
2
0
2
0
0
1
0
0
0
1
0
0
1
0
0
2
2
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
2
0
2
0
0
2
1
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
1
0
0
1
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
2
1
0
2
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
1
1
2
0
2
0
2
0
0
0
0
1
0
2
2
0
0
1
1
0
0
2
1
0
0
2
0
2
1
0
0
0
0
1
0
0
0
0
0
2
2
1
0
1
2
2
2
0
0
0
0
0
0
0
0
0
0
2
0
1
2
1
0
0
1
1
0
0
1
0
1
1
0
0
1
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
2
0
2
0
2
0
1
0
2
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
2
2
0
0
0
2
3
0
1
0
0
2
0
0
1
0
0
0
0
0
1
1
2
0
1
2
2
0
0
0
1
0
1
2
0
2
0
2
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
2
2
0
1
0
0
0
1
0
0
0
0
1
0
2
0
2
1
1
2
0
0
0
2
2
0
0
1
2
1
1
2
0
2
0
1
0
2
0
2
1
1
1
0
0
0
0
0
0
0
0
1
1
1
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
4
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
2
0
2
2
0
0
0
0
0
2
1
2
0
0
1
0
1
2
0
0
3
0
0
1
0
2
7
1
0
0
2
0
2
2
0
1
0
0
0
0
2
1
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
2
0
0
0
2
1
0
0
1
3
0
0
0
0
1
2
0
0
0
1
0
1
1
0
1
2
0
1
0
1
0
0
0
1
0
0
0
1
2
2
2
2
0
0
1
1
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
2
0
0
1
2
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
2
1
0
0
0
2
1
0
0
0
0
2
0
0
0
0
2
0
0
1
0
2
0
0
0
0
1
1
0
0
0
0
0
2
1
0
0
0
0
3
0
0
0
1
1
2
0
0
0
2
0
2
0
0
1
2
1
0
0
2
2
0
1
0
0
0
2
2
0
2
2
2
0
0
1
0
0
1
0
0
0
0
0
2
0
3
2
0
0
0
0
2
1
1
0
1
0
1
0
2
0
1
0
0
0
0
2
0
0
1
0
0
2
1
1
0
1
0
1
0
0
0
2
0
0
1
0
0
2
0
0
2
0
6
0
0
2
0
0
2
0
0
1
0
1
0
1
0
0
0
3
0
0
2
0
0
1
0
0
0
1
0
2
0
0
1
0
0
0
1
1
0
0
0
0
1
1
2
2
0
0
2
1
1
0
2
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
1
0
0
0
2
2
0
0
0
2
0
0
1
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
2
0
0
0
0
0
2
0
0
1
1
2
1
0
1
1
0
0
0
0
0
2
0
0
0
2
2
4
0
0
0
0
0
0
0
1
0
1
1
3
0
0
0
0
0
0
0
2
0
0
2
0
1
2
0
0
0
2
0
0
1
1
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
1
2
0
2
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
3
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
2
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
2
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
1
0
1
1
0
3
0
2
0
0
1
0
0
3
0
0
0
1
0
2
2
0
0
2
0
0
2
0
2
0
2
2
0
2
2
0
0
2
2
0
0
2
2
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
2
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
1
0
1
0
0
0
0
1
0
0
2
1
0
0
0
1
2
0
2
2
0
2
1
2
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
2
2
0
2
0
0
0
0
1
0
3
2
3
2
0
2
0
0
1
1
0
1
0
2
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
2
1
2
0
1
0
0
1
1
0
0
0
0
0
0
0
0
3
0
1
0
0
2
0
0
1
0
2
1
1
2
0
1
0
2
0
2
2
0
1
0
1
1
2
0
1
0
2
2
0
1
0
1
0
0
2
0
2
1
0
0
1
1
0
2
2
2
1
0
0
0
0
2
1
1
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
2
3
0
0
0
0
2
2
0
0
1
1
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
2
1
3
4
0
0
2
1
1
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
1
2
0
0
0
0
0
1
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
2
0
2
0
1
0
0
1
0
0
5
0
0
2
2
2
0
2
3
0
0
1
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
1
1
1
2
0
1
0
0
1
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
3
0
0
0
1
1
2
2
0
0
4
2
0
0
0
0
0
1
1
0
1
0
1
0
0
3
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
1
0
2
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
2
0
1
2
0
0
0
1
0
0
3
0
0
0
1
1
0
2
0
2
0
2
0
1
0
3
0
1
0
0
1
0
0
2
1
0
0
0
2
0
3
1
0
2
0
0
0
2
0
0
2
0
1
2
0
0
0
1
1
2
0
2
0
0
0
0
0
0
0
2
0
1
1
0
2
0
0
0
0
0
2
0
0
2
2
1
0
0
2
1
1
1
0
0
0
0
1
0
2
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
2
1
1
3
2
0
0
0
0
1
1
1
1
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
1
0
0
1
0
1
0
0
0
1
1
0
0
1
0
0
0
0
1
1
0
0
2
0
0
0
2
0
2
2
0
0
2
3
0
1
0
1
1
0
1
1
2
3
0
0
1
2
0
0
2
0
0
2
0
4
2
0
1
0
2
0
0
0
1
3
1
2
1
1
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
1
1
0
1
2
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
2
2
2
0
0
0
0
1
0
2
0
0
0
0
0
2
0
1
0
4
1
0
2
0
0
1
2
0
1
0
0
0
0
1
0
2
0
1
0
1
0
0
0
0
1
0
0
1
0
0
2
1
1
0
0
1
0
0
0
0
1
0
0
1
1
2
2
0
0
0
0
1
0
0
2
2
0
0
1
0
2
0
0
0
1
2
0
0
3
0
0
1
1
1
1
1
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
2
2
0
2
0
0
2
0
0
2
0
1
0
0
0
0
3
0
1
0
1
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
1
1
0
0
0
2
0
0
2
0
0
2
2
0
0
2
2
4
1
0
2
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
1
3
0
0
0
2
3
3
0
2
0
1
0
1
1
0
0
0
0
0
1
0
0
0
2
2
2
1
0
1
0
0
2
0
0
0
0
1
1
0
1
2
1
0
2
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
4
0
1
0
1
2
0
0
0
1
0
0
0
0
0
2
1
0
1
2
0
0
1
2
2
2
0
3
1
0
0
0
0
1
0
0
2
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
2
2
0
2
0
0
0
3
0
2
1
0
0
0
0
0
0
0
0
1
1
0
0
1
2
3
0
0
1
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
1
0
0
0
2
0
0
0
1
2
0
0
0
1
0
1
0
2
0
2
1
2
0
2
2
2
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
2
0
0
2
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
2
0
1
0
1
2
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
4
1
1
4
2
0
0
0
0
0
0
0
0
1
2
1
1
0
2
0
0
0
0
1
1
0
2
1
0
0
0
1
0
1
0
0
0
0
1
2
0
1
0
0
2
0
0
0
0
0
0
1
0
2
0
0
2
0
1
0
2
2
0
1
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
2
2
0
1
0
0
0
1
0
1
0
2
0
0
0
1
0
0
3
0
0
2
1
0
0
1
2
0
0
0
0
5
0
0
2
1
0
0
0
2
0
2
0
2
0
0
2
0
3
1
2
0
0
1
2
1
2
1
2
1
0
0
0
0
1
2
1
1
0
1
0
0
1
2
0
2
1
0
0
1
0
0
2
0
2
0
2
0
0
0
0
0
0
0
2
2
2
0
0
1
0
1
0
2
0
2
1
1
17
0
3
2
6
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
1
2
4
2
0
2
0
0
2
0
2
2
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
1
1
1
1
2
2
1
0
2
0
1
3
0
0
0
0
0
2
0
2
4
0
0
1
0
1
0
1
2
1
1
0
0
1
2
0
0
0
2
0
0
2
2
1
1
2
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
1
1
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
2
0
1
0
0
2
0
0
5
0
0
2
2
2
1
2
0
0
2
1
2
0
1
1
0
0
0
0
1
0
2
1
1
3
0
0
0
2
1
0
0
0
0
0
2
0
1
0
0
2
0
1
0
0
0
2
1
2
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
1
1
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
1
3
2
1
1
0
0
0
1
0
0
0
1
2
1
2
2
0
0
0
1
1
0
1
0
1
1
2
1
1
0
0
0
0
0
1
2
0
0
2
1
2
0
0
0
0
0
1
2
0
2
0
2
1
1
0
0
1
0
1
0
1
0
0
1
2
0
0
0
2
0
2
1
0
0
0
0
0
0
0
2
0
0
2
2
0
2
1
2
0
1
1
0
0
0
0
1
1
0
0
0
2
0
0
0
2
3
0
0
0
2
0
0
0
0
2
0
0
0
1
0
2
0
0
1
0
0
0
0
1
0
2
0
1
0
1
2
0
0
0
2
0
0
0
0
1
0
0
0
0
1
2
0
0
0
2
0
2
1
0
0
0
0
0
0
2
0
0
1
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
1
0
2
0
0
0
0
1
0
2
0
2
0
0
0
2
0
2
1
0
0
0
0
0
1
0
2
2
0
1
0
1
2
0
1
2
2
1
0
0
0
0
2
2
1
0
2
1
0
0
2
1
1
2
1
0
0
0
2
0
2
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
1
0
2
0
1
0
0
2
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
2
0
0
0
0
1
1
2
0
0
2
1
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
1
2
2
1
0
2
3
1
2
2
1
0
1
0
0
2
4
0
1
2
2
2
1
1
0
2
2
0
1
2
2
2
0
0
0
1
0
0
1
0
0
2
1
2
0
0
0
1
0
1
0
0
0
1
1
0
1
1
0
0
2
0
0
2
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
2
0
1
0
0
0
0
1
0
0
2
2
0
0
0
0
0
2
1
0
0
1
1
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
2
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
2
1
1
0
1
0
1
0
1
0
1
2
1
2
0
0
0
0
0
0
0
2
0
1
0
1
2
0
0
1
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
1
0
0
3
0
0
0
0
0
2
1
2
0
0
2
0
0
0
0
1
2
0
1
1
0
3
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
2
0
0
0
0
0
2
1
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
1
0
0
2
0
2
0
0
0
5
2
3
0
0
0
0
2
0
0
0
0
1
2
0
1
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
2
2
0
0
2
2
2
2
0
0
2
0
0
0
0
2
1
0
0
0
0
3
2
1
2
0
2
0
11
1
0
2
1
0
0
0
0
2
0
0
2
2
2
1
0
0
0
0
1
0
0
2
0
0
0
0
2
1
0
0
0
2
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
2
0
1
2
0
0
0
2
0
1
0
0
0
0
0
0
0
1
2
1
2
0
0
0
2
1
0
1
0
0
0
0
0
1
0
0
2
2
0
0
0
0
1
4
0
0
0
1
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
2
0
2
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
1
0
0
0
2
1
0
1
1
0
2
0
1
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
2
0
2
0
3
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
2
1
1
2
0
1
1
0
0
2
0
1
1
0
0
0
0
0
0
1
1
0
1
1
0
1
0
0
0
1
0
1
0
4
1
1
2
0
1
1
2
0
2
1
2
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
2
2
0
2
0
0
0
0
0
1
1
1
0
0
0
0
1
1
1
0
0
1
0
2
1
0
1
0
1
1
1
2
1
1
0
0
2
2
0
0
0
0
0
0
0
1
2
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
1
2
1
0
0
2
0
2
0
0
4
0
2
0
1
0
1
0
0
0
2
0
0
0
2
2
0
0
0
2
1
0
1
3
0
0
1
2
1
1
0
1
0
0
0
0
0
2
3
0
0
1
1
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
1
1
0
0
0
0
2
1
0
0
2
0
0
1
1
0
0
0
2
2
1
1
0
2
0
0
2
0
0
0
0
0
0
2
1
2
0
2
2
0
2
0
1
0
1
0
2
1
2
0
0
1
0
1
0
0
0
1
1
0
0
3
0
0
2
2
0
1
0
0
0
1
1
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
3
0
2
0
2
2
1
0
0
0
2
0
0
0
0
1
2
0
0
0
0
2
0
0
2
0
1
0
0
0
3
0
0
1
0
1
5
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
2
0
1
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
1
0
2
1
0
0
0
0
0
0
1
2
1
0
0
1
1
2
1
2
0
0
0
1
1
2
1
0
1
1
0
2
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
1
0
1
1
1
0
5
0
0
0
3
2
0
2
0
0
5
1
0
0
0
0
2
2
0
0
0
1
0
0
2
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
2
0
0
0
0
2
0
0
1
1
0
1
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
2
1
1
2
0
0
0
2
1
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
3
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
5
0
0
0
0
0
0
0
0
3
0
0
2
1
0
1
0
1
1
0
0
0
0
2
0
0
2
0
2
0
0
1
0
2
1
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
2
3
1
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
2
0
3
0
0
3
1
0
2
0
0
2
1
0
0
0
0
1
0
0
0
0
2
1
1
0
0
1
0
0
2
0
0
0
2
2
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
1
2
0
0
0
1
0
0
1
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
2
1
1
0
2
0
0
1
0
2
0
0
2
0
0
0
0
0
2
1
0
0
0
2
0
0
3
1
0
0
2
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
2
0
2
2
0
2
2
1
0
0
0
1
2
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
2
0
2
0
0
0
1
0
0
0
0
1
2
0
0
0
1
2
0
2
0
0
0
1
0
2
2
1
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
1
0
1
2
1
1
0
0
0
0
0
0
0
0
2
1
1
0
0
0
2
1
2
2
0
0
1
0
0
2
0
0
3
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
4
2
2
0
0
1
0
0
1
0
1
1
0
0
0
0
2
0
0
0
0
1
2
0
2
0
1
1
2
2
0
0
0
2
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
1
6
0
2
0
0
0
0
0
1
1
3
0
0
0
2
0
0
0
0
1
0
2
2
0
2
0
0
2
1
0
0
2
0
2
2
0
0
1
0
0
0
4
1
1
0
2
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
1
2
1
1
0
0
0
2
0
0
0
0
0
1
1
0
0
2
0
1
0
2
0
0
2
1
0
2
0
2
0
1
0
0
2
0
0
0
0
1
4
0
0
2
2
0
1
1
0
0
1
1
1
2
2
0
1
2
0
2
0
0
0
0
1
1
3
2
0
0
1
3
1
0
0
2
0
1
0
0
0
0
0
0
0
0
1
3
2
1
0
0
2
0
0
0
3
1
0
0
0
0
1
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
2
0
2
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
1
0
0
0
1
2
1
0
2
0
2
1
0
0
0
0
0
0
2
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
2
2
2
1
0
2
0
1
2
0
2
0
0
1
0
0
0
0
2
0
1
2
2
0
1
0
0
0
2
1
3
0
0
0
0
0
1
2
0
1
1
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
7
1
0
0
0
1
1
2
1
2
1
0
0
2
1
0
0
1
1
0
2
0
0
0
0
1
1
2
0
0
0
0
0
5
0
2
0
0
0
2
2
3
0
0
2
0
1
0
1
0
2
0
0
0
2
0
0
0
0
2
0
0
2
1
1
0
0
0
2
0
2
2
0
2
1
0
1
0
0
1
2
2
0
0
1
1
2
1
0
0
1
2
0
2
5
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
2
2
1
0
0
0
1
0
1
2
0
0
1
0
1
0
2
0
0
0
1
0
0
4
0
1
1
1
1
0
0
0
2
0
3
0
0
0
1
2
0
0
0
1
0
2
0
0
1
0
1
1
0
4
0
0
0
0
1
4
2
0
1
2
0
0
0
0
0
2
2
0
0
0
2
1
2
0
2
1
2
0
1
3
0
4
0
3
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
5
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
2
0
0
2
0
0
0
0
2
1
0
2
0
0
3
0
2
0
0
0
1
0
0
0
2
0
1
1
0
0
1
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
1
0
2
0
1
0
2
0
0
0
1
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
1
0
2
1
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
2
0
0
0
0
2
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
3
1
0
0
1
0
1
1
0
0
0
2
0
0
0
2
0
0
0
1
1
0
0
1
0
0
0
1
1
1
0
2
0
2
0
1
0
0
1
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
1
1
0
0
1
0
0
0
1
0
0
1
2
0
2
0
2
0
0
1
2
1
0
0
1
2
0
0
0
0
2
0
0
0
2
1
1
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
2
0
1
1
0
0
0
0
0
2
0
1
1
1
3
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
3
0
2
0
0
0
0
0
1
0
1
1
2
0
0
0
0
0
1
1
0
0
1
0
1
1
0
0
0
0
1
0
0
0
2
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
2
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
3
0
0
2
0
1
0
0
1
2
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
8
0
0
0
0
0
2
1
2
0
0
0
0
0
0
2
1
2
0
0
0
2
1
0
1
0
0
0
1
0
1
0
4
0
0
1
0
1
2
1
1
0
0
2
0
0
1
1
0
1
1
0
0
0
0
0
2
0
1
1
2
2
1
0
1
0
0
0
0
0
1
0
0
0
2
0
0
2
0
2
0
1
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
1
0
2
0
2
0
0
1
0
1
1
1
2
0
2
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
2
2
0
0
0
0
0
1
0
0
1
0
1
0
0
0
3
1
0
0
0
0
0
1
1
1
0
0
0
0
1
1
0
0
0
0
1
2
1
0
0
0
1
1
1
1
0
0
0
0
0
1
0
2
0
0
0
1
3
0
1
2
0
1
0
0
1
0
0
0
0
1
0
3
1
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
2
1
1
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
1
1
0
0
0
0
2
0
0
0
2
2
0
1
1
1
1
0
1
2
2
0
0
0
0
0
1
2
0
0
0
0
2
2
0
0
0
0
2
3
1
0
1
3
1
0
2
2
0
0
1
0
1
0
3
2
1
0
0
2
0
0
0
1
11
4
1
1
0
0
0
0
0
0
0
3
0
0
1
4
0
0
2
1
0
0
1
0
0
2
0
0
1
0
2
0
0
0
0
0
0
2
2
2
1
2
0
0
0
1
1
0
0
2
0
0
0
0
2
1
2
0
1
0
1
2
0
3
0
1
0
2
0
0
0
2
0
1
0
1
0
0
0
0
1
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
1
0
0
0
0
2
0
2
0
0
1
2
0
0
2
0
2
1
0
0
2
2
0
0
2
0
1
2
1
0
0
0
0
0
0
2
0
0
0
0
0
3
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
1
1
0
0
1
0
0
1
1
0
1
2
2
1
0
0
0
0
0
0
1
1
0
0
4
2
0
0
0
0
2
0
0
0
2
1
2
0
0
0
1
0
0
1
0
1
0
2
0
0
1
0
0
0
0
1
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
1
1
0
0
0
0
0
0
1
2
1
0
1
0
0
0
2
2
0
1
0
2
0
1
1
1
0
0
1
0
2
0
1
2
0
1
0
0
0
0
0
2
0
2
0
1
0
0
0
0
1
2
0
0
0
0
4
0
0
0
0
1
0
0
1
0
2
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
1
0
2
2
0
2
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
1
0
0
2
0
0
0
2
0
0
2
0
1
0
1
3
0
0
0
0
2
0
2
0
0
1
2
0
0
2
0
0
4
1
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
3
2
0
0
1
0
0
0
0
0
2
0
2
0
0
2
0
2
0
0
2
0
2
0
2
0
0
0
3
0
1
2
2
0
0
0
0
1
0
2
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
2
1
0
1
0
0
3
0
1
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
1
1
1
2
0
2
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
1
2
0
0
1
0
1
1
0
1
0
0
0
1
0
0
2
2
1
1
0
0
1
1
0
0
0
1
0
1
0
0
1
0
0
1
0
1
0
1
1
2
1
2
1
0
0
1
0
0
1
0
2
0
1
0
1
0
0
0
0
1
0
0
5
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
2
0
0
2
0
1
0
0
0
0
0
2
0
0
0
2
0
0
1
4
0
0
1
0
0
1
0
0
6
0
0
0
0
0
1
1
0
0
4
3
2
0
0
0
0
1
3
1
1
0
1
1
0
0
0
0
0
0
0
1
0
1
2
0
0
2
4
0
0
2
1
0
0
0
2
2
1
0
2
1
0
0
1
0
0
0
0
0
2
0
2
0
2
0
2
1
0
2
0
0
0
2
0
1
2
0
1
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
1
2
0
0
0
2
0
0
2
0
1
2
0
0
1
0
0
0
0
0
0
2
2
0
0
2
2
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
1
0
1
2
0
0
0
0
1
0
0
2
0
1
1
1
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
3
1
0
2
0
2
0
0
1
1
0
0
0
0
0
1
1
2
2
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
2
2
2
0
0
2
0
0
3
0
0
2
0
2
1
0
0
0
0
0
3
0
0
0
1
0
1
1
2
0
0
1
0
2
0
0
0
1
0
2
0
0
0
1
0
2
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
3
0
0
0
0
0
0
0
1
2
2
0
0
1
0
1
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
3
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
1
2
1
0
1
0
2
0
0
1
0
0
0
0
0
1
1
0
0
0
2
2
0
1
1
2
0
0
0
0
2
0
2
1
0
0
2
0
0
2
0
0
2
2
1
1
2
2
0
0
0
0
3
0
2
0
0
3
0
0
1
2
2
0
0
0
0
1
1
0
0
0
0
0
2
0
0
1
1
0
0
1
2
0
0
0
0
0
2
2
1
0
1
0
2
0
0
0
0
0
2
2
0
1
0
0
1
0
2
1
0
0
2
0
1
0
0
0
1
0
0
0
0
2
2
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
2
0
2
0
0
2
0
0
0
3
0
0
0
0
2
0
0
0
0
2
1
0
0
0
1
1
0
2
1
0
0
0
1
1
0
0
0
1
2
0
2
0
2
0
0
1
0
1
3
1
2
2
0
0
0
0
0
0
0
0
1
0
2
0
2
2
0
2
0
1
2
0
0
0
1
0
0
0
1
2
0
1
1
1
0
1
0
0
0
0
0
2
1
0
0
1
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
1
1
0
0
2
2
0
0
2
1
0
0
0
0
1
0
0
2
2
2
0
1
1
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
4
0
0
1
0
2
0
0
0
0
1
0
0
0
1
0
0
1
1
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
2
0
0
1
0
1
0
0
2
2
0
0
0
0
1
1
1
0
2
1
1
1
2
1
1
2
1
2
0
0
0
2
0
0
3
0
1
1
0
2
1
0
0
0
0
0
0
3
0
0
1
0
1
0
0
0
1
2
0
0
0
2
1
0
1
0
0
0
1
2
0
0
0
2
0
2
2
1
1
0
0
0
0
0
0
0
0
0
2
3
2
0
0
1
0
0
0
2
0
0
0
2
1
0
0
0
1
0
1
0
1
0
0
0
0
0
1
1
0
0
1
0
2
2
0
2
1
1
0
2
1
0
0
0
0
1
3
0
0
0
0
0
2
1
0
1
0
0
1
1
0
1
0
0
2
2
2
0
1
0
0
2
2
1
1
1
0
2
1
0
2
0
1
2
0
0
0
0
0
1
1
1
0
0
1
0
0
0
3
0
2
1
0
0
0
0
0
1
2
0
0
0
0
0
2
1
0
0
1
0
0
1
0
0
0
1
0
0
1
2
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
1
2
2
0
1
2
0
1
2
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
5
0
2
0
0
0
1
2
1
0
0
0
1
0
0
1
0
0
1
0
1
1
0
0
0
0
1
0
0
2
1
0
1
1
0
0
1
0
0
1
1
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
3
0
0
0
1
0
0
1
0
1
1
0
0
1
1
2
4
0
0
0
1
2
1
0
2
0
0
1
1
0
1
0
0
0
0
0
1
1
1
1
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
2
0
0
1
3
2
0
1
0
0
2
0
0
0
1
1
0
2
1
1
0
1
0
0
0
0
2
0
0
1
2
0
2
0
0
1
1
1
0
2
2
0
0
2
0
2
0
0
2
1
0
0
0
2
0
0
0
0
2
0
0
2
0
1
0
2
0
2
1
2
0
0
2
1
0
0
1
0
2
2
1
1
0
0
0
1
1
0
1
0
1
1
1
2
0
0
0
0
1
0
2
2
0
1
0
2
0
1
1
0
0
2
0
0
0
1
2
0
0
1
2
0
1
3
1
2
3
0
1
0
0
0
0
0
0
0
1
0
4
0
0
1
0
0
1
0
0
0
3
0
0
0
0
2
2
0
2
0
2
0
0
2
1
1
0
0
0
0
1
2
2
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
1
0
2
1
1
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
2
1
1
0
2
0
0
2
0
1
2
2
1
1
0
1
2
0
0
0
0
2
0
2
0
2
0
0
2
1
2
0
0
0
1
0
0
0
0
2
0
0
4
0
0
0
0
1
0
0
1
0
0
2
0
1
2
2
0
0
2
0
1
3
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
2
0
1
0
0
0
0
0
1
1
2
0
2
0
0
0
0
0
0
1
0
2
0
1
0
0
1
0
2
0
2
0
0
0
0
0
0
1
0
2
0
1
1
1
0
0
1
1
0
0
0
0
1
1
0
0
1
1
0
0
2
0
0
0
0
0
0
1
1
0
0
2
0
2
1
0
0
1
0
0
0
1
0
2
0
2
1
2
1
2
0
0
0
1
0
2
0
0
1
0
0
0
2
0
0
0
1
2
0
0
2
0
0
2
0
0
2
0
1
0
0
0
0
1
0
3
1
0
0
0
0
0
1
0
1
0
0
0
2
0
2
0
0
2
1
0
2
0
1
0
0
0
1
1
0
0
0
0
1
2
0
0
1
2
0
0
0
0
0
0
3
2
1
0
0
1
1
0
1
0
0
3
0
2
2
0
0
0
1
1
0
2
0
2
0
0
1
0
0
2
2
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
1
0
2
1
2
1
2
0
1
0
0
0
0
1
2
2
1
0
0
2
2
0
0
1
3
0
1
2
0
1
1
0
0
0
0
1
1
2
0
0
1
1
0
1
2
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
1
0
1
1
0
3
0
0
0
1
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
1
2
1
2
1
0
0
1
0
0
0
0
2
1
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
1
2
0
1
0
0
0
2
0
0
1
0
1
0
0
1
1
2
0
0
0
0
2
0
2
0
1
0
2
0
2
1
0
0
1
1
0
0
0
1
1
1
1
2
0
1
2
1
0
0
0
0
1
0
0
0
1
0
1
0
2
0
1
2
1
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
1
2
1
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
1
0
0
1
1
5
0
1
0
2
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
1
0
3
0
0
0
2
0
0
2
0
0
1
0
0
0
0
1
2
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
1
1
0
0
2
0
0
0
0
1
2
2
2
0
0
0
0
0
0
3
2
2
2
0
1
0
0
0
0
4
0
0
0
2
0
0
2
0
2
2
0
0
2
0
0
0
0
1
0
0
0
1
0
2
1
0
0
0
2
4
0
1
0
0
1
0
1
1
1
1
2
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
1
1
0
1
1
0
1
0
0
0
0
0
1
0
1
0
2
0
2
0
0
0
3
0
1
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
1
0
0
2
1
0
3
0
2
1
0
0
2
0
1
0
2
0
0
1
0
0
1
0
1
1
1
2
1
1
2
1
0
1
0
2
0
1
0
0
1
0
0
2
2
0
0
2
0
0
0
3
0
0
0
0
0
3
1
0
0
0
1
0
3
0
1
1
1
0
2
0
2
0
1
3
0
0
1
1
0
0
0
1
1
0
1
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
1
0
0
2
0
0
1
0
1
1
2
0
0
2
0
2
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
2
1
0
2
1
0
3
0
0
1
0
0
1
0
1
0
0
0
1
0
1
0
1
0
2
0
0
0
0
0
0
2
0
0
2
2
0
2
2
0
0
0
0
0
0
2
0
1
0
0
0
0
1
1
0
1
2
3
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
2
0
2
2
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
1
1
0
0
1
0
2
0
0
1
0
0
0
0
2
0
0
2
1
2
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
2
1
1
0
0
0
4
0
0
1
0
2
1
2
0
0
2
0
3
0
0
0
0
0
2
2
2
1
2
0
2
0
2
2
0
0
2
2
0
2
0
0
4
0
0
0
1
0
0
2
0
0
1
1
0
0
1
2
0
0
0
2
1
3
1
2
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
2
0
1
2
2
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
1
0
0
2
0
1
0
0
0
0
0
0
0
0
2
1
0
0
1
2
0
1
0
0
0
0
3
0
0
1
0
2
0
1
0
0
1
0
0
2
0
1
2
0
0
0
0
0
0
1
0
1
0
2
2
0
1
0
0
1
0
0
2
0
0
1
0
0
2
0
1
1
0
0
1
0
2
1
0
1
0
2
1
0
0
1
0
1
2
1
2
1
2
0
0
0
0
0
2
0
1
1
0
0
1
0
0
0
0
1
2
0
0
0
1
3
2
0
2
0
0
0
0
2
1
0
0
0
1
0
0
1
0
2
0
2
1
0
0
0
0
0
0
0
2
1
0
1
1
0
0
1
2
0
2
1
0
2
0
0
1
0
1
0
1
0
0
2
2
0
0
2
2
1
2
0
0
0
0
1
1
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
2
0
0
0
0
1
0
0
1
0
1
0
1
1
0
0
0
0
0
0
2
2
0
2
2
0
0
0
0
0
2
0
0
0
0
1
2
0
1
1
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
3
0
0
0
1
0
1
0
0
3
0
0
1
2
0
0
3
0
0
2
1
0
0
0
3
1
4
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
1
0
0
0
1
0
0
0
0
2
0
0
2
0
2
0
0
0
2
0
0
4
1
1
3
0
0
0
0
2
1
1
0
2
0
0
1
3
0
0
0
0
0
2
1
1
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
1
0
1
2
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
2
0
1
0
0
2
2
0
0
0
0
0
0
2
2
0
2
0
2
0
0
1
1
0
0
0
2
0
0
0
0
0
1
0
1
1
0
1
4
1
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
2
0
0
1
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
2
0
0
2
1
0
0
1
1
0
0
0
0
1
0
1
1
1
2
1
0
0
1
0
4
0
4
2
2
0
0
0
0
3
0
0
0
0
0
3
0
2
1
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
1
2
0
0
0
1
0
2
0
0
0
2
2
0
0
1
0
1
2
0
0
0
0
0
1
0
1
0
0
0
2
2
0
0
0
0
0
2
2
0
0
0
0
0
1
3
0
2
2
0
0
0
0
1
0
1
0
1
0
0
0
2
0
2
0
0
0
2
0
0
1
1
0
2
1
0
0
0
0
0
2
0
0
0
0
0
3
0
2
1
0
0
0
1
1
0
2
0
2
0
1
0
1
3
0
2
0
0
2
0
0
0
1
0
0
0
1
0
1
1
1
1
0
0
0
0
1
0
0
0
0
6
0
1
3
2
3
0
2
2
0
0
2
2
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
1
0
2
2
0
0
2
0
0
0
0
1
2
0
1
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
2
0
0
0
1
0
0
0
2
1
0
1
0
0
0
0
0
2
0
2
2
2
1
0
0
0
0
0
2
0
2
0
1
2
0
0
0
1
0
1
0
0
0
1
0
1
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
2
0
2
2
0
0
1
0
0
1
0
0
0
0
2
1
0
1
0
2
2
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
2
1
1
1
2
0
3
0
1
0
0
0
0
0
2
0
1
2
2
2
1
1
2
1
0
0
0
0
2
0
0
1
0
0
0
2
2
0
2
0
0
0
1
0
2
0
0
2
0
2
1
2
0
0
0
2
0
0
2
2
0
0
0
2
0
1
0
2
0
0
0
0
0
1
0
0
2
0
4
1
0
2
0
0
0
0
0
1
0
2
1
0
0
0
2
1
0
0
0
1
0
1
0
1
1
2
0
2
4
1
0
0
1
2
0
0
1
1
0
2
2
2
0
1
2
2
0
1
0
2
1
1
0
0
4
0
2
2
0
0
0
0
0
0
1
2
2
0
4
1
2
0
0
2
0
0
0
0
2
0
1
1
0
0
0
1
0
0
0
0
3
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
1
1
0
4
3
0
1
1
0
2
0
0
1
0
1
0
0
0
0
0
1
2
1
1
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
1
2
2
0
0
0
0
0
1
0
0
0
0
2
2
0
2
0
0
0
0
2
0
1
0
0
0
0
0
2
1
0
0
0
0
0
3
1
1
0
0
1
0
0
1
2
0
0
0
0
2
0
0
2
0
0
1
2
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
1
2
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
1
2
0
0
1
0
0
0
1
2
1
0
0
0
0
2
0
0
0
0
2
0
1
0
2
3
2
2
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
3
0
0
0
1
2
0
0
1
1
0
2
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
1
1
1
2
1
2
1
0
0
1
2
1
0
0
0
0
0
1
0
2
1
0
0
2
0
0
0
0
0
1
0
0
1
1
2
0
0
1
0
0
0
0
0
0
0
1
2
2
0
1
0
0
0
0
1
1
1
2
1
0
0
0
0
0
0
0
1
1
0
2
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
2
0
1
0
1
0
0
2
0
0
0
0
2
2
0
1
1
1
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
2
0
2
0
0
3
1
0
0
0
2
0
0
3
0
0
3
0
0
1
0
1
1
2
0
0
0
0
3
0
1
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
1
1
0
1
1
0
1
0
2
0
2
0
0
1
1
0
1
2
1
0
1
1
1
0
0
0
2
0
0
0
0
0
0
1
0
0
4
1
0
0
0
1
2
0
1
0
0
1
0
0
1
0
0
1
2
1
0
0
0
0
0
0
0
0
3
0
0
2
2
0
0
0
1
2
2
0
1
0
0
0
0
0
1
1
2
2
2
0
1
0
1
0
0
2
2
0
2
0
2
1
0
0
0
0
1
2
0
0
0
0
2
1
2
0
0
0
0
0
2
0
0
1
0
0
0
1
2
0
0
0
0
2
0
1
0
2
0
2
0
1
2
0
0
1
0
3
0
0
0
1
2
3
0
0
0
0
0
2
2
0
2
0
2
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
1
0
2
0
2
1
1
2
0
2
0
1
2
0
0
2
0
0
1
2
0
0
1
0
0
0
0
1
2
0
0
0
1
0
1
0
0
2
2
2
2
3
0
2
1
6
1
0
1
0
0
0
2
2
0
0
2
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
1
0
1
0
1
2
0
0
0
0
1
2
0
0
2
2
0
0
1
0
0
0
1
0
1
2
0
1
2
0
1
5
14
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
2
0
0
2
0
1
0
0
0
0
0
0
2
0
1
0
1
0
0
1
1
0
2
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
1
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
2
0
1
0
0
1
0
0
0
0
0
0
0
3
0
2
1
0
0
0
1
0
0
0
1
1
0
0
0
0
2
2
0
1
0
2
0
0
1
0
0
0
0
2
0
0
4
0
0
0
1
2
0
0
0
0
0
0
0
0
2
2
0
1
0
1
0
0
0
0
2
1
2
1
0
3
0
0
0
2
0
1
0
0
1
0
2
1
0
0
1
0
0
0
2
2
0
2
0
0
1
0
0
0
0
1
3
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
1
2
0
0
0
1
1
2
0
1
2
0
0
0
0
2
0
0
2
0
1
0
0
0
1
0
0
0
1
0
1
0
1
2
1
1
0
0
0
0
2
4
2
0
1
0
0
0
0
2
1
0
1
2
0
3
1
2
0
0
0
0
1
0
0
0
1
2
2
0
0
2
2
0
0
1
0
1
0
0
0
0
3
2
0
2
0
2
0
0
1
0
0
3
0
0
0
2
0
0
0
2
0
0
0
2
0
0
1
1
2
0
0
0
0
2
1
1
2
0
0
0
0
0
0
1
0
0
2
1
2
2
1
0
0
0
1
0
0
0
0
2
3
0
0
2
0
0
2
0
1
1
0
0
2
0
2
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
1
2
0
2
2
2
3
1
0
0
2
1
0
0
0
0
2
1
1
0
1
0
0
0
2
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
1
0
1
0
0
0
1
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
2
1
0
0
0
0
0
1
0
0
0
1
2
0
0
1
0
0
0
0
3
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
1
1
0
2
0
0
2
0
2
0
0
0
1
0
0
1
0
2
0
0
1
0
0
0
0
0
0
3
2
1
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
1
1
2
0
0
0
3
0
0
2
1
0
1
2
0
0
1
2
0
0
0
1
2
0
0
1
3
0
0
2
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
3
0
0
0
0
0
1
1
0
1
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
1
0
2
0
0
0
0
1
1
1
1
1
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
1
2
0
0
1
0
1
0
0
0
2
0
1
0
0
2
1
0
0
1
0
0
1
0
1
7
0
0
0
1
3
0
2
4
1
0
1
2
0
0
0
0
0
0
0
1
2
0
0
2
0
1
2
2
2
0
1
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
3
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
3
2
0
2
0
0
0
5
1
0
1
1
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
1
0
2
0
1
0
0
2
2
0
2
0
2
0
0
0
2
0
0
1
1
0
0
0
1
0
1
2
0
1
0
2
0
0
2
0
0
2
0
1
1
0
0
1
1
2
0
0
2
1
1
0
2
2
2
2
2
0
0
0
1
0
2
2
1
1
0
1
2
0
0
2
0
2
1
2
1
0
2
1
0
0
0
0
2
0
1
0
2
0
0
0
1
2
0
1
2
2
0
0
1
1
0
0
2
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
4
0
0
1
0
1
1
1
2
0
0
2
0
0
0
0
1
0
0
3
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
2
1
0
0
0
0
0
0
0
4
0
1
2
2
3
0
0
0
0
4
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
1
2
2
0
0
1
2
0
0
0
0
0
1
1
0
0
3
1
1
0
1
1
0
0
0
0
0
0
2
2
2
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
2
2
0
0
0
1
0
0
1
2
8
1
0
0
0
0
1
0
0
0
0
0
1
2
1
0
0
0
1
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
3
1
0
0
0
2
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
1
0
2
1
0
0
0
2
2
0
0
0
0
0
1
1
0
3
0
0
2
3
2
0
0
1
0
2
2
0
2
4
1
0
4
0
0
2
0
0
0
2
0
1
0
0
1
1
1
0
0
2
0
1
0
1
0
2
2
0
0
1
0
0
0
1
0
1
0
0
1
1
0
2
0
1
0
1
1
0
0
0
0
1
0
2
0
1
0
2
3
0
0
0
1
7
0
0
0
0
1
0
0
1
1
1
3
0
0
0
0
0
0
1
0
0
1
2
2
0
0
0
0
1
0
0
0
0
0
0
4
1
0
1
0
0
0
2
0
0
1
0
1
0
0
2
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
3
1
0
0
0
0
1
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
1
2
0
0
0
1
0
0
1
0
1
0
2
1
0
0
1
0
0
0
0
2
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
2
2
2
0
0
0
0
0
1
2
1
2
0
2
1
0
0
0
2
0
1
1
1
0
0
0
0
0
2
0
1
2
0
0
1
0
2
0
2
0
1
1
0
3
0
0
0
0
2
0
2
1
0
0
2
0
0
2
0
0
0
1
2
0
0
1
3
0
0
1
0
0
1
2
0
0
0
0
2
0
0
0
0
3
0
0
0
3
2
0
0
0
0
0
0
0
2
1
1
0
0
1
2
0
1
1
1
2
0
2
0
0
0
1
0
1
0
1
1
0
0
1
0
0
0
2
0
0
1
1
0
1
2
2
1
0
2
0
0
1
0
0
0
2
2
3
0
0
2
1
2
0
0
0
2
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
2
0
0
0
2
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
1
1
0
1
0
0
2
0
2
0
0
1
0
4
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
1
2
0
0
2
0
2
0
2
1
0
2
1
1
0
2
0
0
1
2
0
1
2
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
2
2
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
3
1
2
0
0
0
2
1
1
1
2
2
0
0
2
0
0
2
0
1
0
0
2
0
0
2
1
2
0
0
0
0
0
0
0
2
4
0
2
0
1
1
0
0
2
0
2
1
0
0
1
2
2
2
1
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
1
2
0
0
0
0
1
0
1
2
0
0
0
0
0
2
0
1
0
0
0
1
1
0
0
0
1
2
0
0
2
0
0
0
1
0
0
1
1
0
2
0
2
2
0
0
0
0
0
1
0
2
0
0
0
1
1
0
0
2
1
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
2
2
0
2
0
1
3
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
1
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
2
1
2
2
2
1
0
0
2
1
0
0
0
0
0
2
0
0
2
0
1
0
1
0
0
1
2
0
2
0
0
2
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
2
0
0
1
0
0
0
2
0
0
2
2
0
0
0
2
2
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
2
0
0
1
2
2
1
0
0
0
0
0
1
0
1
0
1
2
1
0
0
1
0
2
2
0
1
3
2
2
0
0
0
2
0
1
0
0
1
1
0
0
0
0
1
0
1
1
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
1
1
4
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
3
2
0
0
0
2
0
0
1
0
0
0
2
0
0
0
1
2
0
2
0
0
0
0
0
2
0
0
0
5
0
2
0
2
0
2
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
3
2
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
2
2
2
0
2
2
0
0
1
0
0
1
2
0
0
2
1
2
0
1
4
0
0
0
0
3
0
0
0
0
1
1
0
0
1
0
2
1
2
0
1
1
0
1
2
0
0
0
1
1
0
1
1
0
0
0
0
0
0
1
0
1
2
1
0
1
0
0
0
0
2
1
1
0
0
0
1
0
1
0
0
3
2
1
0
0
0
0
0
2
0
1
0
2
0
0
0
0
2
1
0
1
1
1
0
2
0
1
0
0
0
1
2
2
1
0
2
0
0
0
2
2
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
2
2
0
1
1
1
1
2
0
2
2
2
0
0
2
2
2
0
1
2
0
0
0
2
0
0
1
0
1
0
1
2
1
0
1
1
0
0
2
1
0
0
2
2
0
0
0
0
1
0
1
2
0
0
1
1
2
1
0
8
0
0
1
0
1
1
0
0
1
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
1
2
0
2
0
3
1
0
0
2
1
0
0
3
1
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
1
0
0
0
0
1
3
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
1
1
0
2
0
1
1
2
3
2
0
1
0
0
0
1
2
0
0
2
0
0
0
1
1
1
2
0
2
0
1
2
0
0
1
0
1
2
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
2
2
0
2
2
0
0
1
1
0
0
0
0
0
2
2
0
0
0
0
1
1
0
0
1
0
2
1
1
1
0
0
0
0
0
0
2
2
0
3
0
2
0
2
0
2
3
2
0
2
3
0
2
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
2
1
1
0
0
0
0
0
0
2
0
1
0
2
2
2
2
0
0
0
0
0
0
0
1
2
0
0
1
2
0
1
0
0
1
0
2
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
2
0
2
0
1
0
1
1
0
0
0
0
3
0
0
1
2
0
2
0
0
0
0
0
0
2
1
0
1
2
2
1
0
0
0
1
0
0
1
0
1
2
0
1
0
0
2
1
1
0
0
2
0
0
2
0
0
0
0
2
2
0
0
2
0
2
0
0
0
1
0
0
1
1
1
0
0
0
0
2
0
0
0
0
0
0
1
0
1
1
0
0
0
0
2
1
0
2
1
2
1
0
0
0
2
0
0
3
1
0
0
0
1
0
2
1
0
0
2
0
0
1
0
0
1
0
0
0
2
0
0
0
1
1
1
1
2
0
0
0
0
2
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
1
2
0
0
2
0
0
2
0
1
0
1
1
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
1
0
1
1
0
0
1
0
0
1
0
2
2
0
1
0
0
1
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
3
3
0
0
0
0
3
2
1
0
1
2
1
1
0
2
0
0
2
1
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
2
0
0
0
1
0
0
0
0
2
0
2
0
2
2
0
0
0
1
0
0
1
0
1
0
0
0
1
2
1
0
0
2
0
1
0
1
0
0
0
3
0
0
0
1
0
2
0
2
0
0
0
2
1
0
0
0
2
1
0
0
0
0
0
1
2
0
0
2
0
2
0
1
0
1
0
0
3
0
0
1
1
1
0
0
2
2
0
0
1
1
1
0
1
0
0
1
2
0
2
0
1
0
0
0
0
1
2
1
0
0
0
2
0
0
1
0
2
0
2
2
0
1
0
0
0
0
1
0
1
0
2
3
0
1
0
0
3
1
2
1
0
0
0
2
2
2
1
1
1
2
1
0
0
0
0
0
1
0
0
0
0
1
2
2
0
0
0
2
0
0
0
0
0
2
2
0
2
0
0
1
2
0
0
0
0
0
1
0
1
0
0
1
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
2
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
1
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
2
0
0
0
1
0
1
0
2
0
0
4
0
0
0
1
0
0
0
0
0
0
0
3
0
0
2
0
1
2
1
0
2
2
1
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
2
1
1
2
2
0
0
0
0
1
2
0
0
0
1
1
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
2
1
2
1
1
0
2
2
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
1
0
0
0
1
2
1
0
0
1
0
3
1
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
5
1
0
0
0
0
0
2
0
2
2
1
0
0
10
0
1
0
0
0
1
1
0
2
0
1
0
0
0
1
1
0
0
0
2
0
1
0
0
2
0
2
0
0
0
3
0
1
0
0
0
0
2
0
0
0
0
2
0
0
1
1
0
0
2
0
1
0
1
2
0
2
2
0
2
0
0
0
1
2
0
2
0
0
1
0
2
0
2
0
0
2
2
0
0
0
0
0
0
0
1
1
0
0
1
2
2
1
0
2
0
1
0
1
1
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
2
0
2
1
0
0
1
1
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
1
0
0
0
0
1
1
0
1
2
2
2
1
2
0
2
0
0
0
0
0
1
1
1
0
0
2
0
0
0
2
0
0
0
6
0
1
0
0
0
1
0
1
0
1
0
0
0
1
1
1
0
0
0
2
0
0
1
0
0
0
1
1
1
1
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
2
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
2
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
1
0
2
1
1
2
0
0
1
0
2
0
0
0
0
2
2
0
2
0
0
1
2
1
0
0
1
0
1
0
0
0
0
0
0
2
2
0
0
1
1
0
4
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
2
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
1
1
2
0
1
1
2
0
2
1
0
2
0
0
0
0
0
0
3
0
1
1
0
0
2
0
2
0
2
2
0
0
0
1
0
2
0
0
1
0
0
1
1
2
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
1
2
0
0
1
0
1
2
0
0
0
0
2
2
1
0
1
0
0
2
1
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
1
2
2
0
0
1
0
5
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
2
0
2
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
1
0
2
2
1
0
1
2
0
0
0
0
0
0
1
0
2
1
2
0
1
1
0
0
0
0
0
2
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
2
0
0
0
3
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
2
0
0
2
0
1
0
1
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
1
2
1
1
0
0
0
2
0
0
2
1
0
1
0
2
1
0
0
0
0
0
2
3
3
0
2
2
1
1
2
0
0
0
0
0
0
0
0
2
0
0
2
7
1
0
2
1
0
0
2
0
1
1
3
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
3
0
0
1
0
0
0
1
0
0
0
1
0
0
0
2
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
3
2
0
1
0
0
1
0
3
0
1
0
0
0
1
0
2
2
0
4
0
0
2
2
0
0
0
2
0
2
2
2
0
0
2
2
0
0
0
0
2
1
0
2
0
0
0
1
1
1
0
2
0
1
0
0
0
0
0
1
1
0
1
0
2
2
0
0
0
0
2
0
2
0
2
0
0
2
1
0
0
0
0
1
1
0
0
1
0
0
1
2
0
0
1
0
0
1
0
2
1
1
0
2
0
1
0
0
1
0
0
0
2
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
2
0
0
1
0
0
1
0
2
0
0
0
1
0
2
2
0
1
0
2
0
1
0
0
1
0
0
0
0
1
0
0
2
0
2
0
0
1
0
0
0
1
1
2
2
0
1
0
0
0
0
0
0
1
4
2
1
1
0
1
1
1
0
0
2
2
2
2
0
1
1
0
0
0
3
0
0
0
0
0
2
2
4
0
2
1
1
0
0
1
1
3
0
0
1
2
0
1
0
1
1
0
0
0
0
0
1
0
0
1
0
2
1
1
1
2
2
0
0
0
0
1
0
0
0
0
0
2
0
0
1
1
0
1
0
2
1
0
0
0
0
1
0
2
0
0
1
2
0
1
2
0
0
1
2
0
0
0
0
2
0
0
0
0
1
0
0
0
1
2
0
1
0
0
0
1
2
1
0
0
1
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
2
1
1
0
0
0
0
1
1
0
0
2
0
0
0
2
0
1
1
2
0
0
0
0
0
0
0
0
2
1
1
3
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
3
0
2
0
0
0
0
1
0
1
2
0
0
2
2
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
2
0
2
0
0
1
1
1
2
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
2
0
0
0
1
0
2
2
0
2
1
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
2
0
2
0
0
0
0
0
3
1
0
0
1
0
1
1
0
2
0
1
3
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
2
0
1
0
2
2
2
0
0
0
0
0
0
0
0
0
1
0
2
1
1
0
0
0
1
0
0
2
0
0
1
0
0
1
0
0
0
0
2
2
0
1
2
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
2
0
2
0
0
1
1
2
0
1
0
2
0
0
1
0
0
2
1
2
1
0
0
0
0
0
0
0
3
0
0
0
1
2
0
1
0
2
0
2
0
1
3
0
1
1
0
1
0
0
0
1
0
2
0
0
0
0
2
1
0
0
0
1
1
0
0
0
0
2
0
0
0
0
2
0
1
0
1
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
1
0
0
0
0
0
0
1
0
2
2
1
0
1
1
0
0
0
2
2
0
2
1
0
0
1
0
0
2
1
0
0
2
0
0
0
2
0
0
1
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
2
0
0
2
0
0
0
0
0
2
0
5
1
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
1
2
0
1
0
2
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
2
0
3
0
2
0
1
0
3
2
0
0
1
0
0
1
3
1
0
0
0
0
0
0
0
2
2
1
1
0
0
0
2
2
0
1
0
0
1
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
2
1
2
0
0
0
0
0
0
6
0
1
3
0
0
0
0
0
1
0
3
3
0
0
0
2
0
1
0
0
0
1
0
1
1
0
0
0
0
2
1
1
3
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
2
1
0
4
2
0
2
0
0
4
4
1
0
1
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
2
3
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
3
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
2
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
1
0
1
1
2
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
2
0
2
2
0
0
2
0
0
0
0
0
0
0
1
1
0
0
1
2
0
0
2
0
1
2
0
0
2
2
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
4
1
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
2
0
0
2
0
1
1
0
0
2
0
0
0
0
0
2
1
0
0
1
2
2
0
0
0
0
0
1
2
0
0
0
1
0
2
0
2
2
0
2
1
0
2
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
2
1
0
1
2
0
0
2
0
0
0
0
2
1
3
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
1
0
1
3
4
1
0
0
0
0
2
0
1
0
1
1
0
3
2
2
0
0
0
0
2
0
1
1
0
0
1
0
1
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
3
0
0
2
1
1
0
1
1
2
1
2
0
1
0
0
1
2
1
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
1
0
1
3
0
0
0
2
0
0
2
0
0
3
0
0
4
2
0
1
0
2
0
3
0
1
0
0
2
0
1
2
1
2
0
2
0
0
0
0
0
2
2
1
2
0
0
5
2
0
0
0
0
0
2
2
2
0
0
1
2
2
0
0
2
0
0
0
0
1
1
1
0
0
0
2
0
1
0
0
0
0
3
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
1
1
3
0
0
2
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
1
0
3
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
1
0
0
1
0
0
0
3
0
0
0
5
1
2
0
0
0
0
0
2
2
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
2
0
0
2
0
0
0
2
2
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
1
1
0
2
0
0
0
0
0
0
0
1
0
0
1
2
1
2
2
5
0
0
2
0
0
0
0
0
0
0
0
0
2
2
2
0
1
3
0
0
0
2
0
0
0
2
0
1
0
0
0
0
1
2
1
0
0
1
2
0
0
1
0
0
0
0
0
1
0
2
0
2
1
1
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
2
2
0
1
0
0
1
0
0
0
0
1
1
2
0
1
0
2
0
0
1
2
2
0
0
0
1
0
0
2
0
0
0
1
1
0
0
0
0
0
1
0
1
0
1
2
0
1
2
0
0
0
1
0
0
1
2
0
0
1
1
0
1
2
2
0
0
0
1
0
0
0
2
0
1
2
1
0
0
0
3
1
0
0
2
1
0
1
1
7
0
1
1
0
1
0
0
0
0
0
0
0
1
2
0
0
0
1
1
0
1
1
0
0
0
2
0
0
1
1
0
0
0
0
0
2
0
4
1
0
0
0
0
2
0
2
1
0
1
1
1
1
2
0
2
1
0
2
1
0
0
0
0
1
0
0
2
0
3
1
0
1
2
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
4
0
0
2
0
2
1
0
0
0
0
0
2
1
0
0
1
2
0
0
1
0
1
0
0
0
1
0
1
2
0
1
0
0
0
2
2
2
0
0
0
1
0
0
3
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
1
0
0
1
0
0
0
1
0
2
1
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
2
2
1
0
2
0
0
0
0
0
1
0
0
2
0
0
2
0
0
1
0
0
1
1
0
1
0
0
0
2
1
0
0
0
0
0
2
2
0
0
1
2
0
1
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
2
2
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
2
1
1
0
1
1
0
3
1
1
0
0
0
1
0
0
1
0
2
0
0
0
1
0
0
0
1
0
3
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
1
1
0
2
0
0
2
0
2
2
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
2
1
1
0
0
1
0
1
1
0
0
1
0
0
0
0
2
2
2
0
1
1
0
0
0
0
0
0
0
2
2
2
0
3
2
0
0
2
0
0
0
0
0
0
2
2
2
2
2
0
1
0
0
0
1
1
0
3
1
1
0
0
3
1
0
2
2
0
0
0
1
1
1
0
1
0
0
0
0
1
0
0
1
5
0
0
1
0
1
0
0
0
1
1
0
0
2
2
0
1
0
0
0
2
2
0
1
1
1
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
3
1
1
1
2
0
2
1
0
0
1
0
2
2
0
1
1
0
1
2
0
0
2
2
0
0
0
1
1
2
3
0
0
2
0
0
2
0
1
1
0
0
0
0
0
1
1
2
1
0
2
2
0
2
0
2
0
1
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
1
2
1
0
0
0
12
0
0
1
0
0
2
0
0
1
1
0
0
0
0
0
0
0
2
0
1
0
0
4
0
1
0
1
2
0
0
2
2
0
0
2
0
0
0
1
0
1
0
0
0
0
0
2
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
1
1
0
0
0
5
0
0
0
0
0
2
0
0
1
0
0
2
1
0
1
0
0
1
0
0
0
0
1
2
0
0
0
0
1
2
0
0
0
0
1
2
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
2
1
1
1
0
2
3
0
1
1
0
0
0
0
1
0
2
2
0
0
0
2
2
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
1
1
0
0
0
1
0
2
0
1
2
0
2
2
2
0
0
0
1
0
0
1
0
0
0
0
1
0
2
1
0
0
2
5
0
0
0
0
1
2
3
0
0
1
0
1
2
0
0
0
3
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
2
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
1
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
2
2
1
0
1
0
0
0
0
0
0
2
0
2
2
0
1
2
0
2
0
0
0
0
0
1
1
0
0
1
1
2
2
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
3
1
2
0
0
0
0
0
0
1
0
0
0
1
0
0
3
2
1
0
2
0
0
3
0
0
2
0
0
0
1
0
0
2
0
0
2
0
0
1
1
0
2
0
2
1
0
0
0
0
2
1
3
0
1
0
0
0
1
0
0
0
1
2
0
1
1
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
1
2
0
0
1
1
1
2
0
1
0
1
0
0
0
2
0
0
0
0
1
1
1
0
2
2
0
1
0
0
4
2
1
0
2
2
0
1
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
2
2
1
0
0
0
0
1
0
2
2
0
0
1
1
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
1
2
1
0
0
0
0
0
0
1
1
1
0
2
2
0
0
1
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
2
2
1
0
0
18
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
2
0
0
2
2
0
2
0
0
1
0
2
0
2
2
0
0
0
0
0
0
1
0
0
2
0
0
2
2
2
4
2
0
2
0
0
0
1
2
1
0
0
0
0
0
0
2
1
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
1
0
0
0
0
0
0
0
0
2
1
1
1
0
0
0
0
1
0
2
0
6
0
0
0
0
0
0
2
1
0
1
0
2
0
0
0
0
0
1
0
2
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
2
0
0
1
0
0
0
2
1
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
1
0
0
0
1
0
1
0
0
0
0
1
1
0
2
0
0
0
2
0
2
2
2
1
0
1
3
0
0
0
1
0
0
0
0
0
2
2
1
0
1
0
0
0
1
2
0
1
0
0
1
2
0
0
0
0
0
0
1
0
1
0
2
0
3
2
0
0
0
0
2
1
1
0
1
0
0
1
0
0
2
0
2
0
0
0
0
1
0
1
1
0
0
1
0
1
0
1
0
0
2
0
1
0
0
1
0
1
0
0
0
0
0
3
0
3
0
0
0
2
0
2
1
0
0
1
1
0
1
0
0
0
2
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
4
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
2
2
0
2
2
0
2
0
2
2
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
1
0
2
1
0
0
0
0
1
0
0
0
2
1
2
2
0
0
0
0
0
0
0
0
0
2
2
2
2
1
1
1
2
3
1
1
0
0
0
1
0
0
0
0
0
2
1
1
5
0
0
0
2
1
1
1
0
2
0
1
0
0
1
2
0
0
0
2
0
2
5
2
0
1
0
3
0
0
0
0
2
0
0
0
2
3
2
0
0
0
0
1
0
1
3
1
1
0
0
0
0
2
2
1
0
1
0
0
0
1
0
0
2
0
0
0
2
0
1
0
0
1
0
0
0
2
0
0
0
0
1
2
0
2
0
0
0
0
2
1
0
1
0
0
1
2
1
0
2
1
0
2
0
0
0
2
0
0
0
2
0
1
1
0
0
0
1
0
0
0
1
1
4
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
1
0
0
0
1
0
4
2
0
0
0
2
0
1
0
3
0
0
2
0
1
2
0
1
0
0
2
0
0
0
0
1
0
2
0
0
2
0
1
0
2
0
0
1
0
1
0
0
0
2
0
0
0
0
1
1
0
1
0
0
1
1
0
0
1
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
5
2
0
0
2
1
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
3
1
0
2
0
1
2
0
0
2
2
2
2
2
0
0
3
0
0
0
0
0
0
2
1
1
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
1
0
2
0
0
2
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
2
0
0
2
0
0
1
1
0
1
0
2
0
0
0
0
1
1
0
0
2
0
0
0
1
0
0
2
0
0
0
1
0
2
0
0
0
2
2
4
0
0
0
1
2
0
2
1
0
0
1
0
2
3
0
0
1
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
2
1
0
0
3
0
3
1
0
2
0
0
0
2
0
2
0
0
1
0
0
1
3
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
2
0
0
0
0
3
0
1
1
0
0
0
0
0
1
0
2
1
0
1
2
2
0
0
2
0
2
0
0
0
0
0
0
0
1
0
1
1
2
0
6
2
0
1
2
0
2
2
2
0
4
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
2
1
2
0
2
0
2
2
0
1
2
0
0
0
1
0
0
2
2
0
0
0
1
1
2
1
2
2
0
1
2
1
0
1
0
0
0
1
1
1
0
0
3
0
0
0
2
2
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
2
0
0
1
1
0
3
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
3
2
0
0
0
0
2
0
0
0
1
0
0
1
2
0
0
0
0
2
0
2
0
0
0
1
2
0
0
2
1
0
0
1
0
0
0
1
0
2
0
0
0
1
1
0
0
1
2
0
0
1
0
1
0
0
3
1
2
1
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
1
1
2
1
2
0
3
1
2
3
0
0
0
0
0
0
2
1
2
0
2
0
1
0
1
1
0
2
0
2
0
0
0
2
0
0
0
1
0
2
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
1
2
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
2
0
0
2
1
0
1
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
1
2
0
2
0
0
0
0
0
2
0
0
0
1
1
0
2
0
1
2
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
2
0
1
0
1
1
0
2
0
1
1
2
0
0
0
2
0
0
0
0
0
2
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
1
0
2
1
1
0
0
0
0
2
1
1
0
2
0
2
0
0
1
2
0
0
0
2
0
0
0
1
0
0
0
2
0
2
0
0
1
1
1
3
2
2
1
0
0
0
0
1
0
2
0
0
0
0
1
1
2
1
0
0
0
0
0
0
0
1
0
0
2
0
0
2
1
0
0
0
3
1
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
3
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
1
2
0
0
2
1
2
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
1
2
0
2
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
1
0
3
0
0
0
2
2
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
2
0
0
1
0
2
2
0
1
0
0
0
0
1
0
1
1
1
2
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
2
0
0
2
0
0
0
0
0
1
1
1
0
0
0
0
0
1
2
0
0
1
0
0
0
1
1
0
1
0
0
2
0
1
2
0
2
0
0
0
2
2
0
2
1
0
0
0
3
0
0
1
1
2
0
1
0
0
4
0
1
0
0
0
0
2
1
0
1
2
2
1
1
0
0
1
0
0
0
2
1
0
0
1
2
0
0
0
0
0
0
2
0
1
0
2
2
1
0
2
0
0
0
2
2
0
0
1
1
1
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
1
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
1
0
0
0
0
0
1
1
3
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
2
1
1
0
0
3
0
3
1
2
0
0
0
0
1
0
1
0
0
0
0
2
1
0
0
0
0
8
2
2
0
2
0
0
0
0
0
0
0
0
0
0
1
1
2
2
0
0
2
0
0
0
1
0
0
2
0
1
2
1
0
0
1
0
1
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
2
2
0
0
0
1
0
2
0
0
0
1
0
1
0
0
4
2
1
0
1
0
0
0
0
0
0
0
0
2
0
1
2
0
2
0
2
0
0
3
0
0
0
1
1
0
0
2
0
0
1
1
2
0
0
2
2
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
3
0
1
0
1
2
0
0
1
2
0
0
0
0
1
0
0
0
0
0
2
1
0
2
0
2
1
0
0
0
2
0
0
0
2
7
1
0
0
0
1
0
1
2
1
0
0
4
0
0
0
2
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
2
1
2
2
0
0
0
0
1
1
2
2
0
0
0
1
0
0
1
0
0
3
0
0
1
0
2
2
0
1
1
0
0
2
0
0
0
2
0
1
2
1
0
2
2
2
1
0
0
0
0
2
0
0
0
2
2
1
0
0
1
2
0
1
2
0
0
0
1
0
0
0
0
2
2
0
2
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
2
0
0
2
0
0
1
0
0
0
0
0
2
1
2
0
2
1
2
0
0
0
3
0
0
1
1
0
0
0
0
2
0
0
0
1
1
3
0
0
0
0
0
0
0
0
2
2
0
1
0
2
0
1
2
0
0
1
0
1
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
1
2
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
1
3
2
0
2
0
0
0
1
2
0
2
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
2
0
0
3
3
0
0
0
0
1
0
1
0
1
0
1
0
0
4
0
0
0
0
0
0
0
2
3
2
0
1
0
0
0
0
0
2
0
1
0
1
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
1
2
0
1
0
2
0
2
0
1
0
2
0
0
1
0
0
0
0
2
2
0
2
0
2
1
0
1
0
1
0
0
3
1
1
2
2
1
0
0
2
1
0
0
2
1
0
0
2
0
2
0
0
0
0
2
0
1
0
0
0
2
1
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
2
1
2
0
1
1
1
0
1
0
3
0
0
0
0
0
1
0
2
2
2
0
1
2
1
0
0
0
1
4
3
0
0
1
0
2
1
0
0
0
1
0
0
1
1
0
2
2
2
1
0
0
0
0
1
0
2
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
2
2
0
6
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
1
4
0
0
1
0
0
0
0
0
0
0
1
2
2
0
1
0
0
1
0
0
0
0
1
0
1
0
0
2
0
1
1
0
0
1
0
0
0
2
0
1
0
0
2
0
0
0
0
1
0
2
0
0
1
1
0
2
1
0
1
0
0
0
0
0
0
2
2
1
0
2
0
0
2
2
0
1
1
1
0
2
0
0
0
0
0
0
0
1
2
2
0
2
1
0
0
1
0
0
0
0
0
0
0
2
0
1
1
1
0
1
2
0
0
0
0
0
1
2
0
0
0
2
0
1
2
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
2
0
0
2
0
0
1
0
0
0
3
0
2
2
0
2
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
3
2
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
2
0
1
0
1
0
0
0
3
0
0
0
0
0
2
1
1
2
0
2
1
0
0
0
1
0
0
0
2
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
2
1
0
0
0
0
2
0
1
0
1
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
2
2
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
1
1
1
1
1
0
1
2
0
1
2
0
0
1
0
0
1
1
2
0
0
0
2
0
2
0
0
0
0
0
1
0
0
2
0
0
0
2
0
2
1
2
1
0
0
0
2
0
1
2
0
0
0
1
0
0
3
1
1
0
0
0
0
0
0
0
0
0
1
0
2
2
0
2
0
0
0
0
0
2
0
2
0
2
0
0
1
1
0
0
0
0
2
2
0
0
2
3
2
0
0
3
0
0
0
1
1
0
0
8
3
2
1
0
2
1
0
1
1
0
0
0
0
0
1
2
0
0
0
1
2
0
0
2
0
1
1
1
2
3
0
2
0
0
2
0
0
0
0
0
3
0
1
0
2
0
2
1
2
0
0
0
1
2
0
3
0
2
2
1
2
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
1
0
3
2
0
0
1
0
0
2
0
0
0
1
0
1
2
0
0
0
2
2
0
0
0
0
0
0
1
1
2
2
0
1
0
2
0
3
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
1
0
2
2
0
0
1
1
0
0
0
0
2
0
0
0
0
3
1
0
2
2
2
0
1
0
4
0
0
0
0
1
1
0
1
2
0
0
0
3
1
0
2
0
0
1
0
1
0
1
2
0
0
0
1
0
2
0
0
0
0
0
1
0
1
1
0
0
1
0
2
0
2
0
4
1
0
1
0
2
2
0
1
0
0
2
0
0
0
2
3
1
0
1
0
0
1
0
0
0
1
1
0
2
2
2
0
1
0
0
1
1
0
0
1
1
0
0
0
0
2
2
2
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
2
0
2
1
2
0
0
1
0
2
0
3
4
0
0
0
1
0
0
2
2
1
0
3
2
0
0
0
2
2
2
1
1
0
0
0
1
2
0
0
2
0
2
0
1
2
2
2
2
1
1
0
0
1
1
2
2
0
0
2
0
0
0
1
0
1
0
0
0
0
3
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
1
0
2
2
0
2
1
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
1
0
0
1
0
3
1
0
0
1
0
0
3
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
3
2
1
2
1
1
1
0
0
2
1
1
0
4
0
0
0
1
1
2
1
1
0
1
0
0
1
1
2
1
1
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
1
2
0
2
1
0
2
0
0
0
0
2
1
0
1
0
2
0
2
2
0
0
0
0
0
1
0
2
0
1
1
0
0
0
1
2
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
1
0
1
0
2
1
0
0
0
3
0
0
0
1
0
0
1
2
0
1
0
0
0
0
3
0
0
1
1
0
0
0
0
0
2
2
0
0
2
2
0
0
1
2
0
0
0
0
0
0
0
0
1
1
0
0
0
2
1
2
2
0
0
0
0
0
2
0
0
0
0
0
2
1
1
1
2
0
2
0
2
0
0
0
0
0
3
0
2
0
1
1
0
0
1
2
0
1
0
1
1
0
4
0
0
1
3
2
1
0
0
0
1
0
0
2
1
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
1
2
1
0
0
2
0
0
1
1
3
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
1
0
0
0
0
7
1
1
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
2
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
2
2
0
0
0
2
1
0
0
0
0
2
1
0
0
2
1
0
0
0
2
0
0
0
0
0
2
2
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
2
1
2
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
2
1
0
3
0
0
3
0
0
0
2
0
1
1
0
0
0
2
1
0
1
2
0
2
0
0
0
2
0
2
2
0
2
0
0
0
0
0
0
1
2
0
2
0
0
4
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
2
0
2
1
0
2
1
7
0
0
1
0
0
1
1
0
3
1
2
1
0
1
0
0
0
2
2
2
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
3
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
2
1
1
0
1
0
2
0
1
1
2
0
1
1
0
1
2
0
0
0
0
1
2
0
0
0
0
1
0
0
1
0
1
0
0
1
2
0
0
0
2
0
0
0
0
2
5
1
2
0
0
0
1
0
1
0
0
0
1
2
0
0
1
5
2
2
0
2
1
0
1
2
0
0
4
0
2
0
2
0
1
0
3
0
2
0
0
0
0
0
2
2
0
0
0
0
0
3
2
0
0
0
0
3
8
0
4
0
2
0
0
1
0
2
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
2
0
0
0
0
1
0
1
0
1
0
0
0
2
0
1
0
0
1
1
0
0
0
0
0
1
0
1
2
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
2
0
1
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
2
1
1
0
0
2
0
2
0
2
0
2
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
3
0
2
1
0
0
0
2
1
2
0
0
0
0
2
2
0
2
0
3
2
1
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
2
1
0
2
1
2
0
0
0
0
0
0
0
1
0
1
0
2
1
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
3
0
1
1
0
0
0
0
2
0
0
2
1
0
0
2
0
1
1
0
1
0
1
0
0
0
0
2
0
2
1
0
2
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
1
0
0
0
0
2
0
0
0
2
0
0
2
0
0
2
2
1
0
1
0
0
3
0
0
0
0
1
2
0
2
0
3
1
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
1
1
0
0
0
0
1
0
1
1
0
0
1
2
0
0
2
0
0
0
1
1
0
0
4
0
0
0
0
0
0
0
0
0
2
0
2
3
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
1
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
3
1
0
0
0
2
0
0
0
1
0
1
1
0
0
0
0
1
1
0
3
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
2
2
0
1
0
3
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
2
1
0
0
1
0
1
0
2
0
0
0
0
1
1
0
1
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
2
0
1
0
1
1
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
1
4
1
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
1
2
0
1
2
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
2
2
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
1
1
1
0
0
0
2
0
2
0
0
0
2
1
0
2
1
0
0
1
0
0
0
1
1
0
2
2
0
2
0
0
0
4
1
0
2
1
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
2
0
0
2
2
2
1
1
0
2
0
0
0
0
1
0
2
3
1
0
0
0
2
3
0
0
0
2
2
0
2
0
0
0
1
1
1
0
0
2
1
0
2
1
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
1
0
0
0
0
2
1
2
0
0
0
0
1
1
0
2
1
0
0
0
0
1
1
0
0
1
1
0
2
0
0
0
0
4
0
1
0
1
1
1
2
0
0
0
0
0
1
1
3
1
1
0
2
1
0
3
0
1
0
1
2
0
0
0
0
1
2
2
0
0
1
2
0
1
0
0
0
0
0
0
3
0
1
0
0
0
0
0
1
1
0
1
0
0
0
1
1
2
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
5
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
3
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
2
1
0
1
2
2
0
3
0
2
1
2
1
1
0
0
3
2
2
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
2
0
0
0
0
1
0
2
0
1
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
1
2
1
0
2
3
1
0
0
0
2
0
1
0
1
0
1
0
3
1
0
0
2
1
0
1
0
1
0
5
0
0
1
0
0
0
0
0
1
1
0
3
1
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
1
2
2
0
1
2
0
0
2
2
2
1
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
2
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
1
1
1
2
1
0
0
0
2
0
2
0
0
1
3
5
1
0
0
1
0
0
0
0
0
0
2
0
2
1
1
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
3
0
2
3
0
0
0
2
0
0
2
0
0
0
0
2
3
1
2
2
0
2
1
2
0
0
2
0
1
0
0
1
0
0
0
0
2
0
2
0
1
0
1
0
0
0
0
0
0
1
0
0
2
0
1
5
0
0
1
0
0
0
0
0
0
0
0
0
2
2
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
3
1
1
0
1
0
0
0
0
2
1
1
0
0
1
0
0
0
0
0
0
0
2
0
2
0
1
2
0
0
0
0
0
0
0
2
4
0
3
0
2
0
1
0
1
1
0
0
0
1
1
1
1
0
0
0
0
1
0
0
0
0
2
1
2
1
0
0
1
1
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
2
0
1
2
1
0
2
1
0
2
0
1
0
0
0
0
1
0
0
1
0
3
0
0
0
2
1
1
1
0
0
0
0
2
1
0
3
0
0
0
0
0
2
1
1
0
0
0
0
0
0
4
2
1
2
0
0
0
0
0
0
0
0
2
1
1
1
0
0
0
0
3
0
4
0
0
0
1
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
2
0
0
0
0
1
0
0
0
0
1
0
4
1
1
3
0
2
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
2
0
2
0
2
0
2
0
1
0
2
0
1
0
1
5
0
0
0
0
1
1
2
0
1
0
0
2
0
1
0
0
0
0
1
0
3
0
0
0
0
2
1
2
0
1
3
0
1
0
0
2
2
2
0
1
0
1
0
0
1
2
1
2
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
2
1
0
1
0
0
0
2
2
0
1
0
2
1
0
0
1
0
0
1
0
0
1
1
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
3
0
0
2
2
2
0
0
2
0
2
0
1
2
1
1
0
0
0
0
0
1
0
0
1
2
0
0
1
1
1
3
0
0
1
2
0
0
1
2
0
0
0
0
1
0
0
0
0
1
0
0
2
1
1
1
2
2
0
1
2
0
0
0
1
2
0
2
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
1
1
0
0
1
0
1
2
2
0
1
0
0
0
0
0
2
0
0
0
0
1
1
0
1
5
0
0
2
0
0
0
0
1
1
0
2
0
0
0
1
2
1
0
1
1
0
0
1
1
1
0
0
0
0
0
1
1
1
0
0
0
1
4
0
1
0
0
0
1
0
0
2
0
1
2
2
0
0
0
1
0
2
2
1
3
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
1
1
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
1
0
2
2
2
0
0
0
1
2
0
1
1
0
1
0
1
0
2
2
0
2
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
2
2
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
1
5
0
0
0
0
0
2
0
2
1
2
2
0
0
0
3
2
0
0
1
1
0
0
2
0
1
0
3
0
1
0
0
2
1
2
0
2
0
0
1
0
0
2
0
0
0
2
2
0
1
1
1
2
0
2
0
2
0
1
0
0
0
2
2
0
0
2
0
2
1
0
1
0
0
1
0
0
1
6
0
0
0
0
1
0
0
0
0
0
2
0
2
0
3
0
0
2
0
1
1
0
2
0
0
1
2
0
2
1
1
0
7
0
0
0
1
0
0
0
0
0
2
2
0
2
0
0
0
2
0
1
4
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
1
1
0
2
1
0
0
0
2
2
0
0
1
0
3
0
0
0
0
0
0
0
2
1
0
0
2
2
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
1
0
2
0
0
2
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
1
0
2
2
0
1
0
1
0
0
0
0
1
1
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
1
2
2
0
0
0
1
0
2
2
2
2
0
0
1
1
0
0
0
0
2
0
0
0
2
3
3
0
0
0
0
1
3
0
2
0
2
0
2
0
2
0
2
0
0
1
0
0
2
0
0
0
1
0
0
2
0
0
1
1
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
2
1
0
0
2
0
0
0
0
0
2
2
2
0
0
1
0
0
0
0
0
0
1
1
2
0
0
0
1
0
1
1
0
0
2
0
0
2
0
2
0
0
1
0
1
1
0
1
0
1
0
1
0
0
2
3
1
3
1
0
1
1
0
1
0
0
2
0
0
2
0
0
1
2
0
1
0
0
2
0
2
0
1
0
2
0
0
2
0
0
1
2
1
0
1
0
0
0
0
0
1
0
0
0
1
0
1
2
0
0
1
0
2
1
1
0
2
0
0
2
0
2
2
1
0
1
1
0
0
1
0
1
2
0
0
2
0
2
0
0
0
1
1
0
0
0
0
4
0
0
0
1
0
0
0
2
1
2
0
2
0
0
0
0
0
1
0
4
0
2
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
3
0
2
0
0
0
2
0
1
2
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
2
1
0
2
0
0
0
3
0
0
1
2
0
0
0
1
1
2
0
0
0
2
0
0
0
2
0
2
2
0
0
0
1
0
0
3
0
0
0
2
1
0
1
1
0
0
0
1
0
0
0
1
1
2
0
0
2
0
0
2
2
1
0
0
2
1
2
0
0
2
0
0
2
2
1
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
2
2
1
2
2
0
0
1
0
1
0
1
2
2
0
0
2
0
0
1
0
0
2
0
0
0
1
0
1
2
0
0
1
2
1
0
1
0
0
0
0
4
0
0
0
0
0
2
1
0
0
1
2
0
0
0
0
0
3
1
2
1
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
1
2
0
2
2
1
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
1
2
0
0
0
0
1
0
2
1
0
0
2
0
1
0
0
1
1
0
0
1
2
1
0
0
1
0
0
0
0
1
1
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
1
1
0
3
0
2
1
1
0
0
1
0
0
2
0
1
0
0
1
0
0
0
0
2
0
1
2
1
1
0
1
0
1
0
3
1
1
0
0
0
1
0
9
0
0
0
0
0
0
0
1
1
2
0
1
1
0
1
0
2
1
0
0
0
0
0
2
1
0
2
0
0
0
3
0
0
0
0
1
0
0
1
0
0
0
0
2
2
0
0
2
0
0
2
2
0
2
0
0
0
0
0
0
1
1
0
1
2
0
0
1
0
2
0
1
0
0
1
0
0
0
1
0
3
0
0
0
1
1
0
2
1
0
0
2
3
0
0
1
0
0
0
2
0
0
0
0
2
1
2
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
1
0
2
0
2
1
0
1
0
0
0
0
0
0
2
1
0
1
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
4
2
0
0
0
0
1
1
0
0
2
0
0
0
0
2
0
1
0
0
0
0
2
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
2
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
2
1
0
0
2
0
2
0
0
2
0
0
2
0
0
0
0
2
2
0
0
0
3
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
2
0
1
1
1
0
1
0
0
0
0
2
0
1
0
2
0
1
2
1
0
0
0
2
0
1
1
0
0
0
2
1
1
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
2
1
0
0
0
0
1
0
1
0
3
0
0
0
1
1
2
2
1
3
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
2
2
0
0
0
0
1
1
0
2
1
1
0
0
0
0
1
0
1
1
0
0
3
0
0
2
0
0
1
0
0
1
0
3
2
1
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
1
0
0
0
0
0
1
2
0
0
0
0
1
0
1
1
1
0
0
1
0
0
1
0
0
0
0
2
1
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
2
2
2
0
0
0
0
2
0
1
0
2
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
1
1
2
1
0
0
0
0
1
0
0
0
0
2
1
0
2
0
2
0
0
2
0
0
0
0
2
0
0
2
1
0
0
1
0
0
1
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
2
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
1
0
2
1
2
0
0
0
0
0
0
1
0
2
2
2
0
0
0
2
2
0
2
0
0
0
1
0
1
2
1
0
1
0
0
2
0
0
1
1
1
0
0
1
2
0
0
0
1
0
1
0
0
1
1
3
1
0
1
0
2
1
2
0
0
0
2
0
1
2
0
0
0
1
0
0
0
1
2
0
0
1
0
0
0
2
0
0
2
3
0
0
2
0
2
2
0
2
0
0
0
5
2
0
0
0
0
1
0
0
0
2
0
0
0
1
2
0
1
0
0
1
2
1
0
0
0
1
1
1
0
0
2
1
10
1
0
1
0
0
0
0
0
1
0
3
2
0
2
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
1
0
0
2
0
0
0
2
0
2
2
0
0
1
0
0
0
0
1
0
0
0
0
3
0
0
0
0
1
0
2
0
0
0
6
0
1
0
0
1
2
2
0
0
1
0
0
2
0
0
2
1
2
0
0
0
0
2
2
0
0
1
0
0
0
0
0
2
2
0
0
0
1
2
0
0
0
0
1
2
1
0
0
0
1
0
0
1
2
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
2
0
0
0
4
0
1
2
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
2
1
0
0
0
0
2
1
0
0
0
0
2
1
0
0
0
0
2
0
1
5
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
1
0
1
2
2
0
1
0
0
0
0
0
1
1
1
1
0
0
3
0
1
1
0
0
0
1
0
0
0
1
1
0
0
0
2
0
0
0
0
0
2
2
0
1
1
0
0
3
0
0
0
1
0
1
0
2
1
2
1
2
1
0
1
0
0
0
0
0
0
0
2
1
0
3
0
1
1
0
0
5
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
2
3
2
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
1
0
0
0
0
1
2
2
3
1
0
0
1
6
0
1
0
0
0
0
2
1
2
0
2
2
2
1
2
0
0
0
0
1
0
3
6
1
0
1
2
0
3
0
0
0
0
0
1
0
1
2
0
0
0
0
1
0
0
0
0
3
0
0
1
0
0
2
2
1
1
0
0
0
0
0
1
0
0
2
1
0
0
2
0
2
1
0
0
2
0
0
2
2
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
3
0
2
2
0
1
0
6
0
1
1
0
2
0
0
3
2
0
1
2
0
0
0
0
0
0
3
0
0
0
0
3
2
3
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
2
0
1
0
0
0
0
1
2
0
2
0
1
1
0
2
1
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
1
2
0
1
0
0
0
0
0
1
1
0
0
1
0
1
1
2
0
0
0
0
2
0
0
0
0
1
2
0
0
1
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
2
2
0
0
0
0
1
2
1
1
0
0
0
2
0
1
2
2
0
1
0
0
0
2
0
0
0
3
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
2
2
0
2
0
0
0
0
0
1
0
0
1
0
1
0
1
2
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
2
2
2
1
1
0
3
0
0
0
1
0
0
0
0
2
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
2
0
1
2
0
1
2
0
0
0
2
0
0
1
0
0
2
2
0
0
0
0
2
2
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
1
1
1
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
2
0
0
2
0
0
0
2
0
1
0
0
0
5
2
0
3
0
0
0
0
2
1
0
1
0
0
2
2
0
2
0
2
0
1
2
0
2
2
0
0
0
0
0
0
3
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
1
1
2
0
1
0
2
0
1
0
0
0
2
0
0
0
2
0
0
2
0
2
2
0
0
2
3
2
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
3
2
1
0
0
0
0
1
2
0
0
0
1
0
0
0
0
3
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
2
2
0
0
0
1
2
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
2
3
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
3
1
0
0
1
0
0
2
0
0
1
0
0
0
0
0
2
2
6
0
2
0
1
0
0
2
0
2
1
7
1
0
0
0
0
0
0
0
1
0
0
1
0
1
2
0
2
0
0
0
2
1
0
1
2
0
1
3
2
0
0
0
0
0
0
0
0
2
2
0
1
0
1
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
3
1
2
0
0
0
1
0
1
1
0
0
1
1
0
1
2
1
1
2
0
0
0
0
0
3
0
0
0
0
0
0
1
0
3
0
3
4
0
2
3
0
2
0
4
0
1
2
0
0
0
1
0
0
0
3
0
2
1
0
0
0
0
2
1
2
0
2
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
1
2
0
2
1
1
1
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
2
1
0
2
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
6
0
2
1
0
0
0
0
0
0
0
1
2
1
0
1
1
1
2
0
0
2
0
0
3
0
0
0
1
0
2
0
1
2
1
1
0
2
1
1
2
1
0
0
1
0
0
0
2
1
0
0
2
0
1
0
1
0
0
2
2
1
0
1
1
0
0
3
0
0
0
0
1
2
1
0
0
1
2
0
0
0
2
0
0
0
1
1
2
0
1
7
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
1
2
1
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
4
0
1
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
35
2
3
0
1
1
3
0
0
2
0
1
0
1
0
0
1
1
0
2
1
0
0
1
0
0
2
2
2
0
0
0
0
0
0
0
0
1
2
0
2
1
0
1
0
0
2
3
0
0
2
0
0
2
0
0
0
0
1
1
3
0
0
0
0
2
0
0
0
0
3
0
3
0
1
1
1
1
2
2
1
0
0
3
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
1
4
1
0
0
1
0
2
2
0
2
0
3
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
2
0
2
2
1
0
5
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
3
2
1
1
0
1
2
1
0
2
1
0
0
1
0
0
0
1
1
1
0
2
2
2
0
0
0
0
1
0
0
1
0
0
2
0
2
1
0
1
1
1
0
0
0
0
0
0
0
2
0
0
1
0
0
1
2
0
2
2
0
3
1
1
0
0
1
0
0
0
0
0
0
3
2
0
2
0
0
2
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
3
2
1
0
0
1
1
1
1
0
2
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
2
0
2
1
0
1
2
2
0
1
0
0
2
2
0
1
0
0
0
0
1
0
0
0
0
1
1
1
0
1
1
0
0
0
1
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
2
0
1
0
0
0
2
1
0
0
0
3
0
0
0
2
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
2
2
1
0
0
0
1
1
0
0
2
0
1
2
1
2
0
0
0
0
5
2
1
2
2
0
0
0
1
2
0
0
0
2
0
1
1
1
1
0
2
1
0
0
1
0
3
1
1
0
0
0
2
0
2
2
0
2
2
0
1
0
0
0
1
0
0
0
2
2
1
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
1
0
0
1
2
0
1
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
2
2
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
3
1
0
1
0
2
0
3
1
1
2
1
0
0
0
0
0
0
0
1
2
0
0
1
2
1
2
0
0
1
2
2
0
0
0
0
2
1
0
0
1
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
2
0
1
1
0
0
0
1
0
1
2
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
2
0
2
0
0
0
2
0
0
0
3
0
0
0
0
0
1
3
2
2
0
0
0
0
0
0
2
2
0
1
0
0
3
2
0
1
0
6
0
0
1
0
2
0
1
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
1
0
1
0
1
2
0
0
0
0
0
0
0
0
0
3
0
1
1
0
0
0
1
0
1
2
2
2
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
3
0
1
1
2
0
1
0
0
0
1
0
0
0
1
0
0
0
1
1
2
0
1
0
0
1
3
0
2
1
0
1
0
1
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
2
0
0
0
0
1
1
0
2
0
0
0
2
0
0
1
0
2
0
0
1
0
2
0
0
0
0
0
2
2
0
0
0
1
0
3
0
0
0
1
1
0
0
0
0
0
3
0
2
0
1
0
2
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
2
2
0
0
2
0
3
0
0
2
0
0
1
2
0
0
0
1
0
0
0
1
1
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
2
2
2
0
0
0
0
0
1
0
2
0
1
1
0
0
0
3
0
0
1
0
0
1
2
1
0
0
1
1
0
2
2
0
0
0
2
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
2
0
0
0
0
2
0
0
2
0
0
0
0
0
1
2
0
0
0
0
2
1
2
0
1
0
0
0
2
0
1
1
0
1
0
0
0
0
0
1
2
0
1
2
1
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
2
2
2
0
0
0
0
1
0
1
0
0
0
0
2
2
0
0
0
1
2
0
0
1
1
0
0
0
0
1
1
3
1
2
2
0
0
0
0
0
0
0
0
0
3
0
0
1
2
0
0
2
4
0
1
0
2
0
2
0
2
0
0
0
0
1
0
2
2
0
0
1
0
0
0
0
0
1
0
0
1
0
2
0
0
2
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
6
0
0
1
0
3
0
0
0
1
0
0
2
0
3
0
4
0
0
0
2
0
2
2
0
1
0
0
2
0
0
1
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
2
0
0
0
6
0
0
0
0
1
0
0
0
3
0
1
1
0
0
0
0
0
1
2
0
0
0
2
0
1
0
2
1
0
0
0
2
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
1
2
1
0
2
2
0
1
0
2
0
1
0
0
0
0
2
0
0
2
0
1
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
2
0
2
0
0
0
2
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
1
2
1
0
0
0
1
0
0
1
0
0
1
1
2
0
0
1
0
2
1
1
0
0
0
2
2
0
0
1
0
0
0
0
0
1
0
4
3
0
0
0
0
2
2
0
0
0
0
2
0
0
0
2
2
0
0
1
0
0
0
1
1
2
1
0
0
0
0
2
0
2
1
2
2
0
2
0
0
2
2
1
1
0
0
0
3
0
3
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
2
0
1
0
0
15
1
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
2
0
0
0
0
2
0
1
0
1
0
2
1
2
2
0
0
2
0
0
0
0
0
0
0
1
2
0
1
0
1
1
0
1
2
0
0
3
0
0
2
0
0
0
1
0
0
0
1
1
1
0
0
1
2
2
0
0
0
0
2
1
0
0
2
0
0
0
2
2
0
2
1
1
2
1
0
0
0
2
1
0
0
0
2
0
0
2
0
1
0
1
0
1
0
3
0
2
1
0
1
7
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
2
0
0
0
1
0
2
0
0
0
1
0
1
0
1
0
0
1
1
0
1
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
2
0
0
0
1
1
1
0
0
0
0
0
1
1
0
1
0
3
2
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
1
0
0
1
0
1
2
0
2
0
0
1
0
0
1
0
2
0
0
2
0
2
2
3
2
0
1
0
1
2
2
0
0
2
2
1
1
0
0
0
0
1
0
1
2
1
0
0
1
1
0
1
0
0
2
2
2
0
0
0
0
0
1
1
2
1
2
1
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
1
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
3
0
1
1
1
1
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
2
1
0
0
0
2
0
0
2
0
2
0
2
0
0
0
0
3
0
2
2
1
0
0
0
1
0
1
1
0
0
0
0
0
2
2
2
1
0
0
1
2
1
1
2
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
2
0
0
0
0
1
2
1
2
1
1
0
0
0
2
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
2
0
2
2
0
0
1
0
1
1
0
1
0
2
2
0
0
2
0
0
0
0
1
0
1
0
0
0
1
1
1
3
2
0
2
0
1
2
0
0
0
0
1
2
0
0
2
0
0
1
3
0
0
0
0
2
1
1
0
0
2
0
1
0
2
2
0
0
0
0
0
1
0
0
5
0
0
1
0
2
0
2
2
0
0
2
1
2
0
0
1
0
2
1
0
1
1
0
2
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
2
0
0
1
1
2
0
0
1
0
3
0
0
2
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
1
3
2
0
1
0
1
0
2
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
3
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
2
2
0
0
1
1
2
1
2
1
0
2
1
0
0
2
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
1
0
0
1
0
1
2
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
1
0
0
2
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
1
1
0
0
0
0
2
0
2
0
0
0
0
2
1
0
1
0
2
0
0
2
1
2
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
3
1
1
0
2
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
1
2
2
0
2
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
1
0
1
0
2
1
1
1
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
2
0
2
1
1
2
1
0
0
0
18
0
2
0
0
2
0
0
0
2
0
0
1
2
2
1
0
0
1
0
1
2
0
0
3
0
0
0
0
2
1
1
0
0
0
0
2
0
0
0
1
0
1
0
2
0
0
0
1
1
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
4
0
0
1
1
2
1
0
0
0
2
0
0
2
2
0
1
1
0
1
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
1
1
0
2
0
1
0
0
0
0
2
0
2
1
0
1
3
0
0
1
0
2
3
0
0
0
1
0
0
1
2
0
1
0
2
1
1
1
0
0
2
1
1
0
0
1
0
0
2
0
0
1
1
4
1
0
2
0
0
3
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
3
2
3
1
2
2
0
1
2
0
1
1
0
0
0
0
1
2
2
0
0
0
1
1
2
2
0
1
1
2
2
0
2
0
1
2
1
2
0
1
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
4
1
2
0
1
0
0
1
1
0
1
0
1
0
0
1
1
0
0
0
0
1
0
0
1
1
2
0
2
2
0
0
0
1
0
0
0
1
0
0
0
0
2
2
0
0
0
0
2
0
2
2
0
0
1
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
3
0
0
1
1
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
3
1
1
1
0
1
0
2
0
0
0
1
0
0
0
1
2
2
1
0
2
1
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
3
2
1
2
0
2
0
0
0
0
1
0
1
0
2
0
1
2
0
1
2
0
0
0
0
2
0
1
2
0
0
0
2
2
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
2
1
0
0
0
2
0
0
1
2
0
0
1
2
0
2
0
1
0
0
0
1
0
0
0
7
0
0
1
0
0
0
2
2
2
0
1
0
2
0
0
0
0
1
2
1
0
0
0
0
0
1
2
1
0
0
0
0
0
1
1
0
0
0
5
0
0
1
2
0
1
1
2
2
0
2
1
0
1
2
1
0
0
2
2
0
0
2
2
2
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
3
1
0
1
1
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
1
2
0
0
0
0
0
1
0
0
1
0
2
2
0
0
0
2
2
2
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
2
2
4
0
2
0
0
2
0
2
0
0
0
0
0
1
2
0
0
0
1
2
1
0
1
0
0
0
2
0
0
0
2
0
0
2
0
0
0
2
0
0
1
0
1
0
0
0
1
2
2
0
1
4
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
2
0
0
2
0
0
0
1
0
0
0
0
0
1
0
2
0
0
1
1
0
0
1
0
0
0
2
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
1
0
0
2
2
0
1
0
0
1
2
0
2
0
0
0
0
0
0
0
1
3
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
1
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
2
1
0
1
0
2
0
2
0
2
0
0
0
2
0
2
1
2
0
0
2
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
2
0
1
1
0
0
0
1
0
0
0
1
0
0
2
0
1
0
1
0
1
3
0
0
0
1
3
0
0
0
2
0
0
1
0
1
0
0
2
0
0
1
1
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
2
1
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
2
0
2
0
0
2
0
0
0
2
0
0
0
0
2
0
2
0
0
1
0
0
1
0
2
2
0
0
0
2
2
0
0
1
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
2
2
0
2
0
0
0
2
1
0
1
0
0
1
1
0
0
0
2
0
2
2
0
1
1
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
2
2
4
1
2
0
0
0
2
0
0
1
0
0
0
2
0
0
1
0
0
0
1
0
0
1
0
0
0
2
0
2
2
0
0
2
2
1
0
0
1
0
1
0
2
0
0
0
0
1
1
1
1
1
0
0
0
0
0
1
0
2
0
0
2
2
0
0
0
0
2
0
4
2
0
0
2
0
1
0
0
0
0
0
0
0
5
0
1
0
0
1
0
0
0
1
0
1
0
3
1
0
1
2
2
1
1
0
0
0
1
0
1
0
2
0
0
1
1
0
1
0
0
0
2
3
0
0
1
0
0
0
1
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
2
2
0
0
1
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
1
2
0
2
0
0
2
1
0
0
0
0
0
1
2
0
1
1
0
0
1
1
1
0
4
0
0
0
0
2
0
0
0
0
0
1
0
2
1
0
1
0
2
0
2
1
0
1
2
0
0
1
0
3
0
0
2
0
2
0
2
0
1
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
2
1
0
0
2
1
0
1
1
2
2
0
3
0
0
1
1
0
1
1
0
1
1
1
1
0
0
3
0
1
1
0
0
2
0
0
1
0
0
1
1
0
0
0
0
0
1
1
1
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
2
0
0
0
3
2
1
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
1
1
0
2
0
0
1
0
0
0
2
0
0
0
0
0
1
2
0
0
1
0
2
0
0
0
0
0
0
4
0
0
0
2
0
0
2
1
0
0
1
0
0
0
0
2
1
0
0
0
2
0
1
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
1
0
2
1
2
0
0
2
1
1
2
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
1
0
1
0
0
0
1
0
2
0
1
0
0
0
1
1
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
2
0
3
0
0
0
0
1
0
4
1
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
6
0
1
0
0
0
1
0
1
0
0
0
0
2
1
0
0
1
0
0
2
1
0
0
0
0
2
0
0
0
0
1
0
0
1
1
0
0
1
0
1
0
1
2
0
2
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
2
2
0
0
0
2
0
0
1
0
0
1
1
0
0
0
1
1
1
1
2
2
1
0
0
0
0
1
0
0
0
1
0
0
1
2
2
2
0
2
5
0
0
1
0
0
2
0
0
1
2
0
0
1
0
2
0
0
1
0
2
0
0
2
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
2
0
2
0
0
0
0
1
0
1
1
0
0
0
0
0
0
3
0
0
2
0
4
0
0
0
2
2
0
0
0
0
2
1
0
0
0
0
0
1
0
0
1
2
1
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
3
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
2
1
1
0
0
0
0
0
0
0
2
0
0
3
2
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
4
0
2
1
2
0
0
0
0
1
1
0
0
0
0
2
1
1
0
2
2
1
1
0
3
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
2
0
4
3
0
0
0
1
2
2
2
2
0
0
0
1
0
1
0
0
1
0
0
1
2
0
1
1
1
0
1
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
1
0
0
0
0
2
0
0
0
0
1
3
1
0
0
2
1
2
0
2
1
0
0
2
2
0
2
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
1
0
1
0
1
1
2
0
0
2
0
0
0
0
0
3
0
1
1
0
2
2
0
2
0
0
0
1
0
0
2
0
0
0
2
0
1
0
0
2
0
1
0
1
2
0
0
0
0
0
2
0
0
1
0
0
3
0
0
2
0
0
0
0
0
2
0
2
0
4
0
1
0
2
1
0
0
0
1
0
0
2
0
0
0
2
0
0
2
0
2
0
2
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
3
0
0
0
2
1
2
0
0
2
0
0
2
1
0
1
1
0
1
0
2
3
1
0
2
0
2
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
1
0
1
0
0
0
0
0
2
2
0
0
0
3
2
1
0
1
2
0
0
2
0
2
0
2
0
2
0
0
0
0
0
0
0
3
0
1
2
0
2
0
0
0
0
0
1
0
3
2
0
0
1
0
0
1
0
0
0
0
1
0
0
2
0
1
1
0
0
2
0
0
0
0
0
2
0
2
0
2
0
2
0
1
3
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
1
0
1
0
2
0
1
0
0
0
0
1
2
0
0
0
2
0
0
0
1
0
0
3
0
0
0
0
1
0
1
2
0
0
0
2
1
2
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
1
0
2
0
2
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
1
0
0
0
0
2
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
3
2
0
0
1
0
1
0
3
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
2
1
2
0
2
0
0
0
1
3
2
1
1
1
1
1
0
1
0
0
0
0
0
0
0
1
2
0
1
1
1
0
0
1
0
0
1
0
0
0
1
1
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
2
1
2
0
2
0
0
0
0
2
0
1
0
0
1
0
0
0
0
2
1
1
0
0
0
0
2
1
1
1
0
0
1
0
2
1
0
1
1
1
0
2
0
0
0
0
1
0
1
1
2
0
0
0
3
0
0
3
0
1
0
2
1
1
0
0
0
0
2
4
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
1
0
2
0
0
0
2
0
1
1
2
0
1
0
0
1
0
2
0
0
1
2
0
2
2
0
0
0
0
1
0
1
3
1
0
2
2
2
1
0
1
0
2
0
3
0
2
0
1
0
0
2
1
0
0
1
2
2
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
2
0
0
2
1
0
3
0
1
0
0
0
1
0
1
1
1
0
0
0
1
2
2
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
2
0
2
1
1
0
0
1
0
0
0
0
1
0
0
0
4
0
0
0
0
1
0
2
0
0
0
1
2
0
2
2
0
2
0
1
0
0
0
1
1
0
0
0
1
1
0
0
0
1
3
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
1
1
2
0
0
0
0
0
1
1
0
0
0
0
0
0
2
1
0
0
1
1
0
1
1
0
0
0
0
1
2
2
1
1
0
2
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
1
0
2
2
0
0
0
2
0
0
1
0
0
2
3
2
1
2
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
2
1
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
1
0
2
0
0
0
0
0
0
1
0
3
1
1
1
0
0
0
0
2
1
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
4
0
3
0
2
0
2
1
2
0
0
2
0
0
2
0
0
1
0
0
2
0
0
1
0
0
2
0
3
0
3
0
0
0
0
0
0
1
1
0
0
0
0
1
2
0
0
0
1
2
1
0
0
1
0
2
0
1
0
0
0
0
0
0
0
2
1
2
0
2
0
3
2
0
0
0
3
0
3
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
1
2
1
2
0
0
2
0
0
0
3
1
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
2
1
0
4
0
2
0
0
1
1
0
0
0
1
0
0
1
0
0
0
1
2
0
0
2
0
1
0
0
0
1
0
1
0
1
2
0
2
0
0
1
0
0
0
2
1
0
0
0
0
1
0
0
0
0
1
2
0
1
0
2
0
0
0
0
2
1
1
0
1
2
0
0
2
0
0
2
0
0
1
1
2
3
1
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
2
0
2
1
1
0
0
0
2
0
0
1
2
0
0
0
0
1
0
1
0
2
1
0
0
1
2
2
0
0
0
0
1
0
1
0
1
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
1
0
1
0
2
2
0
1
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
1
1
0
0
1
2
0
0
0
2
0
0
0
0
3
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
2
1
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
1
0
0
0
0
0
1
0
1
2
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
2
0
0
0
2
0
0
2
2
0
4
0
2
1
0
0
2
1
1
2
0
1
0
2
0
0
1
0
2
0
1
0
2
2
0
0
0
0
0
1
0
0
0
0
1
2
0
0
2
0
4
0
0
0
2
2
0
0
0
2
0
0
1
1
0
1
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
1
0
0
1
0
1
0
0
2
0
2
0
0
1
0
2
0
2
0
0
2
0
0
0
0
0
1
0
2
1
0
0
2
2
0
0
2
1
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
2
0
2
0
0
2
0
0
0
2
0
0
2
1
0
0
0
2
0
0
1
0
2
0
0
1
0
2
0
0
1
0
0
0
2
0
2
0
0
0
0
0
1
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
1
0
0
0
2
3
1
1
0
4
0
0
2
0
1
0
0
2
0
2
0
3
0
0
0
1
0
2
0
3
0
0
6
0
0
0
1
3
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
2
1
1
0
1
0
1
1
0
0
2
0
2
1
0
0
0
1
0
0
0
1
0
0
0
1
0
2
0
0
0
2
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
2
0
0
2
2
0
0
0
0
1
1
0
0
1
0
1
0
1
0
1
0
1
1
2
2
0
0
0
0
0
1
1
1
0
0
0
1
2
1
2
0
2
1
2
3
0
0
2
0
4
3
1
0
0
1
0
0
1
1
0
0
2
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
1
1
0
2
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
1
0
0
1
0
2
1
0
0
1
0
2
0
0
1
0
1
0
4
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
2
0
0
2
2
2
0
2
0
0
0
1
0
0
2
0
0
2
0
4
0
0
3
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
2
1
0
0
1
0
3
0
7
2
0
0
1
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
1
0
1
0
1
2
0
0
0
1
0
0
0
1
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
3
1
0
0
0
0
1
2
0
2
2
0
1
0
2
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
1
2
0
0
0
1
5
2
0
0
0
0
0
2
0
1
1
1
0
0
0
0
0
0
2
0
1
0
0
0
1
0
2
0
2
0
2
0
0
2
0
0
0
2
0
2
2
0
1
1
0
0
0
0
1
0
1
2
2
1
2
0
1
0
0
0
0
0
0
0
0
0
0
2
5
2
2
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
1
0
0
2
2
2
0
1
0
1
0
0
1
0
0
1
0
0
0
1
1
2
0
1
0
0
1
0
0
1
0
2
0
0
0
0
0
2
1
2
0
0
0
1
0
0
0
2
1
0
1
2
0
0
1
3
0
0
1
0
0
9
2
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
3
2
0
0
0
1
0
0
0
2
0
0
2
0
2
0
1
0
0
0
1
2
4
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
2
0
0
2
1
2
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
2
2
2
1
1
2
2
0
0
1
2
0
2
1
0
0
0
0
0
0
0
2
0
2
0
0
1
1
2
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
2
0
2
0
0
1
0
0
0
0
3
0
0
2
2
2
0
0
2
1
0
0
1
0
0
1
0
0
0
0
2
0
0
1
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
2
0
1
2
0
0
0
2
0
2
0
0
0
0
2
0
2
1
1
2
2
0
0
0
0
0
1
0
0
1
0
0
2
1
3
0
1
0
0
0
2
0
2
0
0
2
0
0
1
0
1
2
0
0
0
2
0
3
0
0
0
0
2
0
2
0
0
0
0
0
0
2
1
2
0
0
0
2
3
0
2
0
0
0
2
0
2
0
1
0
0
0
1
0
1
0
1
2
0
0
1
1
1
1
0
1
0
0
0
0
0
0
0
1
1
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
3
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
2
1
0
2
0
0
1
0
0
1
0
0
0
2
2
2
0
0
2
1
0
0
0
1
1
0
0
0
0
1
3
1
0
1
0
0
0
0
0
1
0
1
0
1
0
0
2
3
0
0
2
2
1
0
0
0
0
0
0
1
2
2
2
0
0
2
0
2
0
0
1
1
0
0
0
1
2
0
1
0
0
0
0
1
2
0
0
0
0
1
0
1
0
1
3
0
0
0
0
0
1
1
1
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
2
0
0
0
2
0
0
1
0
1
2
0
1
0
0
2
0
0
1
1
1
0
0
2
2
0
1
0
0
1
2
1
0
3
0
0
2
1
0
0
0
0
0
0
1
0
2
1
0
0
2
0
0
1
1
0
0
0
0
0
0
0
1
0
0
2
1
1
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
1
2
2
0
0
2
0
1
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
1
2
0
0
2
2
0
0
1
0
0
0
0
0
1
0
0
0
0
3
0
1
0
0
0
2
1
1
1
2
0
1
2
0
0
0
4
0
0
0
1
0
0
0
2
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
1
2
0
1
1
0
1
0
0
0
2
0
0
0
0
1
0
0
0
2
2
0
3
0
1
0
0
1
3
1
1
1
0
0
1
0
2
0
1
0
1
0
1
0
0
0
3
0
1
0
0
1
0
1
0
2
0
2
0
0
1
2
0
0
0
0
0
1
0
0
0
2
1
1
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
1
0
1
0
0
0
0
1
0
0
2
0
0
0
1
2
0
0
0
0
0
0
1
0
2
0
0
0
0
1
1
2
1
3
2
1
1
2
0
0
0
1
0
1
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
1
2
0
0
0
0
1
1
0
0
0
0
0
0
2
1
0
1
0
1
1
1
1
2
0
1
0
0
2
0
1
2
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
1
2
0
1
2
0
0
0
1
0
1
3
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
3
0
4
0
2
0
0
0
1
1
1
0
3
0
0
0
0
2
1
2
0
1
0
0
1
2
0
0
0
0
1
0
0
0
0
1
0
1
2
1
0
0
0
0
1
0
0
1
0
2
0
1
1
0
0
0
0
2
2
0
0
0
0
1
0
5
1
1
0
1
0
1
0
0
1
2
0
0
0
0
2
2
1
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
1
1
0
2
0
0
2
2
1
0
0
1
0
1
0
1
1
0
0
0
2
0
1
0
1
0
1
0
0
2
0
0
0
1
0
1
0
0
0
2
0
1
2
0
1
0
0
4
2
2
0
1
0
1
1
1
0
1
2
0
0
1
2
0
0
0
0
1
0
2
0
0
1
0
0
1
1
2
0
2
1
0
1
1
1
0
1
1
0
2
0
0
1
1
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
2
1
1
0
0
0
1
1
2
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
1
2
1
1
0
1
1
0
0
0
2
2
0
0
0
0
1
1
2
2
0
0
0
0
1
0
2
0
1
0
2
0
0
1
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
2
0
1
0
1
0
0
1
0
1
1
0
0
2
0
0
1
0
2
2
0
2
1
0
1
2
2
2
1
0
0
0
0
0
0
2
0
1
8
1
0
1
1
0
0
1
0
0
0
10
0
0
0
0
1
1
0
0
0
1
0
2
0
0
0
0
0
4
0
0
0
2
0
2
0
0
2
1
2
0
0
0
0
0
0
0
1
2
0
3
1
2
2
0
0
2
0
0
0
0
4
2
0
0
2
0
0
0
2
0
2
1
0
2
0
0
0
2
0
0
1
0
0
1
2
2
0
1
0
0
0
0
1
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
1
1
0
0
1
2
0
0
0
1
0
0
0
0
0
1
0
2
0
1
0
0
0
0
2
2
0
2
0
2
1
1
2
0
0
0
3
1
0
2
0
0
0
0
2
0
1
1
1
0
0
2
0
2
0
1
0
0
0
1
2
0
0
1
3
0
0
1
1
2
1
0
1
0
2
0
0
0
0
0
0
0
2
1
0
2
1
0
0
2
2
0
1
0
0
0
0
0
0
1
2
0
1
0
0
3
1
0
0
0
0
0
1
1
2
0
0
1
0
0
0
0
1
0
1
2
1
0
2
0
0
2
0
2
2
0
2
0
0
2
0
0
1
2
0
2
0
0
1
0
0
0
1
0
1
2
0
2
0
0
0
0
1
2
2
2
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
1
2
1
0
0
0
0
1
2
0
0
2
1
0
0
1
0
0
2
2
1
1
0
2
2
0
0
0
2
0
0
2
2
3
1
0
0
2
0
0
0
2
2
0
2
2
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
2
2
0
1
2
2
0
2
0
0
0
0
2
2
0
0
0
0
3
0
2
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
2
0
2
2
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
1
0
3
1
1
0
0
0
2
1
2
2
0
0
3
0
0
4
2
2
1
0
0
0
1
0
0
0
1
0
2
0
1
1
0
0
0
0
2
0
0
0
2
1
0
1
0
2
0
0
0
1
0
0
1
1
1
0
2
0
0
2
2
1
0
1
1
1
0
3
3
0
1
1
0
0
0
1
0
0
1
4
2
0
1
0
2
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
1
2
0
2
1
1
0
0
2
1
0
0
0
0
2
0
0
0
2
0
0
0
1
1
1
0
0
1
0
0
0
0
1
0
0
1
1
0
1
1
0
0
0
0
2
1
0
1
4
0
0
0
1
0
0
0
1
0
2
0
0
0
1
3
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
2
1
1
0
0
0
0
1
0
2
1
0
1
0
0
0
2
0
0
0
2
0
3
0
1
0
0
0
2
0
0
2
0
2
1
0
1
0
2
0
1
0
0
0
0
0
2
0
1
0
1
2
2
1
0
0
0
2
0
0
0
0
1
0
1
4
0
2
0
2
0
2
2
0
0
0
0
0
0
0
0
1
2
1
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
1
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
2
0
0
1
2
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
1
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
1
2
0
3
2
0
0
0
0
2
0
0
0
0
0
0
1
2
0
2
0
0
0
2
0
1
0
1
2
2
0
1
0
1
1
0
0
0
0
1
0
1
0
1
2
0
0
2
0
1
1
2
1
0
0
0
0
0
0
0
0
3
0
1
0
3
0
0
0
1
2
1
0
0
0
2
1
6
0
0
2
1
0
0
1
1
0
0
3
2
1
2
2
2
1
0
0
0
2
0
3
0
0
0
0
0
2
0
0
1
0
1
0
1
0
2
0
1
2
2
1
1
0
0
4
1
0
0
2
0
0
0
0
0
1
0
2
1
0
2
0
0
2
0
1
2
2
0
0
0
2
0
0
2
0
0
0
0
2
0
1
0
1
0
0
0
0
0
1
0
1
3
0
0
0
1
1
1
0
0
0
0
1
1
2
0
0
0
0
1
1
0
2
0
0
1
2
2
0
2
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
2
2
0
1
1
0
1
3
1
0
3
0
0
0
2
0
0
1
1
0
2
0
0
0
2
2
0
1
0
0
0
1
2
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
1
2
0
0
1
0
0
2
1
0
0
0
0
2
0
0
2
2
0
1
2
0
2
0
1
1
1
0
0
2
1
1
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
2
2
1
0
0
0
0
2
0
2
0
1
1
1
1
0
0
1
2
0
0
2
0
0
0
0
1
0
1
1
0
2
2
0
0
0
2
1
0
1
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
11
0
3
2
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
4
0
1
0
2
0
0
0
4
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
1
2
0
2
0
1
1
0
2
2
0
0
2
1
2
0
0
1
0
0
0
1
0
0
0
0
2
1
0
0
3
1
0
0
1
0
1
0
1
2
0
0
2
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
2
1
0
0
0
3
1
0
0
2
2
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
1
0
0
0
0
0
1
2
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
3
0
3
0
0
3
2
2
0
0
0
0
1
1
0
1
1
2
1
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
2
0
0
1
1
1
0
0
2
1
0
0
2
0
1
1
0
1
2
0
1
0
0
2
3
1
1
0
0
1
2
0
0
0
0
0
0
1
0
2
1
1
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
3
1
0
1
2
2
0
0
2
2
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
1
2
0
1
0
1
1
0
0
0
2
0
0
0
0
0
2
0
0
2
1
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
1
0
0
1
0
2
0
0
4
1
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
3
0
1
0
0
0
0
2
0
0
0
0
2
0
2
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
2
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
1
2
1
3
0
0
0
2
3
0
0
1
0
2
0
1
0
0
0
0
2
0
2
0
0
0
0
2
2
0
0
0
0
2
2
0
0
1
0
1
0
3
1
4
2
2
0
0
0
1
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
1
2
0
0
1
2
0
0
0
0
1
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
2
0
0
1
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
2
1
0
0
0
0
0
2
0
0
1
0
0
2
0
2
0
0
1
0
1
0
2
2
0
0
0
2
4
0
0
0
0
0
1
1
0
0
0
2
0
0
2
2
1
0
0
2
2
0
0
0
2
0
2
0
2
0
2
0
2
0
0
0
0
0
2
1
0
1
2
1
1
2
2
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
1
0
1
0
1
3
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
1
0
0
0
0
0
1
0
0
2
0
1
2
0
0
1
0
0
1
0
1
1
0
0
0
1
0
0
2
0
1
0
1
0
2
1
3
2
0
1
2
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
1
0
0
0
2
0
1
1
0
0
0
0
0
2
0
0
0
0
2
1
1
0
2
0
1
0
0
1
0
0
0
0
0
0
2
0
0
3
0
2
0
0
0
2
0
0
0
0
0
2
2
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
2
2
1
0
2
0
1
0
0
1
1
1
2
0
0
0
1
1
1
0
0
0
0
0
0
1
0
2
0
1
0
0
0
1
2
0
0
1
0
0
0
2
0
2
0
1
0
0
0
2
0
2
1
0
2
0
0
0
2
0
0
1
0
0
1
1
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
3
0
2
0
1
0
1
0
2
0
1
0
0
0
2
0
0
1
0
0
0
0
0
2
1
0
0
2
0
1
2
0
1
2
1
1
0
0
1
1
1
1
0
0
0
0
0
1
2
2
2
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
1
2
0
0
0
1
2
0
0
2
2
2
0
2
2
1
1
0
0
0
0
0
0
0
3
1
2
0
0
1
0
0
0
1
0
0
4
1
1
0
2
0
0
0
1
1
0
0
0
2
2
1
3
2
0
2
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
1
1
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
2
0
2
3
2
0
0
2
0
0
0
0
2
0
1
2
0
1
2
0
1
0
2
0
0
2
1
2
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
1
1
0
0
1
1
2
0
0
0
1
0
1
0
0
1
1
1
0
0
0
0
0
1
1
0
1
0
1
1
0
0
4
1
0
1
2
1
2
0
0
0
1
2
6
2
0
0
1
2
0
0
0
0
2
1
0
0
1
1
0
0
0
0
1
1
0
1
0
2
0
2
0
1
0
1
1
0
0
1
1
0
2
0
2
0
0
0
0
0
1
1
2
0
1
0
0
0
0
0
2
0
1
1
1
0
2
2
1
0
0
0
2
0
0
0
0
2
1
0
0
1
0
3
0
0
0
0
1
1
3
1
0
0
0
0
1
0
0
2
2
0
1
2
0
2
0
2
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
1
0
1
0
1
0
0
0
0
0
0
1
2
0
0
0
1
2
0
2
0
1
0
0
0
0
2
1
2
0
0
1
0
2
0
2
1
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
2
0
1
0
0
2
2
0
0
2
0
0
0
0
0
0
1
0
2
2
0
1
1
0
0
0
0
0
1
0
2
1
0
2
0
0
0
0
3
0
1
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
1
1
0
2
0
0
0
1
1
2
0
1
0
0
1
2
0
0
0
2
2
0
0
0
1
0
0
1
0
2
5
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
1
0
0
0
2
0
0
1
0
0
0
0
2
1
1
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
3
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
2
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
1
2
2
0
1
0
0
1
1
0
0
1
2
0
0
1
1
0
1
1
0
0
0
0
1
1
0
0
1
1
0
0
0
2
2
0
0
3
0
0
1
0
0
0
0
0
0
9
2
2
0
1
1
0
0
0
0
2
0
2
0
2
1
0
0
2
0
0
0
2
0
0
1
0
0
2
0
0
1
1
1
0
2
1
0
1
2
0
0
0
0
2
2
2
1
0
0
0
0
0
1
0
0
0
0
2
2
2
2
0
1
0
0
0
0
2
0
0
0
0
2
1
1
0
0
0
2
0
0
1
2
2
0
0
0
0
0
0
2
0
1
1
2
1
1
0
0
0
0
1
0
1
1
0
0
0
1
2
1
0
0
0
0
2
0
0
1
1
0
2
0
0
0
0
0
0
3
2
0
1
0
0
3
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
2
0
1
0
0
0
0
0
0
1
0
0
2
1
0
1
0
1
0
1
2
0
0
0
0
1
2
0
2
0
0
1
2
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
2
2
0
0
0
1
0
0
1
0
0
0
1
0
0
2
0
0
1
2
1
0
0
0
0
1
1
2
1
0
0
0
2
2
0
0
1
0
0
2
0
1
0
0
1
0
0
1
0
1
0
0
0
1
0
2
0
0
0
1
1
2
2
0
2
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
1
0
2
0
1
1
3
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
2
0
1
0
1
0
3
0
1
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
1
1
2
0
1
0
3
0
0
2
2
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
1
0
2
0
2
0
2
0
3
1
0
0
1
0
0
1
4
1
1
0
1
0
0
0
0
0
0
1
1
0
0
2
0
0
0
1
0
2
0
1
0
0
0
1
0
2
2
0
1
1
1
8
0
0
0
1
0
1
0
2
1
0
1
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
1
0
0
0
2
0
0
1
2
0
2
0
0
7
3
0
0
0
0
0
0
1
2
0
1
0
0
0
0
1
0
0
1
2
0
0
1
0
2
3
0
1
0
0
0
2
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
3
0
2
1
0
0
0
1
0
1
2
2
0
0
2
0
3
1
0
1
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
2
0
0
1
1
0
0
0
2
0
2
0
2
0
0
2
2
0
0
1
1
2
0
0
3
2
0
0
0
1
0
2
1
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
1
1
0
7
0
2
0
0
0
0
0
0
2
0
0
0
1
0
1
2
3
1
1
0
1
0
0
1
2
1
2
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
1
0
1
0
1
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
2
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
3
0
1
0
0
2
2
0
2
1
0
1
1
2
0
0
0
0
2
1
2
4
0
1
0
1
0
1
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
1
0
0
0
2
0
0
0
0
0
1
1
0
2
2
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
2
0
0
2
0
0
0
0
5
0
0
1
0
2
0
0
0
0
0
0
0
0
3
0
3
0
0
0
0
0
0
0
2
0
0
0
0
3
0
1
0
0
1
1
0
2
0
0
1
1
0
0
0
0
1
0
1
1
2
0
2
2
0
0
0
2
0
1
0
0
0
0
0
1
0
4
0
0
3
0
0
0
1
0
0
1
0
2
0
2
2
2
0
0
0
0
0
1
2
1
0
0
0
0
0
0
1
1
0
0
0
1
2
3
0
4
0
2
4
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
2
0
0
0
2
0
0
0
1
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
1
0
0
1
3
0
0
0
2
2
1
0
1
1
0
0
1
1
0
0
0
1
0
2
1
1
0
0
0
1
2
2
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
1
3
0
2
0
0
0
2
2
2
0
0
0
0
0
2
2
2
0
0
0
0
2
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
1
3
0
0
0
0
0
0
1
1
2
0
1
0
0
0
1
0
0
0
2
0
2
1
1
0
0
2
0
1
1
1
0
1
0
0
0
0
1
1
0
1
0
0
2
0
0
0
2
1
0
2
0
1
0
0
0
0
0
1
0
2
2
0
2
0
1
0
0
0
0
0
2
1
0
0
0
0
0
1
2
0
0
0
0
2
2
0
2
1
0
0
0
0
1
0
0
0
0
1
0
1
0
2
0
1
2
2
0
0
0
0
1
3
0
2
2
2
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
2
2
0
0
1
0
0
0
0
1
0
0
0
2
0
2
1
0
1
0
0
0
1
0
0
0
1
4
2
1
0
0
1
0
1
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
1
0
1
0
0
0
1
1
0
0
2
0
0
3
1
1
1
0
0
1
0
1
2
0
0
1
1
0
1
0
0
0
0
0
2
1
2
0
0
0
2
0
1
1
1
2
0
0
2
1
0
0
1
0
0
0
0
2
2
0
2
1
0
2
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
5
0
2
0
0
0
0
0
0
2
0
2
0
1
1
0
2
0
1
4
1
0
1
0
0
0
2
0
0
0
2
1
0
2
0
0
0
1
0
0
0
0
3
0
0
1
2
2
0
0
0
0
1
1
0
0
0
2
0
0
0
4
1
2
0
0
2
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
1
2
0
0
0
1
0
1
2
0
0
0
0
0
0
2
1
0
0
0
0
0
6
0
1
0
0
2
0
1
2
1
0
0
2
2
0
0
0
0
1
0
2
0
0
0
0
1
2
3
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
1
0
2
0
1
3
0
1
0
1
0
2
2
0
0
0
1
1
0
0
0
0
1
2
0
0
0
0
0
1
0
2
0
2
0
3
0
0
3
0
1
2
0
3
0
0
0
0
1
2
0
0
0
0
0
2
0
1
1
1
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
1
2
0
0
2
2
4
1
2
0
0
0
3
2
0
2
3
2
2
1
1
1
1
0
1
0
1
2
0
3
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
1
0
2
1
1
1
2
0
0
1
1
1
2
0
1
0
0
0
2
0
2
1
2
0
0
2
0
0
0
0
0
0
2
0
1
0
0
1
1
2
0
2
2
2
1
1
0
1
0
2
1
0
1
0
1
0
0
0
1
0
0
0
0
3
1
0
2
0
0
0
0
0
4
1
0
1
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
4
2
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
3
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
1
0
0
1
0
2
1
0
2
1
1
0
0
2
3
0
0
2
0
2
0
0
1
4
0
0
1
1
0
0
0
0
0
2
0
1
0
0
0
0
2
1
0
0
1
1
1
1
0
2
1
0
0
0
0
0
0
0
0
1
1
0
0
1
1
1
2
2
0
0
0
0
0
0
2
1
0
1
0
0
0
1
0
2
0
0
0
1
1
1
2
1
0
0
0
0
1
0
2
1
0
2
0
0
0
1
2
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
2
0
2
0
0
2
0
1
2
0
1
1
0
0
2
2
0
0
0
0
1
0
0
0
0
2
2
0
2
2
1
0
0
0
0
0
0
0
1
0
0
1
2
1
2
0
1
0
0
0
2
0
0
0
0
1
0
0
2
0
0
1
0
0
1
0
0
5
0
0
1
0
0
1
0
1
0
1
0
0
2
2
1
2
0
0
0
1
1
2
1
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
1
2
0
0
0
0
0
0
0
1
0
2
2
1
1
0
0
1
1
1
0
0
0
0
0
0
0
1
4
0
0
0
1
1
0
0
0
2
0
0
3
0
0
5
0
0
0
2
1
0
1
0
0
1
1
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
1
0
0
0
0
2
0
0
3
0
2
0
0
2
1
1
1
0
1
0
0
0
1
0
0
2
0
0
0
2
0
0
2
0
0
0
2
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
1
1
1
0
1
0
1
2
0
2
1
1
1
2
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
2
2
0
1
2
0
1
2
1
1
0
3
0
2
0
0
3
3
0
1
1
2
0
1
0
0
2
0
0
0
2
2
0
1
2
0
0
0
0
0
0
0
0
0
1
1
0
2
1
0
2
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
3
1
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
2
0
0
0
1
2
1
3
1
1
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
2
1
2
1
0
0
1
1
0
0
1
2
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
1
1
0
0
0
0
1
0
1
0
0
2
0
1
1
2
0
0
0
2
1
2
0
0
0
0
1
0
1
2
0
1
0
1
2
0
1
0
0
0
0
1
2
0
0
0
0
0
0
1
0
2
1
1
0
1
3
0
0
0
2
3
1
0
2
1
0
2
0
2
0
0
2
0
2
0
2
0
0
2
0
0
2
1
0
0
0
2
0
0
1
1
0
3
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
2
1
0
0
0
0
0
0
1
2
0
3
0
1
0
3
0
0
0
2
0
3
0
1
2
0
2
0
0
0
0
0
0
1
0
0
2
0
1
2
2
0
0
1
2
2
1
0
0
2
0
2
0
2
2
2
1
1
1
2
0
0
0
0
1
1
2
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
3
0
1
1
2
0
0
1
3
0
0
1
2
1
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
2
2
1
0
2
0
0
0
2
0
2
2
0
2
0
0
1
0
0
2
0
0
1
0
3
0
0
1
0
0
1
2
1
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
2
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
5
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
3
2
1
1
2
0
0
2
0
0
0
0
0
2
1
0
2
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
2
0
0
2
0
2
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
1
0
1
1
1
0
0
1
2
0
2
0
1
0
1
0
1
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
2
1
0
0
1
0
0
3
0
0
0
0
1
2
3
2
0
0
4
1
0
1
0
0
1
2
0
0
2
2
1
2
0
0
1
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
2
1
0
1
0
2
0
0
0
2
0
1
1
0
3
0
0
0
0
2
0
6
0
2
0
0
1
1
0
1
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
1
0
2
0
4
2
0
2
2
2
0
0
0
0
0
2
1
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
5
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
1
0
0
2
1
0
1
0
0
0
1
0
0
2
1
0
0
0
1
1
2
2
0
0
0
0
0
0
0
1
2
2
1
0
0
2
0
0
0
2
0
0
0
0
1
3
0
0
1
2
0
3
0
0
0
1
0
0
2
1
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
2
0
0
0
2
1
1
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
2
0
1
0
2
0
0
0
0
1
0
0
2
0
1
0
2
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
2
0
2
0
0
1
0
1
0
1
0
1
1
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
1
2
0
0
0
1
2
0
0
1
2
0
0
1
0
0
0
0
0
2
2
1
1
0
0
0
1
0
1
1
0
0
0
0
2
0
2
0
0
0
1
1
2
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
1
0
2
0
0
0
1
0
0
0
1
0
1
0
1
0
1
0
0
0
0
1
0
3
8
2
0
0
0
0
1
0
0
0
0
2
2
0
1
0
0
5
0
0
0
0
2
2
1
0
2
0
2
1
1
0
1
0
0
0
2
0
0
1
0
0
2
0
0
1
2
2
0
0
0
0
1
0
2
0
1
2
0
3
0
0
1
2
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
2
0
1
1
0
0
2
2
0
0
0
1
0
3
1
2
0
0
0
0
0
0
0
0
1
1
0
1
0
1
1
0
1
0
1
0
1
0
2
0
2
0
0
0
0
0
0
0
3
0
0
0
1
2
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
4
0
2
0
1
0
1
0
1
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
2
0
0
1
0
1
0
2
0
1
1
0
1
0
1
1
0
0
0
0
1
0
1
0
2
0
1
0
0
2
0
0
0
1
1
2
0
0
2
0
0
0
0
1
0
3
0
0
0
0
0
1
2
0
0
0
0
2
0
1
0
1
0
0
0
0
0
1
0
0
2
0
2
1
1
1
2
0
1
4
0
0
0
0
1
0
2
0
2
2
0
0
0
0
0
2
0
1
3
0
0
0
1
0
1
0
0
0
1
0
0
0
2
0
0
1
0
2
0
1
2
0
2
2
0
2
2
0
0
0
0
0
2
0
2
1
1
0
0
1
0
1
0
1
2
0
2
0
2
0
0
1
0
2
3
2
0
0
0
0
0
0
1
0
1
2
0
0
0
1
2
0
0
1
2
1
0
1
1
0
2
2
0
1
2
1
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
2
0
0
1
0
2
0
1
1
0
0
0
0
1
0
1
2
1
1
0
0
0
9
0
2
0
1
0
2
0
1
0
0
0
2
8
0
0
0
0
2
1
0
0
0
0
1
1
8
0
0
1
0
0
0
1
2
0
4
0
0
0
0
0
2
0
0
0
0
2
2
1
1
0
0
2
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
1
2
0
2
1
1
2
1
0
1
2
0
0
0
0
0
0
1
1
0
2
0
0
1
0
1
0
0
0
0
1
2
1
0
0
0
2
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
1
0
0
0
0
1
2
1
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
1
3
0
4
1
1
2
0
1
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
2
0
0
1
2
1
0
0
0
0
0
1
0
0
0
2
2
2
1
2
4
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
3
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
2
0
1
0
0
2
2
0
2
3
2
0
0
2
1
0
0
0
3
0
0
0
0
3
0
2
0
0
2
0
0
0
0
0
0
0
0
2
1
1
1
1
1
0
0
0
0
1
0
2
1
0
0
2
0
0
0
1
1
1
0
1
1
2
0
2
1
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
1
1
0
0
0
0
2
0
1
2
0
0
2
1
0
1
2
0
0
1
0
1
3
1
0
0
1
0
0
2
2
0
0
2
0
1
1
1
0
0
1
0
0
0
0
1
0
1
0
2
0
0
1
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
2
1
1
0
1
0
0
0
0
1
2
0
2
1
1
0
0
1
0
0
2
0
0
0
0
2
2
2
0
0
0
0
0
2
1
2
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
2
0
0
1
1
2
0
0
0
0
2
0
0
0
0
0
1
0
1
2
0
0
1
1
0
0
0
1
1
0
1
1
0
2
0
2
0
1
2
0
0
2
0
0
2
0
1
0
0
4
0
0
2
0
1
2
0
0
0
0
0
0
1
0
0
0
2
1
0
0
2
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
2
2
2
0
0
0
0
2
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
1
0
0
0
3
1
0
2
0
0
0
1
1
0
0
1
1
0
1
1
1
2
0
0
0
0
1
0
1
1
1
1
0
0
0
0
2
2
2
0
0
1
0
2
0
1
0
1
2
0
0
2
1
1
0
1
0
0
0
1
0
0
0
0
0
0
3
2
0
1
0
0
2
0
0
1
0
2
0
0
0
0
0
0
1
1
1
2
0
2
0
0
0
0
2
0
2
2
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
2
2
0
0
1
0
0
1
0
3
0
0
3
2
0
1
0
0
0
0
2
1
0
0
0
0
2
1
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
2
1
2
3
0
0
0
1
0
0
1
0
1
0
1
0
1
0
2
0
1
2
0
0
0
4
2
0
1
0
0
0
0
1
2
0
0
0
3
0
1
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
1
1
3
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
2
0
0
2
1
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
1
2
0
0
1
1
1
0
0
0
0
0
0
2
2
1
0
0
0
0
1
5
1
1
1
0
0
0
0
0
1
0
2
0
0
1
0
2
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
2
1
0
1
0
0
0
1
2
0
0
0
0
0
1
0
1
2
0
0
0
1
1
0
0
0
0
1
1
0
1
0
1
1
0
0
0
1
2
0
0
1
2
2
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
2
0
2
2
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
2
2
1
0
0
1
0
2
2
0
2
2
0
0
0
1
1
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
1
1
0
0
0
0
1
0
0
1
0
1
1
0
1
0
4
2
2
2
0
1
2
0
1
0
0
0
2
3
1
0
1
1
1
2
2
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
1
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
2
1
1
0
0
0
0
2
2
0
0
0
0
2
1
0
0
0
0
1
0
0
2
1
0
1
2
0
0
0
0
1
2
1
1
0
0
0
0
0
0
2
1
2
2
1
0
0
0
0
0
1
0
2
2
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
2
0
1
1
0
2
0
0
0
3
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
3
0
3
1
0
1
0
2
0
1
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
1
0
1
0
0
2
0
2
2
0
2
1
0
1
0
2
2
1
0
0
0
0
1
0
0
1
2
0
0
0
0
2
1
2
1
0
2
0
0
0
1
0
0
1
0
1
0
2
0
0
2
0
0
0
0
0
2
1
1
0
0
2
0
2
1
0
0
1
0
0
0
0
1
0
1
0
1
0
1
0
0
0
2
1
2
0
2
2
0
1
0
2
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
2
1
0
2
0
2
0
1
2
0
1
0
1
0
0
2
1
0
0
0
0
2
0
0
0
1
0
1
0
2
0
2
0
1
0
1
0
2
0
0
1
0
0
0
0
1
0
2
1
2
1
0
0
2
1
0
0
1
1
0
0
3
0
0
0
1
0
0
0
0
0
0
2
1
0
1
2
1
0
1
4
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
2
0
0
0
1
3
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
1
0
0
0
2
1
0
2
0
1
2
2
0
0
1
1
0
0
1
0
0
1
2
2
2
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
3
0
0
2
0
0
1
0
2
0
0
0
0
2
1
0
2
0
2
0
0
0
0
0
2
2
0
0
2
0
1
0
2
1
0
0
0
2
0
0
0
2
0
0
0
0
3
0
0
1
0
1
2
1
0
2
0
0
1
0
1
0
0
0
2
0
0
2
0
0
0
1
0
1
0
1
2
0
0
0
2
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
1
0
1
0
2
0
0
2
0
0
1
0
2
0
0
0
0
0
1
1
1
2
2
0
0
0
2
0
1
2
0
0
2
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
1
2
0
0
0
0
2
1
0
1
0
0
0
2
2
1
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
3
0
0
2
0
2
0
1
0
1
1
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
2
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
1
1
4
0
0
0
0
0
2
0
0
0
0
2
0
0
2
1
1
0
0
2
1
0
0
0
0
2
2
2
0
0
0
0
0
0
1
1
2
0
0
0
2
0
0
1
0
1
2
0
0
3
1
1
0
0
0
0
0
2
3
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
1
0
1
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
1
0
0
2
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
1
0
0
1
1
1
0
0
0
2
1
0
1
0
1
0
1
2
1
2
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
2
1
0
1
2
0
2
0
0
1
0
0
0
0
1
2
1
1
0
2
2
0
1
0
0
1
0
1
0
2
1
0
0
1
0
2
0
0
0
1
1
2
0
0
0
1
0
1
1
0
0
2
0
0
1
0
0
2
0
2
3
1
2
0
1
6
0
0
1
0
0
0
1
2
0
0
0
0
4
0
2
2
0
0
0
2
0
0
1
2
1
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
2
1
0
0
1
0
1
1
0
0
1
0
0
0
0
2
0
0
0
0
1
0
2
0
1
0
2
0
0
0
0
0
3
1
1
1
0
1
3
0
0
2
0
0
2
2
0
0
0
0
2
2
0
1
0
0
2
1
4
3
1
2
0
0
0
0
0
2
2
0
0
0
1
1
2
0
2
0
2
1
0
1
0
0
0
1
0
0
0
2
3
1
0
0
2
0
2
0
0
1
2
0
0
0
0
2
3
0
2
1
0
0
0
0
1
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
1
2
2
0
0
1
2
1
0
2
1
0
1
2
0
0
0
2
1
0
0
1
0
0
1
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
1
2
1
1
0
0
0
0
1
0
0
1
0
2
1
0
1
0
0
1
0
0
0
2
3
0
0
2
2
2
0
0
1
0
0
0
0
0
0
0
1
2
0
2
0
2
1
2
0
1
1
0
0
2
2
2
1
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
2
1
0
0
0
5
0
0
0
0
0
1
0
2
1
1
0
0
0
3
0
0
2
0
1
3
0
0
0
0
2
1
1
0
0
0
0
0
2
1
2
3
0
1
0
1
1
2
1
0
0
1
0
0
2
1
0
0
2
0
0
1
0
0
0
0
0
1
0
0
2
0
1
1
0
0
2
0
0
0
0
2
1
0
0
1
0
2
0
0
2
2
0
0
2
0
2
0
1
0
0
0
1
3
0
0
0
0
2
2
0
1
0
0
0
2
1
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
1
2
0
0
0
0
1
0
0
1
0
0
0
0
0
2
2
1
0
1
0
0
0
0
0
0
1
0
0
0
0
3
0
2
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
3
0
1
2
0
1
0
1
0
2
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
1
0
0
0
1
2
1
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
2
0
3
1
0
2
0
3
1
0
0
0
1
1
0
0
3
1
1
0
1
0
0
1
1
2
1
0
0
0
0
0
0
1
0
0
0
0
0
5
0
1
0
0
0
0
0
1
2
1
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
2
0
1
0
3
0
0
1
0
2
5
2
2
0
0
0
1
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
2
0
2
1
0
0
2
1
0
1
0
0
1
2
0
1
2
3
0
3
1
0
0
0
2
0
2
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
2
1
2
0
0
0
2
0
0
0
0
0
1
0
0
1
0
2
0
0
2
2
2
0
0
1
0
0
0
0
0
0
0
3
1
2
0
1
0
2
0
1
1
0
1
0
0
1
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
2
0
1
2
0
2
2
1
0
0
1
0
0
0
0
1
0
2
0
0
2
2
0
0
0
0
2
0
0
1
1
0
2
0
1
1
0
1
2
0
0
2
1
0
0
4
3
1
0
0
1
0
3
0
2
2
1
0
0
0
0
2
0
2
0
1
0
0
1
0
1
3
1
0
0
0
0
2
0
0
1
2
2
0
0
0
0
1
0
2
0
0
0
0
0
0
1
1
0
4
0
0
1
0
1
0
1
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
2
0
0
2
2
0
5
0
0
0
0
1
0
0
2
1
1
0
0
0
0
0
2
1
0
1
0
0
0
1
0
0
0
0
1
0
2
2
0
0
0
0
2
1
2
0
0
0
2
2
1
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
2
0
1
2
5
0
0
0
1
1
1
1
2
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
2
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
1
1
0
0
0
1
1
0
1
0
0
0
0
2
0
0
1
1
2
3
0
2
0
2
1
1
0
1
2
0
0
0
0
0
2
0
0
0
2
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
2
0
2
0
0
2
1
2
0
1
2
0
2
0
2
0
0
0
0
0
2
0
2
0
1
0
2
0
1
1
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
2
0
1
0
2
0
0
1
0
0
2
0
1
0
0
0
0
0
1
0
1
1
0
0
0
3
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
2
0
0
2
0
1
1
2
7
1
0
0
0
1
0
0
0
1
2
2
2
0
1
0
0
0
1
1
1
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
1
1
0
1
0
1
0
2
0
0
2
0
2
0
1
1
1
0
0
0
2
2
0
1
0
0
0
0
0
1
2
0
0
1
1
0
1
0
0
2
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
1
0
0
0
0
2
1
0
0
0
0
1
2
0
1
0
1
0
2
0
0
1
2
2
0
2
2
1
0
0
0
2
2
1
1
0
3
0
0
0
0
0
0
1
1
0
0
0
2
2
1
0
1
0
1
0
0
2
0
2
2
0
0
0
0
0
3
2
0
1
0
0
0
0
0
2
2
0
1
0
0
2
2
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
3
1
0
0
2
0
1
0
0
0
0
4
2
0
1
1
1
0
3
2
0
0
2
0
1
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
2
0
0
4
0
0
2
1
1
2
1
2
3
0
0
2
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
2
0
1
0
1
0
2
0
1
2
0
0
2
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
1
0
1
2
0
0
2
0
5
1
1
0
0
2
0
0
1
0
0
0
1
0
2
0
0
2
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
3
0
0
0
2
2
0
0
1
0
0
0
2
0
0
3
2
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
2
2
0
2
0
3
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
1
2
0
2
1
1
0
1
2
2
2
0
0
0
0
0
1
2
1
2
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
1
0
2
0
2
0
0
2
2
0
0
0
0
0
1
2
0
2
0
0
0
0
0
2
1
0
0
0
2
0
0
2
1
0
1
0
0
0
0
0
2
1
1
1
0
0
2
0
2
2
0
0
6
0
0
2
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
1
0
1
0
1
2
1
0
2
0
0
0
0
1
1
2
0
0
1
0
0
2
0
0
0
3
1
1
2
0
1
1
1
2
1
2
0
0
0
1
0
3
1
1
0
0
1
1
1
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
1
1
2
0
0
0
0
0
2
0
1
0
0
2
1
1
0
0
1
2
0
0
0
2
3
1
0
0
2
2
0
0
2
0
0
0
0
0
1
1
0
1
2
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
2
0
0
1
2
0
0
0
0
0
0
2
0
0
2
2
1
0
0
0
0
0
0
1
1
0
2
0
0
0
0
2
0
2
0
0
2
1
0
2
1
0
2
3
0
0
2
0
0
0
0
0
0
0
2
0
1
2
1
0
0
0
2
0
1
0
1
0
0
2
0
0
0
2
5
0
0
0
0
2
0
0
1
0
2
0
0
1
0
0
0
1
0
2
3
0
2
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
1
0
2
1
0
2
0
0
1
0
2
0
0
0
1
2
0
0
0
1
0
0
0
0
2
0
1
0
0
2
1
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
8
1
0
2
2
0
0
0
1
3
2
1
0
0
2
0
0
0
0
1
0
2
0
0
0
0
2
4
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
3
0
0
0
2
1
0
1
0
1
0
0
0
0
2
0
2
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
2
2
1
2
0
1
0
0
0
0
1
0
0
0
2
0
0
1
1
0
1
0
1
0
0
0
0
2
0
1
1
0
1
0
0
0
0
2
1
0
0
2
0
0
0
1
0
0
1
0
0
2
2
0
1
0
0
2
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
3
0
1
0
1
3
1
0
0
0
1
0
0
0
0
0
0
0
0
1
2
1
0
1
0
0
0
3
2
0
0
0
0
2
4
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
1
0
0
1
0
2
2
0
0
0
0
0
0
1
0
2
1
0
0
0
2
0
0
1
0
2
1
0
1
0
0
0
0
3
2
1
0
1
1
2
0
0
1
0
1
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
2
0
1
0
0
3
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
2
0
0
1
1
1
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
1
1
2
3
2
0
0
0
0
0
1
0
3
0
0
0
1
0
2
2
2
2
0
2
0
2
1
0
0
0
0
0
0
0
0
2
0
0
2
1
2
3
0
0
0
1
0
2
0
0
2
0
2
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
1
0
2
0
1
2
0
2
0
1
0
0
3
0
0
0
1
0
0
0
2
0
3
0
1
2
1
0
0
0
2
0
0
2
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
1
0
0
0
1
0
2
1
0
0
1
0
0
0
2
0
1
1
2
2
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
1
1
0
2
1
0
0
2
3
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
4
0
1
0
1
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
1
1
0
2
0
2
0
0
0
0
0
1
0
0
0
1
1
3
1
0
2
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
2
0
0
0
2
2
0
2
2
2
0
0
0
0
0
0
0
1
2
0
2
2
0
0
1
2
0
0
1
0
2
0
0
2
0
0
0
3
0
0
0
2
1
2
1
0
0
0
0
2
0
2
0
0
0
1
3
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
1
0
2
0
1
1
0
2
1
0
2
0
4
0
0
0
1
0
0
0
0
1
1
1
2
0
0
0
2
0
1
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
1
0
0
0
1
1
0
0
0
2
2
2
0
1
0
0
0
1
0
0
1
0
1
1
0
0
0
0
2
0
1
1
0
0
0
2
2
1
0
2
0
0
0
0
0
0
0
1
2
0
0
1
0
0
2
0
2
0
0
0
3
0
0
1
0
0
1
0
2
0
2
2
0
0
0
0
0
0
0
0
2
0
2
2
2
1
2
0
0
1
0
1
2
2
0
0
0
0
0
0
1
2
3
0
2
1
2
1
0
1
0
0
2
0
0
0
0
0
1
0
0
2
0
0
2
0
0
3
0
1
0
0
1
0
1
1
1
0
2
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
2
2
1
0
1
0
0
1
1
0
2
1
1
0
2
1
0
0
0
1
0
4
0
1
0
0
0
0
0
1
0
0
2
0
0
0
1
0
1
1
0
2
0
1
0
0
0
0
2
0
0
1
0
0
0
2
2
1
0
0
0
0
2
0
0
2
2
2
2
0
1
0
0
2
0
0
1
0
0
1
0
1
2
0
0
1
1
0
0
0
0
2
2
1
0
0
2
0
0
0
1
2
1
0
0
6
0
1
2
0
0
0
1
0
1
2
0
2
1
2
2
0
0
1
0
1
0
0
0
1
0
0
3
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
4
1
2
0
1
0
0
1
1
0
0
0
2
0
0
2
1
2
0
0
0
1
0
0
2
2
3
0
0
0
0
1
0
0
2
0
2
0
0
3
0
0
2
2
0
0
0
2
2
0
0
0
1
0
1
0
4
0
1
0
0
0
2
0
2
2
0
0
2
2
2
0
0
0
0
1
0
0
0
1
1
0
0
1
0
2
0
0
0
0
1
0
0
0
0
1
0
2
0
0
3
0
0
5
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
2
2
0
1
0
0
0
0
1
0
0
0
0
0
2
0
1
1
0
0
2
0
0
1
2
0
0
0
0
0
1
2
0
0
2
2
0
0
0
0
0
1
0
0
0
0
1
1
2
0
1
0
0
0
0
0
2
1
2
0
0
0
2
0
2
0
1
0
1
0
2
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
1
1
1
0
1
0
0
0
2
0
1
0
0
0
0
1
0
2
2
4
0
0
2
2
1
1
0
0
0
0
0
2
0
2
0
0
1
1
1
0
0
0
2
2
1
1
0
0
0
0
1
0
1
0
1
0
0
0
2
0
0
0
2
2
1
0
2
0
2
0
0
0
4
1
0
0
0
0
0
0
2
0
0
2
0
1
0
2
0
0
1
0
2
0
0
0
2
2
1
0
0
0
0
0
0
0
3
1
0
0
0
0
2
0
0
4
0
1
1
0
1
2
0
0
2
9
0
0
0
0
0
2
1
0
0
1
0
1
0
1
0
1
0
2
0
0
1
2
0
0
0
2
0
1
0
0
2
2
0
0
0
1
0
0
2
0
3
0
0
1
1
0
0
0
2
2
0
1
3
4
0
0
0
2
0
0
4
0
1
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
1
0
0
0
1
2
0
2
1
1
0
0
2
1
0
0
0
0
0
1
0
0
0
2
0
1
0
1
2
0
0
0
1
0
0
1
2
0
1
2
0
0
1
0
0
0
0
0
0
0
1
0
2
1
1
1
0
0
1
0
0
0
0
3
2
0
2
0
0
2
0
2
1
0
1
2
0
1
0
0
0
2
0
0
2
0
2
2
0
1
0
1
2
2
1
2
0
1
1
0
3
0
0
0
0
1
1
2
0
2
0
0
2
0
0
0
0
2
1
0
0
1
1
2
0
0
0
0
0
2
2
0
0
1
7
0
0
0
0
2
0
1
3
1
0
0
2
0
0
0
1
1
2
1
1
1
0
0
2
0
0
2
1
2
1
1
0
2
1
0
2
1
0
0
0
0
0
0
5
1
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
3
3
0
0
1
0
0
0
0
0
1
2
0
0
0
2
0
2
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
2
1
0
0
0
2
2
0
0
0
2
0
2
1
1
1
0
1
0
1
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
1
1
0
1
4
0
0
0
1
2
0
0
0
0
0
0
0
1
2
1
2
0
0
2
1
1
1
2
0
0
0
2
0
0
4
0
1
0
1
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
2
1
0
0
0
1
3
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
3
2
1
0
0
1
1
0
0
2
2
1
0
2
0
0
0
0
1
1
1
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
2
0
1
0
0
2
0
2
2
0
0
0
0
0
0
2
0
0
2
0
0
1
1
0
0
2
0
1
2
2
0
2
0
0
1
0
1
0
0
2
2
2
0
0
0
1
0
0
2
0
0
1
2
1
2
0
0
0
2
0
1
1
0
2
0
2
2
0
0
1
2
1
0
0
0
0
2
0
2
0
1
1
0
1
0
0
2
0
0
0
0
1
1
1
2
0
0
1
1
0
2
0
0
0
1
0
1
0
0
0
0
4
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
1
0
0
2
0
1
1
0
0
0
0
1
2
0
1
2
0
0
0
0
0
3
0
0
0
1
2
2
1
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
2
2
0
1
0
0
2
2
0
0
0
0
1
0
0
1
1
0
0
1
0
2
0
0
1
0
0
0
0
1
2
0
2
0
0
0
2
2
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
2
0
0
5
2
0
1
2
0
0
0
0
3
1
1
2
2
0
0
2
0
3
0
0
0
2
0
0
0
0
0
0
0
2
0
2
2
0
2
2
0
2
3
0
1
2
0
0
1
2
0
0
2
0
0
2
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
2
0
1
0
0
2
0
2
0
0
0
0
0
1
2
1
0
0
3
0
1
0
0
0
0
1
1
1
1
0
2
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
1
0
1
1
0
2
0
3
1
1
0
1
2
0
1
0
0
1
0
0
0
2
1
0
0
0
0
0
3
0
1
0
0
0
2
1
2
0
1
1
0
1
0
0
0
0
1
0
2
0
0
2
1
0
0
2
0
2
0
3
0
1
2
1
0
0
0
0
2
1
0
0
0
1
0
0
0
0
2
1
0
0
2
1
0
0
2
1
0
2
2
0
1
0
0
2
1
0
2
0
0
2
1
0
2
0
1
0
1
0
1
0
0
0
0
0
1
0
1
2
2
0
0
0
2
1
0
0
1
0
0
0
0
0
1
0
0
0
0
2
1
1
0
0
1
0
2
0
0
1
0
0
2
1
0
2
2
2
2
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
1
2
0
0
2
0
0
0
1
0
0
2
1
0
0
1
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
2
0
0
0
0
1
0
2
0
3
1
0
2
0
0
3
2
1
0
1
0
0
0
2
2
1
0
0
1
0
1
0
0
0
0
0
1
1
0
0
2
1
1
0
1
0
0
0
0
0
0
0
2
1
1
0
0
5
2
0
0
0
2
3
0
0
0
1
0
0
2
0
0
0
0
1
0
0
1
0
1
1
2
1
0
2
1
0
0
0
0
0
0
1
1
0
0
1
0
1
3
0
1
0
0
1
0
2
1
1
0
0
0
2
0
0
0
1
0
1
0
2
5
0
0
2
0
0
2
0
0
2
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
4
0
0
2
0
0
0
0
0
0
0
0
0
2
2
2
2
0
1
0
0
1
1
1
2
1
0
2
0
1
1
2
0
1
2
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
1
0
3
1
0
0
1
0
1
0
0
0
0
0
0
1
2
0
0
1
0
1
0
0
1
1
0
0
0
0
0
2
0
0
2
0
0
1
2
1
0
0
0
2
0
1
0
0
0
3
0
0
0
0
1
0
1
1
0
4
0
0
0
0
0
0
0
0
0
1
0
0
2
2
1
2
2
0
1
0
0
0
0
0
3
0
0
2
2
0
2
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
1
0
2
0
0
1
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
2
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
2
1
0
1
0
0
0
1
1
0
0
0
1
0
1
2
0
0
0
0
0
0
0
2
0
4
0
0
0
0
0
2
0
1
0
0
0
1
0
1
0
2
0
0
0
0
1
0
2
1
0
2
2
0
1
0
0
2
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
1
0
0
1
0
0
1
1
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
1
0
0
2
0
0
1
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
1
0
0
0
1
0
0
0
2
2
0
0
0
0
0
1
0
1
0
0
1
0
2
2
0
2
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
1
0
2
0
0
0
0
0
1
0
0
0
1
1
2
0
0
0
1
1
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
3
0
1
2
0
1
0
3
1
0
5
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
2
1
0
0
2
0
0
2
1
0
3
0
0
0
0
0
1
0
1
0
1
2
1
0
1
1
0
2
0
0
0
0
0
0
0
0
1
2
1
2
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
2
0
0
2
2
0
2
0
2
0
0
0
0
6
0
0
1
2
2
2
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
2
0
2
0
0
0
0
2
1
0
0
1
1
3
2
0
1
1
1
0
3
1
2
0
0
0
1
0
2
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
2
2
2
1
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
2
2
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
1
0
2
0
0
2
1
0
2
0
0
1
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
2
0
1
1
2
0
0
1
0
2
2
2
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
2
1
2
0
0
1
0
2
0
2
0
1
0
1
1
2
0
0
3
1
0
2
0
1
1
0
0
1
0
1
2
0
2
1
1
2
0
0
0
0
2
0
2
0
1
0
0
0
3
1
0
0
0
0
0
1
0
1
0
0
3
0
1
0
2
1
0
2
0
2
2
0
0
0
0
3
0
0
0
3
0
1
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
1
2
0
0
1
1
0
0
1
0
2
0
0
0
0
1
1
0
0
0
2
0
2
0
0
0
0
2
1
0
1
0
3
0
2
0
0
1
0
0
1
1
0
2
0
0
0
0
0
0
0
3
0
1
0
0
0
2
2
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
2
1
2
1
0
0
0
1
2
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
1
1
0
2
0
2
0
0
1
0
2
0
1
0
1
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
2
1
2
0
0
0
2
0
0
1
0
1
0
1
2
0
0
2
0
2
0
1
0
1
0
2
0
2
0
0
2
0
0
2
3
0
0
0
0
0
2
1
2
0
2
0
0
0
0
0
1
0
1
0
2
0
0
0
0
1
0
1
1
0
2
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
2
1
1
0
0
0
2
1
1
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
2
1
0
1
0
2
0
0
1
1
0
2
1
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
2
1
0
0
1
2
2
0
0
0
0
1
0
0
0
0
0
0
2
0
2
1
0
0
1
0
0
0
0
0
0
1
3
0
0
0
2
0
0
0
2
0
2
0
2
2
0
0
0
0
1
0
0
1
0
2
2
1
0
0
0
0
0
0
0
1
0
0
2
2
0
1
0
0
1
0
0
0
0
0
1
1
0
1
0
0
1
0
2
0
1
0
0
2
0
0
0
0
0
5
0
0
1
0
0
0
0
0
0
1
1
0
2
0
2
0
3
0
0
1
1
0
2
0
0
0
2
0
0
1
0
1
0
1
0
1
0
2
1
1
0
0
0
8
1
1
1
0
0
2
1
1
1
2
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
1
1
0
2
0
1
1
0
0
0
0
1
2
0
0
0
0
1
2
2
2
0
0
2
0
0
1
0
3
0
0
0
0
1
0
0
3
0
0
0
1
0
2
2
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
1
1
2
0
0
0
1
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
2
2
1
4
0
2
0
0
1
0
0
1
0
1
1
1
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
1
0
1
0
0
2
2
0
0
0
0
1
1
2
0
0
0
1
1
0
1
0
0
2
3
0
2
0
0
0
0
0
1
2
0
0
2
0
0
2
1
2
0
6
0
1
2
0
2
2
1
1
2
1
2
1
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
2
1
0
0
0
2
0
0
2
1
0
0
1
0
4
0
0
0
0
1
1
0
0
3
1
0
1
0
0
0
0
1
1
2
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
1
0
1
2
0
0
1
0
2
0
3
0
0
0
0
2
1
0
0
0
2
0
2
2
0
0
0
1
0
0
0
0
0
2
0
0
0
2
1
1
1
0
2
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
1
0
2
0
0
2
0
0
1
2
0
0
0
0
1
2
0
0
2
0
1
0
0
2
0
0
0
1
2
0
0
0
3
0
0
1
2
1
3
1
2
1
0
0
0
0
0
0
2
0
1
0
1
1
0
0
0
0
2
0
1
1
1
0
2
0
0
2
2
0
2
0
1
0
1
0
0
0
1
0
0
0
2
2
0
0
2
0
0
1
0
0
2
0
1
1
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
2
1
2
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
2
0
0
1
0
0
0
0
3
0
0
1
2
1
0
0
4
0
1
0
3
1
0
0
0
2
0
1
0
0
0
1
0
3
0
0
2
1
0
0
2
0
0
5
0
2
0
1
2
0
2
1
1
1
2
2
0
2
0
0
2
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
1
1
1
2
1
0
2
0
0
0
2
0
0
0
0
0
2
0
0
10
0
1
0
1
1
0
2
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
3
1
0
0
0
0
3
0
0
0
0
1
0
4
0
0
1
0
0
0
2
0
0
1
0
1
0
0
0
2
1
0
1
0
1
0
0
1
0
2
0
0
0
2
0
0
0
1
1
1
0
0
0
0
2
1
1
0
0
2
0
0
0
0
1
1
0
2
1
1
2
0
0
1
2
0
0
2
0
2
2
0
2
0
0
0
1
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
4
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
4
2
0
1
0
0
0
2
0
0
0
0
0
0
3
0
0
1
0
1
2
2
1
1
0
0
0
0
0
0
0
1
1
0
0
4
4
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
2
2
0
0
0
2
0
0
0
0
0
1
0
1
1
0
0
0
0
1
2
0
0
0
0
2
0
3
0
1
0
2
0
0
0
0
1
0
0
3
2
1
2
1
0
0
0
0
1
1
2
0
0
0
1
2
0
0
0
0
0
2
0
1
0
2
0
1
0
0
1
2
1
0
0
2
6
0
0
1
1
1
1
1
2
1
0
2
0
1
0
2
1
2
0
0
0
2
0
1
0
2
0
0
2
0
0
1
3
0
0
0
0
1
2
3
1
0
2
0
2
0
1
0
0
0
0
1
0
2
0
0
1
0
0
0
2
0
2
0
1
1
1
0
0
2
0
1
0
0
0
1
1
0
2
2
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
1
0
1
2
2
0
1
2
1
1
0
0
0
2
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
1
0
0
2
1
0
0
2
0
0
2
0
2
0
0
0
2
2
0
0
0
0
0
1
1
0
0
1
0
0
2
0
0
0
0
1
0
0
0
2
0
2
2
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
1
1
0
2
0
0
0
1
2
1
2
1
2
0
1
2
0
2
1
0
3
0
2
2
2
0
0
2
0
11
3
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
2
0
2
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
2
0
0
1
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
2
5
1
0
1
0
0
0
0
0
0
4
0
0
0
1
2
0
0
1
2
2
2
2
0
1
0
1
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
1
2
0
0
2
0
0
0
0
1
2
0
1
0
0
0
2
2
0
0
0
0
0
1
0
2
2
0
1
0
1
1
1
2
2
0
2
1
0
0
0
0
0
1
2
1
0
1
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
4
0
4
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
1
0
3
2
2
0
0
0
0
0
2
0
1
2
0
0
1
0
0
1
0
2
0
6
1
0
2
1
0
1
2
0
0
0
1
0
1
2
0
1
2
2
0
0
1
1
1
3
0
0
0
0
0
0
0
0
0
2
0
0
2
3
2
2
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
2
1
0
1
0
2
0
2
0
0
2
0
0
0
0
0
1
0
0
1
0
2
0
0
0
2
0
0
2
0
1
0
0
1
1
0
1
0
0
1
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
1
2
0
0
0
2
0
0
0
0
0
1
0
1
0
0
1
1
2
1
0
0
0
2
0
1
1
0
1
2
0
0
2
0
0
0
1
0
0
2
0
0
0
1
0
2
1
0
2
0
1
2
1
0
0
0
0
2
0
0
0
1
0
1
2
2
0
0
0
0
0
2
0
0
1
0
0
3
0
0
2
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
1
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
3
0
2
0
1
0
0
0
1
0
0
2
0
1
0
0
2
0
1
0
0
0
1
0
0
1
0
0
0
2
2
1
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
3
2
2
1
1
1
0
0
0
2
1
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
2
1
2
0
0
1
0
0
1
0
0
0
0
0
2
0
1
0
1
1
0
0
0
0
0
0
2
1
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
2
2
1
1
0
0
0
1
0
0
2
0
0
0
3
0
0
1
0
0
1
0
0
0
0
0
0
1
2
2
1
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
2
3
0
0
1
0
0
0
2
0
0
0
1
0
2
0
1
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
2
1
2
0
2
1
0
2
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
2
1
0
0
0
1
1
1
0
0
1
2
0
0
2
0
2
0
1
1
4
2
0
0
2
0
0
0
0
2
1
0
0
0
0
1
1
0
1
0
2
2
1
1
2
0
2
1
1
0
0
2
0
2
0
3
0
0
0
2
0
0
0
2
0
3
0
1
2
0
0
1
1
0
0
0
0
0
1
1
0
0
0
2
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
2
1
1
1
2
3
2
1
0
2
0
0
0
0
0
0
1
2
1
0
0
2
2
2
0
1
0
0
0
0
0
1
1
1
0
0
0
0
3
0
0
0
3
2
3
1
0
0
2
0
2
1
1
0
0
1
0
1
0
2
2
2
0
0
1
2
0
1
0
0
2
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
2
1
0
0
1
2
0
0
1
0
0
2
0
1
2
0
1
7
0
0
0
0
0
0
0
0
0
0
3
2
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
2
2
3
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
1
0
2
1
0
0
0
2
1
2
1
2
0
0
0
0
0
1
0
2
0
2
0
1
0
1
0
1
1
0
0
1
0
0
0
1
0
0
0
3
1
0
0
0
0
0
2
0
1
2
0
1
0
0
0
2
0
0
3
0
4
0
2
0
2
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
2
1
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
1
1
2
3
2
2
1
2
0
2
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
2
0
3
1
1
0
0
0
1
0
0
2
1
2
3
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
2
2
1
0
1
1
0
1
0
4
0
0
0
2
0
0
1
0
0
0
0
1
2
0
0
2
2
1
4
0
1
0
0
1
2
1
1
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
1
0
3
0
2
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
2
0
1
1
0
2
0
1
0
0
0
1
0
1
1
2
0
0
1
0
2
0
2
0
0
0
1
0
0
2
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
1
0
2
1
1
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
2
1
2
0
0
1
0
1
2
0
2
0
0
2
0
0
0
1
0
0
0
1
0
3
1
0
0
0
0
0
0
0
2
0
0
0
3
1
1
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
2
2
0
0
0
1
2
0
0
1
0
0
0
5
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
2
3
0
0
2
0
1
2
1
1
1
1
0
2
0
0
1
1
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
1
2
0
0
0
1
0
0
0
2
0
0
0
1
1
0
5
1
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
2
2
0
2
1
2
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
1
2
0
0
0
1
0
0
2
1
0
0
0
0
1
1
0
0
0
1
0
0
2
2
0
0
2
0
0
0
2
0
2
0
0
0
0
2
1
2
0
0
0
0
3
0
2
0
0
0
0
2
1
1
1
0
0
0
0
2
2
1
1
2
0
0
1
2
2
0
0
0
0
0
0
2
0
0
1
0
1
0
0
1
0
2
0
2
3
1
2
2
0
2
0
2
0
0
2
0
1
0
1
0
2
0
0
1
0
0
0
0
1
0
0
2
0
1
0
1
1
1
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
1
1
2
0
2
0
4
0
1
2
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
1
3
1
1
1
0
0
0
1
2
1
0
0
0
3
0
1
2
2
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
1
0
0
1
2
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
2
0
0
2
0
1
0
2
0
0
0
2
1
0
0
2
1
0
2
2
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
2
0
0
0
1
0
0
1
2
0
0
0
0
3
0
0
0
0
0
0
2
2
0
0
0
2
1
0
0
0
2
2
3
0
1
0
0
0
0
3
0
0
0
0
0
1
0
0
2
1
1
1
1
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
1
1
2
0
1
0
0
2
2
0
1
0
0
1
0
0
0
0
3
0
0
0
1
0
0
1
0
3
0
0
0
0
1
1
0
1
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
2
1
2
2
0
0
1
0
2
1
0
0
1
1
0
0
0
0
1
2
2
1
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
2
0
0
0
1
0
2
0
3
1
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
2
2
1
0
0
0
0
0
0
2
0
1
2
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
2
1
0
2
0
0
0
1
0
2
0
1
0
1
1
1
0
0
2
0
0
2
0
2
2
0
1
3
0
0
1
2
0
1
0
1
0
0
0
1
0
2
1
1
0
0
0
1
0
2
1
0
0
2
0
2
0
0
2
0
0
0
1
1
0
2
0
0
0
2
0
1
0
0
0
0
0
1
1
1
2
0
1
0
0
0
1
0
2
0
0
2
0
0
0
0
1
1
0
2
0
2
0
3
0
1
0
4
1
3
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
2
0
2
0
0
1
0
0
1
0
0
0
0
0
2
0
4
0
4
2
0
0
0
1
2
0
1
0
1
0
0
0
0
1
0
0
2
1
0
0
0
0
2
0
0
3
2
0
0
0
0
0
2
0
1
0
9
1
0
0
1
2
0
0
0
2
1
2
0
1
2
2
1
0
0
1
0
0
1
0
0
0
0
3
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
4
0
4
1
1
0
1
0
0
2
1
0
1
1
1
1
1
0
0
0
2
2
0
0
1
2
2
0
2
0
2
2
2
0
0
1
1
2
1
0
0
1
1
0
0
0
2
0
1
1
0
2
0
0
2
0
0
1
1
1
0
0
0
1
0
0
0
0
1
2
1
0
2
0
0
0
0
2
0
1
0
0
1
0
1
1
0
0
2
0
2
1
0
0
0
0
0
0
1
2
0
0
0
1
3
2
0
0
0
1
0
3
0
0
0
1
1
0
3
0
0
1
2
0
1
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
2
1
2
0
2
0
2
2
2
0
1
0
0
1
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
1
2
0
1
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
2
0
2
1
0
0
2
1
1
0
0
0
1
0
1
2
0
0
0
0
0
0
0
1
1
3
1
3
0
1
1
3
0
2
0
1
0
0
0
0
0
1
2
0
0
0
2
5
1
1
2
0
2
0
2
1
0
1
0
1
0
0
3
0
0
0
2
1
0
1
0
2
0
2
2
0
3
0
0
1
1
0
0
0
2
1
0
0
0
0
2
1
0
2
0
2
0
0
2
0
0
3
0
2
1
0
0
2
0
0
2
0
2
0
2
1
0
2
0
0
0
2
0
0
0
0
0
2
0
2
0
2
1
2
0
0
1
0
0
0
0
0
2
0
2
0
1
0
0
0
1
0
0
0
2
1
0
2
0
1
0
0
0
0
0
0
0
1
0
4
0
1
0
0
2
0
0
2
2
0
0
0
0
1
0
0
0
0
0
3
0
0
2
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
2
0
0
1
0
0
0
1
0
0
1
1
2
0
0
1
1
0
1
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
3
0
1
3
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
2
1
0
2
0
0
1
0
2
1
3
2
0
0
5
0
2
2
1
2
0
0
0
0
2
0
6
0
1
0
1
0
2
0
0
1
0
0
0
2
2
0
0
2
0
0
2
2
1
0
2
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
2
0
2
2
0
4
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
1
0
1
0
1
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
3
2
0
1
0
2
2
0
2
0
1
0
0
1
2
0
2
3
0
0
1
0
0
0
0
1
2
0
3
3
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
2
2
2
2
0
0
1
0
0
2
0
0
2
0
4
0
0
1
0
2
0
0
1
0
0
2
0
2
1
0
0
0
2
1
0
2
0
0
0
0
0
2
1
1
0
0
2
0
0
0
1
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
2
0
2
4
1
0
1
1
0
0
0
0
0
0
1
0
3
0
0
1
0
1
0
0
1
1
2
0
0
2
1
0
1
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
1
2
0
2
0
2
0
0
0
0
0
0
2
12
2
0
1
0
0
0
0
2
0
0
0
1
0
0
2
2
0
1
3
0
0
0
1
0
0
0
0
1
2
0
1
0
0
0
2
1
1
0
0
2
0
0
0
0
3
2
2
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
2
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
2
0
4
0
1
3
1
0
0
2
2
0
0
1
0
3
0
0
2
0
0
0
2
0
0
1
0
0
2
0
0
2
0
0
2
1
1
0
0
2
1
0
0
1
0
0
1
0
0
1
0
1
0
0
0
1
0
2
0
1
1
1
0
0
0
1
2
0
0
0
1
0
1
1
3
0
2
2
2
1
1
0
0
3
2
2
0
0
2
0
0
0
1
1
0
1
0
0
2
2
0
1
0
0
1
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
1
1
0
0
2
0
1
2
2
2
0
0
0
0
3
1
0
2
0
2
2
1
0
0
1
0
0
1
0
1
3
0
2
1
0
0
0
2
0
1
0
1
2
0
0
2
0
1
0
2
0
2
2
2
0
0
1
1
2
0
0
0
0
1
2
0
0
0
0
1
0
1
1
0
0
1
0
0
2
2
2
0
0
2
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
3
0
0
0
2
2
1
0
0
2
0
1
0
0
0
0
0
2
0
0
0
2
1
2
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
2
0
1
9
1
2
1
2
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
2
3
1
0
1
1
0
2
0
0
1
0
0
1
1
1
0
2
1
0
0
0
0
1
0
0
1
0
0
0
2
2
1
1
0
0
0
1
0
0
1
1
2
0
2
0
2
0
1
0
2
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
3
4
2
0
5
0
0
1
0
0
1
0
0
0
0
2
0
0
0
3
2
0
0
1
0
0
1
0
0
0
2
1
0
0
0
0
0
0
8
0
0
1
0
0
2
0
0
1
2
1
0
0
0
2
0
0
0
2
0
0
0
2
0
0
2
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
1
0
2
0
0
2
0
1
0
0
0
1
0
1
0
2
2
0
1
0
0
1
0
2
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
1
0
1
0
2
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
1
1
0
1
2
0
1
0
0
1
0
0
0
0
2
2
0
1
1
2
0
2
2
3
1
0
1
0
0
2
2
0
0
2
0
0
0
0
0
1
0
1
1
0
2
0
3
2
0
0
0
0
1
1
0
0
0
2
1
0
1
1
0
1
0
0
0
1
2
2
0
0
0
0
0
0
1
0
1
0
2
0
0
1
0
0
0
0
2
0
0
1
1
0
2
1
0
0
0
3
2
0
1
2
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
3
0
1
1
0
4
0
0
0
0
0
2
2
1
0
0
0
0
1
0
2
0
0
0
0
2
0
2
2
0
2
0
0
1
1
0
1
0
0
0
0
0
0
2
0
0
2
0
2
1
2
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
2
0
0
0
0
0
2
2
1
0
0
0
1
0
2
0
2
0
2
0
0
0
1
2
0
0
1
2
1
0
0
2
2
1
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
1
4
0
1
0
0
1
0
0
1
0
1
0
0
0
0
1
0
1
0
2
0
0
1
0
0
1
1
0
0
0
1
2
2
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
1
1
2
0
0
0
0
2
0
0
2
0
0
0
0
0
1
1
2
1
1
1
2
0
0
1
0
3
1
0
0
1
0
2
2
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
2
1
0
0
0
1
1
0
0
2
0
2
0
1
0
0
0
0
1
2
0
1
0
0
0
0
3
0
1
0
2
0
1
2
0
1
0
1
0
0
0
0
1
0
2
2
0
0
1
2
1
2
2
0
0
1
0
2
0
0
2
1
1
1
2
0
0
1
0
0
0
1
0
3
0
0
0
1
2
2
1
1
1
2
1
0
0
2
0
1
2
0
2
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
1
1
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
1
2
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
1
2
0
3
0
0
2
1
0
1
0
2
0
0
0
0
0
2
1
1
1
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
1
1
1
2
0
0
0
2
1
0
0
0
2
0
2
0
0
1
0
1
1
0
2
0
0
2
0
1
2
0
0
0
0
1
0
0
0
2
1
1
0
0
0
2
3
0
0
3
0
1
1
2
0
2
0
2
0
2
0
0
0
0
0
1
0
0
0
2
1
1
0
2
3
0
2
0
0
0
2
0
1
1
0
0
2
0
1
0
2
0
0
0
0
1
1
1
1
1
2
0
0
0
0
0
0
0
0
0
0
1
7
0
0
0
1
0
1
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
1
1
1
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
1
2
0
2
1
0
0
2
0
0
1
0
1
0
1
1
0
4
3
1
2
0
2
0
0
0
0
0
0
1
2
0
0
2
0
0
0
2
0
3
0
3
3
0
0
1
2
3
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
2
1
0
0
1
0
0
1
0
0
0
1
1
0
0
1
2
1
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
2
0
2
0
1
2
2
0
0
0
0
2
0
1
1
3
0
0
0
1
2
0
3
2
0
0
1
0
0
0
0
2
2
1
0
0
0
1
0
1
2
2
0
1
0
1
2
0
0
1
0
0
1
1
0
1
2
2
0
3
1
1
0
0
1
0
1
0
0
1
1
0
2
1
2
3
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
2
0
2
0
2
2
0
0
1
0
0
0
0
0
2
0
1
0
0
0
1
0
0
1
2
0
0
0
2
1
0
2
0
3
1
0
0
4
2
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
1
0
1
0
2
0
0
0
2
2
0
0
1
2
1
0
1
0
0
1
0
0
0
0
2
0
0
2
1
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
2
7
0
1
0
0
1
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
2
0
1
1
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
2
1
2
0
0
0
3
0
0
3
1
0
0
0
0
0
0
3
1
0
0
2
0
0
0
0
0
0
1
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
3
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
5
0
0
0
2
1
2
0
2
0
2
1
0
2
0
2
2
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
2
2
1
0
0
1
0
0
0
0
1
1
0
1
2
3
0
0
2
0
2
0
0
3
0
0
1
2
0
1
0
0
0
2
0
0
0
0
2
1
0
2
0
0
0
1
1
0
1
0
0
2
0
0
1
2
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
1
0
0
2
2
0
0
0
0
1
0
0
2
0
1
0
0
0
2
2
0
2
0
0
0
2
2
0
0
2
2
0
2
2
2
0
0
2
0
0
0
1
0
2
0
1
0
0
0
1
0
1
0
12
0
3
0
0
0
0
2
0
1
1
0
3
0
0
0
0
0
0
1
0
0
0
2
0
1
0
2
1
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
2
2
1
0
1
1
0
0
0
2
0
0
0
2
0
2
2
0
0
0
0
1
0
2
2
0
2
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
2
0
2
1
0
0
0
0
0
0
0
2
0
1
0
1
0
0
1
0
2
1
0
0
0
1
0
0
0
2
0
0
0
2
0
3
0
1
0
0
0
1
3
3
2
0
0
2
1
1
0
0
0
0
1
0
0
1
2
0
2
0
0
0
0
1
0
1
0
2
0
0
0
0
2
1
0
1
2
0
2
0
0
0
3
2
0
1
0
2
0
0
1
0
1
3
0
0
1
0
2
0
0
0
0
0
0
0
3
3
0
0
1
0
0
0
0
0
0
1
2
0
1
2
0
0
1
0
0
0
0
1
0
1
1
3
0
3
2
1
1
0
2
1
0
0
0
0
0
1
0
2
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
1
1
2
1
3
0
0
2
0
0
0
1
2
0
2
0
0
0
2
0
6
0
2
0
1
2
0
0
2
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
1
0
0
0
2
2
0
0
1
0
2
0
0
0
0
2
0
2
0
0
1
0
0
0
1
2
0
0
0
2
5
3
0
5
2
1
0
2
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
2
0
4
0
0
3
3
2
1
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
2
0
0
1
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
1
1
0
1
0
0
2
0
2
0
0
2
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
2
0
0
0
0
1
0
0
0
3
0
1
1
0
0
0
1
0
2
0
1
0
1
1
0
1
0
0
2
0
0
1
2
1
1
1
1
0
0
0
2
1
1
1
2
0
0
1
1
0
0
2
0
2
1
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
2
1
0
0
1
1
1
0
1
0
2
0
3
1
0
0
0
2
3
0
1
0
1
0
0
0
0
2
0
0
0
0
1
2
0
0
0
2
2
1
1
2
0
6
0
1
2
0
0
2
0
0
1
1
1
1
0
0
0
0
2
0
0
2
0
2
1
1
1
0
1
0
1
0
0
5
2
0
0
2
0
0
0
2
1
2
0
2
1
0
0
0
0
2
0
1
0
1
0
2
0
2
0
1
0
0
0
0
1
2
0
1
0
0
0
1
1
0
1
0
0
5
1
0
1
1
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
2
1
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
2
0
0
1
0
0
2
0
0
0
0
1
1
0
2
0
0
0
0
2
0
0
0
0
2
0
1
3
1
0
1
0
0
0
0
0
0
2
0
0
1
1
1
0
0
0
0
1
1
1
0
2
1
0
1
0
0
0
1
0
2
0
1
2
0
1
0
1
1
0
0
0
0
0
2
0
0
1
0
2
1
1
0
2
0
0
0
1
0
0
0
0
1
1
2
0
0
0
0
0
2
0
0
1
0
1
2
0
0
2
1
0
0
0
0
0
2
2
0
0
0
0
7
1
0
7
2
0
0
0
0
0
0
1
1
0
1
2
0
1
4
0
0
2
0
0
1
0
0
1
0
1
3
0
0
0
2
0
0
2
0
0
1
0
0
1
1
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
1
0
2
0
1
0
0
2
1
0
1
2
2
0
0
0
0
0
1
0
2
0
0
2
2
0
0
0
2
0
2
0
0
0
2
0
0
0
0
4
2
0
1
0
0
0
0
0
0
0
4
0
0
0
2
0
3
0
0
2
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
2
3
0
0
0
2
1
0
0
0
0
1
0
0
0
1
2
0
0
4
2
0
0
1
0
0
5
0
2
0
0
0
1
2
1
0
0
0
0
0
2
2
1
0
5
2
0
0
0
1
0
0
0
2
1
0
0
0
1
0
0
2
1
0
0
0
1
0
2
0
0
0
1
1
0
2
0
1
0
2
0
1
2
0
0
0
2
0
0
0
2
0
3
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
1
0
0
1
0
0
0
2
0
0
0
2
1
0
0
3
2
0
1
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
6
0
1
0
1
1
0
0
1
0
0
1
0
2
0
0
0
0
0
2
0
0
1
1
1
0
3
0
0
0
0
1
2
2
7
0
0
0
0
3
1
3
0
1
0
0
0
0
2
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
2
2
0
2
0
0
0
1
0
0
1
0
0
1
2
0
2
0
0
0
0
0
2
0
0
1
1
0
0
0
2
1
0
1
1
0
0
1
1
0
0
0
0
0
0
0
2
2
1
0
2
0
4
0
0
2
0
1
1
1
0
2
2
1
0
0
1
0
0
0
1
0
0
2
2
1
2
0
0
2
2
1
0
0
1
0
1
0
0
0
2
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
1
0
0
0
2
0
0
4
0
0
0
0
0
0
3
0
2
0
0
2
1
0
2
0
0
1
0
0
0
0
1
0
7
2
0
0
2
0
1
0
0
0
0
1
0
2
1
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
1
7
0
0
0
1
2
0
1
0
0
1
2
0
0
0
0
0
0
0
0
1
1
0
0
2
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
2
0
2
0
2
0
1
1
3
0
1
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
1
1
0
0
3
3
3
0
0
1
0
0
1
1
2
2
0
0
0
0
0
0
0
0
1
0
0
1
2
1
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
3
0
0
0
0
0
1
0
1
0
0
0
0
1
4
2
0
2
0
2
0
2
2
0
0
0
0
0
0
2
2
0
1
0
0
2
2
0
0
3
1
0
0
0
0
2
2
0
0
1
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
1
2
0
2
2
0
0
2
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
1
1
0
2
0
1
24
1
0
0
1
0
0
2
0
0
0
2
9
1
2
0
3
2
1
0
0
2
1
0
0
1
0
0
0
1
0
0
0
2
2
2
0
0
0
0
0
1
2
0
0
1
0
0
2
0
0
0
0
0
0
2
3
0
0
0
1
0
1
0
2
1
0
1
0
0
1
0
0
1
0
1
2
2
3
0
0
3
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
2
1
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
2
2
0
2
3
0
1
0
0
0
1
0
2
2
1
0
2
0
2
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
2
2
1
0
2
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
1
0
2
0
2
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
2
0
0
0
1
0
0
0
0
3
2
0
0
2
1
0
2
1
0
0
0
0
0
0
1
1
0
2
2
0
1
1
0
1
0
1
0
2
0
0
0
0
1
0
0
2
2
1
0
2
0
1
0
0
2
0
1
2
1
0
0
0
1
1
2
0
1
0
0
2
0
1
0
0
0
1
1
0
1
0
0
0
2
2
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
2
0
0
2
0
0
1
0
1
1
0
0
0
0
2
1
0
1
0
2
0
1
0
0
1
2
0
0
1
0
2
0
0
4
0
0
0
0
0
2
3
0
0
0
0
1
0
1
2
1
1
0
1
0
0
0
2
0
0
0
2
1
1
0
0
1
0
0
0
0
1
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
2
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
1
0
0
1
0
2
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
2
0
0
0
2
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
1
1
0
2
3
0
1
1
0
0
2
0
0
2
0
0
0
0
1
2
0
0
0
0
0
2
2
0
2
2
0
0
3
0
0
2
0
1
0
0
1
0
2
1
5
0
0
0
1
0
3
2
0
0
0
0
0
0
1
2
0
3
0
0
0
0
2
0
1
0
0
2
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
4
0
2
0
0
0
0
0
1
0
6
2
0
0
0
0
2
2
0
0
2
0
0
1
2
2
0
0
1
1
2
3
1
0
1
0
0
0
0
2
1
2
0
0
2
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
1
2
2
0
2
1
0
0
1
0
1
0
1
0
0
2
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
1
2
0
0
0
0
2
0
0
0
2
0
0
0
3
0
0
0
1
2
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
1
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
2
0
2
0
1
1
1
0
0
0
1
2
2
0
0
0
0
1
0
0
2
0
0
2
0
0
1
2
2
0
0
0
0
0
2
1
0
3
0
1
0
2
0
0
1
0
2
2
0
0
0
0
0
0
5
0
0
1
1
0
0
0
0
0
0
0
3
0
1
2
1
0
0
0
1
0
1
0
0
1
0
0
2
0
0
0
0
1
0
0
0
1
0
0
2
1
1
0
0
2
0
0
2
0
2
0
0
0
0
2
0
1
0
0
0
0
0
2
2
0
0
0
0
2
2
2
0
1
2
2
0
0
0
1
0
0
0
2
1
2
2
2
1
2
0
0
0
0
1
0
0
0
1
1
1
0
0
1
0
2
0
1
0
1
0
0
0
0
0
0
0
0
4
1
0
1
0
1
1
1
0
1
0
0
0
0
0
1
1
2
0
0
2
0
2
2
0
0
2
0
2
0
0
0
0
0
2
0
2
1
0
1
0
1
0
0
0
0
0
1
1
1
2
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
1
0
1
2
0
0
0
2
2
0
1
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
1
0
0
3
0
2
0
2
0
0
2
0
0
0
0
2
2
4
0
1
0
0
0
1
0
2
1
1
1
1
0
1
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
2
2
1
0
0
0
0
0
2
0
2
0
0
0
1
0
2
0
0
2
0
1
0
0
0
1
2
0
0
0
2
1
1
0
0
2
0
3
1
1
2
0
1
2
2
0
2
0
0
0
2
0
2
1
0
0
2
0
1
4
0
1
0
0
0
0
1
1
0
0
8
2
2
0
0
2
0
0
4
1
1
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
1
2
1
1
2
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
2
0
2
1
2
2
1
0
0
0
0
0
0
1
1
1
2
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
2
2
0
0
1
6
0
2
0
2
0
0
0
0
0
2
0
1
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
1
0
0
1
1
0
0
0
0
0
2
0
1
3
2
0
1
0
0
0
2
1
1
2
1
0
1
2
2
2
0
0
2
0
0
1
2
0
0
0
1
0
0
0
2
0
1
1
0
2
0
2
1
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
1
0
2
2
0
0
0
0
0
6
0
0
2
0
1
1
0
2
1
1
2
0
0
7
0
0
0
0
2
2
0
0
1
1
0
2
0
0
0
0
2
0
1
4
0
0
2
0
4
0
0
2
0
2
0
0
0
0
2
0
0
1
1
0
3
4
1
0
0
0
1
0
0
0
0
0
0
0
2
2
1
1
2
0
0
0
0
3
0
0
1
0
1
0
0
0
1
2
0
0
2
1
2
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
1
2
2
0
2
0
1
0
0
1
0
0
0
1
0
2
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
1
2
0
2
0
2
0
0
0
1
1
2
0
0
2
1
0
0
0
2
2
0
0
0
0
1
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
2
0
1
0
0
0
0
0
0
0
1
2
0
1
0
0
0
2
0
0
2
2
0
2
0
0
0
1
1
0
0
0
1
0
0
2
0
1
1
0
0
1
0
0
2
0
2
0
0
2
0
3
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
1
0
1
0
0
2
1
1
0
4
0
2
2
1
1
0
0
0
0
1
0
0
0
0
0
2
0
2
1
0
0
2
0
0
1
0
0
1
0
0
0
0
0
2
0
2
0
0
0
1
2
0
2
0
2
0
0
0
2
0
0
1
2
1
0
1
0
0
1
2
0
0
1
0
0
0
0
0
0
0
1
3
1
1
0
0
0
0
0
2
0
1
0
1
1
0
0
0
2
0
0
4
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
1
1
2
0
0
1
1
0
0
0
0
0
1
2
2
0
0
0
0
0
2
0
2
0
0
0
0
3
0
0
1
0
1
1
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
1
2
1
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
1
2
2
0
0
0
0
0
1
0
1
1
0
1
2
1
0
0
1
2
0
0
0
2
0
0
0
2
1
0
0
0
1
1
0
1
2
0
0
0
1
0
0
1
0
1
2
1
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
2
2
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
1
2
1
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
15
0
1
0
0
1
0
3
0
0
2
1
0
0
0
1
0
1
0
3
0
3
3
0
0
0
0
0
0
1
0
0
2
2
0
0
1
1
2
0
1
1
0
0
0
1
0
1
2
0
2
0
0
0
0
0
1
0
1
0
1
0
1
0
0
2
2
0
0
0
1
0
2
0
0
0
0
0
2
1
0
1
2
2
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
2
2
2
0
2
1
0
1
1
0
2
0
1
0
0
1
1
0
2
0
0
0
0
0
0
0
2
0
1
0
1
1
0
0
4
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
2
0
0
1
0
0
2
0
0
0
0
1
0
0
1
1
0
0
1
0
1
1
1
0
2
2
0
2
0
2
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
1
1
2
1
2
0
2
2
1
1
0
1
0
1
1
0
2
0
0
2
0
2
3
0
0
1
0
1
0
0
0
0
0
1
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
1
0
0
0
0
1
0
2
0
0
0
0
0
1
3
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
1
0
0
2
1
2
0
2
2
0
1
0
0
0
0
2
1
2
0
1
1
0
0
1
2
1
2
0
0
3
0
0
2
0
2
1
0
2
0
1
2
0
0
0
2
0
0
1
2
1
3
0
0
0
0
1
0
1
0
0
1
2
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
2
3
1
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
3
1
0
2
0
0
0
1
2
0
1
0
0
1
0
0
0
0
1
2
0
2
0
0
1
0
2
1
1
0
0
0
1
2
0
1
2
0
1
0
1
2
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
3
0
0
0
0
0
0
0
0
2
1
0
0
1
0
1
0
0
0
0
0
0
0
0
2
4
0
0
0
0
2
0
0
0
0
0
2
1
1
0
2
0
2
1
1
2
1
0
2
2
2
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
2
1
2
2
0
0
0
1
3
2
3
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
1
2
0
0
0
3
0
1
1
0
0
0
0
0
1
2
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
1
0
2
2
0
0
0
2
1
2
2
2
0
0
1
0
1
0
0
0
2
1
0
1
0
0
2
0
1
1
0
0
0
0
1
0
0
1
1
0
0
2
0
2
1
0
1
2
3
0
0
0
1
2
0
0
0
3
0
0
1
1
0
2
0
0
2
0
0
0
1
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
3
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
4
0
0
3
1
0
0
0
2
0
0
0
3
0
1
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
1
1
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
1
1
0
0
3
2
0
2
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
2
2
1
0
1
1
0
0
0
0
0
0
0
0
0
2
2
1
1
0
1
0
0
2
2
0
2
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
2
2
2
0
0
0
0
0
1
2
2
0
0
0
0
3
0
1
0
0
1
1
0
1
1
0
1
0
0
4
1
1
0
2
0
0
1
0
0
2
2
0
0
1
1
2
0
0
0
0
0
1
2
0
0
0
0
2
0
1
0
2
0
0
0
2
0
2
2
0
0
1
2
0
2
2
2
2
1
0
1
1
0
0
1
0
2
1
0
0
2
1
0
0
0
0
1
0
0
0
0
0
2
2
2
2
0
0
2
1
0
0
0
0
1
0
2
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
2
5
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
1
3
2
1
0
3
1
0
0
0
0
1
0
0
2
2
1
2
0
2
0
0
2
0
0
0
0
0
0
0
4
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
2
1
1
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
2
4
0
0
0
0
1
1
0
0
2
0
1
0
1
1
0
1
0
0
0
1
0
2
0
0
0
0
4
1
0
0
0
0
0
2
0
1
0
2
0
0
2
2
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
2
1
0
2
2
0
0
2
0
1
2
0
1
1
0
0
2
0
0
2
1
1
0
0
0
0
2
1
1
0
0
2
1
0
0
0
0
0
8
2
1
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
2
0
0
2
2
0
0
2
2
0
0
1
2
0
0
0
2
2
2
2
0
0
2
0
0
0
0
1
0
1
0
0
0
0
2
2
0
1
0
0
2
0
0
0
1
1
0
1
1
0
1
1
0
0
2
1
0
0
1
0
0
2
0
0
0
0
2
0
0
0
1
0
1
0
2
0
1
0
0
0
2
1
0
0
0
5
2
0
0
2
1
0
2
0
1
0
0
0
0
2
1
0
0
0
2
0
2
0
1
1
2
1
0
0
2
0
2
0
0
1
1
1
0
1
0
2
3
1
0
0
2
2
0
0
0
0
2
0
0
3
0
0
0
0
0
0
1
0
0
0
1
0
1
1
2
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
2
0
0
0
0
0
1
1
3
0
0
2
0
1
0
0
0
0
2
0
1
0
0
1
0
1
0
0
1
0
1
0
1
0
2
4
0
0
1
0
0
1
0
0
0
0
2
2
0
0
0
0
1
1
1
2
0
0
0
0
0
0
0
0
3
0
0
0
0
2
2
1
0
0
0
0
2
0
2
0
0
0
1
2
0
2
0
1
0
2
1
1
0
0
0
0
0
1
0
1
2
0
1
0
0
2
0
0
1
0
2
0
0
2
2
1
0
0
2
0
2
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
3
0
0
2
0
0
0
1
1
1
2
0
0
1
1
1
0
0
0
0
1
0
0
1
1
0
1
0
1
0
2
0
2
0
0
0
0
2
0
1
1
1
2
0
2
0
0
0
2
1
0
1
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
1
2
0
1
0
1
0
1
0
0
0
2
0
0
0
0
1
1
0
0
1
2
0
3
0
2
1
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
3
0
1
0
0
0
0
1
0
2
0
1
0
2
0
2
0
0
0
0
1
0
0
1
0
0
2
2
2
0
1
0
2
0
0
2
0
0
6
0
0
1
2
0
0
0
1
0
0
0
1
0
0
2
0
2
0
0
0
0
2
0
3
0
0
3
1
0
1
2
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
3
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
1
2
1
0
2
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
1
2
1
4
2
0
0
0
0
2
0
0
5
1
1
0
0
2
0
1
0
0
1
1
0
0
0
2
2
0
2
2
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
3
0
0
0
1
1
0
0
0
1
0
2
0
2
0
2
0
2
2
1
2
3
0
0
0
1
1
0
0
0
0
0
2
2
1
0
0
2
2
1
2
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
2
0
2
2
0
3
0
2
0
0
0
2
0
0
1
0
0
0
0
2
2
2
2
0
0
0
0
1
1
2
0
2
1
0
2
1
0
1
2
0
0
2
1
0
2
0
0
2
2
0
0
1
0
0
1
0
1
1
0
0
0
5
0
2
0
1
0
1
2
2
1
0
1
0
1
1
0
1
0
2
0
0
0
1
0
0
0
2
1
0
0
2
0
0
2
1
1
0
1
1
0
0
0
0
0
3
1
0
0
0
2
1
0
0
0
1
0
0
2
0
0
0
0
1
0
1
0
1
0
1
3
0
0
0
0
0
0
1
0
4
0
0
1
0
0
2
2
2
0
0
0
2
0
0
0
0
0
0
0
3
2
0
1
2
1
0
0
2
0
0
1
2
0
2
2
0
0
0
0
1
0
0
2
0
0
1
0
2
2
0
1
0
1
2
0
0
0
2
2
0
0
1
1
2
0
1
1
0
1
0
1
0
0
0
0
3
2
0
0
2
1
0
2
0
0
2
1
0
0
2
0
1
2
0
3
0
1
3
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
2
0
1
0
0
0
0
2
2
2
3
0
0
1
0
0
3
0
1
0
2
2
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
2
1
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
1
0
0
0
0
2
2
1
1
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
2
0
1
0
1
0
1
2
1
0
0
1
2
0
2
0
1
2
0
0
1
1
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
5
0
0
1
0
0
0
2
0
1
0
1
1
2
0
2
2
0
2
1
0
0
0
0
1
2
0
2
0
1
1
1
0
0
0
2
0
0
2
1
0
0
0
0
1
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
1
1
2
0
0
0
2
0
0
0
1
2
0
0
1
0
1
1
1
2
0
1
2
1
0
0
0
0
0
0
1
0
2
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
2
0
3
0
0
0
0
2
0
0
1
0
0
3
0
3
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
2
1
2
1
0
5
0
5
0
1
0
0
0
3
0
0
4
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
1
2
1
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
2
1
2
1
0
2
2
1
0
1
1
1
1
0
0
0
0
0
1
0
0
0
2
1
2
0
0
0
0
0
0
1
0
2
0
0
0
2
0
2
2
0
1
0
1
0
0
0
0
2
1
0
0
0
2
1
2
7
0
3
0
1
0
0
0
1
0
1
0
0
3
1
0
1
3
0
0
0
0
3
0
0
1
0
0
0
2
0
2
1
1
0
3
0
0
0
0
0
2
0
2
0
0
0
0
0
3
3
2
1
0
1
0
1
0
0
0
0
1
1
0
0
3
0
0
2
0
2
2
0
0
1
0
1
1
2
0
0
0
0
1
2
1
1
2
1
0
0
0
1
0
2
0
2
0
0
0
0
0
1
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
2
2
1
3
0
0
0
0
2
0
2
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
1
0
1
0
0
1
3
2
0
1
0
1
11
1
0
0
1
1
2
0
0
0
2
0
0
0
2
0
2
0
0
2
2
1
0
0
0
0
0
0
2
2
0
0
0
3
2
0
0
0
0
2
0
0
0
0
0
2
2
2
0
1
0
1
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
2
4
1
0
0
2
0
0
2
0
1
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
1
0
0
0
0
2
0
2
0
0
0
1
0
0
2
0
2
2
1
0
0
2
0
0
0
4
1
1
2
2
0
0
0
0
0
0
2
0
2
1
0
1
3
1
0
1
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
1
1
1
1
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
1
3
1
0
0
0
0
0
0
0
2
1
0
0
0
1
1
0
0
0
0
2
0
0
1
1
0
0
0
1
2
0
0
1
1
0
0
2
1
0
2
0
0
0
1
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
4
0
0
1
1
0
1
1
2
1
0
2
3
3
2
0
0
0
2
0
0
2
0
0
7
0
1
0
0
1
1
2
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
3
1
1
0
0
0
1
0
2
0
2
2
0
2
0
0
0
2
0
0
0
0
0
2
0
1
1
0
1
0
1
1
0
0
0
1
0
1
2
2
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
2
0
0
2
2
3
0
0
0
0
1
2
0
2
1
1
2
2
0
0
0
0
2
0
2
0
0
0
2
1
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
1
1
1
0
2
0
0
0
1
0
2
0
1
0
0
0
0
0
3
0
1
1
2
2
0
0
2
0
1
0
0
1
2
1
2
0
0
0
0
0
0
0
0
1
0
0
2
0
2
5
1
0
2
0
1
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
2
0
0
1
0
0
0
1
1
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
2
1
0
0
0
3
0
0
0
0
1
0
0
1
2
1
0
0
1
0
0
1
0
0
0
0
2
1
0
0
2
0
2
1
0
1
0
2
0
0
1
4
7
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
1
2
1
2
0
0
0
0
0
0
1
0
0
0
1
1
3
2
2
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
1
1
0
2
0
1
0
0
0
0
0
1
0
1
3
1
2
0
0
0
0
0
2
2
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
2
0
1
0
0
1
4
1
0
0
0
0
0
1
0
2
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
2
0
1
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
2
0
1
0
0
0
0
1
2
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
1
0
1
2
0
1
0
1
0
2
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
2
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
1
1
2
0
2
0
0
1
1
2
0
0
0
2
0
1
1
2
1
2
0
3
2
0
1
0
0
1
0
0
2
0
0
2
1
0
0
2
1
1
1
1
0
0
0
0
2
0
1
2
1
2
2
2
0
0
0
0
0
1
0
0
2
0
5
1
1
0
0
1
2
1
2
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
1
0
2
0
0
2
2
0
0
0
0
2
0
2
3
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
2
0
2
0
1
0
0
0
1
1
0
0
0
0
2
1
2
0
0
1
0
0
0
0
0
0
1
0
0
0
1
2
0
0
3
0
0
0
0
3
0
1
0
2
2
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
1
4
1
0
5
0
0
2
0
0
2
2
1
0
1
0
0
0
1
5
0
0
1
0
1
0
0
2
0
0
4
0
1
2
0
2
1
0
1
0
0
0
0
2
0
1
0
2
1
0
1
0
0
1
0
0
2
0
0
0
1
2
2
2
1
3
0
2
0
3
2
0
0
0
0
0
4
0
0
2
3
0
2
2
2
1
2
0
0
2
7
0
0
0
0
0
0
0
0
3
0
0
0
0
2
2
2
2
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
2
0
1
0
1
2
2
0
0
0
0
0
2
0
0
0
0
0
0
1
1
2
1
2
0
0
0
0
1
2
0
0
1
0
1
2
0
0
1
0
1
1
0
1
2
2
0
1
0
1
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
2
2
2
0
0
1
2
0
1
0
3
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
1
0
2
2
0
0
0
0
2
0
1
2
1
2
0
1
1
0
0
1
0
1
0
0
0
4
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
1
0
3
2
0
0
0
1
1
0
2
3
0
0
2
1
0
2
1
2
1
2
2
0
0
0
0
0
1
0
3
0
0
0
2
0
0
0
0
2
0
2
0
2
0
0
1
0
0
1
2
1
0
2
1
0
0
0
0
1
0
1
0
0
0
0
2
0
0
1
2
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
3
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
2
0
2
2
0
1
0
0
0
0
2
2
0
0
0
0
1
1
0
1
1
1
0
0
2
0
2
0
1
0
1
0
0
0
0
1
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
1
0
1
0
3
2
0
2
0
0
0
0
0
0
0
2
0
1
0
2
0
2
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
2
2
0
2
1
1
0
0
0
0
0
0
0
2
0
0
1
3
1
1
2
2
0
0
2
0
0
0
1
3
0
0
0
2
2
2
1
0
1
0
0
0
0
1
0
0
2
0
1
2
0
2
0
0
1
2
0
1
1
1
1
0
0
1
2
0
0
0
0
1
0
1
0
2
0
0
2
2
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
2
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
2
2
1
2
0
1
0
1
0
2
0
0
0
0
0
0
0
1
2
0
2
1
2
0
0
0
2
2
0
2
0
1
2
2
2
0
1
0
0
0
0
2
1
1
1
2
2
0
0
0
1
1
0
1
6
2
1
0
1
1
0
0
0
2
0
0
2
0
0
0
1
1
2
1
1
0
1
0
0
1
0
0
0
1
2
0
0
2
0
1
1
1
0
0
1
0
1
2
0
0
2
0
0
0
1
0
0
0
1
2
0
1
0
1
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
1
0
2
0
0
0
1
1
1
2
0
0
1
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
2
2
0
0
0
1
1
0
0
1
0
0
0
0
2
0
0
0
1
0
0
1
0
3
2
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
2
0
2
1
0
0
3
1
0
1
0
0
0
0
1
1
0
2
0
0
2
0
0
0
2
0
2
2
0
2
0
0
0
1
1
1
0
0
0
2
1
0
0
0
1
1
0
1
0
3
1
0
2
0
0
2
0
2
0
2
0
3
0
0
0
0
0
0
1
3
1
0
1
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
3
1
2
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
2
0
0
1
1
0
1
1
0
0
0
0
2
0
0
0
1
0
0
2
0
1
4
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
2
0
0
0
2
0
0
2
0
0
0
0
0
2
1
0
1
2
0
0
0
2
0
0
0
0
4
0
2
0
0
0
0
0
1
0
2
0
0
1
0
2
4
0
0
2
0
0
0
0
2
0
2
0
0
0
0
3
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
1
0
2
0
1
0
0
0
1
0
1
1
0
0
1
2
0
0
0
0
0
2
0
1
0
2
0
1
0
1
1
0
0
0
0
0
0
0
3
1
4
0
0
0
0
1
0
1
0
0
1
0
0
1
1
2
0
0
0
1
1
1
0
0
0
0
2
2
2
1
0
0
1
2
2
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
1
2
2
0
0
0
0
1
0
0
2
1
0
1
2
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
2
0
0
1
0
1
0
0
0
0
2
2
0
0
0
0
0
2
0
2
1
0
2
1
2
1
0
0
0
0
0
2
0
2
0
0
0
0
3
0
1
0
0
2
0
1
0
0
0
0
0
1
0
0
0
1
1
2
1
1
2
1
0
2
0
0
1
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
1
0
2
0
0
1
0
3
0
0
0
0
0
2
1
0
0
1
1
0
0
2
1
0
2
0
0
1
1
0
0
3
1
2
0
1
0
2
2
0
0
0
0
0
0
1
0
0
1
0
2
0
0
1
0
0
0
2
0
0
1
0
1
2
0
1
3
0
2
0
1
0
1
2
0
2
0
0
0
0
0
0
1
1
0
0
0
0
1
0
2
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
3
1
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
2
0
2
0
0
0
0
0
1
2
1
0
0
0
2
0
0
0
1
1
0
0
2
2
0
2
0
0
0
0
0
2
1
2
1
0
2
1
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
1
2
1
0
0
1
0
0
0
5
2
0
0
0
2
0
0
0
1
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
1
0
2
0
0
1
0
0
2
0
0
0
1
0
1
0
2
1
0
2
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
2
2
0
0
1
0
1
0
0
1
0
0
1
0
2
1
0
1
1
0
0
3
0
0
0
2
0
0
0
1
0
2
2
1
2
0
0
0
1
0
2
0
0
1
0
2
0
1
0
0
1
1
0
0
0
1
0
1
1
0
0
1
0
0
1
0
0
2
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
2
2
0
0
1
2
0
1
1
0
0
0
1
1
0
0
2
0
1
0
2
2
0
1
1
0
0
0
1
2
2
1
0
0
0
0
0
1
2
0
1
0
2
0
0
1
0
2
2
0
1
2
0
0
0
2
0
0
0
1
0
2
0
0
1
2
0
1
0
0
0
0
1
0
1
0
1
1
0
0
1
0
2
0
0
3
0
0
0
1
0
0
0
0
1
1
1
1
2
0
0
2
2
0
1
1
0
0
2
0
0
2
0
0
1
0
2
0
1
0
0
0
0
2
0
0
0
1
1
0
1
0
0
0
0
1
0
2
0
0
0
0
1
1
0
0
0
0
0
2
1
0
0
2
0
0
2
0
1
2
2
1
0
0
0
4
2
0
0
0
1
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
1
1
0
2
1
1
1
0
2
0
1
0
1
0
0
0
1
0
1
0
0
0
2
1
0
0
1
0
0
1
0
0
0
0
3
0
1
0
0
0
0
2
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
10
0
0
1
1
0
1
3
2
0
3
0
1
1
1
0
1
0
1
2
2
1
0
2
0
0
1
0
2
0
2
0
0
0
1
0
0
2
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
3
1
2
1
2
2
0
2
2
0
1
0
0
2
1
0
1
0
2
0
1
0
0
1
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
1
0
1
0
0
1
0
2
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
2
0
2
0
0
0
0
2
1
0
2
0
1
0
3
0
0
1
2
0
1
0
0
1
2
0
0
0
1
0
0
6
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
2
0
1
0
0
0
0
1
0
1
1
2
0
0
0
0
1
0
3
0
1
1
0
0
0
1
1
3
3
0
0
1
0
1
0
1
0
0
2
2
2
0
2
0
0
0
0
0
1
0
0
0
2
0
0
5
1
0
0
2
2
1
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
1
2
0
1
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
2
0
2
0
1
1
3
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
1
2
0
0
1
0
0
0
0
0
0
0
0
1
0
4
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
1
0
0
0
0
1
0
0
0
1
1
1
0
2
1
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
2
0
0
0
0
1
1
2
3
2
1
0
2
0
1
2
2
0
0
0
0
0
1
0
0
2
0
2
0
2
1
0
0
0
0
0
0
2
0
1
0
1
1
0
0
0
2
0
2
0
0
2
2
4
2
0
1
0
0
0
0
0
0
0
1
0
2
0
1
1
0
0
0
2
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
1
2
1
0
0
2
0
0
0
2
1
2
2
1
0
1
1
1
1
0
0
0
0
2
0
1
2
1
0
3
0
0
0
0
1
1
0
1
0
0
1
0
1
0
0
0
1
1
3
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
3
0
1
0
1
0
0
2
0
2
0
0
2
2
1
0
0
0
0
1
2
0
2
2
1
0
0
0
1
1
0
0
0
0
2
0
0
2
4
0
0
0
2
0
4
0
0
1
2
0
0
2
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
2
0
0
1
0
1
0
4
0
0
0
0
1
0
1
2
0
1
0
4
1
2
0
0
2
0
0
1
2
1
0
0
0
2
0
0
0
1
1
4
0
0
2
0
0
2
0
0
0
0
1
0
0
2
2
0
0
0
1
2
0
0
0
1
0
0
1
1
0
2
0
0
1
0
0
0
0
1
0
2
2
1
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
1
0
0
3
0
0
2
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
2
0
0
0
1
0
0
0
1
0
1
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
2
3
0
0
0
1
0
2
2
0
0
2
2
0
0
1
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
1
2
3
0
0
0
0
2
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
1
1
0
0
0
2
2
0
1
0
2
0
0
2
0
0
2
0
0
2
1
2
1
2
1
2
0
0
3
1
0
0
2
1
3
0
0
2
1
0
0
2
1
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
2
2
0
0
0
0
1
1
1
2
2
1
0
0
0
2
1
2
1
1
0
1
1
0
1
2
0
1
0
0
0
0
0
0
2
2
0
0
1
0
0
2
1
0
1
0
0
2
0
0
0
0
1
0
0
0
0
1
6
1
1
1
1
0
1
2
0
0
0
1
0
0
0
0
1
2
0
0
1
1
0
2
0
2
0
0
2
0
0
0
1
2
2
0
0
0
0
0
1
0
0
0
0
1
0
0
7
2
0
0
0
0
1
0
0
1
0
0
0
2
0
1
1
2
0
0
1
0
0
2
0
0
2
0
1
0
0
0
0
2
2
0
0
1
0
0
0
0
0
1
2
0
1
0
0
2
0
2
0
0
1
0
1
0
2
2
0
0
0
0
0
1
0
0
2
2
0
2
0
0
0
0
1
2
1
0
2
0
0
0
2
1
0
0
0
1
0
1
1
2
0
2
0
0
0
1
0
1
1
2
1
2
1
0
0
1
0
0
0
0
0
4
0
0
1
0
2
0
1
0
0
0
0
0
0
2
0
2
0
0
0
1
0
2
0
0
2
1
2
0
2
0
0
0
0
0
1
1
1
0
0
0
4
3
2
2
0
2
0
0
2
0
2
1
0
0
2
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
2
1
0
0
0
1
0
0
1
1
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
1
1
1
2
2
0
0
1
0
0
2
2
0
0
0
0
1
0
0
2
2
0
1
1
0
0
1
0
0
2
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
2
0
0
1
0
0
0
2
2
2
2
0
1
0
0
1
0
0
2
2
0
2
0
0
0
1
1
1
2
0
0
0
0
2
1
0
0
1
0
0
2
2
1
0
1
0
0
0
2
1
0
0
0
2
1
2
2
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
2
0
0
1
2
0
1
0
2
0
0
1
0
0
1
0
0
0
0
2
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
1
0
0
0
0
1
1
2
0
0
1
1
0
0
2
1
0
0
0
1
0
0
1
2
0
1
0
2
0
0
0
0
1
0
2
0
0
0
0
2
0
2
0
2
2
0
0
0
2
1
1
1
0
0
0
1
0
2
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
4
2
2
0
0
4
1
0
1
0
0
0
0
2
0
0
2
2
0
0
2
0
2
0
0
0
0
0
0
1
6
0
0
2
0
0
0
0
0
1
2
1
0
0
0
0
0
0
1
0
0
3
1
1
0
1
2
0
0
0
0
0
2
0
2
1
0
2
0
0
1
1
0
0
0
0
2
0
0
0
1
0
0
0
4
1
0
2
2
1
1
1
0
0
0
0
2
0
0
0
0
3
0
2
0
0
1
0
0
0
0
4
0
0
1
1
1
0
0
2
3
2
3
1
2
0
0
1
0
0
0
1
0
0
0
0
0
1
0
2
0
1
0
1
2
0
0
0
3
0
0
0
0
2
0
0
0
1
0
2
2
0
0
1
0
1
0
0
2
1
0
0
0
2
0
1
0
1
0
0
0
1
0
2
2
2
1
0
2
0
0
2
0
0
1
0
4
1
0
0
0
1
2
0
0
0
0
1
0
1
1
0
0
0
0
2
2
0
1
0
0
0
4
2
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
2
2
0
2
0
0
0
0
1
2
0
2
0
0
2
0
1
0
0
1
0
2
1
0
1
0
0
1
2
2
0
2
0
0
0
2
1
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
2
0
0
0
2
1
2
1
1
0
0
2
0
0
0
0
0
0
2
1
1
0
0
1
0
1
2
1
0
0
1
0
0
2
0
0
2
2
0
2
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
2
0
0
0
0
1
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
1
2
2
0
0
0
2
0
2
1
1
2
2
0
2
0
1
0
0
0
0
1
1
0
0
0
0
0
2
1
1
0
0
0
2
0
2
0
0
0
0
0
0
2
1
2
2
0
1
2
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
1
2
1
0
0
0
2
0
0
0
0
2
1
1
2
1
1
0
2
5
0
1
1
2
0
0
2
1
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
1
2
1
0
1
5
1
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
1
0
1
0
0
0
1
3
0
0
0
0
1
1
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
3
2
0
0
0
0
1
2
2
1
1
0
0
0
0
2
2
0
0
0
1
0
1
0
0
2
2
1
0
2
2
0
1
0
1
2
0
0
3
0
1
0
2
0
2
0
0
2
0
0
0
1
0
0
1
2
0
0
0
0
0
2
1
0
0
1
3
0
2
2
2
0
2
0
0
0
2
0
0
0
2
1
1
0
1
3
0
0
0
0
1
0
0
1
0
1
0
0
2
2
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
2
2
0
0
1
0
2
1
0
0
1
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
1
2
2
0
2
0
0
1
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
1
2
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
1
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
4
0
2
2
0
0
0
0
0
0
5
0
0
0
1
0
2
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
1
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
2
2
0
0
0
1
0
0
0
1
2
0
0
2
0
2
2
2
0
1
0
0
0
1
0
0
2
0
0
2
0
1
2
0
2
0
2
0
7
0
0
0
0
0
0
3
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
2
1
0
0
0
2
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
2
0
0
1
1
2
0
0
0
0
2
0
0
3
1
0
0
0
2
2
0
1
0
1
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
2
2
1
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
2
0
1
1
0
2
0
1
1
0
0
0
0
1
0
2
0
0
2
1
2
3
0
1
1
0
1
2
0
1
4
0
1
0
0
0
1
1
0
2
0
1
0
0
0
0
2
0
2
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
1
2
0
0
1
0
0
0
0
0
3
1
1
0
0
2
1
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
1
0
2
2
0
2
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
2
0
1
1
0
0
0
2
0
1
1
0
0
0
2
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
1
2
0
0
0
2
0
0
2
0
0
1
0
0
0
0
2
0
2
0
0
0
1
1
2
0
0
0
1
0
1
0
0
0
0
0
0
0
2
2
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
2
0
2
2
2
0
3
2
1
0
1
0
0
2
1
0
0
0
1
0
3
2
0
0
0
0
0
1
0
1
2
1
2
1
0
0
0
0
0
1
0
0
1
1
0
1
1
0
2
0
0
1
0
0
1
1
2
0
1
0
0
1
0
0
0
1
0
0
0
0
2
2
0
1
0
0
2
0
2
2
0
2
1
0
0
0
0
0
0
1
0
0
1
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
1
2
0
0
0
1
0
0
0
2
0
2
2
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
2
1
1
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
3
1
0
2
0
0
0
0
0
1
0
1
2
1
0
2
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
2
1
0
0
0
0
1
1
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
1
2
1
2
0
1
1
0
2
0
2
0
2
0
3
0
0
0
1
2
2
0
2
2
0
0
0
2
0
1
0
0
0
0
2
0
0
1
0
1
0
0
5
0
0
0
0
0
2
0
1
0
2
0
3
0
1
1
0
1
0
0
1
0
2
0
2
0
0
1
1
0
2
0
0
2
1
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
2
0
0
0
0
0
0
1
1
2
1
0
0
0
2
0
0
0
0
3
1
0
2
2
1
0
0
1
1
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
2
0
0
1
0
0
0
1
2
0
2
0
0
1
0
0
2
0
1
0
0
0
0
0
0
2
2
0
0
0
0
2
1
0
0
1
0
0
2
0
1
0
0
0
0
0
0
1
0
1
2
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
2
0
0
2
2
0
2
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
2
0
2
2
0
1
0
1
1
0
3
0
0
0
2
0
1
0
0
2
1
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
2
0
3
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
1
1
0
0
0
0
1
2
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
4
2
0
0
0
2
1
0
0
0
1
1
0
0
0
0
0
2
0
0
1
2
3
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
1
0
0
0
2
1
0
0
0
1
1
1
0
2
2
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
1
0
1
1
0
0
0
0
1
2
2
0
0
0
0
0
2
2
0
1
1
0
0
0
0
2
0
0
3
1
0
0
0
2
0
0
0
0
2
1
0
2
1
0
2
1
0
1
2
0
0
2
0
2
2
0
2
1
0
0
8
0
1
0
2
0
2
0
1
0
0
1
2
0
2
0
1
0
0
1
1
0
4
0
1
2
0
0
0
1
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
1
0
0
0
0
2
0
0
0
3
1
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
2
1
0
1
1
2
0
2
1
1
1
1
2
1
0
2
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
2
4
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
1
2
0
0
0
4
0
2
1
1
0
0
0
0
2
0
3
1
0
0
0
1
1
0
1
1
1
0
0
0
2
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
2
0
1
2
2
2
1
0
0
1
0
0
1
0
2
3
0
1
0
2
2
0
0
1
0
0
1
0
2
3
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
3
2
1
1
0
2
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
2
2
1
0
0
0
1
1
0
1
0
0
0
1
0
2
0
1
0
0
0
0
1
0
1
0
0
1
0
1
0
1
1
0
1
0
2
0
1
0
0
0
0
0
2
0
1
0
0
0
0
1
1
1
1
0
1
0
2
0
1
1
0
1
2
1
0
1
0
0
1
0
2
0
0
0
0
1
0
0
2
1
0
0
1
2
1
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
2
1
1
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
6
0
2
0
0
1
0
0
0
0
0
0
1
3
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
1
0
1
0
0
0
2
2
0
1
0
0
1
2
0
0
2
0
0
2
0
1
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
2
0
0
0
0
3
1
0
1
0
0
0
2
0
2
0
0
2
1
0
1
0
0
1
1
2
0
0
0
0
0
2
0
0
0
2
1
0
0
7
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
2
2
2
2
2
0
1
2
0
0
2
0
0
0
0
0
0
0
0
2
2
1
0
1
1
0
0
0
1
2
2
2
2
0
3
1
1
0
0
2
0
1
0
1
1
0
0
0
0
2
0
2
1
1
0
0
1
2
7
2
0
0
2
0
2
0
0
0
2
1
3
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
2
1
3
0
0
2
1
3
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
2
2
0
0
2
0
0
0
0
5
1
3
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
2
0
0
0
2
0
2
0
0
1
2
0
0
1
0
0
0
1
0
0
0
0
3
0
2
0
1
0
0
2
0
0
1
1
0
2
1
0
0
2
0
2
0
1
1
2
0
0
2
1
0
2
0
2
0
1
0
0
0
0
1
2
0
1
2
2
1
0
0
0
1
2
0
0
1
1
0
1
1
0
0
0
0
0
0
0
2
0
0
1
0
2
0
2
0
0
0
2
0
0
0
0
1
1
2
0
0
2
1
0
1
0
0
1
5
0
1
0
2
2
0
0
1
1
0
0
1
0
0
1
0
2
2
0
1
0
1
1
2
2
0
0
2
1
0
0
0
1
2
0
0
3
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
1
2
2
1
2
2
0
0
0
0
0
0
1
2
0
2
0
0
0
0
1
2
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
1
0
2
0
0
0
1
1
1
0
1
0
0
1
0
3
3
0
1
0
1
2
0
0
2
1
0
1
1
1
0
3
1
0
0
2
0
0
1
2
0
1
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
2
0
0
1
2
2
0
0
0
0
1
1
0
0
0
2
2
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
1
1
0
1
2
0
0
0
0
1
3
1
0
1
1
1
1
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
1
1
0
1
0
0
0
0
2
1
0
1
4
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
5
0
0
2
0
2
2
1
0
2
0
0
0
0
1
0
2
0
0
0
2
2
0
0
0
0
2
1
1
0
1
0
2
0
1
0
2
0
0
0
2
1
2
0
2
2
0
0
2
1
0
2
0
0
1
0
1
0
1
0
0
2
1
0
1
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
1
0
2
1
3
0
1
0
3
0
0
0
0
0
0
0
1
3
1
0
0
0
0
0
2
1
2
0
0
0
2
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
6
0
1
2
1
0
0
0
0
2
1
2
2
1
1
1
0
0
1
0
2
4
0
2
0
2
0
1
0
1
1
1
0
1
1
0
0
0
1
0
1
0
0
2
3
0
0
0
0
0
0
0
0
0
1
0
1
3
0
2
3
0
0
0
1
0
0
1
0
0
1
0
1
0
0
2
0
0
2
1
0
2
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
1
2
1
1
0
0
0
1
0
1
1
0
0
2
1
0
1
2
1
0
2
0
0
0
2
0
0
0
0
1
2
2
1
0
1
0
0
1
0
0
3
0
0
2
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
2
3
0
0
1
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
2
0
2
0
0
2
2
0
0
4
2
0
0
3
0
0
1
2
1
0
0
2
0
0
1
0
1
0
1
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
3
1
0
0
4
0
0
0
0
2
0
2
2
0
0
0
0
8
0
0
0
0
0
2
1
1
0
0
0
1
0
0
3
0
1
0
2
0
2
0
1
0
1
0
0
1
0
0
0
4
0
0
1
1
0
1
2
1
0
1
0
0
0
1
2
1
2
0
2
0
0
0
0
2
2
0
1
0
0
4
0
2
0
1
1
0
1
2
0
0
2
0
1
3
1
0
0
0
1
0
0
0
1
0
0
2
0
2
1
0
2
0
0
1
0
0
2
0
2
0
2
0
1
2
0
0
0
1
0
0
1
0
2
1
1
1
0
1
0
0
2
0
0
1
2
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
2
0
0
0
0
0
1
0
2
1
0
0
1
1
0
1
2
0
0
0
2
0
0
0
1
2
0
3
0
0
0
0
1
0
0
0
0
0
2
2
0
0
2
1
1
0
2
2
0
0
0
0
2
1
0
0
0
0
0
2
1
2
0
1
0
0
0
0
0
2
0
0
3
0
0
0
0
0
2
1
0
0
0
2
0
1
1
0
0
0
1
1
0
2
0
0
0
0
2
0
0
1
0
1
0
0
0
2
0
0
0
0
0
1
2
0
2
3
0
1
1
0
2
0
1
1
0
0
0
1
2
0
0
1
1
2
2
2
1
0
1
0
0
2
1
0
0
0
3
1
0
4
2
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
1
0
2
3
0
0
0
2
0
1
2
2
0
1
0
2
0
1
0
0
1
3
0
0
2
1
0
0
1
0
0
1
0
1
1
0
0
1
2
0
1
1
0
2
0
0
0
0
2
0
1
0
1
0
5
0
0
0
0
1
0
0
0
0
0
1
1
0
2
0
0
0
1
0
2
2
1
1
0
1
1
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
4
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
1
1
0
1
0
0
0
1
2
0
2
1
0
1
4
2
0
2
0
2
0
3
0
1
3
2
1
1
0
0
0
2
0
0
0
1
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
2
1
1
0
2
0
0
0
0
2
2
0
0
0
2
1
0
0
2
0
0
1
0
0
1
0
2
0
0
0
0
2
2
2
0
2
2
3
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
1
1
0
3
0
1
0
2
0
0
2
0
0
4
0
0
0
2
2
1
0
0
0
0
1
0
0
0
0
0
2
1
2
0
0
0
1
0
0
2
1
0
0
2
2
0
0
0
0
0
0
0
2
1
2
1
0
1
0
2
2
0
0
1
2
0
0
1
0
2
0
0
0
0
2
2
0
0
0
0
1
2
0
1
0
0
0
0
0
2
0
1
0
2
2
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
1
0
2
0
0
0
1
0
2
2
0
0
0
1
2
0
1
2
0
0
0
0
1
0
0
1
0
1
2
0
2
1
2
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
2
0
0
2
0
0
0
0
2
0
1
2
1
0
2
0
0
0
1
1
1
0
0
0
0
0
1
0
1
0
0
3
0
0
0
1
0
3
0
0
0
0
0
2
0
0
1
1
0
2
2
0
0
0
2
2
0
2
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
2
0
0
2
2
0
0
2
0
0
0
2
0
0
0
1
0
0
2
2
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
3
1
2
1
2
1
0
0
0
1
0
0
0
0
2
2
0
1
0
1
0
0
2
2
0
2
2
1
0
0
2
2
2
1
0
0
1
0
0
2
0
1
0
0
0
2
0
0
0
0
1
0
0
1
0
2
2
0
0
0
3
0
0
0
0
2
1
0
0
1
0
0
3
1
0
0
0
5
2
2
2
0
0
2
0
4
1
0
0
1
0
1
0
2
0
2
0
0
0
0
0
0
0
0
1
2
0
2
0
0
1
0
0
0
0
2
1
2
0
0
0
0
0
0
0
1
1
0
2
0
0
0
2
0
1
0
0
4
0
0
2
1
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
2
1
1
2
2
0
0
0
0
0
1
2
1
0
0
0
0
8
2
2
0
0
1
0
0
2
1
0
1
2
1
0
0
1
0
0
0
0
2
1
1
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
2
0
0
0
0
2
0
1
0
0
1
1
0
1
0
1
1
0
2
2
0
1
2
0
2
2
0
1
1
2
0
0
0
2
0
2
0
0
2
2
2
1
0
2
2
1
2
0
2
0
2
2
0
2
1
3
2
3
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
1
1
0
0
0
1
0
2
4
2
0
2
0
3
0
0
1
0
1
0
0
2
3
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
2
1
0
0
0
0
1
0
0
0
0
1
1
0
0
2
0
0
1
0
0
1
0
0
0
0
0
1
1
0
3
0
0
0
0
1
0
0
2
0
0
1
0
0
0
2
1
0
2
1
0
0
0
1
1
1
0
0
0
0
2
2
2
0
0
0
2
0
0
1
1
0
0
0
2
0
1
0
3
0
1
1
3
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
2
0
1
0
0
2
1
1
0
1
0
0
0
1
0
0
2
2
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
2
0
2
0
0
2
0
2
0
0
0
2
1
1
0
0
1
1
2
0
0
0
0
2
0
0
0
0
3
0
0
11
2
0
0
0
1
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
1
2
0
0
1
0
0
2
0
1
0
1
0
0
0
0
0
0
2
0
2
1
0
2
1
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
1
2
1
2
1
2
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
1
2
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
1
2
0
0
1
0
0
2
2
2
0
1
0
1
2
2
0
1
0
0
1
0
2
2
1
0
0
0
0
2
0
1
2
1
1
0
0
0
1
2
2
0
0
0
0
0
0
0
0
2
1
1
3
0
0
0
2
1
1
1
0
1
0
2
2
0
2
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
1
1
2
0
0
0
0
1
0
2
0
0
0
0
1
0
2
1
0
0
0
0
1
0
0
0
2
0
2
0
0
1
1
0
2
2
0
0
0
0
0
2
2
1
0
1
0
0
2
2
0
1
1
0
2
0
0
2
1
0
0
2
0
0
0
1
0
0
0
1
2
3
1
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
3
0
0
0
0
1
0
1
0
1
0
1
0
0
2
2
1
0
1
0
1
0
0
0
0
2
0
1
2
0
1
0
2
2
2
0
1
0
3
0
2
0
2
0
1
2
0
0
1
0
0
0
1
1
1
0
0
0
0
1
0
0
1
2
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
2
2
2
0
0
2
1
2
2
1
0
0
0
0
0
0
2
0
0
0
1
0
1
2
0
0
1
2
1
2
0
1
0
0
0
2
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
2
2
0
0
2
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
2
1
0
0
0
0
0
0
0
0
0
1
0
2
2
1
1
1
0
2
2
1
1
0
0
0
0
2
2
1
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
1
2
1
1
0
1
0
1
0
0
2
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
3
1
0
1
0
1
1
2
0
0
1
0
5
2
1
0
0
0
0
0
1
1
1
1
1
0
0
3
0
2
0
0
1
0
0
0
0
2
0
1
0
1
0
2
0
0
1
0
0
0
3
0
1
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
1
2
0
1
2
3
0
0
1
0
0
0
2
3
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
2
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
1
2
0
0
2
2
0
1
2
1
2
0
0
1
0
0
0
0
1
2
0
2
1
0
0
1
3
0
2
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
2
2
0
1
2
2
1
0
0
0
0
0
0
0
1
0
1
0
1
2
1
1
1
2
0
0
2
0
2
2
0
0
4
0
1
0
2
0
0
0
0
1
1
0
1
0
3
0
2
0
2
0
2
3
0
0
0
2
0
0
2
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
3
0
0
0
0
0
2
0
0
1
0
0
0
1
2
0
0
0
2
0
1
3
0
2
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
2
0
7
0
2
1
0
0
0
1
2
0
0
0
2
0
1
1
2
4
1
0
0
2
0
0
0
2
2
0
0
0
4
0
1
0
0
2
0
0
2
1
1
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
2
1
0
2
2
0
0
1
0
0
2
0
1
0
0
2
0
0
1
1
0
2
0
0
1
1
0
2
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
1
1
1
0
0
1
2
1
1
2
0
0
0
0
0
1
2
0
1
0
0
1
1
0
2
0
0
0
2
1
0
1
2
1
0
1
0
0
0
0
2
0
1
0
0
1
0
2
0
0
0
1
0
0
0
0
1
0
1
1
1
0
0
0
0
2
0
1
0
4
1
1
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
1
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
1
1
1
2
2
1
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
1
0
2
1
0
0
0
1
0
1
1
1
2
0
0
0
1
0
0
2
2
1
1
0
0
0
0
2
0
0
1
1
0
2
0
0
2
0
0
1
1
0
2
0
0
0
1
2
0
1
0
1
2
1
1
2
0
0
0
0
1
1
2
1
0
0
0
0
0
0
2
0
2
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
2
1
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
5
1
0
0
0
1
1
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
2
1
1
2
0
3
1
0
0
0
0
2
2
0
0
2
2
0
0
0
0
1
1
2
0
1
0
0
0
2
1
0
1
3
2
0
1
1
0
2
0
0
0
0
2
0
2
1
0
0
1
0
1
3
0
1
0
0
0
0
0
0
0
2
2
1
2
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
3
0
1
0
0
1
0
0
2
2
0
0
1
0
0
3
2
0
1
0
0
0
2
2
0
1
1
0
0
1
0
0
0
0
1
1
1
0
0
2
0
0
0
0
0
3
0
0
2
1
0
0
0
2
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
2
0
0
0
1
2
0
0
1
0
0
0
1
0
0
1
0
0
3
0
2
0
1
1
0
0
1
2
0
0
0
0
0
2
1
0
1
0
0
0
0
2
0
1
0
1
0
0
0
0
2
2
1
1
1
1
2
2
2
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
1
0
2
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
2
0
0
1
1
2
2
1
1
0
2
0
2
0
0
0
0
2
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
3
2
0
1
2
2
0
0
1
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
1
1
0
0
0
0
0
2
0
2
0
0
0
0
1
0
1
6
0
0
0
2
0
2
0
0
0
1
0
0
0
2
2
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
2
1
0
1
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
2
1
0
2
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
2
0
2
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
2
2
0
1
2
0
0
0
1
2
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
3
0
0
2
1
0
0
0
0
0
0
0
0
0
2
1
0
0
2
1
0
0
0
0
1
0
0
0
2
2
0
0
0
2
3
0
1
0
0
2
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
1
0
0
0
0
0
1
2
0
0
1
0
1
0
1
2
1
0
3
1
1
0
1
0
1
1
0
0
0
3
0
0
0
0
2
0
1
0
0
0
2
0
0
2
1
2
1
2
0
0
0
0
0
2
0
1
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
3
1
2
2
0
0
0
0
0
0
0
0
0
0
0
4
2
0
2
2
0
2
0
1
1
0
0
2
1
1
0
0
0
1
0
0
1
1
0
1
0
1
1
2
0
0
0
0
0
2
0
0
0
1
1
0
0
0
2
1
0
0
0
0
2
2
0
0
2
2
0
1
1
0
0
0
0
0
1
1
2
2
0
0
0
0
0
0
0
1
0
1
0
2
1
1
1
0
1
0
0
0
1
1
0
2
0
3
2
2
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
1
0
2
1
2
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
2
0
1
1
0
1
0
0
0
0
2
0
1
0
0
0
2
0
0
2
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
2
0
0
1
0
0
0
0
0
2
0
2
0
0
1
0
0
1
2
0
1
0
0
2
2
1
1
0
2
0
0
1
1
0
0
2
0
0
0
0
2
2
0
0
0
1
0
1
2
0
0
0
2
0
0
0
0
2
0
2
0
0
2
1
2
1
0
2
0
0
1
0
0
0
0
3
1
2
0
2
0
2
1
1
2
0
2
2
0
1
2
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
2
0
1
0
0
2
1
0
1
0
0
0
0
0
1
1
2
0
0
2
0
0
1
1
2
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
3
0
1
0
1
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
1
0
0
2
0
2
0
0
0
1
2
0
1
0
1
0
0
0
0
0
0
0
2
0
0
1
0
2
1
1
0
0
0
2
1
0
0
0
0
0
1
1
0
1
0
2
0
0
0
1
0
3
0
1
0
1
0
0
1
2
0
0
2
1
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
3
1
1
0
0
0
0
1
2
0
0
0
0
0
0
2
2
0
0
2
2
2
1
1
2
4
0
0
2
0
0
0
0
0
1
1
1
2
0
0
1
0
1
3
0
1
0
0
0
3
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
2
0
0
0
2
0
1
1
1
0
1
1
0
1
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
3
1
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
1
3
0
2
1
2
1
3
1
0
0
0
0
0
0
1
0
1
2
0
0
0
1
1
0
1
0
0
1
2
0
0
1
0
0
0
0
0
0
2
0
2
0
2
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
1
0
2
1
0
0
2
0
2
1
1
0
0
2
2
0
2
0
2
1
1
2
0
0
0
1
2
0
1
1
0
0
0
2
2
1
0
0
1
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
2
1
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
1
0
1
0
0
0
0
0
2
0
2
0
2
1
0
0
0
1
2
0
2
0
1
0
0
1
1
0
2
0
2
1
0
0
0
1
1
2
0
1
0
0
2
0
0
2
1
1
0
0
2
0
1
1
1
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
6
0
0
0
0
2
0
0
2
1
0
0
2
0
1
1
1
0
1
0
0
1
2
2
0
0
0
2
0
0
0
0
0
0
0
1
4
0
1
0
2
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
1
0
0
1
2
2
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
1
0
1
0
1
0
0
0
1
0
0
0
2
0
0
2
0
0
1
0
0
0
1
0
2
1
2
1
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
2
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
3
3
0
1
0
0
0
1
0
3
0
0
0
0
2
0
0
1
1
0
0
1
2
0
2
2
0
0
0
0
0
0
1
1
1
2
2
2
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
3
0
1
0
2
1
0
0
2
0
2
0
0
0
0
2
1
0
0
0
0
4
0
0
2
0
0
1
0
0
0
1
0
3
0
1
1
0
1
0
1
2
2
2
0
0
0
2
1
2
0
2
0
1
0
2
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
1
0
1
1
0
0
0
3
1
0
2
2
0
2
0
4
0
1
2
0
0
1
0
1
0
2
0
1
1
0
0
1
2
0
1
0
2
2
0
0
0
0
1
0
2
0
0
2
0
2
0
0
0
2
0
0
0
0
2
0
0
7
0
0
0
1
0
0
0
0
0
0
0
2
2
3
2
1
0
2
0
1
1
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
1
0
0
1
2
0
1
2
0
0
0
0
3
0
1
0
0
0
0
0
1
2
0
0
1
1
0
2
0
1
0
2
1
1
3
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
1
0
2
0
0
2
0
0
1
0
2
2
2
0
0
3
0
0
2
0
0
0
0
2
0
1
0
2
1
0
2
0
0
0
0
1
3
0
0
0
0
0
0
0
0
2
0
1
2
0
0
2
1
0
2
2
1
0
1
1
0
0
0
3
1
0
0
2
0
0
0
2
2
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
1
1
1
0
2
0
1
0
0
0
0
0
1
0
0
0
1
0
0
2
0
2
0
0
0
2
2
0
0
1
2
0
0
0
0
0
2
0
0
0
0
4
1
0
0
0
0
1
2
0
2
1
0
1
2
0
1
1
0
0
0
0
2
0
0
0
0
0
1
0
1
0
1
0
0
0
0
2
0
0
0
0
0
1
0
1
0
2
0
1
0
0
1
0
1
2
0
0
1
1
0
0
3
0
0
2
0
0
0
0
0
1
0
2
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
1
2
0
1
0
0
0
1
0
2
0
0
0
1
0
0
1
3
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
2
0
0
0
0
1
1
0
0
0
2
0
0
1
1
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
2
2
2
1
2
0
2
0
0
0
2
0
0
0
0
0
0
3
2
2
1
1
0
1
0
0
0
2
1
2
0
2
0
0
0
0
2
2
0
1
0
1
2
1
1
3
0
1
0
1
3
0
0
0
0
0
0
0
2
2
0
2
0
0
1
0
0
0
0
1
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
9
0
2
1
2
0
2
0
1
1
2
1
1
2
0
0
0
2
0
1
0
0
1
0
2
0
0
2
0
0
0
1
0
3
0
0
0
0
1
1
0
1
0
2
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
1
1
0
0
0
0
2
2
3
0
1
2
1
2
2
0
2
1
2
2
0
0
0
1
0
2
0
2
0
0
1
0
1
1
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
2
2
0
0
3
0
2
1
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
1
1
1
1
0
0
2
0
0
2
0
0
0
0
1
1
1
0
1
0
0
2
2
0
0
2
2
2
0
0
3
2
1
0
0
2
1
2
2
2
0
0
1
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
2
0
0
2
2
0
1
0
2
0
2
2
0
1
0
2
0
2
0
1
0
0
0
0
1
0
0
0
0
1
0
1
2
2
1
0
0
0
1
2
0
2
0
1
1
1
0
0
2
0
0
0
1
1
4
1
2
0
0
0
0
0
1
0
0
2
1
0
2
2
0
0
1
0
0
0
2
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
2
2
0
1
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
2
2
0
0
0
2
2
0
0
0
0
0
0
14
1
0
0
0
0
0
0
2
0
0
6
0
2
0
0
0
0
1
0
0
0
0
2
0
0
1
2
0
1
1
1
2
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
4
0
1
0
0
0
0
0
0
0
1
2
2
0
0
0
1
0
2
0
0
1
1
0
1
0
2
0
1
0
0
1
1
1
0
0
0
1
0
0
0
0
3
2
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
1
2
1
2
1
1
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
3
0
0
0
0
1
2
0
3
2
1
1
0
0
1
1
0
2
0
0
0
0
0
2
0
1
0
0
1
1
0
2
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
1
0
0
0
0
0
2
4
0
0
2
0
0
0
1
0
0
3
0
0
0
0
2
0
0
1
0
1
0
0
1
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
1
1
1
1
1
0
2
5
2
0
1
0
1
0
1
0
0
0
0
2
3
0
1
0
0
0
2
0
1
0
0
0
0
0
0
3
2
0
2
0
0
2
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
2
0
2
3
0
0
0
0
0
0
0
0
0
0
0
3
0
1
4
2
0
0
2
0
0
0
1
0
1
0
2
0
1
0
1
1
0
1
2
0
0
0
2
0
2
1
0
0
1
0
0
1
0
0
0
0
2
1
1
2
0
0
0
1
2
1
0
1
0
1
0
0
0
0
0
0
1
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
3
4
0
2
2
0
2
1
2
0
0
0
0
2
0
1
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
2
0
0
0
0
1
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
1
2
0
0
2
2
0
0
0
1
0
0
2
1
1
1
2
1
2
0
0
0
1
0
1
0
2
0
0
0
2
2
0
0
0
1
0
0
0
2
1
0
0
0
1
0
0
2
1
0
0
1
0
1
0
0
1
1
2
0
0
1
0
1
0
1
1
0
1
0
0
2
2
0
0
0
3
3
0
0
1
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
2
1
0
0
1
0
2
1
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
1
2
1
2
1
2
0
0
0
0
4
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
1
0
0
5
0
0
0
1
0
0
1
1
3
0
1
0
2
1
0
1
0
1
1
2
0
0
1
0
0
0
2
0
0
0
1
2
0
0
0
0
0
1
0
1
0
2
1
1
2
1
0
0
1
0
0
0
0
3
1
0
1
0
1
1
0
2
0
1
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
1
1
2
0
1
1
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
1
3
2
1
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
3
0
2
0
0
0
0
0
1
1
0
1
1
2
0
0
0
1
0
1
2
0
0
0
0
1
0
0
1
3
1
2
1
0
2
0
0
0
2
0
0
0
1
0
0
0
3
0
0
1
0
2
3
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
2
0
2
2
0
0
2
2
0
0
2
0
0
1
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
1
0
1
0
0
1
1
1
0
0
0
1
0
0
0
1
0
3
0
2
0
0
0
0
2
0
1
2
2
0
0
2
2
0
0
2
2
0
0
2
0
0
2
1
0
0
0
0
2
1
2
2
1
1
1
0
1
1
0
0
2
0
0
0
0
3
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
2
1
0
2
0
0
2
1
0
0
2
1
0
1
0
2
0
2
0
2
3
0
0
0
1
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
1
0
2
1
0
0
2
2
2
0
2
0
0
0
1
0
2
0
0
2
0
1
0
1
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
2
0
0
1
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
1
2
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
1
2
2
0
1
0
0
0
0
0
3
0
1
0
0
0
1
2
2
0
2
2
1
0
2
1
2
2
1
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
1
0
0
2
0
1
0
0
0
0
2
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
2
1
0
2
0
0
1
0
1
0
1
0
2
0
0
1
2
0
0
0
2
0
0
0
2
1
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
4
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
1
2
1
0
1
0
0
0
0
1
0
0
2
0
0
0
0
1
1
1
0
2
2
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
3
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
1
1
2
1
0
0
0
0
2
1
0
1
2
0
1
0
0
0
1
0
1
0
2
0
0
0
0
1
0
2
0
2
1
1
0
0
0
2
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
2
3
1
2
0
0
3
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
1
1
0
1
1
2
0
0
0
2
1
1
0
0
1
0
0
0
2
3
0
0
0
0
0
0
2
1
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
4
1
1
0
0
2
0
1
0
0
0
1
0
0
0
2
0
2
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
1
0
2
3
0
1
0
1
1
0
0
0
0
0
2
0
0
1
0
2
2
1
0
0
0
1
0
1
0
0
0
2
2
0
1
2
2
0
1
1
2
0
0
0
2
0
2
0
1
1
0
1
0
3
0
0
0
0
0
1
0
1
0
2
0
0
1
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
1
2
0
1
1
0
0
2
0
1
1
2
0
0
2
0
2
4
1
0
0
0
0
1
1
0
0
0
2
1
1
0
0
2
0
2
0
0
0
0
0
1
0
1
0
2
0
2
0
0
0
0
2
0
0
0
0
2
1
0
1
0
0
2
0
1
0
2
0
0
2
0
0
0
0
0
2
0
1
2
0
0
1
0
1
0
2
0
2
0
1
0
0
1
0
0
0
1
0
3
0
2
0
1
1
0
0
0
1
2
0
1
0
0
0
0
0
0
0
1
1
0
2
2
1
2
0
0
0
0
0
0
0
1
0
2
2
0
1
0
1
3
2
2
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
2
2
1
0
0
0
2
0
0
0
0
0
1
0
0
2
3
0
3
2
2
0
0
0
0
2
0
1
0
0
0
0
1
1
0
0
2
2
0
0
2
0
2
0
2
0
0
0
0
0
0
1
2
2
4
0
0
1
1
0
0
2
0
2
0
0
0
0
1
2
1
2
0
2
0
2
0
2
0
0
0
0
1
1
0
0
0
2
0
2
0
0
1
0
0
2
0
1
0
2
0
0
0
0
0
2
0
3
1
0
0
2
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
2
0
0
1
0
0
0
0
1
3
0
2
0
0
2
2
0
1
2
0
0
0
0
0
1
3
0
1
1
1
1
0
1
1
5
2
0
0
0
0
2
0
1
0
0
0
1
0
0
1
0
1
2
0
0
0
0
1
0
0
1
0
1
0
2
0
0
0
0
2
1
1
0
0
0
1
0
0
0
2
1
2
0
0
1
1
0
1
2
0
0
2
0
0
1
0
2
0
0
0
1
0
2
1
0
0
1
0
0
0
1
2
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
1
0
0
1
0
1
0
0
0
2
0
2
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
1
0
1
2
2
0
2
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
3
2
0
2
0
0
0
1
2
1
2
2
0
0
0
0
0
3
0
0
2
2
0
0
0
1
1
0
0
0
2
1
1
1
0
2
0
0
0
0
1
0
1
0
1
2
1
2
0
0
0
0
0
0
1
0
0
0
1
0
2
0
2
0
1
0
1
0
2
1
0
0
0
0
0
0
1
1
2
0
0
2
1
0
0
0
2
1
0
0
0
1
2
0
2
0
1
0
0
0
1
0
2
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
1
0
0
0
1
1
0
0
1
0
0
0
2
2
0
0
0
1
2
2
0
0
0
0
0
2
0
0
0
1
0
0
1
1
2
2
2
2
0
0
0
4
0
0
0
0
0
0
1
1
0
1
2
1
1
0
0
0
1
0
1
2
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
2
1
0
2
1
0
1
0
2
0
2
0
0
2
0
0
2
0
1
0
0
0
0
1
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
1
2
2
2
1
1
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
2
2
1
0
0
3
0
1
0
1
2
0
0
2
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
2
4
1
0
5
1
1
0
0
1
0
0
0
0
0
0
1
0
0
3
1
0
1
0
0
0
0
0
0
0
0
1
2
2
1
1
0
1
3
0
1
1
2
0
2
2
1
1
0
1
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
2
0
0
1
0
0
0
4
0
1
1
4
2
0
0
0
0
1
2
0
1
2
0
0
0
0
0
1
1
0
1
1
0
0
1
2
1
1
2
0
1
0
0
1
0
1
1
0
3
0
0
2
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
3
0
0
0
1
2
0
1
0
0
2
1
2
2
0
1
0
0
1
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
2
0
0
0
0
2
2
0
0
0
1
1
2
0
2
2
0
0
0
0
0
1
0
0
0
0
2
1
0
1
0
1
0
0
0
0
0
0
3
0
1
0
0
0
0
1
2
1
2
0
0
2
1
0
1
1
1
0
0
1
0
0
0
0
0
1
3
0
0
1
0
0
0
1
2
2
2
0
0
0
0
2
0
0
2
1
0
0
1
0
0
1
0
0
3
4
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
2
3
2
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
1
1
0
0
0
0
0
2
0
1
1
0
2
0
0
2
1
0
1
0
0
0
1
0
0
0
0
2
2
0
5
0
0
0
0
0
0
1
0
0
2
1
2
0
0
1
1
2
0
0
1
1
2
2
0
0
0
0
1
2
1
0
0
2
1
0
1
0
3
0
0
0
0
0
0
1
0
0
0
3
0
1
0
0
2
0
0
1
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
1
0
2
0
1
2
2
0
0
2
1
3
2
1
1
1
0
0
1
2
1
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
2
2
0
1
1
0
0
2
0
0
0
0
1
0
0
0
0
2
2
0
2
0
2
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
2
0
1
2
0
0
0
0
2
0
2
0
0
0
0
0
2
2
0
1
2
2
0
0
2
0
0
0
0
2
0
0
1
0
2
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
2
0
2
0
0
0
2
0
1
1
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
1
0
2
1
1
2
2
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
3
0
0
1
0
2
0
0
0
0
0
0
2
0
0
1
0
0
1
0
4
0
0
2
1
0
0
1
2
0
2
1
3
0
1
0
2
1
0
0
0
1
0
2
0
1
1
0
0
1
0
2
0
0
0
0
0
1
0
1
0
2
1
1
2
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
2
1
2
0
0
0
1
1
1
0
0
1
1
0
0
1
2
0
0
0
2
0
0
0
2
0
2
0
2
0
2
1
2
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
2
1
0
0
1
0
0
0
0
0
0
0
1
0
2
0
2
0
0
1
2
2
2
0
1
2
1
2
3
2
2
0
0
0
2
1
0
1
2
0
0
1
0
0
0
0
1
1
0
1
0
0
1
2
2
0
0
0
1
2
0
0
2
2
0
2
1
1
2
0
0
1
3
0
2
1
3
0
0
0
0
0
2
0
0
2
0
0
0
0
2
2
0
0
1
1
0
2
0
0
2
0
0
0
0
0
0
0
0
1
1
0
1
1
2
0
0
2
0
0
0
0
1
0
1
1
3
2
0
0
0
2
0
0
1
0
2
2
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
2
0
2
1
2
0
0
0
0
0
0
1
0
1
1
1
0
1
0
0
0
2
2
1
2
2
3
0
0
2
0
0
0
0
0
2
0
2
1
0
0
0
0
2
0
5
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
1
1
2
0
0
0
1
1
2
0
0
1
0
0
1
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
2
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
1
1
1
2
0
0
0
0
0
0
1
0
2
1
0
0
0
0
1
0
0
0
3
0
0
0
1
2
0
0
2
2
1
1
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
2
0
0
0
0
0
0
0
1
1
1
0
0
1
0
1
2
0
2
0
0
0
0
0
0
2
3
0
0
0
0
2
0
0
0
0
0
0
9
0
0
0
0
0
2
5
0
0
0
2
1
0
0
2
0
0
2
0
1
1
2
0
0
0
0
0
0
0
1
2
0
2
0
0
0
1
0
0
0
2
0
1
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
1
1
0
0
0
0
2
0
0
0
0
5
2
0
1
1
0
2
0
0
1
0
0
2
0
0
0
2
2
0
1
1
1
0
0
0
0
0
0
0
1
2
1
0
0
2
0
0
0
2
2
2
0
0
2
0
1
0
0
1
0
0
0
1
0
2
2
4
0
0
0
2
2
1
2
0
2
1
1
2
1
3
1
0
0
2
0
1
1
0
0
0
2
0
0
0
0
1
2
1
1
0
0
1
2
0
0
1
0
0
0
1
0
2
0
1
0
3
0
0
0
0
0
1
0
0
2
1
2
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
2
1
0
2
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
3
0
1
0
0
2
0
1
0
0
2
0
2
0
0
0
1
2
0
1
0
0
1
2
1
0
0
0
1
2
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
3
0
1
0
1
2
1
0
0
0
0
2
2
0
2
0
0
1
0
1
0
1
2
0
3
0
0
0
1
0
0
0
2
2
0
4
0
0
2
0
1
0
0
2
0
0
1
3
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
2
2
0
0
1
1
0
1
0
0
2
0
2
0
0
0
1
1
1
0
0
0
0
4
0
0
2
0
1
0
0
1
0
0
1
0
0
0
2
0
3
1
1
0
0
0
0
0
0
1
2
0
2
0
0
1
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
1
0
0
1
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
1
2
1
0
0
0
0
0
1
1
1
0
0
0
0
0
2
2
0
0
0
0
1
1
0
1
2
0
0
2
0
0
0
2
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
2
0
1
0
0
1
2
0
2
0
0
0
0
0
1
6
0
0
0
1
2
0
0
0
4
0
2
1
0
0
0
0
0
0
2
0
1
0
0
2
2
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
2
2
1
1
0
4
0
2
0
2
0
1
0
1
0
0
0
0
1
0
0
1
1
0
2
0
0
0
0
0
1
1
0
2
0
0
0
2
1
0
0
0
1
0
1
3
2
0
1
2
0
2
0
1
2
0
0
0
0
0
0
0
0
1
1
0
2
2
0
0
1
2
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
2
0
2
2
1
0
1
0
0
0
0
1
2
1
2
0
0
1
0
2
1
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
1
0
1
2
2
0
0
0
0
1
0
2
0
2
2
0
0
0
1
0
1
0
2
0
1
0
1
0
1
0
0
0
0
0
0
3
1
0
0
0
1
0
2
0
1
1
1
0
0
0
0
0
0
0
1
0
1
2
1
0
2
2
0
0
0
1
2
0
0
0
0
0
2
0
0
0
1
2
2
0
0
0
2
0
3
0
1
0
1
2
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
1
0
2
0
1
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
2
0
0
0
0
1
1
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
1
0
2
0
0
1
0
1
0
0
0
3
0
0
1
0
1
0
0
2
0
0
0
0
2
0
0
0
2
0
1
1
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
2
0
0
1
0
0
1
2
2
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
1
1
1
0
0
0
1
1
2
0
2
0
0
2
1
0
0
0
1
1
0
0
0
0
0
0
0
4
1
2
0
0
1
0
0
1
1
0
2
0
0
0
2
2
1
2
0
0
2
0
0
0
0
2
0
2
1
0
0
1
2
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
2
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
3
0
0
1
0
1
1
1
0
1
0
0
1
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
2
0
0
1
0
1
1
2
0
0
1
1
0
0
1
2
2
2
0
0
0
0
0
2
0
0
1
1
1
0
2
0
0
0
0
0
3
0
0
0
0
2
0
2
3
0
2
0
0
0
0
1
2
0
0
0
0
2
2
0
2
0
0
2
0
0
0
0
0
2
2
0
2
0
2
0
2
0
1
2
3
2
0
0
2
2
0
2
0
0
1
0
0
0
1
1
0
2
0
0
0
0
1
2
2
0
0
3
0
1
0
0
0
0
0
1
0
0
2
2
2
0
1
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
1
0
1
0
0
1
2
2
0
0
3
0
0
0
2
0
2
0
0
2
1
0
0
0
0
0
0
1
0
0
1
2
0
0
2
2
1
0
0
0
0
0
0
0
0
2
1
0
2
1
2
0
2
0
1
1
2
0
0
0
0
3
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
1
1
0
0
1
3
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
1
2
0
2
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
2
2
0
0
0
0
2
2
0
0
0
1
2
0
0
2
1
2
0
0
0
0
1
2
1
0
1
0
1
0
0
0
0
1
0
0
0
1
2
0
1
1
1
1
0
0
2
0
2
2
1
2
1
1
0
1
0
0
0
2
2
2
2
0
0
2
4
3
1
2
4
0
0
4
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
1
1
2
0
0
0
0
1
0
2
1
0
1
2
1
2
1
0
1
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
1
4
2
0
2
0
1
0
2
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
3
1
2
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
1
1
2
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
1
1
2
0
0
0
0
0
1
1
0
2
0
0
0
1
2
0
0
0
0
2
3
2
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
2
2
0
0
1
9
0
1
0
2
1
0
0
1
2
0
0
2
1
0
1
2
0
0
0
1
2
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
1
1
2
2
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
2
3
2
2
0
0
0
1
0
0
0
0
0
2
1
1
1
0
0
0
1
0
1
0
1
0
0
6
0
0
0
1
0
3
1
1
1
2
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
2
1
0
0
2
2
0
2
0
1
0
2
0
2
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
3
0
1
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
1
1
0
0
0
0
0
0
2
0
2
2
2
0
1
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
1
0
2
1
0
0
2
0
2
1
2
1
1
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
4
2
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
4
2
0
2
0
1
0
0
0
1
0
2
1
1
0
0
0
0
0
2
1
0
2
2
0
0
2
1
2
0
2
1
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
2
0
3
0
0
2
1
0
2
2
0
0
0
1
2
1
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
2
1
0
0
2
1
2
1
0
2
1
0
2
0
0
1
1
1
2
2
0
1
2
0
0
0
2
0
0
1
0
0
0
2
1
2
0
2
0
0
0
2
1
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
1
1
0
1
2
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
1
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
3
0
0
3
1
1
1
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
1
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
2
1
0
0
3
0
0
1
0
0
0
0
0
1
1
2
1
0
1
0
0
0
0
2
0
2
0
0
1
0
1
1
0
0
2
0
0
1
0
0
1
0
0
1
3
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
2
2
2
0
2
3
0
0
0
2
1
1
1
0
1
0
0
2
0
0
0
0
0
0
2
2
0
0
2
2
1
0
0
1
1
0
0
2
2
0
1
1
0
0
1
2
1
3
0
0
0
1
0
0
2
0
2
0
1
0
0
0
1
0
0
1
0
1
0
1
0
0
0
2
2
2
0
0
2
0
2
0
0
0
0
0
1
2
1
5
0
0
0
0
1
0
1
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
2
0
1
0
1
5
2
0
0
2
0
0
0
1
1
0
0
2
1
0
4
0
3
0
3
2
0
2
1
2
0
2
1
1
0
0
0
2
1
0
0
0
0
2
2
1
0
0
2
0
0
2
1
2
1
0
0
2
0
0
2
0
0
2
1
2
5
0
2
0
1
1
1
1
0
0
0
2
0
0
0
0
1
1
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
2
1
0
0
0
0
1
4
2
0
1
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
2
1
0
0
0
3
0
1
0
0
0
0
2
2
2
2
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
1
2
1
0
0
0
0
0
1
0
0
0
0
0
3
0
0
1
1
0
1
2
1
1
0
1
0
1
0
0
0
2
2
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
1
0
2
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
1
0
1
1
0
0
0
1
1
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
2
6
0
0
0
0
2
1
0
0
1
0
0
2
0
1
0
1
3
0
0
1
0
1
1
2
0
0
0
0
0
1
1
2
0
1
0
1
0
0
0
2
2
0
0
2
0
0
0
0
1
2
2
1
0
0
0
0
2
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
1
0
2
0
0
1
0
2
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
3
1
0
0
0
0
0
0
2
0
2
2
1
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
2
0
3
0
2
1
0
1
1
0
0
1
2
0
0
0
0
1
3
1
0
0
1
2
1
1
2
0
0
2
2
1
0
0
0
2
0
0
7
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
1
1
1
0
2
0
0
0
0
0
1
0
1
2
3
0
0
2
1
1
0
0
0
0
1
0
0
0
0
0
3
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
2
0
2
0
0
1
2
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
1
1
0
0
0
0
0
2
1
0
1
2
0
0
2
2
0
2
0
0
1
1
2
0
0
1
0
0
2
0
0
3
3
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
1
0
0
0
2
2
0
0
1
1
1
0
3
0
0
0
1
1
0
1
0
1
1
3
0
0
0
1
1
0
0
0
0
0
0
3
0
2
5
2
0
0
0
0
1
0
0
0
2
2
0
0
0
0
2
0
2
0
0
0
0
2
0
0
1
0
2
0
0
1
0
0
2
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
2
0
2
4
0
0
0
0
0
2
0
0
0
1
1
0
2
1
0
0
0
0
2
0
0
0
0
0
2
0
5
0
1
2
0
0
1
0
0
0
1
0
1
2
2
0
1
0
0
2
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
2
1
1
1
0
0
1
1
0
2
0
1
0
0
0
0
1
0
0
1
2
0
1
0
0
2
0
0
1
0
0
1
1
0
2
0
1
0
0
0
0
1
1
2
0
2
0
2
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
1
1
0
0
1
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
2
0
0
0
1
0
2
0
3
0
0
0
0
0
3
0
0
2
0
1
0
0
0
2
0
1
0
2
1
0
0
2
0
1
2
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
1
0
0
2
0
1
1
2
4
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
1
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
1
2
1
0
0
4
2
2
0
0
0
2
2
0
2
0
2
0
0
0
0
2
2
2
1
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
4
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
2
0
0
0
0
0
0
2
0
0
1
2
0
2
1
1
1
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
1
2
0
2
1
2
1
2
0
1
2
0
0
0
0
0
1
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
1
1
0
0
0
0
2
1
0
0
0
0
0
0
1
0
2
2
0
0
0
0
1
0
2
0
0
1
0
0
1
0
0
0
2
2
2
0
0
0
0
0
1
0
0
2
0
0
0
2
1
1
0
1
1
2
0
1
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
2
2
1
1
1
0
1
0
0
1
3
0
0
2
0
1
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
2
1
0
0
2
2
0
2
2
0
0
0
1
1
0
2
2
0
0
1
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
2
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
2
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
2
2
0
0
1
0
0
0
1
1
0
1
2
0
2
1
0
2
2
2
0
0
1
0
4
0
2
1
2
2
0
0
0
0
2
2
1
0
0
0
0
1
0
0
0
0
2
0
2
2
0
0
2
1
2
0
0
2
2
0
0
0
1
0
0
0
0
1
1
1
1
0
0
0
1
1
0
0
2
1
2
1
0
0
0
0
2
0
2
1
0
2
1
0
0
1
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
1
0
1
0
0
0
0
1
0
0
1
2
2
0
0
2
0
0
2
1
2
0
0
2
0
0
0
0
2
0
1
0
2
0
3
0
0
0
0
0
1
1
2
2
0
0
0
1
1
0
0
0
0
0
2
0
3
0
2
0
1
1
0
2
0
0
1
1
2
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
2
1
0
2
0
0
1
1
0
0
0
3
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
1
0
0
0
0
1
0
1
0
0
2
0
0
1
0
2
2
1
0
0
0
0
1
1
1
2
0
0
1
2
0
2
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
2
0
0
4
0
0
0
2
2
1
1
0
1
0
1
0
1
1
0
1
0
0
0
1
0
0
0
0
1
2
2
2
1
0
1
0
0
1
2
0
0
1
0
1
0
0
0
1
0
2
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
2
0
4
3
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
2
0
0
1
2
2
1
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
1
0
0
0
0
1
0
0
0
2
1
0
0
1
0
0
0
0
0
0
2
2
0
1
0
2
0
3
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
2
2
1
2
0
2
1
1
2
0
0
0
0
0
0
2
0
1
0
1
1
2
0
1
1
0
0
0
1
0
0
0
1
0
2
1
0
0
1
0
1
0
0
2
0
2
0
1
1
1
0
1
3
0
2
2
1
0
2
0
0
0
0
0
2
1
1
1
1
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
1
3
0
1
1
0
1
2
0
0
1
0
0
1
1
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
1
1
1
0
0
3
2
1
0
0
2
0
0
1
1
0
0
4
3
0
1
1
0
0
0
0
0
0
0
2
0
1
2
0
1
2
1
0
1
2
2
1
1
0
0
0
2
1
2
0
2
0
0
0
2
3
0
0
0
0
0
0
0
1
2
0
0
2
0
1
0
0
2
0
0
0
2
0
1
2
0
2
0
0
1
0
0
2
0
0
0
2
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
2
2
0
1
0
0
2
0
0
2
1
0
2
0
2
0
0
1
0
2
2
0
0
0
0
1
0
0
1
0
2
4
1
2
1
2
0
0
0
1
0
0
0
0
2
1
0
0
6
2
0
1
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
1
0
9
0
1
2
2
0
0
2
0
0
1
2
0
0
0
1
2
0
0
0
0
1
0
1
2
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
2
0
1
2
0
0
0
1
0
1
0
0
0
2
2
1
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
2
1
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
2
1
0
0
2
0
0
0
1
2
2
0
0
0
1
2
0
1
0
0
1
0
0
0
1
0
0
2
0
0
0
1
2
2
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
2
0
1
0
0
0
2
2
2
0
0
1
2
1
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
2
0
0
2
0
0
2
0
0
2
0
1
1
0
1
0
0
0
0
0
0
2
2
0
1
0
2
1
0
0
0
2
0
0
0
0
2
0
0
1
1
2
0
0
0
2
1
0
2
1
0
0
0
0
2
0
0
0
2
0
2
2
0
0
0
0
2
0
0
0
0
2
2
0
1
1
0
1
0
0
1
0
0
1
0
2
0
0
0
1
0
1
0
1
1
2
0
1
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
1
0
0
1
0
0
0
1
0
2
9
0
0
2
2
0
0
2
0
0
2
1
0
0
0
0
0
0
0
2
2
0
2
1
0
0
0
0
0
0
0
1
1
0
0
2
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
1
1
2
0
0
0
2
0
0
2
0
1
1
0
0
0
0
0
2
0
0
0
2
0
5
1
0
0
0
2
0
1
0
0
0
1
0
2
0
4
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
4
1
0
0
2
0
1
1
2
0
0
2
0
1
0
0
0
0
1
0
0
2
0
1
0
0
1
0
1
2
0
0
0
1
2
1
0
1
0
0
2
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
1
2
2
0
0
0
0
0
2
0
2
0
0
2
0
0
1
0
0
0
3
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
2
0
0
4
0
0
0
0
0
0
0
0
2
2
0
1
0
2
0
0
1
0
0
0
0
3
2
2
3
0
2
0
0
0
0
0
1
0
0
1
1
0
1
0
2
0
0
2
1
0
4
0
0
0
2
1
0
2
2
0
0
0
0
0
2
0
0
0
0
2
2
2
1
0
0
0
2
0
1
2
0
2
1
0
1
0
0
2
0
2
0
2
0
0
1
0
4
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
2
0
0
0
3
0
0
2
2
1
0
0
3
2
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
2
1
0
0
0
0
1
0
0
0
0
1
0
2
2
2
0
0
1
0
0
4
2
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
2
1
2
0
0
0
1
1
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
2
0
2
0
2
1
0
0
0
0
1
0
2
2
3
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
1
0
2
1
1
0
1
1
0
2
0
0
0
1
0
0
2
2
0
2
0
0
0
0
1
2
1
0
2
1
0
0
0
0
0
0
0
0
2
2
0
1
0
1
2
2
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
1
1
0
0
0
0
1
2
0
3
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
1
0
2
0
0
1
0
2
0
2
2
0
0
0
0
0
2
0
0
2
2
0
1
2
3
0
2
0
0
0
1
2
0
2
1
0
2
1
0
0
2
2
0
1
2
0
3
2
0
0
0
1
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
2
0
2
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
2
2
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
2
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
1
0
0
1
0
0
0
0
3
1
0
1
2
1
0
0
0
0
0
0
2
2
0
1
2
1
0
2
1
0
0
0
1
0
0
2
0
0
2
1
0
0
0
1
1
0
0
2
0
2
0
0
0
1
0
0
2
2
0
0
0
1
0
0
1
1
0
0
0
0
0
2
1
1
3
0
0
0
0
0
0
0
0
2
0
2
2
2
0
0
0
0
0
2
0
1
1
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
2
0
1
1
2
0
1
1
0
0
2
0
2
2
0
0
0
0
0
0
2
0
1
1
0
1
0
0
0
0
2
0
1
0
0
0
2
1
0
0
0
0
1
0
1
0
1
0
0
3
0
3
2
1
1
0
0
0
1
1
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
1
0
2
0
2
0
0
2
0
1
2
1
0
1
0
2
0
3
0
0
0
1
0
1
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
1
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
2
0
1
0
0
0
1
0
0
0
0
1
0
2
0
0
1
1
2
0
0
0
3
0
0
0
0
0
1
1
1
1
2
0
0
0
1
0
1
0
0
3
0
0
0
1
0
2
1
2
0
1
2
2
0
2
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
1
0
1
0
0
2
1
0
0
2
1
0
0
2
2
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
1
0
1
1
1
1
0
0
0
0
3
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
2
0
1
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
2
1
2
0
0
0
0
1
0
1
2
0
0
0
0
0
1
0
0
2
2
0
0
1
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
2
1
0
2
0
0
0
0
1
2
0
0
0
0
0
0
1
0
2
0
0
0
0
1
2
0
2
0
2
0
0
1
0
2
2
0
0
0
0
0
0
0
2
1
0
2
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
2
1
2
0
0
1
0
0
0
0
0
1
0
2
0
1
0
1
0
2
2
0
1
2
0
0
2
2
0
3
0
1
0
1
0
0
0
0
0
0
1
1
1
1
0
0
0
1
0
0
0
1
0
0
2
0
0
2
0
0
0
0
5
1
0
0
0
0
0
1
0
0
1
2
2
0
1
0
0
0
0
1
0
2
0
1
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
3
0
1
0
1
1
0
0
1
0
1
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
2
0
1
0
0
0
2
0
1
0
2
0
1
0
3
2
0
0
1
0
0
1
1
0
0
1
2
2
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
2
0
6
0
0
0
0
0
2
1
0
0
1
1
2
1
2
0
0
2
4
0
1
2
2
0
0
1
2
0
0
0
2
0
0
4
2
1
1
1
1
0
0
0
1
2
0
2
0
0
1
0
0
5
2
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
2
0
0
0
1
0
0
0
1
0
0
2
0
0
1
0
0
0
3
2
1
0
1
2
0
0
2
0
1
0
1
0
0
1
0
0
1
0
0
1
0
1
0
2
3
0
0
0
2
0
1
0
0
3
0
0
1
0
0
0
2
0
0
0
1
2
0
0
2
0
0
0
0
1
0
3
2
2
0
1
0
0
1
0
0
2
0
0
0
0
0
0
1
1
1
0
0
0
0
2
1
1
0
0
1
0
0
0
1
2
0
0
0
1
2
0
0
0
0
0
0
1
1
1
0
0
2
0
1
2
1
0
0
0
0
0
0
2
2
0
0
0
1
0
2
0
0
1
0
2
0
0
1
2
2
0
0
0
0
0
1
0
2
1
1
0
0
0
0
2
2
2
2
0
2
1
0
1
0
2
0
0
1
1
0
0
0
1
0
0
4
0
2
0
1
0
0
1
0
0
0
0
0
2
2
0
1
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
2
1
0
1
0
3
1
1
0
1
0
0
0
1
2
2
0
2
0
0
1
2
0
2
1
1
0
0
1
3
0
2
2
1
0
1
4
0
0
2
0
0
1
0
0
0
1
0
0
0
0
1
2
0
1
1
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
3
0
2
0
0
0
1
0
1
0
2
1
2
0
0
1
0
0
1
2
0
0
0
1
0
1
2
1
0
0
2
0
0
0
0
0
0
2
0
2
0
0
3
2
2
0
0
0
0
1
1
0
0
1
1
0
2
1
0
1
3
0
0
1
0
0
1
2
2
0
0
1
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
2
0
2
3
2
1
0
0
0
0
0
2
6
1
2
0
0
1
0
0
2
0
1
2
1
0
2
1
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
2
1
0
0
2
1
0
0
0
0
2
2
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
2
1
1
2
0
0
1
0
2
0
0
0
1
0
0
0
2
0
0
1
0
0
2
1
0
1
0
0
0
2
3
0
0
2
1
1
0
2
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
1
1
2
1
2
2
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
2
1
2
0
0
0
0
2
0
1
0
1
0
0
2
1
0
0
2
1
0
0
1
0
1
0
0
0
0
0
2
0
1
1
0
2
0
0
0
2
1
0
5
1
1
0
0
0
1
2
0
0
0
3
0
0
0
2
0
0
0
0
1
0
0
0
1
0
1
0
0
2
1
0
0
0
2
0
1
0
0
1
2
1
2
0
0
0
3
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
2
0
1
2
2
0
1
0
0
0
2
0
0
0
0
0
0
3
0
0
2
0
0
0
0
2
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
3
0
1
0
1
0
0
0
1
0
0
2
0
2
0
1
0
2
0
1
2
0
0
0
0
4
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
2
2
0
2
1
2
0
0
0
0
0
2
0
1
1
0
2
0
0
3
0
0
0
0
2
0
0
0
0
1
0
0
2
2
0
2
2
0
3
0
0
1
0
2
0
1
1
0
0
2
0
0
1
0
0
0
0
0
2
2
0
0
2
0
0
0
1
1
0
1
0
0
1
0
1
1
2
0
1
1
1
0
2
2
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
1
0
1
0
0
0
0
3
1
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
1
2
0
1
0
0
1
1
0
0
1
2
2
0
2
0
0
2
1
1
2
0
0
0
1
0
2
2
2
1
0
2
1
0
0
0
0
0
1
0
2
1
0
0
0
0
0
1
0
0
0
0
0
2
1
1
0
0
0
0
0
0
1
1
0
1
0
1
1
2
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
1
0
1
0
1
3
4
0
2
2
2
0
0
1
0
2
0
0
0
1
1
1
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
1
2
2
0
0
0
1
0
1
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
4
1
2
0
2
0
0
1
0
1
1
1
0
0
0
0
2
0
1
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
1
2
0
0
2
0
0
0
0
0
0
0
1
2
1
1
0
2
0
2
1
0
0
0
0
1
0
1
0
0
0
0
0
1
2
0
0
0
2
2
0
1
2
0
0
0
0
1
0
0
0
3
0
0
1
1
2
2
0
0
1
1
1
2
0
1
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
1
1
0
1
0
1
1
2
0
1
0
0
0
1
2
0
0
0
0
2
0
1
0
0
2
0
1
0
1
0
0
0
0
0
2
0
0
1
1
2
0
1
1
0
0
0
0
2
0
1
2
0
0
0
1
0
0
0
0
2
2
0
0
1
1
1
2
0
0
0
1
1
0
0
2
0
0
0
0
0
1
0
1
1
0
0
0
0
2
0
2
0
0
0
1
1
0
0
0
2
0
2
0
1
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
2
0
0
0
2
0
0
0
2
0
0
1
0
0
0
1
2
4
0
0
0
0
0
0
0
0
0
3
0
0
0
2
1
1
2
0
0
2
0
0
0
2
0
0
0
0
1
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
2
1
0
2
2
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
2
0
1
2
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
1
1
1
0
1
0
0
2
2
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
3
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
2
0
0
2
1
0
2
1
0
0
0
0
0
1
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
2
0
0
1
1
1
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
4
0
2
0
0
0
1
0
0
0
0
2
0
0
2
1
2
2
2
1
2
1
0
2
0
1
0
0
0
0
0
3
0
0
0
1
2
1
0
0
3
0
2
1
1
2
1
0
1
0
2
0
0
0
0
2
0
1
0
1
0
0
0
1
1
1
0
0
0
2
1
0
2
1
3
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
2
0
0
1
0
0
0
2
1
1
0
2
2
0
0
4
0
0
1
1
0
0
0
2
1
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
1
0
2
1
0
0
0
1
2
0
1
0
1
0
0
1
1
0
1
0
1
2
0
2
0
0
1
0
0
0
1
0
0
2
0
0
0
0
1
0
2
0
0
0
3
1
0
0
1
0
1
0
0
1
0
1
0
1
0
1
0
0
0
0
0
3
1
2
0
1
0
0
1
2
0
0
0
0
0
2
2
0
0
2
0
1
1
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
3
0
0
0
0
0
0
0
1
0
0
1
0
2
1
0
2
1
1
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
2
2
0
2
0
0
0
0
0
1
0
0
2
0
0
0
4
0
1
0
2
0
1
2
0
0
0
0
0
0
1
2
0
0
0
1
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
2
0
2
2
0
0
1
2
2
0
0
1
0
1
0
0
1
0
2
2
1
0
0
1
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
2
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
1
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
2
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
1
1
0
1
0
0
0
0
0
0
0
2
0
0
1
2
2
2
0
0
0
0
1
2
0
0
2
1
2
2
1
0
0
0
1
3
0
0
2
1
0
2
2
0
0
1
2
0
2
2
3
0
0
2
0
0
2
0
2
2
1
0
1
0
0
0
0
0
1
1
0
4
2
0
0
1
0
0
0
0
0
1
1
0
0
0
3
0
2
0
0
0
1
0
0
0
2
0
2
0
0
0
0
1
0
0
1
0
0
0
0
2
2
1
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
6
0
0
1
0
0
0
2
0
0
2
0
0
0
0
2
0
1
3
0
0
0
2
0
2
0
0
0
2
0
1
0
2
2
0
2
0
1
0
2
2
1
0
0
2
1
0
0
0
0
0
2
0
2
0
1
0
2
2
0
0
1
0
0
0
1
0
2
0
0
0
1
0
0
1
2
1
2
0
0
0
1
0
0
1
0
0
0
0
1
0
0
2
1
0
2
0
0
0
3
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
1
0
0
0
1
0
1
0
0
0
1
3
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
2
0
0
1
0
0
2
0
2
1
0
0
0
1
2
0
0
0
2
0
0
0
5
0
0
0
1
0
0
0
1
0
0
1
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
2
1
1
0
0
0
0
0
1
1
1
0
1
0
0
1
2
0
0
0
0
0
2
1
0
1
0
0
1
2
0
2
0
0
1
0
0
0
1
0
2
1
0
2
1
0
1
0
0
1
1
1
0
0
1
1
1
0
1
1
1
0
0
1
1
1
5
0
0
2
0
0
0
0
2
1
1
2
0
0
2
0
0
1
0
0
0
0
0
0
1
1
0
0
2
0
7
0
1
0
1
1
0
0
0
0
1
1
0
1
2
0
0
2
1
2
1
0
1
0
0
0
3
0
2
0
1
0
0
0
0
0
0
2
2
1
0
0
2
0
0
0
1
0
1
0
0
1
0
1
0
0
0
1
0
1
0
0
2
0
2
0
0
1
0
0
0
1
1
1
1
0
2
0
0
0
1
2
0
0
0
4
0
0
2
0
1
2
2
1
1
0
1
1
0
0
2
0
0
0
2
1
0
0
0
1
2
0
2
0
0
2
2
2
2
0
1
1
0
1
2
1
1
2
1
0
2
1
0
0
1
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
8
0
1
1
0
1
1
0
1
0
1
2
2
1
0
0
1
1
0
0
0
3
0
1
0
0
1
2
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
1
0
0
0
2
0
0
0
3
0
0
0
0
2
0
1
0
3
0
2
1
2
2
0
0
0
2
0
1
0
0
2
0
0
2
0
0
0
1
1
0
1
0
1
0
0
1
2
1
0
0
2
1
0
0
2
1
0
0
0
3
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
4
0
1
0
1
0
0
1
2
0
4
0
0
0
0
0
0
1
1
0
2
0
1
0
2
0
1
0
0
0
2
0
0
0
2
0
1
0
0
2
0
1
1
0
2
0
0
0
0
2
0
0
1
1
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
2
0
0
1
0
0
0
1
0
2
2
1
1
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
1
0
0
0
1
1
0
2
2
0
0
0
1
0
1
0
1
0
2
0
0
2
2
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
1
2
0
2
0
1
0
0
1
0
0
3
0
0
0
0
1
0
2
2
0
0
1
0
0
0
0
0
0
0
1
2
0
0
1
2
2
0
0
2
2
0
0
3
0
0
0
0
2
0
0
2
1
0
2
1
2
0
0
0
0
2
0
0
0
0
1
1
1
2
1
0
0
1
0
0
0
2
1
0
2
0
4
2
0
0
1
0
2
1
2
0
0
0
1
2
0
0
2
0
0
2
1
2
0
0
0
0
0
1
1
0
1
0
3
0
0
0
1
0
2
2
0
0
0
0
1
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
2
2
0
2
0
2
0
0
0
1
0
0
0
2
0
0
1
1
2
0
0
4
0
1
0
1
0
0
1
0
1
2
0
0
0
0
1
0
1
0
0
2
0
0
0
2
2
0
0
0
0
0
1
0
1
0
3
0
0
0
0
0
0
0
0
2
0
0
3
0
2
0
2
0
0
1
0
0
2
1
0
1
1
0
0
0
0
0
0
2
1
2
0
2
1
1
3
1
2
0
0
0
2
0
0
2
2
0
0
0
0
1
7
3
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
1
1
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
1
1
0
2
0
0
2
0
2
1
1
0
0
2
1
0
0
1
0
0
0
0
0
1
1
0
0
0
2
0
2
0
0
1
1
0
0
0
0
0
2
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
2
1
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
1
2
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
2
1
2
0
2
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
2
2
0
0
1
0
2
0
0
1
2
0
0
1
0
1
3
0
2
0
1
0
2
1
0
0
1
0
3
2
1
0
0
0
0
2
0
0
1
0
1
0
2
1
1
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
2
0
1
2
0
0
0
3
0
0
2
0
2
1
2
1
1
1
0
1
1
0
0
0
1
2
0
0
0
1
0
2
0
1
2
2
1
1
0
0
1
2
0
0
0
0
0
1
0
0
0
1
1
2
0
5
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
1
2
2
0
0
0
0
0
1
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
3
0
0
0
2
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
2
0
1
0
1
0
0
0
0
0
0
1
2
1
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
1
0
0
0
0
1
1
2
2
0
0
0
0
0
3
0
0
2
2
2
0
1
1
0
1
0
0
0
0
1
1
0
0
1
2
0
0
0
1
0
0
0
0
0
0
3
0
3
0
2
0
1
0
0
0
0
1
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
3
0
0
0
0
0
1
0
1
0
3
0
1
2
2
0
0
1
0
2
0
0
1
0
0
0
0
1
0
0
1
1
3
0
0
1
0
0
0
1
0
0
2
0
1
0
2
0
0
1
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
1
0
1
2
1
0
1
0
0
2
0
0
0
0
2
1
0
1
2
2
0
0
1
0
0
0
2
0
1
1
2
0
0
1
0
1
0
2
2
2
0
1
1
0
1
0
1
1
0
0
0
9
1
0
0
0
0
2
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
1
0
0
1
0
2
0
0
0
0
0
2
0
2
0
0
0
3
0
0
0
0
0
0
0
0
1
0
2
1
3
1
0
0
0
0
0
0
2
1
0
0
2
1
1
2
0
1
2
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
1
2
0
1
0
0
0
0
1
1
1
2
0
0
0
0
2
1
0
1
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
1
4
2
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
1
0
0
2
2
0
0
0
0
0
3
0
0
2
2
2
0
0
0
0
0
0
2
0
0
2
0
1
0
2
0
0
0
0
3
0
0
0
0
0
3
0
0
3
0
0
0
0
1
2
1
2
0
0
1
0
0
0
0
2
1
3
0
2
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
1
0
0
1
0
0
0
0
0
2
0
2
0
1
2
0
0
0
0
0
0
1
0
0
0
2
0
1
1
2
0
2
0
0
2
0
1
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
1
0
1
1
1
0
1
0
0
0
0
2
0
2
0
0
0
0
2
0
2
0
1
0
0
0
1
0
3
0
0
2
1
0
0
2
0
7
1
0
0
0
0
2
3
0
0
0
3
0
0
0
2
0
2
0
0
2
0
0
0
1
2
0
0
0
0
0
0
2
1
0
2
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
3
2
2
4
0
0
1
0
0
0
0
1
2
3
0
0
0
0
2
2
0
0
0
1
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
2
0
0
1
0
1
1
1
0
0
2
0
3
0
0
1
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
1
0
1
0
2
0
1
1
2
0
2
0
1
2
3
1
0
2
2
0
1
2
2
0
2
0
0
0
0
0
0
0
3
1
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
3
3
0
0
1
2
1
2
1
2
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
1
1
0
0
1
0
2
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
1
0
1
0
0
2
2
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
2
0
1
0
0
0
2
0
3
0
0
1
0
1
1
2
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
1
0
2
0
1
0
0
1
0
2
0
2
0
2
1
2
0
0
2
1
0
2
0
1
0
0
0
0
2
0
2
0
0
1
2
2
0
1
0
1
2
0
1
0
0
0
2
2
0
1
0
1
1
0
0
0
0
0
2
2
0
3
0
2
1
0
0
2
1
1
0
0
0
1
0
0
0
2
0
0
1
1
0
0
0
0
2
1
3
2
0
1
0
1
0
2
0
0
1
2
0
1
0
3
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
2
1
0
0
0
1
2
0
1
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
1
0
0
1
0
2
0
2
0
0
0
2
2
1
1
0
2
2
2
0
1
0
1
0
0
0
1
1
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
1
0
0
1
0
0
2
1
0
0
0
0
0
0
4
2
0
0
2
0
0
1
0
1
0
0
2
0
0
0
2
0
2
0
0
0
1
2
2
0
2
0
2
1
2
0
0
0
0
2
1
0
2
0
0
2
0
0
0
0
0
1
2
2
0
0
1
2
0
0
0
1
0
1
0
2
0
1
1
0
2
0
4
1
0
1
1
0
0
2
0
0
2
2
0
2
2
0
0
2
0
2
2
0
0
0
0
0
2
0
0
0
1
2
0
0
0
2
1
2
0
0
0
2
1
0
0
0
1
2
2
0
1
0
0
0
0
0
1
0
1
0
2
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
2
2
2
0
2
0
1
0
2
1
2
0
0
0
0
1
2
2
1
2
1
0
2
0
0
1
0
0
0
1
0
2
0
2
0
0
2
0
0
0
1
0
0
0
0
2
0
0
2
2
0
3
0
2
0
0
0
0
0
0
1
1
0
1
0
1
2
1
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
2
0
0
2
0
0
0
0
2
1
0
0
2
2
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
2
0
0
1
0
2
0
1
0
2
0
0
0
2
0
2
1
1
0
2
4
1
0
0
0
4
0
0
0
1
2
0
2
0
0
0
2
0
0
3
0
1
2
2
0
1
0
3
2
0
0
2
2
0
0
0
1
0
0
0
0
0
0
2
1
0
0
1
0
0
1
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
1
0
1
1
0
1
0
0
1
2
0
0
1
0
2
0
0
1
0
4
0
2
1
1
1
0
0
1
0
2
1
0
1
0
2
0
1
0
1
1
0
1
2
1
1
0
0
0
0
0
0
1
0
1
0
2
0
0
1
2
0
0
0
2
1
0
0
2
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
2
0
0
2
0
1
0
0
0
2
0
0
2
0
0
2
1
0
1
0
1
1
0
0
0
2
0
0
0
3
0
1
0
0
0
0
1
0
1
0
0
2
1
0
0
1
0
0
0
0
2
0
3
0
0
0
0
1
2
0
0
0
3
0
1
2
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
1
0
2
0
0
1
0
2
0
1
0
2
2
1
0
2
1
0
0
1
1
0
1
1
2
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
2
2
2
0
2
0
1
0
0
1
0
0
0
0
0
1
0
1
0
2
2
2
0
1
0
1
0
2
0
0
3
0
0
1
0
1
0
0
1
1
0
2
0
0
1
3
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
1
0
0
0
1
0
0
2
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
2
2
0
2
0
0
2
0
0
2
2
2
1
0
0
2
1
0
0
3
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
3
3
2
5
0
0
1
0
1
0
0
3
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
1
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
1
1
2
0
1
1
2
1
2
0
0
0
0
2
0
1
0
0
0
0
0
1
2
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
1
1
0
0
0
1
2
0
0
0
0
2
0
2
2
2
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
3
2
0
0
0
1
1
0
0
2
0
0
0
0
0
1
1
3
1
0
0
0
2
0
0
0
0
2
3
0
2
0
0
0
0
1
1
0
0
0
2
0
0
1
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
2
0
1
0
0
0
1
0
0
0
1
0
1
1
2
0
0
0
1
1
2
0
0
0
0
2
0
0
0
0
1
0
1
0
0
4
3
0
1
0
2
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
2
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
1
0
2
0
2
0
0
0
5
1
0
1
1
0
1
1
0
1
0
1
0
2
1
1
0
0
2
1
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
2
0
0
0
0
3
1
2
0
2
0
0
0
0
0
2
2
0
0
5
0
0
0
0
0
0
2
2
2
0
1
0
2
0
2
2
0
1
2
0
0
0
2
3
0
0
0
2
2
0
0
2
0
1
0
2
1
0
0
0
2
2
2
0
1
2
0
0
1
0
1
0
0
0
1
0
0
0
0
2
1
1
0
0
1
2
0
0
1
0
1
1
2
0
0
0
0
0
0
0
2
0
0
0
2
1
1
0
0
2
1
2
0
2
0
0
2
0
0
1
0
0
2
0
0
2
0
0
0
0
0
4
0
0
1
0
1
0
2
1
0
0
1
2
0
0
2
0
0
0
6
2
1
2
0
0
2
0
0
1
0
0
0
1
2
0
0
0
2
2
2
2
1
0
1
2
0
2
0
1
0
2
1
1
2
2
1
0
0
0
0
1
1
1
0
1
0
1
0
0
0
2
1
1
0
2
1
0
0
0
1
2
0
0
2
1
0
0
1
2
0
0
0
0
0
0
2
2
3
1
0
2
1
0
3
0
0
3
0
0
0
0
0
1
0
1
0
0
0
0
2
0
2
0
2
1
0
1
0
1
0
0
0
0
1
0
0
0
1
1
1
1
0
0
0
0
0
0
2
2
0
0
0
2
0
1
2
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
1
0
0
0
1
1
0
2
1
0
0
0
0
1
2
2
1
2
0
0
0
1
0
2
0
2
2
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
2
6
0
1
2
1
0
0
1
2
0
0
2
0
1
0
0
0
2
0
1
0
1
0
0
4
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
2
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
1
1
1
0
1
1
0
1
2
0
5
1
0
1
0
1
0
0
3
0
1
1
0
1
0
0
0
0
0
0
2
2
2
1
0
0
2
0
0
2
2
0
0
0
2
1
0
0
0
0
2
2
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
2
2
0
1
1
0
0
2
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
2
8
2
0
0
0
0
0
1
0
0
2
0
5
1
1
0
0
0
2
2
2
1
0
1
0
0
0
1
0
0
1
2
0
2
0
2
0
0
2
0
2
1
2
2
1
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
2
0
3
0
0
1
2
1
0
2
2
0
1
0
1
0
0
0
2
1
2
1
2
1
0
0
0
1
0
1
0
0
1
2
1
1
2
2
0
0
1
0
1
2
0
0
2
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
2
2
0
1
0
0
3
2
0
0
1
1
0
0
0
0
2
0
0
0
0
1
0
0
1
0
2
0
0
1
1
2
2
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
2
2
0
0
2
0
0
0
0
0
0
0
1
3
0
1
1
0
1
0
0
1
0
1
0
0
0
0
1
0
0
2
0
1
0
3
0
0
1
0
0
0
0
0
1
2
0
1
1
0
2
2
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
1
0
0
2
0
0
2
2
0
0
1
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
2
0
2
0
1
1
0
3
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
1
0
0
1
0
0
2
1
0
1
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
2
0
0
2
0
1
0
0
0
1
1
0
0
0
0
0
0
1
2
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
2
1
2
0
0
1
0
0
1
0
2
0
0
2
0
0
2
2
0
1
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
2
1
0
0
1
0
0
1
0
1
1
0
0
0
0
1
1
0
0
0
0
2
3
0
1
2
2
1
2
1
0
0
2
2
0
1
0
0
0
4
0
0
2
0
2
0
0
0
0
0
0
0
1
0
1
0
1
1
2
0
0
0
0
4
0
0
2
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
1
1
1
0
0
0
1
2
0
0
0
1
0
0
2
0
0
0
2
0
0
2
2
2
0
0
5
2
0
0
0
0
0
1
2
0
2
0
0
0
1
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
2
0
0
0
1
2
0
0
0
0
0
0
1
2
0
2
0
0
2
2
0
2
2
0
0
0
2
2
0
1
0
2
0
0
0
0
0
1
0
1
0
0
2
2
1
0
1
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
5
0
0
1
1
1
0
0
1
2
0
1
0
0
2
0
0
0
2
0
0
1
3
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
1
2
0
1
0
0
2
2
3
0
1
0
0
4
0
0
0
0
0
2
0
0
1
3
0
2
2
2
0
0
2
1
1
4
0
2
0
1
0
1
0
1
0
0
1
1
0
0
1
0
0
0
1
0
0
1
1
0
1
2
1
0
1
2
1
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
2
1
2
0
1
0
1
0
1
1
0
1
0
0
0
1
1
0
0
4
0
0
0
0
0
2
0
1
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
2
2
1
0
0
0
0
0
0
1
0
0
0
2
2
1
2
0
0
0
0
2
0
1
0
1
1
0
0
0
1
2
0
0
0
0
0
1
0
0
0
2
0
0
3
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
3
0
1
0
0
0
0
2
1
1
1
1
0
2
1
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
2
0
1
0
0
1
0
2
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
1
1
0
1
2
1
1
0
3
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
2
0
0
0
0
3
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
1
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
2
1
1
1
0
0
2
0
1
1
0
0
0
1
1
1
0
1
0
1
1
2
0
2
0
0
0
0
0
0
2
1
2
2
2
0
0
2
2
1
1
0
1
1
0
1
0
1
0
2
1
2
2
0
0
3
0
0
0
1
0
1
0
1
0
0
2
0
0
2
0
0
0
0
0
0
2
1
0
2
0
0
0
2
0
2
0
0
0
0
1
0
2
0
0
1
2
0
2
0
2
0
0
0
1
0
0
0
0
0
0
1
0
4
2
0
0
0
1
0
1
0
1
1
3
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
1
1
0
1
0
0
0
0
1
0
2
2
1
0
2
3
2
0
2
0
0
0
0
2
1
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
2
0
1
3
0
0
1
0
2
0
1
0
2
1
0
0
0
0
0
1
0
2
0
1
0
2
0
0
0
1
2
2
1
2
0
0
0
0
0
0
0
0
0
1
1
2
0
0
2
1
1
1
0
3
0
0
0
3
0
2
1
0
1
1
1
0
2
2
1
0
0
0
1
0
1
2
0
0
0
0
0
1
2
1
0
4
0
1
0
0
0
2
0
0
0
1
0
0
1
1
0
0
0
0
0
1
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
1
0
3
0
0
0
0
0
1
0
2
0
2
1
0
0
2
1
0
0
0
1
2
1
0
2
1
2
1
0
0
0
0
0
1
2
0
1
1
0
0
1
0
0
0
1
0
3
1
2
2
1
1
1
2
1
0
0
0
0
1
2
1
0
1
3
2
1
0
0
0
0
2
2
0
0
0
0
0
2
0
0
2
2
2
0
2
0
0
3
0
0
0
0
2
0
0
1
2
1
0
1
0
0
1
0
3
0
2
0
2
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
2
1
2
1
0
2
0
2
0
0
0
0
0
2
0
0
1
1
0
0
2
1
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
4
2
0
2
0
1
0
0
0
0
0
0
0
0
0
1
2
2
2
0
0
0
3
1
2
2
2
1
1
0
2
1
2
0
0
2
1
2
0
0
2
0
0
0
0
0
0
3
0
1
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
1
1
0
0
2
2
0
0
1
0
0
0
0
0
0
2
2
0
0
0
1
0
2
0
1
0
0
0
0
0
2
1
1
0
0
0
0
0
0
2
2
3
0
0
0
2
1
0
2
0
0
1
2
0
0
2
0
2
1
0
3
0
1
0
0
0
2
2
2
2
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
2
0
0
0
1
1
0
1
0
5
0
0
0
0
0
0
2
0
2
0
0
2
0
2
0
0
0
0
0
0
2
0
0
2
2
0
2
0
1
0
0
0
2
1
0
0
0
0
0
0
0
2
1
0
0
0
1
0
2
1
3
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
1
0
2
0
0
1
1
0
0
0
0
0
0
2
1
1
0
0
0
2
0
0
2
0
1
1
3
0
5
1
1
0
0
0
1
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
2
0
2
2
2
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
1
1
2
0
0
1
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
1
2
0
1
0
1
0
0
0
0
2
2
1
0
0
0
1
2
0
0
2
1
3
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
1
1
0
2
2
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
2
0
0
2
0
0
0
0
2
1
1
0
0
0
2
0
0
0
0
0
0
0
2
3
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
1
0
0
0
2
1
0
0
0
0
2
1
1
1
0
0
0
1
2
0
0
1
1
2
0
0
2
0
1
1
1
0
0
0
0
1
0
0
2
0
0
2
0
0
1
2
2
0
0
1
3
3
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
1
1
0
1
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
2
0
0
0
1
1
0
0
0
0
2
2
2
0
0
2
1
2
1
1
0
2
0
0
0
1
0
0
0
0
2
0
0
0
1
2
2
1
2
1
3
0
0
0
1
1
0
2
0
1
0
0
0
0
0
7
0
1
0
4
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
2
0
2
0
0
0
0
2
0
0
0
2
1
0
2
1
0
0
0
0
0
1
0
0
1
0
1
1
0
2
0
0
1
0
0
0
1
0
1
0
0
1
0
1
2
2
0
1
3
0
0
3
0
0
0
0
1
2
0
0
0
0
1
0
0
0
2
0
2
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
1
2
2
0
0
2
0
0
0
0
1
2
1
0
1
0
2
0
1
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
1
0
2
0
0
0
0
3
0
2
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
1
0
2
3
0
2
1
1
0
0
2
1
2
0
2
1
0
1
0
0
1
0
0
0
2
2
0
1
0
0
0
0
2
0
1
0
4
3
2
0
0
2
0
0
0
1
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
2
0
1
1
0
2
1
0
0
0
0
0
0
0
1
0
2
0
0
4
0
2
0
3
0
0
2
2
0
0
3
3
2
0
0
0
0
2
0
0
1
0
1
0
1
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
1
1
1
1
0
0
0
0
1
2
0
0
0
0
0
1
1
0
1
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
2
0
0
2
0
1
0
1
0
0
2
2
0
2
0
1
0
2
0
1
0
0
0
2
0
2
0
2
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
2
0
1
1
1
0
0
1
1
0
0
0
0
11
0
2
1
0
0
0
1
0
3
0
1
0
0
2
0
0
0
0
0
0
0
1
1
1
0
0
0
0
2
0
1
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
2
2
0
0
5
0
1
0
0
1
0
1
3
0
2
0
2
1
0
0
0
0
1
2
0
1
1
2
0
0
0
2
1
0
0
0
0
0
1
0
0
3
0
2
0
0
0
1
0
1
0
0
0
0
0
1
2
1
0
0
0
0
0
0
1
1
0
0
2
1
1
1
2
2
0
0
0
1
0
0
0
2
0
1
0
2
1
2
0
1
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
4
0
0
0
0
0
1
0
1
0
2
0
0
1
0
0
0
0
4
2
0
1
0
2
0
2
0
1
0
0
0
2
1
0
0
0
0
3
0
1
2
0
0
0
0
1
0
0
2
0
1
1
1
1
0
0
1
0
0
1
2
0
0
0
2
2
1
0
0
0
0
2
0
0
0
0
1
0
0
1
1
0
0
0
2
0
0
1
0
0
2
0
0
0
1
1
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
2
0
1
2
0
1
0
0
0
1
0
1
1
0
2
0
0
1
2
0
0
0
0
3
0
0
1
0
0
2
0
0
1
1
0
0
2
0
0
3
0
0
1
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
2
0
1
0
1
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
1
0
2
0
0
2
0
0
0
0
0
1
1
2
0
1
1
1
0
0
2
0
3
0
0
0
2
0
1
1
2
0
2
0
1
0
0
0
1
2
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
1
2
2
0
0
1
1
0
0
0
0
1
0
1
1
0
0
0
0
1
2
2
2
0
2
0
0
2
0
0
0
2
0
1
1
0
0
2
2
3
1
7
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
1
2
0
0
0
0
1
1
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
2
1
0
4
0
2
0
2
0
0
0
0
0
0
1
2
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
2
1
2
0
0
0
2
0
0
1
1
4
2
1
0
1
0
2
0
0
1
0
0
0
1
0
0
0
1
2
2
0
1
0
1
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
2
0
0
0
0
0
0
0
0
0
1
2
3
1
2
1
1
1
0
1
1
0
0
0
2
1
0
0
4
0
0
2
1
1
0
2
0
1
0
0
0
0
2
1
0
0
1
0
3
0
0
1
0
0
0
0
0
1
0
0
0
2
3
0
0
2
0
2
0
1
2
0
0
0
2
0
1
4
0
1
0
1
2
0
0
0
2
1
2
0
0
1
0
0
0
2
0
0
0
2
2
0
0
4
1
1
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
1
1
2
0
0
0
0
1
0
0
2
0
1
1
0
0
1
1
4
1
0
0
1
2
0
0
2
2
0
0
0
2
1
0
0
1
0
0
0
2
2
0
0
0
0
0
1
2
0
0
2
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
3
0
2
1
0
3
2
0
0
0
0
2
0
0
0
2
2
0
0
2
1
1
2
2
0
1
0
0
1
0
0
1
2
1
1
1
0
0
0
0
0
0
0
0
4
0
0
0
1
1
1
2
0
0
1
0
0
1
0
2
0
1
1
0
0
2
1
1
0
0
1
3
0
2
1
1
1
0
0
1
3
4
0
0
0
1
0
0
2
0
2
0
0
0
0
1
0
0
1
0
0
2
2
1
0
2
2
0
1
0
1
2
0
2
0
0
1
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
1
0
2
1
2
0
1
0
0
2
1
0
0
1
0
0
1
0
1
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
3
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
2
1
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
2
2
2
0
1
0
0
0
2
0
0
2
0
0
0
1
1
0
0
0
0
2
0
0
1
0
0
2
2
1
1
0
2
1
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
1
0
0
0
1
0
0
2
0
0
0
0
0
1
0
1
2
1
0
0
1
1
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
2
1
0
2
0
1
0
2
2
0
0
0
0
0
0
0
0
1
0
2
1
0
1
0
0
1
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
2
2
6
0
1
0
0
0
0
1
0
1
0
1
0
2
1
1
0
2
2
2
0
0
0
1
0
0
0
0
2
3
1
1
0
1
0
2
0
0
1
2
0
3
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
2
2
1
0
2
1
1
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
1
0
2
0
1
3
0
1
0
1
1
0
0
1
0
3
2
0
0
1
2
0
1
3
1
1
0
0
1
0
0
0
2
0
2
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
3
0
2
0
0
0
0
0
0
0
0
3
0
2
1
1
1
1
2
0
0
3
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
2
2
2
0
0
1
1
2
1
0
0
2
1
1
2
0
0
2
1
2
1
2
0
0
0
3
2
1
0
1
1
1
0
1
0
1
2
3
2
1
0
0
1
2
0
3
0
0
0
0
0
0
3
1
0
0
0
1
0
1
0
0
0
2
3
0
2
0
0
1
7
1
0
2
0
1
0
1
2
0
0
0
2
0
0
2
0
1
1
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
2
0
2
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
2
2
1
0
0
0
2
0
0
0
0
1
0
0
0
2
1
0
0
0
1
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
2
0
0
0
1
2
2
0
0
0
1
0
0
0
0
1
2
1
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
1
1
1
0
0
1
3
1
0
1
0
1
0
2
0
3
0
2
2
0
0
0
0
1
2
0
0
1
1
2
0
0
0
2
0
0
1
1
0
0
0
0
0
2
0
1
0
1
0
0
0
0
1
2
2
0
2
1
2
1
0
1
0
1
0
0
0
1
2
0
0
4
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
3
0
1
0
2
3
0
0
1
0
0
0
0
0
0
0
2
1
0
0
1
0
2
0
3
2
0
2
2
2
1
0
0
0
0
4
0
2
0
0
0
0
1
0
0
1
0
2
2
0
0
1
1
3
1
0
0
2
0
1
0
2
0
0
0
0
2
2
0
0
0
0
2
2
0
0
0
0
1
0
0
8
0
0
1
0
1
1
0
0
0
1
1
2
0
2
0
0
0
0
1
2
0
1
1
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
1
0
3
1
0
0
2
0
0
0
0
2
2
0
0
1
1
0
2
1
0
0
0
0
1
2
0
0
0
1
1
2
0
1
1
0
0
0
0
0
0
0
0
2
0
3
0
1
0
0
2
1
0
0
2
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
2
1
5
0
0
1
1
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
1
0
0
0
0
0
2
0
1
0
0
0
2
2
0
0
1
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
2
1
0
1
0
1
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
1
1
0
1
1
0
0
0
2
1
0
2
2
0
5
1
1
2
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
2
3
0
0
0
0
0
1
1
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
1
2
0
2
0
0
0
0
2
1
0
0
0
0
2
1
0
2
0
0
0
1
0
1
0
1
2
1
1
0
2
0
0
2
2
0
0
0
2
0
0
0
0
0
1
1
0
0
2
0
0
2
1
1
0
0
0
0
1
0
1
1
0
2
0
0
0
0
2
0
0
0
2
2
0
0
1
0
1
1
1
0
1
0
0
0
1
1
0
0
0
2
0
1
1
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
3
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
2
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
4
0
0
0
0
0
1
2
0
0
0
2
2
1
0
0
1
1
1
2
0
0
1
1
0
1
0
0
0
0
0
2
2
0
0
0
0
1
2
1
0
2
0
0
1
0
0
0
1
2
0
1
0
0
2
1
0
1
1
0
0
1
2
1
0
1
0
2
0
0
0
1
0
2
2
2
0
0
1
1
0
0
2
1
0
1
0
1
0
0
1
1
0
0
0
1
0
2
4
0
1
0
0
0
0
1
0
1
1
1
0
2
2
0
2
0
0
1
0
1
0
0
0
2
2
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
1
1
2
5
1
0
0
1
2
3
0
0
1
0
2
1
1
0
2
0
0
0
1
0
0
0
0
2
2
0
0
0
0
2
0
1
0
2
0
0
2
0
0
0
0
0
0
0
1
0
2
2
1
0
0
3
0
0
0
1
0
0
0
1
2
0
2
0
2
0
0
2
1
0
0
2
2
3
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
1
0
0
0
1
2
0
0
2
0
0
1
0
0
0
2
2
0
0
2
0
2
1
1
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
2
0
2
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
2
3
0
1
0
0
0
0
1
2
1
2
1
1
2
0
0
0
0
0
2
2
2
0
0
0
0
0
2
2
2
1
2
0
0
4
0
2
1
1
1
0
2
0
2
1
2
0
0
0
0
1
0
2
0
0
0
0
1
0
2
0
0
0
0
2
0
2
0
2
0
1
1
1
0
0
1
0
2
1
0
1
1
0
0
2
2
1
0
0
0
0
2
2
0
0
2
2
0
2
1
2
2
0
0
1
0
0
2
0
0
0
0
0
0
0
1
1
0
1
0
0
3
0
0
0
0
2
1
0
0
0
0
0
2
1
2
0
1
0
2
0
1
2
2
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
1
2
0
0
2
3
2
0
1
0
0
0
0
0
1
0
0
0
1
0
0
3
0
1
0
0
3
0
0
2
2
2
0
0
0
0
2
0
2
0
0
0
0
1
1
2
0
0
1
0
0
1
0
4
0
3
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
2
2
0
2
0
1
0
1
1
0
0
0
0
1
2
0
2
0
0
2
0
0
0
0
0
0
0
1
2
2
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
2
0
0
1
1
2
0
0
1
2
0
0
1
0
1
0
0
2
0
0
1
0
0
2
0
2
1
0
2
0
0
0
0
0
3
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
2
0
0
0
0
1
0
1
1
0
0
0
0
0
1
2
0
0
0
0
0
0
1
2
1
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
2
1
2
1
2
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
1
2
1
0
1
0
0
0
0
0
1
0
2
1
2
0
0
0
3
0
0
0
0
1
0
0
0
0
1
1
1
0
2
2
0
0
0
0
2
1
0
1
0
0
0
2
0
2
0
1
2
0
0
0
2
2
0
2
0
4
1
2
0
1
0
1
2
0
0
0
3
2
0
0
0
2
2
1
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
4
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
4
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
1
0
0
1
2
2
1
1
0
1
0
1
2
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
3
0
1
2
2
0
0
0
1
0
0
2
0
0
0
0
3
0
1
1
1
0
1
2
0
2
2
1
1
0
0
0
0
0
1
2
0
1
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
1
2
3
0
1
0
0
0
1
1
0
0
0
0
1
1
0
2
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
2
0
0
0
0
0
1
0
0
0
2
0
0
0
1
2
0
2
2
1
2
0
2
0
0
2
0
1
0
0
1
0
0
3
1
3
3
2
0
0
4
0
0
0
0
0
0
1
0
1
0
0
0
0
2
2
0
0
0
2
1
2
0
0
0
0
0
0
0
2
1
1
0
0
1
2
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
4
0
0
2
0
0
0
2
0
0
0
8
0
0
1
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
2
2
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
1
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
1
0
1
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
1
1
0
0
0
0
3
1
0
2
0
0
0
1
2
0
2
0
2
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
4
2
0
0
0
0
2
1
0
1
2
0
0
0
0
2
0
0
0
0
1
1
1
2
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
2
1
2
0
1
0
1
0
2
0
5
1
2
1
0
0
0
1
2
1
2
1
0
0
2
1
0
2
2
3
2
1
0
0
0
0
0
1
0
2
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
2
0
0
0
0
1
0
2
1
2
1
1
1
0
2
1
0
0
0
2
2
0
0
1
0
1
1
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
2
0
0
0
2
1
0
0
1
0
0
2
0
0
2
2
0
0
0
2
0
2
0
2
0
1
2
0
1
2
0
0
0
2
0
2
0
0
0
1
1
6
0
0
1
2
0
0
0
1
0
1
0
0
1
0
0
0
3
4
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
2
1
1
0
0
0
0
0
0
0
0
0
2
0
0
2
2
4
0
0
1
0
1
0
2
2
0
2
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
3
0
0
1
1
2
1
1
0
2
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
2
2
0
2
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
3
1
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
1
1
0
0
2
0
1
0
0
0
1
0
0
2
1
0
1
0
2
2
0
0
2
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
2
2
0
2
0
0
1
1
2
2
2
1
0
3
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
1
0
1
2
1
0
0
2
0
0
1
0
0
1
0
0
1
0
1
1
0
1
0
0
1
1
0
0
3
0
0
2
0
1
0
0
0
0
0
0
1
0
1
1
1
0
0
1
1
0
2
1
0
2
2
0
0
0
0
0
2
2
0
1
2
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
2
1
0
1
2
0
0
0
0
2
0
0
1
1
2
0
0
0
0
1
0
0
0
0
0
2
0
0
1
1
1
1
1
0
1
1
2
1
0
0
0
1
0
1
0
0
2
0
2
0
0
2
0
1
0
0
0
2
0
0
0
0
1
0
0
2
0
1
2
2
0
1
0
0
0
2
0
1
0
2
1
0
2
1
1
1
2
2
0
1
0
0
0
0
0
0
2
0
0
2
0
0
2
1
1
0
0
1
2
0
2
2
0
0
1
2
2
0
1
0
0
1
2
0
1
2
0
2
0
0
2
1
0
1
0
3
1
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
2
0
1
0
0
1
0
0
0
1
0
0
0
1
0
1
1
2
0
0
0
0
1
1
1
0
0
0
0
2
0
2
1
1
0
0
1
0
0
0
1
0
2
0
2
2
3
3
0
0
2
0
0
2
0
2
0
0
0
1
3
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
2
1
2
2
0
0
0
1
0
2
1
1
2
0
4
0
0
0
0
1
4
0
0
0
0
0
0
2
1
0
0
2
1
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
2
0
0
0
0
1
2
2
0
0
1
0
0
1
0
2
0
3
0
0
1
0
2
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
2
0
3
2
1
0
2
0
0
1
0
1
2
0
2
0
0
0
2
0
1
1
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
2
1
0
1
1
2
1
1
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
2
2
2
0
1
0
0
0
0
0
2
2
0
0
1
1
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
3
1
3
2
0
1
0
3
1
0
2
0
1
0
0
0
1
0
2
0
0
0
0
0
1
2
1
1
0
0
1
2
0
1
0
0
0
1
0
1
0
7
0
2
1
0
0
0
2
2
1
0
1
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
2
1
0
0
0
0
2
1
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
3
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
1
0
2
1
0
2
0
1
1
0
1
3
0
2
0
0
2
0
1
0
1
0
2
2
0
0
0
2
0
1
0
0
0
0
0
0
0
1
2
2
0
1
0
2
2
0
0
0
0
2
0
0
1
0
0
0
1
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
2
2
2
0
0
0
2
2
0
2
1
0
2
1
0
0
1
0
0
3
0
0
1
0
2
0
0
0
0
2
0
0
0
1
0
0
1
2
0
0
0
2
0
0
0
2
2
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
2
2
0
0
1
1
0
0
1
0
0
2
0
2
0
1
1
0
0
1
0
0
0
2
0
6
2
2
1
0
0
2
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
3
2
0
2
1
1
0
8
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
1
1
0
1
2
0
0
0
1
2
1
2
0
2
0
0
0
1
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
1
0
2
1
0
0
0
0
0
2
0
0
1
1
0
1
0
0
1
3
0
0
0
0
0
0
2
1
2
0
1
1
2
0
0
1
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
2
2
0
2
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
3
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
1
0
0
7
3
0
0
0
1
0
1
0
0
2
0
1
1
0
3
0
0
0
0
0
1
0
1
1
2
2
0
3
0
0
0
1
3
0
0
0
0
0
0
2
0
3
0
2
0
0
2
0
2
2
0
0
1
1
0
2
1
0
0
0
0
0
2
0
2
0
2
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
2
2
1
0
0
0
0
1
2
0
1
0
0
0
0
2
0
1
0
2
0
0
0
0
1
0
2
0
1
0
1
0
0
7
2
1
1
0
0
0
1
0
2
0
0
0
0
0
0
2
0
2
0
0
0
3
0
2
1
1
0
0
1
0
0
0
0
0
0
1
0
1
0
2
1
1
0
0
2
0
1
0
1
0
2
1
0
2
0
1
0
0
1
0
2
3
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
1
2
2
1
1
1
2
0
1
1
0
1
0
0
2
0
1
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
2
0
0
0
0
0
0
1
3
2
1
0
0
0
0
0
0
1
0
2
0
1
2
0
2
0
0
1
2
0
0
0
0
2
1
0
1
0
0
0
0
3
0
2
1
0
0
2
1
2
0
0
0
0
2
0
0
1
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
1
1
0
2
0
2
2
1
0
0
1
0
1
0
1
1
0
0
1
0
0
0
0
2
0
0
1
0
2
0
1
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
1
0
1
3
0
2
1
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
1
1
0
0
0
0
1
1
0
2
0
0
1
0
0
0
1
3
0
0
0
0
3
2
0
0
1
0
1
1
0
0
0
0
0
1
2
0
0
1
0
0
0
2
0
0
0
0
0
2
0
1
2
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
1
2
2
0
0
0
2
0
1
2
0
1
0
2
0
0
2
0
1
1
0
0
2
1
1
0
0
0
1
0
0
0
0
0
2
0
2
0
0
2
0
2
0
0
0
0
1
0
1
1
0
0
2
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
2
2
0
1
0
0
0
1
2
0
0
0
2
0
0
2
1
0
0
0
1
1
0
1
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
2
1
0
1
0
1
0
0
0
0
1
0
0
1
0
2
0
0
0
0
1
0
0
0
1
0
2
0
2
0
1
0
0
0
0
1
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
2
1
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
2
0
0
3
1
0
0
8
0
0
2
2
0
1
2
2
0
1
0
2
1
0
1
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
2
4
2
0
1
1
0
4
2
0
0
0
6
0
2
0
0
1
0
0
0
0
2
1
0
2
2
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
2
0
2
0
1
0
0
0
2
0
0
0
0
0
2
2
0
0
0
2
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
2
0
0
0
1
1
0
0
0
0
1
2
0
2
2
0
0
0
1
1
2
0
0
0
0
2
0
2
0
0
1
1
0
1
0
0
0
0
2
1
0
0
0
2
1
1
0
0
1
0
0
0
1
0
2
2
1
0
2
2
0
2
0
0
0
3
0
2
1
0
5
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
1
0
0
0
1
1
0
0
0
1
4
1
2
1
2
0
2
0
0
0
1
0
2
0
0
0
1
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
2
2
0
0
0
2
2
0
0
0
1
0
0
0
0
1
0
1
0
0
2
1
0
0
0
1
2
1
0
0
0
0
2
1
0
0
2
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
1
1
2
2
0
2
0
0
0
0
0
1
0
0
0
0
0
5
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
2
0
1
1
0
0
2
0
0
0
0
2
0
2
2
0
2
0
0
0
2
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
3
0
1
0
0
0
2
0
0
0
2
1
1
2
2
0
0
2
0
1
1
0
0
0
1
2
0
1
1
0
2
2
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
2
0
2
0
3
1
0
0
1
0
3
0
0
3
0
0
0
0
0
1
0
0
2
2
2
1
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
2
0
0
0
1
2
0
0
1
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
3
2
1
0
0
0
0
0
1
0
2
0
0
5
1
0
0
0
0
0
0
1
0
0
0
1
2
2
0
1
0
2
0
2
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
2
0
3
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
1
1
0
0
0
0
0
0
1
0
0
2
2
0
1
0
0
0
1
0
0
0
2
0
0
2
0
0
1
1
2
0
2
1
1
0
0
0
1
1
2
1
1
0
1
0
2
1
0
0
0
0
0
2
1
1
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
2
0
1
0
0
2
0
0
0
0
2
1
0
0
0
2
0
0
2
2
0
0
0
1
0
1
0
0
2
0
1
0
1
0
0
1
2
0
1
0
2
0
0
1
0
2
0
1
0
1
0
0
0
0
12
2
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
1
0
1
2
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
3
0
1
0
0
0
0
1
0
0
0
0
1
2
1
1
3
2
0
0
0
0
0
0
0
0
0
0
2
3
1
2
0
1
0
2
0
0
0
0
0
2
1
1
0
0
0
0
0
5
2
2
0
0
2
1
0
2
0
0
0
1
0
1
1
0
2
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
2
1
0
0
0
0
2
0
0
0
2
2
2
1
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
4
2
0
0
0
0
0
1
2
0
1
0
1
0
0
2
0
0
0
0
2
2
0
2
1
0
0
0
0
2
2
1
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
2
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
2
1
3
2
2
1
0
0
2
0
2
2
0
1
1
0
0
0
0
1
0
0
3
0
0
0
2
0
2
0
1
1
0
0
1
2
1
0
0
1
3
1
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
2
0
2
0
1
0
0
0
2
2
0
1
2
0
2
0
0
0
0
1
1
0
0
0
2
0
2
0
0
0
0
2
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
1
0
2
2
0
2
2
1
1
0
1
0
2
0
0
0
0
0
2
2
0
0
2
2
2
0
2
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
2
1
2
1
2
0
1
0
1
0
0
2
0
0
2
1
0
0
1
2
0
0
0
2
0
1
0
1
2
0
0
0
0
0
1
2
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
1
2
0
0
0
0
1
1
0
0
1
0
0
0
2
0
2
0
0
0
0
1
1
1
0
0
2
0
9
1
1
0
1
3
1
1
0
0
0
0
0
0
0
0
0
1
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
3
0
1
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
1
0
0
0
2
0
2
0
1
0
0
1
0
1
4
0
0
0
0
0
0
1
3
2
0
0
0
1
2
0
2
1
0
0
0
0
0
2
0
0
0
0
0
1
0
1
2
1
0
0
0
0
0
2
0
2
0
0
1
2
0
1
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
1
1
0
1
1
1
0
1
0
2
0
0
1
0
0
1
2
0
0
0
2
0
2
0
0
1
0
2
0
1
0
0
1
0
1
0
0
1
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
1
0
0
0
1
0
2
1
1
0
0
0
0
0
0
2
0
0
0
0
0
3
1
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
2
2
2
1
0
0
0
2
0
2
0
0
0
1
0
1
0
1
0
0
1
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
2
1
0
0
1
2
0
0
1
2
0
1
0
1
1
0
1
2
0
2
0
0
2
2
1
0
0
2
0
0
0
0
2
0
0
0
0
2
0
2
0
2
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
1
1
2
0
2
0
0
0
0
0
3
2
1
0
1
0
0
1
1
2
0
0
0
2
1
0
0
0
2
0
0
0
3
0
2
1
2
0
0
0
0
0
0
2
0
0
2
2
2
0
0
0
0
0
4
0
0
1
2
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
1
0
1
1
1
0
1
0
0
0
2
0
1
0
0
1
2
0
0
0
0
0
0
0
1
1
1
1
0
0
2
0
0
0
0
0
2
1
0
1
0
2
0
0
0
0
0
0
0
0
0
3
1
4
1
0
0
2
0
1
2
0
0
2
0
1
0
0
2
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
1
0
1
2
1
0
2
0
1
1
0
2
2
0
0
0
2
3
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
3
3
3
2
0
1
1
0
1
0
0
1
1
1
2
0
0
0
0
2
0
0
0
0
1
1
1
2
0
1
0
2
0
0
3
1
2
0
1
0
0
0
0
2
0
0
2
0
1
0
0
0
0
2
0
0
0
0
2
2
0
0
0
2
0
0
2
0
1
1
0
1
0
0
2
1
0
1
1
1
0
0
0
0
3
2
2
1
0
0
0
1
0
0
1
0
2
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
3
0
0
0
0
1
0
0
0
2
0
1
0
2
0
1
0
5
2
2
0
0
1
0
0
1
0
0
0
0
2
0
1
1
0
0
1
1
0
2
0
0
0
2
0
2
0
0
0
0
0
1
1
0
1
2
0
1
1
0
2
1
3
0
0
1
1
0
0
0
2
2
0
1
0
5
2
0
0
0
0
1
0
1
0
2
1
0
2
2
5
0
2
0
0
0
0
0
2
0
2
0
0
2
1
0
0
0
1
1
0
0
0
2
0
0
1
0
0
2
0
2
1
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
2
0
0
0
0
0
1
0
1
0
2
0
1
2
2
0
1
0
0
0
1
0
0
0
0
1
2
0
1
0
2
0
1
0
0
1
0
0
0
2
0
1
0
0
2
1
0
0
2
2
0
2
0
2
0
1
1
0
0
0
0
0
2
0
0
1
0
0
2
0
1
1
1
0
0
0
0
0
1
0
0
1
0
2
1
0
0
0
0
0
2
1
0
0
0
0
2
2
2
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
1
0
2
0
2
0
2
0
2
0
0
1
1
0
0
0
1
1
0
0
2
1
0
0
0
2
1
0
0
3
0
0
0
0
0
1
2
0
2
0
0
0
0
3
0
0
1
2
0
2
2
2
2
0
1
0
0
0
1
0
1
0
2
2
0
0
2
2
0
0
0
1
0
1
0
0
6
0
1
0
0
0
0
0
0
1
1
2
2
0
0
1
0
0
1
0
0
2
0
0
1
3
0
0
1
0
0
0
0
2
0
2
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
1
1
1
0
0
0
1
1
3
4
0
2
0
0
0
0
1
0
0
0
2
2
0
0
2
0
0
0
3
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
2
0
2
1
0
0
0
2
0
2
3
1
0
1
0
0
0
1
0
0
0
0
0
3
0
0
0
0
1
0
1
0
0
2
1
1
0
2
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
2
0
0
2
0
1
0
1
1
0
1
2
1
1
2
0
2
0
2
2
0
0
0
2
1
0
0
0
2
0
0
1
0
1
0
2
3
0
0
0
2
0
1
2
0
1
2
1
1
0
4
0
0
4
0
0
0
0
0
0
1
0
0
1
1
0
2
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
1
0
0
1
0
1
2
0
0
1
0
0
0
0
0
1
1
0
2
0
1
0
2
0
0
3
0
0
0
1
0
0
1
1
0
0
0
0
2
0
0
0
1
1
0
0
0
0
2
0
1
1
2
0
0
0
1
0
0
0
0
2
1
2
2
1
1
0
0
0
1
0
1
0
2
0
0
0
2
0
2
0
2
0
2
0
0
0
1
0
1
0
0
1
0
2
0
0
0
3
0
0
0
1
0
0
0
2
2
0
2
0
0
0
1
1
0
1
0
0
0
0
0
2
0
1
1
0
0
0
0
1
0
2
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
1
0
2
3
0
0
0
1
0
0
1
1
1
2
0
2
1
1
0
1
0
1
1
1
1
0
2
0
0
2
3
0
0
0
0
0
1
1
0
3
0
1
0
0
0
3
1
0
2
2
1
0
1
0
0
7
0
0
1
0
1
3
0
2
0
2
7
0
2
1
0
0
1
0
0
1
2
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
1
0
0
0
0
1
2
0
1
0
0
0
0
2
0
2
2
0
0
1
0
0
1
1
0
0
0
1
2
0
0
0
1
0
1
0
2
2
2
0
0
1
2
1
0
1
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
1
1
2
2
0
1
2
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
2
0
0
0
0
0
1
0
0
0
2
0
0
1
0
1
0
1
1
0
0
2
0
1
0
1
2
0
0
2
1
2
1
1
0
1
0
0
0
2
2
1
1
0
0
0
1
0
0
1
2
1
0
2
2
0
2
0
0
2
0
0
0
0
1
0
0
3
0
2
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
2
1
0
0
1
0
2
2
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
3
2
0
0
0
2
2
3
1
0
0
0
0
2
1
0
0
1
0
0
0
0
0
2
1
2
0
2
0
1
0
0
2
1
0
1
0
1
2
0
0
0
0
2
0
0
0
0
0
1
2
1
0
0
0
0
0
1
2
0
2
0
0
0
0
2
2
0
0
2
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
1
0
3
3
0
2
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
1
0
1
0
2
0
1
1
0
0
1
0
2
2
0
0
1
0
0
3
2
0
0
0
0
2
0
1
1
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
1
0
1
0
0
2
2
1
0
0
2
0
0
0
1
0
1
0
0
0
0
1
0
1
0
2
0
1
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
1
1
1
0
1
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
1
0
1
2
1
0
2
0
0
0
2
0
0
1
0
1
0
2
0
0
1
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
3
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
3
0
0
1
0
0
2
0
2
2
1
0
0
1
3
0
0
0
0
0
0
0
2
1
0
0
1
2
0
0
0
0
0
1
0
0
2
1
2
0
0
0
0
0
2
1
2
0
1
0
1
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
2
0
0
0
0
1
0
2
0
0
0
2
0
2
2
0
0
1
0
1
1
0
0
0
0
2
1
0
1
1
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
1
2
0
1
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
2
0
2
0
0
4
1
0
0
0
1
0
2
0
0
0
0
0
0
0
1
2
0
2
1
0
2
0
0
2
1
1
2
0
2
0
0
0
0
1
2
0
0
0
0
2
2
0
1
2
1
0
0
0
1
1
1
3
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
1
2
1
0
2
0
0
22
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
2
1
0
0
1
0
0
0
0
1
2
1
0
0
0
0
0
0
3
0
1
0
0
2
0
1
0
0
0
0
0
0
2
0
2
0
0
0
1
1
2
1
0
0
0
0
0
1
2
0
1
0
0
0
0
0
1
1
1
0
2
0
0
2
0
0
5
0
0
0
0
2
0
0
0
0
0
1
0
2
0
1
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
1
0
2
3
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
1
2
6
0
0
0
0
0
1
3
0
0
0
1
0
0
0
2
1
2
2
0
2
2
0
0
0
0
0
0
0
1
2
0
2
0
2
0
1
1
0
0
0
1
0
0
2
1
2
0
1
2
1
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
1
0
0
1
1
1
1
0
1
0
0
2
0
0
0
1
0
0
1
2
1
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
1
3
2
2
0
2
0
0
0
1
1
0
2
2
2
0
0
2
1
0
2
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
2
2
1
0
0
0
0
0
2
0
0
0
1
0
0
2
2
0
0
2
0
0
0
1
0
1
1
0
0
1
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
2
0
0
0
3
1
0
1
0
2
3
2
0
1
3
0
0
0
1
0
0
2
2
8
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
1
1
0
0
0
0
1
0
0
1
0
2
0
2
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
3
0
2
2
0
0
2
1
0
0
1
2
0
0
0
0
2
2
1
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
1
2
0
0
4
1
0
0
0
0
3
0
2
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
3
1
2
0
0
1
1
0
1
0
0
0
1
0
0
0
0
1
2
0
3
1
0
1
0
2
0
0
0
0
1
0
2
0
0
0
0
1
1
0
1
1
0
0
0
1
2
0
2
2
1
0
0
1
0
1
0
0
2
2
1
2
0
2
2
1
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
2
0
2
0
1
0
0
1
0
0
0
3
1
4
2
0
1
0
2
0
0
1
0
0
1
3
0
1
0
0
1
2
0
0
0
0
0
2
3
2
1
2
2
2
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
1
1
0
0
1
1
1
0
0
1
2
0
0
0
1
0
0
0
1
0
0
1
1
1
2
0
0
1
0
1
0
1
1
1
2
2
2
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
2
0
0
0
2
0
0
1
0
1
0
0
2
0
2
0
0
2
0
1
0
4
0
1
0
0
0
0
1
0
0
0
3
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
1
0
2
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
1
2
0
0
2
2
0
0
0
0
0
1
2
0
2
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
2
0
2
0
0
0
2
0
0
1
1
1
2
0
0
1
0
0
0
0
1
0
5
1
0
0
0
1
1
2
2
0
0
1
0
0
1
2
0
0
2
1
2
0
0
0
1
0
2
0
0
0
0
0
1
1
0
0
1
1
0
0
0
1
2
0
1
2
0
2
2
0
2
0
0
0
2
1
1
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
1
0
2
0
2
1
0
0
0
0
0
1
1
0
0
3
2
0
0
0
0
0
0
0
2
1
0
0
1
0
1
0
0
0
0
0
1
0
0
2
2
1
1
0
1
3
0
1
0
1
0
0
1
2
1
2
0
1
0
2
0
0
1
2
0
1
0
0
2
2
1
1
1
1
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
2
1
1
0
1
2
2
0
0
0
0
0
2
0
0
4
2
0
0
2
2
2
2
2
0
0
1
0
0
2
1
0
0
0
0
1
0
0
1
2
1
1
0
0
0
0
2
2
0
2
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
3
0
0
1
0
1
0
1
1
1
1
0
0
0
1
0
0
0
1
2
5
0
0
0
0
0
2
0
0
1
0
0
2
1
0
0
1
0
1
0
1
3
0
0
0
1
4
0
0
0
4
0
1
2
0
0
0
0
2
2
0
1
0
0
1
0
2
2
1
0
0
0
0
2
0
2
0
0
0
3
1
0
3
1
1
0
0
2
2
0
1
0
0
0
0
0
1
1
0
0
1
0
2
0
2
1
0
0
0
0
2
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
2
0
0
1
0
2
1
1
2
3
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
1
2
0
0
0
1
1
0
2
1
0
0
0
2
0
0
0
0
2
0
0
0
2
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
2
0
0
3
2
0
0
0
0
0
0
0
2
2
2
0
0
0
1
2
2
3
1
0
0
1
2
0
3
0
2
1
0
0
0
2
0
0
1
1
0
2
0
1
0
0
1
0
1
0
1
0
1
0
2
1
0
2
0
1
0
0
0
0
1
2
0
1
0
1
1
0
0
0
0
0
2
0
3
2
1
1
0
0
2
0
0
2
0
0
1
0
0
0
0
2
0
0
1
0
2
1
0
1
1
0
1
0
0
0
1
0
0
0
1
0
2
0
0
1
1
1
0
2
0
5
2
0
1
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
1
0
0
2
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
2
2
0
2
0
1
1
0
0
0
0
1
2
2
0
0
0
0
0
2
2
0
1
0
0
1
1
0
0
1
0
0
3
0
0
1
2
0
2
0
1
0
0
1
0
0
0
2
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
3
2
0
1
1
0
1
0
0
1
0
0
2
0
0
1
1
0
0
0
1
1
0
1
1
0
0
0
1
2
0
1
2
0
2
0
2
0
1
3
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
1
1
2
0
0
0
1
0
0
0
1
0
2
0
0
2
0
0
0
1
2
0
0
1
2
2
3
0
1
0
0
0
0
2
0
1
1
0
0
2
1
2
2
1
0
0
2
1
1
2
0
0
0
2
0
0
0
2
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
2
1
2
2
2
0
1
1
0
1
0
0
1
0
0
0
1
1
1
0
0
1
2
1
1
0
0
0
0
0
1
0
0
0
0
2
2
2
2
1
2
0
0
5
1
2
0
3
0
0
1
0
0
0
1
0
1
0
2
0
2
2
0
0
0
1
0
1
2
0
0
1
0
6
1
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
2
0
2
0
2
0
2
0
0
1
1
0
0
0
0
0
2
2
0
2
0
1
0
1
1
2
0
1
2
2
0
2
1
1
0
0
0
0
1
1
0
0
0
0
0
0
2
0
2
0
1
1
1
1
2
0
2
1
0
0
1
0
0
0
2
0
0
0
0
2
0
0
1
0
0
1
0
1
0
0
0
0
1
2
0
0
4
0
2
0
1
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
4
0
1
0
1
0
1
3
0
0
0
1
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
1
1
0
0
2
1
0
1
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
1
2
3
1
0
0
1
7
1
0
2
0
0
0
0
2
0
1
0
0
1
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
2
1
0
2
0
1
0
1
0
0
2
1
0
0
0
0
1
0
1
0
2
0
0
0
0
1
0
0
1
0
1
0
0
2
0
0
2
0
0
0
0
0
1
2
0
1
0
0
0
1
0
0
0
0
0
1
2
2
0
0
2
0
0
2
0
0
2
0
2
0
2
0
2
0
1
0
0
1
2
1
1
0
0
0
2
0
0
1
1
0
2
0
0
0
1
0
1
0
0
0
0
1
0
0
2
2
0
1
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
1
0
0
2
0
1
0
0
2
2
2
0
0
2
0
0
1
0
0
0
0
0
1
0
0
1
1
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
1
2
0
2
2
0
0
0
0
0
1
0
1
0
0
1
2
3
0
1
1
0
1
0
1
2
2
1
1
0
0
2
1
2
1
0
1
0
0
1
0
0
0
0
0
0
2
0
2
2
2
0
0
0
0
0
1
0
0
0
0
1
1
0
2
1
0
2
0
2
3
1
0
1
0
0
0
5
1
2
0
2
0
0
0
1
2
0
1
0
0
2
0
1
0
2
1
0
2
2
1
0
2
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
2
2
0
0
0
0
2
2
1
0
2
1
0
2
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
2
0
2
0
0
0
0
1
0
0
0
0
2
2
2
4
0
2
0
0
0
0
2
0
0
0
0
1
0
0
2
0
1
0
1
2
0
0
0
0
0
2
1
1
0
1
0
0
1
1
0
3
1
1
0
4
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
2
2
1
0
2
2
0
3
0
0
0
0
0
2
3
0
1
0
2
0
0
2
2
2
3
0
0
0
0
0
1
2
1
0
0
0
0
1
1
0
2
1
3
1
0
1
0
0
0
0
8
0
0
0
0
0
1
0
1
2
0
2
0
1
0
0
1
0
2
1
0
3
0
0
0
2
0
0
2
0
0
0
5
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
3
0
2
2
2
1
1
2
0
0
0
0
1
0
1
0
0
0
0
0
2
0
1
3
2
1
1
0
2
0
1
1
0
0
0
0
2
0
0
1
0
1
0
1
1
1
0
0
1
0
0
1
0
0
0
2
1
0
2
2
0
2
0
0
3
0
0
2
3
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
1
0
0
0
1
0
2
1
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
3
2
2
0
1
2
1
1
1
0
0
0
0
2
0
1
3
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
3
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
1
2
0
1
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
1
3
0
2
0
1
1
3
0
0
0
2
2
3
2
1
2
0
0
0
0
0
0
1
2
0
2
0
0
2
2
0
1
1
0
0
2
0
1
2
1
1
0
0
0
1
2
0
1
0
1
0
0
2
2
0
0
0
2
0
0
0
1
0
0
1
0
0
3
1
0
1
0
0
0
0
2
2
1
2
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
4
0
1
2
1
0
0
0
0
0
2
0
2
2
5
2
0
3
1
0
0
0
1
2
1
0
0
2
1
0
0
0
0
1
0
1
0
0
1
1
2
2
0
0
1
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
2
0
1
0
1
0
2
0
1
0
2
0
2
0
1
0
0
0
2
0
0
0
0
2
4
1
0
0
0
3
3
0
1
2
2
1
3
2
2
0
0
0
0
0
2
1
2
0
1
0
1
2
2
0
0
0
2
1
0
0
0
0
0
0
0
2
1
1
0
0
0
1
2
0
0
0
2
1
0
1
1
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
2
0
0
2
0
0
2
0
0
0
0
2
1
0
0
0
1
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
1
2
3
0
0
0
0
0
0
0
3
0
2
0
0
2
2
0
0
1
0
0
2
0
0
0
3
1
1
1
0
0
0
2
0
0
5
2
0
2
1
0
0
2
0
0
0
0
0
0
2
2
1
1
0
1
1
0
2
0
2
0
0
0
0
0
0
0
2
0
1
3
1
4
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
1
2
0
2
0
0
0
0
0
0
3
1
1
0
0
1
0
2
1
0
1
1
2
2
0
0
4
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
3
0
0
1
0
0
2
1
0
0
1
1
0
1
0
3
0
2
2
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
2
0
0
3
0
1
0
2
0
1
2
1
0
1
0
0
0
1
1
2
2
0
1
0
0
0
8
1
0
0
0
2
0
0
0
1
0
1
4
0
0
0
2
0
0
0
1
0
0
2
2
0
0
0
0
0
1
2
0
2
2
0
0
0
1
0
1
0
1
0
2
2
1
2
0
1
0
1
0
0
1
0
0
0
0
3
1
0
0
0
0
2
0
0
1
1
1
1
0
0
0
0
2
0
2
2
0
0
1
1
0
0
0
0
2
1
0
2
1
0
0
0
0
2
0
1
2
0
1
1
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
1
2
1
2
0
0
0
0
0
1
0
0
0
1
0
1
0
1
2
1
0
0
0
0
0
2
0
0
1
2
0
2
1
1
2
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
1
1
1
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
1
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
1
2
1
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
3
0
2
0
0
1
0
1
0
2
2
1
2
0
0
1
0
1
2
0
0
3
2
1
0
0
1
1
2
0
0
2
2
0
0
2
0
0
2
0
0
0
0
0
2
2
0
0
0
2
2
0
0
2
0
0
0
0
0
0
1
2
2
0
1
0
1
0
0
0
0
0
1
1
1
2
0
0
1
1
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
1
0
0
0
0
3
0
0
0
0
1
1
0
0
0
0
3
1
0
0
0
2
2
0
0
0
0
0
1
1
2
0
0
0
1
2
0
0
1
0
2
3
1
0
0
1
0
0
0
0
0
2
2
1
0
0
2
0
0
0
0
0
2
0
0
2
0
0
1
2
2
0
1
0
2
3
0
0
0
0
2
1
0
0
0
1
0
0
1
0
0
1
1
2
1
0
0
2
0
1
0
0
2
0
1
1
1
3
0
0
0
0
2
0
0
0
2
2
0
2
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
2
0
1
0
0
0
3
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
1
0
2
0
1
1
0
0
2
0
0
1
1
0
0
2
1
2
0
0
2
0
2
1
0
0
0
0
0
0
0
0
1
0
2
0
1
2
0
0
0
0
0
1
0
2
0
0
0
0
0
1
2
2
0
1
0
2
0
0
1
1
2
0
0
1
0
2
1
0
0
0
0
1
0
0
0
2
0
1
0
2
2
0
2
0
1
2
0
2
1
0
0
2
0
1
0
1
0
0
1
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
1
2
0
0
2
0
0
1
2
0
0
0
0
4
0
1
0
0
6
0
0
2
1
10
0
0
0
0
0
1
2
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
1
1
0
2
3
0
2
1
1
0
0
1
0
0
0
0
0
2
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
3
0
0
2
1
0
0
0
1
0
5
0
1
0
0
1
0
0
0
4
0
0
0
3
1
0
0
0
2
2
1
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
1
0
2
0
0
2
1
0
0
0
0
1
0
0
1
0
0
1
0
1
0
2
0
0
0
2
0
2
1
1
1
0
0
0
0
1
0
0
2
0
2
0
2
0
1
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
2
2
0
1
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
1
1
1
0
0
0
0
0
1
0
0
1
2
0
0
0
0
2
1
0
0
0
1
0
1
0
2
0
0
0
0
2
2
2
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
2
2
1
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
1
1
0
0
0
1
1
0
1
0
0
1
0
0
1
0
2
0
0
0
1
2
0
0
0
2
1
0
0
0
0
1
0
0
2
1
1
0
1
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
9
2
0
0
1
2
0
1
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
2
1
1
0
0
2
2
0
2
0
0
0
0
0
2
1
0
0
2
2
0
0
0
0
0
0
0
1
0
2
1
2
0
2
2
0
0
0
0
2
0
2
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
1
2
2
1
2
5
1
0
0
0
0
2
2
0
0
0
2
2
0
0
0
0
0
2
2
0
0
0
0
0
0
1
2
0
0
0
0
0
1
2
2
0
0
0
1
0
2
0
0
0
2
0
2
1
1
1
0
2
0
0
2
1
1
0
1
0
0
2
0
3
0
0
0
0
0
1
1
2
0
3
0
2
0
1
0
0
1
0
0
2
1
1
1
0
0
2
0
0
1
0
0
0
1
0
0
0
0
2
0
0
2
3
0
2
0
0
2
0
5
0
0
0
0
0
1
0
1
2
0
0
0
0
2
1
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
1
1
0
0
0
0
1
0
2
0
0
0
3
1
1
0
0
1
0
0
0
0
0
0
1
3
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
1
0
0
0
0
3
0
0
0
0
2
2
0
1
0
1
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
1
2
0
1
1
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
2
2
0
0
6
0
2
0
0
1
0
1
0
1
2
0
1
0
0
0
0
1
0
0
0
3
0
1
0
0
3
1
1
0
0
0
0
0
0
2
2
0
0
0
1
0
0
1
0
0
0
0
1
1
2
1
2
2
0
0
1
2
0
0
2
1
0
0
2
0
0
1
0
1
4
1
0
0
1
2
1
0
1
0
0
1
0
0
1
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
2
1
2
2
2
0
0
1
1
7
2
0
0
0
0
0
2
0
2
0
0
1
0
1
0
0
0
2
0
0
1
0
1
0
0
0
0
2
0
1
0
2
2
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
1
0
2
0
0
2
0
2
0
3
0
0
0
1
0
3
0
0
1
0
0
0
0
0
2
0
0
0
2
2
2
0
2
0
2
0
0
0
2
0
0
0
0
1
1
1
2
1
1
0
0
0
0
0
0
2
1
2
0
0
1
0
1
0
0
0
2
1
0
0
0
0
0
1
2
0
1
2
1
0
2
2
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
2
2
0
0
1
0
2
0
1
4
0
2
0
0
0
2
1
0
0
1
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
3
2
0
0
0
0
2
0
1
0
3
0
2
0
0
0
1
0
0
1
0
0
2
2
0
2
1
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
2
0
0
3
3
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
1
0
0
2
0
0
0
0
1
2
0
2
0
0
1
0
1
1
1
1
0
2
0
0
1
2
2
2
0
0
0
0
1
0
0
0
0
5
0
0
0
0
3
1
1
0
0
0
0
2
0
1
1
2
0
2
2
2
2
0
0
0
0
2
4
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
6
0
0
0
0
0
0
2
0
0
0
2
0
2
0
2
0
1
0
2
2
0
0
0
0
2
2
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
1
2
0
1
1
0
0
0
0
1
1
0
2
0
0
0
0
0
1
0
0
1
0
0
2
0
0
1
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
3
0
0
0
2
0
1
2
1
2
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
2
0
1
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
2
0
0
1
0
1
1
0
2
0
0
1
0
0
0
1
0
3
2
0
2
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
1
1
2
2
0
0
0
1
0
3
3
0
0
1
0
0
2
0
1
2
2
1
0
0
0
1
2
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
1
2
0
2
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
2
0
2
0
1
0
2
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
2
2
2
1
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
3
0
0
0
1
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
2
0
2
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
3
1
0
2
0
0
0
1
0
0
2
2
1
0
0
2
1
1
0
2
0
0
0
2
0
0
1
1
0
0
0
3
0
0
1
1
0
0
0
1
1
0
0
1
0
0
0
1
1
2
0
0
0
0
3
2
1
0
0
0
1
2
1
2
1
2
0
0
1
1
3
1
0
0
0
0
0
0
1
1
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
1
0
2
1
0
2
0
0
0
0
0
0
1
0
0
0
2
1
0
1
2
1
0
0
0
0
0
1
0
0
3
2
2
0
0
1
0
0
0
1
0
0
0
0
2
0
2
1
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
1
0
0
2
0
0
0
2
0
2
0
0
1
0
2
1
0
0
0
1
0
0
2
0
0
1
0
0
0
6
0
1
0
0
0
0
1
0
0
0
2
2
2
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
2
0
2
1
0
0
1
0
0
4
1
3
0
2
0
0
2
0
2
2
0
1
0
0
1
0
1
2
0
2
0
0
0
1
2
2
0
1
1
2
1
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
1
0
0
3
0
2
0
0
0
0
0
1
2
1
0
2
0
1
0
0
0
3
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
2
0
1
2
0
0
0
2
0
0
0
0
0
0
1
2
1
0
0
0
0
2
1
0
0
2
0
0
0
0
1
0
2
0
2
1
0
2
0
0
2
2
1
0
0
0
0
2
2
0
0
0
0
1
0
3
0
2
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
1
2
0
2
0
2
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
2
0
0
0
2
0
1
0
0
0
1
1
0
1
1
2
0
1
0
1
0
2
2
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
3
0
3
2
0
0
5
2
0
0
0
0
0
0
4
0
1
2
0
0
2
2
2
2
1
2
2
3
0
0
0
2
0
0
0
0
1
2
1
0
0
1
0
3
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
1
2
0
0
0
1
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
1
2
0
0
0
0
1
2
0
0
0
0
0
0
1
0
2
2
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
3
2
2
0
0
1
0
1
0
0
0
0
1
1
2
1
0
0
0
1
1
1
2
2
1
0
0
1
0
0
0
0
2
2
0
1
0
0
0
0
0
1
2
0
0
0
2
0
0
0
2
0
0
0
2
0
1
1
0
2
0
2
1
0
0
2
2
0
0
0
0
2
2
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
2
0
1
0
0
2
0
2
0
1
0
0
0
0
0
1
0
1
2
2
0
0
1
1
2
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
2
3
2
0
0
2
0
1
2
0
1
0
3
1
2
2
0
0
0
1
1
0
0
2
0
2
0
1
0
0
0
2
1
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
2
3
1
0
0
0
2
0
0
2
0
0
0
1
1
0
0
0
0
0
0
2
2
1
0
0
0
1
0
0
0
1
1
0
0
0
2
0
0
0
0
0
1
0
0
3
2
0
0
0
0
2
0
2
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
3
2
2
0
0
3
2
0
3
0
0
2
0
0
0
0
1
0
2
1
0
0
1
0
0
1
1
0
3
2
2
1
0
1
0
0
0
0
1
0
0
2
3
1
0
2
0
0
0
0
0
0
0
1
2
1
1
0
1
0
0
0
1
1
0
0
0
1
1
3
2
1
0
0
0
1
2
0
1
2
0
0
1
1
0
2
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
2
2
3
0
1
1
0
2
2
0
0
2
0
0
2
0
0
0
2
0
0
1
0
1
0
4
1
2
0
0
2
0
6
0
0
0
0
0
0
1
0
0
0
0
2
1
5
0
2
2
0
2
0
0
0
0
0
0
0
1
2
0
1
0
0
2
0
0
1
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
1
0
1
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
2
2
0
0
1
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
3
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
1
0
1
0
1
1
2
1
0
0
1
1
0
3
2
1
0
1
0
1
2
2
0
0
0
0
1
0
0
2
2
0
1
0
0
0
0
0
0
1
0
1
0
1
2
1
0
1
0
1
2
0
1
0
1
2
0
3
0
0
0
0
1
1
3
1
0
0
0
2
0
0
0
0
1
0
2
0
0
2
0
0
1
0
0
1
1
2
1
1
1
0
0
0
0
2
1
0
0
0
1
0
2
2
0
0
0
0
0
2
0
2
2
0
2
2
0
2
2
0
2
0
0
2
0
2
2
1
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
1
1
0
0
1
1
0
0
2
0
1
0
0
0
0
0
1
2
0
2
1
1
2
0
1
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
8
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
2
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
1
2
2
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
2
1
0
0
3
0
2
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
2
0
2
0
0
0
2
1
2
1
0
0
0
1
2
0
0
0
0
0
2
0
1
2
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
1
2
0
0
1
0
0
1
4
0
1
0
0
1
0
0
0
0
0
2
0
1
0
0
0
2
2
1
2
0
2
2
0
0
0
1
2
0
0
0
0
1
1
0
2
0
0
0
2
0
0
0
1
1
2
0
2
2
0
0
0
0
0
4
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
1
0
1
2
0
2
2
1
2
0
0
0
1
0
1
0
0
2
1
1
0
0
1
0
0
0
1
2
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
2
2
0
0
3
0
2
1
0
1
0
0
0
1
0
1
0
2
1
0
0
0
0
2
0
0
0
0
0
1
0
1
0
2
0
0
0
1
3
0
0
0
0
0
2
2
0
0
1
0
0
0
4
1
0
0
0
2
2
0
1
2
0
1
0
0
0
1
1
2
2
1
1
2
0
1
0
1
2
1
0
0
0
2
0
1
1
1
0
2
0
0
0
0
1
0
0
1
1
0
0
0
1
2
2
2
0
1
1
2
0
1
0
2
0
1
1
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
2
0
1
0
0
1
2
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
2
0
2
0
1
3
0
4
1
0
0
2
0
0
0
2
0
0
0
2
1
2
1
0
0
0
3
4
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
1
1
2
1
0
0
0
2
1
0
0
1
0
2
0
0
1
0
0
0
1
2
0
2
2
0
0
1
2
0
1
2
0
0
0
1
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
1
0
0
1
1
2
2
0
0
0
0
0
1
1
2
0
0
0
2
1
1
0
0
0
1
0
0
0
2
1
0
0
0
1
2
0
2
2
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
1
2
0
2
1
2
2
2
0
0
2
3
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
2
0
1
3
1
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
3
0
1
0
0
0
1
1
0
0
1
1
0
3
0
1
2
0
0
0
0
3
0
1
0
2
0
0
0
2
1
0
2
0
0
0
1
0
0
1
1
0
1
0
2
0
0
1
0
1
1
0
2
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
2
1
0
1
0
0
0
0
2
0
0
2
1
1
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
2
1
2
0
2
2
0
0
0
1
0
0
0
0
2
0
0
1
1
0
1
0
1
0
0
1
0
0
0
0
2
0
0
1
0
1
0
0
2
2
0
2
0
0
0
0
1
2
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
2
1
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
2
0
0
0
4
0
0
1
3
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
1
3
0
0
0
1
0
0
0
1
2
0
1
2
0
0
0
0
0
2
0
0
0
0
1
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
1
0
2
1
0
0
2
2
0
0
0
0
1
1
1
0
0
2
0
0
2
1
0
1
0
2
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
2
0
0
1
0
0
1
0
0
2
1
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
1
2
0
2
1
0
0
2
0
0
2
4
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
2
1
1
0
2
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
1
2
4
0
0
0
1
0
2
0
0
1
0
2
0
0
0
0
0
1
0
2
0
0
2
0
2
0
2
0
2
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
1
2
1
1
1
0
0
0
2
2
0
0
1
0
0
0
0
2
0
2
0
2
0
2
0
0
2
0
2
2
2
0
0
2
2
0
1
0
0
2
0
0
0
1
0
0
4
2
2
0
0
2
0
0
0
0
0
0
1
0
0
2
2
0
2
2
1
0
0
0
1
0
0
0
0
2
0
2
0
1
0
0
0
0
2
2
3
0
0
0
2
2
0
0
1
2
2
1
2
2
0
0
0
0
0
1
0
0
0
0
0
2
1
0
2
0
2
0
0
1
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
1
0
0
0
1
0
0
0
1
0
0
0
2
2
0
1
2
2
1
1
1
0
2
0
1
0
1
0
0
0
0
0
2
0
2
2
0
1
0
0
4
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
3
0
0
1
0
1
1
2
0
0
1
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
2
2
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
2
4
0
0
0
1
0
2
1
1
0
0
2
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
2
0
4
1
1
0
2
2
1
3
0
2
0
0
1
0
0
0
0
0
1
0
1
0
1
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
1
2
1
0
2
1
0
0
2
0
0
0
0
0
2
0
1
0
0
0
1
2
0
1
0
2
1
0
0
0
0
0
0
0
0
8
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
2
2
0
1
1
0
1
2
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
1
1
0
0
0
1
2
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
1
2
0
1
1
0
0
0
0
1
2
2
0
1
0
0
1
0
0
0
2
0
0
0
0
1
1
0
2
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
2
1
0
0
0
0
0
1
3
0
0
0
0
1
0
2
2
2
0
1
0
0
1
0
0
0
0
0
0
0
1
0
2
2
0
0
2
0
0
0
2
0
2
2
2
1
0
0
1
2
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
3
2
2
1
0
1
0
2
1
3
1
0
2
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
3
4
0
1
1
1
0
1
2
0
2
0
0
2
1
0
0
0
0
1
0
0
2
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
2
2
3
0
0
0
0
2
1
0
2
0
0
0
0
0
2
0
0
1
2
0
1
0
2
1
0
0
2
2
2
1
0
0
2
0
0
1
0
2
0
0
1
0
0
0
0
0
1
3
2
0
0
2
0
1
1
2
1
0
0
4
1
0
0
1
1
0
0
1
0
0
0
1
1
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
1
2
2
0
1
0
0
0
1
0
0
2
0
0
0
0
1
0
0
1
4
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
2
0
3
0
0
2
0
0
0
0
3
0
0
2
3
2
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
2
2
1
0
0
0
0
1
0
1
0
0
1
1
0
2
0
0
0
1
2
0
1
1
2
1
1
0
0
1
0
0
1
2
0
1
1
0
0
0
0
1
0
0
0
2
2
2
0
2
2
0
2
0
0
2
2
0
0
0
0
1
2
1
0
0
2
2
0
0
0
1
1
0
0
2
0
0
1
1
0
0
1
0
0
2
1
0
2
0
0
2
1
0
4
1
0
1
2
0
2
0
2
0
0
0
1
1
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
1
2
0
0
0
0
2
1
2
0
1
2
2
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
1
1
0
0
1
0
0
0
1
0
0
0
2
0
2
0
2
1
2
0
0
0
0
0
2
0
1
2
0
1
0
0
0
1
0
1
0
0
0
1
4
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
4
0
0
0
2
0
0
0
1
3
1
0
1
2
3
0
0
0
3
1
0
0
0
2
0
1
1
0
0
0
0
2
0
0
0
2
1
0
0
0
2
0
0
1
0
1
2
3
1
2
0
2
0
0
2
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
2
1
0
2
2
0
1
0
1
1
0
1
0
2
2
0
1
0
0
1
0
0
1
1
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
2
2
1
2
0
0
2
1
0
3
0
1
2
0
0
1
0
0
0
0
0
1
2
0
1
0
0
0
2
0
1
2
0
1
1
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
1
0
2
2
1
2
1
0
0
0
2
1
1
1
2
2
1
0
0
1
0
0
0
0
1
0
2
2
1
0
1
3
0
1
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
2
0
0
1
0
0
0
0
1
2
1
0
0
0
0
1
0
1
2
0
0
0
1
2
0
1
1
2
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
1
2
1
1
0
1
0
1
0
2
0
0
0
1
2
0
0
0
2
0
2
0
0
1
0
1
1
0
0
0
2
0
2
0
0
0
2
0
0
1
0
0
2
0
0
2
0
0
4
0
2
2
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
2
0
0
0
1
2
1
2
0
1
0
0
0
2
0
1
0
0
2
3
0
0
2
0
1
0
1
0
2
1
1
0
0
0
2
1
3
0
0
0
2
2
0
0
2
0
0
1
0
5
4
0
0
0
0
1
2
0
1
0
1
0
0
0
0
0
2
0
0
0
0
1
0
1
1
0
2
0
0
1
0
1
2
2
0
0
3
1
1
2
1
0
0
0
0
0
0
1
2
1
0
0
0
0
0
1
0
0
0
1
0
2
0
1
0
0
0
2
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
2
0
1
2
0
0
0
0
0
1
1
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
1
0
1
2
2
1
0
1
1
3
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
2
0
1
2
2
0
0
0
1
0
2
0
0
5
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
1
0
0
0
2
0
2
0
3
0
0
0
2
0
0
0
0
0
2
0
1
2
0
0
2
2
2
2
0
1
0
0
2
1
2
2
0
2
0
0
0
0
0
0
1
3
1
0
2
1
0
2
0
1
0
0
1
0
0
1
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
2
2
3
0
2
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
1
0
0
1
1
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
1
1
0
0
0
2
1
0
0
0
0
1
0
1
0
0
0
1
1
3
1
2
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
1
2
0
2
2
0
2
0
2
2
0
0
0
2
1
2
0
0
0
2
1
0
2
1
0
0
0
0
0
4
0
0
0
0
3
1
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
2
0
3
0
0
0
2
2
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
2
4
2
0
0
2
0
1
1
1
0
1
2
2
0
0
0
1
0
0
0
0
0
2
0
1
0
0
1
0
2
1
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
1
2
1
1
4
0
2
0
0
0
1
1
0
0
0
0
2
2
0
1
1
0
0
2
2
0
0
2
1
0
2
0
1
0
1
2
0
1
0
1
0
0
0
1
0
0
1
0
1
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
3
0
0
0
0
1
1
2
0
0
1
2
0
2
0
0
1
0
0
0
0
2
0
3
2
0
0
0
0
0
2
2
2
0
0
2
0
0
0
2
0
2
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
1
2
0
0
1
0
2
0
0
0
0
1
1
1
0
0
2
2
0
0
0
0
0
1
0
2
2
0
1
2
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
1
2
1
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
2
1
2
0
0
0
0
0
2
0
1
0
2
0
1
2
0
0
0
2
0
2
0
0
2
5
1
1
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
1
1
0
0
0
0
1
1
2
0
1
0
2
0
0
1
2
0
1
2
0
0
0
0
0
2
1
0
1
0
0
0
1
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
1
2
0
0
2
0
1
1
0
1
0
0
0
0
2
0
0
0
0
2
0
3
0
1
0
0
0
4
0
0
0
1
0
0
0
0
2
2
0
4
0
0
0
0
2
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
2
1
0
2
0
0
1
2
2
2
1
0
0
0
1
0
1
0
0
0
1
2
0
2
1
0
2
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
1
1
0
2
2
0
0
2
2
0
0
0
0
0
1
0
0
1
0
3
0
0
2
0
1
0
0
0
0
1
0
1
2
1
1
2
2
0
0
0
0
0
1
0
0
0
0
2
1
1
1
2
1
0
2
0
2
3
1
0
0
0
0
1
0
1
0
0
0
0
0
0
2
2
0
0
0
3
2
2
0
0
0
0
0
2
0
2
0
0
0
0
1
3
0
0
0
0
0
2
2
1
0
1
0
1
1
2
1
2
2
0
0
0
1
0
1
0
1
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
3
1
1
0
2
1
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
1
2
0
0
0
0
1
1
0
0
2
0
0
1
0
0
0
0
1
0
3
0
5
3
0
0
0
0
0
1
0
1
0
2
0
0
0
2
0
0
1
2
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
1
0
0
1
1
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
2
0
1
0
0
2
0
1
0
0
2
2
0
0
0
1
0
0
0
0
0
4
1
1
0
2
0
1
0
2
2
0
0
2
0
0
0
2
0
0
0
0
2
0
1
1
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
2
2
0
0
2
0
2
2
0
2
2
1
0
2
0
1
3
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
2
1
1
0
0
0
0
0
2
1
1
0
0
1
0
0
0
0
2
0
0
2
0
0
1
0
1
3
0
1
0
0
0
0
2
0
1
0
0
1
0
0
0
2
0
1
0
0
0
0
0
1
2
0
0
0
2
0
0
1
0
0
0
0
2
0
2
2
0
0
1
1
1
2
0
0
0
1
2
0
0
1
1
1
0
1
0
0
1
0
3
2
2
0
0
0
0
2
0
2
0
0
2
0
2
0
2
0
0
1
0
0
0
1
2
1
0
1
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
1
0
0
1
0
0
1
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
2
0
2
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
1
0
1
0
1
1
0
0
2
2
0
1
0
0
0
0
1
0
0
0
3
0
1
2
0
1
0
0
0
0
0
0
2
0
2
0
2
1
2
0
2
0
1
0
0
0
1
0
1
1
0
2
1
0
0
1
1
1
2
0
0
1
0
0
0
0
2
1
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
2
2
0
0
2
0
1
2
0
1
2
0
1
0
1
0
0
0
0
0
1
0
2
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
2
0
0
4
2
0
1
0
0
0
0
0
0
1
1
2
0
0
0
2
1
0
1
3
1
2
1
2
2
1
0
0
0
1
1
0
0
0
0
0
0
8
0
0
2
0
0
0
0
3
1
1
0
0
1
0
0
1
1
0
1
0
0
2
0
1
1
0
0
1
0
2
0
1
1
0
0
0
0
0
0
0
0
2
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
2
0
2
0
2
1
0
0
2
0
0
0
1
1
2
2
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
1
0
0
2
0
0
0
1
2
1
0
1
0
2
2
1
0
0
0
1
0
0
2
0
0
0
1
0
3
0
0
0
2
0
0
0
0
2
2
0
2
0
2
0
1
0
0
0
3
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
2
2
0
1
5
2
2
0
0
1
0
0
1
0
0
0
0
0
3
0
4
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
1
2
1
0
0
1
1
1
2
1
0
2
0
0
0
0
0
0
2
0
2
0
3
0
0
0
1
0
0
0
2
0
0
1
0
1
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
1
2
0
0
2
1
0
2
0
0
0
0
0
1
0
1
1
0
2
0
1
0
2
0
0
1
0
1
0
2
0
1
2
2
0
1
0
3
0
0
0
1
0
0
2
2
0
0
0
1
0
0
1
1
1
0
1
0
2
0
0
0
3
1
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
2
0
2
0
0
0
0
0
3
0
2
0
0
0
0
2
2
1
2
0
0
0
0
0
2
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
2
0
1
0
2
1
0
0
2
1
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
1
1
2
0
1
0
0
0
1
0
0
0
1
0
2
0
2
0
2
2
0
0
2
0
0
0
0
1
2
0
1
0
0
2
2
0
0
1
0
1
0
1
0
1
2
1
1
0
0
0
3
0
0
0
2
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
2
0
0
0
0
0
1
0
1
1
2
1
0
0
1
1
0
0
0
2
0
0
0
0
0
1
1
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
1
2
0
1
2
1
2
0
1
0
0
2
0
0
2
0
2
0
2
1
0
2
1
0
0
0
1
0
0
0
0
0
0
0
2
0
2
2
1
0
0
0
2
1
0
0
0
0
1
0
0
0
1
0
0
2
5
0
2
1
0
0
0
0
0
1
3
0
2
0
0
0
0
0
0
1
1
1
1
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
1
0
0
0
2
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
2
0
0
1
1
0
0
2
2
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
3
0
2
1
1
1
1
2
0
0
0
0
1
0
0
1
0
0
1
2
5
0
0
1
2
0
1
0
0
0
0
0
1
1
0
0
0
2
0
0
1
0
0
2
6
0
0
0
1
1
0
2
0
0
0
1
1
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
2
0
2
2
0
0
0
0
0
0
0
1
1
0
0
4
0
2
0
0
1
2
0
0
0
0
0
0
0
0
2
2
1
2
0
0
0
0
2
1
2
2
1
2
0
1
2
0
0
0
1
0
0
3
0
0
0
1
0
0
0
2
0
2
0
1
2
3
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
2
0
3
0
1
0
1
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
2
2
3
0
0
0
1
2
0
0
2
2
0
0
0
0
0
1
0
0
0
0
2
0
1
2
2
2
0
0
0
0
0
0
1
0
0
1
0
1
2
0
0
2
0
2
0
0
0
1
0
0
0
2
0
2
0
0
0
2
1
0
0
2
1
0
1
1
0
0
1
0
0
2
0
0
0
4
2
0
2
0
0
0
0
0
0
0
1
0
0
0
2
2
0
3
0
2
2
0
0
0
2
0
2
0
1
0
0
0
2
2
0
0
0
2
0
0
0
3
0
0
1
1
2
0
1
0
1
2
2
2
0
4
1
2
0
0
0
0
0
2
0
0
0
2
1
1
2
0
0
0
0
0
1
2
0
0
0
1
1
2
1
2
1
0
0
2
0
1
0
0
0
0
0
0
0
1
2
1
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
1
2
0
1
0
2
2
0
0
0
0
0
2
0
0
0
0
2
0
1
0
1
1
0
0
0
1
0
2
3
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
3
0
0
0
1
1
0
2
0
0
1
0
2
2
0
0
0
0
1
2
0
0
1
2
0
1
2
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
2
0
1
1
1
0
0
0
0
1
0
1
0
0
0
1
1
0
2
1
0
0
0
0
0
0
2
2
0
1
2
0
2
2
0
0
2
0
2
0
0
0
0
1
3
0
0
2
0
0
1
0
1
0
0
1
0
0
0
2
3
2
1
1
0
1
2
7
2
1
2
0
0
1
0
2
0
0
0
2
0
0
1
1
0
2
2
3
0
0
2
0
1
0
1
0
2
1
1
0
0
0
1
1
1
1
2
1
0
0
0
2
0
0
0
0
0
1
0
0
2
1
0
0
0
0
2
0
0
0
0
2
0
0
1
0
1
0
1
0
2
0
0
1
0
1
0
1
0
1
0
0
0
1
0
2
0
0
1
0
0
1
1
1
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
2
0
2
0
0
0
1
0
0
0
0
0
2
1
0
2
0
1
1
0
1
0
0
0
1
0
2
0
1
1
1
3
1
0
1
0
1
0
0
0
0
0
1
0
2
0
0
1
0
0
0
2
0
0
0
1
0
1
2
2
2
0
1
1
2
2
1
0
1
0
1
0
0
1
2
1
0
1
0
2
1
2
0
0
0
0
1
0
2
0
0
0
0
2
2
2
0
2
0
0
0
1
0
0
0
0
2
1
1
0
2
1
0
0
1
2
1
0
2
0
3
0
3
0
0
0
0
2
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
1
2
0
0
0
0
1
0
0
0
5
0
0
2
17
0
0
0
0
7
0
0
1
2
0
2
0
1
0
0
0
0
0
0
2
2
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
2
2
0
0
0
2
0
2
0
1
1
0
0
2
2
4
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
2
0
2
0
0
0
0
0
1
0
2
0
1
0
0
0
1
0
1
1
0
0
2
1
0
2
0
2
1
16
2
0
2
2
0
0
0
1
0
0
0
0
2
2
0
2
0
2
0
0
0
0
1
0
0
0
0
2
0
0
1
2
0
1
1
2
0
3
2
1
0
2
2
2
3
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
2
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
2
2
1
0
0
0
1
2
0
1
0
0
0
1
2
0
0
1
0
1
0
0
0
0
1
0
0
1
2
3
0
2
0
2
1
0
2
0
2
2
1
0
1
0
1
1
0
0
2
0
0
2
1
1
2
0
2
0
2
2
0
0
2
1
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
2
1
0
0
0
2
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
1
0
1
1
0
0
0
3
0
2
0
0
0
0
0
2
0
0
0
1
2
0
0
1
0
0
0
2
2
2
2
0
2
0
1
2
0
0
0
1
0
4
0
0
2
0
0
1
2
0
1
1
0
0
0
2
2
6
0
0
0
2
0
0
0
1
0
0
0
0
2
0
1
0
0
2
0
0
0
2
0
0
0
1
3
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
1
2
1
0
2
0
3
1
0
1
1
0
0
2
1
1
0
2
1
0
1
1
1
1
1
0
0
1
2
1
0
1
0
0
0
2
0
0
2
0
0
0
2
1
0
1
3
1
2
0
0
2
0
0
1
0
0
0
0
2
0
0
0
5
1
0
1
2
0
2
1
1
0
0
0
1
0
0
1
1
0
2
2
0
0
2
0
2
1
0
1
0
1
2
1
2
0
2
0
1
0
0
2
0
0
0
0
0
0
0
3
0
1
2
0
0
2
0
0
0
0
0
1
0
0
0
1
2
0
1
0
0
0
0
2
0
0
1
1
0
1
0
0
0
1
1
0
0
2
2
0
0
1
0
2
0
2
2
0
0
1
0
0
1
0
0
1
0
2
0
2
0
1
1
0
0
1
1
0
0
2
2
1
0
0
0
1
0
0
0
2
0
0
1
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
2
1
0
1
3
0
1
6
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
2
0
2
0
0
1
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
2
0
0
0
1
2
0
0
0
4
0
0
2
2
1
0
2
0
1
0
0
0
1
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
3
0
1
0
0
0
1
0
0
0
0
0
1
4
0
2
1
1
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
1
0
0
1
1
1
0
0
1
0
2
2
0
0
0
0
0
0
0
7
0
1
2
2
0
2
2
0
0
0
0
2
0
0
2
2
0
3
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
3
1
0
0
0
2
0
0
0
0
2
1
2
0
2
1
0
1
0
0
2
0
2
1
0
0
1
0
0
0
0
0
2
8
0
2
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
1
0
1
0
2
1
0
2
0
0
0
0
0
1
2
0
1
2
1
1
0
2
0
0
2
1
1
3
0
0
0
1
0
0
1
2
1
2
0
1
1
1
2
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
2
2
2
0
0
2
0
0
0
0
0
0
3
0
0
2
2
0
0
2
0
0
0
2
0
2
0
0
2
2
0
2
0
1
0
2
0
0
0
2
0
1
2
1
0
0
0
1
3
0
0
0
2
2
1
1
0
0
4
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
1
2
0
2
0
2
2
1
0
0
1
0
1
0
2
0
2
0
0
0
0
1
2
1
0
1
0
2
0
0
0
0
2
0
1
0
1
0
0
0
2
1
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
2
1
2
0
0
0
0
0
0
1
1
2
0
0
1
0
1
0
0
0
0
0
0
2
2
0
2
1
0
0
3
2
0
0
0
1
0
2
0
0
0
2
2
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
2
2
2
0
0
0
3
0
0
0
0
0
1
2
0
0
0
2
0
0
1
1
0
0
2
0
0
0
1
0
0
0
1
2
0
2
2
1
0
0
0
2
1
1
0
0
2
2
0
0
0
2
2
0
1
3
0
0
0
0
0
1
0
0
3
2
0
1
2
2
0
0
0
1
0
1
0
0
0
0
0
0
2
0
1
1
1
2
3
0
2
2
2
2
0
0
3
0
1
0
0
1
1
0
0
2
0
0
0
1
0
1
0
0
1
2
0
0
0
0
2
0
0
0
1
0
2
0
1
0
1
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
4
0
0
1
0
0
1
0
1
2
1
0
0
0
2
1
0
1
0
0
0
0
0
0
0
2
2
1
1
1
0
0
1
0
1
2
0
0
0
1
2
0
1
1
0
0
0
1
0
1
0
1
1
1
0
2
1
0
1
0
0
1
0
2
1
1
0
1
0
0
2
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
1
2
0
2
2
0
1
2
1
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
2
0
1
0
1
0
1
1
1
0
0
0
3
0
0
0
0
2
1
0
0
0
0
1
0
2
0
2
1
3
0
0
0
0
0
2
0
0
1
0
0
0
2
1
0
0
0
1
0
2
0
2
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
2
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
1
1
2
0
1
2
0
4
0
0
2
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
2
0
2
3
1
0
1
0
3
0
0
0
0
0
0
3
1
0
0
0
0
0
0
2
0
3
0
2
0
2
0
2
2
1
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
1
0
0
2
0
0
0
0
2
4
0
0
0
0
1
0
0
2
3
0
2
2
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
2
0
1
0
0
0
0
2
0
0
1
2
0
0
0
2
1
0
0
1
0
1
0
1
1
1
0
2
2
2
1
0
1
0
1
1
0
0
0
2
0
0
0
1
0
1
2
0
1
0
0
0
0
1
2
0
3
0
2
0
1
0
2
1
2
0
1
2
2
2
0
0
1
0
0
0
2
1
1
0
0
0
2
0
2
2
1
0
0
1
0
0
2
1
0
0
2
0
0
1
1
1
2
0
2
1
0
0
1
0
0
2
0
0
2
2
0
0
0
0
3
1
1
2
0
1
1
0
0
0
2
1
0
0
4
0
0
0
0
0
0
0
2
2
4
0
0
1
0
2
0
0
0
0
0
2
0
0
2
0
0
2
1
2
0
0
0
0
2
0
0
0
2
0
2
2
0
0
0
2
0
0
1
0
0
0
0
0
2
2
0
0
0
0
1
0
1
0
2
1
1
0
0
5
0
0
1
0
2
0
0
0
0
2
0
1
0
0
0
1
2
0
1
2
0
2
0
0
0
2
0
0
0
1
1
0
2
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
1
0
0
1
0
0
0
0
2
1
0
0
2
0
2
0
0
0
0
0
1
0
1
0
1
2
0
0
1
0
0
0
0
0
0
0
0
1
0
1
3
1
1
3
0
0
0
0
1
2
0
0
0
2
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
1
0
2
0
1
0
2
0
0
1
2
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
2
2
0
0
2
0
2
0
0
0
0
0
0
3
1
0
1
0
0
2
1
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
4
0
2
2
1
0
0
1
0
0
2
1
2
2
0
0
0
2
0
0
0
1
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
1
1
0
1
2
0
1
1
1
0
0
2
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
1
0
1
0
2
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
1
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
2
1
2
0
1
0
4
2
0
0
0
0
0
2
2
1
0
0
1
0
2
0
0
1
0
2
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
3
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
2
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
2
0
1
0
2
0
0
0
0
1
0
0
1
0
0
1
0
1
0
2
2
0
1
2
0
1
0
0
0
0
1
2
2
0
1
2
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
2
1
0
0
0
1
0
0
1
2
2
0
0
1
0
1
0
2
0
2
0
0
0
0
0
4
0
0
1
1
0
2
0
0
1
2
0
0
1
2
2
3
0
2
0
0
0
0
0
0
0
0
2
0
3
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
2
2
1
0
0
0
2
0
2
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
1
0
0
0
1
1
1
0
0
2
1
1
2
0
1
0
0
1
0
0
1
1
0
0
1
0
0
2
0
0
0
0
0
1
5
0
2
0
0
0
0
0
2
0
0
2
2
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
1
0
0
0
2
0
0
0
2
3
2
1
2
1
0
1
1
2
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
1
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
3
3
1
1
1
1
0
1
2
2
0
2
2
0
0
1
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
1
1
0
2
0
3
0
0
0
0
1
0
0
0
2
2
0
0
0
2
0
0
2
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
2
4
0
0
0
0
1
2
2
0
3
2
0
3
0
0
0
1
1
0
0
0
0
2
0
1
0
0
3
2
0
0
0
0
0
0
0
0
2
0
1
2
0
0
1
0
0
2
0
2
2
1
0
1
0
1
4
4
2
0
0
0
0
2
0
0
1
2
0
1
0
0
0
0
1
0
2
0
0
0
1
2
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
1
0
0
0
0
1
0
0
2
3
0
0
1
0
0
4
1
1
2
0
0
1
0
2
1
0
0
1
2
1
0
0
1
0
2
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
2
0
0
0
4
0
0
0
0
0
2
4
0
1
0
2
2
2
0
2
1
0
1
0
0
0
1
0
2
2
0
0
0
2
0
3
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
2
1
2
0
1
1
0
0
0
0
0
2
2
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
1
2
1
0
2
0
0
0
0
0
1
1
1
1
3
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
2
1
0
0
0
1
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
1
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
6
0
0
0
2
0
0
0
0
2
0
1
0
0
2
0
2
0
0
0
0
0
2
2
2
0
1
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
2
0
1
2
1
0
1
2
0
0
0
2
1
0
2
0
0
4
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
2
2
2
0
2
2
0
0
2
1
1
0
0
0
0
1
2
0
0
0
2
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
1
2
0
0
2
0
0
0
0
1
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
2
0
1
0
1
2
0
0
1
0
0
1
2
0
1
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
1
0
0
0
2
2
1
0
0
0
2
0
1
0
2
2
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
1
0
0
0
2
0
0
0
1
0
0
0
3
1
0
0
0
0
0
0
2
0
1
2
1
2
0
1
0
0
0
1
1
2
1
0
0
1
0
0
0
0
4
0
0
1
0
2
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
3
1
0
1
0
0
1
2
0
0
0
1
0
0
0
0
2
2
2
0
2
2
2
0
1
0
0
1
0
1
0
0
1
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
1
0
2
0
0
0
0
1
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
2
1
0
0
1
0
0
0
1
0
0
0
2
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
4
1
0
0
0
2
0
1
0
0
0
0
1
0
1
1
1
2
0
2
0
3
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
2
2
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
3
0
0
0
0
0
0
0
1
0
0
1
1
2
0
0
2
1
0
0
0
0
1
1
5
2
0
0
1
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
2
1
0
0
1
0
2
0
0
0
1
1
0
0
0
1
1
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
2
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
1
2
2
2
2
1
0
0
0
0
0
0
0
0
3
0
1
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
2
0
2
0
1
1
0
0
0
0
0
0
0
0
0
3
1
1
0
1
2
0
1
0
0
1
2
0
0
0
0
0
0
0
2
0
3
2
0
0
7
2
0
0
1
0
0
1
0
0
1
0
4
0
1
1
1
0
0
1
1
0
1
0
2
0
0
0
0
0
2
2
1
0
0
2
0
0
0
0
2
0
1
0
2
2
1
0
2
0
1
0
2
0
0
0
2
4
0
3
1
0
1
1
0
0
0
0
0
2
0
2
1
0
1
0
1
2
0
3
0
0
2
0
0
0
2
0
1
3
2
0
2
0
1
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
1
2
2
2
2
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
2
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
3
0
0
2
1
0
0
2
0
1
2
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
1
0
1
0
1
2
1
0
0
1
0
0
0
1
1
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
2
1
1
0
1
0
0
0
1
0
2
0
3
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
2
0
0
1
0
0
1
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
1
0
2
0
0
2
0
1
0
1
2
2
0
1
2
0
0
1
1
0
2
0
0
0
0
2
0
0
2
1
1
1
2
0
2
0
2
0
0
0
1
0
2
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
2
0
0
2
1
0
1
0
1
2
2
5
0
0
1
0
1
2
0
1
0
0
2
2
0
2
0
2
0
1
0
0
0
0
1
0
1
0
0
0
2
0
2
0
2
0
0
0
0
2
5
0
3
0
0
0
0
0
0
0
0
0
2
1
2
0
2
3
0
0
0
0
0
0
1
0
0
2
1
2
0
0
0
0
0
3
0
0
0
0
1
2
0
0
1
0
0
3
0
0
0
2
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
4
0
1
0
0
2
0
2
0
1
2
0
1
0
0
2
2
2
0
1
0
0
1
0
0
0
1
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
1
0
0
0
2
0
1
1
0
1
1
0
0
0
1
1
8
0
0
1
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
1
0
0
1
0
0
0
1
1
1
2
3
1
0
0
1
1
0
0
2
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
2
0
1
1
0
1
0
1
0
1
0
0
1
0
0
2
3
1
0
0
0
0
0
1
0
1
0
0
0
2
0
1
0
0
0
2
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
2
0
0
0
1
0
0
2
1
3
0
1
0
0
2
0
2
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
1
0
4
0
0
0
2
1
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
3
0
1
1
0
0
0
1
0
1
1
0
1
0
2
0
1
1
0
2
2
0
1
0
1
0
1
0
0
1
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
1
1
2
0
2
1
0
1
1
1
0
2
1
2
0
0
0
2
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
2
0
0
0
2
0
0
0
1
2
0
2
0
0
0
0
3
2
1
0
2
0
0
2
0
0
2
0
0
0
1
1
0
0
0
1
2
1
0
0
0
2
0
0
0
0
1
2
1
2
0
0
0
0
0
1
0
2
0
0
2
0
0
2
1
0
0
1
0
0
0
0
0
1
2
0
0
0
0
3
0
2
0
0
0
0
1
2
1
0
2
0
2
1
0
2
0
1
2
2
0
0
0
0
0
0
2
0
0
1
2
1
2
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
2
0
1
3
1
3
2
0
0
0
0
1
1
0
1
0
0
0
1
1
0
1
0
2
2
1
0
0
0
0
0
0
0
1
1
0
2
0
1
0
0
1
1
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
2
1
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
1
1
0
0
1
0
2
0
0
0
0
0
0
0
1
2
0
2
0
0
3
0
1
0
2
2
2
1
0
0
2
0
0
0
0
1
0
1
0
1
2
0
0
2
1
2
1
0
2
2
0
1
1
0
2
0
0
1
2
0
2
0
0
1
1
5
0
0
0
2
0
0
2
0
1
0
0
2
0
1
1
0
0
0
2
1
0
0
0
0
0
0
0
1
1
3
0
0
0
1
1
0
2
0
0
1
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
1
2
1
0
0
0
0
0
2
0
2
1
0
1
0
0
0
2
1
0
2
2
3
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
4
1
0
1
1
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
1
2
0
0
1
1
1
1
0
1
0
0
0
0
0
0
0
1
0
0
2
1
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
2
0
1
0
2
0
0
0
0
2
0
2
0
7
2
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
2
0
1
1
0
1
2
0
0
0
1
0
0
0
0
0
0
2
2
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
1
0
2
0
0
0
0
1
0
0
0
3
0
2
3
0
1
1
2
2
2
0
0
0
0
2
2
2
0
2
0
2
2
1
1
0
0
0
0
3
0
0
0
0
3
0
1
3
0
1
1
0
1
0
2
0
2
0
0
2
0
0
1
0
1
2
1
4
0
0
0
0
0
2
1
0
2
0
0
0
1
1
2
2
0
0
0
0
2
0
2
0
3
0
0
1
1
0
0
2
0
2
1
0
2
1
0
1
0
2
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
1
1
2
0
0
0
0
0
1
2
0
2
0
2
0
0
0
0
1
0
2
6
2
0
0
2
0
0
2
0
1
0
0
2
0
0
0
2
0
0
0
1
1
0
1
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
1
2
0
0
0
1
1
0
0
2
0
2
1
0
0
1
0
0
2
0
1
2
0
0
0
0
2
0
0
0
0
0
2
1
0
1
0
1
0
2
0
0
1
2
0
1
0
0
0
0
0
0
0
2
0
0
0
2
1
1
2
0
0
0
1
0
0
3
0
1
0
1
0
1
0
2
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
1
1
0
0
2
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
1
2
0
0
0
0
0
1
0
0
0
2
0
2
0
1
1
0
0
1
0
0
0
0
0
2
2
0
2
3
0
2
0
1
1
0
0
1
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
2
0
0
0
1
0
1
0
0
0
0
1
0
0
1
1
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
1
2
0
1
0
0
0
2
2
0
1
0
0
0
1
0
0
2
0
1
2
2
2
0
1
0
0
2
0
2
0
0
3
0
0
0
0
0
2
1
1
0
0
0
1
1
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
1
1
0
2
0
2
0
0
0
0
1
0
0
0
0
1
0
0
1
2
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
1
1
6
0
1
2
1
0
1
2
0
2
0
2
2
0
8
0
0
1
0
2
1
0
0
0
0
0
1
0
1
2
0
0
2
0
0
0
2
0
0
2
1
0
1
1
1
3
0
1
0
0
1
1
2
2
2
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
5
1
0
0
0
0
1
0
0
0
1
1
0
0
1
2
1
0
0
0
2
0
1
1
2
0
2
0
0
2
0
1
0
0
1
1
1
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
1
0
0
0
0
1
0
0
2
2
0
2
0
0
0
0
2
0
2
1
0
2
0
1
0
0
0
3
1
0
0
1
1
0
1
1
0
0
0
0
0
0
1
0
1
2
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
4
0
0
0
2
2
0
0
0
0
0
2
1
0
0
0
2
0
1
0
0
2
1
0
1
0
0
2
2
0
1
2
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
1
0
1
2
2
2
0
0
0
0
0
0
1
2
0
2
0
0
0
2
3
1
2
0
0
1
2
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
1
0
1
0
3
0
0
0
0
1
4
2
0
0
2
0
0
0
0
0
0
2
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
1
2
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
2
0
1
0
0
0
1
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
1
0
0
0
0
1
3
2
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
1
3
0
0
0
0
3
1
0
0
0
0
0
2
0
1
0
0
0
0
2
0
1
0
0
1
2
0
0
1
1
0
0
1
1
2
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
2
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
2
1
1
1
1
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
1
0
1
1
0
2
3
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
2
0
0
0
3
0
2
3
1
1
2
0
0
2
0
0
2
0
0
0
2
0
0
1
1
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
1
1
2
0
0
0
0
1
2
0
1
0
1
0
1
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
2
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
1
0
0
2
0
0
0
1
0
0
1
0
1
0
0
2
0
0
0
0
1
0
0
0
0
1
0
3
0
0
2
0
0
1
0
1
2
0
3
0
2
0
0
2
2
0
1
1
0
0
1
2
0
0
1
0
0
1
0
2
0
0
0
0
1
0
1
0
0
4
1
1
1
1
0
0
2
0
0
2
0
2
1
2
0
1
0
0
0
2
0
1
0
0
2
0
1
0
0
0
1
0
0
1
0
0
0
2
2
3
0
0
0
3
0
0
0
0
0
3
0
1
2
2
0
0
0
0
0
2
0
3
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
2
0
0
1
0
2
0
1
1
0
0
0
0
0
2
0
0
0
0
0
2
3
0
2
0
0
0
0
0
0
0
0
0
1
0
2
2
0
1
0
0
1
0
2
2
1
1
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
2
2
0
0
0
1
2
0
0
2
1
0
0
0
0
0
0
2
0
0
1
0
0
2
1
0
0
0
3
1
0
0
0
0
0
0
0
0
0
2
1
0
1
2
2
1
1
0
1
0
3
1
0
1
0
0
1
0
3
0
2
0
1
0
2
1
2
0
0
2
0
2
0
2
0
1
0
0
1
2
1
0
2
1
0
2
0
5
2
0
0
0
2
2
0
0
1
1
0
1
3
0
0
0
1
0
0
0
0
3
1
1
0
0
1
0
2
1
0
0
0
0
1
2
0
0
0
0
0
1
1
0
0
5
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
2
2
0
1
1
0
0
0
0
0
0
0
0
2
1
1
0
1
0
0
0
0
0
1
1
0
0
3
0
0
2
0
1
0
0
0
0
1
2
0
0
1
0
0
0
1
0
2
1
1
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
1
0
0
2
0
0
0
1
0
3
0
1
0
2
0
0
1
0
0
1
1
0
2
2
0
1
0
1
0
2
0
0
2
0
0
0
2
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
3
0
1
1
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
3
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
3
0
0
2
2
2
4
0
2
0
0
0
0
1
2
0
0
0
6
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
1
0
2
0
2
0
1
0
0
0
0
1
3
0
0
0
0
1
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
4
0
2
2
0
0
0
1
0
0
0
2
0
2
4
0
0
0
1
1
0
0
0
1
0
1
2
2
0
2
1
0
0
1
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
2
0
0
0
0
1
0
1
1
1
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
1
0
2
0
2
0
0
2
0
2
1
0
0
0
0
1
0
2
2
0
0
1
0
1
0
0
1
0
1
1
0
0
0
2
2
1
1
0
0
2
0
0
0
2
2
1
1
0
0
2
0
2
1
1
1
1
1
0
2
0
0
0
0
0
2
0
0
2
2
0
1
0
2
0
0
2
2
1
0
0
0
0
2
1
4
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
2
2
3
0
0
0
0
0
0
1
0
0
1
1
0
2
2
0
0
0
0
2
0
0
2
0
0
2
0
2
0
1
0
0
0
1
0
0
1
0
2
1
1
0
1
0
0
0
0
0
1
1
0
0
3
2
1
2
0
0
0
0
0
0
1
0
1
2
1
0
0
0
1
1
0
0
2
1
0
1
1
0
2
1
0
1
2
0
3
1
2
0
2
0
2
2
2
3
0
0
0
1
0
0
1
0
1
0
0
2
0
0
2
1
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
5
0
0
0
0
0
0
0
0
1
2
0
0
0
2
1
0
0
0
0
0
2
1
0
0
0
0
2
1
0
1
1
0
2
2
2
1
0
0
0
0
1
0
0
2
1
0
1
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
3
0
2
0
0
1
1
0
0
0
0
2
0
2
0
0
0
2
3
0
0
0
0
0
0
0
2
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
2
0
1
2
0
0
0
0
1
2
0
0
0
0
1
2
0
4
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
2
0
0
0
2
0
1
0
0
2
0
1
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
1
2
2
0
0
2
0
0
0
0
2
0
1
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
2
0
0
0
0
0
0
2
3
0
0
0
2
0
0
0
2
0
0
2
1
0
4
1
0
1
2
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
2
2
0
2
0
0
2
0
0
2
0
1
1
0
1
1
2
0
2
1
1
0
1
0
0
2
3
1
2
0
0
2
1
0
0
0
0
0
0
3
0
0
0
2
2
0
0
0
0
0
2
1
0
0
2
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
2
1
1
0
2
0
1
2
2
0
2
1
2
3
1
0
0
0
2
0
1
2
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
2
0
2
0
0
0
0
0
2
1
0
2
1
4
2
3
1
2
1
0
0
0
1
0
0
0
1
0
0
0
0
2
2
0
1
0
0
2
0
0
2
0
1
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
3
0
2
0
2
0
0
0
0
1
0
0
1
0
0
2
0
0
3
1
0
0
0
2
2
1
0
1
2
1
1
2
1
1
0
0
1
0
1
1
0
0
2
2
0
0
0
1
2
0
1
0
0
2
2
2
1
0
2
1
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
2
1
1
2
0
0
0
0
0
0
2
1
0
0
2
0
0
0
1
0
2
1
1
0
1
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
2
2
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
2
2
2
2
1
0
0
1
0
0
0
0
0
0
2
1
0
2
1
0
0
2
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
2
0
0
0
3
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
1
2
1
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
2
0
2
0
2
2
0
0
0
0
0
3
0
0
0
2
2
0
1
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
1
2
0
0
2
2
0
0
2
0
2
0
0
1
1
0
0
0
2
1
1
0
6
2
0
1
2
0
2
0
0
2
0
1
0
1
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
2
4
0
0
0
2
0
1
0
0
2
0
1
1
0
2
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
1
1
0
1
0
0
4
0
0
1
0
0
0
2
0
1
1
0
0
2
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
2
0
1
0
0
0
0
2
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
1
0
5
0
0
0
1
0
1
0
1
1
0
2
2
0
0
1
0
0
2
0
0
1
0
1
2
1
0
0
1
1
0
0
1
0
1
2
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
2
1
2
1
1
2
2
0
0
0
0
0
1
0
0
0
1
0
0
1
2
1
0
0
0
1
0
0
0
1
1
0
2
1
6
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
1
0
2
2
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
2
1
2
0
2
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
1
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
2
0
1
0
1
0
0
0
2
0
0
1
0
0
0
2
0
1
2
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
2
1
0
1
0
2
0
1
1
1
2
1
0
0
1
0
1
0
1
1
0
0
4
0
2
0
1
0
1
2
0
0
0
0
1
0
2
0
0
0
1
2
2
1
3
0
0
0
0
0
2
0
0
0
0
1
1
0
1
1
0
0
0
1
0
0
0
1
0
2
0
0
0
0
3
3
1
1
2
2
1
0
0
1
0
2
0
0
0
1
0
1
0
0
2
0
1
2
0
0
1
0
1
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
1
1
1
0
0
2
2
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
2
2
0
0
2
0
2
0
2
1
0
1
2
1
0
1
2
0
2
1
0
0
0
1
0
0
0
0
0
1
0
0
2
0
2
0
0
2
0
0
0
1
0
0
4
1
2
1
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
1
2
0
0
0
2
2
0
0
0
3
1
2
0
0
2
1
2
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
1
2
2
1
2
0
1
1
1
0
1
0
0
2
0
0
0
0
0
1
0
6
0
0
1
0
1
0
1
0
0
0
0
0
0
2
2
0
0
0
0
1
0
1
1
1
2
0
0
1
0
0
0
0
2
0
1
0
1
0
0
1
2
0
0
0
1
0
1
3
0
2
3
0
0
2
0
0
1
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
1
0
2
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
2
1
0
0
1
0
0
0
0
1
0
2
0
0
0
1
0
1
0
2
2
1
0
0
1
2
0
0
2
1
0
0
0
0
0
0
0
0
1
0
2
0
1
1
0
1
0
2
0
1
0
1
1
0
0
0
0
0
1
0
0
0
2
3
0
0
2
0
0
0
2
0
0
1
1
0
0
5
0
0
0
2
1
0
2
1
0
0
2
0
0
2
0
0
0
1
1
2
0
0
0
0
1
1
0
2
0
0
1
0
1
0
2
0
0
1
0
0
0
1
0
0
0
3
0
1
0
0
2
1
1
0
0
0
0
2
2
1
2
1
1
0
0
0
0
1
0
0
0
1
1
1
0
1
0
0
0
0
1
0
0
0
0
2
0
0
4
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
2
0
0
1
2
0
0
1
0
2
1
0
0
1
1
0
0
1
2
0
0
0
0
0
0
2
2
2
4
0
0
1
2
2
1
0
2
0
1
0
0
0
1
0
0
0
0
0
2
2
0
0
1
0
2
1
0
0
0
0
0
1
2
1
0
0
0
0
0
3
2
0
3
0
0
0
0
0
2
1
1
0
0
0
0
0
1
0
2
0
0
0
2
0
1
0
0
2
0
0
1
0
1
0
0
2
2
0
1
2
0
2
0
1
0
0
0
0
0
0
0
2
0
2
2
1
1
0
0
0
0
0
3
2
0
0
0
2
0
0
1
0
0
2
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
2
0
8
2
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
3
0
0
0
2
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
1
1
1
2
0
0
2
1
2
0
2
4
0
0
2
2
0
0
1
1
0
0
0
2
0
0
1
0
0
2
0
0
0
2
2
2
0
1
3
0
0
0
0
0
1
0
0
0
0
0
2
1
4
2
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
2
2
2
0
0
0
2
0
1
0
1
0
1
2
1
1
2
0
1
0
0
0
0
0
3
1
0
0
0
3
2
1
2
1
2
0
0
0
1
0
0
1
0
0
0
2
2
0
2
2
0
2
0
1
1
0
2
0
1
0
0
2
0
0
2
0
2
0
0
0
1
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
1
1
0
0
0
0
0
2
0
2
2
1
2
2
0
0
1
0
0
0
1
1
0
0
2
0
0
0
2
2
0
0
1
0
2
0
2
0
0
1
0
0
1
0
0
0
0
1
0
3
0
0
1
0
0
1
0
2
2
2
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
1
0
1
2
0
0
2
0
0
2
3
0
0
2
1
0
0
0
1
1
1
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
3
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
2
1
0
1
2
1
1
0
0
0
0
1
2
0
0
1
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
2
1
0
1
0
0
1
0
0
0
0
2
2
0
1
0
0
1
1
0
2
0
1
0
2
1
0
0
0
0
0
0
2
1
0
2
0
0
2
0
0
1
3
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
2
1
1
0
0
0
0
2
2
0
2
0
0
2
0
0
3
0
0
0
0
2
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
1
2
1
1
0
1
2
2
2
0
2
2
0
1
0
3
0
1
0
0
0
0
2
2
1
2
0
1
0
2
0
0
2
1
0
1
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
2
6
0
1
0
2
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
3
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
1
2
0
0
1
0
2
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
2
1
0
1
1
0
0
0
0
0
0
1
0
0
2
1
2
0
1
0
3
0
2
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
3
0
2
1
1
0
0
0
3
2
0
1
1
0
0
2
4
1
2
0
1
0
0
0
0
0
0
2
0
1
3
1
2
1
0
0
1
0
0
0
0
0
1
0
2
1
0
0
0
3
2
0
0
0
1
0
0
2
1
0
2
1
0
0
0
1
0
1
1
2
0
2
0
0
0
0
1
0
0
0
2
0
1
1
2
0
0
0
2
2
1
2
0
0
0
0
0
2
0
0
1
1
3
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
4
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
2
2
1
0
1
0
2
0
1
0
1
1
1
0
4
2
2
1
0
0
1
1
1
2
1
0
1
0
0
0
2
0
2
0
0
0
1
0
1
0
1
1
0
2
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
2
2
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
2
0
1
2
1
0
0
0
0
0
2
0
0
0
0
4
1
0
2
0
2
2
0
0
1
2
0
0
0
0
1
0
0
0
1
1
0
2
0
0
1
0
0
2
0
0
0
0
0
0
1
1
2
0
2
0
0
0
2
0
1
2
2
2
2
0
0
2
0
0
0
1
1
0
0
0
2
0
1
0
0
0
0
0
0
3
2
0
1
3
0
0
1
2
0
0
0
0
0
0
0
2
0
1
1
2
0
0
0
1
0
0
0
0
2
1
1
0
1
0
0
1
0
2
0
2
0
1
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
2
1
0
1
1
0
1
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
2
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
2
2
0
0
0
0
1
0
0
2
0
2
0
2
2
0
2
0
1
2
0
1
0
0
1
1
0
0
0
2
1
2
2
0
0
1
0
0
1
2
0
0
3
0
2
1
0
0
0
1
0
0
3
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
1
2
0
0
0
1
0
0
2
0
0
0
0
2
0
0
1
0
2
1
0
0
1
2
1
1
2
1
0
2
0
0
1
2
0
0
0
1
4
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
1
1
0
0
3
0
0
0
0
1
1
0
0
0
4
3
2
1
1
2
0
0
2
0
0
2
0
2
1
2
0
0
2
0
5
0
1
0
0
2
0
2
0
0
4
0
2
0
0
0
0
0
0
0
1
0
1
0
2
0
0
2
0
0
0
1
2
0
1
0
2
0
0
0
2
0
0
2
0
2
0
2
2
0
1
1
3
0
1
2
0
1
0
0
1
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
1
0
0
1
1
2
0
1
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
2
2
0
1
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
1
2
0
1
1
1
0
0
1
0
1
2
3
0
0
0
3
0
1
0
2
1
2
0
0
1
0
3
1
2
2
0
1
0
0
0
0
1
0
6
0
0
0
2
0
0
2
0
0
0
2
1
2
0
0
0
0
0
0
2
0
0
2
0
1
2
0
0
0
0
0
0
0
4
0
0
0
0
0
1
2
3
0
0
0
0
0
0
0
1
0
1
0
2
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
1
0
0
0
1
1
2
0
2
2
0
0
0
0
1
0
1
1
0
0
2
0
1
0
0
0
0
2
1
0
2
0
2
2
0
0
2
2
0
3
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
2
0
3
2
0
4
0
0
0
0
2
0
0
2
0
0
1
1
0
0
0
0
2
2
2
0
0
0
0
0
1
0
0
0
2
2
0
2
0
2
1
1
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
1
0
0
2
1
1
1
0
0
1
1
0
3
1
1
0
2
0
1
0
1
0
0
0
0
1
1
0
0
0
3
0
1
0
2
2
0
1
0
1
1
0
1
1
1
0
0
0
2
0
2
1
2
1
0
2
0
2
1
3
1
0
0
2
0
3
2
3
0
0
0
2
0
0
1
0
0
0
2
0
0
2
0
0
1
0
2
2
0
0
1
2
2
0
0
0
2
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
3
1
0
2
2
0
2
0
1
2
2
0
0
1
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
1
1
2
2
0
2
2
2
2
1
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
2
2
0
0
1
1
2
0
1
1
0
1
0
0
1
0
0
0
1
0
2
1
0
0
2
0
0
1
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
1
0
2
2
0
0
0
1
2
1
0
2
0
2
0
0
0
0
0
0
0
2
0
2
0
0
1
2
2
1
1
1
1
0
2
0
0
1
0
2
1
1
0
0
2
1
2
1
0
1
0
1
0
1
0
0
0
0
1
2
2
1
0
0
0
0
0
2
0
1
0
2
2
0
1
2
4
1
0
0
1
0
0
0
0
0
1
1
0
0
2
2
0
0
0
0
0
0
1
0
1
1
1
0
0
1
1
2
0
0
2
0
3
0
0
1
0
0
2
0
0
1
2
1
0
0
2
0
1
0
2
1
0
0
0
2
0
0
0
0
0
1
0
0
1
1
0
1
0
0
2
3
1
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
2
1
0
2
0
0
2
0
0
1
2
0
0
3
0
0
0
0
2
0
0
0
2
2
0
0
0
1
5
0
0
2
0
2
1
0
2
0
0
2
0
0
0
1
1
0
0
0
2
0
0
0
1
2
0
2
2
1
2
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
1
0
1
0
0
2
2
0
0
0
0
1
2
0
0
3
0
1
1
0
1
0
2
1
1
0
1
0
1
0
0
2
2
2
0
0
0
0
0
0
6
3
0
0
0
2
0
0
0
0
1
0
1
0
0
2
0
1
0
2
1
1
1
0
2
0
0
2
1
2
0
0
0
2
0
0
2
0
1
2
1
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
2
2
0
0
2
0
2
1
1
0
1
2
2
1
2
0
0
2
2
2
0
1
0
1
1
0
0
1
0
0
0
2
0
2
1
2
0
0
0
0
2
0
2
0
2
0
2
0
0
2
0
0
1
0
0
0
1
1
0
0
2
0
1
0
1
2
0
0
0
1
2
0
2
0
0
1
0
2
2
0
2
3
0
0
0
0
1
0
0
2
3
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
1
1
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
1
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
2
0
0
0
0
2
0
1
1
0
0
0
1
0
1
2
0
2
1
2
1
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
2
1
1
0
0
1
0
0
0
0
0
2
0
0
5
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
2
1
0
1
2
0
0
0
0
3
0
0
0
0
2
0
1
0
2
0
1
0
0
2
0
0
2
0
1
0
0
2
0
0
0
2
0
1
0
0
0
0
0
2
0
1
0
2
1
0
1
0
1
2
2
0
2
2
0
0
0
3
0
4
0
1
0
1
0
0
0
0
0
2
1
0
0
2
3
0
0
0
1
1
1
0
0
0
0
0
1
1
0
2
2
1
0
2
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
2
1
0
3
0
1
0
0
0
2
1
2
1
0
0
2
0
1
0
2
2
0
2
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
2
1
0
1
2
1
0
2
1
2
1
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
2
2
2
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
3
1
1
0
0
0
0
0
1
0
2
1
2
3
1
1
0
0
1
2
0
0
0
2
1
0
3
1
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
1
2
0
4
0
1
0
0
1
3
0
1
0
2
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
2
1
0
1
0
0
0
0
2
2
0
0
0
2
0
2
2
0
1
0
0
0
0
2
0
1
0
0
2
0
0
1
2
0
1
1
0
2
0
0
3
0
0
0
0
0
0
4
0
0
2
0
0
2
1
0
0
2
0
0
2
1
0
0
0
0
0
1
0
0
2
0
1
0
0
2
2
0
0
2
2
0
0
3
0
0
0
0
0
2
0
0
0
2
0
0
2
0
1
0
2
1
0
0
0
0
2
0
0
1
0
1
0
2
0
2
0
0
0
2
0
0
0
2
0
0
2
1
6
1
0
2
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
2
0
0
1
1
0
1
0
0
2
2
1
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
2
2
2
0
0
1
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
6
3
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
1
1
0
1
3
0
2
1
0
4
0
0
2
0
1
0
0
0
0
0
0
1
0
0
1
2
2
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
2
1
1
0
0
2
0
0
0
8
0
0
1
0
0
0
1
1
0
1
0
0
2
0
1
0
4
0
1
0
0
0
2
0
0
3
2
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
2
1
1
1
0
0
1
2
1
0
0
0
0
2
1
0
1
0
0
1
0
0
0
2
2
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
2
1
1
0
0
0
1
0
2
2
0
1
0
0
1
0
2
2
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
3
0
0
3
1
1
2
0
0
2
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
1
2
0
0
2
2
1
7
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
2
0
2
0
2
0
0
2
0
0
0
2
1
0
2
0
1
0
2
1
1
0
0
1
0
0
3
0
2
0
0
2
0
1
0
0
0
2
0
1
2
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
2
0
2
1
1
0
0
2
1
0
2
2
0
1
1
2
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
1
1
2
1
0
0
0
1
1
2
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
1
4
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
1
0
0
0
1
0
1
1
0
0
2
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
2
3
0
0
3
0
1
0
0
0
1
2
1
0
0
0
0
1
0
2
0
0
0
1
0
0
0
2
0
2
0
0
0
3
2
0
0
0
0
0
1
0
1
2
0
0
2
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
5
1
0
0
0
0
1
2
0
2
0
1
0
0
0
0
4
2
0
1
2
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
2
0
1
2
2
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
1
0
2
0
1
0
0
0
2
0
1
2
1
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
2
1
0
2
0
1
2
0
1
0
0
1
1
0
2
0
1
1
1
0
0
2
0
0
0
1
1
0
0
0
3
0
0
1
1
1
1
2
0
0
0
1
0
0
9
1
1
1
1
0
2
0
1
1
0
0
1
0
0
0
0
0
3
0
2
1
1
2
1
2
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
1
0
0
2
1
2
1
2
0
2
0
0
1
0
2
1
0
2
0
1
0
0
0
0
0
3
2
0
2
0
0
0
1
0
0
1
2
0
0
1
0
0
2
5
0
2
0
0
0
0
0
1
0
1
1
0
2
0
0
0
0
0
2
0
0
0
0
1
0
2
0
2
1
0
0
0
0
1
2
0
0
0
1
1
0
0
0
0
2
2
3
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
1
1
0
0
2
0
2
1
0
0
0
4
1
0
0
1
2
2
0
0
1
2
0
1
0
1
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
1
0
1
2
0
1
0
0
1
0
0
1
0
2
0
2
2
1
1
0
0
0
2
0
0
0
0
0
4
0
2
0
2
1
3
0
1
2
0
0
2
0
0
3
0
1
0
2
2
0
1
0
0
1
0
0
1
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
2
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
1
2
0
2
0
0
0
0
1
0
2
0
0
1
0
0
2
0
1
0
2
1
0
2
0
1
0
2
0
0
0
2
0
2
0
0
0
1
2
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
1
2
1
0
0
2
2
0
1
1
1
0
3
0
0
0
0
0
0
1
0
2
2
0
0
0
2
0
1
1
0
0
0
0
4
2
0
1
0
0
2
0
0
1
0
0
1
1
2
0
0
3
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
1
0
2
0
0
1
2
3
0
1
1
2
0
1
0
2
0
0
0
2
0
0
0
2
3
0
0
2
0
0
0
0
0
0
0
0
1
4
2
0
2
0
0
1
2
0
0
0
0
2
0
0
0
2
0
0
2
0
2
0
0
0
0
1
0
0
2
0
2
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
2
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
2
0
1
0
0
0
0
1
2
0
1
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
1
1
1
0
1
0
1
0
0
0
0
0
0
0
2
0
0
1
0
1
2
0
0
1
0
1
2
3
0
2
0
0
2
1
0
0
0
2
2
0
2
0
0
0
1
0
0
3
0
0
1
2
0
0
0
2
0
0
1
0
0
0
0
0
0
1
2
2
2
0
0
0
2
0
2
2
0
3
0
0
0
1
0
0
0
1
0
2
0
1
0
2
0
0
0
0
1
0
1
0
0
1
1
0
2
1
0
0
0
1
0
1
0
0
0
3
2
0
1
0
0
0
0
2
2
1
0
0
1
0
0
1
1
0
0
2
0
1
2
0
0
1
0
1
0
2
0
0
0
0
1
0
1
0
0
0
1
2
0
0
0
0
1
0
0
0
2
0
2
2
1
0
0
4
0
0
0
2
0
0
0
0
0
1
1
1
0
1
1
0
0
2
2
0
2
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
6
2
3
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
2
2
0
1
0
2
0
1
0
0
2
0
1
0
1
2
0
2
0
1
0
0
0
0
0
0
1
2
0
0
1
0
1
0
2
0
0
0
0
4
0
0
0
0
2
0
0
1
1
0
0
1
0
0
3
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
2
0
1
0
0
0
2
1
0
2
0
1
0
0
2
0
0
2
1
1
0
0
0
2
1
0
1
1
0
2
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
1
1
2
0
0
0
2
0
0
0
0
1
1
1
0
1
0
3
0
2
0
2
0
0
0
0
1
0
1
1
0
0
0
1
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
3
1
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
2
0
0
0
0
0
0
2
1
0
2
0
2
1
0
0
0
1
0
0
2
1
0
0
0
1
0
2
1
0
0
0
2
1
2
0
1
1
2
3
0
0
1
0
0
2
1
2
0
2
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
2
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
2
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
4
0
1
0
0
0
2
0
0
0
0
1
0
1
2
0
2
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
6
1
1
0
2
0
0
0
0
2
1
1
0
0
2
4
0
0
0
2
1
0
1
2
0
0
2
0
0
1
0
0
2
2
2
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
2
1
1
0
2
2
1
1
0
1
2
0
0
0
0
1
0
2
0
0
0
2
3
1
0
0
3
0
0
2
1
0
0
2
0
0
1
2
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
2
0
2
1
0
0
0
2
1
0
2
1
1
0
1
0
2
2
0
0
0
0
2
0
2
1
2
0
0
0
0
2
1
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
2
2
2
0
0
1
0
0
0
1
0
0
2
1
0
2
1
0
0
0
0
1
0
0
2
0
1
0
0
3
0
0
1
0
1
1
0
0
0
1
2
2
2
3
0
2
0
0
2
0
0
0
1
2
1
0
1
2
0
0
2
1
0
1
1
0
0
1
0
0
2
0
0
0
0
0
0
2
1
0
2
1
0
0
0
0
0
0
0
0
2
0
0
4
0
0
1
0
2
0
0
1
0
0
0
0
0
2
2
1
0
0
0
0
0
2
3
0
0
1
2
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
1
2
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
1
2
1
0
0
0
0
0
0
0
2
1
1
0
1
0
3
1
2
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
3
0
0
1
1
0
0
0
1
0
0
2
0
0
0
0
0
1
4
0
0
0
0
1
0
1
1
0
0
1
7
0
1
0
0
1
1
2
0
2
2
0
0
1
0
0
0
0
2
0
0
0
1
1
0
0
0
1
0
0
1
0
0
2
0
0
1
1
0
1
0
1
2
0
1
0
0
1
1
0
0
1
2
1
0
2
0
0
1
0
0
0
1
1
1
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
2
1
1
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
2
1
2
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
4
0
2
0
2
0
0
0
1
0
0
0
0
0
0
1
2
1
1
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
1
0
0
2
0
0
2
1
2
0
0
0
0
0
0
0
1
2
0
0
1
0
0
2
0
0
0
0
1
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
3
1
0
0
0
0
1
1
0
0
0
0
0
3
0
0
0
0
0
0
2
2
1
2
0
0
0
0
0
0
2
1
0
1
2
0
0
0
1
0
1
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
2
2
0
0
0
0
1
2
0
1
1
0
6
0
2
0
1
1
1
2
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
2
1
1
2
1
0
2
1
0
5
1
2
0
1
0
0
2
1
2
1
1
1
0
2
0
1
0
1
2
0
1
1
0
0
2
1
1
0
0
0
2
2
0
0
0
1
1
0
2
1
2
1
0
0
0
0
2
0
1
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
3
0
2
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
3
2
1
1
2
0
0
0
2
2
0
0
0
1
2
0
2
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
1
2
0
0
0
3
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
1
2
2
1
1
4
2
3
0
1
0
0
0
0
0
1
0
3
0
0
0
0
2
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
2
1
0
1
1
0
0
0
1
0
0
0
0
0
0
2
1
1
2
0
0
0
0
0
0
0
2
1
1
0
0
0
0
2
1
9
3
0
3
0
1
2
0
0
2
0
0
0
0
1
0
0
1
2
0
1
1
0
1
0
1
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
3
1
0
1
2
0
0
0
0
0
1
0
2
0
1
0
0
0
2
0
0
1
0
3
0
0
0
0
0
0
0
1
0
0
1
2
0
2
0
1
0
0
2
0
2
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
2
2
0
0
2
0
1
1
0
0
1
1
0
2
0
1
0
1
1
0
0
0
0
2
0
0
0
0
0
2
1
1
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
2
0
0
2
0
2
2
1
1
1
2
0
0
0
0
0
0
0
0
2
0
2
1
0
2
1
0
0
2
0
0
2
1
1
3
0
0
0
1
2
1
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
2
1
1
0
2
1
0
2
2
0
0
2
0
1
1
0
0
1
0
0
2
0
4
1
0
0
1
0
0
2
0
0
0
1
2
2
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
2
0
1
0
0
0
0
1
0
0
1
2
0
1
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
2
2
1
0
1
2
2
0
4
1
0
0
0
1
1
2
0
0
0
3
1
0
0
1
2
0
0
0
0
0
1
0
0
2
1
2
1
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
2
2
0
1
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
2
1
0
1
1
2
2
0
0
0
0
0
0
1
2
0
0
1
2
1
0
1
0
0
1
0
0
0
2
2
2
0
2
1
0
0
1
0
1
0
1
2
2
0
2
0
0
1
2
0
1
0
0
2
2
2
1
1
2
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
2
0
0
1
2
0
2
1
0
0
0
1
0
0
0
0
0
3
0
2
0
0
0
2
0
0
0
1
1
2
2
1
0
0
0
0
0
1
2
3
0
0
1
0
0
0
1
1
0
0
2
2
0
0
0
0
1
2
0
1
0
1
0
0
2
1
0
1
0
1
0
2
2
2
2
1
2
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
2
0
2
2
2
0
1
2
2
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
1
0
2
2
2
0
3
1
0
1
1
1
2
0
2
0
0
0
2
1
0
1
0
0
0
2
0
0
0
2
0
1
2
0
0
0
1
2
1
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
2
2
0
0
1
0
0
0
0
1
2
0
2
0
0
0
0
2
3
0
0
0
1
2
2
1
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
2
1
0
0
0
1
2
2
2
3
0
0
2
0
0
0
2
0
0
1
0
2
1
0
1
2
0
0
2
0
1
0
0
1
0
0
0
1
0
2
0
0
3
1
0
0
0
0
2
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
1
1
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
1
0
0
0
3
1
0
0
2
0
0
0
1
1
3
0
1
0
2
0
0
2
0
1
0
1
2
2
0
2
0
0
2
0
2
0
0
2
0
1
0
0
0
3
1
1
0
0
0
2
0
1
0
0
2
2
1
0
0
2
0
0
1
0
0
1
0
2
2
0
0
0
2
1
2
1
0
0
2
2
0
0
0
3
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
1
2
0
0
0
0
2
2
0
0
2
0
3
2
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
3
0
0
0
0
2
1
1
0
0
0
0
1
0
0
0
1
0
1
0
0
1
1
0
2
0
1
0
0
0
0
1
0
0
0
0
4
0
0
0
2
2
0
2
2
0
3
0
2
1
0
1
2
1
0
0
0
0
0
0
2
0
0
0
1
1
0
0
1
4
0
0
0
2
0
0
0
0
2
0
1
0
0
0
2
1
0
1
0
0
2
1
0
1
2
1
0
0
0
0
0
2
2
0
2
2
0
0
0
2
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
1
1
2
2
0
0
0
0
2
0
0
2
0
0
0
0
1
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
1
3
0
0
2
0
2
0
1
0
0
1
0
0
3
1
0
0
2
0
0
2
0
0
0
2
0
4
0
0
2
2
0
0
0
1
1
0
0
0
2
2
2
1
0
1
0
0
0
2
0
1
1
2
0
1
2
1
0
0
0
0
0
0
1
0
2
0
0
1
0
1
1
2
0
1
0
0
0
0
2
0
0
2
0
1
0
0
1
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
2
1
0
1
0
2
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
2
0
0
1
0
2
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
3
0
1
0
0
0
2
0
0
2
0
0
2
0
0
1
0
2
0
0
1
0
2
0
1
0
0
2
1
0
2
0
1
1
0
1
2
0
0
1
0
2
1
2
0
1
1
0
0
0
0
0
1
0
0
0
2
1
2
0
0
0
1
1
0
2
0
0
2
2
1
0
0
0
0
2
1
2
0
1
0
0
2
3
0
0
0
0
0
0
2
0
2
0
2
4
0
0
2
0
0
3
1
1
0
1
0
2
0
0
0
2
1
0
0
1
0
0
0
0
1
0
0
2
0
2
0
2
0
0
0
3
0
0
2
1
0
0
1
1
0
1
1
0
0
0
1
0
2
0
2
0
0
0
0
2
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
1
0
1
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
1
1
0
0
0
2
0
0
0
0
2
0
2
0
1
0
0
2
1
1
0
0
0
0
6
0
2
2
0
1
0
0
0
1
1
0
0
2
2
0
0
0
0
0
0
1
1
0
2
2
1
2
0
1
0
0
1
1
0
1
0
0
1
1
1
0
0
0
1
0
2
0
0
1
0
0
0
1
1
0
2
1
0
0
1
1
0
1
0
1
1
1
0
2
0
0
0
0
0
0
0
0
0
3
1
0
0
1
0
1
2
2
2
0
0
0
0
0
1
1
3
0
1
0
1
0
0
2
0
0
2
1
0
0
0
0
1
0
2
2
2
0
2
0
0
0
2
0
2
4
3
2
0
4
1
0
2
0
2
1
0
0
2
0
0
0
0
0
0
1
0
1
0
0
2
1
0
0
0
0
0
1
4
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
2
1
0
2
2
3
0
1
0
1
0
0
0
1
1
2
2
0
2
1
1
0
2
0
0
0
3
2
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
1
2
0
0
2
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
1
0
2
1
2
1
0
0
0
0
1
0
1
2
1
1
1
2
0
0
0
0
0
0
2
0
1
1
0
1
0
0
1
2
2
0
0
0
2
0
0
0
0
1
0
0
2
1
2
2
0
0
0
0
0
0
0
3
2
2
1
0
0
0
0
2
2
2
1
2
0
0
0
0
0
2
2
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
1
0
2
2
1
0
0
0
2
2
2
2
0
2
0
0
2
2
0
0
0
2
0
0
2
0
0
2
0
0
0
0
1
0
1
3
0
1
0
0
0
1
2
1
1
0
1
2
2
0
0
0
0
1
0
0
2
1
1
0
1
1
0
0
0
0
2
2
0
0
0
3
1
2
0
3
0
2
2
0
1
2
0
1
1
0
0
5
0
1
0
2
2
3
0
0
0
0
1
1
2
2
3
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
2
1
3
0
0
0
0
0
1
0
0
2
3
0
0
1
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
1
0
1
2
0
0
1
0
0
0
0
2
0
0
1
1
1
0
0
0
2
0
1
0
2
0
0
0
0
0
2
0
1
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
2
0
2
1
0
0
0
0
0
1
1
1
1
0
0
0
1
2
1
0
0
0
2
1
1
2
1
1
0
0
0
0
0
2
1
1
1
2
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
1
1
0
1
10
0
2
0
1
4
2
0
1
2
0
1
1
1
1
0
1
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
2
0
0
1
0
0
4
0
0
0
2
1
1
0
0
1
0
1
0
0
0
0
0
3
2
0
0
0
0
0
1
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
1
1
0
1
4
1
0
0
0
1
1
1
0
0
0
0
0
1
1
0
0
0
0
0
2
1
0
0
0
1
0
4
0
0
0
0
0
2
2
0
0
1
0
2
1
1
1
1
0
0
1
0
0
0
0
1
3
0
1
0
0
2
0
0
1
1
2
0
2
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
1
1
0
2
2
0
0
0
1
0
1
0
1
0
1
0
0
1
0
1
0
0
0
1
0
0
2
1
1
1
0
2
1
1
0
2
1
2
0
0
0
0
2
0
2
2
2
2
1
0
0
0
0
2
3
2
3
0
0
0
0
0
1
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
1
0
7
0
0
3
0
0
0
3
0
2
0
0
0
2
1
0
0
1
1
0
0
1
0
0
0
3
1
0
0
0
0
0
0
2
3
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
1
0
0
0
1
2
2
0
1
1
0
0
0
0
0
2
1
0
0
3
0
0
1
1
0
6
0
0
0
0
0
0
3
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
3
0
0
1
0
0
0
2
0
0
6
0
0
0
1
1
0
0
0
3
2
2
2
1
2
0
2
2
0
1
1
1
0
0
0
2
0
0
2
2
0
1
1
3
0
0
2
0
0
1
1
0
0
0
0
0
2
0
0
2
2
1
0
0
0
0
1
1
0
0
1
1
2
0
0
1
0
0
0
0
1
0
0
2
2
2
2
1
0
0
0
2
0
0
0
1
0
0
0
1
1
1
1
2
0
0
2
0
1
0
2
0
2
0
0
0
0
2
0
0
0
0
1
0
0
1
0
1
0
0
2
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
2
0
0
1
2
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
2
0
2
0
1
2
0
0
0
2
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
3
2
0
2
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
2
0
2
0
0
1
0
0
1
0
2
2
0
2
0
2
0
0
0
0
0
0
2
0
0
0
3
0
0
3
2
2
1
0
0
0
0
0
2
2
0
2
0
1
1
0
3
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
2
0
0
0
2
0
2
0
1
0
2
2
2
0
0
2
2
1
0
0
0
0
0
0
1
2
0
0
0
0
1
2
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
2
2
1
0
0
0
2
2
0
0
2
1
0
0
0
1
0
0
2
0
1
2
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
1
3
2
0
0
0
0
0
0
0
1
1
2
0
0
1
0
2
2
1
1
0
0
2
3
1
1
0
0
0
3
0
0
0
0
0
1
1
0
0
0
2
0
1
1
0
0
3
0
0
0
0
0
0
3
3
0
2
0
1
1
1
1
0
2
0
1
0
2
1
1
0
0
0
2
0
0
0
2
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
1
0
0
1
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
2
0
0
0
0
1
1
2
2
0
0
0
0
0
0
7
0
1
0
2
0
0
2
0
0
0
0
0
0
0
2
2
2
0
1
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
1
0
2
2
0
1
0
2
2
0
2
0
0
0
0
1
6
2
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
1
2
2
0
0
2
0
2
2
0
1
0
0
0
0
1
0
0
0
0
1
0
2
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
3
0
2
0
0
0
0
2
0
1
0
1
0
2
0
2
2
1
1
1
0
0
2
1
0
0
2
0
0
0
0
2
0
1
0
0
1
0
0
0
1
0
2
1
1
2
0
0
1
0
0
0
1
0
1
2
1
0
0
0
0
1
3
1
0
2
1
1
0
0
0
1
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
2
0
1
0
1
0
1
1
1
2
0
0
1
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
1
0
2
0
0
1
0
0
0
3
1
0
0
1
0
0
2
2
1
0
0
0
0
0
1
0
2
2
0
2
0
0
0
0
1
0
1
0
0
1
0
1
2
0
0
0
0
2
2
1
0
0
0
1
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
1
0
1
0
2
1
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
2
2
2
0
2
0
0
1
0
0
0
2
2
0
0
0
1
0
0
2
0
0
0
2
3
0
0
1
0
1
1
1
2
1
2
1
2
0
0
1
2
0
3
0
0
1
0
2
0
0
1
0
2
0
0
0
0
0
2
0
2
0
0
2
0
1
1
2
2
0
0
2
1
1
0
0
0
2
0
0
0
0
2
0
3
0
2
1
0
2
1
1
0
0
2
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
2
0
1
1
0
0
0
0
1
2
0
1
0
1
0
0
0
0
2
2
1
2
1
0
2
2
0
0
0
0
1
2
1
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
4
1
0
0
2
0
2
0
2
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
1
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
2
0
1
1
0
0
1
0
0
0
0
1
1
0
5
0
0
0
1
0
1
2
0
0
0
1
1
0
0
2
0
0
1
1
0
0
0
0
4
2
0
0
0
1
0
0
0
1
2
1
1
0
0
0
2
0
0
0
1
0
2
1
0
0
1
0
0
0
1
2
0
0
2
1
1
2
1
2
0
2
1
0
0
2
0
0
0
0
1
1
2
0
1
0
0
0
2
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
2
2
0
1
1
0
0
0
0
0
1
0
0
1
2
0
2
2
2
2
0
2
0
1
2
3
0
1
0
0
1
3
0
0
1
1
1
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
2
1
0
0
0
1
0
2
0
1
0
2
1
0
0
0
0
2
0
1
2
1
0
0
2
0
2
0
0
0
1
2
1
1
1
0
1
3
0
1
0
0
2
0
0
0
1
1
2
1
0
0
0
0
1
1
0
0
0
2
0
2
0
0
0
1
0
0
2
0
0
0
0
1
0
2
1
0
1
2
1
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
1
0
0
1
2
2
1
0
1
0
0
2
0
2
0
0
0
0
1
0
1
0
0
0
2
2
0
0
2
0
0
0
1
1
2
0
2
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
6
0
2
0
1
0
0
1
1
0
0
2
1
1
0
0
2
0
0
1
1
0
0
2
1
0
0
2
0
0
1
2
1
0
0
1
0
1
1
1
0
0
0
3
2
0
0
1
0
2
0
2
0
1
0
1
0
0
2
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
2
0
2
0
0
0
0
2
0
0
0
2
1
2
0
0
0
0
0
2
0
0
2
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
2
1
0
1
1
0
1
0
1
1
0
2
1
0
0
1
0
1
1
1
1
1
0
2
0
2
0
0
0
0
0
0
2
0
0
2
2
0
0
3
3
1
0
0
1
0
0
0
2
0
1
0
0
0
0
0
1
2
0
0
2
0
1
0
0
1
0
0
0
0
0
2
1
0
0
3
0
1
0
0
0
0
1
0
0
0
1
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
2
2
2
0
0
0
0
3
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
3
0
1
2
1
0
0
1
1
2
0
1
2
0
0
0
0
0
2
2
2
0
0
0
1
1
1
2
1
0
0
1
1
1
1
2
2
1
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
1
2
1
2
4
0
0
0
0
2
0
0
0
0
0
0
0
2
1
2
1
2
0
0
0
2
0
0
2
2
0
1
1
0
0
2
0
0
0
1
0
1
0
2
0
0
2
0
0
2
1
1
0
1
0
1
0
0
0
2
1
0
0
0
2
2
1
0
1
0
0
3
0
2
1
0
0
0
1
0
0
0
1
0
0
1
0
2
0
0
0
0
0
1
0
0
2
1
0
0
0
3
0
0
0
0
2
1
1
0
0
0
1
0
0
1
1
0
0
2
0
0
2
2
1
2
3
0
0
0
1
0
1
0
0
2
2
0
0
3
0
2
0
0
0
0
0
2
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
1
1
2
2
0
0
1
0
0
2
0
3
1
1
0
0
2
0
1
2
0
1
0
1
2
0
1
1
0
1
0
2
0
0
0
2
1
0
1
0
0
2
0
0
0
1
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
2
3
0
0
0
2
0
2
0
3
0
0
2
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
2
1
1
0
3
0
3
2
0
0
0
2
0
0
0
1
0
1
1
0
1
0
0
1
0
0
0
2
0
0
1
0
0
0
1
0
2
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
2
2
0
1
0
0
0
0
2
2
2
0
1
0
1
0
2
0
2
0
0
0
2
0
1
0
0
2
0
0
0
2
0
1
0
0
0
2
0
0
1
0
0
0
0
1
0
0
1
1
0
0
2
0
0
0
1
0
0
2
0
0
0
1
0
2
0
4
0
1
0
0
0
1
0
0
2
0
3
0
0
1
0
1
0
0
0
0
2
2
0
1
0
0
1
1
0
0
0
1
1
1
2
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
2
3
2
0
1
0
0
0
0
0
2
0
0
2
1
0
0
3
2
0
1
0
0
1
0
3
2
0
0
1
3
2
0
0
0
0
1
0
0
0
2
0
0
0
1
1
0
0
0
0
0
1
0
1
1
2
0
0
0
1
0
0
0
1
0
2
0
0
0
0
1
0
1
0
0
0
0
0
2
2
0
0
1
0
1
0
1
2
0
3
0
1
0
0
2
0
0
0
1
2
0
0
0
0
10
0
0
0
1
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
3
0
0
0
0
1
0
1
0
0
1
1
0
1
1
0
0
2
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
1
0
1
3
0
0
1
1
0
0
0
0
1
2
0
1
1
0
0
0
1
0
1
2
0
0
0
0
1
1
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
2
2
0
2
0
1
2
0
0
1
2
0
1
3
0
0
0
0
2
1
1
1
1
0
0
1
0
0
2
0
1
2
0
0
0
1
1
1
0
0
0
1
1
2
0
2
0
0
1
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
3
1
0
2
0
1
0
2
0
0
1
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
2
0
2
0
0
1
2
0
2
2
0
0
0
0
0
0
0
1
0
2
0
0
2
1
0
0
0
0
1
2
0
0
1
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
3
0
2
0
2
1
0
2
0
1
2
0
0
2
2
1
0
2
0
1
2
2
0
2
1
2
1
0
0
1
4
2
0
1
1
0
0
0
1
0
0
0
0
0
1
2
2
0
0
1
0
2
2
0
2
0
0
0
1
0
0
2
3
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
2
3
0
0
0
1
0
0
0
0
2
0
2
0
1
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
2
2
0
0
2
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
3
0
0
0
0
0
0
2
0
0
2
1
1
0
2
0
1
0
0
0
1
0
1
1
0
1
1
0
2
0
1
1
1
1
0
0
0
1
1
1
0
1
0
0
0
0
0
0
4
1
3
0
1
0
1
2
0
0
1
2
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
2
3
1
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
1
0
1
0
1
0
1
2
0
0
0
0
1
1
0
0
0
2
0
1
1
2
0
0
2
3
0
0
0
0
0
1
0
1
0
0
0
0
1
0
2
0
3
1
0
0
0
9
0
2
0
2
0
1
0
0
0
1
1
2
1
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
1
1
0
7
0
2
0
0
5
2
0
0
2
0
1
2
0
1
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
1
0
0
0
0
0
1
0
0
2
0
2
1
0
0
0
0
1
1
0
0
0
1
1
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
2
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
2
0
2
1
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
2
0
1
0
0
1
0
0
0
0
0
1
1
0
0
1
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
1
1
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
2
1
0
2
2
2
0
1
2
1
1
0
0
0
1
1
1
2
0
0
2
0
0
0
1
2
0
2
0
0
2
1
0
0
0
0
0
2
1
0
0
1
0
0
0
1
0
1
1
1
0
2
0
2
0
0
0
1
0
2
0
0
0
0
0
2
1
2
2
1
1
0
0
0
0
0
0
0
1
2
2
1
0
0
0
1
0
1
0
0
2
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
1
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
1
0
1
0
1
3
0
0
0
1
0
1
0
0
1
0
1
1
0
0
0
0
2
2
2
0
0
0
0
0
0
2
0
2
0
0
0
2
1
0
1
2
1
2
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
1
0
0
1
0
0
0
0
0
1
0
1
1
0
2
0
0
0
1
0
0
2
1
1
1
0
0
0
0
2
1
0
0
0
0
2
1
0
0
2
0
2
2
0
0
0
2
0
1
2
1
0
4
0
1
0
2
0
0
3
0
1
1
1
1
0
0
1
2
0
1
0
1
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
1
0
2
3
0
0
2
0
0
0
0
2
0
0
0
0
2
1
1
0
0
1
1
1
0
0
0
0
2
2
1
1
1
1
2
0
0
2
0
2
2
2
0
0
0
0
1
2
0
0
0
0
0
0
1
0
2
1
0
0
1
1
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
1
1
0
0
1
0
1
4
1
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
2
1
1
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
1
2
0
1
1
0
2
0
0
0
2
0
0
2
2
2
0
1
0
0
0
0
1
0
1
2
1
2
0
0
1
0
0
0
1
0
1
0
0
0
1
1
3
0
0
1
0
2
1
2
1
0
1
0
0
2
1
0
3
1
0
2
0
0
0
0
2
2
0
2
0
0
1
0
2
0
0
0
0
2
2
3
2
1
1
0
0
0
2
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
1
1
2
0
0
1
2
0
0
0
0
1
1
0
1
0
0
2
0
0
0
1
2
0
0
3
0
0
1
0
0
0
0
2
0
1
1
1
0
1
0
2
2
0
2
0
0
2
2
0
0
0
1
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
2
0
1
2
0
0
2
0
1
0
2
2
0
1
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
1
0
0
2
2
1
0
0
0
0
0
2
0
1
0
2
0
2
1
1
3
0
2
1
2
0
1
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
1
2
0
0
0
2
0
2
0
2
1
0
0
1
0
0
1
0
1
0
2
0
1
1
0
0
0
0
0
0
0
0
2
0
1
0
2
0
1
2
1
0
2
0
0
1
1
0
2
0
0
0
0
0
3
2
1
0
0
3
1
2
0
0
3
0
1
4
0
0
0
2
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
3
0
2
1
1
1
2
3
1
0
2
0
0
1
0
0
1
2
0
2
0
0
0
1
0
1
1
0
1
0
0
2
0
1
1
0
0
1
5
0
0
3
0
1
0
0
0
0
0
2
2
2
0
0
2
0
1
0
0
0
1
0
0
1
0
0
2
0
1
2
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
1
0
0
0
1
2
0
0
2
2
6
1
1
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
2
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
1
2
2
2
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
3
1
0
0
1
1
0
2
0
0
0
3
1
0
0
0
1
3
0
2
1
0
0
2
1
2
0
2
2
0
1
2
0
1
0
0
2
1
2
0
2
0
2
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
2
3
0
2
0
2
2
5
2
0
0
0
0
0
1
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
5
2
1
1
1
0
1
3
1
1
0
0
0
1
0
0
0
0
3
0
1
0
0
0
0
2
0
0
2
2
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
1
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
2
0
0
0
2
0
1
0
0
0
0
2
0
0
0
1
1
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
3
2
1
4
0
2
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
2
0
0
2
1
0
1
0
0
0
0
0
0
0
1
0
2
4
0
3
0
0
0
0
0
0
0
3
2
2
2
0
2
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
2
2
0
0
0
2
0
3
0
0
0
2
1
0
0
0
2
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
2
0
0
2
2
1
0
2
0
2
0
1
1
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
2
0
1
0
1
0
0
0
1
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
1
0
2
2
1
0
0
0
2
0
2
8
0
0
0
0
1
2
2
0
0
0
1
2
0
0
1
1
0
0
2
0
0
2
0
2
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
3
1
0
0
0
1
2
0
1
0
1
0
1
2
2
2
0
0
1
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
2
0
1
1
0
0
2
2
0
1
0
0
0
0
0
0
1
0
1
0
1
1
0
2
0
0
2
0
1
0
0
0
0
2
0
0
0
2
0
1
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
1
2
0
0
1
0
2
0
0
2
2
0
0
1
0
2
4
0
0
0
0
0
0
2
1
1
1
0
1
1
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
1
0
0
2
2
0
2
0
0
1
2
1
1
1
1
0
0
2
1
0
1
0
2
0
1
2
0
0
2
0
0
0
0
2
2
0
0
0
1
0
2
2
2
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
2
1
0
0
1
0
2
0
0
2
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
2
0
1
0
0
0
0
0
1
2
0
1
2
0
1
0
2
1
0
1
0
1
2
0
1
0
0
0
0
2
0
0
1
0
0
0
1
0
0
1
0
0
1
0
1
1
0
1
2
0
0
0
2
0
0
0
0
0
2
0
1
3
1
2
2
0
2
2
3
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
1
0
2
0
2
0
2
0
0
1
2
0
0
1
0
1
0
0
3
0
0
0
0
1
0
2
1
0
0
1
0
0
0
0
2
2
0
0
0
1
0
0
0
1
2
1
0
1
0
1
1
1
0
0
0
0
0
2
2
0
0
0
2
0
1
0
1
0
1
0
1
5
2
0
0
0
2
0
1
1
2
0
1
0
2
0
0
0
1
1
1
0
2
2
1
0
0
1
0
0
0
0
2
0
0
2
1
0
1
0
0
0
1
0
1
0
0
0
0
3
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
1
0
1
0
4
1
0
0
1
1
0
0
1
1
0
0
0
0
1
0
2
2
2
2
0
3
0
0
0
0
0
0
1
0
1
0
2
1
1
0
2
0
2
0
2
1
0
3
2
2
4
0
0
1
1
0
0
2
0
0
0
1
1
2
0
0
2
0
2
1
2
2
2
1
0
0
2
0
0
2
1
0
0
1
1
0
0
2
0
2
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
2
0
2
1
2
1
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
1
2
0
0
0
0
0
0
0
1
0
0
1
0
1
2
0
0
0
2
0
3
0
1
1
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
7
2
2
2
0
0
1
2
0
0
1
2
2
6
0
2
0
0
0
1
1
0
2
1
2
0
0
0
2
1
0
0
0
0
0
1
2
0
2
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
1
5
0
1
0
0
2
0
1
0
0
0
0
0
3
0
1
0
1
0
2
0
0
1
0
0
0
0
0
2
1
0
0
0
1
2
0
0
2
0
0
0
0
1
0
0
3
1
0
0
0
0
0
1
2
0
0
0
1
0
2
1
1
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
2
2
2
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
2
2
0
1
0
0
0
1
0
0
2
0
1
0
0
0
0
1
0
2
0
3
0
2
0
0
0
1
2
0
0
1
0
0
0
0
0
2
2
1
2
0
0
0
0
0
0
1
0
0
1
2
1
1
1
0
2
0
2
3
0
0
2
2
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
2
0
1
0
0
0
2
0
1
2
0
2
1
0
0
0
0
2
0
0
0
0
2
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
1
0
2
1
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
2
0
1
0
0
1
0
1
0
0
0
0
2
0
2
0
0
0
3
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
1
2
1
0
0
0
0
2
0
2
2
0
2
1
0
2
1
2
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
3
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
1
0
1
0
1
0
1
0
1
0
0
2
0
1
2
1
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
2
1
0
0
1
0
0
2
0
2
0
2
1
2
0
0
1
0
0
1
0
0
1
3
2
2
0
0
0
0
1
1
0
0
0
0
2
0
0
3
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
3
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
2
0
2
0
0
0
0
2
0
1
2
0
0
0
0
0
0
2
0
0
0
2
0
2
2
2
1
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
2
0
2
0
0
0
1
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
3
0
0
0
0
0
0
0
3
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
2
0
1
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
3
0
1
2
2
0
2
0
0
2
1
0
0
0
1
0
2
0
1
2
0
2
2
2
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
2
2
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
2
0
0
0
0
2
0
0
1
0
0
1
1
0
0
2
0
0
0
0
0
3
2
2
0
2
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
5
1
1
0
0
2
0
0
2
0
1
0
1
0
0
0
0
0
2
0
2
1
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
1
0
1
0
0
2
0
0
2
2
1
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
2
0
2
0
0
2
2
0
1
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
1
2
0
2
0
0
1
1
2
1
0
0
2
0
2
0
0
0
0
0
2
0
2
1
0
0
2
0
1
0
1
2
0
1
0
1
0
2
2
1
0
1
0
2
0
0
2
1
0
2
0
0
0
0
0
0
0
3
1
0
0
2
2
0
0
0
0
0
1
0
0
0
1
2
0
3
0
1
0
2
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
1
2
0
0
2
2
0
0
0
2
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
2
2
2
0
2
1
1
2
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
3
1
0
1
0
0
0
0
1
3
0
0
1
2
2
0
2
0
2
1
0
1
1
0
0
1
0
0
1
0
0
1
2
0
2
0
0
1
0
2
0
3
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
1
0
2
0
0
0
1
0
0
0
1
5
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
1
2
0
0
2
0
2
0
0
0
2
1
1
1
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
1
0
0
0
2
2
2
0
0
1
0
0
1
1
0
2
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
1
0
1
0
0
2
0
0
0
2
0
0
0
1
0
0
3
1
0
0
0
2
0
0
0
0
2
0
2
2
0
1
0
0
0
1
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
2
0
1
1
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
1
1
0
0
3
0
0
2
2
2
2
2
1
0
2
1
1
3
0
2
2
0
0
1
0
1
0
0
2
0
1
0
1
0
2
0
0
0
1
2
2
0
0
2
0
1
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
1
0
0
2
0
2
1
0
1
0
1
2
0
1
0
0
0
0
3
0
1
2
0
0
0
0
2
0
1
0
0
0
2
0
3
3
0
0
1
2
0
0
0
1
4
2
0
1
0
1
0
0
0
1
0
0
2
0
0
2
0
1
0
0
0
0
0
0
2
1
0
1
2
1
1
1
0
1
2
0
0
0
2
1
2
1
0
0
0
2
0
0
0
0
0
2
3
1
0
0
0
1
2
2
0
0
1
2
0
0
0
1
0
1
0
0
0
1
1
1
2
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
2
0
2
1
0
1
0
2
1
1
0
0
0
0
1
1
0
0
0
1
0
0
1
1
2
0
3
0
0
0
0
2
0
2
1
0
0
0
0
0
1
2
0
1
0
2
2
0
0
2
2
1
0
0
0
2
0
0
2
0
0
0
0
2
1
0
1
0
2
0
1
0
0
0
0
0
1
0
5
1
1
0
0
0
2
0
0
2
0
0
0
0
0
1
1
1
2
1
0
3
1
0
0
0
0
0
0
0
2
0
0
2
0
0
1
1
2
0
0
1
3
0
2
0
1
0
2
0
0
0
0
2
1
0
0
1
1
1
0
0
1
0
0
1
2
0
2
0
0
0
1
2
0
1
1
0
0
0
1
0
0
3
1
2
0
0
0
0
0
0
0
0
0
1
1
0
2
0
1
0
0
2
1
1
0
0
0
2
0
1
0
0
0
0
0
4
1
0
2
1
5
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
2
0
0
2
0
0
0
3
0
0
1
0
0
2
1
0
0
1
0
0
0
1
0
1
0
0
1
2
0
1
2
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
2
0
2
0
0
0
1
0
0
2
1
0
0
1
0
0
1
0
0
2
0
0
1
0
0
2
1
0
2
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
2
2
0
0
0
1
0
0
1
1
0
1
0
0
2
0
1
1
0
2
1
1
0
2
1
0
0
1
0
1
0
0
0
0
0
0
1
1
2
0
2
0
1
0
0
2
0
0
2
0
0
1
1
1
2
0
3
1
0
0
0
0
3
0
0
0
3
0
0
1
0
0
2
0
0
1
2
1
2
0
1
2
0
0
0
0
0
0
0
2
2
0
1
1
0
1
0
2
0
0
1
0
0
0
0
2
0
0
2
1
3
0
0
2
2
0
1
0
1
0
0
1
1
0
0
1
0
1
3
0
1
2
1
2
0
0
0
0
0
0
0
2
1
0
0
1
0
2
0
2
0
1
0
0
0
0
1
1
1
0
2
0
1
0
0
0
0
8
2
0
2
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
2
0
0
0
1
0
0
0
1
1
1
1
2
0
1
1
0
0
0
2
1
2
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
3
1
1
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
1
1
0
0
2
1
0
0
0
0
0
2
2
0
0
1
0
2
0
2
0
0
0
1
0
2
0
0
0
1
2
0
0
0
0
0
1
1
0
2
0
0
0
0
0
1
0
0
1
2
0
0
1
0
0
2
0
0
1
0
0
0
0
0
1
1
0
2
0
0
0
2
0
0
1
0
0
0
2
0
2
0
0
0
0
1
0
0
1
0
0
1
0
0
0
3
1
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
2
0
0
0
0
0
1
1
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
1
1
1
0
1
0
1
0
0
2
0
2
0
1
0
1
2
0
0
1
0
1
0
1
0
1
2
0
1
1
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
1
1
0
0
0
0
2
1
0
0
1
0
0
1
1
0
1
0
1
0
1
2
1
0
0
1
0
1
1
0
0
0
1
0
6
2
0
0
0
0
0
2
3
0
2
0
2
2
0
2
2
1
1
1
1
0
0
4
0
1
1
2
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
1
3
0
0
0
0
0
0
2
1
0
0
0
0
0
5
1
1
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
1
0
0
2
0
0
0
0
1
1
0
0
0
1
0
2
0
0
0
1
2
0
0
0
0
0
1
0
1
0
0
0
2
0
0
2
0
1
0
2
0
0
1
1
1
2
1
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
4
2
0
1
0
2
1
2
1
0
0
0
0
2
0
1
0
0
0
2
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
1
0
1
0
0
0
1
0
3
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
2
0
0
2
0
0
2
2
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
2
0
0
1
1
0
0
2
2
0
0
0
0
0
0
0
1
1
0
2
2
0
0
0
0
0
0
0
2
1
0
1
2
0
0
0
0
0
1
1
1
0
0
0
0
1
0
1
2
0
0
1
2
2
2
1
0
0
0
1
1
2
1
0
1
0
0
0
2
1
0
0
0
0
0
2
2
1
2
2
1
0
0
0
1
0
2
2
2
0
0
0
0
0
0
1
0
2
1
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
2
1
0
0
1
0
1
2
2
0
1
0
0
1
1
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
1
2
0
1
1
0
2
0
1
0
2
0
1
0
0
0
1
0
2
1
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
2
2
1
1
0
0
0
0
1
0
2
1
0
0
2
2
0
0
2
0
0
1
0
0
0
2
0
2
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
1
0
3
0
0
1
0
0
3
2
2
1
0
0
2
1
0
2
1
0
0
0
0
1
0
0
2
0
0
1
2
0
0
2
0
1
2
0
0
0
1
1
2
4
0
1
2
0
2
2
2
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
2
2
0
2
2
0
2
0
1
1
0
2
0
2
0
0
1
0
2
1
1
0
0
0
0
2
3
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
1
2
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
2
0
0
1
1
1
0
0
0
0
0
0
0
0
1
1
2
0
0
0
1
0
0
2
0
0
1
1
2
1
0
0
0
0
1
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
1
1
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
1
0
0
0
2
0
0
1
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
6
2
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
1
1
0
1
0
2
0
0
0
0
0
1
2
2
2
0
0
0
0
2
2
0
2
0
1
2
0
0
2
2
5
1
2
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
2
1
0
0
0
0
1
1
0
0
2
0
1
0
1
2
0
1
0
1
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
3
0
1
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
2
0
0
0
0
0
2
1
2
0
0
3
0
0
0
2
0
2
1
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
1
1
1
0
0
0
1
2
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
2
0
2
0
2
0
0
2
0
0
1
0
0
1
0
0
2
2
1
3
0
0
2
0
0
2
0
2
0
1
2
0
1
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
1
0
1
2
0
0
1
0
1
0
1
0
0
0
0
0
0
2
2
0
2
0
0
0
1
0
0
0
2
1
1
2
0
0
1
0
2
0
0
0
1
2
0
2
1
0
0
0
3
2
0
2
0
0
0
1
1
0
2
0
0
0
0
0
0
2
0
1
0
1
0
0
2
2
0
0
2
3
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
3
3
0
0
1
1
2
1
0
0
1
0
0
0
0
1
1
1
2
0
0
0
0
0
0
0
0
0
2
0
0
1
1
1
2
1
0
1
0
1
0
0
0
1
1
0
0
0
5
0
2
0
0
0
0
1
2
0
2
0
2
0
0
1
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
1
0
1
0
0
0
0
1
0
2
0
2
2
1
0
0
1
0
0
1
0
4
0
0
2
1
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
3
0
0
2
0
1
0
0
0
0
3
0
3
0
0
0
1
0
1
0
0
1
2
0
2
0
2
2
0
1
1
0
1
1
1
0
0
1
1
0
0
2
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
1
2
0
0
0
3
0
2
0
1
0
2
2
1
1
0
1
0
2
0
2
2
2
0
2
0
0
2
0
0
1
0
1
0
1
0
0
2
1
0
1
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
1
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
2
0
2
3
0
0
2
0
0
0
1
0
2
1
1
2
1
1
1
1
0
0
1
1
1
2
0
2
0
0
0
0
2
0
1
0
0
2
2
0
0
1
0
2
0
1
2
1
0
0
2
0
1
2
0
1
2
1
0
0
0
1
1
0
0
0
1
2
0
2
0
0
0
1
1
0
2
0
0
1
0
0
0
0
0
0
0
2
1
0
0
1
1
0
0
1
0
1
0
1
0
0
0
1
2
0
1
0
1
0
0
0
0
0
0
1
0
1
0
2
0
3
1
0
0
0
1
1
2
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
2
1
1
2
1
0
2
1
0
0
0
1
0
0
0
0
1
2
0
0
1
0
2
1
0
0
0
0
0
1
0
2
0
0
1
0
0
0
2
1
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
3
2
0
0
4
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
3
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
1
0
3
2
0
0
0
1
0
0
0
1
1
2
0
0
0
0
2
0
1
2
0
0
0
3
0
2
0
0
0
0
1
0
2
0
0
0
1
2
0
1
0
2
0
1
0
0
0
0
1
0
0
2
0
1
2
0
0
0
0
3
1
0
0
2
1
0
1
0
1
0
1
4
0
4
2
2
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
1
0
0
0
2
0
1
2
0
2
0
2
0
0
0
0
0
1
0
0
6
0
2
0
1
5
0
2
2
0
1
0
0
0
0
0
1
1
0
1
0
1
2
0
4
0
0
0
0
3
2
0
1
0
2
2
0
0
0
0
0
1
1
0
1
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
1
0
2
0
1
0
0
1
0
2
0
0
0
0
0
3
2
2
1
2
0
0
1
1
2
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
2
1
0
0
0
1
1
0
0
1
1
1
2
0
1
2
0
1
0
0
0
2
2
1
1
1
0
2
0
0
0
1
0
0
0
0
1
2
2
0
0
0
0
0
2
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
1
1
0
0
0
2
2
1
1
0
0
2
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
3
0
1
0
1
3
0
1
0
2
0
0
0
1
0
2
0
1
1
0
0
1
0
1
0
0
1
1
1
1
0
0
2
0
1
0
0
1
0
0
0
2
1
0
1
1
0
0
0
2
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
2
0
0
0
1
0
0
0
0
0
2
1
1
0
1
1
2
0
0
0
2
0
0
0
0
0
0
1
3
1
0
1
2
0
1
2
0
0
1
1
0
2
0
2
0
0
0
2
1
0
1
0
2
0
0
0
0
0
1
1
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
2
0
1
2
0
1
0
1
0
2
1
2
0
1
0
0
0
0
3
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
2
1
0
0
0
1
0
1
0
0
0
0
2
0
0
1
0
0
0
2
2
0
0
0
1
2
1
0
0
2
0
1
2
0
0
0
0
2
0
1
0
0
3
4
2
2
2
2
0
1
0
0
1
1
0
0
0
2
0
1
1
0
2
1
0
8
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
3
0
0
0
2
2
3
0
0
0
2
0
0
0
1
1
0
2
0
0
0
0
0
0
2
0
1
2
2
6
0
2
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
1
0
0
2
1
0
2
0
0
0
0
0
0
2
1
0
0
0
0
2
2
0
1
1
0
0
0
0
2
0
1
0
1
0
0
0
2
1
0
0
2
0
0
0
0
0
1
0
0
1
2
0
2
2
0
0
2
0
0
1
0
2
0
1
0
1
2
1
1
2
0
0
2
0
0
4
0
2
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
1
2
0
2
0
0
0
0
1
0
0
2
2
0
0
0
2
0
1
0
2
1
0
0
0
1
0
0
0
1
2
1
1
0
0
0
0
0
2
0
0
0
2
1
2
0
0
0
3
2
1
1
9
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
2
1
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
1
2
0
2
1
1
0
0
2
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
1
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
2
2
0
0
0
0
0
0
0
1
0
0
1
0
0
4
1
1
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
2
2
1
0
1
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
1
2
1
0
1
1
5
2
0
0
2
1
0
1
2
1
0
0
0
0
0
0
2
1
1
2
0
0
1
3
1
0
0
0
2
2
0
0
0
2
0
1
1
1
1
0
0
1
2
0
2
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
1
2
0
0
0
0
1
0
0
2
0
0
2
0
2
0
0
0
2
0
0
7
2
0
0
1
0
0
1
2
0
0
0
0
0
1
4
2
0
1
1
0
3
0
2
0
1
0
2
1
0
0
0
1
0
0
0
0
1
2
1
0
2
0
0
0
0
0
0
2
0
1
0
0
0
2
0
1
0
2
0
0
0
0
0
3
0
0
0
0
0
2
0
0
2
0
0
0
5
0
2
2
0
2
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
2
0
0
1
1
0
2
0
0
2
0
2
0
0
2
0
3
1
2
2
0
0
0
0
0
0
0
1
0
0
2
2
0
0
2
0
0
0
0
0
2
0
0
1
1
0
2
0
7
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
2
1
2
0
1
2
1
1
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
2
0
3
0
2
0
3
0
0
1
1
0
0
1
1
2
0
0
1
0
0
2
0
0
2
0
2
0
0
0
1
1
1
2
1
0
0
0
2
0
0
0
0
1
1
0
1
0
1
0
0
1
0
1
0
0
0
1
0
0
0
2
0
1
2
2
0
0
1
0
0
0
0
2
0
2
1
0
1
0
0
1
1
2
2
0
2
0
0
1
0
0
0
2
0
0
2
1
1
1
0
0
0
2
1
0
1
1
0
0
1
0
0
2
2
2
2
0
0
2
0
0
0
0
0
0
2
0
0
2
0
1
1
0
2
0
1
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
1
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
1
1
0
9
2
0
0
1
0
1
0
2
0
0
0
1
1
2
0
0
2
0
0
1
0
0
0
2
0
1
2
0
1
0
1
1
1
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
2
0
0
2
0
0
0
1
1
0
1
0
0
3
1
0
1
0
1
0
0
0
2
0
1
0
0
0
1
2
1
0
0
2
0
2
0
1
0
0
0
2
1
0
0
0
0
1
1
0
0
0
0
1
3
0
0
1
2
0
0
1
1
0
0
3
0
0
0
0
0
0
0
2
0
0
1
0
2
2
1
0
0
0
1
0
0
1
2
2
0
0
0
0
0
1
0
2
2
2
1
0
0
0
0
1
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
1
2
0
1
3
0
1
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
1
0
1
0
2
0
0
0
2
3
0
1
1
1
0
2
0
0
1
0
0
0
0
0
2
1
1
3
1
2
1
0
0
0
0
0
1
1
0
0
0
0
0
0
2
2
0
0
0
1
1
0
3
0
1
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
1
1
1
0
1
0
2
2
2
0
0
1
2
0
0
0
1
1
0
0
0
1
1
0
0
1
0
1
0
0
0
1
2
2
0
1
1
0
2
1
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
2
0
2
0
0
0
0
1
0
2
0
0
2
1
2
0
0
2
0
0
2
0
0
1
0
0
0
0
2
0
1
1
0
0
0
1
0
0
0
0
0
0
1
4
2
0
0
0
0
2
0
0
0
0
0
1
1
0
2
0
1
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
1
1
1
0
3
2
1
0
0
0
0
0
1
1
2
2
0
2
2
0
0
0
0
0
2
2
0
2
0
0
0
0
2
1
0
0
2
1
0
2
0
0
0
2
0
2
1
0
0
1
0
0
0
1
2
0
1
0
1
0
3
0
0
1
3
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
1
2
1
2
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
4
0
0
2
2
0
0
0
0
2
1
1
2
1
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
2
0
2
1
1
3
0
0
0
1
1
0
0
1
2
0
1
2
0
0
0
0
0
0
2
4
1
0
0
1
1
0
1
0
1
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
1
0
0
2
0
2
0
0
0
2
1
0
0
0
1
2
0
0
0
0
2
1
0
2
1
0
0
0
0
1
2
1
0
2
0
2
0
2
0
0
0
0
7
0
1
5
1
0
2
4
0
1
1
0
2
2
0
0
0
1
2
2
1
1
0
0
0
1
0
2
1
2
0
0
0
0
0
0
1
1
0
2
1
0
0
1
2
0
1
2
0
2
0
1
1
0
0
0
0
0
2
1
0
0
0
0
1
2
3
0
0
0
0
0
0
0
0
1
0
0
0
2
1
2
0
2
0
0
0
0
0
3
0
2
1
2
0
0
1
0
0
0
0
0
2
1
1
0
2
0
0
2
0
0
1
1
0
0
1
0
0
0
2
1
0
1
0
1
0
1
1
0
2
1
0
2
0
1
0
0
0
0
2
0
0
0
1
0
0
0
1
0
1
1
0
2
0
0
2
1
0
0
2
0
0
0
2
1
2
0
1
0
1
2
0
0
1
2
0
0
0
2
1
1
24
0
1
1
2
0
1
0
0
1
1
0
0
1
1
2
1
2
0
0
0
3
0
1
0
2
1
0
1
0
1
0
0
2
0
0
0
1
0
3
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
1
0
0
1
0
2
0
0
0
1
0
0
0
0
0
1
1
0
2
0
0
2
2
0
1
0
1
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
2
2
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
1
0
0
5
0
0
1
0
0
0
2
0
3
1
1
1
1
2
0
3
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
2
0
0
0
0
2
0
0
2
0
0
1
0
0
2
1
0
1
0
2
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
3
2
0
2
0
1
0
2
1
2
0
0
0
2
2
0
0
0
0
0
2
2
1
0
2
0
2
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
1
0
2
0
2
1
0
0
0
2
1
1
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
1
2
1
0
0
2
0
0
2
0
0
0
0
2
0
0
1
0
0
2
2
0
1
1
1
0
1
1
0
4
0
0
1
0
2
1
1
2
0
2
0
1
2
0
2
0
0
2
2
2
1
0
0
0
0
0
2
0
1
1
0
0
1
0
2
2
0
0
0
0
1
2
0
0
0
0
0
0
1
1
1
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
5
1
0
2
0
0
1
0
1
0
2
0
0
1
1
2
1
1
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
4
0
1
1
1
0
2
0
0
2
1
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
1
0
0
2
0
3
0
0
0
1
0
2
0
3
0
2
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
2
0
1
1
2
0
3
1
0
2
1
1
0
0
0
0
0
0
1
0
1
0
1
0
1
2
1
0
0
0
0
2
2
0
0
2
0
1
0
1
1
0
2
0
0
2
1
3
0
2
0
0
0
0
1
0
0
1
2
4
0
0
0
0
0
0
1
1
1
2
0
0
1
1
1
0
1
2
2
2
0
0
0
0
0
1
1
0
2
0
1
0
2
0
0
0
0
0
2
1
2
0
0
0
0
0
1
2
1
0
0
1
1
0
0
0
0
0
2
1
0
0
0
0
4
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
2
0
1
0
1
2
0
0
1
3
0
3
2
3
0
0
0
0
0
0
0
2
0
0
2
1
0
0
3
0
1
0
1
0
0
0
0
1
0
0
2
0
0
2
0
2
1
1
0
0
2
0
0
1
0
0
2
0
0
2
2
0
1
0
0
0
0
1
2
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
2
1
0
0
1
0
1
0
0
0
2
2
2
0
0
0
0
0
2
2
0
0
1
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
1
2
1
2
3
0
0
0
2
1
0
0
0
0
2
2
0
1
0
1
2
0
1
1
1
1
2
0
1
0
0
0
2
2
0
1
0
1
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
2
0
0
1
0
0
0
0
2
1
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
2
1
1
0
2
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
2
2
0
2
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
2
0
1
0
0
2
0
0
0
1
2
2
4
0
0
1
0
1
2
0
2
0
0
0
0
2
0
0
2
0
0
0
2
1
0
0
0
3
3
0
0
1
0
0
2
2
0
0
0
2
1
0
1
0
2
0
1
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
2
2
2
1
0
1
1
0
0
0
0
0
0
1
1
0
0
2
0
1
2
1
1
0
0
0
0
2
0
1
1
0
0
1
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
1
1
0
1
0
3
0
1
1
1
0
2
0
0
0
0
0
0
1
1
1
0
1
4
0
0
6
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
2
0
0
1
1
0
0
1
4
0
0
0
1
0
1
1
0
0
2
5
0
0
0
0
0
4
2
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
2
3
2
0
0
0
2
2
0
1
0
0
2
1
0
0
1
0
0
2
4
2
0
0
0
2
0
1
2
2
0
1
2
2
0
1
2
2
0
0
0
1
7
1
0
0
0
0
0
1
0
2
0
0
1
0
0
2
1
2
1
2
0
0
2
0
0
0
1
2
3
0
1
1
0
1
0
2
1
1
0
2
0
2
0
1
2
2
1
0
0
0
0
0
1
2
0
0
1
1
0
0
7
0
0
0
2
0
0
0
2
0
0
1
0
0
1
2
0
2
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
1
1
0
2
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
2
0
0
2
2
0
1
0
0
0
2
1
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
1
1
2
2
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
3
1
2
1
0
0
0
0
1
2
0
1
0
1
0
0
1
1
7
1
0
0
0
1
0
1
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
2
0
1
2
2
2
1
0
1
0
1
0
0
2
0
0
2
0
2
0
2
2
1
0
2
2
0
0
0
0
0
0
2
0
0
2
2
1
0
0
1
0
0
0
0
1
0
2
0
0
1
1
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
1
2
2
0
0
2
0
1
2
0
0
2
2
0
2
1
1
0
1
0
0
0
5
0
3
0
0
0
0
0
0
0
0
2
1
1
1
0
0
0
2
0
1
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
2
1
1
0
1
0
0
0
6
0
0
0
0
1
0
0
0
1
0
2
1
0
0
0
0
1
0
0
1
1
4
0
0
0
0
0
0
1
0
1
2
0
0
0
0
3
1
0
0
0
0
0
0
0
1
0
0
5
0
0
1
2
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
1
0
1
0
0
1
2
0
1
1
2
10
0
1
0
0
0
0
0
4
0
0
0
0
1
3
1
0
2
0
0
0
0
0
1
0
0
0
2
0
1
0
0
1
0
1
0
1
2
0
1
2
1
0
0
1
0
0
0
5
1
1
1
0
0
2
0
0
1
0
0
1
1
0
0
0
0
0
1
0
2
0
2
0
1
0
0
1
1
1
0
0
0
2
0
0
2
0
0
0
1
0
0
0
3
1
1
1
1
0
4
3
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
2
1
2
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
2
1
1
0
0
3
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
3
0
2
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
4
1
0
2
0
0
2
0
2
1
0
2
2
0
0
2
0
0
1
0
2
0
1
0
0
1
0
0
0
0
0
0
0
2
2
2
0
1
2
0
0
0
0
1
0
0
1
0
1
1
0
2
2
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
1
0
0
0
2
1
0
1
0
0
0
0
1
0
0
0
0
0
2
0
1
0
2
0
2
0
1
2
2
1
0
1
0
2
2
0
1
1
3
0
1
0
0
0
2
2
1
2
1
2
0
2
0
2
0
0
0
0
1
2
0
0
0
1
2
1
2
1
0
0
0
0
0
1
2
2
0
0
0
0
2
0
0
0
0
1
2
0
1
2
0
0
0
0
0
1
0
1
0
2
2
0
2
1
0
0
2
0
0
0
0
0
0
3
0
0
2
0
1
3
0
0
0
0
0
2
0
0
0
0
0
0
2
1
1
2
0
1
0
2
0
0
1
2
0
1
0
2
1
0
0
0
0
0
1
2
3
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
1
2
1
2
2
2
0
0
2
1
0
2
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
1
2
2
0
1
0
0
0
2
1
2
0
0
0
0
0
0
2
2
0
0
4
0
0
2
2
2
1
2
0
1
0
0
0
0
0
2
2
0
3
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
1
1
2
0
0
0
5
3
0
0
0
1
0
2
1
0
2
1
0
0
0
2
1
0
0
0
0
0
2
1
2
4
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
1
0
1
0
2
0
0
0
1
0
1
0
0
1
1
0
2
0
1
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
1
1
0
0
0
2
0
0
3
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
1
1
1
1
2
0
0
0
1
0
3
0
2
2
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
1
2
2
0
0
0
0
5
1
2
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
2
1
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
1
0
2
0
2
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
2
2
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
1
2
0
0
1
0
0
2
2
2
1
0
0
0
0
0
0
2
0
2
0
3
0
4
0
2
2
0
2
1
0
0
0
2
2
1
1
0
1
9
0
0
0
1
0
2
0
1
0
1
0
2
1
0
1
1
2
0
0
0
1
1
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
2
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
4
0
0
0
1
6
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
1
0
0
1
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
2
0
0
2
0
2
0
1
0
0
0
2
0
0
1
1
2
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
3
2
1
0
0
1
0
0
0
0
0
1
0
0
0
3
0
1
1
0
0
0
1
0
2
0
0
2
2
2
2
1
0
0
2
2
0
0
1
0
0
1
0
2
0
0
0
2
0
0
2
2
0
0
2
0
0
1
0
0
0
0
2
0
1
0
0
2
0
0
1
0
0
1
2
2
0
1
1
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
1
1
0
3
0
0
0
1
3
0
2
0
0
3
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
2
1
0
0
0
0
0
2
0
0
1
0
2
0
1
0
2
0
4
0
0
0
1
0
0
2
0
3
0
1
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
1
2
2
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
1
2
2
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
2
0
0
1
2
2
2
0
0
2
0
1
0
0
1
1
2
2
0
0
0
0
1
0
2
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
1
0
2
0
0
1
2
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
1
1
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
2
1
0
0
0
2
2
0
0
0
2
0
0
0
0
4
1
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
2
0
0
0
0
0
0
0
0
3
1
2
1
0
0
0
0
0
2
1
2
0
0
2
1
0
0
1
0
0
0
2
1
3
2
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
2
0
3
0
0
0
0
0
1
0
0
2
1
0
1
0
0
0
1
0
0
0
1
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
1
0
1
0
0
0
1
0
1
0
0
0
2
1
0
0
0
0
2
1
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
2
2
0
0
1
2
1
1
0
0
0
1
2
2
0
0
1
0
0
0
1
0
0
2
2
0
0
2
1
2
0
0
0
0
0
0
1
0
0
9
1
0
0
0
0
2
0
2
0
0
0
0
1
1
0
0
2
2
0
1
1
0
0
1
0
1
2
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
2
0
0
0
1
1
1
1
0
2
0
0
0
0
1
0
1
0
3
1
2
2
0
0
2
0
0
2
0
0
0
0
0
1
0
1
0
0
0
3
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
2
1
0
0
0
2
0
0
0
0
0
2
1
0
2
1
0
1
2
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
2
2
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
2
2
0
0
0
1
1
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
1
2
1
0
0
2
1
2
1
2
0
0
0
1
0
2
0
1
1
2
0
1
1
0
0
1
0
2
0
1
0
0
1
0
0
0
0
0
2
1
1
0
1
2
0
0
1
0
0
0
3
0
0
0
0
1
0
0
0
0
1
0
0
1
2
0
0
2
2
1
0
0
2
0
0
0
0
0
2
0
0
1
1
1
0
1
0
2
2
0
0
1
0
0
0
1
0
0
1
0
0
1
1
2
0
3
0
0
1
0
1
0
0
0
0
1
2
0
2
0
0
2
2
1
0
0
0
0
1
1
0
0
1
0
0
2
0
2
0
1
0
1
1
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
2
1
1
1
0
0
2
1
0
0
0
2
0
2
0
1
2
0
3
0
0
2
0
1
0
0
1
2
0
2
1
0
1
0
2
0
0
0
1
1
1
0
2
2
1
0
1
0
0
0
1
1
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
2
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
1
0
0
0
0
2
2
0
1
1
0
2
2
0
2
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
1
2
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
2
1
0
2
1
0
2
0
1
2
1
0
0
1
2
2
2
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
5
0
0
1
0
0
0
0
0
0
1
2
0
0
2
2
1
0
2
0
0
1
1
0
0
0
0
1
1
0
0
0
0
2
2
0
1
1
2
0
1
0
0
0
0
2
1
0
0
0
0
0
2
0
2
0
0
1
0
0
1
1
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
2
0
1
0
2
0
0
0
0
0
1
0
1
0
0
2
0
0
0
1
0
0
1
0
0
0
0
1
0
2
0
0
1
2
0
2
0
0
1
0
1
0
0
0
0
0
0
3
0
0
0
1
0
1
4
0
0
0
0
0
2
1
0
0
0
0
1
1
0
0
0
0
1
1
0
2
0
0
2
2
0
1
0
0
1
0
0
0
0
0
0
2
1
1
0
0
0
0
3
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
2
1
1
2
0
1
0
2
0
0
0
2
0
0
2
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
1
0
0
1
0
2
2
0
0
0
1
1
2
0
0
0
1
0
2
0
0
0
0
2
1
0
2
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
1
1
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
3
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
1
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
2
0
2
0
0
1
2
0
0
0
0
1
0
2
0
0
2
1
2
0
0
0
0
0
1
3
0
0
0
0
0
2
1
0
0
1
0
1
1
0
0
0
0
0
1
3
0
2
1
2
0
2
0
1
0
0
0
0
0
0
0
0
0
1
2
2
1
2
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
3
2
0
0
0
0
2
3
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
2
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
3
2
0
0
2
0
0
0
0
0
0
0
0
2
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
2
3
0
1
1
0
2
0
1
0
2
2
0
2
0
2
0
0
0
1
0
1
2
0
2
0
0
0
1
0
0
2
1
0
1
0
0
2
0
0
0
2
2
0
0
0
0
0
0
2
2
0
0
0
1
0
0
1
1
1
0
0
0
0
2
6
2
0
2
0
7
1
2
0
2
2
0
2
0
1
0
0
0
0
0
1
1
2
0
0
1
0
0
1
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
4
3
1
2
0
0
1
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
1
2
0
0
2
2
0
0
1
1
1
2
2
0
0
0
0
0
1
0
1
0
4
1
0
0
1
1
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
1
0
0
0
0
1
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
2
0
0
2
0
2
2
2
4
1
1
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
6
0
1
2
1
1
1
0
0
2
0
0
1
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
1
0
1
0
2
0
2
0
0
0
0
0
0
2
1
0
0
0
2
2
0
0
0
0
0
1
3
1
0
0
0
0
0
2
2
0
0
1
2
0
2
2
1
0
0
0
1
0
0
0
0
0
0
3
0
1
0
2
0
0
0
0
0
1
0
0
0
2
0
2
2
0
2
1
0
0
0
0
2
0
2
2
0
1
0
2
2
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
1
1
0
0
2
0
0
0
1
1
1
3
0
0
1
0
1
0
2
0
0
1
0
1
0
2
2
0
0
0
2
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
1
2
0
2
0
0
0
0
0
1
2
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
3
0
1
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
2
2
0
0
0
1
1
0
2
1
0
0
0
0
2
0
1
0
0
0
2
0
2
1
0
1
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
3
0
0
1
2
1
0
0
1
1
0
0
0
1
0
1
1
0
0
0
0
0
2
0
1
2
0
0
1
0
0
2
1
1
1
0
0
0
0
1
0
1
2
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
2
0
0
2
0
1
2
0
0
1
1
2
1
0
1
0
1
0
0
0
0
2
0
0
1
1
0
0
0
0
2
1
0
0
2
0
2
0
0
1
0
1
0
0
1
0
0
2
1
0
0
0
1
0
1
4
2
0
0
0
0
1
0
0
0
0
1
2
0
0
1
0
0
3
0
2
0
1
0
0
1
2
0
0
0
2
1
0
0
2
2
3
2
1
2
1
1
0
0
0
1
1
0
0
1
3
0
0
0
0
0
1
0
0
2
1
0
1
1
1
2
0
0
0
0
1
2
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
4
2
0
0
2
0
0
1
0
0
1
0
1
0
1
0
0
0
1
0
1
2
0
0
0
0
2
0
2
0
2
2
1
1
0
2
0
2
0
2
0
1
2
0
1
0
1
0
3
0
0
2
0
0
2
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
2
0
0
2
0
2
0
2
0
0
2
0
0
0
0
0
0
0
3
0
2
0
2
0
2
0
0
0
2
0
0
2
2
0
0
2
1
2
0
1
3
2
0
2
0
0
1
1
0
0
2
0
0
0
0
2
2
0
0
1
0
2
2
0
2
0
0
0
2
1
0
0
2
0
2
0
0
0
0
0
2
0
1
0
0
2
0
0
2
0
1
2
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
1
1
0
0
0
0
1
0
0
1
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
1
0
2
0
0
0
2
2
2
1
0
0
0
2
1
0
0
0
0
2
0
0
1
0
1
0
3
0
0
2
2
0
2
0
0
0
1
2
0
0
0
2
2
1
0
2
2
2
0
0
1
0
1
1
2
0
3
0
2
2
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
2
0
2
1
0
0
0
0
0
1
1
0
2
0
0
2
0
0
0
0
2
0
0
1
2
1
0
0
2
0
0
0
0
1
0
0
3
0
1
0
0
0
2
0
0
0
1
1
1
0
1
2
1
0
2
0
1
2
1
0
1
0
0
0
0
1
0
1
0
2
0
0
0
0
2
1
0
0
0
0
0
2
0
0
1
1
0
1
0
0
2
2
0
2
0
0
1
0
1
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
2
0
0
0
1
0
0
0
2
2
3
0
0
0
0
0
0
0
2
2
0
1
0
0
2
3
0
1
3
1
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
1
1
2
0
0
3
1
2
0
0
0
0
0
0
0
2
0
2
0
0
2
1
1
0
2
2
0
2
0
0
1
0
0
0
0
0
0
1
0
0
1
0
2
1
1
1
1
0
2
0
0
2
0
0
0
1
0
0
2
0
2
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
5
1
0
0
0
0
0
0
1
2
0
0
0
0
1
2
3
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
1
1
1
2
2
2
1
0
0
0
0
1
5
1
0
0
0
0
0
1
0
2
0
0
1
3
0
1
2
2
0
1
0
0
0
0
2
0
0
3
0
0
1
1
0
0
0
0
0
0
0
2
0
1
2
2
0
0
2
0
0
2
0
1
0
1
0
1
2
0
1
0
1
0
2
0
0
0
1
1
0
1
0
1
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
3
1
0
2
0
0
1
0
1
1
0
0
0
2
2
0
1
0
0
0
0
0
0
1
0
3
0
0
2
0
0
0
1
1
0
0
1
0
0
1
2
1
0
0
2
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
2
0
0
0
0
1
1
0
1
0
0
2
2
0
2
1
0
1
0
2
0
0
0
2
1
2
1
0
2
1
1
0
2
0
0
1
0
4
0
2
2
0
1
0
0
0
0
0
0
0
0
1
1
0
0
2
3
0
2
0
0
3
0
1
0
1
1
1
0
0
0
0
1
1
0
2
2
2
2
0
2
2
0
0
2
0
0
0
0
0
1
2
3
0
2
0
0
0
0
0
0
0
0
1
2
1
2
0
0
2
0
0
0
0
1
1
0
0
1
1
0
1
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
2
0
0
0
0
0
1
0
0
2
2
0
0
1
0
0
1
2
2
1
2
0
0
1
0
0
1
1
0
0
2
0
0
0
2
2
0
0
1
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
2
2
0
0
0
1
2
0
2
0
2
1
0
0
0
1
2
0
0
2
1
3
1
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
2
0
2
0
2
2
0
1
0
0
0
3
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
4
0
0
2
0
1
1
1
1
2
0
3
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
1
1
2
0
0
0
2
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
2
0
2
0
0
2
1
1
1
0
2
0
1
0
1
1
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
2
0
0
0
0
0
0
1
2
0
1
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
1
1
1
0
0
0
2
1
0
0
0
0
2
0
1
0
0
0
2
2
0
2
1
1
0
1
2
0
0
0
0
0
1
0
0
2
1
0
0
1
0
0
1
0
0
0
1
2
1
0
0
2
0
0
1
0
0
0
0
0
0
2
0
2
1
0
0
2
1
3
2
1
0
0
1
0
0
0
0
4
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
2
0
2
2
2
0
1
1
1
3
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
1
1
0
0
0
0
3
0
0
1
3
2
0
0
0
1
0
0
0
0
0
0
1
1
1
1
0
1
0
0
0
1
0
1
2
0
2
0
0
0
0
0
0
0
0
1
2
1
0
1
0
0
0
0
1
0
0
0
0
0
1
1
1
0
2
1
0
0
2
1
0
1
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
3
2
0
0
0
0
4
0
2
0
2
2
0
0
0
2
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
1
1
0
1
0
2
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
2
0
3
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
2
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
3
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
1
0
2
0
2
0
2
0
0
0
1
0
2
0
0
0
0
1
1
0
1
0
0
0
2
2
0
3
0
0
1
0
0
0
0
2
1
3
2
0
0
0
0
1
0
2
2
0
1
0
0
0
1
1
1
0
0
0
2
2
0
1
2
2
0
1
0
2
1
0
2
0
0
0
0
2
1
0
0
2
0
0
0
0
1
2
0
0
2
1
1
0
1
0
0
0
0
0
1
0
0
1
0
2
0
0
2
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
1
0
2
1
2
0
0
0
1
0
3
3
3
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
1
0
2
2
2
0
0
1
0
1
0
1
0
0
0
0
0
0
0
2
0
1
1
0
0
0
1
0
2
0
0
0
0
0
0
0
2
1
2
0
0
1
0
1
0
1
2
0
1
1
0
0
0
0
0
1
1
0
2
0
0
0
1
0
0
0
0
0
0
1
2
2
0
1
0
2
2
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
1
2
2
0
1
0
0
0
0
0
0
0
1
2
2
2
1
2
1
1
1
0
1
1
0
2
1
1
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
2
2
0
0
0
1
1
0
0
0
0
2
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
2
1
2
1
0
2
0
1
0
1
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
2
0
0
3
0
2
0
1
2
0
0
0
0
0
0
0
1
1
0
1
0
2
1
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
1
1
0
2
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
2
0
1
0
1
0
1
0
0
1
0
0
1
2
0
1
0
2
0
1
2
1
0
0
2
1
2
1
0
1
1
0
2
1
0
0
1
0
0
2
1
0
1
1
1
0
0
0
2
1
1
0
2
1
0
2
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
2
2
1
0
0
2
1
0
0
4
0
2
1
0
1
2
2
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
2
0
3
0
0
2
0
0
2
0
0
1
1
0
0
0
0
0
0
0
2
2
1
0
2
1
0
0
0
0
0
1
1
2
1
0
2
0
1
0
2
0
2
0
1
0
0
1
0
0
0
1
0
1
0
0
1
0
0
3
0
2
0
0
0
0
0
0
0
2
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
1
3
0
2
2
0
0
2
0
2
0
1
3
0
0
2
0
0
2
0
0
0
1
1
0
0
1
2
1
2
0
0
0
0
0
0
2
0
0
2
0
0
1
0
1
1
1
0
0
0
0
0
0
0
3
0
0
0
2
2
0
0
0
2
1
0
1
1
0
1
0
2
0
0
3
0
0
0
1
0
0
0
0
2
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
1
2
1
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
1
0
2
2
0
0
0
2
0
0
0
0
2
1
1
0
0
2
1
0
2
0
0
1
0
0
1
0
0
0
0
2
0
2
0
3
0
0
1
1
3
0
0
0
1
1
2
0
2
0
3
3
0
0
0
3
2
1
0
1
0
0
0
0
0
1
2
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
2
2
0
1
0
1
0
0
1
2
0
1
0
2
0
0
0
0
0
1
0
1
0
2
0
1
2
0
2
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
1
0
1
2
2
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
3
0
4
2
3
0
2
0
0
2
0
0
0
2
1
0
0
0
1
2
0
2
1
2
0
0
1
2
0
2
0
0
0
0
2
0
1
2
0
0
2
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
5
1
0
0
0
0
0
0
0
0
0
2
2
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
1
1
0
0
0
0
2
0
2
0
1
0
0
0
1
0
1
0
0
1
1
0
2
0
0
0
0
1
0
0
0
1
0
3
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
1
0
0
1
1
0
2
0
1
1
1
1
2
0
0
0
0
0
0
0
2
0
0
1
0
1
2
1
0
0
0
1
2
0
0
3
2
2
0
0
0
2
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
1
0
2
3
1
0
0
2
1
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
2
0
0
2
4
1
0
0
1
0
1
1
0
1
0
2
0
0
0
0
0
2
0
0
0
0
1
1
0
0
2
0
2
1
0
0
0
1
2
0
0
2
0
2
2
1
0
1
0
1
2
0
0
2
0
0
0
2
1
2
0
2
0
0
1
0
0
2
1
1
2
0
0
2
0
0
0
0
0
4
1
0
2
0
1
1
0
0
0
0
0
2
0
0
1
0
1
0
0
1
1
0
0
1
2
3
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
3
2
0
0
0
1
0
0
0
1
0
1
0
0
0
1
1
0
2
0
0
0
0
2
0
0
0
0
2
1
0
0
0
2
0
1
0
2
0
0
2
0
1
2
1
0
2
1
2
0
0
0
1
1
1
1
0
2
0
0
0
0
1
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
1
3
0
1
0
0
2
1
0
0
2
1
1
0
0
0
0
1
0
2
0
2
1
0
0
1
1
1
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
2
0
2
2
2
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
3
0
0
1
0
0
0
0
1
0
2
0
1
0
1
0
0
0
0
1
1
2
0
0
0
0
0
0
1
2
0
2
1
0
2
0
0
1
0
0
0
2
2
1
1
1
0
0
2
0
0
1
1
0
2
0
0
0
0
1
1
1
0
0
0
2
0
0
0
2
1
0
0
2
1
2
0
2
0
0
0
0
2
1
2
0
0
1
1
0
0
2
2
1
0
0
2
0
1
0
2
0
0
0
0
2
0
1
2
1
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
2
0
2
0
0
2
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
1
1
2
0
0
0
2
0
0
0
0
0
1
0
3
0
0
0
2
1
0
0
3
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
2
1
0
0
0
0
0
1
0
2
0
0
0
0
2
1
0
1
1
0
0
1
0
2
0
2
1
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
2
0
0
0
0
0
2
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
1
1
1
1
0
0
0
1
1
1
0
1
2
1
0
1
0
0
0
3
0
1
2
1
0
1
0
0
0
0
1
2
1
0
0
0
0
1
2
0
2
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
2
0
2
2
0
0
0
0
0
3
0
0
0
0
0
1
0
1
0
0
0
0
2
0
1
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
4
0
0
2
0
0
1
0
2
0
0
1
2
2
0
4
2
0
3
1
0
0
0
2
1
2
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
3
0
0
0
0
2
0
2
0
0
1
0
1
0
1
2
0
0
0
0
0
1
0
4
1
0
1
0
0
0
1
0
0
0
3
0
2
0
1
0
0
0
0
2
2
0
0
0
2
0
0
0
0
2
0
2
0
0
2
1
0
1
3
0
0
0
1
0
0
0
0
0
0
0
1
3
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
2
1
2
1
1
1
0
0
0
0
0
1
0
0
1
0
0
2
2
0
1
2
1
2
1
1
0
2
0
0
2
1
0
0
1
2
2
1
3
1
0
0
0
1
2
0
1
0
3
1
2
0
2
1
1
2
0
0
0
1
0
0
0
0
0
2
1
2
0
0
1
1
0
2
0
0
2
1
2
0
1
0
2
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
1
2
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
2
0
0
1
1
0
0
0
1
1
2
1
0
0
1
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
2
2
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
2
2
2
0
0
0
1
0
0
2
0
0
1
3
0
0
1
2
0
0
2
0
1
0
0
2
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
1
0
0
0
0
2
1
0
2
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
1
0
2
0
0
2
0
0
1
2
0
1
1
0
0
1
0
0
2
2
0
1
2
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
3
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
2
0
2
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
3
2
0
5
2
0
0
1
2
0
0
1
0
0
2
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
1
4
0
2
1
0
0
0
0
2
2
0
0
4
2
0
0
0
1
0
0
2
0
0
0
0
2
0
1
1
0
2
0
0
1
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
5
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
1
0
0
2
0
2
0
1
3
2
0
2
0
0
2
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
3
1
0
2
0
2
1
0
1
1
0
0
2
0
0
0
0
0
0
2
0
3
0
1
3
0
3
0
0
2
0
0
0
0
0
1
0
0
0
7
1
1
0
12
2
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
1
0
1
1
1
0
0
0
0
0
0
0
12
0
0
2
3
1
0
0
1
0
3
0
0
1
0
2
0
2
2
0
0
0
0
0
2
2
0
0
2
0
2
2
3
0
0
0
2
0
0
0
0
0
2
2
2
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
1
0
2
0
2
0
1
0
2
2
1
1
0
0
2
1
6
0
4
2
1
2
2
0
2
0
1
2
1
0
2
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
2
1
3
6
2
2
0
2
1
2
0
0
2
2
0
0
0
0
1
0
0
0
0
2
2
0
2
2
0
0
2
0
0
0
2
2
0
0
0
0
2
4
1
2
0
1
0
0
0
1
1
0
2
2
2
1
0
2
0
0
0
0
1
1
0
2
0
1
1
2
2
0
0
1
0
1
2
2
0
0
1
0
2
0
3
0
2
2
2
2
1
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
3
2
2
2
0
0
0
0
0
0
0
0
2
2
2
1
2
0
2
0
2
0
0
2
0
0
2
2
0
0
2
0
0
0
0
0
1
2
2
1
2
0
0
1
0
1
0
1
0
0
2
0
2
2
2
0
0
1
0
0
3
0
0
0
0
2
1
2
0
0
0
0
1
2
0
0
1
2
1
0
2
1
0
0
0
0
0
1
0
2
0
0
0
2
0
2
1
2
0
0
1
2
1
0
2
0
1
1
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
1
2
0
0
2
3
2
2
0
0
0
0
0
0
2
1
0
0
0
0
2
1
1
0
0
1
2
0
3
0
0
0
2
0
2
0
0
0
0
0
0
0
1
1
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
1
0
0
6
2
2
0
0
2
0
0
0
0
0
1
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
1
0
0
1
2
2
1
1
0
0
0
1
0
0
1
0
0
0
1
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
2
1
2
2
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
2
0
2
1
1
0
3
0
3
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
2
2
0
1
0
3
2
0
2
2
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
2
0
2
2
0
0
0
2
2
2
0
0
1
0
0
0
0
0
0
0
1
1
0
0
2
2
2
1
0
1
1
0
0
1
1
1
0
0
0
0
1
0
0
1
2
1
0
0
1
1
0
1
0
0
2
0
0
0
0
2
1
0
0
2
0
0
0
0
2
2
1
1
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
1
0
0
0
1
2
1
2
1
1
0
0
0
0
0
1
0
0
2
0
0
2
1
2
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
3
0
0
0
0
0
0
1
0
0
0
2
1
0
1
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
2
3
2
0
0
0
1
0
0
0
0
0
1
0
0
0
2
2
1
2
0
1
0
0
0
2
3
0
0
0
0
0
0
0
2
0
0
0
2
1
1
0
0
0
1
0
2
1
0
0
0
2
0
0
2
0
1
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
3
0
2
2
2
2
2
1
0
0
0
0
0
0
0
1
1
0
1
0
2
0
0
0
0
2
1
0
1
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
2
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
1
2
1
0
0
0
0
0
0
2
1
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
4
2
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
3
0
0
1
0
1
0
0
1
0
0
2
0
0
0
3
2
0
0
0
0
3
0
0
0
0
0
1
0
1
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
1
0
2
0
0
1
0
0
1
0
1
0
0
0
0
1
0
2
0
2
2
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
2
0
2
1
1
1
1
0
2
0
0
0
0
0
0
1
2
0
0
0
0
2
0
1
0
1
3
0
0
0
0
0
0
0
0
0
2
0
2
2
2
1
0
0
0
0
0
1
0
1
0
1
0
0
1
0
2
1
0
1
1
0
0
0
2
0
0
0
2
2
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
1
0
0
0
1
1
0
0
0
2
0
0
0
0
1
0
1
0
0
2
1
1
2
0
2
3
0
0
0
0
0
0
2
0
0
0
1
1
0
0
1
1
0
0
2
0
0
0
0
0
1
0
0
0
0
3
0
2
2
0
3
1
3
0
0
0
0
2
0
0
0
0
0
1
2
1
0
0
0
0
1
2
1
1
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
2
2
0
0
2
1
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
2
0
2
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
3
2
2
1
1
3
1
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
1
2
0
0
2
1
2
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
3
0
1
1
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
1
0
0
2
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
1
0
0
1
0
0
0
1
0
2
0
0
2
0
0
0
0
0
2
2
1
2
0
0
1
0
1
0
0
1
0
0
0
2
0
2
0
0
0
2
0
0
0
0
3
0
3
0
0
0
0
2
1
0
1
2
1
2
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
2
1
0
0
0
0
0
0
1
0
0
3
0
2
0
0
0
0
0
2
0
0
0
5
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
2
1
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
1
0
0
2
1
0
1
0
0
0
0
2
0
0
0
0
2
3
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
2
0
0
1
0
0
0
1
2
0
0
2
2
0
0
2
1
1
2
1
0
0
0
1
2
1
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
2
2
2
2
2
0
0
0
0
1
0
2
0
0
3
0
0
0
3
0
2
1
2
0
0
1
1
0
2
1
0
0
0
0
2
6
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
1
2
0
0
1
0
2
0
0
0
1
0
1
2
2
0
2
1
2
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
2
2
0
2
0
1
0
0
0
0
3
0
0
0
0
2
0
1
2
0
1
0
2
2
0
0
0
2
0
0
0
2
2
0
1
0
2
1
0
0
0
0
0
1
0
2
2
1
0
2
0
2
2
0
1
0
1
0
1
1
2
0
0
0
0
2
0
0
0
0
0
1
2
1
0
0
2
0
0
0
2
1
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
3
0
0
0
0
0
2
0
0
1
2
0
2
1
0
1
0
0
0
1
0
0
0
1
0
4
0
1
1
1
0
1
0
2
1
2
0
4
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
2
2
0
0
2
1
2
0
2
2
2
0
0
0
1
0
2
0
0
1
0
0
1
1
1
0
0
0
0
2
1
0
0
1
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
1
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
2
0
1
1
0
0
0
1
2
0
1
0
0
0
0
0
0
0
2
0
2
2
1
2
0
4
0
1
0
0
0
0
2
2
2
0
2
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
1
2
0
0
0
0
1
0
2
0
0
0
0
2
1
0
2
0
0
0
0
1
2
0
0
0
0
0
0
2
0
1
0
0
1
1
2
0
0
0
0
0
0
3
0
1
2
0
3
0
0
0
2
1
3
1
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
3
2
1
0
0
2
2
0
1
0
1
0
2
0
1
0
0
5
1
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
1
2
2
1
1
0
0
2
0
0
1
0
3
0
2
5
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
3
0
0
2
0
0
0
1
0
0
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
1
0
0
2
0
2
0
2
0
0
0
2
0
0
2
1
2
0
0
0
3
0
0
0
0
0
0
0
1
2
0
2
1
1
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
1
0
6
0
0
1
0
1
0
1
0
2
0
2
1
0
2
2
1
2
1
1
0
0
1
0
0
0
1
2
1
0
1
2
1
0
0
1
0
2
0
0
1
0
0
2
0
2
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
1
0
0
2
1
0
1
0
0
1
0
1
0
2
0
0
2
1
0
0
0
0
2
0
0
0
0
1
2
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
2
0
2
0
2
0
1
0
0
0
1
1
1
0
2
0
0
0
2
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
2
0
1
0
1
0
0
0
0
1
1
0
0
1
3
0
0
0
3
1
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
1
1
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
2
0
1
0
0
0
0
2
1
0
0
1
1
0
3
0
0
0
1
1
0
0
0
0
1
0
1
0
1
0
2
0
0
0
0
2
0
2
0
1
0
0
0
0
0
1
0
2
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
2
0
0
0
1
0
1
0
2
4
0
0
0
0
2
0
0
0
2
2
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
2
0
1
1
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
2
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
1
0
1
0
2
1
0
0
1
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
2
1
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
3
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
4
0
0
0
2
1
0
2
1
0
0
0
2
0
0
2
1
1
0
0
0
2
0
0
0
0
1
0
2
0
0
1
0
0
1
0
0
1
0
0
1
0
0
1
1
2
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
2
0
0
0
3
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
1
0
0
1
1
2
0
1
0
2
0
0
0
2
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
1
0
2
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
2
0
0
1
0
2
0
2
0
0
0
2
0
2
2
0
2
0
2
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
3
0
2
1
3
0
1
2
0
2
0
0
0
1
3
1
0
2
1
0
0
0
0
0
0
0
2
2
1
1
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
1
0
1
0
0
0
1
1
2
1
0
0
0
2
1
1
0
2
0
1
1
0
0
0
0
2
0
0
0
1
0
0
0
1
2
0
0
0
1
0
2
0
0
2
0
0
0
2
2
3
2
2
1
0
0
0
2
0
1
0
0
1
2
2
0
0
0
1
1
0
0
2
2
1
0
0
0
0
2
0
0
3
0
0
0
0
0
2
0
0
0
2
2
0
0
0
2
1
1
0
1
1
0
0
0
1
0
1
0
1
0
0
1
1
2
0
0
0
0
0
0
0
3
0
1
0
1
0
0
0
0
0
1
1
0
0
0
2
0
2
0
0
0
2
0
0
1
2
0
1
0
0
0
0
1
0
1
2
0
2
0
1
1
0
0
0
0
0
0
2
1
0
2
0
2
0
2
1
2
0
0
1
0
0
0
1
2
2
0
0
1
0
0
0
1
2
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
2
2
1
1
0
2
2
0
0
0
0
0
0
1
0
0
0
1
0
2
0
1
3
1
0
0
0
1
3
0
1
2
0
0
0
0
0
0
1
0
1
1
1
2
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
1
1
1
0
0
1
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
3
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
2
0
1
2
0
0
0
1
0
0
0
0
1
1
1
2
2
0
1
0
0
1
0
2
0
0
0
0
1
1
0
1
1
0
0
1
3
2
1
2
2
0
1
0
0
0
0
2
0
1
1
2
0
1
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
2
2
0
2
0
1
0
0
0
0
1
0
1
0
2
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
1
0
2
2
1
0
0
0
2
2
0
2
2
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
7
1
0
0
2
1
2
0
0
0
1
0
0
2
1
2
0
2
0
2
0
0
0
0
1
0
0
0
2
0
2
0
0
0
1
1
0
2
0
1
3
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
1
0
1
1
0
0
2
2
1
2
1
0
2
1
0
1
0
0
0
1
0
2
2
0
0
0
0
0
2
0
0
0
2
1
0
0
1
0
1
0
2
0
1
1
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
2
1
0
1
2
1
2
0
1
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
4
0
0
0
0
1
0
2
0
0
2
0
1
0
0
0
0
0
0
2
1
0
2
1
1
1
0
0
1
2
0
0
0
0
0
1
2
2
0
0
1
0
0
2
0
0
1
0
1
1
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
3
2
0
0
0
0
0
3
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
1
0
2
0
0
0
1
0
0
0
0
1
2
2
0
2
0
0
0
1
3
0
0
0
0
0
2
2
0
0
1
2
2
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
4
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
1
0
2
2
0
2
0
2
2
1
0
1
0
0
1
0
0
0
1
2
0
1
0
0
1
2
1
1
2
5
2
1
0
0
1
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
1
1
1
1
0
0
1
1
0
0
0
0
1
2
2
0
0
2
0
0
2
0
0
2
0
1
1
0
1
2
0
2
0
0
0
1
1
0
0
0
0
0
0
3
0
0
0
0
0
1
1
3
0
2
1
0
0
2
0
0
0
0
0
0
1
0
2
0
1
0
1
0
0
0
2
2
0
0
0
0
0
0
0
2
0
1
1
1
0
0
2
0
0
0
0
1
0
0
2
0
1
0
1
0
0
0
0
1
0
1
0
0
3
1
0
0
0
1
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
1
3
1
1
0
2
0
1
1
0
0
0
2
1
0
1
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
1
0
2
2
0
0
0
1
0
0
0
0
0
2
1
1
1
2
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
1
0
0
0
2
0
1
2
1
1
0
2
0
0
2
0
0
0
1
0
0
2
0
1
1
1
0
0
0
0
1
2
0
2
0
0
0
0
2
0
0
2
0
3
0
0
2
0
0
0
0
0
0
1
0
2
1
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
1
2
0
0
1
0
2
0
0
2
0
0
0
1
0
0
0
2
1
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
1
0
0
2
0
0
2
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
2
0
1
2
0
0
0
1
0
0
2
2
0
0
1
0
1
0
0
0
1
2
0
0
0
0
0
0
0
1
1
2
0
2
0
0
0
0
0
2
0
0
1
1
0
0
0
0
3
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
2
2
0
0
0
2
1
0
0
0
0
1
0
2
0
2
0
0
0
0
0
1
0
1
0
0
2
0
0
0
1
1
0
0
0
1
2
1
0
0
2
0
0
1
2
0
0
0
0
0
2
0
0
0
0
2
3
0
0
2
1
0
2
3
0
1
2
0
0
0
0
0
0
0
1
0
0
0
1
1
2
0
0
0
0
1
2
1
0
0
1
2
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
3
1
2
0
2
0
0
0
0
2
0
0
2
0
3
0
2
2
2
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
2
0
0
1
0
0
0
1
0
2
0
0
2
0
1
2
0
1
0
0
1
0
0
0
0
0
2
1
2
1
0
0
0
2
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
4
3
2
0
1
1
0
0
1
0
0
0
0
2
1
0
0
2
0
0
0
2
0
0
1
0
1
1
0
1
0
2
0
0
2
0
0
3
1
0
0
0
2
0
2
0
1
1
1
2
0
0
0
0
1
0
1
0
2
0
1
2
1
0
0
0
0
0
4
0
1
0
0
0
1
0
0
3
1
0
0
1
1
2
0
1
0
1
0
2
0
0
0
0
1
0
0
2
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
2
0
1
2
1
0
0
1
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
5
0
0
1
0
0
2
0
1
0
0
0
0
0
0
1
1
2
0
1
0
0
0
0
4
1
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
2
1
0
0
0
0
2
1
0
1
0
0
0
2
0
0
0
1
0
0
2
0
0
2
1
0
0
2
0
0
0
2
0
0
1
0
0
0
1
0
2
0
0
1
0
2
2
0
1
1
0
1
0
1
0
0
0
0
0
0
2
2
1
1
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
3
0
1
0
0
0
0
2
0
0
2
1
1
1
0
0
0
0
2
0
0
0
0
0
0
0
1
1
2
0
0
1
2
0
0
0
0
0
1
3
0
0
2
0
0
4
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
1
3
2
0
0
3
2
0
0
0
0
1
0
0
0
0
0
2
0
1
2
0
7
0
1
2
4
2
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
1
0
0
2
0
1
0
0
1
0
1
0
2
5
1
0
0
2
0
0
1
0
0
0
1
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
2
1
1
0
2
1
0
0
1
1
0
1
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
2
1
0
2
0
0
2
0
2
2
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
2
0
1
1
2
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
2
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
2
0
1
0
0
0
2
0
2
1
0
2
1
0
0
2
1
0
1
1
1
0
1
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
2
2
1
2
0
0
0
0
0
0
3
1
0
2
0
0
1
0
0
0
1
0
0
2
2
0
0
0
1
1
1
2
1
0
1
2
0
2
0
2
0
2
0
0
0
2
0
2
0
0
0
2
0
1
0
2
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
2
2
2
0
0
2
0
0
0
1
1
1
1
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
2
0
0
2
0
0
0
5
0
2
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
2
1
1
0
0
0
0
0
2
0
0
0
1
0
2
3
0
0
0
0
0
1
2
0
0
0
0
2
2
1
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
1
0
1
2
3
0
0
1
0
2
2
0
1
0
0
0
1
0
4
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
1
0
1
1
0
0
0
2
0
0
1
0
1
3
1
0
2
0
0
0
0
1
0
1
1
2
2
0
0
0
0
0
0
1
3
0
1
0
1
0
0
0
0
2
0
2
1
0
0
0
0
0
1
3
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
2
0
1
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
2
1
2
0
0
1
0
2
0
0
0
0
0
0
0
1
2
1
0
0
1
0
0
1
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
2
1
2
0
0
0
0
0
1
0
0
1
0
0
0
1
0
2
0
0
0
3
0
2
2
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
1
0
1
2
0
1
2
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
1
0
2
0
1
2
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
1
0
0
2
0
1
0
0
2
0
2
0
2
1
0
0
0
1
0
0
0
0
0
0
2
2
2
1
0
0
2
2
0
0
0
0
2
0
0
2
0
0
0
0
0
1
2
0
2
1
0
0
2
3
2
0
0
2
0
0
1
0
0
0
0
2
0
0
0
2
1
0
0
0
2
3
0
1
2
0
0
0
1
1
1
2
0
0
2
0
0
1
0
0
1
1
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
1
2
2
0
0
1
0
2
0
0
0
0
2
0
1
0
2
2
0
0
2
0
0
4
1
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
1
0
2
0
2
0
0
1
0
1
0
0
2
0
2
1
0
1
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
1
2
0
2
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
3
0
0
0
1
0
0
1
1
0
1
0
2
0
0
0
2
2
0
2
0
2
0
0
0
0
2
1
0
0
0
0
1
0
1
0
0
2
2
1
0
0
0
2
0
0
0
3
2
2
2
0
0
0
1
0
1
1
0
2
1
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
2
2
0
1
1
0
0
0
1
0
2
1
1
1
0
0
0
1
0
1
0
0
0
2
0
0
0
1
0
1
0
0
1
0
1
0
0
1
1
1
0
0
0
0
3
0
1
1
0
2
2
0
0
0
2
1
1
1
0
0
0
2
0
0
0
0
0
0
2
2
1
0
0
0
1
0
1
0
0
0
0
0
1
2
0
0
2
0
3
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
1
0
1
0
0
0
1
0
1
1
0
1
0
0
2
1
0
0
0
1
0
0
1
4
0
0
1
2
0
2
0
0
2
0
0
0
0
2
0
0
0
2
0
1
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
1
0
2
2
0
1
0
0
0
0
0
2
2
2
0
0
0
2
2
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
2
2
2
0
0
1
0
2
1
0
0
2
3
2
0
1
0
0
0
1
0
0
0
0
1
1
0
1
1
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
1
0
0
1
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
1
2
1
0
1
1
0
0
0
0
0
0
0
1
0
2
0
1
0
1
2
1
1
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
3
1
0
0
0
0
1
1
0
1
2
2
0
1
2
1
0
0
1
0
0
0
0
2
1
0
0
1
0
0
1
2
0
1
0
0
0
0
0
0
1
1
0
0
0
2
0
2
0
0
0
3
0
1
0
0
0
1
2
1
0
1
0
0
0
3
1
0
0
0
2
0
0
0
0
0
1
1
0
0
2
1
2
0
1
0
0
0
0
2
0
0
0
2
0
1
0
1
0
0
1
0
1
0
0
1
2
0
0
0
0
0
1
0
0
0
1
3
2
0
1
2
0
0
1
2
1
1
0
0
1
0
2
0
0
1
0
2
2
0
1
2
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
2
0
2
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
2
1
2
0
7
2
1
0
2
2
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
1
2
0
1
0
0
0
2
2
0
0
0
1
2
1
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
1
0
1
1
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
1
1
0
0
0
0
0
1
0
0
1
0
0
1
3
3
1
0
2
0
0
0
0
0
1
0
0
1
1
2
1
0
0
0
1
2
1
0
0
0
0
0
0
0
2
2
1
0
1
0
0
0
1
0
2
1
3
0
0
0
0
0
0
0
1
3
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
1
0
0
0
0
1
0
2
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
3
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
2
1
0
1
1
2
0
1
2
0
1
2
2
0
0
0
1
0
1
0
0
0
0
0
2
1
0
0
1
0
0
1
0
0
0
1
0
2
1
2
1
0
2
0
0
1
1
0
0
0
2
0
2
0
0
0
0
2
1
0
0
0
1
0
3
2
0
0
2
1
0
1
2
0
2
0
0
13
0
0
0
0
0
1
0
0
0
1
0
2
2
0
0
1
0
2
1
0
0
0
0
2
0
0
0
0
2
0
2
0
0
1
2
0
1
0
1
1
0
2
1
2
1
0
2
0
0
3
1
0
0
0
0
1
0
0
2
0
0
1
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
1
2
0
2
0
2
2
0
0
2
0
0
1
3
1
0
1
1
1
0
0
0
0
2
0
2
2
0
2
1
0
0
0
0
0
0
0
1
0
2
1
1
0
0
0
0
0
2
0
0
2
0
2
1
0
0
0
0
1
0
1
0
0
2
0
0
0
2
0
1
1
1
0
1
1
1
0
0
0
0
2
0
0
0
0
0
3
0
0
0
2
1
2
2
0
0
1
0
0
0
1
0
0
2
1
0
1
0
2
2
0
2
1
2
0
0
0
1
2
0
1
1
0
0
0
0
2
1
0
0
0
1
0
1
0
0
0
2
6
0
0
2
0
0
1
0
2
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
2
0
0
2
0
0
1
0
0
0
1
0
1
0
2
0
2
0
0
1
0
0
0
2
0
0
0
3
0
2
1
1
2
0
0
0
0
3
0
0
0
0
1
0
0
0
1
0
0
0
2
0
2
1
0
1
6
0
2
0
1
0
1
0
1
1
2
0
0
0
1
1
2
2
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
1
0
0
1
0
1
0
2
0
0
0
1
0
3
0
0
0
1
0
2
0
0
0
0
2
2
1
4
2
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
2
1
0
0
0
2
0
1
4
2
1
1
2
1
0
0
0
1
0
0
0
1
0
1
0
2
1
0
2
0
2
1
0
0
0
0
1
2
1
0
0
1
0
0
0
0
0
0
3
0
2
2
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
2
0
1
6
0
2
0
0
0
1
0
0
2
0
0
0
1
1
0
1
2
1
0
2
0
0
1
1
0
0
2
0
2
0
2
2
0
2
2
0
1
0
1
0
1
0
0
1
0
1
0
0
0
1
0
0
0
3
2
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
1
0
1
0
0
1
2
0
2
0
1
0
0
0
2
0
1
0
2
0
0
1
1
0
2
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
1
2
0
0
0
2
0
0
0
2
1
0
0
2
0
2
1
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
3
0
0
0
0
0
0
0
0
3
1
0
0
0
1
2
4
0
4
2
0
2
2
0
0
0
0
0
0
2
0
1
0
1
0
2
0
1
1
1
0
0
0
1
0
0
0
2
2
2
1
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
1
0
0
2
1
0
0
0
0
1
0
1
1
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
1
1
2
0
0
1
0
0
0
1
0
0
2
2
0
0
0
0
0
2
1
1
0
1
2
0
1
0
0
0
1
0
0
0
0
2
1
1
0
0
0
0
2
0
2
1
2
0
2
0
0
2
0
0
0
1
0
0
0
2
2
2
0
0
2
0
0
0
1
0
0
0
0
1
2
0
0
2
2
0
0
2
4
0
2
0
0
0
0
0
2
0
2
0
1
0
0
0
2
0
0
0
5
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
2
0
1
0
0
1
0
0
0
6
0
2
0
0
1
1
1
0
2
2
0
0
0
0
0
0
1
0
0
1
2
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
1
0
0
1
2
0
0
0
0
4
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
1
1
2
0
0
2
0
0
0
2
0
3
0
1
0
0
0
0
2
0
2
3
0
0
2
0
0
0
1
0
1
2
2
1
0
0
1
0
0
0
1
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
1
0
0
0
1
0
2
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
1
0
0
1
3
2
1
1
0
0
0
2
0
2
0
2
0
0
2
1
0
0
0
0
0
0
0
0
2
2
1
1
0
0
4
3
2
0
0
3
3
0
1
0
0
2
0
0
0
7
2
1
1
1
2
0
1
0
1
0
0
2
2
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
5
1
0
0
0
0
2
0
0
0
0
3
0
0
0
0
2
0
0
1
1
2
2
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
2
0
0
0
0
1
0
0
1
0
0
2
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
1
2
1
2
0
0
1
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
1
0
2
0
1
0
2
0
0
0
0
2
1
0
0
5
0
2
0
0
0
0
0
2
0
2
1
1
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
2
2
0
1
0
0
1
0
0
0
1
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
1
0
2
0
1
2
0
0
0
1
0
0
0
0
2
1
0
2
0
5
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
2
2
2
0
1
0
0
0
0
5
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
1
0
0
1
0
0
0
0
0
0
2
1
0
0
0
2
0
1
0
0
0
2
0
0
0
3
0
0
0
0
0
1
0
1
1
0
2
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
2
2
1
1
0
0
0
0
0
0
1
3
2
0
0
0
2
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
2
4
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
1
0
2
1
0
0
0
2
1
0
0
0
0
0
0
1
0
2
0
1
0
0
2
0
2
0
0
3
0
0
3
0
0
1
2
2
0
1
0
0
0
2
0
0
1
0
0
0
1
1
1
1
1
0
2
0
0
1
0
1
1
1
1
0
0
1
0
1
0
2
2
0
0
0
0
0
2
0
2
1
0
1
2
1
0
0
0
1
2
1
0
0
3
0
0
0
0
0
0
0
0
0
0
1
2
2
0
1
0
2
0
1
1
0
0
1
0
2
0
1
0
1
0
1
0
0
0
1
2
2
0
0
0
4
1
1
0
1
1
0
1
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
1
0
0
1
0
1
0
5
0
1
1
0
0
0
0
0
2
1
0
0
0
1
6
0
0
0
2
1
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
2
2
0
2
1
0
0
1
1
0
1
2
0
0
0
0
0
0
0
1
5
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
1
2
0
0
0
1
0
0
2
0
1
1
1
1
0
0
0
0
2
0
2
0
2
1
0
0
2
1
1
0
4
0
0
0
0
1
0
2
0
0
0
1
1
0
2
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
2
1
0
0
2
0
0
0
2
0
1
0
0
0
1
0
0
2
1
1
0
1
1
0
0
0
0
1
3
1
0
2
0
2
0
0
0
0
0
1
1
0
0
0
0
3
0
0
0
0
1
0
0
0
0
1
2
2
0
0
1
2
0
0
1
0
2
1
0
1
1
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
1
4
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
1
0
2
0
0
1
1
2
0
0
1
0
2
2
0
0
1
2
0
1
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
1
1
1
0
0
2
0
0
2
2
1
2
0
0
0
0
2
1
0
2
0
1
2
1
0
2
0
0
0
0
1
0
1
0
2
1
2
0
0
1
1
0
0
2
0
1
4
0
0
0
1
2
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
2
0
0
2
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
1
2
0
1
1
0
0
1
0
1
0
2
0
0
0
0
2
2
0
1
1
2
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
2
0
0
1
0
1
2
1
0
0
0
0
0
3
0
2
0
0
0
0
0
1
0
2
0
0
0
1
1
3
0
0
0
0
0
0
0
0
3
1
0
2
0
2
2
1
1
0
1
0
0
0
0
1
0
2
0
0
3
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
2
0
2
1
3
0
0
2
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
2
0
1
0
0
2
0
0
0
2
1
2
0
1
0
2
2
2
2
0
2
0
0
1
0
0
2
0
2
1
0
2
1
1
2
0
1
0
0
0
1
1
0
2
0
0
0
0
0
2
1
0
1
0
2
0
0
0
0
0
7
0
0
0
1
0
0
1
0
2
1
1
0
1
0
0
2
0
2
0
0
0
1
0
0
1
0
0
0
2
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
3
0
2
2
0
3
1
2
0
0
2
0
1
0
0
1
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
2
0
1
2
1
0
2
0
0
0
0
1
0
0
1
0
2
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
1
2
0
0
0
2
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
2
2
0
5
0
0
0
0
1
0
2
0
0
0
1
0
3
1
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
3
0
1
0
0
1
0
2
2
0
1
0
1
0
0
0
2
0
1
2
0
0
0
2
2
0
1
1
0
2
2
1
0
0
2
0
0
0
1
0
0
0
1
0
3
0
0
0
0
0
0
0
0
1
0
0
1
1
0
4
1
1
2
4
0
0
2
0
0
2
0
0
0
1
1
0
0
0
1
0
1
0
1
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
1
1
0
1
0
0
0
2
0
0
2
0
0
4
0
0
0
2
3
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
1
2
0
2
2
0
2
0
1
0
0
0
2
0
1
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
1
2
2
0
1
0
0
0
1
1
2
0
1
0
0
1
2
1
3
2
0
1
0
0
0
0
0
0
0
0
2
2
0
1
0
0
1
0
4
1
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
1
2
0
2
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
1
0
0
6
2
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
2
0
2
0
2
0
1
0
0
0
1
0
0
0
0
2
2
0
2
2
2
2
0
3
2
7
0
1
0
0
0
0
3
2
0
0
0
2
1
2
0
0
0
0
1
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
2
2
0
0
0
0
1
3
1
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
1
3
0
0
1
0
1
0
3
2
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
2
1
0
0
1
1
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
2
0
0
0
0
3
1
0
3
2
0
1
2
0
0
0
1
0
2
0
4
1
1
1
0
1
1
2
0
1
0
1
3
0
0
0
0
0
0
0
0
2
0
1
1
1
0
2
1
2
0
0
0
0
0
0
2
0
0
2
2
0
0
2
4
1
0
0
1
2
0
0
2
0
0
1
0
2
1
0
0
0
1
1
0
2
1
0
0
0
0
2
0
1
2
1
0
0
0
0
0
0
0
1
1
0
2
2
0
0
1
1
1
1
0
0
0
0
0
1
1
0
0
2
2
2
2
0
1
0
0
0
1
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
1
0
1
0
0
1
2
2
3
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
4
2
0
0
0
0
0
0
1
2
2
0
0
0
0
0
2
2
2
0
0
1
0
0
0
0
0
3
0
0
1
1
2
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
1
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
1
0
3
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
2
0
0
1
0
1
1
2
0
0
2
0
1
0
2
2
0
1
2
0
3
1
0
0
0
1
0
0
0
0
0
0
1
2
0
1
0
0
1
1
2
0
0
2
2
0
2
0
1
0
0
0
0
0
0
3
0
1
0
2
0
2
0
0
0
1
0
2
0
2
2
0
0
0
2
0
1
0
0
0
3
1
0
0
0
0
2
0
0
1
0
1
0
1
1
2
0
1
2
1
0
2
0
0
0
0
2
1
0
1
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
2
0
0
0
0
0
0
1
0
2
0
0
1
1
0
0
0
0
0
0
0
0
1
1
2
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
2
3
2
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
2
0
0
2
0
0
2
2
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
3
2
0
1
0
2
0
0
0
0
4
0
0
2
2
1
0
0
0
0
0
0
1
2
2
1
0
2
0
1
0
1
0
2
0
2
0
0
1
0
0
2
2
0
2
0
0
0
0
0
1
0
1
0
0
0
0
2
2
0
2
0
2
0
1
0
0
2
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
2
0
1
2
1
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
1
1
0
0
1
0
1
0
1
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
3
0
0
0
2
0
1
1
0
0
2
0
0
0
0
0
1
0
0
1
0
0
2
2
0
0
0
2
1
2
0
1
5
2
0
0
2
7
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
1
0
1
0
1
0
1
1
2
2
3
1
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
1
2
0
1
0
0
0
1
2
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
2
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
1
0
0
1
0
0
0
1
1
1
0
1
2
2
2
0
0
0
0
0
1
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
1
3
1
0
1
0
0
0
1
1
1
1
0
0
0
0
0
1
2
0
2
0
2
0
1
1
0
3
1
1
0
2
0
0
0
0
0
1
0
2
0
1
0
1
0
0
1
1
2
2
0
0
2
1
1
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
2
0
0
0
1
1
0
2
0
1
0
0
0
0
0
0
0
2
7
1
0
0
0
0
0
2
0
0
2
1
0
0
1
0
1
2
0
2
0
2
0
2
2
0
3
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
1
2
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
1
0
2
3
0
0
1
0
0
2
1
0
1
0
1
0
0
0
0
2
1
2
0
0
4
0
0
0
2
0
2
2
2
2
0
0
0
1
0
0
4
0
0
0
2
0
1
2
0
2
0
2
0
3
1
0
1
1
0
0
1
0
1
0
1
2
0
2
2
0
1
0
0
0
0
0
0
0
0
1
0
2
1
0
0
2
0
2
0
0
0
0
1
1
2
0
0
0
0
1
0
2
1
0
0
2
0
0
0
0
1
0
0
1
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
3
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
1
0
2
0
2
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
2
5
2
0
0
2
0
2
2
0
0
0
0
1
2
0
0
1
1
2
0
0
0
0
1
2
0
1
0
0
2
0
2
2
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
2
0
1
2
0
2
0
0
0
2
2
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
1
2
1
0
2
0
1
0
0
0
0
0
0
1
2
1
0
0
1
2
1
0
2
0
1
6
0
0
0
0
0
0
1
0
0
1
0
1
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
2
0
0
0
0
1
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
1
1
1
0
0
2
2
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
2
0
2
0
2
2
0
0
0
0
3
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
2
1
0
2
2
2
0
2
1
1
0
0
0
2
1
1
0
0
3
2
0
1
1
0
0
0
0
0
0
1
0
0
1
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
2
2
1
2
3
0
2
1
0
0
1
2
0
0
0
0
3
2
0
1
0
0
0
1
2
0
2
2
1
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
1
0
1
0
1
1
2
0
0
2
2
2
0
0
0
1
3
0
0
0
2
0
0
0
5
0
0
0
1
0
0
0
2
0
0
1
0
1
0
2
0
0
0
2
1
1
1
1
2
2
0
0
0
0
2
2
1
1
2
1
0
1
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
2
0
0
0
1
1
1
0
0
0
2
0
4
2
0
1
0
1
1
0
1
0
2
0
1
0
1
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
1
0
1
0
0
0
2
1
1
0
0
1
2
0
0
4
0
2
2
0
0
0
1
3
0
1
0
2
0
0
0
2
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
1
0
2
2
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
2
0
0
0
0
1
0
0
1
0
0
2
1
1
1
0
0
0
2
0
0
1
0
1
1
1
2
0
0
0
0
0
0
0
2
0
0
2
1
0
2
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
3
2
1
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
2
0
0
0
0
1
2
0
0
0
0
2
0
1
0
2
0
2
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
5
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
2
1
0
0
0
2
0
0
1
0
0
0
1
0
2
0
2
0
0
1
0
0
1
0
2
2
0
1
0
0
0
1
2
0
0
0
0
0
0
2
1
0
0
0
0
1
0
1
1
0
0
2
2
0
2
0
0
0
2
0
1
1
2
0
1
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
2
2
1
0
1
1
0
0
1
2
0
0
1
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
3
0
2
0
0
0
0
1
2
0
0
0
0
0
1
3
1
0
0
2
0
0
0
0
0
0
0
0
1
2
0
4
1
0
1
0
1
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
1
0
2
0
2
1
0
0
0
2
0
2
0
0
0
0
2
0
1
0
0
1
2
2
0
1
0
1
0
2
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
2
0
0
0
1
1
1
0
0
0
1
2
0
2
0
1
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
1
2
0
1
1
2
1
2
0
1
2
2
0
1
0
0
0
0
0
2
0
0
0
1
2
1
1
0
0
0
1
0
0
3
1
0
0
0
1
1
0
0
0
0
0
2
0
1
0
0
2
0
2
0
1
2
2
0
0
0
0
1
0
0
2
1
1
0
0
1
0
0
1
0
0
1
1
0
0
0
1
0
0
0
3
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
1
1
2
3
0
0
0
1
2
2
2
0
0
1
0
0
0
2
0
0
0
1
1
0
0
0
0
2
0
0
0
0
1
1
4
0
0
0
0
0
0
1
0
1
1
3
1
0
0
0
0
1
1
0
2
2
0
1
1
0
0
1
2
1
0
0
0
2
2
0
0
1
0
0
0
2
2
0
0
0
0
0
2
0
0
0
2
3
0
2
0
0
4
1
1
2
1
1
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
1
0
0
1
0
1
2
1
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
2
3
3
2
0
0
1
0
2
1
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
1
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
2
0
1
2
1
0
2
0
1
0
1
2
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
2
1
0
0
0
0
1
0
0
0
0
0
2
0
1
1
0
2
1
0
0
0
1
0
3
0
0
0
1
0
2
2
1
1
1
0
0
2
0
0
3
0
2
0
1
0
2
2
0
0
2
0
1
1
0
0
0
1
0
0
2
2
0
2
0
0
0
0
0
0
3
3
2
0
1
0
1
2
0
0
0
0
2
2
0
2
1
0
2
0
0
3
0
0
0
0
0
0
0
0
1
2
2
2
0
1
3
0
2
2
1
0
0
2
0
2
1
0
0
0
0
1
0
2
3
0
0
0
0
1
2
2
0
1
0
2
0
0
3
0
2
0
1
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
2
0
0
0
0
0
0
1
1
2
0
0
0
2
0
0
0
0
0
0
0
0
3
2
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
5
0
0
1
1
0
0
2
0
0
1
0
0
0
0
1
1
2
2
0
2
3
0
0
1
0
0
0
1
0
0
1
0
0
2
0
0
0
1
0
2
0
2
3
1
0
0
2
4
0
0
1
0
0
0
2
0
1
0
6
0
2
0
2
2
0
0
0
1
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
5
0
0
0
1
0
0
1
0
1
0
0
1
0
0
1
6
1
0
0
0
0
0
3
0
0
2
0
1
1
0
0
2
0
0
2
0
1
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
2
0
1
0
0
1
1
0
2
0
2
1
0
2
0
0
2
3
2
0
1
2
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
1
2
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
1
0
0
2
2
1
0
0
2
0
2
2
0
0
1
2
0
2
2
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
2
0
0
1
2
2
0
2
0
2
1
0
1
0
0
1
0
0
2
0
0
0
0
1
1
2
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
2
0
1
0
0
0
0
1
0
1
2
0
1
0
0
0
0
2
0
1
0
2
0
2
1
0
1
0
0
0
1
0
0
0
3
0
1
1
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
3
1
2
0
0
0
3
0
2
2
1
2
0
0
2
1
0
3
0
2
0
0
0
2
2
0
1
0
0
0
0
0
0
0
1
2
0
0
0
1
2
0
0
0
1
2
2
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
1
0
1
2
0
0
2
2
1
0
0
0
1
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
1
2
2
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
2
0
0
2
1
0
0
0
0
0
1
2
1
0
0
1
1
1
0
0
1
1
2
1
0
1
2
0
1
0
2
0
1
1
0
2
0
0
2
1
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
1
0
1
0
2
0
1
2
2
0
0
1
0
0
0
5
1
1
0
2
1
0
0
0
2
0
0
2
0
0
1
0
2
0
0
0
1
0
0
0
0
3
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
2
2
0
0
0
1
0
1
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
1
2
0
1
0
2
0
0
0
1
1
2
1
0
0
0
2
0
0
1
0
1
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
1
2
0
0
0
0
1
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
2
0
1
1
0
2
0
0
1
1
0
1
0
1
0
1
0
1
0
4
0
0
1
0
0
0
0
0
0
0
0
1
2
1
0
2
0
0
2
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
1
0
1
0
1
0
2
1
1
2
2
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
2
1
1
0
0
0
0
2
2
0
2
0
2
0
0
0
0
2
2
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
1
0
2
0
1
0
2
0
0
0
1
0
2
1
1
0
2
1
2
0
1
0
1
0
0
0
1
0
2
0
2
1
1
2
1
1
0
3
2
0
2
0
0
0
2
1
0
0
0
3
2
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
2
1
0
0
0
0
2
0
0
0
1
2
0
0
0
1
0
0
1
0
3
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
3
0
0
0
2
0
0
2
0
3
1
0
0
0
2
0
0
1
0
0
0
1
0
0
0
2
1
0
1
0
0
1
0
2
6
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
2
1
1
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
2
0
0
0
2
0
0
2
2
1
0
0
1
0
0
2
0
2
0
0
1
0
1
0
2
7
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
10
0
0
0
2
0
0
0
2
1
0
0
1
0
0
2
1
0
0
0
0
0
0
1
0
1
0
0
2
2
0
0
0
0
0
2
2
0
0
2
0
0
1
0
0
0
2
0
0
2
0
2
0
0
0
0
1
1
0
0
0
0
1
1
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
1
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
1
2
0
3
1
2
1
2
2
0
1
0
0
0
0
2
0
0
2
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
2
2
0
0
1
2
0
0
0
0
0
0
0
2
0
2
0
1
1
0
0
0
2
1
0
0
2
3
1
1
0
2
2
0
1
0
0
1
0
0
0
2
2
0
2
0
2
0
0
0
1
0
0
0
2
1
0
3
1
1
0
0
0
0
0
1
0
2
1
1
0
0
0
1
0
0
2
0
0
1
0
1
1
2
2
1
1
1
0
0
0
0
0
2
2
0
1
2
0
0
1
0
1
0
0
0
2
0
0
1
1
0
1
2
1
1
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
4
0
3
0
0
1
2
2
0
2
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
2
0
1
3
2
0
1
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
1
2
0
3
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
1
3
0
1
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
1
0
2
0
0
1
2
0
0
1
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
1
2
0
1
0
0
1
0
4
0
0
3
2
0
0
1
0
0
0
2
0
0
0
0
2
1
2
0
0
0
0
0
0
0
1
0
0
2
1
1
0
2
0
0
2
0
0
0
2
0
0
0
0
0
2
1
0
0
1
0
2
0
2
1
0
0
2
2
2
0
0
1
0
2
0
0
1
0
0
1
0
1
0
0
0
2
0
0
1
0
0
0
0
3
2
1
0
1
3
0
0
1
0
2
0
0
0
0
0
0
2
0
1
2
0
0
2
0
2
0
0
0
1
0
2
0
1
2
1
0
1
0
0
1
0
0
0
2
0
0
0
1
0
0
1
0
0
0
2
0
1
1
0
0
2
1
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
2
2
2
0
0
2
0
0
2
0
1
1
0
1
0
2
2
1
1
1
1
2
0
0
0
2
1
1
0
0
0
1
1
1
0
1
0
0
0
1
0
3
2
0
2
2
2
0
2
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
1
2
2
0
2
0
3
3
0
0
2
2
2
0
0
0
2
0
0
1
2
0
2
1
0
1
3
0
0
0
0
0
0
0
0
1
1
0
0
2
2
2
1
0
0
0
2
0
0
0
0
2
1
0
2
0
0
0
0
0
0
2
2
2
0
0
0
0
1
0
0
0
3
0
2
1
0
1
0
2
0
0
0
0
2
1
2
0
5
0
3
0
2
0
0
0
2
0
0
1
2
1
0
0
0
0
0
0
0
1
1
0
0
2
3
2
2
0
0
2
0
2
0
0
0
2
0
1
0
0
1
0
2
0
0
1
2
0
0
0
0
2
1
1
2
2
1
1
0
0
2
0
1
0
0
2
0
0
0
2
0
0
1
0
0
0
0
3
1
1
0
1
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
1
0
3
0
1
0
0
0
0
0
2
4
0
1
0
0
1
1
2
2
0
2
2
2
0
0
2
0
0
0
4
1
0
0
0
0
0
1
0
0
0
0
2
0
1
2
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
2
0
1
0
2
0
0
1
1
1
0
0
0
0
3
1
2
2
0
1
0
2
1
0
1
0
0
0
0
1
0
0
0
0
1
2
1
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
2
0
0
1
2
2
2
0
0
2
2
1
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
2
0
0
3
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
2
0
3
2
0
1
1
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
2
0
0
1
0
0
0
2
1
1
0
1
2
1
1
0
0
3
2
0
0
0
0
0
1
1
0
2
0
2
1
1
1
0
1
1
0
0
0
0
1
2
0
1
1
2
1
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
2
2
0
0
0
0
1
1
0
2
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
1
3
1
3
2
0
0
0
1
0
1
0
0
1
0
0
2
0
0
0
1
1
1
2
1
0
1
2
2
0
0
0
1
1
0
0
2
0
1
0
0
0
0
1
0
2
4
1
0
2
0
0
0
0
0
2
2
1
2
2
0
1
0
2
0
2
0
0
3
0
0
2
0
0
1
0
0
1
0
1
0
0
2
2
0
0
2
0
1
2
0
0
0
0
1
0
1
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
1
0
0
1
0
0
2
6
1
1
1
2
0
0
1
0
0
2
0
0
0
0
3
0
1
0
1
0
2
0
0
0
2
0
0
0
0
0
1
2
2
0
2
0
0
0
1
1
0
0
2
2
1
0
2
0
0
0
0
0
1
1
0
0
2
2
3
0
2
2
0
4
0
1
1
0
0
0
0
0
0
1
0
3
0
0
0
0
3
3
1
2
0
2
0
0
0
0
0
0
0
2
1
0
1
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
2
0
1
0
0
0
2
1
0
0
2
0
0
1
2
0
1
0
1
0
3
0
0
0
0
2
0
2
1
2
0
0
0
0
0
0
2
0
2
0
0
2
2
0
0
0
2
2
0
0
0
0
2
0
1
0
0
2
2
0
0
0
0
2
0
3
1
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
3
0
0
0
1
0
2
0
1
0
0
0
0
2
2
1
0
1
2
0
0
4
1
2
1
0
0
2
0
0
0
11
0
2
2
1
2
2
2
1
0
2
1
1
0
4
2
0
0
0
0
1
0
0
0
1
1
1
0
1
0
0
2
1
0
2
0
1
2
2
2
0
0
2
0
2
0
1
0
1
0
1
2
0
0
0
0
2
1
0
0
0
0
0
0
0
2
4
1
1
0
0
1
1
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
1
0
1
1
2
0
0
0
2
0
1
2
0
2
1
0
1
0
0
1
1
2
3
1
2
0
0
2
1
1
0
0
3
0
1
0
1
0
0
0
1
0
0
2
1
0
0
1
2
1
0
0
1
2
0
0
1
1
1
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
2
0
0
3
0
0
2
2
1
2
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
2
0
2
1
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
3
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
3
2
1
2
2
2
1
1
0
2
1
0
0
1
2
2
1
0
0
0
0
0
0
0
2
2
0
0
2
0
2
0
0
0
0
0
1
1
2
0
0
1
0
0
0
0
1
4
2
0
3
0
0
0
0
2
0
0
2
0
0
1
1
0
2
1
0
0
0
0
1
0
0
0
0
2
0
1
0
2
1
1
0
0
1
2
1
2
0
1
2
0
0
3
0
1
0
0
0
0
2
0
0
2
1
1
0
0
0
0
0
0
0
1
1
0
0
0
2
0
1
0
1
1
1
0
0
1
2
1
0
0
1
1
0
0
0
1
2
0
6
2
2
0
1
2
0
0
2
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
3
0
2
2
0
2
0
0
0
1
0
1
1
0
0
0
1
1
0
2
1
0
2
1
2
2
0
1
2
0
0
0
0
0
0
0
0
1
0
0
2
0
1
1
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
2
3
2
2
0
2
0
2
0
0
1
0
0
0
1
0
0
1
0
0
0
0
2
0
1
0
0
3
0
0
0
0
3
0
2
1
0
0
3
0
2
1
0
0
2
0
0
0
0
2
0
0
0
0
2
2
2
0
2
0
0
2
0
2
0
0
0
2
1
1
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
1
2
1
1
0
0
2
0
0
0
1
1
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
1
0
2
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
4
0
1
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
2
1
2
1
2
0
0
1
2
0
0
0
0
0
0
0
2
0
1
1
0
2
0
0
0
1
6
1
2
0
0
2
2
0
0
0
2
0
0
0
1
0
2
1
2
1
1
0
0
2
0
2
0
0
1
0
0
1
0
0
1
0
0
0
0
0
2
0
0
1
0
1
1
1
0
2
0
0
1
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
2
0
0
2
1
0
0
0
0
2
0
2
2
1
0
1
1
2
3
1
2
1
0
2
0
1
0
0
2
1
5
0
0
0
0
0
0
2
0
2
1
2
1
0
0
0
1
2
0
2
1
3
0
2
0
1
2
1
0
0
1
0
0
1
0
2
1
2
1
0
1
0
0
1
0
1
0
0
1
0
0
2
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
2
0
1
0
0
0
2
0
0
0
1
1
2
1
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
3
0
0
0
1
2
0
2
0
1
0
0
1
0
0
0
1
2
2
0
2
2
0
0
0
1
0
1
0
0
0
0
0
1
1
1
2
0
1
1
0
1
0
2
0
0
1
0
0
1
0
2
1
0
0
0
0
1
0
0
2
2
2
0
1
0
2
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
2
0
0
2
0
0
0
2
0
2
2
1
0
0
0
1
0
1
2
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
2
1
0
2
0
0
0
0
0
0
1
1
0
0
1
0
0
1
1
2
0
1
0
1
0
0
2
1
0
1
1
0
3
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
1
0
2
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
1
2
0
2
0
2
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
1
2
2
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
1
2
0
0
3
2
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
2
0
2
0
0
2
0
2
0
1
1
2
0
0
1
0
0
0
1
2
0
0
0
1
1
0
0
0
0
1
0
0
2
1
0
1
0
0
0
0
2
0
1
0
0
0
1
2
0
3
2
2
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
2
0
2
0
1
0
0
0
0
0
0
1
0
1
1
0
2
0
0
1
0
2
0
0
2
0
0
0
4
1
2
0
2
0
0
2
2
0
1
1
0
2
2
1
0
0
2
1
0
0
0
1
2
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
2
2
1
0
2
0
1
3
0
0
2
1
0
0
1
0
0
2
1
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
3
0
1
0
0
1
0
0
0
1
2
0
1
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
2
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
2
2
0
1
1
1
3
3
0
0
0
0
0
0
0
2
0
0
2
0
3
0
0
1
0
0
1
1
1
0
0
1
1
0
2
0
2
1
0
0
0
2
1
2
0
0
0
2
0
1
0
1
0
1
0
1
1
0
0
2
2
2
0
0
2
1
0
1
2
0
2
3
1
0
0
0
1
0
0
0
2
3
1
0
2
1
0
0
2
0
0
3
1
1
0
0
2
2
0
1
0
0
1
1
0
0
0
0
0
0
0
0
2
1
0
1
1
0
0
1
0
0
0
2
0
0
1
0
2
0
1
0
0
0
0
0
2
0
0
2
2
0
1
0
0
0
0
0
1
1
0
0
2
0
0
1
0
0
0
1
0
0
2
0
2
0
1
1
1
2
0
1
0
0
2
0
1
0
1
0
0
0
0
0
1
0
0
1
1
2
0
2
0
0
1
0
1
0
0
2
0
0
0
2
0
1
0
0
1
0
0
0
0
2
2
1
2
0
0
1
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
6
0
0
2
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
1
2
2
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
1
0
1
0
1
0
2
0
0
0
0
0
0
0
3
2
0
0
0
1
0
1
2
1
0
0
0
0
0
0
1
1
1
0
0
1
0
0
1
0
0
0
0
2
0
1
2
0
0
2
0
0
0
1
0
0
1
0
0
2
2
0
0
0
3
1
2
2
1
0
1
2
0
0
2
0
2
0
0
0
0
2
3
2
0
0
0
1
0
1
0
1
0
2
0
1
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
1
0
0
2
0
2
0
2
2
0
0
3
0
1
2
1
1
0
2
1
1
1
2
2
2
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
1
1
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
2
1
0
0
0
1
0
0
0
2
1
0
0
0
2
2
0
2
2
2
1
0
0
0
1
0
0
0
1
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
4
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
1
0
2
0
1
0
1
1
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
2
2
0
1
3
0
6
0
1
0
3
3
0
0
2
0
1
0
0
2
0
0
0
2
0
2
2
2
0
0
0
0
1
2
1
0
1
0
0
2
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
2
1
1
2
0
0
0
1
0
0
2
0
1
0
2
2
1
0
0
0
0
2
1
3
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
1
1
1
0
0
1
3
0
0
2
0
1
0
3
0
1
0
0
2
0
1
0
0
0
0
0
0
2
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
1
0
0
2
0
0
2
0
2
0
0
0
1
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
2
2
1
0
0
1
0
0
0
0
5
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
3
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
2
1
1
0
2
0
0
1
0
2
1
2
0
0
0
2
1
0
0
2
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
6
0
0
0
0
0
0
0
2
2
0
0
0
7
0
0
2
0
0
0
1
1
2
2
2
0
0
1
2
0
0
1
2
0
0
1
0
0
0
0
2
0
2
2
0
1
0
2
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
1
1
1
0
0
2
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
1
0
2
0
0
0
0
0
1
0
0
0
1
0
0
3
0
0
1
0
0
0
0
0
2
0
0
2
0
1
2
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
4
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
2
1
1
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
1
1
0
1
2
0
0
0
1
0
0
1
4
1
2
0
1
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
1
0
0
0
2
0
2
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
1
1
1
0
0
2
0
1
0
0
2
0
1
1
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
2
1
2
0
1
0
1
2
0
0
1
0
1
0
1
0
2
0
0
0
0
2
3
2
0
0
2
1
0
0
0
0
2
2
0
0
0
2
0
1
2
0
2
1
0
0
1
0
2
0
1
0
0
0
2
0
1
0
2
0
0
0
0
0
1
0
0
0
1
0
1
0
2
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
1
0
1
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
1
2
0
0
0
2
0
1
1
0
0
3
2
0
2
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
1
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
2
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
2
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
2
2
0
2
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
1
0
2
0
0
2
0
1
0
2
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
4
0
2
2
0
1
0
1
1
0
0
0
2
1
1
0
0
0
0
2
1
2
1
2
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
1
0
2
0
0
1
1
0
0
0
0
0
1
1
0
2
2
0
0
2
1
1
0
0
0
1
0
0
1
1
0
1
1
1
0
2
0
0
0
0
0
0
0
1
1
1
0
1
2
0
1
1
1
1
3
2
1
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
2
1
0
0
0
2
1
0
2
0
0
4
1
1
0
1
0
0
1
0
2
0
0
0
2
1
0
0
0
0
0
0
2
2
0
0
2
0
1
2
2
0
1
0
1
1
1
1
0
3
0
0
1
1
2
0
2
0
1
0
2
0
0
2
2
1
0
2
0
0
0
0
1
2
0
0
1
0
0
0
1
0
0
2
0
2
1
1
1
0
0
1
2
2
4
0
1
1
0
0
2
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
2
2
0
2
0
0
0
1
0
1
0
1
0
2
2
0
0
0
0
2
3
2
1
0
2
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
2
1
3
2
2
0
0
2
0
0
0
0
3
0
1
0
0
0
0
1
1
2
0
0
0
0
0
2
2
1
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
2
0
0
2
1
0
0
2
3
0
0
1
2
1
0
1
0
1
1
0
2
0
2
0
0
1
1
0
1
3
2
1
1
0
0
0
0
3
1
1
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
2
1
2
0
2
0
0
0
8
0
1
1
0
0
0
2
0
0
1
0
0
1
0
1
1
0
0
2
0
0
3
2
2
5
3
0
0
0
1
0
0
0
1
3
0
1
1
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
1
0
1
1
0
2
1
1
0
0
0
1
0
0
0
0
0
2
0
0
2
1
0
0
2
0
0
0
0
3
0
2
2
0
1
0
0
1
0
1
0
0
1
2
1
2
1
0
0
0
2
2
0
0
0
1
1
0
0
0
2
1
0
2
0
1
2
0
0
3
0
0
0
0
0
6
1
0
1
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
2
1
0
1
2
0
0
0
1
5
0
2
1
0
0
0
0
2
0
0
0
1
0
2
0
0
2
0
0
0
2
1
2
0
0
2
2
0
0
0
0
2
1
0
0
1
0
4
0
2
0
0
0
1
0
2
2
0
0
3
1
2
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
1
0
0
2
1
1
0
0
2
0
1
2
0
0
2
0
0
2
2
0
0
0
1
1
1
0
0
0
0
1
3
0
0
0
2
0
0
1
1
0
0
1
1
0
0
2
0
2
0
0
0
0
2
1
1
0
2
0
1
1
0
0
1
0
0
1
2
0
0
0
1
2
1
0
5
2
0
0
0
0
1
2
2
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
1
0
1
1
2
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
1
2
2
0
1
0
1
2
0
2
0
0
0
0
0
0
0
3
4
2
0
0
0
1
2
1
0
0
0
1
0
0
0
1
2
0
1
0
0
1
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
3
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
1
0
2
0
0
0
0
2
0
0
1
1
1
0
1
0
0
0
1
1
1
2
2
0
2
0
2
2
0
1
0
1
2
1
0
0
0
0
2
0
1
0
0
0
2
0
0
0
1
0
0
0
0
3
1
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
2
0
0
0
1
0
1
0
1
1
0
1
0
0
0
0
0
0
1
1
2
0
0
0
0
2
2
3
1
0
2
0
2
0
0
0
2
1
1
0
0
1
1
2
1
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
2
0
0
3
0
2
1
0
0
1
0
2
1
0
0
2
0
3
0
0
0
0
1
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
2
1
0
0
0
0
0
2
0
2
0
0
1
0
2
2
0
0
0
0
0
0
0
1
0
0
1
0
2
0
2
0
0
0
2
0
2
1
0
2
0
0
1
0
0
0
2
0
1
0
0
2
0
1
0
0
1
0
2
0
0
3
2
4
0
0
0
0
0
1
0
0
1
1
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
1
0
0
2
1
1
2
0
0
1
0
0
2
3
1
2
0
0
1
0
0
0
2
0
2
0
0
0
0
0
1
0
0
2
0
1
0
4
2
0
0
1
1
2
1
0
0
1
1
2
0
0
0
0
1
1
1
2
2
0
1
0
0
2
2
0
1
0
0
2
0
1
0
2
2
0
0
1
2
2
0
0
0
0
0
0
0
1
2
0
0
1
1
1
1
0
2
0
0
2
0
1
0
1
0
1
0
1
0
0
0
2
1
1
0
0
0
2
0
2
0
0
0
0
0
2
0
0
2
0
2
0
1
0
0
0
1
0
0
0
2
0
0
0
2
2
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
2
0
1
1
0
0
2
0
0
2
0
0
0
0
1
0
1
1
0
1
0
1
0
1
2
0
0
0
0
0
0
1
2
0
2
0
0
0
0
1
1
0
0
0
3
0
2
0
2
0
0
0
0
1
0
0
1
2
0
0
2
0
0
0
0
1
0
0
1
0
0
1
0
2
1
2
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
9
0
1
2
0
1
1
0
2
1
0
0
0
2
0
1
0
0
1
0
0
1
0
0
0
0
2
0
0
1
1
1
2
0
1
0
0
0
2
1
0
1
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
2
1
1
0
1
1
0
0
0
3
0
1
0
2
0
0
0
1
2
0
0
0
0
0
0
1
4
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
4
0
0
0
0
1
0
0
0
0
0
0
2
1
0
2
0
1
0
2
0
0
1
1
0
0
0
0
2
0
0
2
1
1
2
2
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
4
0
0
2
2
0
0
0
0
1
0
1
0
0
2
0
4
3
0
0
0
0
2
0
1
1
1
0
1
0
2
0
0
1
1
0
0
0
0
1
1
2
1
1
3
0
0
2
1
2
1
0
0
1
0
1
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
3
1
0
2
2
2
0
0
0
1
0
0
2
2
1
0
2
0
0
1
0
0
0
0
1
0
2
2
0
0
0
0
0
0
2
0
2
2
0
0
5
0
1
2
0
0
1
0
0
1
1
0
1
3
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
2
0
2
0
0
0
0
0
1
0
1
0
0
0
0
1
2
0
2
0
0
2
0
1
2
0
1
0
0
0
0
2
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
1
0
2
0
0
1
0
1
2
2
1
2
0
0
1
0
2
0
2
0
2
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
2
2
0
0
0
0
0
0
1
2
1
0
1
1
0
2
0
0
0
0
1
0
0
2
1
0
0
0
1
2
0
0
0
0
0
2
0
1
0
0
0
1
2
0
1
1
0
0
0
1
0
1
0
1
2
1
0
0
0
0
0
0
0
0
2
0
0
0
1
3
1
0
1
0
2
3
1
0
0
0
0
0
0
0
1
0
0
0
2
2
0
2
1
0
2
0
0
1
0
0
0
2
2
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
1
1
0
0
2
1
0
2
2
0
3
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
1
0
0
1
0
0
1
2
1
1
2
0
2
1
0
1
0
2
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
1
0
1
0
3
1
0
2
0
0
1
0
2
1
1
0
0
0
2
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
1
1
0
0
2
1
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
2
2
1
0
0
0
0
1
0
0
2
0
1
0
0
0
1
2
1
0
1
0
0
0
0
2
0
0
0
0
2
2
1
0
0
2
0
2
0
0
0
0
0
0
0
1
1
2
0
0
2
1
0
2
1
2
1
0
0
0
0
1
2
1
0
0
0
0
0
0
1
0
1
0
0
0
2
1
2
2
1
0
0
0
0
0
0
1
0
0
2
0
2
2
0
1
0
0
0
2
0
0
2
2
0
2
0
0
0
0
0
0
0
0
2
0
0
2
1
2
0
0
1
0
2
2
1
0
0
0
0
1
0
0
0
2
0
0
1
1
2
0
0
0
0
2
1
0
0
1
1
0
0
0
0
1
0
2
0
1
0
0
0
6
1
0
0
0
0
2
2
1
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
3
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
3
1
0
1
1
0
2
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
1
1
0
0
1
1
0
1
1
2
0
1
2
2
0
2
1
0
0
0
0
0
3
2
2
0
0
2
1
0
1
1
4
3
2
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
2
0
0
1
0
0
0
0
0
1
0
2
0
0
3
0
0
2
0
1
0
0
0
1
0
0
0
0
2
0
2
0
0
0
1
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
1
0
0
2
0
0
0
0
1
1
0
0
1
1
0
1
0
0
0
0
0
0
2
1
0
0
1
1
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
2
2
0
0
1
0
0
1
0
0
0
2
0
0
2
0
2
2
0
0
0
2
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
2
0
2
0
1
1
0
0
0
0
1
1
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
7
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
3
2
0
0
0
0
0
0
2
0
0
0
1
0
0
1
2
0
1
0
0
0
2
0
1
2
2
0
1
2
0
0
0
2
0
0
1
0
4
0
0
0
0
0
0
1
0
0
1
2
0
1
0
0
1
1
1
1
1
0
0
0
0
2
0
2
2
3
0
2
1
1
0
2
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
1
1
0
0
0
0
0
2
0
0
0
1
0
1
1
1
0
1
1
1
0
0
0
0
1
2
1
0
0
1
1
2
0
2
0
0
2
0
1
0
1
0
2
1
0
0
0
2
0
2
0
0
0
1
0
2
0
2
2
0
2
0
0
2
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
2
0
3
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
2
1
0
0
1
2
0
2
0
1
2
1
0
3
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
2
0
1
0
2
0
1
0
0
0
0
2
0
0
1
0
2
0
0
0
2
2
0
0
2
0
2
1
1
0
0
2
0
2
1
2
1
0
1
1
0
2
1
0
0
0
0
0
0
0
1
0
1
0
1
2
0
2
0
1
0
0
0
0
1
2
2
0
0
0
1
0
0
1
0
0
0
1
0
0
2
1
2
2
1
0
0
0
0
0
0
1
1
1
0
0
1
0
1
0
1
0
0
2
0
0
1
1
0
1
2
0
1
1
1
0
1
0
0
0
0
2
0
1
1
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
1
2
1
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
2
0
2
1
0
0
2
1
4
0
0
2
1
0
1
0
0
0
1
2
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
2
0
1
0
3
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
1
1
1
1
0
0
0
2
2
0
1
1
2
0
1
1
0
0
0
2
1
2
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
4
0
0
0
0
1
1
0
0
0
2
0
0
0
0
2
0
0
0
1
1
1
1
5
1
2
0
0
0
2
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
1
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
2
0
0
2
1
2
0
2
0
0
1
1
0
0
0
1
0
2
1
2
0
2
1
0
1
1
0
0
0
0
0
0
2
1
2
2
0
2
0
0
0
2
4
2
0
0
0
1
0
0
0
2
0
0
2
0
2
0
0
0
1
0
1
3
0
2
0
1
0
0
2
0
0
2
2
0
0
2
1
1
0
2
0
0
3
0
0
0
4
0
0
0
0
2
0
0
0
0
2
0
1
0
2
0
0
2
3
0
0
1
2
0
0
2
0
1
0
2
2
0
0
1
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
1
0
1
2
4
1
0
2
0
2
0
2
1
0
0
2
0
2
0
3
0
1
1
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
2
2
1
3
0
0
2
0
0
1
0
1
1
1
1
2
0
0
1
2
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
1
2
2
2
0
2
0
1
1
1
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
2
0
4
2
0
1
2
0
2
0
0
0
1
1
0
0
2
0
0
2
0
2
0
2
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
2
0
2
0
2
0
2
0
0
2
1
0
2
0
1
2
2
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
2
1
0
0
0
2
1
0
2
0
0
1
2
1
0
0
2
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
2
0
1
2
0
1
2
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
2
0
2
0
1
2
0
0
0
0
0
0
0
1
1
0
2
0
0
0
1
0
1
2
0
1
0
0
4
0
1
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
2
2
0
0
0
0
1
1
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
1
1
0
0
0
2
2
0
0
0
1
1
2
0
0
1
1
0
2
2
0
0
1
1
2
0
0
3
1
1
0
0
1
2
1
1
0
0
0
0
0
2
0
0
0
0
1
1
1
2
2
1
0
0
0
1
0
2
0
0
0
0
0
1
0
0
1
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
1
0
1
0
0
0
1
0
2
0
0
0
1
2
2
0
0
0
0
0
1
0
2
0
0
0
0
1
1
1
0
0
3
1
1
2
0
1
0
0
0
0
3
0
0
1
0
0
2
1
1
0
1
0
1
0
1
0
2
0
0
0
0
0
1
3
0
0
0
2
1
0
1
0
2
0
0
1
0
2
0
2
1
0
2
0
0
2
0
0
0
0
0
0
2
1
1
0
0
1
0
1
0
1
0
0
0
0
1
2
2
0
1
0
2
0
2
0
0
2
2
0
0
0
0
2
0
2
0
0
1
3
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
2
1
2
2
1
1
0
0
0
2
1
0
2
3
1
0
2
0
0
0
0
2
1
0
1
0
0
2
2
0
0
0
0
1
0
0
2
0
1
1
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
2
0
1
2
0
0
1
0
0
1
0
2
0
0
0
1
0
0
1
0
2
0
0
2
2
2
0
0
1
2
0
0
0
1
0
1
2
0
0
0
1
1
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
2
1
0
0
3
0
2
0
0
1
0
1
1
1
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
1
1
0
0
0
1
1
0
0
0
0
0
1
0
2
0
0
0
1
1
1
2
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
1
0
0
1
9
3
1
0
0
0
0
1
2
0
0
2
2
1
2
0
1
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
3
0
0
1
0
1
2
0
2
0
0
2
0
0
4
0
0
2
0
0
0
0
0
0
1
1
1
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
7
2
2
0
0
2
0
7
0
0
0
1
0
1
0
0
0
0
1
1
0
1
0
2
2
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
2
0
1
0
2
0
0
2
0
1
0
1
0
0
1
0
0
0
2
2
0
0
0
2
1
1
1
0
0
2
0
1
0
2
0
2
0
0
1
0
1
1
2
0
0
0
0
0
3
2
0
0
2
2
0
0
1
0
0
1
0
0
1
1
0
2
0
0
0
2
0
0
0
2
2
2
0
0
0
0
0
0
0
0
2
0
3
0
1
0
2
2
0
2
2
0
0
2
1
0
2
1
0
0
1
0
0
0
0
0
0
2
1
2
2
0
0
0
1
0
0
0
2
1
0
0
3
0
1
9
1
1
0
0
0
2
0
0
2
2
0
0
0
0
0
2
0
2
0
0
0
1
1
0
0
2
0
0
2
0
2
0
3
1
0
1
1
1
2
0
0
1
2
2
0
2
1
0
0
0
1
2
1
0
1
0
0
1
1
0
2
0
2
0
0
0
2
0
0
0
0
1
0
0
1
2
1
0
0
2
0
0
3
2
0
2
1
0
0
1
0
2
0
0
0
0
3
1
0
1
1
0
0
0
0
0
1
0
2
0
0
1
0
0
0
2
0
0
0
3
0
0
0
0
2
0
1
0
1
0
0
0
0
2
0
0
1
0
1
1
1
0
1
0
0
1
0
0
1
0
0
0
2
2
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
1
1
0
2
0
1
0
0
0
2
0
0
2
1
0
0
1
0
2
0
1
0
2
0
5
0
1
0
0
1
0
0
0
2
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
3
0
0
1
0
0
2
1
1
0
0
0
0
0
0
2
2
0
0
0
0
1
0
1
1
0
1
1
2
1
0
2
0
2
0
0
2
0
0
2
1
2
0
1
0
0
0
0
2
2
1
0
0
0
0
0
0
2
0
2
6
1
0
0
0
0
2
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
1
1
2
0
2
2
0
1
0
0
1
2
1
1
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
3
2
2
1
0
0
0
0
0
1
0
3
0
0
0
2
0
1
0
0
0
0
2
1
3
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
1
2
2
0
0
0
0
0
2
0
0
0
1
0
0
2
1
1
1
1
0
0
0
1
0
0
0
0
2
0
6
0
0
0
0
1
2
2
1
2
0
0
0
0
0
2
0
1
0
0
4
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
3
0
1
0
2
1
0
0
1
0
0
0
2
1
2
1
1
0
1
0
0
0
0
0
0
0
0
1
2
3
6
0
1
2
0
2
1
1
1
0
0
0
0
0
1
0
0
2
0
1
2
0
2
0
0
0
2
1
0
0
2
1
0
2
0
0
0
1
0
0
0
0
1
0
2
2
1
0
1
1
0
2
0
0
1
1
2
0
0
1
0
2
0
1
0
2
0
2
0
0
2
0
0
0
2
2
0
0
0
1
0
0
0
2
1
0
0
0
2
1
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
1
0
5
1
0
0
2
2
0
0
0
2
0
0
1
1
0
0
0
3
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
1
3
0
1
0
0
1
0
0
0
0
2
1
0
1
0
0
0
1
1
0
0
1
0
0
0
0
2
1
0
0
0
0
2
2
0
0
0
0
1
5
0
6
1
3
2
2
0
0
0
1
0
2
2
1
0
0
0
3
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
1
2
2
0
0
0
6
0
0
0
1
1
0
0
0
1
3
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
2
2
0
0
0
0
0
1
0
0
0
1
2
1
2
0
0
0
1
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
1
1
0
0
0
1
2
0
0
1
0
1
0
0
0
3
1
2
0
4
0
0
1
2
0
0
0
0
1
0
0
0
0
2
0
2
1
0
0
2
0
0
1
0
1
0
0
2
1
1
0
2
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
3
2
2
0
0
0
1
0
2
2
0
0
0
0
2
0
0
0
1
1
0
1
0
0
2
0
2
1
1
0
0
0
0
0
0
0
1
0
0
1
0
2
1
2
0
1
1
0
1
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
2
0
0
0
0
1
0
0
10
2
1
0
3
2
0
0
0
0
0
0
2
0
2
0
1
3
0
1
0
2
0
0
0
1
0
0
0
0
2
0
2
0
1
0
1
2
0
0
0
2
0
1
0
1
0
2
0
2
0
0
0
1
1
0
0
0
0
1
3
2
0
2
2
0
0
0
1
2
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
2
3
3
0
0
1
0
1
0
2
0
0
0
1
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
2
0
2
1
0
0
0
0
2
0
0
1
0
1
0
2
0
0
0
0
1
0
1
2
1
2
1
1
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
2
0
2
0
0
0
1
1
1
0
0
1
2
0
1
0
0
1
0
0
0
1
1
3
3
0
2
0
1
0
1
1
2
1
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
2
0
1
0
0
0
2
0
1
1
0
2
0
1
0
0
2
2
1
1
1
0
1
0
0
4
0
2
2
0
1
2
2
3
0
1
0
2
0
0
0
0
3
1
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
2
5
0
0
1
1
1
0
0
1
0
0
1
1
0
2
0
2
0
0
1
0
0
1
0
1
2
1
0
0
0
0
1
1
2
0
2
2
2
1
0
1
0
2
0
1
2
1
2
0
0
0
0
0
0
1
0
2
1
0
0
0
3
0
0
2
0
2
0
0
0
0
1
0
0
1
0
2
0
1
3
0
0
1
0
0
0
1
1
2
0
0
0
2
0
0
0
2
3
0
0
0
0
0
1
0
1
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
1
3
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
2
0
3
2
0
2
0
2
0
0
0
2
0
0
1
2
0
0
1
0
0
0
0
0
1
0
2
0
1
0
1
1
3
2
2
0
0
0
0
1
0
2
0
0
1
0
0
1
1
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
2
0
1
0
0
1
2
1
0
2
0
2
2
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
1
2
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
1
0
0
2
0
0
1
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
4
0
2
0
0
1
0
1
0
1
3
0
1
1
0
0
0
2
0
0
0
1
0
0
1
2
1
0
3
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
2
1
0
0
2
0
2
0
0
1
1
0
2
2
0
2
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
2
0
0
3
0
0
0
0
0
1
0
1
0
3
1
2
0
0
2
2
1
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
1
0
0
2
0
1
1
0
0
2
0
0
0
0
0
0
2
0
0
0
4
0
1
0
0
1
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
1
0
1
0
2
1
0
0
0
2
5
1
0
0
1
1
0
0
0
0
1
2
0
0
1
0
0
0
2
0
1
0
0
1
0
0
0
1
2
0
1
0
1
0
1
0
1
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
1
2
0
0
0
0
2
0
1
0
1
0
0
0
2
2
2
3
3
0
0
0
2
2
1
0
2
2
2
0
1
0
0
2
2
2
0
0
1
1
0
0
1
0
1
0
2
0
1
0
2
0
0
0
0
2
0
1
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
1
1
1
2
0
0
1
0
0
0
0
1
1
0
0
1
1
0
0
0
1
1
1
0
2
1
0
0
0
0
0
4
0
1
0
0
0
0
1
1
0
0
2
1
0
1
0
0
0
0
1
0
0
2
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
1
0
0
2
2
0
1
0
2
1
0
2
0
2
1
0
1
2
1
0
1
1
0
0
0
0
0
2
2
0
1
0
0
0
2
2
0
2
2
0
0
0
0
0
2
2
1
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
1
1
0
0
0
7
2
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
1
2
0
2
1
1
2
0
2
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
1
0
0
0
2
2
0
1
0
0
2
3
0
0
0
2
0
2
2
0
0
1
0
0
1
3
1
1
0
0
1
0
0
2
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
1
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
1
0
2
1
0
1
0
0
0
0
0
0
0
1
1
2
0
0
0
2
0
1
0
2
1
2
0
0
1
0
0
20
0
0
0
2
0
1
0
0
0
0
2
0
2
2
1
0
0
3
1
1
0
1
0
1
0
1
0
0
0
2
1
0
0
1
0
0
0
1
2
1
0
1
1
1
0
1
1
1
0
2
2
0
0
1
0
1
0
0
2
0
2
0
0
0
1
0
0
0
1
2
2
3
0
0
2
2
1
0
0
1
1
0
0
0
0
1
0
0
1
0
2
0
0
0
1
1
0
2
2
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
2
0
2
0
0
0
2
0
1
2
0
0
0
0
0
3
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
2
1
0
0
0
0
1
0
1
0
0
1
0
1
0
1
0
2
0
0
2
1
0
1
0
1
1
1
2
0
2
0
2
0
2
0
0
0
0
0
0
3
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
1
0
0
1
0
0
0
0
1
0
2
0
2
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
2
0
0
0
0
2
0
0
2
0
2
0
0
1
2
0
0
0
0
0
1
2
0
2
2
2
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
1
0
0
2
0
0
0
1
0
0
1
2
0
2
0
1
0
0
2
0
0
0
0
0
1
1
2
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
2
2
0
1
0
0
2
2
0
2
0
2
0
0
2
1
1
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
2
0
1
1
0
2
0
0
0
0
0
1
0
2
0
1
1
2
3
0
0
1
0
0
0
0
0
0
1
2
1
0
0
0
2
0
0
1
1
3
2
0
1
1
0
2
1
0
1
1
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
1
0
1
2
2
2
0
0
2
0
1
2
2
1
0
0
2
2
0
2
3
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
2
0
1
2
1
0
0
3
0
2
1
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
1
2
0
0
0
2
0
0
0
1
1
1
1
0
0
0
0
1
0
6
1
0
2
0
1
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
6
0
2
1
0
0
2
2
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
2
0
0
0
0
0
1
1
1
2
0
1
2
0
0
0
1
0
1
1
0
2
1
2
0
1
0
0
0
2
3
0
1
2
2
2
2
1
0
0
0
1
0
0
0
4
2
2
0
0
0
1
2
0
0
0
0
2
2
0
1
0
0
1
0
0
0
0
0
2
1
1
0
0
3
0
2
0
0
0
1
0
1
0
0
0
0
0
1
2
1
0
0
2
0
2
2
0
2
1
2
0
0
0
0
0
0
0
3
0
0
2
0
0
2
0
0
3
0
0
1
0
0
1
0
0
0
0
2
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
2
0
0
1
0
0
1
0
0
1
0
0
1
0
2
0
1
1
2
1
2
0
2
1
0
1
0
0
1
2
0
1
1
0
0
0
0
0
0
0
0
2
1
0
4
2
0
1
0
0
0
2
2
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
2
0
1
0
0
2
0
1
1
0
0
0
0
0
1
0
0
2
2
2
0
1
2
0
1
0
0
2
0
0
1
1
2
0
0
1
0
1
0
1
4
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
1
0
0
1
0
0
4
0
0
0
1
0
1
0
1
0
0
1
0
0
1
2
0
0
1
1
0
0
2
1
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
2
1
0
2
1
0
1
1
0
2
0
2
0
0
2
0
2
0
0
0
1
2
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
3
0
0
2
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
2
1
2
0
0
0
0
1
0
0
0
1
0
0
0
0
1
2
2
0
0
0
0
2
0
0
3
1
0
0
1
0
0
2
1
0
0
1
0
0
1
1
0
2
2
2
1
0
1
0
2
0
1
3
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
2
0
2
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
2
1
0
0
2
0
0
0
0
0
0
2
0
3
0
2
0
0
1
2
0
0
1
2
5
0
0
0
2
0
3
1
0
0
2
0
1
2
1
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
2
1
0
1
0
1
0
2
0
0
1
2
0
0
1
2
0
1
2
0
0
1
1
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
2
0
1
1
0
1
1
0
2
1
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
2
0
1
0
0
1
0
2
0
0
1
0
1
2
4
0
0
1
0
0
0
2
0
0
1
0
0
2
3
0
2
2
0
0
0
2
0
3
0
1
0
0
2
1
0
2
0
0
0
2
0
2
0
0
1
0
1
1
0
1
1
0
1
0
0
2
0
1
2
2
1
0
0
0
0
0
0
0
2
1
1
1
0
0
0
0
0
2
0
0
2
1
2
0
0
3
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
1
0
3
1
0
0
1
0
1
0
0
2
1
0
1
1
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
1
0
0
0
2
0
2
0
0
0
0
0
3
0
0
1
0
1
0
0
0
0
0
1
1
0
0
1
2
0
0
1
0
0
0
4
0
2
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
2
0
2
0
1
2
0
3
0
0
0
1
0
0
0
0
0
0
0
2
2
1
2
0
1
1
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
1
3
0
0
1
0
1
1
2
2
0
0
1
1
0
0
0
0
2
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
1
0
0
2
0
0
0
2
0
1
0
0
1
0
1
2
1
0
2
1
0
0
0
2
1
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
1
0
1
0
3
1
2
0
1
3
0
1
0
0
2
0
0
0
2
0
0
0
0
1
1
1
0
3
0
2
1
0
1
0
0
0
0
1
2
0
0
0
0
2
0
0
1
2
0
0
1
1
1
2
2
2
0
0
2
0
0
0
0
2
2
0
0
0
0
2
0
1
5
0
0
2
0
1
1
0
2
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
3
0
0
0
0
0
1
0
0
0
2
1
2
0
0
1
0
1
0
0
0
1
1
0
2
0
1
1
0
0
1
0
1
3
1
0
0
1
1
0
0
1
0
0
0
0
0
0
1
2
2
0
1
0
0
1
2
2
0
0
2
0
1
0
1
2
0
0
0
0
1
0
3
2
2
0
1
0
0
2
0
0
1
2
0
0
0
1
1
2
0
1
1
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
1
0
0
1
0
2
2
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
4
0
0
0
1
0
1
2
2
1
0
0
0
1
2
4
4
2
1
0
1
0
1
2
0
0
1
0
0
0
1
1
0
0
0
0
1
1
0
1
0
1
0
0
1
2
1
0
0
1
0
2
0
0
1
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
3
0
0
2
0
1
0
1
0
0
0
2
0
0
0
0
0
2
1
0
1
2
0
0
0
2
1
0
0
2
2
0
0
0
0
0
1
0
2
1
0
0
2
2
0
1
5
2
1
0
2
0
0
2
1
0
0
0
0
2
0
0
2
0
1
1
0
0
3
2
0
0
0
0
3
4
0
3
0
0
1
0
0
0
1
0
0
0
0
0
1
2
2
0
2
2
0
1
2
0
1
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
4
1
0
0
0
2
1
2
0
0
1
1
1
0
0
2
0
2
2
0
0
0
0
0
0
0
1
1
0
3
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
1
0
1
0
0
1
0
1
0
0
2
0
0
0
0
2
2
2
2
0
0
0
0
0
2
0
1
1
0
0
0
0
9
0
0
1
0
0
1
0
0
1
0
0
0
2
0
0
2
0
0
0
2
1
2
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
2
1
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
1
2
4
0
1
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
2
1
0
1
1
1
0
0
0
1
1
0
1
1
2
1
2
2
2
0
1
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
1
0
0
2
0
0
0
1
2
1
1
0
0
0
0
0
1
1
1
0
1
0
2
2
0
0
0
2
0
0
1
2
1
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
2
1
0
0
2
0
0
0
1
2
1
1
0
0
0
0
0
2
2
1
0
0
1
0
0
0
1
2
0
0
1
2
0
0
0
0
0
1
0
0
1
2
0
0
1
2
2
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
1
0
0
0
2
1
0
2
0
0
0
0
0
1
0
0
0
0
2
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
2
0
0
0
0
2
0
1
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
2
1
2
1
0
0
0
0
1
1
2
0
1
0
0
0
2
1
0
5
0
0
0
0
1
2
0
0
0
5
1
0
0
0
0
0
0
0
2
0
1
2
1
0
2
0
0
1
1
0
1
2
0
0
2
2
0
0
0
1
0
0
0
0
1
0
0
0
6
0
1
0
2
0
0
2
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
2
1
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
2
0
2
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
3
1
0
0
2
2
0
1
2
0
1
0
1
1
3
0
1
0
4
0
1
0
0
2
3
1
0
0
0
2
2
0
0
0
1
1
2
0
0
0
3
1
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
1
0
0
3
0
0
1
0
0
0
1
0
0
0
0
2
0
0
2
1
1
0
1
2
0
1
0
0
0
0
1
2
2
1
2
0
0
2
0
1
0
0
0
0
2
0
0
2
0
0
1
3
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
1
1
0
0
0
2
0
0
1
0
0
1
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
2
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
2
0
2
0
1
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
3
2
0
0
0
1
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
2
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
1
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
1
0
2
1
1
0
0
0
2
0
5
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
1
1
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
1
3
0
0
0
0
0
2
1
0
1
1
1
0
1
0
1
0
2
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
2
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
1
2
0
0
1
0
0
2
0
2
0
0
0
1
0
2
0
0
4
0
1
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
3
0
0
1
1
0
1
1
3
0
0
0
2
0
2
0
4
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
2
1
1
0
0
0
2
2
1
1
2
1
2
0
0
2
0
0
3
0
0
2
3
3
0
0
0
0
0
0
0
2
0
1
0
2
0
2
0
1
0
4
2
0
1
0
0
0
0
0
0
2
0
1
1
2
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
1
2
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
1
2
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
1
1
1
0
1
0
1
1
2
0
2
0
0
2
1
0
1
0
0
0
1
0
3
1
2
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
2
0
0
2
0
2
5
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
3
0
0
2
1
0
2
2
2
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
2
2
1
2
2
1
2
0
0
0
0
2
1
0
1
0
0
0
0
0
2
0
0
0
0
1
1
1
1
0
1
0
1
0
1
0
0
0
2
0
0
2
0
0
1
0
2
0
0
0
0
0
0
1
1
0
0
2
0
1
0
0
1
0
1
1
2
0
0
0
2
0
0
1
2
0
0
2
0
0
0
0
2
0
0
2
2
0
0
0
0
0
1
0
1
2
0
0
0
1
0
1
0
0
1
1
0
1
0
0
0
2
1
1
0
0
2
0
0
0
1
0
0
0
2
1
1
0
1
2
0
2
0
0
0
0
0
2
0
1
0
3
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
1
1
0
0
1
0
2
1
0
1
0
1
0
0
0
1
0
2
0
1
2
0
2
0
1
2
1
0
0
1
0
1
1
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
2
0
0
2
1
0
0
0
0
2
0
0
1
1
0
1
0
0
0
2
1
0
0
0
1
0
2
2
0
0
1
2
0
2
0
0
0
0
2
0
0
0
2
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
2
0
0
2
1
0
0
0
1
0
0
2
1
2
1
2
0
0
0
2
1
1
0
0
0
0
2
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
1
1
1
0
0
0
2
1
2
0
1
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
2
0
0
0
0
0
7
2
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
3
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
4
0
0
1
0
0
2
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
2
0
3
0
1
0
2
1
0
2
0
1
0
1
0
2
2
1
1
1
1
0
0
2
0
0
1
0
2
0
0
0
2
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
1
0
3
0
0
1
0
3
0
2
2
0
0
2
0
1
0
0
0
0
0
2
0
2
1
2
1
0
0
0
0
2
0
0
0
2
2
0
2
0
0
0
1
0
1
2
0
1
0
0
3
0
0
3
0
0
1
4
0
2
2
1
0
0
2
0
1
0
0
0
0
0
2
2
2
1
3
0
0
0
0
3
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
2
0
0
0
2
1
0
2
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
2
2
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
1
2
0
0
2
2
0
1
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
1
2
0
0
0
0
2
1
0
0
0
0
0
1
2
1
0
2
0
0
0
2
0
0
1
2
0
0
0
0
2
2
0
7
0
0
0
0
0
1
3
0
0
1
0
0
0
0
0
0
0
0
0
2
1
2
0
1
0
0
1
0
2
0
0
0
0
0
0
0
2
2
0
2
0
0
0
2
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
3
2
0
0
1
0
0
0
1
0
0
0
1
0
2
0
2
3
0
0
1
0
2
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
2
0
2
0
1
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
6
1
1
1
2
0
2
0
0
2
0
0
0
0
1
0
2
0
0
1
0
0
2
0
0
0
1
2
0
9
1
2
1
1
1
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
3
2
0
1
2
0
2
0
0
0
0
0
0
0
1
1
0
2
0
1
7
0
0
5
0
0
0
0
3
0
0
0
0
0
1
1
0
0
1
2
0
2
1
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
1
0
2
0
1
2
0
2
0
1
0
1
0
1
0
2
2
1
1
1
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
4
1
0
2
0
0
0
1
0
2
0
0
0
0
0
0
2
2
2
0
0
2
0
1
1
2
2
1
1
0
0
0
0
3
0
0
0
1
1
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
2
2
0
0
0
0
1
0
0
2
0
0
1
2
0
0
0
0
1
0
0
4
0
2
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
2
0
0
2
0
0
0
1
2
0
1
2
0
2
0
0
0
0
0
2
0
1
0
1
0
0
0
9
1
0
0
1
1
0
0
0
0
2
0
0
0
0
2
1
0
1
1
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
2
0
2
0
2
0
0
1
0
2
0
1
0
0
0
1
2
0
0
0
0
1
1
1
0
0
0
0
0
2
1
0
1
0
0
2
0
0
0
2
2
2
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
2
0
2
6
0
0
0
0
0
1
0
0
0
3
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
1
0
0
2
1
0
1
1
0
1
0
0
2
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
1
0
2
0
2
0
0
0
2
0
0
1
0
0
0
1
7
0
0
0
0
1
1
0
0
1
0
2
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
2
1
1
0
0
1
3
2
0
1
0
1
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
1
0
1
0
0
0
0
0
0
0
2
2
0
0
2
1
0
0
2
0
0
2
1
1
2
0
0
0
0
1
1
0
0
0
0
0
2
2
0
1
0
0
1
0
0
0
0
0
0
1
2
0
0
0
1
0
1
1
0
1
0
0
0
2
0
1
0
0
1
2
2
0
0
0
2
1
1
2
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
1
1
0
2
1
0
0
0
0
1
0
2
0
0
0
1
2
1
2
1
0
1
1
0
0
0
0
0
0
2
0
0
0
2
0
2
1
0
2
0
2
1
0
0
0
1
0
1
3
2
0
0
0
0
2
1
1
1
0
1
0
0
0
0
0
0
2
0
0
0
3
3
0
2
0
1
0
1
0
0
0
1
1
0
1
2
0
0
0
0
0
0
0
1
0
0
2
0
0
1
2
2
0
1
0
3
0
1
1
0
1
1
0
0
0
1
0
1
1
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
1
0
0
0
0
2
2
1
0
0
0
1
0
0
0
0
2
0
2
0
2
0
0
1
2
0
0
2
1
0
0
0
0
2
0
1
0
0
2
0
2
0
0
0
0
1
2
0
0
2
1
2
1
0
0
2
1
2
2
1
2
2
1
1
0
0
0
2
0
0
0
1
0
0
1
0
1
1
1
0
0
0
0
2
0
1
0
1
2
1
0
0
1
1
0
0
0
1
0
0
0
1
0
0
2
1
0
0
1
0
2
0
1
0
0
0
0
0
0
3
0
0
0
0
2
0
1
1
0
1
0
0
0
1
0
2
0
0
0
2
0
1
2
1
2
0
1
1
0
0
2
1
1
1
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
1
2
1
0
1
1
0
0
0
0
0
0
0
1
2
0
1
0
2
0
0
0
0
2
3
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
2
0
1
0
2
1
0
0
1
2
2
0
0
2
0
0
1
0
1
0
0
1
0
0
2
1
0
0
1
0
2
1
2
0
0
0
0
0
0
0
0
2
2
1
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
2
0
0
0
1
0
0
0
0
0
0
1
1
1
2
0
0
1
0
0
0
2
2
0
0
0
0
2
1
1
2
0
0
0
0
2
2
0
0
2
0
0
0
1
1
0
0
0
1
2
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
2
0
1
0
3
0
1
0
2
0
0
0
1
1
0
0
0
3
1
0
0
0
2
0
0
2
0
0
1
0
2
0
0
0
0
0
2
0
0
0
2
1
2
0
2
3
0
2
0
0
1
2
1
0
0
2
0
0
1
0
0
0
1
1
0
0
2
1
2
1
0
0
0
0
0
0
0
1
2
1
0
0
0
1
0
0
1
1
2
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
4
1
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
3
0
0
1
2
1
0
0
2
0
1
2
0
1
0
0
1
0
2
0
0
0
0
0
0
3
0
0
0
2
1
0
2
2
0
0
0
4
0
0
0
0
0
0
0
0
2
2
0
1
1
2
0
1
0
0
1
1
1
0
0
0
2
1
0
0
1
0
0
1
0
2
0
1
0
1
2
0
1
1
0
0
0
0
0
0
1
0
3
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
6
0
0
0
2
0
2
1
0
0
0
1
1
0
1
0
0
0
1
1
2
0
0
1
0
2
0
2
0
1
2
0
0
1
0
2
0
0
2
2
1
0
0
0
3
1
3
0
0
1
1
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
1
0
1
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
1
0
2
0
0
0
0
1
2
3
0
0
0
0
0
1
0
2
2
0
0
0
1
0
2
1
1
0
2
0
0
0
0
0
1
0
2
0
0
0
0
3
0
2
0
0
0
0
0
1
1
0
0
2
1
0
0
1
0
2
0
0
2
1
1
0
0
0
0
0
2
0
0
0
2
2
0
2
1
0
0
1
1
2
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
1
1
1
1
2
0
0
0
0
0
3
0
0
1
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
1
4
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
3
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
2
2
0
1
0
0
0
2
0
2
0
1
3
0
1
0
0
0
0
2
0
1
0
0
1
0
0
2
0
0
0
0
2
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
1
0
0
2
0
0
0
1
0
0
0
2
0
0
1
1
0
0
4
0
0
2
1
0
0
0
0
0
2
1
2
1
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
1
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
1
0
0
1
0
2
0
2
0
0
1
2
0
2
2
0
0
1
0
1
2
0
1
0
1
2
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
1
0
0
2
0
0
0
1
1
0
1
0
0
1
1
0
0
1
0
2
0
0
2
0
0
1
0
1
0
3
1
0
0
0
2
1
2
0
0
1
2
0
1
2
0
2
2
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
1
0
1
0
3
2
2
2
0
0
0
1
0
0
2
0
0
0
0
1
0
2
1
0
0
2
0
2
0
1
0
0
0
1
0
0
2
1
0
0
2
1
1
0
2
1
1
1
0
0
0
0
1
0
1
0
0
0
0
0
2
3
0
0
5
0
1
0
0
0
0
2
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
2
0
0
3
0
0
0
0
0
2
2
0
0
2
3
1
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
2
1
1
1
0
0
1
0
2
0
2
0
0
1
0
0
1
1
0
1
1
1
0
0
1
1
1
0
2
2
3
2
0
1
1
3
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
1
2
2
1
2
2
0
1
0
2
0
1
2
0
0
0
0
0
2
0
1
1
0
1
2
0
0
0
0
2
1
2
2
1
0
0
0
0
0
0
0
0
0
2
0
0
1
2
2
2
2
2
0
0
2
1
2
0
0
0
1
2
0
1
0
2
0
0
0
0
0
3
0
1
2
0
0
1
0
2
1
2
0
0
0
0
0
1
0
0
0
2
1
0
0
1
0
0
0
0
0
2
2
0
1
0
0
0
1
0
0
1
0
2
2
0
0
0
0
0
0
0
1
0
0
2
2
0
2
1
0
1
0
0
2
0
0
0
0
0
3
4
0
0
0
2
0
0
0
3
0
0
1
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
4
0
0
1
0
1
0
1
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
1
0
1
0
1
0
0
0
2
0
0
0
2
1
1
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
2
0
2
0
0
2
0
0
0
0
0
0
0
1
1
0
0
1
0
2
0
0
0
1
0
1
0
0
0
3
1
0
0
1
2
0
0
0
3
2
0
1
2
0
0
1
0
0
0
0
1
0
3
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
2
1
0
1
1
2
0
0
0
1
2
2
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
2
1
1
2
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
1
0
1
1
2
0
1
1
0
0
0
2
1
0
2
0
0
7
0
0
1
0
2
2
0
0
0
0
0
2
2
0
2
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
3
0
2
0
0
0
0
0
0
2
0
2
0
0
0
2
8
2
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
1
0
1
1
1
0
2
0
0
0
0
1
0
1
0
1
2
0
1
1
2
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
1
1
0
0
1
0
3
0
0
0
0
2
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
2
1
0
1
0
0
0
0
0
0
0
2
1
0
1
0
0
1
0
1
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
1
0
2
2
1
0
0
0
1
3
0
0
1
1
0
0
1
0
1
0
2
0
0
1
0
0
0
0
3
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
2
2
0
2
1
0
1
2
2
1
0
0
0
2
0
0
1
0
1
0
0
0
4
0
2
0
0
0
0
0
0
1
1
0
0
1
1
0
0
2
2
0
0
0
0
1
1
0
1
0
0
2
0
2
0
2
1
0
1
1
0
0
3
0
2
0
2
1
1
0
0
2
0
2
1
2
0
0
2
0
0
0
2
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
3
2
0
0
0
0
0
0
0
1
1
2
1
2
1
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
2
2
1
0
2
2
0
0
2
2
0
0
0
1
0
2
0
1
0
0
2
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
2
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
5
0
0
3
0
0
0
0
2
3
0
0
0
0
1
0
0
0
1
0
0
0
1
2
0
0
1
0
2
0
2
0
1
1
1
0
0
1
0
2
0
1
0
0
0
2
1
2
2
0
3
0
1
2
4
0
0
0
0
2
0
1
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
1
0
0
0
2
1
1
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
2
1
0
0
1
1
0
2
3
1
0
1
2
0
2
2
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
1
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
2
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
2
1
0
0
1
2
1
1
3
0
0
0
0
2
0
0
1
0
0
0
2
0
2
0
0
1
0
1
1
0
1
0
0
2
0
3
0
0
0
0
2
0
0
0
1
2
2
0
1
0
0
1
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
2
0
1
2
1
2
0
0
0
0
1
0
2
0
1
0
0
0
1
0
0
2
3
0
2
1
0
0
0
0
0
1
0
0
0
0
0
1
0
3
0
0
1
0
0
0
1
1
2
1
0
0
0
1
7
3
1
1
2
2
1
1
1
0
0
0
2
0
1
0
0
0
0
0
1
0
1
0
1
0
0
1
1
0
0
1
0
0
1
0
1
0
0
1
0
0
2
3
1
0
2
0
3
0
1
0
0
0
2
0
2
0
0
2
1
0
2
2
1
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
1
0
3
0
0
0
2
2
0
3
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
4
0
2
0
0
0
1
1
0
0
2
2
0
2
2
0
0
2
0
2
0
0
0
0
0
1
0
1
0
0
0
0
1
1
2
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
2
0
0
1
0
0
2
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
3
0
1
2
1
1
2
2
3
0
0
2
0
2
0
0
2
0
2
0
0
1
1
0
1
0
1
2
2
0
1
1
2
0
1
1
0
1
0
0
1
0
0
0
0
0
0
2
0
0
1
1
0
4
0
0
0
2
0
0
0
2
1
1
0
4
4
1
0
2
2
2
2
0
0
1
0
2
0
0
0
0
1
0
0
2
0
1
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
3
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
2
2
1
1
1
0
2
0
2
0
0
0
0
0
0
2
0
0
1
0
3
2
1
0
1
2
2
0
0
2
0
0
0
2
0
0
0
0
1
0
1
0
0
1
1
0
2
0
2
1
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
3
1
0
0
1
2
0
0
1
0
0
2
2
0
0
0
0
0
0
1
0
1
0
0
1
2
0
0
1
0
0
0
1
0
0
0
1
0
1
1
2
0
0
1
2
0
0
1
2
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
2
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
2
0
0
1
0
1
1
0
0
1
1
0
1
0
0
0
0
0
3
1
0
2
0
1
2
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
2
0
1
1
0
0
2
1
1
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
2
0
0
0
0
1
3
0
0
1
0
2
0
0
0
0
3
0
1
0
2
0
0
0
0
2
1
2
0
2
3
2
1
0
2
0
2
2
2
0
0
0
0
3
2
0
0
0
0
0
2
0
0
0
1
2
2
0
2
0
0
0
1
1
0
3
3
0
0
3
1
0
1
0
0
0
2
0
1
2
1
0
0
0
0
0
0
0
0
2
2
0
1
1
3
0
0
1
0
0
0
1
0
0
1
2
0
0
2
0
0
0
0
1
2
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
1
0
2
1
0
0
0
1
0
1
0
2
1
0
2
0
0
0
1
1
2
0
0
1
2
1
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
1
1
1
1
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
2
1
1
0
2
0
0
0
3
2
1
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
1
2
0
1
0
0
0
2
1
0
0
0
0
1
3
1
0
0
0
1
1
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
2
0
0
0
2
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
2
1
0
1
0
0
0
0
0
2
0
2
1
0
0
0
2
2
0
0
0
0
0
0
2
1
2
0
0
0
1
1
2
1
0
0
0
2
0
0
1
1
0
2
0
0
0
0
2
2
1
0
0
0
2
0
0
0
1
1
1
0
0
0
0
2
1
0
1
3
0
0
2
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
1
2
2
2
1
0
0
0
1
0
0
0
2
2
1
0
0
0
0
1
2
0
0
2
0
0
2
0
1
0
0
0
1
0
2
0
0
1
0
1
0
1
1
0
2
0
2
2
0
2
0
0
2
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
1
0
0
0
0
1
0
2
0
0
3
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
3
1
0
0
1
3
0
2
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
2
0
0
1
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
1
1
2
0
0
0
0
2
0
0
0
2
1
0
1
1
3
0
0
3
0
0
0
0
0
0
1
3
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
2
3
0
0
1
0
0
0
0
0
1
0
2
0
2
1
1
0
0
0
2
0
0
0
2
0
0
1
0
2
1
0
0
0
0
2
0
0
0
0
1
0
0
2
4
0
0
1
0
2
2
0
0
0
0
0
0
1
0
2
0
0
1
3
1
0
0
1
0
0
1
0
0
0
0
2
0
0
0
3
0
2
0
0
0
0
2
0
0
2
1
2
1
2
2
2
1
0
0
1
0
0
1
0
1
2
1
0
3
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
2
0
2
0
1
0
2
0
2
0
0
0
3
0
0
1
0
2
1
1
0
0
1
0
0
2
0
0
1
1
1
0
0
2
1
0
0
0
0
0
1
1
0
0
0
0
2
1
0
0
0
1
2
0
0
0
3
1
2
1
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
1
2
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
2
0
2
1
1
2
1
0
0
3
0
2
0
1
0
0
2
2
1
2
0
0
1
0
2
2
0
2
1
0
0
0
0
0
0
0
1
0
2
1
1
2
1
0
0
1
1
0
0
0
0
0
0
2
2
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
3
1
2
2
1
0
0
1
0
0
0
0
0
1
0
1
2
1
2
1
1
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
1
2
2
0
2
1
1
0
0
1
0
1
0
1
0
1
0
0
1
1
0
0
1
2
0
0
0
0
0
1
2
2
0
0
0
0
1
0
0
1
0
0
1
0
1
1
0
1
2
0
4
0
1
0
1
0
0
2
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
1
0
1
0
2
0
0
0
1
0
1
2
0
0
0
2
0
1
2
1
3
0
0
0
2
0
0
3
2
0
0
0
0
0
1
0
1
0
0
3
0
0
0
0
1
1
0
2
0
2
0
0
1
2
0
0
2
0
2
0
0
1
1
1
0
0
0
2
0
0
0
0
0
2
0
0
0
2
1
0
0
1
0
1
1
0
0
0
1
0
0
0
9
0
0
0
1
0
4
0
2
2
0
0
0
1
0
1
0
0
1
0
0
0
0
0
2
2
0
3
0
0
2
2
1
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
2
0
0
1
1
0
2
2
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
2
0
2
2
0
1
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
1
1
0
0
1
0
0
3
0
0
0
0
0
0
0
2
1
0
0
0
0
2
1
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
3
0
0
2
0
2
0
0
0
0
0
1
1
0
1
0
4
0
2
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
2
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
1
2
1
0
0
0
2
18
0
0
0
1
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
2
0
2
2
1
2
0
2
0
1
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
3
4
1
0
1
0
0
0
1
1
1
3
0
0
0
2
4
0
0
0
0
0
0
1
0
0
0
0
1
2
0
1
0
0
0
2
0
0
1
0
0
2
0
0
0
0
1
0
0
0
1
2
0
0
0
2
0
0
1
0
0
2
0
0
1
2
0
0
0
0
3
2
2
0
0
1
1
0
1
1
0
0
1
0
2
1
0
0
2
0
0
2
0
2
1
0
0
0
1
0
0
1
0
0
0
2
0
2
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
1
1
2
0
2
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
1
1
0
0
0
0
0
0
0
7
1
0
0
0
2
2
2
0
1
0
2
2
0
0
2
1
0
0
0
0
0
0
1
2
0
1
1
2
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
2
1
0
0
0
1
2
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
2
1
0
2
1
0
0
0
0
0
2
0
1
1
1
0
0
0
0
2
2
3
0
1
0
2
1
1
0
1
1
0
0
1
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
2
0
2
1
1
0
0
1
1
0
1
2
0
3
0
1
1
1
2
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
2
2
2
0
2
0
0
0
1
0
1
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
1
1
2
0
0
0
1
0
0
2
0
1
2
1
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
3
0
1
2
2
0
0
1
0
2
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
2
2
2
1
0
5
0
2
0
2
0
1
0
0
2
2
2
2
0
0
1
0
0
0
0
0
1
0
0
0
2
2
2
1
0
5
0
0
2
1
0
0
1
1
0
2
1
1
1
1
2
0
0
0
1
0
0
0
1
1
0
0
0
2
0
0
1
1
0
0
2
0
1
0
1
0
1
0
0
1
2
1
0
0
1
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
4
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
1
3
0
0
2
2
1
0
0
0
0
2
0
1
0
0
0
2
0
0
2
0
0
0
1
0
1
2
2
0
0
0
1
2
0
0
0
0
2
1
1
0
0
1
0
2
0
1
1
2
1
0
2
3
0
1
0
0
0
0
0
3
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
1
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
1
0
1
2
0
1
0
1
2
0
0
0
1
0
1
7
2
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
1
1
2
0
1
0
0
2
2
0
1
0
0
0
1
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
2
0
0
2
2
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
2
1
0
0
0
0
2
0
2
3
0
0
1
0
0
1
2
0
0
0
2
1
0
0
0
1
0
0
0
0
0
2
0
0
0
2
1
0
0
1
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
1
2
1
0
0
0
0
0
4
2
0
1
2
0
2
2
0
0
2
0
1
1
1
0
0
1
0
0
1
1
0
0
0
3
1
1
1
0
0
0
1
1
1
0
1
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
2
0
2
0
1
0
0
0
0
0
1
0
3
2
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
1
2
1
2
2
1
0
0
0
1
2
1
0
1
1
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
3
0
0
0
0
3
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
2
0
1
1
2
0
1
1
0
0
0
1
1
1
0
0
0
0
1
0
0
0
1
1
1
1
0
2
0
0
0
2
0
0
2
2
3
0
0
2
0
0
0
0
1
3
1
0
2
2
0
2
1
0
0
0
0
1
0
0
1
0
0
0
2
1
3
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
2
1
1
2
0
0
0
0
0
0
2
0
0
0
1
1
0
0
2
1
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
2
2
2
2
0
0
0
0
0
0
0
1
0
0
4
2
2
0
0
2
0
0
2
2
7
0
2
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
2
2
0
0
0
1
3
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
2
0
1
0
0
0
0
1
0
1
1
1
2
2
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
2
0
0
0
2
0
2
0
0
0
2
0
1
1
1
1
0
0
0
2
0
1
0
1
0
3
0
2
2
1
0
0
1
0
0
0
2
2
2
0
0
0
1
0
0
0
0
2
2
0
1
0
0
2
0
0
0
1
1
2
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
2
2
1
0
1
1
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
3
1
1
2
0
1
2
2
0
0
2
0
0
0
3
0
0
0
0
1
0
1
0
0
0
0
2
1
0
0
1
2
0
0
1
0
0
1
0
0
0
2
2
0
2
0
0
2
0
0
0
0
1
0
1
0
0
1
2
0
0
0
1
0
0
0
0
2
2
0
0
1
0
1
0
0
0
1
1
1
0
0
0
4
0
0
0
1
0
0
0
1
0
0
1
0
1
2
2
0
1
0
2
0
1
0
0
2
2
1
0
0
1
2
2
0
0
2
2
1
3
2
0
2
1
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
1
1
0
0
0
1
2
0
2
0
0
0
1
4
0
0
1
2
1
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
1
0
2
0
1
2
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
2
3
2
0
1
1
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
2
2
1
0
0
0
0
0
0
1
1
2
0
1
1
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
1
1
1
0
0
0
0
2
0
2
11
0
2
0
0
0
1
1
0
2
0
2
2
0
0
0
0
0
0
0
0
1
2
2
1
0
0
2
0
0
0
1
0
0
1
1
0
0
2
0
1
1
0
1
0
0
1
0
1
0
0
3
0
1
0
0
2
0
0
1
0
0
0
1
1
0
1
0
2
0
0
2
2
1
1
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
4
0
1
1
2
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
2
2
0
2
1
2
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
1
2
1
1
0
2
1
1
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
1
1
2
0
0
1
1
3
0
1
0
1
0
2
0
0
1
0
0
1
1
1
2
0
0
0
0
0
0
2
0
0
0
1
2
1
0
1
0
0
0
3
1
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
2
0
2
0
2
2
0
0
2
0
0
2
0
0
2
0
0
1
2
0
0
2
0
0
1
0
2
1
0
0
0
2
1
0
1
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
2
0
0
1
2
0
1
0
0
1
2
0
0
0
2
0
0
0
1
0
2
1
0
0
1
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
1
0
0
1
0
0
1
0
2
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
1
1
2
0
1
4
1
1
0
0
1
0
0
0
1
1
0
0
0
0
2
0
1
1
0
0
0
2
0
0
2
1
0
0
0
0
1
0
2
2
0
0
2
0
0
2
0
0
1
0
0
6
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
3
0
1
0
0
3
0
2
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
1
2
0
0
0
0
1
2
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
1
0
3
2
0
1
1
0
0
2
0
0
1
0
0
0
1
2
0
1
0
1
0
0
0
1
0
0
0
1
0
2
0
0
0
1
0
0
0
2
0
0
2
0
2
2
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
1
1
0
2
2
2
1
0
0
1
0
1
0
2
0
0
0
1
1
0
2
1
0
0
0
0
0
2
0
1
0
0
1
0
1
0
0
2
0
2
1
1
0
1
0
1
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
1
0
2
0
0
0
1
1
0
0
0
0
0
2
0
0
2
0
1
0
0
2
1
0
1
1
2
1
1
0
0
0
1
4
0
2
0
3
1
0
1
2
0
1
0
0
1
1
1
1
0
0
0
0
1
1
0
1
0
2
0
0
1
0
2
1
0
0
0
0
1
0
2
1
0
0
0
0
0
2
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
4
0
1
0
0
1
0
1
0
2
2
0
1
1
0
0
0
3
0
2
1
1
0
0
0
0
0
0
0
1
0
2
0
0
2
0
1
0
2
1
2
2
0
0
0
2
2
1
0
1
0
1
0
1
0
2
0
0
2
0
1
2
1
0
0
0
0
3
2
2
0
2
0
0
1
0
0
2
0
1
0
0
0
0
0
0
2
2
1
0
0
2
0
2
0
0
1
0
0
1
1
0
1
2
1
3
0
3
2
0
2
0
2
2
1
2
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
1
0
1
0
2
0
0
1
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
1
2
3
0
0
1
1
0
0
2
0
1
0
0
0
0
1
0
0
2
0
0
2
1
0
0
2
2
0
0
1
2
0
0
0
0
1
0
0
1
2
1
0
0
2
2
0
0
0
2
0
0
0
1
1
0
0
0
0
0
2
2
1
0
0
1
0
0
0
2
1
1
2
0
0
0
0
0
2
0
0
0
1
1
0
0
1
1
0
0
0
2
0
0
0
0
0
0
1
1
3
0
0
1
0
0
0
0
1
2
2
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
1
2
0
1
0
2
0
1
0
0
0
0
2
1
0
2
0
2
0
1
2
1
0
2
2
0
2
0
1
1
0
0
1
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
1
0
2
0
0
0
0
0
1
0
2
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
1
2
2
0
0
0
2
0
0
0
0
1
0
0
1
0
0
2
1
2
1
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
3
0
0
3
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
1
0
0
3
1
1
0
1
2
0
1
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
1
0
0
1
0
0
1
0
0
2
0
0
3
2
0
1
0
0
0
2
1
0
0
0
0
0
1
0
0
1
0
0
2
0
2
1
1
1
1
0
0
2
1
0
1
2
0
1
1
0
1
0
1
0
1
0
2
2
0
2
0
1
0
1
0
2
2
0
1
0
0
0
1
1
0
0
0
0
2
1
1
1
0
1
0
0
1
0
0
0
0
1
0
1
2
0
2
1
0
4
3
0
3
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
2
0
0
0
0
0
0
1
1
2
1
0
0
0
2
0
1
0
1
0
2
0
0
2
2
0
0
0
2
1
2
2
1
0
1
0
1
0
2
0
0
0
0
0
2
2
0
2
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
3
0
0
1
0
0
1
1
0
0
0
0
2
0
2
0
0
1
0
0
1
1
0
1
0
2
2
0
0
0
1
0
1
0
0
2
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
1
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
4
0
1
2
0
2
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
2
1
0
0
0
0
3
1
0
0
0
0
1
2
2
0
0
0
2
1
0
1
0
0
2
0
0
1
2
0
0
2
5
0
2
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
1
2
2
1
0
0
0
0
2
1
0
0
0
1
1
0
0
0
2
0
0
1
2
1
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
1
2
1
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
2
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
2
0
1
0
0
2
0
0
0
0
3
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
2
2
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
2
0
2
1
1
0
0
0
1
2
1
3
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
2
1
0
0
0
1
2
0
0
0
0
0
2
0
0
1
0
1
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
1
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
3
2
0
0
0
2
0
0
0
0
0
1
2
2
0
0
0
0
2
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
1
0
2
1
0
0
0
2
0
2
0
0
1
0
1
0
0
0
0
2
2
0
0
1
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
3
0
0
0
2
2
0
0
0
0
1
2
1
0
1
0
0
0
0
1
0
0
0
0
0
1
1
2
0
1
0
1
0
1
0
2
0
0
0
1
0
0
1
2
0
0
1
3
1
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
2
1
0
1
0
1
1
0
3
1
0
3
1
3
0
3
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
1
5
0
0
0
0
0
0
0
0
2
0
0
4
0
0
1
0
0
0
0
0
0
2
0
0
1
1
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
1
2
1
0
0
1
0
0
0
0
2
1
2
2
1
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
3
1
0
3
0
0
1
0
1
1
1
1
0
2
1
0
0
0
0
0
0
0
0
0
0
2
1
2
2
0
0
0
1
1
0
0
0
1
0
2
0
2
1
2
2
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
1
1
0
2
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
1
2
2
0
0
1
1
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
3
0
2
0
0
0
1
0
1
2
3
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
2
1
0
1
0
1
1
0
0
0
0
0
8
0
2
1
0
0
0
1
2
2
0
3
0
0
0
0
2
0
0
1
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
4
0
1
0
0
0
0
0
0
1
1
1
0
1
0
0
1
1
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
2
0
1
1
2
0
1
2
1
3
0
0
3
0
0
1
0
2
0
2
1
2
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
1
1
0
0
0
2
2
1
0
0
1
1
0
0
1
3
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
2
1
2
0
1
0
0
0
0
0
1
0
2
2
2
0
1
0
1
0
0
0
2
0
1
1
0
0
0
0
1
0
0
1
0
0
1
1
0
0
2
2
0
0
0
0
2
6
0
0
0
1
0
2
1
0
0
2
0
0
1
0
0
1
0
0
0
2
1
0
0
1
0
0
0
0
0
1
1
2
0
1
0
1
2
0
0
1
0
1
0
0
1
1
1
0
0
0
0
1
0
0
0
2
0
0
2
0
4
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
1
4
0
0
2
1
0
0
0
0
4
0
0
2
1
0
0
2
0
0
0
0
3
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
1
0
0
2
0
0
2
0
0
0
0
0
1
2
2
1
1
0
0
0
1
1
1
0
2
0
0
0
2
0
0
1
0
2
1
0
2
1
1
1
0
0
1
1
2
0
0
0
1
0
1
1
2
2
0
0
1
0
0
0
2
2
0
1
1
0
1
0
0
2
6
0
0
1
0
4
0
0
0
0
0
0
0
1
2
0
1
0
0
0
1
1
1
1
0
2
2
0
0
1
0
0
2
0
3
0
0
0
0
0
0
1
1
0
0
1
0
2
1
2
0
0
0
0
1
0
2
0
0
0
1
1
0
2
1
0
2
0
0
0
2
0
6
0
0
2
0
1
0
0
2
1
0
0
1
2
0
0
0
0
0
0
1
0
2
1
0
1
2
2
1
0
1
1
0
0
2
2
2
0
0
2
0
0
0
0
2
0
0
2
2
0
3
0
1
0
1
3
1
0
2
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
2
2
1
2
0
3
0
0
0
0
2
1
0
0
0
0
0
1
1
0
1
0
0
2
1
0
0
0
0
0
0
1
1
1
0
2
0
1
0
1
0
0
1
1
1
0
1
0
0
2
0
0
3
0
0
3
1
0
2
0
0
1
0
2
0
0
2
0
2
0
0
0
2
0
2
0
2
0
0
0
1
0
0
2
1
0
0
0
2
0
0
0
0
1
0
2
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
1
0
0
1
0
0
2
2
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
3
1
0
3
0
1
2
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
1
1
1
1
0
0
2
0
0
2
0
2
1
0
0
2
0
1
2
0
1
2
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
2
0
2
2
0
0
0
0
0
1
7
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
1
0
2
0
0
0
0
2
0
1
2
0
1
0
1
1
2
0
2
0
2
0
4
0
0
0
2
0
2
0
0
0
2
0
2
0
2
0
1
2
0
1
0
0
1
0
0
2
1
2
0
2
2
2
2
2
1
0
1
0
0
2
0
0
0
0
1
0
0
1
0
1
3
1
2
0
0
0
2
1
0
0
2
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
2
0
0
0
1
1
0
0
2
0
10
3
0
0
0
1
0
0
0
0
0
0
0
2
1
2
5
1
0
1
0
1
3
0
2
0
0
0
0
2
1
0
0
2
0
0
0
2
0
1
0
0
4
0
2
0
0
0
1
0
1
0
0
1
2
0
0
2
0
0
1
0
2
0
1
0
0
1
2
2
1
1
2
1
0
0
2
0
1
0
0
0
1
1
2
1
0
0
2
0
0
0
0
0
0
0
0
0
3
0
2
0
2
2
1
0
0
0
1
2
0
0
1
0
1
0
0
0
2
0
2
2
1
0
0
0
0
0
1
2
0
2
0
0
0
4
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
2
0
3
2
0
2
0
2
0
0
0
2
0
0
1
0
1
0
3
0
0
0
1
0
0
2
0
1
1
0
0
0
1
0
2
1
0
2
0
0
0
2
1
1
1
0
1
0
2
0
1
0
0
0
0
0
2
2
1
0
2
2
2
0
2
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
1
0
0
2
0
0
2
0
1
0
1
0
0
3
1
0
0
0
0
0
1
2
2
1
1
0
1
1
0
0
2
1
0
2
2
2
0
0
0
0
2
0
0
2
0
0
1
2
2
0
1
0
0
1
1
2
0
0
0
3
0
0
0
0
1
0
0
0
1
0
1
2
0
1
0
0
0
0
1
2
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
1
2
1
0
0
0
0
0
0
0
0
2
0
1
1
1
1
0
0
0
0
1
0
0
0
2
0
1
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
3
0
0
1
0
2
1
1
0
0
2
0
2
0
0
2
2
0
1
0
0
0
1
0
0
0
2
0
0
0
1
1
0
1
0
2
2
0
1
2
1
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
2
1
0
2
0
0
3
0
0
2
0
2
0
0
2
0
0
0
1
1
0
0
2
0
1
0
1
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
1
0
3
2
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
2
2
2
0
2
1
2
0
2
2
0
3
0
0
2
1
0
3
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
1
0
2
2
0
0
0
0
0
2
0
0
3
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
1
2
0
2
1
0
0
2
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
1
2
0
0
0
1
1
1
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
1
0
2
1
0
0
1
0
4
0
0
0
0
0
1
0
2
0
0
0
1
2
2
0
0
0
0
1
1
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
1
2
3
0
0
0
0
0
0
1
0
0
1
2
0
1
2
1
0
0
0
1
1
2
1
0
0
0
1
2
2
0
2
0
0
0
0
0
0
0
0
3
0
4
1
0
3
0
0
2
2
1
0
1
0
0
0
0
1
3
0
0
1
0
1
0
0
2
0
2
0
0
2
0
0
0
1
0
1
1
0
0
0
1
0
1
2
0
0
0
0
0
1
3
0
0
2
2
0
2
0
0
1
0
0
2
1
4
1
0
0
0
0
0
2
0
0
2
2
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
2
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
1
1
2
0
0
0
0
0
4
1
0
0
0
0
2
2
1
1
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
2
0
0
1
3
0
1
1
0
0
1
2
3
0
0
2
0
0
1
0
0
0
0
1
0
2
1
0
0
1
2
1
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
3
0
2
0
0
0
1
0
1
0
0
0
0
0
2
1
0
0
2
1
0
0
2
0
0
2
0
0
0
0
2
2
0
2
0
1
0
1
2
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
1
0
1
1
0
0
0
2
0
0
1
0
0
0
1
1
2
3
0
0
0
0
0
0
0
0
0
0
1
2
1
1
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
2
2
2
0
0
0
0
0
2
2
0
2
0
2
0
0
0
0
1
1
0
4
0
1
2
1
1
0
3
0
0
0
2
2
0
0
0
0
1
2
7
0
0
2
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
2
2
0
1
0
0
0
0
0
0
1
2
1
0
2
0
0
0
0
2
0
0
0
1
1
2
0
0
0
1
1
0
0
2
0
0
0
0
2
0
2
0
0
0
2
0
0
0
1
0
0
0
1
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
1
1
0
0
0
0
0
2
0
0
2
1
0
0
0
2
2
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
2
2
1
0
0
1
0
2
3
0
0
0
1
0
0
2
2
1
2
0
2
2
0
2
0
2
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
1
1
0
0
0
0
0
2
1
2
0
0
1
0
0
0
1
0
0
2
1
0
0
2
0
1
1
2
1
0
0
1
0
1
2
2
0
0
0
0
0
0
1
1
0
0
1
2
0
0
0
0
1
0
2
0
2
2
2
2
0
0
1
2
0
0
2
0
1
1
0
1
0
1
0
1
1
0
0
0
1
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
3
0
0
0
0
0
1
0
0
2
0
0
2
2
0
0
0
1
1
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
2
0
1
3
0
0
2
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
4
0
1
0
0
1
0
1
0
0
0
2
0
2
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
2
2
2
0
1
5
1
0
0
0
2
1
0
0
0
0
2
2
1
0
0
2
2
1
2
1
2
2
2
1
2
2
0
0
1
0
0
1
1
0
0
2
1
0
1
0
0
2
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
1
0
1
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
2
2
0
0
2
2
0
0
1
0
1
0
0
1
1
2
1
0
2
2
1
2
3
0
1
3
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
2
0
2
3
0
0
0
0
0
0
0
1
0
2
1
2
0
1
0
0
2
0
0
2
1
0
2
1
2
2
1
0
1
2
0
0
0
1
1
0
2
0
0
1
0
0
2
2
1
1
1
0
1
0
0
1
1
1
0
0
1
0
2
1
0
2
0
0
0
0
0
0
2
1
1
2
0
0
3
0
0
1
1
0
0
2
0
1
2
0
0
1
0
1
0
1
1
0
0
1
1
1
1
0
2
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
2
0
1
0
0
0
0
1
1
0
0
2
1
2
1
0
0
1
0
0
0
1
1
0
0
0
1
2
0
0
1
1
3
0
0
0
0
0
1
2
0
2
0
0
1
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
2
0
0
3
2
0
1
1
0
0
2
0
0
0
2
0
1
1
0
0
2
0
0
2
0
4
1
0
2
0
0
0
0
0
2
2
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
2
2
0
0
0
2
0
0
0
0
0
1
0
0
3
2
0
0
0
0
0
0
2
0
2
0
0
0
1
2
0
0
2
2
1
2
3
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
6
0
0
2
2
0
0
2
0
1
1
1
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
1
0
1
0
1
0
0
2
0
1
1
0
0
0
0
2
0
0
2
1
0
0
0
1
2
0
1
2
0
0
2
1
0
1
0
0
2
3
2
2
0
3
0
0
0
3
0
2
0
2
0
0
0
2
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
2
2
0
0
0
0
1
0
1
0
0
0
0
1
1
0
2
0
0
0
0
2
2
0
2
1
0
0
0
1
0
1
1
0
0
0
2
2
0
0
0
0
0
2
2
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
2
2
0
0
0
0
1
0
1
0
1
3
0
0
0
2
2
3
0
0
0
0
1
1
0
0
0
0
2
2
3
0
0
2
0
0
0
0
0
1
0
1
0
1
0
2
1
0
0
0
0
0
0
0
2
5
1
0
1
0
0
1
0
0
0
2
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
1
2
2
2
0
0
1
0
2
1
2
0
0
0
1
0
2
2
0
0
1
0
1
2
0
0
2
0
0
0
2
0
2
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
1
0
2
4
2
0
2
0
1
0
0
0
1
0
0
0
1
2
0
2
0
2
0
0
1
0
0
1
0
1
0
4
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
2
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
2
1
0
1
0
1
0
0
0
0
0
2
2
0
1
0
0
0
0
2
0
0
0
1
0
2
2
0
0
0
2
2
1
0
0
0
0
2
0
0
0
0
2
0
1
0
2
2
0
0
0
0
0
2
1
0
0
0
1
2
1
0
0
1
0
4
2
0
1
1
0
0
0
0
1
2
0
1
0
1
0
0
1
0
1
1
0
2
1
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
2
1
2
0
0
3
0
0
3
0
0
0
0
0
2
0
0
0
1
1
0
2
1
0
0
1
1
0
2
0
4
2
0
0
1
0
0
0
2
2
2
0
1
0
0
0
0
0
0
1
2
0
1
1
1
0
0
0
0
0
0
1
1
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
2
0
0
0
0
2
1
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
1
3
0
0
0
0
1
0
0
0
1
0
3
0
0
2
0
1
0
0
0
0
0
2
0
0
0
2
1
0
0
1
2
0
1
0
0
1
0
2
1
1
1
2
2
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
2
2
0
2
0
0
2
1
0
2
2
5
0
0
1
2
2
2
0
0
0
1
0
0
0
0
0
2
0
0
2
1
0
1
0
3
1
0
1
2
0
1
0
1
0
0
0
1
0
0
0
2
0
1
0
1
0
0
1
2
0
0
0
0
0
2
0
0
2
6
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
1
0
2
2
0
1
1
0
0
0
0
1
0
0
0
1
1
0
0
0
3
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
2
0
0
1
0
2
0
0
0
0
0
0
2
2
2
0
2
1
0
0
2
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
2
1
1
0
0
1
2
1
1
0
0
1
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
1
2
2
0
0
1
2
3
2
0
0
1
0
0
0
0
0
0
0
1
0
1
2
0
3
0
2
0
0
0
1
0
0
0
0
1
0
2
4
0
0
0
2
0
0
1
2
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
3
0
0
0
0
2
3
3
0
0
0
0
0
1
1
0
0
2
2
0
1
1
0
0
0
2
2
3
1
0
0
0
1
2
1
0
1
2
0
0
2
1
0
2
0
2
2
1
0
0
0
2
1
0
0
1
0
0
2
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
1
0
0
1
1
0
0
0
0
1
0
0
5
0
0
0
0
5
0
0
0
2
0
1
2
0
0
1
0
2
0
0
0
0
0
0
3
2
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
1
0
0
0
2
0
2
0
2
1
2
0
0
0
1
1
2
0
0
1
0
2
0
0
0
1
2
2
4
0
0
0
1
0
1
0
0
0
0
0
1
0
0
2
2
0
2
1
1
2
0
2
0
0
0
2
1
0
0
0
0
1
1
1
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
2
2
0
1
0
1
0
1
0
0
0
0
0
1
0
2
0
1
0
0
3
1
0
1
0
1
2
0
1
0
2
0
2
2
0
0
0
0
0
1
0
0
1
0
0
1
1
2
0
0
2
1
0
1
2
0
0
0
0
0
0
1
1
0
2
2
0
1
1
2
1
2
0
0
2
0
1
2
2
1
2
0
1
2
1
0
1
2
0
0
1
0
2
1
0
1
0
2
0
1
1
1
0
0
1
1
0
0
2
0
0
0
0
2
1
1
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
1
0
0
1
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
1
1
0
0
0
0
0
2
1
2
0
0
0
0
0
1
0
0
2
0
1
2
0
2
1
2
1
0
0
1
0
1
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
4
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
2
4
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
2
0
0
3
2
0
0
0
0
0
0
1
0
0
6
4
0
1
0
0
0
0
0
1
2
2
1
0
0
2
0
0
1
2
0
0
0
2
0
0
1
1
0
1
0
0
0
1
0
2
2
0
0
1
2
1
0
0
0
1
0
1
2
0
0
2
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
2
1
1
0
4
0
1
0
1
0
0
2
0
0
0
2
2
0
0
2
0
0
0
0
0
1
0
1
1
0
1
3
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
2
0
2
2
0
3
2
1
0
0
1
2
1
0
0
3
0
0
2
0
1
1
0
1
2
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
1
2
2
0
0
0
0
1
1
0
0
0
2
2
2
2
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
2
1
0
2
0
0
1
3
1
1
2
1
0
1
1
0
0
0
0
2
1
2
0
1
0
2
0
0
2
1
0
0
2
0
0
0
0
2
0
0
0
1
0
2
1
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
1
2
3
0
0
0
0
1
0
0
3
0
0
2
0
1
2
1
1
0
1
0
2
0
0
1
0
0
0
0
0
0
0
2
1
2
0
0
0
1
0
2
0
2
1
0
0
2
0
0
0
0
0
1
1
1
0
0
0
0
0
0
2
0
0
2
0
1
0
1
0
0
2
0
0
1
0
2
0
0
0
1
1
0
0
0
0
0
0
2
0
0
1
1
1
0
0
2
1
0
2
0
2
0
0
0
0
0
0
1
1
0
0
1
2
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
3
0
1
0
1
0
1
0
2
2
1
0
0
0
1
0
1
0
0
0
1
0
0
1
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
2
0
1
0
1
1
0
0
0
0
0
1
0
1
2
1
0
0
2
1
2
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
1
0
0
0
1
2
0
1
2
1
0
2
0
0
1
2
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
4
1
2
1
1
0
0
0
1
1
0
2
0
0
0
0
0
0
1
2
0
0
0
5
2
0
2
0
0
0
2
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
3
2
0
0
2
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
4
0
2
2
0
0
2
1
0
2
0
1
0
1
1
1
0
0
0
0
1
0
0
2
1
1
2
0
1
0
0
0
0
0
0
2
0
5
0
0
0
2
0
2
1
4
1
0
2
0
1
0
2
0
0
1
0
2
0
0
0
0
0
0
1
2
0
0
2
0
2
0
0
0
0
0
2
0
1
0
0
0
2
0
1
1
1
0
0
0
2
0
2
0
2
0
1
1
0
1
0
0
0
2
0
1
0
0
0
2
0
1
1
1
0
1
1
0
2
0
0
2
1
2
0
0
0
2
2
0
1
1
0
0
0
0
2
0
1
4
1
0
2
0
0
0
0
0
0
1
1
2
2
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
1
1
1
1
0
0
2
0
2
2
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
1
0
0
0
0
0
0
0
0
0
4
1
0
1
0
0
0
0
0
0
2
1
0
0
1
0
2
0
0
2
2
0
0
0
0
0
1
0
1
1
0
1
0
1
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
3
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
2
1
0
2
1
0
0
2
0
0
1
2
0
2
0
0
0
1
0
1
0
2
0
1
0
0
0
0
2
0
0
1
0
2
0
2
2
0
1
2
0
2
0
0
0
2
2
1
0
0
0
2
1
3
0
0
0
0
0
0
0
0
1
4
0
2
2
0
0
0
0
0
1
1
1
0
1
1
0
0
0
1
0
0
2
2
0
1
0
0
2
0
1
0
0
0
1
0
0
1
1
2
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
1
1
0
0
0
2
0
0
1
1
2
0
0
0
0
1
0
0
1
2
1
2
2
2
0
2
1
0
0
0
0
0
2
0
0
0
0
2
0
3
0
0
0
0
1
0
0
2
0
0
2
2
0
0
1
0
1
2
0
1
0
0
0
0
0
1
0
0
0
0
1
2
1
0
1
2
0
1
0
0
2
3
0
1
1
2
2
1
6
0
0
0
1
0
1
2
1
0
2
1
0
2
0
0
0
0
0
2
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
1
0
0
2
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
5
0
1
1
1
1
2
1
0
1
0
0
0
0
0
2
2
1
0
1
0
0
0
1
2
0
0
0
0
2
0
0
0
1
0
0
0
2
4
0
0
1
0
0
0
1
0
0
0
4
0
2
0
0
1
1
0
2
0
0
3
1
0
1
0
0
0
1
2
0
0
0
2
0
0
0
2
1
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
1
1
0
0
3
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
1
0
0
0
1
1
0
0
1
0
0
1
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
1
3
1
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
2
0
0
1
2
0
0
0
3
0
0
3
0
2
0
1
0
0
0
2
3
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
2
0
2
0
0
0
1
0
0
0
3
0
0
0
1
0
2
1
1
1
0
2
0
0
0
0
0
4
0
1
0
2
1
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
2
0
0
1
0
1
0
2
0
2
2
2
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
1
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
2
0
1
1
1
0
1
1
2
0
0
1
6
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
1
0
0
1
0
0
1
0
0
1
2
1
0
1
1
0
2
0
2
0
0
0
0
0
0
0
0
1
1
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
2
2
0
2
0
0
1
0
2
0
0
0
0
0
1
0
2
1
1
0
0
0
2
2
0
0
0
0
0
0
1
0
0
3
0
2
0
0
2
1
0
0
0
1
0
2
3
0
2
0
1
2
0
0
0
0
0
0
1
0
0
2
0
0
1
2
0
0
1
0
0
1
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
2
1
0
0
1
0
2
2
1
2
0
2
0
0
0
0
3
0
0
2
2
0
0
0
0
0
1
0
2
0
0
1
1
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
2
0
0
2
1
1
0
0
1
1
0
0
0
0
2
0
0
1
0
0
2
0
1
0
0
0
1
1
0
0
2
0
0
0
0
0
0
1
0
1
1
0
1
2
0
0
0
0
0
2
0
1
3
2
0
2
2
0
1
0
2
1
0
0
0
0
0
2
1
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
1
0
1
1
0
0
0
0
0
0
0
0
0
2
3
1
1
0
0
2
0
3
0
0
2
0
0
2
0
0
0
0
3
0
2
0
0
4
0
0
0
0
0
0
0
0
13
1
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
1
0
2
0
2
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
1
1
2
2
0
1
0
0
1
1
0
0
1
2
1
1
0
1
0
2
0
0
0
2
2
1
0
0
0
0
0
3
0
2
2
1
0
2
0
0
0
0
2
1
0
0
0
2
0
1
1
0
0
1
0
0
0
0
1
0
1
0
1
2
0
0
0
2
0
0
0
0
0
0
3
0
0
2
1
0
0
1
0
1
2
0
2
0
2
2
1
0
2
0
2
2
1
0
0
0
1
0
2
0
0
1
3
0
0
1
2
2
0
0
1
2
2
1
0
0
2
2
3
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
3
1
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
1
0
0
1
1
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
1
2
0
2
0
0
0
0
1
2
1
3
0
3
1
0
0
0
1
0
0
3
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
1
1
0
0
0
1
1
0
0
0
0
0
2
0
1
1
1
0
0
0
0
3
0
0
2
2
0
0
0
0
0
0
2
1
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
1
1
2
1
0
0
0
2
1
0
0
0
2
1
0
0
0
0
0
2
0
0
0
2
0
1
1
2
1
1
0
0
1
0
0
0
0
0
1
0
1
0
2
1
0
2
0
0
0
0
0
0
1
0
0
0
2
0
2
0
1
0
2
0
0
0
0
0
2
0
2
0
1
1
0
1
0
0
0
1
2
0
1
2
2
0
0
0
0
0
2
2
1
0
2
2
3
0
1
1
0
0
1
0
3
1
0
0
0
0
0
1
1
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
2
0
0
0
0
0
1
1
1
0
2
0
0
2
0
0
0
0
0
2
1
1
0
0
0
3
1
0
0
0
2
0
1
0
0
0
2
0
2
1
0
1
1
1
0
0
0
0
0
1
0
0
2
0
0
0
1
1
0
5
0
0
0
2
2
1
0
0
1
2
0
0
2
0
0
1
1
0
2
0
0
2
0
2
0
2
3
1
0
0
2
0
0
0
0
0
2
1
2
0
0
0
2
0
2
0
0
0
0
0
0
0
2
2
0
0
4
0
0
0
1
2
1
1
0
0
0
0
2
2
0
2
2
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
2
0
0
0
0
1
0
0
0
2
1
0
0
3
0
2
0
1
0
1
2
2
1
0
0
2
3
2
0
1
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
2
0
2
1
0
0
1
2
0
0
0
0
1
0
0
2
0
1
2
0
0
0
2
1
3
2
0
0
2
0
6
0
0
1
0
0
0
0
2
0
0
0
0
1
0
1
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
2
2
0
1
0
0
0
0
1
1
1
2
2
0
0
0
0
0
0
0
0
0
2
1
1
1
1
0
1
0
0
2
2
1
2
0
0
2
1
0
0
1
0
0
0
1
0
0
2
2
0
1
1
0
1
0
0
1
0
1
0
0
0
1
2
3
1
1
2
0
0
0
0
1
2
2
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
1
1
2
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
4
1
1
0
0
1
2
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
2
0
0
0
1
1
0
2
0
0
0
0
2
0
0
0
2
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
1
1
0
3
0
1
0
0
2
0
1
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
2
3
0
2
0
0
1
2
0
0
2
1
1
0
0
2
2
2
1
0
1
1
2
2
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
2
1
1
1
0
0
2
0
0
0
2
0
2
0
2
2
0
2
2
0
0
0
0
0
1
1
2
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
2
1
0
1
0
0
2
2
1
1
1
0
0
0
0
0
0
1
1
2
1
3
0
1
0
0
0
2
1
0
0
5
0
0
1
0
0
0
0
0
2
0
0
0
0
1
1
2
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
1
0
2
0
0
1
0
2
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
2
0
2
0
0
0
1
2
2
0
1
2
0
0
0
1
1
1
0
2
1
2
0
0
0
1
1
0
0
1
1
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
1
1
0
2
0
0
3
0
0
0
2
1
0
2
0
0
0
2
1
2
0
0
1
0
2
0
0
0
0
2
1
1
5
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
1
1
0
0
2
0
1
2
1
1
3
0
0
2
0
0
0
0
0
0
0
1
2
1
0
1
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
2
0
1
0
1
2
0
0
0
2
0
1
0
1
0
0
2
2
0
0
0
2
2
0
0
0
0
0
0
0
1
0
1
0
2
0
1
0
2
0
0
0
2
0
0
0
0
0
1
1
0
2
0
0
0
1
0
0
1
0
2
0
0
1
3
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
1
1
2
3
1
0
2
1
0
0
0
0
0
1
1
0
3
2
0
0
0
0
0
1
2
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
2
1
0
1
1
0
2
0
3
2
2
1
0
1
1
0
0
2
1
1
0
0
0
0
1
0
0
1
0
0
1
2
0
0
1
0
3
2
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
1
2
2
1
0
2
0
0
2
0
0
0
1
0
0
2
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
1
2
2
0
0
0
0
0
1
0
0
1
0
0
0
0
2
1
2
2
0
1
0
2
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
2
1
0
2
0
2
1
0
2
0
0
0
0
0
0
6
0
0
1
1
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
1
0
1
0
1
0
0
2
0
1
0
0
1
0
2
1
0
0
5
0
0
0
1
0
0
0
2
0
0
0
0
2
2
2
2
3
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
1
1
0
0
0
1
0
2
1
0
2
2
7
0
0
4
0
0
0
0
2
1
2
0
2
0
0
1
0
1
0
1
0
0
1
0
0
0
2
0
0
0
2
2
0
2
0
0
1
0
1
2
3
0
2
0
2
0
1
0
1
1
0
0
1
2
1
0
0
0
0
0
0
1
0
0
1
2
3
0
0
2
1
2
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
1
0
0
1
0
1
0
1
2
0
0
2
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
3
0
1
2
1
0
2
0
2
2
1
2
4
0
0
0
2
2
0
0
0
2
0
0
0
0
0
1
0
2
5
0
1
0
0
0
1
0
0
0
0
1
2
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
1
1
2
0
1
1
0
0
2
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
2
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
2
2
0
0
2
0
0
0
1
0
3
2
3
0
2
0
2
0
0
0
0
2
2
1
2
1
2
2
1
1
2
1
0
2
0
0
1
0
0
1
0
2
1
1
0
0
0
0
0
1
1
0
0
0
1
1
0
0
1
0
0
0
2
2
0
1
0
2
0
0
2
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
1
0
1
2
1
0
1
0
1
0
0
0
1
2
0
1
0
1
2
2
2
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
2
2
1
0
0
0
0
0
2
0
0
0
0
0
1
2
0
1
0
0
0
0
1
0
1
0
2
2
1
0
1
0
0
0
0
1
0
0
2
2
1
2
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
1
0
2
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
1
1
0
0
0
0
2
1
2
0
3
1
2
2
2
1
0
0
0
1
1
3
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
3
0
1
0
2
2
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
1
2
0
0
0
1
0
0
1
0
0
0
1
2
0
0
1
0
0
1
0
0
5
0
0
1
2
1
0
0
0
0
2
1
0
2
0
0
1
0
1
0
0
0
0
0
0
0
2
0
1
1
0
2
1
0
0
0
0
2
1
0
1
0
1
0
0
0
2
2
0
0
0
0
0
1
2
0
0
0
0
2
1
0
0
0
0
1
0
1
2
0
0
0
0
0
0
1
1
2
0
0
0
0
1
0
1
2
2
0
0
1
0
0
0
3
1
2
0
0
2
1
0
1
1
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
2
2
2
1
0
0
0
0
2
1
2
1
0
0
0
0
4
1
0
2
1
0
0
1
0
0
0
1
3
1
1
3
2
1
3
4
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
2
1
1
0
0
2
0
2
0
3
2
1
0
0
0
2
1
0
0
0
0
0
1
0
1
0
2
1
0
0
0
1
0
2
0
0
1
0
0
0
0
0
1
1
0
1
0
1
0
0
1
3
1
0
0
0
3
0
1
2
0
1
1
0
0
0
0
1
0
0
2
2
0
0
1
2
1
0
0
0
1
2
0
0
0
0
0
0
1
2
0
1
0
0
0
1
1
0
0
0
0
2
1
5
2
0
1
1
0
0
0
0
2
0
1
0
0
2
1
0
0
0
0
2
0
2
0
0
1
3
1
0
2
0
0
0
2
0
0
0
1
0
1
0
0
2
0
0
1
0
2
1
0
0
2
1
1
0
0
0
0
0
1
2
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
2
4
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
1
2
1
0
0
4
1
0
0
0
2
2
1
0
0
0
0
2
2
0
1
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
1
2
0
2
0
0
0
1
1
0
0
2
2
1
0
0
0
1
1
0
2
0
0
2
0
1
1
0
0
1
0
0
0
0
2
2
2
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
1
1
2
0
1
2
0
2
0
1
0
1
3
1
1
0
2
1
1
0
0
1
0
0
0
2
0
2
1
0
1
0
1
0
0
0
2
1
0
0
0
1
0
1
0
0
2
0
2
0
2
2
1
1
1
1
1
3
2
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
2
2
2
0
0
0
1
0
1
0
0
1
0
2
0
0
1
0
1
1
0
2
1
0
1
0
0
0
0
0
3
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
2
1
1
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
2
0
2
1
0
2
0
0
0
2
0
1
0
2
1
0
0
1
1
0
0
0
2
0
1
0
0
0
2
0
1
0
0
0
0
1
0
0
0
1
1
1
2
2
2
0
2
0
0
5
0
0
1
2
0
0
1
0
1
0
0
1
0
0
2
0
1
0
1
0
0
0
0
0
0
1
0
2
2
0
0
1
0
0
2
0
0
0
2
0
3
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
1
0
0
1
1
2
1
0
0
1
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
2
2
2
0
0
1
1
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
2
1
0
3
4
4
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
2
0
1
2
1
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
1
2
1
1
0
0
1
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
1
1
2
0
2
0
0
1
0
0
0
0
0
1
0
4
0
1
2
2
0
0
0
1
0
0
0
2
2
0
0
0
0
1
1
0
0
1
0
2
0
0
0
2
2
0
0
0
6
0
0
0
2
1
0
2
0
0
2
0
0
0
1
1
2
0
0
0
0
0
2
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
2
0
2
0
0
2
1
1
0
0
0
2
0
0
0
0
1
2
0
0
0
2
2
1
0
0
2
0
2
0
1
0
0
0
0
1
1
0
1
1
0
2
1
0
3
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
3
0
0
1
2
3
0
0
0
0
1
0
0
0
0
0
0
1
0
2
1
1
0
0
0
0
2
2
1
0
0
2
0
3
0
0
1
2
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
1
0
2
0
2
0
2
1
1
0
1
1
0
1
1
0
2
0
1
0
1
0
0
0
2
0
0
2
2
0
1
1
0
0
0
0
2
0
1
1
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
2
0
3
2
0
1
2
0
0
0
2
0
0
0
0
1
0
2
0
0
1
0
0
2
0
0
0
1
2
0
2
0
1
0
1
0
0
0
1
0
2
1
0
3
0
0
0
1
0
0
0
2
2
0
0
0
0
0
1
1
0
0
0
0
2
0
1
0
0
3
2
0
0
1
0
0
0
1
0
2
2
0
0
2
0
0
0
1
2
1
2
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
6
0
4
0
0
0
0
0
5
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
4
0
0
2
0
1
0
0
1
0
0
0
2
0
0
1
0
0
0
0
1
0
0
4
0
3
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
3
3
0
0
0
0
2
1
1
0
0
0
2
0
2
0
0
0
1
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
3
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
2
0
0
2
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
3
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
1
1
2
2
0
0
0
0
0
0
2
0
0
3
0
1
2
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
1
0
3
0
2
2
0
0
2
0
0
0
0
1
0
0
1
2
2
0
2
0
1
0
0
1
0
0
1
0
0
0
0
2
0
4
2
0
0
1
2
2
0
1
0
0
0
0
1
0
10
1
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
3
1
0
0
0
0
2
0
0
0
2
0
0
0
0
18
0
3
0
1
0
1
0
0
0
1
0
1
1
0
0
0
0
1
0
0
2
0
0
0
1
1
0
0
3
0
2
2
1
2
1
0
2
0
2
0
1
0
2
0
0
1
1
1
1
1
1
1
0
0
0
1
0
0
1
1
1
0
1
2
0
0
1
0
2
0
0
2
0
1
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
3
0
0
0
0
0
2
1
0
1
0
3
0
0
0
1
2
0
0
0
0
0
0
1
0
0
2
2
1
0
1
0
2
2
0
1
0
0
0
0
1
1
0
0
0
2
0
2
0
1
0
1
2
0
0
0
0
0
0
0
2
1
2
0
0
2
2
0
0
0
1
0
1
2
0
0
0
0
0
0
0
1
0
2
2
2
1
0
0
0
0
0
0
0
0
2
0
1
0
0
1
1
0
0
0
0
0
0
0
2
2
3
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
1
0
2
1
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
1
0
0
2
0
0
2
0
0
1
0
1
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
5
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
3
0
0
0
0
0
3
1
0
0
0
0
2
0
1
0
0
1
0
0
0
0
2
0
1
0
0
0
0
3
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
1
0
1
1
0
1
1
0
0
0
1
0
0
0
1
0
2
0
0
2
0
1
0
2
0
1
0
2
0
0
0
1
0
2
0
0
0
3
0
2
1
0
3
0
2
0
2
1
2
1
2
2
0
1
0
0
0
1
0
0
0
1
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
3
1
2
0
1
2
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
6
0
0
0
0
4
0
0
0
0
2
0
2
3
2
2
0
2
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
2
0
0
0
1
0
0
0
2
0
1
0
0
2
0
0
1
0
1
0
0
0
1
0
1
0
0
0
1
1
2
0
1
0
0
0
0
0
0
0
0
1
1
0
3
1
0
2
2
1
0
1
0
0
0
0
1
1
0
0
1
2
0
0
2
0
2
0
0
0
2
1
0
0
0
2
0
0
0
2
1
0
0
1
0
2
1
0
1
0
0
2
0
1
1
0
0
0
2
0
0
1
0
0
2
3
0
0
0
0
1
0
2
0
0
1
2
0
1
2
2
0
0
0
0
0
0
0
0
0
2
3
0
2
1
0
2
0
1
0
0
0
2
0
2
0
0
0
0
0
1
0
0
2
1
2
1
1
0
0
2
0
0
0
0
0
0
0
1
2
2
2
1
0
0
0
0
0
0
0
2
2
2
0
0
0
3
0
2
0
1
0
0
0
0
2
0
1
0
0
2
0
0
2
0
2
0
0
1
1
2
0
2
0
0
0
2
0
0
0
2
1
0
2
0
1
0
0
0
3
1
0
2
0
0
0
0
2
1
0
2
0
1
0
0
1
0
0
0
0
1
0
0
1
0
1
0
1
0
0
2
1
0
1
0
3
0
0
1
1
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
1
0
0
0
2
0
2
0
0
0
0
0
2
0
0
2
0
0
1
2
0
4
2
0
2
1
2
0
0
0
0
0
2
0
0
1
2
0
0
2
0
2
0
2
0
0
0
1
0
0
0
3
0
0
0
2
1
0
0
0
0
0
4
0
0
2
2
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
2
0
0
1
2
0
0
0
0
0
0
1
0
0
0
2
0
1
0
1
1
0
0
4
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
1
2
0
0
2
1
1
0
0
0
2
0
1
0
0
0
1
1
0
0
0
1
0
2
1
1
0
1
0
2
0
0
1
0
0
2
2
0
1
1
0
2
2
0
2
1
0
0
0
1
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
1
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
2
2
0
0
0
0
0
1
0
1
2
0
1
1
0
0
0
0
2
1
0
0
0
2
1
0
0
0
0
1
2
2
0
0
1
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
1
2
0
0
0
1
2
0
0
2
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
2
0
2
0
1
1
0
0
2
1
2
0
0
2
0
2
1
2
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
2
3
0
0
0
0
0
0
0
2
0
0
0
0
1
1
1
1
0
0
0
0
1
2
0
2
0
0
2
0
2
0
2
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
2
1
2
1
2
0
0
1
1
0
1
2
3
0
2
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
1
0
1
2
0
0
2
0
3
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
3
1
0
0
0
0
1
1
0
2
0
2
0
1
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
1
2
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
1
0
0
2
0
2
1
1
1
0
0
0
2
0
0
0
0
2
0
1
2
0
1
0
3
0
1
0
0
2
0
0
0
0
0
0
2
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
2
0
0
0
1
0
1
0
6
0
0
0
2
2
2
0
0
0
1
0
2
0
2
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
1
2
2
2
2
2
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
3
2
1
2
0
0
0
1
0
2
0
0
0
1
0
0
0
0
1
0
0
1
2
1
2
2
0
3
2
0
0
2
2
0
3
0
0
1
2
5
0
0
2
0
1
0
0
3
0
2
2
0
4
0
0
0
2
1
1
0
0
0
0
1
0
2
0
0
1
0
0
2
0
1
0
1
1
0
2
0
0
0
2
0
2
0
0
1
1
2
2
2
0
0
0
0
0
0
0
0
1
0
1
0
1
1
2
0
0
0
1
0
0
1
0
2
0
1
2
0
1
2
0
2
0
1
1
0
0
0
0
2
2
0
1
0
2
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
1
2
0
0
1
0
0
0
2
1
0
0
0
0
2
0
0
1
1
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
1
0
2
0
0
2
1
1
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
2
1
0
0
0
1
0
0
1
0
0
0
3
0
0
1
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
2
0
1
1
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
1
0
0
2
1
0
0
0
0
2
0
1
0
0
2
2
1
1
2
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
2
0
0
1
2
0
0
0
4
2
0
3
2
1
0
0
2
0
0
0
0
0
2
1
0
2
3
0
2
0
0
2
0
0
0
0
0
0
1
0
2
0
0
1
2
0
0
0
0
0
2
1
0
2
0
1
0
2
0
0
0
0
0
1
0
2
0
0
0
1
0
1
1
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
3
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
2
3
0
1
2
0
0
0
0
0
0
1
3
2
0
0
0
1
2
0
0
1
1
0
0
0
0
2
1
1
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
1
0
1
0
0
1
0
1
1
0
2
0
0
1
0
0
0
0
1
0
2
1
0
0
2
0
1
0
0
2
0
0
0
0
2
1
0
0
0
4
2
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
2
0
2
2
0
0
0
0
0
1
0
2
0
2
0
0
2
1
0
0
0
0
2
0
1
0
1
0
2
0
0
2
0
0
0
0
0
1
0
0
2
0
2
2
0
1
0
0
3
0
0
0
0
3
0
1
0
0
1
0
0
1
0
0
0
0
1
0
1
0
2
2
0
1
1
0
2
0
1
0
0
1
2
2
0
0
1
2
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
1
1
3
1
0
0
0
1
1
0
3
0
0
0
0
0
0
0
3
2
0
2
0
2
2
0
0
1
2
1
2
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
1
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
1
0
0
2
0
3
0
2
1
0
3
0
2
0
1
2
0
0
0
0
1
2
0
0
0
2
0
0
0
2
3
0
2
0
2
0
0
1
1
0
1
0
0
0
0
0
2
2
0
0
0
1
1
0
1
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
1
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
2
1
1
0
1
2
0
2
2
0
0
1
0
2
2
1
2
2
0
0
1
1
3
1
0
0
0
0
0
2
2
0
0
0
1
0
2
0
1
0
0
0
0
0
1
0
2
2
2
0
0
0
2
1
0
0
0
2
2
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
1
2
2
0
0
2
0
0
0
2
2
2
1
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
1
0
0
1
1
2
0
2
1
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
2
1
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
2
2
2
0
2
0
1
0
0
2
0
0
1
0
1
0
2
2
0
0
0
0
0
2
0
0
0
0
2
3
1
0
1
0
1
2
1
2
0
1
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
2
2
0
0
0
2
1
2
0
0
0
0
0
2
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
2
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
1
0
1
0
0
1
1
2
0
0
1
0
0
2
0
0
1
0
0
0
1
1
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
2
1
0
0
0
1
0
2
1
1
0
0
1
0
4
0
2
2
0
0
0
1
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
2
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
1
0
0
1
0
1
0
1
0
1
2
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
2
1
0
2
0
0
0
2
2
0
2
2
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
2
0
0
2
0
0
0
3
0
1
0
1
0
0
0
0
1
0
0
1
4
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
2
0
0
2
1
3
0
2
0
0
0
0
1
5
0
2
1
0
2
0
1
1
1
0
3
0
0
2
0
2
1
0
2
1
1
0
0
0
1
1
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
3
2
1
0
0
2
0
1
1
0
0
0
2
0
1
0
3
0
0
0
0
0
0
1
0
0
1
1
2
0
0
0
2
1
0
2
0
2
0
0
2
0
0
0
2
1
2
0
1
1
1
1
0
0
1
1
0
0
2
1
0
1
0
0
0
0
2
0
0
0
1
0
0
2
0
1
0
2
0
0
2
0
0
1
1
0
0
0
0
2
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
2
0
1
1
3
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
1
2
0
1
2
0
0
0
0
1
1
0
1
2
3
2
2
0
0
0
2
4
0
0
0
3
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
2
2
1
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
2
2
0
0
0
0
0
0
0
1
1
0
1
0
2
0
1
0
0
0
0
1
0
2
2
2
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
2
0
0
2
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
1
2
0
0
0
1
0
1
1
3
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
2
0
2
0
0
1
0
0
1
1
0
0
1
2
0
2
0
0
0
2
1
0
0
0
0
1
1
0
2
3
2
0
0
0
0
1
0
0
0
2
2
0
0
1
0
0
1
2
0
1
4
0
0
0
1
0
0
0
2
0
0
2
0
0
0
1
0
0
0
2
0
0
1
3
0
0
0
0
2
0
1
2
0
0
0
0
1
0
0
0
0
0
2
1
0
1
0
0
0
2
0
2
2
0
2
0
0
1
1
0
0
0
0
0
1
0
1
0
0
1
0
0
2
2
0
0
1
0
0
1
0
2
2
2
0
0
1
2
0
1
0
1
0
1
0
2
2
0
0
1
0
2
1
0
1
0
1
0
0
2
0
0
0
4
1
1
0
0
2
0
1
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
2
2
0
0
0
1
2
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
1
0
0
0
0
1
1
0
0
2
0
0
1
0
5
0
2
0
0
1
0
0
0
0
1
1
2
0
2
0
0
2
0
3
2
0
0
0
0
0
0
2
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
2
0
0
2
2
0
2
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
2
2
2
2
0
2
0
0
0
1
2
0
0
0
0
1
0
2
2
0
0
2
0
2
0
0
0
0
1
0
0
2
1
1
0
0
0
4
1
0
0
0
2
0
0
2
1
1
0
2
2
2
0
0
0
0
1
0
1
0
0
0
0
0
2
0
5
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
2
0
0
0
0
2
2
2
1
0
2
2
0
0
2
0
0
1
2
0
2
2
1
2
1
0
0
0
0
0
1
0
0
3
2
0
0
2
0
0
0
0
2
0
0
0
0
1
2
0
0
0
2
0
2
1
1
0
0
1
0
0
0
1
1
0
0
1
0
0
0
2
1
0
2
3
0
2
0
0
1
0
2
1
2
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
1
0
0
0
0
0
1
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
2
1
2
0
2
0
2
0
2
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
1
0
0
0
1
0
2
1
0
0
3
0
2
1
1
0
0
0
0
2
0
1
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
2
2
0
1
0
0
0
0
1
0
1
1
0
0
1
1
0
0
1
0
0
0
0
0
0
1
2
2
0
0
0
1
2
0
0
0
2
0
0
0
2
1
1
2
0
0
2
0
0
0
0
0
0
3
2
0
1
2
2
3
1
0
0
0
0
1
0
0
1
0
0
0
2
1
0
2
1
0
0
0
0
1
1
1
0
2
2
2
0
0
1
1
0
2
0
2
0
2
1
2
0
0
2
1
0
0
2
0
0
0
2
0
0
1
1
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
1
0
0
0
2
1
0
2
0
0
2
0
0
1
0
1
0
0
0
1
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
1
0
2
2
0
0
0
1
0
2
0
0
1
0
0
0
1
1
0
0
0
0
1
1
2
0
0
2
0
2
0
3
2
1
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
1
0
0
0
2
0
1
0
1
0
0
2
0
3
0
2
0
0
0
1
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
2
0
2
0
0
0
0
0
0
1
0
2
0
0
0
2
1
1
1
2
1
0
0
0
0
0
0
3
1
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
2
0
2
1
2
1
0
8
1
0
2
2
0
2
0
0
0
0
1
0
0
2
1
0
1
0
0
2
0
0
0
2
2
0
1
0
2
0
0
0
2
2
0
0
1
0
0
2
2
0
0
0
2
0
2
0
0
1
1
2
0
1
0
0
1
0
2
0
0
0
1
0
1
0
0
1
0
0
2
0
0
1
1
2
0
0
0
1
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
2
1
0
1
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
2
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
3
0
1
0
0
2
2
0
0
0
1
1
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
1
0
0
4
0
3
0
3
2
0
1
0
0
2
0
0
2
0
0
0
0
2
0
1
1
0
0
1
2
0
2
2
0
0
1
0
0
0
0
0
0
2
2
1
2
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
3
0
2
0
0
0
0
1
0
2
0
0
0
0
1
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
2
0
1
0
0
0
0
1
0
1
0
0
4
0
1
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
2
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
2
1
0
0
0
1
0
0
1
0
0
0
0
2
0
2
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
2
0
0
0
3
0
0
0
0
0
0
1
1
0
2
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
2
1
3
0
0
0
0
0
0
0
0
1
1
0
2
0
0
2
0
0
0
0
0
2
0
3
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
2
1
0
0
0
0
1
1
3
2
4
2
0
0
0
1
0
0
1
0
2
0
0
2
3
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
1
2
1
0
1
0
1
2
2
0
0
0
0
0
2
2
0
0
0
0
0
0
2
2
1
2
2
0
0
1
0
2
0
0
2
0
0
1
0
0
1
0
0
0
0
2
0
0
0
1
4
1
0
2
0
1
0
1
0
4
3
2
0
0
2
1
2
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
1
1
1
0
0
1
0
1
0
1
0
0
0
0
1
0
3
2
0
0
0
0
0
0
0
2
2
1
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
5
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
1
1
0
0
3
0
1
0
1
2
2
0
2
1
2
2
1
0
0
1
2
0
0
1
2
0
1
0
2
0
2
0
1
0
2
1
2
1
2
0
0
0
0
0
2
0
0
1
0
0
0
0
2
1
0
0
0
1
0
0
1
1
2
2
2
1
0
0
0
1
2
0
0
1
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
2
0
1
0
2
0
1
1
0
0
1
1
2
0
0
0
1
2
2
0
0
0
0
1
2
1
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
1
0
1
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
2
0
7
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
2
0
2
0
0
2
0
0
1
0
3
0
2
2
0
2
0
1
1
0
0
1
1
0
0
0
2
0
1
0
2
0
1
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
2
1
0
2
0
0
1
0
0
0
1
2
0
1
0
2
3
0
0
0
1
0
0
1
0
0
2
0
0
0
0
1
0
1
2
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
2
2
2
0
0
0
0
0
0
1
1
0
1
0
0
3
0
0
0
0
1
2
0
0
2
0
0
6
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
2
1
0
2
0
0
3
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
1
0
2
0
0
2
0
0
2
0
0
0
2
0
2
1
0
0
1
0
0
0
1
0
2
2
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
2
0
0
2
2
1
1
0
0
0
0
0
2
0
0
0
2
0
0
0
1
4
0
2
0
0
0
2
0
0
0
0
2
0
0
0
2
2
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
2
0
1
0
2
0
0
1
0
0
2
0
2
0
0
1
0
0
3
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
2
0
3
0
0
0
0
2
0
0
0
0
0
1
2
0
2
2
1
2
2
0
2
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
1
0
3
0
0
2
0
0
1
3
0
0
0
0
0
1
0
0
4
2
0
0
0
1
1
2
1
1
0
0
1
0
2
1
0
0
0
1
2
0
2
1
1
0
4
2
0
0
0
1
1
2
0
2
2
0
0
0
0
0
0
0
2
0
1
2
0
0
0
1
0
0
0
2
3
0
0
0
0
0
2
2
1
0
1
2
0
0
1
0
0
2
2
0
0
0
2
1
2
0
0
2
1
0
0
0
0
0
1
2
2
0
0
2
0
1
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
1
0
0
2
0
0
2
0
0
0
0
2
3
0
7
1
0
0
0
2
0
0
0
0
0
2
2
2
2
0
2
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
2
0
2
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
3
1
0
2
1
1
0
2
0
0
0
1
0
0
1
0
0
2
0
0
0
3
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
1
0
0
1
0
1
1
1
2
1
1
1
0
0
0
2
3
0
0
0
0
0
0
0
1
1
2
0
1
0
2
0
0
0
0
1
0
0
2
2
0
0
0
0
1
3
0
2
2
0
2
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
1
0
1
2
0
1
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
1
1
0
1
0
2
0
2
0
0
1
0
0
1
2
1
2
0
0
1
0
0
0
1
0
0
1
0
1
0
2
2
0
1
0
0
0
1
2
0
0
1
2
2
1
1
0
1
0
0
0
0
0
1
0
1
0
0
1
0
2
8
1
0
0
2
0
2
0
0
0
0
0
0
4
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
4
0
0
0
0
0
0
1
1
0
0
0
0
2
1
0
0
0
2
1
0
2
0
3
2
2
1
0
0
1
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
3
1
1
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
1
3
0
0
1
0
0
0
0
0
1
0
1
0
2
0
0
0
2
2
0
2
0
3
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
2
4
0
0
0
0
2
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
1
2
2
2
0
1
3
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
2
2
2
1
0
2
2
2
1
0
0
0
0
0
1
0
2
2
0
0
0
1
1
0
0
0
1
1
0
0
2
1
2
0
0
1
1
1
0
0
2
2
0
0
0
0
0
2
2
1
1
1
0
1
2
0
0
3
0
0
0
1
0
0
0
1
0
0
1
0
3
0
2
0
0
0
1
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
2
0
2
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
2
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
1
0
0
2
0
0
2
0
0
2
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
2
1
2
1
2
1
1
0
0
0
3
1
2
2
1
1
1
3
0
2
1
0
2
1
0
1
1
0
0
0
0
0
0
0
1
0
2
0
1
0
0
2
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
1
0
3
0
1
1
0
4
2
2
0
1
0
2
0
0
2
0
0
0
0
0
0
0
2
0
1
0
1
0
0
1
2
0
2
0
0
0
0
0
0
0
0
1
2
1
0
0
2
2
0
0
0
0
0
0
1
0
0
0
3
0
0
2
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
2
3
1
0
0
0
0
2
1
2
0
1
0
1
2
0
0
0
1
0
1
0
0
0
1
3
1
0
0
1
1
1
0
0
2
0
0
0
0
1
2
2
2
2
0
0
0
0
0
0
0
2
1
0
2
0
2
1
0
0
0
1
1
0
0
0
2
1
2
1
2
0
0
0
0
0
2
2
0
1
2
0
2
0
0
2
0
0
0
1
1
1
1
1
0
4
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
4
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
2
3
0
0
2
0
0
3
1
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
1
1
0
0
0
2
2
0
0
0
0
1
1
1
1
0
0
0
2
2
0
0
1
0
0
1
1
0
1
0
1
2
2
0
1
0
0
2
2
0
1
0
2
0
0
0
2
0
0
0
3
1
0
0
2
0
0
1
1
0
0
0
2
0
1
1
1
0
0
0
0
3
0
2
0
1
0
0
1
0
0
0
0
2
1
0
1
0
0
0
1
0
1
0
2
0
2
0
1
2
0
0
0
1
1
0
0
0
0
2
2
0
1
0
0
0
0
0
2
0
1
0
2
2
1
0
2
0
1
0
1
0
1
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
2
2
1
0
1
0
0
0
1
2
1
3
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
2
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
1
2
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
2
0
0
1
0
4
0
0
0
1
0
0
2
0
4
2
0
1
1
0
11
0
0
0
0
1
0
2
2
2
0
1
0
0
2
2
0
1
0
0
0
0
2
1
0
0
1
0
0
0
1
1
0
0
0
2
0
0
1
2
2
0
0
0
0
1
1
2
0
0
1
0
0
0
0
0
0
2
2
0
2
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
5
0
0
2
0
0
0
2
0
0
0
1
0
0
0
1
0
2
0
0
1
0
2
0
0
1
2
0
1
3
0
1
0
2
3
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
1
2
0
0
0
2
0
0
2
1
2
0
0
0
2
1
1
0
0
0
0
0
0
0
10
0
0
0
0
1
1
1
1
0
0
0
0
0
2
0
1
1
1
1
1
0
3
1
0
0
1
0
0
0
0
0
1
1
0
1
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
2
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
6
2
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
3
1
0
2
0
0
0
0
0
0
0
1
0
0
0
1
1
2
0
0
0
2
0
0
0
0
0
0
2
1
0
0
1
2
0
0
0
2
0
0
0
2
0
2
0
0
2
0
0
0
0
0
2
0
0
2
0
0
3
1
0
1
2
1
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
3
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
1
3
2
2
1
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
2
2
0
0
0
1
0
0
2
0
0
0
0
0
1
1
0
0
2
0
0
0
1
0
1
0
1
2
0
2
2
0
1
0
4
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
2
1
1
0
1
0
0
4
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
4
2
2
0
1
0
0
0
1
0
0
0
2
0
2
0
0
0
0
2
1
2
0
1
0
3
2
0
0
0
0
1
2
2
1
1
1
0
0
0
2
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
1
0
2
0
0
3
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
1
0
0
1
0
0
0
0
0
0
1
0
0
2
1
0
1
0
0
0
2
0
0
0
2
0
0
0
2
0
1
2
0
0
0
3
2
2
0
0
0
1
0
0
1
0
0
0
1
0
1
1
0
1
2
1
1
1
1
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
1
2
1
1
0
0
0
0
0
1
2
1
1
0
0
0
0
0
1
2
1
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
2
0
0
1
1
0
0
0
4
2
2
2
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
2
1
0
2
0
2
0
0
1
2
0
0
0
2
0
0
0
3
0
2
1
0
2
0
1
0
0
0
0
2
1
0
1
1
0
2
1
1
0
1
2
0
0
2
0
0
2
0
0
2
0
5
1
2
0
0
0
2
0
2
1
3
1
0
0
0
0
0
0
2
0
2
4
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
2
2
0
1
0
0
1
1
1
0
1
0
0
3
0
0
0
2
1
0
1
1
2
0
2
1
0
0
0
0
0
3
0
0
1
1
1
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
4
0
1
0
2
0
2
0
2
0
0
0
0
0
2
1
0
5
0
0
1
2
1
0
0
0
1
0
1
0
0
1
0
2
0
0
1
0
2
0
0
2
0
0
2
1
0
2
0
0
0
0
0
1
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
2
0
2
0
0
2
0
0
0
1
3
2
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
2
1
0
2
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
2
0
2
0
0
0
2
1
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
2
0
1
0
1
2
0
0
1
1
3
0
0
0
1
1
0
1
1
0
0
0
0
0
1
0
1
0
1
1
0
2
0
0
1
0
0
1
0
1
1
1
0
1
0
0
0
0
0
1
0
0
0
2
1
0
1
2
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
2
0
0
0
1
2
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
2
0
0
0
2
0
2
0
2
1
0
0
0
1
2
0
1
1
1
0
0
0
0
1
0
0
0
0
2
0
0
1
1
0
1
0
2
0
0
0
0
1
1
0
1
2
0
0
1
0
0
2
2
0
2
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
2
0
0
0
0
2
1
0
1
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
2
0
1
0
0
0
2
0
2
1
0
0
0
0
2
0
0
1
1
0
0
0
0
2
2
0
0
0
1
1
0
0
1
2
1
0
0
0
0
0
1
0
0
2
0
0
0
2
0
1
0
0
1
0
0
1
1
1
0
0
2
1
0
1
0
2
1
0
2
2
0
2
0
0
0
0
3
0
0
1
1
2
2
0
1
0
0
0
1
0
0
2
0
0
0
1
2
0
0
2
0
2
0
0
0
0
0
1
0
1
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
4
1
2
0
0
0
0
0
0
0
0
0
4
2
0
0
1
2
3
2
0
0
2
1
2
0
1
0
0
0
0
2
2
0
0
0
2
2
0
1
0
0
1
0
0
0
0
1
0
2
0
0
2
0
1
2
1
0
0
2
0
1
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
4
1
0
1
1
2
0
0
0
0
0
1
0
0
2
2
0
0
1
0
0
0
2
0
0
1
0
0
2
0
0
0
0
2
0
0
1
1
0
3
0
0
2
0
2
1
0
2
0
1
0
0
1
1
0
0
0
0
1
0
0
1
0
0
1
1
2
0
0
0
0
2
0
0
2
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
3
0
0
0
0
0
0
0
0
1
0
0
4
0
0
1
0
0
3
0
0
1
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
2
1
2
2
0
1
0
0
1
1
0
3
0
0
2
0
0
2
1
0
1
2
0
0
1
1
3
2
0
2
0
1
2
0
1
0
0
1
2
2
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
2
2
0
1
0
0
0
0
0
0
0
2
1
0
2
1
0
0
0
1
0
0
0
0
0
0
0
2
0
3
0
1
1
1
1
1
2
2
0
0
1
1
2
1
0
1
0
0
0
0
0
1
0
2
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
3
1
0
2
3
0
0
0
1
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
2
2
0
1
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
3
0
2
0
0
1
0
1
4
2
0
0
0
0
1
2
0
5
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
3
2
1
0
2
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
2
1
0
3
0
1
0
1
0
0
0
0
1
0
2
0
2
0
3
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
2
0
1
0
0
0
0
1
0
0
1
0
0
0
0
3
1
0
0
0
0
1
0
2
0
1
0
0
0
1
0
0
1
2
0
0
0
0
1
1
0
0
0
2
0
1
0
0
0
0
1
1
1
0
1
0
2
0
0
1
0
0
0
0
0
2
0
0
0
2
2
1
0
0
1
1
1
1
0
1
0
0
0
0
0
0
4
2
0
0
2
2
0
2
1
0
1
2
2
0
0
0
0
0
0
0
2
0
0
1
0
2
2
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
2
0
0
2
0
0
2
0
1
0
2
2
0
0
0
0
2
2
1
0
0
1
0
1
1
0
0
0
2
0
1
0
0
2
2
0
2
0
0
0
1
1
2
2
0
0
0
1
0
0
1
0
1
0
2
0
2
0
0
1
2
2
0
1
2
0
0
0
2
1
2
0
1
1
0
0
1
0
0
2
2
1
1
2
0
1
1
2
1
0
0
0
2
0
1
2
0
3
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
2
2
0
0
1
0
0
1
1
0
0
2
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
1
2
0
1
0
0
2
1
4
0
0
0
0
1
1
2
0
0
0
0
0
2
5
1
0
1
0
2
2
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
2
0
1
1
1
0
0
0
0
0
0
1
2
0
0
0
0
1
0
1
1
0
0
0
1
0
2
0
0
2
0
0
2
0
0
0
1
2
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
3
2
2
1
2
0
0
0
2
0
0
0
1
2
1
0
1
1
0
2
1
0
0
0
0
1
0
0
0
0
0
1
2
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
2
1
0
0
2
1
0
0
2
2
0
1
0
0
1
0
1
0
1
0
2
0
2
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
1
2
0
2
0
2
0
0
0
0
0
0
0
0
4
1
2
0
0
0
0
2
0
0
0
0
3
2
0
0
2
0
1
2
0
0
2
1
0
2
0
1
0
0
0
0
1
1
0
2
0
0
0
2
1
0
0
0
0
0
0
1
0
1
0
2
0
0
2
1
0
0
0
0
0
0
0
1
1
2
0
2
0
0
0
1
0
0
0
1
0
0
1
3
0
0
0
2
1
0
6
0
0
3
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
2
1
1
0
1
2
2
0
0
0
1
0
1
0
2
0
0
0
0
0
1
0
0
2
0
0
2
1
0
2
0
0
0
0
0
1
0
0
0
1
0
0
5
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
2
2
0
1
0
0
0
0
0
1
0
0
1
0
1
2
0
0
2
1
0
1
0
0
4
0
0
1
2
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
2
1
0
0
1
1
2
0
0
1
1
1
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
1
1
0
2
2
1
0
2
2
0
0
0
0
0
0
1
0
3
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
1
0
1
0
4
2
1
0
0
0
1
2
0
0
0
0
3
0
2
2
1
0
0
0
0
3
0
2
1
1
0
1
2
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
2
1
0
0
1
0
0
0
0
0
1
1
0
0
3
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
2
2
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
1
1
1
0
2
0
0
2
0
1
0
2
0
1
1
0
3
0
1
0
2
0
0
0
0
0
0
2
0
0
3
0
3
1
0
0
1
1
0
0
1
0
2
0
0
0
0
0
1
0
0
1
0
2
1
0
1
0
0
2
0
0
0
0
2
0
1
0
2
0
2
0
3
0
0
2
2
0
0
0
1
1
0
0
0
4
2
0
0
2
0
0
1
0
1
0
2
1
2
0
2
2
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
2
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
1
2
0
1
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
2
2
1
0
2
1
0
0
0
0
0
0
0
2
0
1
2
2
4
1
0
0
1
2
0
1
2
0
0
0
0
0
0
2
0
0
0
1
0
1
2
0
0
0
2
0
1
0
1
0
0
0
2
0
1
0
1
1
2
0
0
0
0
0
0
1
0
1
1
0
0
1
2
0
0
1
0
1
1
2
0
1
2
4
0
0
1
1
1
1
1
0
2
0
2
0
0
1
0
0
2
1
0
2
2
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
2
2
0
0
1
0
0
0
1
0
0
2
2
0
0
0
1
0
0
0
0
2
1
1
2
0
1
0
0
0
0
1
1
0
0
0
1
0
2
2
0
0
0
0
2
2
0
0
0
2
0
2
1
0
0
3
0
0
0
0
2
2
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
1
0
1
2
0
0
5
0
1
0
0
0
1
0
2
0
0
0
1
1
2
0
0
2
0
0
1
2
1
1
0
0
2
0
0
0
0
0
0
2
2
0
0
0
1
0
2
0
0
2
2
2
0
2
0
0
1
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
1
2
0
0
0
0
2
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
3
1
0
2
0
0
0
0
3
0
2
0
2
2
2
0
2
0
0
1
3
0
1
0
0
1
1
0
0
0
1
1
0
0
1
0
1
0
0
3
2
1
0
1
0
2
0
0
1
1
0
2
1
0
1
2
0
2
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
2
1
0
2
0
1
0
0
0
0
0
1
0
0
0
3
0
0
0
0
3
0
0
0
0
2
0
0
1
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
1
1
1
1
0
0
0
1
0
2
3
0
1
2
0
0
3
0
0
1
1
0
1
2
2
0
0
0
0
0
2
0
0
0
3
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
2
0
0
0
1
1
0
0
0
0
0
1
2
2
0
0
0
0
0
2
0
2
0
2
0
0
1
0
1
0
0
0
1
0
0
1
0
1
0
1
0
1
0
2
0
1
0
1
0
0
0
1
0
0
0
1
0
1
0
0
2
2
1
0
2
0
0
1
0
0
0
3
0
0
2
0
3
2
0
0
1
2
0
0
0
2
0
2
2
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
2
0
0
1
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
1
1
1
0
1
1
3
0
1
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
1
1
1
1
2
2
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
1
0
0
0
0
0
2
1
0
2
1
1
0
0
0
0
0
2
0
0
2
2
0
0
0
0
5
1
1
1
0
2
1
0
2
2
0
0
0
0
0
1
1
0
1
0
1
1
0
0
0
0
0
0
2
2
2
2
0
0
1
0
2
0
0
0
1
0
0
0
1
0
1
1
1
0
1
0
0
0
1
2
0
0
0
1
0
0
0
0
1
2
0
0
0
0
3
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
1
0
1
2
2
2
0
2
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
1
0
0
0
0
0
2
1
0
2
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
2
0
0
1
0
0
1
0
0
1
0
1
4
0
0
0
1
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
2
0
2
0
1
0
5
1
0
0
0
2
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
2
2
0
0
2
0
0
0
1
1
0
0
0
2
1
1
2
1
0
0
0
0
0
2
0
0
0
2
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
1
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
2
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
2
0
0
0
0
1
1
0
0
0
1
0
0
0
1
2
2
0
0
0
0
0
0
2
0
0
2
0
1
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
1
0
0
0
1
3
1
0
0
1
2
1
0
0
0
2
0
0
0
1
0
0
1
1
1
0
0
2
1
1
2
0
0
2
2
0
1
2
0
0
0
1
2
3
0
1
1
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
2
0
1
0
1
2
0
2
0
1
0
2
0
1
0
0
1
0
1
1
0
4
0
1
2
0
0
0
0
2
1
2
0
0
1
0
1
0
0
1
0
0
0
1
3
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
1
0
0
2
0
2
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
1
0
1
2
2
1
2
0
0
0
0
1
2
0
1
0
0
0
2
2
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
2
1
0
2
0
0
0
0
1
1
0
0
0
1
0
0
0
1
2
2
0
1
8
0
0
1
0
1
1
0
1
2
0
0
2
0
1
2
2
0
0
2
0
0
1
0
0
1
0
0
1
2
0
0
0
0
0
0
1
0
2
1
3
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
2
3
0
0
0
0
1
2
0
0
1
0
0
0
2
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
4
2
4
0
0
0
0
0
0
1
0
5
0
0
0
1
0
1
1
2
0
0
2
2
0
2
1
0
0
2
2
0
2
0
0
0
0
0
1
0
1
0
0
0
2
0
1
0
0
0
2
3
0
2
0
1
0
2
0
0
1
0
0
1
0
2
2
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
3
0
0
0
0
0
1
0
2
2
1
0
2
0
1
0
1
0
0
0
3
1
0
0
2
2
0
0
1
2
0
0
0
1
1
0
0
0
1
0
0
0
2
1
0
2
0
1
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
1
2
2
0
0
0
0
2
1
1
2
1
0
1
3
2
1
0
0
2
2
0
0
2
0
0
1
0
2
1
0
2
0
0
0
2
1
0
0
2
0
0
1
0
0
0
0
0
0
1
0
2
2
1
0
0
1
0
1
0
2
0
4
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
1
1
0
2
1
1
2
2
0
0
2
0
0
0
0
0
1
1
0
2
0
2
1
2
0
0
0
0
1
1
0
0
2
1
1
0
0
0
1
0
0
0
0
0
0
3
1
0
1
2
0
0
0
1
0
3
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
3
0
0
0
2
3
0
0
1
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
3
0
4
1
0
2
2
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
2
0
2
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
2
3
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
3
2
0
0
0
2
1
0
0
1
0
0
0
0
2
0
1
0
0
1
2
4
0
0
0
2
1
1
1
1
0
0
0
0
1
0
1
0
0
0
1
0
1
1
0
0
0
1
0
2
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
2
0
1
0
2
0
1
2
0
0
0
0
2
0
2
1
0
2
0
0
0
1
1
1
0
1
1
0
1
0
2
2
2
1
0
1
0
0
0
1
0
1
1
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
1
0
0
0
1
2
2
0
0
0
1
1
0
0
0
1
1
0
1
0
0
0
0
2
1
2
1
0
0
0
4
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
3
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
2
0
0
0
0
1
0
0
0
2
0
1
2
2
0
0
0
0
0
2
2
0
0
2
1
0
0
0
0
2
1
0
0
0
0
0
1
0
0
1
1
3
1
0
0
0
0
1
0
2
1
1
0
1
0
1
0
1
1
0
0
0
0
0
2
0
0
2
2
1
2
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
4
0
1
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
2
2
0
1
0
0
2
0
2
0
0
0
0
1
0
9
2
1
0
0
2
2
0
0
1
1
2
1
2
2
0
0
0
2
4
0
1
0
0
0
0
0
3
0
2
2
0
1
2
0
2
2
0
0
0
0
1
2
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
1
2
3
2
1
0
0
1
1
0
1
0
0
1
0
1
0
1
0
1
0
0
0
0
1
0
0
0
1
2
2
2
2
0
0
2
1
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
2
0
0
0
1
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
2
0
1
2
1
2
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
1
2
0
2
2
2
1
0
1
1
0
3
3
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
1
0
0
0
2
2
2
0
0
0
3
2
2
0
0
2
0
0
0
1
2
2
0
0
0
1
0
0
2
0
0
0
3
0
2
0
0
0
3
2
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
2
0
0
3
0
0
0
0
0
2
2
0
1
0
0
0
2
1
1
0
1
0
0
0
1
1
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
3
1
0
0
0
2
2
0
0
0
2
0
2
2
0
3
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
1
1
0
1
1
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
2
1
0
0
2
0
1
0
0
1
0
2
1
0
0
2
0
2
0
0
0
2
1
6
1
2
1
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
1
0
2
1
0
0
0
0
0
0
4
0
0
0
0
2
0
0
1
0
1
0
1
0
2
0
2
0
2
0
2
0
0
0
1
0
1
2
1
0
0
0
0
0
1
0
1
0
1
1
1
0
0
0
0
0
2
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
1
2
0
2
1
0
0
0
0
1
0
3
0
2
2
0
2
0
0
0
0
0
0
3
0
1
2
0
0
0
0
2
0
0
2
0
0
0
1
2
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
2
2
1
0
0
2
0
2
0
2
2
0
0
0
1
2
0
0
1
1
0
0
2
1
2
0
2
1
0
0
2
1
1
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
2
2
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
1
0
1
2
0
0
0
2
0
1
0
0
0
1
0
0
1
0
0
1
0
0
2
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
2
2
0
0
0
2
0
0
0
2
1
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
1
1
0
0
0
0
0
2
0
1
0
2
0
2
0
1
0
0
1
2
2
0
0
1
0
0
1
2
0
1
1
0
2
0
1
0
0
2
0
0
2
0
0
0
0
0
1
2
0
0
0
0
1
0
0
1
0
0
1
0
0
2
0
0
0
0
2
2
0
0
1
1
0
0
0
3
0
0
1
1
0
0
2
1
1
1
0
1
0
2
0
2
0
0
0
0
0
2
0
1
0
1
2
0
0
0
0
0
0
0
1
0
0
3
1
0
1
0
0
0
0
2
0
0
3
0
3
1
0
0
0
1
0
0
0
1
0
2
0
0
0
1
0
1
4
0
2
0
0
0
0
1
1
0
0
2
0
2
0
0
0
0
1
2
2
0
1
0
2
0
2
0
0
2
2
1
2
1
0
0
0
3
0
0
2
0
0
2
1
0
0
2
0
0
1
2
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
1
0
0
2
1
0
0
3
0
0
0
1
1
0
0
0
0
2
0
1
1
1
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
1
0
0
0
2
2
0
0
3
0
0
1
1
0
0
1
1
2
2
0
0
2
0
2
0
1
7
0
0
2
0
0
2
0
0
2
0
0
1
2
0
2
0
0
0
0
2
0
1
0
0
0
2
0
0
1
2
2
0
0
0
0
0
2
1
2
0
0
1
0
1
1
2
0
2
1
0
0
3
0
1
0
0
2
0
0
1
0
0
0
0
0
2
1
0
2
0
2
0
0
0
0
1
0
0
2
2
0
0
0
1
1
2
1
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
1
0
1
2
0
2
1
0
2
0
0
0
0
0
1
1
0
0
0
2
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
1
1
2
2
3
0
0
0
0
0
1
0
2
1
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
1
2
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
1
1
3
0
1
0
2
0
2
0
4
0
0
1
0
1
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
1
1
0
0
0
3
0
0
1
4
0
0
2
0
0
2
0
1
0
0
2
0
2
0
2
0
1
0
0
0
0
2
0
1
2
0
0
0
2
2
2
0
0
0
0
0
0
1
0
2
2
0
0
0
2
0
0
0
0
1
0
0
1
2
0
2
2
0
0
0
0
1
2
0
0
0
0
2
0
0
1
0
1
0
0
2
0
2
0
0
1
2
0
0
0
0
0
2
1
1
0
0
0
1
0
2
1
0
0
0
0
0
0
2
2
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
1
0
2
0
1
1
2
0
0
0
2
1
0
0
0
0
0
2
0
0
2
1
0
3
0
0
2
2
0
0
2
0
0
2
2
2
3
2
2
3
3
0
0
2
0
2
0
0
0
2
2
0
0
0
0
0
2
0
0
0
2
1
4
0
0
2
2
0
2
0
0
0
0
0
1
0
0
0
2
4
0
0
0
1
1
1
2
0
0
0
0
4
2
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
2
1
2
3
0
0
0
0
0
0
1
0
2
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
1
1
3
0
1
1
0
1
0
1
1
0
2
0
0
0
0
0
0
0
3
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
1
2
0
1
2
0
0
0
0
0
0
2
1
1
0
3
2
0
0
0
1
0
0
0
1
1
0
2
2
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
1
1
1
0
1
0
1
0
0
2
0
1
1
0
0
3
0
0
1
0
4
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
2
2
0
0
1
0
2
0
0
3
1
0
1
2
0
0
0
0
2
0
0
1
1
1
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
1
1
2
1
2
2
0
0
10
0
1
1
0
0
1
0
2
0
0
0
0
1
2
0
2
0
0
2
0
2
1
0
0
0
0
0
0
0
0
2
0
2
0
2
1
0
2
0
2
2
0
0
0
2
0
0
0
3
0
1
0
0
0
0
2
3
2
0
0
0
0
2
1
0
2
0
1
2
0
1
1
0
1
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
2
0
1
0
1
0
1
0
0
1
0
1
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
2
2
1
0
1
0
2
0
0
0
1
0
0
0
1
0
0
2
0
0
0
1
0
0
1
1
0
0
2
0
0
0
0
0
0
2
0
1
1
0
0
2
1
2
0
6
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
2
0
0
1
0
0
0
0
0
3
0
1
0
0
0
0
0
0
2
0
2
0
2
1
2
1
7
0
0
0
1
2
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
1
1
0
0
2
1
2
0
2
2
1
2
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
1
0
0
2
0
2
1
1
0
0
0
1
0
0
1
1
0
1
0
1
0
0
0
0
2
0
0
0
0
1
0
0
1
2
0
1
1
1
0
2
0
0
0
0
0
0
0
0
1
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
1
2
0
0
2
2
2
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
2
2
3
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
2
1
2
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
3
2
0
1
0
0
2
1
0
0
0
1
1
2
2
2
0
0
0
1
1
1
0
0
2
1
2
0
0
0
0
2
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
2
1
1
2
2
1
0
0
0
2
0
2
0
0
0
2
0
0
2
2
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
1
0
0
0
1
2
0
0
2
0
2
1
0
1
0
1
0
0
0
0
0
1
0
2
2
0
0
0
0
1
1
2
0
0
1
0
1
1
0
0
0
1
1
2
2
0
2
0
1
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
2
2
0
1
0
0
2
0
1
0
0
0
1
2
2
1
0
0
0
0
0
0
2
0
0
2
1
0
0
1
0
0
0
0
1
2
2
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
1
1
0
0
0
1
0
2
0
2
0
0
0
2
0
2
0
0
1
1
0
0
2
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
1
1
0
2
2
0
0
2
0
0
0
0
0
0
0
0
1
1
0
1
0
1
1
0
1
1
0
0
1
0
0
2
0
0
0
0
0
0
2
1
2
0
1
2
0
0
0
0
1
1
2
2
1
2
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
2
0
2
0
2
0
0
0
0
3
0
0
0
2
2
0
0
2
0
0
2
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
1
3
0
1
0
1
1
1
0
0
0
2
0
1
0
0
0
0
2
0
1
0
1
0
0
0
0
2
1
0
0
0
0
0
1
0
0
1
0
2
4
0
1
0
1
1
0
2
0
0
1
0
1
0
0
0
1
0
0
0
0
2
0
0
0
1
1
1
2
0
2
1
0
0
2
0
0
2
4
0
0
0
0
2
2
0
0
0
2
0
0
2
2
0
3
1
0
0
1
0
0
0
1
0
2
2
0
0
2
1
0
0
2
2
0
1
1
5
0
0
1
0
0
0
0
2
0
1
0
0
2
0
0
1
0
0
0
2
2
0
0
2
0
2
0
2
2
0
1
0
0
0
0
0
0
5
0
0
0
0
0
2
2
0
2
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
1
1
0
1
2
1
3
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
1
0
2
0
0
0
1
0
0
0
0
2
0
0
2
2
2
0
0
0
0
0
0
0
3
1
0
0
0
7
0
0
2
0
0
2
0
0
0
0
0
0
1
1
2
2
0
3
1
0
0
2
0
1
0
0
1
2
0
0
0
1
2
0
0
0
2
0
5
2
0
1
0
0
0
0
2
0
2
0
1
1
1
1
0
0
0
3
0
5
0
0
1
2
0
1
1
2
0
0
1
0
0
1
1
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
3
1
1
2
1
2
0
1
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
1
1
2
1
0
0
2
2
0
2
2
0
0
0
0
0
2
1
0
0
0
0
0
2
0
2
0
2
1
0
0
2
0
0
1
0
1
1
0
0
0
0
0
2
0
0
1
0
2
0
1
0
0
1
1
0
0
0
0
2
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
1
0
2
0
0
0
1
2
1
0
0
2
0
2
0
0
1
0
1
1
0
1
0
3
1
0
0
2
2
1
0
1
0
0
2
1
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
1
0
2
0
1
1
0
0
1
2
0
0
2
2
2
0
0
1
0
0
0
2
2
2
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
1
2
0
2
0
0
0
0
0
0
0
2
2
0
1
1
1
0
1
1
0
0
0
0
2
0
0
2
0
0
0
2
0
2
0
1
0
2
0
1
0
0
0
4
0
1
0
3
0
3
2
1
7
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
2
0
0
3
0
3
1
0
0
0
0
1
0
1
1
1
0
0
0
0
1
2
0
2
0
1
1
0
2
1
0
1
0
0
2
0
3
2
1
0
2
1
0
0
0
2
0
0
1
1
0
1
1
0
2
1
0
0
0
0
0
1
0
0
0
0
4
0
2
0
0
0
2
2
1
1
0
2
0
0
3
1
0
0
2
2
1
1
1
1
2
0
0
0
2
0
0
0
0
0
1
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
2
1
2
1
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
1
3
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
2
1
1
0
1
0
1
0
0
0
1
0
1
0
0
2
0
2
2
0
2
1
0
0
0
0
1
0
0
2
1
2
0
0
0
3
1
0
0
0
0
0
0
2
0
1
1
1
1
1
0
0
0
1
1
1
0
1
0
0
1
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
2
1
0
1
0
0
1
2
1
2
1
0
1
0
1
0
2
0
0
0
0
2
0
2
2
0
0
0
0
1
1
0
0
0
1
0
1
0
2
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
3
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
1
0
1
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
2
4
3
0
0
0
0
3
1
0
2
0
1
0
0
0
3
0
0
0
2
1
2
0
0
0
0
0
0
1
0
0
0
2
1
0
1
1
0
2
0
1
1
0
0
0
0
0
2
2
1
0
0
0
1
0
0
0
0
0
0
2
1
2
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
1
0
0
2
2
0
2
0
1
0
3
0
0
1
1
2
0
0
0
1
0
0
1
0
2
0
0
0
0
0
2
2
0
1
0
2
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
2
1
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
2
2
0
2
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
3
2
1
2
0
2
1
0
0
0
2
0
0
2
3
0
0
0
1
0
0
0
0
0
1
2
1
0
0
0
0
1
3
1
0
0
1
0
0
0
2
2
1
1
0
0
2
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
2
0
2
0
0
0
0
1
2
0
0
0
1
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
3
2
0
2
0
0
1
0
0
0
0
0
2
0
1
0
2
2
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
1
0
0
2
0
2
1
0
0
1
0
0
1
0
0
1
1
0
1
0
2
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
1
0
1
1
0
0
0
1
0
0
2
1
0
0
2
0
0
0
2
1
1
2
2
0
2
1
0
0
1
0
0
0
0
0
0
2
0
2
1
0
0
1
0
0
2
0
0
0
0
2
0
1
2
0
0
1
0
0
1
0
0
1
2
1
0
0
0
1
0
1
0
0
2
0
2
0
0
2
0
0
2
0
0
0
1
0
0
1
1
0
0
1
0
2
0
0
0
0
2
0
2
0
0
0
0
2
0
1
2
0
1
1
0
2
2
1
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
1
1
0
3
2
0
3
2
0
3
0
0
1
0
0
2
0
2
1
0
0
2
1
0
2
0
2
1
2
0
1
0
2
0
0
2
2
1
2
2
0
1
2
0
1
2
2
2
0
2
0
1
0
0
0
1
1
0
2
2
0
2
6
1
0
0
0
0
2
1
0
0
0
0
2
0
1
1
1
0
0
1
1
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
1
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
2
0
3
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
2
2
0
0
0
0
0
1
1
0
0
0
1
0
2
1
2
2
1
1
4
1
0
2
0
0
0
0
0
1
2
0
0
0
0
1
0
0
1
1
3
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
1
2
0
0
3
2
2
1
0
1
0
2
0
0
0
0
1
0
0
0
1
0
0
2
1
0
0
1
0
1
2
2
4
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
2
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
2
2
1
0
2
0
2
1
0
0
2
1
2
0
1
0
2
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
1
0
0
1
0
2
0
0
0
0
0
2
1
1
2
1
2
0
0
1
1
1
0
2
0
0
0
0
0
1
0
1
0
0
1
0
0
2
0
2
2
0
0
0
2
0
1
1
0
0
2
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
2
1
0
0
0
0
0
0
3
2
0
1
2
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
1
1
1
0
0
0
0
0
1
0
2
0
1
0
2
1
2
2
0
2
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
2
0
1
0
2
4
0
0
1
1
0
0
0
0
1
0
0
0
2
2
1
0
1
0
0
1
0
2
1
0
0
0
0
3
2
1
1
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
1
2
0
0
0
1
0
2
0
0
0
0
1
0
2
2
2
0
2
1
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
2
2
0
1
2
0
0
1
2
0
0
0
0
0
2
0
2
2
1
0
0
0
1
0
0
0
2
0
1
2
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
1
0
5
2
2
2
0
0
2
2
0
0
1
0
2
0
0
1
0
0
2
0
0
0
0
2
1
1
1
0
0
0
2
0
0
1
2
2
2
0
1
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
2
1
0
1
0
0
0
2
0
1
1
0
0
0
0
0
0
0
3
0
1
2
0
2
0
2
2
0
0
2
2
0
1
0
1
0
0
0
1
0
3
0
1
1
0
0
1
1
0
1
0
0
0
0
1
2
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
2
0
2
0
0
4
1
0
2
1
0
0
0
0
0
1
2
0
0
2
1
0
0
0
2
0
3
0
0
0
1
1
0
0
0
0
0
1
1
0
1
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
2
2
0
0
0
3
0
2
0
7
1
0
1
1
1
0
0
3
2
2
2
0
1
1
1
0
2
2
0
0
0
1
0
2
0
0
0
0
0
2
0
0
1
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
1
1
1
0
0
1
0
0
1
0
0
4
1
0
0
1
0
0
0
0
0
2
0
1
1
0
1
0
0
1
0
0
0
0
1
1
0
1
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
4
2
0
0
2
0
0
2
0
0
2
0
1
0
0
0
2
1
0
2
0
0
0
3
0
1
1
1
2
0
0
0
2
0
2
0
0
1
0
0
1
1
1
0
0
0
0
5
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
1
0
0
0
1
0
0
4
0
2
1
0
0
1
3
2
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
2
0
2
0
2
0
1
0
3
1
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
1
0
0
0
1
0
0
3
0
0
0
1
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
3
0
2
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
1
2
0
3
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
3
1
1
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
1
1
0
0
1
0
2
2
0
0
0
0
3
0
0
0
0
0
2
0
0
0
1
0
2
1
2
1
0
3
2
2
0
0
2
1
2
2
0
0
2
0
2
0
1
1
2
0
1
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
1
0
0
1
1
0
3
2
2
1
1
0
0
1
0
1
1
2
1
2
0
1
1
0
0
0
0
1
0
0
2
0
0
1
1
2
0
0
0
0
1
1
0
1
0
1
0
0
0
1
1
0
0
1
0
0
1
1
2
0
1
2
0
1
0
0
1
0
0
2
0
1
0
0
0
1
0
0
2
0
0
1
0
0
0
1
0
0
0
0
1
1
2
1
0
0
0
0
1
0
0
2
0
2
0
0
0
0
1
0
0
1
1
2
2
0
0
2
0
2
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
1
0
0
0
2
1
1
1
0
0
0
1
0
0
2
2
0
0
0
0
0
2
0
0
2
0
0
0
2
3
2
0
0
1
0
2
0
0
0
2
0
2
1
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
3
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
1
2
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
1
1
1
0
2
0
1
0
0
1
0
2
0
1
0
1
0
0
1
0
0
0
2
0
1
0
0
0
1
0
1
1
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
2
2
0
0
0
2
2
0
2
1
0
2
0
1
2
1
2
1
2
1
0
0
2
1
2
2
0
2
1
0
0
0
2
1
2
0
0
1
2
1
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
3
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
1
0
0
1
0
0
0
0
1
0
0
1
0
2
1
0
2
0
0
2
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
2
1
0
0
2
0
1
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
1
0
2
2
0
2
0
0
0
0
1
2
0
0
2
0
2
0
2
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
2
1
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
1
2
0
1
0
0
1
0
0
0
1
3
0
2
3
0
0
0
0
0
0
1
0
0
0
1
0
2
0
1
0
0
0
0
3
0
0
0
0
0
0
1
0
0
2
0
1
0
1
2
0
0
1
0
0
0
0
0
0
2
2
1
0
0
0
2
0
1
0
7
1
0
0
1
0
0
1
0
0
0
0
0
0
0
2
2
2
1
0
0
0
0
0
1
2
0
0
2
0
0
0
0
2
2
2
0
0
0
1
2
0
2
2
0
1
1
0
0
0
1
2
1
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
1
1
2
0
0
1
0
1
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
2
1
0
2
0
2
0
0
2
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
2
2
1
0
3
0
1
1
0
0
0
0
1
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
1
0
0
0
0
0
0
2
1
2
0
0
3
0
0
0
0
0
1
0
2
0
0
0
2
2
1
0
0
0
0
1
1
2
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
1
1
0
0
0
3
0
1
1
0
4
0
1
0
2
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
2
1
0
1
2
0
0
0
0
0
0
0
2
2
0
1
2
0
0
2
0
0
1
0
0
1
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
2
0
2
2
0
2
1
0
0
0
0
0
0
0
2
2
0
1
2
1
0
0
0
1
2
0
2
0
0
0
0
2
0
0
0
0
0
1
0
1
2
1
3
0
0
0
2
2
2
1
2
0
0
0
0
0
2
2
0
2
1
2
0
0
0
1
1
2
1
0
2
0
0
1
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
3
1
4
0
2
1
0
0
1
0
0
0
0
2
1
0
1
0
4
0
0
0
2
0
1
0
0
2
0
1
0
0
1
0
0
1
0
2
0
0
2
0
0
2
0
1
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
1
1
3
0
1
1
2
2
0
2
1
1
0
1
2
0
0
0
0
2
0
4
0
1
0
2
0
0
0
2
0
1
1
1
0
0
0
0
1
2
2
0
0
0
1
0
1
2
0
0
0
0
0
2
0
0
0
2
2
2
0
1
0
3
2
0
0
1
1
0
0
0
1
0
0
4
2
1
0
0
0
2
0
0
0
0
1
1
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
1
1
1
0
0
1
0
0
1
1
2
0
0
0
0
0
0
1
2
4
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
2
1
0
0
3
0
0
0
0
1
0
3
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
5
0
0
0
0
1
0
0
0
0
1
1
0
0
4
0
0
0
0
0
0
0
0
1
2
2
0
1
0
0
0
0
3
0
2
1
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
1
0
0
0
2
1
2
0
5
0
1
0
2
0
2
1
3
0
0
0
0
2
0
1
0
0
0
0
0
1
3
0
0
0
2
0
0
0
0
0
0
1
2
0
0
1
0
1
2
0
1
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
1
0
0
3
1
1
1
0
0
0
0
0
0
6
0
0
1
0
0
0
0
2
0
2
0
0
1
2
0
0
0
2
0
0
1
2
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
2
0
0
2
0
0
0
0
3
0
0
1
0
0
0
1
1
2
2
2
1
0
0
0
0
0
1
2
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
1
0
1
0
2
0
0
1
1
0
0
0
0
0
1
2
0
0
0
0
1
2
0
0
0
2
0
1
0
0
2
0
2
0
1
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
1
2
0
0
0
2
1
0
0
0
0
2
0
0
2
2
1
0
2
0
0
1
0
1
0
0
1
0
1
0
2
2
0
0
0
0
0
0
0
2
2
1
0
1
0
1
0
0
1
1
1
1
0
2
1
0
0
0
0
0
2
0
0
0
2
2
2
0
0
0
0
2
1
1
0
2
0
0
0
0
0
1
0
2
0
2
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
3
0
0
2
0
0
2
0
0
0
0
2
0
2
1
0
0
1
0
0
1
0
0
2
0
0
0
0
1
2
0
2
0
0
0
6
0
0
2
0
0
1
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
2
0
2
1
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
1
0
0
2
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
1
2
0
3
1
1
1
0
0
0
3
0
1
0
0
0
0
0
0
1
2
2
0
0
0
2
0
2
0
1
1
3
2
0
0
0
0
3
2
0
0
3
2
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
5
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
2
0
1
1
1
1
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
2
0
2
0
1
0
0
2
0
3
1
0
0
0
0
0
1
0
2
0
0
0
2
1
0
0
1
0
0
0
0
1
0
1
0
2
0
0
0
2
1
0
0
0
2
0
2
0
0
1
0
0
0
0
1
0
1
0
1
0
1
0
0
0
1
0
0
1
0
1
2
0
0
1
2
0
1
0
0
0
1
0
0
0
0
1
1
0
2
2
0
0
0
0
0
0
1
2
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
3
0
3
0
0
1
0
0
0
0
0
0
0
1
1
0
3
1
0
1
2
0
2
0
0
0
3
0
0
0
0
0
2
1
2
0
0
0
0
1
2
0
2
0
0
0
0
3
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
1
0
0
1
0
0
0
0
0
0
3
0
2
0
2
0
1
1
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
2
0
2
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
2
0
0
1
2
0
1
1
0
2
2
2
0
1
2
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
2
0
0
4
0
0
0
2
1
3
0
0
2
0
0
0
0
0
0
0
0
0
5
0
1
2
0
0
0
2
2
2
0
0
0
2
3
2
0
0
0
2
0
1
0
0
0
1
1
5
2
2
0
0
0
2
1
0
0
0
0
0
2
8
1
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
2
0
1
0
0
1
1
0
0
2
0
2
2
0
0
0
0
0
1
1
2
0
1
1
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
2
2
0
0
3
0
0
1
1
2
0
2
0
2
0
0
0
1
0
0
1
1
0
2
0
1
2
0
0
0
1
0
0
1
0
2
0
2
1
0
2
0
0
2
2
1
0
0
1
2
2
0
0
0
1
2
0
0
2
1
2
2
0
1
0
0
0
0
0
1
0
2
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
3
1
2
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
1
2
0
0
2
2
2
0
2
0
0
2
2
0
2
0
2
0
0
0
0
0
1
1
0
0
1
0
0
0
0
2
0
2
2
1
2
0
2
1
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
2
0
2
0
2
0
0
2
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
1
2
0
3
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
2
1
2
0
0
0
1
0
2
0
0
0
0
0
0
3
0
3
1
0
0
0
1
0
2
0
0
0
0
1
0
0
1
0
0
0
1
0
2
1
2
0
1
2
0
0
3
0
0
1
0
0
0
0
0
2
1
1
1
0
0
1
0
1
0
2
0
0
1
0
0
0
0
1
2
0
2
0
0
0
0
2
0
0
1
0
0
2
0
1
0
0
2
2
0
0
2
0
1
0
3
0
2
0
0
1
2
1
2
1
1
0
1
0
1
2
2
0
1
2
0
1
2
0
0
1
0
1
2
0
0
0
2
0
0
0
0
1
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
2
2
0
2
0
2
2
1
1
2
0
0
0
0
0
2
0
0
1
2
0
2
0
0
2
0
0
0
2
0
1
1
0
0
0
0
0
0
0
2
2
2
0
0
1
2
0
2
0
2
0
0
1
0
0
0
0
0
2
1
2
0
0
1
0
0
0
1
0
3
0
2
1
0
0
2
0
2
0
1
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
2
1
0
2
0
2
0
2
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
1
2
1
2
0
0
0
0
0
2
0
0
1
0
0
2
0
2
1
0
1
1
0
0
1
2
0
0
0
0
0
0
2
2
2
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
3
0
0
2
0
0
0
0
2
1
8
0
0
2
0
0
3
0
0
2
0
1
0
3
1
0
1
3
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
1
2
1
0
1
0
0
3
0
0
0
3
1
0
0
2
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
1
0
0
0
1
0
1
0
0
2
2
0
0
0
3
2
0
1
0
2
0
0
0
1
2
0
1
1
0
0
0
0
2
1
2
1
1
0
0
2
0
2
1
1
4
0
2
0
1
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
1
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
1
1
1
0
1
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
3
0
0
0
0
2
2
1
0
0
1
0
2
0
3
0
0
0
2
0
0
1
1
0
2
2
0
0
0
1
1
0
1
0
1
0
0
0
0
0
2
2
2
2
1
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
1
1
2
3
0
0
0
1
0
2
1
0
1
0
0
0
0
2
2
1
1
2
0
2
1
0
1
1
2
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
2
0
1
0
0
0
0
0
1
0
1
2
0
0
1
0
0
0
0
0
1
3
0
0
0
0
1
1
0
1
0
0
4
1
0
0
2
0
0
1
2
0
2
0
0
0
3
2
0
5
0
1
0
0
0
0
0
3
1
3
0
2
2
0
0
0
2
0
1
2
2
0
0
1
1
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
2
2
0
1
2
1
0
0
2
2
2
0
0
1
0
2
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
1
2
0
1
1
1
2
1
6
0
0
0
2
0
2
0
0
1
0
0
2
0
0
0
0
2
0
1
1
0
0
4
0
0
1
0
2
1
2
0
0
0
0
1
0
0
2
0
1
0
2
2
1
0
0
0
0
1
2
0
0
2
0
1
0
0
2
0
2
0
0
0
0
6
2
0
1
0
0
0
1
1
0
0
0
1
0
1
2
2
2
0
1
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
1
0
1
0
0
2
1
0
1
0
0
0
1
0
0
4
0
0
1
1
0
0
0
2
0
0
0
2
0
0
0
2
1
2
0
2
0
0
1
0
3
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
1
0
0
0
1
1
1
0
1
1
1
0
0
0
0
0
0
1
2
1
1
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
2
2
1
0
2
0
0
1
0
0
0
3
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
2
2
0
2
2
0
0
2
0
1
0
0
2
0
1
2
0
1
0
0
0
1
2
0
0
1
0
2
1
0
1
0
1
0
1
0
2
2
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
3
0
1
0
0
0
0
0
2
0
0
0
0
0
7
0
3
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
1
0
2
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
2
1
5
2
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
2
0
0
0
2
0
0
2
1
0
1
0
2
0
0
4
0
1
0
0
0
0
0
0
0
0
1
2
2
0
0
1
0
0
0
0
0
2
0
1
2
0
0
0
0
2
0
1
0
0
0
2
0
1
2
0
0
0
2
0
0
0
1
0
3
2
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
3
0
0
0
0
1
2
0
1
0
0
0
0
1
0
0
0
2
1
1
0
2
0
1
2
0
0
0
1
2
0
0
0
0
0
2
0
1
2
1
5
0
0
1
0
1
0
1
2
1
0
0
1
0
0
0
0
0
2
2
1
0
0
0
2
1
1
1
0
2
1
0
0
1
0
1
0
2
0
0
2
0
0
1
0
0
0
0
0
1
0
0
1
0
2
0
2
1
0
0
2
2
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
1
0
2
0
0
0
0
0
1
2
1
0
1
2
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
2
2
2
0
0
0
2
4
0
2
0
3
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
1
1
0
0
1
1
0
2
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
1
0
2
2
0
0
1
0
3
0
1
1
0
0
1
0
0
0
0
0
0
2
0
1
2
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
2
1
0
1
0
1
0
0
0
2
1
4
2
2
1
0
1
2
1
1
1
2
1
0
0
0
0
0
2
0
0
2
0
1
2
2
0
0
0
0
1
2
0
2
0
0
2
2
3
0
2
0
0
0
0
3
0
2
0
0
0
2
1
1
1
0
4
0
1
0
0
1
0
4
0
0
0
1
1
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
2
2
2
2
0
1
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
3
2
0
0
1
0
0
0
0
1
0
0
0
0
0
2
2
3
0
1
1
0
1
4
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
3
0
0
0
0
0
1
1
0
0
2
0
0
1
0
2
1
0
0
0
0
2
0
0
2
0
0
1
0
2
1
1
0
1
0
2
0
0
1
0
0
0
0
0
0
0
1
1
0
0
2
2
1
2
0
2
0
1
2
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
1
0
2
0
0
0
1
0
0
0
2
0
0
0
0
1
4
0
0
0
0
0
0
0
1
1
1
0
0
0
0
2
0
2
2
2
2
1
1
0
0
0
0
0
0
2
2
0
0
0
0
1
2
0
2
0
1
0
0
0
2
1
2
1
2
0
1
0
0
2
0
0
1
0
1
0
2
1
1
0
2
1
0
0
1
1
0
0
0
4
1
0
0
2
0
0
1
1
0
0
1
0
1
0
2
1
0
0
0
2
2
5
0
2
1
0
3
0
0
0
1
2
0
2
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
1
2
0
0
1
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
1
0
2
1
0
0
2
1
0
0
1
0
1
1
0
0
0
2
0
2
1
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
1
2
0
0
2
0
0
0
0
0
2
1
0
1
1
0
2
0
1
0
0
0
0
0
0
1
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
2
2
1
0
2
0
0
0
1
2
0
1
0
1
1
0
2
0
1
0
0
1
0
0
2
0
2
0
0
0
3
0
0
0
1
2
0
0
0
0
2
3
0
1
0
1
2
0
0
1
1
0
0
2
2
0
0
0
0
0
0
2
1
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
2
0
3
2
2
2
0
2
1
1
0
1
0
2
1
0
3
0
1
0
0
2
0
2
0
0
0
1
1
2
0
0
2
0
0
0
7
1
2
0
0
0
2
2
0
2
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
2
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
1
0
2
0
0
2
0
3
0
0
0
0
2
2
1
1
0
1
0
0
0
0
0
0
1
2
1
0
0
0
0
2
1
0
0
0
0
1
0
0
1
0
0
1
1
0
3
0
1
0
1
1
0
0
1
0
0
0
0
1
0
1
0
0
2
2
1
1
0
0
1
1
0
0
0
0
0
0
2
2
0
0
0
1
1
1
0
0
2
0
0
0
4
0
1
2
1
0
0
0
0
0
0
2
0
1
0
2
0
0
0
1
1
2
0
0
1
0
0
0
1
2
1
0
2
2
1
0
0
0
0
0
0
0
1
0
1
0
2
0
0
1
0
0
0
3
3
0
0
2
0
0
0
0
2
0
0
1
2
2
0
0
0
1
0
2
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
2
1
1
0
2
0
1
0
0
0
0
2
0
0
0
0
2
1
1
0
0
1
1
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
1
0
2
2
1
2
0
1
0
0
0
0
0
2
1
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
2
1
1
2
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
1
1
3
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
1
1
0
0
0
0
0
1
1
0
2
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
2
0
0
2
0
0
3
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
1
2
1
0
1
2
0
0
2
0
2
2
0
0
0
2
2
0
0
1
1
0
0
1
0
1
0
2
1
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
1
0
0
1
1
0
0
0
2
0
0
0
0
0
0
1
0
1
0
1
0
1
2
0
0
0
0
0
2
1
0
0
1
5
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
1
2
0
0
0
2
2
0
0
0
2
2
0
0
2
0
2
0
1
0
0
1
2
1
0
2
0
0
0
0
1
0
1
0
1
0
2
2
0
0
2
1
2
1
0
1
0
0
1
0
0
0
0
1
1
1
0
0
1
1
0
1
0
3
1
0
1
2
0
0
0
1
0
2
0
2
1
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
1
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
1
0
1
1
0
0
0
1
4
1
0
0
0
1
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
9
1
0
0
0
2
0
0
0
1
0
0
0
0
2
0
1
0
1
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
2
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
1
1
0
1
2
1
0
2
0
2
1
0
1
0
0
2
1
0
0
0
0
0
0
1
3
0
1
0
0
2
0
0
1
0
0
0
1
0
1
2
0
0
2
0
0
1
0
0
0
0
1
1
0
2
0
0
0
1
0
0
2
2
0
0
0
1
0
2
0
1
2
2
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
4
0
0
0
0
2
1
2
0
0
2
1
0
0
1
0
0
0
0
2
3
1
0
0
0
0
0
1
2
3
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
3
0
1
3
0
0
3
0
0
1
1
0
1
0
2
0
2
0
0
2
0
0
0
2
0
2
2
2
1
2
0
1
4
0
3
0
1
2
0
0
1
0
1
1
1
0
0
0
1
0
3
0
3
2
2
1
0
0
0
2
1
0
1
0
1
2
0
1
0
0
0
0
0
0
1
1
0
1
2
1
1
2
0
2
0
0
1
1
2
1
1
0
1
0
0
0
0
0
0
0
0
2
1
1
0
0
0
2
1
0
2
0
0
1
0
0
0
0
1
0
0
1
2
1
0
1
0
0
0
0
0
0
1
3
6
0
0
0
0
1
0
1
2
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
3
0
0
0
0
1
2
0
1
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
2
0
1
1
0
1
0
1
2
0
1
0
0
0
0
0
0
0
0
1
1
2
0
1
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
2
1
1
0
2
1
0
0
2
0
0
1
1
0
0
2
0
0
1
0
0
1
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
3
0
1
0
0
0
0
1
0
0
2
0
1
1
0
2
0
0
0
0
0
1
1
2
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
2
3
3
0
2
0
0
0
0
1
1
2
0
0
0
0
0
2
0
4
0
2
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
1
2
0
0
1
0
2
2
1
0
0
1
2
1
0
2
0
0
4
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
4
0
0
1
1
2
0
0
2
0
0
0
2
0
2
0
2
0
2
1
0
0
0
0
2
2
0
1
1
1
1
2
0
2
0
0
0
0
0
1
2
0
0
0
3
1
2
0
0
0
0
0
0
0
0
1
1
2
1
0
0
0
0
0
0
0
1
2
2
1
0
0
2
0
1
0
0
2
0
2
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
2
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
2
0
1
1
0
2
0
1
2
2
0
2
2
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
2
5
1
1
2
0
0
0
0
0
0
2
0
3
2
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
2
0
0
2
0
3
1
2
0
0
0
0
0
0
1
2
0
1
1
1
0
0
1
2
0
1
0
2
0
0
0
3
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
3
0
1
1
0
1
0
0
0
0
0
2
0
0
1
0
1
0
0
1
0
1
0
2
0
2
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
3
0
0
0
1
2
0
0
0
0
0
0
0
2
0
1
0
2
8
0
5
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
2
0
0
0
1
0
1
2
1
1
2
0
0
0
1
0
1
2
2
1
0
1
1
0
2
0
0
2
0
0
0
1
1
2
2
0
1
0
0
0
3
0
0
0
0
2
1
0
0
0
0
0
0
0
1
1
0
2
0
0
0
1
2
0
2
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
2
0
0
0
0
2
2
0
1
1
2
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
2
1
0
0
2
2
0
0
0
1
0
2
2
0
0
0
0
0
0
5
0
0
0
0
1
0
1
1
2
0
0
0
1
1
1
0
0
0
2
0
1
0
0
1
2
0
0
1
1
0
0
1
2
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
1
2
0
0
1
0
0
2
0
0
0
2
0
0
0
0
2
0
1
0
0
0
1
2
1
2
3
0
0
0
2
0
0
0
0
0
1
2
1
2
0
0
0
2
0
0
1
0
0
0
2
3
1
0
1
0
0
0
1
2
0
0
0
1
1
0
2
0
0
0
1
1
2
1
3
0
2
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
3
2
2
3
0
0
0
0
0
1
2
1
0
0
1
2
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
1
1
2
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
2
2
0
0
1
0
0
2
0
0
2
0
2
2
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
3
1
0
0
1
1
2
1
1
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
4
1
1
0
0
1
1
0
0
1
1
1
1
0
2
2
0
0
2
0
0
2
0
0
2
0
0
0
0
0
1
0
0
1
0
0
1
2
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
2
0
0
1
1
2
1
0
0
0
2
0
0
0
1
0
1
2
1
0
0
1
0
0
1
0
4
0
1
0
0
0
0
0
2
1
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
3
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
1
4
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
3
0
0
0
1
0
0
0
1
0
1
2
0
0
1
0
0
1
0
1
2
0
0
0
0
0
0
0
2
1
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
2
0
0
0
1
0
2
2
1
0
0
0
2
0
3
2
0
0
0
1
0
0
0
0
1
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
8
2
0
1
2
0
1
1
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
1
1
1
0
2
0
0
0
2
0
0
0
4
2
0
1
0
0
0
2
0
0
0
2
0
0
0
0
1
2
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
4
2
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
2
0
1
0
0
1
0
2
0
0
1
0
2
0
1
1
0
1
0
0
1
0
0
0
0
1
2
0
0
0
1
2
2
1
2
0
0
0
2
0
0
0
0
2
0
0
2
2
0
2
0
0
0
0
0
2
1
3
0
1
0
0
1
0
0
2
0
0
0
0
0
3
1
0
0
1
0
0
2
0
0
1
0
1
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
1
0
3
0
0
0
0
1
0
2
0
0
2
0
1
0
1
1
0
0
0
0
0
0
0
0
2
3
0
2
0
0
1
0
0
0
0
2
1
0
0
0
0
2
0
2
0
0
0
1
1
0
1
0
0
0
4
0
0
0
0
1
1
0
0
1
0
0
3
0
2
0
0
0
1
2
0
0
0
0
0
0
2
1
0
0
2
0
0
2
0
1
0
1
0
1
0
2
2
0
0
0
0
0
0
0
1
2
2
1
1
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
1
2
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
2
2
1
0
2
0
3
1
0
0
0
0
0
0
3
0
2
0
0
0
0
7
0
0
2
0
2
0
1
0
0
1
0
0
0
0
0
1
0
2
0
0
2
0
1
0
0
0
0
3
2
0
0
2
0
0
1
2
0
0
0
0
0
2
1
0
3
1
2
0
1
0
0
0
0
0
2
0
1
0
2
0
1
2
0
1
0
0
1
1
0
2
2
0
0
0
0
1
0
1
0
0
0
0
1
0
2
0
0
0
0
2
2
0
2
0
0
1
2
0
0
0
2
0
2
2
0
0
0
0
0
2
1
1
0
0
0
1
0
1
1
0
0
2
0
1
0
0
1
2
0
1
0
1
0
1
0
0
0
0
1
0
2
0
0
1
0
0
0
1
3
1
1
0
0
0
2
0
2
0
2
0
1
0
0
2
0
2
0
2
1
0
0
0
2
0
0
0
0
0
0
2
0
2
0
1
0
2
1
0
0
0
1
2
1
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
2
2
0
1
3
1
0
2
1
2
0
1
3
1
2
1
2
1
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
3
0
0
0
0
0
0
1
2
0
0
1
1
1
2
0
0
0
1
0
0
2
0
2
1
2
0
1
0
0
0
0
0
1
0
2
0
3
1
0
0
0
0
2
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
1
1
0
1
0
1
2
0
1
2
1
0
0
1
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
2
2
0
3
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
5
1
2
1
0
0
0
0
0
1
0
3
0
0
1
0
0
0
0
2
0
2
2
2
3
2
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
3
1
2
2
0
1
0
0
1
0
0
2
1
0
0
0
0
0
0
1
1
0
1
0
2
1
1
0
0
0
1
0
2
0
1
2
0
0
2
0
0
1
1
0
1
0
0
0
0
1
1
2
0
0
3
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
2
2
0
0
0
2
2
0
0
0
3
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
1
0
0
2
2
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
2
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
1
0
2
2
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
1
0
0
0
2
0
0
1
0
3
0
1
0
0
0
1
0
0
0
0
1
0
2
0
2
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
1
1
0
0
2
0
2
0
0
0
1
0
0
0
1
2
0
3
0
2
0
1
1
1
2
0
1
1
0
0
1
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
2
1
0
0
0
1
2
0
2
1
2
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
1
2
0
0
0
0
1
1
1
2
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
2
0
0
0
0
0
2
0
1
0
0
2
1
2
0
1
1
2
3
0
0
5
1
1
0
0
0
2
0
1
1
0
0
0
2
1
0
0
0
1
0
0
0
2
1
1
0
2
0
2
0
0
2
0
2
0
0
0
1
0
2
0
0
0
1
0
1
0
0
0
2
0
0
1
0
4
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
4
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
1
1
1
2
0
0
1
1
2
0
0
0
0
0
0
0
2
2
1
0
0
2
1
0
0
2
0
2
2
2
0
0
2
1
0
2
2
0
1
2
2
0
3
2
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
2
0
0
2
0
1
0
1
0
1
2
0
1
2
0
1
0
2
2
0
2
2
0
0
0
1
0
1
0
0
1
0
0
3
2
2
0
0
0
0
0
2
1
2
0
0
3
0
1
0
0
0
0
2
2
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
2
1
0
2
0
0
2
0
0
0
2
0
0
0
0
1
1
0
0
3
2
1
1
0
2
0
0
2
0
1
1
3
0
0
2
1
0
0
1
2
2
0
0
1
0
3
0
1
0
2
0
0
1
0
2
1
1
0
0
1
0
2
0
1
2
0
2
3
2
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
3
0
1
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
2
0
0
1
0
2
0
0
0
2
1
2
0
1
1
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
1
0
2
2
1
0
0
0
0
0
0
0
0
1
0
1
2
0
2
1
0
0
1
0
0
0
2
2
0
0
0
0
2
1
0
2
0
0
2
2
0
0
0
0
0
0
2
1
0
0
0
2
2
1
1
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
2
0
0
1
0
0
3
0
0
1
1
1
0
0
0
0
4
1
1
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
1
1
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
1
1
0
1
0
2
0
2
1
1
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
2
2
2
0
2
1
0
0
0
0
0
2
2
0
2
2
2
0
0
0
2
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
2
0
2
0
2
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
2
1
1
0
2
3
0
1
0
0
1
0
1
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
2
0
1
1
1
0
2
0
1
0
1
0
2
0
1
1
0
2
0
0
0
0
0
0
1
5
0
0
0
2
0
0
0
2
0
0
1
0
2
0
0
2
0
2
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
3
0
0
1
2
0
1
3
2
0
2
1
1
0
2
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
2
1
1
0
0
0
2
0
0
2
0
1
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
1
1
0
4
2
0
0
0
1
4
0
0
2
0
1
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
1
1
1
0
2
2
0
0
0
1
0
2
0
2
0
1
0
3
1
2
0
1
0
0
0
2
1
0
1
0
1
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
1
2
2
1
0
0
0
0
0
3
2
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
2
2
0
0
1
0
2
0
0
0
1
0
0
0
0
1
1
0
0
1
2
2
0
0
0
0
1
0
0
0
3
1
0
0
0
2
0
1
0
2
1
1
2
0
0
0
0
2
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
3
1
2
0
1
0
1
9
0
0
0
0
0
1
0
0
1
2
0
0
0
0
1
1
0
0
1
0
0
1
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
2
2
2
0
0
0
0
0
0
0
0
1
1
2
2
0
0
2
0
2
3
0
0
2
2
0
1
0
0
0
0
1
0
0
0
0
0
2
0
1
2
0
1
2
0
2
0
0
0
0
1
0
0
0
1
1
1
0
0
1
2
0
0
0
1
0
0
1
0
2
0
2
2
4
0
2
0
1
1
0
1
1
0
0
0
0
0
0
0
2
1
0
0
0
2
0
1
1
1
0
2
0
0
0
0
0
0
3
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
1
11
2
1
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
3
3
3
0
1
0
0
2
0
1
0
0
0
1
0
2
2
0
0
2
2
1
0
0
0
0
0
0
0
1
2
0
0
2
0
2
0
0
0
0
1
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
1
0
1
2
1
0
2
1
0
0
0
1
2
0
0
0
0
1
0
0
0
1
1
1
0
0
1
1
1
0
0
0
1
0
2
0
0
2
1
1
0
0
0
0
0
1
2
1
0
2
1
0
0
0
0
1
0
4
2
1
0
2
0
1
1
0
6
0
0
2
4
0
1
0
1
0
0
0
1
0
1
0
1
0
2
0
2
0
0
2
1
0
0
0
2
2
2
0
1
2
0
0
16
1
2
0
1
1
0
0
0
2
0
0
0
2
1
0
1
2
0
2
0
0
0
0
1
2
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
2
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
1
2
2
2
2
0
1
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
2
0
2
1
0
0
0
0
2
1
0
0
1
0
0
0
0
0
1
0
0
2
2
2
0
0
0
0
2
0
0
0
2
1
1
0
0
0
0
1
1
0
0
0
0
1
0
2
2
0
0
1
0
0
1
0
0
0
0
0
2
3
2
1
0
0
1
0
0
0
0
3
1
0
0
0
1
2
0
2
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
2
0
0
0
2
0
2
2
0
1
0
3
0
0
3
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
1
2
0
0
2
2
0
1
0
0
1
2
0
0
1
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
1
1
2
0
2
1
0
0
2
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
1
0
2
0
2
0
0
1
2
2
1
0
0
0
0
0
0
0
0
1
0
0
2
1
0
1
0
0
0
0
1
0
0
0
1
0
2
1
0
0
0
2
0
0
0
3
0
0
0
0
2
1
1
1
0
0
1
0
1
0
0
0
1
1
2
0
0
0
1
0
6
0
0
0
0
8
0
0
0
0
1
0
0
0
1
2
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
2
0
1
3
0
2
0
2
0
0
2
2
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
1
3
0
0
1
1
2
0
0
0
3
0
0
0
0
0
0
0
2
0
2
0
0
2
1
0
2
0
0
0
0
1
0
2
0
1
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
2
2
0
0
2
0
0
0
0
1
0
2
0
2
0
1
2
0
0
0
0
0
0
2
0
0
0
1
1
0
2
0
0
1
0
0
0
0
3
0
0
1
0
0
0
0
0
0
2
0
0
1
1
0
0
0
2
1
1
0
0
2
0
1
2
1
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
2
0
1
0
2
1
0
0
0
0
1
0
0
0
0
0
1
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
2
1
1
0
3
0
0
0
1
1
1
1
0
0
1
0
0
1
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
1
1
2
0
0
0
2
0
2
2
2
0
0
2
1
0
0
0
2
0
2
1
1
1
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
1
0
0
0
1
1
0
0
4
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
2
0
0
1
0
0
2
0
1
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
2
0
0
0
2
0
1
0
1
2
0
1
0
0
1
0
0
3
2
0
0
1
0
1
1
0
0
0
0
2
0
0
0
2
0
0
0
0
2
2
0
0
2
2
0
0
2
1
0
0
0
1
2
0
0
1
1
1
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
1
2
1
0
0
1
0
1
1
2
0
0
0
0
2
0
0
1
3
1
1
1
1
0
0
2
1
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
1
2
0
0
0
1
0
2
2
0
2
0
0
0
0
0
3
0
0
0
1
0
0
0
0
1
0
1
0
0
1
2
2
1
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
1
0
0
0
1
1
0
0
1
2
2
0
1
0
0
1
1
0
0
0
1
0
2
0
0
0
1
2
1
0
1
0
0
0
0
2
0
0
1
0
1
2
0
0
0
0
2
0
0
2
2
0
0
0
0
1
1
0
0
2
2
0
0
0
0
0
0
3
0
0
0
0
1
1
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
2
0
2
1
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
1
0
2
0
2
0
1
2
2
0
2
0
0
2
0
0
3
0
0
0
0
1
0
0
0
0
0
0
1
0
2
2
2
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
1
0
0
2
0
2
2
2
1
0
0
0
2
0
1
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
1
0
1
0
0
3
1
0
0
1
0
0
1
1
1
0
2
0
1
2
0
0
2
1
0
4
2
2
0
0
0
0
0
0
0
2
0
2
1
0
0
0
1
2
0
3
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
2
2
0
2
2
0
0
0
0
0
0
0
0
1
2
2
0
0
1
0
2
0
2
0
0
0
0
2
0
0
1
1
0
0
0
2
1
0
2
0
0
0
0
1
0
0
0
0
2
1
0
1
1
1
0
0
0
2
1
2
1
1
1
0
2
0
0
4
0
0
1
1
0
0
0
1
0
1
0
0
1
0
0
2
0
2
0
1
0
0
2
2
2
0
1
1
1
0
0
0
0
0
2
0
0
0
1
0
2
1
0
1
0
0
0
0
0
0
0
0
2
4
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
3
0
2
0
0
2
0
0
0
0
2
2
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
2
0
1
1
1
0
3
0
3
0
2
0
0
2
1
0
0
0
0
1
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
1
2
0
1
0
0
0
2
0
2
1
1
0
0
0
2
4
0
3
0
0
0
0
1
0
0
0
2
0
0
0
1
0
2
1
0
0
0
3
1
1
2
0
1
0
0
0
0
2
0
0
0
0
1
1
2
0
1
0
0
0
2
0
1
0
0
2
0
1
2
1
1
0
0
0
0
0
2
0
0
0
2
0
0
2
0
3
0
1
2
1
0
1
0
1
2
0
0
1
1
1
0
0
0
0
2
0
0
0
0
2
2
1
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
2
1
0
2
2
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
1
1
1
1
2
0
0
0
0
1
0
1
0
0
2
0
0
3
0
1
2
0
1
0
0
0
4
0
1
0
2
0
0
2
0
0
0
0
2
2
0
3
0
1
2
0
0
4
1
1
1
0
1
0
0
0
2
0
3
0
0
0
0
2
0
2
2
1
0
0
1
0
2
0
2
0
2
1
0
2
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
1
2
1
2
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
1
0
0
0
0
2
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
2
0
1
0
0
1
1
1
0
1
1
0
2
0
2
1
0
0
2
0
1
0
1
0
0
2
0
1
0
0
0
4
9
2
0
0
0
0
0
0
1
0
1
0
2
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
5
0
0
2
0
2
0
1
0
0
0
0
0
0
2
0
0
1
0
0
1
0
1
0
0
1
2
0
0
1
0
0
0
1
0
2
0
0
2
0
1
1
0
2
0
0
0
0
0
0
0
0
1
2
2
0
0
1
3
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
2
2
0
1
0
0
0
1
0
0
0
0
1
1
0
1
1
0
1
1
0
3
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
7
1
0
1
1
0
0
0
0
1
0
0
1
1
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
1
0
0
0
0
2
0
0
0
1
0
1
0
0
2
0
1
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
2
1
0
0
0
2
1
2
0
0
0
0
1
2
0
0
0
0
2
0
0
2
2
0
0
0
0
3
1
1
1
2
2
2
0
1
0
2
0
1
1
3
0
0
0
0
0
0
0
0
0
1
2
0
0
1
1
2
0
2
1
0
0
2
2
2
1
0
0
0
0
0
0
2
0
0
2
0
2
0
0
2
0
0
0
2
1
1
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
3
0
0
0
2
0
0
0
2
0
2
1
3
2
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
2
2
2
0
1
3
1
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
1
5
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
2
1
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
2
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
1
0
0
0
0
1
1
0
1
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
8
0
0
0
1
2
1
0
0
2
0
0
0
0
1
0
0
0
1
0
2
1
0
0
2
0
1
1
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
2
2
1
0
0
0
2
2
1
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
1
0
1
0
1
1
2
0
0
1
0
1
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
1
0
0
0
0
0
0
1
1
1
1
0
2
0
0
1
0
1
1
1
0
0
2
0
0
0
2
2
0
0
1
1
0
2
0
0
2
0
1
0
0
3
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
2
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
3
0
1
0
0
0
1
0
0
0
0
0
1
2
0
4
1
0
0
2
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
2
0
1
0
2
0
1
0
1
1
0
0
0
0
1
2
2
2
0
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
1
1
0
0
1
3
3
2
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
4
0
1
2
0
0
0
0
0
0
0
0
2
0
1
0
0
1
3
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
3
0
2
1
1
0
2
0
0
0
0
1
0
0
0
2
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
2
2
1
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
3
0
1
2
0
2
1
1
0
1
1
0
0
0
0
1
2
2
0
1
0
0
0
0
0
0
0
2
0
1
0
2
1
4
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
2
0
0
1
2
0
1
0
0
0
0
3
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
1
2
1
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
2
0
0
0
1
2
2
0
0
0
0
0
1
2
0
1
2
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
1
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
1
2
3
0
2
0
0
0
0
2
0
2
1
0
0
0
0
1
1
1
0
2
1
0
1
0
0
0
1
2
1
0
0
0
0
0
0
0
0
1
0
2
2
0
1
0
0
0
2
1
0
2
0
1
0
0
0
1
0
0
0
1
0
0
1
1
0
0
1
0
2
0
0
2
1
1
0
0
2
0
0
1
0
0
0
0
1
1
0
0
0
1
1
0
1
0
0
2
0
2
2
2
0
0
0
2
0
2
2
0
0
2
0
0
0
0
0
2
0
0
0
2
1
0
0
0
1
2
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
2
0
0
1
0
2
2
0
2
4
0
0
0
1
1
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
1
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
1
0
0
0
1
0
2
0
0
1
0
0
0
1
2
0
0
2
0
2
0
0
1
2
0
2
0
0
0
0
0
1
1
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
1
2
2
0
0
2
2
0
0
2
2
0
2
2
1
0
2
0
0
2
0
0
0
1
0
0
1
0
0
0
2
0
1
2
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
1
3
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
1
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
3
1
2
0
0
0
0
0
0
2
1
0
2
1
2
0
2
2
0
1
0
1
1
0
0
2
0
0
1
0
0
2
0
0
0
0
0
1
2
0
0
2
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
1
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
3
1
0
0
1
0
2
2
0
0
0
0
0
1
0
0
0
0
5
0
1
0
0
1
0
5
1
5
0
0
2
0
1
0
0
0
0
0
0
1
1
0
1
1
0
1
1
0
2
0
1
1
1
0
0
0
0
0
0
1
1
0
0
0
2
2
0
0
1
0
2
0
0
2
0
0
0
0
1
2
2
0
3
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
1
1
0
0
0
1
0
0
1
0
2
2
0
0
0
0
0
0
0
0
1
0
2
0
2
0
2
0
0
0
1
0
1
2
5
0
0
0
1
1
0
1
1
3
2
0
0
0
1
0
1
0
0
0
2
0
0
1
0
1
0
0
2
0
0
1
1
2
0
1
1
0
1
0
4
2
0
1
1
2
1
0
2
0
1
0
2
0
2
3
1
0
0
1
2
2
0
2
0
0
0
2
0
2
2
2
0
1
1
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
2
1
1
2
1
0
0
0
1
2
0
4
0
0
0
0
1
2
0
0
0
0
0
0
2
1
0
1
0
1
1
1
2
0
0
0
2
0
0
0
0
2
2
0
2
1
0
2
0
1
0
0
1
0
2
0
1
0
0
1
0
0
1
0
2
2
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
1
0
0
0
2
2
0
1
0
0
0
0
1
0
2
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
2
0
0
2
0
0
2
0
1
0
1
0
1
0
0
0
0
0
2
2
0
1
0
0
0
0
0
1
0
1
0
2
2
1
1
2
0
0
0
0
1
0
1
0
1
0
0
0
2
1
0
2
0
1
0
2
0
0
0
3
0
0
2
0
0
0
0
3
1
2
2
1
2
1
0
0
0
0
0
1
3
1
0
0
0
0
0
0
0
2
3
0
3
1
1
0
1
0
3
0
1
1
0
0
0
0
1
0
0
0
0
2
0
0
1
2
0
0
1
0
2
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
1
2
7
2
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
2
2
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
1
0
0
0
2
0
2
0
3
0
0
2
0
0
1
0
2
0
1
0
2
2
1
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
2
2
1
0
0
0
0
1
1
1
2
0
2
1
0
0
0
2
0
1
2
1
0
0
1
0
2
1
0
2
1
2
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
1
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
1
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
1
1
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
1
2
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
3
0
0
1
0
0
0
0
1
0
0
0
3
1
0
2
0
0
1
0
0
0
1
0
0
0
0
1
2
0
0
2
2
0
1
1
1
2
1
2
4
2
1
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
2
0
0
1
0
2
1
0
1
0
1
0
0
2
0
1
0
1
1
0
1
0
0
0
0
2
0
0
0
0
2
0
3
1
2
0
0
0
0
2
0
0
0
0
1
0
2
3
1
0
0
0
2
2
0
2
1
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
3
0
0
1
0
0
2
0
0
0
1
2
2
2
0
0
0
0
0
2
0
1
0
0
1
2
0
1
2
0
1
0
0
0
2
0
2
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
2
4
0
0
0
1
0
0
1
0
0
0
3
0
0
1
0
0
0
1
0
2
0
2
0
0
0
1
1
0
1
0
2
1
0
1
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
1
1
0
0
0
0
2
1
1
1
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
2
0
3
2
0
0
2
1
1
1
0
2
0
0
0
2
2
1
2
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
2
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
1
1
3
1
0
0
2
0
2
1
0
2
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
1
1
0
1
0
2
0
0
0
0
0
3
0
0
0
2
2
0
1
0
2
2
0
0
1
0
0
0
0
0
0
1
0
0
1
2
2
0
0
1
0
1
0
0
0
0
2
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
2
1
0
0
0
2
1
2
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
3
1
0
0
0
0
0
2
2
1
0
1
0
1
0
1
2
0
0
0
1
1
0
0
2
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
1
0
1
0
1
2
0
2
0
0
0
0
0
0
0
3
0
0
1
0
1
1
1
1
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
2
0
2
1
1
0
2
1
0
0
2
1
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
1
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
2
2
2
0
0
0
0
2
0
1
1
0
0
0
1
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
1
0
0
0
1
2
0
1
0
2
1
2
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
2
2
5
2
0
0
1
0
0
0
1
1
0
0
0
2
0
0
1
0
1
2
0
0
0
0
0
0
1
1
1
1
0
0
1
0
0
2
0
0
0
3
0
0
2
0
1
2
0
0
2
0
0
1
0
0
0
0
1
1
0
0
0
0
2
0
0
0
1
2
1
0
0
0
0
0
2
1
0
0
0
0
1
4
1
0
2
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
2
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
3
1
1
0
1
1
0
1
2
0
0
0
0
0
0
0
1
1
4
0
0
4
0
0
0
7
0
1
0
1
0
1
1
1
0
0
2
0
0
0
1
2
0
0
0
0
0
2
0
0
0
1
2
1
0
0
0
0
2
0
2
0
2
2
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
1
1
0
0
0
0
2
0
2
2
1
0
0
1
0
1
1
2
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
1
1
0
0
2
0
0
0
1
3
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
2
0
1
2
0
0
0
1
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
2
2
0
0
0
0
0
0
3
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
1
0
0
2
1
0
1
0
0
0
0
0
2
2
0
1
3
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
2
0
0
0
0
1
2
1
0
1
0
0
1
0
1
0
2
2
1
1
3
0
0
2
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
5
0
1
2
1
1
1
1
0
0
2
0
2
2
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
2
2
0
0
0
2
0
0
4
3
1
0
2
1
0
2
0
1
2
0
1
0
2
0
2
0
2
0
0
0
0
1
0
0
2
1
2
0
2
0
0
0
2
0
3
0
1
0
0
0
0
1
0
1
0
2
1
0
0
0
2
0
0
0
0
1
0
0
2
0
0
1
0
0
0
1
1
2
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
1
0
1
0
0
0
0
1
1
1
2
0
2
2
0
2
2
5
1
0
3
0
0
2
1
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
2
0
1
0
0
1
0
0
1
0
0
0
0
1
1
0
0
1
0
2
1
2
2
3
2
0
0
0
1
0
0
1
1
2
0
0
0
0
1
0
0
0
2
0
1
0
0
0
1
0
0
2
0
2
2
2
3
0
2
1
4
0
0
0
2
0
0
1
0
0
0
2
0
0
0
2
0
0
1
0
0
0
2
1
0
1
0
0
0
0
1
0
2
0
0
0
0
1
0
2
2
0
1
0
0
0
2
0
2
0
1
0
2
0
0
0
0
1
0
0
0
1
2
1
0
1
1
0
3
0
2
0
0
0
0
0
0
0
1
2
1
3
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
2
0
0
0
0
2
0
2
0
0
2
1
2
2
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
2
0
0
0
0
2
1
2
1
0
0
2
1
0
0
1
0
0
0
0
0
0
0
1
1
1
0
1
1
0
0
0
0
0
0
1
2
0
0
0
0
0
1
1
2
2
1
2
0
0
0
2
0
4
0
0
2
0
1
1
0
0
1
2
0
0
0
1
0
0
3
2
0
1
0
0
0
0
1
2
2
0
2
0
3
1
0
0
1
0
0
0
2
1
2
2
2
0
0
0
1
0
5
2
2
0
1
0
0
1
0
0
1
0
2
1
0
3
0
1
8
0
1
1
0
2
0
0
2
2
0
2
0
2
2
1
1
1
0
2
0
1
0
2
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
2
1
0
2
0
0
2
0
0
2
1
1
0
0
2
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
2
2
0
2
1
2
0
0
0
1
1
1
0
2
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
2
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
1
2
2
0
1
0
2
1
2
2
0
0
0
0
0
0
2
1
2
0
1
1
0
0
2
2
0
0
4
0
1
0
1
1
1
0
1
2
0
0
1
1
2
1
0
1
0
0
1
0
0
0
0
0
2
2
0
0
0
0
1
2
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
3
0
2
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
1
2
0
0
0
1
0
2
0
0
0
0
2
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
2
2
0
0
0
0
0
0
0
2
3
1
0
2
0
0
1
2
0
0
0
0
0
0
2
1
0
0
2
0
0
0
1
2
1
1
3
0
2
4
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
1
1
0
1
0
0
0
2
0
1
0
0
0
1
0
1
0
1
0
2
0
0
2
2
2
1
1
0
2
3
2
1
0
0
0
1
1
1
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
3
2
0
0
0
1
1
2
1
1
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
2
1
4
0
0
2
0
0
0
4
0
0
0
0
2
0
0
0
0
1
2
2
0
0
0
2
0
2
0
0
0
0
2
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
1
0
1
1
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
1
0
0
0
1
2
0
0
2
2
0
0
0
0
6
0
2
1
0
0
2
0
0
0
0
0
0
0
1
2
0
2
0
1
0
0
0
0
0
0
1
0
0
1
2
1
0
2
0
1
0
2
2
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
2
0
2
0
2
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
1
0
0
2
1
0
0
0
1
0
0
0
2
0
0
0
0
0
1
2
1
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
1
1
1
0
2
0
1
0
1
0
0
0
0
0
2
0
1
1
0
1
0
0
1
1
0
0
2
2
2
0
1
1
0
0
0
0
0
0
0
2
2
1
2
0
2
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
1
2
0
1
0
0
0
1
1
1
2
0
0
1
1
2
0
0
1
0
1
0
0
0
1
2
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
2
0
0
1
2
0
2
0
0
1
0
1
5
0
2
0
0
0
0
2
1
2
2
3
1
0
2
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
4
2
0
1
2
0
0
1
1
0
1
0
0
1
0
4
0
0
2
1
1
1
0
1
1
0
0
0
1
2
1
1
0
0
1
0
0
0
0
0
1
0
0
0
2
2
2
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
1
1
0
4
2
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
1
0
2
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
2
3
1
2
0
0
0
1
0
1
2
0
1
1
0
0
0
1
1
0
0
0
0
1
1
2
1
0
0
2
0
0
1
1
0
2
0
0
0
0
1
0
0
0
1
0
1
0
0
2
0
0
0
1
0
0
2
0
2
0
1
0
0
0
1
2
0
2
0
0
0
0
1
0
0
0
0
2
0
1
0
0
1
0
0
1
1
0
1
0
1
1
0
2
0
0
1
0
0
1
2
2
0
0
0
0
0
2
1
1
2
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
4
0
0
0
1
1
0
1
0
0
0
0
0
1
2
2
1
2
0
1
0
1
0
1
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
2
2
1
2
0
0
1
0
1
2
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
2
1
1
0
1
2
0
2
0
0
4
1
0
1
0
0
2
0
0
2
0
0
2
2
0
0
2
0
0
0
0
0
2
0
2
0
0
2
1
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
1
0
0
4
1
1
2
0
1
0
0
1
0
0
2
1
1
1
1
0
0
2
1
0
0
2
0
1
2
1
2
0
0
1
3
2
0
0
0
0
0
0
0
0
0
1
0
3
0
0
1
2
0
0
0
2
0
0
1
0
2
3
0
1
0
0
0
4
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
2
1
0
0
0
1
1
0
0
2
0
0
0
0
1
4
2
0
0
0
1
0
0
0
0
2
0
0
1
2
0
0
3
0
0
0
2
0
2
1
0
1
3
0
0
0
2
2
1
0
0
1
0
0
2
2
0
0
2
0
0
3
2
0
0
0
0
1
1
0
2
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
2
1
1
0
0
1
1
0
0
0
0
0
1
2
0
0
2
0
0
3
0
0
0
0
1
0
1
1
2
0
2
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
1
0
1
0
1
1
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
1
0
1
1
1
0
0
0
1
0
0
0
1
0
2
0
0
0
2
0
0
1
2
0
2
1
2
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
1
1
0
0
2
0
0
0
0
2
0
1
1
0
0
0
0
0
0
2
1
1
1
1
0
3
0
0
0
0
0
1
2
1
0
2
0
0
1
0
2
0
0
0
0
0
1
0
1
2
2
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
2
1
0
2
0
0
2
1
2
0
3
2
0
2
0
0
3
0
1
1
0
0
0
4
0
1
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
2
3
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
1
1
0
0
0
2
2
0
3
0
0
1
0
0
0
0
0
2
2
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
3
1
1
0
1
0
2
1
0
0
1
0
1
0
0
0
1
0
0
0
1
0
2
1
0
0
0
0
1
0
1
1
0
0
1
0
0
1
0
2
1
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
2
0
0
3
0
1
0
0
1
0
0
1
1
2
1
0
1
0
0
1
0
0
6
3
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
2
0
1
0
1
1
0
0
0
0
1
2
0
2
0
0
0
0
1
1
1
0
0
1
2
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
2
0
0
0
0
0
0
5
0
1
0
1
0
2
3
0
1
1
1
0
1
0
0
1
1
2
0
0
0
0
1
0
0
2
3
2
0
0
0
2
0
2
3
0
0
0
2
1
1
0
4
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
3
0
1
0
1
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
2
1
1
0
0
0
1
0
2
1
2
0
1
1
0
1
0
0
0
3
0
0
1
1
2
0
2
1
0
1
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
2
1
0
0
0
2
0
0
0
2
2
3
1
0
0
0
0
1
2
2
2
0
1
0
1
0
1
0
1
0
2
2
1
0
0
2
2
0
4
0
2
0
0
0
0
0
0
0
1
2
0
0
0
1
2
0
0
1
1
1
1
2
2
2
2
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
2
2
0
0
1
1
0
1
0
0
0
1
0
0
2
0
0
0
0
0
1
2
0
1
1
0
0
0
1
0
3
1
1
1
2
0
0
0
2
1
0
0
1
0
0
0
0
0
2
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
2
2
0
1
0
2
0
0
0
1
2
2
0
0
1
1
0
1
0
2
3
1
2
0
0
0
2
0
2
0
1
0
0
0
2
0
0
0
1
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
1
0
2
0
2
1
1
0
0
0
2
1
0
0
0
1
0
0
1
1
1
1
0
1
2
0
0
2
0
0
1
0
2
0
2
3
1
0
0
2
0
2
0
2
0
0
0
0
0
0
0
1
0
1
0
2
1
0
0
0
2
0
2
0
2
2
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
3
1
0
3
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
1
0
1
1
1
1
0
1
1
0
2
0
0
0
0
0
0
3
0
0
2
0
1
0
0
0
0
1
0
0
2
2
0
1
0
0
1
0
2
0
1
2
0
1
2
2
1
0
0
1
1
0
0
1
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
2
1
3
0
2
1
0
2
0
0
2
0
2
0
1
0
0
2
2
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
3
0
0
1
0
0
0
1
0
1
1
2
1
0
1
2
1
0
0
2
0
1
3
0
2
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
2
0
1
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
1
3
0
1
0
0
2
0
0
2
0
2
0
0
0
0
0
2
2
0
0
0
2
0
2
0
1
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
2
0
1
1
0
0
2
0
0
0
1
0
1
0
0
0
4
1
0
0
0
0
0
0
0
1
2
0
0
2
0
2
0
0
0
0
1
2
1
2
0
0
1
4
0
0
0
0
0
2
2
1
0
0
0
1
0
0
0
2
1
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
5
0
1
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
2
0
2
0
1
2
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
2
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
1
0
0
0
0
0
0
2
1
0
0
2
0
1
0
2
0
1
0
2
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
2
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
2
1
2
1
0
0
0
0
2
3
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
2
0
2
1
1
0
0
2
1
2
0
0
0
0
0
1
2
0
0
2
2
1
0
0
0
0
0
2
0
1
0
1
0
0
3
2
0
2
0
0
0
1
0
0
0
0
8
2
0
2
0
2
0
1
0
0
0
0
0
5
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
2
0
0
0
0
1
0
0
1
1
1
2
0
0
2
0
1
0
0
0
0
1
0
0
1
2
0
0
0
0
2
0
1
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
1
1
0
0
0
3
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
1
1
0
0
1
1
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
2
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
3
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
3
0
0
0
0
1
0
0
2
1
1
0
0
3
0
0
0
1
0
0
2
0
2
0
0
2
0
0
1
1
0
0
0
0
0
1
2
0
0
0
2
1
2
1
1
0
1
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
1
1
0
0
2
0
0
3
1
0
2
0
1
0
1
0
0
2
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
2
1
0
0
0
0
0
0
0
2
2
0
0
0
2
3
0
0
0
0
0
1
0
0
2
0
0
2
0
0
2
0
0
0
0
1
1
4
0
1
2
0
0
0
0
0
0
0
0
1
1
0
1
0
2
0
2
1
0
0
0
0
0
1
0
0
1
1
0
1
0
0
3
0
0
0
0
0
1
0
0
0
2
0
1
0
0
2
0
0
2
0
0
0
0
1
0
0
1
0
0
2
0
2
0
2
2
4
3
0
0
2
0
0
0
2
0
2
0
2
0
2
0
2
0
0
0
0
1
0
1
0
1
0
0
0
1
3
0
0
0
0
0
0
0
0
2
1
0
1
2
0
0
2
2
1
0
1
0
2
0
0
0
1
0
2
1
2
0
2
0
0
2
2
1
1
2
0
0
0
2
3
0
1
2
0
0
0
0
3
0
2
0
2
0
2
0
0
1
2
2
0
0
2
0
0
1
0
0
2
0
0
2
1
2
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
1
1
0
1
0
0
0
3
0
0
1
0
0
0
0
2
0
0
0
1
1
0
2
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
4
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
2
1
0
1
1
1
0
1
1
0
2
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
2
2
2
0
1
0
2
2
0
0
3
0
0
0
0
1
2
0
1
0
0
2
2
2
2
2
1
2
1
0
2
0
0
0
0
0
1
0
0
2
0
4
2
4
5
0
1
0
0
0
0
0
3
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
1
0
0
0
0
2
2
1
1
2
2
3
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
1
2
2
0
2
0
0
0
3
0
1
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
1
0
0
1
0
1
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
1
0
1
1
0
0
2
0
2
1
2
0
0
0
2
0
1
0
3
0
0
0
1
1
0
0
0
2
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
1
1
0
1
0
2
0
0
2
1
2
2
1
0
0
0
0
1
2
1
0
0
1
0
2
1
0
1
1
0
0
1
2
2
1
0
2
0
0
2
0
0
1
0
0
1
2
0
0
0
0
2
0
0
1
2
2
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
1
2
1
0
0
0
0
2
2
2
0
3
2
0
1
0
0
0
0
2
0
0
0
0
1
0
0
1
1
2
2
2
0
0
3
0
0
0
0
0
2
1
0
2
1
2
2
1
2
1
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
1
2
0
0
0
1
1
2
0
0
0
2
0
2
1
1
0
1
0
0
2
0
0
0
2
0
0
1
0
0
0
0
1
0
2
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
1
2
0
1
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
2
0
2
2
0
1
1
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
1
0
1
2
1
0
0
1
0
2
1
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
2
2
0
0
2
2
1
0
0
1
0
0
0
2
1
0
0
0
0
2
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
2
2
0
2
0
0
0
2
0
2
0
0
0
1
0
2
0
0
0
0
1
1
2
0
0
2
0
1
0
0
1
2
0
0
0
2
1
1
3
5
0
2
0
0
1
0
0
1
1
0
0
0
2
1
0
1
8
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
1
2
0
0
0
2
1
2
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
4
0
2
1
0
0
0
2
0
0
2
1
2
2
1
0
0
0
0
2
0
0
0
0
0
0
2
0
1
2
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
1
2
0
3
1
0
0
0
1
1
0
2
0
0
0
0
0
2
1
0
1
1
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
2
0
0
1
0
1
0
0
1
0
1
1
0
2
1
0
3
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
2
2
1
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
2
0
1
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
1
1
0
0
1
0
2
4
2
0
1
1
0
0
0
0
0
2
0
0
0
2
0
3
1
0
0
0
2
0
0
0
1
1
0
0
2
0
2
0
0
0
1
0
0
0
2
1
2
0
0
0
0
0
2
2
1
1
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
1
0
0
3
1
0
0
0
0
1
3
0
0
1
2
2
0
0
0
2
1
1
0
0
0
1
2
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
1
0
0
1
3
0
0
2
0
3
0
0
1
0
2
0
0
1
2
0
0
0
2
1
0
2
0
0
0
1
0
2
0
0
0
1
0
2
0
0
2
0
0
2
0
1
0
0
0
1
2
2
0
2
1
0
1
0
1
0
0
2
0
0
0
2
2
2
0
0
1
1
2
1
2
0
0
2
2
1
0
0
0
0
0
1
0
0
2
2
0
0
0
2
4
0
0
0
1
0
0
0
2
1
0
1
0
1
2
0
0
2
0
0
1
0
0
2
0
0
0
0
0
1
3
2
0
1
0
1
0
1
1
2
0
1
0
0
0
0
0
0
2
0
1
0
2
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
2
1
0
0
0
0
2
1
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
2
1
0
0
2
0
0
0
0
0
2
0
0
0
1
0
1
0
2
2
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
2
0
0
2
0
0
1
0
0
0
0
0
2
2
0
0
0
0
1
0
2
2
1
0
0
1
0
0
0
0
2
2
0
0
1
1
0
1
1
0
2
0
0
0
1
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
2
1
2
1
1
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
1
1
2
0
0
1
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
1
3
0
0
0
0
1
0
2
1
2
1
2
0
0
0
0
2
0
1
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
4
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
1
1
2
2
1
0
1
1
0
2
0
0
0
0
1
0
0
2
2
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
3
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
2
0
0
2
2
1
0
1
0
1
0
2
0
1
0
0
1
0
0
1
4
1
0
0
0
0
1
2
0
0
0
0
0
0
2
2
0
0
1
2
0
0
0
0
1
1
0
0
3
0
2
0
0
2
0
0
0
1
1
1
1
0
1
1
0
0
1
2
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
1
2
0
0
0
0
2
2
2
0
0
1
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
1
1
1
1
0
1
1
0
0
0
1
0
0
0
2
0
0
0
1
0
0
1
0
0
2
0
0
0
0
2
0
1
0
0
0
0
3
2
0
4
0
1
1
0
1
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
2
1
0
0
0
0
0
0
1
0
0
2
0
0
0
1
1
0
0
1
0
1
2
0
2
1
1
0
1
0
0
0
0
1
0
1
0
2
0
0
2
2
1
2
2
2
0
0
1
2
0
0
1
0
1
0
1
0
0
0
2
2
0
3
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
1
2
5
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
1
1
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
2
0
1
1
0
2
1
0
1
0
0
2
0
1
0
0
0
2
1
2
1
1
2
0
0
0
0
1
0
0
2
0
2
1
0
0
3
0
0
0
0
2
1
0
0
2
0
1
0
0
1
0
0
0
1
2
1
0
0
0
2
1
4
0
0
0
0
2
0
1
0
0
1
0
0
0
0
2
2
3
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
2
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
2
1
0
0
0
1
1
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
2
1
1
1
1
1
2
6
2
0
1
1
0
2
3
0
0
0
1
1
1
1
1
2
0
1
1
0
1
0
1
3
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
3
0
3
2
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
4
0
0
0
0
1
0
2
0
0
0
0
0
1
0
1
2
1
0
0
0
0
1
2
1
0
1
2
0
0
0
0
0
0
1
0
0
0
1
1
0
2
0
1
2
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
2
0
0
0
0
0
1
0
0
0
0
2
1
0
1
2
0
0
2
1
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
4
2
0
0
0
1
0
0
3
1
0
0
0
0
0
1
0
2
0
2
2
0
0
2
1
0
2
0
0
0
0
1
0
2
0
0
0
0
0
6
2
0
0
1
0
0
0
0
0
2
0
2
1
0
0
0
1
1
0
0
0
0
0
2
2
1
0
0
1
1
0
1
3
2
0
1
0
3
0
0
1
1
1
0
0
0
0
1
2
0
0
2
1
2
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
1
2
2
0
0
2
2
0
2
0
2
0
0
0
1
2
0
0
0
1
2
1
2
0
2
0
1
0
0
0
0
1
2
0
0
3
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
2
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
1
0
2
1
2
1
0
0
1
0
1
2
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
3
2
0
0
0
0
0
0
0
0
0
5
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
2
0
0
0
0
2
0
0
3
0
2
0
0
0
0
2
3
1
0
1
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
2
1
0
0
2
0
0
2
0
0
1
0
2
2
0
0
0
1
2
0
1
0
0
2
0
0
2
0
0
0
2
0
2
0
0
0
2
0
0
2
2
0
0
0
2
0
0
0
1
0
0
2
0
0
4
0
0
0
1
0
1
0
1
0
0
1
1
0
0
0
2
0
0
1
2
0
0
2
0
0
0
0
0
2
0
0
0
2
0
2
0
2
0
0
0
1
0
1
2
2
0
0
0
1
1
1
0
0
0
2
0
2
1
0
0
2
0
0
0
2
0
0
2
0
2
0
1
0
1
2
0
0
0
0
0
0
0
0
0
5
2
0
2
0
3
1
0
0
1
0
0
2
0
0
1
0
0
1
4
0
0
0
2
0
1
0
1
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
1
0
1
1
1
0
1
0
5
0
2
1
1
0
2
1
0
2
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
1
2
1
0
0
0
2
0
0
0
0
2
0
3
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
2
1
0
0
0
1
1
0
1
1
0
2
0
0
0
0
2
4
0
0
0
0
0
1
2
2
2
0
0
0
1
0
0
0
2
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
2
1
1
2
0
0
2
1
0
2
2
0
0
0
3
2
0
1
1
0
0
1
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
3
0
0
1
1
0
0
0
0
0
0
0
0
0
1
2
1
0
0
1
0
2
0
0
0
2
2
2
0
7
0
0
0
2
2
0
1
2
1
0
0
2
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
2
0
0
2
3
2
0
0
0
1
0
0
2
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
4
1
0
2
2
0
0
2
1
2
2
1
0
1
0
2
0
2
0
1
0
0
0
2
1
0
2
1
0
0
0
2
0
1
0
0
0
0
1
0
2
0
2
0
0
1
0
0
0
1
2
2
5
0
2
0
1
0
0
2
0
0
0
1
0
0
1
0
2
2
1
1
1
0
0
1
2
0
0
0
0
0
0
1
2
2
1
0
1
1
2
1
0
0
0
1
2
1
0
1
2
1
0
0
0
0
2
0
1
1
0
2
0
0
0
2
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
1
0
2
5
2
0
0
0
2
0
0
1
1
0
0
1
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
2
2
0
1
0
2
2
1
0
0
1
0
0
0
0
0
2
0
2
2
0
4
0
0
2
1
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
2
0
2
0
0
0
2
1
0
0
0
2
0
0
1
0
2
2
0
1
0
1
2
0
0
1
1
0
0
1
0
2
0
0
0
0
1
0
2
1
2
2
0
0
2
1
0
2
0
0
1
0
0
0
0
4
1
0
0
0
0
0
1
0
0
0
4
0
0
3
0
0
2
2
0
1
1
0
2
2
2
0
0
0
0
0
2
0
0
2
0
1
2
0
2
1
0
0
0
1
0
1
0
2
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
2
2
2
1
5
3
1
9
0
2
1
0
0
0
2
0
0
2
0
1
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
3
1
1
1
0
0
0
0
2
0
0
0
0
1
0
2
1
2
0
0
1
0
1
2
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
2
0
1
0
1
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
1
2
1
0
0
2
1
0
0
1
0
2
0
0
0
2
2
0
0
0
2
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
2
1
2
0
0
0
2
0
1
0
0
0
1
0
0
0
0
2
0
4
0
0
0
0
1
0
2
0
0
0
2
1
0
2
1
0
0
2
0
0
0
0
1
0
0
0
0
1
0
2
1
2
0
0
0
0
1
0
0
7
0
0
0
0
1
0
0
1
2
0
1
0
0
2
0
1
1
0
4
0
1
2
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
1
2
2
2
0
3
1
0
1
2
0
0
0
0
0
0
0
1
1
0
1
2
0
1
1
0
0
0
0
3
0
1
0
1
0
0
1
1
0
0
0
1
0
0
3
1
0
0
0
0
2
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
3
0
0
0
1
1
2
0
0
0
0
0
2
0
1
2
1
2
0
0
2
4
2
1
0
0
0
0
0
0
0
0
1
0
2
0
0
2
2
2
0
0
0
1
2
0
0
0
1
0
2
0
0
0
0
0
0
3
0
1
0
0
0
2
2
0
0
0
1
0
2
0
0
12
0
2
0
2
1
0
0
0
1
0
0
1
0
0
1
1
2
0
4
0
0
7
0
1
0
0
0
1
0
2
1
0
1
0
1
0
0
0
0
0
2
2
2
1
2
0
2
0
3
0
0
1
1
0
0
1
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
2
0
0
0
2
0
0
0
2
0
1
0
1
0
6
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
1
2
0
0
0
0
0
1
0
0
1
0
2
2
1
2
0
0
0
0
0
0
0
2
2
0
1
1
0
0
0
1
2
1
0
0
0
0
1
3
0
0
1
2
0
0
1
0
0
1
0
2
2
0
1
0
1
0
0
2
0
2
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
2
0
0
2
0
0
2
0
0
0
0
1
1
0
0
0
1
2
0
1
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
1
0
2
2
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
1
0
0
2
0
0
0
0
0
0
2
2
1
0
2
0
0
0
0
0
2
0
2
1
1
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
1
0
1
0
0
0
1
2
1
0
2
0
2
1
2
1
0
2
0
0
0
0
0
0
1
0
0
4
0
0
1
2
0
0
0
1
0
0
0
2
0
0
1
0
2
4
0
0
0
0
2
2
0
2
2
0
1
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
2
2
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
2
3
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
1
2
0
0
2
0
4
2
0
0
0
0
0
0
2
0
0
0
1
2
0
0
2
1
0
1
2
0
0
4
2
0
0
0
0
0
0
2
0
0
0
0
0
0
3
1
2
0
0
0
0
1
0
0
0
1
6
0
2
2
0
0
2
1
0
0
0
0
2
2
0
0
0
2
0
0
0
1
0
2
2
3
0
0
0
0
2
0
0
3
0
1
0
1
0
2
0
2
0
0
1
2
0
2
1
1
2
0
2
3
0
0
0
0
0
0
1
0
1
2
0
2
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
1
0
2
0
2
0
0
0
0
2
2
2
1
1
0
2
0
0
0
0
0
2
0
2
0
0
0
2
1
0
1
0
0
2
0
1
2
2
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
1
0
0
2
2
1
0
0
1
2
2
0
0
0
2
0
0
0
2
0
1
1
1
0
0
1
0
2
0
0
3
2
0
2
1
0
0
2
1
0
0
0
2
1
0
0
0
0
0
0
4
2
0
2
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
1
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
2
2
0
0
0
1
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
1
0
0
2
0
0
1
0
0
1
0
0
2
0
2
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
2
0
2
2
1
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
1
2
3
0
0
2
1
0
2
2
0
0
1
0
0
1
1
0
2
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
1
1
0
1
0
1
1
0
0
0
0
1
3
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
2
2
0
1
0
0
2
1
2
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
1
0
3
2
0
0
0
0
5
2
0
0
0
0
0
0
1
1
0
2
1
2
0
2
0
5
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
3
0
0
0
0
0
2
0
0
0
1
0
0
3
0
0
0
1
0
1
0
1
0
0
0
0
1
2
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
3
0
1
0
2
0
0
0
1
0
1
3
0
1
0
0
2
0
2
1
2
0
0
1
0
0
0
0
1
0
1
2
2
0
0
0
0
1
1
2
0
0
0
0
2
0
0
2
0
0
0
0
0
3
3
1
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
1
0
0
0
1
0
2
0
2
0
0
0
1
5
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
2
1
0
0
1
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
1
0
2
1
1
2
2
2
0
0
0
1
1
0
2
0
0
2
1
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
1
1
0
0
1
2
1
1
0
2
1
1
0
0
0
2
0
1
1
2
0
0
0
3
3
2
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
4
0
2
0
2
0
0
0
0
0
1
0
0
2
0
0
2
1
1
0
1
0
0
0
0
0
0
2
0
0
0
0
1
1
1
0
2
1
0
1
0
0
0
0
1
1
0
3
0
2
0
0
1
0
1
0
0
2
0
0
4
1
1
2
0
0
2
0
0
2
1
0
2
0
0
0
1
0
0
0
1
2
0
0
2
0
1
0
3
0
0
0
1
0
0
1
1
2
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
2
0
18
2
0
0
1
0
1
3
1
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
1
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
2
2
2
4
1
1
4
2
0
0
2
1
0
0
0
0
2
0
0
0
0
1
1
0
0
1
0
1
0
1
0
4
2
0
0
0
1
0
1
0
0
2
2
0
0
0
0
0
1
0
2
0
0
3
2
2
0
0
0
0
0
1
0
0
0
0
2
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
2
0
1
0
0
1
0
0
0
0
2
2
1
2
1
0
0
0
1
0
0
0
1
0
0
1
0
2
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
1
1
2
0
0
0
0
0
0
0
0
0
1
1
2
1
0
0
3
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
2
1
1
0
0
0
0
0
1
0
1
1
1
0
0
3
4
0
0
0
0
2
3
0
0
0
0
0
2
3
0
0
0
0
0
0
2
0
0
2
2
0
3
1
2
0
0
1
1
1
0
0
0
2
0
1
0
0
0
2
1
0
2
2
2
2
0
0
0
0
0
0
2
1
0
0
1
0
0
2
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
1
3
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
2
0
1
1
0
2
0
0
0
1
0
0
0
1
2
0
1
0
2
0
0
2
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
2
1
1
0
0
1
0
0
1
0
2
0
0
2
0
0
0
2
0
4
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
1
3
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
1
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
3
1
0
0
1
0
1
0
0
1
2
0
0
0
1
0
0
0
0
0
2
2
1
1
2
1
2
1
1
1
0
1
2
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
7
2
0
1
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
2
1
2
0
1
2
2
0
1
2
0
1
0
0
0
2
0
0
0
2
0
0
0
1
0
2
0
2
1
0
0
2
0
0
0
1
0
0
2
1
0
0
0
2
0
1
2
0
1
0
2
0
2
1
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
2
2
0
0
0
0
0
2
0
1
0
0
1
0
0
0
2
2
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
1
0
1
0
2
0
0
0
2
2
2
1
0
0
0
0
1
0
1
0
1
2
0
0
0
0
2
0
0
4
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
1
1
0
0
1
0
1
1
1
0
2
0
1
1
0
1
0
0
2
0
0
0
0
0
1
1
1
0
1
0
2
0
0
1
1
1
1
1
2
0
0
0
2
0
0
0
1
0
0
0
0
0
2
1
0
0
1
0
3
1
1
1
2
0
0
2
1
0
0
1
2
1
0
0
2
1
1
1
2
2
0
0
2
0
0
0
0
0
1
0
0
1
0
1
2
2
0
2
0
2
0
2
0
2
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
2
0
0
0
2
3
2
1
0
0
0
0
1
0
0
0
1
0
1
0
0
2
0
0
0
0
2
0
0
2
0
0
0
2
1
2
0
1
0
1
0
0
0
1
2
0
0
1
1
0
0
1
0
2
1
1
2
2
1
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
2
0
0
1
0
0
0
0
0
2
2
0
2
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
2
0
1
1
0
1
0
2
0
1
0
2
0
1
0
2
0
1
1
0
2
1
4
2
2
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
3
0
0
1
0
1
1
0
0
0
2
0
1
0
0
1
0
0
0
0
1
2
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
1
2
2
0
1
1
0
3
0
1
0
0
0
3
0
2
0
0
1
2
0
0
0
0
0
0
0
2
0
1
2
0
2
0
1
0
0
0
0
0
2
1
2
0
0
0
0
0
0
2
1
0
0
1
0
0
3
0
1
2
5
0
1
1
1
1
0
2
0
0
0
2
2
0
0
0
0
0
0
1
0
0
1
1
2
2
4
2
1
0
0
1
0
0
0
3
0
1
2
2
2
1
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
1
2
0
0
2
1
2
1
0
2
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
2
0
2
2
0
0
2
0
0
0
0
0
2
1
0
0
1
0
1
1
2
0
0
0
0
0
2
0
1
2
2
1
0
0
0
2
2
2
2
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
1
0
0
0
0
1
0
2
0
1
0
0
0
1
0
0
0
1
0
2
0
2
0
1
0
1
0
0
0
2
0
0
3
0
1
0
0
0
0
1
0
1
0
2
0
0
2
1
1
1
2
0
1
0
0
1
0
1
0
1
0
0
1
0
1
2
1
0
2
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
1
0
2
0
0
2
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
2
0
0
0
1
0
0
2
0
1
0
0
1
0
0
0
1
0
2
0
2
1
0
0
0
0
1
0
0
0
3
0
0
0
0
0
1
2
0
0
2
0
3
0
1
1
2
0
1
2
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
2
2
0
1
0
0
0
0
0
1
2
0
0
2
1
1
0
1
0
1
0
0
2
0
0
1
0
0
0
0
0
0
2
1
0
2
0
1
0
0
2
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
2
0
0
0
1
2
1
3
0
0
0
1
1
1
0
0
0
0
0
1
1
0
0
0
2
0
1
0
2
0
2
0
6
0
0
0
0
1
0
2
0
1
2
1
2
1
0
1
0
0
0
2
0
1
2
0
0
1
0
1
1
0
0
0
0
1
0
1
0
1
0
0
0
0
1
2
0
0
2
1
0
1
1
1
0
0
0
0
1
0
0
0
0
0
3
1
0
3
1
2
3
1
1
0
0
0
2
0
1
0
1
1
0
0
0
1
3
1
1
0
1
0
2
1
0
0
0
0
0
0
0
0
0
2
2
2
0
0
1
0
2
0
1
0
0
0
0
1
0
1
0
0
0
1
2
2
0
0
0
0
1
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
2
2
0
2
0
1
2
0
1
1
1
0
0
0
1
1
0
0
2
1
2
3
0
0
0
1
2
0
0
2
1
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
2
0
1
0
3
1
0
1
0
0
0
1
1
2
0
3
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
1
0
0
1
0
2
0
2
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
2
0
0
2
2
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
1
1
1
2
1
1
1
0
1
0
0
5
0
0
0
0
0
1
0
0
2
2
2
0
0
0
2
0
2
0
0
3
2
1
2
0
0
0
0
2
0
1
0
0
1
0
0
0
1
2
0
0
2
0
1
0
0
0
0
0
1
2
1
0
0
0
0
0
2
1
0
0
0
0
0
0
2
2
0
0
2
0
0
0
1
1
0
3
2
0
0
2
0
0
0
0
3
0
1
0
1
0
3
0
2
1
1
0
0
1
0
1
2
2
0
0
1
4
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
2
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
1
2
2
2
0
0
1
1
2
0
2
0
0
2
2
1
0
0
2
1
1
0
0
0
1
0
0
1
0
2
0
0
0
1
1
0
1
0
2
0
2
0
0
1
3
1
1
0
2
0
0
3
0
0
0
0
1
0
2
0
0
0
2
0
0
5
0
0
0
3
1
1
0
1
0
0
0
0
2
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
1
0
0
1
0
2
0
1
1
2
0
0
8
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
6
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
2
0
1
2
1
0
1
0
0
2
0
0
0
2
0
0
0
2
2
0
0
0
2
0
0
0
1
0
0
1
0
0
0
2
0
0
1
1
1
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
2
0
0
1
0
0
1
0
1
1
1
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
2
0
1
1
0
2
0
1
0
1
0
1
0
2
0
1
2
1
0
2
0
0
5
0
0
0
2
0
1
1
0
0
0
0
0
0
0
2
1
0
0
0
1
1
0
0
1
1
0
1
1
0
0
1
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
1
0
0
0
1
0
0
0
0
1
2
0
0
0
1
1
0
0
0
0
0
1
1
2
1
0
1
0
0
1
0
0
1
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
2
2
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
4
0
1
1
2
1
0
2
0
0
0
0
1
2
1
2
0
0
0
0
0
0
0
0
1
0
0
3
0
0
1
0
1
2
0
0
1
0
2
0
1
1
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
3
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
1
0
0
1
0
2
0
0
1
0
0
3
0
0
0
0
0
2
0
0
1
1
0
2
0
2
0
2
0
0
0
0
0
0
0
1
2
2
0
2
0
0
0
1
0
1
0
0
0
0
0
0
2
1
0
2
0
5
1
2
0
0
0
2
1
0
1
1
0
0
0
2
0
1
0
1
0
1
1
1
0
0
0
2
2
1
0
0
2
1
2
0
2
1
0
0
0
0
0
0
1
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
2
0
1
2
0
1
2
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
1
0
0
0
0
0
0
3
1
0
2
2
0
0
0
0
1
2
0
1
1
1
0
0
0
0
2
0
1
0
0
0
2
2
1
1
4
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
1
0
2
1
1
0
2
0
0
2
2
0
0
0
1
0
0
1
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
1
0
1
0
2
0
1
2
1
0
1
1
0
1
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
2
0
2
0
0
1
0
0
1
1
1
0
0
2
1
0
0
0
0
1
2
1
2
0
0
0
1
2
0
3
0
0
0
0
1
0
0
3
2
0
1
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
1
0
2
2
0
0
0
1
0
0
0
1
1
0
0
0
2
0
2
0
0
0
2
1
0
0
0
0
2
0
0
0
0
3
0
0
0
1
0
0
0
0
1
0
1
1
1
2
0
0
0
0
1
0
1
0
1
0
1
0
0
1
0
0
0
0
2
1
0
0
2
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
2
0
0
0
0
1
2
0
0
1
3
0
0
2
1
0
0
0
0
1
1
0
0
2
0
0
1
0
3
1
0
0
1
0
0
0
0
0
1
0
1
0
1
2
1
2
0
0
0
0
0
2
0
0
0
1
1
0
0
2
2
1
1
0
0
0
2
0
0
0
0
1
0
2
0
2
1
0
0
0
2
2
0
0
2
0
0
2
0
2
1
0
0
0
0
2
1
0
0
3
0
0
0
2
2
1
0
2
0
1
2
0
1
0
1
1
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
2
2
0
0
4
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
2
2
2
1
0
1
1
0
0
2
0
0
0
0
0
2
2
2
0
0
1
0
1
0
0
0
2
0
0
0
0
1
0
0
2
2
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
6
0
0
2
1
0
0
0
1
0
0
2
0
0
0
2
0
1
2
0
0
0
1
2
0
0
1
1
2
2
1
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
5
0
0
0
0
0
0
1
0
0
2
0
1
2
0
0
1
1
0
0
2
0
0
1
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
1
2
1
2
0
0
0
0
0
1
0
0
3
2
0
0
2
0
0
0
0
1
1
2
1
1
0
2
1
1
1
1
2
0
0
0
1
1
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
2
2
0
1
2
0
0
0
1
0
0
0
0
2
1
1
1
2
0
2
0
0
2
0
1
0
0
0
1
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
1
2
0
0
1
0
0
0
1
0
1
0
0
0
3
0
0
2
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
1
2
0
0
1
0
1
0
0
0
2
1
1
0
0
1
0
0
2
1
0
0
0
3
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
2
2
2
0
2
0
2
0
0
0
0
0
1
0
0
1
0
2
1
2
0
0
0
0
1
2
0
2
0
1
2
1
1
0
0
0
1
0
0
0
0
2
0
0
0
16
2
0
2
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
2
2
0
1
1
2
2
1
1
0
1
1
1
2
2
0
0
6
0
0
2
0
0
0
2
0
0
0
0
2
2
1
1
1
1
1
0
0
0
1
2
0
0
0
0
1
0
1
0
0
2
0
0
1
1
0
0
2
0
2
0
0
0
1
0
2
1
1
2
2
0
0
0
0
0
1
0
0
0
0
0
0
2
1
1
0
0
0
1
0
0
0
0
0
2
1
0
1
2
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
1
1
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
2
0
0
1
0
0
4
3
0
2
1
0
1
0
3
0
0
0
0
1
0
0
0
3
0
2
0
0
2
0
3
0
1
2
0
0
0
0
1
0
2
0
1
0
1
0
2
0
0
1
2
0
0
2
0
2
0
0
2
0
3
1
2
3
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
2
1
2
2
0
0
0
1
0
1
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
2
0
0
2
0
1
1
0
0
1
0
3
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
2
0
1
0
2
0
1
1
0
2
0
2
1
0
1
0
4
0
1
0
0
1
2
4
2
1
0
0
2
0
0
0
0
0
1
0
0
0
1
0
2
2
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
2
0
1
0
1
2
0
0
0
0
0
0
0
1
2
0
0
0
0
2
2
0
0
0
1
0
1
0
1
3
0
0
0
0
0
1
0
0
0
0
1
2
0
0
1
0
0
2
1
1
3
2
0
2
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
3
2
0
0
0
2
1
1
1
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
2
1
0
5
0
2
0
0
0
1
1
0
2
1
0
0
2
0
2
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
2
0
0
2
0
1
1
2
1
0
1
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
1
2
3
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
2
0
1
1
2
0
2
2
0
2
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
1
2
1
0
1
1
0
0
2
0
0
1
1
0
1
0
0
2
0
1
1
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
3
1
2
1
0
1
0
0
0
1
0
0
2
2
0
0
0
1
0
1
1
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
2
1
1
0
0
0
2
0
0
0
0
0
1
1
0
2
2
0
0
1
2
0
1
1
0
0
0
0
0
0
0
0
2
1
0
0
0
1
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
2
2
0
0
0
0
1
0
2
1
0
0
1
1
2
0
2
1
0
1
1
0
2
2
1
0
0
0
0
1
1
0
2
0
2
3
0
0
2
2
0
2
0
0
0
2
2
0
0
0
2
0
1
1
1
1
0
2
2
0
2
0
0
2
0
0
0
0
0
2
0
0
3
0
1
0
0
0
0
0
0
0
0
2
0
2
2
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
2
0
1
1
0
0
0
0
0
2
4
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
3
0
2
0
0
1
0
1
0
0
0
2
1
0
0
2
0
0
0
0
0
2
0
0
1
0
0
1
0
2
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
3
0
2
2
0
2
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
4
0
3
0
2
1
1
1
0
0
2
0
0
0
1
1
2
1
0
0
0
0
0
3
0
2
2
0
0
2
0
2
1
1
0
0
1
0
0
2
1
2
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
2
1
0
0
0
2
0
0
3
0
0
0
0
0
0
1
0
0
3
0
1
0
0
0
0
0
2
0
6
0
0
0
1
0
8
1
2
0
0
0
2
1
0
1
0
0
0
0
1
0
0
2
0
0
2
0
1
0
0
0
0
0
0
1
1
3
0
0
0
1
0
0
0
0
2
2
0
0
3
0
0
0
0
0
0
0
5
0
1
2
0
0
0
1
0
0
1
0
0
0
1
2
0
2
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
3
0
1
1
2
0
1
0
1
2
2
0
2
2
0
2
0
2
0
0
0
0
1
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
3
2
0
0
1
0
0
0
0
2
2
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
1
0
2
0
0
0
3
1
1
2
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
3
0
0
0
2
1
0
0
0
0
0
0
1
2
2
0
0
1
0
0
0
2
0
0
0
1
1
0
1
0
0
2
0
0
0
1
0
0
0
1
0
1
0
0
0
1
1
0
0
0
2
0
0
0
0
1
0
1
2
2
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
2
2
0
0
0
1
0
2
0
2
0
0
0
1
1
1
1
0
1
1
0
0
0
2
0
0
0
0
2
0
0
4
0
0
1
2
1
0
1
0
0
2
0
0
0
0
1
2
0
1
1
0
3
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
2
2
0
2
0
0
1
0
0
0
1
0
2
1
1
0
0
0
1
0
0
0
0
0
0
3
0
0
0
2
0
2
0
0
1
0
0
0
1
1
7
0
2
1
2
0
2
1
1
1
2
0
0
0
0
0
0
5
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
1
0
2
1
0
0
0
2
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
2
0
2
0
1
0
0
0
3
2
0
0
2
0
0
1
1
0
0
0
2
2
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
2
3
0
0
1
1
0
0
1
0
2
0
3
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
2
0
1
2
1
0
0
0
0
1
0
1
2
1
0
0
0
0
1
0
1
1
0
1
1
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
2
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
1
2
1
0
1
1
0
0
1
2
0
0
0
0
2
0
2
1
2
2
1
0
0
1
0
2
0
0
0
1
0
0
0
1
3
1
0
1
0
2
2
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
2
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
1
0
0
0
2
0
4
3
2
0
0
0
1
2
1
0
0
0
0
0
1
0
3
0
0
0
0
1
0
0
0
2
0
2
2
0
0
1
0
2
0
0
1
1
0
0
0
1
2
0
2
1
0
2
2
0
0
0
1
0
5
2
0
0
1
3
0
1
0
2
1
1
1
1
0
1
1
0
0
2
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
1
1
1
0
0
1
0
0
1
0
1
0
1
0
0
2
0
0
0
1
2
0
0
0
0
1
1
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
2
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
2
0
1
2
0
0
0
1
1
0
0
0
0
2
0
1
2
0
0
1
0
1
0
0
0
0
1
1
0
1
0
0
1
0
2
0
2
0
0
2
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
2
0
2
2
0
2
0
0
0
4
0
2
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
1
1
0
1
0
0
0
2
2
0
0
0
2
0
1
0
2
0
1
0
0
0
1
0
0
2
2
0
0
2
1
0
0
0
0
0
1
0
0
1
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
2
0
0
0
2
0
0
2
0
0
1
0
0
4
0
0
3
0
2
0
0
0
0
2
0
1
1
2
0
0
0
0
0
0
0
2
0
1
2
0
0
5
1
0
0
0
0
2
2
0
0
1
0
1
0
1
3
2
2
0
0
0
0
1
1
3
1
0
4
2
0
0
0
1
2
0
0
0
2
0
0
0
0
2
0
2
1
0
0
0
0
2
2
1
0
0
0
0
0
0
0
1
1
2
0
2
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
1
2
1
2
0
0
0
1
0
1
0
2
1
0
1
4
0
0
0
0
1
0
0
2
0
4
1
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
2
0
2
2
2
2
0
0
0
0
1
2
0
0
0
0
0
3
4
1
1
1
0
0
0
0
1
2
0
0
0
0
2
0
0
2
2
0
0
1
0
0
2
2
0
0
0
2
0
0
0
0
0
2
1
0
0
1
0
2
0
0
0
0
1
0
2
0
0
2
1
0
1
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
1
1
0
0
0
1
0
0
0
2
2
0
0
0
2
1
0
0
0
1
2
0
2
0
0
1
1
1
0
2
0
0
0
0
1
1
0
0
0
2
1
0
0
2
0
2
2
0
2
2
0
0
0
0
2
0
0
0
0
1
0
2
1
0
0
2
0
0
1
0
0
0
2
1
1
4
0
2
1
0
2
1
0
0
0
0
0
0
2
1
1
0
1
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
1
0
2
0
2
0
0
0
1
0
0
1
3
0
2
2
0
0
2
0
0
0
0
0
2
0
3
0
1
0
0
0
0
2
0
1
1
0
2
0
0
0
2
0
1
2
0
0
11
0
2
0
0
1
1
0
2
1
0
2
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
4
1
1
2
0
0
0
1
0
0
1
0
1
0
1
0
0
0
2
2
2
0
0
2
1
0
1
0
0
1
0
0
2
2
1
0
0
2
1
0
3
0
0
1
0
0
0
0
2
0
2
0
1
0
1
2
0
0
2
0
0
1
0
0
2
1
0
0
0
0
1
2
1
2
0
3
0
0
0
2
0
0
0
1
0
2
0
3
0
0
0
0
0
0
0
0
2
1
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
2
1
1
0
1
2
2
0
1
1
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
1
0
2
0
1
0
0
1
0
0
1
0
2
1
1
1
0
0
1
0
0
0
1
1
2
0
1
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
2
0
1
1
0
2
0
0
0
0
0
0
2
1
0
0
1
0
3
0
0
1
0
1
2
2
0
0
1
0
1
0
2
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
2
0
1
0
2
2
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
1
2
0
0
0
0
0
3
0
0
0
0
3
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
1
0
2
0
2
0
1
0
0
5
2
0
0
0
0
1
0
0
1
1
0
0
0
0
2
2
2
0
0
0
0
2
0
0
0
0
0
2
0
1
0
1
2
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
1
0
0
0
0
0
1
2
2
0
0
2
0
0
1
0
0
2
0
0
1
0
2
0
2
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
2
2
4
0
3
1
2
0
0
0
0
0
1
0
1
0
0
0
2
2
0
1
0
2
1
0
0
0
1
0
2
0
2
2
0
0
0
0
1
0
1
2
2
0
1
5
2
0
0
0
1
0
1
0
2
0
0
0
0
2
1
3
2
0
0
0
2
0
0
1
1
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
2
0
2
1
0
0
1
1
0
0
0
1
0
0
2
2
2
0
2
0
0
1
1
0
0
0
1
0
0
2
1
0
2
0
0
1
1
1
2
0
1
0
1
0
2
1
0
1
2
0
0
0
0
2
0
0
2
4
0
2
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
1
0
2
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
1
0
2
0
2
0
0
1
2
1
0
0
0
0
0
0
0
2
1
1
2
0
0
2
0
0
0
2
0
2
0
0
0
2
0
0
0
0
2
0
0
2
2
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
3
2
3
0
0
0
0
0
2
0
0
0
1
0
1
0
1
1
2
0
0
1
1
2
0
0
0
2
0
1
0
0
0
0
1
2
1
2
2
0
0
3
0
1
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
1
0
2
2
0
0
1
1
0
0
0
0
4
1
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
2
0
2
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
1
0
0
1
0
0
2
2
0
2
1
0
0
0
1
1
0
0
0
2
0
0
2
1
0
0
2
1
0
2
0
3
0
2
0
0
0
2
2
0
2
0
0
0
0
2
0
0
0
0
5
0
0
2
4
0
0
0
0
1
0
3
1
0
2
3
2
1
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
3
2
0
0
2
1
0
0
2
1
2
0
0
0
0
1
0
0
0
0
2
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
3
0
0
0
0
2
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
2
0
0
0
1
4
0
0
1
1
0
0
3
2
0
0
2
1
2
1
2
0
1
2
0
0
0
0
2
0
0
0
0
2
2
2
2
0
0
0
0
0
0
2
0
0
1
0
1
2
0
0
0
1
0
1
0
0
0
0
7
0
2
1
0
1
0
2
0
0
0
0
0
1
0
0
2
0
0
0
4
0
0
0
0
0
0
0
2
0
4
0
1
0
0
0
2
2
0
2
1
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
1
1
1
2
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
2
0
2
0
1
2
0
2
1
0
2
0
0
0
0
0
0
2
1
0
0
0
2
0
1
1
1
0
2
0
1
1
2
0
0
0
0
2
2
0
1
0
0
2
0
0
0
0
1
0
3
0
1
0
0
4
1
1
0
2
2
0
0
1
0
2
0
2
0
0
2
2
0
2
2
2
1
1
0
0
0
0
1
0
0
0
1
0
1
2
0
2
0
1
2
1
1
0
0
0
3
0
2
0
0
2
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
2
1
1
0
2
0
2
0
1
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
1
0
2
0
2
0
0
1
0
0
0
1
0
0
0
0
3
2
0
0
2
2
0
0
1
1
2
0
0
2
0
2
0
0
1
0
0
0
0
0
0
1
0
0
1
2
0
1
0
0
2
0
0
1
1
1
2
1
1
0
0
2
0
0
0
2
2
0
0
0
0
1
1
0
0
0
2
0
0
1
0
0
0
1
0
2
0
2
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
2
1
0
1
0
0
0
0
0
0
2
0
2
0
0
2
0
2
2
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
7
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
2
1
0
2
1
0
0
2
0
0
0
2
2
0
0
1
0
1
0
0
1
0
1
2
2
0
0
0
1
2
1
2
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
2
2
0
0
0
2
2
1
0
0
0
0
2
1
1
1
1
0
1
2
0
0
0
1
1
0
0
0
0
0
2
0
2
2
1
0
0
0
0
0
2
1
0
0
0
0
0
1
0
2
2
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
3
2
0
0
0
0
0
3
2
0
0
0
0
1
0
0
0
0
2
0
2
0
1
0
0
2
0
1
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
2
0
0
2
0
0
0
0
1
0
0
0
2
0
0
1
1
1
0
2
0
3
2
2
0
0
0
0
0
0
1
2
1
1
0
0
2
0
0
0
2
3
1
1
1
2
0
0
2
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
1
0
1
0
2
0
0
1
2
1
1
0
2
0
1
0
2
2
2
0
0
0
0
2
0
0
0
2
0
0
0
1
2
2
2
0
0
0
0
0
0
0
0
0
1
2
0
0
1
1
0
3
2
2
0
0
0
0
0
0
0
0
2
2
0
1
2
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
1
0
2
0
0
1
0
0
0
2
0
1
2
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
2
0
0
0
1
5
1
0
0
0
2
2
0
0
0
2
0
2
2
0
0
2
0
1
0
0
1
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
1
0
0
0
2
0
0
2
0
0
1
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
2
1
0
0
0
0
1
1
0
0
0
0
1
0
2
1
0
0
2
0
0
3
0
0
0
0
0
1
2
0
2
1
1
2
1
1
1
0
0
0
0
0
1
0
0
2
0
1
0
0
2
1
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
2
2
1
2
1
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
2
1
0
0
1
1
0
0
3
0
1
0
2
0
1
1
1
1
0
0
1
1
0
1
0
0
0
0
1
2
1
0
0
2
1
0
0
0
0
0
1
0
2
0
2
0
1
0
1
0
0
0
1
1
1
0
2
0
2
0
0
0
0
1
0
5
1
0
1
0
0
7
2
2
0
0
0
0
1
0
2
1
2
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
3
1
0
2
0
0
0
1
1
0
1
0
0
1
0
1
0
0
2
0
0
0
0
1
0
2
2
13
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
2
2
0
0
0
0
0
0
1
2
0
0
0
2
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
2
1
0
0
1
0
2
0
1
2
1
0
1
2
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
2
2
0
0
0
0
2
0
1
2
0
0
2
0
0
1
0
0
0
0
0
1
0
1
0
0
1
2
2
0
1
0
0
2
1
1
2
1
0
0
1
1
1
1
1
0
3
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
7
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
2
3
2
2
0
0
0
2
0
0
0
2
0
6
0
0
2
0
0
0
0
0
1
5
0
0
0
0
0
2
0
2
0
2
0
2
0
1
0
0
0
2
0
0
2
2
0
0
0
0
0
0
1
0
1
0
3
1
2
0
2
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
2
0
1
0
0
0
1
0
2
0
1
0
0
0
2
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
2
1
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
1
2
0
0
0
5
0
1
3
2
0
2
2
0
5
0
0
2
2
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
1
2
0
1
0
0
2
1
1
2
0
3
0
0
1
1
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
1
2
0
0
0
1
0
0
2
0
0
1
1
0
0
0
0
2
2
0
0
2
0
0
1
0
1
0
0
0
0
2
0
0
0
1
2
1
1
0
1
1
0
1
0
1
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
2
1
2
0
1
0
1
2
0
0
0
2
0
2
0
0
0
1
2
2
2
0
0
1
0
0
1
0
0
0
5
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
2
1
0
0
2
1
2
0
2
1
0
2
0
2
1
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
5
0
0
0
0
0
0
1
2
0
0
2
0
0
5
0
1
1
0
0
0
0
1
0
3
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
3
0
1
0
0
0
0
0
1
2
0
0
0
0
1
2
0
0
1
1
0
0
0
2
0
0
0
1
0
3
1
0
0
0
1
0
0
1
2
0
2
1
0
0
0
1
0
0
2
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
2
0
0
0
0
0
0
0
2
1
0
0
0
1
3
0
1
2
0
2
1
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
2
0
1
2
0
0
0
1
4
0
0
1
0
1
0
3
0
0
1
2
1
1
0
1
0
0
3
2
0
0
0
0
1
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
1
2
1
0
0
1
0
1
1
0
0
0
2
0
2
0
0
0
0
2
1
0
0
1
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
2
0
2
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
1
0
2
0
0
0
1
0
0
1
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
2
0
0
2
0
1
2
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
1
2
0
0
0
1
0
0
2
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
1
1
0
0
1
0
2
5
1
0
0
0
0
0
1
2
0
1
0
0
0
2
2
0
0
0
0
1
2
1
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
2
1
1
0
5
0
0
2
0
2
1
0
2
0
0
0
1
0
0
2
0
0
0
1
0
0
2
0
1
0
0
0
0
1
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
2
0
2
0
2
2
0
2
0
2
1
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
1
1
1
0
0
2
2
0
2
1
1
2
0
0
0
2
0
0
2
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
2
0
0
0
1
0
1
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
2
0
2
1
1
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
1
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
2
0
0
0
0
0
1
1
1
1
0
0
0
0
0
1
2
1
0
0
0
0
0
1
0
0
1
0
2
0
1
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
3
2
1
0
0
0
3
0
0
1
0
0
0
0
0
6
0
0
0
0
2
0
0
2
0
0
2
0
1
0
0
2
0
0
0
0
0
2
2
0
0
2
2
0
1
2
0
0
2
1
0
0
1
0
0
0
0
1
1
0
0
0
0
2
0
0
1
0
2
2
0
1
1
0
0
0
0
0
0
1
0
2
2
0
0
1
0
0
0
0
0
3
0
0
2
2
0
0
0
1
2
0
0
0
0
2
0
1
0
2
0
0
1
0
3
0
0
0
5
1
2
2
0
1
1
0
0
0
0
0
0
0
3
0
0
1
0
0
1
0
0
0
0
0
2
2
0
0
0
2
2
0
2
2
0
0
1
0
0
2
0
0
1
0
1
0
1
2
0
0
0
0
0
2
1
0
1
0
2
0
0
0
0
2
2
2
2
0
2
0
0
2
0
3
1
0
0
1
1
1
1
2
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
2
2
0
0
0
0
0
2
0
0
3
0
0
0
0
0
2
0
2
0
0
0
2
0
0
2
2
0
1
0
1
0
0
0
1
0
0
2
2
2
1
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
1
0
0
0
1
0
0
3
0
0
1
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
2
2
0
0
1
0
0
0
0
0
1
2
3
0
0
0
0
0
1
0
0
1
1
3
0
0
0
0
2
2
0
0
1
1
0
2
0
0
0
0
0
2
2
0
0
0
0
0
1
1
2
0
0
0
1
2
0
1
1
0
2
0
0
0
1
0
0
0
0
1
2
4
2
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
2
2
0
2
0
1
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
2
1
0
1
0
0
1
1
1
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
2
1
2
0
1
2
0
0
1
0
1
0
1
1
1
0
1
0
0
0
1
1
0
0
0
2
0
0
0
0
2
2
0
2
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
2
1
0
1
0
0
2
2
1
0
2
1
3
0
0
2
1
1
0
0
2
2
1
0
0
0
2
1
0
2
0
2
0
2
1
0
0
3
0
2
0
0
0
0
0
0
0
1
3
0
2
2
0
0
2
0
2
2
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
2
2
0
2
0
0
0
1
0
1
2
1
1
0
2
0
0
1
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
4
0
1
1
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
1
2
1
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
2
2
2
1
0
0
1
0
0
0
0
2
0
0
1
1
1
0
2
0
0
0
0
0
3
0
0
1
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
1
0
1
1
2
0
0
0
0
0
0
0
1
0
1
2
1
1
2
0
1
0
0
1
1
0
0
0
0
0
1
1
0
0
1
1
0
0
2
0
0
0
2
1
2
0
0
0
2
0
1
0
2
0
0
1
2
0
2
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
1
0
1
2
1
1
2
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
3
0
1
2
0
0
2
1
1
2
1
0
0
0
0
0
0
2
0
0
0
0
1
1
0
1
0
0
0
0
1
1
0
1
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
1
2
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
2
1
2
2
1
0
0
0
1
0
0
0
0
2
1
2
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
2
1
0
2
2
2
0
0
0
0
1
0
2
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
1
2
0
1
2
0
0
2
0
2
2
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
3
0
0
0
0
2
0
0
1
0
0
1
1
2
2
1
1
1
1
1
0
1
0
0
0
0
0
0
3
3
2
1
0
2
1
2
0
0
0
0
1
3
0
2
1
0
2
2
0
0
0
0
0
2
0
1
2
4
0
0
0
0
1
0
0
2
0
0
0
2
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
2
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
2
1
0
0
2
2
0
1
1
2
0
0
0
1
2
0
0
2
0
2
0
1
0
1
1
0
0
2
1
0
3
0
1
0
1
1
0
2
1
2
0
0
1
0
1
0
0
0
1
3
0
2
1
0
0
0
2
2
0
0
2
0
0
1
0
2
1
1
2
0
0
2
0
1
0
0
0
1
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
2
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
2
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
2
1
3
0
0
0
0
0
1
0
1
2
1
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
1
0
1
2
0
0
0
0
1
0
2
2
1
1
0
0
0
0
0
2
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
1
1
2
2
0
0
2
0
1
1
0
0
0
2
0
2
0
1
0
0
2
0
0
0
0
1
0
2
0
2
0
0
0
0
1
2
0
0
0
1
1
2
0
0
2
1
0
0
0
0
0
0
2
0
0
0
1
0
3
0
0
0
0
0
1
1
0
2
0
0
1
0
5
0
2
0
0
1
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
2
0
0
1
1
0
2
0
0
1
1
0
1
0
0
0
2
0
1
0
0
0
2
1
0
0
2
0
0
2
0
1
0
1
2
2
0
0
0
0
0
0
0
0
1
0
0
2
1
1
1
1
0
0
2
0
2
0
0
0
0
0
1
0
0
2
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
2
0
1
0
3
0
0
2
0
0
0
0
0
0
2
0
3
1
0
1
0
0
1
0
1
1
0
0
0
0
1
2
2
0
0
1
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
1
1
2
0
0
2
0
0
0
1
2
0
0
1
1
0
0
0
3
1
1
0
0
2
1
0
0
0
2
0
0
1
0
0
0
2
0
1
0
0
1
1
1
0
1
0
0
1
2
0
0
0
0
0
2
0
1
0
0
0
0
2
2
1
0
1
0
0
0
0
4
0
1
1
0
0
0
0
1
0
1
1
0
0
0
2
0
1
2
0
0
3
0
0
0
0
2
0
0
2
0
1
0
0
2
0
2
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
3
0
1
2
2
2
1
0
0
0
0
0
2
1
1
0
0
1
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
2
1
1
0
0
0
0
0
1
2
1
0
0
0
0
0
0
1
2
0
0
2
2
0
0
2
0
1
1
1
0
0
0
0
0
0
0
0
2
0
0
2
0
2
4
1
0
0
0
2
2
0
0
0
0
2
0
0
1
0
0
0
0
1
1
0
0
1
2
1
0
0
5
0
0
1
0
0
0
0
2
0
1
0
0
0
1
0
0
1
2
0
0
0
0
1
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
2
0
0
2
1
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
2
1
0
0
0
0
0
1
0
3
0
0
1
0
1
5
3
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
2
0
0
2
1
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
1
0
1
0
2
0
0
0
3
0
0
1
1
0
0
1
2
1
2
2
2
0
0
1
0
0
0
0
2
0
3
0
0
0
1
0
6
0
1
0
0
1
0
0
0
0
2
2
0
0
5
2
0
0
1
0
0
0
0
2
1
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
2
0
0
1
0
0
0
2
1
1
0
0
0
2
0
0
0
1
2
0
2
2
0
1
1
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
2
0
1
0
2
0
2
1
1
2
0
0
0
1
0
0
1
1
0
0
1
0
1
0
0
0
0
0
2
0
1
2
2
0
0
0
0
0
0
1
0
2
0
1
2
0
0
0
1
2
0
0
1
0
0
0
0
2
2
0
1
0
0
1
2
0
0
0
0
3
0
0
0
2
0
2
0
0
0
2
1
3
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
3
0
0
1
0
3
0
0
0
2
3
0
1
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
1
1
2
3
0
3
2
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
1
1
2
0
0
0
1
2
0
0
0
0
2
0
0
1
1
2
2
1
0
0
0
0
0
1
1
0
0
1
0
0
0
4
2
1
0
0
0
3
3
0
1
1
4
0
0
1
1
2
0
0
0
0
0
2
2
1
0
3
2
1
0
1
0
1
0
0
1
0
0
0
0
0
0
2
8
0
0
0
1
0
0
3
0
0
1
0
1
2
0
1
0
2
1
2
0
0
1
2
0
0
0
0
0
0
0
2
2
1
2
0
0
0
0
0
0
0
1
1
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
1
2
1
3
1
0
0
0
2
0
0
1
0
0
0
1
0
0
0
1
2
0
0
1
0
0
0
0
0
0
2
0
0
2
2
2
1
1
5
2
0
0
2
0
0
0
0
2
0
2
2
0
0
0
0
2
1
0
3
0
3
2
0
0
0
0
1
2
0
0
1
0
2
1
0
3
0
2
0
0
1
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
1
0
2
0
0
2
3
0
0
1
1
0
0
0
0
0
1
1
0
0
1
1
0
1
0
0
2
0
0
0
2
2
2
0
0
0
1
2
0
2
2
0
1
0
0
2
0
0
2
0
0
0
2
1
0
2
1
0
0
1
0
0
0
0
0
0
0
2
0
2
1
0
2
0
0
0
0
0
1
0
2
2
1
2
0
0
0
0
2
1
0
0
0
2
0
0
3
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
2
1
1
21
0
1
0
2
0
1
2
1
0
0
0
0
0
1
2
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
2
2
0
2
0
0
0
0
0
0
1
0
1
0
1
1
0
2
0
2
2
0
0
1
0
1
0
2
0
0
0
0
0
0
2
0
0
2
0
3
0
0
0
0
0
0
3
0
0
0
0
0
2
0
2
1
2
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
1
0
0
1
0
0
1
2
0
0
0
0
1
0
1
0
0
1
2
1
0
0
1
0
0
2
4
2
1
0
2
1
0
0
0
0
1
2
2
2
1
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
1
0
0
0
0
2
2
1
1
0
0
2
0
2
0
0
0
0
2
0
0
0
1
1
0
0
1
4
0
0
0
0
2
0
1
0
2
0
1
2
1
1
2
0
0
2
0
0
1
2
0
1
0
1
1
0
2
0
0
2
2
0
2
1
1
0
1
2
0
0
0
1
0
0
1
0
1
2
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
1
0
2
1
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
2
0
0
1
0
1
0
0
2
0
1
2
0
0
0
1
1
0
0
0
1
1
1
0
0
0
2
2
0
3
0
0
0
0
2
0
3
2
0
0
0
0
3
2
0
0
0
0
1
1
0
0
2
2
2
2
0
0
0
0
5
0
0
0
0
0
1
0
0
0
0
1
2
2
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
2
1
0
0
1
0
2
2
0
0
1
0
0
3
0
2
0
0
1
0
0
2
0
1
0
0
0
0
4
0
0
2
1
0
0
0
0
0
1
0
0
1
0
1
2
1
0
0
0
0
0
2
0
2
0
0
0
3
0
0
2
0
0
0
1
2
1
3
0
0
0
0
0
1
0
2
2
2
1
0
0
0
0
0
0
2
0
0
1
1
0
0
0
1
0
0
0
2
0
1
2
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
1
0
0
2
1
0
2
0
2
2
0
0
1
1
0
1
0
0
1
0
2
0
2
0
0
0
2
0
0
0
1
0
0
0
2
4
0
0
1
0
0
0
0
0
2
1
2
1
2
0
0
1
2
0
1
1
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
2
0
0
2
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
1
2
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
4
1
2
0
0
1
2
2
0
3
0
0
1
0
0
0
0
1
0
1
0
1
0
0
1
0
1
2
2
0
0
1
0
1
0
1
0
2
1
0
1
2
2
1
0
0
2
0
0
0
0
0
1
2
0
2
0
0
0
0
0
1
1
2
0
1
2
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
2
1
0
0
1
2
0
0
2
2
1
0
2
1
2
0
1
0
2
0
1
0
0
0
0
2
1
0
0
1
0
0
0
0
2
4
1
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
2
2
1
1
0
2
0
0
0
0
0
0
0
3
2
1
0
1
2
1
1
1
0
0
2
0
0
0
2
0
1
4
0
0
0
0
3
2
0
1
0
1
0
2
0
2
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
1
1
0
2
0
3
1
0
2
2
2
3
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
1
0
2
0
0
0
0
0
2
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
1
0
0
0
2
0
0
0
0
2
1
0
0
0
2
0
1
2
0
0
0
0
0
0
2
0
2
0
1
5
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
2
0
1
2
1
0
0
0
0
3
1
0
2
0
1
0
2
1
1
1
0
0
2
0
2
1
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
1
0
1
0
1
1
2
3
0
0
0
2
0
0
0
2
1
1
1
1
2
0
1
4
0
0
2
0
1
2
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
1
1
0
1
0
1
0
1
2
1
1
2
0
1
0
0
2
1
3
0
0
2
0
1
2
0
0
0
1
2
1
1
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
1
1
1
1
0
1
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
1
2
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
2
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
2
1
1
0
2
0
0
0
0
0
3
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
1
0
0
1
1
1
0
1
0
2
0
0
2
0
0
0
1
2
0
2
0
0
0
1
0
0
0
0
2
0
2
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
2
1
2
1
1
2
2
0
1
0
2
0
2
1
0
0
0
1
0
0
0
5
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
3
0
2
0
0
2
0
0
0
3
2
0
0
0
0
0
0
1
0
1
1
1
2
0
0
2
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
1
0
0
2
0
0
2
0
1
0
0
0
2
3
0
3
0
0
0
0
0
0
2
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
3
1
0
0
1
1
0
0
0
1
0
0
1
2
1
1
0
2
0
0
0
0
1
1
0
1
0
0
1
3
0
2
0
0
0
0
1
0
1
0
0
0
1
2
0
2
0
0
0
1
1
0
1
1
0
1
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
3
3
1
0
0
1
1
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
1
0
1
2
2
0
0
0
1
0
0
0
0
1
1
1
0
0
1
0
0
2
0
2
0
1
0
1
0
0
2
1
1
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
2
0
3
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
2
0
1
0
1
1
0
0
2
0
0
0
1
0
0
2
2
0
0
0
0
0
0
2
0
1
1
2
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
1
0
0
2
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
2
0
0
1
2
0
2
0
2
1
0
0
1
2
0
0
0
0
0
0
0
1
0
0
2
0
1
1
0
2
2
0
1
2
0
1
0
0
0
2
0
2
0
0
0
0
0
0
3
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
2
0
1
2
2
2
0
0
0
0
0
4
1
0
2
0
0
0
2
0
1
2
2
0
0
2
1
0
0
1
0
0
0
0
0
1
0
2
0
2
0
0
2
1
0
2
1
2
1
0
0
0
1
0
1
1
0
0
0
1
3
2
0
1
3
1
0
2
0
2
1
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
1
0
1
0
0
0
2
0
0
0
0
1
0
2
0
0
0
2
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
4
1
2
4
0
0
0
1
1
0
0
2
1
1
0
0
0
3
0
0
1
0
0
3
2
0
1
0
0
2
0
0
1
1
0
0
0
2
0
0
1
1
1
0
1
0
2
0
2
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
4
0
1
2
2
0
0
1
0
0
0
1
1
1
0
0
0
0
1
1
0
0
0
3
2
1
3
0
1
2
1
0
0
0
0
2
2
1
0
0
0
0
0
0
3
0
1
1
0
0
0
0
1
0
0
2
0
0
2
1
0
0
0
0
2
0
1
0
0
1
1
2
0
1
1
0
0
1
0
1
0
0
0
1
2
0
0
0
2
2
0
0
0
0
0
0
2
1
0
0
0
1
0
3
0
2
0
3
2
0
1
1
0
2
1
0
1
1
0
2
2
0
0
0
0
0
1
0
2
0
1
1
2
2
0
0
0
0
2
1
0
0
0
5
0
1
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
1
0
2
0
1
0
0
1
0
1
1
0
2
0
0
2
0
1
1
2
0
0
0
2
0
0
0
0
0
2
0
2
0
1
0
1
0
2
0
0
1
0
1
0
2
0
0
1
2
0
0
0
0
0
0
0
0
1
0
1
0
2
2
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
4
0
0
1
1
0
0
2
1
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
2
1
0
1
1
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
1
0
1
0
0
1
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
3
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
2
1
0
0
2
0
2
2
0
0
0
0
0
0
0
1
0
2
0
1
2
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
1
0
2
0
1
2
0
0
0
0
0
0
0
0
4
0
2
1
2
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
1
0
1
0
1
0
0
1
0
0
0
1
0
1
2
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
2
1
1
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
2
0
0
2
1
2
0
0
1
1
0
0
0
2
1
2
0
1
2
1
0
0
2
0
0
1
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
2
0
1
1
0
0
1
0
0
0
2
0
0
2
0
2
0
0
0
2
1
1
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
3
2
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
2
1
0
0
0
1
0
0
1
1
0
1
3
4
0
0
0
0
0
0
1
4
0
0
0
0
0
0
3
0
2
1
1
0
0
0
0
0
0
0
0
2
2
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
2
0
0
1
1
0
2
0
3
0
1
1
2
0
0
0
0
1
0
2
0
0
1
0
1
0
1
0
2
0
0
0
0
1
0
1
2
2
2
0
1
0
0
0
0
2
0
0
1
1
0
0
0
0
2
0
0
2
0
0
2
0
0
0
1
0
0
2
0
1
0
1
2
0
1
1
0
0
0
2
0
0
0
0
0
2
0
1
0
2
0
0
2
2
0
2
0
1
0
0
0
0
0
2
1
1
0
1
2
0
0
0
0
0
2
0
0
0
0
0
1
2
0
1
2
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
1
1
0
0
2
1
0
1
2
2
0
0
1
0
1
0
0
0
0
0
0
0
0
2
2
1
0
1
0
0
1
0
4
2
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
1
0
0
0
1
0
1
2
0
1
2
0
0
0
3
1
0
1
1
0
0
2
1
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
2
0
0
2
0
2
3
1
0
2
1
0
0
1
0
0
2
1
0
0
0
1
0
0
0
0
10
1
0
1
0
0
0
1
0
0
0
0
1
0
0
1
3
0
0
0
0
0
0
0
0
1
0
0
1
0
1
2
0
1
0
3
2
1
2
0
1
1
0
0
2
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
2
2
3
0
0
0
0
0
2
1
0
0
1
0
0
2
0
0
0
1
0
0
2
1
0
0
1
0
2
0
2
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
2
0
0
2
0
0
2
0
1
0
2
0
1
2
0
1
0
0
0
1
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
1
0
2
1
0
0
0
3
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
3
0
0
0
3
2
0
0
0
2
1
2
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
2
0
2
1
0
0
0
2
0
0
0
1
0
2
0
0
2
1
0
2
0
0
1
0
1
0
0
0
0
2
2
2
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
2
0
1
0
0
0
0
2
0
0
0
0
0
2
0
5
0
3
2
0
0
1
1
0
2
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
1
0
1
3
2
2
2
0
1
1
1
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
2
0
3
0
2
0
1
2
0
0
0
1
0
0
2
2
0
0
0
1
0
0
0
1
1
1
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
2
0
1
2
0
0
1
0
1
1
0
0
0
2
0
1
0
0
0
0
2
0
2
0
0
2
0
1
2
0
0
0
1
0
3
0
1
2
0
0
0
7
0
2
0
0
0
0
0
0
2
0
3
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
1
1
1
1
2
0
0
0
0
0
1
1
1
0
0
0
2
4
2
0
0
0
0
0
0
1
1
0
1
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
1
2
0
0
1
0
0
0
1
0
1
0
0
2
1
0
3
0
1
2
1
2
0
0
0
0
2
0
0
0
3
0
2
0
0
1
1
0
0
0
2
2
0
2
2
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
2
1
1
0
1
0
0
0
0
0
0
2
0
1
1
0
2
0
0
0
1
1
0
0
0
2
0
2
0
0
0
1
2
0
2
0
1
0
0
0
0
0
0
2
0
2
1
2
2
2
0
0
0
2
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
3
0
0
0
0
2
0
2
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
1
0
0
0
1
0
0
2
0
0
1
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
2
0
0
1
1
0
0
0
0
0
1
0
2
1
0
0
1
0
1
1
0
2
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
1
0
0
0
2
0
1
1
0
1
0
0
0
1
0
0
2
0
2
3
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
2
1
0
0
2
0
0
0
0
1
0
0
6
0
0
0
0
0
0
2
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
2
0
1
0
2
0
0
0
0
1
0
3
0
1
0
0
0
2
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
1
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
2
2
3
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
2
1
1
0
0
0
0
0
0
1
0
1
0
2
0
2
0
0
0
0
0
2
0
0
0
2
4
0
1
2
0
2
0
2
2
0
1
0
0
1
0
0
0
0
0
2
2
6
0
0
0
0
0
0
1
0
1
2
0
0
0
0
2
0
0
0
1
0
1
0
2
0
0
0
0
0
1
0
2
1
1
0
1
0
0
0
3
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
2
2
0
2
0
0
0
0
0
1
1
0
0
0
1
1
0
0
2
0
1
2
0
0
0
0
1
1
0
0
2
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
4
0
0
0
2
0
0
1
0
1
0
0
0
1
0
0
3
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
1
2
1
2
0
0
2
2
0
0
0
0
2
0
0
3
0
0
1
0
0
1
0
0
0
2
0
0
0
0
2
0
0
1
0
2
0
0
0
0
2
1
0
0
3
2
1
0
0
0
1
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
1
2
1
0
0
0
2
2
0
0
2
0
2
0
1
0
0
0
2
1
0
2
0
0
0
0
1
2
1
1
0
0
2
0
0
0
0
0
1
1
3
0
0
1
0
2
1
0
0
0
0
0
0
0
3
1
1
0
2
1
0
0
0
0
0
0
1
0
1
0
0
1
2
0
0
0
0
0
0
0
2
1
0
0
0
0
2
2
1
1
0
1
0
0
0
0
2
1
0
0
1
1
0
0
0
0
0
1
1
0
1
1
0
0
2
1
0
1
0
1
0
0
1
2
0
1
0
0
0
2
3
0
1
0
0
1
0
0
1
1
0
1
1
0
4
2
0
2
1
2
0
0
0
0
2
1
0
2
1
2
1
0
1
2
0
0
2
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
3
1
2
1
0
1
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
2
2
0
2
0
0
0
0
2
1
0
0
0
0
0
2
0
0
1
1
2
0
0
0
2
0
2
0
0
1
3
1
1
0
0
0
0
0
1
0
0
0
1
0
6
0
0
0
1
2
2
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
2
0
1
2
2
1
0
2
1
0
0
0
0
0
1
0
2
2
0
2
1
0
1
2
0
1
0
0
0
2
0
2
0
1
0
1
0
0
2
0
0
1
1
0
1
0
2
0
2
0
0
0
0
1
1
0
0
2
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
8
1
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
2
0
0
2
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
1
0
2
2
0
1
0
1
2
2
1
0
2
0
1
0
2
1
0
1
0
2
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
2
1
0
1
0
0
0
2
0
2
0
2
3
0
0
1
1
0
1
0
4
2
0
1
0
0
2
0
0
1
2
0
0
2
1
0
1
0
2
0
2
1
0
1
0
0
2
0
7
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
3
2
0
1
0
1
1
2
1
0
0
0
2
0
0
2
0
0
0
0
0
1
1
0
0
2
1
0
0
0
1
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
3
0
1
0
0
0
0
0
1
0
0
0
1
0
2
1
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
2
0
0
0
0
3
0
0
2
1
0
2
0
0
1
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
1
0
0
2
2
1
0
3
1
0
0
1
0
2
1
0
0
1
0
0
0
1
1
2
0
1
1
2
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
2
0
0
2
1
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
1
1
0
0
0
0
0
2
0
1
2
2
2
1
0
0
1
0
1
1
2
2
2
0
0
2
0
0
0
1
0
0
2
0
1
1
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
1
0
1
0
2
0
2
0
0
2
0
1
0
0
0
0
0
1
0
0
2
0
0
0
2
1
0
0
2
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
5
2
0
0
0
0
1
0
0
0
4
0
0
0
2
0
1
2
0
1
0
2
1
1
0
1
2
0
0
0
0
0
2
0
3
2
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
3
0
1
0
0
0
0
3
0
0
1
0
0
0
1
1
0
1
0
0
0
0
2
1
0
0
2
0
2
0
1
2
0
0
1
2
0
0
0
0
0
0
0
0
0
2
1
2
1
2
1
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
1
0
0
0
1
0
0
0
1
0
2
0
2
0
0
4
0
0
0
2
2
0
0
1
1
0
1
2
0
2
0
0
1
0
0
1
1
0
0
1
2
0
0
0
0
1
1
0
2
0
0
0
0
1
1
0
0
0
1
0
2
0
2
0
2
0
1
1
0
2
0
2
0
2
1
1
0
0
0
0
0
1
2
0
1
2
2
0
0
1
0
0
0
2
0
0
0
0
0
0
2
1
0
1
1
2
2
0
0
1
0
0
1
0
2
0
2
0
0
0
1
0
1
0
2
2
1
0
1
0
2
0
0
2
1
0
1
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
2
0
1
0
0
0
0
0
3
0
0
0
1
0
2
2
0
1
0
2
2
0
0
0
0
2
0
0
1
1
2
3
3
0
0
1
0
2
3
0
0
0
0
0
0
1
0
0
0
3
0
0
0
2
0
0
0
0
1
2
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
4
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
2
0
0
2
0
0
2
0
0
0
0
0
2
1
0
0
1
0
0
0
0
2
2
0
0
1
0
0
1
0
2
2
0
0
0
2
0
0
2
0
0
0
1
0
1
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
1
1
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
1
1
0
0
0
5
1
0
1
0
2
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
1
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
2
0
0
0
1
1
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
2
1
3
0
0
0
1
0
0
1
2
0
2
0
0
0
0
2
0
0
0
0
1
0
2
2
1
0
0
0
0
2
0
0
0
2
2
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
1
2
1
0
2
0
0
0
0
1
3
0
1
0
2
0
1
0
1
0
0
1
2
1
0
0
0
0
0
0
0
1
0
2
1
0
0
0
1
0
0
1
0
0
3
1
2
0
0
0
0
0
2
1
2
1
2
2
0
2
1
1
0
0
2
0
0
1
0
1
0
0
0
0
0
0
1
0
0
2
1
0
0
1
0
0
0
1
0
1
1
0
0
1
0
2
0
0
1
0
0
2
0
2
0
0
1
0
0
0
1
3
1
0
2
0
1
0
0
1
1
0
0
2
0
0
0
0
0
1
0
2
1
0
0
2
0
0
0
1
1
2
0
0
0
0
1
0
0
0
1
0
3
0
0
0
0
0
0
1
0
1
0
0
2
3
1
0
0
0
0
1
1
0
0
0
0
1
1
0
0
2
0
1
2
0
0
0
2
1
1
0
1
1
2
1
0
0
2
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
2
0
2
2
2
0
1
1
2
2
0
0
0
0
0
0
1
1
0
0
2
4
0
2
0
2
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
2
0
0
0
0
0
0
1
2
0
0
1
0
0
1
0
1
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
2
0
0
2
2
0
0
0
2
0
2
0
1
0
1
0
4
0
1
0
0
0
1
0
0
2
2
1
0
1
1
0
0
0
0
2
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
2
4
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
4
1
0
0
2
0
0
2
0
1
1
0
0
0
0
0
1
2
0
0
2
0
0
0
2
1
0
0
0
0
0
1
0
0
1
0
2
2
0
1
0
0
0
0
0
2
1
0
3
2
0
2
0
0
1
0
0
1
0
0
0
0
2
0
0
1
1
0
1
0
1
2
0
0
0
1
0
1
1
0
0
0
0
2
2
0
2
0
0
0
0
0
2
0
0
2
2
1
0
1
2
0
1
1
0
0
0
2
0
0
0
1
2
0
0
1
1
0
0
0
2
0
1
0
0
0
0
1
2
2
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
3
0
2
1
6
0
1
0
1
0
0
0
0
0
0
1
1
2
2
0
0
0
1
2
0
0
1
0
0
0
4
0
2
1
0
0
0
5
1
5
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
1
1
0
2
1
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
2
0
2
1
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
3
0
0
0
2
0
0
0
6
0
0
2
0
2
2
0
2
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
1
2
0
2
1
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
2
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
2
0
1
2
1
0
1
0
0
1
1
0
1
1
0
1
1
1
7
0
1
1
2
0
4
1
0
5
0
0
0
2
2
0
1
2
1
2
0
0
1
0
0
0
5
0
0
2
2
0
1
0
0
2
0
0
0
0
3
0
0
0
1
0
1
0
2
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
1
2
2
0
0
0
0
1
2
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
1
0
1
0
0
0
0
2
1
0
0
1
0
1
0
0
0
2
1
0
1
0
1
0
0
1
0
1
0
0
1
0
0
0
2
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
3
0
2
0
0
2
0
2
1
2
0
1
1
2
1
1
1
0
0
0
1
1
2
0
2
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
2
0
0
0
2
0
1
1
0
0
3
1
0
0
0
1
0
1
0
0
0
1
1
0
2
0
3
1
2
2
0
0
0
0
0
2
7
0
0
1
2
0
0
1
2
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
3
0
0
4
0
0
1
0
2
0
0
1
0
3
0
0
0
1
2
0
2
0
3
2
2
0
0
0
0
0
1
1
0
5
0
0
1
2
2
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
2
0
0
1
0
1
2
1
0
0
1
0
1
0
0
0
0
1
2
2
1
2
1
0
0
1
1
0
0
0
0
0
0
0
0
2
1
2
0
0
1
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
2
2
1
0
0
0
2
0
0
0
0
0
2
1
0
0
2
0
2
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
1
1
0
0
0
0
2
1
0
2
0
0
1
2
2
0
2
0
0
0
0
1
0
0
0
0
0
2
0
2
1
1
2
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
2
1
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
2
1
1
1
1
1
0
1
0
0
0
0
2
2
0
1
2
1
1
0
2
0
0
0
1
0
1
0
1
2
2
0
2
1
0
2
0
0
0
0
0
0
0
3
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
2
3
0
1
0
0
0
0
1
0
0
0
1
0
1
1
0
1
0
0
2
0
2
1
0
0
0
2
2
1
0
0
0
3
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
2
0
1
0
3
0
0
2
1
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
2
1
1
0
0
0
0
0
0
2
0
0
0
1
1
0
0
2
0
0
2
1
1
0
1
2
0
0
1
0
0
1
0
0
1
0
0
2
2
0
0
0
2
0
0
0
1
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
3
0
0
0
2
0
0
2
1
1
0
1
0
0
1
1
2
0
1
0
0
2
3
1
2
0
2
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
1
1
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
1
2
0
1
1
1
0
0
0
0
2
0
0
1
2
1
0
1
2
0
2
0
1
1
1
0
1
0
2
0
0
2
0
0
1
0
0
1
0
0
1
0
2
2
0
0
0
1
2
0
1
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
1
0
0
0
2
0
1
0
3
0
1
0
0
0
0
1
2
1
1
0
2
2
1
0
0
0
0
1
2
0
2
2
0
0
0
0
2
0
0
1
0
1
0
0
1
2
1
0
0
0
0
1
1
0
2
0
1
0
1
0
0
1
0
0
0
0
0
2
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
2
2
0
0
0
0
2
0
2
1
0
1
3
2
0
0
0
0
2
0
0
0
0
1
1
0
0
0
2
0
1
0
0
0
0
2
1
0
0
0
0
1
0
0
2
0
0
2
0
2
0
0
0
0
2
0
0
0
0
2
0
2
0
1
2
0
1
0
0
0
0
0
1
0
0
0
3
3
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
2
1
0
2
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
2
0
1
0
0
3
0
1
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
1
2
2
0
1
0
1
0
1
1
0
2
1
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
2
0
0
0
1
1
0
0
1
2
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
2
0
0
2
2
0
0
0
0
2
0
2
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
1
2
0
0
0
0
1
0
1
2
0
1
0
2
0
0
0
2
5
0
2
0
0
0
0
4
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
2
0
0
0
0
0
2
0
2
1
0
3
0
1
0
0
0
2
1
1
1
0
1
0
4
2
1
1
0
3
1
0
0
0
0
0
0
2
2
2
0
1
0
0
1
1
2
0
0
2
0
0
1
0
2
2
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
2
0
0
1
0
1
0
2
0
0
0
0
2
0
0
2
2
0
5
2
0
1
0
0
0
0
0
1
2
0
1
0
1
0
1
1
2
1
0
1
0
0
0
1
0
2
2
0
2
0
0
0
0
2
0
1
0
0
0
1
1
0
0
0
4
0
0
0
2
0
2
0
2
2
1
0
1
0
2
1
0
0
1
1
2
0
2
1
0
1
0
2
1
0
0
0
0
0
2
0
1
0
1
1
0
0
0
2
1
0
2
0
1
0
1
3
0
1
1
1
0
2
0
0
0
1
2
1
1
0
0
1
2
0
2
0
0
0
0
1
0
0
1
0
0
1
1
0
0
1
0
2
1
2
2
0
2
0
0
0
0
0
0
0
0
2
1
0
0
2
1
0
0
0
0
0
2
0
0
2
2
0
0
0
1
0
1
2
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
2
2
0
1
1
0
1
2
2
0
0
0
2
0
2
0
0
0
2
1
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
3
0
0
0
2
0
0
2
0
1
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
3
1
0
0
0
0
0
0
0
2
2
0
7
1
1
0
2
0
1
0
3
0
0
0
0
0
1
0
0
2
0
0
2
0
0
1
4
2
0
0
2
2
3
1
1
0
1
0
1
0
0
0
2
1
0
0
0
0
1
0
2
0
0
2
0
2
0
0
0
0
5
2
0
0
0
0
0
0
0
0
1
0
0
2
0
1
2
3
2
0
0
1
0
0
0
2
1
1
1
0
2
0
2
0
0
0
2
0
0
0
0
2
0
0
2
2
0
1
1
0
2
1
0
0
0
0
0
1
0
0
1
2
1
0
2
0
0
0
1
2
0
3
0
0
0
0
1
2
0
2
0
0
1
1
0
0
2
0
3
2
1
0
0
0
3
0
0
1
0
0
0
0
2
2
1
0
0
0
0
2
0
0
0
1
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
3
0
0
0
1
0
0
0
0
0
2
0
1
0
0
1
2
1
1
2
1
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
2
1
2
0
6
1
0
0
1
2
3
1
2
0
1
6
1
2
0
0
1
0
2
0
2
0
2
2
0
0
1
1
0
1
1
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
4
0
1
1
2
1
0
0
0
1
0
2
2
0
4
0
2
0
0
2
0
1
0
1
2
0
0
2
0
0
2
0
0
0
0
0
1
1
2
0
2
0
0
0
0
0
0
0
0
0
2
0
2
2
1
0
2
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
1
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
3
1
2
0
1
2
0
0
2
2
1
2
0
0
0
0
0
0
2
0
0
1
0
0
2
1
0
0
0
0
0
2
0
0
2
2
0
0
0
0
2
2
0
0
2
0
0
1
0
1
0
0
0
2
0
1
1
3
0
0
2
0
0
0
2
0
0
0
1
1
0
0
0
4
1
0
0
1
0
1
0
0
0
0
0
0
2
1
0
0
1
0
0
0
1
3
0
2
0
1
0
0
2
0
0
2
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
1
0
0
0
0
0
0
2
1
1
2
1
0
0
0
2
2
0
2
2
0
1
0
2
0
0
0
1
1
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
3
0
1
1
0
0
0
0
0
0
1
1
0
0
3
2
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
1
2
1
1
0
0
0
1
2
1
2
0
0
0
0
0
1
0
2
0
0
1
1
2
2
1
0
2
0
1
0
2
0
1
0
4
0
0
1
0
7
0
1
2
0
1
0
0
0
0
0
1
0
0
0
0
0
2
2
1
0
0
0
1
3
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
1
2
0
0
2
0
0
0
0
0
1
0
0
1
2
2
0
0
0
0
0
0
2
2
0
0
2
1
1
0
2
1
1
2
1
2
1
0
0
0
0
1
0
1
1
0
2
0
3
1
0
0
0
0
0
0
0
0
0
3
2
1
0
0
1
0
1
0
0
1
0
0
2
1
1
0
0
1
1
0
2
2
5
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
1
0
0
2
1
0
0
1
0
0
0
2
1
0
0
2
0
0
1
1
0
2
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
1
0
1
1
0
1
3
1
0
1
0
1
1
0
0
0
2
0
0
0
0
0
2
2
0
0
2
1
2
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
2
0
2
0
1
1
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
1
0
0
1
1
0
0
1
2
0
1
0
2
0
0
2
2
0
0
0
1
0
1
2
2
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
3
3
0
0
0
0
0
0
2
0
1
0
2
1
1
0
0
3
2
1
0
1
0
0
0
0
0
1
0
0
0
1
0
2
0
2
2
0
0
2
1
2
1
0
1
0
0
0
1
0
2
2
0
0
0
0
1
0
0
2
2
1
0
0
0
1
0
1
0
0
0
0
0
2
0
0
1
1
0
1
0
0
0
2
2
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
3
0
1
0
0
2
0
1
2
0
0
1
0
0
0
0
2
1
0
0
1
0
0
0
2
0
0
0
0
4
0
0
0
0
2
0
2
1
2
0
1
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
2
0
2
1
0
0
1
0
2
1
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
1
2
1
0
0
1
0
3
0
0
0
0
0
0
1
1
0
3
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
1
1
0
2
1
0
0
0
0
3
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
1
1
0
0
1
0
0
0
2
0
2
0
0
1
0
1
0
1
1
0
0
0
2
0
0
0
1
0
0
0
1
2
0
0
0
0
0
1
0
1
0
0
0
0
0
2
1
2
2
0
1
1
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
2
0
0
2
0
0
0
2
2
0
1
1
0
1
0
4
0
0
0
2
1
0
0
1
0
0
2
2
1
0
0
0
1
1
0
2
1
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
3
0
2
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
1
0
0
0
1
0
2
0
0
0
2
0
0
0
3
1
1
0
1
0
0
0
0
0
2
1
2
1
1
1
2
4
0
0
0
0
0
2
0
0
2
3
0
0
0
0
1
1
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
2
2
2
0
2
3
1
0
0
0
1
1
0
2
2
12
1
1
0
0
0
0
2
0
0
1
0
0
3
0
0
0
0
0
0
1
0
0
1
2
0
0
2
2
0
0
2
3
0
2
2
1
0
0
2
0
0
0
0
0
0
1
0
0
2
0
1
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
2
0
0
0
0
0
0
1
2
2
0
0
0
0
2
0
0
1
0
2
5
1
0
0
3
3
0
0
0
2
0
0
0
0
2
1
1
0
0
2
1
0
0
0
0
1
2
2
0
1
2
0
2
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
2
0
0
0
0
0
0
4
2
1
1
0
2
2
0
2
0
0
2
1
0
2
0
2
0
2
0
0
0
0
0
0
0
1
1
0
0
0
2
0
2
2
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
3
0
1
1
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
1
0
0
0
1
0
0
0
4
0
0
2
2
0
2
2
0
1
0
0
0
1
0
0
0
2
0
0
0
2
0
1
2
0
0
2
0
2
2
0
0
0
0
2
1
3
2
0
1
0
0
0
2
0
1
0
2
0
2
2
2
0
1
2
0
0
0
0
0
3
1
0
1
1
0
2
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
1
0
0
1
0
0
1
5
0
0
0
2
0
2
0
0
0
0
1
2
0
0
0
0
0
1
1
1
0
0
0
0
0
0
2
5
3
1
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
1
0
0
2
0
1
0
0
0
0
0
2
1
2
1
0
0
0
0
8
0
0
1
0
0
0
3
1
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
1
1
0
2
0
1
0
0
2
0
0
0
0
2
0
1
0
2
2
1
0
0
0
0
0
0
0
2
1
2
1
1
2
0
0
2
0
0
1
1
0
0
0
2
0
0
0
0
0
0
2
0
3
2
0
0
0
2
2
0
0
0
0
2
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
2
1
0
0
0
0
0
2
0
1
0
2
0
0
0
2
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
1
1
1
1
0
0
0
4
0
0
0
0
0
0
0
1
1
2
0
0
0
1
0
0
1
2
0
0
0
3
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
1
1
1
1
0
1
1
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
2
2
0
1
1
2
0
2
0
2
2
0
2
1
1
1
0
0
1
0
1
2
0
2
0
3
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
1
0
1
0
0
1
1
1
1
2
0
0
0
0
2
2
0
1
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
2
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
2
2
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
2
0
1
0
1
0
0
0
0
2
1
0
0
1
3
0
0
1
0
0
1
1
0
0
7
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
2
0
3
0
2
0
0
0
0
0
1
1
2
2
2
0
0
0
0
1
2
2
0
1
2
0
1
1
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
3
0
0
3
0
2
2
1
1
3
2
0
1
3
1
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
2
2
1
2
4
1
2
1
0
0
0
0
0
2
2
1
0
0
3
0
2
0
0
1
0
0
1
0
0
0
0
2
0
1
2
0
0
1
0
0
3
0
0
1
1
0
0
2
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
2
0
0
0
2
1
0
0
0
0
1
0
0
0
0
2
0
0
1
1
4
0
2
0
2
2
0
2
0
1
2
0
0
3
0
1
0
0
0
0
2
0
2
0
0
1
0
1
0
0
0
0
0
0
1
2
0
0
0
0
1
2
1
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
1
1
0
0
0
0
3
0
0
0
1
5
0
0
0
1
2
0
0
0
1
2
0
0
0
1
0
0
1
2
0
1
0
0
0
2
0
0
3
0
0
0
0
0
0
1
0
2
0
0
1
0
2
0
1
1
0
1
0
0
2
2
0
1
0
0
0
0
2
1
0
2
0
0
0
0
1
0
0
0
0
2
0
1
0
2
0
0
1
1
0
0
0
0
0
0
1
0
1
1
1
2
0
0
0
0
1
2
0
0
0
0
0
0
2
1
1
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
4
1
1
0
0
0
0
2
0
2
0
2
2
0
0
1
2
0
0
0
0
0
0
0
0
3
2
1
1
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
1
2
0
1
0
1
1
2
0
1
0
0
0
2
1
0
2
0
1
0
1
2
1
1
1
0
1
0
1
2
2
0
0
0
0
0
0
4
1
2
0
2
0
0
1
3
0
0
1
2
0
2
0
1
0
0
2
0
0
0
0
2
0
0
1
0
0
2
0
0
1
2
2
0
0
2
1
2
0
2
0
1
0
2
0
2
0
0
0
1
0
2
2
1
0
1
0
2
0
0
0
0
3
1
2
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
1
2
2
0
1
0
0
2
0
1
1
0
2
1
0
1
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
1
0
0
0
0
0
1
1
2
0
0
0
0
1
0
0
1
0
1
0
2
0
0
2
0
3
0
0
3
2
0
0
1
0
0
2
1
1
0
0
1
2
0
2
0
0
0
2
0
1
0
0
0
1
1
5
0
1
0
0
0
0
1
0
0
0
0
0
2
1
0
2
0
0
0
0
2
2
0
0
0
0
2
3
0
0
0
0
2
0
0
0
0
0
1
1
1
1
0
3
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
2
0
2
0
2
0
1
2
0
0
1
2
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
1
0
2
1
2
0
0
1
0
0
0
3
1
0
0
0
0
1
3
0
0
0
1
2
0
0
0
0
2
0
0
1
2
0
2
1
0
0
0
0
2
3
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
4
0
0
3
1
0
0
0
0
0
0
0
0
0
0
1
1
2
2
2
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
2
0
0
0
0
1
0
0
0
3
0
1
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
3
0
0
0
2
2
1
2
0
1
8
3
2
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
1
3
3
0
0
1
0
1
0
0
1
1
1
1
1
0
0
0
1
0
0
1
2
0
1
0
2
0
2
2
0
0
0
0
0
2
0
0
1
2
2
0
0
0
0
2
0
2
0
5
4
0
6
0
1
0
1
1
2
0
0
0
1
1
1
1
0
3
0
2
0
1
2
0
3
1
0
0
1
2
0
0
0
2
1
0
0
0
0
1
1
0
2
0
2
0
0
2
1
0
1
0
0
0
0
0
0
2
2
0
0
0
1
1
0
0
1
0
2
1
1
0
3
0
2
0
0
3
2
0
0
0
0
0
0
0
0
2
0
2
1
2
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
1
2
1
1
0
0
0
1
2
0
0
1
1
0
0
2
0
0
0
1
0
0
0
0
0
2
0
1
2
0
2
0
0
0
2
2
2
0
1
0
0
0
0
1
5
0
0
2
0
3
0
2
0
3
0
2
0
1
2
0
0
0
1
1
1
0
0
0
0
1
0
0
2
0
1
0
1
2
1
0
0
0
0
0
0
0
0
2
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
1
0
0
0
1
0
1
0
0
2
0
0
0
0
2
0
1
0
0
2
6
0
0
1
2
0
2
0
0
1
4
0
0
0
0
0
1
2
2
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
2
2
1
0
1
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
1
1
0
1
1
0
0
3
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
2
1
0
2
1
0
0
0
0
1
2
1
0
1
2
0
0
0
2
1
0
2
0
0
0
0
0
2
1
1
2
0
1
0
0
0
0
1
1
1
0
0
2
2
2
0
0
0
0
2
0
2
0
2
1
0
0
1
1
0
0
1
0
0
2
0
0
2
1
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
3
0
0
1
2
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
2
0
0
2
0
0
2
0
2
1
0
2
0
1
0
2
1
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
1
1
0
0
0
1
0
2
2
2
0
3
2
1
0
1
5
0
0
0
0
1
0
2
0
0
0
2
0
0
1
0
0
0
0
2
0
1
0
0
1
0
0
2
1
0
0
0
0
1
1
0
0
0
1
0
0
1
1
5
0
0
0
1
0
0
2
0
1
0
2
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
1
2
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
1
0
3
0
0
4
0
2
0
0
0
0
1
0
0
0
2
0
0
1
2
0
0
0
2
1
0
2
0
1
1
1
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
2
1
2
2
1
0
0
1
0
1
1
0
0
0
0
0
0
1
1
0
0
2
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
1
0
0
1
1
2
2
0
0
3
0
0
2
1
0
1
1
0
2
0
0
2
0
0
0
0
0
0
0
1
1
7
1
0
2
3
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
1
0
1
2
0
0
2
2
0
2
2
2
0
0
0
0
1
2
1
0
0
0
0
0
0
1
0
1
2
0
0
3
1
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
1
2
2
1
0
0
0
0
0
0
0
3
0
2
0
0
0
1
0
2
1
2
1
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
1
0
0
0
0
1
1
0
1
0
2
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
2
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
2
0
0
0
3
2
0
0
0
0
0
0
0
0
0
2
0
2
1
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
1
0
2
0
1
0
0
4
2
0
0
0
3
0
2
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
1
2
0
0
1
3
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
2
0
0
0
1
0
2
1
0
0
0
1
1
1
0
0
2
0
0
1
1
0
0
2
0
0
0
0
0
2
1
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
4
0
0
2
0
1
1
0
0
0
0
3
1
1
0
0
1
0
2
0
1
0
1
3
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
3
0
3
0
0
1
0
0
1
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
1
1
1
0
0
2
1
0
0
0
2
2
0
0
1
1
0
1
0
0
1
0
1
0
0
0
1
2
0
0
1
2
0
0
0
0
0
2
1
1
0
1
1
0
0
1
0
0
1
0
0
0
0
1
3
1
1
2
0
0
0
0
0
0
0
0
2
0
2
1
0
0
7
2
0
0
3
0
0
0
0
0
0
0
1
0
0
4
0
1
1
1
0
0
0
2
0
0
0
0
0
0
1
2
0
2
2
1
2
0
0
0
1
0
0
0
2
0
2
1
2
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
2
4
2
2
0
0
1
0
0
0
0
0
0
1
0
3
2
0
0
0
1
0
0
0
1
0
1
2
0
4
0
0
1
0
0
0
0
0
1
0
3
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
2
0
2
2
0
2
2
0
2
0
0
0
0
0
0
1
0
0
0
0
1
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
1
0
1
0
1
1
1
0
0
1
2
2
0
0
0
0
0
1
2
0
0
0
0
2
1
1
0
0
4
0
2
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
1
0
0
5
1
0
2
0
0
0
0
0
2
0
0
0
2
2
0
2
3
1
1
0
3
0
3
1
0
0
0
0
0
0
1
0
2
2
2
0
1
1
1
3
1
1
2
2
0
2
0
0
0
2
1
0
1
0
1
1
0
2
2
0
2
2
2
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
1
0
2
2
0
0
0
2
0
0
3
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
1
3
0
0
0
0
0
0
1
2
0
1
0
0
2
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
1
0
1
2
0
1
1
0
1
0
0
0
1
0
0
0
0
1
1
2
0
0
0
0
0
1
1
1
4
0
0
0
0
2
0
1
0
0
0
0
2
0
2
4
0
2
0
1
0
2
0
0
2
2
2
0
0
0
3
0
2
0
0
1
1
0
0
1
2
0
0
2
0
0
0
1
0
1
2
1
2
3
1
0
0
1
0
1
1
1
0
1
0
0
0
1
0
0
0
0
3
0
2
0
2
0
0
2
2
1
2
4
0
0
0
0
0
0
0
0
2
1
0
1
0
0
1
0
1
0
2
0
1
2
2
1
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
3
0
1
0
0
0
0
0
0
0
2
0
2
0
0
2
2
2
1
0
0
2
0
1
1
0
0
0
0
0
0
1
4
4
1
1
0
2
0
1
1
0
0
0
0
0
0
0
0
1
1
2
0
0
2
0
0
0
1
0
1
1
0
2
0
0
0
1
2
0
2
0
1
1
0
0
3
1
1
0
2
1
0
2
0
2
0
0
0
0
0
2
2
0
1
0
2
0
1
0
0
1
0
0
2
0
1
2
2
0
0
0
0
2
1
1
0
2
4
0
0
0
0
1
0
0
0
2
1
0
6
2
0
2
1
2
0
0
0
0
0
2
0
1
1
0
0
0
0
0
1
0
1
0
0
2
1
0
0
3
0
2
0
1
1
0
0
0
0
0
0
1
2
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
1
0
0
2
0
0
0
0
0
1
0
0
3
0
0
2
0
2
0
0
1
0
0
1
0
2
0
0
1
0
0
0
0
0
1
2
1
1
2
0
1
0
0
1
1
0
0
1
0
0
2
0
0
3
0
0
1
0
0
0
2
2
2
0
0
1
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
1
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
3
0
2
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
5
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
2
1
1
0
1
0
1
0
0
2
6
0
0
0
0
0
0
2
0
2
5
2
0
1
1
2
1
3
0
0
3
2
2
0
0
0
1
0
2
2
0
4
2
0
1
2
2
0
1
0
0
2
1
1
0
1
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
2
2
2
0
0
0
1
1
0
0
0
0
2
0
0
2
0
0
0
1
3
0
1
1
2
1
2
2
2
2
0
0
0
0
1
0
0
2
2
1
0
0
0
0
0
0
2
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
1
0
3
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
2
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
3
0
1
1
0
2
0
0
0
3
1
0
0
2
1
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
2
0
2
2
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
6
0
0
0
1
0
0
1
0
0
2
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
5
0
0
1
4
0
2
2
0
1
0
0
0
0
0
2
0
2
2
0
0
1
1
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
1
0
0
0
1
1
1
2
1
1
0
2
0
0
1
0
1
0
2
0
0
0
0
1
1
2
2
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
2
0
0
0
0
0
4
0
0
0
0
1
0
1
0
0
0
1
0
0
2
0
0
0
0
0
3
2
0
0
2
0
2
1
2
1
1
5
0
0
1
2
1
0
0
1
0
0
0
0
2
0
0
0
1
0
1
0
1
0
0
0
2
0
1
0
1
0
0
1
0
1
2
0
0
0
2
2
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
1
1
0
0
0
0
1
1
0
0
1
2
0
2
0
2
1
0
2
0
0
2
2
0
2
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
1
2
2
1
1
0
2
1
0
0
1
0
0
1
0
1
2
0
0
2
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
3
1
1
2
2
0
0
0
2
1
0
0
1
0
0
0
0
1
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
1
0
0
2
0
0
2
2
0
0
0
3
0
0
0
2
0
1
0
4
0
0
1
0
0
2
0
2
0
0
1
0
0
0
0
1
2
0
1
2
0
0
2
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
3
0
0
2
0
0
2
0
2
0
0
0
1
0
0
1
0
2
2
1
0
0
0
1
0
0
0
2
2
1
1
0
2
4
0
1
1
2
3
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
2
1
0
0
1
0
2
2
1
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
1
0
0
0
3
0
0
1
0
0
1
0
0
1
1
0
0
2
0
2
2
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
2
0
1
1
2
0
0
2
1
0
0
2
1
0
0
0
0
0
0
1
1
0
2
0
1
0
0
0
2
0
0
0
0
1
0
0
1
0
0
1
0
2
2
0
0
0
0
0
0
0
2
0
2
0
0
2
1
0
0
1
1
0
0
0
2
0
4
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
1
2
2
0
0
0
0
0
0
0
3
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
2
0
0
0
2
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
2
0
2
0
0
1
1
0
2
0
0
0
2
0
1
2
0
0
0
0
1
1
0
0
0
3
0
0
0
0
0
0
0
1
0
3
1
0
1
0
0
0
1
1
0
1
2
0
0
0
1
0
0
1
0
1
0
1
1
0
1
0
0
2
1
0
1
0
2
2
0
3
0
2
0
0
1
0
2
0
0
0
0
0
0
1
0
0
1
0
1
3
1
2
0
0
0
0
1
0
0
2
0
0
0
1
0
0
2
0
0
2
1
0
0
1
2
0
0
0
0
0
0
3
0
0
0
0
2
1
0
0
0
0
0
2
0
2
2
0
1
2
0
0
0
1
1
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
2
0
1
2
1
0
2
0
1
2
1
0
0
0
0
3
0
0
0
0
0
2
0
0
0
2
0
0
0
2
2
2
0
0
2
0
1
0
2
0
0
1
2
0
1
0
0
0
2
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
1
1
2
0
1
2
2
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
2
2
0
2
0
0
1
2
2
0
0
1
0
0
0
0
0
0
2
0
2
2
1
0
0
0
0
2
0
2
2
2
0
0
1
1
0
0
0
0
2
1
0
0
2
0
1
0
3
0
1
1
0
0
2
3
0
2
2
0
0
1
0
0
1
1
2
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
3
1
0
0
0
2
2
1
2
0
3
0
2
0
0
2
0
1
2
0
4
0
1
0
0
1
2
0
0
2
2
1
0
0
0
1
1
0
0
2
0
0
0
0
1
0
0
0
0
0
4
0
1
0
2
2
2
0
0
2
1
0
0
0
0
0
0
1
0
1
0
2
0
0
0
1
0
0
2
2
1
0
1
0
0
0
0
2
0
1
1
0
2
1
1
1
0
0
0
2
0
0
0
1
0
0
0
5
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
1
2
1
0
0
0
2
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
1
1
1
0
0
0
0
0
3
0
0
0
0
1
0
2
0
1
1
0
0
2
0
0
0
2
2
1
2
0
0
1
0
0
0
2
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
1
1
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
2
2
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
3
1
0
0
0
1
1
0
1
0
0
0
0
0
2
0
0
1
0
2
2
2
1
0
0
2
0
2
0
0
1
0
0
0
2
2
0
1
1
2
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
1
1
0
0
0
1
2
1
0
0
1
1
1
2
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
3
0
0
1
1
0
0
0
1
0
1
1
1
0
0
2
0
0
0
0
0
0
1
0
1
0
0
1
0
2
0
1
2
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
4
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
2
1
0
2
0
2
1
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
1
2
1
0
1
0
0
1
0
0
2
0
0
1
0
1
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
2
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
2
0
2
0
0
0
2
2
1
0
0
1
0
2
2
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
1
0
1
0
2
0
0
1
1
2
2
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
2
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
3
0
2
0
1
0
0
0
0
0
0
1
0
1
1
2
2
2
0
0
2
0
0
1
0
0
0
2
0
1
0
1
0
0
2
0
0
0
0
0
0
1
0
1
0
0
3
0
2
0
1
2
0
0
1
0
0
0
0
0
0
0
2
0
4
0
1
1
0
2
0
0
0
0
2
0
1
0
0
0
0
2
0
1
2
0
2
0
0
0
0
0
2
2
0
0
2
1
1
0
0
0
0
2
1
0
1
0
0
0
0
0
1
0
0
0
2
1
0
1
2
0
0
1
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
3
2
1
0
0
0
2
0
2
1
0
4
0
1
2
1
0
0
0
0
0
2
0
1
0
1
0
0
2
0
0
0
2
0
2
0
2
0
2
0
2
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
4
0
1
0
0
0
0
0
0
0
2
1
2
0
2
0
1
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
2
1
0
1
2
2
0
0
1
0
0
0
0
2
0
2
1
0
0
0
0
2
1
0
0
0
1
0
0
2
0
1
0
0
0
2
2
0
0
0
2
2
2
0
2
1
0
0
0
2
0
0
0
0
0
1
2
0
0
0
1
0
0
1
1
0
0
2
0
2
0
2
2
0
0
0
0
2
1
0
0
0
0
1
2
2
0
1
1
2
0
1
0
0
1
0
0
0
0
3
0
2
2
1
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
2
0
2
0
0
2
1
0
1
0
0
0
0
0
1
2
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
2
1
0
3
0
0
0
2
2
2
2
0
0
0
0
2
1
0
3
0
1
2
2
3
2
2
1
2
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
1
0
2
0
0
0
1
0
0
1
2
2
0
1
2
3
0
0
0
0
0
2
0
1
0
0
0
0
0
1
2
0
2
1
0
0
3
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
1
0
1
1
0
0
0
0
0
2
1
2
0
1
2
3
0
0
1
1
2
1
0
0
2
0
2
0
0
0
2
1
2
1
0
0
0
0
2
0
0
3
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
2
0
1
2
0
0
2
0
2
0
1
2
0
0
0
1
0
1
0
0
1
1
1
0
0
2
1
1
7
1
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
2
2
0
0
0
1
0
2
1
2
0
0
2
0
1
0
0
0
0
1
2
0
0
0
2
0
0
0
2
2
2
2
0
0
2
0
0
2
0
1
1
1
1
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
1
1
0
0
2
1
0
0
1
0
0
1
0
1
1
2
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
3
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
1
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
4
0
2
0
2
0
2
2
0
2
2
0
0
0
0
0
1
2
1
0
0
2
3
1
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
2
0
0
1
2
0
0
0
0
0
0
0
0
2
1
0
0
1
1
0
0
0
1
0
0
0
0
2
2
2
0
0
2
0
0
0
0
0
0
0
1
2
1
0
2
0
0
1
1
2
2
2
3
0
1
1
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
3
0
1
1
0
2
1
0
1
1
0
2
1
0
2
0
0
0
2
0
0
2
2
0
0
2
1
1
0
1
0
0
1
0
2
0
4
1
2
0
0
1
0
1
2
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
1
0
2
0
0
0
1
2
1
0
2
2
0
0
3
4
0
2
1
2
3
0
1
0
0
0
3
2
0
0
0
0
0
1
0
0
1
2
0
1
0
0
2
0
0
2
2
0
0
0
1
0
1
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
2
0
0
0
0
1
2
0
0
0
1
3
1
0
0
0
0
0
2
0
2
1
1
0
0
0
2
2
0
1
0
0
0
0
0
0
0
2
1
0
0
1
1
0
0
1
0
1
2
1
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
3
2
0
2
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
1
1
2
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
2
0
1
0
0
1
2
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
1
1
0
2
0
0
2
1
0
1
0
1
0
1
0
1
0
0
0
2
0
0
2
0
0
1
1
2
0
1
0
0
0
1
1
0
1
1
1
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
2
1
0
2
3
2
0
2
0
1
0
0
0
1
0
1
0
0
0
1
2
0
0
0
2
1
0
0
1
0
0
1
0
0
0
0
2
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
1
0
0
0
2
1
1
0
0
0
0
1
1
5
1
0
0
0
0
1
0
1
0
2
0
2
2
0
0
1
0
1
0
1
1
1
0
0
2
0
0
0
0
0
0
2
0
0
0
1
2
0
0
1
0
2
0
0
2
0
3
3
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
2
0
2
0
1
0
2
2
1
0
3
0
0
0
0
2
0
0
0
1
1
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
1
2
0
0
0
2
0
2
0
2
2
0
1
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
2
0
1
0
0
0
1
2
1
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
1
0
2
3
2
0
2
0
1
0
0
0
2
0
0
0
0
2
2
0
0
2
0
0
0
0
0
2
0
1
0
2
1
0
3
0
0
2
0
1
0
2
1
1
0
2
0
0
0
1
0
2
0
0
1
2
1
2
1
2
0
2
1
0
2
0
0
1
2
0
2
2
0
0
0
0
2
0
0
3
1
0
0
0
1
0
2
0
0
1
0
4
0
0
1
0
0
0
0
0
1
0
0
2
0
0
2
0
2
0
0
5
1
0
0
1
0
0
0
0
2
0
2
2
2
0
1
1
0
1
0
0
0
1
0
1
0
1
0
1
1
1
2
1
5
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
3
0
1
1
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
2
1
1
0
0
0
1
1
0
0
0
1
2
1
0
0
1
2
2
0
0
1
2
0
0
0
0
0
1
2
2
2
0
0
1
2
0
2
1
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
2
1
0
2
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
3
1
1
0
1
2
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
2
1
0
0
1
4
1
0
1
0
0
2
0
1
0
0
0
0
1
0
0
0
0
1
4
0
0
1
0
2
1
0
0
0
0
2
2
0
2
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
1
3
0
2
2
0
1
0
0
0
0
0
0
0
0
1
1
1
0
1
1
0
0
0
2
2
1
0
0
3
0
1
2
0
1
0
0
2
0
2
0
0
1
0
1
0
2
0
1
1
2
1
0
0
0
0
0
0
1
0
2
0
1
2
0
1
0
2
1
0
0
0
0
0
4
0
1
0
0
1
0
1
2
0
0
0
1
1
0
0
0
0
1
0
2
0
1
0
2
2
0
0
2
0
2
0
1
0
1
0
1
0
1
1
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
4
0
0
2
0
0
1
0
0
1
2
0
0
0
0
1
0
0
1
0
2
0
0
1
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
1
2
0
0
2
0
0
0
2
0
0
4
0
0
0
0
0
2
0
2
0
0
1
3
0
1
0
1
1
0
1
0
1
1
0
2
2
2
0
2
0
2
1
0
0
1
0
0
1
1
1
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
2
0
0
0
0
1
1
0
0
1
2
2
2
1
0
0
1
2
0
0
0
0
2
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
1
1
2
1
2
0
0
0
0
0
1
2
1
0
0
0
1
0
1
0
0
2
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
2
2
0
0
0
0
0
0
0
6
1
2
0
1
0
0
0
3
0
0
0
1
2
1
0
1
0
0
2
1
2
0
0
1
0
0
0
1
0
1
1
0
0
1
0
0
0
2
1
0
2
0
1
1
0
0
2
1
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
1
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
2
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
1
0
0
0
2
0
3
0
1
1
0
2
0
2
0
0
0
0
0
0
0
0
0
1
4
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
2
0
0
0
1
0
0
1
0
0
2
2
0
0
0
0
1
2
0
1
0
1
0
0
0
2
3
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
2
1
0
1
1
0
2
2
0
1
2
2
1
1
2
0
4
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
1
0
1
0
0
0
0
0
2
1
2
0
2
0
1
0
0
0
0
2
0
0
3
2
2
2
0
0
0
0
0
1
0
0
2
0
1
1
3
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
1
0
1
2
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
4
2
1
1
0
2
0
0
1
0
0
2
0
0
0
0
0
0
3
1
0
2
0
0
1
0
0
0
0
0
2
0
6
1
2
0
2
2
0
2
2
1
0
1
0
0
3
0
2
0
0
2
2
0
2
0
0
2
0
0
0
0
1
0
0
0
0
1
0
2
1
1
4
0
1
0
0
2
2
0
2
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
1
2
2
0
0
0
0
1
0
0
0
1
0
2
1
0
0
0
2
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
1
0
2
0
0
0
0
0
2
0
0
2
0
0
0
2
2
1
0
0
0
0
2
1
1
0
2
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
1
0
0
0
0
2
0
0
2
0
1
0
0
0
2
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
1
1
2
0
0
0
2
0
2
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
1
1
0
0
2
1
0
0
1
0
0
0
0
2
2
1
3
0
0
1
2
1
0
0
0
1
0
1
1
0
0
1
0
0
2
0
0
0
0
0
0
2
1
1
3
1
0
0
2
0
2
0
1
0
0
0
2
0
0
2
2
0
0
1
0
0
1
0
1
6
0
0
0
1
0
2
2
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
3
0
0
0
1
0
2
0
0
2
0
2
1
1
0
0
1
0
0
0
1
0
0
4
0
1
2
0
0
0
2
2
3
1
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
6
0
0
0
0
0
0
2
0
1
2
0
0
0
2
0
0
0
0
0
2
0
0
0
1
3
1
0
0
0
0
0
2
2
0
0
1
0
0
0
1
1
1
0
2
3
1
2
7
1
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
1
1
0
0
2
0
0
0
1
0
0
0
0
0
1
2
0
1
0
0
0
2
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
2
0
0
1
2
0
0
0
0
0
0
0
0
1
0
2
1
2
0
2
0
2
0
0
0
0
1
1
1
1
2
0
0
0
0
2
0
1
2
0
2
2
1
0
2
1
0
0
0
2
0
1
1
1
1
0
0
1
0
2
0
0
0
0
1
0
0
2
2
0
1
0
0
0
2
0
0
0
0
2
0
0
0
1
1
2
0
2
2
0
3
0
0
1
1
0
2
0
1
3
0
0
2
0
0
2
0
2
0
2
2
0
0
0
2
2
0
2
2
6
2
0
0
0
0
0
1
1
0
2
0
0
0
2
0
1
0
1
0
0
0
1
2
2
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
2
2
0
1
1
0
0
1
0
1
1
1
0
2
2
0
0
0
2
0
0
2
0
1
0
0
2
4
0
0
1
1
0
0
0
1
0
0
1
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
3
1
2
1
0
0
1
1
0
2
0
2
0
1
0
0
0
1
0
0
2
0
0
0
0
0
2
2
2
2
0
0
0
0
1
0
0
1
1
0
1
0
0
0
2
1
0
1
1
0
0
0
0
0
2
1
2
1
0
0
0
1
1
0
0
0
0
2
0
0
3
0
2
2
2
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
3
0
1
1
0
1
1
3
3
2
0
0
0
0
0
0
0
0
1
0
2
1
3
0
0
2
0
2
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
1
0
0
1
0
0
1
0
2
0
0
0
0
0
3
1
2
0
0
1
1
0
0
0
4
1
0
0
2
0
2
1
2
0
1
0
1
2
2
2
0
2
1
0
1
0
0
1
0
2
1
0
0
1
0
1
1
0
1
1
1
2
0
5
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
2
1
0
3
0
0
3
1
0
2
1
2
0
2
1
0
0
0
1
1
0
2
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
2
0
0
0
2
0
1
0
0
1
2
0
0
1
2
1
1
1
0
2
0
0
1
0
0
0
0
2
2
1
2
0
1
2
0
1
1
0
0
1
0
1
0
0
1
0
0
1
0
0
0
3
0
0
3
0
0
0
0
0
1
0
0
0
2
0
0
1
2
0
0
0
1
2
1
2
0
1
0
0
1
2
0
2
0
0
2
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
3
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
1
0
2
0
0
2
1
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
2
0
0
0
3
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
2
1
0
1
1
1
0
3
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
2
2
1
0
1
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
2
0
2
0
0
1
2
1
0
0
1
0
1
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
2
0
0
1
1
0
0
0
0
2
2
0
2
1
0
0
2
0
0
0
2
0
2
0
2
2
0
0
0
0
0
1
0
1
2
0
1
0
0
1
2
0
0
0
0
0
1
0
0
2
0
1
0
1
1
1
0
0
8
0
1
0
0
0
1
0
0
2
0
0
0
2
2
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
2
0
2
2
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
4
0
0
0
0
1
1
0
2
2
0
1
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
2
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
2
0
2
1
0
1
0
0
0
0
0
0
0
0
2
2
0
3
0
2
2
0
0
0
0
1
2
1
2
0
0
0
0
0
0
0
0
0
0
1
2
0
1
2
0
1
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
2
0
1
0
1
0
2
3
0
0
4
0
2
0
0
2
0
0
0
3
0
2
0
0
1
0
0
0
0
1
1
0
0
0
0
0
3
1
0
1
0
1
0
0
0
0
0
0
2
0
0
0
1
1
2
0
0
0
0
0
1
1
0
0
2
0
1
0
0
0
0
0
0
0
2
0
1
0
2
2
0
0
0
0
1
1
5
1
2
2
0
0
3
2
0
1
0
0
0
0
0
1
0
1
0
0
2
0
1
0
0
0
1
0
0
0
2
5
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
1
0
1
3
0
0
0
0
0
0
1
0
0
0
0
2
3
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
2
1
0
0
1
2
1
0
0
2
1
1
2
1
1
0
3
0
2
0
0
0
0
1
0
0
2
5
1
0
0
0
2
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
2
0
1
0
1
2
0
1
0
0
0
2
1
2
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
2
3
0
1
0
0
2
0
2
0
2
2
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
2
4
0
1
0
0
2
1
0
1
0
0
2
0
0
2
0
0
2
0
0
0
0
0
2
1
0
0
0
0
3
0
1
0
2
1
0
0
0
0
0
0
2
1
2
1
0
0
0
1
0
0
0
1
0
1
0
3
0
0
0
0
0
0
0
1
2
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
2
0
0
2
0
1
2
0
2
0
1
0
0
0
0
2
2
0
0
0
0
3
0
2
2
0
0
2
0
0
2
0
2
2
2
0
1
0
1
1
1
0
0
0
0
32
0
0
0
0
0
0
0
0
2
2
1
1
0
0
1
1
6
0
5
2
0
0
2
0
2
1
1
0
2
1
0
0
0
0
0
0
0
0
2
1
1
0
0
1
0
2
0
1
1
2
0
0
0
0
0
1
1
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
1
2
2
0
0
0
2
0
0
0
0
1
1
0
0
1
0
2
0
0
0
0
1
1
0
2
0
3
0
0
0
0
1
0
1
1
0
0
1
2
2
0
0
0
1
2
0
0
0
0
1
0
4
0
0
0
0
0
0
1
0
0
0
2
0
3
3
2
0
0
1
1
0
2
1
2
1
0
2
0
2
0
0
0
2
2
0
1
0
2
1
0
1
0
0
0
2
1
0
1
0
0
0
2
2
0
0
0
1
0
0
0
0
1
0
1
2
0
0
2
0
0
0
2
2
0
2
2
0
0
0
0
0
0
1
2
0
0
1
8
0
1
2
1
0
2
1
2
2
0
1
0
2
3
0
0
1
0
2
0
0
0
1
1
2
0
0
0
2
0
1
0
2
0
0
2
1
1
0
0
0
0
0
0
1
1
0
0
0
3
0
0
1
3
0
2
1
1
1
0
2
0
0
0
0
0
1
0
1
0
2
1
0
0
0
1
0
0
1
4
1
0
0
0
0
0
0
0
0
2
0
0
2
2
2
8
0
0
0
1
0
1
0
2
1
0
0
2
1
0
0
2
1
0
0
1
0
1
0
0
0
0
2
0
2
0
0
0
0
1
0
1
0
2
0
0
1
0
0
2
2
0
0
2
0
0
0
1
1
0
0
0
1
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
3
1
1
1
1
2
0
0
0
1
2
1
1
2
0
0
0
4
2
0
1
0
2
2
0
1
2
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
2
0
0
0
0
1
2
1
0
3
0
0
2
0
0
0
0
1
0
0
0
1
2
1
2
2
0
1
0
0
0
1
0
0
0
0
2
1
3
2
0
0
0
0
1
1
0
2
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
2
0
0
1
0
2
0
1
2
0
0
2
3
1
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
1
2
0
1
0
0
2
0
1
0
0
2
0
0
0
0
0
2
1
0
3
0
0
0
0
0
2
1
0
0
0
0
2
0
0
2
0
0
0
2
1
0
0
2
0
0
2
2
0
0
2
0
2
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
3
0
0
0
1
0
1
0
1
0
1
2
2
0
0
0
1
2
3
3
0
0
0
1
0
0
1
1
0
0
0
1
0
0
1
0
0
1
2
1
1
0
0
2
0
1
2
1
0
0
2
2
0
0
1
0
1
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
1
0
1
0
0
0
0
2
2
2
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
2
0
2
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
2
0
1
1
0
1
0
5
0
0
0
0
3
1
0
0
0
0
0
2
2
0
0
2
0
2
0
0
0
1
0
0
0
3
0
0
2
2
1
0
0
0
1
1
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
1
1
0
0
3
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
2
0
0
0
1
0
1
1
0
0
1
0
1
2
0
0
0
1
2
0
0
1
0
2
1
0
2
1
0
0
2
0
0
1
0
0
0
0
2
0
0
0
1
0
1
0
1
5
1
0
0
0
0
0
1
2
0
2
0
0
0
2
0
0
0
0
2
0
1
1
1
0
0
0
0
0
0
3
0
3
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
2
3
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
1
0
0
1
0
0
0
3
0
2
0
2
0
0
0
0
1
0
0
0
2
0
0
0
1
1
0
1
0
0
0
0
0
2
1
1
0
0
2
0
0
0
0
2
0
0
1
2
0
1
2
0
0
0
1
1
0
1
0
0
0
1
2
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
3
2
3
2
0
0
0
0
2
0
0
1
0
0
1
0
0
1
0
0
0
0
2
1
2
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
3
0
1
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
1
1
0
0
1
0
1
0
0
0
0
2
1
0
2
0
0
2
0
0
0
0
0
0
0
2
1
0
0
3
0
0
0
0
0
0
2
1
0
0
0
0
2
0
3
2
1
0
2
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
1
0
0
0
0
0
0
0
2
1
0
2
0
0
1
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
1
2
1
0
2
0
0
2
2
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
2
0
1
0
0
0
0
1
1
0
3
2
2
0
0
0
0
3
0
0
0
2
2
1
0
1
0
0
0
0
0
1
0
2
0
0
0
1
2
0
2
0
1
0
0
0
2
0
0
0
0
0
2
0
2
2
0
0
1
0
0
0
0
0
2
0
1
0
1
1
0
2
1
0
0
0
0
0
1
1
0
0
0
2
0
1
7
0
1
0
1
2
0
0
0
1
0
0
1
0
1
5
1
0
0
1
2
2
0
1
0
1
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
2
1
1
0
2
0
0
2
1
1
0
0
0
1
2
2
0
2
1
0
1
1
0
0
0
0
0
1
0
0
0
1
2
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
2
1
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
2
0
0
2
2
0
2
0
1
2
1
2
0
2
3
0
0
2
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
2
1
2
0
0
1
0
0
0
1
2
0
1
0
2
0
0
1
0
0
2
0
0
2
0
0
0
1
1
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
2
0
2
1
0
0
3
2
0
1
0
0
0
1
1
1
2
0
0
0
0
1
0
0
0
0
0
0
0
3
0
2
1
0
1
2
1
0
0
1
2
0
3
0
1
1
1
2
2
0
0
0
1
0
0
0
0
0
1
0
2
2
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
1
0
0
1
1
0
2
2
2
1
1
1
0
0
2
1
1
1
0
0
1
1
0
0
0
0
1
0
2
0
2
2
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
2
0
0
1
0
1
0
0
2
0
0
0
0
2
0
0
0
0
2
0
1
0
6
0
0
0
0
0
2
0
1
0
0
0
0
1
0
3
0
0
0
1
0
0
3
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
1
1
0
2
0
0
0
0
1
1
1
1
0
3
0
2
0
0
2
1
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
1
1
0
2
2
0
2
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
2
2
0
0
0
0
1
0
0
1
0
0
1
0
0
1
2
0
2
2
3
0
0
2
2
0
0
3
0
0
1
1
2
1
0
2
0
0
2
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
2
0
2
0
0
1
0
0
1
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
3
0
0
1
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
2
0
0
1
1
1
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
2
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
1
0
1
0
1
1
1
2
0
0
2
3
0
0
1
2
0
0
1
2
0
1
1
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
1
2
0
2
0
1
1
2
2
0
4
1
0
1
0
0
0
1
2
0
4
2
0
1
0
0
1
0
2
0
0
0
1
0
1
0
0
0
2
0
2
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
1
2
2
0
0
0
2
1
1
1
0
0
0
0
0
0
0
0
0
2
1
0
1
0
1
3
0
4
0
0
0
0
1
0
0
1
0
0
2
2
2
2
0
0
0
0
2
2
0
0
0
0
0
3
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
1
0
2
2
0
0
1
1
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
2
1
0
0
1
0
0
0
0
1
3
0
0
0
0
2
2
0
0
0
0
1
0
2
4
0
0
0
0
0
0
0
1
1
1
0
1
0
1
0
1
1
2
0
1
1
0
0
2
1
0
0
0
1
0
0
2
1
2
0
1
0
2
0
0
0
0
1
2
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
2
2
0
0
1
1
0
2
0
0
0
1
0
0
0
2
0
0
1
2
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
2
0
0
1
0
1
2
0
0
0
0
0
0
0
2
1
0
0
0
1
1
1
0
2
2
0
0
1
0
0
0
0
0
0
1
0
1
2
0
3
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
2
0
0
1
0
0
3
0
0
2
0
0
1
2
0
0
0
0
0
1
1
2
0
1
0
0
1
2
1
2
0
1
0
0
0
0
2
0
1
2
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
1
2
2
0
2
2
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
2
2
1
0
2
0
0
0
0
0
0
1
2
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
1
0
2
2
1
2
1
2
0
0
0
0
0
2
0
2
0
1
0
2
2
2
0
1
2
1
1
0
1
2
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
1
1
0
0
0
2
0
1
0
2
0
2
0
0
0
0
0
1
0
1
1
2
0
1
1
0
1
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
2
0
1
0
0
0
2
2
0
0
0
0
2
2
0
0
1
1
0
1
0
0
3
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
4
0
1
0
0
0
0
0
2
0
0
0
0
2
1
0
0
2
1
0
1
2
0
1
1
0
2
0
0
0
0
0
0
0
0
0
1
0
3
0
1
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
2
0
0
0
0
1
2
0
1
0
1
0
0
0
0
2
2
0
0
3
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
2
0
2
0
1
2
0
0
0
0
0
0
0
2
2
0
0
0
1
1
0
0
0
0
0
1
0
1
0
2
0
0
0
1
0
0
0
0
1
1
0
0
0
2
0
0
0
2
0
0
2
1
0
0
0
2
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
2
1
3
0
0
2
0
0
0
2
0
1
0
2
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
1
0
1
0
1
0
2
0
0
0
0
0
2
0
0
1
0
0
0
1
7
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
2
0
0
2
0
2
1
0
1
0
0
3
1
0
0
0
0
1
0
0
0
3
1
0
2
1
0
2
0
0
0
0
1
0
2
2
2
2
0
0
1
2
0
2
2
0
0
0
2
0
1
2
0
2
0
0
1
0
0
0
2
0
2
1
0
0
0
1
0
0
0
1
0
0
0
0
4
0
0
0
3
0
0
0
2
2
0
0
1
2
2
0
1
0
0
1
2
0
1
0
0
0
1
2
0
0
1
1
0
1
0
0
0
2
0
0
1
1
0
2
0
0
2
0
0
2
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
1
0
2
2
0
0
1
3
0
1
2
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
1
0
0
0
0
0
1
0
1
2
0
1
2
0
2
0
0
1
2
0
0
0
1
0
0
3
2
0
1
0
0
3
0
2
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
1
0
0
2
0
0
1
2
0
0
1
0
0
0
0
0
0
2
1
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
2
0
0
0
0
1
0
0
1
2
0
2
0
0
0
1
0
0
0
0
0
0
1
2
2
0
0
0
0
1
2
0
1
0
0
0
3
0
2
1
0
2
1
0
1
2
1
0
0
0
0
0
1
0
2
0
2
0
0
1
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
2
2
0
0
1
2
2
0
0
0
0
0
1
0
1
0
0
0
0
1
0
2
1
0
0
0
1
0
4
0
3
4
3
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
4
2
0
0
0
0
1
2
0
2
2
2
0
0
2
0
0
1
2
0
0
1
6
3
0
2
1
0
0
0
1
2
1
1
2
0
0
0
0
2
0
1
1
0
1
0
1
1
0
2
0
0
0
1
0
0
0
1
0
0
1
2
1
0
0
1
0
0
2
0
0
0
0
1
0
2
4
2
2
0
2
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
2
1
0
2
0
2
0
1
0
2
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
1
0
1
2
0
0
2
0
1
0
0
0
2
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
4
2
2
1
0
0
0
0
2
0
1
1
0
1
1
0
0
0
2
0
0
1
2
0
1
4
0
0
0
0
0
2
3
1
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
4
0
0
2
1
0
0
0
0
0
2
0
0
2
0
0
2
0
0
1
0
0
2
0
1
0
0
2
0
1
0
1
2
1
1
0
0
0
2
2
1
0
0
0
0
0
1
1
2
0
0
0
0
0
0
1
0
2
2
0
0
2
0
2
0
2
0
1
0
0
0
0
0
0
0
0
2
0
1
0
2
2
0
0
1
0
0
0
0
0
0
0
0
2
2
2
2
0
1
0
0
0
0
0
1
1
2
2
0
1
0
0
0
0
0
1
0
2
0
0
0
1
0
2
0
0
0
1
0
0
0
0
1
1
1
0
0
1
0
1
0
0
0
0
1
0
0
1
2
0
1
0
0
1
2
1
0
2
0
0
0
0
0
0
2
0
1
0
0
0
1
1
0
1
1
1
0
2
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
3
2
0
0
0
1
2
0
0
1
1
0
1
0
2
0
0
0
1
0
1
0
0
0
0
4
0
1
0
0
0
2
0
0
0
0
0
2
2
2
1
2
0
2
0
2
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
2
0
0
1
2
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
1
0
1
0
0
2
1
0
0
1
0
0
0
0
2
0
1
0
1
0
3
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
2
1
0
0
1
1
2
1
0
3
0
2
0
1
0
0
4
0
2
1
2
1
1
0
0
0
2
2
2
1
1
2
2
2
0
0
0
2
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
1
1
2
0
1
1
1
2
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
2
1
0
0
1
0
2
0
0
0
2
0
0
0
0
1
0
1
1
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
2
0
2
1
1
2
0
0
2
0
0
2
2
1
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
3
3
1
0
0
0
2
0
2
2
0
0
1
0
0
0
1
0
0
0
0
1
1
2
0
2
0
0
4
1
0
1
2
0
0
0
0
2
0
1
1
0
1
4
0
0
0
0
0
0
0
1
0
1
1
0
2
0
0
1
1
2
0
0
2
2
4
0
0
0
0
0
1
2
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
2
1
2
1
0
0
1
0
0
2
1
2
0
1
0
0
1
0
2
1
0
1
0
2
0
0
0
2
0
0
0
0
0
0
1
2
0
1
0
1
0
1
1
2
2
0
0
0
1
0
0
1
1
0
1
0
0
0
0
8
0
0
2
2
0
0
2
1
1
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
3
1
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
2
2
0
0
0
0
0
1
1
0
1
0
0
0
0
2
0
1
2
0
0
1
1
0
0
0
1
1
0
0
1
2
0
0
3
0
0
0
0
0
2
0
2
0
1
1
1
0
0
2
0
1
0
1
2
0
0
0
2
2
0
1
0
0
0
0
5
0
0
0
0
2
2
0
2
2
0
0
0
0
0
3
0
1
2
0
3
2
0
2
0
1
2
1
0
0
0
2
0
0
1
1
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
1
3
1
0
0
3
0
1
0
2
1
0
0
0
0
0
1
1
0
0
0
0
0
1
1
1
0
1
0
1
0
0
3
1
0
1
0
0
0
0
1
0
2
4
0
0
0
1
1
0
0
0
0
0
0
3
0
2
0
0
0
0
0
1
1
0
2
0
0
2
0
0
1
0
0
0
0
3
1
2
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
1
1
2
0
0
0
2
2
1
0
0
0
4
1
0
2
0
0
1
0
0
0
0
0
2
1
0
0
0
3
0
0
0
0
0
0
2
1
0
1
2
0
2
0
0
1
3
1
0
2
0
0
1
0
0
2
0
1
0
1
0
0
3
0
1
1
0
1
0
0
0
1
1
1
2
1
2
0
0
2
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
4
1
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
1
3
3
0
0
2
0
1
1
1
0
2
0
0
0
1
1
0
0
2
0
2
0
1
1
0
0
0
0
0
1
0
3
0
4
0
1
2
1
0
2
0
0
0
2
0
2
0
4
1
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
2
8
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
2
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
2
0
1
0
0
0
0
1
1
1
1
0
0
1
0
0
1
0
0
0
0
2
0
0
2
0
1
0
1
1
1
0
1
16
0
0
0
0
0
0
3
0
2
1
1
0
0
2
0
2
2
0
1
0
0
0
0
0
0
0
0
3
0
0
3
0
0
0
0
0
2
3
2
2
0
1
2
0
1
0
2
2
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
2
1
0
0
0
1
0
2
1
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
3
0
0
2
0
0
1
0
1
0
0
1
1
0
1
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
1
2
1
0
0
1
0
1
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
1
2
0
0
1
0
2
0
0
0
0
0
0
0
0
1
1
0
2
1
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
1
1
2
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
1
0
0
1
2
0
1
0
2
0
1
0
0
0
0
3
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
3
0
1
0
0
1
3
0
1
2
3
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
1
0
0
0
0
1
3
0
0
2
3
0
0
1
0
2
0
2
0
3
0
0
0
0
0
1
0
1
0
0
2
0
1
0
1
2
0
0
0
0
0
0
0
2
0
0
0
2
2
3
0
0
0
0
0
2
0
0
2
1
2
2
0
0
0
0
3
0
0
0
0
2
0
2
0
0
1
1
1
0
0
2
2
3
1
0
0
1
0
0
2
0
1
0
0
0
0
0
1
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
1
1
0
1
1
0
0
1
2
0
0
1
1
0
0
1
2
2
0
0
0
1
1
0
0
0
2
0
0
0
3
0
1
1
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
2
0
1
2
0
0
0
0
0
2
1
3
0
0
0
2
2
2
0
2
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
1
0
1
0
0
2
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
1
0
0
0
0
1
0
1
2
2
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
1
2
1
1
0
2
0
0
0
0
1
2
1
0
2
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
1
2
2
0
0
1
0
0
2
0
0
0
0
2
0
0
0
2
1
0
1
2
0
0
0
0
1
1
0
0
0
0
2
0
2
0
0
2
0
0
0
1
1
0
2
0
1
1
0
0
1
0
2
0
0
0
2
1
0
0
0
0
0
0
2
1
0
0
1
0
1
0
1
0
0
0
0
0
1
0
1
2
1
0
1
2
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
2
0
0
0
2
1
0
0
0
1
1
0
1
0
1
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
1
0
0
1
0
0
0
0
1
2
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
1
2
2
0
0
1
1
2
0
0
0
1
2
2
0
0
0
0
1
0
2
1
0
1
0
0
0
1
1
0
0
0
2
0
2
0
0
2
0
0
0
2
0
1
0
1
2
1
0
1
0
0
0
1
1
3
0
2
0
2
0
0
0
1
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
2
0
1
0
0
4
0
0
0
0
2
3
0
0
0
1
0
0
0
0
0
2
2
0
2
3
1
0
0
0
0
0
1
2
0
2
1
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
1
2
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
2
0
2
0
0
2
0
1
0
1
3
2
1
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
1
0
2
1
0
0
1
0
2
1
0
2
1
0
1
2
0
1
0
2
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
2
1
0
0
0
2
1
0
0
0
0
1
0
1
0
2
1
0
0
1
0
2
2
0
2
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
2
0
0
1
0
2
0
2
0
2
1
1
1
0
2
0
0
1
2
0
0
0
2
0
2
2
0
2
0
0
0
0
2
0
2
0
1
0
1
0
2
0
0
0
0
2
2
0
2
2
1
0
0
0
0
0
2
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
4
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
2
2
0
1
0
0
3
1
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
1
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
2
1
0
0
2
0
0
0
1
0
1
2
1
1
0
0
0
0
0
0
1
1
4
2
2
2
1
0
2
0
0
1
0
0
0
1
2
0
1
2
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
2
0
1
0
1
0
2
1
0
2
0
1
0
0
0
0
1
0
1
0
2
1
1
0
0
2
0
0
1
2
0
1
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
1
0
0
0
0
2
1
0
0
1
0
0
0
0
1
2
0
0
0
0
0
2
2
0
0
0
0
2
2
0
0
0
0
0
0
2
0
1
0
0
0
0
2
2
1
0
3
3
1
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
1
1
0
2
0
0
0
0
1
1
0
1
0
0
0
0
2
0
0
0
0
2
2
0
0
0
1
0
2
2
0
1
0
0
0
2
0
0
0
2
0
1
0
0
2
0
1
0
0
1
0
0
2
0
0
1
2
2
0
0
1
1
1
0
0
2
0
11
0
0
2
1
0
0
1
0
0
0
0
0
0
4
2
2
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
1
1
2
3
1
1
0
0
0
0
1
0
0
2
0
0
1
0
0
0
3
0
2
1
0
2
0
1
0
4
0
0
2
7
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
2
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
1
0
0
1
0
0
1
0
1
1
1
0
0
1
0
0
0
2
2
0
0
1
1
0
0
2
0
0
0
0
0
1
2
0
0
0
1
0
2
2
2
0
0
3
0
0
0
0
0
0
1
0
0
0
1
2
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
1
0
1
2
2
2
0
2
0
0
0
0
2
0
0
0
0
1
2
3
0
0
0
1
2
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
2
0
2
0
0
1
1
0
0
1
0
2
0
0
1
0
0
0
0
2
0
0
1
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
2
1
0
0
2
1
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
2
0
0
0
0
1
1
0
0
0
1
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
1
1
0
0
0
0
3
0
0
1
2
2
3
0
2
0
0
0
0
3
2
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
1
0
1
0
2
2
0
0
1
1
0
2
2
0
0
0
0
0
1
1
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
2
3
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
2
1
0
1
0
0
1
0
0
0
0
0
1
0
0
2
0
0
1
0
1
2
1
0
0
0
0
0
3
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
2
0
1
0
2
0
1
2
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
2
1
0
0
1
1
2
3
1
0
0
0
0
0
1
0
0
4
2
0
0
0
0
2
0
7
0
0
2
0
1
0
0
1
1
1
0
2
1
0
0
1
0
1
0
0
5
1
1
0
0
1
2
1
0
0
0
1
0
0
2
0
2
1
1
0
0
0
0
0
0
1
2
0
0
1
0
1
2
0
0
0
0
1
0
0
1
2
0
0
0
1
0
2
0
1
0
0
0
0
0
2
1
0
0
0
0
1
1
2
0
0
0
0
0
2
0
2
0
0
0
2
2
1
0
0
0
0
0
2
1
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
1
0
0
2
1
0
1
0
0
0
0
1
0
0
0
0
2
2
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
2
0
0
1
2
1
0
2
0
0
0
0
1
1
1
0
1
3
1
1
0
1
0
1
0
1
0
0
3
0
0
0
0
0
1
1
0
0
0
1
0
0
4
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
2
0
0
5
2
0
2
0
0
0
0
1
0
0
0
0
2
0
0
1
0
1
0
1
0
0
0
0
0
0
1
2
1
0
0
3
3
0
1
0
0
2
0
1
0
0
1
1
0
0
0
2
0
0
3
1
2
1
0
0
0
0
0
1
0
0
0
2
1
2
1
0
0
0
1
0
0
0
2
1
0
2
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
1
0
1
0
1
1
0
0
2
0
1
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
1
0
0
1
0
0
0
2
0
1
0
0
0
0
2
3
0
0
1
2
2
1
3
0
0
0
0
2
0
1
0
0
2
0
0
0
1
2
0
0
0
2
0
8
0
0
0
0
0
2
0
2
3
3
1
0
0
1
0
0
2
0
0
0
0
0
2
2
0
0
1
0
3
0
2
0
0
0
0
2
2
0
0
0
1
0
1
0
0
1
2
2
3
0
3
0
2
0
0
1
0
1
0
0
0
2
2
0
0
0
0
0
2
2
0
0
0
0
12
0
0
0
0
0
0
0
2
1
0
0
0
1
1
0
0
1
0
0
0
0
2
0
0
0
1
2
4
1
1
0
0
1
2
0
1
0
2
0
1
0
0
2
0
0
0
0
0
1
0
0
2
0
3
0
0
0
2
0
0
0
1
0
0
0
0
2
1
0
0
2
1
0
0
0
0
1
0
2
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
2
0
0
1
0
1
1
0
0
2
1
2
0
0
0
2
0
0
0
1
2
1
0
1
1
3
0
0
2
2
2
0
2
1
0
0
0
1
1
0
0
0
2
0
1
2
0
1
0
0
0
0
0
1
0
0
1
1
1
2
2
2
0
1
1
0
0
2
0
0
1
0
2
1
0
2
0
1
0
2
0
2
1
0
0
0
2
0
0
0
1
1
0
1
1
0
0
2
2
3
0
0
0
0
0
2
1
0
0
0
2
0
1
0
0
0
0
1
0
2
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
2
1
0
1
0
3
2
1
0
0
2
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
2
2
1
1
0
1
3
0
0
0
1
0
0
0
0
1
1
2
2
4
0
2
2
1
2
0
0
2
0
0
0
0
4
0
1
0
2
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
1
0
0
0
2
0
2
0
0
0
1
0
1
1
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
1
1
0
1
0
0
1
1
1
1
0
1
2
0
2
0
0
1
0
0
0
1
0
0
0
2
1
2
2
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
1
1
0
2
0
0
1
0
0
0
0
0
3
2
1
0
0
0
0
0
0
3
1
0
2
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
2
1
0
0
1
2
1
0
3
0
0
0
0
1
1
0
0
0
1
0
1
1
2
2
0
0
2
0
0
0
0
2
0
2
2
2
0
2
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
2
1
0
0
0
2
1
0
0
2
0
1
0
0
0
1
0
6
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
1
0
0
2
0
2
0
0
0
0
0
1
0
0
0
1
1
1
1
0
0
2
0
0
0
0
1
0
0
0
0
2
1
1
0
2
0
1
1
0
0
1
0
1
2
1
0
0
0
0
1
0
0
2
0
2
0
1
1
2
0
1
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
1
0
0
1
5
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
1
0
1
1
1
5
0
2
0
0
0
1
1
0
0
0
3
0
2
2
2
1
0
0
1
0
0
0
0
2
0
2
2
0
2
3
1
0
2
1
0
0
2
0
0
0
0
0
1
0
0
5
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
2
1
2
0
0
0
1
0
0
0
0
1
3
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
2
0
1
2
0
2
2
0
0
0
0
1
0
2
0
2
0
0
2
2
1
0
0
0
0
0
2
0
0
1
1
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
2
0
1
1
0
0
0
0
0
0
2
1
0
0
2
1
2
2
0
2
4
0
0
0
0
0
0
0
1
0
3
0
1
0
1
2
0
0
1
0
0
0
1
0
1
0
0
2
2
1
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
3
1
0
0
2
1
0
0
0
0
0
0
0
0
3
2
0
0
0
1
0
2
0
0
0
0
0
3
0
0
0
2
0
1
1
0
1
1
0
2
0
0
1
1
0
1
1
1
0
0
0
1
2
0
0
0
2
0
1
0
1
1
2
0
0
1
0
1
1
0
0
1
0
2
0
0
2
2
0
0
0
0
0
1
2
4
1
3
0
1
0
2
0
0
2
1
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
1
1
2
0
0
1
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
2
0
0
0
2
2
2
0
0
0
2
0
0
3
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
2
0
0
2
0
1
0
0
0
0
0
6
0
0
0
0
2
0
0
0
0
2
0
0
1
1
0
2
1
0
0
1
0
0
2
0
2
2
0
1
0
0
0
0
0
0
0
1
0
1
0
2
0
2
0
0
1
1
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
2
0
0
2
1
0
0
0
2
0
0
0
0
0
0
4
0
2
0
2
0
0
2
0
0
1
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
1
0
0
2
1
1
0
0
0
3
1
1
0
0
1
2
2
1
1
2
0
0
0
0
0
3
1
1
3
2
1
0
0
2
2
1
0
1
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
2
0
1
0
0
0
0
2
0
0
0
0
0
1
1
0
0
1
2
0
2
0
3
0
1
2
0
3
0
0
0
1
1
0
2
1
2
0
0
0
0
0
1
0
2
3
3
0
2
0
0
1
0
2
1
0
0
0
1
2
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
1
0
2
0
2
1
2
0
0
1
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
3
0
1
0
0
1
2
0
2
1
0
1
1
0
1
0
0
1
0
1
0
0
1
0
1
0
0
3
1
0
3
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
1
0
2
2
0
0
2
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
2
2
0
0
0
2
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
2
0
0
0
0
0
3
0
0
2
0
0
0
0
0
1
0
1
1
0
0
0
0
3
2
0
0
0
0
1
1
0
2
1
0
2
0
0
1
1
3
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
1
1
0
0
2
0
0
0
0
0
1
0
1
0
0
0
1
0
3
2
2
2
2
0
0
2
0
0
1
0
0
1
0
0
0
3
0
0
1
0
2
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
2
0
0
1
0
0
2
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
2
0
1
0
1
0
0
0
0
1
0
1
0
0
0
4
0
0
0
0
1
0
0
2
1
0
0
2
2
1
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
2
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
2
1
1
1
0
3
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
1
2
1
2
0
2
3
1
1
0
0
1
0
0
1
0
0
0
0
1
1
0
1
0
1
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
1
2
0
2
0
0
0
2
0
0
1
0
0
0
0
0
1
0
1
0
0
1
3
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
1
1
2
0
0
2
0
0
1
0
2
0
0
0
0
2
0
0
0
3
0
1
0
0
0
1
0
0
0
0
0
0
1
0
2
1
0
1
2
0
0
0
2
1
1
0
2
0
0
0
1
0
1
0
1
0
4
0
0
2
0
1
0
0
0
2
2
0
0
1
0
0
0
0
2
0
0
0
0
0
3
0
0
2
0
0
0
0
3
0
1
2
0
1
1
0
0
0
0
0
1
1
0
2
0
0
0
1
0
2
0
0
2
1
0
0
1
0
2
1
0
1
2
0
0
0
0
0
0
2
0
2
2
0
0
1
0
0
0
2
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
1
2
0
0
1
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
2
1
0
0
1
0
1
0
0
2
0
0
0
2
2
0
2
2
0
1
1
0
0
0
0
0
0
0
1
0
2
1
2
2
0
1
0
0
1
0
0
0
3
1
0
0
1
0
0
0
0
2
0
0
0
2
0
2
2
2
0
0
1
1
0
0
0
0
3
1
2
0
0
0
0
2
0
0
2
2
0
0
2
0
2
0
0
2
0
0
1
1
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
2
1
0
0
0
1
1
0
1
1
1
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
2
1
0
1
0
1
0
0
0
1
0
0
0
2
2
2
0
0
2
1
0
0
0
0
1
1
1
0
0
0
1
0
1
0
0
0
0
0
2
2
1
0
0
0
2
0
0
2
0
0
1
0
0
0
1
1
0
0
1
0
1
0
0
1
1
0
1
2
0
0
3
0
3
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
2
2
3
0
0
0
1
2
0
0
1
0
1
0
0
0
1
0
1
0
0
0
1
0
1
1
2
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
2
1
0
2
1
0
1
0
0
0
1
2
1
0
0
0
1
0
0
1
0
0
0
1
0
2
1
2
1
1
1
2
1
0
1
3
0
0
0
2
0
0
1
0
1
1
6
0
1
0
0
2
0
0
0
2
0
1
0
2
0
1
2
0
2
0
1
0
0
0
0
1
0
0
1
0
2
1
1
0
3
0
0
0
0
0
2
1
1
1
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
1
1
2
0
6
0
0
2
2
1
0
0
0
0
2
1
2
3
0
2
0
0
2
0
2
0
0
0
2
1
2
0
0
0
0
0
1
0
0
0
2
0
2
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
1
0
1
0
0
2
0
0
0
0
0
2
0
2
1
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
2
0
1
0
0
2
1
0
1
0
1
1
2
0
0
1
2
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
2
2
0
0
0
0
4
2
2
0
2
1
2
0
2
1
0
2
2
0
0
0
0
0
0
0
0
4
0
0
1
2
0
2
0
0
1
0
0
0
0
0
0
0
0
1
1
2
2
2
0
0
0
0
0
2
2
0
0
2
2
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
2
0
0
0
0
0
2
0
1
2
1
0
1
0
0
0
1
0
2
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
3
0
0
0
1
0
1
0
2
0
0
2
0
0
0
1
0
0
0
0
2
1
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
2
0
0
2
0
1
2
2
2
0
0
0
0
2
0
0
0
0
1
1
0
0
1
2
2
0
0
1
0
0
0
1
2
2
0
0
0
0
1
1
0
0
1
0
1
1
2
2
1
1
3
1
0
0
0
0
0
0
0
2
0
2
2
0
1
2
1
0
2
1
0
0
0
0
4
2
2
0
0
0
0
1
2
0
1
0
0
0
0
0
0
2
2
1
0
1
0
3
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
1
0
2
0
0
1
0
0
0
0
0
2
3
1
0
1
0
0
0
0
0
0
3
0
0
2
3
1
0
0
0
0
1
0
4
0
1
0
0
1
2
0
2
2
2
2
0
0
0
0
0
0
0
0
1
2
0
2
0
2
0
0
1
0
2
1
0
0
0
1
0
0
2
3
2
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
2
1
1
0
0
1
1
0
1
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
2
0
0
0
0
0
2
1
2
0
0
0
2
0
0
0
1
1
2
0
1
1
2
0
0
1
0
0
0
1
0
0
0
0
2
0
1
0
0
0
1
0
4
2
0
1
2
0
0
1
0
1
0
0
0
1
0
2
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
2
1
0
0
0
0
2
2
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
2
1
1
1
0
0
1
2
2
0
0
2
0
1
2
1
2
0
0
0
0
0
0
0
0
0
1
0
1
1
2
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
2
2
0
0
2
0
0
3
2
0
1
0
1
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
2
2
0
1
0
0
0
4
0
1
0
0
3
0
2
2
1
0
0
0
0
0
0
1
0
0
2
0
1
0
0
1
0
0
0
2
2
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
2
2
1
0
0
0
0
2
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
1
0
0
2
1
1
1
0
1
0
0
2
1
0
0
0
0
0
0
0
2
2
0
2
0
0
0
2
0
2
0
0
2
2
0
1
0
0
2
0
0
0
2
0
0
6
2
2
0
2
0
1
0
0
1
0
0
0
0
1
0
1
2
0
0
2
1
2
0
0
2
0
0
0
0
0
2
2
1
1
1
0
0
0
0
0
1
0
0
1
0
0
1
0
2
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
2
1
1
0
0
1
0
0
0
0
2
0
1
0
2
2
0
0
0
0
0
2
2
1
0
0
0
1
0
0
1
3
2
0
1
2
0
0
3
0
2
1
0
2
1
0
0
0
0
0
2
0
1
1
1
1
0
0
0
0
0
1
1
0
0
0
2
0
0
0
1
0
0
2
0
1
1
1
1
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
2
0
2
1
0
0
1
2
0
2
0
1
2
0
0
1
0
1
0
0
0
2
2
0
1
0
0
0
1
0
2
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
3
0
1
0
2
0
0
2
0
0
0
2
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
1
1
0
0
1
0
0
0
0
2
0
1
0
0
1
1
0
0
1
1
0
2
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
2
0
0
1
0
1
0
0
1
1
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
3
0
2
0
0
2
0
0
0
0
0
1
0
0
2
2
2
0
2
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
2
2
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
3
2
0
0
2
0
0
0
1
0
0
2
0
1
2
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
1
0
0
0
0
2
0
0
3
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
2
0
0
2
3
0
0
0
0
2
2
0
0
0
1
0
0
1
2
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
2
0
2
0
0
0
0
1
0
0
1
0
1
0
0
1
0
2
0
0
0
0
2
2
0
1
0
2
0
2
0
1
0
0
1
0
0
1
2
0
2
0
0
3
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
2
1
2
2
2
2
0
0
0
1
1
1
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
1
3
0
0
4
0
0
0
0
1
0
0
3
0
0
3
2
0
1
2
1
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
1
2
1
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
2
2
0
0
2
0
0
1
1
2
1
1
2
2
2
0
0
0
0
1
0
0
0
0
2
0
2
2
2
0
0
0
0
0
1
1
2
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
1
0
1
1
2
1
0
0
1
2
0
0
0
0
0
1
1
1
2
0
0
0
2
0
0
2
0
0
0
0
2
2
1
0
0
0
1
0
0
1
0
2
2
2
0
0
0
2
0
0
0
0
1
1
0
0
1
0
0
0
1
3
3
0
0
2
2
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
2
1
0
1
2
0
0
1
0
2
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
1
0
1
1
0
2
0
0
1
0
0
0
0
0
0
0
2
0
1
0
2
1
2
0
1
0
0
0
0
0
0
0
0
3
0
2
1
0
0
0
2
0
1
1
1
2
0
0
1
1
0
0
1
0
0
3
1
0
0
9
0
0
2
2
0
0
2
0
2
2
0
1
0
0
0
0
0
1
0
3
0
0
0
1
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
2
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
2
0
0
0
1
0
0
2
2
0
2
1
2
1
0
1
0
0
0
0
1
0
3
0
0
0
2
0
2
0
0
0
0
0
0
2
0
2
0
0
2
0
3
0
0
0
0
2
1
1
0
0
2
3
1
0
0
2
1
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
2
2
0
3
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
1
0
1
1
0
0
0
0
0
0
1
1
3
0
0
0
0
1
0
2
0
0
0
3
2
0
0
2
0
1
2
0
2
0
0
0
0
7
1
1
1
0
0
0
0
1
0
0
1
0
0
2
0
2
0
1
0
0
0
0
0
2
2
0
1
0
0
0
1
0
0
0
2
0
0
2
1
1
0
0
0
3
0
2
0
2
2
0
2
2
1
2
0
1
0
2
0
0
0
0
0
2
1
0
0
2
1
0
0
0
3
0
0
0
0
0
0
0
2
1
0
1
1
0
2
0
0
0
1
1
0
0
1
0
0
0
1
0
0
1
2
0
2
1
2
0
0
1
0
0
2
0
2
0
0
2
0
2
0
2
0
0
0
0
0
0
1
1
0
1
0
1
3
0
0
0
0
1
1
2
0
0
0
2
0
0
1
0
0
0
1
2
2
0
2
0
0
0
0
2
2
0
0
2
1
1
0
0
2
0
0
0
0
0
1
2
0
1
2
0
0
0
0
0
1
0
0
0
2
0
0
0
1
2
2
2
0
1
1
1
1
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
5
0
0
0
0
0
0
0
2
0
0
1
1
1
2
2
0
0
0
1
0
0
0
0
0
0
0
1
0
2
2
0
0
2
0
1
3
0
0
1
2
3
0
1
0
0
1
0
3
0
1
2
1
1
0
1
1
3
0
3
0
0
0
0
2
2
2
0
1
3
0
1
0
0
0
0
0
3
0
1
0
0
0
1
0
0
0
2
1
1
0
3
0
0
0
1
0
2
2
2
0
0
0
0
2
1
1
2
0
2
0
0
0
2
0
2
1
2
2
2
1
2
0
1
0
3
0
0
0
7
0
0
1
2
0
0
0
0
0
1
2
1
1
0
0
2
1
0
1
0
0
1
1
0
4
0
2
1
0
0
0
0
2
2
1
0
0
2
0
0
0
2
0
0
0
0
1
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
2
2
2
0
0
0
1
0
0
2
0
1
0
2
0
1
0
1
0
0
2
2
0
2
2
2
0
2
0
2
2
1
0
1
2
0
2
1
1
0
0
0
0
1
1
0
0
0
1
0
1
0
2
0
0
1
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
1
2
0
1
0
0
1
2
0
2
0
0
0
0
0
0
2
1
1
2
2
0
1
0
1
2
0
2
0
0
0
2
1
1
0
0
1
0
1
0
1
0
0
0
0
0
1
1
1
0
0
2
0
1
0
2
0
0
0
0
0
0
0
2
0
1
2
0
0
1
0
0
0
0
0
0
1
2
1
0
0
1
0
2
0
1
0
1
2
1
0
3
2
0
2
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
1
1
0
2
0
2
0
2
2
0
0
0
2
0
2
0
1
0
2
1
0
0
0
0
0
2
2
1
0
0
0
0
0
0
1
2
2
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
1
0
1
4
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
2
0
1
0
1
1
0
2
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
2
0
0
1
0
2
1
1
1
1
2
0
0
2
0
0
1
0
0
3
0
2
2
0
0
1
2
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
4
1
1
1
2
3
2
2
2
1
0
0
1
1
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
4
1
1
2
0
0
0
0
2
1
0
2
0
0
0
1
0
0
0
1
2
0
2
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
3
0
1
0
1
0
0
0
0
0
1
0
1
2
0
0
1
0
2
3
2
1
0
0
2
0
2
2
2
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
2
1
0
0
0
2
0
0
2
2
2
1
2
1
2
1
4
0
1
1
0
0
0
2
2
0
0
0
0
2
0
0
0
1
1
0
0
2
0
1
0
0
0
4
0
0
2
0
0
0
0
1
0
0
2
0
2
0
1
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
2
1
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
2
2
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
2
1
0
0
0
0
0
0
2
2
1
0
0
1
0
1
0
0
0
1
1
1
0
3
1
0
0
2
1
0
2
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
2
0
0
2
0
1
1
0
1
2
0
0
2
0
0
0
0
2
0
1
0
1
1
1
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
2
0
2
2
0
0
0
0
0
1
1
1
2
0
0
0
2
0
0
0
0
0
0
2
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
1
2
1
1
0
0
0
1
0
0
2
0
1
2
0
1
0
2
0
2
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
2
0
2
0
1
1
0
0
0
1
2
2
2
0
0
0
0
1
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
1
2
1
0
2
0
1
2
0
0
0
0
1
2
1
0
0
1
0
1
2
0
0
0
0
1
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
1
0
2
0
0
2
1
2
1
1
1
0
0
2
0
1
1
0
1
2
0
0
0
0
0
1
0
0
0
0
5
0
0
0
2
0
1
0
0
1
0
0
0
2
1
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
2
0
0
1
0
0
1
1
1
2
0
1
0
1
0
0
0
0
1
0
1
0
1
0
1
2
1
2
1
0
4
0
0
0
0
4
0
1
0
1
0
2
0
2
2
0
0
0
0
2
0
0
0
1
1
0
0
0
0
2
1
0
0
0
3
1
2
1
0
0
1
2
0
0
0
0
0
1
2
0
2
0
0
0
0
3
0
1
0
2
0
3
0
0
0
0
0
0
7
0
0
0
0
0
0
0
2
1
0
2
0
0
0
2
1
0
0
0
0
2
1
0
1
0
0
0
2
2
2
0
0
0
0
1
0
0
2
0
0
2
0
0
2
1
0
0
0
0
0
0
2
0
1
2
1
0
1
1
0
0
2
1
2
2
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
3
0
1
1
0
0
0
1
2
3
0
0
0
0
2
1
2
0
1
3
3
2
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
2
0
2
0
2
0
1
1
0
1
0
0
0
0
2
0
0
0
3
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
2
1
0
0
0
1
1
10
0
0
1
2
0
0
0
1
0
0
1
0
1
0
3
0
0
0
2
2
2
0
0
1
1
2
1
0
0
0
0
4
0
0
2
0
0
1
2
0
1
0
1
0
2
2
1
2
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
2
2
0
0
1
0
2
0
1
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
1
0
2
0
1
0
0
0
1
2
0
0
0
0
1
0
0
0
2
1
0
1
0
0
0
0
2
0
0
2
0
0
0
3
5
0
0
0
1
0
0
0
3
0
0
2
0
2
0
0
0
2
0
0
2
0
0
1
7
0
0
0
0
0
0
0
3
0
2
1
0
0
0
0
0
2
0
0
0
0
0
1
1
0
2
1
1
0
0
2
2
0
0
0
1
3
0
0
2
1
0
1
0
2
0
2
0
0
0
0
0
0
1
0
1
0
0
0
3
2
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
2
0
1
2
2
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
2
1
1
0
1
0
2
0
0
0
0
2
0
1
0
0
2
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
3
0
2
0
0
0
0
0
1
2
1
0
0
0
0
2
0
0
1
2
0
3
0
0
0
2
0
1
0
2
0
0
2
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
1
0
4
2
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
2
0
0
2
0
1
2
1
0
1
1
2
1
0
0
0
0
0
2
1
0
0
3
2
0
0
2
0
0
0
0
0
1
1
1
0
0
1
0
1
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
1
1
1
0
1
0
0
0
2
1
0
1
0
0
0
1
0
0
2
1
0
2
2
0
4
1
0
1
0
1
0
0
0
3
0
2
0
0
0
1
0
0
0
3
0
0
2
2
1
0
2
0
0
0
2
2
1
1
0
1
0
0
1
0
0
4
0
0
1
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
2
0
0
0
1
0
1
0
0
0
0
1
0
0
0
2
1
2
0
0
0
4
0
0
0
0
0
1
0
1
0
1
1
0
2
0
1
1
0
2
0
2
0
2
2
0
1
0
1
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
1
1
2
0
2
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
1
0
0
2
0
0
1
1
0
0
1
0
1
0
0
0
0
2
0
1
0
0
1
0
2
0
0
0
0
0
0
2
0
3
2
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
1
0
2
2
1
0
0
0
2
2
0
0
2
1
0
0
0
1
0
1
2
2
2
0
0
0
0
0
2
0
1
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
2
0
0
2
0
0
1
0
2
1
0
0
0
0
1
0
0
2
0
2
0
3
0
1
0
0
4
0
0
0
2
0
2
1
0
0
1
0
2
0
0
1
0
0
2
2
0
0
0
0
0
2
0
2
0
0
1
0
2
0
0
0
0
0
0
2
2
0
1
2
1
0
0
2
2
0
2
0
1
0
0
1
1
0
0
0
2
2
0
0
1
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
1
0
0
0
1
0
0
1
2
0
2
0
2
0
2
0
1
1
0
1
0
1
3
3
0
3
0
2
0
2
0
0
0
0
1
0
1
0
0
0
2
1
0
1
1
0
0
1
1
1
0
0
2
0
0
0
4
0
0
2
0
2
1
2
0
1
0
2
0
0
1
0
0
2
0
2
2
0
1
0
5
1
0
2
0
0
0
0
0
0
2
1
0
0
0
1
1
0
0
1
0
2
2
0
0
0
0
0
2
2
0
1
0
0
1
2
0
0
2
2
1
0
2
3
1
1
0
0
0
2
0
2
2
0
2
0
1
0
0
2
0
0
1
0
1
1
0
0
0
0
0
2
2
0
1
2
0
1
0
3
1
0
0
2
0
0
0
1
0
0
0
0
0
3
1
1
1
2
2
0
0
1
1
0
1
1
1
0
0
0
0
0
0
1
2
0
0
1
0
0
2
2
0
1
0
0
2
0
0
1
2
0
1
0
2
0
0
0
1
0
0
0
0
0
0
1
2
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
1
2
2
1
1
2
0
1
0
1
2
0
0
0
0
1
0
0
0
2
0
2
1
1
1
0
2
0
0
1
0
0
0
2
0
0
1
2
0
3
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
1
0
5
0
2
2
0
2
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
2
0
0
1
1
0
0
0
2
2
0
0
2
4
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
3
0
0
0
0
0
1
0
1
2
2
0
0
1
0
1
0
2
1
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
2
2
1
1
0
2
0
1
0
2
0
2
1
2
2
1
0
0
0
2
0
2
0
0
0
0
0
0
1
2
0
0
0
0
1
2
2
0
0
4
0
2
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
2
1
0
2
0
0
3
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
1
0
2
0
0
0
0
1
0
0
0
0
5
0
0
0
0
3
1
0
1
2
2
2
1
0
2
0
0
2
1
0
0
0
2
0
0
0
2
0
0
1
2
1
0
0
1
0
0
2
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
2
3
2
0
0
2
0
1
0
0
0
2
2
2
2
0
0
2
0
0
2
0
0
0
0
0
0
1
2
1
0
0
0
0
0
3
2
0
0
0
0
0
2
0
1
0
0
1
0
2
0
3
1
2
0
0
0
1
1
0
0
1
1
0
0
1
0
0
1
1
1
1
1
0
2
0
0
0
2
1
1
0
0
0
1
0
2
2
0
0
2
0
1
0
0
0
1
0
0
0
0
0
1
2
0
2
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
1
2
0
0
2
0
0
2
0
0
1
0
0
0
2
0
0
1
0
0
1
0
0
0
0
2
2
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
1
0
2
0
2
0
0
0
0
1
0
0
2
1
2
0
0
0
0
1
1
0
0
0
2
1
0
0
2
0
0
0
0
1
0
0
0
1
0
1
1
2
0
0
0
0
0
0
0
0
2
2
2
1
0
0
1
0
0
0
0
2
6
0
1
1
3
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
2
0
2
1
1
1
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
2
2
2
0
0
1
0
0
2
0
2
0
1
0
2
2
2
0
0
1
0
0
0
2
2
2
0
0
0
0
0
0
0
2
2
2
0
0
2
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
2
1
1
0
1
1
0
0
0
0
2
0
2
2
1
0
0
2
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
2
0
0
1
0
1
0
2
2
0
2
1
1
0
3
0
0
2
0
2
0
0
1
0
2
1
0
0
0
2
2
0
0
0
0
2
1
1
0
2
0
0
2
0
0
2
0
2
0
1
1
2
0
1
3
0
1
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
1
2
0
0
2
3
0
1
1
0
0
1
0
0
4
0
0
2
0
0
0
1
1
2
0
0
2
2
1
1
0
3
0
0
0
0
0
0
2
1
1
0
1
1
2
1
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
2
0
0
1
4
0
0
1
0
2
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
2
1
0
1
0
2
0
1
0
0
1
1
0
0
0
0
2
0
2
0
0
0
0
0
2
0
1
0
0
0
0
2
2
0
0
2
0
0
2
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
3
0
1
0
0
1
0
2
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
1
0
1
2
0
1
0
2
2
0
0
2
0
0
0
0
0
0
0
2
2
1
0
0
0
0
1
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
2
1
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
2
0
1
0
2
2
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
1
1
0
1
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
2
1
0
0
0
1
0
0
2
4
0
0
2
2
0
0
1
0
2
2
0
0
0
2
0
0
2
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
1
2
0
0
1
0
0
1
1
0
0
1
0
0
0
1
0
5
0
0
2
1
2
0
0
0
1
0
1
0
1
3
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
2
1
0
0
0
1
1
0
2
2
3
0
3
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
3
0
0
0
2
0
1
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
2
0
0
1
0
0
0
0
0
2
0
1
0
2
0
0
0
2
1
0
0
2
0
2
2
0
0
2
2
0
1
0
1
2
0
1
0
0
0
4
0
3
1
0
1
0
1
2
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
1
0
0
2
1
0
1
0
2
0
0
0
0
2
0
1
0
0
2
0
1
1
0
1
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
1
0
0
0
0
4
0
0
0
0
2
0
0
0
0
1
1
1
1
0
0
0
1
0
1
1
1
1
2
2
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
2
0
0
0
0
2
2
1
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
1
0
1
0
2
0
0
0
0
2
0
1
1
0
0
2
0
1
0
0
1
1
1
2
0
0
0
0
0
0
2
0
1
0
0
2
0
0
3
2
0
0
2
0
0
2
0
2
1
2
2
2
1
0
0
0
0
1
2
0
0
0
0
2
0
0
0
1
0
2
2
0
0
0
0
2
0
1
2
0
2
1
0
0
0
1
2
0
0
2
0
0
1
0
2
2
0
0
0
0
3
1
0
0
2
2
2
1
0
0
0
0
0
0
0
0
0
2
1
0
2
0
2
1
0
2
0
1
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
1
1
0
2
0
2
2
2
0
0
0
2
0
0
1
1
0
1
1
1
0
0
0
0
0
1
0
1
1
1
0
2
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
1
0
1
0
3
0
1
0
0
1
1
1
0
0
1
0
2
0
0
0
1
2
0
0
1
2
0
0
0
0
1
0
0
0
0
2
0
0
1
0
2
1
0
1
0
4
0
2
1
0
0
2
0
0
0
0
0
0
0
1
1
0
0
1
2
1
0
1
0
0
1
0
2
0
0
1
2
0
2
0
0
1
2
1
0
1
0
0
2
0
0
0
2
0
2
0
0
1
0
0
0
0
1
0
0
0
0
5
0
0
0
0
0
1
0
0
0
0
10
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
1
0
0
6
0
4
0
1
1
7
0
1
0
2
1
0
1
1
0
2
0
1
0
2
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
3
0
0
2
0
0
1
0
2
3
0
0
0
1
0
2
1
0
0
0
1
1
2
1
0
0
0
0
2
1
0
0
1
0
0
2
1
0
0
0
2
1
1
0
0
0
0
0
0
1
0
2
2
2
2
1
1
0
0
1
0
1
1
0
0
0
0
0
0
2
0
1
3
1
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
3
2
1
0
0
2
1
0
2
0
2
0
0
2
0
0
0
0
1
2
0
0
0
0
2
0
0
2
0
0
0
2
0
2
2
0
0
1
2
2
0
0
0
2
0
0
0
0
1
3
1
1
1
1
0
1
1
2
0
0
1
0
0
1
0
0
1
0
0
1
1
0
0
0
0
2
0
1
2
1
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
2
0
1
0
2
2
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
1
0
1
2
2
0
3
0
0
1
2
2
0
0
2
2
0
0
1
0
2
1
0
0
0
0
2
0
0
0
0
1
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
0
1
1
0
5
0
2
0
0
0
0
3
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
3
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
2
1
1
1
0
0
1
0
0
2
2
0
1
0
2
0
0
0
0
0
1
0
6
0
1
0
0
1
1
1
0
0
0
0
0
0
2
0
0
2
1
0
2
0
2
2
3
0
3
0
0
1
0
2
1
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
3
0
2
2
2
0
1
2
2
2
0
0
2
0
3
0
1
0
1
1
1
2
1
0
0
2
0
0
0
0
0
0
2
2
0
2
2
5
2
0
2
2
1
0
1
0
1
0
3
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
4
0
0
2
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
1
0
0
2
0
0
2
0
0
0
1
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
1
1
1
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
1
1
0
0
0
0
1
0
0
1
0
2
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
2
1
2
0
0
0
0
0
0
1
1
0
2
1
0
0
0
2
0
2
0
2
0
0
2
0
0
0
0
1
0
3
0
0
0
0
0
0
0
2
2
0
0
0
6
1
1
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
1
0
1
2
0
0
0
0
1
0
0
0
1
0
0
0
0
1
2
0
2
3
0
0
1
1
0
0
0
0
1
0
0
2
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
1
1
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
2
1
1
0
0
1
2
0
0
0
2
0
1
1
0
0
2
0
0
0
0
0
0
1
2
0
2
1
0
0
0
0
2
0
2
0
0
2
0
2
1
2
0
0
1
0
0
1
0
2
1
0
0
1
0
0
0
0
2
0
0
0
0
1
3
0
1
1
0
0
0
0
0
1
0
0
0
0
2
1
1
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
1
0
0
1
1
0
0
2
0
0
0
0
0
2
0
0
1
0
2
2
0
3
2
1
0
0
0
2
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
2
0
0
0
2
0
4
1
2
0
0
0
1
0
0
0
0
2
0
0
0
1
0
1
1
0
0
0
12
0
1
0
0
0
1
2
0
1
0
0
0
0
0
0
1
2
0
1
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
1
0
2
1
0
0
1
3
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
2
2
0
1
0
2
0
0
0
0
2
2
4
0
2
0
0
0
0
0
1
1
0
1
1
2
0
0
0
3
2
0
0
1
0
0
0
0
3
2
0
0
0
0
0
0
4
0
1
0
3
0
0
1
0
1
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
1
1
0
0
0
0
0
2
0
1
1
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
2
0
0
0
0
0
2
0
0
1
0
0
1
1
1
0
0
0
2
0
2
0
2
0
1
1
3
0
0
0
0
1
1
0
0
1
0
0
2
1
0
0
0
0
0
2
0
3
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
1
1
0
0
2
1
0
1
0
1
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
2
2
0
1
1
0
0
0
1
0
2
0
2
0
0
0
0
1
2
0
2
0
0
0
1
3
0
0
2
0
2
0
1
0
0
1
0
2
0
0
2
3
0
1
2
0
1
2
1
0
0
0
0
0
1
0
0
0
0
0
2
1
0
1
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
2
1
0
0
2
2
1
1
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
2
0
2
1
2
1
0
2
0
2
0
0
2
0
0
1
0
3
0
0
0
0
0
0
0
0
0
3
0
1
2
0
1
0
3
0
0
0
0
0
1
0
0
0
1
2
2
0
0
1
0
0
0
2
1
1
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
2
1
1
0
2
2
0
0
0
1
0
0
0
2
0
1
0
0
0
0
2
0
2
2
0
1
0
0
0
1
0
1
0
0
0
0
0
0
2
2
1
0
3
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
1
0
1
3
1
1
1
0
0
2
1
2
2
0
0
0
0
1
1
0
1
1
1
0
1
0
0
0
2
0
0
2
0
1
3
1
1
0
0
0
0
0
1
0
1
1
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
2
2
0
1
0
0
2
0
0
0
1
0
0
0
6
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
1
0
0
1
2
1
0
0
1
1
0
1
0
0
0
0
3
0
0
1
0
1
1
0
0
0
0
0
0
2
0
1
2
0
1
0
0
1
0
2
1
0
0
0
0
3
0
0
0
0
2
0
0
2
0
1
0
0
0
0
2
0
0
0
1
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
1
2
1
0
1
0
0
2
1
1
0
0
0
1
0
1
0
1
0
1
2
0
0
1
0
2
0
2
0
2
0
0
1
0
0
0
0
0
0
0
2
0
1
2
0
0
0
2
0
2
1
2
0
2
0
4
0
0
0
0
2
2
0
2
0
0
0
0
2
1
0
0
2
0
3
0
1
0
0
2
3
0
0
0
1
0
0
0
0
0
0
1
2
0
1
2
1
2
0
0
0
0
4
0
0
2
2
2
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
1
0
0
2
0
1
2
0
1
1
1
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
2
1
1
2
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
2
0
2
0
1
0
2
0
0
0
2
1
0
2
0
0
2
0
0
3
1
0
1
0
1
0
2
0
2
0
0
0
0
1
0
2
2
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
1
2
0
2
3
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
2
2
3
0
1
1
1
2
2
0
1
2
2
0
0
0
0
3
0
0
0
0
2
0
0
1
2
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
2
1
0
0
0
1
1
0
1
1
0
1
0
0
2
0
0
2
0
0
0
2
0
0
0
0
2
0
2
0
0
2
0
0
0
0
1
0
1
1
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
2
2
0
0
2
0
1
1
1
3
0
0
0
0
2
0
2
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
1
1
0
0
0
0
0
2
2
1
0
3
2
1
2
0
0
0
1
1
2
2
0
0
0
1
0
0
1
0
0
0
1
2
1
0
1
0
0
0
0
2
2
2
2
3
2
0
0
0
1
0
2
0
0
0
1
0
0
1
2
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
1
0
1
0
2
1
0
2
2
1
0
0
1
0
0
1
2
0
2
2
0
0
0
0
0
1
0
2
2
0
1
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
3
2
0
2
0
0
0
0
0
1
0
0
2
0
3
1
0
2
0
1
0
0
0
0
1
0
1
0
1
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
1
0
2
2
1
0
0
0
0
0
0
0
1
0
0
0
0
1
2
1
1
0
0
0
2
0
2
0
0
0
0
0
1
0
2
0
0
0
1
1
0
2
1
0
0
0
0
0
0
2
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
2
0
5
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
2
3
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
5
0
0
0
0
1
0
2
0
2
0
0
0
1
1
2
0
0
0
0
2
2
0
0
1
4
0
0
1
0
0
0
2
0
0
2
2
0
1
1
1
0
0
0
0
3
0
2
2
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
2
0
1
2
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
2
0
2
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
2
1
0
1
3
4
0
0
0
2
0
0
0
1
2
3
0
0
0
2
2
0
0
0
0
1
0
0
1
0
0
1
1
0
0
2
1
0
2
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
2
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
2
0
0
1
2
1
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
3
0
0
1
0
3
2
0
0
2
0
0
0
2
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
2
2
0
3
0
0
0
1
2
2
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
1
0
1
0
2
0
0
2
0
0
2
0
1
0
1
0
2
1
1
0
0
0
0
0
2
4
0
1
1
0
0
0
3
0
0
0
1
2
0
0
2
1
1
0
0
0
0
1
1
0
1
0
0
2
2
3
0
0
0
0
0
0
4
0
0
0
1
1
0
2
1
0
1
4
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
1
2
0
0
0
0
2
0
0
0
1
1
2
2
2
1
2
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
1
0
0
0
0
3
2
0
0
2
1
0
1
0
0
2
0
0
0
1
0
1
0
2
1
2
2
0
0
0
0
3
0
1
0
0
1
0
2
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
2
0
0
1
1
1
0
0
2
0
0
0
0
0
0
1
0
2
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
2
0
0
2
1
0
0
2
0
2
0
0
2
0
1
0
2
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
2
2
1
1
1
0
2
0
1
2
0
1
2
1
3
0
2
1
0
1
1
2
0
0
0
2
2
2
1
0
2
0
2
0
1
0
0
0
2
1
0
0
0
2
0
0
2
1
0
2
0
0
1
0
0
0
2
1
1
0
0
0
0
0
2
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
2
0
1
0
0
0
2
2
2
1
1
0
2
0
0
3
0
0
2
0
0
1
0
4
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
2
0
0
0
0
0
0
2
0
1
0
2
1
0
2
2
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
1
0
1
0
0
2
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
2
1
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
1
2
1
0
0
0
0
0
1
0
1
2
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
2
0
0
0
0
0
0
1
1
3
1
0
0
0
0
2
0
0
0
0
2
0
0
2
0
1
0
0
0
1
1
2
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
1
1
0
0
2
0
0
1
0
3
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
2
2
0
0
0
0
0
2
1
2
0
1
1
1
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
2
1
0
2
0
3
0
1
0
0
0
0
0
0
1
0
0
1
2
0
0
0
1
2
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
2
1
2
0
1
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
1
2
2
0
0
0
2
2
0
0
0
2
1
0
0
2
0
0
2
1
1
0
0
2
0
0
0
0
1
0
0
0
1
0
1
2
0
0
0
0
0
0
1
0
1
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
2
0
2
1
0
2
0
1
0
1
2
0
0
1
1
0
0
2
0
1
0
0
1
0
0
0
2
1
1
0
0
1
0
0
3
0
0
2
0
0
0
0
0
0
3
1
1
0
1
0
0
0
0
0
1
0
1
1
0
1
1
1
1
0
0
0
1
0
2
2
0
0
1
2
1
0
0
0
1
2
0
0
0
0
3
0
1
0
0
0
0
2
0
0
0
0
1
0
1
0
0
2
0
0
2
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
2
0
2
2
0
2
0
2
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
1
2
5
1
0
0
1
2
1
0
2
1
0
1
0
0
0
0
2
1
1
2
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
1
2
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
2
1
1
0
0
1
1
0
0
0
0
0
0
2
1
2
0
2
1
1
0
0
0
1
2
0
0
0
2
0
2
0
1
1
0
2
1
2
2
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
2
0
0
0
2
1
0
1
0
0
0
1
2
0
0
0
0
0
0
1
2
2
2
0
0
0
0
1
0
0
2
2
0
2
2
0
0
0
2
0
1
0
1
0
1
0
0
0
0
2
2
0
1
0
0
1
0
2
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
1
1
2
0
0
0
1
0
0
1
0
0
0
1
2
0
0
0
0
2
0
1
0
5
1
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
2
1
3
0
0
0
0
0
2
0
2
0
0
0
0
2
4
0
0
1
0
0
1
0
2
0
2
0
2
0
0
1
0
0
0
0
0
2
1
0
2
1
2
0
0
2
1
0
2
0
0
0
0
0
0
0
1
4
0
1
2
0
0
0
2
0
1
0
0
2
0
0
0
0
0
2
0
2
0
2
0
2
0
2
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
1
1
0
2
0
0
0
0
1
0
1
3
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
1
0
2
0
0
1
0
0
0
2
2
0
0
0
1
0
1
0
2
2
0
0
0
2
1
0
2
1
0
2
1
1
0
0
0
0
0
0
0
2
1
0
0
2
2
0
7
2
0
0
5
1
0
0
0
0
1
0
1
2
0
0
0
0
2
0
4
2
0
0
1
0
0
0
0
0
2
1
2
1
1
0
1
0
1
2
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
1
1
0
0
1
0
2
0
0
0
2
1
0
0
2
2
2
2
1
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
3
0
1
0
0
1
0
0
0
0
0
1
1
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
2
0
2
0
2
0
0
3
0
0
0
1
0
4
0
1
0
1
0
0
0
0
1
0
0
2
1
3
2
0
1
2
5
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
2
2
0
0
1
0
1
1
0
0
2
0
2
1
0
1
0
0
0
1
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
1
2
0
0
0
2
2
3
0
0
0
2
2
0
0
0
0
0
0
1
0
2
0
2
2
0
1
0
0
0
1
0
0
2
0
0
2
1
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
2
2
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
1
2
2
2
0
0
0
0
0
0
0
1
1
0
2
1
1
0
0
0
2
1
0
3
0
1
0
0
0
1
1
0
1
0
0
1
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
1
1
0
2
0
1
2
1
2
0
2
0
2
0
1
0
1
1
0
0
1
0
0
2
0
4
0
0
1
2
0
0
1
0
1
0
0
1
2
2
2
0
2
1
0
1
1
2
0
2
2
2
3
1
0
1
0
0
1
1
0
0
0
2
0
1
3
0
3
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
2
1
0
2
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
1
0
0
0
0
0
1
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
1
0
0
0
2
3
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
1
0
2
1
0
0
1
0
3
0
0
0
0
1
1
0
2
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
1
2
0
0
0
0
0
1
0
0
0
0
5
0
0
1
2
0
0
0
0
2
2
2
0
0
1
0
1
0
0
2
1
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
1
0
0
2
0
1
2
0
1
2
0
0
0
0
2
0
2
2
0
0
1
0
0
0
2
0
2
0
0
0
0
2
2
1
1
0
0
0
2
0
0
0
2
2
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
1
3
2
0
1
2
0
0
0
2
2
0
0
1
0
0
2
0
1
0
0
0
2
0
0
2
0
2
0
3
0
2
0
1
0
2
1
0
0
0
0
0
2
0
2
0
0
4
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
1
1
1
0
4
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
2
0
0
2
0
0
0
1
0
0
0
1
0
0
1
1
0
0
1
0
2
1
0
0
1
0
0
0
0
1
2
0
1
1
1
0
1
2
0
2
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
2
2
0
1
0
2
1
0
2
0
0
0
0
0
0
0
1
1
0
0
0
2
2
2
1
0
1
2
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
1
0
0
0
2
0
0
0
0
0
0
1
1
0
0
2
3
0
0
0
1
0
2
1
0
1
1
0
0
0
0
2
0
2
0
1
0
0
2
1
0
0
0
0
2
0
1
2
0
1
0
0
2
0
0
1
1
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
2
0
1
0
0
2
0
0
0
3
0
0
0
0
0
1
0
2
2
0
1
1
2
2
2
0
0
2
0
1
4
2
0
0
2
0
0
0
0
0
1
0
2
2
0
0
1
1
0
2
0
0
0
0
0
0
1
0
2
0
1
1
0
1
0
0
1
0
2
0
3
1
1
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
1
0
0
0
0
2
0
4
2
2
1
0
0
0
0
0
3
0
2
1
0
0
0
1
0
0
1
2
0
0
1
1
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
1
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
1
1
0
0
1
2
0
0
1
0
2
2
0
0
0
2
1
3
0
1
2
0
0
2
1
0
1
1
0
0
0
0
2
0
0
2
0
3
1
0
0
1
0
1
0
1
0
0
0
0
0
1
1
1
0
0
0
1
2
0
0
0
1
1
0
0
1
0
0
0
0
1
1
2
0
1
0
1
0
1
1
1
0
0
2
1
1
0
0
2
2
0
0
0
0
0
0
1
0
2
0
1
0
2
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
3
0
1
2
0
1
0
0
1
2
0
0
2
2
1
2
2
1
1
0
0
0
2
2
0
1
0
0
0
2
0
0
1
0
0
0
2
1
1
0
0
0
0
1
0
0
1
2
3
2
1
2
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
3
2
1
1
0
1
0
0
2
0
0
3
0
2
0
0
2
5
0
0
0
0
0
0
3
0
1
0
0
1
2
0
0
0
0
1
1
0
0
1
0
0
0
2
0
0
2
1
0
0
0
0
0
1
0
1
1
0
0
1
2
0
0
0
0
0
1
1
2
1
0
2
1
2
0
0
0
0
0
0
4
0
0
2
0
0
1
0
1
0
0
2
1
0
0
0
2
2
0
0
0
0
0
0
1
0
2
1
0
2
0
0
2
0
1
0
0
2
0
2
2
1
0
0
2
1
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
1
1
0
1
0
1
0
2
0
0
2
0
0
1
0
0
0
0
0
2
2
2
2
0
0
2
2
1
0
0
0
0
2
1
0
1
3
0
1
1
2
1
0
2
1
2
0
0
5
0
0
0
0
0
0
1
0
0
1
0
0
3
0
1
0
0
0
0
2
0
1
1
1
2
1
1
0
0
2
1
0
0
0
1
0
1
0
3
3
2
1
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
1
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
2
3
0
0
1
0
1
0
0
0
0
1
1
0
0
0
4
0
0
2
0
0
0
2
0
0
1
1
2
2
0
0
0
0
0
0
0
3
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
1
0
0
1
0
0
0
0
1
2
0
0
1
0
0
0
1
1
2
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
2
1
0
0
1
1
0
0
0
0
2
2
0
0
3
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
1
0
2
2
0
0
0
2
0
1
1
1
0
1
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
1
0
0
0
2
1
0
3
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
1
0
0
0
0
0
0
1
0
0
2
0
2
0
1
0
0
2
0
0
2
2
0
2
0
1
1
0
2
0
1
2
2
0
0
2
1
0
1
0
0
3
0
1
0
2
1
1
1
0
0
0
3
2
0
2
2
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
2
1
0
0
0
1
0
0
0
1
0
2
1
0
0
0
0
0
1
1
0
2
2
0
0
1
2
0
0
0
0
0
1
0
0
0
1
0
1
2
0
0
2
0
0
0
2
0
0
1
0
1
0
1
0
1
0
0
0
0
2
1
0
3
0
0
0
0
2
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
1
1
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
2
1
0
0
0
0
0
3
0
0
0
0
1
0
0
0
1
2
0
0
2
0
0
0
2
0
2
2
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
2
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
2
0
0
1
0
0
2
0
0
0
2
1
1
1
2
0
0
1
2
0
0
0
0
1
0
1
2
0
0
0
0
3
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
2
1
4
0
0
0
0
0
0
1
0
0
1
0
1
0
0
2
0
0
3
0
2
3
2
1
1
2
0
0
0
0
0
1
0
0
0
1
0
2
3
1
0
0
1
1
0
3
1
0
1
0
0
0
0
0
2
0
4
0
0
0
0
1
0
0
2
0
0
2
0
2
2
0
1
0
2
2
0
2
0
2
2
0
0
0
1
0
0
0
1
0
1
0
0
0
2
0
2
2
2
0
0
0
2
2
0
0
0
0
1
2
1
1
0
0
2
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
2
1
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
1
1
0
2
1
0
0
0
3
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
2
1
0
0
2
0
2
0
1
1
2
2
1
3
2
0
0
0
2
0
0
0
0
2
2
0
1
0
0
1
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
1
2
0
0
1
0
0
2
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
1
0
1
0
0
3
0
0
0
0
1
0
1
0
0
2
2
2
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
2
0
0
1
0
0
6
1
0
1
1
0
2
0
0
0
0
1
0
0
0
2
0
1
1
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
2
2
0
0
0
1
2
0
1
1
2
1
1
0
0
2
0
0
0
0
1
0
0
2
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
3
1
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
3
0
1
0
0
0
0
0
1
0
2
0
1
0
2
0
0
2
0
0
0
2
0
2
2
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
1
1
0
2
0
0
5
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
2
1
2
0
0
3
0
0
0
0
2
2
2
0
2
0
0
0
1
0
2
0
0
0
0
0
0
2
2
1
0
0
1
0
0
0
0
0
1
1
0
0
0
2
2
0
0
0
0
0
2
0
0
0
2
0
1
0
0
1
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
1
2
0
0
0
0
1
0
2
2
0
0
0
2
2
0
0
0
0
0
2
0
2
1
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
3
0
0
1
0
0
1
1
2
2
0
1
0
0
0
0
0
1
0
0
0
4
0
0
0
0
2
2
0
0
0
0
1
1
0
0
0
0
2
0
1
0
0
0
2
1
1
0
2
0
0
6
0
0
1
1
0
0
0
2
0
4
0
2
0
1
0
0
0
0
2
1
0
0
0
2
2
0
0
2
0
0
0
0
0
0
1
2
1
1
0
0
1
0
0
0
2
1
0
0
2
1
1
0
0
1
1
0
0
0
0
2
0
1
1
2
0
0
1
0
1
0
0
0
0
0
1
0
0
0
2
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
2
1
0
1
0
0
0
0
0
0
2
0
0
2
3
0
2
1
2
3
2
3
0
0
0
2
2
0
0
0
0
1
1
0
6
3
0
0
0
0
0
2
0
0
2
1
2
0
0
1
0
2
0
0
0
0
1
0
0
1
0
0
0
0
2
2
4
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
1
1
0
1
0
3
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
1
0
2
0
0
1
0
0
2
0
1
0
1
0
0
13
2
0
1
0
0
2
3
2
0
2
1
0
1
2
0
0
0
2
3
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
2
1
1
1
0
0
0
0
1
0
0
1
0
1
1
1
1
0
1
2
0
1
0
0
2
0
0
0
0
0
0
2
0
0
6
0
2
0
1
0
0
2
1
0
0
0
0
2
0
1
0
0
0
2
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
1
0
1
0
0
0
0
3
1
0
0
0
0
2
0
0
0
0
3
2
0
0
0
1
0
2
0
1
1
0
1
1
0
2
2
1
0
0
3
2
0
0
0
1
0
0
0
0
0
2
0
0
0
3
3
0
0
0
0
4
0
0
0
0
0
0
0
0
1
1
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
2
2
0
1
1
0
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
2
0
0
2
0
1
1
0
0
1
1
0
0
1
0
0
1
1
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
2
0
2
0
2
0
0
0
0
0
2
1
2
0
0
0
2
0
0
2
0
0
0
0
2
0
1
1
0
0
1
2
0
0
2
0
0
0
3
2
0
0
0
0
2
0
2
4
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
2
1
4
3
1
0
2
1
0
1
0
0
0
0
0
0
0
0
2
1
1
0
2
1
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
2
3
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
2
0
0
0
0
0
0
1
4
0
0
0
2
0
0
2
0
0
2
2
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
2
0
1
2
0
0
2
0
2
1
2
0
0
0
0
0
0
1
0
0
0
1
0
2
0
1
1
0
1
2
0
0
0
0
0
0
2
0
2
0
2
0
0
0
2
0
0
2
0
1
0
1
1
0
0
2
0
0
2
1
0
0
0
0
0
0
1
0
2
0
0
0
1
0
1
0
0
1
0
1
2
2
0
2
0
0
1
0
0
2
0
1
0
1
0
0
0
0
2
0
1
2
3
0
1
1
0
0
2
0
1
4
0
0
0
0
0
2
0
0
0
0
0
1
0
2
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
2
1
0
2
0
0
2
3
0
0
0
0
0
1
1
2
2
0
0
1
0
0
1
0
2
3
0
1
2
0
0
0
0
1
1
0
0
0
0
2
0
1
2
1
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
2
0
0
0
2
3
0
0
1
0
0
0
2
0
0
0
0
1
0
2
2
0
1
1
0
2
2
0
0
0
2
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
2
2
1
1
3
2
0
1
2
0
0
0
0
1
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
3
0
1
2
0
1
2
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
1
2
2
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
2
0
0
0
2
1
0
0
2
5
1
1
0
1
1
0
0
1
0
3
0
4
0
0
0
0
2
0
2
0
2
0
2
0
0
2
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
2
0
0
0
2
2
0
0
0
0
2
0
0
1
0
0
1
1
0
1
2
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
1
0
0
2
0
1
1
0
2
2
0
0
0
0
0
0
2
0
0
4
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
1
0
0
0
1
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
3
0
1
0
3
0
0
0
0
0
0
0
1
2
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
2
0
0
1
3
0
2
2
0
0
2
2
0
0
1
0
1
0
0
0
0
0
2
2
2
0
0
0
0
1
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
1
0
2
0
2
0
0
1
2
0
0
0
0
1
0
0
0
0
2
0
2
0
2
2
2
2
2
1
0
0
3
0
2
0
1
0
2
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
2
2
0
0
0
0
0
0
0
5
2
1
2
0
0
1
0
1
0
0
2
2
0
2
0
1
1
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
2
0
1
0
0
0
2
0
1
0
0
1
0
0
0
0
0
1
1
3
2
0
2
0
0
2
0
0
0
0
0
1
2
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
1
0
0
1
0
0
2
0
2
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
5
1
1
0
0
1
1
0
0
1
0
0
2
2
0
2
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
1
0
2
1
1
2
0
0
0
0
0
0
0
0
2
4
1
0
0
0
2
0
1
2
0
0
0
0
0
2
0
2
0
0
1
8
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
1
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
2
0
0
1
0
0
0
2
2
0
0
1
0
0
1
1
2
2
0
0
2
0
0
2
2
0
0
1
1
2
1
3
0
1
0
0
0
0
1
0
0
1
0
0
0
2
0
1
0
0
2
0
0
1
1
0
0
0
0
0
0
1
2
1
2
0
0
0
1
2
0
0
1
0
0
3
0
3
2
0
3
0
0
0
1
1
2
1
1
2
1
2
0
0
1
0
0
0
0
0
0
0
1
0
0
2
2
0
4
0
0
1
1
1
1
1
1
0
0
1
0
1
0
0
0
0
2
2
0
0
0
0
0
1
1
0
0
4
0
1
0
0
0
0
0
1
0
0
0
0
1
0
2
2
2
2
0
2
0
0
0
1
2
0
1
1
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
2
0
0
2
1
2
1
0
0
1
0
0
0
1
0
0
0
2
1
2
0
0
0
0
0
0
2
0
2
0
0
0
2
2
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
2
1
3
0
1
0
0
0
1
2
2
0
1
0
0
3
0
1
0
1
2
0
0
0
0
1
1
1
0
0
0
0
0
0
1
2
3
0
0
0
0
0
0
0
1
0
1
0
1
2
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
1
0
0
0
2
0
0
1
0
3
0
1
0
0
1
0
1
2
1
0
0
1
0
0
2
0
0
0
2
3
1
0
1
1
1
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
2
0
2
0
2
0
0
0
1
4
0
1
1
2
0
2
1
0
0
2
2
1
0
0
0
0
1
2
1
2
0
0
0
1
0
0
0
2
2
0
0
0
0
1
1
1
5
0
1
0
0
0
2
2
0
0
2
1
0
0
1
3
0
1
0
0
4
0
1
0
2
0
0
0
1
1
0
2
0
0
1
2
3
2
1
0
0
0
1
0
0
2
1
0
0
0
0
0
0
1
0
0
1
2
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
2
1
0
1
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
1
1
0
0
1
2
0
0
0
3
1
0
1
1
0
0
0
2
1
4
0
0
0
0
1
0
0
1
2
2
0
0
2
0
1
0
1
1
0
2
2
0
0
2
0
0
1
1
1
0
0
2
0
2
1
1
0
0
1
0
1
1
0
0
1
2
1
1
0
0
0
0
1
1
0
0
2
0
1
0
0
1
0
2
1
0
0
2
0
0
2
0
0
1
2
0
2
2
1
1
4
0
0
0
9
3
0
0
0
1
0
0
2
0
2
0
0
2
2
0
3
1
0
2
0
0
3
0
0
0
0
2
0
1
0
1
0
0
0
0
0
1
1
0
1
0
0
0
1
1
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
2
0
1
0
1
2
2
2
0
0
2
0
2
1
0
0
1
0
0
0
2
2
0
0
2
1
0
0
0
2
0
0
1
0
0
0
0
1
0
0
1
1
0
1
0
0
2
1
1
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
2
1
1
0
2
2
0
2
0
0
0
4
2
2
0
2
0
1
1
1
0
0
0
0
2
1
0
0
0
1
0
0
0
2
1
0
1
1
0
0
0
0
2
1
1
0
0
1
0
1
0
2
2
2
1
1
0
1
0
1
0
0
0
1
1
1
0
2
0
0
0
0
2
1
1
0
1
1
0
0
0
1
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
1
1
0
2
1
0
0
1
0
0
1
0
0
1
0
1
1
0
1
1
1
0
1
1
0
0
2
1
2
0
1
0
2
1
0
2
0
0
0
1
0
2
1
2
1
0
1
2
1
1
0
1
1
0
0
2
2
0
2
0
0
1
0
0
0
0
0
0
0
1
1
1
1
2
2
1
3
1
2
0
2
0
2
0
0
0
0
0
1
0
1
5
0
0
0
2
0
0
2
2
0
1
0
0
0
1
2
2
1
2
2
0
4
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
2
0
0
0
0
2
0
0
0
0
1
3
1
0
0
0
0
0
0
0
0
0
3
1
1
2
1
0
0
0
2
0
2
0
1
2
0
0
0
2
2
1
0
0
0
1
0
2
0
1
0
0
0
0
1
0
1
0
0
2
1
0
0
0
1
0
0
2
6
1
1
1
0
1
0
2
0
2
2
0
0
2
1
0
1
0
0
1
0
0
0
0
2
1
0
2
0
0
0
0
1
0
1
0
2
0
2
1
2
0
0
1
2
2
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
1
1
0
0
0
1
2
0
0
0
0
0
0
0
2
2
0
0
2
0
1
2
2
0
0
2
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
2
0
1
1
0
2
0
0
5
2
1
2
2
0
0
0
0
1
0
1
0
0
0
0
1
1
2
0
0
0
1
0
0
0
2
1
0
0
1
0
1
0
0
0
0
2
1
2
2
0
2
2
0
1
1
0
0
2
0
0
1
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
1
2
1
0
1
0
0
0
0
0
0
0
1
0
0
3
1
0
0
0
0
1
0
2
0
3
1
0
1
1
2
0
1
0
4
0
2
2
2
0
0
0
0
0
1
0
0
0
1
0
0
2
0
2
0
3
1
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
2
1
2
0
0
2
1
0
0
0
0
0
0
2
1
0
0
2
2
2
0
0
0
0
0
1
1
1
0
0
0
0
2
2
2
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
1
0
0
0
1
1
2
2
0
2
0
2
0
0
2
0
0
0
0
2
0
1
1
2
0
0
0
0
0
0
1
0
0
2
0
3
0
0
1
2
3
0
0
1
1
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
2
0
1
0
1
2
0
2
0
0
2
1
1
0
0
0
0
0
1
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
1
0
0
0
0
0
2
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
2
1
0
0
0
0
0
2
0
1
1
0
0
2
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
2
0
2
0
1
1
0
0
2
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
2
0
1
0
0
0
1
0
2
1
0
0
0
1
0
0
0
2
2
0
0
0
1
0
2
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
2
2
3
2
2
0
0
0
0
1
0
1
3
1
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
2
0
0
0
1
1
2
2
1
2
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
2
0
0
0
1
0
1
0
0
1
1
0
2
0
2
0
0
0
0
0
0
0
0
2
0
3
2
0
0
0
0
2
2
0
1
0
1
0
0
0
2
0
0
0
2
0
2
0
2
0
0
0
0
2
0
1
0
0
0
0
2
1
2
0
0
1
0
1
0
1
0
1
2
1
0
2
0
2
3
0
2
0
0
0
0
3
0
1
5
0
2
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
2
0
1
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
2
2
0
0
0
1
0
0
4
0
1
3
1
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
1
0
2
0
1
0
1
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
2
0
2
1
0
1
0
0
0
0
0
0
0
2
1
2
2
0
0
0
3
0
0
0
0
1
1
1
2
0
2
0
0
0
0
0
0
1
5
0
0
0
0
1
1
0
1
0
1
2
0
2
0
0
0
0
1
0
0
0
0
0
3
0
1
0
0
1
0
1
1
0
1
0
1
0
0
1
1
0
1
0
1
0
1
2
2
1
0
0
1
0
1
2
0
0
2
0
1
1
0
0
1
2
1
2
2
0
1
0
0
1
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
1
0
0
2
0
0
1
0
0
1
2
1
0
0
0
2
2
1
0
0
0
2
0
0
2
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
1
0
2
0
2
0
1
2
0
0
1
1
0
2
2
2
0
0
0
0
1
2
0
0
0
0
2
1
2
5
0
0
2
0
0
2
0
2
1
1
0
0
0
0
2
0
2
0
0
2
0
1
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
1
0
2
0
0
2
0
1
0
0
0
0
0
2
0
1
2
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
2
2
5
2
0
1
5
0
0
0
1
1
0
0
0
0
1
0
0
2
0
1
2
0
0
0
0
2
1
2
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
1
0
2
0
0
0
0
0
3
0
0
1
0
1
0
1
3
0
1
0
0
2
2
0
0
2
1
2
0
1
0
0
0
2
1
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
2
2
0
0
0
0
0
2
0
2
4
1
0
0
2
0
0
0
0
3
3
1
0
2
1
0
0
0
0
0
0
0
0
1
3
1
1
0
0
2
2
1
0
2
1
1
0
0
0
0
0
1
1
2
2
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
2
3
0
0
0
2
2
0
0
1
1
0
0
0
2
2
0
0
0
1
2
0
1
1
2
0
0
0
0
2
0
2
0
0
0
0
1
2
0
1
0
3
2
0
0
0
0
2
2
0
0
0
2
0
3
0
0
0
0
0
1
2
0
0
0
0
1
0
2
0
6
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
2
2
1
2
2
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
1
0
1
2
0
0
1
0
1
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
1
1
0
0
1
1
0
2
0
0
0
0
0
1
0
2
1
0
0
0
1
0
1
0
1
1
2
2
2
0
2
0
0
2
2
3
0
0
0
0
0
0
0
0
1
1
0
2
0
2
1
2
2
0
0
0
0
2
1
0
2
0
1
2
0
1
2
0
0
0
2
0
0
2
0
0
1
0
1
0
0
1
0
4
3
0
1
1
0
2
0
0
1
2
0
0
1
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
1
1
2
1
2
2
0
0
0
0
0
2
1
0
0
1
0
0
2
0
3
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
1
6
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
1
0
2
1
0
0
0
0
0
0
3
1
1
0
2
0
0
0
0
0
0
0
0
1
2
2
0
1
0
0
3
0
0
0
1
0
2
1
0
1
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
2
0
2
1
0
2
0
0
1
0
1
0
1
0
0
2
0
0
0
0
1
2
0
0
1
0
1
0
0
2
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
2
1
2
0
0
1
0
0
0
0
1
0
0
1
1
0
2
1
2
1
1
0
0
0
1
2
0
2
1
0
1
0
0
0
1
0
1
2
1
0
0
0
1
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
3
1
0
1
0
0
0
0
0
0
0
1
2
0
1
1
1
2
0
0
2
2
2
0
0
2
0
0
1
0
1
0
2
1
0
0
0
0
0
2
3
0
0
0
2
0
2
2
0
3
2
1
1
0
2
0
1
1
0
0
4
0
0
0
0
0
0
0
0
2
2
0
2
1
1
0
0
0
0
0
0
1
2
0
2
1
2
0
0
0
0
1
2
0
2
0
0
0
2
0
0
0
1
1
0
0
0
1
0
0
2
0
1
0
1
0
2
0
0
0
2
2
1
1
1
1
0
0
1
0
2
0
0
0
1
0
1
0
0
2
0
1
0
0
0
1
1
0
0
2
1
1
0
3
1
1
1
0
1
1
0
0
0
2
2
1
0
1
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
3
1
1
1
1
0
0
1
2
0
0
0
1
0
1
0
0
0
1
0
2
1
1
0
0
0
0
2
0
2
0
2
0
0
0
0
1
0
1
0
2
0
0
3
0
1
0
1
0
1
0
0
1
1
0
2
2
2
0
0
0
0
0
2
1
1
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
3
1
1
0
2
0
0
4
0
0
2
2
1
0
1
2
0
0
2
0
2
0
2
0
0
1
0
0
2
4
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
2
1
0
0
0
2
1
2
0
1
0
0
0
2
1
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
2
4
0
0
2
2
0
7
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
2
1
0
0
0
2
0
0
2
2
1
0
0
0
1
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
2
0
0
1
0
0
0
1
1
1
0
3
1
1
1
0
0
2
1
0
0
0
0
1
0
0
3
0
1
2
0
2
0
0
1
1
0
0
0
0
0
0
1
0
2
0
0
0
0
9
0
0
2
0
0
0
2
1
0
0
1
1
1
2
1
1
0
0
0
0
2
2
0
2
0
0
0
0
0
2
0
0
0
4
2
1
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
2
2
0
2
0
0
0
1
0
2
1
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
2
0
0
1
0
0
1
1
0
0
0
1
0
2
0
1
0
1
0
0
2
1
1
1
0
1
0
2
0
1
0
0
0
0
3
0
1
0
1
1
0
0
0
0
0
0
1
2
0
1
0
0
1
0
1
0
2
0
1
3
0
0
0
1
1
0
0
2
2
1
0
0
1
0
2
2
1
0
2
0
2
0
0
1
2
0
1
1
0
0
0
1
1
0
0
0
0
0
1
1
2
0
3
0
1
0
0
2
0
0
0
2
0
0
0
2
5
1
1
1
2
0
1
2
1
0
0
0
1
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
2
1
2
2
1
1
0
0
0
0
2
3
0
0
1
0
2
0
0
0
2
1
2
2
0
2
0
1
3
0
1
0
0
0
0
0
0
1
0
0
1
0
2
2
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
1
0
1
0
0
2
2
0
0
0
0
0
1
1
1
1
1
4
2
0
0
1
0
1
0
0
2
0
3
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
1
1
0
0
4
2
0
0
0
1
1
0
2
0
1
0
2
1
1
0
1
0
0
2
2
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
4
0
0
1
4
2
0
0
0
2
2
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
2
1
0
1
2
0
0
0
0
3
1
2
1
2
0
0
0
0
1
0
0
0
0
2
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
3
0
2
0
0
0
2
0
1
1
0
1
0
0
0
0
0
2
1
1
1
2
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
2
2
0
0
2
0
0
2
0
0
2
0
9
0
0
0
0
2
2
0
3
3
1
3
0
0
0
2
1
0
1
0
0
2
1
0
0
1
0
0
0
2
0
0
0
1
0
0
0
1
0
0
6
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
2
2
2
0
0
0
1
1
1
0
2
1
0
0
1
0
2
0
0
1
0
0
0
3
1
1
0
0
2
0
0
0
0
0
0
2
1
2
0
0
2
2
0
1
0
1
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
3
0
0
0
0
0
2
0
1
0
0
2
0
1
0
1
1
0
2
0
0
0
0
0
0
2
0
0
0
0
1
2
1
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
3
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
2
0
0
0
0
0
0
0
1
1
2
2
0
1
7
1
2
0
2
0
0
1
2
0
2
0
0
2
0
1
0
1
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
1
2
1
0
0
0
2
0
1
0
2
2
0
0
0
2
0
0
0
0
2
1
2
0
1
0
0
2
0
0
2
2
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
3
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
2
2
0
0
2
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
2
1
1
0
0
2
0
1
0
0
0
1
0
0
1
0
5
0
1
0
0
0
0
2
0
0
1
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
3
0
0
0
0
0
1
0
0
1
1
0
0
1
0
1
0
0
0
1
1
2
0
4
1
0
1
0
2
0
1
0
2
0
0
1
0
0
0
1
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
2
0
5
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
1
2
0
2
0
0
1
0
0
0
1
0
0
0
2
0
0
1
0
2
0
0
2
0
0
1
1
0
1
1
0
0
1
0
0
0
2
0
0
0
0
2
0
1
2
0
0
0
2
0
0
2
0
1
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
1
2
0
0
0
1
0
1
1
0
0
0
3
1
1
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
2
0
0
2
0
0
2
0
0
0
2
1
0
0
0
1
0
0
0
1
0
2
1
2
0
0
0
2
2
0
0
0
0
0
2
1
0
0
2
0
2
2
2
2
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
2
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
2
0
0
1
0
0
0
3
2
0
0
0
0
2
0
2
0
2
0
0
0
1
3
0
0
0
2
0
2
0
0
0
0
2
0
0
8
0
2
2
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
2
3
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
4
0
0
0
0
1
0
0
1
0
2
0
1
2
0
2
0
1
0
0
2
0
1
0
2
0
0
2
2
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
2
0
0
1
2
2
6
1
0
1
0
3
2
0
0
0
2
0
0
0
0
1
0
0
2
2
0
2
0
0
0
0
0
0
2
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
2
0
2
0
0
0
0
2
1
1
0
1
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
2
1
0
1
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
1
2
0
0
2
0
0
2
0
4
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
3
0
0
1
0
1
0
0
2
0
0
0
0
1
0
0
0
1
1
0
0
0
0
2
0
1
2
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
1
1
4
0
3
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
3
0
0
2
1
0
1
0
0
1
1
2
0
0
0
0
0
0
0
0
2
0
0
2
1
0
2
0
2
0
1
2
0
0
0
5
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
2
2
0
2
0
0
0
2
0
0
0
1
0
2
2
0
2
0
0
0
2
2
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
1
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
1
0
1
0
0
2
0
0
0
0
3
0
2
0
0
0
1
0
0
0
0
2
7
1
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
2
1
1
0
0
0
1
2
2
0
0
3
1
1
0
0
4
2
1
0
0
0
2
0
0
0
0
1
0
0
2
0
0
1
2
1
2
2
0
0
0
0
2
0
2
2
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
2
2
2
2
1
0
0
0
1
0
0
0
1
2
4
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
2
0
2
1
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
1
1
2
1
2
0
0
1
0
1
0
0
0
0
2
2
0
1
0
1
0
2
2
0
2
0
0
0
0
2
0
0
0
0
1
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
2
1
0
1
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
3
0
1
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
1
2
2
0
0
1
0
0
1
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
2
0
0
1
0
1
1
2
0
0
1
0
1
0
1
2
0
0
0
1
2
9
0
1
0
0
0
0
2
2
0
0
0
0
1
0
0
2
0
1
1
0
0
0
0
0
2
1
0
0
1
0
1
0
0
3
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
2
0
1
0
2
0
0
0
1
0
0
1
0
0
0
0
0
1
1
1
0
0
2
2
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
12
0
2
0
0
2
3
0
0
0
0
1
0
2
0
0
1
0
1
1
0
0
1
0
1
0
0
1
1
0
0
2
0
0
0
3
0
0
2
1
2
0
1
0
0
0
1
0
0
0
0
1
1
0
0
1
0
2
0
0
0
0
1
0
1
2
0
2
1
0
2
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
1
2
0
0
2
0
0
0
0
1
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
4
1
0
0
2
2
0
0
1
0
0
0
0
1
3
0
1
0
1
0
1
0
0
0
1
0
0
2
2
2
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
3
0
1
1
0
0
0
1
2
0
1
0
0
1
0
1
2
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
2
0
0
0
0
2
0
2
2
0
2
2
0
0
1
1
0
1
0
2
0
0
0
0
1
0
2
0
0
4
0
0
0
0
1
2
0
1
0
0
0
2
0
2
0
1
2
2
0
2
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
1
1
0
2
0
2
1
1
0
2
0
0
1
0
1
0
1
1
0
0
0
0
1
2
2
2
0
0
2
1
0
0
1
0
0
0
1
0
0
0
1
2
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
1
0
3
0
0
4
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
4
1
0
2
0
0
0
0
1
0
1
2
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
1
1
4
0
1
0
0
0
2
0
1
0
0
1
2
0
4
0
0
0
0
0
1
0
2
2
0
0
2
0
0
2
0
1
1
1
0
0
0
2
0
0
2
0
1
1
1
0
1
0
0
0
1
1
2
0
0
0
0
0
2
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
2
1
2
2
0
0
0
1
0
2
3
1
0
0
1
0
0
1
0
1
0
0
2
0
2
2
0
1
0
0
1
0
0
2
0
1
0
0
0
1
1
0
0
2
0
0
2
0
2
0
0
0
0
0
3
0
3
1
1
1
0
0
0
0
0
2
2
0
1
1
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
1
0
0
2
0
2
0
0
3
0
0
0
0
0
0
2
0
1
0
1
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
2
0
0
0
0
0
1
3
1
1
0
0
0
1
0
1
0
0
1
2
2
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
2
2
2
0
0
1
0
2
0
1
2
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
1
0
0
0
2
0
3
1
1
1
0
2
2
1
0
1
1
1
2
1
0
0
0
0
2
2
0
0
0
0
2
0
2
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
1
0
2
0
1
0
0
0
3
1
2
1
0
0
0
1
1
0
2
0
0
2
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
1
0
0
1
2
0
2
1
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
1
0
1
0
0
0
2
0
0
2
2
0
0
0
1
0
0
1
1
1
1
2
1
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
2
0
2
1
0
0
0
2
0
0
1
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
1
1
2
0
0
3
1
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
4
1
2
1
0
0
0
2
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
3
0
0
1
0
0
0
0
3
0
0
2
0
0
0
1
1
0
0
1
2
1
2
1
2
0
0
0
1
0
0
3
2
0
1
0
0
0
0
0
1
2
0
0
2
0
0
0
0
2
0
10
1
0
2
0
1
0
0
1
0
2
1
0
0
0
1
0
2
0
1
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
1
2
0
2
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
2
0
1
2
2
0
1
2
2
0
0
0
0
0
3
0
1
0
0
0
2
0
0
1
0
1
0
0
0
0
0
2
0
1
0
0
0
0
2
1
1
0
2
2
0
0
1
0
1
0
2
0
1
0
0
1
0
1
0
1
2
1
0
2
2
0
0
2
0
0
0
1
1
0
5
0
1
0
0
0
0
1
1
2
0
0
4
0
2
0
1
2
0
0
3
0
2
0
1
13
0
1
0
0
0
0
0
1
0
2
0
1
0
2
0
2
1
0
0
2
2
2
1
1
1
1
2
2
1
0
0
2
0
0
2
1
0
2
1
1
0
0
0
0
0
2
1
0
4
0
0
0
0
0
0
0
0
0
1
2
2
1
0
0
0
0
0
2
0
0
0
2
1
1
3
1
0
2
1
0
0
0
1
0
0
2
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
2
2
1
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
1
2
0
0
0
0
2
1
0
0
0
0
2
0
0
1
0
2
0
1
0
2
0
0
0
0
2
0
0
0
0
1
1
2
1
0
1
2
0
0
2
0
0
0
0
0
2
0
1
0
1
0
1
0
0
0
4
0
0
0
2
1
0
4
0
4
2
0
0
0
2
0
0
1
2
0
1
2
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
1
2
0
0
1
0
0
1
0
0
1
2
2
0
0
2
1
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
1
0
1
2
0
0
0
0
3
0
0
0
2
0
1
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
1
1
2
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
1
0
1
1
0
2
0
0
0
0
1
0
0
3
0
1
1
0
1
0
1
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
1
0
0
1
2
1
0
0
0
2
1
0
0
1
1
0
0
2
0
1
0
2
1
0
0
1
1
0
0
0
2
0
0
1
2
2
0
0
1
0
0
2
0
0
0
0
2
2
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
1
0
0
2
0
1
1
2
2
0
1
0
0
1
0
0
1
0
2
1
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
1
0
0
0
1
1
0
0
2
1
2
2
0
0
0
2
3
1
0
0
0
2
0
1
1
1
0
0
0
2
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
2
0
0
1
0
0
0
0
2
1
2
3
0
1
1
0
2
1
0
1
0
1
2
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
1
0
1
0
2
2
1
2
0
0
1
0
0
2
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
2
1
2
1
1
0
2
2
3
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
1
2
1
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
1
2
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
1
0
0
2
0
0
0
1
3
2
0
0
1
2
2
0
2
0
0
1
0
3
2
0
0
0
1
0
0
1
0
0
2
0
1
0
0
2
0
0
2
1
0
0
0
0
2
2
0
0
1
0
0
2
0
2
1
1
0
3
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
4
2
0
1
0
0
1
0
0
0
0
2
0
0
3
0
0
0
1
0
0
0
0
1
0
1
0
2
0
1
0
1
1
0
1
0
1
0
1
2
0
1
0
1
1
2
0
2
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
9
0
0
1
0
0
2
1
1
0
0
2
0
0
2
0
2
1
0
1
0
0
1
2
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
2
0
2
0
1
0
2
0
0
0
1
1
0
0
0
0
0
2
0
1
0
1
0
2
0
0
0
1
0
1
0
2
0
0
0
0
1
0
0
0
0
2
2
0
2
0
0
1
1
0
0
0
2
1
0
1
0
0
0
2
0
1
2
2
0
0
1
2
1
0
0
0
0
1
2
2
2
0
1
1
0
1
0
1
0
0
0
1
0
0
2
0
2
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
2
0
0
0
3
0
0
0
1
1
0
0
1
0
3
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
2
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
2
2
0
1
2
0
2
0
2
0
0
0
0
1
0
1
1
0
3
0
0
0
0
1
0
0
0
7
2
0
2
0
2
0
2
0
0
0
0
1
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
3
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
1
2
0
1
0
1
0
1
0
0
0
0
1
0
2
0
4
0
2
2
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
2
0
0
0
2
0
0
3
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
3
1
0
3
0
1
0
0
0
0
2
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
1
1
2
3
1
1
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
2
0
0
0
0
1
2
0
1
0
0
3
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
3
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
1
1
1
0
0
1
0
2
0
0
0
2
0
3
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
1
0
1
1
1
0
1
1
0
0
0
0
2
2
1
0
0
0
0
3
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
2
1
0
1
1
0
1
0
0
2
0
0
0
2
2
2
0
0
2
0
3
2
0
0
0
1
2
0
0
1
0
0
1
0
0
2
0
0
0
1
1
0
0
1
0
0
0
13
0
2
1
0
0
2
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
2
0
2
0
2
2
0
0
3
0
0
0
0
0
2
0
0
0
0
1
0
0
9
0
0
0
0
0
0
1
0
0
1
0
1
2
0
2
2
1
1
0
2
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
3
1
2
0
1
0
1
0
0
0
0
0
0
2
0
2
2
2
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
2
0
0
1
0
0
4
0
1
0
0
0
0
2
0
2
2
1
0
0
1
0
0
2
0
0
0
5
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
2
0
0
1
2
2
0
0
0
0
0
1
0
0
0
0
0
0
2
1
1
0
2
0
0
0
1
0
2
1
2
1
0
0
1
0
0
0
0
0
0
0
0
1
2
2
0
0
0
1
0
1
0
0
0
1
0
0
0
2
0
2
0
0
1
1
0
0
0
0
0
3
1
1
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
2
2
0
0
1
0
0
4
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
2
1
0
3
1
1
2
1
2
0
1
0
0
0
0
3
0
2
1
0
0
0
1
0
0
0
0
2
0
0
1
2
1
0
0
0
0
0
2
1
0
0
0
2
1
0
2
0
2
5
1
0
0
1
1
0
0
0
2
0
0
0
2
2
1
0
0
0
1
0
0
0
2
0
0
0
0
2
2
0
0
0
1
0
0
2
0
2
1
1
0
0
1
2
0
0
2
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
2
1
0
3
0
0
1
4
0
0
1
2
0
0
0
2
3
2
0
0
0
2
0
2
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
1
3
0
2
0
0
0
1
0
2
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
3
0
1
0
0
2
2
0
1
0
0
0
0
0
1
0
0
0
1
2
0
1
0
0
0
0
0
0
3
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
1
1
0
0
0
2
1
0
2
0
0
0
0
0
2
0
1
2
2
0
0
2
0
2
0
0
0
0
2
0
3
0
0
1
0
1
2
0
1
0
1
2
0
1
2
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
1
2
0
1
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
1
0
0
0
2
0
0
3
0
0
1
0
3
1
2
1
2
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
1
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
2
1
0
2
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
1
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
1
0
0
1
2
3
2
1
2
0
0
0
2
0
0
0
3
2
0
0
0
1
1
0
0
0
1
0
4
2
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
2
1
1
0
0
0
1
3
0
0
0
0
0
0
0
6
0
1
0
0
0
0
1
1
0
2
0
2
0
0
0
4
0
0
1
1
0
1
0
0
1
0
2
2
0
0
2
0
0
0
1
1
2
0
0
2
0
2
0
1
0
0
0
0
0
1
1
2
0
0
1
0
2
0
1
0
1
0
0
1
2
2
0
0
0
2
0
3
0
1
3
0
0
1
0
0
0
2
0
0
1
0
0
1
0
0
0
2
1
2
0
0
0
2
1
0
2
0
2
0
0
1
0
1
1
2
0
0
0
0
0
1
0
0
1
0
0
0
1
2
1
0
0
0
0
0
2
2
3
1
2
0
0
3
0
1
2
1
0
1
0
1
0
1
1
0
0
0
4
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
2
2
0
3
0
1
0
0
0
0
2
1
2
0
0
2
1
1
0
0
0
0
0
1
0
3
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
1
1
2
2
0
2
0
0
1
0
0
0
2
0
1
1
0
0
3
2
0
0
0
0
1
2
1
0
0
0
0
0
0
1
1
2
0
1
0
1
2
1
0
0
1
2
0
1
2
1
0
0
0
0
1
1
0
1
1
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
3
0
2
0
1
1
0
2
0
0
2
2
1
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
2
0
0
0
0
2
0
2
0
0
0
2
0
0
0
2
1
1
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
1
0
0
0
1
0
0
0
2
0
2
1
1
0
0
1
1
0
2
0
0
1
2
0
3
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
1
2
2
2
0
0
2
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
1
1
0
0
1
1
0
2
2
0
2
1
0
2
0
0
2
0
0
1
0
0
1
0
0
0
2
0
0
0
1
2
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
2
2
3
0
0
1
2
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
1
0
2
0
1
0
1
0
2
0
0
1
0
0
2
1
2
2
0
0
1
0
0
0
0
0
2
2
1
0
1
0
1
0
1
1
0
1
0
3
0
1
0
2
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
2
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
1
1
0
0
2
1
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
1
0
0
0
0
0
0
1
0
2
0
2
0
0
0
1
3
0
2
0
0
5
0
0
0
0
5
0
0
1
0
0
0
0
2
1
0
0
1
0
1
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
2
0
1
0
0
2
0
0
1
0
0
1
0
0
3
0
0
1
2
0
0
0
0
0
1
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
3
1
0
0
2
2
2
0
0
1
0
0
3
0
0
0
0
1
0
1
2
0
0
2
2
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
1
0
0
0
1
2
2
0
0
2
2
1
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
2
0
3
1
1
1
0
0
2
1
0
0
1
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
1
0
0
0
0
0
0
0
1
1
2
0
0
1
0
1
1
0
0
0
1
0
3
0
0
0
2
1
1
1
1
0
0
0
0
0
0
1
3
2
0
0
0
0
0
0
2
0
2
0
0
0
0
2
1
1
3
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
1
0
0
0
0
1
2
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
2
0
2
0
0
0
2
0
2
0
1
0
0
0
1
0
0
2
0
0
0
1
2
0
0
1
0
0
2
1
1
1
0
1
6
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
11
0
0
0
0
0
0
2
2
0
0
1
0
0
2
0
1
1
0
0
1
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
2
0
2
1
0
0
0
0
1
0
0
0
0
1
0
0
1
1
1
0
0
1
1
0
0
3
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
2
2
0
1
0
0
0
1
0
2
0
0
1
1
0
0
1
0
0
0
0
2
1
1
2
0
0
0
0
0
0
1
0
1
0
1
0
0
0
2
0
0
0
0
2
1
0
1
2
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
1
2
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
1
2
0
0
0
1
2
0
0
0
1
1
2
0
2
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
7
2
0
0
0
3
0
0
0
0
2
2
0
0
0
0
1
1
1
0
1
0
0
0
0
2
0
2
0
0
2
0
1
0
0
0
0
2
0
1
2
0
0
2
0
1
0
0
5
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
2
1
2
2
2
0
0
1
0
0
2
0
0
0
0
2
0
1
0
1
0
1
0
1
2
0
0
1
1
0
0
0
0
0
2
1
2
0
0
1
0
2
0
0
2
0
3
0
0
0
0
0
0
2
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
1
2
1
0
0
1
0
0
1
0
0
0
1
2
0
2
0
0
0
2
0
2
2
0
1
3
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
1
2
0
0
1
1
0
0
1
0
0
0
1
2
0
0
0
0
0
2
2
0
1
1
1
0
0
2
0
0
0
0
1
2
0
0
0
0
0
3
0
0
2
2
0
2
0
0
3
0
0
0
0
0
0
1
0
0
2
3
0
0
0
2
0
0
0
2
1
0
1
0
2
0
0
0
1
0
1
0
2
2
1
1
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
1
2
0
2
0
0
1
0
0
1
2
3
1
0
0
0
2
1
1
0
0
1
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
2
0
1
1
0
1
0
0
0
0
0
0
1
1
1
2
2
2
0
0
0
0
1
2
0
2
0
2
0
2
0
0
2
0
0
1
0
1
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
2
0
1
0
2
1
1
0
0
0
2
0
0
1
2
0
0
0
2
1
0
0
2
1
0
2
1
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
2
1
0
0
0
1
0
3
0
0
0
0
0
3
0
0
0
2
0
2
1
0
3
2
2
2
2
0
2
1
0
0
0
0
0
1
0
1
2
0
2
0
2
0
1
1
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
1
2
1
0
0
0
1
2
0
0
0
3
1
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
3
1
3
0
0
0
0
1
0
1
0
0
0
0
0
2
0
2
2
0
0
0
1
0
0
1
0
0
0
0
0
4
0
1
1
1
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
1
0
1
0
0
0
0
0
1
1
1
2
0
0
2
0
2
0
0
0
1
2
0
0
0
1
1
2
0
0
1
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
2
0
2
1
0
0
2
0
0
0
2
0
0
2
0
1
0
1
1
2
0
2
1
3
0
2
2
0
1
0
3
0
0
2
1
0
0
2
2
0
1
0
0
0
3
2
1
0
0
1
0
0
1
1
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
1
0
2
0
0
1
0
1
1
0
0
0
0
1
1
0
3
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
2
0
2
2
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
2
1
0
1
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
2
1
2
0
2
2
0
2
2
1
0
2
0
0
0
1
3
2
0
0
0
1
0
0
2
0
1
0
1
2
0
1
0
0
0
1
0
0
1
0
2
0
0
1
0
0
0
1
2
1
0
0
0
0
1
0
0
0
1
0
0
2
2
0
0
0
2
0
1
0
1
0
2
0
2
0
0
0
0
2
1
0
0
0
1
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
2
2
0
0
1
0
2
2
2
0
0
2
2
0
0
1
0
2
0
0
2
0
0
1
0
0
2
6
1
2
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
5
2
0
0
0
0
0
4
0
2
1
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
1
0
2
0
0
0
1
2
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
2
1
2
1
0
1
0
1
2
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
1
0
2
0
2
0
1
0
1
0
0
2
1
0
1
1
0
0
0
0
4
0
0
2
0
0
2
1
0
2
0
0
0
0
2
0
3
0
2
0
1
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
1
1
1
0
0
2
0
0
0
2
0
1
2
1
0
0
0
1
1
1
2
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
1
0
2
0
1
2
0
2
0
1
0
0
1
2
2
0
1
0
2
0
0
1
1
0
0
0
0
1
0
2
1
0
0
1
0
1
0
1
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
3
1
0
0
2
0
0
2
0
1
2
2
0
0
0
13
0
0
0
0
2
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
2
1
0
2
2
1
0
1
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
1
0
0
2
0
0
0
3
0
0
2
0
0
1
0
0
0
0
1
0
1
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
1
0
0
2
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
7
3
3
0
0
2
4
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
2
2
2
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
1
2
2
0
0
1
2
0
0
0
0
1
4
0
0
2
1
0
0
0
1
2
1
0
0
0
0
2
0
1
1
0
1
0
2
0
0
0
0
2
0
2
1
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
2
0
1
7
0
0
0
2
2
1
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
2
0
1
2
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
1
1
0
1
0
0
1
0
1
1
0
0
2
0
0
2
1
0
2
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
2
0
0
0
0
3
0
0
0
0
0
0
0
0
2
1
2
0
2
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
2
0
2
1
1
0
0
1
1
0
0
0
1
0
0
0
0
1
3
1
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
1
1
1
1
1
0
0
0
2
0
2
0
1
0
0
0
0
1
0
0
0
0
1
2
0
0
2
2
1
1
0
1
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
2
0
1
0
1
1
0
0
1
0
1
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
1
0
0
2
0
0
0
1
0
2
0
2
0
0
0
0
0
2
0
0
4
0
0
0
2
3
0
0
1
0
0
3
0
1
0
2
1
0
0
1
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
2
1
0
0
0
0
0
0
2
0
0
1
1
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
2
0
3
0
0
0
2
0
0
1
1
0
0
0
1
0
1
2
2
3
0
2
2
0
0
2
0
3
0
3
0
0
1
1
2
3
0
4
0
0
0
0
0
0
0
0
1
1
2
0
1
1
1
0
0
0
0
0
3
0
2
0
2
0
2
0
0
0
0
1
2
0
1
2
0
0
0
0
0
0
1
0
2
1
0
0
0
1
0
1
0
0
2
1
2
0
0
0
0
2
2
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
1
0
0
2
0
0
1
2
0
2
0
0
3
0
0
1
0
1
0
0
0
1
0
1
2
0
1
0
1
0
0
0
0
0
1
1
0
0
2
1
2
0
0
0
0
0
2
2
2
0
0
1
1
0
0
0
0
0
0
2
1
1
0
1
0
1
0
2
1
2
2
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
2
0
0
0
2
0
2
1
0
0
0
2
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
2
1
0
1
2
0
0
0
0
1
0
2
3
2
2
0
1
2
0
1
0
0
0
0
1
1
1
2
0
0
0
1
2
0
0
1
1
1
1
1
0
1
1
0
2
0
0
2
2
0
2
0
1
0
0
0
0
0
0
1
0
1
0
2
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
1
0
0
0
0
2
0
0
1
0
0
1
0
1
1
2
0
3
0
0
2
0
0
2
0
0
1
3
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
1
4
1
0
0
0
0
0
0
1
1
1
1
0
0
0
0
2
0
0
0
0
1
0
0
1
2
1
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
1
2
4
1
2
1
1
0
0
0
1
0
0
0
0
2
0
0
1
0
1
0
1
0
3
3
0
1
0
0
0
2
3
0
3
2
0
0
2
0
0
1
1
2
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
3
0
1
0
0
0
0
1
0
2
0
2
0
0
0
1
0
2
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
1
0
2
0
0
1
0
1
0
0
2
2
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
1
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
1
2
0
2
1
2
0
7
0
2
0
1
0
1
0
1
0
0
0
0
1
1
1
2
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
4
1
0
1
3
2
0
1
0
2
2
1
1
1
0
0
1
0
0
0
0
0
2
2
2
1
0
0
0
2
2
1
2
0
1
0
2
0
2
1
1
0
1
0
0
2
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
1
0
1
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
2
0
1
0
0
0
1
2
0
0
1
1
3
0
0
0
0
1
0
5
0
1
1
1
0
0
1
0
2
0
0
2
0
0
1
1
0
1
2
0
0
3
0
2
1
0
1
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
2
0
1
1
0
2
2
0
0
1
0
2
1
1
0
0
1
0
2
0
1
0
1
2
2
2
0
3
0
2
0
1
1
0
0
1
0
1
0
0
0
0
2
2
0
1
0
0
2
0
0
0
1
1
1
1
0
1
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
1
0
2
0
1
0
0
1
2
2
0
0
0
3
2
0
0
1
2
0
0
2
0
0
0
0
0
0
2
0
0
1
1
1
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
1
1
0
2
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
2
2
0
0
0
0
1
1
0
0
0
0
2
2
0
0
0
0
3
2
1
0
1
2
1
2
0
0
0
0
1
1
2
0
2
0
0
0
1
2
0
0
2
0
0
0
2
1
1
0
0
0
1
0
0
2
0
2
0
0
0
2
1
2
0
2
0
2
0
0
2
0
1
0
2
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
2
2
0
2
0
0
0
1
1
1
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
1
0
0
2
1
1
2
0
0
1
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
2
2
1
0
0
0
0
0
0
0
2
0
1
2
0
0
1
2
2
0
0
0
0
0
2
1
0
2
0
2
0
0
0
0
1
0
0
1
0
3
0
2
3
0
0
1
2
0
0
0
0
0
0
2
1
4
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
3
0
2
0
0
0
1
0
0
0
0
0
1
2
0
1
1
0
0
0
1
1
0
2
3
0
2
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
1
2
1
0
0
1
1
1
2
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
3
0
1
1
0
2
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
2
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
1
1
2
2
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
2
0
2
1
2
0
0
0
2
0
0
2
1
0
1
2
0
0
0
1
0
0
2
1
0
0
1
0
1
2
0
1
0
0
1
1
0
0
2
0
0
0
2
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
2
0
1
0
0
2
0
0
2
0
0
0
1
3
0
1
0
0
2
1
3
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
3
0
0
0
0
0
2
0
0
0
2
0
0
0
1
1
1
0
2
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
3
1
0
2
1
1
0
1
0
0
1
0
1
1
0
1
0
0
0
2
1
0
2
0
3
0
8
0
2
2
2
0
0
0
0
1
0
0
3
0
0
1
0
1
0
0
1
0
0
1
2
0
0
0
1
2
0
1
0
1
1
0
1
1
1
0
2
0
0
0
0
1
2
1
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
21
0
6
1
1
0
0
1
1
0
0
1
1
0
2
0
3
0
1
2
0
0
0
2
1
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
1
1
0
2
0
1
0
0
2
2
0
2
0
2
0
1
2
1
0
1
0
0
0
0
0
0
3
0
0
0
2
0
0
1
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
1
0
0
2
0
0
0
0
1
0
0
2
2
1
0
0
1
0
1
0
1
0
0
0
2
0
2
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
2
0
2
0
2
0
1
0
1
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
3
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
5
3
0
0
0
0
2
0
0
1
0
2
0
2
3
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
2
0
0
0
0
1
2
0
1
0
0
2
0
0
0
0
0
3
1
2
0
0
0
0
0
2
3
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
2
0
1
0
0
0
0
0
3
0
0
0
0
0
0
2
0
2
0
2
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
2
1
2
0
2
0
0
0
0
0
0
1
2
0
0
0
0
1
0
2
0
2
0
0
0
1
1
0
0
0
0
0
3
2
0
0
2
1
0
0
0
2
1
2
0
0
0
1
0
0
0
0
2
3
0
0
0
3
1
0
0
1
2
0
1
2
1
2
0
0
0
0
0
1
0
0
1
2
0
0
1
0
0
0
0
0
0
3
1
1
0
0
0
2
0
1
0
0
1
2
1
0
0
0
1
0
0
2
1
2
0
2
0
1
0
2
0
1
0
1
2
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
3
0
0
1
0
0
0
2
0
0
2
0
1
1
0
2
1
2
1
0
2
0
0
1
2
0
0
1
2
0
1
0
0
0
0
0
1
0
0
1
0
1
0
2
0
0
2
2
1
0
1
2
2
0
1
2
0
0
1
0
0
2
2
0
1
2
1
0
0
1
0
0
0
0
0
1
0
1
1
1
0
0
1
0
0
0
0
0
2
1
2
1
2
0
0
0
0
0
2
1
0
0
2
1
2
0
1
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
1
1
0
2
2
0
2
0
0
0
2
0
0
1
0
0
0
2
1
0
1
1
0
0
1
0
0
0
0
0
1
0
1
1
1
0
0
0
0
2
3
0
2
0
1
0
0
0
1
0
0
0
0
2
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
2
2
0
1
0
0
1
1
0
2
0
0
0
0
1
2
2
0
0
2
0
0
1
0
0
0
0
2
1
1
0
1
0
0
0
1
3
2
0
0
1
0
2
0
0
0
2
0
0
2
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
2
0
1
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
1
2
1
0
0
2
0
0
0
0
0
0
1
0
2
0
1
0
2
0
0
0
0
2
0
0
1
2
1
0
0
2
0
0
0
0
0
0
0
0
1
0
2
1
2
2
0
2
0
0
0
0
2
1
0
1
2
2
0
0
0
1
2
0
0
0
0
0
1
0
0
0
1
0
2
0
1
2
0
0
2
1
0
3
0
2
0
0
0
1
0
0
1
0
0
0
1
2
0
0
1
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
2
1
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
2
1
0
0
1
0
0
0
0
2
1
0
0
0
0
0
1
2
1
2
0
1
0
0
1
0
0
2
1
2
0
2
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
1
0
0
2
0
0
0
1
2
0
0
1
0
1
0
0
1
1
1
0
1
2
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
2
0
1
7
0
0
0
0
1
0
0
2
0
0
0
0
0
4
1
0
0
0
2
1
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
3
2
1
1
0
0
0
4
2
2
0
1
2
0
0
0
0
2
0
1
1
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
2
0
1
0
0
0
0
2
0
3
0
1
1
0
0
0
0
0
1
0
0
1
1
0
0
4
0
0
0
2
0
0
0
1
0
0
1
2
0
1
0
0
1
0
0
0
2
3
0
0
2
2
0
0
0
1
0
1
0
0
2
0
0
1
0
2
0
0
3
1
2
0
2
0
0
2
3
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
4
2
0
0
0
1
1
0
1
0
0
0
0
2
0
2
1
0
0
0
1
0
1
0
0
0
1
0
0
0
2
2
0
0
0
0
1
0
0
1
2
0
0
1
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
1
1
2
0
2
2
0
2
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
2
1
0
0
1
1
1
0
0
0
0
1
0
0
0
2
2
1
0
1
0
2
0
1
0
0
0
1
0
1
0
0
0
1
2
0
2
1
0
0
0
1
2
2
0
0
0
1
1
0
2
2
1
0
0
0
1
0
0
0
0
2
0
3
0
0
2
2
2
1
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
1
0
1
1
2
0
1
0
0
1
1
0
0
0
2
0
0
0
0
0
1
1
2
2
2
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
2
0
2
1
1
0
1
0
0
1
1
0
2
0
1
0
2
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
1
1
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
3
3
0
0
3
0
0
0
3
1
0
0
0
1
0
2
0
1
2
1
0
2
0
0
2
0
2
2
0
0
2
1
0
0
1
2
0
1
1
0
1
0
0
2
0
0
0
0
0
1
1
1
0
0
0
0
2
0
0
0
2
1
1
0
3
0
1
1
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
2
0
0
0
0
2
0
0
0
1
2
0
0
0
0
1
0
0
0
0
2
2
1
1
0
0
0
0
1
0
0
1
0
0
0
2
1
1
0
2
1
1
0
0
0
2
0
0
0
0
1
0
2
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
2
0
0
0
0
1
0
2
0
1
0
0
0
1
4
0
2
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
2
0
0
2
0
2
2
0
0
0
0
1
0
1
2
1
0
2
0
2
0
2
4
0
2
1
0
0
0
0
0
2
1
1
1
3
0
0
1
1
0
0
2
2
0
0
0
2
0
1
2
1
0
0
0
0
0
0
0
1
2
2
0
0
0
0
2
2
0
0
0
0
1
0
2
1
1
0
1
1
0
0
1
2
0
1
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
1
3
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
3
0
1
2
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
2
0
1
1
0
0
0
2
1
0
2
3
2
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
2
0
1
2
0
0
0
0
2
2
0
0
0
0
0
2
1
0
2
1
2
1
1
0
0
0
1
1
1
0
5
0
2
0
3
2
0
1
3
1
0
0
1
0
2
0
0
0
0
0
0
0
1
2
0
0
0
1
2
0
0
0
0
0
0
0
2
0
2
2
2
1
0
0
0
1
1
1
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
2
1
2
0
1
0
0
0
2
2
0
0
0
1
0
2
1
1
1
2
3
0
1
0
2
0
0
2
1
0
0
0
2
0
0
0
3
1
0
0
1
0
2
1
0
2
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
2
1
0
0
1
0
0
0
0
0
0
0
2
0
2
0
1
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
2
0
0
0
0
1
0
2
0
0
2
2
0
2
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
2
0
0
0
1
0
2
2
2
0
0
0
0
1
0
0
0
0
0
0
4
0
0
1
0
0
2
2
0
2
0
0
0
1
0
1
0
0
0
1
1
2
1
1
1
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
1
1
2
0
2
0
1
4
0
0
2
1
0
0
5
0
0
0
0
1
1
2
0
3
2
2
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
2
2
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
1
1
1
4
1
2
0
0
0
2
1
0
0
2
0
0
1
0
1
0
0
0
2
0
2
0
2
1
0
0
0
1
0
0
0
3
0
0
1
0
2
0
0
2
0
5
0
0
0
1
7
2
0
1
2
1
0
2
0
0
0
0
0
0
2
2
1
0
1
0
0
1
0
0
1
0
0
0
0
1
0
1
2
2
0
2
0
4
0
1
0
1
1
1
1
1
0
1
0
1
0
0
0
0
2
2
0
0
1
0
0
0
0
2
0
0
2
2
0
1
2
0
0
0
0
0
0
0
2
0
2
0
0
2
2
2
0
0
0
0
0
2
0
0
0
0
1
0
0
3
0
0
1
0
1
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
3
1
0
1
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
2
2
2
1
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
2
0
2
1
0
0
0
6
0
0
0
0
0
0
0
0
1
4
1
0
0
0
0
0
2
0
1
1
0
0
0
2
4
3
0
0
0
0
0
2
1
1
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
1
0
0
0
1
0
0
2
2
0
0
6
1
0
0
0
0
2
0
0
0
2
0
2
0
2
0
0
1
0
0
0
0
0
2
0
0
2
1
0
0
0
0
1
0
0
1
2
1
0
0
2
0
0
3
1
0
0
2
2
0
1
1
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
3
0
0
0
1
0
1
0
1
1
0
0
0
0
0
2
0
0
2
0
0
2
0
0
2
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
1
2
0
2
0
2
0
0
0
0
0
1
0
2
0
1
0
0
0
2
0
1
0
0
2
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
1
2
0
0
1
0
0
0
0
0
1
2
2
0
1
0
0
0
0
2
0
0
2
2
3
0
0
0
1
2
0
0
0
0
2
0
2
0
0
0
2
1
1
0
0
2
0
0
0
1
2
1
0
0
1
0
0
1
2
0
0
1
1
1
0
0
2
1
0
0
0
1
0
0
0
0
1
0
1
1
0
2
1
0
0
2
2
2
1
1
1
0
1
0
1
2
2
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
1
1
6
0
0
0
1
0
0
0
0
0
2
1
0
0
1
2
0
2
2
0
2
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
1
1
0
2
1
0
1
0
0
0
1
0
0
0
2
0
0
0
0
2
0
1
0
1
0
0
0
0
0
3
2
0
0
0
0
2
0
0
0
0
2
2
0
1
0
0
1
0
2
0
1
0
0
0
0
2
1
2
0
2
2
0
0
1
1
0
3
0
2
0
2
0
0
0
0
0
1
0
0
0
0
2
0
1
0
3
1
0
0
2
0
0
2
1
1
0
0
3
1
1
2
0
1
0
0
2
0
0
1
1
0
0
0
0
0
0
1
2
2
0
0
0
0
1
0
1
0
0
0
1
0
2
2
1
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
1
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
2
3
0
1
1
0
1
0
0
0
3
0
2
0
1
1
1
1
1
2
1
0
1
2
0
0
0
0
0
1
4
1
2
0
2
1
0
2
1
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
2
1
0
0
0
2
0
0
3
0
2
0
0
2
0
0
0
2
2
0
1
1
0
0
1
0
0
0
3
0
1
0
2
0
1
0
0
0
1
0
0
0
1
0
0
1
1
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
1
1
0
0
1
1
0
2
0
0
1
2
2
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
3
0
0
0
2
0
0
0
1
2
2
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
1
0
0
0
2
3
2
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
2
0
1
1
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
1
1
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
2
2
0
0
0
5
1
0
1
0
0
0
2
0
0
2
2
0
0
0
1
1
2
2
0
0
0
1
0
2
0
0
0
0
0
1
0
0
1
0
0
3
0
0
3
3
0
2
0
0
2
1
3
0
1
0
0
0
1
0
0
0
1
1
0
0
1
2
1
0
1
2
1
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
1
0
0
3
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
2
0
1
0
0
0
0
2
0
0
2
0
0
1
0
3
1
0
0
0
0
2
2
2
0
0
2
0
1
1
0
1
0
0
0
2
0
0
0
0
0
2
1
1
0
0
0
1
0
0
0
2
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
2
0
1
2
1
2
0
1
0
0
2
0
2
1
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
1
0
0
2
0
0
2
0
0
2
0
2
2
0
0
0
0
0
0
1
2
0
2
0
0
0
1
2
0
0
2
1
0
0
0
2
1
0
0
0
0
0
0
2
0
0
1
1
0
1
0
0
2
2
2
0
0
0
0
1
0
0
0
2
0
0
0
1
1
0
1
0
0
1
2
0
3
0
0
2
1
0
0
0
2
0
1
0
0
0
1
0
1
0
0
1
0
1
0
1
0
2
0
0
1
0
0
2
1
0
0
0
1
0
0
0
2
6
2
2
2
0
0
2
2
1
0
0
4
1
1
0
0
0
0
1
0
0
0
2
0
0
0
1
0
2
0
2
0
0
0
2
1
0
0
0
2
0
0
0
0
2
2
1
1
0
0
0
0
0
0
0
0
1
1
0
0
2
1
1
0
0
2
1
0
0
0
0
1
0
0
2
2
0
0
0
0
1
1
0
2
0
1
0
0
1
1
0
0
0
2
0
0
1
1
0
0
0
1
1
0
0
0
0
0
3
0
0
0
0
0
0
6
0
2
1
2
0
0
0
1
0
0
6
1
0
0
1
0
1
0
0
1
1
0
2
1
2
0
2
1
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
2
1
3
0
0
0
4
2
2
0
2
1
0
2
2
0
0
1
0
1
0
0
0
0
0
1
0
2
1
1
2
0
0
0
2
2
1
3
1
0
2
2
0
0
0
0
1
2
1
0
0
2
0
2
0
0
0
0
2
1
1
0
2
0
0
0
0
1
2
2
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
2
2
0
0
1
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
1
1
1
0
2
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
2
1
0
1
3
0
3
0
0
0
1
1
1
2
1
2
1
2
0
1
1
0
0
0
1
0
2
2
0
0
2
0
2
0
0
0
0
0
2
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
2
2
0
2
1
0
0
2
1
2
1
0
3
2
0
0
0
2
1
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
2
1
0
0
0
2
0
0
0
2
0
0
0
1
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
2
3
0
0
3
1
1
0
2
1
0
0
3
0
2
0
0
0
2
0
0
2
1
0
0
0
0
0
1
0
1
0
0
2
1
0
1
1
1
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
1
0
0
1
0
1
2
0
0
0
0
1
0
0
2
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
3
2
3
0
3
1
0
1
2
1
0
0
0
0
0
0
0
3
0
2
0
1
2
2
0
0
1
2
0
0
0
0
2
1
2
1
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
2
0
0
2
2
1
0
1
0
0
1
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
2
2
4
0
0
0
0
0
0
0
0
0
0
0
1
6
0
0
2
0
0
2
0
2
0
0
2
0
2
0
0
0
0
0
0
2
0
0
3
2
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
2
2
0
0
0
0
0
0
0
0
0
1
0
0
2
1
1
0
2
0
1
0
0
1
0
2
1
1
0
0
2
0
2
3
0
0
0
1
0
0
1
0
1
0
0
3
2
0
0
1
1
1
1
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
1
1
0
0
2
2
2
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
2
1
0
2
0
2
0
0
1
0
0
2
0
2
0
0
0
4
0
0
2
0
1
1
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
2
0
0
0
2
0
0
1
0
0
1
0
0
1
0
2
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
2
2
0
1
0
0
1
0
0
2
0
0
0
2
0
1
0
0
0
3
2
0
1
0
2
1
0
1
0
0
0
0
2
3
3
0
1
0
0
0
2
0
1
0
2
2
0
0
1
0
0
0
0
1
0
2
0
0
0
0
1
0
0
2
0
1
2
0
0
2
1
0
1
1
0
2
1
1
0
0
2
0
0
0
2
0
1
2
1
2
0
2
0
0
0
1
0
0
0
1
0
2
1
0
0
2
0
0
0
0
0
1
0
1
2
0
0
0
0
1
0
2
0
4
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
1
0
0
0
0
2
0
1
0
1
1
2
0
0
0
2
0
2
1
0
2
0
0
0
0
0
2
1
0
1
1
2
0
0
1
1
0
1
1
0
0
0
1
0
2
0
0
0
0
2
1
0
0
0
0
0
0
1
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
1
1
1
0
2
0
0
0
2
3
1
0
1
1
0
1
0
0
0
0
0
1
0
0
0
2
1
0
0
0
2
0
1
0
0
3
0
0
0
1
0
1
0
0
0
1
1
0
0
1
1
1
0
3
0
2
0
2
0
2
0
0
1
0
0
0
0
2
1
1
1
0
0
0
1
0
2
0
0
0
1
0
1
2
1
0
0
1
0
0
0
0
1
1
2
1
1
0
0
1
0
0
0
0
0
0
0
3
1
0
1
0
0
0
0
1
2
0
0
0
1
1
0
0
0
1
0
0
0
2
1
3
0
7
0
1
1
1
0
1
1
0
0
0
0
0
0
3
0
3
0
0
0
2
0
1
0
2
0
0
1
0
0
0
1
1
2
0
0
1
0
0
0
1
2
1
0
0
0
3
3
0
2
3
0
0
1
0
0
0
0
0
0
0
0
2
1
2
1
1
0
0
0
3
0
2
0
0
1
0
2
1
0
1
0
0
0
2
4
1
0
0
1
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
1
0
0
2
1
2
2
1
3
0
0
0
1
0
0
0
1
1
2
0
1
1
0
1
0
0
0
0
0
1
2
0
0
0
0
0
1
2
6
2
0
0
0
0
0
1
0
0
3
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
1
0
0
0
1
1
0
0
0
2
0
0
0
1
2
0
0
0
2
2
0
1
0
0
1
0
0
1
2
0
2
0
0
0
1
0
0
0
0
1
1
0
0
0
2
0
2
0
1
0
0
0
1
1
0
2
2
2
0
0
2
0
2
0
0
0
0
0
3
0
2
0
0
0
1
0
0
0
1
0
0
0
2
2
2
0
0
0
1
1
0
2
0
0
2
0
0
0
1
0
0
2
1
0
0
3
0
2
2
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
2
0
0
1
1
1
1
0
0
1
2
2
0
0
0
2
2
2
0
0
0
0
0
0
1
0
4
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
3
0
0
0
0
2
0
0
1
1
1
0
0
2
0
0
0
2
1
0
2
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
1
1
1
0
2
0
0
0
2
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
2
2
2
1
2
1
0
2
0
0
0
1
0
0
1
1
0
0
0
0
4
1
0
0
1
0
0
0
0
0
2
1
0
0
0
0
1
2
0
0
0
2
0
2
1
0
5
0
1
1
0
2
0
2
2
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
2
1
0
1
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
2
0
1
0
2
0
2
3
0
1
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
1
8
0
0
0
0
0
2
0
3
0
1
0
0
2
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
1
1
1
0
1
0
0
0
0
3
1
0
0
2
0
0
2
1
0
0
1
0
1
0
1
0
2
0
2
1
0
0
0
0
0
0
1
0
0
3
0
0
1
0
0
1
0
0
1
0
1
0
2
0
0
1
0
0
0
0
2
0
0
0
0
2
0
1
0
0
1
2
0
2
0
0
2
0
2
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
1
1
0
2
0
1
0
0
0
1
0
0
0
1
2
0
0
0
1
0
2
0
0
2
0
0
0
1
0
0
0
1
2
0
0
0
0
0
6
2
2
0
0
0
0
0
0
0
0
1
0
1
1
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
1
0
0
0
2
2
3
0
2
0
0
0
1
0
1
0
0
0
2
1
1
0
0
1
2
1
0
0
0
2
2
0
0
0
0
3
0
1
0
0
1
0
2
0
1
2
1
7
0
0
1
0
0
0
0
0
2
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
2
2
2
2
1
2
1
2
0
0
0
0
0
1
1
0
0
0
1
0
0
2
3
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
1
0
2
0
0
0
3
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
2
2
0
1
0
1
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
3
1
2
0
2
2
0
0
3
0
0
1
0
0
0
0
0
0
1
3
0
1
0
0
2
0
3
0
0
0
2
0
1
0
0
0
0
1
1
0
1
2
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
1
2
2
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
2
0
2
0
0
0
0
2
0
1
2
0
0
1
0
1
3
0
0
0
2
1
0
0
0
1
0
0
0
1
2
2
0
0
1
0
0
0
1
1
1
0
0
0
1
0
2
0
0
0
1
1
0
0
0
0
2
2
0
2
0
0
4
2
0
0
2
0
0
2
1
0
0
0
0
0
5
2
0
1
0
0
0
2
0
1
0
0
2
0
1
1
0
4
0
0
2
2
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
2
1
1
1
0
0
1
0
0
2
0
0
0
2
0
0
1
0
0
0
0
2
1
0
1
2
1
0
0
0
0
2
1
0
0
0
0
0
2
0
0
2
0
2
0
0
0
1
0
1
0
0
0
0
14
0
2
0
2
2
0
0
2
0
3
2
0
0
0
0
0
0
0
1
1
0
2
0
0
0
7
0
1
2
0
0
0
1
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
2
0
0
2
1
2
0
0
0
4
2
0
2
2
2
0
0
1
1
1
0
0
0
2
0
0
0
0
2
2
2
0
0
2
1
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
3
0
0
0
1
1
2
2
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
2
1
0
0
2
0
0
0
0
0
2
0
1
1
0
0
0
1
0
1
0
1
0
0
2
2
0
0
1
0
0
0
2
0
0
0
0
2
0
1
0
1
2
0
0
2
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
2
2
0
0
1
2
1
0
0
1
2
2
0
1
0
1
0
1
1
1
2
0
1
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
2
1
2
0
0
0
1
2
0
2
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
1
0
2
2
1
0
0
0
0
0
0
0
1
2
1
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
2
0
1
1
1
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
1
2
1
0
0
2
0
2
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
1
0
0
2
2
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
2
1
0
1
2
0
0
0
0
2
0
0
0
1
2
0
0
2
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
3
1
0
2
1
1
0
1
2
0
0
0
0
2
0
0
2
1
1
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
2
2
0
0
2
1
0
1
0
0
1
2
1
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
2
2
1
2
0
1
0
2
0
0
0
0
1
0
2
1
2
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
2
0
1
2
0
0
2
2
1
0
0
0
0
1
0
2
0
0
1
0
1
0
0
2
0
0
0
0
2
0
2
1
0
0
0
0
0
0
2
0
2
2
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
2
0
1
1
1
0
0
0
0
2
2
0
0
1
0
1
0
0
0
0
2
0
2
0
0
23
1
2
0
1
0
1
2
0
2
0
1
0
0
0
1
0
0
0
0
2
1
0
3
0
1
1
0
2
2
0
0
1
1
0
0
2
0
0
0
0
0
0
2
1
0
0
0
1
1
1
0
0
1
1
1
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
2
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
2
2
2
3
1
2
0
0
0
3
0
0
0
0
0
0
5
1
0
0
1
2
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
2
2
2
0
0
1
1
0
0
0
1
0
0
0
0
4
0
0
1
0
2
1
2
2
0
0
0
0
0
1
3
1
5
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
1
3
0
1
0
1
0
1
0
0
0
2
1
2
1
0
0
0
2
0
2
0
0
1
3
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
2
0
0
3
0
0
0
1
0
1
0
0
0
0
0
2
1
0
0
1
1
0
1
1
0
0
0
2
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
2
0
1
0
0
1
0
1
2
0
0
2
4
2
0
0
2
0
0
0
2
2
0
3
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
2
0
0
2
0
2
0
1
0
1
0
1
0
0
2
0
1
1
2
0
0
0
0
1
2
0
2
2
0
0
2
0
0
2
1
2
0
1
0
0
0
0
0
0
0
2
1
0
2
0
0
2
0
2
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
4
0
1
0
0
2
1
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
3
0
1
0
0
2
0
0
1
0
2
0
0
0
0
0
1
1
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
2
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
1
2
2
0
1
2
5
0
3
0
2
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
2
2
0
0
1
0
0
0
0
0
1
1
1
2
0
1
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
2
0
1
0
0
0
0
0
0
0
0
3
0
0
1
0
2
3
0
0
1
0
0
0
1
0
0
1
0
0
2
0
1
0
0
0
2
0
0
2
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
1
1
0
0
0
2
1
0
1
2
0
0
0
2
0
0
1
0
0
1
0
2
3
0
2
0
0
3
2
0
2
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
2
0
2
0
0
4
2
0
1
0
0
3
0
3
0
1
0
0
2
2
2
0
0
1
1
0
0
1
1
2
1
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
1
2
2
0
0
0
0
0
1
1
0
0
1
0
0
0
2
0
0
1
1
1
1
0
0
0
0
1
2
0
0
0
2
0
2
0
0
0
1
0
0
0
1
0
2
2
2
1
0
0
0
0
0
0
0
2
1
1
2
0
0
0
0
0
2
0
0
0
1
0
0
1
0
2
2
0
1
1
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
1
1
0
0
0
2
0
0
0
2
0
1
4
1
2
0
0
0
0
0
2
1
1
2
0
0
0
1
0
0
0
2
2
0
1
0
2
0
0
0
1
3
0
1
1
1
2
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
2
0
1
2
0
0
0
0
3
0
0
0
0
1
1
0
0
0
2
0
0
2
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
2
0
2
0
0
2
0
0
3
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
2
1
1
1
0
2
0
2
0
0
0
0
1
0
0
0
0
2
0
0
1
1
3
1
1
0
0
0
0
2
1
2
1
0
0
2
1
0
0
1
0
0
2
0
0
2
1
1
2
0
0
0
0
0
2
0
2
4
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
2
2
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
1
0
0
4
2
0
2
0
3
0
0
0
1
2
1
0
1
0
0
0
0
1
1
2
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
3
1
1
0
0
2
0
0
0
2
0
1
2
0
2
0
2
0
1
0
0
1
1
4
0
1
0
0
1
0
1
1
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
1
2
2
3
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
2
0
2
0
1
0
0
0
2
1
0
0
1
2
0
0
2
0
2
0
0
0
5
2
2
1
0
0
2
1
0
2
0
1
1
3
0
2
2
1
1
0
0
1
3
0
0
2
2
0
0
0
0
2
0
0
1
0
1
2
1
0
2
0
2
1
0
2
2
0
0
2
0
0
0
0
0
0
0
0
2
1
2
1
0
2
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
2
0
0
2
0
0
2
0
1
1
0
2
0
2
1
0
2
0
1
0
0
0
0
0
0
2
2
0
0
0
0
2
2
0
0
3
0
2
0
0
0
1
2
0
0
0
2
0
4
1
0
2
0
1
0
1
0
1
1
0
0
2
1
1
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
2
2
0
3
0
1
12
0
1
0
5
1
0
1
0
1
0
0
0
0
0
0
0
0
2
3
0
0
0
1
0
2
1
0
0
0
0
0
2
0
0
2
0
0
2
2
0
0
0
0
2
1
1
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
3
2
2
0
1
0
0
2
0
0
0
2
0
1
1
0
1
0
1
0
0
0
2
0
0
0
1
0
1
1
0
0
1
1
1
3
0
0
1
0
2
2
0
0
4
4
0
0
2
0
1
4
4
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
1
0
2
0
0
0
2
0
0
1
1
0
0
1
1
2
1
2
1
1
1
2
0
2
0
3
0
2
1
2
1
0
1
1
0
0
1
0
1
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
4
0
2
1
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
1
0
3
0
0
1
0
0
1
0
0
0
0
2
1
0
0
0
1
1
0
1
0
0
2
3
1
0
0
0
1
2
0
0
2
0
0
0
2
0
1
0
2
0
0
0
2
0
0
0
2
0
0
0
2
1
0
0
0
0
1
0
1
0
0
2
1
0
1
2
0
0
0
2
0
0
0
1
0
0
2
0
2
1
1
2
1
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
1
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
3
0
0
1
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
4
0
2
2
0
0
0
3
1
0
0
0
0
0
1
3
2
0
1
0
0
2
0
3
0
0
0
1
0
2
2
1
0
1
0
0
2
2
2
0
0
1
1
0
0
3
0
1
3
2
2
0
1
0
0
2
1
2
0
0
0
1
0
0
0
1
3
0
1
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
2
0
1
1
0
1
0
0
0
2
0
1
1
1
0
1
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
3
1
0
2
0
0
0
2
0
0
2
0
1
0
0
3
0
0
2
0
0
0
0
0
1
0
2
0
0
0
1
0
2
0
2
0
2
2
0
2
1
0
5
0
1
1
1
0
1
1
0
0
0
2
0
0
0
2
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
1
1
0
2
2
0
0
0
0
0
1
0
0
1
0
0
1
0
1
2
2
0
0
1
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
2
2
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
2
0
1
2
1
0
0
1
0
0
2
1
2
1
2
0
0
0
0
0
0
2
1
1
0
0
2
4
2
1
0
0
1
0
1
2
2
2
0
2
0
1
0
2
0
0
2
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
3
1
0
0
2
0
2
0
0
0
0
2
3
0
1
0
0
1
0
1
0
0
0
2
2
2
0
0
1
1
1
2
0
0
1
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
1
2
2
0
0
0
1
0
3
0
0
0
0
2
0
0
1
2
0
0
0
1
0
2
1
1
2
0
1
2
1
2
0
1
1
0
2
0
0
0
0
0
2
2
2
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
3
2
2
0
0
1
0
0
2
0
2
0
2
0
1
0
1
0
0
0
0
2
1
2
0
0
2
0
0
0
0
0
0
0
0
1
2
1
0
1
2
2
0
0
0
2
0
1
0
1
1
0
1
1
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
2
1
0
2
0
1
1
1
2
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
2
0
0
1
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
2
1
0
1
2
1
0
0
1
2
0
0
0
0
0
0
2
0
0
2
1
0
1
0
0
0
0
1
0
1
0
0
0
7
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
2
3
0
0
0
0
2
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
2
2
0
1
1
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
1
1
1
2
0
1
0
0
0
1
0
1
1
0
2
0
0
0
0
1
1
1
0
0
3
0
1
1
1
1
0
0
0
0
0
1
0
0
0
2
0
1
0
4
1
0
0
2
0
0
0
1
0
0
1
1
1
0
0
0
0
0
2
0
0
0
2
0
1
0
1
0
0
1
0
0
0
2
1
0
1
0
3
0
0
0
1
2
0
1
2
2
1
0
0
0
2
1
0
2
1
1
0
0
0
1
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
4
0
1
0
2
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
2
0
3
0
1
0
0
0
1
0
0
0
0
0
0
1
0
3
1
2
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
2
0
1
0
0
0
2
1
0
0
1
2
0
0
0
0
1
3
0
0
1
0
0
1
3
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
2
1
0
0
2
0
0
1
1
2
1
0
2
0
0
0
0
0
2
0
0
1
0
3
1
0
0
2
0
0
0
0
0
0
10
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
3
0
0
0
1
0
0
0
0
3
0
0
2
0
0
1
2
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
2
1
0
0
0
4
0
0
2
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
2
0
1
0
2
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
2
0
0
2
0
2
0
2
0
1
0
0
1
0
0
0
0
1
0
2
3
0
0
0
1
0
2
0
0
1
0
0
0
0
2
1
0
1
1
2
0
0
1
4
2
0
0
1
0
2
0
0
2
2
1
0
0
2
1
0
0
0
1
0
0
0
0
1
1
0
2
0
1
2
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
1
2
0
0
5
2
2
0
0
2
2
0
0
0
2
0
1
0
0
2
0
0
1
0
0
0
2
0
4
2
2
2
2
0
0
0
2
0
2
0
0
0
0
2
2
0
2
0
1
0
1
2
0
1
3
2
1
0
0
2
0
0
0
2
0
0
2
0
1
1
0
0
0
0
0
2
2
0
2
0
1
0
0
0
2
1
1
2
2
0
1
2
0
0
0
2
0
2
1
1
2
0
0
1
1
0
0
0
0
0
2
2
0
0
2
3
1
0
0
2
0
1
0
2
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
1
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
2
1
0
0
0
3
0
0
1
2
0
1
0
0
0
0
0
0
0
1
2
2
1
1
0
0
2
1
1
1
0
2
0
0
0
0
1
0
1
0
0
2
1
1
0
0
1
2
0
0
1
0
0
0
0
2
0
0
0
1
2
1
0
0
1
2
0
0
0
1
0
0
3
0
0
0
0
2
1
0
0
0
0
4
0
0
0
0
2
2
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
1
0
1
0
2
0
1
2
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
2
2
0
1
0
0
2
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
3
0
0
1
0
1
0
0
1
0
1
1
0
0
0
2
2
3
0
0
0
0
0
0
2
0
1
0
0
0
1
0
2
2
1
1
3
1
0
0
0
2
0
2
0
1
2
1
0
0
1
2
2
1
1
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
1
0
1
0
2
1
2
0
0
1
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
2
2
0
3
1
0
1
2
0
0
0
0
2
4
0
0
0
2
0
1
1
0
1
0
1
0
0
2
0
1
0
1
0
0
1
0
1
0
1
1
0
2
1
0
1
0
0
2
0
1
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
2
0
2
0
1
1
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
1
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
1
1
1
2
2
0
0
0
2
2
0
0
0
0
1
0
0
0
2
0
0
1
1
2
0
3
0
0
2
4
0
0
2
2
0
1
1
2
1
0
2
0
0
0
0
2
2
0
0
0
0
2
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
2
0
2
1
0
0
0
0
0
2
0
1
0
0
0
2
2
2
1
0
1
0
0
0
0
1
0
2
0
0
0
0
1
1
0
1
2
0
0
3
1
0
0
0
1
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
2
1
0
2
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
1
0
1
2
0
1
0
1
1
0
3
0
1
0
2
0
2
0
0
3
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
2
1
0
0
2
0
0
0
0
3
1
6
0
2
0
1
0
2
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
2
0
0
0
2
0
3
1
0
3
0
0
1
3
0
0
0
2
0
0
2
0
0
0
0
2
0
0
1
2
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
1
2
2
0
4
1
0
1
1
0
0
2
0
0
0
2
1
2
0
0
0
1
1
2
2
0
0
1
0
0
1
2
0
0
2
2
0
0
0
0
0
0
1
0
2
4
0
1
2
0
0
1
0
0
1
3
0
1
0
0
2
1
1
0
1
0
1
0
2
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
2
1
0
1
0
0
0
0
0
2
1
2
0
0
0
2
2
1
0
0
1
0
2
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
2
0
0
2
0
2
0
0
0
1
0
1
1
1
0
2
1
0
1
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
1
0
2
1
0
2
2
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
1
0
2
0
0
0
5
1
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
1
1
1
0
0
0
1
0
0
1
0
0
2
2
1
2
0
1
0
0
1
0
0
0
2
2
0
0
1
2
2
0
1
0
0
0
0
2
0
2
1
0
1
0
0
2
0
2
3
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
1
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
3
1
3
0
1
0
0
1
2
0
2
0
0
0
0
0
1
2
0
0
0
2
3
1
0
0
0
2
1
0
2
0
0
1
1
1
0
0
1
0
0
0
2
2
2
0
0
0
0
0
0
1
0
0
2
0
1
0
1
3
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
1
2
0
2
0
0
0
0
3
1
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
1
1
1
0
0
0
2
1
0
1
0
0
1
0
0
0
2
0
0
1
0
1
1
4
0
0
2
0
2
0
1
0
0
0
0
0
3
1
1
0
1
0
0
0
0
1
0
2
0
0
1
1
2
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
1
0
0
0
0
2
0
1
2
0
0
0
2
7
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
1
2
0
0
0
0
1
0
1
0
1
2
0
0
0
1
0
2
2
0
0
0
4
2
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
2
2
0
1
0
1
1
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
2
2
1
2
0
0
0
1
0
1
2
1
0
0
2
0
0
0
0
0
0
2
0
1
2
1
0
1
2
0
5
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
6
0
1
0
3
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
1
1
0
0
0
2
2
0
2
0
0
2
2
2
0
2
1
0
0
1
0
0
1
0
0
2
1
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
3
2
0
1
1
0
3
0
0
0
0
0
1
0
2
1
5
0
0
1
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
1
2
0
2
0
0
0
0
1
0
1
0
0
3
1
0
1
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
2
1
0
2
1
0
0
1
0
0
2
2
0
6
1
0
0
0
2
1
2
0
2
2
1
1
0
2
1
0
1
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
2
1
1
0
0
0
1
5
0
0
0
0
2
0
0
0
2
0
2
1
1
2
0
0
0
1
2
1
0
0
0
1
0
0
0
0
1
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
2
2
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
2
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
1
1
0
1
0
0
0
0
2
3
2
1
1
0
3
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
2
2
2
0
0
2
0
1
0
1
0
1
0
0
1
4
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
2
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
2
2
0
1
2
0
2
2
0
0
2
1
2
1
0
0
0
2
1
0
2
2
0
0
1
0
1
0
0
1
0
2
0
2
0
1
0
2
0
0
0
2
0
2
0
1
0
0
0
1
2
0
0
0
0
0
1
1
1
0
0
0
2
0
2
0
2
2
0
0
1
1
2
0
0
0
2
0
0
0
1
1
0
0
0
0
2
0
1
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
2
0
1
0
0
4
2
0
0
2
0
0
1
0
2
1
0
1
0
2
0
0
0
3
0
1
0
0
0
1
0
0
2
2
2
0
0
0
2
0
0
0
1
2
0
0
2
0
0
2
2
0
0
0
0
1
2
0
0
2
0
1
0
1
0
1
0
1
0
2
2
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
1
1
1
0
0
0
0
0
10
0
1
0
0
2
0
0
2
2
1
1
1
0
2
1
0
0
2
0
2
0
1
0
1
0
0
2
1
1
0
0
1
0
1
2
0
0
0
0
1
0
0
0
2
1
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
2
1
1
1
0
0
0
0
2
0
1
0
1
1
0
0
0
0
1
0
0
1
0
0
2
0
2
2
1
0
0
1
2
0
0
0
0
2
3
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
2
0
1
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
2
0
2
0
2
0
1
0
2
0
2
0
0
0
1
0
0
0
0
0
1
0
2
0
2
0
0
2
2
2
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
2
0
0
0
0
0
2
1
2
0
0
1
1
1
3
0
0
0
1
0
0
2
0
0
0
2
0
0
0
1
0
0
1
2
1
2
2
0
0
0
1
0
1
0
0
1
0
0
2
2
0
0
1
0
0
0
0
5
3
0
1
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
2
2
0
2
2
0
0
2
1
0
2
1
0
0
0
0
0
3
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
2
0
2
0
0
3
2
1
0
2
0
1
0
0
3
0
0
1
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
1
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
1
1
3
0
0
0
0
0
0
0
2
0
0
0
1
2
0
1
4
0
1
0
3
0
1
0
0
0
0
0
2
2
0
2
0
0
0
1
0
0
0
0
2
0
2
0
0
3
0
0
0
0
0
0
1
0
0
3
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
1
0
0
1
0
1
2
0
2
2
0
0
0
1
2
1
0
2
0
2
2
0
0
2
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
1
3
2
0
1
0
0
2
1
1
0
0
2
0
0
2
4
0
0
0
0
2
1
0
0
0
0
0
0
1
1
0
1
0
2
0
0
0
4
0
0
4
1
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
2
0
0
0
0
1
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
1
1
0
0
1
0
1
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
2
1
0
0
0
1
0
0
0
0
0
2
2
0
3
1
0
0
2
2
3
0
0
3
2
0
0
1
0
0
0
0
2
0
1
0
0
2
0
2
0
2
0
0
0
2
0
0
2
2
0
0
1
0
0
0
1
0
0
2
1
0
0
1
0
2
0
0
1
2
0
0
0
0
0
2
0
2
0
2
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
3
0
2
0
0
1
1
0
3
0
0
0
0
0
0
1
0
1
0
1
0
0
2
0
1
1
0
1
1
0
0
0
1
2
1
0
0
0
2
2
2
1
3
0
2
1
1
0
1
0
8
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
3
0
0
1
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
2
0
0
2
0
0
0
1
0
0
1
0
1
0
0
0
0
2
0
0
5
0
1
0
0
0
0
1
0
0
2
1
2
1
0
1
0
1
1
0
0
0
1
1
0
1
0
0
4
0
0
2
2
0
0
0
1
0
0
0
0
0
1
0
2
0
2
0
3
0
1
0
0
1
0
0
0
0
0
0
1
2
0
0
1
1
1
0
0
4
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
1
0
2
2
3
1
2
1
1
2
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
2
1
0
2
0
0
2
0
2
2
1
0
1
0
0
0
7
0
1
0
0
0
0
0
0
3
1
0
0
0
0
2
1
0
0
2
0
0
0
1
0
0
2
2
1
2
1
0
0
1
0
1
1
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
2
0
0
2
1
1
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
2
3
1
2
2
2
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
1
0
3
0
0
0
2
0
1
0
2
0
0
2
1
0
0
2
1
0
1
2
2
0
1
3
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
2
2
1
0
0
0
0
2
1
0
2
1
1
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
2
0
0
0
2
1
0
2
0
0
1
0
0
2
0
2
0
0
0
2
0
2
0
0
0
0
0
1
1
1
0
0
0
1
0
2
2
1
0
2
0
2
0
0
1
0
0
0
0
0
0
2
0
0
2
1
0
0
1
1
0
0
4
0
1
0
0
2
3
0
0
0
0
1
0
2
2
0
0
0
0
2
2
1
0
0
1
0
0
4
2
2
0
0
0
1
0
2
2
0
1
1
2
0
1
0
2
1
0
0
1
0
0
4
0
2
2
0
2
0
1
0
0
1
2
0
0
0
0
0
0
1
2
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
2
0
2
2
1
1
1
2
0
2
2
1
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
1
0
0
2
0
0
1
0
2
0
2
1
0
0
2
0
0
0
1
2
2
2
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
3
0
0
0
2
0
0
0
0
0
1
0
0
2
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
1
0
0
0
0
2
2
0
0
1
2
0
0
0
2
0
1
0
0
0
1
0
1
0
0
1
2
0
3
0
0
1
2
2
0
0
0
1
0
0
0
1
0
0
0
0
2
1
0
0
1
0
0
0
0
1
1
2
0
1
1
0
1
0
0
1
1
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
1
0
4
1
0
0
0
1
0
2
1
0
0
2
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
1
0
2
0
0
1
1
1
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
1
1
0
0
2
1
1
0
0
0
0
9
0
2
0
0
1
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
1
1
1
1
0
1
0
0
0
1
0
0
0
1
0
2
1
2
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
1
3
1
0
0
0
1
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
1
2
0
0
2
2
1
1
0
2
0
1
0
0
1
2
1
0
1
2
1
2
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
2
0
0
2
0
0
2
0
0
0
4
0
0
0
0
4
0
1
0
2
0
2
0
1
1
0
2
0
1
0
1
0
0
0
0
2
0
0
1
3
0
1
0
1
2
2
1
1
2
0
2
0
1
0
1
0
1
0
2
1
1
0
2
2
0
0
0
0
0
1
0
2
0
1
2
0
0
0
0
0
1
2
1
0
0
0
0
3
1
1
0
0
0
0
0
0
2
0
2
0
0
1
0
0
2
0
0
0
2
0
3
2
1
1
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
2
0
0
0
0
0
2
0
0
1
0
2
1
0
0
0
2
0
5
0
1
1
0
0
0
0
0
0
0
2
0
0
1
0
0
2
3
0
0
0
0
0
0
2
3
1
0
0
0
1
2
3
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
1
0
0
0
2
0
1
2
4
0
2
0
2
0
0
0
2
0
0
0
0
1
0
2
0
0
2
2
0
0
0
0
0
0
2
2
2
0
0
1
0
1
0
0
0
3
1
1
2
0
1
0
2
0
1
1
0
0
1
2
2
2
2
0
0
0
0
0
1
1
0
0
0
1
0
0
2
0
0
0
2
1
0
0
2
0
0
0
0
0
1
2
0
0
0
1
0
2
0
2
0
0
0
2
0
0
2
0
0
2
0
1
0
0
2
0
2
2
2
0
0
2
0
0
0
0
0
0
2
0
2
2
1
0
2
0
1
2
0
0
0
0
0
0
1
0
0
0
1
0
2
0
1
0
0
0
2
0
4
2
0
0
0
0
0
0
2
1
0
0
2
0
2
2
0
0
2
0
1
0
2
0
0
1
0
2
1
0
0
0
0
0
0
1
0
0
1
0
1
1
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
2
1
1
0
0
1
0
1
0
2
0
1
2
0
0
0
0
2
1
0
0
1
0
1
0
0
0
1
0
0
1
1
2
0
3
0
0
0
0
1
0
0
2
2
0
1
0
0
2
0
1
1
0
0
0
0
1
1
0
1
0
2
0
0
0
1
0
1
3
0
0
0
0
2
2
0
0
2
1
0
1
0
0
0
0
1
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
2
1
0
0
4
1
0
8
0
0
0
2
0
1
1
0
1
1
0
1
0
1
0
0
0
1
0
0
1
2
0
0
2
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
2
0
0
1
0
1
0
2
0
0
2
0
1
1
0
1
0
0
1
2
1
0
0
2
1
0
0
0
2
0
0
0
1
2
0
1
0
0
0
2
0
1
0
1
0
0
0
0
3
0
2
0
0
0
0
2
0
0
1
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
6
3
0
2
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
2
2
0
3
0
1
1
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
1
3
0
1
4
0
0
1
0
0
0
0
0
1
0
2
0
0
1
1
0
1
1
0
0
1
0
0
0
0
0
0
3
0
0
0
1
0
0
0
2
0
0
2
0
2
0
1
0
0
0
0
0
2
1
0
0
0
0
1
2
0
0
1
2
0
0
0
0
2
2
0
2
0
0
0
1
1
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
1
1
0
0
2
0
0
0
2
0
0
0
1
1
3
0
2
1
1
0
2
0
4
0
1
0
0
0
1
1
0
1
1
0
1
2
0
0
0
0
0
0
0
0
1
1
0
0
2
0
1
1
0
0
0
2
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
2
0
2
0
0
2
0
0
0
1
0
2
4
0
2
2
1
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
2
2
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
1
0
1
1
1
0
1
0
1
2
0
2
4
0
2
2
0
0
0
0
2
0
0
0
0
0
2
0
0
2
1
2
0
0
0
0
0
0
1
0
1
2
3
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
1
1
2
0
0
0
2
2
0
0
0
4
2
0
0
0
0
2
0
0
0
0
1
1
0
1
3
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
2
2
1
0
0
0
0
1
0
0
0
0
0
0
2
1
1
1
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
2
0
0
0
3
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
6
1
1
0
0
2
1
0
0
0
2
1
1
2
0
1
0
0
0
1
2
0
0
0
0
2
2
1
0
1
0
0
0
0
1
2
0
1
0
0
1
2
3
0
0
0
1
0
0
0
0
1
0
0
2
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
1
1
0
0
2
2
0
0
0
0
0
2
2
0
0
2
1
0
1
0
1
1
1
1
0
3
0
2
2
0
1
0
1
1
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
1
1
0
2
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
2
2
0
0
0
0
1
0
0
0
3
3
0
2
0
0
0
0
2
2
0
1
0
0
0
0
2
0
0
2
2
3
0
0
0
0
0
2
2
1
2
0
2
0
0
1
2
1
0
0
1
0
2
1
2
0
5
1
0
2
0
0
0
0
0
1
0
1
0
0
2
0
2
1
0
2
0
0
2
0
1
2
2
0
0
0
0
2
0
2
0
0
1
0
0
1
0
0
0
2
1
0
2
0
0
1
2
1
1
0
0
0
0
1
0
1
1
1
2
1
1
1
2
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
2
1
1
1
1
1
0
0
0
1
2
0
1
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
1
1
0
0
2
2
0
1
0
2
0
0
0
1
0
0
2
2
2
1
0
2
0
0
0
1
1
0
0
2
1
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
2
1
0
0
0
2
0
1
0
0
1
1
0
1
0
1
0
2
0
1
1
0
0
0
2
0
1
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
4
0
1
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
1
0
0
0
0
0
0
2
2
0
0
0
0
3
0
0
1
0
3
1
0
0
0
2
0
1
0
0
0
2
0
0
2
1
1
0
1
0
0
0
1
0
0
0
0
2
1
1
0
0
0
1
0
0
0
0
0
2
0
0
2
2
2
2
0
0
0
0
0
2
1
2
1
0
0
1
1
0
0
1
0
0
2
0
1
1
0
1
0
0
0
0
0
0
1
0
1
1
0
1
1
0
0
0
1
0
0
2
2
2
0
2
2
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
3
1
0
0
0
0
0
1
0
2
2
1
2
0
2
0
2
1
0
0
0
0
2
2
0
1
0
1
1
0
2
0
1
2
0
2
0
0
2
2
1
0
2
0
2
0
0
1
2
0
0
0
0
0
1
0
0
0
3
2
2
0
0
0
0
1
2
1
0
0
0
0
0
1
0
1
0
0
1
1
0
1
0
0
2
0
0
0
1
0
0
0
0
0
1
2
0
0
2
3
0
0
0
1
0
1
2
2
0
0
0
3
2
2
0
1
0
0
0
0
0
0
2
0
0
0
1
0
2
1
0
1
0
0
0
0
0
0
3
2
0
0
0
0
0
6
0
0
0
0
1
1
0
0
0
1
0
2
2
0
3
1
0
0
5
1
0
3
0
0
2
1
1
0
1
1
0
0
1
1
0
0
0
0
0
0
0
2
2
0
0
2
0
2
3
1
0
0
1
0
2
0
0
0
2
1
2
0
2
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
2
2
1
0
0
0
1
0
1
2
0
0
0
2
1
0
1
2
0
0
0
0
1
0
0
1
1
0
2
2
0
2
0
1
0
1
0
0
0
1
1
0
0
1
1
2
1
0
2
0
2
2
1
2
0
0
0
0
0
2
3
1
1
2
0
1
0
1
1
2
0
2
5
0
0
1
0
0
2
0
0
0
0
0
1
1
0
0
2
2
0
2
1
2
1
0
2
2
0
0
0
3
1
0
0
1
0
0
1
1
2
0
1
0
2
0
0
0
1
1
0
1
0
2
0
1
1
2
0
0
0
0
0
2
2
0
1
0
0
2
1
2
0
0
0
2
0
0
1
2
0
2
1
0
0
0
0
2
0
0
0
0
2
0
2
0
0
1
1
0
0
0
0
1
4
0
0
2
0
0
0
0
2
0
2
0
0
0
2
0
0
0
1
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
3
0
2
0
0
2
0
2
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
2
0
2
0
1
1
0
0
0
0
2
0
1
0
1
0
2
1
0
0
2
0
0
0
2
0
2
0
2
0
0
0
0
0
0
2
0
2
0
1
0
0
1
0
0
2
1
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
1
1
0
1
2
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
3
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
2
1
0
4
0
1
0
0
0
1
0
0
1
1
0
2
0
0
0
0
1
0
0
5
0
2
2
0
5
0
0
1
1
2
0
0
0
0
1
0
0
0
2
1
0
0
0
1
0
0
1
0
2
0
0
1
1
0
1
1
0
1
0
0
2
1
0
0
0
2
2
2
3
0
0
0
0
0
0
0
1
0
0
2
0
1
1
0
1
0
3
0
2
0
1
0
0
0
0
0
2
0
0
0
2
2
0
2
0
1
0
2
6
2
0
0
1
0
2
1
2
2
0
0
0
0
1
0
0
0
2
0
1
2
0
0
0
0
2
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
1
1
0
0
2
1
0
0
0
0
0
2
0
0
2
0
0
0
1
3
0
0
3
0
2
0
2
0
0
0
2
0
2
1
0
1
0
0
0
2
0
0
0
0
0
1
2
1
1
0
0
2
0
0
1
2
0
1
0
2
0
1
2
1
0
0
2
1
2
0
0
0
0
0
2
2
0
0
1
3
2
2
0
1
1
3
0
1
0
2
0
0
1
0
0
0
2
2
0
0
0
2
3
0
0
1
1
0
0
0
0
2
0
2
0
2
0
0
0
0
0
2
0
2
0
0
0
1
0
1
0
0
0
0
0
3
0
2
0
0
0
2
0
0
0
0
0
0
2
0
1
2
0
0
3
0
0
0
0
2
0
0
2
0
0
0
1
0
0
2
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
2
0
0
1
2
0
0
2
0
1
0
0
0
2
2
0
1
1
3
0
1
0
0
0
0
0
0
0
2
0
2
0
1
1
0
0
2
1
2
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
2
2
0
1
0
2
0
0
2
0
0
1
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
1
2
1
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
3
1
0
1
1
2
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
1
4
0
1
1
1
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
4
1
0
2
2
0
1
0
0
2
2
1
2
0
1
1
0
0
0
1
1
2
0
0
0
0
0
0
0
0
2
2
8
7
0
2
2
1
6
0
1
1
2
0
2
0
0
0
1
0
0
2
0
1
3
0
0
2
1
0
2
2
1
0
0
0
2
1
2
1
0
0
0
1
0
1
0
2
1
2
0
1
3
2
0
1
0
1
1
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
2
1
0
0
0
1
2
2
0
0
0
1
2
0
0
2
0
1
0
0
0
1
0
3
0
2
0
0
1
0
3
0
2
0
1
0
2
0
0
1
0
0
3
0
0
0
3
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
2
0
3
0
0
0
2
0
0
0
0
0
1
0
1
0
1
1
1
2
0
1
1
1
0
0
0
2
0
2
0
0
0
1
1
0
1
1
1
0
0
0
1
0
2
0
0
0
2
1
2
2
1
0
0
0
1
2
0
1
0
0
2
2
2
0
0
2
2
0
10
0
2
0
0
1
0
0
0
1
0
0
0
1
0
1
2
0
0
3
1
1
1
0
0
0
2
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
3
0
0
0
2
0
2
0
0
2
2
2
0
2
2
1
0
1
0
2
0
2
0
2
0
2
0
3
0
0
0
0
0
2
0
2
1
0
2
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
1
1
2
1
1
0
0
0
0
0
0
0
2
0
0
1
1
1
1
0
2
0
0
2
1
0
1
0
1
0
1
0
0
0
0
2
2
0
0
0
0
0
2
2
1
0
0
2
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
2
1
0
0
0
0
1
2
0
1
0
0
0
0
2
2
0
0
3
2
1
0
0
1
0
1
2
0
1
0
3
2
0
0
0
0
2
1
2
0
0
0
2
0
2
0
2
0
0
1
0
1
1
0
0
0
2
1
0
2
0
1
0
0
1
0
2
0
0
0
0
2
2
0
1
0
0
0
2
0
0
0
0
0
0
2
2
2
0
1
0
2
1
1
1
0
0
1
0
1
1
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
1
1
0
0
1
0
3
2
1
0
1
0
2
0
1
0
0
0
0
1
0
0
0
1
0
2
1
0
0
0
2
0
0
0
0
1
1
1
1
0
0
0
2
0
0
0
1
0
2
2
0
1
2
0
2
0
0
0
0
2
0
2
2
0
0
0
0
0
2
2
0
0
0
0
1
0
2
0
1
0
0
2
0
1
2
0
0
1
1
1
1
0
2
1
0
0
0
0
1
0
0
0
1
0
1
1
1
2
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
2
0
1
0
1
0
0
0
2
2
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
2
0
0
1
1
2
0
0
0
0
0
2
0
2
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
2
0
3
0
1
0
1
2
0
0
0
1
0
3
0
0
0
0
2
0
2
0
0
0
0
2
2
0
1
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
1
0
2
1
0
1
0
1
0
1
0
0
2
0
0
2
2
2
0
0
0
0
0
0
2
0
0
3
0
0
2
0
0
0
0
0
0
0
1
2
0
2
1
0
0
2
0
0
1
2
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
1
0
0
0
2
0
2
0
0
0
1
0
2
2
0
0
6
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
1
0
0
1
0
0
2
2
2
0
2
0
0
1
0
0
1
2
2
0
0
0
0
0
0
0
1
0
0
0
0
4
0
1
0
0
1
0
0
2
0
1
0
0
0
2
2
0
1
1
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
5
0
2
0
0
0
1
2
1
0
0
1
0
2
0
0
0
0
0
1
2
1
2
3
1
0
0
2
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
2
1
0
0
1
0
2
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
1
2
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
2
2
2
1
0
0
0
1
0
1
0
0
2
0
0
2
2
0
0
0
1
0
0
0
0
4
1
0
0
2
0
2
0
0
2
1
0
0
0
0
1
0
2
1
2
1
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
3
0
0
2
1
2
0
3
0
2
0
0
2
0
2
0
0
2
0
0
1
1
0
0
0
2
0
0
0
0
0
2
0
0
3
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
1
2
2
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
1
2
1
1
0
0
2
0
0
0
2
0
0
0
2
0
2
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
1
1
1
0
0
0
0
0
2
1
0
0
2
0
0
1
0
0
0
1
1
1
2
0
0
0
2
0
2
1
0
0
1
0
0
0
1
0
1
0
0
0
0
3
0
2
0
0
0
0
1
0
0
0
0
1
2
2
0
3
0
1
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
2
0
0
1
2
0
0
2
0
0
0
0
0
1
2
1
0
0
0
0
0
2
0
1
0
0
0
1
0
2
1
0
0
2
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
1
1
0
0
0
0
0
2
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
1
2
1
2
0
1
0
2
0
0
0
0
0
3
0
0
0
0
0
1
2
1
0
0
0
0
0
2
2
0
1
2
0
0
1
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
2
0
0
2
2
1
3
0
0
1
0
0
0
2
0
1
0
0
0
0
0
2
2
0
1
1
0
2
0
0
2
1
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
3
2
1
0
0
0
2
3
0
0
0
0
1
0
1
0
0
0
2
1
0
0
0
0
0
0
0
2
0
1
2
0
0
0
1
0
0
0
0
2
1
0
0
1
0
2
2
2
0
0
0
3
0
0
0
0
3
0
2
0
1
0
0
0
0
1
1
0
3
1
2
0
2
0
0
0
0
1
0
0
0
0
3
0
1
2
1
0
0
2
2
2
0
1
2
0
1
0
0
0
0
0
1
2
0
0
0
0
0
1
3
0
1
4
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
1
2
0
2
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
3
0
0
0
2
1
1
2
0
0
2
2
3
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
2
0
1
0
0
0
1
1
1
2
2
0
0
2
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
1
0
2
1
1
0
0
0
0
0
0
0
0
2
1
0
4
1
1
1
0
0
1
1
0
2
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
3
0
2
2
0
0
0
0
0
2
2
0
2
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
1
1
0
2
0
0
0
0
1
0
0
2
0
0
0
0
1
1
1
0
0
0
1
0
9
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
1
9
1
0
0
0
0
0
0
0
1
0
0
0
7
0
2
0
1
2
0
2
2
0
0
0
2
2
0
0
0
2
0
2
0
0
3
0
1
0
1
2
0
0
1
1
0
0
1
0
2
0
0
2
1
0
1
0
0
0
0
0
0
0
2
0
2
4
1
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
3
0
1
1
0
0
2
0
0
0
3
0
1
2
1
0
1
0
2
0
2
1
0
2
0
1
1
1
0
0
0
1
2
0
0
0
1
1
0
0
1
0
0
0
1
2
0
2
0
0
0
0
1
2
0
1
0
2
0
0
0
2
1
1
2
2
0
0
1
0
0
0
0
0
1
1
2
0
0
0
0
1
0
2
0
1
0
0
2
2
0
0
0
0
0
2
0
0
0
0
4
1
0
0
2
0
0
2
2
1
1
0
2
1
1
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
3
0
1
0
1
0
1
0
2
1
0
0
0
3
2
0
1
0
0
1
2
0
0
0
1
0
0
1
0
1
0
1
2
2
0
0
0
0
0
2
1
0
0
2
0
1
1
4
0
2
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
4
1
2
0
0
0
0
0
0
0
1
1
2
0
0
1
0
0
0
0
0
1
1
1
2
2
0
2
0
0
0
2
2
0
1
1
0
0
0
0
1
0
2
0
2
0
0
1
2
2
1
0
0
0
0
0
0
2
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
1
0
0
1
2
0
0
1
2
1
1
4
1
2
1
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
2
1
0
0
1
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
1
2
2
0
1
2
1
0
0
1
0
0
2
0
1
0
0
1
1
0
2
1
0
0
3
0
0
0
1
1
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
1
2
0
1
0
1
0
0
0
1
1
0
0
1
0
1
1
0
0
0
0
1
2
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
1
2
2
1
0
0
2
0
0
2
1
0
0
2
1
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
2
1
0
2
2
2
0
0
0
2
2
0
1
0
0
0
2
0
1
0
0
0
1
0
0
1
0
2
1
0
2
0
1
1
0
2
0
0
1
0
10
1
0
8
0
0
0
1
0
1
0
0
0
0
2
1
0
0
0
0
0
2
1
0
2
0
0
2
2
0
0
0
0
2
0
0
3
1
2
0
2
0
0
1
1
0
0
2
2
0
1
0
0
1
0
0
0
0
1
0
1
1
0
2
0
1
0
0
3
0
0
1
0
0
1
0
1
1
0
0
2
0
0
0
0
0
5
1
2
0
2
0
2
1
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
2
2
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
3
0
2
1
2
0
0
0
0
2
0
0
0
0
0
0
3
0
0
1
1
0
0
0
0
0
0
0
1
2
2
3
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
2
0
1
0
1
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
4
1
1
2
0
2
0
0
0
2
0
0
0
0
1
9
0
2
0
1
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
2
0
2
3
0
1
1
0
0
0
1
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
2
2
1
0
0
0
2
0
2
2
0
1
0
2
0
0
1
2
0
0
1
1
1
0
0
3
2
0
0
0
2
1
2
0
0
2
0
0
0
0
0
1
0
3
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
1
2
0
0
2
2
0
1
2
0
1
1
0
2
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
2
1
1
0
1
2
2
0
0
0
1
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
1
2
0
0
1
0
0
0
2
3
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
2
0
0
0
1
0
2
1
0
3
0
1
0
2
0
1
0
0
1
0
0
0
0
0
2
1
1
1
1
1
1
2
1
0
0
2
1
2
0
1
3
0
0
0
0
0
1
2
0
0
2
0
1
0
2
0
0
0
0
1
0
1
1
1
0
2
1
1
0
0
1
2
0
0
3
0
1
2
0
0
0
1
0
0
0
0
2
0
0
3
0
0
0
1
2
0
2
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
2
1
0
0
1
2
0
0
2
1
0
0
0
2
0
0
1
0
0
1
0
2
0
2
2
2
0
2
2
1
0
1
1
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
3
0
0
1
1
0
1
1
0
0
0
1
1
1
0
1
0
0
1
0
0
1
2
2
0
0
0
0
1
0
0
0
0
2
0
1
2
0
0
0
2
0
0
0
0
1
0
0
1
2
0
0
2
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
2
2
0
0
0
0
3
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
2
0
2
0
0
2
0
0
0
2
0
2
0
0
0
0
2
0
0
2
0
2
0
1
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
1
0
0
2
2
0
0
0
2
0
2
0
0
0
0
0
0
0
2
1
0
3
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
2
1
2
0
0
1
0
0
0
0
1
0
3
1
0
1
2
0
2
0
2
0
0
2
0
0
3
0
4
0
0
3
0
0
1
1
2
0
2
2
0
2
0
0
0
0
2
0
0
2
1
0
0
1
0
1
0
0
2
2
1
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
2
0
0
0
2
1
2
0
0
1
0
0
3
0
0
0
2
0
1
0
0
2
1
0
0
0
2
0
0
2
2
3
0
0
0
0
2
0
0
0
2
0
0
0
1
2
0
0
0
0
1
2
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
3
0
0
3
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
8
0
0
0
0
1
0
0
0
1
0
0
0
3
0
0
2
0
2
0
1
0
0
1
0
1
1
2
2
0
0
1
0
0
1
0
0
2
0
1
2
2
1
0
4
0
0
0
1
1
2
0
0
0
0
2
0
1
0
0
0
0
2
2
0
2
0
0
2
0
2
0
0
0
0
3
2
0
0
0
1
1
0
0
0
0
0
1
1
0
0
1
0
0
0
1
3
0
0
2
0
0
0
0
1
3
0
1
0
0
0
0
0
0
1
0
1
0
0
0
2
0
2
0
2
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
2
2
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
3
0
0
0
0
2
1
0
0
0
0
0
1
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
2
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
1
1
0
1
0
3
0
0
2
2
0
1
2
1
1
1
0
2
0
0
0
1
0
0
1
1
2
1
0
2
1
0
1
0
0
1
0
1
0
0
0
0
2
2
0
0
1
3
1
1
1
0
0
1
2
0
0
0
0
2
0
2
2
0
0
0
1
2
6
0
0
1
0
0
0
0
0
0
2
2
0
1
3
0
2
0
0
0
2
0
0
0
0
2
1
0
0
0
1
0
0
2
0
2
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
2
1
0
1
2
2
1
0
0
0
0
0
0
0
0
0
1
0
1
0
3
0
1
0
2
0
1
2
0
1
0
0
1
0
2
0
2
2
0
1
3
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
2
1
1
0
0
0
1
0
0
0
0
0
1
0
0
3
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
3
2
0
0
0
0
0
1
2
0
2
2
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
2
1
1
0
0
0
1
3
0
1
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
1
2
0
0
0
2
1
1
4
0
1
2
0
0
0
1
0
0
2
0
0
3
1
1
1
0
0
1
0
0
1
1
0
1
0
1
2
0
2
0
0
0
2
1
0
2
0
2
2
2
2
0
0
0
1
2
0
0
0
1
1
1
1
0
1
1
2
0
0
0
0
0
0
3
0
2
0
0
6
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
3
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
1
0
3
1
0
1
0
1
0
1
0
2
0
1
0
0
1
1
0
0
0
0
1
0
2
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
1
0
0
0
2
0
0
0
2
2
0
1
0
2
3
1
0
0
0
2
0
1
0
2
0
0
0
1
0
0
0
0
1
0
2
2
1
2
2
0
2
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
2
0
2
1
2
1
0
0
0
1
2
0
1
0
0
0
0
2
0
1
2
1
1
1
0
0
0
1
1
0
0
1
1
0
0
1
1
0
0
1
0
1
0
1
0
0
2
0
1
0
0
2
1
2
1
0
0
2
2
0
1
0
0
0
2
1
0
0
0
0
1
0
0
1
2
0
0
0
1
2
1
0
0
2
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
1
3
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
2
0
0
1
0
0
0
0
0
1
2
0
0
0
2
0
0
1
1
0
0
2
1
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
1
0
0
2
2
2
0
1
1
2
0
2
3
0
0
0
0
0
0
2
0
1
2
0
4
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
1
2
1
0
2
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
2
1
0
2
0
0
0
0
2
0
0
0
1
1
0
0
0
0
1
1
1
0
2
0
0
1
0
0
2
2
1
2
0
1
3
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
1
2
0
0
0
0
0
2
0
0
2
2
0
1
1
0
1
2
2
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
2
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
2
0
2
0
0
0
0
0
0
0
1
0
3
1
0
2
0
0
2
2
0
2
1
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
1
1
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
1
0
0
2
0
0
0
0
1
0
1
0
2
0
0
1
0
0
0
2
2
0
1
0
0
0
0
2
0
0
0
0
2
3
0
0
1
0
2
0
0
0
2
1
0
2
0
0
0
0
1
0
0
2
2
1
0
2
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
1
0
1
0
2
0
3
0
1
0
0
0
0
0
0
0
2
2
2
0
2
0
0
3
0
0
0
1
0
0
1
0
0
0
2
3
1
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
2
0
0
0
2
0
2
2
0
0
0
0
0
0
2
2
0
0
0
1
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
2
0
2
0
0
2
2
1
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
1
0
0
2
0
1
2
0
0
0
0
0
1
1
0
0
0
2
2
2
1
1
1
2
0
1
0
0
1
0
0
0
1
2
0
0
0
0
1
0
0
1
1
2
0
0
2
1
0
0
1
2
0
0
0
1
1
0
0
1
9
1
1
1
0
1
0
0
0
2
0
0
0
0
1
0
2
0
0
1
2
1
0
0
3
1
0
0
1
0
0
0
0
2
2
1
0
0
0
2
2
0
0
1
1
2
0
0
0
0
0
0
1
3
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
2
0
0
1
0
0
0
0
0
1
1
1
1
1
0
0
1
1
1
1
2
0
0
1
2
0
0
1
0
0
1
0
2
0
0
1
0
2
0
0
1
0
0
0
1
1
0
2
3
0
0
0
0
0
4
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
3
2
2
1
1
0
1
0
0
0
0
2
2
0
1
2
0
3
1
0
0
0
0
0
0
1
2
0
1
0
1
0
0
0
0
2
1
0
2
0
0
4
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
1
2
0
1
1
0
0
0
1
1
1
0
0
1
0
2
0
0
0
0
0
0
1
0
1
0
2
0
2
1
2
0
0
1
0
2
0
1
0
1
1
0
0
0
0
0
0
2
1
2
4
0
0
0
0
1
1
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
2
1
0
1
1
0
0
0
1
2
0
1
0
2
1
0
0
2
0
0
0
0
0
0
0
0
2
1
1
1
0
0
1
0
0
1
2
1
1
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
2
0
2
0
3
0
0
0
2
1
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
2
2
2
2
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
1
1
1
2
1
0
1
0
0
1
2
0
2
0
0
0
0
0
0
0
2
3
0
0
1
1
0
2
1
0
0
1
3
0
0
1
0
2
2
1
0
0
0
0
2
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
3
0
0
1
0
0
1
3
1
0
0
0
0
4
0
0
3
2
0
0
0
0
2
0
0
0
3
0
0
1
0
0
1
1
0
0
2
1
0
1
1
0
0
1
0
0
1
2
0
2
0
0
1
0
1
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
2
2
1
0
2
0
0
0
0
0
0
1
0
0
0
1
0
1
0
2
0
0
0
0
2
2
2
0
0
2
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
3
1
0
0
2
0
0
2
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
1
0
0
2
0
0
0
1
0
0
2
0
1
0
1
0
2
1
1
1
1
0
0
1
1
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
2
2
0
0
0
0
0
0
1
0
1
1
1
0
0
2
2
1
0
3
1
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
2
3
0
0
0
0
0
0
0
2
2
0
0
2
1
1
1
2
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
3
0
1
1
1
0
2
0
1
1
0
0
0
0
0
2
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
4
2
0
0
0
2
0
1
0
6
0
1
0
0
0
0
1
0
0
1
2
0
1
0
1
0
2
2
0
0
1
1
0
1
0
1
2
0
1
0
1
0
0
0
0
0
1
1
0
0
1
2
2
0
0
1
0
0
0
0
0
0
1
1
0
0
2
0
1
0
0
0
2
1
1
0
1
0
0
0
0
0
0
2
0
2
1
1
1
2
0
2
0
0
0
0
0
0
2
1
0
2
0
1
0
0
2
0
1
2
2
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
1
1
0
2
2
6
0
2
0
0
0
2
0
1
0
0
2
0
0
1
2
1
0
2
0
0
0
0
1
0
0
2
0
1
2
1
0
1
0
2
2
0
0
0
0
1
3
0
0
0
0
1
2
1
0
0
0
0
1
0
1
2
2
0
0
3
0
1
0
0
0
0
0
3
2
0
0
0
0
0
2
0
1
0
0
1
1
0
1
0
2
2
0
0
0
0
0
0
0
3
1
1
0
1
0
0
2
1
1
3
0
0
2
0
0
0
0
1
2
0
0
0
1
1
0
0
1
0
2
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
2
0
1
1
0
0
1
0
0
0
0
0
0
0
1
2
0
1
1
0
0
2
2
0
0
0
0
0
2
0
1
0
1
0
1
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
1
0
1
1
0
2
0
1
1
0
0
0
2
0
0
0
2
1
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
2
0
0
1
1
1
0
0
2
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
1
1
2
0
1
0
3
0
1
1
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
2
0
1
0
1
0
2
1
1
0
0
1
1
0
1
0
0
0
0
0
2
0
1
0
0
0
2
0
1
0
2
1
0
0
0
0
0
0
0
3
3
0
0
2
0
0
1
0
0
2
0
0
1
2
4
0
2
0
0
1
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
2
2
0
1
0
2
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
2
1
1
0
0
0
0
1
2
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
2
1
1
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
2
2
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
3
0
1
0
0
0
0
2
0
2
1
2
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
2
0
2
0
0
0
0
1
0
1
2
0
0
1
1
2
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
1
1
0
2
0
2
0
0
2
0
2
2
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
1
0
0
3
0
0
0
2
1
2
1
0
0
1
0
0
2
2
0
0
0
0
2
3
1
0
0
0
1
0
0
0
0
1
2
0
0
0
0
1
0
0
2
0
1
0
1
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
2
1
2
0
2
0
2
2
1
0
0
0
1
0
2
0
0
2
0
2
0
2
1
1
0
2
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
2
0
0
2
2
0
0
0
0
2
0
1
1
1
0
0
0
1
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
2
0
1
2
0
0
0
1
0
0
1
0
0
1
0
1
1
0
0
0
3
0
0
0
2
1
2
0
0
3
0
2
0
0
0
0
1
0
2
0
0
0
0
2
1
0
1
0
0
1
2
1
0
0
0
0
2
0
0
0
3
0
0
1
0
0
0
0
0
1
1
0
2
0
2
0
0
2
0
1
0
0
1
0
0
0
0
0
1
0
2
1
0
0
0
0
1
2
0
1
0
1
0
0
0
0
1
0
2
0
0
2
1
0
1
2
0
0
2
1
0
0
0
0
0
2
1
0
0
1
0
0
0
0
2
0
2
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
2
1
0
0
2
2
0
0
0
0
0
1
0
2
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
3
1
1
2
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
1
1
0
0
1
2
0
1
1
1
0
0
1
2
0
1
1
0
1
0
0
1
0
1
1
0
1
2
1
0
1
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
2
1
0
0
2
2
0
0
2
0
2
2
1
0
0
1
0
2
0
2
0
1
0
1
1
0
0
0
0
0
2
0
1
1
0
0
0
0
1
0
0
0
0
1
0
2
2
0
0
0
2
0
0
1
0
2
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
2
0
0
0
1
0
0
1
1
2
0
0
0
2
2
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
1
0
0
2
0
0
1
0
0
1
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
2
0
0
2
1
0
0
0
0
0
0
2
1
2
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
2
2
0
1
0
3
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
2
0
0
1
0
0
2
0
1
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
1
1
1
0
0
2
0
1
0
2
0
2
2
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
1
2
0
0
0
2
0
1
0
0
0
1
1
2
1
2
0
0
0
1
0
2
1
4
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
2
1
2
2
1
0
2
0
0
2
0
2
0
0
0
0
0
2
2
2
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
1
0
2
0
2
2
0
0
3
0
0
0
0
0
1
1
1
0
2
1
0
0
0
0
0
0
1
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
2
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
2
0
0
0
0
0
2
2
0
0
0
1
2
0
0
1
2
0
0
1
0
1
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
1
1
2
0
0
2
0
0
2
3
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
9
1
0
0
0
1
0
0
1
0
1
0
0
0
0
1
2
0
0
0
1
1
1
0
0
0
0
2
0
1
0
0
0
2
0
1
2
2
0
0
0
0
3
0
0
2
0
0
0
0
1
2
0
2
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
2
2
0
0
0
0
1
2
1
0
0
1
0
2
0
1
0
0
1
0
1
2
0
2
1
2
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
2
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
2
0
2
0
2
3
0
0
1
2
2
1
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
2
2
0
0
0
2
0
2
0
0
0
2
5
1
2
0
0
0
2
0
0
2
0
0
0
8
0
0
0
0
2
0
2
0
0
0
2
2
0
2
0
1
0
2
1
1
0
0
3
0
0
0
2
2
2
2
0
0
1
0
0
0
0
0
1
2
1
0
0
0
0
1
2
1
1
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
1
0
0
2
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
1
2
1
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
1
2
0
1
1
0
1
0
2
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
2
3
0
0
1
0
1
0
0
0
0
0
0
2
1
2
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
2
0
2
0
0
0
2
0
4
1
1
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
3
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
3
2
1
2
0
0
1
1
0
0
0
0
0
7
0
0
2
1
1
0
0
0
0
0
0
1
0
0
2
0
1
0
0
2
0
0
0
0
0
0
2
2
0
0
2
0
1
0
0
0
2
1
0
1
1
2
0
0
2
2
2
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
2
0
0
1
0
0
1
1
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
1
1
0
0
0
0
0
1
1
1
4
0
0
0
0
0
2
1
0
2
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
1
0
3
3
0
1
0
0
1
1
0
3
0
3
1
0
0
1
0
2
0
0
0
1
0
1
0
0
1
0
0
0
0
2
0
0
1
1
1
0
1
0
0
0
2
1
0
1
2
1
2
0
2
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
1
2
0
0
2
1
0
0
0
0
0
1
0
2
1
0
0
0
0
1
2
0
0
2
1
0
0
0
0
0
2
2
0
1
1
1
1
2
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
2
0
2
0
0
0
0
1
0
2
0
3
0
0
0
0
2
0
0
2
2
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
15
1
0
0
2
2
0
0
0
0
2
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
7
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
1
1
0
1
0
2
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
2
0
2
0
0
0
0
1
0
0
0
2
0
0
0
1
1
1
0
2
0
0
0
0
0
0
0
0
2
0
1
1
0
2
0
0
2
0
1
0
1
0
0
2
0
2
0
0
1
1
0
1
0
2
1
2
0
0
0
0
7
0
0
0
0
2
2
2
0
0
0
0
0
2
0
0
1
1
0
1
0
1
0
0
0
0
1
1
0
0
0
3
2
2
0
1
1
0
0
2
1
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
2
0
2
2
2
0
0
0
0
2
1
0
0
0
0
1
0
2
0
0
1
0
0
5
1
1
2
1
0
0
0
1
1
0
0
3
0
2
0
0
0
0
2
0
0
2
2
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
1
0
0
2
1
0
1
0
0
0
0
2
2
2
0
0
0
1
0
0
5
2
2
0
0
1
0
0
1
1
0
0
2
2
0
0
0
0
1
2
0
2
2
0
0
0
0
0
0
3
1
2
2
0
0
0
2
1
3
1
1
0
0
0
0
1
0
0
2
0
1
0
0
0
3
0
1
1
0
0
3
0
1
0
0
0
0
0
1
0
0
0
0
0
3
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
2
0
2
3
0
0
1
1
1
0
0
2
0
0
0
1
2
1
0
2
0
4
0
0
0
0
1
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
1
2
0
1
0
1
2
0
0
0
1
0
0
1
0
0
0
3
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
2
1
0
0
2
1
1
0
0
0
0
2
2
3
0
0
0
2
0
0
1
0
0
0
0
2
0
0
2
1
2
2
0
2
2
1
0
0
3
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
2
2
2
0
0
0
0
0
0
2
3
0
2
0
2
2
0
0
0
2
0
1
0
0
0
0
2
0
0
0
3
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
2
1
0
0
0
2
0
1
1
0
2
0
1
0
0
0
0
2
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
3
2
0
0
1
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
1
2
1
2
2
0
0
0
1
1
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
2
0
0
0
5
2
1
0
2
0
0
1
0
0
0
0
0
0
0
1
2
1
1
6
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
1
2
0
1
0
0
0
0
3
0
1
1
0
0
0
3
0
1
0
2
0
0
1
0
0
0
0
0
0
2
1
1
0
0
0
1
1
0
0
0
0
2
0
0
2
0
0
0
0
1
0
1
0
0
2
0
1
1
0
2
0
0
1
1
2
0
0
1
2
2
0
2
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
2
1
1
0
2
0
0
0
4
1
1
1
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
1
2
0
0
0
2
0
0
0
0
0
3
0
0
0
2
0
0
0
2
0
0
0
2
1
0
0
2
0
0
1
0
0
0
2
1
1
0
0
0
1
1
0
0
0
0
0
2
2
1
2
1
1
1
0
1
2
0
0
2
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
1
2
0
2
0
0
2
1
3
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
2
2
0
0
2
0
0
0
0
0
1
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
2
0
0
2
1
0
0
1
0
0
0
0
0
2
0
0
1
1
0
1
1
0
0
0
0
2
0
0
0
1
0
1
0
1
1
0
1
0
0
2
0
0
0
2
6
0
0
1
0
0
0
1
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
4
0
0
2
0
0
0
0
0
1
1
0
0
0
2
0
2
0
0
0
2
0
2
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
2
1
2
0
0
0
0
0
0
3
0
0
0
1
2
0
1
0
0
0
0
1
1
2
0
0
2
0
0
0
0
1
0
0
0
0
3
0
0
0
2
1
0
0
0
0
0
2
0
2
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
1
1
1
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
2
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
3
2
0
2
0
2
0
1
2
1
2
0
0
5
0
0
0
2
1
2
0
1
0
0
1
2
4
0
0
1
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
4
0
0
0
0
1
2
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
2
1
0
0
2
0
0
0
0
0
2
2
0
1
0
1
1
0
0
2
0
0
2
0
1
0
2
0
1
0
0
3
0
0
0
0
0
2
0
1
1
0
0
0
2
1
0
0
0
3
0
1
2
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
2
2
0
0
1
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
3
0
0
1
8
0
1
0
0
0
3
0
1
0
0
0
0
1
2
2
1
0
0
0
1
0
0
0
2
0
4
0
2
3
0
1
0
1
0
0
1
0
0
1
0
0
0
1
2
1
0
1
2
0
0
2
2
1
0
1
1
1
0
0
0
0
1
1
3
1
0
1
1
1
1
1
0
0
0
0
1
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
1
2
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
2
1
0
1
0
0
0
2
0
0
2
8
0
2
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
1
1
1
0
0
2
2
2
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
1
0
0
2
0
0
0
0
1
1
1
0
0
0
0
0
2
0
1
3
0
0
0
1
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
3
0
0
0
0
0
0
0
1
2
1
1
2
0
1
1
0
1
0
2
0
1
2
0
0
0
3
0
1
0
0
2
0
1
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
9
0
1
0
0
2
0
2
0
2
0
0
1
2
2
0
0
0
0
1
0
0
2
1
2
0
2
0
0
0
1
2
0
0
1
0
3
0
0
0
0
3
0
0
3
0
0
0
0
0
0
0
1
0
3
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
3
1
0
0
0
0
2
2
0
0
0
2
2
1
0
2
0
1
2
2
1
3
0
0
2
0
2
2
0
2
2
0
2
0
2
0
1
2
0
1
0
1
0
0
0
0
1
0
0
0
2
0
0
2
0
0
3
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
1
1
0
0
0
0
2
2
1
1
0
3
0
0
1
2
2
2
0
1
0
0
2
2
1
2
4
2
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
3
0
0
0
0
0
0
2
2
0
0
2
0
0
0
4
0
2
0
0
0
0
2
1
0
0
0
0
1
0
1
0
0
2
0
0
1
1
0
0
0
2
0
0
0
0
0
1
2
2
0
0
0
3
0
0
0
0
0
2
0
2
1
1
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
1
1
2
0
1
0
1
1
0
0
3
0
2
1
0
2
1
1
0
0
1
2
0
0
0
1
0
1
0
1
2
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
1
0
3
0
1
1
0
0
0
2
0
0
1
0
0
3
0
1
0
0
0
3
0
1
1
2
1
2
0
0
0
1
1
2
0
1
2
1
0
2
0
2
0
0
2
1
0
0
0
0
1
2
0
2
2
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
1
0
0
0
2
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
4
2
0
0
1
2
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
2
1
0
0
2
0
0
0
2
0
0
0
0
1
2
0
0
2
0
1
2
2
2
1
1
1
0
0
0
0
0
0
1
0
2
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
1
2
0
0
0
0
2
0
0
0
0
1
2
0
0
0
2
1
0
3
1
1
0
0
0
0
1
0
0
1
0
0
1
1
1
0
0
0
2
0
0
1
2
1
0
0
2
0
0
1
0
0
1
0
2
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
1
0
0
2
1
0
0
1
1
1
0
0
1
2
2
0
0
2
2
0
0
0
0
2
1
1
0
2
2
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
4
1
0
2
0
1
1
0
0
0
0
0
2
0
1
0
2
2
1
2
0
0
0
0
2
2
0
1
0
1
0
0
1
0
0
0
1
0
1
1
1
0
0
0
0
1
1
2
3
0
0
0
0
0
1
0
0
2
1
0
0
0
0
3
0
0
2
0
1
1
1
3
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
2
0
1
0
0
0
0
2
2
2
0
1
0
1
2
0
2
1
2
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
1
0
2
0
2
1
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
2
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
2
1
1
0
0
2
0
0
1
2
1
0
1
3
0
0
0
0
1
0
2
0
1
1
0
2
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
2
2
0
1
0
0
0
2
0
1
0
0
0
3
0
2
1
2
0
2
4
0
0
1
2
1
1
0
0
2
2
0
0
2
0
1
0
0
0
0
1
0
2
0
0
0
2
2
0
0
0
1
0
0
0
0
2
2
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
2
1
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
1
0
0
0
2
0
0
1
0
1
0
0
3
1
1
1
0
2
0
2
3
0
0
2
1
0
0
1
1
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
2
2
0
2
0
2
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
1
2
0
0
0
0
1
0
1
0
2
0
2
1
2
1
2
0
4
0
1
2
0
0
0
0
0
0
1
0
2
0
0
2
1
0
1
0
0
0
0
0
2
1
1
0
1
1
2
0
0
0
2
0
0
0
0
2
0
1
2
0
1
1
2
2
0
0
3
0
0
3
1
0
2
0
1
2
0
0
1
0
1
1
0
0
1
0
2
0
0
0
0
0
0
1
0
0
3
0
0
2
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
1
2
2
2
0
0
1
0
0
1
0
1
1
1
1
0
0
0
0
0
0
0
2
0
0
0
2
0
4
0
0
0
0
0
0
4
1
2
0
3
0
1
0
0
1
0
0
2
2
1
3
1
0
0
1
2
2
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
2
0
3
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
2
0
2
0
5
0
1
1
0
2
0
0
1
0
2
1
0
0
2
2
2
1
1
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
2
0
0
0
1
0
3
1
0
0
1
1
0
0
0
1
0
0
0
1
0
0
1
2
2
1
0
0
0
0
2
0
0
0
4
2
0
0
0
0
0
0
1
0
0
1
2
2
0
0
0
0
1
0
1
0
2
0
0
2
2
0
3
0
0
0
1
1
0
0
1
1
0
0
0
0
0
1
2
0
0
2
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
1
1
0
0
1
0
0
0
1
1
0
0
0
2
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
1
2
1
0
2
0
0
2
2
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
2
2
0
2
2
0
2
0
1
1
0
1
0
0
0
1
2
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
2
2
0
4
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
1
0
1
2
1
1
1
0
0
1
0
0
0
0
2
0
1
1
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
2
2
2
0
1
0
1
0
0
1
0
2
1
0
1
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
3
2
0
0
0
0
0
3
0
0
2
1
0
1
0
0
0
0
2
0
1
0
1
0
1
0
0
0
0
1
0
2
0
3
1
0
0
5
1
0
1
0
0
0
0
1
0
0
0
0
0
1
2
2
1
3
1
0
1
1
1
0
0
1
1
0
0
1
0
2
1
2
2
0
0
0
0
1
0
0
0
1
1
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
1
2
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
4
0
0
1
0
0
1
0
1
2
2
2
1
0
0
0
0
0
0
2
0
3
0
2
1
0
1
0
0
2
0
2
0
0
2
0
0
0
0
0
2
0
0
1
1
0
2
0
0
0
0
1
2
0
2
2
1
0
1
0
0
0
0
3
0
0
2
0
2
0
5
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
2
0
1
1
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
1
0
0
1
0
0
1
0
1
0
0
2
0
0
0
0
0
3
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
2
1
0
0
0
1
0
0
2
2
1
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
1
0
0
1
2
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
1
0
1
1
1
0
1
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
2
0
0
0
0
1
0
2
0
0
2
1
1
1
0
2
2
1
0
0
1
2
0
0
0
0
1
2
0
2
2
1
0
1
0
0
0
0
2
2
0
1
0
2
0
2
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
3
0
1
0
0
1
0
0
1
0
1
2
1
1
0
0
1
0
0
1
0
1
1
2
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
2
2
3
2
2
2
2
0
0
0
1
0
0
0
3
0
0
0
0
1
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
1
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
2
0
0
1
0
0
1
0
1
0
2
1
0
2
0
0
0
0
0
0
0
1
2
0
2
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
2
0
2
1
0
0
0
1
0
0
1
2
3
1
0
2
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
1
1
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
2
1
0
0
2
0
0
0
0
0
1
2
1
2
0
0
0
1
2
1
0
0
0
0
1
0
1
2
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
3
0
0
0
0
0
0
2
1
1
0
0
0
0
1
2
0
4
1
2
0
0
0
0
2
0
2
3
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
1
1
0
0
1
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
2
1
2
1
1
0
3
0
0
0
0
0
1
0
0
0
1
1
0
1
0
2
1
0
0
0
1
0
2
1
1
1
0
1
1
1
0
0
0
0
0
1
2
2
0
5
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
2
0
0
3
1
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
2
0
1
0
0
0
6
0
2
0
2
0
0
0
0
2
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
2
0
2
2
0
0
2
0
2
2
1
1
1
2
2
0
5
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
1
1
1
0
0
0
2
2
2
0
1
0
0
0
0
1
2
1
2
1
0
0
1
2
0
3
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
2
1
0
0
0
0
2
0
2
0
1
2
0
0
2
2
0
2
2
1
1
1
1
2
3
0
0
0
2
0
1
4
0
0
0
0
0
1
0
2
0
1
0
0
2
0
1
0
0
0
2
0
0
2
0
0
2
0
2
0
0
1
4
0
0
2
1
2
2
0
1
0
0
0
0
0
1
1
2
1
0
2
2
0
0
2
1
1
0
1
1
1
0
0
0
0
0
2
0
2
2
0
0
1
1
1
2
0
0
0
2
0
0
0
0
0
1
0
1
0
1
1
0
1
2
0
3
0
0
0
0
0
2
2
0
0
0
0
1
2
0
0
2
3
1
0
0
1
0
0
2
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
2
1
0
1
0
1
1
2
0
1
2
2
0
1
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
1
0
0
0
2
0
0
4
0
1
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
1
2
2
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
4
1
0
1
0
0
0
1
0
1
1
1
0
0
0
2
0
0
0
1
0
0
1
2
2
2
0
8
0
0
0
2
1
0
0
1
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
2
4
0
0
0
0
2
2
0
1
0
1
0
0
0
2
0
2
0
0
0
1
5
0
0
2
0
0
4
0
2
0
1
1
0
0
2
0
1
0
1
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
1
0
2
0
3
0
1
0
2
2
0
7
0
0
3
1
2
0
0
2
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
3
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
3
1
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
2
1
1
0
2
0
0
0
0
3
2
0
0
0
0
0
2
1
1
2
2
0
0
0
0
2
1
2
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
2
0
0
0
1
0
1
1
0
0
0
0
2
1
2
0
2
0
1
0
1
0
1
0
1
0
0
2
1
0
2
0
0
0
0
0
0
1
6
0
2
1
2
1
1
2
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
6
0
0
0
0
2
3
0
0
2
0
0
0
0
1
3
0
1
2
1
1
0
1
1
0
0
1
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
2
2
0
0
1
0
0
0
1
0
0
0
0
2
0
0
2
1
0
0
0
1
2
2
0
1
2
0
2
0
0
0
0
1
0
2
2
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
2
0
2
0
3
1
0
2
0
0
0
0
0
1
1
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
3
0
0
0
1
2
2
5
1
2
1
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
1
1
0
0
0
1
2
1
0
0
6
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
3
1
1
2
1
2
4
1
2
0
0
0
0
2
2
0
2
0
0
2
0
0
0
0
0
0
0
1
0
2
1
2
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
2
2
0
1
2
0
0
1
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
1
1
2
1
0
2
0
0
0
0
0
0
0
2
0
0
1
2
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
2
2
2
0
0
2
0
0
0
0
1
4
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
1
0
0
0
0
1
2
2
0
0
1
2
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
2
0
1
0
0
0
0
0
0
2
0
0
2
0
1
0
3
0
2
1
0
0
0
0
2
0
0
0
0
2
0
1
1
0
2
0
1
0
1
1
0
0
0
0
2
2
0
0
0
2
1
2
1
1
0
1
0
0
0
1
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
2
0
2
3
0
0
0
0
0
2
0
0
0
2
0
0
1
2
0
0
2
1
0
0
0
0
1
1
1
0
1
0
0
0
1
2
0
0
0
0
0
0
3
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
2
2
1
0
2
0
0
0
0
3
0
2
5
1
0
0
0
0
0
0
0
3
0
1
0
0
2
0
0
2
0
1
0
2
0
0
2
1
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
2
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
3
2
1
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
1
0
0
0
0
2
0
2
0
0
0
0
1
0
1
0
1
0
0
0
1
0
1
1
0
0
0
0
2
4
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
3
0
0
0
0
0
0
1
0
2
0
3
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
2
0
1
0
1
2
1
2
2
2
1
0
1
1
1
0
1
0
0
0
2
1
0
0
2
2
0
0
1
1
0
1
0
0
0
2
0
2
2
0
1
0
0
0
0
0
2
0
0
0
1
0
0
1
1
2
1
0
1
1
0
0
1
0
3
3
0
2
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
2
2
0
0
0
0
1
0
4
0
0
0
0
0
1
2
0
1
0
2
0
2
0
1
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
2
1
1
0
2
0
0
0
0
1
1
2
0
2
0
1
0
0
0
0
0
2
1
2
0
2
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
1
0
0
0
1
1
0
1
1
1
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
2
0
0
0
0
1
0
2
1
0
0
2
0
0
0
1
0
16
1
0
0
0
1
1
2
2
1
1
2
0
0
2
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
1
0
0
3
1
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
1
1
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
1
7
0
1
1
2
1
0
0
0
0
0
1
0
0
1
0
0
0
3
0
7
0
0
0
0
1
0
2
0
2
0
0
0
0
1
1
0
1
0
0
0
1
1
0
0
0
1
1
0
0
2
2
0
0
0
2
0
0
0
0
0
2
0
0
0
2
2
1
0
8
0
0
0
0
0
0
0
1
1
3
1
0
0
0
0
0
0
1
0
0
0
2
3
1
0
0
0
2
2
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
3
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
2
1
1
1
0
1
2
0
0
0
0
1
0
0
0
0
2
1
1
0
2
2
0
0
1
0
0
1
0
0
2
1
0
1
0
2
0
2
0
1
0
2
2
1
3
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
3
0
0
2
0
4
0
0
0
0
0
4
1
0
0
0
0
0
0
2
0
4
0
1
0
0
1
0
0
0
2
3
0
1
0
1
0
0
2
4
0
2
3
2
2
2
0
0
1
1
1
0
2
0
0
2
1
0
0
0
2
2
1
0
2
2
0
0
0
0
0
2
2
0
0
1
0
2
0
0
1
1
0
0
0
0
1
2
1
2
2
2
2
0
0
2
0
0
0
1
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
1
1
2
1
0
1
0
2
0
1
0
0
2
0
0
0
1
1
1
0
0
0
1
0
1
0
0
0
1
0
4
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
2
0
0
2
0
1
0
2
2
2
0
0
0
0
0
0
0
2
1
2
1
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
2
2
0
2
1
0
2
0
0
0
2
0
0
2
0
1
0
0
0
1
1
1
0
2
1
0
0
4
0
1
0
0
0
2
2
0
0
0
0
1
2
2
1
0
3
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
2
0
1
0
2
0
0
0
0
0
0
0
1
0
1
0
1
0
1
1
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
2
0
0
0
1
1
0
1
0
0
0
0
2
0
0
1
0
0
0
0
1
1
0
0
0
1
0
2
0
1
1
0
0
0
0
0
1
0
1
0
0
1
0
2
2
2
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
2
2
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
3
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
2
1
0
2
1
1
0
0
1
1
2
0
0
0
0
0
1
0
0
1
0
0
0
2
2
0
0
1
0
2
0
1
0
0
2
0
1
0
1
0
0
2
0
0
1
3
2
2
0
0
0
0
0
1
3
0
0
0
1
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
1
2
1
0
0
0
0
1
0
1
1
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
1
0
1
0
0
2
0
2
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
1
2
0
0
1
0
0
0
0
3
0
1
0
0
0
2
0
0
0
0
0
2
1
0
2
0
1
0
2
1
0
1
2
0
0
0
0
0
0
0
1
1
0
0
2
0
0
2
0
0
4
0
1
0
0
0
0
0
1
0
1
1
1
0
4
0
1
0
2
0
0
0
0
0
0
2
0
2
1
0
0
1
1
3
0
0
0
0
2
0
0
0
0
2
0
0
2
0
1
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
2
1
5
2
0
0
1
1
0
0
0
2
2
1
1
2
0
1
0
1
0
0
0
0
2
1
4
0
2
0
1
2
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
4
2
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
2
0
3
1
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
1
0
0
0
0
2
2
4
2
2
2
2
0
0
0
0
2
2
1
0
1
1
0
2
0
0
1
0
0
2
0
0
0
2
1
1
0
1
0
0
0
2
2
2
2
4
1
1
0
0
2
2
1
1
0
1
0
2
2
0
8
0
1
0
0
0
1
0
1
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
1
0
2
2
0
0
0
0
0
0
2
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
2
2
0
1
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
1
2
0
2
1
0
1
0
2
0
0
0
1
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
2
5
0
0
0
0
0
0
0
2
1
0
0
2
3
2
1
2
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
2
0
2
3
2
0
0
0
1
0
2
0
1
2
2
0
0
0
2
1
2
1
0
2
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
2
0
0
0
1
2
1
2
0
0
0
2
0
1
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
2
2
0
0
0
2
0
1
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
1
2
0
2
1
0
0
2
0
2
0
0
1
0
2
1
2
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
1
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
2
2
2
0
0
0
0
2
0
2
0
1
2
0
0
0
0
2
0
0
1
2
0
1
1
1
1
1
1
0
2
1
1
1
2
2
0
2
0
0
2
2
0
0
0
0
0
1
0
0
2
1
0
1
1
2
0
2
2
0
0
1
1
1
0
0
1
0
0
0
1
0
0
0
0
0
2
0
1
0
2
0
1
1
1
2
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
3
0
0
2
0
0
0
3
0
0
1
0
1
1
1
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
1
2
1
0
0
1
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
2
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
1
0
0
2
1
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
1
1
0
1
1
0
0
3
0
2
1
0
0
0
0
0
1
0
0
2
0
0
0
1
1
0
0
0
1
0
1
0
0
1
2
0
0
1
0
0
2
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
2
1
0
0
2
0
0
0
0
1
0
0
0
0
2
0
1
0
2
2
0
0
0
1
0
0
0
2
0
0
1
1
0
0
3
0
0
0
1
2
0
2
0
0
1
1
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
1
0
1
0
2
0
3
1
2
0
0
2
0
0
1
1
1
0
0
1
0
1
0
0
1
2
1
0
0
1
1
2
0
0
2
0
1
0
2
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
2
1
0
0
1
0
2
0
0
1
0
0
3
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
1
0
1
2
2
0
0
0
0
0
0
1
1
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
2
2
0
1
2
0
0
2
1
0
0
2
1
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
1
1
0
1
0
0
1
0
0
2
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
3
0
1
0
1
2
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
2
0
2
0
0
0
2
3
1
0
2
2
0
0
0
2
0
0
2
0
0
3
0
0
0
2
0
0
0
0
0
0
0
1
1
1
0
0
2
0
0
1
1
1
0
0
0
1
0
0
0
1
1
1
1
2
0
0
1
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
4
0
0
0
1
2
2
0
0
0
2
1
0
0
2
0
0
2
0
0
0
0
1
0
0
1
0
2
2
2
0
0
0
0
2
0
0
0
1
0
2
2
1
0
0
0
0
1
2
0
2
2
1
0
0
0
1
0
1
0
0
1
1
4
0
2
0
0
1
0
1
1
1
2
2
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
2
2
0
0
2
0
0
0
0
1
0
0
2
0
2
0
0
3
0
1
0
0
1
0
0
2
0
0
0
0
0
1
2
0
0
1
0
2
1
0
0
0
1
1
2
0
2
2
1
0
0
2
2
0
2
0
1
2
0
0
0
0
0
0
1
1
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
2
0
0
0
0
0
2
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
1
0
2
1
2
0
2
1
2
0
0
2
2
2
0
0
0
0
2
0
0
1
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
1
2
1
1
0
0
1
2
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
2
0
2
2
0
0
2
0
1
0
2
1
0
2
0
0
1
1
2
2
0
1
0
1
0
1
1
0
2
0
0
0
0
0
0
1
0
2
0
0
7
0
0
1
0
0
1
0
1
2
0
1
0
0
1
2
0
0
0
1
0
1
1
0
0
0
0
0
0
0
2
2
0
0
1
0
2
0
3
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
1
0
2
2
1
0
0
0
0
2
0
0
2
0
2
0
0
3
1
0
1
1
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
2
0
2
2
0
1
2
0
2
2
0
0
1
0
0
1
0
0
0
2
1
1
0
0
2
0
3
0
0
1
2
0
3
0
2
1
2
0
0
1
2
0
0
0
0
1
3
2
2
2
0
0
0
0
0
1
0
1
3
2
0
1
2
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
1
2
0
0
1
0
0
0
0
1
1
2
0
0
0
0
2
0
2
2
0
0
0
0
2
1
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
3
3
0
0
0
1
0
2
0
0
0
1
0
4
0
0
0
2
0
1
0
0
0
2
3
0
0
0
0
0
0
0
1
1
0
5
1
2
0
0
1
0
0
0
2
2
0
2
0
1
0
2
2
0
0
2
2
0
0
0
0
0
2
1
1
0
0
0
0
1
1
0
3
0
1
1
2
2
2
0
0
0
2
0
2
2
0
0
0
0
0
2
1
1
0
3
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
2
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
2
0
1
0
1
1
1
1
0
0
0
0
1
2
2
0
0
1
0
3
0
1
0
0
2
0
0
0
2
0
0
0
0
0
2
2
0
2
1
1
0
5
1
0
0
0
3
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
2
0
0
1
1
0
0
1
3
0
0
0
2
1
0
0
0
0
0
0
1
1
0
0
0
0
2
0
2
0
2
0
0
0
1
3
0
0
0
0
0
0
2
0
2
2
3
3
1
0
1
0
1
1
0
0
0
2
1
0
0
1
2
0
1
0
1
0
0
3
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
1
0
0
2
0
0
0
2
1
0
1
0
0
2
0
3
2
0
0
1
0
2
0
0
0
2
1
0
1
0
0
2
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
1
2
0
0
2
0
2
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
2
1
1
0
0
2
1
0
0
0
2
0
0
2
0
0
7
0
2
0
4
0
0
1
0
0
0
0
1
2
0
0
1
0
0
0
0
2
1
0
1
0
0
2
0
0
2
0
0
0
0
1
0
1
0
0
1
2
0
0
3
2
0
2
1
2
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
2
2
0
1
0
0
1
0
0
2
2
0
0
0
0
0
0
1
2
0
0
2
2
0
0
2
2
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
2
0
0
0
0
2
1
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
2
0
1
0
0
0
2
2
0
0
0
2
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
2
1
1
2
0
1
1
0
2
2
0
0
0
0
2
3
2
2
2
0
2
1
2
0
0
0
2
0
0
1
2
2
0
0
0
1
0
0
2
2
0
4
0
0
0
0
0
0
0
0
5
0
0
2
1
0
0
0
0
1
0
1
0
1
0
3
0
0
1
0
2
2
0
0
2
0
1
0
0
1
1
0
3
2
0
0
1
0
0
0
0
0
0
0
1
0
2
1
2
0
0
0
2
0
0
1
0
0
0
0
0
1
1
0
0
0
1
2
0
0
0
2
0
0
1
1
2
2
0
2
0
2
0
3
0
0
2
0
0
0
0
1
1
2
1
1
2
0
1
4
1
1
1
0
1
2
3
3
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
2
1
0
2
0
1
1
1
1
0
0
0
0
2
0
1
0
0
0
1
0
0
1
1
1
0
0
0
0
2
1
0
0
0
2
0
0
1
0
0
0
0
1
1
1
1
0
0
1
2
0
1
2
0
3
0
0
0
0
0
1
1
1
1
0
1
0
0
1
0
0
0
2
1
0
2
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
3
0
2
0
0
1
0
0
0
1
0
0
1
0
2
0
0
1
0
0
1
1
0
0
0
0
0
1
0
2
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
1
1
0
0
0
0
0
2
4
0
1
0
1
0
1
0
0
1
0
0
0
2
0
1
0
2
0
1
2
2
0
0
1
2
0
2
0
1
0
0
1
1
0
0
0
2
0
2
0
1
1
0
0
1
2
4
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
1
0
0
0
0
3
1
0
0
0
0
2
0
0
0
1
0
0
0
0
3
1
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
4
0
0
0
0
2
0
0
0
0
2
2
1
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
2
2
3
0
0
0
1
0
0
3
0
1
2
0
0
0
0
0
0
1
1
0
0
2
3
0
2
0
0
2
0
2
1
0
0
0
0
1
2
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
1
0
1
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
2
0
0
1
0
2
1
2
0
0
1
0
0
0
0
0
0
1
2
2
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
2
0
2
0
0
1
0
1
2
1
0
0
1
0
1
0
0
1
2
0
0
1
1
0
0
2
2
1
0
0
0
0
1
0
2
5
0
2
0
0
0
0
0
0
0
1
0
0
2
0
2
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
2
0
2
0
0
0
0
1
0
0
1
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
2
1
0
5
0
2
2
1
0
0
0
0
0
1
0
2
1
1
0
0
2
2
0
0
0
0
1
1
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
1
0
0
2
0
1
1
0
0
0
2
2
2
0
2
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
1
0
0
1
0
0
3
0
1
0
1
2
0
0
2
0
2
0
3
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
3
0
0
2
1
0
0
0
0
1
0
1
0
1
0
2
0
2
3
0
0
0
0
0
1
2
2
0
0
1
1
0
1
1
2
2
0
0
0
1
0
1
0
0
2
3
0
0
2
7
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
2
0
1
0
0
0
1
1
0
0
0
0
3
1
0
2
0
0
2
0
0
1
2
0
0
0
0
0
0
0
2
0
0
1
1
0
1
1
2
2
0
2
2
0
0
0
0
0
0
0
0
0
0
2
3
0
0
2
2
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
2
0
0
0
0
0
2
1
2
0
0
0
0
1
2
1
0
1
1
1
0
0
0
1
0
0
0
0
1
2
1
1
0
0
0
0
0
0
0
0
0
0
1
2
2
0
3
3
2
2
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
1
2
0
0
2
1
0
0
2
0
0
2
0
1
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
3
0
2
0
2
0
0
0
1
0
0
1
0
0
1
0
1
1
0
0
2
1
0
1
0
2
0
0
2
0
2
0
0
1
2
0
1
1
2
0
0
0
0
2
6
1
0
0
2
2
2
0
0
1
1
1
0
3
0
0
0
0
0
0
1
0
2
0
1
0
0
1
0
0
0
0
1
0
0
1
0
1
1
0
0
3
0
0
3
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
1
1
1
1
1
0
2
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
2
1
0
1
1
1
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
1
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
1
2
0
0
0
0
0
0
2
0
3
1
1
0
0
1
0
2
1
0
0
0
0
0
3
2
0
1
0
0
0
2
1
0
0
0
0
0
0
1
0
1
1
0
1
2
2
0
1
0
1
0
2
1
0
0
0
0
1
1
0
1
2
0
1
1
3
1
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
1
0
2
1
0
0
0
2
0
0
2
1
0
0
0
1
0
1
0
0
0
0
1
0
1
1
0
1
0
2
0
1
0
1
1
0
0
0
0
0
1
0
1
1
2
0
0
0
0
0
2
0
0
0
3
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
1
2
5
1
2
1
0
1
0
0
2
0
0
0
0
1
1
2
1
0
2
0
1
3
0
2
0
1
4
0
0
2
0
2
0
0
2
0
0
1
0
0
1
2
0
0
0
2
1
1
0
0
0
2
0
0
2
0
0
1
0
0
0
1
0
0
0
2
1
0
0
0
1
2
0
0
0
1
2
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
1
0
2
1
2
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
2
0
2
1
1
0
2
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
1
2
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
1
0
0
0
1
1
0
1
0
0
0
0
2
0
0
0
2
1
0
0
1
2
0
1
0
0
2
0
0
0
0
3
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
1
0
2
1
1
0
0
0
1
0
2
0
1
2
0
1
0
0
1
1
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
4
2
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
1
2
0
1
0
0
1
0
1
0
2
1
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
2
1
2
1
0
1
1
0
0
0
0
0
0
2
2
0
2
0
1
0
1
2
0
1
0
0
1
0
0
0
1
2
2
0
0
0
0
2
2
2
0
0
2
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
2
3
2
2
0
3
1
0
2
2
0
1
0
0
0
0
0
0
0
2
0
0
2
1
0
1
0
0
1
1
2
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
2
0
0
2
0
1
4
1
1
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
2
0
0
0
2
1
0
1
1
1
0
0
0
3
0
1
0
0
0
0
2
0
1
0
2
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
2
0
0
1
0
2
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
8
0
0
1
0
1
0
0
1
3
0
0
1
2
1
0
0
0
0
0
0
1
2
0
1
1
2
2
0
0
0
0
1
0
0
1
1
0
0
0
2
0
0
1
0
1
1
1
1
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
3
2
2
0
2
0
1
0
0
0
2
0
0
0
3
0
0
1
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
2
2
0
0
0
2
1
0
0
0
0
0
0
1
0
1
2
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
2
0
1
0
0
2
0
0
0
0
1
0
0
1
1
0
0
0
0
2
1
0
2
0
0
0
0
2
0
0
0
0
2
2
2
2
1
0
0
1
0
2
2
0
0
7
2
0
0
0
2
0
2
0
2
2
2
0
0
0
1
0
1
0
0
2
0
0
0
2
0
0
0
2
2
2
0
1
2
0
1
1
0
2
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
1
0
2
0
1
1
1
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
1
1
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
1
2
0
2
0
0
0
0
2
1
2
0
1
1
1
2
0
2
2
0
0
0
0
0
0
0
1
0
0
2
0
0
1
2
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
2
0
0
0
2
9
0
1
1
0
1
0
2
0
0
0
2
0
0
2
1
0
0
2
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
2
0
0
0
0
2
1
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
2
0
2
1
0
0
0
0
0
0
0
2
1
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
5
1
2
1
0
2
2
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
1
0
1
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
2
2
1
1
1
0
1
1
2
0
0
3
0
0
1
1
0
1
0
1
1
2
0
0
0
1
0
0
1
1
0
2
10
0
2
1
0
1
0
0
2
0
0
0
0
1
0
0
2
0
1
1
1
0
0
0
0
0
2
2
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
2
0
0
0
0
0
2
0
2
0
0
0
0
2
0
1
0
0
0
1
1
2
0
0
2
0
0
0
0
1
0
1
2
0
1
0
0
1
1
0
0
0
0
1
0
0
1
1
0
0
0
2
0
0
2
2
1
0
0
0
1
2
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
3
1
0
0
2
0
2
2
0
0
0
1
2
1
0
0
0
2
2
0
0
2
0
0
2
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
1
0
3
2
1
0
0
2
0
0
0
2
0
1
0
0
1
0
0
2
1
2
1
0
0
1
3
0
1
0
1
0
2
2
0
2
0
0
1
1
2
1
0
2
0
1
0
0
0
0
0
0
0
0
1
2
0
2
1
1
0
0
0
1
0
1
2
0
0
1
2
0
0
0
0
1
0
0
0
2
0
0
0
9
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
7
1
4
0
0
1
1
0
2
0
0
1
0
3
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
1
1
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
2
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
7
0
0
1
1
1
0
0
0
0
0
0
0
0
2
2
0
0
1
0
2
0
1
0
2
0
1
1
2
0
2
0
0
0
0
0
1
2
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
2
1
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
2
0
2
0
0
1
0
1
1
2
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
2
0
1
1
1
0
0
0
2
0
0
0
0
1
1
2
0
0
2
2
0
3
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
1
0
0
2
2
2
0
0
0
0
1
0
1
1
0
0
1
2
1
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
1
0
0
0
1
0
2
0
0
2
0
0
1
0
0
1
2
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
2
1
2
0
2
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
3
0
2
0
0
0
3
0
1
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
2
4
2
1
0
2
1
0
0
1
2
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
2
1
0
1
2
0
0
2
1
0
1
0
0
1
0
0
0
2
0
1
2
0
0
0
0
0
4
0
2
0
2
0
0
0
1
0
2
0
0
0
2
0
1
1
2
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
3
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
1
0
1
0
1
0
2
0
0
0
2
1
2
0
0
0
0
2
0
0
0
2
1
1
1
0
2
2
0
0
0
0
0
2
0
0
0
3
0
2
0
1
2
0
1
0
0
1
0
0
1
0
1
0
1
1
0
0
0
0
0
0
2
0
0
0
1
0
4
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
3
0
2
0
0
2
0
0
0
1
0
2
1
0
0
0
0
2
2
0
0
2
1
0
0
0
0
2
0
0
0
2
1
3
0
0
2
0
1
0
1
0
2
2
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
2
0
2
1
0
0
0
1
0
0
0
2
0
0
0
0
2
1
0
0
2
0
1
1
1
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
2
2
0
0
0
0
2
2
0
0
2
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
2
1
0
0
11
0
2
2
1
0
0
0
0
0
0
0
0
0
2
0
1
3
2
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
1
0
0
0
1
2
0
2
0
0
1
0
0
0
2
0
0
0
0
0
2
0
1
1
0
0
1
0
2
1
1
1
0
0
0
1
2
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
2
2
0
2
0
0
1
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
1
0
0
0
0
2
0
0
2
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
1
0
1
0
2
2
0
2
0
0
0
1
0
0
2
0
1
0
0
0
0
0
2
0
1
0
1
2
0
0
1
1
0
0
2
0
2
0
2
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
2
1
0
3
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
2
1
0
1
0
2
0
0
0
0
0
2
0
1
2
1
0
1
0
0
2
0
1
2
2
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
1
0
2
1
0
1
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
1
2
1
1
1
1
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
2
0
2
0
2
0
0
0
0
1
1
0
1
0
0
0
0
1
4
1
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
2
0
0
1
0
1
0
2
0
0
0
1
2
2
0
0
0
1
0
1
2
1
2
0
0
0
2
0
1
1
1
0
1
3
1
2
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
1
1
0
2
0
1
0
0
0
0
2
0
0
2
1
1
0
1
0
0
0
0
0
1
0
1
0
0
0
7
2
1
0
0
0
0
0
0
0
0
0
2
1
0
1
1
0
2
0
0
0
1
0
0
1
0
2
2
1
0
0
1
0
0
0
0
0
1
2
0
0
0
2
0
1
2
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
1
1
1
0
1
0
2
0
4
1
0
0
1
2
0
0
0
1
0
0
2
1
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
2
1
0
0
2
2
1
1
2
0
1
0
1
0
0
0
2
2
0
0
2
1
0
0
2
1
2
0
1
1
0
1
0
2
1
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
2
1
2
0
0
2
0
1
2
0
1
0
2
0
2
0
2
1
0
0
2
1
1
2
0
1
1
2
3
0
0
1
2
2
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
2
1
0
1
0
3
1
3
2
0
0
0
1
2
0
0
0
2
0
0
0
0
2
1
0
0
2
0
1
0
2
0
0
0
0
0
2
2
4
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
1
0
1
1
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
3
3
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
2
0
2
0
0
0
0
1
0
1
0
1
1
0
0
1
0
0
0
0
0
1
0
0
1
2
1
1
0
0
1
1
0
2
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
1
2
0
0
2
0
0
2
0
0
2
2
0
0
0
1
0
0
0
2
1
2
0
2
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
2
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
2
0
2
0
2
1
2
0
1
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
1
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
1
2
0
1
2
0
1
0
0
2
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
7
1
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
1
0
2
0
2
0
0
0
0
1
2
0
0
0
1
0
0
0
0
2
0
0
0
1
2
0
1
1
0
0
2
1
0
0
0
1
0
0
0
2
0
0
2
1
0
0
0
1
0
2
0
0
2
0
0
1
0
1
3
0
1
1
0
1
0
1
2
0
0
0
0
0
0
2
0
2
0
0
1
0
1
0
0
2
2
0
1
0
2
2
0
1
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
2
1
0
2
1
0
0
0
0
0
1
0
1
0
0
2
2
1
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
1
0
0
0
2
2
2
1
2
1
2
2
0
0
2
2
0
0
1
0
0
1
2
0
3
0
0
2
0
1
1
0
0
0
2
1
2
0
2
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
1
2
1
0
0
2
0
0
0
0
0
2
0
0
2
1
0
0
2
2
0
0
2
2
0
0
0
0
0
2
0
0
1
0
2
1
0
0
0
0
0
2
0
0
0
2
0
1
0
1
0
1
0
0
2
1
0
0
0
2
1
0
1
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
1
0
0
0
1
0
0
0
2
0
0
0
1
0
0
1
0
0
1
1
0
1
0
1
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
2
0
0
0
3
0
2
0
2
0
0
0
2
1
2
0
1
0
1
1
0
0
0
2
2
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
1
0
2
1
0
1
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
2
0
0
0
0
0
2
2
0
2
1
1
0
0
0
1
0
2
1
1
1
5
0
0
0
0
0
1
4
0
0
2
1
0
0
1
0
0
0
7
0
1
0
0
0
1
1
2
0
0
0
2
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
2
3
1
1
2
0
0
0
1
0
1
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
1
0
1
0
0
2
1
2
0
0
0
0
2
0
0
0
0
2
0
0
2
1
1
1
0
0
3
0
1
0
0
0
0
2
2
2
0
2
0
4
1
0
1
0
0
1
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
2
2
0
0
0
0
1
2
0
0
1
0
4
0
0
2
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
1
0
2
0
0
0
1
1
0
0
2
0
0
2
0
0
0
2
0
2
2
0
0
2
0
0
0
0
0
0
0
7
0
0
0
0
0
2
2
2
1
0
2
1
2
0
5
2
1
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
2
2
0
0
1
0
2
2
0
2
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
3
0
3
0
1
0
0
0
2
0
0
1
0
0
0
0
0
1
1
2
0
0
0
0
1
0
0
0
2
0
0
2
1
0
2
0
2
3
2
0
0
0
0
0
0
0
2
0
1
0
1
0
1
0
1
0
0
2
2
0
0
0
2
2
0
2
0
2
11
2
0
0
0
0
0
0
1
1
0
1
1
0
1
0
0
2
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
1
0
0
0
1
3
1
0
0
0
0
0
0
1
0
0
0
0
1
1
1
2
0
0
0
0
4
1
0
2
1
1
0
1
0
0
2
2
0
0
0
0
2
0
1
0
1
2
1
0
0
0
2
0
0
1
1
2
0
1
0
2
2
1
0
2
1
2
0
0
1
1
2
3
0
1
1
0
0
1
3
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
3
1
0
3
0
0
0
1
0
0
2
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
1
2
2
1
0
0
2
0
0
0
0
2
0
0
1
1
0
2
1
4
0
2
2
0
0
2
0
0
0
1
0
2
0
0
1
0
0
1
2
0
0
1
0
0
0
0
0
2
0
3
0
0
0
2
0
1
0
0
0
0
0
0
0
2
2
0
0
1
0
2
0
3
0
0
0
3
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
2
0
2
3
0
0
0
0
0
0
0
2
0
0
2
0
1
0
1
0
2
0
0
2
0
2
0
0
0
0
0
2
1
0
1
2
0
1
0
1
0
1
0
0
2
2
0
0
0
0
0
3
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
1
2
0
1
1
0
0
2
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
4
0
2
0
1
0
0
1
0
0
2
0
0
0
1
0
1
1
0
0
2
2
1
2
0
2
0
2
2
0
1
0
1
0
0
0
0
0
0
1
1
1
0
0
0
2
1
0
0
2
0
0
2
1
0
0
1
0
0
2
2
0
2
0
0
1
0
0
1
0
0
0
3
0
0
1
0
2
2
1
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
1
0
0
7
1
0
2
0
0
0
0
1
2
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
3
0
0
2
1
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
1
1
1
0
0
1
0
0
2
1
8
0
2
0
0
0
0
0
1
2
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
2
1
0
2
0
0
0
1
1
2
0
2
0
2
2
0
1
2
0
0
0
0
0
0
2
0
2
3
0
2
0
1
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
3
0
2
0
2
1
0
0
2
2
0
2
1
1
1
0
0
0
1
1
2
0
1
0
0
4
0
2
1
0
1
1
0
2
0
1
0
0
0
0
0
0
2
1
0
0
2
1
0
1
1
0
1
1
0
0
1
2
0
0
1
0
0
0
0
0
1
0
2
0
2
0
0
1
0
0
1
0
1
2
0
0
1
0
0
0
0
2
2
1
0
0
1
0
0
1
0
2
1
0
0
0
0
0
0
2
0
1
7
0
2
0
3
0
0
0
2
0
0
2
1
0
1
0
0
0
0
1
4
6
0
0
1
2
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
2
2
0
0
0
2
0
0
0
1
0
0
0
2
0
3
0
1
2
7
0
0
2
0
0
0
0
0
1
0
0
2
1
0
0
1
4
1
0
0
2
1
2
0
0
0
1
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
1
2
2
0
0
0
1
0
3
0
1
1
0
0
1
0
0
0
0
0
0
3
1
0
1
0
0
0
0
0
2
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
2
2
1
0
0
0
2
2
0
0
0
1
2
1
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
1
2
0
5
2
2
2
0
0
1
0
2
0
1
2
0
0
0
0
2
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
2
0
2
0
0
2
0
0
2
0
0
1
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
1
2
0
1
0
0
0
0
0
1
0
1
0
2
0
0
1
0
0
1
0
2
0
0
0
0
0
1
0
0
0
1
0
2
2
0
0
1
0
0
2
0
0
0
2
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
2
1
2
1
0
0
0
0
0
2
1
0
0
2
1
1
1
0
0
0
0
0
0
1
0
2
2
1
1
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
1
2
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
1
1
1
0
2
0
1
0
2
0
0
0
0
2
1
2
0
0
0
0
1
2
0
0
0
1
0
0
0
1
0
2
2
0
2
1
2
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
1
0
0
1
2
8
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
2
2
0
0
3
0
0
1
0
1
0
2
0
0
2
0
0
0
0
2
3
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
1
2
3
0
0
1
0
1
0
0
0
0
0
1
1
0
0
1
0
2
0
0
0
0
2
0
4
0
0
0
2
0
0
2
1
0
0
2
0
0
0
0
0
3
1
0
2
0
0
0
2
0
0
1
0
1
0
0
1
0
2
1
0
2
2
0
1
0
2
0
2
0
0
0
0
1
1
0
0
0
1
2
0
0
0
0
0
0
2
0
2
0
2
0
0
0
2
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
3
0
0
0
0
2
0
2
2
0
2
1
1
0
2
0
2
1
1
1
0
1
2
2
0
0
1
0
0
0
1
2
0
0
1
1
1
0
0
1
0
0
2
1
0
0
0
1
2
2
3
2
0
0
0
1
1
1
2
0
0
0
1
0
0
1
2
2
1
1
0
1
1
2
0
0
1
0
1
0
2
0
0
0
3
0
2
0
0
0
4
2
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
2
0
2
2
0
2
2
1
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
2
1
0
0
0
0
1
0
0
0
2
0
0
0
1
2
0
3
0
0
1
0
2
0
1
1
0
0
2
0
0
2
0
1
0
0
2
0
1
0
0
0
1
1
0
2
0
0
0
0
2
2
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
2
1
0
1
0
2
0
1
0
0
0
0
0
1
0
0
0
0
3
0
0
0
2
2
1
0
1
0
1
2
0
0
2
1
0
0
0
0
0
2
2
0
1
2
0
0
2
1
2
0
2
0
1
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
1
0
1
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
1
2
2
1
1
0
0
0
2
0
1
0
1
0
0
0
0
0
0
2
2
1
0
2
0
0
1
1
0
0
1
0
2
2
1
0
2
0
0
2
2
2
0
0
0
3
2
0
1
1
0
2
1
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
4
0
1
3
1
0
0
1
1
1
0
1
1
0
0
0
1
0
0
1
1
1
3
2
0
2
0
0
3
0
0
0
0
0
0
0
5
0
0
0
0
2
2
0
0
0
0
0
2
0
1
1
1
0
0
0
0
0
1
0
0
2
1
0
3
0
0
1
0
1
0
0
0
1
1
0
2
0
0
2
0
0
1
0
0
0
1
0
1
0
1
0
1
1
2
2
1
1
0
0
0
0
0
1
2
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
2
1
1
0
0
0
0
1
0
1
2
0
1
0
0
0
1
0
1
1
0
2
2
0
0
1
0
1
1
1
2
2
1
0
0
2
0
0
1
0
0
2
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
1
1
0
0
1
1
0
0
1
0
0
0
1
0
1
0
3
1
7
0
2
0
0
1
0
0
0
4
0
2
0
0
0
0
2
0
0
0
1
4
2
2
0
0
0
0
2
2
1
2
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
2
0
1
0
0
0
1
2
0
0
0
0
2
2
0
1
1
0
0
0
0
0
3
0
1
0
1
0
1
1
0
0
1
1
0
0
0
0
0
0
1
2
0
2
0
0
0
0
2
1
0
2
2
1
0
0
1
0
2
0
0
0
0
0
0
0
1
2
1
0
1
0
2
1
1
0
0
2
0
0
0
0
0
0
1
2
0
0
0
1
0
1
1
0
0
2
1
1
0
0
0
0
0
2
2
1
1
1
2
0
0
2
1
0
0
1
0
0
0
0
0
1
8
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
1
0
3
0
3
2
0
1
1
3
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
3
0
0
0
1
0
2
0
2
0
2
0
2
1
0
0
2
1
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
2
2
0
0
2
0
0
2
2
0
0
2
0
0
2
0
0
0
1
1
0
2
2
0
1
1
0
1
1
0
0
0
0
2
0
0
1
2
1
1
1
0
0
1
2
0
0
0
0
0
3
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
2
1
0
2
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
2
1
2
1
0
0
0
1
0
2
0
0
1
0
0
4
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
1
0
0
2
0
0
2
3
0
2
0
2
0
0
0
0
0
1
2
0
2
0
0
0
0
0
2
1
0
0
1
1
1
0
0
1
0
0
0
0
2
0
0
0
0
0
1
2
0
2
2
1
2
0
0
0
2
0
0
4
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
1
0
1
1
2
1
0
0
0
2
0
0
1
0
0
0
0
0
2
0
1
0
2
0
4
0
2
1
0
2
0
0
0
0
2
0
2
0
2
0
1
0
0
1
2
0
0
2
2
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
1
0
1
0
0
1
0
2
0
2
0
0
2
0
0
0
0
1
0
1
1
0
1
1
0
0
0
2
0
2
0
2
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
3
0
0
0
1
0
0
1
0
0
1
0
1
2
0
1
0
0
0
1
0
2
0
0
0
2
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
9
0
0
0
0
1
0
1
0
1
1
1
0
0
2
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
2
2
0
1
2
1
0
1
1
1
0
0
2
2
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
1
0
0
0
1
0
1
1
0
0
1
0
1
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
3
1
1
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
1
0
1
1
0
2
1
0
0
0
0
2
0
0
0
1
0
0
0
1
1
1
0
0
1
1
1
0
1
0
0
0
0
1
0
2
0
2
0
0
1
0
1
0
1
1
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
4
0
0
0
2
0
2
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
2
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
1
0
0
0
2
0
0
0
1
0
0
0
2
0
0
5
0
0
0
1
0
1
0
1
0
0
2
2
1
0
0
0
2
0
0
0
4
0
1
0
0
0
1
3
1
1
0
2
0
0
2
1
3
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
2
0
2
0
0
0
2
2
1
0
3
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
2
1
1
1
0
0
0
1
1
0
0
0
0
0
1
1
2
0
1
0
2
0
0
2
0
0
2
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
3
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
2
0
2
0
0
0
2
0
2
0
0
0
1
0
0
2
0
0
1
0
1
2
0
1
0
1
2
0
0
1
0
0
1
1
2
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
1
0
0
0
0
1
0
1
1
2
2
0
0
0
1
0
2
0
2
2
2
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
2
0
1
1
1
1
1
1
0
2
0
1
0
0
3
0
3
0
0
0
0
0
0
1
2
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
2
1
0
0
0
0
2
0
5
0
0
1
0
3
0
0
2
2
0
2
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
3
1
0
0
0
1
0
0
2
2
0
0
0
1
0
1
1
15
0
0
0
3
0
1
0
0
0
1
0
2
1
0
1
0
0
2
0
0
0
2
0
0
2
0
0
2
0
0
2
0
0
0
0
0
2
0
2
5
0
0
2
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
1
2
0
1
1
2
0
1
0
1
0
0
0
0
0
0
2
0
0
1
0
1
0
2
0
0
0
1
0
0
1
0
1
0
0
3
2
2
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
1
0
2
1
3
0
0
0
1
1
0
0
0
0
0
0
0
5
1
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
2
3
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
2
2
2
2
0
0
0
1
1
0
1
0
0
0
1
1
0
2
0
0
2
0
0
1
0
1
0
0
0
2
0
1
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
8
2
0
1
0
0
2
0
0
0
0
4
0
2
0
2
2
1
1
0
0
0
0
1
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
2
0
1
2
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
1
0
0
1
0
1
0
1
0
1
1
2
0
0
1
2
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
2
1
0
0
0
1
0
0
0
0
2
0
0
0
1
1
0
1
1
2
2
0
1
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
2
0
2
0
0
1
0
0
0
1
2
0
2
0
2
1
2
0
1
2
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
2
3
2
0
1
0
1
1
0
2
2
2
0
2
1
1
0
0
2
0
2
1
0
1
0
1
0
2
0
0
2
0
1
0
0
1
2
0
0
0
2
1
0
2
0
0
0
0
1
0
0
0
0
1
1
0
2
1
0
1
0
1
0
2
2
1
2
0
0
0
0
0
1
2
0
0
0
0
2
2
1
0
0
6
2
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
1
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
3
0
1
2
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
1
1
0
2
0
1
0
0
2
0
1
0
0
0
0
1
2
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
1
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
3
0
0
2
0
1
2
2
1
1
0
0
0
1
1
0
0
1
0
1
0
0
2
0
0
0
1
0
0
1
0
2
0
0
2
0
0
0
2
0
1
0
0
1
4
6
0
2
1
0
1
0
2
0
0
0
1
3
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
2
4
0
1
0
0
0
0
0
1
1
0
0
1
1
0
0
1
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
3
2
0
0
1
0
0
2
0
2
0
1
1
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
4
2
0
2
1
0
0
0
0
2
0
0
0
3
0
0
0
4
0
0
0
0
1
0
0
2
0
2
2
2
0
1
0
0
0
0
1
0
0
0
0
0
1
1
3
0
0
0
1
0
0
0
0
0
1
2
0
0
2
0
0
1
0
1
3
2
0
0
0
0
0
2
0
2
0
2
1
0
0
2
0
2
0
0
0
1
0
2
0
2
0
0
6
0
0
0
1
1
1
0
0
0
0
0
0
1
2
2
1
0
0
1
0
0
0
0
0
2
2
0
1
1
1
0
0
1
2
2
2
0
2
1
0
2
2
0
2
1
0
3
0
0
0
2
0
1
0
0
0
0
0
2
0
0
1
0
1
1
0
2
3
0
0
2
2
0
0
2
0
2
0
0
1
0
0
2
1
0
0
2
1
2
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
1
2
0
0
2
0
0
0
1
1
1
2
0
0
1
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
3
1
2
0
0
2
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
1
0
0
0
1
0
0
3
0
1
0
0
0
1
0
2
1
2
1
0
0
1
1
1
0
0
0
2
1
2
0
0
0
0
0
1
1
0
1
0
0
0
2
0
2
1
2
2
0
0
0
2
0
0
0
2
0
1
0
2
0
0
0
3
0
0
2
2
1
0
2
0
0
0
0
0
1
2
2
0
0
0
1
2
0
0
2
0
2
2
1
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
2
1
2
2
2
0
0
0
0
8
0
0
0
6
1
0
0
0
0
2
0
0
1
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
3
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
2
1
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
2
0
1
0
2
2
2
0
2
0
1
0
0
2
0
0
0
3
0
0
1
0
1
1
1
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
2
0
2
1
2
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
2
2
0
0
2
0
0
1
0
1
0
1
1
1
0
0
0
0
0
1
3
0
0
0
2
1
0
0
1
3
1
1
1
2
1
0
0
0
0
0
0
1
0
0
2
2
0
0
1
2
0
2
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
1
1
1
0
0
0
1
0
2
1
2
0
3
1
0
0
0
2
0
0
1
2
0
1
2
2
0
1
0
2
0
0
2
0
0
0
0
0
0
1
2
4
2
0
0
2
2
0
1
2
1
0
1
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
2
2
1
0
0
2
2
1
2
0
0
1
0
2
0
0
0
0
2
1
0
0
2
0
0
1
0
1
2
0
0
0
0
0
1
1
0
2
0
0
0
0
2
1
0
0
2
0
2
0
0
0
1
3
1
0
3
2
0
0
1
0
0
1
2
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
2
0
0
1
1
0
0
0
2
0
0
0
0
0
2
0
1
0
2
1
0
0
0
0
1
0
2
0
0
2
2
0
0
1
0
2
0
2
0
0
0
1
0
1
1
1
0
1
0
0
1
0
2
0
0
0
0
1
0
3
0
1
0
0
0
0
0
2
1
0
1
0
0
0
0
6
2
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
2
0
1
1
0
0
0
2
1
0
2
0
1
2
2
0
0
1
0
0
0
0
1
0
0
0
0
4
0
2
0
0
1
0
0
0
0
2
0
1
1
2
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
1
2
1
0
0
0
2
0
0
0
0
1
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
1
2
0
2
0
0
0
3
0
0
1
2
0
0
1
0
0
1
2
1
2
0
0
1
0
0
0
1
2
0
0
1
0
1
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
2
0
0
1
2
1
0
0
0
0
0
0
2
0
0
1
0
1
2
0
0
0
2
0
0
2
0
0
3
1
1
0
0
1
2
2
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
4
0
2
0
0
1
0
2
2
2
0
2
0
2
0
1
0
1
0
0
0
0
0
1
1
1
0
0
0
2
0
0
0
2
0
2
0
0
0
0
1
2
1
0
0
1
1
0
0
0
0
4
2
2
2
0
0
2
2
0
2
0
0
0
0
1
0
1
0
0
1
0
0
0
2
2
0
1
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
1
2
0
0
0
0
2
0
2
0
1
1
0
1
1
0
0
1
0
0
0
0
1
0
0
1
0
0
1
1
1
1
0
0
0
3
1
0
0
0
1
1
2
2
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
2
2
0
1
2
3
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
1
2
0
2
0
2
0
2
2
2
1
0
2
0
0
0
0
0
0
1
0
0
0
3
0
2
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
1
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
4
2
0
0
1
0
0
0
1
3
5
0
0
0
0
0
1
1
0
0
0
0
0
2
1
0
0
1
1
0
8
2
0
2
0
2
0
0
0
0
0
0
0
0
2
0
2
1
1
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
1
1
2
1
0
0
0
0
0
1
2
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
2
1
2
0
2
0
0
0
1
0
0
0
3
2
1
0
0
0
2
2
2
3
2
1
0
1
0
0
0
0
1
0
0
0
2
0
0
1
0
1
0
1
1
0
1
0
0
1
0
1
0
2
1
0
0
3
0
1
2
1
2
2
0
2
1
0
0
0
0
2
0
0
0
2
0
0
1
1
0
0
1
2
0
0
1
0
0
0
0
2
0
1
2
0
0
0
0
0
0
2
2
0
4
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
3
0
4
0
0
1
0
0
0
0
2
0
0
2
2
0
1
0
2
0
1
0
1
0
2
0
0
0
1
0
4
1
1
2
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
2
0
2
0
0
0
0
1
0
0
1
0
2
0
0
2
0
1
0
0
0
0
0
2
1
0
1
0
0
2
0
2
0
0
1
0
0
2
2
0
0
2
0
0
2
0
1
0
0
0
1
0
0
0
0
2
2
1
0
0
1
0
0
0
0
0
0
1
0
2
2
0
0
2
0
0
0
0
2
0
0
0
2
1
0
2
0
0
0
0
0
0
1
0
0
4
0
0
1
2
0
2
0
3
2
0
0
0
0
0
0
1
0
0
2
0
0
1
1
0
0
1
0
0
0
0
1
1
2
0
0
2
0
0
0
0
0
0
2
0
2
0
0
2
2
0
4
0
1
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
5
0
0
0
0
0
1
0
0
1
0
1
1
1
0
2
2
2
1
0
0
0
1
2
2
0
0
0
0
0
0
0
1
0
2
0
0
0
1
2
0
0
0
0
1
0
1
0
0
1
0
0
0
0
4
0
0
1
0
1
0
0
2
0
0
1
2
1
0
2
0
2
0
0
0
0
0
1
0
0
1
3
0
1
1
2
0
0
0
0
0
0
0
1
1
1
2
0
0
2
0
0
0
0
0
1
1
1
0
0
0
0
2
0
0
2
0
2
0
1
0
1
0
2
1
2
0
0
0
0
0
0
0
0
2
1
0
2
2
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
2
0
0
0
1
0
0
0
0
0
0
3
0
0
0
3
0
1
0
2
0
0
1
1
2
0
1
0
0
0
0
1
0
0
0
1
0
1
2
0
0
2
0
0
0
0
1
0
0
0
2
0
1
0
0
2
0
0
0
0
0
1
0
0
0
1
0
1
0
2
1
2
2
0
0
1
2
1
0
0
0
4
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
1
2
1
0
0
1
1
0
2
0
0
0
0
0
0
0
1
0
1
0
1
2
2
1
0
0
1
0
0
0
0
1
2
2
0
0
0
2
0
0
0
0
4
0
2
0
0
0
0
0
2
1
0
1
2
0
0
0
0
4
0
0
0
2
1
0
1
0
1
0
2
2
1
0
3
1
1
0
1
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
2
1
1
0
2
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
2
1
0
1
4
0
2
0
0
1
3
0
0
3
0
0
2
1
1
0
1
0
1
0
0
1
0
2
0
0
0
0
1
2
2
0
0
0
0
1
2
0
0
0
2
0
1
2
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
1
1
0
2
0
0
0
2
2
1
0
0
0
0
0
2
1
0
2
0
0
0
1
0
0
3
0
0
1
2
0
2
2
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
1
1
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
2
0
2
0
1
0
0
1
1
1
0
1
0
0
1
0
0
2
1
0
0
2
3
0
0
0
1
2
1
2
0
1
0
0
0
0
0
0
0
2
1
2
0
2
2
1
0
0
0
0
0
0
0
0
1
0
2
2
4
0
0
0
0
0
0
0
2
0
0
4
0
1
0
1
0
0
1
0
0
0
3
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
1
1
0
0
0
0
1
0
0
0
1
2
2
0
0
1
1
0
1
0
0
0
2
0
0
0
1
0
0
0
1
0
0
1
0
2
0
0
0
0
2
0
0
1
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
4
0
2
0
1
0
0
1
0
0
0
0
2
1
0
0
0
1
0
0
0
0
1
0
0
0
1
2
2
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
1
0
0
1
2
1
0
0
0
2
2
1
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
3
2
0
0
0
1
0
0
0
1
0
0
0
2
1
2
0
1
0
4
2
2
0
2
1
0
2
0
0
1
0
0
0
0
0
2
0
0
0
2
1
0
1
0
0
2
0
0
1
1
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
1
0
0
0
0
0
1
1
0
0
2
0
2
0
1
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
2
0
0
2
0
2
2
0
0
3
0
1
0
0
1
0
0
0
0
1
0
0
0
2
0
1
1
0
2
0
0
0
1
0
0
0
1
2
0
0
2
2
0
1
2
1
1
1
3
0
0
2
0
1
2
2
1
0
0
0
0
0
0
0
2
1
2
0
2
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
1
2
0
1
0
0
2
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
3
1
1
2
1
1
0
0
0
2
2
0
1
2
0
0
0
0
0
0
0
2
0
0
1
2
1
1
1
0
3
0
0
0
1
2
0
0
2
0
0
0
1
1
2
0
0
1
2
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
1
0
1
0
0
0
1
0
1
2
1
0
2
3
0
2
0
2
1
1
0
0
0
0
1
0
1
2
1
4
2
0
1
1
1
0
0
2
0
1
6
2
1
0
2
1
0
1
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
6
0
0
0
3
0
2
0
1
0
3
0
0
2
0
1
0
4
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
1
3
0
0
2
0
1
0
0
0
2
2
0
0
0
0
0
2
0
0
0
1
3
1
2
1
2
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
1
0
1
0
2
0
0
1
1
1
0
0
1
0
0
0
1
2
1
0
1
1
0
1
0
0
0
0
0
2
1
0
1
0
1
2
1
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
1
0
2
1
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
12
0
0
0
0
0
2
2
1
0
0
2
2
0
0
2
2
0
1
2
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
1
0
2
2
0
3
0
1
0
1
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
1
0
0
0
0
0
2
0
0
0
5
0
0
1
0
2
0
2
2
0
0
0
0
0
1
1
3
0
0
4
1
1
2
0
0
0
0
0
1
0
2
1
0
1
0
0
0
0
0
0
1
0
3
0
1
0
0
0
0
0
0
1
2
0
0
2
0
0
2
1
0
0
0
1
0
0
0
0
0
0
1
1
1
1
3
0
0
0
0
4
0
0
1
0
1
2
0
0
1
1
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
2
0
1
0
0
0
2
0
0
2
0
0
0
0
3
0
2
0
1
0
0
0
0
0
0
0
2
0
1
2
1
0
0
0
1
0
0
1
0
1
1
1
0
0
0
1
0
2
0
0
1
0
0
1
3
2
0
0
0
6
0
0
0
0
0
0
0
1
0
0
2
2
0
2
2
1
2
1
1
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
1
2
0
1
2
0
2
0
0
2
0
1
0
0
0
2
2
0
1
0
3
0
0
0
0
0
1
0
1
0
0
1
0
0
1
2
0
0
0
0
0
0
0
2
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
2
2
0
0
0
2
0
0
0
1
0
1
0
0
2
0
1
0
1
0
0
0
2
1
0
1
3
2
0
0
0
2
1
1
0
1
0
1
0
0
0
0
1
0
0
0
2
0
0
1
0
0
1
0
2
0
1
0
1
1
2
0
0
0
1
1
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
2
2
1
0
0
0
1
0
0
1
0
0
2
2
0
0
1
0
0
0
0
1
1
2
1
1
0
0
1
2
5
2
2
0
0
2
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
1
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
2
2
2
0
0
0
2
0
0
1
0
1
2
0
0
0
0
0
0
0
0
1
0
0
2
2
2
1
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
2
1
0
0
0
0
1
1
2
0
0
0
1
0
0
0
0
0
0
2
0
2
1
0
2
0
2
0
2
2
0
0
0
0
0
1
0
2
0
0
2
1
1
0
0
1
0
0
0
0
0
0
0
0
0
3
1
0
0
0
2
0
0
0
3
0
2
2
0
1
2
0
2
3
2
0
2
0
0
0
2
0
0
0
0
2
0
1
2
2
2
2
0
2
0
0
0
0
0
1
0
1
0
0
1
0
2
2
5
0
0
0
0
0
2
2
1
1
0
0
0
0
1
0
0
1
0
0
1
2
0
2
2
1
2
0
2
0
0
0
2
0
0
1
0
0
0
0
0
1
1
0
0
0
0
2
0
1
0
0
2
2
0
0
0
0
2
0
0
0
1
0
2
0
0
2
0
0
3
2
0
2
0
0
1
0
1
0
1
1
0
0
0
2
0
0
0
2
0
0
1
3
0
3
0
1
0
2
0
0
0
0
0
0
2
2
1
0
0
2
0
0
0
1
0
0
0
0
1
0
7
0
0
0
0
0
0
0
0
0
0
1
2
1
2
0
0
2
0
1
0
0
0
2
0
0
0
0
4
0
0
1
0
1
0
1
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
1
0
0
2
2
1
2
3
1
0
0
0
1
0
0
1
2
0
1
1
0
2
0
0
0
0
1
0
0
1
2
2
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
2
0
1
0
1
1
0
3
0
1
2
1
2
0
0
3
2
1
1
0
0
0
2
2
2
0
1
1
0
0
2
0
1
0
2
0
0
0
0
0
0
3
1
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
1
0
0
0
1
0
2
0
2
0
1
0
0
2
0
0
0
0
2
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
2
3
0
0
0
0
0
1
1
0
0
1
0
2
0
3
3
1
0
0
0
0
2
2
0
2
2
3
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
2
1
2
1
0
0
0
1
2
0
1
1
0
0
0
0
0
0
1
0
2
2
0
2
2
0
2
0
0
1
0
0
0
0
1
3
0
0
0
2
0
1
0
0
0
0
0
0
0
2
2
0
0
0
1
2
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
1
0
2
0
1
0
1
1
1
1
0
0
0
2
0
2
2
2
0
0
2
0
0
2
0
0
2
0
0
0
1
2
1
2
0
0
0
2
0
0
1
1
0
0
0
0
0
0
1
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
2
2
0
0
0
2
1
0
3
0
0
0
2
0
0
1
1
1
0
0
2
2
0
3
0
0
1
1
2
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
2
1
0
0
0
1
2
0
1
0
1
1
0
0
0
0
1
1
0
0
0
1
2
0
0
0
0
1
2
0
0
2
1
0
0
0
0
0
0
0
0
1
1
1
0
2
1
0
0
0
0
1
1
0
0
1
0
0
2
0
2
2
0
1
0
0
0
2
0
3
0
0
2
1
0
0
0
0
0
1
0
0
3
0
0
0
0
2
0
0
2
2
2
0
0
0
0
0
1
0
1
0
1
1
0
1
2
1
2
0
0
1
0
0
0
0
0
1
0
1
0
1
1
0
0
2
0
2
0
0
1
1
0
0
0
0
0
2
0
0
0
0
3
2
0
0
0
2
2
1
0
2
2
2
0
0
0
0
0
0
5
0
2
1
0
0
0
0
0
2
1
0
0
1
1
2
0
0
1
0
0
1
0
0
0
0
3
0
2
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
3
0
1
1
1
0
0
2
1
1
1
0
0
0
0
2
0
0
0
2
0
0
2
0
1
0
2
0
0
0
1
0
0
0
0
1
0
2
0
0
1
1
0
2
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
2
0
0
1
0
2
0
0
2
0
1
0
1
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
3
2
0
2
0
0
0
0
0
1
1
0
1
0
2
1
0
0
2
0
0
0
0
0
0
1
2
0
0
2
1
0
0
2
1
0
2
1
0
0
2
0
2
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
1
0
0
0
1
1
0
2
0
0
2
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
1
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
1
1
2
0
0
0
0
0
0
2
0
0
2
3
1
0
1
2
0
0
0
0
1
0
0
0
0
2
0
1
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
3
2
0
0
0
0
0
0
2
2
0
0
0
1
2
0
2
0
0
2
1
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
2
0
1
1
0
2
0
2
2
0
0
0
1
3
0
0
0
0
0
1
0
0
2
0
0
2
2
2
2
0
0
0
0
0
0
0
0
3
3
0
0
0
1
0
1
1
0
1
0
0
2
0
0
1
0
1
0
0
0
2
2
0
0
0
1
0
0
0
0
1
0
1
0
2
1
0
1
2
3
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
1
0
0
0
0
0
0
1
1
0
2
2
0
0
1
1
0
0
1
0
1
0
0
2
1
0
0
0
0
2
2
2
0
0
0
2
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
1
0
0
0
1
2
3
0
0
2
1
2
2
0
1
0
2
2
0
2
0
0
0
1
0
2
0
1
3
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
1
2
2
2
0
0
0
2
0
0
0
0
1
1
0
0
0
2
0
0
1
0
2
1
2
0
2
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
2
0
1
0
0
0
2
0
1
0
1
0
0
0
2
2
0
0
0
2
0
1
0
1
0
2
2
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
2
1
1
0
0
0
0
0
1
3
0
2
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
1
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
1
2
1
1
1
2
1
0
1
4
1
3
0
1
0
0
2
0
0
0
2
1
0
0
2
0
2
0
0
2
1
2
2
0
0
0
0
0
0
2
0
1
0
0
0
3
1
0
0
1
1
1
1
1
0
1
0
0
2
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
2
0
0
2
0
0
1
0
0
0
0
2
1
0
2
0
0
2
0
0
2
0
1
2
0
0
0
0
2
2
1
0
1
0
0
2
0
2
0
0
2
0
2
0
1
0
0
0
0
0
1
3
0
2
1
0
1
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
2
4
0
0
0
2
2
0
0
3
1
1
0
2
1
1
1
1
0
0
1
2
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
2
1
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
2
3
2
2
0
0
0
0
2
0
2
0
2
0
0
2
0
0
0
0
0
2
2
1
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
2
1
2
0
1
1
0
0
1
0
1
2
0
0
0
1
0
0
1
0
2
1
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
2
2
1
0
0
2
2
0
0
1
0
2
0
0
2
0
0
1
2
0
2
1
0
2
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
2
1
1
1
0
1
0
0
1
0
1
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
2
1
0
1
2
0
2
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
1
0
1
2
0
0
1
0
0
1
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
2
0
1
0
0
0
3
1
1
1
0
0
0
0
0
1
0
1
0
0
2
0
0
2
2
0
0
0
0
2
0
1
0
2
0
0
2
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
3
0
2
0
2
0
0
0
2
0
1
0
0
2
0
0
0
0
3
2
0
2
0
0
0
0
2
0
0
0
0
1
0
2
2
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
2
0
1
1
0
2
0
2
0
2
2
0
0
2
0
1
0
0
2
2
1
2
0
0
0
1
0
2
1
1
0
2
0
0
0
2
3
0
2
2
1
2
2
0
1
0
2
2
0
1
0
3
0
0
0
0
0
2
1
0
2
0
4
0
2
2
0
1
0
0
0
3
0
1
2
0
2
0
0
2
0
0
1
0
1
0
0
2
1
3
0
2
0
2
1
0
0
2
1
0
0
0
0
0
0
1
0
0
0
2
0
1
0
2
1
0
1
2
0
0
1
1
0
3
0
1
1
0
3
1
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
3
0
0
1
0
0
0
0
0
1
0
1
0
2
0
0
2
0
0
0
2
0
0
1
0
0
0
0
2
0
2
0
0
2
0
2
2
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
4
0
3
2
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
3
0
2
2
0
0
1
0
0
2
1
0
0
0
1
0
0
2
2
0
1
0
0
4
0
2
0
0
0
1
0
2
1
0
1
1
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
2
0
0
0
0
2
2
0
1
0
0
0
0
0
0
2
3
0
1
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
1
1
2
0
3
2
0
0
1
2
0
2
0
1
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
3
0
2
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
1
1
0
2
0
0
0
1
0
0
0
0
2
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
1
0
0
0
0
3
0
2
0
0
0
0
1
2
2
1
0
0
2
0
2
0
0
0
2
0
1
0
0
0
0
1
1
2
4
0
2
0
2
0
0
1
0
0
1
0
0
1
0
1
0
0
0
1
1
0
2
0
3
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
3
1
0
0
1
0
0
0
2
0
0
2
0
0
2
0
1
0
0
0
0
1
0
1
2
2
2
0
0
0
2
0
0
3
0
1
0
0
0
0
0
0
0
0
2
0
0
4
0
2
2
0
1
2
1
0
2
1
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
3
2
2
0
0
0
1
1
0
0
0
1
0
1
1
1
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
2
1
0
0
2
0
0
0
1
0
0
2
1
2
2
0
1
1
0
0
0
0
0
0
1
0
0
0
0
2
1
1
2
0
2
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
1
2
1
1
0
4
4
2
0
0
0
0
0
1
2
4
0
1
1
1
0
0
0
0
2
0
0
0
0
0
0
1
2
0
1
1
0
2
0
0
0
2
0
0
0
1
0
0
0
2
0
2
0
2
1
1
1
0
2
0
1
0
0
0
0
2
2
0
1
0
0
0
0
0
0
2
0
0
2
0
1
2
0
0
0
0
0
2
0
0
0
1
0
1
0
1
0
1
0
1
0
0
3
0
0
0
0
0
2
1
0
2
0
2
0
0
0
2
0
2
3
1
3
0
0
1
0
2
0
0
0
0
1
0
0
2
2
1
1
0
2
1
1
0
0
0
2
0
0
1
0
0
0
2
2
1
2
2
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
1
1
1
0
1
0
2
1
0
0
0
0
1
1
1
0
0
0
0
2
0
2
1
0
0
0
0
2
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
1
2
1
0
2
1
0
0
1
1
0
0
0
2
0
0
2
0
0
1
0
0
2
1
0
0
0
1
0
0
0
0
0
1
0
2
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
2
2
0
2
2
1
2
0
1
0
0
0
2
0
0
0
0
0
0
2
1
0
1
0
0
0
1
1
0
1
1
2
2
2
2
2
2
1
0
2
0
0
0
0
0
1
0
4
0
0
0
0
0
2
0
2
0
0
1
0
0
1
1
0
0
0
0
0
2
0
0
1
1
1
1
1
0
0
2
1
1
0
0
0
1
3
0
0
0
2
0
0
0
0
1
2
0
0
0
3
0
2
1
0
0
0
1
2
0
0
0
2
0
0
0
1
0
2
2
0
0
0
5
0
0
0
1
0
0
0
0
2
1
3
0
2
0
0
0
0
0
0
0
2
1
2
0
0
2
0
1
0
0
0
0
2
0
0
0
1
1
0
3
2
0
2
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
2
1
0
0
1
1
2
0
2
0
0
2
3
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
2
0
2
1
0
1
1
0
2
2
0
0
1
2
2
0
0
1
0
1
1
0
1
0
1
0
2
0
0
0
2
2
0
2
1
2
1
0
0
1
2
0
2
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
1
0
0
3
0
2
0
1
0
2
0
2
0
0
1
0
0
2
0
0
0
1
1
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
2
2
2
1
2
0
0
2
1
0
2
2
0
0
0
2
0
3
1
2
0
2
0
0
0
1
1
0
4
0
0
3
0
1
2
0
0
1
0
0
0
0
2
0
1
2
2
0
0
0
1
0
1
0
0
0
1
0
0
1
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
2
2
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
1
0
0
1
0
1
0
0
2
0
0
0
0
1
0
0
2
0
0
2
0
0
1
1
0
1
0
0
1
0
0
1
0
2
0
0
1
2
0
0
0
0
0
1
0
0
2
1
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
2
0
0
1
2
1
0
0
2
2
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
2
2
0
2
0
1
0
0
1
0
2
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
1
0
1
0
0
1
2
2
2
0
0
0
0
2
0
0
1
2
0
2
2
3
1
1
2
0
1
0
0
0
2
0
0
1
1
0
1
3
0
1
3
1
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
2
0
0
1
0
0
2
2
0
0
0
0
0
0
2
1
1
1
2
0
2
2
0
0
0
2
1
0
0
1
0
0
0
0
2
0
2
0
2
0
1
0
2
2
1
1
0
0
1
1
1
0
1
0
0
1
0
2
0
0
0
2
0
0
2
1
0
0
0
1
0
0
1
0
0
0
0
2
0
2
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
1
1
0
1
0
0
1
1
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
8
0
3
0
2
0
0
1
1
0
0
0
0
1
0
5
1
3
0
0
0
0
0
1
0
2
1
0
2
0
0
0
2
1
0
0
0
1
0
1
0
0
0
2
0
2
4
1
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
2
0
1
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
2
0
1
0
2
0
0
0
0
2
2
1
0
1
0
0
0
0
0
2
2
0
0
1
0
2
0
0
0
3
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
2
2
0
0
2
0
0
1
0
0
3
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
1
2
1
0
0
0
2
0
2
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
1
1
1
1
0
0
2
0
2
0
1
1
1
2
0
3
0
2
0
0
1
0
1
0
0
2
0
2
0
1
0
2
0
1
1
0
0
2
0
0
0
3
2
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
1
0
1
0
0
1
1
0
1
0
1
0
0
1
1
1
0
2
1
0
0
2
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
1
1
0
1
0
0
0
3
2
0
2
1
1
0
0
0
0
1
0
1
1
0
0
0
0
0
1
1
0
2
0
0
2
0
0
1
1
1
1
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
2
0
1
1
1
0
0
0
1
0
1
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
1
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
1
0
2
0
0
0
0
1
2
0
1
1
0
0
0
2
0
1
0
1
0
2
0
2
0
1
1
0
0
0
1
0
1
0
0
2
0
1
2
0
0
0
2
1
2
0
2
2
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
2
0
0
2
2
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
1
1
1
0
0
0
1
0
0
0
0
2
0
1
0
0
0
1
0
1
1
2
1
1
0
0
0
0
0
0
0
2
0
2
1
0
0
3
2
0
0
0
1
0
2
0
1
0
2
0
0
0
2
1
1
0
0
3
0
0
0
0
1
3
2
1
0
0
0
1
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
1
2
0
0
0
0
1
1
0
2
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
2
2
0
0
1
0
1
2
0
1
0
0
0
2
0
1
1
0
0
0
0
2
2
0
0
2
1
1
0
0
1
0
0
1
0
0
2
2
2
3
1
1
0
0
0
0
0
1
2
0
1
2
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
2
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
2
2
0
1
1
0
1
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
2
1
0
0
1
0
0
0
2
2
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
3
1
2
1
0
0
1
0
0
1
0
0
2
0
3
1
0
0
1
1
0
0
0
0
1
0
0
0
1
0
1
0
1
0
1
0
0
1
0
2
0
0
1
1
1
1
0
2
0
0
1
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
1
1
2
0
0
0
1
0
2
0
2
1
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
2
1
0
2
0
0
0
1
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
2
1
2
0
2
3
0
1
2
0
0
0
0
2
0
0
0
0
1
1
0
0
0
2
0
0
2
0
1
1
0
1
0
1
2
1
1
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
2
0
0
0
0
1
0
2
1
0
1
0
0
1
2
0
0
0
2
1
0
0
0
0
0
2
0
1
3
0
2
0
0
0
0
1
0
0
0
1
0
2
2
0
2
2
0
0
1
1
1
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
3
2
0
0
0
0
1
1
0
0
0
1
0
0
1
2
0
1
0
2
1
0
3
0
0
0
0
2
1
0
2
0
0
0
2
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
2
0
1
0
0
0
2
1
0
0
0
0
2
2
2
0
2
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
3
3
0
0
0
0
0
0
0
0
0
0
2
1
0
2
8
2
0
0
0
0
0
2
0
0
1
0
0
2
2
0
2
2
0
0
0
1
1
0
0
0
0
2
2
0
0
0
2
1
0
0
0
1
0
1
0
0
0
1
2
1
0
2
0
2
0
1
0
0
0
0
0
0
0
0
1
0
1
3
4
1
2
0
0
0
1
0
0
0
0
1
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
1
2
1
1
3
1
0
0
2
0
1
0
0
0
0
0
0
1
1
1
1
2
0
0
2
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
4
3
0
0
2
2
2
0
0
1
0
3
0
0
2
0
1
0
1
2
1
0
2
1
2
2
0
2
0
0
0
0
2
2
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
1
1
0
0
0
0
0
0
0
2
1
0
0
1
0
0
1
0
0
0
2
1
1
0
0
0
1
2
0
2
1
0
0
0
1
0
0
2
2
1
2
1
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
2
0
0
0
0
2
0
1
3
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
2
2
0
0
0
2
2
2
0
0
1
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
3
2
0
3
0
0
0
0
2
2
0
0
1
0
1
2
0
1
0
2
0
2
0
2
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
3
3
1
0
0
0
3
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
1
0
2
1
0
0
0
2
0
1
1
0
0
1
0
0
0
2
0
0
3
0
1
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
2
1
0
0
1
0
0
2
0
0
1
3
0
1
1
0
2
2
0
0
0
2
0
0
2
2
1
0
1
0
0
0
1
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
1
0
1
2
0
0
0
1
0
2
2
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
1
1
0
0
0
2
0
1
0
3
0
0
2
0
0
2
1
0
1
0
0
0
0
0
0
3
0
2
0
2
0
0
0
0
2
0
3
0
2
2
2
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
2
0
1
0
0
1
0
2
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
1
1
1
0
1
0
0
0
2
0
0
1
0
0
0
0
2
1
1
1
0
0
1
0
0
0
0
2
0
2
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
1
0
0
1
1
0
1
1
0
0
1
0
0
4
0
1
1
0
2
1
0
0
2
0
2
0
1
0
0
2
0
0
1
2
0
1
2
0
0
1
0
0
0
3
2
0
1
0
0
0
0
1
2
2
0
0
2
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
2
0
4
0
0
1
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
1
0
2
2
2
2
2
0
0
0
0
0
2
1
2
1
2
0
0
0
0
0
2
0
0
2
0
0
2
0
2
1
0
0
0
0
0
2
0
0
2
0
0
2
3
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
1
3
1
0
0
0
0
2
0
1
0
0
2
2
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
1
0
2
0
0
1
0
0
0
0
2
0
1
0
0
0
2
1
1
0
0
0
0
0
1
0
0
0
1
1
1
2
0
2
3
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
2
0
0
1
1
0
1
2
0
0
0
0
2
0
0
0
2
2
0
2
0
1
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
1
2
2
4
1
2
0
0
0
1
2
0
0
2
0
0
4
0
3
0
3
4
2
4
0
0
2
1
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
1
0
1
0
2
0
0
1
0
0
2
1
2
1
0
2
2
0
2
0
1
0
0
4
1
1
0
0
2
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
2
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
1
0
2
0
0
0
0
0
0
0
0
5
1
0
0
0
1
2
0
0
2
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
1
3
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
1
2
1
1
3
2
0
6
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
3
0
2
1
2
0
3
0
0
0
0
0
1
0
0
0
0
1
0
0
1
2
1
0
2
1
3
0
0
0
0
0
0
0
0
1
1
1
0
1
0
2
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
2
0
0
2
1
2
0
0
0
0
1
0
1
1
0
0
0
1
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
1
0
0
4
0
2
0
0
0
0
1
0
0
2
2
0
2
0
0
0
1
0
0
0
0
2
2
0
0
0
2
0
1
2
0
0
0
2
0
0
0
2
1
0
0
1
1
0
0
1
0
0
0
1
0
0
2
2
1
3
1
1
2
0
1
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
1
0
0
2
0
0
0
0
1
0
3
0
0
2
0
0
0
0
0
2
0
0
1
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
1
2
0
1
0
1
0
0
0
0
0
0
2
3
0
0
0
0
0
1
1
3
2
2
0
2
0
2
0
2
2
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
1
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
3
1
0
0
0
2
0
0
0
1
2
0
2
1
0
1
1
2
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
2
4
0
0
0
0
3
0
0
0
0
0
1
2
0
0
0
0
1
2
1
0
0
0
0
0
0
0
1
0
2
3
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
2
0
1
1
0
1
1
0
0
0
2
0
2
0
1
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
1
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
1
1
0
4
0
0
1
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
1
1
1
0
0
0
0
2
1
2
1
0
0
2
0
0
0
0
0
0
1
1
0
0
0
2
1
2
3
1
1
1
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
1
1
0
2
2
1
0
0
2
1
1
2
0
1
1
0
0
1
3
1
1
0
0
2
1
0
0
1
0
0
0
2
1
2
2
1
0
0
0
0
0
1
0
0
0
1
2
0
2
0
1
1
2
2
2
0
2
0
2
1
1
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
2
0
0
2
0
1
1
0
0
0
0
2
0
0
0
1
0
1
0
1
0
0
1
3
1
0
0
2
0
2
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
1
1
2
0
1
0
2
5
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
2
1
1
0
0
0
0
0
2
2
2
0
1
0
1
0
0
2
0
0
2
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
2
0
0
0
0
0
2
1
1
0
0
1
0
0
0
2
0
0
0
0
0
0
2
2
0
2
0
2
0
1
0
0
0
1
2
0
0
0
1
0
0
0
0
1
0
0
0
2
0
1
0
0
2
2
0
0
1
2
0
0
0
0
0
1
1
1
0
0
3
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
1
0
1
0
0
0
2
1
1
2
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
2
0
1
1
2
0
2
0
0
1
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
2
0
2
0
2
0
0
0
1
2
0
0
0
2
0
0
2
0
2
0
2
0
2
0
2
0
0
3
1
1
1
0
1
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
1
3
0
0
0
0
0
1
1
1
1
0
1
1
2
4
0
0
0
0
2
1
2
0
1
0
0
0
2
0
0
0
2
2
0
1
1
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
2
0
0
0
0
0
1
0
0
0
3
0
3
1
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
1
0
1
0
0
3
2
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
2
1
0
1
0
0
0
0
0
2
2
0
1
0
0
0
2
1
0
0
2
0
2
0
2
0
1
1
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
1
2
0
1
1
2
1
0
1
2
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
2
0
0
0
0
0
1
1
1
1
0
1
2
2
0
0
0
1
2
0
0
1
0
2
0
0
0
0
1
0
1
0
0
0
0
2
1
2
1
0
1
2
2
0
1
0
0
2
0
0
0
0
0
0
1
0
1
2
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
2
2
0
2
1
0
0
0
0
2
1
0
0
0
0
2
2
0
0
2
0
0
0
2
2
0
0
2
1
0
0
0
1
2
1
0
2
1
2
2
0
0
0
0
1
1
1
1
1
0
2
2
0
2
0
2
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
3
0
0
0
0
1
2
0
4
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
2
1
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
3
1
1
0
0
0
2
0
3
3
1
0
2
0
0
0
0
1
1
2
0
1
1
0
0
0
0
3
1
0
0
0
0
0
2
0
0
0
2
1
0
0
1
0
0
1
2
0
0
1
0
0
0
0
2
2
0
0
2
1
0
1
0
0
1
0
0
1
1
0
3
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
1
2
3
2
1
1
0
1
0
0
2
0
0
0
2
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
3
2
0
0
2
0
0
0
2
0
0
2
0
0
0
1
2
0
0
1
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
2
1
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
2
2
0
0
0
0
3
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
2
0
0
0
0
0
0
0
2
1
3
0
1
0
2
1
2
0
1
1
0
0
0
0
2
1
0
0
2
2
0
2
1
0
0
0
0
0
0
2
0
0
2
0
0
2
3
0
0
0
2
0
1
0
0
0
0
3
0
1
0
0
0
0
1
2
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
1
0
0
1
1
0
0
2
0
0
0
1
0
1
0
0
0
2
0
2
0
0
0
2
1
1
0
1
4
0
2
1
0
0
0
2
1
0
0
0
4
0
2
0
2
0
0
0
0
0
1
0
1
0
0
0
0
2
1
0
0
0
0
2
0
2
0
1
0
0
0
0
0
1
0
0
2
1
0
0
1
0
1
0
0
3
1
0
0
2
0
0
0
1
0
2
2
1
0
1
0
0
2
0
0
0
2
0
0
0
3
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
2
0
1
0
2
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
2
0
0
1
1
0
1
0
2
0
2
0
0
0
2
0
0
0
2
0
1
1
2
0
0
1
1
0
0
0
1
0
0
1
0
2
2
0
0
1
0
2
1
0
0
2
1
0
0
2
1
0
0
0
2
1
2
2
1
1
1
0
0
0
0
0
0
1
2
1
0
3
0
0
2
1
1
0
1
0
0
1
2
0
0
0
0
0
1
0
0
0
2
0
3
2
0
0
1
1
0
0
0
2
0
0
0
0
1
0
1
0
0
2
0
0
2
2
0
2
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
2
0
2
1
1
0
0
0
2
3
1
2
0
0
0
0
0
0
0
1
3
0
0
0
2
0
0
2
0
2
0
0
0
0
0
2
2
2
0
1
2
0
0
0
2
0
0
1
3
0
2
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
2
0
1
0
1
0
0
3
1
0
2
0
0
0
3
1
0
0
2
2
0
1
0
0
0
0
2
0
2
0
0
0
0
0
1
0
1
0
0
1
2
2
2
0
0
0
0
1
0
0
1
0
2
1
1
0
0
1
0
0
0
1
0
2
1
0
0
1
2
2
0
0
0
0
1
0
0
1
0
0
0
1
0
2
1
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
12
0
2
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
2
0
0
0
0
1
0
2
0
1
3
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
2
0
0
0
2
0
1
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
1
0
0
0
2
1
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
3
0
0
1
0
0
0
0
0
1
2
0
1
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
1
0
0
0
2
1
0
0
1
0
0
0
0
0
0
1
1
0
2
1
0
0
0
0
0
2
1
1
1
0
2
0
0
2
0
2
0
0
1
1
0
1
0
2
0
0
0
2
2
0
0
1
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
1
0
2
0
0
0
0
1
0
1
0
2
0
0
0
0
1
0
0
1
0
0
0
1
0
2
1
2
0
0
2
2
1
0
0
0
1
2
0
0
0
0
0
0
5
0
1
2
0
0
0
1
2
2
2
1
0
2
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
1
1
1
1
0
0
1
2
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
2
1
2
2
0
0
0
0
0
0
0
1
0
1
0
2
3
0
0
1
2
2
0
0
2
0
2
0
1
3
0
1
1
0
0
1
0
0
2
1
0
0
0
0
1
0
1
0
0
0
1
1
0
0
2
2
0
0
0
2
0
0
1
1
0
0
0
2
2
0
0
0
0
1
0
1
0
0
0
0
0
0
2
1
0
0
2
1
0
0
0
1
0
0
0
2
2
0
1
2
1
0
0
0
0
1
2
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
1
5
0
0
1
0
1
0
2
0
0
0
0
0
1
1
0
0
0
0
2
0
2
1
1
1
0
0
0
0
2
0
0
0
2
0
0
0
2
1
0
0
2
0
0
1
1
0
1
0
0
2
0
1
0
0
0
0
3
0
2
1
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
1
0
0
0
0
2
1
0
1
0
2
1
0
0
0
0
0
0
0
2
0
1
0
2
1
0
2
2
2
0
0
1
1
0
0
1
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
2
0
2
0
1
2
1
1
2
0
2
1
0
0
2
2
0
0
0
0
2
2
0
1
1
0
0
0
0
0
1
0
2
0
1
0
0
0
2
0
0
0
0
0
1
1
1
2
0
0
2
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
2
2
1
1
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
2
0
1
0
0
1
0
1
0
0
0
2
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
1
1
0
0
0
0
0
0
2
0
4
0
0
0
0
0
2
0
0
1
1
0
1
0
0
1
0
0
1
0
0
2
0
0
0
0
2
3
0
0
0
1
0
2
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
1
0
0
0
2
2
0
3
2
1
0
0
1
0
1
0
0
0
1
2
0
0
0
0
3
2
0
0
2
0
0
1
1
1
2
1
0
1
0
0
1
0
0
0
3
0
0
3
1
0
0
0
0
0
0
2
0
0
0
1
2
0
2
0
0
0
1
1
0
0
1
1
0
0
0
2
3
2
1
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
2
0
2
2
2
0
0
0
0
2
0
0
0
2
2
2
0
0
0
1
2
0
3
1
1
0
1
2
0
1
0
2
0
0
2
1
1
1
0
2
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
1
2
1
0
2
0
0
0
0
2
0
0
0
0
0
2
1
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
2
0
2
0
0
1
1
0
2
1
0
0
0
1
0
1
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
2
0
2
2
2
1
1
0
0
1
0
2
4
0
1
1
0
0
0
1
0
0
0
1
0
1
0
1
2
0
0
0
0
0
1
0
2
0
2
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
1
1
2
0
0
3
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
2
0
0
2
0
0
0
0
2
0
2
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
2
0
0
0
1
0
0
2
1
2
0
0
1
2
0
1
1
4
0
0
0
2
0
1
0
0
2
2
2
1
2
1
1
0
2
2
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
2
1
0
1
0
0
0
0
0
0
2
1
0
0
0
0
2
0
1
0
2
0
2
0
0
0
0
0
0
0
3
6
0
0
0
0
0
2
1
2
0
0
0
0
1
2
0
0
1
2
0
0
0
1
2
1
0
1
0
0
1
0
1
0
0
2
0
0
1
0
1
0
0
0
2
1
0
0
2
1
1
3
0
0
0
2
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
1
0
1
2
0
1
0
0
0
0
1
2
0
1
0
0
0
2
4
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
2
0
1
0
1
0
0
0
0
0
2
0
0
2
1
0
1
2
0
0
0
0
0
0
0
3
0
0
1
2
0
0
0
3
0
1
0
1
0
0
1
0
0
0
0
0
1
0
2
0
0
2
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
1
1
0
2
1
0
4
2
0
0
0
1
0
1
0
0
0
1
0
1
2
1
2
0
0
0
1
0
0
2
1
0
1
0
0
0
1
1
2
0
2
0
0
0
0
1
0
1
2
1
0
1
0
0
1
0
2
2
0
0
0
0
0
0
0
0
1
1
0
0
2
1
0
0
2
2
2
1
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
1
0
0
0
1
0
0
2
1
0
0
0
0
0
0
1
1
0
3
0
2
0
1
0
2
1
0
0
0
1
0
2
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
1
0
0
0
3
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
2
2
0
1
0
6
0
1
1
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
1
0
0
2
1
1
0
0
2
0
1
0
3
1
0
2
2
0
2
2
2
1
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
1
0
0
2
0
0
1
1
0
0
1
0
1
1
0
2
1
2
0
2
1
0
0
0
1
1
0
1
0
0
0
0
0
0
2
0
1
0
0
3
0
0
2
1
1
0
2
0
0
1
0
0
0
1
2
0
0
0
0
0
0
2
0
1
1
2
0
2
0
0
1
0
0
0
0
0
0
1
0
3
2
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
1
2
0
0
2
0
1
0
0
2
0
0
0
0
1
1
2
2
0
2
2
0
0
0
1
0
0
1
0
0
2
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
1
0
1
0
1
2
0
1
1
2
0
0
0
0
0
1
0
0
0
0
0
1
3
0
2
1
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
5
2
2
2
1
1
0
0
2
0
0
1
1
0
0
0
0
2
0
2
0
0
1
0
0
0
0
2
0
1
0
0
0
2
1
0
0
0
2
0
1
0
0
2
2
0
3
0
2
2
1
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
1
2
0
0
0
0
0
1
3
0
0
0
0
0
1
1
0
0
0
0
2
4
0
0
0
0
2
1
1
0
0
2
1
0
1
0
0
0
2
0
0
0
0
2
2
0
0
0
0
4
3
0
1
0
1
0
0
1
0
1
0
0
2
0
0
0
0
6
0
0
0
0
2
0
0
0
2
1
1
0
1
1
0
0
2
0
0
2
0
0
2
2
0
0
1
0
3
0
0
1
0
0
1
2
0
1
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
1
2
1
0
2
2
0
1
1
2
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
1
2
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
2
0
2
0
1
0
4
2
3
0
0
0
2
2
2
0
0
2
0
0
0
3
0
0
0
1
0
0
1
0
0
2
2
0
2
0
2
2
2
0
1
0
2
0
0
0
1
0
0
1
1
0
0
1
0
2
0
0
0
1
2
0
3
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
2
0
0
0
0
0
1
2
3
0
0
0
1
0
0
0
0
3
0
0
0
1
0
0
1
2
0
2
0
1
2
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
2
0
2
0
0
1
1
0
1
0
1
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
1
2
0
0
1
2
0
1
0
2
1
0
0
1
0
1
0
0
0
2
1
2
0
0
0
1
0
0
1
2
0
0
1
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
1
0
2
1
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
1
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
2
0
1
0
0
4
0
0
2
1
2
1
2
0
0
1
0
2
1
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
2
0
0
0
2
0
2
0
2
0
1
0
0
4
0
0
0
0
0
2
0
1
0
1
2
0
0
0
0
2
0
0
0
2
0
2
1
0
1
0
0
0
0
2
0
0
0
0
1
2
0
1
0
0
2
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
2
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
2
2
0
2
0
1
1
0
0
2
1
0
0
1
0
0
1
0
0
0
0
1
2
0
0
1
0
1
2
1
0
1
1
0
1
1
1
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
2
2
2
0
0
0
1
0
0
1
0
1
1
0
2
2
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
1
1
0
2
0
0
0
1
1
0
0
1
2
0
0
0
0
0
2
0
0
2
2
1
2
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
1
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
2
2
1
2
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
2
6
1
0
0
0
1
2
0
0
2
0
1
0
1
2
0
0
0
0
0
0
1
2
0
0
0
1
2
1
0
1
0
0
0
2
0
1
3
2
2
0
1
0
2
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
2
2
1
0
2
0
1
0
0
1
1
0
2
2
3
0
0
0
0
1
2
2
2
0
1
1
2
0
0
2
0
1
0
0
2
0
1
0
0
0
0
1
1
2
0
0
0
0
0
0
2
1
0
0
1
0
2
0
0
2
0
1
0
2
0
2
0
3
2
0
2
0
2
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
2
0
1
1
0
0
2
2
2
2
0
0
0
2
0
2
0
0
4
0
0
2
2
2
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
2
0
2
1
0
1
1
0
0
1
0
2
0
0
0
0
0
1
0
0
0
2
0
1
2
0
0
0
0
3
0
0
2
0
0
2
0
2
1
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
1
1
1
0
1
0
0
0
2
2
0
1
0
2
0
0
1
0
0
0
0
2
0
0
0
2
0
0
2
3
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
3
0
2
0
0
2
2
0
0
0
0
0
0
1
1
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
1
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
1
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
2
0
1
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
3
0
0
0
2
0
0
1
0
0
2
0
0
2
0
1
0
1
0
0
2
1
1
0
2
0
1
0
0
0
0
0
0
0
2
1
1
0
0
2
3
0
2
1
0
2
0
1
3
1
0
0
0
4
0
1
0
0
1
0
2
1
0
0
1
0
0
1
0
0
2
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
2
0
1
0
0
0
0
0
1
1
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
2
1
0
0
2
0
2
0
0
0
0
0
0
3
1
2
0
0
2
1
0
0
0
0
0
1
0
1
0
2
0
2
0
2
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
2
0
1
0
0
0
1
2
0
0
0
1
0
0
2
0
2
1
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
1
0
2
0
0
0
0
1
0
2
1
1
0
0
2
0
0
0
2
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
2
0
2
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
2
0
0
1
0
0
0
0
2
1
1
0
2
0
0
0
1
0
2
0
0
0
1
0
1
0
0
2
0
0
0
0
0
2
2
0
1
0
2
0
0
1
0
1
2
0
2
1
1
0
0
1
0
1
1
0
0
1
1
0
0
2
1
0
0
0
4
0
2
0
0
0
0
0
0
0
2
2
2
1
1
2
0
1
0
2
0
1
0
0
0
2
0
1
2
3
1
0
0
0
0
1
1
0
1
3
0
1
2
0
0
0
0
0
1
2
0
0
0
1
2
0
1
0
2
0
0
0
0
0
2
0
0
0
2
1
0
0
1
0
0
0
1
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
1
2
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
3
1
1
0
0
0
0
0
0
1
1
2
2
2
1
0
2
4
0
0
0
2
1
0
0
0
0
1
0
2
0
0
0
2
0
0
2
1
3
0
2
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
3
1
2
2
0
0
0
0
0
1
0
0
2
1
2
1
1
2
2
0
2
0
0
0
0
0
0
2
0
1
0
0
0
1
0
2
1
0
0
0
1
2
0
2
0
0
1
2
0
1
1
1
0
0
0
0
1
0
0
2
1
0
0
0
2
2
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
2
2
0
0
1
0
0
0
1
0
1
0
1
3
2
2
0
0
0
2
0
1
0
1
0
1
0
0
1
2
0
0
0
2
0
0
0
2
0
0
0
0
0
1
1
2
2
1
0
2
0
0
0
0
0
0
2
1
0
1
0
2
0
0
0
0
1
0
0
0
2
0
2
0
1
0
1
0
1
2
0
0
0
1
0
0
0
2
0
0
0
1
0
0
1
2
0
0
2
0
0
0
0
0
0
2
0
0
1
1
0
2
0
1
1
1
0
0
0
0
1
2
0
1
1
2
0
1
0
0
0
1
1
2
3
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
2
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
2
1
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
3
2
0
1
3
1
0
0
2
1
1
1
1
2
0
2
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
1
0
0
2
3
0
1
0
1
2
2
2
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
1
3
0
0
1
0
1
0
1
1
0
0
0
0
0
3
0
0
2
0
0
0
0
3
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
1
2
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
2
1
1
3
0
2
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
1
0
0
0
2
1
0
0
2
1
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
1
1
2
0
0
1
1
0
0
0
1
0
2
2
2
0
1
0
0
1
0
0
0
0
0
1
2
0
0
0
1
0
1
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
2
0
1
0
0
3
0
1
2
0
2
0
1
2
0
0
1
0
1
0
2
1
0
0
1
1
2
0
0
0
1
0
0
2
0
0
2
0
2
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
1
1
0
0
2
0
0
1
0
0
3
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
1
0
2
0
0
1
0
0
0
3
0
0
2
0
0
0
0
2
1
1
0
0
1
1
0
0
0
1
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
2
2
3
2
4
5
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
2
1
0
0
0
0
1
0
0
0
1
0
1
2
0
0
0
0
0
0
0
2
2
0
2
2
3
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
1
0
0
0
3
0
0
0
0
0
0
1
2
0
1
0
0
2
1
0
2
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
2
1
0
1
2
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
2
0
1
1
0
2
0
0
2
0
2
1
0
1
0
2
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
2
0
0
0
1
2
0
0
0
2
1
0
0
2
0
0
2
0
1
0
0
0
0
1
1
1
0
0
0
2
0
0
2
1
2
0
1
1
1
2
0
4
0
0
0
1
2
2
0
1
0
0
0
2
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
3
0
2
0
0
0
0
3
0
0
2
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
2
0
1
0
2
0
0
0
1
1
0
0
1
1
0
0
0
0
1
0
1
0
1
2
0
0
0
3
0
1
1
2
0
1
3
1
0
0
0
1
2
0
0
1
0
0
0
1
0
2
0
0
0
2
1
3
2
0
0
0
2
0
1
1
0
0
0
2
2
0
0
2
2
1
1
0
0
2
0
2
0
0
0
0
0
2
0
1
1
2
1
0
0
0
2
0
0
2
0
0
2
0
0
3
0
2
0
2
2
0
0
0
1
0
1
0
0
0
2
0
0
0
0
2
0
0
2
1
0
0
1
0
0
0
0
3
2
0
2
2
2
0
0
0
0
2
0
0
0
0
0
2
2
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
3
1
1
1
1
0
0
1
0
0
0
0
0
1
2
0
0
1
0
1
0
1
2
0
1
0
0
0
1
0
0
2
0
0
3
2
1
0
1
2
0
1
1
1
1
0
1
0
0
4
2
0
2
0
1
0
0
1
0
0
0
0
4
0
0
2
0
1
1
0
0
0
1
2
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
2
4
2
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
1
0
2
1
0
0
0
1
2
2
0
1
2
0
2
1
0
2
2
0
0
0
0
2
0
1
0
0
2
2
1
0
2
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
5
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
1
2
0
0
0
0
0
0
0
0
2
2
1
0
1
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
1
0
0
3
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
3
0
2
0
0
0
0
0
0
0
0
1
2
0
0
1
0
3
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
1
0
1
0
2
0
0
0
2
0
0
0
1
2
0
0
2
0
0
0
2
0
0
1
1
0
2
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
1
1
1
1
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
2
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
1
0
1
0
0
0
0
0
0
1
2
1
1
1
0
2
2
0
0
2
0
3
1
1
0
0
0
0
0
0
1
0
0
0
1
2
1
0
0
0
1
0
0
0
0
0
2
0
1
0
0
1
2
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
4
0
0
0
0
0
2
2
0
0
0
0
2
1
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
3
1
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
1
0
0
0
1
1
2
2
0
0
1
0
0
3
0
0
2
0
0
0
0
2
0
2
0
0
1
0
1
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
2
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
2
0
1
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
1
0
0
1
0
2
3
0
1
0
0
2
0
0
1
0
0
0
1
0
2
0
0
0
1
0
5
2
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
2
2
3
1
0
0
1
1
0
0
1
0
0
1
1
0
2
1
0
0
0
2
0
2
0
2
1
2
0
0
1
2
1
0
0
0
0
0
1
0
2
0
2
0
0
1
1
0
0
0
0
0
0
1
2
1
0
2
0
1
2
0
2
0
2
0
1
0
0
0
2
0
0
0
0
0
2
2
0
1
2
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
1
1
0
2
2
0
0
0
1
0
1
2
1
1
2
1
1
3
0
0
2
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
1
0
0
0
3
0
0
0
0
0
0
2
2
1
0
0
0
0
0
1
0
1
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
1
0
3
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
2
0
0
0
0
0
0
0
2
0
0
1
1
2
0
1
0
1
0
0
2
1
0
0
1
2
2
2
0
0
0
0
0
0
1
0
2
0
0
0
1
0
2
0
0
0
0
2
1
0
0
1
0
0
0
0
0
2
0
1
1
0
0
0
1
0
0
2
1
0
0
0
0
1
0
1
0
0
0
1
0
2
0
2
1
1
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
2
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
2
1
2
2
0
1
0
0
3
0
2
0
0
0
3
2
0
2
0
0
0
0
2
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
2
3
0
0
1
0
0
0
2
1
1
2
1
1
0
0
2
0
0
0
0
0
0
0
1
2
0
0
4
0
0
0
0
0
0
0
0
1
3
0
0
0
0
1
1
0
1
0
1
1
2
0
0
0
1
2
0
2
2
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
1
1
0
2
2
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
2
1
0
0
2
2
0
1
0
0
2
2
0
0
1
2
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
2
2
1
1
0
2
2
0
0
2
0
1
1
2
1
2
3
0
1
0
1
1
0
0
0
3
0
1
0
0
1
0
1
0
2
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
2
4
0
1
0
1
1
0
2
1
1
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
2
1
0
0
0
0
1
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
2
0
1
0
0
2
0
0
0
2
1
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
2
1
1
0
0
1
1
0
0
2
0
0
1
2
0
2
2
0
0
0
5
0
2
2
1
0
0
2
0
2
0
0
0
0
1
1
3
2
1
1
1
0
0
0
2
0
0
1
2
0
0
1
2
3
0
0
2
2
1
0
0
0
0
0
0
2
0
5
1
4
0
0
1
0
1
0
2
0
1
1
0
2
0
0
0
1
0
0
0
0
0
1
0
1
1
0
2
0
0
1
0
2
1
1
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
2
1
2
0
0
0
0
0
0
0
2
0
2
0
1
0
0
1
2
0
1
3
0
0
1
0
2
0
0
2
2
0
1
1
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
1
2
0
1
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
1
0
0
2
0
3
2
1
0
0
0
0
1
1
1
0
2
2
0
0
0
1
0
0
0
0
0
2
2
1
2
1
3
0
0
2
1
0
0
2
3
0
1
0
0
1
2
0
0
0
2
0
0
0
1
0
0
3
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
2
1
1
2
0
0
0
1
0
1
1
0
1
2
3
0
0
2
2
1
0
0
0
3
3
2
2
0
0
0
0
0
0
0
3
0
0
0
1
0
2
0
3
0
0
1
2
2
4
0
0
0
0
2
0
1
0
0
0
1
0
0
2
2
0
1
0
1
2
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
1
0
2
2
2
0
0
1
0
2
0
1
0
0
1
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
1
0
0
1
0
0
0
0
2
2
2
2
2
0
3
0
0
0
2
0
0
1
3
0
0
1
0
0
0
0
1
2
1
0
2
2
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
1
0
0
0
0
2
0
0
1
1
0
2
1
2
0
0
0
0
0
1
0
1
3
0
0
0
0
0
0
2
2
0
1
0
1
2
0
1
1
1
0
1
2
1
0
1
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
2
1
0
0
1
0
2
0
0
1
1
0
2
0
0
2
0
0
2
0
2
1
0
1
0
0
2
1
0
3
0
0
0
1
1
1
0
1
0
2
0
0
0
0
2
0
0
0
0
2
0
2
0
1
0
0
1
0
0
0
2
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
1
1
1
0
0
3
0
0
0
2
0
0
0
2
2
0
1
2
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
1
0
2
0
2
0
1
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
1
0
1
0
0
2
0
1
3
0
0
1
0
0
0
1
2
6
1
0
2
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
3
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
1
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
3
1
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
1
2
2
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
3
2
0
2
3
0
0
0
0
2
0
0
0
0
2
0
0
0
2
1
0
0
1
0
0
3
1
0
0
0
0
0
0
0
0
1
3
0
2
2
0
0
2
0
1
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
2
2
1
0
2
0
1
2
2
0
0
0
0
0
0
1
1
0
0
2
0
0
0
3
0
2
2
1
0
1
1
0
0
2
0
2
0
0
1
0
1
0
1
2
0
0
0
2
0
0
1
2
0
1
1
0
0
0
0
0
0
2
0
1
2
0
1
0
1
6
0
0
0
0
1
0
1
0
3
2
0
0
0
1
0
0
0
2
2
2
0
0
1
1
0
0
2
2
0
0
0
1
0
0
0
0
1
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
2
1
5
1
1
0
0
0
0
0
0
0
3
0
2
0
0
0
3
0
0
1
2
1
2
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
1
2
0
1
0
0
2
1
0
0
0
0
0
0
0
1
1
0
0
2
0
1
2
0
1
2
2
0
0
0
0
0
0
0
5
0
0
2
0
0
0
1
2
0
0
0
0
1
2
1
0
1
0
2
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
1
2
0
0
0
0
0
1
2
2
1
0
2
2
2
0
0
0
0
0
1
0
0
1
2
0
0
0
1
0
0
0
0
2
3
0
0
0
0
2
0
1
1
0
0
0
0
1
0
1
2
0
0
0
0
0
0
2
2
2
0
0
1
2
0
1
0
1
1
1
2
2
2
1
0
1
0
0
0
1
1
0
0
1
0
0
2
0
0
2
0
0
0
1
0
0
0
1
0
2
0
0
1
0
0
0
1
1
2
1
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
1
2
2
1
0
0
0
1
1
1
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
2
1
0
2
0
0
1
0
0
0
2
1
0
2
1
2
0
2
1
0
0
1
0
1
0
0
0
1
0
0
2
0
1
2
0
2
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
3
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
2
0
0
1
0
1
2
0
0
0
0
0
2
0
2
2
0
2
0
3
0
0
0
0
0
2
0
0
2
1
0
1
0
0
0
0
2
0
1
0
2
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
2
0
1
1
0
0
0
3
0
0
0
0
2
4
0
2
1
0
0
1
1
0
0
2
2
0
1
1
1
0
0
0
1
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
2
1
0
1
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
4
1
0
2
3
4
0
0
1
0
2
1
0
0
0
1
0
0
0
0
2
1
0
0
1
0
0
2
1
1
0
0
0
0
0
1
2
0
1
0
1
1
1
2
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
2
2
1
0
0
1
1
0
2
0
0
0
4
0
0
2
0
0
1
0
1
1
0
0
2
0
1
0
2
0
2
1
2
0
0
0
0
2
0
2
0
0
0
1
1
1
0
0
0
0
2
0
4
1
0
0
0
0
1
0
2
0
0
0
0
0
1
1
1
1
2
0
1
0
0
2
0
0
0
0
3
0
0
0
1
0
2
0
1
2
4
1
2
2
0
0
3
0
0
0
0
2
2
1
0
2
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
2
2
0
0
0
0
0
1
0
2
1
0
0
0
1
1
1
2
2
0
2
0
0
2
2
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
1
0
1
0
0
2
0
2
0
0
3
0
1
0
0
0
0
1
1
0
0
1
1
0
2
0
0
2
0
0
1
0
2
0
2
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
1
0
1
1
0
0
0
0
0
1
2
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
2
0
0
2
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
2
0
2
3
0
0
1
2
0
3
1
0
0
2
1
0
1
1
0
2
0
1
2
0
1
2
2
2
0
0
0
1
1
0
1
2
0
0
4
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
1
0
2
0
0
2
0
0
0
2
2
1
1
0
0
0
0
1
1
1
1
0
0
2
0
1
1
0
0
0
2
2
0
2
0
0
0
0
1
0
1
0
0
1
0
0
1
0
1
0
0
1
0
1
2
0
1
0
0
0
0
0
0
0
1
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
2
1
2
0
2
0
0
0
2
2
2
1
0
0
1
0
0
2
0
0
1
0
0
0
2
0
0
1
0
1
0
0
0
0
2
0
2
2
0
0
0
0
4
1
0
2
4
0
1
1
0
1
0
0
0
1
1
0
0
0
2
1
0
0
0
1
2
0
0
0
0
2
0
0
0
0
2
0
2
2
2
0
0
0
0
2
1
0
0
1
2
0
0
2
1
0
1
2
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
2
0
2
0
0
0
0
0
0
1
1
1
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
2
0
2
0
0
2
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
2
0
1
0
0
0
0
2
2
1
0
0
0
0
1
0
1
0
0
0
1
2
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
1
1
0
0
2
2
1
0
0
1
0
2
2
0
0
0
0
1
2
0
2
0
2
0
0
2
0
2
0
0
2
0
2
1
0
0
0
0
0
4
2
0
2
0
2
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
2
0
2
0
0
2
1
0
0
2
2
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
1
0
1
0
2
0
0
0
1
0
0
2
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
1
3
1
0
0
2
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
1
2
0
0
0
1
0
0
1
0
0
1
0
0
1
2
2
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
2
0
3
1
1
0
0
1
0
0
1
0
0
2
2
2
0
0
0
0
1
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
3
2
0
0
0
0
0
0
0
0
0
2
0
0
3
2
0
0
1
1
0
2
2
0
0
0
0
0
0
2
1
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
3
0
0
0
1
1
2
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
2
2
0
0
0
0
1
0
1
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
2
1
1
0
0
0
0
0
0
1
2
0
2
0
0
0
0
2
2
0
0
0
0
1
1
0
1
1
2
0
0
0
1
0
0
1
1
0
0
0
0
2
1
0
0
2
1
0
0
0
0
2
2
1
0
2
0
2
0
2
1
0
2
2
0
0
0
1
2
1
0
0
2
2
0
0
3
0
0
2
1
2
0
0
3
0
2
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
2
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
1
1
0
0
0
0
0
2
0
2
1
0
0
0
1
1
2
0
1
2
0
0
0
2
0
2
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
1
1
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
4
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
1
1
0
2
1
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
1
2
0
0
0
2
0
2
0
1
2
0
0
0
0
2
1
1
0
1
1
0
0
0
0
2
1
2
0
0
1
0
0
1
0
0
2
0
0
2
2
5
0
0
0
1
2
2
0
0
0
0
0
3
2
0
0
0
0
2
0
2
1
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
2
2
0
1
1
1
1
0
0
0
0
0
0
0
0
2
1
0
1
0
1
0
0
0
1
0
0
1
2
0
0
1
0
2
0
0
0
0
2
0
1
0
0
2
2
0
1
0
0
1
1
0
2
0
0
1
0
0
1
2
1
0
1
0
0
0
0
1
1
0
4
0
1
0
1
2
2
0
0
0
0
0
0
0
0
3
2
1
0
0
2
0
4
1
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
2
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
3
0
0
2
0
0
0
0
3
0
1
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
2
1
0
1
0
2
2
0
0
1
0
1
0
0
1
2
1
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
1
1
2
1
1
0
0
2
2
1
0
0
5
0
2
1
1
0
0
1
2
0
1
0
1
2
0
0
1
2
1
2
0
0
1
0
0
0
0
1
0
1
2
2
1
1
0
1
3
1
3
0
0
0
0
1
0
1
1
0
1
0
2
2
0
0
1
2
2
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
3
1
0
2
2
1
1
2
0
0
0
2
0
2
1
0
0
0
3
2
1
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
3
0
1
0
3
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
1
1
0
0
0
0
0
2
0
1
0
0
1
3
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
3
0
0
0
0
0
3
2
2
0
0
2
0
2
0
0
2
2
0
0
0
0
1
0
0
1
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
1
1
1
0
0
0
0
1
1
0
2
3
0
0
2
0
0
0
1
2
0
0
0
2
0
0
0
2
0
0
2
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
1
0
2
2
0
1
0
2
0
0
0
0
1
0
0
1
1
2
2
1
0
0
0
1
1
1
2
0
0
0
1
0
0
0
1
0
0
0
2
0
0
2
2
1
0
0
0
2
2
1
0
0
0
0
1
1
0
3
0
0
0
1
0
0
2
1
1
0
2
2
0
0
3
2
4
0
0
0
0
2
0
2
0
0
3
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
2
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
5
0
0
2
0
2
0
0
6
0
0
0
0
1
1
1
0
2
1
2
0
1
1
0
0
0
1
0
0
0
0
2
0
2
0
1
0
2
0
0
0
0
0
0
1
1
2
0
0
1
1
2
0
0
0
1
0
0
0
0
2
0
2
0
1
1
0
2
0
0
0
2
0
1
0
1
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
2
0
1
0
1
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
2
1
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
2
2
0
2
1
0
0
0
0
1
1
1
1
0
0
1
1
0
0
2
1
1
0
1
0
1
0
0
1
0
0
1
0
2
0
1
0
1
2
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
1
3
0
0
0
2
1
0
0
0
0
0
1
0
0
2
0
0
0
0
1
2
1
0
2
1
0
2
2
0
1
0
0
0
1
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
2
2
0
1
0
2
0
0
0
2
0
0
0
1
2
0
0
0
0
0
3
0
0
2
1
2
0
0
1
2
0
0
0
2
0
2
2
0
0
0
0
1
2
2
0
0
1
0
1
1
2
1
0
0
0
1
1
0
0
1
2
2
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
2
0
0
1
0
0
0
1
0
0
1
3
0
2
2
2
0
0
0
0
0
2
0
1
2
0
2
1
0
0
0
0
0
0
3
1
2
0
0
2
0
0
0
0
0
1
2
1
1
0
1
0
1
2
0
0
1
1
1
0
0
0
0
0
0
1
0
2
0
0
1
2
1
4
0
0
0
3
0
0
0
0
0
1
0
0
0
2
0
1
2
0
0
1
0
0
1
1
1
1
2
2
2
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
5
0
0
2
0
0
0
0
0
1
2
2
0
3
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
2
0
1
3
0
2
0
2
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
1
0
1
0
0
3
0
0
0
0
2
0
2
1
1
0
0
0
1
0
2
0
1
1
1
2
0
0
0
0
0
2
1
0
0
1
1
0
1
0
0
0
0
2
0
0
1
2
0
2
0
0
1
0
2
2
0
0
2
0
0
0
0
0
0
0
2
1
3
0
0
0
1
1
0
0
1
1
1
0
1
0
0
0
2
2
0
0
1
0
2
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
2
0
2
2
0
0
1
2
1
0
1
0
0
2
0
0
0
0
0
1
0
0
2
0
0
1
0
1
1
0
0
1
2
0
1
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
3
1
0
0
0
0
0
0
0
1
1
0
0
0
2
2
0
2
0
0
0
0
2
0
0
1
0
0
0
1
0
2
2
0
0
0
4
0
0
0
0
0
0
1
2
1
2
0
2
0
0
0
2
0
2
1
1
1
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
1
1
2
1
0
1
0
0
0
0
0
0
2
1
2
0
2
2
0
0
1
2
0
0
0
1
0
4
1
2
0
0
1
1
2
0
1
1
1
0
2
0
0
0
2
0
0
0
0
2
2
2
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
2
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
1
1
0
0
0
0
0
0
0
0
2
0
1
2
0
0
1
0
1
1
0
2
0
1
0
0
0
2
7
2
1
0
0
2
0
0
0
0
1
2
1
0
0
1
0
3
0
0
1
3
0
0
0
0
0
0
2
1
1
0
0
0
1
1
0
2
0
0
0
0
0
0
2
0
0
4
2
1
2
0
0
0
2
0
2
0
0
1
2
0
0
2
0
0
1
2
0
1
0
3
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
1
0
0
1
1
1
2
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
1
1
1
0
2
0
0
1
0
0
0
0
0
0
1
2
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
2
0
1
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
3
4
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
2
0
1
0
1
0
1
2
0
2
0
0
0
0
1
0
0
1
0
2
0
0
0
1
2
0
0
0
0
0
1
0
0
0
1
0
2
1
0
0
0
0
2
0
1
1
0
0
2
0
0
0
0
0
0
2
1
3
0
0
0
0
0
2
1
0
3
0
1
1
0
0
0
1
0
0
2
0
0
0
0
0
2
1
0
4
0
0
0
1
0
0
1
2
1
0
0
1
2
0
0
3
2
0
2
1
0
1
1
0
0
0
0
1
3
1
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
2
1
5
0
0
0
1
1
2
0
0
1
0
1
0
0
0
0
0
3
2
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
1
0
2
0
1
0
0
1
0
1
0
2
1
1
0
0
0
2
1
0
2
0
0
0
1
1
0
1
0
1
0
0
0
0
0
1
0
0
2
0
0
2
0
2
2
0
0
1
0
0
2
1
0
0
2
1
0
0
0
0
1
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
1
1
0
2
1
0
1
1
0
0
2
0
2
0
2
1
3
2
2
0
0
0
0
0
0
0
3
0
0
0
0
3
0
0
0
2
2
0
2
0
0
0
0
0
1
2
2
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
2
1
0
1
3
0
0
1
1
0
0
0
0
1
2
0
0
1
0
0
1
0
0
1
0
0
2
2
0
0
1
1
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
2
0
0
0
1
1
1
0
2
0
2
1
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
2
0
2
2
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
1
2
0
0
0
1
0
2
0
0
1
1
0
0
3
0
0
0
0
0
0
1
1
1
0
1
0
2
2
0
2
0
0
2
2
0
0
0
3
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
2
4
0
0
0
0
1
0
3
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
1
1
0
1
0
0
0
2
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
2
0
0
1
0
0
0
2
2
0
0
3
0
1
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
2
0
2
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
3
1
2
0
2
0
0
0
1
2
0
0
0
2
0
0
3
1
0
1
0
2
2
1
0
0
2
0
0
0
0
0
0
2
1
0
0
2
0
0
1
1
0
0
0
0
2
1
0
1
0
0
1
1
2
0
3
2
1
0
0
0
0
2
0
0
3
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
2
0
1
2
0
0
2
0
0
0
0
0
0
2
2
1
2
0
0
0
2
0
2
2
0
0
0
0
1
2
2
1
2
0
0
0
1
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
8
0
0
2
0
0
0
0
2
0
1
0
1
0
0
0
1
4
0
0
2
0
2
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
1
0
0
1
0
1
2
2
1
0
0
1
0
0
1
0
2
0
2
0
0
0
2
1
0
1
2
2
0
2
0
2
1
0
0
2
0
0
1
2
0
2
2
1
1
0
2
0
0
0
0
0
0
0
0
2
0
0
2
1
0
2
0
1
1
0
0
2
0
2
0
0
0
0
0
4
0
3
0
1
2
0
1
0
3
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
1
0
0
2
0
0
2
1
0
1
0
2
0
1
0
2
0
0
1
0
0
2
0
0
0
2
0
0
0
0
1
0
2
0
2
0
0
1
0
0
2
1
0
0
3
0
2
0
0
0
0
0
2
2
2
1
0
0
1
2
2
0
0
0
0
0
2
2
0
2
2
0
0
2
1
0
0
0
1
1
0
1
2
0
2
0
0
0
0
1
1
0
0
0
0
0
0
1
2
0
1
0
1
0
0
0
0
2
1
0
1
2
1
2
0
0
0
1
0
0
0
0
0
0
1
0
2
2
0
0
2
0
0
1
0
0
2
0
0
0
1
0
0
0
0
4
0
0
0
0
0
1
2
6
0
0
0
0
1
0
1
1
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
1
0
2
0
1
0
1
0
0
2
0
0
0
0
2
0
1
0
0
0
0
2
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
3
1
0
2
0
2
2
0
0
1
0
1
0
0
0
0
0
1
0
0
1
2
0
0
0
1
0
0
0
2
1
0
3
0
2
0
0
2
0
1
0
0
0
0
2
0
2
0
2
0
2
0
0
0
0
0
1
2
2
0
2
0
2
0
0
0
1
2
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
2
0
0
2
1
1
1
0
0
1
0
0
0
2
0
0
2
0
1
0
2
0
0
0
0
1
1
0
2
1
0
0
0
1
1
0
0
2
1
0
3
2
0
0
3
2
2
0
0
1
0
0
0
0
0
0
0
1
1
0
0
2
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
2
2
0
2
0
2
0
0
0
0
0
0
1
0
1
0
2
1
0
1
1
0
0
0
2
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
2
1
1
0
1
0
0
1
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
1
1
0
1
0
0
2
0
0
0
0
2
0
1
0
2
1
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
1
1
3
1
0
0
0
0
1
0
0
0
3
0
2
0
1
1
2
2
1
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
1
2
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
1
1
0
2
0
1
1
0
0
4
1
0
0
2
2
0
0
0
0
0
0
0
0
3
2
1
0
1
0
0
0
1
0
0
0
0
2
0
0
0
5
0
2
1
0
0
0
1
1
2
0
0
0
0
0
1
0
2
0
0
1
0
1
1
0
1
0
0
2
0
1
1
1
0
0
2
0
0
1
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
2
0
0
2
0
0
1
0
1
0
0
7
1
0
0
2
0
0
0
2
0
1
0
0
2
0
2
0
1
0
0
2
1
0
2
0
0
0
3
0
0
1
0
2
0
1
2
2
0
2
1
0
1
0
2
0
0
0
2
1
0
3
0
0
0
0
1
0
0
0
2
1
1
0
0
0
0
2
0
1
1
2
1
0
2
2
0
0
2
0
2
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
4
0
1
2
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
3
0
0
0
0
2
1
0
1
0
2
0
0
0
0
2
0
0
0
1
2
1
0
0
0
2
0
0
2
0
0
0
1
0
1
0
2
1
0
0
0
2
0
2
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
2
1
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
2
0
1
0
2
0
1
1
0
0
0
0
2
2
1
0
0
0
1
1
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
2
2
0
0
1
0
0
0
0
2
0
0
1
1
0
2
2
0
0
2
1
0
0
2
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
2
1
1
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
1
9
1
0
0
1
0
0
2
2
0
0
2
0
0
0
0
2
0
1
0
1
2
0
0
0
1
0
0
0
1
0
0
1
2
0
0
0
2
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
4
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
3
0
0
0
2
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
1
0
2
0
1
0
0
0
3
0
0
0
0
0
2
0
2
1
0
0
0
0
0
2
1
0
0
1
2
0
0
0
1
0
0
0
0
0
1
0
0
0
1
2
3
0
0
0
0
2
0
2
0
1
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
1
4
2
0
0
0
0
0
2
0
0
0
1
2
0
2
0
4
3
1
0
0
0
0
1
1
2
0
0
0
2
0
0
0
2
1
1
2
2
2
2
0
2
2
2
3
0
0
0
3
0
0
0
0
1
2
0
0
2
1
0
0
0
0
0
2
2
0
0
2
3
1
0
0
0
0
0
0
2
0
0
2
2
0
0
0
4
1
0
0
0
0
2
1
0
1
1
1
0
0
0
2
0
0
0
0
0
1
1
2
0
0
0
1
1
3
1
1
0
0
0
0
0
0
0
2
0
0
1
0
2
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
3
2
2
0
1
0
0
0
1
0
1
2
2
1
0
0
0
0
0
2
3
0
0
1
1
2
0
1
2
0
2
0
2
0
2
0
0
0
1
0
2
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
2
0
1
0
2
3
0
0
0
0
0
0
0
0
0
2
2
2
0
2
0
1
1
0
0
0
2
2
0
0
5
0
0
1
0
2
2
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
1
1
1
0
1
1
1
0
2
2
0
2
0
0
1
0
0
1
0
0
0
2
2
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
1
0
0
1
0
1
0
2
0
0
2
0
1
0
0
3
0
1
0
0
0
0
2
0
0
0
1
0
1
0
0
1
0
0
0
1
0
2
2
1
2
0
2
0
0
1
0
0
0
0
0
2
1
2
0
1
2
0
2
2
0
0
0
1
2
1
0
2
0
0
0
1
0
0
2
1
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
2
0
0
0
1
0
2
0
3
0
0
0
5
2
0
0
3
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
2
0
1
2
0
0
0
1
0
1
2
0
2
2
0
0
0
1
1
0
4
0
2
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
2
1
1
1
1
0
0
0
0
0
1
0
2
1
0
0
0
0
0
2
2
1
2
0
1
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
1
1
1
1
0
0
0
0
0
2
0
2
1
1
1
0
0
0
2
1
0
1
0
1
2
0
0
0
0
2
0
1
0
0
3
0
0
2
0
1
2
1
2
2
0
0
2
0
0
0
0
0
2
0
1
3
2
0
2
0
0
1
0
0
2
2
0
2
0
2
1
0
2
1
1
0
0
1
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
1
0
2
0
2
0
0
1
0
3
1
0
0
2
3
0
1
0
0
0
2
0
5
0
1
1
0
1
0
0
1
1
0
3
1
0
0
0
1
0
2
0
1
0
1
0
1
0
0
0
1
1
0
0
2
0
0
1
0
1
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
5
0
0
1
0
2
0
2
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
2
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
1
0
2
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
1
2
0
5
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
2
2
0
0
1
0
1
1
2
0
0
0
2
1
0
0
0
0
0
0
1
0
0
1
0
0
1
1
2
4
2
0
1
0
1
0
1
0
0
2
0
1
0
1
1
2
0
0
0
0
2
1
2
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
2
1
2
0
0
1
0
3
0
0
0
2
1
2
0
0
3
2
2
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
2
0
0
2
0
0
1
0
0
2
0
0
0
0
0
2
0
1
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
2
0
0
2
0
0
0
1
1
1
0
0
1
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
2
1
2
1
0
2
0
0
1
0
0
2
1
2
0
0
1
1
0
0
0
0
1
2
1
1
0
0
0
4
1
1
2
2
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
1
0
0
0
2
0
0
0
1
1
0
0
0
2
0
0
2
2
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
1
2
0
0
1
0
2
2
0
0
1
0
2
0
0
2
0
0
0
1
0
0
2
1
1
2
0
0
0
0
0
2
0
1
2
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
2
2
2
0
0
0
0
2
1
2
2
2
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
2
0
1
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
1
0
0
0
0
1
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
3
2
1
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
2
2
0
1
3
0
0
0
0
0
1
0
4
1
1
0
0
0
1
0
0
0
0
1
0
2
0
0
0
1
1
2
0
0
0
0
0
1
2
1
0
0
1
2
2
0
2
2
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
1
0
2
2
1
2
0
0
0
0
0
2
0
1
0
2
2
0
1
0
0
2
1
2
2
0
2
0
0
0
0
2
2
1
2
0
0
1
1
2
0
2
2
0
1
0
0
0
0
2
1
0
1
0
0
2
0
0
1
0
0
1
2
0
0
0
0
2
0
0
0
0
4
1
0
2
2
0
0
0
2
0
2
0
0
1
2
1
2
0
2
1
1
0
0
0
0
1
1
1
3
0
0
1
0
0
1
0
2
0
0
2
1
1
1
0
0
0
2
1
2
0
3
0
1
0
0
0
4
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
3
0
1
0
0
0
0
0
2
0
2
0
1
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
2
0
1
1
0
0
0
0
2
0
2
2
2
0
1
0
2
2
2
2
0
0
0
1
0
0
0
0
0
3
0
1
0
0
0
1
1
0
0
0
0
3
0
1
0
0
0
0
1
1
1
0
0
0
0
2
0
0
0
0
2
1
1
0
0
0
0
0
3
0
0
1
0
0
0
1
0
0
0
0
0
0
2
1
0
0
1
3
4
1
0
2
0
0
0
0
0
0
0
2
0
2
1
0
1
2
0
0
0
0
2
0
0
2
0
0
0
2
0
1
0
0
0
2
2
0
0
0
0
0
0
0
1
0
1
0
1
0
2
2
1
0
0
0
0
2
1
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
3
0
0
3
0
0
1
2
0
0
2
0
2
2
0
0
0
0
2
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
2
2
2
0
1
1
1
0
0
0
0
1
0
0
0
5
0
1
1
0
2
0
0
0
0
2
0
0
3
1
2
0
0
0
0
1
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
1
2
0
0
1
0
0
2
1
3
1
1
0
2
0
2
0
2
0
0
0
2
2
0
1
0
1
1
0
1
0
5
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
1
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
2
0
2
2
0
0
0
0
2
0
2
1
0
2
2
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
2
2
0
2
1
0
2
0
0
0
0
0
2
0
1
0
2
1
2
1
0
1
0
0
1
2
0
1
0
0
0
1
2
2
3
0
2
0
2
0
0
0
0
0
0
0
2
1
0
0
0
2
2
2
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
1
2
0
0
2
0
5
0
2
0
0
0
0
0
0
0
0
0
1
1
2
0
0
2
0
0
0
2
0
2
0
1
0
0
2
1
0
1
0
0
0
0
0
0
0
3
0
1
0
0
0
3
0
0
0
0
0
2
1
0
2
0
0
0
2
0
0
1
0
1
1
0
0
0
0
0
0
1
0
1
1
2
1
0
0
6
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
1
4
0
3
2
0
2
0
0
0
1
1
2
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
3
0
0
0
0
3
0
1
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
1
0
2
0
1
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
1
0
0
1
0
0
2
1
0
0
2
2
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
1
0
0
2
1
1
0
1
0
0
0
0
0
0
2
1
2
0
0
1
0
2
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
3
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
1
0
0
0
2
1
0
2
0
0
0
0
2
0
0
7
0
0
1
0
1
1
0
1
0
1
0
0
0
0
0
2
0
0
2
2
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
2
0
1
0
0
1
0
0
2
1
0
1
0
0
0
0
0
2
0
2
0
2
2
1
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
1
1
1
0
0
1
2
2
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
2
0
0
0
1
1
0
0
0
0
0
0
0
6
0
0
0
2
1
0
1
2
1
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
2
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
1
0
1
1
0
0
1
1
1
0
0
2
2
1
0
1
2
0
0
2
0
0
0
1
2
0
0
0
3
0
0
1
0
0
0
0
1
1
0
2
0
2
0
3
0
1
0
0
2
1
2
0
0
0
0
1
1
1
1
0
0
1
0
4
0
0
2
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
1
0
2
1
1
1
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
1
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
2
0
1
2
1
1
1
0
0
1
1
2
0
2
2
0
1
0
2
0
0
2
0
0
0
0
0
2
0
2
0
0
0
2
1
5
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
1
2
0
2
0
0
0
1
2
0
0
2
0
0
0
0
0
0
1
2
1
4
0
0
0
0
0
0
7
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
2
2
1
0
0
1
0
0
0
0
0
1
0
1
1
1
1
0
2
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
1
1
0
0
0
0
1
0
0
0
3
1
2
0
0
0
0
3
1
0
0
0
0
3
1
0
0
0
0
0
2
0
1
2
0
2
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
1
1
1
0
0
0
2
0
0
1
0
0
2
0
0
0
3
2
0
0
2
0
1
1
0
0
0
2
0
2
0
0
0
1
2
1
0
0
0
2
0
0
0
0
2
1
0
1
2
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
2
0
2
2
0
0
0
2
0
1
0
3
0
0
2
1
0
2
0
0
0
0
2
0
1
0
1
0
0
0
0
1
0
1
0
2
2
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
2
2
0
1
1
0
0
0
1
2
0
2
0
2
1
0
0
1
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
2
0
2
3
0
0
0
0
0
0
1
2
0
1
1
0
0
1
0
0
2
0
0
0
0
0
2
0
1
2
2
0
1
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
2
0
0
1
2
0
1
0
0
0
1
4
1
0
2
1
2
0
1
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
1
1
1
1
0
0
0
1
0
0
1
0
0
0
2
0
0
2
0
0
1
2
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
3
2
0
0
0
0
1
0
1
0
2
0
2
1
0
0
0
1
2
0
1
0
1
0
0
3
1
0
0
4
0
1
1
2
0
1
2
0
0
0
1
0
0
0
1
2
0
0
0
0
2
0
0
0
2
4
0
2
1
0
1
0
0
2
0
0
0
2
0
0
2
1
0
0
0
2
0
0
1
1
0
2
1
0
1
0
0
2
0
0
3
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
2
1
0
1
1
0
2
0
1
0
0
0
0
0
0
1
1
2
1
0
0
0
0
0
0
0
1
2
3
0
0
0
0
0
2
0
0
2
0
0
1
1
0
0
2
0
1
0
2
1
0
0
0
0
0
0
0
0
1
1
3
1
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
2
1
0
1
1
0
0
1
1
3
0
0
1
2
1
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
2
0
2
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
1
1
1
2
0
0
1
0
0
0
0
2
1
0
0
0
2
3
0
1
0
0
0
0
3
1
1
1
0
0
0
0
0
2
0
1
1
0
3
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
2
1
0
2
0
2
3
1
0
0
2
2
0
2
0
0
1
1
0
0
0
0
0
1
0
3
0
1
0
0
2
3
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
2
1
0
0
0
0
2
2
1
0
0
0
2
1
2
1
1
0
2
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
2
2
0
0
2
2
1
3
0
0
0
0
0
0
2
1
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
1
2
2
0
0
0
2
1
0
0
0
1
0
2
2
3
0
2
1
0
2
2
0
0
1
0
2
2
0
0
1
0
0
1
2
0
0
0
0
1
0
0
0
0
0
2
3
0
0
2
1
0
0
0
1
2
1
1
0
0
1
2
2
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
1
0
5
1
2
0
1
2
0
0
0
1
1
0
1
2
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
1
0
1
0
3
0
1
0
0
0
2
0
1
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
2
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
2
0
0
1
0
0
0
2
0
0
1
3
1
0
1
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
1
1
0
0
0
2
0
0
2
2
2
0
2
0
0
0
0
0
0
0
1
2
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
1
0
0
0
1
0
1
1
0
1
1
0
1
0
0
0
0
0
1
0
2
1
1
0
0
0
0
0
2
1
0
0
1
1
1
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
2
0
2
1
2
0
0
0
2
1
0
0
0
0
0
0
2
0
5
0
2
0
1
2
1
0
0
0
0
1
0
1
1
2
0
2
1
1
0
0
3
0
2
1
0
2
0
2
0
0
0
1
0
0
0
2
0
1
0
0
0
0
2
1
1
2
2
2
0
0
0
1
0
0
1
1
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
2
0
1
1
2
0
0
0
2
0
0
2
1
0
0
0
0
2
0
0
0
0
0
2
2
3
1
2
0
2
1
0
0
1
1
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
2
2
0
3
0
2
1
2
2
1
2
0
0
0
0
0
0
0
2
1
0
0
0
2
2
1
0
0
2
2
0
0
0
3
0
1
2
0
2
1
0
0
0
0
0
0
2
2
2
2
0
1
0
0
0
0
2
0
2
0
0
2
1
0
0
0
1
0
4
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
2
2
0
0
2
1
0
0
0
4
3
2
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
3
0
0
0
0
1
1
0
0
1
0
2
0
3
1
0
0
0
1
2
2
0
0
0
0
0
2
2
2
2
2
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
1
1
1
2
1
1
0
0
2
0
0
1
0
5
0
2
0
0
1
0
2
0
0
0
0
0
0
2
2
1
1
0
1
0
0
0
1
0
0
0
0
2
0
0
1
0
0
1
1
0
0
0
0
0
3
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
3
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
1
2
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
2
1
2
0
1
1
0
2
0
1
1
1
0
2
2
0
0
1
0
0
1
1
0
1
0
0
1
1
0
2
0
0
0
0
0
5
1
0
0
2
0
1
0
0
1
0
3
0
0
0
1
0
0
2
0
0
2
0
0
0
1
0
0
1
2
0
0
2
1
0
1
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
1
0
1
1
0
0
1
0
0
1
1
0
1
4
0
0
0
0
0
0
0
1
1
1
0
0
2
0
0
0
0
2
0
3
0
2
0
0
1
0
3
0
1
1
1
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
3
1
0
2
0
2
1
0
0
0
0
0
1
1
2
2
0
0
0
1
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
1
0
1
1
0
1
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
2
0
1
1
1
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
2
0
0
1
0
1
1
1
2
0
0
3
1
0
1
0
0
1
1
2
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
2
0
1
2
0
2
0
0
0
0
3
0
0
1
1
2
2
1
2
1
0
0
1
2
2
2
0
0
0
0
0
0
0
0
0
0
0
2
1
1
2
1
2
1
0
2
0
1
2
0
0
0
2
2
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
2
0
2
0
0
0
0
0
0
0
1
0
1
0
1
2
0
0
2
0
1
1
6
0
0
0
1
2
2
1
0
2
0
0
1
0
2
1
0
1
0
0
0
0
0
0
0
0
2
0
1
2
2
2
0
0
0
1
0
3
0
2
1
4
0
0
2
1
0
0
2
0
0
0
0
1
0
0
0
0
1
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
2
0
0
3
0
0
3
0
0
0
0
0
0
0
0
2
0
0
2
3
0
2
0
0
1
0
1
0
2
1
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
1
1
2
0
2
0
0
0
1
1
2
2
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
2
2
1
1
0
0
2
0
1
1
1
0
2
0
0
2
1
0
0
0
2
0
1
1
2
0
0
1
0
0
1
0
1
0
3
0
0
0
0
0
1
2
2
1
0
0
0
0
2
5
0
0
0
2
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
1
2
0
0
0
0
2
0
0
1
2
0
1
0
0
1
5
0
2
1
0
2
0
0
0
0
0
1
0
2
2
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
2
0
1
0
0
4
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
2
2
0
0
3
0
0
1
0
2
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
2
3
0
1
0
0
1
2
0
0
0
0
0
0
1
1
0
3
0
0
2
0
0
0
0
2
2
0
1
2
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
1
2
2
0
1
0
0
0
2
1
0
0
0
2
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
2
1
3
2
2
2
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
1
1
1
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
3
0
0
0
0
0
2
2
0
0
1
2
2
0
0
0
0
0
1
2
0
1
2
1
0
0
0
0
1
0
0
0
0
1
1
2
0
0
1
0
1
1
0
0
2
0
0
0
2
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
2
1
0
2
0
0
0
2
1
0
2
0
0
2
0
5
0
0
0
0
1
2
0
1
2
0
2
2
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
2
0
0
2
0
1
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
1
1
0
0
3
2
0
1
0
2
1
1
0
0
2
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
1
2
1
0
0
0
0
1
0
6
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
2
0
2
0
1
2
0
0
0
0
0
0
1
0
0
2
2
0
2
0
0
0
0
2
0
0
1
2
2
2
0
1
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
1
0
1
1
1
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
2
0
1
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
2
0
2
0
2
1
0
0
1
2
0
0
0
2
0
1
2
1
0
0
0
2
0
0
0
0
0
0
0
1
0
2
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
2
1
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
1
0
0
1
1
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
1
0
1
2
0
2
0
0
1
0
1
0
0
1
0
0
0
1
0
1
2
0
0
1
0
1
0
1
0
0
0
0
0
0
0
2
0
1
1
0
1
0
0
0
0
0
2
0
0
5
0
0
2
1
0
1
0
0
1
0
0
2
2
0
1
0
5
0
0
0
1
0
0
0
0
2
1
0
0
2
1
2
0
1
0
2
0
2
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
2
0
1
0
0
1
1
0
0
0
0
0
0
2
2
2
0
0
2
0
0
3
0
0
1
2
0
0
0
3
2
0
0
1
3
0
0
0
1
0
0
0
2
0
1
2
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
2
1
0
0
2
0
0
0
1
0
0
0
0
2
2
0
2
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
1
0
0
2
0
2
0
0
0
2
0
0
0
2
1
1
2
1
2
2
0
0
2
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
2
0
0
2
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
2
1
0
1
0
0
0
2
1
0
0
0
0
2
0
1
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
3
1
0
0
0
1
0
0
1
0
0
1
0
0
2
0
2
0
0
0
2
0
0
2
1
0
0
0
2
2
0
0
0
0
3
0
2
0
2
0
1
0
3
2
2
4
3
1
0
0
1
1
2
0
1
0
2
0
0
0
2
0
1
0
0
2
0
0
2
0
0
2
2
0
0
0
2
3
0
2
0
0
0
0
2
2
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
2
0
0
2
0
0
0
0
0
2
1
0
2
1
0
1
0
2
0
0
2
0
0
0
0
0
0
0
2
0
3
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
2
0
0
2
0
0
0
2
1
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
1
1
2
0
0
0
2
1
0
0
0
1
2
0
0
0
1
2
0
0
0
0
0
1
2
0
0
2
2
0
0
0
0
0
0
2
1
1
3
0
0
0
2
0
0
0
1
1
2
0
0
0
0
1
0
0
2
0
0
0
2
3
1
0
0
0
1
1
0
0
1
1
1
0
0
0
1
3
0
0
0
0
1
0
0
0
1
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
1
0
0
0
1
2
0
0
2
0
0
0
0
2
0
1
0
0
0
2
2
0
0
2
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
2
1
0
0
0
0
2
0
0
0
2
0
2
2
2
2
0
0
1
0
0
0
2
2
1
2
0
0
0
0
0
0
2
0
2
0
1
0
1
0
0
0
0
3
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
3
1
2
0
0
2
1
0
0
2
2
0
1
0
0
2
0
0
0
2
1
0
0
2
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
2
2
0
1
2
1
0
0
3
0
0
0
0
0
0
0
0
0
2
0
1
2
2
0
1
0
0
1
0
1
3
0
0
0
1
1
2
0
0
2
0
0
0
0
1
2
2
0
0
0
0
0
2
0
2
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
1
2
0
3
2
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
1
2
1
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
2
0
0
0
0
1
2
1
0
2
0
0
2
0
0
0
0
2
1
0
1
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
1
0
0
4
0
0
0
0
0
1
1
0
0
0
1
0
1
2
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
2
0
1
2
1
0
2
0
1
0
3
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
2
0
0
2
1
0
1
0
0
0
0
1
0
3
0
2
0
1
1
0
1
0
1
0
0
0
0
0
1
3
2
3
1
2
1
2
0
0
1
0
0
0
0
5
2
2
0
0
2
1
0
1
0
1
0
0
0
2
1
0
0
0
0
0
3
0
0
2
4
0
2
0
1
0
0
1
0
0
2
0
0
0
1
0
2
2
0
0
0
0
0
0
0
1
0
1
0
0
3
1
0
2
0
0
0
0
0
1
2
1
2
0
1
1
1
0
1
0
2
0
0
0
1
2
2
0
0
2
1
0
0
2
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
1
0
0
2
0
0
0
2
1
0
0
1
0
2
1
0
1
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
2
0
0
1
0
0
1
1
2
0
2
0
0
0
1
0
0
0
1
0
0
0
0
2
0
1
1
0
1
0
1
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
1
0
2
1
0
0
0
2
2
2
0
0
0
0
0
2
0
0
2
0
0
0
0
1
1
2
2
2
0
0
2
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
3
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
1
2
0
0
0
0
2
0
0
0
0
2
1
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
1
2
0
1
0
0
0
0
1
0
0
0
1
2
1
1
0
0
0
1
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
1
3
0
1
0
2
0
1
0
0
0
1
1
0
2
0
2
2
0
0
0
0
0
0
1
0
1
1
1
0
2
2
0
2
3
2
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
1
2
1
2
1
0
0
1
2
0
0
0
0
0
0
0
0
3
0
0
1
2
0
0
2
2
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
3
0
2
0
2
0
0
0
0
1
0
2
0
0
0
1
1
2
0
0
0
2
1
1
2
2
0
0
0
0
0
1
0
0
2
1
1
0
0
0
1
0
0
0
0
1
2
2
0
1
3
0
2
1
2
0
2
1
2
0
2
0
0
0
2
1
0
0
2
0
1
0
0
0
0
0
1
0
0
1
0
0
2
0
1
0
0
0
1
0
0
1
0
2
2
0
0
1
2
0
2
0
2
2
2
1
0
2
1
2
2
0
2
0
0
0
2
0
0
1
0
0
2
1
2
0
0
2
2
0
0
2
1
0
0
0
0
0
0
1
0
0
2
0
2
1
1
1
2
1
0
2
2
0
1
2
0
0
0
2
1
0
0
0
0
1
1
1
0
0
0
0
0
2
0
0
2
1
1
0
1
0
2
1
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
1
1
0
2
0
0
0
6
0
0
2
0
2
0
2
0
0
1
1
2
0
1
3
0
2
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
1
0
2
2
2
2
0
1
0
2
1
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
3
0
1
0
1
1
0
0
1
1
0
0
0
0
2
0
2
0
0
1
0
1
0
0
0
0
0
1
0
0
2
2
0
1
2
0
1
0
0
0
0
0
3
0
1
2
0
0
0
0
2
0
0
1
2
0
0
0
0
1
0
0
0
2
1
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
1
1
1
0
1
0
0
1
0
0
1
2
0
0
0
0
0
1
2
0
0
2
0
0
2
0
1
0
0
1
4
0
0
0
0
2
0
0
0
3
0
0
0
0
0
2
0
0
0
0
3
0
1
0
0
2
1
1
0
2
2
0
2
2
0
0
1
0
2
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
2
2
0
1
2
0
2
1
2
2
0
0
2
0
0
1
0
0
0
2
0
0
0
2
2
0
2
1
1
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
1
0
0
0
1
2
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
1
1
1
0
2
0
0
3
0
0
0
0
0
0
0
1
1
0
0
1
0
0
2
2
0
0
0
1
0
0
0
1
1
0
0
0
3
0
0
0
0
2
1
0
0
3
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
1
2
1
1
0
0
0
0
0
1
0
1
0
2
0
2
0
0
3
0
0
0
0
0
0
0
2
0
0
2
0
1
0
1
0
0
1
2
0
1
0
0
0
2
2
0
2
0
0
0
0
1
1
0
2
1
0
0
0
0
2
0
2
1
1
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
2
1
0
0
1
1
2
0
1
2
3
2
0
0
2
0
0
2
0
1
3
1
0
1
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
1
2
0
2
0
0
0
2
2
1
2
0
0
0
0
3
0
0
0
0
2
0
1
1
0
0
1
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
1
0
1
0
0
0
3
3
0
1
0
0
2
0
0
0
0
0
2
1
0
2
1
0
2
2
3
2
0
0
0
1
0
1
0
1
0
0
0
1
1
2
1
0
0
1
0
2
0
2
0
0
0
0
1
2
0
0
1
1
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
2
0
1
2
2
1
0
0
0
0
0
0
1
0
2
1
0
1
0
2
0
2
3
0
0
2
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
4
0
1
1
0
0
0
0
0
1
0
2
0
2
1
0
0
2
2
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
1
2
0
4
0
0
4
0
0
0
0
0
2
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
2
0
0
0
0
1
0
0
0
0
1
0
3
2
0
0
0
0
0
0
0
0
1
2
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
1
2
0
2
0
0
0
0
1
1
0
1
2
2
0
2
4
0
0
0
0
0
2
2
1
0
1
1
0
0
0
2
0
2
2
4
2
0
1
2
0
0
2
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
2
0
0
0
0
0
2
0
0
1
2
2
1
0
1
0
2
2
0
2
1
1
0
0
0
0
0
1
0
0
2
0
0
1
1
0
1
0
1
0
0
0
2
2
0
1
0
2
0
2
0
2
0
0
0
0
3
0
3
1
2
0
0
0
0
0
0
2
1
1
0
0
0
0
2
0
0
2
2
0
1
0
2
0
0
1
2
0
0
1
0
0
1
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
2
0
1
0
0
0
2
2
2
1
1
2
0
1
3
2
0
0
0
0
2
1
0
0
0
1
2
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
1
1
1
0
0
0
0
0
1
1
0
0
0
1
1
1
1
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
1
1
2
4
1
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
2
0
0
2
0
0
2
0
0
0
0
1
3
1
3
1
0
2
0
0
0
0
0
1
1
0
1
2
2
0
0
1
2
0
2
2
1
0
0
1
2
3
0
0
2
0
0
0
0
2
2
2
1
1
0
1
0
0
0
2
2
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
2
0
0
0
0
0
2
1
2
2
0
0
0
0
0
1
2
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
1
0
1
2
0
0
0
0
0
1
2
1
1
1
0
1
3
1
2
0
1
2
0
0
5
0
0
4
0
1
1
0
1
0
0
2
0
0
0
2
1
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
1
2
2
0
1
0
2
0
0
0
2
0
2
1
0
0
0
0
2
2
0
1
1
1
0
0
0
0
2
0
0
0
1
3
1
0
0
0
2
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
1
2
0
0
0
0
0
0
1
0
3
1
2
1
0
0
0
4
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
2
2
4
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
1
2
1
0
0
1
0
0
0
0
0
1
2
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
2
2
0
0
0
0
2
2
0
2
0
0
0
0
1
1
1
0
0
2
0
0
2
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
4
2
0
0
0
2
1
0
2
2
0
1
2
2
2
2
0
0
2
1
0
0
0
1
1
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
1
1
1
0
0
1
1
0
0
0
2
1
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
2
0
1
0
4
1
2
0
0
0
2
0
0
0
2
1
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
1
0
0
2
2
0
0
0
0
0
1
1
2
3
0
0
3
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
2
4
1
0
1
0
1
3
0
0
0
2
2
0
1
0
0
0
0
0
0
1
0
2
0
0
0
3
1
2
0
1
0
0
0
1
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
1
0
2
0
0
0
0
1
0
0
0
1
1
4
0
0
0
2
0
0
0
3
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
2
1
0
3
0
2
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
1
1
0
1
0
0
1
1
0
2
0
0
0
1
0
1
0
0
0
0
2
0
1
1
0
0
2
2
1
1
0
1
0
0
0
1
2
0
1
1
0
1
0
0
0
0
1
1
3
2
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
2
0
0
2
1
1
0
0
2
0
2
2
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
6
0
0
0
1
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
2
3
0
1
1
0
0
0
2
0
0
0
2
0
2
0
1
1
0
0
0
3
0
3
1
0
0
1
0
0
0
1
2
0
0
0
0
2
2
0
1
2
2
2
0
0
0
0
0
2
2
0
1
0
0
0
0
1
2
0
0
0
0
0
1
1
1
0
0
1
0
0
0
2
0
1
3
0
0
0
0
0
0
3
0
2
2
0
0
0
1
0
0
1
2
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
2
0
2
0
4
0
0
2
0
0
0
0
0
1
2
0
0
0
2
2
1
1
0
0
0
1
2
0
0
0
2
2
1
6
2
0
0
0
0
0
0
0
0
0
2
1
1
0
0
1
0
0
2
0
0
6
1
0
0
0
0
2
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
1
2
3
0
0
2
0
0
1
1
2
1
2
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
4
0
2
0
1
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
1
1
0
1
0
0
0
0
2
3
0
0
0
1
0
2
0
0
1
1
2
1
2
1
0
0
0
0
1
0
0
0
0
2
0
0
4
0
0
3
0
1
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
3
1
0
2
2
0
0
0
0
0
1
0
0
0
1
2
1
0
0
0
0
1
1
0
1
2
0
0
1
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
1
0
0
1
0
0
0
0
0
2
2
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
2
0
1
2
1
0
0
0
0
1
2
1
0
4
2
2
0
0
0
0
0
2
1
2
0
0
1
0
0
0
0
0
0
0
1
1
1
0
1
0
2
0
0
0
0
0
1
1
0
2
1
0
0
1
1
2
0
0
1
1
0
0
2
0
2
4
0
0
0
1
0
0
0
0
0
1
2
2
1
0
0
0
2
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
2
0
1
1
1
0
0
1
0
2
0
0
0
1
0
0
0
2
0
0
1
1
1
2
0
2
0
0
0
1
4
1
3
2
0
0
0
0
0
0
1
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
1
0
0
2
1
2
2
0
0
1
0
1
2
0
3
0
0
0
0
0
2
0
0
2
1
1
0
0
2
0
2
2
0
1
0
2
0
2
1
0
0
0
1
0
1
0
0
1
0
0
0
0
1
2
0
2
2
2
0
1
2
0
0
1
0
2
2
0
0
1
0
0
0
1
2
1
2
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
5
2
0
0
2
2
0
0
0
1
2
1
0
0
1
0
0
0
0
0
1
0
1
1
2
2
0
2
1
1
0
0
2
2
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
2
1
0
0
0
0
2
0
2
0
0
0
0
1
2
1
0
0
0
0
0
2
0
0
0
0
0
0
3
2
0
0
0
2
2
0
0
0
0
2
0
3
6
0
0
1
1
1
2
0
0
1
0
2
0
1
1
0
1
0
0
0
1
0
0
0
2
1
0
2
0
1
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
2
0
0
0
1
0
0
0
1
0
0
0
5
1
2
0
0
0
1
0
0
0
2
0
0
2
0
1
0
0
1
1
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
4
1
0
2
0
0
1
0
0
2
0
2
0
1
2
0
0
1
0
0
1
2
0
0
0
1
0
2
0
2
0
0
0
0
0
1
0
0
1
0
2
2
0
0
1
0
0
0
0
2
0
0
0
0
3
3
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
1
0
2
0
2
0
0
1
0
0
0
1
0
1
0
0
1
0
2
2
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
2
1
0
2
1
2
0
2
2
0
2
0
0
0
0
0
1
0
2
0
0
0
0
2
0
2
3
3
1
0
0
0
1
0
3
2
0
0
1
0
2
0
0
0
1
2
2
0
2
0
0
0
0
1
1
0
0
0
0
0
0
2
2
2
0
2
0
0
1
1
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
1
2
1
0
0
0
1
0
2
0
0
0
0
0
1
1
1
1
0
0
2
0
2
0
1
0
0
1
0
0
0
0
2
0
0
2
3
0
2
0
0
0
0
1
1
0
2
0
0
1
2
2
3
2
2
0
2
1
2
2
1
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
5
0
1
0
1
0
0
2
2
0
1
0
0
0
0
0
1
0
0
0
1
0
2
2
0
0
1
1
0
1
0
0
0
0
1
0
0
0
1
0
0
2
2
0
1
2
0
0
0
0
0
0
1
0
0
0
1
0
1
2
1
0
1
0
0
1
2
1
0
0
1
1
0
1
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
2
2
0
0
0
0
0
1
0
0
0
2
1
2
0
0
0
2
0
0
0
2
0
0
1
2
0
0
0
0
0
2
1
1
0
1
0
1
1
0
1
2
0
0
0
0
0
0
0
2
0
1
0
0
1
0
1
3
0
0
0
1
1
1
0
0
2
1
3
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
2
0
0
1
1
0
0
3
0
0
1
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
2
0
2
2
0
0
3
0
2
0
2
1
2
1
1
0
1
0
1
0
0
1
1
0
0
0
1
0
0
1
0
3
0
2
3
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
1
1
0
0
0
2
0
1
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
2
4
1
1
0
2
0
0
0
0
0
2
0
1
0
0
0
0
1
2
0
0
1
0
6
2
0
2
0
2
3
2
0
0
0
0
0
1
0
1
2
0
0
0
1
0
0
1
1
0
0
2
0
0
2
0
2
0
0
1
0
1
0
0
0
0
0
2
0
1
0
0
2
2
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
1
1
1
0
0
0
2
0
0
1
1
0
2
1
0
2
0
0
2
0
9
0
0
1
0
0
0
2
0
2
1
2
0
1
2
0
0
0
0
0
2
0
0
2
0
1
0
1
0
0
1
2
0
0
0
0
0
1
2
0
2
0
0
2
2
0
3
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
2
1
1
1
0
0
2
2
0
0
1
0
0
1
2
0
2
0
0
1
0
0
0
1
1
2
0
2
0
0
1
0
0
0
1
0
0
0
2
0
1
2
3
0
2
0
2
0
0
1
0
1
1
0
1
1
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
2
1
0
1
0
1
2
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
1
2
0
0
0
0
0
0
2
2
0
0
1
1
1
0
0
0
0
0
0
0
0
2
2
1
0
0
2
0
1
0
1
2
0
2
0
2
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
1
0
0
2
0
2
2
1
1
0
1
0
2
2
0
0
0
2
2
1
0
1
1
2
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
2
2
0
1
0
0
1
0
0
1
0
0
0
0
2
0
0
3
0
2
0
0
0
2
2
0
2
0
1
0
0
0
0
1
1
0
0
0
0
1
2
3
1
2
0
1
0
0
1
1
0
0
2
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
3
0
0
1
0
1
0
0
0
0
0
0
0
2
2
0
0
0
2
1
0
0
0
2
0
0
1
0
0
2
2
0
0
1
0
2
0
1
2
0
0
1
2
2
0
1
0
0
1
0
2
1
0
0
2
0
0
0
1
0
1
0
0
1
1
0
0
0
1
0
0
1
0
0
1
0
2
2
0
2
2
2
2
0
1
2
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
2
1
0
0
2
0
2
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
2
0
0
2
2
0
0
1
0
0
0
2
0
2
3
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
2
2
0
1
2
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
2
2
0
0
0
2
0
0
0
0
2
0
0
2
0
1
2
0
0
0
1
0
1
3
1
0
0
1
0
0
0
1
0
0
0
2
2
3
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
2
0
2
0
1
0
0
0
0
0
2
1
0
0
1
1
2
2
0
0
2
0
0
1
0
1
0
0
0
2
1
1
0
0
0
0
2
0
1
0
1
0
0
0
2
0
2
1
2
0
1
2
2
2
1
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
1
0
0
2
1
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
2
2
0
0
0
2
1
0
0
0
0
0
1
0
0
1
0
4
2
1
2
0
0
0
0
0
3
1
1
0
0
0
0
2
0
0
0
1
2
0
0
0
0
1
1
0
0
0
0
2
1
1
0
1
0
0
3
1
0
2
2
0
2
0
0
0
0
0
1
0
0
0
0
2
2
2
0
3
3
0
0
1
3
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
1
2
3
2
0
3
1
0
2
0
0
0
0
0
2
2
1
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
1
0
0
0
1
1
0
0
0
0
2
0
3
2
0
0
1
0
0
0
0
0
0
2
0
2
3
2
0
0
2
1
1
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
1
0
2
0
2
0
2
1
0
0
0
2
0
1
1
0
0
0
0
0
1
0
0
0
1
0
2
0
0
1
1
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
2
0
0
0
1
1
2
0
0
0
0
0
0
0
0
1
2
3
1
1
0
0
0
0
2
0
1
0
1
0
0
0
1
0
0
10
0
0
2
2
3
3
0
0
0
2
1
0
1
0
2
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
2
1
1
1
2
0
1
0
2
0
2
0
1
1
0
0
2
1
0
2
0
1
2
0
0
0
0
1
2
0
2
0
1
2
2
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
2
2
1
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
2
0
1
0
1
0
2
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
2
0
1
3
0
0
1
1
1
3
1
0
2
0
1
1
0
2
1
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
1
0
1
1
0
1
0
0
2
0
0
1
0
1
0
1
1
0
0
1
0
0
0
1
2
1
0
0
1
0
0
0
0
2
0
0
0
0
2
2
0
0
1
2
1
0
0
0
0
2
0
3
1
0
0
1
0
0
0
2
0
0
2
2
2
1
2
0
0
0
1
1
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
5
0
0
0
1
0
0
0
2
0
0
1
0
2
1
1
0
2
0
2
0
2
3
2
0
2
1
0
0
0
0
1
1
0
1
1
1
0
0
0
0
0
2
0
2
0
0
0
0
2
1
0
2
3
0
1
0
2
2
0
0
0
0
1
0
1
0
0
1
2
1
0
0
1
2
0
0
0
0
0
2
1
0
0
0
2
0
0
1
0
0
0
0
1
0
2
0
2
1
0
0
1
1
1
2
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
9
0
1
0
2
0
4
0
0
0
0
2
4
1
0
0
0
1
2
1
2
2
0
2
0
2
2
1
0
0
0
1
1
0
1
0
0
0
2
0
2
0
1
0
1
2
0
0
0
0
0
0
7
2
0
0
0
3
0
1
1
2
1
2
0
0
0
0
0
2
1
0
0
0
0
4
0
0
1
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
3
0
2
1
2
1
1
0
0
0
2
2
1
1
0
1
0
0
0
2
0
1
0
1
0
0
0
2
1
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
1
0
0
0
1
2
2
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
4
2
1
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
5
2
0
0
0
0
0
2
1
0
2
2
0
0
1
0
0
0
0
0
1
1
2
2
0
0
0
2
2
1
0
2
0
2
1
0
0
0
2
2
2
0
0
3
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
3
0
0
0
1
1
2
2
0
0
0
2
0
2
0
2
0
0
2
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
1
2
0
0
0
1
1
1
0
0
1
0
1
1
0
0
1
0
0
0
3
1
0
1
0
0
2
0
0
0
0
0
0
0
0
1
2
1
1
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
4
2
1
0
1
1
1
0
0
2
0
0
2
0
0
0
2
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
2
0
1
1
2
0
0
0
2
0
1
0
0
0
0
1
1
0
0
0
0
1
1
0
2
2
0
2
2
3
0
3
0
0
1
1
0
2
0
0
1
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
4
0
2
0
0
1
0
1
0
0
1
0
0
2
0
2
0
1
0
1
0
2
2
0
0
0
0
0
1
2
0
2
0
0
0
0
1
0
1
0
0
2
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
5
0
0
6
0
2
0
0
0
0
1
2
0
0
0
1
0
0
1
0
0
0
1
0
0
2
0
0
2
0
1
1
0
1
0
0
1
0
1
2
0
1
2
0
0
2
2
0
1
0
0
0
0
0
0
0
0
2
0
1
2
2
0
3
0
0
1
0
1
1
0
0
4
0
0
1
0
3
1
2
0
0
0
1
2
2
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
1
2
2
0
2
0
0
0
1
0
0
0
0
4
0
0
1
0
1
0
0
1
1
1
7
0
1
1
0
1
2
0
0
2
0
1
0
2
0
1
0
1
0
1
7
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
1
1
1
1
0
1
0
1
0
0
2
0
0
0
2
0
0
0
0
2
3
3
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
1
1
1
1
1
2
0
1
1
0
0
0
0
0
1
0
1
0
0
1
0
1
1
1
0
0
0
0
1
0
3
1
2
1
0
2
1
0
0
0
0
1
1
0
1
1
0
1
2
1
0
0
0
0
0
0
2
1
2
2
0
0
0
0
2
2
0
1
0
1
1
0
0
2
0
0
0
1
0
3
0
1
0
0
0
2
0
1
0
1
2
0
4
1
0
2
1
0
1
1
0
0
2
1
0
0
2
0
0
2
0
1
2
2
1
0
0
0
4
0
0
2
2
1
0
0
0
0
2
0
2
1
0
0
2
0
0
1
0
9
0
1
0
2
1
0
0
0
0
0
2
0
0
1
2
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
2
2
0
2
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
2
3
1
0
0
1
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
4
0
0
1
3
2
0
1
1
2
0
0
0
2
1
2
0
0
1
0
2
0
2
0
1
1
2
0
2
1
1
0
0
0
0
0
2
0
1
1
0
0
2
0
1
2
2
1
2
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
4
1
2
1
3
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
1
2
2
1
0
2
0
2
0
2
0
0
0
2
1
1
2
0
0
0
0
2
0
1
0
0
1
0
2
1
0
0
2
0
0
1
0
1
2
1
0
0
1
0
1
2
0
0
0
0
0
2
2
0
2
0
0
0
1
0
2
0
2
0
3
0
0
2
2
0
1
3
0
0
0
1
0
0
1
0
1
0
1
2
0
0
0
2
3
0
2
0
2
0
2
0
0
1
0
2
2
0
0
3
2
1
3
0
1
4
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
2
0
2
1
2
0
0
0
0
0
2
1
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
2
0
0
0
1
0
1
3
0
1
1
0
0
2
0
0
0
1
0
0
0
0
0
1
3
0
0
1
1
2
1
5
0
1
0
0
0
0
0
2
0
1
2
0
0
2
0
2
1
0
0
0
1
2
0
0
1
3
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
2
2
0
2
0
1
0
0
0
0
0
2
0
0
1
0
0
2
3
0
0
0
0
1
0
0
0
0
1
0
3
0
0
0
0
2
0
0
0
2
1
0
2
0
1
0
0
0
0
2
3
2
1
0
2
0
0
0
0
1
2
0
0
1
0
1
0
0
1
2
0
1
0
1
2
0
2
0
0
1
1
3
0
0
1
1
0
0
2
0
0
2
2
0
0
1
0
1
1
0
1
0
0
0
2
2
1
2
0
0
1
0
0
0
2
3
0
0
0
0
0
0
0
1
2
0
0
0
2
0
2
0
1
2
0
0
0
0
1
0
0
2
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
2
2
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
3
0
0
0
2
0
0
0
2
0
1
0
0
0
1
1
0
3
0
1
2
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
3
1
2
0
0
2
0
0
0
0
0
2
2
1
2
0
0
0
0
0
1
0
1
0
0
0
0
3
2
0
0
1
0
0
2
0
0
0
0
0
2
2
0
0
0
0
2
0
1
2
2
0
0
1
1
2
2
0
0
1
0
1
0
0
2
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
2
0
2
0
0
1
0
6
0
0
2
0
1
0
0
2
1
0
0
0
1
1
0
0
0
0
0
1
0
0
2
1
0
3
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
1
4
1
2
0
0
0
0
0
1
0
0
2
1
1
2
2
0
0
2
0
2
0
1
0
2
2
0
0
0
0
0
1
0
1
0
0
1
0
0
1
2
0
0
0
0
2
2
0
1
1
2
0
0
0
0
0
0
2
0
0
1
2
2
0
0
0
1
0
0
1
0
3
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
2
1
2
1
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
4
1
0
3
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
2
1
0
0
2
0
1
2
0
1
1
0
0
0
1
0
5
2
0
1
1
3
2
0
2
0
2
1
0
0
0
0
0
2
1
1
2
0
2
0
0
1
1
2
0
0
0
0
2
1
0
0
0
0
0
1
0
0
3
0
0
2
2
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
2
0
1
0
4
0
0
1
0
1
0
1
0
0
1
0
0
2
0
0
0
0
2
2
2
0
0
2
1
1
0
0
2
0
1
4
0
0
0
1
0
0
0
0
1
1
0
0
2
0
0
3
0
0
0
0
0
2
0
0
1
2
0
0
1
0
0
2
4
2
1
0
2
0
0
0
0
2
0
2
0
0
3
1
0
0
2
2
1
0
2
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
2
1
1
0
1
0
0
0
0
2
0
0
2
2
1
2
0
1
0
0
2
2
0
2
0
0
0
2
2
0
0
0
0
0
0
2
2
1
0
2
0
0
0
0
1
0
2
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
1
1
0
0
2
1
0
1
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
2
0
2
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
2
3
0
0
2
0
0
1
2
0
2
0
1
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
1
0
0
0
3
0
0
0
2
2
0
0
0
3
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
2
2
1
1
0
0
1
0
0
1
1
2
0
0
0
0
1
0
0
2
0
0
0
2
1
0
2
0
1
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
2
2
0
1
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
2
2
0
1
3
1
0
0
0
2
0
0
0
0
1
2
2
0
0
0
0
0
1
0
2
0
5
2
0
0
0
0
2
2
0
3
2
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
1
0
0
2
0
0
2
1
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
1
1
0
2
2
0
0
0
0
0
2
0
1
2
0
0
2
0
0
0
0
1
0
2
2
3
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
1
2
0
0
0
1
1
0
2
3
0
1
0
0
2
1
0
0
2
0
0
1
0
0
2
0
0
0
1
0
2
0
0
2
1
2
2
0
2
0
9
0
0
0
1
0
0
1
0
0
2
0
0
0
0
4
0
2
0
2
0
0
0
2
0
0
0
1
1
2
0
0
0
0
2
0
0
0
0
0
0
2
2
0
3
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
1
1
0
0
1
0
0
0
0
0
2
0
1
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
1
3
0
0
0
0
1
1
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
4
0
1
2
0
1
2
0
0
2
0
1
2
0
0
0
2
0
0
0
0
0
0
0
1
0
1
2
1
1
0
3
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
2
0
0
0
2
1
0
2
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
1
2
0
0
0
2
0
0
0
1
0
0
0
0
2
0
2
0
3
0
0
0
0
1
0
0
1
0
0
0
2
1
0
0
0
0
1
0
2
2
2
1
0
1
1
0
1
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
2
0
2
1
1
2
1
0
2
1
0
1
0
1
0
0
0
0
0
0
2
0
5
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
3
2
2
0
0
0
0
2
2
0
0
2
2
0
0
0
0
0
0
0
3
0
3
0
0
1
0
2
1
0
2
0
0
2
2
2
0
0
2
0
2
0
1
0
3
0
2
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
1
0
0
2
0
0
1
1
0
0
0
0
1
1
3
0
0
0
1
1
0
0
3
1
1
0
0
0
0
0
0
1
0
0
0
0
2
1
0
1
0
0
0
0
2
0
0
3
1
0
0
2
0
0
2
2
0
1
0
1
0
0
0
0
0
2
2
1
0
0
0
0
1
0
1
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
2
0
0
1
2
0
3
1
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
2
1
1
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
2
0
0
2
0
1
0
1
0
0
0
0
2
0
2
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
2
0
0
1
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
3
0
0
0
0
7
0
1
2
2
2
0
0
1
0
1
1
0
0
0
1
0
0
0
1
0
1
3
2
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
1
3
1
1
0
0
1
0
0
0
0
0
2
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
2
0
0
1
2
0
0
0
0
1
1
0
1
0
2
0
1
1
2
1
0
2
0
2
0
0
0
0
0
2
1
1
1
0
2
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
2
0
6
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
1
2
0
1
1
0
0
0
2
0
1
1
1
1
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
2
2
0
1
2
0
0
2
4
1
1
0
1
0
1
0
1
0
0
1
1
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
1
0
0
0
0
0
2
2
2
0
0
0
0
1
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
2
0
0
0
0
0
1
1
4
0
0
1
1
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
2
2
0
0
1
0
1
2
0
2
0
0
0
0
0
1
1
3
0
0
2
2
0
0
0
0
2
0
1
1
1
2
1
1
0
1
0
1
0
1
1
3
0
0
2
0
0
0
0
0
0
0
0
1
2
0
1
0
0
1
1
7
0
0
0
0
0
0
2
1
2
0
1
2
0
2
0
1
0
1
0
2
1
2
2
1
0
1
0
2
0
0
2
0
0
1
0
1
0
2
1
2
1
2
0
0
0
0
2
1
2
0
0
4
0
2
3
1
2
0
2
2
0
0
2
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
1
1
0
1
0
3
0
1
0
2
2
0
1
0
0
0
0
0
0
0
1
0
2
1
1
2
0
0
0
2
0
0
0
0
3
0
0
0
0
0
1
3
2
0
0
1
0
1
0
0
1
0
0
2
0
0
0
0
0
4
2
0
0
1
0
0
0
0
0
0
0
0
2
5
2
1
0
0
3
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
2
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
2
1
1
0
0
0
0
1
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
2
1
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
1
1
1
0
5
0
0
1
2
1
2
0
0
0
0
0
0
1
1
1
0
0
2
2
0
2
1
0
1
0
0
0
0
3
0
0
0
0
0
0
0
3
0
0
0
2
0
1
2
1
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
2
1
0
1
0
2
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
2
1
2
0
0
1
1
0
2
0
0
0
0
2
0
1
2
0
0
0
0
0
1
2
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
1
2
3
1
1
0
0
0
0
0
0
0
0
0
2
2
2
0
0
1
0
0
0
0
0
0
0
1
1
0
1
2
0
0
5
0
2
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
2
2
0
0
1
0
0
2
0
2
1
0
2
0
0
0
2
1
0
1
1
0
0
0
1
0
2
3
0
0
1
2
0
2
0
0
0
0
0
4
2
1
0
2
1
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
1
0
2
0
0
0
1
0
6
1
0
1
0
0
2
0
0
1
1
0
1
1
2
2
0
3
1
0
2
0
0
0
0
0
1
0
1
1
1
0
0
2
0
1
0
0
0
0
0
0
2
2
2
0
2
0
0
2
0
1
1
0
0
0
1
0
0
0
0
0
0
0
3
2
0
0
2
0
0
1
2
0
0
1
1
1
0
3
0
2
2
2
2
0
0
1
0
0
3
2
0
2
2
0
2
0
0
0
1
0
1
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
2
1
0
0
0
0
2
0
0
0
2
1
1
0
1
1
2
0
2
0
0
2
2
0
0
1
2
0
0
0
0
0
0
0
1
0
2
2
0
0
0
1
1
0
2
0
0
2
3
0
1
1
0
2
0
1
0
2
2
0
1
3
2
2
0
0
1
0
0
0
1
2
0
0
0
2
0
0
2
2
0
0
2
2
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
1
2
0
3
0
2
1
1
1
2
1
0
1
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
1
0
1
0
1
0
0
0
0
1
0
0
2
0
0
1
1
1
0
3
2
0
1
0
2
3
0
0
1
0
0
0
0
2
1
2
2
1
0
0
5
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
2
1
0
2
0
0
0
0
1
1
1
0
0
0
2
0
0
0
1
1
0
0
0
2
0
0
2
1
0
1
0
0
1
1
0
1
2
0
1
0
1
0
0
0
0
1
0
0
3
0
0
0
2
0
0
3
3
0
0
0
0
2
1
0
0
3
0
1
1
0
0
0
0
2
2
2
0
0
0
2
0
2
2
1
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
1
2
0
0
0
0
0
0
2
2
0
2
0
0
0
0
1
1
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
2
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
1
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
2
1
0
2
0
1
1
0
2
0
0
0
0
2
2
0
0
0
0
0
0
2
0
1
0
0
1
0
1
2
1
1
0
4
1
0
0
0
0
0
0
2
1
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
1
0
0
1
2
2
1
0
0
1
0
0
0
2
0
0
0
1
0
2
1
2
0
0
0
2
1
0
0
0
0
3
0
1
0
0
5
0
1
0
0
1
1
3
1
0
0
0
0
3
1
0
0
2
1
0
0
0
2
2
0
2
2
4
0
0
0
0
0
1
0
0
2
1
0
1
0
2
0
0
2
2
0
0
0
1
1
0
1
0
2
0
1
0
0
0
0
1
0
0
1
0
0
0
1
2
2
0
2
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
2
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
2
0
5
0
0
1
0
1
1
0
0
0
0
0
0
3
0
0
0
0
0
2
2
0
0
0
0
1
0
2
2
0
0
1
0
1
0
1
0
0
2
2
2
0
2
0
2
2
1
0
0
2
0
0
2
2
2
0
0
0
1
0
0
1
0
1
1
0
0
0
1
0
2
0
1
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
4
0
1
3
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
1
0
2
0
1
1
1
0
1
0
2
0
0
1
2
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
1
0
2
0
0
1
1
1
3
2
2
1
0
0
0
2
2
1
0
2
2
2
0
2
1
0
2
0
0
0
2
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
2
1
0
1
0
0
0
1
0
1
0
0
0
0
1
2
0
0
1
2
0
1
0
1
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
2
0
0
0
0
1
2
0
0
0
0
0
1
0
0
1
0
0
0
2
2
0
1
4
0
0
0
0
2
2
0
2
0
1
0
1
1
0
3
0
1
1
1
0
6
1
0
0
0
0
1
0
0
2
0
0
2
0
4
0
0
2
0
0
0
1
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
3
0
1
0
0
0
0
2
0
1
0
0
0
1
1
0
5
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
1
0
0
0
0
1
1
2
1
0
1
3
0
0
1
2
0
0
1
2
0
1
0
1
2
0
0
3
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
2
0
2
0
0
0
0
0
2
0
0
1
0
0
1
1
0
0
0
0
0
1
0
1
0
0
3
0
0
0
0
2
3
2
2
0
0
0
1
0
2
0
1
0
0
1
0
0
1
0
2
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
1
1
2
0
0
1
0
0
1
0
4
1
1
0
0
0
0
2
0
0
3
0
0
0
2
0
2
1
0
0
0
1
2
0
1
1
0
2
0
1
1
2
2
0
0
0
2
0
2
1
2
0
0
1
2
0
0
2
2
0
0
0
1
2
2
1
0
0
0
2
0
0
0
1
2
0
1
0
0
1
0
2
0
2
0
0
3
1
1
0
1
1
1
0
0
1
0
0
0
0
2
0
0
1
0
2
1
0
2
2
0
2
0
0
0
1
0
1
0
2
0
0
1
0
0
0
0
0
0
1
2
2
1
0
0
1
0
1
0
0
0
0
1
0
0
0
2
1
0
1
2
2
0
1
0
1
0
1
2
0
0
2
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
2
1
0
2
0
0
2
1
2
0
3
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
1
0
2
1
0
0
1
0
1
2
0
0
0
2
1
1
0
1
0
0
0
2
0
1
0
0
1
0
0
0
0
2
0
1
0
5
0
0
0
2
2
2
0
2
0
1
0
0
0
1
0
0
1
1
1
0
2
0
0
2
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
2
1
2
2
1
0
0
0
0
0
2
1
0
0
2
0
1
1
0
0
0
0
1
0
0
0
0
2
0
0
0
5
0
2
0
0
6
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
2
0
1
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
3
0
1
0
0
0
1
1
0
0
1
0
0
0
0
2
0
0
6
0
2
0
0
0
0
0
1
2
1
0
0
1
0
1
0
0
1
0
0
3
2
0
0
2
1
0
1
0
0
2
2
1
0
0
0
0
1
0
0
1
0
0
1
1
0
1
1
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
2
0
0
0
1
1
2
0
0
2
0
1
0
0
0
2
0
0
0
0
2
0
1
1
0
0
0
0
2
2
0
1
0
2
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
4
0
2
0
0
0
2
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
2
1
0
1
2
0
0
0
2
0
0
0
1
4
1
0
0
2
0
0
0
1
0
0
0
0
2
0
2
2
0
0
0
0
1
1
0
0
0
1
1
0
2
0
0
0
0
0
1
2
0
0
1
0
0
1
2
2
0
0
0
3
0
2
1
2
2
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
2
0
1
1
0
0
1
0
0
0
2
0
0
2
2
0
2
2
0
1
2
2
1
1
2
1
0
0
2
2
2
1
2
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
2
0
0
0
1
1
0
0
0
2
1
2
1
1
0
0
1
0
2
0
0
1
1
0
0
1
0
0
0
1
0
1
0
1
0
1
0
2
1
0
0
0
0
1
1
1
0
1
0
0
0
1
0
0
1
1
1
2
0
0
0
0
0
0
0
2
2
0
2
1
0
0
2
1
0
0
2
0
0
0
0
0
1
1
0
0
2
0
2
2
1
1
0
1
1
0
0
0
2
1
1
2
0
2
0
1
1
0
2
2
0
4
0
0
0
0
1
2
2
2
0
1
0
2
0
1
1
0
3
0
1
1
0
2
1
2
0
0
1
0
0
1
1
2
1
0
3
0
1
0
0
0
2
2
0
0
0
0
1
0
0
6
0
0
0
0
0
0
0
1
0
0
3
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
2
1
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
2
2
0
2
0
0
1
2
1
0
0
0
0
0
1
2
0
0
0
2
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
1
0
0
4
2
0
2
0
0
1
0
2
1
0
1
2
1
0
0
2
0
1
1
0
0
0
1
0
0
0
2
0
0
1
0
1
1
0
2
0
2
2
1
0
0
0
0
0
2
0
1
0
1
2
0
3
0
0
2
1
0
0
1
0
0
0
0
1
0
2
0
1
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
2
1
1
3
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
1
2
1
1
0
1
2
0
0
0
0
0
0
0
0
0
2
0
2
2
1
0
0
1
0
0
3
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
2
0
0
0
0
4
2
0
0
1
0
2
2
0
0
2
2
1
0
2
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
2
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
4
2
3
3
2
0
1
1
0
0
0
0
3
0
2
0
0
2
0
1
0
1
1
1
1
0
1
0
1
0
0
0
0
0
1
0
0
4
0
2
2
2
2
0
1
3
1
2
0
0
1
0
0
0
1
1
0
1
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
1
0
1
0
0
0
0
1
0
0
2
0
1
0
0
2
0
0
1
0
1
0
2
1
0
0
0
1
2
0
0
0
0
2
0
2
2
0
0
0
2
0
1
1
0
0
0
1
2
1
1
2
2
1
0
0
2
0
1
0
0
0
0
2
0
0
1
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
3
0
2
2
0
2
0
0
0
2
0
0
0
2
1
2
1
1
1
0
0
0
0
2
2
2
0
1
1
1
1
0
0
0
2
0
1
0
0
1
0
0
0
0
1
1
0
2
0
0
0
0
0
2
1
0
0
2
2
3
0
0
1
0
0
2
2
1
0
0
1
2
0
1
2
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
1
1
0
0
2
3
0
0
0
2
2
0
0
0
0
0
1
2
0
1
0
0
1
1
0
2
0
0
1
0
1
0
0
2
0
0
0
1
0
1
2
0
1
0
0
0
0
0
0
0
0
0
1
0
2
3
0
2
2
0
1
0
2
1
1
0
0
0
1
0
1
0
0
2
0
0
0
2
0
0
0
1
2
0
1
0
0
1
1
0
1
1
0
0
1
0
0
0
0
2
2
0
1
0
0
0
0
1
2
0
0
1
2
0
0
2
0
0
1
0
2
1
2
1
2
0
0
2
1
0
0
0
0
0
1
1
0
0
1
0
1
2
1
2
1
0
0
0
2
1
2
2
2
0
0
0
2
2
0
2
0
2
0
0
0
0
1
0
0
0
0
1
1
1
0
1
0
1
0
0
1
1
1
0
1
0
0
2
1
1
0
1
1
2
2
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
1
0
0
0
2
2
1
0
0
3
0
2
0
2
0
0
0
2
1
0
2
0
0
0
0
0
2
0
0
0
2
0
1
0
0
1
0
2
0
1
2
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
2
1
0
0
1
0
2
0
3
3
0
0
1
2
1
0
2
0
0
0
2
0
0
0
0
1
1
0
0
0
1
0
0
0
0
2
1
1
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
4
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
2
0
0
0
0
2
0
0
2
0
0
3
0
2
0
2
0
2
0
0
0
0
2
1
2
0
0
0
1
0
2
1
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
2
0
1
0
9
0
0
1
0
1
1
0
0
0
2
1
1
0
2
0
0
0
1
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
1
0
3
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
1
0
0
0
1
0
5
2
3
2
0
0
1
2
0
0
0
0
1
2
1
1
1
2
0
1
2
0
0
0
1
0
1
0
0
0
0
0
1
0
0
2
0
0
2
1
0
2
0
0
0
2
0
0
0
1
0
0
1
0
1
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
2
1
0
0
1
0
0
2
2
6
1
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
1
1
0
0
2
0
2
1
0
0
0
1
2
0
0
3
0
0
0
0
0
1
2
0
0
0
0
2
6
0
1
0
2
0
0
1
1
1
0
2
0
2
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
1
2
2
1
1
1
1
1
0
1
2
1
0
2
0
0
0
2
1
1
0
0
1
2
0
0
0
0
1
0
0
0
2
2
0
4
2
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
1
1
0
2
0
1
0
1
0
0
1
0
0
0
0
0
0
3
0
2
1
0
1
0
0
2
0
0
0
0
0
0
1
2
0
0
2
0
0
1
2
0
0
1
0
2
0
1
1
1
0
2
0
2
0
1
0
0
0
0
0
1
0
0
0
1
0
1
3
0
2
0
2
1
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
1
0
0
0
2
1
1
2
0
3
1
0
0
0
0
0
1
0
0
0
1
0
1
0
2
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
2
0
2
1
0
0
0
0
0
1
0
1
1
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
3
2
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
2
1
0
0
2
6
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
1
0
3
0
0
0
1
1
0
0
2
0
1
1
0
0
0
2
0
1
2
0
1
0
2
2
0
0
0
2
0
0
2
0
2
0
1
0
2
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
1
0
3
0
2
1
0
0
0
1
0
0
0
2
3
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
1
2
1
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
2
2
0
0
0
0
0
0
3
0
1
2
0
0
0
0
1
0
2
4
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
4
2
0
1
0
0
0
1
2
0
1
0
0
0
1
0
1
0
2
0
0
0
2
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
1
2
1
2
3
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
3
0
0
2
1
0
1
0
0
0
1
1
0
0
0
1
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
1
0
1
0
0
2
0
0
2
0
0
2
0
1
0
0
0
1
0
0
0
0
0
1
0
0
2
2
0
2
0
1
0
0
1
0
0
1
0
0
2
1
1
0
0
0
0
0
0
0
2
0
0
2
0
1
0
2
1
0
0
1
0
0
2
1
0
1
0
0
2
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
1
0
2
3
0
0
2
0
0
0
1
3
0
1
0
0
0
0
3
1
0
0
0
0
0
1
1
2
0
3
0
0
0
2
2
2
0
0
0
2
1
0
0
2
1
2
0
2
0
2
0
1
0
2
2
0
2
2
0
1
0
2
2
1
0
0
0
0
2
0
0
2
1
1
0
2
0
0
2
2
0
2
0
0
0
0
0
0
0
1
0
1
0
4
0
1
0
1
2
0
2
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
1
2
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
3
2
0
0
0
0
1
0
0
0
0
0
0
2
1
1
1
0
5
0
0
0
0
0
0
2
0
0
4
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
2
0
1
0
2
0
1
0
2
1
0
3
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
4
0
0
0
0
0
1
2
0
1
2
1
0
2
0
0
0
1
2
0
0
0
0
0
0
0
2
2
0
2
0
0
0
2
0
0
0
2
0
1
2
1
0
0
0
0
2
1
0
2
0
0
2
0
1
8
0
1
0
0
0
0
2
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
1
1
0
2
0
0
1
1
2
0
0
2
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
1
2
1
0
2
0
2
0
2
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
1
2
0
0
3
2
0
1
0
0
2
2
0
0
0
0
0
1
0
2
0
0
2
0
0
2
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
1
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
2
1
0
0
0
0
0
0
3
0
0
0
0
0
2
3
2
0
2
3
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
1
1
0
2
1
1
0
0
1
3
1
0
0
0
0
0
1
0
1
0
0
1
0
0
3
1
0
0
0
0
1
2
0
1
2
0
0
1
1
0
0
0
1
1
2
2
1
0
0
3
0
1
0
0
0
1
0
0
0
1
3
2
0
0
0
1
2
0
0
2
2
2
0
0
1
0
1
2
0
0
0
0
0
2
1
0
0
1
0
0
1
2
0
0
0
0
0
0
0
3
0
2
1
2
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
2
0
3
2
0
2
0
0
4
0
0
1
0
1
1
1
0
0
0
0
0
2
1
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
1
1
2
1
1
0
2
1
2
0
0
0
1
2
0
0
0
2
0
1
0
0
0
1
1
0
1
0
0
0
0
0
2
1
0
0
0
0
2
0
0
2
0
0
1
0
0
0
1
0
0
0
1
0
2
2
0
0
0
1
0
0
0
2
0
0
1
0
2
0
0
0
2
0
0
1
2
0
1
0
0
2
1
0
2
0
0
2
0
0
0
1
0
0
2
1
2
0
0
0
2
1
2
0
0
2
1
1
0
2
0
1
0
0
1
2
0
0
1
6
0
0
0
2
0
0
0
1
0
0
1
0
1
0
0
2
0
1
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
1
2
1
2
0
0
0
1
1
2
0
1
1
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
1
1
0
0
9
0
0
2
0
1
0
1
0
0
2
2
0
2
0
0
0
2
0
0
0
0
0
2
0
2
0
0
3
1
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
1
2
3
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
2
0
1
0
1
2
0
0
0
0
0
1
0
2
0
0
2
2
0
0
0
0
0
0
1
2
0
2
4
1
0
0
0
2
0
0
0
0
0
1
1
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
2
0
0
0
0
2
0
1
0
0
2
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
1
2
0
2
0
0
0
1
1
0
5
2
0
0
0
1
0
2
2
1
0
0
3
0
1
2
0
0
1
0
0
0
3
2
0
1
1
0
4
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
1
2
0
0
0
2
2
0
1
1
0
2
1
0
2
0
0
0
0
2
0
2
0
2
0
0
1
1
2
0
0
0
1
0
0
2
2
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
1
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
3
0
0
0
0
0
0
2
1
0
1
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
1
1
2
2
0
0
0
1
1
0
0
0
0
1
2
0
0
1
2
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
2
0
1
1
0
1
0
0
1
0
0
0
0
2
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
1
2
0
1
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
1
0
2
0
0
0
1
0
0
1
2
0
1
2
0
1
0
0
2
0
2
1
0
1
0
2
0
2
1
0
0
0
3
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
1
0
0
0
1
0
1
2
0
0
1
0
0
0
1
2
0
0
0
0
0
0
1
0
3
0
2
1
0
0
2
0
0
2
0
0
1
2
0
1
1
2
1
1
1
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
3
0
1
0
0
2
0
0
1
0
1
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
2
2
2
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
2
0
4
0
1
1
0
0
2
0
1
1
0
0
2
0
2
1
2
2
0
2
2
0
0
0
0
0
0
1
0
0
0
0
1
0
2
2
0
0
0
1
2
2
0
0
1
0
1
2
0
2
0
0
0
0
2
1
1
2
2
1
0
0
2
9
0
0
0
2
0
0
2
2
2
1
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
1
1
0
0
1
0
0
2
0
2
0
2
2
2
0
0
0
0
2
0
2
2
0
1
0
2
0
0
1
2
0
0
0
1
0
1
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
4
1
0
2
2
0
2
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
1
2
0
0
0
0
0
0
0
0
1
0
3
1
1
2
1
2
0
0
0
1
1
2
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
2
0
2
0
2
0
1
0
0
2
1
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
2
2
1
1
3
0
0
0
0
1
1
0
0
4
1
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
2
3
0
0
0
0
2
2
0
0
0
0
11
0
0
1
0
0
0
0
0
0
1
2
0
0
1
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
1
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
1
3
1
1
0
0
1
0
1
0
2
0
2
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
2
0
2
0
1
0
0
1
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
1
0
0
2
2
0
2
0
0
0
0
0
0
2
0
0
1
2
0
0
0
1
1
0
0
0
0
1
0
0
2
0
0
1
1
0
2
1
1
0
2
0
2
1
0
0
0
0
2
2
0
2
2
0
0
0
0
0
1
0
0
0
0
0
6
0
0
1
0
2
2
0
1
0
2
2
2
0
0
0
0
1
0
0
2
0
0
2
1
0
0
0
0
0
0
0
2
0
1
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
2
0
0
2
1
1
1
0
1
1
2
0
0
0
0
0
2
0
1
0
1
0
2
2
0
2
0
0
1
1
0
0
1
0
0
2
1
2
2
0
0
0
2
2
0
1
1
0
2
2
0
0
0
2
1
0
0
0
0
1
0
0
1
0
0
2
0
0
1
3
0
1
0
0
0
1
2
0
2
0
0
0
1
1
0
0
0
0
0
0
2
0
1
0
1
2
0
2
0
2
2
7
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
2
0
0
0
2
2
0
1
1
0
0
2
0
0
1
1
0
0
0
2
0
2
0
0
2
1
0
0
1
2
2
0
2
0
0
0
1
1
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
2
0
0
0
0
1
2
0
1
0
1
1
2
0
1
0
0
1
0
3
0
2
0
2
0
2
1
1
2
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
2
0
0
0
0
0
0
2
2
0
2
1
0
2
0
2
1
0
2
2
0
0
2
0
0
0
0
0
2
0
0
0
1
0
4
1
1
3
1
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
1
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
2
2
1
3
0
0
0
1
1
0
1
0
0
0
2
0
2
0
3
1
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
2
2
0
2
0
0
1
0
0
0
2
0
1
0
1
2
0
0
0
0
2
1
1
2
0
0
2
0
0
0
1
1
2
0
1
1
0
0
0
0
2
0
2
2
0
2
0
0
0
2
0
0
2
1
0
0
1
0
0
0
1
0
0
0
1
0
1
2
0
0
0
1
0
0
1
1
0
0
0
0
0
2
2
0
0
0
0
2
2
0
0
0
1
1
0
1
1
1
2
2
1
0
3
0
0
1
0
2
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
1
0
2
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
2
1
0
0
0
0
0
2
0
0
0
0
0
0
1
2
1
0
1
0
0
0
0
1
0
2
1
0
1
1
2
0
1
2
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
1
0
1
2
2
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
1
2
0
1
0
2
1
0
0
2
2
0
1
0
1
0
0
0
0
0
0
0
2
1
0
2
0
0
2
0
0
0
1
2
1
0
0
1
0
0
0
2
0
2
0
2
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
2
2
1
0
1
0
0
0
0
5
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
2
2
1
2
1
0
1
0
0
2
2
0
0
0
1
0
0
0
0
0
4
0
1
0
2
1
0
0
0
0
2
1
1
0
0
0
1
1
0
0
0
1
1
1
2
2
0
0
0
0
0
0
2
0
1
0
1
0
0
0
2
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
3
0
2
0
0
1
0
2
1
0
0
0
0
0
1
0
0
3
0
0
2
1
0
2
0
2
0
1
2
0
0
0
0
2
0
0
1
2
0
1
2
1
0
0
0
1
3
2
1
1
1
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
2
1
0
0
4
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
2
5
0
3
0
2
1
3
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
3
0
0
1
2
0
2
0
0
0
0
2
0
2
2
1
3
1
1
0
0
0
6
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
1
0
2
2
2
0
1
4
2
0
0
1
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
1
2
0
0
1
2
0
0
0
0
0
0
0
1
0
0
2
0
1
0
1
0
0
0
1
1
0
2
0
0
0
3
3
2
2
0
0
4
0
2
0
0
2
0
0
0
0
3
2
0
0
1
2
0
1
0
0
0
2
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
4
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
1
0
0
8
1
0
0
1
1
0
0
1
0
1
0
0
0
0
2
5
0
0
2
0
5
0
0
2
0
2
2
1
2
0
2
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
2
2
0
1
0
0
0
1
0
1
0
1
1
2
2
0
0
0
2
1
1
0
2
0
1
2
0
2
2
2
2
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
1
1
2
2
0
0
2
0
1
0
2
2
0
0
0
0
0
0
0
2
0
2
2
0
1
0
0
5
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
2
0
2
0
0
1
0
2
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
1
2
1
0
0
2
0
2
0
0
2
0
2
0
0
2
0
2
0
0
0
0
0
0
2
0
0
1
2
0
0
1
1
1
1
2
0
0
0
0
0
2
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
3
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
2
1
1
0
2
1
0
2
0
1
0
0
1
1
1
0
0
0
2
0
0
0
0
2
0
0
0
1
0
1
0
1
0
3
0
1
0
0
0
0
1
0
1
0
1
0
1
0
1
2
0
0
0
0
0
2
2
2
0
0
2
2
0
0
1
0
0
1
0
2
0
0
1
0
0
0
0
1
0
2
1
0
0
2
0
1
0
0
1
2
0
0
2
0
1
1
2
0
0
0
0
0
2
1
0
0
0
0
2
2
2
0
0
0
0
2
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
2
0
1
0
0
0
1
0
0
0
0
1
0
0
1
1
1
0
2
0
1
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
3
2
0
0
2
0
0
0
0
0
0
3
0
0
0
0
1
2
0
2
1
1
1
1
1
0
0
1
0
2
2
0
0
1
0
0
0
0
1
2
0
1
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
1
0
0
0
0
2
1
0
2
3
0
0
0
0
4
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
1
0
0
3
1
0
1
1
0
1
0
0
1
1
0
2
1
2
0
1
1
1
0
0
1
2
1
0
0
0
2
1
1
0
0
0
0
2
1
1
0
0
0
1
1
0
0
1
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
2
0
0
6
2
0
0
0
2
0
0
0
1
0
1
0
0
1
0
0
0
1
2
1
0
1
0
0
0
0
0
1
0
0
1
0
2
1
2
0
0
1
1
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
2
0
1
0
0
0
0
0
2
2
2
0
1
0
0
0
2
0
1
1
0
0
2
0
0
0
0
1
0
0
2
0
0
0
2
0
2
1
0
3
1
0
2
0
0
0
0
0
1
1
3
0
1
0
2
0
2
0
0
0
1
2
0
0
0
2
0
1
0
2
0
1
2
0
1
3
1
1
0
0
0
7
0
1
1
0
0
2
0
1
0
2
0
0
0
0
1
1
0
0
0
2
1
1
0
0
0
0
2
0
1
1
0
1
0
0
0
0
2
0
0
0
0
2
1
2
0
0
0
0
0
0
2
0
0
2
0
0
2
1
0
1
0
0
2
0
0
0
0
0
0
0
1
2
2
0
0
1
1
2
2
0
2
2
0
0
2
2
0
0
0
0
0
0
2
0
1
1
2
0
0
1
0
1
2
0
0
1
0
3
2
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
2
0
3
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
2
0
0
0
1
0
0
0
3
0
0
3
0
2
0
1
0
1
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
2
1
2
1
0
0
0
1
1
0
4
0
2
0
1
0
0
1
0
0
0
0
2
0
1
0
2
0
1
2
0
0
0
0
2
2
0
1
2
0
0
0
0
0
1
0
1
0
2
0
0
1
0
1
0
0
0
0
0
0
2
0
1
0
0
1
1
2
0
2
1
2
1
2
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
1
1
0
0
0
2
2
2
2
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
1
0
2
1
0
2
1
1
0
0
0
0
0
0
2
0
1
2
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
2
0
1
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
3
1
1
1
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
2
0
2
2
0
0
2
1
0
0
0
0
2
3
1
1
0
2
2
0
0
0
0
0
1
2
2
2
0
1
0
1
0
2
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
2
1
0
0
3
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
2
2
1
0
4
2
0
1
0
0
0
3
0
0
0
0
1
0
2
1
0
1
1
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
2
2
0
2
0
2
0
0
3
1
0
2
1
0
0
0
0
0
0
2
0
0
2
1
0
1
0
0
0
0
0
2
2
1
0
1
0
0
2
1
1
0
1
1
1
2
1
0
1
0
0
0
0
0
0
2
0
2
0
1
0
0
2
0
1
0
0
0
0
2
1
2
1
0
0
0
1
2
2
0
1
1
0
0
0
0
0
0
2
0
2
1
2
2
2
0
0
1
0
1
0
2
1
1
0
0
0
2
4
1
2
1
0
2
0
0
0
2
1
2
2
0
0
0
1
0
0
1
0
3
0
0
1
1
0
4
0
0
0
0
0
0
0
0
2
0
1
2
0
1
2
2
0
2
0
0
0
0
2
3
1
0
0
1
0
0
0
0
0
0
3
2
0
0
0
0
0
1
0
0
1
0
2
2
0
3
0
1
0
0
0
0
0
0
1
0
0
2
2
2
0
2
2
0
1
2
0
0
2
1
0
1
1
0
0
2
0
0
0
1
0
0
0
1
0
1
0
2
0
0
0
1
0
2
0
0
0
2
0
0
0
0
1
1
0
2
0
0
1
2
0
0
1
1
1
0
0
2
0
1
0
2
0
1
2
2
0
0
0
0
0
0
0
1
0
1
0
0
0
1
2
2
0
2
0
0
0
0
0
0
0
1
0
0
2
0
2
1
2
0
1
1
0
0
1
0
2
0
2
0
1
0
0
0
0
0
0
1
1
0
0
1
0
2
0
0
1
2
1
0
0
0
1
0
0
1
0
0
0
1
0
1
2
1
0
3
0
0
3
0
0
2
1
2
0
1
0
0
0
0
2
1
0
2
0
1
0
1
3
0
0
1
0
0
2
1
0
0
1
2
2
3
0
0
2
0
0
1
0
0
0
0
2
0
0
2
0
0
0
1
0
0
1
1
0
0
0
2
0
1
3
2
0
0
2
0
2
2
0
1
1
0
0
0
1
0
3
2
0
5
0
0
2
0
0
0
0
0
0
0
2
1
0
0
2
0
0
2
2
2
2
2
0
0
1
0
0
2
1
2
0
5
0
0
0
0
0
0
0
1
0
2
1
0
2
0
1
2
0
0
2
0
2
0
2
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
2
0
3
0
1
1
0
2
2
0
0
2
0
1
5
0
2
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
2
2
2
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
1
2
0
2
0
1
0
0
1
3
1
1
1
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
2
1
0
0
0
1
2
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
2
0
1
0
1
2
1
1
0
1
0
2
0
0
0
2
0
0
0
1
0
1
1
0
1
1
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
1
1
3
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
2
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
2
0
2
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
7
1
0
1
1
0
0
0
1
0
0
1
3
2
0
0
0
0
2
0
1
0
1
0
0
4
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
1
0
0
1
1
0
0
1
0
0
0
1
0
0
0
1
2
0
0
0
0
0
2
2
0
0
0
2
1
1
0
0
0
0
0
0
1
1
2
0
1
0
0
0
1
0
2
1
0
0
2
0
0
0
0
1
1
0
2
1
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
1
0
1
2
0
0
0
0
1
1
1
0
0
1
0
1
0
1
0
2
0
1
0
2
0
0
1
0
0
0
1
0
0
1
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
1
0
1
1
2
0
0
2
0
2
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
2
1
2
1
0
0
1
2
0
0
0
0
0
0
0
1
1
1
0
0
0
1
2
0
2
0
0
1
0
0
2
1
0
0
1
2
2
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
2
0
2
2
0
0
0
1
0
1
0
1
0
2
6
1
0
1
0
3
0
0
0
3
1
2
0
0
0
0
0
2
0
0
0
2
2
1
0
1
2
2
2
2
0
0
1
1
2
0
2
0
0
0
0
1
1
1
0
0
0
1
0
0
1
3
0
2
0
0
0
2
0
2
0
2
0
0
0
1
0
0
1
0
1
2
0
2
2
1
0
0
0
0
2
2
0
0
1
1
0
2
1
2
0
1
0
2
0
1
0
0
1
1
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
1
3
0
0
0
0
2
0
0
0
1
1
1
1
2
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
1
0
2
2
0
0
0
0
1
0
2
0
1
0
1
0
2
0
0
0
1
0
2
0
0
1
2
0
1
0
0
2
0
0
1
2
0
0
0
1
0
1
0
1
1
0
0
0
0
2
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
2
1
0
2
0
2
0
0
0
2
1
2
1
3
0
2
0
0
3
2
2
0
1
0
0
0
0
1
0
0
0
3
1
0
0
1
2
1
0
2
0
2
0
1
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
2
2
0
0
2
3
0
1
2
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
2
0
1
0
2
0
2
0
0
2
0
1
0
0
2
0
0
1
3
0
0
1
0
2
0
1
0
2
0
2
0
0
0
0
0
1
1
3
2
0
1
2
0
0
0
0
2
1
0
0
1
0
0
0
2
2
0
0
0
0
0
1
1
1
0
0
2
0
1
2
1
2
2
1
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
1
0
2
1
2
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
1
0
0
2
0
2
1
0
1
1
0
1
0
1
0
1
1
0
1
1
1
0
0
1
0
0
0
2
0
0
0
0
1
2
0
0
1
0
1
0
1
0
0
1
0
1
0
0
0
2
0
3
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
1
2
0
0
1
0
0
0
0
2
0
0
3
0
0
1
1
2
0
5
0
0
1
0
0
0
0
2
0
0
2
0
0
0
1
0
1
0
0
2
0
0
2
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
1
2
2
0
2
0
0
1
0
1
3
0
0
0
0
4
1
0
0
2
0
0
0
0
2
1
0
0
0
0
1
1
0
0
2
1
0
1
0
0
0
0
3
0
0
2
0
0
0
2
1
0
0
0
1
2
0
1
2
0
0
0
1
0
2
0
0
0
0
0
1
0
1
0
0
0
0
2
0
1
2
0
0
0
0
2
0
0
0
0
2
2
1
2
0
0
0
0
0
1
0
0
0
0
0
0
4
1
1
1
2
2
2
2
1
0
0
2
0
0
0
0
3
0
0
0
0
3
0
0
1
2
0
0
3
0
0
0
0
2
0
0
0
0
0
0
1
0
1
1
1
1
0
0
0
0
1
0
1
0
1
2
2
1
0
0
1
2
0
0
0
1
0
1
1
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
4
0
0
3
0
0
0
2
1
0
3
0
0
2
0
2
0
2
0
0
2
0
0
0
0
2
0
0
1
0
2
2
0
0
2
0
0
2
2
2
0
1
0
1
1
1
1
1
2
0
0
2
2
0
0
0
0
0
1
7
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
3
2
2
0
2
2
2
0
0
0
2
0
1
4
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
2
2
0
2
0
1
1
0
2
0
0
0
3
0
0
2
0
0
0
0
0
2
2
2
0
2
2
0
1
3
0
0
2
0
0
0
0
0
2
2
2
1
0
2
0
0
0
0
2
0
0
1
0
2
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
2
1
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
1
0
2
0
2
1
0
0
0
0
0
0
0
1
0
0
0
2
1
0
2
0
0
0
0
0
1
0
0
3
0
0
1
5
0
1
0
0
2
0
0
1
3
0
0
0
1
2
0
0
2
2
2
0
0
3
0
0
0
0
2
0
1
0
0
0
3
0
0
2
0
2
2
0
0
0
2
1
0
0
0
3
1
0
0
0
0
1
2
0
1
2
0
0
1
0
0
1
0
0
2
2
0
0
2
0
1
0
2
0
2
0
0
1
1
0
1
0
2
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
2
0
2
0
0
0
0
0
1
1
1
0
0
1
0
0
1
2
0
0
2
2
1
0
1
0
1
1
0
0
0
1
1
0
0
1
0
1
0
2
2
2
0
0
0
0
0
0
2
1
0
2
2
0
1
1
2
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
2
1
2
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
2
1
0
0
0
2
1
0
3
0
0
0
2
0
0
1
0
0
1
2
1
0
1
0
0
0
1
0
2
2
1
1
1
1
0
1
0
3
1
2
0
2
0
2
0
0
0
2
2
0
2
0
0
1
0
0
1
2
0
2
0
0
0
1
1
0
0
1
2
0
1
6
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
4
1
3
1
0
1
0
0
0
0
1
0
0
2
2
0
0
0
2
2
2
0
0
0
1
1
0
1
0
0
1
0
0
0
2
0
1
2
0
0
0
0
2
1
2
2
0
0
1
4
0
0
0
3
0
2
2
0
0
0
0
0
1
0
3
0
1
2
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
1
2
0
1
2
2
0
2
0
1
0
0
1
1
0
0
2
2
0
0
1
0
2
0
2
0
2
0
3
0
0
1
0
2
1
0
2
1
0
1
1
0
0
2
1
1
2
0
0
0
1
1
0
1
0
0
0
1
0
1
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
2
0
0
1
4
0
0
1
2
0
1
1
0
0
0
0
2
0
0
0
0
0
1
2
2
0
0
0
2
0
0
0
2
1
0
0
0
2
2
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
3
0
0
1
0
2
1
0
0
0
0
2
2
0
1
2
2
1
0
2
1
0
1
0
0
1
2
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
2
2
0
2
1
0
0
0
0
0
0
0
0
1
0
2
0
1
2
0
0
1
1
0
1
0
0
1
1
1
1
0
1
1
0
0
1
0
2
0
0
0
2
0
0
1
0
2
1
0
0
0
0
0
0
1
0
1
1
1
2
0
1
0
2
0
0
0
0
0
0
1
1
0
0
0
2
1
0
0
0
1
0
1
1
0
0
0
0
5
0
0
0
2
0
2
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
1
2
0
1
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
1
0
0
2
2
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
1
1
3
0
2
1
1
1
1
0
0
0
1
1
1
1
1
0
3
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
1
1
1
0
0
2
1
0
2
0
0
0
0
1
2
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
2
0
2
0
0
2
1
0
0
0
1
2
2
0
1
2
0
2
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
1
1
0
1
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
3
0
0
1
0
0
0
1
1
0
0
1
1
0
0
2
2
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
3
1
0
0
2
0
0
0
2
2
0
2
1
1
0
2
1
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
5
2
2
2
0
0
0
0
1
2
1
0
1
2
0
2
0
1
0
2
0
1
0
1
0
1
0
2
0
2
0
0
0
0
0
0
0
2
0
2
0
0
3
0
0
1
0
0
2
0
1
0
0
0
0
1
0
3
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
2
0
1
1
0
0
1
0
0
1
0
1
0
0
0
0
1
2
2
0
0
0
0
1
1
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
2
5
2
0
0
3
0
0
0
0
2
0
1
1
5
1
0
0
2
1
1
2
1
0
1
2
0
0
0
0
0
0
0
2
1
0
1
2
2
0
0
0
1
0
0
0
0
0
0
1
0
0
1
2
0
1
2
0
0
2
0
1
0
0
0
0
1
0
0
0
2
3
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
1
2
0
0
0
0
1
0
0
1
0
0
2
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
2
1
0
1
0
0
0
2
0
0
5
1
0
1
0
0
2
0
1
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
3
0
1
1
0
0
0
0
2
3
1
0
0
0
0
0
2
0
0
1
2
1
2
2
2
0
0
0
0
1
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
1
0
0
2
0
2
0
2
1
1
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
2
0
2
0
0
1
0
2
2
1
4
0
0
0
1
1
0
0
0
0
1
0
0
0
0
2
0
0
1
0
1
1
0
1
0
2
0
2
0
0
1
0
2
0
0
0
0
1
3
3
0
2
0
0
0
2
0
0
1
1
0
0
0
2
0
1
0
2
0
2
0
0
1
1
0
0
1
1
2
2
0
1
2
0
0
0
0
3
0
1
2
0
0
0
0
0
1
2
0
0
1
1
1
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
1
2
0
0
0
2
0
2
2
0
0
0
1
3
1
2
1
0
0
2
0
0
2
1
0
1
0
1
0
0
0
0
1
0
1
0
2
2
0
2
1
0
1
0
2
0
0
1
0
1
0
2
0
0
1
0
0
2
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
3
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
2
0
0
0
0
0
1
0
1
1
2
1
0
0
0
1
0
1
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
2
0
2
0
0
0
2
0
2
1
1
2
0
1
0
1
2
0
0
0
1
0
0
0
2
1
1
0
0
0
2
0
0
0
3
0
0
4
0
0
0
1
1
2
0
2
0
1
0
0
0
0
0
0
2
0
1
1
0
0
1
0
0
0
1
0
0
2
3
0
0
0
1
0
1
2
0
1
0
0
0
0
0
2
0
0
1
0
1
0
2
0
0
0
0
0
3
0
2
0
1
0
0
0
0
0
0
0
1
0
1
2
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
3
0
0
0
0
0
1
1
0
2
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
2
1
0
0
1
0
2
0
3
2
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
2
0
1
1
2
0
0
0
0
2
0
3
0
0
0
2
2
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
3
0
0
2
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
1
1
2
1
1
0
0
0
2
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
2
1
3
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
2
0
2
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
1
2
2
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
1
1
1
2
0
1
0
0
0
0
0
1
0
2
0
2
0
1
0
0
0
1
0
0
0
1
0
0
3
1
0
0
10
0
0
3
2
0
2
0
0
0
2
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
3
2
2
1
0
0
2
2
1
1
2
0
0
0
2
0
0
0
0
2
1
0
2
0
0
2
1
0
1
0
1
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
2
1
0
1
0
1
0
0
0
3
1
1
0
1
2
0
0
0
1
0
1
0
0
0
2
1
0
0
1
1
1
0
0
3
0
0
1
0
0
1
1
0
2
0
0
2
2
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
2
2
0
2
0
0
0
0
0
0
0
1
3
0
0
2
1
3
0
0
2
0
2
0
3
0
1
0
2
0
0
1
0
0
0
0
1
0
0
0
2
0
0
3
0
0
1
1
2
2
0
1
0
0
2
0
0
2
0
0
0
0
2
2
0
0
1
1
1
0
0
2
0
0
1
2
0
2
2
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
1
1
1
2
1
0
0
2
1
1
1
2
0
0
0
3
2
0
1
0
0
0
1
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
1
1
2
2
3
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
2
1
0
0
0
0
0
0
3
0
0
1
0
0
0
1
0
1
1
0
2
0
0
0
0
0
1
0
1
1
0
0
0
2
0
0
2
1
0
1
0
1
2
0
1
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
2
1
0
1
2
0
1
1
0
0
2
0
0
0
0
0
1
0
2
2
1
0
0
2
0
0
0
0
0
0
0
1
1
0
2
2
0
0
0
0
2
0
0
2
0
0
2
0
1
1
0
0
0
0
0
1
1
0
0
0
2
0
1
0
0
1
0
1
1
0
2
0
0
2
1
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
1
0
1
0
1
0
0
0
0
2
0
1
1
1
1
0
0
2
0
0
0
0
0
1
0
0
0
1
1
1
0
0
1
0
0
0
0
2
0
0
0
0
1
1
0
2
1
0
2
1
0
0
1
0
0
2
2
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
1
1
1
0
0
2
2
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
1
0
2
0
2
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
2
1
2
0
1
0
0
0
0
2
2
1
0
2
2
1
0
0
1
0
4
0
0
0
1
0
1
1
0
2
1
1
0
0
0
0
0
1
0
0
1
0
2
0
1
0
1
0
0
0
2
2
2
0
1
0
0
2
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
1
1
0
0
0
0
0
0
0
3
0
0
0
2
0
1
0
0
2
0
1
0
0
2
2
0
0
2
2
0
2
1
0
0
0
0
0
0
0
0
0
1
1
2
1
1
0
0
2
0
0
0
1
1
1
0
3
0
2
2
0
0
1
0
0
0
1
0
1
0
0
0
2
0
0
0
0
1
0
0
2
0
2
1
2
0
0
0
0
0
0
0
1
1
0
3
0
1
1
0
0
0
2
0
0
0
2
0
3
0
2
1
1
0
0
0
0
2
0
0
1
0
2
0
0
0
1
0
1
0
2
0
0
0
1
2
3
0
1
1
0
0
2
1
0
2
1
1
0
2
2
0
0
2
0
0
1
2
2
0
0
2
3
1
1
1
2
0
0
0
0
1
1
0
0
0
4
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
3
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
2
0
0
1
0
1
2
0
0
0
1
0
0
0
1
0
0
1
0
0
0
2
0
0
1
0
0
0
2
2
0
0
0
2
0
2
0
0
2
2
0
2
0
0
0
2
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
2
1
0
0
2
0
0
0
2
0
2
0
0
0
0
1
0
1
1
0
1
2
1
1
0
0
0
0
0
0
0
0
0
0
1
3
0
1
0
0
3
2
0
0
0
0
0
2
1
1
2
0
2
0
0
0
0
0
0
0
3
0
2
0
2
1
1
0
1
0
0
1
0
0
0
0
3
1
1
0
1
1
1
0
1
0
2
0
0
0
2
0
1
3
2
2
2
0
2
4
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
1
0
0
1
0
0
1
0
1
0
2
0
0
0
0
0
1
0
2
0
1
0
1
1
2
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
2
2
3
4
0
0
0
1
1
1
0
1
1
0
1
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
1
1
1
0
1
1
0
0
1
2
0
0
3
1
0
1
0
1
0
1
2
0
1
1
0
0
0
0
0
0
0
0
0
1
0
2
1
1
0
0
0
0
0
0
0
1
0
0
1
0
1
1
1
0
0
1
0
1
2
0
0
2
2
2
0
0
0
0
0
0
1
1
1
1
1
0
2
0
0
0
2
1
2
0
0
0
0
0
2
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
2
0
2
1
1
0
2
0
0
0
0
2
0
2
1
0
2
0
1
0
0
0
2
0
2
0
1
0
1
2
0
0
0
0
2
0
1
0
0
0
1
3
0
1
0
0
1
0
1
0
0
1
1
1
0
0
0
2
0
0
0
0
0
0
0
1
0
1
2
0
2
0
0
0
2
1
1
1
0
0
0
0
0
1
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
2
0
1
0
1
0
2
0
0
2
2
0
0
1
2
2
0
0
0
0
0
1
3
0
0
0
2
0
1
0
0
2
1
1
0
0
2
0
3
0
0
0
3
0
0
1
1
0
0
0
1
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
2
1
2
0
0
0
1
0
0
0
1
0
0
1
0
2
0
0
2
0
1
0
1
0
0
0
0
0
1
2
0
2
0
0
0
0
2
1
0
0
0
0
2
0
0
2
0
2
2
0
1
1
1
1
0
2
0
0
3
0
2
0
1
1
1
1
1
2
0
1
0
0
1
2
0
0
0
0
0
1
0
0
0
2
1
0
1
0
0
0
0
0
1
2
0
0
3
0
2
2
2
3
2
0
0
0
0
2
1
0
0
1
0
0
2
2
0
0
2
2
0
1
1
0
0
2
0
0
0
2
0
0
0
1
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
2
0
1
2
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
2
2
0
1
0
2
1
2
0
0
0
0
0
0
2
1
2
0
0
0
0
2
0
2
1
2
2
2
0
0
1
0
1
1
0
0
0
0
2
0
0
0
2
0
0
3
1
0
0
0
0
1
3
0
1
0
0
0
1
0
2
1
1
0
2
1
0
0
0
0
0
0
0
2
1
2
2
2
1
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
2
2
1
5
3
1
0
0
1
0
0
0
0
2
3
2
0
1
1
1
0
0
1
1
0
2
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
2
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
1
0
0
2
1
0
0
0
2
0
1
0
0
0
0
1
1
1
0
0
0
3
2
2
1
0
0
0
2
0
0
2
1
0
0
2
0
1
0
1
1
1
0
3
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
1
1
0
0
0
2
0
3
2
5
0
2
0
2
1
0
2
0
1
0
0
0
0
0
0
0
0
2
0
2
2
0
0
2
1
0
0
0
0
0
0
1
2
0
2
1
0
0
0
1
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
2
1
1
0
0
0
0
0
1
1
0
1
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
2
0
0
2
0
0
0
2
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
1
0
0
0
3
0
2
0
0
0
2
0
0
1
0
0
2
2
0
3
2
1
2
0
0
1
1
2
1
2
0
0
0
1
0
0
0
0
0
1
0
0
2
1
2
0
0
0
0
0
3
1
0
0
0
0
4
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
2
0
0
1
5
0
0
1
2
2
0
0
1
0
0
0
0
0
2
0
2
2
1
2
0
2
0
0
0
0
0
1
1
0
0
0
1
0
0
2
0
2
2
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
2
2
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
5
0
0
0
0
0
1
1
1
0
0
1
0
2
1
2
0
1
0
0
2
0
0
0
0
0
1
1
0
2
2
3
0
0
3
0
0
1
0
0
1
1
2
1
0
0
1
0
0
2
0
0
1
3
0
0
3
1
1
2
0
3
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
2
4
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
1
0
1
2
0
1
1
0
0
2
1
0
0
0
0
1
2
0
0
0
0
0
1
0
2
0
0
0
3
2
0
0
0
2
0
0
2
0
2
2
0
0
1
0
2
0
1
0
0
2
0
3
0
0
6
0
0
0
0
0
0
2
2
0
1
0
1
1
0
0
2
0
1
1
0
0
0
2
0
0
2
0
1
4
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
2
0
2
0
1
0
2
1
0
0
1
0
0
0
0
4
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
1
2
2
1
0
0
1
1
1
2
0
0
0
0
0
0
2
0
0
0
0
0
5
0
2
0
0
0
1
2
0
2
2
0
0
2
0
0
0
0
0
0
0
1
2
0
1
1
0
1
0
2
0
0
0
1
1
0
0
2
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
3
2
0
0
1
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
1
0
1
0
1
0
0
2
0
1
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
2
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
1
0
0
0
0
1
0
1
2
0
1
2
2
0
1
0
0
2
2
2
0
1
1
0
0
2
0
2
1
0
0
1
0
0
2
3
0
0
2
0
0
0
0
0
2
2
2
0
1
2
0
0
0
0
0
0
2
0
0
2
0
0
0
2
2
1
0
0
1
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
1
0
0
2
1
3
0
0
0
1
0
0
0
0
2
2
0
0
1
0
0
1
0
2
0
1
0
0
1
1
5
0
1
1
2
1
0
2
1
0
0
1
1
0
0
1
0
0
0
2
0
0
2
0
2
2
0
1
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
2
0
0
2
1
0
0
0
1
0
1
3
2
0
0
0
0
0
1
0
0
2
1
2
0
0
0
1
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
2
2
0
0
2
0
0
2
0
0
0
2
0
3
0
0
0
0
1
2
6
0
0
1
0
1
0
0
0
0
0
1
1
0
1
0
3
0
2
0
1
2
0
0
0
0
0
1
1
0
2
0
0
0
0
0
1
1
1
0
0
3
2
0
0
1
0
1
0
0
1
0
0
0
3
0
0
0
1
0
0
0
1
3
1
2
0
1
2
0
1
1
0
0
0
0
1
0
0
2
1
0
0
1
2
0
0
0
0
0
0
0
1
0
4
0
0
1
1
1
0
0
0
0
2
0
0
0
1
0
2
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
3
2
0
0
0
0
3
0
2
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
2
2
1
1
0
0
6
2
0
2
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
2
0
0
0
1
0
0
2
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
2
2
0
0
0
0
0
2
1
0
0
3
0
0
2
1
1
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
2
0
2
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
1
1
1
0
2
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
2
0
0
2
2
0
0
0
0
0
1
2
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
1
1
1
0
2
0
1
2
0
1
2
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
2
0
1
1
0
0
1
1
2
0
0
0
2
2
0
2
2
0
0
0
2
0
0
1
0
0
0
2
2
1
0
0
2
0
1
0
0
2
0
0
0
1
0
0
0
1
0
2
0
0
0
2
1
0
0
0
1
2
0
0
1
0
1
0
1
1
1
0
0
0
0
1
0
2
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
1
0
2
0
0
1
0
0
2
0
0
0
0
2
0
1
1
0
0
0
0
0
0
2
0
1
1
0
0
2
2
0
0
0
0
1
1
1
0
0
1
1
0
0
0
0
0
0
2
2
0
0
0
3
0
0
0
0
0
1
0
0
2
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
2
0
1
0
0
0
0
1
0
2
0
2
1
0
1
0
0
2
0
2
0
0
0
0
0
0
2
0
1
2
1
3
2
2
2
0
0
0
2
5
0
1
0
2
0
0
2
0
2
2
1
0
0
2
3
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
3
0
0
1
0
1
0
0
2
0
2
0
0
0
1
0
2
0
0
1
0
0
2
1
0
2
1
1
0
1
1
0
1
0
0
0
2
3
0
0
0
1
2
1
0
0
0
0
0
1
2
1
2
0
1
0
1
2
1
0
2
0
1
0
2
0
0
0
0
1
1
0
0
0
0
1
1
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
1
3
0
1
1
0
2
0
0
3
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
1
1
2
0
0
0
0
1
0
0
2
0
0
0
0
0
2
1
0
0
1
0
0
1
0
1
1
0
0
0
0
1
2
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
2
2
2
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
1
1
2
0
0
0
0
0
2
3
0
0
0
0
0
1
2
1
0
0
0
2
1
2
0
0
1
0
0
0
2
1
0
2
0
0
0
2
0
0
0
1
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
2
2
0
0
0
0
1
0
0
1
0
1
0
0
3
0
0
0
0
2
2
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
1
6
1
0
0
0
0
0
1
2
0
0
0
2
0
0
2
2
0
0
0
1
0
2
0
1
0
0
0
0
2
0
1
1
0
0
0
0
0
0
1
0
0
2
1
3
3
0
3
0
0
0
0
2
2
0
1
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
2
2
0
2
0
1
0
0
0
2
3
2
0
1
0
0
1
0
2
0
1
0
2
0
2
1
0
0
0
0
2
1
0
0
2
0
0
3
0
2
0
1
1
2
0
0
0
1
0
1
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
2
0
1
1
1
2
2
0
2
2
0
0
1
1
1
0
1
0
2
0
0
0
0
1
0
1
0
0
0
0
0
2
1
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
2
1
1
0
2
2
2
0
0
2
1
0
1
0
2
0
2
1
0
0
0
0
0
1
0
0
0
1
2
0
0
2
2
1
0
0
0
0
0
0
1
2
2
0
0
1
0
2
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
2
0
2
0
0
1
2
1
0
2
0
1
0
2
1
0
11
2
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
2
0
0
2
2
0
0
1
0
0
1
0
0
0
1
1
2
1
0
4
1
0
0
1
2
0
0
0
1
3
0
1
0
2
0
2
0
0
0
0
0
0
0
1
2
1
2
0
0
0
1
0
2
0
1
1
0
0
2
0
0
2
0
0
0
2
0
1
0
2
0
0
0
1
3
0
0
2
0
1
1
0
0
0
0
2
1
3
0
0
2
0
0
1
0
0
1
2
0
0
2
0
0
0
0
0
2
0
2
1
1
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
2
0
0
0
1
2
2
0
0
0
0
0
0
1
0
0
1
1
2
0
0
0
1
0
0
0
2
0
2
0
3
0
0
0
0
0
0
2
1
0
1
2
1
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
3
0
0
0
2
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
1
1
2
0
2
1
0
0
0
2
0
2
0
1
1
1
2
0
2
0
0
0
1
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
1
0
2
1
0
2
2
0
2
0
0
3
0
0
0
2
2
1
1
0
0
0
0
1
0
2
0
0
0
2
0
0
0
1
0
0
0
1
1
0
1
0
1
0
0
1
0
1
0
1
0
0
0
1
0
1
0
0
0
2
3
0
0
0
0
0
2
0
2
0
1
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
2
1
0
1
0
2
1
1
0
0
0
0
0
0
2
0
2
1
0
0
2
2
0
2
1
0
1
0
0
0
0
0
0
0
1
1
0
1
0
2
0
1
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
1
0
0
1
0
0
1
2
0
2
0
0
0
0
0
0
1
0
0
3
0
0
2
1
0
0
0
0
0
2
0
2
0
1
1
2
0
2
0
1
0
0
0
2
2
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
2
1
3
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
2
0
0
0
1
0
1
2
0
0
0
1
0
0
1
0
0
0
1
1
0
1
2
2
2
0
0
0
2
2
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
1
0
4
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
1
0
0
2
2
2
1
2
1
0
0
2
0
0
1
2
0
0
1
1
2
1
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
1
2
0
1
0
0
2
0
2
0
2
1
0
1
0
4
0
2
0
2
2
0
0
0
0
1
1
0
0
0
2
0
3
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
3
1
1
0
0
1
1
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
1
1
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
2
0
0
1
0
1
0
1
1
1
0
0
2
1
2
0
2
0
0
0
0
0
0
2
2
1
0
2
0
0
1
2
2
0
0
3
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
2
2
0
2
0
0
1
1
2
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
3
2
0
0
1
0
0
0
1
3
0
0
1
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
1
0
1
0
0
0
1
0
0
2
0
1
1
0
1
0
0
0
2
0
9
2
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
1
2
2
0
0
0
0
0
0
1
0
0
1
0
0
2
1
2
2
0
0
0
0
0
2
0
1
0
0
2
1
1
0
0
1
0
1
2
2
1
0
1
2
0
0
2
0
0
0
2
1
0
0
0
0
0
1
0
0
1
0
2
0
2
0
0
1
0
0
3
0
3
0
0
3
2
0
0
0
0
0
2
2
2
0
1
0
1
0
1
0
0
1
1
2
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
3
0
1
0
0
2
0
2
3
0
1
0
2
0
2
2
0
0
0
0
0
2
1
1
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
1
1
0
0
0
0
2
1
0
1
0
0
2
0
2
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
2
1
0
0
1
0
0
1
2
0
1
0
2
1
2
0
0
2
1
0
1
3
0
2
1
0
0
0
2
2
1
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
2
1
0
0
0
0
2
0
0
0
2
1
0
0
2
0
2
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
1
0
1
0
1
1
1
0
1
0
0
2
0
0
2
0
0
0
1
0
1
0
2
0
0
1
1
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
2
0
0
0
2
0
0
0
2
2
1
0
0
1
0
0
1
0
0
0
2
0
2
0
1
2
0
0
2
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
1
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
2
0
2
0
0
0
0
4
0
0
1
1
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
1
0
1
1
1
0
1
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
1
1
0
0
0
0
0
2
0
1
0
3
0
1
0
1
0
2
0
0
2
2
7
0
3
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
1
2
1
1
0
0
1
3
1
0
1
0
0
0
3
0
0
0
1
0
0
1
0
0
0
2
0
1
1
1
1
1
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
3
0
3
0
0
0
2
0
0
1
2
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
1
3
2
0
0
1
0
0
0
0
0
2
0
2
0
1
0
0
1
0
2
1
0
0
0
4
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
2
0
1
1
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
1
1
0
1
0
0
1
0
0
2
2
3
0
0
0
0
0
0
1
0
2
0
2
1
0
0
0
0
0
1
0
0
0
2
0
1
0
1
0
2
0
1
0
1
3
0
4
0
4
2
0
0
0
0
0
2
1
1
0
0
0
1
0
2
1
0
0
0
0
0
0
2
0
0
0
0
2
0
1
1
0
3
2
0
2
2
0
2
0
2
0
0
1
0
1
0
0
1
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
2
2
0
0
1
0
0
1
0
2
2
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
2
0
0
3
2
2
0
2
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
1
0
1
0
0
0
1
2
0
0
1
1
2
2
1
0
0
0
0
0
3
0
0
0
0
4
2
1
2
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
2
1
0
0
2
0
0
2
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
1
0
2
0
1
2
2
0
0
0
0
0
2
0
1
0
0
2
1
0
0
0
0
0
2
1
2
0
0
1
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
1
0
0
2
2
2
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
1
0
2
1
0
2
0
0
0
0
0
1
1
0
2
0
1
1
1
1
0
1
1
2
0
2
0
1
0
0
0
0
0
1
0
1
1
1
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
2
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
1
0
0
1
0
2
0
0
0
1
0
3
0
0
0
0
1
0
0
2
1
0
2
0
0
0
0
0
0
0
0
4
2
0
0
0
0
1
1
0
0
0
2
0
0
0
0
2
0
1
0
0
2
0
1
0
0
0
2
0
0
3
0
0
0
1
0
0
2
0
2
2
0
0
0
0
2
0
0
1
0
1
1
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
2
1
0
0
0
2
0
0
0
1
2
2
0
1
1
1
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
1
1
0
1
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
1
1
1
0
0
0
0
1
0
2
0
0
0
2
0
0
0
1
2
2
0
0
2
1
1
0
0
0
0
0
0
2
2
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
2
3
2
2
0
3
1
0
2
0
0
1
0
1
1
0
2
0
0
0
0
0
0
3
0
0
2
0
0
0
1
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
1
0
0
1
0
0
0
0
0
2
1
3
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
3
2
0
1
0
0
0
0
2
1
0
0
0
1
2
2
0
0
1
2
0
0
0
0
0
0
2
2
0
2
0
0
2
1
0
0
1
0
0
0
0
0
1
0
2
0
2
1
3
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
1
0
2
0
1
0
0
0
0
1
0
0
0
2
0
4
0
2
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
3
0
1
0
0
0
0
0
2
0
0
1
0
3
0
0
0
0
4
0
1
0
0
0
1
0
4
1
0
2
1
0
0
0
0
0
1
0
0
1
1
1
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
2
0
0
0
2
0
1
2
1
1
2
0
0
0
0
1
1
0
1
0
0
0
0
0
0
2
0
0
1
0
2
0
0
1
2
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
1
0
0
2
0
0
0
3
0
0
1
1
0
0
1
0
2
0
0
0
0
2
0
0
1
0
1
0
1
2
1
0
0
0
0
2
1
0
1
0
0
1
2
0
1
0
0
0
0
1
1
2
0
3
2
2
2
0
0
0
2
0
0
1
1
0
1
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
2
2
0
0
0
0
2
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
3
1
2
0
3
1
0
0
0
0
1
0
1
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
1
0
1
0
2
3
2
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
2
2
0
1
0
1
0
4
0
1
0
2
2
0
1
0
0
2
1
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
1
1
1
0
0
0
1
1
0
1
2
0
1
0
0
0
2
0
0
1
1
0
1
0
2
0
2
2
0
1
0
0
0
0
0
0
0
3
0
2
1
2
0
2
0
0
2
0
3
0
0
0
0
0
0
2
2
1
0
0
0
1
1
0
2
1
0
0
0
1
2
2
0
2
0
0
0
2
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
2
0
1
0
0
0
1
1
0
0
0
0
0
2
0
2
0
0
0
1
1
1
0
0
0
3
3
0
0
0
0
2
0
0
0
2
0
2
1
1
1
0
0
1
1
1
2
0
2
0
1
2
1
2
0
1
0
1
0
2
0
2
0
0
1
0
0
0
2
0
2
0
1
2
0
0
1
2
0
2
0
0
0
1
0
0
0
0
0
2
2
0
0
1
0
2
2
0
3
0
1
0
0
0
0
0
2
0
0
0
0
1
0
2
2
1
0
0
1
0
0
0
0
0
1
0
1
2
1
1
2
2
0
0
2
3
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
2
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
2
0
0
1
4
1
1
0
0
1
0
0
0
2
0
3
2
0
2
0
0
0
0
0
1
0
1
0
2
1
0
0
2
0
0
0
1
0
0
1
0
0
2
1
0
0
1
2
2
2
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
1
0
2
0
0
2
2
2
1
0
1
2
0
2
1
0
0
0
0
1
2
0
0
0
0
2
0
0
1
0
1
1
0
0
0
0
0
0
1
0
2
0
2
1
0
2
0
0
1
0
0
2
0
0
0
2
2
0
0
2
1
1
0
0
0
0
0
1
0
0
0
2
2
2
1
0
1
2
0
1
0
0
0
0
2
1
0
2
1
2
1
0
3
2
0
0
0
1
0
0
0
0
2
0
0
2
2
1
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
2
2
2
2
1
1
1
1
0
2
2
2
0
1
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
2
0
0
0
1
1
1
1
0
1
2
0
1
3
0
0
2
0
2
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
2
0
0
1
0
2
1
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
1
0
2
0
0
2
0
3
0
0
0
0
1
0
0
2
2
0
2
0
2
0
1
0
2
0
2
1
0
0
0
2
0
0
1
0
1
0
0
0
2
0
2
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
1
2
1
0
0
2
0
0
0
2
0
0
2
0
0
1
2
0
0
0
2
0
0
1
0
0
0
2
2
0
1
0
1
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
1
2
1
0
2
0
2
0
0
0
2
0
0
0
0
1
1
3
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
1
1
0
0
2
0
0
2
0
1
0
0
0
0
2
2
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
3
1
0
0
0
2
0
0
0
0
0
2
0
0
1
0
2
0
2
1
0
0
0
0
1
2
2
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
6
0
0
0
2
0
2
0
2
0
0
0
0
0
0
1
0
1
2
0
0
1
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
2
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
1
0
1
1
2
0
0
0
1
0
0
0
1
1
0
0
0
2
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
1
1
1
0
0
2
2
1
1
1
0
0
0
1
2
1
0
2
1
1
0
0
2
0
0
2
0
1
0
0
1
1
1
1
1
0
0
1
0
0
0
4
1
0
0
0
0
1
1
1
1
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
2
0
2
1
0
0
1
2
1
1
0
0
1
0
0
2
0
0
1
1
0
0
0
1
0
2
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
3
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
2
0
1
0
2
0
0
0
1
0
0
0
1
0
1
2
0
0
0
1
1
0
0
2
1
1
0
0
0
0
0
0
0
1
1
1
0
2
4
0
3
0
0
3
0
0
0
1
2
1
0
3
2
0
2
2
1
0
0
0
0
0
0
1
0
0
0
1
3
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
2
1
0
0
0
0
1
0
1
2
1
2
0
1
1
0
0
2
2
1
0
0
1
2
0
0
0
2
1
0
0
0
2
1
0
0
2
0
2
2
0
1
2
3
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
2
2
0
0
1
0
0
1
0
2
3
0
0
0
1
0
2
0
1
1
1
2
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
3
0
0
0
1
0
1
0
2
1
0
0
0
0
2
1
2
1
0
0
0
0
2
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
1
2
1
0
0
0
1
0
1
0
2
2
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
2
2
2
1
0
2
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
1
0
2
1
0
0
1
1
0
0
5
0
0
2
0
0
4
0
1
1
0
0
0
0
1
1
0
2
0
0
0
2
2
0
0
1
0
1
2
0
0
0
0
3
0
0
1
0
0
1
1
0
1
0
1
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
2
0
1
1
0
1
1
1
0
1
0
0
1
1
0
0
2
0
4
0
2
1
0
0
0
0
1
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
2
2
1
0
2
0
0
0
1
0
0
1
2
1
2
0
0
0
0
1
0
0
2
0
0
2
2
0
0
0
0
0
1
0
1
1
0
2
0
1
0
2
0
0
0
0
0
0
0
1
0
1
2
2
0
0
2
0
0
1
3
0
2
1
1
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
2
0
0
0
0
0
2
0
1
0
0
1
0
0
1
2
0
1
0
0
2
0
2
2
0
0
0
1
0
3
0
0
0
0
1
0
0
1
0
0
2
0
2
0
0
0
2
2
0
2
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
2
3
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
7
0
0
1
0
1
0
2
0
1
0
1
2
0
0
0
0
0
2
2
0
0
3
0
1
0
0
0
0
0
0
2
2
0
0
1
0
0
0
1
1
1
0
1
0
0
1
0
0
1
0
0
2
2
0
0
0
0
0
0
6
2
2
2
0
3
0
0
0
1
1
0
3
0
0
0
0
0
4
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
2
2
0
1
1
1
1
0
1
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
2
1
0
1
0
1
2
2
2
3
1
2
0
0
0
2
0
0
0
2
0
0
0
0
2
2
1
0
2
0
0
0
0
2
2
0
0
0
0
0
1
0
1
0
0
0
1
2
1
0
0
0
0
0
0
2
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
2
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
1
1
2
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
2
0
0
2
0
2
0
2
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
2
0
2
0
0
0
2
1
2
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
1
1
0
2
0
0
1
0
0
2
0
0
2
2
0
0
0
0
2
0
2
0
0
0
0
2
0
1
0
0
0
2
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
2
0
0
1
2
0
0
0
2
0
2
0
0
0
0
1
2
0
2
0
0
3
0
2
0
0
0
0
0
2
0
1
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
2
2
2
0
0
0
2
0
1
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
1
2
0
0
1
0
0
1
0
0
3
0
1
0
0
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
2
1
2
1
1
0
1
0
0
1
1
2
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
2
0
0
0
1
1
0
2
0
2
0
2
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
2
1
0
1
0
2
2
0
2
2
0
1
1
3
0
1
0
0
1
0
0
0
2
0
1
0
1
0
2
0
0
1
2
2
0
0
1
2
0
2
0
0
0
0
2
1
0
0
0
0
3
0
1
0
1
0
2
0
1
0
3
2
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
1
2
3
1
0
0
0
0
0
1
2
0
1
0
2
0
0
0
0
1
0
0
1
1
1
0
0
0
2
0
0
0
0
0
1
1
0
0
1
1
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
2
0
0
0
1
2
0
2
2
0
1
0
1
0
2
0
0
0
1
1
1
2
0
0
0
0
1
2
1
1
0
1
0
2
0
2
2
0
2
0
0
2
1
1
0
0
1
0
2
1
4
0
0
0
0
0
0
0
1
0
0
2
2
0
0
1
1
1
2
2
2
1
1
0
1
2
2
1
1
0
1
0
3
0
0
0
1
0
1
1
2
3
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
1
0
2
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
2
0
0
0
0
0
1
0
0
2
0
2
1
2
2
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
1
2
0
0
2
0
0
2
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
3
1
0
0
0
0
0
1
0
2
2
0
0
0
1
0
3
0
0
1
0
1
0
0
0
0
0
2
2
0
0
0
0
2
0
0
1
0
1
1
2
3
0
1
1
1
2
0
0
0
3
4
2
1
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
2
1
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
2
1
2
0
1
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
2
2
2
0
1
1
1
1
0
0
0
2
0
0
2
1
0
2
0
2
0
0
0
0
2
1
2
0
0
0
1
0
0
1
0
0
1
1
1
0
1
2
2
1
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
1
0
0
0
0
2
2
0
0
0
2
2
0
0
1
0
0
1
2
2
0
3
0
1
0
0
5
1
0
0
2
0
0
0
0
3
1
0
0
0
0
2
1
0
0
0
0
3
1
0
0
2
0
0
1
0
0
0
2
2
1
0
0
0
0
2
0
0
0
2
0
0
1
0
0
1
1
2
1
0
0
0
0
1
1
2
2
0
1
2
0
0
1
0
0
0
1
0
1
3
2
0
0
2
0
0
0
0
1
2
0
0
0
0
0
2
1
0
0
0
0
3
0
0
1
2
4
3
0
2
2
0
0
1
0
0
0
0
1
2
0
0
4
2
0
0
0
0
0
0
2
0
2
1
1
0
1
0
0
0
0
1
1
0
2
4
0
0
1
0
1
0
0
0
2
0
1
0
0
2
0
0
0
0
0
1
1
0
1
0
1
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
1
2
0
0
2
1
1
0
0
1
1
0
0
1
0
0
2
2
1
2
1
1
0
1
1
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
1
0
2
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
1
0
2
2
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
2
0
0
6
0
0
1
0
0
0
2
0
2
0
0
1
2
1
2
0
0
0
0
1
0
2
2
0
2
1
2
0
0
0
1
0
0
1
2
2
0
1
1
2
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
2
1
0
0
0
0
0
1
0
0
0
0
4
1
0
0
2
0
0
2
0
2
0
1
0
0
0
0
0
0
2
0
0
2
0
0
1
3
0
2
0
0
2
2
0
0
1
3
1
0
0
0
0
0
1
0
3
0
2
3
0
1
2
2
0
0
0
0
1
0
0
0
2
0
0
2
0
0
2
0
0
0
2
0
1
0
1
0
0
2
0
0
1
0
0
0
0
2
1
0
1
0
0
2
0
0
0
1
2
0
0
0
0
0
0
2
0
1
2
1
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
2
1
0
2
0
0
2
0
2
1
0
1
2
0
0
2
2
2
0
1
0
0
0
0
0
3
0
0
1
2
2
0
1
0
0
1
1
0
2
0
1
0
0
0
2
1
0
0
0
1
0
2
2
0
0
1
0
0
1
1
0
0
0
1
1
0
1
0
2
0
0
0
2
0
0
2
0
0
0
0
2
0
0
1
0
0
2
0
0
0
2
0
0
1
0
1
0
1
1
3
0
2
0
0
0
0
1
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
1
0
2
2
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
1
0
0
1
0
0
1
1
0
2
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
1
1
0
0
0
0
2
0
1
0
0
1
2
0
2
2
1
0
0
0
0
0
0
1
0
1
0
2
0
1
2
1
1
1
0
0
0
0
2
3
2
2
0
2
0
0
0
0
0
0
0
2
2
3
0
2
1
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
1
0
0
2
0
0
2
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
1
0
2
0
2
0
0
0
0
1
0
0
1
1
1
0
0
0
0
1
0
0
0
2
2
1
1
0
0
0
1
0
0
0
2
1
3
0
0
0
0
0
0
2
0
0
4
0
1
3
0
0
1
2
0
0
0
0
0
2
0
0
0
2
2
1
0
0
3
1
1
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
1
1
0
1
1
0
1
0
0
0
0
1
1
2
2
1
0
2
2
0
1
0
0
3
0
0
0
1
0
0
2
0
1
1
1
0
1
0
0
3
2
0
2
1
0
0
1
0
0
2
0
0
1
1
0
0
0
0
0
0
0
1
0
0
2
0
1
3
0
0
0
0
2
1
2
2
1
0
0
0
1
0
0
2
1
1
0
1
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
2
5
0
0
0
2
2
2
0
0
0
0
0
0
0
0
1
1
0
0
3
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
2
1
0
0
0
0
1
0
0
0
0
3
0
1
2
0
0
0
0
2
0
0
2
0
0
2
1
0
0
2
2
0
0
0
2
2
1
1
0
4
1
2
0
0
2
2
3
1
2
0
2
0
0
0
0
1
2
2
0
0
1
1
0
2
1
0
0
2
0
0
1
0
2
2
2
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
4
1
1
1
0
2
0
0
0
1
0
0
2
3
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
2
0
2
1
0
0
1
0
2
0
0
0
0
2
0
0
0
1
2
0
0
0
1
0
0
1
0
0
1
0
1
0
1
4
0
0
1
1
1
0
0
0
1
0
0
2
0
1
0
1
0
1
1
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
1
1
0
2
0
0
1
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
1
0
0
2
2
0
0
1
2
1
1
2
2
0
0
0
1
3
1
0
2
0
0
0
0
0
2
0
1
0
2
1
0
0
1
0
0
1
0
0
0
0
0
1
0
2
0
2
2
0
4
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
1
1
0
0
2
0
0
0
1
0
1
0
1
2
0
0
1
0
0
2
2
2
0
0
4
1
0
0
2
0
0
0
0
2
1
2
1
1
0
1
0
0
2
0
0
2
0
0
0
2
0
0
0
1
0
0
0
1
1
2
0
1
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
2
0
1
0
7
0
0
0
0
0
2
0
0
0
2
0
0
2
1
2
2
0
2
1
0
4
0
1
0
0
2
0
0
3
1
0
0
1
2
3
0
0
0
1
0
0
0
0
0
1
0
0
1
1
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
1
0
2
1
0
0
0
0
0
0
2
2
2
0
0
0
0
0
2
0
1
1
0
0
1
2
1
2
2
0
2
0
0
0
1
2
0
0
0
0
0
0
2
2
0
1
1
1
0
0
0
2
0
1
2
3
1
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
2
0
1
0
0
0
0
3
0
0
2
1
2
1
2
0
0
0
0
0
0
3
0
1
1
2
0
2
1
1
0
0
2
0
0
2
0
2
1
0
0
1
0
1
2
1
1
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
2
0
0
0
2
0
0
0
0
0
2
0
1
1
2
0
4
0
0
1
0
2
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
1
0
0
0
1
2
0
2
2
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
2
2
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
2
0
0
0
2
0
2
1
0
0
0
2
0
0
0
0
2
2
1
0
0
0
0
0
1
0
0
0
2
0
2
1
0
0
0
1
1
2
0
0
0
1
0
1
0
3
2
0
0
0
0
0
0
0
0
0
2
1
1
1
0
1
3
0
0
0
0
1
0
1
1
1
1
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
1
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
2
0
2
4
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
3
2
0
8
1
0
2
0
2
0
1
0
1
0
1
0
3
0
0
0
0
1
0
1
0
2
3
2
1
1
0
1
0
0
2
0
0
0
2
0
0
1
2
0
0
0
0
0
1
0
1
2
2
1
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
26
0
0
1
1
1
0
0
0
0
1
0
0
5
0
0
0
0
0
1
0
0
0
3
0
0
1
1
1
0
0
0
0
3
2
1
0
2
0
0
1
1
0
0
0
2
3
0
0
1
0
2
2
0
0
1
0
0
0
0
1
0
1
0
2
0
0
1
1
0
1
2
0
2
2
2
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
2
1
2
0
0
2
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
2
1
2
0
0
1
1
0
0
2
3
0
0
0
0
2
1
1
0
0
1
0
2
2
0
0
0
2
0
0
0
0
1
0
1
0
2
0
0
0
0
1
0
0
2
0
1
2
0
0
0
0
0
2
2
0
1
2
1
0
3
2
1
0
0
1
0
0
0
2
0
0
2
0
2
1
0
2
0
1
2
0
1
1
2
0
0
2
0
1
0
0
0
1
2
1
0
0
0
0
2
2
0
1
0
0
1
0
2
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
1
2
2
0
0
0
2
0
0
0
0
0
0
0
0
1
1
1
0
15
0
2
0
1
0
1
0
0
2
1
0
0
0
1
0
1
1
1
0
2
0
1
0
0
0
1
2
0
1
0
0
3
0
1
0
0
0
1
0
2
2
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
1
2
2
1
0
0
0
0
2
0
0
1
2
4
0
0
1
0
0
3
0
0
0
0
0
1
0
0
0
0
0
1
1
2
0
1
0
0
0
0
2
1
0
0
1
0
0
2
0
0
1
0
0
0
3
0
0
0
0
0
0
0
2
0
0
1
0
2
1
0
2
0
2
0
0
1
0
0
1
1
1
0
1
0
0
0
0
2
1
0
3
2
1
0
2
0
2
0
2
0
1
2
2
0
0
1
2
1
0
0
0
1
0
0
1
1
3
0
3
0
0
2
1
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
2
0
2
0
0
1
0
0
1
1
2
0
0
0
0
2
0
0
0
2
1
0
1
0
0
0
0
1
1
1
0
1
1
2
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
2
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
2
0
1
2
1
0
0
2
2
0
1
1
2
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
1
1
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
2
0
0
0
1
0
0
0
0
0
2
1
0
0
0
1
0
0
0
3
0
2
0
0
0
0
1
1
1
0
0
2
0
0
0
0
1
2
1
0
0
1
0
0
2
0
2
0
0
0
0
1
1
1
0
0
0
0
2
0
1
0
0
0
0
0
2
2
0
0
1
1
0
2
1
0
0
2
0
0
0
0
0
0
1
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
1
1
0
1
0
2
0
0
0
0
1
1
2
1
1
0
0
1
0
0
0
0
0
2
2
2
0
2
0
0
0
0
0
1
0
1
0
0
0
0
1
2
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
1
0
0
0
1
2
2
0
2
0
0
0
0
2
0
1
0
3
2
0
2
2
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
2
2
1
0
0
0
2
0
2
1
1
1
1
0
1
0
3
0
0
0
1
0
1
2
1
2
2
0
0
2
0
0
0
0
0
1
0
0
0
1
2
0
0
0
1
1
0
1
1
0
0
1
0
1
0
2
0
1
0
5
0
0
1
1
3
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
1
1
0
2
0
0
1
0
1
0
0
0
0
1
1
2
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
6
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
1
2
2
0
0
1
1
1
0
0
2
1
1
0
0
0
0
2
2
0
0
0
0
0
1
0
2
2
2
3
2
0
0
0
1
0
0
1
0
1
0
0
1
0
0
1
0
2
0
2
0
1
0
1
2
2
1
0
0
0
0
0
3
0
1
0
1
0
0
1
2
0
1
2
0
0
0
0
0
0
0
0
0
1
0
1
2
0
2
0
0
1
0
0
0
1
0
1
0
0
0
2
2
1
0
0
2
2
0
1
1
0
2
2
0
2
0
0
0
0
0
0
1
0
2
0
0
2
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
1
0
0
1
0
0
0
0
2
0
1
0
0
1
1
2
0
0
1
1
0
0
0
0
1
0
0
0
0
1
2
1
0
0
3
1
2
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
2
2
1
0
0
0
3
0
1
0
0
1
0
1
0
8
0
2
0
0
0
2
0
0
0
1
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
1
2
2
0
0
0
1
0
0
3
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
1
0
1
3
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
2
0
1
0
1
0
0
0
5
0
0
0
0
1
0
0
2
2
0
0
0
0
0
1
0
1
1
2
0
1
0
2
3
2
1
0
1
2
1
1
0
1
0
2
0
0
0
0
2
1
0
0
1
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
2
1
0
0
1
1
2
0
2
0
0
0
0
0
0
2
0
0
0
4
3
0
0
0
2
0
0
0
0
0
0
1
3
2
0
1
2
2
0
0
4
0
0
0
0
1
2
1
0
1
0
2
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
1
1
0
1
2
1
0
0
0
0
0
0
2
1
0
2
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
1
2
0
1
1
0
5
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
2
0
2
1
2
0
1
1
0
0
0
0
1
1
1
0
0
0
0
1
0
1
1
0
2
0
4
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
2
0
0
2
1
0
0
0
2
0
2
0
0
0
0
1
0
2
2
1
2
0
2
1
0
0
0
0
0
1
1
0
2
0
0
1
0
0
1
0
2
1
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
1
0
1
0
2
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
2
0
0
0
0
2
0
2
0
0
0
2
0
0
1
0
0
0
3
1
0
2
0
2
2
1
0
0
0
1
0
0
0
0
2
2
0
1
0
0
2
0
0
0
1
0
0
1
1
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
1
0
1
2
2
2
1
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
3
0
0
0
0
2
2
0
0
0
0
1
0
1
3
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
2
0
0
0
2
0
1
0
2
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
1
0
2
1
1
1
1
0
6
0
0
0
0
1
2
1
0
0
1
0
0
0
1
0
2
2
0
0
0
0
0
2
5
0
0
2
0
0
0
1
4
0
0
2
0
0
0
2
0
0
2
0
2
0
2
2
1
2
0
0
0
1
1
0
0
3
4
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
3
0
0
0
2
1
0
0
0
1
2
0
2
0
0
0
0
2
0
0
2
1
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
4
0
2
2
0
2
1
1
0
0
3
0
1
2
2
0
2
2
0
0
0
0
0
1
0
0
0
2
2
0
1
2
0
0
0
2
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
1
0
0
2
0
1
0
0
0
0
0
0
0
1
1
2
0
0
2
0
0
0
2
0
2
0
1
0
2
0
2
2
0
2
0
3
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
2
1
0
0
0
0
0
1
1
0
0
0
0
2
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
1
0
0
1
0
2
0
2
1
1
1
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
1
0
0
0
1
1
3
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
1
1
0
0
1
0
1
1
0
1
2
0
0
2
2
0
1
0
2
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
1
1
1
0
0
0
2
1
4
0
1
0
0
5
2
0
1
0
0
0
3
1
0
0
1
2
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
3
2
1
0
0
0
0
1
1
0
2
0
1
0
0
0
0
2
1
1
0
0
0
0
1
0
0
1
0
1
0
0
1
2
1
0
0
0
2
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
1
0
0
2
2
0
0
1
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
2
1
2
1
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
2
0
1
1
1
3
0
2
0
0
0
0
2
2
0
1
0
1
0
2
2
0
0
1
2
1
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
3
1
0
1
0
0
0
1
0
3
0
0
0
2
2
0
0
0
0
0
0
0
1
0
3
0
2
0
0
0
0
0
1
0
1
1
1
0
2
2
1
0
0
0
0
0
0
0
1
0
1
0
1
1
0
2
2
2
0
0
0
1
2
1
1
0
0
2
0
0
0
1
1
0
1
0
0
0
0
0
2
0
0
0
1
1
0
1
0
0
2
0
1
1
2
1
0
1
0
1
0
0
1
2
2
0
1
0
1
0
0
2
2
0
0
0
1
0
0
2
2
2
3
0
1
2
0
0
1
1
0
1
0
2
2
2
0
0
0
2
0
0
0
1
0
1
0
0
2
0
2
0
0
2
1
0
0
0
1
2
0
1
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
3
1
0
0
2
2
1
0
0
2
1
0
10
2
0
1
0
1
2
0
1
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
3
2
2
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
1
1
0
0
0
2
0
1
2
1
0
0
0
1
0
0
0
0
2
3
0
2
0
0
0
0
0
2
0
0
0
0
2
2
2
0
0
0
1
2
0
0
2
0
0
2
2
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
3
1
2
0
1
1
0
0
1
0
2
0
0
2
1
0
1
1
0
0
0
0
0
1
1
0
0
3
0
0
1
0
0
1
0
0
2
0
0
0
0
3
1
0
0
0
1
0
0
2
0
2
0
0
0
0
1
0
0
0
1
2
0
0
0
1
2
3
1
0
0
0
0
0
1
0
0
0
0
2
1
0
1
1
1
0
0
0
0
0
2
0
1
0
2
0
0
0
2
0
0
1
0
0
0
0
1
2
0
2
0
0
0
0
0
2
0
0
0
0
2
2
1
0
0
0
0
0
0
2
0
2
1
1
0
0
0
0
0
2
3
2
0
1
0
1
0
0
1
0
0
0
0
2
0
0
0
1
0
2
0
0
0
2
2
2
0
0
0
0
2
0
0
1
1
4
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
1
0
0
0
2
1
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
1
0
0
0
0
0
0
2
7
1
0
0
1
2
0
0
2
0
0
0
0
2
0
2
0
0
2
3
0
2
2
0
0
1
0
0
3
0
0
0
2
2
1
0
0
1
1
0
1
0
0
0
2
1
2
2
1
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
1
2
3
0
0
1
1
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
2
0
0
2
0
2
0
4
0
0
0
0
2
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
3
2
0
0
0
0
0
0
0
0
2
1
1
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
2
2
2
1
0
0
1
0
0
1
0
1
1
0
2
2
0
1
0
1
0
0
0
3
0
0
2
0
0
0
0
1
4
1
2
0
0
0
1
2
0
0
0
0
2
1
0
0
1
0
2
0
2
0
0
2
2
0
0
2
0
2
1
2
2
2
0
0
0
2
0
0
1
1
1
0
1
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
1
0
1
0
0
0
1
1
0
0
0
2
1
0
0
2
0
0
0
1
0
0
0
0
2
0
2
0
1
1
0
0
1
0
0
2
1
1
0
0
0
2
0
0
2
0
2
2
0
0
0
1
0
0
0
2
0
0
0
1
2
2
2
2
0
2
0
2
0
0
0
0
0
2
0
0
0
0
1
0
1
2
1
1
1
1
0
1
0
0
2
0
2
4
0
1
0
1
0
1
0
0
1
0
0
0
2
2
1
0
0
0
0
1
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
1
1
0
0
0
1
1
0
0
0
2
0
2
1
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
4
1
0
2
1
1
0
0
2
0
0
0
0
0
3
0
2
0
2
2
1
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
2
0
0
1
2
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
2
2
2
1
0
2
1
1
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
2
0
2
0
0
0
1
0
0
1
1
1
0
0
0
0
0
2
2
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
1
2
2
1
0
1
3
0
0
2
1
0
2
0
0
0
2
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
2
0
0
2
0
0
0
0
2
0
1
2
1
1
2
0
2
2
0
0
1
0
2
2
2
1
0
0
2
2
2
1
0
0
0
1
2
2
1
0
0
1
0
2
0
2
2
1
0
0
0
0
2
0
0
1
0
1
0
2
0
0
1
1
0
0
0
1
2
0
0
2
0
0
0
1
0
2
0
0
0
0
0
1
2
0
0
2
1
0
0
2
0
0
2
1
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
1
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
3
1
0
0
0
0
0
2
0
0
2
2
2
0
0
1
1
2
0
0
1
3
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
2
0
0
0
0
2
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
2
3
0
1
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
1
0
0
0
0
2
0
1
0
0
2
0
1
0
1
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
1
0
1
0
1
0
0
1
0
0
2
0
0
0
1
1
0
1
0
0
0
0
0
2
0
1
0
0
2
1
1
1
1
0
0
0
1
0
0
0
1
0
0
3
2
0
0
0
2
0
0
2
0
1
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
2
0
0
2
0
0
0
0
0
0
1
2
0
1
0
2
0
0
0
1
0
0
2
2
0
0
1
0
0
0
0
2
0
0
0
2
0
0
1
0
1
0
0
0
0
0
1
1
0
1
0
4
0
0
1
0
0
2
1
0
2
0
2
0
0
1
0
1
0
0
0
2
1
0
2
0
0
3
0
1
0
1
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
2
1
0
0
0
0
1
0
0
0
1
0
1
0
2
2
0
0
1
4
2
0
1
2
0
1
0
2
0
1
0
0
0
0
0
0
1
1
2
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
1
3
0
1
0
2
0
2
0
2
0
0
0
1
0
0
0
2
1
2
2
0
0
1
0
0
1
0
3
0
0
0
0
1
0
2
2
0
0
0
0
0
1
0
0
1
0
0
1
1
1
0
1
2
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
3
0
0
2
0
0
0
2
0
1
1
2
2
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
1
0
0
2
1
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
2
2
0
0
0
0
5
0
0
1
0
1
0
2
0
0
0
0
1
0
0
0
1
2
1
0
0
0
0
1
0
0
0
0
0
0
1
1
1
2
0
4
1
0
0
0
0
2
2
0
1
0
0
0
1
1
0
5
0
0
1
0
2
0
0
0
2
0
1
0
1
2
0
1
1
0
0
0
0
0
2
0
0
1
0
2
0
0
2
0
1
2
0
0
1
0
0
2
1
0
0
0
0
2
2
0
0
2
0
0
2
0
0
2
3
0
0
2
0
2
1
0
1
2
0
0
0
7
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
1
0
2
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
1
0
0
1
0
0
2
1
1
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
1
1
1
0
0
1
0
1
0
0
2
0
3
1
0
0
1
0
2
0
2
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
2
0
0
0
2
1
2
0
0
0
2
0
5
2
0
2
1
1
1
0
2
0
0
2
0
0
0
0
1
0
0
0
2
0
1
0
1
1
0
0
2
0
2
0
0
0
0
0
1
1
1
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
2
0
0
0
2
0
0
2
1
2
0
0
0
0
0
2
2
0
0
0
1
2
2
2
0
2
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
3
0
0
2
2
0
1
1
0
0
0
0
2
2
0
1
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
1
2
0
0
2
1
1
2
1
0
0
0
0
0
0
0
0
0
0
2
0
3
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
1
0
2
0
0
1
0
0
1
1
1
2
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
1
2
1
1
0
0
0
0
0
0
2
0
1
0
1
1
2
1
0
1
0
1
2
0
1
2
0
2
1
0
0
0
2
0
0
1
2
0
0
1
2
2
0
2
0
0
3
0
0
1
0
0
0
0
0
0
1
1
0
3
1
0
0
0
0
0
1
3
0
2
0
0
2
0
2
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
2
1
2
0
1
0
0
0
2
0
0
0
0
1
0
2
0
0
1
0
0
0
0
2
3
0
0
2
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
3
1
0
0
0
0
0
2
0
0
0
0
2
1
1
0
1
0
0
3
1
0
0
8
0
1
0
0
2
0
1
1
0
1
0
0
0
0
2
0
2
2
0
1
0
1
1
2
2
0
0
3
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
1
0
0
2
2
0
0
2
2
0
2
1
1
0
0
0
0
2
0
0
0
2
0
2
0
0
1
1
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
1
2
0
0
0
0
1
0
0
0
1
2
2
1
0
0
2
2
1
0
0
0
0
0
1
0
0
0
0
4
0
2
2
0
0
0
1
2
0
0
0
0
1
1
0
1
0
1
0
0
0
1
1
0
0
2
0
0
0
2
0
0
1
2
1
3
0
1
0
0
0
1
0
1
3
2
2
0
1
0
2
4
0
1
0
0
1
3
0
2
1
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
1
1
3
0
0
0
2
0
1
0
0
0
0
0
0
2
1
2
1
0
0
0
0
0
1
1
1
0
0
0
1
1
0
0
3
0
2
0
0
2
1
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
2
1
1
1
1
1
0
0
1
1
0
1
3
2
2
0
0
1
0
0
0
1
2
1
1
0
0
2
0
2
1
0
0
2
2
0
0
0
0
0
2
0
0
0
4
1
0
0
0
0
0
0
2
0
1
0
1
3
0
1
0
0
1
1
0
1
0
2
0
2
0
2
0
0
1
2
0
0
0
0
2
1
0
0
0
0
1
0
0
0
1
2
0
1
2
0
0
1
2
2
0
0
0
3
7
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
4
0
0
0
0
0
0
1
0
2
1
0
0
2
0
0
2
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
2
3
2
2
0
2
0
0
0
0
1
0
3
0
0
0
3
1
0
0
2
2
0
2
1
2
2
0
1
0
2
2
0
1
0
0
2
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
1
2
1
0
0
0
0
1
2
0
3
1
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
1
0
1
0
0
1
0
0
0
2
0
0
2
0
0
2
0
0
0
1
0
0
0
1
1
8
0
2
0
0
3
1
1
0
1
2
0
2
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
2
1
0
0
0
1
2
0
2
2
2
0
0
0
0
2
0
0
1
0
0
0
4
1
0
0
2
1
1
0
0
0
0
0
0
0
0
2
0
0
2
1
2
0
0
0
1
2
0
0
0
1
0
1
0
0
1
1
2
1
0
0
2
0
0
1
0
0
0
0
1
0
2
0
1
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
2
0
1
0
2
1
0
2
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
2
1
0
0
2
0
0
1
0
1
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
1
2
0
0
2
1
2
0
0
0
1
0
2
0
0
0
0
1
1
0
0
0
1
2
2
0
0
0
2
2
0
0
1
1
0
2
0
1
2
0
0
0
1
0
0
0
0
0
0
1
0
0
3
0
0
1
2
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
2
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
5
0
1
0
3
2
2
0
2
1
4
0
0
2
0
0
0
0
2
0
0
1
0
1
3
0
1
1
0
0
0
2
0
0
0
0
0
0
2
0
1
0
1
1
1
0
0
1
0
0
0
2
0
2
2
1
1
0
2
1
1
0
0
0
0
1
0
0
0
0
2
0
1
0
2
0
2
1
0
2
2
0
0
2
2
1
0
2
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
2
0
0
2
0
2
2
0
0
1
1
1
1
2
0
0
1
0
0
2
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
2
0
0
2
0
0
0
1
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
2
3
6
0
0
1
0
0
0
1
1
0
1
0
1
1
0
0
2
1
0
2
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
5
0
1
0
0
3
1
0
1
1
3
2
0
0
2
0
0
2
3
0
1
1
0
0
0
0
0
0
0
2
0
0
3
1
0
0
0
1
1
2
2
2
0
1
2
0
1
0
1
0
0
0
0
0
0
1
0
2
4
1
0
1
1
0
0
0
1
0
0
0
6
0
2
0
0
0
0
3
0
0
0
4
1
0
0
0
2
2
3
0
0
0
1
0
0
2
2
2
0
0
1
2
0
2
0
0
0
0
3
0
0
2
0
2
0
0
0
1
1
2
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
2
0
2
1
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
3
0
0
0
2
0
3
1
0
2
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
2
0
0
0
1
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
2
0
1
0
0
0
0
1
1
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
2
0
0
0
2
0
0
0
0
2
0
0
2
0
2
2
0
1
1
0
0
2
2
0
2
0
1
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
2
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
4
0
0
1
1
2
0
0
1
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
1
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
2
1
0
0
0
2
0
2
0
1
0
0
0
1
0
1
0
0
0
1
1
2
1
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
2
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
3
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
1
0
1
1
0
0
0
0
3
1
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
2
2
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
2
3
2
0
0
0
0
0
1
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
1
1
0
2
0
0
1
0
3
0
0
0
0
0
2
0
0
0
0
1
1
2
1
0
0
2
1
0
0
0
1
2
0
2
1
0
1
0
0
0
0
1
0
1
1
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
2
0
2
0
2
0
2
1
0
1
0
0
2
1
0
2
2
0
0
2
2
2
1
2
1
3
1
0
2
2
0
1
0
0
0
1
2
2
2
0
0
0
1
0
1
0
0
0
1
2
0
0
0
1
0
0
3
0
0
2
0
0
0
0
2
2
0
0
0
1
1
1
2
2
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
2
2
0
1
1
0
0
0
0
2
1
1
0
0
0
1
0
0
0
0
0
0
0
2
1
0
2
2
1
2
0
0
0
0
0
0
0
0
2
1
2
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
2
4
1
2
4
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
2
1
0
0
2
0
1
2
2
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
2
0
3
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
2
0
2
0
0
1
0
0
0
0
3
0
2
1
1
0
0
2
0
1
0
0
1
0
0
1
2
2
0
0
0
1
1
2
2
1
0
0
0
0
2
0
0
0
0
0
2
0
1
1
0
0
1
0
0
0
0
2
0
0
0
2
0
1
2
0
0
0
0
1
1
0
1
0
2
0
1
1
1
1
1
0
1
1
0
0
2
5
0
1
0
0
0
2
2
0
0
0
0
0
0
1
1
0
0
2
2
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
1
2
1
1
0
0
2
0
1
1
1
0
2
0
1
1
0
1
0
0
1
2
2
1
0
1
0
1
2
0
0
1
0
2
2
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
4
2
0
2
1
1
1
0
0
1
0
0
2
0
0
1
3
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
1
11
0
2
0
1
0
1
3
2
0
0
0
3
0
2
1
0
2
0
2
0
1
1
0
0
0
2
0
0
0
0
0
3
2
0
1
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
2
1
1
0
3
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
2
1
0
2
0
1
0
2
2
0
0
0
1
1
3
2
0
1
2
0
0
0
2
0
1
0
2
1
0
0
0
1
0
0
2
0
0
0
2
0
1
1
0
0
1
2
0
0
0
0
0
0
0
1
0
1
2
0
0
0
1
2
2
0
0
1
0
0
2
0
0
2
0
0
4
0
0
0
1
0
0
0
2
3
1
1
0
1
2
1
0
0
0
0
1
1
2
1
0
1
1
0
2
1
2
0
0
0
0
2
0
0
2
0
1
1
2
2
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
1
0
0
0
1
0
1
0
0
1
0
0
2
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
1
2
0
0
0
0
0
2
2
1
0
0
1
0
0
0
0
0
0
1
1
2
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
2
4
1
2
2
0
0
0
0
0
0
0
0
0
0
0
2
1
2
2
2
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
2
0
3
0
1
0
0
2
0
0
0
1
2
1
0
0
0
0
1
1
0
0
0
0
0
0
2
2
1
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
2
2
1
0
0
2
0
0
0
2
2
0
0
1
0
1
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
1
0
2
2
0
0
0
1
1
0
0
0
0
0
0
0
1
2
2
2
0
0
1
0
2
3
2
0
0
2
0
2
0
2
0
1
0
0
0
1
3
0
0
0
0
0
2
0
2
0
1
0
3
0
0
0
0
2
0
1
0
2
3
0
1
0
0
1
3
1
1
0
0
1
1
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
1
3
0
0
0
1
0
3
0
1
0
0
0
3
0
1
0
1
0
0
0
1
0
0
1
0
0
3
0
0
0
0
0
0
3
2
3
0
1
1
3
1
0
2
0
2
2
0
0
2
1
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
1
1
0
0
0
2
0
0
2
0
2
2
0
0
2
0
2
2
2
0
1
1
0
0
0
2
0
1
0
0
0
1
0
0
1
0
0
0
4
0
1
1
0
0
2
0
2
1
0
0
3
0
0
1
0
0
2
1
0
11
2
0
0
0
0
0
2
1
0
0
1
0
1
0
0
0
2
2
0
0
0
0
0
2
0
2
3
0
2
0
0
0
3
2
2
0
2
0
1
0
0
1
1
2
3
1
1
1
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
2
1
0
1
1
1
2
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
1
1
1
0
0
0
0
0
1
0
0
0
2
0
1
4
1
0
0
0
1
0
0
0
0
1
0
0
0
2
1
0
0
1
2
0
0
1
0
0
0
0
0
3
0
2
0
0
0
1
3
0
0
0
2
0
1
0
0
0
3
0
0
1
0
1
0
3
0
1
0
2
0
2
2
0
3
1
1
0
1
0
0
2
0
0
0
0
0
2
0
1
0
1
0
0
0
0
2
1
2
1
2
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
2
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
2
0
2
0
0
2
1
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
2
0
3
0
0
2
0
2
4
0
0
0
0
1
0
2
1
0
1
2
0
2
0
1
0
1
0
0
2
1
0
0
1
2
1
1
0
2
1
2
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
1
0
1
0
0
0
0
1
0
0
4
3
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
1
0
1
0
2
1
0
0
0
0
0
2
2
1
0
1
1
0
0
2
0
2
0
0
2
0
0
0
0
2
0
1
0
2
0
2
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
2
2
0
1
1
0
0
0
0
2
0
0
0
1
0
0
2
2
0
3
0
0
0
0
0
0
0
1
0
2
0
2
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
2
1
0
2
0
0
2
0
0
0
2
0
1
0
0
0
0
1
2
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
2
1
0
0
2
2
0
0
0
0
0
0
1
0
0
0
2
0
0
2
1
0
0
0
1
0
1
2
0
0
0
1
0
2
0
2
1
0
0
1
0
0
0
0
1
5
2
1
0
0
1
0
2
0
0
1
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
1
0
2
0
0
1
0
0
0
2
0
0
1
1
2
1
0
2
2
0
0
0
2
0
2
1
0
2
0
0
3
1
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
1
1
2
0
0
0
0
2
1
1
0
0
1
0
0
10
1
0
2
0
0
0
0
0
1
0
2
0
2
0
0
2
0
0
0
1
1
0
0
0
1
0
0
0
2
1
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
2
2
1
3
0
0
1
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
2
1
0
0
0
1
0
0
0
1
0
0
0
1
0
2
0
0
0
2
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
3
0
2
0
0
0
0
0
0
0
4
0
2
1
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
1
2
2
1
0
2
2
1
0
1
0
0
2
2
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
1
1
0
2
0
0
0
0
1
0
0
0
0
1
1
0
2
2
1
1
3
1
0
0
1
1
0
2
0
0
0
0
1
0
1
1
0
2
0
0
2
1
1
1
0
0
0
2
0
1
0
0
0
2
1
1
1
2
0
0
0
0
2
0
2
0
2
3
0
0
3
0
1
0
0
2
1
0
0
2
1
0
0
3
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
1
2
1
0
2
0
0
2
1
0
0
1
0
0
0
0
1
2
1
2
0
1
0
0
0
1
2
0
0
0
1
2
0
0
0
0
1
1
2
0
0
1
0
1
0
1
0
2
0
0
1
0
1
0
0
0
0
0
0
1
2
0
1
2
2
1
2
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
2
2
0
1
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
2
0
1
3
0
0
1
0
2
0
1
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
1
0
0
0
1
0
0
1
0
0
1
2
1
1
2
0
0
0
0
2
1
0
0
0
0
0
2
2
0
0
1
0
0
1
2
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
1
0
2
3
0
0
0
1
0
0
3
0
0
2
1
2
0
2
0
0
0
1
0
2
1
2
0
0
1
1
1
0
2
0
0
1
2
0
1
1
0
0
2
1
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
1
1
0
0
0
2
0
1
1
2
0
0
0
0
2
2
0
1
1
0
0
0
0
0
1
0
0
1
2
0
0
0
2
0
0
1
0
2
0
0
2
0
2
0
1
2
0
0
1
0
0
0
2
3
2
1
2
0
0
1
0
0
0
0
0
0
0
1
0
1
0
2
2
2
0
0
0
0
2
0
0
0
0
0
0
1
1
2
3
0
1
0
0
5
0
0
0
0
0
0
2
0
1
2
1
0
0
0
2
0
0
1
2
2
0
1
0
1
0
0
0
0
1
1
0
2
1
0
0
1
1
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
1
4
2
0
0
0
0
2
0
0
0
2
0
0
3
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
3
0
1
1
0
2
0
0
1
1
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
2
1
0
2
2
0
0
2
0
2
0
0
0
0
0
0
0
2
0
3
1
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
1
1
0
3
0
0
0
1
0
2
0
0
1
1
0
0
0
1
2
1
3
2
0
0
0
0
0
1
1
1
2
0
1
1
0
1
0
1
0
0
2
0
2
1
0
1
5
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
2
1
0
0
1
1
1
0
0
0
0
0
1
3
1
2
2
0
0
0
1
2
1
1
0
0
0
1
0
0
0
0
4
0
3
0
0
2
1
0
0
0
1
2
0
0
0
2
0
0
0
0
1
1
1
1
0
1
1
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
1
1
0
0
1
2
1
0
1
0
2
0
1
0
1
0
0
1
1
1
2
1
0
0
0
0
1
2
0
0
0
0
0
0
2
3
0
1
2
2
1
3
0
0
1
0
0
0
2
1
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
1
0
0
4
2
1
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
1
0
1
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
9
0
1
0
0
0
2
2
0
0
0
0
0
1
2
0
0
0
0
0
1
0
1
0
0
2
1
0
0
1
2
0
0
0
0
0
1
0
0
2
1
0
0
1
2
0
0
0
2
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
2
2
0
2
0
1
2
0
2
0
0
2
1
0
0
2
0
3
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
2
2
0
2
0
0
0
3
2
1
0
1
2
0
0
2
0
1
2
1
1
0
1
1
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
3
1
0
0
2
2
6
1
0
0
2
1
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
1
2
0
0
0
2
0
0
0
1
0
2
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
3
2
0
0
0
1
0
3
0
0
1
0
2
3
1
1
2
0
2
0
0
0
1
1
1
1
0
0
2
0
2
0
1
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
1
0
1
0
0
0
0
3
0
0
0
0
0
2
0
0
1
1
2
0
0
0
2
2
0
1
0
0
1
0
1
0
0
0
2
3
0
0
0
2
0
0
0
1
0
0
1
0
0
0
2
1
0
0
2
1
3
1
0
0
0
0
1
0
1
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
2
0
0
0
0
1
0
0
3
0
2
0
0
0
0
2
0
0
2
0
2
2
0
0
2
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
3
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
1
0
2
2
1
0
2
0
1
1
0
0
0
0
0
2
0
0
0
0
5
0
0
0
1
2
0
2
2
0
1
1
0
1
0
1
2
0
0
2
0
0
0
0
1
0
0
1
0
0
0
1
2
0
0
0
2
0
1
0
1
0
0
1
0
0
0
1
1
1
0
1
3
1
1
0
2
0
0
0
0
2
0
0
0
0
7
0
0
0
1
3
1
0
0
1
0
4
0
0
1
1
1
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
1
0
1
1
1
2
0
0
0
1
0
0
2
0
0
0
1
0
0
1
0
1
0
0
2
2
0
3
1
0
0
9
0
0
3
2
0
0
0
0
2
3
0
0
0
0
0
0
3
2
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
2
1
1
8
0
2
2
0
0
0
2
0
0
1
1
1
0
1
0
0
2
0
0
0
0
3
1
0
0
1
0
0
1
0
0
0
2
0
2
1
0
0
6
0
0
0
2
0
2
1
0
0
0
0
1
0
2
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
2
0
1
1
1
2
2
0
0
2
0
0
0
1
0
0
1
0
0
1
0
0
0
1
2
2
1
0
0
1
2
2
0
2
0
0
0
2
0
0
0
1
0
0
1
0
3
2
0
0
0
1
0
2
1
0
0
1
2
0
2
2
2
0
0
0
1
0
2
2
0
0
2
3
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
2
2
2
0
0
0
0
0
1
1
0
2
0
0
0
2
0
1
1
1
0
0
2
2
0
0
0
0
0
2
1
1
0
2
0
0
0
0
0
1
0
0
0
1
0
4
0
0
1
0
0
0
0
0
1
2
0
0
2
1
0
1
0
0
2
0
0
0
0
0
0
0
1
2
0
0
2
0
1
2
2
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
1
0
2
1
0
0
0
2
0
0
0
1
1
0
0
1
1
0
0
0
1
0
1
0
1
1
0
2
0
0
0
0
1
0
2
2
0
0
0
0
0
0
2
0
1
1
1
0
1
0
2
2
2
1
0
0
2
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
3
2
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
1
0
3
1
2
0
0
0
1
0
0
0
0
2
0
0
2
0
0
1
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
2
2
2
0
1
0
0
0
1
0
0
1
0
2
1
1
2
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
2
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
1
0
0
0
1
0
1
0
0
0
1
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
2
1
1
0
0
0
2
1
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
2
0
0
0
0
1
2
1
0
0
3
2
0
1
0
0
0
0
0
0
0
2
2
0
1
1
0
0
2
0
0
0
0
0
0
2
0
0
3
0
1
0
1
0
0
1
3
2
0
0
1
0
0
0
0
3
0
2
0
1
0
0
2
0
0
0
2
0
0
0
3
2
0
0
1
0
0
0
2
2
0
0
4
0
0
2
0
1
1
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
2
0
1
2
0
0
0
1
0
0
0
0
1
2
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
1
0
2
0
2
0
0
2
0
2
1
2
1
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
2
1
0
0
1
2
0
0
2
0
1
2
1
1
0
0
0
1
2
0
0
0
0
0
1
0
1
0
1
0
2
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
1
1
0
0
2
2
1
0
0
0
0
0
0
0
3
0
0
0
2
1
2
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
2
0
0
2
2
1
0
1
1
2
1
0
0
0
0
0
2
2
0
1
0
1
2
1
2
0
0
0
0
1
0
2
2
0
0
2
0
0
2
0
0
1
1
0
1
0
1
3
1
0
0
0
0
1
1
2
1
0
0
0
2
0
3
0
0
0
2
0
5
0
0
1
0
2
1
1
0
0
4
1
1
1
0
3
0
2
2
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
1
0
1
1
0
0
0
1
0
2
2
0
0
0
1
0
0
2
0
0
0
0
2
0
0
2
2
1
0
2
0
0
1
0
1
0
3
0
0
2
0
1
0
0
0
0
1
0
0
1
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
5
0
0
0
1
0
0
1
0
1
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
2
0
0
0
1
0
1
1
2
2
6
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
1
0
2
0
2
0
1
2
0
0
1
0
2
2
0
1
0
2
0
0
1
1
0
2
0
0
0
1
1
2
1
0
2
1
0
0
2
1
0
0
0
2
2
0
1
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
2
1
0
0
0
0
2
4
2
0
1
1
1
1
2
0
1
3
0
1
1
2
1
0
0
0
2
0
0
0
0
2
0
0
0
1
0
2
0
0
0
2
0
0
0
2
2
0
2
0
0
0
1
0
1
0
0
0
0
3
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
2
0
1
0
2
1
0
0
2
0
0
0
0
2
0
0
1
0
2
2
0
1
0
0
1
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
1
0
1
2
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
2
2
1
0
1
2
0
1
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
1
1
2
0
0
4
0
1
1
1
1
0
1
2
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
2
3
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
1
2
0
0
0
0
0
2
1
0
1
0
4
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
2
0
2
0
0
2
0
7
0
5
2
0
0
0
0
2
1
3
0
3
1
0
0
0
2
0
2
1
1
1
0
1
0
0
3
0
3
0
0
0
0
0
2
2
0
0
0
0
0
0
1
2
2
0
0
2
0
0
0
0
0
0
0
1
1
1
0
0
1
0
1
2
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
1
0
1
1
0
0
0
2
1
0
0
0
1
0
0
0
2
1
0
1
0
2
0
0
0
1
2
3
0
1
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
2
0
0
0
2
0
0
0
1
1
2
0
0
0
0
0
0
1
0
2
0
1
0
1
0
1
2
2
0
2
0
0
0
1
0
3
5
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
2
2
0
2
1
1
2
0
0
0
2
2
0
2
1
1
1
0
3
2
2
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
1
2
0
0
0
0
0
1
0
0
2
0
1
2
1
0
0
2
0
0
2
1
0
3
0
2
0
1
0
0
0
0
0
1
2
1
0
0
2
3
0
0
1
2
0
0
7
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
2
1
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
1
0
0
0
3
2
2
4
2
1
0
0
1
0
0
0
1
2
1
0
0
1
0
2
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
1
2
0
0
2
2
0
0
0
0
0
1
2
0
0
2
0
0
3
0
2
2
1
0
2
2
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
2
0
0
0
0
1
1
0
0
1
2
0
0
0
0
0
1
0
1
0
0
3
0
1
0
0
1
1
2
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
1
1
2
1
0
0
0
2
0
1
1
0
0
0
0
2
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
1
0
0
1
3
2
0
0
2
0
0
1
0
0
0
0
0
2
2
2
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
2
2
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
8
0
0
0
0
2
2
0
2
0
0
0
0
2
2
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
2
2
0
2
0
0
0
2
0
2
0
0
0
1
3
0
0
0
1
0
0
0
0
1
2
0
0
1
3
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
1
1
0
1
0
1
0
0
0
0
0
2
0
2
2
0
0
2
1
0
0
0
0
0
1
0
0
0
2
0
2
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
2
1
0
0
3
0
2
0
0
0
2
0
0
0
1
0
0
0
2
1
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
1
2
1
1
0
0
0
0
2
1
0
0
1
0
0
0
0
2
0
1
0
0
0
0
1
1
0
1
0
2
0
0
0
0
0
0
2
2
1
2
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
1
0
2
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
1
0
1
1
1
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
4
0
2
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
2
1
0
1
0
0
0
0
2
0
0
0
4
0
1
0
0
1
4
1
0
0
0
0
0
0
0
0
2
0
5
0
0
2
1
0
0
1
0
2
0
0
2
0
0
0
1
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
2
0
0
1
0
0
2
1
1
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
2
0
1
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
2
0
0
2
0
0
0
0
1
1
2
0
0
0
0
0
2
0
2
5
0
0
0
0
0
1
0
1
2
0
0
2
0
2
1
2
0
3
1
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
2
0
1
0
2
0
1
0
0
0
0
0
1
0
0
2
0
0
2
2
1
0
2
0
0
0
0
2
2
0
0
1
0
1
0
0
1
0
2
0
0
1
1
0
0
2
0
2
0
1
0
0
0
3
0
1
0
0
1
0
2
2
3
2
0
0
2
2
0
0
0
0
1
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
2
0
0
0
0
0
2
0
0
2
0
0
0
1
0
2
0
0
1
0
0
0
0
2
1
0
2
0
0
0
0
0
0
2
0
0
1
2
0
2
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
1
0
2
0
0
0
0
1
1
2
1
0
1
0
0
0
1
0
0
0
2
1
0
2
0
0
2
0
0
0
1
0
0
0
1
2
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
2
1
0
0
1
0
1
0
1
2
2
1
0
0
1
0
0
2
0
0
0
0
1
2
0
0
0
2
0
1
1
0
2
0
0
0
0
0
0
0
1
1
2
2
0
0
0
2
0
1
0
0
0
1
0
0
0
1
0
0
2
0
0
0
1
0
0
2
0
1
0
0
0
2
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
1
1
2
0
0
1
0
0
0
1
0
1
0
0
0
0
2
0
1
0
0
1
0
2
2
0
0
2
0
0
1
1
0
0
0
0
0
1
1
0
0
2
1
2
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
1
1
1
0
0
0
2
0
0
2
0
0
0
0
2
1
0
0
2
0
0
1
1
0
0
1
0
0
2
0
0
1
0
2
0
0
8
0
0
0
0
1
0
2
2
0
1
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
1
1
2
2
1
2
1
0
0
0
0
0
0
0
1
1
0
0
2
2
0
1
1
0
0
1
0
2
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
1
0
1
0
0
1
0
0
1
2
1
0
0
0
1
1
0
0
0
0
1
1
3
0
2
0
0
0
0
1
0
0
2
0
0
0
2
0
2
0
2
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
1
4
1
0
0
0
1
0
0
2
1
0
0
2
1
1
2
0
1
1
0
2
1
0
0
2
0
2
0
0
0
2
0
0
0
1
0
0
0
1
1
1
0
2
0
2
8
0
0
2
2
0
2
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
2
0
0
3
0
0
2
0
0
0
0
0
0
2
2
0
0
1
3
0
1
0
2
0
0
0
2
0
2
0
1
0
1
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
1
0
0
2
1
0
0
0
0
0
0
2
0
1
1
0
1
0
0
0
0
0
2
0
0
2
0
0
2
0
2
2
1
2
0
1
2
0
0
0
0
0
0
1
1
0
0
3
0
0
1
0
2
0
1
0
0
1
1
0
0
2
1
0
0
1
0
1
0
0
1
0
0
1
2
0
1
1
0
1
0
0
0
0
1
1
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
1
2
0
0
0
0
0
1
0
3
0
0
0
1
0
0
0
0
0
1
0
0
1
2
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
2
0
1
1
0
0
0
0
2
0
4
0
0
0
1
0
0
2
3
2
2
0
0
0
0
3
1
0
1
0
0
0
1
0
2
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
1
0
0
2
1
0
0
0
1
0
0
2
1
0
1
1
2
1
0
1
1
0
0
1
0
0
0
0
0
2
0
0
1
2
0
0
1
0
0
1
0
0
1
2
0
1
0
3
0
2
0
1
2
0
1
0
2
0
0
1
0
0
1
2
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
2
0
0
2
0
1
0
0
0
0
0
1
0
0
7
0
0
0
1
0
1
2
0
1
1
0
2
0
2
0
2
1
0
2
0
0
0
0
2
0
0
2
0
1
0
1
1
2
3
1
0
1
1
2
0
1
2
0
2
0
0
0
2
0
0
1
0
0
0
0
3
1
2
2
0
1
1
0
0
0
0
0
2
2
2
0
1
1
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
3
2
1
1
0
2
2
0
0
0
0
2
0
2
0
2
1
0
2
0
2
0
0
2
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
2
2
1
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
1
2
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
2
2
0
2
0
0
0
0
3
0
0
0
0
0
2
1
0
0
0
0
2
0
1
2
0
0
1
1
0
0
2
0
2
0
1
0
0
0
2
1
0
0
2
0
2
0
0
0
0
0
0
0
3
1
0
0
1
1
1
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
3
0
0
1
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
3
0
0
0
1
2
0
0
1
2
0
2
0
0
0
0
1
2
1
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
5
0
1
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
1
0
1
1
1
0
2
1
0
0
0
1
0
0
0
2
1
1
2
0
1
0
2
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
2
3
2
1
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
1
1
0
0
0
2
0
0
2
1
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
2
2
0
0
0
0
1
0
0
0
2
2
0
0
1
2
2
0
2
0
0
2
0
0
2
0
0
0
0
1
0
1
1
0
1
1
2
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
1
0
1
0
0
0
2
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
1
0
0
0
2
1
2
0
0
2
0
0
0
0
0
0
1
1
0
1
1
0
2
0
1
0
0
0
2
2
0
0
1
0
0
0
0
2
0
0
2
1
0
0
1
0
2
0
0
0
2
2
0
2
2
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
2
2
0
2
0
0
0
0
3
3
1
1
3
0
2
2
0
0
2
0
0
1
0
0
0
0
2
1
0
2
0
2
3
0
0
2
1
1
0
2
0
1
0
1
1
1
0
0
2
1
0
0
0
0
2
2
2
2
0
1
0
2
0
3
2
0
0
1
0
2
0
0
1
2
0
0
1
0
0
0
0
0
2
0
0
0
2
1
2
0
0
0
0
2
1
0
1
2
2
1
0
0
0
3
0
0
1
2
0
2
1
1
0
2
0
0
2
1
1
0
0
0
0
0
0
2
1
1
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
1
1
0
0
2
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
1
0
2
0
2
2
1
2
0
1
2
1
0
0
1
0
1
0
1
0
0
1
0
0
2
1
0
0
2
0
1
1
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
1
1
0
0
0
2
0
2
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
2
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
2
0
2
1
2
0
0
0
2
3
0
0
0
0
1
0
0
1
2
0
1
2
0
0
0
0
1
0
0
2
1
0
3
1
0
0
1
0
2
0
1
0
0
1
0
0
0
0
0
2
0
2
0
2
0
2
0
0
0
1
0
0
2
0
0
2
0
0
2
2
1
0
0
0
1
0
0
0
1
1
1
0
2
0
2
2
0
0
0
2
0
0
0
0
1
0
0
2
2
0
0
0
1
2
0
0
0
0
0
2
1
2
2
1
0
0
1
2
0
1
3
1
1
0
1
0
0
0
0
2
0
2
2
1
2
2
0
0
0
1
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
2
0
2
0
0
1
1
1
0
0
0
2
0
0
0
1
1
0
0
1
0
1
3
1
0
0
0
1
2
0
0
1
3
0
0
0
1
1
0
0
0
0
2
1
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
1
2
0
1
0
0
0
0
2
0
0
0
1
1
0
2
0
0
1
0
0
2
0
1
0
0
2
0
0
2
0
0
0
0
0
1
0
1
0
2
0
0
0
0
2
0
0
1
0
0
0
1
2
0
1
2
1
2
0
0
1
0
2
0
0
0
0
1
0
0
0
2
0
4
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
1
2
0
1
0
0
1
0
0
2
0
2
0
1
0
0
0
0
2
0
1
2
1
0
0
0
1
0
2
1
1
2
0
0
0
1
1
0
0
1
0
0
0
0
2
2
3
1
0
2
0
1
2
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
4
0
2
0
1
0
2
0
0
0
0
0
0
0
2
2
1
0
0
1
0
0
0
0
1
2
0
0
2
1
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
1
0
1
0
4
2
2
2
0
0
0
0
0
1
2
1
1
0
0
2
3
0
0
0
0
0
0
0
2
0
2
0
0
0
1
2
0
0
0
2
2
1
0
0
0
2
2
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
2
1
1
0
0
1
0
3
0
2
0
0
0
2
2
0
1
0
1
0
0
0
0
2
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
2
2
1
0
2
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
1
1
0
0
4
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
1
0
0
1
1
0
2
0
2
0
0
0
2
0
2
0
2
0
0
0
1
2
0
2
0
1
2
1
0
0
0
0
2
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
1
3
0
1
0
1
0
0
0
1
0
0
6
2
0
0
1
0
0
0
0
1
0
2
1
0
2
1
1
0
2
0
0
0
2
0
1
0
1
0
0
0
0
0
2
0
1
0
0
3
2
0
0
0
1
0
0
2
1
0
1
1
0
0
1
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
1
0
1
0
0
3
1
2
1
0
1
3
0
0
1
0
1
0
2
1
1
0
0
0
0
0
0
1
0
1
3
0
2
0
0
0
3
0
0
1
3
2
0
0
0
0
1
0
2
0
0
0
1
0
4
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
2
2
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
1
1
0
0
0
2
1
0
1
0
0
2
1
0
0
0
0
2
1
1
0
0
0
2
0
0
0
0
1
1
2
0
0
3
2
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
2
0
3
0
0
0
0
2
0
1
1
1
9
2
2
0
0
0
0
0
1
2
0
1
0
0
1
1
1
0
2
4
1
0
0
0
1
1
0
0
0
0
0
0
2
1
1
0
1
0
0
0
0
0
2
0
0
0
0
0
2
1
1
0
0
0
0
0
0
1
0
0
1
0
0
2
3
0
0
0
0
1
0
7
1
0
0
0
0
0
0
1
2
1
0
0
0
0
2
0
0
0
0
4
0
0
2
0
0
0
0
0
0
0
0
0
1
2
1
2
1
2
0
0
0
5
1
0
0
0
0
0
1
2
0
2
0
0
0
0
0
2
0
1
0
1
0
0
0
1
2
0
0
0
0
0
1
1
2
0
0
0
2
0
2
0
1
2
0
0
3
1
0
2
3
1
0
0
2
2
1
2
0
1
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
2
0
0
2
1
0
0
0
1
1
2
0
0
0
2
0
1
0
2
0
2
1
1
0
1
1
1
3
0
0
0
0
0
1
0
1
0
1
1
0
0
6
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
2
1
1
0
1
2
0
3
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
1
2
0
0
0
0
1
0
0
2
0
1
2
0
0
0
0
0
1
1
0
2
0
0
0
2
0
1
0
1
0
1
1
1
2
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
1
0
2
2
0
0
0
1
0
0
2
0
2
0
0
0
2
2
1
0
0
3
0
3
2
0
0
0
0
0
3
0
1
0
0
1
2
1
2
0
0
0
2
0
1
0
0
1
1
0
0
2
0
1
2
1
0
0
0
2
1
0
0
1
0
0
1
0
0
0
0
2
2
0
1
0
2
1
0
1
1
3
0
2
0
2
2
2
0
0
0
0
0
0
0
1
0
0
6
0
2
1
0
1
0
0
2
1
2
0
0
0
0
0
0
0
1
0
0
1
0
3
0
0
0
2
2
0
0
0
2
2
1
0
0
0
2
1
0
0
3
0
0
2
1
1
0
0
2
0
2
1
0
1
0
0
0
0
1
0
0
0
0
2
2
1
0
2
2
1
2
1
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
2
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
4
2
2
5
0
2
0
1
0
0
1
0
1
1
0
0
1
0
0
0
0
2
1
1
0
0
2
1
1
0
0
0
1
2
1
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
2
0
0
2
1
2
0
0
0
2
2
0
0
0
0
0
0
2
0
0
3
2
0
0
0
0
0
0
0
0
0
2
0
1
2
1
0
1
0
0
2
0
3
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
1
0
1
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
1
1
0
0
0
0
0
0
2
2
1
1
0
1
0
3
2
2
0
1
0
0
0
0
1
2
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
2
1
0
2
2
0
2
0
0
2
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
1
2
1
0
0
0
0
0
0
2
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
2
3
5
1
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
2
0
1
0
1
0
0
0
1
1
0
1
0
0
0
3
0
0
0
0
2
2
0
2
2
0
0
0
0
1
2
1
2
0
0
0
0
2
2
0
1
0
0
0
0
1
0
2
0
0
2
0
0
0
4
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
2
0
0
2
0
2
0
0
4
2
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
2
0
0
1
2
2
0
0
2
0
0
0
2
2
2
1
0
0
0
1
2
1
1
0
1
0
1
1
0
1
1
2
2
1
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
1
1
0
2
0
0
0
0
2
2
0
0
1
2
0
3
0
1
0
0
2
0
0
1
0
0
0
0
2
0
0
1
2
0
0
0
1
0
2
1
0
2
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
1
0
0
2
1
2
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
3
0
0
1
2
1
2
0
0
1
2
0
2
0
2
0
0
0
2
0
0
0
3
2
0
0
2
1
1
2
0
1
0
0
0
5
2
2
3
0
0
2
0
0
2
2
0
2
1
0
0
0
2
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
2
1
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
1
2
0
0
1
1
0
1
1
0
0
0
0
0
0
1
0
0
0
1
1
1
1
0
0
2
2
0
0
0
2
0
1
1
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
1
0
1
0
0
0
0
1
0
2
0
0
0
1
0
2
2
1
0
3
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
1
2
1
2
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
2
1
0
0
1
1
0
0
0
0
1
0
0
3
0
1
0
0
2
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
2
1
0
4
0
1
1
1
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
1
2
0
1
2
0
2
0
0
0
1
0
2
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
2
2
0
0
2
0
0
2
0
0
0
0
2
1
0
2
1
2
2
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
2
0
1
0
2
0
0
1
0
0
0
2
1
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
1
0
5
0
1
2
0
0
1
0
0
1
0
0
0
2
2
0
0
0
0
2
0
0
2
0
2
1
0
1
2
0
2
2
1
0
0
0
1
0
0
0
0
1
0
1
0
1
2
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
2
1
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
2
0
0
2
1
1
2
1
1
2
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
2
2
0
0
6
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
3
2
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
1
0
4
0
0
1
2
1
0
0
0
1
2
0
2
1
0
1
1
0
1
5
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
2
2
0
1
0
0
2
1
0
0
2
0
1
2
2
0
0
1
0
1
0
0
0
0
2
2
0
1
0
0
2
0
2
0
1
1
0
0
0
0
1
0
0
2
0
2
0
1
2
2
0
0
0
0
0
1
2
0
0
2
2
0
1
1
2
0
0
1
1
0
1
2
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
2
0
1
0
1
0
0
0
2
1
2
0
1
0
2
0
0
2
0
2
0
2
0
0
1
1
0
1
1
0
2
2
0
0
0
1
0
2
0
0
0
0
1
0
0
1
0
1
0
0
2
0
0
0
0
0
1
1
2
0
0
0
0
2
0
4
0
1
0
0
0
0
0
0
0
2
1
0
0
1
0
0
1
1
0
0
0
0
0
0
1
2
1
1
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
2
0
0
0
0
0
1
2
2
2
0
1
0
2
0
2
1
0
0
2
0
2
2
1
0
0
4
1
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
2
0
2
1
0
0
1
0
0
0
0
0
1
1
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
2
0
2
4
0
0
2
1
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
1
1
0
0
0
2
2
0
2
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
2
0
1
0
0
0
1
2
0
2
0
0
0
0
0
0
2
1
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
2
0
2
0
2
0
0
2
0
0
0
0
2
0
0
1
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
1
1
0
1
0
0
3
5
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
2
1
1
0
1
0
0
0
0
2
0
1
1
0
0
0
0
0
0
1
0
2
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
2
0
0
1
1
0
0
2
0
0
1
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
2
1
0
0
2
0
0
0
0
4
0
0
0
1
0
0
0
1
2
3
0
0
0
0
0
0
0
1
1
0
0
2
1
0
0
2
0
2
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
2
2
0
1
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
2
0
2
1
1
1
0
0
0
0
2
0
1
0
1
2
0
0
0
0
0
1
5
0
0
1
0
0
0
1
0
0
0
0
1
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
2
1
0
0
1
0
5
0
0
0
0
1
2
0
0
0
2
1
0
2
0
2
0
0
2
2
1
0
0
0
2
1
0
2
1
0
0
1
2
0
0
0
2
1
2
0
0
0
0
2
0
0
3
0
0
1
0
1
1
0
2
0
5
0
0
1
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
2
2
1
2
0
1
0
2
0
0
0
1
4
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
1
0
0
2
0
0
1
2
0
0
0
0
0
0
2
0
1
0
2
0
0
0
1
1
0
0
0
0
1
0
0
0
1
1
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
1
0
2
1
1
0
1
0
3
0
2
0
2
0
2
0
0
0
0
2
4
0
0
0
2
1
2
0
2
1
0
0
1
0
2
2
0
2
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
2
0
0
0
0
0
1
2
0
0
0
1
5
0
0
0
1
1
0
0
1
0
0
1
0
0
0
6
1
0
0
2
0
0
1
2
0
0
0
0
1
0
1
0
0
0
0
3
2
0
3
0
1
0
0
0
3
1
2
0
2
1
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
1
0
0
0
2
0
0
0
0
2
0
2
0
1
1
2
0
0
0
0
2
1
0
1
1
2
0
2
0
0
0
0
1
0
0
1
0
1
2
2
0
4
0
1
0
2
0
2
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
2
0
3
0
0
0
1
0
0
0
2
0
0
1
0
1
1
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
2
2
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
2
1
0
0
0
1
0
2
0
2
0
0
0
0
0
0
3
0
0
1
0
0
1
2
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
2
2
0
2
2
1
0
2
1
0
1
0
0
0
0
0
3
0
0
0
0
1
1
0
0
0
0
0
2
0
0
1
0
1
0
1
2
2
0
0
0
0
0
1
0
0
0
0
0
2
1
1
0
0
0
1
1
2
2
0
1
0
2
0
0
0
2
1
2
0
0
1
0
2
2
3
2
0
0
1
0
0
0
2
3
2
2
4
0
0
1
1
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
2
0
1
2
0
1
1
0
1
0
2
0
0
0
1
1
0
0
0
1
2
0
0
0
0
0
0
1
0
0
1
2
0
1
0
0
1
0
0
1
1
1
2
0
0
0
0
1
1
2
1
1
0
0
1
0
0
1
1
0
0
1
2
0
0
1
2
1
2
2
1
2
0
0
0
0
2
0
0
4
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
4
0
0
1
0
1
0
0
0
1
5
2
0
1
1
1
0
0
0
1
0
3
0
0
0
2
1
1
0
0
0
0
0
0
1
2
0
0
0
2
0
1
2
2
1
2
0
5
2
0
0
0
1
1
0
0
0
0
0
0
1
1
2
2
0
3
0
2
0
2
0
3
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
2
3
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
3
1
0
2
3
0
2
0
2
0
0
0
0
0
3
0
0
2
0
0
0
0
0
1
0
0
1
2
2
0
0
1
1
0
0
0
0
1
2
1
5
2
0
1
2
1
2
1
0
1
0
2
1
2
0
1
1
0
0
0
1
0
1
0
0
0
1
1
2
1
0
1
0
2
0
1
2
0
0
2
0
0
0
0
3
1
1
2
0
0
0
2
2
0
0
0
1
1
0
2
0
0
2
0
2
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
2
2
1
0
0
0
0
1
0
0
0
1
0
1
0
2
0
0
0
1
1
0
2
2
1
0
0
1
0
0
1
1
0
2
2
1
0
0
0
0
0
0
0
0
2
0
1
2
0
2
0
1
4
3
1
0
0
0
2
3
0
0
2
1
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
1
2
0
0
0
2
0
0
0
0
0
1
2
0
0
3
2
0
3
0
0
0
2
1
0
0
1
0
0
0
2
0
0
0
0
0
0
2
2
1
0
1
1
1
0
1
0
0
1
0
0
0
3
0
2
1
0
0
0
0
0
0
1
0
0
1
3
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
1
0
2
1
0
0
2
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
1
0
0
0
0
1
0
1
0
1
2
0
0
1
2
1
0
0
0
1
1
0
0
2
0
1
0
1
0
0
1
0
2
2
1
2
1
0
0
2
0
0
0
0
1
0
0
1
2
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
2
1
2
0
0
2
1
0
1
0
1
0
0
1
0
0
0
0
2
3
0
2
1
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
2
1
0
0
5
1
0
1
0
2
0
0
0
0
3
0
0
1
0
2
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
2
0
1
1
0
2
2
0
0
0
2
0
0
1
0
1
2
0
1
0
0
0
0
2
0
1
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
2
1
0
0
1
2
0
1
2
0
1
0
3
0
0
0
0
4
0
0
0
0
1
2
0
0
2
1
0
0
0
2
0
1
0
0
0
0
1
0
2
0
1
1
0
0
0
0
2
1
2
1
0
2
0
0
0
1
4
2
0
0
0
2
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
1
0
2
1
0
0
0
1
0
1
0
0
2
1
0
0
1
0
0
0
0
1
2
4
0
0
3
0
0
0
0
0
0
0
1
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
1
0
0
2
3
0
0
0
1
0
0
0
1
2
2
0
0
2
0
0
1
1
0
0
0
0
1
0
0
3
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
1
0
0
1
1
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
1
1
0
2
0
1
1
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
3
1
1
1
1
0
2
2
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
2
0
1
0
2
0
0
0
0
0
2
1
2
0
0
0
0
1
0
0
0
1
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
2
2
1
0
2
2
0
1
0
0
5
2
0
1
1
0
1
0
2
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
1
0
2
1
2
0
0
0
0
0
2
0
0
0
0
0
1
0
1
1
0
0
0
0
0
2
2
0
0
1
0
0
5
0
0
0
1
0
2
0
0
0
1
2
2
1
0
0
0
0
0
0
1
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
1
1
4
0
1
0
1
0
0
1
1
0
0
1
3
1
0
2
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
1
2
1
1
1
2
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
1
2
0
0
0
1
0
2
0
0
1
0
2
0
2
0
2
0
1
0
2
1
0
0
1
1
0
2
0
1
2
0
0
0
3
1
0
1
0
1
1
2
0
1
0
1
0
0
0
0
2
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
1
0
1
1
0
0
0
0
1
1
0
0
0
0
2
2
0
2
1
0
0
2
1
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
2
0
2
1
0
0
2
0
2
2
0
3
1
0
2
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
2
0
0
0
0
3
1
2
1
0
3
0
0
1
0
0
0
0
2
1
1
0
0
0
0
0
0
1
1
0
2
0
0
0
0
1
2
0
2
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
2
0
2
1
0
0
0
0
0
0
1
1
1
0
0
0
1
0
2
0
0
1
2
2
0
1
2
0
0
0
0
0
2
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
1
1
0
0
2
0
0
2
0
0
0
2
0
0
2
1
2
1
1
0
0
6
0
0
2
0
1
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
2
0
2
1
0
2
0
0
0
1
0
1
1
1
2
0
0
0
1
1
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
2
0
1
0
2
1
2
3
0
2
2
0
2
0
0
0
0
1
0
0
1
0
0
1
0
0
0
2
0
0
0
0
2
2
2
0
0
1
1
0
0
0
1
0
0
0
0
2
0
0
0
2
2
0
0
1
2
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
1
2
0
2
0
0
0
0
1
0
0
2
0
1
1
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
1
2
0
4
4
0
1
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
1
0
0
1
0
2
1
0
0
0
0
0
0
0
1
2
0
3
0
1
0
1
0
0
2
5
0
0
1
0
0
0
2
1
2
4
0
0
2
0
0
0
0
2
0
2
3
1
1
2
3
1
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
2
2
0
0
1
1
0
2
0
0
1
0
2
0
1
0
1
0
1
1
2
1
1
2
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
2
2
0
1
1
0
0
0
0
2
1
0
0
1
1
1
1
0
0
0
0
0
2
0
0
0
2
0
1
1
0
1
0
1
0
0
0
0
2
0
3
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
2
0
0
2
0
0
0
0
0
0
1
2
0
2
0
0
1
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
2
0
3
1
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
2
2
0
0
0
0
1
1
0
0
3
0
0
2
0
0
2
2
0
0
1
0
0
2
2
3
0
2
0
2
0
0
1
1
0
1
0
0
0
0
1
0
2
0
0
1
0
0
0
1
2
0
0
2
0
1
0
0
0
0
0
0
1
0
2
0
0
1
2
0
0
0
0
0
2
2
0
0
0
2
0
0
1
0
2
1
0
1
0
0
0
2
0
0
0
0
0
1
0
3
0
0
1
1
0
2
0
1
0
1
0
1
2
2
0
0
0
1
1
1
2
1
1
0
0
0
1
2
0
0
2
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
1
0
2
0
0
0
0
0
0
2
0
0
1
1
0
0
1
1
3
0
0
1
2
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
1
0
0
2
2
0
1
0
2
0
1
0
0
1
0
2
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
2
0
0
4
0
1
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
1
2
1
2
1
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
2
2
2
2
1
0
0
1
2
0
0
0
0
0
0
2
1
0
2
0
0
0
2
1
1
2
0
0
0
0
0
0
1
2
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
1
1
0
0
2
0
2
0
1
3
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
1
0
2
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
1
1
0
0
0
0
3
0
3
1
0
0
0
0
0
0
0
0
1
0
2
0
1
0
1
2
0
0
2
1
2
0
1
1
0
0
3
3
2
0
1
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
0
0
0
7
2
0
0
0
0
1
1
0
0
1
0
2
3
1
1
0
0
2
0
2
0
0
4
1
0
0
0
0
0
0
1
2
2
0
0
0
2
0
0
1
0
0
0
0
0
0
2
3
1
2
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
2
0
1
2
1
0
0
1
0
1
0
0
0
0
0
2
1
0
0
1
0
0
2
0
0
0
1
2
0
0
1
0
0
0
1
0
1
4
0
0
0
0
0
0
1
0
2
1
1
0
2
0
0
0
1
2
1
2
0
2
0
0
1
0
0
0
1
2
1
1
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
6
1
0
2
2
1
0
0
0
0
0
0
0
2
0
4
0
2
0
0
0
2
1
1
0
0
2
2
2
0
2
0
1
2
0
0
0
1
0
3
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
2
0
2
0
1
2
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
2
0
2
0
1
2
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
1
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
2
2
0
0
0
1
0
0
0
2
0
1
0
2
1
0
0
1
0
1
0
0
2
0
1
1
0
0
2
0
1
1
1
2
1
0
0
0
0
3
0
0
3
0
0
1
0
2
1
0
0
1
0
1
3
1
1
1
2
5
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
1
1
0
1
2
1
1
0
1
1
0
0
0
2
0
0
0
0
0
2
0
2
0
1
0
1
1
0
2
2
1
0
2
0
2
0
1
0
0
0
1
1
0
1
0
2
0
1
0
0
0
2
1
0
0
0
0
0
1
0
3
0
0
0
1
2
1
0
0
2
0
0
0
0
0
2
0
0
0
2
1
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
1
0
0
2
0
0
2
0
0
1
1
2
0
2
0
0
0
2
0
0
0
1
0
2
1
0
2
2
1
0
1
1
0
0
2
2
0
0
0
1
1
0
3
0
0
0
0
2
1
0
0
1
0
2
2
0
2
1
0
0
1
2
5
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
1
2
0
0
4
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
1
0
0
0
0
0
0
0
0
5
0
0
0
1
0
1
1
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
2
2
0
1
0
2
1
0
0
2
0
1
2
2
1
0
0
0
0
0
0
0
0
0
1
0
2
2
0
2
0
0
0
2
0
0
0
0
1
0
0
0
1
0
1
1
0
1
1
0
0
0
0
2
2
2
1
0
0
0
0
0
2
0
2
0
1
1
1
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
2
0
0
0
0
1
1
1
0
0
1
1
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
3
1
2
2
0
0
2
0
0
0
1
2
0
0
2
0
0
0
0
2
0
0
5
0
0
0
0
0
0
0
1
1
1
0
0
0
6
1
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
3
0
0
1
0
1
0
2
2
0
2
0
2
0
0
1
0
0
0
1
0
1
0
1
0
0
0
2
0
0
0
2
0
0
1
0
2
0
1
0
2
0
1
0
0
2
2
1
2
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
1
1
1
2
0
2
0
0
0
2
0
0
0
1
0
0
4
2
0
0
0
1
0
0
0
2
2
2
0
0
0
2
0
0
4
1
2
0
0
1
0
0
0
1
0
0
0
1
1
1
2
1
1
0
0
2
1
0
0
0
5
0
0
0
0
0
0
0
0
1
1
1
0
0
2
0
2
1
0
0
1
1
0
0
0
0
3
0
0
2
1
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
4
0
1
0
0
1
0
0
1
1
0
0
2
0
1
1
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
2
1
1
2
0
0
1
2
0
0
0
2
1
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
2
2
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
1
0
0
0
2
2
0
0
0
0
4
2
0
0
0
2
0
0
2
2
1
0
0
2
0
0
0
2
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
2
0
0
1
0
0
1
2
0
0
0
0
1
0
0
2
0
0
0
0
2
0
2
0
3
2
2
0
0
0
2
0
0
0
0
0
1
2
2
2
0
1
2
2
1
0
0
0
3
0
1
0
1
0
0
0
3
0
2
2
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
1
2
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
1
2
1
2
2
2
1
0
1
0
1
0
0
2
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
2
2
1
0
0
2
0
0
0
0
2
0
0
1
3
0
0
2
0
1
0
0
0
0
1
1
0
0
3
0
0
0
0
2
0
2
0
1
2
0
0
0
1
2
0
0
2
2
1
0
0
2
0
0
0
1
0
0
0
0
1
1
0
11
2
0
0
0
1
0
0
0
1
2
0
0
1
0
0
0
2
2
1
1
0
0
0
2
1
0
0
0
1
0
0
3
0
2
0
1
0
1
0
1
0
2
0
2
2
0
0
0
0
0
0
0
2
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
1
0
0
2
2
0
1
0
0
0
1
0
0
0
2
0
3
0
2
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
2
1
0
0
0
2
1
0
2
0
3
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
3
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
1
1
0
1
0
0
0
2
0
0
0
2
0
1
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
1
0
2
1
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
4
0
2
2
0
0
0
0
2
0
3
0
1
3
0
0
1
1
2
0
0
0
1
0
3
0
0
0
0
0
0
2
0
0
0
0
0
3
0
4
0
0
1
0
0
2
1
0
0
2
3
0
0
0
0
0
1
1
0
0
1
1
1
0
0
2
0
0
0
0
0
0
0
1
0
1
0
1
2
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
1
0
2
0
2
0
0
2
1
0
2
0
0
0
0
1
2
0
1
0
2
0
0
0
0
0
0
0
0
1
0
2
2
1
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
1
0
3
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
3
0
2
0
1
0
0
0
0
0
0
2
0
0
0
1
1
0
0
2
0
0
0
1
0
3
0
1
0
0
1
0
2
0
1
0
1
1
0
0
1
0
0
2
0
2
0
2
1
0
1
1
0
0
0
2
0
0
0
1
0
0
0
2
1
2
0
0
1
0
0
1
1
2
1
0
0
0
0
2
0
1
1
0
3
0
1
0
0
0
2
0
1
1
6
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
1
0
2
2
0
1
1
1
2
0
0
0
0
0
1
0
0
0
0
0
2
0
1
2
1
0
2
2
0
0
2
2
0
0
2
0
2
0
1
1
0
2
0
2
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
2
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
1
1
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
2
0
0
0
2
1
1
0
0
2
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
2
0
2
0
0
2
0
2
0
0
2
0
3
3
2
0
0
0
0
0
2
1
1
0
2
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
1
1
1
1
0
0
1
2
0
0
0
0
0
0
0
0
0
2
1
0
2
0
1
1
2
0
0
0
2
2
2
0
0
1
0
2
0
2
0
0
0
0
0
2
1
0
0
1
1
1
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
2
0
1
1
1
0
2
2
2
1
2
0
0
1
2
0
1
0
0
0
0
2
1
1
0
2
2
0
0
1
1
2
1
2
0
1
0
0
1
0
2
0
1
0
0
1
2
2
2
1
1
0
0
0
0
0
1
0
0
3
0
1
0
0
0
1
2
1
1
1
0
2
0
0
1
0
1
0
0
2
0
0
0
1
3
0
0
0
1
0
1
2
1
1
1
0
1
2
0
0
1
1
0
2
0
0
0
1
2
0
0
0
0
0
2
2
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
1
1
0
0
0
0
0
3
0
2
0
0
0
4
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
3
0
1
0
2
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
1
2
2
0
0
2
1
0
0
1
2
0
0
1
0
1
1
0
0
1
0
0
0
2
0
2
2
0
0
0
0
2
0
2
2
0
0
1
0
2
0
1
0
0
0
0
10
3
1
0
1
0
1
0
0
0
0
1
0
0
5
1
0
0
2
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
2
0
0
1
0
0
1
0
1
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
2
0
1
1
2
2
2
0
5
2
1
0
2
1
0
2
2
0
0
0
0
2
1
1
0
2
1
1
0
1
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
2
0
2
1
0
1
0
1
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
1
2
2
1
0
0
0
1
2
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
2
0
1
0
2
0
0
0
2
0
0
0
2
1
0
1
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
2
0
1
0
1
2
1
1
3
2
0
0
0
0
0
0
1
2
11
0
1
0
2
0
0
0
2
0
0
0
1
2
0
1
0
1
1
0
1
1
1
1
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
1
1
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
3
0
1
2
2
0
0
2
0
0
2
2
0
1
1
0
1
0
0
1
0
0
1
2
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
2
1
0
0
2
1
0
0
2
2
0
0
0
1
0
0
0
1
2
0
0
2
0
2
0
0
0
0
0
0
1
1
0
2
0
0
0
2
0
2
1
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
1
2
0
0
1
1
0
0
2
0
0
0
2
0
0
0
1
1
0
1
2
0
0
1
0
2
0
1
1
2
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
2
3
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
3
0
0
0
0
0
1
0
2
1
0
0
2
0
2
1
2
0
0
0
3
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
1
0
1
1
1
0
0
2
4
0
0
0
0
0
0
0
0
0
1
0
2
2
1
1
5
0
0
0
2
0
0
1
2
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
2
2
1
0
0
0
0
0
0
0
2
1
0
2
1
0
1
0
2
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
2
0
0
2
0
0
1
0
2
0
2
0
1
0
0
2
0
2
1
1
0
0
0
0
0
0
2
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
2
0
0
1
0
2
1
0
0
0
1
0
0
0
1
0
1
0
0
2
0
0
0
0
0
1
0
2
1
0
0
1
0
0
0
2
2
0
1
0
0
1
0
0
0
0
3
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
4
0
0
0
0
1
4
2
7
0
0
1
0
0
0
0
0
0
1
0
2
0
2
2
0
0
1
0
0
2
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
2
0
0
2
0
1
1
2
3
0
1
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
1
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
1
0
1
0
2
1
0
0
2
0
2
0
1
2
0
0
0
1
0
0
0
2
1
0
0
1
0
2
0
0
0
1
1
0
0
0
1
1
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
1
0
2
2
2
0
0
0
2
0
0
0
2
2
0
0
0
2
1
0
0
2
1
0
0
0
1
2
2
1
0
1
0
0
0
0
0
2
0
2
1
0
0
0
0
2
0
1
1
2
0
1
0
5
0
0
0
1
1
1
2
2
0
0
0
0
0
0
2
0
2
0
1
0
1
0
2
1
0
0
0
2
0
1
0
0
1
0
0
0
0
0
1
2
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
2
1
2
0
1
1
2
1
0
3
0
2
1
0
0
2
0
1
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
1
2
1
0
0
2
2
2
1
0
2
0
0
2
2
2
0
3
0
0
0
5
0
2
0
2
3
2
0
1
0
1
0
1
0
0
1
2
0
0
2
0
0
1
2
0
1
0
2
0
0
0
1
5
0
0
0
3
0
0
0
0
8
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
1
1
0
2
2
2
0
1
0
0
0
0
0
0
0
1
0
1
0
3
2
0
0
2
1
1
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
3
0
2
2
0
0
2
1
0
0
1
2
0
0
1
1
0
0
0
1
0
0
1
0
1
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
1
0
2
2
2
0
0
0
1
0
1
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
1
2
0
2
2
3
4
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
1
0
2
0
0
1
0
0
2
0
0
1
0
0
0
0
0
2
0
2
1
0
0
0
0
0
1
0
0
1
2
1
0
0
3
0
0
0
2
0
1
2
1
0
0
0
1
1
2
2
0
0
0
2
0
0
0
1
5
2
0
1
1
0
0
0
2
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
3
0
0
0
0
2
0
0
0
3
0
1
2
1
0
0
1
0
0
2
0
1
0
1
0
0
1
0
0
0
0
0
1
3
1
0
0
3
2
0
0
1
2
0
1
0
2
0
1
0
0
2
1
1
0
0
1
0
0
2
2
0
1
0
0
0
1
0
0
0
1
0
0
0
0
2
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
3
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
4
0
1
0
0
1
0
2
0
0
0
0
0
2
0
2
0
0
4
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
2
5
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
2
1
0
2
0
1
1
1
0
0
0
0
1
0
2
0
2
0
1
0
0
0
0
2
1
0
0
1
0
0
0
0
1
0
0
0
1
0
2
0
0
2
0
2
0
0
0
2
0
1
0
0
1
1
0
0
1
0
0
0
0
2
2
0
0
1
0
3
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
4
0
0
2
0
2
0
0
2
2
2
0
0
1
2
0
0
0
0
0
0
1
1
2
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
2
1
1
0
1
0
0
0
0
1
2
1
1
0
0
1
2
0
2
1
2
1
1
0
2
0
1
1
0
0
2
0
0
2
0
2
0
0
0
0
0
1
0
3
2
0
2
1
0
1
0
0
0
2
0
2
0
1
2
0
0
0
0
0
1
0
2
1
1
0
0
2
0
2
0
0
2
1
2
0
2
1
0
2
0
1
2
1
2
0
0
1
0
0
0
2
0
1
0
0
0
1
0
0
1
0
0
3
1
2
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
1
0
0
1
0
1
2
0
1
0
0
0
0
0
2
2
2
1
1
1
0
0
1
1
0
0
2
0
1
0
0
0
0
0
0
1
2
0
1
0
2
0
0
0
0
0
0
0
0
1
2
0
0
2
1
0
2
0
0
0
2
0
0
0
1
1
0
0
0
0
0
1
0
1
2
1
2
5
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
1
1
0
0
1
1
0
1
1
0
0
2
0
0
2
1
2
0
4
0
0
0
6
0
0
0
0
0
0
0
1
0
0
1
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
1
0
1
0
1
2
0
0
0
4
0
2
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
4
0
0
0
2
2
0
1
0
0
0
0
0
0
1
0
2
2
1
0
0
1
0
2
0
2
0
1
3
1
0
2
1
0
0
0
0
0
0
0
2
2
0
2
1
2
1
1
0
0
2
2
1
2
0
0
0
2
4
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
2
0
1
1
1
0
1
0
2
1
0
0
1
1
0
1
0
2
0
0
0
2
2
0
0
1
0
0
2
0
0
0
2
0
2
0
0
3
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
1
0
2
0
0
2
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
2
0
4
0
2
0
0
0
1
0
0
0
1
1
1
0
0
0
0
1
0
0
0
1
2
2
1
2
1
0
3
0
1
0
0
0
0
2
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
2
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
1
2
2
0
1
0
0
0
2
2
0
0
0
1
1
0
0
1
0
0
0
1
2
0
0
0
2
0
0
2
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
16
0
0
0
2
0
0
1
4
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
1
1
1
0
0
2
1
0
2
0
0
0
2
0
0
0
2
1
1
0
0
0
1
1
1
0
2
3
2
1
0
0
0
0
1
1
0
0
0
2
1
0
3
0
0
2
0
0
2
0
1
0
1
1
1
1
0
4
2
1
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
1
0
1
0
2
1
1
2
0
0
2
2
0
0
0
1
0
1
0
2
0
0
1
2
2
0
0
1
0
0
1
0
0
0
1
0
2
0
4
1
1
2
0
0
1
0
0
2
0
1
1
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
2
1
2
1
0
0
0
0
2
2
0
1
0
2
0
2
0
0
0
2
0
1
0
2
0
1
1
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
1
0
1
0
0
1
2
0
0
0
0
0
1
2
3
0
0
0
0
0
0
1
0
1
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
3
2
0
0
0
2
2
0
1
0
1
0
1
2
0
2
0
1
1
1
0
2
1
1
0
1
0
0
1
0
0
0
0
2
0
1
0
0
1
1
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
2
0
4
0
2
0
0
0
3
2
0
0
0
0
0
0
1
0
0
1
0
0
0
1
3
0
0
0
1
0
0
2
0
3
2
2
1
0
2
1
4
0
0
2
2
2
0
0
0
0
0
2
0
1
0
0
2
1
1
0
0
0
0
2
1
3
0
0
1
0
6
0
0
0
2
0
5
0
0
0
0
1
0
2
0
0
2
1
0
1
0
1
0
2
0
0
2
0
3
0
5
1
2
1
0
2
0
0
0
0
3
5
0
0
1
0
0
2
0
1
1
1
0
0
2
1
2
0
0
4
1
0
0
0
2
0
0
2
0
0
0
3
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
3
2
0
0
0
0
2
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
5
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
2
0
1
0
2
0
2
2
0
0
0
0
0
0
0
0
1
0
1
1
2
0
0
0
0
2
2
2
1
2
0
1
1
0
0
2
0
0
2
2
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
1
0
0
0
0
0
1
2
0
2
2
0
1
2
0
0
1
1
1
0
0
0
1
1
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
2
1
0
1
2
0
2
0
0
0
0
1
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
2
3
0
2
0
1
0
1
0
0
0
2
0
0
1
0
0
0
0
0
1
0
3
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
2
1
0
1
0
1
1
2
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
2
2
1
0
1
3
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
1
0
2
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
2
0
1
2
2
0
2
0
1
2
0
1
1
2
0
1
0
0
2
0
0
0
0
0
0
2
0
3
1
0
0
1
2
0
0
0
1
0
0
0
1
0
0
0
0
3
1
2
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
2
2
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
2
1
0
0
1
0
0
1
1
0
1
3
0
0
2
0
0
0
2
0
0
1
2
2
0
1
0
1
0
0
1
2
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
2
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
1
0
0
2
3
2
1
1
2
2
0
0
2
0
1
2
2
0
0
0
0
0
1
1
1
1
3
0
0
2
1
1
0
0
0
0
0
0
1
0
0
1
2
2
3
0
0
3
1
0
0
0
1
2
0
0
2
0
3
0
2
2
0
0
0
0
0
0
0
2
1
1
0
0
1
0
0
0
0
1
0
0
0
2
2
2
0
1
0
1
0
0
0
4
2
0
0
0
0
0
2
2
0
0
0
0
0
2
0
1
0
0
1
0
0
0
1
1
5
0
1
1
0
0
0
0
0
2
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
2
1
0
0
0
0
1
2
0
1
0
0
0
0
0
0
3
3
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
3
0
0
0
2
0
1
1
0
0
1
2
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
4
1
2
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
2
2
2
1
0
1
2
0
3
2
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
2
0
2
0
0
2
1
0
0
0
1
0
3
0
2
2
0
0
3
0
0
0
0
2
2
3
0
0
2
1
1
0
0
0
0
0
1
0
2
0
2
1
0
1
2
0
0
0
0
1
0
0
1
0
2
0
0
2
0
0
0
0
0
1
1
0
0
0
1
0
2
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
2
0
1
2
0
2
0
0
0
0
0
1
1
1
2
0
2
0
0
0
1
1
0
0
0
0
1
2
0
0
0
0
2
0
0
1
0
0
1
1
0
2
0
0
0
2
1
0
1
2
2
0
0
0
4
0
0
0
0
1
0
0
0
2
1
0
0
0
2
0
0
1
1
2
0
2
0
0
2
1
0
0
3
0
1
0
1
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
1
2
0
0
0
2
0
2
1
2
0
0
2
2
0
2
0
0
2
2
0
1
0
1
2
0
0
1
0
0
1
2
0
0
1
0
0
0
0
2
0
2
0
0
1
0
0
2
2
0
2
0
2
2
2
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
1
0
0
1
0
0
0
1
1
0
0
0
1
0
2
0
1
1
0
0
2
1
0
0
0
1
0
0
1
0
0
1
5
1
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
1
1
0
0
2
1
0
1
0
1
1
0
1
1
1
2
3
0
2
0
0
0
1
0
0
0
0
0
0
1
2
2
2
0
0
0
0
1
2
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
1
0
1
2
1
0
1
0
1
0
3
2
2
1
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
2
0
0
0
0
1
1
1
1
0
0
0
0
0
0
2
1
1
1
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
1
2
0
0
1
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
1
1
0
11
2
1
2
2
0
0
0
0
2
0
3
1
0
0
1
0
2
0
1
0
0
1
0
0
0
2
0
1
1
2
2
0
0
0
0
0
2
0
1
2
1
2
2
0
1
2
0
2
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
2
0
0
2
1
1
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
2
0
0
0
2
0
3
0
1
2
0
2
0
0
0
1
0
1
3
0
0
0
1
1
0
2
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
2
0
0
2
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
4
1
0
0
2
0
2
0
3
0
1
2
1
2
1
0
1
0
0
0
2
3
0
0
1
1
0
2
1
0
2
0
0
2
1
2
0
0
1
0
2
1
1
0
0
0
0
0
2
0
0
0
1
2
1
0
1
0
0
0
0
0
1
1
0
0
1
1
0
0
2
0
1
1
2
0
0
2
0
2
1
0
0
2
0
0
0
1
0
0
0
0
0
0
2
1
2
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
8
1
0
2
0
0
1
0
2
0
0
2
0
0
0
1
0
0
1
0
0
0
1
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
1
2
2
0
0
0
2
0
0
1
4
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
2
2
1
1
0
0
0
0
0
0
0
0
0
0
5
0
0
0
1
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
3
4
0
0
2
0
0
0
0
0
0
0
0
0
1
1
2
2
0
0
0
1
0
0
2
1
1
2
2
0
0
0
1
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
1
2
1
2
0
0
2
0
0
0
0
1
0
0
0
3
1
0
0
2
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
3
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
3
0
0
1
2
0
1
0
0
0
3
0
0
0
0
0
3
0
2
1
1
0
0
0
1
4
0
1
2
0
0
1
0
0
0
0
1
0
1
1
0
0
2
0
0
1
2
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
1
1
2
1
1
0
1
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
2
2
0
0
1
0
1
0
0
2
0
0
2
0
0
0
1
1
0
4
0
1
1
0
1
0
0
2
0
0
0
1
0
0
0
0
2
0
1
0
0
2
0
0
0
1
0
0
0
2
0
1
1
0
0
0
1
2
0
0
2
2
0
3
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
2
0
0
0
0
2
0
1
2
1
0
1
1
0
0
0
0
0
1
1
2
1
1
1
0
0
1
0
0
2
0
0
0
2
0
0
0
2
1
0
2
0
4
0
1
0
1
1
1
1
0
1
0
2
3
0
0
2
1
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
3
1
0
1
0
0
0
1
0
2
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
2
0
0
0
0
2
2
0
2
0
1
0
2
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
2
2
0
0
0
0
0
0
0
0
0
2
2
2
1
2
0
0
2
0
0
2
0
2
2
2
2
0
3
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
1
1
0
1
1
1
1
1
2
1
0
2
2
0
0
0
0
0
1
0
0
3
1
0
6
2
0
2
0
2
2
0
3
1
1
0
0
1
0
1
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
1
2
0
3
2
1
2
0
0
2
1
1
0
2
1
0
2
0
0
2
2
0
1
0
0
3
0
0
1
0
0
0
0
0
0
0
0
2
1
2
0
2
0
1
0
0
3
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
2
1
2
0
0
0
0
0
0
3
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
1
2
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
1
0
0
0
2
0
1
0
1
0
0
1
0
0
2
0
0
0
1
11
1
0
2
0
0
1
0
0
0
0
2
3
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
2
0
0
1
0
2
0
1
0
2
0
0
1
0
0
0
0
0
1
1
0
1
2
2
2
0
1
0
0
2
0
0
0
2
0
0
3
2
1
0
2
1
0
0
0
2
0
0
2
0
0
1
0
0
0
1
2
0
2
0
0
2
0
1
0
0
1
1
0
1
1
3
3
0
0
0
0
1
1
0
2
1
2
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
3
1
2
0
2
0
0
0
1
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
5
1
5
0
0
0
2
0
2
0
0
2
0
0
2
0
0
0
2
3
0
0
0
0
1
0
0
2
1
0
1
2
2
1
0
0
0
0
2
0
7
0
0
1
0
2
0
0
0
0
0
0
0
0
1
2
1
1
0
4
1
0
0
2
0
0
0
1
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
2
1
3
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
2
0
2
0
0
0
1
0
0
1
2
0
0
0
1
0
0
0
0
1
0
3
2
2
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
3
0
2
1
0
0
1
0
0
1
0
0
0
0
1
1
1
0
0
2
0
0
0
0
0
2
0
1
1
0
1
1
0
0
0
0
2
0
0
0
1
0
3
2
2
1
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
1
0
1
0
0
0
1
2
0
6
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
4
0
0
1
0
2
0
1
0
0
1
2
0
0
0
0
2
0
2
1
0
1
1
2
2
0
2
2
0
0
0
2
0
0
1
0
1
0
1
2
0
1
0
0
2
0
0
1
0
0
0
2
2
2
0
0
2
1
0
2
0
0
0
0
0
0
0
1
0
0
1
2
0
4
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
1
2
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
1
0
0
0
1
1
2
0
2
0
0
1
1
2
2
0
1
3
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
1
0
1
1
0
0
1
0
0
0
2
2
0
1
0
0
0
0
0
1
2
0
0
0
2
0
1
0
0
0
1
0
0
0
1
0
0
1
2
1
0
0
2
1
0
0
0
2
0
0
0
0
0
0
1
4
2
0
0
0
0
0
2
0
1
0
0
0
1
2
1
0
0
0
0
1
2
0
1
0
2
1
0
0
0
1
1
0
0
0
0
2
2
1
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
2
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
1
1
0
0
0
0
2
0
0
0
0
0
1
0
2
2
0
0
3
0
0
1
2
0
0
0
0
0
0
0
1
0
2
0
1
2
0
1
1
0
1
0
1
0
0
1
0
0
1
0
0
1
0
2
2
2
2
1
1
1
0
0
2
0
2
0
0
1
1
3
3
0
1
0
1
0
1
2
2
0
0
1
0
0
2
1
0
2
0
0
1
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
2
1
1
2
0
0
0
1
2
0
0
0
0
1
1
0
1
0
0
2
0
0
1
0
0
2
1
0
0
0
0
0
1
0
0
2
0
2
0
1
0
1
0
0
0
1
1
0
0
0
0
0
2
2
0
0
1
0
0
1
2
1
3
1
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
3
0
1
0
3
0
0
1
0
2
2
0
1
1
0
2
2
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
2
0
0
0
2
0
2
0
0
0
0
2
0
0
3
1
0
1
0
0
0
0
0
2
1
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
1
2
2
0
0
1
0
0
0
0
0
0
0
1
2
1
2
0
1
0
1
0
1
0
2
2
2
0
0
0
1
1
0
2
0
2
1
1
0
0
1
1
1
1
1
0
0
0
0
0
0
0
0
1
1
2
0
0
2
0
0
3
0
0
0
0
0
2
0
3
0
2
0
0
1
1
0
0
0
1
0
0
0
0
4
0
0
0
0
0
1
0
1
0
0
2
0
1
0
6
0
1
0
3
0
0
2
2
0
2
0
0
2
1
1
0
0
0
0
2
0
17
1
0
2
0
0
0
0
2
0
0
0
0
2
1
0
0
0
2
0
1
0
1
0
1
0
0
0
1
0
0
0
1
1
3
0
1
0
1
0
1
1
2
0
2
1
2
2
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
2
0
0
2
0
1
1
1
1
0
0
0
1
1
0
1
0
0
1
0
0
0
0
2
0
0
0
1
0
1
0
0
0
2
1
0
0
0
0
1
2
1
0
0
0
0
0
0
0
2
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
1
1
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
1
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
1
1
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
2
2
0
0
1
0
0
0
0
0
0
2
0
0
0
1
1
1
1
2
1
0
0
1
0
2
1
0
1
0
1
1
2
0
1
0
0
0
0
0
1
0
1
0
0
1
1
0
0
2
0
0
0
0
1
0
1
1
0
0
0
1
0
0
2
0
1
0
0
1
2
0
0
0
1
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
1
2
2
1
2
0
0
0
0
0
2
1
2
0
1
0
0
0
0
0
0
2
1
0
1
2
1
2
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
2
0
0
2
0
0
0
0
1
1
0
0
0
0
0
1
0
2
0
1
0
1
1
0
1
0
1
1
0
2
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
1
0
1
0
5
0
7
0
2
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
2
1
0
0
0
4
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
2
1
0
0
2
0
0
0
2
0
0
0
1
0
1
0
0
0
1
0
0
2
0
1
0
0
1
0
2
1
2
1
0
0
2
0
0
0
3
0
0
0
0
0
0
0
1
2
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
2
2
0
0
0
0
2
0
1
0
0
0
2
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
3
1
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
2
2
1
0
0
2
0
0
1
2
6
0
2
0
0
0
0
0
0
0
0
2
2
0
0
2
0
2
0
1
1
1
0
0
0
2
0
1
0
0
2
1
0
0
0
2
0
0
0
0
0
0
1
1
0
0
2
0
0
2
1
1
0
2
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
3
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
1
1
0
1
0
2
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
1
3
2
0
2
1
0
2
0
0
0
1
0
0
1
0
2
3
0
0
0
0
3
1
2
0
0
2
0
0
0
0
0
0
0
2
0
1
1
1
0
0
2
0
0
2
0
0
4
1
0
0
1
0
0
0
1
1
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
3
1
0
0
3
2
0
0
0
0
0
0
0
0
2
0
0
0
1
1
1
0
0
0
1
0
0
3
0
0
1
0
1
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
2
0
0
4
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
2
0
0
0
0
0
2
0
1
1
0
2
1
0
1
2
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
1
1
3
0
8
0
0
0
2
2
1
2
0
0
0
0
2
2
1
0
1
1
2
0
0
2
0
0
2
2
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
2
1
0
1
2
2
0
0
0
2
0
0
0
1
2
1
2
2
0
0
1
3
1
0
0
1
3
1
0
1
0
0
3
1
0
1
0
0
0
0
1
2
2
1
1
1
1
0
1
1
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
1
1
0
1
2
0
0
0
1
2
0
0
3
0
3
1
0
0
1
0
0
1
0
0
0
0
2
2
0
2
0
0
0
0
2
4
0
0
2
1
0
2
0
2
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
1
4
0
0
0
0
0
0
0
1
2
0
4
2
0
0
0
0
1
0
0
1
2
2
0
0
0
0
0
1
0
1
2
0
0
0
0
1
0
0
1
0
0
2
0
0
1
2
1
0
0
2
0
0
0
0
0
3
2
2
0
3
0
0
0
0
0
0
0
0
1
2
0
2
1
0
0
0
1
0
2
1
2
1
0
0
3
0
1
1
2
1
0
1
0
0
0
2
2
0
0
1
0
0
1
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
2
1
0
0
0
0
0
1
2
0
2
1
0
0
1
0
2
2
0
1
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
1
0
2
2
0
2
0
0
0
2
0
2
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
2
0
0
0
2
0
0
0
1
0
1
0
0
0
3
0
1
0
0
2
2
0
0
0
0
0
1
0
0
2
0
0
0
0
1
1
0
1
0
0
0
0
0
1
1
0
3
0
0
2
0
0
0
0
0
1
0
1
0
7
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
1
1
0
1
0
0
0
0
0
2
1
0
0
2
1
0
2
1
0
0
1
0
0
0
0
0
2
0
4
0
0
0
0
0
0
2
0
0
0
2
0
1
1
2
0
2
0
0
0
0
1
2
0
0
1
1
0
1
0
0
0
0
2
2
0
2
2
2
1
2
0
0
2
0
0
0
0
0
0
1
0
2
0
0
1
2
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
2
0
1
1
1
0
0
0
0
0
0
0
3
3
1
0
0
0
0
1
0
0
1
0
0
0
1
3
0
0
1
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
2
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
1
2
0
0
0
0
0
2
3
0
0
0
0
1
0
0
0
3
0
1
2
1
1
2
0
1
1
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
3
0
0
1
2
0
0
1
0
2
0
1
1
0
0
0
1
1
1
0
0
2
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
2
0
0
1
1
1
1
0
1
0
1
0
0
0
0
1
0
2
0
2
0
7
2
0
0
3
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
3
0
2
0
0
0
1
9
0
0
0
2
0
0
0
2
1
1
1
0
0
1
2
0
0
1
0
0
1
2
2
0
0
0
0
0
0
3
0
0
0
0
0
0
3
0
0
0
3
0
0
2
2
1
0
1
0
1
1
0
2
1
2
0
0
2
2
0
0
0
0
2
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
2
1
2
0
0
1
0
0
0
0
0
2
1
0
1
0
2
0
0
0
0
0
0
0
2
0
0
2
1
0
2
2
1
0
0
2
3
2
0
1
1
0
0
0
1
0
0
0
0
2
0
0
1
1
2
3
0
0
0
0
2
2
0
1
0
2
0
0
0
1
0
0
0
0
0
0
1
2
2
1
1
0
0
0
0
1
1
0
1
0
1
0
0
1
0
1
1
0
0
1
2
0
0
1
0
0
0
0
1
1
2
0
0
1
1
0
0
0
0
0
0
0
3
0
2
2
0
0
0
0
1
0
2
0
0
1
2
1
0
0
0
0
0
0
2
0
1
0
0
2
2
0
0
0
0
1
0
1
2
1
2
0
0
0
0
1
0
1
1
0
1
0
2
0
1
2
1
0
3
1
1
0
0
0
0
0
1
0
0
2
2
1
1
2
2
0
1
1
1
1
2
2
0
2
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
2
3
0
0
1
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
0
0
0
2
0
0
0
1
2
0
0
2
0
3
0
2
2
0
0
0
0
2
0
0
0
0
0
0
3
0
0
1
0
1
0
1
0
1
0
2
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
3
0
1
1
0
0
1
0
0
0
1
0
0
2
1
0
0
1
0
0
2
0
0
0
0
2
0
0
2
0
2
2
1
1
0
0
0
0
0
0
1
0
0
0
7
2
1
1
1
0
1
0
0
1
0
2
0
0
1
1
0
0
0
0
0
0
0
2
0
2
2
0
0
1
1
0
1
0
0
0
2
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
1
0
2
2
0
0
0
1
2
2
0
0
1
1
0
1
1
0
0
0
1
0
0
0
0
1
2
2
1
0
1
0
0
0
0
0
2
3
0
2
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
6
1
0
0
2
0
0
0
0
0
2
1
0
2
0
0
1
0
0
2
2
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
2
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
1
1
0
1
0
1
4
0
0
0
1
1
1
0
2
1
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
1
2
0
0
0
0
0
1
1
1
1
0
2
0
1
0
0
0
0
2
0
2
2
2
1
0
0
0
0
0
1
0
2
2
0
2
0
0
0
1
2
0
1
1
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
2
2
3
1
1
0
0
1
1
1
0
2
1
0
0
0
0
0
0
0
0
0
1
0
2
2
0
2
2
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
2
0
0
1
1
0
2
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
1
2
2
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
3
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
1
2
1
2
0
0
0
0
1
0
0
0
0
0
1
0
1
2
2
2
0
2
0
0
1
1
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
4
3
0
1
0
0
0
0
0
0
1
0
2
1
0
1
0
1
0
0
0
0
0
1
2
1
0
0
2
1
0
2
0
1
0
1
2
0
0
2
3
1
0
2
0
0
2
1
0
0
3
0
0
0
0
0
1
1
0
0
0
1
1
1
2
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
2
1
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
1
0
0
2
1
1
0
0
0
0
0
1
2
0
2
0
1
0
2
2
0
1
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
2
2
0
0
2
0
1
1
0
0
0
0
2
2
0
0
0
0
0
0
2
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
3
0
0
3
0
0
0
0
0
0
1
0
0
0
0
2
1
2
2
1
0
2
0
0
0
0
0
2
0
1
1
0
1
2
0
0
0
2
2
0
1
1
0
0
0
5
1
0
1
2
0
0
0
2
1
1
0
1
0
0
1
2
0
0
1
0
3
1
0
2
0
1
0
2
0
1
2
0
0
0
0
0
1
3
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
2
0
0
0
0
2
2
0
2
1
0
1
0
1
1
1
2
0
0
2
0
0
0
1
3
0
1
0
0
2
0
0
0
0
0
0
3
1
1
2
1
0
2
0
0
2
1
0
0
1
0
2
0
1
0
0
0
1
2
1
2
0
0
0
0
0
0
2
0
0
0
0
2
1
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
5
0
0
0
0
2
0
2
1
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
1
2
0
0
0
0
0
1
0
0
0
2
0
1
0
0
2
1
1
0
0
1
1
2
2
0
1
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
1
0
2
2
0
2
0
1
0
1
1
1
0
1
2
0
0
0
0
0
0
2
1
0
3
2
1
0
1
0
0
2
1
2
2
1
0
0
1
0
0
1
0
2
0
0
1
2
0
1
2
1
1
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
1
0
0
0
2
3
1
1
2
2
0
0
0
0
2
0
1
2
0
0
1
0
0
0
0
2
1
0
2
1
0
0
0
0
0
1
0
2
0
4
0
0
0
0
0
0
1
1
1
0
0
1
0
2
1
1
0
1
0
0
0
0
0
0
0
1
0
2
0
2
0
1
1
1
1
1
0
1
1
1
1
0
0
0
1
2
0
0
0
0
0
2
2
1
0
1
0
0
0
0
2
0
1
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
1
0
0
0
0
1
0
2
0
1
1
1
0
1
0
1
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
2
1
2
0
0
4
1
0
4
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
2
0
0
0
1
2
0
0
0
0
0
0
0
2
0
1
1
0
1
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
2
1
0
1
0
2
0
0
1
1
1
0
0
0
1
1
1
1
1
1
2
2
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
4
3
2
1
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
1
1
2
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
2
0
1
0
2
2
0
0
2
0
0
2
0
0
0
1
2
0
0
0
0
1
0
0
2
0
0
5
0
0
1
1
0
2
0
0
1
0
1
0
0
0
0
1
0
0
0
2
2
0
1
0
0
1
0
0
0
3
0
0
0
0
0
1
1
1
1
0
0
0
0
1
0
0
0
1
0
0
1
0
2
0
1
0
3
2
0
0
2
0
0
0
0
0
1
2
1
2
0
4
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
2
2
1
1
6
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
1
1
2
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
2
0
0
1
0
0
2
2
1
1
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
1
2
0
0
0
0
0
2
0
0
0
2
3
0
2
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
3
0
2
2
1
0
3
4
0
1
2
0
0
2
0
1
1
0
0
0
2
2
0
2
0
0
0
1
0
0
2
1
0
2
0
0
0
0
0
2
0
0
4
0
0
1
3
0
0
0
0
0
2
0
0
0
1
4
0
0
3
0
0
1
2
0
1
0
0
1
0
0
2
2
0
0
0
0
0
2
0
1
1
0
1
0
0
1
0
0
0
2
0
0
0
0
0
10
1
0
2
0
3
0
1
0
2
1
1
0
2
1
0
4
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
2
0
0
2
1
0
0
2
0
0
1
2
0
2
1
0
0
0
0
0
3
1
0
0
2
0
0
0
3
0
2
0
0
1
2
0
2
3
0
0
0
0
2
2
0
0
2
2
0
0
0
0
1
0
2
0
0
0
1
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
2
1
0
0
0
5
0
0
0
0
2
0
0
2
0
0
2
0
0
0
2
1
0
0
0
0
0
1
0
0
0
1
2
0
0
2
0
0
0
0
0
1
0
1
0
2
0
0
0
1
2
1
1
0
0
1
0
1
0
0
1
0
0
0
1
0
1
1
3
0
1
1
0
2
2
0
2
1
0
0
0
2
0
1
0
0
2
2
0
2
0
0
0
0
0
2
3
0
0
0
0
2
0
2
0
1
2
0
0
1
0
0
0
1
1
0
2
1
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
1
0
0
0
0
1
2
0
2
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
1
1
0
1
0
1
1
0
0
0
1
1
0
1
0
0
0
1
0
0
1
2
0
0
0
0
0
3
0
0
0
0
3
0
0
0
0
1
2
2
0
0
0
2
0
0
0
2
1
1
0
0
0
2
0
1
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
1
7
0
0
1
2
2
1
0
1
1
0
1
2
0
0
0
0
0
3
1
0
0
0
2
1
2
0
0
0
1
0
0
0
2
0
1
2
0
1
0
1
1
1
0
0
4
1
0
1
0
0
2
0
0
0
0
5
0
2
1
0
0
2
2
0
0
0
0
1
1
0
0
0
1
0
1
1
0
0
0
1
2
2
1
0
0
2
2
0
2
0
0
2
0
0
1
0
0
2
0
2
2
1
2
2
0
2
1
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
2
0
0
1
0
0
0
3
0
1
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
1
2
2
1
0
0
3
0
0
0
0
1
0
1
2
0
0
0
0
0
0
2
0
3
3
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
1
0
0
0
2
0
2
2
0
2
0
0
0
1
0
2
0
2
0
1
0
0
0
0
2
0
0
0
1
0
1
2
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
2
2
0
0
1
0
0
1
0
0
0
1
1
1
0
0
0
0
1
1
0
0
1
2
1
0
0
1
0
0
0
1
2
0
0
0
0
1
0
0
2
0
0
3
0
2
1
0
2
0
0
0
0
1
2
1
0
0
0
0
2
1
0
0
1
2
0
1
0
2
2
2
0
0
0
0
1
0
0
1
0
1
2
1
0
4
0
0
0
0
0
0
0
0
1
0
0
2
1
0
1
2
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
1
2
0
0
0
0
2
0
0
0
0
0
2
0
1
0
1
0
0
0
2
1
0
2
1
0
0
0
1
2
0
0
1
0
2
2
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
2
0
2
1
0
0
1
0
0
2
0
3
1
0
1
0
0
0
0
0
0
2
1
1
0
1
1
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
2
1
0
0
1
0
1
0
2
1
0
1
3
2
0
0
0
0
0
3
2
0
0
2
0
0
0
0
0
1
1
2
0
0
0
0
0
2
0
0
0
2
1
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
1
0
1
2
0
0
2
2
0
0
0
0
1
0
0
4
0
0
0
0
1
0
1
0
0
3
0
0
1
0
0
2
0
0
1
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
2
0
0
2
0
0
1
0
0
0
1
0
1
0
0
2
0
0
1
2
3
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
2
0
0
0
2
0
1
2
0
0
1
2
2
0
1
1
2
0
0
2
0
0
0
0
1
1
0
1
0
0
0
1
2
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
4
0
0
1
0
1
1
1
2
0
2
1
2
0
2
2
0
0
1
0
1
4
0
0
0
0
0
1
1
0
2
0
0
2
0
0
0
0
0
2
1
0
0
0
1
0
0
1
1
0
2
2
0
2
0
2
2
1
0
1
2
0
1
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
1
2
0
1
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
2
2
1
0
2
0
0
0
0
0
2
0
2
0
0
2
0
1
1
1
0
0
0
1
1
1
0
0
1
0
1
0
3
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
1
0
0
0
2
0
1
0
2
1
0
0
0
0
0
3
2
0
0
1
2
0
0
3
0
0
0
3
2
1
0
0
2
2
0
1
1
1
0
1
2
0
0
0
0
2
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
1
0
1
2
0
5
1
1
0
1
3
0
1
3
0
2
2
1
0
0
1
0
0
0
0
1
0
0
0
2
0
2
0
0
2
0
0
0
0
0
1
0
1
0
0
0
2
0
1
0
3
0
0
0
0
0
0
0
2
0
1
2
0
0
1
2
2
1
0
0
1
0
2
0
0
4
0
0
0
2
0
0
0
0
2
0
1
0
2
1
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
5
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
1
0
1
0
0
0
0
0
3
0
1
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
1
2
2
0
0
0
0
2
2
0
0
0
0
0
0
2
0
2
0
2
0
2
1
1
2
0
2
1
2
2
1
1
0
0
0
6
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
2
1
1
0
0
3
0
0
0
6
2
2
0
2
0
0
1
1
0
0
0
0
0
3
0
2
0
0
0
0
0
0
3
4
0
0
0
0
1
1
0
0
0
2
1
0
0
2
0
0
2
6
1
1
0
0
0
2
2
0
3
0
0
1
0
0
0
1
0
0
0
0
0
1
2
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
2
0
1
1
0
2
0
1
0
0
2
0
0
0
1
0
1
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
2
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
3
1
1
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
2
2
1
0
0
2
0
0
1
2
1
0
0
0
2
1
2
1
0
1
0
2
0
2
0
0
3
0
0
1
0
2
0
1
2
0
0
0
0
0
2
0
0
1
0
2
0
1
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
4
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
2
2
1
0
0
1
0
2
2
1
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
2
0
1
0
0
5
0
2
3
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
1
0
2
0
0
0
1
0
0
0
0
4
0
0
0
0
2
1
0
0
0
0
2
1
1
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
2
1
1
0
0
0
1
0
1
0
0
0
2
0
1
0
0
1
1
0
0
0
0
0
1
0
0
1
0
2
0
0
4
0
0
0
0
2
2
0
2
3
2
2
1
1
1
1
2
2
1
2
3
0
0
0
1
1
1
0
2
0
2
0
0
1
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
1
2
2
1
2
0
0
0
0
0
0
0
2
3
0
0
0
0
1
0
0
0
0
0
0
1
2
1
0
0
1
1
0
3
0
3
2
2
1
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
1
3
0
2
0
0
0
1
2
2
2
1
0
2
1
0
0
0
0
2
0
2
0
0
0
1
1
0
0
2
0
0
0
0
3
4
0
1
0
2
0
0
1
0
0
2
1
0
1
0
0
2
0
0
2
0
0
1
0
2
2
2
0
0
0
2
2
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
1
2
0
1
1
1
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
2
0
1
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
1
2
1
1
1
2
2
0
0
1
0
0
1
0
2
1
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
1
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
2
1
1
1
0
2
0
0
0
0
0
1
0
2
2
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
1
0
2
1
3
0
0
0
1
1
0
0
0
1
0
1
0
0
1
1
1
0
0
1
0
0
0
0
0
1
2
0
1
0
0
1
0
2
1
1
0
2
1
0
2
0
0
0
2
2
0
0
1
0
1
1
0
0
1
0
1
1
1
0
0
1
0
0
0
2
0
0
2
1
3
2
0
1
0
1
0
1
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
2
0
0
1
3
2
1
2
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
2
0
1
2
1
0
1
0
1
1
1
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
2
0
3
1
0
0
0
0
2
2
0
0
1
0
0
0
1
0
0
1
1
0
0
0
1
0
2
1
0
0
0
0
0
2
1
2
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
1
2
3
1
2
0
0
1
2
2
2
2
0
0
0
0
1
0
2
0
1
1
3
2
2
2
0
2
0
3
0
1
0
2
0
0
0
1
2
1
1
0
0
0
0
1
2
2
1
0
0
0
2
0
2
3
0
0
3
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
2
0
1
0
0
0
1
0
1
0
3
0
0
1
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
3
0
2
0
0
0
1
0
0
2
0
2
1
1
0
1
0
1
0
1
2
1
3
2
2
0
0
0
0
2
2
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
2
0
0
0
2
0
0
0
2
0
0
0
2
2
2
0
0
0
0
0
1
0
0
0
0
0
1
0
1
2
2
0
0
0
1
1
0
6
0
0
0
1
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
2
1
0
0
0
0
1
0
2
0
2
0
1
1
2
0
2
1
1
0
0
0
0
0
0
4
0
0
2
0
0
4
0
0
1
0
1
0
0
0
2
0
0
0
2
1
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
1
2
0
0
0
1
3
0
1
0
0
0
0
0
0
0
0
2
0
3
1
1
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
2
1
0
0
0
2
0
1
2
0
0
1
1
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
2
1
2
2
1
1
1
1
0
0
1
0
0
0
2
1
2
0
0
0
2
5
2
1
0
0
0
1
0
1
1
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
2
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
3
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
2
1
0
1
0
0
0
0
2
2
0
0
1
0
0
1
0
0
0
0
1
2
0
2
0
0
2
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
2
1
1
2
0
0
0
5
2
0
0
0
3
0
0
2
0
1
2
0
2
2
2
0
0
1
1
0
2
0
0
0
0
2
0
0
2
2
0
0
0
0
1
0
2
0
0
1
2
0
0
0
0
2
0
0
2
0
2
1
0
0
0
2
0
0
2
0
0
0
0
0
1
1
2
0
0
1
0
1
0
0
1
0
0
1
1
0
2
0
0
0
0
0
0
1
0
2
1
1
2
2
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
1
0
1
0
1
0
1
0
0
3
0
0
0
0
0
0
2
7
0
2
0
1
2
0
2
0
1
0
1
0
0
0
1
1
0
0
1
2
0
2
0
0
0
0
1
0
0
2
1
0
1
0
2
0
2
0
0
0
0
0
0
0
2
0
2
1
2
0
0
1
0
2
2
0
0
2
2
0
1
0
0
1
0
1
0
0
0
0
0
2
1
0
0
0
2
2
0
2
1
0
0
2
0
0
2
0
3
1
1
0
0
2
0
0
0
0
2
0
0
0
0
0
1
1
1
1
3
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
2
0
1
0
1
1
0
0
0
0
1
2
0
0
1
1
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
3
0
4
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
1
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
1
2
0
0
0
2
0
2
2
0
0
1
0
0
1
2
0
0
4
1
2
1
2
1
0
0
0
2
2
2
0
1
0
0
3
0
0
0
1
0
0
1
0
1
0
0
0
0
0
2
0
1
0
0
0
2
0
0
1
0
0
1
1
2
1
2
0
0
0
2
2
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
2
3
0
0
0
2
0
0
1
0
0
1
0
0
1
0
0
0
2
0
2
2
3
0
2
0
2
0
0
2
2
0
0
2
3
1
0
0
0
1
1
0
0
1
0
0
0
0
2
1
0
1
0
0
0
1
0
1
0
0
0
0
0
2
0
0
2
0
0
0
2
0
1
0
0
2
2
3
2
0
2
0
0
0
0
3
0
0
1
0
0
0
3
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
2
0
0
1
1
0
0
1
2
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
2
1
2
2
0
0
1
2
1
2
3
3
0
0
0
0
0
2
2
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
8
1
2
0
0
0
0
1
0
1
1
2
0
0
0
0
0
1
0
0
0
0
1
0
2
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
3
1
1
0
2
2
2
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
2
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
4
0
2
1
0
0
0
2
1
0
0
1
1
2
2
0
0
0
2
0
1
0
0
6
2
1
0
0
1
0
0
0
0
0
0
0
1
1
2
1
0
0
2
3
0
1
0
0
2
1
0
0
0
1
0
0
0
0
4
0
1
0
2
0
1
1
0
0
0
0
0
2
0
1
2
1
0
0
1
0
0
0
1
2
0
2
0
2
0
0
1
0
1
2
0
1
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
12
2
0
3
2
0
2
1
0
0
0
3
2
1
1
0
0
0
2
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
1
2
0
0
0
0
0
2
2
2
2
0
2
0
0
0
1
2
1
0
0
0
0
0
0
1
2
0
3
1
0
0
2
1
0
0
0
0
4
0
0
2
0
0
2
1
0
0
0
1
0
0
0
0
2
2
2
0
1
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
1
2
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
1
1
2
1
0
0
0
1
0
1
1
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
1
0
0
2
0
1
0
2
0
0
0
0
1
0
2
0
0
1
0
2
0
2
0
0
2
0
0
0
0
1
0
0
2
0
0
1
0
0
2
0
4
0
1
0
0
0
0
0
0
0
2
0
1
2
2
0
0
0
2
0
0
0
0
6
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
1
1
2
4
0
0
0
0
1
0
0
0
0
0
0
2
1
0
1
0
0
1
0
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
3
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
2
1
0
0
0
0
2
1
0
0
0
2
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
3
0
0
0
0
1
2
2
0
2
0
0
1
0
0
0
0
2
0
0
0
2
0
1
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
1
0
2
1
0
1
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
2
2
0
0
0
0
1
0
0
4
0
0
1
0
0
1
3
2
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
1
1
2
0
1
2
1
2
0
2
0
1
1
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
6
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
2
0
0
1
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
1
3
0
0
0
0
1
0
1
1
0
0
0
1
0
0
2
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
1
0
2
1
0
0
1
2
0
0
1
1
0
1
0
2
8
2
1
0
1
2
0
0
1
0
0
0
0
2
0
0
2
1
1
1
1
0
1
0
3
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
2
0
3
2
2
1
1
1
0
1
0
1
0
0
1
0
1
0
0
0
0
0
1
1
2
0
0
1
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
1
2
0
0
1
0
0
0
2
1
0
0
0
2
0
0
4
0
2
2
0
0
0
0
0
0
0
0
0
1
0
1
2
0
1
0
2
0
1
0
1
2
0
0
1
0
0
1
1
2
0
0
2
1
1
0
3
0
1
0
0
0
0
1
2
2
0
0
1
0
0
3
1
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
1
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
2
2
0
1
0
0
2
2
0
1
0
0
1
0
3
0
1
0
0
0
0
1
2
2
0
0
0
1
1
1
2
1
0
4
0
1
0
2
1
1
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
1
1
0
2
0
0
0
1
0
1
0
0
0
0
1
1
0
1
0
0
5
0
0
0
0
1
2
0
0
2
0
1
3
0
0
0
0
1
1
1
0
1
0
0
1
0
1
3
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
3
0
0
2
0
0
0
1
0
2
2
0
1
0
1
0
0
0
0
0
3
0
3
0
2
4
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
1
2
0
1
0
1
0
2
0
1
0
2
2
2
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
1
0
0
1
0
0
2
0
2
2
0
0
1
0
1
0
1
2
0
0
0
0
0
1
1
0
0
1
0
0
0
0
2
0
0
0
1
3
2
0
1
2
0
2
0
0
1
0
0
0
0
3
0
0
0
0
0
2
0
0
0
1
0
2
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
1
2
0
0
0
1
0
0
0
0
2
2
1
1
0
3
0
0
0
2
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
2
0
0
2
2
2
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
3
0
2
0
0
2
0
0
0
2
1
0
2
0
0
0
1
0
0
0
0
1
0
0
0
2
0
3
2
1
0
1
2
0
2
0
0
0
1
2
0
2
1
1
2
1
2
0
0
0
1
0
0
0
2
0
2
0
0
0
0
2
1
1
3
0
0
0
0
2
1
2
0
0
2
0
2
0
1
0
1
0
0
2
0
0
2
0
1
0
1
0
4
1
0
1
2
0
1
0
2
0
1
1
0
0
0
2
0
3
0
3
0
2
1
2
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
3
0
0
0
1
5
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
1
1
3
0
0
0
1
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
2
1
0
1
2
1
0
1
0
3
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
2
0
2
2
0
0
0
0
3
0
0
2
0
0
1
2
1
1
1
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
2
1
0
1
0
0
2
2
1
0
1
0
0
1
1
0
0
2
0
2
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
2
1
0
0
4
0
2
0
0
0
0
0
2
0
2
0
1
0
1
0
2
1
0
0
1
0
0
0
1
2
0
0
1
0
0
1
1
0
1
2
1
0
0
0
0
1
0
0
1
2
0
0
2
1
0
0
0
0
0
1
0
0
3
1
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
1
2
1
2
0
0
1
0
0
0
1
1
2
0
0
0
0
1
0
0
2
6
1
1
0
0
0
1
1
0
0
1
0
0
2
0
0
0
1
1
1
0
1
1
0
0
3
0
2
0
1
1
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
1
2
0
0
0
1
1
0
1
2
2
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
3
2
0
0
0
2
1
0
0
0
0
0
0
1
1
0
0
0
5
0
1
0
0
2
0
1
0
0
0
0
0
0
3
0
0
1
1
0
1
0
0
1
0
2
4
0
2
0
1
1
2
0
0
0
2
0
0
0
1
3
0
1
1
0
0
1
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
2
0
1
0
0
2
0
0
0
3
2
2
0
2
0
0
0
0
0
0
0
0
1
0
0
1
1
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
3
1
0
4
1
2
2
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
2
0
2
2
5
1
1
1
0
0
1
0
0
0
1
2
1
2
0
3
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
2
0
2
1
0
0
0
5
0
2
0
0
0
1
0
1
2
2
2
1
1
0
1
2
0
2
0
0
0
1
0
1
0
2
0
4
0
0
0
2
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
1
1
0
1
0
0
3
2
2
0
0
0
2
0
0
0
2
0
0
0
0
0
1
1
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
2
0
0
0
1
0
0
0
2
1
0
2
0
0
2
0
0
0
0
0
0
2
1
2
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
2
0
0
1
1
0
2
0
0
0
0
1
0
1
0
0
1
0
0
0
3
0
2
1
0
0
0
0
0
0
1
0
0
0
2
1
2
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
2
0
2
2
0
11
0
0
1
0
1
2
0
0
0
0
0
1
0
0
3
0
0
1
0
1
1
1
1
0
0
0
2
1
0
0
0
0
1
0
0
0
2
0
0
0
3
2
0
0
1
2
1
1
0
0
2
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
2
0
0
2
0
0
1
0
0
1
0
0
2
0
0
1
0
0
1
1
0
2
2
1
0
0
0
1
0
1
0
1
0
2
1
0
2
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
1
2
1
0
1
0
0
0
0
0
1
0
0
2
1
0
0
0
0
3
0
2
0
0
0
2
0
0
1
1
0
1
0
0
0
1
0
3
0
1
2
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
1
0
0
0
2
2
1
0
0
0
0
1
0
0
2
1
2
1
0
0
0
0
0
0
0
2
1
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
2
2
1
0
0
2
2
0
2
0
2
0
0
0
2
2
2
2
1
0
1
0
0
1
0
0
0
1
0
0
0
0
2
0
0
1
3
0
0
0
0
0
1
0
0
3
1
0
0
0
0
1
0
2
2
1
0
1
0
1
0
2
0
1
0
1
1
0
2
0
0
1
0
0
4
0
1
2
2
2
0
0
0
0
2
0
0
0
2
0
0
2
0
0
1
1
2
0
0
0
2
0
0
0
0
0
0
0
0
1
1
2
0
1
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
3
0
0
0
2
0
1
0
0
0
2
1
0
0
0
1
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
3
0
1
0
0
0
2
0
2
1
1
0
0
0
0
0
0
0
1
0
2
2
0
2
2
0
2
1
0
1
0
0
0
0
2
3
0
0
1
1
1
0
0
0
0
0
4
2
1
2
0
0
1
0
2
0
0
2
0
0
0
2
2
0
1
2
0
1
0
2
0
2
1
0
0
2
0
1
0
2
2
1
1
0
0
0
3
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
2
0
1
0
0
2
1
0
1
0
0
2
1
0
2
0
2
1
0
1
0
0
0
1
0
1
1
0
0
2
0
0
0
0
0
1
1
0
2
1
0
2
0
0
0
2
1
2
0
0
2
1
2
0
0
0
0
2
1
2
2
0
1
0
7
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
1
1
0
0
1
0
2
2
0
0
1
0
2
0
0
0
0
1
0
1
0
0
1
0
1
0
2
2
0
1
1
0
0
0
0
0
1
0
0
0
2
0
1
0
0
1
0
0
1
1
0
2
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
2
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
2
0
0
0
0
0
1
0
0
2
0
0
1
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
2
0
1
0
1
0
0
0
2
1
1
0
0
0
0
1
0
1
0
0
1
0
0
0
2
1
1
2
3
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
1
1
0
0
0
2
2
0
0
0
1
0
0
0
0
1
0
1
2
0
2
2
4
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
1
2
2
2
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
1
0
1
0
2
2
0
2
0
0
1
1
0
2
2
0
4
0
0
2
0
0
1
0
0
0
0
0
2
1
0
1
2
0
0
1
3
0
5
1
1
0
0
0
0
0
0
0
0
1
0
0
2
2
2
1
2
1
0
0
0
0
1
0
0
2
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
1
0
2
0
0
0
0
2
1
0
1
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
1
1
0
0
1
2
0
0
1
0
0
0
0
5
0
0
0
0
2
0
2
1
2
0
1
1
0
0
0
0
0
2
2
0
0
0
1
0
1
2
1
0
0
0
0
0
2
2
0
1
0
2
2
1
0
0
0
0
1
1
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
1
1
0
0
1
0
0
0
0
5
0
1
0
0
2
0
0
0
0
2
1
0
2
0
0
0
0
2
0
2
0
0
2
0
1
0
0
1
1
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
1
3
0
0
0
0
0
0
0
2
0
0
2
2
0
0
1
1
0
0
1
1
1
1
2
0
0
0
0
0
1
0
2
1
0
0
1
0
0
0
0
0
0
1
1
0
2
1
0
1
0
1
0
1
0
2
0
0
2
0
0
0
0
0
1
0
0
0
1
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
1
1
0
0
1
0
1
0
1
0
3
0
0
0
0
2
2
0
0
0
0
0
0
0
0
3
2
2
1
0
2
2
0
0
0
1
2
0
0
0
0
1
4
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
2
0
2
2
0
0
0
0
0
0
2
0
1
0
1
0
1
1
0
1
1
0
0
1
1
0
3
1
2
0
0
2
2
0
0
1
0
0
0
0
1
0
0
0
0
6
0
0
0
1
2
0
0
1
0
2
2
0
0
0
0
0
2
1
1
0
0
0
0
2
2
2
1
2
0
0
2
2
0
0
0
0
0
0
0
0
3
0
2
0
0
0
1
2
0
2
2
0
0
2
0
0
2
2
0
0
1
1
0
0
2
0
2
0
1
1
0
0
0
0
0
2
1
0
0
0
2
0
0
1
1
0
0
0
0
0
1
0
0
2
0
0
0
2
0
2
2
0
0
1
0
0
3
2
0
2
1
0
0
1
0
0
0
1
2
0
2
0
0
1
2
1
0
0
0
0
0
5
0
1
2
1
0
2
0
2
0
0
2
0
0
1
1
1
2
0
0
2
0
2
0
0
0
2
0
1
0
0
3
0
1
0
0
0
0
2
0
0
2
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
6
1
0
0
0
2
0
0
0
1
1
2
1
1
0
0
0
0
2
0
2
0
1
0
0
0
2
0
2
0
0
1
0
0
2
0
0
0
4
0
0
0
0
0
1
0
2
2
0
0
2
1
2
0
0
0
2
0
0
1
0
0
0
0
1
1
0
0
0
2
0
1
0
0
0
1
0
0
1
2
0
8
0
1
0
0
1
0
0
1
0
1
0
0
2
1
0
2
0
0
0
0
0
0
0
0
2
0
2
2
2
1
1
0
2
1
0
0
0
0
0
0
1
0
0
1
0
2
0
0
2
0
0
3
0
2
0
0
2
0
0
0
2
0
1
0
0
0
0
0
1
2
2
0
0
0
0
2
0
0
0
0
0
0
1
0
3
1
0
0
2
2
1
0
1
2
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
1
1
0
1
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
2
2
0
0
2
2
2
2
1
4
0
2
0
0
2
1
0
0
0
0
0
0
2
0
2
1
0
1
0
0
0
0
2
2
0
2
0
0
0
2
0
0
0
1
0
1
0
2
2
0
0
0
0
0
0
0
0
3
2
0
0
2
0
0
1
2
1
2
0
0
0
1
1
2
0
0
0
0
2
0
0
2
0
0
1
1
0
3
0
0
2
0
0
1
2
0
0
2
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
2
0
1
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
3
0
0
1
0
1
0
0
1
1
0
2
0
2
3
0
0
0
0
2
0
0
0
0
2
2
1
0
2
1
0
1
0
0
1
0
1
0
2
0
1
1
1
0
0
2
1
2
2
0
0
0
1
0
2
2
0
1
0
0
0
0
1
0
1
1
2
0
2
0
0
1
0
0
0
0
2
1
0
0
0
1
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
1
0
0
0
3
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
2
0
3
0
2
0
0
0
1
0
0
0
1
0
0
1
0
1
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
2
2
0
0
0
1
0
3
0
0
0
0
0
0
0
2
0
0
1
2
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
1
3
0
2
0
0
0
0
2
1
1
0
0
2
0
0
1
0
0
1
1
0
1
2
0
2
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
2
1
2
1
0
2
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
1
2
0
2
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
2
0
2
0
0
0
2
1
0
1
0
3
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
4
1
1
0
0
0
2
0
0
0
2
2
0
2
0
1
2
0
2
0
2
0
0
2
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
1
2
1
0
0
0
2
1
0
0
0
0
0
2
1
1
1
0
0
0
0
0
0
2
2
0
0
0
1
0
1
1
0
2
0
0
1
0
0
0
0
0
0
2
3
0
0
0
1
0
2
0
0
0
2
0
3
0
0
0
0
0
0
0
2
1
0
0
1
1
1
2
2
2
2
1
0
0
1
2
0
2
0
2
0
1
2
0
0
0
0
0
0
2
0
0
1
1
0
2
0
2
0
0
0
0
0
1
0
2
2
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
1
1
2
2
0
0
0
0
1
1
1
1
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
1
0
0
1
0
0
2
1
0
0
0
1
1
0
0
0
2
0
1
2
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
2
1
0
1
0
2
0
1
0
1
0
0
2
0
1
1
0
0
1
0
2
0
0
1
0
0
0
0
0
1
0
3
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
2
2
0
0
1
0
2
1
0
2
0
2
1
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
3
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
3
2
0
2
2
1
1
1
0
0
0
2
1
0
0
0
2
1
0
1
0
0
0
0
0
1
1
3
1
0
1
0
1
0
1
0
0
1
2
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
3
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
2
0
1
1
1
1
3
0
0
0
1
1
3
1
0
0
0
0
0
0
0
0
2
0
0
1
2
0
2
0
0
1
0
2
0
2
0
3
0
0
0
0
0
2
1
0
1
2
0
1
0
0
0
2
0
0
1
0
1
2
0
0
0
0
0
0
1
3
0
0
1
1
0
2
0
0
0
0
2
0
1
1
1
1
1
2
2
0
0
2
0
2
0
0
1
0
2
0
0
0
1
0
0
0
1
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
2
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
2
1
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
1
2
0
1
0
0
0
2
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
2
0
0
0
2
0
2
2
0
0
0
1
0
0
0
2
1
0
0
0
0
0
2
0
0
2
1
0
3
2
0
0
0
1
1
0
0
1
0
0
1
1
2
0
2
2
1
1
0
0
0
0
2
1
2
0
0
0
3
1
0
0
0
2
0
0
0
0
0
2
1
2
0
0
1
2
1
0
2
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
2
2
3
0
1
0
2
1
0
0
0
0
2
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
6
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
2
2
2
2
0
1
0
0
2
2
0
0
1
2
0
0
0
0
0
0
2
1
0
0
2
0
0
2
0
1
0
0
0
0
2
1
2
0
0
0
0
3
2
0
3
0
12
1
0
2
0
2
0
0
0
0
0
0
2
2
0
0
2
1
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
4
2
0
0
1
4
0
0
0
0
2
0
4
1
0
0
0
1
3
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
4
0
2
1
2
0
0
0
2
1
0
0
0
0
0
1
0
1
0
1
0
2
3
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
3
2
0
0
0
1
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
1
0
3
2
0
1
1
1
0
0
0
1
0
0
0
0
3
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
2
0
0
1
0
1
2
2
2
0
0
0
0
1
1
0
0
0
0
0
0
0
2
2
1
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
1
0
0
1
0
0
0
2
1
0
2
2
1
5
1
0
0
0
1
1
2
0
2
0
0
0
2
0
1
0
2
0
1
0
1
2
0
0
0
0
0
1
0
0
2
2
2
0
0
0
2
2
0
0
0
2
0
0
2
0
0
3
5
0
1
0
1
0
0
1
2
0
0
1
0
1
0
2
1
2
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
4
0
2
0
0
0
0
1
0
0
0
0
0
2
0
1
1
2
0
0
0
3
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
2
3
1
0
2
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
4
0
0
0
1
1
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
2
2
2
0
0
0
1
0
0
0
3
1
0
0
1
4
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
1
0
0
0
1
0
0
0
2
1
0
0
1
1
4
0
1
0
1
0
0
1
2
2
2
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
2
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
2
2
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
1
1
0
0
2
0
2
3
1
0
2
0
0
0
2
0
0
0
3
1
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
3
0
2
0
0
0
1
2
1
1
0
0
0
1
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
1
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
1
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
6
1
2
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
2
0
0
0
1
0
0
0
4
3
0
2
3
1
1
1
0
0
1
2
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
1
0
0
0
3
2
0
3
1
0
1
1
2
0
1
0
1
0
0
3
0
2
1
0
1
0
0
2
0
0
2
1
1
0
0
3
0
0
2
2
2
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
1
2
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
1
2
1
1
0
0
2
0
0
1
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
2
0
1
2
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
2
0
0
0
0
3
0
1
4
0
0
0
0
2
1
0
0
1
0
0
0
2
0
0
1
2
0
3
0
0
0
1
0
0
3
2
0
0
0
0
0
0
1
1
0
0
3
0
3
0
0
3
0
0
0
0
6
1
0
2
1
0
3
0
0
0
0
0
0
1
0
0
0
1
2
0
1
1
3
1
1
3
0
0
0
0
0
1
0
0
0
2
1
1
0
0
0
2
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
2
0
1
1
0
0
2
0
2
0
0
0
1
1
0
0
0
0
1
0
0
2
0
0
0
6
0
2
0
0
0
1
3
0
1
0
0
0
0
1
0
0
1
1
0
1
0
1
0
1
0
0
0
1
2
1
0
0
1
0
0
0
2
2
0
3
2
0
0
0
1
0
3
0
2
0
0
0
0
0
2
2
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
2
0
0
0
1
1
0
0
1
1
0
1
2
3
1
0
0
2
1
2
2
0
1
0
2
0
0
1
0
5
0
0
0
0
3
0
0
0
2
0
0
2
0
3
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
1
0
0
3
0
2
0
0
0
1
1
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
3
2
0
0
0
0
1
1
1
2
2
0
1
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
1
4
0
1
1
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
3
0
1
0
0
0
1
0
0
1
0
1
0
2
2
0
0
1
0
0
1
1
1
0
0
2
0
2
0
0
0
1
0
0
2
0
1
0
0
0
1
0
0
1
2
2
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
3
0
2
0
0
0
1
0
0
0
0
1
1
2
1
0
0
1
1
0
0
0
0
1
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
1
0
3
1
0
0
2
1
1
0
1
0
0
0
3
2
1
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
2
1
0
0
0
0
2
0
0
2
1
0
2
0
0
1
2
0
0
2
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
2
0
0
1
2
1
0
0
2
0
0
1
0
0
1
0
1
2
0
0
0
0
1
0
0
4
1
0
0
0
0
2
2
1
0
1
0
2
1
1
2
0
0
2
0
2
0
5
2
1
0
2
0
2
0
2
0
1
1
0
1
0
0
1
0
0
0
0
1
0
2
2
0
1
2
3
0
0
0
1
0
2
0
0
0
2
0
0
0
1
0
0
2
1
1
1
0
0
1
0
0
1
2
0
1
2
0
1
0
0
0
2
0
0
0
2
2
0
1
0
1
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
2
1
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
1
1
2
1
0
0
0
0
0
0
1
0
0
2
0
1
2
0
2
2
0
0
0
0
3
0
0
0
0
0
1
1
0
0
0
0
2
0
0
1
1
1
1
0
0
0
0
0
3
2
0
0
2
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
2
3
0
0
2
1
2
0
0
1
2
0
0
3
1
1
0
0
0
0
0
1
1
1
2
2
0
0
0
0
1
0
1
1
1
0
0
2
4
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
3
0
2
0
0
0
0
0
0
1
1
0
0
1
0
0
2
0
0
0
2
0
2
0
1
2
0
2
2
0
0
0
0
1
1
1
2
0
0
2
0
1
0
0
0
0
1
1
0
2
1
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
2
2
0
0
0
2
0
1
0
0
1
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
1
1
1
0
0
2
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
2
4
0
0
0
0
0
0
0
0
0
1
1
1
0
2
2
0
1
2
2
0
1
0
0
2
0
0
0
2
0
0
2
0
2
0
0
0
2
1
2
2
0
2
0
2
0
2
0
2
1
2
0
0
1
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
2
0
2
3
0
1
1
1
0
1
0
0
1
0
0
0
1
0
1
1
3
1
0
2
0
0
0
0
0
4
0
0
0
1
0
0
0
0
2
1
1
0
0
2
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
1
0
0
1
2
0
0
0
1
1
3
0
2
2
1
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
1
0
1
0
1
1
0
0
1
0
1
0
1
0
0
1
0
2
1
0
0
0
0
0
2
0
0
0
2
0
3
2
0
2
0
2
0
0
0
0
1
0
1
1
0
2
0
0
0
1
2
0
2
0
0
2
0
0
1
0
0
1
0
1
0
2
0
0
1
0
0
1
0
1
1
0
2
0
2
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
1
2
0
0
0
2
1
1
0
2
2
0
0
1
0
0
2
2
0
0
0
2
0
0
1
2
2
0
2
0
0
0
0
0
0
2
2
0
0
4
1
1
0
0
0
0
1
0
3
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
2
0
0
2
0
0
2
1
0
1
0
1
0
2
0
0
2
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
2
1
0
0
1
0
0
0
0
1
0
1
0
0
2
0
2
0
0
0
0
0
1
1
1
0
0
1
3
1
2
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
1
0
2
0
0
1
0
2
1
0
0
0
2
0
1
2
2
0
1
0
0
2
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
2
0
3
2
0
0
0
0
2
2
0
3
0
2
0
0
1
2
0
1
0
0
1
1
2
0
1
1
0
2
0
0
0
0
2
0
1
1
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
1
0
0
0
2
0
3
2
0
0
0
0
0
0
0
1
0
1
1
2
0
0
2
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
1
3
0
1
0
2
2
1
0
0
1
0
0
2
0
0
1
0
2
2
1
2
0
0
0
1
2
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
1
2
0
2
2
3
0
0
1
0
0
1
0
0
0
0
0
5
1
2
3
0
1
1
1
2
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
2
1
0
0
0
0
1
0
0
0
0
1
0
1
0
2
1
0
0
0
0
1
1
0
0
0
1
2
0
2
0
2
1
0
0
0
1
0
0
0
2
0
0
1
0
3
0
0
0
0
0
0
0
0
1
2
2
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
1
2
1
0
0
1
0
0
2
2
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
1
1
0
0
0
0
0
0
2
2
2
0
1
0
0
1
0
1
2
0
2
0
0
0
0
2
0
0
0
2
1
0
0
1
0
0
1
0
0
2
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
2
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
1
1
1
0
0
2
1
0
2
2
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
1
0
0
4
1
0
2
0
0
0
0
0
0
0
1
0
0
2
0
2
2
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
4
0
0
1
2
2
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
1
0
0
10
0
2
2
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
3
0
0
1
0
0
0
0
2
0
2
2
2
0
0
3
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
3
0
1
1
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
1
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
2
2
0
0
1
0
0
1
1
2
0
0
2
2
0
0
0
0
1
2
1
0
1
0
0
1
0
2
2
0
0
0
1
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
1
2
0
0
0
0
0
0
0
0
0
0
2
9
1
0
1
0
0
1
0
1
2
2
0
0
1
1
2
0
0
0
2
0
1
1
1
1
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
1
0
2
0
2
0
1
0
2
0
2
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
2
1
0
0
0
2
0
2
0
0
2
1
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
1
2
1
2
0
0
2
0
0
0
1
0
2
0
1
0
0
1
0
1
0
2
1
1
2
0
2
2
0
2
0
0
0
0
0
0
0
1
2
0
2
3
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
2
0
1
3
1
0
0
2
0
0
3
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
2
1
0
2
0
3
1
0
2
1
0
0
1
0
0
0
1
2
1
0
0
0
2
0
0
1
0
0
1
0
0
0
2
2
0
0
0
0
1
1
0
0
1
0
1
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
3
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
3
4
0
0
2
2
0
2
0
0
0
0
0
1
1
0
1
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
1
3
2
0
0
0
0
1
0
1
0
0
2
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
2
0
0
0
0
0
2
0
0
0
0
1
0
1
0
2
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
1
1
2
0
0
0
1
0
0
2
0
1
1
0
0
0
1
0
1
2
0
1
0
0
0
0
0
0
1
2
0
0
0
0
2
0
2
0
1
2
0
2
1
2
0
0
0
1
0
1
2
0
0
0
0
0
2
0
0
1
0
0
1
2
0
0
2
0
0
0
2
0
1
1
0
0
1
0
0
1
0
1
0
0
1
0
0
0
2
0
1
1
1
2
0
0
0
0
0
2
0
0
1
0
0
0
2
1
0
2
0
2
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
3
0
0
0
1
0
1
0
0
0
0
2
1
0
0
0
2
0
4
0
2
1
0
1
2
0
0
0
0
2
2
4
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
2
2
0
0
2
0
1
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
2
1
0
0
1
2
0
2
0
0
2
0
0
0
0
0
2
1
1
0
1
0
0
0
2
0
0
2
1
2
1
0
0
3
2
0
0
0
0
2
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
1
2
0
0
2
0
0
0
2
1
0
2
0
0
0
0
3
0
0
0
0
1
0
1
0
0
0
0
0
2
0
2
0
2
1
0
0
0
2
0
0
1
0
2
1
3
0
0
0
0
0
1
2
0
0
0
0
0
1
0
2
0
1
2
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
2
0
2
0
0
0
2
0
0
0
2
1
0
1
2
0
0
1
1
0
1
2
0
0
1
0
1
2
0
0
3
0
0
2
0
2
0
2
0
0
0
0
2
1
0
1
0
1
2
0
0
0
0
0
0
1
0
0
2
1
0
0
1
0
0
0
0
1
0
0
1
1
2
0
0
1
0
0
1
0
0
0
2
2
2
0
0
0
0
0
0
1
0
2
1
0
0
1
1
0
0
1
0
1
0
0
1
0
0
0
1
0
0
3
0
0
1
1
0
0
2
0
1
0
3
1
0
0
0
2
0
0
0
0
0
1
2
1
0
0
0
1
0
2
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
3
1
0
0
2
0
0
1
0
0
0
2
1
0
0
0
1
2
0
0
0
0
0
1
2
0
2
0
1
1
0
2
1
0
1
0
1
2
0
0
0
1
1
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
1
0
0
0
2
1
1
0
0
0
2
2
1
0
2
2
0
0
0
1
1
2
0
0
0
1
0
1
0
2
0
0
0
1
0
0
0
1
0
3
0
0
0
2
0
2
0
0
2
2
0
2
0
1
2
0
0
0
0
1
2
0
0
1
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
1
1
1
0
0
0
0
4
0
0
1
0
2
0
0
0
0
0
0
2
2
1
0
0
0
2
1
2
2
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
1
0
2
0
1
0
1
1
2
0
0
2
3
1
0
0
0
2
0
1
0
0
2
0
0
0
1
0
1
2
0
4
0
0
1
1
2
0
0
0
0
2
0
0
0
0
2
2
1
0
0
0
0
0
0
0
5
5
0
0
1
0
1
2
4
2
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
1
0
0
0
1
1
0
2
4
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
1
0
0
0
3
1
0
0
0
0
1
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
2
2
2
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
1
1
0
0
0
0
3
0
0
2
0
0
0
1
0
0
2
0
1
0
0
1
0
1
0
0
1
0
0
0
0
1
0
3
0
2
0
0
0
1
2
1
1
0
2
1
0
1
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
1
2
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
3
0
3
0
0
2
0
0
2
0
1
0
0
1
2
0
0
1
3
0
2
1
2
0
1
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
1
0
1
0
0
0
2
2
2
1
1
0
0
2
2
2
2
0
1
0
0
1
0
0
0
1
0
0
2
0
0
2
0
1
1
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
2
0
2
0
2
2
1
0
0
0
0
1
0
0
0
1
1
1
2
0
0
1
2
1
0
0
1
0
1
0
0
2
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
2
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
2
0
0
2
0
1
0
2
0
1
0
0
1
0
0
3
0
0
0
0
1
1
5
2
0
0
0
4
0
1
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
1
1
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
1
0
0
1
1
0
2
0
0
0
0
0
1
0
1
0
0
2
0
0
1
2
0
0
2
1
2
0
0
0
0
0
0
0
1
2
3
0
1
0
2
0
0
0
1
0
1
0
2
1
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
2
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
1
1
1
0
0
0
0
0
1
2
0
0
0
0
0
1
0
3
0
0
0
0
1
1
0
0
1
2
0
0
0
1
0
0
1
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
1
2
2
1
0
0
2
0
0
0
2
0
0
0
0
2
2
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
1
0
2
2
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
1
0
0
1
2
0
2
0
0
2
0
2
0
1
1
0
0
0
0
0
2
1
0
1
0
2
1
0
0
0
0
1
0
0
0
0
0
2
0
1
5
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
1
0
1
0
0
0
1
2
0
1
0
1
0
3
0
2
1
0
0
0
0
1
1
1
1
1
2
1
2
0
1
0
2
0
2
0
2
0
1
0
1
1
0
1
0
0
0
1
2
0
1
0
0
1
0
2
0
0
3
0
2
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
2
0
1
0
0
0
0
2
0
0
0
2
0
0
2
1
2
3
1
0
0
0
0
2
0
2
2
3
0
2
1
2
0
0
2
0
1
0
0
1
0
2
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
2
2
0
0
1
1
2
0
2
0
0
0
0
1
1
0
3
0
2
0
0
0
0
0
2
0
1
0
0
1
2
2
0
2
0
0
0
0
2
0
0
0
0
0
0
2
1
0
2
2
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
3
1
0
0
1
1
0
0
1
2
0
2
0
1
0
0
0
3
0
0
1
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
2
1
1
0
0
0
2
1
2
0
0
0
0
1
2
1
1
1
0
0
1
1
1
0
2
4
0
1
0
2
2
2
0
0
2
2
0
1
0
0
0
0
0
1
1
1
1
1
1
0
0
0
0
2
0
1
0
0
0
0
0
1
0
2
2
0
0
0
0
1
0
0
1
0
1
0
0
0
2
1
0
0
0
0
0
0
0
1
2
0
2
2
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
1
2
0
2
0
2
2
0
1
0
0
2
0
2
0
0
0
2
2
0
1
1
0
0
0
0
1
0
0
2
0
0
0
0
0
1
2
0
2
2
2
2
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
1
2
0
1
1
0
2
2
0
2
0
0
2
0
0
0
0
2
1
0
1
0
2
1
1
1
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
1
0
0
0
2
2
2
1
1
0
0
2
1
0
0
0
0
0
0
1
1
1
0
1
0
1
0
1
0
0
2
0
1
3
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
1
0
0
2
0
0
0
0
0
0
3
0
0
0
0
1
0
2
1
0
0
1
0
0
2
0
2
1
0
3
0
2
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
1
0
0
0
1
2
0
1
1
0
1
0
0
1
2
0
0
2
0
0
0
1
2
1
0
2
0
1
1
0
0
0
0
0
3
0
0
0
2
0
0
2
1
1
0
0
0
0
0
0
0
0
2
0
1
0
1
0
2
0
0
1
2
2
0
0
0
0
2
2
0
2
0
0
0
0
0
2
0
0
2
2
0
1
2
2
0
0
1
2
0
1
0
1
2
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
4
0
0
1
0
0
0
0
1
0
1
0
2
0
0
0
2
0
1
0
2
0
0
1
0
2
0
0
2
1
0
0
1
0
2
0
2
1
0
0
0
0
0
1
1
0
1
0
2
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
2
2
0
1
2
0
0
0
2
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
2
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
2
2
1
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
1
1
0
0
2
0
0
1
0
0
0
1
1
2
1
2
1
0
0
2
0
3
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
1
2
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
2
0
0
2
1
0
1
0
2
0
2
0
0
2
0
0
0
2
0
0
0
2
0
2
2
0
1
1
0
0
0
2
1
0
0
0
0
2
0
1
1
0
0
1
2
0
2
2
0
2
1
0
1
0
1
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
6
0
1
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
1
1
2
1
2
2
0
1
2
1
3
0
0
0
0
0
1
2
0
1
0
0
1
0
0
0
1
0
2
0
2
2
2
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
4
1
0
0
1
0
1
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
1
0
1
0
1
2
1
1
0
2
0
0
2
3
0
3
0
0
2
0
0
0
0
0
1
1
0
0
1
3
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
2
0
0
0
1
0
2
0
0
5
0
2
3
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
3
1
1
0
1
1
2
0
0
0
2
0
1
0
0
2
2
2
2
1
1
0
1
1
0
1
2
2
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
2
3
0
0
2
0
0
0
0
0
0
0
2
0
1
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
2
0
2
1
1
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
1
1
1
1
0
1
0
0
0
1
0
0
2
1
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
2
2
0
1
1
0
0
0
0
0
2
0
0
0
1
0
2
0
2
3
0
1
1
1
0
1
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
1
2
1
0
0
2
0
0
0
0
0
0
0
0
0
2
1
1
2
1
2
0
1
0
0
0
2
0
2
0
0
0
0
1
3
2
1
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
1
2
0
0
0
0
0
1
0
0
2
0
0
0
1
1
2
0
0
0
0
0
0
2
0
0
2
0
1
0
2
2
2
0
1
0
0
2
1
2
0
0
0
0
0
1
1
0
1
2
0
2
1
2
2
0
0
0
1
0
0
3
0
0
2
0
0
2
1
0
0
1
2
0
0
0
0
2
1
1
2
0
0
1
1
2
0
0
0
0
1
1
1
0
2
2
0
2
2
0
0
0
1
1
0
0
1
0
1
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
2
0
0
0
2
1
2
0
0
0
0
1
0
2
1
0
0
0
0
0
7
0
0
3
1
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
1
0
0
2
2
0
0
0
2
0
2
0
0
1
0
0
0
3
0
0
0
0
0
1
2
2
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
2
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
5
2
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
2
0
1
0
0
1
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
1
2
0
1
1
0
0
0
0
0
0
8
0
2
1
0
1
0
0
1
0
2
0
0
2
0
0
0
0
0
0
1
1
0
0
0
2
2
0
0
2
1
0
1
0
0
2
1
0
2
1
0
1
0
1
2
2
1
0
0
0
1
0
0
0
0
2
0
0
0
0
3
0
2
0
1
2
0
2
0
2
0
0
1
0
2
0
1
0
0
0
1
1
0
2
2
1
0
0
0
0
0
0
2
0
2
2
2
2
0
1
0
0
2
0
0
0
0
2
0
2
0
0
0
0
2
2
2
0
2
0
0
0
1
0
1
0
1
2
0
0
0
0
2
2
0
0
1
0
0
0
2
2
1
2
1
0
0
2
2
0
0
0
0
1
1
1
2
0
0
0
0
1
0
0
1
1
2
3
0
0
1
0
0
0
2
1
0
0
0
0
0
0
2
0
0
1
2
1
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
9
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
2
2
0
0
3
0
0
2
0
3
0
0
0
0
1
0
2
0
0
0
0
0
1
1
1
2
0
1
2
2
2
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
2
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
2
2
1
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
1
2
2
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
2
1
0
0
2
0
1
1
0
2
0
2
3
0
0
0
0
0
0
0
2
0
0
0
0
2
1
1
2
0
1
2
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
1
2
3
0
0
2
0
0
0
1
0
0
0
1
1
2
1
3
2
1
0
0
0
0
0
0
2
1
0
0
0
1
1
0
0
0
1
2
0
1
0
0
0
0
2
0
1
1
3
0
1
9
0
1
0
1
0
0
0
0
2
0
0
0
2
1
0
0
3
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
2
1
2
0
2
0
1
0
0
1
2
0
0
2
0
0
1
1
0
0
0
0
0
1
1
0
2
2
2
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
7
1
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
2
0
2
0
0
1
0
3
1
1
0
2
0
2
0
0
0
1
1
1
2
0
2
1
0
0
0
0
0
2
0
3
0
0
1
2
0
0
0
2
1
0
2
0
0
1
0
0
0
1
1
0
1
0
0
0
0
1
2
0
0
0
1
2
0
0
1
0
1
0
1
0
2
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
3
0
0
0
0
2
0
2
2
0
2
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
1
4
0
0
0
1
1
1
2
0
0
2
0
0
0
0
1
0
2
0
1
0
0
1
0
0
0
1
0
0
1
0
0
3
0
1
0
2
1
1
0
2
2
0
0
0
0
0
0
2
1
0
1
0
1
0
1
1
1
0
0
0
0
1
2
0
1
1
2
0
2
0
1
1
1
0
2
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
2
2
1
1
0
0
0
2
0
0
0
0
1
0
2
2
2
1
0
0
0
2
0
0
1
2
0
0
0
2
0
0
0
2
2
2
0
0
1
0
0
0
1
0
0
0
0
2
2
0
0
2
1
0
1
1
2
0
0
3
1
0
1
1
0
1
0
0
0
0
1
0
1
1
0
0
2
1
2
0
0
2
1
1
0
0
2
1
0
0
2
0
2
0
2
0
0
0
2
0
2
0
2
1
0
0
0
0
0
1
0
2
0
0
0
0
1
2
0
2
0
1
1
0
1
0
0
1
1
1
1
0
0
0
0
1
1
0
1
0
0
0
0
0
2
0
0
1
0
0
1
1
2
0
2
1
2
1
2
1
0
0
1
0
0
2
0
0
2
0
0
1
0
0
0
0
1
2
0
0
2
0
1
2
2
1
0
2
2
1
0
0
1
2
2
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
1
1
0
0
1
5
0
0
1
0
0
0
1
0
0
2
1
2
0
2
0
1
1
2
1
0
1
0
2
0
0
0
1
0
0
0
1
3
0
2
0
0
0
2
0
0
0
1
1
0
0
2
2
1
0
0
0
1
1
1
0
2
0
1
0
2
0
0
0
0
0
3
0
3
2
2
0
0
2
0
0
2
2
2
0
0
0
0
2
4
0
3
1
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
2
0
0
1
1
0
0
0
0
0
2
2
0
1
0
0
2
2
1
4
0
0
0
0
0
1
2
0
0
1
0
0
0
2
0
1
2
0
2
0
0
2
2
3
4
0
0
0
0
2
0
1
0
0
0
0
3
0
1
1
1
0
0
0
3
1
1
0
0
2
0
2
0
0
0
0
1
0
0
2
1
4
0
0
1
1
1
0
2
0
1
1
2
2
0
1
1
0
1
1
2
0
0
2
0
1
0
0
2
0
0
0
1
1
1
1
0
1
0
0
0
0
2
0
0
3
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
2
0
0
0
1
0
1
0
2
2
1
1
0
2
1
1
0
0
0
0
0
1
0
0
0
0
1
1
2
2
1
1
0
0
1
0
2
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
1
0
0
0
2
1
2
0
1
0
1
0
0
1
0
0
0
1
1
1
0
0
0
0
0
1
0
0
1
0
0
1
1
2
0
0
1
0
0
0
0
2
0
0
0
2
1
0
2
0
0
0
0
0
1
0
0
1
2
0
2
0
2
0
0
0
3
2
2
0
0
0
1
0
2
0
0
0
1
1
0
0
1
0
0
2
1
0
0
0
0
0
0
0
3
1
0
0
1
0
1
0
2
1
0
0
0
0
0
0
0
2
1
1
0
1
0
0
1
1
2
0
1
0
0
0
2
3
2
1
0
0
1
0
2
1
0
1
2
0
0
0
1
3
0
1
2
2
0
0
2
1
0
0
0
0
2
0
0
0
0
2
0
2
0
0
2
0
0
1
2
1
1
0
2
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
1
1
0
1
1
0
2
0
1
1
0
1
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
7
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
1
1
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
1
4
2
0
0
2
0
0
0
2
0
2
0
0
1
1
2
0
0
0
0
0
3
0
1
0
0
2
2
0
0
1
3
1
0
0
0
1
0
0
0
2
1
1
0
1
2
2
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
1
2
1
0
0
0
0
0
1
0
0
0
2
0
0
1
0
2
1
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
1
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
2
1
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
1
4
0
0
0
0
2
7
0
2
1
0
0
0
0
2
2
2
2
0
0
0
0
1
2
1
2
0
0
3
0
0
2
1
1
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
1
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
2
0
3
0
0
2
0
0
2
1
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
1
0
1
0
1
2
0
1
0
0
0
0
0
0
0
2
1
0
2
3
0
1
2
1
1
1
0
0
0
0
0
1
1
1
0
1
1
1
0
2
0
0
0
0
1
0
2
3
0
0
2
0
0
0
0
0
0
1
1
0
0
1
0
0
2
2
0
1
1
2
1
0
0
0
2
2
0
1
1
0
0
0
0
0
3
0
0
0
1
0
2
2
1
2
0
0
2
0
0
2
1
2
0
2
2
0
0
1
1
0
0
0
0
0
3
1
0
0
0
2
0
0
0
0
1
0
0
0
1
0
1
0
2
0
0
0
0
0
0
1
2
0
0
1
0
0
2
2
0
0
4
0
1
0
0
0
2
0
0
0
0
0
0
2
0
1
1
0
0
0
0
2
0
0
1
0
1
0
0
1
0
0
3
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
1
0
0
2
1
1
0
0
0
0
0
3
0
0
2
0
0
0
0
1
1
0
2
1
1
3
0
0
2
0
0
1
0
0
0
1
0
2
0
0
0
0
0
1
0
0
2
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
1
0
0
1
1
0
0
0
1
0
2
0
1
0
0
1
0
0
1
2
2
0
0
0
0
0
0
2
0
0
2
0
0
1
2
0
0
1
0
1
0
0
1
0
2
0
0
0
1
0
2
1
0
0
0
0
0
2
1
0
1
0
2
1
0
0
0
0
2
0
0
0
0
2
0
1
0
1
0
1
0
2
0
0
0
0
2
0
0
0
2
0
0
1
0
1
0
0
2
0
0
1
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
1
1
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
2
1
0
1
3
1
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
2
0
0
2
1
1
0
0
0
0
0
2
1
1
0
0
1
0
2
0
0
0
0
0
1
0
4
0
2
2
0
0
2
0
0
0
2
0
1
0
0
3
0
0
0
0
0
1
1
1
0
0
2
0
2
2
0
0
2
0
0
0
2
0
1
1
0
0
0
0
2
1
0
2
1
0
0
0
0
0
1
2
0
0
1
0
1
0
1
0
0
0
0
2
0
3
0
0
0
0
0
0
1
0
0
0
0
0
1
5
1
0
1
0
0
0
1
1
2
0
0
0
2
0
0
1
0
0
0
2
2
2
1
0
1
0
0
0
0
2
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
3
0
1
0
0
1
0
2
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
2
0
2
0
0
2
0
2
2
0
0
1
0
2
0
0
1
1
1
0
0
0
4
0
0
0
0
0
0
0
0
1
2
0
2
1
0
1
0
0
0
1
0
1
0
0
0
2
0
0
0
0
1
0
0
1
2
0
0
0
2
1
2
0
2
0
0
0
1
1
1
1
2
2
0
0
0
2
1
2
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
2
1
2
0
0
1
0
1
0
0
2
2
2
0
0
0
2
2
0
1
1
1
2
0
0
1
1
2
2
2
0
0
0
2
1
0
0
2
2
2
0
1
1
2
0
0
1
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
2
1
2
1
1
0
3
0
1
0
0
3
0
2
1
0
2
0
1
0
2
0
0
0
0
0
1
2
3
0
2
0
0
1
0
0
2
0
2
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
2
1
0
2
2
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
1
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
1
0
1
1
2
0
1
2
0
0
0
3
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
1
1
0
0
2
1
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
4
0
0
0
0
0
0
1
0
4
0
2
2
0
2
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
2
1
2
0
0
0
0
0
2
0
0
1
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
3
0
0
1
0
0
5
0
2
0
0
1
0
0
1
0
0
0
0
2
0
0
2
1
1
0
0
1
0
2
1
0
0
0
1
0
0
0
0
0
1
0
2
0
0
2
2
0
1
0
1
0
0
0
1
2
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
1
0
0
2
2
0
0
1
1
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
1
2
0
0
0
2
1
0
2
0
0
2
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
4
0
0
2
0
0
1
1
0
2
0
0
1
1
0
0
1
1
1
0
0
1
0
0
0
1
3
1
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
2
2
0
0
2
2
0
0
0
2
0
2
1
0
2
1
1
0
1
2
0
2
0
0
1
0
0
0
1
0
0
3
0
0
2
0
0
0
0
2
0
0
0
0
3
2
1
0
0
0
5
2
1
0
2
1
0
0
0
1
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
3
0
1
1
1
0
0
0
0
0
0
2
2
1
0
2
2
1
0
1
1
0
2
1
0
0
0
1
0
0
2
2
0
0
1
0
0
0
2
0
2
1
2
0
0
0
0
1
0
0
0
0
2
0
2
0
0
1
1
0
0
0
0
0
1
3
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
1
0
0
3
0
0
1
2
0
2
0
1
0
2
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
1
0
0
0
1
0
1
2
0
0
1
0
0
1
0
1
2
0
0
0
1
0
1
0
1
0
0
0
1
2
5
0
2
2
0
0
2
1
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
1
2
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
2
1
1
0
0
1
1
0
2
0
1
0
0
0
1
0
2
0
0
2
0
1
2
1
2
0
0
2
0
1
2
1
0
0
0
0
0
0
0
0
4
0
1
0
2
0
0
1
1
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
1
1
2
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
1
2
0
2
0
2
0
1
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
1
8
1
2
1
0
1
1
0
0
0
0
0
0
2
0
1
2
0
0
0
1
1
0
2
0
0
0
0
2
0
0
2
1
2
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
2
1
0
2
0
0
2
2
0
3
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
4
0
0
2
0
0
0
1
0
0
0
3
1
0
1
0
2
2
2
1
0
0
0
0
0
0
0
2
2
1
2
0
0
0
0
0
0
2
1
1
0
0
1
0
2
5
0
0
0
1
0
1
0
1
0
0
0
1
1
1
2
1
1
2
2
0
0
0
0
1
2
0
0
2
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
1
1
0
0
2
0
2
0
1
0
1
1
0
1
0
0
0
0
0
2
0
0
0
1
1
1
0
0
2
2
2
0
0
0
1
0
0
0
0
1
0
2
0
0
2
2
3
0
2
0
0
2
1
0
0
0
0
0
0
2
2
2
2
0
0
0
1
0
3
0
0
1
0
0
0
0
1
0
2
0
3
1
0
2
0
1
1
0
1
2
1
2
2
0
1
0
0
1
1
0
1
0
2
1
2
0
2
4
0
0
0
1
2
2
0
0
0
0
0
2
0
2
0
0
1
2
0
0
0
0
2
2
1
1
4
0
0
0
0
0
4
0
0
1
1
0
0
2
3
0
0
0
0
1
1
0
0
2
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
1
3
0
0
0
0
0
1
0
1
0
2
3
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
1
2
3
2
2
2
2
0
0
1
0
0
1
0
1
0
0
2
0
1
1
0
0
1
0
2
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
4
0
1
1
0
0
1
1
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
1
2
0
0
0
1
1
1
0
0
0
1
2
2
0
0
0
0
0
2
0
1
0
0
2
0
1
2
1
0
0
0
0
1
1
0
0
0
2
0
0
0
0
1
0
2
0
0
2
2
0
0
1
0
0
2
0
0
1
0
0
0
0
2
1
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
1
0
1
0
0
1
0
1
1
0
0
0
2
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
2
2
0
1
3
2
1
0
1
1
0
1
0
0
2
2
0
0
1
2
0
0
1
2
0
0
0
0
2
0
2
0
1
2
0
2
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
1
1
0
0
3
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
1
0
1
0
2
0
0
1
0
2
0
3
0
2
1
2
0
2
0
0
2
1
2
1
0
0
1
0
0
2
0
0
2
0
1
0
2
0
0
0
4
2
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
2
1
2
0
2
0
0
0
3
0
0
1
1
0
1
1
0
2
0
0
0
0
2
0
1
1
0
1
0
0
4
2
0
0
1
1
6
2
0
2
0
0
0
0
1
1
1
0
1
2
0
2
0
2
1
0
0
0
1
0
3
0
1
2
1
0
0
0
0
3
0
2
1
0
0
0
1
2
0
1
0
0
0
0
0
1
2
1
0
0
0
1
0
1
0
2
2
0
0
0
2
1
0
2
0
0
0
0
0
0
1
2
0
0
2
0
4
2
0
1
1
2
0
0
0
1
1
0
0
0
2
1
0
0
0
1
0
0
3
2
0
0
0
0
0
0
2
1
0
0
0
0
2
1
2
0
0
0
5
1
0
0
2
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
1
3
0
2
0
0
0
0
0
0
2
0
4
2
1
2
0
0
0
0
0
0
0
1
1
0
2
0
1
3
1
0
0
0
1
3
1
2
0
0
1
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
1
2
1
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
1
0
2
0
1
0
1
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
2
1
2
0
0
2
2
0
0
0
0
3
1
0
0
0
0
1
1
0
0
0
0
2
1
1
0
0
0
0
1
0
2
0
0
0
2
0
2
0
2
0
2
0
0
0
2
1
1
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
2
0
1
1
2
0
0
0
1
2
2
2
2
1
2
0
0
0
0
1
0
0
2
2
4
0
2
0
2
2
1
2
2
0
0
0
3
0
1
1
0
0
2
0
2
2
0
1
0
0
2
0
0
2
0
2
0
1
0
0
0
1
0
0
0
1
3
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
1
2
2
0
0
0
1
0
1
2
0
0
0
2
1
0
0
2
1
1
0
3
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
2
0
0
1
2
0
0
1
1
0
0
0
1
2
0
0
2
0
1
0
0
1
1
0
0
0
1
1
0
0
2
0
0
2
2
1
0
0
1
0
2
0
0
2
1
0
0
0
0
0
3
0
0
0
0
2
1
0
1
0
2
0
0
0
0
2
2
1
1
1
0
0
0
0
0
1
0
2
0
0
0
3
0
0
0
2
0
2
0
0
2
1
0
0
0
0
0
0
2
0
1
1
0
0
0
1
0
2
0
0
0
2
0
0
0
0
1
0
1
1
1
0
0
1
0
1
1
3
0
0
1
0
0
0
2
3
1
1
1
2
0
0
0
1
3
1
1
0
0
0
0
0
2
1
0
0
2
2
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
9
1
0
0
1
0
0
2
0
1
2
3
0
2
0
0
0
1
1
0
1
2
0
0
0
0
0
0
0
2
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
2
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
1
1
1
2
0
2
2
3
0
0
0
0
2
0
1
2
2
0
0
0
1
1
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
2
0
0
0
1
1
0
1
0
0
0
1
1
1
0
0
0
1
2
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
4
2
0
2
0
0
1
0
0
1
0
0
0
2
1
3
1
0
0
0
0
3
0
0
0
0
1
0
1
0
0
2
1
2
0
1
1
2
0
2
2
0
0
0
0
2
0
2
0
0
0
0
3
0
0
2
1
0
1
2
1
0
0
0
0
0
0
0
0
1
1
0
2
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
2
0
0
0
0
2
0
0
0
0
1
2
2
0
0
0
2
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
6
0
0
2
0
0
2
0
0
0
0
0
2
0
1
0
1
0
0
0
0
2
1
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
3
2
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
7
0
0
2
0
2
0
2
2
0
0
0
0
1
1
0
0
0
1
2
2
1
2
0
0
0
1
1
0
0
0
1
2
0
1
0
3
0
0
3
0
1
0
0
4
0
0
0
0
2
0
0
0
0
1
1
0
2
2
0
0
0
0
0
10
0
2
0
0
0
0
1
2
0
0
2
0
0
2
0
2
2
0
1
0
0
2
0
0
3
6
0
1
0
0
0
0
1
0
1
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
1
0
2
2
2
2
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
1
0
0
1
0
0
1
2
0
1
0
0
0
1
3
0
0
2
1
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
2
1
0
2
0
0
1
2
4
0
0
0
0
1
0
0
2
0
2
0
0
2
0
0
0
3
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
2
0
1
0
0
2
0
0
0
1
1
0
0
0
0
1
2
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
2
2
2
1
0
0
2
0
3
0
2
0
2
2
0
0
0
2
2
0
0
0
2
1
0
0
0
0
0
1
0
1
1
2
0
0
0
1
2
0
0
0
0
0
0
3
0
0
3
1
0
1
0
0
0
1
4
2
1
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
1
0
2
0
0
0
0
1
0
0
2
1
2
2
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
3
0
0
0
2
1
2
0
2
0
0
0
1
0
0
0
0
2
1
3
0
0
2
0
0
1
0
0
2
2
1
0
2
1
0
2
0
0
0
3
0
2
1
0
0
1
2
1
2
0
0
0
0
1
1
0
0
2
2
1
0
1
0
0
0
0
0
1
0
0
0
2
2
0
0
0
3
2
2
1
0
0
2
0
2
0
0
1
0
0
0
0
0
0
2
2
0
2
1
0
0
1
1
0
2
0
1
2
1
0
1
0
0
0
2
2
0
0
0
1
0
0
0
2
0
0
2
0
2
1
1
0
2
0
0
0
0
3
2
0
1
0
0
0
1
0
1
0
1
0
1
0
1
3
0
1
0
0
4
2
0
1
0
0
0
0
0
0
0
2
0
0
1
0
1
1
0
1
1
0
0
0
0
0
1
1
2
0
0
1
0
0
0
1
0
0
0
0
1
1
0
2
1
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
3
0
0
1
1
0
0
0
0
2
0
2
0
0
2
3
0
1
0
0
2
0
2
0
0
0
0
1
0
0
0
2
2
0
1
0
0
0
2
0
0
0
0
0
0
1
0
1
1
2
2
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
3
1
0
0
1
0
0
2
0
0
1
2
0
0
0
0
0
1
0
0
3
0
1
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
1
3
0
0
0
0
0
1
0
2
1
0
0
0
0
1
0
1
0
2
1
0
0
0
0
0
0
0
0
1
0
2
2
4
0
2
0
0
0
4
1
0
1
2
0
0
0
0
2
0
0
1
0
1
0
0
0
2
2
2
0
0
0
0
0
1
0
0
2
1
0
2
1
0
0
0
0
1
0
2
1
0
0
0
1
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
1
2
0
0
1
0
1
0
2
2
0
2
1
1
0
0
0
3
0
0
2
1
0
0
0
0
2
1
0
0
1
0
0
0
0
0
2
2
1
0
0
0
1
1
1
2
1
0
2
1
2
0
0
1
0
1
2
0
0
0
0
0
1
0
4
0
3
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
2
1
0
0
0
0
0
0
1
0
0
0
1
1
1
1
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
2
1
0
0
0
0
1
0
2
0
0
2
0
2
1
0
0
0
2
0
0
2
1
1
0
0
2
2
0
0
1
2
0
0
1
0
0
2
0
0
1
0
2
2
5
0
2
1
0
0
1
0
2
0
0
0
2
0
0
0
5
0
0
0
1
0
2
1
0
2
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
1
1
1
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
1
0
0
2
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
2
1
1
3
2
0
0
2
1
0
1
0
0
0
0
3
2
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
2
0
2
2
1
0
0
1
0
0
1
3
1
0
2
1
0
0
0
0
0
3
0
2
0
0
1
0
0
0
0
0
2
2
1
0
0
0
1
1
2
0
3
1
1
0
0
0
0
0
0
0
0
0
3
0
0
0
2
2
1
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
2
0
0
2
0
1
0
0
0
0
2
0
0
2
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
2
0
4
0
1
0
0
0
0
0
1
0
0
0
1
0
2
0
2
0
0
0
2
0
0
0
1
2
3
1
1
0
0
2
2
0
0
0
2
2
1
1
0
0
0
0
0
0
1
0
1
0
0
2
0
2
0
0
1
1
0
0
0
0
1
2
0
2
0
0
0
0
1
0
0
0
0
1
0
1
0
0
2
0
0
2
2
0
0
0
1
4
0
0
0
0
0
0
2
0
2
0
0
1
0
1
2
0
1
0
1
0
1
2
1
1
1
0
1
0
2
0
0
0
0
2
0
0
1
1
1
2
0
1
1
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
2
0
2
1
0
1
1
0
0
0
2
0
0
1
0
0
0
2
0
0
2
0
0
0
2
0
1
0
0
2
1
1
4
0
1
0
0
1
0
0
2
0
2
1
1
0
0
0
0
5
0
0
0
2
2
0
0
0
3
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
1
0
0
0
1
1
0
2
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
1
0
0
0
0
2
0
0
0
0
2
2
2
0
2
0
0
1
2
0
0
0
2
2
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
3
1
0
0
0
0
1
0
0
2
0
2
0
0
0
0
1
0
1
0
0
2
2
0
0
0
0
1
2
0
1
0
1
2
0
0
0
2
2
2
0
0
0
2
2
2
1
2
0
0
0
1
0
0
0
2
0
0
2
1
9
1
0
1
0
0
0
0
2
2
0
0
0
0
0
0
3
2
0
1
2
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
2
1
0
4
1
0
0
0
0
0
0
2
2
0
1
1
2
0
2
0
1
0
2
0
0
0
0
0
0
2
0
0
1
1
0
2
1
1
0
1
0
1
2
2
0
0
0
2
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
3
0
0
0
0
0
2
0
0
1
0
0
2
0
2
2
0
0
2
0
1
0
0
0
2
2
0
0
0
0
0
0
2
0
2
2
0
1
1
0
0
2
0
0
0
0
0
1
0
0
0
0
1
1
0
1
1
1
1
1
0
1
1
0
2
0
0
2
4
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
2
0
0
0
0
1
2
0
0
0
0
1
0
2
0
0
0
1
0
0
2
0
0
1
0
0
0
1
0
2
0
1
0
0
0
2
0
0
0
0
1
0
0
2
0
2
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
1
0
0
0
2
1
0
0
0
0
0
1
0
0
2
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
1
2
0
1
2
0
3
2
0
0
0
1
0
1
1
1
2
1
1
0
0
0
1
2
0
0
0
0
0
2
0
1
0
0
0
0
1
1
0
0
0
2
0
2
1
0
0
0
0
1
0
2
0
0
1
1
0
0
0
0
0
2
0
1
0
0
0
2
0
4
0
1
0
0
0
0
0
2
2
0
2
0
0
2
2
0
1
0
1
2
0
0
3
0
0
2
0
0
0
0
1
0
0
0
1
1
0
1
0
2
0
2
0
0
0
0
0
0
0
3
0
2
0
2
0
2
0
1
0
2
0
0
0
0
0
0
1
1
0
2
0
0
1
2
0
1
1
1
0
1
0
0
1
0
0
0
0
0
0
1
3
0
0
1
2
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
2
3
0
1
1
0
2
0
0
0
0
0
0
0
3
0
2
3
0
1
2
0
0
0
4
2
0
0
1
2
0
0
0
2
2
0
0
2
2
2
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
1
0
2
0
2
0
1
1
2
2
2
1
0
2
0
0
0
1
1
0
0
1
2
1
0
0
0
1
2
0
0
2
0
1
2
0
0
0
0
0
1
0
2
0
0
0
0
0
1
3
1
0
1
0
2
0
2
2
1
0
0
0
0
2
1
0
1
0
1
0
0
1
1
1
0
0
1
0
2
1
1
2
2
0
2
1
2
1
0
1
2
0
0
0
0
1
0
0
1
0
0
1
0
0
2
2
1
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
1
0
2
0
2
1
2
0
0
0
3
0
0
0
0
0
0
0
1
0
1
0
2
0
1
0
2
0
0
1
2
1
2
0
2
2
0
0
0
0
1
0
2
2
0
1
1
1
0
0
0
2
2
0
0
1
1
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
1
3
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
3
2
0
0
0
1
1
0
0
4
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
4
0
0
1
0
0
0
1
1
2
0
0
0
0
0
1
0
1
1
3
0
0
0
0
0
2
0
0
0
0
2
0
1
1
0
1
0
0
1
1
1
3
1
1
2
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
6
0
1
0
0
0
0
0
1
0
0
2
1
0
0
3
0
0
1
0
0
2
1
1
1
2
0
2
0
0
3
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
2
1
0
0
2
1
2
1
0
0
0
1
0
1
0
0
0
2
2
0
2
2
0
0
2
1
1
3
0
0
0
2
0
0
3
0
0
0
1
0
0
0
1
0
3
0
0
2
0
0
1
1
2
0
1
2
1
0
2
0
0
0
2
0
2
0
0
0
2
3
0
0
0
1
1
0
1
2
0
0
1
1
1
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
2
0
0
0
1
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
1
2
1
1
2
1
0
0
1
0
0
0
0
0
1
0
0
2
2
0
0
0
0
3
0
2
0
1
0
2
0
7
0
0
1
0
0
2
2
2
0
1
0
1
0
0
0
2
0
1
1
0
0
1
0
0
1
0
3
1
1
0
2
4
0
2
1
0
0
1
0
0
1
0
2
1
3
0
1
0
0
0
3
0
0
0
2
0
0
2
0
1
0
2
0
0
0
3
2
0
2
1
0
1
2
0
0
2
0
0
0
0
1
2
0
2
0
2
0
0
3
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
1
1
0
0
0
0
0
0
0
0
1
2
0
0
0
3
0
0
0
2
0
1
0
0
3
0
0
0
2
0
0
2
0
1
0
0
0
2
0
0
0
1
1
0
1
0
1
0
0
3
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
1
2
0
0
1
0
0
1
0
2
0
1
1
2
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
2
2
2
0
0
0
0
1
0
0
0
2
0
0
2
2
1
0
1
0
0
0
0
0
0
1
2
1
0
0
0
1
1
0
0
0
0
2
0
0
0
0
1
1
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
2
0
0
0
0
2
1
0
0
1
0
0
0
0
1
0
3
1
2
1
0
0
1
0
2
0
1
2
0
1
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
3
1
0
0
2
1
3
2
1
2
0
0
1
2
0
0
1
0
0
0
0
0
0
0
2
3
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
2
2
2
2
1
0
0
0
0
0
0
0
1
1
0
0
2
1
0
2
0
0
0
1
0
0
1
0
0
0
0
1
1
2
0
0
0
2
0
2
0
0
1
1
0
0
0
0
1
0
0
0
2
1
0
1
2
0
1
1
0
0
0
1
0
0
1
0
0
0
1
2
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
2
1
2
0
0
0
2
1
0
0
1
2
1
0
0
2
0
0
0
1
0
0
2
1
1
0
1
0
2
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
1
0
2
0
0
1
0
2
0
0
0
2
1
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
3
0
0
1
0
2
0
0
2
0
0
0
2
0
1
2
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
1
0
0
1
0
0
2
0
0
0
0
0
1
2
1
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
1
2
1
1
0
0
0
10
0
1
0
0
1
0
0
0
0
2
2
2
0
0
1
1
0
0
0
2
1
1
0
0
4
0
0
0
0
0
9
0
1
0
0
0
0
0
0
0
2
6
0
0
0
0
3
0
0
0
0
0
1
0
1
0
4
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
2
0
3
0
0
2
0
3
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
2
1
0
2
0
0
2
1
2
0
1
0
1
0
2
2
0
0
0
2
0
0
0
1
0
0
2
1
2
1
2
0
0
0
2
0
0
0
0
1
0
2
0
1
3
0
0
2
0
2
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
4
2
0
1
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
1
1
2
1
0
2
0
1
2
0
0
1
0
0
0
1
2
0
0
2
0
0
1
1
0
0
0
1
0
0
1
1
0
0
1
2
0
0
0
1
0
3
0
0
0
0
0
1
3
1
3
0
0
1
1
0
0
1
0
4
1
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
1
1
0
0
0
2
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
1
2
3
0
0
1
0
2
1
1
1
1
0
0
0
0
0
0
0
0
0
1
0
1
1
2
0
2
1
0
2
0
0
0
0
0
2
2
0
0
0
2
2
0
0
2
0
1
0
2
2
0
2
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
2
1
0
1
0
1
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
2
0
4
0
2
0
0
0
3
0
0
0
0
1
0
1
0
0
2
2
0
2
0
2
0
0
0
0
2
1
1
0
1
0
0
1
0
0
2
1
0
1
2
0
2
2
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
1
1
0
0
0
1
0
2
2
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
2
2
0
6
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
2
0
2
0
0
0
1
1
1
0
0
0
0
2
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
2
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
1
2
0
2
1
0
0
0
2
0
0
2
0
1
0
0
0
0
1
0
1
0
0
0
2
0
0
0
2
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
2
0
1
0
2
0
1
2
2
0
0
1
0
0
2
2
0
0
0
0
0
0
0
2
2
2
1
0
2
0
0
0
0
0
1
0
1
0
0
0
2
0
0
4
2
0
0
2
0
0
2
1
0
0
2
0
0
2
2
0
0
0
0
0
0
0
1
0
0
1
1
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
1
0
1
0
2
0
1
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
2
1
0
2
1
1
0
0
0
2
0
0
0
0
0
1
2
7
0
1
1
0
0
0
0
0
2
0
0
0
2
1
0
1
0
0
4
1
0
0
0
2
0
2
0
0
2
0
1
1
1
1
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
2
2
0
0
0
8
3
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
1
0
0
1
0
0
2
3
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
1
0
0
3
0
2
2
2
0
0
0
1
1
1
0
2
0
2
0
0
0
2
2
0
0
0
0
0
1
0
1
0
2
0
1
2
2
2
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
1
2
0
0
1
0
0
1
0
1
0
2
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
2
2
1
0
0
0
1
2
0
2
0
0
0
1
1
1
4
2
0
0
0
0
0
0
0
0
2
0
0
2
0
1
2
1
0
2
0
0
1
0
1
0
0
0
0
2
2
0
3
0
2
0
0
0
0
0
0
1
1
0
0
2
1
1
0
0
2
0
2
0
1
0
0
0
0
1
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
5
1
0
0
0
0
2
0
0
1
0
1
0
0
2
0
1
1
0
1
0
2
2
0
0
0
2
2
0
2
0
0
0
2
2
0
0
3
0
0
1
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
1
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
2
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
3
3
2
0
0
1
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
1
0
0
2
2
0
0
1
0
0
1
10
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
6
0
0
0
0
0
2
0
0
3
2
0
0
0
0
0
0
0
0
0
1
2
0
1
1
0
0
0
2
1
0
0
0
0
0
1
0
1
0
0
0
0
0
2
2
1
1
0
2
0
4
0
0
1
2
2
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
2
1
1
1
0
2
0
0
2
1
2
0
2
0
0
0
0
1
1
2
0
2
0
0
2
0
0
0
0
1
2
0
0
1
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
1
0
2
1
1
0
2
0
0
1
1
0
2
1
0
2
0
2
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
1
0
0
2
0
1
0
0
0
0
0
1
0
2
1
2
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
2
0
1
2
1
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
2
1
1
0
0
0
0
0
2
1
0
0
0
0
1
0
3
0
0
0
0
0
2
0
1
0
0
2
1
0
0
1
2
0
0
0
0
0
1
2
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
2
1
0
0
0
2
2
1
0
0
2
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
2
2
0
0
0
0
1
0
0
2
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
1
2
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
3
1
0
4
0
1
0
0
0
0
1
0
0
0
0
1
2
1
0
0
0
2
1
2
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
2
2
1
0
0
0
0
2
1
0
2
0
1
0
0
0
0
2
1
0
0
0
1
0
0
0
0
1
0
2
0
1
0
0
0
0
2
1
0
2
0
0
0
2
0
0
2
0
0
2
0
2
0
2
0
2
0
0
0
0
0
1
2
2
1
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
2
0
0
1
2
1
1
2
2
1
0
1
0
0
2
0
0
0
2
1
0
0
2
0
0
2
0
2
0
0
3
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
1
0
1
0
0
0
0
2
0
2
3
0
0
2
0
0
1
1
0
1
0
1
0
1
0
0
2
1
0
2
1
0
0
0
4
1
1
2
0
0
0
3
2
0
0
0
1
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
2
0
1
0
1
0
1
1
0
0
0
4
0
2
0
1
2
0
2
1
1
0
2
0
2
2
1
1
0
0
1
0
2
3
1
0
0
0
0
2
1
7
0
0
0
2
0
0
0
0
2
0
2
0
1
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
3
0
0
0
2
2
0
2
2
0
2
0
2
1
2
0
1
2
0
0
0
1
0
0
1
0
1
0
0
2
1
0
0
0
1
1
0
0
2
0
1
1
0
0
1
1
0
0
1
1
0
0
0
3
2
2
0
2
2
0
0
0
0
4
0
0
0
0
3
0
0
2
0
13
2
2
0
1
1
0
1
1
0
0
0
2
0
0
1
0
1
2
0
0
3
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
2
1
0
2
0
1
0
0
1
0
2
2
2
0
0
0
4
0
1
0
0
2
2
0
0
0
0
2
0
2
0
2
1
0
1
1
0
1
1
0
2
1
0
2
3
0
0
0
0
0
2
0
0
0
1
0
2
0
2
0
0
0
2
0
2
0
0
2
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
1
1
0
0
0
1
0
2
0
0
1
1
0
3
0
0
0
1
0
0
0
0
0
2
1
0
0
0
1
0
1
0
0
0
1
2
2
1
0
0
0
2
2
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
2
0
2
0
0
0
2
2
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
1
0
0
1
0
0
0
0
0
2
0
0
1
0
0
2
2
2
2
2
0
0
2
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
2
2
2
1
0
1
0
0
0
0
0
0
0
0
0
3
0
1
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
2
0
0
2
0
3
0
0
0
0
2
1
0
0
2
1
0
1
0
0
1
0
0
0
0
2
0
0
0
0
2
3
0
0
0
1
0
0
0
0
0
1
0
2
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
2
2
1
0
0
0
0
0
0
3
1
0
0
3
0
1
0
0
0
2
1
0
3
2
0
2
2
1
0
0
0
0
2
1
2
0
2
0
0
1
1
0
0
2
0
1
2
2
1
0
3
0
2
0
0
0
1
2
3
0
0
0
0
0
1
0
2
2
0
1
0
0
0
1
0
1
1
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
2
0
2
2
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
1
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
2
2
4
0
0
2
0
1
0
1
0
0
2
2
0
0
2
0
1
0
0
1
0
0
2
3
0
0
3
0
0
0
3
2
2
0
0
0
0
2
2
2
0
1
0
2
0
2
0
1
2
2
1
0
0
5
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
1
0
2
0
0
2
1
1
0
1
1
0
1
0
0
1
0
0
0
0
2
0
2
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
1
1
1
0
2
2
0
1
0
2
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
2
2
0
3
0
0
2
0
3
2
0
1
0
1
0
1
0
0
0
2
2
0
0
0
1
0
0
2
0
1
0
0
1
0
2
2
1
0
0
0
1
0
0
2
0
1
2
1
2
2
1
1
1
0
2
1
1
0
2
1
3
1
0
1
2
1
0
2
0
0
0
2
0
0
1
0
1
2
0
1
0
0
1
0
1
0
2
0
0
0
0
0
1
2
0
2
2
0
0
0
2
0
0
0
2
0
0
2
0
2
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
4
1
0
2
1
0
0
0
1
0
2
1
2
0
0
1
1
0
1
0
0
2
0
0
0
2
0
0
0
3
0
0
0
0
1
1
1
0
1
0
1
0
2
1
1
0
1
1
0
4
0
3
0
0
0
0
2
1
0
2
1
2
0
0
0
0
2
0
0
1
0
0
2
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
1
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
3
0
1
2
0
0
2
0
0
1
0
0
0
2
0
2
1
0
1
2
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
3
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
1
0
1
0
0
1
1
0
0
0
0
0
2
1
0
2
1
0
2
1
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
1
0
1
0
2
0
2
2
0
1
1
2
0
4
2
0
0
0
0
0
1
2
2
0
2
2
2
0
1
0
0
2
0
1
1
1
1
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
4
0
2
0
0
0
0
1
1
0
0
2
0
0
0
2
1
0
0
1
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
1
2
0
0
2
0
1
0
2
0
1
0
0
0
0
0
0
2
1
0
0
2
1
0
1
0
0
1
4
0
0
0
0
2
1
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
2
1
0
0
0
0
0
1
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
1
1
0
2
0
0
1
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
2
1
0
0
0
2
0
3
0
1
0
0
0
0
0
0
1
1
1
1
0
2
2
1
0
0
0
2
1
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
1
1
0
1
0
0
2
0
1
0
0
2
0
0
0
2
0
2
0
0
0
1
0
2
2
2
3
0
2
0
0
1
0
0
2
0
0
0
2
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
2
1
0
1
0
2
3
0
0
1
0
1
0
0
1
1
0
0
2
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
2
1
1
0
0
0
2
1
1
0
0
0
1
0
1
0
0
0
0
0
0
2
0
1
0
1
2
0
0
0
0
0
1
2
0
6
0
0
0
0
0
1
0
0
4
0
1
1
0
1
1
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
2
0
2
1
1
2
0
0
1
1
1
1
1
0
2
0
0
0
2
0
3
2
0
1
1
2
2
1
0
0
2
0
0
3
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
4
0
1
2
0
1
1
1
0
0
2
0
3
0
0
0
1
1
0
0
0
0
0
1
0
1
0
1
0
0
0
2
0
0
1
0
0
1
0
0
0
0
2
2
2
2
2
1
0
2
0
0
1
0
2
0
0
1
0
2
1
2
1
2
2
2
0
1
0
0
0
0
0
0
2
2
0
2
2
0
0
0
0
2
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
3
1
0
2
0
0
0
1
0
0
3
0
0
1
1
1
1
0
1
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
2
2
0
0
0
0
0
1
0
0
2
0
1
1
0
1
0
2
0
0
0
1
0
2
1
1
0
0
1
0
0
1
0
0
1
2
5
1
0
1
0
2
2
1
0
0
0
2
0
3
0
1
0
0
0
0
3
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
1
0
0
3
0
0
2
5
0
0
0
1
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
1
0
1
1
0
0
0
1
2
0
2
2
0
1
0
0
1
2
2
2
3
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
2
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
2
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
2
0
0
1
0
0
0
0
1
0
1
0
0
0
1
14
0
0
0
2
1
0
0
2
2
0
2
0
0
0
0
4
0
2
0
0
0
1
0
1
0
2
0
2
0
2
0
0
0
1
0
0
0
0
0
1
2
2
1
0
1
0
0
0
1
0
1
1
1
0
0
2
1
0
2
1
0
0
0
0
0
2
3
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
2
0
1
1
0
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
2
1
2
3
2
0
1
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
1
2
2
0
0
0
0
2
0
0
0
0
3
1
2
2
0
0
0
1
3
1
0
2
0
0
0
0
9
0
1
0
4
0
0
0
1
2
0
0
2
2
2
0
0
0
2
0
2
0
0
1
0
0
0
2
0
0
1
1
0
0
0
0
2
0
1
2
1
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
2
0
0
2
1
0
0
2
2
0
1
0
2
2
0
0
0
0
2
0
0
1
0
0
0
0
2
1
0
2
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
1
1
0
1
0
1
0
2
0
0
0
0
0
5
1
0
0
0
0
0
2
0
0
1
0
2
1
0
2
0
0
0
0
2
0
0
0
1
0
0
0
1
1
0
2
2
0
0
2
0
0
0
2
0
1
0
1
2
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
1
3
0
0
0
2
0
1
2
3
0
0
0
0
0
0
0
2
0
2
0
2
0
0
1
2
2
0
0
0
2
0
1
0
0
0
0
1
2
1
2
0
0
0
1
0
2
1
2
1
1
2
0
0
2
0
1
0
1
2
0
0
0
1
0
0
0
0
1
2
1
1
1
3
2
0
0
0
0
0
0
1
0
2
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
2
2
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
1
0
0
1
2
0
2
0
0
3
0
0
3
0
2
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
2
0
0
0
1
0
1
0
0
0
1
0
1
1
0
1
0
0
0
0
2
0
0
1
0
0
1
0
3
0
3
0
0
1
0
2
0
0
1
0
0
0
0
1
0
0
0
0
2
0
2
0
0
1
0
0
1
0
2
2
0
2
0
0
0
0
0
1
2
2
0
0
2
0
2
1
1
0
2
0
2
1
0
0
0
0
2
2
2
0
0
0
1
1
2
0
2
0
0
2
1
0
0
2
0
0
0
2
0
0
0
3
0
1
0
3
0
0
0
0
0
0
2
0
1
2
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
2
0
2
0
1
0
0
2
1
0
0
1
0
1
0
1
2
0
2
0
0
4
2
0
0
0
3
2
0
1
0
2
0
0
2
0
1
1
0
2
0
1
0
0
0
2
1
2
3
0
0
0
2
0
2
1
0
2
0
0
0
1
0
0
2
0
0
1
1
0
0
0
1
3
0
2
0
0
2
0
1
1
0
1
2
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
1
1
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
2
2
2
0
1
2
0
0
1
0
1
0
2
0
3
1
0
1
2
0
0
0
0
1
2
0
0
0
0
1
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
2
0
2
0
1
1
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
1
2
0
0
1
1
2
0
0
0
1
2
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
1
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
1
1
1
2
2
0
2
1
0
0
1
0
0
2
0
1
2
2
2
0
0
1
2
0
0
0
0
0
0
0
0
2
1
1
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
3
0
0
1
0
0
0
3
0
1
1
0
0
1
0
0
0
2
0
2
2
1
3
0
1
0
0
3
5
0
2
2
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
4
1
0
1
0
1
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
2
0
0
2
0
3
3
0
1
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
1
1
0
0
1
2
0
1
2
0
0
0
0
0
2
0
2
1
0
1
1
3
0
2
0
1
2
0
0
0
2
1
0
0
0
0
0
2
0
0
2
0
0
1
2
0
0
1
0
0
2
0
0
1
0
0
1
0
2
0
0
2
3
2
0
0
2
0
0
2
1
0
0
0
0
2
2
1
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
2
2
0
0
1
1
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
1
0
1
0
1
0
0
1
2
0
1
1
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
1
0
1
1
0
1
0
2
0
0
0
0
2
0
0
2
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
2
1
0
0
1
2
0
0
0
0
2
0
0
1
0
0
1
1
0
0
1
0
0
1
0
0
0
0
1
2
0
2
0
0
0
2
1
0
1
1
0
0
0
0
0
0
1
1
0
0
1
6
0
1
0
0
0
0
1
0
2
0
0
0
1
1
0
2
0
1
0
0
0
0
0
0
0
2
0
3
0
0
0
0
2
0
0
0
0
0
0
0
1
2
2
0
1
2
0
2
0
1
0
2
0
1
0
2
0
0
0
0
0
0
0
0
2
2
1
2
0
0
0
0
0
0
0
1
0
2
1
1
2
1
0
2
2
0
0
0
3
2
0
0
1
2
1
0
0
0
0
2
0
0
2
0
0
2
2
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
2
2
0
1
2
0
0
0
0
1
0
1
0
0
0
1
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
1
2
0
0
0
0
0
1
0
2
0
2
0
2
1
1
2
1
0
0
0
1
2
0
0
0
0
0
0
2
3
1
2
1
0
2
0
0
0
0
0
0
2
1
1
1
0
0
0
0
0
1
2
0
0
0
0
0
0
3
0
0
0
2
2
1
1
2
0
2
2
0
1
1
2
0
0
1
0
0
1
0
2
0
0
0
0
2
2
0
0
0
0
0
4
0
2
0
0
0
0
1
2
2
0
2
3
3
0
0
2
0
1
2
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
1
1
0
0
0
1
1
1
0
0
2
0
0
0
0
0
3
0
0
0
2
0
1
1
1
1
0
1
0
0
0
1
0
0
0
3
0
0
1
0
0
0
1
2
2
0
2
0
0
0
0
2
3
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
2
0
1
0
0
3
0
0
2
0
0
0
2
2
0
0
1
0
2
1
0
0
0
0
0
0
0
3
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
1
0
2
2
2
0
0
0
0
0
3
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
1
0
0
1
0
0
0
2
0
0
1
0
1
2
0
0
1
2
2
0
0
0
0
2
2
0
0
0
1
0
3
0
3
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
2
0
1
0
1
0
0
0
0
1
1
0
1
0
0
2
0
0
0
2
0
0
1
2
0
0
0
0
0
0
1
2
0
2
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
2
1
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
1
2
2
0
0
0
0
0
1
2
0
0
2
0
1
0
0
1
0
0
0
0
2
1
0
1
0
1
0
3
0
0
0
2
0
2
3
0
1
0
0
0
2
1
0
0
0
2
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
1
2
0
2
2
2
2
0
1
0
0
1
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
3
0
1
0
0
0
1
0
0
0
0
0
2
0
2
1
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
2
2
4
1
0
0
0
0
1
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
1
2
2
0
0
1
0
3
0
2
1
2
2
0
1
0
1
1
1
2
2
0
0
0
0
3
0
0
0
0
2
0
0
0
0
2
1
1
1
0
0
0
0
0
2
0
0
1
1
0
1
0
2
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
2
0
1
0
0
0
1
0
0
0
0
4
0
0
0
0
0
2
0
1
9
0
1
0
1
1
0
0
0
0
8
0
0
1
0
0
3
0
0
1
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
1
0
0
0
1
2
1
0
0
0
1
0
0
0
1
0
1
2
0
0
0
0
1
1
0
0
2
0
1
2
1
0
0
0
0
0
2
2
0
0
1
0
1
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
1
2
1
2
0
1
0
0
1
0
0
0
0
1
0
2
0
0
2
1
0
0
0
0
1
0
0
0
2
0
1
4
0
2
2
0
0
4
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
4
0
2
1
0
2
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
3
0
1
1
0
0
0
0
0
1
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
2
2
1
0
2
0
1
0
0
3
0
0
1
0
0
1
0
0
1
0
0
2
2
1
0
1
0
1
0
2
0
1
0
2
0
0
0
0
1
2
2
0
0
0
0
0
2
0
0
1
0
2
0
0
0
1
2
1
0
2
0
0
0
1
0
0
0
1
0
0
1
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
1
2
2
2
2
2
2
1
0
2
1
0
0
1
0
2
0
0
1
0
0
1
2
1
1
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
2
2
0
0
0
2
1
0
0
0
2
0
1
0
2
2
0
0
0
0
0
0
2
0
0
0
2
2
3
2
0
2
1
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
1
0
2
1
1
0
2
0
0
0
0
0
0
0
1
2
1
1
0
0
3
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
3
0
1
1
0
0
2
0
3
2
0
0
0
0
3
1
2
3
1
0
0
0
6
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
3
2
0
1
0
0
2
0
1
0
0
1
1
0
1
0
0
0
0
0
2
1
0
2
2
0
0
2
2
0
0
1
2
0
1
0
0
0
0
0
3
2
0
2
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
1
1
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
2
1
0
2
0
2
0
0
2
1
2
3
2
0
1
0
0
0
1
3
2
0
0
1
2
0
0
0
0
0
2
0
3
2
0
0
0
0
0
2
0
1
0
0
1
1
0
0
1
1
0
0
2
1
1
0
1
2
1
0
0
0
0
0
3
0
2
1
0
0
0
0
2
0
0
0
3
1
0
0
0
1
0
0
0
0
1
0
2
0
2
0
0
1
2
1
2
0
0
2
2
3
1
0
0
0
0
0
0
1
2
0
0
1
2
0
0
0
2
2
2
0
3
0
2
1
0
0
0
0
2
0
0
0
1
0
0
0
2
2
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
2
0
1
0
0
2
0
1
0
0
2
0
0
2
0
1
0
4
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
2
0
0
1
0
0
0
1
2
2
0
2
2
0
0
0
1
0
1
0
0
1
2
1
0
0
2
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
1
1
0
0
0
0
2
1
2
0
2
0
0
2
2
0
2
2
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
2
0
2
0
2
0
0
2
0
0
1
0
2
0
0
0
0
2
2
1
1
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
1
2
2
0
1
0
0
0
0
1
2
0
0
1
0
1
3
1
0
0
1
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
1
0
2
2
0
2
0
0
1
0
2
0
2
3
0
0
0
0
2
0
1
0
0
2
0
0
2
0
1
0
0
1
1
0
1
2
1
0
2
1
0
0
1
0
0
1
0
1
0
0
1
0
0
0
2
0
1
1
2
0
1
2
0
2
0
0
0
0
2
2
0
1
0
0
3
2
1
0
0
0
1
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
2
1
5
0
0
2
0
2
1
1
0
0
2
0
2
1
2
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
2
2
0
1
0
1
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
1
0
2
0
2
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
2
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
2
0
1
0
0
0
2
1
0
2
0
1
0
2
2
0
1
1
0
0
2
2
0
1
1
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
1
0
1
0
2
0
0
0
0
0
2
0
0
0
0
2
2
1
0
0
0
0
1
3
0
2
2
1
0
0
0
0
0
1
2
1
0
2
1
0
0
1
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
3
1
0
0
0
2
2
0
0
0
0
0
1
3
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
1
1
2
0
1
0
3
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
2
0
0
2
0
0
0
2
0
0
1
2
0
0
0
0
2
0
0
0
2
0
1
1
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
2
0
2
0
0
4
0
0
0
0
0
0
0
0
1
2
1
0
1
0
0
0
0
0
1
2
1
6
0
0
2
0
2
0
0
0
0
0
0
2
0
2
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
3
0
4
0
1
0
0
2
0
1
1
0
1
0
0
2
0
0
1
1
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
2
1
1
0
0
1
0
0
0
0
1
3
0
0
1
0
0
0
2
0
1
2
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
2
2
0
0
0
0
0
0
2
1
0
2
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
1
2
1
0
0
0
0
0
2
0
0
0
1
3
1
0
0
1
0
0
2
0
0
0
0
0
1
1
1
0
4
0
2
1
2
0
1
0
0
0
2
2
0
0
2
2
0
0
1
1
0
0
0
2
2
1
1
0
0
0
0
0
1
2
0
0
2
2
0
0
0
0
1
0
2
0
0
2
0
0
2
0
2
2
2
0
0
0
2
0
0
1
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
3
2
1
0
1
1
2
4
0
0
0
2
0
0
0
0
1
0
1
0
0
1
2
0
2
2
0
0
2
2
0
2
0
0
1
0
0
0
0
2
0
0
0
5
0
0
0
0
0
0
1
0
1
0
0
2
1
0
4
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
7
2
0
0
2
0
1
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
1
2
0
0
2
3
0
1
0
0
0
1
0
0
1
0
1
0
0
1
0
0
2
0
0
0
0
2
1
0
0
0
1
0
0
1
0
0
2
2
0
0
1
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
2
3
0
2
2
0
0
0
0
1
1
0
0
1
0
1
0
2
0
2
0
0
0
1
2
1
1
0
1
0
0
0
0
0
0
0
0
1
0
2
1
0
1
0
0
4
1
0
1
1
0
2
0
1
0
1
0
0
0
0
0
4
2
0
2
0
0
1
0
0
0
0
2
0
0
1
0
0
0
1
0
4
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
3
1
0
1
0
0
2
0
0
0
0
0
1
1
1
0
0
2
0
1
0
1
0
3
3
0
0
0
1
2
2
2
0
1
0
2
0
0
7
2
0
1
0
2
0
0
0
0
0
0
0
0
0
2
2
2
1
0
0
0
2
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
1
2
0
0
0
2
0
0
2
2
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
2
2
0
2
1
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
2
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
1
0
0
0
0
0
0
0
0
0
2
2
3
0
0
1
2
0
2
0
0
0
1
0
0
0
0
1
0
1
0
2
0
2
0
1
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
1
0
1
0
0
1
1
2
0
0
2
0
0
0
0
0
1
0
0
0
1
2
3
2
1
2
0
0
0
0
1
2
3
2
2
0
0
0
0
0
3
1
0
0
1
2
0
0
0
2
0
2
0
0
2
0
2
0
0
0
0
0
1
0
2
0
0
2
1
0
0
2
2
1
0
1
0
0
0
0
0
2
2
1
1
0
1
0
2
0
0
2
0
1
2
2
0
0
0
0
0
3
0
0
0
2
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
1
2
0
2
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
1
2
1
0
0
0
0
0
0
1
2
2
2
0
0
4
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
2
0
1
0
0
2
0
2
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
1
2
0
0
1
0
2
0
0
2
0
1
2
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
2
0
2
0
0
0
2
0
0
0
2
2
0
0
1
1
0
0
0
0
0
2
0
0
0
1
0
4
0
0
2
0
2
0
1
0
2
0
0
0
2
2
2
0
0
0
0
0
1
0
2
1
0
0
2
1
0
1
0
0
0
1
3
0
0
0
0
1
0
0
2
1
2
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
2
0
0
0
0
2
0
2
0
1
2
2
0
0
0
2
0
0
0
1
0
0
0
1
0
0
1
0
1
0
1
0
1
2
0
1
0
0
2
1
0
0
0
0
0
1
0
0
1
2
0
0
0
2
0
1
0
1
0
0
1
2
0
0
2
2
1
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
5
0
0
2
1
1
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
1
0
0
0
1
2
0
2
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
2
0
0
0
2
0
0
1
2
0
1
0
2
1
1
0
0
1
0
2
2
0
2
1
0
3
2
0
2
2
0
0
1
0
0
2
0
2
2
1
0
0
0
1
0
0
2
0
1
0
2
0
2
0
0
0
3
0
0
0
0
2
0
0
0
0
0
2
1
0
2
1
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
2
1
0
2
0
0
2
0
0
0
1
0
0
1
1
0
0
0
0
0
2
2
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
2
1
1
1
0
0
0
0
0
0
0
2
2
2
0
2
0
1
2
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
1
1
0
0
3
1
0
2
0
0
2
2
2
0
1
0
1
0
2
1
0
1
1
0
0
0
0
1
2
0
1
0
0
0
2
1
1
2
0
0
0
0
0
0
1
0
0
2
0
1
0
2
0
0
2
0
2
2
0
0
1
2
1
2
0
0
1
1
0
1
1
0
2
1
2
0
0
1
0
0
1
0
2
0
2
0
1
2
0
0
0
0
2
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
2
0
1
1
0
0
0
0
1
1
0
0
2
0
1
2
0
0
2
0
0
0
3
0
2
1
0
0
2
0
2
2
1
0
0
2
2
0
0
2
0
2
1
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
2
2
0
0
2
0
0
0
1
0
2
0
0
0
0
0
1
0
2
2
0
0
2
0
0
1
0
0
0
0
0
1
0
0
2
0
2
0
0
1
0
0
0
0
0
0
1
1
1
2
1
0
0
0
0
2
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
2
0
1
0
2
0
0
2
2
1
0
1
1
0
0
0
0
3
0
0
0
1
1
1
0
2
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
2
0
0
1
0
0
2
2
0
2
0
1
0
2
0
0
0
0
0
0
1
1
0
0
1
0
0
2
0
2
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
2
0
2
1
0
0
2
2
1
5
2
0
2
1
0
0
0
0
0
0
0
2
2
0
2
3
0
0
1
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
2
3
0
2
1
5
0
0
1
0
0
1
2
0
0
0
0
0
2
0
0
0
1
0
2
0
0
3
0
2
1
0
0
0
0
0
0
1
0
1
2
0
0
2
0
0
0
0
1
0
0
0
0
1
2
2
1
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
3
2
0
1
0
2
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
2
1
2
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
1
1
1
0
2
0
0
0
2
3
0
0
0
0
1
2
0
1
0
0
1
0
2
0
1
0
1
0
0
0
0
0
0
1
0
1
0
2
0
0
1
0
1
1
0
0
0
0
1
2
2
0
1
0
0
2
0
2
1
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
2
0
2
0
1
1
2
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
2
3
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
3
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
2
0
0
0
0
1
1
1
0
0
0
0
0
2
0
2
0
1
1
0
2
0
2
5
0
0
0
1
0
0
2
2
2
0
0
0
0
2
2
1
2
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
2
2
0
0
0
0
0
2
0
0
2
0
0
2
2
1
0
0
0
0
0
0
0
0
0
1
2
0
0
2
1
1
1
0
0
3
2
1
0
0
0
0
2
2
1
0
2
1
0
2
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
1
0
2
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
5
0
0
0
3
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
1
0
2
2
2
0
0
4
0
1
2
1
0
0
0
0
0
0
0
0
0
1
2
0
1
3
0
1
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
3
1
0
0
0
0
0
0
1
1
2
0
1
0
2
0
0
0
0
2
0
1
1
0
0
0
1
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
1
5
1
0
0
1
0
0
0
2
1
0
13
0
3
0
0
0
0
0
1
0
2
1
2
0
0
0
0
0
5
2
2
0
0
2
1
1
0
2
2
0
2
0
0
0
0
0
0
2
1
0
0
0
1
0
1
2
0
1
2
0
0
0
2
0
0
1
0
0
1
1
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
1
1
1
0
2
0
0
2
2
1
0
3
0
2
0
0
0
0
0
0
1
0
0
2
0
1
2
0
1
3
2
0
1
2
0
2
2
0
2
0
1
1
0
0
0
2
2
0
0
2
0
1
1
0
0
0
0
1
0
0
1
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
3
0
2
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
1
0
2
0
1
0
0
0
3
0
1
0
2
0
2
0
0
0
0
2
1
0
0
0
0
1
2
2
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
1
0
0
0
1
0
1
0
0
0
0
2
0
1
1
0
0
0
1
1
2
0
0
1
0
1
2
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
2
0
0
0
3
0
0
1
0
0
0
0
0
2
2
1
0
2
0
0
0
0
0
5
1
0
0
0
1
0
0
0
2
0
2
0
0
0
0
2
0
0
0
1
0
1
0
2
2
2
2
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
1
0
1
0
0
0
2
0
0
0
0
0
2
2
0
1
1
0
0
0
0
2
0
2
2
0
2
2
0
0
0
1
0
0
2
2
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
1
0
0
2
0
2
0
0
0
0
2
1
1
0
0
1
0
0
0
1
0
2
0
0
0
2
0
0
0
1
0
1
0
0
1
1
0
0
2
0
1
1
0
0
2
0
0
0
2
0
0
2
1
1
3
0
0
0
0
0
2
0
0
0
0
0
0
2
2
1
2
0
0
2
1
0
0
0
0
0
2
4
2
2
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
1
2
0
1
0
2
0
1
0
0
1
0
0
1
2
0
0
1
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
1
2
0
0
0
0
0
2
1
0
0
0
0
1
0
2
0
2
0
1
1
0
1
1
0
1
0
0
2
1
2
0
2
1
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
1
0
2
2
0
0
1
2
0
0
1
0
0
0
0
1
0
1
0
1
0
0
1
1
2
2
1
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
1
1
0
0
2
0
0
0
2
1
10
1
0
0
2
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
3
1
1
0
1
4
2
3
2
0
0
1
3
0
0
1
4
0
0
2
0
0
0
0
0
1
2
1
1
2
0
0
0
1
1
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
1
1
0
0
1
1
0
0
0
0
0
0
1
2
1
2
1
0
0
0
0
0
2
0
1
0
0
0
0
3
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
2
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
2
0
2
0
0
0
0
0
2
3
1
2
2
0
1
0
0
2
2
0
2
0
1
2
1
0
1
2
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
1
0
2
0
1
0
1
0
0
3
1
1
0
1
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
2
0
2
0
2
0
2
0
0
2
2
0
1
0
2
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
2
2
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
1
2
0
0
0
2
0
0
0
1
0
0
0
2
0
2
0
2
1
0
1
0
0
0
0
1
1
0
2
1
1
0
0
0
2
0
0
0
2
1
0
0
1
2
1
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
1
1
0
1
0
1
2
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
1
0
0
3
2
1
1
0
0
2
0
0
0
2
1
0
0
0
2
0
2
2
0
0
0
0
2
0
0
0
1
1
0
0
1
0
2
1
1
0
0
1
0
1
1
1
0
1
0
1
2
0
1
0
2
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
2
0
0
0
2
2
0
0
3
0
0
1
0
0
0
0
0
1
0
0
2
0
0
1
1
0
0
0
0
1
1
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
2
0
2
2
0
2
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
1
2
0
0
0
0
0
2
2
1
0
2
1
0
1
0
0
1
2
0
0
0
1
0
0
1
3
1
1
1
0
0
0
2
0
0
2
1
0
0
0
1
1
0
2
0
2
1
2
0
2
0
0
0
2
1
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
3
2
0
2
2
0
1
0
0
2
2
0
3
0
2
0
0
1
0
1
0
0
1
0
0
0
0
0
2
0
2
0
0
0
1
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
2
2
1
0
2
1
0
0
1
1
2
2
1
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
3
0
1
0
0
1
2
2
2
0
2
0
1
0
0
1
0
2
0
3
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
2
2
0
2
1
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
2
1
0
0
0
1
0
0
1
1
2
0
0
0
0
1
0
0
0
0
1
0
2
1
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
2
0
0
2
0
1
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
1
0
2
0
0
1
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
3
0
0
1
0
0
2
0
2
2
0
0
6
2
0
0
0
1
2
5
0
0
0
2
0
0
2
0
2
0
0
0
0
1
0
0
3
0
0
0
1
0
0
3
1
2
0
0
0
0
1
0
0
2
0
1
0
0
0
1
0
0
0
2
0
0
0
0
2
2
0
0
3
1
1
1
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
2
2
1
1
1
1
0
2
1
1
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
1
2
0
0
0
1
0
2
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
1
0
2
0
1
1
0
2
0
0
1
0
0
0
1
0
0
2
1
1
1
0
0
0
1
0
1
1
0
0
0
2
0
2
0
1
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
1
1
0
1
1
0
0
0
2
2
0
0
0
1
2
1
0
0
2
0
2
0
2
0
2
0
2
0
0
1
1
0
0
0
3
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
4
1
0
0
1
0
0
1
3
1
1
1
0
0
1
1
2
2
2
2
0
1
0
0
0
2
0
1
2
2
1
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
2
1
0
1
0
0
0
1
0
1
2
2
2
0
2
0
0
3
0
0
0
1
0
0
4
3
0
2
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
1
1
0
0
0
0
1
1
0
0
1
1
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
2
2
1
1
3
0
0
0
3
0
0
2
0
2
0
0
0
0
2
1
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
2
0
0
1
2
2
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
2
1
0
0
2
0
0
0
1
0
0
0
0
0
0
3
0
0
2
0
2
0
0
1
0
0
1
2
0
2
0
0
0
0
0
0
1
0
0
0
2
0
4
1
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
1
3
2
2
0
0
2
0
0
0
1
0
0
1
2
0
0
2
0
0
0
1
1
2
2
0
0
1
0
0
1
0
0
5
1
0
2
0
0
4
2
0
1
0
0
1
1
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
2
2
0
1
0
1
1
0
1
0
2
2
0
2
0
0
2
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
1
1
0
0
1
0
0
2
0
1
0
0
0
3
1
0
0
0
0
2
0
0
0
0
3
0
1
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
2
1
2
0
0
1
0
0
0
1
2
1
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
1
0
1
0
0
2
1
0
2
0
0
1
0
0
2
0
0
0
1
0
0
1
2
0
0
0
0
2
0
0
2
2
0
4
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
2
1
0
1
0
0
1
0
0
0
0
0
0
2
1
2
1
2
0
1
0
0
1
0
0
0
1
1
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
2
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
1
0
0
0
0
1
1
0
0
0
3
0
1
4
0
0
0
0
0
1
0
0
1
1
2
0
0
0
1
2
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
1
0
0
0
2
1
0
2
0
0
1
0
1
0
0
0
0
0
2
0
1
0
2
0
0
2
0
0
1
1
0
1
0
0
0
0
0
0
0
0
2
0
2
2
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
1
2
0
0
2
0
0
1
0
0
2
1
0
0
2
0
3
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
2
0
1
1
0
0
0
1
2
0
0
0
0
0
1
1
0
0
0
2
1
0
1
1
1
0
1
0
1
1
0
0
0
1
1
0
2
0
2
2
0
0
1
1
0
1
0
0
0
2
0
3
0
2
2
0
1
1
2
0
0
0
0
2
0
0
1
2
0
1
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
2
1
0
2
2
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
1
0
0
0
0
1
1
1
1
1
0
2
0
1
0
0
2
0
2
0
0
2
0
1
0
0
2
0
2
4
1
0
0
0
0
0
0
0
0
0
1
0
2
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
2
0
1
0
0
2
2
1
3
2
0
0
1
0
0
1
1
0
2
0
2
0
1
1
0
0
1
2
2
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
2
0
0
2
2
0
0
1
1
1
1
0
1
0
2
0
0
0
0
0
0
1
1
0
0
1
1
2
2
2
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
2
1
0
0
1
0
0
0
2
0
0
1
0
2
1
2
0
0
0
1
0
0
0
0
0
2
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
2
1
2
0
0
0
1
0
0
0
1
1
2
0
0
3
0
0
0
2
0
0
2
0
1
0
0
0
1
0
2
2
1
1
0
2
0
1
0
0
0
1
1
0
0
2
1
2
0
0
0
1
2
0
0
1
1
0
2
0
1
0
0
0
2
0
2
0
0
0
2
0
3
0
0
1
0
0
1
0
0
0
0
0
0
2
1
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
1
0
2
1
1
2
0
2
0
0
0
2
0
1
2
1
2
0
0
0
0
1
1
0
1
0
0
0
0
1
0
3
2
2
0
0
1
0
1
1
1
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
2
1
0
0
0
0
0
1
2
0
0
0
2
0
0
4
2
0
1
2
0
1
4
0
2
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
2
0
0
0
0
2
0
1
3
0
0
0
1
0
0
2
2
1
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
1
1
1
0
1
1
0
0
2
0
1
2
0
0
4
0
1
2
2
2
2
2
1
0
0
1
0
0
3
0
0
2
0
0
0
0
2
1
2
0
0
0
0
0
2
0
0
0
0
3
2
0
0
1
0
0
2
0
1
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
1
1
0
1
0
3
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
3
0
0
0
2
1
2
0
0
0
0
0
0
1
2
0
0
4
0
0
0
0
2
2
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
3
0
1
2
1
0
2
2
0
1
2
2
2
1
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
1
1
2
0
2
0
0
0
1
1
1
1
1
0
2
1
0
0
2
1
1
2
0
2
0
2
0
2
0
0
0
0
0
0
0
0
2
2
0
0
2
0
1
0
0
0
4
0
1
0
1
0
1
0
2
0
1
2
0
0
2
0
1
1
0
0
1
1
0
0
0
0
0
0
0
2
2
1
1
1
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
2
2
0
0
0
1
2
1
0
0
0
0
0
0
1
2
1
0
0
0
1
0
1
0
4
0
0
0
0
2
0
2
0
2
0
1
0
0
1
2
0
2
0
3
0
0
1
0
1
0
1
5
0
0
0
2
1
1
0
0
0
1
2
0
0
0
2
1
2
1
1
1
0
0
0
0
0
2
0
1
2
0
1
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
2
0
0
0
2
1
0
0
2
1
2
2
0
2
0
0
0
0
0
0
0
2
1
3
0
0
0
0
0
0
0
0
0
5
0
1
0
0
0
0
0
2
0
1
1
0
3
0
0
1
2
1
0
1
1
0
0
2
0
0
0
0
0
2
1
0
0
0
2
0
3
0
0
0
0
2
0
0
0
1
2
0
2
1
0
0
1
0
0
0
2
0
3
0
0
2
0
0
0
0
0
0
0
2
0
4
0
0
0
0
0
2
0
0
1
1
0
3
0
0
0
0
1
1
0
0
2
0
0
0
2
2
1
0
2
0
1
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
3
0
0
1
0
0
0
2
0
2
0
1
1
2
0
0
0
0
0
0
0
2
2
2
2
0
0
0
0
0
0
0
0
2
0
0
2
3
0
1
1
1
2
0
2
0
0
1
0
0
0
0
0
0
2
0
0
2
3
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
2
1
0
0
0
0
0
0
2
1
0
0
2
1
1
2
0
0
1
1
0
2
0
0
1
0
1
0
0
0
0
0
2
0
2
0
4
0
0
1
2
2
0
3
0
2
2
0
2
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
1
0
2
0
1
0
0
2
0
0
2
2
0
1
1
0
0
0
3
0
0
0
1
2
1
2
0
2
0
0
0
0
1
1
0
2
1
0
2
0
0
0
2
1
2
0
1
3
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
1
0
1
1
0
2
1
2
1
0
0
0
2
0
0
0
0
2
0
1
0
0
1
0
3
0
0
0
1
0
0
1
0
0
2
2
1
0
2
1
1
0
2
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
1
1
0
3
2
2
0
1
0
1
1
0
2
1
0
1
0
1
1
0
0
1
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
6
0
2
0
1
0
2
0
2
0
1
0
0
2
2
0
1
0
1
0
1
0
1
1
1
0
2
0
1
3
0
0
0
0
0
2
1
1
0
0
2
0
0
0
0
0
0
0
3
1
1
1
0
0
2
0
0
2
0
0
0
1
0
1
0
0
0
3
1
2
0
0
2
2
0
2
2
1
1
1
0
2
0
0
2
2
0
0
0
1
0
0
1
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
2
0
1
0
0
3
2
2
0
1
1
1
0
0
0
1
0
0
0
6
1
1
0
0
0
5
1
2
0
0
2
0
0
1
1
0
2
0
1
0
0
2
0
2
0
0
2
2
2
1
2
2
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
2
1
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
1
1
2
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
7
2
2
0
0
0
0
1
0
3
1
0
0
0
1
2
0
2
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
1
2
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
5
1
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
1
0
1
0
2
1
0
1
0
0
0
0
3
2
0
1
1
0
2
1
0
0
0
0
2
1
2
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
2
1
0
1
0
2
0
0
0
2
0
2
0
1
1
2
1
0
0
0
0
0
3
0
1
0
1
0
0
0
0
0
2
0
0
0
2
0
2
2
0
0
0
2
1
0
1
0
0
1
0
0
1
4
0
2
2
0
2
1
0
0
0
0
1
0
0
0
2
3
0
0
0
0
0
0
1
2
0
0
0
1
1
1
0
0
0
0
2
0
0
1
0
0
0
1
1
2
0
2
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
2
2
2
1
2
2
0
0
0
0
0
1
0
0
3
0
1
0
1
1
0
1
0
1
2
0
0
2
0
0
0
0
1
0
2
1
1
1
0
2
0
2
0
0
1
3
0
0
0
0
0
3
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
2
0
2
0
0
0
0
1
0
0
0
1
1
0
3
1
1
0
0
3
2
0
0
1
1
2
1
0
1
0
0
0
2
2
2
0
2
2
2
0
0
0
0
0
0
1
0
0
1
0
1
1
1
0
0
1
0
0
0
2
0
0
0
2
0
2
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
2
1
0
1
0
2
0
1
2
2
6
1
0
0
0
0
0
0
2
2
2
1
1
0
0
0
0
4
0
0
0
0
0
0
0
0
1
5
2
0
2
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
1
1
0
3
1
0
0
0
0
0
0
0
2
0
0
0
0
1
1
1
0
1
0
2
1
0
0
1
0
1
1
1
0
1
1
0
0
0
0
0
3
0
0
3
2
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
1
0
1
1
2
1
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
2
0
0
1
0
2
3
0
0
0
1
0
0
0
0
0
2
0
4
1
0
0
0
0
1
2
6
2
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
1
0
0
0
1
0
2
0
0
1
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
4
1
0
0
0
0
0
0
1
0
0
2
0
2
0
0
1
0
2
1
0
1
0
0
0
0
0
0
0
3
0
2
1
1
0
2
2
2
0
0
2
0
1
2
0
0
0
0
0
3
0
0
2
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
2
0
2
1
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
2
0
0
1
1
0
0
1
2
0
0
1
2
2
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
1
1
0
0
0
2
0
1
0
1
2
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
2
2
0
0
1
0
0
3
1
2
1
0
0
0
0
0
2
1
2
1
1
0
0
3
0
0
3
0
2
0
1
2
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
5
2
2
2
3
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
1
0
0
2
0
0
0
1
0
1
0
1
1
0
0
0
2
1
0
0
1
1
0
0
0
0
0
2
0
1
1
0
2
2
0
1
0
2
5
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
2
0
2
2
1
0
0
0
0
2
2
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
1
2
2
0
1
0
1
0
3
0
0
5
1
0
0
0
0
0
1
0
0
1
0
1
2
2
1
3
0
0
0
2
0
0
0
1
0
1
1
2
1
0
0
2
0
0
0
0
2
2
1
0
0
0
2
6
2
6
1
2
0
1
0
2
0
2
0
0
0
0
0
0
0
0
1
1
2
0
1
0
1
0
1
2
1
0
1
2
0
0
1
0
0
2
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
1
1
2
0
1
2
0
0
3
1
1
1
2
0
2
0
0
2
2
0
0
2
0
2
0
1
3
0
0
0
0
1
2
2
2
0
2
2
0
0
0
2
0
0
1
2
1
2
0
0
2
0
0
1
0
0
1
1
1
1
0
0
2
1
0
1
0
0
2
0
0
1
0
0
0
1
0
0
3
0
0
0
0
1
0
2
2
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
2
1
0
0
1
0
1
1
1
0
2
0
2
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
2
1
1
0
0
0
3
2
0
0
0
2
0
0
1
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
1
4
1
2
0
0
0
1
1
0
0
0
1
1
0
3
0
0
0
0
2
0
0
0
1
0
0
0
1
2
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
2
3
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
1
2
0
0
1
0
0
0
0
0
0
1
0
2
0
3
1
0
0
2
0
0
0
0
1
2
0
1
0
0
0
0
0
2
1
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
7
1
0
0
0
0
0
2
0
2
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
3
0
1
1
0
0
0
0
0
0
1
1
0
1
1
0
2
0
0
1
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
2
2
4
1
0
0
2
0
1
0
0
0
0
0
0
0
0
2
1
2
0
0
2
0
1
0
0
0
0
2
2
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
2
2
0
0
2
1
0
0
0
1
0
1
0
2
0
0
0
1
1
2
0
1
0
0
0
1
0
1
0
0
1
0
0
0
2
0
0
0
0
1
1
0
2
2
2
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
2
0
2
0
0
0
1
0
1
0
0
2
2
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
1
1
2
0
0
0
0
0
0
1
0
2
0
1
0
2
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
3
1
2
2
3
1
0
2
1
0
0
0
0
0
0
0
0
1
2
1
0
0
0
1
0
1
2
0
0
1
2
1
1
2
0
0
0
0
0
0
1
2
0
0
0
0
1
1
0
0
0
2
0
0
0
0
1
1
0
1
2
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
2
0
2
1
0
1
0
1
0
2
2
2
2
0
0
0
0
0
1
0
1
1
0
1
0
0
1
0
0
0
2
1
0
2
0
0
0
0
1
2
0
0
2
0
0
0
0
0
2
0
0
0
1
1
2
0
1
0
0
1
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
2
0
2
1
0
1
0
2
2
1
0
0
0
1
0
0
0
2
2
0
0
0
3
2
2
1
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
2
0
4
1
0
6
2
0
2
2
1
1
0
1
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
1
1
2
0
1
2
1
0
2
0
1
1
0
0
0
3
0
0
2
1
0
0
1
1
0
1
1
0
2
2
0
1
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
2
1
1
0
1
0
2
1
0
0
0
0
0
0
1
2
0
2
0
0
0
1
0
2
0
2
1
0
0
0
0
1
2
0
0
2
0
0
1
3
0
0
0
0
0
0
2
0
0
2
0
2
0
1
0
0
0
2
0
0
0
0
0
0
1
1
0
1
0
0
1
2
4
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
2
0
0
2
0
0
0
0
2
0
2
0
5
0
0
2
1
1
0
3
0
0
0
0
2
1
2
0
1
3
1
0
0
2
1
1
2
0
0
2
0
0
0
0
2
1
0
0
1
2
0
1
0
1
0
0
2
1
0
1
0
0
2
0
1
0
2
0
0
0
0
2
0
0
0
2
1
3
3
0
0
0
1
1
1
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
1
2
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
3
0
0
0
2
0
0
0
0
0
1
2
3
2
1
1
0
2
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
1
0
2
0
1
1
1
0
0
1
0
2
0
0
1
0
2
0
2
1
0
0
0
2
2
0
0
1
0
1
2
0
0
2
1
1
0
0
1
0
0
0
0
2
2
1
0
0
1
2
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
2
1
0
2
1
1
0
2
0
0
0
0
0
0
0
0
2
1
0
1
2
2
0
2
0
2
0
2
0
0
0
0
0
1
0
2
1
2
0
0
0
0
0
0
0
1
1
0
2
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
4
2
1
2
0
0
1
1
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
3
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
1
0
0
9
0
0
2
0
0
0
0
2
0
0
3
2
0
0
0
0
1
0
2
0
1
1
0
1
0
1
0
3
0
0
0
0
0
0
1
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
2
0
2
0
0
0
0
1
5
0
0
0
0
3
1
0
2
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
2
1
0
2
0
0
1
1
0
2
0
1
0
0
1
0
0
0
0
0
0
4
0
0
0
2
0
1
0
0
1
2
0
0
0
1
1
0
0
2
0
1
1
0
0
1
0
0
0
0
2
0
1
2
2
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
2
0
2
0
2
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
2
0
0
2
2
0
1
0
0
0
0
0
2
0
0
1
0
0
3
0
3
0
1
0
2
3
1
0
2
0
0
0
1
2
0
1
2
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
2
0
0
2
0
0
1
0
0
1
1
0
0
2
1
0
0
0
1
2
0
0
0
1
0
0
2
0
2
0
0
0
0
1
0
0
0
0
2
0
1
1
1
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
1
0
1
0
0
1
0
1
0
0
1
0
0
0
0
1
0
1
1
1
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
1
0
2
0
0
2
0
0
0
0
0
1
0
0
1
2
0
0
0
2
1
0
0
0
3
0
0
0
0
1
0
0
0
1
2
0
1
0
2
0
1
2
0
2
0
1
0
2
0
1
3
1
0
0
0
0
1
0
1
0
0
0
1
2
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
1
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
2
0
2
4
0
0
0
0
0
1
0
1
0
0
0
0
0
2
1
0
2
0
0
2
0
0
0
1
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
2
1
0
0
1
0
2
0
0
0
0
0
3
0
1
0
0
0
0
1
1
3
0
1
0
0
0
1
2
2
0
0
0
1
1
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
2
2
1
0
0
2
1
3
0
0
0
2
0
0
0
0
0
0
0
0
1
1
1
0
1
0
4
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
1
0
0
0
2
1
1
1
0
1
0
1
1
1
0
2
2
0
0
0
0
1
0
0
1
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
8
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
2
0
0
2
0
0
2
2
0
1
0
0
0
0
0
0
0
0
2
0
0
1
2
1
0
0
0
0
1
1
0
2
0
2
0
0
0
2
0
0
0
1
0
0
0
2
2
0
2
0
0
7
1
0
0
0
2
0
0
0
0
0
2
1
1
0
0
0
0
2
3
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
2
0
1
3
0
2
0
1
1
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
4
0
2
0
0
0
1
0
0
1
1
1
2
0
2
0
0
2
0
1
0
1
0
1
1
1
0
0
0
0
1
0
1
0
1
0
1
2
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
2
0
0
2
1
0
0
0
0
1
0
1
0
2
1
0
2
1
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
1
0
2
1
2
2
0
0
0
3
2
1
1
0
0
0
3
0
1
0
0
0
1
0
0
0
0
0
2
1
0
1
0
0
0
0
1
1
0
1
0
1
0
1
0
1
0
0
4
0
1
0
0
0
0
0
0
1
1
2
0
1
0
0
2
0
2
2
2
0
1
1
0
0
1
0
1
2
0
2
0
0
0
1
1
0
2
0
0
2
2
2
0
2
1
2
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
2
1
0
1
0
1
2
3
1
2
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
3
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
1
0
2
0
1
0
1
0
0
1
0
0
1
0
0
2
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
3
0
0
0
0
1
0
0
0
0
1
1
0
1
0
2
0
0
2
0
2
0
0
1
0
1
0
0
0
0
0
0
2
0
0
1
1
0
0
1
2
1
0
0
0
0
0
2
2
0
1
0
0
2
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
2
2
0
0
0
2
1
0
1
0
0
0
2
3
0
2
0
1
0
0
0
2
0
2
0
1
0
0
2
1
0
2
0
0
3
0
0
0
0
2
0
1
1
3
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
2
1
0
0
0
2
0
2
1
0
1
3
0
2
0
2
0
0
0
0
1
0
0
2
2
2
0
1
0
0
1
0
2
0
1
0
1
0
0
0
0
1
1
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
2
0
0
0
0
0
0
1
1
0
0
0
5
0
3
0
0
2
2
0
0
1
0
2
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
2
1
2
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
2
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
4
1
2
0
0
2
2
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
2
0
2
0
0
0
0
0
3
1
0
2
0
0
0
1
0
0
0
0
0
1
2
1
0
2
1
0
0
0
2
1
1
2
0
0
0
2
0
0
0
0
2
2
1
0
2
0
0
1
0
0
0
0
1
0
3
0
2
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
2
2
2
0
0
0
1
0
2
1
1
0
0
0
0
0
2
0
0
1
2
0
0
1
0
2
1
2
2
0
0
1
0
0
0
0
0
2
2
0
0
0
2
2
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
2
0
4
0
0
1
0
0
1
0
0
0
0
1
2
0
0
2
0
0
1
0
2
5
0
0
0
1
7
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
2
2
0
0
0
1
0
2
0
2
0
2
0
0
1
0
1
1
0
2
0
2
2
0
0
0
2
2
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
2
1
0
1
0
1
0
0
0
0
1
2
1
0
0
0
0
2
1
0
1
0
0
1
0
0
0
1
1
0
0
0
2
0
0
0
1
1
0
0
0
0
0
1
0
0
2
1
1
0
1
0
1
1
0
0
0
0
1
0
0
0
0
1
1
0
2
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
1
1
1
0
0
0
0
2
1
0
0
1
0
1
0
0
2
0
0
1
0
0
0
1
2
2
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
2
2
1
1
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
2
0
2
0
0
0
0
0
1
3
0
0
1
0
3
0
1
0
0
0
1
2
0
0
0
0
3
0
0
0
3
1
0
1
0
0
0
2
0
0
2
0
1
4
1
1
1
2
0
0
1
0
2
0
2
1
1
1
1
3
0
0
0
0
0
2
0
0
0
0
2
0
1
0
1
2
0
1
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
3
0
0
1
1
3
2
1
1
2
0
1
0
0
0
1
0
1
0
0
0
2
0
0
2
0
0
1
1
1
2
2
0
0
2
1
1
0
2
2
0
1
1
0
1
0
0
0
0
0
0
0
2
0
3
2
0
0
0
2
0
0
1
0
0
0
2
2
0
0
0
3
0
12
2
2
0
2
0
0
2
2
0
2
0
2
2
0
0
0
0
0
0
0
1
2
0
0
2
3
1
2
2
0
0
2
2
0
1
0
2
2
0
0
0
2
0
0
0
1
0
0
1
0
2
2
2
2
0
1
0
10
0
0
2
0
0
2
0
2
1
0
2
0
0
0
0
0
0
1
1
0
1
0
0
2
0
2
2
2
0
1
0
0
2
0
1
0
0
2
0
0
0
2
0
0
1
0
0
4
0
0
1
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
2
2
0
0
3
0
0
0
2
1
0
0
1
1
2
0
0
2
0
1
0
0
1
0
2
0
0
0
4
1
0
0
1
0
0
1
0
0
2
0
0
2
1
0
2
2
0
0
0
0
2
2
1
2
2
0
1
1
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
1
0
0
2
0
0
1
0
0
0
2
0
0
2
1
0
0
3
2
0
1
0
0
0
0
0
2
2
0
0
11
0
2
2
0
0
2
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
1
0
0
1
0
2
0
0
0
2
0
0
0
2
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
2
0
1
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
2
1
1
0
1
0
0
0
1
0
1
0
0
0
0
1
0
2
1
2
0
2
1
0
0
0
0
1
2
1
3
0
2
2
0
2
1
0
1
1
2
0
0
0
0
1
0
0
0
0
0
1
3
0
0
1
1
2
0
1
3
1
0
0
0
0
0
0
0
3
0
2
0
1
0
0
1
0
0
1
2
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
2
0
1
0
2
0
1
0
0
0
0
0
1
2
0
1
2
0
0
1
0
0
2
1
0
0
2
0
0
0
2
0
0
0
1
0
2
0
0
2
0
0
2
0
1
0
0
2
0
0
1
0
2
0
0
0
0
3
1
1
0
0
0
0
1
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
2
0
0
0
2
0
1
0
0
1
0
0
0
0
0
1
3
0
1
1
1
0
0
2
0
0
0
1
0
0
0
0
1
2
0
0
0
1
2
1
1
0
0
0
2
0
2
0
0
0
0
1
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
1
0
1
0
1
2
1
0
0
1
2
1
0
1
1
0
1
0
0
4
0
2
0
1
0
1
2
0
1
0
1
0
1
0
2
0
0
0
0
2
1
0
0
0
1
0
0
0
2
0
0
0
2
2
0
2
0
0
0
2
0
1
0
0
0
2
1
4
0
0
2
2
0
0
2
0
0
0
2
1
2
0
0
2
0
0
1
0
1
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
3
0
2
0
1
0
0
1
0
0
2
0
0
1
1
0
0
0
0
2
0
1
0
1
0
0
1
0
2
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
4
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
1
2
0
2
0
1
2
0
2
0
0
0
1
2
1
0
0
1
0
0
0
0
2
0
1
0
1
3
3
0
2
0
1
1
2
0
3
0
0
1
2
0
2
0
1
2
3
0
0
2
2
0
0
0
2
2
0
0
0
0
0
0
0
0
2
1
2
2
0
1
0
2
2
1
6
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
2
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
3
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
2
2
2
2
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
1
0
0
2
2
0
0
1
0
0
2
0
2
2
1
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
2
1
0
0
0
0
2
0
0
2
1
0
0
0
1
0
0
0
2
2
2
1
1
0
0
1
0
0
0
0
2
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
1
0
1
1
1
0
1
0
4
0
0
0
0
3
0
0
7
0
0
1
1
0
0
1
0
0
1
0
0
0
1
1
2
0
0
0
2
0
0
2
2
0
0
2
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
3
0
1
1
0
0
0
0
0
0
1
0
1
2
0
2
0
2
1
0
0
1
0
2
1
2
0
0
0
0
0
0
0
2
0
1
0
2
0
0
1
0
0
0
0
2
1
1
0
0
1
0
1
0
0
1
0
2
0
0
0
0
4
0
0
0
1
0
2
0
0
0
0
0
0
0
3
1
0
2
0
0
0
2
2
1
0
0
1
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
2
2
0
2
0
0
2
1
0
0
2
0
0
0
1
0
0
2
4
0
3
0
0
1
0
0
2
1
0
1
0
2
3
0
0
0
0
2
1
1
0
0
0
0
2
1
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
2
1
0
1
0
2
0
0
0
1
1
0
2
0
2
0
0
0
0
2
0
0
0
2
0
6
1
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
2
0
0
1
1
1
0
0
0
1
1
0
0
2
2
0
0
0
0
0
2
2
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
6
1
2
0
2
2
1
1
0
0
1
0
0
0
1
2
2
0
0
1
0
1
1
2
0
0
1
0
0
0
0
4
0
0
0
2
0
0
1
2
1
2
1
2
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
1
0
1
0
0
2
1
2
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
1
0
0
1
0
0
2
1
0
0
0
0
2
2
0
0
2
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
2
0
1
1
0
2
0
1
2
2
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
1
0
0
0
1
0
2
1
0
1
2
0
0
0
0
0
2
1
2
0
2
2
0
2
1
0
0
1
1
2
0
2
0
2
0
2
0
0
0
2
0
1
0
0
0
3
2
0
2
0
0
5
0
0
0
2
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
1
0
1
1
0
2
3
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
1
4
1
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
2
0
0
1
0
3
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
1
2
3
0
4
0
0
2
0
0
0
1
0
0
2
0
1
0
0
1
0
2
0
0
0
3
0
2
1
0
1
1
3
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
2
0
1
0
0
0
0
2
2
0
0
0
0
0
2
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
2
1
0
0
1
0
1
0
0
0
2
0
0
2
0
2
2
0
0
0
0
0
2
2
2
0
3
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
1
0
0
2
0
0
2
4
2
0
0
2
0
0
0
2
0
0
0
1
0
1
0
0
0
0
2
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
1
0
0
0
1
0
1
1
2
0
0
0
1
0
0
2
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
1
1
0
1
0
0
1
2
0
0
0
0
2
0
1
1
0
0
0
0
0
2
0
0
0
2
1
0
2
0
0
0
1
0
1
2
0
1
2
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
1
2
1
1
1
1
1
1
0
1
0
0
0
0
3
0
0
2
3
0
2
0
2
0
0
1
0
0
1
0
1
0
2
0
0
0
0
0
1
2
0
1
1
0
0
2
1
0
0
0
0
0
0
2
0
2
0
0
0
0
2
4
0
2
0
0
0
2
1
1
0
0
0
0
0
0
3
0
0
0
3
0
0
0
1
0
0
0
2
0
0
4
2
2
0
0
0
0
0
2
1
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
2
0
2
2
0
0
0
0
1
1
0
0
0
2
1
0
0
0
0
8
0
1
0
0
0
0
2
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
2
0
1
0
1
0
1
0
0
0
0
2
0
0
0
0
2
0
2
1
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
2
2
0
1
0
2
0
2
1
1
2
0
0
1
1
2
0
0
1
0
0
2
1
0
1
2
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
2
1
2
0
1
0
2
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
2
0
0
0
1
0
0
1
2
0
0
0
0
1
1
0
0
0
2
2
0
0
2
1
0
0
1
2
0
1
0
1
0
0
2
2
2
0
0
2
1
0
0
2
0
0
1
1
0
1
1
0
0
0
0
0
1
0
1
0
0
2
3
0
0
0
2
0
0
0
0
0
1
0
0
1
1
0
0
0
2
0
1
0
0
0
0
0
1
0
1
1
0
2
0
4
0
2
2
0
0
0
1
0
2
1
1
0
0
1
2
1
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
1
1
0
0
0
1
0
2
1
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
4
0
0
1
0
3
0
0
0
0
0
2
0
1
1
0
1
2
0
2
0
0
1
1
1
0
2
2
0
0
2
0
1
0
1
2
0
0
2
0
0
5
1
0
1
2
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
2
0
1
0
0
0
0
1
1
0
2
1
0
1
0
0
0
1
1
1
2
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
1
0
1
0
1
0
0
2
0
2
1
0
1
1
0
2
1
0
0
1
2
0
0
1
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
1
0
1
1
2
0
2
2
0
2
2
1
1
0
1
0
0
0
2
2
1
1
1
0
2
0
1
0
0
0
0
0
0
1
1
2
0
0
0
3
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
2
2
0
0
0
2
1
0
2
0
0
0
1
1
1
0
0
1
0
0
1
1
0
1
0
0
0
2
0
2
1
0
1
0
0
1
0
1
0
0
0
1
0
1
0
0
2
0
2
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
2
2
1
1
0
2
0
2
0
0
1
1
1
0
1
0
2
0
1
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
1
2
0
0
0
2
0
0
2
0
1
0
0
1
0
0
2
0
3
1
0
0
1
2
0
0
0
0
0
1
1
0
0
2
0
1
1
1
2
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
2
0
0
0
1
1
2
0
0
0
0
2
0
3
1
1
0
0
0
0
0
0
2
0
0
1
0
0
2
0
2
2
0
2
0
0
0
0
0
1
0
0
0
1
3
0
0
0
0
0
2
0
0
1
0
2
2
0
2
0
2
0
0
0
2
0
3
0
4
0
0
1
0
0
0
2
2
7
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
2
4
0
0
0
0
1
1
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
1
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
2
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
2
0
1
0
0
1
0
2
0
0
1
0
2
0
0
1
2
0
0
1
0
2
0
1
0
0
2
1
0
0
2
2
3
0
0
1
0
0
0
1
0
0
2
0
0
0
1
0
0
2
0
0
2
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
1
0
0
2
1
1
1
0
0
2
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
2
0
1
0
0
2
0
0
2
0
0
0
1
0
1
0
2
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
1
0
0
0
2
0
1
0
0
1
1
0
0
2
1
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
2
1
2
0
2
0
0
2
0
1
2
0
1
0
0
3
0
4
1
2
1
2
0
1
0
1
0
0
0
0
3
1
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
2
0
1
2
1
2
1
0
0
2
0
2
0
1
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
1
0
0
0
2
0
1
2
0
0
0
0
0
1
0
2
1
0
0
0
0
0
1
3
0
0
1
0
0
0
2
0
0
2
1
1
1
0
0
1
0
0
2
0
0
0
0
1
2
2
0
0
1
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
2
1
0
1
0
0
0
0
1
2
0
1
0
0
0
0
1
2
1
2
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
1
1
2
2
0
0
1
0
2
1
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
2
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
2
2
0
0
3
2
1
0
0
0
2
0
0
0
0
1
0
2
1
0
2
1
0
2
2
3
0
1
2
2
0
0
0
1
2
0
0
0
1
0
0
1
4
1
0
0
0
1
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
2
0
1
0
1
1
0
2
1
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
2
0
0
2
2
1
0
0
0
2
0
1
0
1
0
1
0
0
1
3
1
0
2
1
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
1
1
0
2
0
2
0
0
0
1
0
3
1
0
1
1
0
0
2
0
0
0
1
0
2
1
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
2
1
0
1
0
0
1
0
0
2
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
2
1
0
3
0
2
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
2
2
0
0
2
1
1
1
0
1
0
0
1
2
1
0
0
0
0
3
0
0
0
0
1
1
0
1
0
0
2
0
0
0
0
1
2
1
2
0
0
3
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
2
0
1
3
0
0
0
0
0
2
2
0
0
1
1
1
0
1
0
0
0
1
2
0
2
0
0
0
2
1
1
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
3
1
0
0
1
0
0
1
2
0
0
0
0
0
6
2
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
2
0
3
0
0
3
0
0
0
0
1
1
0
0
0
2
0
2
0
0
0
0
0
2
2
0
0
0
0
2
0
0
1
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
1
2
0
1
1
0
0
0
0
1
0
0
2
1
2
2
0
1
2
1
0
0
2
0
3
0
0
0
0
0
1
2
1
1
0
0
0
1
0
2
0
0
0
1
0
1
2
2
0
1
2
1
0
2
0
0
1
1
2
0
1
0
2
1
1
2
0
0
1
0
0
0
2
0
2
1
0
0
0
0
1
0
1
0
0
3
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
2
2
0
0
0
0
1
0
0
1
2
1
2
0
0
0
0
0
2
0
0
0
0
0
2
0
1
2
0
0
1
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
2
1
2
0
0
2
2
1
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
2
0
1
2
0
0
0
0
0
0
0
1
0
3
1
0
0
2
0
0
1
1
2
0
2
1
1
0
0
2
0
0
1
0
0
0
2
1
0
0
2
0
0
2
0
0
0
0
2
0
0
2
0
0
2
0
2
0
1
0
1
0
0
3
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
3
2
0
2
0
2
1
0
0
0
2
2
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
3
2
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
2
1
0
0
1
0
0
1
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
1
0
0
0
1
0
0
0
1
1
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
1
3
2
0
2
0
1
2
0
0
0
0
0
8
1
1
0
0
0
0
1
2
2
0
0
1
0
2
0
0
2
1
0
2
2
0
0
0
0
0
1
1
0
0
0
2
2
0
0
2
1
0
0
1
0
0
2
0
2
0
0
2
5
1
0
0
0
0
2
0
0
0
1
1
1
0
0
1
1
0
2
2
1
2
2
1
2
1
0
3
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
8
1
0
0
3
4
0
2
2
0
0
0
2
1
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
2
0
1
1
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
2
0
0
0
2
0
5
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
3
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
1
0
0
0
0
0
2
0
1
1
1
0
0
1
0
1
0
1
0
2
2
0
0
2
1
1
1
1
0
0
1
0
1
0
0
1
0
0
0
1
9
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
2
0
1
0
8
2
2
1
2
0
0
0
1
0
0
0
2
1
0
0
0
0
1
2
0
2
0
2
1
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
2
0
0
2
0
0
0
0
2
1
2
1
0
0
0
2
0
1
0
2
0
0
0
1
0
0
2
0
0
2
0
2
0
0
2
0
0
0
1
0
1
0
1
0
0
2
5
0
0
2
0
1
1
1
0
2
2
1
12
0
0
3
0
1
0
0
0
0
1
3
0
1
0
1
0
1
0
1
0
0
0
2
2
1
0
0
2
0
0
2
0
1
0
2
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
1
1
0
0
0
4
0
0
0
0
0
4
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
1
0
2
1
1
0
0
0
2
2
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
2
3
0
0
0
0
2
1
0
2
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
1
0
1
1
2
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
2
1
0
0
0
1
0
1
2
1
3
0
1
0
1
0
0
0
3
0
0
0
0
1
0
2
0
0
0
1
0
2
1
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
2
2
0
0
0
2
1
1
0
1
0
2
0
0
0
0
0
2
0
1
2
0
0
2
0
1
0
0
0
2
2
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
1
1
1
0
0
1
0
0
2
2
0
0
0
1
2
0
1
0
2
0
1
0
0
1
0
0
0
0
2
0
0
3
0
0
0
0
1
0
0
0
0
2
1
0
0
2
0
0
1
1
1
0
0
0
0
2
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
8
1
0
2
0
0
0
1
0
2
0
1
2
0
0
0
1
0
0
0
0
0
0
1
1
0
1
2
0
0
0
0
0
2
0
0
1
0
2
2
0
0
0
1
0
2
0
1
0
0
1
0
1
0
0
1
1
0
2
0
0
1
0
0
0
0
0
0
2
1
0
2
0
2
0
2
0
0
0
1
4
1
0
2
1
0
1
0
1
0
0
0
0
0
0
1
2
0
0
0
1
1
7
1
2
2
0
1
2
0
1
0
1
2
1
2
2
0
0
2
2
3
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
3
0
1
1
1
1
0
3
0
0
1
2
0
2
0
2
0
0
0
0
0
0
2
0
2
0
1
0
2
0
0
1
2
0
0
0
0
0
1
0
2
0
0
2
2
0
0
1
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
2
1
1
0
1
2
1
0
0
0
3
0
0
0
0
0
2
2
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
2
2
0
2
0
0
0
1
0
0
0
0
1
2
0
0
1
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
1
1
0
0
0
1
2
2
0
0
0
1
0
2
0
1
0
2
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
1
1
2
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
2
1
0
0
0
0
0
2
0
1
0
1
0
0
2
0
0
0
0
0
2
1
2
0
1
0
0
2
0
0
0
1
0
1
0
0
0
2
0
0
0
0
1
2
1
0
2
0
1
0
0
1
0
2
0
1
1
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
3
0
1
0
0
1
1
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
1
0
2
1
0
1
0
0
1
2
0
0
2
0
1
3
0
1
0
0
1
0
0
0
1
1
0
0
1
1
0
0
0
1
1
1
0
0
2
0
0
0
0
0
0
0
0
1
2
2
0
1
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
2
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
1
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
2
0
0
2
0
0
0
1
1
0
0
0
0
0
2
2
2
2
0
0
0
0
0
3
0
0
0
0
0
1
1
0
0
2
1
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
1
2
0
0
0
0
2
0
1
2
1
2
0
0
0
0
0
0
3
0
0
0
0
1
0
2
0
2
0
1
0
1
3
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
2
0
0
1
1
0
3
0
0
1
0
3
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
2
2
2
0
0
0
1
0
1
2
0
1
0
1
0
0
2
0
0
1
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
1
2
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
1
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
3
2
0
0
0
0
2
2
1
0
1
0
0
0
1
0
0
0
2
1
0
3
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
2
0
0
2
0
0
2
0
0
1
2
1
0
2
2
2
1
0
0
0
0
2
1
0
0
0
7
1
2
0
2
0
2
2
1
0
2
2
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
2
0
0
0
0
1
0
2
0
1
0
0
0
0
2
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
3
0
2
0
0
0
0
1
1
1
0
1
0
2
1
0
0
0
1
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
1
0
0
0
0
2
0
1
2
1
0
2
0
0
0
0
0
0
0
0
0
2
1
0
2
0
2
1
0
2
0
0
1
1
1
0
0
0
0
0
1
0
0
0
2
0
0
3
0
0
0
2
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
2
1
2
1
0
0
0
2
4
0
0
5
0
0
0
0
1
0
0
3
0
2
2
2
1
2
0
0
0
0
0
2
0
0
4
1
0
1
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
2
2
0
0
0
2
0
3
0
2
3
0
0
0
2
1
2
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
2
1
0
0
1
1
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
2
0
0
1
0
0
0
2
0
0
0
0
5
0
1
0
1
0
1
0
2
2
0
0
2
2
3
0
2
0
2
0
1
0
1
1
2
0
0
1
2
0
1
2
2
2
1
2
0
0
0
1
0
0
1
0
1
2
0
0
3
2
0
0
0
2
0
0
0
0
2
1
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
2
0
0
0
2
0
2
0
2
0
1
1
1
0
0
1
0
0
0
2
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
1
1
0
0
0
2
0
0
0
2
0
2
1
0
1
0
0
0
1
1
0
2
2
2
1
2
0
0
0
2
0
2
0
0
0
0
0
1
2
0
2
0
0
1
0
0
0
1
0
1
3
0
1
2
2
0
0
0
2
0
0
0
2
2
0
1
2
1
6
0
0
0
0
0
0
0
0
1
0
5
0
1
0
0
0
0
0
0
0
1
1
3
1
0
0
0
0
0
1
2
2
0
1
1
0
2
0
0
0
1
0
0
2
0
0
2
2
0
0
1
1
0
3
0
2
0
0
1
0
0
0
2
0
0
0
1
1
0
0
2
1
0
0
1
2
1
0
0
0
0
0
1
1
1
0
0
1
0
0
0
1
1
2
2
1
0
0
0
1
2
0
1
0
3
0
1
0
0
0
0
0
1
0
0
2
0
0
0
1
0
2
0
1
0
1
2
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
2
0
1
0
2
0
1
0
0
0
0
2
2
0
0
0
1
0
0
1
2
2
1
2
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
2
0
2
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
7
0
0
2
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
2
1
1
2
1
0
0
0
0
1
0
0
0
0
1
0
0
1
2
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
1
0
0
0
1
2
2
1
0
1
0
1
0
1
0
2
0
0
0
0
1
1
0
0
0
1
0
2
1
1
2
0
0
0
1
1
0
0
0
2
1
1
0
1
0
0
0
0
1
0
0
1
1
1
0
0
1
2
1
0
0
0
2
0
1
3
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
2
0
2
0
2
2
2
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
2
0
0
2
2
0
0
2
0
0
2
0
0
2
0
0
1
1
0
2
0
0
0
0
1
1
2
0
2
2
0
2
0
1
1
0
0
2
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
2
0
2
2
0
0
5
0
2
0
3
3
0
0
0
0
0
2
0
1
0
1
0
2
0
0
0
0
2
0
1
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
1
0
2
0
0
1
2
0
1
0
0
1
0
1
1
0
2
0
0
0
1
0
0
2
0
0
0
0
2
0
0
1
2
0
1
2
0
0
0
0
0
0
1
2
0
1
2
2
1
0
1
2
0
1
0
0
0
0
0
1
1
5
0
0
3
1
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
2
0
0
2
0
3
0
0
0
2
5
0
0
1
0
0
2
0
0
0
0
1
0
0
2
0
1
1
0
0
2
0
0
1
0
0
0
0
2
2
0
0
0
1
0
2
1
0
0
0
1
3
0
0
0
0
0
0
0
0
2
1
0
0
3
0
0
0
0
0
0
0
0
1
0
0
1
0
2
1
2
0
0
0
1
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
1
2
2
0
2
2
2
1
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
2
0
0
0
0
1
0
2
0
0
2
0
2
0
0
1
0
0
0
0
0
0
1
0
1
2
2
0
0
0
1
0
1
2
0
0
0
0
1
0
1
2
0
1
1
1
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
2
2
1
0
2
1
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
1
1
1
0
0
2
0
0
0
1
2
0
1
2
1
0
1
1
0
0
0
1
1
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
1
0
0
0
2
1
1
1
0
2
0
0
2
1
0
0
3
0
1
0
0
0
0
1
1
0
0
0
0
2
1
0
0
0
0
2
0
0
2
0
1
0
2
0
0
1
1
1
0
0
0
0
1
0
3
0
0
1
0
0
1
0
0
1
0
0
2
0
0
2
0
0
3
0
0
1
0
0
2
1
2
0
0
0
1
2
0
1
2
0
0
0
0
0
0
0
0
0
0
2
3
3
2
0
1
0
2
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
1
1
2
2
1
2
2
0
0
0
1
0
0
0
0
2
2
0
1
0
0
2
0
0
0
1
1
0
0
0
2
0
2
0
0
0
1
1
2
2
0
0
0
0
0
2
0
2
0
1
0
0
0
4
0
0
0
0
0
1
1
0
0
3
0
1
2
1
2
0
0
3
0
0
0
2
4
0
2
1
1
3
0
2
0
0
1
0
0
0
4
1
0
3
1
0
0
1
0
2
0
0
1
0
2
3
0
2
1
0
0
0
0
1
0
0
2
0
0
0
2
0
1
2
3
0
0
0
0
2
0
0
2
2
2
3
2
0
0
0
0
1
1
1
2
0
0
1
0
1
1
1
0
0
2
0
0
2
0
0
1
0
0
1
0
0
1
2
1
0
1
0
1
0
1
1
0
2
3
2
1
0
0
0
0
1
1
7
0
0
2
1
1
1
2
2
0
0
0
0
0
0
1
0
2
0
1
0
0
0
2
0
1
0
0
2
0
0
2
0
0
0
1
0
2
2
1
2
0
0
0
0
1
0
0
0
0
0
2
2
1
0
0
2
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
1
1
0
2
5
1
0
0
0
1
0
0
2
1
0
2
0
0
0
0
1
1
1
0
0
2
0
0
0
0
2
0
1
0
1
2
0
0
0
3
0
0
0
1
0
0
3
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
1
0
2
2
0
0
0
0
0
0
0
2
1
0
2
2
0
1
1
3
4
1
1
0
0
1
1
0
2
0
1
3
0
0
0
1
2
0
2
0
0
1
1
0
0
0
3
0
0
0
0
2
0
0
1
0
0
1
2
1
0
0
0
2
0
0
0
0
1
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
2
1
0
6
0
5
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
2
1
0
0
2
3
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
2
2
1
1
0
0
1
0
0
0
0
0
2
0
2
0
0
0
2
0
1
0
0
1
0
2
2
2
0
0
0
0
2
0
0
0
0
0
1
2
0
1
2
0
2
0
0
1
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
1
0
0
0
1
0
2
0
0
0
2
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
1
0
0
2
2
1
1
1
0
0
0
0
0
0
3
1
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
1
2
0
1
1
0
1
0
0
0
1
0
3
0
2
1
1
0
2
0
2
0
0
2
0
0
0
1
0
0
1
0
2
4
1
0
0
2
1
0
0
1
1
0
2
0
1
2
2
0
2
2
0
2
0
2
1
0
1
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
2
0
2
2
0
2
0
1
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
2
1
1
2
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
1
2
1
0
1
1
2
0
0
0
1
1
0
0
0
2
2
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
1
0
0
0
1
0
1
1
0
0
1
2
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
2
2
0
0
1
1
0
0
2
1
0
2
2
0
0
0
2
1
0
0
2
1
0
0
2
3
0
1
0
0
0
2
0
1
1
2
0
1
0
1
0
0
1
2
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
4
2
0
0
2
1
0
0
0
0
2
1
0
0
1
0
2
1
2
0
0
1
1
0
1
0
2
0
1
2
0
0
4
0
2
1
0
0
0
0
0
1
0
2
1
2
0
2
0
1
0
0
0
1
0
2
0
0
0
0
1
2
0
0
0
0
4
2
1
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
2
0
2
2
0
0
0
2
0
0
2
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
2
0
1
0
0
2
2
0
3
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
1
0
1
0
0
2
0
0
0
1
0
0
1
2
2
0
0
2
1
2
2
0
2
0
0
0
0
0
0
2
0
1
0
2
0
0
2
0
0
0
0
0
2
0
1
0
0
2
1
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
5
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
2
0
0
0
1
0
2
0
1
0
0
0
0
0
2
0
0
2
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
1
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
2
0
1
0
0
1
1
0
2
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
2
1
0
0
0
1
0
0
0
0
0
0
2
0
0
2
2
2
1
0
0
1
0
0
1
1
0
0
0
1
1
0
0
0
1
1
1
0
1
0
2
0
1
0
0
0
0
2
1
0
0
0
1
3
0
1
2
0
0
2
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
1
0
0
1
0
2
1
2
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
3
1
1
1
2
0
0
2
2
1
0
0
2
1
2
0
0
0
0
2
0
0
0
1
1
2
1
0
2
0
0
0
2
0
1
1
0
0
0
0
2
2
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
1
1
0
4
2
0
1
0
1
0
1
0
1
1
1
0
2
0
0
2
0
0
2
0
0
2
0
0
2
0
0
2
0
1
0
0
2
1
0
1
0
1
0
0
2
0
0
0
1
0
0
1
0
4
1
2
0
0
1
2
0
0
0
0
1
2
0
0
1
2
1
1
3
3
2
3
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
2
2
0
2
0
1
2
0
0
0
0
0
2
0
0
0
1
1
0
1
0
2
1
2
0
0
0
0
2
2
2
0
2
0
0
0
0
0
2
1
0
0
1
1
0
0
0
0
0
0
0
2
2
0
0
1
0
1
2
0
2
0
2
0
0
0
0
0
2
0
1
0
2
1
0
0
1
0
5
0
0
0
0
1
1
0
7
1
2
1
0
0
0
0
1
2
0
0
0
0
0
0
2
1
0
0
2
1
1
0
0
0
0
1
0
0
1
0
0
2
0
2
0
0
0
0
2
1
0
0
2
0
1
1
5
1
1
0
3
0
0
0
1
0
0
0
2
2
0
2
0
0
0
0
0
0
2
0
0
1
0
4
0
0
2
0
3
0
2
2
0
0
0
1
0
1
2
0
0
2
0
2
0
0
0
0
2
1
0
0
1
1
2
1
2
0
0
0
0
1
0
0
0
0
0
0
2
2
0
1
0
0
1
3
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
2
2
2
2
0
0
0
2
0
0
0
1
0
0
0
2
1
0
0
0
1
1
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
2
0
1
2
0
0
0
0
0
3
1
2
0
0
1
0
0
0
0
2
1
0
0
0
0
0
3
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
1
0
2
2
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
1
2
1
0
0
0
0
1
0
0
0
0
1
0
2
0
1
0
2
2
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
1
2
0
0
0
1
0
0
0
3
0
1
3
0
0
3
2
0
2
1
0
1
2
0
0
0
1
0
0
0
0
1
0
0
1
2
0
0
2
0
2
2
0
0
0
0
0
0
0
0
1
0
1
1
2
0
0
0
0
0
1
1
0
2
2
2
0
1
2
0
1
1
2
0
0
3
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
2
0
0
1
1
0
0
4
1
0
0
0
0
0
0
3
2
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
2
1
0
0
0
0
1
1
1
0
0
0
0
0
0
2
0
1
0
0
2
2
0
0
0
0
0
1
0
0
2
1
1
2
0
1
2
0
0
0
1
0
0
1
0
2
2
0
0
0
0
0
0
0
1
2
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
2
0
1
3
0
0
1
0
1
0
0
0
0
2
2
0
0
1
2
0
0
0
0
0
0
0
2
0
2
3
0
0
0
2
1
0
0
2
0
0
0
1
2
4
0
2
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
2
5
1
0
0
0
0
0
2
0
1
0
2
2
1
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
1
2
2
0
0
0
1
2
2
0
2
1
1
0
0
1
0
0
0
0
2
0
1
0
0
2
1
0
0
0
0
1
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
2
2
2
1
0
0
2
1
0
2
0
0
1
0
0
0
2
0
0
0
0
0
1
2
2
2
2
1
0
0
0
0
0
8
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
1
1
0
2
0
0
0
0
0
0
0
2
2
1
1
2
0
2
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
2
1
0
0
0
2
0
0
0
0
0
2
1
0
0
0
1
2
2
3
0
1
0
2
0
0
1
0
0
0
0
1
1
0
0
2
1
0
1
0
0
1
1
1
0
1
1
0
0
1
0
1
0
0
0
0
2
0
0
2
2
0
0
0
2
1
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
1
0
1
1
0
0
0
1
0
0
1
0
1
1
0
2
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
1
1
0
1
3
0
0
0
2
0
2
0
0
0
0
1
0
0
1
0
0
1
0
1
1
3
0
0
0
0
0
2
0
1
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
2
0
0
1
0
0
0
1
0
2
0
0
0
1
0
0
2
0
3
2
2
2
0
0
2
0
0
0
1
1
0
1
2
0
0
0
1
0
0
0
0
2
2
0
1
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
2
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
3
1
0
0
0
0
0
2
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
1
4
0
0
1
0
2
1
0
1
0
1
0
0
2
0
0
0
2
0
0
0
1
3
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
1
0
0
0
1
2
0
1
0
1
1
0
2
2
0
0
1
2
0
1
1
0
0
0
0
1
0
0
1
0
0
2
0
1
1
0
0
0
0
0
2
3
3
0
0
0
2
0
0
1
1
2
0
0
0
1
0
0
0
2
2
0
1
0
1
0
2
0
0
5
0
1
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
1
2
0
0
0
1
1
1
0
2
0
0
2
0
0
0
0
1
0
0
1
2
0
0
2
0
0
0
0
2
0
0
0
0
4
2
0
0
2
0
0
0
0
0
1
0
2
1
2
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
1
0
1
2
0
0
2
1
0
2
1
2
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
1
1
0
0
0
0
2
1
0
2
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
1
2
2
0
0
0
2
0
0
1
1
0
0
0
0
0
2
0
0
0
2
0
0
3
0
0
1
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
3
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
2
0
2
1
0
0
1
0
0
2
0
2
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
2
1
1
1
0
0
1
0
0
0
1
0
0
2
1
1
0
0
2
0
0
1
1
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
1
2
0
0
0
0
2
0
0
0
0
2
0
2
3
0
0
1
1
2
0
0
0
0
0
0
1
1
2
0
0
0
1
1
2
1
1
0
2
1
0
0
0
0
2
0
1
0
0
0
0
2
0
0
2
0
1
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
1
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
1
0
2
0
0
0
2
0
0
2
0
2
2
2
0
0
0
1
1
1
9
0
2
2
0
1
0
0
0
0
2
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
3
2
0
0
0
1
0
0
0
1
0
2
0
0
0
3
0
1
2
1
2
2
2
2
2
0
0
1
0
0
1
0
0
0
2
0
0
1
0
0
0
2
1
2
0
0
1
0
0
0
1
0
0
1
0
0
0
2
0
1
0
0
1
0
0
1
1
0
9
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
3
0
2
0
2
1
0
0
2
2
1
0
0
1
0
1
0
0
3
1
1
1
1
0
1
4
0
0
1
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
1
1
2
2
1
0
0
0
0
0
0
1
0
1
1
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
1
0
1
2
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
2
1
2
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
1
2
0
0
0
1
3
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
2
0
2
0
0
1
1
1
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
1
0
0
0
0
1
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
2
2
0
0
0
0
2
0
1
1
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
1
0
0
2
0
0
0
1
1
1
0
0
0
3
1
2
0
0
0
0
0
0
0
1
2
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
1
1
0
0
0
2
1
0
0
2
0
1
2
0
1
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
1
1
1
0
0
2
1
2
0
0
0
3
4
1
0
0
0
2
0
0
2
0
0
1
3
0
2
0
5
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
4
0
2
0
2
0
0
0
0
1
0
0
2
1
0
0
0
1
0
0
0
1
0
1
0
1
3
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
1
1
2
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
2
0
1
2
2
2
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
1
1
0
0
2
0
1
1
0
0
2
0
1
0
0
0
0
2
0
0
0
1
1
0
7
0
1
0
0
0
0
0
2
2
0
3
1
0
0
2
1
1
0
0
1
0
0
0
1
2
1
0
0
1
2
2
2
0
0
0
2
2
0
0
0
2
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
5
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
1
1
2
0
0
1
0
0
0
1
0
0
2
0
1
2
2
0
0
1
1
0
0
0
1
0
0
0
1
0
0
2
0
1
2
0
0
0
0
2
0
0
0
1
3
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
2
1
0
3
2
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
2
0
0
2
0
0
2
0
0
0
0
0
1
1
0
3
2
0
0
0
0
0
1
0
0
0
0
1
0
3
0
0
0
0
0
2
0
0
2
0
0
0
0
5
2
2
1
2
0
0
1
0
1
0
0
2
0
2
0
0
0
1
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
3
5
0
1
0
0
1
0
0
2
0
2
2
0
1
0
1
0
2
1
0
1
0
2
0
0
0
1
0
0
2
1
0
1
0
0
1
1
2
1
0
1
0
0
2
0
2
1
0
0
0
0
0
0
0
2
1
0
2
0
0
0
2
0
0
0
0
0
0
2
0
2
1
0
0
2
0
3
2
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
1
1
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
2
1
1
0
0
2
0
2
1
0
1
1
0
0
0
2
0
0
2
0
3
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
2
0
0
0
0
2
0
1
0
0
1
1
0
0
0
0
2
0
0
1
0
2
1
0
0
2
0
0
0
0
0
2
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
2
1
0
0
2
2
2
2
1
2
0
2
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
2
1
1
0
0
1
0
0
1
0
0
0
0
2
1
0
0
0
2
2
1
1
2
1
0
1
0
1
1
0
0
0
0
0
2
0
1
0
0
0
0
1
1
2
0
0
1
2
1
0
0
0
1
0
0
2
0
1
0
0
2
0
0
1
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
2
0
0
0
3
2
0
0
1
1
0
2
1
1
2
0
1
2
0
2
0
1
0
2
2
1
0
0
2
0
0
0
0
1
3
0
0
1
0
2
0
0
0
1
2
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
1
0
0
0
1
0
1
0
0
0
1
2
2
1
0
0
0
0
2
2
0
1
1
0
0
2
0
0
1
0
2
2
0
2
0
1
0
0
0
0
0
1
2
2
1
0
0
0
0
2
0
0
2
6
0
0
0
0
1
1
0
0
0
3
0
1
0
0
0
0
0
0
1
0
2
0
0
2
0
0
1
0
1
0
0
1
2
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
2
2
2
1
2
0
4
0
2
1
0
1
0
0
1
2
0
0
0
0
1
0
1
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
2
0
0
1
0
1
1
2
0
2
3
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
1
0
2
0
0
0
1
0
0
0
1
0
0
0
1
0
2
2
1
0
0
0
2
2
2
0
0
0
0
0
0
0
2
2
2
1
2
0
1
0
0
0
2
0
3
1
0
0
2
0
0
2
1
0
3
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
2
2
0
2
0
0
1
1
0
0
0
2
0
2
0
0
1
0
0
5
0
0
2
0
0
0
0
0
2
1
0
1
0
2
2
0
0
0
0
0
1
0
0
3
0
1
0
2
1
0
0
0
0
1
0
0
0
0
2
2
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
3
0
0
2
1
3
0
0
2
1
1
0
4
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
2
0
1
0
0
0
1
0
1
2
0
0
0
3
1
0
1
2
2
0
0
0
1
1
1
1
1
1
0
2
0
2
1
1
0
1
0
0
0
0
0
2
1
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
3
0
2
0
1
0
1
1
0
2
2
1
2
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
3
1
0
0
0
0
0
0
2
0
2
0
0
0
0
2
1
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
1
0
0
0
2
0
2
1
0
0
0
0
1
0
0
1
3
0
0
0
0
0
2
1
0
0
0
4
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
1
2
1
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
2
1
0
3
0
0
0
1
0
0
2
0
1
0
0
1
2
0
2
0
0
0
2
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
1
0
0
1
2
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
2
1
0
0
0
0
0
1
0
1
0
0
0
4
3
3
0
0
0
0
1
0
1
1
1
2
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
1
0
2
0
1
2
0
0
0
0
1
0
2
2
0
0
0
2
0
1
0
0
2
2
0
1
1
0
0
2
2
2
0
0
1
0
1
0
0
0
0
0
0
2
0
2
0
2
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
2
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
2
1
0
4
1
0
0
2
0
0
0
0
0
5
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
2
0
0
1
1
1
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
2
2
0
0
2
1
0
1
0
0
0
0
1
0
0
1
1
0
2
0
0
1
0
0
2
0
0
0
3
0
0
1
0
0
1
0
0
3
0
0
1
0
0
2
1
2
0
0
1
1
0
1
0
3
0
0
1
2
2
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
1
1
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
1
0
1
2
2
1
0
2
1
0
0
0
0
0
0
2
2
0
3
0
0
1
1
1
0
0
1
0
0
2
2
0
1
0
0
1
0
2
0
3
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
2
0
2
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
2
2
0
0
0
0
0
2
0
0
1
2
0
1
0
1
0
0
1
0
0
0
0
1
0
0
1
0
2
0
0
2
0
1
1
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
1
3
0
0
0
2
0
0
0
1
2
0
0
0
2
0
2
0
0
1
3
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
3
1
0
0
1
1
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
2
2
1
1
0
0
0
1
0
0
0
1
0
0
2
0
1
0
1
1
0
2
1
3
0
0
0
2
0
4
0
1
0
2
0
0
1
2
0
1
1
2
0
1
0
2
0
1
0
1
0
0
0
0
1
0
0
0
2
0
0
0
1
0
1
2
0
0
0
2
0
0
1
0
1
2
1
2
2
0
0
0
1
0
0
2
0
0
2
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
1
2
0
1
2
2
2
0
1
1
0
0
3
2
0
0
0
0
0
2
3
0
0
0
0
0
2
0
2
0
0
0
2
1
0
2
0
0
2
2
2
0
2
1
1
0
0
0
0
1
0
0
2
0
13
1
3
0
0
1
0
0
0
1
0
0
0
2
1
1
2
0
0
0
2
0
2
0
0
0
2
3
0
0
0
1
0
1
0
2
0
0
0
3
0
0
0
0
2
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
1
1
1
0
2
0
0
4
1
1
1
0
0
0
2
1
1
0
0
1
0
3
0
0
0
0
0
0
2
1
0
1
0
0
1
1
0
2
1
2
2
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
2
1
0
0
0
1
2
1
1
1
0
2
1
0
2
0
0
1
0
0
1
0
3
2
0
0
1
2
0
1
0
0
2
0
1
0
0
1
3
0
0
2
0
0
0
0
1
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
2
1
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
6
0
0
0
2
1
2
1
1
0
0
0
2
2
0
0
0
2
1
0
0
0
1
2
0
2
3
0
0
0
2
0
2
0
1
0
0
0
2
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
1
0
1
0
0
1
2
0
0
0
0
2
0
0
1
0
0
2
0
2
0
0
0
0
0
0
2
0
0
2
2
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
2
0
1
0
1
2
0
1
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
1
0
1
0
2
0
0
1
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
2
0
1
1
0
0
0
2
1
4
1
0
2
0
0
0
1
1
0
3
0
0
0
0
1
0
1
6
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
3
2
0
1
1
2
0
2
0
1
2
1
0
0
0
0
2
0
2
0
0
0
2
2
0
2
2
1
0
4
1
0
1
0
0
1
2
0
2
0
0
2
0
0
2
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
1
0
1
2
0
2
0
0
0
1
2
0
0
0
2
2
2
0
0
1
0
2
0
0
0
2
0
0
1
0
2
0
3
1
0
0
2
1
0
0
0
2
1
0
2
1
0
1
2
0
1
0
0
0
1
1
1
0
0
0
1
2
0
0
0
2
0
0
0
2
0
0
1
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
2
0
0
0
1
1
0
0
0
0
2
1
0
0
2
2
3
0
0
0
0
2
0
2
0
3
0
0
0
3
1
0
0
2
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
2
1
1
0
1
1
0
0
1
0
0
1
0
2
1
0
5
2
0
0
0
1
0
0
0
0
0
0
1
1
1
0
2
2
2
0
0
0
0
3
0
0
0
1
0
0
0
2
2
0
1
1
0
0
1
1
0
2
0
1
0
1
0
0
0
0
1
0
0
1
0
0
1
2
0
0
0
0
0
2
1
0
0
1
1
2
2
0
0
2
0
0
0
0
0
1
0
2
0
1
2
0
0
2
0
1
2
2
1
0
0
1
1
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
3
0
0
0
0
2
0
0
0
0
1
0
0
2
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
2
2
0
0
0
0
0
0
0
1
2
1
2
1
1
0
2
0
0
0
2
1
1
0
0
1
0
0
1
1
0
0
0
1
2
1
0
0
1
2
0
3
0
0
0
0
0
0
2
0
2
0
0
2
0
0
1
0
0
1
0
0
0
0
1
1
0
0
1
0
2
1
1
1
0
1
1
0
2
1
0
3
0
4
3
2
1
1
2
4
0
2
2
2
2
0
0
0
0
1
1
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
2
0
1
0
1
2
0
2
0
1
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
2
1
2
0
0
1
0
0
2
0
0
2
0
1
0
2
0
1
0
0
1
0
0
0
1
0
2
0
0
0
1
0
0
0
0
2
2
0
2
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
2
1
0
0
0
2
0
0
0
0
2
3
0
0
0
0
0
0
2
0
0
1
3
0
3
0
2
2
1
2
2
0
2
1
0
2
0
1
0
0
1
0
1
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
1
0
2
0
0
2
2
0
2
4
1
2
2
0
1
0
0
2
0
0
3
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
2
0
0
2
0
0
0
0
2
0
0
2
2
2
1
2
3
0
2
0
0
3
0
1
0
3
2
1
0
0
0
0
1
0
0
3
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
3
0
1
1
1
0
0
0
0
0
1
2
1
0
2
0
0
1
2
0
0
2
2
0
0
0
4
2
2
0
2
0
0
0
0
0
0
0
0
1
2
0
0
1
0
2
0
2
2
0
3
1
0
0
0
0
0
1
0
0
1
0
2
1
0
0
1
0
2
0
2
0
0
0
0
4
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
2
1
0
3
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
1
0
1
0
2
1
2
0
0
0
1
0
1
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
2
0
2
1
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
2
0
0
2
3
1
0
1
0
1
1
0
2
0
0
0
2
0
0
2
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
1
1
2
0
3
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
1
0
0
0
1
0
0
1
5
0
0
1
0
0
0
0
1
0
1
0
2
2
2
0
0
0
0
1
1
1
2
0
2
0
2
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
1
2
0
2
2
1
0
0
2
2
1
1
0
1
0
0
2
1
1
1
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
2
0
1
1
0
0
0
1
1
0
0
0
0
3
0
0
0
0
0
0
2
1
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
4
0
0
0
0
2
0
1
1
0
1
0
0
0
1
2
0
0
0
1
0
2
0
0
2
0
0
0
2
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
2
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
1
2
0
4
0
2
0
4
0
0
1
1
2
0
0
2
1
0
1
0
0
0
2
1
0
0
0
2
0
0
0
1
2
0
0
0
2
2
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
1
1
10
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
2
0
1
0
2
1
0
0
0
0
2
0
0
2
2
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
2
0
1
2
2
0
0
0
2
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
2
0
0
0
4
0
0
4
2
0
0
0
0
1
0
0
2
0
1
0
0
1
0
1
0
0
0
0
0
1
1
0
2
2
0
0
2
0
1
1
2
0
1
0
2
0
0
1
0
2
0
0
1
2
2
2
0
2
0
0
1
0
0
0
2
0
1
0
1
2
2
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
2
0
3
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
2
1
0
2
3
2
1
0
0
0
2
0
2
0
0
1
1
1
0
1
0
0
0
0
0
2
1
2
0
0
0
2
0
0
2
2
1
0
1
1
0
0
0
0
1
0
1
1
0
1
2
0
0
0
0
0
0
2
2
1
0
1
2
0
2
1
0
0
2
0
0
0
2
0
1
2
0
0
1
0
0
1
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
3
2
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
2
0
0
1
0
1
0
0
1
0
0
0
0
2
2
0
0
2
0
0
0
2
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
10
0
0
0
5
2
0
2
0
2
0
0
0
0
2
2
0
0
1
0
2
0
0
0
0
0
1
0
0
1
0
1
0
0
1
1
0
1
0
0
0
3
0
0
1
0
0
2
0
0
2
0
0
0
1
1
2
2
2
0
0
4
0
0
0
2
2
0
0
2
2
0
1
0
1
0
1
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
2
0
1
0
0
0
0
0
0
0
1
0
2
1
0
1
0
0
5
0
0
0
1
1
0
1
0
1
0
0
2
0
0
1
2
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
1
2
0
2
0
0
0
0
2
0
0
0
2
1
0
0
0
2
0
0
0
0
1
0
0
0
1
1
0
0
1
2
0
1
0
1
0
1
2
0
0
0
1
0
1
0
0
2
3
2
0
1
0
0
0
0
0
1
0
2
1
1
0
0
0
0
0
1
0
0
1
2
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
6
1
2
0
0
0
1
1
0
3
0
0
0
0
0
0
0
2
0
0
3
0
5
0
0
0
0
0
0
0
2
1
0
2
0
0
2
0
0
0
1
0
2
2
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
2
1
0
0
1
0
1
0
0
0
0
0
2
0
1
2
2
1
0
0
0
0
2
2
0
0
0
1
0
2
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
4
2
0
0
1
0
1
1
2
0
1
3
0
2
0
1
2
0
0
4
2
1
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
1
1
0
2
0
0
1
0
0
1
0
1
2
0
0
0
0
1
2
2
0
2
2
1
0
0
1
0
0
0
0
1
0
2
2
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
1
0
1
1
0
0
0
0
2
0
0
0
2
1
0
0
3
0
0
0
0
0
0
0
0
2
1
2
0
1
0
0
0
1
0
1
0
2
0
0
0
1
0
1
0
0
1
1
2
0
0
1
0
1
0
0
0
0
1
0
0
2
0
2
1
3
0
2
2
0
1
0
1
2
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
1
1
1
0
1
0
0
0
2
0
1
0
0
3
0
0
2
0
0
1
1
0
0
0
1
2
0
1
0
1
2
0
0
1
2
0
2
0
0
2
0
0
1
2
0
0
2
0
0
0
0
0
7
0
1
0
0
1
0
0
1
0
0
1
0
2
0
0
0
0
1
0
0
3
1
0
0
0
0
1
1
0
0
0
1
0
0
2
1
0
1
0
0
0
0
1
0
2
0
0
1
1
2
1
1
0
0
0
0
1
4
2
2
0
0
3
2
0
0
1
0
0
0
0
0
0
1
2
1
0
0
1
1
0
0
0
0
1
0
3
0
0
0
0
2
0
0
3
0
2
2
1
0
0
0
0
0
0
3
0
2
2
0
0
2
0
0
0
0
1
0
0
2
0
1
0
2
0
0
0
2
1
0
0
0
0
1
0
0
1
0
2
0
1
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
2
2
0
2
2
0
0
0
2
0
0
1
0
1
0
0
0
2
0
0
0
3
2
0
0
0
0
1
2
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
1
0
1
1
2
2
0
0
0
0
0
0
2
0
0
0
1
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
1
0
0
0
0
1
0
2
0
0
0
2
2
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
3
0
0
1
0
0
0
2
0
0
0
1
0
2
0
0
0
2
0
0
0
1
0
1
0
0
0
1
0
1
1
0
1
0
0
0
2
0
0
2
0
1
0
0
1
2
2
1
0
0
0
0
1
0
0
1
0
2
0
0
0
0
2
2
1
2
1
2
2
1
1
1
0
2
1
0
0
0
0
0
0
0
0
0
2
1
0
1
3
2
0
2
1
1
2
2
1
0
2
0
0
0
0
2
3
1
2
0
1
0
0
0
2
2
0
0
1
0
0
2
0
1
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
2
1
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
2
1
1
0
0
0
0
0
0
0
0
1
0
2
0
1
2
1
0
0
0
0
0
2
1
0
1
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
1
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
3
1
3
3
1
1
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
2
0
2
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
2
1
1
2
0
2
0
0
2
1
0
1
0
2
0
0
3
0
0
0
0
0
0
0
2
1
4
0
0
0
0
0
1
0
1
1
0
0
3
0
0
2
3
3
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
1
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
2
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
2
1
0
3
0
0
0
2
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
1
1
1
0
0
2
2
0
0
1
0
0
2
1
0
0
1
1
0
0
0
1
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
9
0
2
0
0
0
1
0
2
0
1
0
0
0
0
3
0
0
0
0
0
1
2
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
1
2
0
1
2
0
0
0
0
0
0
0
0
1
0
2
0
1
0
2
1
0
0
1
0
0
0
1
2
0
0
0
0
1
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
2
0
1
0
1
0
1
0
2
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
1
0
2
1
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
9
2
0
1
0
1
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
1
0
1
0
2
0
1
0
1
0
0
4
0
0
0
0
2
0
0
1
2
0
6
2
2
2
0
0
2
2
0
0
3
1
0
2
2
2
1
0
0
1
0
0
0
0
1
0
0
2
0
1
0
1
2
0
0
0
0
1
2
0
1
1
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
2
2
2
1
0
1
0
2
0
0
0
0
1
0
1
0
0
2
2
0
0
2
2
0
1
0
0
0
2
0
0
0
2
1
2
0
0
2
1
0
0
0
0
0
0
0
0
2
2
2
2
0
3
1
1
0
0
2
2
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
4
1
2
0
1
0
3
0
0
0
0
1
0
0
3
1
0
0
2
1
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
4
0
1
1
0
0
1
0
2
0
0
0
0
1
0
1
0
0
2
0
1
2
1
0
2
0
0
3
0
0
0
1
0
1
2
1
2
1
0
0
0
2
0
0
0
1
0
2
0
0
1
0
3
1
0
2
0
0
1
0
0
0
0
0
2
2
0
0
1
2
0
0
0
1
1
1
2
0
0
0
2
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
2
0
0
0
0
2
0
0
0
2
2
0
2
0
2
0
0
0
1
0
0
2
2
0
0
0
3
1
0
0
0
2
0
2
0
0
1
0
1
0
0
2
0
0
2
0
0
0
1
2
0
0
0
0
0
2
0
0
0
1
0
0
0
2
1
0
0
2
2
0
0
0
0
0
1
1
0
2
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
2
0
0
0
0
0
2
1
0
2
0
0
1
0
0
1
3
2
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
2
0
3
0
2
0
1
0
1
0
2
1
3
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
2
0
1
1
0
2
2
0
2
2
2
2
2
0
0
2
0
0
0
0
1
1
0
0
1
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
1
2
0
2
0
0
2
0
0
0
1
2
0
2
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
1
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
1
0
0
0
0
2
1
0
0
1
0
1
2
1
2
0
1
0
0
0
1
2
0
1
0
0
2
0
0
0
0
0
0
1
0
2
0
2
0
2
0
1
1
0
2
0
0
0
0
0
1
0
0
0
0
2
0
1
1
0
0
1
0
0
1
2
0
1
0
0
2
0
0
0
1
0
0
0
1
1
2
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
2
1
0
1
1
1
0
2
0
0
0
0
0
0
3
0
0
0
4
0
0
2
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
2
0
1
0
1
0
0
0
0
1
0
0
0
1
0
1
0
1
2
0
0
0
0
0
0
1
0
2
3
2
1
1
0
0
0
2
0
1
0
0
0
1
1
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
1
1
0
0
0
4
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
2
2
0
0
0
2
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
1
1
0
1
1
1
2
2
1
4
2
4
2
0
0
2
0
0
0
0
1
2
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
1
0
2
1
2
1
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
1
0
2
1
1
1
2
2
0
1
0
0
0
2
2
1
2
0
0
0
0
1
0
0
0
0
2
5
0
2
0
2
0
0
0
3
2
0
0
0
1
0
1
0
0
0
0
2
0
0
0
2
0
0
2
0
0
2
2
0
0
0
2
1
0
1
1
1
0
2
0
0
0
0
0
0
1
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
4
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
2
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
5
2
0
0
1
0
2
0
0
1
0
0
0
0
0
4
0
2
1
0
0
0
1
0
1
0
2
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
1
2
0
1
2
0
1
0
0
0
0
2
0
0
1
0
0
0
1
1
0
0
0
0
2
0
0
0
2
2
0
0
1
0
0
1
0
2
2
0
0
0
0
1
0
1
1
1
0
1
2
1
2
0
1
0
2
0
1
1
0
1
0
0
0
0
0
2
2
0
0
1
0
0
0
9
1
2
0
0
0
0
2
0
0
2
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
1
0
0
2
0
0
1
0
2
0
0
0
2
0
3
0
0
0
0
2
0
2
0
2
1
0
0
0
1
0
0
2
0
2
1
2
0
0
0
1
0
0
1
0
1
0
0
1
1
0
1
0
0
1
0
0
0
0
1
0
2
2
1
0
1
0
1
0
0
0
0
2
2
1
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
3
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
2
2
0
0
0
0
0
0
2
0
0
2
1
1
0
3
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
1
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
3
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
2
2
0
1
0
0
0
4
0
2
0
0
1
1
3
0
0
0
0
0
0
2
3
3
0
1
2
0
0
1
0
0
2
2
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
1
0
0
1
0
0
1
0
4
0
1
2
0
1
1
0
1
0
0
0
0
2
0
2
0
1
0
1
0
0
0
4
0
0
0
1
0
0
0
1
0
1
0
0
2
3
1
2
2
0
0
0
0
2
0
4
1
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
2
1
0
0
1
0
0
2
0
0
0
2
0
2
2
1
0
2
3
0
0
2
0
0
1
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
1
3
2
1
0
1
2
0
1
1
0
1
0
0
0
1
1
1
1
0
0
2
2
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
2
3
0
2
1
1
0
1
0
2
0
2
2
0
0
0
0
0
0
0
0
2
2
1
3
0
0
1
0
0
0
2
1
2
0
0
1
1
0
1
2
0
3
0
0
1
0
0
1
1
2
1
2
0
2
0
0
0
0
2
0
2
0
0
1
1
2
2
2
2
8
0
0
1
1
2
0
0
1
2
2
2
0
1
0
1
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
1
2
0
0
2
1
0
0
0
2
0
0
1
0
2
0
0
2
1
0
0
0
1
0
1
2
0
0
0
0
1
0
0
2
1
0
0
1
3
0
1
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
2
0
0
1
0
2
0
1
1
0
0
1
1
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
1
2
1
0
0
0
0
0
1
0
0
0
0
0
1
3
0
1
0
1
2
0
0
0
0
0
1
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
2
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
1
1
1
1
1
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
2
0
1
0
1
0
2
0
2
0
2
0
1
0
2
0
0
0
2
1
0
2
1
1
1
1
0
2
1
0
0
0
1
0
0
0
0
0
2
1
0
0
1
2
1
1
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
1
1
2
0
0
2
0
1
0
0
0
1
0
0
0
2
0
2
3
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
2
2
0
0
0
0
2
2
0
0
0
0
0
1
1
0
0
0
1
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
2
0
0
0
0
1
1
0
0
0
0
0
0
2
4
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
2
0
0
1
0
0
0
1
1
1
0
0
0
1
0
0
2
2
3
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
1
0
4
0
1
1
1
0
0
3
0
0
0
0
0
0
0
2
1
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
1
2
0
0
0
1
0
1
0
0
0
0
0
1
0
1
1
1
0
0
0
0
2
1
0
0
0
0
2
2
2
1
0
2
0
0
0
0
1
0
0
0
1
0
0
1
3
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
1
1
0
0
0
0
0
2
0
3
1
0
3
0
1
0
0
1
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
2
0
2
2
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
2
2
2
1
2
2
0
0
0
1
0
2
2
0
1
0
2
1
0
0
0
0
2
0
1
0
0
0
0
1
4
0
0
0
0
0
0
0
0
1
1
0
2
0
0
1
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
1
0
2
1
0
0
0
1
0
1
0
0
0
1
1
0
0
0
1
2
2
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
1
0
1
2
0
0
0
2
0
0
0
0
1
0
2
0
0
0
1
1
2
0
0
0
0
0
2
2
2
1
0
2
0
0
0
0
0
1
2
0
1
0
0
3
0
0
0
3
0
2
0
0
0
0
2
0
2
0
0
2
3
1
0
2
0
1
0
0
0
0
2
0
1
0
0
0
2
0
0
3
2
0
0
2
0
0
1
0
0
0
3
2
2
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
1
0
0
0
0
1
1
0
0
0
3
0
0
2
1
1
0
0
0
0
1
0
0
0
2
2
0
2
0
0
0
0
0
0
0
2
2
2
1
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
2
0
2
1
0
2
2
0
0
0
0
0
0
0
2
2
0
2
0
0
1
0
0
2
0
0
3
0
0
1
0
2
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
2
3
2
1
0
2
0
0
2
0
2
2
0
0
4
3
0
1
3
0
0
0
0
1
2
0
0
0
0
1
2
0
0
0
1
1
2
0
0
1
0
0
0
0
2
0
1
0
3
0
1
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
1
0
2
0
0
1
0
2
2
3
1
2
2
2
0
2
1
0
1
2
0
0
0
1
0
1
0
2
0
0
0
0
1
1
0
2
0
1
0
2
1
0
0
0
0
1
0
2
0
1
0
2
0
3
2
0
0
0
1
0
4
2
1
0
3
1
1
0
0
0
0
0
0
0
1
0
2
3
0
0
0
2
0
0
2
0
0
2
0
0
0
0
1
2
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
1
0
0
1
2
2
0
0
3
0
0
1
8
0
0
1
2
1
2
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
1
0
0
1
0
1
0
2
0
0
1
0
0
1
0
1
0
0
0
1
0
0
2
0
2
0
1
0
0
0
2
1
1
0
0
0
0
1
0
2
0
0
3
0
1
0
0
1
0
3
0
0
2
2
0
3
0
0
0
1
1
0
0
2
1
0
1
1
2
0
1
0
2
0
0
0
0
0
0
0
0
2
0
1
1
2
0
1
3
1
0
0
2
0
1
1
0
0
0
0
1
0
0
2
0
0
2
0
0
0
2
0
2
0
3
2
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
1
1
0
0
0
0
0
0
0
2
1
0
0
1
2
2
0
0
0
0
1
0
2
1
0
1
1
0
0
0
0
1
1
0
1
1
1
0
0
0
2
0
0
2
0
2
3
0
0
0
2
0
0
0
2
1
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
2
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
1
2
2
0
1
0
3
0
0
2
0
0
1
0
0
0
1
2
0
2
0
1
0
2
2
0
1
0
0
1
2
3
0
1
0
1
2
2
0
0
0
0
0
0
0
2
1
0
1
0
0
2
0
0
1
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
1
1
0
0
0
2
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
1
2
1
0
0
0
1
0
2
0
1
0
0
0
0
2
0
0
2
0
1
0
0
2
0
1
2
1
0
2
2
0
0
0
1
0
0
1
0
0
0
2
2
2
1
1
0
0
1
1
2
0
0
3
2
0
0
2
3
0
3
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
1
0
2
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
1
3
0
0
0
0
4
3
1
2
1
0
2
1
2
0
3
2
0
0
0
0
2
0
1
0
1
0
2
0
1
0
1
0
0
1
0
1
1
2
0
0
0
0
0
0
0
0
0
1
2
0
1
2
1
0
0
2
2
3
0
0
0
0
0
0
0
0
1
0
2
2
2
0
0
0
2
0
0
1
1
0
1
2
2
1
2
2
0
2
0
1
1
2
0
1
0
0
1
1
2
0
1
6
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
1
2
0
0
0
0
1
0
3
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
1
2
0
0
0
2
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
2
0
0
0
1
0
1
0
0
1
0
1
0
0
1
1
0
0
0
0
0
2
0
2
2
0
0
2
0
0
0
0
1
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
2
1
0
1
0
0
1
0
2
0
2
2
2
0
0
0
0
0
3
0
0
1
0
1
2
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
4
0
0
0
0
2
0
3
1
0
0
2
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
1
2
2
2
0
0
0
0
0
1
0
1
1
0
1
0
0
0
1
2
1
1
0
0
0
0
0
1
0
2
0
1
2
0
0
0
2
2
1
2
0
0
0
0
1
0
0
1
0
0
0
0
0
1
2
0
2
0
0
0
2
0
0
0
1
2
2
0
1
1
0
2
0
0
1
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
2
0
0
0
1
2
0
0
1
0
0
0
0
0
1
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
1
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
2
0
1
2
0
0
0
0
0
1
2
0
1
0
0
3
0
1
0
0
2
0
0
1
2
3
0
2
1
0
1
3
1
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
4
0
1
0
1
2
0
4
0
1
0
0
0
0
0
1
0
1
2
1
0
1
0
0
0
0
1
0
2
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
4
0
1
0
0
1
2
0
0
0
1
0
1
0
0
0
1
2
2
0
0
1
0
0
0
0
2
0
0
2
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
1
1
0
2
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
6
2
1
1
1
0
0
0
1
2
0
2
0
0
0
0
0
2
0
0
0
1
0
0
1
1
0
0
2
0
0
0
0
0
2
0
2
1
0
0
1
0
0
2
0
1
1
0
1
0
0
0
0
0
0
0
0
1
1
0
2
3
0
2
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
3
1
0
1
1
3
0
2
0
0
0
0
2
2
2
2
0
2
1
0
0
1
0
0
1
2
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
2
0
2
0
1
0
0
0
1
0
0
0
0
1
0
1
0
4
0
0
0
1
0
0
0
2
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
2
0
0
0
0
0
2
1
0
1
0
0
0
0
0
2
4
0
3
0
1
1
2
0
5
0
0
0
0
0
0
2
1
0
0
1
1
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
1
0
0
0
0
0
2
3
0
0
1
1
0
1
1
0
2
2
0
2
0
1
0
0
0
1
0
0
1
0
0
0
0
2
4
1
0
0
1
0
0
0
0
0
0
2
2
0
0
1
1
1
0
0
0
0
0
0
3
0
1
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
1
1
0
0
0
0
0
0
2
0
1
1
1
0
0
1
0
2
0
0
1
0
0
0
2
1
0
0
1
0
2
1
0
0
0
1
0
0
2
0
2
0
1
2
0
1
0
0
2
0
2
0
0
0
2
0
0
1
0
1
0
1
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
2
0
0
2
0
2
2
0
1
0
0
3
0
2
0
1
0
3
1
1
1
0
0
0
0
0
2
1
0
0
0
2
2
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
1
2
0
4
0
1
0
0
0
1
1
1
0
0
1
0
2
0
1
0
0
0
0
2
0
1
0
1
0
1
0
0
0
2
0
0
0
1
0
4
0
0
0
1
2
0
1
0
1
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
1
0
2
3
0
1
0
0
1
2
0
1
0
0
0
2
3
0
2
0
0
0
0
0
1
0
2
2
2
0
2
0
0
2
0
0
0
0
1
4
0
0
2
0
0
0
0
2
0
3
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
2
0
2
1
2
2
1
0
2
0
0
0
2
4
0
2
0
0
0
0
0
0
2
2
3
0
0
0
0
0
0
2
0
2
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
2
1
0
2
0
1
0
2
0
1
0
0
2
2
0
0
0
2
2
0
1
0
0
2
1
1
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
1
0
0
1
0
0
0
0
1
2
2
1
2
2
2
0
0
0
1
2
2
0
0
0
0
0
2
0
0
1
1
0
0
0
2
0
2
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
2
0
0
1
0
0
0
1
3
0
0
1
0
2
0
0
0
0
2
4
2
2
0
0
1
2
2
0
2
1
0
0
1
1
2
0
2
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
1
1
0
1
1
0
1
2
0
0
1
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
2
2
0
0
0
1
0
1
1
0
1
2
0
1
1
0
0
3
2
0
0
0
2
0
0
0
1
2
0
0
0
0
1
0
1
1
0
0
1
1
2
0
0
0
0
3
0
2
1
0
2
1
2
0
0
3
1
4
0
0
0
0
0
1
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
1
0
2
0
2
3
2
3
0
0
0
2
2
0
0
2
0
0
0
1
0
0
0
0
0
0
2
2
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
1
0
1
0
1
0
2
0
0
0
1
0
0
0
0
0
2
1
2
0
3
2
0
0
0
2
2
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
2
1
0
2
0
1
0
0
1
1
0
2
0
2
0
2
0
2
0
0
0
2
0
0
2
0
0
0
0
6
0
1
0
0
0
0
0
0
0
0
1
0
2
1
0
1
1
1
2
4
5
2
0
0
2
1
0
0
0
0
2
0
0
0
0
1
0
0
0
1
1
0
2
0
0
1
0
0
0
1
0
2
0
0
0
0
2
0
2
0
2
0
0
2
0
0
0
0
3
1
0
0
0
0
0
1
0
2
1
0
1
2
1
1
0
0
1
0
2
1
2
0
0
1
0
0
0
3
0
1
1
2
2
1
0
1
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
2
0
2
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
2
3
0
0
0
0
2
0
0
0
2
0
3
1
2
0
1
0
2
0
0
1
0
0
0
0
2
1
0
0
1
0
2
1
0
0
0
0
0
1
2
1
0
0
2
0
0
0
0
0
1
2
3
0
0
0
0
0
2
2
0
3
0
2
0
2
2
0
0
0
1
2
1
0
0
0
2
0
0
0
1
0
1
1
0
1
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
1
0
0
1
2
2
0
0
0
0
2
0
0
0
1
0
0
0
3
0
0
0
0
2
2
0
2
2
1
0
0
1
2
1
0
0
0
1
0
0
4
0
1
1
1
0
0
1
2
0
2
0
0
2
0
0
2
0
0
1
0
1
0
0
1
1
2
2
0
1
0
0
1
0
0
0
0
0
0
1
0
2
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
3
0
0
0
1
0
0
2
1
0
1
1
0
0
0
0
3
1
0
0
2
0
0
2
3
0
2
2
1
1
0
0
2
0
0
1
0
0
0
2
1
0
2
2
0
0
0
2
2
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
1
3
0
0
2
1
4
1
0
12
0
1
0
2
2
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
1
2
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
3
2
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
1
2
0
0
1
0
0
0
1
0
0
1
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
3
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
2
0
1
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
2
1
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
2
2
0
0
2
2
2
1
0
0
2
1
2
2
4
1
0
0
0
1
0
2
1
2
1
1
0
1
0
3
0
0
0
1
3
2
2
3
2
0
1
0
0
0
0
0
1
2
1
2
2
2
0
0
1
0
0
0
2
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
1
0
2
0
0
0
3
0
4
2
0
0
0
0
0
2
1
2
0
1
0
0
2
1
0
1
0
2
0
0
1
0
0
1
0
0
3
0
0
0
1
2
0
0
2
0
0
0
2
0
2
0
3
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
1
0
2
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
1
1
0
0
0
2
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
1
2
0
0
0
0
2
0
1
0
0
2
0
0
2
2
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
2
2
2
0
0
0
2
1
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
2
0
0
2
1
1
1
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
2
2
0
2
1
0
0
2
2
0
3
0
0
1
0
0
2
1
0
1
1
0
0
2
0
0
0
0
0
1
1
0
1
1
0
0
1
0
0
0
0
1
1
1
1
0
0
1
1
0
0
0
0
2
0
2
0
0
1
0
0
0
1
2
1
0
2
2
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
2
1
0
1
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
2
2
1
0
0
0
0
0
1
2
1
2
1
0
0
0
1
0
0
1
1
0
0
0
0
3
1
0
1
1
0
2
1
2
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
2
0
0
1
0
0
0
0
0
0
3
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
2
0
0
0
0
0
2
0
1
0
1
0
2
2
0
0
0
0
0
1
0
0
0
2
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
1
0
4
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
4
2
0
0
1
0
0
0
0
2
1
0
0
0
3
0
0
2
0
0
1
0
2
0
2
0
0
0
2
0
1
0
2
0
2
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
1
2
0
1
0
0
0
0
0
0
0
0
1
2
1
1
0
0
2
0
2
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
5
2
1
0
0
0
3
0
0
0
1
1
0
0
1
0
0
2
2
2
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
2
4
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
1
1
0
1
1
1
0
0
1
0
0
0
2
0
0
0
0
2
1
2
0
0
1
0
0
0
2
0
0
2
0
1
0
0
0
1
0
0
0
2
0
2
0
2
2
1
0
0
1
0
0
0
0
2
0
1
0
2
0
2
1
0
0
0
0
2
0
1
0
0
0
1
2
1
0
0
0
0
0
2
0
2
0
0
0
2
2
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
2
3
2
2
0
0
0
2
0
1
0
0
1
0
0
2
1
0
0
1
1
0
0
2
1
2
2
0
3
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
1
0
1
0
3
0
0
0
0
0
0
0
0
0
1
3
1
0
0
0
0
0
2
1
0
1
2
0
3
0
0
3
0
0
0
1
1
1
0
1
2
0
0
2
0
0
0
2
1
0
1
1
0
2
2
0
0
1
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
1
1
0
3
2
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
1
2
1
0
0
0
2
0
2
0
1
0
1
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
1
0
3
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
1
1
2
2
0
0
1
0
0
0
0
2
0
0
2
0
1
0
0
0
2
1
1
0
0
1
0
0
0
0
1
0
0
4
1
1
1
0
0
0
0
0
2
0
1
0
0
1
1
2
0
1
0
0
1
1
0
2
0
0
2
2
2
0
1
0
0
0
0
0
0
0
0
1
0
3
0
0
2
0
2
1
2
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
1
1
0
0
0
0
0
2
1
0
0
2
0
1
1
2
1
0
0
3
0
0
0
0
0
2
2
0
2
1
1
0
0
0
2
2
1
0
2
2
1
2
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
4
2
2
0
0
1
5
1
2
2
0
0
0
2
0
3
0
0
0
0
1
2
0
2
2
0
1
0
0
0
0
1
0
0
0
2
1
0
0
1
2
0
1
0
0
0
2
0
1
0
0
1
1
1
0
0
2
0
0
1
1
0
1
1
2
2
0
0
1
3
0
1
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
2
0
2
0
0
1
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
1
1
0
1
1
0
0
0
0
1
1
0
0
0
0
2
0
2
0
2
0
2
0
0
1
5
0
0
0
0
0
0
1
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
1
0
0
0
0
0
1
0
2
2
1
0
2
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
2
1
0
0
0
1
2
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
1
0
1
2
1
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
3
1
0
0
0
2
0
0
1
0
2
0
0
0
1
0
2
0
0
0
0
0
1
1
0
3
2
1
0
0
0
0
0
0
2
1
0
0
0
1
2
0
0
0
1
1
1
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
1
2
0
0
0
0
0
0
1
0
2
0
3
2
1
0
0
0
0
0
0
1
2
0
0
1
1
0
0
0
0
0
0
0
2
1
0
3
0
0
0
0
0
2
0
0
0
2
0
0
2
0
2
0
0
0
2
1
2
2
0
0
0
0
1
2
2
1
0
0
2
0
0
1
1
0
0
0
2
2
1
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
2
2
2
0
0
0
1
0
2
0
0
0
2
0
1
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
2
0
1
0
1
3
1
0
0
0
0
0
2
0
0
0
1
2
0
0
2
0
3
2
0
0
0
2
1
0
1
0
0
1
1
2
1
0
0
1
0
1
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
2
0
2
2
0
1
0
0
0
0
0
0
0
2
0
2
2
1
0
2
0
0
1
0
0
3
0
0
0
2
0
1
1
0
0
2
2
0
1
0
0
2
2
0
1
0
0
2
2
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
3
0
0
0
0
1
0
2
0
0
1
8
0
0
0
2
2
1
1
2
0
1
0
1
1
0
2
0
0
1
0
0
0
0
0
1
2
0
0
2
0
2
0
0
2
0
1
1
1
0
0
1
0
0
3
0
0
2
0
1
0
0
2
1
0
0
0
0
0
0
2
1
1
0
0
1
1
0
0
0
2
0
2
0
0
2
2
1
0
0
0
0
0
1
1
0
0
2
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
1
3
0
0
1
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
1
0
0
0
0
0
0
3
2
1
0
0
0
0
2
3
0
1
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
1
1
0
0
1
2
0
0
1
2
1
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
1
0
2
1
0
0
0
3
2
0
2
0
0
0
0
1
0
1
2
0
1
0
1
2
0
0
3
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
2
0
2
0
0
1
0
1
1
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
2
0
2
0
1
0
0
0
1
0
0
0
0
0
1
0
2
0
0
1
0
2
1
1
0
0
0
2
2
1
0
2
2
2
1
0
2
0
0
0
2
0
2
0
0
2
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
1
1
2
0
0
1
1
0
1
0
0
0
2
0
0
1
1
1
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
2
1
2
0
0
0
0
0
0
0
0
2
2
1
1
2
0
0
1
2
0
0
0
0
0
0
3
2
0
0
0
0
0
5
2
0
0
2
0
0
0
0
0
1
1
0
0
1
1
1
0
1
0
0
0
1
0
0
0
0
0
2
2
0
0
1
0
0
1
1
0
0
0
2
0
0
1
1
2
0
0
0
0
2
2
0
0
0
2
0
0
1
1
0
1
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
2
0
0
2
3
0
0
0
0
0
0
1
0
1
0
0
0
0
2
2
0
5
2
2
0
0
0
0
1
2
0
0
2
2
0
1
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
6
0
1
1
0
1
0
2
1
1
0
0
1
1
0
1
1
2
0
2
2
1
0
0
0
2
1
0
0
0
2
0
0
0
2
2
0
1
2
0
0
3
0
0
0
0
0
1
0
2
1
0
0
3
2
0
0
2
0
2
0
0
2
0
0
2
0
2
1
1
1
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
2
2
0
2
0
2
0
0
0
0
2
0
0
1
0
0
1
0
0
0
1
3
0
0
0
1
0
0
2
1
0
0
1
0
0
1
0
0
0
3
0
2
0
0
1
0
3
0
1
0
0
0
0
0
0
0
3
1
0
2
2
2
0
1
1
0
0
1
2
1
0
0
2
0
0
1
0
1
0
0
0
2
1
0
1
0
2
1
0
0
0
2
0
0
0
0
1
0
0
0
0
2
2
2
1
1
0
0
0
0
0
0
1
2
2
0
0
1
2
0
0
0
1
0
0
0
0
2
0
2
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
1
0
0
0
0
0
0
1
1
0
4
0
0
0
2
0
0
0
0
0
0
1
0
1
0
2
1
1
0
2
0
2
0
0
0
3
0
2
1
0
1
0
0
2
0
1
1
0
0
0
0
0
2
0
0
0
4
0
1
0
2
0
2
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
2
2
0
0
1
0
1
2
0
0
2
0
2
0
0
1
0
2
2
0
0
0
0
2
1
2
0
0
0
2
0
2
0
0
0
2
3
0
1
2
0
0
0
1
0
0
2
0
0
0
0
0
1
2
2
1
0
0
0
3
0
0
2
1
0
0
2
1
0
1
0
0
0
1
2
0
0
1
0
0
0
0
0
2
3
2
0
0
1
0
2
2
1
1
0
0
0
0
3
0
4
0
0
0
0
0
0
1
0
3
0
1
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
2
1
0
0
1
1
2
0
0
0
0
0
3
0
1
0
2
0
2
0
0
0
2
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
1
1
1
0
0
2
0
0
2
0
1
0
1
0
1
0
0
1
0
0
2
1
0
0
0
0
0
2
0
4
2
0
0
8
1
0
0
2
2
0
1
0
2
0
2
2
2
0
0
3
0
1
2
0
1
1
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
2
2
0
0
2
0
1
0
1
1
0
0
1
0
0
0
0
1
2
2
1
0
1
4
2
3
2
0
0
0
0
2
0
0
0
2
0
0
2
0
1
2
0
0
0
0
0
0
2
0
1
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
2
0
1
0
0
1
0
0
6
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
1
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
1
0
2
1
0
0
0
2
3
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
2
1
1
0
1
3
1
9
0
0
0
0
0
0
1
0
0
2
2
0
2
2
0
0
0
1
1
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
1
2
0
0
0
0
2
0
3
0
1
0
0
0
0
0
1
0
2
2
0
2
2
2
0
2
0
2
0
1
0
0
1
0
1
1
1
0
0
3
0
0
1
0
2
1
0
0
0
2
0
0
2
0
2
1
2
0
0
0
0
0
0
0
1
1
0
1
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
3
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
1
2
0
1
2
0
2
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
6
0
0
0
0
1
0
1
0
2
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
2
0
0
0
1
0
0
0
3
2
2
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
8
0
2
3
0
0
0
0
2
0
0
2
2
0
0
0
0
2
0
1
0
0
0
1
0
1
2
1
0
1
0
2
0
1
0
0
0
1
1
0
0
0
0
0
0
2
2
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
1
2
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
1
0
0
2
3
0
0
0
0
1
1
0
0
2
0
2
0
1
0
0
1
0
0
0
2
0
2
0
0
0
0
0
4
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
2
2
0
3
0
0
0
0
2
1
2
0
0
0
0
0
1
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
2
2
1
2
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
1
2
2
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
2
2
2
0
0
0
0
0
0
0
0
2
1
2
0
1
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
1
0
0
2
3
0
1
0
2
0
0
3
2
0
0
0
2
2
2
1
2
2
0
0
2
0
0
1
1
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
3
0
2
0
0
0
3
0
2
0
0
0
0
0
0
0
3
0
0
0
2
0
0
1
0
0
2
0
0
0
0
1
2
1
2
0
0
2
0
0
0
0
0
0
3
1
0
0
0
2
1
0
0
0
1
2
1
0
0
0
1
0
2
0
2
0
0
0
0
1
0
0
0
1
0
0
0
1
0
2
0
1
0
0
0
2
0
2
0
1
0
1
0
0
1
2
0
1
1
2
0
0
2
2
0
0
0
1
0
1
2
0
0
0
0
0
3
0
0
0
0
1
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
1
1
0
2
2
0
1
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
3
1
1
0
1
0
1
0
0
0
0
1
0
0
0
1
1
0
0
1
1
0
0
1
1
0
0
0
0
0
2
0
1
0
1
0
2
0
0
2
0
0
0
1
0
0
2
2
0
0
0
0
0
1
0
0
2
4
0
0
0
0
2
1
0
1
0
0
0
0
2
2
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
1
2
0
0
1
2
1
2
2
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
1
1
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
1
0
2
2
1
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
5
0
1
1
2
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
1
0
2
1
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
1
2
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
4
0
0
0
2
0
0
0
0
2
2
1
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
4
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
1
2
0
1
3
0
0
0
0
0
0
1
0
1
0
1
0
0
2
1
0
0
0
0
1
1
1
0
0
0
1
0
2
0
2
0
0
2
1
2
0
2
0
0
0
1
0
0
0
0
1
0
0
3
1
0
2
1
0
1
1
0
0
2
0
0
2
0
2
1
1
1
1
1
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
2
0
0
2
1
0
2
0
2
1
0
1
0
2
0
0
3
5
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
5
2
2
0
0
1
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
1
1
1
0
0
0
0
1
0
2
0
2
2
1
0
2
0
0
0
1
1
0
2
2
0
1
2
1
0
0
0
2
2
0
0
1
2
1
0
0
0
0
1
0
1
0
2
0
2
0
0
0
2
0
2
3
4
0
0
1
0
2
3
0
2
0
0
1
0
0
0
0
0
1
0
0
2
1
1
0
0
0
1
1
0
2
2
1
2
2
0
3
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
2
0
1
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
2
2
0
0
1
0
0
0
1
0
0
1
0
1
2
0
0
2
0
0
0
1
0
2
2
0
0
1
0
0
0
2
1
0
1
0
0
0
0
1
1
2
0
0
2
0
1
0
2
2
2
1
0
0
0
1
2
0
2
0
0
2
0
0
1
3
0
1
1
0
0
0
2
0
0
0
2
2
1
2
0
2
1
1
0
2
0
0
1
0
0
2
0
2
0
0
2
2
0
0
0
0
0
0
2
0
2
1
2
0
0
0
0
1
2
0
0
1
0
1
0
0
2
1
1
0
0
5
0
0
0
0
0
0
2
1
0
0
2
0
4
0
0
0
1
2
1
0
0
1
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
1
2
0
1
1
0
0
0
1
1
1
0
0
0
0
0
0
0
2
1
0
0
1
0
0
2
0
2
0
0
1
0
0
0
0
0
0
2
1
2
0
0
0
1
1
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
1
0
0
1
2
2
0
2
2
1
0
2
0
1
2
0
0
0
1
0
2
0
2
0
0
0
0
0
1
0
0
2
0
0
1
2
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
2
2
1
0
0
0
3
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
1
2
0
2
0
0
0
0
0
1
2
0
0
0
0
1
1
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
2
1
0
1
0
2
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
2
2
0
2
2
0
5
0
2
1
0
0
0
0
1
0
0
0
2
1
0
0
0
1
0
0
1
0
1
0
0
0
0
1
1
1
1
1
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
4
1
1
1
0
0
0
1
2
0
0
1
0
0
0
0
1
2
0
0
2
2
1
0
1
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
4
1
0
0
0
2
0
0
2
1
0
0
2
2
3
0
0
1
1
0
0
0
0
3
0
2
0
1
0
0
1
0
0
1
0
0
0
1
0
2
0
0
0
2
3
2
2
1
2
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
4
2
1
2
1
0
0
2
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
2
0
0
1
0
0
1
2
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
3
1
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
1
0
2
2
2
1
2
0
2
2
1
0
1
2
0
2
2
2
2
0
0
1
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
3
0
0
0
1
2
0
1
0
0
0
2
0
2
1
0
2
0
0
2
0
0
0
0
2
1
0
2
0
0
0
0
0
0
2
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
3
0
0
0
2
0
1
2
1
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
3
0
0
2
0
4
1
0
2
1
2
0
0
0
2
2
1
1
2
2
0
0
2
0
1
0
1
2
1
1
1
0
0
2
0
0
0
1
0
0
2
1
0
1
0
0
0
0
0
0
0
1
2
0
1
2
1
0
0
1
2
2
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
1
1
0
0
0
1
0
0
1
1
0
1
2
1
1
0
0
2
2
1
0
0
0
3
1
0
0
0
2
1
0
0
0
0
0
1
2
2
1
0
0
1
1
0
0
2
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
2
0
2
0
0
2
0
0
2
3
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
2
0
0
3
0
2
0
0
0
0
2
1
1
0
0
0
1
0
2
1
0
1
0
0
1
0
2
0
0
1
2
0
0
0
0
0
2
1
0
0
0
1
0
0
0
2
0
1
0
1
2
1
2
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
1
0
0
0
2
3
1
0
0
2
0
1
1
2
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
2
2
0
1
2
2
0
2
0
1
0
1
0
2
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
1
1
0
0
3
2
0
2
0
1
0
0
0
1
1
2
0
0
0
0
1
0
4
0
1
2
0
0
2
0
0
0
0
0
0
0
1
2
1
2
0
1
0
0
0
2
1
0
2
2
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
1
0
1
1
2
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
1
0
1
2
0
0
1
0
1
1
0
1
0
0
0
2
0
0
0
0
1
0
0
2
2
2
0
0
0
0
1
0
0
2
1
0
1
2
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
1
0
2
0
4
1
0
0
0
2
0
0
0
0
0
0
2
6
0
2
0
1
0
1
1
0
0
0
2
0
2
0
0
3
0
2
2
0
0
0
0
0
0
2
1
4
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
2
0
0
0
2
0
0
0
2
2
1
0
0
0
0
0
0
1
0
1
0
0
0
1
1
2
0
2
0
1
0
0
1
3
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
2
0
1
0
2
0
0
2
2
0
0
0
0
0
0
1
2
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
2
2
0
0
0
0
0
1
0
0
0
2
0
2
1
2
0
0
0
0
0
0
0
0
2
1
0
0
1
0
1
3
1
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
2
2
1
0
0
2
0
1
0
0
0
0
1
0
2
0
2
0
3
2
0
0
0
2
1
0
0
0
2
0
0
0
2
0
0
0
1
1
0
2
1
0
1
2
0
0
0
2
1
0
1
0
0
0
0
0
0
5
0
1
1
0
0
0
2
0
1
0
0
2
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
2
1
1
0
0
0
0
4
3
0
0
0
2
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
6
0
0
0
0
0
1
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
3
1
0
0
0
1
0
4
0
1
1
0
1
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
9
4
1
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
2
0
0
1
0
0
2
0
2
0
0
2
2
0
0
0
0
0
0
0
2
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
4
0
1
0
0
0
2
0
0
0
1
2
0
2
1
2
1
1
0
3
1
2
1
0
0
1
0
1
0
2
1
2
0
0
1
0
4
0
2
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
2
0
2
0
1
0
2
1
2
1
1
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
1
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
2
0
1
2
2
0
0
0
2
1
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
1
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
2
0
0
0
0
0
1
1
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
1
0
0
0
1
0
0
1
0
0
2
0
1
0
3
1
1
2
0
2
0
0
0
0
2
0
0
2
0
0
0
1
1
1
0
0
0
0
0
2
0
0
0
1
0
4
0
0
0
2
0
0
1
2
0
0
2
0
1
1
0
2
2
1
1
0
2
2
0
1
0
0
0
1
0
0
1
0
0
1
0
0
2
1
0
0
0
1
0
0
2
2
0
1
0
2
1
0
0
0
1
0
0
3
2
0
4
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
1
1
1
1
0
0
0
1
0
0
2
0
0
0
0
2
0
0
1
2
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
2
0
2
2
1
1
1
0
0
0
2
2
0
1
0
0
0
1
3
0
2
1
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
3
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
2
0
0
0
1
1
0
1
2
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
1
2
2
0
0
0
0
0
2
0
2
0
1
0
0
2
2
3
0
0
0
0
1
0
0
4
0
1
0
0
0
0
2
1
0
0
0
1
0
2
0
2
0
1
0
2
2
0
1
0
0
0
0
1
0
2
0
0
0
0
1
0
1
1
1
0
0
2
2
1
0
2
0
2
0
0
0
0
0
2
0
0
1
0
0
1
0
0
1
0
0
0
0
3
1
1
0
1
0
0
2
0
2
0
1
0
0
1
0
3
2
2
1
1
0
0
0
0
0
4
1
1
0
3
0
2
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
2
0
0
0
1
0
0
0
0
0
3
0
0
3
1
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
2
2
3
0
3
0
0
0
0
0
0
3
1
0
2
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
2
0
2
1
0
0
1
0
0
0
0
2
1
0
1
0
0
0
0
2
2
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
1
0
0
1
2
0
0
0
2
0
2
0
0
0
0
1
0
1
0
0
2
0
2
0
0
2
2
0
2
1
0
0
0
1
0
0
0
1
0
0
0
1
1
1
0
0
1
0
0
1
0
0
2
1
0
0
2
0
1
0
0
0
2
2
0
1
0
2
1
0
0
2
0
0
1
1
1
0
1
0
0
0
2
2
0
0
0
0
4
0
0
1
0
0
1
0
2
1
2
1
1
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
2
1
0
1
0
0
2
0
2
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
2
0
2
1
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
3
0
0
1
0
2
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
1
0
2
1
1
0
3
0
1
0
0
0
0
0
3
0
0
1
2
2
2
0
0
0
0
0
2
2
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
2
1
1
0
1
2
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
1
0
2
0
0
0
1
0
1
0
0
2
0
0
2
2
0
0
1
2
0
0
2
1
2
0
0
0
2
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
1
0
0
1
0
0
2
0
2
0
0
0
0
0
1
1
2
0
0
0
1
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
1
0
0
0
2
1
1
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
3
0
2
1
1
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
1
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
1
3
0
1
0
0
0
0
0
0
0
0
8
0
0
1
0
1
0
2
0
0
1
0
0
1
2
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
3
2
2
0
0
0
0
0
0
2
4
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
2
0
1
0
2
0
1
0
1
0
0
0
2
0
1
2
2
1
0
0
2
2
1
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
1
0
0
0
2
0
1
0
1
2
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
4
2
2
1
1
0
0
0
1
2
0
0
0
0
1
0
0
0
1
2
0
3
2
0
0
0
0
3
2
0
1
0
1
2
2
0
0
0
1
0
2
0
2
0
0
2
0
1
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
2
1
0
0
0
2
0
2
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
1
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
2
0
0
0
0
0
1
1
3
1
0
1
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
5
0
2
2
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
5
0
2
0
0
2
0
0
0
0
1
0
0
2
1
2
0
2
0
1
1
1
2
0
1
2
0
1
1
0
3
0
2
0
0
1
0
0
2
1
2
0
0
1
2
1
2
1
0
0
0
3
0
0
0
0
1
0
0
0
0
0
1
0
2
0
1
1
2
0
0
2
0
0
1
0
1
0
0
1
0
0
0
2
0
1
0
1
0
0
1
0
1
0
0
2
0
1
0
0
1
0
0
1
1
0
1
0
2
0
1
0
0
0
2
0
1
0
0
1
2
0
0
0
0
0
1
1
0
0
0
2
0
1
0
1
2
1
2
0
1
0
0
0
2
0
0
5
0
0
0
2
1
0
0
0
0
0
1
2
0
2
0
1
2
0
0
0
0
0
0
0
0
0
1
2
0
1
0
1
1
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
1
1
0
2
2
2
0
0
0
1
0
1
0
1
0
0
0
0
0
2
0
1
1
1
0
1
0
0
0
0
0
1
0
2
0
0
2
0
1
1
0
1
0
2
0
0
0
0
0
2
1
0
0
1
0
2
0
0
0
1
1
2
0
0
0
0
0
1
1
0
0
0
0
3
0
1
0
0
2
0
0
1
2
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
1
0
0
2
0
0
2
0
0
1
0
0
0
0
1
0
1
0
0
2
0
0
2
0
1
0
2
2
0
1
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
2
1
2
0
2
0
0
1
0
0
0
0
0
0
1
2
0
0
2
0
1
0
0
0
0
2
0
2
0
1
0
2
2
2
2
0
1
0
1
1
2
1
0
0
5
0
0
1
0
1
0
0
2
0
0
2
2
0
0
0
0
0
2
0
0
0
0
1
1
0
0
2
1
2
2
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
1
2
1
2
0
0
1
2
2
1
0
0
0
0
0
2
0
0
0
2
0
2
0
2
0
0
0
0
0
1
1
1
1
1
1
1
0
0
1
0
1
0
2
0
0
2
0
0
1
0
0
0
1
0
0
0
1
0
0
1
1
0
1
1
0
0
0
1
0
0
2
0
0
0
0
0
1
1
0
1
0
2
0
2
0
0
0
2
0
0
0
0
2
2
0
0
1
2
0
0
0
0
0
1
0
1
0
2
0
0
2
0
0
1
0
1
0
0
0
0
0
0
2
0
0
1
1
1
0
1
0
0
0
1
2
0
0
0
1
0
2
0
2
1
2
0
0
0
0
0
1
0
2
0
0
1
0
0
1
0
0
0
3
0
0
0
0
2
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
2
1
0
0
0
1
0
2
0
3
0
1
0
0
2
0
7
0
1
0
2
2
0
0
0
1
0
0
0
0
1
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
3
0
2
1
0
1
2
0
0
0
0
0
1
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
1
2
4
1
2
0
0
0
2
2
0
0
0
0
1
2
1
2
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
3
1
2
0
0
2
0
1
2
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
2
0
2
0
1
0
0
1
0
2
1
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
1
0
2
0
1
1
0
2
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
1
0
1
1
2
2
2
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
1
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
1
1
0
0
0
2
0
2
1
2
1
3
1
0
2
1
0
0
0
0
0
1
0
1
0
0
1
1
1
0
1
0
1
0
2
2
0
0
0
1
1
0
1
0
2
0
1
0
1
0
0
0
0
0
2
1
1
2
1
0
3
0
2
0
0
1
0
2
1
0
0
0
4
2
0
1
0
2
0
2
0
0
0
0
2
0
2
0
2
0
2
0
1
0
0
4
1
0
1
2
0
1
1
0
0
1
1
0
0
2
0
0
0
0
4
0
0
2
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
3
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
1
1
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
2
2
1
0
3
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
1
0
0
0
0
0
1
0
1
0
0
1
2
2
0
1
0
0
0
1
0
3
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
2
2
2
2
0
0
0
1
0
2
0
0
2
0
0
0
0
2
1
0
0
0
1
2
0
0
2
0
0
1
2
1
1
2
1
2
0
2
1
0
0
1
0
1
1
1
0
1
0
0
0
0
1
0
2
0
0
0
2
0
1
2
0
2
0
1
1
0
1
0
1
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
2
0
1
0
2
0
0
1
0
2
0
0
0
0
0
0
0
3
1
0
1
2
0
1
0
0
1
1
0
0
1
1
2
0
0
1
3
0
0
2
1
0
0
0
0
0
1
2
0
1
0
0
0
1
1
1
0
0
0
1
0
0
1
1
2
0
0
2
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
1
2
2
0
0
0
1
1
0
2
0
0
0
1
2
0
0
5
0
4
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
1
2
0
1
0
0
0
2
0
0
0
0
0
1
1
0
0
1
0
2
0
1
3
3
0
0
0
0
0
1
0
2
0
0
2
1
2
0
2
0
0
0
1
0
0
2
0
1
0
0
0
1
2
0
1
4
2
2
2
0
1
1
2
0
1
0
1
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
1
0
1
3
0
2
0
2
0
0
3
2
2
0
0
2
2
0
0
0
2
0
0
0
0
0
0
3
0
1
0
1
0
0
0
0
0
0
2
0
0
1
0
2
2
2
1
0
0
0
0
2
1
0
0
1
0
0
1
0
2
0
0
0
2
0
0
0
2
1
0
1
0
0
0
1
0
0
4
0
0
1
1
0
0
0
2
0
0
1
0
0
1
0
1
0
0
0
0
0
5
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
1
0
0
3
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
1
0
0
2
1
0
1
0
0
1
0
0
0
0
0
0
0
2
0
2
1
0
1
0
0
0
0
0
0
0
1
0
2
0
0
2
0
2
0
0
0
1
0
0
3
2
1
1
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
1
0
0
1
0
2
2
1
0
0
0
0
0
1
2
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
5
0
1
0
0
0
0
0
0
1
0
0
2
0
1
2
0
1
1
0
0
0
0
0
2
0
1
0
0
0
0
3
0
0
0
0
0
3
0
1
0
0
0
2
1
0
0
0
0
1
1
0
1
0
0
2
0
0
1
0
0
2
4
0
0
0
0
0
1
2
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
2
0
0
1
4
2
2
0
0
2
1
2
0
0
1
0
0
0
0
2
1
0
1
0
0
0
2
0
0
2
0
1
0
0
0
0
2
0
0
0
3
0
0
5
0
0
0
0
1
0
0
0
2
2
0
1
1
0
0
0
0
0
1
0
0
2
1
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
1
0
0
1
2
0
2
0
0
0
1
0
0
0
1
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
1
1
2
0
0
0
0
1
2
0
1
0
0
1
0
0
1
0
0
6
1
2
0
2
2
0
0
0
0
2
0
0
1
0
2
1
1
1
0
0
1
1
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
3
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
1
0
0
0
0
0
0
1
0
2
1
1
1
1
0
1
0
0
3
1
1
0
0
0
2
0
1
1
2
0
0
0
0
0
1
2
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
2
2
0
1
0
0
0
0
0
4
0
3
1
1
0
2
2
0
2
0
1
2
2
0
1
2
5
0
2
0
1
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
2
1
1
0
0
0
1
0
0
0
0
1
0
2
0
2
2
0
0
0
0
1
0
2
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
1
2
2
1
2
0
0
1
0
0
0
2
0
0
0
0
1
2
0
0
0
0
2
0
1
1
1
0
1
0
0
0
1
0
0
1
0
3
0
1
0
0
0
1
0
0
1
0
0
1
1
1
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
2
0
0
0
1
0
1
0
2
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
1
2
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
1
1
0
1
0
0
1
0
2
0
0
0
0
1
25
0
0
0
0
1
0
2
2
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
1
2
0
0
1
1
1
1
0
0
0
0
0
0
3
1
0
1
0
0
1
2
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
3
0
0
0
0
0
1
2
2
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
3
0
0
0
1
0
1
1
1
0
4
0
1
1
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
1
2
0
0
2
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
1
2
0
1
0
2
0
0
0
0
0
0
1
0
0
5
0
2
0
2
0
2
1
2
0
2
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
1
0
3
2
0
1
0
1
0
1
0
1
0
2
0
0
0
1
0
0
0
2
0
1
0
0
1
0
2
1
0
0
0
0
1
0
0
2
0
0
1
0
0
0
3
0
2
0
1
0
0
0
2
1
0
1
1
0
0
0
0
0
0
1
1
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
2
0
1
2
2
1
1
0
1
2
0
2
1
1
0
0
1
0
0
2
0
0
2
1
4
0
0
1
0
1
5
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
2
0
0
2
0
0
0
1
0
1
0
1
0
0
2
2
0
1
0
2
2
3
2
0
0
0
0
0
0
2
0
0
0
0
10
0
0
0
0
0
0
2
0
2
2
0
2
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
2
0
0
0
0
0
0
0
0
2
0
0
4
0
0
1
0
2
0
0
0
0
1
1
0
2
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
2
1
0
0
1
0
1
2
1
1
2
0
2
3
1
0
2
0
1
1
3
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
2
1
2
1
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
2
0
0
0
0
2
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
1
0
1
0
2
0
0
1
1
0
0
2
2
2
0
0
2
0
0
1
0
2
0
0
1
2
0
0
2
1
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
5
0
0
2
0
0
0
2
2
0
2
0
0
0
2
0
0
2
0
1
2
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
2
1
2
0
0
0
0
1
0
0
0
0
2
0
2
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
1
0
0
0
2
0
0
1
0
1
0
1
0
0
0
0
2
1
2
0
2
2
0
2
0
0
0
2
1
0
0
1
0
0
1
0
0
0
0
0
1
1
0
1
2
0
0
2
2
0
0
0
0
0
0
2
0
0
0
1
0
3
3
1
0
0
0
0
2
0
1
0
1
0
0
2
1
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
2
0
0
0
1
1
0
0
0
1
0
1
2
1
0
0
0
0
0
2
0
0
0
0
0
1
0
1
1
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
2
1
0
0
2
0
0
0
0
3
0
0
0
0
2
0
2
0
0
0
0
1
1
0
1
0
0
0
2
0
0
0
0
0
1
0
1
0
0
4
0
0
0
2
0
1
0
2
2
0
2
0
1
0
1
0
0
0
2
1
0
0
1
1
1
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
2
2
0
0
0
0
2
0
2
2
2
1
1
2
2
0
0
1
1
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
2
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
1
0
0
0
0
0
0
2
1
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
1
0
3
0
0
0
0
0
0
2
1
2
0
2
0
0
0
1
0
1
0
0
0
1
0
1
0
2
1
2
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
2
0
0
0
0
1
1
0
1
0
0
1
0
2
0
1
0
0
0
0
0
1
0
0
0
2
1
2
0
0
0
2
0
2
0
2
3
2
0
2
0
0
0
0
2
0
0
1
0
3
0
2
2
0
0
0
2
0
1
0
2
3
0
0
0
1
2
0
0
0
0
1
0
0
2
0
0
2
0
0
2
0
0
0
7
0
2
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
2
0
0
0
1
0
1
1
0
1
0
0
2
0
0
0
2
0
2
0
0
1
2
2
2
2
0
0
0
0
2
0
0
0
2
0
0
0
0
2
2
1
0
0
0
2
0
0
2
2
2
0
1
2
0
2
0
0
2
0
0
0
0
0
2
0
2
1
2
4
0
1
1
0
0
11
1
0
0
0
0
2
0
1
0
3
1
1
0
0
1
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
2
0
0
2
0
0
0
1
0
0
0
0
2
1
1
0
0
0
0
1
1
1
1
0
1
1
0
0
1
0
2
0
0
2
2
0
1
0
0
0
0
4
1
0
0
1
0
0
1
2
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
3
0
0
0
1
0
0
0
0
0
2
1
1
0
0
0
1
0
1
0
0
0
2
1
0
0
1
0
0
2
0
0
2
0
0
2
2
0
0
0
0
0
0
2
1
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
4
0
0
0
2
0
2
1
0
0
0
0
2
3
0
0
0
0
0
0
1
0
1
0
0
2
1
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
1
3
0
1
1
2
0
0
2
2
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
2
0
2
0
0
2
1
1
0
0
1
0
1
0
2
0
0
2
0
2
0
0
0
1
2
0
1
0
2
1
0
2
2
0
0
0
0
0
1
0
0
0
1
0
0
2
2
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
4
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
1
2
0
0
0
2
0
2
2
2
0
0
0
1
0
0
0
0
0
1
0
0
1
0
2
2
2
0
1
2
2
0
0
2
3
0
0
2
1
0
0
0
1
2
1
0
0
0
1
1
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
2
0
0
0
1
0
1
0
0
0
1
2
0
0
0
2
0
0
2
1
1
1
1
0
0
0
0
0
1
0
0
2
0
2
0
1
0
1
8
1
0
0
2
1
0
1
1
1
1
0
0
0
1
0
0
2
0
1
0
0
2
0
0
0
0
1
1
2
2
0
0
1
1
1
2
0
0
0
2
1
0
0
0
0
0
1
0
2
1
0
2
1
2
3
0
0
0
0
0
0
0
0
2
1
0
0
2
0
2
0
0
0
0
0
0
2
1
1
1
1
0
1
0
2
0
0
2
1
0
2
1
0
2
0
2
1
0
0
3
0
0
0
0
0
0
2
2
2
2
1
0
0
0
1
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
1
0
1
1
1
0
1
1
1
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
2
0
0
1
1
0
0
0
0
1
0
0
0
1
2
0
0
1
0
1
0
4
0
1
0
0
0
0
0
0
5
0
2
0
0
0
3
4
0
2
0
2
0
0
0
0
2
0
0
0
1
2
1
0
0
0
2
2
0
0
0
0
0
1
0
2
0
1
1
0
0
0
1
2
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
2
0
2
0
0
2
0
0
0
0
0
0
0
0
1
1
2
1
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
1
2
0
0
2
2
0
1
0
2
1
0
1
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
3
3
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
4
2
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
1
2
1
0
0
1
0
0
0
2
1
0
0
0
2
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
2
0
1
0
0
0
1
0
0
0
1
0
0
2
2
2
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
2
0
0
1
2
0
1
0
1
2
2
2
0
0
1
0
3
0
2
2
0
1
0
1
0
1
0
1
1
0
1
0
3
0
1
1
0
0
0
0
0
1
0
1
0
5
0
0
0
0
0
0
1
1
2
0
0
3
0
0
1
0
2
2
0
3
0
0
0
0
1
2
1
0
0
0
0
2
2
3
1
0
0
0
2
0
0
3
0
2
0
0
2
1
0
0
1
0
0
0
0
2
1
0
3
2
0
1
0
1
0
0
1
1
0
0
3
2
0
0
0
2
0
2
0
2
0
0
2
2
0
3
0
0
1
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
1
0
3
0
0
0
1
0
1
1
1
0
1
1
0
0
1
0
1
2
0
2
1
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
2
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
1
2
0
0
1
0
1
0
1
0
0
1
1
2
0
1
0
0
1
0
1
1
2
2
0
0
0
0
2
0
0
2
0
0
2
0
2
0
3
0
0
0
0
1
2
2
2
0
1
0
1
0
1
0
0
1
0
0
0
0
0
2
1
0
2
1
0
1
0
1
0
0
0
0
0
0
5
2
2
0
0
0
0
2
0
1
0
0
0
2
2
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
2
2
1
0
1
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
2
0
0
0
0
2
2
0
0
0
1
0
1
2
1
0
0
2
0
0
0
1
3
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
2
0
2
0
1
0
0
1
0
2
1
0
0
0
2
0
0
0
1
2
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
1
1
1
2
0
1
0
0
0
0
0
0
0
4
1
0
1
0
2
0
0
0
2
0
0
0
0
2
0
0
0
1
2
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
2
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
1
0
2
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
2
1
0
3
1
2
0
1
1
0
0
0
0
0
1
0
1
0
2
2
0
0
1
1
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
3
1
3
0
0
0
2
1
0
2
2
2
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
3
2
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
1
1
0
0
2
0
2
2
1
2
0
1
2
5
0
0
1
0
0
0
1
0
0
1
0
0
0
0
3
0
1
2
0
2
2
2
0
0
0
0
1
1
0
1
0
2
0
1
0
0
1
1
0
0
1
0
2
2
0
0
2
0
1
2
0
0
0
0
0
0
0
1
0
2
0
2
0
1
0
1
0
0
2
0
0
2
3
0
0
1
2
0
1
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
1
0
0
0
2
0
2
1
0
0
1
0
0
0
0
0
2
0
0
2
0
3
0
0
0
2
0
0
0
0
0
2
2
0
0
0
4
0
0
0
1
2
2
0
0
0
2
1
2
2
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
2
2
0
1
0
0
2
0
2
2
1
1
0
0
0
4
2
0
1
0
0
0
0
0
1
0
0
0
2
1
1
2
0
0
0
2
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
2
1
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
4
2
0
1
0
0
0
1
0
0
0
1
0
0
0
0
2
1
1
0
0
1
0
1
3
3
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
4
0
0
0
1
1
0
1
0
0
0
1
0
0
0
1
2
1
0
0
0
2
0
0
0
0
1
0
1
0
0
0
3
0
0
0
4
0
1
0
0
0
0
0
0
1
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
1
0
1
2
0
0
0
1
0
0
0
1
0
2
0
1
0
0
0
0
3
1
0
0
1
0
0
1
0
0
2
0
2
0
3
0
0
1
0
0
0
3
0
2
2
1
0
1
0
0
1
0
0
1
2
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
1
0
0
2
1
1
0
2
0
0
0
1
0
0
2
0
0
0
2
1
0
1
0
1
1
2
0
0
1
0
0
2
2
0
0
1
0
0
6
0
0
0
0
1
1
1
1
3
0
1
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
2
0
0
0
0
0
2
0
0
0
3
3
0
2
0
3
0
0
0
0
1
2
0
1
1
0
2
0
2
2
1
1
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
1
1
0
0
0
2
0
1
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
2
1
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
1
1
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
1
0
1
0
0
0
0
2
3
2
0
0
0
0
0
1
0
0
1
0
0
1
0
2
0
0
0
2
2
1
0
0
2
0
1
0
1
3
0
0
1
0
0
2
2
0
0
2
0
0
1
2
1
0
3
0
0
0
1
0
2
2
1
2
0
2
0
2
0
0
2
0
1
0
2
0
0
1
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
1
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
1
0
1
2
0
1
2
1
2
2
0
0
0
0
1
0
1
0
0
1
0
0
1
0
3
0
0
0
1
1
1
0
1
0
3
2
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
2
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
1
2
1
1
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
3
0
0
2
3
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
1
1
1
1
0
0
1
0
2
2
0
1
0
0
0
1
1
0
0
2
0
2
0
4
0
0
0
0
0
1
1
0
2
0
0
0
1
0
0
1
0
0
2
2
0
0
1
1
0
1
0
0
1
2
0
0
1
1
3
2
2
1
2
0
0
0
2
0
0
0
5
0
0
0
1
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
1
0
2
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
3
2
0
2
1
2
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
4
2
2
1
0
0
2
0
1
0
0
0
2
1
0
1
2
0
1
2
2
2
2
2
0
2
2
0
2
0
0
0
0
0
0
2
5
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
3
2
0
2
2
0
1
2
1
0
1
1
0
2
0
2
1
1
1
2
0
0
0
1
0
0
2
1
0
3
2
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
1
2
0
0
0
2
1
0
0
2
0
1
0
0
0
1
3
0
0
0
0
0
0
1
2
2
0
2
2
2
0
0
1
0
0
0
2
1
0
2
0
2
1
0
0
1
0
0
0
0
0
1
0
0
1
2
1
0
1
0
1
0
0
0
0
1
0
1
0
1
1
0
2
0
0
0
1
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
3
2
3
2
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
1
0
1
1
0
0
1
0
0
0
0
0
1
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
3
2
0
0
2
2
1
1
0
0
0
0
0
0
0
0
1
2
0
2
0
2
0
0
1
1
0
0
1
2
0
1
2
1
0
1
1
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
1
0
1
0
1
2
0
0
0
3
0
3
0
0
0
2
1
0
0
0
0
6
0
1
0
0
0
0
2
0
0
0
2
2
1
2
0
2
0
2
0
0
1
1
0
0
0
0
2
1
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
2
0
1
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
2
0
1
2
0
0
0
1
1
0
0
0
2
1
1
0
2
1
1
0
0
2
2
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
2
1
0
2
0
0
3
0
0
0
0
1
0
1
0
0
0
2
0
0
2
0
0
0
0
1
1
1
0
0
0
0
0
3
0
1
2
0
0
1
1
0
0
1
0
0
0
2
0
1
0
0
0
2
0
1
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
1
0
0
1
1
0
1
0
3
0
1
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
1
0
1
2
1
0
1
0
2
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
2
1
1
0
0
0
0
0
0
1
0
2
1
1
3
1
0
0
2
0
0
1
0
0
1
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
3
1
0
0
2
1
1
2
0
0
1
0
1
1
0
2
0
0
0
0
0
0
2
2
1
0
2
0
2
0
0
1
0
0
0
2
0
0
1
0
1
2
0
0
0
0
0
0
3
2
1
2
0
0
0
0
0
0
2
0
0
1
0
2
0
2
0
1
0
0
2
2
1
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
1
0
1
1
2
0
1
0
0
0
0
0
1
0
0
0
0
2
1
0
2
0
0
1
4
0
0
0
0
1
2
0
0
0
0
2
0
1
0
2
2
2
2
0
0
1
2
1
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
3
0
0
2
0
1
0
3
1
0
0
2
0
0
0
1
1
0
1
0
2
2
1
0
0
0
0
0
2
0
0
0
1
2
0
1
0
2
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
1
0
2
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
3
0
0
2
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
1
2
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
1
1
0
2
0
0
0
0
0
0
0
2
1
2
3
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
3
0
0
0
1
0
0
1
0
0
1
0
2
0
2
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
2
0
1
1
0
0
2
0
0
2
0
2
0
0
0
1
2
0
2
1
1
2
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
1
1
1
1
0
3
2
1
0
0
2
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
2
0
5
0
2
0
1
1
0
0
0
0
0
2
1
2
0
0
1
2
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
4
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
4
3
0
1
2
0
0
0
1
1
0
2
0
2
1
1
1
0
2
0
6
0
1
0
0
0
1
2
1
0
0
1
0
0
0
2
1
0
4
0
0
2
0
0
0
1
2
2
1
1
1
0
0
2
0
2
0
0
0
1
0
2
2
0
0
2
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
2
0
0
2
2
1
0
1
2
1
0
1
1
2
0
0
0
0
1
1
2
2
0
0
0
0
0
0
0
3
0
2
0
1
2
0
0
1
2
0
0
0
1
1
2
0
1
2
0
0
0
0
1
1
1
0
0
1
1
0
2
0
0
1
0
0
1
0
0
1
2
0
0
0
0
0
2
0
1
2
0
1
0
1
0
0
1
0
4
1
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
2
1
1
2
2
1
0
0
2
2
3
0
0
0
2
0
0
0
0
0
1
1
2
0
2
2
1
1
1
5
0
2
0
2
1
2
2
0
0
0
0
0
1
0
0
1
0
0
2
2
2
0
2
2
1
0
1
0
2
0
1
0
0
1
2
0
0
3
0
0
1
0
0
1
1
0
0
0
1
1
2
0
0
0
0
0
2
0
4
0
0
0
2
0
0
1
0
2
1
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
2
1
0
2
2
0
0
0
1
0
0
0
3
0
0
0
0
2
0
1
2
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
1
0
2
0
0
0
1
0
2
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
2
2
0
2
1
0
1
2
0
2
1
0
0
0
0
0
0
0
1
2
2
4
0
1
1
0
0
0
1
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
2
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
2
0
0
2
1
1
2
1
0
0
0
0
1
2
2
1
0
1
1
2
0
1
0
0
0
1
0
0
0
1
1
1
2
0
0
2
2
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
2
0
2
0
0
1
0
1
0
0
0
1
2
0
0
0
0
1
1
2
2
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
4
0
0
2
2
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
2
0
2
0
2
2
0
2
0
1
0
0
0
1
0
1
0
0
2
1
0
2
0
0
0
0
2
0
2
0
0
2
0
0
1
1
0
0
0
1
0
0
2
1
0
2
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
3
0
2
0
1
0
0
3
0
0
0
0
2
1
1
0
0
0
2
0
0
0
0
1
2
2
0
1
1
0
1
2
2
0
0
1
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
1
0
0
2
0
0
2
1
2
0
0
0
2
0
1
0
0
0
1
0
2
0
1
0
1
0
2
0
0
1
0
1
0
0
0
0
0
0
2
0
1
1
0
0
0
0
1
0
0
1
2
2
1
0
0
2
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
2
0
0
1
6
0
0
0
0
2
0
2
1
0
1
0
2
0
0
0
0
4
0
0
1
0
1
0
2
0
1
2
0
0
0
2
1
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
1
1
0
0
0
0
2
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
1
3
0
2
1
1
1
0
0
0
2
1
0
4
3
0
2
0
0
2
0
0
1
0
0
0
2
1
1
2
0
2
0
0
0
0
0
2
0
0
0
0
0
3
0
0
2
0
1
1
0
0
1
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
1
2
1
0
0
2
0
0
0
2
1
2
1
1
0
2
0
0
0
2
0
0
0
0
0
3
2
0
2
0
0
0
0
3
0
2
0
0
2
0
2
0
1
1
0
1
1
1
0
1
1
1
0
0
0
0
4
0
0
1
0
1
3
0
0
1
2
2
1
1
1
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
1
0
1
0
0
0
1
1
1
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
1
0
0
0
1
1
0
2
0
2
0
2
0
0
2
0
1
0
0
1
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
1
0
1
1
0
0
0
0
0
0
1
1
0
0
2
1
0
1
2
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
3
1
0
0
2
2
0
0
1
0
1
0
0
2
2
2
0
1
2
0
0
1
0
0
0
2
0
1
0
2
0
0
2
2
3
0
0
0
1
0
1
1
1
0
2
0
0
2
0
0
1
2
0
2
1
0
2
1
0
2
1
2
0
0
0
0
0
1
0
0
2
1
0
0
0
0
2
0
2
2
0
3
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
8
0
2
0
3
2
1
0
1
0
2
0
0
0
1
0
0
2
0
0
0
2
0
1
0
2
0
0
1
0
0
0
0
0
3
0
1
0
0
0
2
0
0
2
3
1
0
0
1
0
0
1
0
2
0
0
0
1
1
0
0
0
1
2
2
1
1
1
0
0
2
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
2
0
1
0
1
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
3
0
0
0
0
0
2
0
0
2
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
1
0
0
0
2
2
2
2
0
0
0
2
2
0
0
1
1
1
0
1
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
3
0
0
2
3
0
2
1
0
2
0
0
0
2
2
0
0
0
0
1
2
0
0
0
1
0
0
0
1
1
2
0
0
0
0
2
0
0
0
0
1
0
0
1
2
0
3
1
0
1
0
0
2
0
0
0
1
0
0
0
0
0
3
0
0
0
4
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
1
0
1
2
1
2
2
2
0
0
0
0
3
0
2
2
0
1
0
3
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
2
0
0
3
0
2
0
0
1
2
1
0
0
2
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
3
0
2
0
1
1
0
0
0
1
0
0
1
0
1
0
0
0
0
1
2
0
1
0
2
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
2
2
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
2
1
0
1
3
0
2
1
1
0
0
0
0
0
0
2
1
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
2
0
0
1
0
1
0
0
1
0
1
1
0
0
1
0
0
1
2
0
1
2
0
1
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
1
0
2
0
1
0
2
0
0
1
0
1
0
0
1
2
0
0
0
1
0
0
2
0
0
0
1
0
2
0
0
1
1
0
1
1
0
0
2
0
0
2
2
0
0
2
0
0
0
0
0
4
0
2
1
1
0
0
1
0
0
1
0
2
0
0
1
1
0
3
0
0
0
0
2
0
0
2
2
1
0
0
0
1
0
1
0
2
3
0
2
0
0
0
1
0
6
0
0
0
2
1
0
0
0
1
0
0
0
0
0
2
4
2
1
1
2
0
1
0
2
0
2
1
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
1
1
0
2
1
0
0
0
2
0
2
2
1
2
0
2
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
1
0
0
0
1
0
0
1
2
0
1
2
0
0
1
2
0
1
0
0
1
0
0
0
1
0
1
0
1
1
0
0
0
4
0
0
0
0
0
0
2
0
2
3
0
0
3
0
2
0
0
0
1
1
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
2
2
0
2
2
4
1
0
0
0
0
1
0
0
0
0
0
0
2
0
2
2
0
0
0
1
0
0
0
0
2
2
3
0
0
0
0
0
0
2
1
1
0
0
0
2
0
0
2
1
0
0
0
1
0
0
0
0
0
0
4
1
2
0
0
0
1
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
5
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
2
0
2
2
0
0
1
1
1
1
0
0
2
1
0
0
0
0
0
0
2
1
0
0
0
0
1
0
2
3
0
0
0
0
1
1
0
0
0
2
0
2
0
1
2
2
0
0
0
2
1
0
0
2
2
2
1
0
0
2
0
2
1
0
0
0
2
0
0
1
1
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
1
0
2
0
0
1
0
0
0
1
0
0
0
2
0
0
2
0
1
0
2
1
0
0
0
0
2
1
0
0
0
0
0
0
0
3
0
0
0
2
0
2
0
0
0
2
0
2
1
2
0
3
0
2
0
2
1
0
5
0
0
0
1
2
0
0
1
0
0
1
2
1
0
0
0
0
1
0
0
0
0
2
0
0
1
2
0
0
0
0
0
1
2
2
0
0
1
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
1
2
0
0
0
2
0
1
0
0
2
2
1
0
2
2
2
0
1
0
0
1
0
0
0
2
0
2
1
2
0
1
0
0
1
0
2
0
0
0
1
1
2
0
0
0
1
1
2
0
2
2
0
0
0
0
2
1
0
2
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
1
0
1
1
0
1
0
0
1
0
0
0
0
2
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
4
0
1
0
1
0
2
0
1
0
0
0
0
0
0
1
0
0
0
2
2
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
3
1
1
0
0
0
0
1
1
2
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
3
0
2
0
0
0
0
0
2
1
2
0
2
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
1
0
1
1
2
0
1
1
0
2
0
0
0
0
1
1
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
2
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
1
2
2
5
0
0
0
0
0
0
2
0
0
1
2
2
0
1
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
1
0
2
1
0
0
4
4
0
0
0
0
0
1
0
1
1
0
0
0
1
1
1
2
0
0
2
0
0
2
0
0
0
0
1
0
0
0
1
2
0
1
1
1
1
2
0
2
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
3
0
0
1
0
2
0
2
2
0
1
0
1
1
0
2
4
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
1
0
0
1
4
1
0
0
0
2
0
0
2
0
0
2
1
0
3
1
1
0
0
0
0
2
0
0
7
2
0
1
0
2
0
2
0
0
0
0
0
3
0
2
2
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
3
0
1
0
0
1
2
1
2
1
0
0
0
0
2
1
0
0
0
2
0
1
0
0
0
1
2
0
0
0
0
1
2
2
1
2
0
0
0
0
3
1
0
1
0
1
2
1
0
2
2
0
0
0
1
0
1
0
1
2
0
0
0
1
2
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
2
1
0
1
0
0
3
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
2
2
0
0
0
1
1
0
0
2
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
2
1
1
2
0
0
2
0
0
1
3
1
0
0
0
1
2
0
2
1
0
0
0
2
0
4
0
2
1
0
0
2
0
0
1
0
1
0
1
1
0
0
0
0
0
0
1
2
3
1
0
0
2
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
2
0
0
3
0
0
0
2
1
0
1
1
0
1
0
4
0
0
1
0
3
1
2
0
2
0
0
0
0
2
0
1
1
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
1
1
1
0
2
0
2
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
3
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
2
2
0
0
2
0
1
0
0
0
3
0
1
0
0
1
2
0
1
0
1
2
0
2
0
2
0
2
2
2
0
0
2
1
1
0
0
0
1
1
0
0
2
0
0
0
2
0
0
0
2
1
2
0
1
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
2
0
2
1
0
0
2
0
1
0
1
2
0
0
3
0
0
2
0
1
0
0
1
0
0
0
1
2
0
2
2
1
1
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
1
0
0
0
0
0
2
0
1
1
2
0
2
0
2
1
2
0
1
0
0
1
4
0
0
1
0
0
1
0
0
0
0
1
5
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
2
1
1
1
0
3
0
2
0
0
1
0
0
0
1
0
0
1
1
2
1
1
0
0
0
1
0
0
0
0
0
2
2
0
0
2
0
2
0
1
2
0
0
1
1
0
2
0
0
1
0
1
0
0
0
0
2
0
0
0
2
2
1
0
0
0
0
0
0
1
0
0
2
0
2
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
2
0
1
1
2
0
2
0
1
2
0
0
1
0
0
0
0
1
2
0
0
0
0
2
1
0
2
0
0
1
1
2
0
0
0
0
0
0
1
3
0
2
1
0
0
2
1
0
0
0
0
0
2
2
2
0
2
0
0
0
0
0
2
1
0
0
1
0
0
0
0
1
0
1
0
1
1
0
1
0
0
0
4
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
1
0
1
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
2
4
0
1
1
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
3
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
1
0
0
0
0
0
1
0
0
2
0
2
0
2
2
2
1
0
0
0
0
0
1
1
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
1
1
0
0
1
0
1
2
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
2
0
0
0
2
2
1
3
1
1
0
2
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
2
2
1
0
0
2
0
0
2
2
0
0
0
0
0
0
0
1
2
0
1
1
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
1
0
0
1
0
0
0
0
1
0
3
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
1
1
0
0
0
2
0
0
0
0
2
1
1
0
0
0
1
0
0
2
1
0
1
2
1
0
0
2
0
0
0
0
1
0
0
0
0
3
2
0
2
1
2
0
0
1
0
0
3
2
1
0
0
0
0
0
0
1
0
2
2
0
1
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
2
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
2
1
0
1
3
1
0
0
1
2
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
1
2
1
0
0
0
0
1
0
2
2
0
0
0
0
0
3
0
1
0
0
0
1
2
0
1
0
3
0
2
0
2
2
0
0
0
0
0
2
2
0
1
0
0
0
0
0
2
2
0
2
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
3
2
2
0
0
0
0
0
0
0
0
0
5
0
0
1
0
2
0
2
0
2
0
0
2
0
0
0
1
0
0
0
1
3
2
2
1
0
1
0
1
2
3
1
0
0
0
1
3
1
1
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
4
1
1
0
1
3
0
0
0
1
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
1
0
1
0
2
1
0
1
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
3
0
0
0
0
4
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
2
0
2
1
3
0
1
0
3
0
0
0
0
0
1
0
0
0
2
0
2
0
0
1
0
0
1
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
3
0
2
0
0
2
2
1
0
0
0
0
1
0
0
0
1
1
1
2
2
1
0
1
2
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
2
1
1
0
0
0
2
1
1
3
0
2
2
2
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
2
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
1
0
1
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
3
0
0
0
0
3
0
0
0
2
0
0
1
0
0
0
1
0
0
0
7
0
0
0
0
2
0
0
0
0
0
0
2
1
7
2
0
0
0
0
0
0
0
2
1
0
0
1
0
2
1
0
0
0
0
0
0
2
0
0
0
3
0
0
2
2
0
0
1
0
1
0
2
2
0
0
1
0
0
0
0
4
0
0
0
0
0
2
0
0
2
0
0
1
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
2
0
1
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
2
0
2
0
0
1
1
0
0
2
0
1
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
1
1
1
0
0
2
0
0
0
0
1
0
1
0
0
0
2
2
0
3
0
0
0
2
1
1
0
0
0
0
0
1
1
0
0
1
0
0
2
1
2
1
0
0
2
0
0
0
2
2
2
0
0
0
5
1
0
0
0
0
1
0
1
1
1
0
0
0
2
0
2
0
0
0
2
0
0
2
0
0
8
0
0
1
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
1
2
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
1
0
0
1
0
2
2
0
0
2
0
2
1
0
2
0
0
0
2
1
0
0
1
0
1
1
0
1
1
2
1
0
0
2
1
0
0
0
1
0
0
1
0
0
0
0
1
0
2
0
2
0
1
0
0
0
1
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
2
0
2
1
0
0
0
0
0
2
1
2
2
0
0
1
0
0
0
0
0
1
1
0
0
1
2
0
1
2
0
0
2
0
0
0
0
1
1
0
1
0
0
0
2
0
2
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
4
0
0
1
1
0
2
1
0
0
0
2
1
0
0
0
0
1
2
0
2
0
2
0
2
1
0
1
1
0
0
0
0
0
2
1
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
2
0
0
0
0
1
0
0
0
3
0
0
5
2
3
1
1
6
1
0
1
0
0
0
0
1
1
0
0
1
1
0
2
0
1
0
0
0
0
0
0
1
1
0
0
0
0
2
1
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
1
2
0
1
0
2
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
2
0
0
1
1
0
2
3
0
0
0
0
2
0
0
0
1
0
0
0
0
0
4
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
2
0
2
2
0
1
1
0
0
0
0
2
2
0
1
0
1
0
0
2
0
1
0
2
0
1
0
0
0
1
2
0
0
1
0
0
0
1
1
1
0
2
2
0
0
2
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
3
2
0
0
0
0
1
0
2
0
1
1
1
0
0
2
0
2
0
0
1
0
1
0
1
0
1
1
0
3
2
0
0
0
2
1
2
1
5
0
1
3
0
0
1
0
0
0
0
0
2
0
1
0
0
1
0
0
1
0
0
0
0
2
0
0
2
1
0
0
0
0
0
2
0
1
0
1
0
0
1
0
1
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
2
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
1
1
1
0
1
0
0
2
2
1
1
0
3
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
2
0
0
1
2
0
0
1
2
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
3
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
2
1
0
0
0
0
1
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
2
1
0
0
0
2
1
0
0
2
0
0
2
4
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
1
2
1
3
2
0
2
3
0
1
0
2
1
0
0
0
2
0
1
1
0
2
0
1
0
0
0
0
2
1
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
4
0
2
1
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
5
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
1
4
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
1
3
0
1
2
0
0
0
2
0
0
0
0
6
0
0
0
1
0
1
3
1
0
0
0
0
0
0
0
1
3
1
0
2
0
0
0
1
0
0
2
2
0
0
0
2
2
0
1
3
0
0
2
1
2
0
0
0
1
2
0
1
2
1
0
0
3
1
1
0
2
0
0
2
2
0
0
0
0
2
0
0
0
0
2
1
0
0
0
1
0
0
1
0
0
0
0
2
1
0
1
0
0
1
0
0
0
1
0
0
1
1
1
0
0
1
0
0
0
0
1
0
0
4
1
0
0
0
1
0
2
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
1
0
0
1
0
1
0
0
0
3
0
0
0
0
1
0
0
0
2
0
2
2
2
0
0
3
0
0
0
2
3
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
3
0
0
0
0
0
0
2
0
1
2
0
2
2
0
0
2
2
0
0
0
0
0
0
3
0
0
2
2
0
0
2
0
0
1
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
2
1
0
0
1
0
2
0
2
0
0
3
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
1
1
0
1
2
0
1
1
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
9
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
1
1
2
1
3
0
1
2
0
0
0
2
0
2
0
0
0
1
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
4
0
1
2
1
0
2
2
1
1
1
2
2
0
2
0
1
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
2
0
0
1
0
1
1
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
2
0
0
2
2
0
0
1
0
0
2
0
1
0
1
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
1
2
0
0
2
0
0
2
0
1
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
1
0
3
0
0
0
0
1
1
2
0
1
2
1
8
0
2
0
3
0
0
0
3
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
2
0
0
0
0
1
0
1
1
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
2
2
0
0
1
0
3
0
0
0
0
0
0
1
1
1
0
1
0
1
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
1
1
1
0
0
0
0
1
0
0
1
0
0
3
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
2
0
1
0
1
0
1
0
0
0
2
0
0
0
2
2
0
0
0
0
1
2
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
3
2
0
1
0
0
0
0
1
2
0
2
0
1
0
1
0
2
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
1
3
0
0
1
0
0
0
0
0
0
0
1
0
2
1
0
0
1
0
1
0
2
0
2
1
2
1
0
3
2
2
0
2
1
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
1
2
2
1
1
0
2
0
2
0
0
1
0
0
0
0
2
3
0
2
1
2
0
0
1
0
2
0
0
2
0
2
1
2
0
1
2
1
0
0
1
1
1
0
0
0
0
0
1
0
0
1
0
2
0
1
0
0
1
0
0
2
0
0
0
2
0
0
1
0
1
0
0
1
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
1
0
0
1
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
2
0
0
0
1
2
0
1
0
0
0
2
0
0
2
0
0
0
2
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
2
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
1
1
1
1
0
1
2
2
0
0
0
0
0
2
1
0
1
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
2
2
0
0
0
2
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
1
0
0
0
2
0
0
0
1
0
0
1
2
0
1
2
0
0
2
0
0
1
0
5
1
0
2
2
0
1
2
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
1
0
0
1
0
0
0
2
1
2
0
1
1
0
0
0
2
0
2
0
2
2
1
0
0
2
0
1
1
0
0
0
1
1
0
1
1
1
0
1
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
4
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
2
0
0
0
2
0
1
1
0
2
2
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
3
2
4
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
2
0
1
0
0
0
1
2
0
0
0
2
0
0
0
0
2
0
2
1
4
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
2
0
1
0
0
1
0
0
0
2
0
1
0
0
0
0
1
0
0
0
1
3
0
0
2
0
0
0
0
1
0
8
2
0
1
0
5
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
1
1
0
2
3
0
0
0
0
0
1
2
0
1
0
2
0
0
2
1
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
1
0
0
1
0
0
0
1
1
0
0
1
0
0
0
2
0
0
0
0
1
2
0
0
1
0
0
0
0
1
0
0
1
2
0
0
0
0
2
2
0
0
2
0
0
0
2
0
0
0
1
0
0
0
1
1
0
0
0
1
0
1
0
1
0
0
0
0
2
1
1
1
2
0
1
0
0
0
1
2
0
0
2
0
1
2
0
0
2
0
2
2
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
2
0
1
1
1
0
1
2
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
2
2
1
0
2
1
0
2
0
0
2
0
0
0
1
0
0
1
2
0
1
2
1
0
2
0
0
0
1
0
3
0
1
0
0
0
0
1
0
0
0
0
3
0
1
0
0
0
2
0
2
0
0
0
0
0
2
0
1
0
2
2
0
1
1
0
0
0
2
0
0
2
0
1
0
1
0
2
0
0
1
3
0
2
1
1
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
1
2
1
0
0
0
2
0
0
1
0
2
0
2
1
0
0
1
1
1
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
1
0
2
2
0
2
0
2
0
0
1
0
0
3
0
1
0
1
2
0
2
0
0
2
2
0
2
0
1
1
0
1
2
2
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
2
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
4
0
0
1
0
0
0
2
0
1
1
0
0
0
1
3
0
1
1
1
0
0
1
2
0
3
0
2
0
0
0
0
0
0
1
1
0
2
0
0
2
0
0
1
1
0
0
1
0
2
1
2
0
0
0
0
1
0
1
1
0
1
0
0
1
1
0
0
0
1
0
2
0
0
0
2
0
2
0
1
1
2
2
2
0
0
0
0
2
0
1
0
1
0
0
2
0
2
0
1
0
2
2
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
2
2
0
0
3
0
2
0
0
0
0
0
1
0
1
1
0
0
0
0
2
0
0
1
0
0
2
2
0
0
2
2
3
0
0
1
0
0
0
0
0
1
0
2
2
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
3
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
3
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
2
1
0
2
1
0
0
2
0
0
0
1
2
2
0
0
1
0
0
2
0
0
0
0
2
1
0
0
0
0
0
1
2
1
2
0
0
0
1
0
0
0
1
0
1
1
2
0
1
0
0
0
1
1
0
1
0
2
0
0
0
3
3
0
0
0
0
1
1
0
1
0
2
0
0
4
0
1
1
0
2
1
0
0
0
2
1
0
0
1
0
1
2
0
0
0
0
0
0
0
0
2
1
2
2
0
0
0
0
3
1
1
0
1
0
1
2
0
0
0
2
2
0
0
0
2
1
0
0
0
2
0
0
4
1
0
0
0
1
0
2
0
0
0
0
1
0
0
1
1
3
1
1
0
0
2
0
1
0
0
0
0
3
0
0
0
2
0
2
0
0
1
0
0
1
0
1
0
0
1
2
0
1
2
0
0
0
0
1
2
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
1
0
2
1
1
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
1
0
1
0
0
0
0
2
0
2
1
3
0
2
0
1
0
0
0
1
0
0
2
0
0
2
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
2
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
1
0
2
0
1
0
0
2
0
0
0
1
1
1
0
0
0
1
2
0
0
2
2
2
0
0
0
0
1
0
0
0
0
1
0
2
0
2
2
1
1
0
1
2
3
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
1
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
1
2
0
0
1
0
3
0
0
1
0
0
0
0
0
2
0
2
0
0
3
1
2
0
0
0
0
1
0
0
2
0
0
3
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
1
0
2
0
0
0
1
1
2
0
2
1
1
0
0
0
2
0
2
0
0
2
2
0
0
1
2
1
0
0
0
0
2
0
0
0
1
0
0
2
1
0
2
0
0
0
2
3
0
2
2
0
0
2
0
0
2
0
0
0
0
0
1
0
0
1
1
1
0
0
1
3
0
0
0
2
0
1
0
1
2
2
0
0
1
2
2
2
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
2
0
1
0
0
2
0
0
1
0
0
2
0
0
0
1
1
2
0
0
1
0
0
2
1
0
1
2
0
1
0
1
1
0
1
2
2
0
1
1
1
0
1
0
1
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
1
0
1
0
0
2
0
2
0
0
0
0
0
2
0
0
1
2
1
0
0
1
1
2
0
0
2
0
0
0
0
3
0
0
0
0
0
0
1
2
3
0
1
2
2
1
2
0
0
0
3
0
1
1
0
0
0
1
0
0
1
0
1
1
1
1
0
0
0
0
0
2
0
0
0
2
0
0
2
2
1
2
0
0
0
2
0
1
0
1
1
2
1
1
0
0
0
0
2
2
0
0
1
0
0
0
1
0
2
0
1
1
1
0
0
0
2
0
0
0
0
0
0
7
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
1
0
0
2
0
0
0
0
0
0
1
1
0
4
1
2
0
0
0
0
0
0
2
1
0
0
0
0
1
1
0
0
0
0
0
2
3
0
0
1
0
0
2
1
0
2
0
0
2
0
2
0
0
0
0
0
2
0
2
0
0
2
0
1
0
0
0
0
0
0
0
1
1
1
0
1
0
1
1
0
2
0
0
2
1
0
1
1
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
2
4
0
2
0
2
0
0
0
0
2
2
0
1
0
0
0
0
2
1
1
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
1
0
2
1
2
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
1
0
2
0
2
0
0
2
2
1
0
1
2
2
0
1
1
0
3
2
0
0
1
2
1
0
0
3
0
2
0
0
1
0
2
0
1
1
0
1
1
0
0
1
0
0
1
0
0
0
1
1
0
0
1
0
2
0
0
0
0
2
0
0
3
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
1
2
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
1
3
1
0
1
1
0
0
2
1
2
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
2
0
0
0
0
0
0
2
2
0
2
0
1
1
0
0
0
5
0
0
1
0
0
2
0
0
0
2
0
0
3
2
1
0
0
0
2
0
1
3
0
1
2
0
0
0
0
1
1
0
0
0
0
0
2
1
2
0
0
2
1
0
0
0
0
0
1
0
3
0
0
0
1
1
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
1
2
0
0
1
0
0
2
0
0
2
1
0
0
0
0
0
5
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
4
1
1
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
1
2
0
0
1
2
0
0
0
0
1
0
0
0
0
0
2
0
1
1
2
0
0
1
0
7
0
0
0
1
1
1
1
2
0
1
0
2
0
0
1
0
1
2
0
0
0
1
0
1
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
2
1
0
0
0
2
0
0
0
0
0
0
1
1
0
4
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
2
0
2
3
0
0
0
0
0
1
0
2
1
2
0
2
0
0
0
0
0
1
2
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
1
2
0
0
0
0
1
2
2
0
0
1
0
0
0
1
1
1
2
4
0
1
0
2
1
0
2
1
0
0
0
1
0
1
0
0
2
0
1
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
2
0
1
0
0
0
0
0
0
1
1
1
0
2
0
0
0
0
1
0
1
2
0
2
1
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
1
2
0
2
0
0
0
1
2
1
0
2
0
2
0
0
1
0
1
0
0
1
1
0
1
0
0
1
2
0
1
2
2
0
1
0
2
0
3
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
1
1
1
0
0
0
0
0
2
1
0
0
2
0
0
2
0
0
0
1
3
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
2
1
0
0
1
0
0
0
2
1
0
0
0
1
0
2
1
1
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
2
0
3
0
0
0
2
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
5
0
0
0
0
0
0
0
2
0
2
2
3
1
1
1
0
1
0
0
0
0
2
0
0
1
1
2
2
0
0
2
0
0
1
0
0
2
0
0
2
0
1
1
2
0
4
0
0
0
0
0
0
1
0
0
3
0
2
0
2
0
0
2
0
0
1
0
4
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
2
2
0
0
3
0
0
0
2
1
0
2
2
0
0
0
1
2
0
0
2
0
0
1
2
0
0
1
0
1
0
1
0
1
0
1
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
1
0
0
0
0
1
1
0
0
0
0
0
0
2
1
2
0
0
1
0
0
0
1
0
0
1
2
0
2
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
3
1
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
1
2
0
0
2
2
0
0
2
0
0
1
0
2
0
0
2
0
0
0
0
1
2
0
0
0
0
0
2
0
2
0
0
0
2
0
0
2
0
2
0
1
0
1
0
1
1
0
0
0
2
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
2
0
0
0
1
0
2
1
2
0
2
0
0
0
0
2
0
2
0
0
2
6
0
0
1
1
0
0
0
0
2
0
0
0
1
0
4
2
2
0
2
0
0
1
0
0
2
0
2
1
0
0
1
1
2
0
1
0
0
0
0
1
2
0
2
2
1
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
1
1
0
0
2
1
1
0
1
0
2
3
2
2
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
2
1
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
2
0
0
0
1
0
1
1
1
0
1
0
2
0
1
0
0
0
0
0
1
0
0
1
1
2
0
0
0
0
0
0
0
0
1
0
0
1
2
1
1
0
1
0
0
1
0
0
2
0
0
0
2
0
0
0
2
2
2
0
0
2
0
0
0
0
0
0
2
1
0
0
2
0
0
2
1
0
0
0
0
0
0
0
2
0
2
2
0
0
1
0
0
0
0
2
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
2
0
2
2
0
2
2
0
0
0
1
0
1
2
0
0
0
0
2
0
0
0
2
4
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
1
0
1
0
0
2
1
0
3
1
2
0
0
0
1
1
2
1
1
0
0
1
0
0
2
0
1
0
2
0
0
0
0
1
0
0
0
0
1
2
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
2
0
0
0
1
0
0
2
0
0
1
0
0
0
0
3
0
0
1
1
0
0
0
0
0
0
2
0
0
3
0
1
0
0
0
2
1
0
0
0
1
1
0
3
1
0
0
0
2
0
2
1
1
0
1
1
0
0
0
0
1
0
1
0
0
2
0
0
2
2
1
0
1
1
0
1
2
1
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
2
2
2
2
0
3
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
1
0
0
0
0
0
0
0
0
2
2
2
1
2
1
0
0
2
0
1
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
1
0
2
0
0
2
0
0
2
1
1
0
0
2
0
0
2
0
0
1
0
2
1
0
0
1
1
1
1
1
2
2
0
2
1
0
1
2
3
0
2
0
0
0
1
0
1
0
2
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
1
0
0
1
0
3
0
0
1
0
1
2
0
0
1
1
2
0
2
1
2
2
1
0
0
0
0
0
1
2
2
0
0
0
2
0
0
1
0
0
0
0
1
0
1
0
0
2
4
0
0
0
2
0
0
1
2
2
2
1
0
0
4
1
0
0
0
0
1
0
0
1
0
2
0
1
0
0
0
0
0
0
1
2
0
2
0
0
2
0
1
0
2
0
1
1
0
0
0
1
0
0
1
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
2
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
3
0
0
0
0
0
0
0
2
0
2
2
1
0
0
0
1
2
1
0
2
1
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
2
0
0
0
3
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
2
0
1
0
2
0
0
1
0
0
0
0
1
1
0
0
0
0
0
4
0
0
2
0
0
0
2
3
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
2
3
0
0
2
0
0
0
0
3
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
1
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
3
2
1
1
0
0
0
0
0
1
0
0
3
0
0
0
0
0
6
0
0
1
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
1
2
1
2
0
0
1
0
0
3
0
0
2
1
0
1
0
0
3
1
0
0
1
0
2
0
0
0
0
1
1
0
0
1
0
2
0
0
0
0
0
0
0
0
2
2
1
0
0
1
0
0
0
0
0
1
2
1
1
0
2
0
1
0
2
0
1
0
1
2
0
0
0
0
2
1
1
0
0
0
0
1
1
0
0
1
2
0
0
2
0
0
3
0
1
4
0
0
0
0
0
1
0
1
2
2
0
0
0
0
0
0
0
0
1
0
2
2
0
0
1
3
11
2
0
0
6
1
0
0
2
0
1
1
0
0
1
0
0
1
1
2
1
0
0
1
1
0
1
0
0
0
0
3
0
0
0
0
0
0
0
1
2
3
0
1
0
1
1
3
0
0
0
0
0
2
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
1
2
1
0
1
1
0
0
0
0
0
0
0
2
1
0
0
2
0
2
0
1
2
0
0
0
0
0
1
0
7
0
0
3
2
0
0
0
1
2
2
0
2
0
2
0
1
0
2
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
3
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
2
0
3
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
4
1
0
0
0
2
0
0
0
0
0
2
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
1
1
2
0
2
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
1
0
0
0
0
0
0
0
0
1
3
1
3
2
2
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
1
2
2
1
1
0
1
0
1
1
0
0
2
0
1
0
0
0
0
1
1
0
1
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
3
1
0
2
0
0
1
1
2
0
0
0
0
1
1
0
1
2
0
5
0
0
0
0
0
0
2
0
1
1
1
0
0
0
0
0
2
1
2
0
0
0
3
1
0
0
0
2
2
0
2
0
0
3
0
0
2
0
0
1
0
0
1
0
2
1
0
1
2
0
0
0
0
0
1
0
2
2
1
0
0
0
0
1
1
2
0
3
2
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
2
0
0
1
0
0
0
0
1
0
2
1
1
0
1
0
2
0
0
0
2
0
0
1
1
0
1
1
0
0
2
0
0
2
2
1
2
0
0
1
0
0
2
0
2
0
3
0
2
0
2
1
2
1
0
0
0
0
3
2
2
0
1
0
0
1
2
0
2
0
0
1
1
0
1
0
2
2
0
1
0
2
0
0
0
2
0
0
0
1
0
2
1
2
2
0
1
2
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
1
1
0
2
0
0
0
2
0
3
1
0
0
2
2
0
1
2
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
2
2
0
0
0
2
1
0
0
1
1
2
2
0
0
1
0
1
0
0
2
0
1
0
2
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
1
0
0
2
3
0
0
0
2
1
0
0
0
1
2
2
1
2
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
2
0
0
2
1
0
0
2
0
0
2
0
0
0
0
3
1
0
0
0
0
0
1
3
0
0
1
1
0
0
0
1
0
2
0
0
0
0
0
1
0
1
0
2
1
0
0
2
0
1
1
1
3
1
2
0
0
2
1
0
0
0
0
0
0
2
1
0
0
1
0
0
4
0
2
0
2
2
1
0
2
0
0
1
0
0
0
0
2
1
0
0
1
6
0
0
3
0
5
0
1
0
2
0
0
0
0
1
2
1
2
0
0
1
0
0
0
2
1
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
1
2
0
0
0
2
0
2
0
0
0
0
0
1
1
1
0
1
0
0
1
1
1
0
2
0
2
2
0
1
2
0
0
1
1
0
0
2
0
0
3
0
0
0
1
3
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
2
0
2
0
0
0
1
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
2
0
1
0
2
1
0
0
0
0
1
2
0
2
1
1
2
1
0
0
0
1
0
0
0
0
0
0
1
2
0
2
0
0
1
0
2
0
3
3
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
2
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
6
0
1
1
0
0
0
0
1
1
1
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
1
2
0
1
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
1
2
0
0
0
0
0
2
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
1
2
1
0
0
0
2
2
0
2
1
0
1
2
1
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
2
3
0
0
0
2
1
1
1
1
0
1
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
2
0
0
2
1
0
2
0
0
2
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
2
2
2
1
1
2
0
0
1
2
0
0
0
1
0
1
1
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
3
0
0
2
0
1
0
0
0
0
0
0
0
2
1
0
0
1
0
0
1
0
1
0
0
1
2
0
1
2
0
0
0
0
0
0
1
0
0
0
2
0
1
1
0
0
2
0
0
1
2
0
4
0
0
4
0
0
1
0
0
0
3
0
0
0
1
0
0
0
0
0
2
1
0
1
1
0
1
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
11
0
0
0
0
0
0
1
0
0
0
2
1
0
0
2
2
0
1
0
3
1
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
1
7
1
0
0
0
0
2
0
0
0
0
1
1
3
0
1
3
1
0
0
2
0
2
0
0
0
0
2
2
1
1
1
1
0
0
0
1
0
0
1
2
0
1
0
0
1
0
2
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
2
1
0
0
2
0
0
1
2
0
1
0
1
1
2
1
0
2
0
0
2
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
2
0
2
0
3
0
1
0
1
0
0
2
0
0
2
0
1
2
2
0
0
0
0
2
2
0
0
2
0
1
0
1
0
0
2
2
0
0
0
0
2
0
1
0
0
0
0
2
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
1
0
2
0
1
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
3
1
1
0
2
0
0
0
0
0
0
2
0
1
2
0
1
0
0
0
2
0
1
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
2
0
2
0
0
2
0
0
1
0
0
0
0
0
0
2
1
0
1
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
1
0
0
0
2
1
0
1
0
0
0
2
0
0
0
0
1
1
0
0
1
1
0
2
1
0
0
0
0
1
0
0
1
1
0
1
0
0
2
0
0
0
0
0
1
2
0
0
2
0
0
0
1
0
0
2
1
0
0
1
1
2
0
0
0
1
2
0
1
2
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
2
2
1
0
0
0
2
2
2
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
1
0
0
0
1
0
1
1
2
0
0
0
0
0
0
0
0
4
0
1
4
0
2
0
0
0
1
0
0
0
0
0
1
0
1
0
0
2
0
2
1
0
0
3
2
0
1
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
3
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
1
1
1
1
0
1
1
0
0
0
1
0
0
0
2
0
0
0
1
0
1
1
0
0
1
0
0
0
1
2
0
0
0
1
1
0
2
0
3
0
0
2
1
0
0
0
0
0
1
1
0
0
1
0
0
2
1
0
0
1
1
0
1
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
1
2
1
0
0
2
0
0
1
1
0
0
0
1
2
0
0
1
1
3
0
0
0
1
1
0
0
0
0
0
0
0
0
1
2
0
2
0
0
1
0
2
0
2
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
2
1
0
0
0
0
0
0
0
1
0
0
0
0
1
2
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
3
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
2
0
2
0
0
2
0
0
2
0
0
0
0
1
1
1
2
0
0
0
0
0
1
1
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
2
2
0
0
2
0
2
6
0
0
2
1
0
0
0
1
0
2
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
2
0
2
1
0
2
1
0
0
0
2
0
2
0
2
2
0
0
0
1
0
3
1
0
0
0
2
0
0
0
0
1
0
2
2
0
0
1
2
0
0
0
1
1
1
0
0
0
3
0
0
2
0
1
1
1
0
2
1
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
2
0
0
1
2
0
0
2
2
0
1
0
1
2
1
2
0
2
0
1
0
0
2
1
0
0
0
0
0
0
0
2
1
2
0
1
0
1
0
2
1
1
0
0
2
2
1
2
0
3
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
4
1
2
0
0
2
0
2
0
1
2
0
0
0
2
0
0
0
1
2
0
1
2
0
1
3
2
2
0
2
0
2
2
2
0
2
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
2
0
1
0
1
0
0
0
0
1
2
1
2
2
1
0
0
2
0
0
1
0
0
1
0
0
0
0
2
0
0
2
3
1
1
0
0
2
0
1
1
1
1
0
0
0
0
0
0
0
0
3
2
1
0
0
0
0
2
1
0
0
0
0
2
0
1
1
2
0
0
0
1
1
1
2
0
0
2
1
0
0
0
0
0
0
1
2
0
0
3
1
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
4
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
5
0
0
1
0
3
0
0
2
0
0
0
4
2
0
1
0
0
1
0
1
0
0
0
2
0
0
0
1
0
0
0
0
2
1
0
0
1
0
0
0
0
1
0
0
2
1
0
5
1
0
0
2
0
2
0
0
0
0
2
1
1
0
1
0
0
2
1
0
0
1
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
2
0
2
1
1
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
1
0
0
2
0
0
0
2
0
0
0
2
0
0
2
0
0
0
1
3
0
2
1
1
1
1
0
0
0
0
0
1
0
2
0
0
1
0
1
0
1
1
0
0
1
0
0
0
0
2
3
2
0
0
2
0
0
0
0
2
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
1
1
0
0
2
2
0
0
1
0
0
1
0
2
1
0
1
0
2
1
2
0
0
0
1
2
3
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
4
0
0
0
0
1
0
0
2
0
2
0
1
0
1
1
0
0
2
2
1
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
2
0
0
0
0
2
0
0
2
0
0
0
2
1
0
0
0
1
0
2
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
2
0
0
0
0
2
0
0
2
2
2
0
0
0
1
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
3
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
1
0
4
0
2
1
1
2
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
1
1
1
2
0
0
0
0
1
0
0
0
0
0
0
3
0
0
1
2
0
2
0
1
1
0
2
0
0
1
0
0
2
3
0
2
1
0
0
0
2
0
2
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
1
0
0
0
1
2
0
0
0
2
0
2
0
1
0
2
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
3
0
0
0
0
3
0
0
1
0
0
3
1
0
2
0
0
0
2
2
1
3
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
1
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
3
3
2
0
2
1
0
2
0
0
0
0
0
0
0
3
1
2
0
0
0
0
2
1
0
0
0
2
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
1
1
0
1
0
0
0
0
0
1
0
0
0
2
0
2
0
2
0
0
1
0
0
2
0
0
0
1
2
1
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
1
2
2
0
1
0
2
1
0
2
0
0
1
0
0
0
0
2
0
2
2
0
1
0
0
1
0
0
1
0
0
1
0
0
5
2
0
0
1
0
0
2
0
0
0
1
0
1
1
1
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
3
0
0
1
0
0
0
0
0
0
1
0
2
0
1
0
1
0
0
0
1
0
0
0
2
0
0
1
1
0
0
0
1
0
0
1
0
1
2
2
0
0
1
2
1
0
0
0
0
0
0
0
2
0
2
1
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
2
0
1
1
0
0
0
0
0
1
0
0
2
0
0
2
2
0
1
0
0
0
1
0
1
0
1
1
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
1
2
1
2
0
0
2
1
0
1
0
0
1
0
1
2
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
2
2
0
1
0
2
0
0
1
0
0
2
1
0
0
0
0
0
3
6
0
2
0
1
2
5
2
1
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
4
1
1
0
2
2
0
0
0
3
0
1
0
0
0
1
2
0
1
0
0
0
0
0
2
0
2
0
0
2
2
1
0
2
0
0
0
0
0
2
0
1
2
0
2
0
0
0
0
0
2
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
3
2
1
0
2
0
2
0
1
0
1
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
1
0
0
0
0
0
2
0
0
0
1
0
1
0
1
2
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
2
2
0
0
0
0
0
0
0
2
2
0
2
0
1
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
2
3
0
0
1
0
1
0
0
0
0
2
0
0
0
1
2
0
0
1
0
1
1
1
0
1
0
2
0
1
0
2
0
0
0
2
2
0
1
0
0
1
0
1
1
1
1
2
0
0
0
1
0
2
2
0
0
2
3
1
0
5
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
1
0
0
0
0
0
0
0
1
0
2
0
0
1
0
2
0
0
0
0
2
2
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
1
2
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
1
2
0
1
1
1
0
1
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
2
1
0
1
1
0
1
1
2
0
0
0
1
1
2
0
2
0
0
0
0
1
0
2
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
2
0
0
1
0
0
0
0
0
0
0
0
2
2
2
0
2
0
0
0
0
0
0
0
0
2
0
0
1
1
2
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
2
0
1
3
0
1
0
3
0
0
2
1
2
1
1
0
0
1
1
0
0
1
2
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
3
0
2
0
2
2
0
2
0
0
2
0
0
0
1
0
1
4
1
2
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
2
2
0
0
2
0
1
0
0
2
0
1
1
0
0
0
0
0
1
1
2
0
3
0
0
0
0
0
0
0
1
0
1
0
1
0
2
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
1
0
0
5
0
0
0
0
1
2
0
1
0
1
2
2
0
0
1
0
1
0
0
2
2
0
0
2
1
0
0
1
0
0
0
2
0
0
0
0
1
0
0
1
0
0
1
0
1
1
1
1
2
1
0
0
2
0
0
0
0
0
2
0
1
0
0
2
0
2
0
0
1
0
0
1
1
1
0
2
2
0
0
0
1
3
0
0
0
0
2
1
0
1
0
8
4
0
1
0
0
0
0
1
0
2
0
0
0
1
2
2
0
0
0
2
2
0
0
0
3
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
2
0
2
0
2
0
0
0
0
0
0
0
0
2
0
3
1
0
0
0
0
0
0
2
0
2
1
0
2
0
0
2
0
0
0
0
0
0
0
2
1
0
1
0
1
0
0
2
0
2
0
0
0
2
2
0
0
1
1
0
1
0
2
0
0
1
0
0
0
0
0
0
2
0
1
0
0
2
0
2
0
2
0
0
0
1
2
2
0
0
0
0
1
0
0
2
0
1
0
0
0
1
2
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
2
2
0
0
2
2
1
0
0
0
2
1
0
1
0
2
0
0
0
0
0
0
2
1
1
1
0
1
1
0
1
0
1
0
0
0
0
2
0
0
0
0
0
1
1
0
1
0
3
1
0
2
1
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
2
0
2
1
0
0
0
1
1
0
0
0
0
0
0
0
2
1
1
0
1
0
0
2
1
0
2
0
0
1
2
2
0
0
0
3
0
0
0
0
0
0
0
0
2
0
2
3
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
1
0
2
0
0
0
0
2
2
0
0
1
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
3
2
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
2
0
0
0
2
0
1
0
0
0
0
2
1
0
0
0
1
1
0
0
0
0
0
1
2
0
1
1
0
0
0
2
0
1
0
0
1
2
0
1
0
0
2
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
1
2
0
2
2
1
0
0
0
0
1
0
0
0
2
0
3
0
0
2
0
0
0
0
0
1
2
0
0
0
0
3
2
0
1
2
0
1
0
0
0
2
0
0
1
1
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
3
1
1
0
0
0
0
0
0
1
0
0
4
0
2
0
0
0
0
1
0
1
4
0
2
0
1
0
1
1
0
1
0
0
0
0
0
2
1
2
0
0
1
0
0
0
2
0
0
3
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
2
0
0
0
1
0
0
2
2
0
0
0
1
0
0
0
1
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
1
0
0
1
0
0
1
0
0
0
2
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
1
0
1
0
2
0
0
0
0
0
2
0
0
0
3
5
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
1
3
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
1
1
1
0
0
0
0
1
0
0
1
0
2
0
0
2
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
2
0
0
0
2
2
0
0
1
0
1
1
1
0
0
0
1
1
0
0
2
2
0
0
0
0
0
2
2
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
3
1
0
1
0
0
0
1
1
0
0
1
1
0
3
1
0
0
0
0
2
1
1
0
2
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
2
0
0
0
0
5
2
2
2
0
1
0
0
0
2
0
0
2
1
1
0
0
0
2
0
0
0
2
0
0
0
2
1
0
3
0
3
0
2
0
0
1
0
0
0
1
1
2
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
3
0
0
2
0
1
0
0
1
0
1
1
0
0
0
0
0
2
0
2
0
0
2
2
0
0
0
2
0
1
2
0
0
0
0
1
0
0
0
0
1
0
0
1
0
2
0
0
0
0
3
1
1
0
0
1
0
0
2
1
2
0
0
0
2
3
0
0
0
0
1
0
1
1
1
0
0
0
0
0
1
0
0
0
0
2
0
0
1
1
0
2
0
2
0
0
0
2
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
1
0
1
1
1
0
0
1
0
2
0
0
0
1
2
1
2
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
1
0
1
0
4
2
0
0
1
0
0
1
0
2
0
0
0
2
0
0
1
0
0
0
2
1
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
3
0
2
1
0
2
0
0
0
0
0
1
1
1
1
0
1
0
1
3
2
0
0
0
2
0
2
0
2
2
2
0
0
0
0
0
2
2
0
7
0
0
0
0
0
2
0
0
2
0
1
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
2
0
0
1
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
2
0
2
2
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
1
0
0
0
2
2
0
1
0
2
2
0
2
0
0
0
2
0
0
1
0
2
0
0
0
1
0
0
1
0
0
2
0
2
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
2
1
0
0
0
0
2
0
1
3
0
1
0
4
0
4
3
0
0
0
1
1
1
0
0
0
0
0
6
0
3
0
0
0
0
0
0
2
1
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
5
1
0
1
2
4
0
0
1
0
2
0
0
2
0
1
0
2
0
0
0
3
0
0
0
0
0
1
0
1
0
0
2
0
1
1
0
0
0
0
1
0
0
0
0
3
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
4
1
2
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
3
2
2
1
0
0
0
0
0
0
4
1
2
0
0
0
0
0
2
0
0
0
5
1
1
1
0
0
2
0
0
0
1
1
1
0
0
1
1
0
0
1
0
1
1
0
0
2
0
2
1
0
0
0
1
1
2
0
0
0
1
2
0
2
0
0
0
2
0
2
1
2
2
0
0
0
6
0
1
0
0
1
2
1
0
0
0
2
2
1
1
2
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
9
0
1
0
1
0
0
1
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
2
0
1
1
1
0
2
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
1
0
2
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
5
2
1
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
2
2
1
0
0
1
0
0
0
0
0
0
1
2
0
0
1
1
2
0
0
0
0
0
0
0
2
1
1
0
2
1
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
2
0
2
2
1
2
0
1
1
2
0
1
0
0
0
0
0
0
0
0
0
1
1
2
0
0
2
0
1
1
0
1
0
0
1
0
0
0
2
0
0
0
0
2
0
1
2
0
0
1
0
0
0
0
0
1
2
2
0
0
2
2
1
2
0
0
2
0
0
1
2
2
0
0
2
1
1
0
0
0
0
0
0
0
2
4
1
2
0
0
2
0
0
0
0
4
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
1
1
2
0
0
1
2
0
0
1
1
0
0
1
1
0
0
1
0
5
0
0
0
2
2
0
0
0
2
0
1
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
2
1
1
2
0
0
0
0
0
0
1
0
0
2
1
2
0
0
0
0
0
0
2
1
1
0
0
1
0
0
0
1
0
0
2
2
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
1
2
0
2
0
2
0
0
0
0
1
0
2
0
0
1
2
0
0
2
4
0
1
2
1
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
1
2
0
0
1
2
0
0
2
0
0
1
1
0
0
1
0
0
3
0
2
1
0
2
0
0
1
1
3
2
0
3
0
0
1
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
5
0
0
0
0
0
2
2
0
0
0
0
0
0
1
1
1
1
2
0
2
0
0
1
0
2
2
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
1
2
0
1
2
0
0
1
0
0
2
0
2
1
0
2
2
0
0
2
3
0
3
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
2
2
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
2
2
0
2
0
1
0
7
0
0
2
1
0
0
2
1
0
1
0
0
0
0
2
1
0
1
0
1
0
0
0
2
0
2
3
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
2
1
0
0
0
0
1
2
0
2
1
0
0
0
1
2
0
2
0
0
0
2
0
0
2
4
0
0
0
0
2
0
2
0
0
0
1
2
0
1
0
0
0
1
2
0
1
0
1
0
0
0
2
0
0
0
2
0
0
1
0
1
1
0
1
2
0
0
1
1
0
0
2
2
0
0
1
1
0
3
1
0
0
0
0
0
1
0
0
0
0
3
0
0
0
4
0
0
2
2
0
2
0
0
1
0
1
2
2
0
0
2
0
1
2
1
1
0
1
0
2
1
3
4
0
0
0
0
0
0
0
0
0
0
2
3
0
0
2
0
0
2
0
1
1
0
0
3
2
0
0
0
2
0
1
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
1
2
2
0
0
1
0
2
0
0
0
0
0
2
1
0
0
0
0
3
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
1
0
0
0
2
2
0
0
2
3
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
1
0
0
2
1
0
0
0
2
2
0
0
0
2
0
3
0
0
0
2
0
0
2
0
2
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
2
0
1
1
0
0
0
1
0
3
0
1
2
0
0
0
0
0
3
0
2
0
0
0
0
0
1
0
1
0
0
1
0
0
0
2
2
1
2
1
2
1
0
0
0
0
0
2
2
0
2
0
1
2
0
2
3
1
0
0
2
0
2
0
0
0
0
2
0
0
1
2
0
0
0
2
2
0
2
0
0
0
0
0
2
0
0
0
0
2
0
2
2
0
2
5
0
2
0
0
2
0
0
3
1
0
2
0
1
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
1
0
2
0
0
0
1
0
0
1
2
0
1
0
0
0
0
0
1
1
0
2
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
1
2
1
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
2
0
0
0
1
0
0
2
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
3
0
0
1
0
2
2
0
0
0
1
1
1
0
3
0
0
2
0
1
0
0
1
0
0
1
1
3
0
1
0
0
3
0
2
1
0
1
0
0
2
0
2
0
1
0
2
0
0
0
0
0
1
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
1
5
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
1
2
2
0
1
0
0
0
0
0
2
2
2
0
0
0
0
2
0
2
4
1
1
1
0
0
0
0
0
2
1
0
0
0
0
0
2
2
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
2
0
0
0
0
1
0
1
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
2
1
0
0
2
2
2
3
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
3
0
1
2
3
6
0
0
3
1
2
0
2
0
0
0
0
0
0
0
2
0
1
2
0
0
3
0
1
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
2
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
1
1
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
1
0
2
2
1
1
2
2
0
0
0
1
0
0
0
2
2
0
2
0
0
2
0
0
0
0
2
7
0
0
0
0
1
0
0
2
3
1
1
2
0
0
0
0
0
2
1
2
0
1
0
2
1
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
1
1
2
1
2
0
1
0
0
0
0
0
2
0
0
0
1
0
2
1
0
0
0
0
0
0
0
1
1
1
0
0
0
2
0
0
0
1
0
2
1
0
0
0
1
0
0
0
2
0
2
2
1
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
1
1
1
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
5
0
2
1
2
0
0
2
1
0
2
1
2
0
2
0
0
0
0
2
1
2
1
2
1
0
0
0
0
2
1
1
2
0
0
0
1
0
2
0
0
0
0
0
2
3
2
0
0
1
1
2
0
0
0
0
1
0
0
0
2
0
0
2
0
1
2
1
2
0
0
0
0
0
2
0
2
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
1
0
2
1
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
2
0
0
1
0
0
0
1
2
0
0
0
0
1
2
0
0
0
0
2
0
0
1
2
2
0
2
0
1
1
2
0
0
0
1
0
1
2
2
0
1
1
0
1
0
2
1
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
3
0
0
0
2
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
2
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
3
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
2
0
0
0
1
2
0
1
0
0
2
2
1
0
2
0
0
0
0
0
0
1
1
0
1
2
2
0
0
0
0
1
1
0
0
2
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
1
0
1
2
0
0
0
0
2
4
0
2
0
0
1
0
2
0
1
1
0
0
2
1
1
0
0
0
2
0
0
2
0
0
2
0
2
0
0
0
2
0
2
0
0
0
0
2
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
1
2
0
0
0
2
0
1
0
1
1
0
0
0
1
0
1
0
1
0
0
2
1
2
1
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
1
0
1
3
0
0
0
2
1
1
0
0
2
0
0
1
0
0
1
0
1
0
0
2
2
0
1
0
0
2
2
1
0
1
0
0
0
0
0
0
1
3
0
0
0
0
1
1
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
2
2
0
0
0
1
2
0
0
1
2
1
2
0
2
0
1
1
2
0
0
1
2
1
0
2
0
0
0
0
0
0
0
1
0
1
1
0
0
1
2
1
1
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
2
1
2
2
2
0
0
0
0
3
0
0
2
0
0
0
2
0
0
0
1
0
2
0
0
1
0
2
0
0
1
2
1
2
0
2
1
1
0
0
0
0
1
0
0
0
0
1
2
0
0
1
2
0
0
0
0
2
1
1
1
0
1
1
0
0
0
0
1
2
2
0
0
0
0
0
2
1
0
3
2
0
0
0
0
0
0
1
2
0
0
1
0
2
2
0
0
2
2
2
2
0
1
0
0
2
2
0
2
2
0
1
0
0
0
2
2
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
2
2
0
0
1
0
0
2
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
1
1
2
0
0
0
2
1
0
0
1
0
0
2
0
1
0
0
1
0
0
0
0
0
1
0
1
2
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
3
0
1
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
3
0
0
2
0
0
0
0
0
0
1
0
2
0
2
1
2
1
0
0
0
1
0
0
0
2
0
2
0
0
3
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
2
0
0
2
1
0
0
0
0
0
0
0
1
1
0
0
1
0
1
2
0
2
2
0
0
0
2
1
0
2
0
0
0
1
0
0
0
0
0
1
0
1
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
1
2
0
2
0
1
1
0
0
2
0
0
0
2
0
1
0
1
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
4
2
1
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
1
1
1
2
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
1
2
0
0
0
1
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
2
1
0
1
0
1
0
0
0
0
2
0
0
0
2
0
1
0
2
0
0
0
0
0
1
0
0
1
0
0
2
0
0
1
0
0
0
1
1
0
0
2
2
1
0
0
2
0
1
0
0
0
6
1
1
0
0
0
3
0
0
1
1
0
1
0
3
0
0
2
1
0
0
2
1
0
0
1
1
0
1
0
0
0
1
0
2
1
0
0
0
0
0
0
1
2
0
0
2
0
0
0
1
1
0
0
0
1
1
0
0
1
0
0
1
0
0
0
1
2
0
0
0
0
2
2
0
0
2
0
2
1
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
2
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
3
0
2
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
1
0
0
1
0
0
2
2
0
0
0
1
0
2
1
0
1
1
0
0
2
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
2
1
0
0
0
0
0
1
0
0
1
0
2
2
0
2
0
2
1
0
0
3
2
1
1
0
0
0
0
2
0
0
0
0
0
0
1
2
0
1
3
0
0
1
0
1
2
1
0
0
2
0
0
0
0
0
0
2
1
0
2
0
3
2
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
1
0
2
2
0
2
0
0
1
1
0
0
1
0
3
1
1
3
0
2
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
2
0
0
0
3
0
0
2
3
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
2
2
3
0
0
1
0
0
1
2
0
0
2
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
5
0
2
0
0
2
0
0
0
3
2
0
0
3
0
0
2
1
1
2
0
0
0
1
2
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
3
0
2
0
0
1
1
1
0
2
0
0
0
0
2
3
0
0
0
0
2
0
0
1
0
0
0
1
2
2
1
2
0
2
0
0
0
5
1
0
1
2
1
3
0
1
1
0
0
2
0
0
3
0
5
2
0
0
0
2
0
0
0
2
0
0
0
0
0
2
5
1
0
0
2
0
2
1
2
0
2
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
1
1
0
2
0
0
0
0
0
0
0
0
2
2
0
1
2
0
0
0
1
0
0
0
0
2
3
2
1
0
0
0
0
0
0
2
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
2
0
0
1
0
1
1
1
0
2
1
1
0
0
0
0
0
1
1
0
1
0
0
0
0
2
0
2
1
0
0
0
0
0
1
1
0
0
1
1
0
0
2
1
0
2
0
0
2
0
0
0
0
2
2
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
2
0
1
2
0
1
0
2
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
2
0
3
0
1
0
2
0
0
1
1
0
0
0
0
1
3
2
0
2
0
0
1
0
2
0
0
0
0
1
1
0
0
0
0
1
1
2
0
2
0
1
0
2
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
2
0
0
0
1
0
1
0
0
0
1
0
0
0
2
0
0
0
3
0
0
1
1
1
0
0
2
1
0
0
2
1
0
0
1
0
0
0
0
0
2
0
1
2
0
0
1
0
1
1
2
2
0
0
2
2
2
1
2
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
1
0
0
1
0
0
2
1
3
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
4
0
2
0
0
1
3
0
1
2
0
0
0
0
0
2
0
1
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
1
1
0
1
0
0
1
0
1
1
0
0
1
0
0
2
0
0
2
0
1
0
0
1
2
1
0
2
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
1
1
0
0
0
1
2
2
4
1
2
0
0
2
0
1
2
2
1
0
2
1
0
4
1
0
1
0
0
0
1
1
0
0
0
1
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
2
1
1
1
0
0
0
0
3
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
2
0
0
0
2
0
2
0
0
0
2
4
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
1
3
2
0
0
1
1
0
2
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
4
0
0
2
0
0
1
4
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
4
2
1
0
2
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
4
0
2
2
0
0
0
0
0
1
0
1
2
0
0
1
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
3
2
0
2
0
0
0
3
0
2
4
1
0
2
0
0
1
1
2
0
1
2
2
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
1
2
0
1
1
1
0
0
0
0
0
0
0
0
1
1
0
3
1
1
2
0
0
2
0
0
1
2
0
0
1
1
0
2
2
0
0
2
0
0
1
1
0
0
0
0
1
0
1
0
2
0
2
1
1
0
1
2
0
1
1
3
1
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
2
1
3
0
1
0
2
3
1
0
2
0
2
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
1
2
0
0
1
0
2
0
1
0
2
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
2
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
1
1
0
1
2
0
0
0
0
0
2
4
0
0
0
0
0
1
0
1
4
0
2
0
1
1
0
0
0
0
2
1
0
0
0
2
0
1
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
6
3
0
0
1
1
0
0
0
2
0
1
0
0
1
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
5
0
0
1
0
0
2
3
2
0
0
2
0
0
1
1
0
0
0
0
0
0
0
4
1
3
0
0
0
3
2
0
1
0
0
3
0
0
0
2
2
0
1
0
0
2
0
3
2
1
0
0
1
2
0
2
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
2
0
0
1
0
1
1
0
2
0
1
0
0
0
2
0
1
0
0
0
0
0
0
1
0
2
2
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
1
1
0
1
0
0
0
1
1
0
1
1
0
0
2
2
0
1
0
0
0
0
0
2
0
0
2
0
1
0
1
1
0
0
2
2
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
1
0
2
1
0
1
0
0
1
0
0
0
0
0
1
2
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
2
1
0
0
0
0
0
0
3
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
1
0
1
0
0
0
1
3
2
1
1
0
0
1
2
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
3
0
1
1
5
0
0
0
0
0
2
0
1
1
1
0
2
1
0
0
0
0
2
0
1
2
1
2
0
0
0
0
0
0
2
2
0
0
0
0
0
1
1
1
0
0
0
1
1
2
0
0
0
2
1
3
0
0
0
2
0
0
0
1
0
2
0
0
0
1
1
0
0
0
0
0
2
1
0
1
1
1
0
1
0
0
0
0
0
0
0
1
0
0
2
1
0
0
2
0
1
0
2
0
1
0
2
1
0
0
0
0
1
0
4
0
2
9
0
0
1
1
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
2
0
0
2
0
2
0
2
1
0
0
2
1
0
0
2
0
0
0
1
0
1
0
0
0
2
2
1
0
1
0
1
0
1
0
0
1
7
0
1
0
0
2
0
2
2
0
0
0
2
0
0
1
2
0
1
0
0
0
0
2
0
0
0
1
0
0
2
1
0
0
0
0
0
3
1
2
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
1
0
2
0
0
0
0
1
0
0
2
0
1
1
0
1
0
0
0
0
2
0
2
0
2
0
0
2
2
1
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
1
1
0
0
2
0
1
2
0
0
0
2
1
0
0
2
0
0
3
0
1
0
0
0
0
0
1
0
0
2
0
0
0
1
1
0
2
0
1
0
1
0
0
2
0
2
0
1
0
0
0
0
1
1
0
2
0
1
0
0
0
0
0
0
1
1
0
0
0
1
1
0
1
0
1
2
0
0
0
0
2
2
0
0
0
0
0
0
1
0
1
0
2
2
1
0
2
3
0
0
0
0
1
0
1
1
2
2
1
0
1
0
0
2
2
1
1
0
2
1
0
0
0
2
2
0
0
0
0
1
1
2
3
0
0
1
0
2
0
2
0
1
1
2
0
0
3
0
0
1
2
0
0
2
0
0
0
0
0
2
1
0
3
0
0
0
1
0
0
0
0
2
0
0
1
0
2
0
0
2
0
1
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
2
0
2
0
0
0
2
1
0
1
0
1
0
1
0
2
2
0
0
0
0
5
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
2
2
1
0
3
0
1
2
1
0
0
0
1
0
1
0
0
0
0
0
3
0
2
4
3
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
2
0
2
2
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
2
2
2
0
1
0
0
0
0
0
1
1
2
0
3
1
0
0
0
0
0
0
0
1
4
1
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
3
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
2
2
0
0
1
0
0
0
2
0
0
0
4
0
2
0
0
2
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
1
0
2
0
0
0
0
0
2
0
0
3
0
0
0
0
2
2
4
0
0
0
0
1
1
2
0
0
0
2
3
0
0
0
1
0
1
1
0
0
0
0
2
0
3
0
0
1
0
1
0
0
0
0
0
2
1
1
0
1
2
0
3
1
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
2
0
2
3
0
0
0
0
0
1
2
0
0
2
3
0
0
0
0
0
0
2
0
1
1
0
1
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
1
2
2
1
1
1
0
2
2
0
1
1
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
1
2
1
0
0
0
0
0
0
2
0
1
1
1
0
0
2
2
2
1
0
1
1
0
0
0
1
0
0
0
0
2
1
0
0
0
1
0
0
1
0
1
0
0
0
0
2
0
0
0
0
2
1
1
0
2
0
0
1
2
1
2
0
0
0
0
2
1
0
0
0
1
0
2
0
0
0
0
2
0
2
1
0
0
2
2
0
0
1
0
2
0
0
0
2
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
1
0
2
1
0
0
0
0
0
0
1
0
1
2
0
0
1
0
0
0
0
1
2
0
6
2
0
0
1
0
0
0
1
0
0
2
1
0
0
0
0
1
0
1
0
0
2
0
1
2
0
0
6
0
0
0
0
1
1
0
0
0
0
1
2
1
0
0
0
0
1
0
1
0
0
2
0
0
1
0
0
1
0
0
0
2
0
1
0
0
1
2
0
0
2
2
0
0
0
0
0
0
2
1
0
0
0
2
0
0
1
2
0
0
0
2
0
1
2
1
0
0
0
0
0
1
1
2
0
0
2
0
1
0
0
2
0
0
1
1
0
2
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
2
2
1
0
1
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
1
1
0
1
1
1
0
0
0
0
1
0
0
0
1
2
2
0
1
1
1
2
0
0
0
0
0
0
2
0
0
2
1
0
4
0
0
0
0
1
2
2
0
0
0
0
2
2
0
0
2
0
1
0
2
0
0
0
1
0
0
0
0
2
2
0
0
2
0
2
0
0
0
0
0
2
0
0
3
1
2
0
0
0
0
0
2
1
0
2
2
0
2
0
2
0
0
0
2
0
0
2
0
3
1
0
0
0
0
1
2
1
0
1
0
0
0
2
1
0
0
0
2
0
0
0
0
0
2
0
0
2
1
1
0
1
0
0
0
1
2
0
0
0
0
0
0
2
1
0
0
1
0
0
2
0
0
0
1
2
0
0
0
1
0
0
0
1
0
1
0
1
1
0
1
0
0
1
0
2
1
0
0
1
2
2
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
2
1
1
2
0
0
1
2
0
0
2
0
1
1
2
1
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
1
0
0
0
0
2
0
1
1
0
0
0
0
1
2
0
0
1
0
2
0
2
0
2
2
0
0
0
0
2
1
1
2
0
1
0
0
0
1
0
0
1
1
2
0
1
0
0
2
0
2
2
0
0
0
2
0
0
0
0
0
0
2
2
0
2
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
1
0
1
2
1
2
0
1
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
2
1
2
0
0
0
0
0
2
0
2
2
0
2
0
0
0
0
0
1
1
0
3
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
3
0
0
0
0
0
0
0
2
1
0
0
2
2
0
3
1
1
0
0
0
0
0
1
0
2
0
0
1
1
0
2
0
2
0
0
1
0
1
1
0
2
0
2
2
0
1
1
0
1
0
1
0
1
3
2
0
0
0
2
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
2
0
1
2
0
1
0
1
0
0
0
0
0
2
1
0
1
0
0
2
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
1
0
2
1
1
0
1
1
0
0
0
1
0
0
1
1
0
0
2
0
1
1
2
1
0
1
0
2
0
0
0
1
0
0
0
0
1
0
0
2
0
1
0
0
2
2
0
0
0
0
1
0
1
0
2
0
2
0
0
1
0
0
1
0
0
0
0
0
1
0
1
2
2
0
0
2
1
0
1
0
2
1
0
2
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
2
1
0
0
1
2
1
0
2
0
1
0
0
1
0
0
2
1
0
0
0
0
0
0
1
3
0
0
0
0
2
0
0
0
2
0
0
2
0
1
0
2
0
0
2
1
0
0
2
2
2
1
0
3
2
0
0
0
0
0
2
0
0
0
0
1
2
0
0
2
0
0
0
0
0
1
0
0
1
1
2
0
2
1
0
2
0
1
0
2
0
0
1
1
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
1
2
2
0
2
1
2
0
2
2
3
0
0
0
0
0
2
0
2
0
0
0
2
1
0
0
0
0
0
2
0
0
2
0
1
1
0
1
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
3
0
2
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
1
1
0
2
0
0
0
1
1
1
0
0
0
1
3
1
1
0
0
1
2
0
0
1
0
0
1
2
0
0
2
0
1
0
0
0
1
2
0
0
2
2
0
0
0
0
0
0
2
0
0
1
2
0
0
2
2
0
0
0
0
2
0
2
1
1
0
0
0
1
0
0
1
0
0
0
1
0
1
1
0
0
0
2
1
2
2
1
1
0
1
0
1
0
0
2
2
1
0
0
0
0
2
0
0
0
1
0
3
0
0
0
0
2
0
0
2
1
1
0
2
0
0
0
1
2
0
0
0
2
2
0
1
0
0
2
0
0
0
0
0
1
0
0
1
2
0
0
0
1
0
0
0
0
0
2
0
0
1
2
3
0
0
1
2
0
0
0
0
0
2
0
1
1
0
0
0
0
0
2
3
0
2
2
0
0
0
0
1
0
1
0
0
0
2
2
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
2
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
2
2
0
2
0
0
1
0
1
0
0
1
2
0
2
0
0
0
0
0
2
0
1
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
2
0
0
1
1
1
0
0
2
1
0
0
0
0
2
2
1
2
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
1
0
0
2
1
0
0
0
0
2
0
0
0
1
1
0
2
0
0
2
2
1
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
2
2
0
2
0
1
0
3
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
5
0
0
0
1
0
0
0
0
1
0
0
2
1
2
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
1
2
2
0
2
0
0
2
0
1
0
0
1
0
0
3
2
0
0
1
0
0
1
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
2
1
0
0
2
0
2
1
2
1
2
2
0
0
0
0
0
2
0
1
0
0
2
0
0
0
2
0
0
0
0
0
2
1
0
1
1
0
1
1
0
0
2
0
0
0
0
0
0
0
1
0
4
0
0
1
0
1
2
0
2
0
0
2
0
0
0
0
0
1
0
0
4
1
0
2
0
0
0
0
2
2
0
0
0
1
1
1
0
0
1
0
0
0
2
1
0
1
0
0
1
0
0
0
0
0
1
0
0
2
0
3
2
0
0
0
1
0
0
0
0
2
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
1
0
2
2
0
2
0
0
0
1
0
0
2
0
1
0
0
0
0
0
1
1
0
2
0
0
2
1
2
2
0
0
0
0
1
2
0
0
0
0
0
0
2
1
1
0
0
0
1
2
0
2
0
0
0
0
0
1
2
2
0
0
1
1
0
2
2
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
5
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
2
1
0
0
0
2
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
1
2
0
0
2
0
2
0
0
2
0
1
0
0
2
0
0
0
2
0
3
0
0
0
2
1
0
1
1
2
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
1
0
0
2
1
2
0
0
0
0
0
0
3
1
0
2
2
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
2
2
0
0
1
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
2
0
1
0
0
0
2
3
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
2
2
0
0
0
0
2
0
0
2
1
0
1
2
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
2
0
0
1
2
0
3
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
2
0
0
1
0
1
1
0
0
0
2
0
0
1
0
0
1
0
0
3
0
1
0
0
1
0
1
0
2
2
1
0
0
0
0
1
0
2
0
2
0
0
1
0
1
1
1
2
0
0
0
0
0
0
0
0
1
1
5
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
2
1
0
0
2
2
1
2
0
0
0
0
0
1
0
3
0
2
0
0
2
1
0
0
1
0
2
0
1
1
0
0
1
2
0
1
0
2
0
0
0
0
2
1
0
0
0
0
0
0
2
2
1
2
0
0
1
0
2
2
0
0
1
2
0
2
0
0
0
0
0
1
0
0
2
0
0
0
1
2
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
1
0
1
3
0
2
0
0
0
2
0
1
3
0
0
0
0
0
2
2
0
0
0
0
2
0
2
0
0
0
2
0
1
2
0
3
1
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
1
2
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
3
0
0
1
2
1
0
0
0
2
0
0
0
2
0
0
0
1
0
0
1
2
0
0
0
0
0
0
2
0
0
2
1
0
2
0
0
0
0
1
0
0
0
0
0
0
1
2
2
0
0
1
0
0
0
1
1
0
2
0
2
1
2
1
2
1
0
0
0
2
0
1
0
2
0
1
2
0
0
1
2
1
0
0
0
2
0
2
2
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
1
0
2
0
1
0
0
1
0
1
0
0
0
0
1
0
1
0
2
0
0
1
6
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
1
3
2
0
2
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
4
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
3
0
0
0
0
2
1
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
1
0
0
2
2
1
1
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
1
2
2
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
1
0
1
1
2
1
2
2
2
1
0
2
0
2
0
0
1
0
0
0
0
1
1
0
0
0
2
0
0
2
0
2
0
0
0
1
1
1
2
1
0
0
1
0
1
0
0
0
1
0
0
0
1
0
2
0
1
2
0
0
0
1
0
3
0
0
7
2
0
0
0
0
1
1
0
0
1
1
0
0
0
1
0
2
0
0
1
2
0
0
2
2
0
2
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
1
0
0
1
1
1
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
2
0
0
1
0
2
0
1
0
0
1
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
2
2
0
2
0
1
0
2
1
2
1
0
0
0
2
0
0
0
1
2
0
0
0
0
1
0
0
0
1
0
0
0
2
2
0
2
2
2
0
0
2
1
0
0
3
0
0
0
0
3
5
0
0
2
0
2
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
1
0
0
2
1
2
0
0
1
0
0
0
2
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
2
0
1
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
1
1
2
0
0
2
0
0
0
0
1
1
0
1
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
2
0
1
0
1
0
0
1
2
0
0
2
0
2
2
0
3
0
0
0
0
3
2
0
0
2
0
2
0
1
0
0
2
0
0
1
2
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
1
1
1
0
0
1
0
2
2
0
0
0
1
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
2
1
2
0
0
2
0
0
0
2
0
0
1
0
0
2
0
1
0
0
3
0
0
2
0
0
0
1
0
2
0
1
2
2
0
0
2
1
0
0
2
2
2
0
2
1
1
2
0
1
1
0
0
1
1
2
0
0
2
0
2
1
1
1
0
0
0
0
2
0
0
2
0
0
0
1
1
0
0
0
3
1
0
0
0
1
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
2
2
2
1
0
2
2
0
1
0
0
1
3
0
2
2
0
2
5
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
2
0
2
2
0
0
1
0
3
1
0
0
0
0
0
0
0
2
1
1
2
0
1
0
0
0
0
1
0
2
1
0
1
1
0
0
3
2
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
2
2
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
2
0
1
0
0
0
1
1
0
1
0
0
0
0
2
1
0
0
1
0
0
0
2
0
0
2
0
0
2
0
0
2
0
0
0
1
0
2
0
2
2
0
0
0
0
4
0
0
0
2
0
1
0
2
0
0
0
0
1
0
0
2
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
1
0
2
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
2
0
1
0
0
0
1
2
2
0
0
1
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
1
0
0
1
2
0
1
2
1
0
1
0
0
0
1
1
0
0
0
2
0
0
2
1
0
1
1
0
0
0
2
0
2
0
0
2
0
0
0
0
2
0
0
2
0
2
0
0
0
0
3
0
1
0
0
0
2
0
0
0
3
2
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
2
0
0
0
2
1
2
3
1
5
0
2
1
0
0
0
1
0
0
0
1
0
0
1
0
0
3
2
0
1
0
1
0
0
1
2
0
0
0
1
0
0
0
2
2
0
0
0
0
0
1
0
0
3
0
1
1
1
0
1
1
0
0
0
2
0
0
0
0
1
0
2
2
0
0
1
0
0
0
2
2
2
2
1
5
1
0
1
1
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
1
0
1
0
0
0
0
0
0
7
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
2
2
1
1
0
0
1
0
1
0
0
0
2
0
0
2
4
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
4
2
0
0
1
0
1
1
0
2
0
0
2
0
1
0
0
0
1
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
1
2
2
0
0
0
0
0
1
0
0
0
0
0
2
0
9
0
0
2
0
0
0
0
3
0
2
0
5
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
1
2
1
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
2
0
0
1
0
0
1
0
2
0
0
0
0
2
1
1
0
0
1
0
0
0
0
0
0
2
0
0
3
0
2
0
1
0
0
0
0
0
0
0
0
0
2
1
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
2
1
2
1
0
2
0
0
0
1
0
0
2
1
0
0
0
2
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
1
0
1
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
1
0
2
3
0
1
1
0
2
0
1
0
0
0
2
0
0
0
0
0
0
2
0
1
3
3
2
1
1
1
0
0
1
0
0
0
0
3
2
0
0
0
0
0
0
0
0
1
0
0
3
1
2
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
1
0
2
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
1
1
0
0
0
0
2
1
0
2
1
2
0
0
0
0
0
0
2
2
0
0
1
0
0
1
1
0
0
2
0
0
0
1
2
0
1
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
2
1
0
1
0
0
0
0
1
0
2
0
2
0
2
0
2
2
0
0
2
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
1
2
1
0
0
0
0
1
1
1
1
2
0
2
0
0
0
1
1
0
1
0
0
0
2
0
0
0
1
2
2
0
0
2
2
2
2
0
1
0
0
0
1
1
2
0
0
2
0
0
0
1
2
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
2
1
0
0
0
2
0
0
1
0
0
0
2
2
2
1
2
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
3
2
1
0
2
0
1
0
0
0
0
1
2
1
1
0
3
1
2
0
0
0
0
1
1
0
0
0
0
2
1
1
1
0
2
0
0
1
0
0
1
2
0
0
0
2
0
2
1
0
0
2
2
0
0
0
0
1
0
1
0
4
0
2
0
0
0
2
0
1
2
1
0
1
2
0
0
1
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
1
2
1
2
1
0
0
0
0
0
0
1
0
2
0
2
0
3
0
2
0
0
0
0
0
2
0
0
2
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
1
0
0
0
0
3
2
0
0
0
2
1
0
0
1
0
0
0
0
0
2
2
0
3
0
0
0
1
0
0
3
0
0
0
2
1
0
2
2
0
0
0
0
0
2
0
1
0
2
0
1
2
0
1
0
0
1
2
0
2
1
0
1
0
0
0
2
0
0
1
0
2
0
1
0
0
1
0
2
0
0
1
0
0
0
2
0
1
0
0
1
2
1
0
0
0
3
0
1
2
0
0
0
2
2
0
0
1
0
2
0
0
0
0
1
2
1
0
2
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
2
0
1
0
0
0
1
0
0
2
0
1
1
0
0
2
0
2
0
0
1
0
0
0
0
0
0
1
1
0
1
1
2
0
0
3
0
0
1
0
0
0
0
0
0
0
0
2
2
0
1
0
0
1
1
0
1
0
0
1
0
1
0
0
2
0
1
0
0
0
0
0
1
0
0
0
2
0
1
1
0
1
0
0
0
2
0
0
5
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
2
0
1
1
0
0
1
0
1
1
1
1
0
0
3
0
0
1
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
1
0
0
2
2
0
0
2
0
0
1
0
0
1
0
3
0
0
0
0
1
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
3
2
0
0
1
0
3
0
0
2
1
0
0
1
0
1
1
0
2
0
0
0
1
0
0
0
0
0
2
0
3
1
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
2
3
0
0
2
1
0
2
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
2
2
0
0
0
2
0
0
0
0
1
2
2
0
1
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
3
0
0
0
4
0
1
1
1
0
2
0
0
1
1
2
1
0
2
1
0
0
1
0
1
0
0
0
1
2
1
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
1
2
1
0
0
0
3
0
0
0
0
0
1
0
2
0
0
1
1
0
2
0
0
2
0
0
2
2
3
0
0
0
4
0
0
0
0
0
0
2
0
1
1
0
0
0
2
2
1
2
2
1
1
1
0
1
0
1
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
2
1
0
0
0
2
1
3
2
0
1
0
0
0
1
1
2
0
2
3
0
2
0
1
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
1
0
0
1
2
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
10
3
0
0
0
1
2
0
0
2
0
1
0
0
0
0
1
0
0
2
1
0
2
2
0
2
0
0
0
1
0
2
0
0
0
0
1
1
0
0
1
2
0
0
1
1
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
1
0
0
2
1
2
2
1
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
1
0
1
0
0
3
0
1
1
0
0
0
0
2
0
1
0
0
1
0
0
0
1
2
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
2
0
1
0
0
2
0
0
2
2
0
0
0
1
1
0
0
0
0
1
2
0
0
0
0
3
0
1
0
0
0
1
0
1
1
1
2
2
1
0
2
0
0
0
1
0
0
2
2
1
2
0
2
2
0
0
1
4
2
0
0
1
1
0
0
2
0
0
1
0
0
0
0
1
0
5
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
1
0
0
0
2
0
1
0
0
0
1
0
1
2
1
0
0
3
0
0
2
0
1
1
0
0
2
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
2
2
0
1
2
2
2
1
0
0
0
0
1
0
0
0
2
0
0
0
8
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
4
1
0
2
0
1
1
0
2
0
0
0
0
0
2
0
0
1
2
0
0
2
0
0
0
1
0
0
0
2
0
0
2
1
2
0
1
0
0
2
1
0
1
2
1
0
2
0
0
2
0
0
0
0
0
0
0
1
0
4
0
0
0
0
1
0
0
0
0
1
1
1
3
0
1
1
0
1
1
0
1
0
0
2
0
0
2
1
1
1
1
0
2
1
0
0
0
0
0
2
0
2
0
2
1
1
1
0
0
0
0
2
1
2
0
0
0
0
2
0
0
0
1
1
0
1
2
1
2
2
0
0
0
1
1
0
2
1
0
1
0
0
0
2
0
0
2
0
0
0
0
2
0
0
2
1
2
2
1
0
2
0
0
1
2
1
3
0
0
0
1
2
2
3
0
0
0
2
1
0
1
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
2
2
0
1
2
2
0
0
1
0
0
0
0
2
0
2
0
0
0
1
2
0
1
0
2
0
1
0
0
0
0
1
0
0
0
1
3
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
1
3
0
1
1
0
0
1
0
0
2
0
2
1
2
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
2
0
0
1
1
1
0
0
3
0
2
0
0
2
1
0
1
2
0
2
0
1
2
0
1
1
0
0
2
2
1
0
2
1
0
0
2
0
0
2
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
2
1
2
0
0
2
0
2
0
2
0
1
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
1
0
1
0
0
2
0
0
0
2
0
0
0
2
0
1
2
2
0
0
1
0
2
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
1
0
1
0
2
1
2
0
0
0
0
1
0
1
0
1
1
0
1
2
0
1
0
2
1
0
1
0
0
1
1
1
0
0
0
0
3
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
1
1
1
0
2
0
0
0
0
1
0
1
1
0
0
0
0
1
0
2
0
1
1
0
0
1
0
1
0
1
1
0
1
1
0
0
2
1
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
2
0
1
1
1
1
1
3
2
0
0
2
0
0
1
0
1
1
0
0
1
0
1
1
0
0
2
0
1
1
2
1
1
2
1
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
1
0
0
0
0
0
0
1
2
1
0
1
0
0
2
0
2
0
2
0
1
1
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
2
0
0
2
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
2
0
1
0
0
2
0
0
0
1
0
0
2
1
0
1
0
0
0
1
0
0
0
0
1
5
0
1
0
1
2
0
1
0
0
2
1
0
1
0
1
0
0
0
2
0
0
0
1
0
1
0
2
2
2
0
0
2
0
0
1
0
0
0
0
0
1
2
1
0
0
1
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
1
2
0
3
0
0
0
0
1
0
1
0
0
1
1
0
1
0
4
0
0
0
1
0
1
0
0
0
0
2
0
0
0
2
0
2
0
2
0
0
0
0
0
1
1
2
0
0
0
2
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
2
1
0
0
1
1
0
1
0
0
2
1
0
0
1
2
0
0
0
2
2
0
2
2
2
0
0
5
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
2
0
1
0
0
0
0
0
1
2
1
0
0
2
0
0
0
1
1
0
2
0
2
0
1
0
1
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
1
0
1
1
0
0
0
0
3
0
1
0
0
0
1
0
0
2
1
1
1
3
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
3
2
2
0
0
0
1
0
3
0
2
0
0
2
1
2
0
1
0
0
0
1
0
2
1
0
1
2
0
0
0
2
0
0
1
0
0
0
1
0
0
0
2
1
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
1
0
0
0
2
2
0
0
2
2
0
0
1
0
1
0
2
0
0
0
0
0
1
0
3
0
1
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
1
3
0
0
1
1
0
2
0
1
0
0
0
0
0
2
1
0
1
0
0
1
0
0
0
1
1
0
0
1
2
0
2
1
0
0
1
0
1
0
0
0
2
4
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
2
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
1
0
1
4
2
1
0
0
0
0
0
1
0
1
0
2
0
0
2
1
0
0
1
0
0
1
0
0
0
2
0
0
0
1
3
3
0
0
0
0
0
0
0
0
0
0
2
1
0
1
1
1
1
0
0
2
1
0
0
2
0
0
0
0
1
2
2
1
1
0
0
0
1
0
2
5
2
3
0
0
0
0
1
0
0
2
0
1
0
0
0
0
2
0
0
2
3
0
0
1
0
1
0
0
0
0
0
1
0
0
0
3
0
1
1
1
0
0
1
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
2
1
1
2
0
0
0
0
0
0
0
0
0
0
2
1
0
1
2
0
0
0
1
1
2
0
1
1
2
2
1
0
0
1
0
0
0
0
2
1
2
2
2
0
0
0
0
2
0
0
2
0
2
0
0
0
1
0
0
3
2
0
0
2
1
0
0
0
0
0
0
0
2
1
0
0
1
0
0
2
0
0
1
0
2
0
0
1
1
2
1
0
2
0
0
1
2
2
1
2
0
0
0
2
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
2
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
2
2
3
0
0
0
0
2
0
0
0
0
2
0
0
2
1
0
0
2
0
1
0
0
1
0
2
0
0
1
0
1
0
2
2
1
0
2
0
1
2
2
0
0
0
1
0
0
0
0
2
0
0
0
0
2
2
2
1
0
6
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
3
0
0
1
0
0
2
0
0
2
1
0
2
0
1
2
0
0
0
2
1
2
0
0
0
0
0
2
0
2
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
1
2
0
0
2
0
1
0
1
0
2
0
0
0
0
2
1
0
1
0
0
0
0
1
2
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
2
1
0
0
0
0
1
0
2
0
1
1
0
1
0
0
0
0
0
1
0
2
2
0
0
0
0
0
2
2
0
2
1
1
3
0
0
0
0
1
1
0
0
0
0
0
0
0
2
2
0
2
0
1
0
0
0
2
0
0
0
2
1
0
1
0
2
0
0
0
0
0
2
0
1
3
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
2
1
1
2
1
0
0
1
0
0
2
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
2
2
0
0
0
0
1
1
0
0
0
0
0
1
1
2
2
0
0
0
5
1
10
1
1
0
1
0
0
2
1
0
0
3
0
2
0
1
0
2
1
0
2
1
1
0
1
2
0
0
0
0
2
0
1
0
1
0
1
0
1
0
0
0
1
2
0
2
2
0
0
0
1
0
2
0
0
0
1
0
1
0
0
2
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
1
3
0
0
0
0
2
0
1
0
2
4
1
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
1
7
0
0
0
0
0
0
0
2
2
0
0
1
0
2
0
0
2
1
0
2
0
0
0
0
0
2
0
0
0
2
1
0
1
1
0
2
0
0
3
1
0
0
2
0
0
0
2
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
2
2
0
1
0
0
0
4
0
1
0
0
1
1
0
1
1
2
1
0
0
1
0
0
2
0
2
0
1
1
1
0
1
0
1
1
0
0
0
1
2
0
0
2
1
0
1
0
1
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
2
1
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
1
0
0
3
0
1
2
0
0
0
0
1
0
1
4
0
0
0
2
1
0
0
2
1
0
1
1
0
0
0
1
0
0
0
0
0
2
2
1
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
2
2
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
1
1
0
1
2
2
0
2
0
2
0
0
0
0
1
0
0
2
0
2
1
2
1
1
0
0
0
1
3
1
1
0
0
0
1
2
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
2
0
3
1
0
0
0
2
0
0
1
0
1
0
2
0
0
0
0
1
0
2
0
1
1
0
1
0
1
0
0
0
0
0
2
2
0
2
2
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
1
0
2
0
1
3
0
1
1
0
0
0
1
2
1
0
2
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
2
0
0
1
0
0
2
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
1
1
1
0
3
0
0
1
4
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
1
2
0
0
2
2
0
2
0
2
3
0
0
0
1
1
2
0
0
1
1
1
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
1
0
6
0
0
0
0
0
1
2
2
1
0
0
1
0
1
0
1
0
0
2
0
2
0
0
0
1
0
0
0
2
0
2
0
0
2
2
0
2
1
1
1
0
0
2
0
0
1
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
2
1
2
0
0
0
0
7
0
1
1
0
0
0
0
0
1
0
0
3
0
0
2
0
0
0
1
0
0
0
0
1
0
0
1
2
1
0
0
3
0
0
1
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
1
2
2
0
0
0
2
1
1
0
0
2
1
0
0
1
0
2
1
1
1
0
0
0
1
0
0
2
0
1
0
0
2
2
0
2
1
1
0
1
2
0
0
0
0
0
0
2
0
2
0
1
2
0
0
0
0
1
0
0
0
1
0
5
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
2
0
0
0
0
2
0
0
2
1
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
2
0
0
2
0
0
0
0
1
3
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
2
1
0
0
1
0
2
0
0
0
2
2
2
0
0
0
0
0
0
0
0
4
2
0
0
0
2
1
0
1
1
0
0
0
2
2
0
0
0
2
0
1
0
2
0
1
0
2
2
1
0
2
0
0
0
0
0
2
0
1
1
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
2
0
0
1
0
1
0
0
1
1
0
2
0
2
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
1
2
0
1
1
2
0
0
0
0
0
1
2
0
0
2
1
1
1
0
0
0
1
0
2
0
0
0
0
1
0
2
0
2
0
0
1
0
0
1
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
3
0
0
1
0
0
0
0
0
0
0
0
0
2
0
3
0
0
1
2
1
0
0
0
0
2
2
0
0
0
0
1
5
0
0
0
0
0
1
1
0
0
2
0
0
0
1
0
2
2
1
1
1
0
2
0
0
0
0
0
0
2
0
0
1
1
2
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
2
1
0
3
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
3
0
3
2
0
0
3
0
2
0
0
2
0
2
2
0
0
3
0
0
1
0
0
1
0
0
0
1
0
1
3
0
0
2
0
0
0
2
0
2
0
1
0
0
1
0
3
0
2
0
0
1
2
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
4
2
0
0
0
1
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
5
0
0
0
0
0
1
0
0
3
0
0
0
3
1
0
0
0
1
0
0
0
0
4
2
2
0
1
0
2
0
0
1
0
1
0
0
0
0
1
0
0
3
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
1
0
0
0
2
1
0
0
0
1
0
0
1
0
0
0
0
2
2
2
0
0
0
0
0
0
2
0
0
0
1
1
0
2
0
0
2
1
2
0
0
1
2
0
0
0
0
2
1
0
2
0
0
0
3
0
2
0
1
0
0
0
0
2
2
5
0
0
0
2
1
2
2
0
1
2
1
2
0
0
1
2
0
0
2
1
0
4
1
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
2
2
0
0
0
0
2
1
0
2
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
1
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
2
2
0
1
0
2
0
0
1
0
0
2
2
0
2
0
0
0
0
0
1
0
2
0
3
2
0
0
0
0
3
0
1
0
0
2
1
0
2
2
0
0
0
1
0
0
0
0
0
1
2
0
2
2
0
0
1
0
1
1
0
0
1
0
1
1
0
0
0
2
1
0
0
0
0
0
2
3
0
1
0
0
0
0
1
2
0
0
0
0
2
0
0
2
1
1
0
2
0
1
1
0
0
0
0
3
0
1
2
0
2
0
0
0
1
2
0
0
0
0
0
2
1
0
0
0
0
0
1
0
1
0
2
1
1
0
2
2
1
1
1
0
0
0
0
1
0
2
2
0
2
2
1
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
2
0
0
4
0
0
1
2
0
0
0
0
1
0
0
2
1
0
1
0
0
0
1
0
0
0
0
2
0
0
2
2
0
0
2
1
0
1
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
2
2
1
0
0
2
1
2
1
0
0
2
0
1
0
2
0
2
1
2
1
1
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
2
2
0
0
0
0
1
1
0
0
0
2
0
2
0
0
0
1
0
2
0
1
1
0
0
2
0
0
2
0
3
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
3
0
0
0
0
0
0
0
1
2
0
0
1
0
1
0
0
0
1
0
1
0
0
0
2
0
1
1
0
0
2
0
0
0
2
2
1
0
0
2
0
0
0
0
2
0
0
1
2
0
0
1
3
0
3
2
1
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
2
0
1
1
0
1
2
2
0
0
1
3
2
0
1
2
0
0
1
0
0
2
0
0
1
0
0
0
2
0
0
0
1
2
0
2
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
1
0
0
2
2
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
1
0
1
0
4
0
0
1
1
0
2
0
1
0
0
0
0
2
2
0
1
0
2
0
0
0
0
2
2
1
1
0
0
0
0
0
0
0
0
2
2
0
2
0
0
2
0
0
2
0
2
0
1
0
0
2
0
0
0
0
1
1
0
1
0
1
2
1
0
1
0
0
1
2
0
0
0
1
0
0
1
2
0
0
0
2
2
0
0
0
1
1
0
2
0
1
0
0
2
0
2
0
1
1
0
2
0
2
0
1
0
2
0
0
0
0
1
2
2
1
0
0
1
0
0
0
2
0
0
1
0
0
0
2
0
0
1
0
2
0
1
1
0
2
0
0
2
0
1
1
0
1
2
0
0
0
1
2
1
3
0
0
1
0
2
0
0
1
2
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
2
1
0
2
0
0
0
0
2
1
2
1
0
2
2
0
3
0
0
0
0
0
0
0
0
0
0
2
1
2
3
3
0
1
0
2
0
0
0
2
0
1
2
1
2
0
0
1
0
1
1
0
0
1
0
0
0
0
0
1
1
1
0
0
0
2
0
0
1
1
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
1
1
1
0
1
2
1
2
1
1
0
2
0
0
1
0
1
2
0
0
0
1
1
0
1
1
1
2
1
0
0
1
0
0
2
2
0
0
0
1
1
2
0
1
1
0
1
0
1
0
0
2
0
5
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
1
4
0
2
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
2
1
0
0
1
0
1
0
3
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
1
0
0
1
0
2
0
2
0
0
2
0
0
0
2
0
0
0
2
2
0
1
1
0
2
0
0
0
1
0
0
1
2
0
0
0
0
0
2
1
0
0
1
0
0
2
0
0
0
0
0
1
0
2
2
0
0
0
1
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
2
0
2
2
0
0
0
0
0
0
0
3
0
0
0
2
2
0
0
1
2
0
0
0
3
0
0
0
0
0
2
0
0
0
0
1
0
2
0
2
2
0
0
0
0
1
2
2
0
0
0
0
0
2
0
0
0
1
1
0
1
1
2
0
1
0
0
0
2
0
2
0
0
0
1
0
1
0
1
0
0
2
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
1
0
1
0
0
3
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
3
0
2
0
0
2
0
0
2
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
4
0
0
2
0
0
1
3
1
1
0
0
1
1
0
2
0
0
2
2
0
0
1
0
0
0
0
2
1
1
2
0
1
0
0
0
1
1
3
1
2
1
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
2
0
0
1
0
0
2
2
0
0
0
0
3
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
1
0
2
0
2
0
2
0
2
0
1
0
2
0
0
1
0
0
0
0
0
0
1
0
0
1
1
1
0
1
6
0
1
0
0
0
2
2
0
0
0
0
2
0
2
1
0
0
0
0
2
0
2
0
3
0
0
0
0
0
1
2
0
0
0
0
2
9
1
0
0
2
1
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
2
2
0
2
0
0
4
0
0
0
0
0
0
0
0
1
1
1
0
2
2
0
2
0
1
0
0
0
1
0
0
0
2
4
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
2
0
2
0
0
1
2
1
0
0
0
1
0
2
2
0
0
2
0
2
0
0
3
2
2
1
1
1
0
0
0
0
1
0
1
1
2
0
1
1
1
0
0
0
0
0
0
0
1
2
0
2
0
1
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
1
1
0
0
3
0
0
2
2
0
1
0
2
2
0
2
2
0
1
0
1
0
0
0
1
1
1
1
0
0
3
0
0
2
1
1
1
2
0
4
0
1
2
0
2
1
0
0
0
2
1
2
2
0
0
2
0
4
1
1
1
1
2
1
1
0
1
0
0
0
1
2
0
0
2
2
0
0
0
0
0
2
0
1
0
2
0
0
0
0
2
0
0
0
1
2
2
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
1
0
1
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
1
0
0
0
2
1
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
2
3
0
1
0
1
0
2
0
2
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
2
0
2
2
0
0
2
0
0
0
0
2
0
0
1
1
0
0
1
2
0
0
0
0
0
1
0
0
0
2
0
0
2
0
2
1
1
0
0
1
0
2
0
0
0
0
2
0
2
0
0
2
2
0
0
0
0
1
2
2
0
0
0
0
2
2
0
2
0
0
2
1
0
0
0
0
0
0
1
2
0
2
3
2
2
0
0
0
0
1
0
0
1
0
0
1
0
0
0
2
1
1
3
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
2
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
4
0
1
2
0
0
0
0
0
0
0
0
1
0
2
0
0
3
0
0
0
0
0
0
2
2
0
2
0
0
2
0
0
0
1
0
2
2
2
0
0
0
0
0
0
1
0
0
2
0
2
1
0
0
0
1
0
0
1
2
2
2
2
0
0
0
2
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
1
1
1
0
2
0
0
1
1
0
2
1
0
0
1
2
0
0
0
0
1
1
2
2
0
1
2
1
2
0
0
0
0
0
0
3
0
1
2
2
0
1
0
2
0
0
1
0
1
2
0
2
0
2
0
0
2
2
2
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
1
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
4
0
2
0
0
0
2
0
2
0
0
0
1
1
0
0
0
0
0
1
2
2
0
1
0
4
0
1
2
0
0
1
2
0
0
2
3
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
1
0
0
0
1
0
2
0
0
2
0
0
0
0
0
1
0
0
0
1
0
2
1
0
3
2
0
0
0
2
0
1
0
0
0
1
0
0
0
0
2
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
5
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
1
2
0
1
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
2
2
1
0
0
0
1
1
0
0
1
1
0
2
0
0
3
0
0
2
0
0
0
2
0
2
1
2
0
0
2
0
0
1
1
1
0
1
0
0
2
2
1
1
0
0
2
1
0
0
2
0
1
0
0
2
0
1
0
0
2
3
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
1
2
1
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
1
1
0
0
0
0
1
0
2
1
0
0
0
2
0
0
0
1
0
0
0
2
1
0
0
0
1
0
1
1
0
0
0
0
0
1
1
0
2
0
0
2
0
0
1
0
0
0
0
0
1
2
0
0
0
2
2
0
0
0
1
0
2
1
0
1
0
0
1
0
0
1
0
0
2
1
0
0
0
0
0
2
2
1
0
1
0
0
0
0
0
4
2
2
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
2
0
2
0
0
2
0
2
1
0
0
2
0
0
0
1
1
0
0
0
0
0
1
2
0
2
0
0
0
1
1
1
0
0
1
0
0
0
0
2
0
0
1
0
0
1
2
0
0
0
1
2
2
3
0
0
2
1
3
2
0
0
0
0
0
0
0
0
4
0
0
0
0
1
1
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
1
2
2
1
0
3
1
2
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
2
1
0
0
0
2
2
1
2
3
2
0
0
0
0
1
2
0
7
2
0
0
0
0
0
0
3
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
2
1
2
0
0
0
0
0
0
0
0
1
0
1
0
3
0
0
0
0
2
0
0
0
1
2
3
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
2
1
2
0
0
0
1
0
1
0
0
0
3
0
0
2
1
0
1
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
1
0
0
0
2
0
3
0
0
0
0
0
2
0
0
0
5
0
4
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
2
1
0
0
0
0
0
0
1
2
0
2
0
1
0
0
0
1
2
2
0
1
0
3
0
1
2
0
1
1
0
0
1
1
0
0
2
0
1
0
0
1
0
0
0
1
0
2
3
1
0
2
3
1
1
1
1
0
0
0
1
3
6
2
0
1
0
0
0
1
0
1
2
2
0
0
0
0
0
2
0
0
0
0
2
1
0
1
0
2
0
1
0
0
0
0
1
0
1
0
1
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
1
1
0
0
2
0
1
1
0
2
2
0
0
2
1
1
0
1
1
0
1
0
0
0
0
2
4
1
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
3
5
0
0
1
2
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
1
0
2
0
0
0
3
1
0
1
2
2
1
2
0
0
0
1
0
0
0
0
1
0
0
0
3
0
0
0
0
0
1
0
2
0
0
3
0
2
0
0
0
1
0
0
0
2
1
0
1
0
0
2
0
2
0
0
0
0
0
1
0
1
0
0
2
0
0
1
2
0
0
1
0
2
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
2
0
1
1
0
0
1
0
2
1
0
2
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
4
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
1
2
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
2
0
2
0
1
0
2
1
0
0
0
2
0
0
0
0
0
2
0
0
0
1
2
1
1
2
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
1
0
0
4
2
2
3
1
0
0
2
0
1
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
2
1
2
0
1
0
0
2
0
1
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
2
0
1
1
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
2
2
0
0
3
0
0
1
1
1
0
0
0
0
0
2
1
1
0
0
2
0
0
0
0
0
0
0
1
1
3
2
0
1
0
2
1
1
0
0
1
0
0
2
0
0
3
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
1
1
2
0
1
0
0
0
1
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
2
0
2
0
0
1
0
0
0
2
0
2
0
0
2
0
0
0
1
2
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
1
0
0
0
2
0
0
1
0
2
0
1
1
1
2
0
0
0
0
0
1
0
2
0
1
0
0
2
2
0
0
0
2
0
0
4
0
0
0
0
2
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
2
0
2
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
2
0
2
0
2
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
4
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
6
0
0
0
0
2
0
0
1
0
0
0
2
0
2
1
0
2
0
1
2
0
0
0
1
1
2
0
0
2
0
0
0
1
2
0
0
0
1
1
0
0
0
2
0
0
1
1
0
0
0
1
2
0
0
0
1
0
0
2
0
1
1
1
0
0
2
1
0
0
2
0
1
0
0
0
2
0
0
3
0
0
0
0
2
0
1
0
2
0
0
0
2
1
1
2
2
1
0
0
0
1
2
1
0
1
2
1
2
2
0
0
0
0
1
2
0
0
2
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
1
1
0
0
2
1
0
1
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
2
3
1
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
2
2
5
0
0
0
4
2
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
5
0
0
0
0
0
0
1
1
0
1
0
0
1
0
2
0
0
0
0
0
1
2
2
0
1
0
2
0
0
2
0
1
2
0
1
0
0
0
2
2
0
0
0
2
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
1
0
0
0
0
1
0
2
3
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
2
2
0
0
1
0
0
1
0
1
0
1
1
1
0
2
0
0
1
3
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
3
2
0
0
0
0
0
0
2
0
1
1
0
1
1
2
0
0
1
2
0
0
2
0
1
2
2
0
0
0
1
0
0
3
0
0
0
0
1
0
2
0
0
2
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
1
1
2
2
1
0
0
0
0
0
0
1
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
1
2
0
0
0
1
0
2
0
2
2
0
2
2
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
1
0
1
1
0
2
1
0
2
0
0
1
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
2
0
0
0
2
2
0
0
0
0
0
1
0
4
0
0
0
0
2
3
1
2
0
2
0
1
0
0
0
2
0
0
0
7
1
0
0
2
1
0
0
2
2
0
0
0
1
0
0
1
0
2
0
0
0
1
0
0
2
0
1
2
2
2
0
0
0
0
1
0
0
2
0
1
0
0
0
2
0
1
1
0
0
2
0
1
0
1
1
0
1
2
0
0
0
0
2
1
1
0
0
2
2
0
0
0
0
0
1
1
0
0
1
0
1
0
1
0
0
2
0
1
0
0
2
0
0
1
0
0
0
1
0
1
0
0
0
1
1
1
0
0
1
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
2
1
1
0
0
0
0
0
2
0
0
0
2
2
0
2
0
0
1
2
0
0
0
0
0
3
0
0
0
1
2
2
0
0
0
1
0
0
2
0
0
0
2
1
1
2
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
1
1
0
0
1
0
0
3
2
2
1
0
2
1
0
2
1
0
1
0
0
1
1
0
0
0
0
0
0
0
2
1
2
2
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
1
0
0
3
1
0
0
0
0
2
0
0
1
0
1
2
2
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
1
2
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
2
1
0
1
2
0
0
0
0
1
2
2
0
0
1
0
0
1
1
0
2
0
0
0
2
2
0
0
2
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
3
0
0
0
0
0
0
0
0
2
1
0
0
2
2
1
1
0
0
0
4
0
0
0
0
5
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
2
2
0
2
1
0
1
1
0
0
0
2
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
1
0
0
7
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
2
1
1
1
0
0
0
0
0
2
1
2
0
0
0
0
0
0
2
0
0
0
1
2
1
2
2
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
1
0
0
0
0
2
4
0
0
0
0
1
1
4
0
1
1
0
0
1
3
1
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
1
0
0
2
2
1
0
1
1
1
0
1
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
2
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
1
1
0
3
1
1
0
0
0
0
0
2
2
0
2
0
1
0
5
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
1
2
0
1
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
1
1
1
1
0
1
0
1
1
1
0
0
0
0
4
0
1
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
2
1
2
2
0
2
0
0
2
0
0
1
0
0
1
2
2
2
0
0
0
1
1
0
0
0
2
1
0
0
0
0
2
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
2
1
0
2
0
1
0
0
0
0
6
0
0
1
0
2
1
0
2
0
0
0
2
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
1
1
1
1
0
2
0
2
0
3
0
0
0
0
0
0
0
1
1
0
4
0
1
0
0
2
1
1
2
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
2
0
0
0
1
1
0
0
0
0
1
0
1
0
0
1
2
0
1
0
0
0
0
3
0
0
0
0
2
2
0
0
0
0
2
0
2
0
0
1
0
0
2
0
2
0
0
0
1
0
0
1
1
0
0
0
4
0
1
0
1
1
1
0
2
2
2
0
2
0
2
0
1
0
0
1
0
0
0
0
2
1
0
1
1
1
2
1
1
0
0
0
0
0
1
0
0
2
0
0
0
3
0
0
1
1
1
1
0
0
0
0
2
2
0
1
1
0
0
0
2
0
1
0
0
0
1
1
0
0
0
2
1
0
1
0
0
0
0
1
2
0
0
1
2
2
0
1
2
0
2
2
2
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
2
0
0
0
2
1
0
0
1
1
0
2
2
1
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
2
0
2
0
0
0
0
2
2
0
0
0
0
2
1
0
2
1
2
0
1
0
0
1
0
0
1
1
0
0
0
0
1
2
0
2
0
0
1
0
0
1
0
0
0
2
1
0
0
0
0
0
0
2
0
0
1
1
0
0
0
2
2
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
2
0
1
1
0
0
0
2
1
2
2
1
0
1
2
0
0
0
0
0
2
0
0
0
1
1
0
0
0
1
0
0
1
0
0
2
1
1
2
0
2
0
0
0
2
2
3
0
0
0
2
0
2
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
1
2
0
1
0
0
2
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
1
0
0
0
2
0
2
2
0
0
2
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
3
0
2
2
2
1
2
0
1
0
0
0
1
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
3
0
1
0
0
0
0
2
0
1
1
0
2
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
1
1
2
1
0
1
0
0
2
0
0
0
0
0
1
0
0
1
2
1
0
0
1
0
0
2
0
0
0
0
3
0
0
2
0
2
0
0
0
1
6
0
1
1
0
0
0
0
2
0
1
0
1
0
4
1
0
0
2
0
1
0
1
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
2
1
2
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
9
1
0
1
2
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
1
0
0
0
2
0
0
0
2
0
1
0
0
0
2
2
2
1
0
2
2
1
2
0
1
0
1
0
1
0
2
1
2
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
1
2
0
0
0
0
2
1
1
0
1
2
0
0
2
1
2
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
1
2
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
1
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
1
2
0
0
1
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
1
0
6
0
0
2
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
1
1
0
0
0
0
2
0
0
0
2
0
2
0
1
1
0
0
0
3
2
2
2
0
0
0
0
2
0
0
0
2
0
0
0
0
1
2
0
1
1
2
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
2
0
0
3
1
0
0
0
0
1
1
0
2
0
2
0
1
2
0
1
1
0
0
1
1
0
0
0
0
1
2
0
0
2
2
0
0
0
2
0
0
1
0
0
3
0
0
0
0
2
2
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
1
0
2
2
0
0
0
0
1
0
0
0
2
1
0
0
2
2
2
0
0
1
0
0
2
0
0
0
0
1
0
0
0
2
0
0
3
0
0
1
0
2
2
2
0
0
0
0
0
0
0
0
0
2
1
1
0
2
0
0
0
1
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
2
1
0
2
0
0
0
1
0
0
1
0
2
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
1
0
1
0
0
1
1
0
1
0
0
0
0
3
1
3
0
0
2
1
2
0
0
2
2
0
0
0
1
0
0
2
0
2
0
0
1
1
2
1
0
0
0
2
0
0
0
1
2
0
0
1
1
0
0
1
0
0
0
1
0
0
1
0
8
1
0
1
1
1
2
0
1
1
0
1
0
2
2
0
0
0
0
0
2
2
0
0
0
3
0
0
0
1
0
0
2
0
1
2
1
0
0
0
1
1
1
0
1
1
1
0
0
0
0
0
0
0
1
2
3
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
1
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
2
0
3
1
0
0
2
0
1
0
0
0
0
1
0
2
0
2
0
2
0
0
0
2
1
1
0
2
3
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
1
1
0
0
1
0
0
0
0
0
1
1
2
2
0
0
2
0
0
0
1
2
0
2
2
0
0
2
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
3
2
0
0
2
0
0
2
0
0
2
0
1
0
0
0
2
0
2
2
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
3
0
1
0
1
0
0
0
0
1
1
0
1
1
2
0
1
0
0
0
0
0
1
1
2
0
0
0
0
2
0
0
1
0
7
1
2
2
0
0
0
0
1
1
0
0
1
1
2
1
0
2
0
0
2
0
0
1
2
2
0
0
2
0
1
0
0
0
1
2
3
2
0
0
0
0
0
1
0
1
2
0
0
0
0
2
0
0
0
1
0
3
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
2
2
0
0
0
2
2
0
0
2
0
2
0
1
0
1
0
0
1
1
0
2
0
2
0
1
2
2
4
2
0
2
0
2
0
1
0
0
2
0
0
2
0
0
2
1
2
0
0
1
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
1
0
0
2
0
0
1
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
1
0
4
0
0
3
0
0
0
1
0
1
2
1
0
0
0
0
2
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
2
2
0
0
0
0
0
2
0
3
0
1
2
0
0
0
0
1
0
3
2
2
2
0
0
0
2
3
1
0
3
0
0
0
2
2
2
0
4
0
0
3
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
3
0
2
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
2
0
0
0
2
0
2
1
1
0
0
1
0
0
0
0
0
1
2
2
0
2
0
2
0
0
0
1
2
0
0
0
0
1
2
2
1
0
0
2
1
0
0
0
0
0
1
0
1
2
0
1
0
0
0
0
2
2
0
0
1
2
2
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
3
0
2
1
0
2
0
1
0
0
0
3
0
1
0
0
0
3
2
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
2
2
0
4
1
0
0
0
1
2
6
0
0
0
2
1
0
0
2
2
0
0
0
2
2
1
0
0
0
0
0
1
0
0
2
0
0
2
0
2
0
1
0
0
0
0
1
0
0
0
0
2
1
0
0
0
2
2
0
0
2
1
2
0
0
0
1
0
2
0
1
1
0
0
0
0
2
3
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
2
1
2
0
0
0
0
2
0
2
0
1
0
0
0
2
0
0
0
0
6
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
2
2
2
3
0
0
1
0
2
0
0
0
0
0
0
2
0
2
1
0
0
0
0
2
1
1
0
0
0
2
0
1
2
3
0
0
0
2
2
0
1
2
0
1
2
3
0
0
0
1
1
1
1
0
1
0
1
0
0
1
0
2
0
0
2
2
0
0
0
0
2
2
0
0
0
1
0
0
2
0
5
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
1
2
0
0
0
0
0
0
1
2
0
2
1
0
1
0
0
2
1
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
2
1
0
0
0
0
0
0
0
0
1
2
0
1
0
0
1
0
0
0
1
2
1
0
2
0
0
0
2
0
0
0
1
0
1
0
1
0
0
0
4
0
1
2
2
1
1
2
2
0
0
2
2
3
3
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
1
2
0
1
0
0
0
0
0
1
1
0
2
1
0
2
0
1
0
1
0
0
0
2
0
0
0
1
2
0
0
0
0
2
0
0
3
0
0
2
0
0
0
1
2
0
0
0
1
0
1
0
0
0
1
2
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
1
0
0
0
2
0
2
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
2
0
0
0
0
1
0
2
0
1
0
0
0
0
0
2
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
4
0
0
1
1
0
5
0
1
2
2
0
0
0
1
2
0
0
0
0
0
0
0
2
0
2
0
2
2
2
2
2
0
0
0
0
1
0
0
0
2
1
0
0
2
1
3
0
1
1
2
0
0
0
2
0
2
0
0
1
1
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
2
2
0
2
0
0
2
1
2
1
0
0
1
0
0
0
0
0
1
0
0
1
0
2
2
0
2
0
0
2
0
2
0
0
3
1
1
0
1
0
2
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
2
1
0
0
0
2
1
2
0
0
1
1
2
0
0
0
2
2
0
1
1
0
0
0
0
2
0
0
0
0
1
1
1
2
1
2
0
2
0
0
2
0
0
0
0
2
0
0
4
0
0
1
4
0
0
0
1
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
1
0
0
1
1
1
0
1
0
0
1
1
2
0
2
0
1
0
1
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
2
1
1
0
0
0
0
1
1
3
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
2
1
0
0
0
3
1
0
1
0
0
1
0
2
0
0
2
0
0
0
1
0
2
0
2
0
0
0
0
1
0
2
0
0
0
3
0
0
0
0
1
2
0
1
0
2
0
0
1
0
0
0
1
0
0
0
3
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
2
1
2
0
2
0
0
1
0
0
3
0
0
0
0
0
1
0
0
2
1
1
0
0
2
0
0
1
0
1
0
0
2
0
0
2
0
1
2
1
1
0
0
0
2
0
0
0
0
0
0
0
1
0
1
1
2
0
2
0
0
0
0
1
2
0
2
0
2
0
0
1
0
1
0
1
2
1
2
0
0
0
0
0
2
2
1
0
1
0
0
3
0
1
0
0
0
0
1
0
1
0
1
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
1
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
1
2
0
1
0
0
1
0
1
0
1
1
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
2
0
0
2
2
0
0
1
0
0
0
2
2
1
0
0
1
0
2
0
0
0
1
1
0
0
0
0
1
2
2
0
0
0
2
0
0
0
0
0
2
1
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
1
2
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
1
0
0
2
3
1
0
0
0
1
0
0
0
0
2
1
0
1
0
2
0
0
0
0
2
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
3
1
0
0
2
2
1
0
5
0
0
0
0
0
0
0
1
1
0
1
0
0
2
1
0
2
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
1
2
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
3
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
1
0
0
1
2
0
1
0
2
0
0
2
0
0
0
0
0
1
1
0
1
0
0
0
0
2
1
0
0
0
0
0
0
1
0
2
0
0
0
2
0
1
2
0
0
0
2
0
0
0
0
0
0
1
2
2
2
0
1
0
1
0
0
2
0
1
0
1
2
0
0
0
0
2
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
2
2
0
1
0
0
0
0
1
0
0
0
0
2
0
2
0
0
1
0
1
0
0
0
0
1
0
2
0
2
0
0
0
1
0
0
2
0
0
2
1
1
1
1
1
1
0
0
0
0
0
2
0
0
0
0
0
2
0
1
2
0
0
1
0
0
1
0
0
0
1
0
2
0
0
0
2
0
0
4
0
2
2
1
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
1
2
1
1
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
2
1
2
1
0
0
0
1
3
2
1
0
1
1
0
2
0
0
1
0
1
0
1
0
1
0
1
1
0
0
1
1
1
1
0
1
2
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
2
2
2
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
3
1
1
2
2
1
2
1
0
0
1
0
0
0
0
1
0
2
1
1
2
1
2
2
0
0
0
3
0
3
0
0
0
2
1
0
0
0
0
0
3
0
0
0
1
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
1
0
1
0
0
2
1
0
0
2
0
0
0
1
2
0
1
1
2
0
0
0
0
1
0
0
0
2
1
0
0
1
1
0
1
0
0
2
0
0
0
1
0
2
0
0
0
2
1
2
1
1
1
2
0
2
6
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
2
2
0
1
1
0
2
0
2
4
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
2
0
0
0
0
0
0
2
1
0
1
0
0
0
2
2
0
0
2
0
3
0
1
0
1
0
0
0
2
4
0
2
2
1
0
0
0
1
2
0
2
0
0
0
1
0
0
0
2
0
1
0
2
0
1
0
0
0
2
0
0
2
0
0
0
1
2
0
0
0
0
0
1
0
1
0
0
0
3
2
1
3
0
2
0
0
2
0
0
0
0
4
1
0
1
1
0
3
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
2
0
2
0
1
2
0
0
0
2
1
2
0
0
2
1
0
1
0
1
2
0
0
2
1
0
0
0
1
1
0
0
1
2
3
0
0
0
2
1
2
1
2
0
0
0
1
0
2
2
0
0
0
0
0
1
2
0
0
1
1
2
1
0
2
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
1
1
0
2
1
1
1
0
2
0
0
2
0
0
0
0
0
1
0
0
0
1
11
1
2
0
1
0
0
0
2
0
1
0
0
1
0
0
0
2
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
3
1
0
1
2
2
1
4
0
0
1
0
2
1
1
0
0
0
0
1
2
0
1
0
2
0
0
0
2
1
0
0
0
0
0
0
0
1
2
0
2
3
0
0
3
0
1
0
0
0
0
0
1
0
2
0
0
1
1
0
2
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
3
0
2
1
2
0
0
0
2
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
2
1
0
0
2
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
1
0
3
0
0
0
0
2
0
2
2
2
2
0
2
0
1
1
4
2
0
2
1
1
0
0
0
0
0
0
0
2
3
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
2
0
2
0
8
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
1
0
0
2
2
0
1
0
0
0
0
3
0
0
1
0
0
0
0
1
3
0
0
0
0
0
1
1
0
0
0
1
2
0
0
3
0
2
2
0
0
0
0
0
0
2
0
0
2
1
0
2
0
0
2
0
2
0
0
0
0
0
3
3
0
0
1
2
0
0
0
0
1
0
2
2
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
2
0
0
0
0
0
0
0
2
1
0
1
0
1
0
0
0
0
1
0
1
1
0
2
0
3
0
1
2
0
0
0
2
0
0
2
0
1
0
3
0
2
0
0
0
1
2
0
0
0
0
2
0
1
0
0
0
0
2
0
4
1
1
0
0
1
1
0
0
0
2
0
1
0
1
0
2
0
0
1
0
1
1
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
1
0
1
0
2
0
2
2
0
0
0
0
0
1
0
0
1
2
0
0
2
0
1
0
1
0
2
2
0
0
2
0
0
0
3
0
0
0
0
1
0
0
0
0
2
0
4
0
1
2
2
0
1
3
0
3
14
0
0
0
0
0
1
2
0
0
2
2
1
1
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
2
1
0
0
0
1
0
0
1
0
0
2
1
1
0
0
0
1
0
1
1
0
0
1
2
2
0
0
1
0
0
0
0
2
2
0
0
1
0
2
1
2
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
2
0
0
0
1
2
7
2
0
0
0
0
0
0
1
0
0
1
0
0
1
2
0
2
1
2
0
1
1
2
1
1
0
1
1
0
1
2
0
2
0
1
0
0
0
0
2
0
0
0
1
2
2
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
2
0
0
1
2
2
1
2
0
0
0
0
0
2
0
0
1
1
1
2
0
0
0
0
0
0
1
2
2
0
1
0
2
1
0
0
0
1
0
2
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
1
2
2
0
2
0
0
0
0
0
0
0
0
0
0
1
1
1
1
2
6
0
0
0
0
0
1
0
1
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
2
1
1
0
2
0
0
0
1
0
0
1
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
2
0
4
1
0
2
1
2
0
0
0
0
0
0
0
0
2
0
2
2
0
1
2
0
1
0
1
2
2
0
0
0
0
1
0
3
0
0
2
1
0
2
7
0
1
0
0
1
0
0
0
1
0
2
1
0
1
1
0
0
0
1
1
0
0
0
2
0
0
1
0
0
0
0
0
0
2
2
0
0
2
0
1
0
1
1
0
0
2
2
2
0
1
2
3
0
0
0
0
0
0
1
0
1
0
1
2
1
0
0
1
0
3
0
1
0
0
2
0
0
2
1
1
0
0
0
1
0
2
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
2
2
0
1
0
2
0
2
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
1
1
0
1
0
0
0
2
0
0
0
0
1
0
1
0
2
0
1
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
1
0
1
0
2
0
0
1
0
0
2
2
0
0
1
0
0
0
0
1
1
0
0
0
1
0
3
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
3
2
0
0
1
0
2
1
0
1
0
0
0
0
1
3
1
0
0
0
0
0
1
2
0
0
4
0
0
1
0
2
0
0
0
2
0
1
0
0
0
2
1
2
2
2
0
0
1
2
0
2
2
2
0
0
1
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
1
2
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
3
2
1
2
0
0
0
2
0
1
3
0
2
0
1
0
3
2
0
0
2
2
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
1
1
0
2
0
1
0
4
0
1
2
2
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
3
2
0
1
1
0
0
0
0
0
1
0
1
0
0
1
3
0
0
0
0
1
2
2
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
1
0
1
0
0
2
0
0
0
1
2
0
0
0
0
0
1
3
0
0
0
0
2
2
2
1
1
0
0
2
1
2
0
0
0
0
0
0
1
0
1
2
1
0
1
1
0
2
0
1
0
1
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
2
1
1
2
0
3
0
0
2
0
2
2
0
1
2
0
0
0
1
2
1
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
2
0
1
0
0
0
0
1
2
1
0
0
0
1
0
0
0
0
1
1
2
0
2
0
2
0
0
2
0
1
0
2
1
0
0
2
0
0
2
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
2
0
1
2
2
0
0
2
0
0
2
1
0
0
2
0
0
0
0
0
0
0
2
2
2
0
0
2
0
1
1
0
0
1
0
0
0
0
2
0
0
3
0
0
1
0
1
1
0
2
1
0
0
0
1
0
1
0
0
3
0
1
0
0
1
0
1
0
0
1
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
2
0
2
0
1
2
1
0
0
0
0
2
2
2
0
0
0
2
0
1
0
0
1
2
1
0
0
2
0
0
1
1
0
0
0
0
1
2
0
0
0
0
2
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
2
0
0
0
0
3
0
0
0
1
0
0
2
2
0
0
2
0
3
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
2
0
0
2
0
0
0
0
1
0
1
0
0
0
1
1
0
0
2
0
1
2
1
2
1
0
0
2
0
2
0
1
0
0
2
0
0
0
1
1
0
1
2
1
0
0
0
1
1
0
0
1
0
2
0
0
1
0
0
0
0
1
0
0
3
3
0
0
0
1
0
2
0
2
0
1
0
0
0
2
2
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
3
2
3
1
2
1
2
0
0
0
0
0
0
1
0
1
2
0
1
4
0
1
0
0
0
0
0
1
2
1
0
4
1
2
0
2
1
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
2
1
0
1
1
2
0
0
1
1
0
0
0
0
0
0
1
1
2
0
0
1
0
2
0
1
1
0
0
1
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
1
0
0
2
0
2
0
0
1
1
1
1
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
1
0
1
1
0
1
0
2
0
0
2
0
0
2
1
2
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
2
1
0
1
0
1
1
0
2
2
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
3
0
0
0
2
0
0
3
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
2
0
0
0
0
3
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
2
0
0
0
1
2
0
0
0
2
0
0
0
0
2
0
2
0
0
1
0
0
0
1
4
0
3
0
0
0
0
0
2
0
0
0
0
1
1
0
1
1
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
1
2
0
2
0
1
0
2
0
0
0
1
0
2
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
6
2
0
0
2
0
0
2
0
0
0
0
0
3
1
3
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
1
1
0
0
1
0
2
0
0
0
3
0
0
0
0
1
0
3
0
2
0
2
0
0
0
0
2
1
0
1
1
0
2
1
2
0
2
3
2
0
0
1
0
0
0
0
0
3
0
1
0
1
2
2
0
3
0
1
1
1
2
0
0
0
0
0
0
0
1
0
0
1
2
2
0
0
0
0
0
0
0
1
2
0
0
2
1
2
1
0
2
0
0
2
1
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
1
2
0
1
2
0
1
0
0
0
0
0
0
0
2
2
2
0
3
2
0
0
2
2
1
2
2
0
2
0
0
0
0
4
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
2
1
0
0
1
0
1
2
0
1
0
0
0
0
0
1
0
2
0
0
0
0
1
0
2
0
2
0
0
1
0
0
2
0
0
0
0
2
0
2
0
0
0
1
0
1
2
2
2
1
0
2
2
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
2
1
2
0
2
1
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
2
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
2
3
0
3
0
1
0
0
1
1
0
0
2
0
0
0
2
0
0
0
2
0
1
0
1
0
1
0
0
0
0
0
1
1
0
1
2
0
0
2
0
1
0
2
0
3
0
0
1
2
0
0
0
0
0
0
1
2
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
2
0
1
0
0
1
0
1
0
1
2
0
0
0
1
2
0
1
1
0
0
2
0
0
3
1
0
0
0
0
0
0
2
2
0
0
1
2
0
0
0
1
0
1
1
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
2
1
1
1
1
0
0
0
0
1
6
0
0
0
0
1
1
0
0
2
1
2
0
2
1
0
2
1
0
0
2
0
2
4
0
2
2
0
2
1
1
1
2
2
0
0
2
0
0
1
1
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
4
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
2
1
0
2
0
0
2
0
0
0
0
0
0
1
3
0
1
0
1
0
0
0
1
1
0
2
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
4
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
2
1
2
4
0
0
0
2
1
0
0
0
0
0
0
2
0
0
1
1
0
0
0
1
2
1
2
0
0
0
2
0
0
2
0
1
0
1
2
0
2
0
2
1
1
0
1
0
0
2
0
0
2
0
2
0
0
2
1
0
0
0
1
2
1
1
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
1
1
0
1
0
0
2
2
2
1
0
0
0
0
0
1
0
0
0
2
1
3
1
3
0
0
1
1
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
1
0
2
0
0
0
0
0
2
0
2
0
0
1
0
0
0
2
0
0
2
2
0
0
0
0
1
0
0
0
1
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
3
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
1
1
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
2
0
0
0
1
0
3
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
2
2
0
0
0
1
3
0
0
2
2
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
1
0
2
2
0
2
1
2
1
1
2
0
2
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
1
2
0
0
1
3
1
0
2
0
0
1
0
1
1
1
1
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
2
1
0
1
2
0
1
1
0
0
1
0
0
0
1
2
0
0
0
0
2
2
3
0
1
0
0
1
2
0
0
0
0
1
2
0
0
0
0
1
2
0
0
0
1
0
0
0
2
0
0
0
3
0
1
1
3
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
1
0
1
1
0
2
0
2
0
0
0
0
2
0
2
0
0
0
2
0
1
1
0
0
0
0
0
0
0
1
1
2
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
1
0
1
0
2
1
1
0
0
3
1
0
0
0
0
0
0
2
0
0
2
0
0
1
0
1
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
1
1
2
2
0
0
1
0
1
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
1
2
0
0
1
0
0
0
3
0
0
0
0
0
0
2
0
0
0
1
0
1
0
1
1
0
1
0
0
1
0
1
4
1
1
0
1
0
0
0
0
2
2
0
1
0
0
0
2
0
0
2
2
1
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
2
0
0
0
0
0
1
0
2
1
0
1
1
0
1
2
1
0
2
0
1
0
0
0
1
2
1
1
0
0
0
1
0
1
0
1
0
0
2
1
0
0
0
1
0
3
0
2
0
3
0
2
2
0
0
0
0
0
0
0
0
0
2
1
2
0
2
2
0
0
0
2
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
2
0
2
2
0
1
2
0
2
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
3
0
0
0
0
0
2
0
0
1
1
1
0
0
2
2
0
0
1
1
2
0
0
2
0
0
0
2
0
3
2
0
0
0
2
0
0
0
0
0
0
1
2
1
0
0
0
2
0
0
1
0
0
2
0
1
0
1
0
0
1
0
2
0
0
2
1
1
0
1
0
2
1
1
0
0
0
0
0
1
1
0
0
0
0
0
2
1
2
0
3
2
0
0
1
2
0
0
0
0
2
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
2
1
2
3
1
0
0
0
1
0
2
1
0
0
0
0
2
0
0
2
0
2
0
0
2
0
0
0
0
1
0
0
0
2
0
1
1
1
0
1
0
0
0
1
2
2
1
0
0
1
0
0
0
0
2
0
1
2
2
0
0
0
0
0
0
0
0
1
1
1
0
0
0
2
0
1
0
2
2
0
2
3
2
2
2
0
2
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
3
1
0
1
2
0
0
0
1
2
0
1
2
0
1
2
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
2
2
0
0
0
0
0
0
0
1
2
0
2
0
0
1
0
0
1
0
0
0
0
0
2
1
0
2
0
2
1
0
2
2
1
0
0
2
1
2
0
0
0
2
0
0
0
2
0
2
2
0
0
2
1
2
0
0
2
0
0
2
0
2
0
0
1
2
1
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
2
2
0
3
0
1
0
0
1
0
0
2
0
1
0
2
1
0
1
0
2
2
2
1
2
2
0
2
2
0
1
0
0
0
0
1
0
2
1
0
1
2
0
1
0
2
2
0
0
0
2
4
1
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
2
0
1
2
2
0
0
0
2
0
0
0
0
0
2
0
1
0
1
0
0
0
0
2
0
0
0
0
2
1
1
2
1
1
1
3
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
1
2
2
1
1
0
2
1
0
0
0
1
0
2
0
1
0
2
2
2
0
0
0
0
2
0
0
0
0
2
2
0
0
0
2
1
0
0
0
0
0
0
3
1
0
0
1
0
0
0
1
0
1
0
0
0
1
2
0
0
0
0
0
2
0
2
0
0
0
0
0
1
2
0
1
0
0
0
0
0
1
2
0
2
1
0
2
2
1
0
2
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
2
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
4
2
1
3
2
1
3
1
0
3
0
0
0
0
0
1
1
0
0
0
1
0
0
2
0
0
1
0
0
1
4
2
0
0
0
0
2
2
0
0
1
2
1
1
0
0
1
0
0
1
0
0
0
0
2
2
1
2
1
2
0
2
0
0
0
1
0
0
2
0
1
2
2
3
1
0
1
2
0
1
0
2
0
0
0
0
0
1
1
1
2
2
0
0
0
2
1
2
0
1
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
1
0
0
2
0
1
0
0
0
0
1
1
2
0
0
0
0
1
0
1
0
0
2
0
0
0
0
2
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
2
2
2
0
1
0
0
0
0
2
0
0
2
1
1
1
0
0
0
0
0
2
0
0
0
0
0
1
1
1
2
0
0
2
0
1
1
0
2
1
4
0
0
1
1
2
0
1
0
1
2
2
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
2
0
2
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
1
0
0
0
2
0
1
0
0
2
0
0
0
1
2
0
1
1
0
0
0
0
0
4
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
2
0
1
0
2
1
0
0
1
0
1
2
1
0
2
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
1
0
2
2
0
0
1
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
2
0
1
0
0
0
0
1
0
0
0
0
0
1
2
2
1
1
0
0
0
1
0
0
1
0
1
0
2
1
0
0
1
0
2
1
2
0
1
0
1
0
0
0
0
0
0
2
1
1
1
0
2
1
0
2
0
1
1
0
0
2
1
0
0
0
0
0
2
0
1
0
0
1
0
1
0
2
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
2
1
1
0
0
1
1
0
0
0
2
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
2
1
0
2
0
1
1
0
0
0
0
3
2
0
1
0
1
0
1
0
0
1
2
0
3
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
3
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
2
1
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
2
0
0
0
1
1
0
2
2
0
1
1
0
0
0
1
0
0
2
0
0
0
3
0
1
0
0
2
0
0
0
0
4
0
0
1
0
0
1
0
0
0
2
0
1
0
1
0
0
1
1
2
0
0
2
2
1
0
0
2
0
0
1
0
0
0
0
0
1
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
1
0
4
1
2
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
2
2
0
0
2
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
2
2
0
3
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
5
1
2
0
0
0
2
0
0
2
1
0
1
2
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
2
0
2
0
1
3
1
1
0
0
1
0
0
0
1
1
2
0
0
2
1
0
1
0
0
0
0
2
2
0
0
0
0
0
1
1
0
2
1
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
2
2
0
0
0
4
0
0
0
0
0
0
1
1
2
0
2
0
3
0
0
0
1
1
0
0
0
2
0
0
2
1
2
0
0
0
0
0
1
0
0
1
0
2
2
1
0
2
2
0
2
0
1
2
0
0
0
2
0
2
2
0
1
0
0
1
0
1
0
1
0
0
0
0
1
2
0
0
1
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
1
0
1
1
0
2
1
0
2
1
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
2
0
2
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
2
3
0
1
0
0
0
0
1
0
0
0
2
0
1
0
0
1
0
0
0
1
0
2
0
1
0
0
0
0
1
1
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
2
1
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
2
0
0
1
0
0
1
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
2
1
0
0
2
0
0
1
1
0
0
1
2
1
0
0
0
3
0
2
0
0
2
1
0
0
1
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
3
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
2
0
0
2
0
2
0
1
2
0
0
0
0
1
1
0
2
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
2
0
1
1
0
0
0
0
0
0
0
0
1
0
2
1
2
0
0
1
0
0
3
1
1
0
0
0
2
0
0
0
1
2
2
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
1
2
0
2
0
0
0
2
0
1
0
1
0
0
1
1
0
0
0
0
1
0
1
0
2
0
1
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
4
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
4
0
0
2
0
0
0
2
0
1
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
2
0
0
0
0
0
2
2
0
1
0
0
2
2
1
0
0
0
1
0
0
0
0
1
1
1
1
0
0
0
1
0
0
1
0
1
1
1
0
1
2
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
2
1
2
0
0
1
1
0
0
0
0
0
2
0
0
1
0
0
0
1
1
2
0
2
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
2
0
0
0
2
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
2
1
0
0
1
0
2
0
0
1
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
2
2
0
2
0
1
1
4
0
0
0
2
0
0
0
0
2
2
0
1
0
2
0
1
0
0
0
1
1
1
2
1
0
0
1
2
0
0
0
0
0
0
1
0
1
0
0
1
2
1
1
1
0
2
0
1
1
0
2
0
0
1
1
1
0
0
0
0
0
0
2
1
0
4
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
1
0
2
2
1
0
1
0
0
1
1
1
1
0
1
0
2
0
0
0
0
1
2
1
0
0
2
0
1
1
1
2
1
0
2
0
0
0
0
3
0
1
0
2
0
6
0
0
1
1
0
2
0
0
0
0
0
1
1
0
0
0
1
2
1
1
0
0
2
0
0
2
0
0
0
2
1
0
2
1
1
2
1
0
0
1
0
1
0
0
0
2
0
1
0
0
0
0
1
3
1
1
0
0
2
0
0
0
0
1
0
1
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
5
1
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
2
0
1
1
0
1
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
1
2
0
1
0
0
0
0
2
1
0
0
0
1
1
0
0
0
1
0
2
1
0
1
0
0
0
0
0
2
1
0
0
2
2
0
0
0
1
1
0
0
1
0
0
0
2
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
3
2
2
0
2
1
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
1
2
1
1
0
2
0
1
0
0
0
0
0
2
2
1
0
2
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
2
2
2
0
2
0
2
2
0
0
3
0
2
1
0
0
0
2
0
1
0
0
0
1
2
2
0
2
2
0
0
0
0
0
0
1
2
0
0
0
0
2
1
1
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
3
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
1
0
0
0
2
0
0
2
1
0
0
2
2
1
0
1
0
0
0
1
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
1
2
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
2
0
0
2
2
0
2
0
2
0
0
0
1
0
0
1
0
2
1
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
2
0
2
1
3
0
0
2
1
0
0
0
2
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
1
1
1
0
0
0
0
1
0
0
2
0
0
1
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
2
2
0
0
0
0
0
2
2
0
0
1
0
7
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
1
1
1
0
0
0
1
2
0
2
0
1
0
3
0
2
0
1
0
0
0
1
1
1
0
1
1
0
1
2
0
0
1
3
0
0
0
0
2
2
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
3
0
1
0
1
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
1
2
0
2
0
2
0
1
3
2
0
0
1
3
1
1
0
1
0
2
0
3
0
0
0
0
0
0
0
0
1
1
2
1
0
0
0
0
0
0
2
2
2
1
0
2
2
0
0
0
2
0
0
2
0
0
1
0
3
0
1
0
0
0
1
0
2
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
1
3
0
0
0
0
2
2
0
0
0
1
0
0
1
1
0
1
1
0
0
2
0
1
0
0
1
1
0
0
1
0
2
0
0
6
0
0
1
2
0
1
0
2
0
0
0
0
0
0
0
1
1
0
2
2
0
0
0
0
1
0
0
1
2
2
1
0
0
0
0
0
0
0
0
1
2
1
0
0
0
1
0
0
2
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
3
0
1
2
0
0
2
0
1
1
2
1
0
0
0
1
0
0
0
0
0
0
0
4
0
0
2
0
1
0
0
1
1
2
1
1
1
0
2
3
0
0
2
0
1
0
0
0
0
1
0
0
0
2
1
0
0
1
0
2
4
0
0
2
0
1
0
1
0
1
0
1
2
0
2
3
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
2
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
2
0
0
1
0
2
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
1
3
2
0
0
0
0
0
2
2
2
1
3
1
2
0
1
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
1
1
1
0
2
0
0
0
1
2
2
0
0
2
2
1
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
1
0
1
1
1
0
0
0
1
0
2
0
0
1
2
0
0
0
0
0
1
2
2
1
0
0
0
0
1
0
1
1
0
4
2
2
2
0
0
1
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
2
0
5
2
0
0
1
0
0
0
0
0
0
3
2
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
4
0
1
4
0
0
0
0
1
0
2
1
1
1
1
2
0
1
0
1
0
2
0
0
0
1
2
1
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
2
1
0
2
0
1
2
0
2
2
2
0
2
0
0
0
2
1
0
0
0
1
2
1
1
1
0
0
0
2
1
3
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
2
0
1
1
0
1
0
2
0
1
2
0
1
0
0
1
2
0
0
2
0
2
0
0
0
0
1
0
0
0
1
1
0
2
2
0
2
0
0
0
0
1
2
0
2
0
0
0
0
1
1
1
2
1
1
0
2
2
2
0
0
3
0
1
1
0
2
1
3
0
2
1
1
0
1
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
1
2
0
1
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
4
0
0
0
1
0
0
1
0
0
2
1
0
0
1
0
2
0
0
0
1
2
0
1
0
2
0
0
0
0
0
1
2
1
6
1
0
2
0
2
0
0
0
0
0
2
0
1
2
1
2
0
0
0
0
0
0
0
2
0
0
2
0
0
2
2
0
0
1
0
0
1
0
0
0
0
2
0
2
2
2
1
0
0
0
2
1
2
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
2
2
1
2
0
1
2
0
1
0
0
0
5
0
3
0
1
0
0
2
2
4
0
1
1
2
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
2
0
2
0
0
0
1
0
1
0
1
1
0
2
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
1
0
0
0
2
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
4
0
2
1
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
2
2
0
2
1
0
0
1
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
3
0
1
0
0
0
2
1
1
0
2
0
2
2
0
0
0
2
0
2
0
0
1
0
0
2
1
0
0
2
0
0
0
1
1
2
0
1
0
0
1
0
0
1
0
1
0
2
3
2
2
1
0
0
1
2
0
2
0
0
1
0
2
2
0
1
0
4
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
1
1
2
0
0
0
0
1
0
1
2
1
0
2
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
1
0
1
0
1
0
1
0
2
0
0
1
1
0
0
0
0
0
1
1
2
0
0
1
0
0
0
0
2
2
1
0
0
0
0
1
0
0
0
1
2
0
0
2
3
0
2
0
0
0
0
0
0
0
0
2
0
1
0
3
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
2
1
0
0
1
0
4
0
0
0
0
0
0
0
1
1
2
0
0
2
0
1
0
0
0
0
0
0
0
0
1
3
3
0
2
1
0
0
0
0
1
0
1
0
0
0
0
0
1
2
1
0
0
2
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
1
0
2
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
1
0
1
1
1
0
2
0
2
0
2
1
0
2
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
1
0
0
0
1
1
1
0
0
0
3
0
0
0
0
1
0
0
1
1
4
0
0
5
1
0
2
0
1
0
2
1
0
0
0
0
2
1
0
0
0
1
0
1
0
0
2
3
1
1
1
2
0
0
0
2
0
0
1
0
0
2
1
0
0
2
1
3
0
0
0
2
0
0
0
2
0
0
1
1
0
0
0
0
1
2
1
0
2
2
0
0
0
0
0
2
2
2
1
2
1
1
3
4
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
1
1
0
1
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
1
0
1
0
1
0
0
3
0
0
0
0
0
1
1
0
2
2
0
2
1
0
0
0
0
1
0
2
2
0
2
1
2
1
4
2
1
0
0
1
1
2
0
0
0
0
1
0
0
2
0
1
0
0
0
2
0
0
0
2
2
2
0
1
0
2
1
0
0
0
2
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
1
0
1
1
1
2
0
0
0
2
2
0
1
0
2
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
1
2
0
0
2
1
0
2
0
0
2
0
0
0
0
1
0
2
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
1
1
0
0
3
0
0
0
0
1
0
1
0
0
0
0
0
0
2
1
0
0
1
2
0
1
0
0
0
1
1
0
1
0
2
0
0
2
0
0
0
0
1
2
2
3
0
0
2
0
1
1
1
2
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
3
0
0
0
0
2
2
1
1
2
0
0
5
0
2
0
1
0
1
1
4
0
0
0
0
4
0
2
0
1
2
1
0
3
0
0
0
1
0
1
0
1
0
0
0
0
2
1
0
0
0
4
1
1
0
0
0
1
0
0
0
2
2
0
0
0
2
0
0
0
0
0
2
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
2
2
1
0
1
0
0
0
2
0
0
0
0
1
2
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
3
3
1
2
0
0
0
2
1
1
0
0
1
2
1
0
0
2
0
0
1
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
2
2
2
0
2
3
1
2
0
0
2
0
1
0
0
0
0
0
0
1
0
2
0
0
2
0
1
0
1
0
0
0
1
2
0
2
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
1
0
0
1
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
2
0
2
0
2
1
0
0
0
2
0
0
0
0
1
2
1
1
0
0
4
2
1
0
1
0
0
0
0
0
0
0
1
0
2
1
0
0
2
2
0
2
0
0
0
1
0
2
2
0
0
2
2
2
3
0
1
2
0
0
0
1
2
0
0
0
2
1
0
0
2
0
0
1
0
0
1
0
2
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
3
0
0
2
0
0
1
0
1
0
2
0
1
0
3
0
1
0
0
1
0
1
0
2
0
0
2
0
0
0
3
1
0
0
0
2
0
0
0
1
0
0
0
0
2
1
0
0
0
0
1
2
2
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
2
0
1
1
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
2
0
0
1
0
1
0
0
0
1
1
0
2
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
2
1
0
0
1
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
2
1
0
0
0
2
0
0
2
0
1
1
0
0
2
0
0
0
2
0
0
2
1
0
0
1
0
0
0
1
2
1
0
0
0
1
2
2
3
0
0
0
1
0
0
0
6
0
0
2
0
0
0
0
0
2
2
0
0
0
1
0
2
0
0
0
0
2
0
0
1
0
0
0
0
2
0
1
0
0
1
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
2
0
0
0
0
0
0
3
0
0
0
5
0
0
0
0
2
0
0
0
0
2
1
0
0
1
0
0
0
0
1
0
1
0
1
1
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
1
1
0
0
0
0
1
0
1
0
0
2
1
1
1
0
1
2
0
2
0
0
1
0
0
1
2
2
1
0
0
0
2
2
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
2
0
0
2
0
0
0
2
2
0
2
2
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
1
1
2
0
0
1
0
1
2
2
0
0
1
0
1
0
0
1
2
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
2
0
2
0
1
0
2
0
2
0
0
3
1
1
1
0
0
0
2
1
0
0
2
0
0
0
2
0
3
0
0
2
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
7
0
1
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
10
0
0
1
1
0
0
2
1
2
0
1
2
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
3
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
2
2
2
2
0
0
0
0
1
2
0
2
1
1
0
1
1
0
0
1
2
1
1
2
0
0
0
0
2
0
1
0
0
0
0
2
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
1
0
2
0
0
0
2
1
1
2
0
1
0
0
1
0
2
2
0
1
0
1
1
0
1
0
0
0
0
3
0
0
1
1
0
0
2
2
2
2
0
1
0
1
0
2
1
0
0
0
0
2
0
0
1
0
0
3
1
0
0
0
0
0
0
1
2
0
2
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
4
2
0
2
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
1
2
1
0
0
0
2
2
2
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
2
2
0
1
5
0
0
2
0
0
0
1
0
1
0
1
0
2
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
3
1
2
0
0
2
0
0
0
1
2
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
2
0
0
2
0
2
0
0
0
0
1
0
1
0
2
1
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
1
1
0
0
0
1
0
2
2
0
1
2
0
1
0
1
0
1
2
1
3
1
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
3
0
0
0
1
0
0
1
2
0
0
0
2
1
0
0
1
1
3
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
1
0
1
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
2
0
2
2
0
0
0
0
0
1
1
1
1
0
0
1
1
1
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
5
1
2
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
1
1
1
1
0
1
0
0
2
1
0
0
0
3
0
0
0
2
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
2
0
0
0
0
0
3
0
2
0
0
1
1
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
2
0
0
0
1
1
0
1
1
0
2
2
2
0
3
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
1
2
0
0
2
0
1
0
2
2
0
0
1
2
0
0
0
0
0
3
0
1
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
2
2
0
1
1
1
0
3
0
1
1
0
1
1
0
0
0
0
0
0
3
0
1
0
2
2
2
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
1
1
1
0
1
0
2
0
1
0
2
0
0
0
0
2
2
0
1
0
2
2
1
1
1
1
0
2
1
0
0
0
0
0
2
0
0
0
0
1
1
0
0
2
0
2
2
2
0
0
1
0
0
0
0
3
0
0
0
0
2
2
2
0
0
0
1
0
3
0
0
0
0
0
2
3
0
3
1
1
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
2
0
0
1
0
0
4
0
0
0
1
0
2
0
0
1
2
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
3
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
1
0
1
2
0
0
5
2
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
2
0
1
0
0
0
2
0
0
1
1
3
0
0
1
1
0
0
0
2
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
2
0
0
0
2
1
0
1
2
0
3
0
0
0
1
1
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
1
0
2
0
0
2
0
1
0
1
2
1
0
0
0
0
0
1
0
1
0
3
0
0
2
2
0
0
2
2
3
0
0
0
0
0
1
0
0
0
2
1
2
2
2
0
0
2
0
0
1
1
0
0
0
1
0
0
0
0
2
0
2
2
2
2
0
1
0
0
0
1
2
1
4
0
1
1
0
0
0
2
0
2
2
0
0
0
0
4
3
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
3
0
2
1
0
0
0
0
1
2
0
0
0
2
0
0
2
1
0
0
2
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
2
0
0
1
1
0
1
0
2
2
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
2
0
1
0
0
2
0
2
0
0
0
2
0
2
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
1
0
0
0
0
1
2
0
0
0
0
3
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
1
0
2
1
2
1
0
1
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
2
0
1
0
2
1
1
0
3
1
2
0
2
3
0
1
0
0
0
0
0
1
1
0
1
0
0
1
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
1
0
0
2
0
0
1
0
0
2
0
0
1
2
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
1
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
2
1
0
0
1
0
1
1
0
6
0
0
0
0
0
0
1
2
0
1
2
2
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
1
0
2
2
4
2
0
2
2
0
0
0
0
2
0
2
1
2
2
0
1
0
2
0
0
0
2
2
0
3
0
1
0
0
0
2
0
0
0
0
0
1
0
1
0
1
1
0
0
0
2
2
0
1
0
1
1
0
0
0
0
1
0
2
0
0
1
3
0
2
0
2
0
0
0
0
0
1
0
1
1
0
1
0
2
0
0
2
2
0
1
0
0
0
0
0
0
0
0
3
1
0
0
2
0
1
0
0
0
1
1
0
0
1
2
0
1
2
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
4
1
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
1
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
1
0
0
2
0
0
2
0
0
0
0
1
2
1
0
0
1
0
1
2
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
1
2
2
1
1
0
4
0
0
0
0
2
0
0
0
2
0
1
0
2
0
0
0
0
0
1
0
2
1
1
0
0
0
0
0
3
0
0
0
0
1
2
0
1
0
2
0
0
0
0
0
1
0
0
1
0
2
2
1
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
2
0
2
2
0
0
0
0
0
0
1
1
0
2
0
0
1
1
1
0
1
0
0
0
0
0
2
0
1
0
2
2
0
0
0
2
1
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
2
0
0
0
0
0
2
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
2
0
0
0
1
2
0
0
1
0
0
0
0
0
1
2
0
2
3
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
1
0
0
2
1
0
2
0
2
2
0
0
0
0
1
0
2
0
0
1
0
2
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
2
0
2
2
0
2
0
0
0
2
1
0
0
2
0
0
0
0
1
1
0
2
0
0
1
2
0
0
1
0
2
0
2
2
1
3
0
0
1
0
0
0
0
0
1
0
0
1
1
1
1
0
0
0
0
0
0
0
2
0
0
2
0
5
2
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
2
0
0
0
1
0
0
2
1
0
0
2
0
0
2
3
0
0
2
0
1
0
0
2
0
2
1
1
0
1
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
1
1
0
0
2
2
0
1
0
0
2
2
0
0
1
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
3
0
1
0
1
0
2
0
0
0
0
1
0
1
0
0
3
0
0
2
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
1
1
0
1
1
1
0
0
2
0
0
0
1
2
0
0
0
0
1
0
1
0
0
0
3
0
2
2
1
1
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
2
2
1
0
1
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
2
0
1
0
0
2
0
2
2
1
0
0
0
0
0
0
0
2
3
2
1
1
2
1
1
0
0
0
0
0
1
0
2
1
0
1
0
2
0
0
0
0
1
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
1
2
0
1
0
0
0
0
0
0
2
0
0
0
0
2
1
1
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
1
1
0
0
0
3
0
0
2
0
0
2
0
2
1
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
2
0
2
0
1
0
2
0
0
0
0
1
0
0
0
1
1
1
0
0
2
2
0
0
2
2
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
2
2
2
0
2
0
0
3
0
0
0
2
0
2
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
2
2
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
2
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
2
1
2
1
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
2
0
0
0
2
0
1
0
2
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
2
2
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
1
2
2
1
0
1
2
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
2
1
0
0
0
0
0
0
1
2
2
0
0
0
2
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
2
0
0
0
0
2
2
0
1
2
1
1
0
0
0
2
0
0
1
2
1
0
2
0
0
1
1
0
1
0
1
4
0
1
1
0
1
0
1
0
0
2
0
0
1
1
0
0
0
0
2
2
0
0
0
1
0
1
0
0
1
1
2
2
0
1
0
2
1
1
0
1
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
2
0
0
2
1
2
1
0
1
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
1
0
1
3
1
0
0
1
0
0
0
1
0
2
1
0
1
0
0
2
2
0
1
0
1
0
2
2
2
1
0
0
3
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
1
0
0
1
2
0
0
2
0
0
0
0
0
5
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
2
2
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
1
2
2
0
0
0
0
0
1
2
0
0
1
3
0
0
0
0
0
2
2
0
0
0
0
0
2
2
0
0
1
0
0
0
2
0
0
0
0
4
1
2
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
4
0
0
0
2
0
0
0
1
0
1
0
0
0
0
1
2
1
2
0
0
1
0
0
0
1
1
0
0
0
6
0
0
0
2
0
0
2
2
1
0
0
0
3
0
1
1
0
2
0
1
0
1
0
2
1
0
2
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
2
1
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
1
0
2
2
2
0
2
0
1
0
1
0
0
0
2
1
0
1
0
0
0
1
0
2
0
0
0
1
0
0
2
0
1
0
0
1
0
1
1
0
0
0
0
1
1
1
1
0
2
0
2
0
1
2
0
0
0
2
0
4
1
0
0
0
0
0
2
0
2
1
0
0
0
0
1
0
6
1
0
1
2
0
0
0
1
3
0
0
0
0
0
0
2
2
1
0
0
0
0
2
2
1
3
0
0
0
0
0
0
0
0
0
1
5
0
0
2
0
1
0
2
0
0
0
0
0
1
0
3
1
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
1
3
0
0
1
0
0
0
2
0
0
0
2
1
1
0
0
1
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
1
0
2
2
0
0
1
0
0
0
1
2
0
0
0
0
1
0
2
1
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
1
0
1
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
3
1
0
0
0
0
1
0
0
2
1
0
0
0
0
0
2
1
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
2
2
0
2
0
1
0
1
1
0
0
0
0
1
0
2
0
1
0
0
0
2
0
2
1
0
0
2
0
2
0
2
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
2
0
0
0
1
1
1
0
1
0
0
0
1
2
0
2
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
3
0
0
2
0
0
0
1
0
1
0
0
0
0
1
4
1
0
0
0
2
0
0
1
2
1
0
0
2
2
1
0
0
4
2
1
0
1
0
1
0
2
2
2
2
0
1
0
1
1
0
0
2
0
0
1
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
1
0
1
0
0
0
2
0
2
0
0
2
1
0
2
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
1
1
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
3
0
0
1
1
1
0
0
0
0
2
2
0
0
3
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
2
1
2
1
0
0
1
0
0
2
1
1
0
0
0
0
0
0
2
0
0
1
2
0
2
2
2
0
0
0
1
0
2
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
2
0
0
0
0
2
2
0
0
0
0
2
2
0
1
0
1
0
0
0
3
0
5
2
0
0
0
0
0
0
1
2
0
0
1
1
0
0
2
0
1
1
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
1
1
3
2
2
2
1
0
0
0
0
2
1
0
1
0
0
0
0
2
1
0
0
0
0
1
2
2
0
3
2
0
0
2
1
1
3
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
3
0
1
0
0
0
0
1
2
0
2
1
0
0
2
0
0
0
2
0
0
1
1
0
0
0
0
0
3
2
0
1
1
0
1
0
0
0
0
0
0
1
0
2
0
2
2
0
0
2
1
1
0
0
0
0
2
0
2
0
2
2
2
0
0
0
0
0
1
0
0
1
0
2
3
0
1
0
0
0
1
3
0
0
0
2
0
0
0
0
1
3
1
1
1
2
0
2
0
0
2
0
1
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
3
0
2
2
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
2
2
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
2
0
0
2
0
0
2
0
0
2
0
2
0
0
0
0
2
4
0
4
0
0
1
0
0
2
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
2
7
2
0
0
0
2
2
0
0
0
1
2
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
1
1
0
0
3
0
0
0
0
2
1
1
0
0
0
1
2
0
1
0
0
0
0
1
0
0
1
0
0
2
2
0
2
0
0
1
1
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
1
0
0
0
2
1
1
0
0
1
0
0
0
1
3
0
0
0
0
0
1
1
0
0
1
0
0
3
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
3
2
1
2
1
0
2
0
1
0
2
1
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
1
0
2
2
0
2
0
1
4
0
0
1
2
1
1
0
0
0
0
0
1
0
1
2
4
1
0
0
0
2
1
0
0
0
2
0
0
1
1
0
1
0
0
0
2
0
0
0
0
2
3
1
0
0
2
0
0
2
0
0
2
0
1
1
0
0
0
2
1
2
1
1
0
0
0
0
1
0
0
1
0
2
0
1
0
1
2
2
2
0
0
0
1
0
0
2
0
0
0
0
0
1
0
2
0
0
0
2
0
0
2
0
3
0
0
0
0
2
0
0
1
0
1
0
3
1
1
2
0
0
1
0
0
1
0
0
0
1
0
1
0
2
0
0
0
2
0
2
0
2
0
1
0
0
5
0
0
1
1
1
1
0
0
0
0
0
0
0
0
4
1
0
2
1
0
2
0
0
0
0
2
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
2
1
2
1
0
2
1
2
0
0
0
1
1
2
1
0
0
1
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
4
1
3
0
0
1
0
0
0
0
0
2
0
0
0
1
2
0
0
5
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
1
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
1
0
0
1
2
1
0
1
0
1
0
0
1
1
0
2
1
0
0
0
0
0
0
3
0
1
3
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
2
2
1
0
0
1
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
4
1
0
0
1
0
1
1
0
0
0
0
1
1
0
0
1
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
1
1
1
0
0
0
0
0
2
0
2
0
0
2
1
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
2
0
2
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
2
2
2
0
0
0
0
1
2
0
0
1
2
0
2
0
0
1
0
2
0
2
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
2
1
0
1
2
0
0
0
0
1
0
2
0
0
1
2
1
2
0
0
0
0
1
0
1
0
0
1
0
0
0
2
0
1
0
0
2
1
0
0
0
2
0
0
0
2
0
2
2
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
2
3
1
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
1
1
0
0
1
1
2
0
2
0
2
1
2
1
1
2
0
0
0
1
0
0
0
0
1
2
1
0
1
0
4
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
2
0
2
1
2
0
0
0
2
0
2
2
0
0
2
0
0
1
0
1
0
0
0
0
1
0
2
2
2
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
1
1
0
0
0
2
0
1
0
0
1
0
0
1
2
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
2
0
0
1
1
0
1
3
0
0
0
2
0
0
0
0
0
0
0
2
0
2
2
1
1
0
0
0
0
0
1
0
0
0
2
1
2
0
0
0
0
0
0
0
2
0
2
0
1
2
1
0
0
0
2
0
1
0
0
2
1
2
0
0
4
1
0
0
0
0
0
3
0
1
0
0
0
1
0
0
0
0
2
0
0
0
3
0
2
0
1
0
0
2
2
0
0
0
0
0
1
1
0
0
2
2
0
0
1
0
0
0
2
0
2
0
0
2
2
2
0
2
0
0
0
0
2
0
1
0
0
0
1
0
0
2
1
2
0
0
2
0
2
2
0
1
1
0
0
2
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
1
0
1
2
4
0
1
0
2
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
3
1
0
0
0
0
0
1
1
4
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
1
0
0
2
2
0
0
0
2
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
1
1
0
0
1
2
1
1
0
1
0
1
0
0
0
2
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
1
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
2
0
1
0
2
0
2
0
1
1
1
0
0
0
1
0
2
1
0
0
2
0
0
1
1
1
0
0
0
1
0
1
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
2
2
0
0
1
2
1
0
0
1
0
1
0
0
0
0
0
4
0
0
1
0
0
0
2
1
0
0
2
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
2
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
1
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
1
0
2
1
1
2
0
1
0
2
0
0
0
0
0
2
1
0
2
1
2
0
1
0
2
0
2
0
0
0
0
0
0
2
1
1
0
1
0
2
0
0
0
0
0
1
0
0
1
2
0
0
0
0
1
1
0
1
2
0
2
0
0
1
0
0
0
0
1
2
0
2
0
2
0
0
0
1
0
0
0
0
0
1
0
0
3
0
0
0
0
2
0
0
1
1
0
0
0
1
0
0
0
0
2
0
0
2
3
2
0
0
2
0
2
2
0
0
0
2
0
0
1
1
0
0
0
2
0
1
0
1
0
2
1
2
0
2
1
1
0
2
0
0
0
0
0
1
1
0
0
2
2
0
1
0
2
0
0
2
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
1
0
2
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
2
0
0
0
0
2
0
2
1
0
0
1
0
6
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
2
0
2
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
3
0
0
1
0
1
0
0
2
0
0
0
2
2
3
0
0
0
3
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
1
0
1
0
0
0
0
0
2
3
1
3
2
1
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
2
0
2
7
0
0
0
0
10
2
0
0
2
0
2
2
2
0
2
0
0
0
1
1
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
1
0
0
2
1
0
0
0
2
0
0
0
2
0
2
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
1
0
2
0
0
1
1
0
0
0
1
1
0
1
0
3
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
1
1
2
0
1
2
0
0
0
0
0
0
0
2
1
0
2
0
0
0
1
1
1
0
2
1
0
0
1
0
0
0
2
0
2
0
3
0
0
1
0
2
0
1
0
0
0
2
0
0
1
1
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
5
1
0
1
2
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
3
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
2
0
1
2
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
1
0
1
5
0
0
0
0
2
1
0
6
0
0
1
2
0
0
1
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
1
0
0
0
2
0
1
0
0
2
0
1
0
2
0
0
0
0
2
3
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
4
0
0
1
0
1
2
0
2
0
0
0
0
2
2
0
0
0
0
1
1
0
0
0
2
1
1
3
0
0
0
0
3
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
2
1
0
1
0
0
2
0
0
0
0
0
2
1
0
0
0
1
1
0
0
0
1
0
0
0
1
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
2
1
0
0
0
0
1
2
0
0
1
0
1
0
0
0
0
0
1
2
2
1
2
2
0
0
0
1
2
2
1
1
1
0
0
0
0
0
5
0
1
0
0
1
0
1
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
1
1
0
0
2
1
0
0
1
1
2
0
1
0
2
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
2
2
0
0
0
1
2
2
0
0
0
0
0
2
1
0
0
0
0
0
1
0
1
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
1
0
1
0
2
0
1
0
2
5
1
0
0
0
0
1
0
0
3
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
3
2
0
0
3
1
0
1
0
1
2
0
0
0
0
0
0
0
2
2
0
1
0
4
0
0
2
0
1
1
1
0
0
2
0
0
0
0
0
0
0
1
0
2
0
1
0
0
2
0
0
0
1
0
0
0
1
0
0
2
0
1
0
0
12
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
4
0
0
0
1
1
0
0
0
2
0
0
2
0
1
0
1
0
0
0
0
0
1
2
0
1
0
0
0
2
2
0
0
1
0
2
0
1
1
0
0
0
0
2
2
2
0
1
1
0
0
0
0
1
0
3
0
0
0
2
2
0
2
0
0
1
3
2
2
0
1
2
0
2
0
0
0
0
0
0
1
2
0
2
2
0
1
0
0
0
1
0
1
1
0
1
1
0
2
0
2
0
1
0
2
3
0
0
0
0
2
0
0
1
0
0
0
2
1
0
0
2
0
2
3
1
2
0
0
0
1
2
0
0
0
2
0
0
0
0
2
2
0
1
1
0
0
0
1
2
0
4
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
2
1
0
0
0
0
2
2
0
0
0
0
1
0
1
0
0
0
2
0
1
1
0
0
0
1
0
0
0
1
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
3
0
0
0
3
0
2
0
1
0
2
0
0
2
0
0
2
0
0
1
2
0
0
1
2
2
1
0
0
0
2
2
0
0
0
0
1
0
1
0
0
0
1
1
2
1
1
0
1
0
0
0
3
1
0
0
1
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
1
0
2
0
0
2
0
1
0
2
1
1
2
0
0
1
2
0
0
1
1
3
0
0
0
2
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
1
1
0
1
1
2
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
2
0
2
0
0
0
0
0
0
1
0
0
1
0
0
2
1
2
1
0
0
1
2
0
2
2
0
0
0
0
2
2
0
0
1
0
1
0
0
2
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
3
2
0
3
2
1
0
0
3
2
1
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
1
2
2
0
0
0
0
0
1
0
0
2
2
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
1
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
1
2
2
0
2
0
1
1
2
2
1
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
2
1
0
2
2
0
2
0
2
0
0
2
0
0
2
0
1
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
1
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
2
0
4
0
0
0
2
0
0
2
0
1
0
2
3
0
0
1
0
0
0
0
2
0
0
2
1
1
0
2
0
0
0
0
0
0
2
0
1
0
0
2
0
0
2
2
0
0
0
2
0
0
1
0
0
0
2
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
3
2
2
2
0
0
0
0
4
2
0
0
1
0
0
0
0
1
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
1
1
0
0
0
2
8
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
1
1
2
0
1
0
0
1
0
1
2
1
0
1
0
2
1
2
1
0
0
1
1
0
0
0
0
0
2
0
0
2
0
0
0
0
1
1
0
0
3
1
0
0
0
0
0
2
0
0
2
0
2
0
0
0
1
0
2
0
2
2
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
1
0
3
0
0
0
0
2
0
0
1
2
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
1
0
1
0
1
0
2
1
0
0
1
0
2
0
0
0
2
0
2
0
0
0
0
0
0
3
2
0
1
0
1
0
1
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
1
2
0
1
0
1
0
0
0
0
0
0
0
1
2
0
0
0
4
0
0
0
0
0
1
2
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
3
0
1
2
0
0
0
0
0
1
0
0
0
0
2
0
2
2
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
2
2
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
2
0
2
0
0
0
0
1
0
3
0
0
0
1
0
2
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
1
2
0
0
0
0
2
2
0
2
0
1
0
1
0
1
0
1
0
0
0
0
2
1
2
0
0
0
0
1
0
0
1
0
2
2
2
1
0
0
1
0
2
0
1
0
2
2
0
1
0
0
0
0
0
0
0
0
1
4
1
1
1
0
2
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
3
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
1
1
1
1
0
0
0
2
1
0
1
2
0
0
1
0
2
0
2
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
2
0
0
0
0
0
0
1
0
1
0
2
2
0
0
0
0
1
0
0
1
2
0
0
0
1
2
2
0
1
1
0
0
0
1
0
0
0
0
3
1
0
0
0
0
2
0
1
2
0
1
0
2
1
2
0
2
2
0
2
0
0
0
0
2
0
0
0
2
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
1
2
2
3
1
2
2
0
0
1
0
1
0
0
0
0
2
0
2
2
0
0
2
0
2
2
2
0
0
2
1
2
2
0
0
0
0
0
0
1
1
0
2
1
0
0
2
1
1
2
0
2
0
0
1
0
2
1
5
1
2
0
2
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
2
0
0
0
2
1
0
0
1
0
2
1
0
0
2
0
0
2
0
0
2
0
0
0
4
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
3
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
1
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
1
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
3
0
2
0
2
1
0
2
2
0
2
2
0
0
0
0
0
2
0
0
2
2
2
0
0
1
2
0
2
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
1
1
0
0
0
0
2
2
0
2
0
0
1
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
2
0
0
2
2
0
2
0
3
1
0
1
2
0
0
2
0
1
1
1
1
2
0
0
0
0
0
0
2
0
0
3
1
0
1
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
1
2
1
0
0
5
1
1
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
2
0
2
0
0
0
1
2
1
0
1
0
2
1
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
3
0
0
2
1
2
0
2
0
0
0
2
0
0
2
0
0
0
1
0
0
1
2
0
0
0
2
0
1
2
2
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
1
2
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
1
2
2
0
0
0
2
0
0
2
2
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
1
2
0
2
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
2
1
0
0
0
2
0
1
0
0
2
2
0
3
0
1
0
0
0
2
0
2
2
0
1
3
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
1
0
1
0
1
0
0
2
0
0
0
0
2
1
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
2
0
0
0
0
1
3
0
1
0
0
1
1
2
1
1
0
0
1
0
0
3
0
0
0
1
0
0
0
1
0
0
0
2
2
0
0
0
1
0
0
0
1
0
1
0
0
0
1
1
1
2
0
0
2
1
0
0
0
0
0
0
0
2
0
0
1
1
1
0
4
0
0
3
0
0
0
0
0
1
0
1
0
1
1
0
2
1
0
2
0
2
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
1
1
0
2
5
0
0
0
2
1
3
1
0
0
0
0
2
2
0
2
0
0
0
0
0
2
0
2
0
2
1
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
3
0
0
2
1
1
0
1
0
0
2
0
3
0
2
0
0
2
0
2
2
0
1
2
1
0
0
0
0
0
0
0
1
1
0
1
14
0
1
0
0
0
2
0
0
0
2
1
0
0
0
4
2
0
1
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
3
0
2
2
0
1
0
1
0
0
0
0
0
2
0
1
0
0
0
0
2
1
1
0
2
1
1
0
0
1
0
0
2
1
0
0
0
0
0
1
0
1
0
0
1
2
0
0
0
2
2
0
0
0
2
2
3
2
2
1
0
0
0
0
2
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
1
2
0
1
0
1
0
0
3
2
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
1
0
0
0
0
0
0
2
0
0
2
0
0
3
1
0
2
2
1
0
3
0
1
0
0
0
0
1
1
0
1
1
0
0
1
0
0
0
0
2
5
0
3
2
0
0
2
1
1
0
1
0
1
0
1
0
1
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
3
0
0
0
2
0
2
0
0
0
0
2
0
1
1
1
0
0
2
0
0
0
5
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
1
1
1
1
0
0
0
1
0
0
0
0
2
0
1
0
0
3
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
1
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
2
0
0
2
2
0
0
0
0
0
0
0
2
0
0
2
2
1
0
0
2
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
4
0
0
0
0
0
1
1
0
2
0
0
0
0
1
0
0
3
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
1
0
2
2
0
1
0
0
0
0
0
0
2
0
0
2
0
0
19
0
1
0
0
0
0
0
2
0
0
0
0
2
1
0
0
2
2
0
0
0
2
1
0
0
2
0
2
1
2
0
2
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
4
0
1
0
3
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
2
0
1
1
0
1
1
0
4
0
0
0
1
2
0
0
0
1
0
0
1
1
0
1
2
2
0
0
0
0
1
0
1
1
1
0
0
0
2
0
0
2
4
2
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
1
0
2
0
1
1
2
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
2
0
0
0
0
0
2
0
2
0
1
1
0
1
1
0
2
1
0
2
0
0
3
0
0
2
0
1
0
0
1
2
0
1
0
0
0
0
0
0
2
2
0
2
0
0
0
0
3
0
0
1
1
0
0
0
0
0
2
0
0
2
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
2
5
2
0
2
3
0
0
0
0
0
1
1
1
0
1
1
0
0
0
2
2
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
1
1
0
1
0
1
0
0
2
0
2
1
2
1
0
1
0
0
1
2
1
0
0
1
0
0
0
0
1
3
0
1
0
0
0
0
1
0
0
0
0
0
2
0
1
3
0
2
0
0
0
0
2
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
2
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
1
0
2
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
1
1
0
1
2
0
0
0
2
2
1
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
1
0
2
0
2
0
0
2
0
1
1
0
0
0
0
0
1
0
0
1
0
0
2
0
2
2
0
2
0
0
0
0
0
0
0
0
1
4
2
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
2
2
2
0
2
2
0
0
1
2
1
0
1
1
0
1
0
0
0
0
0
0
0
3
0
0
0
2
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
2
0
3
0
2
1
0
0
2
2
0
0
0
0
0
1
0
1
1
0
0
0
2
1
0
0
0
1
0
0
0
1
2
2
0
0
1
1
0
1
2
2
0
0
0
0
0
0
2
0
0
0
0
3
0
1
0
0
0
2
0
0
1
2
1
0
1
0
1
0
0
4
0
0
0
0
0
1
0
2
1
0
0
0
2
0
0
0
1
2
0
1
0
0
0
0
0
1
2
0
1
1
2
1
2
0
2
0
0
2
0
0
2
0
1
0
0
0
1
0
0
0
0
0
3
0
1
1
0
1
0
0
1
0
1
0
0
0
0
0
0
2
2
0
0
0
2
0
0
1
0
0
1
0
4
1
1
0
0
1
1
2
0
2
1
0
2
0
2
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
1
0
2
1
0
2
0
2
2
0
1
2
0
0
0
0
0
6
0
0
2
0
1
1
0
0
0
1
2
1
1
1
2
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
3
2
0
0
1
2
0
0
3
0
1
2
0
0
2
0
0
0
0
0
0
2
1
1
1
0
1
0
2
0
1
0
0
0
0
0
0
2
1
3
1
0
0
2
0
1
1
2
1
0
2
1
2
0
1
0
0
0
3
0
0
1
1
0
0
0
0
0
0
0
1
1
0
1
0
2
2
0
1
0
2
0
0
1
0
0
0
1
0
0
1
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
2
1
0
2
0
0
0
0
2
0
0
2
2
0
1
0
0
0
0
0
1
0
1
0
0
0
2
0
3
2
0
2
3
0
0
1
1
2
0
0
0
0
0
0
0
0
0
3
0
1
2
0
2
0
0
0
2
1
1
0
0
0
0
1
1
0
0
0
0
1
1
0
2
0
0
0
0
3
0
0
0
0
0
1
1
0
0
0
1
0
0
2
0
2
2
2
0
1
0
2
0
0
2
0
0
0
2
1
0
2
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
2
0
3
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
2
1
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
1
3
2
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
2
0
0
0
1
1
3
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
1
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
5
0
0
1
2
0
0
1
0
1
1
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
2
2
0
0
2
1
0
1
0
0
0
0
0
2
2
0
1
1
0
0
2
0
0
0
1
0
0
1
0
2
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
7
0
1
2
2
2
0
0
0
1
0
0
2
0
0
0
2
0
1
1
0
1
0
0
0
0
2
0
0
3
0
2
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
1
0
2
0
1
1
0
0
0
0
0
2
0
0
0
2
0
1
4
0
0
2
0
0
0
1
0
1
1
0
1
1
0
0
0
0
0
0
0
1
0
0
2
0
0
2
1
2
0
0
2
2
1
0
0
2
0
1
1
0
0
0
0
1
2
0
1
0
2
0
0
0
0
0
0
2
0
1
2
1
1
0
0
0
1
0
0
0
2
0
0
0
2
0
2
1
1
1
0
0
0
0
0
1
0
0
0
2
0
0
0
1
1
0
2
3
2
0
0
0
0
1
2
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
1
0
0
0
0
0
0
2
0
1
0
2
0
1
2
0
0
2
0
2
0
2
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
1
1
3
0
1
0
1
0
0
0
2
0
0
1
0
2
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
1
1
1
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
1
0
2
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
2
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
1
0
0
1
2
0
0
0
0
0
1
0
2
0
1
0
0
2
0
0
2
0
2
1
2
1
0
0
0
0
2
0
0
9
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
1
0
1
0
1
1
2
0
0
0
0
1
0
2
2
0
0
0
0
0
0
2
0
2
0
2
1
0
2
0
1
0
1
0
1
0
0
0
2
1
1
0
0
0
0
0
1
0
0
2
2
0
0
1
1
0
0
0
4
2
0
0
0
0
0
2
0
0
0
1
0
1
0
2
1
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
2
3
0
1
0
0
2
0
1
1
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
2
0
2
0
0
0
0
1
0
0
2
1
0
2
0
0
0
0
1
1
0
0
1
2
0
0
0
0
3
1
0
0
0
2
0
0
0
0
0
2
1
0
1
1
1
0
2
2
0
0
0
0
1
0
2
0
0
1
0
1
0
0
2
0
0
2
1
0
1
2
0
0
0
0
3
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
2
2
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
1
1
2
3
2
0
0
2
0
1
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
1
1
0
0
2
0
2
0
2
0
0
2
1
0
2
0
0
2
0
0
1
0
0
0
1
1
0
1
0
0
1
0
2
2
1
2
1
1
0
0
1
0
0
0
1
1
2
0
0
0
2
0
0
2
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
1
0
0
0
0
0
2
0
2
0
1
0
1
0
0
1
1
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
1
2
1
1
0
1
0
0
1
1
1
0
1
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
1
2
2
2
0
0
2
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
3
1
0
0
0
0
0
0
0
0
2
0
0
2
2
0
2
0
0
0
0
0
1
0
2
1
0
0
0
0
0
1
0
0
2
1
0
0
0
1
2
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
2
0
0
0
1
0
0
2
0
0
2
1
1
1
1
0
0
0
2
2
2
2
0
1
0
0
0
2
0
1
0
2
0
0
1
0
1
0
0
0
0
1
2
3
0
0
0
2
0
0
3
2
0
1
0
0
0
0
0
3
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
2
0
0
0
0
2
2
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
2
0
1
0
0
1
0
2
0
0
2
2
0
0
2
0
0
2
0
0
2
0
0
0
1
0
6
0
0
1
1
1
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
1
3
0
2
0
2
1
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
2
0
1
1
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
2
2
2
1
0
2
0
2
2
0
0
1
1
1
1
0
3
0
2
0
0
0
1
1
0
1
1
0
0
0
2
0
0
0
0
2
2
0
2
0
0
0
0
0
2
1
0
0
1
0
0
0
2
0
0
0
0
0
1
0
2
2
0
0
0
2
0
0
2
0
2
1
0
0
2
0
0
2
0
0
2
0
0
1
1
0
2
2
0
0
2
3
1
0
1
2
0
7
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
1
2
2
0
1
0
0
0
1
0
0
1
1
2
1
0
0
0
0
0
1
0
0
2
2
0
1
0
0
0
0
1
0
0
1
1
1
2
3
0
0
0
1
0
1
3
2
2
2
4
1
0
0
0
1
0
2
0
0
0
1
1
1
0
0
1
2
3
0
0
0
1
2
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
1
0
0
0
2
1
1
1
0
0
0
1
0
0
0
1
2
1
2
1
0
1
1
1
0
2
0
0
0
0
1
0
0
2
1
0
1
0
2
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
1
1
0
0
0
0
2
0
1
1
1
2
1
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
2
2
0
0
1
1
1
1
2
0
1
0
0
0
2
0
1
0
1
1
1
0
0
0
0
0
0
0
1
2
0
0
0
1
0
1
0
0
0
2
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
2
0
2
0
0
1
0
0
0
2
0
1
2
0
2
0
0
1
2
2
0
0
1
1
0
0
1
0
0
1
0
2
0
0
1
0
0
0
0
2
1
0
1
0
0
1
0
0
1
1
0
2
0
0
0
0
1
0
2
2
0
2
0
0
3
0
0
0
0
0
2
0
0
0
1
3
1
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
2
2
0
2
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
2
0
2
0
4
0
1
0
2
0
0
0
0
0
0
0
0
1
1
0
2
1
1
1
0
0
0
1
2
2
2
2
0
2
1
1
2
0
2
2
1
0
2
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
3
0
0
1
2
1
1
3
1
0
0
2
0
2
0
1
0
1
0
0
2
0
0
0
1
0
1
2
1
1
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
3
0
1
0
0
2
1
0
0
0
0
0
0
2
1
0
0
2
0
2
0
1
0
1
0
0
2
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
1
0
0
2
2
2
0
0
1
1
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
2
2
0
1
0
1
0
0
1
0
3
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
1
2
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
2
2
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
1
1
0
2
0
1
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
2
0
2
2
0
2
1
0
2
2
0
1
2
0
0
2
1
0
0
0
0
2
1
0
0
0
0
2
1
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
1
0
1
1
2
0
0
0
0
1
2
2
0
1
0
0
2
0
1
1
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
1
2
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
4
2
3
0
1
0
0
0
3
0
0
2
1
0
0
2
0
0
0
1
0
0
0
0
0
0
2
2
1
0
0
2
1
0
2
1
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
3
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
1
1
0
0
1
2
0
0
0
2
2
0
0
2
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
2
0
2
0
1
1
0
2
0
0
0
1
0
1
2
1
3
0
1
0
0
2
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
1
1
1
0
2
0
1
2
0
3
0
0
0
0
0
2
0
0
0
1
0
2
2
0
1
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
2
0
2
0
1
0
0
0
1
0
1
0
2
0
0
1
0
1
1
0
1
0
0
0
0
2
2
0
0
0
0
5
0
1
0
0
1
0
2
1
2
1
0
3
0
0
1
1
1
0
2
0
0
0
0
2
0
2
0
2
1
2
2
0
0
1
1
0
2
2
2
0
0
0
0
1
0
0
0
1
0
0
0
2
1
6
0
2
0
0
1
1
0
0
2
3
1
2
1
0
0
0
1
0
0
0
1
0
1
1
0
1
0
2
0
2
0
0
0
2
1
0
1
1
0
0
0
0
0
0
0
1
2
0
0
0
0
1
2
0
1
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
1
2
2
0
0
0
3
0
0
2
0
2
0
0
0
1
0
1
0
0
0
0
1
0
0
0
2
0
1
0
1
1
2
0
1
0
0
0
1
0
0
0
0
0
0
2
0
2
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
1
1
2
2
0
0
0
2
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
1
0
0
0
1
0
1
2
3
0
0
3
0
0
0
0
0
0
0
1
0
1
2
0
1
0
1
0
2
2
2
3
0
0
0
0
0
2
0
0
1
0
2
0
0
0
2
0
0
2
0
0
2
1
2
1
0
0
1
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
1
0
2
4
2
0
2
2
0
0
3
0
0
2
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
1
0
1
2
0
0
0
1
0
0
0
0
0
0
0
2
3
2
1
0
0
0
1
0
1
2
1
2
0
1
0
0
0
0
2
0
2
0
2
1
0
1
0
2
0
0
0
2
0
2
1
0
0
0
0
0
0
2
0
2
0
0
1
2
0
0
0
0
0
0
0
3
0
6
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
1
2
2
1
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
2
1
0
0
1
2
2
0
1
1
1
1
0
2
1
0
0
2
1
1
0
0
0
0
2
2
0
0
1
0
2
1
1
0
0
0
0
1
1
0
1
0
0
0
1
0
2
3
0
0
1
0
0
0
0
0
2
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
2
0
1
0
0
3
0
0
1
1
2
0
2
0
1
0
1
1
2
2
0
0
2
0
0
2
0
2
0
1
0
0
0
2
1
0
1
5
1
0
0
0
2
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
1
3
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
2
1
0
0
2
2
1
2
0
0
2
0
0
0
2
1
0
1
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
1
1
0
2
2
1
0
2
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
1
2
0
0
1
0
0
0
1
1
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
2
1
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
1
1
1
0
2
0
1
0
0
1
0
1
0
1
2
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
1
0
0
1
0
0
0
0
3
0
0
0
0
1
0
3
0
0
1
0
0
0
0
1
0
3
2
0
0
2
0
2
3
0
0
0
2
0
2
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
8
0
2
0
2
0
0
3
1
4
0
2
0
0
0
0
0
1
3
0
0
0
0
2
1
1
0
0
0
2
0
0
0
0
2
0
2
0
0
0
1
0
1
0
1
0
1
2
0
0
1
0
2
1
0
1
1
0
2
0
0
0
2
2
2
1
1
2
0
2
0
0
0
2
0
0
0
0
0
0
0
1
1
2
0
0
1
0
0
0
1
0
0
2
0
1
1
0
0
2
0
0
0
2
1
3
2
0
0
0
1
0
2
0
0
0
0
0
2
0
2
0
1
0
0
1
1
3
0
0
0
0
0
1
0
1
2
0
0
1
0
0
0
0
2
2
0
1
2
0
0
1
1
2
0
0
2
0
0
1
0
0
1
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
2
0
0
2
1
0
0
2
2
4
2
0
1
0
1
2
0
0
2
1
0
0
0
0
0
0
0
0
1
1
2
1
2
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
1
0
2
1
0
0
0
0
0
2
0
0
0
0
2
0
0
1
5
0
0
0
2
0
0
2
0
1
2
0
1
0
2
1
0
1
1
1
0
0
2
2
2
0
0
0
0
0
0
0
1
3
0
0
0
1
1
2
0
0
0
0
0
1
0
0
0
2
2
0
0
2
8
0
2
0
0
2
0
0
1
1
1
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
2
1
0
0
0
0
1
0
2
0
1
0
2
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
1
1
0
2
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
2
0
0
3
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
2
2
1
0
0
2
1
0
1
0
0
0
0
0
1
0
1
0
1
1
0
1
0
0
0
1
2
2
1
0
1
0
0
2
0
0
0
0
0
3
0
0
0
2
2
2
0
1
9
1
1
0
2
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
2
1
2
0
3
2
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
2
0
0
2
0
2
0
0
0
0
1
1
0
0
1
2
0
0
1
3
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
1
0
0
0
1
0
0
1
1
0
0
0
2
2
0
0
0
0
3
0
1
0
0
0
2
2
0
0
0
2
0
1
0
0
0
0
3
0
0
0
0
0
1
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
1
2
0
2
0
0
0
1
1
0
2
0
0
0
0
0
0
0
2
2
0
1
0
1
0
2
0
2
0
0
2
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
3
1
0
0
0
0
1
1
2
0
1
1
0
0
0
1
1
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
1
2
1
0
0
1
0
0
0
0
0
1
0
2
0
0
1
0
0
2
2
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
2
1
2
2
0
0
0
1
0
0
1
0
0
2
2
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
1
0
0
0
2
0
0
0
0
1
0
2
1
1
0
2
0
0
2
1
0
0
0
1
2
2
0
0
0
1
0
0
1
0
0
2
1
0
0
0
2
0
1
0
2
2
0
0
1
1
3
0
0
0
0
0
2
0
0
0
1
2
1
0
0
1
0
1
0
0
0
0
0
2
1
0
2
0
1
1
0
0
0
0
0
0
0
0
2
0
2
1
1
0
1
2
1
0
0
2
2
1
0
0
0
2
0
0
0
0
0
2
0
2
0
0
3
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
2
1
2
2
0
0
0
0
2
0
0
0
0
0
0
1
1
3
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
2
0
3
0
2
0
1
2
1
1
0
0
1
2
0
0
0
2
0
0
1
0
0
0
1
2
0
0
0
4
0
2
0
0
0
0
2
2
1
0
0
2
0
0
1
0
1
2
0
0
0
0
0
0
0
0
2
1
4
0
0
1
0
0
0
0
0
0
0
0
1
0
3
0
1
0
0
0
2
0
1
1
0
0
0
0
1
0
2
2
0
1
0
0
1
0
0
0
1
0
0
0
1
0
1
1
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
1
0
0
1
0
0
0
0
1
0
0
0
0
2
2
1
1
1
2
0
0
1
1
0
0
0
0
2
0
1
0
2
1
0
1
0
2
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
1
0
0
0
2
0
1
0
1
1
0
2
0
0
1
2
0
0
1
0
1
2
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
2
0
2
0
2
0
0
0
0
0
0
0
3
1
2
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
1
2
2
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
2
0
0
0
0
2
1
0
0
2
2
0
1
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
1
0
1
1
0
2
1
1
1
0
0
1
0
0
0
1
0
0
1
2
0
1
2
0
0
0
1
2
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
3
2
3
0
0
0
1
1
1
0
0
0
1
0
0
2
2
0
0
0
0
0
2
0
0
1
4
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
1
2
0
0
1
0
0
0
0
0
3
0
0
3
0
1
0
0
0
0
0
1
0
0
2
1
0
1
0
1
0
2
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
2
3
2
0
2
0
2
0
2
0
0
0
1
0
0
0
1
2
0
0
2
0
0
1
0
0
0
2
0
2
0
1
0
0
0
0
2
3
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
1
2
1
0
0
1
0
0
0
2
0
0
0
2
0
4
0
0
0
0
1
1
0
0
1
0
1
0
0
0
1
0
1
2
3
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
2
2
0
0
1
0
2
0
0
2
0
2
0
0
0
0
0
0
2
0
1
0
2
0
3
1
2
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
8
2
0
0
0
3
0
0
3
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
2
1
0
2
0
0
2
0
0
3
0
0
1
1
0
0
0
2
0
0
0
1
2
1
0
0
0
1
0
0
0
2
0
2
0
0
0
2
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
2
0
0
2
0
1
0
0
0
0
1
0
2
1
1
2
0
0
1
0
0
0
4
1
0
1
0
0
0
1
2
2
0
2
0
1
0
0
2
1
0
0
2
2
2
0
0
0
2
0
0
0
2
1
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
6
0
1
0
0
0
0
1
1
0
1
2
0
0
1
0
0
1
0
1
0
0
1
1
1
0
0
0
1
2
0
0
0
0
1
0
0
1
2
0
3
0
0
0
1
0
0
1
0
1
0
0
2
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
1
2
0
0
1
2
6
0
0
0
2
1
0
2
0
1
1
0
1
0
0
0
0
0
1
2
2
0
2
1
2
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
2
1
0
1
0
0
0
0
1
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
1
2
0
1
0
0
0
1
0
0
0
0
0
0
2
0
3
1
1
0
0
0
4
2
0
0
0
0
1
0
0
1
0
0
0
2
2
1
2
1
2
1
0
1
2
1
0
1
2
0
0
1
0
0
2
1
2
2
0
0
0
0
0
0
1
1
0
1
0
2
0
1
0
1
1
0
1
0
1
0
0
1
0
2
0
0
1
0
3
0
0
2
0
1
0
0
0
0
0
0
0
1
2
2
1
0
0
2
2
0
4
2
1
0
0
1
1
0
2
1
1
2
0
0
0
0
0
1
2
2
0
1
1
0
0
2
0
1
1
0
0
0
0
2
1
0
1
2
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
2
0
0
1
0
0
1
0
0
1
0
1
2
0
2
1
0
1
0
0
2
0
0
2
2
1
0
2
0
0
0
0
2
2
0
1
1
0
0
0
1
0
2
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
1
1
2
0
1
1
1
2
2
0
0
0
0
0
0
2
1
2
0
0
0
0
0
1
2
0
0
0
1
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
1
0
0
2
2
1
0
0
1
0
2
0
1
0
0
0
2
2
0
0
0
0
0
0
3
0
0
1
0
0
2
4
2
0
0
0
2
0
0
0
0
1
2
0
0
1
0
1
0
2
1
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
1
1
0
1
0
2
0
0
2
0
0
4
1
1
2
0
2
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
1
1
1
0
1
0
0
0
0
2
1
0
2
0
3
2
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
1
1
0
1
1
2
1
0
0
0
0
1
1
2
2
0
2
0
2
0
1
1
1
0
1
2
2
1
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
2
2
0
0
1
0
0
0
1
2
0
0
0
2
0
1
2
0
0
0
0
0
0
0
3
1
0
0
2
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
2
0
0
0
2
0
0
0
1
1
0
2
0
0
1
2
0
2
0
2
1
0
4
2
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
3
0
2
2
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
1
1
0
2
0
1
2
0
2
1
0
0
2
0
1
0
2
2
0
1
1
2
2
0
0
0
1
2
0
0
0
4
0
3
0
0
0
0
0
1
2
2
0
0
1
0
2
1
0
2
0
0
2
1
0
0
2
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
2
0
0
0
1
2
0
0
0
1
0
3
2
0
0
0
0
0
0
2
0
0
1
0
0
1
0
2
2
0
0
1
0
2
1
0
0
0
0
0
0
0
3
1
0
0
0
1
2
1
2
1
1
2
0
0
2
0
3
1
1
0
0
2
0
0
0
1
0
0
0
0
0
2
0
1
0
1
0
0
1
0
1
0
0
0
0
0
1
1
0
1
2
0
0
1
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
2
2
1
0
0
1
0
1
0
0
2
0
2
0
0
2
0
0
1
0
0
0
1
0
0
3
0
2
2
2
0
0
0
2
1
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
2
2
2
0
0
2
0
0
0
2
2
0
0
1
3
0
1
1
2
1
2
2
0
0
0
2
1
0
0
2
2
1
0
0
0
0
2
1
0
0
1
1
0
0
0
5
0
1
0
0
1
2
2
0
2
2
0
3
1
2
1
0
2
0
2
1
0
2
0
2
0
0
0
1
1
2
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
4
0
0
0
1
0
1
2
2
0
0
0
1
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
2
0
2
2
0
0
0
0
0
0
0
2
0
0
1
2
0
0
1
0
0
1
2
0
0
0
6
0
1
0
0
3
0
0
1
1
0
0
0
0
2
0
0
0
0
3
0
1
0
0
0
0
0
0
1
0
1
1
1
0
0
2
0
0
0
0
0
0
1
0
2
1
2
0
1
0
0
2
0
1
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
1
2
0
0
2
2
0
2
0
2
0
0
1
2
1
0
0
0
0
0
0
0
1
0
0
0
1
2
0
2
1
1
0
0
0
0
1
1
2
2
0
0
0
1
0
0
0
0
2
3
1
0
0
0
1
1
1
1
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
1
2
0
2
0
0
0
0
0
1
2
0
0
2
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
2
0
3
0
1
1
2
0
2
1
2
0
0
2
0
0
0
0
0
0
0
14
0
7
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
2
1
1
0
0
0
0
1
0
0
0
2
2
0
0
0
0
1
4
2
2
0
1
0
0
0
0
1
2
1
0
0
0
0
2
0
0
2
0
0
1
0
0
1
0
0
0
2
2
2
1
0
0
0
0
3
0
0
1
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
2
1
0
0
2
0
2
1
2
1
0
2
0
0
0
0
1
0
1
0
1
0
0
0
1
1
2
0
2
1
0
2
0
2
0
0
1
1
1
0
3
0
0
0
0
0
0
4
0
0
2
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
6
0
0
0
2
0
0
3
11
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
1
0
0
2
0
0
1
1
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
3
1
0
0
1
4
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
2
1
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
1
1
0
2
0
0
2
0
2
0
2
0
0
2
0
1
0
2
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
1
2
1
0
2
0
2
0
1
1
2
2
0
2
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
1
2
0
0
0
0
2
0
2
0
2
0
0
2
2
0
0
0
0
0
0
1
0
0
0
2
0
0
1
2
2
0
2
1
0
0
1
1
1
1
1
0
0
0
0
0
0
2
0
1
3
0
1
1
0
0
2
0
0
0
0
1
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
3
1
0
2
0
0
1
0
0
0
2
1
0
0
2
2
1
1
0
2
0
1
0
0
0
0
0
0
2
0
1
2
0
4
0
0
0
1
1
0
1
0
0
1
1
1
2
0
2
0
2
0
1
0
0
0
2
0
1
1
1
0
0
0
0
0
0
1
5
0
2
0
0
1
0
0
1
1
0
0
0
1
0
2
1
0
2
1
2
1
0
0
0
0
0
2
2
0
0
3
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
1
0
1
0
2
0
0
0
1
1
0
2
0
0
0
2
1
0
0
0
0
0
0
2
0
2
1
0
0
0
2
0
0
0
1
0
0
2
1
1
0
0
2
0
0
2
0
0
1
3
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
2
0
0
1
0
0
1
0
0
1
0
0
0
0
0
2
0
2
0
1
2
0
0
0
0
0
0
0
0
2
0
1
1
0
2
2
0
0
1
0
2
1
3
0
2
0
0
0
0
0
0
2
1
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
1
2
0
8
0
0
0
0
0
2
3
0
2
0
1
2
2
0
1
0
0
0
0
0
2
2
2
0
2
0
0
0
2
0
0
0
2
0
2
0
0
0
2
0
0
1
0
0
2
0
0
0
0
2
0
2
0
2
0
1
2
0
2
1
2
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
1
2
2
2
0
0
2
0
0
0
1
0
1
0
2
0
0
2
0
2
0
0
0
0
2
0
0
0
1
0
0
2
1
2
1
2
2
0
1
2
1
0
0
1
0
0
0
2
0
0
1
2
0
0
0
1
1
0
0
1
0
0
0
2
0
1
1
2
0
0
0
0
0
0
0
1
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
1
1
0
1
1
0
0
0
0
0
2
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
2
3
0
2
0
2
0
1
1
0
0
0
3
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
6
0
0
3
0
1
0
0
0
0
0
0
0
1
0
1
2
2
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
1
3
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
2
1
0
0
0
0
0
3
0
0
0
0
1
1
3
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
2
2
0
2
0
0
1
0
0
0
2
1
4
1
2
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
1
0
3
2
0
0
0
0
2
0
1
2
0
0
0
2
0
0
0
0
0
2
0
1
0
2
0
1
2
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
1
0
2
1
1
0
0
0
2
2
5
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
2
0
0
0
0
0
2
0
1
0
0
2
0
2
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
1
1
0
0
1
1
1
0
1
0
0
0
0
3
0
0
2
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
2
0
0
2
1
1
1
0
0
0
0
2
6
2
0
1
3
0
0
0
1
0
0
0
0
0
0
0
2
1
0
2
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
2
0
0
0
2
0
1
0
1
2
1
1
0
0
0
3
0
0
2
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
3
0
1
0
2
0
0
2
0
0
0
2
1
0
0
1
3
0
0
0
0
1
0
1
0
0
4
0
4
1
2
0
2
0
0
0
2
0
2
0
1
1
0
0
0
0
0
0
0
0
2
2
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
1
0
2
0
0
0
1
0
2
0
0
4
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
1
0
0
0
3
0
0
3
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
9
2
2
2
1
1
0
0
0
0
0
0
0
0
1
0
3
0
1
1
1
2
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
1
0
1
0
1
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
2
1
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
1
1
0
0
1
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
2
0
0
1
1
0
0
0
1
0
0
0
0
0
2
2
1
1
0
0
0
1
2
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
1
1
2
1
1
0
1
1
0
0
2
0
2
2
2
0
0
0
0
1
0
2
0
0
0
0
0
2
0
2
0
0
0
2
1
1
0
0
8
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
2
0
2
0
0
2
2
2
0
2
0
2
3
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
1
0
0
0
0
1
2
0
1
2
1
0
2
0
0
1
0
1
0
2
0
1
2
1
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
1
0
2
0
0
0
2
0
0
0
0
0
1
2
0
1
2
0
2
0
0
2
0
1
0
0
0
0
0
2
2
0
0
2
0
2
1
1
1
2
1
0
0
0
0
1
0
1
0
0
0
0
1
2
1
1
1
0
0
0
5
1
0
0
0
3
0
0
1
0
0
1
0
0
0
0
0
0
1
0
3
0
0
0
0
0
1
0
0
0
0
0
1
2
1
0
0
1
0
3
1
0
0
2
0
0
0
0
0
2
2
3
0
0
0
2
0
2
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
1
0
0
0
1
2
0
2
2
0
0
0
1
1
0
0
0
0
0
2
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
2
1
1
2
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
2
0
2
2
1
2
0
0
1
0
0
0
0
0
0
1
0
2
0
0
3
1
1
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
2
0
0
0
0
3
0
1
2
2
0
2
0
2
0
3
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
4
2
0
0
0
1
0
0
1
0
1
0
1
0
2
1
0
0
0
0
0
0
0
0
2
1
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
1
1
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
1
1
0
0
2
0
2
0
1
0
0
3
2
2
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
1
0
0
0
2
0
1
0
0
1
1
0
0
0
0
1
1
0
2
0
1
0
2
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
2
0
0
0
2
0
0
1
2
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
2
0
0
2
0
0
1
2
2
0
0
1
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
1
2
0
2
1
3
0
0
0
0
0
0
0
0
1
2
1
0
1
2
0
0
0
1
2
0
1
2
1
0
0
3
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
2
0
0
2
2
0
0
2
0
2
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
2
1
1
0
2
1
0
0
0
0
1
0
0
0
0
1
2
1
0
1
0
1
0
0
0
2
0
2
2
0
1
2
0
2
0
2
0
0
0
1
2
0
0
0
4
0
2
1
2
1
0
0
1
2
0
2
0
3
0
0
0
1
0
2
0
0
0
0
1
2
0
0
0
0
0
2
0
0
2
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
1
0
1
0
2
1
1
0
2
0
0
1
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
8
3
0
2
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
2
2
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
2
2
0
1
0
4
1
0
0
0
0
0
0
3
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
3
0
2
0
0
3
0
1
1
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
1
1
2
0
0
0
2
1
3
1
2
0
0
1
1
0
1
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
2
1
0
0
1
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
3
1
1
2
1
0
0
1
0
2
0
2
4
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
2
0
0
0
0
2
1
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
1
1
1
2
0
0
0
1
0
2
0
0
2
2
0
0
1
3
0
0
2
0
2
3
1
1
0
0
0
2
0
1
2
0
0
1
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
1
0
2
0
1
1
3
2
0
0
0
0
1
0
0
0
0
2
0
2
0
1
2
0
0
0
1
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
3
0
1
0
0
1
0
0
0
0
1
0
0
1
0
1
0
2
0
1
1
0
0
1
0
1
1
0
0
0
0
0
2
0
2
0
1
0
1
0
0
1
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
2
0
0
0
1
0
0
1
2
0
0
0
0
0
0
1
0
1
0
1
1
2
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
1
2
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
1
2
0
3
1
0
0
1
0
0
0
0
0
0
0
0
2
1
1
1
0
0
0
0
2
0
0
2
0
1
2
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
3
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
1
0
0
2
1
0
0
2
1
0
0
0
2
0
4
2
1
1
2
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
2
1
0
0
2
1
0
2
2
2
0
1
3
0
0
0
0
1
0
0
1
0
0
2
1
0
0
0
1
0
0
0
0
2
2
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
5
1
2
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
2
1
0
0
0
1
2
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
1
2
0
0
2
0
0
0
0
2
0
0
1
0
1
0
1
1
2
1
0
1
0
1
0
0
0
0
0
2
1
2
0
0
1
2
2
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
1
2
0
0
2
0
1
0
2
1
0
2
0
0
0
0
2
2
1
0
0
0
2
0
0
0
1
0
0
0
0
1
1
0
0
0
2
0
2
0
0
2
1
0
0
2
1
0
0
0
0
0
0
1
0
0
2
0
1
0
1
0
2
0
1
0
2
2
1
0
0
0
2
2
2
2
0
1
1
0
0
0
0
3
1
0
0
2
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
2
0
2
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
1
0
3
0
0
3
0
2
0
0
0
0
0
1
0
0
1
2
0
2
0
1
0
2
0
2
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
1
2
0
2
0
2
2
0
3
0
2
0
0
0
0
0
0
0
1
0
1
0
1
0
0
2
0
2
0
2
2
0
1
1
1
0
1
0
0
0
0
0
2
0
0
0
0
1
0
3
0
0
1
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
1
2
2
2
0
2
0
0
0
0
0
2
0
0
0
2
2
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
4
0
1
0
0
2
1
2
2
2
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
1
0
1
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
2
1
0
0
2
1
0
2
0
0
0
0
2
2
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
2
2
1
1
0
1
1
2
0
0
0
0
0
2
3
0
0
0
1
2
0
2
0
0
0
2
1
2
0
0
0
0
0
2
2
2
0
0
0
1
0
1
0
2
1
1
0
1
0
1
0
0
0
0
0
0
0
0
2
2
2
1
0
0
0
0
0
2
0
0
2
1
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
2
0
2
2
0
0
0
1
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
1
1
0
0
1
0
3
2
0
0
2
2
0
1
2
0
0
2
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
1
0
2
0
0
1
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
1
1
1
1
0
1
0
0
1
0
0
0
0
0
2
0
4
1
1
0
0
2
0
0
0
6
0
0
0
0
0
0
1
2
2
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
2
0
1
0
0
2
0
0
2
0
0
1
2
0
0
2
0
1
1
1
0
2
0
0
0
0
0
1
0
0
1
1
1
0
0
2
0
0
0
1
0
0
0
0
0
2
2
1
0
0
1
2
0
0
0
0
1
0
0
2
0
2
0
0
0
2
0
0
2
0
0
0
1
0
2
0
0
0
1
0
2
0
3
0
0
1
1
1
0
1
0
1
2
3
0
0
1
0
0
0
0
0
0
0
2
1
0
2
1
1
0
1
1
0
0
0
1
0
2
2
3
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
2
0
0
2
0
1
0
1
2
2
1
0
0
0
1
0
0
0
0
0
1
2
4
0
0
0
2
0
2
0
0
0
0
1
0
2
1
0
1
0
0
0
0
0
0
0
2
0
1
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
2
3
2
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
1
1
0
0
2
0
0
1
0
0
2
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
1
1
2
1
2
0
0
2
1
1
1
2
0
0
2
0
2
0
0
2
0
2
0
2
0
0
0
0
2
1
1
0
0
1
2
0
2
1
1
2
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
2
0
0
2
1
1
0
2
0
2
2
2
0
0
1
0
0
0
0
1
1
1
2
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
3
1
2
1
1
0
0
2
0
2
2
0
0
1
2
0
0
0
0
1
0
0
0
2
0
0
1
1
0
0
0
2
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
1
2
0
0
0
6
0
1
2
0
2
0
2
0
0
0
0
0
2
1
2
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
1
0
0
0
2
0
0
2
1
0
0
2
1
0
1
0
2
2
0
0
1
0
0
2
0
0
1
0
4
2
0
0
0
0
0
1
0
0
1
1
0
0
2
2
3
1
2
0
0
1
0
0
1
1
1
0
0
0
2
0
1
0
0
0
2
2
2
0
1
1
0
0
0
0
0
0
0
2
2
0
0
0
0
2
2
0
0
0
0
2
0
1
1
1
0
0
2
1
0
0
1
2
1
0
0
0
2
1
0
0
3
3
0
2
0
0
0
2
0
3
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
3
2
1
0
0
0
0
0
1
2
1
0
0
0
0
0
0
1
2
2
2
2
0
1
0
0
3
0
3
0
0
0
2
0
2
0
0
2
0
0
2
0
0
0
0
0
1
1
0
2
0
0
1
1
0
0
0
2
2
2
0
0
0
3
0
0
2
0
0
0
1
0
1
3
1
0
0
2
0
0
1
0
2
1
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
2
0
0
0
0
0
1
2
0
0
0
2
2
2
1
0
0
2
1
2
0
0
1
0
0
0
2
2
0
0
2
0
1
0
1
2
1
0
0
0
0
0
1
0
0
2
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
1
1
0
1
2
0
0
0
0
0
0
1
0
2
0
0
0
1
2
0
3
2
2
0
3
1
0
2
2
0
0
0
0
0
2
0
3
2
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
2
1
0
0
0
2
0
2
0
2
2
0
0
0
2
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
2
2
0
0
0
1
0
0
0
0
0
2
1
0
0
0
1
0
0
0
2
0
2
1
0
2
0
0
0
2
0
1
0
4
0
0
2
0
1
0
2
0
0
1
1
0
0
1
0
0
1
1
1
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
2
2
1
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
2
0
0
4
0
0
1
2
1
0
0
0
1
0
0
0
0
2
1
0
0
0
3
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
5
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
1
0
1
0
0
0
0
2
1
0
1
0
0
0
0
2
0
2
0
0
0
2
0
0
0
3
0
2
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
1
2
0
2
2
2
0
0
0
1
0
0
0
0
0
0
2
1
0
0
1
1
0
2
2
0
0
1
0
0
2
1
0
0
1
0
1
0
0
3
0
2
0
0
0
2
0
0
2
0
0
0
0
0
3
0
2
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
3
1
3
0
2
2
0
2
0
1
1
2
0
0
0
2
0
1
2
0
0
0
1
1
2
1
1
1
0
1
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
1
0
2
2
0
0
0
0
0
0
1
1
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
1
0
0
0
0
1
0
2
1
1
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
2
3
0
1
0
0
0
0
2
1
1
0
0
2
2
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
3
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
1
0
1
1
0
0
1
2
0
0
1
1
0
0
3
2
0
0
0
0
0
1
0
0
2
2
0
0
0
2
0
2
2
0
1
1
0
0
0
1
2
0
0
0
2
0
0
0
1
0
0
0
0
2
2
0
0
0
6
2
3
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
2
0
3
0
0
0
0
1
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
2
1
0
0
0
0
1
0
1
2
2
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
2
0
0
0
1
1
0
0
2
2
0
1
0
0
2
2
1
0
3
1
0
2
0
0
5
0
0
2
2
0
2
1
1
0
0
0
0
1
4
0
0
1
2
1
2
1
0
0
0
0
0
0
1
0
2
0
2
2
2
0
0
2
2
0
0
0
0
0
1
0
1
2
0
0
2
0
3
0
1
2
0
0
0
0
0
1
0
0
0
0
2
0
0
2
1
0
0
0
2
2
3
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
2
0
1
0
0
1
4
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
1
0
1
0
2
0
0
2
1
4
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
2
1
0
0
0
0
0
0
0
0
1
1
0
3
0
0
0
2
0
2
0
0
0
0
0
1
0
0
1
0
1
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
1
0
1
2
0
0
0
0
1
1
1
2
1
0
1
0
0
2
3
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
2
2
0
0
3
2
0
0
1
0
1
0
0
0
2
1
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
1
2
0
2
0
0
1
1
0
0
1
0
0
0
0
0
0
2
0
1
0
1
2
0
2
0
4
0
2
2
1
0
0
0
1
0
1
0
1
1
0
0
1
6
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
1
0
2
0
0
0
0
0
1
0
1
1
0
2
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
1
1
2
1
0
2
2
1
0
0
1
5
0
0
0
0
5
0
0
0
1
0
0
0
0
0
0
1
0
1
0
2
1
0
1
0
3
0
2
0
1
0
2
0
0
1
1
1
0
1
0
0
0
0
0
1
1
0
2
0
2
0
2
0
0
0
0
2
0
2
0
0
0
2
1
0
0
0
0
2
0
2
1
0
0
1
0
2
0
0
0
1
2
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
2
1
0
0
0
0
1
1
1
2
0
0
0
2
0
0
0
2
2
0
0
0
0
1
0
0
0
2
0
1
0
1
0
1
0
0
0
0
2
0
0
0
1
1
0
0
0
2
0
0
1
0
4
2
0
1
2
1
0
2
2
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
1
0
1
0
0
0
0
0
1
2
0
0
2
1
0
0
1
0
2
0
0
0
0
0
0
2
1
2
2
0
1
0
0
0
1
0
0
1
2
0
1
0
0
0
0
7
1
0
1
0
0
0
0
0
0
1
0
2
0
1
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
3
0
0
1
0
1
0
0
2
0
0
1
1
0
0
2
1
2
2
2
1
1
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
1
0
1
1
0
0
2
1
0
2
0
1
0
1
0
1
0
0
2
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
2
2
0
2
0
2
0
0
4
0
1
0
0
1
0
0
0
2
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
4
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
1
0
1
0
0
1
2
0
0
0
2
1
0
0
2
2
0
2
2
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
1
3
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
3
3
0
0
0
0
0
0
0
0
1
2
0
2
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
1
2
2
0
1
2
1
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
1
1
2
0
0
0
0
1
1
0
0
0
0
0
2
2
0
0
2
1
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
1
1
0
0
0
2
1
1
3
0
0
0
0
2
0
0
0
0
2
1
1
1
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
2
0
1
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
1
2
0
2
2
1
0
1
0
0
1
0
0
0
1
1
0
0
2
1
1
2
0
0
0
0
2
1
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
1
1
1
0
2
2
0
0
1
0
1
2
0
1
0
0
1
0
0
1
1
0
1
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
1
2
1
0
0
4
1
0
0
1
0
0
0
1
1
0
0
0
0
0
2
0
1
0
2
1
0
0
0
0
1
0
2
0
2
0
1
0
0
0
0
0
0
2
0
1
2
1
1
0
0
0
1
0
0
0
1
0
2
0
0
2
0
0
0
0
0
1
0
0
0
2
3
0
1
0
4
2
2
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
1
0
3
0
1
0
2
0
1
0
1
1
0
0
1
0
2
0
3
0
2
0
2
0
2
2
1
0
0
1
2
0
1
0
2
0
3
0
2
0
1
0
0
0
1
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
1
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
1
0
1
2
2
2
2
0
0
0
1
0
0
0
0
0
0
0
3
0
1
0
1
0
0
0
0
2
2
2
0
0
0
1
0
1
0
3
0
0
0
0
0
0
1
2
0
2
0
0
0
0
2
0
0
0
2
0
2
0
0
2
0
0
1
0
0
1
0
0
0
0
1
2
2
2
1
0
0
0
1
0
2
3
0
0
0
0
2
0
0
1
0
1
1
0
2
1
1
0
0
1
1
0
0
0
0
0
2
1
0
2
0
1
0
0
1
1
0
2
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
1
0
2
0
0
3
0
0
0
1
1
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
1
1
2
0
0
0
1
0
0
0
2
0
0
0
0
1
2
1
2
0
0
0
2
0
2
0
0
0
0
0
0
2
2
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
1
1
2
1
0
0
1
0
0
0
0
0
0
0
2
3
0
0
2
0
2
2
0
1
0
0
0
0
2
1
0
0
1
0
2
0
2
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
2
0
0
0
3
1
0
1
2
0
1
1
1
0
0
0
1
2
0
2
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
1
0
2
0
0
2
1
0
2
0
1
2
0
0
0
0
1
3
0
1
1
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
2
1
1
0
0
0
1
2
1
0
0
0
2
0
1
0
2
0
1
2
3
0
0
0
0
1
0
0
2
2
0
0
0
2
2
1
0
0
2
0
0
0
2
1
1
0
0
0
2
2
0
0
0
0
0
0
2
1
0
2
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
2
0
0
2
2
0
0
1
0
2
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
2
0
0
1
0
2
2
1
3
0
0
1
2
0
1
2
0
1
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
1
3
0
0
1
1
0
1
0
0
1
0
0
0
2
1
1
1
1
0
1
1
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
2
0
0
1
0
2
0
0
0
0
0
2
1
0
2
2
0
0
1
0
2
0
0
2
0
0
0
2
0
0
1
0
1
0
0
2
0
0
0
0
0
2
1
0
0
0
2
0
0
2
0
0
2
2
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
1
1
0
0
0
0
1
0
0
2
1
0
0
2
1
0
0
0
0
0
2
0
0
3
2
0
0
0
0
1
0
1
2
2
0
2
0
2
0
2
0
2
0
0
0
0
0
2
0
2
0
1
0
0
0
0
1
0
0
2
0
0
2
0
1
0
1
0
1
3
0
2
1
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
1
1
2
0
0
0
0
2
0
1
3
3
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
2
0
2
0
1
0
1
0
2
0
3
1
3
0
2
1
0
0
2
0
3
0
0
0
0
2
0
0
0
0
0
1
1
0
2
0
0
0
0
0
2
1
0
0
0
0
0
2
1
0
2
0
2
0
0
2
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
2
0
1
0
0
0
1
0
0
0
1
0
0
2
0
1
1
2
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
2
0
0
1
2
2
0
1
0
2
1
1
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
2
0
0
0
2
0
0
0
0
1
0
0
2
0
0
1
1
2
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
1
0
1
0
1
0
0
1
1
0
0
0
1
2
2
0
3
0
2
0
0
2
0
0
2
0
1
0
0
0
0
2
0
0
0
0
2
0
2
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
1
2
0
0
2
0
0
1
2
0
0
0
0
0
0
2
0
0
0
1
0
1
0
1
1
1
0
0
4
2
1
1
0
0
0
0
0
0
0
0
1
0
2
1
1
1
0
2
0
0
0
1
0
1
2
0
0
0
0
0
2
0
2
0
1
1
1
0
1
0
0
0
0
0
0
0
0
2
0
0
1
1
1
0
1
0
2
0
0
3
0
0
2
0
0
2
2
1
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
3
0
0
1
0
3
0
1
0
0
2
0
0
0
0
0
0
1
1
0
0
0
2
2
0
0
1
0
2
2
0
0
2
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
2
2
4
0
2
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
1
1
2
2
0
0
2
2
2
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
1
2
0
1
0
0
1
0
0
0
0
0
2
1
0
3
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
2
0
1
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
2
0
0
0
0
0
1
2
0
2
0
0
2
0
0
0
2
3
0
0
0
0
0
0
1
1
0
1
2
0
1
0
0
0
0
0
2
0
2
2
2
0
0
0
0
0
1
0
0
2
0
0
0
1
2
0
2
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
3
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
2
0
2
0
0
2
0
0
1
1
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
1
0
0
3
0
0
1
1
0
1
0
2
2
0
0
0
0
0
0
2
1
0
2
1
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
2
1
0
1
0
0
0
0
1
2
0
0
0
1
0
2
1
2
2
0
0
0
2
2
0
0
0
0
2
0
0
0
0
2
0
0
2
0
2
0
0
0
0
2
1
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
2
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
2
0
0
1
1
2
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
1
3
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
1
0
1
0
0
2
1
0
0
0
1
0
7
1
2
2
0
0
1
4
2
0
2
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
3
1
2
3
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
3
0
0
1
3
0
2
0
1
0
0
0
0
1
0
0
0
2
0
2
2
2
0
1
0
2
0
0
0
0
1
1
2
0
1
0
0
0
0
0
0
0
0
2
0
1
1
1
0
0
0
1
2
2
2
0
0
0
0
0
1
0
0
1
1
0
1
2
1
0
2
0
0
2
1
0
1
1
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
1
0
0
0
1
1
2
2
0
0
1
0
0
2
0
0
3
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
3
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
2
0
0
0
1
0
0
1
1
0
0
2
0
2
0
0
0
0
2
0
1
0
1
0
2
0
0
2
1
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
1
1
0
3
2
1
0
2
0
0
2
0
1
1
0
0
0
2
1
1
1
1
2
1
0
1
1
0
0
0
0
0
1
2
0
1
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
1
0
2
0
2
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
2
2
0
0
0
0
3
0
0
2
0
0
2
0
1
0
0
0
1
1
1
0
0
2
0
6
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
2
1
3
2
0
1
0
0
2
0
0
1
0
2
1
0
2
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
1
2
0
0
0
0
0
0
0
0
0
2
1
1
1
3
1
0
1
0
1
0
1
2
0
1
2
0
2
1
0
0
0
1
0
2
1
4
1
1
0
0
0
1
2
0
0
1
1
1
2
2
1
2
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
2
0
0
1
1
0
0
2
1
0
0
0
2
0
1
1
0
0
1
0
1
1
2
0
2
2
1
0
0
0
0
0
1
1
0
2
3
0
1
0
0
1
1
2
1
0
0
0
2
0
0
0
1
1
0
0
2
2
0
0
1
2
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
2
0
2
0
0
0
0
0
0
0
1
1
0
2
0
0
2
1
1
0
0
1
1
1
0
2
0
0
2
0
0
1
0
0
1
0
2
0
2
1
1
1
2
2
0
1
1
0
0
0
1
0
0
2
0
2
0
2
0
0
2
2
1
0
0
0
1
1
0
1
0
0
0
1
0
2
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
1
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
2
0
1
1
0
0
2
2
0
1
2
0
0
1
0
0
1
2
0
1
0
0
0
0
1
2
1
1
1
0
2
0
0
0
2
1
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
2
0
0
0
1
0
2
0
0
1
0
1
0
3
0
0
0
0
2
1
0
2
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
2
3
0
2
1
0
1
1
0
0
0
0
1
0
0
0
2
0
1
0
1
2
2
1
2
0
2
0
0
2
2
0
2
0
3
0
0
0
2
0
1
0
1
1
1
1
0
2
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
3
0
0
0
1
0
0
3
0
0
1
0
1
0
0
1
0
0
1
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
2
0
2
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
1
1
1
2
0
1
2
0
2
2
1
0
2
2
1
0
1
0
0
0
2
0
1
0
0
0
0
3
0
0
1
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
1
0
0
0
1
1
0
0
0
1
1
0
0
1
0
2
0
0
0
0
0
2
2
2
0
0
0
0
0
0
2
0
0
2
1
0
0
2
0
0
0
0
0
1
0
0
2
0
0
1
0
2
1
0
0
2
0
0
2
0
1
5
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
2
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
1
0
0
1
3
0
0
0
3
0
2
1
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
3
0
0
0
1
3
2
0
1
0
1
0
0
0
0
2
0
1
1
0
0
1
1
1
0
1
0
0
0
0
1
1
2
0
1
2
0
0
0
2
1
2
1
1
0
0
0
0
0
0
0
1
2
0
2
3
0
0
1
2
2
0
1
1
1
2
0
0
0
0
2
2
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
1
0
2
2
0
0
2
0
0
0
0
2
1
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
1
1
0
1
2
0
0
0
0
0
0
0
1
1
2
0
1
0
0
9
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
2
2
1
0
0
0
1
1
2
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
2
0
2
2
0
0
0
0
0
2
1
1
2
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
1
0
2
1
0
0
0
0
2
0
1
0
0
3
2
0
0
0
0
1
2
0
3
0
1
0
0
0
0
6
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
1
1
0
1
0
0
0
1
1
1
2
1
0
0
0
0
2
0
0
1
2
0
0
0
0
0
1
4
0
1
0
0
0
4
0
0
0
2
0
0
0
1
0
2
2
0
0
0
1
1
0
0
0
0
4
0
1
2
1
1
2
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
1
1
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
2
2
0
0
0
2
0
0
2
0
0
2
0
0
1
1
0
2
0
0
0
2
0
1
0
1
0
0
2
1
2
0
0
2
2
1
3
0
0
0
1
0
0
0
1
2
3
1
0
2
1
0
0
2
0
0
0
2
1
2
0
1
0
0
1
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
1
0
0
1
0
0
0
0
0
2
0
0
2
0
1
0
2
0
0
0
2
2
0
1
0
1
2
2
1
0
0
1
2
0
0
0
0
0
1
3
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
2
2
0
0
1
1
0
0
0
2
0
2
1
0
0
0
0
2
0
2
0
0
0
2
1
2
0
0
0
0
0
0
1
3
1
0
2
0
0
0
1
1
0
2
0
0
2
0
1
0
0
0
0
0
1
2
0
0
0
1
0
0
2
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
6
0
0
0
1
0
0
0
0
0
0
0
0
0
4
1
0
1
0
1
1
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
2
2
0
2
0
0
0
0
1
2
2
0
0
0
0
1
1
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
2
0
2
0
1
0
1
0
0
1
0
1
0
4
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
1
0
2
1
0
0
0
2
0
2
0
2
1
2
1
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
2
1
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
1
0
2
2
0
0
1
3
0
2
0
1
0
0
1
1
1
2
0
0
0
0
2
0
1
0
2
0
1
2
2
2
0
2
0
1
0
0
0
0
0
2
2
1
0
0
0
0
1
0
0
0
0
0
0
2
0
2
1
0
2
0
0
0
0
0
1
3
1
0
2
1
0
0
0
0
0
2
0
0
0
0
3
0
1
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
1
0
0
2
1
0
0
0
1
1
0
1
1
0
1
0
0
0
0
0
5
0
0
0
0
4
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
4
0
0
0
0
0
1
1
2
2
0
0
0
0
2
2
0
0
2
0
0
0
2
2
0
0
2
0
0
0
0
0
0
4
0
0
0
1
0
1
0
0
0
0
0
1
2
0
0
0
2
2
1
0
2
0
0
3
2
1
0
2
0
0
2
0
2
0
0
0
1
2
1
0
0
1
0
0
0
0
1
0
1
1
2
2
1
0
0
0
0
0
3
0
0
2
0
0
0
2
0
1
1
0
0
1
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
3
2
0
0
0
0
2
0
2
0
0
0
0
0
1
2
5
0
0
0
0
2
0
1
2
3
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
1
3
0
0
2
0
0
0
0
0
0
1
3
0
0
0
1
5
0
2
2
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
2
0
2
0
0
0
1
0
0
0
0
0
1
0
2
2
2
0
0
1
0
2
0
0
1
2
0
2
0
1
2
0
0
0
2
0
0
2
2
2
0
0
0
1
1
2
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
1
1
0
2
0
2
2
0
1
0
2
0
2
2
5
2
0
0
0
2
0
0
2
0
1
0
0
0
0
0
3
0
0
0
2
0
0
0
0
1
0
0
1
2
0
0
0
0
2
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
1
0
0
1
1
0
0
3
0
0
2
0
0
0
0
0
0
0
1
0
1
1
4
0
0
0
0
0
2
0
2
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
1
2
0
1
2
2
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
3
0
0
0
0
0
0
0
2
0
0
2
0
2
3
0
0
2
0
0
0
0
0
0
1
0
0
1
1
1
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
1
2
1
0
0
2
0
0
1
0
0
0
2
2
2
0
1
0
1
0
2
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
3
2
0
1
0
0
2
1
1
2
1
2
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
1
2
0
0
0
1
0
0
0
4
0
0
1
0
0
0
1
2
2
2
0
0
0
1
0
0
1
2
1
1
1
0
0
0
0
0
0
0
3
0
0
1
1
1
1
0
0
1
0
0
0
1
0
1
0
2
2
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
1
0
0
1
0
0
0
1
1
0
0
3
0
0
2
0
2
0
1
0
0
1
3
0
0
0
1
2
1
2
1
1
1
0
0
1
2
0
0
1
0
1
0
1
1
5
0
0
0
0
0
0
0
0
2
0
0
0
2
0
3
1
2
1
0
0
0
0
0
0
3
2
0
0
0
0
2
0
0
2
0
1
0
3
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
1
2
0
2
0
1
0
0
0
1
0
1
0
0
2
0
2
0
1
0
0
0
2
1
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
1
0
1
0
1
1
2
0
2
0
0
2
0
0
2
0
2
3
0
0
0
1
0
1
0
2
2
1
0
2
0
1
1
0
2
0
0
0
0
0
1
0
0
1
2
2
2
0
0
0
2
0
0
1
0
0
2
0
1
0
2
0
0
1
0
0
0
0
0
0
2
0
2
0
0
1
2
0
0
0
0
2
0
0
1
1
2
0
1
1
0
2
0
5
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
2
2
0
0
0
3
0
0
0
0
0
2
1
1
1
1
0
0
0
1
3
0
3
0
0
0
0
1
2
1
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
1
0
0
0
2
0
0
1
2
0
1
0
2
0
0
1
0
1
2
0
0
0
1
3
0
0
0
0
0
1
0
1
0
0
0
1
0
1
2
1
0
1
0
2
0
1
2
0
0
0
2
0
0
1
2
1
1
2
1
1
0
4
0
0
2
0
0
1
0
0
0
2
0
1
0
0
0
0
1
2
0
0
1
0
2
0
1
2
0
0
0
2
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
2
1
0
0
1
0
0
0
2
1
0
2
0
0
0
0
4
1
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
3
2
2
0
2
2
3
0
0
1
2
2
1
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
3
0
0
1
2
2
2
0
1
0
0
0
2
0
0
1
2
1
1
2
0
1
1
0
4
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
2
1
2
1
0
0
0
0
0
1
0
0
0
3
0
0
0
0
3
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
2
2
0
2
0
0
0
3
0
0
1
0
0
0
2
0
0
0
1
0
1
0
2
0
0
1
0
0
1
0
0
2
0
0
1
0
0
0
0
0
1
0
0
2
2
0
0
1
0
0
1
2
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
1
2
0
0
1
0
2
0
0
0
2
1
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
2
1
0
0
0
0
1
0
1
0
0
1
1
0
1
0
2
0
0
2
0
2
0
0
1
2
0
0
0
1
0
0
1
0
0
1
0
3
2
0
0
1
2
0
0
2
1
2
0
0
0
2
0
0
0
2
0
0
0
1
1
0
2
2
2
0
0
0
2
2
2
2
1
0
0
2
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
1
0
2
2
0
0
0
1
2
0
1
2
0
3
1
1
0
0
0
0
0
0
1
0
3
0
1
0
0
1
1
1
0
2
0
0
2
0
0
0
1
2
0
0
0
0
2
1
1
3
2
1
2
0
1
0
1
0
0
0
0
1
2
1
0
1
2
0
0
1
0
0
1
0
2
0
0
0
2
0
1
0
0
0
2
0
1
1
0
2
0
0
2
0
1
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
4
0
0
2
2
0
0
2
1
2
0
2
1
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
3
0
0
1
0
0
1
0
0
2
2
0
0
0
0
0
0
0
2
1
0
0
4
1
1
0
0
0
0
0
2
0
1
1
0
0
0
0
0
1
1
0
1
0
0
0
0
1
2
1
0
0
0
2
0
0
2
0
0
0
1
2
0
0
0
1
0
0
2
1
0
1
1
0
0
0
0
0
0
0
2
0
0
0
2
2
1
1
0
0
1
2
0
0
0
1
2
2
0
0
0
0
0
1
0
2
2
0
0
0
0
0
1
0
1
0
0
2
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
1
2
0
0
0
0
0
0
0
3
0
2
2
0
0
1
1
0
0
1
0
2
0
3
0
0
1
1
2
0
1
0
1
2
1
4
2
0
0
1
1
0
0
2
0
0
0
0
0
0
2
0
1
0
2
0
0
2
0
0
2
0
0
0
2
0
1
2
0
3
2
0
0
2
2
0
0
2
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
1
0
1
0
0
2
0
6
1
0
0
2
0
0
0
0
1
3
2
0
0
1
1
0
4
0
0
1
0
0
2
0
2
0
1
0
0
1
0
0
0
2
0
0
1
1
0
2
0
1
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
2
0
0
0
0
2
1
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
2
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
2
0
1
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
2
0
1
2
0
3
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
3
0
3
6
0
0
0
2
2
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
2
0
1
0
0
1
1
1
1
0
2
2
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
2
0
0
1
1
1
0
1
1
0
2
1
0
0
0
0
0
2
0
2
0
0
1
0
0
2
0
0
0
1
2
1
1
0
0
0
0
1
2
2
2
0
0
0
0
2
1
0
0
0
2
2
0
0
2
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
1
0
0
1
1
0
2
0
2
2
0
0
1
0
0
0
0
2
1
1
0
0
0
3
2
0
0
0
2
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
3
0
1
0
1
1
2
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
1
1
1
1
0
0
0
2
0
0
4
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
2
0
0
0
0
2
0
1
1
2
0
3
1
0
1
0
1
0
0
2
0
2
2
0
0
2
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
3
1
0
1
0
1
1
3
2
0
1
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
1
2
0
0
1
0
0
0
1
0
0
0
3
0
1
1
2
1
1
0
0
0
2
0
0
1
0
2
3
0
0
0
2
0
0
0
0
2
0
2
1
0
2
0
0
0
0
0
1
0
2
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
1
2
1
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
1
0
1
2
0
0
3
0
0
0
0
2
0
0
0
2
0
1
1
0
0
2
0
0
2
0
0
0
3
2
0
0
1
0
0
0
0
0
0
0
0
2
0
1
1
1
0
1
2
0
1
0
0
1
0
0
3
0
0
0
0
2
0
0
2
0
1
1
1
0
0
1
1
0
1
0
1
0
0
0
2
1
1
0
0
0
2
0
3
1
3
0
0
0
0
1
1
0
2
1
0
0
0
3
1
0
0
0
1
0
1
0
0
0
0
0
1
0
2
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
1
1
0
0
2
0
0
2
2
1
1
0
0
0
0
1
1
4
0
2
0
0
0
2
3
1
1
0
0
1
0
0
0
2
0
0
0
2
0
1
0
2
0
0
0
0
1
2
3
1
0
0
0
0
0
4
0
0
2
0
0
0
2
2
0
0
0
0
0
2
1
2
0
0
2
0
2
0
1
0
0
0
0
0
1
1
2
1
2
1
0
0
0
0
0
0
0
0
3
0
0
0
0
1
1
1
0
0
0
0
0
2
1
0
1
1
1
0
1
0
0
1
0
2
0
1
0
0
0
1
0
0
5
0
0
2
0
0
0
0
0
4
1
0
0
1
0
3
0
0
1
0
0
2
0
0
2
0
1
0
0
6
0
0
0
1
0
0
0
1
0
2
0
0
2
1
0
0
0
2
0
0
1
0
0
1
4
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
3
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
1
2
2
0
0
0
0
0
1
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
1
0
2
0
4
0
0
0
1
0
3
0
0
0
2
0
1
2
2
0
0
0
0
0
1
0
1
0
0
2
2
0
0
0
0
0
0
2
0
1
2
0
0
3
0
0
1
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
3
0
2
2
0
0
0
0
0
0
0
1
2
2
0
0
2
0
0
0
3
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
1
0
1
0
0
1
0
0
0
0
2
2
0
1
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
1
2
0
0
0
1
2
0
1
2
0
1
1
0
2
0
1
0
0
0
2
0
2
1
0
0
0
1
0
1
0
1
0
1
1
0
0
3
1
1
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
2
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
2
2
2
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
2
1
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
3
2
0
0
0
0
3
0
1
0
0
1
0
2
1
1
1
0
2
0
0
2
2
0
0
0
3
0
0
1
0
1
0
2
0
1
0
0
0
0
0
1
1
0
0
0
0
0
2
2
0
0
1
0
0
1
0
0
0
1
0
0
3
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
1
0
0
3
0
0
0
2
0
0
0
0
1
2
1
0
0
0
2
0
0
0
2
0
0
0
2
1
0
2
0
0
1
3
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
2
0
0
0
0
1
1
0
0
2
0
0
0
0
2
1
0
0
1
0
0
1
0
2
0
0
1
2
0
0
0
0
0
1
0
1
0
0
2
0
0
0
2
0
0
0
2
0
0
2
2
1
0
0
0
0
1
0
0
0
2
0
0
1
0
1
2
0
0
0
0
0
0
0
2
0
1
5
2
0
2
2
1
0
2
0
0
0
1
0
0
2
0
2
0
0
1
0
0
1
0
0
1
2
2
1
1
0
2
1
1
0
2
0
0
1
0
0
0
0
1
0
2
0
1
0
1
2
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
2
2
0
0
0
2
2
0
2
2
0
2
0
3
0
0
0
2
0
0
0
0
1
0
1
0
0
1
1
0
1
0
1
0
1
0
2
0
2
0
1
2
0
0
0
0
1
0
0
2
0
0
0
2
1
1
0
1
0
0
1
1
2
0
2
1
2
0
2
2
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
1
0
1
2
1
0
0
1
0
0
1
2
0
1
0
0
0
0
2
0
2
0
0
0
0
0
1
2
0
1
0
2
1
2
0
0
0
1
0
0
1
0
0
2
0
1
2
0
0
2
0
0
0
2
0
1
0
0
0
1
2
0
1
0
1
1
1
3
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
1
2
0
0
1
0
2
2
0
0
0
0
0
0
2
1
2
1
4
0
0
0
2
2
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
1
2
0
0
0
1
0
2
4
0
0
0
2
0
1
2
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
2
0
3
0
0
2
0
0
2
2
0
0
0
0
2
1
0
2
2
2
0
0
3
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
3
0
0
0
0
0
1
0
1
0
0
0
0
2
0
1
0
0
2
0
0
0
0
2
0
0
2
0
2
0
0
1
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
2
0
1
0
1
0
2
0
0
0
0
2
0
2
2
0
0
0
3
3
2
1
2
0
0
0
1
0
0
1
0
2
0
0
0
0
1
2
1
0
0
0
0
0
1
0
1
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
1
1
1
1
2
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
2
2
0
1
1
0
0
0
1
0
0
1
1
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
1
1
1
0
0
2
1
1
0
0
2
0
0
0
0
0
1
1
0
2
0
2
2
1
0
1
0
1
4
0
0
0
1
2
0
2
0
0
0
1
2
0
1
2
0
1
0
0
0
2
0
2
0
2
0
0
1
0
2
0
1
2
0
0
1
0
1
0
0
0
0
0
1
1
0
1
1
2
1
0
0
1
1
0
1
0
0
0
0
0
2
2
0
3
0
0
1
0
0
3
2
0
0
1
0
2
1
0
0
0
0
2
0
2
0
2
0
0
0
0
0
1
2
2
1
0
2
1
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
2
0
0
2
2
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
2
2
0
1
0
1
5
0
1
0
2
0
1
0
0
3
0
0
0
1
0
0
0
0
3
0
1
0
0
1
1
2
2
0
0
0
0
1
0
0
1
0
1
1
2
0
0
0
1
0
1
0
2
0
2
0
1
0
1
0
0
0
0
2
0
0
1
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
2
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
2
0
1
0
0
0
1
2
0
0
1
0
0
0
1
2
0
0
0
2
1
0
0
0
0
1
0
2
0
0
1
2
0
0
0
1
0
0
0
2
0
0
0
1
2
0
0
0
0
3
2
1
0
0
0
0
2
3
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
2
2
1
1
0
0
0
0
1
2
0
0
2
0
2
0
0
0
0
0
1
2
3
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
2
1
2
0
1
0
0
0
2
0
0
0
2
2
1
2
0
1
0
0
0
2
0
0
1
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
2
0
1
0
0
1
0
1
0
1
0
1
0
0
0
0
0
2
1
0
1
0
0
1
0
3
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
2
2
0
1
2
2
0
1
0
0
1
0
1
2
0
0
0
1
1
1
0
0
3
0
1
1
0
0
1
0
0
0
0
1
2
0
0
6
1
0
0
0
2
0
0
0
0
1
0
2
0
2
0
0
0
1
0
0
4
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
3
1
0
0
2
1
1
2
2
4
0
1
2
1
0
0
0
1
0
1
3
2
0
0
0
1
1
0
2
0
0
0
0
0
1
0
0
2
0
2
0
0
1
2
2
0
0
0
0
0
0
0
0
1
2
0
2
0
1
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
2
0
2
0
0
1
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
1
1
0
0
0
2
1
0
3
0
0
0
1
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
1
1
1
1
0
1
0
1
0
0
0
0
0
3
1
2
0
0
0
2
0
2
2
2
1
1
0
0
1
1
0
2
0
0
0
3
0
0
0
2
2
2
0
2
0
2
0
0
2
2
1
0
0
0
0
1
2
0
0
0
1
1
0
0
1
2
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
1
3
0
2
1
0
0
2
0
0
0
1
0
2
0
2
0
2
0
0
1
0
1
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
4
0
1
0
0
0
0
2
0
1
0
0
1
2
1
0
1
0
0
0
1
1
1
1
0
0
0
0
0
0
2
0
0
0
0
1
2
0
2
0
0
0
3
0
0
0
0
1
0
1
1
0
0
0
0
2
1
0
2
1
0
1
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
2
2
1
0
3
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
1
0
0
0
2
1
0
0
0
0
1
1
0
0
0
4
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
2
1
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
1
0
0
0
1
2
1
0
2
2
0
3
0
0
0
0
1
4
0
0
0
0
2
2
0
1
2
2
0
0
0
1
0
0
2
0
1
0
2
0
0
0
1
1
1
0
7
1
0
2
1
0
0
0
1
0
0
3
1
1
0
0
0
1
1
2
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
4
0
0
0
0
0
2
0
2
5
0
0
1
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
3
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
2
0
0
1
0
0
0
0
0
2
0
0
0
1
0
2
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
3
0
0
0
1
2
0
0
0
1
0
0
0
0
2
1
0
0
3
0
0
0
1
0
0
0
3
0
1
2
0
0
1
1
0
0
0
2
2
0
4
2
3
0
0
1
1
0
1
0
0
1
1
0
0
2
0
0
0
1
0
0
0
0
2
2
1
0
0
0
1
1
0
0
2
1
1
0
0
1
0
0
0
1
2
0
0
0
0
0
1
4
2
2
0
0
2
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
1
4
2
1
0
0
2
2
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
1
0
0
2
0
0
2
0
0
2
0
2
0
4
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
1
2
0
0
1
2
0
1
1
2
2
0
0
1
0
0
0
0
1
0
0
0
1
2
0
0
1
0
0
0
2
0
0
0
1
3
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
2
0
2
1
0
1
1
1
0
0
0
1
0
0
6
0
0
2
0
1
0
0
0
0
0
0
0
3
2
2
0
2
1
0
2
3
0
0
1
0
1
2
0
0
0
0
0
0
1
2
0
1
0
1
2
1
0
0
0
2
0
0
0
2
0
1
1
0
0
1
0
0
0
0
1
3
0
0
0
2
0
0
0
2
2
0
0
0
1
2
0
2
2
0
1
2
0
1
0
0
0
0
0
2
1
1
1
1
0
0
0
2
1
2
0
0
0
0
2
0
0
2
0
0
0
3
3
0
3
0
2
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
1
0
3
0
0
3
0
2
1
2
0
0
0
1
0
2
0
0
0
0
2
0
0
1
2
1
0
2
1
1
0
1
0
1
0
0
2
1
1
2
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
2
2
1
0
0
0
0
0
2
0
0
1
0
2
1
2
0
0
1
0
2
0
0
1
0
2
1
0
0
4
0
2
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
1
1
0
0
0
0
0
3
0
5
0
1
0
0
0
0
1
0
0
0
0
0
2
2
1
0
0
1
0
0
1
2
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
5
0
0
1
0
0
0
1
1
0
0
3
1
0
1
0
0
0
0
3
0
0
2
2
2
2
1
1
1
1
0
2
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
2
2
0
0
0
0
2
2
0
0
0
0
1
1
0
1
0
0
0
0
2
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
1
0
1
0
2
1
0
0
0
2
2
0
0
1
2
2
0
2
0
2
0
0
0
0
1
0
1
0
1
0
2
0
1
1
0
0
0
3
0
1
2
0
0
0
1
0
2
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
2
2
2
2
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
3
1
0
1
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
3
0
0
0
0
0
2
0
1
1
0
0
1
0
1
0
0
0
0
0
1
1
0
1
1
0
1
0
1
0
0
0
1
0
0
1
0
2
1
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
1
0
0
3
0
1
1
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
3
1
1
0
2
0
0
1
1
0
0
0
0
0
1
0
0
0
1
2
0
0
2
1
2
0
0
0
0
0
0
2
0
1
0
1
0
1
2
0
2
0
0
0
1
0
0
0
0
0
0
0
2
1
2
1
0
0
0
1
0
1
0
0
2
0
0
0
1
1
2
0
0
0
0
0
0
2
0
0
0
0
0
2
1
2
0
2
2
0
0
1
0
0
1
1
0
0
2
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
2
2
1
1
0
0
1
0
0
1
0
0
2
0
5
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
2
1
0
0
0
1
0
2
0
0
1
0
1
1
1
0
0
0
0
1
0
0
0
0
0
2
2
0
3
0
0
0
1
0
1
0
2
0
1
0
0
0
0
0
0
1
0
1
0
1
1
0
0
4
0
1
2
2
2
1
0
0
0
0
0
2
1
1
0
0
0
0
6
0
0
2
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
2
1
0
0
0
0
1
1
0
0
2
2
0
2
1
0
0
1
1
0
1
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
1
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
3
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
1
2
0
0
0
2
0
0
0
2
0
1
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
1
1
0
0
0
0
0
0
0
1
5
0
0
0
0
2
2
0
0
0
0
2
0
0
1
0
0
2
0
1
0
2
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
1
1
0
0
0
0
0
1
1
0
0
0
1
1
1
0
0
0
0
1
2
0
0
0
0
1
0
0
0
2
2
1
0
1
0
0
0
1
6
1
0
0
0
0
0
0
0
0
2
0
1
0
3
0
0
0
0
0
1
2
1
1
2
0
0
1
0
0
0
0
2
0
1
2
0
1
0
1
2
0
0
0
1
1
0
2
1
2
0
0
0
0
0
0
1
0
3
0
1
0
0
0
0
0
2
0
0
0
2
2
2
0
0
1
0
2
0
2
2
1
0
0
0
0
1
0
1
2
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
3
3
1
2
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
2
2
0
0
1
0
0
1
2
0
0
0
1
0
1
0
2
2
0
1
0
0
1
2
1
0
0
1
0
2
0
0
0
2
1
0
0
0
0
4
0
0
0
2
1
2
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
2
0
0
2
1
3
0
0
0
0
2
1
0
1
0
1
3
2
1
0
2
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
2
0
0
1
0
0
1
0
0
2
0
0
0
0
0
3
0
0
1
0
0
0
0
2
1
0
0
2
0
1
0
0
0
0
1
0
2
1
0
1
0
0
1
0
3
0
1
0
0
0
0
2
2
3
0
0
1
0
2
2
0
0
0
0
0
1
1
0
0
0
2
1
1
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
1
2
0
0
0
0
1
0
1
0
0
0
0
1
0
0
2
1
0
1
1
0
1
0
0
0
2
2
1
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
3
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
2
0
2
2
0
1
1
2
0
0
0
0
0
2
0
0
1
0
1
0
2
1
0
0
0
1
0
0
0
2
2
0
0
2
0
0
1
1
2
0
0
1
1
2
0
0
0
0
0
2
0
2
3
0
0
1
0
0
1
3
4
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
1
0
0
0
1
1
1
2
0
0
0
0
0
1
0
3
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
1
0
2
0
0
0
0
0
0
1
0
0
0
3
0
0
1
0
0
0
0
1
1
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
1
6
1
1
0
1
2
1
0
2
0
3
2
0
0
0
2
2
1
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
2
1
2
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
2
1
2
2
0
0
2
0
0
0
2
2
0
0
0
0
1
0
1
0
0
0
0
2
0
1
2
1
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
1
1
0
0
2
0
2
0
3
1
0
0
0
0
0
0
0
0
2
1
0
0
0
3
2
1
0
0
0
0
1
0
2
1
2
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
1
0
0
1
0
1
0
0
0
2
2
0
1
0
1
1
1
0
2
0
1
1
0
0
0
0
2
0
0
0
1
0
0
3
0
0
0
0
2
3
0
0
3
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
2
2
1
0
0
0
1
2
0
1
1
0
0
0
2
0
2
2
0
0
0
0
0
0
0
1
0
0
0
2
1
0
1
0
0
2
0
1
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
3
0
2
1
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
2
1
2
0
1
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
1
2
0
0
2
0
0
0
0
0
2
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
2
1
0
1
2
2
0
1
2
0
0
3
1
1
2
0
0
0
0
2
2
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
2
1
3
1
1
0
2
0
0
0
0
0
2
4
0
0
1
0
1
0
0
0
1
0
1
0
0
2
1
0
2
0
1
0
2
2
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
3
0
0
0
0
1
0
2
0
0
0
2
0
1
0
0
0
0
0
2
0
0
1
1
0
0
0
0
2
0
0
1
0
2
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
2
1
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
3
0
1
0
0
0
0
0
0
0
1
0
1
1
3
1
0
1
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
2
2
2
2
2
0
0
0
0
0
0
0
0
1
2
1
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
2
0
1
0
0
2
0
4
1
0
2
0
0
1
0
0
0
0
0
0
0
0
1
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
2
2
0
0
1
0
1
0
0
0
0
0
1
1
0
1
1
2
1
0
0
1
0
0
0
2
1
0
0
2
0
0
2
0
0
0
2
0
1
0
1
2
2
0
0
1
1
0
1
2
0
0
1
0
0
0
0
1
0
2
0
1
2
1
1
0
1
1
2
0
0
0
0
0
0
0
0
0
1
0
0
3
1
0
1
0
1
0
0
0
2
0
1
0
0
0
2
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
1
1
2
2
0
0
0
0
1
0
0
0
0
0
2
2
0
2
0
1
0
1
0
0
0
1
0
0
1
0
0
2
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
3
0
1
1
2
0
0
1
0
0
2
1
6
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
2
0
0
0
0
1
2
0
0
1
0
2
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
2
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
2
0
0
2
0
0
0
0
0
0
2
0
2
0
2
0
0
2
0
0
0
0
1
0
0
0
0
1
1
2
0
2
0
3
3
2
1
1
3
2
1
1
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
2
0
1
0
0
0
3
0
1
0
1
2
0
0
2
2
0
0
0
3
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
2
1
0
1
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
1
0
1
4
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
2
1
0
0
0
0
1
0
0
0
0
4
1
1
2
1
0
0
1
0
1
2
1
0
0
0
2
2
0
0
0
0
0
0
2
1
0
1
0
1
0
0
1
3
0
0
0
0
0
1
0
0
0
2
0
3
1
0
0
0
2
1
1
1
0
0
4
1
1
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
2
2
2
1
2
1
0
0
1
2
0
0
2
3
0
0
1
2
0
0
0
2
0
0
1
1
0
1
2
2
0
0
0
0
1
0
0
1
0
2
0
2
1
0
2
0
1
1
0
0
0
0
0
2
0
0
1
0
0
3
0
0
0
2
0
1
0
0
0
0
2
0
2
1
1
0
1
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
2
2
0
0
0
0
0
0
0
1
2
0
0
0
2
0
1
1
0
0
3
0
1
0
1
0
2
0
3
0
0
0
1
0
0
0
0
0
2
0
2
0
0
1
0
2
0
0
0
0
0
2
1
0
2
4
1
1
0
0
0
0
0
0
0
0
1
0
1
0
3
0
1
1
0
0
2
0
1
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
1
1
0
2
0
2
2
1
0
0
0
3
1
0
1
0
1
0
0
1
0
0
0
0
2
2
2
1
1
1
0
0
0
0
2
1
0
0
0
1
0
0
1
1
0
2
2
0
1
1
0
1
0
0
1
0
2
2
1
0
0
0
2
1
0
0
1
0
2
0
1
0
0
2
0
0
1
2
0
2
0
0
1
1
0
0
0
0
0
2
1
2
1
1
0
1
2
0
1
1
3
0
0
0
0
0
0
0
1
1
0
2
0
1
0
2
1
2
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
2
0
0
1
2
0
1
2
1
0
0
0
1
0
5
0
0
1
1
0
0
0
2
2
2
0
2
1
0
0
2
0
2
1
0
1
1
0
0
1
1
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
2
0
2
0
0
0
0
2
2
0
0
0
0
1
2
0
1
0
0
0
25
0
2
1
2
0
0
0
0
0
0
1
2
2
4
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
2
1
0
3
1
0
0
0
1
0
0
2
0
0
0
2
0
0
1
1
0
0
1
0
2
0
0
3
0
1
0
0
2
1
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
1
0
1
3
1
1
0
0
2
0
0
0
0
0
1
1
1
0
1
7
0
1
2
0
1
1
1
2
0
2
0
1
0
0
2
2
0
0
1
0
0
0
0
2
0
0
1
0
1
0
1
0
1
0
2
0
2
0
2
0
0
1
0
0
0
1
1
0
2
1
0
0
0
0
2
0
0
0
2
1
2
0
0
0
0
1
3
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
5
0
0
1
1
0
0
0
0
2
0
1
1
0
0
3
3
2
2
1
0
0
0
2
0
0
0
2
0
1
0
1
0
2
0
0
0
1
0
0
0
0
0
2
0
2
1
0
2
1
0
1
1
0
0
1
0
2
0
1
0
1
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
2
0
2
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
3
0
1
1
0
2
0
0
0
0
1
0
0
2
0
2
0
0
0
1
3
0
0
2
2
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
1
2
0
2
0
0
0
1
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
2
0
0
0
2
0
0
1
1
0
1
1
0
1
0
0
3
0
1
1
0
1
2
2
2
0
0
0
1
1
0
0
0
0
2
0
0
1
1
3
0
1
0
0
3
1
0
0
0
0
2
0
0
1
1
0
0
0
0
0
1
0
2
3
0
0
1
0
2
0
1
0
0
1
0
2
3
0
0
0
0
2
5
1
0
2
2
2
2
0
0
0
0
2
2
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
2
0
2
0
0
2
0
2
0
0
2
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
2
1
0
0
1
0
0
2
3
1
0
0
2
2
0
0
0
0
0
0
0
1
1
0
0
2
0
1
0
0
1
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
1
0
0
0
0
2
1
1
0
1
1
0
1
0
0
0
2
7
0
2
0
1
2
0
0
0
1
0
0
2
2
0
1
0
1
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
2
2
1
0
0
0
0
1
0
1
0
1
0
0
1
1
0
2
0
0
2
1
4
0
1
0
0
2
0
0
0
0
0
1
0
0
2
0
1
0
1
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
2
0
1
0
1
0
0
1
0
0
1
0
0
1
2
0
1
1
0
2
1
2
2
0
2
0
0
0
2
0
0
1
0
0
0
1
0
2
0
2
0
0
0
0
4
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
2
1
0
0
0
2
0
0
1
0
0
0
2
0
1
2
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
1
1
0
2
0
0
0
2
1
3
2
0
0
0
2
0
0
0
0
0
0
2
1
0
0
2
1
2
2
0
0
0
2
3
1
2
6
0
0
2
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
1
2
2
1
3
0
2
2
0
0
0
0
0
0
1
2
2
0
0
0
0
1
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
2
0
2
2
1
0
1
0
0
0
3
0
1
0
0
0
0
2
1
0
0
1
1
0
0
1
1
1
0
1
0
0
2
0
0
0
0
2
0
0
0
1
0
0
1
2
0
0
3
0
2
0
0
1
0
2
0
2
1
0
0
0
1
0
3
0
0
0
2
0
1
1
0
0
1
0
0
1
2
0
1
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
5
0
0
0
0
1
0
1
0
6
0
1
0
2
0
0
0
0
0
5
0
0
2
0
1
2
1
1
2
1
0
2
0
0
0
0
0
0
0
2
2
2
2
1
0
0
0
0
2
0
0
1
0
2
2
2
0
0
0
0
1
0
1
0
0
0
1
0
2
1
0
0
0
0
0
1
0
1
0
2
2
2
0
0
3
0
0
3
0
0
1
2
0
0
1
1
0
0
0
0
1
1
2
2
0
0
1
1
0
0
0
2
0
0
0
1
0
1
0
2
0
0
0
0
2
1
0
0
1
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
1
1
1
1
0
0
1
2
0
1
3
1
0
1
0
0
0
0
2
3
0
0
1
0
0
2
1
0
0
0
3
2
0
0
0
0
2
1
0
1
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
2
0
1
0
0
0
2
0
2
2
2
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
1
2
0
1
0
0
0
0
1
0
0
0
3
0
0
0
0
0
2
2
0
0
0
0
2
0
1
0
2
0
2
1
0
2
1
0
0
0
0
2
0
0
0
1
2
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
3
0
2
0
0
1
0
0
0
2
0
0
2
2
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
1
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
2
0
1
1
0
0
0
0
1
1
0
0
2
0
0
0
0
1
0
0
2
0
2
0
1
0
1
0
1
1
0
2
1
1
0
0
3
1
0
2
0
0
0
0
0
0
1
1
1
0
1
0
0
0
2
0
0
0
0
0
1
1
0
0
1
1
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
2
2
0
1
0
0
0
0
0
1
2
0
0
1
1
0
0
0
0
2
0
0
2
0
1
1
0
4
0
0
1
2
0
0
0
0
1
2
0
2
2
0
2
0
2
2
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
1
0
0
1
0
0
2
0
0
0
2
1
1
1
2
0
0
0
0
2
0
1
1
3
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
2
1
0
2
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
2
0
2
1
2
1
1
0
0
1
0
1
1
2
0
1
0
0
0
0
0
0
0
0
2
1
0
2
0
0
1
1
1
4
0
1
0
0
0
2
0
0
0
1
3
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
1
0
1
0
0
2
2
0
0
0
0
0
2
0
0
0
1
0
0
0
1
1
2
1
0
2
0
0
0
2
2
0
0
0
0
0
0
0
2
1
0
0
0
0
1
2
0
0
0
0
2
2
0
0
0
0
1
2
0
2
0
2
1
0
2
0
0
0
2
0
0
0
2
0
0
0
1
0
1
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
3
2
1
2
0
2
0
1
0
6
0
0
0
0
0
1
0
0
1
1
0
0
2
1
3
0
2
0
0
2
0
1
1
3
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
1
2
1
1
0
1
0
0
2
0
0
2
0
2
0
1
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
2
0
0
0
0
0
0
1
0
0
2
0
2
0
0
1
0
3
2
2
0
2
0
0
1
0
0
1
0
0
0
2
0
0
0
3
0
0
0
2
0
2
0
0
2
0
0
0
0
0
2
1
0
4
0
0
0
1
0
0
1
1
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
2
1
2
1
2
0
2
2
0
0
0
0
1
0
1
1
0
0
0
0
1
2
0
0
0
0
1
1
0
0
0
0
2
0
2
0
0
1
0
1
0
2
0
0
0
1
1
0
0
1
5
2
1
0
0
2
1
4
1
0
0
2
1
2
1
1
0
0
0
0
2
0
0
0
1
0
0
1
0
2
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
3
0
0
0
0
0
1
0
2
0
2
0
1
2
0
0
2
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
1
1
3
1
1
1
0
1
0
0
1
1
0
0
0
1
1
0
1
0
0
1
0
0
0
2
3
2
1
2
1
0
2
2
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
1
2
0
0
1
1
1
2
2
0
1
0
0
1
0
0
0
0
1
2
0
0
0
1
0
2
0
0
0
2
0
0
0
1
0
0
1
2
0
1
2
0
0
0
0
5
0
0
2
2
1
0
2
0
0
0
0
2
1
1
1
0
2
1
0
0
2
0
0
1
0
2
1
0
10
0
0
2
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
1
0
0
0
2
1
0
0
0
2
0
0
0
1
0
0
2
1
0
0
0
0
0
2
0
0
0
1
1
0
0
3
0
2
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
1
1
1
0
1
2
0
0
1
0
2
1
2
2
2
0
0
0
2
0
0
1
0
0
1
1
0
0
0
3
1
2
0
2
1
0
0
0
0
0
0
0
1
0
1
2
0
2
0
0
0
0
0
1
1
2
0
1
0
3
0
0
0
1
0
0
2
0
1
1
0
0
0
0
0
0
0
0
1
2
0
0
2
0
2
0
0
1
1
0
0
0
0
0
0
1
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
2
0
0
0
0
0
1
1
1
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
2
1
0
0
1
2
0
2
0
3
0
0
0
0
1
0
2
3
0
0
1
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
2
1
5
0
0
0
0
0
0
1
1
0
1
1
0
0
0
2
0
0
2
0
0
0
0
0
1
0
2
0
2
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
1
0
0
7
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
2
0
3
0
0
0
1
0
0
2
2
0
2
1
1
1
0
0
1
0
0
0
0
2
0
1
1
0
2
0
2
0
2
2
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
1
2
0
0
2
0
2
0
2
2
0
0
2
0
2
0
0
0
0
0
2
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
8
0
0
1
0
0
0
2
2
0
3
0
2
2
0
0
1
1
0
0
0
0
0
2
2
0
0
0
1
3
0
2
0
0
1
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
1
2
0
1
0
2
0
3
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
2
0
0
2
0
2
0
1
2
1
1
0
0
0
2
0
2
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
2
0
0
1
0
1
0
0
1
0
1
0
2
0
2
0
0
2
2
0
1
0
0
0
0
2
0
0
0
0
2
0
1
1
0
0
0
2
1
4
0
0
0
0
2
0
2
0
0
0
0
2
2
1
0
1
0
0
3
1
2
2
0
0
0
1
0
0
6
2
0
2
2
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
1
0
2
0
0
0
1
0
0
0
2
1
1
0
0
2
0
2
1
0
2
2
2
0
1
0
0
2
3
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
2
1
2
0
0
2
0
1
0
1
0
1
0
0
2
1
0
2
2
0
0
0
0
1
1
1
0
2
5
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
1
2
0
0
1
0
1
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
3
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
2
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
2
0
0
0
0
0
2
1
0
1
1
0
0
2
0
1
2
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
1
0
1
4
1
1
1
0
0
0
0
4
0
0
0
2
0
0
1
1
0
0
2
1
0
2
2
2
0
2
0
0
0
0
1
2
2
0
0
0
0
1
2
0
0
0
0
1
0
0
0
2
0
2
0
1
2
0
2
0
1
0
0
1
1
2
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
1
2
2
0
0
0
0
0
0
0
1
0
0
1
0
0
2
1
0
1
0
0
0
0
0
0
2
0
1
2
0
0
0
0
2
1
1
1
2
0
0
1
0
0
2
0
1
2
0
0
0
2
0
1
2
1
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
2
0
0
0
3
0
0
0
2
0
0
3
0
0
0
0
0
1
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
2
0
0
2
2
0
0
1
2
1
0
0
2
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
1
2
0
0
1
0
2
2
0
2
1
3
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
2
2
0
0
0
0
1
0
0
2
2
1
0
0
2
0
2
0
0
0
1
0
0
0
2
0
3
0
0
2
0
1
2
1
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
4
1
0
1
1
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
1
1
1
1
0
0
0
1
0
2
3
2
2
1
0
1
0
0
1
0
0
0
1
0
0
2
1
1
2
0
1
0
0
0
0
0
3
0
0
0
0
2
0
2
1
0
0
0
1
2
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
2
2
2
0
0
0
2
0
0
0
0
2
0
0
2
0
2
0
2
0
0
1
0
2
2
0
0
2
0
0
1
3
0
1
1
0
0
2
0
0
1
1
0
0
0
0
0
1
1
0
1
2
2
0
0
0
1
0
2
1
0
0
1
0
2
0
0
1
1
0
1
0
0
0
0
0
1
0
0
2
0
0
1
2
2
1
0
0
0
0
0
0
1
2
0
4
0
0
1
1
0
2
0
0
0
0
1
0
2
0
0
0
0
2
1
0
2
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
4
0
2
0
0
0
0
0
0
2
0
2
0
1
0
4
2
0
0
1
0
0
0
0
2
0
2
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
2
0
2
1
0
0
1
0
2
0
3
1
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
5
0
1
1
1
0
0
1
2
2
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
1
1
0
0
0
2
0
0
0
3
0
0
0
2
1
2
2
0
0
0
0
0
1
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
1
0
1
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
1
1
4
1
0
0
2
0
0
1
0
0
0
0
0
2
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
1
1
0
2
4
1
2
3
3
1
1
2
0
0
0
0
0
1
0
0
2
1
1
0
0
0
0
2
1
0
0
2
0
0
5
0
2
0
2
0
2
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
1
0
1
1
0
0
0
0
1
0
1
1
1
0
0
2
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
2
1
1
2
0
0
0
1
1
0
0
1
0
1
0
1
1
0
2
0
0
0
0
3
0
1
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
2
0
3
2
0
0
0
0
0
0
0
0
1
2
1
0
0
1
0
2
0
0
0
0
1
1
1
0
0
2
0
1
0
3
0
0
1
0
0
0
0
0
0
0
1
1
2
0
5
2
1
1
0
0
0
0
0
3
1
0
1
0
2
3
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
2
0
1
0
1
0
0
0
0
0
1
0
2
1
0
3
0
0
0
1
1
2
0
1
0
0
2
2
0
1
0
2
0
0
0
2
1
1
0
0
0
2
1
0
2
0
0
0
0
4
1
0
0
0
2
2
1
0
1
0
0
2
0
0
0
0
1
0
0
0
1
0
1
0
1
2
2
1
0
2
1
0
1
0
0
0
1
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
1
0
0
2
0
0
1
2
0
0
0
0
0
1
0
0
1
0
1
0
0
0
2
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
1
1
0
1
0
0
0
0
0
1
0
2
2
0
2
0
2
1
0
0
2
1
1
0
0
0
0
0
2
0
0
1
2
0
0
1
0
1
1
0
2
0
2
1
1
1
0
0
0
2
1
2
0
0
0
1
2
0
2
0
0
2
0
0
0
1
0
0
0
0
1
1
0
0
3
1
0
0
1
0
0
0
0
2
0
3
0
0
0
3
0
0
2
1
0
1
0
0
0
0
0
1
0
2
1
1
0
0
1
0
0
1
2
0
1
0
0
1
0
0
0
0
0
0
0
2
3
0
1
0
0
2
0
0
0
2
1
0
0
0
0
2
2
2
0
0
0
0
0
0
0
1
0
0
2
0
1
0
2
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
1
0
1
0
2
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
3
0
0
0
1
0
2
1
0
0
0
0
0
0
2
2
2
1
1
2
0
1
1
2
1
0
0
2
0
0
0
0
0
0
0
0
0
1
2
2
1
0
0
1
0
2
1
1
2
0
2
0
2
0
3
0
1
0
0
2
0
0
2
2
1
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
1
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
2
2
0
0
0
2
0
0
0
1
1
0
0
0
0
1
0
0
2
1
2
0
0
2
0
1
0
2
0
7
2
0
0
0
1
2
1
0
5
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
2
0
0
0
0
3
2
2
0
1
0
0
0
1
0
0
2
1
0
1
0
0
1
0
0
2
0
0
6
0
0
2
1
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
1
0
1
1
1
0
0
0
0
1
2
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
2
0
1
1
1
0
0
0
0
2
0
2
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
2
2
2
0
2
2
1
0
0
0
2
0
0
0
0
0
0
1
1
0
1
1
1
0
0
0
2
2
2
1
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
1
1
0
1
0
2
1
0
0
1
0
2
0
2
2
1
0
0
1
0
0
2
0
2
1
0
0
1
0
0
2
2
0
0
1
0
3
1
2
2
0
1
0
0
0
9
0
0
0
2
1
0
0
0
1
0
0
0
0
1
1
1
1
2
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
3
1
0
0
0
0
1
2
0
2
0
0
0
0
0
2
0
2
0
1
1
0
0
1
0
1
1
2
1
0
0
0
0
0
2
1
0
0
2
1
0
0
2
2
1
1
1
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
2
0
3
0
0
1
2
2
0
0
0
0
0
1
0
0
1
3
0
0
1
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
6
0
1
0
0
1
0
2
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
1
0
0
0
2
1
2
0
1
0
1
0
1
0
0
2
0
0
3
1
0
0
0
0
1
1
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
2
0
2
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
3
1
0
1
0
0
2
2
0
2
0
0
0
0
1
4
0
2
2
1
0
0
2
1
0
0
1
2
0
0
1
0
5
0
0
0
0
1
0
2
0
0
3
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
1
2
0
0
2
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
1
0
1
0
0
0
2
0
0
1
0
2
1
0
0
0
1
2
0
1
0
0
0
0
0
2
2
1
0
2
0
0
1
4
0
1
0
1
3
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
1
0
0
0
0
1
0
1
0
2
0
2
0
0
1
0
1
1
0
2
0
0
0
0
1
0
0
1
0
2
0
0
3
0
2
0
1
0
0
1
2
0
0
0
0
0
0
0
0
1
2
0
2
2
0
0
1
0
0
2
2
0
0
0
1
0
1
1
0
0
2
0
2
0
0
0
0
0
0
0
2
2
1
0
0
2
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
2
0
0
2
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
1
2
1
0
0
2
0
2
0
0
0
0
1
0
0
0
2
0
1
1
0
1
0
4
1
0
0
1
2
0
1
0
1
1
0
2
0
1
0
2
0
0
1
0
0
1
2
1
2
0
2
0
1
2
2
1
0
0
0
0
0
0
0
0
0
0
0
2
6
0
0
0
0
0
2
0
0
0
1
0
3
0
1
0
0
0
0
1
2
0
0
0
0
1
2
0
1
0
2
0
1
1
0
1
0
1
1
2
0
3
0
1
0
0
0
0
0
1
0
1
0
0
1
1
0
1
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
2
1
0
1
2
0
0
0
0
2
0
1
0
0
0
2
2
0
0
2
1
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
1
0
1
3
1
3
0
2
1
1
2
1
0
1
0
1
0
1
0
0
2
2
0
0
1
0
0
0
0
1
0
1
0
2
0
0
3
0
1
0
1
2
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
2
1
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
1
1
2
1
0
0
0
2
0
0
2
0
2
1
2
0
1
0
0
0
1
0
0
0
0
0
3
0
2
0
2
2
0
1
0
0
2
0
1
1
2
0
0
0
0
0
1
2
0
1
0
0
0
0
0
1
1
0
0
2
0
0
0
2
1
2
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
1
1
0
2
0
1
2
1
0
0
0
0
0
0
0
0
2
0
0
1
3
0
1
3
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
2
2
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
3
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
3
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
2
0
0
0
0
0
1
0
2
3
0
2
0
1
1
2
0
0
0
2
0
1
1
0
1
0
2
0
1
0
0
2
0
0
1
1
0
2
0
2
2
0
1
2
0
1
2
0
0
1
2
0
1
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
3
2
0
1
0
0
0
0
1
0
1
0
0
0
1
1
0
2
0
0
0
6
0
0
0
1
2
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
2
2
0
0
2
0
1
0
2
0
0
2
2
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
3
1
0
0
0
0
0
2
0
0
0
1
0
1
2
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
3
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
1
2
2
1
2
0
2
0
0
1
2
2
0
0
0
0
2
0
0
2
0
0
2
0
0
2
2
0
2
0
0
0
0
3
2
0
2
0
0
0
0
0
0
0
0
0
2
3
1
1
0
2
0
2
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
1
0
0
0
0
0
1
2
1
0
3
0
1
2
0
0
0
0
0
0
0
0
2
1
1
0
1
0
1
0
0
1
0
0
0
0
0
2
0
2
0
2
2
0
0
0
2
0
0
1
1
0
1
0
0
2
0
1
0
0
0
0
2
1
3
1
0
3
0
2
0
0
0
0
0
2
0
2
0
0
0
2
1
0
0
1
0
0
0
0
0
2
0
0
0
0
1
4
0
2
0
1
1
1
0
0
0
1
0
0
1
2
0
1
0
0
2
2
2
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
2
0
1
0
0
1
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
2
1
0
0
0
2
0
0
0
3
0
0
1
0
1
2
0
0
1
0
0
0
0
1
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
1
0
1
2
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
2
2
1
0
0
0
2
0
0
0
1
0
0
1
0
0
1
0
2
0
1
0
1
0
0
2
0
0
1
2
2
0
0
4
1
1
0
1
1
0
2
0
1
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
6
0
2
0
2
2
1
1
0
0
0
0
1
0
0
0
2
0
2
1
0
1
2
1
0
1
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
2
2
0
0
1
0
0
0
0
0
2
0
0
1
0
0
1
1
0
0
0
2
1
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
3
0
0
2
1
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
2
1
1
0
3
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
1
0
1
0
1
0
0
0
3
0
0
0
2
1
0
1
0
0
1
0
0
0
0
2
1
0
1
2
0
2
0
2
1
0
0
0
1
0
1
2
0
0
0
2
2
0
0
2
0
2
2
0
1
0
0
0
0
1
2
2
1
0
0
2
0
3
1
0
0
0
1
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
2
1
2
2
1
0
1
1
0
0
0
2
0
0
1
0
0
2
1
0
1
1
1
0
2
2
2
0
0
1
0
1
0
0
2
2
0
1
2
0
0
0
0
1
1
0
1
0
2
1
1
2
0
0
2
0
0
2
0
1
2
0
0
0
1
0
1
0
1
1
1
2
0
2
0
0
0
1
0
2
1
0
1
3
0
0
1
0
0
1
0
0
0
0
2
2
0
1
0
1
2
0
0
1
3
1
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
2
1
1
0
0
0
3
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
2
0
0
2
0
1
0
2
0
2
0
0
0
0
0
0
2
0
1
0
0
4
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
1
0
0
1
0
0
0
0
1
2
0
3
0
0
0
0
1
0
0
0
0
2
2
1
1
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
1
0
0
2
0
1
1
2
1
0
0
0
0
3
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
6
0
1
1
2
0
0
0
0
0
1
1
2
1
1
0
0
0
2
0
2
2
0
0
0
2
1
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
2
2
0
0
2
2
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
2
2
1
0
0
0
0
2
0
0
1
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
1
0
2
1
2
0
0
0
2
1
1
0
0
1
0
2
0
0
0
0
0
0
0
1
1
0
3
1
1
0
0
0
2
0
2
1
1
0
0
0
0
0
2
0
2
0
1
2
2
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
1
2
0
0
3
0
0
2
0
1
1
1
0
1
0
2
0
0
1
0
1
0
0
0
2
1
2
1
0
1
0
0
2
1
0
0
0
2
1
0
2
1
0
0
0
2
0
0
1
0
0
1
0
1
2
0
0
1
0
0
0
1
0
0
2
0
0
1
1
6
0
0
0
0
0
2
0
0
1
2
0
1
0
2
0
0
0
0
1
0
0
0
0
2
0
1
2
0
0
2
0
0
0
0
2
1
1
0
0
0
0
2
0
0
3
2
0
2
0
2
2
0
0
0
2
0
0
0
0
2
0
0
1
1
2
0
2
0
0
2
2
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
1
2
0
0
2
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
2
3
0
0
1
0
0
0
1
0
0
0
0
2
0
1
0
0
2
0
0
2
2
0
0
0
2
0
0
0
2
0
0
0
2
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
1
2
2
0
0
0
2
1
0
1
1
0
0
2
0
1
2
1
0
2
0
0
2
2
0
0
0
0
0
0
0
3
0
1
0
0
0
0
1
0
0
0
3
0
2
0
0
0
2
0
2
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
2
1
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
1
2
1
1
0
0
2
3
0
0
0
0
1
1
2
2
2
0
0
1
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
1
0
0
1
0
0
1
0
2
0
0
1
1
0
2
0
0
0
0
1
0
1
0
3
2
1
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
2
1
0
1
0
0
0
0
2
0
1
1
1
2
1
0
1
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
2
0
2
3
0
1
0
0
2
1
0
0
4
0
0
1
0
2
0
0
0
0
0
6
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
1
0
2
2
0
1
0
0
0
0
1
0
2
0
2
2
0
0
2
0
0
2
0
0
0
1
0
1
0
2
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
1
0
0
0
0
0
0
1
2
2
1
3
1
0
0
0
0
0
1
0
0
1
0
0
2
0
2
0
0
0
1
0
0
0
0
1
2
1
0
2
0
0
0
0
0
0
2
2
0
3
1
2
2
0
0
0
2
1
0
0
1
2
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
3
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
2
1
0
1
0
0
2
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
2
0
2
0
2
2
2
0
0
2
0
0
0
0
2
1
1
1
0
0
0
0
0
2
2
0
1
0
0
0
0
1
0
2
0
0
0
0
1
1
1
2
2
0
0
2
1
1
2
0
0
0
0
0
0
1
2
1
0
2
2
0
0
1
0
0
1
0
0
3
0
1
0
0
0
3
0
0
0
1
0
2
2
0
4
0
2
0
0
1
2
2
0
4
0
0
1
0
0
0
0
1
0
0
2
2
1
0
3
0
0
1
0
2
0
2
0
0
3
0
2
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
3
0
2
0
2
0
1
0
0
0
0
2
1
2
1
0
0
1
2
0
0
2
0
0
0
0
0
1
2
2
2
0
0
1
0
2
1
2
2
0
0
0
1
2
2
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
1
2
2
1
2
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
1
0
1
0
0
0
2
0
0
1
2
0
1
0
0
2
4
0
3
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
2
1
2
0
0
0
1
1
0
1
0
2
0
2
0
1
2
2
0
0
2
0
2
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
2
1
0
1
0
0
1
0
2
0
1
0
2
0
0
0
0
0
0
0
1
1
0
1
0
1
1
0
0
2
1
0
0
1
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
2
1
2
0
0
1
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
2
1
2
0
0
1
0
0
1
0
0
0
0
0
0
2
0
2
0
1
0
2
0
0
0
2
1
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
1
2
0
0
0
0
1
0
1
0
0
0
2
2
0
0
4
1
0
0
0
2
0
0
2
0
0
4
0
0
2
1
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
2
1
1
1
1
0
0
1
0
1
2
2
1
0
0
0
0
1
0
3
1
1
0
2
0
0
1
0
0
2
2
0
0
2
4
0
0
1
0
0
0
0
0
1
1
1
0
0
1
0
0
2
1
2
0
0
0
0
0
2
0
0
0
1
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
5
2
2
0
0
1
1
0
0
0
0
2
0
2
0
2
2
2
3
0
0
0
1
0
0
0
0
0
0
2
1
0
0
1
2
0
2
0
0
2
0
0
1
3
0
2
2
1
2
1
1
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
3
1
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
2
0
2
0
2
1
0
0
2
1
0
0
0
0
0
0
1
2
0
2
0
1
1
0
0
0
2
2
1
0
1
1
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
1
2
1
0
1
1
2
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
2
0
1
0
0
1
3
2
0
1
2
0
0
1
1
0
0
0
0
1
0
0
0
2
1
3
0
0
1
0
0
0
0
2
0
0
1
0
0
1
2
0
0
0
0
0
1
0
2
0
0
0
0
2
0
2
0
0
2
1
0
0
0
1
0
2
0
2
2
1
2
0
0
1
0
0
1
0
0
0
0
2
0
0
2
1
0
2
0
1
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
2
3
2
0
0
0
0
0
0
0
2
0
1
0
2
1
0
2
2
0
0
0
0
0
0
0
2
0
1
1
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
1
0
1
1
0
0
0
0
1
0
0
0
1
0
0
1
2
2
2
2
0
1
0
1
0
0
1
2
0
0
0
2
0
2
1
0
0
1
0
0
1
2
1
0
1
0
2
4
0
0
0
0
1
0
4
1
0
0
0
0
0
0
0
1
1
1
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
3
2
2
1
0
1
0
0
0
0
0
0
0
0
2
0
0
2
1
2
0
2
0
0
0
0
1
2
1
1
0
0
2
0
0
2
1
0
2
0
1
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
1
0
0
1
2
0
2
1
0
0
0
2
0
0
0
0
1
0
2
1
0
2
0
1
0
0
0
2
0
1
1
1
0
0
1
0
2
0
1
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
2
2
1
1
1
0
0
0
1
1
0
0
0
0
0
1
0
2
2
2
0
2
0
0
0
1
0
1
0
1
2
0
0
0
1
0
0
0
0
1
0
2
1
0
0
1
0
4
2
0
0
0
0
0
2
3
2
2
0
1
0
0
0
2
0
0
0
0
0
0
0
4
1
1
2
1
0
0
0
0
1
0
0
1
0
2
2
1
0
2
2
0
0
0
4
0
2
0
0
0
2
0
1
1
0
0
0
0
0
1
1
0
0
1
0
1
0
0
1
2
0
2
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
2
0
0
3
0
1
0
1
0
1
0
2
0
0
0
1
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
1
1
0
0
0
2
0
0
2
1
2
0
0
0
0
2
0
2
1
1
2
1
0
0
0
0
1
0
1
0
0
0
2
1
1
0
0
0
2
0
1
0
0
0
1
0
0
0
2
1
0
0
1
0
0
0
0
2
0
2
0
2
0
1
0
0
1
0
0
1
0
2
0
0
0
0
0
1
1
0
1
0
0
0
2
0
1
0
0
2
1
0
0
0
1
2
0
2
0
0
0
0
0
0
2
1
0
0
2
1
1
0
0
0
0
0
2
1
0
0
0
1
0
1
0
0
0
1
0
0
1
1
1
0
0
1
0
0
1
5
0
0
0
0
0
0
0
2
0
0
0
1
0
2
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
1
1
0
0
1
6
1
0
3
1
2
0
0
0
2
1
0
1
0
1
0
0
0
1
2
0
1
0
1
1
0
0
1
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
2
2
0
0
2
1
0
0
1
0
0
0
1
0
0
0
2
0
0
2
0
0
1
0
1
0
0
0
0
1
0
1
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
2
0
2
1
2
0
0
0
2
0
1
2
1
0
2
1
0
0
1
8
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
1
0
1
0
1
1
2
1
1
2
0
0
3
0
1
2
0
0
0
2
0
0
2
0
1
1
2
0
0
1
0
2
0
2
2
0
0
2
2
0
0
1
0
0
0
0
0
1
0
0
2
1
0
0
0
1
0
2
0
2
0
2
3
0
0
0
0
1
0
0
0
2
0
0
0
0
1
1
0
1
0
0
1
1
0
0
0
1
1
0
2
0
0
1
2
0
1
0
0
0
1
0
0
0
1
0
0
0
2
2
1
0
0
0
2
1
0
2
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
2
0
3
2
3
0
0
0
1
0
3
0
1
1
2
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
1
1
0
0
0
0
2
1
2
2
0
0
1
0
0
0
2
1
1
0
1
0
0
2
2
0
0
2
2
1
0
0
0
0
1
0
0
0
0
2
2
0
0
2
0
0
0
0
0
2
0
0
0
0
2
1
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
2
2
1
1
0
1
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
1
3
0
0
1
0
3
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
2
1
0
0
2
2
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
3
0
0
0
1
0
0
0
2
3
1
0
0
0
0
1
2
0
2
0
2
2
0
1
2
0
2
0
1
0
2
0
0
0
1
0
2
0
0
2
2
0
0
0
2
0
0
0
2
1
0
1
2
0
1
1
0
0
0
0
0
2
0
2
0
1
0
1
0
0
1
2
0
1
0
0
1
3
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
2
1
0
0
2
1
0
2
1
0
0
0
2
2
0
0
0
0
0
0
1
0
1
0
1
0
0
0
2
2
0
0
0
2
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
2
2
0
0
0
1
0
2
0
1
0
0
2
0
2
0
0
2
0
0
0
1
1
0
0
0
2
0
0
2
0
2
0
0
0
2
0
0
1
2
0
0
0
0
0
5
0
0
0
0
0
0
1
0
0
2
0
1
0
1
0
0
0
0
0
0
0
2
1
0
1
0
0
0
2
0
2
0
0
2
2
0
0
2
0
1
0
0
0
0
1
1
2
2
0
1
0
0
0
0
0
0
1
1
0
0
1
2
0
0
0
0
0
0
0
0
1
1
0
0
0
3
0
0
0
0
0
1
1
1
1
0
0
1
2
0
3
0
2
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
1
0
3
0
1
1
0
2
0
0
0
0
2
0
0
2
0
2
0
0
6
2
2
0
1
2
2
0
0
0
0
1
1
0
1
0
0
2
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
2
1
0
1
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
2
1
0
0
1
0
0
0
1
3
0
0
2
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
1
0
1
0
1
0
0
0
0
0
2
10
1
0
0
0
0
2
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
3
0
0
0
0
2
0
2
0
1
0
0
1
0
0
1
0
2
0
2
1
2
0
0
0
2
2
0
0
0
0
0
0
0
1
0
1
2
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
2
6
0
0
0
1
0
0
0
4
1
2
1
2
0
0
0
0
0
1
0
0
1
0
1
2
0
0
1
3
0
1
1
0
0
0
0
2
0
2
1
0
1
0
0
0
0
2
0
1
3
0
0
0
2
1
0
1
2
0
0
2
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
2
0
2
0
0
0
0
1
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
0
1
1
1
0
0
0
2
0
0
0
2
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
1
2
0
0
1
1
1
0
2
0
1
0
1
0
0
2
0
1
0
0
2
2
0
0
0
0
0
1
0
0
1
0
0
0
2
0
1
1
1
0
0
0
0
0
0
0
0
1
1
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
1
0
2
0
1
0
0
0
0
1
1
0
2
0
1
0
0
2
0
0
0
0
4
0
1
0
1
0
0
2
0
0
0
1
0
0
1
2
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
3
0
0
0
0
1
1
2
0
8
1
0
0
0
1
0
0
0
3
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
2
0
0
2
0
1
0
0
0
2
0
0
3
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
2
0
0
0
1
2
0
0
0
0
0
0
4
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
4
0
2
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
2
0
0
0
0
0
1
0
1
1
1
1
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
1
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
2
0
0
2
0
3
1
0
1
1
0
0
0
0
0
1
0
2
2
0
0
1
0
0
0
0
1
0
0
1
0
0
0
2
1
2
0
3
0
2
0
2
2
0
0
0
4
2
0
0
1
0
2
0
0
1
1
2
1
0
2
1
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
1
2
0
4
2
0
0
1
0
1
2
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
2
1
0
0
2
1
0
0
2
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
9
0
2
0
0
0
0
2
1
2
0
0
2
0
2
0
0
0
0
0
2
0
1
0
1
1
0
0
2
0
0
1
2
0
1
1
1
1
5
1
2
2
0
2
0
1
0
2
0
0
0
0
2
0
0
0
2
2
0
0
1
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
1
2
0
0
0
0
0
0
1
2
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
1
0
2
0
0
2
0
2
1
0
0
0
0
2
0
0
0
10
0
2
2
2
1
0
0
2
2
0
0
0
1
1
0
0
0
0
0
0
3
2
1
2
0
0
0
0
0
2
1
3
0
0
2
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
3
3
0
1
1
1
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
1
0
1
0
0
2
0
2
0
2
1
1
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
3
0
1
0
0
0
1
1
0
0
1
0
0
1
0
1
1
2
0
0
0
1
1
0
0
0
1
2
1
2
0
1
0
3
2
1
1
2
0
0
0
0
0
3
9
0
0
1
0
0
0
1
0
0
0
0
0
0
0
3
1
1
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
2
2
0
0
1
2
0
0
0
0
0
1
2
1
0
0
2
2
0
0
2
0
0
0
0
2
0
1
0
0
1
0
0
0
1
0
1
0
0
13
0
0
2
0
2
2
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
1
1
0
0
0
1
2
1
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
2
0
0
1
0
2
0
3
0
2
0
0
1
0
0
2
0
0
0
0
1
0
1
0
1
3
1
0
1
1
2
0
0
0
1
0
0
0
0
1
3
2
0
1
0
2
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
2
0
1
2
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
1
0
1
0
2
2
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
2
0
0
0
2
1
2
3
0
2
0
2
1
0
0
0
1
1
0
0
0
0
0
0
0
2
3
0
0
0
2
0
0
2
0
2
0
0
1
0
0
0
0
1
2
1
0
0
0
0
1
0
1
2
0
0
1
0
2
0
0
0
1
0
2
1
0
0
1
0
0
1
0
1
0
1
1
0
0
0
0
2
0
2
0
0
1
2
0
0
0
2
0
2
1
1
2
0
0
0
0
1
0
0
0
0
1
0
1
0
0
2
0
0
0
2
2
0
3
1
0
1
0
0
3
0
0
2
1
0
0
0
2
2
0
0
2
0
0
1
0
0
0
0
1
0
0
0
1
1
0
1
0
1
2
0
0
2
0
0
2
1
0
2
1
0
2
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
1
1
1
2
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
1
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
2
2
0
0
1
0
1
0
1
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
2
1
2
1
0
0
0
1
0
2
0
0
0
1
2
0
0
0
0
0
0
1
2
0
0
0
2
1
1
2
0
1
0
1
2
0
2
0
0
0
0
0
1
0
0
1
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
1
0
2
2
0
2
2
2
2
1
2
1
0
0
1
2
1
2
0
0
2
1
2
5
0
0
2
1
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
2
1
0
0
2
4
0
0
0
1
0
2
1
2
0
0
0
2
1
2
0
2
0
0
2
2
1
1
0
1
0
3
0
0
2
0
0
0
1
0
2
2
2
0
1
2
0
0
0
0
0
2
1
1
0
0
0
1
0
1
1
1
0
2
0
1
2
0
0
0
0
0
3
1
4
2
1
1
1
0
2
0
0
0
2
0
1
0
0
0
0
2
1
1
0
2
0
1
2
0
1
0
0
0
1
0
2
0
2
0
0
3
2
0
0
0
0
0
1
0
1
0
0
2
0
1
0
0
1
0
0
0
1
0
1
0
0
0
1
1
2
0
0
0
2
1
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
1
1
0
2
0
1
0
0
0
3
0
0
0
2
2
0
0
0
1
1
2
0
0
0
0
1
1
3
0
0
0
0
0
0
0
0
0
1
1
0
1
0
2
1
0
0
0
2
0
2
0
0
2
0
0
1
1
0
2
0
2
2
0
0
0
0
0
0
1
0
0
1
0
1
0
2
1
0
0
0
0
1
0
0
1
0
0
0
1
0
1
1
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
2
2
0
1
0
0
0
0
2
2
2
0
0
1
2
0
0
0
1
0
2
0
1
1
3
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
2
0
2
0
0
3
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
1
0
0
0
3
0
1
2
0
2
2
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
2
0
0
2
0
0
2
0
0
3
0
2
0
0
0
1
2
0
0
1
0
0
0
0
0
1
1
0
5
0
2
1
0
0
1
2
0
0
1
0
2
2
0
3
1
0
0
0
1
0
0
2
2
3
0
0
0
2
0
4
0
0
0
0
2
0
0
2
1
0
0
0
1
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
1
2
0
1
0
0
2
0
0
2
1
2
2
2
0
0
0
0
4
0
0
0
2
1
0
0
0
0
0
1
0
0
1
2
0
0
0
1
0
0
0
0
1
0
1
0
2
0
1
0
1
0
0
0
0
1
2
1
0
0
2
0
0
0
1
0
1
1
1
0
2
0
0
0
0
1
0
0
0
1
0
2
1
3
0
0
0
2
2
0
0
0
0
0
0
0
1
0
2
0
0
2
2
1
0
0
0
1
0
0
0
0
2
2
2
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
2
0
1
0
0
1
0
0
0
0
0
0
2
0
0
1
1
0
1
0
1
0
0
0
2
0
0
0
0
0
1
1
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
5
1
0
1
2
1
0
1
0
0
0
2
0
2
0
0
1
0
2
0
0
2
0
0
2
2
0
1
1
0
0
3
2
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
3
0
1
0
1
1
2
0
0
0
0
2
0
1
2
1
0
0
0
0
0
3
0
0
0
0
0
0
0
2
1
0
3
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
2
0
1
0
2
0
1
0
2
0
2
0
0
0
1
1
1
0
0
1
2
0
1
0
1
0
0
0
0
1
0
0
2
1
0
0
0
0
2
0
2
0
0
3
0
0
0
2
1
2
0
0
1
0
0
2
2
2
0
0
2
1
0
2
0
1
2
0
0
2
1
0
0
0
2
2
0
1
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
1
0
1
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
3
2
1
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
1
0
0
2
0
0
2
1
0
0
0
1
0
1
0
0
0
0
0
0
4
0
1
0
0
0
0
1
2
0
1
0
1
0
0
0
0
0
0
0
0
0
1
2
1
1
1
0
0
1
0
3
1
0
0
0
2
0
0
0
0
0
2
0
2
2
0
1
0
0
1
1
2
0
0
0
0
0
0
0
4
0
1
0
0
2
0
0
0
0
0
1
2
2
0
1
1
2
0
0
2
0
1
0
0
2
0
0
1
0
0
0
0
1
0
2
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
3
0
2
0
1
0
0
0
0
2
0
0
0
1
0
0
0
3
2
0
0
0
0
2
1
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
1
0
0
1
0
2
1
1
1
0
0
1
1
0
0
1
0
1
0
0
1
0
0
2
0
0
0
0
0
0
3
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
2
0
0
1
0
0
1
0
3
1
0
0
1
1
0
1
0
1
0
1
1
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
5
0
2
1
0
1
0
2
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
3
0
0
0
2
0
1
0
0
2
0
0
0
0
0
2
0
0
1
0
2
0
2
1
0
0
1
0
0
0
0
2
3
0
2
0
0
1
0
1
0
0
0
0
0
1
2
2
0
0
2
0
2
0
3
1
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
1
2
1
0
1
0
0
0
0
0
1
0
0
1
0
0
3
1
1
0
1
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
2
0
1
0
0
1
0
1
0
0
0
0
0
0
1
2
0
1
1
0
1
1
1
0
0
0
0
0
1
0
1
1
0
2
0
0
1
0
0
0
2
0
2
1
1
2
0
0
2
2
0
1
0
0
2
0
2
1
1
0
0
0
0
0
2
0
0
0
2
1
0
0
1
1
0
2
0
0
2
0
0
4
2
0
0
0
0
0
0
2
0
0
2
0
0
1
2
1
0
0
2
0
0
2
1
2
0
0
0
0
2
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
1
1
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
1
0
0
0
3
2
0
2
0
0
1
0
0
0
1
0
0
0
1
0
1
0
2
1
0
2
2
0
0
0
3
1
0
0
1
2
2
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
5
0
1
0
1
0
0
2
0
0
0
0
1
1
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
5
0
0
0
2
0
1
0
0
1
0
0
1
0
0
2
2
1
2
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
2
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
1
1
2
0
2
0
0
2
1
2
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
2
0
0
1
0
0
2
1
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
3
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
4
1
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
1
2
1
0
0
1
1
2
0
0
0
0
2
0
0
0
0
0
2
1
0
2
0
2
0
0
0
0
3
1
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
8
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
2
0
3
0
0
1
0
0
0
1
0
0
0
0
0
2
1
0
0
0
2
0
4
0
1
0
1
1
1
1
0
0
0
2
0
0
1
0
0
0
2
2
0
4
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
1
2
0
0
1
0
1
1
0
2
0
0
0
2
0
3
2
1
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
1
0
1
2
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
2
1
0
0
0
1
0
2
0
1
0
0
2
0
0
0
0
0
0
2
2
0
0
3
1
0
0
2
0
1
3
2
0
0
0
1
1
0
1
0
0
0
0
0
0
0
4
0
2
1
1
1
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
2
0
1
0
0
0
0
0
2
0
0
0
0
2
1
2
2
0
2
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
2
0
2
1
0
0
0
0
2
0
3
0
0
0
0
1
0
0
1
1
0
0
0
0
1
4
1
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
2
2
2
0
0
0
0
2
0
1
0
2
1
0
1
2
0
1
1
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
2
2
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
2
0
1
0
0
0
0
0
1
2
0
0
2
1
0
0
0
0
0
2
0
2
3
3
0
1
1
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
2
0
0
0
2
0
1
0
3
0
0
0
1
0
0
0
0
0
1
0
0
1
0
2
2
0
4
2
0
0
2
1
0
1
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
1
0
0
1
0
0
0
1
1
1
0
0
1
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
2
0
0
0
0
0
2
0
2
2
0
2
0
0
3
2
2
0
0
3
2
2
0
2
0
0
2
2
0
0
0
0
2
0
2
0
2
0
0
2
0
2
0
0
1
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
2
1
1
2
0
0
2
0
1
0
1
0
1
0
0
0
0
0
4
2
0
2
1
0
1
0
0
1
2
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
1
1
1
0
0
0
0
0
2
0
1
2
1
2
0
0
1
0
0
2
1
0
0
0
0
0
1
1
0
1
1
0
0
0
0
2
4
1
2
1
1
0
1
0
0
3
0
0
2
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
4
5
2
0
0
0
2
1
0
0
0
1
2
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
2
0
0
0
2
0
0
0
0
1
0
0
1
1
2
0
0
0
0
0
0
0
0
1
1
0
1
0
0
2
3
0
0
1
2
0
0
0
2
0
2
0
0
1
0
1
0
2
0
0
0
0
0
0
1
0
3
0
2
0
0
0
0
0
0
0
1
1
0
1
0
2
10
0
0
0
2
2
2
1
0
0
1
2
2
0
1
0
1
0
0
0
0
0
0
2
0
0
1
1
2
0
1
2
2
2
0
1
1
0
0
0
0
2
1
0
2
0
0
1
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
2
2
0
0
0
1
0
0
0
0
1
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
1
0
1
1
0
0
2
0
2
0
0
0
0
0
0
1
2
0
0
1
0
0
1
0
0
0
2
1
0
1
1
2
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
1
0
1
1
1
0
0
0
1
0
0
0
0
1
1
3
2
0
0
1
2
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
3
0
1
0
0
0
0
1
2
0
2
2
1
2
0
0
1
3
0
0
2
0
2
2
0
0
2
0
0
0
0
1
0
7
0
0
0
0
0
0
2
0
2
1
0
0
1
2
0
1
0
0
0
1
2
0
0
0
1
0
0
1
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
1
0
0
1
0
0
0
2
1
1
2
1
0
0
0
1
1
2
0
0
0
0
0
0
0
1
2
0
0
6
0
1
0
0
0
1
3
1
0
1
0
1
1
0
0
0
2
0
0
1
3
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
3
0
0
0
0
1
1
0
2
1
0
0
2
1
0
0
2
0
0
1
0
2
1
1
0
2
0
0
0
0
0
2
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
1
0
1
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
2
0
0
2
0
0
1
2
0
1
1
0
2
1
0
6
0
2
1
2
0
1
0
0
0
1
0
0
2
0
0
0
1
0
1
1
0
0
0
0
2
2
2
0
1
0
2
0
0
0
0
1
0
0
0
0
0
2
1
0
0
2
0
0
0
1
0
2
0
0
0
1
0
0
0
2
0
2
1
0
2
0
2
0
0
0
0
2
0
0
0
0
2
4
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
1
1
1
0
1
0
0
1
2
2
0
0
0
1
0
0
1
0
2
0
0
1
0
1
0
1
0
1
0
1
0
0
1
2
0
0
1
2
0
1
6
0
0
0
1
2
0
0
0
0
2
0
1
0
0
1
0
0
0
1
1
1
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
1
2
0
1
0
2
2
2
2
1
2
0
0
0
1
0
0
0
1
1
1
1
0
1
2
2
0
1
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
8
0
0
0
0
0
0
0
2
0
1
2
1
2
2
2
3
0
2
0
2
0
0
0
0
0
1
2
0
2
0
1
0
0
0
1
1
0
2
0
1
0
0
2
0
1
2
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
2
2
2
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
1
1
0
2
0
0
2
1
0
0
2
2
0
2
0
2
1
0
2
0
0
0
0
1
0
1
0
2
2
0
1
0
0
0
0
0
1
0
1
2
1
0
0
0
0
0
1
3
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
2
0
1
0
0
3
1
1
0
0
0
1
1
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
2
0
0
0
1
3
0
1
1
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
1
0
2
0
2
0
0
0
0
2
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
2
2
0
0
1
0
1
0
1
0
0
2
0
1
0
0
0
1
0
1
0
0
0
0
1
2
0
0
1
0
0
0
3
0
2
0
0
0
2
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
2
0
1
0
1
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
2
1
0
2
2
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
1
0
0
0
0
1
0
2
0
0
0
0
0
2
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
3
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
1
2
1
1
0
3
0
0
2
0
0
0
0
0
0
0
1
2
0
1
6
1
2
4
0
0
2
0
2
0
0
0
2
2
0
0
0
0
2
2
2
1
0
0
0
0
0
0
0
0
1
2
0
2
0
1
1
0
1
2
0
0
1
0
0
1
1
2
1
0
0
2
1
0
2
0
0
0
0
0
2
0
1
0
0
0
0
1
2
0
0
1
1
0
0
1
1
2
0
0
0
2
0
0
2
4
0
2
2
2
1
0
0
1
0
0
0
0
0
2
0
0
1
1
0
0
0
0
2
0
1
0
0
0
0
1
2
3
2
0
2
0
1
0
0
0
0
0
2
0
0
2
1
1
0
0
0
1
0
0
0
2
1
2
1
1
0
0
0
2
2
1
0
1
0
0
0
0
2
0
1
0
1
0
0
1
0
0
0
0
0
0
1
1
2
0
2
1
1
0
1
0
0
1
1
0
0
0
0
0
0
1
2
1
0
1
0
0
0
0
2
0
0
0
0
2
2
0
2
0
0
2
0
0
0
0
0
1
0
4
0
1
0
0
1
2
0
0
2
0
1
2
0
0
0
0
0
1
0
1
2
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
2
0
0
2
0
0
2
0
2
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
2
0
1
2
0
1
2
0
0
0
2
2
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
1
0
1
0
2
0
0
2
0
2
2
1
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
2
0
1
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
2
0
0
0
1
1
1
2
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
2
0
0
1
0
1
2
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
1
0
3
0
0
0
0
2
0
0
1
2
2
0
1
2
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
1
2
0
0
0
2
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
1
2
0
1
0
1
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
2
1
0
0
0
2
0
2
0
1
0
2
0
0
1
1
0
2
2
3
1
0
3
0
0
0
1
0
0
0
0
1
2
3
0
2
1
0
1
2
1
0
0
0
0
2
2
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
2
2
0
0
1
0
0
0
0
1
0
0
0
0
2
1
2
0
0
2
0
0
0
0
0
0
0
0
0
2
2
2
2
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
3
2
1
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
1
2
0
0
0
0
0
1
2
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
2
2
0
2
0
0
0
0
1
0
1
2
0
2
1
1
0
0
0
1
0
1
0
0
2
0
1
1
0
0
0
1
0
1
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
1
2
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
5
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
1
0
1
0
1
0
1
1
0
2
2
0
0
0
0
0
0
0
0
0
6
0
1
0
0
0
0
0
0
2
0
2
3
0
0
0
0
3
0
0
0
2
2
0
0
0
2
0
0
0
1
0
2
0
2
2
0
2
0
2
0
0
1
2
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
3
1
0
0
2
1
0
0
0
0
1
0
0
1
1
1
0
1
0
2
0
1
2
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
1
0
0
1
0
0
2
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
1
0
2
2
0
1
2
0
0
0
1
0
2
2
0
0
0
2
0
0
1
2
3
0
0
2
1
2
2
0
0
2
2
1
1
0
0
3
0
0
0
0
2
2
1
0
0
0
1
0
2
0
1
2
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
4
2
0
0
0
0
0
1
0
1
0
1
1
0
1
0
1
2
1
2
3
0
0
0
0
1
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
2
0
0
0
1
1
0
2
0
0
1
0
0
2
1
2
0
2
0
1
0
1
3
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
4
1
1
0
0
1
2
0
0
0
1
1
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
0
1
0
1
2
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
1
2
0
0
1
1
0
1
4
0
0
1
0
0
0
0
2
0
1
0
0
2
3
0
1
0
1
0
0
0
2
2
0
0
0
2
1
1
0
0
0
2
1
0
1
11
2
0
2
1
0
0
2
0
1
0
0
0
1
0
0
0
1
0
0
0
2
0
3
2
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
2
0
0
3
0
1
0
2
0
0
0
0
0
0
0
1
0
0
2
1
0
2
0
1
0
1
0
0
1
0
2
0
1
0
0
0
1
0
0
2
0
2
0
0
0
0
1
2
0
0
0
1
1
2
0
1
0
2
1
0
2
0
0
0
1
1
0
2
0
2
0
1
0
2
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
2
2
0
0
1
0
0
1
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
3
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
2
1
3
0
0
0
1
0
0
0
3
0
0
0
0
0
0
4
0
1
0
0
0
2
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
1
0
0
1
0
2
2
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
2
3
0
0
2
0
0
2
0
0
1
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
2
0
0
2
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
3
2
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
1
2
0
0
1
0
0
1
0
0
0
0
0
0
3
0
1
0
0
0
0
3
3
0
2
0
1
0
0
0
3
0
0
0
0
2
0
1
1
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
1
1
0
0
1
2
0
0
0
0
0
1
2
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
1
1
0
0
0
1
2
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
1
2
0
0
2
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
1
1
0
1
0
2
2
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
1
2
0
2
0
0
0
2
0
0
2
0
0
2
0
1
0
1
0
0
0
1
2
0
0
0
1
2
0
1
0
0
0
2
0
0
0
2
0
3
0
0
0
0
0
1
0
2
1
1
0
0
0
0
2
1
0
0
1
2
0
1
0
1
1
2
0
0
2
2
0
1
1
0
0
1
2
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
2
2
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
1
1
0
2
0
0
1
2
0
1
1
0
0
0
2
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
1
0
2
0
0
1
2
1
2
1
5
0
2
0
1
1
2
0
2
0
0
0
0
0
1
0
1
0
2
1
0
0
2
2
0
0
2
0
0
0
1
2
0
1
0
2
2
0
0
0
2
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
1
0
0
0
0
0
0
0
1
2
1
0
0
0
2
0
0
1
2
1
1
0
1
0
2
0
0
0
3
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
1
2
1
0
2
2
0
2
1
0
1
0
0
0
2
1
1
0
0
0
2
2
1
0
2
1
0
0
0
1
2
0
0
0
2
1
1
2
0
0
2
0
2
2
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
2
1
0
0
0
2
1
0
0
2
1
1
0
0
0
2
0
0
0
1
0
1
0
0
0
2
0
1
2
0
1
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
1
0
0
0
1
0
0
3
2
2
2
1
0
0
1
0
0
0
1
2
0
0
3
0
0
0
0
0
0
1
0
0
1
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
2
1
2
0
0
1
1
0
2
0
0
0
2
0
0
0
0
2
1
0
0
2
0
2
0
3
2
1
0
0
0
0
1
0
0
1
1
2
0
3
1
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
3
0
0
2
0
1
2
2
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
1
1
0
2
2
0
1
0
1
0
1
2
0
0
2
3
0
0
1
0
2
0
1
1
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
2
0
1
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
1
1
1
0
0
2
3
0
0
0
1
2
0
1
2
1
0
3
0
1
0
0
2
0
0
0
0
0
0
0
2
2
0
3
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
1
0
0
1
1
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
4
2
0
1
1
0
1
2
0
0
1
4
0
0
0
2
0
0
1
2
0
1
0
0
0
2
0
0
1
0
2
0
0
0
0
2
1
0
0
1
5
0
0
1
0
1
4
1
0
1
2
2
0
0
1
1
0
1
1
0
0
0
1
1
0
0
0
2
0
0
2
2
0
1
0
4
2
1
0
0
5
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
2
0
1
1
0
0
0
0
0
2
1
0
2
0
0
0
0
1
0
0
4
0
0
0
0
0
0
1
1
2
0
1
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
2
2
2
0
2
0
2
1
0
2
2
0
1
0
1
1
1
2
1
0
2
1
2
0
0
0
2
0
1
2
0
0
0
0
2
1
0
0
2
0
1
0
0
0
0
1
0
0
0
1
0
2
0
2
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
2
0
2
2
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
3
0
0
0
0
1
0
1
0
0
0
0
0
1
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
3
2
1
2
0
0
2
0
0
2
2
0
0
0
2
0
1
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
1
4
2
1
1
2
0
0
0
1
0
0
0
0
1
0
1
0
0
2
1
1
3
0
0
2
0
2
1
2
0
0
1
0
2
0
0
1
2
4
0
0
0
0
0
0
0
0
1
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
2
1
0
0
0
2
1
0
0
3
1
2
1
2
0
0
0
1
0
3
0
1
1
2
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
1
2
0
0
0
0
2
2
1
1
0
0
1
0
1
0
2
2
0
0
1
0
2
2
0
0
0
1
2
0
1
0
1
2
1
3
0
1
0
0
2
0
0
2
1
2
0
0
2
0
0
0
0
2
0
1
0
4
1
2
1
0
0
0
1
1
2
1
1
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
2
1
1
0
0
2
1
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
1
2
2
0
0
0
0
0
7
2
0
0
1
3
0
1
0
1
0
2
0
0
2
1
2
2
1
0
0
0
0
0
0
0
0
0
0
10
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
2
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
3
2
2
0
0
0
0
0
0
0
1
0
1
0
1
13
2
0
0
0
0
0
0
2
0
2
0
4
0
0
0
2
1
0
0
0
0
0
0
2
0
1
1
1
0
2
0
1
0
0
1
2
0
0
1
0
0
0
1
0
2
0
0
2
0
2
0
2
0
1
0
0
0
0
0
0
1
0
1
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
5
0
2
0
1
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
1
1
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
1
0
1
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
3
0
1
2
0
0
1
0
1
0
0
0
2
2
0
0
2
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
1
0
0
0
0
2
2
0
0
0
2
1
0
0
2
0
1
2
0
0
0
0
1
1
2
0
4
0
0
1
0
0
4
1
0
0
0
2
1
1
2
0
0
1
0
0
0
2
0
0
0
1
1
0
0
1
0
2
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
1
0
0
2
0
0
1
2
0
0
0
2
0
0
1
0
1
0
1
2
0
0
0
0
1
0
0
0
0
2
0
0
2
0
1
0
2
0
0
0
0
2
0
0
2
0
1
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
1
2
0
0
1
0
0
0
0
2
0
1
2
2
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
2
0
2
0
1
0
0
0
1
2
2
2
0
0
0
0
0
0
2
0
0
1
1
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
1
0
1
5
0
1
1
0
2
0
0
0
2
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
2
2
0
0
1
0
1
0
0
2
0
0
2
2
1
0
0
0
0
0
2
1
0
0
0
0
1
0
0
3
0
2
2
0
0
0
2
1
0
0
0
0
1
0
0
1
0
0
2
0
1
1
0
0
0
0
0
0
2
2
0
0
0
0
3
2
0
0
2
0
1
0
0
0
1
0
0
2
0
2
0
2
2
0
0
2
1
0
0
0
2
0
0
1
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
2
0
2
0
1
0
0
0
1
1
2
0
0
0
2
0
1
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
2
0
1
0
0
1
0
0
0
0
0
2
1
0
1
0
0
2
0
0
0
0
2
0
0
2
1
1
0
0
1
2
0
0
1
1
0
0
2
2
0
1
0
2
0
0
2
0
2
1
0
0
0
0
2
0
0
0
2
0
1
1
0
0
1
0
0
2
0
0
2
0
0
2
0
0
2
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
2
2
0
2
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
2
3
0
2
2
0
0
0
1
2
0
1
0
0
0
0
0
0
4
1
2
0
0
0
2
0
0
2
2
1
0
0
0
0
2
2
1
0
0
1
0
1
2
0
3
0
0
2
1
0
0
3
1
0
0
2
0
0
0
3
2
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
1
0
3
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
1
1
1
0
0
1
0
0
1
0
0
0
1
0
0
2
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
1
1
0
1
1
2
0
1
2
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
2
1
0
0
1
0
1
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
2
0
0
2
0
0
0
0
0
0
3
0
1
2
0
0
4
2
1
0
2
2
1
0
0
0
0
3
1
0
1
0
0
1
2
1
0
0
0
0
2
0
0
0
1
0
1
0
0
1
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
2
1
1
0
1
0
1
1
1
0
1
2
1
0
0
1
3
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
1
1
0
0
1
3
0
0
0
0
0
0
2
1
2
2
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
1
1
0
0
0
2
1
1
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
1
0
2
0
0
2
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
1
2
0
1
0
0
1
1
0
2
0
2
2
1
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
2
0
1
1
1
2
2
0
1
0
1
0
0
2
0
0
1
2
0
0
0
0
0
2
0
2
0
1
0
0
0
2
2
1
0
0
0
0
0
0
2
2
0
0
0
0
2
2
0
0
0
1
1
0
0
1
0
2
0
1
1
2
0
3
2
0
0
1
1
1
1
1
0
0
0
2
1
0
0
1
0
2
1
2
0
0
0
1
0
3
1
0
1
0
0
2
0
0
1
0
0
2
2
0
0
0
0
0
0
2
0
3
0
0
0
2
1
2
0
0
0
1
2
0
0
2
0
2
0
0
0
0
1
2
2
0
0
0
0
0
2
2
1
3
0
0
0
0
0
1
0
0
0
0
0
0
1
2
2
0
0
2
7
0
0
0
1
0
0
0
0
2
0
0
0
1
0
1
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
6
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
3
0
0
1
0
1
2
0
2
0
2
0
0
1
0
2
0
0
0
2
0
2
0
2
0
1
0
2
0
0
2
3
2
0
0
0
2
0
0
0
1
0
1
0
3
0
0
1
0
2
0
0
1
0
2
0
2
0
2
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
3
0
2
0
0
0
1
0
1
2
2
0
2
1
0
0
0
2
2
0
0
0
0
0
6
2
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
1
2
0
0
0
0
1
1
0
1
0
2
0
0
2
2
0
2
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
2
2
0
1
0
0
0
1
0
0
2
0
2
0
0
1
2
0
2
0
0
0
1
2
0
0
0
0
2
1
1
0
0
0
1
0
0
2
0
1
1
0
0
0
0
0
1
2
0
2
0
2
0
0
1
0
0
4
0
0
0
1
0
1
2
2
2
2
0
0
0
0
0
0
0
0
0
1
1
0
0
3
0
1
0
0
0
0
0
0
0
0
1
0
1
2
1
1
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
1
3
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
2
0
2
1
1
2
2
0
0
1
0
0
3
1
0
0
0
1
1
3
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
1
1
0
0
0
0
0
0
0
1
0
1
2
2
0
0
1
3
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
2
1
2
4
2
2
1
1
0
1
0
2
0
1
0
0
0
1
2
1
0
1
0
0
0
0
0
2
1
2
0
0
0
0
2
2
3
0
0
0
0
2
0
4
1
1
0
0
0
0
0
0
0
2
2
0
0
1
0
1
0
5
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
1
1
0
2
0
0
0
0
0
2
2
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
3
0
1
0
1
0
0
1
1
0
0
1
0
0
2
0
0
0
4
0
0
0
1
2
1
1
0
0
0
1
0
0
0
2
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
2
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
1
1
2
0
2
2
1
0
2
0
0
2
1
1
0
2
0
0
0
2
2
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
1
0
1
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
1
0
0
2
0
2
0
0
1
0
0
2
0
0
0
0
3
0
0
0
0
0
0
1
1
1
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
2
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
2
1
2
0
0
0
0
2
0
1
0
2
2
0
2
0
0
0
2
0
1
2
0
3
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
1
1
1
0
0
1
0
2
0
0
1
0
2
0
1
3
0
0
1
1
0
2
0
0
0
1
2
0
3
2
0
0
0
0
0
0
4
0
0
2
2
0
2
2
0
0
1
0
1
0
2
1
0
0
2
0
0
1
2
0
1
2
1
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
2
1
3
2
1
2
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
1
3
0
2
0
1
2
0
0
0
0
0
3
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
1
2
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
3
0
0
0
0
0
0
0
2
1
0
2
1
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
1
2
0
2
0
2
0
0
2
0
0
2
1
0
2
0
0
2
0
2
0
1
0
2
0
0
2
0
2
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
1
0
2
1
0
0
0
1
0
0
0
0
2
0
0
3
0
0
0
2
0
0
2
0
1
0
2
1
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
2
2
0
0
1
1
1
1
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
2
1
1
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
2
2
1
0
4
0
0
0
0
0
0
2
0
0
2
0
0
2
1
2
2
0
0
2
0
0
2
0
2
2
0
0
2
0
0
0
0
2
1
1
0
0
0
1
1
2
1
1
0
0
1
0
5
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
3
0
1
0
0
2
0
4
0
0
0
0
1
0
0
0
3
1
0
0
2
1
1
0
1
0
0
0
1
2
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
8
2
1
0
0
0
0
0
0
1
1
0
0
1
0
1
1
0
0
0
0
2
0
0
2
2
0
0
1
0
1
0
0
1
1
0
2
2
0
3
0
1
3
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
1
1
0
4
2
0
0
0
3
1
1
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
2
0
0
2
1
1
1
1
0
2
0
0
0
0
2
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
1
1
0
0
2
0
0
0
0
1
1
0
0
0
0
2
1
1
2
0
0
0
2
0
1
2
0
5
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
1
0
2
0
0
1
1
1
1
0
1
0
0
1
2
1
1
1
1
0
0
0
1
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
1
2
7
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
1
1
2
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
1
0
0
0
2
2
0
0
0
2
1
0
2
0
2
2
1
1
1
0
2
0
2
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
2
0
0
0
0
0
2
2
0
0
0
1
2
0
2
0
0
0
0
3
2
1
2
0
0
1
0
0
1
0
0
2
0
1
0
1
0
2
0
2
0
0
0
1
0
0
1
0
0
0
0
2
0
0
1
0
0
2
0
0
2
0
0
0
2
0
1
0
1
2
1
1
0
2
0
2
0
1
2
1
0
1
0
0
1
0
0
1
1
1
2
2
1
1
1
1
0
0
0
0
0
3
0
0
0
2
1
2
0
0
1
0
0
0
2
3
0
3
0
0
2
0
0
0
0
2
0
0
0
3
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
1
0
0
0
0
2
1
0
0
0
0
1
0
2
1
2
0
0
0
2
0
2
2
2
0
0
1
0
0
2
1
0
0
0
0
1
0
0
0
1
0
0
0
0
3
2
0
0
1
0
2
2
0
0
0
0
0
0
2
0
2
0
0
0
0
2
2
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
1
1
0
0
0
0
0
0
2
1
0
3
0
0
0
3
0
0
0
0
2
0
1
0
0
0
0
1
0
0
3
2
0
0
0
1
2
0
3
0
0
0
0
2
0
1
1
0
0
0
1
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
1
0
0
1
0
1
2
2
0
0
0
0
2
0
0
0
0
1
0
1
0
0
2
0
0
1
0
0
2
0
1
0
0
0
1
0
4
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
5
1
6
0
1
0
0
2
1
1
0
0
0
0
0
0
0
2
1
1
2
0
2
1
0
2
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
2
1
0
0
0
2
2
0
0
2
0
0
0
0
2
2
1
1
1
0
2
2
0
2
0
0
0
1
1
0
1
1
0
0
0
0
2
0
0
0
0
3
0
2
2
0
1
0
0
2
0
2
0
1
0
0
0
0
0
2
2
0
0
3
2
1
2
1
0
0
0
2
0
0
0
1
2
1
0
0
0
0
2
1
0
0
0
0
0
0
1
0
2
0
1
0
0
0
1
2
0
1
1
0
4
2
1
0
1
0
0
2
0
0
0
0
2
0
0
0
0
4
2
1
0
0
1
0
2
0
0
0
0
1
0
0
1
2
0
0
3
3
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
1
0
1
0
1
0
0
0
0
2
1
2
0
0
1
2
2
0
0
0
1
0
2
0
2
0
0
0
3
1
2
0
0
0
2
0
0
0
0
2
0
0
1
0
0
2
0
2
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
2
0
2
0
0
1
0
1
0
2
1
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
2
1
2
0
0
0
0
1
2
0
1
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
1
2
1
3
2
0
0
2
0
1
0
2
0
0
2
0
0
1
0
0
2
0
0
0
2
0
2
0
2
0
0
0
2
1
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
1
1
0
0
2
0
0
0
0
3
0
0
1
1
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
1
3
3
2
1
2
0
0
0
0
0
0
1
0
0
0
0
2
4
2
2
0
0
0
0
2
1
0
0
2
1
0
0
0
1
2
0
2
0
0
2
3
2
0
0
0
0
0
3
1
0
0
4
1
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
4
1
0
0
0
0
1
0
2
1
0
0
0
1
0
1
0
0
2
0
1
0
0
0
1
1
0
0
0
5
2
0
0
0
0
0
0
0
1
1
1
0
2
2
0
2
2
0
2
0
0
1
0
0
0
0
0
2
1
1
0
0
2
1
0
0
0
0
0
1
0
1
0
2
0
0
0
2
0
1
0
0
1
1
0
0
0
0
0
1
0
2
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
3
1
0
1
2
2
0
2
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
2
0
2
0
1
0
0
2
1
1
0
0
0
0
0
0
0
1
1
0
0
2
0
0
1
0
0
1
0
1
1
1
0
0
2
0
2
2
0
0
0
2
0
2
0
1
0
0
1
0
0
0
2
0
2
0
1
0
0
0
0
1
0
1
1
0
0
0
0
3
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
1
2
0
1
0
1
0
0
2
0
1
1
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
3
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
3
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
2
2
2
2
2
0
0
0
0
0
0
3
0
2
0
0
1
2
0
0
2
1
2
0
2
2
0
0
0
2
0
2
0
2
0
2
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
2
2
1
1
0
2
2
2
1
0
1
0
2
0
0
2
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
1
1
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
1
3
0
1
0
0
3
2
0
2
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
9
2
1
0
0
0
0
0
0
3
0
0
1
0
0
1
2
2
0
1
0
0
0
0
1
0
2
0
2
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
1
0
1
0
2
0
0
0
1
0
0
2
0
0
0
1
2
0
1
0
2
0
0
1
3
0
0
0
0
2
2
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
1
0
1
2
4
0
0
1
0
0
2
0
0
0
1
2
1
0
1
0
0
0
0
1
2
0
2
2
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
1
1
0
2
0
0
0
1
0
0
2
0
0
0
1
1
0
0
2
1
2
0
0
1
2
0
3
0
0
0
0
2
0
2
0
1
0
2
0
1
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
2
0
0
2
2
0
0
1
0
2
0
0
1
0
0
0
0
2
0
2
3
0
2
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
2
0
0
0
1
3
1
0
2
1
1
0
1
0
0
0
1
0
0
2
0
1
3
0
1
0
0
2
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
1
2
0
0
0
0
1
0
2
2
2
0
0
0
0
2
0
1
1
0
2
2
0
2
2
0
0
1
2
0
0
1
0
0
0
0
0
1
2
1
0
0
0
0
0
2
2
2
0
1
0
4
2
0
0
0
1
2
2
2
1
0
0
1
0
0
0
0
0
1
2
2
0
0
0
0
1
1
2
0
1
0
1
0
0
0
2
5
0
0
0
2
2
0
1
2
0
1
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
2
1
2
2
0
0
0
2
1
0
1
1
0
0
0
0
0
0
0
0
1
1
1
2
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
1
0
0
0
2
0
0
0
0
2
0
0
0
1
1
0
0
0
0
1
1
0
2
4
0
0
0
2
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
1
0
3
0
0
1
0
0
2
0
0
0
1
0
0
1
0
2
0
2
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
1
3
0
0
2
3
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
1
3
0
0
1
0
0
1
0
2
1
2
0
0
1
0
3
0
2
2
0
2
2
0
0
2
0
2
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
2
1
2
0
1
1
0
2
0
0
0
2
1
2
3
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
3
1
2
0
0
0
0
0
0
0
1
0
0
1
0
0
1
2
0
1
0
0
0
0
2
0
0
1
0
1
2
0
0
0
1
0
1
0
1
0
0
0
0
2
0
0
1
0
1
1
1
0
1
1
0
0
0
1
0
0
0
2
1
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
1
0
2
1
0
1
2
0
0
0
0
1
0
2
0
1
1
2
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
2
0
0
0
0
1
1
1
1
1
0
2
0
0
0
1
0
0
0
0
0
0
0
2
2
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
1
2
1
1
0
0
0
0
0
1
1
1
0
0
0
2
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
1
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
2
0
1
2
2
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
2
0
1
2
0
0
0
0
2
0
0
1
0
0
2
1
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
2
0
1
0
0
0
0
1
2
0
0
2
0
2
0
1
0
0
2
2
0
0
2
0
2
0
2
2
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
2
0
0
0
1
3
2
1
0
2
0
0
0
1
0
1
0
1
0
0
0
1
0
1
0
0
1
2
0
1
0
0
0
0
0
2
0
0
0
2
1
0
2
0
1
1
0
0
0
2
0
1
0
0
0
0
1
1
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
2
0
1
0
0
2
0
0
1
2
0
0
1
0
0
0
2
2
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
2
0
0
0
2
0
1
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
2
1
1
0
0
0
2
1
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
2
1
2
2
0
2
0
0
0
0
2
1
0
0
0
0
1
0
0
2
2
0
0
0
1
1
0
0
0
2
0
0
2
2
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
2
1
0
2
0
0
1
0
2
0
1
2
0
0
0
2
2
1
0
0
0
0
1
0
2
0
0
0
1
1
0
0
1
1
0
0
0
0
0
2
0
0
2
4
0
0
1
1
0
0
2
0
2
1
0
0
5
2
1
0
0
3
0
0
1
0
0
2
2
0
2
2
0
1
2
2
2
0
0
0
1
0
2
1
0
2
2
0
0
0
1
1
0
1
0
2
0
0
1
0
0
2
0
0
0
0
2
1
0
0
1
0
0
0
0
0
2
0
2
1
0
4
0
0
2
0
0
0
0
1
1
0
0
0
1
2
0
2
0
1
2
0
1
5
2
0
0
1
0
2
0
1
2
0
0
1
0
1
1
0
0
0
0
2
0
2
0
3
1
1
2
0
0
0
1
0
0
0
0
2
1
0
1
1
0
2
1
0
0
1
0
0
0
1
9
2
0
0
2
0
0
0
1
5
0
0
0
2
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
1
0
0
1
2
0
2
2
2
0
0
0
0
0
1
0
0
0
1
0
0
1
0
2
0
1
0
0
1
1
1
2
1
2
0
0
0
1
3
0
0
0
0
0
0
0
2
2
2
0
0
1
1
0
1
3
2
1
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
1
1
0
0
0
0
0
1
1
3
0
2
0
0
1
0
1
1
0
0
0
1
3
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
1
3
0
0
0
0
2
0
6
0
2
0
1
0
0
2
1
1
1
0
0
1
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
4
0
0
1
1
2
0
0
2
5
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
1
2
1
0
0
2
1
2
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
3
0
1
1
0
2
0
2
2
0
0
0
2
2
1
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
1
2
0
1
0
0
0
2
0
1
0
1
0
0
1
0
1
0
2
0
0
0
0
0
0
2
1
2
2
1
2
0
0
0
2
2
1
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
2
0
1
0
0
1
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
1
0
2
0
0
0
2
2
0
1
2
0
0
0
0
2
1
0
0
0
1
0
2
0
1
0
2
0
0
0
1
0
0
0
1
0
0
2
3
0
1
0
0
1
1
0
2
3
0
0
2
0
1
0
0
2
2
0
0
0
0
1
0
2
1
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
1
1
0
0
0
2
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
2
0
0
2
0
0
2
0
0
1
0
1
1
2
0
1
2
2
0
0
2
1
0
2
0
0
1
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
1
2
1
0
0
0
0
1
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
1
0
2
0
1
0
0
0
0
2
0
2
0
0
0
0
1
0
0
2
0
0
1
2
3
0
2
0
2
0
2
2
0
2
0
1
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
1
2
0
1
1
0
2
2
0
0
3
0
0
0
1
1
0
0
1
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
1
0
0
3
2
0
0
0
0
1
0
0
1
3
0
1
2
0
0
0
0
0
2
0
0
1
2
0
0
0
2
1
1
0
2
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
1
3
0
1
1
5
2
0
2
0
1
1
2
0
0
0
0
0
0
1
3
1
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
1
2
0
2
1
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
2
0
2
0
0
2
0
2
2
1
0
0
0
2
11
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
1
2
2
1
0
2
0
0
0
0
0
2
3
0
1
0
1
0
1
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
2
0
0
2
0
0
1
2
0
2
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
3
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
3
2
0
0
1
1
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
2
0
2
2
1
0
0
0
0
0
0
1
1
2
0
0
0
1
0
1
0
2
1
1
0
0
2
0
0
0
2
1
2
0
0
0
0
2
0
1
1
0
0
7
0
1
0
0
0
0
0
0
0
0
0
1
2
0
1
0
1
1
0
1
0
1
0
0
0
0
0
1
0
0
2
0
0
2
0
0
1
0
0
2
2
1
0
0
0
0
0
0
0
4
2
2
1
0
0
0
1
0
2
0
2
0
0
1
0
0
0
3
0
2
0
0
0
1
0
0
2
0
0
1
0
2
1
0
0
2
0
2
1
0
0
0
3
0
1
0
0
0
0
2
1
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
5
0
0
0
1
0
1
2
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
2
0
1
1
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
1
2
1
0
2
2
0
0
0
1
0
0
1
0
0
0
2
2
7
0
2
0
0
0
4
1
1
2
2
1
0
1
1
1
0
0
2
0
0
1
1
0
1
1
1
0
1
2
0
0
0
0
0
0
0
0
1
1
2
2
1
0
1
1
0
2
1
1
0
0
2
1
2
2
0
0
2
1
0
0
2
0
0
1
0
0
2
0
0
2
2
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
4
3
0
1
0
0
0
1
1
1
0
0
2
0
1
1
2
0
2
2
0
2
1
0
2
0
0
0
0
1
2
1
0
2
1
0
1
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
3
1
0
0
0
0
2
1
3
2
0
0
0
2
0
0
0
0
1
0
4
0
2
0
0
0
1
0
2
0
0
1
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
2
1
2
0
1
0
0
0
2
0
0
0
0
2
0
0
1
0
0
1
0
0
1
1
1
0
0
0
0
2
0
2
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
2
0
1
0
3
0
2
0
1
0
0
0
2
0
0
2
1
1
0
0
0
2
0
0
0
0
1
0
2
0
2
0
0
2
0
0
0
1
0
0
0
0
0
1
1
0
1
1
0
0
1
0
2
0
0
2
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
1
0
1
0
1
2
0
0
0
2
0
2
1
0
0
1
0
0
1
0
1
0
0
0
2
0
0
0
1
0
0
1
0
0
1
1
0
2
1
0
2
1
1
2
0
1
0
0
1
0
0
0
1
0
0
0
2
0
1
0
1
0
2
0
2
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
2
0
2
0
0
0
1
0
2
0
0
0
2
0
1
1
0
0
0
0
1
0
2
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
3
0
0
2
0
1
0
0
0
1
0
2
2
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
2
0
0
0
0
0
0
1
1
0
2
2
0
1
2
1
2
1
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
2
3
2
1
0
0
1
0
0
0
2
0
0
2
2
0
2
0
2
0
1
1
2
1
0
1
0
2
3
1
2
0
2
0
0
0
0
2
0
0
2
2
0
0
0
0
2
0
0
0
1
1
0
0
0
0
2
0
2
0
0
0
2
1
0
1
0
0
0
2
0
1
0
0
0
0
0
1
1
0
2
0
0
1
0
0
2
1
0
1
1
0
0
0
5
2
0
1
0
0
0
0
5
0
2
0
1
0
0
0
0
2
0
0
2
0
1
0
2
1
3
4
0
0
1
2
1
0
0
0
0
2
0
0
0
0
0
2
0
1
2
0
0
1
1
0
0
2
1
0
0
2
0
1
0
1
2
0
0
1
1
0
0
0
3
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
2
0
0
1
2
0
0
2
0
0
0
0
2
3
3
2
0
0
1
2
0
1
0
0
1
1
0
0
0
1
0
0
0
1
0
0
2
0
1
0
0
0
2
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
1
1
1
0
0
1
0
0
2
1
0
0
2
2
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
2
1
1
0
1
1
0
0
0
2
2
0
1
0
0
1
0
0
0
1
2
0
0
1
0
0
1
0
2
2
0
1
0
0
0
0
1
0
0
4
1
0
0
0
3
0
3
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
2
0
1
2
0
0
1
2
0
0
0
1
2
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
1
0
2
1
1
0
0
0
1
2
0
0
0
0
0
0
0
3
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
1
0
0
2
1
0
0
1
1
0
1
0
0
0
2
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
1
2
2
0
0
2
0
0
0
0
0
1
2
1
1
0
0
0
0
0
2
0
2
8
0
1
2
0
0
1
1
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
1
0
2
1
0
0
0
0
2
0
1
0
0
1
0
1
2
0
0
2
1
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
2
2
0
0
2
1
1
1
0
0
2
0
0
2
2
0
1
2
0
0
0
1
1
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
2
1
0
0
0
0
1
1
0
0
0
0
0
1
2
0
3
1
1
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
3
0
0
0
0
0
2
0
2
1
0
1
2
0
0
0
0
1
0
4
2
0
0
0
0
0
2
0
0
0
1
1
0
1
0
0
4
0
0
0
0
0
2
0
0
0
2
0
0
0
3
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
3
0
0
0
1
0
2
2
1
0
1
0
2
0
0
0
0
0
0
2
0
0
1
1
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
2
0
2
0
0
2
2
0
1
1
0
1
0
0
0
0
2
0
2
0
0
0
2
0
0
2
0
1
0
0
2
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
2
1
0
0
0
1
0
4
1
0
1
0
0
0
0
0
0
0
5
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
1
0
0
3
1
2
0
2
0
0
0
0
1
0
0
1
0
2
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
2
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
2
0
0
1
0
1
2
2
2
0
1
1
0
1
0
0
0
0
0
1
0
0
1
3
0
0
0
0
0
2
0
0
2
1
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
2
0
0
2
0
2
0
0
0
0
1
0
0
0
1
2
0
1
0
2
2
0
2
3
0
1
0
0
2
0
2
1
2
1
0
1
0
0
0
0
0
2
1
2
0
1
0
1
2
0
0
2
1
0
0
2
2
0
0
0
1
0
0
0
0
2
1
0
1
1
0
2
2
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
2
0
0
0
4
0
0
0
0
2
0
0
0
5
1
0
2
0
0
0
1
0
2
0
0
0
2
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
2
2
0
0
2
1
1
0
0
0
0
1
0
0
0
0
0
2
2
0
0
1
0
0
0
0
1
0
1
0
0
1
1
0
0
0
2
0
0
0
1
0
0
0
2
2
1
0
0
1
1
0
2
0
0
0
0
7
0
0
0
0
1
0
0
1
1
0
2
2
0
0
0
2
2
0
0
0
1
0
1
0
0
0
0
2
2
0
2
0
2
0
1
2
0
0
4
2
2
0
2
0
0
0
0
0
2
1
2
0
0
0
0
1
1
1
0
0
0
1
2
2
0
1
0
0
1
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
2
2
0
1
1
2
0
2
1
0
0
0
0
4
1
0
0
0
2
0
1
2
1
0
0
0
1
0
0
0
0
1
2
0
0
0
2
1
2
0
2
0
0
0
0
2
2
0
0
0
0
0
1
2
0
0
1
0
0
4
1
0
0
1
1
0
0
2
3
0
1
2
0
0
3
2
0
0
1
0
2
1
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
3
1
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
1
0
2
0
2
2
0
0
0
0
2
0
0
0
2
0
1
2
0
0
2
1
2
1
1
1
0
0
0
0
0
1
0
2
1
0
1
0
1
0
0
0
0
0
0
1
1
2
0
0
0
1
0
1
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
1
0
1
2
0
0
1
2
0
2
0
1
1
0
2
2
0
2
2
0
0
0
0
1
2
0
0
0
0
0
0
2
1
0
1
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
1
0
0
1
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
1
0
0
0
2
0
3
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
1
0
0
2
1
0
1
2
0
1
0
0
1
0
0
0
1
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
2
2
0
0
0
1
1
2
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
2
0
2
0
0
0
0
1
0
1
0
1
1
2
0
0
2
0
0
0
0
2
0
0
2
1
0
0
3
0
0
0
0
2
2
0
2
1
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
1
1
1
1
2
2
0
1
0
0
0
0
0
1
0
1
0
1
1
0
0
2
0
1
0
2
0
1
0
0
0
1
1
0
2
2
0
0
0
0
0
4
4
1
2
0
0
0
3
2
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
1
0
0
2
0
1
0
0
0
0
1
0
0
0
2
1
0
0
2
1
0
0
1
0
2
2
0
0
1
3
2
2
0
0
0
0
0
2
0
2
1
0
0
3
0
1
0
2
0
1
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
2
2
0
0
0
0
0
0
1
0
1
1
1
0
1
2
0
0
1
0
1
1
0
0
0
2
0
0
0
1
0
0
0
0
2
1
0
0
0
1
2
1
0
0
0
0
0
0
0
2
0
2
1
0
0
2
2
1
0
0
0
0
3
0
1
0
0
3
1
0
0
2
0
0
1
0
0
0
1
3
0
3
2
0
0
2
1
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
5
0
2
0
0
4
0
0
1
0
2
0
2
0
1
0
2
0
1
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
1
1
0
3
0
1
0
2
3
0
0
0
3
0
1
2
2
0
0
3
2
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
1
0
2
1
0
1
1
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
2
2
0
0
1
1
1
1
0
1
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
1
4
0
1
0
1
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
7
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
1
0
0
0
0
2
1
1
0
0
0
1
1
2
2
1
0
0
2
1
0
0
2
0
1
1
0
1
1
1
0
1
1
0
0
1
0
0
0
0
0
1
1
3
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
2
1
2
0
0
0
0
0
0
1
0
0
0
0
0
5
0
2
1
1
0
2
0
0
1
1
1
1
0
0
2
2
1
1
1
0
0
0
0
1
0
0
0
0
1
0
1
2
0
0
0
0
2
0
0
0
3
0
0
1
0
0
0
0
0
2
0
0
1
0
1
0
0
2
0
2
3
1
2
1
0
0
0
0
1
0
0
0
2
0
0
0
1
1
0
1
0
0
0
0
0
2
0
0
0
1
1
0
1
2
0
0
2
1
0
2
0
1
2
1
2
0
0
0
0
0
0
2
1
0
0
0
0
1
3
0
0
2
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
2
0
2
2
0
0
1
1
1
0
0
0
1
0
0
0
0
0
1
0
2
1
0
0
2
0
0
0
1
0
2
1
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
4
1
0
0
1
0
2
0
0
0
1
0
0
0
0
1
0
0
0
3
1
0
0
2
0
0
2
1
0
1
0
1
1
1
0
0
0
2
0
2
1
1
1
2
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
2
0
0
2
2
1
1
1
0
0
0
2
0
1
0
0
4
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
2
0
1
1
3
2
0
0
0
1
0
1
0
0
0
1
0
2
1
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
1
0
0
1
0
2
0
2
2
2
0
0
0
0
0
1
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
2
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
1
0
0
1
1
0
0
0
2
0
1
2
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
2
2
1
2
0
0
1
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
1
0
0
2
0
1
1
0
0
0
0
0
0
0
3
0
0
1
1
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
1
1
2
0
0
2
4
2
1
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
2
1
1
0
2
0
0
0
0
0
0
0
1
0
0
1
0
2
1
1
0
2
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
2
0
2
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
2
0
2
1
0
1
1
0
0
0
0
0
2
0
6
1
1
0
0
2
0
1
2
0
0
0
2
0
1
2
1
0
0
0
0
1
0
2
2
1
1
2
2
1
0
1
0
1
1
2
0
0
0
0
2
0
0
2
0
2
0
0
0
0
2
0
0
0
1
0
0
1
0
2
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
1
1
2
0
0
1
1
1
2
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
2
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
1
2
0
0
0
0
0
0
2
0
3
0
0
2
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
2
2
1
0
0
0
2
1
2
1
0
2
0
0
0
0
0
0
2
0
2
0
1
0
0
1
0
2
0
0
1
0
1
0
0
0
0
0
0
3
0
2
2
0
1
2
0
2
0
0
0
0
1
1
0
0
0
0
0
0
2
0
1
0
1
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
2
1
0
0
2
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
3
0
0
0
0
2
3
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
2
2
0
2
1
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
2
1
1
1
1
1
0
0
0
3
0
2
1
0
0
1
0
1
1
0
3
1
0
1
0
0
2
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
2
0
0
0
0
1
0
0
1
0
1
0
2
2
0
0
0
0
1
2
0
1
0
0
2
2
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
2
1
1
0
0
0
1
0
2
2
2
2
0
2
0
1
2
0
0
0
0
0
2
1
0
0
0
0
0
0
2
1
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
2
4
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
1
2
0
0
0
2
0
3
1
0
2
2
1
0
2
2
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
1
2
2
1
0
0
0
0
0
2
1
0
1
0
0
0
1
0
0
0
2
0
0
2
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
1
0
2
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
2
0
2
2
0
1
0
0
5
1
0
0
0
1
1
0
2
0
0
1
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
1
2
1
1
0
0
0
0
0
1
2
1
0
5
2
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
2
0
0
1
0
0
0
3
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
2
2
0
0
1
0
1
0
0
1
0
2
3
0
0
0
2
0
0
0
1
0
0
1
0
0
2
2
0
1
1
2
2
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
2
0
2
1
0
0
0
0
2
2
0
0
2
1
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
3
0
0
0
1
0
0
0
0
1
2
0
0
0
2
0
0
1
1
0
0
0
0
1
0
2
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
2
0
7
0
2
2
0
0
1
2
2
2
0
1
0
1
1
0
0
0
0
1
0
0
1
0
0
1
0
1
1
0
2
0
0
0
1
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
2
2
0
1
0
1
0
0
0
0
0
0
1
0
2
1
0
0
5
2
0
0
0
1
0
1
1
0
0
1
0
2
1
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
2
0
0
0
0
1
0
2
0
0
2
0
1
0
2
2
0
0
1
0
3
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
1
1
2
1
1
0
0
1
1
0
0
0
0
1
0
1
0
0
2
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
1
2
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
2
3
0
0
0
0
1
3
0
1
0
1
0
0
0
1
1
0
0
1
0
1
0
0
2
0
0
2
2
2
2
0
2
0
0
0
2
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
1
2
1
0
0
2
0
0
0
0
0
0
1
2
3
0
0
2
4
1
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
4
0
2
2
0
2
0
0
0
0
0
0
1
0
1
0
0
0
2
1
1
0
0
0
0
1
0
0
2
0
2
2
0
1
1
0
0
1
0
0
2
0
2
0
2
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
2
2
6
0
0
2
0
0
0
0
1
0
2
0
0
0
2
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
1
1
0
0
0
2
0
2
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
1
1
2
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
1
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
2
2
0
0
0
2
1
2
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
2
0
1
0
2
0
0
0
2
0
0
0
1
1
0
1
0
0
0
3
2
1
2
0
2
0
1
0
0
2
3
0
1
1
1
0
0
2
0
0
1
1
2
0
0
0
1
0
2
0
0
0
1
1
0
0
0
0
0
1
0
0
2
0
1
2
0
0
0
1
1
0
2
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
1
2
0
2
2
0
1
2
1
0
1
0
0
5
2
2
1
0
1
0
0
0
0
0
2
0
1
0
1
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
1
0
0
1
0
0
0
0
1
1
1
0
0
0
1
0
2
1
0
0
0
1
3
0
1
0
0
1
0
7
2
2
1
0
0
0
2
0
0
0
0
0
0
2
1
2
0
0
2
0
2
0
1
1
0
2
0
0
0
0
2
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
1
0
0
0
0
2
1
0
0
0
0
0
0
2
0
2
2
0
0
2
2
0
0
3
0
1
0
0
0
0
1
1
0
1
0
1
0
0
1
0
1
0
0
1
2
0
0
0
0
0
1
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
3
1
0
1
0
2
2
0
0
1
0
1
0
2
1
2
1
0
0
1
1
0
0
0
0
1
1
0
2
2
2
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
1
0
0
0
0
0
1
0
0
2
2
1
0
0
2
1
1
0
2
0
0
0
0
0
2
0
0
1
1
0
1
0
1
1
1
0
0
0
1
0
1
0
0
2
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
1
0
4
0
2
1
0
0
0
1
4
0
0
0
0
0
1
0
0
0
0
0
1
2
2
0
0
1
0
0
1
1
0
1
0
0
1
0
2
0
2
0
0
0
2
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
2
1
2
0
0
0
0
0
0
1
2
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
2
1
0
0
2
0
2
2
0
1
0
0
0
2
0
1
1
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
2
2
0
0
1
0
1
1
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
1
2
2
0
3
0
0
0
2
1
0
0
2
2
0
0
0
2
0
2
0
1
1
0
0
1
2
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
2
0
0
2
0
0
1
3
0
0
0
0
2
0
1
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
2
0
0
1
2
0
1
0
0
2
2
2
2
0
2
0
2
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
1
0
0
0
2
3
0
2
0
0
0
0
1
0
0
1
1
0
0
0
0
3
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
3
0
2
0
0
2
0
0
0
0
1
0
0
0
0
1
2
0
1
0
1
1
0
0
0
1
0
2
0
0
0
2
0
1
2
0
0
3
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
2
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
2
0
0
2
3
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
2
4
0
0
0
1
1
0
0
2
0
0
0
0
1
0
0
0
1
1
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
6
2
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
3
1
0
0
0
4
0
1
0
2
1
0
1
0
0
0
0
0
3
2
0
0
0
2
0
3
0
0
2
1
1
2
1
1
0
1
0
2
0
0
1
1
0
1
0
0
1
0
3
1
0
2
2
0
0
1
1
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
2
1
2
0
0
0
0
0
0
0
0
2
2
0
2
3
0
3
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
2
0
0
1
0
0
0
1
1
2
0
2
0
2
0
0
1
0
3
0
0
2
2
0
0
0
0
2
1
0
1
0
0
0
2
2
1
0
0
1
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
1
0
0
0
0
2
1
0
0
0
0
2
1
0
0
0
2
0
0
0
0
5
2
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
2
3
2
0
0
0
0
0
0
1
0
0
2
2
0
0
1
0
1
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
1
0
0
0
0
0
1
0
2
0
0
0
1
2
1
1
1
0
3
1
2
1
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
1
0
1
4
0
0
2
0
1
0
0
1
0
0
2
0
2
2
0
1
1
1
0
0
2
0
1
0
0
1
0
0
1
2
0
2
2
0
0
0
3
0
2
1
2
1
0
2
1
0
2
1
2
2
2
0
1
0
0
0
0
0
0
2
0
1
2
0
0
0
2
0
2
1
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
1
0
2
0
2
0
1
0
0
1
0
2
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
2
1
2
0
0
1
0
0
2
0
0
0
0
0
1
0
0
1
0
1
0
2
0
0
0
0
0
2
1
0
0
0
0
1
0
1
1
0
0
1
0
0
2
0
0
2
0
1
0
0
0
0
0
0
3
2
2
1
0
1
0
0
1
1
2
0
1
0
0
0
2
0
0
1
0
0
0
0
1
2
0
0
0
1
1
0
1
1
2
0
1
0
1
0
0
0
0
1
0
0
2
2
1
1
0
1
0
1
2
0
0
1
0
1
0
0
0
0
2
0
0
0
1
1
1
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
2
0
0
1
0
0
2
2
2
1
0
1
1
1
1
2
0
0
0
0
1
0
1
0
2
2
0
2
0
0
2
0
0
1
4
0
0
0
2
2
0
2
1
0
0
0
0
0
0
2
1
0
0
2
1
2
2
1
0
1
0
0
2
2
1
0
1
0
1
2
0
0
2
0
0
0
0
1
1
0
0
2
0
1
0
1
0
1
0
0
2
0
1
2
0
0
0
0
0
0
0
3
0
1
0
2
0
0
3
0
1
0
0
0
0
0
1
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
1
2
0
2
0
3
0
0
0
1
0
1
3
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
1
2
1
0
0
2
2
0
0
1
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
2
3
0
0
2
3
2
1
0
0
0
4
2
2
0
0
0
0
1
0
0
1
0
3
0
0
0
0
0
0
1
0
2
1
0
2
0
2
1
0
0
5
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
2
2
0
3
2
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
1
0
0
0
2
1
1
2
2
0
2
2
0
0
0
0
0
0
0
1
2
0
0
1
0
0
1
0
0
0
2
0
0
1
1
2
0
0
0
0
1
1
3
3
0
0
0
0
2
3
0
0
0
0
1
0
0
0
1
0
2
2
0
2
1
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
1
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
1
2
0
0
0
0
2
0
0
0
3
0
0
1
2
0
1
1
0
0
0
1
0
0
2
0
0
3
1
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
2
1
0
0
0
2
0
1
1
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
1
1
0
0
0
2
2
2
0
2
0
0
1
1
2
0
2
0
3
3
0
0
0
0
1
0
0
0
0
10
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
2
1
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
1
2
0
0
0
1
2
1
0
0
0
0
2
2
0
0
1
0
0
0
1
2
0
0
1
3
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
2
1
2
1
6
5
0
0
0
0
0
3
2
2
0
1
0
0
1
0
0
0
0
0
2
0
2
1
0
0
1
0
0
1
0
0
2
0
0
0
1
1
0
0
0
0
0
3
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
2
1
0
0
2
0
0
1
2
0
0
0
2
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
4
0
0
0
0
0
0
0
1
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
2
0
0
2
2
0
0
0
0
0
0
4
2
0
0
2
0
0
0
1
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
2
1
2
0
0
0
1
1
2
0
2
1
0
0
0
0
2
0
1
0
0
2
0
0
0
0
2
2
1
0
0
0
1
2
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
2
1
0
0
0
0
2
0
0
1
2
0
0
0
0
0
6
2
0
0
0
0
0
1
0
1
0
1
0
0
2
0
1
2
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
2
0
1
0
0
2
0
2
0
2
0
2
0
0
2
2
0
0
2
2
0
2
0
0
0
2
0
0
0
1
2
0
1
0
0
0
3
0
1
1
0
2
0
2
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
2
0
2
1
1
0
0
0
0
3
0
0
0
2
2
2
0
0
0
1
1
0
0
1
1
0
0
0
0
0
1
2
1
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
3
0
1
0
1
0
0
0
0
0
1
2
1
2
0
0
0
0
0
0
1
2
0
2
2
1
0
0
0
0
0
1
0
2
0
1
2
0
0
2
2
4
2
0
0
2
3
0
0
0
2
2
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
1
1
0
1
1
0
0
1
0
1
2
2
2
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
3
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
2
0
2
1
3
0
1
0
0
1
0
2
0
0
0
0
0
1
2
0
0
0
2
1
0
3
2
1
0
0
0
0
2
0
2
0
2
2
1
1
2
0
0
1
2
1
0
1
0
0
0
0
0
0
1
0
0
0
2
2
1
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
2
0
0
0
0
1
0
2
1
0
1
2
0
1
2
0
4
0
0
0
0
0
0
0
2
2
0
0
0
1
2
0
2
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
1
0
3
1
0
1
0
2
0
0
0
0
0
0
0
2
0
4
0
0
0
2
0
1
0
2
0
2
1
0
1
1
0
2
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
1
0
0
0
0
0
0
1
5
0
0
0
0
2
0
2
0
0
2
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
1
2
1
0
0
0
1
0
1
0
0
0
0
1
0
0
1
2
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
1
0
2
0
1
2
2
0
1
2
0
0
0
0
2
0
0
0
3
4
0
2
0
1
0
1
0
0
0
0
0
0
0
1
0
0
2
0
2
0
1
0
1
1
2
0
0
1
2
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
2
1
0
2
1
0
0
0
1
0
1
0
1
0
0
0
1
0
0
2
1
0
0
0
1
0
0
0
1
0
2
0
0
1
1
1
2
0
0
2
2
0
1
0
1
2
2
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
2
2
0
0
1
0
2
0
1
1
0
0
0
2
0
1
2
2
2
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
4
0
0
0
0
0
9
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
1
0
0
1
0
1
2
0
0
0
1
0
0
0
0
0
0
2
1
1
0
0
2
1
1
1
1
1
0
0
2
0
0
1
0
1
0
2
0
1
1
1
0
0
2
2
0
0
2
2
3
1
1
1
0
2
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
2
2
2
0
1
1
0
0
1
2
1
0
0
2
0
0
2
0
0
0
0
1
2
0
1
1
2
1
0
0
0
0
1
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
2
3
2
0
0
2
2
0
0
0
0
0
0
0
1
0
0
1
0
3
2
0
0
0
2
0
2
0
0
2
0
2
0
2
1
1
1
0
2
1
2
0
1
0
1
0
2
0
2
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
2
1
0
0
0
2
2
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
1
0
1
0
0
0
0
0
0
2
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
2
0
0
0
2
0
0
0
1
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
1
0
0
0
0
0
1
0
1
1
1
6
2
0
2
1
3
0
0
1
2
1
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
2
2
1
1
0
2
2
0
0
0
0
1
0
0
1
1
2
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
1
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
3
1
2
1
0
0
1
1
0
1
0
0
2
0
1
0
0
0
0
1
2
1
0
0
1
0
2
0
2
2
0
0
0
1
0
0
2
0
2
0
0
0
0
0
1
0
1
3
1
0
0
4
0
0
0
2
0
0
0
0
0
1
2
0
0
2
0
2
1
0
0
0
1
0
0
0
2
1
0
2
0
1
2
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
2
0
0
2
2
2
0
1
0
0
0
2
0
0
2
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
1
3
0
0
0
0
0
1
1
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
2
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
1
0
0
2
1
0
0
1
0
0
2
2
0
0
1
0
0
0
0
0
0
0
1
2
2
1
2
0
0
2
0
1
1
1
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
3
2
2
2
1
0
0
2
0
0
1
1
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
1
2
0
1
0
1
0
1
1
0
0
2
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
2
3
1
1
2
0
0
0
1
0
2
0
1
1
2
1
1
2
0
0
2
0
0
1
0
2
0
1
1
0
0
0
0
0
1
1
1
0
0
0
0
2
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
2
1
0
1
0
0
0
2
0
0
0
0
0
1
0
1
1
0
0
2
1
1
0
2
0
0
1
1
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
4
0
1
0
2
2
0
0
0
0
1
0
2
1
0
0
1
0
0
0
0
4
0
0
0
0
2
0
0
1
0
2
0
2
0
0
0
1
0
0
0
0
0
0
1
2
0
2
1
0
1
0
3
2
1
2
2
0
1
0
0
0
1
0
1
0
1
2
0
0
0
1
0
1
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
3
0
1
2
0
0
0
0
2
0
0
3
1
2
0
0
1
0
2
0
1
0
0
0
0
2
0
0
2
0
2
1
0
2
2
1
0
0
0
0
2
0
0
0
1
0
0
0
2
1
1
0
0
0
2
0
2
0
1
1
2
0
0
0
0
0
2
0
0
1
0
1
2
0
0
2
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
2
2
0
0
2
0
0
0
0
0
0
0
2
0
2
0
1
3
0
0
2
0
2
0
0
0
2
0
0
1
0
1
0
1
0
0
0
1
3
0
0
0
1
0
1
0
0
0
0
4
0
2
0
0
1
0
0
0
0
0
0
0
5
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
1
1
0
0
2
0
0
0
2
1
0
0
2
1
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
2
2
0
1
0
1
0
0
2
0
2
1
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
3
0
0
0
0
0
4
0
1
0
0
0
1
0
1
0
2
0
0
0
0
0
1
1
0
2
0
2
2
2
0
0
0
0
0
1
0
0
1
4
0
1
1
1
0
1
0
2
0
0
1
0
1
0
2
0
0
0
1
2
2
0
2
2
0
0
1
1
0
2
2
1
0
0
0
1
2
2
0
0
0
0
1
0
1
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
2
1
0
2
0
1
0
3
0
1
0
2
1
0
2
0
0
1
0
1
1
0
0
0
1
0
1
0
3
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
1
0
0
1
0
2
0
0
0
2
1
0
1
0
0
2
0
1
0
3
0
1
0
3
0
1
0
2
1
0
0
0
1
0
0
0
0
2
0
0
1
0
1
0
4
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
2
0
0
2
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
2
2
1
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
3
0
2
0
2
0
0
1
1
2
2
0
0
0
1
3
1
0
0
0
0
3
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
1
2
0
0
1
0
0
2
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
2
0
0
0
1
0
2
0
2
0
1
0
3
2
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
2
0
0
2
0
0
2
0
0
0
0
1
0
0
1
2
0
0
1
0
0
0
0
0
0
2
1
0
2
1
1
0
2
0
0
2
0
0
2
0
0
0
1
1
1
1
0
2
0
1
0
0
0
0
2
2
0
0
0
2
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
1
2
0
0
2
1
1
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
2
0
0
0
2
0
2
1
1
0
2
0
0
2
0
0
0
1
1
1
0
2
1
2
2
1
0
2
2
0
2
1
0
0
0
0
0
2
2
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
3
0
0
1
1
1
2
0
2
0
1
0
0
1
0
0
0
2
3
1
2
0
0
0
0
0
0
0
0
0
1
2
1
1
0
0
0
0
0
1
2
1
0
0
0
1
0
0
0
2
0
0
0
1
0
0
2
0
2
1
0
0
0
0
0
0
2
0
0
1
1
2
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
2
2
0
0
0
0
0
0
1
1
0
0
2
2
0
0
0
1
2
1
0
0
2
0
0
0
0
1
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
3
0
1
0
0
0
1
0
2
0
2
2
0
1
0
0
0
1
0
2
0
0
0
2
0
0
3
0
1
0
1
0
0
0
1
0
0
1
0
1
2
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
1
1
0
0
0
1
0
1
3
2
1
0
1
1
1
2
1
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
2
2
0
0
1
1
1
0
0
0
1
0
0
2
0
1
1
0
1
0
0
1
2
0
0
2
0
2
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
5
1
0
0
1
0
0
0
0
0
2
3
3
0
0
0
1
0
0
0
2
3
0
1
0
0
0
0
0
0
1
0
0
1
2
0
0
2
2
0
0
0
0
0
1
1
0
3
0
2
2
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
1
2
1
0
0
0
1
2
0
0
0
0
2
0
0
1
0
1
1
0
0
3
2
0
0
0
2
0
0
2
2
2
0
0
4
0
7
0
0
0
2
2
0
0
0
1
3
2
0
1
0
0
0
2
0
1
3
0
0
2
0
0
0
0
3
2
0
0
0
2
1
0
0
1
0
1
0
0
0
2
1
1
0
0
0
0
0
0
3
2
1
1
0
0
0
0
0
0
0
0
0
2
2
0
4
0
0
2
0
0
0
2
0
0
1
0
0
0
0
3
0
0
1
0
2
0
1
0
2
3
0
1
2
3
0
0
0
0
0
1
0
2
2
2
2
0
0
0
0
1
0
1
0
0
0
0
0
2
1
0
1
2
1
1
0
0
2
1
0
0
1
0
0
0
5
0
0
1
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
2
0
0
0
1
1
2
1
0
1
0
0
0
0
2
0
0
0
0
4
0
0
1
0
0
0
2
3
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
1
0
0
0
0
2
2
1
2
0
0
0
0
2
0
1
0
0
1
0
0
0
3
0
0
0
1
0
0
1
0
0
0
0
0
0
2
1
1
1
0
1
1
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
2
2
1
1
1
2
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
1
1
3
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
4
0
0
0
0
1
0
0
0
2
0
1
0
1
0
0
0
0
0
1
2
0
0
1
1
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
1
1
2
3
1
4
0
0
2
0
0
1
2
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
1
0
0
2
2
0
0
2
0
0
0
2
0
1
3
0
0
1
0
1
0
0
0
1
1
0
0
2
2
2
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
2
0
0
0
0
1
1
0
0
1
0
0
2
1
0
1
0
0
0
0
3
0
0
1
0
1
1
0
2
0
2
0
0
3
1
0
2
1
0
0
0
0
0
2
3
2
0
0
0
2
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
5
0
1
0
0
0
0
0
0
0
0
2
0
3
2
0
2
0
0
2
0
0
2
0
2
0
0
0
0
0
0
2
0
0
1
0
0
2
2
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
1
2
2
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
2
1
2
1
2
2
2
1
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
2
2
1
2
0
0
0
2
1
0
0
0
2
0
0
2
0
1
0
0
0
0
0
2
0
1
0
0
1
1
2
0
0
2
1
0
2
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
3
2
0
2
2
2
1
1
1
0
0
1
0
0
0
0
0
0
1
0
0
1
2
1
0
0
0
0
0
2
0
2
0
0
2
3
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
2
2
0
0
2
0
0
1
3
0
2
0
2
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
2
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
2
1
1
0
0
7
0
2
0
0
1
0
0
0
0
0
0
1
0
0
2
0
2
1
0
1
2
0
1
3
2
0
1
2
1
0
0
0
0
0
1
0
0
2
0
3
0
2
1
2
0
2
1
2
1
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
1
1
0
0
2
1
0
1
2
1
0
0
1
1
0
0
0
0
0
0
1
0
0
1
1
2
0
0
0
0
0
0
2
0
1
3
0
0
0
1
2
2
1
2
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
1
0
4
2
2
0
0
1
0
2
0
0
0
0
1
0
1
0
0
0
2
2
0
0
0
1
2
0
0
0
1
1
2
0
0
1
2
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
1
0
1
0
2
0
0
0
0
0
1
0
1
0
1
2
0
0
0
2
0
0
0
0
0
2
2
0
0
0
2
1
2
1
1
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
4
0
1
2
0
0
2
0
0
0
4
0
1
0
0
0
0
0
2
2
0
0
1
0
0
0
1
1
1
0
0
2
2
2
2
0
0
0
1
0
2
1
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
4
0
0
2
0
0
0
0
2
2
4
2
1
1
0
2
2
2
2
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
1
2
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
1
2
0
0
1
0
0
1
1
1
0
0
0
0
0
1
2
1
0
1
1
2
2
2
0
0
0
0
0
3
0
0
0
1
0
0
2
0
0
0
1
0
2
0
1
1
1
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
2
1
1
0
0
0
1
0
1
1
1
0
0
0
1
0
0
1
0
0
1
2
0
1
0
0
2
0
1
2
0
0
0
2
0
1
0
0
0
0
0
0
4
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
3
0
3
0
1
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
2
0
2
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
1
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
3
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
1
1
1
3
0
0
2
0
2
0
0
2
0
1
1
8
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
2
3
2
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
2
0
1
0
0
2
0
1
0
0
0
0
2
0
2
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
2
0
2
3
2
0
2
0
0
2
0
0
0
1
3
0
0
0
1
0
5
0
0
0
0
0
0
2
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
2
0
0
2
0
0
1
2
0
0
0
0
0
2
0
1
0
0
2
0
0
0
2
1
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
4
0
1
1
0
0
2
1
1
0
0
0
0
0
0
1
0
1
0
0
2
0
2
0
1
0
0
0
2
2
0
1
0
0
2
2
10
0
2
0
0
2
0
1
0
1
0
3
2
0
1
0
0
1
0
1
0
0
2
1
0
2
0
1
0
0
1
0
0
0
2
0
0
2
1
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
1
1
0
1
0
1
0
1
0
2
0
0
2
1
0
0
0
0
2
2
0
0
0
2
0
0
1
0
0
3
0
2
1
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
1
0
0
0
0
4
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
2
1
1
0
0
2
0
1
0
0
0
2
0
1
2
0
0
1
0
0
2
0
0
2
0
0
0
1
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
2
2
0
4
0
0
0
0
0
1
0
0
2
0
1
1
0
0
0
0
1
1
2
0
0
0
0
1
1
0
0
0
1
1
0
0
2
0
0
0
0
0
2
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
2
2
1
1
0
0
1
0
0
0
0
2
0
2
0
0
1
1
1
1
0
0
0
1
4
0
1
2
1
1
0
3
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
1
0
0
0
1
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
2
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
2
1
0
1
0
1
0
1
0
0
1
0
0
0
2
0
0
0
2
0
0
0
2
1
0
1
0
6
0
0
0
2
1
1
2
0
0
0
0
0
0
1
1
0
0
1
0
1
2
0
0
0
2
0
0
1
0
0
0
0
2
2
2
0
0
0
1
0
2
0
2
0
0
1
0
0
0
1
1
2
0
0
1
0
0
0
0
0
0
2
1
0
2
2
0
0
0
0
0
1
1
0
1
0
2
0
0
0
0
0
0
2
0
0
0
1
1
1
0
0
0
0
2
0
0
1
1
0
1
0
0
0
1
1
0
0
0
1
1
1
2
0
0
0
1
0
0
0
2
0
0
2
1
0
0
0
2
0
1
0
1
0
0
0
1
1
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
2
1
2
0
0
1
0
1
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
1
0
1
0
2
1
0
0
0
2
0
0
1
1
0
0
0
1
2
0
1
2
0
0
2
0
0
2
0
0
0
0
2
0
1
0
1
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
1
1
0
0
0
0
2
0
2
0
0
0
0
1
2
0
0
1
0
0
2
0
0
2
0
1
0
0
1
0
0
2
2
0
0
0
1
0
0
0
0
0
0
2
0
0
2
1
2
0
0
0
0
0
2
0
0
2
0
2
0
0
0
2
0
2
1
1
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
2
0
2
1
0
1
0
0
1
2
0
3
2
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
1
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
3
0
0
3
1
2
3
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
2
0
3
0
1
2
2
0
2
2
2
0
1
3
0
0
0
0
0
0
2
0
0
1
5
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
2
1
0
0
3
2
0
2
0
2
0
0
2
2
1
0
1
0
0
0
2
0
0
2
1
0
3
2
1
1
0
0
1
2
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
2
2
2
0
2
0
1
0
1
0
1
0
0
0
0
1
0
0
0
1
2
0
1
0
0
0
2
2
0
0
0
2
0
0
2
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
1
3
0
1
0
0
0
2
1
0
0
0
3
0
0
2
1
0
1
0
0
1
0
0
1
0
1
0
1
1
0
0
2
0
0
1
2
0
2
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
1
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
1
2
0
0
0
0
2
1
0
0
0
2
2
2
0
0
3
2
2
0
0
2
0
0
0
0
1
0
0
2
0
1
4
1
0
2
0
1
2
1
0
0
1
0
0
1
2
2
0
2
1
2
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
2
1
2
1
0
0
0
1
1
2
1
1
2
0
0
2
0
0
1
1
0
0
1
0
0
0
0
2
2
0
1
1
0
1
0
1
0
0
2
2
0
1
0
0
0
0
3
0
0
1
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
1
2
0
2
0
0
3
1
1
1
0
0
1
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
1
1
0
1
0
1
0
1
2
0
1
0
0
2
0
0
1
1
2
0
0
0
2
2
1
2
0
1
0
2
0
1
0
0
2
5
0
0
0
2
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
2
0
1
1
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
2
1
1
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
4
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
2
0
1
2
0
0
2
0
1
2
0
0
0
0
0
0
2
1
0
1
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
1
1
0
0
5
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
2
0
0
1
1
1
1
0
0
1
4
0
0
0
3
1
0
2
1
1
0
1
0
1
3
0
0
0
2
0
0
1
0
0
0
0
0
2
2
0
0
0
0
1
1
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
2
0
2
0
1
1
2
0
2
2
0
0
0
0
0
0
0
0
4
1
0
1
0
0
0
0
2
0
1
0
2
2
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
1
2
0
0
0
3
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
1
1
1
0
0
0
0
1
2
1
2
0
0
0
0
1
0
0
1
0
2
0
2
1
2
2
0
4
2
0
0
0
5
0
0
0
0
0
0
2
1
0
0
0
1
0
0
1
0
0
0
1
2
2
0
0
0
0
0
1
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
2
1
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
5
2
1
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
2
0
2
0
1
1
0
0
0
0
1
2
0
0
0
2
1
0
0
1
2
0
0
0
1
0
0
0
0
0
2
0
2
1
1
0
0
2
1
2
0
0
2
0
0
1
1
0
0
2
0
2
1
1
1
1
0
0
2
0
1
1
0
0
0
1
1
2
2
0
0
0
1
0
0
2
0
2
0
1
0
0
1
1
0
0
0
0
0
2
0
3
0
1
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
2
0
2
0
1
2
0
0
1
0
0
1
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
1
0
2
0
0
1
2
0
2
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
3
2
0
2
1
2
0
0
0
1
0
2
0
0
0
0
0
0
2
2
1
0
0
0
1
0
0
2
0
2
0
3
0
2
1
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
2
0
2
1
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
1
1
0
0
0
2
0
0
0
2
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
1
1
0
1
0
2
2
1
1
0
0
0
0
1
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
2
2
1
0
0
0
0
0
0
2
2
0
1
0
2
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
2
0
0
2
2
2
0
0
0
0
2
4
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
2
1
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
2
0
2
2
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
2
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
2
0
0
0
0
0
2
1
1
2
2
2
0
0
2
0
1
0
1
2
2
0
0
0
0
0
0
0
0
0
1
0
0
1
2
1
0
0
2
0
3
1
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
2
2
0
1
0
3
0
0
0
1
0
0
1
0
1
2
1
1
1
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
1
1
3
1
0
0
1
0
0
0
2
0
1
1
0
2
1
0
0
0
2
2
0
0
0
0
2
2
0
0
2
0
0
3
0
1
0
0
0
2
0
0
0
1
1
2
0
0
0
0
0
0
2
0
1
0
2
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
2
0
0
0
0
2
0
0
0
2
1
2
2
0
1
0
0
0
2
0
2
1
2
0
0
1
0
1
1
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
2
0
1
0
1
0
0
0
2
0
0
0
1
0
0
0
2
0
1
2
2
0
2
0
2
0
0
0
0
0
1
1
0
2
0
0
0
4
1
2
0
0
1
0
0
0
2
1
0
0
0
0
1
0
0
2
1
0
1
0
0
0
1
0
2
0
4
2
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
3
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
2
2
0
2
0
2
0
0
0
1
2
0
0
0
0
0
0
1
0
4
0
0
2
0
2
2
0
0
2
0
0
1
0
0
1
1
0
0
2
1
0
0
2
0
2
2
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
2
0
2
0
0
2
0
1
2
2
0
0
2
0
0
0
0
2
2
0
3
1
0
2
0
2
0
1
1
0
2
2
2
3
1
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
2
0
0
2
0
1
2
1
1
2
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
2
0
1
1
1
1
0
1
0
0
0
2
1
1
2
0
0
2
0
0
0
2
0
0
0
2
2
1
0
1
0
2
1
0
0
2
2
0
0
1
0
0
0
3
0
0
0
2
0
0
0
2
1
0
0
0
0
1
2
0
3
0
0
2
0
0
1
0
0
3
3
0
2
0
1
0
0
1
0
0
0
0
2
0
1
1
0
0
1
0
2
0
2
2
0
0
1
2
2
0
0
0
1
0
1
0
0
1
1
2
0
0
0
0
0
1
0
0
2
5
2
0
2
1
2
2
0
0
0
0
1
0
0
1
1
1
0
0
1
0
2
1
1
2
0
0
0
1
0
0
0
1
0
1
1
0
2
0
2
0
0
1
0
2
1
0
0
1
0
0
1
1
0
2
0
0
1
0
2
2
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
6
1
0
2
2
0
0
3
1
0
1
0
0
2
0
0
0
2
3
0
0
1
1
2
0
0
0
2
0
0
0
0
2
2
1
0
1
0
0
0
2
0
0
0
0
1
0
3
1
0
0
1
0
0
0
1
0
0
0
0
1
0
2
1
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
1
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
2
1
0
1
2
0
2
1
2
0
0
0
2
1
0
0
1
0
0
0
1
1
0
2
0
0
2
0
0
4
0
2
0
2
0
0
2
1
1
1
0
0
1
2
2
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
4
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
2
0
1
2
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
3
0
0
0
2
1
0
2
0
0
0
0
0
1
0
0
0
2
2
1
0
1
1
0
0
0
0
2
0
2
0
2
1
0
0
1
2
0
0
1
0
1
0
0
0
0
2
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
1
0
1
2
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
4
0
1
0
0
0
2
0
0
1
0
0
1
1
0
0
0
0
0
1
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
2
0
2
0
0
2
0
2
1
2
1
0
0
0
0
1
0
0
0
1
2
1
0
0
0
0
1
0
2
2
2
2
1
2
0
0
0
0
0
2
2
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
1
2
0
0
2
1
2
2
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
3
2
0
0
1
2
1
0
1
0
0
6
0
4
1
2
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
2
0
0
1
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
1
0
1
0
0
0
2
0
0
4
0
1
0
0
2
2
2
0
0
0
0
2
2
0
0
0
0
0
1
0
5
0
1
0
1
2
0
2
1
0
0
0
1
2
0
0
0
0
3
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
2
1
1
2
0
1
1
0
2
2
0
0
1
2
0
0
0
0
2
1
0
0
0
0
1
0
0
2
0
0
0
0
1
1
0
2
2
0
0
0
1
1
1
0
0
0
0
0
1
0
0
1
0
0
2
1
0
1
2
2
0
0
1
1
2
0
0
0
1
0
0
0
0
0
0
1
0
1
2
0
3
0
2
0
2
0
1
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
1
0
2
2
2
1
0
0
0
0
0
0
0
1
0
2
2
1
0
1
1
1
0
0
0
1
0
1
1
0
0
2
2
1
0
0
0
0
1
0
2
1
0
0
2
2
0
0
1
2
0
0
0
2
0
0
1
1
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
5
1
0
1
0
0
0
0
0
1
0
0
1
1
1
2
0
0
2
1
0
2
0
1
3
0
0
0
0
0
0
0
0
2
2
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
1
1
0
1
0
0
2
2
0
1
0
0
1
2
2
0
0
0
1
0
1
2
0
0
0
1
0
1
1
0
2
0
0
1
2
2
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
2
2
0
0
1
0
1
0
0
0
0
1
1
0
2
0
2
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
1
2
0
0
1
1
1
0
0
1
0
0
2
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
2
2
3
5
2
0
2
0
0
2
1
0
0
4
2
1
0
0
0
1
0
2
0
4
0
0
3
0
2
2
0
0
0
0
0
0
0
0
0
0
0
8
0
1
0
0
0
1
0
0
0
1
0
0
2
0
3
0
2
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
1
0
2
1
1
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
1
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
2
1
0
1
2
2
0
0
0
0
0
2
4
0
2
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
2
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
2
0
1
0
3
0
1
0
2
0
1
0
2
2
0
0
0
0
1
0
2
1
0
0
1
1
0
2
0
0
0
0
2
2
0
0
0
2
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
2
0
0
1
2
1
0
2
0
0
0
0
0
0
0
3
1
0
0
0
1
1
0
0
2
0
1
0
2
2
2
0
0
0
0
0
1
0
0
0
1
1
2
0
1
1
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
1
2
0
7
1
0
0
0
0
0
0
2
0
0
1
1
2
2
2
1
0
0
1
0
0
0
0
1
0
0
1
1
2
0
0
2
2
0
2
0
0
0
1
0
2
1
2
3
0
0
0
0
0
0
3
0
0
0
0
4
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
1
0
1
1
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
2
2
0
0
1
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
1
4
0
0
0
0
1
0
0
1
1
0
0
0
2
1
2
3
1
2
0
3
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
1
2
0
1
2
0
0
0
1
2
0
0
0
1
0
1
1
2
0
2
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
2
0
0
1
0
0
1
0
0
2
0
2
2
0
0
3
0
0
0
0
1
2
1
0
0
0
0
0
1
1
0
0
0
2
0
1
2
2
0
0
0
0
0
0
2
2
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
1
1
0
0
0
0
0
0
2
3
1
2
0
0
0
2
2
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
1
0
0
3
0
0
0
0
0
2
0
0
1
0
0
2
2
0
2
0
0
1
2
2
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
3
0
1
0
0
1
0
2
0
2
2
0
0
1
0
0
0
0
0
2
0
0
1
0
0
1
1
0
0
0
0
2
3
2
2
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
2
1
0
2
0
1
1
3
0
0
0
1
0
0
1
1
0
0
0
0
1
0
2
0
0
0
0
0
0
2
1
0
1
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
1
0
2
1
0
2
0
0
0
0
0
2
0
2
0
1
0
0
0
0
4
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
5
3
1
0
0
0
2
1
1
0
0
1
0
1
2
1
1
4
0
2
1
0
0
2
0
0
2
0
0
0
0
2
2
0
2
0
0
2
0
0
0
2
0
1
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
4
1
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
1
1
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
12
0
0
0
0
0
0
1
0
0
1
0
1
4
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
4
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
3
2
0
2
1
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
2
0
2
1
0
2
0
0
2
0
0
0
0
2
0
0
2
1
0
0
0
0
1
1
1
1
1
2
0
0
1
2
2
0
0
0
0
2
3
1
0
1
2
0
1
0
1
0
1
0
0
2
2
0
0
0
0
2
0
0
1
0
1
2
0
2
0
0
0
1
0
0
0
1
0
0
0
0
3
2
0
0
2
0
1
0
0
2
2
0
1
0
0
0
0
2
0
0
0
0
0
2
1
0
1
0
1
3
0
1
2
2
0
2
0
0
0
1
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
1
0
2
2
2
1
1
2
1
2
0
0
0
0
2
2
0
0
0
2
0
2
0
0
0
1
0
0
0
0
1
1
2
0
2
1
0
0
1
2
0
0
3
1
2
2
0
1
0
0
0
4
2
0
0
1
2
0
0
0
2
0
0
2
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
2
0
0
2
0
0
0
0
0
1
0
2
0
0
2
2
0
2
2
1
1
0
1
0
3
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
2
1
0
0
0
2
0
0
0
0
0
2
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
1
0
2
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
1
2
0
0
0
3
1
1
0
0
0
0
2
1
2
0
1
0
1
0
0
1
0
2
1
1
1
0
0
2
1
0
3
0
0
1
1
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
2
0
2
1
1
1
0
3
0
1
0
0
0
1
1
2
0
2
1
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
2
0
0
0
1
2
2
0
0
2
0
0
2
0
0
1
0
0
0
2
1
0
2
0
0
0
0
0
3
0
2
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
2
1
2
1
0
0
0
1
0
2
0
0
0
0
0
0
1
1
3
0
0
0
0
0
0
2
0
1
2
0
2
2
0
1
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
2
0
2
0
1
1
0
1
2
0
0
0
1
0
1
0
0
0
0
1
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
2
2
0
2
0
2
2
0
0
0
0
3
2
0
0
1
0
0
0
0
2
2
0
0
2
0
2
0
0
0
0
1
0
2
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
1
3
0
0
2
1
1
0
2
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
2
1
0
2
0
0
2
0
1
0
0
0
0
0
1
0
1
0
0
0
7
3
0
0
2
0
0
0
0
1
0
0
0
2
1
0
0
0
0
2
0
0
1
2
1
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
2
0
0
2
0
2
0
1
0
0
0
2
0
0
0
1
1
0
0
0
2
0
0
0
0
2
1
0
0
1
1
1
0
2
0
0
1
0
2
1
0
0
1
2
0
1
0
2
0
2
1
2
0
0
2
1
0
0
2
0
0
0
1
0
2
0
2
0
0
2
1
0
6
0
0
0
0
1
1
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
5
0
0
0
0
1
1
0
0
0
0
0
1
1
2
0
1
0
0
1
0
0
1
0
0
0
0
0
1
1
2
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
1
0
1
0
0
1
0
1
0
0
2
0
0
2
0
0
1
0
1
1
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
3
0
0
0
0
0
2
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
1
0
1
0
0
1
0
0
2
0
0
0
2
1
0
0
2
2
2
0
0
1
0
1
0
2
0
2
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
1
0
0
2
0
2
0
1
2
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
1
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
3
0
0
0
2
0
0
0
0
1
0
0
1
0
1
1
0
2
0
0
0
0
1
0
1
2
0
0
0
0
1
2
0
0
1
2
0
1
0
1
0
0
1
2
1
0
3
0
0
2
0
2
1
2
0
2
0
0
0
1
0
1
0
0
2
1
1
1
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
2
0
0
1
0
1
0
0
0
0
0
2
1
1
0
0
3
0
1
7
0
3
2
0
2
2
0
0
0
2
0
0
1
0
1
0
3
2
2
1
2
2
3
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
1
2
2
2
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
2
2
1
1
1
1
0
0
0
2
1
1
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
1
0
0
0
1
0
0
0
1
2
0
0
0
1
0
3
2
1
1
0
0
2
0
0
0
0
0
2
1
2
0
4
0
0
0
0
0
0
0
0
3
2
2
0
2
2
0
1
0
0
0
0
0
0
4
2
0
1
0
1
2
1
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
4
0
1
2
0
1
2
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
2
1
0
1
0
2
0
1
1
0
0
0
3
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
1
0
1
2
0
1
2
0
0
2
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
5
0
0
1
4
2
1
0
0
2
0
1
1
0
2
2
3
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
3
1
0
0
0
0
0
2
2
2
0
1
0
2
0
0
0
1
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
3
2
3
0
0
0
0
3
1
0
0
2
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
2
0
2
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
1
2
2
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
2
2
4
0
0
0
0
5
0
4
0
0
1
1
0
0
2
0
1
0
2
1
3
0
2
0
0
0
0
0
0
1
0
0
2
0
1
0
1
0
2
0
1
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
3
0
2
0
0
0
0
1
0
0
0
1
0
1
0
0
0
2
0
0
2
2
0
3
2
1
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
1
2
0
1
1
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
1
0
0
1
0
2
3
1
0
0
0
0
0
2
2
2
1
0
0
0
0
2
1
1
0
1
0
0
1
0
0
2
0
0
0
0
1
8
0
2
1
1
0
0
2
0
1
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
2
0
0
0
0
0
1
0
2
1
1
0
0
1
0
1
0
2
3
6
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
1
1
0
0
0
1
1
1
0
0
0
1
0
2
0
2
0
2
2
2
0
1
0
1
1
2
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
5
2
2
0
0
1
0
0
0
0
2
0
0
2
0
2
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
1
2
1
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
2
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
1
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
1
4
2
2
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
2
2
3
0
0
3
0
0
0
1
0
0
0
0
0
1
0
0
1
3
0
0
0
2
2
1
2
2
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
2
1
2
2
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
2
2
0
1
0
2
0
0
0
0
0
0
0
0
1
0
2
1
0
0
1
0
2
1
3
0
0
0
1
1
1
1
0
0
1
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
1
2
0
1
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
1
0
0
5
1
0
1
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
2
0
3
0
0
1
1
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
2
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
2
1
1
0
0
0
1
1
1
0
0
1
0
3
0
0
1
2
1
0
2
2
1
0
0
2
0
1
0
1
0
1
0
1
0
0
0
3
0
0
0
1
2
0
0
0
0
0
0
1
1
2
0
3
1
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
2
1
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
1
2
0
0
1
0
0
1
0
0
1
2
1
0
0
0
2
1
0
1
0
0
0
1
0
0
1
2
0
0
0
1
0
0
0
0
0
1
2
0
0
0
2
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
3
0
0
2
3
0
1
2
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
4
0
0
1
1
2
0
1
2
1
1
2
0
1
0
0
0
1
1
0
0
0
2
2
2
1
0
0
0
0
0
0
0
0
2
0
2
0
2
1
0
0
0
0
2
1
0
2
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
2
2
0
0
1
1
0
1
1
0
2
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
1
1
0
1
2
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
2
2
2
0
0
2
2
0
1
0
0
1
1
0
0
0
1
2
3
2
1
1
1
0
0
0
0
1
2
0
0
0
3
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
2
1
0
0
0
1
0
0
2
0
0
0
4
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
2
1
0
0
0
0
1
0
0
0
1
0
2
0
2
1
0
1
0
1
0
0
0
0
1
0
0
0
1
2
2
0
2
0
0
0
1
2
0
0
0
0
1
0
0
2
0
2
1
2
0
1
0
0
2
0
1
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
2
0
1
0
2
0
1
0
1
2
2
0
1
0
0
2
0
0
0
0
0
0
1
1
2
0
1
1
0
0
0
0
2
0
2
0
0
2
0
0
0
2
2
0
0
0
0
0
1
1
1
0
1
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
4
2
1
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
2
0
0
0
0
1
3
1
0
3
0
0
0
1
0
2
0
0
2
1
0
0
1
0
0
0
0
0
0
0
2
0
1
1
1
3
0
0
0
0
2
2
1
2
0
2
1
2
1
1
0
1
0
1
1
0
0
0
0
0
0
0
0
2
0
0
2
0
3
0
0
0
0
0
2
2
1
0
3
1
0
0
1
2
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
1
0
2
0
0
2
2
2
0
0
0
0
0
1
1
0
0
1
0
0
1
0
1
0
2
0
0
0
0
0
2
1
0
3
2
0
0
0
2
1
0
1
0
0
0
2
1
0
0
2
0
0
0
0
0
2
0
1
2
0
3
2
0
2
0
0
0
0
0
0
0
0
2
0
0
2
4
0
0
0
0
2
1
2
0
1
0
0
1
0
2
0
2
0
2
0
0
2
0
2
2
0
0
1
0
1
2
0
2
2
1
0
1
2
2
0
0
0
0
2
0
1
0
0
1
1
2
0
0
0
2
0
1
0
2
2
0
0
0
0
0
1
0
0
2
1
2
1
0
1
0
0
2
0
0
0
1
1
0
0
1
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
1
0
1
0
1
0
0
0
2
0
0
2
0
1
1
1
1
0
0
0
1
0
1
1
1
0
1
1
0
1
1
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
2
2
0
0
0
2
0
2
0
0
0
0
2
0
2
2
2
0
2
1
1
2
1
2
0
0
0
2
0
0
1
3
2
0
0
2
2
0
0
0
12
0
0
0
0
0
0
1
2
0
0
0
2
0
2
1
0
0
0
0
0
0
2
2
1
0
0
0
1
0
0
1
1
0
1
0
1
0
0
0
2
0
0
0
2
0
0
2
2
0
1
2
0
2
0
0
0
2
0
2
0
1
0
0
0
0
0
2
0
1
0
2
0
0
1
0
0
2
0
2
0
0
2
2
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
1
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
2
1
1
1
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
2
2
1
0
1
0
2
2
0
0
0
2
0
0
1
5
1
0
2
0
1
2
0
0
1
0
2
0
0
2
2
0
2
0
2
0
0
1
1
0
2
0
1
2
0
0
0
0
0
0
0
2
0
0
3
0
0
1
0
0
2
0
0
0
0
2
1
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
1
0
0
0
0
2
0
0
7
2
0
0
0
0
0
1
1
1
2
0
3
2
0
0
0
1
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
2
0
0
2
2
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
2
0
0
1
0
2
2
1
0
2
0
2
0
0
0
1
0
1
0
0
1
0
0
1
0
0
1
2
1
1
1
0
3
0
0
2
3
0
0
0
0
2
0
0
3
0
1
1
0
0
4
0
1
0
2
1
1
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
2
1
2
0
2
0
2
2
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
4
1
0
0
0
3
0
0
0
1
0
0
1
0
0
2
1
0
1
0
0
0
0
1
2
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
3
0
0
0
1
0
0
0
0
3
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
1
2
1
0
0
0
0
0
0
2
2
0
0
0
1
1
0
2
1
0
1
0
0
0
1
0
0
0
0
1
2
1
2
2
2
0
2
0
0
2
2
0
0
2
0
1
1
0
0
2
0
0
2
0
0
1
0
0
2
0
0
1
1
2
0
0
1
2
0
0
0
0
0
0
2
0
2
1
1
0
0
0
0
0
0
2
2
0
0
1
1
2
1
0
1
0
1
2
2
0
0
1
0
0
0
0
2
2
3
2
0
0
2
1
0
3
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
2
2
2
2
1
0
1
1
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
2
1
0
0
0
0
3
0
0
2
1
1
2
0
0
0
0
0
2
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
2
2
0
1
0
0
1
0
1
0
0
2
0
0
1
0
0
0
2
0
0
0
1
2
0
0
1
1
0
2
0
2
1
0
1
2
2
1
1
0
0
2
1
2
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
3
0
2
3
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
2
0
1
0
1
1
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
2
1
0
1
0
3
0
1
2
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
4
0
0
1
2
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
1
3
0
2
0
1
0
0
0
2
2
0
0
0
0
2
1
1
2
0
0
2
2
0
2
0
1
0
2
0
0
3
0
2
0
0
3
0
0
0
0
0
0
2
3
2
0
1
1
2
2
0
0
2
0
0
2
0
2
1
2
0
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
2
2
0
0
2
2
0
2
2
1
0
0
1
0
0
0
0
0
2
2
0
0
2
2
0
1
3
1
0
3
0
0
1
2
0
0
1
0
1
0
0
2
0
2
0
0
0
2
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
1
2
0
0
0
0
0
2
1
0
0
0
2
1
0
1
1
1
0
0
0
3
0
3
1
0
1
0
0
0
1
1
1
0
0
0
0
0
1
0
2
0
1
2
0
1
1
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
1
0
0
2
0
2
0
2
2
0
1
1
0
3
0
1
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
2
0
1
0
0
1
1
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
1
2
0
1
0
0
0
2
0
2
0
0
0
1
1
0
1
0
2
1
1
2
2
1
0
0
0
1
0
0
2
0
2
1
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
2
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
1
1
2
1
0
0
1
0
2
0
0
0
1
2
1
0
0
0
4
2
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
2
2
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
1
0
0
0
2
0
2
2
1
1
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
2
2
0
1
0
2
2
2
2
1
4
2
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
2
2
2
3
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
11
2
0
0
0
1
0
1
0
1
1
0
0
2
0
0
0
1
0
2
0
2
0
1
1
0
2
0
0
1
0
3
2
2
0
0
0
0
0
1
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
2
0
4
0
2
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
1
0
1
0
2
0
0
2
0
0
0
2
2
0
0
3
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
2
2
2
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
4
0
2
2
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
2
2
1
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
1
1
0
0
0
1
0
0
0
1
0
2
0
0
2
0
1
2
2
0
0
0
2
0
0
0
0
0
1
2
2
0
0
0
1
0
1
0
0
0
0
0
0
1
0
2
0
0
0
2
1
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
1
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
4
1
0
0
0
0
0
0
0
1
0
3
0
1
1
0
1
0
0
1
0
2
1
1
0
0
0
0
0
3
1
0
0
0
0
1
2
1
0
0
0
1
1
0
0
2
2
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
1
0
2
0
2
0
1
0
1
1
0
2
2
0
0
1
0
0
0
1
0
0
0
0
0
2
0
1
0
2
1
2
0
0
1
0
0
0
1
0
0
0
2
2
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
1
0
1
0
0
0
0
1
0
0
0
0
2
0
0
5
0
0
0
4
0
0
1
0
2
1
0
1
0
0
0
2
0
1
0
1
0
0
1
1
0
0
0
0
2
1
0
0
2
0
0
2
2
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
2
0
0
2
2
1
0
0
0
0
2
0
0
0
0
0
2
1
2
1
0
1
0
2
0
0
1
1
0
8
1
0
0
1
0
0
2
0
1
0
2
2
0
0
0
0
5
0
0
0
0
2
0
0
0
0
0
2
0
2
1
0
1
2
0
2
1
0
0
1
2
1
0
0
0
0
0
1
0
0
2
0
0
0
0
2
2
2
0
0
2
2
3
0
2
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
2
0
0
0
0
2
0
2
0
1
0
0
0
2
0
0
0
0
1
2
0
1
2
2
0
0
1
2
0
0
0
3
0
1
1
0
1
8
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
2
0
0
0
0
6
1
0
0
0
1
0
0
1
0
0
0
0
0
2
1
0
1
0
0
2
0
2
1
2
1
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
1
2
2
0
1
0
2
0
1
1
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
4
0
0
0
0
0
2
0
0
0
1
3
1
2
0
0
0
0
1
0
2
2
0
0
0
0
2
3
0
0
0
1
1
2
3
0
0
0
0
0
2
2
0
2
2
0
0
0
1
0
0
1
0
0
1
2
1
1
0
1
1
1
0
1
0
0
0
0
1
0
2
1
0
1
2
2
0
0
0
0
4
0
0
0
2
0
0
1
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
1
2
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
1
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
2
1
0
0
0
0
0
1
0
0
0
1
0
3
0
0
0
0
0
2
0
0
0
0
1
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
3
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
3
0
2
0
0
0
0
0
2
0
2
0
1
0
1
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
1
2
1
0
1
0
0
1
0
0
0
0
0
2
0
0
2
0
0
1
2
0
0
0
0
0
1
0
1
2
1
0
0
0
0
0
3
0
0
0
1
2
1
2
0
0
1
0
0
0
0
0
0
1
0
0
0
2
2
0
0
2
1
1
0
0
2
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
2
2
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
1
2
2
1
0
0
2
2
9
3
1
0
0
2
0
0
0
0
1
0
2
0
0
0
2
0
2
2
2
0
0
0
1
0
0
0
0
0
1
1
0
2
1
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
1
2
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
2
1
0
0
0
0
1
0
0
0
1
0
2
0
1
2
0
1
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
2
2
0
1
1
0
2
0
2
0
0
2
1
2
1
0
0
0
0
2
1
2
0
0
0
7
0
3
0
0
0
2
0
2
0
1
1
0
2
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
1
2
0
1
0
0
1
1
2
0
1
0
0
2
2
2
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
1
2
0
2
0
1
0
1
2
5
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
1
0
1
2
0
1
2
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
1
2
1
1
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
1
0
2
0
0
2
0
1
0
0
0
0
2
1
0
1
3
0
1
0
2
0
1
3
4
1
0
0
0
1
0
0
2
0
0
2
0
0
1
0
1
2
2
0
2
0
0
0
1
3
0
0
1
0
0
0
1
0
1
0
2
0
0
0
3
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
1
0
1
0
1
0
0
0
0
1
0
1
0
0
5
0
2
0
0
0
0
1
2
1
2
0
1
0
2
0
0
2
0
1
0
0
1
1
3
0
0
0
0
2
3
0
1
0
2
0
0
0
0
0
0
0
1
1
1
0
1
2
0
1
2
2
1
0
2
0
0
0
1
0
1
2
1
0
2
2
2
0
0
0
0
0
0
2
0
0
2
0
1
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
2
1
0
2
0
0
0
1
1
2
0
3
0
0
0
0
2
0
0
0
2
1
1
13
0
0
0
2
0
1
1
0
0
0
0
1
1
0
0
1
1
2
0
1
1
0
0
0
2
2
0
0
1
0
0
0
0
1
2
2
2
2
0
0
0
1
0
0
0
0
2
2
1
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
3
0
2
0
0
2
0
2
2
4
0
2
0
0
1
1
1
1
0
2
0
1
0
0
2
1
0
0
1
0
0
1
1
0
2
0
2
1
0
2
0
0
0
0
0
2
1
0
1
2
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
1
0
0
2
0
0
2
0
0
2
0
1
4
1
1
2
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
2
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
1
0
3
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
2
2
1
0
2
0
1
2
0
0
0
0
0
0
0
0
1
1
2
0
1
1
1
2
0
0
1
0
1
0
2
0
0
0
2
2
1
0
1
1
0
0
0
0
0
2
1
0
2
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
2
2
0
1
0
0
0
2
1
1
2
0
0
0
0
2
2
0
0
1
2
0
1
0
1
0
1
1
2
0
0
0
2
0
0
0
2
0
2
1
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
4
2
0
2
2
0
0
0
0
1
0
2
0
2
0
0
0
0
2
0
2
2
1
0
0
2
1
0
0
2
0
0
0
0
2
0
0
0
0
1
0
3
0
0
1
0
1
0
0
0
0
0
0
2
0
0
1
2
0
0
1
0
0
2
2
0
0
0
0
0
1
2
1
0
0
0
0
0
0
3
1
0
0
2
0
0
0
0
0
2
0
0
0
1
2
0
2
1
0
1
2
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
1
1
2
0
0
1
0
2
0
0
1
0
0
0
0
2
0
0
0
0
2
0
1
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
1
0
2
7
0
2
0
0
0
2
1
2
0
0
0
0
1
1
0
0
0
2
0
4
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
2
1
1
0
0
2
0
0
2
0
0
2
0
0
0
0
1
1
3
0
2
1
0
0
0
0
0
0
0
2
0
0
1
1
0
0
1
2
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
2
2
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
3
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
3
0
2
0
2
1
1
0
0
0
0
1
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
3
0
3
0
0
0
0
0
1
3
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
1
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
3
1
0
2
0
1
0
1
2
2
1
0
0
0
0
2
0
0
1
2
0
0
0
2
0
0
1
0
0
2
0
0
0
2
2
0
0
0
0
0
2
1
0
1
1
1
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
1
1
0
0
0
2
2
0
0
1
1
0
0
4
0
0
0
0
3
1
0
0
0
0
2
0
0
0
2
0
0
3
1
0
0
0
0
0
2
2
0
0
0
0
0
2
0
2
0
1
0
2
0
0
0
0
0
1
1
1
0
0
0
1
2
0
0
0
1
0
2
0
0
0
1
0
1
0
0
1
0
2
0
1
0
0
2
2
0
0
0
0
0
0
1
1
0
0
2
0
0
0
3
0
0
1
1
0
0
0
0
0
0
2
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
2
0
1
1
0
2
0
1
0
0
0
1
0
0
0
2
1
0
0
1
0
0
0
2
0
0
1
0
0
1
1
2
0
3
0
0
0
0
0
0
1
0
1
1
0
0
2
0
0
1
2
0
2
0
1
1
0
0
0
2
2
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
2
2
2
2
0
2
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
1
0
0
2
0
1
0
2
0
0
2
1
0
1
1
0
0
0
2
1
0
0
0
2
0
0
0
0
2
2
0
0
2
2
0
2
0
1
0
0
0
0
2
0
0
1
2
0
1
0
0
0
0
2
1
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
1
0
2
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
1
2
0
0
2
0
0
0
1
2
0
3
0
2
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
2
1
0
0
0
0
0
0
0
0
0
0
4
1
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
2
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
1
0
0
2
2
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
4
2
0
1
0
1
0
2
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
2
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
1
2
0
2
0
2
0
1
0
2
2
0
1
0
0
0
1
1
2
1
1
0
0
0
2
0
1
2
0
0
0
1
0
1
0
2
0
0
0
0
0
0
3
0
2
0
0
1
0
1
0
0
0
0
0
1
1
2
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
1
0
3
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
3
1
0
0
0
0
1
1
0
0
0
2
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
2
0
2
1
0
1
1
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
1
2
0
0
0
2
1
0
3
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
2
0
0
0
0
0
0
1
2
0
1
1
0
1
1
0
0
1
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
2
2
1
0
0
0
0
0
1
0
0
0
2
1
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
1
1
3
2
0
0
1
1
1
0
0
0
2
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
3
1
1
1
1
0
0
1
12
0
2
2
0
0
3
1
0
0
0
2
0
1
0
0
3
0
0
0
0
0
3
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
1
2
2
0
0
0
3
0
0
0
0
1
0
0
0
1
2
0
0
2
3
2
0
0
1
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
2
0
0
0
2
0
0
0
2
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
1
2
0
0
0
2
3
3
0
0
0
2
0
0
0
0
1
0
1
0
1
0
0
0
6
2
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
3
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
1
1
2
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
3
2
3
2
0
4
0
1
1
1
0
0
1
0
0
0
1
0
0
0
0
2
2
0
0
0
0
2
0
0
0
1
1
1
0
0
0
0
1
0
2
1
2
0
1
2
1
0
0
0
0
3
3
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
3
0
0
0
0
0
0
7
0
0
0
2
0
0
2
0
2
0
1
1
0
2
0
2
2
0
0
1
0
0
2
0
1
0
1
0
0
0
0
1
0
1
0
2
0
0
0
0
1
1
0
0
0
0
2
0
1
0
0
0
1
2
0
0
0
0
0
2
0
3
2
1
0
0
0
1
2
2
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
1
1
2
0
0
0
1
0
0
5
1
1
0
0
0
0
0
3
0
0
1
2
0
0
0
1
0
1
0
1
2
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
1
0
1
2
0
2
0
0
0
1
0
2
0
1
0
0
2
0
0
2
0
0
0
2
1
0
0
0
0
0
0
1
1
0
0
2
0
1
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
2
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
3
0
0
1
0
2
2
0
1
0
0
0
0
0
0
0
1
2
0
2
0
2
0
0
2
1
0
0
2
1
0
2
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
1
1
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
1
0
2
1
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
1
2
1
0
0
0
0
1
0
0
0
1
0
0
3
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
2
2
0
0
2
0
0
0
2
2
0
0
0
0
0
2
2
1
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
1
2
0
0
0
2
1
0
1
0
0
1
2
1
0
0
0
2
0
0
0
0
0
0
1
2
1
0
3
0
2
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
1
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
2
2
0
0
1
1
2
0
0
2
1
2
0
0
0
1
5
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
2
6
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
2
1
2
0
0
0
0
0
0
0
1
0
1
0
0
0
3
0
1
2
1
0
0
0
1
0
0
2
0
0
0
3
1
1
0
0
2
0
0
0
0
3
2
0
0
0
0
3
0
0
0
0
4
0
0
0
2
0
1
0
2
0
2
0
3
1
1
0
2
0
0
1
4
1
0
2
1
1
2
0
0
0
0
2
0
0
0
0
0
0
0
3
0
1
0
0
0
1
0
0
0
1
0
2
1
2
1
1
0
0
1
2
2
1
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
1
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
1
1
2
3
0
0
0
0
0
0
0
5
0
2
0
0
2
2
1
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
1
2
0
1
2
2
0
2
2
0
0
0
0
0
2
0
2
0
0
0
0
1
2
2
1
0
2
3
0
0
0
0
1
0
0
2
0
2
2
0
0
0
0
0
0
1
1
0
0
0
1
0
0
2
2
0
0
1
0
1
2
1
0
2
0
0
0
0
2
0
0
0
0
1
0
0
2
2
0
1
1
0
1
0
2
0
0
0
0
1
2
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
3
0
0
2
2
1
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
1
1
1
1
1
0
2
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
2
0
1
0
0
0
0
0
0
0
0
1
2
0
1
5
0
0
0
0
0
1
0
1
0
2
2
1
1
0
1
3
1
0
2
1
5
0
0
0
1
0
0
2
2
2
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
2
1
0
0
0
0
0
0
0
1
3
1
2
0
0
0
0
0
0
0
3
1
3
0
0
1
0
1
1
1
0
1
2
0
0
0
1
0
0
1
0
0
0
2
0
0
2
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
1
2
1
1
1
1
2
0
0
2
0
0
0
0
2
0
0
1
0
0
8
0
2
0
5
1
0
2
1
3
1
0
3
1
0
1
1
1
1
0
1
0
0
0
0
0
1
2
1
0
2
0
2
0
0
1
0
0
0
1
1
1
0
0
2
0
1
2
3
0
2
3
2
0
1
0
0
0
0
2
0
0
2
0
2
1
0
0
1
0
2
1
0
0
1
0
2
0
0
1
1
2
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
2
2
2
1
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
3
2
4
0
0
0
0
0
0
0
0
1
1
2
2
0
2
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
1
2
5
0
1
0
1
0
0
3
0
1
0
2
0
0
0
0
2
0
0
2
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
2
1
2
2
0
0
1
0
0
0
0
0
2
2
2
0
0
0
0
1
0
1
1
1
2
1
0
0
2
0
0
0
1
0
0
0
2
2
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
2
0
0
0
2
0
0
1
1
0
0
1
0
0
1
0
1
0
1
2
0
0
2
0
1
2
0
1
1
1
0
0
0
0
2
0
1
1
0
1
0
0
1
0
4
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
1
1
0
0
1
2
1
2
2
0
0
2
0
0
1
2
0
0
2
0
0
0
0
0
2
0
1
2
0
0
0
2
0
0
1
0
0
0
0
0
1
2
2
0
0
0
0
1
2
0
0
0
0
2
0
2
0
0
0
2
1
0
0
0
0
0
0
0
2
0
2
0
0
1
2
2
0
1
1
0
1
2
0
2
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
1
0
2
0
2
0
0
1
2
0
1
3
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
2
2
1
0
4
0
1
1
0
0
0
1
0
0
1
0
0
0
3
0
0
0
0
0
0
0
3
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
1
1
1
1
0
0
2
2
1
2
0
2
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
2
0
0
2
0
0
2
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
1
2
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
4
2
0
0
0
2
0
2
0
0
0
0
0
0
2
2
0
0
0
2
1
0
0
2
2
0
1
0
0
0
0
0
2
2
1
0
2
1
2
1
0
1
0
1
0
0
2
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
1
2
0
1
1
2
0
0
0
1
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
1
0
0
2
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
1
1
0
0
1
0
0
0
2
0
0
1
2
2
1
5
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
4
0
1
0
0
0
1
2
1
1
2
0
1
0
2
1
0
0
0
1
2
1
0
0
0
0
1
0
1
0
2
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
1
0
1
1
0
0
0
0
2
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
3
3
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
2
1
0
0
0
1
0
1
0
1
0
2
1
0
0
0
0
1
0
0
1
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
2
0
2
0
0
1
1
0
2
0
1
0
0
1
2
0
0
0
0
2
3
1
2
0
1
0
2
0
0
2
0
1
0
1
0
0
0
0
0
0
2
2
0
2
0
0
1
0
2
0
2
3
0
2
2
0
0
0
0
0
0
1
0
0
0
3
2
0
0
2
0
1
0
0
0
1
2
0
1
0
0
0
0
1
0
1
0
0
2
0
0
3
2
2
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
2
0
3
2
1
2
0
0
1
0
2
1
0
1
1
1
0
0
1
0
2
0
2
2
0
0
1
1
1
2
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
1
0
1
2
3
0
0
0
0
1
1
0
0
0
0
1
1
1
0
0
0
0
2
0
2
1
1
2
8
2
2
1
0
1
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
1
1
0
3
0
0
2
0
0
2
1
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
2
2
2
1
0
0
0
1
1
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
2
0
0
2
0
2
0
0
0
0
4
3
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
2
0
2
0
1
2
0
0
1
0
1
0
0
0
1
0
0
0
0
2
0
2
0
1
0
0
0
3
0
0
0
2
1
0
2
2
2
0
0
2
0
0
0
0
0
0
1
0
0
2
1
1
0
1
1
0
1
0
0
0
2
1
0
0
0
0
0
0
1
0
0
2
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
1
2
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
2
1
1
0
0
2
0
0
2
0
0
2
0
2
0
0
0
2
1
1
0
0
2
0
0
2
0
0
0
0
0
1
0
0
1
0
1
0
1
1
0
2
0
0
0
0
1
0
2
0
0
2
0
0
1
1
1
0
0
0
1
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
1
2
1
0
0
2
0
0
1
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
2
0
1
1
3
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
2
0
0
2
1
1
1
0
1
0
2
0
4
2
0
2
1
0
0
1
2
0
0
0
2
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
2
2
1
0
1
0
0
0
0
2
1
0
2
2
0
0
1
0
1
2
0
0
1
0
0
1
2
0
0
0
1
0
0
0
3
0
0
0
0
0
1
0
0
1
1
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
1
0
0
0
2
0
1
0
1
2
1
0
2
1
0
1
5
0
0
2
2
1
1
2
0
0
0
2
1
1
1
0
0
1
2
2
0
0
0
0
2
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
2
0
2
2
0
0
0
0
0
1
1
2
1
0
0
1
0
0
0
1
2
0
0
0
0
0
1
0
0
1
1
2
0
3
0
1
2
1
1
1
1
0
2
3
1
1
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
1
0
0
0
0
0
0
0
1
1
0
1
0
0
2
0
2
0
0
0
0
0
0
2
1
0
0
0
1
0
3
2
0
0
0
0
0
0
1
0
0
0
3
2
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
1
2
0
2
0
0
2
2
0
0
0
0
2
0
3
0
0
1
2
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
2
2
2
1
0
2
1
0
0
1
0
2
1
0
0
0
0
2
0
1
0
0
0
0
0
3
0
1
1
0
0
1
0
0
2
1
0
1
0
2
0
0
0
6
0
0
1
0
0
0
0
1
0
0
2
2
0
0
0
0
0
1
2
2
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
1
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
2
1
0
0
2
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
2
0
2
2
0
0
0
1
1
2
0
0
1
0
0
1
0
0
0
0
0
0
2
2
3
1
0
0
0
1
0
0
0
0
2
0
1
1
0
2
3
1
2
0
1
2
1
0
2
2
0
1
0
2
0
1
1
0
1
1
0
2
1
0
1
2
0
2
0
0
1
0
1
0
0
0
0
1
0
0
0
2
0
0
0
1
2
0
0
2
0
0
0
2
0
1
0
1
2
1
0
0
0
0
1
0
0
6
0
0
1
0
0
2
0
1
0
2
2
1
0
0
0
1
0
2
0
0
0
0
2
2
0
0
0
1
0
2
0
2
0
2
0
0
0
0
0
1
2
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
2
0
1
3
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
2
2
0
0
0
1
0
0
1
1
0
0
2
0
1
0
0
0
1
1
0
0
0
0
1
2
0
0
0
2
1
0
0
0
0
0
2
0
3
2
0
1
2
0
2
0
1
0
0
1
2
1
2
2
1
0
1
0
3
0
0
0
1
0
0
0
0
2
1
0
0
1
0
2
0
0
0
2
0
2
2
0
0
0
0
0
0
0
1
0
0
0
2
0
1
2
0
2
1
0
0
2
1
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
2
0
0
0
0
2
0
1
0
2
1
0
1
2
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
1
1
1
1
0
2
0
2
1
0
2
1
0
1
0
1
0
0
0
4
0
0
1
1
0
1
0
0
1
0
0
1
2
1
0
0
1
0
0
1
0
0
1
0
2
2
0
0
0
0
0
0
1
0
0
1
0
0
3
1
1
0
0
2
0
0
0
0
0
0
0
0
1
2
1
0
0
2
2
0
1
0
0
0
2
0
2
2
0
2
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
2
0
0
1
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
1
0
0
0
1
0
1
0
0
3
0
0
0
0
2
2
0
2
0
0
0
0
0
0
3
0
0
2
0
0
2
2
0
1
0
1
2
1
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
1
0
1
0
0
0
2
0
2
0
0
2
0
0
1
0
1
0
0
0
0
0
2
0
0
1
1
0
0
0
2
0
0
0
0
2
2
0
0
0
1
0
1
0
0
0
0
0
0
1
2
0
2
1
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
1
2
1
0
0
0
0
1
0
2
0
0
2
0
2
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
2
0
0
1
0
2
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
2
1
2
0
0
2
0
1
0
0
0
0
0
3
0
1
0
0
0
1
1
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
2
0
0
1
2
1
0
0
0
0
1
0
0
2
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
1
1
0
1
1
0
2
2
1
0
0
0
1
0
0
0
2
0
0
0
1
0
0
5
1
0
0
0
0
0
1
2
1
0
1
2
1
0
2
1
0
0
0
2
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
2
0
1
4
0
0
0
2
0
1
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
2
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
1
0
1
0
0
0
0
2
0
0
2
0
0
0
0
1
0
2
0
0
0
2
0
1
0
0
1
3
0
0
0
2
0
2
1
1
0
0
0
0
0
0
0
3
0
0
0
0
1
0
4
0
0
0
0
0
0
1
3
0
0
2
0
0
2
0
1
0
0
0
2
0
0
1
0
0
0
0
2
1
1
0
1
0
1
2
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
1
1
2
0
0
0
0
0
2
2
0
0
0
2
1
0
2
0
2
2
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
1
0
0
0
2
1
0
0
1
0
0
2
0
0
1
0
1
0
0
2
2
1
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
2
0
1
2
0
0
0
1
3
2
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
3
3
1
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
2
0
1
0
0
0
0
0
0
1
2
1
0
0
0
1
2
3
0
0
2
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
2
2
1
0
0
1
0
1
0
0
2
0
2
0
2
0
0
1
2
0
1
2
1
0
0
1
2
5
0
0
0
2
0
0
1
0
0
0
0
2
0
2
1
1
0
0
0
2
0
2
1
0
0
0
0
1
0
1
0
1
0
2
0
2
0
0
0
0
1
3
0
2
2
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
2
1
0
0
0
0
0
0
2
0
1
0
0
0
2
1
0
0
0
5
0
1
0
2
4
0
1
2
0
0
2
0
1
1
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
2
2
0
0
1
0
1
0
1
1
1
0
1
0
0
2
1
0
0
1
0
0
0
1
1
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
3
1
0
0
2
0
1
2
0
0
1
0
2
1
2
0
1
0
2
0
0
0
0
0
0
1
1
0
2
0
0
0
2
0
1
0
2
1
1
0
0
2
2
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
6
0
0
1
0
2
1
0
0
1
0
2
0
2
0
2
2
1
0
2
0
2
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
1
0
0
1
0
0
0
0
0
3
1
0
0
1
0
0
1
0
1
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
1
0
0
0
1
3
2
0
0
0
0
2
0
0
1
0
4
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
1
1
0
0
0
0
0
1
0
0
1
0
1
1
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
3
0
1
2
2
0
0
0
0
0
1
1
0
2
0
0
1
0
1
0
0
0
0
0
0
2
0
1
1
0
1
0
0
0
0
0
0
2
1
2
0
0
0
1
1
0
1
0
1
0
0
0
0
0
2
0
1
2
1
4
2
0
0
1
0
0
2
0
10
0
0
1
0
0
1
2
2
0
0
0
0
1
2
0
0
0
0
2
0
0
0
2
1
2
0
0
2
0
0
0
1
0
0
0
0
2
0
0
4
0
1
0
0
1
0
0
1
2
0
1
0
1
0
3
2
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
3
0
1
0
2
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
2
0
0
1
2
0
0
2
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
3
1
1
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
1
0
0
0
1
2
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
2
0
4
2
1
1
0
0
0
1
1
0
0
0
0
0
2
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
2
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
2
2
0
0
2
0
2
0
2
2
1
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
3
2
0
0
0
0
0
0
0
0
1
1
0
1
1
1
0
0
0
0
1
0
0
2
0
0
2
2
0
1
0
0
1
0
0
1
0
0
1
0
0
0
2
0
0
1
0
1
2
0
0
2
1
0
2
0
0
0
0
0
0
2
2
1
1
0
1
2
2
0
2
0
0
0
1
0
0
1
2
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
2
0
1
0
2
0
0
2
1
0
1
0
0
0
2
0
3
2
0
0
2
0
0
1
0
0
2
2
0
0
1
0
0
0
1
0
0
1
2
0
0
1
0
0
1
1
1
0
1
1
1
0
2
2
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
1
2
0
1
0
2
2
0
0
1
2
0
0
0
0
2
0
0
1
0
0
1
0
0
0
4
0
0
2
0
0
0
0
0
0
1
2
0
0
0
1
2
1
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
2
0
0
2
0
0
0
1
2
1
0
1
0
0
1
0
0
2
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
1
0
2
0
1
0
1
2
1
0
2
0
1
2
0
0
0
0
0
0
2
0
0
2
0
1
2
0
2
0
1
0
0
0
0
1
0
0
0
1
0
1
0
2
0
0
2
2
1
0
2
0
0
0
3
1
0
0
0
0
2
0
2
2
0
2
0
0
2
1
0
0
0
0
2
0
0
5
0
0
2
0
0
1
0
0
0
0
1
0
0
1
0
0
2
3
0
0
1
2
0
1
0
1
2
0
0
0
2
0
0
0
1
0
0
0
2
1
2
0
0
2
0
0
0
0
0
0
1
0
1
2
0
2
1
0
1
0
0
0
1
1
1
1
0
1
3
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
1
1
2
0
2
0
0
0
0
0
0
1
3
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
2
0
0
2
2
0
2
0
0
0
0
0
1
0
0
2
2
2
2
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
1
2
0
0
0
1
0
2
2
0
0
1
1
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
1
1
0
2
2
0
0
0
0
0
0
0
0
2
3
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
2
1
0
4
0
0
0
1
2
2
0
0
0
0
2
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
1
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
1
2
1
1
1
0
1
0
1
0
0
1
2
0
1
1
2
0
0
2
1
0
0
0
0
0
1
1
0
0
0
1
2
2
0
2
1
0
0
0
1
0
1
2
0
1
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
1
0
2
0
0
1
2
2
0
2
2
4
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
1
3
0
3
0
0
0
0
0
0
1
1
2
0
0
1
0
2
0
0
0
0
0
1
1
0
1
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
2
0
2
0
0
2
0
1
1
1
0
1
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
1
2
0
2
0
0
1
6
0
0
0
1
0
1
0
2
3
0
0
0
0
0
0
1
1
2
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
2
0
0
1
0
3
0
0
1
1
1
1
0
1
0
1
2
0
2
0
1
0
0
0
0
0
0
0
2
0
4
0
0
0
1
1
0
0
0
0
0
2
0
0
5
1
1
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
2
0
0
2
0
1
0
2
0
2
0
0
2
0
1
1
0
2
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
1
0
1
2
2
0
0
0
1
1
0
0
2
1
0
0
2
2
0
1
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
2
0
2
2
0
0
1
1
0
0
0
1
1
2
2
0
0
1
2
1
0
2
4
0
0
1
2
1
2
1
0
0
1
0
2
0
1
2
0
0
1
0
0
0
0
0
3
0
0
1
0
1
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
1
0
2
2
0
0
1
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
2
3
2
1
0
0
1
0
0
0
0
1
0
0
0
2
2
1
1
4
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
1
0
1
2
0
2
0
0
2
1
0
0
2
2
1
0
0
2
0
0
0
2
0
2
1
2
0
0
1
0
1
1
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
2
0
1
0
0
1
2
1
0
0
0
1
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
2
0
1
0
0
0
0
2
0
2
2
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
2
2
0
1
0
0
1
0
0
0
2
1
0
1
0
0
0
0
0
1
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
2
0
2
2
0
0
4
0
0
0
2
0
1
2
1
3
2
1
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
2
2
2
0
2
0
0
2
1
2
2
4
0
2
1
1
2
0
2
0
1
0
0
3
0
0
0
1
0
0
0
2
2
0
0
0
1
0
0
2
1
2
0
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
2
2
0
0
0
0
0
0
0
1
0
1
0
2
2
2
1
0
0
1
0
1
1
1
0
0
2
0
0
0
0
0
1
0
1
0
2
0
0
0
0
1
2
0
1
0
1
1
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
1
0
2
0
1
0
2
1
1
2
1
4
1
1
2
4
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
1
0
0
0
1
0
1
0
0
1
1
0
2
0
0
0
0
0
1
0
1
0
1
0
0
0
2
0
0
1
1
0
2
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
1
0
0
1
1
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
1
2
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
2
0
1
0
0
2
0
0
0
1
0
0
2
0
1
6
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
1
0
1
0
2
0
0
0
0
1
0
2
2
0
3
2
0
0
3
0
0
0
0
2
0
1
0
2
1
2
1
0
0
1
2
5
0
1
2
1
0
1
1
0
1
1
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
2
0
0
1
0
1
2
1
0
0
2
0
2
1
2
0
0
0
0
2
0
0
0
0
0
1
0
3
0
0
0
0
0
0
1
1
0
2
2
2
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
2
2
0
1
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
2
2
0
2
0
1
1
0
0
1
0
0
0
0
2
0
0
2
0
2
0
2
2
1
0
1
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
2
1
0
1
0
0
0
2
2
1
1
0
2
1
0
1
0
1
2
0
1
0
0
0
1
0
0
0
2
1
0
2
1
0
1
0
1
0
2
0
0
0
0
2
1
2
0
0
2
0
2
0
1
0
0
1
1
2
0
1
0
2
1
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
2
1
0
0
0
0
2
2
0
2
0
2
0
2
0
1
2
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
2
3
0
0
0
0
0
1
0
0
2
0
0
1
0
0
1
0
0
0
1
0
0
1
2
1
1
0
0
0
0
0
0
2
1
0
2
2
0
1
0
0
1
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
2
2
0
0
1
0
2
1
2
0
0
0
0
0
0
0
0
0
1
2
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
1
1
0
1
0
1
2
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
3
0
3
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
2
1
0
0
0
0
0
1
1
2
3
0
0
1
2
2
0
0
0
0
0
0
0
0
0
6
4
0
0
2
0
0
0
0
1
0
0
2
0
2
0
0
1
2
0
2
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
2
1
1
0
2
1
0
2
0
0
2
0
0
1
0
0
2
0
1
2
1
0
1
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
2
0
1
0
1
0
0
2
0
0
1
0
0
2
0
0
0
0
0
1
1
0
1
0
2
0
0
0
0
1
0
1
0
0
2
0
2
1
0
0
0
0
2
2
2
0
3
0
1
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
1
1
0
1
0
0
0
0
1
3
2
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
3
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
1
0
0
2
0
2
0
1
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
2
1
0
0
0
0
0
2
0
0
0
1
2
0
2
0
0
0
0
0
1
0
0
0
0
3
3
0
3
0
0
2
0
0
0
0
2
0
0
1
2
0
0
0
1
0
0
2
1
0
0
0
0
0
1
1
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
1
0
2
0
0
0
5
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
2
0
0
0
2
1
0
2
0
0
0
0
0
2
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
2
2
1
0
0
0
0
0
0
0
1
1
0
0
2
1
0
2
0
2
0
1
0
1
2
0
0
0
0
1
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
1
2
2
0
2
2
0
0
0
0
2
0
1
0
0
0
1
0
2
0
0
3
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
1
0
2
0
0
0
1
0
0
1
0
0
2
2
2
0
2
0
0
2
0
1
1
1
2
0
1
2
0
3
2
0
0
1
0
0
0
1
0
2
2
0
1
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
1
0
2
0
0
0
3
0
0
0
0
0
1
2
2
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
5
0
0
1
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
3
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
4
2
1
1
1
0
0
0
0
0
2
0
0
1
0
0
0
2
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
1
1
1
0
2
1
0
1
2
2
1
2
0
1
0
0
0
2
0
0
0
2
0
0
2
0
2
2
0
2
0
0
0
2
1
2
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
2
0
0
0
1
0
0
1
1
0
0
0
2
1
0
0
2
0
1
0
1
1
1
2
0
0
0
3
1
0
1
0
0
2
2
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
8
0
1
1
0
0
0
2
1
2
0
2
0
0
1
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
2
0
1
2
0
0
0
1
1
0
0
0
0
0
0
0
2
1
2
1
0
0
1
2
0
1
2
0
1
0
1
3
1
0
0
0
1
0
0
1
2
1
0
0
0
1
2
0
0
0
0
4
0
1
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
4
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
3
0
0
1
0
0
0
0
2
2
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
1
0
2
0
0
2
0
0
1
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
1
2
2
0
2
0
0
0
0
0
2
1
0
2
0
0
0
2
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
2
1
0
2
0
1
2
0
2
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
2
2
0
2
0
0
2
0
0
0
1
1
0
2
0
2
0
0
2
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
2
1
1
0
1
0
0
2
0
1
2
1
0
0
0
1
2
0
0
2
0
0
0
2
0
0
1
0
1
0
2
0
0
1
0
0
1
0
0
2
2
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
7
3
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
2
1
0
2
2
0
0
0
1
1
0
0
0
0
0
1
2
0
0
0
1
2
2
2
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
2
0
1
2
1
1
0
0
0
0
2
0
0
0
1
1
1
1
0
0
0
0
0
0
2
0
3
1
0
3
0
1
0
0
1
0
2
0
0
0
0
0
0
1
0
0
1
0
2
0
2
0
2
0
0
0
1
1
1
1
1
2
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
2
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
5
1
2
0
1
1
0
0
0
0
2
0
1
0
0
0
0
2
0
0
1
0
1
0
1
0
0
0
0
0
2
0
0
0
0
1
1
0
0
1
2
1
0
1
2
1
0
0
0
0
2
0
1
0
0
0
1
1
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
2
1
0
0
1
0
2
0
1
0
0
3
0
0
0
2
0
2
2
0
0
0
1
2
0
0
0
1
2
0
1
0
0
0
0
0
1
1
0
2
0
0
0
0
1
0
0
0
1
0
0
3
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
1
2
0
1
0
0
0
0
1
0
0
0
1
0
0
1
1
1
0
0
0
0
0
1
3
0
2
2
2
0
1
1
0
2
2
0
0
0
1
0
0
1
1
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
2
0
0
4
0
0
0
0
0
0
1
2
1
2
0
0
1
0
0
2
0
0
1
0
0
1
1
0
0
3
3
0
3
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
1
0
0
0
2
1
1
3
1
1
2
0
0
0
0
2
0
1
0
0
0
2
1
0
0
0
0
0
1
1
0
0
0
0
2
0
0
1
0
3
0
0
0
0
0
5
1
1
0
0
2
0
0
2
2
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
2
1
0
0
1
0
0
0
2
0
0
0
1
0
0
1
2
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
2
0
0
0
0
2
0
1
0
0
0
1
4
0
0
1
0
0
0
0
0
0
2
3
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
1
2
3
2
0
2
0
0
1
2
0
0
0
4
0
0
0
2
0
0
0
1
0
0
1
0
0
1
0
2
1
1
2
2
0
0
0
2
0
1
0
0
0
1
1
2
0
2
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
1
0
0
2
2
0
2
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
1
2
0
0
0
0
2
2
0
1
0
2
0
0
2
0
2
0
1
0
2
0
0
3
1
1
0
0
2
0
0
1
0
0
0
0
2
1
1
1
0
0
1
1
1
0
0
0
0
1
0
0
1
0
2
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
1
0
2
0
0
0
0
1
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
2
1
2
0
0
2
0
0
0
0
0
3
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
2
0
0
0
2
0
2
2
0
0
0
0
2
0
2
8
0
0
0
0
0
1
0
0
0
1
0
0
0
2
1
0
1
1
1
2
0
0
5
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
1
2
1
0
2
0
0
1
0
0
2
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
2
5
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
1
2
0
2
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
2
1
0
1
1
1
0
8
0
1
0
1
0
2
1
0
0
1
2
1
0
1
1
0
0
0
0
1
1
1
1
0
3
0
2
0
2
1
1
0
1
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
2
0
2
2
0
0
2
0
2
0
1
0
0
3
0
2
0
0
0
0
1
1
1
0
2
0
1
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
2
0
0
0
1
1
0
0
0
0
0
0
2
2
0
2
0
1
0
0
0
0
0
3
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
1
2
2
2
0
0
0
2
0
0
0
0
0
2
0
1
2
2
0
2
0
0
0
0
2
1
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
2
1
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
2
1
2
2
4
0
0
0
1
0
1
0
0
1
2
2
0
0
0
0
0
0
0
2
0
2
0
2
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
1
0
2
2
1
1
0
0
0
1
0
2
0
0
1
0
0
1
2
0
0
0
0
1
3
2
1
0
0
3
0
1
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
2
0
0
0
1
1
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
3
1
0
3
1
0
0
0
0
0
0
1
0
0
1
1
1
2
0
0
1
1
0
0
1
0
4
0
2
0
0
0
0
0
3
2
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
2
0
0
2
2
1
0
0
0
0
0
0
1
2
0
2
1
0
0
2
0
0
0
1
0
0
1
0
0
2
1
1
0
0
0
0
0
0
2
0
0
0
3
1
1
0
0
0
2
0
2
0
1
0
1
0
2
0
0
1
2
1
0
0
0
3
1
1
0
0
0
2
2
0
1
0
0
0
0
0
2
0
0
0
2
0
1
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
1
0
2
0
1
1
0
2
2
2
0
1
0
1
1
1
3
0
0
2
1
0
0
0
5
1
2
1
0
0
2
0
0
1
0
0
0
2
2
0
1
2
1
0
1
3
0
2
1
2
0
0
0
0
0
1
0
4
0
6
0
2
2
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
1
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
2
1
0
2
0
1
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
1
0
3
0
0
2
1
0
0
0
0
0
1
2
0
1
0
1
1
2
0
1
0
2
0
0
0
3
0
2
0
0
1
3
0
1
0
1
1
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
1
2
1
0
2
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
2
1
2
0
0
1
0
0
1
0
1
1
2
0
0
1
0
2
0
0
0
2
1
0
2
0
0
0
0
2
0
0
0
2
1
0
0
0
0
1
0
0
0
0
1
0
0
2
0
1
0
1
0
0
1
0
0
0
0
1
0
2
1
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
2
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
2
1
0
0
0
1
0
2
0
0
0
0
2
1
1
1
0
1
0
3
0
2
1
0
1
0
1
0
1
0
0
0
0
0
2
2
0
0
0
2
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
1
1
0
1
2
0
0
2
2
1
0
0
1
0
1
0
0
0
2
0
1
0
0
4
2
1
1
0
0
0
0
0
0
0
0
1
2
0
2
1
2
0
0
0
1
1
0
1
0
0
0
2
0
0
0
1
1
0
0
1
0
2
0
0
4
1
0
0
0
1
0
3
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
3
2
0
0
0
0
1
1
1
5
0
2
1
0
0
1
0
2
0
1
1
0
1
1
0
0
3
0
2
1
1
2
0
0
1
2
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
3
1
2
0
1
1
0
0
0
1
1
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
1
0
1
0
0
0
4
1
0
1
2
0
1
0
3
0
1
0
0
0
1
2
0
1
2
0
1
1
4
0
0
0
0
1
0
1
0
0
0
1
2
0
0
2
0
2
1
0
0
2
0
0
0
0
2
0
0
2
0
0
2
4
0
1
0
0
0
0
1
2
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
1
2
0
0
0
2
0
1
1
0
0
2
1
0
2
0
0
1
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
2
2
1
0
2
0
0
2
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
2
0
2
2
3
2
0
0
0
0
2
0
0
0
2
0
2
2
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
5
0
0
1
0
0
2
1
0
0
0
1
2
0
0
0
0
0
0
1
0
2
1
0
1
1
2
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
1
2
0
1
1
0
0
0
1
1
0
0
1
0
0
0
1
2
0
1
0
2
2
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
1
2
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
1
0
1
2
3
0
2
1
0
1
0
0
0
1
0
0
2
2
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
1
0
2
0
0
1
2
0
0
0
2
0
0
2
1
0
2
2
1
0
1
2
6
2
2
0
0
1
1
0
0
0
0
1
0
2
0
1
1
1
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
2
2
0
0
0
2
0
0
0
2
2
0
0
0
1
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
3
1
3
0
1
2
0
2
2
0
0
2
0
0
2
0
0
1
1
0
0
2
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
2
0
0
7
0
1
0
1
0
0
0
0
0
0
1
0
2
2
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
1
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
2
0
1
4
1
2
1
2
0
0
0
0
0
2
2
1
0
0
0
1
0
0
1
1
1
3
0
0
0
2
2
0
0
0
1
2
0
1
0
2
0
0
2
0
2
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
1
0
1
2
0
2
0
2
1
0
1
0
2
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
2
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
2
1
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
2
2
0
0
3
0
0
0
0
2
0
0
0
0
0
1
3
0
1
5
0
1
1
0
0
1
1
0
2
0
0
0
1
0
2
0
0
0
0
3
2
2
0
0
1
0
1
1
2
0
0
5
0
0
0
1
2
1
1
0
1
1
1
0
2
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
2
0
0
2
0
1
0
2
0
3
0
0
0
0
2
0
0
2
2
0
0
0
0
1
1
0
2
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
1
2
1
0
0
1
2
0
0
0
0
2
0
1
0
0
8
0
0
0
2
0
2
0
0
1
0
4
1
2
0
1
0
0
0
0
3
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
1
0
0
2
0
1
0
2
4
1
1
0
0
1
0
0
0
0
0
0
2
2
0
0
0
2
1
1
1
2
0
2
0
2
2
0
1
1
0
2
2
0
0
0
0
2
0
0
2
1
1
0
1
1
2
0
0
0
0
0
0
1
0
0
0
3
1
0
1
1
0
0
0
1
1
2
0
2
0
0
0
0
3
0
0
0
2
3
0
0
0
1
2
0
0
0
0
0
0
0
1
3
0
1
0
0
0
0
0
2
0
0
2
0
1
1
2
1
2
0
1
0
2
0
0
1
0
0
0
0
0
1
3
0
0
0
0
0
0
0
1
0
0
1
2
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
3
0
2
1
1
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
1
1
0
0
0
0
1
0
0
0
2
1
1
0
0
1
3
1
0
0
0
1
1
1
0
2
0
0
0
0
1
2
6
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
4
0
0
0
1
0
0
0
1
2
1
0
0
0
1
1
0
2
0
0
0
0
0
1
1
0
1
0
0
0
2
0
1
1
2
2
0
1
0
0
0
2
1
0
0
2
1
0
0
2
0
0
0
1
0
0
0
0
0
2
2
2
0
0
0
0
0
0
2
2
1
0
3
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
1
1
0
0
0
1
2
2
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
1
1
0
2
0
0
1
0
0
2
0
0
1
2
0
1
0
0
1
3
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
1
1
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
1
2
0
0
2
0
0
0
0
1
1
2
0
0
0
0
1
3
0
1
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
2
4
2
0
0
0
1
0
2
1
0
1
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
1
0
2
0
1
0
0
0
3
3
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
1
0
0
2
1
0
0
2
0
1
0
0
0
0
1
1
0
0
1
0
0
2
2
0
2
0
0
0
0
0
0
1
2
0
0
0
2
0
0
2
2
0
0
2
2
0
2
2
0
0
2
0
0
1
1
0
0
0
0
0
1
1
1
0
0
0
0
2
3
0
0
0
0
1
2
1
0
1
0
0
0
1
0
0
3
0
2
1
0
0
1
1
1
0
2
4
0
0
0
0
0
0
2
1
1
1
0
2
0
0
1
0
0
0
2
0
1
1
0
0
1
2
0
0
0
0
2
0
2
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
2
0
1
0
0
2
0
0
0
1
0
0
0
0
1
0
1
0
1
2
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
2
1
2
4
1
1
0
0
1
0
0
0
2
0
0
0
1
1
0
1
0
1
1
0
0
2
0
0
1
1
1
2
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
1
2
1
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
4
2
0
0
0
1
2
0
2
0
2
0
0
2
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
5
0
1
1
1
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
4
0
0
0
0
0
2
2
2
2
1
0
0
1
0
2
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
2
0
2
0
3
1
0
0
0
0
0
0
1
0
0
0
0
2
2
1
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
2
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
2
1
1
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
1
0
0
0
0
0
0
2
1
0
2
1
0
0
1
2
1
0
2
1
0
0
2
2
0
0
0
0
0
1
1
5
2
2
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
2
0
2
0
0
0
1
0
2
1
2
0
0
0
0
2
0
0
2
1
0
1
0
0
2
0
0
0
0
2
1
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
6
0
0
2
0
0
1
1
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
2
2
2
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
1
2
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
2
0
1
1
1
2
2
1
0
2
0
0
1
2
0
3
1
2
0
3
0
1
2
0
0
0
0
1
1
1
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
9
1
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
3
0
0
4
0
0
1
0
0
1
2
0
0
1
2
1
0
0
0
0
1
2
0
0
1
1
2
0
0
0
0
0
1
0
1
2
0
2
0
0
0
0
2
0
0
0
0
0
2
0
2
2
1
0
0
0
0
0
1
2
2
0
1
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
2
1
0
0
1
0
0
0
2
1
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
2
0
0
0
3
1
0
3
0
1
0
0
0
0
1
0
0
0
2
0
0
1
0
1
0
0
0
0
3
1
0
0
0
0
1
1
0
0
0
0
0
2
0
2
2
5
0
0
0
0
0
0
2
0
1
0
0
1
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
1
1
1
0
2
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
4
1
2
0
1
1
1
0
0
0
0
2
1
2
0
0
2
0
0
0
1
0
0
0
0
1
2
2
0
0
1
2
0
0
0
2
0
2
1
2
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
2
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
2
2
0
1
0
1
2
1
0
2
0
0
0
0
0
1
0
0
0
1
0
2
1
2
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
2
5
1
1
2
0
2
0
0
0
0
0
0
0
0
2
0
0
2
2
2
0
0
0
2
0
0
0
1
1
2
1
1
0
0
3
0
0
0
2
2
0
0
2
2
0
0
0
2
2
0
0
0
3
0
0
1
0
1
1
0
2
0
0
2
2
0
0
0
0
0
0
0
0
1
1
0
0
2
0
1
4
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
1
0
0
2
1
0
0
0
0
4
2
0
0
0
0
4
1
1
0
0
0
0
1
0
0
2
0
0
2
3
2
0
2
1
0
0
0
1
4
1
0
2
0
2
0
0
0
0
2
2
0
0
0
1
0
0
1
0
0
0
0
1
0
0
2
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
2
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
3
0
1
0
0
0
0
2
0
1
2
0
2
0
0
2
1
1
1
0
2
0
0
0
1
0
0
2
0
2
0
0
1
2
2
0
0
0
2
2
0
0
2
0
0
1
0
0
0
0
9
1
1
0
0
1
4
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
2
0
2
0
0
0
1
1
0
0
1
0
2
0
1
1
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
4
3
0
0
2
0
0
3
0
1
0
1
0
0
3
0
1
2
0
1
2
0
0
1
0
1
0
1
2
0
0
0
1
0
0
2
1
0
0
0
2
0
0
2
0
1
2
1
0
0
2
0
0
0
3
0
2
1
0
0
1
0
2
1
0
2
1
2
2
1
0
0
0
2
0
1
0
0
2
3
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
3
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
2
2
1
0
0
0
2
0
1
0
0
2
0
0
0
2
0
1
0
4
0
2
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
2
1
0
0
2
0
1
2
0
1
2
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
2
0
1
1
0
0
0
1
2
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
3
0
0
0
1
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
2
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
6
0
1
0
0
4
0
1
1
0
0
0
2
1
0
2
0
0
0
3
3
2
0
2
3
3
1
0
0
0
1
2
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
1
0
0
0
2
1
2
2
0
2
2
0
0
0
1
0
1
1
1
0
0
0
1
0
0
0
0
1
0
1
0
1
0
1
0
2
0
2
0
0
2
0
1
1
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
1
4
0
0
0
0
1
0
0
1
0
1
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
3
0
0
0
2
1
0
0
3
2
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
2
0
1
0
2
0
1
0
0
0
0
4
0
0
0
0
0
0
0
1
2
0
1
0
3
2
0
0
1
0
1
1
1
0
1
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
3
0
1
0
0
0
0
0
0
1
0
2
0
2
1
0
0
1
0
0
1
0
1
0
0
0
0
3
2
0
2
0
0
2
0
0
2
0
0
1
0
0
2
0
2
2
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
2
0
0
0
1
2
0
2
2
1
0
1
0
0
0
5
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
3
0
0
1
2
1
2
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
2
0
1
0
1
0
2
0
0
0
1
0
0
2
3
0
0
1
1
2
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
1
2
0
1
1
0
0
0
0
1
3
3
1
1
0
0
1
1
0
2
0
2
1
3
2
2
0
0
2
2
0
1
0
0
0
0
0
0
0
0
1
2
2
1
0
0
2
0
1
1
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
2
0
2
0
2
1
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
1
2
2
0
0
0
2
1
0
0
1
2
0
0
0
0
1
0
0
1
1
1
3
0
1
0
1
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
2
0
3
0
0
1
0
0
1
0
0
0
2
0
1
0
2
2
0
0
0
0
1
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
1
2
0
0
0
0
0
1
2
0
0
0
0
2
2
0
2
0
1
1
0
0
2
0
1
0
0
0
0
2
0
2
1
0
0
1
1
1
2
1
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
2
2
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
1
0
0
0
1
2
0
0
0
0
0
5
0
0
0
1
0
0
3
0
0
0
0
1
0
1
0
2
0
0
1
0
2
0
0
1
0
0
2
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
1
2
0
3
0
1
2
0
2
1
0
2
0
4
2
2
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
1
1
2
0
0
0
0
0
0
1
0
0
0
0
1
2
0
1
2
2
0
0
2
2
0
2
0
1
0
2
0
0
0
0
2
0
1
0
2
2
0
1
0
1
0
0
1
0
1
1
0
0
1
1
0
1
0
3
0
1
2
2
0
0
0
1
1
0
0
0
3
0
0
1
0
0
2
0
2
1
0
0
0
0
0
1
0
2
0
1
1
1
0
0
0
1
0
0
1
2
1
0
0
1
0
0
0
0
2
2
1
2
0
2
1
2
0
0
0
0
2
0
0
1
0
0
0
2
0
1
2
0
2
0
0
1
0
1
0
0
1
0
2
1
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
1
0
2
2
0
1
0
2
3
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
2
0
3
0
0
1
0
2
0
8
0
0
0
1
0
2
2
0
0
0
2
0
0
0
2
0
0
0
0
2
1
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
1
1
1
2
0
2
3
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
2
0
1
1
0
2
0
0
2
0
2
2
0
0
1
0
0
0
0
2
0
0
0
0
0
1
2
0
2
3
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
2
0
0
1
3
0
0
0
0
0
0
0
0
3
0
0
0
2
0
3
0
1
1
2
1
0
0
0
0
0
1
0
1
0
2
3
0
0
1
0
0
1
2
0
0
1
0
0
0
0
2
1
0
0
2
0
0
1
0
1
1
0
1
0
0
0
1
2
0
1
0
2
0
0
0
1
0
1
0
0
0
1
0
1
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
2
0
0
0
0
0
0
2
0
1
1
0
3
2
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
2
1
0
0
1
3
0
0
1
3
1
0
2
0
0
1
0
0
0
2
0
1
2
0
0
0
0
1
2
2
1
0
0
0
0
0
2
1
2
1
0
0
0
3
0
0
0
0
0
0
0
1
0
2
0
2
0
2
0
1
0
2
0
0
3
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
2
0
2
0
0
0
0
2
1
0
0
0
0
1
0
0
1
1
0
2
2
1
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
3
1
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
2
2
0
1
0
0
1
1
0
0
0
0
2
0
1
1
0
1
0
2
0
0
2
2
2
2
0
2
0
1
0
0
0
2
2
0
0
3
0
0
2
0
0
0
0
0
0
2
0
0
1
2
1
0
0
1
0
1
0
2
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
2
0
2
0
2
1
1
1
2
0
2
0
0
0
0
0
1
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
3
0
1
1
1
1
0
0
0
0
4
2
2
0
0
0
0
0
0
0
2
0
1
1
0
1
2
0
2
0
1
1
0
2
2
0
2
0
18
3
0
0
2
1
2
0
0
0
1
2
1
1
2
1
0
0
1
2
0
1
0
1
0
0
0
2
1
1
1
0
0
1
0
3
0
0
1
0
0
1
0
1
1
2
0
0
0
1
0
0
0
0
2
0
0
2
2
2
0
1
3
0
0
2
1
1
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
2
0
1
0
0
0
0
0
0
0
2
2
0
2
0
2
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
2
1
0
0
0
0
0
1
2
2
1
1
2
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
2
1
1
2
0
0
1
1
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
3
1
1
0
0
0
1
2
0
0
0
0
2
0
0
0
1
0
1
2
0
0
0
1
1
0
3
2
0
2
1
0
1
0
0
1
0
0
0
2
1
0
2
1
0
2
0
0
0
0
0
0
2
2
2
0
2
0
1
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
1
1
0
0
1
0
0
2
0
1
0
0
0
0
0
0
1
0
5
0
2
0
2
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
1
1
0
0
0
0
0
0
0
1
0
2
0
2
0
0
2
0
2
1
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
1
0
2
2
0
0
1
0
2
1
2
1
2
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
2
0
0
1
0
1
0
2
0
2
2
0
2
1
0
1
1
0
0
2
0
0
0
1
0
0
0
0
2
0
3
0
0
2
1
1
0
0
0
2
2
0
1
0
0
0
2
0
0
0
1
0
0
1
0
0
2
0
0
0
0
2
1
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
3
1
0
0
0
0
1
1
0
0
0
0
2
2
0
0
0
0
1
0
0
3
2
1
0
0
2
0
0
1
1
0
1
2
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
2
0
0
2
0
2
1
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
3
2
0
0
0
0
0
0
2
1
0
2
2
1
2
0
3
0
2
3
0
1
0
0
0
1
0
0
2
0
2
0
0
0
2
3
1
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
3
0
0
0
2
0
2
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
1
2
0
0
0
0
2
1
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
3
1
1
0
0
0
3
2
0
1
1
2
2
0
0
0
2
0
1
0
0
0
0
1
2
0
0
0
2
0
0
0
2
2
1
0
0
1
0
0
0
0
0
1
0
0
2
0
1
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
2
1
0
0
0
0
2
2
0
0
0
2
0
0
0
2
0
0
1
0
3
0
0
0
1
3
0
0
0
0
0
0
0
0
2
1
2
0
0
0
1
1
0
1
1
0
0
0
2
0
0
0
2
2
2
0
0
0
3
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
1
1
0
0
2
0
0
0
0
1
0
0
3
0
0
2
0
2
0
0
1
2
2
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
1
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
1
0
0
3
0
1
1
0
0
2
1
2
2
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
1
1
2
2
0
0
1
0
1
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
1
2
0
0
2
0
0
2
0
1
2
0
1
0
0
0
0
0
0
1
0
0
2
3
2
0
0
0
0
0
0
1
1
2
0
0
0
0
0
1
2
2
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
1
0
3
2
2
0
1
1
0
0
0
2
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
3
0
2
0
0
0
1
0
0
0
0
2
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
3
0
0
1
0
0
0
2
1
2
0
2
0
0
1
0
0
2
0
3
0
1
0
1
1
2
2
0
0
0
0
0
0
1
2
2
1
1
2
2
0
0
0
2
0
1
1
0
0
1
0
0
0
1
0
2
1
0
0
0
0
2
0
0
1
0
0
1
1
2
0
0
0
0
2
0
0
0
0
0
2
2
2
0
1
2
0
0
0
2
0
0
0
0
2
2
0
1
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
1
0
0
1
0
0
2
0
1
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
2
1
2
0
2
0
1
1
0
0
0
0
0
0
2
0
0
1
2
0
1
1
0
1
2
2
0
0
0
1
1
0
0
0
0
0
2
1
1
0
0
0
2
0
2
1
2
0
0
0
0
0
0
2
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
2
2
2
0
2
0
0
0
2
0
0
0
2
0
0
0
1
1
1
0
0
2
0
0
0
2
3
0
0
0
0
2
2
1
2
0
2
0
1
0
0
0
0
3
0
0
2
2
1
2
0
0
0
0
0
0
0
2
1
0
1
2
1
0
1
0
1
1
0
0
2
1
2
0
1
0
0
2
0
0
2
0
4
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
3
0
0
2
0
0
0
0
0
2
0
2
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
3
0
0
3
0
0
0
0
0
0
0
0
1
2
0
0
2
0
1
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
3
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
2
0
0
2
2
0
1
0
0
1
2
0
0
1
1
2
2
0
0
0
0
1
0
0
1
0
0
4
0
3
0
1
0
1
1
0
0
1
0
2
0
1
0
1
2
0
0
0
0
0
1
2
0
0
2
0
0
2
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
1
1
0
0
2
1
1
0
1
0
0
1
0
1
2
0
0
0
0
0
0
0
0
1
2
0
0
3
1
0
0
1
4
0
0
0
1
1
0
0
2
0
0
0
1
0
0
2
0
0
0
0
1
2
0
2
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
1
1
0
2
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
1
0
2
0
0
1
0
3
0
0
1
0
2
0
0
0
0
0
0
0
0
1
2
1
0
2
0
2
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
3
0
0
0
1
1
1
0
1
0
0
2
2
0
0
0
0
2
0
1
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
3
0
0
1
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
1
0
4
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
1
1
0
0
0
1
2
1
2
1
0
0
0
0
0
0
1
0
0
0
0
0
2
2
2
2
2
0
0
2
0
0
0
0
1
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
2
2
0
0
0
2
0
2
2
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
1
1
0
2
1
0
2
1
1
0
1
0
3
2
0
0
0
0
2
0
0
1
0
1
0
0
0
2
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
2
0
2
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
2
0
1
0
0
0
2
0
2
0
1
0
0
2
0
1
2
1
0
0
0
0
0
0
2
2
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
5
2
0
1
2
0
0
1
0
0
4
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
6
2
0
2
2
2
0
1
1
2
2
0
0
1
2
2
0
0
1
2
1
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
1
0
2
2
0
2
0
0
0
2
0
1
2
2
1
2
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
1
0
0
2
5
2
1
2
1
0
2
0
0
2
0
1
2
0
0
0
1
2
1
1
2
0
0
0
2
0
0
1
1
0
2
2
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
2
2
2
2
1
0
2
2
0
1
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
1
0
2
0
0
0
1
2
1
2
2
0
3
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
2
1
2
1
0
0
0
1
0
0
0
0
2
2
1
0
0
1
2
2
3
1
0
0
1
0
1
1
0
0
1
0
0
3
0
0
1
1
0
0
0
1
0
1
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
1
0
0
8
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
2
0
0
0
0
1
2
0
0
0
0
2
0
0
1
1
2
0
2
0
2
3
1
0
0
0
0
1
0
1
0
0
2
1
2
0
1
1
3
0
0
0
0
0
0
2
0
0
2
0
0
0
1
1
0
1
1
1
1
0
1
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
3
0
2
0
1
0
0
0
2
0
0
1
0
0
0
0
2
0
3
2
0
2
0
0
0
1
0
1
1
4
0
0
0
3
1
0
0
2
1
1
0
2
0
2
0
5
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
1
2
2
0
0
1
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
1
2
2
2
0
1
0
0
0
2
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
1
1
3
1
2
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
2
1
0
0
0
1
1
2
2
0
0
1
0
0
0
0
1
0
0
0
2
1
0
0
2
1
1
1
0
3
1
0
0
0
2
0
0
1
0
2
0
0
0
1
0
0
0
1
1
1
0
0
0
0
1
0
1
0
0
1
0
1
1
0
0
2
2
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
2
1
0
0
0
2
1
0
0
0
0
0
1
0
2
1
0
0
0
0
1
1
2
1
0
0
0
0
2
0
0
1
1
1
0
0
1
0
1
0
0
0
1
0
0
1
2
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
1
2
0
1
2
0
0
0
1
1
2
2
0
0
2
0
0
0
0
0
1
2
2
1
0
0
0
0
2
1
1
0
0
0
0
3
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
1
2
2
0
0
1
0
0
0
0
1
0
2
3
0
0
0
4
0
0
0
0
0
0
2
2
0
2
2
0
0
0
1
0
0
0
0
2
0
2
2
2
2
2
0
0
2
1
0
0
2
1
0
0
0
0
0
2
2
0
0
0
0
2
0
2
0
0
1
1
0
0
0
0
2
0
0
1
0
0
0
0
2
1
0
0
0
0
2
2
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
1
0
1
0
0
2
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
1
2
0
0
2
0
2
0
0
1
0
0
0
0
2
0
2
1
0
0
0
2
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
1
0
0
1
1
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
1
1
0
2
0
0
0
0
2
2
0
0
2
0
0
2
2
0
2
0
2
2
1
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
6
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
2
1
1
1
1
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
2
0
0
2
0
0
2
0
0
1
0
2
0
1
0
2
2
2
1
2
0
0
4
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
2
1
2
0
0
0
0
1
0
0
2
0
0
0
0
4
0
2
1
0
2
0
0
2
0
2
1
1
1
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
2
0
1
0
0
0
0
1
0
0
0
1
2
0
0
2
2
0
0
0
2
0
0
0
1
1
0
1
2
1
0
1
1
0
2
0
0
0
0
0
2
0
0
1
0
1
2
4
1
0
1
1
0
0
2
0
0
0
1
1
0
0
0
1
2
0
0
1
0
0
0
0
0
0
2
1
0
2
1
2
0
1
0
0
0
0
4
1
0
0
0
0
0
0
1
0
1
1
0
1
0
1
3
0
2
2
0
0
0
0
0
2
1
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
1
0
0
2
1
1
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
2
3
0
1
0
0
2
2
0
0
1
2
1
0
0
2
1
0
0
1
15
0
0
0
0
0
0
0
2
2
0
1
0
1
0
1
1
0
2
0
0
3
3
1
0
0
0
0
4
1
2
0
0
2
3
0
0
0
0
0
0
2
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
2
0
1
0
3
0
1
1
0
2
0
0
0
0
2
1
0
0
0
1
0
2
2
3
0
2
0
0
1
0
2
0
0
2
0
1
2
1
0
3
0
0
0
2
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
2
1
2
0
0
1
0
0
0
1
0
1
0
0
0
0
0
2
0
2
2
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
1
0
0
0
1
0
1
1
0
0
1
0
2
0
1
1
0
2
1
2
2
1
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
1
3
0
1
0
0
0
0
0
0
0
2
0
2
0
0
1
1
0
0
0
1
1
0
2
0
4
0
1
2
0
2
0
0
1
1
1
1
0
2
0
0
1
2
0
2
1
0
1
0
0
2
0
0
0
2
0
3
1
0
0
0
2
1
0
0
0
1
1
1
1
1
0
2
0
1
3
0
1
0
1
0
2
0
0
1
0
2
2
2
0
0
2
0
1
1
0
1
1
0
0
2
0
0
1
1
0
1
2
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
2
0
0
0
2
0
0
0
1
1
0
1
0
1
0
0
0
1
2
0
0
0
0
1
0
0
1
0
0
0
0
1
0
3
0
0
0
0
0
0
1
0
0
0
2
2
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
2
0
0
0
1
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
2
2
0
0
0
0
2
1
1
0
2
0
0
0
2
2
0
0
0
3
0
0
0
2
2
2
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
2
3
1
0
1
0
0
0
2
0
0
1
0
0
3
0
2
0
0
1
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
3
2
2
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
1
0
1
1
2
1
1
0
0
0
0
2
0
0
1
2
2
0
5
0
1
0
0
1
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
1
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
2
0
2
2
0
0
1
0
2
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
1
0
3
0
1
1
0
0
0
0
2
2
0
0
0
0
0
1
0
1
0
2
0
0
0
1
0
0
0
0
0
1
2
0
0
0
2
2
0
2
0
3
0
0
1
1
1
1
2
1
0
1
0
1
0
2
0
0
0
1
0
1
0
0
2
1
0
0
3
0
2
0
1
0
0
0
1
0
0
1
2
0
0
0
1
1
2
1
0
1
0
0
2
0
0
0
0
2
0
2
2
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
1
0
1
5
0
0
0
0
1
0
1
0
0
0
1
1
2
1
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
2
1
0
0
0
1
0
0
0
0
0
2
0
1
0
2
0
1
0
0
2
0
1
0
0
0
2
0
0
0
0
2
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
2
1
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
3
0
1
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
2
0
0
0
2
0
0
2
0
0
1
1
0
0
0
2
2
1
1
2
1
0
2
1
2
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
2
0
1
0
2
0
2
0
0
0
0
1
0
2
2
0
0
2
0
0
1
0
2
0
1
0
0
0
2
0
0
2
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
1
1
0
2
0
0
1
2
2
1
0
0
0
1
0
0
2
0
0
0
1
2
0
0
0
2
0
0
2
0
0
0
2
0
2
0
2
1
2
0
0
0
0
0
0
0
0
1
0
2
0
2
0
2
0
0
0
1
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
1
0
2
1
2
2
0
0
0
0
0
0
0
0
2
1
1
0
2
1
1
0
0
1
2
0
0
0
0
0
0
0
2
1
1
0
2
0
0
0
0
0
1
2
0
2
0
0
0
2
0
1
0
0
1
0
1
1
0
0
2
3
0
0
1
2
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
2
1
1
0
1
1
0
0
0
1
1
2
0
0
0
0
0
0
2
0
0
0
2
0
0
3
0
1
2
0
1
2
0
0
2
2
0
2
0
1
0
0
0
0
1
2
0
2
2
1
2
2
2
2
1
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
1
0
0
0
2
0
0
2
1
0
0
0
1
0
0
2
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
3
1
1
0
1
1
0
0
1
0
0
0
0
0
1
0
1
2
0
0
0
1
2
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
2
0
2
0
2
0
0
2
0
2
2
0
2
0
0
0
0
0
1
1
0
2
0
0
1
0
2
0
2
0
1
1
2
0
2
2
0
1
0
0
0
0
0
0
0
0
1
1
2
0
2
0
2
0
0
0
1
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
3
2
1
0
0
1
1
0
0
1
2
0
0
0
0
1
0
0
0
1
1
0
2
0
0
0
0
0
2
1
1
0
1
0
2
0
0
0
3
0
1
2
1
2
0
0
2
0
0
0
0
2
0
0
0
0
1
2
0
1
0
1
0
2
0
0
0
2
0
1
0
3
1
0
0
0
2
1
1
1
0
2
0
0
0
0
1
0
1
0
0
2
0
0
0
1
2
1
0
0
0
0
0
1
1
1
1
0
0
0
1
1
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
1
2
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
2
2
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
1
1
0
0
0
0
0
1
2
0
0
0
2
2
0
0
0
3
0
0
1
0
2
0
0
0
0
0
0
0
0
3
0
2
0
0
0
1
0
0
1
2
0
2
1
0
0
0
1
0
0
2
0
0
1
0
2
0
0
2
0
0
0
2
0
2
0
1
0
0
0
3
0
0
0
0
0
0
0
2
0
2
0
0
2
1
0
0
0
1
2
0
1
0
2
1
0
0
2
2
0
0
0
0
2
0
0
0
1
0
0
0
2
2
2
2
0
0
0
0
0
1
0
2
0
3
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
1
0
0
0
0
0
2
2
1
0
0
0
0
1
1
1
0
0
0
4
2
1
3
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
2
0
1
3
0
0
0
2
1
0
1
1
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
2
1
1
0
0
0
1
0
2
2
5
0
1
0
0
0
0
0
1
0
0
1
2
0
1
2
0
1
0
0
0
0
2
2
0
2
2
0
0
1
1
1
2
0
0
0
1
0
0
0
0
1
0
1
3
1
0
2
0
0
1
1
1
0
0
2
0
0
0
1
2
0
0
0
1
0
1
0
0
0
0
1
2
0
0
0
0
5
0
0
0
0
0
0
0
1
0
2
2
2
1
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
2
0
0
1
0
2
0
2
1
0
1
1
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
1
0
0
1
0
0
0
0
2
1
0
0
1
0
0
2
2
6
1
0
2
1
0
0
1
1
2
0
0
1
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
1
2
1
0
0
1
1
2
1
2
2
0
0
0
0
0
1
0
0
0
0
1
0
1
1
2
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
2
2
0
0
2
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
1
2
0
0
0
0
2
0
2
0
1
0
0
0
0
2
2
1
1
1
1
0
1
0
0
0
0
0
1
0
1
2
0
0
1
0
0
2
0
0
0
1
0
0
1
1
2
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
2
0
0
0
0
0
0
0
0
3
0
0
2
0
0
1
0
2
0
0
0
1
0
0
1
0
1
0
0
1
0
2
0
0
0
2
0
0
2
1
0
2
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
1
3
0
0
1
2
1
0
0
0
1
0
1
0
0
2
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
2
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
2
2
1
0
2
0
0
2
0
0
1
0
2
1
0
0
0
0
1
0
1
0
0
1
0
0
1
2
0
0
2
0
0
0
0
0
0
0
1
0
7
2
0
2
1
2
0
2
0
1
0
0
0
0
0
0
3
1
1
0
1
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
1
2
2
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
2
1
0
2
0
1
3
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
3
1
2
0
0
4
0
1
1
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
2
1
0
0
2
0
0
2
0
2
0
1
1
0
0
0
0
0
2
2
0
1
1
2
1
1
1
1
0
0
0
1
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
1
0
2
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
1
1
0
0
2
1
1
0
0
1
0
0
0
1
0
0
0
0
0
4
0
2
6
1
0
0
0
3
0
0
0
0
0
2
2
0
0
1
2
0
1
0
1
0
0
0
1
1
2
2
0
0
1
0
0
0
0
0
2
1
1
0
0
0
1
3
0
2
0
1
1
0
0
0
0
1
0
0
0
0
0
2
3
1
0
1
3
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
2
0
2
0
1
0
1
0
0
0
0
0
0
0
4
0
0
0
0
3
0
1
1
2
0
0
0
0
2
0
1
0
0
1
0
1
0
1
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
1
0
0
0
0
3
0
2
1
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
1
0
0
0
0
0
0
0
2
0
1
2
2
0
0
0
2
0
2
0
2
0
0
0
1
1
2
0
0
1
1
0
1
0
1
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
2
1
0
1
0
0
1
0
2
1
0
2
1
0
0
1
0
0
3
1
0
2
0
0
0
1
0
2
0
1
0
0
1
0
0
0
0
1
0
0
0
2
2
1
0
1
2
0
1
2
1
1
0
0
0
0
0
0
0
0
0
6
1
1
2
1
0
1
3
0
0
2
1
0
0
2
0
1
0
1
3
0
1
2
0
0
0
2
0
0
1
0
0
1
0
2
0
0
2
0
0
1
0
2
1
0
0
0
1
2
0
0
1
1
0
2
0
0
0
0
0
1
0
0
2
0
0
2
0
2
1
0
0
1
1
0
0
2
0
1
0
0
0
1
0
0
0
0
2
4
0
0
0
0
1
1
0
1
2
3
0
4
0
0
0
2
2
0
0
2
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
2
1
2
0
0
2
2
1
0
2
0
0
0
0
1
0
1
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
2
0
2
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
2
0
3
1
0
0
2
0
0
0
0
0
3
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
2
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
5
2
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
2
0
0
0
1
2
0
0
0
1
0
3
0
0
0
0
1
0
0
2
3
0
0
0
0
0
1
1
0
1
1
0
0
5
0
0
0
1
0
0
0
0
0
2
1
0
0
0
1
0
0
0
2
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
1
2
0
0
2
0
0
1
0
2
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
2
2
0
1
0
0
0
0
2
2
2
0
0
0
0
1
0
1
0
0
1
0
1
1
0
0
0
2
2
0
1
1
1
2
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
2
0
3
0
0
0
2
0
0
0
0
0
0
0
1
0
2
2
1
0
0
0
0
0
1
0
1
0
1
0
0
2
2
1
0
0
0
0
2
1
0
0
0
3
0
0
0
1
1
2
0
1
3
1
0
0
0
5
0
0
0
1
1
2
2
1
0
2
0
0
2
0
2
0
1
0
1
1
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
2
0
0
0
3
1
2
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
2
1
0
0
1
0
1
0
0
0
2
0
1
0
0
2
1
0
0
2
0
1
0
0
1
1
0
0
4
0
2
2
1
0
1
0
0
0
0
0
0
0
3
0
0
1
2
0
0
0
1
2
0
0
2
0
0
1
0
0
0
1
0
0
1
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
2
0
0
0
1
2
0
0
2
0
1
2
0
2
0
0
0
0
2
0
1
2
0
1
0
0
0
1
0
2
2
0
0
0
1
0
1
0
0
4
0
0
0
0
1
0
0
0
2
0
0
0
1
0
2
0
0
0
0
2
0
1
1
0
2
2
0
0
0
0
0
2
0
0
0
1
2
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
3
0
0
0
0
0
2
2
0
1
0
0
0
0
3
2
0
0
0
1
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
2
0
0
2
2
2
1
1
0
2
0
0
0
0
0
2
1
0
0
1
2
0
0
1
0
3
0
0
0
3
2
1
0
0
0
0
2
1
2
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
2
1
0
0
3
0
0
0
1
0
0
4
0
0
1
3
0
0
2
1
0
0
0
0
1
0
2
4
1
0
0
0
0
1
0
0
2
0
0
1
0
2
0
0
2
0
0
2
0
0
0
0
0
2
1
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
5
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
2
1
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
1
2
0
1
0
0
1
1
0
1
0
0
0
0
1
0
1
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
1
1
2
4
2
0
0
2
0
0
0
0
2
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
1
0
0
1
1
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
2
1
0
0
2
0
2
0
2
0
1
0
0
0
0
0
2
2
0
0
2
0
2
0
1
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
1
0
2
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
2
0
2
0
0
3
2
0
0
0
0
0
1
0
1
0
0
1
0
0
1
2
0
0
0
2
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
2
0
2
0
0
0
1
2
2
2
0
0
0
2
0
1
3
0
0
2
2
2
3
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
2
0
1
6
1
0
0
2
0
0
0
1
1
0
0
0
0
2
0
0
1
1
0
0
0
0
2
2
0
0
0
0
0
2
0
3
0
1
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
3
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
3
0
0
1
0
1
1
2
1
1
2
1
0
2
0
2
2
0
0
0
1
0
0
0
0
0
1
2
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
2
2
3
1
2
0
1
1
0
0
0
2
2
0
0
0
2
0
0
0
2
0
0
0
1
0
0
3
0
0
0
0
1
0
2
1
0
2
0
0
0
0
2
0
0
2
1
0
0
2
2
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
1
0
2
0
0
0
0
0
0
0
2
2
0
1
0
0
0
1
0
0
1
0
0
2
1
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
1
1
0
0
0
0
1
1
0
1
0
0
0
0
0
1
1
0
1
2
0
1
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
1
0
0
0
2
2
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
1
1
0
1
0
0
1
2
0
1
0
0
2
2
0
3
0
1
0
0
0
0
1
0
0
0
2
2
0
2
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
3
0
0
2
1
0
1
1
0
1
0
2
0
1
1
0
0
0
1
0
1
2
1
0
1
0
1
0
0
2
2
0
0
0
1
0
2
0
0
0
0
0
0
2
1
0
0
0
1
1
2
0
1
2
0
0
2
0
2
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
1
2
0
0
0
0
3
0
0
2
3
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
2
1
0
1
0
0
2
0
0
0
1
0
0
1
2
2
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
3
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
6
1
0
1
0
0
0
1
2
2
0
0
0
0
0
1
1
0
0
0
1
0
1
2
0
0
0
3
0
0
0
0
2
0
0
2
0
2
0
0
2
1
0
0
1
2
3
0
0
0
0
0
1
0
0
0
2
0
0
0
3
0
0
0
0
0
0
2
4
0
2
2
0
0
0
2
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
2
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
3
0
0
0
0
2
2
3
0
3
0
0
1
0
2
0
0
1
0
2
2
0
0
0
1
0
1
2
0
2
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
1
2
1
0
0
2
1
0
0
0
0
1
1
1
0
0
1
0
0
1
0
0
0
0
0
2
0
0
2
0
1
2
0
0
0
0
0
0
0
0
2
0
2
1
0
2
0
0
1
0
0
3
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
2
0
0
2
1
0
0
2
0
0
0
0
0
0
2
0
1
0
1
3
0
3
2
0
1
2
3
0
0
1
0
0
0
0
0
0
0
1
2
0
0
1
0
1
0
1
0
0
0
0
2
0
0
1
0
2
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
2
1
0
1
0
0
2
0
0
0
0
2
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
1
2
0
2
1
0
1
0
1
0
0
0
0
0
2
2
0
2
0
0
2
0
0
0
2
0
0
1
2
0
0
0
1
0
0
2
1
0
0
0
2
1
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
2
0
1
0
2
0
0
2
2
1
0
0
0
0
2
0
1
0
2
2
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
1
0
1
1
1
6
2
2
0
0
0
0
0
0
5
0
0
1
0
0
1
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
3
2
0
0
0
0
1
1
1
2
0
0
0
2
1
2
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
2
3
0
0
0
0
0
2
2
0
1
1
0
0
1
2
0
1
0
1
0
2
0
0
0
1
0
1
1
4
3
1
1
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
2
2
1
0
0
3
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
1
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
4
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
5
1
2
0
13
2
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
2
0
0
0
0
1
2
0
0
1
1
2
0
0
2
0
1
2
0
2
2
1
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
1
3
0
0
0
0
0
0
0
0
1
0
0
1
1
2
1
0
0
1
2
0
0
0
1
1
0
0
2
0
0
0
2
2
0
0
2
0
0
0
5
0
0
0
0
2
1
0
1
1
0
0
2
0
1
0
2
0
0
0
3
0
0
0
0
3
1
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
1
0
1
0
1
0
2
1
3
2
0
0
0
1
0
0
0
0
0
0
1
0
2
0
2
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
1
0
0
1
1
0
2
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
1
2
2
0
2
1
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
2
2
0
2
2
0
2
0
2
1
0
0
2
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
2
0
1
0
0
2
0
0
1
0
0
0
1
1
0
1
0
0
2
1
0
1
0
2
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
1
1
1
2
1
1
0
1
1
0
1
1
0
2
0
0
0
0
2
0
0
0
0
1
0
0
2
1
6
0
1
0
0
0
0
2
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
2
2
0
1
0
0
0
0
1
2
0
0
0
1
0
1
3
0
0
1
0
1
0
0
0
1
1
2
0
2
2
0
1
0
0
1
0
0
0
1
0
0
3
0
1
0
1
0
0
0
0
2
1
0
0
1
0
0
0
0
0
2
0
2
2
11
0
0
1
1
0
1
0
0
0
0
0
2
0
0
0
2
2
2
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
2
1
1
0
0
0
0
0
1
1
0
1
2
0
2
0
0
1
0
1
1
0
2
2
2
0
1
2
1
0
2
0
1
0
0
0
0
0
2
2
1
1
2
0
0
0
1
0
0
1
0
3
0
0
2
3
1
2
1
0
0
0
0
0
2
2
2
0
1
0
0
2
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
1
1
1
5
0
0
0
1
2
7
0
0
0
1
0
0
0
0
2
0
1
0
1
1
2
0
2
0
0
0
0
0
1
2
0
1
0
0
1
1
0
0
1
0
0
0
0
2
8
0
2
2
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
1
0
2
0
0
1
0
0
2
1
0
0
0
0
1
0
2
0
0
2
1
2
0
0
0
2
0
0
0
2
1
0
0
2
0
2
0
0
0
0
1
0
0
0
2
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
2
2
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
2
2
0
0
0
0
0
0
0
1
1
0
0
0
2
3
0
1
0
2
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
1
1
0
0
0
0
2
0
0
1
0
2
0
2
2
1
0
1
0
0
0
0
0
3
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
1
2
1
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
2
2
0
1
0
0
0
1
0
0
1
2
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
1
1
0
1
0
1
0
0
1
1
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
1
2
1
0
0
3
0
0
0
0
0
0
2
0
0
2
0
0
0
1
1
0
0
1
1
0
2
0
1
0
0
0
0
0
0
3
0
1
0
0
0
0
1
0
0
2
9
0
2
0
0
0
0
1
0
2
0
3
0
2
0
1
0
0
2
0
1
0
1
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
3
4
0
2
0
0
1
0
0
0
0
0
2
2
0
0
0
1
1
0
2
0
2
2
0
0
0
3
0
0
0
0
0
2
0
2
0
0
1
0
0
0
1
0
0
0
1
3
2
2
0
1
0
2
2
0
0
0
1
1
0
1
3
0
0
0
0
0
0
3
2
7
0
0
1
0
0
2
2
0
0
2
0
0
1
0
0
0
1
1
0
0
0
1
0
0
1
1
1
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
6
2
0
0
1
1
0
2
0
2
2
0
0
0
0
1
0
0
2
2
0
0
2
2
0
0
0
0
0
0
0
0
0
1
2
1
0
0
3
0
1
0
0
2
0
0
2
0
0
0
0
2
0
0
2
1
0
2
2
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
2
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
2
0
2
1
0
0
1
0
0
2
0
3
0
1
0
0
1
0
0
0
0
1
1
2
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
2
0
2
3
2
1
0
2
3
0
0
0
0
0
3
2
1
0
1
0
1
3
1
1
0
0
0
2
0
0
0
2
0
0
0
0
2
2
0
0
0
0
1
2
0
1
0
2
0
0
0
0
3
0
0
0
2
1
0
1
0
1
0
0
2
0
1
0
1
0
0
0
0
1
0
0
2
0
0
2
0
0
0
2
0
5
1
1
0
0
2
0
0
0
0
1
0
1
1
0
1
0
0
0
2
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
4
0
2
0
0
1
2
0
0
0
2
1
0
1
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
1
0
2
2
1
1
0
0
0
1
1
0
0
0
0
2
0
1
0
1
0
2
0
1
0
0
0
1
1
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
2
0
0
1
0
1
4
1
0
2
0
0
1
1
2
0
2
0
0
2
0
1
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
2
2
2
2
0
1
2
0
0
1
1
1
1
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
2
0
1
0
1
0
1
1
1
0
1
0
0
1
1
2
1
1
0
2
2
1
0
2
1
1
0
0
0
2
0
0
0
0
3
2
0
0
2
0
0
0
0
3
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
1
2
0
0
1
0
1
0
1
0
0
1
1
1
1
1
1
2
0
0
2
0
2
0
0
0
1
5
0
0
0
0
2
0
0
0
1
2
2
0
0
0
1
0
0
2
1
1
2
0
2
2
0
1
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
3
0
2
0
0
0
0
2
0
0
0
1
2
1
1
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
2
0
0
2
0
1
2
0
0
1
0
0
0
0
1
1
0
0
1
0
0
2
0
2
0
0
2
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
1
0
0
0
1
0
0
0
1
2
0
0
2
0
2
1
0
1
1
0
0
2
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
1
0
0
0
3
0
0
2
0
3
0
0
1
0
2
0
0
1
0
0
0
2
0
0
0
0
1
2
1
0
0
0
1
0
0
1
0
2
0
0
0
1
0
2
1
0
0
1
1
1
0
0
0
0
0
1
0
0
1
0
1
0
2
0
2
0
0
0
0
4
0
0
1
0
2
0
2
2
1
0
0
0
0
2
0
0
2
1
0
0
0
0
1
0
0
2
2
4
0
0
2
2
0
1
0
1
1
0
0
0
0
0
0
2
2
0
0
0
0
6
1
1
0
0
0
1
2
2
0
2
1
0
0
0
2
0
0
0
0
2
1
1
1
2
2
0
0
1
2
0
0
0
0
0
2
2
2
4
0
2
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
1
2
0
2
0
2
2
0
0
2
2
0
0
0
2
1
0
2
0
0
1
0
1
0
2
0
0
1
2
0
0
0
0
2
0
1
0
2
0
0
0
1
1
0
0
0
0
0
0
1
0
1
1
0
0
1
0
2
0
2
2
0
1
2
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
2
0
2
2
1
0
0
2
0
2
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
1
2
0
0
1
0
0
0
2
2
0
0
2
0
0
1
0
1
0
1
0
1
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
1
0
1
0
0
0
2
2
2
1
1
0
0
2
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
2
2
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
2
0
1
0
0
2
0
0
0
2
0
0
1
0
0
1
1
0
0
0
0
1
3
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
3
1
1
0
0
1
0
1
0
0
1
0
2
0
0
0
2
0
0
0
0
1
1
0
2
0
3
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
2
2
0
1
1
0
2
1
0
2
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
3
0
2
1
1
0
0
0
2
2
2
0
0
2
3
1
0
0
3
1
2
1
1
2
0
0
0
0
1
2
1
0
0
0
0
2
2
0
9
0
0
0
0
2
1
0
1
0
0
1
0
0
0
1
0
0
1
1
2
0
1
2
0
1
0
1
0
0
0
1
0
0
1
0
0
0
4
0
0
0
0
0
1
2
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
1
0
6
0
1
2
1
0
0
0
1
0
2
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
2
1
0
0
2
0
2
0
1
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
1
2
0
0
0
1
0
0
0
1
0
0
0
1
0
0
2
0
0
0
1
2
0
0
2
2
0
0
1
1
1
1
0
0
0
2
1
1
0
0
0
0
0
0
0
1
1
1
0
0
2
0
0
0
0
0
2
0
0
0
3
0
1
0
1
3
2
1
0
0
0
2
0
0
1
0
0
0
1
2
0
1
1
0
0
0
0
2
0
0
2
0
0
1
0
0
2
1
0
3
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
2
0
1
1
2
2
1
0
0
1
1
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
2
0
0
1
2
0
0
1
0
1
0
2
0
1
0
0
0
2
2
0
0
1
1
2
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
2
2
0
1
0
2
0
0
0
1
0
1
1
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
1
1
2
2
0
0
0
0
0
2
0
0
4
0
3
0
0
1
0
0
0
1
1
0
1
1
1
2
2
0
0
0
0
0
0
0
1
1
1
2
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
1
0
0
1
0
0
0
1
0
2
0
0
0
0
0
2
3
0
1
0
2
1
0
0
1
0
1
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
2
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
2
2
0
0
0
1
0
0
1
0
1
0
0
0
0
1
1
3
0
0
0
1
0
2
1
1
0
0
0
0
0
0
0
2
0
0
0
1
1
0
2
1
0
1
0
0
0
2
0
1
0
0
2
1
1
0
2
0
0
0
2
1
0
1
0
2
0
0
0
1
0
0
0
0
0
2
1
2
1
0
0
0
0
2
2
2
1
0
1
0
1
1
0
1
0
1
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
2
0
0
2
0
1
0
1
1
0
3
1
1
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
1
0
2
2
0
0
0
0
0
2
0
2
0
0
2
1
0
0
0
0
3
0
2
2
0
1
2
1
0
1
0
0
0
2
0
0
1
1
0
0
0
1
3
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
2
2
0
2
0
1
1
2
1
0
0
0
1
1
2
0
0
0
0
2
0
2
2
0
1
0
0
2
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
2
0
2
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
2
2
0
1
1
1
0
0
0
0
2
0
2
0
0
0
0
1
2
1
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
2
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
2
0
2
0
0
0
1
0
3
1
0
0
0
1
1
0
0
0
0
1
1
0
0
2
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
3
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
3
2
1
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
2
2
0
0
0
3
2
1
0
0
0
1
0
1
0
2
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
2
0
0
2
0
0
2
0
0
2
0
0
0
0
2
1
2
0
0
0
0
2
0
0
0
0
0
1
1
0
3
0
1
2
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
1
0
3
0
3
0
2
2
0
0
2
3
0
0
0
0
5
0
1
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
2
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
3
0
0
0
1
0
0
1
2
1
1
0
0
1
0
0
0
3
0
1
0
0
0
0
0
2
0
1
2
1
2
1
0
0
4
1
0
1
0
0
0
0
0
1
0
1
1
0
1
0
0
1
0
2
1
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
1
0
0
1
2
0
0
2
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
5
0
1
1
1
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
1
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
1
0
2
2
0
0
2
2
0
0
0
0
1
0
0
0
2
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
3
1
2
0
0
0
0
0
0
3
2
0
0
2
2
0
0
0
2
0
0
0
0
0
0
1
1
0
1
2
0
0
0
0
0
0
0
1
2
0
0
2
2
0
0
0
0
0
2
2
0
2
0
2
0
3
3
0
0
0
2
2
0
0
0
1
0
0
0
0
0
6
1
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
3
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
2
0
2
0
0
0
2
0
0
0
0
0
1
0
1
0
2
3
0
0
0
0
0
2
2
0
1
0
2
2
0
1
2
0
0
0
0
0
0
2
1
2
1
0
0
0
0
0
0
0
1
0
0
0
0
2
1
1
0
0
0
0
2
3
2
0
0
0
0
0
0
2
0
0
2
0
1
0
1
0
0
2
2
0
0
0
0
0
2
0
1
0
1
0
2
1
0
2
0
0
1
0
0
3
2
0
2
0
2
0
2
0
0
0
2
0
0
0
1
0
2
0
0
0
2
0
2
0
0
0
0
2
0
2
1
0
0
0
2
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
2
0
0
1
0
0
0
0
1
2
0
0
0
2
0
0
2
0
0
0
1
0
0
1
1
0
2
2
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
3
0
0
1
2
0
0
1
2
2
0
2
0
5
0
0
0
0
1
0
0
0
0
0
0
2
1
1
1
0
0
0
0
0
2
1
1
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
1
2
0
0
0
0
0
0
0
0
2
1
0
0
0
2
1
1
1
1
0
2
0
0
1
0
1
1
0
1
2
0
3
0
0
2
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
2
0
2
1
2
0
1
0
0
0
1
0
0
1
2
3
2
0
0
0
3
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
2
0
2
0
0
0
2
0
0
1
0
0
0
0
0
1
0
4
0
0
0
0
2
0
2
0
1
0
2
0
0
0
6
0
0
0
0
0
2
1
0
0
1
2
0
3
0
0
0
1
2
0
0
0
0
1
2
0
2
0
0
0
0
0
1
0
2
1
0
1
0
0
0
0
1
0
0
0
0
0
1
2
2
0
2
0
1
1
0
3
0
0
0
0
0
0
0
1
1
2
0
0
0
0
1
0
0
0
1
1
1
2
0
0
0
2
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
2
0
0
0
0
2
0
0
0
0
0
1
1
2
1
2
0
0
1
1
0
0
0
0
1
0
2
0
0
1
0
2
2
0
2
0
1
2
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
2
0
2
2
1
2
1
0
0
0
2
3
1
2
0
2
2
1
1
3
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
3
1
1
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
2
0
1
1
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
2
2
0
0
0
2
0
2
0
1
0
2
0
0
2
1
1
0
2
1
0
1
0
1
2
2
0
0
1
1
2
0
0
2
0
0
2
0
2
0
0
0
0
0
1
0
2
2
2
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
2
0
3
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
3
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
2
0
0
2
0
1
1
0
0
1
0
1
1
1
1
0
0
2
0
0
2
2
0
2
0
2
3
0
2
2
0
0
0
0
0
1
0
1
2
2
0
0
0
0
0
1
0
2
1
0
0
0
0
2
0
0
0
2
0
0
0
0
2
1
1
2
2
2
0
0
1
0
1
0
1
0
0
0
1
0
0
1
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
2
2
0
1
0
0
0
0
0
1
2
0
0
1
2
0
0
0
1
0
0
2
1
0
0
1
0
0
0
2
1
1
0
0
0
1
0
0
1
2
2
0
1
2
0
1
3
0
0
0
3
0
1
0
0
0
1
1
0
0
0
1
0
0
1
0
1
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
3
2
0
0
1
1
3
0
0
1
0
0
0
0
0
2
0
0
0
0
1
2
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
2
0
1
0
0
1
2
1
0
0
0
0
0
1
2
2
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
2
0
1
3
0
0
0
3
0
0
0
0
0
0
1
0
5
0
0
2
1
2
2
2
0
0
2
0
2
0
0
1
0
0
2
3
0
2
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
1
2
0
0
2
0
2
1
0
0
0
1
0
2
0
0
0
0
2
0
2
0
1
1
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
3
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
4
2
1
2
4
0
1
0
0
2
0
0
0
0
0
0
1
2
2
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
1
2
2
1
0
1
0
2
1
2
1
1
2
1
1
0
0
0
0
0
2
0
0
0
0
1
0
1
1
0
0
2
1
2
0
1
2
2
0
0
0
0
0
2
1
0
1
0
1
0
0
1
0
0
0
0
0
1
1
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
1
0
2
1
2
0
0
0
0
0
3
1
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
1
2
1
0
5
0
0
0
2
0
0
0
0
2
2
0
1
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
1
2
1
0
0
0
0
2
0
0
2
0
2
0
3
0
0
2
1
0
0
2
1
1
0
1
0
1
1
2
2
0
2
0
1
1
0
0
0
0
2
1
0
0
2
1
2
5
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
1
1
1
0
0
2
0
0
2
0
1
3
0
0
2
0
0
2
0
2
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
2
1
2
0
2
0
0
2
0
0
0
0
0
4
2
0
2
0
0
0
1
0
1
1
1
0
1
1
1
0
0
1
0
0
0
0
2
4
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
2
2
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
3
0
0
0
0
0
2
0
0
1
2
2
0
0
0
0
0
1
0
2
0
0
2
0
1
0
0
0
0
0
0
0
2
0
3
0
0
0
1
2
0
0
3
0
1
0
2
0
1
1
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
4
6
0
1
2
0
1
0
1
0
1
0
0
0
0
0
3
0
2
0
2
5
1
1
2
0
1
2
0
1
0
2
0
0
0
1
1
0
0
3
0
3
2
0
0
0
0
3
0
0
0
0
1
0
0
0
0
1
0
0
1
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
2
0
1
0
0
0
0
2
1
0
1
0
2
0
0
2
1
0
2
0
2
0
4
1
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
2
1
0
0
0
0
0
1
1
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
2
0
0
0
1
0
0
0
0
1
1
2
0
1
0
0
0
0
2
0
0
2
0
2
1
2
1
1
3
0
2
2
0
1
0
2
0
2
1
0
2
1
0
1
0
0
2
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
2
0
0
0
2
0
0
0
1
2
1
0
1
0
0
2
2
1
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
2
1
2
2
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
1
1
0
1
0
1
1
0
1
1
1
0
0
0
0
1
2
1
0
0
0
0
1
0
1
3
0
0
0
0
0
1
0
0
1
1
0
0
0
0
2
0
3
0
1
1
2
0
1
0
0
0
0
2
0
0
0
1
2
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
1
1
0
1
2
1
2
1
0
2
4
1
0
0
2
2
1
0
1
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
1
1
2
0
2
4
0
0
0
1
0
0
0
2
0
2
2
0
1
0
0
0
2
0
1
0
0
1
0
0
2
0
0
2
2
0
1
0
1
0
2
0
0
0
1
0
1
0
0
1
0
0
1
0
2
0
0
0
1
2
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
2
0
0
1
1
0
2
0
0
0
0
0
2
1
2
0
0
0
0
4
0
2
0
2
2
0
0
1
0
0
0
0
0
0
1
1
2
0
2
0
0
0
2
0
1
0
0
0
0
1
1
0
1
0
0
2
0
1
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
1
0
2
0
2
2
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
3
0
2
0
0
0
2
0
0
0
2
2
0
0
0
0
4
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
2
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
1
1
0
1
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
2
2
2
0
1
0
2
0
2
0
0
0
2
0
0
0
0
2
0
0
0
2
1
0
0
0
0
1
0
3
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
2
0
2
0
0
0
2
2
0
0
0
0
0
4
0
0
0
0
0
2
2
0
0
1
1
0
1
2
2
2
2
2
0
2
2
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
1
0
0
2
1
2
1
2
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
1
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
1
0
0
0
2
0
0
0
0
2
1
1
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
1
1
0
0
2
0
0
1
0
2
2
0
2
2
1
1
2
0
0
1
2
0
0
0
0
0
0
1
0
1
1
1
0
0
1
1
0
1
0
2
1
0
0
2
1
0
2
0
0
1
2
0
1
0
0
2
0
0
0
0
2
0
0
0
0
1
0
1
0
0
1
2
0
2
0
0
2
0
0
1
0
2
1
0
0
1
0
0
2
0
2
1
1
0
1
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
1
1
1
0
1
0
3
0
0
0
0
0
0
0
0
0
0
1
2
0
2
1
0
1
0
0
0
1
0
0
0
2
0
0
0
0
1
0
2
0
0
0
1
0
0
0
1
0
4
0
0
0
0
1
0
0
2
0
0
1
0
2
0
0
0
0
0
0
1
2
2
2
0
3
0
0
0
0
0
2
2
2
0
0
0
0
0
0
1
0
0
0
2
1
0
2
2
0
2
1
0
1
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
1
2
0
1
0
1
0
0
0
1
2
1
0
1
0
0
0
0
1
0
2
0
2
0
0
2
2
0
2
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
1
0
0
2
0
0
0
1
0
0
0
3
0
0
0
1
0
0
1
0
0
2
1
0
0
3
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
1
1
0
0
1
0
2
0
0
0
0
1
1
0
1
1
0
0
0
0
2
1
0
0
2
0
0
2
0
0
2
2
0
4
0
0
1
3
0
0
0
0
1
0
0
0
0
1
0
0
2
2
0
3
2
0
1
1
0
0
2
0
0
1
0
0
0
0
2
1
0
0
2
0
0
0
1
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
2
2
0
1
0
2
2
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
1
2
1
0
1
0
0
1
0
2
0
0
0
0
0
0
0
1
2
2
0
0
1
0
0
0
0
0
0
0
2
0
5
0
0
1
0
2
2
2
0
0
0
0
1
0
0
0
0
1
3
0
0
0
0
0
2
0
2
1
1
0
2
3
1
0
0
0
1
0
2
0
2
0
0
2
2
0
0
0
1
0
0
1
1
0
1
0
0
0
0
9
0
3
4
0
1
0
0
0
0
2
0
1
1
2
1
0
0
0
1
2
0
0
0
0
0
2
1
0
1
2
0
0
0
1
0
0
0
2
0
1
0
1
0
0
1
0
0
0
0
2
0
1
0
0
0
1
3
0
1
2
0
0
2
0
0
0
0
0
3
1
0
0
2
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
1
0
0
0
2
1
0
1
0
2
2
3
1
0
0
0
2
0
0
0
0
1
0
1
3
0
0
0
0
1
0
0
0
0
0
0
0
2
2
2
1
2
2
0
1
0
0
0
0
0
0
2
2
1
0
2
1
0
0
1
0
0
1
0
0
0
1
0
2
0
0
2
0
1
2
0
1
0
2
0
0
0
0
2
1
0
1
0
0
4
0
1
0
2
0
0
1
0
0
0
1
1
0
0
0
1
0
1
1
2
0
0
0
0
1
0
2
0
1
0
2
0
0
0
1
0
0
2
1
0
0
1
1
0
1
0
0
2
0
0
0
0
2
1
3
0
0
0
0
0
0
2
0
0
2
0
0
0
0
3
0
0
0
2
2
2
0
0
0
0
2
0
1
1
1
0
0
0
1
0
2
0
0
2
1
3
2
0
0
1
0
0
0
2
0
1
1
1
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
5
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
1
1
1
0
2
0
1
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
2
0
2
2
0
2
1
2
0
0
0
0
1
1
0
0
1
1
2
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
1
3
1
2
2
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
1
0
0
0
0
0
1
0
1
1
0
0
1
0
1
0
0
1
0
0
0
0
1
0
1
0
0
2
1
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
6
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
1
0
1
0
0
0
3
1
2
2
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
4
1
2
1
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
2
0
0
1
2
1
1
2
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
2
0
0
1
0
0
0
1
0
0
0
0
2
0
2
2
2
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
3
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
1
0
0
0
0
3
0
0
2
0
0
2
0
2
2
2
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
1
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
1
1
0
2
0
0
0
1
2
0
1
2
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
2
0
1
0
2
1
0
1
0
1
0
0
0
2
0
0
1
3
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
1
0
1
0
2
0
1
3
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
3
2
0
0
0
0
0
0
1
0
0
1
0
0
3
1
2
0
1
0
0
0
0
0
0
0
0
2
4
1
0
2
0
1
0
1
1
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
1
1
0
0
2
0
0
1
0
0
1
1
1
0
2
0
2
1
0
0
0
0
2
1
0
2
0
0
0
0
2
0
2
1
0
0
0
1
0
0
2
0
0
0
1
0
0
0
2
1
2
0
0
0
5
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
1
0
2
0
0
2
2
0
0
0
2
0
0
0
0
0
0
1
2
0
2
1
0
0
0
0
0
0
2
0
0
0
0
1
2
2
0
0
2
2
0
0
0
0
0
2
1
0
1
2
2
0
1
2
0
0
2
2
0
1
0
0
0
0
2
2
0
1
0
1
2
1
0
1
0
0
0
1
2
0
2
0
1
0
0
0
2
2
0
2
1
0
0
0
0
2
0
2
0
1
2
0
1
0
0
0
0
1
0
0
2
0
0
1
0
0
0
2
1
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
2
0
2
2
0
0
0
0
2
0
0
0
0
2
0
0
1
1
1
0
0
0
1
15
0
0
2
0
0
3
0
2
0
1
1
0
0
2
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
2
0
0
0
0
2
2
3
0
0
0
1
2
0
0
3
0
0
0
1
0
0
0
3
1
0
0
0
0
3
0
1
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
2
0
0
1
3
0
0
0
2
0
2
1
0
2
0
0
0
0
1
1
0
2
0
1
0
0
0
0
0
0
0
1
0
1
0
1
2
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
0
2
1
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
2
1
2
0
0
0
0
0
0
4
0
0
1
0
1
0
1
0
1
1
0
1
0
2
0
3
0
0
0
4
0
0
2
0
0
0
0
1
1
0
0
0
0
1
0
0
0
2
0
2
0
0
2
0
0
0
0
1
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
1
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
2
2
0
1
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
1
2
2
0
0
2
0
0
0
1
0
0
0
2
2
0
0
0
0
1
1
1
1
1
0
0
2
0
0
1
2
0
1
1
1
1
2
0
0
0
2
1
0
1
0
0
3
0
0
3
0
0
0
2
0
0
0
0
0
1
1
0
0
1
2
0
2
0
0
0
0
0
1
1
2
0
1
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
1
0
0
2
4
2
2
0
0
0
2
0
0
2
0
1
0
0
0
2
2
1
5
0
0
1
0
0
0
1
2
0
0
0
0
0
1
0
2
2
2
2
1
0
0
2
0
1
1
1
0
0
0
1
0
0
0
2
2
1
1
0
1
0
0
2
1
2
1
0
0
1
0
1
0
0
2
0
0
2
0
0
2
3
1
0
0
0
0
0
0
0
2
0
0
0
2
1
1
0
0
1
0
0
0
1
2
0
1
0
0
0
0
0
2
2
0
0
0
2
1
0
0
0
0
3
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
1
0
1
2
2
0
0
1
1
2
0
2
0
0
2
0
0
0
2
0
1
0
1
0
0
0
0
2
2
0
0
1
0
3
0
2
0
2
2
0
2
0
0
0
1
0
1
0
0
1
0
2
0
0
2
2
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
7
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
2
1
0
0
0
0
1
3
0
0
2
0
0
0
0
8
0
1
0
0
1
1
0
2
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
2
0
2
0
0
0
0
2
0
1
1
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
1
1
2
3
0
0
0
0
0
1
2
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
2
1
0
0
2
0
0
0
0
2
2
0
0
0
1
0
2
0
1
0
1
1
2
0
2
0
0
0
0
1
0
0
0
3
0
0
0
1
0
0
0
1
0
1
2
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
1
2
0
1
2
0
4
2
0
0
0
1
0
0
2
0
0
1
1
1
0
2
1
1
0
0
0
1
0
1
2
0
1
0
0
0
0
1
0
2
0
2
0
1
0
0
1
0
0
0
1
1
1
2
0
0
0
0
0
0
0
2
0
0
2
3
0
0
0
2
0
0
0
0
0
0
1
2
1
0
0
1
2
0
0
1
2
0
0
0
0
0
0
1
0
2
3
0
0
0
0
2
0
2
1
1
0
2
0
1
0
2
0
2
0
0
1
0
0
1
3
0
1
1
2
2
2
0
0
1
2
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
2
1
0
2
0
0
1
0
2
0
0
0
0
0
0
0
2
0
1
0
2
0
1
2
0
2
2
0
3
0
0
0
2
0
1
0
2
2
4
0
0
0
0
1
0
1
2
0
1
0
0
1
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
3
2
2
1
0
1
0
0
0
2
0
0
0
1
2
0
0
0
3
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
3
0
0
0
0
0
1
0
0
0
0
2
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
3
2
2
2
0
1
2
0
1
0
0
0
2
2
0
0
1
1
0
1
0
0
1
2
0
0
1
0
1
1
0
0
0
1
0
0
0
2
1
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
2
1
0
2
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
7
0
0
1
0
0
1
0
0
1
0
2
0
1
1
0
1
1
0
1
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
2
2
0
1
1
1
0
0
0
0
2
0
4
2
0
1
1
0
0
2
1
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
2
0
2
0
0
1
0
2
0
1
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
2
0
4
0
0
2
0
0
0
2
2
1
2
2
0
2
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
2
0
1
0
0
0
0
1
0
0
0
0
1
3
0
0
0
0
0
1
1
2
2
1
2
2
2
2
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
4
0
1
1
0
1
0
0
0
2
0
1
1
0
1
2
0
0
1
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
2
3
0
0
0
0
0
0
2
2
0
0
2
0
2
0
0
1
0
0
0
2
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
2
2
1
2
2
0
0
1
1
0
1
2
0
0
0
0
0
2
2
1
0
2
2
0
2
1
1
0
0
2
0
0
0
1
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
1
0
0
0
1
0
0
2
2
0
0
2
0
0
0
0
0
0
2
0
0
0
1
1
0
2
2
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
2
2
0
0
4
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
5
0
3
0
1
1
1
0
0
1
0
0
0
0
1
0
0
0
0
3
1
2
0
0
0
2
1
0
0
2
0
0
0
0
0
2
0
1
0
2
0
1
0
2
0
2
2
0
2
2
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
3
0
1
3
0
0
0
0
0
3
1
2
0
0
2
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
2
1
1
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
1
1
1
2
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
2
0
0
1
0
0
0
2
0
0
1
1
3
0
1
0
0
0
0
1
0
0
1
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
1
1
2
0
0
0
1
2
0
2
2
0
2
0
0
0
6
0
0
0
0
0
0
0
0
1
1
0
0
0
2
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
1
1
0
2
2
1
3
0
0
0
0
2
1
2
0
1
0
0
0
0
0
2
0
1
2
0
1
0
0
0
2
2
0
4
0
0
0
0
0
0
2
2
0
0
1
0
1
0
0
0
2
0
3
0
0
3
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
2
0
0
2
0
1
0
0
2
0
0
0
0
1
0
0
0
2
0
0
2
1
2
0
0
0
1
0
1
0
1
2
0
0
0
2
0
0
2
2
1
0
2
2
0
2
1
0
1
1
0
1
1
1
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
4
2
0
1
0
0
2
0
0
0
0
0
0
0
0
2
1
2
0
0
0
1
0
2
2
0
0
0
0
0
2
0
1
0
1
0
1
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
2
0
1
2
0
0
2
0
2
0
2
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
2
0
0
2
1
0
0
1
2
0
1
1
0
0
0
0
1
0
0
0
0
0
2
2
1
0
0
0
1
2
0
0
0
2
1
2
0
0
1
2
0
1
1
0
1
1
0
0
0
2
1
1
2
0
0
1
0
1
0
0
1
1
1
1
1
1
1
1
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
2
0
0
1
0
0
0
1
1
3
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
4
1
0
0
1
0
0
1
1
0
0
0
0
1
0
2
0
1
0
2
1
0
0
2
0
2
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
1
1
2
0
0
2
1
0
1
0
0
0
2
0
1
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
2
1
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
6
1
0
0
0
1
0
0
1
1
0
1
2
0
2
0
0
0
2
0
1
0
0
0
0
0
0
2
1
4
2
1
1
0
2
1
3
0
0
1
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
2
2
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
2
1
2
1
0
2
2
2
0
0
0
0
2
0
0
0
1
0
2
0
1
0
0
0
0
1
0
0
0
4
1
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
2
2
0
1
1
1
2
2
0
0
1
2
0
0
1
2
0
0
2
0
0
0
1
0
1
0
1
1
0
0
2
0
0
0
1
2
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
2
0
0
0
1
0
0
0
0
2
2
0
6
0
0
0
2
0
2
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
1
0
1
0
0
1
0
0
0
0
2
2
3
1
1
2
1
2
0
0
0
1
0
0
0
1
2
0
0
1
0
1
0
0
0
0
0
0
1
0
2
0
0
1
1
0
2
1
0
0
0
0
0
0
2
0
0
0
1
1
0
0
2
0
0
0
1
1
0
1
0
0
0
0
1
3
1
0
0
0
0
0
1
0
0
2
2
0
0
0
1
1
1
0
3
0
1
1
0
1
0
1
0
1
0
0
1
0
0
0
0
0
2
1
1
0
2
1
0
1
0
0
0
2
0
0
2
1
1
0
1
0
1
1
2
1
0
5
0
0
0
0
0
0
0
0
1
1
1
0
0
2
1
2
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
2
0
0
1
0
2
0
0
0
2
0
1
1
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
1
2
0
1
0
2
0
0
1
0
3
0
1
0
0
0
0
0
2
0
1
0
0
0
1
1
1
1
2
2
0
0
0
2
1
0
1
1
0
1
1
0
1
0
1
0
0
1
0
0
0
2
0
1
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
2
1
2
1
0
0
0
1
0
0
2
0
1
0
1
1
1
1
0
2
0
0
0
2
0
0
0
1
2
1
0
0
0
3
2
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
2
0
1
0
0
1
0
2
1
0
0
0
0
0
1
3
0
0
0
0
0
0
2
0
1
1
1
0
2
1
2
0
2
0
0
0
2
1
0
2
0
2
0
0
0
2
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
1
0
2
0
1
0
1
2
0
3
1
0
0
0
0
1
0
0
2
0
0
0
2
2
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
1
1
0
2
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
2
2
0
1
1
1
0
0
0
0
1
0
0
2
1
0
0
0
0
1
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
1
0
1
0
0
0
0
0
0
1
1
0
1
1
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
1
1
0
0
1
1
0
0
1
2
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
1
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
1
1
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
3
0
0
2
3
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
1
0
0
0
0
0
1
0
2
0
1
2
1
0
1
0
0
4
0
0
0
0
2
2
0
0
0
0
0
2
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
2
1
1
0
2
0
1
1
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
4
0
1
1
0
2
2
0
0
0
0
1
3
0
2
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
1
0
1
0
2
0
0
0
1
0
0
0
0
0
1
2
1
0
2
1
0
0
0
0
4
0
2
2
2
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
1
0
0
0
0
2
0
0
1
0
1
0
2
0
0
1
0
2
0
0
1
0
0
0
0
2
2
2
1
0
2
1
0
0
1
0
0
2
0
1
1
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
1
0
0
2
0
3
0
0
2
1
0
0
1
0
0
1
0
2
0
1
2
0
0
1
0
2
0
0
2
2
0
0
0
2
1
0
1
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
2
0
0
2
0
1
0
2
1
0
0
1
0
0
1
2
0
1
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
1
1
0
0
0
1
0
0
0
2
0
2
0
2
0
0
0
0
0
0
2
0
0
0
1
0
4
5
0
2
0
0
2
0
0
0
1
0
1
1
2
2
0
0
0
1
2
10
0
0
4
1
1
0
2
0
0
2
0
0
1
2
1
0
0
0
2
2
1
0
0
1
0
0
0
0
0
0
1
3
0
0
1
1
0
0
1
0
0
1
0
1
0
1
0
1
3
0
0
0
1
0
3
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
3
1
1
0
0
1
1
0
0
0
0
0
0
0
0
1
2
3
0
0
0
0
2
0
0
0
1
0
0
1
0
2
1
2
0
2
0
0
0
3
1
2
0
0
0
0
0
0
0
0
0
2
2
1
2
0
0
0
0
0
2
0
0
2
0
0
0
0
1
1
2
0
1
0
1
0
0
0
2
1
0
2
0
0
0
2
0
0
0
0
0
0
0
1
1
2
0
0
0
0
2
1
0
2
0
1
2
0
2
0
0
0
0
0
1
0
0
2
0
0
1
0
2
0
0
0
0
2
0
0
0
2
0
2
1
1
2
1
0
0
0
0
0
0
1
1
0
2
0
2
2
0
2
2
1
0
0
2
0
0
2
1
0
2
0
1
2
1
0
2
0
0
0
0
0
1
0
0
1
1
0
0
0
0
2
1
0
2
3
0
0
0
0
2
0
1
0
0
1
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
2
1
0
0
0
0
0
0
1
1
0
1
1
0
0
2
1
0
1
1
0
0
0
1
0
1
0
1
0
2
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
2
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
1
0
2
0
0
0
0
2
2
0
0
0
0
0
2
0
2
2
0
0
1
0
2
0
0
2
1
1
2
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
1
1
0
0
2
2
0
1
0
0
0
0
0
2
2
2
1
1
0
2
0
0
0
0
2
1
0
1
0
0
1
1
1
0
2
0
0
0
0
0
2
2
0
0
2
2
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
2
2
0
0
0
0
1
0
0
0
2
0
2
1
2
0
2
0
0
0
1
0
0
1
1
1
2
0
0
0
0
0
0
0
0
0
2
1
0
0
2
1
1
0
0
0
0
2
0
0
0
1
0
0
1
0
2
1
10
0
1
1
0
0
2
0
1
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
2
0
0
0
1
2
0
0
0
0
2
0
0
4
2
0
0
0
0
0
0
0
0
2
0
2
3
1
1
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
1
1
1
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
2
2
0
1
1
0
0
0
0
0
0
9
1
0
0
0
0
0
1
1
1
0
4
0
2
0
0
1
2
0
0
0
0
0
0
2
1
0
1
0
0
2
1
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
2
0
2
0
1
4
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
1
0
2
0
0
0
0
1
1
2
0
0
2
0
0
0
2
0
1
2
1
0
0
1
0
0
0
2
2
0
2
0
3
2
0
0
0
0
0
0
0
4
0
1
1
1
0
2
0
0
0
0
0
0
1
0
1
1
1
2
0
0
1
0
2
0
1
7
0
0
1
0
0
2
2
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
1
1
0
1
0
0
1
2
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
2
1
3
0
0
2
0
0
0
2
0
2
1
0
0
0
0
0
1
1
0
0
1
4
2
0
0
2
0
0
1
2
2
0
0
0
0
0
2
0
0
3
0
1
1
0
1
2
0
0
2
2
0
0
0
0
0
2
5
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
1
0
2
0
0
2
0
0
1
0
3
0
2
0
1
0
2
2
1
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
1
3
0
2
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
1
1
0
0
1
0
0
2
0
0
0
0
0
0
0
1
1
0
2
0
0
0
2
0
0
0
2
0
0
0
1
0
0
1
0
0
1
0
0
3
0
2
0
0
1
0
1
0
1
4
0
0
0
2
0
2
0
2
1
2
0
0
0
0
1
1
2
2
1
0
1
0
0
0
2
0
0
2
0
0
0
2
0
0
2
0
2
0
0
0
0
0
2
0
2
1
0
2
1
2
2
0
1
0
0
0
0
1
0
0
1
0
2
2
0
0
0
1
0
0
2
0
0
0
0
0
2
2
0
0
0
0
1
1
2
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
3
0
0
0
0
0
0
0
2
0
1
0
1
0
1
0
0
0
0
1
2
0
1
2
0
5
2
1
0
0
0
1
0
0
0
1
0
0
0
0
1
10
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
1
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
2
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
2
2
0
1
0
0
0
0
2
0
0
0
2
1
0
1
0
0
0
0
0
1
0
0
2
1
2
2
1
0
0
0
0
0
0
0
1
2
0
0
0
1
1
1
0
0
0
0
2
1
0
2
1
1
2
0
2
0
0
0
0
0
3
3
2
0
0
0
0
0
2
3
2
0
0
0
1
1
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
2
0
0
0
1
0
0
2
0
0
0
2
0
0
1
0
1
0
0
0
3
1
0
3
2
0
0
0
2
1
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
2
2
2
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
2
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
1
0
2
1
0
1
0
0
2
1
0
1
2
2
0
2
0
0
3
0
0
3
1
0
3
0
1
0
0
2
0
2
1
0
0
1
0
0
0
2
1
1
0
0
2
0
0
2
1
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
1
2
0
1
2
0
2
1
0
2
0
2
0
1
2
1
0
0
2
0
0
1
2
4
1
2
2
1
0
1
1
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
2
3
0
0
0
0
2
0
0
0
0
2
0
2
0
1
0
1
0
0
0
0
0
1
0
1
2
0
0
2
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
1
0
1
0
0
0
1
1
1
2
1
0
0
0
0
0
0
2
2
2
0
1
2
0
1
0
2
0
0
2
2
0
0
2
0
1
0
0
2
1
0
2
0
0
6
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
2
0
1
0
0
1
0
0
0
2
0
1
0
0
3
0
2
2
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
1
0
3
0
1
1
0
3
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
2
2
0
0
3
2
0
0
0
0
1
2
0
2
0
0
0
0
1
0
0
1
2
0
0
2
0
2
0
1
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
1
0
0
0
1
0
0
1
4
0
0
0
0
0
2
1
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
1
2
0
0
0
1
0
1
0
0
8
2
0
1
0
1
0
2
2
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
2
1
0
1
2
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
2
0
2
0
2
0
0
0
0
2
0
0
2
0
2
1
2
0
0
0
0
1
2
0
0
0
2
0
0
2
2
0
3
0
0
0
1
1
0
0
0
0
0
2
2
0
0
2
0
3
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
1
2
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
1
0
2
0
3
2
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
2
1
1
1
0
2
0
0
1
0
1
0
0
0
1
2
0
0
0
1
1
0
2
0
0
0
2
0
0
2
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
2
0
1
0
2
2
1
0
1
1
2
2
0
0
0
1
0
0
1
0
0
0
0
2
0
0
1
0
0
0
1
1
0
2
1
3
0
0
0
2
0
1
2
0
0
0
0
0
2
0
0
1
0
0
0
2
2
1
2
1
0
1
0
2
0
0
0
0
0
2
0
2
0
0
0
0
1
1
0
0
1
0
0
2
2
0
1
0
0
1
0
0
2
0
1
0
4
0
0
0
2
1
0
0
0
1
0
0
2
0
2
0
2
0
0
0
0
0
1
0
2
0
0
0
3
0
0
1
2
0
0
3
0
0
0
0
2
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
2
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
1
0
1
1
0
2
2
0
0
0
0
1
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
1
0
2
0
2
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
3
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
2
2
1
1
0
0
0
0
1
0
1
3
0
2
0
0
0
0
0
0
2
0
2
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
1
1
0
0
0
2
2
1
0
3
2
2
0
0
0
0
1
0
0
2
0
0
0
2
1
0
0
1
1
1
3
0
0
0
2
0
1
1
0
0
2
2
0
0
2
2
0
0
0
0
2
1
0
0
0
0
0
3
0
2
0
2
1
0
0
0
0
0
0
2
0
0
2
1
2
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
3
2
0
2
0
1
0
1
0
0
0
2
0
0
0
1
0
0
1
0
1
0
0
3
2
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
2
0
0
0
1
0
0
2
2
1
1
0
0
0
2
0
0
0
0
0
1
0
0
0
1
1
2
1
1
0
0
1
1
0
0
3
0
0
0
0
1
1
0
2
1
0
0
3
0
0
0
1
2
1
1
0
0
0
0
0
0
2
0
0
1
0
2
0
1
0
0
0
2
0
1
0
0
0
0
2
1
0
2
2
3
0
1
0
1
0
0
1
1
0
0
0
0
0
1
2
0
0
1
0
1
0
2
3
1
0
0
0
2
0
0
0
0
0
2
0
2
1
0
2
2
2
0
2
0
0
0
0
1
0
0
1
1
0
1
0
0
3
0
0
0
0
0
0
2
0
0
1
0
1
0
0
1
1
2
2
1
0
1
1
0
1
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
1
1
0
0
1
1
0
0
0
0
2
0
1
0
2
1
0
2
1
0
0
0
0
0
3
3
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
2
0
0
0
0
1
0
0
2
0
0
0
1
0
3
0
0
1
0
2
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
1
0
0
2
0
0
0
1
1
0
0
0
0
0
3
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
2
0
0
3
2
1
0
2
1
0
1
0
0
0
1
0
0
1
2
1
0
0
1
0
4
2
1
0
2
2
0
0
0
1
1
2
0
1
1
0
0
1
1
0
1
0
2
0
1
2
1
1
0
0
0
1
1
0
0
0
0
1
0
1
0
1
1
0
0
1
0
0
0
0
0
1
2
0
0
0
1
0
0
0
2
2
0
0
1
1
0
0
0
1
0
1
1
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
10
0
0
0
3
1
1
0
1
1
0
0
0
1
0
0
0
1
0
0
1
0
2
0
1
2
0
0
0
2
0
0
2
0
2
0
0
1
0
0
1
1
0
0
1
1
0
0
0
0
1
2
0
1
1
1
0
0
1
0
0
2
0
1
0
1
0
2
0
2
0
1
1
2
2
0
0
2
1
0
0
0
0
0
2
2
2
0
1
0
1
0
0
0
2
0
0
0
0
0
1
0
2
2
0
0
0
2
0
1
0
0
0
3
0
0
0
1
0
0
0
0
0
2
0
2
1
0
0
2
0
0
0
1
2
0
0
1
0
2
0
2
1
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
2
0
1
2
0
2
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
2
0
0
0
3
0
2
0
2
0
1
0
0
1
0
0
0
6
0
1
0
2
3
0
0
2
0
0
0
1
2
0
0
0
1
0
1
1
1
0
0
0
0
2
0
0
0
1
2
1
2
0
1
0
1
2
1
0
2
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
1
1
0
1
0
2
0
0
1
0
0
1
0
2
0
0
2
1
0
0
0
0
1
0
1
0
2
0
0
0
1
0
0
0
0
1
1
6
1
2
0
1
0
0
0
0
0
2
1
1
0
1
0
0
0
1
1
2
1
2
2
0
0
0
0
0
0
0
0
3
0
0
2
0
1
0
0
2
2
1
0
2
0
0
0
0
0
0
2
1
0
2
0
1
0
1
2
0
0
0
1
2
0
2
2
0
2
1
1
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
1
2
0
0
0
2
0
0
2
0
2
2
0
2
0
0
0
1
3
0
0
0
2
1
1
0
2
1
1
0
0
0
0
1
0
2
1
1
0
1
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
1
0
0
3
1
1
2
0
1
2
0
0
0
0
3
3
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
2
1
0
0
0
3
1
0
1
2
0
4
0
2
1
1
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
3
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
2
2
0
1
0
0
0
0
2
0
1
0
0
3
0
2
0
0
0
1
0
0
0
2
0
1
0
0
0
2
0
1
1
0
0
2
0
2
1
0
1
6
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
3
2
2
0
2
2
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
1
1
0
1
0
2
0
0
1
1
1
0
0
2
0
0
1
1
0
0
0
0
0
0
0
1
1
0
1
0
2
1
3
0
2
1
0
0
2
0
0
7
0
0
2
0
1
2
1
1
0
0
0
0
1
1
0
0
0
2
1
1
2
0
2
0
1
0
0
2
0
0
0
0
0
2
1
0
1
1
1
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
1
0
0
2
0
0
0
3
1
0
3
1
0
0
2
0
0
0
0
0
1
0
0
0
3
1
0
0
0
0
0
2
0
0
2
0
0
0
2
1
0
0
0
4
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
2
0
0
2
0
0
0
2
3
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
2
1
0
0
0
2
0
0
1
1
0
0
0
0
1
0
0
3
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
1
1
2
0
0
0
1
0
0
2
0
1
0
0
3
2
0
0
0
1
0
0
0
0
2
2
8
2
1
2
1
1
0
0
0
0
0
2
2
0
1
0
0
0
1
1
0
1
1
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
2
0
0
0
1
1
0
0
2
1
0
2
0
0
0
0
2
0
1
0
1
0
0
2
2
2
0
0
0
2
0
0
0
1
1
1
2
3
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
2
0
0
0
0
2
0
2
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
2
0
2
1
1
2
2
0
1
2
0
0
0
1
0
0
0
0
1
0
0
2
2
1
0
3
1
0
0
1
0
0
2
1
0
1
0
0
0
2
2
1
0
2
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
2
2
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
7
2
0
0
0
0
2
2
0
0
0
0
0
3
0
2
0
1
0
0
2
0
0
0
2
1
0
0
2
0
1
2
0
3
2
0
2
0
0
0
0
1
0
0
2
0
0
0
1
1
0
0
1
2
0
1
2
0
1
0
0
1
1
1
0
1
0
0
0
2
0
0
0
0
0
1
0
2
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
2
2
1
0
0
0
2
0
0
0
0
0
0
2
0
0
3
0
0
0
0
1
0
1
2
1
0
0
2
0
0
0
0
0
0
1
1
0
0
2
4
0
3
0
0
1
0
0
2
0
0
2
1
1
0
1
0
1
0
0
0
0
2
2
1
0
0
0
2
0
5
0
1
0
2
0
2
0
0
2
0
0
0
1
0
1
1
2
0
0
2
1
0
0
2
0
0
0
0
0
2
0
0
4
0
1
0
2
0
0
0
1
0
1
0
0
0
1
0
0
2
0
0
0
0
1
0
0
3
2
2
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
3
0
2
0
0
0
0
0
0
3
1
0
2
0
1
0
2
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
3
1
2
0
1
2
0
1
0
0
0
2
0
0
0
1
0
2
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
3
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
2
0
3
0
2
0
1
0
4
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
1
0
0
1
0
0
0
2
2
0
4
0
0
0
0
0
2
2
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
3
1
1
2
0
0
1
2
2
2
0
0
0
0
0
0
1
0
0
0
2
1
0
2
0
0
0
0
1
0
2
0
2
0
2
0
0
0
0
2
3
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
3
0
0
0
0
0
0
0
2
2
0
2
2
2
0
2
2
1
0
2
0
6
0
0
0
1
0
1
2
0
0
0
2
0
0
0
1
0
0
0
1
0
2
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
1
2
1
0
5
0
2
0
2
0
0
2
0
1
0
0
1
0
0
0
1
0
0
0
0
0
2
1
0
1
3
1
1
0
0
1
0
0
0
1
2
0
0
0
0
0
0
1
1
0
2
2
0
0
2
0
0
0
2
0
0
0
1
0
0
0
1
1
1
1
0
2
0
1
0
0
2
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
1
1
0
0
1
0
1
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
2
0
2
0
0
0
1
1
0
1
1
1
0
2
0
0
2
1
2
1
2
1
2
0
0
0
2
0
0
1
0
1
0
1
0
2
2
2
1
0
0
0
3
1
0
0
0
1
1
0
2
0
1
1
2
1
0
0
0
0
0
1
2
2
2
0
0
3
1
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
1
4
1
0
1
2
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
1
0
0
0
0
1
0
0
2
0
0
0
1
0
2
0
0
1
0
0
0
1
0
0
1
0
0
1
2
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
2
0
0
0
0
1
0
0
2
2
1
1
0
1
0
1
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
2
1
0
1
2
0
2
1
1
0
1
0
0
0
1
0
1
1
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
2
2
0
0
0
1
0
1
1
3
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
3
2
0
0
0
0
1
1
0
0
2
0
0
2
0
1
0
0
2
0
29
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
2
0
2
1
0
0
0
0
2
0
1
0
2
0
0
0
0
0
1
2
0
1
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
2
0
0
1
2
1
2
0
0
0
1
0
0
2
2
1
1
0
1
0
0
0
0
0
2
1
0
1
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
1
3
3
2
0
1
1
0
2
0
2
0
1
2
1
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
1
1
2
2
0
0
0
2
0
1
2
1
1
2
0
3
0
0
0
2
0
0
1
0
2
0
1
0
8
2
0
1
0
1
0
1
0
1
1
0
2
0
0
0
0
2
0
0
0
2
0
1
0
2
0
1
1
2
0
1
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
2
2
1
1
2
3
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
3
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
2
0
0
2
1
0
1
0
0
0
0
0
1
2
0
2
0
0
2
0
1
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
2
0
0
2
0
0
2
0
0
1
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
1
0
0
0
1
0
0
1
2
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
2
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
1
1
1
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
3
0
1
0
0
0
1
2
4
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
1
0
0
0
2
0
0
0
2
0
1
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
1
2
3
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
2
1
0
1
2
0
0
0
0
3
0
0
0
0
1
2
0
0
0
0
0
1
2
0
0
0
0
1
0
2
3
6
0
0
0
2
0
1
3
0
1
2
1
1
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
3
0
0
0
0
0
2
1
0
0
2
0
2
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
1
2
0
0
0
0
2
0
0
2
4
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
2
0
0
1
0
0
0
2
2
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
4
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
2
2
0
1
0
1
0
1
2
0
0
2
2
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
2
1
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
1
1
1
0
0
1
0
0
0
0
2
0
0
2
0
1
0
1
0
0
0
4
0
0
1
1
0
0
0
3
0
0
1
0
0
1
0
0
0
2
0
1
0
0
1
0
1
2
0
0
0
1
0
2
0
2
1
0
0
0
0
2
2
1
0
0
0
0
2
2
1
0
0
0
2
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
2
1
2
0
0
0
0
0
0
1
0
0
2
1
0
0
0
1
0
1
2
2
1
2
0
0
1
0
0
1
1
2
1
2
0
0
0
1
0
0
0
0
0
0
3
2
0
2
0
0
0
1
1
4
0
1
1
1
0
0
2
0
4
0
0
0
2
5
0
0
0
0
0
1
0
3
1
0
2
2
1
0
0
1
1
0
0
2
0
1
0
1
0
0
0
2
2
2
0
1
0
0
0
2
1
2
1
0
0
0
2
2
2
1
0
0
0
1
0
0
0
1
0
2
2
0
0
2
0
0
0
1
0
1
0
0
2
1
2
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
1
0
0
1
0
0
2
2
0
0
0
0
0
0
2
2
1
2
0
0
0
0
0
1
2
0
0
0
0
3
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
2
0
3
1
0
0
0
0
0
0
2
0
0
0
4
0
3
2
0
0
0
0
0
1
0
2
1
0
1
0
0
0
0
1
0
2
0
0
0
1
2
0
0
0
0
3
2
0
2
2
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
2
0
1
0
1
0
0
0
2
0
0
0
2
0
0
1
0
0
2
0
1
0
0
0
2
0
1
0
0
0
1
0
2
2
3
0
2
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
1
1
1
1
2
0
1
2
0
0
1
0
0
2
0
1
0
3
2
0
0
1
0
0
0
3
0
0
0
0
2
0
1
0
0
1
0
0
1
1
0
2
0
1
0
0
0
0
0
0
0
3
0
0
2
0
0
3
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
2
1
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
2
2
4
0
2
0
0
0
1
3
1
0
1
1
7
0
1
0
0
0
0
0
0
0
2
0
0
0
2
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
2
0
1
0
1
0
0
2
0
2
0
0
2
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
1
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
2
0
1
0
0
3
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
2
0
0
0
0
1
2
0
0
2
2
0
0
0
2
2
0
0
0
0
0
1
0
2
0
0
0
0
6
0
0
1
1
0
0
0
0
4
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
1
2
0
2
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
2
1
1
1
0
0
1
0
0
2
0
3
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
3
2
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
3
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
1
0
1
0
0
0
2
2
0
0
0
0
1
0
0
5
0
0
0
0
2
0
0
0
0
1
1
1
0
0
0
1
2
0
0
0
1
0
0
0
0
1
0
2
0
0
0
2
0
0
2
1
1
0
0
1
2
2
0
2
0
0
1
0
0
0
0
0
2
2
0
2
0
2
0
0
0
1
2
0
1
1
0
2
1
0
0
1
0
0
1
1
2
0
0
2
0
1
0
0
0
0
0
1
2
1
2
0
2
1
0
2
0
2
0
0
0
2
0
0
1
3
2
0
0
0
0
0
0
0
0
2
0
0
0
2
2
1
1
0
0
0
0
0
0
0
2
1
2
2
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
2
0
0
0
0
2
1
1
2
0
0
1
2
2
1
1
0
0
0
2
0
0
2
2
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
2
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
1
0
0
0
3
0
0
1
0
2
2
0
0
0
0
1
0
1
0
1
1
0
0
0
1
0
0
0
1
0
0
1
0
2
0
0
0
3
2
0
2
0
0
0
0
0
0
2
2
0
1
0
0
2
0
0
0
0
0
1
1
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
1
2
0
2
0
2
0
1
1
0
0
1
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
3
0
2
0
2
0
0
0
0
2
0
1
1
2
0
0
0
0
0
0
0
1
0
2
3
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
1
1
0
0
2
0
2
0
0
1
0
3
0
0
0
0
0
2
1
0
0
2
1
0
4
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
2
0
2
1
0
0
0
2
0
0
1
0
0
0
0
0
0
2
2
2
2
2
0
0
0
2
0
0
1
0
0
0
5
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
4
0
1
0
1
1
0
0
2
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
2
0
0
0
0
2
1
2
0
0
0
0
0
2
2
1
0
1
1
0
2
0
0
1
0
0
0
0
0
0
0
2
0
1
1
1
1
3
0
0
0
0
2
0
0
1
0
2
0
0
2
0
1
0
1
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
3
2
0
0
2
0
1
0
0
2
0
0
2
0
0
0
0
0
0
2
0
1
0
0
2
0
0
1
2
0
0
0
1
0
0
0
1
0
0
1
0
2
0
0
2
0
0
0
1
1
0
0
1
0
1
0
2
0
1
0
1
2
0
0
1
0
0
0
0
0
0
1
0
0
1
1
1
0
1
0
2
0
0
0
0
0
2
1
0
0
0
2
0
1
0
0
1
0
0
2
0
1
0
1
0
2
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
1
0
0
0
2
0
3
2
0
2
0
1
1
3
0
2
1
0
2
0
0
3
0
0
0
0
1
1
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
3
2
3
1
1
0
0
2
0
3
0
1
0
0
4
0
1
0
0
0
0
1
2
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
2
2
1
0
3
0
0
1
0
0
2
2
0
0
1
2
0
0
0
2
0
0
1
2
0
1
2
0
0
0
0
0
3
0
2
2
2
0
0
0
0
2
2
0
1
0
0
0
0
0
2
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
1
0
1
1
2
2
0
0
0
3
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
3
2
6
0
1
2
0
0
0
0
0
2
1
0
2
0
1
1
2
0
1
0
1
0
0
0
0
0
0
0
1
1
1
1
1
2
0
2
0
0
1
2
1
3
1
0
0
0
2
1
0
1
2
0
4
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
3
1
2
0
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
1
1
0
6
0
1
0
0
1
0
0
1
2
0
0
2
1
0
0
1
0
1
1
1
0
0
0
0
2
0
0
0
4
0
0
1
1
0
1
0
0
1
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
7
1
0
0
1
1
2
0
0
1
1
0
2
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
2
0
0
0
4
2
0
1
0
0
0
0
0
2
0
0
1
0
2
0
1
0
0
0
0
0
1
0
0
0
0
3
1
0
0
4
0
0
2
2
0
1
0
0
0
5
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
2
0
0
2
0
0
0
1
0
1
1
0
0
1
1
0
0
2
0
0
1
1
0
0
0
2
0
0
0
0
0
1
2
1
1
0
2
0
0
0
0
0
3
0
0
0
0
0
0
1
0
3
0
2
2
0
0
2
0
0
1
0
0
2
1
2
2
0
0
0
0
0
0
1
0
0
0
0
5
0
0
2
3
0
0
0
0
0
0
0
2
0
2
2
2
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
1
1
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
1
0
0
2
1
0
1
0
1
2
2
0
1
1
0
0
0
2
1
0
0
0
0
1
0
4
4
0
1
1
0
2
0
0
2
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
2
0
0
0
1
0
1
0
1
0
0
0
0
2
0
0
0
2
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
5
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
1
0
0
2
2
1
0
1
2
1
2
1
1
0
0
0
0
0
1
1
2
0
0
0
1
0
0
1
0
0
0
2
0
2
0
0
1
1
0
0
0
0
4
0
2
0
3
1
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
2
0
2
0
1
2
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
1
1
2
2
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
2
2
0
0
0
0
1
3
2
0
2
1
2
0
1
0
0
0
0
0
0
0
1
0
2
0
2
2
0
0
0
0
0
1
1
2
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
1
0
1
2
0
0
0
1
1
2
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
1
4
0
0
2
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
1
0
2
0
0
1
0
2
0
0
0
0
2
0
3
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
1
4
0
0
0
0
1
0
1
0
0
4
2
0
2
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
1
0
0
1
1
2
2
1
0
0
0
0
0
1
1
1
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
3
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
1
1
0
0
0
2
0
0
1
0
0
0
3
0
0
1
0
0
0
0
2
0
0
0
1
0
1
2
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
2
1
1
0
0
0
0
0
4
0
0
0
0
3
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
10
0
1
1
0
1
0
0
2
5
2
1
0
0
0
1
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
1
0
2
0
1
0
1
2
0
0
0
0
0
3
0
2
0
0
1
0
0
0
0
0
0
0
0
9
0
0
0
1
0
0
0
2
1
0
1
0
0
0
0
1
3
0
1
0
0
1
0
2
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
2
0
0
0
1
1
2
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
2
2
0
0
0
0
2
0
0
0
0
2
0
0
0
1
2
0
0
3
1
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
1
2
0
2
0
0
2
0
3
0
2
0
4
0
1
1
1
0
0
0
3
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
1
0
1
1
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
1
0
1
1
0
0
0
2
1
0
0
1
0
2
0
0
2
0
1
1
0
3
1
2
0
0
0
2
0
0
2
0
2
0
1
2
1
1
0
0
1
0
0
0
0
0
2
0
4
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
1
2
0
0
0
0
0
2
0
0
2
0
2
1
0
1
2
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
2
2
0
1
0
0
0
1
0
5
0
0
0
0
0
0
0
1
1
0
1
1
1
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
2
1
1
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
1
1
2
0
1
1
0
0
0
3
3
0
0
2
0
2
2
0
0
2
0
1
1
0
0
0
1
0
0
0
2
1
0
0
0
3
2
0
0
0
0
0
0
1
1
0
2
0
2
0
0
0
4
0
2
0
1
0
0
2
0
2
2
2
0
0
2
0
0
0
2
0
0
2
0
1
1
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
1
1
1
1
0
0
0
2
0
0
0
1
1
0
1
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
3
0
1
0
0
1
0
0
1
4
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
2
0
1
1
2
2
0
1
0
2
2
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
2
2
2
0
1
0
0
2
0
0
0
1
0
0
0
0
0
1
1
0
0
10
2
0
2
0
0
0
0
0
0
0
2
0
2
0
0
2
2
1
0
1
0
0
0
0
2
0
1
1
0
2
2
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
1
0
0
0
1
1
0
2
2
0
0
1
0
0
0
0
0
0
1
1
0
1
0
2
2
0
2
1
1
2
1
0
0
2
1
2
0
0
0
0
0
2
1
0
0
2
0
1
1
0
2
0
0
2
1
0
0
1
0
0
2
0
2
0
2
0
0
0
2
0
0
0
0
0
1
0
2
2
1
0
1
0
2
1
0
2
0
0
0
1
1
2
1
2
1
0
0
0
0
0
0
2
1
0
0
0
2
1
0
1
2
0
1
1
0
1
0
0
2
1
0
0
1
0
0
1
2
0
1
0
0
0
2
0
0
0
2
1
0
0
0
7
1
3
5
0
0
1
1
0
0
0
0
0
0
1
5
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
3
2
0
2
0
0
0
1
1
2
4
0
0
0
0
0
2
2
0
2
0
0
0
1
0
0
0
0
1
0
0
2
0
2
0
0
0
1
0
1
0
0
2
0
0
2
0
0
1
0
2
2
1
0
0
0
0
2
1
0
0
0
1
1
0
0
1
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
2
0
1
0
0
0
0
0
1
0
1
0
1
1
0
1
0
1
1
0
2
0
1
0
1
0
0
2
2
0
1
1
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
2
1
0
2
2
1
0
2
0
2
2
0
0
1
0
1
1
2
2
0
2
0
0
0
0
0
2
2
1
1
1
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
2
1
0
2
0
0
0
0
2
3
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
2
1
0
0
1
0
0
2
0
2
2
0
2
2
0
1
2
0
0
0
0
0
2
2
3
1
0
1
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
1
1
2
0
0
1
0
0
0
0
1
0
2
0
2
0
0
2
0
0
0
0
0
2
5
0
0
0
0
0
1
0
0
2
2
1
0
1
0
0
0
1
3
0
2
2
0
2
0
1
2
2
0
0
0
0
0
0
0
2
0
0
2
2
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
2
1
2
3
0
0
0
0
2
0
0
0
0
0
2
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
1
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
1
0
2
0
2
2
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
5
0
0
0
0
7
0
3
0
1
1
1
0
0
2
2
2
0
0
0
0
0
1
0
0
2
0
3
0
2
2
0
0
0
2
1
2
0
2
2
2
2
0
0
0
1
0
0
0
1
4
2
0
0
2
0
1
0
0
1
2
1
0
0
0
0
1
2
1
0
0
1
0
0
2
0
0
2
2
0
0
0
1
0
0
0
2
1
2
1
1
1
0
0
0
0
2
0
2
0
0
0
1
1
0
1
0
2
2
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
1
2
0
0
0
0
0
1
0
6
0
0
1
0
0
0
1
2
0
1
1
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
2
0
0
0
0
0
0
1
1
0
1
0
1
0
1
0
0
0
2
2
0
2
0
0
2
0
0
1
0
0
3
5
2
0
2
1
0
0
0
2
0
0
1
0
1
0
0
2
0
0
0
2
2
0
0
0
3
1
2
2
0
0
0
1
0
2
0
0
0
0
0
0
1
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
2
2
1
0
1
0
1
1
2
2
0
2
0
1
0
0
0
3
0
0
0
0
0
2
1
0
0
1
1
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
2
1
3
0
0
0
0
0
0
0
0
1
4
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
2
2
1
0
3
2
0
3
2
1
1
0
0
2
0
0
1
2
0
0
1
0
0
1
0
0
2
0
0
1
0
0
0
1
2
1
3
0
0
0
1
0
2
0
0
0
0
2
0
0
1
0
0
1
2
0
0
0
0
2
0
1
0
2
0
2
1
0
0
0
0
0
0
1
1
0
2
0
0
1
0
1
0
0
0
2
0
2
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
1
0
0
1
1
2
0
2
0
1
1
0
3
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
1
0
1
3
0
0
0
1
1
1
0
0
0
0
0
0
1
2
2
0
0
1
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
3
1
1
0
1
0
2
2
0
2
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
1
0
0
0
0
0
1
2
0
2
1
3
2
2
1
1
1
0
1
0
0
2
1
2
0
0
1
0
3
0
1
0
3
0
0
1
0
0
1
0
0
4
0
1
0
0
0
0
0
1
1
2
1
2
0
0
0
2
0
1
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
2
2
1
0
0
0
0
0
0
0
2
0
0
1
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
1
2
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
3
1
0
0
0
1
1
0
0
1
1
0
0
0
0
0
2
0
1
0
0
0
1
1
4
2
1
0
0
1
0
0
0
2
0
1
0
0
0
0
2
1
0
0
0
0
0
0
2
0
2
0
2
0
2
1
0
2
3
1
1
0
0
0
0
0
1
1
0
0
2
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
2
1
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
2
2
2
2
2
0
0
1
1
0
0
0
1
1
0
0
0
1
2
0
1
0
0
0
1
1
0
2
1
0
4
0
2
0
0
0
3
0
1
0
1
0
0
0
0
0
0
0
1
0
0
2
0
1
2
0
0
0
0
1
0
0
0
2
2
1
0
0
1
0
0
1
0
0
2
0
2
0
1
3
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
1
0
0
0
0
0
2
1
1
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
1
2
1
0
0
1
2
0
0
0
1
0
0
0
0
2
0
0
2
2
1
0
1
0
0
2
1
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
1
1
0
0
0
0
1
0
2
0
1
2
2
0
0
0
1
0
1
1
0
1
0
1
0
0
0
3
0
1
0
0
0
0
0
0
0
2
0
0
1
2
2
0
0
1
0
2
0
0
0
1
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
2
1
0
0
0
0
0
0
0
1
2
2
2
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
3
2
1
1
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
5
0
4
1
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
2
0
3
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
1
2
0
2
0
2
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
2
3
0
0
1
1
0
2
0
0
0
1
0
2
0
0
0
2
0
0
1
1
2
1
0
0
0
0
1
2
1
0
1
2
0
0
2
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
1
1
1
1
1
0
1
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
2
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
2
2
2
0
0
0
1
1
0
0
1
0
0
1
0
0
1
0
1
2
0
1
2
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
2
0
0
1
0
0
0
1
0
0
4
0
0
2
0
2
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
1
2
1
0
0
0
1
4
0
0
0
1
0
0
1
1
0
0
2
1
2
2
0
0
0
1
2
0
0
2
0
0
2
2
2
0
2
0
0
0
3
0
0
0
0
2
2
0
0
1
2
0
0
0
0
1
2
0
0
0
0
0
2
1
1
0
0
0
0
2
0
0
2
0
2
1
0
0
2
1
0
0
0
2
2
0
1
1
2
0
2
1
0
1
0
0
0
0
1
0
1
1
2
0
0
0
0
1
1
3
2
0
2
0
0
0
0
2
0
0
1
1
1
1
0
0
0
2
2
0
2
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
2
2
0
0
0
2
1
0
2
2
0
2
1
0
1
1
0
1
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
2
1
0
0
0
0
2
2
0
0
1
0
0
1
2
0
0
1
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
1
1
2
0
0
0
0
2
0
1
1
1
1
0
0
0
1
0
1
0
0
0
0
0
1
0
2
1
0
1
0
0
0
0
1
1
0
1
0
1
2
1
0
0
1
0
0
0
2
2
0
1
2
1
1
1
1
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
1
1
1
1
0
1
0
1
0
0
0
0
1
2
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
1
2
1
0
0
0
1
0
2
1
2
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
3
2
0
1
1
0
0
0
2
1
1
1
2
0
0
0
0
0
2
0
1
0
2
0
1
0
1
1
0
1
0
2
0
7
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
1
2
0
2
1
0
0
0
0
0
2
0
0
0
1
1
2
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
1
1
0
1
0
1
0
0
1
2
0
0
0
0
2
0
2
1
0
0
1
2
0
0
2
2
1
0
0
0
0
2
0
0
1
3
0
2
1
1
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
3
0
0
0
1
0
1
1
0
0
2
0
1
0
0
2
0
1
0
0
0
0
0
3
2
0
0
0
0
1
2
0
0
0
2
0
0
0
1
0
0
0
0
2
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
2
1
0
2
2
2
0
1
0
0
0
0
0
2
2
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
2
0
0
0
3
0
0
2
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
2
0
2
4
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
2
0
1
0
3
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
2
1
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
4
2
0
0
2
0
3
0
0
0
2
0
1
1
1
0
0
1
2
0
0
0
1
0
0
0
1
2
0
0
0
2
0
1
0
0
1
0
2
1
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
4
0
3
0
2
1
0
0
0
2
0
0
0
0
0
2
0
0
2
2
0
0
0
1
5
0
0
0
0
1
1
0
0
1
1
0
0
1
0
2
0
0
2
1
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
2
2
2
3
2
0
0
0
1
0
2
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
1
1
0
0
0
2
1
2
0
1
2
2
0
0
2
1
0
0
2
1
0
0
0
1
0
0
0
2
0
2
1
1
0
0
1
0
2
0
2
2
0
0
1
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
1
0
2
0
0
2
0
0
0
3
0
3
3
0
1
0
0
1
1
2
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
2
2
1
0
0
1
2
0
0
0
3
0
0
2
0
0
1
0
0
0
0
0
2
1
1
1
0
2
2
2
1
2
1
0
1
0
0
1
0
0
0
0
0
0
2
1
1
0
0
0
2
0
0
1
4
0
1
0
0
2
1
1
0
2
2
0
4
0
0
0
2
0
0
0
2
2
4
0
0
0
0
2
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
1
2
1
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
1
0
2
0
0
1
0
2
0
0
2
1
0
0
0
0
0
0
2
0
2
1
0
0
0
2
0
0
2
0
0
0
11
0
0
1
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
1
0
2
2
2
2
0
0
1
0
0
1
0
0
8
0
0
0
9
0
2
0
0
2
0
1
2
0
0
2
2
0
0
0
2
2
1
0
1
0
0
0
2
2
0
0
0
0
0
0
1
0
1
2
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
2
2
0
0
1
0
2
0
0
0
0
0
0
0
4
2
0
0
0
0
0
1
1
0
0
2
0
2
2
0
0
1
5
0
0
0
0
2
0
0
1
1
0
1
0
2
0
0
2
2
0
0
0
0
3
0
0
2
0
2
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
3
0
0
1
0
0
0
0
0
1
1
0
0
0
2
1
0
0
0
0
1
0
0
1
2
2
0
0
0
0
0
1
4
0
0
1
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
1
0
2
0
1
1
0
0
0
1
0
2
1
2
0
0
2
2
0
3
0
2
1
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
2
0
1
1
0
1
0
0
3
1
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
6
1
0
0
1
1
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
2
2
0
0
2
1
2
0
1
0
1
0
0
0
0
0
1
2
0
0
2
0
1
0
0
0
0
0
0
1
2
2
2
0
2
0
2
1
0
0
1
0
0
0
0
2
0
0
0
2
1
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
1
2
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
1
2
0
0
0
1
1
0
0
0
0
0
2
1
0
2
0
2
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
2
0
1
0
0
0
1
0
0
1
0
2
0
0
2
0
2
0
0
2
0
0
0
2
0
0
0
2
0
0
0
1
0
0
1
2
0
0
1
0
0
0
2
0
0
2
2
1
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
2
0
2
1
0
1
2
2
0
0
0
0
3
1
2
0
1
0
2
0
1
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
2
0
0
1
2
0
0
2
2
1
2
0
0
1
0
0
0
0
1
0
1
0
2
1
2
0
0
1
0
2
0
0
0
1
0
0
0
0
0
2
0
1
0
3
0
0
0
2
0
1
0
2
0
0
1
2
0
0
0
3
2
0
0
1
0
1
3
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
3
0
2
1
0
0
0
0
2
0
0
0
2
0
0
0
1
2
1
0
1
0
1
0
0
2
1
0
4
0
1
2
0
0
2
1
4
0
2
0
1
0
0
2
2
3
0
0
0
0
0
1
0
0
1
0
0
0
0
3
0
2
0
2
0
2
0
0
0
1
0
0
0
0
0
0
1
2
2
0
2
2
1
1
0
2
0
1
1
0
0
0
2
0
0
0
1
1
0
2
0
1
2
1
0
0
1
0
0
2
1
0
0
1
0
0
2
1
1
0
0
0
1
0
0
0
2
3
0
0
1
1
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
2
0
3
0
0
1
1
0
0
0
2
0
0
1
0
0
2
0
0
0
2
0
1
1
0
0
0
1
2
0
0
0
0
0
1
1
1
0
0
2
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
2
2
1
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
2
2
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
1
0
0
2
0
1
0
2
0
0
0
0
0
0
0
2
1
1
0
4
2
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
1
0
1
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
1
2
0
0
1
0
1
2
0
0
1
0
1
2
1
0
0
0
0
1
1
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
3
1
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
2
2
0
2
0
0
0
0
0
1
0
3
0
0
1
0
0
2
0
0
0
0
0
0
2
2
2
0
0
1
0
0
2
0
2
0
0
0
0
2
1
0
1
0
1
0
2
2
0
0
0
0
1
2
6
3
2
0
0
0
0
2
4
0
0
0
2
0
0
0
0
2
0
0
1
2
0
0
0
0
2
0
1
0
0
0
1
2
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
1
0
1
2
0
0
0
0
2
0
0
0
0
0
1
1
2
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
2
1
0
2
0
0
3
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
2
0
0
0
0
2
1
0
1
0
0
0
0
1
0
0
0
0
1
3
0
2
0
0
2
0
1
0
0
0
2
0
1
0
2
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
1
1
1
0
2
0
2
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
1
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
1
1
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
1
1
2
1
2
0
0
1
0
0
1
0
0
2
0
0
0
0
1
2
1
0
0
0
2
2
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
1
0
2
2
2
0
0
0
0
0
0
0
2
1
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
2
1
0
2
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
1
0
2
1
0
0
0
1
0
1
1
0
0
0
0
1
0
1
1
0
2
0
0
2
1
2
2
0
0
1
3
2
0
0
0
0
0
2
1
0
1
0
0
0
0
2
0
0
2
0
2
0
0
0
1
0
1
0
0
1
0
0
1
0
0
1
3
0
0
3
1
0
0
0
0
0
5
0
0
0
0
2
0
0
2
1
0
2
0
0
2
0
1
0
0
0
0
2
1
1
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
2
2
1
2
1
0
0
0
7
0
1
0
0
0
0
0
0
2
2
0
2
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
1
0
0
2
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
2
0
2
0
1
2
0
0
2
1
0
0
2
0
0
1
0
0
2
0
1
0
0
0
0
2
0
0
0
0
2
2
0
6
0
1
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
2
2
2
2
1
0
0
0
0
0
0
2
0
2
0
2
0
0
2
2
0
0
2
0
2
0
0
3
0
2
0
0
1
1
0
0
1
0
2
4
0
0
1
0
0
0
0
0
2
0
0
1
2
0
2
2
1
0
1
0
0
1
0
0
0
2
2
0
0
1
0
0
1
0
1
0
0
0
1
0
1
0
0
2
0
1
0
0
0
0
0
0
2
2
3
0
0
2
0
1
0
1
1
0
1
0
2
0
2
1
3
0
2
0
0
2
0
2
0
0
2
1
0
2
1
1
0
0
1
0
2
0
2
0
0
2
0
0
2
0
0
1
0
0
1
3
1
0
1
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
2
0
1
2
0
0
2
0
0
0
0
2
0
0
1
0
0
2
1
0
3
0
0
1
0
0
0
0
0
3
1
2
0
2
2
0
0
0
0
0
0
1
0
2
0
1
0
0
0
1
2
0
0
2
1
2
0
0
0
1
0
0
0
0
1
1
0
1
0
0
2
2
0
0
0
2
2
0
1
0
0
0
0
0
2
0
0
5
1
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
1
1
0
0
2
1
0
2
0
0
2
0
3
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
4
0
2
0
1
0
0
1
2
1
1
1
1
0
0
2
0
0
1
0
0
0
0
0
2
2
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
2
0
1
0
0
0
0
1
1
0
0
2
1
0
0
0
0
1
0
0
0
1
0
2
1
2
0
2
0
2
0
2
0
0
3
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
1
2
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
2
0
2
0
1
0
0
1
0
2
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
1
1
1
1
0
0
0
1
2
1
3
2
0
0
0
0
1
0
1
1
0
0
0
0
2
2
0
0
0
0
1
0
1
1
1
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
2
1
2
0
2
1
2
1
2
0
1
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
2
1
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
1
1
0
1
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
1
0
2
0
2
1
0
0
0
0
1
0
1
0
0
0
1
0
2
0
1
1
0
0
2
3
1
0
0
4
0
0
0
0
0
0
2
2
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
1
0
1
1
0
1
2
0
0
2
1
0
0
0
0
0
1
2
3
0
0
0
2
0
0
0
0
1
0
0
2
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
3
1
0
0
0
0
0
2
1
2
1
0
0
1
0
0
0
0
0
0
2
0
1
1
0
0
0
1
2
0
2
2
2
2
1
2
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
3
1
0
0
0
0
0
1
0
1
1
1
0
1
0
0
0
0
0
0
0
2
0
1
3
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
2
3
1
0
0
2
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
2
0
2
0
1
0
0
0
0
0
0
0
1
0
1
0
0
3
0
2
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
2
0
0
0
0
1
1
0
0
2
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
2
0
0
1
0
1
0
5
0
0
0
2
1
0
0
0
0
0
0
0
0
1
1
0
0
1
5
0
0
3
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
1
2
2
0
2
1
0
0
1
2
0
0
1
0
3
1
0
0
0
1
2
1
1
0
1
1
2
0
0
0
0
0
2
3
0
0
0
0
1
0
0
0
0
2
2
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
3
2
2
0
2
0
0
1
0
0
1
0
0
0
0
2
0
0
2
0
2
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
3
0
1
0
0
1
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
1
1
6
0
0
0
0
0
1
0
0
2
0
0
2
0
2
0
0
1
0
2
0
0
0
0
0
2
0
0
2
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
1
1
1
2
1
0
0
0
1
1
1
0
0
0
0
2
0
0
1
1
3
1
2
1
1
0
0
2
2
0
3
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
2
0
2
0
2
1
0
2
0
2
0
0
2
0
0
0
1
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
1
0
0
2
0
1
0
0
1
3
2
0
2
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
2
0
0
4
0
0
1
0
0
2
0
2
0
0
0
1
0
0
2
0
0
0
0
2
0
1
2
2
0
0
0
2
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
2
2
0
1
0
0
2
2
0
0
1
0
0
0
0
0
1
2
0
1
1
0
2
0
0
0
0
1
0
0
0
2
0
0
1
2
1
0
2
1
0
0
0
0
0
0
0
0
0
0
6
0
0
7
2
1
1
0
0
0
2
2
0
0
0
2
0
0
0
0
0
1
1
1
1
2
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
3
0
2
0
0
1
2
2
0
0
1
0
0
5
0
0
0
0
1
0
1
2
0
0
0
0
2
0
0
0
0
0
2
1
2
0
0
0
1
1
0
0
0
0
0
1
2
5
0
0
0
0
0
0
1
0
0
4
0
2
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
2
1
2
2
0
2
3
1
0
0
0
0
0
0
1
1
1
2
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
1
1
0
0
0
0
4
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
1
2
0
0
0
0
2
0
0
3
0
1
0
0
0
0
0
0
0
0
2
1
2
1
0
0
1
0
0
0
0
0
1
2
2
2
0
0
0
2
0
1
1
0
2
1
2
0
0
0
0
0
1
0
0
2
2
0
0
0
0
2
1
0
0
0
1
0
3
1
0
0
0
0
0
0
0
0
0
3
0
1
0
0
1
0
2
0
0
2
0
0
2
0
0
0
0
0
0
2
0
1
2
1
0
0
0
0
1
2
1
0
0
1
2
0
0
0
2
0
2
0
0
0
1
2
0
1
0
0
2
2
1
2
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
3
0
0
0
1
3
2
3
2
0
2
2
0
0
2
3
0
0
0
2
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
2
2
0
2
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
1
0
0
2
2
0
2
1
0
2
2
0
0
0
2
1
2
0
1
1
0
0
1
0
0
1
0
0
0
3
0
0
0
2
0
0
0
0
0
0
1
2
1
2
0
2
1
0
1
2
0
0
2
0
0
0
0
0
0
1
0
1
0
0
2
2
0
0
0
2
1
0
0
0
1
1
2
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
1
1
0
1
0
2
2
2
1
1
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
2
0
2
0
0
1
2
0
2
0
0
2
2
0
2
0
0
2
2
0
1
3
0
0
0
2
0
0
1
2
0
1
0
0
1
1
1
1
0
0
0
1
0
0
2
1
0
1
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
3
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
4
0
2
2
0
0
0
0
2
0
0
1
0
0
2
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
1
1
2
0
0
1
0
0
0
0
1
0
1
0
0
2
1
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
2
2
1
2
0
0
0
0
2
1
0
0
2
0
0
0
1
0
0
2
0
0
0
3
0
1
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
1
1
2
0
0
0
0
1
1
0
0
0
0
2
0
2
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
2
2
0
1
0
2
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
2
1
2
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
1
0
2
0
0
0
0
2
0
1
1
1
1
0
0
2
1
2
0
0
0
0
1
2
1
0
0
2
2
0
0
0
0
0
0
2
2
1
0
0
1
0
1
2
0
0
6
0
0
2
0
2
0
0
1
1
1
0
1
3
1
0
0
0
2
0
2
0
0
0
0
1
0
0
0
1
0
2
1
0
0
1
0
1
0
0
2
0
2
1
0
0
0
0
0
0
1
2
0
0
0
4
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
1
0
0
0
1
0
1
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
2
0
0
0
2
0
1
2
0
0
1
2
1
0
1
0
0
1
0
1
7
1
1
1
0
1
0
0
0
2
0
1
0
2
0
1
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
2
2
2
0
1
1
0
0
3
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
2
0
0
0
2
0
2
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
2
0
0
2
0
0
0
3
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
2
0
0
1
0
1
0
0
0
0
1
1
2
3
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
1
0
2
0
0
1
0
0
2
0
0
0
0
2
0
1
0
2
0
2
1
0
4
3
1
0
0
0
0
0
0
1
0
2
0
1
0
1
2
2
0
1
0
0
0
2
2
1
0
0
1
0
1
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
2
0
2
0
0
1
0
0
2
0
1
0
0
2
0
0
2
1
2
0
2
1
1
0
1
2
0
1
1
0
2
0
2
0
2
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
2
2
0
2
2
1
0
0
2
0
0
1
0
0
2
0
1
0
1
1
0
0
0
0
1
0
2
1
1
2
2
0
0
2
0
2
1
0
0
1
0
2
1
0
0
2
1
0
2
1
0
0
1
0
0
0
0
0
1
1
0
1
1
2
0
0
1
0
2
1
1
0
0
0
1
0
2
0
2
1
2
0
0
0
2
0
1
0
0
0
0
0
0
1
1
0
2
0
0
1
1
0
1
0
0
1
1
2
5
0
2
1
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
5
0
0
0
9
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
1
1
2
0
0
0
0
2
0
0
1
1
1
0
0
1
2
0
3
1
2
1
1
2
0
4
0
1
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
1
1
2
0
1
2
1
0
0
1
0
1
1
0
0
0
0
0
0
3
0
0
0
0
3
0
0
1
1
0
0
0
0
0
1
1
0
0
2
0
2
1
1
0
0
0
0
1
0
2
0
0
2
1
0
1
0
0
0
0
2
0
1
1
0
0
1
2
0
2
1
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
1
1
2
0
0
1
0
0
0
0
0
2
1
1
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
2
1
1
0
2
0
2
2
0
0
3
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
2
0
1
1
0
0
0
2
0
2
0
0
0
0
1
2
0
0
0
0
0
1
0
1
0
0
0
3
0
0
0
2
1
0
2
3
0
2
0
0
0
0
1
0
0
0
1
1
0
0
1
1
2
0
2
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
1
1
0
1
0
0
0
0
3
0
0
0
1
0
6
0
0
0
0
2
0
0
0
1
0
0
1
0
2
1
2
2
1
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
5
0
0
2
0
2
0
0
0
0
2
1
0
0
0
0
1
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
2
2
1
0
0
0
2
1
2
2
0
1
0
0
0
2
0
0
1
0
0
1
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
2
0
0
1
0
2
1
1
0
2
0
0
0
0
0
0
2
0
0
1
0
0
2
2
0
0
1
0
0
0
0
0
0
2
2
2
0
2
0
0
6
0
0
0
0
2
0
0
2
0
0
2
1
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
2
1
1
0
0
0
0
0
0
0
1
2
0
2
2
0
0
0
1
1
1
0
0
0
2
1
0
1
0
1
0
1
2
2
1
0
0
0
0
1
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
1
0
0
1
2
2
1
1
1
1
1
3
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
1
2
0
1
0
1
0
0
0
0
0
0
0
1
0
0
3
0
0
0
2
0
1
2
2
1
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
1
0
0
2
0
0
0
0
0
2
2
2
0
2
0
0
0
0
3
0
0
0
0
2
0
1
2
0
0
1
0
0
2
0
0
1
0
0
1
3
0
0
0
0
0
2
1
0
0
2
0
1
3
1
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
2
1
0
0
0
0
0
1
0
1
0
0
0
0
2
1
0
1
0
1
1
1
1
0
0
0
0
0
0
2
0
1
0
1
0
2
0
2
0
0
0
2
0
0
0
0
0
1
2
0
2
3
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
2
0
0
2
0
0
1
1
2
0
0
0
1
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
1
2
0
0
0
0
0
1
0
2
0
2
0
1
0
0
1
2
1
0
1
3
0
1
0
3
3
1
2
0
0
0
1
2
0
2
1
0
1
0
1
0
0
0
3
0
0
2
0
0
0
0
0
2
1
0
0
2
0
0
2
3
1
1
0
0
0
0
0
1
0
0
0
0
0
2
2
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
2
1
0
2
2
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
1
0
1
0
1
3
1
2
0
2
0
0
0
2
2
0
0
0
0
0
3
0
1
0
0
1
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
1
0
2
1
0
2
0
0
0
2
0
0
0
0
2
0
2
0
0
0
1
2
1
0
2
1
0
0
0
0
0
2
0
2
0
0
1
0
2
0
4
0
0
0
1
2
1
0
0
0
2
1
0
1
0
0
0
0
2
2
0
0
1
2
2
1
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
1
0
2
1
0
0
0
1
0
2
0
1
2
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
1
2
0
3
0
0
0
0
0
3
1
1
0
0
0
0
4
2
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
1
1
0
0
2
0
1
0
1
2
2
0
0
0
2
2
0
0
1
0
2
0
0
0
2
1
0
0
2
1
1
1
2
0
0
1
1
0
2
0
0
0
2
0
1
0
0
2
0
0
0
1
2
0
0
0
0
2
4
1
1
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
1
0
2
2
1
0
2
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
3
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
3
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
2
1
0
1
0
0
5
0
6
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
1
2
0
0
0
1
1
0
2
1
1
2
2
1
0
0
2
2
2
0
1
2
0
1
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
3
0
0
2
2
0
1
1
1
2
0
0
0
0
2
0
1
2
0
1
0
0
2
2
1
0
0
0
1
0
0
2
2
0
0
1
0
2
0
0
2
0
1
1
0
0
1
0
0
1
2
0
1
1
0
0
0
0
0
4
0
0
0
0
1
2
1
2
0
0
1
0
2
2
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
2
0
4
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
3
0
1
0
2
0
1
0
0
0
1
0
0
0
1
1
1
0
0
0
0
1
0
0
1
0
0
3
0
0
0
0
0
0
0
0
1
0
1
2
0
0
1
1
0
0
2
0
0
0
0
0
0
0
2
1
2
1
0
0
2
0
1
0
0
0
0
0
0
1
0
2
0
1
0
0
1
0
0
0
0
0
2
1
1
1
0
0
1
0
3
1
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
2
0
4
1
1
0
0
0
0
0
0
2
0
0
2
4
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
2
1
0
0
0
0
5
0
0
0
1
1
0
1
0
0
1
3
0
2
0
1
0
1
0
0
1
2
2
1
0
2
3
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
1
0
0
1
1
0
1
0
2
1
0
2
3
1
0
1
1
1
3
1
0
3
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
3
3
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
1
0
1
0
2
1
0
0
0
2
0
3
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
2
0
2
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
1
0
0
0
0
1
0
0
2
0
0
1
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
3
0
2
0
2
0
0
2
2
0
0
0
0
1
1
0
0
0
0
1
2
0
0
0
1
0
0
1
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
1
1
1
2
0
1
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
1
0
0
2
0
0
0
1
0
0
0
0
1
0
3
2
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
2
2
0
0
0
1
0
1
0
0
1
0
0
0
0
2
0
2
1
0
1
0
1
0
2
0
0
0
2
0
0
7
1
0
1
0
2
1
0
0
0
0
0
2
0
0
8
0
0
0
0
1
0
2
1
0
0
0
2
0
0
0
0
0
1
1
0
1
0
0
0
1
2
0
0
1
0
2
0
1
4
0
1
2
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
1
0
0
0
1
0
0
0
2
1
3
1
0
2
0
0
0
0
0
3
0
3
0
0
0
0
1
0
0
2
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
2
0
1
0
1
1
0
0
0
0
0
1
0
1
0
0
2
2
0
2
2
1
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
2
2
2
0
0
0
0
0
1
1
2
1
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
4
1
0
1
0
0
1
0
0
2
0
0
2
0
0
1
0
0
1
0
2
0
0
1
0
1
0
0
2
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
2
0
1
0
0
1
0
1
1
0
2
0
1
1
3
0
0
0
3
0
0
2
0
1
0
2
0
0
2
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
2
2
1
1
2
2
0
2
0
0
0
0
0
0
0
2
1
0
0
0
1
0
2
0
0
1
0
2
2
1
2
0
0
0
0
1
2
0
0
2
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
2
0
0
0
2
1
0
0
0
0
0
0
2
1
1
3
1
1
1
1
0
1
0
0
0
0
0
1
0
1
0
0
1
1
2
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
2
2
1
2
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
3
2
1
0
2
0
0
0
1
0
2
3
1
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
1
1
0
5
1
0
2
0
0
1
0
0
2
1
1
2
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
2
2
0
0
1
0
0
2
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
2
0
0
1
0
1
2
2
0
1
1
0
2
0
0
0
0
0
0
0
0
1
0
1
2
0
2
1
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
2
1
1
1
2
0
1
0
0
0
1
1
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
3
1
1
0
2
6
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
2
2
3
0
0
0
0
1
0
0
0
0
2
0
0
1
1
2
0
0
0
1
2
0
0
0
1
1
1
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
1
2
1
1
0
3
0
1
1
0
0
0
0
0
0
2
0
2
1
0
0
0
2
0
1
0
1
0
1
0
1
1
0
0
2
0
1
0
0
2
0
4
0
0
0
0
2
2
0
0
1
0
0
1
0
2
0
1
2
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
1
2
0
1
0
0
1
0
2
0
2
0
0
2
0
1
3
1
0
2
1
1
0
0
0
1
0
1
0
0
0
0
3
1
0
0
0
0
0
0
0
0
1
0
3
2
2
1
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
1
1
0
1
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
2
0
3
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
1
1
0
0
0
0
3
0
0
0
1
3
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
1
0
0
1
0
2
0
1
0
0
2
0
1
0
0
0
1
0
2
1
0
2
0
0
1
1
0
0
1
0
0
2
2
1
2
0
0
0
0
1
1
2
0
3
0
0
0
0
0
0
0
1
1
1
4
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
5
0
2
2
3
1
1
0
2
0
1
0
1
0
0
2
0
1
0
1
0
0
2
0
1
0
1
1
1
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
2
0
2
3
2
0
0
3
1
0
0
0
2
1
0
0
0
1
1
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
1
0
0
0
1
0
2
0
1
0
0
0
0
0
2
0
0
0
2
0
1
0
0
1
0
0
2
0
0
1
2
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
2
2
1
0
0
1
1
0
1
0
0
0
0
1
0
2
1
0
0
1
0
0
0
2
0
2
2
0
0
1
0
1
0
0
0
0
2
0
2
1
1
1
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
2
1
0
0
1
2
0
0
0
0
0
1
0
1
0
0
0
0
2
0
1
1
4
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
2
0
0
1
0
0
3
0
0
1
0
0
2
1
3
1
0
0
0
1
2
1
1
0
0
0
0
0
2
0
2
0
0
0
0
2
2
0
3
0
0
2
0
2
4
3
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
6
1
0
0
0
3
1
0
0
0
0
0
4
2
0
1
4
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
1
1
1
0
0
0
0
3
0
0
0
2
0
1
1
0
2
0
1
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
2
0
2
0
0
0
0
0
2
0
0
1
0
0
0
3
1
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
3
0
1
0
0
1
0
1
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
2
1
1
0
2
2
2
1
1
1
0
0
0
0
0
0
2
0
2
1
1
0
0
0
0
0
0
0
0
1
0
1
0
1
2
1
0
0
0
3
1
0
0
0
0
1
0
1
0
1
0
0
2
2
0
3
0
0
2
0
0
0
1
1
0
0
1
0
0
2
1
0
1
2
0
1
0
0
0
0
0
0
0
0
6
1
0
0
0
0
0
0
1
1
0
1
0
4
0
0
0
1
0
0
0
2
0
0
0
0
2
1
0
2
2
0
0
1
1
0
0
1
1
0
0
0
0
1
1
1
0
2
0
2
1
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
2
2
2
0
0
2
0
2
0
1
0
1
0
0
0
1
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
1
0
2
0
0
1
0
0
0
3
0
0
0
1
2
0
0
2
1
0
0
2
0
1
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
3
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
2
3
0
1
0
7
2
0
1
0
1
0
0
0
0
1
2
0
0
0
0
1
0
0
2
0
0
1
0
0
2
1
0
0
2
1
0
2
0
0
3
2
0
0
0
0
0
0
2
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
1
2
1
0
1
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
2
1
1
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
1
1
0
0
1
2
0
0
0
0
0
2
2
2
0
0
2
0
1
1
0
0
2
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
1
1
0
0
0
0
0
0
1
1
0
4
2
1
2
0
2
0
3
0
0
0
0
1
0
0
0
1
0
0
1
1
0
1
1
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
1
1
0
0
0
1
3
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
2
0
0
1
0
2
0
2
0
2
1
3
0
2
0
0
0
0
0
0
0
2
4
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
1
1
2
1
0
0
0
0
1
2
0
1
3
0
1
0
2
0
1
0
0
0
2
2
0
0
1
0
0
0
0
0
0
6
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
2
1
0
0
0
3
2
1
0
0
1
1
0
0
1
1
1
2
0
0
0
1
2
2
1
2
0
2
0
0
0
1
1
2
0
0
0
2
2
5
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
2
0
0
1
0
0
0
0
0
2
1
0
0
1
0
0
3
2
0
2
0
0
4
0
1
2
2
0
0
1
2
1
0
0
0
0
2
1
0
0
0
3
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
1
0
1
1
1
0
1
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
1
0
1
2
0
0
1
0
0
0
0
1
0
2
0
2
0
2
1
0
0
2
3
1
0
0
1
2
0
1
2
0
0
6
0
2
1
0
0
2
0
0
0
0
0
0
2
1
0
2
0
0
0
1
0
2
0
0
1
1
0
0
2
0
1
0
0
0
2
0
3
2
1
0
0
0
2
0
0
2
1
2
0
1
0
2
1
0
1
1
1
0
2
1
3
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
3
0
0
2
1
0
0
0
0
1
0
1
0
1
2
0
0
0
0
0
1
2
0
0
0
0
0
2
2
0
0
0
1
1
0
1
2
0
0
2
0
0
0
0
1
2
1
2
2
1
0
1
0
2
2
0
2
0
0
0
1
0
3
0
1
2
3
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
3
0
0
0
2
0
0
2
1
0
0
0
0
2
2
0
1
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
2
0
1
2
0
1
0
0
1
0
3
2
0
0
1
2
0
0
1
0
0
0
0
1
1
1
0
0
0
2
0
2
0
1
2
2
1
2
0
0
0
0
3
0
1
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
3
0
0
2
0
0
2
0
2
1
0
1
0
0
2
0
1
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
1
2
1
1
0
1
0
0
2
1
0
1
2
0
0
0
2
1
1
3
0
1
4
1
0
0
0
0
1
0
0
0
0
1
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
2
1
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
1
1
1
0
1
1
2
1
1
0
0
1
3
0
0
1
2
0
0
0
0
0
1
2
2
0
0
0
1
1
0
2
2
1
0
2
1
0
0
3
1
1
0
0
0
0
0
0
0
3
0
2
0
2
0
0
1
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
2
1
0
0
0
0
0
3
0
1
0
0
1
1
1
0
0
0
0
2
0
1
0
0
0
0
0
1
0
1
3
0
0
1
1
1
0
0
1
0
0
2
0
2
1
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
1
0
1
0
0
1
0
0
2
0
0
1
2
2
0
1
2
0
0
0
2
1
0
0
2
0
0
1
0
0
0
0
4
0
1
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
1
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
1
0
1
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
2
1
2
0
2
2
0
0
0
2
1
0
1
3
1
2
1
2
1
1
2
0
2
1
0
0
0
0
0
0
0
2
0
2
0
0
1
0
1
0
0
2
0
1
0
4
0
0
1
1
0
0
3
2
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
2
2
1
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
1
2
0
1
0
0
0
0
2
0
0
7
0
0
0
0
0
0
1
0
1
0
0
2
0
1
0
0
0
0
0
1
0
0
0
2
0
1
2
2
0
0
0
0
0
2
0
1
0
1
0
0
2
0
2
0
0
2
0
2
2
0
0
0
0
1
2
1
0
0
1
0
0
2
3
0
3
0
0
2
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
3
0
0
2
2
0
0
0
1
0
0
0
2
1
0
0
2
0
1
1
0
1
0
0
0
0
1
0
0
2
0
0
0
0
2
1
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
1
1
0
0
1
0
0
1
0
0
0
0
2
2
0
2
0
2
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
4
2
0
0
0
3
2
0
0
1
0
2
1
2
0
2
2
0
0
0
2
0
0
0
1
0
1
1
0
0
0
2
0
0
1
1
1
0
0
0
2
1
0
1
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
3
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
2
0
2
0
0
1
2
0
1
0
0
0
0
1
2
1
0
0
0
0
0
1
0
0
1
0
0
0
1
2
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
1
0
0
0
6
0
0
1
0
0
0
1
0
0
1
2
0
0
0
0
1
0
1
0
0
0
0
3
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
1
1
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
2
2
2
0
0
1
0
0
0
0
1
0
0
0
0
0
2
2
2
0
0
0
1
2
0
0
0
0
0
1
0
2
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
4
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
1
2
2
0
1
0
1
0
2
1
2
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
2
1
0
0
0
2
2
1
0
0
1
0
0
0
0
0
0
0
0
2
1
3
0
0
1
0
0
0
0
0
0
0
1
0
2
0
2
0
2
1
0
0
0
0
0
2
0
2
0
1
1
0
0
0
0
1
0
2
4
0
2
0
0
1
1
0
1
2
1
1
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
2
0
0
1
0
2
1
2
0
0
1
0
0
1
2
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
2
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
2
2
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
2
0
2
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
3
2
3
0
0
1
1
1
1
2
0
0
0
2
0
0
3
2
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
2
2
0
0
1
0
0
0
2
0
0
0
1
1
0
3
2
2
1
0
0
0
1
1
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
1
0
0
0
4
0
2
0
0
1
0
0
0
0
1
2
0
2
0
0
0
1
1
0
0
0
2
2
0
2
0
0
1
4
0
1
0
0
0
2
2
0
0
0
1
0
3
0
2
1
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
3
0
0
0
2
1
0
0
0
2
0
2
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
1
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
1
2
2
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
4
3
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
2
0
0
1
1
2
1
0
0
2
3
3
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
2
0
2
0
0
0
1
1
3
0
1
0
1
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
2
0
0
3
2
0
0
0
2
0
2
0
0
1
0
1
0
0
1
0
0
0
1
2
0
2
0
0
0
0
2
2
1
0
2
2
2
0
0
1
0
2
1
1
0
1
3
1
0
0
0
0
0
1
1
0
0
0
0
0
1
1
2
0
2
0
0
2
3
1
2
0
2
0
0
0
0
0
0
1
0
0
0
0
2
1
1
1
0
0
0
0
2
2
1
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
1
2
0
0
0
3
1
1
2
2
0
0
2
0
0
1
0
0
2
0
0
0
3
2
0
2
0
3
1
0
0
0
1
0
0
0
0
2
0
0
0
2
0
1
0
1
0
0
0
0
3
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
2
0
2
0
1
1
0
2
2
2
1
0
0
0
0
2
0
2
0
0
2
0
2
0
2
0
2
0
0
1
0
0
1
0
0
0
2
1
0
0
0
1
2
0
0
0
0
1
0
1
1
2
0
0
2
0
0
1
0
0
0
1
0
1
0
0
0
0
1
1
0
2
1
0
0
0
2
0
0
0
0
0
1
2
0
1
0
0
0
2
0
0
0
0
0
3
2
3
0
1
0
0
2
0
0
0
0
0
0
0
0
3
2
2
0
0
0
2
0
0
0
2
0
0
0
0
0
1
2
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
4
1
3
0
3
0
1
0
0
0
2
0
0
1
0
0
0
0
2
2
1
2
0
0
1
0
0
1
0
0
0
1
3
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
3
0
0
2
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
2
0
2
0
0
0
2
0
0
1
2
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
1
2
0
2
0
0
0
1
1
2
1
1
0
0
1
0
2
0
2
0
0
0
1
0
2
1
2
2
2
0
3
0
0
0
2
0
0
1
0
1
0
0
1
0
1
1
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
2
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
1
1
1
0
0
2
0
0
0
0
2
0
0
2
0
0
1
0
1
0
1
0
0
0
0
0
0
2
2
0
0
1
0
0
2
2
0
0
0
2
0
0
0
2
0
0
3
0
1
1
0
0
0
2
0
2
0
0
0
0
2
0
1
1
0
1
1
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
2
0
0
1
2
0
0
0
0
2
2
0
0
1
2
2
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
3
0
0
0
0
0
0
1
2
0
0
1
0
0
1
0
0
1
2
0
2
1
0
0
0
2
0
2
2
3
1
0
0
0
1
0
0
1
1
2
1
0
0
3
0
0
0
1
0
0
0
1
2
2
0
2
1
1
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
2
0
0
1
0
2
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
2
0
1
0
0
0
1
0
0
0
0
2
1
0
2
2
1
0
0
0
3
1
2
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
2
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
1
1
0
1
1
1
0
2
0
0
0
0
0
1
0
2
1
0
2
1
2
1
3
0
0
1
0
0
1
0
2
1
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
1
1
1
1
0
1
2
0
2
0
0
2
0
0
2
1
1
0
1
3
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
1
2
0
0
2
0
1
0
1
1
0
0
0
0
2
1
1
0
0
0
2
1
0
1
1
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
2
0
1
0
3
0
0
0
2
3
0
3
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
3
2
0
0
0
0
2
0
0
0
1
0
0
1
0
1
0
2
2
1
0
0
0
0
1
0
0
0
0
0
2
1
2
0
0
0
1
1
0
2
1
0
0
0
2
0
0
1
0
0
1
0
2
1
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
2
2
2
0
0
0
0
1
0
1
0
0
2
2
0
2
2
0
4
0
0
0
1
2
0
0
0
2
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
1
0
0
0
2
1
1
0
2
1
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
2
1
0
0
0
2
1
0
1
0
3
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
2
0
1
2
0
0
0
0
0
0
1
1
0
0
0
0
0
2
1
0
0
2
0
1
0
1
0
0
3
0
0
2
1
3
0
1
0
0
0
2
2
0
1
0
0
0
2
1
2
0
0
0
0
0
2
0
0
2
0
0
2
0
0
2
0
0
0
3
2
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
2
0
0
0
0
0
1
2
0
1
0
1
0
0
0
1
1
0
0
0
2
0
1
2
2
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
0
0
1
0
0
2
4
0
0
0
0
0
2
2
0
0
0
0
1
1
0
0
0
0
2
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
2
2
0
0
1
0
2
0
0
1
0
4
0
1
0
0
0
0
0
2
2
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
1
2
2
0
0
0
0
1
0
2
0
2
0
1
0
1
0
0
0
1
0
0
0
3
0
1
0
1
3
0
1
2
0
0
0
0
0
0
1
1
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
1
0
2
0
0
0
0
0
1
2
2
1
0
0
1
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
2
3
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
1
1
2
1
0
0
1
0
2
0
0
1
0
0
2
2
0
1
0
0
1
0
0
1
0
2
0
0
0
0
1
2
1
0
0
0
0
1
2
0
0
1
0
0
0
0
2
0
2
1
0
2
0
1
1
0
0
2
0
1
1
0
0
2
0
0
0
0
0
0
0
0
1
2
0
2
0
0
2
0
0
0
1
0
0
2
1
0
2
0
0
0
0
2
1
0
2
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
2
2
0
0
2
0
0
1
2
1
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
2
0
4
0
0
0
0
0
4
0
0
0
0
2
0
0
2
0
1
2
0
1
1
3
1
0
0
1
0
2
0
2
2
1
0
0
1
0
1
11
0
0
0
0
1
2
0
2
0
2
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
1
0
0
1
2
0
0
4
0
0
1
0
0
2
0
0
0
4
0
0
0
0
0
1
1
2
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
1
0
0
2
0
0
1
0
0
0
2
0
0
2
0
2
0
1
0
0
0
0
1
0
2
0
0
0
1
1
0
1
0
0
0
1
2
1
1
2
0
2
0
0
1
1
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
1
0
0
0
1
2
0
2
4
0
0
0
0
2
2
0
2
2
2
1
0
0
0
1
0
0
1
0
1
0
0
2
1
0
1
2
2
2
1
0
0
0
2
0
0
1
2
0
0
0
0
0
0
2
2
1
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
2
0
0
0
6
0
0
0
2
0
0
0
1
3
0
0
0
2
0
0
0
0
2
0
0
2
0
0
2
1
1
1
0
0
1
0
0
0
1
0
0
1
1
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
1
2
1
0
1
0
3
0
0
1
1
0
0
0
0
1
2
0
0
0
2
1
0
2
0
0
3
1
0
0
0
0
1
0
5
2
2
0
0
0
0
0
8
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
2
3
0
2
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
1
0
0
1
2
0
0
2
1
0
0
0
0
2
0
0
2
0
0
0
1
1
0
0
0
1
1
0
0
0
0
1
1
0
0
0
1
0
0
0
1
2
0
1
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
2
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
1
1
0
0
1
2
0
0
0
0
0
3
0
2
0
0
1
0
2
0
1
0
1
3
0
0
1
0
0
0
1
0
0
0
2
1
0
1
2
0
3
0
1
0
0
0
1
2
2
0
1
0
1
0
0
0
1
1
0
0
3
0
0
0
1
2
0
0
1
2
2
1
1
0
0
0
0
0
0
1
0
0
2
3
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
2
0
0
2
1
1
0
1
0
0
2
0
0
0
1
2
1
2
0
1
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
2
0
1
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
1
0
5
2
1
0
0
1
0
0
1
0
0
0
0
0
1
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
2
2
0
0
2
1
0
0
2
2
0
2
0
0
1
0
0
1
0
0
1
0
0
2
0
0
1
0
0
0
0
0
2
0
2
0
0
0
1
0
0
1
1
1
0
0
0
2
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
1
0
1
2
0
0
0
0
0
0
2
2
1
0
0
2
0
0
1
0
0
1
0
0
0
0
0
1
0
1
2
0
2
0
0
1
0
0
0
1
0
0
0
2
2
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
1
0
0
0
0
0
0
0
2
2
0
2
2
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
2
1
1
0
0
2
0
0
1
2
0
1
0
2
0
3
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
3
2
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
1
2
2
0
0
3
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
2
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
4
2
0
5
0
0
2
2
0
0
0
2
0
0
1
1
0
3
0
0
0
1
0
0
1
2
1
0
0
0
0
0
0
0
0
1
3
1
0
0
0
0
0
0
0
0
0
5
1
0
0
3
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
3
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
2
3
0
0
0
0
2
0
0
2
1
2
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
2
1
0
0
1
0
1
0
0
2
4
1
0
0
0
1
0
0
0
2
2
0
0
0
0
3
0
0
1
0
1
0
0
3
0
1
0
2
0
3
1
0
1
0
3
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
2
1
0
1
3
0
0
0
2
0
0
0
1
0
3
0
0
0
0
1
0
0
1
0
2
0
0
0
0
2
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
2
2
0
1
0
0
2
0
2
0
0
0
0
2
1
1
0
4
2
0
0
0
0
1
0
0
0
1
2
0
1
3
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
3
0
0
1
0
4
0
0
0
1
0
0
2
0
0
0
1
1
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
2
2
0
0
0
0
2
1
0
0
1
0
0
1
0
0
0
0
2
0
0
2
2
0
2
0
0
0
0
2
1
2
0
0
0
0
1
1
0
2
0
2
0
3
1
2
2
1
2
0
2
1
0
0
2
0
0
3
1
0
0
1
0
2
0
0
0
1
0
1
0
0
1
0
2
1
0
1
1
0
1
0
1
0
0
0
0
3
2
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
1
4
0
0
2
0
1
0
0
2
2
0
0
1
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
2
3
0
0
1
1
2
0
1
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
1
0
1
0
0
0
0
3
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
1
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
1
0
2
1
2
0
1
0
1
0
1
0
0
1
0
1
2
0
0
0
0
1
0
0
0
0
2
1
0
2
2
2
1
0
1
0
1
0
0
2
0
2
0
1
1
0
0
0
0
2
0
0
1
1
2
1
0
1
1
0
0
3
1
0
0
1
0
0
1
0
2
1
0
0
0
0
2
1
4
0
4
0
1
1
0
0
0
1
0
3
2
0
2
0
2
2
0
0
2
0
2
0
0
0
2
0
0
0
1
0
0
1
0
2
0
0
0
0
0
1
0
2
2
0
1
0
1
0
1
0
0
0
1
1
2
2
0
0
0
0
0
0
2
0
0
0
3
1
2
2
0
0
4
2
0
2
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
1
0
0
0
0
0
1
0
0
2
0
0
2
0
0
2
2
0
0
0
1
0
2
0
0
1
2
0
2
0
0
0
0
3
2
0
0
2
0
0
2
0
0
0
1
0
1
1
2
0
0
0
0
0
1
0
1
0
2
0
0
0
0
1
1
0
0
0
1
0
2
0
2
2
0
2
0
0
0
0
3
0
0
1
0
1
0
0
0
0
2
0
1
0
0
0
0
1
2
0
0
0
1
0
1
1
2
0
2
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
4
0
2
0
0
0
0
1
0
1
0
0
1
0
1
1
0
0
3
1
1
0
2
0
1
0
0
0
0
2
0
1
0
0
0
1
2
2
0
1
0
0
4
0
0
2
0
0
0
2
0
1
0
1
1
0
0
0
1
1
1
2
0
0
3
0
0
2
0
0
0
1
0
0
2
3
1
2
0
0
1
2
2
0
0
0
1
1
2
1
0
0
0
0
0
2
0
2
0
0
1
1
1
1
0
2
0
2
1
0
0
0
0
1
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
1
3
0
0
2
2
1
2
2
1
0
0
2
2
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
1
2
2
0
0
0
0
1
1
0
0
0
1
2
0
0
3
0
0
0
2
1
2
3
0
4
0
1
0
0
0
0
1
1
0
0
1
2
0
0
0
0
0
0
1
0
0
0
2
0
2
4
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
3
2
0
0
1
0
2
1
0
1
0
0
0
2
0
0
0
2
1
0
0
0
0
1
2
2
0
0
0
0
2
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
3
0
0
1
0
2
0
3
2
0
0
1
0
0
0
1
0
2
6
2
0
1
0
2
0
0
0
4
0
0
2
2
2
0
0
2
2
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
5
0
0
0
0
0
0
1
2
2
2
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
8
0
0
0
2
1
1
1
0
0
1
0
1
0
2
2
0
0
0
0
0
0
0
1
2
1
0
0
1
2
1
1
2
2
0
0
0
0
0
1
1
0
0
2
0
0
0
1
0
2
2
0
0
1
0
2
0
0
2
2
0
0
1
0
0
1
2
2
0
0
0
2
6
0
1
2
0
0
0
0
0
0
0
0
0
3
0
0
2
2
1
0
0
0
2
2
1
2
0
1
3
1
2
3
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
2
0
1
0
0
0
2
0
1
0
0
0
0
2
2
0
0
0
2
0
0
1
2
0
2
2
0
0
0
0
0
0
0
6
0
0
0
2
2
0
2
0
0
0
2
4
0
0
2
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
1
3
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
1
0
1
0
1
0
0
2
0
0
0
0
2
2
2
0
0
0
1
0
2
0
1
1
0
0
0
1
1
0
0
0
0
0
2
1
0
1
5
0
0
0
2
2
0
2
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
2
1
2
0
0
0
0
1
0
0
0
1
0
0
0
2
0
2
1
1
2
0
0
0
2
0
2
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
2
1
1
2
0
0
1
2
2
2
1
1
2
0
2
0
0
4
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
4
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
1
1
0
1
2
1
2
0
0
0
0
0
1
2
0
2
0
2
2
0
0
0
0
0
0
3
0
1
1
0
0
0
0
1
1
0
2
2
0
0
1
1
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
2
1
1
0
2
0
0
0
0
1
0
0
2
1
0
1
0
2
0
0
0
1
2
0
0
1
0
0
0
1
0
0
0
0
0
0
2
2
1
2
0
2
0
0
2
0
0
2
0
0
0
1
0
0
2
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
2
1
2
0
3
0
0
0
1
0
0
2
0
0
1
1
0
2
3
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
1
1
2
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
1
0
2
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
1
1
0
0
0
1
0
2
2
0
0
0
0
0
0
1
0
2
0
1
0
0
1
0
1
2
0
1
0
2
0
0
1
0
1
2
0
0
0
0
3
0
1
1
0
0
0
3
0
3
0
2
2
0
0
1
1
0
0
1
0
2
0
2
2
0
1
0
2
0
1
0
0
2
0
2
2
1
0
2
1
0
0
0
4
0
1
1
0
0
2
1
0
0
0
0
1
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
1
0
5
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
2
0
0
0
2
1
1
0
0
0
2
1
0
0
0
2
0
0
0
3
0
1
0
2
2
0
2
0
0
3
0
0
0
0
0
0
0
2
2
1
0
1
2
1
0
0
3
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
1
2
0
1
0
1
1
0
0
0
1
1
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
2
1
2
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
1
0
2
0
0
2
0
0
1
2
1
0
0
2
0
2
0
0
1
2
0
0
2
0
0
0
1
2
0
1
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
1
1
3
0
0
0
0
1
0
0
0
3
2
1
0
2
0
2
2
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
2
3
0
0
0
0
2
1
1
0
1
0
2
2
0
0
2
0
0
0
1
1
0
1
0
0
2
2
0
1
0
0
0
1
0
0
2
0
1
2
0
2
0
3
0
0
0
0
1
0
0
2
3
1
2
0
1
2
0
0
2
2
0
1
0
0
0
0
0
0
0
4
0
0
3
0
1
0
0
0
0
0
1
0
0
2
1
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
3
0
0
0
0
0
0
2
0
1
0
0
1
0
0
2
0
0
0
1
1
0
0
0
1
0
2
2
0
0
1
1
0
0
0
2
0
1
2
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
3
0
0
0
1
2
0
0
2
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
3
1
0
2
0
1
2
0
1
0
1
2
0
1
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
1
0
1
2
0
0
0
0
2
0
1
0
2
2
1
1
0
0
0
0
0
0
0
2
0
0
2
1
1
0
0
0
0
0
2
0
1
1
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
1
0
0
2
0
1
1
2
0
0
1
0
4
2
2
0
1
0
0
0
0
0
0
0
0
0
2
1
2
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
3
0
2
0
0
0
1
2
0
2
0
1
1
0
0
2
0
1
1
0
3
0
0
0
0
0
3
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
2
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
3
0
0
1
0
0
0
0
0
2
0
0
0
0
1
2
4
2
0
0
2
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
2
1
0
1
0
0
0
0
2
1
0
5
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
2
0
0
0
0
0
1
0
1
0
0
1
0
3
1
0
0
0
0
0
1
2
0
2
0
1
0
1
2
0
0
1
0
0
2
0
0
0
1
1
0
1
0
2
0
0
0
0
0
0
0
0
1
2
0
2
1
0
1
0
0
0
0
0
0
3
1
0
0
0
2
2
1
0
0
0
0
1
0
1
0
0
1
0
0
1
1
0
2
1
1
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
2
0
2
0
0
1
0
3
0
0
0
1
0
1
3
0
0
0
0
1
0
0
1
2
0
2
0
2
0
0
0
0
1
0
0
0
0
8
2
0
1
0
0
0
1
3
3
0
0
0
0
1
0
0
0
2
1
0
1
0
0
0
0
1
0
2
0
0
0
1
0
0
0
1
0
2
2
0
1
1
0
0
0
0
0
3
0
1
0
0
2
2
0
2
0
0
2
1
1
0
0
0
2
2
0
0
2
0
0
0
0
1
1
0
0
1
0
3
0
1
0
3
0
2
1
0
2
0
0
2
2
2
0
4
0
1
0
1
2
2
0
0
2
0
0
0
2
0
0
0
0
0
2
2
3
0
1
0
0
1
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
3
0
0
0
1
1
1
1
0
3
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
2
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
3
4
0
0
1
0
1
0
0
1
0
4
0
0
3
0
0
0
0
0
1
2
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
1
0
0
2
1
0
1
0
1
0
0
0
0
0
2
0
1
2
0
0
2
1
0
1
0
2
0
0
0
2
2
0
0
0
0
0
2
2
1
0
0
0
1
1
0
1
1
0
2
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
3
2
1
2
0
2
0
0
0
1
1
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
2
0
0
6
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
1
0
0
2
0
0
1
1
0
0
0
0
2
0
0
2
0
2
2
0
0
0
0
0
1
2
0
0
0
1
2
0
0
1
0
0
0
0
0
0
2
1
0
1
0
0
3
1
0
0
0
0
2
1
0
2
2
0
0
2
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
1
0
2
0
1
0
0
1
1
0
0
1
0
0
0
0
2
0
0
2
0
0
4
0
0
0
0
1
2
0
1
0
0
2
0
0
0
1
1
1
0
1
0
0
0
1
0
0
3
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
1
2
0
1
1
0
2
2
0
2
1
0
3
1
1
0
0
0
2
0
0
1
2
2
0
1
1
0
0
0
0
0
0
2
1
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
2
0
0
1
0
0
3
0
0
0
0
0
0
1
0
0
2
0
1
2
0
0
1
2
0
2
0
2
0
0
0
3
0
0
0
0
2
2
0
0
1
0
3
1
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
2
0
0
0
0
0
2
0
0
2
0
2
2
1
1
2
0
1
0
1
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
2
2
0
1
0
2
2
1
0
3
1
0
0
1
1
0
0
0
0
2
0
0
2
0
0
2
2
1
2
1
0
0
1
0
1
1
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
1
1
2
0
2
2
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
1
2
2
2
2
0
0
1
0
0
0
2
1
1
0
2
0
0
0
2
1
1
0
0
0
1
1
2
0
0
2
1
1
2
0
0
0
0
0
0
0
2
0
2
0
0
0
2
5
0
0
0
2
1
0
2
1
1
0
0
0
0
0
2
0
0
1
0
0
2
2
0
2
0
0
0
0
0
2
0
1
1
2
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
7
1
0
0
0
0
1
1
2
2
2
0
1
0
0
0
0
0
0
0
1
1
0
0
1
1
0
1
0
2
0
0
0
0
0
1
2
1
1
0
0
1
0
0
0
0
0
1
1
0
2
0
0
3
0
1
2
0
2
0
1
1
1
0
0
0
2
0
0
0
0
2
0
1
0
0
0
2
1
0
1
2
0
0
1
0
0
0
2
0
1
2
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
2
2
2
0
0
0
0
2
1
0
0
1
1
3
0
0
0
0
0
1
2
0
0
2
2
1
0
1
0
0
0
0
0
0
1
3
0
0
1
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
1
3
1
0
0
0
0
0
0
0
0
1
1
1
2
0
2
0
0
0
0
2
0
0
1
0
0
2
0
2
0
2
0
0
0
0
0
1
1
2
0
1
0
4
0
1
0
0
2
2
1
0
0
2
3
2
0
0
2
2
0
0
0
1
0
0
0
0
1
0
0
2
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
7
0
0
0
2
0
1
0
0
1
1
0
7
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
2
0
0
2
0
1
2
2
0
0
0
3
1
0
1
0
0
0
2
1
0
2
1
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
2
0
0
0
0
1
2
1
0
1
0
0
1
2
0
0
1
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
2
1
0
0
3
0
0
0
0
0
1
0
1
2
1
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
2
0
0
0
0
2
0
2
0
0
2
2
0
0
2
0
1
1
0
0
1
0
0
0
1
0
2
1
0
2
0
3
0
0
2
2
0
2
0
1
1
0
2
0
2
0
0
0
0
0
1
0
0
0
1
2
2
0
0
2
1
0
0
0
2
0
0
1
0
0
1
0
0
0
1
0
0
2
1
0
2
0
0
0
0
0
0
0
3
1
0
0
1
0
0
1
1
0
2
0
1
2
2
1
0
2
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
2
2
1
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
2
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
1
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
1
0
1
0
2
2
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
1
0
1
0
0
0
1
1
0
2
1
1
0
0
0
0
0
0
0
2
0
4
3
2
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
3
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
1
2
0
0
0
0
1
0
0
1
0
0
0
0
5
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
2
1
0
1
0
0
1
0
1
0
1
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
2
2
0
0
1
0
0
2
0
2
2
0
2
0
0
0
1
0
1
2
0
0
0
0
1
0
0
0
1
2
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
1
0
1
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
5
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
3
2
0
0
1
0
0
2
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
1
0
1
0
0
2
0
0
0
1
0
0
1
1
0
0
2
0
0
0
1
1
2
1
1
2
7
0
0
0
1
0
2
1
1
0
1
0
1
2
0
2
2
1
2
0
0
0
2
2
0
2
0
0
0
1
0
0
0
0
0
2
2
0
1
2
1
0
0
1
0
0
0
0
1
4
0
1
0
0
1
0
1
0
1
2
0
0
0
2
0
1
0
0
0
0
0
2
2
0
1
2
1
0
0
0
0
2
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
1
0
2
0
2
2
2
2
1
0
0
0
0
1
1
0
1
0
1
0
2
2
0
1
0
0
1
0
0
0
1
0
2
1
0
0
0
1
0
1
3
0
0
1
0
0
0
0
0
0
0
0
0
3
2
0
1
0
1
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
2
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
2
0
1
0
3
0
1
0
2
0
0
0
2
0
0
3
2
0
0
0
1
3
0
2
0
0
0
1
1
2
0
2
1
3
2
1
0
2
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
1
2
1
0
1
1
0
0
0
0
0
0
1
1
2
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
5
0
0
0
4
2
2
2
0
2
0
0
3
0
1
1
0
2
0
1
0
2
0
0
1
0
1
0
0
1
1
2
1
0
0
0
0
2
1
1
0
0
1
2
0
3
0
0
0
1
1
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
1
1
0
0
0
0
1
0
1
0
2
1
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
1
1
0
2
0
2
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
2
0
0
2
0
4
0
0
0
0
3
0
1
4
0
1
0
0
2
0
0
1
1
0
0
1
2
2
0
0
0
2
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
2
0
0
0
2
2
0
2
1
1
0
0
0
2
1
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
1
0
3
0
0
0
0
0
2
0
1
1
2
1
0
0
2
2
0
0
2
0
2
3
0
0
0
0
2
0
2
0
2
0
1
3
1
2
0
1
1
0
2
0
0
0
0
0
1
2
0
0
0
0
0
1
2
2
0
1
2
0
2
1
2
0
1
0
0
0
2
0
0
1
2
1
2
1
1
0
3
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
3
1
1
0
1
0
0
0
1
0
0
0
0
2
0
5
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
3
0
0
1
1
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
1
1
0
0
0
0
0
2
0
0
2
0
2
1
0
1
0
2
0
0
0
0
0
0
1
1
4
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
1
0
0
0
0
1
0
0
1
1
0
0
1
2
0
1
1
0
0
1
0
1
0
0
2
0
1
2
1
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
4
1
1
0
0
2
0
2
0
1
0
2
2
0
0
0
0
0
2
0
3
2
0
0
1
1
1
2
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
1
1
1
0
1
1
2
2
0
0
0
0
0
0
0
2
0
1
0
0
1
0
1
1
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
1
1
2
1
1
2
0
0
2
2
0
1
0
0
0
0
2
2
2
0
0
2
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
4
0
0
1
0
0
0
0
0
2
1
1
2
1
2
2
0
0
1
0
0
0
0
0
0
0
0
0
3
4
1
1
0
0
2
0
0
1
0
0
0
0
0
1
0
2
0
2
2
1
2
0
0
0
0
0
0
0
1
1
0
0
2
2
0
0
2
0
1
0
0
1
2
0
0
2
0
0
0
2
0
1
0
0
0
0
1
1
0
0
0
0
2
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
3
1
0
2
2
0
2
1
2
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
1
0
1
0
1
0
0
0
0
0
2
2
0
0
0
2
0
1
0
3
0
0
1
1
2
2
0
2
1
0
2
0
2
0
0
1
0
1
0
1
2
0
0
0
2
0
2
0
0
0
2
0
0
0
0
1
0
0
2
0
0
1
0
0
1
2
0
0
1
1
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
3
0
0
0
0
0
2
1
2
0
0
2
2
0
0
1
0
0
2
0
1
2
0
2
1
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
1
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
1
0
0
2
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
1
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
1
1
0
1
2
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
1
0
0
1
0
1
0
3
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
2
1
0
2
2
0
0
1
0
2
0
2
0
0
0
1
2
0
0
0
2
2
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
1
1
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
2
0
2
1
0
0
2
0
0
0
2
1
2
0
1
0
2
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
6
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
3
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
2
1
1
0
1
2
0
0
2
1
1
2
2
1
0
0
0
2
1
0
2
1
0
0
0
0
1
0
0
2
0
0
0
2
3
0
0
0
0
1
0
0
0
0
1
2
1
0
2
2
0
0
3
0
0
0
0
0
2
2
0
1
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
5
0
0
0
1
0
2
0
0
0
0
0
1
0
0
1
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
1
0
0
1
1
0
0
3
2
0
0
0
0
0
0
1
1
1
1
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
1
6
0
0
0
2
0
1
0
0
0
1
0
2
2
1
0
0
0
1
1
2
0
2
1
0
0
2
1
1
1
0
2
0
1
0
0
1
0
0
0
1
0
0
0
2
0
2
0
0
0
1
3
0
1
2
0
0
2
0
1
0
0
0
2
2
0
2
0
0
0
0
0
0
0
2
0
1
0
5
0
0
0
0
0
0
2
0
1
0
0
0
1
2
0
2
1
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
2
0
2
2
2
1
0
0
0
1
1
2
0
2
2
1
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
2
2
0
0
1
0
2
2
1
2
0
4
1
1
0
2
0
1
0
2
2
0
1
0
0
0
0
2
0
0
1
0
0
0
2
2
0
0
0
0
0
0
2
0
2
0
1
2
3
0
0
0
2
2
0
0
0
1
1
0
0
0
0
0
0
0
0
2
2
0
2
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
1
0
2
0
0
0
0
0
2
0
1
2
0
0
0
1
1
1
1
1
0
1
1
1
0
2
2
1
2
0
0
2
0
1
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
1
0
2
2
0
0
1
0
2
1
2
0
0
1
0
0
2
0
0
0
1
1
0
0
2
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
1
0
0
0
1
1
3
1
0
0
0
0
2
2
0
0
0
0
0
2
0
2
1
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
1
4
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
3
4
0
2
0
0
0
0
0
1
2
0
0
0
0
0
2
2
0
0
2
2
0
0
0
1
0
0
1
1
1
0
1
0
1
0
0
0
0
0
2
1
1
3
0
0
0
0
0
1
0
0
2
0
0
1
2
0
0
0
1
0
0
2
1
2
0
0
0
5
0
0
0
0
0
2
2
2
2
0
0
0
1
0
0
0
2
1
2
0
1
2
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
2
0
1
2
0
1
0
2
0
0
1
0
1
0
3
0
2
0
0
2
0
2
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
2
0
1
1
1
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
2
2
0
2
0
1
1
2
4
0
2
0
0
0
0
1
1
0
0
2
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
1
1
0
2
0
0
2
0
0
0
2
0
2
0
1
0
2
2
0
0
0
0
0
2
3
0
2
0
0
2
0
2
0
2
0
0
2
2
0
0
0
0
2
0
0
3
3
1
0
2
1
0
0
3
0
1
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
1
0
0
3
0
4
0
0
0
1
2
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
2
1
1
2
0
2
0
0
3
1
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
2
0
0
0
0
0
1
2
2
2
0
0
0
1
0
2
0
2
2
0
2
1
1
1
9
0
0
2
2
0
0
0
0
0
1
2
1
2
0
0
0
1
0
0
2
0
0
0
0
2
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
1
1
0
0
0
0
0
0
0
0
1
0
2
1
2
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
2
0
0
0
0
2
2
0
1
3
0
0
2
0
2
0
0
1
2
0
4
0
0
1
2
2
0
0
1
0
2
1
0
0
0
0
3
0
0
1
1
0
0
1
1
0
0
1
0
0
3
0
0
2
0
0
0
3
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
1
0
0
1
0
0
1
2
2
0
2
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
3
1
1
2
0
0
0
1
0
2
0
0
2
1
0
0
0
2
0
0
0
0
1
2
0
1
2
0
0
1
0
0
0
0
1
0
0
0
4
0
0
0
0
0
2
2
0
1
0
0
1
0
1
2
3
0
0
0
0
2
0
0
0
2
0
0
0
2
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
2
0
2
2
1
2
2
0
0
2
0
0
0
1
1
0
0
0
3
0
3
0
0
2
1
0
0
0
0
0
0
2
0
0
0
1
3
2
1
1
1
1
0
2
1
0
0
1
0
0
0
0
2
0
0
0
0
2
0
2
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
2
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
1
0
0
2
2
0
0
2
1
0
0
0
0
0
0
0
0
2
2
2
1
0
0
2
0
0
3
0
0
0
0
1
2
2
0
1
0
0
2
1
0
1
0
2
1
0
2
0
2
0
0
0
0
2
2
3
0
1
0
1
0
0
0
0
0
1
0
2
0
2
1
0
2
0
0
1
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
2
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
2
0
0
2
2
1
0
0
0
0
0
2
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
1
0
1
3
0
1
0
0
0
0
0
0
0
0
1
1
1
2
0
0
2
0
2
1
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
3
3
0
2
1
0
0
0
0
2
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
1
2
2
0
2
0
2
1
0
2
0
1
0
0
0
3
1
3
2
4
0
1
1
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
2
2
0
0
0
0
1
0
2
2
1
2
2
0
0
0
0
0
0
0
0
0
0
4
0
0
2
1
0
1
0
0
0
0
1
0
1
0
2
0
0
1
2
0
0
0
0
1
1
3
2
0
2
0
1
0
0
0
2
0
0
2
1
1
0
2
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
2
2
2
0
1
0
0
1
0
1
0
0
0
0
1
0
2
1
0
0
0
0
1
0
1
0
0
0
2
0
1
1
0
2
0
1
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
3
2
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
1
1
0
1
0
0
2
1
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
2
3
0
1
1
0
0
0
3
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
1
1
0
0
3
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
2
0
0
2
0
0
0
2
2
2
0
0
0
3
1
0
0
0
1
0
1
1
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
2
1
1
0
1
0
1
2
0
0
1
0
2
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
2
0
2
0
0
0
0
0
2
1
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
3
2
2
2
0
3
0
1
0
2
2
0
0
2
4
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
1
0
2
0
0
0
0
0
0
2
1
1
0
0
1
0
0
1
2
0
0
1
3
0
0
1
1
0
0
3
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
2
0
0
2
0
2
2
1
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
2
1
0
0
1
0
0
1
2
1
0
0
0
0
1
0
0
0
2
0
0
2
0
1
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
2
0
1
1
0
0
0
0
1
0
0
2
0
2
0
0
1
0
0
0
0
2
0
2
0
0
2
1
2
1
0
0
0
0
0
0
0
2
2
2
0
0
2
1
0
0
1
0
1
1
0
1
1
0
0
0
2
2
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
1
1
0
1
0
0
1
0
2
0
2
0
0
0
1
1
2
2
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
1
0
0
0
1
2
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
1
0
2
1
1
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
2
0
1
0
2
1
0
2
0
0
1
0
2
2
1
0
0
0
1
3
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
2
2
2
0
2
0
1
0
0
2
1
0
1
0
0
0
0
2
0
2
0
0
0
0
4
0
0
0
0
2
0
0
2
0
0
5
0
0
2
1
2
0
0
2
0
0
1
1
1
0
1
0
1
3
0
0
2
0
0
1
1
1
2
0
0
0
2
0
0
0
1
0
2
0
0
2
1
1
0
2
0
2
0
0
1
0
0
1
0
0
0
0
2
0
1
0
1
5
2
0
0
2
0
3
0
0
2
0
0
3
0
1
1
0
0
1
4
0
0
1
0
0
0
0
0
0
2
0
1
0
1
1
2
1
0
2
1
4
1
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
2
0
2
0
0
0
0
0
1
3
1
1
1
2
1
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
1
0
0
0
3
0
3
0
0
2
0
0
0
0
2
0
1
0
0
1
2
0
0
1
0
0
2
2
0
0
0
2
0
0
1
1
0
0
0
1
2
1
1
0
0
0
1
0
1
0
2
0
2
2
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
2
0
1
0
0
1
0
2
0
0
2
0
1
3
0
0
0
0
0
0
0
1
1
0
0
4
2
0
0
0
0
0
1
1
4
0
0
0
0
0
0
0
2
1
0
0
0
2
1
0
1
0
2
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
2
0
1
0
0
0
0
1
0
0
1
0
2
0
1
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
1
2
1
0
1
0
0
2
0
2
0
1
0
1
0
0
0
1
0
0
0
2
2
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
2
1
0
0
0
1
0
0
0
0
0
2
1
0
0
2
0
0
0
2
0
2
0
0
0
0
1
2
0
1
0
0
0
3
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
2
2
1
0
0
1
1
0
1
0
2
1
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
2
0
2
0
1
0
0
0
0
0
0
1
2
1
0
0
1
2
0
1
1
3
1
0
1
0
2
0
0
2
0
2
0
0
1
0
1
0
0
2
2
0
1
0
1
2
0
0
0
1
0
0
0
0
0
0
1
0
0
1
3
1
0
2
2
0
0
0
0
2
2
2
1
0
1
1
1
1
0
2
1
1
2
0
1
0
0
0
0
0
2
3
0
0
1
1
0
1
0
0
0
0
2
2
2
1
1
0
0
2
0
2
0
0
0
2
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
2
1
2
2
0
0
0
1
0
0
2
2
1
0
0
0
0
1
1
1
3
0
0
1
0
0
2
1
2
2
2
0
1
0
1
1
1
2
1
1
0
0
0
0
4
1
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
2
1
3
0
0
3
1
2
2
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
2
0
4
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
2
2
0
0
1
0
0
1
2
1
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
3
0
0
0
2
0
1
2
0
2
0
0
2
0
0
0
2
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
2
3
1
0
0
1
0
0
0
1
0
0
0
2
0
0
2
0
0
0
1
1
0
0
2
0
0
0
1
1
0
0
0
0
2
0
1
0
0
2
0
2
0
0
0
0
2
2
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
4
0
1
0
0
1
3
1
2
2
0
0
0
0
2
0
1
0
1
2
2
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
2
0
2
2
2
2
0
0
0
0
0
0
0
0
0
0
0
2
1
2
2
0
0
0
1
0
0
0
0
1
2
0
0
2
2
0
0
2
2
0
0
0
0
2
0
2
1
0
0
2
2
0
0
0
0
0
1
2
0
0
1
0
0
1
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
1
0
0
1
2
1
2
0
0
1
1
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
1
1
0
1
3
1
0
1
0
0
0
1
3
0
0
1
2
0
0
0
0
0
2
1
0
0
0
0
1
1
1
1
0
1
0
0
1
0
0
0
2
2
0
1
0
0
0
0
1
0
0
2
1
0
0
0
0
0
3
0
2
0
1
2
0
0
0
0
2
2
0
0
2
0
2
0
4
0
0
1
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
1
2
0
0
2
2
1
0
0
0
2
1
0
0
1
0
1
0
2
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
2
1
1
2
0
0
0
2
0
2
0
0
0
0
3
2
1
0
0
1
0
0
1
1
3
0
0
0
0
1
0
0
5
2
0
1
2
1
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
1
0
0
0
0
3
1
1
0
0
1
0
2
0
1
2
0
0
2
1
1
0
0
0
2
0
1
0
2
2
0
0
0
0
2
2
0
0
0
3
2
0
0
2
0
0
2
0
0
0
3
1
0
0
0
1
0
1
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
1
2
1
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
1
0
0
3
0
1
0
0
0
0
2
0
0
0
0
2
0
0
1
1
0
0
4
2
0
0
0
0
2
0
0
2
2
0
0
2
0
0
0
0
1
0
0
0
0
0
1
2
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
1
1
0
3
1
0
1
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
2
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
3
0
0
1
0
0
0
0
2
1
0
0
0
0
1
0
1
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
3
2
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
1
2
0
0
0
0
2
0
2
0
0
2
0
2
2
0
0
0
0
0
3
0
1
2
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
3
0
0
0
2
1
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
4
0
1
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
1
0
0
2
0
0
1
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
2
1
0
0
2
0
0
0
1
2
0
1
0
2
0
0
0
1
0
0
0
2
0
1
0
0
3
1
0
2
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
1
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
2
1
2
1
0
1
0
0
2
2
5
2
1
0
0
0
0
0
0
0
0
0
2
1
0
0
2
1
2
0
2
0
0
2
1
0
0
2
0
0
2
0
0
0
2
0
0
0
0
1
1
1
0
2
0
0
1
1
0
2
2
2
0
2
0
1
1
1
0
1
0
2
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
1
2
0
2
0
1
2
0
0
0
2
1
1
0
0
1
0
0
1
0
0
2
0
0
1
2
2
1
0
0
0
0
0
2
0
0
0
0
3
1
1
0
1
2
0
2
2
4
0
1
0
0
0
0
0
0
0
2
0
2
0
0
2
0
3
0
0
2
0
2
1
1
0
0
2
1
1
1
0
0
0
0
1
1
2
0
2
0
2
1
3
0
0
1
0
0
0
1
0
2
0
2
7
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
2
2
0
2
0
2
0
0
0
1
0
2
1
0
0
0
0
1
3
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
1
1
0
1
1
2
0
1
0
0
0
0
0
0
3
0
0
2
0
2
2
0
0
0
0
0
0
2
0
2
1
2
0
0
2
0
1
0
0
0
2
0
0
1
0
0
0
1
0
2
1
0
2
2
0
0
0
1
1
2
1
0
0
0
0
0
2
1
0
0
0
0
1
1
0
1
0
0
3
2
1
0
0
1
0
0
2
0
0
0
0
1
2
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
1
1
0
0
0
0
1
0
0
1
0
1
0
1
2
0
0
0
0
1
0
1
0
0
0
0
1
1
0
2
1
1
0
2
1
0
2
1
0
0
2
1
0
2
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
1
0
2
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
1
1
0
0
2
0
1
0
2
0
2
0
1
0
0
1
0
0
0
2
0
0
0
1
2
0
0
0
1
1
1
0
0
4
1
0
0
0
2
0
0
2
0
0
0
0
0
1
2
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
1
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
2
0
0
0
2
0
0
0
1
0
0
1
0
0
1
2
0
2
0
1
0
2
2
0
0
10
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
1
0
0
2
0
0
0
2
1
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
2
0
0
0
0
0
2
2
0
0
0
2
0
2
2
0
2
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
2
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
1
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
2
2
1
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
2
0
0
0
2
0
1
0
2
0
1
2
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
3
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
1
2
0
0
1
0
0
0
3
0
1
1
0
0
0
0
2
0
1
0
0
1
2
0
0
0
0
0
1
2
0
0
0
0
1
1
1
1
0
0
0
2
0
1
2
6
0
2
0
0
0
1
0
0
2
0
0
0
0
2
1
0
0
0
0
0
2
0
3
0
0
2
1
0
0
2
1
2
0
3
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
2
2
1
0
2
1
0
2
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
2
2
1
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
1
2
0
1
0
0
1
0
0
1
0
3
0
0
2
0
0
2
0
2
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
3
1
0
0
2
1
1
0
1
2
0
0
3
0
2
1
0
0
0
1
0
0
2
0
2
0
2
0
0
2
2
4
2
1
0
2
0
0
0
0
0
0
0
0
0
0
4
2
1
2
0
0
0
1
2
0
3
0
0
0
0
0
2
1
0
2
2
2
0
0
1
0
3
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
2
0
1
2
7
0
0
0
0
0
1
1
2
1
0
0
0
0
0
2
2
2
2
1
0
2
2
0
0
0
2
1
2
2
0
0
0
0
0
0
0
1
1
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
2
0
2
2
0
0
0
0
0
0
0
0
0
3
1
0
1
0
0
0
0
2
1
2
0
0
2
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
3
0
3
1
0
2
0
0
2
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
1
1
1
0
0
2
4
0
0
2
2
4
2
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
2
2
2
0
1
2
1
0
0
0
0
0
3
0
1
1
0
0
0
2
0
0
0
0
1
3
0
0
2
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
2
6
0
1
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
2
1
1
2
2
0
1
0
0
0
0
0
0
2
0
1
1
1
0
0
0
0
1
2
0
0
0
0
0
1
0
2
2
0
0
0
2
4
3
2
0
0
0
0
2
0
0
0
0
0
3
0
1
2
0
0
1
0
0
1
1
1
2
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
2
1
0
0
2
0
0
0
1
0
0
0
3
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
1
0
0
2
0
1
1
0
0
0
2
0
0
2
0
1
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
1
1
1
1
1
0
0
2
1
0
0
2
0
1
2
0
0
2
0
0
0
0
2
0
0
0
0
1
2
1
1
0
0
0
0
0
0
2
2
2
1
0
0
1
1
0
0
0
3
1
0
2
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
3
0
0
1
2
0
0
1
1
0
0
0
1
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
2
2
0
0
0
1
1
2
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
2
0
0
0
2
0
0
2
0
0
0
2
1
0
1
0
0
0
0
1
0
2
0
1
2
0
0
0
0
0
0
2
2
4
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
2
0
0
1
1
3
0
2
0
0
0
1
0
1
2
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
1
0
0
1
2
0
0
1
1
0
1
0
0
1
0
1
0
1
1
2
0
0
3
0
0
1
0
0
0
0
1
1
2
0
2
0
0
1
0
0
0
0
2
0
0
1
2
1
0
2
0
0
0
1
2
0
0
1
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
3
0
1
0
1
0
0
3
0
1
0
1
0
0
0
2
0
0
1
0
0
2
0
0
1
0
1
0
2
0
0
0
2
0
3
0
0
1
2
0
0
0
2
0
1
0
0
0
1
1
2
0
0
1
2
0
1
0
0
0
1
2
0
2
1
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
1
2
0
0
1
2
0
0
2
1
2
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
2
0
5
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
2
1
2
0
0
0
0
1
0
0
0
0
2
0
0
0
2
1
0
2
2
0
0
1
0
0
0
0
0
0
1
0
2
0
2
0
0
0
1
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
2
1
1
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
1
0
1
2
0
1
0
2
0
0
0
2
0
2
1
0
0
0
0
0
1
0
0
3
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
2
0
0
2
0
1
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
2
0
1
1
1
3
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
3
1
0
0
0
0
2
0
3
4
2
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
3
1
2
0
0
0
0
1
0
2
0
1
2
0
0
0
0
2
0
0
0
1
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
2
2
3
0
0
2
0
1
1
1
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
2
0
2
0
0
1
2
0
1
0
9
0
1
1
0
0
0
1
2
0
0
1
0
1
0
0
2
0
0
0
0
1
2
1
2
0
2
0
0
0
7
2
1
1
0
0
0
1
0
0
0
1
2
1
0
0
2
0
1
2
0
0
2
0
0
1
0
0
1
2
0
0
0
0
1
1
0
0
0
2
2
1
2
1
1
0
0
0
0
1
1
0
0
2
0
1
0
0
0
0
0
1
2
1
0
0
0
0
0
2
0
0
0
1
0
1
0
1
2
2
0
1
0
1
0
0
2
0
0
0
2
1
0
0
0
3
1
1
1
0
1
0
0
0
0
0
0
0
0
2
2
0
1
0
0
2
0
0
0
1
1
2
0
1
0
1
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
2
0
0
1
0
0
0
0
2
0
0
2
2
0
0
0
2
2
0
0
3
0
2
0
2
0
2
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
1
2
0
0
2
1
0
0
2
1
0
1
0
0
0
0
0
0
2
1
0
0
2
0
3
0
2
0
0
2
0
0
1
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
4
2
1
0
1
0
0
0
0
0
1
0
0
0
0
2
0
2
2
0
0
0
1
2
0
1
1
2
1
0
1
1
2
0
2
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
1
2
0
2
0
0
1
1
1
2
0
0
2
0
2
0
0
0
0
1
0
0
0
2
0
2
1
0
0
1
0
1
0
2
0
0
0
0
1
0
3
2
0
0
0
2
0
0
0
2
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
2
1
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
1
1
0
1
0
2
1
0
2
1
1
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
2
2
0
2
0
0
0
1
1
0
2
2
2
0
0
2
0
0
2
0
0
0
0
0
2
0
2
0
2
0
1
1
0
2
1
2
2
2
0
0
1
0
0
0
2
0
2
1
0
2
1
1
0
0
0
0
1
1
0
0
0
0
3
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
2
2
2
0
0
3
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
2
0
0
2
4
0
0
0
0
1
1
0
2
0
0
0
1
0
0
0
0
0
6
0
1
0
3
0
1
0
0
0
0
1
0
1
0
1
1
0
0
1
1
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
1
2
2
0
0
1
0
0
0
1
0
1
3
1
0
1
1
0
2
0
0
2
1
0
0
2
0
0
0
1
0
0
0
0
1
0
0
2
0
1
2
1
0
0
0
1
0
0
0
2
0
1
0
0
0
4
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
1
2
1
0
0
0
0
0
2
0
4
0
1
0
0
2
1
0
0
0
2
0
0
0
0
1
1
0
0
2
0
0
0
0
1
0
2
1
2
0
0
0
0
1
0
0
0
1
0
0
0
2
1
0
1
0
0
0
2
0
0
0
0
0
2
0
0
2
0
2
2
1
2
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
2
0
0
0
2
0
2
0
2
0
0
2
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
3
0
0
2
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
1
0
0
2
0
0
0
2
1
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
2
0
3
0
1
2
0
1
2
2
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
4
0
0
0
0
2
0
0
0
0
0
2
2
0
0
2
0
2
0
1
0
3
1
0
0
0
1
0
3
1
2
0
0
0
0
2
0
0
0
0
1
0
2
0
0
1
1
0
1
0
1
0
0
0
0
0
1
1
0
2
0
3
2
1
2
1
0
2
0
0
0
2
0
0
2
1
0
1
0
2
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
1
0
0
0
0
1
2
0
0
0
0
1
0
0
0
1
1
1
2
1
0
0
1
1
0
1
0
1
0
0
0
0
1
1
0
1
2
0
1
0
0
0
1
0
0
0
0
0
2
0
1
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
2
2
0
0
0
2
0
2
1
0
2
0
0
2
2
0
0
0
0
0
1
0
2
0
0
0
2
0
2
1
0
0
2
0
0
0
2
0
2
1
0
0
0
2
0
0
0
2
0
0
0
2
1
2
1
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
1
1
1
1
2
2
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
2
0
0
0
0
0
3
0
2
0
0
0
2
0
1
0
0
2
0
0
3
0
0
0
2
0
1
2
2
0
0
1
1
0
1
0
0
0
0
1
0
1
0
2
0
0
0
0
2
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
1
0
1
0
0
1
1
1
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
2
0
0
0
1
0
2
1
0
0
1
0
0
0
0
0
0
1
2
0
1
1
0
1
0
1
2
0
0
1
0
1
0
0
0
0
0
0
0
2
0
2
1
0
0
2
0
0
2
0
0
0
0
0
0
5
0
0
0
0
0
1
2
2
2
0
0
0
0
0
1
1
0
2
1
2
0
1
5
0
0
0
0
0
1
0
0
1
3
0
0
2
1
0
1
0
1
0
0
0
0
0
2
0
1
0
0
0
2
0
1
0
0
2
0
2
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
2
0
2
0
0
1
1
0
0
0
0
0
0
2
1
2
0
0
2
1
1
0
0
2
1
0
1
0
0
1
0
2
1
2
1
2
0
0
0
0
1
0
0
0
0
0
0
2
0
2
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
1
2
0
1
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
1
1
0
0
0
0
1
0
2
0
0
2
0
0
0
2
0
0
0
0
1
2
0
0
1
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
1
2
0
0
1
1
2
2
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
1
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
2
2
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
3
2
1
0
2
0
1
2
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
2
0
0
2
0
0
0
2
2
0
0
2
0
1
1
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
2
2
1
0
0
2
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
2
0
0
1
1
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
4
0
0
0
2
1
0
0
0
0
4
0
1
1
0
0
0
2
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
7
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
1
0
0
1
2
0
0
1
0
1
0
0
0
0
0
0
0
2
0
1
1
0
1
0
0
0
0
0
0
2
2
0
0
0
1
0
1
2
0
0
0
0
1
0
0
0
1
1
1
1
0
2
2
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
2
2
1
2
0
0
0
2
3
1
1
0
1
0
0
3
0
0
0
2
0
0
0
0
0
0
0
2
0
2
1
0
2
0
0
4
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
3
1
0
0
0
0
0
1
3
0
1
2
0
0
0
1
0
1
0
2
1
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
2
2
0
0
2
1
1
0
3
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
2
1
0
0
0
2
0
3
0
0
2
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
2
0
2
2
1
2
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
3
2
0
1
1
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
2
0
0
0
2
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
1
0
0
0
1
1
2
1
1
0
2
0
0
0
2
0
0
0
1
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
2
0
2
0
0
1
2
0
0
2
0
3
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
1
0
0
1
0
2
0
2
0
0
2
0
0
2
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
3
0
0
2
0
0
2
0
0
0
0
1
0
0
1
0
1
0
2
0
0
1
2
2
0
0
1
7
1
0
0
1
0
1
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
2
2
1
0
0
2
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
2
1
0
0
2
2
0
2
3
0
0
1
1
2
1
0
2
0
0
0
1
0
0
1
0
0
0
1
0
1
1
0
2
0
0
0
0
0
1
0
0
0
0
1
1
0
2
0
0
2
0
1
0
0
0
2
0
0
1
2
0
2
1
0
0
1
0
2
0
2
2
2
2
1
0
1
2
0
1
0
1
3
0
2
0
0
1
0
0
2
0
0
0
0
2
1
0
2
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
9
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
2
0
2
1
2
0
0
0
0
2
0
2
2
0
1
0
2
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
1
0
0
0
2
2
0
1
4
1
2
0
0
0
0
1
0
0
1
2
0
0
1
0
0
0
0
1
0
2
0
0
1
0
0
1
0
2
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
2
2
0
1
0
0
0
0
1
1
0
2
0
1
0
1
0
0
0
0
0
1
0
2
0
2
0
0
1
0
0
2
0
3
0
1
1
0
0
1
0
2
0
2
2
0
0
1
0
1
0
0
1
1
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
2
0
2
0
0
0
2
2
1
1
0
0
2
0
0
2
0
0
0
2
0
2
0
0
1
0
1
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
2
0
2
2
0
0
2
1
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
4
0
1
0
0
0
0
0
0
2
0
0
1
2
0
0
0
2
0
0
0
0
0
1
0
0
0
2
2
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
2
0
0
1
0
2
0
0
2
0
2
0
0
1
0
0
1
0
0
0
0
0
0
1
2
1
2
0
0
2
0
1
0
0
0
1
0
0
0
3
2
1
2
0
2
0
1
0
0
0
0
0
2
2
0
2
1
3
0
0
0
0
0
0
0
0
0
0
1
5
0
0
2
0
3
2
0
2
0
0
0
3
0
0
0
0
2
2
1
1
0
0
1
0
7
0
0
1
0
1
1
2
0
2
0
3
0
2
2
0
2
0
0
0
2
1
0
0
2
1
0
2
0
0
0
0
6
1
0
0
0
3
0
0
0
0
1
3
0
0
2
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
3
0
0
3
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
1
1
1
1
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
1
2
0
0
1
2
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
2
1
0
2
0
1
4
0
0
0
1
1
0
0
0
2
0
2
0
0
1
1
0
0
0
0
2
0
1
0
0
2
0
0
1
1
0
0
0
1
0
0
0
0
2
0
0
0
1
0
1
1
0
2
0
0
0
2
0
0
1
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
2
0
0
2
1
2
0
0
0
2
0
0
0
0
0
3
0
0
2
0
0
0
2
1
0
2
0
0
3
0
1
2
2
0
0
0
0
2
0
0
1
3
1
0
1
1
0
0
2
2
1
0
0
0
0
0
0
0
0
2
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
7
0
1
0
2
1
2
0
0
0
0
2
0
0
1
0
1
0
0
0
1
1
0
2
1
0
0
0
0
0
1
0
0
0
1
1
1
1
0
2
0
0
0
0
0
1
1
0
0
0
2
3
0
0
0
2
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
2
1
0
0
0
0
4
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
1
2
0
0
1
0
0
0
1
0
0
0
1
2
0
0
1
0
0
1
0
1
0
2
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
1
1
1
0
0
2
1
1
0
1
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
4
0
2
2
1
1
0
0
0
0
0
0
0
0
0
2
2
0
1
2
2
0
0
0
2
1
2
2
0
0
0
0
0
1
1
2
0
1
0
0
1
2
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
3
0
2
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
1
0
0
2
1
0
0
0
3
0
0
0
3
0
2
0
0
2
0
1
0
0
0
0
2
1
0
0
0
1
1
0
1
0
0
0
0
1
0
1
0
0
1
0
0
3
0
2
4
1
1
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
2
0
0
2
0
0
0
2
2
0
1
0
0
0
1
1
0
0
0
0
1
1
2
0
1
2
0
2
2
1
0
0
0
1
1
0
2
0
0
0
0
0
0
0
2
2
2
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
3
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
1
0
0
4
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
2
1
0
1
1
0
2
0
2
1
0
0
1
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
1
1
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
1
0
0
1
0
2
0
0
4
2
2
0
2
0
0
0
2
1
1
1
0
1
0
0
1
0
0
3
2
0
0
1
0
0
2
2
0
0
0
1
1
0
1
0
0
1
0
0
0
0
2
0
0
0
0
2
2
0
0
2
0
2
0
2
0
0
0
0
0
0
1
2
0
1
1
0
1
0
0
0
0
0
2
2
0
1
2
0
0
0
2
3
0
0
0
0
0
2
0
0
0
2
2
1
2
1
0
0
0
1
2
0
0
0
0
0
0
1
1
0
0
0
0
1
2
0
0
2
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
2
0
1
1
1
0
2
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
2
2
0
3
0
0
0
2
1
2
0
0
0
0
0
0
1
0
5
0
1
0
0
1
1
2
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
3
0
0
2
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
1
0
0
1
0
2
1
0
0
2
1
2
0
0
1
2
0
0
0
0
1
0
1
0
0
1
0
2
0
0
0
1
0
0
3
0
0
1
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
2
3
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
2
0
0
0
1
2
0
0
2
0
0
0
0
0
0
2
4
0
0
2
0
1
1
0
0
0
2
0
4
1
0
2
2
1
1
0
2
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
1
0
0
2
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
1
2
0
0
0
0
0
0
0
0
0
4
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
1
1
0
0
0
0
0
4
0
2
1
0
0
2
0
0
2
2
3
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
1
1
0
3
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
1
1
0
0
2
1
0
2
0
2
0
1
0
0
0
0
2
1
1
1
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
2
2
2
1
0
1
0
3
0
0
1
0
0
0
0
0
0
2
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
4
2
1
1
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
3
0
0
1
0
0
3
0
0
0
1
1
0
0
1
1
1
2
0
0
0
2
0
1
0
0
2
0
1
0
1
1
0
0
0
1
0
0
0
0
2
1
0
0
1
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
2
0
5
0
1
1
2
0
0
0
1
0
0
0
2
2
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
1
2
0
0
2
1
0
2
3
2
2
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
2
1
1
0
1
2
0
0
1
0
1
0
0
0
0
2
1
0
0
2
2
1
1
0
1
0
0
1
0
1
2
0
0
0
0
1
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
1
1
1
0
2
0
0
2
1
0
0
1
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
3
2
1
0
0
0
2
0
1
0
0
0
2
0
0
0
1
0
2
0
1
0
1
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
1
4
0
0
0
2
2
1
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
5
1
1
0
2
2
0
0
1
2
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
2
2
0
1
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
4
0
1
0
0
0
3
1
1
1
0
2
0
0
0
0
2
0
1
0
0
0
0
1
1
2
0
2
2
0
0
2
0
2
1
2
2
0
0
2
0
2
0
0
2
0
2
2
2
1
3
0
1
2
0
0
1
0
0
2
0
0
1
0
0
2
1
0
0
0
0
2
0
2
1
0
1
0
0
0
1
0
3
0
0
0
1
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
2
0
2
2
1
0
2
0
2
0
1
1
0
1
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
2
0
0
0
0
0
7
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
2
5
0
0
0
0
1
0
0
2
1
1
2
0
1
0
1
0
0
2
0
2
1
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
2
0
0
1
0
0
0
0
1
2
0
3
0
0
2
1
3
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
4
0
0
0
0
0
1
2
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
2
0
2
2
0
1
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
1
1
0
0
0
0
1
0
0
2
0
1
1
0
2
0
2
0
0
2
0
2
2
0
0
2
0
0
3
2
2
2
0
0
0
0
2
0
5
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
2
0
0
1
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
1
1
1
0
0
2
0
0
1
0
2
2
0
1
0
2
0
0
0
2
0
0
0
0
0
1
0
1
0
2
0
1
0
2
0
1
0
0
0
1
0
1
0
1
0
1
0
0
1
0
0
2
2
0
0
0
0
2
0
1
0
2
0
0
0
0
2
2
0
2
2
0
0
1
0
0
0
2
2
3
0
0
0
1
0
0
0
0
1
2
2
0
0
2
0
0
1
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
1
1
2
1
1
0
0
1
0
0
2
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
2
0
1
5
0
0
0
0
0
0
0
1
1
0
0
1
2
0
2
2
0
0
2
1
2
0
0
0
0
0
0
2
0
0
1
0
1
0
0
1
0
2
3
1
0
0
0
5
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
1
0
0
0
0
0
0
0
1
2
0
1
0
2
1
0
0
0
1
0
0
1
2
1
1
2
0
0
0
0
0
3
0
0
0
1
1
1
0
4
0
0
0
0
1
0
0
2
1
0
0
2
0
1
0
0
1
1
1
2
0
0
2
0
0
1
1
2
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
1
0
0
1
0
2
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
3
0
0
0
2
1
0
2
0
0
0
2
0
1
0
0
2
0
0
0
1
0
0
0
0
2
3
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
2
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
2
0
0
0
0
0
2
0
1
2
0
0
1
1
1
0
0
0
3
0
2
2
0
0
2
0
0
0
0
2
0
2
0
1
0
2
0
0
2
2
0
1
1
0
0
1
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
2
2
0
1
0
1
0
0
7
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
2
2
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
2
0
0
1
2
0
1
1
0
0
1
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
1
1
0
1
0
0
0
0
0
0
2
0
4
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
1
1
0
0
0
2
2
0
0
0
1
0
2
0
0
1
0
0
0
1
3
0
2
0
0
1
1
0
0
0
0
2
0
3
2
2
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
1
1
0
1
0
0
2
2
1
2
1
0
1
0
0
1
1
0
1
0
0
1
0
0
0
0
1
2
1
1
2
2
0
0
0
0
0
0
2
2
0
0
2
0
0
0
1
0
0
0
2
1
1
0
0
0
0
0
0
1
1
1
0
0
0
1
1
0
2
1
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
2
1
0
1
0
0
0
2
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
2
1
0
0
1
0
0
2
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
4
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
2
1
0
2
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
2
1
1
0
0
0
0
1
0
1
0
0
0
2
2
0
0
0
2
2
0
0
2
0
0
0
1
0
0
3
0
0
0
0
0
2
0
0
0
6
0
0
0
1
0
0
0
0
0
0
0
0
1
0
3
0
2
1
0
2
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
2
2
2
1
1
1
0
0
0
0
1
0
0
2
0
2
0
0
1
0
0
1
0
0
1
0
0
0
0
1
1
2
1
1
0
0
2
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
2
0
3
1
0
1
0
0
0
1
0
2
2
0
1
0
0
0
2
1
2
0
0
0
1
0
0
0
2
3
2
0
0
0
2
0
1
0
2
0
0
0
0
2
0
1
2
0
1
1
0
0
0
2
1
0
0
1
3
0
0
0
0
3
0
2
0
0
0
1
0
0
0
3
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
4
1
0
0
1
0
0
2
0
1
0
2
0
0
1
0
0
2
2
1
0
0
2
0
1
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
1
0
0
1
0
3
0
1
0
0
0
2
3
1
1
1
1
1
0
0
0
1
0
0
2
1
1
0
0
2
0
2
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
1
0
2
2
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
2
2
0
0
1
0
0
0
0
0
3
0
0
2
0
2
2
0
0
0
0
0
0
2
0
1
0
0
0
1
1
0
2
1
0
0
1
0
0
0
1
0
2
0
0
0
0
0
4
0
0
2
0
2
2
2
0
1
2
1
0
0
3
0
0
0
0
2
0
0
2
0
0
1
0
1
2
2
0
1
0
0
0
4
3
2
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
3
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
1
0
1
1
0
0
0
0
0
3
0
1
0
2
2
0
0
0
0
2
1
0
0
0
0
0
3
0
2
0
5
0
2
2
0
2
2
2
1
0
0
2
1
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
1
1
0
2
1
1
2
2
0
2
0
0
0
2
1
1
0
1
1
0
0
3
0
0
0
1
1
2
0
2
0
0
2
0
0
2
1
2
0
0
0
0
0
0
0
0
1
0
1
2
2
0
0
0
2
0
0
0
0
1
1
1
1
4
0
1
2
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
1
2
0
2
0
0
2
0
0
0
1
2
2
1
0
2
0
0
0
0
2
2
0
0
0
0
0
2
0
0
1
2
1
0
0
0
0
1
0
0
0
1
0
2
0
2
2
0
0
2
1
2
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
3
0
0
0
3
1
0
0
1
0
2
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
2
2
1
0
2
0
0
0
1
0
0
2
1
0
0
0
0
2
0
0
0
0
2
1
0
0
2
0
1
0
1
1
0
2
1
0
0
0
0
1
1
1
0
0
0
1
2
0
1
2
0
0
2
0
0
1
0
0
2
0
2
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
2
2
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
1
2
2
0
1
0
0
0
1
1
0
0
2
0
0
0
1
0
1
0
0
0
4
1
0
0
0
0
0
0
1
0
1
1
0
0
2
2
0
0
0
1
0
2
0
0
0
1
1
0
0
2
2
2
1
0
0
0
2
0
3
2
2
0
1
0
0
0
0
0
2
0
0
1
0
0
0
2
2
1
1
1
0
2
0
0
2
1
2
0
1
0
2
0
1
0
2
2
0
0
0
1
0
2
1
0
1
1
0
0
0
2
0
0
0
0
0
2
0
0
0
8
0
0
0
1
1
2
0
1
0
0
0
1
1
0
2
2
0
2
0
1
2
1
2
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
1
1
0
0
2
1
0
1
0
0
2
2
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
1
2
0
2
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
1
2
1
0
0
0
1
2
0
0
0
0
1
1
2
0
2
0
0
2
0
0
1
0
2
0
0
0
1
2
0
1
2
0
0
3
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
2
0
2
0
0
1
2
0
0
1
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
2
1
3
0
0
0
2
1
0
1
0
0
0
2
1
0
0
0
0
0
1
0
0
2
2
0
2
0
0
1
0
0
0
0
0
0
1
0
0
1
0
2
2
2
1
0
0
0
2
0
0
0
0
2
1
0
1
2
0
2
2
0
1
0
1
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
1
1
2
0
2
1
0
4
0
0
0
6
1
1
0
1
1
0
2
0
0
1
0
1
0
0
0
0
2
2
1
1
2
5
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
2
0
0
0
1
0
2
0
0
0
0
1
0
0
1
0
1
0
1
0
1
0
0
0
0
1
0
0
1
1
2
1
0
0
1
0
0
0
1
0
3
0
0
1
1
0
1
1
0
1
1
0
3
2
1
2
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
2
1
1
0
2
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
2
1
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
1
0
0
1
0
0
0
0
1
1
0
1
0
0
1
0
0
2
3
2
0
0
0
2
0
2
0
0
0
0
2
2
0
1
0
1
0
1
2
0
0
0
0
0
0
1
0
0
2
2
0
4
0
0
1
3
0
1
2
0
0
0
1
1
1
0
2
0
0
0
0
0
0
2
0
0
0
0
4
0
1
1
0
0
0
1
0
2
2
2
0
0
1
1
1
0
0
1
0
0
0
0
3
3
0
0
0
0
0
0
3
0
0
1
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
2
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
3
0
1
0
0
0
0
0
2
0
1
0
0
2
1
1
0
0
0
1
0
1
0
2
2
0
0
0
0
0
0
0
0
1
0
0
2
2
2
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
1
0
0
2
0
1
0
0
0
0
0
0
2
2
10
0
0
0
0
0
2
0
2
0
1
0
0
0
1
2
2
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
2
1
1
0
0
2
0
2
0
1
0
0
0
0
2
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
2
0
0
1
0
0
2
2
0
1
0
1
0
0
3
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
7
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
2
2
0
2
0
2
0
0
0
1
0
0
2
2
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
1
0
0
0
0
2
0
0
2
0
2
3
0
0
0
2
1
0
0
0
1
0
0
4
1
0
0
1
0
3
0
2
2
0
1
0
1
0
2
2
0
0
0
0
3
2
3
0
1
1
0
0
1
0
0
4
0
0
0
0
1
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
3
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
2
0
0
1
2
0
0
1
0
0
0
2
1
0
1
0
0
0
0
2
0
0
2
0
2
1
2
0
0
3
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
1
0
0
2
1
1
0
1
0
0
2
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
3
0
0
2
1
0
0
0
0
1
1
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
1
2
0
0
0
1
0
0
0
3
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
1
0
2
0
0
3
2
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
1
2
0
0
1
0
1
1
3
1
0
1
0
2
0
1
0
2
0
0
2
0
0
1
0
0
0
0
0
0
2
0
1
0
1
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
1
3
0
1
1
0
0
0
1
0
0
0
0
3
1
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
2
2
2
0
0
1
0
0
2
0
0
2
0
2
1
2
3
0
0
0
0
0
1
0
2
1
0
1
1
0
0
0
1
3
0
0
0
0
2
1
0
0
0
3
0
1
0
0
0
0
0
1
0
1
0
2
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
1
1
2
0
0
0
0
6
1
0
0
0
2
0
2
2
0
1
0
1
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
3
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
1
1
1
0
1
2
0
0
1
2
0
0
0
2
0
0
2
0
0
0
0
1
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
2
0
1
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
1
0
0
0
0
1
2
0
1
0
1
0
0
0
0
2
1
2
0
0
0
0
1
0
1
3
2
0
1
3
0
0
1
0
0
0
0
1
0
0
0
2
0
2
0
0
2
0
0
2
1
0
0
0
1
0
2
2
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
1
0
0
0
3
1
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
3
0
0
5
0
0
1
1
1
1
0
0
1
1
0
0
2
0
0
2
2
0
0
0
1
0
1
2
1
0
0
0
0
0
0
0
1
1
1
0
2
1
0
2
1
0
0
0
0
0
0
0
8
0
0
0
0
0
0
0
2
0
1
0
3
2
2
1
0
2
2
0
0
0
0
1
0
3
1
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
2
0
2
3
0
0
0
0
2
0
3
0
0
1
2
0
0
0
0
0
2
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
2
1
0
1
0
1
0
2
2
2
0
0
0
0
1
0
0
0
0
0
0
2
1
1
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
3
0
1
1
2
0
0
0
0
0
2
0
1
0
0
6
0
1
2
0
0
2
0
0
0
0
1
2
0
0
0
2
2
0
0
0
0
0
1
0
0
1
0
1
0
2
0
1
0
0
2
1
0
0
2
0
0
2
0
1
0
0
0
2
3
3
2
0
0
0
0
1
0
0
0
0
1
0
2
0
1
0
2
1
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
1
0
1
0
0
3
0
0
0
0
1
0
0
0
1
0
0
0
2
2
0
1
0
0
2
0
0
0
0
0
1
2
1
1
0
0
0
0
2
2
0
1
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
1
1
0
0
0
1
0
0
0
0
1
0
0
2
1
2
0
0
0
0
0
0
1
6
3
0
0
2
0
1
0
0
2
0
1
0
0
0
2
0
0
0
2
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
2
1
0
0
1
2
0
0
0
2
2
0
1
1
0
0
0
0
2
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
2
1
0
0
0
0
0
2
2
0
0
1
1
0
1
0
2
0
1
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
5
0
2
1
2
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
2
0
1
0
2
0
2
2
0
2
0
2
1
1
2
1
0
1
0
2
1
2
1
2
0
1
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
1
0
1
0
0
2
0
2
0
0
1
0
1
0
1
4
2
1
0
2
1
3
2
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
3
0
0
2
0
1
0
0
0
1
0
0
0
0
2
0
0
1
0
0
1
0
0
2
1
0
0
1
1
0
2
0
1
0
1
2
1
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
1
1
0
0
0
0
0
0
2
0
1
0
0
1
1
0
0
2
1
0
0
0
2
0
0
2
2
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
1
0
1
0
1
0
0
0
0
0
1
2
0
0
1
1
1
0
0
0
2
2
0
3
1
1
0
1
0
2
1
0
0
0
0
2
0
0
0
1
0
0
1
1
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
2
2
0
0
1
0
0
0
1
0
2
2
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
3
0
0
0
0
0
1
1
0
0
0
0
2
0
2
0
0
0
2
0
0
0
2
0
0
1
1
1
0
0
3
1
2
0
0
0
2
0
0
1
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
4
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
3
1
2
0
0
0
1
0
1
0
0
0
0
0
0
0
1
3
0
2
2
0
0
0
3
0
0
1
2
0
0
1
1
2
1
2
0
0
0
1
0
0
0
3
0
0
0
0
2
2
0
3
0
1
1
1
0
2
0
1
0
2
0
1
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
3
0
0
0
1
1
0
0
0
0
0
1
0
1
2
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
3
0
0
1
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
1
1
1
0
0
0
0
1
3
0
0
0
2
0
2
0
0
0
0
0
1
0
0
1
1
0
0
0
2
0
1
0
0
1
2
0
0
0
0
0
2
0
0
1
2
1
0
0
1
1
0
0
1
0
0
0
0
0
1
0
2
0
0
0
2
0
3
1
0
0
1
1
0
0
0
0
0
0
0
0
1
2
0
1
1
3
0
0
2
3
1
2
0
2
0
1
0
0
0
0
0
1
0
0
0
1
2
0
2
1
0
4
2
0
0
0
1
2
0
2
0
2
0
3
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
1
2
0
2
1
0
0
1
2
0
2
1
0
2
2
1
0
0
0
0
0
1
0
1
0
1
0
2
0
2
0
3
1
0
0
0
1
0
2
0
1
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
2
0
0
1
0
1
0
2
1
0
3
3
1
0
2
0
0
0
1
0
0
0
3
0
0
0
1
0
0
0
0
0
0
2
0
1
1
3
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
2
0
2
0
0
2
2
0
2
0
7
0
0
0
0
0
3
0
1
1
0
0
0
1
2
0
2
0
1
0
0
0
1
4
1
2
0
2
0
0
0
1
0
1
0
1
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
1
0
0
0
2
4
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
1
4
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
2
1
0
0
0
1
0
2
0
0
1
0
0
0
1
0
1
1
0
0
2
2
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
1
0
0
2
1
0
0
1
0
0
0
0
4
2
2
0
1
1
0
2
1
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
2
0
2
1
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
1
1
2
2
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
2
1
0
2
0
0
0
0
0
0
2
0
0
1
2
0
0
2
0
0
2
0
2
1
1
1
0
2
1
0
0
0
2
0
0
1
0
0
1
0
0
0
0
2
0
0
0
1
1
2
0
0
0
0
1
2
0
0
0
0
2
1
3
0
0
2
0
0
0
1
0
2
1
0
1
0
0
0
0
2
1
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
1
2
1
3
0
2
0
1
0
1
0
1
0
0
1
2
0
0
1
0
1
0
0
0
0
0
2
0
2
0
0
0
1
3
2
0
0
2
0
0
1
2
0
1
2
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
2
2
2
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
4
0
0
0
0
0
1
0
0
2
2
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
2
1
2
0
0
0
0
0
1
0
0
0
1
3
0
0
0
0
1
0
0
0
0
0
3
0
0
3
0
3
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
1
0
4
1
0
2
0
2
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
2
0
0
0
0
0
0
1
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
2
0
0
1
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
1
2
2
1
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
1
2
0
0
0
1
0
2
0
3
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
2
1
0
0
2
0
1
0
1
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
1
2
0
0
0
0
1
0
3
2
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
2
0
0
0
1
2
0
0
1
0
0
2
2
3
0
0
0
0
0
0
0
0
1
1
2
0
0
1
0
0
0
0
0
2
0
0
0
2
1
1
0
0
0
0
0
0
2
0
1
1
1
1
2
1
0
3
0
0
2
0
0
0
0
1
1
0
2
0
0
0
2
0
1
2
0
0
2
0
0
1
0
0
0
0
3
0
0
2
1
1
0
1
0
0
0
1
2
1
0
2
0
1
0
1
0
0
3
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
1
0
0
0
2
0
0
1
2
1
0
1
0
3
0
0
0
2
0
2
0
0
0
3
0
0
1
0
0
1
1
0
0
0
0
1
0
1
1
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
4
0
0
2
1
0
0
0
1
0
1
2
1
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
6
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
2
0
0
4
4
1
1
0
0
0
0
1
2
0
0
2
3
1
1
3
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
1
0
0
3
0
2
0
0
2
2
0
1
1
0
0
2
2
2
0
0
0
0
0
2
1
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
2
1
3
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
1
2
0
0
0
1
2
0
0
0
0
2
1
1
2
1
1
0
0
0
1
0
1
2
2
0
0
4
0
1
2
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
2
2
3
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
1
1
0
2
0
1
0
0
0
0
2
2
0
2
1
2
2
0
4
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
2
2
0
0
1
0
0
1
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
3
0
0
2
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
1
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
2
0
2
0
0
0
1
1
0
0
0
1
1
0
0
2
0
0
1
1
0
0
0
0
0
5
1
2
0
0
0
0
2
0
1
0
0
2
1
0
1
0
0
0
0
0
2
1
0
0
0
2
2
0
0
2
3
0
0
0
0
1
0
0
0
2
1
0
0
1
0
0
2
2
0
0
2
0
0
2
1
0
1
1
0
0
0
1
0
3
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
2
1
0
1
1
0
4
1
0
1
1
0
0
0
1
0
0
0
2
1
0
1
2
0
2
1
1
0
0
1
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
1
0
0
0
0
2
0
0
2
2
0
0
0
1
0
0
0
2
0
0
0
2
1
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
2
1
0
0
1
1
0
2
0
0
0
0
0
0
1
0
1
1
1
0
0
2
1
1
0
0
1
0
0
2
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
4
0
0
2
2
3
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
1
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
2
1
1
0
0
1
0
0
0
0
3
0
2
0
2
2
0
0
0
2
1
1
0
0
0
0
0
1
2
0
0
0
0
1
2
2
2
0
0
2
0
0
0
0
2
0
2
0
1
0
4
1
0
0
1
0
0
0
0
0
2
1
1
0
0
0
0
0
1
0
0
2
0
0
0
1
0
2
1
0
1
0
0
0
1
1
4
0
0
0
0
3
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
1
1
2
0
0
1
0
2
0
1
0
2
0
0
0
0
0
0
0
1
2
0
0
2
2
0
2
3
2
1
1
0
2
1
0
0
0
0
0
0
2
2
2
4
2
1
2
0
0
0
0
0
0
0
1
0
0
4
0
1
2
0
0
1
2
0
0
0
0
3
2
0
0
2
0
2
1
0
2
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
1
0
0
0
2
0
0
0
1
2
0
0
0
0
3
2
2
0
1
0
0
3
0
2
2
0
0
2
0
2
2
1
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
2
2
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
3
0
0
0
2
0
1
0
0
0
3
1
0
0
1
0
0
0
0
2
1
0
0
0
0
2
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
2
0
1
2
0
0
2
0
1
1
1
0
2
2
0
0
0
1
2
2
2
0
2
0
0
8
2
0
0
1
0
1
1
0
0
2
2
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
2
0
0
2
2
0
2
0
0
0
2
2
0
0
0
2
0
2
0
0
0
2
4
2
0
0
0
2
0
0
0
0
0
0
2
5
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
2
3
0
2
0
3
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
2
0
2
1
3
0
2
0
1
1
0
0
0
0
0
0
2
0
0
0
0
1
2
3
0
0
1
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
1
0
0
2
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
2
2
2
0
1
0
0
1
0
1
2
0
0
1
0
0
0
0
0
1
1
1
0
0
4
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
6
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
2
0
0
0
0
3
0
0
0
0
0
0
0
1
0
1
3
0
0
0
2
2
0
0
2
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
2
0
1
0
1
0
0
0
0
0
0
0
2
0
0
3
0
3
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
1
2
0
0
1
0
2
1
0
0
0
0
0
0
3
2
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
3
0
0
1
1
0
0
2
0
1
2
0
0
0
0
0
3
0
0
0
2
0
0
0
2
1
0
0
1
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
1
0
0
1
2
1
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
1
1
2
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
1
1
1
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
2
0
0
1
2
2
2
2
0
0
0
0
2
0
0
0
1
0
0
0
0
2
1
1
0
0
2
2
2
2
0
1
0
1
0
1
0
0
0
0
0
2
0
2
3
0
2
0
0
2
1
0
0
0
0
2
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
1
1
0
1
1
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
2
2
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
1
0
3
0
2
0
0
0
2
0
0
1
2
0
1
0
0
0
0
2
0
0
0
1
0
1
0
0
0
2
1
0
0
0
2
0
2
2
0
0
0
0
3
2
0
1
0
1
0
0
2
2
0
0
0
1
2
1
0
0
1
1
1
0
0
0
0
1
0
1
2
0
0
1
0
0
2
0
0
2
0
1
0
0
0
0
2
0
2
0
2
2
2
0
0
1
0
1
0
1
0
1
2
2
0
2
0
2
1
2
1
0
1
0
0
1
2
0
0
0
0
1
0
0
2
0
2
0
2
0
0
3
0
0
0
2
0
2
0
2
3
0
0
1
2
0
2
1
0
0
3
0
0
0
0
0
0
0
0
0
1
7
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
1
2
1
3
0
1
0
1
0
0
1
2
1
0
1
1
0
2
0
0
0
0
2
0
0
2
0
1
2
2
2
2
0
0
1
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
2
0
0
1
3
0
0
0
2
0
0
0
1
0
0
2
2
2
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
2
2
1
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
1
0
2
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
2
2
2
2
1
0
0
0
0
3
0
2
0
2
0
1
0
0
2
1
1
0
0
0
0
0
1
2
0
0
3
0
2
0
0
0
1
0
0
2
0
3
0
1
0
2
0
0
0
1
2
0
0
0
2
0
0
2
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
1
0
1
1
0
3
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
2
0
0
1
0
0
1
0
1
0
0
0
2
1
1
0
0
2
1
0
0
7
0
1
1
0
0
0
1
1
2
0
0
0
1
0
2
0
2
0
0
0
2
0
2
1
0
0
1
0
0
0
2
0
2
1
1
0
1
0
0
1
0
0
2
0
0
0
0
0
3
2
0
1
1
1
0
0
1
0
0
1
0
0
2
0
2
0
2
1
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
2
2
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
2
0
0
0
2
2
0
0
1
0
0
0
0
0
1
1
2
0
1
0
0
0
1
0
2
2
0
2
0
2
0
3
0
0
2
0
0
0
2
0
1
1
0
0
0
0
2
0
2
1
0
0
0
0
0
1
0
3
0
0
0
0
0
0
1
2
1
2
0
0
1
0
0
0
2
2
2
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
1
0
1
2
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
2
1
2
2
0
0
1
2
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
3
2
0
2
1
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
2
3
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
1
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
1
0
0
2
0
0
1
0
2
0
0
2
1
0
0
0
0
0
0
0
0
1
0
1
0
2
0
1
0
0
1
0
0
2
3
2
0
0
0
0
0
2
0
0
0
1
0
2
1
0
0
0
0
0
1
3
0
0
2
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
1
0
2
1
0
1
1
1
0
1
0
2
0
0
0
0
2
0
0
0
0
2
1
0
0
0
1
2
1
0
1
2
2
0
2
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
2
0
0
0
0
1
0
2
2
1
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
2
2
0
2
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
4
0
0
1
0
0
2
0
2
0
2
0
0
1
2
0
0
0
0
0
0
0
0
2
0
2
0
0
2
2
0
0
0
1
0
2
0
0
1
0
0
0
2
0
1
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
3
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
2
1
1
0
0
0
0
1
0
4
7
2
2
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
1
0
2
2
0
0
0
0
0
1
1
2
1
1
6
0
0
2
0
1
1
0
2
0
0
0
0
1
0
0
2
1
0
0
0
0
0
2
2
2
2
3
0
0
0
2
1
0
0
0
0
0
1
0
2
0
0
1
4
0
0
0
2
0
2
0
0
2
0
0
0
0
2
1
0
0
2
0
0
0
0
2
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
2
1
0
2
1
0
0
0
0
0
2
0
0
0
0
0
3
0
1
2
1
1
0
0
0
0
0
0
0
2
0
3
0
0
0
2
0
0
0
0
1
1
0
0
2
1
0
0
4
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
2
0
0
1
1
0
0
1
1
0
0
0
1
0
1
2
0
0
1
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
2
1
0
0
0
2
1
0
0
1
2
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
2
2
2
0
1
1
1
0
0
0
1
0
0
0
2
0
2
0
0
2
0
1
0
1
0
0
0
0
0
2
0
2
2
2
2
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
1
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
1
1
0
2
0
0
1
2
1
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
4
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
2
0
0
0
2
2
0
0
2
1
0
2
0
2
2
0
0
0
0
0
2
1
2
4
1
0
0
0
1
0
0
1
0
2
1
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
1
0
1
0
0
0
1
0
1
0
1
0
0
2
2
2
0
7
0
0
0
2
2
0
0
0
0
2
0
0
3
0
0
2
0
1
0
0
0
0
1
0
2
0
1
0
2
0
2
1
1
0
0
0
1
2
1
1
0
0
0
2
1
0
2
0
2
0
0
0
0
0
0
1
0
0
0
2
1
2
0
0
0
2
2
0
1
2
0
0
0
0
0
2
2
0
2
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
2
1
0
1
0
0
2
0
1
0
0
0
1
1
2
0
1
0
0
0
0
2
2
0
0
0
0
1
0
0
1
1
3
2
0
0
0
1
1
1
0
7
0
1
1
1
0
0
0
0
2
0
0
0
0
4
2
0
0
3
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
2
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
3
2
1
0
1
0
0
0
0
2
0
1
0
0
1
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
1
1
0
2
2
2
1
3
2
1
0
0
0
2
3
1
1
0
0
0
0
0
0
0
0
2
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
3
0
0
2
0
2
0
0
1
0
0
1
0
0
0
0
0
1
1
1
2
0
0
1
0
1
0
1
0
0
1
0
0
2
2
0
0
0
1
1
0
0
0
2
0
1
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
3
0
0
3
2
2
1
3
0
0
0
0
0
0
0
3
0
2
0
0
1
0
1
1
0
1
2
0
2
0
2
0
1
0
0
0
0
0
0
1
0
2
0
1
0
0
0
1
2
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
1
1
2
0
0
2
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
4
0
0
1
1
1
0
1
0
2
0
0
0
2
0
2
1
0
0
1
0
2
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
3
1
2
0
1
1
0
0
1
1
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
1
2
0
0
0
0
2
0
0
0
2
1
0
0
2
2
0
0
0
0
0
0
0
2
0
2
0
1
2
0
0
1
0
0
2
1
0
2
1
0
0
0
2
2
1
2
0
0
0
0
0
2
3
0
0
2
0
0
0
2
0
0
0
0
0
0
2
7
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
3
0
0
3
0
0
2
0
3
0
0
0
0
3
1
1
1
0
0
0
0
5
2
0
0
0
0
2
1
1
0
0
2
0
0
0
1
0
1
0
1
0
2
2
2
0
2
0
0
1
0
0
0
0
2
2
2
2
1
1
0
1
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
1
3
2
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
1
0
0
0
2
1
0
0
0
0
0
1
0
1
0
0
2
2
0
2
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
1
0
0
0
0
0
0
2
0
0
2
0
2
0
2
0
0
0
0
3
0
1
1
1
2
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
3
0
1
1
0
0
0
2
0
6
0
0
0
0
0
2
1
0
1
0
2
0
1
0
0
0
2
1
0
1
0
1
4
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
2
0
1
2
0
0
0
3
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
1
2
2
0
2
1
0
0
0
0
2
2
0
1
0
0
0
0
0
2
0
0
0
2
0
0
2
1
0
0
1
0
0
0
1
0
0
1
1
2
1
0
0
1
0
0
1
1
0
0
1
0
0
0
1
2
1
11
0
2
0
0
1
0
4
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
2
2
1
3
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
1
2
1
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
1
0
2
2
1
0
1
2
0
0
0
0
1
0
0
1
0
0
0
0
2
0
1
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
2
1
0
0
1
0
0
2
0
0
0
1
0
0
0
1
0
2
2
0
0
0
1
1
0
1
2
0
2
0
0
0
1
0
1
0
2
1
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
1
0
0
0
2
0
0
0
4
0
0
2
1
0
0
0
2
0
0
0
1
0
0
2
2
4
2
0
0
0
2
1
0
0
0
0
1
1
0
1
2
0
0
1
1
0
2
0
0
0
0
1
0
2
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
2
0
2
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
2
2
0
0
1
0
0
0
2
0
0
0
4
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
1
0
2
0
0
0
0
1
0
0
2
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
2
0
1
1
0
0
1
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
2
1
0
0
0
0
1
1
0
0
2
0
0
2
1
1
1
0
1
0
0
9
0
1
0
0
2
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
2
0
0
0
0
0
0
2
0
6
0
1
1
0
2
0
0
0
0
1
1
0
0
0
1
0
1
1
0
2
0
1
0
0
0
1
1
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
2
1
2
0
0
2
0
0
2
0
1
0
1
0
1
0
0
1
2
1
0
0
2
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
1
2
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
1
0
3
2
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
2
0
0
0
1
0
0
0
2
1
0
1
2
0
5
1
0
3
0
0
0
0
0
2
0
0
2
0
1
1
0
0
0
0
2
1
0
4
0
0
0
0
0
0
2
1
2
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
1
1
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
2
1
0
0
0
0
0
1
0
1
0
3
0
0
2
0
0
0
1
2
1
0
1
0
1
2
0
0
0
1
0
4
2
0
0
1
0
0
0
2
2
3
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
2
0
3
2
0
0
1
1
2
1
1
0
0
0
0
1
2
2
2
1
0
0
0
0
2
1
0
0
0
1
2
0
0
0
0
2
0
0
2
0
0
2
1
0
0
1
0
2
0
0
0
1
0
0
1
0
0
0
0
2
1
2
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
2
1
0
0
2
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
2
0
0
2
0
1
0
2
2
0
2
2
0
2
8
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
1
2
0
0
0
3
2
2
0
1
1
0
0
1
0
0
0
0
2
1
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
2
0
0
0
0
2
1
0
2
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
1
1
1
2
0
0
1
1
0
0
0
0
2
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
1
0
2
0
2
0
0
0
1
2
0
1
0
1
1
0
2
0
0
0
1
0
0
2
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
2
0
0
2
0
1
0
1
0
2
2
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
2
2
0
0
0
2
0
0
0
2
1
0
0
3
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
1
0
2
0
2
0
1
2
0
0
0
0
2
0
0
0
0
3
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
2
2
0
1
1
1
1
2
0
0
0
1
0
1
0
0
2
1
0
0
0
2
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
5
0
1
2
1
0
0
2
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
2
1
0
0
2
2
0
2
0
2
0
0
0
2
0
0
2
0
0
2
1
2
0
4
0
1
0
0
0
2
0
0
0
0
0
2
6
2
1
1
0
0
0
2
0
0
2
0
1
1
0
1
2
0
0
0
2
1
2
1
0
2
1
0
0
1
1
0
1
1
0
2
2
0
0
0
2
2
2
0
0
0
1
3
0
1
0
1
2
0
3
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
3
1
2
0
0
0
2
0
0
1
0
2
3
0
0
2
0
0
0
2
0
0
0
0
2
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
1
0
0
1
1
2
0
1
0
0
5
0
0
0
0
0
0
1
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
2
0
1
1
0
0
2
0
1
0
0
0
0
0
2
0
2
0
1
0
0
0
0
1
0
0
1
0
3
1
0
0
0
1
3
4
1
2
0
0
2
1
0
2
0
2
0
2
0
3
0
0
0
0
0
2
0
0
1
0
2
0
0
0
1
0
1
3
0
1
0
0
0
2
1
0
0
0
1
0
0
0
0
2
0
2
2
1
0
0
0
0
1
2
0
2
0
1
0
2
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
1
0
3
0
0
2
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
3
2
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
1
0
0
0
2
0
0
2
1
2
0
2
0
0
0
1
1
1
2
0
0
2
0
1
0
1
0
0
2
2
2
3
0
0
1
0
0
0
0
2
0
1
0
0
1
2
0
1
0
0
2
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
1
0
1
3
0
2
0
0
2
1
0
0
1
1
2
2
1
1
0
0
0
1
1
2
2
0
0
0
3
0
0
1
0
0
2
0
0
0
0
0
2
0
2
3
2
1
2
2
0
0
0
2
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
2
0
1
0
0
1
0
0
0
0
0
0
0
2
1
0
0
2
0
0
1
2
2
2
0
0
1
0
0
0
2
1
0
0
1
1
0
0
2
2
0
0
0
0
0
0
0
0
2
2
2
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
2
1
0
0
0
0
0
2
1
0
0
0
0
0
2
1
2
0
0
2
2
1
0
0
11
0
1
1
0
0
1
0
3
1
0
0
0
0
8
0
0
0
0
1
0
0
0
0
0
2
0
1
2
0
1
0
2
3
2
0
0
2
2
2
2
0
1
0
1
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
2
0
0
0
0
0
0
2
0
0
0
1
1
0
0
1
0
0
1
2
0
1
0
2
1
1
0
0
1
0
0
0
1
0
1
0
0
0
0
3
1
1
0
0
2
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
3
0
1
2
0
2
1
0
0
2
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
1
0
1
0
0
2
1
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
3
1
2
2
1
0
0
0
0
0
0
1
0
0
0
0
0
1
2
1
3
0
0
1
2
0
1
2
0
0
0
1
0
0
0
0
0
2
0
2
0
0
1
0
0
0
1
2
0
0
0
2
0
2
0
0
2
1
0
0
0
0
0
0
1
0
0
0
1
0
2
1
0
0
0
3
0
0
1
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
1
1
1
0
2
0
0
0
0
0
0
1
1
2
0
0
0
2
0
1
0
0
0
0
1
0
0
1
0
0
1
0
3
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
2
2
0
0
1
0
0
0
3
0
0
0
3
2
0
0
0
0
0
1
0
0
0
0
2
0
0
2
1
0
1
0
0
0
1
1
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
1
0
2
0
0
0
0
1
0
0
2
1
2
0
0
0
0
3
0
1
2
2
0
0
0
1
0
0
0
1
1
2
1
0
1
1
0
1
0
0
2
1
1
2
0
0
2
0
0
2
1
3
2
0
0
0
0
2
1
1
1
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
2
0
0
0
2
0
0
1
1
1
0
2
1
0
0
0
2
0
0
2
0
2
1
0
2
5
0
2
0
2
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
1
2
0
1
0
0
2
0
1
2
0
2
0
1
2
0
1
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
1
0
1
0
0
2
0
0
2
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
1
2
1
0
0
0
0
0
0
1
0
2
0
0
0
3
0
0
1
2
0
0
1
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
2
0
2
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
2
0
1
0
0
0
1
0
1
0
0
2
0
0
0
1
0
1
0
1
0
2
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
1
1
3
1
0
2
1
0
0
2
0
0
2
0
0
1
1
2
0
2
2
0
0
0
0
1
0
1
2
0
0
2
0
2
0
0
2
0
0
0
1
1
0
1
2
0
0
0
2
2
1
1
0
0
3
1
0
1
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
1
0
2
2
0
0
0
2
2
0
1
2
2
2
1
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
1
1
2
0
0
0
0
2
0
1
0
0
0
1
1
2
1
1
2
0
0
2
0
0
2
0
0
0
0
1
0
1
1
0
0
0
2
0
0
2
0
2
2
0
0
0
1
1
0
0
1
0
2
0
2
1
0
0
0
0
2
0
0
0
0
1
0
0
2
1
2
0
1
0
0
0
0
0
0
0
1
0
2
0
0
1
1
0
2
0
1
2
0
0
0
0
1
0
0
2
0
2
0
0
1
0
0
2
0
0
2
2
5
0
0
1
0
2
0
0
0
0
1
2
0
3
1
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
1
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
1
2
0
0
0
0
1
0
1
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
2
1
0
0
0
1
0
0
1
0
1
8
2
0
0
0
0
1
0
0
0
1
2
1
0
1
0
7
0
0
0
0
1
1
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
2
0
2
0
1
2
0
0
0
1
1
0
1
0
0
0
2
0
1
3
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
2
0
2
0
2
2
0
0
1
1
2
1
0
1
0
0
0
0
0
0
0
2
0
1
0
0
1
0
1
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
1
0
2
0
0
0
0
1
1
1
0
0
1
0
1
0
2
2
0
1
1
1
1
0
2
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
2
0
1
0
2
1
0
2
1
0
2
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
1
0
1
2
2
2
0
1
2
0
0
2
0
0
1
1
0
2
0
1
3
0
0
2
0
0
0
1
0
2
3
2
2
0
2
0
0
2
1
2
1
0
0
0
2
2
1
0
0
0
0
1
1
0
0
2
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
2
1
0
0
0
0
1
0
0
2
1
0
1
0
0
2
2
0
2
0
2
0
1
2
0
1
5
1
2
0
0
2
0
1
0
0
1
0
0
1
0
2
1
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
2
0
0
0
1
0
1
0
1
0
0
1
0
3
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
1
2
1
0
0
2
1
2
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
1
1
0
2
1
2
1
2
0
0
0
0
0
0
0
1
1
1
0
2
0
0
0
1
0
0
0
1
3
0
1
0
0
0
0
0
1
2
0
0
1
1
0
0
0
0
0
0
0
2
0
1
1
0
1
1
0
1
1
0
2
0
2
0
0
0
2
0
0
0
0
0
0
1
0
5
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
3
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
4
1
0
0
0
0
0
0
0
1
0
0
2
1
0
0
1
0
0
0
0
2
4
0
3
1
0
2
1
2
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
3
0
0
0
0
0
2
1
1
1
0
2
1
0
1
0
0
1
2
0
0
1
0
0
1
2
0
3
2
0
1
0
0
0
0
2
1
1
1
0
0
0
0
1
2
0
2
1
0
1
0
2
1
0
2
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
2
2
0
0
0
1
0
1
0
2
2
0
0
1
1
0
0
2
1
0
1
0
2
2
0
0
0
1
2
0
0
0
2
0
0
1
0
0
1
0
0
0
1
2
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
3
1
0
0
2
1
0
0
0
0
0
1
2
3
1
2
0
1
0
0
2
0
0
1
0
3
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
2
0
0
0
0
0
0
0
2
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
2
0
1
2
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
2
2
0
0
0
2
0
0
0
0
0
0
2
0
0
1
2
0
1
0
1
2
0
0
0
3
0
0
0
0
0
0
0
0
2
2
0
2
0
0
2
0
1
2
0
1
0
0
0
0
0
1
0
0
2
0
1
1
0
0
1
0
0
0
2
0
0
1
1
0
1
1
1
2
2
0
0
1
0
0
0
3
3
0
0
2
0
0
0
0
2
2
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
1
0
2
2
1
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
1
0
0
2
2
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
2
2
2
1
0
0
0
1
0
3
2
0
0
3
0
1
0
3
0
0
1
0
0
2
0
2
1
0
0
2
0
0
1
0
0
0
0
0
0
0
3
2
0
0
1
0
2
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
2
1
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
3
4
0
1
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
1
1
1
0
0
0
0
2
2
0
1
1
0
4
1
0
2
0
0
2
0
0
2
0
0
1
2
0
1
1
0
2
0
0
1
0
1
0
0
2
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
2
1
0
0
0
0
2
0
0
1
1
1
0
0
0
2
0
0
0
0
1
1
2
0
0
0
2
2
0
0
0
0
0
1
0
1
1
0
0
1
0
0
2
0
0
0
0
0
1
1
0
1
0
0
0
0
1
2
1
1
0
0
1
1
0
1
0
1
0
0
0
0
0
2
2
0
0
0
3
2
0
0
1
1
0
1
2
0
0
0
0
0
0
0
3
0
0
2
1
0
0
0
0
1
2
0
4
2
1
0
0
0
0
1
0
0
0
2
0
2
1
0
0
2
0
0
0
1
1
0
3
0
1
2
0
1
2
0
0
1
0
1
0
2
0
1
2
0
1
0
1
2
0
2
1
0
0
2
0
0
0
2
1
0
0
0
0
0
2
1
0
0
2
0
1
0
2
0
0
0
1
0
0
0
0
1
2
2
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
1
1
4
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
2
1
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
1
2
0
2
0
0
0
2
0
0
0
2
0
0
1
0
0
0
2
0
2
2
4
0
0
1
1
3
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
2
0
0
0
1
0
2
2
1
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
2
2
0
2
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
4
0
1
2
0
2
0
0
1
0
1
2
1
0
2
0
0
0
0
0
2
0
0
1
0
0
0
1
1
0
2
2
0
0
2
2
2
0
1
2
0
2
0
0
0
4
0
0
1
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
1
2
1
0
0
0
0
1
1
1
0
1
0
2
1
0
1
2
1
0
1
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
2
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
4
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
2
2
0
3
2
0
0
0
2
1
0
1
2
0
1
0
1
0
1
0
0
0
0
0
0
1
0
1
0
1
2
0
0
0
0
0
0
0
1
2
2
5
2
0
0
0
0
0
1
0
0
2
1
0
2
2
0
2
0
1
0
0
5
2
0
1
0
0
0
0
0
0
2
0
5
0
2
0
2
1
1
0
1
0
0
0
0
1
0
0
0
3
2
2
0
0
0
2
3
1
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
2
0
2
0
0
2
2
2
4
0
0
1
0
0
1
1
0
0
1
1
0
0
3
1
0
1
1
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
1
2
0
1
0
0
2
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
1
0
2
1
1
1
1
1
2
0
0
2
0
1
0
2
0
1
1
0
0
0
1
2
0
0
0
0
1
0
0
0
1
0
1
2
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
5
0
2
0
0
0
0
2
0
0
0
0
2
5
0
0
0
0
1
0
1
0
0
2
0
2
2
0
0
1
1
0
0
2
0
0
0
0
1
0
0
1
0
3
1
0
0
0
0
0
4
0
2
1
0
0
2
0
0
0
2
3
0
0
0
1
1
2
3
0
1
0
1
0
2
1
0
0
0
0
0
0
2
1
2
0
0
1
0
1
0
0
0
0
0
1
0
1
1
0
1
0
0
2
0
0
1
2
1
0
0
0
0
2
0
2
2
0
0
1
0
2
0
1
0
1
3
0
0
2
0
0
0
0
0
0
0
0
2
1
2
0
2
0
0
0
0
0
2
2
0
0
2
1
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
3
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
1
3
0
0
1
0
1
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
3
1
0
0
0
0
2
2
0
0
2
0
0
2
0
2
1
0
0
1
2
1
0
0
0
0
0
0
0
0
1
0
2
1
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
3
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
4
0
1
0
0
0
0
1
0
2
0
2
0
2
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
3
3
1
0
2
0
1
1
1
0
0
4
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
3
0
0
0
1
0
0
0
1
2
1
1
0
0
0
1
2
0
1
0
0
0
0
2
0
2
0
0
0
0
0
1
0
6
0
2
0
0
1
3
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
2
1
1
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
1
2
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
1
1
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
2
0
0
2
0
1
4
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
2
0
0
0
0
3
0
0
2
0
2
0
1
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
1
1
2
0
0
2
0
0
0
0
0
0
2
2
2
0
1
0
2
2
1
0
2
2
0
1
1
0
0
0
0
1
0
0
0
0
1
6
1
1
0
1
0
0
0
0
1
4
0
0
1
2
0
2
0
2
0
0
0
1
0
2
1
2
1
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
2
2
2
1
2
1
0
0
0
0
1
2
1
0
1
0
1
1
0
1
0
0
0
1
2
0
0
2
2
0
1
0
3
0
2
0
0
0
1
0
0
0
2
1
2
0
2
2
0
2
0
0
1
0
0
2
2
0
0
0
0
1
0
0
0
0
0
1
1
0
0
2
1
1
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
2
0
2
2
0
0
0
4
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
4
0
2
0
0
0
0
2
0
1
1
0
0
1
1
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
2
0
1
2
0
0
0
1
0
0
1
1
0
3
2
4
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
1
0
2
0
1
0
0
1
0
0
0
0
1
0
0
0
2
1
0
2
0
0
0
2
0
1
1
0
0
1
1
0
3
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
2
2
3
0
0
0
0
0
1
1
1
0
1
0
2
2
1
0
0
0
0
0
0
0
1
1
1
0
0
0
3
0
1
1
1
1
0
3
0
1
0
0
0
0
0
0
0
0
0
0
2
2
1
2
2
2
0
0
3
2
0
0
1
2
1
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
1
0
0
1
0
1
2
2
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
2
1
0
0
1
2
1
0
0
0
0
2
1
0
0
0
2
0
0
2
2
1
1
0
0
1
0
1
0
0
2
0
0
0
3
0
1
3
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
3
0
0
0
0
1
2
2
0
2
0
2
0
2
1
0
1
0
0
0
0
0
0
0
2
0
1
1
2
0
0
1
0
1
0
2
0
1
0
2
1
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
4
0
0
2
0
2
0
0
0
0
1
0
0
2
0
0
0
0
2
1
0
2
0
0
2
0
1
0
0
0
0
1
0
1
0
0
2
1
0
0
1
2
0
0
0
1
2
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
2
2
1
2
0
0
0
0
0
0
2
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
1
2
2
0
1
1
0
0
1
0
0
0
2
2
0
2
0
0
1
2
0
2
0
0
1
1
0
0
0
0
3
1
0
3
0
0
1
0
1
1
0
0
0
1
9
0
0
0
0
2
0
0
1
2
0
0
0
2
0
1
0
0
0
1
2
0
2
0
1
0
0
0
1
0
0
0
5
0
0
1
2
1
0
1
0
0
0
2
0
0
0
3
0
3
0
1
0
1
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
2
0
1
0
1
0
0
2
0
2
1
1
1
2
0
2
1
2
0
2
1
2
0
0
0
2
0
0
1
1
0
0
0
3
0
0
1
0
0
1
1
1
0
0
0
0
1
2
2
2
1
0
0
0
1
0
0
3
1
0
1
0
1
0
1
0
1
0
0
0
0
0
1
0
0
1
0
2
0
0
1
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
3
0
2
2
0
2
0
0
0
0
1
0
1
0
0
1
2
1
0
0
0
0
2
1
0
0
2
1
0
0
2
0
0
0
4
2
0
0
1
2
0
0
0
0
2
2
0
0
1
1
2
0
1
0
0
0
0
2
0
1
0
1
2
2
3
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
2
1
0
0
0
0
1
0
0
0
1
3
0
2
1
0
0
0
1
1
1
0
0
0
0
0
2
0
0
1
2
0
1
0
1
2
1
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
2
2
0
0
0
0
2
2
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
3
1
1
0
0
0
1
0
0
4
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
2
0
0
0
4
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
1
0
0
1
2
0
1
1
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
1
0
0
2
0
1
0
5
2
0
2
3
0
2
2
0
1
0
0
1
2
0
1
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
2
0
4
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
2
0
1
0
0
0
0
0
0
0
0
0
1
1
2
2
1
3
0
0
1
0
0
1
0
2
2
0
0
0
0
1
2
0
2
0
0
0
1
0
0
0
0
3
1
0
2
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
1
2
2
2
0
1
1
0
0
3
0
2
0
0
2
1
2
1
1
0
3
0
2
0
1
0
2
0
0
0
0
2
2
1
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
4
1
0
0
0
2
0
1
0
0
0
0
0
2
0
2
1
0
0
1
0
0
3
0
0
0
0
1
0
1
0
2
0
2
0
1
0
0
0
1
0
2
0
0
1
2
0
0
2
0
0
0
0
0
1
0
2
0
1
1
0
2
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
2
0
1
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
3
2
0
0
0
0
0
0
2
1
0
0
2
1
0
1
0
1
0
0
0
1
0
2
2
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
4
2
1
0
0
0
0
0
2
0
2
1
1
0
1
2
0
0
1
0
2
0
1
0
2
0
0
0
0
1
1
4
0
0
0
1
1
2
0
0
0
0
0
0
1
2
0
1
3
0
2
2
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
1
0
0
3
0
2
0
1
0
1
3
0
1
0
0
0
1
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
2
0
2
0
1
0
0
2
0
0
0
0
0
1
2
0
0
1
0
1
0
0
0
0
1
1
0
0
2
0
0
1
1
2
0
0
0
0
1
0
0
2
0
1
2
1
0
0
0
0
3
0
0
0
2
0
1
0
0
1
0
0
1
0
2
0
1
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
2
0
1
0
1
2
0
0
0
0
2
0
2
0
0
1
1
0
1
1
0
0
0
0
2
0
2
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
2
0
2
1
1
2
0
2
0
2
2
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
2
0
1
0
2
1
0
0
1
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
1
0
1
0
1
1
0
1
1
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
2
0
0
2
2
0
0
0
0
0
3
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
2
0
0
0
1
0
2
0
0
2
0
0
0
1
0
0
0
0
2
1
0
0
0
0
1
0
1
1
0
2
2
0
2
0
0
0
2
0
0
0
0
2
0
2
1
0
0
2
0
0
4
0
2
1
0
1
0
0
1
0
0
0
2
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
1
1
0
1
0
0
2
2
0
1
0
0
1
0
0
0
0
0
2
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
2
0
1
2
1
2
0
0
0
0
0
0
1
2
2
1
0
0
1
0
1
1
0
0
0
0
1
2
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
1
1
2
0
0
2
0
1
0
0
2
0
0
2
0
0
0
1
0
0
2
0
0
1
0
1
0
2
1
1
0
0
0
2
2
2
0
2
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
1
0
2
1
0
0
0
0
1
1
0
2
2
1
1
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
1
1
0
1
0
0
2
0
3
1
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
1
0
0
2
0
0
1
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
3
0
0
2
0
0
1
0
0
0
2
0
0
0
2
2
0
0
0
2
0
2
1
0
2
1
0
2
0
1
2
1
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
2
2
4
0
0
0
0
2
2
1
2
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
1
1
1
0
0
0
1
0
0
1
0
0
4
0
1
0
1
0
0
1
6
0
1
0
0
1
0
0
5
0
0
0
0
1
2
2
0
1
0
1
0
0
0
1
1
8
0
0
0
1
0
2
0
1
0
1
0
1
0
0
0
0
0
2
1
0
0
1
0
1
0
0
0
1
0
0
0
2
2
0
1
0
1
0
2
1
1
0
4
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
1
1
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
1
1
1
0
0
1
1
1
0
1
0
1
1
0
1
0
0
1
1
0
0
0
0
2
2
0
0
2
0
0
1
1
4
1
0
1
0
0
0
0
1
0
0
0
0
1
1
5
0
1
2
2
0
0
0
1
0
0
0
1
0
2
0
0
1
3
0
0
0
1
0
0
1
1
0
0
0
0
3
0
1
0
0
1
2
0
1
1
1
0
1
1
2
1
2
0
0
1
2
2
1
1
1
0
0
0
0
0
0
2
3
0
0
2
1
1
2
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
2
4
2
0
0
1
0
2
0
0
2
0
0
1
0
0
1
2
0
0
0
0
0
1
0
0
2
1
0
0
0
0
2
1
1
2
0
0
0
0
0
0
1
0
0
2
1
0
0
0
2
0
0
2
0
2
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
1
1
0
0
0
2
1
0
0
0
2
0
0
0
0
2
0
0
2
2
0
2
2
2
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
1
1
1
0
2
0
0
0
1
0
1
0
2
0
0
0
0
0
2
0
2
2
2
0
0
0
0
1
2
0
0
2
0
0
0
0
0
1
1
2
0
1
0
1
0
2
0
0
1
0
2
0
0
0
0
0
0
0
2
1
0
2
2
0
0
0
2
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
1
0
0
0
1
0
1
1
1
0
0
0
0
1
3
1
0
0
0
0
0
0
0
0
2
1
1
2
0
0
0
2
2
4
0
2
0
0
2
1
2
0
0
1
0
0
0
2
0
0
0
1
1
0
0
0
1
0
0
1
6
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
4
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
1
0
0
0
2
1
0
0
1
0
0
2
0
0
2
1
0
0
0
1
0
0
1
1
0
3
0
0
1
0
0
0
0
0
1
0
1
0
1
3
1
0
0
1
0
1
0
3
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
1
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
2
2
1
0
1
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
1
0
2
0
0
0
0
1
1
0
0
1
2
0
2
0
1
1
2
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
3
1
2
0
3
0
2
2
0
1
2
0
0
0
0
1
1
1
1
0
0
0
0
0
0
2
1
0
2
0
2
1
0
0
0
1
0
0
0
0
1
1
0
2
3
0
0
0
0
0
0
0
0
0
1
0
2
0
3
0
2
0
2
1
0
0
2
0
0
3
0
0
1
2
1
2
1
0
0
1
2
2
0
1
0
0
0
1
1
1
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
1
0
0
2
1
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
1
0
1
0
2
0
2
2
0
0
2
1
2
1
1
2
3
0
0
0
0
0
0
0
0
1
1
1
1
1
0
0
0
0
0
1
0
2
2
0
1
0
0
1
1
0
0
0
0
1
1
0
2
1
0
2
0
0
0
0
0
0
0
1
2
0
1
2
1
0
0
2
0
2
0
0
0
0
0
0
2
0
2
1
0
1
0
0
0
0
0
0
2
1
0
2
1
2
0
0
0
2
0
0
0
0
0
4
0
0
2
0
0
0
0
2
1
0
0
2
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
3
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
1
1
2
0
2
1
0
2
2
0
0
2
0
0
0
0
0
2
0
2
0
2
0
0
0
0
1
0
0
2
0
1
0
0
1
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
8
2
0
0
0
1
0
0
2
0
0
3
0
1
0
2
0
0
0
1
1
2
0
2
0
1
0
1
0
2
0
0
0
0
0
0
0
3
1
1
0
1
1
0
1
0
1
0
1
1
0
0
0
2
0
1
0
2
3
0
0
0
0
1
0
0
1
1
0
1
2
0
0
0
0
0
0
0
1
2
0
0
1
0
0
3
0
0
0
0
0
2
1
2
0
0
2
0
0
0
1
0
0
0
2
1
1
2
0
1
0
0
1
0
0
0
0
0
0
1
0
2
0
1
0
2
0
0
0
2
1
0
0
0
2
1
0
0
0
1
0
1
0
0
1
2
1
0
0
0
0
2
1
1
0
0
0
0
2
0
2
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
2
1
1
0
0
0
1
2
0
1
0
0
0
0
0
0
0
2
0
1
3
0
0
2
1
0
1
0
0
1
0
0
0
0
0
1
1
1
0
0
1
1
2
0
0
2
2
2
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
2
0
2
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
2
1
1
0
1
1
0
0
0
0
0
2
0
0
0
0
1
2
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
7
2
0
1
0
0
2
0
0
2
1
1
0
0
1
0
1
0
2
0
0
1
1
3
0
1
0
1
0
0
3
1
0
2
0
0
2
0
0
2
2
2
1
1
0
0
0
0
1
2
0
0
0
0
3
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
2
0
1
2
1
1
0
0
0
2
0
0
0
1
0
1
0
0
0
1
1
0
1
2
0
0
2
2
1
0
2
0
0
1
0
2
0
2
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
2
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
3
0
1
0
0
0
0
0
1
0
0
1
0
2
2
1
0
0
0
0
2
0
1
0
0
0
1
2
0
1
1
0
1
0
0
1
2
0
0
2
0
0
0
1
0
0
4
0
0
3
0
1
1
2
0
0
0
0
0
2
0
0
2
0
1
2
0
0
0
0
0
0
1
0
2
2
0
0
2
2
0
2
2
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
1
2
0
0
0
2
1
0
0
2
0
1
0
0
0
0
1
0
0
0
3
0
2
2
0
0
2
1
0
0
0
0
0
1
0
0
2
2
1
1
1
1
0
0
0
2
2
0
2
0
0
1
2
0
0
1
2
0
0
2
0
0
1
0
1
2
2
0
0
0
2
0
0
1
1
0
2
2
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
1
2
0
2
0
0
0
0
0
0
2
3
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
3
0
0
0
0
2
1
1
0
1
0
1
0
0
0
2
0
1
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
1
0
0
0
1
5
0
2
0
1
1
0
0
2
2
1
2
0
0
1
0
1
2
0
1
2
0
0
0
1
2
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
1
0
2
0
0
8
2
0
2
0
1
0
0
2
1
1
0
2
0
0
0
1
0
2
1
3
0
0
0
0
0
2
1
0
0
0
3
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
2
2
0
0
1
0
2
0
0
2
1
0
0
1
0
0
2
2
0
0
0
2
1
2
0
0
2
0
2
3
2
1
0
1
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
1
2
0
0
0
1
2
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
1
0
0
2
1
0
0
0
1
0
0
1
0
0
1
0
1
2
1
0
0
2
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
1
2
3
0
0
0
1
1
0
1
0
0
0
2
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
1
0
0
0
1
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
2
0
0
2
0
0
2
2
0
0
3
0
0
2
1
1
1
1
0
1
0
2
0
0
1
0
1
1
0
1
0
2
0
0
0
0
2
1
1
1
1
2
0
1
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
1
3
0
1
0
0
0
0
0
1
0
0
0
1
0
1
1
0
1
0
0
1
1
0
0
0
2
3
0
0
1
0
1
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
1
3
0
0
3
0
0
0
2
2
0
0
0
1
0
0
0
0
1
2
0
2
2
2
1
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
1
0
2
0
1
0
2
0
0
2
2
1
2
1
2
0
0
0
1
0
0
1
2
0
3
0
1
0
0
0
1
2
0
1
1
0
0
0
0
1
2
0
1
0
2
0
0
5
1
1
1
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
2
2
0
2
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
2
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
1
2
1
2
0
0
0
0
0
0
1
0
1
0
2
0
0
2
2
0
1
0
0
1
1
0
3
0
2
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
2
1
0
0
0
1
0
1
0
0
0
1
2
0
0
0
0
0
2
0
0
0
2
2
0
2
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
1
2
4
0
2
3
0
0
2
0
0
2
0
2
2
0
0
2
0
1
0
2
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
1
1
1
2
1
0
0
0
0
2
1
1
2
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
3
1
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
2
0
0
0
0
0
0
2
1
0
0
5
0
0
0
0
0
0
0
0
2
1
2
2
0
2
0
0
0
1
0
0
0
0
0
0
1
1
2
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
1
0
2
2
0
0
0
1
0
2
0
0
0
0
0
1
0
2
0
0
1
0
2
2
0
0
0
0
2
0
0
1
0
1
2
1
0
0
2
0
0
2
0
1
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
2
1
1
2
0
3
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
1
1
0
0
2
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
1
0
1
2
0
0
0
1
0
0
0
0
0
2
1
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
2
0
2
0
1
1
1
0
0
1
2
0
2
0
2
0
0
2
0
0
0
1
0
3
0
0
0
0
1
1
0
2
0
2
5
1
0
1
0
1
1
0
1
0
0
0
0
0
2
2
0
0
0
0
1
2
2
1
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
1
2
0
0
1
2
2
2
1
0
0
0
0
1
2
0
1
0
2
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
1
2
2
0
2
0
2
1
2
0
1
0
1
1
1
2
0
3
2
0
0
0
0
1
2
1
0
1
0
0
2
0
1
0
0
2
0
0
0
0
2
1
0
2
1
2
1
2
1
0
0
0
1
0
2
0
1
2
0
2
0
0
2
0
1
2
0
0
2
0
0
0
0
0
1
2
0
0
2
0
1
0
0
1
0
0
2
0
1
0
0
1
0
0
0
2
0
0
2
0
2
2
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
2
1
0
2
0
1
2
0
0
1
0
0
2
2
0
0
0
0
2
0
2
1
2
1
0
0
0
0
0
2
2
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
1
1
2
1
0
0
0
0
2
2
0
2
0
0
1
1
0
0
1
0
0
0
1
3
2
0
2
0
0
0
0
3
0
1
0
1
0
0
2
1
0
0
0
0
2
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
1
2
0
0
0
0
0
2
1
0
0
0
0
2
0
2
0
0
1
0
0
0
1
0
0
0
0
1
2
0
0
2
0
0
0
0
2
0
0
2
0
0
0
1
0
0
2
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
2
1
0
1
0
0
0
0
2
0
2
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
2
2
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
3
1
1
0
2
0
0
1
2
0
0
1
1
0
2
1
0
0
1
2
0
0
0
0
0
0
1
0
1
4
0
0
0
0
0
2
0
3
0
2
0
1
0
0
1
2
0
0
2
0
2
2
0
0
2
2
0
1
1
0
0
0
1
3
0
0
1
0
0
0
0
0
0
0
0
1
2
2
0
2
1
5
1
1
2
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
1
1
1
0
1
2
0
2
0
2
0
2
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
3
2
2
0
2
2
2
0
0
2
0
0
0
3
0
0
0
0
0
0
1
0
0
2
2
0
0
1
0
2
0
0
0
1
0
0
0
2
3
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
1
1
2
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
2
1
2
1
0
1
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
1
0
0
0
2
0
0
1
0
0
0
4
0
1
1
0
0
2
7
0
0
0
0
1
0
2
0
0
2
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
2
1
0
1
1
1
1
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
1
1
0
1
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
2
0
1
2
1
1
2
0
1
2
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
2
0
0
0
2
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
1
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
1
0
0
2
1
0
0
2
2
0
2
0
0
0
0
2
0
0
2
0
0
0
1
0
0
3
0
0
0
0
0
0
0
1
0
0
3
2
3
0
0
0
1
0
0
0
2
6
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
1
2
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
2
1
1
2
1
1
2
2
1
2
0
0
0
3
0
0
0
2
0
0
2
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
1
1
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
1
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
2
0
1
1
0
1
0
0
0
2
1
0
0
0
0
2
1
1
0
1
2
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
2
1
0
2
0
2
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
2
0
1
2
0
2
0
0
0
2
0
0
3
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
2
1
0
0
1
0
0
0
0
3
2
0
0
0
0
0
2
1
0
0
2
1
0
1
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
2
2
2
0
1
0
1
2
0
0
2
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
2
2
1
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
2
0
1
1
0
0
2
0
0
1
0
0
0
1
0
0
0
2
2
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
2
3
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
2
0
1
0
2
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
2
2
0
0
0
2
3
0
0
0
0
0
0
2
2
1
0
0
0
0
2
1
0
2
2
0
0
3
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
2
1
2
2
0
0
0
0
0
0
0
0
0
0
3
0
2
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
2
0
1
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
1
2
0
0
2
2
0
0
2
0
0
3
2
0
0
1
0
0
0
0
1
1
0
3
2
0
1
1
0
0
2
0
1
2
1
1
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
2
0
2
0
3
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
2
1
0
1
0
0
2
0
0
0
0
0
0
2
0
0
2
2
0
2
0
0
2
0
0
2
0
1
0
0
0
0
2
1
2
0
0
0
1
0
2
2
0
1
0
0
0
1
2
2
0
2
2
0
0
0
1
0
0
3
2
2
0
0
1
1
0
1
0
0
0
0
0
0
2
0
1
0
1
2
0
0
1
0
1
2
0
2
0
0
0
0
0
0
2
0
1
0
0
2
1
1
0
1
2
2
2
0
0
0
0
1
0
0
1
1
1
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
2
0
0
1
1
0
2
0
0
0
0
0
0
2
0
2
2
0
0
1
0
0
0
0
1
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
2
0
2
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
2
0
2
0
2
0
0
1
0
0
0
2
0
2
0
0
2
2
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
1
1
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
2
0
2
2
0
0
0
0
1
0
0
0
0
0
2
1
0
1
0
2
0
0
0
0
0
2
0
0
0
2
0
0
2
0
1
0
1
0
3
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
3
1
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
4
1
0
0
1
0
0
0
2
0
1
0
1
0
0
0
0
0
2
1
2
1
0
0
2
0
1
0
0
0
0
3
0
0
0
1
2
0
0
2
1
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
3
2
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
2
1
1
2
0
0
0
0
2
0
0
1
2
0
0
0
2
2
1
1
0
1
3
1
2
0
1
0
0
0
1
0
0
2
1
2
0
2
3
0
2
0
0
0
2
1
0
0
0
0
0
0
1
1
2
0
0
2
0
0
0
2
1
0
0
2
2
1
2
2
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
8
0
0
0
2
0
2
0
0
2
2
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
2
1
2
0
1
0
0
0
0
4
0
0
0
0
3
0
0
0
0
0
0
0
0
4
0
2
0
0
1
0
1
0
0
0
0
2
0
0
1
0
2
2
0
0
3
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
1
0
1
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
3
0
0
0
2
0
1
0
0
1
0
0
1
0
0
1
1
1
0
0
0
0
1
0
1
0
2
0
3
0
2
0
1
0
0
2
6
0
0
2
0
0
0
0
1
0
0
3
2
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
1
1
0
2
0
1
1
1
0
1
0
0
1
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
3
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
6
2
2
0
0
2
0
7
0
3
0
2
0
0
0
0
0
0
1
1
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
2
2
0
1
0
0
2
2
0
0
0
0
3
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
2
1
0
2
0
0
1
0
0
2
0
0
1
2
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
1
0
0
2
0
2
2
0
0
2
1
0
2
0
1
0
0
0
1
2
0
1
1
0
0
0
2
0
1
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
1
1
1
1
0
0
0
0
2
1
0
1
0
0
2
0
0
0
0
1
0
0
0
3
0
2
0
0
2
0
0
0
1
0
0
1
2
1
0
0
0
1
0
2
2
0
2
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
1
1
0
1
0
2
0
0
0
1
3
0
0
0
1
0
0
0
0
0
0
1
0
0
2
2
5
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
1
0
1
0
2
0
2
2
0
5
0
2
0
0
0
0
0
0
2
0
1
1
0
1
1
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
1
0
2
0
1
0
0
2
1
2
5
2
0
0
1
2
0
0
0
0
0
1
0
1
0
1
0
0
1
0
2
1
0
0
1
0
0
2
2
2
1
0
0
0
1
1
2
2
2
1
1
2
0
0
0
1
2
2
1
0
0
2
0
2
0
0
0
0
0
1
0
0
1
1
2
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
3
0
0
0
3
0
3
1
0
0
0
2
0
0
0
1
1
2
0
0
1
0
0
2
0
1
2
0
0
1
0
1
1
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
2
0
0
0
2
0
0
0
4
0
0
1
2
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
2
0
2
0
2
0
2
0
0
2
0
2
1
0
1
2
0
1
2
0
0
0
0
0
0
1
0
1
2
0
1
1
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
2
2
1
0
0
2
2
0
1
2
1
0
0
0
2
0
0
4
1
0
2
0
0
1
0
2
0
0
0
1
1
1
1
0
0
2
2
2
0
2
1
0
0
3
0
1
2
2
0
1
0
0
0
0
0
0
0
0
2
3
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
1
1
1
0
0
0
0
0
0
1
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
1
1
3
2
1
1
0
0
1
0
0
0
0
0
1
2
0
0
0
0
2
0
0
1
1
0
1
0
0
0
0
0
2
2
0
1
0
0
0
0
1
3
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
2
0
3
0
0
0
1
0
0
3
1
0
0
2
1
0
0
0
0
0
0
2
1
0
0
1
1
3
0
0
3
0
0
4
0
0
1
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
3
1
0
2
2
0
0
2
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
1
1
0
1
1
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
1
1
0
0
0
2
0
2
1
0
0
0
0
0
0
1
1
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
2
0
0
1
1
0
0
0
0
1
0
1
1
0
2
0
2
0
2
0
0
0
0
6
0
0
1
1
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
1
0
0
2
0
0
0
0
0
0
3
0
0
2
1
2
0
1
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
2
1
2
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
1
2
0
0
2
3
3
1
2
0
3
2
2
0
0
0
0
0
1
1
3
0
0
3
2
0
0
1
1
1
2
0
0
0
0
0
1
0
0
1
1
0
1
0
1
0
0
1
0
0
0
2
0
2
2
0
0
0
1
1
0
1
0
0
0
2
0
0
0
2
0
4
1
0
1
0
0
0
0
2
2
0
0
3
0
0
0
0
0
0
1
1
0
0
2
2
0
1
0
0
1
0
0
1
0
3
2
0
0
2
0
0
0
1
0
0
0
0
1
1
1
2
2
2
1
0
0
1
0
0
1
0
1
2
0
0
0
2
1
1
2
2
0
0
0
1
1
0
0
2
0
0
0
0
0
2
0
0
0
0
3
0
1
1
1
2
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
1
0
2
1
1
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
1
0
8
2
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
4
2
0
1
0
0
0
0
0
4
0
1
0
1
1
0
2
2
2
2
0
0
2
2
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
1
0
2
1
0
0
0
1
2
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
2
0
0
2
0
1
0
1
1
0
0
0
2
2
1
0
2
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
2
3
1
0
1
0
0
0
1
2
0
2
0
3
1
2
0
0
1
2
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
2
0
0
0
0
0
2
2
0
3
0
0
2
0
0
0
2
0
1
0
0
1
0
0
1
2
0
0
0
0
2
0
2
0
0
0
0
0
0
3
0
0
0
0
1
0
0
2
0
0
1
1
1
0
0
0
2
0
0
1
1
0
0
0
0
0
1
0
0
0
1
1
0
4
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
1
2
0
0
0
0
1
2
0
2
0
1
0
0
1
0
0
3
0
0
3
2
0
1
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
2
2
0
1
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
2
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
3
0
1
1
0
1
0
0
0
2
0
0
0
2
1
0
0
0
0
1
1
1
2
1
0
2
0
0
2
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
1
0
3
0
0
0
0
1
0
0
2
2
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
1
1
0
2
2
1
0
0
0
0
1
2
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
2
0
1
2
1
0
0
1
1
2
0
0
3
0
0
0
0
4
0
1
0
2
1
0
0
2
3
2
1
0
0
0
0
0
1
2
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
1
1
1
0
0
0
0
1
0
0
1
2
1
2
0
0
0
0
0
2
0
2
2
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
3
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
2
0
0
7
0
1
2
0
2
0
1
0
3
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
1
0
0
2
0
0
1
0
1
0
0
2
0
1
2
0
1
0
0
0
1
1
1
0
0
0
1
0
3
2
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
2
3
0
3
0
0
0
0
0
0
0
0
1
2
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
2
0
2
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
5
0
1
0
1
1
0
1
1
1
0
0
0
0
0
2
0
0
0
1
1
0
2
1
0
2
1
2
1
1
0
0
3
0
1
0
0
0
0
0
3
1
0
0
2
0
2
2
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
2
3
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
2
1
0
1
1
0
3
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
2
1
1
0
0
1
0
0
0
1
0
0
1
0
2
0
0
2
0
0
2
0
0
0
2
0
0
0
1
2
1
1
0
0
0
1
0
2
1
1
0
0
0
1
0
0
0
0
0
0
1
0
2
1
0
1
1
0
2
0
2
2
0
0
2
2
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
1
1
1
2
1
0
1
0
0
0
0
2
1
1
2
1
0
1
1
0
0
1
0
0
0
1
0
1
0
0
0
2
0
0
0
2
2
2
0
0
1
1
1
2
0
1
0
0
0
0
0
2
1
0
0
2
2
0
0
2
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
6
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
1
2
1
1
1
2
1
1
0
0
0
0
1
0
2
0
2
0
4
0
2
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
1
0
2
1
1
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
2
1
0
0
0
0
0
2
1
0
2
1
5
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
2
1
0
0
0
2
1
0
0
1
0
1
0
0
0
2
0
1
0
3
0
1
0
2
0
2
0
0
2
2
1
2
0
1
0
2
0
0
0
3
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
2
1
1
0
1
0
1
0
0
0
1
1
0
3
0
2
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
2
1
0
0
0
1
2
2
0
1
0
0
0
1
1
1
0
1
0
0
0
0
2
3
2
0
1
2
0
1
0
0
0
0
0
1
1
0
0
3
0
0
3
0
1
0
0
0
0
3
0
0
2
0
2
0
2
0
2
1
0
0
0
1
2
2
1
3
0
0
1
1
0
0
0
0
0
0
1
0
0
2
0
2
0
1
2
0
1
0
1
0
0
0
0
1
0
2
2
0
1
1
0
0
0
2
0
1
0
5
0
0
2
3
1
0
1
2
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
3
0
0
0
3
2
0
1
0
1
0
0
1
1
0
1
0
1
0
0
0
2
1
0
2
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
1
0
0
0
2
1
3
2
0
0
0
1
0
0
2
0
1
0
1
0
0
0
0
1
2
1
1
0
1
1
0
1
0
1
1
2
2
0
0
0
0
0
1
0
1
0
0
0
2
1
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
1
0
0
1
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
2
0
0
4
0
1
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
2
0
1
1
0
0
0
0
0
0
1
2
0
1
0
0
2
0
1
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
1
4
1
1
0
0
1
0
0
0
0
2
2
0
0
0
3
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
2
2
0
0
1
4
2
2
0
0
0
0
0
0
0
2
1
0
1
0
1
0
1
2
0
0
0
2
0
2
0
1
1
0
0
2
1
1
1
0
1
0
0
1
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
2
1
1
0
2
0
0
0
1
2
1
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
1
0
0
1
2
2
2
2
0
1
0
1
0
2
0
2
0
0
0
0
0
2
3
0
0
0
1
0
0
0
0
2
0
2
1
0
1
0
0
3
1
0
0
2
0
0
0
1
0
1
1
2
0
0
1
2
0
0
0
0
2
1
2
0
1
0
2
0
2
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
4
2
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
2
0
0
2
0
2
2
2
0
1
2
1
0
0
0
0
0
1
0
1
0
0
0
2
0
0
1
0
0
0
2
0
2
1
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
1
1
1
0
2
0
0
1
0
0
0
2
0
0
3
0
0
1
0
0
1
0
1
2
0
0
5
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
1
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
2
2
0
0
0
0
2
2
0
2
0
1
1
1
1
0
0
0
0
1
0
0
0
0
2
0
1
3
1
0
0
0
2
0
1
2
2
0
0
0
0
1
3
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
1
2
0
2
0
0
0
1
2
1
0
0
0
1
2
0
0
0
1
0
0
1
0
2
0
2
0
0
0
0
1
0
0
1
0
0
2
2
2
1
0
0
0
0
1
0
1
1
0
0
1
0
0
4
0
0
2
0
0
0
0
3
1
0
1
2
2
1
0
1
2
0
1
0
0
0
0
0
1
0
0
1
1
1
1
0
0
0
0
0
2
0
2
1
0
0
0
0
0
2
0
1
1
2
1
1
0
1
0
3
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
1
1
0
2
0
0
0
0
1
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
2
1
1
1
1
0
0
0
0
1
0
2
0
1
0
0
2
0
2
0
0
1
0
1
0
0
0
0
0
0
1
0
3
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
1
1
1
0
0
0
3
1
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
1
1
2
0
0
1
2
2
1
0
1
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
1
0
0
0
1
1
0
0
0
0
0
1
2
0
2
0
0
2
2
1
0
0
1
0
2
0
0
0
1
0
2
0
0
1
0
1
2
3
0
0
0
0
2
0
2
0
1
0
0
1
0
2
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
1
0
0
2
0
0
0
1
2
0
0
0
0
0
1
2
2
0
0
0
1
2
0
0
1
0
1
0
0
0
0
3
0
2
2
3
0
0
0
2
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
2
1
1
0
0
1
2
0
0
0
0
1
1
0
0
2
0
0
1
0
1
0
0
1
0
2
0
0
0
0
0
2
0
0
1
0
0
2
0
0
1
0
0
2
2
0
2
0
0
0
1
2
0
1
0
0
2
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
1
0
3
2
0
1
2
2
0
0
3
0
2
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
2
0
0
2
0
1
1
0
0
2
1
0
2
0
2
1
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
2
3
1
0
0
1
0
1
2
0
1
0
0
0
2
0
0
2
0
2
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
3
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
2
0
0
1
1
0
0
0
2
2
1
1
0
0
0
0
0
1
2
0
0
0
0
2
2
0
1
2
2
0
0
0
2
0
1
0
0
2
0
0
2
0
0
0
0
0
0
3
1
0
0
3
0
0
0
2
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
2
2
0
1
2
0
2
0
0
0
1
1
1
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
1
0
0
0
1
2
0
0
0
1
2
1
0
1
0
0
1
2
0
0
0
0
0
1
2
0
0
0
0
4
0
0
0
0
0
0
2
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
2
2
1
2
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
2
0
2
0
0
1
1
0
0
0
2
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
3
2
0
0
1
1
0
2
1
0
0
1
1
1
2
0
2
0
2
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
2
0
2
0
0
2
1
0
0
0
0
2
0
0
0
0
2
0
3
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
1
1
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
1
0
0
0
0
2
0
1
2
0
1
0
0
1
0
0
0
0
1
2
0
0
2
0
0
1
0
1
1
0
1
0
0
0
1
0
1
2
2
2
0
2
0
2
2
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
3
0
0
0
0
2
0
1
0
0
1
1
0
0
0
2
0
2
0
0
0
0
0
0
3
2
0
0
1
1
0
0
1
0
0
0
0
0
2
1
0
0
0
1
1
1
0
1
3
0
1
0
2
0
0
0
0
0
0
3
2
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
1
2
0
0
4
0
0
0
0
0
0
2
0
0
1
1
2
0
1
2
2
0
0
0
0
2
1
0
0
2
0
2
0
1
0
0
0
0
1
0
0
2
1
0
0
0
1
0
0
0
2
1
2
0
1
2
0
0
0
2
0
0
0
0
1
1
0
0
1
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
1
1
3
0
0
0
0
0
0
0
1
2
2
1
0
1
0
2
0
0
2
0
0
0
2
1
0
3
1
3
1
1
0
0
0
0
0
0
0
2
0
1
1
1
0
0
2
1
0
0
0
0
1
0
0
2
2
0
2
2
0
0
0
1
2
1
0
0
1
2
0
0
3
2
0
0
0
0
0
2
0
0
0
1
0
1
0
0
2
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
1
0
2
0
0
0
2
1
5
0
0
0
0
0
2
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
7
1
1
0
0
0
0
2
2
0
1
0
0
2
0
0
0
0
0
2
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
1
1
2
1
0
0
0
1
0
0
1
1
0
1
0
0
0
2
1
0
0
0
0
0
2
0
2
0
1
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
1
2
2
1
0
0
2
2
3
0
1
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
2
0
0
0
0
0
0
0
2
2
0
0
1
1
0
1
0
0
0
0
1
0
1
0
0
0
2
0
0
1
1
2
0
1
0
0
1
0
0
2
2
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
2
1
0
0
3
0
0
0
0
0
0
3
0
0
1
0
0
0
0
2
0
1
0
2
2
0
1
0
0
2
1
0
0
0
1
2
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
1
1
0
2
2
0
0
0
2
3
0
2
0
0
0
2
2
0
1
2
0
1
0
0
2
1
0
0
2
0
1
1
0
0
0
0
0
0
0
0
1
0
2
0
3
0
0
1
0
1
0
0
4
2
0
0
0
1
0
1
2
0
2
2
2
2
1
0
2
3
2
1
4
2
2
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
2
0
0
1
0
2
2
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
4
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
1
0
1
2
0
1
0
0
0
1
0
0
0
2
0
0
0
0
1
2
0
0
1
1
2
0
0
1
1
2
0
2
1
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
1
2
0
0
1
0
0
0
3
0
2
0
2
4
1
1
0
1
0
0
1
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
2
2
2
2
0
0
1
0
0
2
0
1
2
0
2
1
0
0
0
0
1
0
0
0
1
0
2
2
1
0
0
0
0
0
1
0
0
1
0
1
0
0
2
0
0
2
0
1
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
8
0
0
2
2
0
0
0
2
0
2
2
0
0
1
0
0
0
5
0
0
0
0
0
0
1
0
1
2
1
0
0
0
0
0
0
1
0
1
1
2
2
0
2
0
0
2
0
0
2
0
0
0
2
2
0
1
0
0
0
2
2
0
2
0
0
0
0
2
1
0
2
0
0
0
1
3
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
2
3
0
0
0
0
0
1
3
0
0
1
0
0
0
1
0
0
2
0
2
0
0
1
0
0
0
2
0
0
1
1
1
0
2
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
4
2
1
0
1
1
0
0
0
0
0
0
0
0
0
6
0
0
1
0
0
0
0
1
0
0
2
2
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
1
0
0
0
0
2
2
0
2
1
1
0
0
1
0
1
1
2
0
0
2
1
3
0
2
1
0
0
0
2
1
0
0
0
1
1
0
1
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
4
0
0
2
0
2
3
2
0
1
0
0
0
2
0
0
1
0
0
0
1
2
1
2
0
0
1
0
2
0
0
0
0
2
1
1
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
2
0
0
1
0
0
2
0
0
0
0
1
0
0
1
0
0
1
1
2
0
1
0
2
0
0
0
0
0
0
0
0
0
3
2
0
0
0
2
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
1
0
0
0
0
0
0
3
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
1
0
0
0
1
0
0
1
0
3
0
0
0
0
1
0
1
1
0
0
0
0
0
1
2
0
0
0
2
1
0
0
0
0
0
3
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
1
0
0
3
0
0
0
0
2
1
1
0
0
0
1
1
0
0
0
0
1
0
0
1
0
1
2
0
0
0
0
3
2
2
0
1
1
2
0
0
0
0
0
0
0
1
0
2
2
0
0
2
0
2
0
0
0
0
1
0
0
1
1
0
0
0
0
2
0
1
3
2
3
0
0
0
0
0
1
0
0
1
1
2
0
0
0
1
0
0
0
0
2
0
2
0
0
2
0
0
2
1
1
1
2
0
11
0
2
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
1
0
1
0
4
0
1
0
0
1
0
1
1
1
0
0
0
0
0
1
1
0
1
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
1
2
0
1
0
0
1
0
0
0
1
5
1
0
0
2
0
0
1
0
0
0
0
0
0
1
2
0
0
1
2
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
3
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
1
0
1
0
0
1
1
1
2
0
0
0
0
2
0
0
1
0
0
0
2
0
2
0
0
2
1
0
0
1
2
0
2
2
0
0
0
1
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
2
0
2
4
0
0
1
5
0
1
0
0
1
1
1
0
1
2
0
0
2
0
2
0
0
2
1
0
0
1
2
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
2
0
0
0
1
0
3
0
2
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
2
2
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
1
2
1
2
0
0
0
2
0
0
1
0
0
0
2
0
0
1
1
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
2
0
1
0
0
1
0
0
2
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
1
2
0
3
1
0
0
3
1
0
0
1
0
0
0
1
2
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
1
0
0
0
1
0
2
0
0
2
0
1
0
0
2
0
0
0
0
0
1
2
2
1
1
1
1
1
2
0
0
1
0
0
0
2
0
2
1
1
0
1
0
2
1
0
0
1
0
1
2
0
0
0
3
0
0
0
0
0
0
4
0
1
1
1
0
0
0
0
2
0
1
1
0
0
2
0
1
0
2
0
1
0
0
0
0
0
0
1
2
0
0
2
0
0
1
0
3
0
0
1
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
3
1
0
0
2
1
2
0
0
1
0
0
0
0
0
0
0
0
1
0
2
3
0
0
1
2
2
1
0
2
0
0
0
2
0
2
0
0
0
0
0
0
1
1
0
0
0
0
1
2
0
0
0
0
2
0
0
1
1
2
0
1
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
2
1
0
0
1
0
0
2
0
2
0
2
0
1
0
0
0
0
0
0
0
1
0
2
2
0
1
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
2
2
0
1
0
0
1
0
0
0
1
2
2
0
0
0
0
0
1
1
0
2
0
2
1
0
0
0
1
2
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
2
0
1
0
0
1
1
0
2
1
0
1
0
0
0
0
1
0
2
1
0
0
2
2
0
0
0
0
1
2
0
0
2
0
2
0
0
0
2
0
0
0
2
0
1
0
2
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
2
0
0
1
0
0
2
0
0
0
1
1
2
0
1
0
0
0
0
0
0
2
0
2
0
2
0
1
2
0
0
1
0
0
0
0
2
0
1
0
0
1
0
2
2
0
0
0
0
0
0
2
0
1
1
0
2
0
1
1
0
2
0
0
0
0
0
1
1
0
1
2
0
1
0
0
0
2
0
0
1
0
2
1
2
0
0
2
0
1
2
0
0
0
0
1
0
2
0
0
1
0
2
0
1
1
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
2
0
0
0
0
0
2
0
0
0
0
1
4
1
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
1
2
1
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
2
0
2
0
0
0
0
0
2
1
0
0
1
1
0
0
0
0
0
0
0
3
1
0
0
2
0
0
0
1
0
0
0
0
2
0
2
1
2
0
0
0
1
2
2
0
0
3
0
2
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
2
0
1
0
1
0
0
0
2
4
0
0
0
0
0
0
2
2
0
1
0
1
1
0
0
0
0
0
0
1
0
2
1
2
0
1
2
2
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
2
0
2
0
0
1
0
1
3
0
1
0
2
0
0
0
0
0
0
1
2
2
1
0
0
0
1
0
0
0
4
0
1
0
2
2
0
0
0
0
6
0
2
1
0
1
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
2
3
0
1
1
0
0
0
2
0
1
0
0
1
0
0
0
0
1
0
1
0
1
0
0
1
3
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
4
0
0
1
1
0
3
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
1
0
1
1
0
0
0
2
2
1
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
1
0
1
2
2
0
2
2
2
0
0
1
2
1
0
0
0
0
2
0
0
0
0
0
1
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
2
0
2
2
0
2
1
2
1
0
0
0
1
1
0
1
0
2
1
0
0
1
0
1
0
2
1
1
0
0
0
0
0
0
0
2
3
0
2
0
0
0
0
0
2
0
2
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
2
2
0
0
0
2
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
2
2
2
1
2
0
2
0
2
0
0
1
0
1
2
0
2
5
0
0
0
0
0
0
2
3
1
0
0
0
0
0
0
0
1
3
2
0
3
1
0
0
0
0
0
2
0
1
3
0
0
0
0
0
0
2
0
0
2
1
0
0
3
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
4
0
1
2
0
0
0
1
0
0
1
0
0
0
1
0
1
2
0
0
0
2
0
2
0
1
1
0
2
2
0
0
3
0
2
0
0
0
0
1
3
1
1
0
1
0
0
0
0
2
0
0
1
1
0
0
0
0
2
0
3
1
1
2
2
0
0
0
0
0
0
1
0
0
1
1
0
2
0
0
2
2
1
0
2
2
0
0
1
0
1
1
0
1
0
0
2
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
1
2
0
0
0
2
1
0
1
0
0
0
0
0
0
0
2
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
2
0
1
2
0
1
0
0
1
1
0
0
0
0
1
0
1
1
0
2
0
1
3
0
2
1
2
0
3
2
2
0
1
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
1
1
2
2
0
0
0
0
0
0
1
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
1
1
2
0
1
0
1
1
0
2
0
0
0
2
0
0
0
0
0
0
0
1
2
0
2
0
1
0
0
2
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
2
0
1
2
0
4
2
0
0
1
1
0
2
0
1
0
0
1
0
1
2
1
0
1
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
3
0
1
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
1
0
2
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
3
0
0
0
0
0
2
0
2
2
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
2
2
2
0
2
0
1
0
3
0
1
0
0
0
2
0
0
1
0
2
0
2
2
0
0
0
1
0
1
0
1
0
0
1
1
0
2
0
1
0
2
1
0
0
2
1
0
0
1
0
2
1
0
0
0
3
2
0
0
0
0
0
3
2
0
0
0
2
0
2
0
0
2
1
2
0
3
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
1
2
2
1
1
0
3
1
4
0
0
1
1
0
2
0
0
1
2
0
0
0
2
0
0
0
0
0
0
1
0
2
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
2
0
0
1
1
0
1
0
0
1
2
0
1
2
0
0
1
0
1
0
0
0
1
1
0
0
0
0
6
2
0
1
0
2
0
0
0
0
0
2
0
0
2
1
1
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
2
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
1
1
0
0
2
1
1
1
0
0
1
2
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
1
1
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
1
0
0
0
2
1
0
0
1
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
2
2
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
2
0
0
1
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
2
1
2
0
0
3
0
0
0
0
0
2
1
0
1
0
0
0
1
0
0
1
0
1
1
3
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
2
1
1
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
1
0
0
1
0
0
2
0
1
0
0
2
0
0
0
1
0
0
0
2
1
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
1
2
3
1
0
1
0
0
0
1
0
0
2
1
0
2
1
0
1
0
0
1
1
2
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
3
2
0
0
1
3
2
1
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
2
0
0
0
0
1
1
2
0
1
0
2
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
1
0
0
2
0
0
1
0
3
0
3
0
0
0
1
0
1
1
0
0
0
0
1
0
0
2
0
2
0
0
1
1
1
0
0
2
0
0
2
0
1
0
1
1
0
2
2
0
0
0
2
0
0
2
3
0
0
0
1
0
0
0
0
2
0
2
0
4
2
0
1
2
0
0
0
1
0
0
2
2
2
2
0
0
0
2
0
0
2
0
0
1
0
0
2
1
1
0
0
0
0
0
1
0
0
1
1
1
0
2
0
2
1
0
0
0
0
1
0
1
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
2
0
0
1
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
2
0
1
0
0
1
2
0
1
0
0
0
0
3
2
2
0
0
0
0
2
0
4
2
2
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
3
2
0
1
0
2
2
0
1
1
0
0
2
0
0
1
0
2
0
2
0
2
1
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
1
0
2
0
4
2
0
0
2
0
0
0
2
0
2
1
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
2
2
2
2
0
0
1
0
2
0
0
3
1
1
0
0
0
0
0
2
0
0
1
2
0
1
2
0
0
2
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
2
1
1
0
2
2
0
0
2
0
0
2
0
1
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
2
0
1
0
0
3
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
1
2
2
0
2
1
2
0
0
0
0
2
0
0
1
0
0
2
1
2
1
1
2
0
0
2
0
0
0
2
0
1
0
0
1
0
0
2
0
0
0
0
0
0
1
0
1
0
1
0
0
0
4
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
2
0
0
2
0
2
0
1
1
0
0
0
0
0
2
0
0
2
0
0
0
2
1
0
1
1
0
0
0
0
0
0
3
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
1
0
0
0
0
2
2
1
1
3
0
1
0
0
1
2
1
0
0
2
0
4
3
1
0
0
0
0
0
0
1
0
0
2
0
0
0
1
1
2
3
0
0
1
1
0
0
0
0
0
0
2
1
2
0
2
1
0
0
0
1
1
0
0
1
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
0
1
2
0
0
1
1
0
0
0
0
0
0
0
0
1
2
0
0
1
0
1
0
1
5
0
0
1
0
0
0
0
0
1
0
0
0
1
3
0
0
2
0
0
0
1
0
0
0
1
0
3
1
0
2
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
1
0
1
0
0
2
0
0
0
0
2
2
0
1
0
0
0
0
2
0
0
0
1
2
1
0
0
0
0
0
0
0
1
0
2
0
2
0
1
0
1
1
1
0
1
0
0
0
2
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
2
2
0
0
0
1
1
0
1
1
2
1
0
0
1
0
2
2
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
3
1
0
2
1
0
1
0
2
0
0
0
0
2
0
0
2
1
0
0
0
2
0
0
0
1
2
0
2
0
2
0
0
0
0
0
0
1
2
0
1
0
2
0
1
0
0
0
0
0
0
1
0
0
2
1
0
0
1
0
2
0
0
0
0
0
2
0
2
2
0
1
0
1
0
0
0
0
0
0
0
0
2
0
1
2
0
2
0
0
1
0
1
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
1
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
2
2
1
0
0
2
2
2
0
0
1
0
1
1
2
0
1
0
2
3
2
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
1
1
0
1
4
0
2
0
0
0
0
0
0
1
1
0
0
0
1
1
3
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
1
0
0
3
2
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
1
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
2
0
1
2
1
0
0
0
0
0
0
0
2
0
1
0
0
0
1
2
0
0
0
0
2
1
0
0
1
1
1
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
1
0
2
0
0
0
2
1
1
1
0
0
0
0
0
0
1
0
2
0
0
1
1
0
0
0
2
0
0
1
0
1
3
0
0
1
0
0
0
2
1
0
2
0
1
0
2
4
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
3
0
2
0
0
1
0
1
0
0
0
0
2
0
1
0
1
0
0
0
2
0
0
2
2
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
2
1
1
2
0
0
0
1
1
1
0
0
0
2
0
2
0
1
0
1
1
1
0
1
0
1
0
0
1
0
0
2
1
0
0
1
0
0
0
0
1
0
2
1
0
0
0
0
0
0
2
2
0
0
2
3
0
0
0
2
0
0
1
0
0
1
0
0
0
1
0
0
0
2
0
0
1
2
1
0
0
0
2
0
0
0
3
0
0
0
1
0
2
0
0
2
0
0
0
2
1
0
2
0
0
0
0
0
0
2
0
4
1
0
2
2
0
1
1
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
1
2
4
0
2
2
2
0
0
2
1
0
1
1
2
3
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
2
1
2
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
2
4
0
0
0
1
0
0
1
1
2
0
1
0
2
1
1
0
0
0
0
0
1
1
0
1
0
0
0
1
2
0
0
1
0
2
2
3
2
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
4
0
0
0
1
0
1
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
2
2
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
1
1
0
0
2
2
0
1
2
2
0
0
0
0
0
0
0
2
2
0
1
0
0
1
0
0
0
0
1
0
0
0
2
0
1
0
1
2
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
2
0
2
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
2
2
0
2
2
3
0
0
2
1
1
0
0
1
0
2
0
2
0
3
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
1
1
0
0
1
2
1
2
0
0
0
0
1
2
0
0
0
0
0
1
1
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
2
0
2
1
0
0
2
0
2
1
2
1
1
1
0
0
0
0
1
1
1
0
0
0
2
1
0
0
0
0
0
0
0
1
1
1
0
1
2
0
0
0
0
0
2
0
1
0
0
0
0
2
2
0
0
4
1
1
0
3
0
1
1
0
0
0
0
0
0
1
1
1
0
0
0
0
1
1
0
2
2
0
0
0
0
0
0
0
0
1
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
1
1
1
0
2
0
0
0
1
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
4
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
1
1
0
0
0
0
0
2
0
0
1
0
0
2
0
1
1
0
0
0
0
0
0
1
0
2
0
2
1
1
0
3
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
2
0
1
2
0
0
2
2
2
0
1
0
0
2
0
0
0
0
1
0
0
1
0
2
0
1
2
2
1
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
2
0
0
1
0
0
0
2
1
0
2
0
0
1
0
0
0
2
0
0
0
2
0
1
0
0
2
2
1
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
2
1
2
0
0
2
3
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
1
0
2
3
0
2
0
0
0
0
1
0
0
2
2
2
0
0
2
0
1
0
2
2
2
0
0
0
0
2
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
2
1
0
1
0
1
0
2
0
0
0
1
0
0
2
1
0
0
0
2
0
0
0
0
0
1
1
2
1
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
2
1
0
0
0
0
1
2
0
1
3
2
0
0
2
0
2
0
3
0
2
2
0
0
1
0
0
0
2
1
2
1
0
0
0
0
2
0
0
0
0
1
1
2
0
0
1
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
3
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
1
0
1
0
0
2
0
2
2
1
0
0
0
2
0
0
1
0
0
2
0
0
1
0
0
0
1
1
1
0
0
1
2
0
2
0
0
0
3
0
0
1
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
2
0
1
0
1
0
2
0
0
2
2
1
0
2
1
0
3
0
2
1
3
1
0
0
1
0
0
1
2
0
0
0
0
1
0
1
0
0
4
0
2
0
0
0
0
0
1
0
0
0
2
2
3
0
0
0
0
0
0
2
0
2
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
2
1
0
1
0
2
0
0
2
0
0
3
0
2
2
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
2
0
0
2
0
0
0
0
1
1
0
0
0
2
0
0
0
2
0
0
0
2
2
0
0
0
0
2
0
2
0
1
2
2
2
1
0
2
1
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
1
0
0
0
2
0
1
0
1
1
0
1
0
1
0
2
1
0
0
1
1
2
0
0
1
3
0
1
0
2
0
2
0
0
0
1
0
2
0
0
1
0
3
0
0
0
0
1
1
2
0
0
2
0
0
1
0
0
3
0
0
2
0
0
0
0
1
2
0
0
0
3
3
0
0
0
3
0
1
2
0
0
0
0
0
0
2
0
0
2
0
2
2
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
1
1
0
1
0
0
0
2
0
2
0
0
0
0
1
0
0
1
0
0
2
2
0
0
1
0
2
1
0
0
0
2
0
2
0
0
0
0
1
0
0
0
1
0
0
1
0
3
0
1
0
1
1
0
1
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
2
1
1
2
1
2
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
2
0
1
0
2
0
0
1
1
2
0
0
0
2
0
2
0
0
0
1
0
2
0
0
0
0
1
1
0
0
0
0
1
1
2
1
2
0
0
0
0
0
0
1
0
2
1
0
0
1
1
0
0
0
2
0
0
1
1
2
2
2
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
1
2
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
2
2
0
1
2
2
0
2
0
0
0
1
1
0
2
0
0
2
0
0
1
0
0
1
1
1
0
1
1
0
1
0
2
0
0
3
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
2
0
0
1
0
0
0
2
2
1
2
0
1
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
2
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
2
2
0
0
0
0
1
0
1
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
1
0
2
0
0
2
1
0
2
0
2
0
0
0
1
2
1
0
0
0
0
0
0
1
2
2
1
2
0
0
2
0
0
0
2
2
1
2
0
0
0
1
2
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
1
0
2
0
0
0
0
0
0
0
0
1
1
1
2
0
0
1
0
1
0
0
0
0
0
2
1
0
0
1
0
0
2
0
1
0
1
2
0
1
0
2
2
1
0
0
0
2
0
0
1
0
2
1
0
0
1
0
1
0
0
1
0
3
0
0
1
0
1
0
2
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
2
0
0
1
0
0
1
0
0
2
0
0
0
2
1
0
1
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
2
0
1
1
0
0
1
1
0
0
0
0
2
0
0
2
3
0
1
0
0
0
0
0
0
0
1
2
0
0
1
0
0
2
2
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
1
1
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
2
0
2
0
2
0
2
6
1
0
0
0
6
0
0
1
1
2
2
0
0
1
0
0
2
0
2
0
1
0
1
2
0
0
0
1
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
2
2
0
4
0
1
1
1
2
0
1
0
2
1
0
2
0
0
1
1
1
1
0
2
2
0
0
0
0
0
2
0
0
2
1
0
2
0
0
0
0
2
1
0
2
1
1
0
2
0
1
2
2
0
2
0
1
0
0
2
2
0
2
2
0
0
0
2
0
0
1
1
0
2
0
0
1
1
1
2
0
0
0
1
2
0
0
0
1
0
0
0
2
0
0
0
2
1
1
0
0
0
2
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
1
1
0
0
2
2
0
0
0
2
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
2
0
2
2
0
2
2
2
0
2
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
2
2
0
2
2
0
2
1
0
1
0
1
0
2
0
2
0
0
0
2
0
1
0
2
0
1
0
0
0
0
1
0
2
0
0
1
0
2
2
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
2
1
0
4
0
0
0
0
0
0
0
3
0
0
0
1
0
0
1
0
0
1
0
2
0
2
1
0
2
2
0
0
1
0
1
0
0
0
0
1
0
0
1
0
2
1
1
0
0
0
1
0
2
1
1
0
2
0
0
0
0
0
1
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
2
0
2
0
0
2
1
0
0
0
2
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
1
12
0
3
0
0
2
0
0
0
2
2
2
2
0
2
0
2
0
0
1
0
1
2
0
0
1
1
0
1
0
2
1
0
0
0
0
1
4
1
0
2
2
0
2
0
0
0
1
0
1
0
1
1
0
0
0
2
2
1
0
0
0
1
2
0
0
2
0
0
0
1
2
0
0
0
0
0
0
1
0
0
2
2
0
4
8
2
0
0
0
0
0
1
0
1
0
2
1
0
0
1
0
1
1
1
1
0
1
1
0
0
0
1
0
0
0
4
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
1
2
1
0
0
0
1
0
2
0
0
0
0
2
0
2
2
0
1
0
0
0
2
1
0
0
2
0
2
0
0
0
4
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
3
2
0
0
2
0
0
2
1
2
2
0
3
1
2
0
2
0
0
2
2
0
0
0
0
1
0
0
0
0
0
3
2
2
0
2
1
3
2
0
2
2
0
0
0
1
0
0
0
1
0
1
5
0
0
0
2
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
1
1
1
1
0
0
0
0
3
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
1
0
1
0
0
1
0
0
0
0
2
3
0
0
0
0
0
0
1
0
0
0
0
1
1
1
1
0
0
0
0
0
0
2
0
1
2
1
2
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
1
2
0
0
0
0
0
1
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
2
0
0
1
0
2
0
0
0
2
1
1
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
2
0
0
0
0
0
0
0
1
2
1
0
2
0
0
0
0
1
1
1
0
0
0
0
0
0
2
0
0
3
1
0
1
2
0
0
0
1
1
1
0
2
1
0
2
0
1
0
0
0
0
1
1
3
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
2
0
0
1
3
0
1
1
2
0
1
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
2
0
1
0
0
0
0
0
1
1
0
0
0
1
2
2
3
0
0
0
0
3
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
3
2
0
3
1
0
0
2
1
0
0
0
1
0
0
1
1
2
0
1
2
0
2
0
0
2
0
2
0
2
0
0
0
1
0
0
1
0
0
0
1
0
1
1
0
0
3
0
0
0
1
2
2
0
2
0
0
0
0
0
0
0
0
3
1
1
1
0
3
0
1
2
0
0
0
0
0
0
0
2
1
1
0
0
1
0
1
2
0
0
2
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
2
2
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
1
2
1
6
0
0
0
1
1
2
0
0
0
3
0
0
1
0
0
0
2
2
2
0
1
0
1
0
0
1
0
2
0
1
2
0
0
0
0
0
3
0
0
0
0
1
1
2
0
2
0
1
0
2
0
0
0
1
0
0
0
2
2
0
1
0
0
0
1
0
0
2
2
0
0
0
0
0
0
1
0
0
0
1
2
2
0
0
1
0
1
0
0
1
0
0
2
0
0
1
1
0
0
0
0
1
0
2
0
0
0
1
2
2
2
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
1
0
2
1
1
0
2
2
0
1
0
2
1
0
0
0
0
3
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
1
2
0
0
0
0
0
2
2
0
1
2
0
2
0
1
0
1
0
2
0
0
0
0
0
1
0
0
2
4
0
0
0
1
0
0
0
1
0
0
0
2
2
0
0
0
0
1
0
0
0
3
0
0
0
1
0
0
0
1
0
2
0
0
1
2
0
2
0
0
2
0
1
1
0
0
0
0
0
0
1
2
0
1
2
0
0
3
0
1
0
2
6
0
0
2
3
0
0
1
2
0
0
0
0
0
2
0
1
0
0
0
3
0
0
0
1
1
0
1
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
2
1
2
2
2
0
0
0
0
0
2
1
0
0
0
1
2
0
0
0
2
0
2
2
2
0
0
2
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
2
1
0
0
2
0
2
0
0
1
3
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
5
2
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
1
0
1
0
1
0
0
0
0
2
0
0
2
0
2
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
2
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
1
0
3
0
0
0
0
2
0
0
0
0
0
1
2
0
0
1
0
1
0
0
0
0
2
0
1
1
0
0
0
0
0
0
1
1
0
0
1
1
0
2
1
0
0
0
0
0
2
0
1
1
1
0
0
0
2
0
0
0
2
1
0
0
2
2
2
0
0
0
2
0
0
1
0
1
0
2
0
0
0
0
0
2
0
0
1
1
0
0
0
1
0
2
0
1
1
1
0
0
1
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
2
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
1
0
3
0
3
0
2
0
1
1
1
0
1
1
1
0
0
1
0
1
0
0
0
0
0
1
2
0
2
1
1
0
0
1
0
2
0
1
0
0
1
2
0
1
0
1
1
0
0
1
0
2
2
0
0
0
0
0
0
0
1
0
0
0
2
1
1
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
1
0
0
0
2
1
0
1
2
0
0
0
0
0
2
0
2
0
2
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
3
1
2
0
1
0
0
0
2
2
0
1
1
0
0
2
0
0
0
1
0
2
0
0
2
0
1
0
0
0
1
0
1
2
0
0
3
0
0
0
1
2
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
1
2
0
2
1
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
2
1
0
1
1
2
0
2
2
0
0
0
0
0
0
0
2
0
0
1
0
0
2
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
1
2
0
2
2
0
1
0
0
0
0
0
1
0
2
0
0
1
2
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
1
0
0
1
0
1
1
1
2
0
2
0
3
0
0
1
2
0
0
1
0
0
0
0
1
0
2
0
1
0
1
1
0
1
1
0
0
2
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
2
0
2
0
0
2
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
2
1
2
2
0
2
2
0
0
0
0
0
1
0
2
1
0
0
0
2
0
1
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
2
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
2
1
0
1
1
0
1
0
0
0
0
1
0
0
3
0
0
0
0
0
1
0
2
1
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
1
0
2
2
0
2
0
0
0
0
0
0
0
1
2
2
2
0
1
2
0
0
2
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
2
0
1
1
0
2
0
0
0
2
2
1
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
1
0
0
2
0
2
0
2
0
1
1
0
2
0
0
1
0
0
0
0
2
0
1
2
0
1
1
0
0
0
0
0
0
0
0
4
2
0
0
1
0
0
0
0
0
0
1
2
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
2
3
0
1
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
1
0
0
0
2
1
0
0
1
1
0
5
1
1
0
2
0
0
0
0
0
0
2
0
1
0
1
0
0
2
0
0
2
2
2
0
0
2
0
0
0
4
0
0
1
0
0
0
1
0
0
0
0
0
2
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
2
0
2
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
3
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
2
0
1
0
0
1
2
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
1
0
2
0
0
2
0
2
0
1
2
0
0
0
0
0
0
0
1
0
1
1
2
0
0
0
0
1
2
2
2
1
0
0
1
0
0
0
2
0
3
1
0
0
0
0
0
0
0
1
1
0
0
0
2
2
0
0
1
0
1
1
1
0
2
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
2
0
2
0
0
0
1
2
1
2
0
0
2
0
0
2
1
1
0
2
0
0
0
0
2
2
1
0
2
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
2
0
0
0
0
3
0
0
2
0
0
2
1
0
0
2
2
1
0
0
0
0
0
2
2
0
0
2
1
0
0
0
1
3
0
0
0
2
0
0
1
0
1
0
0
0
1
1
0
1
0
1
0
1
0
0
3
1
0
0
0
0
0
0
2
0
1
0
2
0
0
3
1
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
1
0
0
2
1
1
0
1
1
0
0
0
1
2
1
0
0
2
0
0
0
0
2
0
0
0
0
3
0
0
1
0
0
0
1
0
1
2
2
1
2
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
2
2
1
1
0
2
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
2
1
1
1
0
1
1
0
0
0
0
0
2
2
0
0
0
0
0
0
3
1
0
0
0
1
0
1
0
0
2
8
0
2
1
2
0
0
1
2
1
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
1
1
0
1
0
0
1
0
0
2
0
0
1
1
2
0
6
0
0
0
2
1
2
1
1
0
0
0
0
0
0
0
0
2
1
1
2
0
0
0
0
0
0
0
1
1
2
0
0
2
0
0
0
0
0
1
3
0
0
0
0
0
0
2
0
1
0
1
0
3
2
0
0
0
2
0
0
0
0
0
2
0
0
2
1
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
6
0
2
0
0
1
0
0
2
0
0
2
0
0
0
0
1
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
2
2
0
0
0
1
0
1
0
1
1
0
0
1
0
0
0
1
2
0
1
0
1
0
0
0
1
0
0
0
0
0
2
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
2
1
0
2
0
0
0
0
0
0
1
0
1
0
1
0
0
2
1
0
0
1
0
1
0
0
0
4
2
2
1
0
1
1
0
0
1
1
0
0
1
4
1
0
0
2
2
0
0
0
2
3
2
0
0
2
1
0
0
0
0
0
0
2
2
0
2
3
0
0
1
0
1
2
0
1
0
1
0
1
0
0
0
0
1
0
0
1
1
2
2
0
0
0
2
0
0
0
1
2
0
2
2
0
2
0
0
2
0
0
1
0
0
0
1
0
0
1
0
1
1
1
0
1
1
0
2
1
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
5
0
0
1
0
1
0
0
1
2
0
0
0
0
0
1
0
1
1
0
2
0
0
0
2
0
1
0
0
0
3
1
0
0
1
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
1
1
3
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
2
0
0
0
0
2
0
2
0
0
1
0
0
0
2
0
2
2
0
0
0
3
0
0
2
0
0
0
0
0
0
2
2
0
1
0
0
1
0
1
0
0
1
1
0
0
1
1
0
1
0
0
5
0
0
0
1
0
0
1
2
1
0
0
2
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
1
1
1
0
0
2
1
2
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
3
1
1
2
0
2
0
0
2
0
0
0
0
2
0
0
0
2
2
0
1
1
0
0
0
0
0
1
1
0
2
2
2
0
2
2
2
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
2
2
0
2
0
2
1
0
0
2
2
1
1
0
1
0
1
0
0
0
0
1
0
0
1
0
3
0
2
0
1
0
0
2
1
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
1
0
0
2
0
0
3
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
2
0
2
1
0
0
0
1
0
0
0
0
0
1
0
0
2
0
2
0
1
0
1
0
1
2
0
0
0
0
3
1
1
0
1
1
1
0
3
0
0
0
2
2
2
1
2
0
0
0
1
1
0
1
1
0
0
0
2
0
2
0
0
0
0
2
0
0
2
0
0
0
0
1
3
0
1
1
0
0
0
0
1
1
0
0
2
2
0
2
2
0
1
0
0
0
1
1
3
0
2
1
2
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
2
0
2
0
0
0
0
2
3
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
2
1
0
1
2
0
0
0
0
2
0
1
0
1
1
0
1
1
2
0
3
2
0
2
0
1
0
0
0
0
0
2
2
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
3
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
1
0
1
0
1
0
2
2
2
0
0
0
0
0
0
0
1
0
2
0
1
0
2
0
0
0
2
1
0
2
0
0
0
0
0
1
1
0
0
1
2
0
2
0
0
2
0
0
0
2
0
0
2
2
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
1
2
0
0
2
2
2
2
0
0
0
1
0
0
0
1
0
0
0
0
1
0
2
2
0
0
0
2
0
1
0
1
1
0
0
1
2
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
1
1
0
1
0
0
0
0
2
2
3
0
0
2
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
1
1
2
2
1
2
2
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
2
0
0
0
0
1
3
0
0
0
1
0
0
1
0
0
1
0
0
0
3
1
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
1
2
0
2
2
0
1
1
2
0
0
0
0
1
0
0
2
0
0
0
0
0
1
2
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
2
2
0
0
2
0
2
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
2
1
1
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
2
1
0
2
0
2
0
0
2
0
0
1
0
2
0
1
0
0
0
0
0
1
0
2
0
1
0
1
0
0
1
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
2
1
0
2
0
0
1
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
1
1
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
2
0
0
1
0
1
0
0
0
0
0
1
3
1
0
0
2
0
0
1
0
0
0
0
0
1
0
0
2
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
2
0
0
0
0
1
0
1
0
3
2
0
0
1
0
0
0
0
0
0
1
0
0
2
3
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
5
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
2
0
1
1
1
0
0
0
2
0
1
0
0
2
0
0
0
0
2
0
0
2
3
0
2
2
2
0
0
0
0
2
0
0
1
0
2
1
1
1
1
1
0
0
0
3
0
0
2
1
0
2
0
1
0
0
1
1
2
1
2
2
0
1
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
2
0
0
1
3
1
0
0
0
0
0
0
1
0
1
2
0
3
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
4
2
0
2
1
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
1
1
2
0
1
0
0
2
0
1
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
2
0
2
1
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
3
0
0
0
0
0
0
0
1
0
1
0
0
2
0
1
2
1
2
0
1
0
1
0
0
1
0
2
0
0
0
0
3
0
3
0
1
0
0
0
1
0
1
0
0
2
0
2
0
2
0
1
1
1
0
1
0
1
2
2
0
2
1
0
1
1
1
0
0
0
0
1
2
0
1
0
2
0
0
2
0
2
0
0
2
1
1
1
2
0
0
0
2
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
2
5
0
0
0
2
0
0
1
0
0
1
0
2
0
2
1
0
0
1
0
1
0
0
1
2
0
2
1
0
2
2
0
4
1
0
0
1
0
0
0
0
0
0
1
2
0
2
2
2
0
0
0
3
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
2
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
2
4
0
2
2
2
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
1
1
1
2
1
0
2
0
3
2
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
2
5
0
2
0
2
0
0
0
0
0
1
1
2
0
0
2
0
0
2
1
0
0
2
2
1
1
0
0
1
0
0
2
2
0
0
0
0
2
0
0
0
1
0
2
0
0
1
0
0
2
0
3
1
0
0
0
0
0
2
0
1
0
3
0
0
0
0
2
2
1
0
2
1
0
1
0
0
0
0
0
0
6
0
0
1
0
0
1
0
1
0
0
0
0
0
0
2
0
4
1
0
0
0
2
1
0
0
0
0
0
0
2
0
1
0
0
2
1
0
1
0
0
2
0
1
0
0
1
2
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
1
2
0
2
1
1
1
0
0
0
1
0
2
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
1
2
2
3
0
0
1
0
2
0
0
0
3
2
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
2
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
1
0
1
0
1
2
2
4
0
0
0
0
0
1
0
0
1
2
0
0
2
0
0
1
2
2
2
0
0
1
0
0
0
1
2
0
2
1
0
0
0
2
0
1
2
0
0
0
0
0
2
1
0
0
0
0
2
0
1
0
0
1
0
0
0
0
1
1
0
0
0
1
1
1
0
0
2
0
0
1
0
1
0
0
0
0
1
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
1
2
2
0
1
2
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
1
9
1
0
0
0
1
0
1
2
3
2
2
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
1
0
0
1
8
2
0
1
2
0
1
0
0
2
1
2
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
1
0
3
0
2
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
1
1
0
1
2
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
2
0
3
1
1
1
2
0
0
2
0
1
0
0
1
2
0
0
1
0
0
0
1
0
1
1
3
0
2
3
0
1
0
0
0
2
0
0
2
1
0
2
0
0
0
0
1
0
1
1
0
0
1
2
1
0
0
0
0
0
1
1
1
0
0
2
1
0
1
0
0
0
0
0
2
0
0
0
1
1
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
2
1
0
0
3
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
3
0
0
0
0
2
0
0
1
0
0
1
2
2
0
0
2
2
0
0
2
2
2
0
2
0
0
0
0
0
0
1
0
0
2
1
0
2
0
2
0
0
0
2
1
0
0
0
1
1
1
0
2
0
1
0
1
1
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
1
2
2
2
0
0
2
1
2
0
1
0
0
1
0
2
0
0
0
0
0
2
0
2
1
0
4
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
3
1
2
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
2
1
0
2
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
2
2
2
2
0
0
2
0
0
0
0
0
0
2
2
6
0
0
0
2
0
0
0
0
0
0
3
0
1
0
2
2
2
0
0
2
0
0
2
0
0
0
0
3
0
2
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
1
1
0
0
2
0
0
1
0
5
3
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
1
0
0
0
2
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
2
0
0
2
0
0
0
1
0
1
0
2
2
0
2
0
1
1
0
0
0
0
0
2
0
1
0
0
0
1
1
1
0
0
4
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
2
1
0
2
0
1
1
0
0
0
1
0
2
0
0
1
0
0
0
1
1
0
0
0
1
0
0
1
1
0
1
0
1
0
0
0
1
0
0
0
2
1
0
0
0
0
2
0
1
0
1
0
2
0
0
1
2
2
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
2
0
1
0
0
1
0
0
1
2
1
1
0
1
0
1
0
0
2
2
2
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
1
2
0
3
0
0
2
2
0
0
0
1
1
0
1
0
0
3
0
0
0
2
0
0
2
0
0
1
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
2
0
1
0
0
0
1
1
2
0
1
0
0
0
2
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
1
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
2
0
0
0
2
3
0
0
0
2
0
2
1
0
2
2
0
0
1
0
2
0
2
0
0
1
0
0
0
1
0
1
0
2
0
2
1
0
1
0
1
0
0
0
0
2
0
1
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
1
1
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
2
0
2
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
2
0
2
0
1
1
0
0
0
0
2
0
0
1
0
2
1
0
2
0
0
0
0
0
0
0
0
2
0
2
1
2
1
1
0
1
0
2
0
0
2
0
0
0
0
0
0
1
2
0
0
0
2
1
0
1
0
2
2
1
0
0
0
1
2
0
0
0
0
2
0
0
2
0
0
0
2
1
1
1
1
2
0
3
0
0
0
0
0
0
2
2
1
1
2
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
1
2
2
0
1
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
2
2
2
0
0
0
0
0
0
1
2
1
0
0
0
2
0
0
2
1
2
0
0
1
2
0
2
1
0
2
0
0
1
0
1
1
1
0
2
2
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
1
0
1
0
2
0
0
0
0
0
3
0
0
0
2
1
1
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
2
0
0
1
0
0
0
2
0
0
1
1
0
0
0
1
1
0
0
0
0
2
0
0
0
3
0
0
1
1
0
0
2
2
2
0
2
0
0
1
0
0
2
0
2
0
0
1
2
0
0
5
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
1
1
2
1
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
1
0
0
0
0
0
0
1
1
0
2
0
0
1
2
0
0
2
1
0
0
0
0
2
0
0
1
0
0
2
0
0
1
3
0
0
0
0
2
2
0
2
0
0
2
0
1
0
1
1
0
1
0
0
2
2
0
1
0
1
0
0
0
0
2
0
0
1
0
2
0
0
0
0
2
0
0
2
2
0
0
2
0
1
0
0
0
0
0
0
0
2
1
1
0
0
1
2
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
1
0
0
1
0
1
0
0
0
1
0
2
0
1
2
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
2
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
11
0
0
0
1
2
0
0
1
1
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
1
1
2
0
2
4
5
0
0
2
0
0
0
0
0
0
2
0
2
2
1
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
2
0
0
0
1
1
0
0
0
0
0
1
0
1
1
0
0
0
0
1
1
2
0
1
2
2
0
0
2
0
0
0
0
0
0
0
3
0
2
1
0
0
2
1
0
0
0
2
0
0
0
3
0
0
0
0
0
1
0
1
2
0
0
1
2
0
1
0
0
2
0
0
0
1
0
0
1
1
3
0
0
1
0
1
0
1
0
1
0
0
0
0
2
0
2
0
3
1
0
0
0
0
0
0
2
0
0
5
3
0
0
1
0
0
0
0
0
2
1
0
1
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
1
2
1
2
0
1
1
2
0
0
0
2
0
1
1
0
1
0
0
9
0
2
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
1
0
1
0
0
2
0
1
0
0
0
2
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
1
0
0
0
0
0
1
0
1
1
1
1
0
0
4
2
0
0
0
0
2
1
2
2
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
1
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
2
1
0
0
1
0
0
1
0
3
1
0
2
0
0
2
0
0
1
0
1
1
0
0
2
1
0
0
0
0
0
0
0
1
1
1
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
12
0
2
0
0
0
2
1
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
2
1
0
0
0
0
1
1
0
2
1
0
0
0
1
0
0
0
2
1
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
2
0
2
2
0
0
2
1
0
0
0
1
0
0
2
0
1
0
0
1
2
0
1
2
1
0
0
0
0
2
2
2
0
2
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
2
0
0
0
1
0
1
1
0
0
0
1
1
0
1
2
1
1
0
1
2
0
0
1
0
0
0
2
2
0
3
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
3
0
0
0
1
1
1
1
0
1
2
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
2
0
2
2
1
0
0
2
1
0
0
0
0
0
0
2
0
2
2
1
0
0
1
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
1
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
1
0
2
0
1
2
0
1
0
2
0
0
0
3
0
0
1
0
0
0
0
1
0
0
0
1
2
1
1
1
0
1
0
1
0
0
0
0
0
2
1
1
2
0
0
0
2
1
0
0
2
0
0
0
1
0
2
0
1
0
2
0
1
0
0
0
0
1
1
0
1
0
0
2
0
0
0
0
0
0
0
0
2
3
0
2
1
0
0
2
0
1
0
0
2
0
0
0
1
0
0
0
0
0
1
0
1
0
0
2
1
2
0
0
1
0
1
0
1
0
0
1
0
1
1
0
2
0
0
0
1
0
1
1
0
2
0
0
2
0
1
0
0
2
0
0
0
1
0
4
1
0
1
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
1
2
1
0
0
0
1
0
0
0
0
1
2
2
2
0
0
1
2
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
3
0
1
0
3
0
0
1
0
0
1
1
0
2
0
3
0
0
0
1
0
0
0
0
0
1
2
0
2
0
0
0
2
0
0
1
2
0
0
0
0
0
1
1
1
0
1
0
2
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
2
1
0
0
2
2
0
1
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
1
2
1
2
0
0
0
0
0
1
2
0
0
2
0
0
1
0
1
0
0
1
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
1
0
0
1
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
1
0
1
2
2
2
4
0
0
1
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
2
0
1
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
2
0
0
0
0
2
2
2
0
1
1
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
2
1
0
0
1
1
0
1
1
0
1
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
3
0
1
1
2
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
1
0
0
2
0
1
0
0
1
0
0
4
0
2
0
0
1
0
0
0
0
1
0
1
1
3
0
0
0
0
0
0
2
1
0
0
1
2
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
2
1
2
2
0
0
0
0
2
3
0
0
0
2
1
0
0
0
0
1
1
0
0
1
0
2
1
1
0
1
0
2
1
0
0
0
0
1
2
2
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
1
2
2
2
0
0
2
1
0
1
0
0
0
6
1
0
0
0
0
2
0
0
6
0
0
2
0
0
0
2
0
1
0
4
2
0
0
0
0
0
1
1
1
2
1
0
2
0
0
0
0
0
0
0
1
1
1
0
1
2
2
0
2
0
0
1
0
2
0
0
0
0
1
0
0
1
0
0
1
0
0
0
2
0
1
0
0
0
0
2
0
2
0
3
1
0
0
0
0
1
0
0
0
0
0
0
2
2
0
1
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
2
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
4
0
0
0
0
1
0
0
2
0
2
0
1
0
0
2
0
1
1
0
0
0
0
2
2
0
1
0
3
0
0
0
0
2
1
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
1
0
0
0
0
0
0
3
0
0
0
0
0
1
0
2
1
0
0
1
0
1
2
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
1
2
0
0
0
2
0
0
0
0
3
0
0
1
0
0
0
0
0
1
0
0
2
0
0
1
1
0
0
0
0
2
2
0
0
0
1
0
0
0
2
0
0
2
1
0
0
0
2
0
0
0
0
0
1
2
1
0
0
0
0
0
3
0
1
1
0
0
0
1
0
1
0
3
0
0
1
0
0
0
0
0
1
1
2
0
0
0
0
2
0
0
0
0
1
0
2
2
0
0
0
0
2
3
2
0
1
0
0
2
0
0
0
1
0
0
1
0
2
0
0
0
0
2
0
1
0
0
2
0
0
1
0
0
1
2
0
1
2
0
0
0
0
1
0
1
1
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
2
2
2
0
1
0
0
3
0
0
0
2
0
0
0
0
2
0
2
1
0
0
4
0
1
0
1
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
1
1
0
0
2
0
0
0
0
2
0
0
0
1
0
1
1
1
2
0
1
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
2
1
0
1
2
2
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
2
1
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
2
0
1
3
2
1
1
1
0
2
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
1
0
2
0
1
2
1
0
1
2
0
0
2
2
0
2
0
1
2
0
0
0
0
0
2
0
0
0
3
2
2
1
2
0
2
0
2
0
0
0
0
8
1
2
0
0
0
0
2
1
0
2
2
0
2
1
2
0
0
0
3
2
2
0
2
0
0
1
0
0
1
2
0
2
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
2
0
0
0
2
0
2
0
0
0
0
2
1
0
3
2
0
0
0
1
1
0
1
1
1
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
1
2
0
1
3
2
0
0
2
0
0
2
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
2
2
0
1
4
0
2
2
1
0
0
0
3
0
0
1
0
0
0
0
1
0
0
2
3
1
1
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
2
0
1
0
2
2
0
0
3
0
1
0
0
2
0
1
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
7
2
0
1
2
0
0
1
1
0
1
0
2
2
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
1
0
0
1
0
0
1
0
1
0
2
1
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
2
1
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
1
0
2
2
1
0
0
0
2
0
2
0
0
0
1
0
2
2
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
3
0
2
0
2
2
1
0
0
0
1
1
0
1
0
0
2
0
0
0
2
0
2
0
0
2
1
3
0
3
0
2
3
0
0
2
0
0
1
0
1
1
1
0
0
2
0
0
0
0
0
0
2
0
0
1
0
2
4
0
1
0
0
2
2
0
1
0
0
0
0
0
0
0
2
0
2
0
1
0
0
1
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
1
1
2
1
0
0
1
1
2
0
0
1
0
0
0
0
1
0
2
0
0
1
2
2
1
0
2
0
2
1
0
0
0
0
1
0
3
2
0
0
0
0
1
2
2
2
4
0
0
0
1
1
0
0
0
2
1
1
0
0
0
2
0
0
0
0
0
2
0
0
0
1
2
0
0
2
1
2
1
0
0
2
1
0
0
0
2
0
0
0
1
0
0
2
1
0
1
2
0
1
1
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
1
1
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
1
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
1
0
4
0
2
1
0
0
0
2
0
0
0
0
2
0
0
0
2
0
1
0
0
2
0
0
0
0
0
1
2
0
0
0
0
2
1
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
1
1
2
0
2
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
2
1
0
0
0
2
0
2
1
0
1
0
2
0
0
1
2
2
2
0
4
0
1
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
1
0
2
0
0
1
0
0
0
2
0
1
2
1
2
0
0
0
0
0
2
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
1
0
0
2
0
2
0
1
0
1
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
3
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
3
0
0
0
1
0
0
2
2
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
1
0
0
2
0
1
6
0
2
1
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
1
1
1
0
0
2
0
0
2
0
0
0
2
2
0
0
0
3
2
4
1
1
3
1
1
0
0
0
0
0
0
0
0
0
2
0
3
1
0
0
0
0
1
2
0
0
1
0
0
2
0
1
0
0
0
0
1
0
0
0
0
6
0
0
0
2
1
0
1
0
2
0
2
1
0
1
1
2
1
3
2
0
0
0
1
0
2
0
0
0
1
1
2
0
0
0
0
0
0
0
2
1
1
0
0
8
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
3
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
3
0
0
2
2
1
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
1
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
2
1
0
1
0
1
1
0
2
3
2
1
2
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
3
0
0
1
0
1
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
1
1
0
2
1
0
0
0
0
0
2
0
0
2
2
2
0
0
0
0
0
0
1
0
0
2
0
0
0
2
2
0
2
1
3
0
1
0
0
2
0
0
3
0
1
0
0
0
0
0
0
1
0
0
2
1
0
0
2
2
0
1
2
2
4
2
0
2
0
0
2
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
2
1
1
0
0
0
2
1
0
0
0
0
2
2
0
0
0
1
0
2
0
0
0
0
0
0
0
2
2
2
2
1
0
0
2
0
0
0
0
1
1
0
1
0
0
0
2
1
1
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
3
0
2
2
0
0
1
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
2
1
3
0
2
0
0
2
5
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
2
0
2
1
0
0
0
2
2
0
0
1
0
0
1
2
0
2
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
3
0
0
0
0
1
2
0
1
0
0
2
0
1
1
0
2
1
0
1
0
2
2
0
2
0
0
0
0
0
0
1
5
0
0
2
2
2
2
1
2
0
0
0
0
1
1
1
0
1
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
7
2
0
0
1
0
0
2
0
2
2
0
0
0
0
1
0
1
0
0
0
1
0
0
0
2
0
0
1
0
0
2
5
1
0
0
0
0
0
2
0
1
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
2
0
0
0
3
0
0
0
1
0
1
0
0
0
1
1
0
0
1
2
3
2
0
0
0
0
0
1
3
2
0
0
1
2
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
1
1
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
1
0
4
0
1
0
0
1
0
0
0
0
1
1
0
1
0
0
2
1
0
0
1
1
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
1
0
1
2
2
1
0
0
2
2
1
2
2
1
2
0
0
2
2
0
0
1
0
0
0
0
4
1
2
2
0
0
0
0
1
1
0
0
0
1
0
2
0
0
2
2
0
2
0
0
1
0
1
0
0
0
0
0
3
2
0
1
0
0
1
0
2
0
1
0
0
1
0
2
2
0
0
2
3
0
0
0
0
2
0
0
1
0
2
0
1
0
2
0
0
0
2
0
0
0
0
0
0
4
2
1
0
0
1
1
1
0
0
0
0
1
0
2
1
0
0
0
0
1
0
0
0
0
1
0
0
2
2
1
0
0
0
0
0
1
1
0
1
2
0
1
0
0
0
0
1
3
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
2
0
0
0
0
1
1
0
0
1
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
1
2
0
0
1
0
0
0
2
0
0
0
1
0
0
3
0
2
0
0
2
1
2
3
0
1
1
2
1
2
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
1
0
2
0
0
2
2
0
2
0
1
0
0
0
2
3
1
2
1
2
0
0
1
0
0
2
3
0
0
0
0
2
0
0
0
0
1
0
1
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
3
1
2
0
2
0
4
3
0
0
0
0
0
0
3
2
0
0
0
0
1
0
0
2
0
2
0
2
0
0
0
0
2
2
0
0
2
0
1
2
2
0
0
0
0
0
0
1
0
0
0
1
1
2
2
0
0
0
3
0
0
0
1
0
2
0
2
1
0
0
0
0
0
2
0
0
2
2
0
0
0
0
1
3
1
1
0
0
0
0
2
0
0
0
1
0
2
1
0
0
0
0
0
1
0
2
0
1
2
2
1
2
3
0
3
1
0
0
0
0
1
0
0
0
0
0
0
2
0
2
1
2
0
0
2
9
0
1
0
0
0
0
2
0
1
2
0
0
1
0
1
1
0
0
0
2
0
0
2
0
0
0
2
2
0
0
2
2
0
1
0
1
0
0
0
0
0
0
3
1
1
0
1
0
0
0
2
2
1
0
0
2
2
0
2
1
0
2
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
2
1
0
2
0
0
0
0
0
1
0
0
0
2
2
0
0
1
0
0
0
0
2
0
0
0
1
2
2
1
1
1
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
3
0
0
2
0
2
2
1
0
2
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
1
0
0
3
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
2
0
0
0
0
1
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
2
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
3
1
2
1
0
1
2
0
0
0
0
0
0
0
0
0
0
4
0
0
0
3
2
1
1
0
2
2
0
0
0
1
0
0
1
0
1
2
0
1
0
0
1
2
0
1
1
0
0
2
0
0
0
1
0
0
2
0
0
0
2
0
0
1
0
0
0
2
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
2
1
1
0
0
2
2
0
0
1
2
2
0
2
0
0
1
0
0
1
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
3
0
0
0
1
3
0
0
0
1
2
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
3
0
0
0
1
0
2
1
0
0
1
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
1
0
0
1
1
2
0
0
2
1
1
0
0
0
2
2
0
0
1
4
2
0
1
0
1
0
0
1
2
1
0
0
0
0
0
0
0
0
0
1
3
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
2
1
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
2
0
0
0
0
0
0
0
1
1
3
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
2
0
0
0
0
0
1
1
0
0
1
1
1
0
4
2
1
1
0
0
1
0
2
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
1
0
0
4
0
2
1
0
2
1
0
2
0
2
1
2
1
0
0
0
1
0
0
1
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
2
0
1
0
2
1
1
3
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
1
2
0
0
0
0
1
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
1
1
2
0
1
0
1
1
0
0
2
1
0
0
0
1
1
1
2
1
2
0
0
0
2
0
1
0
0
0
1
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
2
2
1
1
0
0
3
1
0
0
0
1
0
1
0
0
1
0
2
0
0
0
0
2
1
1
2
0
1
5
0
1
0
0
2
2
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
1
0
2
0
2
1
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
7
0
1
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
2
0
0
0
1
2
1
1
0
0
0
0
0
0
0
0
0
2
0
0
1
1
2
2
0
0
1
1
0
0
0
1
1
0
0
0
0
2
0
1
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
1
1
0
2
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
3
0
1
2
2
0
0
0
0
0
0
0
2
0
1
1
0
1
0
0
2
0
1
0
0
2
0
0
2
2
2
0
0
0
2
0
0
0
0
1
0
2
0
0
0
2
0
0
0
2
1
0
0
2
0
1
0
0
0
1
2
0
0
0
2
2
0
0
0
0
4
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
3
0
0
2
2
2
1
0
0
0
0
0
0
0
0
1
0
1
2
0
0
3
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
2
0
0
0
0
0
0
1
0
2
0
2
0
1
0
2
2
2
1
0
0
1
1
0
1
1
0
2
0
2
2
3
1
1
2
1
0
0
2
1
0
1
0
1
0
0
1
1
2
0
0
0
0
0
2
0
2
0
2
2
0
2
0
1
3
0
0
1
2
0
0
0
0
0
0
0
3
1
1
0
1
0
0
0
1
1
0
2
2
0
1
1
0
2
0
0
0
0
0
0
1
0
0
1
2
2
0
1
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
1
1
0
0
3
2
0
0
0
1
0
2
0
0
0
0
2
0
1
0
1
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
2
0
1
1
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
1
0
2
1
1
2
0
2
0
0
0
2
0
2
0
0
0
0
0
0
1
2
2
0
2
0
0
0
0
0
0
2
0
2
1
0
1
2
2
0
1
3
0
0
1
2
0
2
0
2
0
0
0
0
1
0
1
0
2
1
1
0
1
0
1
0
0
0
0
0
0
1
0
2
1
0
1
0
0
0
0
0
2
1
1
0
0
2
1
0
0
0
2
0
1
0
0
1
0
2
1
1
0
2
0
1
0
0
0
1
5
1
0
3
0
2
2
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
2
2
0
0
1
0
0
0
2
1
2
3
0
2
9
5
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
2
0
1
0
2
2
2
0
0
0
0
0
3
1
2
2
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
3
0
0
2
0
2
0
2
1
0
2
0
0
0
3
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
1
0
1
1
2
0
1
1
0
0
0
0
1
2
0
0
3
0
0
1
0
0
0
0
1
0
0
1
0
1
0
1
1
1
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
1
0
1
0
1
0
1
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
2
1
2
1
0
2
0
1
0
0
0
1
0
3
1
2
0
0
0
9
0
1
2
2
0
0
0
0
0
3
2
0
1
0
2
2
0
0
1
0
1
0
1
2
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
3
0
0
1
0
1
0
0
0
2
2
2
0
2
0
2
0
2
0
0
0
1
0
0
3
1
0
2
0
0
0
1
0
0
2
0
0
0
0
2
2
0
0
0
2
2
0
0
1
0
0
0
2
0
0
1
0
1
2
0
0
0
2
0
0
0
0
3
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
3
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
3
3
0
1
0
8
2
0
1
0
1
1
0
0
1
2
1
0
1
1
0
0
0
0
0
0
1
2
0
0
0
0
1
0
2
1
0
2
0
0
2
1
0
0
0
1
1
0
0
2
0
0
0
0
0
1
2
2
0
1
0
1
1
1
0
0
0
0
1
0
1
0
1
0
0
1
0
1
0
0
2
1
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
2
2
4
0
0
2
0
0
0
0
2
1
0
0
1
2
2
0
0
0
1
1
0
0
2
4
0
0
1
0
1
1
0
0
0
0
0
2
1
1
1
0
0
0
0
0
2
0
0
0
1
1
0
1
0
0
2
2
2
0
2
2
0
0
1
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
2
2
2
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
1
1
2
1
1
2
1
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
1
1
0
0
0
2
2
0
3
0
0
0
1
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
4
0
0
0
1
1
0
0
0
0
0
0
0
0
3
2
1
0
2
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
1
1
2
0
2
1
0
0
0
1
0
0
0
0
0
5
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
2
2
0
2
2
0
2
0
2
0
0
0
2
0
1
0
0
0
0
2
0
2
0
0
2
1
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
1
0
0
0
1
1
0
0
0
0
3
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
2
1
0
2
0
1
1
3
0
2
0
0
1
0
0
0
1
0
0
0
2
0
1
2
3
2
0
0
0
2
2
1
1
0
0
2
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
1
3
1
0
0
2
0
0
0
0
0
0
3
1
2
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
2
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
2
1
0
0
1
0
0
2
0
0
1
0
0
0
1
0
1
1
1
0
1
0
2
0
0
0
0
0
0
0
1
2
1
1
2
0
1
0
2
0
0
0
0
0
1
2
0
2
0
0
2
0
0
0
0
1
3
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
3
2
0
3
0
0
0
2
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
1
1
0
1
1
1
0
1
1
2
2
0
1
1
0
1
0
1
0
0
0
0
0
1
2
0
0
2
0
0
0
2
0
1
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
2
0
0
3
0
0
0
0
0
0
1
0
0
2
0
0
0
1
1
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
1
0
2
2
1
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
3
1
2
2
0
0
1
2
1
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
1
0
2
2
2
0
1
0
0
1
0
0
1
0
1
0
0
0
2
2
0
0
0
3
0
2
2
0
0
0
0
2
1
0
0
1
0
2
2
1
0
1
0
0
2
1
0
2
0
1
0
0
2
1
0
0
0
1
0
2
2
0
0
1
2
4
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
1
2
2
1
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
1
1
0
2
0
0
1
2
1
0
2
0
0
0
0
2
0
2
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
2
0
2
2
0
0
2
0
1
0
0
0
0
1
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
1
1
0
0
0
1
3
0
3
2
2
0
0
2
3
0
0
0
0
0
2
0
1
0
0
0
2
0
1
0
0
0
2
2
2
1
2
0
0
3
0
2
0
0
0
5
0
0
0
1
0
0
0
1
0
0
0
1
0
3
0
2
0
0
2
2
1
0
2
0
1
0
0
0
0
0
1
6
0
1
0
2
1
0
0
1
0
0
0
0
2
0
0
0
1
0
2
2
0
1
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
1
2
2
1
2
0
2
2
1
0
1
0
2
2
0
1
0
0
1
0
0
2
2
0
3
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
1
0
0
0
2
0
2
0
0
0
1
0
0
1
0
1
2
1
2
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
1
3
3
2
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
2
0
0
0
1
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
1
2
2
0
0
2
0
1
1
0
0
0
2
0
2
1
0
0
0
2
2
0
2
1
0
0
0
0
0
0
1
0
0
2
0
0
2
0
1
0
1
1
1
0
1
2
2
0
0
0
0
1
2
2
0
0
2
2
2
0
2
0
0
2
0
0
0
2
0
0
0
6
0
0
0
1
0
0
0
0
1
2
0
0
0
0
1
0
3
0
0
0
0
0
1
0
0
1
2
0
2
0
0
0
0
0
0
0
0
1
1
1
0
2
1
0
0
2
0
3
0
1
3
0
0
1
2
0
0
0
1
0
0
1
0
0
1
0
0
1
2
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
3
2
0
0
1
1
0
2
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
2
1
1
0
2
0
0
0
0
0
1
0
0
1
0
2
1
0
1
0
0
1
0
1
2
0
0
0
2
0
2
3
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
7
0
2
0
1
0
1
0
2
0
2
0
0
0
0
0
0
3
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
1
0
1
2
0
0
2
2
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
2
0
1
1
1
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
2
0
1
0
0
1
2
0
0
2
0
0
0
2
0
2
2
0
0
4
2
0
0
1
1
0
2
0
1
0
0
2
0
1
2
2
0
2
0
1
0
2
0
1
0
0
0
1
0
2
1
1
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
2
0
1
0
0
1
2
0
2
2
0
2
0
0
1
2
0
0
2
1
2
0
0
2
1
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
3
0
0
2
0
0
0
1
1
0
0
1
0
0
4
0
0
1
1
1
3
3
0
1
2
0
1
0
2
2
0
0
0
1
0
0
7
0
1
2
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
2
0
0
1
1
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
1
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
1
2
0
1
0
0
0
0
0
0
0
2
0
0
1
1
1
0
2
0
2
3
0
0
0
0
1
1
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
1
4
0
2
2
1
0
2
0
1
2
0
2
1
0
2
1
0
0
2
0
0
0
0
1
2
1
0
2
0
2
4
2
0
0
1
0
0
0
1
0
0
2
0
0
4
0
1
1
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
2
0
0
0
3
0
1
2
3
0
0
0
2
0
0
2
1
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
1
2
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
2
0
0
1
0
0
2
2
0
0
0
0
0
2
0
1
0
2
2
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
2
1
0
0
0
2
1
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
2
1
0
1
0
0
0
2
10
0
0
0
3
1
2
1
1
0
1
0
2
0
0
1
0
3
0
1
0
0
0
2
0
0
0
0
0
0
2
0
1
4
0
2
0
1
1
0
1
0
0
0
0
1
2
1
1
0
2
2
1
0
0
2
0
2
0
1
0
0
0
0
2
1
0
0
2
2
0
0
1
0
1
0
0
2
0
1
0
1
0
3
0
0
0
1
0
1
0
0
0
1
0
0
3
0
0
1
1
1
0
2
0
0
0
1
0
0
1
1
3
1
1
2
0
2
0
0
0
1
0
2
0
0
2
2
0
0
0
0
3
1
4
0
0
0
0
0
2
2
2
0
0
1
0
4
2
0
1
2
2
0
1
2
0
0
2
0
0
0
1
0
1
0
0
0
1
0
0
0
3
0
0
0
0
1
2
0
0
1
0
0
0
2
2
0
0
0
1
0
2
0
0
0
2
0
0
1
1
0
0
0
1
0
4
0
0
0
1
0
0
1
1
0
1
1
2
0
1
0
0
0
2
1
2
0
0
1
1
0
0
0
1
3
1
0
0
2
0
0
0
2
1
0
1
2
0
3
0
2
0
0
0
0
1
0
2
1
0
0
0
2
0
0
0
0
2
0
1
0
1
0
0
1
4
0
2
2
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
2
0
0
1
0
1
0
1
1
0
0
2
2
0
2
0
1
0
2
0
2
0
0
0
2
0
1
0
2
0
0
1
0
2
0
0
2
0
0
0
0
0
2
1
0
1
1
0
1
0
0
1
0
1
0
2
0
2
2
2
1
0
0
0
0
1
1
0
0
0
1
1
0
1
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
2
2
0
0
0
3
0
2
1
0
0
2
0
1
1
0
0
0
0
2
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
4
0
0
0
1
2
0
0
0
3
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
3
0
2
0
0
0
2
2
2
1
0
0
0
2
0
2
0
3
0
0
1
1
0
1
2
0
0
0
2
0
0
3
0
0
2
0
1
0
0
1
0
0
0
0
0
2
2
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
1
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
2
2
1
0
0
1
1
0
0
0
1
0
0
2
0
0
0
0
1
1
1
1
0
0
0
2
0
2
0
0
2
0
0
2
0
0
2
1
0
0
2
0
0
2
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
1
1
2
1
0
0
1
0
0
0
0
0
2
0
0
2
2
2
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
1
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
1
0
1
0
1
0
2
1
2
0
0
0
0
0
0
2
2
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
2
1
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
2
2
2
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
2
0
0
2
2
0
0
1
1
0
0
0
0
0
0
0
0
2
0
2
0
3
2
0
2
0
2
0
0
0
1
0
0
2
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
2
0
0
2
2
1
0
1
0
0
0
0
0
0
3
2
0
2
0
0
1
0
2
0
0
2
0
0
0
1
0
0
0
1
0
1
0
0
0
2
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
2
0
2
0
0
0
1
1
2
1
1
2
0
0
0
0
2
0
0
1
1
2
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
5
1
0
1
1
0
2
0
2
2
1
2
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
1
0
3
0
0
1
1
0
2
1
0
0
0
0
0
0
1
0
2
0
1
0
0
2
0
0
13
0
0
0
0
0
2
2
1
1
0
2
3
1
0
0
0
0
0
0
0
2
0
1
0
1
0
1
1
1
0
0
0
0
0
1
1
1
0
0
0
3
0
1
0
0
1
0
1
0
1
0
1
0
1
1
0
0
0
0
0
2
0
0
2
0
0
0
0
1
2
0
1
0
0
0
0
0
3
0
0
0
2
1
1
0
0
0
0
1
1
1
1
0
2
0
0
2
0
1
0
0
0
0
0
0
0
1
0
1
0
2
0
1
0
2
3
0
0
1
0
2
0
0
1
0
0
0
0
2
2
0
0
0
1
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
3
1
0
0
2
1
3
1
1
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
1
0
0
0
0
2
1
0
0
0
1
1
0
0
0
0
0
2
0
0
2
0
1
2
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
2
0
1
0
2
2
0
0
1
0
0
3
0
0
1
0
0
0
0
0
1
0
3
0
0
0
2
1
0
0
0
0
1
0
0
0
1
1
2
0
2
0
0
1
2
0
0
0
0
2
1
0
1
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
1
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
1
2
0
0
0
0
4
0
0
1
2
0
0
1
1
0
0
0
0
0
2
2
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
3
0
0
0
0
0
0
1
0
2
0
2
0
0
0
1
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
1
2
2
0
0
1
2
0
0
0
1
0
0
1
0
1
1
1
2
0
1
0
0
2
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
1
0
1
1
2
1
0
1
0
2
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
2
1
0
0
0
0
0
1
2
2
2
0
3
2
0
1
2
0
0
1
2
0
2
0
0
1
2
0
0
0
0
6
0
0
1
0
0
0
0
1
3
0
2
1
0
0
1
1
0
0
2
1
0
0
0
0
0
0
2
0
1
1
2
0
0
1
1
2
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
1
0
0
0
0
1
0
1
1
0
0
0
1
0
2
1
3
0
0
0
0
2
2
0
1
1
0
0
0
1
1
2
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
2
0
0
1
2
0
0
1
2
0
0
0
2
0
0
0
0
0
3
0
0
1
0
0
3
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
1
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
2
1
1
2
0
3
0
0
0
0
0
0
0
1
0
0
2
2
1
0
1
0
1
1
2
0
0
3
2
0
0
3
1
2
1
1
0
0
0
2
0
0
2
1
0
1
0
0
1
0
0
1
1
0
0
1
1
0
0
0
0
2
1
0
0
3
0
2
1
0
1
1
0
0
0
0
0
0
0
1
0
3
2
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
1
2
1
0
0
0
0
0
0
0
0
0
0
1
2
0
2
1
0
2
0
2
0
0
0
0
0
0
2
0
1
2
3
0
0
0
0
0
2
1
2
0
0
2
0
2
0
1
1
0
0
2
2
1
2
1
0
0
0
0
2
0
0
0
0
2
0
0
1
2
3
0
0
1
0
0
0
0
1
0
0
0
0
2
0
2
1
1
1
0
0
1
0
1
1
0
0
2
2
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
1
2
0
0
1
0
0
0
0
2
2
0
0
0
0
0
1
0
0
1
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
2
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
1
2
0
0
2
0
0
2
1
2
0
0
0
0
1
2
1
1
1
1
1
0
0
1
0
2
2
0
0
1
2
0
0
0
0
0
0
0
0
2
1
2
0
1
2
0
0
0
2
0
0
2
0
3
0
0
1
0
0
1
0
0
1
0
0
0
2
2
0
1
0
2
0
0
0
0
0
2
2
0
2
1
0
3
0
0
2
0
0
0
1
1
0
1
0
0
0
1
1
3
1
0
0
2
1
2
1
0
2
0
1
0
2
0
2
0
1
0
0
0
0
0
0
0
1
0
1
0
0
2
0
1
1
2
2
0
0
4
0
1
2
1
0
0
2
1
2
0
1
1
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
3
0
0
2
1
0
1
2
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
3
0
0
3
1
0
1
0
0
1
0
0
1
0
0
1
0
0
0
2
0
2
0
0
0
1
0
2
0
2
0
0
1
0
0
0
1
0
0
0
0
0
1
2
0
1
0
0
2
2
0
1
0
0
0
1
8
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
1
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
2
2
0
0
0
1
2
0
0
2
3
0
0
0
1
1
0
0
0
0
0
0
1
2
1
0
0
2
0
0
1
0
0
1
1
0
0
0
1
1
1
0
0
1
0
1
2
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
1
1
3
1
4
1
2
0
2
2
1
0
2
1
0
2
2
0
1
0
2
2
0
2
0
0
0
1
1
1
0
0
1
2
1
2
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
1
1
1
1
0
0
1
1
1
1
0
2
0
2
0
1
1
0
2
0
0
0
0
0
0
1
0
0
0
0
1
2
0
2
0
0
0
1
2
0
0
0
0
0
0
0
1
1
0
1
0
0
0
2
0
2
1
1
0
0
1
2
0
0
2
2
0
2
1
1
0
0
1
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
2
2
1
0
0
0
0
0
0
1
2
0
0
0
2
1
1
4
2
0
0
1
0
0
0
2
0
0
2
0
3
1
1
0
0
0
0
3
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
1
0
2
2
0
2
0
2
2
0
0
2
1
0
0
0
0
0
2
2
0
0
0
1
0
0
1
0
0
1
0
0
0
2
1
1
2
0
0
0
0
2
0
1
0
2
0
0
2
0
0
0
2
0
0
2
0
1
2
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
1
2
5
2
0
0
1
0
0
0
1
1
1
0
1
2
0
0
0
2
1
2
2
0
1
0
1
0
1
0
0
0
2
2
1
2
1
2
0
0
0
2
0
0
0
0
2
0
3
1
0
3
0
0
0
0
2
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
2
1
1
0
0
0
1
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
1
0
1
1
2
0
1
1
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
3
2
0
0
0
1
0
0
0
0
0
0
4
2
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
2
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
3
0
2
1
2
3
1
1
0
2
0
3
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
1
0
1
2
1
2
0
2
0
0
1
0
0
1
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
1
1
0
0
0
2
2
2
1
0
1
0
0
2
0
0
0
1
0
1
0
1
0
0
3
0
0
0
2
0
0
0
1
2
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
2
2
0
2
1
0
0
0
0
0
3
2
0
1
0
0
0
2
0
0
0
0
0
2
0
2
0
1
1
1
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
2
1
0
0
0
2
1
2
0
2
0
2
2
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
1
1
0
1
0
0
4
0
0
0
1
0
1
3
2
0
0
1
0
1
0
0
2
5
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
2
1
0
0
0
1
0
1
0
0
3
0
1
0
1
0
0
0
1
0
0
2
0
2
1
0
3
3
0
1
2
1
0
0
2
0
1
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
2
1
2
0
3
0
0
0
0
1
1
0
2
1
0
1
0
0
3
2
1
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
1
1
1
1
1
0
0
2
2
1
3
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
2
0
0
0
0
0
0
0
1
2
1
0
0
0
0
1
0
0
1
0
2
1
0
0
0
1
0
1
0
0
1
0
0
2
0
3
0
1
1
2
0
0
2
0
0
1
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
2
0
1
0
0
1
3
1
1
0
2
0
3
0
0
0
0
2
0
0
0
0
1
0
0
0
1
2
1
0
2
0
0
0
0
3
0
0
1
0
0
0
0
0
0
2
0
1
1
0
2
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
2
0
1
2
0
1
0
1
0
1
2
1
0
0
0
0
0
0
2
2
0
0
1
3
0
0
1
1
0
0
0
1
0
0
1
1
0
0
2
2
0
0
0
1
1
2
0
2
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
2
2
2
0
0
2
0
0
3
1
0
0
0
2
0
0
0
1
0
0
2
0
1
2
0
0
0
0
0
0
0
2
0
0
1
2
1
0
0
2
0
0
0
0
2
0
2
3
0
0
1
0
0
1
1
1
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
1
1
2
1
2
2
3
0
1
1
0
0
0
1
0
0
0
0
1
0
1
0
1
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
5
1
2
2
2
1
2
1
1
0
0
0
0
0
2
2
0
0
0
0
1
1
2
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
2
1
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
2
0
1
0
0
2
1
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
1
0
2
0
2
2
2
2
0
1
0
0
0
1
0
2
3
0
0
0
2
1
0
0
2
1
0
1
1
0
2
2
0
2
0
2
0
0
3
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
1
1
0
2
0
0
0
2
0
2
0
1
0
2
2
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
1
1
0
0
0
1
0
0
3
0
2
2
0
0
0
1
1
0
1
1
1
2
0
0
2
0
0
0
2
0
0
0
0
2
2
2
0
1
0
2
0
1
0
2
2
0
0
2
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
3
0
0
2
0
0
2
1
4
2
1
1
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
3
0
0
2
0
0
0
2
0
1
2
2
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
3
2
0
0
0
1
0
1
2
0
1
0
0
1
0
0
0
0
0
2
1
2
2
0
2
2
0
0
0
2
0
0
0
0
0
0
3
1
1
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
1
1
1
0
0
1
1
1
1
0
2
0
0
0
0
0
2
1
0
0
0
2
2
2
0
0
2
1
0
0
0
0
0
1
0
2
0
0
1
0
0
2
0
0
0
2
0
0
1
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
2
0
2
3
0
0
0
0
0
0
1
0
0
0
0
0
1
3
0
0
2
2
0
2
2
1
1
0
2
1
0
0
0
2
0
1
0
0
1
1
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
2
0
0
0
0
0
0
1
1
0
0
2
0
0
0
1
0
0
2
0
1
2
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
1
2
1
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
1
2
0
1
2
2
0
1
0
1
0
0
1
0
0
2
0
1
1
0
2
0
1
0
0
0
0
0
0
0
0
2
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
2
0
1
0
0
0
0
0
1
0
0
0
1
1
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
5
0
2
0
0
1
0
1
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
1
1
0
2
1
2
0
0
1
2
1
0
0
0
0
1
0
0
0
0
3
0
0
1
0
0
0
2
0
2
1
0
0
0
0
0
0
3
0
1
1
0
2
0
0
5
1
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
1
1
2
0
0
1
0
1
0
0
1
1
0
0
1
1
2
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
2
0
1
0
0
0
0
1
1
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
4
0
1
2
0
1
1
1
0
0
0
0
2
1
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
2
2
0
2
2
1
2
0
0
2
0
0
0
0
0
3
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
2
0
0
0
1
1
0
2
0
2
2
2
2
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
1
1
0
1
0
1
0
0
0
3
2
2
0
1
0
0
0
0
0
0
1
0
0
0
2
1
1
0
0
0
0
1
1
0
2
2
0
0
0
0
0
0
1
1
1
0
1
1
0
2
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
2
0
2
0
2
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
3
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
2
0
2
1
0
0
1
1
2
0
0
2
0
2
1
0
2
0
2
0
0
1
0
0
0
2
0
0
2
0
0
2
0
2
2
0
0
1
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
1
0
3
0
2
1
0
0
0
2
0
0
0
0
2
1
0
1
1
0
1
0
0
2
0
0
2
0
1
2
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
1
1
0
1
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
2
3
0
0
0
0
1
2
2
0
0
0
0
2
0
0
0
0
0
0
1
1
1
2
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
1
1
1
2
0
4
0
0
2
2
1
0
0
0
0
0
0
2
2
0
1
0
0
1
1
0
0
2
1
1
0
2
1
0
0
1
0
0
1
0
1
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
1
0
3
0
0
0
0
3
0
0
0
2
0
0
1
0
2
0
1
0
0
0
0
0
0
0
2
1
0
1
0
0
0
1
0
0
0
2
0
2
0
0
2
0
0
0
1
1
2
2
0
0
0
0
0
0
0
2
2
1
1
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
2
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
3
0
1
2
1
1
0
1
0
1
0
0
0
0
0
2
0
0
2
0
0
1
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
2
0
0
0
2
0
1
0
0
2
0
0
0
1
0
1
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
2
2
1
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
2
1
0
1
0
0
1
1
0
2
0
0
0
0
0
3
0
1
0
0
0
1
2
1
0
1
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
1
0
0
0
2
3
0
0
0
0
2
2
2
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
4
2
0
0
1
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
1
1
0
0
0
0
0
0
0
0
2
0
2
1
1
0
2
0
1
1
0
2
0
1
0
1
2
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
2
0
0
1
1
0
2
0
0
0
2
2
1
0
0
0
0
1
1
0
2
0
0
2
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
2
0
1
4
2
0
2
2
0
0
1
0
0
2
0
0
0
2
0
1
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
2
0
0
0
1
0
0
1
2
3
1
2
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
2
1
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
2
0
1
2
0
0
0
0
1
0
1
1
0
0
0
0
1
2
0
3
0
1
0
1
1
0
0
0
1
0
0
1
1
2
0
3
2
0
0
1
1
2
0
0
0
0
0
0
1
0
1
0
0
2
0
2
2
0
0
0
0
2
0
0
2
2
0
0
2
0
0
1
0
0
1
0
2
1
0
0
0
0
0
2
0
1
2
0
0
0
2
2
0
1
0
2
1
2
0
0
0
1
2
3
0
0
1
0
0
0
0
0
1
2
2
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
2
2
1
1
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
2
0
0
2
0
1
1
0
0
0
0
0
1
2
2
1
0
0
0
2
0
1
0
2
0
1
2
1
0
0
0
0
0
0
0
1
2
0
1
0
0
1
1
0
2
0
0
0
1
1
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
2
0
0
1
1
0
0
0
2
0
0
2
0
1
0
0
1
2
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
2
2
1
0
1
0
2
0
0
1
0
2
0
0
0
0
0
2
0
0
1
2
2
2
0
0
1
0
2
0
0
1
0
0
0
1
0
2
1
0
0
0
4
0
0
0
2
0
0
2
0
2
0
2
1
2
0
0
0
0
0
0
0
1
0
2
0
2
0
0
1
0
0
0
0
0
0
0
4
0
1
2
0
1
0
0
0
0
0
1
1
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
1
0
0
2
0
0
0
2
3
0
0
0
0
2
2
0
0
0
0
3
0
2
0
1
2
0
0
0
0
2
0
1
4
0
0
1
2
1
0
2
3
1
1
0
1
1
0
1
0
0
0
0
3
0
0
0
2
0
0
0
0
0
3
0
1
0
0
0
0
0
1
2
0
0
2
2
0
0
1
0
0
2
0
0
1
1
1
0
0
2
2
0
0
1
0
2
0
0
1
2
2
0
1
0
0
1
1
1
0
0
0
0
2
1
2
0
0
0
0
0
0
1
1
0
0
1
0
0
3
2
2
0
0
0
0
2
0
1
0
0
0
1
0
2
0
1
0
1
0
0
0
1
2
1
2
0
1
0
2
0
0
0
0
1
1
0
2
0
0
1
0
2
1
0
2
1
0
2
1
0
1
1
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
1
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
2
4
0
0
1
1
1
0
2
0
1
0
0
0
1
1
0
2
0
0
0
2
0
0
1
0
0
0
1
2
2
2
0
2
0
0
0
0
2
0
1
0
2
0
1
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
2
2
0
0
0
0
1
2
2
0
0
3
0
0
0
0
0
0
1
1
2
0
0
0
2
1
1
2
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
1
2
3
0
0
2
1
0
0
0
0
2
1
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
3
0
2
0
1
2
2
2
3
0
0
0
0
0
0
8
0
2
2
0
1
0
1
0
0
0
0
0
2
0
0
2
0
2
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
3
0
0
0
1
2
2
0
0
0
1
0
0
0
2
2
2
1
2
0
2
0
0
2
0
0
1
0
1
1
0
1
0
0
1
2
1
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
1
8
2
0
0
1
4
0
0
2
1
0
1
1
0
2
2
0
0
0
2
0
2
0
2
0
0
2
0
2
0
2
0
0
0
0
1
2
2
0
2
1
1
2
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
2
0
1
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
1
0
0
0
0
1
2
0
1
1
0
2
0
0
2
0
1
0
0
0
2
1
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
1
2
1
0
0
0
2
0
0
1
0
1
0
1
6
0
1
2
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
1
1
0
0
0
2
0
0
0
0
2
1
0
0
2
0
1
2
0
1
2
0
2
1
1
1
0
0
1
1
0
0
0
0
0
0
0
1
1
2
0
1
0
1
1
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
3
0
0
2
1
0
0
2
0
2
1
2
1
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
1
1
0
0
2
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
1
0
0
0
1
3
0
3
0
2
1
0
0
0
0
0
0
0
2
0
2
1
0
1
3
0
0
0
1
1
1
2
2
0
0
0
1
2
1
0
0
1
1
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
1
0
0
1
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
2
0
1
1
0
0
1
0
0
0
0
1
0
2
0
2
0
0
3
0
2
2
2
2
0
0
0
0
0
0
0
0
2
2
0
0
1
0
2
1
0
0
2
0
0
0
0
1
0
0
0
1
1
1
0
0
2
0
0
0
1
2
0
0
0
0
1
1
2
0
2
2
1
0
0
1
0
0
1
1
1
0
1
0
2
2
0
3
1
0
0
0
1
0
2
0
1
0
1
0
0
0
3
1
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
2
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
2
0
2
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
1
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
1
2
3
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
1
0
0
1
2
0
2
1
1
0
0
2
1
1
0
1
0
2
0
1
0
0
0
0
2
0
0
0
1
0
3
2
0
0
1
0
0
0
0
1
0
1
0
0
0
1
1
2
0
0
0
1
0
0
2
0
0
0
2
1
1
0
0
0
0
2
5
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
1
2
2
1
0
0
0
1
0
2
1
0
2
0
0
2
0
1
0
0
0
0
0
0
2
0
0
1
0
0
2
2
0
1
0
0
3
1
1
0
0
0
0
2
0
0
1
2
0
0
0
0
2
1
0
2
0
0
0
1
0
0
1
2
0
1
0
1
0
0
0
0
0
0
2
0
0
0
1
0
1
3
2
0
1
0
2
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
1
2
0
2
0
0
0
0
1
0
0
0
2
0
2
0
2
0
0
0
1
0
0
1
0
0
0
1
1
2
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
1
1
0
5
1
0
3
0
0
0
0
0
0
2
0
1
0
0
0
3
2
2
0
1
0
1
0
0
0
2
0
1
0
2
0
0
0
0
0
0
1
1
0
0
1
0
3
0
3
0
0
0
1
2
0
0
1
1
1
0
0
0
0
1
0
0
0
0
2
2
0
0
1
1
0
0
0
0
0
0
0
0
3
1
0
0
2
0
2
0
0
0
0
0
0
2
0
1
0
1
0
1
2
1
1
0
0
2
1
2
1
2
3
2
3
0
2
2
1
1
1
1
0
1
1
0
2
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
1
2
3
0
0
1
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
3
1
0
2
0
1
2
0
0
0
2
0
0
0
2
0
0
0
1
0
0
1
2
0
0
1
1
0
0
1
0
0
0
1
2
1
0
0
0
0
1
0
2
0
1
0
2
0
0
1
0
0
0
2
0
1
0
1
1
2
1
0
0
1
0
2
0
2
0
2
0
2
1
2
0
0
0
1
1
0
0
2
0
0
0
2
0
2
1
0
2
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
1
0
0
0
4
1
0
0
0
0
0
1
0
0
0
1
0
3
1
1
0
2
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
2
0
0
0
0
7
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
2
0
0
1
0
1
0
0
0
2
2
0
0
0
0
2
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
2
0
1
1
2
0
0
0
2
0
0
0
0
0
0
2
2
2
2
0
1
0
0
1
1
0
0
0
1
1
0
0
0
2
0
0
0
2
2
2
0
0
1
0
0
2
1
2
0
2
0
0
5
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
1
1
0
2
3
1
2
1
0
0
1
0
0
0
2
0
0
2
1
2
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
2
0
2
0
2
1
2
2
0
0
1
2
0
2
0
1
0
0
2
0
0
2
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
1
0
0
2
0
0
0
0
0
0
2
1
1
0
1
0
1
1
1
0
2
2
0
0
1
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
1
1
0
0
1
0
1
0
0
0
2
3
0
2
0
1
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
1
2
1
3
0
0
0
0
0
0
0
2
0
2
1
0
0
2
2
0
1
0
0
2
1
0
2
2
1
1
0
0
0
0
1
2
0
0
0
0
2
2
0
0
0
1
1
3
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
1
1
2
0
1
2
0
1
2
0
2
0
0
1
0
1
0
0
0
0
2
2
0
0
1
0
0
2
1
0
0
0
0
0
0
0
2
1
2
1
0
1
0
0
0
2
2
2
0
1
0
0
0
2
2
2
0
0
1
1
1
0
2
0
1
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
1
2
0
0
0
1
1
0
1
2
0
0
1
0
0
0
0
1
2
2
1
2
1
1
0
0
0
2
0
0
0
1
0
0
2
0
0
0
1
0
2
0
1
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
1
0
1
1
2
1
0
1
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
2
0
2
2
0
0
2
0
0
0
2
0
0
0
1
0
1
2
0
0
0
0
0
4
1
0
1
1
0
0
0
0
0
1
0
0
0
1
2
0
0
0
14
0
2
0
0
0
0
0
0
1
0
0
0
1
0
2
0
1
3
1
1
0
0
0
0
0
3
0
2
0
0
2
1
2
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
2
2
0
1
2
1
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
1
0
0
3
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
2
0
1
1
0
0
0
1
0
0
1
1
0
1
0
1
0
2
1
0
1
2
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
6
0
0
0
1
0
2
0
2
0
0
0
0
2
2
1
0
1
0
1
0
2
0
1
0
0
6
2
0
0
0
0
0
1
0
0
1
0
6
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
2
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
2
1
0
0
1
0
0
0
2
0
0
0
2
0
0
1
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
1
2
0
2
2
0
0
0
0
0
0
1
1
0
0
0
0
0
2
2
0
0
0
0
0
2
2
0
0
0
2
0
1
0
0
0
0
0
0
8
5
2
0
0
0
0
2
0
2
0
0
0
1
0
0
1
2
2
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
3
0
2
0
1
0
0
1
0
2
3
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
5
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
1
1
2
2
0
0
0
0
0
0
0
0
3
0
0
1
0
1
0
0
0
1
0
0
0
2
0
1
2
0
0
0
0
0
2
1
0
0
0
3
2
2
1
6
0
2
2
1
2
1
0
0
0
0
0
0
2
1
0
1
0
0
0
0
2
0
2
0
0
0
2
1
0
0
0
0
0
0
0
1
1
0
0
2
0
1
0
2
0
2
1
2
0
1
0
0
0
4
0
2
0
0
1
1
0
0
0
0
0
2
0
0
0
1
0
1
1
1
2
1
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
2
1
0
0
2
3
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
2
0
0
2
2
6
1
0
0
2
0
0
0
0
0
3
0
0
2
0
0
0
0
1
2
0
0
2
0
0
0
3
0
0
0
2
0
0
0
0
2
2
1
0
0
0
2
2
1
2
1
0
0
0
2
0
2
0
0
0
0
3
2
0
0
0
3
2
1
0
0
1
0
0
2
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
1
0
3
2
0
0
1
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
1
0
0
1
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
1
1
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
2
1
0
2
0
1
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
1
0
0
0
3
0
2
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
2
0
1
1
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
1
1
0
3
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
2
0
0
0
0
1
2
0
2
0
0
0
1
2
2
0
0
0
0
0
0
1
0
0
0
2
0
3
2
1
2
1
0
0
0
0
0
2
2
0
0
0
0
1
0
1
1
0
0
0
0
2
0
1
0
0
2
6
0
0
0
0
2
1
0
3
0
0
0
2
1
0
0
1
0
0
0
0
0
0
1
2
0
1
3
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
2
0
2
2
1
1
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
1
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
2
1
0
0
0
0
4
0
1
2
0
0
1
0
0
0
0
3
2
2
3
0
0
0
2
0
0
0
0
0
2
2
3
0
2
1
0
0
0
0
1
1
3
2
1
0
0
2
0
0
1
1
0
0
0
0
0
2
0
1
0
0
0
2
1
1
1
0
2
0
1
0
1
0
0
0
3
0
2
0
1
2
0
0
0
0
3
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
1
0
0
0
1
0
0
1
0
0
0
0
1
0
1
1
3
0
0
0
0
0
0
0
2
0
0
1
0
1
0
2
0
0
0
0
0
5
1
0
2
0
1
1
0
0
0
0
0
1
0
1
1
0
0
0
2
0
0
0
2
2
1
0
1
0
0
0
0
0
4
1
0
0
2
2
2
0
0
1
0
2
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
2
0
1
1
2
0
0
0
1
0
4
2
0
1
0
0
0
0
0
0
1
0
1
0
0
1
1
0
1
0
0
0
0
1
2
0
0
0
0
1
0
0
1
2
0
0
0
3
0
1
2
0
0
0
0
0
0
1
1
0
0
0
2
1
0
2
0
0
0
0
0
0
2
0
0
2
1
1
0
0
0
0
2
0
2
2
0
1
0
0
2
3
0
0
0
0
0
0
2
1
1
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
2
0
1
0
0
0
0
2
1
0
0
1
0
0
0
2
0
1
0
0
0
0
1
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
3
1
1
0
1
0
2
1
0
0
1
1
0
0
0
0
2
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
1
1
0
0
0
0
0
2
1
0
0
0
1
0
1
1
0
0
2
0
3
2
0
0
1
0
2
0
3
0
0
0
0
1
1
4
3
0
2
1
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
1
1
0
0
0
2
1
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
2
1
0
0
2
0
1
2
1
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
8
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
2
3
0
0
0
2
0
0
0
0
0
2
1
2
0
0
0
0
1
2
0
0
0
0
0
0
2
2
1
1
0
1
0
0
0
2
0
2
2
0
0
0
1
4
0
0
0
2
0
0
0
1
0
2
0
1
0
0
0
1
0
2
0
3
2
0
0
0
0
0
0
0
0
0
0
4
0
2
2
2
0
2
0
0
0
0
1
0
0
2
1
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
1
1
0
1
1
1
1
0
0
2
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
2
1
0
0
0
0
0
3
0
0
1
0
0
0
1
1
1
0
0
0
2
0
0
2
0
1
0
0
2
1
0
2
0
5
1
0
0
0
0
2
2
1
0
2
2
2
1
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
1
2
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
3
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
2
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
1
1
0
0
0
0
2
0
1
4
0
2
2
1
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
1
0
0
0
3
0
2
1
0
0
0
0
2
2
0
1
2
1
0
1
0
0
3
1
0
0
0
0
0
0
1
0
0
0
2
1
4
2
3
0
0
2
0
0
2
2
0
1
0
5
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
2
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
2
0
0
0
0
1
0
0
1
0
0
0
0
2
2
0
0
3
0
2
2
0
2
0
2
0
0
0
0
0
2
2
0
0
1
0
2
2
0
0
1
1
0
0
1
0
2
1
0
0
0
1
0
0
1
0
0
1
1
2
0
0
0
0
0
0
0
0
1
3
1
0
0
1
0
7
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
2
1
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
2
1
2
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
3
0
0
0
0
1
0
0
0
0
0
0
0
1
2
1
1
0
0
0
0
0
2
0
1
0
0
1
3
0
0
0
0
2
2
0
2
0
0
0
2
0
0
2
4
1
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
3
0
1
0
0
2
0
4
0
1
2
3
0
0
0
0
0
0
0
0
0
1
2
0
2
0
1
1
1
0
0
0
1
0
0
2
0
0
2
2
0
1
1
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
2
0
0
0
1
3
2
2
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
1
1
1
2
1
0
0
1
0
0
1
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
1
0
0
1
0
1
0
2
1
1
0
2
1
0
0
1
0
2
0
0
0
2
1
0
0
2
0
0
0
1
0
0
0
1
0
1
1
0
0
0
2
0
1
2
2
1
1
3
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
3
2
0
0
0
1
2
1
0
2
0
2
0
0
1
4
2
0
2
2
0
0
3
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
2
0
1
2
0
2
1
0
0
0
0
1
1
0
1
0
0
0
2
1
3
0
0
0
0
1
0
0
0
2
2
0
0
2
0
2
0
1
1
0
2
1
0
2
0
0
3
1
0
1
1
1
0
0
0
0
0
4
0
2
2
0
0
0
2
0
0
2
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
2
0
1
2
0
0
0
2
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
2
0
1
2
0
0
0
1
0
0
0
2
0
2
0
0
0
1
0
0
1
0
0
0
1
0
0
2
0
0
2
0
1
0
0
0
2
1
1
2
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
2
1
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
2
1
2
0
2
1
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
2
1
2
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
2
1
0
0
0
1
0
0
2
0
0
0
0
1
1
2
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
1
1
2
0
0
0
2
5
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
3
0
2
1
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
2
0
2
0
1
0
2
0
2
1
0
2
0
0
2
0
0
2
2
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
2
1
1
0
1
1
0
0
0
1
1
0
0
0
0
1
0
0
1
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
1
0
1
0
1
0
1
2
0
1
2
0
1
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
1
0
0
0
2
0
1
1
0
0
0
0
1
0
0
0
0
2
3
0
4
0
0
2
1
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
2
0
0
0
1
1
2
0
0
2
0
0
1
0
2
2
0
0
2
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
2
1
0
0
0
0
0
0
2
2
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
2
0
0
2
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
2
0
1
0
3
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
1
0
1
0
2
0
2
0
1
1
3
4
0
0
1
0
2
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
2
2
0
1
0
0
0
0
0
2
0
1
0
0
1
1
0
3
0
1
1
0
0
0
0
2
2
2
1
0
1
0
0
0
1
1
2
0
2
0
0
0
1
0
1
1
0
0
0
0
2
0
0
0
0
0
2
1
1
0
0
3
1
0
0
0
0
1
2
2
3
0
0
0
2
0
0
0
1
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
1
0
0
2
0
2
1
1
1
2
0
3
0
1
1
0
1
0
0
0
0
0
0
3
0
0
0
1
1
0
0
0
2
3
5
0
0
0
0
0
2
0
2
0
2
2
0
0
2
0
1
0
0
6
0
0
3
0
0
0
2
1
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
2
0
0
0
0
1
0
0
0
2
1
0
0
0
2
0
0
1
0
1
1
1
1
1
0
1
0
0
0
1
1
0
2
0
0
0
0
2
0
2
2
0
2
1
0
0
1
3
0
0
0
1
0
0
1
0
3
0
2
2
0
0
2
2
0
0
2
1
2
1
1
1
2
0
1
0
0
0
0
1
0
0
0
0
1
1
1
0
1
1
0
0
0
2
0
1
0
2
0
0
0
0
0
2
1
0
0
2
0
1
2
0
1
1
0
0
1
2
2
0
2
0
0
0
0
2
0
1
2
1
0
0
1
0
1
0
0
2
0
0
1
0
2
0
0
0
2
2
0
2
2
0
0
0
0
0
3
0
2
0
0
3
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
3
0
0
0
0
2
2
2
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
1
0
0
0
0
3
2
0
0
0
0
2
1
0
0
0
0
0
2
0
3
0
0
2
1
0
1
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
1
1
0
0
0
0
4
0
0
0
0
2
2
0
0
0
0
2
0
2
0
0
0
0
0
1
0
2
0
0
0
0
2
0
2
0
2
0
0
2
0
1
0
0
1
2
0
0
0
0
0
0
2
3
0
2
2
0
1
0
0
0
0
0
0
0
3
0
2
0
1
1
0
0
0
2
0
0
0
1
0
1
0
2
0
1
1
3
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
4
2
0
0
0
0
1
0
0
0
1
1
2
0
1
0
0
0
0
1
1
3
0
0
0
1
0
3
0
0
2
2
0
0
1
0
0
0
1
1
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
2
0
0
1
0
0
1
1
1
1
0
0
1
2
0
0
0
0
0
0
2
0
0
1
1
3
0
0
0
0
2
2
3
0
0
0
2
0
1
0
0
1
2
2
0
1
1
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
4
0
2
1
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
2
0
0
2
1
0
2
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
2
2
0
0
0
1
0
0
0
2
0
3
0
0
1
0
0
0
2
0
0
0
1
0
0
0
1
0
2
0
0
2
0
0
0
1
0
2
2
0
1
0
0
0
0
1
0
0
0
2
0
0
0
2
2
0
0
0
0
2
1
0
2
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
2
0
0
0
2
2
1
0
0
0
2
2
0
1
0
0
0
2
1
0
0
1
0
0
0
2
0
2
1
0
1
0
1
2
0
0
2
0
0
1
0
3
0
0
1
0
0
0
0
1
1
0
1
1
0
1
0
2
0
2
2
1
1
1
0
1
0
0
1
1
1
0
2
0
0
2
0
0
1
0
0
0
2
0
1
0
0
7
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
2
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
2
0
2
0
2
0
0
0
2
0
0
0
1
0
1
0
2
1
2
0
0
2
0
0
0
1
0
0
1
0
0
2
0
0
1
0
0
2
0
0
0
0
1
1
0
0
2
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
2
2
0
1
1
0
0
0
0
1
0
0
0
1
6
0
0
0
2
0
1
2
0
1
2
0
1
2
0
0
0
1
0
3
0
2
0
1
0
1
0
1
2
2
0
2
1
0
0
0
0
0
0
0
3
1
1
0
2
1
1
1
0
0
0
0
0
2
0
1
2
0
0
0
1
0
0
0
2
2
0
0
0
1
2
0
0
0
0
0
1
1
0
3
0
0
1
0
1
1
3
1
1
0
1
2
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
1
0
2
1
2
2
2
2
0
1
1
0
0
0
0
0
0
0
0
0
2
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
1
1
1
1
1
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
3
0
0
0
0
0
0
2
0
1
0
0
2
2
0
0
0
1
1
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
1
1
1
2
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
4
0
2
0
1
0
0
1
2
0
0
1
1
0
0
1
0
0
0
0
1
2
0
2
0
0
2
2
0
0
1
0
0
0
0
1
1
2
0
0
0
0
2
1
2
0
1
2
1
0
0
0
0
0
0
0
2
0
2
0
1
1
0
1
0
0
0
1
0
2
0
3
0
0
0
1
0
1
1
0
0
1
0
0
0
2
0
1
0
0
2
1
2
2
2
0
1
0
2
0
0
1
0
0
2
0
0
0
2
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
4
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
2
2
0
0
1
0
1
0
2
2
0
0
1
0
0
0
1
0
2
0
1
0
3
0
2
2
0
0
0
8
0
2
0
0
2
0
0
3
0
0
0
0
0
0
0
2
2
1
0
0
0
2
0
2
2
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
4
2
0
0
0
2
1
1
4
0
0
1
0
0
0
0
0
0
0
0
0
2
0
3
1
0
0
0
0
0
4
0
2
0
0
1
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
2
0
1
0
1
1
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
1
1
2
2
0
0
0
0
1
0
0
0
1
1
0
2
0
0
0
1
0
0
0
1
2
0
0
0
0
0
1
2
0
4
1
0
0
4
0
2
0
0
0
0
2
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
2
1
0
1
0
0
0
0
1
2
1
1
0
0
0
2
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
2
0
1
0
1
0
0
0
0
2
0
0
1
1
0
3
0
0
2
0
0
0
0
0
0
0
0
1
2
1
3
1
0
0
1
2
2
0
0
1
1
0
1
1
0
0
3
0
0
0
2
0
0
1
0
1
2
0
0
1
0
0
0
0
0
0
1
3
0
0
1
0
0
0
0
1
0
0
0
0
1
0
2
0
0
1
1
0
2
0
0
2
0
0
0
1
0
2
0
0
1
1
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
3
0
2
1
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
1
2
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
16
0
0
0
0
1
0
2
0
0
2
0
0
2
0
2
0
0
0
2
0
1
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
1
0
2
0
2
1
0
0
0
1
0
0
0
0
0
2
0
2
0
1
0
0
0
2
2
0
1
0
1
0
1
1
1
0
2
0
1
1
2
0
2
0
2
2
0
0
2
1
2
0
0
3
4
0
8
0
0
0
1
2
2
1
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
2
0
1
1
0
1
0
0
0
4
1
0
0
3
1
1
2
2
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
3
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
1
2
0
0
0
0
0
2
0
2
1
0
0
0
3
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
1
1
6
0
0
1
2
0
0
2
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
1
0
2
1
0
0
2
1
0
2
1
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
1
0
0
2
2
1
0
2
2
0
1
0
0
0
1
1
1
0
1
0
2
1
0
0
0
0
0
0
0
0
2
0
2
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
3
0
0
3
1
1
0
0
1
0
0
2
1
0
0
0
1
0
0
0
0
0
2
0
0
0
1
2
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
1
3
1
0
2
0
0
0
0
1
0
2
0
2
0
1
0
0
0
1
2
1
0
0
0
0
0
2
1
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
2
0
0
6
0
0
2
0
0
1
0
1
2
0
0
0
0
2
2
0
1
0
2
1
0
1
1
1
0
0
2
1
1
1
0
0
0
0
0
0
2
1
0
2
1
0
1
0
2
1
0
3
0
0
1
0
2
2
0
1
2
0
0
1
1
0
1
0
1
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
2
1
0
0
0
2
2
2
2
2
0
0
1
0
1
0
0
1
0
2
0
0
0
2
0
0
0
0
1
0
1
2
0
0
0
0
1
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
1
0
0
1
2
0
2
1
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
2
3
1
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
2
0
1
0
0
1
0
0
0
2
2
0
1
1
2
0
1
0
1
2
0
0
0
0
1
0
0
2
1
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
1
1
0
0
2
4
2
3
0
2
0
0
0
1
0
0
0
1
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
1
0
1
0
0
0
2
0
0
1
0
0
0
2
0
0
0
1
0
0
2
1
0
0
5
0
2
1
0
0
0
0
0
0
0
2
0
0
0
1
0
1
1
0
3
0
0
0
4
0
0
0
0
2
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
1
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
2
0
1
0
0
0
0
2
1
0
0
1
2
1
0
0
0
0
0
0
1
0
0
3
0
2
0
0
0
0
1
2
0
0
0
0
1
1
0
2
2
2
1
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
2
0
1
0
0
0
0
5
0
0
0
0
1
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
3
1
0
2
0
2
2
1
2
0
1
0
1
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
1
2
0
1
2
0
1
0
0
0
0
0
0
0
1
0
1
0
2
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
3
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
2
0
0
2
2
0
0
0
0
1
0
0
0
0
0
3
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
3
0
2
0
0
1
0
1
0
1
0
1
2
1
2
2
2
2
1
1
0
0
2
1
0
0
1
2
0
0
0
1
0
2
0
0
0
0
0
1
1
0
0
0
1
1
1
1
1
0
0
0
3
0
1
0
0
0
0
1
0
0
0
2
1
8
1
0
2
0
0
0
0
0
1
0
1
0
1
1
2
1
0
0
0
2
1
2
1
0
2
0
2
0
0
0
0
0
1
0
0
2
1
0
1
0
2
0
0
0
2
1
2
0
0
1
0
0
2
1
0
1
0
0
0
0
0
0
0
2
1
0
0
2
0
0
3
0
2
1
0
0
0
0
0
2
2
0
3
1
1
0
1
0
0
0
2
0
1
0
0
1
0
0
1
2
0
0
0
1
1
0
0
1
0
0
0
0
2
0
0
2
0
0
1
0
1
0
0
0
0
1
1
2
1
0
0
2
0
1
1
0
0
1
0
0
0
2
0
0
1
0
2
4
0
0
0
0
2
2
0
2
1
0
0
0
2
0
0
0
0
2
0
0
1
1
1
0
3
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
3
2
1
0
0
2
0
2
0
1
0
0
1
2
0
0
0
1
0
0
0
0
0
0
2
1
0
1
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
2
1
0
1
1
0
0
1
2
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
2
2
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
1
0
2
1
0
2
0
0
0
0
0
2
2
1
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
2
1
0
0
0
2
0
0
2
0
2
1
2
1
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
2
1
1
1
4
0
1
0
1
0
0
1
1
2
0
1
0
0
0
0
0
0
0
0
2
1
0
1
0
0
1
0
2
0
0
0
2
0
0
1
1
0
2
0
0
0
0
1
1
0
0
0
0
0
2
1
1
1
0
1
0
0
0
0
1
0
1
1
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
1
0
1
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
3
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
1
0
0
2
0
0
0
1
1
1
2
1
0
0
0
1
0
0
0
2
1
0
1
0
0
2
3
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
1
2
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
1
3
0
0
0
1
0
1
2
0
0
1
2
3
1
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
2
0
1
0
0
0
1
2
0
0
0
0
0
0
2
0
0
2
0
0
2
1
0
0
1
0
0
0
0
2
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
2
1
1
0
0
0
1
1
2
0
0
0
1
0
0
2
2
0
2
0
1
0
0
0
2
0
0
0
2
1
0
0
0
1
2
0
1
0
2
0
0
1
1
2
0
3
0
0
1
1
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
2
1
0
1
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
1
1
3
1
1
0
0
2
0
2
1
0
2
0
0
0
0
1
0
0
0
0
1
1
0
0
0
2
1
0
0
0
0
1
2
2
2
0
0
0
2
3
0
0
1
2
2
0
0
0
0
1
2
2
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
2
2
0
2
0
1
0
0
2
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
1
1
1
0
1
0
0
0
1
0
0
1
2
0
0
0
2
0
0
0
0
1
0
0
0
0
2
2
2
0
0
0
0
0
2
2
0
0
0
1
2
2
2
2
0
0
0
1
0
1
0
0
3
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
1
2
2
0
1
0
0
2
2
0
1
2
0
0
2
2
1
2
0
0
0
4
0
2
2
0
0
2
0
0
0
0
2
0
1
2
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
1
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
2
0
0
0
2
1
0
2
1
0
0
0
0
0
0
2
0
2
0
0
1
3
0
2
0
0
1
0
0
2
1
1
0
0
0
0
0
1
3
0
1
0
2
0
0
1
0
2
2
0
2
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
2
1
0
0
0
1
0
1
0
0
0
0
0
1
1
1
0
1
0
2
0
0
1
0
0
0
0
2
1
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
2
1
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
3
0
0
2
2
0
0
0
0
0
0
2
1
2
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
3
2
0
2
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
2
2
0
1
2
0
0
0
1
0
2
0
0
0
0
0
1
0
0
1
2
1
0
1
0
0
2
0
0
2
0
0
1
1
0
0
0
0
3
0
1
0
1
0
1
0
1
0
2
2
0
0
1
0
0
0
0
1
2
2
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
1
1
2
1
0
1
0
1
0
0
0
0
1
0
0
1
0
2
0
0
0
0
1
0
0
2
1
0
0
0
0
0
1
0
2
0
2
1
2
1
2
0
2
2
2
1
2
1
1
0
0
0
0
0
0
1
0
0
2
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
3
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
9
0
2
0
2
0
0
1
0
0
1
0
2
0
0
0
1
0
3
0
0
1
1
0
1
2
0
4
0
2
3
0
0
0
1
0
2
2
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
2
0
2
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
2
1
0
2
0
0
0
1
1
1
0
0
2
0
0
0
0
0
1
0
2
0
1
2
1
0
1
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
2
2
0
2
1
0
0
0
0
0
2
0
2
0
1
0
2
2
0
0
1
0
0
0
0
0
0
0
2
1
0
3
0
1
1
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
2
0
0
0
1
2
1
1
0
0
2
1
0
2
0
0
2
0
0
1
0
0
0
0
2
1
0
0
1
2
2
0
0
2
0
0
0
0
0
0
0
2
0
0
1
1
0
0
1
0
0
0
0
1
0
0
2
1
0
1
0
0
1
0
0
0
0
0
1
1
2
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
2
0
2
0
2
0
0
3
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
2
0
1
0
0
0
0
1
1
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
2
2
0
0
1
2
1
0
0
0
0
0
0
2
2
0
0
2
0
0
1
1
0
0
0
1
2
0
2
2
0
2
0
1
0
1
0
0
2
0
0
0
2
1
0
0
0
1
1
0
3
0
0
2
0
3
1
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
1
1
2
0
0
0
1
2
2
1
0
0
0
0
0
0
1
0
0
1
2
0
0
0
2
0
0
0
1
0
2
2
0
0
0
0
1
5
0
0
1
0
0
2
0
0
0
0
0
1
1
0
0
0
2
3
0
0
0
0
0
0
1
0
0
0
2
3
0
1
1
0
0
0
0
0
2
0
0
0
1
0
2
0
1
0
0
0
1
0
2
0
0
0
2
0
0
2
0
2
3
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
2
0
3
0
0
1
0
2
2
3
0
1
0
0
0
0
0
2
1
0
2
0
0
0
2
0
0
0
0
0
1
1
0
0
1
2
0
2
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
2
0
6
0
1
2
2
0
0
2
0
2
2
2
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
1
0
2
2
1
0
0
0
0
2
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
5
0
0
0
0
0
3
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
1
0
0
0
1
2
0
2
0
0
3
0
0
5
0
1
1
0
0
1
0
0
0
0
1
0
0
2
0
0
1
0
0
2
0
0
1
1
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
1
0
2
2
0
2
1
1
0
2
0
0
0
2
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
2
0
1
0
2
2
0
1
0
0
1
2
1
0
0
2
0
0
2
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
3
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
2
1
0
0
0
0
0
1
0
0
1
3
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
2
2
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
4
2
2
1
2
0
1
1
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
2
0
2
2
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
1
0
0
0
0
2
0
0
1
0
0
2
0
1
0
0
2
1
2
0
0
0
0
0
0
0
0
2
0
2
0
1
0
3
0
0
2
2
1
1
2
0
0
2
0
2
0
0
0
1
0
0
0
2
0
0
1
0
0
0
2
0
1
0
0
1
2
0
0
0
0
1
1
2
1
2
0
2
0
2
0
0
0
0
0
2
2
2
0
0
0
0
0
3
0
0
0
0
0
0
1
2
0
1
0
1
0
1
0
0
0
0
2
1
0
0
0
0
7
0
0
0
1
3
1
1
0
2
1
0
0
1
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
4
0
0
2
0
0
2
1
1
0
0
0
0
1
1
1
0
0
0
2
2
0
0
0
0
2
2
0
1
1
0
0
1
2
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
1
0
0
2
1
2
0
1
1
1
0
0
1
0
0
0
0
0
0
0
2
1
0
2
1
0
1
0
1
0
2
0
2
0
2
0
0
0
2
0
0
0
4
0
1
1
0
1
0
0
0
0
0
0
2
0
0
0
1
1
1
2
1
1
0
0
0
1
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
2
2
0
3
0
0
0
0
2
0
0
1
3
2
1
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
2
2
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
2
0
0
1
1
2
0
0
2
1
0
0
0
0
1
0
1
0
1
0
1
0
0
0
2
2
0
0
0
2
1
0
1
0
0
2
0
1
0
1
0
0
1
1
0
2
0
0
2
0
0
1
0
1
1
0
1
0
0
0
0
2
0
1
0
2
2
0
0
0
0
0
2
0
2
2
1
2
0
0
0
0
2
0
0
0
0
1
1
1
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
2
0
1
0
0
2
1
0
0
0
0
1
0
2
0
0
0
1
2
1
1
0
0
0
2
1
0
0
1
2
2
0
0
0
0
0
0
1
0
0
0
1
2
0
0
1
0
2
0
0
1
0
0
0
0
1
1
0
1
1
2
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
2
0
1
3
2
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
2
0
2
2
0
0
2
0
0
0
2
2
3
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
2
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
2
0
1
0
0
0
2
0
0
1
0
2
1
0
0
0
0
0
1
1
2
2
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
1
2
0
0
1
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
1
3
1
3
0
2
0
0
0
1
2
0
0
0
2
2
3
1
0
0
1
1
1
0
1
1
2
0
0
1
1
0
1
2
0
1
0
0
2
0
0
1
0
0
0
1
0
0
0
2
0
1
0
0
2
1
0
0
2
0
0
0
2
1
0
1
0
0
1
0
0
1
2
2
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
3
0
0
0
0
0
0
2
2
2
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
2
2
1
1
0
2
0
1
2
1
0
1
0
0
1
2
2
0
0
0
1
0
0
2
0
0
1
1
2
0
0
0
0
1
1
1
1
0
1
0
0
1
2
0
0
0
1
0
0
1
1
0
2
0
3
1
1
0
0
0
0
0
0
0
2
0
2
0
2
0
2
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
1
0
2
2
0
1
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
4
0
2
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
2
1
2
0
0
2
2
2
0
2
0
2
0
1
0
0
0
1
2
0
0
0
1
0
1
2
1
1
0
0
1
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
2
0
0
2
2
1
0
0
0
1
2
0
2
1
2
0
0
0
2
1
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
1
0
0
2
4
1
0
0
0
0
0
0
0
1
2
0
0
1
1
0
0
1
0
1
0
1
0
1
0
0
1
2
0
1
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
3
0
0
1
0
1
0
3
0
1
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
1
2
0
2
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
2
0
0
0
2
0
0
1
0
0
0
0
2
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
3
0
0
1
1
0
0
0
0
2
0
1
0
0
0
1
0
1
2
0
0
1
0
0
0
0
0
0
2
1
0
0
3
0
2
0
0
2
0
0
1
2
0
2
0
0
0
0
2
0
0
1
2
3
2
2
0
0
0
0
2
0
2
0
2
0
0
1
0
0
1
0
0
1
0
1
1
0
1
0
0
0
0
0
1
1
2
1
0
0
2
0
2
0
1
1
0
0
2
2
0
0
0
0
0
1
0
3
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
2
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
2
2
0
4
0
0
0
2
0
1
2
1
1
1
0
0
0
0
0
0
2
0
0
0
1
0
1
1
2
2
2
0
0
0
0
0
1
0
0
0
0
0
0
1
2
1
0
0
2
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
2
0
0
0
1
2
0
0
0
0
0
2
0
0
2
0
0
0
2
1
0
0
0
0
2
0
1
2
0
0
0
0
2
1
1
0
2
1
0
0
1
0
0
0
2
1
2
0
1
1
0
1
2
0
0
0
2
1
0
2
0
1
0
2
0
3
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
2
0
2
0
1
0
0
2
0
0
0
1
0
2
0
2
0
2
0
2
0
0
0
2
0
0
2
0
0
1
1
0
0
2
0
1
0
0
0
0
2
1
1
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
2
1
1
0
2
1
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
2
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
1
3
1
0
0
0
0
0
2
1
2
0
2
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
2
0
0
0
1
2
0
2
0
0
0
0
3
0
0
0
2
2
2
0
0
0
0
0
2
0
2
0
1
0
0
1
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
1
0
2
2
0
0
0
0
2
0
0
0
1
2
0
0
0
0
2
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
2
2
1
0
0
1
1
0
0
0
1
0
0
0
0
0
2
0
2
0
0
3
2
3
2
1
0
0
1
1
0
2
0
0
1
0
0
0
0
0
2
0
0
1
0
0
2
1
1
0
2
1
2
0
0
2
1
0
0
0
1
2
0
0
2
0
0
0
0
0
2
1
0
1
2
0
1
0
0
0
2
0
0
2
2
0
1
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
1
0
3
0
0
0
0
0
2
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
2
2
1
1
0
0
2
3
0
0
1
1
1
0
0
2
0
0
0
1
0
0
0
0
1
0
1
2
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
1
4
0
3
0
0
0
0
0
0
1
0
2
2
0
0
1
2
2
0
1
2
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
2
2
0
0
0
1
0
0
1
0
3
1
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
1
1
4
0
0
1
0
1
1
2
1
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
2
0
2
2
1
0
0
0
0
3
0
0
0
0
2
0
0
0
0
2
0
0
0
2
2
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
2
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
4
0
0
0
0
0
4
0
1
2
0
1
0
0
0
0
0
0
1
1
2
0
1
1
1
1
0
0
0
0
0
1
1
2
0
1
0
0
0
0
2
1
2
0
1
0
0
2
0
0
0
1
0
0
0
0
1
0
1
3
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
1
0
0
2
1
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
3
0
0
0
0
0
2
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
3
1
1
1
1
0
0
1
0
1
0
1
1
0
0
2
0
0
0
4
1
0
1
0
2
1
0
0
0
0
0
0
1
0
0
2
0
0
1
2
2
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
1
2
2
0
1
0
0
2
0
4
0
2
1
1
0
1
0
1
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
3
0
1
1
0
0
0
2
0
1
1
0
0
0
0
2
0
1
3
0
1
1
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
3
0
0
1
1
2
0
2
1
0
0
0
1
0
1
2
2
0
0
0
1
0
0
1
0
0
2
0
1
0
0
0
0
0
0
1
2
3
2
0
0
2
0
0
1
0
0
1
0
0
1
2
1
0
0
0
0
1
1
1
0
2
0
2
1
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
2
0
1
2
0
0
0
2
0
0
0
0
1
0
0
1
0
2
1
0
0
0
0
0
2
0
0
0
1
1
1
0
0
1
1
0
2
1
0
1
2
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
1
0
1
0
1
5
0
0
1
0
1
2
0
0
0
1
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
1
1
0
0
2
0
0
0
2
0
0
0
1
2
1
1
2
1
0
0
2
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
3
0
0
0
1
0
1
0
0
0
1
3
0
1
0
0
0
0
1
0
2
2
1
1
0
0
1
0
1
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
1
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
1
0
0
1
0
0
0
1
1
0
1
1
0
0
0
0
1
1
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
2
0
1
2
1
2
0
1
0
0
0
0
0
2
0
0
1
1
2
0
0
1
0
0
0
0
2
1
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
3
0
0
2
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
1
2
2
0
2
0
0
0
0
0
1
1
2
0
0
0
2
2
0
0
0
0
1
0
0
1
0
2
0
0
2
0
0
2
0
0
2
3
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
3
4
1
0
3
2
0
0
0
0
0
0
0
0
1
1
0
0
2
0
1
0
0
3
0
0
2
2
0
1
0
0
0
0
3
4
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
1
2
0
2
2
0
0
2
0
0
0
1
0
1
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
2
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
2
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
2
0
0
0
1
2
0
1
0
0
0
0
0
1
0
4
0
2
0
0
1
1
0
0
0
0
1
0
0
0
2
0
0
1
0
1
1
2
1
1
1
2
0
0
0
0
2
1
0
0
1
0
0
2
0
0
0
2
0
0
1
1
0
0
1
2
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
2
0
0
0
2
1
0
0
0
1
2
1
1
0
0
0
1
0
0
0
0
0
1
2
0
0
2
0
1
0
0
1
2
0
2
0
0
0
1
0
1
0
0
1
0
4
0
2
0
0
2
2
0
0
0
3
2
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
1
1
0
0
0
2
3
0
0
0
0
0
0
0
1
2
2
1
1
0
2
0
0
1
0
0
0
2
1
1
2
0
2
2
1
0
2
0
0
2
1
0
0
0
0
3
0
2
1
2
1
1
0
1
1
0
1
2
0
0
0
0
0
1
0
0
0
1
0
0
0
2
1
0
0
0
0
0
1
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
1
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
2
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
1
1
0
3
0
2
0
1
1
0
1
0
6
0
1
0
0
0
1
2
0
0
0
0
1
1
0
0
0
1
0
0
2
0
1
0
0
0
2
1
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
2
0
0
1
0
2
1
2
0
1
2
0
0
0
0
0
0
1
2
0
0
0
1
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
2
1
2
0
1
0
2
0
0
0
0
0
0
1
2
0
1
0
2
0
1
0
0
1
0
2
0
1
0
0
2
2
2
0
0
2
0
0
0
1
2
0
0
0
1
0
1
0
2
0
0
0
0
5
0
2
0
1
2
0
0
2
0
1
0
0
1
0
0
0
0
2
1
1
0
0
0
1
1
1
2
0
0
0
2
0
0
2
2
0
1
0
0
0
0
0
0
1
0
2
1
0
2
0
0
0
1
0
0
0
0
0
2
0
1
1
1
1
0
2
2
2
2
0
2
2
0
0
0
0
0
2
2
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
1
1
0
0
1
1
0
1
0
0
0
0
0
0
1
3
0
0
0
0
1
0
0
1
0
0
0
2
1
1
0
0
0
1
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
1
1
0
0
0
0
0
2
1
0
1
2
0
2
0
0
0
0
1
0
2
0
0
0
1
0
2
2
0
2
1
1
0
0
0
0
3
1
0
0
0
0
3
1
0
0
1
0
1
2
0
0
0
1
1
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
2
0
0
1
0
1
0
0
3
0
0
0
4
1
1
0
3
0
2
0
3
2
0
0
0
0
0
2
0
0
4
0
1
0
0
1
0
1
0
0
0
2
0
0
2
1
0
1
0
0
0
1
1
2
0
0
0
0
0
0
0
1
3
0
0
2
0
0
0
2
1
1
1
1
2
0
1
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
2
0
0
1
1
0
0
1
2
0
0
0
2
2
0
5
0
0
0
0
1
0
0
0
2
2
0
0
1
0
1
2
0
1
0
0
1
0
0
0
2
2
0
1
1
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
1
0
0
0
0
1
0
0
1
0
2
0
0
0
1
0
2
0
0
0
0
0
0
1
1
0
0
0
2
2
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
2
0
1
0
1
1
0
0
1
0
0
1
2
0
0
2
0
1
2
2
2
0
0
0
0
0
0
1
0
2
1
0
2
0
0
3
0
0
2
2
3
1
2
0
0
0
1
0
0
0
1
0
0
2
1
2
2
0
0
2
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
5
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
2
0
0
2
0
0
0
0
2
2
0
2
1
0
0
1
0
0
0
0
0
2
0
2
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
2
2
3
2
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
1
2
0
0
0
0
0
1
2
2
0
2
3
1
2
0
1
0
1
0
0
0
1
0
0
2
1
0
1
1
0
0
0
0
2
0
0
2
0
0
0
1
1
1
0
0
2
0
0
2
0
0
0
0
0
1
0
3
0
0
0
1
0
2
0
0
0
2
0
0
2
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
2
1
0
0
2
0
2
2
2
1
0
0
2
1
4
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
2
0
1
1
0
0
0
0
1
0
0
1
1
2
1
0
2
1
0
0
0
0
2
0
0
2
0
0
2
0
0
1
0
0
1
2
0
1
0
2
0
0
0
1
2
0
2
2
2
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
1
0
2
0
0
0
0
1
0
0
0
0
2
0
2
1
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
1
0
0
3
0
2
0
2
0
0
0
0
0
3
0
0
0
1
0
0
1
0
0
0
4
0
0
2
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
2
1
0
0
2
0
0
0
1
0
0
2
0
1
0
1
0
0
2
0
1
0
0
0
0
0
1
6
2
2
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
2
0
1
0
2
1
1
1
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
2
0
2
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
2
2
2
0
1
0
0
0
2
0
0
1
0
0
0
2
0
2
0
0
3
0
0
0
0
0
2
0
0
0
1
0
0
2
0
2
0
2
2
0
1
2
1
2
2
0
2
0
1
0
2
3
0
0
3
0
1
0
2
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
5
2
0
2
1
0
0
1
0
0
2
0
0
0
0
2
2
0
1
0
0
0
0
2
0
2
0
2
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
2
1
1
2
1
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
2
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
2
1
1
0
0
0
0
2
0
2
0
0
0
1
1
1
0
1
0
0
0
0
0
0
1
0
0
1
1
1
0
1
2
0
0
0
1
1
0
0
1
3
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
2
2
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
1
0
1
2
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
2
0
0
1
1
2
0
0
0
0
0
0
2
0
2
1
0
1
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
2
1
0
2
0
0
2
0
0
2
1
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
2
1
1
0
0
0
1
0
0
0
0
2
1
0
0
1
0
2
0
0
0
0
0
0
0
1
1
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
3
0
0
0
0
0
0
0
1
0
1
0
2
0
2
2
3
2
0
0
0
2
0
0
2
0
0
0
0
2
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
1
0
1
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
2
0
2
1
2
0
0
0
2
0
2
0
0
2
0
1
0
1
0
3
0
0
1
1
1
2
2
0
1
0
0
0
0
2
2
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
1
0
2
1
0
0
3
0
1
0
0
1
0
0
0
0
2
0
1
6
0
0
0
1
0
2
0
2
0
0
0
1
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
1
2
1
1
0
0
0
0
0
1
0
2
0
0
1
0
0
2
0
1
1
0
0
0
0
0
0
0
0
1
2
0
2
1
0
0
2
0
1
0
0
1
0
0
4
0
0
2
0
0
2
1
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
2
0
1
1
0
4
3
0
3
2
1
0
0
0
0
2
0
2
0
0
1
1
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
1
1
1
0
0
0
0
0
1
1
2
0
1
0
0
0
1
0
1
0
6
0
1
0
0
0
0
0
1
0
0
0
0
0
5
3
1
2
0
0
0
1
0
2
0
2
1
1
0
0
0
2
0
0
2
2
1
1
1
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
5
0
0
5
1
0
0
2
2
3
0
0
3
1
0
0
0
1
0
0
0
0
0
0
0
1
0
3
0
0
0
1
1
0
0
0
1
0
0
0
0
2
0
1
0
2
2
0
1
0
1
0
2
0
1
0
1
1
0
1
0
0
0
0
0
1
0
0
2
2
0
0
0
0
1
0
0
1
0
2
0
0
0
2
0
2
0
1
1
0
1
0
0
0
0
0
2
1
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
1
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
3
0
2
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
3
2
0
3
0
2
0
1
0
0
0
0
0
0
0
0
0
2
3
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
7
0
2
2
0
0
2
0
2
0
0
1
0
0
0
1
2
0
0
0
0
0
0
1
1
0
0
0
0
3
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
3
1
1
2
1
2
2
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
1
0
0
1
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
1
0
1
0
1
0
1
2
0
0
1
0
0
0
0
0
2
0
3
1
2
0
0
0
0
0
4
1
1
1
0
0
1
0
0
2
0
0
0
0
1
0
1
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
3
0
1
0
0
1
2
2
2
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
3
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
1
0
1
1
0
2
0
0
3
0
1
0
0
2
1
0
0
1
2
2
0
2
0
3
0
3
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
1
1
0
0
0
0
1
2
1
2
0
0
0
0
1
2
2
1
2
0
0
1
0
0
0
2
0
1
2
1
1
1
2
2
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
1
1
0
0
0
0
2
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
2
0
0
2
2
0
0
2
0
3
0
0
0
0
0
3
1
0
0
0
1
0
0
1
1
0
1
2
0
0
2
0
2
0
0
0
1
1
2
1
0
0
0
0
0
1
0
2
0
0
3
1
0
2
0
0
0
1
2
0
0
0
2
0
2
2
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
2
3
0
0
2
0
1
0
0
0
1
1
0
1
1
0
0
0
0
2
0
0
0
1
2
1
2
0
0
0
0
1
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
3
0
0
2
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
2
0
0
1
0
0
2
0
0
2
0
1
0
1
2
1
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
3
1
0
1
2
2
0
0
0
1
2
0
2
0
0
2
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
2
0
0
0
0
0
0
0
0
2
1
4
0
0
0
1
1
2
1
2
2
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
2
0
0
2
1
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
2
1
0
0
0
1
2
2
2
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
1
0
0
0
0
0
2
0
2
2
0
2
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
1
2
0
2
0
2
1
3
1
0
0
2
0
1
0
0
0
0
0
2
0
2
2
1
0
3
2
0
2
1
0
0
0
2
0
0
1
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
1
1
1
0
0
0
0
2
2
0
0
2
0
2
0
0
1
2
2
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
1
0
0
0
0
0
0
1
1
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
1
0
0
2
0
1
2
1
0
0
0
0
0
1
0
0
0
0
2
2
2
0
2
0
0
1
0
2
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
1
0
2
2
0
2
2
0
0
2
7
0
2
0
2
1
0
1
2
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
1
2
1
3
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
2
0
2
0
1
0
1
0
0
0
3
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
1
0
0
0
1
0
1
2
0
1
2
3
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
2
2
0
2
1
0
1
1
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
3
1
2
0
0
0
1
0
2
0
0
1
0
2
1
1
0
0
0
1
2
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
1
3
1
1
1
1
0
0
4
0
2
0
3
0
0
1
0
1
0
1
0
0
1
0
0
0
0
2
2
0
0
0
0
2
2
2
0
0
2
0
0
1
1
0
1
0
0
1
0
2
2
1
1
1
1
2
0
0
0
0
0
0
0
0
2
0
1
0
0
2
2
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
2
0
2
2
1
0
0
2
0
0
2
0
1
0
1
0
1
0
3
0
0
1
0
1
0
1
2
1
0
1
0
0
0
1
0
2
0
0
0
0
0
1
1
1
0
0
0
0
0
2
0
1
0
0
1
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
1
2
0
0
0
1
0
2
0
0
0
0
0
1
2
0
1
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
1
1
1
1
1
1
0
1
1
0
1
2
0
2
0
2
1
2
2
1
0
2
0
2
0
0
0
0
0
2
2
2
1
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
4
2
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
1
0
0
1
0
0
3
0
0
0
1
0
0
0
0
1
1
2
0
1
2
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
2
1
0
1
0
1
0
0
1
0
0
0
2
3
0
0
2
0
1
0
2
0
1
0
0
0
0
0
0
2
0
0
1
0
1
0
2
2
0
0
1
1
0
0
1
0
2
0
1
0
2
0
1
0
0
1
1
0
0
0
0
1
1
0
0
0
1
0
0
4
1
0
0
0
1
0
0
0
0
1
2
1
1
0
0
1
0
2
0
1
0
1
0
4
0
2
2
1
0
0
2
0
0
0
0
1
0
0
1
1
0
0
0
2
0
0
1
0
0
0
0
1
3
0
0
0
0
0
3
3
0
1
0
2
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
3
3
0
0
2
0
2
1
1
0
2
1
0
0
1
0
0
0
2
0
0
4
2
2
0
0
0
0
0
0
0
2
0
0
0
1
3
0
2
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
1
1
0
0
0
2
2
2
0
2
0
3
2
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
1
0
0
2
0
1
1
0
0
1
1
0
0
2
2
3
0
0
0
0
0
0
1
1
1
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
1
0
0
0
2
0
0
0
0
2
0
2
0
0
2
0
2
0
0
0
0
2
0
1
0
0
1
0
0
0
0
1
0
0
0
0
2
1
0
0
1
0
2
2
0
0
2
2
3
2
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
4
1
0
2
1
0
1
1
0
0
0
0
0
0
0
1
2
0
2
1
0
0
0
0
2
1
2
0
0
1
1
0
3
0
0
0
0
0
3
0
0
1
0
2
0
0
0
1
0
1
1
2
2
1
0
2
2
0
3
0
1
0
2
0
1
0
1
2
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
1
1
0
3
0
1
0
0
0
0
0
0
1
0
0
1
2
2
0
0
0
2
1
2
2
1
0
2
0
0
0
0
2
2
0
1
0
0
3
2
0
1
3
0
1
0
0
2
0
0
0
1
1
2
0
0
2
0
0
0
1
0
0
0
0
2
1
0
0
1
0
2
0
1
0
0
2
0
0
0
0
0
2
1
1
2
2
0
0
2
0
0
1
0
2
0
0
0
1
0
1
0
0
2
0
0
1
0
0
0
0
0
1
2
1
3
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
2
0
1
2
0
0
0
0
0
0
2
0
0
0
2
0
2
1
0
2
2
0
0
2
0
2
2
0
0
1
0
1
1
0
0
0
0
0
0
2
1
0
0
5
2
0
0
0
0
0
0
0
1
2
1
0
0
0
1
2
0
0
0
2
0
2
0
1
0
0
0
2
0
0
1
2
1
1
3
0
0
2
0
1
0
1
0
0
1
0
0
2
0
0
0
2
0
0
2
0
1
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
1
1
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
2
0
2
1
0
0
0
3
1
0
0
0
1
1
2
0
3
0
0
0
0
2
0
2
0
0
1
0
0
0
0
1
1
2
0
1
0
0
0
2
2
2
0
0
2
0
0
0
2
1
0
0
0
2
0
0
1
0
3
0
0
0
0
2
1
0
0
0
0
2
0
0
0
1
0
2
1
0
0
0
1
0
1
1
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
1
2
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
4
0
2
1
0
0
0
1
0
0
2
1
0
0
0
0
2
0
2
0
0
0
1
3
0
0
0
0
0
2
0
0
1
2
0
0
0
1
0
0
2
0
0
2
2
2
0
1
2
5
0
0
1
1
2
2
2
0
1
0
2
2
0
1
0
0
2
0
0
0
3
2
0
0
6
0
2
0
0
2
1
0
0
0
1
0
0
2
0
1
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
1
0
1
2
1
0
2
1
0
1
0
2
0
1
0
0
0
0
0
1
0
3
2
0
2
0
0
2
2
2
2
1
0
1
0
3
0
1
1
0
2
1
0
0
0
0
2
0
1
2
0
0
0
0
0
1
0
0
0
3
0
0
0
0
1
2
2
0
2
1
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
1
0
1
2
1
0
0
0
0
0
2
0
1
1
0
2
0
2
1
0
0
0
0
0
0
0
1
1
0
2
1
0
2
3
2
1
0
0
0
0
2
0
0
0
2
0
1
1
0
0
0
3
2
0
0
2
0
0
1
0
0
2
0
0
1
0
2
0
0
1
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
3
0
0
2
4
2
1
0
0
2
1
0
0
0
1
0
2
0
0
0
1
2
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
2
0
0
2
4
3
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
2
2
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
1
0
2
0
5
0
0
0
0
0
0
1
1
0
0
0
1
1
0
2
0
0
0
0
0
1
0
1
0
0
2
0
0
0
1
0
0
2
2
0
0
0
0
2
0
2
0
1
0
0
2
0
1
1
4
1
0
1
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
3
0
0
0
1
0
0
1
1
0
2
0
0
0
2
0
2
0
1
0
0
3
0
0
2
2
0
2
0
2
0
0
0
3
1
2
0
0
0
2
0
1
0
0
0
2
0
2
0
2
1
0
0
1
0
0
1
0
0
0
1
0
0
0
2
0
2
1
2
2
0
0
0
0
0
0
1
1
0
0
0
3
2
1
1
0
0
0
0
0
0
1
0
0
3
2
2
0
0
0
0
0
0
1
0
0
0
0
1
0
2
2
1
0
0
0
0
0
1
0
0
0
0
8
2
0
1
2
0
0
2
0
0
0
0
0
1
0
0
0
2
1
1
0
0
0
1
2
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
2
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
2
2
0
0
2
0
0
0
0
0
1
1
2
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
2
1
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
2
2
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
2
1
1
0
0
0
0
0
1
0
3
0
1
2
0
2
0
0
1
2
2
0
3
0
0
0
0
0
1
0
0
2
0
0
0
0
1
1
3
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
3
7
0
3
1
3
0
0
2
0
2
2
1
2
2
2
0
2
0
0
0
0
2
0
0
1
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
2
2
0
3
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
2
2
1
1
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
3
0
2
1
2
0
1
0
0
1
2
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
2
0
0
1
1
0
0
2
2
0
0
0
0
1
2
0
0
1
0
0
3
1
0
0
0
1
0
1
2
2
2
2
0
1
1
2
0
2
0
2
2
0
0
1
0
0
0
0
2
1
0
0
2
2
4
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
1
0
0
0
0
2
2
2
0
0
0
0
0
0
0
3
0
0
0
4
0
2
0
2
2
0
2
0
0
0
0
0
1
1
2
0
0
0
0
0
0
2
0
0
1
3
2
0
2
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
2
0
0
2
2
2
2
0
2
2
1
1
2
0
2
0
1
0
1
0
0
0
0
1
1
2
2
2
2
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
1
1
0
2
0
0
0
0
3
0
0
0
1
2
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
1
2
0
0
1
2
0
0
0
0
2
0
1
1
0
1
0
1
2
2
0
0
1
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
2
0
2
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
4
0
0
0
0
1
1
0
0
0
1
0
0
0
2
2
1
0
2
0
0
1
0
0
0
0
2
0
0
3
0
0
0
0
0
2
1
1
0
2
2
2
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
1
2
2
0
2
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
3
0
0
0
0
0
7
0
0
0
0
0
0
1
0
0
0
2
1
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
2
0
1
0
0
2
0
0
0
0
0
1
2
0
1
0
1
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
1
1
2
0
0
0
2
0
1
0
0
0
2
0
0
1
1
0
2
0
0
0
0
0
0
1
0
0
1
2
2
0
2
0
1
0
0
1
2
0
1
2
0
0
0
0
1
0
1
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
1
0
6
2
0
2
0
0
1
0
0
2
0
0
2
1
0
1
0
2
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
2
1
0
0
0
0
1
1
0
1
3
0
2
0
1
2
1
0
0
0
0
2
2
0
0
0
0
1
0
1
0
2
0
1
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
3
0
0
0
2
0
0
1
1
0
0
1
0
0
0
0
0
0
0
2
2
0
0
1
2
1
0
1
0
1
0
0
0
1
0
2
1
0
1
0
2
0
1
0
0
2
0
0
0
1
0
0
1
2
0
1
0
1
0
2
1
0
0
2
2
0
0
0
0
1
0
1
0
0
0
2
0
0
1
2
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
2
0
2
2
2
0
0
0
0
0
0
1
0
2
0
0
1
1
1
1
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
2
2
0
1
0
0
2
1
0
0
0
0
0
0
1
5
2
5
0
2
0
0
0
0
1
0
0
1
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
2
0
0
2
0
2
0
1
3
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
1
1
3
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
1
0
0
1
0
2
2
0
0
0
0
0
0
0
2
0
2
0
0
3
1
0
0
0
1
0
2
1
1
0
0
1
0
1
2
0
2
1
0
0
1
2
0
0
0
4
0
0
0
2
1
0
0
0
0
0
0
1
2
2
0
0
1
0
0
7
0
0
0
0
1
0
0
1
3
1
0
0
2
2
0
0
0
2
1
2
0
0
0
0
0
1
0
0
0
2
1
1
0
1
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
1
0
1
0
0
3
0
0
0
0
0
0
0
0
3
0
0
0
2
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
1
1
3
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
1
0
2
0
0
1
0
1
2
0
2
2
0
1
2
2
2
2
0
0
0
2
0
1
1
0
0
0
1
2
0
2
0
1
0
0
0
0
0
0
1
0
0
0
2
0
3
0
0
0
0
1
0
0
1
0
0
2
0
0
2
0
2
0
1
0
2
0
2
0
1
0
2
0
0
0
0
1
0
1
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
1
0
2
0
0
0
0
0
2
1
0
2
1
0
0
0
0
0
0
0
1
0
2
2
0
0
0
2
1
0
0
0
1
2
0
0
0
0
0
0
0
0
2
2
0
0
1
0
1
0
1
1
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
1
0
1
0
2
0
2
0
0
0
1
1
0
1
0
0
0
0
0
2
0
0
0
2
2
0
2
1
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
2
0
0
2
2
0
1
3
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
2
0
0
1
2
1
0
0
1
0
0
0
0
0
1
1
0
0
0
3
0
1
0
3
0
0
0
0
2
0
0
1
0
1
0
2
0
0
2
2
0
0
0
0
3
0
1
2
2
1
0
2
2
0
0
0
0
1
1
1
0
0
0
12
1
0
0
2
1
2
3
0
2
1
3
2
2
1
1
0
0
0
0
0
2
0
1
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
2
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
1
2
0
0
0
0
0
2
2
1
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
3
0
1
2
0
0
2
0
0
4
1
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
1
2
0
0
0
1
1
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
3
0
0
1
0
2
0
0
0
0
0
1
2
0
0
0
0
0
2
2
2
1
0
1
0
0
0
4
1
1
0
0
0
1
0
1
0
2
0
0
2
2
0
0
0
0
0
3
0
0
1
4
0
1
1
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
3
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
1
0
2
1
0
1
2
2
2
0
0
0
1
5
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
2
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
1
0
0
2
1
1
0
0
2
0
0
0
0
1
3
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
1
9
0
2
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
4
0
0
2
2
0
0
1
1
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
1
0
2
0
0
0
1
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
4
0
0
0
2
2
0
1
0
0
1
0
0
0
1
0
0
0
0
2
0
3
0
0
2
3
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
1
0
1
0
0
1
0
0
2
0
2
0
2
1
0
2
0
1
0
0
2
2
1
0
0
0
1
0
2
0
2
0
0
0
0
0
0
2
0
1
0
1
1
2
0
0
2
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
2
0
0
0
0
0
0
1
1
2
0
2
2
1
0
2
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
2
0
0
0
0
0
2
2
0
0
1
1
0
2
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
1
1
0
1
1
1
0
0
2
0
0
0
2
0
2
3
0
0
1
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
2
4
0
0
1
0
0
0
1
2
0
0
0
1
2
0
0
1
0
2
0
2
0
2
0
0
0
2
2
0
0
3
1
0
0
0
0
2
0
0
2
1
1
0
0
0
1
1
0
0
0
2
2
0
0
0
0
2
2
1
0
0
1
1
0
0
0
2
0
0
2
2
0
0
1
3
0
1
0
0
0
0
0
0
1
0
1
1
1
0
1
1
0
1
0
1
0
1
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
2
0
2
0
0
0
0
0
1
0
6
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
2
1
0
2
2
0
2
0
2
2
0
0
1
0
1
0
2
0
0
0
0
0
0
0
1
1
0
1
1
1
2
0
0
2
0
0
0
0
0
2
0
0
1
0
2
1
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
2
1
0
0
2
0
1
1
0
0
0
0
2
0
0
2
0
0
1
0
0
1
1
2
1
0
0
1
0
2
2
0
0
0
1
1
0
1
0
0
2
0
1
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
3
0
0
0
2
0
0
2
0
0
0
2
0
0
1
0
2
0
0
2
0
0
0
0
2
1
1
0
1
1
0
0
0
0
1
0
2
0
0
0
0
1
2
1
0
0
3
3
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
1
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
1
2
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
1
2
1
0
0
0
3
0
0
3
0
0
2
0
0
2
0
1
0
1
1
2
0
1
2
0
0
0
0
0
2
1
2
0
1
0
0
0
1
2
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
2
2
2
2
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
2
1
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
2
0
0
0
1
0
2
5
0
0
1
1
0
1
0
1
0
2
0
0
0
0
3
0
0
0
0
0
1
1
0
0
2
1
0
0
0
2
0
1
0
2
0
0
1
0
0
1
0
0
2
0
4
0
2
1
1
1
1
0
2
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
2
0
0
0
0
0
2
0
0
3
0
0
1
0
5
1
1
0
0
1
2
0
2
2
0
0
2
0
2
2
0
0
0
0
0
0
0
0
3
0
2
0
1
0
0
0
0
2
0
1
4
0
0
0
0
2
0
0
0
0
0
2
0
0
1
1
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
1
1
2
0
2
0
0
1
0
1
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
2
0
0
3
0
4
0
1
0
0
0
3
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
2
0
0
0
1
2
0
1
0
0
0
0
3
1
2
2
2
0
0
0
0
0
0
1
1
1
1
0
3
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
2
0
0
0
0
0
0
2
1
1
1
2
0
0
0
0
2
1
2
1
0
2
0
2
0
0
0
0
0
0
1
2
0
1
0
1
0
0
3
0
0
0
1
0
0
0
2
0
0
1
1
1
0
0
0
0
0
0
0
1
2
0
1
2
2
1
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
1
0
2
0
0
0
1
0
2
0
0
0
0
1
3
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
2
0
2
1
1
2
0
0
0
0
0
3
1
2
1
0
2
1
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
1
1
1
1
2
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
2
2
0
0
0
0
0
2
0
0
2
0
3
0
1
0
0
1
0
0
7
0
0
0
1
2
0
0
0
0
0
0
3
1
1
0
0
0
2
0
1
1
1
0
0
0
0
0
0
1
0
0
1
0
2
0
1
0
1
2
0
1
1
1
0
2
0
0
0
1
0
0
1
0
1
2
1
0
1
2
2
0
0
0
0
0
2
0
0
0
0
0
0
2
2
1
1
0
0
0
0
2
2
2
0
0
1
1
0
1
2
0
2
0
0
0
2
0
0
0
1
0
0
0
2
1
1
1
1
2
0
0
0
2
0
0
0
1
1
2
2
0
1
2
0
0
2
0
2
0
0
2
0
0
0
0
2
2
1
0
0
0
0
2
0
1
1
0
1
1
0
0
0
1
1
2
3
0
1
0
1
0
1
0
0
0
0
1
0
1
0
1
0
0
2
0
0
1
2
0
0
0
0
0
0
0
1
1
0
0
2
2
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
2
0
2
0
0
2
2
0
0
0
0
1
0
1
1
1
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
1
0
0
0
0
0
0
1
1
2
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
2
0
0
1
3
1
0
0
0
0
0
1
0
3
2
1
0
2
0
0
1
0
0
0
2
2
1
2
0
0
0
0
0
1
0
1
1
0
0
2
2
0
0
0
0
2
1
0
0
0
0
1
2
1
2
0
0
0
0
2
0
0
5
2
0
2
0
2
2
0
0
1
0
0
0
0
0
2
3
0
0
0
1
2
0
0
2
2
0
2
3
1
0
1
0
0
1
0
0
0
1
0
4
2
0
2
2
0
0
0
1
2
2
2
0
2
0
0
0
0
2
0
0
2
1
1
2
1
0
1
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
2
0
0
1
0
0
0
0
1
2
0
0
0
0
0
2
0
0
1
1
0
0
2
0
0
2
0
0
0
0
3
0
0
0
0
0
0
1
2
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
1
1
1
0
0
0
0
0
0
0
0
1
0
0
2
1
0
2
2
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
2
0
0
0
1
0
0
2
0
1
0
2
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
4
1
0
0
0
1
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
1
0
2
1
0
0
3
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
2
2
2
2
0
0
0
1
2
1
0
1
0
0
0
0
1
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
1
0
1
0
1
1
2
1
2
2
2
1
0
0
2
0
2
0
2
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
2
1
0
1
2
0
2
0
0
0
0
0
0
0
0
1
1
2
0
1
0
1
0
1
1
2
0
0
0
0
0
0
1
0
2
2
1
0
0
0
2
0
0
0
0
1
1
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
1
1
2
1
1
0
0
2
2
0
2
0
2
0
0
2
0
0
0
2
1
2
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
1
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
2
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
2
2
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
1
0
0
0
0
0
0
0
1
1
1
0
2
0
2
2
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
1
0
0
0
1
1
0
0
0
2
1
0
1
1
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
2
0
0
3
1
0
1
2
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
1
1
0
0
0
2
0
0
1
0
0
1
1
0
1
0
0
0
0
1
0
0
0
2
0
0
1
0
1
0
0
0
0
0
2
2
0
0
1
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
2
0
1
2
0
0
0
0
0
1
0
0
2
0
0
0
2
2
1
0
1
0
1
2
0
0
2
0
2
0
0
0
0
1
0
1
2
0
0
0
0
0
1
0
2
0
0
0
0
2
0
3
0
1
0
0
0
0
1
0
0
0
2
0
2
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
1
2
0
1
0
1
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
3
0
0
0
0
0
1
4
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
3
1
0
0
0
3
1
0
0
1
1
0
0
0
0
2
0
0
0
2
1
0
0
2
1
0
0
0
2
0
2
0
0
3
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
1
0
1
0
0
2
0
2
0
3
2
2
0
0
1
0
2
0
0
2
0
2
2
0
2
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
2
2
0
0
2
2
0
0
1
0
1
0
3
1
0
0
0
1
2
0
0
1
0
1
0
0
0
0
0
2
2
0
1
0
2
2
0
1
1
0
0
0
1
0
1
1
1
0
0
0
0
2
0
0
0
2
0
0
0
1
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
2
0
0
2
0
0
3
0
0
0
3
1
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
2
0
2
0
2
0
0
0
0
0
2
1
1
2
0
3
0
1
0
1
0
0
0
0
2
0
0
0
0
0
2
2
2
0
2
2
2
0
0
0
3
0
0
0
1
0
0
0
1
2
2
0
1
0
1
2
0
0
0
0
2
0
0
0
2
1
3
2
0
0
0
0
0
1
2
1
3
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
2
0
1
1
0
0
0
0
3
0
1
0
0
0
0
1
0
1
0
2
2
0
0
2
1
2
0
0
2
0
2
0
0
3
1
0
0
1
0
0
0
0
0
1
2
0
0
2
1
0
2
2
0
0
0
0
0
0
2
1
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
4
2
0
2
3
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
1
0
1
1
6
0
3
2
0
2
2
1
1
0
0
0
0
1
0
1
2
0
1
0
0
2
1
0
1
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
2
0
0
0
1
0
0
0
1
0
0
2
1
0
0
0
0
0
0
1
2
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
2
0
0
0
0
1
0
0
0
2
1
0
2
0
0
2
1
0
2
0
0
1
0
0
3
1
2
0
3
1
0
1
2
1
3
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
1
2
1
0
1
0
1
0
0
2
2
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
1
2
0
0
0
0
2
0
2
0
0
0
1
0
0
0
4
1
1
0
0
2
0
0
0
0
2
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
3
0
0
1
0
0
0
0
1
0
0
2
3
1
2
0
0
0
1
0
0
2
1
0
2
0
1
0
0
2
2
2
0
5
0
0
0
1
3
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
1
0
2
0
2
0
1
0
3
1
0
1
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
2
0
0
0
1
0
0
0
0
0
2
0
0
1
1
3
0
0
0
1
0
0
0
0
0
0
2
2
1
0
2
2
7
0
0
2
1
0
0
0
1
1
0
2
0
0
0
3
2
0
0
1
3
2
0
0
0
0
0
0
0
0
1
3
0
1
0
0
1
0
2
0
0
1
0
1
0
3
0
0
2
0
1
0
0
0
0
0
1
0
0
1
0
0
1
1
2
0
2
0
1
0
0
0
0
0
0
0
0
0
1
1
0
2
1
0
2
1
0
0
0
2
0
2
0
2
1
0
0
0
0
0
2
1
1
1
0
0
1
0
0
0
1
0
1
0
1
0
0
0
1
1
0
0
0
1
0
1
2
1
1
0
0
0
0
0
0
0
0
1
0
0
0
6
0
0
0
0
0
1
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
2
0
0
2
0
0
1
0
0
1
2
0
0
0
1
0
1
1
0
0
0
0
0
2
0
2
0
0
0
0
2
1
1
2
0
1
0
0
1
3
0
0
0
0
2
0
0
1
1
0
1
0
0
1
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
2
0
1
1
0
0
0
2
0
0
2
0
0
0
1
0
2
0
2
0
0
0
0
1
2
0
2
0
3
3
2
0
2
0
0
0
0
0
0
0
0
1
1
3
0
0
0
0
1
1
0
0
1
2
0
0
0
0
2
0
0
0
2
0
2
1
0
0
0
0
0
2
1
1
0
0
0
0
0
2
0
0
0
2
2
1
3
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
1
0
1
1
0
0
0
0
2
0
0
2
0
1
0
3
0
0
0
0
0
1
3
6
1
0
0
0
0
0
1
1
0
2
0
0
2
0
2
0
0
1
3
0
1
2
0
2
0
0
0
0
2
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
2
1
2
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
2
1
0
0
1
0
0
0
0
0
0
3
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
1
0
0
1
0
1
0
0
0
0
2
0
0
3
0
0
0
1
1
1
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
2
1
0
0
0
1
0
0
3
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
1
0
0
2
0
1
0
2
2
2
0
0
0
1
0
0
2
0
0
0
0
2
0
0
1
0
0
2
0
0
0
1
3
2
0
1
0
2
0
0
2
3
0
0
0
1
0
1
0
0
0
1
0
0
2
0
0
0
0
4
0
1
0
0
0
0
0
0
2
2
1
1
0
0
0
0
1
0
0
0
2
1
0
0
0
0
4
0
0
0
0
0
2
1
0
0
2
0
0
0
2
0
2
0
0
2
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
1
2
1
1
0
0
2
1
0
1
2
0
2
1
1
1
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
2
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
1
0
2
1
0
0
0
0
0
0
0
1
0
0
1
0
3
2
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
2
2
1
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
1
0
2
0
1
1
1
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
3
0
0
1
0
0
0
2
1
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
1
7
0
0
0
2
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
1
0
2
1
1
0
0
0
0
2
2
1
0
0
2
1
0
0
0
2
1
0
0
0
0
0
0
0
1
2
0
1
1
2
2
0
2
0
1
1
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
2
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
2
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
1
2
1
0
1
0
0
2
2
1
0
0
2
0
3
1
0
0
0
0
2
2
3
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
2
0
0
0
2
0
1
0
1
3
0
0
0
1
2
1
0
0
3
2
0
0
0
0
2
0
1
0
1
0
2
0
0
0
2
0
0
2
0
0
0
0
2
0
3
1
0
1
0
0
2
2
0
0
2
1
0
1
2
0
1
0
0
1
0
1
2
0
0
0
0
1
1
0
2
0
0
0
1
0
0
1
1
0
0
0
1
0
2
0
0
1
0
0
2
0
2
0
0
2
0
1
0
2
0
0
1
0
0
0
0
1
0
3
1
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
5
0
0
1
0
1
0
0
2
0
0
0
0
1
2
0
0
1
0
1
0
2
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
2
1
2
0
2
0
2
1
0
0
1
0
2
0
2
0
0
2
2
0
2
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
3
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
2
1
0
0
1
0
2
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
2
2
0
0
1
0
0
0
1
1
3
0
0
0
1
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
1
0
1
1
2
0
0
2
3
0
1
3
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
1
0
0
0
2
0
2
0
0
0
1
0
2
0
0
0
1
2
1
0
0
0
0
0
0
0
1
4
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
7
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
2
2
2
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
3
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
2
1
1
0
0
0
2
1
1
1
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
1
1
1
0
0
1
2
1
1
0
0
0
0
0
0
3
1
0
0
1
0
0
0
1
0
0
2
0
2
0
0
1
0
0
0
2
0
0
0
0
0
1
1
0
1
1
0
2
0
0
0
3
2
1
0
1
0
0
1
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
2
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
4
0
0
0
2
1
0
0
1
0
2
0
0
0
0
2
0
2
2
0
0
1
0
1
0
0
0
0
0
2
0
1
1
1
0
2
1
2
0
0
0
1
0
0
2
0
0
1
1
1
0
0
1
2
0
0
0
0
2
0
0
2
1
0
1
0
1
2
2
0
0
0
0
0
0
0
0
0
1
3
0
0
2
0
0
1
0
0
1
0
0
5
2
0
2
1
1
2
2
1
0
1
0
1
1
0
0
0
1
1
0
1
1
0
3
0
0
0
1
1
2
2
1
0
1
0
1
2
1
0
0
0
0
1
1
3
0
1
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
5
0
0
1
0
0
0
0
0
1
2
0
0
0
1
0
2
0
2
3
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
3
1
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
1
1
1
0
2
0
0
0
0
2
0
0
0
1
0
1
1
0
0
1
2
0
0
2
0
0
2
0
0
0
2
0
0
0
0
1
3
0
2
1
2
0
0
1
1
1
3
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
2
2
2
1
0
1
2
0
0
0
0
1
0
0
1
1
2
0
0
0
0
0
1
0
1
0
1
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
1
0
0
0
0
2
0
2
1
2
1
5
0
1
0
0
0
0
1
2
1
0
2
0
3
2
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
2
0
1
0
0
0
1
0
2
1
0
3
0
0
2
1
1
3
0
1
0
0
2
0
1
0
0
0
0
2
0
1
0
0
0
0
0
2
0
2
0
0
3
1
0
0
2
0
0
0
0
0
0
2
2
0
5
0
0
2
0
0
0
0
1
0
1
0
0
1
0
0
2
0
0
0
0
0
2
0
3
0
0
0
2
1
2
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
1
0
1
2
0
0
1
1
0
0
2
0
0
0
2
3
0
1
0
0
0
0
0
0
0
0
0
1
1
0
3
1
0
0
0
2
1
0
1
4
1
0
0
5
1
6
1
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
2
0
2
2
1
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
1
1
0
1
1
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
1
0
1
2
0
0
0
0
0
0
0
0
2
0
2
0
2
0
1
2
2
0
0
0
1
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
1
1
0
2
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
2
0
3
0
1
0
0
0
0
5
2
0
0
0
0
0
2
0
2
0
0
0
2
1
1
0
0
0
2
9
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
1
1
0
2
0
2
0
0
2
1
2
1
0
0
0
0
0
2
0
0
0
0
0
3
1
0
1
0
0
0
1
2
1
0
1
0
0
2
0
0
0
0
1
0
0
1
1
1
1
0
0
0
0
2
2
1
0
1
0
0
0
2
0
2
1
2
0
2
0
0
3
1
0
0
1
0
0
0
0
3
1
2
1
0
0
0
0
1
2
0
0
0
0
0
1
0
1
0
1
2
0
0
0
0
0
0
2
0
0
5
0
0
0
0
0
0
0
0
0
2
2
0
4
0
2
3
0
0
0
1
2
0
2
2
0
0
1
0
0
0
0
2
0
0
3
1
0
2
0
2
0
2
2
0
2
1
1
2
1
0
1
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
2
2
0
0
1
0
6
2
1
0
0
0
0
0
1
1
1
0
0
0
0
0
2
0
1
1
0
0
0
0
0
2
2
0
1
2
0
0
0
0
0
0
1
2
0
0
1
1
0
0
0
0
2
0
1
1
0
0
2
1
0
1
0
2
3
0
0
0
0
0
1
1
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
2
0
0
1
0
0
0
0
0
2
1
1
0
2
2
0
1
1
0
0
0
0
0
0
0
1
0
1
1
0
3
0
0
2
0
0
2
1
0
0
1
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
2
3
0
0
0
0
0
0
0
0
2
0
0
4
1
0
2
2
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
1
0
2
0
0
2
0
0
0
0
1
0
2
0
0
2
1
0
0
1
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
2
0
3
0
1
0
1
0
1
2
0
0
1
0
0
0
0
1
1
0
2
1
0
1
0
1
0
2
2
2
1
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
1
0
0
1
2
0
0
1
0
1
0
1
0
0
0
0
0
2
1
0
2
0
0
2
4
1
0
1
0
0
2
0
0
0
1
1
1
0
0
1
3
2
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
2
2
0
0
0
0
0
2
1
3
0
0
4
1
0
1
0
3
3
0
2
0
0
0
0
2
0
2
1
1
0
0
0
1
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
1
0
1
0
0
1
0
0
2
0
0
1
1
0
1
0
0
0
0
0
7
0
0
2
1
0
0
0
2
1
0
1
1
0
2
0
0
1
0
3
0
0
4
2
0
0
1
0
0
2
0
0
1
0
0
0
2
1
0
0
0
1
0
0
0
0
2
0
0
1
2
0
0
0
1
2
1
0
0
0
0
1
2
1
0
0
0
1
0
0
0
0
0
0
1
0
7
0
1
2
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
5
2
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
2
0
2
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
2
0
1
1
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
2
0
1
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
1
0
1
0
2
0
0
1
2
1
4
2
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
2
1
1
0
4
0
1
2
2
3
1
0
0
0
1
0
0
1
0
0
0
2
0
0
0
3
0
0
0
2
0
0
0
1
2
2
0
0
2
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
4
1
0
2
0
0
2
0
2
2
2
0
0
1
2
1
2
0
0
0
1
0
0
0
0
0
3
0
0
0
0
1
0
2
1
2
1
2
0
1
2
1
0
0
0
1
0
1
1
0
2
0
0
0
2
0
0
0
0
0
1
2
0
2
1
1
0
0
0
0
2
2
0
0
0
1
0
1
1
1
0
1
0
0
2
0
0
0
0
1
2
2
1
1
0
1
0
0
2
0
0
1
0
2
0
0
2
2
0
0
0
1
2
0
0
1
0
0
0
0
3
0
1
2
0
1
0
0
0
1
1
0
0
0
1
2
1
1
1
0
0
0
3
0
0
0
0
0
0
0
2
1
0
1
0
0
2
0
1
0
1
0
1
2
0
2
0
1
2
2
0
0
0
2
0
0
0
1
0
0
2
2
0
2
2
0
2
0
0
0
1
0
1
2
0
1
2
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
2
1
0
0
2
0
2
2
0
0
2
0
0
0
2
0
1
2
2
0
0
0
0
0
2
4
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
2
1
0
0
2
0
1
1
0
0
0
0
0
0
1
0
2
0
0
0
0
1
1
2
0
0
0
2
0
0
0
0
1
2
0
0
0
1
0
0
0
0
1
3
0
0
2
3
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
2
0
2
0
0
1
2
0
2
0
0
2
1
0
0
0
0
1
0
0
0
1
2
2
0
1
2
0
0
0
2
1
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
1
0
0
0
2
0
0
3
0
0
0
1
0
0
0
1
0
0
0
0
1
0
2
1
0
0
1
2
0
2
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
1
1
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
1
1
0
2
1
0
2
2
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
1
1
0
3
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
2
2
1
0
2
2
2
2
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
1
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
2
2
0
0
1
1
0
0
2
0
1
2
0
0
0
1
0
1
0
0
0
0
2
0
2
1
0
0
1
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
2
3
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
1
2
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
2
0
0
0
2
0
3
2
0
0
0
0
0
2
1
2
0
0
0
0
0
2
2
2
0
0
0
0
1
0
1
2
0
2
0
0
0
0
0
0
1
1
0
1
1
0
0
1
2
0
0
0
1
0
0
0
0
0
2
2
1
0
2
2
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
1
0
0
1
1
0
0
2
4
0
0
0
2
0
2
0
0
1
3
0
1
0
0
2
1
0
0
0
0
0
1
0
2
4
0
0
0
0
0
1
2
2
0
0
0
0
0
0
2
1
2
2
0
1
0
0
1
1
0
2
0
0
0
0
1
0
1
1
0
2
0
0
0
1
1
0
0
0
1
2
0
0
1
1
5
0
1
0
2
4
2
1
0
1
0
0
0
2
0
0
0
0
2
0
0
0
2
2
1
0
0
0
0
1
0
0
2
1
0
0
0
0
2
2
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
1
1
0
2
0
0
0
1
0
0
0
2
2
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
2
1
2
0
2
0
2
0
0
0
0
1
0
0
2
1
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
1
0
2
0
2
1
0
1
0
1
2
1
0
0
0
0
0
1
2
5
1
1
0
1
0
0
0
0
2
2
0
0
2
0
0
0
0
0
2
0
0
1
1
0
0
0
1
0
1
1
2
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
2
2
2
0
0
0
2
0
0
0
0
0
0
1
2
3
1
2
0
0
0
0
2
2
0
1
0
3
2
0
0
1
0
0
1
0
2
0
2
2
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
2
0
0
1
3
1
2
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
1
1
1
2
0
0
0
0
2
1
0
2
0
0
1
2
0
0
0
1
0
1
0
0
1
2
2
2
0
0
2
0
0
0
0
2
1
0
0
0
0
0
1
0
1
0
0
0
2
0
0
1
3
2
0
0
1
0
0
0
2
2
1
0
0
2
0
0
2
0
1
0
0
1
1
1
1
1
2
0
0
1
0
0
0
0
0
0
2
0
0
0
2
1
0
1
0
0
0
0
2
0
0
1
2
2
0
0
1
1
2
0
0
0
0
2
2
1
1
0
1
0
0
0
3
1
0
0
0
2
0
0
0
0
2
0
1
2
0
0
0
0
2
0
0
2
0
0
1
0
1
0
2
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
2
1
1
1
1
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
2
0
2
1
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
1
1
2
0
2
2
2
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
5
0
0
0
0
0
1
0
0
1
1
0
0
0
2
1
2
2
0
0
0
0
2
0
0
3
0
2
0
0
0
1
0
0
0
1
1
0
2
1
0
0
0
0
2
0
2
0
2
0
0
2
0
3
1
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
2
2
1
0
2
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
1
0
2
2
0
0
1
2
0
2
2
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
1
2
0
0
0
1
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
1
2
1
0
0
0
4
0
1
1
0
0
0
2
2
3
2
1
0
0
0
2
0
1
1
0
0
0
2
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
1
2
0
0
0
0
2
0
0
0
0
0
2
1
1
0
0
0
0
0
4
2
0
0
2
0
0
0
1
3
0
0
0
2
0
0
1
1
0
2
0
0
0
1
0
0
2
0
0
0
0
5
1
1
0
2
0
2
0
1
3
0
1
2
0
2
2
0
0
2
0
0
0
0
0
0
2
1
0
1
0
0
1
0
0
2
0
0
3
1
0
2
0
0
3
0
0
0
0
3
0
2
0
1
0
0
0
1
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
2
3
2
2
0
1
2
0
0
0
0
2
1
0
0
2
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
1
3
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
1
1
3
0
0
1
0
0
1
0
1
0
0
1
1
1
0
0
0
1
0
0
0
1
2
4
2
0
2
0
1
2
0
0
0
1
1
0
2
0
0
1
3
1
0
2
1
0
0
0
0
0
2
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
2
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
4
0
1
1
0
1
2
0
0
1
0
0
0
2
0
0
0
0
1
0
1
0
2
1
0
0
1
0
0
0
1
1
0
0
0
1
1
0
0
0
2
0
0
1
0
0
3
1
0
4
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
3
0
0
0
0
2
2
2
0
1
1
0
0
0
0
0
0
0
0
0
2
0
2
1
0
1
1
0
1
1
2
2
0
0
0
1
0
2
0
1
1
0
3
0
0
0
1
2
2
1
2
1
0
1
0
2
1
0
0
0
1
0
2
0
0
2
2
0
2
0
0
0
0
1
2
1
1
1
1
0
0
0
0
0
1
0
0
2
0
1
1
0
0
0
0
0
0
1
3
1
0
0
2
1
1
2
2
0
1
0
2
1
1
2
0
2
0
5
0
0
0
0
2
0
0
2
0
1
0
0
0
2
0
2
0
0
1
0
0
1
0
0
2
0
0
0
2
0
0
3
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
1
2
1
3
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
2
0
2
1
3
0
3
2
1
1
0
1
0
0
1
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
1
0
2
0
0
1
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
1
0
0
3
2
0
1
2
0
0
0
1
0
0
2
0
2
0
0
0
0
0
1
0
0
0
1
1
0
2
0
1
0
0
0
0
0
0
1
0
2
2
2
0
0
2
0
0
2
0
0
2
0
0
2
1
0
2
0
0
1
1
0
0
2
0
0
2
0
2
0
0
1
0
0
0
0
2
2
0
0
0
0
0
1
0
0
3
0
2
0
0
0
0
1
1
0
2
0
0
0
2
0
1
0
0
0
2
0
1
0
2
0
0
0
0
0
1
0
0
1
0
1
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
2
1
0
3
0
0
0
2
0
0
0
2
2
2
0
0
2
2
2
1
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
1
0
0
0
2
0
2
2
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
2
0
0
0
0
2
0
0
2
1
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
3
1
0
1
2
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
2
1
2
2
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
2
0
0
1
2
0
0
0
0
1
0
0
2
1
1
0
0
2
2
0
1
2
1
3
1
0
1
0
0
0
2
0
0
0
2
0
0
2
0
2
0
0
0
2
0
1
0
1
1
1
0
2
0
0
3
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
2
0
1
1
0
2
0
0
0
2
0
1
0
0
0
0
1
2
0
0
1
4
0
0
2
1
0
1
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
2
1
2
2
0
1
0
0
0
1
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
2
0
0
2
1
0
2
0
0
0
0
0
0
1
0
0
2
1
0
0
0
1
1
0
0
0
0
0
3
2
0
3
0
0
0
2
2
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
2
1
0
0
0
0
1
0
2
0
3
2
0
2
1
1
3
0
0
2
0
0
0
0
0
2
0
1
1
1
0
0
0
0
0
1
0
2
1
0
0
0
0
0
1
2
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
2
0
0
0
2
0
0
2
0
0
0
0
0
0
1
2
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
2
0
0
1
0
0
2
2
0
2
2
0
0
0
0
2
3
0
2
2
0
0
0
0
2
2
0
0
1
0
3
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
2
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
2
2
0
0
0
0
0
2
1
2
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
1
1
0
0
0
0
1
1
1
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
1
1
1
0
0
0
2
1
0
2
0
0
0
0
0
0
1
0
0
1
1
2
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
1
1
1
1
0
1
0
0
1
0
0
2
1
0
0
1
1
3
2
0
0
2
0
1
1
0
0
0
0
2
2
2
0
0
0
0
1
1
0
0
2
1
1
0
1
0
0
0
0
1
0
1
0
0
0
2
0
0
0
4
0
0
1
2
2
4
1
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
3
0
0
0
1
0
2
2
0
2
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
2
1
0
1
0
0
1
0
0
0
0
0
1
1
1
0
0
0
2
0
1
0
0
0
1
2
1
1
1
1
0
3
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
2
2
0
1
0
0
0
0
2
2
0
0
2
1
0
0
0
0
1
1
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
1
0
2
1
0
0
0
0
0
2
0
1
0
0
0
1
0
0
2
2
0
0
0
0
0
1
3
2
0
1
1
0
0
0
0
0
2
0
3
0
0
2
1
1
0
0
1
0
0
0
0
0
2
0
1
1
0
0
2
0
0
1
0
8
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
7
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
2
0
1
0
1
0
0
0
0
2
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
1
2
0
1
1
1
0
0
1
0
0
0
0
0
0
2
1
1
0
2
0
1
1
2
0
0
1
0
0
1
0
1
2
0
0
1
2
1
0
0
0
0
1
1
0
1
2
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
3
0
0
3
2
0
0
0
0
0
1
1
0
1
0
1
3
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
4
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
1
0
2
3
0
1
1
0
0
0
1
0
0
1
0
4
0
2
0
0
0
0
3
2
0
0
1
2
0
1
2
2
0
2
0
0
1
0
0
1
0
0
0
1
0
0
3
2
2
2
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
1
0
0
1
1
0
0
0
1
1
0
0
1
0
2
0
2
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
2
1
2
1
0
0
0
0
0
1
1
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
3
0
0
0
0
0
0
1
0
3
0
0
0
0
2
0
0
0
0
0
0
2
1
0
2
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
1
0
1
0
2
2
0
2
0
1
0
1
2
1
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
1
1
2
1
2
0
0
0
0
0
0
1
0
0
2
0
2
0
2
0
0
2
0
0
0
2
2
0
0
0
0
2
1
0
2
1
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
2
2
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
3
2
0
2
0
0
0
0
0
0
0
3
1
2
1
2
0
0
4
0
0
0
0
0
1
0
0
2
0
0
0
1
1
0
0
0
1
0
0
0
2
0
2
0
0
0
2
0
0
1
1
2
1
0
1
0
1
0
2
3
2
0
1
1
2
0
1
0
0
0
0
0
1
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
2
0
0
2
2
1
0
0
0
0
0
0
0
0
0
2
0
1
2
0
1
0
0
0
0
2
1
0
1
2
0
2
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
3
0
0
0
0
0
0
2
0
1
0
1
2
0
0
0
1
0
1
0
2
1
0
0
0
0
0
0
0
1
1
0
0
0
2
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
1
0
0
0
2
0
1
0
0
0
0
1
0
2
0
0
1
0
1
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
2
1
0
0
1
2
0
0
1
0
1
0
0
0
0
0
0
2
1
0
2
2
2
0
0
0
2
1
1
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
1
2
0
0
0
0
0
1
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
2
2
2
0
1
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
3
1
0
0
0
1
2
2
1
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
1
2
0
0
2
1
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
4
0
1
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
2
2
0
1
0
1
1
0
2
1
0
0
0
1
2
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
2
0
0
0
0
1
1
2
1
0
0
0
0
2
2
0
0
2
0
0
2
2
2
2
1
2
0
2
0
3
0
1
0
1
0
2
0
0
1
4
0
0
2
2
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
2
3
0
2
1
0
2
0
1
1
0
1
1
0
0
2
1
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
1
0
2
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
5
0
0
1
0
2
3
0
1
0
2
0
1
0
0
0
0
2
0
0
3
2
0
1
0
3
0
0
2
0
0
0
2
0
0
0
1
2
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
3
0
1
2
0
0
0
0
0
1
2
0
1
0
0
1
2
0
1
1
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
3
0
1
1
0
0
0
0
0
0
1
2
1
0
0
2
0
0
0
0
2
0
0
1
1
0
0
2
0
0
0
0
0
2
0
0
0
2
1
0
1
0
0
0
0
0
2
1
0
0
0
0
2
0
1
2
1
0
2
0
0
0
0
1
1
1
0
0
2
1
1
0
0
0
0
0
2
0
0
2
1
2
3
1
0
0
0
0
0
0
0
2
0
2
4
0
0
0
1
0
2
0
0
0
0
3
0
1
0
3
0
0
0
1
0
0
0
0
3
0
0
0
0
0
1
2
0
0
1
0
0
0
0
2
1
2
2
2
2
3
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
2
0
1
0
0
0
1
0
1
0
1
2
0
0
2
1
0
0
0
1
0
1
1
2
0
0
1
0
0
0
0
0
0
0
1
2
0
2
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
2
2
2
2
1
0
0
1
1
0
0
1
0
0
0
1
0
1
2
0
1
0
2
0
1
0
3
2
0
0
1
1
2
0
0
0
3
1
0
0
0
0
0
0
1
0
1
0
0
1
0
2
1
2
0
1
0
0
2
2
0
1
0
0
0
0
0
1
0
0
1
4
0
0
2
0
2
0
0
2
0
2
0
0
0
1
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
1
2
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
4
0
0
0
0
0
0
0
1
1
0
2
0
1
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
1
0
3
0
0
0
0
0
0
2
0
2
0
0
0
1
2
0
1
3
1
0
0
2
0
0
0
2
1
1
0
1
0
0
0
0
0
1
2
2
0
3
0
0
0
1
0
0
0
0
1
1
0
0
1
1
0
1
1
3
0
0
0
0
1
2
2
1
0
0
2
0
2
0
0
0
3
0
4
0
0
0
0
0
0
0
0
0
0
2
1
2
0
2
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
1
2
2
0
0
1
1
0
0
0
2
0
1
0
0
0
1
0
0
0
0
1
0
3
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
1
0
1
0
0
1
2
1
1
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
1
2
0
0
0
1
0
0
0
0
2
2
1
0
1
0
0
2
2
0
2
0
1
0
0
2
0
0
1
1
0
1
0
0
0
1
2
2
2
2
2
0
0
1
0
0
2
0
0
0
2
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
1
0
0
2
1
0
1
1
0
0
0
0
0
0
7
0
0
0
0
1
0
1
0
1
0
2
0
2
2
1
1
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
1
2
0
0
0
2
0
3
0
0
0
0
2
2
0
1
0
2
0
0
0
1
0
1
0
1
0
1
2
0
0
1
2
0
1
1
0
1
3
2
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
1
0
0
0
0
0
0
2
2
0
2
0
2
0
0
0
2
0
0
0
0
0
1
2
2
0
1
0
0
1
0
5
0
5
0
2
0
2
0
1
0
1
0
0
0
3
0
1
0
1
0
2
0
0
0
1
0
0
3
0
1
0
0
1
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
1
2
0
0
1
0
0
0
2
0
2
0
0
0
0
1
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
2
0
1
2
0
0
4
0
2
2
0
0
0
0
0
0
0
0
0
0
0
9
0
0
1
0
0
1
0
0
0
0
2
0
0
1
0
0
1
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
2
2
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
2
0
1
2
2
2
2
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
1
1
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
1
1
1
0
0
2
2
0
0
0
0
3
2
0
1
2
0
1
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
2
0
0
1
0
0
2
2
2
0
0
0
2
0
2
0
2
0
0
0
2
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
1
0
2
0
0
0
0
0
2
1
0
0
0
0
0
3
0
0
0
0
0
1
1
1
0
2
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
2
1
1
0
2
0
0
2
0
0
2
0
0
0
0
0
1
1
0
1
2
1
2
1
1
0
1
2
1
0
0
1
2
0
2
2
0
0
2
0
2
1
2
2
0
0
0
0
0
0
3
0
0
0
0
1
3
0
2
4
0
0
1
0
0
0
0
2
0
0
1
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
1
0
2
0
0
1
1
0
0
1
0
0
2
0
0
0
1
0
0
0
2
0
0
0
2
0
0
1
2
1
0
2
0
0
0
11
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
2
1
1
0
0
0
0
0
0
2
0
2
0
2
0
0
0
2
0
2
0
0
0
0
0
1
0
23
0
0
2
0
1
0
2
1
2
0
2
1
2
0
0
0
6
2
0
0
0
0
0
0
1
0
2
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
2
2
0
4
0
2
1
2
0
0
2
0
2
0
2
2
0
1
1
0
0
0
0
0
1
0
0
1
0
0
1
2
2
0
0
2
0
2
0
0
0
0
0
0
0
3
0
0
1
2
0
0
0
2
0
0
0
0
0
0
2
2
2
0
0
2
0
0
0
1
0
0
0
0
2
0
1
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
2
0
0
0
0
2
0
0
0
0
2
2
1
1
0
2
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
1
0
1
0
2
0
0
1
0
0
0
2
1
0
0
0
1
2
1
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
1
7
2
0
4
0
0
1
8
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
2
4
2
0
0
0
2
1
1
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
2
1
1
2
2
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
2
1
1
0
1
1
0
2
0
0
1
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
2
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
1
0
0
1
2
0
0
1
0
0
0
2
2
2
1
1
1
0
0
7
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
1
1
0
0
1
0
0
2
0
0
1
1
1
0
0
1
2
0
1
0
0
0
0
0
2
2
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
2
0
0
0
2
4
2
1
2
0
0
2
2
1
0
0
2
1
1
0
0
1
1
0
0
1
0
3
4
0
0
0
0
0
1
1
1
0
0
0
2
0
1
1
0
0
1
2
1
0
0
1
0
2
3
0
0
2
0
0
0
2
1
0
0
2
0
1
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
4
0
1
0
1
0
0
2
0
0
2
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
3
0
0
2
0
0
0
0
2
0
0
1
0
2
2
1
0
2
0
0
0
0
2
1
0
0
0
0
2
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
2
0
1
0
1
0
0
0
2
1
0
0
2
2
0
2
3
2
3
0
2
0
0
0
0
0
2
2
1
2
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
3
0
2
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
1
0
0
1
0
2
0
1
0
2
1
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
2
0
2
0
2
1
0
0
1
0
0
2
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
1
0
0
0
2
1
0
1
2
0
2
0
0
2
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
3
2
2
1
1
1
0
0
2
0
0
0
0
1
0
0
2
0
0
2
1
0
0
1
0
0
1
0
0
2
2
1
0
1
0
0
1
1
0
0
0
3
0
0
2
3
0
0
0
1
0
1
0
0
0
2
1
0
1
0
0
4
1
2
0
2
0
0
0
2
0
0
1
0
2
0
0
2
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
2
0
3
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
5
4
0
0
0
0
2
1
1
0
1
0
1
0
1
3
0
0
1
0
1
2
0
0
0
2
2
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
2
1
0
0
2
1
0
0
0
0
2
0
2
0
0
0
0
2
2
1
2
2
0
0
1
0
2
1
1
0
1
2
0
3
0
0
2
0
0
0
0
1
0
2
0
1
0
2
0
1
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
2
0
0
2
0
0
0
1
0
2
0
1
0
2
0
1
0
4
0
0
1
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
1
0
0
2
0
1
2
1
0
0
0
1
0
0
0
0
0
1
0
2
0
0
2
1
1
0
1
1
3
0
0
0
1
0
0
1
0
0
2
0
0
0
1
0
0
0
3
0
0
0
0
1
0
0
0
1
2
1
0
0
2
0
2
0
0
2
1
0
0
0
0
0
1
2
0
0
1
0
2
0
1
0
1
1
0
0
0
0
2
1
0
0
0
0
3
0
0
0
0
2
0
1
0
0
0
1
0
0
2
2
2
0
2
0
2
5
0
1
0
0
0
2
0
0
0
1
0
0
0
2
1
0
3
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
2
0
0
2
0
1
2
2
0
1
2
0
0
1
1
0
0
0
2
0
0
1
0
0
3
0
2
0
0
2
2
0
0
0
0
0
0
1
1
0
2
1
0
2
0
0
0
1
0
1
0
1
2
2
0
2
1
0
2
0
0
2
0
0
0
0
1
0
0
1
2
0
0
0
1
2
0
3
0
0
0
1
0
3
1
2
0
2
1
0
0
0
0
0
0
0
1
0
2
1
0
1
0
0
2
0
0
0
0
0
0
2
0
2
0
2
0
0
0
2
0
0
0
0
1
0
0
1
0
2
0
0
0
2
0
2
1
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
1
3
2
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
2
2
0
0
1
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
2
1
0
0
0
2
4
0
2
1
0
0
2
0
1
0
0
1
0
0
1
0
2
1
0
2
0
0
2
0
1
1
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
2
0
2
0
0
0
1
2
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
6
0
3
0
0
1
2
1
0
0
0
0
1
0
0
0
2
0
0
0
0
1
2
0
0
0
2
2
0
0
0
1
1
0
0
1
0
1
1
1
0
0
1
0
1
0
0
2
2
0
1
0
0
3
0
0
0
0
0
0
0
0
0
1
1
0
1
0
5
1
2
0
2
0
0
1
0
0
0
0
0
0
1
5
0
0
1
0
0
0
0
2
4
0
0
2
0
1
1
0
1
2
0
1
0
0
0
2
0
0
2
0
0
1
0
1
0
0
0
2
0
1
0
3
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
2
2
0
2
1
2
1
0
1
0
0
1
2
0
1
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
1
0
2
1
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
2
2
0
1
0
0
2
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
1
2
0
0
0
0
6
2
2
0
0
0
0
2
2
0
1
0
0
1
0
1
2
1
0
1
1
0
2
0
0
1
1
0
0
1
0
0
1
4
3
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
1
2
2
4
1
1
0
1
0
0
0
2
0
0
0
2
0
2
1
0
2
2
0
0
0
1
0
2
0
0
0
0
0
1
1
0
0
3
2
0
2
1
0
0
2
2
0
0
2
0
0
0
0
1
1
0
0
0
0
2
1
1
0
2
3
0
0
0
0
1
0
0
0
3
0
1
0
0
2
3
0
0
0
0
1
2
1
2
0
0
0
0
0
2
2
1
0
0
0
0
0
1
0
0
2
0
2
1
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
1
2
1
1
1
0
0
0
2
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
1
2
0
1
2
0
1
0
0
0
0
2
2
0
2
0
2
0
2
1
2
0
2
0
2
0
0
2
1
0
0
0
1
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
1
1
1
1
0
1
0
1
0
1
0
2
0
1
0
1
1
0
1
0
0
0
2
1
0
0
1
1
0
3
0
0
0
0
1
3
0
1
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
2
2
0
0
2
0
0
0
1
1
1
1
0
0
2
0
1
0
0
1
1
2
0
1
1
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
2
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
1
0
3
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
2
0
1
2
0
0
0
2
0
0
2
1
1
1
0
0
0
2
2
0
0
0
1
0
0
5
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
3
1
2
1
0
0
0
0
0
0
2
0
2
0
0
0
2
0
1
2
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
3
0
0
0
2
0
0
0
1
1
0
1
0
0
0
1
2
0
0
1
0
0
0
0
1
0
1
0
0
1
0
1
2
2
2
0
0
0
2
0
1
3
2
0
1
0
0
1
2
1
0
4
0
1
0
0
0
2
0
0
0
0
0
1
2
0
0
0
2
1
1
0
2
0
0
0
0
0
0
1
0
2
0
1
0
0
0
1
0
1
1
0
1
0
2
0
1
2
0
0
0
2
0
3
2
0
1
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
2
1
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
1
2
0
3
2
1
3
0
0
1
1
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
1
0
2
0
0
1
1
1
0
1
1
0
0
0
0
0
2
0
2
0
1
2
2
0
0
0
1
0
0
0
1
0
1
1
0
0
2
0
0
2
0
0
0
3
0
2
0
1
0
0
0
1
0
0
0
2
0
0
2
0
1
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
3
0
0
0
1
1
3
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
2
0
1
2
1
0
0
2
0
0
2
0
0
1
0
0
2
2
0
0
0
1
2
0
0
1
0
0
1
0
0
0
2
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
1
0
0
0
1
1
1
0
1
0
0
0
0
2
0
1
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
1
0
0
4
0
0
1
2
0
0
0
3
1
2
0
2
1
2
0
1
1
2
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
1
0
0
2
0
2
1
0
0
0
0
0
0
0
2
2
2
0
1
0
0
2
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
3
0
3
0
0
0
5
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
1
2
2
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
2
0
0
0
2
0
0
2
2
2
0
0
0
0
0
2
2
0
0
1
1
2
3
0
0
0
0
0
2
0
0
2
3
0
2
1
0
2
0
0
0
1
0
0
4
0
1
0
0
1
0
0
4
0
0
2
0
0
2
0
1
1
0
2
0
0
1
0
0
1
1
2
0
0
2
0
2
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
2
0
2
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
1
1
0
0
0
0
0
1
3
2
0
0
0
4
0
0
2
0
1
2
1
2
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
1
0
3
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
2
2
1
0
0
0
0
0
0
1
1
2
0
0
0
0
0
1
0
0
3
0
0
0
4
0
1
2
0
3
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
2
1
0
0
0
1
1
0
0
1
2
0
0
0
0
0
0
6
1
2
0
1
0
0
0
2
0
2
0
0
0
0
0
1
2
2
2
0
1
0
2
4
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
1
1
1
0
0
0
4
0
0
0
0
0
0
0
2
0
0
1
2
0
0
1
1
1
0
0
0
0
0
2
3
1
0
0
1
2
0
2
0
2
0
0
0
0
1
0
0
0
2
1
0
0
0
2
0
0
2
1
1
0
0
1
0
0
0
0
0
2
2
0
0
0
1
0
0
2
1
2
1
1
0
0
1
1
0
0
0
2
1
0
0
0
1
1
0
1
2
0
2
2
0
0
0
0
0
1
1
2
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
2
1
0
0
0
4
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
2
1
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
2
0
0
2
0
0
0
0
2
0
2
0
0
1
0
2
1
0
1
0
0
0
0
2
2
0
2
1
0
1
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
4
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
3
2
0
0
1
0
0
0
0
0
0
1
2
2
1
1
1
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
2
0
0
2
0
0
1
1
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
2
1
0
1
0
0
0
2
0
1
4
0
0
2
1
0
2
2
0
0
0
0
0
2
2
2
0
0
2
1
0
2
0
0
2
0
0
1
1
0
0
0
2
0
0
0
0
0
1
0
2
3
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
2
1
2
0
3
2
0
1
0
1
0
1
2
0
0
2
1
0
0
0
0
0
2
0
0
2
2
1
1
2
2
0
2
2
0
0
1
0
0
0
1
0
0
2
2
0
2
1
0
2
1
0
0
0
0
0
2
1
1
0
0
0
0
0
2
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
5
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
4
0
0
0
2
0
0
1
1
0
0
0
1
0
0
1
2
1
1
0
0
0
0
0
0
0
2
0
1
0
0
1
2
2
0
0
0
1
1
1
0
1
0
2
0
0
0
0
0
0
0
0
1
2
0
0
2
0
2
1
0
0
1
0
1
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
1
2
0
0
1
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
3
0
0
2
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
2
0
2
0
0
0
1
0
0
1
0
0
2
0
2
2
0
1
2
0
2
0
1
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
2
0
3
1
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
3
0
2
0
2
0
0
0
1
0
0
0
0
2
0
1
0
2
1
2
0
0
0
1
2
1
0
0
0
0
0
0
0
1
1
0
0
0
1
2
0
0
2
0
0
0
2
0
0
2
0
0
2
0
0
2
1
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
2
1
2
0
1
0
0
0
0
0
0
1
1
0
1
1
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
2
1
0
0
2
0
0
1
1
0
1
0
2
0
2
0
0
0
0
1
3
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
1
0
2
0
1
0
0
3
0
0
0
0
1
0
0
0
0
0
2
1
1
0
0
2
0
1
1
0
1
0
0
1
0
0
1
0
0
0
1
1
1
0
0
0
2
0
0
0
0
1
0
1
3
0
0
0
1
2
0
4
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
1
2
0
0
2
2
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
2
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
1
2
3
0
0
2
0
0
1
1
1
1
0
0
0
1
2
2
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
1
1
0
1
2
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
1
2
0
0
3
2
0
0
2
0
0
0
1
0
0
1
0
2
0
2
2
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
3
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
1
2
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
1
0
1
0
0
2
0
0
0
1
0
0
1
0
2
0
0
1
2
1
0
1
0
2
2
0
0
1
2
0
0
0
0
0
0
0
0
1
0
2
2
2
2
4
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
3
0
1
0
2
1
0
0
1
0
0
0
2
0
0
2
0
0
0
0
1
1
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
2
0
0
0
2
1
0
0
2
0
0
1
1
0
0
0
1
1
1
1
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
2
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
4
2
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
2
2
0
1
0
0
1
2
7
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
1
2
1
1
2
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
2
0
1
2
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
2
0
0
0
0
2
0
1
0
2
6
0
0
0
1
1
0
0
0
0
0
0
1
2
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
2
0
2
1
1
0
0
0
0
0
0
0
0
0
1
0
2
1
0
1
0
0
0
2
0
2
1
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
3
0
1
2
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
1
0
0
2
0
0
2
0
0
0
1
5
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
2
0
1
1
0
0
0
0
2
2
1
1
0
0
0
2
1
1
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
2
0
0
0
2
0
0
2
0
0
0
0
1
2
0
2
0
1
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
2
2
0
2
0
1
2
0
0
0
0
3
0
2
0
0
2
1
0
0
0
0
1
2
2
0
0
0
0
0
2
0
3
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
2
1
1
0
2
0
0
0
1
0
2
0
0
0
0
1
0
3
0
4
1
2
0
0
0
1
1
1
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
2
0
0
5
2
0
4
0
1
0
2
0
0
0
0
1
8
0
0
0
0
1
0
2
3
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
1
0
0
3
1
0
0
0
1
2
0
0
1
0
0
0
0
1
0
0
3
0
0
0
0
2
0
0
1
3
2
2
2
0
1
0
2
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
2
1
0
0
0
0
1
0
1
2
1
0
0
0
1
1
2
0
0
0
0
2
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
2
0
0
1
0
2
1
2
0
0
1
0
0
0
0
2
6
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
1
0
0
2
1
0
0
1
0
0
0
2
2
0
0
0
0
3
1
0
2
1
1
2
2
0
0
0
0
1
0
2
3
1
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
1
0
0
2
0
0
2
0
0
2
0
0
2
0
1
2
0
0
0
0
0
2
0
1
2
0
1
0
0
0
1
2
0
2
2
1
0
0
0
0
0
0
0
0
0
0
1
3
1
0
2
0
0
0
1
0
1
2
2
0
0
0
1
0
1
0
0
2
0
0
1
0
1
1
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
4
0
0
0
0
0
0
2
2
1
1
0
0
0
0
0
0
0
2
2
0
1
0
0
1
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
10
2
0
0
0
0
2
2
2
2
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
2
1
0
1
0
0
1
0
2
1
1
0
0
1
1
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
3
0
1
0
0
0
2
2
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
2
1
2
2
0
0
0
0
0
1
0
2
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
1
2
2
0
1
2
2
0
1
1
0
0
0
4
1
0
2
1
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
1
1
0
0
1
0
3
2
0
2
0
0
0
1
2
1
0
0
0
0
0
2
2
1
2
0
0
0
2
0
1
2
1
0
0
0
0
0
2
0
2
1
1
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
1
0
0
0
0
0
2
0
0
0
1
0
0
2
0
2
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
1
1
0
0
2
2
0
0
0
0
0
3
0
1
1
0
1
0
2
0
0
1
0
2
2
0
5
2
7
0
1
1
0
0
1
2
2
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
1
0
0
1
0
2
0
1
0
4
2
0
2
0
0
2
1
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
3
1
0
1
6
2
2
1
1
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
2
0
2
0
0
0
0
0
0
0
1
2
0
0
1
1
0
1
0
0
0
0
1
1
1
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
2
1
0
0
2
0
2
0
1
0
0
0
0
2
1
0
1
0
3
0
0
2
2
1
2
0
0
0
0
2
1
0
0
0
0
0
1
1
2
0
2
0
1
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
2
3
1
0
0
0
0
0
0
1
1
0
0
0
1
4
1
2
0
0
0
0
2
1
2
0
0
2
0
1
1
0
0
0
0
1
1
0
1
2
0
0
0
1
1
0
0
1
2
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
5
4
0
1
1
3
0
2
2
2
0
0
1
0
0
0
0
0
2
1
2
0
1
0
0
1
0
1
1
0
0
0
0
0
0
1
0
2
1
0
1
1
1
0
2
1
0
0
0
1
1
2
2
0
0
0
0
2
0
1
2
0
1
1
0
0
0
0
0
0
2
0
2
1
0
0
0
1
3
1
0
2
2
0
0
0
0
1
0
0
0
0
1
0
0
2
2
0
0
0
0
1
0
0
1
0
1
0
0
2
0
1
1
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
2
0
2
0
2
0
1
0
0
1
0
0
0
2
1
0
0
0
0
2
0
3
2
2
1
1
2
0
0
1
0
1
0
0
3
0
2
2
0
1
0
0
1
1
2
0
2
1
0
0
0
0
0
0
1
0
0
3
0
0
4
0
1
0
0
1
1
0
0
2
0
2
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
1
1
1
1
1
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
3
0
0
0
0
0
1
1
1
1
0
1
2
0
2
0
1
1
0
0
2
4
1
2
0
2
0
2
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
3
0
1
1
0
2
3
2
0
3
1
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
2
1
0
0
2
0
0
0
1
2
0
0
0
0
1
0
2
0
1
0
2
1
0
2
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
1
3
1
2
0
2
0
1
0
1
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
3
0
0
0
1
0
2
0
0
2
1
0
0
0
1
2
2
0
0
0
1
0
2
2
0
2
0
0
0
0
0
2
0
1
0
0
0
0
1
2
0
0
1
2
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
2
2
0
0
2
2
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
1
0
1
0
1
2
0
0
0
0
1
0
2
0
2
0
0
0
1
0
0
2
0
2
2
2
3
0
1
2
2
0
1
0
0
2
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
2
0
1
1
0
0
0
0
1
0
2
2
0
1
0
0
0
0
1
1
0
0
4
0
2
2
0
0
0
1
0
0
2
0
3
1
0
0
2
0
0
0
0
1
0
0
0
0
1
1
2
0
1
0
0
2
0
0
0
0
1
2
0
1
0
0
2
1
0
1
1
0
2
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
3
0
0
0
0
0
2
0
1
1
0
0
1
1
1
2
2
1
0
0
0
0
3
0
1
2
1
0
0
2
0
0
0
0
0
0
0
0
0
1
1
1
0
2
0
2
0
3
0
1
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
2
0
0
0
0
2
0
1
0
0
0
1
0
1
0
0
0
0
0
2
0
1
1
2
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
4
0
0
1
0
1
0
0
2
1
3
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
1
2
2
0
1
1
2
3
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
2
2
1
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
1
2
0
0
3
0
0
0
0
2
0
3
0
0
0
0
2
2
0
0
0
1
3
0
2
0
0
0
3
0
0
0
2
0
2
2
0
0
2
0
0
2
0
0
2
1
2
0
1
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
1
1
0
0
1
0
0
0
2
0
0
1
2
0
1
0
0
0
2
0
0
2
0
0
0
1
0
2
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
2
0
1
2
0
2
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
2
0
2
1
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
2
1
0
0
0
0
1
0
0
2
0
0
0
3
0
0
0
0
1
0
0
1
0
0
0
1
0
2
0
1
2
2
2
0
2
0
1
0
0
0
1
0
1
0
0
2
1
2
0
0
0
0
0
0
2
1
0
0
1
0
0
1
0
0
0
1
3
0
0
0
0
0
0
1
1
3
1
2
1
1
0
2
2
1
1
0
6
0
2
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
2
3
0
0
0
0
0
0
1
2
1
0
0
2
1
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
2
0
2
2
0
3
0
0
1
0
0
2
2
1
0
0
1
0
0
2
0
0
0
0
2
2
0
0
0
1
1
0
2
0
2
0
0
0
0
2
0
0
0
2
0
1
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
1
0
2
2
0
0
1
0
0
0
1
2
0
1
0
0
1
1
0
0
2
1
1
0
1
0
0
0
2
1
0
2
1
2
0
1
0
0
1
0
0
0
1
0
0
0
3
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
4
0
0
0
0
0
0
0
3
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
2
0
1
0
1
0
1
0
2
1
2
0
1
1
1
0
0
0
0
1
0
0
1
2
1
0
0
1
2
0
0
0
0
0
1
0
0
0
0
1
0
1
0
2
1
1
1
0
0
0
1
0
0
1
0
2
0
0
0
0
2
0
1
0
2
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
1
0
1
0
3
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
1
0
0
2
2
0
2
0
1
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
1
0
1
0
1
0
1
0
0
0
2
0
0
1
2
1
0
2
1
0
1
0
0
0
1
0
0
0
1
0
0
1
2
3
0
0
0
4
1
0
0
2
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
1
1
1
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
4
0
0
0
1
2
1
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
3
1
0
1
2
0
2
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
1
1
1
1
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
1
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
1
1
1
0
1
1
1
0
6
1
1
1
0
0
0
1
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
1
0
1
3
0
4
0
1
2
0
0
0
1
0
1
0
0
0
1
0
1
2
0
0
0
0
0
2
1
2
2
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
1
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
2
0
2
0
2
1
2
0
0
1
0
2
1
1
0
0
0
1
2
0
0
0
1
0
1
0
1
2
0
0
0
0
1
0
0
2
5
0
1
0
1
0
1
0
2
1
0
0
0
0
0
1
2
1
1
0
0
0
0
0
1
4
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
1
1
0
0
2
1
1
0
0
0
0
1
0
0
0
0
1
2
0
2
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
2
2
0
0
1
1
0
0
0
1
0
0
4
1
1
0
0
0
0
1
1
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
2
0
0
0
0
0
1
1
1
0
0
0
0
0
0
2
1
1
1
2
0
0
1
0
2
2
0
0
1
0
0
0
2
1
0
1
0
1
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
2
2
0
1
2
0
2
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
2
1
0
1
0
3
0
0
3
0
0
1
0
4
0
0
0
0
0
2
1
0
0
0
2
0
2
0
1
3
0
0
2
2
1
0
0
1
0
2
1
1
0
0
0
1
2
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
2
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
2
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
2
0
0
0
0
0
2
0
0
1
2
0
0
0
0
2
0
1
0
0
0
0
1
0
2
0
0
1
0
1
1
1
0
0
0
0
1
1
0
2
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
2
0
2
0
0
1
0
0
2
0
2
1
0
0
0
0
0
2
2
0
0
2
0
0
0
2
0
2
0
0
0
0
1
0
0
0
1
0
1
2
0
0
0
2
0
0
0
0
2
2
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
2
0
0
1
0
0
0
0
2
1
3
2
0
1
0
0
2
1
1
0
0
0
0
0
0
0
0
2
0
1
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
3
0
0
0
0
0
3
0
0
2
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
3
0
0
0
0
0
2
2
0
2
0
0
0
0
2
0
1
1
0
0
0
0
2
1
0
0
0
0
2
2
0
0
0
1
1
0
0
0
0
0
0
1
3
2
1
3
0
0
2
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
1
0
0
0
2
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
2
0
0
0
0
2
0
0
2
0
2
0
2
0
0
0
0
0
1
2
1
0
1
2
1
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
2
2
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
2
1
0
1
1
1
3
0
0
0
0
0
2
0
1
0
0
2
1
0
0
1
1
0
0
0
0
0
1
0
2
0
0
1
0
2
0
3
0
1
0
2
0
2
0
3
1
0
2
1
1
0
0
0
0
0
1
0
1
0
0
0
2
2
1
1
2
0
0
1
1
0
0
1
0
2
2
1
0
0
0
0
0
2
0
2
2
0
0
0
2
0
0
2
0
0
2
0
2
2
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
3
0
0
1
0
0
0
1
0
2
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
2
2
3
0
0
1
0
2
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
2
1
0
0
1
0
0
2
0
2
2
2
0
0
0
3
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
2
0
1
0
4
0
0
0
0
0
2
1
2
2
0
0
0
0
0
0
2
0
0
1
0
1
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
1
0
2
0
6
0
0
0
1
1
2
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
4
0
1
0
2
0
0
2
2
0
0
4
1
0
0
2
3
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
5
0
0
1
0
0
3
2
2
0
1
0
0
0
0
3
0
0
0
0
0
1
0
0
0
2
0
1
0
2
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
2
4
3
0
1
0
0
2
0
1
0
0
1
1
0
2
1
0
0
2
1
0
0
0
0
1
2
0
1
1
2
0
0
0
2
2
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
2
1
0
0
1
0
0
1
0
1
0
3
1
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
1
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
2
1
2
1
0
0
1
0
0
1
0
0
2
1
1
9
2
2
1
0
2
0
0
2
1
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
2
1
1
0
0
1
0
0
0
2
0
2
0
1
0
0
0
2
1
2
0
0
0
2
1
1
0
0
0
0
1
1
0
1
0
1
0
0
1
0
2
1
2
0
2
4
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
1
0
1
0
1
2
0
0
1
1
0
0
0
2
2
0
1
0
0
1
0
0
2
0
0
3
2
0
0
2
1
2
1
0
0
0
0
0
1
1
1
0
2
2
0
0
1
0
2
2
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
2
0
0
0
1
1
3
0
2
0
0
0
0
0
0
0
2
1
2
0
1
0
1
0
1
1
0
0
2
2
1
1
2
0
0
0
0
1
1
0
1
2
2
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
2
0
1
0
2
0
0
0
1
0
2
1
0
0
2
0
0
2
0
0
0
2
0
0
0
0
2
2
1
0
0
0
0
0
1
2
2
0
0
0
0
1
0
2
0
0
1
0
0
0
1
2
0
1
0
2
0
4
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
2
2
0
2
0
2
0
0
0
0
1
0
2
1
0
0
0
2
0
0
0
0
0
0
0
4
1
2
0
2
2
1
0
1
2
1
0
1
1
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
1
2
0
0
0
0
0
0
2
2
1
0
0
2
1
0
0
0
0
2
0
1
2
2
0
2
0
0
0
0
0
2
0
0
0
0
0
1
2
0
1
0
0
2
0
0
0
0
0
4
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
2
0
0
0
0
2
0
0
0
2
0
1
0
2
1
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
2
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
1
1
2
2
0
0
2
0
0
0
0
2
1
1
0
0
0
0
0
2
0
1
1
0
0
0
1
3
2
2
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
1
0
2
0
0
2
0
0
0
0
0
2
1
0
1
0
0
0
1
0
0
0
2
0
0
2
0
3
3
2
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
1
1
0
1
0
1
2
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
2
0
1
0
0
0
0
2
2
0
2
2
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
3
0
2
0
2
0
1
0
0
1
0
0
2
3
1
0
0
0
0
0
2
0
2
0
0
1
0
0
2
1
0
0
2
0
3
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
1
0
1
0
0
0
1
0
0
0
2
0
0
2
1
0
0
1
0
0
0
1
0
0
0
1
0
1
2
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
2
0
2
1
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
4
0
0
2
1
0
0
0
1
0
0
0
3
2
0
0
0
3
0
1
0
2
0
4
2
0
0
0
2
0
2
0
2
1
2
1
3
2
1
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
3
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
2
2
0
2
0
0
1
0
0
1
1
1
1
1
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
2
1
0
1
0
0
3
0
1
0
0
0
0
0
4
0
2
2
1
0
0
2
0
0
0
0
1
0
0
2
0
0
1
2
2
0
1
0
0
0
0
0
0
2
2
0
2
0
0
0
2
2
0
2
0
0
1
0
1
2
1
0
0
0
1
0
0
0
1
0
1
0
1
0
3
0
0
0
0
2
0
0
0
0
4
2
2
1
2
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
2
1
1
0
0
0
2
1
1
2
14
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
1
2
2
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
3
0
2
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
1
1
4
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
1
1
1
1
0
0
0
2
2
1
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
1
0
2
0
1
0
0
0
0
0
1
0
0
1
1
0
2
0
2
1
0
0
0
1
0
0
0
0
2
0
1
0
0
0
1
1
3
0
0
1
0
2
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
2
0
0
0
0
3
2
0
1
0
1
0
0
0
2
2
0
0
0
2
1
1
0
1
1
1
2
1
1
1
0
0
0
0
3
1
2
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
1
1
0
0
0
0
1
0
0
0
2
1
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
1
2
0
1
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
4
0
1
0
0
2
0
0
0
1
3
2
1
2
1
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
2
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
2
1
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
1
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
1
0
2
0
0
0
0
0
1
1
0
2
0
0
0
0
1
0
2
0
1
2
0
0
0
2
0
1
0
2
2
1
0
0
0
0
1
2
0
3
0
0
0
2
0
2
1
0
0
0
0
0
0
2
0
2
0
1
1
0
1
2
1
0
0
1
0
0
0
3
0
2
0
0
2
0
0
1
0
0
1
0
0
1
0
0
4
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
1
2
1
1
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
1
0
1
1
0
0
0
2
2
0
0
0
2
0
0
0
1
0
1
2
1
2
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
1
1
0
0
0
0
2
0
2
2
1
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
3
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
1
2
0
1
0
0
0
2
1
1
0
0
1
1
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
1
1
1
2
2
2
1
0
2
0
0
2
0
0
1
0
2
2
0
0
0
1
0
0
6
0
0
1
0
1
0
0
0
1
0
2
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
1
2
0
1
1
0
0
1
0
1
0
0
0
0
0
0
5
0
0
0
0
1
0
0
2
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
1
0
0
1
0
0
0
2
2
0
2
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
2
2
0
1
0
0
2
0
2
0
2
0
0
0
3
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
1
2
1
0
0
0
1
6
0
2
0
0
0
0
1
0
0
2
4
0
1
0
0
1
1
2
0
0
0
2
2
0
0
0
0
1
0
1
1
0
1
0
0
0
0
2
0
0
0
3
0
0
0
0
1
0
0
0
0
2
1
0
0
0
1
0
0
1
0
0
2
0
1
0
0
0
0
1
0
3
2
1
0
0
2
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
1
0
2
0
2
0
0
2
3
2
0
2
3
0
0
2
0
0
0
0
2
0
2
0
1
3
0
1
0
0
1
0
0
0
0
0
4
1
1
1
0
0
2
0
0
0
2
2
1
0
0
1
0
2
0
1
2
0
0
2
0
0
1
0
1
0
1
0
0
1
0
3
2
2
0
0
0
2
1
0
2
0
0
0
0
0
1
1
1
1
0
0
0
1
1
2
1
0
3
1
0
1
2
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
2
0
1
0
0
2
1
0
2
1
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
1
2
1
0
0
2
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
2
0
0
2
0
4
0
0
0
2
0
0
0
0
2
2
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
1
2
0
1
0
0
2
2
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
2
0
1
2
2
0
1
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
1
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
6
1
0
2
0
1
0
0
0
1
1
0
1
2
2
0
1
0
0
0
0
2
0
2
2
0
0
0
0
2
2
0
1
1
2
1
0
0
0
2
0
1
2
2
1
1
2
0
0
0
1
3
0
0
0
0
0
0
0
0
1
0
0
1
0
2
2
0
1
1
1
0
1
1
1
2
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
1
0
2
0
1
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
1
0
3
0
1
2
1
0
2
0
0
0
1
1
2
0
0
1
0
1
0
0
0
0
2
0
0
1
0
0
2
2
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
2
0
1
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
1
2
2
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
2
0
0
2
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
2
0
0
1
1
0
1
0
0
2
7
1
0
2
0
0
2
0
1
0
2
0
2
1
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
1
0
1
0
1
0
2
0
0
0
0
0
3
2
1
0
2
0
0
0
0
0
2
1
0
1
2
0
0
1
2
0
0
0
1
2
2
0
0
2
1
0
0
0
0
1
2
0
0
0
0
0
0
0
2
1
1
0
0
0
1
0
2
0
1
2
2
0
0
0
0
0
0
1
1
0
1
2
2
0
0
0
2
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
2
0
0
0
1
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
2
0
1
0
0
0
0
0
0
0
2
2
2
0
0
2
0
1
0
2
0
1
1
1
1
1
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
2
1
2
0
0
0
1
0
2
0
0
2
1
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
1
0
0
0
3
1
0
1
1
0
1
0
0
2
2
1
0
0
0
1
0
1
0
0
0
0
2
0
0
2
0
0
0
1
2
1
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
3
0
1
1
0
0
2
0
0
0
0
0
2
0
0
1
0
0
1
2
0
2
0
0
2
2
1
0
0
1
0
0
0
1
1
1
0
0
0
1
0
1
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
1
1
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
4
0
1
1
0
0
2
1
0
0
2
0
0
0
0
3
0
0
0
0
2
0
0
2
1
0
1
0
3
1
0
2
0
0
0
0
0
0
0
0
1
0
0
3
1
0
0
2
0
0
0
2
0
1
0
1
2
0
0
0
0
0
3
2
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
1
0
0
1
0
9
2
0
3
1
0
2
0
0
0
0
3
0
1
2
0
0
0
3
0
0
2
0
1
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
2
1
0
2
0
1
0
0
2
0
2
0
1
1
0
3
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
1
0
0
0
2
0
2
3
0
0
0
0
3
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
2
2
1
1
2
0
1
1
1
1
0
0
0
1
0
0
0
0
0
2
1
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
2
1
1
0
2
0
0
2
0
1
0
0
0
2
0
2
0
2
2
0
0
0
0
2
0
3
0
2
2
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
7
0
1
0
0
0
0
0
0
0
0
1
1
2
0
0
2
0
1
0
0
3
0
0
2
0
0
0
0
0
0
0
1
0
2
0
1
0
2
2
0
0
0
0
0
0
2
1
0
0
0
0
1
2
2
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
2
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
1
2
0
0
1
0
0
0
0
0
0
2
0
0
2
1
0
1
0
0
0
0
1
0
0
2
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
1
0
0
0
0
4
0
2
0
0
0
2
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
4
0
0
2
0
3
0
0
0
2
2
0
2
1
2
1
0
1
0
0
0
1
0
2
0
0
3
1
1
0
4
0
0
1
1
0
0
0
2
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
1
1
2
2
0
2
0
0
0
1
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
2
0
1
0
0
1
0
2
2
0
0
0
3
0
0
2
1
0
0
0
2
3
1
0
0
2
0
0
0
1
2
0
0
0
1
2
0
0
0
1
0
2
0
0
0
2
0
0
2
0
0
0
0
1
0
1
0
0
2
9
0
0
0
1
0
0
1
0
0
0
1
0
2
1
0
0
0
1
0
0
0
4
0
2
0
1
0
0
0
0
1
7
0
1
1
1
0
0
0
0
0
0
0
0
1
2
1
2
2
0
0
0
0
1
0
0
1
0
2
2
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
3
0
1
0
1
0
0
2
0
2
0
0
0
0
1
2
0
0
0
0
0
2
0
0
2
1
0
0
3
1
1
0
1
0
0
0
0
0
2
0
1
1
0
3
0
0
1
1
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
1
2
0
0
0
0
2
0
0
1
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
2
3
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
2
0
0
1
0
0
0
2
0
0
1
0
0
0
1
2
0
0
2
0
2
0
0
0
2
0
1
0
0
0
0
0
4
1
0
1
0
0
0
0
0
0
0
0
2
0
2
0
3
0
1
0
2
0
0
0
3
0
0
0
0
0
2
0
2
1
0
0
1
1
0
0
0
1
2
0
2
3
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
2
0
1
1
0
0
2
1
0
0
0
2
1
0
1
0
0
2
0
2
0
2
0
3
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
2
1
1
1
2
0
0
0
1
0
1
1
2
1
1
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
2
2
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
2
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
1
2
0
0
0
5
2
1
0
1
0
2
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
1
0
2
2
1
0
0
0
2
0
2
0
2
0
1
0
0
0
5
0
0
2
2
1
2
0
0
0
2
0
0
1
0
0
0
0
2
1
1
0
0
0
0
1
1
0
0
3
1
0
1
2
1
0
1
0
1
0
0
0
0
0
2
0
2
2
0
2
0
0
0
2
1
0
0
0
0
0
0
1
0
2
1
0
0
0
2
2
0
2
0
1
0
0
1
1
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
2
0
1
2
1
0
0
0
2
2
0
3
2
0
1
0
0
0
1
0
0
1
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
2
2
3
1
0
2
1
0
0
0
0
0
0
2
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
3
2
2
0
0
2
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
2
1
1
0
0
0
0
1
1
0
0
0
1
0
2
0
0
0
2
0
1
0
1
0
0
2
0
0
1
3
2
1
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
4
1
0
0
2
2
0
2
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
1
1
0
0
2
2
1
1
0
0
1
2
0
1
2
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
2
1
0
2
0
2
0
0
1
1
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
1
2
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
2
0
2
1
0
2
0
0
2
1
0
0
0
4
1
2
1
2
2
0
0
1
1
0
0
2
0
0
0
0
1
0
0
1
0
0
1
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
2
0
2
0
0
0
1
1
2
1
0
2
0
2
0
0
0
1
0
2
2
4
0
0
1
0
0
0
2
0
1
0
2
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
2
0
1
2
0
0
1
3
1
1
0
2
0
1
0
0
0
0
0
0
2
0
0
0
1
0
2
2
0
0
0
0
2
0
0
1
0
0
1
1
0
0
1
1
0
1
0
0
0
0
0
1
0
1
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
3
0
0
0
0
1
1
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
1
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
2
2
1
0
2
0
0
2
0
2
0
2
0
1
0
0
0
0
2
2
1
0
2
0
0
0
2
1
0
0
0
2
0
0
0
0
0
2
1
2
0
1
1
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
2
2
0
2
0
0
4
2
0
0
2
0
0
0
0
0
0
0
1
0
1
2
0
0
2
0
0
1
2
0
0
2
1
0
1
0
0
0
1
2
0
1
0
0
3
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
2
0
1
1
0
0
1
2
0
0
1
0
0
0
0
0
2
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
2
0
5
3
2
0
0
0
0
0
2
0
0
2
0
0
1
0
2
0
0
1
2
1
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
2
4
1
0
2
1
0
1
0
0
1
2
2
0
0
0
0
0
0
3
0
0
0
1
0
2
1
2
1
1
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
2
2
1
0
0
0
0
0
0
1
0
1
0
1
2
0
2
2
0
3
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
1
0
0
0
0
0
3
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
2
2
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
1
2
0
2
0
2
1
0
0
0
0
0
0
0
1
0
2
0
2
1
0
0
0
1
2
0
0
0
0
0
1
0
1
1
2
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
1
0
0
1
1
1
1
0
1
0
0
0
0
0
2
2
1
1
2
0
1
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
2
0
1
1
2
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
1
0
0
0
0
0
2
0
0
1
0
0
1
2
1
0
0
1
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
1
0
0
0
4
2
0
0
0
1
0
0
0
1
0
0
2
1
0
1
0
0
1
0
0
1
0
0
0
2
1
2
0
1
2
13
0
0
0
0
0
2
2
0
1
0
0
1
0
0
2
2
2
1
1
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
2
0
1
0
0
2
1
0
0
0
1
0
2
0
1
1
0
2
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
1
2
0
0
0
0
0
2
0
2
0
0
0
2
1
3
0
0
0
0
1
1
0
2
0
1
0
1
0
2
0
1
2
0
1
0
0
0
3
0
0
2
0
9
0
0
0
0
0
1
0
2
0
0
0
1
1
0
1
2
1
0
0
1
0
3
0
1
0
0
2
2
2
0
0
0
2
0
1
2
0
0
0
1
0
1
1
0
0
1
0
1
1
0
2
0
0
1
1
0
0
0
0
3
0
0
0
0
0
1
2
2
2
0
1
1
3
0
1
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
1
0
1
3
0
1
7
1
2
0
0
2
0
0
0
0
2
1
0
0
0
2
2
0
2
0
1
0
0
0
0
0
4
0
0
1
1
0
0
2
0
0
0
0
2
0
0
1
2
0
0
0
2
1
0
2
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
1
0
2
0
0
0
1
2
1
1
0
1
0
0
0
0
2
1
2
0
0
2
0
0
1
2
0
2
0
1
0
1
0
0
0
1
1
0
1
2
0
0
2
0
0
2
0
1
0
0
2
0
0
0
1
0
2
0
0
2
0
0
1
0
0
2
1
0
1
0
2
0
1
0
0
0
0
2
0
0
0
0
2
0
2
0
0
1
0
2
0
0
0
2
0
2
0
1
0
0
0
1
2
2
0
3
0
0
0
0
1
0
0
1
2
0
0
1
2
0
0
0
0
1
2
0
0
0
0
1
2
2
1
0
0
0
2
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
3
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
2
0
2
0
0
0
0
0
0
0
1
1
0
2
0
0
0
1
0
0
2
0
2
2
0
0
1
4
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
1
2
2
1
0
1
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
1
0
0
0
1
0
6
0
0
0
0
0
0
5
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
1
2
1
1
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
1
0
0
2
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
2
3
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
2
1
1
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
2
0
0
2
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
3
1
2
2
0
1
0
0
0
2
2
0
0
0
1
0
2
1
1
2
0
2
0
2
0
2
0
0
3
0
2
0
0
0
2
0
2
2
3
1
0
1
0
0
0
0
8
2
2
2
0
0
0
0
0
0
1
2
0
0
2
2
2
2
0
4
1
0
0
2
0
2
2
1
0
0
0
0
1
1
1
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
1
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
1
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
2
0
0
1
0
0
0
2
0
0
0
2
0
1
0
1
0
2
0
1
0
2
0
0
1
0
0
4
1
0
0
0
0
0
2
0
0
0
1
0
0
2
2
0
0
2
2
2
2
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
2
1
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
2
1
0
2
0
2
1
0
1
0
0
0
0
0
0
1
0
2
2
0
2
2
2
0
1
2
0
0
0
0
1
2
0
0
1
0
0
0
1
2
0
2
1
0
0
0
0
0
0
0
1
3
0
0
0
2
0
2
0
2
0
5
2
2
0
0
1
0
0
0
1
0
1
0
2
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
1
1
0
0
0
1
2
0
0
0
0
2
0
0
2
0
0
1
2
1
2
0
0
0
1
2
0
2
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
1
1
0
1
0
0
0
0
0
0
0
2
0
1
1
0
0
1
2
1
0
0
0
2
2
0
2
2
0
0
3
0
0
0
0
2
1
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
2
0
2
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
1
0
0
0
0
1
0
0
2
1
0
1
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
1
0
0
0
1
0
0
0
1
0
1
1
0
0
0
2
1
0
1
0
1
0
1
0
0
2
0
0
1
0
1
0
0
1
0
1
0
0
0
0
1
2
1
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
1
2
1
1
0
2
1
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
2
0
1
0
0
1
2
1
0
0
0
0
0
1
0
0
0
0
0
1
6
0
0
2
0
1
1
0
2
0
0
1
0
2
2
2
2
0
0
1
0
0
2
3
1
0
2
0
0
2
0
0
4
0
0
1
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
2
0
0
0
7
1
0
2
1
2
0
1
2
0
0
1
0
0
1
0
1
0
0
2
1
2
0
0
1
0
0
0
0
0
1
1
0
1
1
0
0
2
0
0
2
1
0
2
1
2
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
2
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
3
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
2
0
0
0
0
1
1
0
2
1
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
4
1
1
1
1
0
2
0
1
0
0
1
0
0
0
0
2
0
0
1
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
2
4
1
1
0
2
0
1
4
0
0
0
2
0
0
2
2
0
0
1
1
0
2
0
0
0
0
1
1
1
0
0
0
1
0
0
0
3
0
0
2
0
1
0
0
0
1
4
2
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
2
0
0
2
1
0
0
0
0
0
1
2
0
2
0
2
0
2
2
0
2
2
1
0
2
0
2
1
0
1
1
0
1
0
0
0
0
0
0
0
7
0
0
2
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
1
2
2
1
0
2
0
0
2
0
1
0
0
0
0
2
0
0
2
0
1
2
0
1
0
1
0
0
0
2
0
0
2
0
1
0
0
0
2
1
2
1
3
0
1
0
0
0
0
2
0
0
1
3
0
1
0
0
1
0
0
0
0
2
0
1
2
1
0
0
1
0
3
1
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
2
1
1
0
2
0
0
0
0
1
0
0
2
2
1
2
1
1
0
0
0
2
1
0
0
1
1
1
0
3
2
2
0
1
1
0
1
0
0
2
0
3
2
2
0
0
1
0
1
0
0
0
0
2
0
1
0
1
1
2
1
0
0
2
2
0
0
0
0
2
1
0
0
0
0
2
0
0
2
1
2
0
1
1
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
2
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
2
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
2
0
2
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
4
0
3
0
3
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
2
1
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
1
0
0
0
0
0
2
1
2
0
2
0
0
0
1
2
0
1
0
0
0
3
0
1
0
1
0
2
2
0
0
0
2
0
0
0
0
1
1
6
2
0
2
2
0
1
0
0
0
0
2
0
1
3
0
0
2
0
0
0
2
2
0
2
0
0
0
0
0
1
0
0
0
1
2
0
1
1
1
2
0
0
2
0
2
1
2
1
1
0
1
0
0
0
0
0
1
2
1
0
0
0
0
2
2
1
0
0
2
1
0
1
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
2
2
0
3
0
0
0
0
2
1
0
0
4
0
0
2
2
1
2
2
0
1
3
1
0
0
1
0
0
2
0
1
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
2
1
1
1
2
1
0
0
2
0
1
1
1
0
1
0
2
1
0
0
0
0
2
1
2
0
0
0
2
0
2
0
2
2
2
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
1
0
3
0
1
0
0
1
2
0
0
1
0
1
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
1
2
1
0
0
0
0
0
0
0
0
1
0
2
0
0
1
1
3
0
1
0
0
0
1
1
0
2
1
1
2
2
2
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
1
2
1
0
1
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
2
2
0
0
0
0
0
2
1
2
2
1
2
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
1
0
0
2
2
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
2
2
2
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
1
3
3
2
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
1
0
0
2
5
0
0
0
3
0
4
0
0
0
0
1
2
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
1
3
1
2
1
1
1
0
0
1
0
0
0
0
1
1
3
0
0
0
0
0
0
2
2
0
3
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
1
0
2
0
0
0
1
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
2
0
0
0
2
0
0
2
1
0
0
0
3
0
2
0
0
1
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
5
0
0
0
2
0
1
2
1
0
1
0
0
0
0
2
0
0
0
2
0
2
0
0
0
2
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
1
0
1
2
0
1
0
0
3
0
0
2
0
0
0
0
1
0
0
2
0
1
0
2
0
2
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
1
2
2
0
0
2
0
1
1
0
1
1
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
2
0
1
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
1
0
0
1
0
1
2
1
0
2
0
0
0
1
0
0
1
0
0
1
2
0
0
0
0
2
2
2
1
0
0
0
1
0
1
0
0
1
0
0
2
0
1
2
0
0
2
2
1
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
2
1
2
0
2
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
2
2
0
1
2
0
1
0
2
2
0
0
0
1
0
0
1
0
0
0
0
2
2
0
2
2
0
0
0
3
0
0
0
0
2
0
1
0
2
0
0
0
1
0
0
1
0
0
0
1
0
0
0
2
0
0
2
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
2
2
1
0
0
0
2
1
3
1
0
2
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
3
0
1
0
0
2
2
2
3
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
2
1
0
0
1
0
0
1
0
2
2
0
1
0
2
1
0
0
0
0
0
1
0
2
2
1
0
0
1
1
0
0
0
2
0
2
0
2
0
1
0
0
1
2
0
0
0
0
0
2
0
0
1
2
0
0
0
0
3
1
2
0
0
1
0
1
1
0
0
0
2
1
0
0
0
0
0
0
1
0
2
0
1
0
1
2
2
2
1
1
2
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
1
2
0
0
0
2
0
0
1
2
0
0
2
0
0
0
0
0
0
0
1
0
0
2
1
2
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
1
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
1
1
1
0
0
0
2
0
0
0
0
2
2
2
0
0
1
1
0
0
1
0
0
0
1
1
0
0
1
1
0
0
0
0
2
2
0
1
0
0
3
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
2
0
0
2
0
2
1
0
0
1
0
0
1
0
0
2
0
1
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
2
0
2
0
1
1
1
1
1
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
1
1
1
1
0
0
0
0
0
0
1
3
2
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
1
0
0
1
0
0
2
0
0
0
0
0
1
2
1
0
0
0
0
2
1
0
2
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
1
0
2
1
0
2
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
2
2
2
0
0
0
0
1
1
1
3
0
1
0
0
0
1
0
0
0
2
1
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
1
3
0
0
0
1
0
0
0
0
0
1
2
2
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
2
1
1
0
2
0
1
0
4
0
0
2
2
2
0
1
0
1
0
1
0
0
1
0
0
1
2
0
2
0
0
0
2
0
1
1
0
0
0
0
1
0
2
0
1
0
0
1
0
0
0
2
2
0
0
0
0
0
1
2
0
0
1
0
0
0
2
0
0
0
0
2
1
1
1
0
0
0
0
0
0
1
3
1
1
0
0
0
1
0
0
1
1
1
0
0
2
1
0
0
2
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
1
0
4
0
0
0
5
0
0
0
0
1
0
0
1
0
2
1
0
0
0
0
0
0
2
2
0
2
2
0
1
0
0
0
0
0
2
0
0
2
0
2
2
0
2
0
1
2
2
0
1
2
0
0
2
1
2
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
2
2
0
0
0
0
0
2
1
1
0
1
0
1
0
2
0
2
1
0
0
0
1
0
0
2
0
0
0
0
2
2
0
2
0
0
0
1
0
0
1
1
0
0
0
0
2
1
0
1
0
0
0
1
0
0
0
0
0
2
0
2
2
0
0
0
2
0
0
0
2
0
0
2
0
0
1
0
0
0
2
0
2
0
0
0
1
2
2
0
0
2
0
0
2
3
0
2
1
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
1
0
2
0
0
0
1
0
0
0
0
1
0
2
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
1
2
0
2
0
3
2
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
2
0
1
1
2
0
1
1
3
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
1
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
1
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
1
0
1
1
0
1
0
0
2
1
0
2
0
0
1
0
1
0
0
0
2
0
2
0
1
0
0
1
0
0
1
1
2
0
4
2
2
1
0
1
2
0
0
0
1
1
2
1
0
0
1
0
2
0
0
0
0
0
1
3
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
2
1
1
0
0
1
3
0
0
0
0
1
0
0
0
0
2
2
1
0
0
0
4
0
1
0
3
2
1
0
0
1
0
1
0
0
0
0
0
2
2
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
2
2
0
0
2
0
1
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
1
4
0
0
4
2
0
0
0
0
0
2
1
0
0
1
0
0
1
0
2
0
0
2
0
0
0
0
1
0
1
1
0
0
1
2
2
0
0
0
2
1
1
0
0
2
1
1
0
1
2
2
1
0
1
2
0
0
1
0
0
0
0
0
3
0
2
0
3
2
2
1
0
1
0
0
0
0
2
0
0
2
0
0
1
1
2
1
3
2
0
0
0
1
0
2
1
2
0
1
0
0
2
0
8
1
0
0
0
1
0
1
2
0
0
0
2
2
0
0
0
1
1
3
1
0
0
0
1
2
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
2
0
1
1
0
0
1
0
1
0
2
0
0
2
0
3
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
2
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
1
1
0
0
1
0
2
0
0
0
0
0
0
0
1
1
2
0
0
2
0
1
0
0
0
0
0
0
1
0
4
0
2
0
0
0
0
1
0
2
1
2
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
3
0
2
1
0
0
0
2
2
2
0
0
0
0
0
0
1
0
1
2
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
1
2
2
2
1
1
0
1
0
0
0
0
0
2
0
1
0
0
1
0
0
1
0
0
1
1
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
2
2
4
3
0
0
2
0
0
1
0
2
1
0
1
2
0
0
0
1
0
0
0
1
2
0
0
2
1
0
0
1
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
1
2
0
0
2
2
1
0
0
2
2
0
0
0
2
0
1
1
0
0
0
0
0
1
1
0
0
2
0
1
2
1
1
0
0
0
0
0
2
0
3
2
1
0
1
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
4
0
0
1
2
0
0
0
0
0
1
0
1
0
0
2
2
0
1
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
2
0
0
0
0
0
2
0
1
0
0
0
2
0
0
2
0
0
1
0
0
2
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
1
1
0
1
0
1
0
0
2
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
2
0
2
1
0
0
0
0
2
0
4
0
2
0
0
0
1
2
1
0
1
5
0
0
0
1
0
1
0
0
0
0
2
1
0
0
0
2
1
3
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
2
0
0
0
2
1
0
2
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
1
0
1
0
2
0
0
0
2
2
2
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
2
1
0
1
0
2
1
0
0
0
0
3
1
0
0
0
0
0
1
0
0
2
0
0
2
0
0
2
0
0
0
0
0
2
0
1
2
0
0
0
2
0
0
1
2
0
1
1
2
0
1
1
0
1
0
2
0
1
0
0
0
1
0
0
0
2
0
2
1
0
2
0
0
0
0
0
2
0
0
2
0
1
2
1
3
0
0
0
0
0
3
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
2
0
0
1
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
1
3
2
0
2
0
2
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
2
0
0
0
2
1
2
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
1
0
2
1
0
0
2
0
1
0
0
1
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
1
1
0
1
0
0
0
0
3
0
0
0
0
0
2
3
0
0
0
0
3
1
1
2
0
1
0
1
1
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
3
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
2
1
0
1
0
2
0
2
2
0
0
0
2
2
1
2
0
1
0
0
2
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
1
1
0
0
2
2
0
0
0
1
0
1
1
0
1
2
0
0
0
0
0
0
0
0
3
0
1
0
0
0
3
1
0
0
2
2
1
2
2
0
0
0
0
0
0
0
2
0
0
0
2
2
0
2
0
0
0
5
0
2
0
0
0
2
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
2
2
0
2
1
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
4
1
1
1
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
1
1
2
0
2
0
0
4
2
0
2
3
2
0
0
0
2
1
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
2
2
2
1
2
0
0
2
2
0
0
0
2
0
0
1
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
1
2
2
2
0
0
2
3
0
2
0
1
0
1
0
0
2
0
1
0
1
0
0
0
2
2
0
0
0
0
0
0
0
2
3
0
0
1
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
1
2
0
2
2
0
0
0
0
1
0
1
0
1
0
0
0
3
0
0
0
2
0
2
0
0
2
1
0
0
3
3
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
2
2
2
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
3
0
0
0
0
1
0
2
0
0
0
0
1
0
1
0
3
2
0
1
0
0
2
0
1
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
1
2
0
0
0
0
3
1
0
0
2
1
0
0
0
0
1
1
1
1
0
0
2
1
2
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
1
0
0
2
0
1
0
1
0
0
1
1
2
0
0
2
1
0
0
0
0
0
0
1
0
2
1
0
1
0
1
2
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
2
1
0
3
0
0
1
2
0
0
0
0
1
0
0
0
3
0
2
0
0
0
0
0
1
0
1
2
2
0
0
2
2
0
0
1
0
0
2
1
0
2
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
1
1
1
0
0
0
0
3
0
0
0
0
0
2
1
0
0
2
0
0
2
2
1
0
2
1
0
0
2
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
5
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
1
2
0
0
0
2
2
1
0
0
0
0
0
1
0
0
0
1
1
0
3
0
2
0
2
2
1
2
0
2
2
1
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
1
2
0
0
0
0
1
0
0
0
1
0
2
0
0
0
2
2
0
0
0
1
1
2
0
1
0
2
0
1
0
0
2
2
1
0
0
0
0
0
0
2
1
0
0
2
2
0
0
0
0
2
0
12
2
0
0
0
1
0
1
0
0
0
1
2
0
0
2
0
2
0
0
0
2
0
0
0
0
1
2
0
0
0
2
1
1
0
0
2
0
4
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
2
1
1
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
1
0
1
0
1
0
2
1
0
0
0
0
0
2
0
2
0
1
2
0
0
2
2
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
2
1
2
2
0
2
0
0
2
0
0
0
1
2
0
2
0
0
0
1
1
0
0
2
0
0
0
0
0
1
0
0
1
2
0
0
0
2
1
0
1
0
0
1
0
0
2
0
2
0
0
0
0
0
5
0
0
1
0
1
2
0
0
1
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
1
0
2
0
0
0
0
0
0
1
2
0
0
2
3
0
1
1
0
0
0
0
2
2
0
0
1
0
0
2
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
2
0
3
0
0
1
0
0
1
0
0
2
0
0
2
0
0
1
0
0
0
0
2
1
0
0
0
4
1
2
2
0
2
0
0
1
0
0
0
0
0
3
0
0
0
0
2
0
2
1
0
1
2
0
0
0
2
0
2
0
0
1
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
2
2
0
0
1
0
0
0
0
0
1
0
0
1
0
2
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
1
2
2
0
2
0
1
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
2
1
0
2
0
2
0
0
2
0
0
2
0
1
1
0
0
1
1
0
0
3
0
4
0
0
1
0
0
0
1
1
1
0
0
0
2
2
0
2
0
0
0
1
0
0
0
1
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
2
1
1
3
2
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
1
1
0
0
0
0
0
3
0
0
3
1
0
0
2
0
6
0
0
2
1
0
0
0
0
1
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
2
0
0
0
2
0
1
0
0
0
0
0
0
0
2
2
1
0
1
0
0
1
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
3
0
0
0
0
3
1
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
1
0
1
0
0
1
1
1
0
0
2
1
2
0
7
0
0
3
1
0
0
2
0
2
1
1
1
0
0
0
0
2
0
1
2
0
1
2
0
0
0
1
0
0
0
2
0
0
0
4
2
0
1
0
0
1
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
1
0
0
2
0
2
0
1
0
1
1
0
1
3
0
0
2
2
0
0
0
0
1
0
3
0
0
0
0
0
0
1
0
1
0
0
0
1
2
0
2
2
0
0
0
1
1
0
0
2
0
2
0
1
2
0
0
2
3
0
0
1
0
2
0
0
0
1
0
0
2
2
1
0
0
0
0
0
2
4
0
1
0
0
1
0
0
1
0
0
1
1
0
2
0
0
0
2
0
0
1
0
1
1
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
3
0
0
1
0
0
1
2
0
2
0
0
1
0
0
1
0
2
0
0
0
0
2
2
0
0
0
1
0
0
2
0
1
2
0
0
1
0
0
0
1
0
1
0
0
1
1
0
0
0
0
2
2
2
0
0
0
1
0
0
2
1
0
0
1
2
1
0
0
1
0
1
0
0
0
0
0
2
0
2
0
3
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
2
1
2
0
4
0
0
0
1
0
0
0
0
2
2
0
1
3
0
0
1
0
2
1
0
1
0
0
2
0
2
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
2
0
0
0
0
5
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
2
2
6
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
1
2
0
11
0
0
1
0
1
0
0
3
0
1
0
2
0
1
0
0
0
0
0
0
0
0
1
2
0
0
1
0
2
1
1
1
2
0
1
0
0
0
1
0
1
0
0
2
3
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
2
1
2
0
2
0
1
0
1
0
0
0
1
0
0
1
0
1
0
1
0
1
0
1
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
1
0
0
2
2
0
1
0
0
2
0
1
0
0
1
2
0
0
0
0
0
1
0
0
0
3
0
0
1
0
0
0
2
1
0
1
2
0
0
1
0
2
0
0
0
0
0
0
2
0
0
2
2
1
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
2
0
1
1
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
1
0
2
0
1
0
0
1
1
0
1
2
0
1
1
0
0
0
5
2
0
0
2
0
0
3
1
0
0
0
0
0
0
0
1
0
2
0
0
0
1
1
0
0
2
0
1
0
2
2
0
0
0
0
0
0
0
0
1
0
3
0
0
2
1
1
0
0
0
0
0
1
0
1
0
0
2
0
0
0
1
2
0
3
0
2
0
0
2
1
2
0
1
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
9
2
0
1
1
0
0
0
3
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
2
0
0
2
0
0
0
2
0
0
3
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
2
1
0
2
0
2
0
2
1
0
0
0
1
0
2
0
0
0
3
0
0
0
0
1
2
0
0
1
0
0
0
0
1
2
2
0
0
0
0
0
0
0
1
1
0
1
0
0
3
0
0
2
0
3
0
0
2
0
0
0
2
0
0
1
1
2
0
2
2
0
0
3
2
0
0
1
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
1
0
1
0
0
1
1
0
1
0
0
0
3
0
0
1
0
0
0
0
1
0
0
0
0
2
3
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
2
0
0
0
0
0
1
3
2
0
0
4
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
1
0
2
1
0
0
1
1
0
0
0
0
0
2
0
1
0
2
4
0
0
1
2
0
0
1
0
2
0
1
3
0
1
0
0
0
0
1
0
0
0
0
2
0
3
0
0
0
0
1
1
1
1
0
0
0
0
2
0
0
0
1
0
2
1
0
1
0
0
0
0
2
0
1
0
2
0
1
0
0
0
1
2
1
2
1
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
3
0
1
0
0
2
2
0
0
0
0
0
3
0
0
0
0
0
0
0
2
1
0
1
2
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
2
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
1
2
1
0
0
0
0
1
0
0
2
1
0
2
1
2
0
1
2
1
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
1
0
1
2
0
2
2
0
2
3
0
1
2
0
0
1
2
0
0
0
0
2
0
1
1
1
2
2
0
3
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
2
0
1
0
1
0
0
2
0
1
0
0
2
0
0
0
0
0
2
0
0
1
0
0
1
0
2
0
1
1
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
2
2
0
2
0
0
1
0
0
0
2
2
0
1
1
0
0
0
1
0
2
0
2
0
0
2
0
1
1
0
1
0
0
2
2
0
0
0
0
0
1
0
0
0
0
1
0
2
4
0
0
2
0
0
0
0
0
1
0
2
2
1
0
0
2
2
0
0
2
0
0
0
0
2
0
5
2
1
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
4
1
0
0
0
0
1
0
0
1
2
3
1
0
1
2
0
1
0
0
0
0
4
0
0
0
0
2
2
2
0
2
1
1
0
0
0
0
2
0
0
2
0
0
0
1
1
0
0
0
2
1
1
0
0
1
0
1
1
0
0
2
3
0
1
0
1
1
0
1
0
0
2
0
0
0
2
0
0
0
0
1
0
2
1
0
0
1
1
1
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
1
1
0
0
0
0
1
1
0
1
0
0
1
0
0
3
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
1
2
0
0
1
0
1
1
0
2
1
0
0
0
0
0
0
2
0
0
2
0
1
0
0
2
0
2
2
0
1
2
0
0
0
1
0
0
0
0
1
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
3
0
0
1
2
0
0
1
0
0
0
1
0
2
2
0
0
2
1
2
2
4
2
0
0
0
0
0
1
2
2
1
0
0
1
0
0
0
0
0
2
0
1
0
0
0
1
0
1
1
0
0
1
0
0
0
2
0
1
0
1
0
1
2
2
0
0
2
1
0
1
0
1
0
1
0
0
0
4
1
2
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
1
0
0
1
2
0
0
0
0
1
2
1
1
0
0
0
1
0
0
2
2
0
1
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
2
2
2
1
0
0
0
2
0
2
1
2
1
0
0
0
1
1
2
1
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
3
0
0
0
1
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
1
1
1
0
2
1
1
0
2
0
0
1
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
1
1
1
1
1
1
0
0
0
1
2
1
0
1
1
0
2
0
0
0
0
1
2
0
2
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
3
0
3
0
0
2
0
0
0
2
0
2
0
0
0
0
1
2
0
0
0
0
3
0
2
2
2
0
1
0
0
0
0
3
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
2
2
0
1
0
0
0
0
1
2
0
2
0
0
2
2
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
2
2
2
2
1
0
1
1
0
1
0
0
0
0
2
1
0
1
0
1
2
0
0
1
0
0
0
1
0
0
1
2
1
0
0
0
0
1
0
2
2
2
0
3
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
2
0
1
1
1
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
2
0
0
0
2
1
0
0
2
0
0
0
1
0
0
2
0
2
0
2
0
2
0
1
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
1
0
2
2
0
0
1
9
1
0
0
0
0
0
0
0
2
1
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
1
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
2
0
2
2
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
2
1
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
2
2
1
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
2
0
2
0
2
0
0
0
2
1
1
0
0
3
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
1
0
2
1
1
0
0
0
0
0
0
1
2
0
2
1
0
0
3
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
2
1
0
0
0
0
2
1
1
1
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
2
1
0
2
0
1
0
0
1
0
1
2
0
2
3
0
1
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
1
0
1
2
1
2
2
0
0
1
0
2
0
0
0
0
0
2
3
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
1
0
2
2
0
0
0
0
2
0
3
0
1
0
0
1
1
0
1
1
1
2
0
2
1
2
0
1
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
2
0
1
1
2
0
0
0
0
1
0
0
3
2
0
2
0
0
0
0
1
2
0
1
0
1
1
0
2
1
2
1
0
0
0
2
0
0
0
0
0
2
0
2
1
0
0
2
0
0
1
0
0
2
2
0
1
0
1
1
2
1
1
0
0
0
1
0
1
1
2
0
0
1
0
0
0
0
0
2
1
0
0
2
1
2
1
0
0
0
1
0
0
1
0
0
1
2
0
0
1
0
2
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
1
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
4
0
4
0
2
0
0
0
0
0
1
0
0
0
0
1
0
2
1
1
1
0
0
0
2
0
0
0
2
1
0
0
0
0
0
1
0
2
0
1
1
0
2
1
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
2
1
0
0
2
0
0
0
2
4
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
2
0
0
0
1
2
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
1
2
0
0
0
1
0
0
0
2
2
0
0
0
1
0
0
1
1
0
0
1
0
1
0
0
0
0
0
2
0
2
0
2
2
0
0
0
0
1
1
0
0
0
0
0
2
0
2
2
0
0
0
0
0
1
0
0
0
0
0
4
0
0
1
0
0
0
0
2
0
0
0
1
0
2
0
1
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
1
0
1
0
2
1
0
0
0
1
0
0
2
1
1
0
0
2
1
0
2
2
0
1
0
2
1
0
0
2
0
2
0
0
0
2
0
1
2
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
2
0
1
0
0
2
3
2
2
1
0
1
2
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
1
2
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
2
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
1
1
1
1
0
0
0
2
0
2
0
2
1
0
1
0
0
0
0
3
1
2
0
2
0
0
0
1
0
0
0
3
0
0
0
0
1
1
0
0
0
0
0
2
3
0
0
0
0
0
0
3
2
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
1
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
1
1
1
0
1
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
3
1
0
0
1
1
0
0
0
0
0
0
1
0
2
0
1
2
1
0
0
3
1
1
0
0
0
0
0
0
0
2
0
0
0
1
1
1
2
2
0
1
0
0
0
1
2
0
1
0
0
3
0
2
1
1
0
0
0
0
0
0
0
1
0
0
0
3
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
1
1
0
1
1
2
0
2
0
1
0
0
2
3
1
2
0
0
2
3
1
0
0
0
2
0
2
0
1
0
0
0
0
2
1
0
2
0
1
0
2
0
0
1
1
2
1
0
0
0
0
0
0
2
0
0
1
0
2
2
1
0
0
0
0
0
1
0
1
0
2
0
1
0
0
1
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
1
0
1
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
1
0
0
1
1
1
3
0
0
1
0
2
0
0
0
0
0
0
0
2
3
0
0
0
0
2
2
0
2
1
1
0
1
3
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
2
2
2
2
2
0
0
1
0
0
0
0
2
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
1
2
0
0
1
0
0
2
1
0
1
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
15
0
0
0
0
0
0
0
0
3
0
2
1
0
0
1
0
4
2
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
1
0
0
2
0
2
0
1
1
0
1
0
2
0
0
1
0
0
0
2
0
2
0
0
0
0
1
1
0
0
0
2
0
2
1
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
2
0
1
1
0
0
1
0
2
1
0
0
1
0
0
0
0
0
1
0
2
0
0
3
2
2
0
2
0
1
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
2
1
1
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
5
1
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
2
0
0
1
2
0
0
0
0
0
0
2
0
1
0
0
0
3
2
0
0
0
0
0
0
0
1
0
3
0
0
1
0
1
0
2
0
0
0
1
2
1
0
0
0
0
2
0
1
0
0
0
2
2
0
0
2
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
1
0
3
2
2
0
1
2
0
2
1
1
0
1
0
0
0
4
2
0
1
0
0
0
0
0
0
5
0
0
2
0
1
0
0
0
1
0
0
1
0
2
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
1
0
2
1
0
1
0
0
0
0
2
1
0
1
1
0
2
0
0
0
0
0
0
2
0
1
1
1
2
1
0
0
0
0
1
0
0
0
0
2
1
0
1
2
0
0
0
0
1
1
1
0
0
1
0
0
0
2
0
1
0
0
0
0
1
0
1
0
2
2
0
0
2
1
0
0
2
0
2
0
0
0
1
1
1
0
1
2
0
2
0
0
1
0
1
1
0
1
0
1
0
0
0
0
0
3
0
0
0
0
0
2
2
3
0
0
2
2
0
0
1
3
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
2
0
0
1
0
0
0
1
2
1
0
0
0
0
0
0
0
0
2
2
0
3
0
0
0
0
1
0
1
0
0
1
0
2
0
0
0
0
1
0
0
3
1
0
0
0
1
0
0
2
2
0
2
0
2
0
0
0
2
0
2
0
1
0
0
1
0
5
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
3
2
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
1
0
0
0
1
2
0
1
2
0
0
0
0
0
1
0
1
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
2
0
2
0
4
2
0
0
2
1
2
1
0
0
0
0
0
0
0
2
1
0
2
2
2
1
2
2
1
1
0
0
0
3
0
0
0
2
2
0
0
2
0
2
0
2
2
2
0
1
0
2
0
1
1
1
0
1
0
0
2
2
0
0
3
0
0
2
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
1
2
0
0
0
0
0
2
0
1
0
0
1
0
2
0
0
0
0
0
1
0
0
0
5
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
3
2
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
2
2
1
0
1
0
0
0
0
1
1
0
0
1
0
0
1
0
0
1
1
0
0
0
2
2
1
0
0
1
0
1
0
0
0
0
0
0
0
1
2
1
2
0
1
0
0
2
0
2
2
1
1
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
2
0
0
0
0
2
0
0
0
0
0
2
0
0
1
3
3
0
1
0
2
0
0
0
2
3
0
0
0
1
0
0
0
0
0
2
0
0
1
1
0
0
0
2
0
0
0
0
1
0
0
0
2
0
2
0
0
1
0
1
0
0
0
2
2
0
0
0
0
0
0
2
0
0
1
0
1
1
0
2
0
1
0
0
0
2
0
0
1
2
0
0
1
0
0
0
2
0
0
0
2
0
0
2
1
0
0
0
1
0
0
0
0
3
0
1
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
2
2
0
1
8
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
1
0
0
0
2
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
1
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
2
1
0
0
0
0
1
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
3
2
2
0
2
1
0
0
1
0
0
0
1
1
3
0
0
0
0
1
0
1
0
0
1
0
0
1
2
0
1
2
0
2
2
0
0
0
1
1
1
0
0
7
0
0
0
0
1
0
0
1
1
0
0
2
2
2
1
0
0
0
1
2
1
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
2
1
0
0
2
2
4
2
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
2
0
0
1
0
2
1
1
1
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
1
4
2
0
0
1
0
0
0
1
0
3
0
2
0
0
1
0
2
0
0
0
0
0
0
1
0
0
4
2
0
0
0
1
2
0
0
0
2
0
0
4
0
4
1
2
0
1
1
2
0
0
0
1
2
0
0
2
1
2
0
0
0
1
0
0
0
0
2
0
1
2
0
0
2
0
1
0
1
0
0
0
0
1
1
0
1
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
1
0
1
1
2
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
1
0
1
0
3
0
2
0
2
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
1
1
1
2
0
0
0
0
1
0
0
1
2
3
0
0
1
0
0
1
0
0
1
0
2
2
1
0
0
0
0
2
2
0
3
0
0
0
1
0
0
1
0
1
0
3
0
0
0
0
0
0
2
1
0
0
2
1
3
0
0
0
1
0
0
0
1
0
5
1
2
0
0
2
0
0
2
1
2
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
2
1
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
1
2
3
0
0
1
1
2
0
0
0
3
1
1
1
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
1
0
0
2
0
1
0
1
0
0
0
1
0
0
1
0
0
2
0
1
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
2
0
1
0
1
0
2
2
0
1
0
0
2
0
0
0
0
0
1
1
0
0
0
0
1
2
1
0
0
0
1
3
2
2
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
2
2
2
1
1
0
0
0
0
2
0
1
0
0
1
0
0
2
0
0
0
2
1
0
0
1
0
2
0
0
0
0
0
3
4
1
1
0
0
0
1
3
2
1
0
0
0
1
0
4
0
0
0
0
0
0
2
1
0
0
0
1
3
1
3
2
0
1
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
2
0
0
0
0
2
1
2
0
2
2
0
2
1
2
0
1
0
0
2
1
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
2
1
0
0
0
1
2
0
2
1
2
2
3
0
2
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
2
1
0
0
0
0
0
5
3
0
2
0
0
0
0
1
1
0
1
0
0
0
2
2
2
0
0
0
0
1
0
2
0
0
0
0
0
3
2
0
0
1
1
0
0
0
0
0
2
1
0
1
0
2
2
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
2
1
0
0
3
1
0
2
0
0
1
1
3
0
1
1
2
0
0
0
2
0
1
2
0
0
2
0
2
1
1
0
0
2
1
2
2
2
0
2
2
1
2
0
2
0
0
0
0
0
2
1
3
0
1
0
2
0
0
0
0
0
0
0
1
2
2
2
1
0
0
0
1
0
0
0
0
0
1
0
1
1
0
2
0
0
0
2
1
0
0
0
2
0
0
0
5
0
0
0
2
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
2
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
1
1
0
1
3
0
0
0
0
0
2
1
0
0
2
0
2
2
0
0
1
0
0
1
0
0
0
2
0
0
0
1
0
0
2
2
0
1
0
0
2
0
0
2
2
0
0
3
1
0
0
0
0
0
2
0
0
2
0
2
1
0
0
0
0
1
0
1
2
0
3
0
0
0
0
2
0
0
1
0
0
0
0
1
1
0
2
0
1
0
0
1
2
0
0
2
1
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
3
1
0
1
0
0
1
1
0
0
0
0
0
2
0
12
0
0
0
0
1
2
0
0
2
2
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
1
0
0
2
0
2
2
1
0
2
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
1
0
1
0
0
0
1
0
1
1
0
0
1
0
0
2
0
2
2
0
0
0
4
0
0
2
1
1
0
0
0
1
0
1
1
1
0
0
0
0
0
0
1
0
2
2
1
0
1
0
0
1
0
0
0
2
0
2
0
3
0
1
2
2
0
0
0
0
2
0
0
0
0
2
0
0
1
1
1
0
2
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
2
0
2
1
0
2
0
2
0
0
1
0
0
0
1
2
1
1
8
2
1
1
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
2
0
0
2
0
2
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
2
1
0
0
1
0
0
2
1
0
0
0
2
0
0
10
1
0
0
0
0
0
0
0
1
0
2
0
0
2
1
1
1
0
0
0
2
0
1
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
2
0
0
1
2
0
0
0
0
2
0
0
0
2
2
0
0
2
0
0
3
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
2
3
0
2
0
0
1
0
1
0
0
0
0
0
0
1
2
2
0
0
0
2
0
0
3
1
0
0
2
0
0
0
0
1
2
0
0
1
3
0
0
0
0
0
1
0
0
2
0
0
1
1
1
3
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
5
0
0
0
1
0
2
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
2
4
1
1
0
2
0
0
0
0
0
1
2
0
0
0
2
2
2
1
0
1
0
0
0
0
2
2
0
0
0
2
0
1
0
2
2
1
0
0
2
1
2
1
0
2
0
0
0
0
0
1
1
0
0
0
0
0
1
2
0
0
3
0
2
2
0
1
0
0
0
0
2
1
0
1
0
0
0
1
2
0
2
2
1
0
0
0
0
0
0
0
1
1
0
0
1
0
1
3
0
0
0
0
1
2
0
0
2
0
0
0
1
0
0
0
0
2
0
1
0
0
2
0
0
0
1
0
3
0
2
0
8
0
2
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
1
0
0
2
1
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
1
1
1
0
2
0
0
0
0
2
0
0
1
2
2
0
0
0
0
0
0
0
1
0
2
2
0
0
1
0
0
0
2
0
0
0
1
1
0
1
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
2
0
0
0
2
0
1
0
0
0
0
1
0
1
0
2
1
1
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
2
0
2
0
2
1
2
0
0
2
0
1
1
0
0
0
2
1
0
0
0
1
0
0
0
0
0
3
2
0
1
2
0
0
0
3
0
0
0
0
0
1
0
0
3
0
3
2
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
1
0
0
0
0
0
0
2
0
1
1
0
0
2
1
0
0
2
0
0
2
1
2
0
0
0
0
0
1
0
2
2
3
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
1
5
0
0
1
1
2
0
0
2
0
0
1
2
0
0
0
0
0
2
0
0
0
1
0
1
0
2
0
2
0
3
0
1
1
1
0
0
2
0
0
0
0
0
1
2
0
2
1
0
1
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
2
0
0
0
0
2
0
0
1
2
0
2
2
0
0
0
2
0
1
1
2
0
0
0
0
2
0
1
0
0
2
2
0
0
0
2
2
0
0
0
0
4
0
0
0
2
0
2
1
0
2
2
2
0
0
0
0
0
1
1
2
0
0
1
0
1
0
0
0
2
2
2
0
2
1
0
0
1
0
0
0
0
1
0
0
0
3
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
1
0
0
1
0
2
2
1
0
0
2
0
0
1
2
0
0
2
0
0
0
1
1
0
0
0
2
0
0
2
0
0
2
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
2
0
1
0
0
2
0
0
0
2
0
2
2
0
2
2
2
0
3
1
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
1
0
0
2
0
0
0
2
0
3
0
2
0
3
0
2
0
0
0
0
0
2
1
0
1
0
2
0
0
1
0
2
0
0
0
2
0
0
0
0
1
2
0
1
0
2
0
0
2
3
2
2
2
2
0
0
0
2
1
0
0
1
0
0
0
0
2
0
0
1
0
1
0
0
0
2
0
0
0
1
1
0
0
0
0
3
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
1
2
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
6
0
0
0
0
0
0
0
0
2
0
0
0
1
1
1
0
0
1
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
1
0
2
2
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
2
0
0
0
1
0
2
0
0
2
1
0
2
1
0
0
1
0
0
0
2
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
2
1
0
2
1
0
0
2
0
2
0
0
0
2
1
1
1
0
0
0
2
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
2
0
2
1
0
0
0
0
0
2
0
0
0
0
2
0
1
1
0
0
0
0
2
0
0
0
2
1
0
0
0
1
0
0
1
0
2
0
0
0
0
1
2
2
0
0
1
0
0
2
0
2
0
1
0
0
0
3
0
1
1
0
0
1
0
0
0
3
0
1
0
0
1
0
0
2
2
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
1
2
0
0
0
0
0
0
1
1
2
2
0
0
0
1
1
0
0
0
2
1
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
2
0
0
1
0
0
2
1
0
0
0
0
0
1
0
1
0
1
0
5
0
0
0
0
0
2
0
5
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
2
0
0
0
2
0
1
0
1
0
0
0
2
1
3
0
0
0
0
2
0
2
1
0
1
0
2
2
0
0
3
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
3
0
0
0
0
2
0
0
2
4
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
2
0
1
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
1
0
2
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
1
0
0
4
2
0
1
2
2
1
0
4
0
0
1
1
0
0
1
2
2
1
0
0
2
2
0
0
1
1
0
0
0
1
0
0
0
1
1
0
3
1
0
0
0
0
2
0
0
0
2
0
1
0
0
1
1
0
0
2
2
0
1
0
0
0
0
1
0
1
2
2
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
3
1
0
0
0
1
0
2
2
1
0
1
1
0
2
0
1
0
0
2
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
1
0
0
2
0
2
0
0
2
0
0
2
0
4
0
0
0
1
0
0
0
1
0
0
1
2
0
0
1
2
0
0
0
1
1
0
3
2
0
0
2
1
2
0
0
0
1
2
0
2
10
1
0
0
2
2
2
2
2
2
1
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
2
0
0
2
2
3
0
0
2
1
1
0
1
0
1
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
1
0
0
0
2
1
0
2
0
2
0
0
0
0
1
1
0
0
0
0
0
0
2
0
3
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
1
2
1
0
1
0
1
0
1
2
1
0
1
0
3
0
2
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
1
2
2
1
0
0
0
2
0
0
0
0
0
1
0
0
1
1
0
0
2
2
0
0
2
0
0
2
0
1
0
1
0
0
1
0
0
0
2
2
0
2
0
1
0
2
0
2
0
2
1
0
2
0
2
0
1
1
2
0
2
5
0
2
0
2
0
1
0
0
0
2
0
5
0
0
0
2
2
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
2
0
1
2
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
7
0
0
0
0
6
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
2
0
0
2
2
0
2
1
0
3
2
2
0
0
0
0
0
0
1
0
1
1
2
0
1
0
0
0
2
2
2
0
0
2
1
0
1
0
1
0
0
0
0
0
1
1
2
0
0
2
1
0
2
0
0
0
0
0
1
1
1
2
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
1
2
1
0
0
2
2
0
1
0
0
2
0
0
4
0
2
0
0
1
0
0
0
0
2
0
0
0
3
0
1
0
0
1
2
0
0
2
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
1
1
1
0
0
0
1
0
1
0
0
0
3
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
4
1
3
0
2
1
0
0
0
2
0
1
0
2
0
0
1
1
0
2
0
1
1
0
0
0
0
1
2
0
0
0
2
0
1
0
2
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
2
1
1
1
0
1
0
0
0
0
0
0
1
0
2
1
0
2
0
0
0
2
0
0
1
0
0
0
0
0
2
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
1
0
2
1
0
0
0
0
2
1
0
2
2
0
0
0
2
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
2
1
1
1
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
2
2
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
1
0
1
1
0
1
0
0
2
1
0
0
1
1
0
0
0
0
1
2
0
2
0
0
0
1
0
0
0
2
0
0
0
2
0
1
0
0
2
0
1
0
0
1
0
0
0
0
1
1
0
0
2
0
0
3
2
1
0
0
1
1
1
0
0
1
3
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
2
0
0
0
1
0
0
0
2
0
0
0
2
0
1
0
2
1
0
1
0
0
2
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
2
2
0
2
1
0
3
0
0
0
0
0
1
0
0
5
2
0
1
0
0
0
0
7
0
0
1
0
1
2
0
1
4
0
2
0
0
0
0
0
0
1
2
0
1
0
0
3
1
2
2
1
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
3
2
0
0
2
0
2
1
0
0
1
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
1
0
1
0
2
2
0
0
0
0
0
0
1
0
0
0
2
0
2
0
3
1
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
2
2
0
0
0
0
2
0
0
1
2
0
0
1
2
0
0
0
0
1
0
1
1
0
1
2
2
0
0
0
0
0
2
0
0
2
0
1
1
0
0
0
2
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
1
0
0
1
1
2
0
1
1
0
0
2
0
2
2
2
1
0
0
0
0
0
2
0
0
0
1
0
0
1
0
2
2
1
0
0
0
0
0
0
4
0
0
0
0
2
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
2
2
0
1
0
0
0
1
1
2
1
1
0
0
1
0
1
1
1
2
0
2
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
2
3
0
0
0
0
0
0
0
1
1
0
0
2
0
2
1
2
2
0
0
0
0
0
2
2
0
0
0
0
1
1
1
1
2
0
0
0
0
1
1
0
0
1
0
2
7
3
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
3
0
2
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
1
0
0
2
2
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
2
0
0
0
2
1
0
1
0
0
0
0
1
3
0
2
1
2
0
2
0
4
1
0
1
0
0
2
0
2
0
0
0
2
0
2
0
1
0
1
0
0
2
2
3
2
0
2
0
0
1
1
0
2
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
1
1
0
2
2
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
1
3
2
3
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
2
0
2
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
2
2
0
2
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
2
0
2
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
1
0
0
2
2
0
0
0
0
0
1
0
0
0
1
0
0
2
3
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
1
1
0
0
2
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
1
1
0
0
1
0
1
0
0
1
0
1
0
0
1
1
0
0
1
0
1
2
1
0
0
0
0
0
0
2
0
2
1
0
0
0
1
0
0
2
2
0
2
0
1
0
2
0
0
0
0
1
2
0
0
1
2
0
0
0
0
0
1
1
0
1
1
0
0
1
0
2
2
3
0
0
3
2
0
0
2
0
1
0
0
0
0
4
0
0
0
0
0
1
4
0
1
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
2
0
0
1
0
1
1
1
1
0
0
1
2
1
0
1
0
2
1
3
0
0
2
0
0
1
0
2
0
0
0
0
0
2
0
2
1
0
0
2
1
0
0
0
1
6
1
0
0
0
0
0
0
2
2
1
0
1
1
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
1
0
1
3
0
0
0
1
0
0
2
0
0
0
0
15
1
0
0
0
0
0
0
1
0
2
0
2
1
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
1
2
0
0
0
2
0
1
3
2
0
4
3
0
2
0
1
1
0
3
0
1
0
0
2
2
2
2
0
0
3
1
0
0
0
0
0
2
0
1
0
1
0
0
0
0
1
0
2
0
0
0
0
2
1
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
2
2
2
0
1
0
0
0
0
0
0
0
0
1
0
0
2
2
2
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
1
3
0
0
2
0
0
2
0
0
2
2
0
2
0
2
2
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
2
3
1
2
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
1
0
2
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
4
0
0
2
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
1
5
2
0
0
0
0
4
0
2
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
2
0
0
1
0
0
2
5
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
2
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
3
2
1
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
2
1
0
0
0
1
0
0
2
0
0
2
0
1
0
1
0
2
0
0
0
2
0
2
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
1
0
2
2
0
2
0
0
0
0
3
0
0
1
0
2
2
2
0
1
1
0
0
0
2
1
0
2
0
0
1
0
2
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
2
1
0
0
0
4
2
2
1
0
2
1
2
1
2
2
1
2
1
0
0
0
0
0
2
0
1
0
2
0
2
0
1
2
0
0
2
0
0
2
1
0
1
0
2
0
0
2
1
0
1
0
0
2
2
0
0
0
0
0
0
7
0
0
0
0
0
2
0
0
1
2
1
0
0
0
1
1
2
0
0
0
0
0
3
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
2
0
0
2
0
1
0
0
1
2
2
2
1
0
0
1
0
0
1
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
4
0
0
1
2
2
0
2
1
1
2
0
0
2
2
0
0
1
2
8
0
1
0
0
2
0
0
2
4
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
2
0
0
0
1
0
0
1
0
1
0
2
1
0
2
0
1
1
0
1
1
0
0
0
0
0
0
1
1
2
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
4
1
0
0
0
2
0
0
2
2
0
0
0
0
1
0
0
1
0
0
0
1
0
0
2
0
0
0
2
0
10
0
0
0
0
1
1
0
1
2
1
0
4
0
0
0
2
0
0
0
0
2
0
2
0
0
0
2
1
0
1
1
4
0
0
1
1
0
0
0
0
1
0
1
0
2
0
2
0
0
0
0
5
2
0
3
1
2
2
0
2
0
0
0
0
0
0
1
0
1
1
0
1
0
0
1
0
0
2
2
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
2
0
1
3
0
0
2
0
0
0
0
1
0
0
0
0
1
2
0
0
2
2
3
0
1
0
0
0
2
0
0
1
0
0
0
0
3
0
1
0
2
0
0
0
1
0
0
2
0
0
2
0
1
0
0
0
0
1
2
2
1
0
0
3
0
4
0
0
1
0
1
0
2
1
0
1
2
0
1
0
2
0
2
0
0
1
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
1
0
0
2
0
0
0
0
0
4
1
0
0
0
1
0
2
2
0
1
0
1
0
0
0
0
0
1
0
3
0
1
1
0
1
2
0
0
0
0
1
0
2
1
2
3
0
1
1
1
0
0
0
0
3
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
2
1
1
0
3
0
0
0
1
1
0
0
1
0
0
3
0
0
0
0
2
0
0
1
0
2
2
0
2
2
0
0
2
0
2
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
1
0
2
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
2
0
1
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
2
2
2
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
2
0
0
0
2
0
2
0
1
2
0
2
1
2
0
2
0
2
2
1
2
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
1
0
0
0
0
1
0
1
0
0
0
2
0
1
0
0
0
0
3
0
0
1
0
2
0
0
0
0
0
1
1
0
0
2
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
1
2
2
1
0
1
3
0
0
1
0
0
0
2
0
2
1
2
2
0
0
0
0
0
0
1
1
1
0
1
0
1
0
0
0
0
2
0
0
0
2
0
0
2
0
0
2
2
1
2
4
0
0
0
4
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
7
2
2
0
0
0
0
0
0
1
0
0
0
2
0
0
1
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
2
1
0
2
1
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
2
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
1
1
2
0
0
2
0
0
0
0
2
0
0
1
2
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
2
0
0
1
2
0
0
2
0
0
1
0
1
2
0
1
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
1
2
2
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
2
2
0
0
1
0
0
1
0
0
0
0
1
0
0
1
3
1
0
2
1
0
0
2
2
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
1
0
1
0
3
0
2
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
2
0
0
0
1
0
0
0
2
2
1
0
1
0
2
0
2
2
0
1
2
1
1
0
0
3
2
0
0
0
0
0
0
0
2
0
0
3
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
2
0
2
0
0
0
0
0
0
0
1
1
0
2
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
2
1
2
3
0
0
0
0
2
0
0
2
1
0
1
0
0
0
1
2
2
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
1
0
1
1
2
0
2
0
1
2
0
0
1
0
0
1
0
0
1
0
2
0
0
1
0
0
0
0
0
2
0
0
1
1
1
0
0
0
0
2
1
0
1
0
1
0
3
0
0
1
0
1
2
0
2
0
4
0
1
3
0
0
0
3
0
0
3
9
0
0
0
4
0
0
0
2
2
0
2
0
0
2
0
0
2
1
0
0
0
0
0
2
2
0
2
0
0
0
1
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
2
2
2
2
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
2
0
4
1
1
0
0
0
2
0
0
1
0
6
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
2
0
0
2
0
1
1
0
0
1
1
1
0
2
0
0
0
0
0
4
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
5
0
0
1
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
1
2
1
0
1
0
0
3
2
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
1
0
0
0
1
0
3
2
0
0
1
0
0
1
2
0
0
0
0
2
0
1
2
1
0
0
0
1
0
0
4
0
0
0
0
2
0
1
0
1
1
2
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
2
0
1
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
1
0
0
0
2
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
3
0
1
0
1
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
2
1
2
1
1
0
0
0
0
0
0
1
0
2
0
0
1
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
2
0
1
0
0
1
0
1
0
2
1
2
0
0
0
1
0
1
2
0
0
2
2
1
2
1
2
0
0
3
0
1
1
0
0
0
3
0
0
2
0
0
0
1
1
1
1
0
0
1
0
0
0
0
2
0
0
1
0
0
0
2
2
0
0
1
0
0
0
1
0
1
0
0
0
0
2
2
1
0
0
1
2
0
0
1
0
1
2
2
1
3
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
2
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
1
2
0
1
2
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
2
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
5
0
3
3
1
0
1
0
2
1
0
2
2
2
0
2
1
0
2
2
0
0
0
0
0
0
1
0
1
2
2
0
0
0
0
0
0
1
0
0
2
0
0
1
2
2
0
0
0
2
0
1
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
1
2
1
0
0
1
3
0
1
2
0
0
3
0
1
2
0
2
2
0
0
0
2
0
1
1
0
2
0
0
0
2
0
2
4
0
2
0
0
1
1
0
2
0
3
2
1
0
0
0
0
1
2
0
1
0
1
2
1
2
0
0
0
0
2
0
0
1
1
1
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
1
0
0
2
2
0
1
4
0
0
2
0
1
1
1
0
0
0
0
0
2
1
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
1
0
2
2
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
2
0
0
2
2
0
0
1
0
2
0
0
0
2
0
0
0
1
2
2
2
1
0
2
0
1
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
2
0
0
1
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
1
2
1
0
1
0
0
1
0
0
1
0
0
0
1
0
0
2
1
0
0
0
0
0
0
2
1
0
3
2
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
3
2
2
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
2
0
2
3
1
0
0
0
0
0
0
1
1
0
0
0
0
0
3
1
2
0
0
0
1
1
0
0
0
0
0
2
0
0
2
0
0
0
2
1
1
0
0
0
20
1
0
2
1
3
0
0
0
2
0
1
1
0
0
2
0
0
1
1
0
2
1
1
0
0
0
0
0
2
1
2
0
0
0
2
0
1
0
0
2
1
1
3
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
1
2
1
0
0
0
0
2
1
0
0
0
3
2
0
0
0
0
1
0
0
0
1
0
2
2
0
2
0
0
0
0
0
1
0
0
0
2
2
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
9
1
1
0
0
0
0
1
0
0
2
0
0
0
0
0
2
2
3
0
0
0
1
0
1
1
0
0
1
0
1
0
1
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
2
2
0
4
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
2
2
0
1
2
1
0
0
0
0
0
0
2
2
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
1
1
0
0
3
1
5
2
0
0
0
2
0
2
0
0
0
1
2
2
2
0
2
0
1
2
0
0
2
3
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
1
0
1
2
1
2
0
0
2
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
2
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
3
0
0
2
0
4
1
0
2
1
1
0
1
0
0
0
0
2
0
0
0
1
0
2
2
1
0
3
2
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
1
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
2
2
1
0
2
2
1
0
0
0
0
0
1
0
0
3
2
0
1
1
0
0
0
0
1
2
0
0
0
0
1
2
1
0
0
2
1
0
2
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
3
0
0
0
0
1
0
0
1
0
0
2
0
0
2
0
0
0
0
0
2
1
0
1
1
2
2
0
0
0
0
0
2
2
2
0
0
0
0
5
2
0
0
0
0
0
0
0
0
1
0
2
2
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
2
0
0
0
2
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
2
2
2
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
3
2
0
1
1
0
0
0
1
2
1
0
0
1
0
0
0
2
0
0
2
1
0
0
0
2
0
0
1
1
0
1
0
0
0
1
0
0
1
0
0
2
0
0
0
1
0
2
0
0
1
0
0
2
1
0
0
0
0
0
0
2
0
0
2
1
0
0
3
1
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
1
2
1
0
1
0
0
0
1
0
0
2
0
2
1
0
1
0
1
0
1
0
0
2
0
0
0
0
1
2
0
1
0
0
0
0
0
2
1
0
0
0
0
0
2
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
1
0
2
0
0
0
2
0
2
0
0
0
0
0
0
1
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
2
2
2
0
0
1
0
2
0
0
0
0
1
0
0
0
2
0
0
0
1
0
2
1
2
0
0
1
0
2
0
0
0
0
0
0
3
2
0
1
0
2
0
1
0
2
0
1
1
0
0
0
1
1
2
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
2
0
3
0
1
1
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
2
1
0
2
1
0
1
2
0
1
0
3
2
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
3
2
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
2
1
2
0
1
0
2
0
4
0
0
2
1
2
1
0
2
0
0
0
1
1
4
2
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
2
2
0
1
1
2
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
1
2
0
0
0
0
3
0
0
0
0
1
0
1
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
2
0
0
2
2
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
2
2
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
1
2
0
1
0
3
2
0
1
2
0
1
0
0
0
4
0
2
0
0
2
1
1
0
0
1
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
1
0
0
0
4
0
0
0
1
2
0
0
1
0
0
0
0
1
1
2
2
0
1
0
0
2
0
2
2
0
0
0
1
0
0
2
1
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
2
0
0
1
0
0
1
0
0
0
1
0
0
0
1
2
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
1
0
1
0
0
0
0
1
0
1
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
2
1
0
1
0
1
0
0
2
0
0
2
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
2
2
0
1
0
1
0
2
1
0
2
1
0
0
0
0
0
1
2
1
1
1
3
0
2
0
0
1
1
0
1
0
0
1
0
0
2
0
2
1
0
2
1
0
0
0
0
0
0
3
0
1
0
2
0
4
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
1
0
1
1
0
2
0
0
0
0
2
0
2
1
1
0
1
2
2
0
2
0
1
0
2
0
2
2
0
0
0
0
0
1
2
3
0
0
0
0
0
0
2
2
1
2
1
1
1
2
0
1
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
3
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
1
0
0
0
1
1
2
0
1
0
0
2
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
1
0
0
1
2
0
0
1
1
0
0
0
0
0
1
1
2
0
0
0
1
1
1
2
0
0
1
0
0
0
1
1
0
0
1
0
1
0
2
2
0
0
0
0
2
0
2
1
2
1
0
0
0
0
0
0
2
0
1
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
1
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
1
1
2
0
0
2
0
0
2
0
0
2
1
0
0
2
1
2
0
1
0
0
1
1
0
0
0
0
0
1
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
2
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
2
1
3
0
0
0
0
2
0
0
2
1
2
1
0
1
1
0
0
0
2
1
0
0
0
0
2
2
0
0
1
0
1
0
0
2
0
1
4
0
1
0
3
2
0
0
0
2
0
0
0
0
1
0
0
1
2
0
0
0
1
0
0
0
1
0
2
4
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
2
1
2
2
0
2
1
2
1
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
3
1
2
2
0
1
0
2
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
1
1
0
0
0
2
0
1
0
3
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
2
0
1
0
1
0
0
1
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
3
0
0
2
1
0
0
0
0
0
2
0
0
0
2
0
0
1
1
1
0
0
2
2
0
0
2
0
0
0
0
2
0
1
2
0
2
0
1
0
1
0
1
0
2
0
1
0
0
0
0
0
2
0
0
2
3
0
1
0
0
2
0
0
0
2
1
0
2
2
0
1
0
0
0
2
0
2
1
4
0
1
0
0
1
0
0
0
0
5
0
1
2
0
0
0
0
0
4
0
1
1
2
2
0
0
2
0
0
0
3
2
1
2
2
0
0
0
0
0
0
0
0
0
1
1
0
2
1
0
0
1
0
0
0
2
2
0
1
0
4
0
2
1
0
0
0
4
0
2
0
0
0
0
0
2
0
0
2
2
1
0
2
0
0
0
2
0
1
0
3
0
2
0
1
0
0
0
0
0
0
2
1
0
2
0
0
0
0
1
0
2
0
2
0
1
0
0
2
0
0
0
2
2
2
0
0
2
0
0
1
2
1
0
0
0
0
0
2
1
0
0
1
0
0
2
0
0
0
1
0
0
1
0
0
2
0
1
0
0
0
1
0
1
0
0
0
2
0
0
0
0
1
2
1
0
1
2
0
0
0
1
0
1
0
2
1
0
1
0
0
2
2
0
0
0
2
2
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
2
0
3
0
0
0
2
2
2
0
1
0
0
1
0
2
2
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
1
0
0
2
2
1
1
0
0
1
0
0
0
0
0
1
0
0
0
2
0
2
0
0
2
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
2
0
0
1
2
0
2
0
1
0
0
2
0
2
0
0
0
0
0
2
0
0
1
0
1
0
0
3
2
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
1
0
2
2
0
0
2
0
0
2
2
2
0
0
2
0
2
0
1
1
5
2
0
0
1
1
0
0
0
0
1
3
0
2
0
2
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
2
0
0
2
0
0
0
0
0
1
2
0
2
0
0
2
2
0
1
1
0
0
1
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
1
1
2
0
1
2
2
0
3
2
0
0
0
2
1
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
2
1
2
0
2
1
0
0
0
2
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
1
0
0
1
2
1
1
0
0
0
2
0
0
2
1
0
2
1
0
1
0
0
2
0
0
0
1
1
3
0
1
1
0
0
2
0
0
1
0
1
0
0
0
2
0
0
2
2
0
0
0
0
8
0
0
0
1
0
0
2
0
2
0
1
0
5
1
5
0
1
1
1
1
0
0
2
0
1
2
2
0
0
0
0
2
1
0
2
0
0
2
2
2
0
1
0
0
2
0
0
0
2
0
0
0
0
2
0
2
2
2
1
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
2
1
0
2
0
0
2
1
0
0
1
0
1
3
0
2
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
2
0
2
0
1
0
2
0
0
0
1
0
0
0
0
0
0
3
1
0
1
0
0
0
1
0
0
2
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
2
0
2
0
1
0
0
0
0
0
1
0
0
0
1
1
4
2
1
0
0
0
2
2
0
0
1
0
0
1
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
2
0
0
2
2
0
0
2
0
2
0
0
0
2
3
0
0
2
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
0
0
1
1
2
0
0
1
0
0
0
1
0
0
1
0
0
1
0
2
0
0
1
0
2
2
0
0
0
1
1
0
0
2
0
2
1
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
1
0
1
0
0
2
2
2
0
2
0
0
0
0
0
1
0
0
0
1
0
2
0
1
0
0
0
0
0
2
1
0
1
1
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
2
1
0
0
1
0
0
0
1
0
1
2
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
1
2
0
0
0
2
2
2
0
1
0
0
2
0
1
0
2
0
0
1
0
0
0
0
0
1
0
3
0
0
0
0
0
0
2
0
0
0
2
2
2
0
1
2
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
1
2
2
2
2
0
0
0
1
0
2
0
1
1
0
0
0
0
0
0
1
0
0
3
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
1
2
0
0
1
1
2
0
1
0
1
2
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
1
2
0
0
0
3
2
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
1
1
2
2
0
0
2
0
2
0
1
0
0
2
0
1
2
0
0
0
0
0
1
0
1
1
0
2
2
0
2
1
0
2
0
3
1
0
1
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
1
2
2
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
1
2
0
0
2
0
2
2
2
0
0
0
0
2
0
0
1
1
1
0
0
1
0
0
0
0
0
2
0
0
2
1
1
3
0
0
1
0
1
0
0
1
1
0
0
0
2
1
0
2
0
0
1
1
0
0
0
2
0
2
1
1
0
0
1
0
0
0
0
2
0
1
0
1
1
0
1
0
1
0
0
2
2
1
0
2
0
2
0
2
0
2
0
0
0
0
0
2
0
0
1
0
1
1
0
1
0
0
2
0
0
1
3
1
4
0
0
0
2
0
0
0
1
2
0
2
1
2
0
0
2
0
1
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
1
0
0
1
0
0
1
1
0
0
0
0
1
2
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
2
0
2
1
1
0
0
0
0
0
2
2
0
0
2
0
1
1
0
1
0
2
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
2
1
1
0
0
0
0
0
0
1
0
0
0
2
1
1
2
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
1
2
1
0
1
0
4
2
0
0
0
0
0
0
0
0
3
0
0
1
0
2
0
0
0
0
0
2
0
1
2
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
2
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
4
0
1
0
2
1
1
0
0
0
2
0
2
0
0
0
1
0
0
1
0
0
0
1
1
1
0
1
1
0
0
0
0
2
0
2
0
0
2
0
0
0
0
1
0
0
0
1
0
0
2
2
0
0
2
0
1
1
1
0
0
0
2
0
2
0
0
1
2
0
0
0
1
0
2
1
1
0
0
0
2
0
0
2
0
2
0
0
1
0
0
0
2
0
0
0
1
0
0
1
0
2
0
0
2
0
2
2
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
2
2
1
0
0
0
0
0
0
0
2
0
2
0
1
2
1
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
2
0
0
5
0
0
2
1
0
1
3
2
0
2
1
0
2
1
0
0
0
2
0
2
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
2
1
0
0
0
0
0
0
2
0
1
3
2
2
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
1
0
2
0
0
1
0
0
2
2
0
0
2
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
1
3
2
0
1
2
0
2
0
2
0
0
0
1
0
2
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
2
1
0
1
0
0
0
0
1
0
2
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
3
2
0
1
0
0
0
0
2
1
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
1
2
2
0
2
0
1
1
3
0
0
0
0
3
2
0
2
0
0
0
0
1
0
1
3
0
1
1
1
2
0
0
1
0
0
0
1
0
1
0
1
0
2
0
0
0
1
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
3
1
0
1
0
2
0
0
3
0
0
0
2
0
0
2
0
0
1
1
0
1
1
3
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
3
2
1
1
1
0
1
1
2
2
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
3
0
0
0
0
1
1
0
1
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
2
0
0
0
0
0
1
0
2
0
0
0
2
2
1
1
0
0
0
1
0
0
0
0
2
0
2
2
0
0
0
2
0
0
0
2
0
2
0
0
0
2
0
2
0
2
0
0
2
0
0
0
1
0
0
1
0
1
0
0
2
0
0
0
0
2
0
0
0
0
1
0
1
0
2
0
0
2
0
0
1
1
1
0
1
0
0
0
1
1
2
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
2
2
2
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
2
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
1
1
1
0
2
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
2
0
1
0
0
0
0
1
2
0
0
0
0
0
8
1
2
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
2
0
0
0
0
1
0
2
2
0
0
2
1
0
0
0
0
0
0
1
1
2
0
0
2
1
0
1
1
0
0
1
1
0
3
0
0
0
1
0
0
2
2
0
0
0
0
0
1
0
2
9
0
2
0
0
2
1
0
0
0
2
0
3
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
5
1
0
2
0
0
0
2
0
1
0
0
2
0
1
2
1
0
0
1
0
0
2
0
0
0
0
0
2
1
2
0
2
1
0
2
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
2
0
0
0
0
1
1
2
0
0
0
1
0
1
0
0
1
1
0
0
3
2
2
3
0
0
0
0
0
0
2
0
0
2
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
1
0
2
0
1
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
1
1
0
0
4
2
0
0
0
0
2
2
1
2
0
0
0
1
0
2
0
2
0
2
5
0
0
3
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
2
0
2
2
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
2
0
2
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
2
1
1
2
2
0
0
1
1
2
1
0
0
0
0
0
0
2
0
0
2
0
0
1
1
0
0
0
0
0
0
1
0
1
4
3
3
2
1
0
0
1
0
1
4
0
0
2
0
1
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
1
1
1
0
0
2
0
1
0
3
0
0
0
0
2
0
0
2
0
0
2
0
0
0
2
0
0
2
0
0
0
0
2
0
0
1
0
1
0
1
5
0
2
0
1
0
0
0
2
1
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
1
0
0
0
1
0
2
2
2
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
2
3
1
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
1
1
0
0
1
2
0
0
0
1
0
2
0
2
0
0
1
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
2
0
2
0
0
2
0
0
1
0
0
1
1
0
0
0
0
2
1
2
0
4
0
0
0
0
2
0
0
1
1
0
0
2
0
0
0
0
2
2
2
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
2
0
0
1
0
0
0
2
2
2
2
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
2
0
0
1
0
0
1
0
2
2
1
1
0
0
0
0
0
0
2
0
2
1
2
0
0
0
0
1
2
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
1
0
1
1
1
1
0
1
2
0
1
2
3
0
2
0
0
1
0
2
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
1
0
8
2
0
0
0
1
2
0
0
1
0
1
1
0
0
2
0
0
0
0
1
1
0
0
2
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
3
0
1
0
0
0
0
1
1
0
2
0
1
0
0
0
0
1
1
0
0
2
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
1
0
2
1
2
0
0
1
0
2
1
1
0
1
0
2
0
0
1
0
0
0
0
1
0
2
2
2
0
0
2
0
2
0
0
0
1
0
1
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
1
1
0
0
1
0
2
2
1
1
0
0
0
1
0
0
1
1
0
0
0
2
2
0
0
2
1
0
0
0
0
3
0
0
1
2
0
0
1
6
0
0
1
1
2
0
0
1
0
0
0
0
0
0
2
0
0
0
2
2
2
1
0
0
0
0
0
2
0
4
0
0
0
0
0
1
0
3
0
0
0
2
1
0
0
1
2
0
2
1
1
0
1
0
1
2
0
0
1
0
2
1
0
0
0
0
0
0
1
1
0
1
0
0
1
0
2
0
4
0
2
0
2
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
1
1
0
2
0
0
0
0
0
0
1
2
1
0
2
0
0
2
0
1
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
1
2
0
0
1
0
0
0
0
0
2
2
1
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
2
2
2
1
1
0
1
1
0
0
0
1
0
2
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
2
1
2
0
0
1
0
0
0
0
0
0
3
1
0
0
0
0
0
1
1
0
2
0
0
0
1
0
0
0
2
0
0
2
0
1
0
0
0
0
1
2
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
1
2
0
1
1
0
0
2
2
0
2
0
2
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
1
2
1
0
0
0
0
0
1
0
1
0
1
1
1
0
1
0
0
0
2
0
0
1
0
0
1
3
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
2
1
1
0
2
3
0
0
2
0
0
0
3
2
0
0
0
0
0
1
1
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
2
1
0
0
0
2
1
0
1
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
9
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
2
1
3
0
1
0
0
0
2
0
0
0
0
0
2
0
0
1
1
0
1
0
2
0
0
0
0
0
0
0
0
1
2
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
3
0
0
1
1
0
0
1
0
1
0
2
2
0
0
0
0
1
0
0
0
2
0
2
3
2
1
1
0
0
0
0
2
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
1
0
0
0
2
1
2
3
0
0
3
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
2
0
0
2
2
1
0
2
1
0
0
0
1
4
0
0
1
0
4
2
2
0
1
0
0
1
2
2
0
0
2
1
0
0
2
1
2
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
2
0
0
2
1
0
1
0
2
0
0
0
0
0
0
0
2
1
2
1
1
0
3
0
3
0
0
0
2
1
0
0
0
1
0
0
0
0
6
2
0
2
0
1
0
0
2
0
2
0
0
2
0
0
2
0
0
1
2
2
0
0
0
0
0
0
0
2
3
0
0
2
1
0
0
2
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
2
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
2
1
0
2
3
1
0
0
0
0
1
0
1
1
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
3
0
3
0
0
0
1
0
0
0
0
2
0
0
0
1
1
2
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
2
0
0
1
1
0
0
1
2
2
2
0
0
0
2
0
0
0
1
2
0
2
1
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
1
1
1
0
0
0
1
0
2
1
0
0
0
2
0
0
2
0
0
0
1
0
0
0
1
0
0
2
0
0
0
1
1
0
3
0
0
0
0
2
0
0
1
2
1
1
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
1
1
0
0
0
1
1
0
1
2
0
1
2
1
0
1
2
2
0
1
0
1
0
0
1
2
1
0
2
3
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
1
0
0
2
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
2
1
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
3
2
1
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
1
2
0
1
0
1
0
0
0
2
1
0
1
1
0
0
2
0
0
0
0
0
0
1
0
1
0
0
2
0
2
0
2
0
3
2
0
0
1
2
0
2
1
2
0
0
2
1
0
0
0
0
0
0
0
1
1
0
2
2
2
2
1
2
2
0
0
2
0
1
1
1
0
2
0
1
0
3
0
0
0
0
1
0
0
1
0
0
1
1
0
1
1
0
0
0
0
2
2
0
0
0
1
1
0
0
1
0
0
0
16
0
2
1
0
0
2
0
2
0
0
0
0
2
0
3
0
0
0
2
0
1
0
0
0
0
1
0
2
0
1
0
0
0
2
0
0
0
0
2
1
0
0
1
1
0
2
0
2
0
0
0
0
1
1
0
0
2
1
0
0
1
0
0
0
2
0
2
2
0
0
0
2
0
2
0
0
0
0
0
2
0
2
1
0
1
2
0
2
2
1
0
0
1
1
0
0
0
0
1
2
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
2
4
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
1
2
0
0
1
0
1
0
0
0
1
0
0
3
0
0
2
1
0
1
0
2
1
0
0
0
2
0
0
1
2
0
0
0
0
2
1
0
2
0
0
0
0
0
1
0
2
2
0
0
0
2
2
0
0
0
0
0
0
2
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
3
2
2
2
0
0
0
0
0
3
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
1
2
0
0
2
4
0
2
0
0
0
2
0
1
0
0
2
1
0
0
0
0
0
0
0
1
2
0
0
1
0
2
2
0
0
0
0
2
0
2
0
0
0
1
0
0
3
2
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
2
0
2
2
0
0
0
0
0
0
2
1
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
1
2
1
0
0
1
1
3
0
0
0
0
0
0
1
1
2
1
0
0
0
0
4
0
0
0
0
1
0
0
0
0
1
0
2
1
3
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
1
0
1
1
0
1
1
0
0
1
0
0
0
0
1
0
0
2
0
0
0
2
0
0
2
0
0
0
2
0
0
2
0
0
5
1
4
1
2
0
2
0
0
2
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
2
0
0
0
1
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
1
0
0
0
4
3
0
0
0
1
0
0
0
2
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
1
0
1
2
2
0
2
2
0
0
0
3
0
0
0
2
3
2
2
0
0
0
2
2
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
3
2
2
0
0
2
2
1
3
0
0
1
0
0
1
0
1
2
0
0
1
0
1
1
2
0
2
4
2
0
2
0
0
2
2
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
5
2
0
2
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
2
0
1
2
1
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
2
2
0
0
2
1
0
1
0
0
0
1
2
0
2
2
1
0
0
3
2
0
1
0
1
1
0
2
1
0
2
1
0
0
1
2
0
1
1
2
0
2
0
0
2
0
1
0
0
0
0
0
2
0
0
2
0
2
1
0
0
1
1
0
0
2
2
0
5
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
2
0
2
1
0
0
0
1
0
0
0
1
0
2
0
0
0
1
0
0
0
1
0
0
1
1
0
2
0
0
1
0
2
1
0
0
0
0
2
0
0
0
2
0
1
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
4
0
0
0
1
1
0
0
1
1
2
0
0
0
0
0
0
0
1
0
3
0
2
2
1
0
0
0
0
0
0
2
0
3
0
0
0
0
2
0
1
1
0
0
0
0
0
1
0
2
0
0
0
2
1
2
2
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
2
0
3
1
2
0
4
0
1
0
1
1
0
3
0
0
1
2
0
0
0
2
0
0
0
0
0
2
0
2
0
1
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
1
2
2
0
2
0
0
0
1
0
0
2
0
2
0
2
1
1
0
0
1
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
1
1
1
0
0
1
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
2
2
0
1
0
0
0
1
0
1
0
2
0
0
2
0
2
0
0
2
0
0
0
0
1
0
0
1
0
3
2
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
1
0
2
0
0
1
2
2
0
0
2
0
0
1
0
0
0
1
0
2
0
0
2
0
0
1
0
0
0
2
0
0
0
1
2
0
2
0
1
0
0
1
1
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
2
0
0
0
3
1
0
1
2
2
0
2
1
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
1
0
0
1
1
2
2
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
2
0
0
0
0
2
2
1
0
1
1
0
0
0
2
1
1
0
0
1
0
1
0
0
2
1
0
0
1
2
1
0
2
0
2
0
0
0
3
0
0
0
2
0
0
0
2
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
2
0
0
0
0
1
2
0
0
1
2
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
1
0
0
1
1
0
0
2
1
1
0
2
0
0
1
1
0
0
2
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
2
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
3
0
0
3
0
1
2
0
1
0
0
1
1
0
0
0
0
2
0
0
0
2
1
0
0
0
1
2
2
0
0
1
2
0
0
1
0
2
2
0
2
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
3
0
0
2
3
0
1
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
1
1
0
0
3
2
3
0
1
0
0
0
1
0
0
0
1
2
0
2
0
2
0
1
1
0
1
1
0
0
0
1
2
0
2
0
0
0
1
2
0
0
3
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
1
0
0
2
1
2
0
1
0
0
0
1
0
2
1
1
0
0
0
0
0
0
0
0
0
1
1
1
0
2
0
0
0
0
0
0
1
0
2
0
2
0
1
0
4
0
0
0
2
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
1
0
0
2
0
0
0
1
0
1
2
0
1
1
0
1
2
0
2
0
3
2
0
1
0
0
0
3
0
0
2
0
1
0
0
0
0
0
2
0
0
0
3
0
2
0
0
1
4
1
0
0
0
0
0
2
0
0
2
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
1
2
0
2
1
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
3
2
1
2
1
2
1
1
0
0
0
0
2
2
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
2
0
3
0
1
0
0
3
3
0
1
0
0
1
1
0
0
0
0
0
1
2
1
1
0
1
0
2
2
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
3
0
1
1
1
0
0
0
2
0
0
2
0
0
0
0
2
2
0
1
0
0
2
0
0
0
1
0
1
0
0
0
1
1
2
0
0
1
1
1
1
0
2
0
0
2
0
3
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
2
0
0
1
1
0
1
0
0
1
2
0
1
1
2
0
2
0
0
0
2
2
16
0
0
1
0
0
0
2
0
0
9
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
2
0
0
2
0
2
2
0
1
0
0
0
1
0
0
0
1
3
0
0
0
1
1
0
0
0
0
2
3
0
1
0
2
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
1
1
2
2
0
1
2
1
0
1
0
1
0
0
1
1
0
0
4
0
0
1
1
2
0
2
2
0
0
0
0
1
0
0
0
0
1
1
0
0
1
1
2
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
2
0
2
1
2
0
0
2
0
0
1
0
1
0
1
2
2
0
2
0
0
2
0
0
1
2
0
0
0
1
0
2
0
2
2
0
0
1
0
1
0
2
1
0
0
0
0
2
1
0
1
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
1
0
1
2
2
1
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
2
1
1
1
1
0
1
2
1
0
0
0
0
0
1
0
0
0
1
1
3
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
2
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
2
0
0
1
0
4
1
0
1
1
0
2
0
0
0
0
0
0
2
2
0
2
0
1
1
0
0
0
0
1
2
2
0
0
0
1
2
4
0
5
2
0
0
0
0
4
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
1
2
1
0
2
1
0
0
2
0
0
0
0
0
2
0
0
2
1
0
4
0
0
2
0
1
3
0
0
0
2
0
0
0
0
0
0
1
0
2
2
0
1
0
1
0
2
0
0
0
0
1
1
1
2
0
0
0
1
0
3
0
0
0
2
0
0
0
2
1
1
2
0
0
0
0
0
2
2
1
0
1
0
0
4
2
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
2
1
0
0
0
1
0
0
0
2
0
3
0
0
2
0
0
0
0
0
0
0
1
0
2
1
0
1
1
2
2
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
2
2
0
1
0
0
1
0
0
2
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
4
0
0
1
0
1
0
1
0
0
0
1
1
1
0
0
2
0
0
0
1
0
2
2
0
0
1
2
0
3
2
0
0
0
2
0
1
0
0
2
0
0
0
0
1
0
0
1
0
2
0
2
1
1
1
1
0
1
0
0
2
4
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
3
2
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
1
0
2
2
0
1
2
2
0
0
0
1
0
1
0
0
1
0
0
0
2
1
1
1
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
3
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
1
0
6
0
2
2
2
1
0
1
1
1
1
1
1
0
2
2
1
1
0
1
0
2
0
0
1
0
1
0
0
0
0
2
0
8
0
0
0
0
2
0
0
1
0
1
2
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
5
1
0
1
0
0
2
0
1
0
0
5
2
0
0
1
0
0
0
0
0
0
0
3
0
2
0
0
2
2
0
2
0
1
0
0
0
1
0
0
0
0
0
0
1
0
2
2
0
0
0
1
0
0
1
2
0
1
0
0
0
0
0
1
0
2
0
0
2
2
0
1
1
0
1
0
0
0
0
1
1
0
0
2
0
0
0
0
0
3
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
2
0
2
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
1
1
2
1
2
0
0
0
2
0
2
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
1
2
1
0
1
2
2
1
0
2
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
2
0
1
1
1
0
1
0
1
0
2
1
0
0
0
2
0
1
0
0
2
0
0
2
0
0
0
0
0
0
2
1
2
1
0
0
0
0
0
3
1
0
1
0
0
0
1
2
0
0
2
0
0
1
0
0
0
0
0
1
1
0
2
0
0
1
1
0
0
3
1
2
0
0
3
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
1
1
0
0
0
0
0
5
0
1
0
0
2
2
0
0
0
1
2
2
0
0
0
2
0
1
0
1
0
1
1
0
0
0
0
0
0
1
0
2
0
0
0
1
0
1
2
0
0
2
2
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
1
1
2
0
0
0
1
2
0
0
2
0
2
1
0
0
0
1
0
0
0
0
2
0
0
0
1
0
2
0
2
0
0
0
0
0
0
2
0
1
0
1
0
0
3
0
0
2
0
0
3
2
0
2
0
0
0
1
0
0
2
2
0
0
2
1
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
1
2
2
1
0
0
0
0
0
2
1
1
3
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
1
0
2
0
0
0
0
1
0
0
0
0
1
0
0
1
1
2
0
0
3
2
0
5
2
1
2
0
2
0
0
0
0
2
1
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
3
0
2
1
0
0
1
0
0
0
0
0
0
2
1
2
0
2
0
0
0
0
0
0
0
0
1
1
0
1
0
2
3
0
2
0
2
0
1
2
0
0
2
0
0
2
0
0
1
1
1
1
1
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
2
0
0
0
1
1
2
0
0
0
2
0
3
0
0
0
4
0
0
1
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
2
0
1
2
2
0
0
2
0
0
0
1
0
0
0
0
0
3
0
0
0
0
1
0
2
0
0
1
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
3
0
2
1
0
1
2
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
1
1
0
2
2
0
1
0
2
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
2
0
0
0
1
4
1
0
0
0
1
1
2
1
0
0
2
3
0
0
0
1
0
0
1
0
0
0
0
0
2
2
0
1
1
2
0
0
0
0
0
0
3
0
0
3
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
2
0
1
1
2
0
2
0
0
0
0
1
2
0
2
0
0
0
2
1
2
0
0
1
1
0
0
0
0
2
0
0
1
0
3
3
0
0
1
2
1
0
0
0
1
0
0
1
2
0
0
1
0
0
0
0
0
2
0
2
0
0
2
0
0
0
1
0
2
0
0
2
0
0
0
0
0
2
0
1
2
0
0
0
0
2
0
1
2
0
4
0
0
0
1
0
2
0
2
0
1
0
2
1
1
2
0
0
1
0
1
1
0
0
0
0
0
0
2
0
1
2
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
2
2
2
0
0
2
2
0
1
0
1
0
1
0
2
1
0
2
1
1
0
0
0
1
0
0
0
0
2
0
0
5
0
0
0
2
3
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
1
2
0
0
0
0
0
0
2
2
1
0
0
1
2
3
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
2
2
0
1
0
1
0
0
0
2
0
2
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
1
0
0
2
0
0
2
0
0
0
0
2
1
2
0
1
0
0
2
0
0
1
1
0
0
0
0
1
2
1
0
1
0
0
0
0
2
0
0
3
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
1
2
0
0
0
2
1
0
0
0
0
0
0
2
0
3
0
0
1
2
0
0
0
1
2
0
0
0
0
1
1
0
2
2
0
0
0
1
1
0
0
0
2
0
2
0
1
0
0
0
0
1
0
1
2
2
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
2
0
1
2
0
0
0
1
0
1
0
0
0
0
0
2
1
1
1
1
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
3
0
0
0
1
2
0
1
1
0
0
1
2
0
2
0
2
0
0
0
1
1
0
0
0
2
1
2
0
0
0
0
0
0
1
0
0
0
7
4
0
0
0
0
0
0
2
0
0
2
1
1
1
0
0
0
1
0
1
1
0
1
2
11
0
0
0
2
3
1
0
0
1
0
2
3
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
2
2
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
2
0
2
1
1
1
0
0
0
2
0
0
0
2
0
0
0
1
2
1
0
0
0
1
0
1
0
2
0
0
1
0
2
0
1
0
0
1
0
0
1
0
2
0
0
3
0
1
0
1
0
2
2
1
0
0
0
2
0
0
1
0
1
0
0
1
0
1
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
2
1
0
2
0
0
0
0
1
2
1
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
1
1
0
0
0
1
2
0
0
0
0
1
2
0
0
1
0
0
0
0
1
0
1
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
2
0
0
0
2
0
2
0
2
0
0
2
0
1
0
0
1
0
1
0
0
2
0
0
0
0
1
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
1
0
2
0
2
0
0
0
0
0
0
1
2
0
3
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
1
0
0
1
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
2
2
2
2
2
0
0
0
0
0
2
1
0
0
0
1
1
1
0
0
1
0
0
1
0
3
2
0
1
2
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
1
1
0
0
0
1
1
0
2
0
0
0
2
4
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
2
2
1
0
1
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
1
0
5
0
2
1
2
0
0
0
1
0
0
2
1
0
2
0
0
0
2
1
0
2
0
0
0
0
0
0
2
0
0
1
0
0
2
2
0
0
1
0
0
0
0
1
0
0
2
0
2
0
0
0
0
2
0
1
3
0
2
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
2
0
0
0
3
0
1
2
1
0
2
0
0
2
0
0
1
1
0
0
1
0
2
0
1
0
0
0
0
1
1
0
0
0
2
0
1
2
0
0
0
0
0
0
2
0
2
2
2
2
0
1
0
0
0
2
0
0
1
0
1
0
0
0
2
2
0
0
2
0
2
0
0
0
0
0
1
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
2
0
0
2
2
0
0
1
0
2
2
0
0
1
0
0
1
2
7
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
1
0
0
2
1
0
0
0
1
0
0
0
0
1
1
0
0
1
1
1
0
0
0
0
0
1
1
1
1
0
0
0
1
2
0
1
3
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
3
0
1
0
0
0
0
3
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
1
0
2
1
2
0
0
0
1
0
2
1
0
0
1
2
0
1
0
0
0
0
0
1
0
0
1
1
2
0
1
0
0
0
0
1
3
2
0
0
1
0
0
2
0
2
0
0
2
1
2
0
0
0
0
0
0
0
1
0
2
1
0
2
2
1
0
1
0
0
0
1
2
0
1
0
1
1
1
1
0
0
2
0
0
0
0
2
1
2
0
1
0
0
0
0
0
3
0
0
0
10
0
1
0
0
2
0
4
1
0
2
0
2
2
0
0
2
0
1
0
2
0
0
2
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
2
2
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
6
0
0
1
3
0
0
0
0
0
0
3
0
1
0
0
2
0
0
0
1
0
0
2
0
0
2
0
0
1
0
2
0
1
1
3
0
2
1
0
0
0
3
2
0
0
1
2
0
0
0
0
0
0
2
0
0
0
4
1
1
2
0
0
0
1
1
0
2
0
0
0
0
0
0
2
0
2
1
2
4
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
2
2
0
1
0
0
0
1
0
0
0
6
2
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
1
0
0
1
4
0
1
0
2
2
0
0
0
0
0
1
0
0
1
2
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
3
0
1
0
0
1
1
0
2
1
0
0
0
0
1
6
2
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
1
0
2
2
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
1
2
0
0
1
2
0
2
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
1
1
0
0
3
1
0
2
2
0
0
0
0
0
0
0
0
2
0
0
1
2
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
6
1
0
2
0
2
0
2
1
0
2
2
0
0
0
0
0
0
1
2
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
2
0
0
1
2
1
0
0
0
2
2
2
0
0
0
0
1
0
0
2
3
0
2
0
2
1
1
0
1
1
1
0
0
0
1
0
2
1
0
0
0
0
1
0
1
0
0
0
1
1
1
0
0
0
1
0
0
3
0
1
1
1
2
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
1
2
2
1
1
2
0
0
0
0
2
0
0
1
2
0
0
0
0
1
2
2
2
0
2
1
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
2
0
2
1
0
0
0
0
1
1
1
2
0
0
0
0
1
0
1
0
1
0
0
2
1
0
0
0
1
0
0
1
1
1
0
0
1
0
0
1
0
1
1
0
0
0
2
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
2
0
0
0
1
0
1
1
0
0
0
0
0
2
0
0
0
0
0
2
1
0
1
1
0
0
0
3
0
0
0
0
2
0
2
0
2
1
0
0
2
0
0
0
2
2
0
1
0
2
0
0
2
0
1
1
0
0
1
2
1
1
2
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
2
0
0
2
0
0
0
2
2
0
2
0
0
0
0
0
0
0
1
0
2
0
0
1
0
1
0
0
0
0
2
2
0
2
3
0
0
2
0
0
2
0
2
0
2
1
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
2
0
1
0
0
0
1
0
2
0
1
0
2
1
1
1
0
1
1
1
0
0
0
1
0
0
0
6
2
0
0
0
2
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
3
0
1
1
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
3
0
1
0
0
0
0
0
2
3
0
0
1
0
1
2
0
1
0
0
0
1
0
1
2
0
1
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
2
1
2
1
0
0
0
3
0
1
0
0
0
0
0
1
0
0
3
0
2
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
1
1
2
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
3
0
1
0
0
2
0
2
0
0
1
2
2
0
0
0
3
0
3
1
0
2
2
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
2
0
1
0
0
2
0
3
0
2
2
1
0
0
0
3
1
0
0
0
0
0
2
0
1
2
0
2
0
0
0
0
0
0
1
1
0
0
0
0
3
1
0
1
2
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
1
0
0
1
1
1
0
2
1
0
1
0
3
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
1
2
0
0
0
0
0
0
0
2
0
2
1
2
0
0
0
0
1
2
0
2
0
3
2
0
2
0
0
2
1
1
2
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
2
3
2
0
0
1
1
0
0
0
2
0
0
0
0
0
2
0
0
1
1
0
0
0
0
1
0
0
0
2
1
1
1
0
0
1
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
2
0
1
0
0
0
0
2
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
3
0
2
0
3
0
2
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
2
2
0
1
0
0
1
0
1
0
1
0
0
2
0
0
2
2
0
0
1
1
0
2
1
0
2
2
1
0
0
0
0
0
0
2
1
0
0
1
0
1
0
0
2
2
0
2
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
2
1
0
1
0
1
2
0
0
2
1
0
2
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
4
1
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
2
2
0
1
0
2
3
0
0
0
0
2
1
4
1
2
0
0
0
1
1
1
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
1
0
1
0
0
0
0
0
0
2
2
1
1
1
0
2
0
2
0
0
1
3
1
0
0
0
0
2
2
0
1
1
0
0
2
2
0
2
0
2
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
5
0
0
2
0
0
0
1
0
2
1
0
0
0
1
2
0
0
1
0
0
2
0
0
0
2
0
0
2
0
0
2
1
1
1
0
0
0
0
0
2
0
0
0
2
2
0
7
0
0
0
2
0
2
1
2
2
1
0
0
0
0
0
1
1
2
0
1
1
1
0
1
1
0
2
0
1
0
0
0
3
0
0
0
0
0
0
0
0
2
1
1
2
0
0
0
0
1
0
0
0
1
0
0
0
2
0
2
0
1
0
3
2
0
1
2
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
1
1
1
0
0
0
0
1
2
2
0
2
0
2
0
1
0
0
0
0
0
1
0
2
0
2
0
1
0
2
0
0
0
0
2
0
1
1
0
1
0
2
0
0
2
0
0
0
0
0
1
0
1
0
0
1
5
1
0
0
0
1
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
2
2
0
2
0
3
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
1
0
0
0
1
2
2
1
0
0
0
0
2
0
1
2
0
1
1
0
5
0
0
2
0
0
0
0
0
2
0
2
2
1
4
0
0
0
1
0
0
0
1
0
0
1
3
0
2
0
0
0
0
0
0
0
1
2
0
2
0
0
0
1
0
0
0
0
0
1
2
0
0
2
2
1
0
2
1
0
0
0
1
0
0
2
0
0
1
0
1
1
1
2
0
0
1
1
2
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
2
2
1
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
1
0
1
0
0
0
0
2
4
0
2
1
2
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
1
1
0
0
2
0
0
0
1
1
3
0
0
0
1
0
0
0
2
0
0
1
0
0
0
1
0
0
0
3
1
0
2
0
1
0
0
0
0
2
0
1
2
0
0
0
0
0
2
1
0
2
0
1
0
2
0
1
0
0
0
2
0
0
0
0
2
0
2
0
0
0
2
1
0
1
0
0
0
1
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
3
2
1
0
0
2
0
2
0
1
2
3
0
0
1
0
0
0
2
2
0
1
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
1
0
0
0
1
1
2
1
0
0
0
0
0
0
2
2
0
2
0
0
0
1
0
0
0
2
0
0
0
1
2
0
0
0
0
2
1
0
2
0
0
2
0
0
0
0
0
0
0
2
2
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
2
2
2
0
2
0
2
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
3
0
1
1
0
3
0
0
0
2
0
1
0
1
0
1
1
1
0
1
0
2
2
0
0
2
0
0
0
0
0
2
0
2
1
2
2
0
0
3
0
0
0
1
0
0
0
1
1
2
1
0
0
0
0
2
2
3
0
0
2
0
0
0
0
0
0
0
0
0
3
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
2
0
0
2
0
0
0
0
0
2
0
0
0
7
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
1
0
2
0
0
2
1
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
1
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
1
3
0
0
0
4
1
0
1
1
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
4
2
1
2
0
1
0
0
0
1
0
0
0
0
0
0
0
2
2
1
0
0
0
0
1
0
0
1
1
2
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
1
0
2
0
3
2
0
0
0
1
0
2
0
0
1
1
2
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
4
0
2
0
0
0
2
0
0
0
0
3
0
0
2
2
0
2
0
0
1
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
3
0
2
0
1
2
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
2
0
1
0
2
1
0
0
0
3
0
0
0
0
1
0
1
0
0
0
2
2
1
0
1
0
1
2
2
0
0
0
0
0
2
0
0
2
2
1
1
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
2
0
0
0
0
0
2
2
2
0
0
0
1
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
2
1
0
0
0
1
0
0
1
0
0
2
0
3
1
0
0
0
0
0
0
0
2
0
2
1
2
0
0
0
0
0
0
1
0
0
1
0
1
1
1
0
0
0
0
2
0
1
2
2
0
1
1
0
1
0
0
0
2
0
1
0
0
2
1
0
1
2
2
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
1
0
0
0
0
1
2
2
0
0
0
0
0
0
0
1
1
0
1
2
0
0
0
0
2
0
0
1
0
0
0
0
2
1
2
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
1
1
0
0
1
0
1
1
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
2
0
0
0
0
1
0
2
0
0
0
0
3
0
0
0
2
0
2
2
0
1
2
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
2
2
2
0
0
2
0
0
1
2
0
0
2
0
1
0
1
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
1
0
0
0
2
0
2
1
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
2
1
2
0
0
0
4
2
0
0
0
0
2
0
1
1
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
1
2
1
0
0
0
0
2
0
0
1
2
0
2
2
2
0
0
1
1
2
0
0
0
0
2
1
2
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
1
0
0
2
2
0
1
0
0
1
0
0
0
2
1
3
0
0
0
1
0
0
0
1
2
0
0
0
0
1
1
0
1
0
0
0
0
0
2
0
2
0
2
0
0
1
0
1
0
2
0
0
0
0
0
0
1
0
0
1
1
2
1
2
0
2
2
1
0
0
6
1
2
0
0
0
1
1
0
4
0
0
2
1
2
1
0
0
0
0
0
0
1
1
1
0
0
2
0
0
0
2
0
0
2
0
0
0
0
1
0
1
1
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
1
0
1
2
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
1
2
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
1
0
0
2
0
2
0
0
0
8
0
0
0
3
0
1
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
2
0
2
0
1
1
1
2
3
0
0
0
0
1
2
0
0
1
1
0
1
1
0
0
0
1
0
0
1
2
0
0
0
0
0
0
1
0
2
0
0
0
3
2
0
2
2
0
0
0
2
2
0
0
0
0
0
1
0
0
2
0
0
1
0
0
1
0
1
2
3
1
0
0
0
1
1
0
1
2
1
2
0
0
2
1
3
0
1
0
0
0
1
0
0
3
1
1
2
0
1
1
0
0
1
2
1
2
0
2
0
6
2
0
2
0
1
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
2
1
0
0
0
0
2
0
0
3
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
1
0
1
0
0
1
0
0
2
0
0
2
0
1
0
2
0
1
0
1
0
0
1
0
0
1
0
1
1
0
2
0
1
0
0
0
1
2
0
0
0
1
0
1
0
0
0
0
0
1
0
1
2
0
0
0
0
1
1
2
0
2
0
0
0
1
0
1
0
0
0
0
0
1
2
0
1
0
2
1
0
0
0
0
0
0
0
0
1
2
1
2
0
0
1
1
0
0
1
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
1
4
0
0
0
2
2
1
3
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
1
2
1
0
0
0
1
1
0
1
0
0
0
0
2
0
1
0
0
0
2
2
0
0
0
2
2
0
1
1
0
1
1
0
0
1
0
0
2
0
0
0
0
0
1
2
2
2
0
0
0
0
0
1
1
0
0
0
1
0
2
0
0
1
0
1
2
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
2
0
1
5
0
1
0
0
0
2
0
1
0
1
0
0
0
1
0
0
0
4
2
0
1
0
2
1
1
0
1
0
0
2
0
0
0
0
0
0
2
1
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
1
1
2
0
0
0
0
0
2
0
0
0
0
9
0
0
3
0
0
1
0
0
1
1
0
0
1
0
2
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
1
0
0
0
0
1
2
2
2
0
1
0
0
1
0
2
2
0
0
0
2
1
0
0
1
1
0
1
0
1
0
2
0
1
0
0
0
1
1
0
1
1
0
2
2
2
0
0
3
0
1
1
0
1
1
0
3
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
2
1
0
2
0
0
1
2
0
2
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
2
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
1
0
0
0
0
2
0
0
2
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
3
1
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
4
0
0
2
2
2
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
1
0
0
0
0
4
0
0
2
0
0
1
2
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
2
1
0
0
0
0
2
1
0
0
0
2
0
2
0
0
1
0
2
1
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
2
0
1
0
0
3
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
1
2
0
2
0
2
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
1
0
1
1
3
0
1
1
0
2
1
0
0
2
3
0
0
0
2
2
1
0
0
1
0
0
0
2
0
1
0
0
0
1
0
1
2
4
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
1
0
2
0
1
2
2
0
0
2
2
1
0
0
0
0
0
2
0
0
0
2
2
1
0
2
1
0
0
0
2
1
0
1
0
3
0
0
1
2
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
1
0
1
1
1
0
0
2
0
1
2
0
1
0
0
0
2
0
2
1
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
2
1
0
0
2
0
2
0
0
0
0
1
1
0
0
0
0
1
0
0
0
2
0
3
0
0
0
0
0
0
2
1
2
2
1
0
0
0
0
1
1
0
0
0
0
1
0
2
0
0
1
2
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
2
1
3
0
1
0
0
1
0
0
0
1
2
1
0
0
0
0
2
1
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
2
0
1
0
2
0
0
0
0
0
1
0
0
0
0
1
1
0
2
0
0
0
0
2
1
2
0
0
0
1
2
1
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
2
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
1
0
1
1
1
0
2
1
0
0
0
0
2
0
0
2
0
0
0
2
0
1
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
2
0
2
1
0
0
0
2
1
0
0
0
0
0
1
0
1
2
0
2
2
0
1
3
1
0
2
0
0
0
2
0
0
0
0
3
0
0
0
2
0
0
1
0
1
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
1
1
2
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
2
1
1
0
2
0
2
1
0
1
0
1
2
1
0
1
0
1
1
0
0
1
1
0
0
0
0
1
0
2
0
3
0
2
1
4
0
0
0
0
2
0
2
2
0
0
0
0
0
0
1
2
0
0
1
0
1
0
0
0
1
1
1
2
0
0
1
1
2
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
2
0
2
1
0
0
0
0
0
0
0
1
2
1
0
0
0
2
1
0
0
1
1
0
0
0
0
2
0
1
6
0
0
0
0
0
3
0
0
0
2
0
1
0
0
2
0
2
0
0
0
2
0
0
0
1
2
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
2
0
4
2
0
1
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
3
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
1
2
2
0
0
1
2
2
0
0
2
0
0
0
0
1
0
0
0
1
2
2
2
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
2
1
2
0
0
2
2
0
0
3
0
0
2
3
0
0
0
0
1
0
1
1
0
0
12
0
1
0
0
3
0
0
1
0
2
0
1
0
0
0
4
0
0
0
0
0
2
0
0
0
0
1
0
0
0
5
0
0
1
1
0
0
0
0
1
0
0
1
0
0
1
3
0
1
0
0
0
2
2
0
0
0
2
0
2
0
0
0
1
0
1
2
0
0
0
2
0
0
1
0
0
0
0
2
1
0
0
0
0
0
1
2
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
1
0
3
0
0
0
1
0
1
0
0
0
1
2
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
1
1
0
1
0
1
1
1
2
0
0
0
0
2
0
1
0
0
1
0
0
0
0
2
0
2
0
0
0
0
1
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
2
1
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
4
4
0
2
0
0
0
1
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
2
2
0
0
3
0
3
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
1
2
2
0
1
0
2
0
0
2
2
0
1
0
0
0
0
0
3
1
1
0
0
0
3
0
2
2
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
2
2
1
1
0
0
0
0
3
0
3
0
0
0
1
0
1
0
1
2
3
2
0
0
0
2
0
1
0
0
1
0
1
0
0
3
1
0
0
0
1
2
0
0
2
0
0
1
0
0
1
4
0
0
1
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
2
0
0
2
1
1
0
2
0
2
0
0
0
1
0
0
0
2
0
0
2
0
1
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
1
1
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
3
0
0
0
2
0
0
0
0
0
4
0
0
0
0
0
1
0
0
1
0
2
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
1
4
0
0
3
1
0
0
2
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
1
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
3
0
2
1
0
0
0
1
1
1
0
1
2
1
2
0
0
1
0
2
0
0
1
0
1
0
0
1
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
1
0
0
0
3
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
2
0
0
0
0
1
2
2
0
0
0
0
2
0
0
3
0
2
0
0
0
0
2
1
0
0
0
2
0
1
0
1
1
1
1
0
0
1
0
0
0
1
1
0
3
2
0
2
0
0
1
0
0
2
0
0
1
0
0
2
0
1
1
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
2
0
2
0
0
0
0
0
2
0
2
4
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
1
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
2
0
2
1
0
0
0
0
0
2
0
0
2
1
0
1
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
2
2
0
0
1
0
2
0
1
2
1
2
0
0
0
1
2
0
0
0
1
0
2
0
1
1
0
0
1
0
1
2
0
1
0
1
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
3
2
0
0
2
1
0
2
0
1
0
2
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
2
1
1
0
2
2
0
1
0
0
0
0
0
2
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
1
0
0
0
2
0
0
0
1
0
1
0
3
2
1
2
2
2
1
2
0
0
0
2
0
0
1
0
9
0
1
1
0
0
0
0
2
2
0
0
0
1
0
0
0
1
0
2
0
1
0
0
0
0
2
3
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
1
1
0
1
1
0
0
2
2
0
0
1
2
0
2
0
0
2
0
0
0
0
2
4
0
2
0
0
1
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
2
1
1
1
0
0
0
0
1
0
2
1
0
2
2
0
3
1
0
0
1
1
1
3
0
1
0
1
0
2
1
1
1
0
0
0
1
2
0
0
0
2
0
0
4
0
0
0
1
0
0
2
0
1
1
2
2
0
1
1
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
7
0
0
0
0
0
2
2
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
2
2
0
1
3
0
2
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
1
2
2
1
0
0
0
0
5
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
2
0
0
0
0
0
2
0
1
2
0
0
3
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
1
1
0
2
0
1
2
6
0
2
0
0
2
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
3
0
0
2
0
0
0
2
0
1
0
0
0
2
0
0
0
0
2
1
0
0
1
0
0
2
0
1
0
2
0
0
1
0
0
1
0
0
2
2
0
0
0
2
0
0
0
2
2
0
0
0
2
0
1
2
2
1
1
0
0
0
2
0
0
1
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
1
0
1
0
2
0
0
0
0
0
2
2
0
0
2
0
1
2
0
0
0
0
0
1
1
1
0
2
0
0
0
13
0
2
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
3
0
1
0
0
0
0
0
2
1
0
2
1
0
0
0
1
0
0
4
1
1
0
1
0
2
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
1
0
0
0
1
3
2
2
0
1
0
0
1
0
0
0
0
1
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
1
2
2
0
2
0
0
0
2
1
0
0
0
1
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
1
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
2
0
0
1
1
2
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
2
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
2
0
0
0
1
0
0
0
0
1
0
0
2
2
0
0
0
2
0
1
2
0
0
0
0
2
0
0
1
3
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
1
1
2
0
1
0
1
0
2
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
1
0
1
0
0
1
0
0
0
2
0
0
0
1
1
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
1
1
0
0
0
0
1
2
0
2
2
0
2
0
0
0
0
0
0
1
0
0
2
4
0
0
1
1
2
0
1
0
0
1
2
0
1
0
0
0
2
0
1
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
3
1
0
0
2
0
0
0
2
1
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
1
2
1
2
0
0
1
0
0
0
0
2
2
1
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
1
0
0
0
0
3
2
1
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
2
2
1
1
1
0
0
2
0
0
2
0
0
0
0
1
2
0
0
0
0
1
0
1
3
1
0
2
1
1
2
0
0
0
0
2
1
0
0
0
0
0
2
0
0
1
0
0
2
2
0
0
0
0
1
0
0
2
0
1
0
2
0
1
0
0
0
0
0
0
1
2
1
0
0
0
0
1
0
1
0
0
1
2
0
2
1
0
0
0
1
0
2
0
0
0
1
2
0
0
0
0
0
2
1
0
1
1
0
0
0
2
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
2
0
0
1
1
2
1
0
2
1
0
1
1
2
0
0
1
0
1
2
0
0
2
2
0
2
0
1
1
0
0
2
0
0
0
0
1
2
0
0
0
0
0
2
3
0
0
0
0
0
1
0
1
0
0
0
2
1
0
0
1
2
0
5
0
1
0
2
0
0
0
1
0
0
0
1
2
0
0
0
2
0
1
1
1
0
1
0
0
0
0
0
0
1
1
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
1
0
1
0
0
2
0
0
1
0
1
2
0
0
1
0
0
0
0
5
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
2
1
0
1
1
0
1
0
3
0
0
0
0
0
0
0
8
0
0
2
0
0
1
2
0
2
0
0
0
1
0
1
0
0
0
0
2
0
1
0
0
2
0
1
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
3
0
1
0
2
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
1
1
0
1
0
0
2
0
0
1
0
0
0
1
0
1
2
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
2
2
3
1
1
0
0
1
1
0
1
0
0
0
1
20
0
0
0
0
0
1
0
2
1
1
0
0
0
2
2
0
0
0
2
2
1
1
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
2
2
1
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
1
3
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
2
1
0
0
0
1
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
1
0
1
0
1
0
0
3
1
1
0
0
0
1
2
0
2
2
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
2
3
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
4
0
2
0
0
0
0
1
1
0
2
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
2
1
0
0
0
3
0
2
2
0
0
1
0
0
1
0
0
0
0
1
1
0
1
2
2
0
0
0
1
0
0
1
0
0
0
0
0
1
3
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
1
0
0
0
0
1
1
0
2
0
2
0
1
0
2
0
0
0
0
0
0
1
0
0
2
1
2
0
0
0
2
1
1
0
0
2
1
0
2
0
0
2
0
0
0
0
0
0
0
3
3
0
0
1
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
1
1
2
1
2
0
0
2
0
0
0
1
2
0
1
1
2
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
2
0
2
2
0
0
1
1
1
1
0
0
1
2
1
0
0
0
0
0
2
1
0
2
0
0
2
0
2
1
0
1
0
0
0
0
0
3
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
3
0
0
0
0
2
2
2
0
1
1
2
1
1
0
0
0
0
2
0
0
0
1
2
1
0
1
2
0
0
0
2
1
1
0
0
0
1
0
1
3
0
2
2
2
2
0
0
1
1
0
0
0
1
0
1
0
0
3
2
1
0
0
0
1
2
3
2
0
1
0
0
0
0
2
2
0
0
0
2
0
0
0
0
3
0
0
0
3
0
1
0
0
0
0
0
2
2
0
1
2
0
3
0
0
0
2
0
0
2
0
0
1
0
0
1
0
0
0
0
3
1
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
1
0
2
1
0
0
1
2
0
0
0
0
0
2
0
0
0
3
0
0
3
0
2
0
0
0
0
0
0
0
0
0
2
4
5
0
3
0
1
0
2
0
4
0
1
1
0
0
0
0
0
2
5
2
0
0
2
0
0
0
1
1
4
0
2
1
0
2
0
0
2
0
1
0
0
2
1
0
0
0
0
3
0
2
2
1
0
1
2
1
2
1
1
0
0
0
0
0
3
0
2
0
0
0
0
0
1
2
1
0
0
0
1
0
1
0
1
1
1
1
0
1
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
1
0
2
0
0
1
0
0
2
1
0
0
0
0
1
0
0
0
0
0
2
1
2
0
0
0
2
0
0
0
2
1
0
0
2
0
0
2
1
0
0
1
0
2
2
0
1
0
0
4
5
2
1
3
1
0
0
0
2
0
2
1
0
2
0
0
0
0
0
0
1
3
1
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
2
0
2
0
2
2
0
0
0
0
2
0
1
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
2
1
1
2
2
0
0
0
0
0
0
0
2
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
2
2
0
0
1
0
0
2
0
0
1
2
0
0
1
0
1
0
0
0
0
0
3
2
1
0
2
0
0
4
0
0
0
0
0
0
3
0
0
0
1
1
0
2
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
2
0
1
0
1
0
0
0
3
0
0
0
0
0
0
0
1
1
2
0
0
1
2
0
0
0
0
2
1
0
0
0
0
1
1
1
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
1
2
1
0
0
0
1
0
2
0
0
0
0
0
0
1
0
2
0
3
1
3
0
0
1
0
0
2
1
2
0
1
0
1
0
5
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
3
0
0
0
0
2
1
0
1
0
1
0
1
2
1
2
2
1
2
2
1
0
1
2
3
0
0
0
0
1
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
3
0
1
0
1
2
0
0
0
1
0
0
0
1
0
2
2
0
1
0
0
0
0
0
2
3
0
0
0
2
0
9
2
0
0
0
2
2
2
0
0
1
0
0
0
1
4
2
0
0
1
0
2
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
1
0
1
1
5
3
0
0
2
0
0
0
1
0
0
0
0
2
0
0
1
0
0
1
0
0
2
1
2
0
1
1
1
1
1
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
3
0
0
0
0
0
2
1
1
0
0
0
1
0
3
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
2
2
0
1
1
1
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
2
2
2
0
1
0
0
0
0
2
2
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
1
2
1
0
0
1
0
0
3
1
1
0
2
0
0
1
0
0
0
1
0
1
0
0
0
2
1
0
2
3
0
0
0
0
0
0
0
1
0
0
1
2
2
2
0
2
2
1
1
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
2
1
0
0
0
2
0
1
0
0
0
0
0
1
2
0
0
2
0
0
2
0
3
1
1
2
1
0
0
0
0
0
2
1
0
0
0
0
1
0
3
0
0
0
1
3
0
0
0
0
2
2
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
2
2
1
0
0
0
0
0
0
2
0
0
5
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
2
1
2
0
6
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
1
0
1
0
0
0
2
0
0
1
0
1
0
2
0
0
2
0
0
0
2
0
0
2
1
2
0
3
0
2
0
0
1
1
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
2
1
0
0
0
2
1
2
1
0
0
0
1
1
1
0
0
1
0
0
2
3
0
0
0
1
1
1
0
0
2
2
1
1
0
0
2
0
2
1
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
2
1
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
1
1
0
0
0
0
0
2
2
0
0
0
1
1
2
0
0
0
0
0
2
1
0
0
2
0
1
0
0
0
0
0
0
4
0
1
1
12
2
0
1
2
0
0
0
2
1
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
3
0
0
1
1
2
2
0
0
0
2
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
3
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
1
0
1
2
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
1
0
0
0
0
0
1
2
2
1
1
2
0
2
1
0
1
0
0
0
2
0
1
1
0
2
0
0
2
0
1
0
0
1
2
0
1
2
1
0
0
4
0
0
0
0
0
1
2
1
0
4
0
0
1
1
0
0
2
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
1
0
0
0
2
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
2
1
6
2
0
2
0
0
1
0
2
0
0
0
0
0
2
2
1
0
2
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
2
0
0
0
1
2
0
2
0
2
0
2
0
0
0
0
0
1
1
0
1
2
0
0
2
0
2
1
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
2
1
0
0
0
5
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
1
0
0
1
0
0
1
0
0
2
0
0
2
2
0
0
0
0
2
0
2
0
2
0
1
0
1
3
0
2
2
1
0
0
0
1
3
0
0
0
0
1
0
2
0
0
0
0
1
0
0
8
2
2
1
1
2
0
2
0
0
0
0
2
3
0
0
0
0
1
1
0
1
0
3
0
0
0
1
2
2
0
0
3
0
0
0
0
1
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
14
1
0
0
0
2
1
1
0
0
0
1
0
0
0
0
0
1
2
0
2
0
0
0
0
0
2
1
3
1
1
1
0
0
0
0
0
0
0
1
0
0
0
1
1
2
0
0
0
0
2
0
0
0
0
1
1
2
0
0
1
1
0
0
2
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
1
1
0
1
0
3
0
3
1
0
0
0
0
0
0
2
0
0
1
0
2
0
1
2
0
1
1
0
0
0
0
1
2
3
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
1
2
2
0
2
2
5
1
2
2
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
2
2
2
0
0
0
1
0
0
0
0
0
0
0
1
0
2
1
0
0
1
2
1
0
0
0
0
2
0
0
2
0
2
0
0
1
1
0
0
0
0
1
0
0
2
2
1
1
1
0
0
2
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
2
0
2
1
2
0
2
0
1
0
0
1
1
0
0
1
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
1
0
1
0
0
0
2
0
1
0
1
0
0
0
1
0
0
2
0
0
1
1
0
0
1
2
3
0
2
0
2
0
0
0
0
2
1
0
1
0
0
1
2
4
0
0
0
1
2
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
2
2
0
0
1
0
1
0
0
0
0
2
0
0
0
0
1
0
2
0
0
1
1
0
2
0
0
0
1
0
2
0
0
0
1
0
0
1
2
0
0
0
2
0
0
0
0
0
1
2
2
0
0
0
0
0
0
1
0
2
0
0
1
0
2
1
0
1
1
2
0
4
0
0
4
1
0
1
4
1
0
0
0
1
0
0
0
1
3
0
0
0
0
0
2
0
2
1
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
2
0
0
2
2
0
0
2
0
0
0
1
0
0
0
1
0
0
2
2
0
0
1
0
0
0
2
1
0
0
0
0
0
2
1
0
1
0
0
1
2
2
0
1
0
0
2
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
1
0
1
0
2
1
2
0
0
2
0
0
0
0
1
2
0
0
0
0
1
0
0
1
0
1
0
0
0
2
0
2
0
1
0
0
2
2
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
1
2
0
0
1
2
0
0
0
1
2
2
1
0
2
0
0
2
0
0
1
1
0
1
0
0
2
0
0
0
0
1
0
1
0
0
2
0
0
0
1
0
1
0
1
1
0
0
1
1
0
0
0
0
2
1
1
0
0
1
0
3
0
0
0
0
0
0
0
1
0
3
2
1
2
3
0
0
0
0
1
0
3
0
1
0
1
0
2
0
1
2
0
1
0
1
0
0
0
2
2
1
3
0
0
0
0
0
0
0
0
3
0
2
0
1
0
2
2
0
1
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
2
1
0
0
1
0
2
1
0
0
2
0
0
2
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
2
2
2
1
0
0
0
0
0
0
0
2
2
0
0
0
2
1
0
0
0
2
0
0
2
0
2
2
2
0
0
0
2
2
0
0
0
0
2
3
1
0
5
0
0
0
0
2
1
1
2
0
0
0
0
1
0
0
2
2
1
0
0
2
1
1
0
1
0
2
0
0
0
2
0
2
0
1
0
0
0
0
2
0
1
0
1
0
1
0
0
0
0
0
0
0
1
1
1
1
2
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
2
0
0
0
0
1
0
2
0
2
0
0
0
0
2
0
0
0
1
0
2
0
2
2
1
0
0
2
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
1
0
0
2
0
0
1
0
1
3
0
0
0
0
2
0
0
0
0
2
1
0
0
1
0
1
2
0
2
0
0
0
2
0
1
2
0
1
0
2
0
0
1
0
0
0
2
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
2
1
1
1
2
0
0
1
1
0
0
2
0
0
2
0
0
2
0
1
0
1
0
0
0
0
0
0
1
2
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
1
2
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
1
0
1
1
0
0
2
0
2
2
1
0
0
0
3
0
2
0
2
0
0
0
0
0
0
2
0
2
2
2
0
1
2
0
0
0
3
0
1
0
0
1
0
2
0
1
0
4
0
0
0
0
3
0
0
1
1
0
0
2
0
1
0
2
1
0
1
0
0
0
0
0
0
0
2
2
2
2
0
0
0
0
0
2
3
0
0
0
0
0
2
0
0
2
0
0
1
1
1
1
0
0
1
0
0
2
1
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
2
1
0
0
1
1
1
0
0
0
0
0
1
3
1
0
2
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
1
1
0
0
0
0
2
0
1
0
0
1
0
0
1
0
0
0
1
0
1
0
1
1
1
0
0
2
0
0
0
2
0
0
0
2
0
1
2
0
0
1
0
0
1
1
1
3
2
0
2
1
0
0
0
2
2
1
1
0
0
2
2
2
1
0
0
2
1
0
0
0
2
0
0
0
0
0
2
0
1
2
2
0
2
0
0
0
0
0
0
0
2
2
2
0
0
1
0
2
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
1
2
0
1
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
3
2
2
0
0
2
2
0
0
2
2
0
0
0
0
0
2
0
1
0
0
1
1
0
1
0
1
0
1
2
1
0
0
0
2
0
0
0
2
0
0
2
0
0
2
1
1
0
1
2
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
2
2
0
0
1
3
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
1
2
1
0
0
1
0
1
0
2
0
0
0
0
2
2
1
0
0
0
0
0
0
1
0
0
0
2
1
2
2
0
0
1
1
0
1
0
1
3
0
0
2
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
2
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
1
1
2
2
0
0
0
2
0
0
1
0
1
0
0
0
0
2
1
4
0
0
0
0
1
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
1
0
1
0
0
0
2
5
0
0
2
0
0
1
1
0
1
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
1
0
2
0
0
2
0
0
0
2
1
0
0
1
0
2
0
1
2
0
0
0
0
0
0
0
1
1
1
2
0
2
0
0
0
0
0
0
0
6
0
0
2
0
2
0
0
1
0
0
0
0
2
0
1
0
0
0
0
1
0
5
1
0
0
2
0
0
1
2
3
1
0
0
2
0
0
0
2
0
1
0
1
0
0
2
0
0
0
1
0
0
0
0
1
0
1
2
1
5
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
1
0
1
0
0
2
0
2
0
3
2
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
3
1
0
1
0
2
0
0
0
2
0
1
1
1
0
2
0
0
1
0
1
2
2
1
2
1
0
2
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
2
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
1
1
3
1
0
1
2
0
1
0
2
1
0
0
0
1
0
0
0
1
0
0
2
1
0
0
3
2
0
0
4
2
0
1
0
2
0
2
0
4
0
1
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
1
1
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
2
2
2
0
0
0
1
0
0
1
2
0
0
0
2
0
0
0
0
0
2
0
1
3
2
2
0
0
0
0
1
0
0
1
0
2
2
2
0
0
3
0
0
0
0
0
2
0
1
0
0
2
2
3
0
0
0
0
0
0
0
2
1
0
1
0
2
0
1
0
3
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
1
0
0
1
0
0
0
0
0
0
0
2
2
0
2
0
1
2
1
2
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
3
1
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
1
2
0
1
2
1
7
0
0
1
2
0
0
1
2
2
1
2
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
1
0
2
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
1
0
4
0
0
0
0
1
0
0
0
0
2
0
0
2
0
1
2
0
0
1
0
0
0
1
2
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
1
0
1
3
0
0
0
2
1
2
0
0
0
0
1
0
1
2
0
2
0
1
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
3
2
1
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
1
1
0
0
0
1
0
4
0
0
0
0
2
0
0
1
1
0
0
1
0
0
2
3
2
0
1
2
2
0
0
0
0
0
2
0
1
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
1
1
0
1
0
0
0
3
3
0
0
1
0
2
1
1
0
2
0
0
0
0
2
0
0
0
1
1
0
2
1
0
1
0
0
0
0
2
0
2
0
2
0
2
0
2
0
2
3
1
1
0
0
0
1
0
1
0
0
1
0
2
0
2
0
1
0
0
1
0
0
0
0
2
0
0
0
2
2
0
2
0
0
0
2
0
2
0
0
0
0
0
1
3
0
0
0
2
0
0
0
0
0
0
1
0
2
1
2
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
2
1
0
0
0
3
0
0
0
0
2
1
0
0
2
1
1
2
2
0
0
0
0
3
1
0
0
0
1
0
1
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
2
2
2
2
0
0
2
2
0
1
0
0
0
0
2
0
1
2
0
0
0
0
1
0
0
0
1
3
1
1
1
1
5
0
0
0
1
0
0
0
0
2
1
1
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
1
0
0
0
0
2
0
1
0
2
0
2
2
0
1
2
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
1
0
0
1
2
1
0
0
2
0
1
2
0
1
2
0
0
0
1
0
2
0
0
0
1
0
0
1
0
1
2
0
0
2
2
0
0
2
0
0
0
3
0
2
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
1
2
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
1
0
2
0
0
1
1
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
8
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
3
2
0
2
1
0
0
2
0
3
1
2
4
0
0
0
0
2
1
1
1
2
0
1
1
1
0
0
1
0
0
1
2
0
0
0
1
3
1
0
1
0
0
0
1
0
0
1
0
0
2
1
0
2
0
0
0
2
2
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
2
1
1
2
2
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
2
2
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
3
0
1
0
0
3
0
0
1
1
0
2
0
3
0
0
2
1
0
0
0
1
0
0
1
0
1
1
0
0
2
2
2
0
0
1
0
0
0
0
2
0
1
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
2
2
0
0
0
0
2
1
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
2
0
3
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
3
0
3
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
2
0
1
0
2
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
4
0
2
0
4
0
0
1
1
0
2
0
0
1
0
0
0
2
2
2
0
2
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
2
1
2
0
0
0
2
0
0
0
1
1
0
1
1
0
0
3
1
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
1
2
1
0
1
0
0
1
0
2
1
0
0
1
2
1
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
1
0
0
0
2
0
1
0
0
0
1
1
2
1
0
1
0
0
1
0
0
0
1
3
2
1
0
2
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
2
1
0
0
1
0
0
2
0
2
2
1
0
3
2
1
1
1
1
0
0
1
2
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
2
1
0
1
2
2
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
3
2
1
0
1
0
1
0
0
4
0
0
0
2
0
1
2
0
0
0
2
0
2
3
0
0
0
0
0
0
1
0
2
1
0
1
1
0
0
0
0
0
0
2
0
1
0
2
2
0
0
2
0
2
1
0
0
0
0
2
0
1
0
0
0
0
0
2
2
0
1
1
0
0
0
2
4
0
0
1
0
1
0
0
2
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
2
3
2
0
0
0
0
2
0
0
0
1
1
1
0
2
0
1
2
0
0
0
0
0
0
0
3
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
2
0
1
0
1
0
0
2
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
2
1
0
0
0
2
0
0
1
1
2
1
0
0
0
0
0
1
2
2
0
3
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
4
0
0
0
0
3
1
0
0
2
0
1
2
0
0
1
1
0
0
0
2
0
0
0
0
0
0
2
0
0
7
2
0
4
2
2
0
0
0
0
0
0
1
0
1
0
1
0
2
0
3
0
0
1
0
1
2
1
0
0
1
0
0
0
0
2
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
2
2
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
1
0
0
1
1
0
0
0
2
0
1
0
2
0
1
0
3
0
1
0
0
0
0
0
2
0
0
0
0
0
4
0
0
2
0
0
2
0
2
2
0
0
0
1
2
0
0
0
1
0
0
0
1
2
0
1
0
0
0
0
0
2
0
2
0
1
0
1
2
0
1
0
0
2
1
0
2
0
2
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
1
7
0
0
2
2
0
0
0
2
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
2
1
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
2
1
2
3
0
0
0
1
2
0
0
0
0
5
0
0
2
0
2
0
0
0
0
2
2
1
0
2
0
2
2
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
2
1
1
0
0
0
4
0
2
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
1
0
0
0
0
0
0
0
3
0
1
0
2
0
0
0
1
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
2
0
2
1
0
0
1
0
0
3
1
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
3
2
0
0
2
0
0
0
2
0
2
2
2
0
1
0
0
1
2
0
2
0
0
0
0
1
0
0
0
0
2
0
1
0
2
2
0
0
0
1
1
0
0
2
0
0
2
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
2
0
2
1
0
1
1
0
2
0
0
1
0
0
1
0
0
2
0
0
0
0
0
3
0
0
0
0
3
0
1
0
1
0
1
3
0
1
1
0
0
0
1
2
0
0
1
0
1
0
1
1
1
0
1
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
7
1
0
0
0
0
0
0
0
2
0
1
0
0
2
0
1
0
0
0
0
0
0
2
1
0
0
2
1
1
2
2
0
0
0
0
0
2
0
1
0
2
1
0
0
0
1
2
0
0
2
0
2
0
0
0
0
0
0
0
0
1
2
0
2
0
1
0
0
0
2
0
0
0
0
4
0
2
0
3
0
0
2
0
2
2
0
1
0
0
0
2
0
1
1
0
0
0
2
2
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
2
2
1
1
0
0
0
0
2
0
0
2
2
0
0
0
0
0
1
0
0
2
2
0
2
1
0
0
0
1
0
0
0
3
1
0
0
1
0
1
1
2
0
0
4
1
3
1
1
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
1
2
0
0
0
0
2
0
0
0
0
1
1
1
0
0
0
1
2
0
0
0
0
2
1
0
1
3
1
0
1
1
2
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
6
0
1
1
0
0
1
0
2
1
0
2
0
0
0
0
0
0
2
3
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
2
0
1
1
0
0
0
2
1
1
0
2
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
2
0
0
1
0
16
0
2
2
0
0
1
0
0
2
0
1
1
0
0
2
1
2
1
0
0
0
0
0
0
0
2
2
0
0
2
0
2
0
0
6
0
1
1
0
2
0
2
2
0
0
0
1
0
1
2
0
0
0
0
0
1
0
0
2
2
1
0
1
1
0
0
0
2
1
0
1
1
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
1
1
0
1
2
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
2
0
0
2
1
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
3
1
3
0
1
2
0
1
0
1
0
0
0
0
0
0
2
0
0
1
4
0
0
0
0
0
2
1
2
0
2
2
0
1
4
2
0
0
1
0
1
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
1
0
1
0
2
0
0
0
4
0
0
0
0
0
0
2
2
2
0
1
0
0
0
0
0
1
2
0
0
1
1
0
1
1
1
1
1
0
0
1
2
0
0
0
2
0
0
0
0
2
1
0
2
0
4
0
1
0
0
1
0
0
0
0
0
1
2
0
0
0
1
1
1
2
0
0
2
2
0
3
1
0
0
2
2
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
1
0
1
0
0
0
0
0
2
2
0
0
1
0
2
1
0
0
0
3
0
0
0
1
0
0
1
0
0
2
1
1
1
2
1
0
0
2
1
2
0
0
2
2
0
0
0
0
0
1
2
2
0
0
0
0
0
3
0
0
0
2
0
1
2
0
0
0
0
3
2
2
0
0
2
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
2
0
0
0
2
1
2
0
0
0
1
0
2
0
1
0
0
0
0
1
1
1
0
0
1
2
3
0
2
1
2
0
0
0
0
2
0
0
2
0
0
1
1
1
2
0
1
1
1
0
2
0
0
2
0
0
1
0
0
1
1
1
0
0
2
1
0
2
2
1
0
0
1
0
0
2
0
1
0
0
2
0
0
2
0
1
0
1
0
0
0
1
2
2
0
0
0
2
0
1
0
2
3
0
0
0
0
2
1
0
0
0
2
0
0
1
1
0
0
0
1
0
0
2
0
0
0
2
0
2
1
1
2
0
0
1
0
0
0
0
0
2
5
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
1
3
0
0
0
0
2
0
1
0
0
1
0
1
1
0
1
1
0
0
0
1
0
0
0
0
1
2
0
1
0
2
1
1
1
0
2
0
0
0
0
2
1
0
0
0
2
0
0
2
0
0
1
1
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
9
0
1
0
0
0
1
0
0
0
0
0
0
1
0
3
3
3
0
0
0
0
0
0
0
1
0
1
2
0
0
0
1
0
0
0
2
0
0
0
1
2
2
1
0
2
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
1
0
2
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
3
0
0
0
0
2
0
3
0
3
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
1
1
0
2
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
4
0
0
0
1
0
0
0
0
1
2
1
0
1
0
0
0
1
2
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
1
0
1
1
0
0
2
0
0
1
1
2
1
0
0
1
1
0
0
1
0
0
1
0
1
0
0
0
0
0
2
1
0
0
0
1
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
2
1
1
0
1
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
3
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
2
1
0
2
0
2
0
0
0
1
7
1
1
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
2
0
2
1
0
0
0
1
1
0
0
2
2
0
0
0
0
0
0
0
1
2
0
0
0
2
0
1
0
2
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
2
2
0
0
1
0
0
2
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
3
1
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
1
1
0
2
0
1
2
0
0
2
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
2
0
0
1
0
0
0
1
1
0
1
2
0
0
3
2
0
2
0
2
0
0
1
0
3
1
3
1
0
0
0
1
0
0
0
2
2
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
2
0
1
1
2
0
0
0
0
0
0
0
1
2
2
1
1
1
1
1
1
1
0
1
1
0
1
0
2
2
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
2
3
0
0
2
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
1
1
0
0
0
0
2
2
0
0
2
0
2
0
2
0
1
0
0
0
0
1
1
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
1
1
0
0
0
1
2
2
1
2
1
2
1
0
2
0
1
0
1
0
0
0
3
0
1
0
0
0
0
0
0
2
1
2
0
0
0
2
0
0
0
0
1
0
2
0
0
0
2
0
0
0
1
0
0
1
0
0
0
1
0
1
0
1
1
0
2
1
0
1
0
1
1
2
0
0
3
0
2
0
0
0
0
0
3
0
0
0
0
1
2
2
0
1
1
0
2
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
2
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
5
0
2
0
0
0
0
1
0
2
2
0
2
0
0
1
0
0
0
2
1
0
0
0
1
0
2
0
2
0
0
0
0
0
2
0
0
0
3
2
0
2
1
1
0
1
0
0
1
2
0
0
0
0
0
0
0
0
3
1
0
1
0
0
0
0
0
0
0
0
2
1
0
2
1
3
0
0
1
0
0
1
0
2
0
1
0
0
1
0
0
0
2
0
2
2
1
1
1
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
2
0
3
0
1
0
1
1
0
0
0
0
0
3
2
0
1
0
0
0
1
2
2
0
0
2
1
0
0
0
0
0
0
0
0
2
1
0
1
0
0
1
0
1
0
0
0
0
2
0
3
1
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
1
0
1
1
1
0
0
2
0
0
1
1
1
0
0
1
2
2
0
1
1
0
0
1
2
2
0
2
0
0
0
0
0
1
2
1
0
0
0
0
2
2
0
2
1
1
0
0
2
0
2
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
1
1
1
0
0
1
0
2
0
1
0
1
0
2
2
0
0
1
0
0
0
0
0
0
1
0
0
1
2
0
0
1
0
0
0
2
0
1
1
0
0
0
1
0
2
1
2
0
2
2
3
1
0
0
0
0
0
3
0
2
2
0
1
0
0
1
0
0
0
0
0
2
0
2
2
3
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
1
1
0
0
1
0
0
0
1
1
2
0
1
1
1
1
2
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
1
0
2
0
0
0
1
0
0
0
0
1
2
1
0
0
0
0
0
1
0
0
0
0
1
1
1
0
2
1
3
0
0
0
0
0
0
0
2
0
2
4
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
2
0
1
1
0
1
0
0
2
0
1
2
0
0
0
1
0
0
3
2
0
0
0
0
1
0
0
2
0
1
2
0
2
0
0
0
0
1
2
1
0
2
0
0
1
1
0
1
0
0
0
2
0
1
0
0
0
2
0
1
2
2
0
0
0
1
0
0
0
0
2
1
2
0
0
0
0
0
1
2
0
0
0
2
0
2
0
0
1
0
0
0
0
0
2
0
0
3
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
1
2
1
0
1
0
1
2
0
0
0
0
0
0
0
0
0
2
3
3
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
2
1
1
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
2
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
1
1
0
1
1
1
0
0
0
0
1
1
0
0
0
3
0
0
1
0
2
0
0
0
1
1
2
0
2
0
0
0
0
0
0
0
1
1
2
1
0
0
2
1
1
1
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
2
0
1
0
0
0
3
1
2
0
0
0
0
2
0
2
0
0
0
1
2
0
0
2
0
1
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
2
1
0
2
1
1
0
0
0
0
2
2
1
0
0
0
1
2
0
0
2
2
0
0
0
2
0
2
2
0
4
2
0
0
0
2
1
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
2
0
0
1
1
0
0
2
0
0
1
0
2
0
0
0
1
3
0
0
0
0
0
0
1
1
0
0
2
2
1
2
2
0
0
0
2
0
0
0
0
3
0
2
0
2
0
2
0
2
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
3
1
0
0
0
0
0
1
2
2
0
0
2
0
0
2
1
0
0
0
0
0
2
0
2
1
0
0
0
1
2
0
3
0
0
1
2
2
0
0
0
0
1
0
0
0
0
0
0
1
3
0
1
2
0
0
1
0
1
0
1
0
0
2
2
0
0
0
3
1
0
0
0
0
0
1
1
0
0
0
1
0
2
0
0
0
0
1
1
0
0
2
0
0
1
0
1
1
0
2
0
0
1
1
1
2
1
0
0
1
2
0
0
0
0
0
0
6
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
6
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
3
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
1
0
0
1
1
2
0
2
1
1
0
0
0
0
0
0
1
0
1
0
1
1
0
2
0
0
2
0
4
0
1
0
1
1
0
0
0
1
0
0
0
2
0
1
0
2
1
2
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
3
1
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
1
0
2
0
2
0
2
0
0
0
2
1
0
1
0
2
1
2
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
2
2
1
2
0
0
0
0
0
0
1
3
0
0
0
0
2
3
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
2
0
0
2
0
0
0
1
3
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
1
0
0
0
0
2
2
0
0
1
0
1
0
0
1
2
2
0
0
2
2
0
0
0
2
0
0
2
1
0
2
0
2
1
0
1
1
0
0
0
0
1
0
2
0
0
1
0
1
1
2
2
2
2
0
1
2
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
3
1
1
0
2
1
0
2
0
0
0
0
0
0
1
0
3
0
0
0
2
2
0
0
1
0
0
0
0
0
2
0
0
1
0
1
0
3
0
1
0
0
0
0
1
0
0
1
0
0
0
0
3
2
2
0
3
0
0
1
1
1
1
0
1
0
0
1
2
0
0
0
1
2
0
2
0
0
0
1
0
0
1
1
0
2
0
0
0
0
1
0
0
0
2
0
1
2
1
2
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
1
0
1
2
0
0
0
1
0
0
2
1
0
0
2
0
0
0
2
0
0
1
2
1
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
2
1
0
2
2
0
1
0
1
2
2
0
0
0
1
0
0
0
0
1
1
0
2
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
2
0
0
0
0
0
0
2
0
2
0
2
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
1
1
0
0
1
1
1
0
0
0
2
0
0
2
2
0
0
0
0
0
1
2
1
1
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
1
4
0
2
1
0
1
2
0
1
3
1
0
0
0
0
0
0
1
0
1
0
0
0
2
2
0
0
2
0
0
0
0
0
1
0
2
1
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
2
1
1
1
0
0
2
2
2
0
0
2
2
1
0
2
0
0
2
0
1
0
0
0
1
1
0
0
0
2
0
2
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
2
0
0
1
0
2
0
1
0
0
0
2
2
2
3
2
0
2
0
1
0
0
1
4
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
2
1
1
0
2
0
0
0
2
0
1
0
0
0
0
0
2
0
0
1
2
0
0
0
0
2
0
0
0
2
0
0
1
0
2
0
2
8
0
1
4
3
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
1
0
0
2
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
3
0
0
1
3
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
2
2
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
1
1
2
0
0
0
0
0
2
0
0
1
1
0
0
1
0
1
0
0
2
0
0
1
0
1
2
0
0
2
1
0
2
0
1
0
0
0
0
0
0
2
0
2
0
0
0
2
0
2
0
0
0
0
2
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
2
0
1
2
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
2
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
1
5
0
0
1
0
1
0
1
2
2
3
0
2
2
0
2
0
1
0
1
0
0
1
0
2
1
0
0
0
1
0
0
0
0
1
0
4
1
1
0
0
1
3
0
0
2
0
1
0
0
0
0
1
5
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
1
0
2
2
0
0
0
2
0
0
2
2
0
2
0
0
0
0
0
1
0
1
0
1
2
2
0
1
0
1
0
0
0
0
2
0
0
0
1
3
0
0
0
0
1
0
2
0
1
13
0
0
0
0
0
0
0
0
0
1
1
1
0
2
0
1
0
0
0
0
2
0
0
1
0
3
2
0
2
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
5
0
2
0
0
0
0
2
0
0
0
1
1
2
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
2
0
0
2
2
0
0
0
1
0
0
0
2
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
2
1
1
0
0
2
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
1
0
2
2
2
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
2
3
0
0
0
0
0
0
0
0
0
2
0
1
1
1
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
1
1
0
0
0
0
2
0
1
0
1
0
1
1
0
0
0
0
0
2
0
0
2
1
0
2
2
2
0
0
0
1
1
1
0
2
0
0
2
2
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
2
0
1
2
0
1
3
0
0
0
0
1
0
1
0
0
0
0
0
0
1
2
0
1
0
0
0
1
0
0
2
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
1
2
0
2
0
2
1
2
2
0
0
2
1
0
2
0
0
0
1
0
0
1
2
2
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
7
0
2
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
2
0
1
2
0
0
0
0
1
1
7
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
2
0
1
1
0
0
0
2
0
0
0
1
0
2
0
1
2
0
0
0
5
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
1
0
1
0
1
0
0
2
1
0
0
0
2
0
0
2
0
0
1
0
1
2
0
0
0
2
1
0
2
0
2
2
2
0
0
0
0
0
1
2
0
0
1
0
1
0
0
2
0
1
0
0
0
0
1
2
0
0
0
0
2
0
1
0
0
0
2
0
1
0
1
0
1
0
0
0
1
0
2
0
2
0
1
2
2
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
2
0
1
1
0
0
0
0
1
1
0
1
0
1
1
3
0
1
1
1
0
0
0
0
1
0
0
2
2
0
0
0
1
0
0
1
0
2
0
1
1
0
0
0
0
1
0
0
2
2
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
2
0
2
2
0
1
0
0
2
0
1
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
2
0
2
1
0
2
0
0
0
0
4
0
0
1
2
1
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
9
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
2
0
0
0
1
1
2
0
1
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
1
1
1
0
1
2
0
1
2
0
2
0
1
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
3
2
0
0
0
0
0
3
0
2
5
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
2
0
2
0
2
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
2
0
1
2
1
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
3
3
2
0
0
1
0
0
1
2
0
0
0
2
0
2
1
0
0
0
2
1
0
1
2
0
0
0
0
2
0
0
0
0
2
0
1
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
1
0
1
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
1
0
2
2
0
0
0
1
0
1
0
0
0
0
0
1
0
2
2
0
5
0
3
0
0
0
0
0
1
1
0
0
2
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
1
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
2
0
1
2
0
0
1
0
1
0
0
1
0
2
3
2
0
0
0
4
0
0
1
2
0
0
0
0
2
3
0
0
0
0
2
0
1
0
1
0
2
1
0
1
2
0
0
0
0
0
2
2
0
2
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
4
0
0
0
1
2
0
0
0
0
0
1
1
0
0
0
0
2
0
1
0
0
1
0
1
1
0
0
1
0
0
0
1
1
0
1
1
2
0
0
2
0
0
1
0
0
0
0
1
0
2
1
0
2
2
0
2
0
0
0
2
2
1
1
1
0
0
0
0
0
1
1
0
0
0
2
0
1
0
0
0
0
0
2
0
1
0
1
2
0
0
0
2
1
0
2
1
0
0
0
0
1
0
1
2
0
0
0
2
0
0
2
0
0
1
2
0
0
0
0
2
0
0
0
1
0
2
0
2
1
0
2
1
0
2
0
2
0
0
0
0
0
2
0
2
0
0
2
0
0
0
2
3
0
0
0
1
2
0
0
0
0
0
1
5
1
0
2
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
2
2
0
0
0
0
2
2
2
0
0
0
1
0
0
0
0
1
3
0
0
1
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
2
2
1
0
0
0
2
2
2
0
1
0
0
3
0
0
0
3
3
1
0
0
0
0
0
0
2
0
0
1
0
1
2
0
1
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
2
0
0
0
1
2
2
0
0
0
0
2
0
0
4
0
0
2
2
0
2
0
0
0
1
2
0
0
0
1
0
2
2
0
0
0
0
0
2
0
0
0
2
1
1
0
0
1
1
0
2
0
0
0
2
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
2
1
2
0
2
0
0
0
0
0
2
1
0
1
0
0
0
1
1
0
0
1
0
2
0
0
0
0
2
0
0
1
2
0
2
3
0
0
0
2
1
0
0
1
0
0
1
0
0
0
0
0
1
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
1
0
0
2
4
0
0
2
0
0
0
2
1
1
2
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
6
2
0
0
2
0
0
1
0
0
1
0
0
0
0
0
2
0
1
0
4
1
2
2
0
0
0
2
3
0
0
2
1
0
0
0
1
3
2
0
0
2
0
1
0
0
0
0
2
2
0
1
0
0
0
0
2
1
1
0
1
0
0
0
1
0
1
1
2
0
1
1
0
3
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
2
0
0
0
1
2
1
0
2
0
0
1
0
3
0
2
2
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
2
0
1
0
0
0
0
0
0
1
0
0
2
0
0
2
1
0
2
0
1
1
1
0
0
0
0
3
0
1
0
1
1
0
2
0
0
0
1
0
0
1
0
0
0
2
0
0
2
0
0
0
0
1
0
1
0
0
0
1
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
1
0
1
0
1
1
2
2
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
3
0
0
0
0
1
1
1
1
0
0
0
0
0
1
1
0
2
0
0
0
2
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
2
0
1
0
2
0
0
0
1
2
0
1
0
0
0
0
2
2
2
0
0
2
1
2
0
1
0
0
2
1
0
1
0
0
2
0
0
0
0
0
1
2
0
0
0
1
1
1
14
0
2
1
0
0
0
0
0
0
0
0
2
3
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
2
0
0
7
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
1
0
2
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
1
0
0
2
0
1
0
1
2
1
0
0
0
2
2
0
0
0
0
2
0
2
0
0
0
0
1
0
3
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
5
0
1
0
2
1
2
0
3
0
0
0
0
0
4
0
3
0
0
1
1
0
0
1
0
1
0
0
2
0
1
0
1
0
0
0
1
0
2
0
1
1
0
0
1
0
1
0
0
0
2
0
1
1
0
1
2
1
0
0
0
0
0
2
0
2
0
0
0
0
0
2
2
0
0
0
0
0
2
0
2
0
0
2
1
0
0
0
0
5
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
2
0
0
2
1
2
0
1
0
0
0
2
2
0
0
0
1
2
0
1
1
0
2
0
3
2
0
2
1
0
2
0
0
0
2
2
1
1
0
2
0
0
0
0
0
0
1
0
1
2
0
1
1
1
2
0
1
0
0
0
0
2
0
0
0
2
0
0
0
1
1
2
0
0
0
0
0
0
1
3
6
0
2
2
0
0
2
1
0
0
0
2
0
2
1
2
2
0
0
1
0
2
0
0
0
0
0
1
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
3
0
0
0
0
0
2
1
2
0
0
2
1
2
0
0
0
1
0
0
0
0
0
1
4
0
0
2
2
0
0
1
0
2
3
0
1
1
0
2
0
1
0
0
0
0
2
0
0
0
0
2
2
3
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
1
0
0
2
0
0
1
0
0
0
0
2
1
0
0
0
0
0
1
0
2
0
0
0
2
0
0
1
1
0
0
0
1
0
0
0
0
2
0
1
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
1
0
0
1
0
1
0
2
0
0
0
2
1
0
2
1
0
1
0
0
0
1
0
0
0
1
1
2
2
0
0
0
1
2
2
0
0
4
0
1
2
0
0
1
0
2
0
2
1
0
1
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
2
1
2
2
1
0
0
0
0
0
1
0
0
1
0
0
1
2
0
2
0
0
0
0
1
0
1
0
1
0
1
3
0
2
0
0
0
0
2
2
1
2
0
2
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
1
1
2
1
0
1
2
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
2
0
0
0
1
0
1
0
0
0
1
0
0
3
0
0
0
2
0
2
0
0
2
0
1
1
0
0
3
0
1
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
2
1
2
0
0
0
0
3
2
1
0
2
1
1
0
0
0
2
4
1
0
0
2
0
0
2
1
0
4
1
0
0
1
1
0
2
0
0
0
0
2
1
1
1
1
0
1
0
0
0
1
2
0
0
0
0
2
0
0
2
5
0
0
3
1
0
0
0
0
0
0
2
1
1
2
0
0
2
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
3
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
2
2
1
0
0
2
1
2
0
0
0
0
2
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
2
0
0
0
2
2
2
1
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
1
6
0
3
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
2
0
2
0
0
0
0
1
0
0
0
2
0
0
3
0
1
0
3
0
2
0
1
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
1
0
0
1
0
0
0
0
2
0
0
0
4
0
0
1
2
0
0
2
2
0
0
1
0
0
0
4
1
1
1
0
0
1
3
0
2
1
0
2
0
1
2
1
1
2
1
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
1
1
0
0
2
0
0
0
2
2
0
1
2
1
1
1
1
3
1
0
0
1
1
1
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
1
0
2
0
1
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
1
0
2
0
0
1
0
0
0
3
0
0
2
1
0
1
0
2
1
0
0
0
0
2
2
2
2
0
0
0
0
1
2
0
0
0
0
2
0
1
1
0
0
0
0
0
0
1
0
0
0
0
3
0
1
1
1
0
0
7
1
0
3
0
2
0
0
0
0
2
1
0
0
0
0
1
2
6
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
2
0
3
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
1
2
1
1
0
0
1
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
2
0
2
0
2
1
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
2
1
1
0
0
2
4
1
0
2
0
1
0
0
0
1
0
2
0
0
0
0
3
0
1
2
0
0
1
0
0
2
1
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
9
2
0
0
0
0
1
0
1
0
0
0
1
1
0
0
2
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
2
0
0
2
0
2
0
1
0
2
0
0
0
6
0
2
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
1
0
0
2
1
0
0
2
1
1
0
0
0
2
0
2
1
1
0
0
0
0
0
0
2
0
1
0
0
2
0
1
2
0
0
0
2
2
0
2
0
0
1
0
1
0
0
1
1
0
0
0
2
0
1
4
0
0
0
4
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
2
2
0
0
0
1
0
2
0
0
0
1
0
1
2
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
2
5
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
2
2
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
1
2
0
1
0
0
2
0
0
0
0
1
2
2
2
2
1
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
2
0
1
2
0
0
0
2
2
0
2
2
1
0
2
2
0
0
2
0
2
1
0
5
0
0
1
0
0
0
0
0
5
0
0
2
3
1
0
0
1
0
0
0
2
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
1
0
0
1
0
2
0
2
0
0
0
1
0
2
0
0
0
1
1
0
1
0
0
0
1
0
1
2
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
2
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
2
1
0
0
0
0
0
2
2
0
1
0
0
1
0
1
1
2
1
0
1
0
0
2
0
0
1
0
1
0
2
0
0
0
0
2
2
2
0
2
1
1
0
0
0
0
0
2
0
2
0
2
0
0
0
2
1
1
0
0
0
2
0
0
2
1
0
0
2
0
1
0
0
0
2
0
0
1
0
0
0
4
0
0
0
0
2
2
1
0
1
0
1
1
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
2
0
2
2
0
0
1
0
0
0
0
2
2
1
0
2
1
0
2
2
0
2
0
0
1
0
0
1
0
0
0
0
0
2
2
2
1
2
0
2
2
0
0
1
4
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
3
0
2
1
1
2
0
1
0
0
1
0
0
0
0
0
1
3
2
0
1
0
2
1
2
0
0
0
1
0
1
0
2
0
0
2
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
3
1
0
0
0
1
2
0
2
2
1
0
0
0
0
0
0
0
2
4
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
3
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
1
1
3
0
1
0
1
0
0
0
0
0
2
2
2
1
0
1
0
2
1
0
2
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
1
0
3
0
0
0
0
0
0
0
0
0
1
2
0
3
0
0
2
0
1
0
0
0
1
0
0
3
0
0
1
0
0
0
1
0
3
0
0
0
0
2
2
1
2
1
0
0
1
1
0
2
2
0
0
1
1
1
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
1
0
1
0
2
0
0
1
1
1
0
0
2
1
1
1
2
0
0
0
3
0
0
0
0
0
2
0
1
2
0
0
1
0
3
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
3
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
1
2
2
0
0
2
0
1
0
0
1
2
0
0
0
1
2
1
1
0
2
0
2
2
0
2
0
0
1
4
0
0
2
0
3
0
0
0
2
0
0
2
1
2
0
1
7
0
0
2
1
1
0
0
1
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
2
0
0
1
0
2
0
0
0
1
0
0
1
0
0
2
0
1
0
1
1
2
0
0
0
0
3
1
2
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
2
0
1
1
0
0
0
2
0
0
0
1
2
1
1
3
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
3
1
2
0
1
0
0
0
0
0
2
0
0
1
0
0
2
2
1
0
0
1
2
0
0
0
5
0
1
0
1
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
2
2
0
1
0
0
0
2
0
3
1
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
2
1
0
0
0
0
0
2
2
0
0
0
0
0
1
2
0
0
1
2
1
0
0
0
0
0
1
0
2
0
1
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
2
0
2
0
5
0
1
0
1
0
0
2
0
0
0
0
0
1
2
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
2
1
2
1
0
1
0
0
1
0
0
0
0
1
2
0
0
2
1
0
1
0
2
1
0
2
1
1
0
0
0
1
2
0
0
0
0
2
0
0
0
0
4
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
2
0
1
0
0
3
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
2
2
1
0
0
0
2
0
0
0
2
1
0
0
1
3
0
0
0
0
0
0
0
0
2
0
1
1
0
0
1
0
1
0
0
3
2
0
2
0
0
0
1
3
0
0
2
0
1
0
0
0
0
1
1
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
1
2
0
0
0
0
0
0
1
0
2
0
2
0
2
0
3
0
0
2
0
2
10
2
0
2
0
2
0
0
0
3
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
2
0
2
0
1
0
0
2
0
0
2
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
1
2
0
1
0
0
0
2
0
3
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
1
0
1
2
0
1
2
0
1
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
2
0
1
2
0
2
1
0
0
0
0
2
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
3
1
0
2
0
1
0
1
0
2
0
2
1
2
0
0
0
0
0
3
0
0
1
2
2
0
2
1
0
2
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
1
0
0
2
0
0
2
1
0
1
0
0
0
0
2
2
1
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
1
0
0
0
0
3
0
0
1
0
0
1
0
2
0
3
1
2
0
0
1
2
0
0
1
0
2
0
2
1
2
0
1
2
3
2
1
2
0
0
0
2
0
0
2
2
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
2
1
2
0
3
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
1
0
2
0
0
2
0
0
1
0
0
0
0
0
0
2
2
0
0
1
2
2
1
0
1
0
0
1
0
0
1
1
3
0
0
0
3
0
0
0
2
0
1
0
0
3
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
2
0
2
0
0
2
2
1
0
0
0
1
3
0
0
0
0
0
2
0
1
2
2
2
0
0
0
0
0
1
0
0
1
1
2
0
0
1
0
0
1
0
0
2
0
0
0
0
1
2
0
0
0
0
2
0
1
0
0
0
1
0
0
2
0
2
1
0
0
0
0
0
1
3
1
0
0
1
0
3
0
0
1
2
0
0
0
0
1
1
0
0
0
2
1
4
0
3
2
0
3
0
0
0
0
1
2
0
0
1
0
0
2
3
0
0
3
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
2
1
0
0
1
0
2
1
0
0
2
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
1
1
0
0
1
1
2
0
2
0
0
0
2
0
2
1
0
0
1
0
0
0
0
0
0
2
0
0
1
1
0
0
0
2
0
2
0
0
0
1
0
1
0
0
2
0
0
2
0
2
0
0
0
0
2
2
0
0
1
0
0
0
0
0
1
0
1
0
2
0
1
0
0
2
0
0
1
0
0
0
0
0
2
1
0
2
0
1
0
0
0
0
2
1
2
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
2
0
2
2
0
2
0
0
0
2
2
0
2
0
0
2
0
1
1
0
0
1
0
2
0
0
0
0
0
3
0
1
0
1
0
1
0
2
0
0
0
0
0
0
1
1
2
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
2
0
1
0
0
0
2
0
0
0
1
0
2
2
0
0
0
0
0
0
0
2
0
1
1
1
2
0
0
3
0
1
0
1
0
0
4
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
2
0
1
1
0
0
2
0
0
2
0
0
0
0
0
0
1
2
2
3
0
0
0
0
1
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
1
0
2
1
2
1
1
2
0
0
0
0
2
0
0
0
1
1
0
0
0
0
2
0
2
0
0
0
0
2
0
1
0
0
1
0
0
0
4
0
0
0
2
0
0
0
0
1
1
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
2
1
0
1
1
1
1
1
0
0
1
0
0
1
0
0
1
1
2
0
0
0
0
1
2
2
1
0
0
2
2
2
0
2
0
0
0
3
0
0
0
1
0
0
2
2
0
0
0
0
0
6
0
0
0
0
0
0
3
0
2
2
0
1
0
0
2
2
0
3
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
5
0
0
0
0
0
0
0
1
1
2
0
2
0
0
3
0
2
0
2
0
1
0
0
0
1
0
2
0
0
0
1
1
0
1
1
0
0
0
0
4
2
0
0
1
0
0
2
2
2
0
0
1
0
0
1
2
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
2
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
1
0
0
1
0
2
0
2
0
0
0
0
3
0
0
0
0
1
1
0
0
0
3
0
0
0
1
2
2
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
1
3
1
2
1
0
1
0
1
2
0
0
2
0
0
0
0
2
1
1
0
1
2
0
0
1
0
0
1
2
0
0
0
0
0
0
1
2
0
2
0
0
0
0
1
1
0
1
1
0
2
2
2
0
0
2
0
0
1
0
0
0
2
0
0
0
2
1
0
0
0
2
2
0
0
0
1
2
1
0
0
0
2
3
3
0
2
2
0
1
1
0
0
0
0
0
0
1
3
0
2
0
0
2
1
0
2
9
1
0
3
0
0
2
1
1
1
0
0
0
1
0
0
1
0
0
0
0
2
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
2
2
0
0
1
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
5
2
0
1
1
0
0
0
0
2
0
2
0
0
0
2
1
0
1
1
1
0
0
0
0
0
0
0
5
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
3
0
2
0
0
0
1
0
0
1
0
2
0
1
0
0
0
1
0
0
3
0
1
0
0
0
0
0
0
2
1
1
0
0
0
2
0
0
0
1
1
0
2
0
0
0
1
0
1
0
1
0
0
0
0
0
2
2
0
2
0
0
0
1
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
2
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
1
1
0
2
0
0
0
0
1
3
0
0
2
0
0
0
0
0
0
1
1
2
0
1
0
0
0
0
0
1
0
0
2
2
0
1
0
0
0
0
0
2
0
1
0
1
0
0
2
1
2
0
0
2
3
1
1
1
1
3
1
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
1
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
1
1
0
2
1
0
3
0
0
1
2
0
2
0
0
0
1
0
1
0
0
0
0
1
0
1
2
1
2
0
2
0
1
2
0
0
0
0
0
0
0
1
0
0
2
2
0
1
1
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
1
0
0
0
2
1
0
1
2
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
2
0
2
1
0
2
0
0
2
0
1
1
3
0
0
0
0
2
1
0
0
2
0
0
0
0
2
0
0
2
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
2
0
1
0
2
0
0
0
2
0
0
0
2
0
1
1
4
0
1
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
3
2
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
1
1
1
0
0
1
0
0
2
0
0
0
0
1
2
0
0
2
0
0
2
0
0
1
2
0
0
0
0
0
1
0
0
0
3
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
2
0
0
2
1
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
2
1
0
0
0
2
1
1
0
0
1
0
7
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
2
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
1
2
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
3
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
2
0
2
0
0
1
1
0
1
0
0
0
0
1
2
0
0
0
1
2
0
2
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
1
2
1
0
0
0
0
0
2
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
3
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
2
2
1
0
0
0
2
0
0
0
0
0
2
0
0
0
2
1
1
1
0
0
0
1
0
2
1
0
0
2
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
2
0
2
1
0
1
1
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
2
0
0
0
1
1
2
0
0
2
1
0
0
7
0
3
1
0
0
0
0
0
0
0
2
2
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
1
2
1
0
0
2
0
0
0
1
1
0
0
0
0
0
2
1
0
1
1
2
0
0
0
1
0
0
0
0
0
1
0
1
0
2
1
0
1
1
0
0
1
0
5
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
2
0
2
0
1
2
0
1
1
2
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
2
0
0
2
1
1
0
0
2
0
0
2
0
0
0
0
0
0
1
2
0
0
0
2
2
0
0
0
1
1
0
0
0
0
0
1
0
0
0
2
1
0
0
1
1
0
0
2
0
0
0
0
0
0
0
2
1
0
0
2
0
1
0
2
1
0
0
2
2
0
0
0
0
0
0
1
0
2
0
3
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
2
0
0
2
1
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
2
1
1
2
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
5
2
1
0
1
0
1
0
0
2
0
0
0
0
0
3
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
2
2
0
1
0
0
0
2
0
1
4
0
0
2
0
0
0
1
0
0
1
3
0
0
0
2
0
1
0
0
0
1
0
0
0
4
0
1
0
2
0
0
0
1
0
0
3
0
0
0
2
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
4
0
2
0
0
0
1
0
1
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
2
0
0
0
2
1
0
0
1
0
0
2
2
2
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
2
1
2
0
2
1
0
0
0
0
2
2
1
0
0
2
2
0
1
1
2
0
0
2
0
0
1
0
0
2
2
0
0
0
3
0
0
1
0
2
0
1
0
2
0
0
0
0
0
2
0
1
0
2
0
1
1
0
0
1
0
2
2
0
0
1
0
0
0
0
1
2
2
0
0
0
3
0
2
0
0
0
2
0
0
0
3
1
0
0
0
0
2
0
2
0
0
3
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
1
2
0
1
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
3
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
1
1
0
1
0
1
0
2
2
2
0
0
2
0
0
0
4
0
0
2
1
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
6
0
0
2
2
0
2
2
0
0
2
0
0
1
0
0
0
0
1
0
0
4
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
1
0
1
1
0
0
0
0
1
1
1
2
2
0
0
4
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
1
0
0
2
0
1
0
2
0
0
0
1
0
0
1
0
1
0
1
0
0
0
1
0
0
0
2
0
2
0
0
1
0
0
0
0
0
2
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
3
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
2
2
1
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
3
0
2
0
0
0
2
2
0
2
1
0
4
3
2
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
2
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
2
0
0
0
2
0
0
0
1
2
1
0
0
0
0
0
1
1
2
0
3
3
1
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
2
2
0
0
0
1
2
0
1
0
0
2
0
0
0
2
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
1
3
0
0
0
0
2
0
1
0
1
1
2
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
2
0
0
2
0
2
1
3
2
0
0
0
2
0
0
0
0
1
0
2
0
2
0
0
3
1
0
0
0
0
2
0
0
0
1
0
0
2
2
2
1
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
2
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
3
0
2
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
3
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
3
0
0
2
0
2
2
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
2
0
2
0
0
0
0
0
1
2
0
0
2
0
0
1
1
0
0
2
1
0
0
1
2
0
2
0
1
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
2
5
2
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
1
0
0
1
0
2
2
0
1
4
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
1
0
0
0
2
1
2
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
1
0
1
1
2
0
0
2
0
0
2
0
2
0
0
2
0
2
0
1
0
2
0
2
2
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
2
1
2
0
0
0
0
0
0
1
2
0
0
1
2
0
0
0
0
0
2
2
0
2
0
0
2
2
0
0
0
1
0
2
0
0
0
2
0
0
1
0
1
0
1
1
1
0
2
2
0
0
2
0
2
0
4
0
0
0
1
3
0
0
0
0
2
0
0
1
0
2
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
2
0
1
0
0
2
0
1
1
0
0
0
0
1
0
0
0
1
1
2
1
0
0
0
2
0
2
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
1
2
0
1
0
1
2
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
1
2
3
0
3
0
0
1
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
3
0
1
2
0
0
1
2
0
0
0
0
2
0
0
2
0
3
1
0
2
1
0
1
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
2
2
1
0
0
0
0
1
0
2
5
0
0
2
0
1
0
0
0
1
0
1
2
0
2
0
0
2
2
2
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
2
0
1
0
0
0
2
1
0
0
1
0
0
2
1
0
0
0
2
0
2
0
0
0
0
4
0
1
0
2
0
1
0
0
2
0
1
2
2
0
0
0
1
2
0
0
0
1
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
1
0
0
0
0
0
0
1
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
1
0
5
0
0
1
0
0
0
2
0
0
0
1
0
0
1
8
3
0
0
2
1
0
0
0
0
2
1
1
1
1
2
2
0
2
1
0
1
1
0
0
1
3
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
2
0
1
0
1
2
0
4
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
1
2
0
1
0
0
1
0
0
2
0
1
2
0
0
0
0
0
3
0
0
0
0
0
1
1
0
0
1
0
1
1
0
0
1
2
2
0
1
0
0
0
3
0
1
0
0
0
1
0
0
1
0
0
0
0
2
2
2
0
0
1
0
0
0
2
1
0
2
2
0
0
1
0
0
0
1
1
0
0
0
1
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
1
2
0
3
0
3
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
1
2
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
1
3
2
2
2
2
0
1
0
0
2
2
0
0
0
0
0
0
2
2
0
2
0
0
0
2
0
0
2
0
0
0
2
0
2
0
1
0
0
0
1
0
0
0
1
1
0
3
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
1
1
2
2
2
0
0
1
0
0
1
0
0
0
0
1
2
0
2
0
0
0
0
0
1
0
0
7
1
0
0
0
0
1
0
0
0
2
1
0
0
1
3
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
2
0
1
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
3
0
0
2
0
1
0
1
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
1
2
1
1
2
0
3
0
0
0
0
0
0
2
0
0
1
2
0
0
0
2
0
2
0
0
1
0
0
0
1
2
2
1
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
2
1
0
0
1
1
0
1
0
0
1
1
1
1
0
0
0
1
0
2
2
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
1
2
1
0
0
3
0
0
0
1
0
0
1
0
2
0
0
3
0
1
0
0
2
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
2
0
2
2
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
1
1
1
0
0
1
2
0
0
0
1
0
0
0
0
0
1
0
3
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
1
2
0
2
1
0
0
0
0
0
0
0
0
0
4
1
0
0
1
0
1
1
0
0
0
2
0
0
0
0
1
0
0
0
1
2
2
0
0
0
0
1
2
0
2
1
0
0
0
0
0
0
1
2
0
0
2
0
0
0
1
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
1
2
0
0
1
0
0
2
0
0
0
2
0
1
0
0
1
1
0
1
0
0
2
2
1
0
1
0
2
0
0
0
0
2
0
1
0
0
1
1
0
2
2
0
0
2
0
0
3
1
0
0
0
0
0
1
1
0
1
0
1
0
2
1
0
1
2
0
1
0
0
0
0
0
0
2
0
0
1
2
0
0
0
1
2
0
2
1
1
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
2
3
1
2
1
0
0
0
0
0
1
0
0
0
0
0
0
2
2
6
0
1
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
1
0
0
0
0
1
0
2
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
2
1
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
2
0
1
0
0
0
1
0
0
0
0
0
0
1
1
1
2
0
2
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
2
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
2
0
0
0
2
0
3
2
1
0
3
0
0
0
0
0
0
0
0
3
1
1
0
0
1
1
0
0
2
1
0
2
11
0
0
2
0
2
0
2
0
0
0
1
0
0
1
0
0
0
0
2
2
0
0
1
1
1
2
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
2
3
0
0
0
1
1
0
2
2
0
2
0
0
1
1
0
2
2
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
1
2
2
0
0
0
0
0
0
0
0
2
0
2
1
1
0
0
0
0
0
0
0
2
3
0
1
0
1
0
2
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
1
2
1
0
0
0
2
0
0
2
2
0
2
0
1
0
1
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
2
4
0
0
2
2
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
2
2
1
2
0
2
1
1
2
0
1
0
0
0
0
0
1
3
0
0
0
0
0
0
2
1
0
0
0
1
0
0
3
0
0
1
2
0
0
0
2
2
0
2
1
0
1
0
0
1
0
0
0
0
0
2
0
1
3
0
0
0
0
0
0
1
0
0
2
1
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
2
1
0
0
0
0
0
0
1
1
2
1
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
2
1
0
2
0
2
1
0
1
1
0
1
0
0
2
0
1
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
1
1
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
2
0
1
4
2
0
0
0
0
2
0
0
0
0
1
2
0
3
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
3
0
1
1
0
0
0
0
0
0
0
2
0
1
1
0
2
2
0
0
1
1
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
2
7
1
0
0
2
0
2
0
0
1
0
0
0
0
0
1
0
1
2
0
0
0
2
0
0
0
0
1
0
0
0
1
0
1
2
0
0
0
2
2
0
0
0
1
0
0
2
0
0
1
0
0
2
0
0
1
1
1
1
0
0
1
0
0
0
0
0
0
0
0
1
1
3
0
0
0
0
0
0
0
2
0
2
0
3
5
0
1
0
0
0
0
0
1
2
1
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
2
0
0
0
0
1
3
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
1
0
0
2
0
2
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
1
2
0
1
0
0
2
0
0
0
1
1
2
0
1
1
0
0
1
0
0
2
0
0
2
0
2
0
0
0
1
0
2
0
2
0
0
0
0
0
0
1
1
0
0
0
0
1
1
1
0
1
2
0
0
1
0
0
0
1
2
0
0
0
1
2
0
2
2
0
0
0
0
0
1
1
0
3
0
0
2
0
0
0
2
0
0
0
2
0
1
0
1
0
0
0
0
2
0
1
0
0
0
2
2
0
2
4
0
1
2
0
0
2
0
2
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
1
0
2
0
1
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
1
1
0
0
0
0
2
0
0
0
1
1
2
0
1
0
0
0
1
1
2
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
2
0
2
2
0
0
3
2
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
2
0
2
2
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
1
0
0
0
0
5
0
0
1
3
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
1
0
1
0
0
2
2
0
2
0
0
0
2
0
1
1
0
0
0
0
0
2
0
0
1
2
0
0
1
0
2
1
1
0
0
1
0
0
1
0
1
1
1
2
1
0
0
0
2
0
2
2
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
2
0
0
2
1
0
2
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
1
0
0
0
1
2
0
2
0
4
0
0
0
1
0
0
6
0
0
0
2
0
0
0
1
2
0
3
1
1
0
0
0
0
0
0
0
0
0
4
1
0
3
2
0
0
0
1
0
2
0
0
0
0
2
1
2
0
0
2
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
3
0
0
0
0
0
1
2
2
2
0
2
2
0
4
1
0
0
0
0
1
0
0
0
0
1
2
0
0
0
2
2
0
1
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
2
0
3
0
1
1
0
1
0
2
0
0
0
1
1
0
0
0
0
1
2
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
1
0
2
1
0
0
0
0
1
0
1
0
0
5
1
2
1
1
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
2
0
1
0
0
1
0
1
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
2
0
0
0
0
5
0
1
2
0
0
2
1
0
0
1
0
0
0
0
1
2
0
0
0
2
0
0
0
1
0
1
0
0
2
0
2
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
2
0
0
2
0
0
2
2
1
1
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
1
2
0
0
2
2
0
0
0
1
1
2
0
2
0
0
0
0
4
1
2
0
1
4
0
0
0
0
0
2
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
2
2
2
2
0
0
0
0
1
1
2
0
0
1
0
1
2
0
1
0
2
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
2
1
1
0
0
0
0
0
1
2
0
0
2
1
0
1
1
2
0
1
0
1
2
0
0
0
0
0
1
1
0
0
0
2
1
1
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
1
1
2
0
0
0
2
1
0
0
2
0
0
2
0
1
1
0
0
0
2
2
0
2
0
2
2
0
2
0
2
1
0
2
0
0
0
0
1
1
0
0
2
0
0
0
2
0
0
0
1
1
0
0
0
2
1
2
0
0
0
2
0
5
3
0
0
2
0
0
2
1
0
2
0
1
2
1
1
1
2
0
0
0
0
2
0
1
1
0
0
0
1
0
0
0
0
2
0
2
0
0
0
1
2
2
2
0
1
0
0
0
0
1
1
0
0
2
1
0
0
1
0
0
0
2
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
2
0
0
0
2
2
0
0
0
1
0
0
0
0
0
2
2
1
1
1
0
0
0
0
2
1
0
0
1
0
1
0
0
2
0
0
0
2
0
1
2
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
4
0
0
0
1
0
2
1
1
1
1
0
0
1
0
2
1
2
0
0
0
0
0
0
2
1
0
0
1
1
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
2
2
2
0
2
2
0
0
0
0
1
0
2
0
2
1
0
2
0
1
0
1
2
0
0
0
0
0
1
2
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
1
0
0
1
2
0
1
0
0
0
0
1
0
2
2
1
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
2
1
0
0
0
4
2
1
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
1
0
4
0
0
2
2
0
5
0
0
0
2
0
0
0
0
1
3
0
1
0
2
0
0
1
1
1
2
0
2
0
0
0
0
0
2
1
1
1
0
2
2
0
1
2
2
0
0
0
1
0
2
2
0
0
0
1
1
0
0
0
1
4
0
0
0
2
0
0
0
2
1
2
0
0
0
2
0
0
0
0
0
0
0
1
2
1
0
0
0
1
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
1
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
1
0
2
1
0
0
0
0
1
0
0
0
2
2
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
2
0
0
1
0
2
1
0
0
1
0
0
2
2
0
0
0
0
1
2
0
2
2
1
1
0
0
0
0
2
0
0
0
1
2
0
0
0
1
2
0
1
0
1
2
0
2
1
2
0
0
0
1
0
2
0
0
2
0
0
0
0
1
0
1
0
3
0
2
0
0
0
2
3
0
0
2
1
0
2
0
0
0
1
1
0
0
1
0
0
2
1
0
2
0
0
1
0
0
0
0
0
1
0
0
2
0
0
2
2
3
0
1
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
2
1
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
1
0
2
0
0
0
0
4
0
1
3
0
1
1
0
0
1
0
0
0
2
0
0
2
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
2
0
0
2
0
1
2
0
0
2
0
1
0
0
1
1
0
2
0
0
0
0
0
0
3
0
1
1
0
2
1
0
1
0
0
0
0
0
0
0
0
2
0
0
1
1
1
0
0
0
3
0
0
0
1
0
0
0
2
0
0
0
1
2
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
1
0
1
1
0
1
0
2
1
1
0
2
0
1
0
0
1
0
1
1
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
4
2
0
0
0
0
0
3
1
0
0
1
0
0
2
0
1
2
1
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
1
0
0
0
0
0
2
0
0
0
2
1
1
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
2
0
0
0
0
2
1
0
2
0
2
0
0
1
2
2
0
0
0
0
0
1
0
0
2
1
1
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
1
2
0
1
2
0
0
2
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
2
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
2
0
12
0
0
2
1
0
0
0
0
0
2
0
2
0
1
0
0
0
0
1
1
0
1
1
0
1
0
4
3
0
0
0
0
0
0
0
0
0
2
0
5
0
0
0
0
0
0
0
0
2
1
0
1
2
0
0
0
2
1
0
0
0
2
0
0
2
1
0
1
0
1
2
1
0
2
0
0
0
0
0
2
0
0
2
1
2
1
0
0
1
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
2
0
0
1
0
0
1
2
0
0
0
0
1
0
0
1
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
2
1
2
0
0
2
0
0
1
0
2
1
0
2
2
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
2
2
2
0
0
0
1
0
1
6
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
2
0
1
1
2
0
0
2
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
2
2
2
0
0
2
0
3
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
3
4
0
0
0
0
3
2
2
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
2
1
1
0
0
0
0
0
0
1
2
0
0
3
0
1
2
0
2
0
1
2
1
0
0
1
0
0
0
0
1
2
1
0
0
0
0
2
0
0
2
1
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
2
0
0
0
1
0
0
1
1
1
0
0
2
0
0
2
0
0
0
2
0
0
0
1
0
0
2
1
0
0
0
0
0
1
1
2
2
0
1
2
0
0
0
0
0
2
2
0
0
0
0
0
1
1
1
0
1
1
2
0
1
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
2
0
0
1
0
0
0
1
0
2
2
0
0
0
3
0
1
1
1
0
2
1
0
0
0
0
2
0
1
0
2
0
0
2
0
0
0
0
0
0
1
0
0
2
1
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
2
0
0
0
0
1
0
1
0
0
0
0
2
0
0
1
0
1
1
0
0
0
1
0
2
2
0
0
1
0
1
0
0
0
0
3
0
0
0
1
2
0
0
1
0
0
3
0
0
0
1
1
0
0
0
0
0
2
2
0
0
0
1
0
2
0
0
0
0
0
0
1
0
2
1
0
1
0
0
0
0
0
1
1
0
1
0
0
0
1
0
2
0
0
0
1
0
0
1
1
1
2
0
0
1
2
1
2
0
2
0
0
0
0
1
0
2
0
0
0
0
2
1
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
2
0
1
1
0
1
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
2
0
0
3
1
0
0
2
0
2
0
0
2
0
0
0
0
0
2
0
6
0
2
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
2
1
0
1
0
0
0
4
0
1
0
1
2
0
0
0
0
2
0
0
0
0
0
2
0
0
1
3
0
0
3
1
1
0
0
1
1
0
0
0
1
0
0
0
0
0
3
0
0
1
1
0
0
1
2
0
0
0
2
0
1
3
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
1
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
2
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
4
2
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
2
0
0
0
0
2
0
0
1
2
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
1
1
0
2
0
0
0
0
0
2
2
0
2
0
2
1
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
2
1
0
2
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
1
3
0
1
0
0
0
1
0
1
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
2
0
1
0
0
2
0
0
0
2
0
0
0
0
2
0
2
0
0
0
1
0
0
0
2
2
0
1
2
0
2
0
1
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
2
0
0
1
3
0
0
0
0
0
0
0
1
2
4
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
1
0
0
2
1
1
1
0
0
1
0
3
0
2
0
0
0
0
0
1
0
0
1
2
0
1
1
0
0
1
0
0
0
2
2
1
1
1
0
1
0
2
2
0
0
0
1
0
0
2
0
0
2
0
2
1
0
0
0
0
1
0
0
2
0
0
0
3
1
2
0
0
0
0
0
2
0
1
0
0
0
0
1
0
2
2
0
0
1
0
1
0
1
0
1
2
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
1
0
0
2
0
0
0
0
0
1
0
2
0
1
0
0
2
2
1
2
1
2
0
4
2
3
0
0
0
0
2
0
1
0
2
0
1
0
0
0
3
0
0
0
2
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
2
1
0
0
0
1
1
2
1
2
0
0
0
2
2
1
0
2
2
0
0
3
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
3
0
2
0
1
0
0
3
0
0
0
0
1
0
2
0
7
0
0
2
0
2
0
0
2
1
1
0
1
1
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
5
0
1
0
0
0
2
3
1
0
1
0
0
1
0
0
0
1
0
0
0
0
2
3
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
2
1
1
0
1
0
0
2
0
1
0
0
0
0
2
0
2
0
0
0
3
0
0
1
0
0
0
2
1
2
2
2
0
1
0
1
0
0
1
0
1
2
0
1
0
0
0
0
0
1
0
0
2
2
0
0
1
2
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
2
0
1
2
3
0
0
0
0
0
2
0
0
0
0
0
2
3
0
3
0
0
0
0
0
2
0
0
1
7
2
2
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
2
2
1
0
0
1
1
2
2
1
0
0
1
2
0
0
2
0
2
2
2
0
2
0
0
0
0
0
0
1
0
3
3
1
0
1
0
0
2
0
0
0
2
0
0
1
0
0
0
0
2
0
1
0
0
2
2
2
0
0
0
3
0
0
0
0
2
0
0
0
1
0
0
0
1
1
0
0
0
1
0
2
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
3
1
0
0
0
2
0
0
1
0
1
1
0
0
0
2
1
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
1
0
0
1
0
2
0
2
0
0
1
0
0
0
1
0
2
0
0
1
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
1
1
0
2
2
0
0
0
1
0
1
2
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
1
0
0
0
3
0
2
0
2
0
0
1
0
2
1
2
1
2
0
0
0
2
0
2
2
2
0
0
0
0
1
0
2
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
2
0
3
0
0
0
0
0
0
0
1
2
1
1
2
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
4
2
0
0
2
1
0
1
2
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
2
0
0
1
0
0
0
1
0
3
0
0
0
2
1
2
0
1
0
0
0
0
0
1
0
0
0
0
2
1
0
0
2
1
1
0
3
0
1
0
2
0
0
1
0
0
1
1
0
0
0
0
0
1
1
2
0
0
0
3
0
1
0
0
1
0
3
0
0
0
0
0
0
4
0
0
2
0
2
0
0
0
0
1
2
0
2
0
2
0
2
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
1
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
2
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
2
0
1
0
2
2
7
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
3
2
2
0
0
1
2
2
0
0
2
1
0
2
2
0
0
1
0
0
1
0
1
0
1
0
2
1
0
0
1
0
0
1
0
0
0
0
1
0
0
3
2
2
0
1
0
0
1
0
2
2
0
2
2
3
2
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
1
1
0
0
0
0
0
1
0
1
1
0
0
0
1
0
2
0
0
0
0
0
1
0
0
2
2
0
2
0
2
0
0
0
1
0
0
0
0
0
2
1
0
0
2
0
1
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
1
0
1
0
1
1
1
0
1
0
0
0
1
0
3
0
0
0
1
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
1
1
0
2
2
0
0
1
0
1
0
0
0
2
0
3
2
2
3
1
0
0
3
0
0
0
0
1
0
0
1
0
2
0
2
1
0
0
2
0
0
3
2
0
0
0
1
2
1
0
0
2
0
0
0
0
1
1
0
0
0
0
0
2
2
0
0
0
0
1
0
1
1
2
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
3
0
1
0
0
0
0
2
0
0
0
0
2
0
3
1
0
2
1
0
0
1
0
1
0
2
0
0
1
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
1
2
2
0
0
2
0
0
0
0
0
0
1
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
2
0
1
0
2
1
0
1
1
2
0
1
0
0
2
0
1
0
1
1
2
0
0
1
0
0
0
0
1
1
0
0
1
1
2
0
1
0
1
0
2
0
1
2
0
0
0
1
0
0
1
2
1
1
1
0
1
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
1
1
0
1
0
0
1
0
0
1
0
0
3
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
1
0
2
2
0
2
0
1
0
0
1
1
0
0
1
2
0
0
0
0
2
2
0
0
2
0
1
1
0
0
0
2
0
0
1
0
0
0
2
1
0
0
0
0
2
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
4
0
2
1
0
0
1
3
2
0
0
1
0
0
1
0
0
4
0
2
0
0
0
2
0
2
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
4
0
0
2
1
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
1
0
0
1
0
2
0
0
0
1
2
0
0
0
0
1
0
0
1
0
0
1
1
2
0
0
0
2
1
0
1
3
2
0
1
0
0
0
1
1
2
0
1
4
2
1
1
0
1
2
3
3
3
0
0
0
2
0
0
0
2
0
1
2
2
0
0
0
1
0
2
2
1
0
3
0
2
0
0
1
0
0
3
2
0
0
0
1
0
1
0
1
1
0
0
0
0
1
1
0
0
0
0
0
1
1
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
2
2
2
0
1
0
0
0
0
1
0
0
0
2
0
2
1
1
1
0
0
0
0
0
0
0
2
0
1
0
2
0
2
0
1
2
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
2
1
0
0
1
1
0
0
1
0
1
0
1
2
0
0
4
1
0
0
0
2
0
0
1
1
0
0
0
1
0
0
0
0
2
0
0
1
0
2
2
0
0
0
0
1
1
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
3
0
2
0
0
1
0
0
0
2
0
0
1
1
0
2
0
2
2
0
1
2
1
0
0
2
1
1
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
2
0
1
0
0
1
1
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
2
0
3
0
2
1
0
1
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
2
1
0
1
0
0
1
0
0
0
0
0
0
1
1
1
1
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
2
0
0
0
2
0
2
0
0
0
0
1
2
1
0
0
0
0
1
0
0
0
1
1
0
0
1
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
2
2
0
1
1
0
1
0
2
4
0
3
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
2
0
2
0
2
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
1
2
0
2
0
0
0
0
0
0
0
2
2
1
0
0
1
1
2
0
0
2
1
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
1
2
2
0
1
0
0
0
2
0
0
0
0
3
1
0
2
1
0
2
0
0
2
0
0
2
2
1
0
1
0
0
0
0
1
3
0
0
0
0
0
2
0
2
0
1
2
0
0
2
0
1
2
0
0
1
7
0
0
0
0
0
4
1
1
3
0
1
0
0
0
0
0
2
1
0
2
1
0
0
3
2
0
0
0
0
1
0
1
2
0
0
0
0
2
1
4
2
1
0
0
1
1
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
2
0
1
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
2
0
2
2
0
2
0
0
2
4
0
0
0
0
1
2
2
0
0
0
0
0
1
0
1
2
1
0
2
1
1
0
0
0
1
1
1
0
0
1
1
1
2
0
0
0
5
0
0
0
0
0
0
2
2
1
0
0
0
2
0
1
0
0
3
0
2
0
0
0
0
0
2
0
1
0
2
0
0
0
0
1
2
0
2
0
1
1
0
1
0
1
0
0
2
0
0
2
1
0
0
0
0
4
2
1
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
1
0
2
0
3
0
0
1
4
2
0
2
2
1
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
1
0
0
3
0
1
0
0
2
0
0
0
1
2
0
1
0
0
1
2
0
0
2
0
0
0
0
0
2
0
1
1
0
1
1
0
1
0
0
0
2
0
0
0
4
0
2
0
1
1
0
0
0
2
0
2
1
0
2
0
0
2
3
0
1
2
0
1
0
0
0
0
0
0
2
0
2
0
2
1
1
0
0
0
2
1
0
0
2
1
0
0
0
0
0
1
1
2
2
0
0
0
0
0
2
2
1
0
0
0
0
1
0
2
0
0
0
0
0
2
0
2
0
0
2
2
2
0
0
0
0
0
0
0
1
0
0
1
2
0
0
1
0
0
1
2
3
1
0
2
2
1
1
2
0
0
2
0
0
0
1
0
1
0
0
1
0
1
0
0
0
1
1
1
0
0
0
2
0
2
2
2
2
0
0
1
2
0
2
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
2
0
2
1
0
2
0
0
0
0
0
0
1
2
0
0
0
2
1
0
2
3
0
1
0
0
0
1
0
2
0
0
0
0
1
2
2
2
0
1
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
1
3
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
2
1
0
0
2
0
0
1
0
0
2
0
0
2
0
1
0
0
0
0
2
1
2
0
0
3
2
0
0
2
2
0
0
1
2
2
2
2
0
0
0
0
0
0
0
2
0
0
2
0
1
2
0
0
0
0
0
0
0
0
6
0
2
0
0
0
0
0
0
2
2
2
0
0
3
0
0
0
0
1
0
2
0
0
0
0
6
0
1
0
0
0
1
0
0
0
0
1
0
0
2
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
11
0
0
2
2
1
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
1
2
0
0
0
1
1
1
0
1
0
2
0
0
2
0
0
0
1
0
0
2
0
1
0
0
1
1
1
0
1
0
0
2
1
0
2
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
3
1
1
0
2
0
2
0
0
1
0
2
1
0
0
1
0
2
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
5
2
0
0
0
0
0
0
1
1
0
0
2
0
0
2
0
2
0
2
2
0
1
1
3
0
0
0
0
1
4
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
1
0
1
0
0
0
0
1
0
2
1
1
0
1
0
2
0
0
0
0
0
2
0
1
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
4
0
0
1
0
2
2
0
0
0
7
0
0
0
0
2
1
1
2
2
0
0
0
0
0
0
0
3
1
0
0
3
0
0
0
0
0
0
1
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
3
1
0
0
2
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
2
1
0
0
0
2
1
2
0
2
1
1
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
1
1
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
3
1
0
0
0
0
1
0
0
0
0
2
0
0
0
3
2
0
0
2
1
0
0
1
0
1
0
0
0
1
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
1
2
0
1
0
1
2
1
0
0
0
1
0
1
2
0
0
2
0
1
2
1
0
0
1
2
0
1
0
0
0
0
2
2
2
0
0
0
2
1
0
0
2
0
0
1
0
0
0
0
2
2
0
0
2
1
2
1
0
0
2
0
0
0
2
0
0
0
3
0
0
2
0
1
0
0
1
2
1
3
1
0
0
0
0
0
2
1
0
1
1
0
0
2
2
1
2
0
0
0
1
0
0
1
2
0
3
0
1
1
0
0
2
1
0
0
2
0
0
0
2
0
0
2
0
3
0
0
0
2
0
0
2
0
0
0
1
0
2
0
0
1
0
2
0
0
0
0
0
1
2
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
3
1
1
2
0
1
0
1
0
1
0
1
0
0
0
2
1
0
0
2
0
1
1
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
2
0
0
1
0
1
0
0
0
0
0
1
0
2
1
1
1
2
0
1
0
1
2
0
0
0
1
2
1
0
0
1
2
0
0
2
1
0
2
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
2
0
0
1
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
1
0
0
3
1
1
2
0
2
0
1
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
1
2
0
2
1
0
0
0
0
1
1
0
2
0
0
2
1
0
0
2
0
0
1
2
1
0
0
2
3
0
0
2
0
0
0
2
0
3
2
0
2
0
0
2
0
0
1
1
0
0
0
0
4
2
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
2
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
2
0
0
0
0
1
2
1
0
2
0
0
0
0
2
0
0
1
1
0
2
0
0
0
0
0
2
3
0
0
0
0
0
2
0
1
0
0
1
1
1
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
2
0
1
0
0
0
0
0
2
1
2
0
0
0
0
0
1
3
2
2
2
1
0
0
0
2
0
0
1
1
0
0
2
0
0
1
1
1
0
0
2
0
0
0
0
0
4
0
0
2
0
2
0
2
0
0
3
0
1
1
0
2
2
2
0
0
1
0
0
1
1
2
0
1
0
0
1
1
0
3
1
0
1
0
1
0
0
0
2
1
0
0
2
0
0
0
2
0
0
1
0
0
0
0
1
2
0
1
2
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
1
0
0
1
2
0
0
1
0
0
0
0
2
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
2
0
2
2
0
0
1
0
0
0
1
0
1
1
1
0
3
0
2
0
0
0
0
1
0
0
3
4
0
2
3
0
0
0
3
2
0
2
0
1
0
0
1
2
2
0
0
0
0
0
0
5
0
2
0
0
0
0
0
0
1
0
2
0
0
1
0
2
0
2
0
0
0
0
1
0
0
0
1
2
0
0
0
0
2
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
2
0
1
0
2
0
0
1
1
1
1
0
6
0
1
0
0
1
2
0
1
1
1
2
0
0
1
0
1
1
0
0
1
1
2
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
1
0
0
0
0
2
1
0
2
3
1
0
0
0
1
0
0
2
2
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
1
0
0
1
0
2
1
1
1
0
0
0
2
1
0
0
1
0
0
0
0
1
2
0
1
0
1
0
0
0
0
2
0
0
0
0
3
1
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
2
0
3
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
6
0
0
0
0
1
2
0
0
0
0
0
1
0
1
0
2
0
0
0
0
1
0
0
1
0
0
1
2
0
0
1
0
2
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
1
0
2
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
2
2
0
0
1
0
1
0
1
1
0
1
0
2
0
0
0
0
4
0
1
0
1
0
0
0
1
0
0
2
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
1
1
2
4
2
0
0
2
2
0
0
2
0
3
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
2
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
1
2
1
1
5
1
0
0
2
0
0
2
0
1
2
1
0
0
1
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
1
2
0
1
0
0
0
1
2
0
0
2
0
3
0
1
2
2
0
0
1
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
2
0
1
0
1
0
3
2
0
0
0
0
0
0
0
0
2
0
0
1
2
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
5
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
2
1
0
2
0
1
2
3
1
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
2
1
0
0
2
0
1
2
0
0
0
0
3
0
2
1
0
0
0
1
1
2
1
0
0
1
0
2
1
0
0
1
1
1
2
0
1
0
0
2
0
0
0
1
0
2
0
0
1
0
1
0
0
2
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
1
1
0
0
0
0
1
0
0
0
2
0
0
1
0
3
0
1
0
0
0
1
2
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
1
1
0
0
11
1
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
2
1
1
1
0
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
1
2
0
2
0
2
2
0
0
2
0
0
0
2
0
0
0
1
0
1
0
0
2
0
2
1
2
0
0
2
0
1
0
3
1
0
0
0
1
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
1
1
1
1
2
0
0
1
0
0
1
2
1
0
0
2
2
0
0
0
0
0
0
0
0
2
2
2
0
0
2
0
1
1
0
0
1
0
2
2
0
0
2
0
0
0
2
0
0
2
0
2
0
1
0
1
0
2
1
0
2
2
2
0
2
0
0
0
0
1
4
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
2
0
0
1
0
0
0
0
2
1
0
0
3
2
0
0
2
3
0
1
2
0
0
2
0
0
1
0
2
0
0
1
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
1
3
0
0
2
0
2
0
0
0
1
1
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
2
3
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
2
0
0
0
1
0
3
2
0
1
0
0
1
1
1
0
2
1
0
0
0
1
4
0
0
0
1
0
0
0
1
1
0
0
2
0
0
0
0
0
1
0
1
2
0
0
1
2
2
0
3
0
0
0
1
0
0
1
2
0
0
0
1
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
2
2
0
2
2
0
0
1
0
0
0
1
1
0
0
1
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
2
0
1
0
0
1
0
0
2
0
0
0
0
1
0
1
2
1
0
0
0
2
0
0
0
0
0
1
1
0
3
1
2
0
0
0
0
0
0
0
2
2
1
0
0
0
1
0
1
0
0
2
1
0
1
1
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
1
1
0
0
0
0
0
0
0
2
1
0
2
2
1
0
0
0
3
0
1
0
0
0
0
0
0
3
0
1
2
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
2
0
1
2
0
0
0
2
0
0
0
1
0
2
2
0
1
0
0
0
0
1
0
2
0
0
0
2
0
1
0
0
0
0
1
1
0
0
0
0
0
2
1
0
0
0
2
0
1
1
0
0
0
1
0
1
2
2
0
2
0
2
1
1
2
0
1
0
2
0
2
0
3
0
0
0
1
1
1
0
1
1
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
2
2
1
2
2
0
1
0
0
1
0
0
2
1
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
2
2
0
1
2
0
0
0
0
0
0
1
0
2
3
0
0
0
1
0
0
0
0
1
0
2
1
2
0
2
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
2
2
1
2
0
2
0
0
0
0
0
1
0
0
2
2
2
0
0
0
0
0
2
0
0
0
2
0
0
2
0
2
0
0
0
3
4
1
0
3
2
0
1
0
0
1
0
0
1
1
0
2
2
1
0
1
0
1
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
2
2
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
2
0
0
0
3
0
0
0
0
1
0
2
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
1
2
0
0
0
3
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
2
1
1
0
0
1
0
2
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
1
1
0
2
1
2
1
1
1
2
1
0
2
0
0
1
0
0
0
0
2
1
2
2
1
0
2
1
2
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
3
0
1
0
1
1
2
2
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
1
1
0
1
0
0
1
2
0
0
0
0
1
2
0
0
0
0
1
1
0
0
0
1
1
0
2
0
2
0
1
1
0
0
0
2
0
0
0
2
0
0
0
1
0
2
0
1
0
0
1
2
2
2
0
1
0
0
0
0
2
0
0
0
0
1
2
0
0
1
0
0
2
0
2
0
1
0
0
0
2
0
0
0
1
0
0
1
0
0
0
1
0
2
0
0
1
0
0
2
1
0
0
1
0
0
0
0
1
0
0
1
1
0
0
2
0
0
2
0
2
2
1
2
0
1
1
0
0
1
0
1
1
0
0
2
0
0
2
0
0
0
0
0
3
1
0
0
0
0
0
1
5
4
0
2
0
0
1
0
0
1
2
0
0
0
1
0
0
0
0
0
2
2
0
1
2
1
0
0
0
0
1
2
0
0
1
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
2
2
0
1
0
0
0
2
0
0
1
0
0
0
1
1
0
0
2
0
1
0
2
0
1
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
3
1
3
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
1
1
0
1
1
0
1
0
0
0
2
0
2
0
0
0
0
2
0
2
2
0
0
0
0
1
0
2
1
1
0
2
0
0
0
0
0
0
2
1
2
0
0
0
2
0
0
1
0
0
1
0
0
2
0
2
0
0
0
1
1
2
1
0
0
0
2
2
0
2
0
0
2
0
1
0
0
0
0
2
0
0
1
1
1
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
3
1
0
2
2
2
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
1
1
0
0
0
1
0
0
0
0
2
1
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
2
2
0
0
2
1
0
0
0
1
0
0
2
1
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
1
2
1
0
0
0
1
0
3
2
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
1
0
0
0
2
2
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
2
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
2
0
0
2
0
0
2
0
0
0
1
0
1
0
0
0
0
1
2
0
0
0
0
0
1
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
3
2
0
0
0
2
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
2
0
2
0
2
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
2
0
1
2
0
2
1
0
0
2
0
2
0
0
2
0
1
6
0
2
2
0
2
0
2
2
1
0
0
2
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
1
0
2
0
1
0
0
0
3
0
2
0
2
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
3
0
0
4
0
0
0
0
0
0
1
1
2
1
2
0
0
0
0
0
1
2
1
0
0
0
0
1
0
0
0
2
0
2
1
0
0
0
0
3
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
2
2
0
2
2
2
0
1
0
0
0
0
0
2
1
2
0
0
0
0
0
2
1
0
0
0
3
2
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
2
0
1
0
3
0
1
2
0
0
0
1
1
0
0
2
0
0
0
0
1
0
1
1
1
0
0
0
0
0
2
2
0
1
0
0
0
1
1
0
0
0
0
4
0
0
0
1
0
2
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
2
1
2
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
5
0
1
2
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
1
4
0
0
0
0
1
0
0
2
1
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
3
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
1
2
0
0
2
0
0
0
1
0
0
0
1
0
1
0
1
1
0
0
3
0
0
0
0
0
0
2
1
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
4
2
2
0
0
3
0
0
0
1
0
0
0
0
0
1
2
1
2
0
0
0
0
1
0
2
3
0
0
0
0
0
2
0
0
0
0
2
0
2
1
0
1
0
0
0
2
0
0
2
0
1
0
0
0
0
1
0
0
0
1
2
0
2
1
0
1
0
0
2
0
0
0
0
1
0
0
1
1
0
0
2
0
0
0
0
0
4
0
2
2
0
0
2
2
0
1
0
0
0
0
2
1
2
2
0
0
1
14
2
0
0
0
0
0
2
2
1
2
0
0
1
1
0
2
0
0
0
0
2
2
3
0
0
0
1
2
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
2
1
0
0
0
0
2
0
2
1
1
3
1
0
0
1
2
0
0
0
2
0
0
0
4
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
1
0
0
1
1
0
2
0
0
2
0
0
1
1
1
0
1
0
2
0
2
0
0
2
1
0
0
0
3
0
3
1
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
2
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
2
0
1
0
0
0
2
1
1
0
0
0
2
0
0
0
0
2
0
1
0
2
1
0
1
0
0
1
2
0
0
2
2
1
2
1
0
0
0
0
4
1
0
0
0
2
1
0
0
0
0
2
0
2
0
1
0
2
0
2
1
0
0
1
0
0
2
0
2
1
0
2
0
1
0
0
0
1
1
0
0
0
0
0
0
2
1
0
0
0
1
1
0
1
2
1
2
0
0
0
0
2
2
1
0
1
0
0
2
2
0
0
1
0
2
4
0
0
0
1
1
2
0
0
0
1
0
1
0
0
1
0
3
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
2
1
2
0
0
0
0
0
4
0
0
0
0
2
0
1
2
0
0
1
2
0
0
0
0
0
0
0
1
0
0
1
3
1
0
2
1
0
2
0
0
2
0
0
2
0
0
2
0
0
0
1
0
2
0
2
1
0
0
2
0
2
0
0
1
1
0
0
0
1
0
0
2
0
0
0
2
0
0
3
1
0
0
0
0
3
0
1
0
0
0
2
0
3
0
0
0
0
0
1
2
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
1
0
1
1
1
1
0
0
0
1
0
0
0
0
1
2
2
0
1
0
0
1
0
0
1
0
0
0
1
2
0
2
0
0
1
4
0
1
1
0
0
0
1
0
1
0
1
0
4
3
0
0
0
0
2
1
0
2
0
0
0
0
0
2
2
0
0
0
2
1
1
3
0
0
2
0
2
0
0
1
1
0
0
2
4
5
0
2
2
2
1
0
0
3
0
1
0
1
0
2
0
0
0
0
0
1
1
0
2
0
1
2
2
0
0
0
0
2
0
0
0
0
0
0
1
2
2
2
4
0
0
1
0
0
0
0
2
0
1
1
0
0
1
0
0
1
1
0
2
0
2
0
0
1
2
1
0
1
1
0
1
0
0
1
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
1
1
0
2
1
2
0
0
2
0
2
0
1
0
0
0
0
2
0
0
0
1
0
2
0
0
1
1
0
0
0
0
1
0
1
1
0
2
0
0
1
0
0
0
0
1
0
0
0
0
2
2
2
0
0
0
0
1
2
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
4
0
0
2
1
1
1
0
1
2
0
2
0
0
0
2
2
0
1
0
2
0
0
1
0
0
4
0
0
0
0
0
1
1
0
4
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
1
1
2
0
2
2
2
3
1
0
0
2
1
0
1
0
0
0
0
0
0
2
0
0
1
1
0
0
1
0
1
0
0
0
0
2
1
0
0
1
0
0
1
0
2
1
1
0
0
0
0
0
0
1
0
4
0
0
1
0
0
2
2
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
2
2
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
3
0
1
0
0
2
0
0
0
0
1
1
1
0
0
0
0
4
0
0
0
0
0
0
0
0
2
1
2
1
0
2
4
0
1
1
1
2
0
0
1
1
0
1
0
0
0
0
0
0
0
2
1
0
1
0
1
1
0
0
0
0
1
2
0
0
2
0
0
2
0
0
0
3
0
1
1
1
0
1
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
1
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
1
0
1
0
1
1
3
0
2
3
0
0
0
0
2
0
0
0
0
2
2
0
0
0
1
2
0
0
0
0
2
0
0
2
0
0
1
1
1
2
0
0
0
0
1
2
1
0
3
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
3
0
0
0
0
0
2
1
0
1
1
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
2
0
2
1
1
2
0
2
0
2
1
0
0
0
0
1
2
1
1
1
0
0
0
0
0
1
2
2
0
2
1
0
0
0
4
0
2
3
1
1
0
0
1
0
0
2
0
0
0
0
0
0
1
1
1
1
2
1
0
1
1
0
1
0
3
0
3
4
0
1
2
0
1
0
0
0
1
2
1
0
3
1
0
0
2
0
0
1
0
1
0
0
0
0
2
1
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
2
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
1
0
2
2
0
0
1
1
0
2
0
0
1
0
0
0
0
2
0
0
1
1
1
1
0
0
2
1
0
1
0
0
0
0
0
2
0
0
2
0
2
0
0
2
0
2
0
1
0
0
0
2
0
0
1
1
1
0
0
2
0
0
0
0
1
0
2
0
1
0
0
1
3
0
2
0
0
1
0
2
3
2
0
0
0
1
0
0
0
0
3
1
2
0
2
0
1
1
2
0
0
1
0
1
1
0
2
1
2
0
0
1
2
0
0
0
0
0
2
2
0
1
1
2
0
2
1
1
1
1
0
0
1
1
1
0
2
1
0
0
0
0
0
1
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
1
1
0
0
1
2
1
2
0
0
4
0
1
2
0
0
0
0
0
0
0
0
2
2
2
0
0
1
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
1
0
1
0
1
0
1
0
0
2
0
1
0
1
0
0
0
1
0
1
1
0
1
1
1
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
2
1
0
1
2
2
0
0
2
1
5
0
0
0
2
1
2
0
2
0
0
1
0
2
1
0
1
0
0
1
0
1
0
1
0
0
2
0
0
0
2
0
3
0
2
0
0
1
2
1
0
0
0
0
1
3
0
2
0
2
0
0
1
1
2
0
0
0
0
2
1
0
0
0
0
0
0
1
0
2
1
1
1
0
0
0
0
1
0
0
0
1
1
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
2
0
2
1
0
0
0
2
0
1
0
2
2
0
1
0
0
1
1
0
0
0
2
0
0
1
5
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
1
2
0
0
1
0
3
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
2
0
1
1
0
0
0
0
0
0
2
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
3
0
1
0
0
0
1
2
0
0
1
0
0
3
0
0
0
0
2
1
0
0
0
1
0
1
2
0
0
0
1
2
0
0
0
0
0
0
1
0
0
1
0
0
1
3
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
1
0
0
0
2
2
1
0
0
1
0
2
0
1
1
2
0
2
0
0
0
0
2
2
1
0
0
2
0
0
1
0
2
2
1
0
0
0
2
0
2
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
1
0
0
0
2
0
1
0
2
0
1
0
7
0
1
0
0
0
3
1
1
1
0
0
2
1
1
0
0
1
0
0
0
0
0
2
0
0
1
0
1
0
0
0
1
0
3
0
0
0
2
1
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
2
1
1
0
1
0
2
2
0
0
0
0
0
0
2
0
0
1
2
0
1
2
2
0
2
0
0
1
1
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
1
0
2
2
1
2
0
0
2
2
0
0
2
0
0
0
0
0
2
0
2
2
0
0
2
5
0
0
2
1
0
0
3
0
0
2
0
2
0
0
0
0
0
0
0
1
1
3
0
0
0
2
0
0
0
0
2
0
1
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
2
2
2
0
2
0
2
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
1
0
2
0
3
1
2
0
0
0
0
2
0
1
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
1
1
0
0
1
0
0
0
2
2
1
0
0
0
0
0
2
1
0
2
2
0
0
0
3
2
1
1
0
0
2
1
0
0
0
2
1
0
2
0
0
1
0
0
0
0
0
1
0
3
3
1
2
3
2
1
1
2
0
0
0
1
4
0
1
0
0
1
2
0
2
0
0
1
1
0
1
0
0
2
0
2
2
0
0
0
0
1
0
4
0
0
0
0
0
3
2
2
0
0
2
0
0
1
5
0
1
0
0
0
1
0
1
0
2
0
0
2
1
0
0
1
0
0
0
1
0
0
3
0
0
0
2
0
0
1
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
1
2
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
2
2
0
0
2
1
0
0
0
0
1
2
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
1
2
1
0
1
0
1
0
1
0
0
0
0
0
3
0
1
0
2
0
0
0
0
1
0
2
0
0
1
0
0
2
0
1
1
2
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
1
0
0
1
5
0
2
0
0
0
0
0
0
2
1
2
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
2
0
3
0
0
1
0
0
2
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
1
0
2
2
0
1
0
1
0
0
1
0
0
0
0
0
2
2
0
0
0
2
1
3
1
0
1
0
0
1
1
0
0
1
1
0
0
1
0
0
0
1
0
0
0
4
2
0
2
0
1
2
0
0
0
3
1
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
6
1
0
3
0
1
2
0
0
0
1
2
1
0
2
0
0
0
0
1
0
0
0
0
2
0
2
0
1
0
1
0
0
0
0
0
0
0
2
2
0
3
0
0
0
0
0
0
1
0
2
1
0
1
0
0
1
0
0
0
1
0
2
0
1
2
1
0
0
0
0
0
2
1
0
0
0
0
0
2
1
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
2
2
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
3
0
2
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
2
2
0
0
0
0
1
1
0
4
0
0
0
0
0
2
0
0
1
3
0
0
0
1
2
2
0
1
2
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
1
1
2
0
1
1
0
2
0
0
0
1
0
0
0
1
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
1
0
0
0
0
2
0
0
0
0
1
2
2
0
1
2
2
0
0
0
2
0
1
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
1
0
2
1
0
0
2
0
2
0
0
0
0
0
0
1
0
2
0
0
2
0
1
0
1
0
1
0
0
0
0
2
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
1
0
2
1
0
0
1
0
1
0
0
1
0
0
0
0
2
0
0
0
0
2
0
2
0
0
1
0
0
0
1
0
0
2
0
0
0
0
3
0
2
0
0
1
1
3
2
0
0
0
0
0
1
0
1
1
0
0
2
0
0
2
0
1
0
0
0
1
3
1
0
1
0
2
2
1
0
2
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
2
1
2
0
0
2
0
0
2
1
2
0
0
0
2
0
0
0
1
0
0
1
0
0
1
0
2
0
2
2
1
0
1
2
0
2
1
0
2
0
0
0
0
0
0
0
1
1
2
1
0
0
1
0
0
0
1
2
0
0
1
0
0
1
3
2
2
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
4
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
1
1
0
0
0
2
1
0
2
0
2
2
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
2
1
3
2
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
1
2
2
0
0
2
0
0
0
1
2
1
1
0
1
0
0
1
1
1
0
0
0
0
0
2
0
2
0
0
0
0
2
0
3
1
0
1
0
2
0
0
0
0
0
0
0
0
1
2
0
0
2
2
0
0
0
1
1
0
2
0
1
1
1
0
0
0
0
1
0
2
2
0
0
0
0
2
0
0
1
1
2
0
0
3
2
1
1
2
1
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
2
2
0
1
0
1
0
0
0
0
0
1
0
0
2
3
0
2
0
0
0
0
1
1
0
3
2
0
2
0
0
0
0
0
13
2
1
0
0
0
1
3
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
4
0
0
0
0
0
0
4
1
0
0
3
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
3
0
1
1
0
0
2
0
0
0
0
2
2
0
2
1
1
0
0
0
1
1
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
4
1
0
0
0
2
0
0
0
1
0
0
3
0
5
0
0
0
1
0
0
0
0
2
0
0
0
3
0
2
0
0
1
0
2
2
0
1
2
1
1
0
0
1
0
0
1
1
0
0
1
2
1
0
0
2
1
0
0
1
1
0
1
0
1
1
0
0
0
0
0
0
2
0
0
2
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
2
0
0
0
0
2
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
2
0
3
1
2
0
1
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
2
1
1
0
2
0
0
2
1
0
2
0
0
0
0
0
0
1
0
0
1
0
1
1
2
0
2
5
0
2
0
1
0
0
0
2
2
2
0
0
1
0
1
2
0
2
1
1
1
0
0
0
2
0
0
1
1
0
2
0
0
0
1
2
0
0
2
0
0
0
0
0
2
2
0
0
1
0
1
2
2
0
2
0
0
0
0
2
0
1
0
2
0
0
2
0
2
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
2
0
0
0
1
0
1
0
1
3
2
3
0
0
1
0
2
4
0
2
0
0
0
2
2
0
0
1
0
2
0
2
0
0
2
2
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
1
2
0
1
0
0
0
0
0
0
2
0
0
2
2
1
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
2
2
0
0
1
1
0
0
0
1
3
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
2
1
1
2
0
2
1
0
0
0
0
0
0
0
0
0
0
2
2
3
1
0
2
0
0
0
0
2
1
0
0
0
4
0
0
0
0
0
1
0
5
0
0
0
0
2
0
2
0
4
2
0
0
0
0
0
0
0
2
1
1
0
1
0
0
2
0
1
0
2
2
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
2
0
0
0
2
0
0
0
0
2
2
1
0
1
0
1
0
2
1
0
0
1
1
1
0
0
2
2
1
4
0
0
3
2
2
2
2
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
1
0
3
0
0
1
2
2
2
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
8
0
3
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
1
0
0
0
1
1
1
0
1
0
0
1
0
2
2
0
1
0
0
0
2
2
2
0
1
0
3
0
3
0
2
3
0
0
0
0
0
1
2
0
0
1
0
2
1
0
0
1
0
2
2
2
0
0
1
0
0
0
0
0
1
0
1
0
0
2
0
0
2
1
1
1
1
0
0
2
0
0
1
0
0
0
0
0
0
0
1
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
1
2
0
1
0
0
1
1
0
0
0
0
1
0
0
0
2
1
1
2
2
2
2
0
2
0
1
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
2
0
0
0
2
2
1
0
1
0
2
0
3
0
1
0
0
1
0
1
0
0
0
4
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
2
0
0
0
0
2
2
3
0
0
1
0
0
2
0
0
0
0
0
2
2
0
0
0
2
0
2
2
0
1
0
0
0
0
0
0
0
3
0
2
0
0
2
0
1
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
2
1
1
0
1
1
1
0
0
0
0
0
2
0
0
2
0
0
2
0
1
2
1
0
0
2
2
1
1
2
0
1
0
0
1
0
0
0
2
0
0
0
1
1
3
0
1
0
0
2
0
0
1
1
1
3
1
0
0
0
0
1
2
0
2
0
0
0
2
0
0
0
1
0
0
0
0
1
2
0
2
0
2
2
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
1
1
0
0
2
1
0
0
0
0
0
0
0
1
3
0
0
0
0
1
0
2
0
1
2
0
2
0
0
0
2
0
0
0
1
3
0
0
0
0
0
1
0
0
3
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
1
2
0
2
0
0
0
0
1
1
2
0
1
2
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
2
1
0
1
0
1
0
0
0
1
0
0
2
1
0
0
0
1
0
0
0
2
0
1
2
2
0
1
0
0
0
0
2
0
1
0
0
0
0
0
1
2
0
0
0
0
2
1
0
0
0
1
2
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
2
1
1
2
2
0
0
0
1
0
0
0
0
1
0
1
0
2
0
0
0
0
2
3
0
0
0
2
5
1
2
1
1
0
0
3
0
2
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
1
3
1
0
0
0
1
0
0
0
0
0
1
0
1
2
1
0
0
0
0
0
2
0
1
8
0
1
0
0
0
1
0
2
0
0
2
1
0
1
0
0
0
0
0
0
0
1
0
0
2
0
2
1
0
0
1
0
0
0
1
2
1
2
2
0
0
2
2
0
0
0
0
0
0
0
1
3
1
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
1
2
0
0
0
2
0
0
0
2
2
1
0
0
2
0
0
1
2
0
0
0
0
2
1
0
1
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
1
0
0
2
1
0
3
0
0
1
0
0
0
1
2
1
0
0
0
0
0
1
0
2
0
2
0
1
0
0
2
2
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
2
2
2
1
0
0
0
0
0
1
1
0
0
0
0
0
2
1
0
3
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
1
2
0
3
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
1
1
5
0
5
2
0
0
0
0
0
0
0
1
0
2
0
2
2
0
0
2
0
0
0
1
0
1
0
0
3
0
1
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
5
1
0
2
0
0
0
0
2
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
2
0
0
0
0
2
0
1
1
0
9
0
2
5
0
0
0
0
2
1
0
0
0
1
0
0
1
0
0
1
0
0
0
2
2
1
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
2
0
2
2
0
1
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
2
2
0
2
2
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
2
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
2
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
1
0
0
2
0
0
2
0
1
1
0
0
0
3
1
1
2
0
0
0
0
2
1
0
1
0
0
2
0
0
0
0
0
0
0
0
1
1
1
1
1
0
0
0
0
2
0
0
0
0
1
0
2
2
2
2
0
0
4
1
2
0
0
0
2
1
0
1
2
0
0
0
0
0
0
2
0
0
0
1
1
1
0
0
2
1
0
1
2
0
1
2
0
9
2
0
1
2
0
0
0
0
2
0
0
1
0
1
0
0
2
1
2
0
1
0
1
3
4
0
0
0
4
0
1
1
1
1
3
1
1
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
2
0
0
2
0
0
0
1
2
2
0
0
3
0
2
0
0
1
0
0
0
2
2
0
0
0
0
0
1
0
1
0
0
0
2
0
0
2
0
1
0
0
0
0
2
0
0
0
2
0
2
1
2
0
1
0
0
0
0
0
0
2
3
0
0
0
1
0
0
2
0
0
0
3
1
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
2
0
2
0
1
2
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
2
0
1
0
7
1
2
0
0
0
1
0
0
0
0
1
1
2
0
1
3
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
2
1
0
2
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
2
0
0
0
2
0
0
1
0
0
2
0
3
0
3
0
1
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
1
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
1
0
0
2
1
1
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
1
0
1
0
0
0
0
0
2
0
2
0
2
0
0
1
0
2
4
0
0
1
0
1
0
0
2
1
0
1
0
0
1
1
2
3
0
2
0
1
0
0
0
2
0
2
0
0
2
0
1
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
4
0
0
0
2
0
1
1
0
0
0
2
0
0
2
2
0
0
3
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
2
0
0
0
2
1
2
0
1
0
0
0
0
0
0
2
0
1
2
2
0
0
0
0
0
1
2
1
2
0
1
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
3
1
1
2
0
0
0
0
0
0
5
0
1
2
0
0
0
0
0
2
2
0
0
2
0
0
0
0
4
0
0
0
0
2
0
2
2
2
0
2
1
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
4
0
1
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
2
1
1
0
0
1
0
0
0
1
3
0
1
0
0
1
2
0
2
1
0
0
0
2
0
0
1
0
2
7
0
1
0
0
0
0
2
1
0
1
1
1
0
1
3
1
0
3
0
2
0
0
1
1
2
0
0
0
2
0
1
2
2
0
0
0
0
1
0
0
0
0
2
1
0
2
1
2
0
2
1
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
2
1
1
2
0
2
0
2
1
0
1
0
2
2
2
2
0
2
0
0
0
1
1
2
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
2
2
0
0
2
0
2
2
0
0
0
0
0
1
0
2
0
0
2
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
2
1
1
0
0
2
2
2
14
0
1
0
0
2
1
1
2
1
0
0
0
0
2
0
2
0
0
2
0
0
0
0
1
3
1
1
1
0
0
0
0
2
0
3
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
2
0
1
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
3
0
2
2
2
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
2
2
1
0
0
0
0
0
0
1
0
0
1
0
0
2
0
2
2
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
4
1
0
0
0
0
0
0
0
0
3
0
2
2
0
0
0
0
2
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
2
0
0
2
0
0
0
0
2
1
0
0
2
0
0
1
3
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
1
0
1
0
2
0
0
0
2
2
1
0
0
2
1
1
2
3
0
2
2
0
0
0
0
0
2
2
0
0
0
0
0
0
2
1
0
1
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
4
0
1
0
1
2
2
0
1
1
0
1
0
1
1
0
0
0
0
1
0
2
0
0
0
2
0
0
1
0
1
0
0
2
2
0
0
0
0
0
0
1
0
1
0
0
0
0
3
1
2
0
0
2
2
0
1
0
1
1
1
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
1
2
2
1
0
0
1
2
0
0
0
1
1
1
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
2
0
1
1
0
1
2
1
2
0
1
0
0
0
3
2
0
0
2
0
1
2
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
1
2
1
0
3
0
0
0
0
0
2
0
0
1
1
0
0
0
1
2
1
1
0
1
0
0
2
0
1
1
0
2
2
2
0
5
0
1
0
0
0
0
0
0
1
0
0
0
0
2
1
2
0
2
0
0
0
1
0
3
2
1
0
0
0
2
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
2
1
1
0
1
0
2
0
2
0
1
0
0
0
0
1
1
0
0
2
0
0
0
2
0
0
2
0
0
0
0
1
0
2
1
0
0
0
0
2
1
0
0
1
0
0
0
2
2
0
2
0
0
1
0
0
0
2
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
4
0
0
1
0
2
0
0
2
4
2
7
0
0
2
0
0
0
1
0
0
2
2
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
2
0
2
0
2
0
0
1
1
1
0
1
3
1
0
2
1
0
1
1
0
0
3
0
1
0
0
0
0
0
0
2
0
1
1
0
4
0
0
0
0
2
1
1
0
0
2
1
2
0
0
2
2
0
2
0
1
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
2
0
0
2
0
0
6
1
0
2
0
0
0
0
0
0
0
3
1
1
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
2
0
1
1
0
0
2
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
2
0
1
1
0
2
0
1
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
2
1
1
0
0
2
1
0
0
1
0
0
0
0
4
2
4
0
1
0
0
0
0
1
1
1
0
0
1
0
0
2
1
0
4
2
0
0
0
2
0
1
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
2
1
2
2
0
2
0
0
0
2
0
0
2
0
1
0
0
0
2
0
1
0
2
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
1
0
2
0
0
0
1
2
0
0
0
0
0
2
1
0
0
0
0
2
1
0
2
0
0
2
0
1
0
0
0
0
0
1
3
1
1
1
2
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
4
0
0
1
2
2
0
0
0
0
0
0
1
0
0
2
0
1
1
0
0
1
1
1
0
0
1
2
0
1
2
0
0
1
1
1
0
1
1
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
1
0
0
0
0
1
1
4
2
2
0
0
0
0
0
0
2
1
0
0
1
0
1
0
2
0
0
0
0
0
0
0
1
2
2
1
0
1
1
1
0
1
1
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
1
0
1
2
0
2
0
0
1
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
1
0
1
0
2
0
0
0
1
0
1
0
0
0
0
0
0
1
6
0
0
0
0
2
0
3
0
2
0
0
0
1
0
2
0
0
3
1
0
1
0
1
0
1
2
1
2
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
1
1
0
0
0
0
2
0
0
0
2
1
0
0
1
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
2
1
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
1
2
2
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
2
4
0
0
0
0
1
0
1
0
0
0
2
0
2
0
0
0
0
2
2
3
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
2
2
2
2
0
0
0
2
0
0
2
0
0
0
0
2
0
0
1
0
0
0
2
2
0
2
2
2
2
0
0
0
2
1
1
0
0
0
0
2
0
1
0
1
0
0
0
0
0
2
1
2
2
2
0
0
2
2
2
0
0
1
2
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
3
0
0
2
0
0
0
0
2
0
0
2
0
2
2
1
2
1
0
0
0
2
0
0
0
0
0
0
0
0
6
3
0
0
0
0
0
0
1
2
0
0
1
0
1
2
0
4
0
0
2
0
0
0
0
0
0
0
1
1
0
1
1
0
0
1
0
2
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
1
0
2
1
0
0
0
1
0
5
1
2
0
1
0
0
1
0
0
0
0
1
0
1
0
2
0
2
1
0
2
0
0
0
0
0
2
0
2
1
2
0
0
2
0
1
2
0
0
1
0
0
0
0
2
0
0
0
0
1
2
0
2
0
0
1
0
0
1
0
2
2
0
0
1
0
0
2
0
0
1
1
1
0
0
0
0
0
0
0
2
2
0
0
1
1
0
0
0
0
0
2
2
1
0
0
0
0
0
1
1
0
1
0
0
0
1
0
2
0
2
0
0
2
0
0
0
0
4
0
2
1
1
0
1
2
1
1
0
0
1
0
0
0
0
6
1
0
2
3
0
0
0
2
0
4
0
0
0
1
0
0
0
1
0
1
0
0
1
1
0
1
2
1
0
2
0
0
0
0
0
1
1
0
0
0
0
0
2
1
2
0
0
1
0
2
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
1
1
0
1
0
1
1
0
0
1
2
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
5
0
1
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
1
1
1
0
0
0
0
3
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
2
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
2
0
2
2
0
2
1
0
0
4
1
3
0
0
0
1
0
0
2
0
0
0
1
0
0
2
0
1
3
0
2
1
0
2
0
2
0
2
1
0
0
0
2
2
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
1
5
1
1
0
0
2
0
0
0
1
1
1
2
1
2
2
0
0
0
1
1
0
0
0
0
2
0
1
2
0
1
0
0
0
2
1
1
0
0
1
1
1
2
2
0
2
0
1
2
1
0
0
0
0
0
0
1
2
0
0
1
0
0
0
1
0
1
1
0
0
0
0
1
2
1
0
2
0
0
2
0
0
1
1
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
1
2
0
0
0
0
1
0
0
0
0
0
2
0
0
1
1
0
1
0
0
0
0
2
0
0
0
0
1
0
0
3
2
1
0
2
0
0
0
0
0
2
1
1
0
1
0
1
0
0
0
2
0
3
0
0
0
0
0
2
0
0
0
0
0
3
1
2
1
1
0
0
0
0
0
0
0
1
2
0
1
1
0
0
0
0
1
0
2
2
0
0
0
1
1
0
0
0
0
0
2
0
2
0
0
0
0
1
0
1
1
1
0
1
1
0
1
0
2
0
0
2
0
1
1
1
2
1
1
0
1
1
2
1
1
0
0
0
3
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
2
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
2
0
0
1
0
1
0
0
4
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
2
0
1
1
0
2
0
2
0
2
2
1
0
0
2
0
0
0
0
0
0
2
2
0
0
2
1
1
0
5
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
2
0
0
0
1
2
1
2
0
0
0
2
0
0
0
2
2
1
0
1
0
0
0
4
0
0
2
0
0
0
0
1
2
0
0
2
0
0
3
0
0
0
1
0
2
1
0
3
2
0
0
0
0
0
0
0
0
0
1
1
0
0
2
2
0
0
1
0
0
0
0
0
1
0
1
0
0
2
2
2
0
1
2
0
2
0
0
0
0
2
2
1
0
0
2
0
0
2
1
0
1
0
0
0
0
0
1
1
0
1
0
0
1
0
0
2
2
1
1
1
3
0
0
0
1
0
0
0
4
0
0
2
1
1
1
0
0
0
0
0
2
0
0
1
2
2
0
2
0
2
0
2
0
0
1
5
0
2
2
0
0
1
2
0
0
0
0
1
0
0
0
0
3
1
5
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
2
0
2
2
1
1
1
0
0
0
2
0
0
2
0
2
1
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
5
0
0
2
0
0
1
1
2
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
1
1
0
0
1
0
0
1
1
0
2
0
0
0
1
0
0
2
2
0
0
2
2
0
2
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
1
2
0
1
0
0
2
0
0
2
0
0
0
2
0
2
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
3
0
2
0
0
0
0
3
3
2
2
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
1
0
0
1
0
0
1
2
2
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
1
1
0
2
0
0
1
0
0
3
0
0
0
1
0
0
0
1
0
0
0
2
1
0
2
1
0
1
0
0
0
0
4
0
0
1
1
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
2
1
1
0
0
0
0
1
0
0
2
1
0
0
2
0
0
0
1
0
1
6
2
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
1
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
2
0
1
0
2
2
1
0
2
1
2
0
2
0
2
0
0
0
0
1
0
0
2
2
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
2
1
2
0
1
0
1
0
0
1
0
1
0
0
2
1
0
0
0
1
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
1
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
2
0
2
1
0
1
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
2
1
0
1
2
0
1
0
1
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
2
0
0
0
0
0
1
1
0
0
0
1
2
2
1
0
0
0
2
2
0
2
1
1
1
0
0
5
1
0
2
2
1
1
2
2
3
1
2
1
2
0
0
0
2
0
2
0
0
0
0
2
0
2
0
1
0
0
0
0
2
2
2
0
1
1
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
2
0
0
1
1
2
0
0
0
1
0
1
0
2
0
0
1
0
0
0
0
0
0
1
2
0
0
1
0
1
0
0
0
4
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
3
0
0
0
2
0
0
0
1
0
0
0
0
2
1
2
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
3
0
0
0
1
0
3
2
1
0
1
0
2
0
0
0
0
0
1
1
1
0
0
2
0
1
2
0
0
1
0
2
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
2
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
2
0
0
0
3
1
1
0
0
3
0
2
1
2
0
2
1
0
2
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
1
2
0
0
0
0
0
2
0
1
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
2
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
2
0
1
0
0
0
0
2
1
0
1
0
2
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
1
0
0
3
0
2
1
0
1
0
1
0
0
2
0
0
2
0
0
0
2
0
0
2
0
2
2
0
0
0
0
0
2
2
0
0
0
0
1
0
2
0
0
0
1
0
3
2
0
0
1
1
0
0
0
1
0
2
0
0
0
1
0
1
1
0
0
0
2
2
0
1
2
1
3
2
0
0
0
1
0
0
0
2
1
0
1
6
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
1
2
0
1
1
0
0
0
0
2
0
10
1
0
0
1
0
0
1
0
0
0
0
0
0
0
2
3
2
0
1
0
1
0
0
0
3
0
0
0
0
0
1
2
0
0
2
2
1
0
1
0
2
0
0
0
2
0
1
0
0
2
0
0
0
2
0
1
0
0
2
0
2
0
0
7
0
0
1
2
0
0
2
0
2
0
0
1
2
0
0
0
1
0
0
0
0
0
0
2
0
2
1
1
0
0
0
0
0
2
0
0
0
2
0
2
0
0
1
0
0
0
1
0
1
2
6
0
0
0
0
1
0
1
2
0
0
2
0
0
0
2
0
2
0
1
0
0
0
2
2
1
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
1
1
0
2
0
0
0
0
0
2
0
0
1
1
1
1
0
0
1
2
0
0
0
0
1
0
0
0
2
0
0
0
0
3
0
2
0
0
0
0
1
1
0
0
0
0
1
2
1
2
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
6
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
2
1
0
0
0
0
2
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
1
2
0
2
0
0
0
0
0
0
0
2
1
2
2
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
4
0
0
0
0
0
1
0
0
2
0
0
1
0
0
1
0
2
2
1
0
2
2
0
1
0
1
0
2
0
2
1
0
1
1
1
0
0
0
0
1
0
0
0
2
3
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
3
3
2
1
1
5
0
0
0
0
0
2
0
0
2
2
1
2
0
2
2
0
2
2
1
1
0
0
0
0
1
0
2
0
1
0
0
0
0
4
0
3
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
1
0
1
2
0
0
0
0
0
0
1
3
2
0
0
0
0
1
0
5
2
2
0
0
1
1
0
2
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
3
2
0
0
1
0
2
1
0
2
0
0
2
0
1
0
0
0
0
0
5
0
0
0
2
0
2
1
0
0
0
0
2
0
1
0
27
1
1
2
1
0
1
0
0
2
0
2
0
0
0
0
2
0
1
0
2
0
1
0
0
0
2
1
0
0
2
2
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
1
0
4
1
0
0
2
0
0
1
0
2
0
0
0
0
0
0
2
0
0
1
0
1
0
2
0
0
1
0
2
0
0
0
3
0
0
0
0
2
0
0
1
2
0
0
2
1
0
1
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
2
2
0
0
2
1
2
0
0
1
0
0
0
0
1
1
0
0
0
2
2
2
1
0
0
0
0
0
0
2
0
2
0
0
1
2
0
1
0
0
0
0
1
0
1
1
0
0
1
1
1
0
0
1
1
0
0
0
0
0
3
0
1
0
0
0
1
0
0
2
2
2
2
0
0
0
0
0
0
2
1
1
0
0
1
2
0
0
2
2
0
0
2
2
0
2
0
0
1
0
0
0
0
2
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
3
0
0
0
1
0
0
1
2
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
2
3
1
0
1
2
0
1
1
0
2
0
2
0
1
2
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
2
0
1
2
2
1
0
2
0
0
0
0
1
0
2
0
0
1
0
1
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
2
1
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
3
0
1
0
0
0
0
0
2
0
0
1
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
2
0
1
0
0
0
0
0
0
3
1
0
1
0
0
3
0
0
0
0
1
2
1
1
2
0
0
2
3
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
3
0
0
0
2
0
0
2
2
2
11
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
1
0
2
0
1
0
2
0
1
0
0
1
0
2
0
2
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
4
0
0
0
1
0
0
2
0
2
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
2
1
0
0
1
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
1
5
0
1
2
0
0
1
2
0
0
0
0
1
0
1
0
2
0
0
2
0
2
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
1
2
2
0
0
0
0
1
2
1
0
2
0
0
0
0
3
2
0
2
0
0
1
0
0
2
0
1
0
0
1
0
2
0
0
3
1
2
0
1
0
2
0
0
0
1
1
0
0
1
0
2
2
0
0
0
0
1
0
1
0
0
3
0
1
1
1
0
0
0
0
0
0
2
2
0
0
0
1
0
3
0
0
0
1
1
0
0
2
1
0
0
0
0
0
0
2
2
1
3
3
2
0
0
0
0
2
0
0
2
0
1
1
0
0
0
0
0
2
2
0
0
1
0
0
0
2
0
0
1
0
0
0
1
0
1
0
0
2
1
0
0
0
1
0
2
0
2
2
1
2
0
0
0
0
0
0
0
0
2
2
0
0
1
1
2
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
1
0
1
1
1
0
0
0
1
3
2
0
2
1
2
2
0
1
1
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
3
0
2
2
0
0
0
2
1
0
0
2
0
1
0
2
1
2
1
0
4
1
0
0
0
0
0
0
2
1
2
2
0
2
1
1
1
0
2
0
0
0
0
0
0
1
0
1
0
0
1
1
1
1
0
0
1
1
2
1
2
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
1
1
1
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
2
0
0
0
2
0
0
1
1
0
1
0
1
0
0
0
0
0
1
1
1
0
0
0
2
0
2
0
1
0
2
0
1
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
1
0
0
0
0
0
2
2
0
0
0
2
0
2
2
0
0
0
0
2
2
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
2
1
0
1
0
2
0
0
1
0
2
0
1
0
3
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
1
1
0
2
0
0
2
1
0
0
2
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
2
2
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
3
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
1
1
0
2
0
0
1
0
1
0
1
2
0
1
0
0
0
0
0
0
0
3
2
0
1
0
0
0
0
0
0
0
2
0
0
9
0
1
0
1
0
0
1
0
1
0
0
0
1
0
0
1
2
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
2
0
0
1
0
1
1
0
1
2
1
1
0
0
0
0
0
1
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
1
2
0
0
0
1
0
2
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
1
1
0
0
2
1
0
0
2
1
2
1
0
0
0
0
2
0
0
2
1
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
1
2
1
1
2
1
2
0
0
1
0
0
0
0
0
0
0
0
2
1
1
0
0
0
1
0
0
2
2
2
0
0
0
1
1
0
0
1
0
0
2
0
0
2
0
1
1
2
0
0
2
2
2
0
0
0
2
0
0
0
1
0
0
1
0
2
0
1
3
0
0
1
2
0
0
0
0
2
0
0
0
0
1
0
3
0
0
0
3
2
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
2
2
2
0
0
1
2
0
2
2
1
1
0
0
2
0
1
0
0
1
0
1
0
0
2
0
0
0
2
0
0
0
0
1
0
1
2
0
0
0
0
2
0
2
2
3
0
0
1
0
0
0
0
0
2
0
2
0
0
2
1
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
1
1
0
1
1
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
2
2
1
0
0
1
0
0
1
0
3
0
2
2
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
3
0
0
0
0
2
1
0
2
0
1
0
0
2
0
0
3
0
0
0
0
0
0
0
1
1
0
1
2
0
0
0
0
2
0
0
2
2
1
2
0
0
1
0
1
0
2
2
0
3
0
2
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
1
0
0
0
2
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
2
1
0
0
0
0
2
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
1
1
0
1
0
2
0
3
0
0
1
0
0
4
1
0
0
0
3
2
0
0
0
2
1
1
1
0
3
2
0
0
0
0
2
0
2
1
0
0
1
0
1
0
0
0
0
0
2
0
2
1
0
0
1
0
4
2
1
3
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
2
0
2
2
1
0
2
2
2
0
0
0
0
0
2
0
3
2
2
1
0
2
2
0
2
3
4
0
1
0
2
1
0
0
0
0
0
0
2
1
0
0
2
0
0
0
2
0
0
2
0
0
1
0
2
0
0
0
0
1
7
2
0
0
1
1
1
0
1
0
0
0
0
2
0
0
0
0
2
0
2
0
1
1
0
0
0
1
0
0
0
2
0
0
1
0
0
0
2
0
1
2
1
1
2
2
1
0
0
5
2
0
0
0
0
0
0
1
0
0
0
2
4
1
0
0
1
0
1
0
0
2
0
1
0
0
1
0
2
0
1
2
1
0
2
0
0
0
2
0
0
0
2
2
0
0
0
0
1
1
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
1
0
1
2
2
0
0
1
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
4
1
2
0
2
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
1
0
0
0
4
0
0
0
0
2
0
2
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
5
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
2
0
1
1
1
0
0
0
0
1
2
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
4
2
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
2
0
0
2
2
0
2
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
1
2
0
1
1
0
1
0
0
0
0
2
2
0
0
0
1
1
2
0
2
2
2
0
0
2
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
1
0
0
0
1
0
5
0
2
0
0
0
1
4
0
0
0
1
0
1
0
2
0
0
0
0
3
1
0
2
1
1
0
2
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
2
3
8
0
0
0
0
0
0
2
1
2
1
0
0
0
0
0
0
0
0
0
1
0
2
0
2
2
0
1
1
0
0
2
3
0
0
0
0
2
0
0
2
0
2
2
0
0
2
2
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
1
0
2
0
1
1
0
0
0
2
0
0
2
0
2
1
1
0
1
1
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
2
1
1
1
2
0
0
2
0
2
1
2
1
2
0
0
0
0
0
0
0
0
2
1
0
0
1
2
0
0
1
0
1
2
1
0
0
0
1
0
0
2
1
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
1
2
1
0
0
0
0
1
4
0
0
1
0
0
2
0
1
1
0
0
2
0
0
0
0
0
1
0
0
0
1
1
2
0
0
0
2
0
0
0
1
0
1
0
1
0
0
2
0
0
2
0
0
0
2
1
1
1
0
2
1
1
0
0
0
3
1
0
2
0
1
1
1
0
1
2
0
0
0
0
0
0
7
0
0
2
0
3
2
0
2
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
1
1
0
1
1
1
0
1
0
0
0
0
1
0
0
0
0
1
2
0
2
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
2
2
1
0
0
2
0
0
2
1
1
1
0
0
0
0
2
0
2
2
0
1
1
1
0
0
2
1
0
0
0
2
0
0
0
0
2
1
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
3
0
1
0
0
1
0
2
0
0
2
3
0
0
0
2
0
0
0
2
0
0
0
2
1
0
0
0
0
2
0
0
0
1
1
0
0
0
0
2
1
0
2
1
0
0
0
0
0
1
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
1
0
0
0
2
0
0
0
2
0
2
2
1
2
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
1
2
0
0
0
0
1
2
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
1
0
1
0
0
0
0
0
0
1
0
1
2
2
3
0
0
0
0
0
0
2
0
0
2
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
5
0
1
2
0
1
0
4
2
1
0
0
0
0
0
1
1
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
2
1
0
0
1
0
0
1
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
1
0
1
0
0
0
1
0
0
2
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
1
2
0
0
2
1
0
0
0
2
5
2
0
3
2
0
0
0
2
0
1
0
2
0
1
0
0
0
1
0
3
2
0
0
1
3
0
0
1
0
0
0
0
0
0
1
1
2
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
1
0
0
1
2
0
2
0
0
0
0
2
0
1
0
2
1
0
0
0
1
1
1
0
0
0
0
2
0
2
0
2
0
2
1
1
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
2
1
0
0
0
0
0
1
0
1
1
2
6
0
2
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
3
0
0
0
1
0
0
0
0
0
0
1
3
0
2
4
2
2
1
0
0
0
0
1
0
2
1
2
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
1
1
1
1
1
0
3
0
2
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
1
0
2
0
2
1
0
0
0
1
1
1
2
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
2
0
2
3
0
0
0
1
0
5
1
0
1
0
2
0
0
0
1
3
2
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
2
1
0
0
2
1
0
0
0
1
2
0
0
0
0
0
5
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
2
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
2
0
3
0
1
1
0
0
0
0
0
0
1
2
0
0
2
0
0
0
1
1
2
1
2
0
0
0
0
0
2
0
1
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
3
0
1
0
2
0
0
2
1
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
1
2
0
2
2
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
1
1
1
4
0
2
0
1
2
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
1
0
3
2
1
0
0
1
1
0
0
0
0
0
0
0
0
2
1
3
0
0
1
1
0
0
0
0
0
0
1
0
0
3
0
0
0
3
0
2
0
4
1
4
1
1
1
0
0
0
0
1
1
0
1
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
1
1
0
0
1
0
0
0
2
0
3
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
2
0
1
1
0
0
0
1
0
0
0
2
0
0
1
2
2
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
2
2
0
0
0
1
0
1
1
0
2
0
0
2
0
0
0
1
1
0
2
0
0
1
1
1
0
0
0
0
0
0
2
1
3
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
1
0
1
0
0
1
2
1
0
2
0
0
2
0
0
5
2
0
0
0
0
0
0
0
3
0
0
0
4
3
2
0
2
0
0
0
0
0
1
3
1
0
2
0
0
2
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
2
1
2
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
2
0
2
1
0
0
0
1
1
2
0
0
0
2
0
0
1
0
0
0
2
0
0
1
0
0
0
2
0
1
0
1
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
2
0
2
2
0
1
0
0
2
0
1
2
2
2
0
0
0
2
0
0
0
4
1
0
2
0
0
2
0
1
2
2
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
2
0
2
2
0
2
0
2
1
0
0
0
0
0
0
2
0
4
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
4
0
2
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
1
2
2
0
0
2
1
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
1
2
1
0
1
0
0
1
1
2
2
2
1
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
3
0
1
1
1
2
1
0
0
2
0
0
1
0
0
0
2
0
0
0
2
0
2
1
0
1
0
0
0
0
1
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
1
0
2
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
2
0
0
0
2
1
2
3
0
0
2
0
0
0
0
2
1
0
0
0
0
0
1
1
1
0
0
2
0
0
0
1
2
1
2
0
0
3
0
1
2
0
1
2
0
2
1
0
0
1
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
1
0
3
0
1
0
0
2
0
0
0
0
0
0
2
0
1
2
2
0
0
0
0
0
0
2
0
0
0
2
1
0
0
2
0
0
0
2
0
1
2
0
0
0
0
1
0
1
0
0
0
0
1
3
2
0
3
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
1
1
3
0
0
4
0
0
0
2
0
2
0
0
0
2
1
0
0
0
0
1
0
0
0
0
1
0
0
2
2
0
0
0
2
0
0
1
1
0
0
2
0
0
1
2
0
0
2
0
0
1
0
0
0
1
1
0
2
0
0
0
1
1
0
0
0
2
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
2
0
1
0
0
0
0
0
0
2
0
2
0
0
0
1
2
2
0
0
0
2
0
0
0
0
0
0
3
2
1
0
0
0
0
0
1
0
0
1
0
0
1
0
3
2
0
0
0
1
0
0
1
0
0
0
0
1
0
2
1
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
2
2
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
2
1
0
1
1
1
0
1
1
3
0
0
0
0
0
1
0
0
0
2
1
2
0
1
2
0
0
1
0
0
0
0
0
2
1
0
4
1
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
2
1
0
1
0
1
1
0
0
0
1
0
0
2
0
3
1
2
2
2
2
0
0
0
0
2
1
2
0
0
0
1
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
2
1
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
4
1
2
2
2
0
2
1
2
0
0
0
0
0
1
1
0
0
0
2
0
2
0
0
0
0
3
5
0
1
0
2
2
0
0
0
2
0
0
0
2
3
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
2
1
2
0
0
1
1
1
0
0
2
0
0
3
1
0
0
0
0
0
0
0
0
2
0
4
1
0
1
0
3
0
0
0
0
1
0
1
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
2
2
0
0
0
2
2
0
0
1
1
0
0
1
1
0
0
2
0
1
0
0
0
0
2
0
0
0
1
3
0
0
0
1
0
1
0
2
0
2
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
2
1
0
0
3
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
1
0
1
0
0
2
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
2
2
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
1
0
2
2
0
0
0
0
0
1
0
0
3
2
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
2
2
0
0
0
2
2
0
0
1
0
0
2
0
0
0
0
2
0
0
1
2
0
1
0
2
0
0
1
1
0
2
2
2
0
0
2
0
0
0
0
0
2
0
0
3
0
2
1
0
0
0
2
0
0
0
0
0
0
1
1
0
0
1
0
0
0
2
1
0
1
0
2
2
0
0
1
2
0
0
0
1
0
0
1
1
0
2
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
2
1
0
0
1
0
2
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
1
1
0
0
0
2
2
0
0
0
0
0
0
2
0
0
1
0
2
0
2
0
0
0
6
1
1
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
2
2
0
2
2
1
0
0
1
0
0
2
2
1
1
1
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
2
1
0
0
2
0
1
0
1
0
1
0
1
1
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
1
2
0
2
0
0
0
3
0
2
0
1
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
3
2
0
0
0
1
2
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
2
1
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
3
0
0
0
2
0
0
2
1
0
0
0
0
1
0
3
2
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
2
0
0
2
2
0
0
0
0
1
0
2
0
0
1
0
0
2
2
2
2
0
1
0
0
0
0
0
0
1
0
0
0
0
2
1
0
2
1
1
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
1
0
0
2
0
0
2
0
0
0
2
0
0
0
1
0
0
0
1
2
0
0
2
0
1
0
0
0
1
0
2
2
0
0
2
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
1
1
1
0
2
2
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
3
0
3
0
0
0
1
1
0
0
2
2
0
0
0
2
0
0
0
0
2
1
0
1
0
0
0
0
2
2
1
0
1
0
0
0
1
0
0
0
0
2
1
0
0
0
1
3
0
2
0
0
0
0
1
2
0
0
1
0
0
0
2
0
0
0
0
3
1
0
2
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
3
0
1
0
3
0
0
1
0
1
0
1
0
0
2
2
0
0
0
0
1
2
0
0
0
0
1
0
1
0
0
1
0
3
0
2
1
0
0
2
1
1
0
0
0
0
0
2
0
3
1
0
0
1
0
0
0
1
2
0
3
0
1
0
2
2
2
0
3
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
2
2
0
5
2
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
1
1
0
1
2
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
2
1
0
1
0
1
0
0
0
0
0
1
1
2
0
1
0
0
0
0
0
0
0
1
1
2
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
1
2
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
1
0
0
1
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
1
0
1
0
0
2
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
5
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
2
0
0
2
1
0
0
2
2
2
0
0
0
0
1
0
2
1
0
0
1
2
0
0
0
0
0
1
0
1
0
0
3
0
1
0
0
0
1
0
0
0
0
0
0
1
2
0
2
0
0
0
0
1
0
0
1
0
0
2
0
0
0
1
1
0
2
1
0
0
1
2
1
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
2
0
0
0
0
1
4
2
0
0
0
0
0
1
1
2
0
0
0
0
0
2
1
0
2
0
2
1
0
1
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
2
2
1
0
1
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
2
1
2
0
1
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
2
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
2
2
0
0
0
0
0
1
0
0
2
0
0
0
2
2
1
1
0
0
1
2
3
0
0
0
0
0
0
2
1
6
0
1
0
1
0
1
0
1
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
3
0
1
1
0
0
0
1
1
0
0
1
0
0
0
0
0
1
2
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
2
2
0
1
1
1
0
1
0
0
0
0
0
1
0
0
2
0
0
2
2
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
1
0
1
1
2
0
2
0
2
0
2
0
2
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
2
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
2
1
0
0
0
1
0
1
0
1
2
0
0
0
2
2
1
0
0
0
0
0
4
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
1
0
0
2
3
0
0
1
0
0
0
0
0
1
0
0
0
2
2
0
0
2
1
0
0
0
0
0
0
1
1
0
1
0
2
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
2
2
2
0
0
2
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
1
2
0
0
2
0
2
0
0
2
0
0
1
0
1
1
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
2
0
0
0
1
0
0
0
0
2
2
2
0
0
2
0
0
0
2
0
1
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
2
0
0
0
0
1
2
0
1
2
2
1
1
1
2
0
0
0
1
1
0
0
0
0
1
2
0
1
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
1
0
0
1
2
0
2
0
0
2
2
0
2
1
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
2
0
0
1
0
0
0
3
2
1
0
0
1
2
0
0
0
0
0
1
0
1
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
4
1
0
0
1
0
0
1
0
3
1
2
0
0
1
1
2
0
2
0
0
0
0
2
0
0
1
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
1
0
2
2
0
2
1
1
0
1
3
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
2
0
1
2
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
2
1
2
2
0
0
0
0
0
1
1
0
0
1
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
1
1
0
2
0
0
0
1
2
0
0
3
2
0
0
2
0
0
0
0
1
1
1
0
2
1
2
0
1
0
0
0
0
1
1
0
0
1
0
0
2
0
2
0
0
0
1
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
2
2
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
2
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
1
0
0
2
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
2
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
2
2
2
0
0
2
0
2
2
1
0
0
0
0
0
2
1
0
0
0
0
0
1
9
0
2
2
0
0
2
2
0
1
0
2
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
15
0
1
0
1
1
3
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
2
1
0
0
1
0
0
1
0
2
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
1
1
1
0
0
0
0
1
3
0
2
2
0
2
1
0
2
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
1
0
2
0
0
2
0
0
2
0
0
2
0
0
0
1
2
0
1
2
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
2
0
0
0
2
0
1
2
2
1
0
0
2
0
0
0
2
1
0
0
2
0
1
0
0
1
1
0
0
2
2
1
0
2
0
1
2
0
0
1
0
3
0
1
0
0
0
1
2
0
2
0
0
2
0
0
0
1
0
2
0
0
0
2
0
0
2
1
3
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
2
0
1
0
0
0
1
0
2
1
1
3
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
2
0
0
2
0
0
0
2
0
1
1
0
2
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
3
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
2
2
0
0
0
0
0
0
1
2
1
0
0
0
1
0
0
0
0
2
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
2
0
0
3
0
0
1
0
1
0
2
2
0
2
2
0
4
0
0
0
0
1
0
0
2
2
0
2
0
0
0
0
0
0
3
0
2
1
0
2
0
2
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
2
1
0
2
0
2
0
0
0
0
2
0
0
0
1
0
1
0
0
0
2
2
0
0
0
0
0
2
0
0
3
2
0
0
0
0
0
2
3
1
1
1
0
3
1
0
0
3
1
0
2
0
0
0
0
0
1
0
0
0
2
2
0
0
1
0
1
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
1
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
2
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
2
1
0
0
1
1
0
2
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
2
1
0
0
0
0
1
1
4
1
0
0
0
0
0
1
1
0
0
2
0
1
0
2
2
0
0
0
0
0
1
1
0
3
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
1
0
2
4
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
1
2
0
2
0
0
0
0
2
1
0
0
0
0
1
2
4
2
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
2
2
0
1
2
2
1
1
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
3
1
0
1
0
0
0
0
0
0
0
0
0
2
0
1
1
1
0
0
1
0
0
0
2
0
2
1
0
0
0
0
0
0
0
1
1
2
0
0
2
2
0
0
0
1
0
1
2
3
0
0
2
1
0
0
2
0
1
0
1
0
0
0
2
1
2
0
0
1
0
0
1
2
0
1
3
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
2
2
0
2
1
2
1
0
0
1
0
0
0
0
0
0
1
0
1
2
0
0
0
3
0
3
0
1
0
0
1
0
0
2
0
2
0
2
2
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
3
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
1
0
1
1
2
2
0
5
1
1
1
0
0
0
0
0
0
3
0
0
0
2
1
1
2
2
0
0
0
0
0
0
2
2
0
0
0
2
0
0
2
1
1
2
1
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
2
0
0
0
0
2
0
0
1
0
3
0
0
0
2
0
0
2
0
0
1
2
1
0
2
0
0
0
0
1
0
4
0
0
0
0
0
2
0
1
0
0
0
1
0
2
0
0
0
0
1
0
0
1
3
3
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
3
2
0
0
2
2
1
0
0
1
0
0
0
0
0
3
2
0
0
0
1
2
0
0
0
2
0
2
1
2
0
0
0
0
2
2
0
0
0
0
2
0
1
0
0
2
1
0
0
0
0
2
0
1
1
1
1
0
2
1
0
0
0
3
0
0
0
2
0
2
0
0
1
1
0
1
1
1
2
0
2
0
1
0
1
0
0
0
0
0
0
0
2
1
0
1
2
0
2
0
1
0
0
1
2
2
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
2
0
2
0
2
0
1
0
1
0
3
0
0
0
0
4
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
2
0
1
0
1
0
2
1
1
2
0
1
6
1
1
0
0
0
0
2
0
0
0
0
1
1
2
1
1
0
0
0
1
0
0
0
0
0
0
1
2
1
0
2
2
2
1
1
0
0
3
0
1
0
2
0
0
0
2
1
0
0
0
0
0
2
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
1
0
1
2
0
0
0
0
0
0
2
0
0
2
0
0
2
1
0
1
1
0
0
0
0
0
2
0
1
2
0
0
1
0
0
2
3
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
1
0
3
1
2
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
1
1
0
0
1
2
0
0
1
0
2
6
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
2
0
0
1
0
0
2
0
1
1
0
4
0
0
0
0
2
0
0
0
2
0
1
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
1
1
1
0
1
0
0
0
1
0
2
0
2
0
1
0
2
0
2
0
0
2
1
0
3
3
0
1
0
1
2
0
0
2
0
0
2
0
0
1
0
1
0
0
0
0
1
2
0
0
2
0
0
1
0
0
1
1
2
2
1
0
1
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
2
0
2
0
1
0
1
0
0
0
0
1
0
2
0
1
1
0
2
1
0
0
0
0
2
0
1
0
1
2
3
0
0
0
1
0
0
1
0
1
3
0
2
0
0
1
0
0
0
2
0
0
0
2
0
2
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
4
2
1
0
0
2
0
0
0
0
1
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
1
0
0
0
1
2
1
0
0
0
0
2
0
1
0
2
0
0
0
0
1
2
0
0
2
1
2
0
0
0
0
2
1
0
0
0
0
1
0
0
0
3
0
0
1
2
1
0
0
0
0
0
0
1
2
0
4
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
1
1
0
2
0
2
0
10
0
0
2
1
1
0
0
1
0
0
1
2
0
0
0
2
0
1
1
0
2
0
0
1
0
2
0
0
0
3
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
2
2
2
0
2
1
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
2
0
2
1
1
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
2
2
0
0
0
0
2
1
1
2
0
2
0
1
0
0
1
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
2
1
0
0
0
0
1
3
2
1
0
0
0
3
1
2
0
2
0
0
1
0
1
4
0
3
0
1
1
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
2
0
0
0
1
2
0
0
1
0
2
0
2
0
0
1
0
1
0
0
0
0
2
2
0
1
1
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
1
2
2
0
1
1
2
0
1
2
0
0
1
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
1
2
1
0
1
0
0
1
0
0
0
0
2
0
0
1
2
2
2
0
0
0
0
3
0
0
0
0
0
0
1
0
0
1
0
0
2
2
0
0
0
0
0
1
0
1
2
2
0
0
1
0
1
0
4
3
0
1
1
0
0
0
1
0
1
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
2
0
2
1
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
1
0
0
2
1
0
0
2
1
0
0
2
0
0
2
2
0
2
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
2
0
0
0
1
1
2
0
0
0
0
0
0
0
11
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
1
0
2
2
3
0
0
0
2
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
1
0
0
1
5
0
0
0
2
0
0
1
2
0
0
4
0
2
2
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
2
0
0
0
2
0
2
1
3
0
0
1
0
0
2
0
0
2
0
0
0
0
1
0
2
0
0
0
3
0
0
0
1
1
0
0
3
1
5
2
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
5
0
0
1
0
0
0
0
0
0
2
0
0
0
1
2
0
2
2
2
1
0
1
0
0
0
2
0
1
1
1
0
0
1
0
2
0
0
1
0
0
1
0
0
0
0
0
2
2
3
3
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
1
2
2
0
1
0
2
0
0
1
0
0
2
0
0
2
2
0
2
2
0
0
0
0
1
0
0
1
0
1
0
0
2
0
1
0
0
0
2
0
0
2
1
0
0
0
3
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
1
0
1
0
0
1
0
0
0
0
2
0
2
0
1
2
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
3
0
1
4
0
0
1
2
0
0
1
0
2
0
0
0
0
0
1
2
2
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
3
0
0
0
0
0
0
2
0
2
0
1
0
0
0
2
0
0
0
1
1
1
0
1
0
0
2
0
1
2
3
0
2
0
1
0
1
0
0
0
0
2
1
0
0
0
2
0
3
2
0
0
1
0
0
2
0
1
2
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
5
0
0
2
1
1
0
2
2
1
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
3
0
1
0
1
2
1
0
0
2
0
0
1
0
0
0
0
2
0
0
0
1
0
0
2
2
2
0
0
0
0
0
0
0
1
3
2
1
4
0
1
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
2
1
0
2
0
0
1
1
0
1
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
3
1
2
1
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
1
0
1
0
2
1
0
1
5
0
0
2
2
0
0
2
0
0
0
3
2
1
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
2
0
0
1
0
0
0
2
0
0
1
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
1
0
0
1
0
0
0
2
1
0
2
2
0
0
0
0
2
2
1
0
1
2
0
0
0
0
0
2
1
1
0
1
1
4
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
1
1
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
1
0
1
1
0
0
0
2
1
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
1
0
2
3
0
0
0
2
0
2
2
1
0
0
3
0
0
1
0
0
0
1
0
0
2
2
0
2
0
2
1
2
0
0
0
0
1
0
1
2
2
0
0
1
2
2
2
0
1
0
0
2
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
2
0
0
0
2
0
1
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
1
1
0
0
2
0
0
0
3
1
0
2
2
0
2
0
0
1
0
2
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
2
1
1
0
2
0
1
0
1
2
0
2
0
2
0
0
0
0
1
0
0
2
0
0
1
0
0
1
2
0
0
0
1
0
1
0
0
1
0
1
1
0
0
0
0
3
1
0
0
2
0
2
0
0
2
2
2
0
1
0
0
1
0
2
0
0
0
2
2
0
1
0
0
1
0
1
1
0
1
0
0
1
0
0
0
7
1
0
1
0
0
2
0
2
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
1
2
0
1
0
0
0
0
1
0
1
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
2
0
2
1
1
3
0
1
1
0
2
1
0
2
2
0
0
4
0
0
0
0
0
0
0
0
3
0
0
0
0
1
1
2
0
1
0
0
2
2
0
0
1
0
1
0
0
1
1
2
2
0
0
1
1
2
1
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
2
2
1
1
1
1
2
0
1
0
0
0
0
0
0
0
2
0
0
1
1
1
0
2
0
0
2
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
1
4
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
1
0
0
0
1
3
0
0
0
0
0
2
0
0
0
0
0
2
2
0
1
1
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
10
2
0
0
0
0
3
0
2
0
4
0
1
0
0
0
1
0
0
1
1
0
1
2
0
0
0
1
0
0
2
2
2
1
4
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
6
0
1
0
0
0
0
0
1
0
0
1
1
0
1
5
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
1
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
1
0
3
2
0
5
0
2
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
2
1
0
0
0
5
2
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
3
2
0
0
1
2
1
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
2
0
1
0
0
0
0
0
3
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
1
0
1
2
0
1
0
0
0
0
2
0
1
1
0
2
0
0
2
1
0
0
2
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
3
2
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
2
1
1
0
1
0
0
0
0
0
0
0
0
0
1
2
0
2
0
1
1
0
1
0
0
0
0
0
0
1
2
0
0
1
1
2
0
2
0
0
2
0
0
0
2
0
2
2
1
2
0
0
1
0
4
0
0
3
0
1
0
1
1
1
1
2
0
2
0
2
0
1
0
2
1
0
0
0
2
1
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
2
0
1
0
1
2
0
0
1
1
2
1
0
0
2
0
0
0
0
1
2
0
2
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
1
2
2
1
2
2
0
0
0
2
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
1
0
0
2
1
0
0
1
0
0
0
0
0
0
1
0
2
1
1
1
0
0
3
0
0
1
6
0
0
0
0
0
2
0
2
1
1
1
0
1
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
2
0
0
0
2
0
0
0
0
0
0
2
1
4
0
1
2
3
0
2
1
2
0
0
2
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
2
0
0
0
1
2
1
3
0
0
0
2
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
1
0
1
2
0
0
1
1
0
0
2
0
0
2
0
1
0
0
2
1
2
1
1
1
0
0
0
0
2
0
0
0
0
0
2
2
1
0
1
1
1
0
0
0
0
1
3
1
0
0
0
1
2
2
0
0
0
0
2
0
1
1
2
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
2
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
2
2
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
3
2
2
0
0
0
0
0
2
3
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
2
0
0
1
0
0
2
0
0
0
0
0
0
2
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
1
2
0
0
0
0
0
1
0
1
0
1
0
0
2
2
2
0
1
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
6
2
0
0
2
0
0
1
0
1
0
0
0
0
0
2
0
0
1
1
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
1
1
0
1
0
0
2
2
0
1
1
0
0
1
2
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
2
0
0
0
1
2
1
0
2
0
0
2
0
0
1
0
0
1
1
1
0
0
2
1
0
0
2
0
0
2
0
0
0
2
0
0
1
0
0
2
0
2
0
0
2
0
1
0
0
0
0
1
2
1
0
0
0
0
2
0
1
1
2
0
2
0
0
1
0
1
2
1
0
2
0
2
2
3
0
0
1
0
0
2
1
0
0
0
0
0
2
1
0
0
0
1
0
1
0
1
2
0
0
0
3
0
2
0
0
0
0
0
0
0
2
2
0
1
0
0
2
0
0
0
2
1
0
1
2
0
0
2
0
0
1
0
2
0
0
1
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
2
0
0
2
1
1
0
0
0
1
2
0
2
0
0
0
0
0
1
2
0
0
0
1
2
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
3
0
0
2
0
1
3
1
0
1
1
1
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
2
0
0
1
0
0
0
0
1
0
1
0
2
0
2
0
0
1
0
1
0
0
0
0
1
0
1
1
0
0
2
0
0
2
2
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
2
0
1
2
1
2
1
4
0
0
1
1
2
0
0
0
0
0
2
0
0
1
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
1
0
0
0
3
0
2
0
0
0
3
0
0
1
0
0
0
0
0
0
1
1
2
3
0
2
0
0
1
0
0
0
2
0
0
0
2
1
1
0
1
0
0
1
0
0
0
0
2
2
0
0
1
0
0
0
0
0
2
0
2
1
1
0
2
0
1
1
0
0
0
0
0
0
2
1
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
2
2
0
0
0
2
2
0
0
1
0
1
0
2
0
0
2
1
3
0
6
0
0
0
0
0
0
0
0
0
3
1
2
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
3
1
0
0
0
3
1
0
1
1
0
0
0
0
0
2
0
1
1
1
0
1
0
2
2
0
0
1
3
0
0
0
0
0
2
2
2
0
1
1
0
0
0
0
0
1
1
2
0
0
2
2
0
0
1
2
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
1
0
2
0
1
0
2
0
1
1
0
2
0
1
0
0
0
0
1
2
0
0
1
1
0
0
0
0
0
0
0
0
3
0
2
0
3
0
3
0
0
1
0
0
0
0
2
0
0
1
1
0
0
0
0
0
2
2
2
2
1
0
0
0
0
0
0
0
2
0
0
1
0
1
0
2
1
0
0
0
1
0
1
1
2
1
2
0
1
0
0
0
0
0
0
0
2
0
0
4
0
1
0
1
1
1
0
0
1
0
1
0
2
1
0
0
0
0
1
0
0
0
0
2
0
0
0
2
1
0
0
3
1
0
0
0
0
3
0
0
0
1
0
0
0
0
2
0
1
0
0
1
0
0
3
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
2
1
0
0
2
2
1
0
2
1
0
1
0
1
0
2
2
0
0
0
0
0
0
1
0
3
3
0
2
0
2
2
0
2
1
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
2
0
0
0
1
1
0
0
1
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
4
2
0
0
0
0
0
1
1
0
0
0
0
0
2
0
1
0
0
0
0
1
2
0
1
0
0
0
0
2
2
0
0
0
0
0
0
2
1
2
0
0
1
1
0
0
0
2
1
1
0
0
0
0
1
0
1
0
1
0
1
7
0
0
0
1
0
0
1
0
0
1
0
0
0
3
1
0
0
1
1
3
0
0
1
0
0
0
0
0
0
2
1
0
0
0
1
1
1
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
1
2
2
1
0
1
0
0
0
5
4
0
0
0
3
4
0
0
1
2
1
2
0
0
0
0
0
0
0
0
0
2
2
0
0
2
2
0
0
0
0
0
0
0
2
2
2
2
0
0
1
0
2
0
1
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
2
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
1
0
1
0
1
0
0
0
2
2
2
0
0
0
0
0
0
1
0
2
0
1
0
0
0
2
0
0
2
1
0
0
0
1
0
0
0
1
0
1
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
2
1
1
0
0
2
0
0
1
2
0
1
2
0
2
0
0
1
0
0
1
3
0
2
0
2
0
2
1
0
1
0
1
0
3
0
0
1
0
1
1
0
0
0
0
1
1
0
0
2
0
2
0
0
0
0
2
1
2
0
0
0
2
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
1
1
0
1
0
3
0
0
1
0
2
0
2
2
0
0
0
0
0
1
1
0
0
1
0
2
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
3
0
0
0
0
1
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
3
1
2
2
0
0
2
0
0
1
0
1
0
2
0
0
0
0
0
0
0
1
2
0
0
2
0
0
4
2
0
2
0
0
1
1
2
0
2
2
0
0
0
0
2
0
3
1
1
0
2
0
0
0
0
1
0
0
0
0
2
3
3
0
0
2
0
0
0
0
0
1
0
3
0
0
0
4
0
2
0
3
1
0
0
2
0
2
0
1
1
1
0
0
0
0
1
1
0
2
0
0
2
2
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
2
0
2
1
0
0
1
0
0
0
0
4
0
2
0
0
3
1
0
0
0
2
0
2
0
0
2
0
2
1
1
0
0
0
0
0
1
2
0
0
4
0
0
0
0
2
0
0
0
1
0
2
1
0
0
2
0
1
0
0
2
1
0
0
0
0
0
2
1
1
0
0
2
1
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
2
0
0
0
0
2
0
2
2
2
2
0
0
0
0
0
2
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
1
0
0
0
2
2
2
2
0
0
0
1
0
0
1
1
0
2
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
2
1
0
0
0
1
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
2
0
1
0
0
1
0
1
0
3
1
2
0
0
0
2
3
0
0
0
0
2
1
2
0
0
2
0
0
2
0
0
2
0
1
0
2
0
2
1
1
0
1
2
2
1
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
1
0
2
2
0
0
0
0
2
0
0
0
1
2
0
1
2
2
0
1
0
0
0
2
0
3
0
1
0
0
0
0
0
2
0
0
0
0
2
1
2
0
1
0
0
0
0
0
0
0
2
2
1
0
0
0
0
1
0
3
4
2
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
2
2
1
2
0
2
1
2
1
1
0
0
0
0
0
0
2
1
1
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
2
0
0
2
1
0
0
2
2
0
1
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
2
1
0
0
0
0
1
1
0
0
3
1
1
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
2
0
2
0
0
0
0
0
1
1
0
0
0
0
2
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
2
1
1
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
1
1
2
0
2
1
0
0
2
0
0
2
0
0
0
0
0
0
2
2
0
2
0
2
2
2
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
1
1
0
0
2
0
0
1
1
0
2
1
0
0
3
2
1
0
2
0
0
0
2
2
3
1
1
1
0
0
0
1
1
0
1
0
2
2
0
0
0
0
0
0
0
0
1
1
0
2
0
0
1
2
0
1
2
0
2
0
2
0
0
0
0
0
0
1
0
1
2
2
0
1
0
0
1
0
0
2
0
0
0
2
1
2
0
0
1
4
1
0
2
1
0
2
0
1
2
0
0
1
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
1
1
1
0
1
1
0
0
0
0
0
0
0
2
2
2
1
1
0
0
1
1
0
0
0
0
0
1
2
1
0
1
2
4
0
0
1
0
1
2
0
0
0
1
0
1
0
0
0
0
1
2
0
0
1
2
1
3
0
0
0
0
0
0
1
1
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
3
1
0
1
2
0
0
1
0
2
0
1
1
0
0
0
0
0
0
1
0
0
0
2
2
0
2
0
2
0
0
0
2
0
2
2
0
1
0
1
2
0
1
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
1
0
2
1
0
0
1
0
0
0
0
0
1
0
1
1
1
1
0
0
0
0
2
1
2
2
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
7
0
1
0
0
1
1
0
0
0
0
0
1
50
0
0
0
0
0
0
1
0
0
2
1
2
0
2
0
0
1
0
0
2
0
1
2
0
0
0
0
4
0
2
3
0
0
0
0
0
1
2
0
2
1
0
1
2
3
0
0
1
1
0
2
0
2
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
2
0
2
0
2
2
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
3
2
1
0
2
0
0
0
2
1
2
0
2
0
2
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
1
1
1
4
1
2
0
0
0
2
0
1
0
1
1
2
2
0
0
2
0
1
0
1
2
0
1
1
1
0
0
0
0
0
0
1
1
0
1
0
0
1
0
2
2
0
2
2
0
2
0
2
0
1
0
0
2
1
0
0
0
0
1
0
2
0
1
0
2
0
0
4
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
2
0
0
0
2
0
1
2
0
2
0
0
2
0
0
0
2
2
0
2
0
0
0
0
0
0
0
2
2
0
1
0
2
0
0
1
0
2
0
2
0
0
2
2
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
1
0
2
0
0
0
2
0
0
0
0
0
6
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
2
2
0
2
1
2
1
0
0
1
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
1
0
2
0
0
0
1
0
1
2
0
0
0
0
1
0
1
0
1
2
2
0
1
0
0
0
1
2
1
0
0
0
0
0
1
5
3
0
2
1
1
0
0
0
1
0
1
1
1
0
3
3
2
0
0
0
0
1
1
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
2
1
0
0
0
0
0
1
0
1
0
0
1
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
2
1
0
0
0
1
2
0
0
2
1
0
0
0
1
2
0
0
0
2
0
0
0
0
2
2
1
2
1
2
0
2
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
2
2
1
0
2
2
0
1
0
0
0
2
0
0
0
1
0
2
0
1
0
0
0
0
2
0
1
0
0
0
3
0
3
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
1
0
2
0
4
0
0
0
0
0
0
1
0
1
2
2
0
0
0
0
0
2
2
2
0
0
0
0
1
1
1
0
0
0
2
2
2
0
0
0
1
0
1
0
0
0
0
0
0
4
0
1
2
0
0
0
0
2
2
0
0
0
1
1
0
2
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
2
0
0
1
0
0
2
0
0
0
0
0
0
1
0
1
2
1
0
0
0
0
0
1
0
1
0
1
1
3
0
2
0
1
2
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
2
2
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
2
2
0
1
0
0
0
0
2
1
1
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
1
0
2
0
2
0
0
3
0
0
0
2
1
2
0
0
0
2
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
2
1
0
0
0
0
1
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
2
1
2
0
0
1
1
2
2
0
1
0
0
0
0
1
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
2
1
0
4
2
0
1
0
1
2
2
2
0
0
0
0
0
0
1
0
2
0
0
2
0
1
2
0
0
4
0
0
0
1
1
0
0
0
2
0
0
0
0
0
3
0
0
1
1
2
1
2
2
1
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
2
2
0
4
0
0
0
0
1
1
2
0
0
3
0
0
0
0
0
0
0
1
1
1
0
2
1
0
0
0
1
0
0
0
1
1
1
1
1
0
0
0
1
1
0
2
0
0
0
0
3
0
2
0
2
0
3
1
1
0
0
0
0
0
0
2
0
4
0
0
1
0
1
0
0
2
0
1
0
0
0
1
0
0
1
0
0
0
2
2
0
0
2
2
0
0
0
0
0
0
0
0
2
0
2
0
0
1
1
3
2
0
2
0
2
2
1
0
0
2
2
0
0
0
0
1
0
0
2
0
0
0
1
0
0
1
2
2
3
0
2
2
2
2
2
0
2
2
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
2
1
0
1
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
1
0
0
0
1
1
2
0
2
1
0
3
0
0
0
0
1
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
2
2
2
1
2
2
0
1
1
1
0
0
0
0
2
1
1
0
3
0
0
0
0
1
0
0
0
1
0
0
0
2
0
2
0
0
3
2
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
1
0
0
0
1
0
1
0
0
2
2
0
1
0
0
0
0
2
2
0
1
0
0
2
0
3
1
2
2
0
2
0
0
2
0
1
1
2
2
0
1
0
1
1
0
0
0
0
2
0
2
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
1
0
2
2
0
0
0
2
0
0
0
2
0
0
1
2
0
0
0
1
0
0
2
1
2
0
0
0
0
0
2
0
1
0
0
1
2
0
1
0
1
2
0
0
0
0
2
0
1
1
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
1
2
0
1
0
1
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
1
0
2
1
2
0
0
0
3
0
0
0
3
1
0
0
1
0
1
2
1
0
0
0
7
0
0
0
0
1
2
0
0
0
2
1
0
0
0
1
3
0
1
2
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
1
1
2
0
0
1
0
2
0
0
1
0
0
0
2
1
2
0
1
1
0
2
0
1
0
1
2
2
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
2
0
0
1
0
0
0
1
2
0
0
0
0
0
2
0
1
2
0
1
2
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
2
1
3
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
2
0
1
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
5
2
0
5
0
2
0
0
0
0
2
2
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
1
0
1
0
2
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
2
0
0
2
0
1
2
0
1
1
0
2
0
0
3
0
0
1
2
0
0
0
0
1
0
1
0
2
0
0
0
1
2
0
0
0
0
0
0
1
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
2
2
0
1
5
1
2
1
0
0
0
0
0
3
0
0
3
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
1
2
0
0
0
0
0
2
0
0
2
2
2
0
2
0
0
2
0
1
0
1
0
4
0
2
0
0
0
0
1
0
2
0
0
0
1
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
1
0
2
1
1
2
1
1
0
1
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
1
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
3
2
0
0
0
0
0
1
0
2
0
0
0
0
2
1
0
2
0
0
0
0
2
0
0
2
0
3
1
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
2
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
1
0
0
1
2
0
0
1
2
1
0
0
0
0
0
1
0
0
0
0
0
0
5
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
1
0
1
0
2
2
1
2
0
4
1
2
0
0
1
0
2
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
1
2
2
1
0
2
0
2
0
1
0
0
0
0
0
0
0
2
1
2
0
0
0
0
3
2
0
0
0
2
0
0
0
0
2
1
0
2
0
0
0
0
1
3
0
0
1
0
2
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
2
0
1
0
2
2
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
1
0
2
0
0
0
0
2
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
1
0
2
1
0
2
0
1
8
0
0
0
0
1
0
4
2
1
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
1
0
2
1
1
0
0
0
0
0
4
1
2
2
0
0
0
1
0
0
2
0
1
0
0
0
2
0
2
2
0
0
1
1
2
2
0
0
0
0
4
1
0
0
0
0
0
0
0
0
2
0
2
0
2
1
1
0
0
0
1
1
0
1
0
0
0
2
0
1
2
0
0
2
0
0
0
2
1
1
0
0
1
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
5
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
1
1
0
0
0
0
2
1
2
2
0
1
0
0
0
1
0
2
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
2
0
2
0
0
2
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
2
0
0
1
0
2
0
0
1
0
2
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
2
0
0
0
2
0
0
0
1
0
0
2
0
1
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
3
0
2
0
0
0
0
0
0
0
0
2
1
1
0
0
1
0
0
1
0
2
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
2
1
1
0
0
2
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
1
2
0
0
1
1
0
1
1
0
0
0
2
1
2
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
1
0
3
0
1
0
0
1
0
0
2
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
2
2
1
0
0
0
1
1
1
0
0
0
1
2
0
2
0
1
0
0
2
0
1
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
2
2
0
2
0
0
0
3
0
1
0
2
0
1
3
0
2
0
2
0
2
0
6
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
1
2
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
2
2
1
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
1
2
0
0
0
1
0
0
2
1
1
1
0
0
0
1
0
0
0
1
2
0
1
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
2
3
0
0
2
2
0
0
2
1
0
2
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
1
1
1
0
2
0
2
2
3
4
2
2
1
0
0
0
2
0
2
0
0
0
0
0
0
1
1
2
1
0
2
0
0
0
2
0
0
2
2
3
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
1
2
0
0
2
0
0
0
1
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
1
1
0
2
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
2
3
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
2
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
1
2
1
0
0
2
0
0
2
0
0
2
2
1
1
2
0
2
2
0
0
3
0
0
0
2
0
2
0
1
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
1
0
2
0
0
2
0
0
0
2
0
1
0
1
2
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
1
0
0
0
2
1
2
0
1
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
2
1
0
0
0
0
1
2
2
1
0
2
1
0
2
2
1
0
0
4
0
0
2
1
0
2
0
0
0
0
1
2
0
0
0
0
2
1
1
0
1
0
1
0
0
2
1
1
0
0
1
2
0
1
1
0
0
0
0
1
0
0
0
2
0
3
1
0
0
0
0
0
0
0
0
2
0
2
0
1
0
1
0
1
0
1
0
2
1
0
0
1
0
0
2
0
0
2
0
0
1
0
0
2
0
2
0
0
0
0
1
0
0
2
0
0
0
1
1
0
1
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
3
2
2
0
0
2
0
0
0
2
0
0
0
0
2
1
0
0
2
11
1
1
0
0
1
1
0
0
1
0
0
0
0
0
2
2
0
1
0
0
0
0
0
2
1
0
1
1
2
0
2
0
2
2
3
0
0
1
0
1
1
0
2
0
0
1
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
2
0
2
0
2
2
0
1
2
0
1
2
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
3
0
2
0
1
1
0
2
0
2
0
2
2
0
0
2
1
0
2
0
1
2
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
2
0
1
2
1
1
0
0
0
2
2
0
0
0
2
0
2
2
0
0
1
2
0
1
1
0
0
0
1
0
1
0
0
0
1
0
0
2
0
2
0
2
0
0
2
0
0
0
1
0
0
0
0
2
0
0
2
1
0
0
1
0
3
1
0
0
2
1
0
1
2
0
1
3
0
0
2
0
2
0
1
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
2
1
0
1
0
1
0
3
0
0
2
2
0
2
2
2
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
2
1
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
2
1
2
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
2
0
2
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
1
2
1
2
2
1
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
1
2
0
2
1
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
1
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
1
0
0
0
0
1
2
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
2
2
1
0
2
0
0
1
0
0
0
0
1
2
0
1
1
0
2
2
5
2
0
0
0
0
2
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
1
0
0
1
0
0
2
1
0
0
0
0
2
0
0
0
2
0
0
0
0
1
1
0
0
2
0
0
0
0
0
1
0
0
0
1
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
2
2
0
0
0
0
1
0
0
1
1
0
0
1
0
1
0
3
2
0
1
0
0
0
0
0
0
2
2
0
2
0
0
1
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
2
1
2
0
0
1
0
2
0
0
0
0
0
2
2
1
1
1
3
0
0
0
3
1
0
2
2
2
1
0
0
0
0
2
0
2
2
1
0
0
0
2
0
0
1
0
2
0
1
2
2
0
0
1
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
2
2
2
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
1
0
1
1
0
1
0
0
0
0
0
0
3
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
3
0
2
0
2
2
0
0
0
2
0
1
0
0
2
1
0
0
0
0
0
1
0
2
0
0
0
1
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
1
1
0
0
0
0
0
0
0
2
1
2
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
2
2
1
0
1
0
0
0
0
0
0
1
2
1
1
2
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
1
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
2
1
0
1
0
1
0
0
0
0
0
2
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
1
1
2
0
2
1
1
0
1
0
0
0
3
0
0
0
0
4
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
2
1
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
2
1
2
0
0
0
0
1
1
0
0
1
1
0
0
0
2
0
0
0
3
0
0
0
2
0
2
2
5
0
0
1
1
0
2
0
0
2
0
2
0
0
2
1
2
0
0
0
2
0
2
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
4
2
3
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
1
2
0
0
2
0
2
0
0
1
0
1
0
0
0
2
0
0
1
1
0
1
0
0
1
0
2
1
2
1
0
0
0
1
0
0
6
0
0
2
0
0
4
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
2
0
1
2
0
0
2
2
0
1
2
0
0
0
1
1
1
0
1
0
1
2
2
0
0
0
2
0
2
2
1
1
1
0
0
0
0
2
0
0
0
1
2
0
4
1
0
0
2
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
2
0
0
0
0
0
2
0
0
0
0
1
2
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
2
3
0
0
0
0
0
0
13
2
2
0
0
0
1
2
0
0
1
1
0
0
2
0
2
2
0
0
1
0
0
0
0
0
0
0
5
3
1
0
2
0
0
0
0
0
1
0
4
0
4
0
1
0
0
1
1
2
0
0
0
0
4
2
2
0
0
0
2
0
2
1
2
2
1
0
0
2
1
2
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
4
0
0
2
0
1
0
0
0
0
1
0
0
4
0
0
0
0
0
0
2
2
2
0
1
2
0
2
0
1
2
0
0
1
0
0
3
0
2
0
0
0
1
0
0
0
0
1
0
2
0
0
1
0
0
0
2
0
1
0
2
0
0
0
2
1
0
1
0
0
2
0
0
0
0
0
0
0
1
0
4
0
1
0
0
0
1
1
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
2
0
2
1
2
0
0
0
0
2
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
2
3
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
2
2
0
0
1
0
0
0
0
0
0
0
2
0
0
2
1
1
0
1
2
0
0
0
2
0
2
0
0
0
1
3
1
0
0
1
2
0
0
0
0
1
1
1
0
0
0
0
1
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
1
0
2
0
1
1
0
2
0
3
0
0
2
0
0
0
0
2
2
0
0
1
1
0
0
0
0
1
0
0
2
0
0
0
0
3
0
0
0
0
1
1
0
1
0
2
0
2
2
0
0
0
1
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
2
1
0
1
0
0
1
1
0
0
0
2
0
1
0
0
0
0
2
0
2
1
0
0
2
2
2
0
0
0
2
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
2
1
1
0
0
0
2
0
0
0
1
0
0
0
2
1
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
1
4
0
0
1
0
0
0
1
1
0
2
2
0
0
0
2
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
1
1
3
0
0
1
0
0
1
0
1
1
1
0
2
2
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
2
1
4
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
2
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
0
1
2
0
0
2
0
0
2
0
0
1
1
0
1
0
0
2
0
0
0
2
0
0
0
2
0
2
1
0
0
0
2
0
0
0
0
0
0
1
0
2
1
2
2
0
1
3
0
1
0
2
0
0
0
0
2
2
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
3
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
4
2
0
1
1
2
1
1
0
0
0
0
0
4
1
0
2
0
0
2
2
0
0
0
0
0
0
2
0
1
0
0
2
3
0
0
0
0
1
0
2
2
0
0
0
0
0
1
0
0
0
0
1
2
0
1
1
0
0
0
1
2
1
0
1
2
1
1
0
1
0
0
0
2
2
0
0
0
0
0
0
1
3
0
2
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
1
3
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
1
2
0
1
1
0
0
1
0
0
0
0
2
0
0
0
1
2
1
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
1
0
0
0
2
0
0
0
2
1
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
1
3
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
1
1
1
0
0
2
1
2
2
0
2
0
0
0
0
1
0
0
0
4
2
0
0
0
0
0
2
0
1
2
1
0
2
0
0
2
3
0
0
0
0
0
1
0
0
1
0
3
0
0
0
1
0
0
2
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
2
0
1
1
2
0
0
0
0
1
0
0
2
0
2
0
0
1
2
0
2
10
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
1
2
0
1
0
0
0
0
0
1
0
0
2
1
0
0
0
1
2
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
4
0
0
0
1
0
1
0
0
1
1
1
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
1
2
0
0
0
0
1
0
0
0
0
1
2
2
0
1
0
1
0
0
2
2
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
1
1
0
0
2
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
1
2
0
0
2
0
3
0
1
1
0
0
1
0
1
2
1
4
0
0
2
2
0
0
0
0
0
1
0
0
1
2
1
0
2
0
0
0
0
0
0
0
0
2
0
2
0
2
0
1
0
0
1
1
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
2
2
1
1
0
4
4
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
2
1
0
1
0
1
0
0
0
0
1
0
0
2
0
0
2
0
0
0
1
0
1
0
0
0
2
0
0
1
0
1
0
0
1
0
0
0
0
4
0
0
0
2
0
1
2
2
0
0
2
1
0
1
1
1
0
1
0
1
0
2
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
2
0
0
1
0
2
2
0
0
0
0
0
0
0
3
1
0
0
1
0
0
0
0
0
1
2
0
0
2
3
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
2
0
2
1
1
2
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
2
1
0
3
0
0
0
0
0
2
0
0
2
0
4
1
0
1
2
0
0
1
0
0
2
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
4
5
1
0
0
2
0
2
1
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
2
1
0
0
0
0
0
2
2
0
2
1
0
0
8
0
1
0
0
1
0
2
0
0
1
0
0
0
0
1
0
0
0
2
2
0
0
2
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
2
2
0
2
0
0
1
2
0
0
0
2
0
2
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
2
1
0
0
1
0
1
0
0
0
2
1
1
1
0
0
2
0
2
1
1
0
0
1
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
1
0
0
1
0
0
0
2
2
1
0
0
0
0
0
2
3
3
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
2
2
2
0
0
2
2
0
1
0
0
0
0
0
0
3
0
1
0
0
0
1
2
1
0
4
1
0
0
0
2
0
2
1
1
0
0
0
2
0
1
0
0
2
1
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
2
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
3
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
5
2
0
0
0
0
0
0
0
2
0
2
1
2
0
0
0
2
2
0
1
0
0
0
1
0
2
0
1
1
2
1
2
0
0
0
1
0
2
2
0
0
0
0
0
0
4
1
0
0
0
2
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
2
4
0
2
0
0
0
2
0
2
0
0
0
2
0
0
0
1
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
3
2
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
3
3
0
0
0
0
0
3
1
1
0
2
0
2
0
0
2
0
0
2
1
1
0
0
1
2
0
0
0
0
1
2
0
1
2
0
1
1
2
1
0
0
2
0
0
0
2
0
0
0
1
0
2
2
0
0
2
0
0
1
2
0
0
0
2
0
2
0
0
1
1
2
0
0
2
0
2
0
0
1
1
0
0
0
0
1
0
0
0
0
0
2
0
1
0
2
0
0
0
1
2
1
0
0
1
0
2
2
0
1
0
0
0
1
1
0
0
2
2
1
0
0
0
0
0
2
3
0
1
0
0
1
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
2
2
2
3
0
0
1
0
0
0
0
0
0
0
0
2
1
2
0
0
2
1
0
0
1
2
2
0
0
2
0
0
0
2
0
1
0
2
1
2
0
0
0
0
0
1
0
1
0
0
2
0
2
2
0
2
0
2
2
0
0
1
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
3
0
0
0
1
2
1
2
0
1
2
0
0
0
1
0
1
1
0
0
2
0
3
0
0
1
0
0
1
0
0
0
2
3
2
0
0
3
0
2
0
0
2
0
0
1
1
1
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
3
0
1
0
1
0
1
0
2
0
0
1
1
1
2
0
0
0
0
0
1
0
0
0
2
0
2
0
2
2
1
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
1
0
0
1
0
0
1
1
2
2
0
0
0
1
0
0
0
0
1
1
0
1
1
0
0
2
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
1
0
2
1
0
0
1
1
0
0
0
0
1
1
2
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
2
0
0
1
0
3
0
0
3
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
1
0
0
2
0
2
2
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
1
0
1
2
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
1
2
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
2
2
0
2
0
1
0
1
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
2
1
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
1
0
0
0
0
0
1
2
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
2
2
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
3
2
0
1
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
1
2
2
0
0
0
2
1
1
0
0
0
0
1
2
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
2
0
0
0
0
0
0
0
2
1
0
1
2
0
0
0
2
1
0
0
0
0
2
0
1
0
0
1
2
0
0
1
0
0
0
0
0
2
0
0
2
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
1
2
0
1
0
0
0
0
2
0
0
1
0
2
1
0
1
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
2
0
0
1
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
1
0
1
2
0
3
0
0
0
1
1
0
0
3
0
0
1
0
0
2
0
0
0
2
0
0
0
3
0
2
0
0
0
0
0
1
3
1
1
1
0
2
1
0
4
0
0
0
0
0
6
0
0
0
1
0
0
1
0
0
0
0
2
2
0
2
0
0
1
1
1
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
2
1
0
2
0
1
0
0
1
2
1
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
2
0
0
0
0
0
0
2
2
2
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
2
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
1
0
0
0
2
1
0
0
0
0
1
0
1
0
0
0
0
2
1
2
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
1
2
0
2
0
0
0
0
0
1
0
0
0
2
0
2
0
2
0
0
0
2
0
0
0
1
0
3
0
3
0
2
2
0
0
0
2
2
1
0
0
1
2
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
4
2
0
0
2
0
0
0
0
1
2
0
0
2
0
2
0
0
0
0
0
0
0
4
0
0
0
0
1
0
2
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
2
0
7
1
1
0
2
0
2
2
1
0
0
0
1
0
0
0
0
2
0
2
1
3
2
0
0
0
0
0
1
0
0
0
0
2
0
1
1
2
0
0
0
0
3
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
2
0
0
0
1
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
4
1
0
0
1
0
0
0
0
0
2
0
1
0
0
1
1
0
0
0
0
0
2
2
1
0
0
0
0
0
0
1
0
1
0
2
2
1
2
2
0
2
0
1
0
0
1
2
0
2
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
1
0
3
0
0
3
0
0
1
0
0
2
0
0
1
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
3
0
2
1
1
2
0
2
0
2
2
2
0
0
0
2
2
2
1
0
0
0
6
0
0
0
4
0
0
2
0
1
0
1
0
0
0
2
0
0
2
0
0
2
1
1
0
0
0
0
0
1
0
1
0
0
4
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
2
0
2
0
1
0
0
0
0
0
0
0
0
1
0
3
0
0
0
1
0
3
0
0
1
0
1
1
0
0
0
1
2
2
3
0
1
0
3
1
0
0
1
0
2
0
0
2
0
0
1
2
0
0
2
2
0
0
2
0
1
0
0
0
0
0
0
0
2
1
1
2
0
1
1
0
0
0
1
2
1
2
0
0
0
0
0
1
1
0
0
0
2
0
2
0
0
0
1
0
0
0
1
1
2
0
2
2
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
3
2
0
2
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
2
0
1
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
5
0
0
0
0
2
0
0
1
2
0
0
2
0
2
1
0
2
0
1
0
0
0
0
3
1
1
0
0
0
2
1
0
0
0
0
1
2
2
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
3
1
0
5
0
1
1
2
0
0
2
1
2
0
1
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
3
0
0
0
0
1
1
0
0
2
0
0
1
0
1
0
1
0
2
0
0
1
0
0
0
0
0
0
2
0
2
0
2
0
1
0
0
3
0
2
0
1
2
0
0
0
0
0
0
0
1
0
2
0
2
4
0
5
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
2
2
0
0
0
2
0
0
2
0
0
2
2
0
2
0
1
0
1
0
0
2
0
0
1
1
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
1
0
0
0
3
2
0
1
1
0
0
0
0
2
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
2
0
1
0
2
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
3
0
0
0
1
2
0
0
0
2
0
1
1
0
2
0
0
2
0
2
1
0
0
0
0
0
0
2
1
1
0
1
0
0
3
0
0
1
0
0
1
2
0
0
0
0
0
1
0
0
0
2
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
1
2
0
0
0
2
6
0
1
0
0
2
0
0
1
2
0
1
0
2
0
1
0
2
0
0
2
0
0
0
2
0
2
0
0
1
1
0
1
2
2
0
0
0
0
0
0
0
3
2
0
0
2
0
0
0
2
0
1
2
0
0
0
1
1
1
2
0
0
1
1
0
0
2
0
0
2
1
0
2
0
0
0
2
0
1
1
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
1
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
1
0
2
0
0
2
0
0
1
1
0
2
0
0
0
0
1
2
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
1
2
0
0
0
0
1
1
0
0
0
1
0
2
0
2
0
2
0
0
0
0
1
0
0
0
0
0
1
0
4
0
0
2
0
0
2
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
1
1
2
0
0
1
0
2
0
1
2
0
1
0
0
0
1
2
1
2
0
0
3
0
4
0
0
1
1
2
0
0
0
0
2
1
0
2
1
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
1
1
1
0
0
0
2
1
0
2
0
0
0
3
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
5
0
0
0
0
0
2
0
2
0
0
2
1
0
0
0
0
0
1
0
3
2
0
0
0
2
0
0
0
0
0
1
1
0
0
1
1
3
2
0
1
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
2
2
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
1
2
2
0
0
0
1
0
2
2
2
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
2
1
0
2
2
1
0
0
3
0
1
2
0
0
2
0
0
0
0
0
2
1
1
0
2
1
2
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
1
0
0
1
0
1
2
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
3
1
2
1
0
1
1
0
0
2
0
2
0
2
1
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
1
2
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
2
0
2
0
1
0
1
1
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
2
2
4
1
0
1
0
0
0
0
4
0
0
1
0
1
0
2
0
0
0
2
0
0
0
1
0
0
1
0
0
0
1
1
2
0
0
0
0
0
0
2
1
0
0
0
1
3
0
2
2
2
0
2
1
0
0
0
0
0
0
2
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
2
2
0
1
2
0
1
2
0
0
1
2
0
0
2
2
0
0
2
2
1
1
2
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
1
2
0
0
1
0
1
1
0
1
3
0
2
0
1
0
0
0
0
2
2
0
1
2
0
2
0
0
0
1
0
0
2
0
2
0
0
0
0
1
2
0
0
0
0
0
0
1
2
0
0
0
1
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
2
1
0
2
0
0
0
2
2
0
0
0
2
0
0
2
4
0
0
0
2
0
1
0
0
0
0
2
0
0
2
0
0
3
2
0
0
0
0
2
4
1
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
2
0
2
2
2
0
0
0
2
0
0
2
2
2
1
3
0
0
0
0
0
1
0
1
0
3
2
0
0
2
0
0
1
1
2
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
3
0
0
2
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
1
1
0
2
0
0
0
1
1
0
1
5
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
2
0
1
1
0
2
0
0
2
0
0
1
1
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
2
0
0
2
0
1
0
0
1
0
0
1
2
1
1
2
0
0
0
0
1
0
0
1
3
0
0
1
0
0
0
2
2
0
1
0
1
0
0
0
0
0
1
2
0
0
1
0
0
0
0
1
1
0
0
0
1
1
0
0
1
2
0
0
3
0
0
0
0
0
0
0
0
0
1
2
1
1
0
0
0
0
0
0
0
1
2
2
0
1
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
2
0
1
2
0
0
0
0
0
2
2
0
1
0
0
1
0
0
0
0
4
0
1
0
1
0
2
0
0
0
1
1
0
1
2
2
1
0
0
3
1
3
1
0
0
0
0
2
2
0
0
0
0
0
2
0
1
1
0
1
0
0
2
0
0
0
0
0
0
2
0
2
0
1
0
0
2
0
0
0
0
0
0
2
1
0
0
2
1
0
1
1
0
0
0
2
3
0
0
0
1
2
1
2
0
0
1
3
0
0
0
0
1
0
2
0
0
1
0
0
0
3
0
1
0
0
1
1
2
1
2
0
2
2
0
1
0
0
0
0
1
0
2
2
0
1
2
0
0
0
2
1
0
0
3
2
2
2
0
0
0
1
2
3
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
2
0
1
3
2
0
0
1
1
0
0
2
0
2
0
1
0
1
1
0
2
1
2
0
2
0
0
0
0
1
0
2
0
0
0
0
2
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
1
2
0
0
1
2
1
2
1
0
0
0
0
0
0
1
0
0
0
2
0
1
2
0
0
0
0
0
0
1
0
6
1
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
1
0
2
3
0
0
0
0
0
0
1
0
2
0
1
2
2
1
0
2
0
0
0
2
2
0
3
1
1
0
2
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
1
0
0
0
0
0
3
0
1
0
0
0
1
0
1
0
0
0
0
2
2
0
0
3
0
1
0
1
0
0
1
1
0
0
0
2
0
0
1
0
0
0
1
0
0
3
0
0
4
0
1
1
0
1
0
1
0
2
2
2
0
0
0
1
0
2
1
0
0
2
1
0
1
1
0
0
0
0
2
0
1
0
0
0
1
1
2
0
0
2
0
3
0
1
0
0
0
0
0
0
0
2
0
1
0
1
0
1
2
0
0
2
0
2
0
0
1
0
0
0
2
2
0
1
0
1
0
1
2
1
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
1
1
0
1
1
0
1
0
0
0
3
0
0
0
1
0
0
0
0
0
1
2
2
0
1
0
2
3
0
0
1
0
1
0
1
0
1
2
0
0
0
0
1
2
0
0
0
1
0
0
0
4
0
0
1
0
0
0
2
0
0
0
1
2
2
0
0
0
1
2
1
0
2
1
0
0
0
1
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
2
0
1
2
0
0
0
0
2
2
2
0
0
0
1
0
0
0
0
0
1
0
2
2
0
0
0
0
2
0
0
0
1
1
0
0
0
1
2
1
2
1
0
0
0
0
2
1
0
1
0
0
0
0
2
1
2
0
0
0
0
0
0
1
2
1
2
2
0
2
0
0
0
0
0
0
2
0
0
1
1
0
2
1
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
2
1
0
0
1
0
0
0
0
1
0
0
0
1
2
0
0
3
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
2
2
0
2
2
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
1
1
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
1
0
4
2
2
0
0
1
0
1
0
0
2
0
1
2
0
1
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
2
1
2
1
0
2
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
1
1
0
0
0
0
1
0
0
1
0
1
0
2
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
3
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
1
2
3
1
0
2
2
0
0
0
0
0
1
0
0
1
4
1
0
0
2
2
2
2
0
0
0
1
0
0
2
0
0
2
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
2
2
0
0
0
0
0
0
1
0
0
2
0
2
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
2
0
1
0
0
0
0
2
2
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
2
0
0
1
0
0
0
0
0
7
0
0
0
0
0
0
0
0
1
0
0
0
3
1
0
0
0
1
0
2
0
0
0
2
0
0
1
0
0
0
0
1
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
2
2
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
1
1
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
1
2
2
0
4
1
1
0
0
0
2
2
0
0
0
0
0
1
2
0
2
2
0
1
0
0
2
0
0
2
0
2
0
0
1
0
1
0
0
1
1
0
0
0
2
1
1
0
0
0
2
1
0
1
0
1
2
9
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
2
2
2
1
0
4
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
3
0
1
0
0
1
2
1
0
0
2
0
1
0
2
1
0
0
0
0
2
1
0
0
1
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
5
0
0
0
0
0
1
1
0
1
0
0
2
0
0
2
1
0
0
1
0
1
0
0
1
0
2
0
0
0
2
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
2
0
0
0
1
0
3
2
0
1
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
2
0
1
0
0
0
0
1
2
0
2
0
0
0
1
0
0
2
2
1
0
0
0
0
2
0
1
0
0
2
0
2
1
1
0
0
0
2
2
0
1
2
0
1
0
2
2
0
0
0
0
0
0
0
0
2
2
0
0
2
2
0
0
0
0
2
0
0
0
0
1
2
1
0
0
0
0
0
0
1
0
2
1
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
1
2
0
0
2
2
0
0
3
0
0
1
0
0
0
1
0
0
0
0
2
0
0
1
1
0
2
2
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
1
0
2
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
2
0
0
0
1
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
2
0
0
1
0
1
2
0
0
0
1
1
1
0
1
1
0
1
0
0
1
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
1
2
1
0
0
1
1
0
0
0
0
0
0
0
2
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
4
2
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
3
0
1
0
2
4
1
0
0
0
2
2
1
0
1
0
0
0
0
2
0
2
0
0
0
1
0
2
0
0
1
0
1
0
0
0
2
6
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
2
1
0
3
0
2
0
0
0
1
1
2
1
0
2
0
0
0
1
0
0
0
0
0
0
2
1
0
1
0
2
2
0
1
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
1
1
0
0
0
0
1
1
0
0
2
1
1
0
0
0
1
3
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
1
1
1
2
3
0
1
0
0
0
0
0
0
0
2
0
0
4
5
1
0
0
0
2
0
0
2
0
0
0
0
3
0
0
0
0
5
0
0
1
0
0
1
0
0
0
0
3
1
0
0
1
0
2
0
1
2
0
1
0
1
0
0
1
0
0
0
0
2
3
1
2
2
0
0
0
0
0
1
2
2
0
1
2
0
2
2
0
0
0
0
1
3
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
2
1
2
1
0
2
0
0
1
0
0
0
0
0
2
3
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
1
1
0
0
0
0
2
0
1
2
2
0
0
0
0
0
2
0
4
0
0
0
0
1
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
1
1
0
0
1
2
1
2
2
2
0
2
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
1
2
2
0
0
0
0
0
1
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
2
2
1
0
1
0
2
0
0
0
0
0
0
0
0
1
0
1
1
1
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
1
0
2
0
0
2
0
5
1
0
2
0
2
0
0
0
0
0
1
0
3
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
2
0
0
1
0
2
0
1
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
2
2
0
0
0
1
0
1
2
0
1
0
2
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
2
0
0
2
1
0
0
1
0
0
0
1
0
0
3
1
2
3
0
0
0
0
0
0
0
1
2
2
0
2
0
0
1
2
0
1
1
1
1
0
1
0
0
0
0
0
2
0
4
0
0
0
1
0
0
0
0
1
1
0
0
0
2
0
1
0
0
2
0
1
0
0
0
1
0
0
0
1
2
0
0
0
0
2
0
0
0
2
1
4
0
2
1
2
0
2
0
0
3
0
0
0
0
0
1
2
0
1
0
0
0
0
1
1
1
0
6
1
2
1
0
2
0
0
0
0
3
1
0
0
1
0
0
0
2
1
0
0
1
1
0
0
2
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
2
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
1
0
1
0
0
0
1
2
0
0
0
2
2
0
0
0
1
0
0
0
2
1
2
0
0
0
0
4
0
0
0
3
0
0
0
1
1
1
1
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
2
0
0
0
2
0
0
1
2
0
0
0
0
0
2
0
1
0
0
1
0
0
0
2
0
0
0
2
0
0
4
0
0
1
0
1
1
2
2
1
0
0
1
0
1
0
1
0
0
0
0
1
2
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
1
0
0
2
2
1
0
1
0
0
0
0
0
2
0
0
2
0
1
1
0
0
1
1
2
0
0
0
5
0
0
0
0
0
0
0
2
0
0
0
2
2
1
1
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
2
0
1
1
0
0
1
1
0
3
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
2
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
2
1
0
2
0
2
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
4
1
4
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
3
1
0
0
0
1
0
2
0
0
0
0
0
2
0
0
2
0
2
2
0
1
2
2
0
1
1
2
0
0
2
1
1
0
0
1
2
1
1
0
0
0
3
0
0
3
0
0
1
0
0
1
0
0
0
0
0
1
3
0
0
0
0
0
0
1
3
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
3
0
0
1
0
1
0
2
0
0
0
0
2
2
1
0
0
1
0
0
0
0
0
1
2
1
1
0
2
2
0
0
0
1
2
2
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
2
0
2
2
0
0
0
1
1
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
1
2
0
1
1
0
0
1
1
1
0
0
1
0
2
0
1
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
3
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
2
0
0
1
2
0
0
1
2
0
2
0
0
1
0
0
1
0
0
1
0
0
1
2
1
0
0
0
0
0
2
0
2
0
0
1
0
0
1
0
0
0
0
3
0
0
0
2
0
0
2
0
0
1
2
0
0
0
0
2
0
0
0
0
1
2
2
2
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
2
4
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
2
0
0
2
0
0
0
2
1
0
2
1
0
2
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
1
0
0
2
2
0
0
0
2
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
2
1
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
3
2
1
0
0
1
1
0
2
1
0
0
1
0
0
2
0
4
0
1
0
0
0
0
6
0
0
1
0
1
0
0
0
2
0
1
0
1
0
8
2
3
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
2
1
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
2
0
0
1
0
0
3
0
2
0
1
0
0
0
0
0
1
1
7
0
3
0
2
0
1
0
0
0
2
2
0
2
0
1
1
0
0
2
0
0
0
0
5
0
3
0
0
0
1
0
0
1
1
1
0
1
2
0
1
0
1
0
0
1
0
0
0
0
0
0
1
1
0
2
2
0
0
1
0
0
0
0
3
0
0
0
0
0
1
0
1
0
0
0
2
0
0
1
0
4
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
2
2
0
0
1
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
1
0
2
0
0
1
0
1
1
1
0
0
0
0
2
1
0
0
0
1
1
0
0
0
0
1
1
1
2
0
1
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
1
1
0
1
2
2
2
2
1
2
2
0
0
1
5
0
0
2
3
0
0
0
2
1
0
0
0
0
2
0
0
0
1
0
0
0
1
2
0
0
2
0
0
0
0
0
2
0
0
2
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
1
0
2
2
0
1
0
0
3
0
0
1
5
0
0
0
0
1
0
1
1
2
0
0
0
0
2
2
0
0
0
2
0
1
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
2
0
2
2
0
2
2
0
1
2
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
1
0
1
2
0
1
0
0
2
3
0
0
1
1
0
0
0
1
0
2
2
0
2
0
1
0
2
0
0
2
1
0
1
1
2
1
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
2
1
0
2
0
0
0
0
1
0
0
2
4
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
2
0
2
0
1
1
1
0
0
2
0
4
0
1
0
0
0
0
0
1
0
0
0
3
0
0
2
0
0
0
0
0
2
1
2
0
2
0
2
0
0
0
0
0
1
0
0
0
2
2
1
2
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
2
0
2
0
1
2
0
0
1
1
1
0
0
0
2
0
1
0
0
1
0
0
0
0
0
1
1
2
0
1
1
0
1
0
0
0
1
0
0
1
1
0
2
1
0
1
0
0
0
0
0
0
0
0
0
2
1
0
2
0
1
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
2
0
0
0
2
2
0
2
1
1
0
0
0
0
1
2
0
1
0
2
1
0
2
1
0
0
2
0
1
0
0
1
1
0
0
2
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
1
0
0
0
0
3
0
0
0
0
0
1
2
0
2
1
0
0
0
0
0
0
1
2
1
3
2
0
0
1
0
1
0
2
2
1
2
1
0
1
0
2
0
1
0
1
2
0
1
2
0
0
0
1
2
0
0
2
0
0
1
1
0
0
2
0
0
1
2
0
0
1
0
0
0
0
0
1
1
0
0
0
1
1
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
3
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
3
4
0
1
0
0
2
0
2
0
0
1
0
0
1
2
0
0
0
0
0
3
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
3
1
0
0
0
0
0
2
0
1
0
0
0
3
0
2
0
0
1
0
1
1
0
0
0
0
3
0
1
0
0
2
0
3
0
2
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
1
1
12
3
0
0
2
3
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
2
2
0
2
0
1
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
2
0
1
1
2
2
1
0
2
1
3
0
2
2
1
0
2
1
0
0
0
0
0
0
0
1
2
0
0
2
0
3
1
0
0
2
1
0
0
2
0
2
0
2
1
0
0
3
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
2
0
0
0
2
2
2
0
0
0
0
0
0
2
0
2
1
0
0
0
3
0
0
1
0
1
2
1
0
0
0
0
2
0
0
2
1
0
2
0
1
0
0
0
0
1
2
1
0
0
1
2
0
0
2
1
0
1
0
0
1
0
0
0
1
0
0
0
2
0
0
0
1
0
1
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
1
2
0
0
0
1
2
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
4
0
1
0
0
0
2
1
0
1
6
0
0
0
0
0
0
0
1
1
0
0
2
0
1
0
1
1
0
0
3
0
1
0
1
2
0
0
0
2
0
0
2
0
1
0
2
0
0
0
0
1
0
1
0
1
0
0
2
0
2
0
1
0
1
0
1
2
0
3
2
0
0
0
2
0
0
2
0
0
2
0
1
2
0
1
2
0
0
2
1
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
1
0
0
0
2
0
0
1
0
0
2
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
1
2
0
1
1
2
0
2
2
1
0
0
0
2
1
1
1
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
2
0
1
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
2
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
2
1
2
0
0
0
0
0
0
0
3
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
1
0
1
0
1
3
0
0
0
1
0
0
0
1
0
0
1
0
2
0
0
0
4
2
1
0
2
0
0
0
1
0
0
0
2
0
3
0
0
2
2
0
0
0
2
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
1
0
0
1
0
3
0
0
0
1
0
2
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
1
0
0
2
3
1
1
0
2
2
3
2
0
0
0
3
2
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
2
1
1
1
0
0
0
0
0
1
0
0
0
0
2
2
1
3
0
1
0
0
0
1
0
2
2
2
0
0
0
1
2
0
0
3
0
0
0
0
0
0
3
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
1
0
2
7
0
0
0
2
2
0
1
0
1
0
3
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
1
2
1
2
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
2
0
2
2
0
0
2
2
0
0
1
0
0
0
0
1
1
0
1
0
0
1
0
1
0
0
2
0
1
7
0
2
1
0
0
0
1
0
1
0
0
0
0
0
3
2
0
1
0
2
4
0
1
0
0
0
0
0
2
1
0
0
0
0
1
0
2
0
0
1
1
1
1
1
0
0
0
2
0
0
0
2
1
0
0
0
1
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
2
0
2
0
2
0
0
1
0
0
0
0
2
1
2
0
0
0
0
0
1
1
0
0
0
3
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
3
0
1
0
0
2
0
0
0
0
0
0
2
0
2
2
0
2
2
1
0
0
1
2
0
2
0
0
0
0
1
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
1
0
0
0
0
1
0
2
1
1
1
0
0
2
2
0
0
0
0
6
0
0
0
2
1
2
0
0
4
0
0
0
0
0
0
2
1
4
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
1
1
0
0
0
0
1
2
1
1
2
0
0
2
2
0
1
0
0
0
0
0
0
1
2
0
1
2
0
0
0
2
0
0
0
0
0
2
1
0
0
0
2
1
0
0
0
0
2
2
1
0
0
0
2
2
0
1
0
1
0
0
0
2
0
2
7
0
1
2
0
0
0
0
0
0
0
2
2
1
0
0
0
0
1
2
0
0
1
0
0
1
1
0
2
2
0
0
0
0
3
0
0
0
1
0
2
0
2
0
0
1
2
2
2
0
0
0
1
1
1
0
0
0
0
4
1
2
0
0
0
0
0
3
0
1
0
2
2
0
0
2
2
0
0
0
2
0
2
0
2
0
0
1
0
0
0
0
0
0
2
0
0
1
2
0
0
2
2
1
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
1
0
2
1
2
3
0
0
0
0
2
0
1
0
2
0
2
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
1
0
2
0
1
2
2
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
3
1
0
6
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
1
0
0
2
0
0
0
0
0
4
0
2
0
4
2
0
0
0
0
2
2
0
3
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
2
0
2
0
2
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
5
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
2
2
2
0
0
0
0
1
2
0
0
1
0
0
0
0
1
0
2
0
0
2
1
0
0
0
1
0
1
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
1
0
0
1
3
1
0
0
1
0
0
0
2
0
2
0
1
2
2
0
0
0
2
2
0
0
1
1
0
0
0
0
0
0
0
1
2
0
2
2
0
0
0
0
0
0
0
1
1
1
0
1
0
0
2
2
0
0
0
2
0
0
1
0
1
2
0
0
0
0
1
0
2
0
0
0
1
0
1
0
0
0
2
1
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
1
0
0
0
3
0
2
0
0
0
0
0
0
0
1
5
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
1
0
0
2
0
1
1
0
0
1
0
2
2
1
0
0
0
0
0
1
0
0
3
1
1
0
1
0
0
2
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
1
0
2
2
0
0
0
2
0
0
0
2
0
1
0
0
0
3
0
0
1
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
2
0
1
0
0
1
0
1
0
1
2
0
1
4
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
1
0
0
2
1
2
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
1
0
0
0
0
2
0
1
0
2
1
0
0
0
0
0
0
1
0
2
1
0
3
3
0
1
3
2
0
2
0
0
0
2
1
0
0
1
2
1
0
0
0
2
0
0
0
1
0
2
0
0
0
0
1
2
0
0
0
0
0
0
1
2
2
1
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
2
2
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
1
0
1
2
0
0
0
0
0
1
1
0
3
2
0
0
1
2
0
0
1
0
0
3
0
2
1
0
2
1
0
0
2
0
2
0
0
1
0
0
0
2
1
0
1
2
0
1
0
0
3
0
0
0
0
0
2
1
2
0
0
2
0
1
1
0
0
2
0
1
0
0
0
0
2
0
0
4
0
0
0
0
0
0
4
0
1
1
2
2
1
2
0
0
2
1
2
0
2
0
0
2
0
1
0
0
0
0
2
1
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
2
2
0
2
2
3
0
0
0
0
0
0
2
0
1
0
0
0
2
2
0
0
2
0
0
0
0
2
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
1
0
2
0
0
1
0
0
0
0
0
1
2
0
0
0
1
0
2
2
0
0
2
0
0
0
0
1
0
2
1
0
0
0
1
0
0
0
2
2
0
0
1
0
2
0
1
1
0
0
0
0
2
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
2
2
1
0
2
0
0
0
2
0
2
0
3
0
0
1
2
0
0
2
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
4
0
0
0
2
0
0
2
0
0
1
1
0
0
0
0
2
1
1
0
0
0
0
0
2
1
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
2
0
1
1
0
0
0
1
0
2
2
0
0
0
1
0
0
0
0
0
1
0
0
0
3
2
1
0
1
0
1
0
1
0
2
0
0
1
1
0
0
1
0
0
1
1
0
0
1
4
1
2
0
1
0
1
2
1
0
1
0
2
2
0
0
0
0
0
1
2
2
1
0
1
0
1
1
2
2
0
0
1
0
0
0
2
0
0
0
2
0
1
0
1
1
0
0
2
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
2
3
0
0
0
0
1
0
2
1
2
0
2
2
3
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
2
1
1
1
0
0
0
0
1
1
4
0
1
0
0
0
0
1
1
0
0
1
0
2
0
0
2
0
1
2
1
1
2
0
1
0
0
1
0
1
0
0
0
0
0
2
1
0
1
4
0
1
0
0
0
2
2
1
0
0
0
0
1
2
1
0
0
0
2
0
0
1
1
0
1
2
0
2
2
1
3
3
0
0
0
0
0
0
1
0
0
0
0
0
2
2
1
0
0
0
1
0
0
1
1
1
0
0
0
0
1
1
0
1
0
0
0
0
2
1
0
0
0
0
1
1
0
0
2
2
0
0
0
2
0
2
0
0
0
2
2
0
0
2
0
2
0
1
1
2
0
0
1
2
0
1
2
0
1
0
1
2
0
0
2
1
0
2
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
2
0
2
0
2
0
1
0
1
0
1
1
0
0
0
0
0
2
0
0
1
0
1
0
0
2
1
2
0
4
0
1
0
1
0
0
2
0
0
0
2
0
1
0
0
1
1
0
0
1
2
3
2
1
1
2
2
2
3
1
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
2
2
1
1
0
0
0
2
0
1
1
0
4
1
0
1
0
1
0
2
0
0
0
0
1
0
2
2
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
2
0
1
0
0
1
1
2
0
0
2
2
0
0
0
0
0
2
0
4
0
2
3
0
1
0
0
1
0
0
1
2
0
4
0
1
2
2
0
0
0
0
2
2
0
1
0
2
1
0
0
1
1
0
0
0
2
0
0
0
0
3
1
0
2
0
0
1
2
0
2
0
0
1
0
0
0
0
0
2
1
2
2
0
2
1
0
0
2
0
0
0
0
0
2
0
0
2
2
0
0
0
2
0
1
0
1
0
1
0
1
0
2
0
0
1
0
0
0
0
1
2
0
1
0
0
0
1
2
0
2
1
0
1
2
4
0
1
1
0
2
0
1
0
0
2
2
0
0
0
0
1
0
0
1
1
1
1
2
0
2
0
2
1
0
0
0
1
0
0
0
0
2
2
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
2
0
0
0
0
0
1
2
2
0
2
0
0
0
3
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
5
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
1
1
0
1
2
3
0
4
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
1
2
0
2
0
0
0
0
0
2
0
2
1
0
0
2
0
1
0
1
0
1
0
2
0
0
0
1
0
2
1
0
2
1
0
2
0
2
0
1
1
2
0
0
0
0
0
0
0
0
0
2
1
0
0
2
2
0
0
0
0
0
2
0
2
0
0
2
0
2
0
0
0
2
2
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
1
0
1
0
2
2
2
1
0
0
0
1
1
0
0
0
1
2
0
2
2
1
0
0
0
0
2
1
1
1
0
1
0
0
2
0
0
2
0
0
0
0
0
3
0
0
0
1
0
0
0
0
2
2
1
0
1
0
0
0
0
0
0
1
0
2
0
4
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
3
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
8
0
0
1
0
1
1
0
0
2
0
1
1
2
0
0
0
2
0
0
0
0
0
2
0
1
1
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
1
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
1
0
0
0
1
1
2
0
1
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
1
0
2
2
0
0
0
1
0
0
2
4
2
0
2
0
0
0
0
4
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
2
2
1
1
0
0
1
0
0
0
1
0
0
2
0
1
0
0
0
0
1
1
0
2
0
2
0
1
2
1
2
0
2
2
2
1
0
0
1
2
2
2
2
2
0
0
0
2
0
2
0
0
0
0
0
3
1
0
0
0
0
0
2
0
0
0
2
2
0
0
2
2
0
0
0
0
2
0
2
0
0
2
1
1
0
0
1
3
2
2
0
0
0
0
0
2
3
0
1
0
0
2
0
0
0
0
0
0
0
0
2
2
1
0
2
0
0
0
0
0
0
0
2
1
2
0
0
0
2
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
2
2
2
0
1
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
1
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
1
0
2
0
0
0
0
0
0
1
0
1
0
2
1
2
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
1
0
1
0
2
2
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
2
2
2
0
2
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
4
1
0
2
0
1
0
2
0
0
0
2
2
2
2
2
1
0
0
0
1
0
1
1
0
2
0
1
3
0
1
0
1
0
0
0
2
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
3
0
0
0
2
1
1
0
0
0
0
2
0
0
0
2
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
2
0
1
0
4
1
0
0
0
1
0
0
1
0
2
0
0
0
0
1
0
0
3
0
0
0
0
1
3
0
0
0
1
0
0
1
0
2
1
2
0
2
0
0
2
0
2
0
0
0
1
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
2
0
0
2
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
1
0
2
1
2
0
0
0
0
2
0
0
1
0
0
0
0
2
1
0
0
0
0
0
2
0
1
0
2
1
0
0
1
2
0
0
0
0
1
1
0
1
0
0
0
2
2
1
0
1
2
1
0
2
1
0
2
0
0
1
2
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
2
0
1
0
0
2
0
1
0
0
0
0
1
0
1
3
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
1
1
5
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
2
2
0
0
0
0
2
0
0
0
1
2
1
2
2
0
0
3
0
0
2
0
2
0
0
0
0
0
0
1
0
2
0
2
0
0
1
1
0
2
0
0
2
0
0
0
0
0
0
0
0
2
2
2
2
0
1
0
2
0
0
1
0
5
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
1
0
2
2
0
0
2
0
2
2
0
0
0
0
1
0
0
2
1
3
1
0
2
0
0
1
1
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
2
2
0
2
0
2
0
0
2
0
2
1
1
0
0
0
0
1
0
0
2
0
0
1
0
0
2
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
1
2
0
0
2
1
0
0
0
1
1
0
0
0
2
2
2
0
1
0
0
0
0
1
1
0
0
0
1
1
0
0
1
0
2
1
5
2
2
2
0
1
0
0
0
0
0
2
2
2
0
0
1
0
0
0
2
0
0
0
1
1
1
2
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
2
2
0
1
0
0
0
0
0
1
1
0
0
0
4
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
2
2
2
1
2
1
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
1
0
0
0
0
2
0
2
2
0
1
2
0
1
0
0
0
2
0
0
0
1
0
0
1
1
2
0
0
0
0
0
0
1
0
0
1
2
0
2
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
1
1
1
1
2
0
2
1
0
3
2
0
0
0
2
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
3
0
3
0
2
2
0
0
0
1
0
1
0
1
0
0
2
0
0
0
1
2
0
1
2
1
1
0
1
1
0
0
0
0
0
1
2
0
0
0
1
2
1
4
0
1
2
2
0
0
0
0
2
0
0
0
0
2
0
2
0
1
0
2
2
1
0
3
0
1
0
0
0
1
0
0
1
0
0
0
0
0
2
2
0
3
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
2
3
2
0
0
1
2
0
0
0
0
0
3
2
1
0
0
2
0
0
0
0
0
0
1
0
0
2
1
0
2
0
0
0
0
0
0
2
0
1
2
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
2
4
0
0
1
2
2
0
0
1
1
0
3
0
1
0
0
0
0
1
0
2
0
1
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
2
0
0
2
0
3
2
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
4
2
0
0
2
1
0
0
0
0
0
1
1
0
0
1
0
0
3
0
1
0
2
1
0
1
0
2
2
0
1
0
1
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
1
0
0
0
2
0
1
2
2
0
3
2
0
0
0
0
0
0
1
2
2
1
2
1
1
2
1
0
1
0
1
0
1
1
0
0
0
0
0
0
0
2
2
1
2
2
1
0
1
0
0
0
1
0
0
0
0
2
0
0
0
2
0
1
0
0
0
1
2
0
1
0
0
0
1
0
0
0
1
0
1
0
2
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
3
0
1
1
0
1
2
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
2
3
1
0
1
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
2
0
2
4
2
0
0
1
2
0
2
0
0
1
1
0
0
0
2
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
4
2
1
2
0
0
0
0
0
1
0
0
1
0
1
2
0
0
0
3
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
2
0
0
1
0
1
0
2
0
1
2
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
2
0
1
0
1
2
0
0
0
0
0
0
0
2
1
2
0
2
1
1
0
0
0
3
2
0
0
2
0
0
0
1
2
1
0
0
0
1
1
0
0
1
0
2
0
0
2
0
2
2
0
0
0
1
0
2
0
0
2
0
0
2
2
2
1
2
0
0
1
0
0
0
1
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
2
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
2
0
0
0
2
3
2
2
0
0
0
0
0
2
0
0
0
0
0
1
4
0
1
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
7
0
0
1
0
0
0
1
0
1
0
1
0
0
2
0
1
6
0
0
1
0
0
1
2
0
0
0
0
0
0
3
0
0
0
1
0
0
1
1
0
2
0
2
1
0
0
0
0
0
1
0
0
0
1
1
0
2
1
2
0
0
0
0
1
0
2
1
0
2
0
0
0
2
2
0
1
0
0
0
2
0
0
2
0
1
0
0
1
1
1
6
0
0
2
0
1
0
0
1
1
0
0
0
0
0
0
3
1
1
0
2
0
0
1
0
2
0
1
2
1
0
2
2
0
2
0
0
0
1
0
2
0
0
2
0
0
2
2
0
0
0
3
1
1
0
2
0
0
0
0
0
1
1
4
2
0
0
0
1
0
0
0
0
2
0
1
0
0
2
0
1
0
1
1
0
0
2
0
0
2
1
0
0
1
1
3
0
0
2
1
0
0
2
0
0
0
1
0
0
2
0
1
0
0
0
0
0
4
0
2
0
2
1
0
1
0
1
2
0
0
2
0
1
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
2
2
0
1
0
1
0
0
0
1
0
0
2
0
0
3
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
1
0
2
0
2
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
2
2
0
1
0
0
1
0
0
0
2
2
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
1
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
1
1
0
1
2
2
2
0
1
0
0
1
0
1
2
0
6
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
2
0
0
2
2
2
0
0
0
0
0
0
0
0
0
1
0
2
1
1
0
0
0
0
0
0
2
0
2
0
1
0
0
1
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
2
1
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
1
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
1
2
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
1
2
2
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
2
1
0
2
0
0
2
0
0
0
0
0
0
0
1
1
1
2
0
0
1
0
0
0
0
0
2
2
1
0
3
1
0
0
0
0
1
2
9
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
3
0
0
2
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
3
1
0
0
1
2
0
1
0
1
0
1
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
1
1
1
0
1
0
1
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
1
1
0
0
2
1
1
2
2
0
0
1
0
0
1
2
0
0
2
1
0
2
2
0
1
2
0
0
0
0
0
1
0
0
0
2
3
2
1
0
1
3
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
1
1
0
1
0
0
0
0
1
2
0
0
0
0
1
1
1
2
2
1
1
1
0
0
0
0
0
1
2
0
0
2
1
1
2
2
0
0
1
1
1
1
0
0
0
0
2
0
1
0
1
0
0
0
0
0
1
0
1
0
1
1
2
1
0
0
2
0
0
0
0
0
0
1
3
2
0
0
2
0
1
0
0
0
2
1
1
2
0
0
0
0
1
0
1
0
1
0
1
0
1
0
1
1
0
0
0
0
2
0
0
0
2
0
1
2
2
0
0
0
3
2
0
0
0
0
1
0
1
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
3
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
2
0
0
0
0
1
0
3
2
2
1
1
0
0
0
2
1
0
0
0
0
0
0
2
2
2
0
1
0
0
1
1
0
0
2
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
2
0
3
0
2
0
1
0
2
0
2
2
0
0
0
0
2
0
0
0
2
1
0
0
3
1
1
2
0
1
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
1
2
0
1
0
2
0
0
0
0
2
1
2
1
0
1
0
0
1
0
0
2
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
2
1
0
2
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
2
0
0
2
2
2
0
0
1
2
0
0
0
0
0
1
0
2
1
0
2
0
0
2
0
1
0
2
0
2
1
1
3
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
1
2
1
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
1
0
1
0
0
1
2
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
1
2
1
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
1
2
2
0
0
0
0
0
2
0
0
3
0
2
0
0
2
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
1
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
3
0
0
0
0
0
2
0
2
0
0
1
0
0
2
1
0
0
1
2
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
2
1
0
0
0
0
0
8
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
2
1
0
1
1
1
2
0
0
2
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
1
0
2
1
1
2
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
2
0
2
0
0
0
2
0
2
0
0
2
1
0
0
0
0
2
0
2
0
2
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
1
0
1
2
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
2
0
2
0
2
2
0
1
0
0
0
0
2
1
0
0
0
0
1
1
0
1
1
2
0
0
2
1
0
0
2
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
2
0
0
2
0
2
2
0
0
0
0
0
0
1
0
0
1
1
0
0
0
2
1
0
1
2
0
0
1
1
0
0
0
0
2
1
0
0
0
2
0
0
0
0
1
1
0
0
0
2
0
2
2
3
0
2
0
2
2
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
7
1
0
2
0
0
0
1
1
1
0
1
1
1
1
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
2
3
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
1
0
1
0
1
2
0
0
0
0
0
0
0
0
0
3
0
1
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
1
1
1
0
0
0
0
0
0
0
2
0
1
0
1
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
2
0
2
1
4
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
1
3
2
0
0
0
0
0
2
1
0
2
1
0
0
0
0
1
0
0
1
0
2
0
1
1
0
0
1
2
0
2
0
2
0
0
2
1
0
1
0
1
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
1
1
0
0
1
2
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
2
1
1
0
0
0
2
0
0
0
2
2
1
0
0
0
3
0
0
0
0
2
2
0
0
0
1
2
0
0
0
1
1
1
0
1
0
1
3
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
2
0
2
1
1
2
2
0
0
2
0
0
0
0
2
0
0
0
0
2
1
0
0
0
1
2
0
0
0
1
0
1
0
2
0
0
0
1
0
2
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
1
2
0
0
1
0
0
0
2
1
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
1
1
2
2
0
0
1
2
1
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
2
0
2
2
2
0
0
0
2
0
0
2
0
0
0
0
1
0
0
1
2
0
1
0
0
0
0
6
1
0
1
0
0
1
0
3
0
0
0
0
2
0
0
1
1
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
2
0
4
0
1
0
1
2
1
3
0
0
0
0
0
0
0
0
2
0
1
2
2
0
0
0
0
2
2
0
0
1
0
0
0
2
1
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
1
0
0
1
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
1
1
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
2
1
0
2
2
0
1
0
0
0
2
1
2
0
0
0
0
1
0
1
0
1
0
0
0
0
0
2
4
0
0
0
0
0
0
1
0
3
2
0
1
0
1
0
1
0
0
0
1
0
0
0
0
2
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
2
2
0
2
2
0
0
1
2
1
0
0
1
1
0
0
0
1
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
1
0
2
0
0
2
1
1
0
0
3
0
2
1
0
1
2
0
1
0
2
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
4
1
0
2
0
1
0
2
1
0
0
1
2
0
0
2
1
1
2
0
1
1
0
0
0
0
2
0
0
0
0
9
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
1
1
0
0
0
0
3
0
1
2
0
0
2
1
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
2
0
0
1
3
0
2
0
0
2
0
0
0
1
2
0
0
0
1
0
0
1
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
1
1
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
3
0
0
0
0
2
0
2
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
8
2
3
0
0
0
0
0
1
0
1
0
2
0
1
0
1
0
0
1
0
0
0
2
0
1
2
0
0
2
0
0
1
0
0
0
3
2
2
0
0
0
1
1
0
2
1
0
0
2
1
0
1
0
0
0
2
1
0
0
0
0
0
1
0
0
2
0
0
2
0
2
0
0
0
0
1
0
0
0
1
1
2
0
0
2
0
0
2
1
0
0
0
1
1
0
0
0
0
2
0
2
2
1
0
0
0
2
3
2
1
1
1
0
0
0
0
0
2
0
0
0
1
0
1
0
1
2
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
2
0
0
0
0
0
1
1
2
0
1
0
1
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
2
1
0
0
0
3
2
0
2
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
1
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
1
2
0
2
3
0
0
0
2
0
2
0
1
1
0
0
1
1
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
2
0
0
0
0
2
1
0
2
0
0
0
2
0
1
2
2
0
1
0
0
0
0
0
0
0
1
0
1
2
0
2
0
1
2
5
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
1
0
0
0
0
3
0
1
0
0
0
0
2
2
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
1
0
1
0
0
2
0
3
2
0
4
0
2
0
0
0
2
0
1
1
0
1
0
1
0
2
1
0
0
0
2
2
0
0
0
1
0
2
2
2
2
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
3
1
0
1
0
1
2
0
2
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
5
0
0
0
0
0
0
0
0
2
0
0
1
1
2
0
0
2
0
2
1
1
1
0
0
1
1
2
0
2
0
0
1
0
0
0
2
1
2
1
1
2
0
3
0
0
1
2
0
0
0
0
0
1
2
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
1
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
1
1
3
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
1
0
0
0
1
0
0
0
3
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
6
0
0
0
0
0
1
2
0
1
0
0
0
0
1
1
3
0
0
0
0
0
0
1
1
1
0
2
0
0
0
0
2
1
0
0
0
2
0
0
0
0
1
0
2
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
1
0
2
0
0
0
2
1
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
1
0
2
2
2
0
2
2
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
5
1
0
0
1
1
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
2
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
2
0
1
0
0
0
2
0
0
0
1
1
2
1
2
2
0
0
0
2
0
0
0
0
0
0
5
0
2
0
0
1
0
0
0
0
0
0
0
2
0
2
1
1
2
1
0
1
0
0
3
0
1
0
1
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
1
1
3
0
0
1
0
0
0
0
1
0
1
2
0
2
1
0
0
0
2
3
0
0
3
0
0
1
0
0
0
1
0
0
2
2
0
2
1
0
2
0
2
0
0
1
2
2
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
1
0
0
0
0
0
2
0
2
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
1
1
0
0
2
2
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
2
1
0
4
0
0
1
0
0
1
0
0
0
0
1
2
0
2
1
0
1
2
0
0
0
0
0
0
0
0
2
3
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
2
1
2
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
3
2
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
2
0
0
1
0
0
2
0
0
2
0
2
0
2
2
0
0
0
0
0
0
1
1
0
1
0
1
0
2
0
1
0
0
2
0
1
2
0
2
1
0
1
0
0
0
0
2
0
0
0
0
2
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
7
1
3
0
0
2
0
2
0
0
0
0
0
0
0
1
0
2
0
1
0
0
1
1
0
0
3
0
4
2
2
0
0
0
0
2
2
1
0
0
1
0
0
2
0
0
1
1
0
0
1
0
3
0
1
0
0
0
0
0
1
0
1
2
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
3
0
0
1
2
0
0
0
0
2
2
0
0
0
2
0
1
0
0
0
0
0
0
2
1
1
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
2
0
2
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
1
0
1
1
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
1
0
1
1
1
1
1
0
2
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
2
1
0
2
0
0
2
2
0
0
0
0
2
1
1
1
0
2
0
2
1
0
3
0
2
0
0
1
0
0
1
0
1
0
1
1
0
2
0
4
0
0
0
0
0
0
2
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
3
1
1
0
2
0
0
0
0
1
1
1
1
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
1
0
2
0
0
0
0
2
0
2
1
3
0
2
1
0
1
0
2
1
0
0
4
2
1
0
0
0
1
0
2
0
1
1
0
0
0
2
1
0
0
1
0
0
0
3
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
2
0
2
4
1
1
0
0
3
0
0
0
2
1
0
1
0
0
0
2
0
0
1
2
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
1
2
0
0
3
3
0
0
3
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
2
0
1
0
1
0
0
2
0
0
2
0
0
0
1
2
2
0
1
1
0
0
0
0
1
1
0
0
0
2
1
0
3
1
0
1
2
1
2
0
2
0
0
3
1
0
0
0
2
0
0
3
0
0
0
2
0
0
4
0
0
0
0
0
0
0
2
0
0
0
2
1
1
0
0
0
2
0
0
0
0
1
2
0
1
0
0
0
0
1
0
0
0
1
1
0
0
2
1
0
0
0
2
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
2
1
1
0
0
2
0
0
2
0
1
0
1
0
0
2
2
1
0
1
0
1
0
2
0
0
0
2
2
2
0
3
1
0
2
1
1
2
3
5
0
3
0
0
1
0
1
0
0
1
0
0
0
0
1
2
2
2
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
2
2
0
0
0
0
2
2
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
2
1
1
0
2
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
2
0
0
0
0
0
0
0
1
0
0
1
2
0
2
0
0
0
2
0
1
2
2
0
1
0
3
0
0
0
0
0
2
0
0
1
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
3
0
0
0
0
0
2
1
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
2
1
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
2
2
0
1
0
0
0
2
0
0
2
0
0
0
0
0
2
1
1
0
0
0
0
0
1
3
2
1
0
0
0
0
0
1
0
3
1
0
1
0
0
0
2
0
0
0
4
0
1
2
2
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
1
3
2
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
1
0
0
2
0
3
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
2
2
0
0
0
1
2
0
1
1
0
0
0
0
1
0
2
1
0
0
2
2
1
0
1
3
0
1
0
1
1
0
0
0
0
0
2
2
0
0
2
0
0
2
0
1
0
0
0
0
1
0
0
2
1
0
1
0
0
1
0
2
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
2
0
1
1
0
0
0
0
0
2
0
2
0
1
2
0
0
2
1
0
2
0
1
2
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
1
1
0
1
0
0
0
0
2
0
0
2
2
0
1
0
0
0
2
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
1
0
0
0
1
1
0
0
0
1
1
0
0
2
2
0
0
0
0
0
2
1
1
1
0
2
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
1
1
0
2
0
1
1
0
2
1
0
0
0
0
1
0
1
0
0
1
0
2
0
2
2
0
0
1
1
0
1
0
1
0
0
0
0
1
0
0
2
0
0
4
0
2
1
0
0
0
0
1
0
0
1
3
0
0
0
1
0
0
0
2
1
0
2
0
0
2
1
2
0
0
2
2
2
0
4
0
0
1
0
0
0
1
0
0
0
0
3
0
0
0
0
1
0
1
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
1
0
3
0
0
0
2
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
2
2
0
0
0
0
0
0
0
1
1
0
0
1
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
2
0
6
1
0
2
2
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
1
2
1
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
2
0
0
2
0
0
2
2
2
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
2
0
2
2
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
2
1
1
2
0
0
1
0
0
1
3
0
2
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
2
2
0
2
0
2
0
0
0
0
0
1
3
1
0
0
1
0
0
2
2
0
0
2
0
0
0
2
7
1
0
0
1
1
0
0
0
1
0
3
2
2
0
0
2
0
0
3
2
1
1
1
0
0
0
0
0
2
1
2
0
2
0
0
0
4
0
0
1
0
3
0
0
0
0
0
0
0
0
0
2
2
2
2
1
0
2
0
0
2
0
0
0
0
2
2
0
0
0
0
1
1
0
0
1
0
0
1
0
1
2
0
0
4
1
0
1
0
1
0
0
0
0
2
0
0
3
0
0
1
0
0
0
0
0
1
0
0
2
0
1
0
0
1
0
3
0
0
2
1
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
1
2
0
1
0
1
0
0
0
0
0
1
0
0
2
4
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
6
0
0
0
0
0
1
0
3
0
0
2
0
0
0
0
0
0
1
2
0
0
1
0
2
0
1
1
1
0
0
0
0
2
2
1
0
2
0
0
0
0
0
0
1
2
0
0
0
0
2
2
1
0
0
0
0
1
0
2
2
0
0
2
0
0
1
1
2
1
0
2
0
1
0
2
1
1
1
0
0
0
1
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
2
1
4
1
0
2
0
0
1
1
0
1
0
2
0
1
2
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
2
1
0
5
3
0
0
0
0
0
1
2
2
2
0
2
2
0
0
0
0
0
2
1
1
0
0
0
0
1
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
2
0
0
2
2
0
0
0
2
3
0
1
0
0
0
0
0
2
0
1
0
0
0
0
2
1
0
0
1
0
0
2
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
2
0
0
0
1
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
2
0
0
1
0
1
0
0
1
0
0
0
1
2
0
0
0
0
0
2
2
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
2
2
2
1
0
0
0
1
0
0
0
2
2
1
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
2
0
1
0
1
2
2
0
0
0
0
2
1
0
1
1
2
0
1
0
0
0
0
2
0
0
0
2
0
0
3
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
3
2
0
2
1
0
0
1
0
0
0
2
0
1
2
0
0
1
2
0
0
0
2
0
0
0
0
2
0
1
2
2
0
1
0
0
0
0
1
1
3
0
0
1
2
0
0
1
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
2
0
0
0
1
0
0
0
0
2
2
0
2
0
0
2
2
0
2
1
0
0
0
0
0
2
1
0
1
2
0
0
0
1
0
1
2
1
0
0
1
0
1
0
2
1
3
0
2
0
2
3
2
0
1
0
0
0
0
1
4
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
1
1
0
0
1
0
1
0
2
2
0
4
0
0
1
2
0
0
0
0
0
0
1
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
3
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
2
1
0
1
2
2
2
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
2
2
1
0
0
0
0
2
0
0
0
2
2
2
0
3
2
0
1
2
0
0
2
1
2
0
0
1
0
1
1
3
0
0
0
1
0
0
2
0
1
0
0
0
1
0
2
0
0
0
0
0
2
2
0
2
1
0
0
2
0
0
3
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
2
0
1
2
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
1
1
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
6
1
1
0
0
2
0
1
2
0
0
0
1
0
0
0
0
0
0
1
1
3
0
0
0
1
1
0
2
1
0
2
0
0
2
2
0
0
2
0
0
0
2
0
0
0
2
0
0
2
1
0
2
0
1
0
2
0
0
0
2
0
0
0
3
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
3
2
4
2
1
1
0
0
0
0
0
0
0
1
1
0
0
0
2
0
2
1
0
1
1
0
1
1
0
1
0
0
0
1
0
0
0
0
0
5
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
1
0
0
0
0
0
2
1
0
0
1
0
0
1
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
4
2
0
2
0
0
0
1
0
0
0
2
0
2
0
0
0
1
0
2
0
0
2
0
1
0
0
0
3
2
2
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
2
0
0
0
2
0
0
0
1
0
0
4
0
0
0
2
0
0
0
1
0
0
0
0
2
0
3
0
1
2
1
2
1
1
1
0
2
0
0
0
0
0
1
0
1
0
0
0
0
2
3
0
1
2
2
1
1
0
0
0
1
0
0
0
2
1
1
2
0
1
1
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
3
0
0
0
0
2
3
1
0
0
1
2
1
1
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
2
1
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
3
3
0
1
3
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
1
2
0
0
0
0
0
3
0
1
1
0
0
0
2
0
0
2
0
0
0
0
1
3
0
0
0
0
0
0
0
1
1
2
0
0
0
2
2
2
0
2
0
0
1
2
0
0
0
0
3
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
1
2
2
0
2
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
1
0
0
1
0
2
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
3
2
0
1
1
0
2
0
2
2
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
2
0
0
0
0
0
1
1
2
0
1
0
0
0
0
4
0
0
0
0
1
0
0
0
1
1
2
0
2
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
2
0
2
0
3
0
3
2
0
1
0
0
0
1
0
0
0
0
1
0
2
1
2
0
1
0
0
0
0
0
0
2
1
0
1
0
2
1
0
1
0
0
1
0
0
2
1
1
0
1
0
2
0
0
2
1
2
0
2
0
0
0
1
0
0
3
0
0
1
3
0
0
0
1
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
2
2
0
2
2
1
2
0
0
1
0
0
0
0
0
0
2
3
2
0
0
0
0
0
2
2
0
0
0
0
1
1
2
0
1
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
3
0
1
0
0
0
3
0
1
1
0
1
0
0
0
1
0
0
2
0
2
0
1
0
3
1
0
1
2
2
0
2
0
0
0
0
0
0
2
0
0
3
0
0
0
2
0
3
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
1
3
1
1
1
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
2
0
1
2
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
2
2
4
0
1
1
0
0
1
1
0
0
0
1
2
0
2
0
1
2
0
0
2
0
2
0
0
0
0
0
0
0
1
3
1
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
3
1
2
0
2
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
2
0
2
2
0
0
0
1
2
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
1
2
2
0
0
0
0
0
2
0
0
2
0
2
0
0
0
2
1
1
0
0
0
1
1
2
0
0
3
1
0
1
0
2
1
1
2
0
2
2
0
0
0
0
1
0
2
1
2
0
0
0
2
0
0
0
0
0
1
0
1
2
2
0
0
0
0
0
0
0
0
1
0
0
0
1
3
0
0
0
0
0
0
1
0
0
0
0
1
1
0
2
1
0
1
0
1
0
0
0
1
0
0
2
0
0
2
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
1
0
0
2
0
1
2
1
0
1
0
1
0
1
0
2
0
0
1
0
0
0
0
2
2
1
0
0
0
0
3
0
0
0
2
0
1
1
1
0
0
0
0
0
1
2
0
1
1
1
2
1
1
0
0
0
1
0
2
0
0
1
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
2
1
0
0
0
2
0
2
1
0
0
0
0
0
2
2
2
2
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
2
0
2
2
0
1
2
2
0
0
0
0
0
0
1
0
0
1
2
1
1
0
0
0
0
1
1
3
0
0
2
2
1
1
0
1
1
0
0
0
1
0
0
0
0
3
0
0
0
0
1
0
0
2
0
0
0
0
2
0
1
0
0
2
0
0
2
0
0
0
0
2
0
1
0
2
1
0
0
1
2
1
0
0
1
3
1
0
0
0
0
0
0
1
2
2
1
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
1
0
0
0
2
0
2
0
1
0
0
2
0
2
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
2
0
1
2
1
0
1
0
0
1
0
1
0
0
2
2
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
2
0
0
2
0
0
1
0
1
0
0
1
1
1
0
0
2
0
2
2
0
0
0
1
2
0
1
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
2
1
0
0
1
0
0
0
0
1
0
2
4
3
0
0
0
1
0
0
2
0
1
0
0
0
0
1
0
1
1
0
2
2
1
0
0
0
0
0
1
0
0
2
0
0
0
2
2
2
0
0
0
1
0
0
0
2
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
2
0
0
7
1
1
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
1
1
2
0
1
0
1
0
0
1
2
1
0
0
1
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
1
4
2
2
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
2
1
2
0
2
0
2
1
0
0
0
0
0
0
2
0
0
2
0
0
0
1
1
0
2
0
0
0
0
0
1
0
0
0
1
2
0
2
2
0
0
0
0
0
0
0
0
0
1
2
0
1
0
2
0
2
1
0
1
0
0
1
2
0
4
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
1
0
1
0
0
2
0
0
1
0
2
0
0
0
1
0
2
0
0
0
2
2
0
2
0
1
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
5
0
1
0
1
0
1
4
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
1
3
0
0
0
0
5
0
0
2
2
0
2
0
0
1
1
2
0
1
1
2
3
0
0
0
2
0
0
2
0
0
0
1
2
2
1
1
0
0
0
0
0
0
2
0
0
2
0
3
0
0
0
2
0
0
1
0
0
0
2
4
1
0
0
0
2
0
0
2
0
2
0
1
1
0
2
0
2
0
1
0
0
0
0
1
2
0
0
0
1
0
0
0
0
2
0
0
0
1
1
0
1
0
1
4
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
2
1
0
0
1
0
0
1
0
0
2
2
0
0
2
2
0
2
1
0
1
0
0
0
2
0
1
0
0
0
1
2
0
1
0
0
0
0
2
0
1
1
0
2
0
1
0
0
0
0
2
0
0
1
2
0
0
3
1
0
5
0
1
0
0
0
1
0
0
3
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
2
0
0
1
0
0
1
0
1
2
3
0
0
2
0
0
2
0
0
0
1
1
0
0
0
1
2
0
3
0
1
0
2
0
1
0
0
1
0
0
0
0
1
0
0
1
2
0
0
1
0
0
0
1
2
1
0
1
0
0
2
0
1
0
2
0
0
0
2
21
2
0
0
1
0
0
1
2
0
3
0
0
0
2
0
1
0
2
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
1
1
0
0
2
0
2
1
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
3
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
4
0
0
2
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
3
2
1
0
0
2
2
2
0
0
0
0
1
1
0
0
0
2
1
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
2
0
0
0
2
0
2
2
0
2
0
0
2
0
0
1
2
8
0
0
2
1
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
2
0
2
0
2
2
0
0
1
0
0
0
2
1
2
2
1
0
0
2
0
0
0
3
0
2
0
0
0
1
1
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
2
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
1
1
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
1
0
2
0
2
0
0
0
0
2
0
2
0
2
3
0
1
0
2
0
2
0
0
1
2
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
2
2
0
0
2
0
3
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
1
1
0
4
1
0
0
0
0
1
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
2
1
0
0
0
0
2
2
0
1
2
0
0
2
0
0
0
5
1
1
3
0
0
0
2
0
1
2
0
0
0
0
1
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
1
2
0
0
0
3
1
0
0
0
1
2
0
0
1
0
2
0
0
1
0
3
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
2
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
1
0
0
3
0
1
0
0
1
0
0
0
0
0
2
2
1
0
2
1
0
1
0
1
2
0
0
0
0
0
0
0
2
0
0
0
1
1
0
1
1
0
1
0
1
0
0
0
0
0
1
0
0
0
2
0
1
0
1
0
1
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
1
2
0
0
0
2
0
2
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
2
0
0
1
0
2
1
0
1
0
0
0
0
0
2
0
0
0
1
0
1
1
2
1
1
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
1
0
0
2
0
2
0
1
1
2
0
0
0
0
0
0
1
0
1
0
0
1
2
0
1
0
0
1
2
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
1
0
1
2
1
1
0
0
0
0
0
1
0
0
2
2
0
0
1
1
0
2
0
0
0
0
1
1
1
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
2
2
0
1
0
0
0
0
0
2
0
0
0
0
3
0
0
3
1
1
0
1
0
0
2
0
1
1
0
2
0
0
0
0
3
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
1
0
0
2
5
0
0
1
2
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
2
0
2
1
2
4
1
1
1
0
1
0
0
0
0
0
0
0
0
1
2
0
3
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
2
1
0
0
2
0
0
0
0
0
0
1
1
0
0
1
0
1
2
1
0
0
1
0
2
0
0
1
0
1
0
0
0
3
2
0
4
0
2
0
0
0
0
1
0
0
0
0
1
1
1
2
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
4
2
1
0
0
1
0
0
0
0
0
0
1
0
0
1
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
1
2
0
0
2
0
0
0
1
0
0
2
1
1
0
1
0
2
2
0
2
2
0
0
0
3
1
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
2
0
1
5
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
2
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
1
2
2
1
0
0
0
2
0
0
0
1
0
0
0
3
1
0
0
0
0
2
0
0
0
0
0
0
1
1
1
0
0
0
2
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
2
4
0
0
0
0
0
2
1
0
0
0
0
2
2
0
0
2
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
1
1
0
0
2
0
0
0
1
0
0
1
2
0
0
0
0
2
0
2
0
1
0
2
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
1
2
0
0
0
2
0
0
2
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
2
0
0
0
1
0
0
1
1
1
0
0
1
0
0
0
0
2
0
2
0
2
0
1
1
1
0
2
0
0
2
0
0
0
0
0
2
3
0
2
2
0
0
0
1
1
2
0
0
0
2
0
0
0
0
2
1
1
1
0
0
0
2
0
1
0
0
1
0
2
0
2
0
0
0
1
2
1
0
1
2
0
1
0
0
0
1
0
0
0
1
0
0
1
1
0
0
1
0
1
0
3
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
2
2
0
2
1
2
1
1
0
0
0
0
0
2
1
0
2
0
0
1
2
1
2
1
0
0
0
0
0
2
2
2
0
0
0
0
1
0
0
2
3
0
0
0
0
1
0
0
1
2
1
2
0
1
1
2
0
0
0
0
0
1
0
1
0
0
1
2
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
6
0
0
0
0
2
0
2
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
1
2
0
0
2
1
0
0
0
0
0
0
1
2
0
1
2
1
0
2
1
0
0
0
0
0
2
1
0
6
0
0
0
0
1
1
1
1
0
0
0
2
2
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
1
2
2
1
0
0
1
0
0
0
0
0
1
0
2
0
0
2
0
2
0
0
0
0
0
0
0
2
2
0
2
0
1
1
0
0
0
1
0
0
0
1
1
0
0
1
0
3
2
0
0
0
1
0
0
0
0
0
0
1
6
2
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
1
1
0
1
0
0
1
0
0
1
2
0
1
0
1
0
1
1
2
0
2
0
1
1
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
1
2
2
2
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
1
0
0
2
0
1
1
0
0
3
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
1
1
0
0
0
2
0
0
0
3
1
0
4
1
1
0
1
2
2
0
3
0
1
0
2
0
0
0
0
2
0
0
0
3
2
0
0
2
1
0
0
0
2
0
0
0
0
0
0
2
0
0
2
2
1
0
2
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
2
0
0
0
1
0
0
1
0
1
2
2
0
1
1
0
0
0
1
1
0
2
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
3
0
2
0
1
0
0
1
0
0
0
2
3
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
1
2
0
2
0
0
0
1
0
0
0
2
2
1
0
0
0
2
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
5
0
0
2
2
0
0
1
0
0
0
1
0
0
0
2
0
0
1
0
0
0
4
1
1
0
0
2
2
0
0
0
3
1
0
0
2
1
0
0
2
1
1
0
1
0
0
0
0
0
1
2
0
0
0
0
0
1
1
0
2
0
1
0
0
0
0
2
0
0
0
0
1
0
0
2
1
0
2
0
0
0
0
2
0
0
0
0
0
0
1
2
0
1
0
1
0
0
0
2
0
0
2
2
1
0
1
0
0
1
0
0
2
0
1
2
0
0
0
4
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
2
0
0
0
1
0
3
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
2
2
0
0
0
2
0
0
2
0
0
2
0
2
0
0
1
0
0
0
3
1
0
0
1
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
2
2
0
0
2
0
2
1
0
1
0
1
0
0
2
2
0
0
0
2
1
0
0
1
0
0
1
0
0
1
1
2
0
0
0
2
0
1
0
3
0
1
1
0
0
1
2
2
0
1
0
1
1
2
2
0
1
1
0
2
0
0
0
1
0
2
0
0
0
2
2
0
1
0
0
2
1
0
2
0
0
1
0
0
0
0
2
0
0
1
1
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
2
0
2
0
2
0
2
0
1
2
0
0
0
0
0
0
2
0
3
0
0
0
0
0
3
1
0
0
0
0
2
0
0
2
2
0
0
1
0
0
0
0
0
2
2
0
0
1
0
0
0
2
0
0
0
1
2
0
0
1
3
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
1
0
0
2
0
2
0
1
2
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
1
0
0
1
0
0
0
0
2
1
0
0
2
0
1
1
1
0
1
0
0
2
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
1
1
0
0
2
0
0
0
0
0
4
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
2
1
0
0
1
0
0
1
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
1
3
0
1
0
0
2
0
0
1
0
2
0
0
1
0
0
2
0
2
0
0
1
0
0
1
0
1
2
0
0
3
0
1
0
0
0
0
2
2
1
0
0
0
0
0
0
0
1
0
2
0
2
0
0
2
2
0
2
0
0
0
0
2
0
0
0
0
0
0
1
1
2
0
0
2
0
0
0
1
0
2
0
0
0
1
0
0
0
1
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
1
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
2
1
0
2
0
0
0
3
0
1
0
1
1
0
2
1
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
1
1
0
0
1
0
0
0
0
0
0
1
0
1
1
1
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
2
2
1
0
0
1
1
0
0
2
0
0
0
1
0
1
0
0
0
0
0
3
1
0
2
0
0
0
0
0
0
0
1
0
0
1
1
0
7
0
0
0
1
0
1
0
1
0
0
2
1
2
0
0
2
0
2
2
0
2
0
1
0
0
0
0
0
2
0
1
0
2
2
0
0
0
0
0
1
1
1
0
2
0
0
0
0
0
0
1
0
2
1
0
0
0
0
2
2
2
2
0
2
2
2
1
0
0
4
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
2
0
0
1
0
0
0
0
0
1
0
3
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
1
2
0
0
0
0
0
2
2
1
0
2
1
0
0
0
0
2
0
1
0
0
2
0
0
1
3
0
1
0
0
0
1
2
0
2
0
0
4
1
0
1
1
0
0
2
1
3
0
0
0
2
2
0
2
0
0
0
0
0
0
0
2
1
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
1
0
0
0
2
0
1
2
0
0
2
2
0
2
0
0
0
0
0
0
0
2
0
1
1
2
0
1
1
1
0
2
0
0
0
0
2
0
0
2
0
0
0
1
2
1
0
6
2
0
0
0
0
0
2
0
2
0
0
0
3
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
2
2
0
2
0
0
0
0
0
0
1
5
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
2
0
1
0
0
2
1
1
2
0
1
0
1
0
1
1
0
0
0
2
0
0
0
0
2
1
2
0
0
2
2
0
2
2
0
0
0
0
0
1
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
2
0
1
0
1
2
0
0
0
0
0
0
2
5
0
0
1
1
0
0
1
0
0
0
0
0
0
2
0
0
0
1
2
0
0
2
0
0
0
1
1
0
0
2
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
2
1
0
0
1
0
2
1
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
2
0
0
1
2
2
0
0
2
0
0
1
2
2
0
0
0
1
0
1
0
2
0
0
7
0
0
1
0
0
0
0
0
2
0
0
0
0
2
1
1
2
0
0
2
0
2
1
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
1
0
2
2
1
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
2
0
0
2
0
1
0
0
2
0
0
2
1
0
2
1
2
1
0
2
1
2
0
0
1
0
0
2
2
1
0
2
0
0
0
0
1
0
0
0
2
1
2
2
0
2
2
0
1
1
2
0
0
0
1
2
0
2
0
0
8
7
0
0
0
2
0
1
0
0
0
0
0
0
1
0
2
0
0
2
0
0
2
0
2
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
1
1
1
0
0
0
2
0
0
0
0
1
1
2
0
0
0
0
3
2
0
0
0
1
0
0
0
2
0
0
3
0
0
0
2
1
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
1
2
0
2
1
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
2
1
1
1
0
0
0
0
3
4
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
1
0
2
0
3
0
1
0
0
0
0
2
0
2
0
1
0
0
1
1
0
0
0
1
1
1
0
3
0
2
0
0
1
0
0
1
0
2
1
0
1
1
0
1
0
1
0
0
3
0
0
2
1
2
0
0
2
0
0
0
1
0
1
0
2
0
0
2
0
0
1
1
0
0
1
0
0
0
0
1
2
0
0
2
0
2
0
2
0
0
0
0
0
0
0
2
1
1
1
0
0
2
0
0
0
0
0
0
2
1
0
0
0
1
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
2
3
0
2
0
1
0
0
2
0
0
0
0
1
1
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
1
2
1
0
1
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
2
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
1
1
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
1
0
0
4
0
1
0
0
2
1
2
0
0
0
0
0
0
0
2
3
1
0
2
2
0
0
2
1
2
0
2
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
2
2
2
0
0
1
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
2
0
1
6
0
0
1
1
0
0
1
1
0
0
0
1
1
0
3
0
2
0
0
2
1
2
0
2
0
3
0
1
3
0
0
0
0
0
1
0
0
0
3
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
4
0
1
0
0
0
0
0
2
0
0
0
2
1
0
0
0
2
1
1
0
3
1
0
1
2
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
5
1
2
0
1
0
2
0
0
2
0
0
0
1
0
0
5
2
0
0
6
0
0
0
0
0
1
0
0
0
0
0
2
2
2
0
0
0
0
1
2
0
2
0
0
0
0
1
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
10
0
0
3
2
0
0
0
1
0
0
1
0
0
0
2
0
1
0
0
0
1
0
0
0
0
2
4
0
2
0
0
0
3
0
0
2
0
0
1
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
2
2
2
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
2
0
0
1
2
0
0
1
0
2
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
2
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
2
1
1
0
1
0
0
1
2
2
0
1
0
1
1
2
0
0
0
0
0
0
0
1
0
0
1
0
3
2
0
0
2
0
0
0
0
5
0
0
2
0
0
0
0
1
0
2
1
0
2
0
0
0
0
0
0
0
2
0
0
0
1
1
0
1
0
0
3
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
1
0
1
3
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
1
1
0
0
0
0
0
2
2
0
0
1
1
0
0
2
2
0
1
0
0
2
1
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
2
1
5
0
0
0
0
1
2
2
0
0
0
1
1
0
2
0
0
2
0
0
2
0
0
0
0
0
0
2
1
0
0
1
2
1
2
0
2
0
0
2
1
0
1
0
0
0
1
1
2
2
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
10
0
0
3
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
1
3
2
0
0
0
1
1
1
0
0
2
0
0
0
0
0
1
0
0
0
1
2
1
0
2
0
0
0
0
0
1
1
1
0
1
2
0
1
0
0
1
2
0
0
0
1
0
0
1
1
0
4
0
0
2
0
2
1
1
0
0
0
0
1
0
0
1
2
1
1
1
0
0
2
0
0
2
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
3
1
2
0
2
0
0
0
0
0
1
0
0
2
0
0
2
2
1
0
1
0
0
0
2
1
1
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
3
0
1
0
2
2
1
1
0
0
1
0
0
0
0
1
2
2
0
1
0
0
0
0
0
0
0
0
0
1
1
0
3
1
2
1
0
0
1
3
0
0
3
1
0
0
0
0
1
1
0
0
0
2
0
0
0
2
0
0
0
2
1
0
1
1
0
0
0
0
0
0
1
0
1
0
2
2
2
0
2
2
0
0
1
1
1
1
1
2
0
0
0
0
0
0
0
2
0
0
3
5
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
2
0
0
0
0
1
1
2
0
2
0
0
1
1
1
1
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
2
0
0
1
2
2
0
0
2
0
0
3
0
1
1
2
1
0
0
0
0
1
2
0
0
3
0
1
0
3
0
0
0
0
0
1
0
0
0
0
2
1
2
0
0
0
1
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
3
1
1
1
0
0
0
2
1
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
7
2
2
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
1
0
0
1
0
2
1
0
0
0
2
0
1
0
0
0
1
0
2
0
0
1
0
0
0
0
2
0
0
0
2
0
0
1
1
2
0
0
4
0
0
0
0
0
0
0
0
2
3
0
0
0
0
2
0
1
0
0
1
0
0
2
0
0
0
0
2
0
1
0
0
0
1
0
2
0
0
0
0
5
0
2
0
1
0
1
1
0
0
1
2
1
0
0
0
2
0
0
0
2
0
0
0
1
0
0
1
0
0
2
1
1
2
1
1
0
0
1
0
1
0
0
0
3
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
2
2
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
1
2
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
1
2
0
2
0
0
2
0
2
0
0
2
2
0
2
0
1
2
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
3
0
0
2
0
1
0
4
2
0
0
2
2
0
1
0
1
1
0
1
0
0
2
0
2
1
2
0
0
3
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
3
0
0
2
1
1
1
1
0
0
6
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
1
1
3
1
0
2
1
0
0
2
1
0
0
0
0
2
1
1
0
0
0
0
2
0
2
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
1
0
0
0
1
3
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
4
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
2
0
1
0
0
0
0
1
1
0
0
2
0
0
2
0
0
2
0
0
1
2
0
1
0
0
1
2
0
0
3
2
1
0
1
0
1
0
0
1
2
0
2
2
0
0
1
0
2
0
2
2
2
0
2
0
0
0
2
0
0
0
0
3
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
1
1
0
1
0
0
0
0
2
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
2
2
1
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
1
0
0
2
1
0
1
2
2
0
0
0
0
0
3
0
0
0
2
0
0
0
0
1
0
0
0
0
2
3
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
3
2
0
0
1
1
0
0
0
0
0
0
0
2
2
0
0
1
2
0
0
0
1
0
0
0
2
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
1
0
0
0
2
0
1
0
0
2
0
0
0
0
2
1
0
1
1
0
1
0
0
1
1
0
1
0
0
0
0
1
2
1
0
0
2
2
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
2
0
0
0
1
0
0
1
0
1
0
0
0
0
3
2
0
1
2
0
0
0
1
2
0
1
0
1
0
0
0
2
0
1
0
3
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
2
2
0
1
0
2
0
0
0
0
0
0
1
1
1
1
0
2
2
2
0
0
2
0
4
2
1
0
0
1
2
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
2
0
2
0
0
0
0
0
0
0
1
1
3
0
2
0
0
1
0
0
0
0
0
4
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
2
0
2
0
0
0
1
1
2
2
2
0
0
2
0
0
0
0
3
0
0
0
0
0
0
1
0
1
0
2
2
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
2
2
0
0
1
0
0
1
0
1
1
0
0
2
0
0
1
0
4
0
0
0
1
0
2
0
0
1
0
0
0
2
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
4
0
0
0
0
2
0
0
1
0
1
2
0
2
0
0
2
0
0
0
2
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
4
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
2
0
2
1
0
0
2
1
0
0
0
1
0
0
0
1
0
1
0
0
0
2
1
0
0
2
2
1
0
1
0
1
0
2
0
1
0
2
0
0
0
3
2
0
0
0
3
0
2
2
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
1
0
0
0
0
1
0
1
1
1
0
1
0
0
0
1
0
0
0
1
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
2
0
0
0
1
0
0
0
2
0
2
0
0
0
1
0
0
0
1
0
1
0
0
3
4
0
0
0
0
0
0
0
2
0
0
2
0
1
0
2
0
0
0
0
0
0
0
1
0
1
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
2
0
0
1
2
2
0
0
1
2
1
2
3
0
0
0
0
0
0
1
0
2
4
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
2
0
0
0
1
0
3
1
0
0
0
1
0
0
1
2
2
2
2
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
1
0
7
0
0
0
1
2
1
1
1
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
2
0
0
0
0
0
1
1
2
0
0
0
0
0
0
2
1
4
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
2
0
0
2
0
0
0
0
0
1
1
1
1
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
1
0
4
0
0
0
0
0
2
0
4
0
1
0
2
0
0
2
1
0
0
1
1
0
2
1
2
0
0
2
0
0
0
2
2
0
0
1
1
0
0
0
2
0
2
0
1
0
0
0
2
1
0
0
1
0
0
4
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
3
0
0
1
1
0
2
0
0
0
0
2
0
0
0
0
0
5
3
0
0
0
0
0
0
1
1
0
1
0
1
1
1
0
0
0
2
0
0
2
0
2
0
2
3
0
1
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
2
2
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
2
0
0
2
0
1
2
0
2
0
0
2
0
0
1
0
1
0
0
3
0
1
0
0
0
0
0
0
0
2
0
0
2
0
2
2
2
0
0
1
1
0
0
0
0
0
0
2
2
0
0
0
1
0
1
0
2
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
2
0
0
1
1
0
0
0
0
0
0
1
1
2
2
0
0
1
0
0
0
0
3
0
0
2
1
0
0
0
0
2
0
1
2
0
3
0
0
2
0
3
0
6
2
3
1
4
2
0
1
2
0
2
0
0
1
1
1
0
1
2
0
0
0
0
2
2
0
0
2
0
0
0
1
0
0
1
0
0
0
2
0
2
3
0
0
2
0
2
0
0
0
1
3
0
2
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
2
0
0
0
0
3
1
1
1
0
0
0
0
3
1
1
0
0
0
1
0
0
0
0
2
0
0
0
1
2
0
1
0
2
1
0
1
1
0
0
2
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
1
0
0
3
0
0
2
0
0
0
0
0
3
0
0
0
2
0
1
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
2
2
0
2
0
0
0
1
0
0
0
0
0
0
2
2
1
2
2
0
0
0
0
0
0
0
0
1
0
0
1
1
0
2
2
0
0
0
1
2
0
0
2
0
3
6
1
1
2
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
3
0
0
0
0
1
1
2
2
2
0
0
1
0
1
0
0
0
0
0
2
0
0
1
2
5
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
2
0
1
1
0
1
1
2
0
1
0
0
0
1
2
1
1
1
2
1
3
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
4
0
2
0
1
1
3
0
0
0
0
0
0
1
1
0
0
0
0
2
1
0
0
0
0
0
0
0
2
4
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
2
2
1
0
0
0
0
1
0
1
2
2
0
1
0
1
2
0
3
0
0
0
0
1
0
0
1
0
1
0
0
1
0
2
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
1
2
4
0
1
2
0
2
0
0
0
2
0
0
1
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
1
2
2
0
0
2
0
1
1
0
0
0
0
0
2
0
0
0
0
3
2
0
1
0
1
0
2
0
2
0
0
0
0
2
1
2
0
0
0
1
0
2
0
1
0
2
2
0
0
4
0
0
0
0
0
0
1
0
0
5
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
1
0
0
0
0
1
1
0
0
2
1
2
0
2
0
0
0
2
3
0
2
2
3
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
2
0
2
0
0
3
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
2
0
4
0
0
0
0
0
1
0
1
0
0
1
0
0
0
2
0
0
0
0
2
0
1
0
0
2
0
6
2
0
3
2
1
0
1
1
0
0
1
2
2
1
0
1
2
0
0
0
0
2
0
0
2
1
1
0
0
0
1
0
0
0
0
0
0
1
0
2
1
0
0
1
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
1
0
0
2
0
2
0
0
0
0
1
0
1
0
0
0
2
1
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
2
1
1
0
0
0
0
0
2
0
0
1
0
0
0
0
2
2
3
0
0
2
1
2
0
1
1
0
1
0
0
0
1
0
2
0
2
2
0
3
0
2
0
0
1
1
0
1
2
1
0
3
2
0
2
1
0
0
2
0
2
1
0
0
0
0
0
1
1
1
4
0
1
0
0
0
0
0
2
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
1
2
0
0
0
0
1
0
2
0
1
0
0
0
3
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
3
1
4
1
0
0
1
0
2
6
0
0
0
0
0
1
2
2
0
0
2
3
0
0
0
0
0
6
0
0
2
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
1
0
2
2
1
0
1
0
0
2
2
4
0
0
1
1
0
2
0
0
1
0
2
0
2
2
1
1
0
0
2
0
0
0
2
0
0
1
0
0
0
1
2
2
2
1
0
0
1
2
2
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
1
2
0
5
0
1
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
2
0
0
2
0
2
0
1
0
2
0
0
0
0
2
1
1
0
2
0
0
2
2
0
0
2
1
0
4
1
2
3
1
2
1
0
0
1
0
1
2
0
2
0
0
0
1
1
0
0
1
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
2
0
1
0
1
1
0
0
0
0
1
0
3
1
0
0
1
0
0
1
0
2
0
0
2
0
0
0
0
0
0
1
1
0
0
1
0
1
1
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
2
2
3
0
1
0
0
1
0
1
0
2
1
0
2
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
1
0
0
0
0
0
2
1
4
1
0
0
2
0
0
1
1
1
0
4
0
0
0
0
0
0
1
0
3
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
2
1
2
0
1
0
2
0
1
1
0
0
1
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
3
2
0
2
2
0
0
0
0
2
3
0
0
0
0
0
0
0
2
0
2
0
1
2
1
1
1
0
0
0
2
2
0
0
1
2
0
0
0
0
2
1
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
1
2
0
2
0
2
2
0
0
0
0
0
0
2
2
0
0
2
4
2
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
1
3
0
0
0
0
1
0
0
1
3
0
1
2
0
0
0
2
2
1
1
1
0
1
0
0
0
2
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
1
2
0
0
2
0
0
2
1
0
1
0
5
0
0
0
0
0
0
2
1
0
1
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
1
2
0
1
2
0
0
2
3
1
2
0
0
0
1
0
2
0
1
0
1
2
0
0
0
2
2
0
0
0
0
0
4
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
2
0
0
1
2
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
2
0
2
0
2
2
2
2
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
5
0
0
0
0
2
0
0
0
0
0
0
3
2
0
2
0
0
0
0
0
2
1
1
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
1
4
2
1
2
0
1
1
0
0
0
1
0
0
2
0
1
0
1
0
0
2
0
0
1
0
0
2
0
1
0
0
1
0
0
0
0
0
6
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
2
0
2
2
0
0
2
0
0
0
3
2
2
0
0
1
2
0
0
0
0
2
2
0
1
2
0
2
0
1
2
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
4
0
0
2
3
0
1
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
1
1
0
0
1
0
2
2
0
2
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
1
0
1
0
0
0
0
1
0
0
0
0
0
1
2
1
3
0
2
0
1
1
0
0
1
0
0
4
0
2
0
1
0
0
0
2
0
0
0
2
3
0
0
0
0
2
0
1
0
0
0
2
2
0
0
0
2
1
0
0
2
0
1
0
0
1
0
0
0
0
2
0
2
1
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
2
1
1
0
2
0
1
0
0
0
0
2
1
2
3
0
3
0
3
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
2
1
0
0
0
1
0
2
1
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
2
2
2
2
2
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
2
1
0
1
2
0
0
0
0
0
2
0
2
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
2
0
0
0
1
0
0
1
0
1
1
6
0
0
1
1
1
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
2
0
3
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
2
1
1
2
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
2
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
4
0
0
0
0
0
2
0
0
2
1
1
0
1
0
0
0
0
1
2
1
0
2
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
1
0
0
0
0
0
0
1
2
0
2
0
0
0
1
0
0
0
0
0
1
2
2
2
0
0
2
1
0
0
2
1
0
0
0
2
0
2
1
0
1
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
8
0
0
1
0
1
1
2
3
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
2
0
4
0
1
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
2
0
1
0
1
0
2
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
2
1
2
0
2
0
0
0
0
0
0
0
1
3
0
0
0
1
0
0
2
1
1
3
0
2
3
2
1
2
2
0
2
2
1
1
0
0
0
0
0
1
0
2
1
0
1
0
0
0
1
2
0
1
0
0
2
0
0
0
0
0
0
3
0
2
0
0
1
2
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
1
0
0
0
0
1
0
0
2
2
2
2
0
0
0
2
2
0
2
0
3
0
0
3
1
1
0
0
0
2
3
1
0
3
2
0
2
0
2
0
0
2
0
1
3
1
0
2
2
0
0
0
1
1
2
0
2
0
0
2
0
0
1
0
1
1
0
0
2
0
1
0
0
0
2
1
0
0
0
1
1
3
0
0
0
0
0
0
0
1
0
0
0
1
0
2
2
3
1
1
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
2
1
2
0
0
0
1
0
0
0
0
1
0
0
1
1
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
2
0
4
0
0
0
2
0
2
0
0
0
0
0
1
0
6
1
1
0
1
0
0
2
1
0
0
2
0
0
2
0
0
1
1
0
0
1
0
0
1
0
1
1
1
0
0
0
2
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
1
2
0
1
0
0
0
0
1
2
0
0
0
0
1
1
0
2
2
0
0
0
0
2
2
0
0
0
0
0
1
0
0
1
0
2
0
0
1
0
0
2
0
0
0
1
0
0
1
0
1
0
2
0
1
0
0
2
0
0
0
0
1
0
0
1
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
1
0
2
2
0
0
1
0
0
0
0
1
2
0
1
1
2
0
0
1
0
2
1
1
1
0
5
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
2
1
1
0
0
0
0
2
0
2
0
0
1
0
2
0
2
0
0
0
1
0
0
0
0
1
0
1
2
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
2
0
2
0
0
2
0
0
1
2
0
1
0
0
0
1
0
1
1
3
1
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
2
2
0
0
2
1
0
0
0
4
0
0
0
0
0
1
0
0
2
0
0
1
1
3
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
1
0
0
0
0
0
1
0
0
2
0
3
0
0
2
1
0
0
0
2
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
2
0
1
2
1
1
0
0
0
1
2
0
0
1
0
0
0
0
0
3
1
0
2
0
0
2
2
0
1
1
0
1
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
2
2
1
0
0
0
0
1
0
0
1
2
2
0
0
0
0
0
0
1
2
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
1
1
1
0
0
0
0
2
0
2
2
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
1
0
1
0
0
1
0
0
2
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
3
0
2
0
1
0
0
0
2
2
0
2
6
0
0
0
0
0
0
0
2
0
0
0
1
0
2
2
0
0
0
2
0
0
0
0
1
0
2
0
0
1
1
0
2
0
0
2
1
1
0
0
0
0
0
1
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
2
2
0
0
1
1
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
2
1
0
1
0
0
0
1
0
0
0
1
0
0
0
4
2
1
0
0
0
0
2
1
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
3
0
0
0
1
0
1
4
0
1
2
0
1
0
0
1
0
1
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
1
1
0
0
0
0
2
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
2
2
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
1
0
1
1
0
0
0
0
1
2
0
0
0
0
0
0
2
0
1
0
0
0
3
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
2
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
2
1
1
0
2
0
0
2
0
1
0
1
0
2
0
0
0
0
1
0
1
0
0
2
2
0
2
0
0
0
1
1
2
0
2
0
2
0
1
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
2
0
2
0
2
1
0
2
0
0
0
1
0
1
0
0
0
1
0
0
0
2
2
0
0
2
1
0
0
1
2
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
1
1
1
2
0
0
0
0
2
1
1
1
0
0
3
0
0
0
2
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
1
2
1
0
0
0
2
1
0
2
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
2
1
1
0
0
0
0
0
2
0
0
4
0
0
0
2
2
6
3
1
1
0
0
1
0
0
0
0
2
0
0
0
2
3
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
2
0
0
0
0
2
2
0
1
0
1
0
1
1
0
2
0
2
1
0
0
1
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
2
0
0
0
1
2
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
6
2
1
0
0
0
0
0
0
2
1
3
2
0
2
0
0
1
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
1
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
2
2
1
0
1
0
0
2
0
0
0
0
1
0
0
2
1
1
1
0
1
0
0
2
1
0
0
0
0
0
0
0
0
3
0
2
0
0
0
1
1
0
0
1
0
2
0
0
0
0
0
1
0
0
2
0
1
0
0
0
2
1
0
0
0
1
1
0
0
0
0
0
0
2
0
2
0
2
0
0
0
2
0
0
0
2
0
0
0
0
3
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
1
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
1
0
1
2
0
0
0
0
0
1
1
0
1
0
2
0
2
0
0
0
1
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
3
0
2
0
0
1
0
2
0
1
0
1
2
0
0
0
0
0
0
0
1
2
1
0
1
2
0
0
0
0
1
0
0
0
2
0
1
0
2
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
1
0
1
0
1
0
0
0
0
2
0
2
2
0
2
2
0
2
1
0
2
1
0
0
0
0
0
2
0
0
1
0
0
0
0
3
2
0
1
0
0
0
0
2
0
0
2
1
1
0
0
0
0
0
0
0
1
2
0
2
2
0
1
0
2
0
0
0
0
0
4
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
1
2
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
2
0
0
2
2
1
0
0
1
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
2
0
0
0
0
1
0
1
1
3
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
2
0
1
0
2
0
1
0
0
0
2
0
0
0
0
1
0
0
0
1
0
2
2
3
0
1
1
2
1
0
2
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
1
2
0
0
1
1
0
1
0
3
0
0
0
0
0
2
0
1
2
1
0
0
0
0
1
2
0
0
0
1
2
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
3
1
0
0
2
0
0
0
2
0
3
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
3
0
0
0
0
0
0
0
0
1
2
0
0
2
1
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
2
0
0
0
0
2
0
2
0
1
0
2
0
0
1
0
2
1
0
0
0
0
0
0
2
0
0
1
0
1
2
1
0
1
1
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
1
2
0
0
1
0
0
0
2
0
2
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
2
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
1
0
2
1
0
2
0
0
2
2
0
1
3
0
0
0
0
0
0
0
1
0
0
2
1
0
0
2
0
0
1
1
3
0
2
1
2
1
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
1
3
0
0
1
2
0
0
0
0
1
0
0
0
1
2
2
0
0
0
0
0
0
0
3
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
2
1
3
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
1
0
2
0
2
0
0
0
0
1
0
0
0
0
3
0
0
1
0
0
0
2
0
2
0
0
0
0
2
2
2
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
2
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
2
0
0
1
2
2
2
2
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
1
2
0
1
0
1
0
0
1
1
1
0
0
0
2
0
2
2
2
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
2
1
0
0
0
3
0
3
0
2
0
2
0
0
0
0
0
0
1
2
0
0
0
7
0
0
1
1
0
0
2
0
0
0
0
0
1
2
0
3
1
0
0
0
1
0
0
1
1
1
0
0
1
0
0
0
2
1
2
1
2
0
2
0
1
0
0
2
0
0
2
0
1
1
0
0
0
0
2
1
5
0
0
0
1
0
0
1
0
2
0
1
1
1
0
1
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
2
0
1
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
1
2
0
0
0
1
0
0
2
0
2
0
0
0
1
0
0
1
0
0
0
0
0
1
0
2
1
1
0
0
1
0
0
2
1
2
2
0
0
0
0
2
0
2
0
1
2
2
0
0
0
1
0
0
2
1
0
1
0
0
0
0
2
2
1
2
1
2
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
2
0
4
0
0
2
2
0
2
0
0
0
0
0
2
2
2
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
1
1
0
0
1
1
0
0
2
1
1
0
0
0
0
1
0
2
0
1
0
0
1
1
1
0
0
2
0
0
0
1
0
2
0
0
0
3
0
1
2
0
0
0
0
0
2
3
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
2
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
2
2
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
2
0
0
0
2
2
1
2
1
0
2
1
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
6
2
1
2
0
1
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
1
1
0
0
2
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
1
0
2
0
0
0
0
1
0
0
2
2
0
0
1
1
0
3
1
0
2
2
3
1
0
0
0
0
0
1
0
0
2
3
2
0
0
0
0
0
0
0
0
1
0
2
0
3
0
2
2
0
0
0
1
0
0
1
0
6
0
1
1
0
1
2
2
0
1
0
0
0
3
1
0
0
0
0
0
1
2
0
1
0
0
1
1
1
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
1
2
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
3
1
2
0
1
2
0
0
0
0
0
0
2
2
0
1
0
3
0
0
0
0
0
3
0
0
2
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
1
1
0
0
0
0
1
0
0
0
3
0
2
1
0
0
0
0
0
0
2
0
0
1
0
0
0
1
1
3
0
1
0
3
0
0
0
0
0
2
0
1
0
1
1
0
1
0
0
2
0
0
0
0
0
4
0
0
0
0
1
0
0
2
0
0
1
0
0
0
1
0
1
0
1
2
0
0
1
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
1
2
0
0
0
1
2
0
1
0
0
1
0
0
1
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
2
0
0
2
0
0
3
0
0
0
2
0
2
0
0
0
1
1
2
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
2
0
0
3
0
0
0
4
0
2
2
0
0
0
3
1
0
1
1
0
0
0
0
1
2
0
0
0
0
1
0
0
3
0
0
0
0
0
2
1
2
2
1
0
1
1
2
0
1
2
0
0
1
0
0
2
2
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
2
0
2
0
0
0
0
2
1
0
2
1
0
0
0
1
0
0
2
0
0
0
0
1
2
0
0
0
1
0
1
0
0
2
1
0
0
0
0
0
0
3
1
0
1
0
2
2
0
0
0
1
0
0
0
2
1
0
0
0
1
2
2
0
1
0
0
2
2
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
2
1
0
0
0
0
1
1
0
0
0
0
2
1
0
2
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
1
0
0
0
0
0
0
1
0
0
1
0
0
2
0
1
0
2
0
0
0
0
0
0
2
0
0
4
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
1
5
3
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
2
1
0
0
0
2
0
1
0
2
0
2
0
0
0
0
0
0
0
1
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
1
0
0
0
2
0
6
0
0
0
3
0
2
0
1
0
0
0
0
0
0
0
1
0
1
2
0
0
2
0
0
0
0
0
1
0
0
2
1
0
0
1
0
0
0
0
0
1
0
1
0
1
1
0
2
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
3
0
1
1
1
2
0
0
0
0
0
0
0
0
2
3
1
0
0
0
2
1
1
1
2
0
0
0
1
3
2
0
3
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
1
0
2
3
0
2
1
3
0
0
0
0
0
2
1
0
0
0
0
1
0
1
0
0
0
0
0
1
1
1
1
0
0
1
0
0
2
2
0
0
1
1
1
1
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
1
0
0
1
0
0
2
0
0
0
1
0
0
1
1
1
0
0
2
0
0
5
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
2
0
3
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
1
0
1
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
2
0
2
2
0
2
1
2
1
1
0
0
2
2
2
2
1
1
0
1
0
0
0
0
2
1
2
0
0
1
0
0
0
0
0
0
1
0
0
0
3
1
2
0
1
1
0
0
2
2
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
1
2
0
0
0
0
1
1
0
1
2
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
2
1
0
0
0
0
0
1
1
0
0
0
0
2
0
2
0
2
0
1
0
0
0
2
0
1
0
0
2
2
0
1
0
0
3
0
0
0
0
1
1
0
1
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
4
0
0
0
1
0
0
2
0
0
1
1
2
2
0
0
0
0
1
2
2
1
0
0
2
0
2
0
0
2
0
1
1
0
1
0
0
3
0
0
0
2
2
0
2
0
3
0
0
0
0
2
0
0
0
2
0
0
0
1
1
0
0
0
0
2
3
0
0
0
2
1
0
1
0
0
1
1
0
2
0
0
0
0
0
2
0
2
1
0
0
2
1
0
0
0
0
0
0
2
0
0
0
4
1
1
0
0
0
0
1
1
2
1
0
1
0
2
1
1
0
1
0
0
0
0
0
2
2
0
0
0
2
1
0
0
0
0
3
2
1
1
0
0
0
2
1
0
0
0
1
0
0
0
0
0
2
0
1
1
1
0
0
2
0
0
4
0
1
2
0
0
0
0
0
0
1
0
2
1
0
2
0
0
0
0
2
3
0
2
0
1
2
1
0
0
0
1
2
0
0
2
0
0
0
2
0
1
0
1
2
0
0
1
0
0
0
3
0
0
0
0
2
0
0
2
0
0
0
0
2
2
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
2
0
0
2
1
0
2
0
0
1
0
1
0
1
0
0
0
1
0
0
2
0
0
0
1
0
2
0
0
1
1
2
0
2
1
0
0
1
0
0
0
1
0
3
1
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
1
1
1
0
2
0
0
0
0
0
2
0
1
1
0
1
2
0
0
1
0
0
1
1
0
1
0
2
1
0
0
0
0
0
2
0
0
0
1
0
2
2
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
2
2
2
0
0
2
1
0
1
1
0
0
2
2
1
0
0
0
0
0
2
0
0
2
0
3
2
0
0
1
1
0
0
0
0
0
2
0
1
0
1
2
0
0
2
2
2
1
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
4
0
0
0
0
1
0
3
0
0
1
0
1
0
1
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
8
2
0
3
2
0
2
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
3
0
0
1
0
1
3
2
2
2
0
0
1
0
1
0
0
0
2
3
0
0
0
0
2
0
0
0
0
0
2
0
2
1
1
1
0
5
0
1
0
0
0
2
0
2
1
1
0
2
0
0
0
2
2
0
1
0
0
0
1
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
2
2
0
2
0
0
4
0
1
0
2
1
0
1
0
0
0
0
0
0
2
1
0
0
3
0
0
2
0
0
0
2
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
1
0
1
0
0
0
0
2
0
1
2
3
0
1
0
0
2
0
0
1
1
0
1
0
2
0
1
1
2
0
0
1
2
0
0
2
2
1
1
0
2
0
2
3
0
0
2
2
1
2
0
0
0
0
0
0
2
0
2
0
0
2
1
0
0
2
0
2
1
1
0
0
0
2
0
0
2
0
0
0
1
1
0
0
1
2
2
3
0
0
2
0
0
2
0
0
0
0
1
2
0
1
0
0
2
2
0
0
2
4
0
0
2
1
2
1
0
2
2
1
2
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
2
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
2
1
0
0
1
2
2
1
0
2
0
0
0
2
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
2
2
1
0
1
0
0
1
2
0
0
0
0
0
0
2
2
2
0
0
1
0
0
5
0
0
2
0
1
1
0
0
0
1
1
0
1
2
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
1
0
2
0
0
2
0
2
2
0
2
0
0
0
0
0
0
1
0
0
1
2
1
2
1
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
1
0
0
1
1
0
2
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
2
1
1
0
0
0
0
2
2
0
3
1
0
0
0
0
2
0
2
0
1
0
0
0
0
2
0
0
0
0
2
0
0
2
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
1
0
2
0
0
1
0
0
1
1
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
2
0
0
3
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
2
1
1
2
1
2
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
5
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
1
0
2
2
0
1
2
0
0
0
1
1
0
2
1
0
0
0
0
0
0
0
1
0
0
2
0
0
1
2
0
0
0
3
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
1
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
1
0
0
3
0
0
0
0
1
0
2
0
0
0
1
0
0
2
0
2
2
0
3
0
0
2
0
0
1
0
1
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
2
0
2
0
0
1
0
0
0
2
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
1
1
0
1
0
0
0
2
1
0
1
0
1
0
0
0
0
0
0
0
1
2
0
1
0
0
0
1
0
1
0
0
0
2
2
1
0
0
0
0
1
1
0
0
2
0
1
0
0
0
2
0
0
0
0
0
2
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
1
2
2
1
0
0
0
0
0
0
2
0
0
1
0
0
2
2
2
2
0
0
1
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
1
0
1
1
0
1
0
0
0
1
1
2
1
0
2
0
2
1
0
0
0
0
1
0
0
0
2
0
0
2
0
0
2
0
0
0
0
2
2
2
1
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
2
0
0
0
1
0
0
1
1
1
0
0
0
1
0
0
0
0
1
0
1
0
2
0
2
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
3
2
1
2
2
3
0
0
3
0
1
0
0
0
0
2
0
0
2
0
0
0
1
0
0
2
1
0
0
1
1
1
1
2
1
0
1
2
0
0
0
0
0
0
1
0
2
0
1
0
2
1
0
0
2
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
1
0
0
0
2
0
0
2
0
0
2
1
1
0
0
0
0
2
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
2
2
0
1
0
2
0
0
0
0
0
0
1
0
1
1
2
2
0
2
0
3
0
1
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
3
0
2
0
0
0
0
3
3
1
0
0
0
0
1
0
0
0
2
0
0
1
1
2
2
1
0
0
1
2
2
0
0
1
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
2
0
1
2
0
0
0
1
0
0
0
1
2
0
2
1
0
0
0
0
1
0
2
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
2
1
1
0
1
1
1
1
0
1
1
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
2
0
2
1
3
1
0
0
0
0
2
0
2
0
1
0
0
1
0
2
1
0
0
0
1
0
2
0
0
0
5
1
0
0
2
0
0
0
0
1
0
0
2
0
2
1
0
1
0
0
0
2
0
0
1
2
2
0
0
1
2
0
0
1
2
0
0
2
0
0
0
0
0
1
0
1
0
0
2
0
2
0
0
0
0
0
0
2
1
0
0
2
0
2
0
0
0
0
0
1
1
1
2
0
1
1
2
2
0
2
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
2
0
2
0
2
0
0
0
0
0
0
2
0
0
1
0
2
3
0
3
0
1
0
0
1
0
2
0
1
0
1
0
0
2
0
2
2
1
0
0
0
0
0
2
0
1
5
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
2
0
2
1
1
1
0
0
1
2
0
2
0
0
5
0
0
1
0
0
2
2
0
0
1
2
1
1
0
0
2
0
0
0
3
2
0
1
0
0
0
0
0
1
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
1
0
1
0
2
0
0
0
1
0
0
2
2
2
1
0
0
1
3
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
1
1
0
2
0
0
1
0
0
0
0
0
0
2
1
0
2
0
2
0
1
1
0
0
2
2
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
2
0
0
0
0
2
0
0
0
1
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
2
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
2
0
1
5
2
1
0
0
2
0
1
2
2
0
1
0
2
2
0
0
0
0
0
2
3
0
0
1
0
0
1
2
0
0
0
2
0
0
1
0
0
2
0
0
1
1
1
0
0
1
1
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
5
1
0
0
3
1
2
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
2
0
0
2
0
2
1
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
1
0
1
0
0
0
0
0
0
2
0
1
0
0
2
0
1
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
2
3
1
0
0
3
0
2
0
2
0
0
0
0
0
0
1
0
2
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
2
0
0
0
1
0
2
0
0
2
1
0
1
0
0
0
0
0
2
0
0
1
0
0
1
0
1
0
1
1
1
0
1
1
0
0
0
1
2
0
0
0
2
0
1
10
0
1
0
3
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
2
0
0
1
2
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
5
0
0
0
2
0
0
0
0
0
2
0
3
2
0
0
0
0
0
0
0
1
0
3
2
0
2
3
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
3
1
0
3
0
1
2
0
0
0
2
0
0
1
2
0
0
0
1
0
0
0
1
0
0
0
1
1
2
0
2
0
0
0
0
0
0
2
1
0
0
1
0
1
0
0
0
1
1
4
1
0
1
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
2
0
0
1
1
1
0
0
0
3
0
0
0
0
2
0
2
0
0
0
2
0
0
0
1
0
0
0
2
2
0
0
0
0
1
1
0
1
0
0
2
0
2
0
0
2
0
0
0
1
3
1
0
1
0
0
0
0
0
2
2
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
2
1
0
0
1
3
1
0
0
0
0
1
2
2
0
0
0
0
2
0
0
0
0
2
0
0
7
2
1
0
1
0
1
0
1
2
1
1
0
2
0
2
0
1
2
0
0
0
0
0
1
0
0
2
0
0
1
0
2
0
2
0
0
2
1
0
0
2
0
0
0
2
0
1
0
2
2
2
1
0
0
0
0
0
0
2
0
0
0
1
0
2
1
2
1
7
2
0
1
0
0
0
2
0
0
1
1
0
2
2
2
0
0
0
0
0
2
0
0
2
2
1
0
1
0
0
0
2
0
2
0
1
2
0
1
2
0
0
2
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
3
0
0
0
0
0
1
3
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
3
0
0
0
0
0
1
0
1
1
0
0
0
2
1
1
2
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
1
0
1
2
0
2
0
1
0
2
1
0
0
0
0
1
0
2
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
1
0
0
0
0
2
0
0
0
0
0
1
2
0
2
1
0
0
0
0
2
0
0
1
0
1
0
0
2
0
1
0
0
0
1
0
0
1
0
2
2
1
2
0
1
0
0
0
0
0
0
0
0
0
3
2
1
0
3
0
0
0
2
1
0
2
1
1
0
1
0
0
1
0
2
0
2
1
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
1
1
0
1
2
1
0
2
2
0
0
2
0
0
2
2
0
0
0
0
3
1
0
3
0
2
0
0
2
0
2
1
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
1
0
0
1
1
1
1
0
2
0
0
2
0
1
0
2
0
0
0
0
1
2
0
0
1
2
2
0
0
1
2
0
0
0
1
1
0
2
2
0
0
1
0
1
0
2
0
0
1
2
0
0
1
0
2
0
1
0
0
4
0
2
1
2
0
2
2
0
0
3
1
0
3
0
6
1
0
2
0
0
0
0
0
1
1
1
2
0
2
0
0
0
1
2
2
0
0
0
0
2
0
2
2
0
0
2
0
1
0
0
0
2
0
1
1
2
1
1
1
0
0
0
0
0
2
0
0
1
1
2
0
0
1
1
0
1
0
0
1
0
1
3
1
2
0
2
2
1
0
0
0
0
0
0
2
0
0
0
1
0
1
1
0
0
1
2
0
3
1
0
2
0
0
0
0
2
0
2
0
2
0
0
1
0
0
0
0
1
1
2
0
2
0
0
0
0
0
1
2
0
0
0
0
0
1
0
1
1
2
1
0
1
0
0
0
1
4
2
3
0
0
0
2
0
2
2
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
2
1
1
0
2
0
0
2
1
0
0
0
0
0
2
1
2
0
2
0
0
1
0
1
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
3
0
0
2
1
0
0
0
2
0
1
2
0
1
0
0
2
1
2
0
0
0
0
1
1
0
1
1
0
2
0
0
0
0
1
1
0
0
0
2
0
2
0
0
0
4
2
0
1
0
0
2
2
2
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
1
1
0
0
0
0
0
1
2
0
0
2
2
0
2
0
0
0
1
0
2
0
1
1
2
0
2
1
0
0
2
1
2
0
1
1
0
2
0
1
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
2
0
1
0
0
0
2
1
0
0
2
2
4
0
0
0
2
0
0
0
1
0
1
0
0
0
0
1
2
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
3
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
1
1
2
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
3
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
1
1
2
0
1
0
5
1
0
2
1
3
0
0
0
2
0
1
0
0
0
0
1
0
2
0
1
0
1
0
2
0
2
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
1
0
0
0
1
2
0
1
0
2
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
2
1
1
0
0
7
1
2
1
0
0
0
2
0
2
0
0
0
1
1
0
2
0
0
0
2
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
4
2
2
0
0
0
0
0
2
0
0
1
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
3
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
1
0
2
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
1
2
0
2
1
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
1
0
0
0
0
0
2
1
0
0
0
1
3
1
0
2
1
0
0
1
2
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
1
0
0
0
4
1
1
1
0
1
0
0
1
2
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
2
0
2
1
0
0
0
1
2
3
0
0
0
0
0
0
1
1
0
1
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
1
1
2
0
0
2
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
2
2
1
0
0
0
0
1
0
0
1
0
1
2
1
0
2
2
1
1
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
3
0
1
2
2
0
1
0
1
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
1
0
1
2
0
2
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
1
0
0
0
0
1
2
2
0
0
3
2
0
2
0
6
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
1
2
0
1
2
1
1
0
0
2
0
0
0
2
2
0
0
0
0
1
0
0
0
0
1
2
0
0
0
1
0
0
0
2
2
1
0
0
0
0
1
0
2
0
1
1
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
1
0
2
1
1
1
2
2
2
3
0
2
2
3
2
0
0
0
0
2
2
0
0
1
0
2
0
0
0
2
2
0
2
0
0
0
0
0
0
1
0
2
2
2
0
0
0
1
0
0
2
0
0
0
0
2
0
2
1
2
0
1
0
0
0
2
0
0
0
0
1
0
0
0
1
0
1
0
0
5
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
2
0
3
0
1
1
2
0
1
0
2
1
0
0
2
1
0
2
3
2
0
0
0
0
2
0
0
0
1
2
1
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
1
2
0
1
0
1
2
1
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
2
0
0
0
0
2
1
0
0
1
0
1
0
0
0
0
2
1
1
2
0
2
1
0
0
0
0
1
0
3
0
0
3
0
0
0
0
0
1
1
2
3
0
0
1
2
2
1
0
1
0
2
1
1
0
2
0
1
0
1
0
0
0
0
0
0
0
2
2
0
0
1
1
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
1
2
0
1
0
0
0
0
2
0
2
0
1
2
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
1
0
0
2
0
0
2
2
0
0
2
1
0
1
1
0
1
2
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
4
0
1
1
0
0
1
0
2
1
0
0
3
0
1
2
2
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
1
0
1
0
0
2
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
9
0
0
0
0
2
0
0
0
2
0
2
0
0
1
0
0
2
2
0
0
2
0
0
0
1
0
0
2
1
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
7
0
1
1
0
2
0
1
3
4
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
2
1
0
1
0
0
2
1
2
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
2
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
2
2
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
1
0
1
0
3
0
0
0
2
0
3
0
0
0
0
2
0
0
0
0
2
0
1
0
0
1
0
0
0
1
0
0
2
1
0
3
3
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
1
0
0
2
0
0
2
2
0
2
0
0
0
0
1
1
1
1
3
0
0
0
0
1
1
0
0
0
0
1
2
0
0
1
1
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
1
0
0
1
1
0
1
0
2
2
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
1
1
0
2
0
0
0
1
2
2
1
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
2
0
0
0
1
2
1
0
0
1
2
2
0
1
0
0
0
1
0
0
0
6
0
0
0
0
5
2
0
0
2
1
0
1
2
2
0
0
1
0
1
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
1
2
0
0
2
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
3
1
1
1
0
0
0
2
2
0
0
0
0
2
0
0
2
3
1
0
0
0
1
0
3
0
0
0
1
2
0
0
1
0
0
0
0
0
1
0
0
0
1
0
2
0
0
1
0
0
0
1
0
1
2
1
1
0
1
0
2
0
0
2
0
0
0
0
0
0
2
0
0
1
1
2
0
0
1
1
0
2
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
2
2
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
2
1
1
1
1
0
0
1
0
0
0
0
0
2
2
1
0
2
0
0
2
0
0
0
1
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
2
1
0
0
2
0
2
1
0
0
0
2
0
0
0
2
2
0
0
1
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
1
0
1
1
0
0
0
0
0
0
1
0
1
0
0
2
2
0
0
1
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
2
2
2
0
3
0
2
0
1
3
1
1
0
0
2
0
1
1
0
0
1
2
2
0
3
0
0
0
2
2
0
0
0
0
1
1
1
0
2
0
0
1
1
2
1
0
0
0
1
0
1
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
4
2
0
0
0
0
0
2
1
0
0
1
0
0
4
0
1
1
2
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
2
1
2
0
0
0
1
0
3
1
1
1
0
2
1
1
0
0
2
1
0
0
0
2
0
1
0
0
2
0
1
0
0
1
0
2
0
0
0
0
2
0
2
0
0
0
0
1
0
0
1
0
2
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
1
0
0
0
2
1
0
0
0
0
0
0
0
2
0
2
0
1
0
3
0
0
0
0
0
1
1
0
0
1
1
1
2
0
0
1
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
9
2
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
2
2
0
0
2
2
2
0
0
2
1
2
0
1
1
0
0
1
1
0
0
3
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
2
0
1
0
2
0
2
0
0
2
2
1
0
0
1
2
3
0
0
0
5
0
0
0
0
0
0
0
2
2
0
0
0
2
1
0
2
0
2
2
2
0
0
2
2
2
0
1
0
0
2
2
0
2
0
0
1
2
1
0
1
1
0
0
1
0
0
2
0
2
0
0
0
3
1
0
0
0
2
0
1
2
0
0
0
0
0
0
2
0
0
4
0
2
0
0
0
1
0
2
0
0
2
0
0
1
0
0
1
2
0
0
0
4
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
3
0
0
2
0
0
0
0
0
1
0
1
0
0
2
2
1
0
0
1
1
0
0
1
0
0
1
2
2
0
1
2
2
0
2
0
0
0
0
1
3
0
0
0
3
0
0
0
0
2
0
0
0
0
0
1
0
1
1
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
2
0
0
2
0
1
1
1
2
0
2
1
0
0
0
0
0
0
4
0
0
1
0
1
0
1
0
0
2
0
0
0
0
0
1
1
0
0
2
2
2
0
1
0
0
0
0
3
1
0
0
0
0
2
2
2
1
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
2
1
0
0
2
2
0
1
0
0
0
0
1
0
2
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
2
0
0
1
0
2
0
2
0
0
0
2
0
0
1
0
1
2
0
2
2
1
1
0
1
1
0
0
0
0
0
1
1
2
2
0
0
0
0
0
1
0
2
0
0
0
0
3
0
1
0
2
2
0
0
1
0
2
0
2
1
0
2
0
0
2
0
2
1
3
1
0
0
0
1
0
0
0
0
0
1
3
0
2
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
2
1
2
3
0
0
2
1
0
0
0
1
2
0
1
2
1
1
1
0
1
2
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
1
1
0
0
2
0
1
0
0
2
2
0
0
0
0
1
0
0
0
2
2
2
2
0
0
1
1
1
2
1
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
4
0
0
2
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
3
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
1
0
1
0
0
0
3
1
0
0
0
0
1
0
0
1
1
0
0
1
0
0
2
2
0
1
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
3
0
0
0
2
0
1
0
0
0
2
0
0
3
0
1
0
0
0
1
0
0
1
2
0
0
0
0
0
4
0
0
0
1
0
2
1
2
0
1
2
2
4
0
0
2
0
0
3
0
1
0
2
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
1
1
0
0
0
1
1
0
2
0
2
0
1
1
2
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
2
2
0
2
0
0
0
0
2
0
1
1
3
0
0
1
2
0
0
1
0
2
2
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
3
0
3
0
0
1
4
0
0
1
2
1
0
1
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
1
2
0
0
0
1
2
1
0
0
2
0
0
3
1
1
0
0
0
1
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
2
2
2
0
0
0
1
1
0
3
2
2
0
1
0
0
2
0
0
1
1
0
2
0
0
0
1
0
2
3
2
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
2
0
2
2
0
0
5
0
1
0
0
0
0
0
0
0
0
0
0
3
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
2
2
1
1
0
2
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
1
0
0
1
1
2
0
0
4
1
1
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
3
1
1
0
0
0
0
2
2
4
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
1
0
0
0
1
3
0
2
0
0
0
1
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
3
1
0
2
0
2
0
1
0
1
0
0
1
2
0
2
1
0
7
2
2
0
2
0
0
3
0
0
0
1
0
2
2
1
1
0
1
0
0
2
0
0
0
0
0
1
1
0
1
0
0
0
3
0
2
0
0
0
2
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
2
1
2
1
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
2
0
1
0
2
1
1
0
0
2
0
1
2
0
0
1
0
0
0
0
0
3
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
2
0
0
0
0
2
0
2
1
0
0
1
2
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
2
2
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
2
0
0
1
1
0
0
0
0
0
1
0
1
1
1
1
3
0
0
0
2
0
0
2
0
2
2
0
0
0
1
1
0
1
0
0
0
2
3
0
1
0
0
0
0
1
1
0
0
1
2
1
2
0
0
0
1
2
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
5
0
2
0
2
0
0
2
1
1
0
0
2
0
0
2
1
1
0
0
2
2
0
0
0
0
0
0
0
1
1
2
0
0
2
0
3
0
0
0
1
1
0
0
2
0
0
0
0
0
1
2
0
0
0
2
0
0
0
2
0
1
0
0
0
2
1
1
0
0
0
1
0
0
0
1
1
0
0
0
1
1
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
6
0
2
0
0
0
2
0
0
1
0
0
0
0
2
1
1
2
2
1
1
2
0
0
1
0
0
0
0
0
2
0
2
0
0
2
2
0
0
0
1
0
1
2
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
2
0
0
0
2
0
0
0
0
2
0
2
3
0
2
0
0
2
1
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
2
0
0
1
2
0
0
2
1
1
0
2
0
2
2
0
0
0
0
0
0
1
0
0
3
0
2
0
0
0
0
2
0
0
0
2
1
3
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
1
2
1
0
0
0
1
0
0
0
0
0
1
0
2
1
0
0
3
2
0
0
2
0
2
2
1
0
1
0
0
0
0
0
3
0
0
0
1
0
1
0
2
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
1
0
2
2
0
0
0
0
2
0
0
0
1
1
0
1
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
1
0
3
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
2
0
1
0
2
2
0
1
0
0
2
2
1
1
1
0
0
2
0
2
0
1
1
0
0
0
1
1
0
0
0
0
0
1
3
2
0
0
1
0
2
1
0
1
0
1
2
0
0
1
0
1
2
0
2
1
0
0
0
1
0
1
1
2
0
0
1
0
0
1
0
2
2
0
1
0
0
1
0
0
0
2
0
0
2
0
0
0
1
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
2
1
0
0
1
0
0
0
2
0
2
0
0
0
1
2
0
3
0
0
2
0
2
2
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
1
2
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
1
1
1
0
0
0
0
1
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
2
2
3
0
2
0
2
0
1
0
2
1
2
2
0
1
0
0
0
0
0
0
0
0
0
0
3
1
0
0
2
0
0
0
0
0
2
2
2
2
0
0
0
1
0
1
2
2
2
0
0
0
2
0
0
0
0
0
2
0
1
1
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
1
3
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
2
0
1
1
0
2
0
1
2
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
1
0
1
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
4
0
1
1
0
2
7
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
1
0
0
0
0
0
1
3
0
0
0
1
1
0
2
0
2
0
1
0
1
1
0
0
1
0
1
1
0
2
2
1
0
0
0
0
2
0
0
2
0
1
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
2
0
0
0
1
0
0
1
2
0
0
0
0
2
2
0
2
1
0
0
2
1
0
0
4
1
0
0
2
0
0
0
1
0
2
1
0
2
1
2
0
0
3
0
1
0
3
2
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
3
0
0
1
2
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
2
1
0
0
1
1
0
2
0
0
1
2
1
0
0
1
0
0
2
2
0
0
1
1
0
0
0
0
2
2
0
0
1
0
0
0
1
1
1
1
0
0
0
4
1
0
0
2
1
0
1
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
2
0
0
0
0
0
0
3
1
2
0
4
0
0
0
1
0
0
0
2
1
0
0
2
0
0
1
0
0
0
0
0
1
0
0
2
1
1
0
3
0
2
0
0
2
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
2
0
1
0
2
0
0
0
2
1
2
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
1
0
2
0
0
0
2
0
0
0
2
0
1
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
3
0
1
1
0
1
0
2
0
1
2
1
0
1
0
0
0
5
1
0
0
2
0
0
2
4
0
0
1
0
1
0
0
0
0
0
0
0
2
1
0
2
1
0
0
3
0
0
0
0
0
0
1
0
0
0
1
2
0
2
0
0
0
1
0
1
0
0
1
0
0
4
2
0
1
0
2
2
1
0
0
0
0
1
1
0
3
0
0
2
1
0
1
0
0
1
0
3
0
0
0
0
2
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
2
1
0
1
1
2
1
0
0
0
0
0
0
0
2
2
2
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
1
2
0
1
0
4
0
1
0
0
0
0
0
0
2
2
0
0
0
1
2
0
1
1
0
1
2
0
0
1
0
0
2
0
0
2
0
1
1
0
0
2
0
2
2
0
0
0
0
2
0
0
0
0
0
0
1
1
1
0
0
0
1
1
0
0
1
2
0
2
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
2
0
1
0
1
0
0
2
0
0
0
0
0
0
2
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
2
2
0
0
0
2
1
0
1
0
0
0
0
0
1
0
2
0
0
2
0
0
0
1
1
0
0
0
0
0
1
0
0
3
0
0
0
0
1
0
3
3
2
1
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
2
0
5
3
1
0
2
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
1
0
0
1
2
2
0
0
0
3
1
1
0
3
0
0
1
1
0
2
2
2
0
0
1
0
1
0
0
0
0
0
0
0
0
2
1
2
2
0
1
0
0
0
2
1
2
0
2
0
0
0
0
2
0
0
1
1
0
1
0
0
0
0
1
2
1
0
0
0
0
0
0
2
1
0
1
0
0
0
0
1
1
1
0
0
0
0
0
2
0
0
0
0
0
0
1
1
2
2
0
0
0
0
0
0
3
0
0
2
1
0
1
2
0
1
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
2
2
0
2
1
0
1
3
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
3
1
2
0
0
1
0
2
0
0
0
2
0
1
0
0
1
0
1
1
0
0
2
0
1
0
1
0
0
0
0
1
0
0
2
0
0
1
2
0
1
0
0
2
0
0
0
0
2
2
0
1
1
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
1
0
2
2
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
1
1
1
0
1
0
2
0
2
1
0
0
1
1
0
0
0
2
1
1
0
0
1
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
1
0
2
0
2
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
2
2
0
1
0
0
0
0
0
0
0
2
1
0
0
2
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
5
0
0
0
0
1
0
0
0
0
0
1
0
2
1
0
0
1
1
1
0
2
2
1
0
1
2
1
0
0
1
2
0
2
2
5
0
0
0
0
2
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
1
0
0
2
2
1
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
3
2
2
0
0
3
1
1
0
0
2
0
1
0
0
1
0
2
2
0
0
0
0
1
0
0
1
0
1
1
0
0
0
1
2
2
0
0
1
1
0
0
0
0
0
0
0
2
0
0
2
2
2
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
2
0
0
0
1
1
0
2
0
0
1
0
0
0
2
1
0
1
0
0
1
0
0
0
0
1
0
0
2
0
3
2
0
2
1
2
2
0
0
0
1
0
2
3
0
0
0
1
0
0
2
1
0
2
1
1
0
0
0
0
0
1
0
2
2
1
1
1
0
0
0
0
0
1
2
0
1
1
0
0
0
0
0
2
0
2
1
0
0
1
4
0
1
0
0
0
0
0
0
1
2
0
1
1
0
0
0
1
0
0
0
2
1
0
2
3
0
1
0
3
0
0
0
1
1
0
1
7
1
0
0
0
2
2
2
0
2
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
3
2
0
2
0
0
1
0
2
3
0
0
0
0
0
1
0
1
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
2
3
0
0
0
0
2
0
0
2
0
0
2
2
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
2
1
2
0
0
2
2
0
0
0
0
3
0
2
1
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
3
2
2
1
1
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
2
0
0
0
0
0
0
1
0
0
2
0
0
1
2
0
0
2
0
0
0
0
0
0
0
1
1
2
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
2
0
0
0
0
0
0
1
2
0
1
2
0
2
0
0
0
2
1
1
1
0
1
0
0
2
0
0
0
0
1
2
1
0
0
2
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
1
2
2
4
0
0
0
0
0
2
0
1
0
0
2
0
1
0
2
0
0
0
0
0
0
2
3
1
0
0
0
0
1
2
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
1
0
1
1
0
2
2
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
1
1
0
0
1
1
0
1
3
0
0
0
0
1
1
0
2
0
0
1
0
0
0
0
0
1
0
2
1
2
0
0
0
0
2
0
0
1
0
5
0
0
2
0
1
0
0
0
0
2
2
0
0
1
0
1
0
0
0
2
0
0
0
0
0
2
4
0
0
3
0
0
1
0
0
2
0
0
0
2
0
0
0
6
0
0
0
2
0
0
0
0
0
2
3
2
2
0
0
0
0
1
0
2
2
2
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
1
0
1
0
2
1
0
0
0
1
0
0
0
0
1
1
1
0
0
1
1
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
2
0
0
3
0
2
2
0
0
0
0
2
2
0
0
0
0
1
0
1
0
1
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
2
1
2
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
1
2
1
2
0
0
1
0
0
0
2
0
1
0
0
1
0
2
0
1
1
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
2
0
0
1
1
0
0
1
1
0
1
0
2
2
0
1
0
0
1
0
0
0
0
0
2
2
3
0
0
0
1
1
0
0
2
1
0
0
0
0
2
0
0
2
1
0
0
0
0
5
0
2
0
0
0
0
0
0
2
2
1
1
0
0
0
0
0
0
1
1
0
0
1
2
0
0
0
0
5
0
0
0
2
0
0
0
2
0
1
2
1
2
0
1
1
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
2
2
3
0
0
0
0
0
0
1
0
2
0
0
0
0
1
1
0
2
0
0
2
2
0
0
2
2
0
2
2
4
1
0
0
0
1
0
0
2
1
0
2
0
1
1
2
0
0
2
0
1
0
0
1
0
0
2
0
0
1
0
4
1
0
0
0
0
0
0
1
2
2
0
2
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
1
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
2
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
2
1
0
0
1
0
0
2
0
1
0
1
3
0
0
0
0
0
0
2
2
1
0
2
0
0
0
0
2
0
2
0
2
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
4
0
2
0
0
2
0
0
2
2
1
0
2
1
0
1
0
2
0
1
1
0
0
2
0
0
0
0
0
0
0
1
2
1
0
0
0
0
2
0
0
0
2
0
2
3
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
3
1
0
0
0
0
2
1
1
0
2
0
4
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
2
2
3
2
0
2
1
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
1
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
2
2
1
0
0
2
2
2
0
0
2
0
0
1
1
0
0
2
0
3
1
1
2
1
0
0
2
2
0
0
1
0
0
0
2
1
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
1
1
0
0
0
0
0
1
0
0
2
1
1
1
2
0
0
1
0
2
0
1
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
2
0
0
0
4
0
0
2
0
0
2
1
0
1
0
0
1
2
0
1
0
0
0
0
0
1
3
3
1
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
2
2
0
0
1
0
0
2
0
2
0
0
0
2
0
1
1
0
0
2
0
0
0
1
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
2
2
1
0
0
2
0
0
1
0
0
0
0
0
0
2
1
4
1
1
1
0
0
0
0
3
0
0
1
1
0
2
1
1
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
1
3
2
1
2
0
0
2
2
0
0
1
2
0
2
1
0
1
0
0
2
1
0
0
1
0
1
0
2
0
1
0
0
1
0
0
1
1
0
0
1
0
1
0
2
2
0
1
1
3
1
2
0
1
1
0
0
0
0
3
1
1
0
0
0
3
0
0
0
2
3
1
2
0
0
3
0
0
1
2
0
0
1
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
1
1
0
1
2
0
0
0
2
0
1
0
0
0
0
0
0
1
1
0
0
2
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
1
2
2
0
2
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
2
2
0
1
0
2
0
1
0
0
0
1
2
0
2
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
2
2
0
0
0
0
1
2
2
2
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
3
0
1
1
0
1
1
0
0
3
0
0
0
0
3
0
0
2
0
2
2
0
0
0
1
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
2
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
1
1
0
2
1
0
0
0
1
2
0
1
0
1
1
1
0
0
1
2
2
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
1
3
0
0
1
0
0
1
0
0
1
1
0
2
0
0
0
0
1
0
1
0
0
1
0
1
0
1
3
2
0
1
0
0
2
0
0
0
0
1
2
0
2
0
0
0
0
0
0
1
1
0
2
2
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
2
1
1
2
2
0
0
2
0
0
0
2
2
1
0
0
0
0
0
0
1
1
2
1
2
2
0
0
0
0
1
0
1
2
0
2
0
0
2
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
2
0
0
2
0
2
2
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
2
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
4
1
1
3
0
2
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
2
0
2
1
2
0
0
0
0
2
1
0
1
2
0
0
0
0
0
2
1
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
1
1
0
1
0
2
0
3
0
2
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
3
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
1
1
1
0
2
1
0
0
0
0
0
1
1
0
2
1
0
0
0
0
2
0
1
0
0
2
2
1
2
1
0
0
0
1
2
0
2
0
0
0
0
0
1
1
0
2
0
0
0
2
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
2
0
1
1
2
0
2
0
0
0
0
1
2
2
0
0
0
1
0
0
2
1
0
0
1
0
0
0
1
0
2
2
0
0
0
2
0
0
0
0
0
1
1
0
1
1
0
0
1
0
1
1
0
2
0
0
0
1
1
0
0
0
0
0
1
1
0
4
2
1
0
0
0
1
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
2
0
2
0
1
1
1
0
0
0
1
0
1
1
0
2
1
0
0
0
3
0
2
0
0
2
3
0
1
0
0
2
0
1
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
3
0
1
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
2
2
0
0
0
0
0
1
0
0
1
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
3
0
0
0
2
0
2
0
0
1
1
0
0
0
2
0
0
0
0
0
0
3
0
0
2
0
0
1
0
0
1
3
0
2
2
0
0
2
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
1
1
2
0
0
2
0
0
2
2
1
1
2
1
0
3
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
1
2
0
0
0
0
0
1
2
2
0
1
2
2
1
0
0
0
1
5
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
2
1
0
0
0
0
0
1
2
2
2
0
0
0
0
0
3
1
2
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
2
3
0
1
1
0
0
0
0
0
13
0
1
0
2
1
0
0
0
2
0
3
0
0
5
2
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
2
0
0
2
2
0
0
0
0
0
2
0
0
1
3
0
0
2
0
0
0
0
0
2
1
0
3
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
1
1
0
0
0
0
2
0
0
2
0
0
1
0
0
2
2
0
0
0
1
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
3
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
2
1
0
2
0
2
0
2
2
1
0
0
0
0
2
1
1
2
0
2
0
2
0
1
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
1
0
0
1
1
0
0
0
2
2
0
1
0
0
0
0
2
0
0
0
0
0
1
1
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
1
2
0
0
1
0
0
1
1
3
0
0
1
0
0
1
1
0
0
2
0
0
0
0
2
0
0
2
0
1
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
2
1
0
2
2
2
0
2
0
2
0
2
0
0
0
0
0
2
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
2
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
1
1
1
0
0
0
0
1
2
0
0
2
0
0
0
0
1
2
0
1
0
1
0
0
0
1
2
0
2
0
1
0
0
2
2
0
0
0
0
0
0
2
1
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
1
0
2
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
3
3
0
1
0
0
0
2
1
0
0
0
2
0
0
0
0
1
0
3
0
0
0
1
2
0
1
0
2
0
0
2
1
0
0
2
2
0
0
0
0
0
0
0
0
2
1
2
0
1
1
0
0
0
1
0
3
1
0
0
2
0
0
0
0
0
0
6
0
0
2
0
1
0
0
0
0
0
0
0
0
1
3
1
1
2
2
0
0
0
1
0
0
1
0
0
2
0
2
1
0
0
0
2
0
2
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
2
0
0
0
0
0
0
2
3
0
0
2
1
4
2
0
0
0
1
2
0
0
1
0
2
0
2
0
0
0
3
0
0
2
1
0
0
1
1
0
0
4
0
2
1
0
2
0
0
2
0
0
2
0
0
0
1
0
2
0
0
0
1
1
1
1
0
1
0
0
1
1
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
1
1
0
0
2
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
1
1
1
2
2
0
1
0
2
0
1
0
1
1
1
2
2
0
1
2
2
0
1
0
0
0
0
3
0
2
0
0
2
0
0
0
2
1
0
0
1
0
0
2
0
1
2
0
0
0
0
0
1
2
1
1
0
0
0
0
2
0
2
1
0
0
0
0
0
1
0
0
0
2
0
0
2
1
3
2
1
0
0
2
0
1
0
2
2
0
2
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
4
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
1
1
1
0
1
1
1
0
1
0
0
0
0
0
1
1
2
0
1
0
0
0
1
0
0
0
0
3
1
0
0
1
2
1
2
2
0
0
0
0
1
1
1
0
2
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
1
0
2
0
1
0
2
0
0
0
0
0
1
0
0
0
0
1
0
1
2
0
1
0
2
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
3
1
2
1
1
1
1
2
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
1
0
0
0
1
1
0
0
0
1
0
0
0
0
3
0
2
0
2
2
0
2
0
2
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
2
2
0
1
0
0
0
2
0
0
0
0
2
0
0
0
2
1
1
2
0
2
0
0
2
2
0
1
0
1
0
0
0
0
0
0
0
2
2
0
1
0
1
0
0
2
0
3
2
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
1
3
1
0
0
0
1
0
0
0
0
0
1
0
2
0
0
1
3
0
1
0
0
0
0
1
0
0
1
0
1
1
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
2
1
2
0
1
2
0
0
0
0
0
2
1
0
2
2
1
2
0
4
1
0
0
1
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
4
2
0
0
0
3
0
0
4
0
0
2
0
0
0
2
2
0
0
0
0
0
0
1
0
3
0
1
2
0
0
0
1
0
2
2
1
0
0
0
0
2
3
0
0
0
0
1
1
0
1
0
1
2
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
3
1
0
1
1
0
2
0
2
0
2
4
0
0
0
0
1
1
0
0
1
0
2
0
0
0
2
0
0
0
0
0
2
0
1
0
1
1
0
0
0
0
0
1
0
0
2
1
0
0
1
3
0
1
0
0
1
0
0
4
2
0
1
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
1
2
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
2
0
0
2
6
0
2
2
2
0
0
0
0
0
1
2
0
0
0
0
1
0
2
2
1
0
1
0
1
0
2
0
0
0
0
0
0
2
0
2
2
0
0
1
0
1
2
0
0
1
0
1
0
0
1
2
1
0
0
2
0
3
0
0
2
2
3
0
2
0
0
0
1
1
2
0
2
0
1
0
0
0
0
2
1
0
0
1
0
0
0
1
0
0
1
0
2
0
4
1
0
0
1
1
0
0
2
0
0
2
0
0
0
1
1
0
1
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
1
0
0
1
2
0
2
0
0
1
0
0
2
1
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
7
0
0
2
1
0
0
2
0
3
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
1
0
1
0
0
2
2
0
1
0
0
0
0
0
2
0
0
0
0
0
2
2
1
1
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
2
2
0
1
0
0
2
0
0
1
0
0
2
2
0
0
1
1
0
0
1
0
2
2
0
0
0
0
3
1
2
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
3
0
0
0
1
0
0
0
0
1
0
0
0
0
2
2
2
2
2
0
1
0
0
1
0
0
0
2
0
0
2
0
1
0
2
0
0
2
0
0
2
0
0
0
1
0
0
1
1
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
1
2
3
3
0
0
0
2
1
0
0
0
0
0
1
0
1
0
1
1
1
0
0
1
2
0
0
0
0
1
0
1
1
0
2
0
0
0
0
2
2
3
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
2
1
0
0
1
0
2
0
0
0
0
0
2
0
1
0
0
2
0
2
2
1
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
3
0
2
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
2
0
1
0
1
0
0
0
1
0
0
0
0
0
2
0
2
0
1
3
0
1
2
0
1
0
0
0
2
1
0
0
0
1
2
2
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
2
0
0
0
5
0
2
0
0
3
0
0
0
2
0
0
2
2
1
0
3
1
0
2
0
1
0
2
0
1
2
2
0
0
0
2
1
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
2
1
0
0
0
3
0
0
0
1
0
0
0
0
0
1
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
2
2
0
1
2
1
0
1
0
0
1
0
0
0
0
2
2
0
0
2
2
0
2
0
0
0
1
1
0
0
0
1
0
1
0
0
1
1
2
0
0
2
0
2
0
0
0
0
0
0
1
0
1
1
2
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
1
0
0
1
1
2
2
1
0
0
0
0
6
2
0
0
0
0
0
2
3
2
0
0
0
0
0
2
0
3
0
2
0
0
1
1
2
0
1
1
0
0
0
0
0
2
0
2
1
2
0
0
0
1
0
0
0
0
0
0
0
1
2
1
2
0
0
0
0
0
2
2
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
1
0
2
0
0
2
0
2
2
0
1
0
0
0
2
0
1
1
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
2
3
0
0
0
0
3
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
2
1
2
2
0
1
0
0
2
0
0
0
2
0
0
1
1
0
0
0
2
0
0
2
0
0
0
1
2
0
0
0
1
0
1
1
0
0
2
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
2
0
2
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
1
0
1
0
2
0
0
0
3
2
0
0
0
0
1
0
0
0
0
1
1
2
0
1
0
0
2
0
0
0
1
1
1
0
0
0
0
0
2
2
2
2
0
0
2
0
0
0
1
2
1
1
0
1
2
1
1
0
1
0
0
0
0
1
3
0
0
1
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
2
0
2
0
0
0
1
0
1
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
2
1
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
2
0
2
0
0
1
0
2
0
0
0
2
2
0
0
0
0
0
0
3
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
2
1
3
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
2
2
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
3
3
0
0
0
0
0
0
0
2
0
0
2
0
2
5
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
1
1
1
0
0
2
0
0
6
2
3
0
2
0
0
0
1
0
0
2
0
0
3
1
0
1
1
1
1
0
0
1
1
0
0
2
0
0
1
2
0
0
0
2
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
3
0
0
0
0
0
2
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
8
0
0
1
0
2
0
1
0
2
1
1
0
2
2
4
0
0
3
0
0
2
2
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
5
0
0
1
1
1
0
0
0
2
1
0
1
0
2
0
1
0
0
0
1
0
3
2
0
2
2
0
2
1
1
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
2
2
0
0
0
0
0
1
0
2
0
1
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
1
1
0
1
0
0
1
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
3
0
1
1
2
0
2
0
0
1
2
1
2
0
0
0
1
0
0
0
0
0
2
0
3
0
0
1
0
0
2
0
2
0
1
0
0
1
0
1
3
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
2
0
2
1
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
1
2
1
0
1
0
0
0
2
1
2
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
2
0
0
0
2
0
2
0
0
0
1
0
0
1
0
2
0
0
1
0
0
0
0
2
1
2
0
3
0
0
0
0
2
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
7
1
0
0
0
0
1
1
0
0
0
0
2
0
1
0
1
0
0
0
0
2
1
0
0
2
1
1
1
2
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
13
0
0
0
3
0
0
2
0
0
0
1
0
0
0
0
0
2
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
1
3
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
2
2
6
0
1
0
0
1
1
2
0
2
0
0
0
0
0
3
2
1
0
0
0
2
0
1
2
0
1
0
0
2
0
0
1
1
0
1
0
2
0
0
0
1
0
2
0
2
0
0
0
0
0
2
0
2
0
0
0
2
1
0
1
0
1
0
0
0
0
1
1
0
0
0
1
0
0
2
0
0
0
0
0
1
2
0
0
2
1
1
0
1
0
2
0
0
0
2
0
1
1
0
0
0
0
0
2
0
1
0
1
0
0
0
0
1
0
1
0
1
0
1
0
0
0
1
2
0
0
0
0
1
0
2
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
2
0
0
1
0
0
0
0
1
0
1
1
0
0
0
1
0
0
1
1
2
0
0
0
0
0
0
2
0
1
0
0
0
3
0
1
1
0
1
0
0
0
0
0
0
1
2
2
0
2
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
2
2
1
2
0
0
0
0
0
0
0
0
1
3
2
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
1
0
1
2
0
1
3
1
0
0
1
2
2
0
0
0
1
2
0
0
0
2
0
1
1
0
0
2
0
0
0
0
0
1
1
0
0
0
0
1
1
0
1
2
0
0
4
2
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
2
2
1
0
2
1
0
0
0
0
3
2
0
0
1
0
3
0
2
0
1
1
0
0
0
0
0
0
5
2
0
2
0
1
0
0
2
1
1
2
0
0
0
2
0
1
0
0
0
0
6
1
1
0
0
0
0
0
0
0
2
1
0
0
1
1
0
0
0
0
0
0
4
1
0
2
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
1
1
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
3
0
0
0
1
2
0
0
2
0
1
0
0
0
0
0
1
0
2
0
1
0
0
2
1
0
3
0
2
0
2
1
0
0
1
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
2
1
1
0
0
1
0
1
0
1
0
2
0
2
1
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
1
2
0
1
0
1
2
0
0
1
2
0
0
0
0
2
1
0
0
0
0
0
2
1
0
0
0
2
2
0
0
2
1
0
0
0
0
0
2
0
0
0
1
2
0
1
2
2
0
2
0
0
1
0
0
1
0
1
0
0
0
0
0
2
0
1
2
0
1
2
0
0
1
0
1
0
2
0
0
0
0
2
0
0
0
0
1
2
0
1
0
2
1
4
0
0
1
0
0
1
0
2
2
0
2
2
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
2
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
2
1
0
0
0
1
2
1
2
0
0
0
0
1
1
0
2
0
1
0
0
0
3
0
0
2
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
1
2
0
1
0
0
0
0
2
1
0
0
1
0
0
0
2
2
1
0
0
0
1
2
1
0
0
0
0
1
2
2
1
3
0
0
1
0
0
0
1
1
2
2
2
0
2
1
0
0
1
0
0
1
0
1
0
0
0
0
0
1
2
0
0
3
0
0
0
2
1
0
4
2
0
0
0
0
4
2
1
0
2
2
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
2
1
0
0
0
1
2
2
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
1
0
2
0
3
0
0
0
1
0
1
1
1
0
0
1
0
2
0
0
0
0
2
0
0
0
2
2
1
2
0
0
3
0
0
0
0
3
2
0
0
0
1
0
0
1
0
0
1
0
0
1
2
1
0
2
1
2
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
4
0
1
0
0
1
0
0
1
0
2
0
2
1
2
0
0
0
1
0
0
0
2
0
0
2
0
0
2
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
1
6
1
3
2
0
0
1
0
0
0
2
0
0
1
0
0
0
1
1
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
1
3
2
0
0
0
2
1
0
2
0
0
0
2
1
0
0
2
2
2
1
1
2
0
1
1
2
1
0
0
0
2
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
1
1
1
1
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
3
0
1
1
0
1
0
2
0
0
1
0
0
1
1
1
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
2
4
0
1
2
0
1
0
0
0
2
0
1
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
1
1
1
0
0
1
1
1
0
0
0
0
1
2
0
0
1
0
1
1
1
0
0
0
0
0
0
2
0
4
4
0
0
0
1
4
5
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
1
1
2
2
1
0
2
1
2
2
0
0
1
0
1
0
0
1
1
0
2
0
0
2
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
1
1
0
0
1
0
0
1
1
1
1
0
0
0
1
0
0
2
0
0
1
2
0
0
0
1
0
0
0
0
1
0
0
0
1
1
1
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
2
2
1
0
1
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
2
1
0
0
1
0
1
1
0
1
2
2
1
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
1
0
2
0
0
1
2
0
2
0
0
1
0
0
0
0
2
0
1
0
0
1
1
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
2
1
7
0
1
4
2
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
3
0
2
1
0
0
0
0
2
1
0
0
0
0
0
0
1
2
1
1
0
0
0
0
0
3
0
0
0
0
2
0
0
2
0
0
1
0
0
1
0
0
2
0
0
0
2
1
0
0
0
0
1
0
0
1
0
0
1
0
1
1
1
2
1
0
0
0
0
0
1
0
0
1
0
2
0
3
0
1
0
1
0
0
1
2
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
2
1
0
0
0
0
0
2
1
0
2
1
0
1
0
0
2
0
0
1
0
0
1
2
0
0
2
2
0
0
0
0
0
0
1
0
0
0
1
0
1
2
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
3
0
0
0
2
2
0
0
0
2
0
0
0
1
1
0
0
0
0
2
2
0
2
0
1
0
2
1
1
0
0
2
3
0
0
1
0
1
0
0
1
0
1
1
0
0
2
0
1
1
0
0
0
0
1
0
2
2
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
1
1
2
0
7
1
2
0
2
0
0
0
2
1
0
1
3
2
0
2
1
0
2
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
2
1
0
1
0
0
1
0
2
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
1
1
0
1
4
0
0
0
0
3
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
3
1
1
0
0
0
1
0
0
0
0
1
0
0
2
2
0
1
0
2
0
0
0
2
0
0
2
0
2
1
0
1
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
2
2
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
1
0
2
3
0
0
0
1
0
2
0
2
0
2
0
0
2
2
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
3
1
0
0
0
0
1
0
1
0
2
0
0
1
1
0
1
0
2
2
3
1
1
2
0
1
0
0
0
2
0
0
0
2
0
1
0
0
0
3
0
1
0
0
0
1
0
0
0
2
6
0
2
2
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
2
0
0
0
0
0
0
2
1
0
0
0
1
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
2
2
2
1
0
0
1
2
0
0
0
0
2
0
0
0
2
2
0
2
0
0
0
2
0
0
2
1
0
0
0
2
0
2
0
0
0
1
1
0
2
0
1
2
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
1
2
2
2
0
1
0
0
1
1
0
0
0
0
1
0
0
2
2
2
1
0
0
0
1
0
0
0
1
2
0
3
1
0
0
3
0
0
2
0
0
0
0
2
0
0
0
0
2
0
2
0
0
2
1
1
0
1
0
0
0
0
2
0
0
1
0
0
0
0
2
0
2
0
2
0
0
0
0
0
2
2
1
2
1
1
0
1
1
0
0
0
1
2
0
3
1
0
1
0
0
0
2
0
0
0
0
0
1
0
3
0
2
0
1
0
0
0
1
2
0
0
0
4
1
2
0
0
0
0
2
0
0
0
2
0
2
0
2
0
0
0
0
1
1
3
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
1
1
0
2
1
2
0
0
2
1
0
0
0
0
1
2
2
2
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
2
2
0
2
0
0
0
0
2
0
1
0
0
0
1
0
0
2
2
0
4
0
0
0
0
0
0
1
0
0
1
0
2
0
0
2
1
0
0
0
0
1
0
0
0
0
0
1
0
0
2
1
0
0
0
1
0
2
0
1
2
1
1
0
0
0
0
1
0
0
0
0
0
2
0
1
1
1
0
1
0
2
0
0
0
0
0
0
1
0
2
0
0
0
2
1
2
1
0
1
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
2
0
0
1
2
0
0
0
2
3
0
2
0
1
0
0
0
2
0
0
0
1
0
1
0
2
0
1
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
1
1
0
0
0
1
2
2
0
2
0
1
0
0
0
0
2
0
2
1
0
0
0
0
1
1
0
0
0
1
2
0
1
1
0
0
1
0
4
0
0
0
0
0
2
1
2
0
0
0
2
0
0
1
0
2
2
0
1
2
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
1
2
0
2
3
2
0
2
0
2
0
1
0
1
0
0
1
1
0
0
2
0
1
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
3
2
0
0
1
1
1
0
0
0
0
3
0
0
0
1
0
0
1
1
0
0
2
2
1
0
0
0
0
0
1
0
1
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
1
0
2
0
0
1
0
2
0
2
0
0
2
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
2
0
2
3
0
1
0
0
0
0
0
1
1
0
1
0
0
0
1
0
1
0
1
0
0
0
2
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
4
0
0
0
0
0
0
2
1
0
0
0
0
0
2
2
0
0
2
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
1
0
0
2
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
1
0
1
3
0
0
0
2
0
1
2
0
0
0
0
0
1
0
1
0
0
0
2
0
2
0
0
0
0
4
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
4
2
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
3
1
1
0
0
0
0
0
0
0
0
2
0
0
1
1
1
1
0
0
1
0
0
0
2
1
1
0
0
2
1
1
1
2
1
1
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
2
0
0
0
0
2
0
2
0
1
1
4
0
1
3
0
0
0
0
0
2
1
1
0
0
0
0
3
2
0
1
0
0
0
0
2
0
0
2
1
2
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
1
0
0
1
1
2
1
0
0
0
0
0
2
2
0
2
0
1
0
0
0
0
0
0
2
1
1
2
0
1
2
1
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
1
1
0
1
0
0
1
1
0
1
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
1
1
0
0
1
2
2
3
0
0
1
0
2
0
0
1
0
2
2
0
0
0
0
0
1
2
1
2
0
1
0
2
1
0
0
1
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
2
0
1
0
2
0
2
0
0
2
0
0
0
0
0
2
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
2
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
2
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
2
0
0
1
2
1
1
0
2
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
3
2
1
1
2
0
1
0
0
0
1
1
0
1
0
0
1
1
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
3
0
1
2
1
2
2
0
2
2
0
0
2
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
1
0
0
1
1
2
0
0
0
2
0
0
0
0
0
0
0
0
3
0
1
1
0
2
0
0
0
1
0
0
0
0
1
0
0
2
0
0
1
1
1
2
0
0
0
1
0
2
2
0
0
0
0
0
0
2
1
0
0
1
1
2
0
0
0
0
2
3
0
2
1
0
0
0
0
0
0
2
1
0
0
0
1
2
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
2
1
1
0
0
0
1
0
1
0
2
4
0
0
2
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
2
0
1
5
0
0
0
2
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
1
0
3
0
1
0
0
0
0
1
2
2
1
2
0
2
2
0
1
4
1
0
1
2
2
2
0
0
2
0
0
0
0
0
1
0
0
2
1
0
2
0
0
0
3
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
3
0
2
0
2
0
0
2
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
1
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
1
1
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
4
2
0
0
0
0
1
0
1
0
1
0
2
0
0
0
0
2
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
2
2
2
0
0
1
0
0
2
0
1
2
1
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
4
0
0
0
1
0
0
2
1
0
0
2
1
1
2
0
1
0
2
1
0
0
1
2
2
0
0
0
1
0
4
0
0
4
4
0
1
1
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
2
0
1
2
0
0
2
2
0
0
0
0
1
1
0
0
2
1
0
2
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
2
0
0
0
3
0
0
0
1
0
0
2
0
0
1
0
0
2
4
1
0
2
0
3
1
0
0
0
0
1
0
2
2
1
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
2
0
1
1
0
0
1
1
0
0
2
0
1
2
2
0
0
2
0
0
0
2
0
0
0
0
1
0
0
2
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
1
0
1
1
0
0
0
1
2
2
2
0
1
1
0
1
0
0
0
2
0
2
0
0
2
0
0
2
2
0
0
0
4
1
2
0
0
0
3
0
0
2
0
1
1
1
1
0
0
0
1
1
0
0
2
1
0
2
0
0
2
0
0
0
0
0
2
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
1
0
1
0
0
0
0
0
2
1
2
2
0
0
0
1
0
0
1
0
0
2
1
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
1
2
0
0
0
0
0
3
0
0
0
0
1
0
2
1
0
0
1
0
0
0
2
0
0
1
1
2
2
2
1
0
0
0
0
0
0
2
1
0
1
2
0
0
0
0
0
0
0
0
2
0
1
1
1
0
1
4
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
2
1
1
0
1
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
3
1
1
0
1
0
0
1
2
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
1
0
3
0
1
1
0
3
0
1
0
1
0
1
0
3
0
1
0
1
2
0
0
1
2
0
0
1
0
0
2
0
0
0
0
2
2
0
0
2
0
0
0
2
0
0
0
2
1
1
0
0
0
1
0
0
0
0
0
1
0
1
0
1
2
0
0
0
3
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
1
0
0
0
0
0
0
1
0
1
0
2
1
0
3
2
1
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
2
0
2
0
1
2
0
0
0
0
0
2
0
0
0
3
0
0
2
2
0
0
0
1
0
3
2
2
0
0
1
0
1
1
0
1
1
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
2
0
0
6
2
3
0
2
4
0
0
0
0
0
0
0
0
0
6
0
1
0
0
1
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
1
0
0
1
0
1
4
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
3
2
0
0
2
0
1
1
0
0
1
0
0
0
1
2
0
1
0
0
0
0
2
2
1
0
0
2
0
0
0
1
0
2
2
0
0
2
1
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
1
1
0
1
1
2
0
0
0
0
1
1
0
0
0
1
1
1
0
0
2
0
2
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
3
0
0
0
2
4
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
4
3
2
2
0
2
1
0
0
0
2
0
0
0
1
0
2
0
0
0
0
3
6
0
2
0
2
2
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
1
0
0
2
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
2
1
2
0
2
2
2
0
0
2
0
0
0
2
1
1
0
0
0
0
2
2
0
0
0
0
0
2
0
0
1
2
0
0
0
1
0
2
0
0
1
0
2
1
0
2
1
0
4
1
0
0
0
0
0
0
0
0
1
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
3
2
1
2
2
0
0
0
0
0
0
0
0
3
1
2
2
1
0
3
2
0
0
0
1
0
0
2
1
0
0
0
2
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
6
1
0
0
0
2
1
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
1
1
1
0
1
0
1
0
3
1
2
0
2
1
0
1
0
1
0
0
1
0
0
2
2
0
0
3
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
1
2
0
0
0
1
0
1
0
2
0
1
3
1
0
1
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
2
0
0
0
1
0
0
1
0
1
0
0
1
0
0
1
2
0
0
2
0
0
0
1
2
0
1
0
1
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
5
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
2
2
1
0
0
0
0
2
0
2
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
2
0
0
0
0
2
1
2
0
0
1
1
0
0
2
6
0
0
0
0
2
1
2
2
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
3
0
0
0
2
2
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
3
0
0
0
1
0
0
1
3
0
2
0
2
0
0
0
0
0
0
1
0
0
0
2
1
3
1
0
1
2
1
2
0
1
0
0
0
0
0
0
0
3
1
0
1
1
0
2
1
0
0
2
0
2
0
0
0
0
0
0
2
0
0
1
0
1
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
1
0
1
0
0
1
0
0
1
2
2
0
0
0
0
0
0
2
0
1
0
0
1
2
0
0
2
0
0
0
0
0
0
1
0
0
1
0
2
0
2
2
0
0
2
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
2
0
2
3
0
0
1
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
1
4
2
0
1
0
0
0
1
2
2
2
0
1
0
0
1
1
0
6
0
1
1
0
0
1
0
1
0
2
2
1
2
1
0
2
0
1
0
2
2
1
1
1
0
2
0
1
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
2
0
0
1
0
1
1
1
0
1
1
0
2
2
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
3
1
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
1
1
3
1
2
2
0
0
0
0
0
1
2
0
0
2
1
3
0
0
1
1
0
0
1
0
1
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
1
2
0
2
0
0
2
0
3
2
1
0
2
0
0
2
0
0
0
2
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
2
0
0
0
1
0
0
2
0
0
1
1
0
1
1
2
0
0
1
2
2
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
1
0
0
0
0
0
2
1
0
0
1
2
0
1
0
0
0
0
0
2
2
2
1
0
2
2
0
0
1
1
0
0
0
2
1
0
1
1
0
3
3
1
0
0
2
1
1
4
0
0
0
0
0
1
2
0
2
0
0
0
1
1
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
5
0
1
0
0
0
2
0
0
0
1
2
1
0
1
4
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
4
0
2
2
0
0
0
0
0
2
2
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
2
0
1
2
1
6
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
2
0
2
0
0
0
0
0
1
0
0
0
2
0
0
1
1
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
2
2
0
1
0
2
0
2
0
0
0
0
1
1
2
1
0
2
0
0
0
0
5
2
0
0
1
0
0
0
0
0
2
0
0
0
1
0
1
0
0
2
1
0
2
2
0
0
4
0
0
0
2
0
0
2
2
0
2
0
0
0
0
0
0
0
0
1
2
0
0
1
1
0
1
2
2
0
0
1
0
0
0
0
2
0
3
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
1
1
0
1
0
4
0
0
0
0
0
0
1
0
0
3
0
1
1
0
2
0
1
0
2
0
1
1
0
2
0
0
0
0
0
2
0
2
0
2
0
0
2
0
0
0
2
0
0
2
1
2
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
1
0
1
2
3
0
2
1
0
0
0
0
2
2
0
0
0
0
0
1
0
0
2
1
2
0
1
0
1
0
0
0
1
0
0
0
0
0
0
4
2
0
1
0
0
0
2
3
1
0
1
2
0
3
2
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
1
0
2
0
0
0
2
1
0
1
0
3
2
0
3
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
3
1
0
1
0
1
0
0
0
0
0
0
1
2
0
1
0
0
1
0
1
0
2
0
1
4
0
0
0
0
3
0
0
3
2
0
1
0
0
0
2
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
3
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
2
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
2
1
1
0
0
0
1
0
0
0
1
0
0
3
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
1
3
2
0
1
0
1
1
0
0
1
1
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
2
2
2
2
4
0
1
0
0
1
0
0
0
0
0
2
0
1
0
3
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
1
2
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
3
0
1
0
1
0
1
2
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
1
2
0
1
0
1
1
1
0
2
1
0
0
0
0
0
0
0
0
1
2
0
2
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
2
0
0
0
0
0
1
1
0
3
0
0
1
1
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
2
1
0
0
0
1
1
0
0
2
1
3
1
1
0
0
1
1
1
0
2
0
0
0
1
2
2
0
0
0
0
0
1
2
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
1
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
1
1
0
0
2
2
0
2
0
0
0
0
2
0
4
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
1
1
2
2
4
0
0
0
0
0
0
0
0
2
2
1
0
2
4
0
0
1
0
1
0
0
0
0
1
2
0
0
0
0
1
0
1
0
2
0
0
0
1
0
2
0
0
2
2
0
0
0
0
0
2
0
2
1
0
2
3
2
0
2
0
0
2
0
5
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
1
0
0
0
1
3
1
0
2
0
2
0
1
2
0
2
2
1
0
0
2
0
0
0
1
0
0
0
0
0
1
1
1
0
2
2
1
0
0
0
1
0
1
0
1
1
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
1
0
1
0
1
1
2
4
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
1
0
2
0
0
1
1
2
0
0
4
2
1
0
0
3
0
2
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
3
1
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
5
0
0
0
0
1
0
0
1
0
1
0
2
0
0
0
0
0
0
2
0
2
0
0
1
1
1
0
0
0
0
0
1
0
1
0
0
4
2
0
0
2
1
0
0
0
2
2
0
0
0
2
0
0
0
3
1
2
2
3
2
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
1
0
0
5
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
1
2
0
2
0
0
1
0
1
0
0
1
0
0
0
2
1
1
0
0
2
0
0
1
0
2
0
2
0
1
1
2
2
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
1
2
2
0
2
0
0
3
1
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
2
0
2
1
3
0
0
0
0
0
0
2
0
1
0
3
0
0
0
0
0
0
0
1
3
1
0
1
4
0
2
0
1
0
0
0
1
0
0
1
0
0
1
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
2
0
1
0
0
0
0
0
0
0
0
1
1
1
1
1
1
2
1
0
1
0
2
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
2
0
0
2
2
0
1
0
1
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
1
0
0
0
0
1
0
0
0
0
10
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
2
1
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
2
0
1
0
3
2
2
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
1
2
1
0
0
0
0
1
0
0
1
0
0
1
0
3
1
2
0
1
0
2
0
0
0
0
2
0
1
0
2
2
1
0
0
1
0
0
0
2
1
0
1
0
0
0
2
0
1
0
0
1
1
0
0
1
0
4
2
0
0
1
2
0
0
2
2
0
0
2
1
1
2
1
0
0
0
1
0
0
0
2
0
0
2
0
1
0
0
0
1
0
0
0
1
0
2
4
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
1
0
2
0
1
0
0
0
2
2
0
3
0
1
0
0
1
1
0
1
0
2
0
1
0
2
0
0
0
0
0
2
1
1
0
0
1
0
0
0
0
1
2
1
0
0
0
2
0
0
0
1
0
0
2
0
1
0
1
2
2
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
3
1
0
2
0
0
0
1
2
0
0
0
5
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
1
1
2
0
0
0
1
2
1
3
2
0
0
2
0
1
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
1
0
2
1
0
2
0
1
1
0
0
1
0
0
1
0
0
0
0
2
0
0
2
0
3
3
2
0
0
0
1
2
0
0
1
0
0
4
0
0
0
0
0
2
1
0
1
0
1
0
0
0
0
2
0
2
3
1
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
3
0
1
1
0
0
1
0
2
1
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
3
2
0
0
0
0
1
0
0
0
0
0
5
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
1
3
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
2
0
1
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
2
0
2
0
0
0
2
2
0
0
0
0
1
2
0
0
0
1
0
2
2
0
1
0
0
0
2
0
0
0
0
1
0
1
1
3
0
2
0
0
0
0
1
0
1
0
0
0
0
0
1
0
2
0
3
0
0
2
0
0
0
2
2
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
4
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
1
1
2
1
0
1
0
0
0
1
2
0
3
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
1
1
0
0
2
2
1
0
2
0
0
0
0
0
1
0
1
1
1
0
0
0
0
1
5
0
2
0
0
2
1
0
2
2
1
0
0
0
0
0
0
2
0
2
1
0
0
0
1
1
0
0
5
0
0
0
0
0
0
0
1
2
0
0
1
0
1
0
0
1
0
0
2
1
0
0
2
0
0
1
1
2
2
0
0
0
0
0
2
0
0
0
1
0
2
2
1
0
0
2
0
0
0
1
3
1
2
0
0
11
0
0
10
1
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
3
0
0
1
0
0
0
0
6
1
1
0
2
0
0
0
0
0
0
0
0
0
1
0
2
2
1
1
2
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
3
0
0
1
0
0
0
1
0
0
1
1
1
0
0
2
2
0
1
0
1
0
1
2
0
0
0
2
0
0
0
2
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
2
0
1
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
1
3
0
0
1
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
3
1
1
0
0
2
1
0
0
2
0
2
0
0
1
1
2
0
2
0
1
0
3
0
0
2
0
0
1
0
0
1
2
0
0
0
1
0
0
3
1
0
0
0
3
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
3
2
0
1
0
1
0
3
1
0
0
2
0
0
0
2
2
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
1
4
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
2
0
3
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
2
1
0
0
0
1
0
2
3
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
2
0
1
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
2
0
0
0
1
0
0
2
0
0
0
0
0
1
1
0
2
1
0
0
0
1
0
7
2
2
2
0
2
2
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
4
0
1
0
0
2
0
2
2
0
2
0
1
0
0
2
0
0
0
2
2
0
0
0
2
0
0
2
1
2
0
1
0
0
0
0
2
2
1
0
0
1
1
3
0
0
0
0
0
1
0
3
0
0
0
1
0
0
0
0
2
0
0
0
1
2
0
0
0
0
2
2
3
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
2
0
0
3
1
0
0
0
1
0
4
2
2
0
0
1
1
2
0
0
0
1
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
1
2
2
0
0
2
0
1
0
0
1
0
0
1
0
1
3
0
1
0
0
0
0
0
0
1
1
0
0
1
1
0
1
2
0
0
2
0
0
1
0
0
2
0
0
2
0
0
0
0
1
0
1
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
2
2
1
2
0
0
1
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
1
1
0
1
1
1
0
0
0
1
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
1
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
2
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
2
0
2
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
2
0
0
0
0
4
0
0
0
1
2
0
1
0
0
1
2
2
0
0
0
0
2
2
2
2
1
0
0
0
0
0
0
2
5
0
0
0
2
0
0
0
2
2
2
1
0
0
0
0
0
1
0
0
0
0
0
3
0
0
1
1
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
3
0
0
2
1
1
0
0
0
2
1
6
2
0
2
0
0
0
0
0
0
1
1
0
1
1
2
3
2
0
0
0
2
0
0
1
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
2
0
2
0
0
2
2
2
2
0
1
1
1
0
0
0
0
3
0
1
0
0
1
0
1
0
0
0
0
0
2
1
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
2
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
8
0
0
1
0
0
0
2
2
2
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
1
0
3
0
0
1
0
1
0
0
0
1
1
0
0
1
0
0
0
3
2
2
2
0
0
1
2
0
2
3
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
2
0
0
0
2
0
0
0
0
2
2
1
0
0
2
0
0
0
0
2
2
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
1
0
0
0
2
0
0
1
0
0
0
0
2
0
2
0
2
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
2
0
1
0
0
0
2
0
3
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
1
1
1
0
0
1
0
2
2
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
1
2
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
1
2
0
2
0
1
2
0
1
2
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
3
2
1
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
1
1
2
0
0
1
0
0
0
2
0
0
0
0
2
0
0
3
3
2
0
0
0
2
0
2
4
3
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
1
2
1
1
0
0
2
0
0
0
0
2
0
1
3
0
0
1
0
0
0
2
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
2
0
2
1
0
1
0
0
0
0
1
0
2
0
2
0
2
0
1
0
0
1
0
0
0
1
0
1
0
0
0
1
0
1
3
0
1
0
0
0
0
2
2
1
0
2
0
0
0
0
0
1
2
0
0
0
0
0
2
0
2
2
1
1
0
0
0
3
0
0
0
2
0
1
2
0
3
0
1
0
0
1
1
2
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
2
2
1
1
0
1
2
0
0
1
0
2
0
0
0
1
1
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
2
0
1
0
0
2
0
0
0
0
0
0
1
0
0
1
0
3
0
0
0
1
0
0
2
0
1
0
0
2
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
1
1
0
0
2
0
0
1
2
2
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
2
0
0
2
0
0
3
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
2
0
0
1
1
1
0
2
1
0
0
0
1
1
0
2
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
2
1
1
1
0
2
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
2
1
2
2
0
3
2
2
0
0
0
0
0
1
0
0
0
0
0
2
2
2
1
2
1
1
2
0
0
0
2
3
1
1
0
0
0
0
0
0
2
0
0
0
0
0
2
3
1
0
0
2
0
1
0
0
0
0
0
0
1
0
1
0
3
0
0
0
0
1
0
0
0
1
1
0
2
2
0
1
0
0
0
1
2
3
0
1
0
2
2
1
1
0
0
1
0
1
0
0
0
0
0
2
0
1
3
1
0
0
0
0
2
0
0
2
1
1
0
1
0
0
0
0
1
2
0
0
0
1
0
0
2
0
2
0
0
0
0
0
2
0
0
2
0
4
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
2
0
2
0
0
0
0
1
0
0
1
2
1
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
3
0
2
0
4
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
2
0
0
2
0
0
1
2
3
1
2
2
0
0
0
4
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
2
1
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
1
0
1
1
0
0
2
0
0
0
1
2
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
2
2
0
0
0
1
0
1
0
0
0
0
0
0
2
6
2
1
2
0
0
1
0
2
4
2
1
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
2
0
0
1
0
0
2
0
0
0
0
2
2
2
2
0
0
0
1
0
0
1
2
0
0
0
0
0
1
2
0
0
0
3
0
0
1
1
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
3
0
0
0
2
0
2
0
0
0
2
0
0
0
1
0
2
0
0
2
0
2
4
0
1
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
4
0
0
1
1
3
0
1
3
2
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
1
1
0
0
0
0
0
1
1
0
0
1
2
2
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
2
2
0
0
1
1
0
0
0
0
0
0
2
0
0
2
0
0
1
2
0
1
0
3
0
0
1
4
2
0
0
0
1
0
0
0
0
1
0
1
1
2
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
2
1
0
3
0
2
0
0
0
2
1
0
0
0
0
2
2
0
1
0
1
0
0
0
0
0
0
1
2
1
0
0
0
1
2
0
1
0
2
0
1
2
0
0
1
2
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
2
0
0
1
0
1
0
2
2
0
0
0
1
1
0
1
0
0
1
2
0
0
0
0
1
0
0
0
2
0
0
0
0
1
2
2
0
1
0
0
1
0
0
2
0
0
0
0
1
0
0
2
2
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
4
0
0
1
0
0
1
0
2
2
0
2
0
1
1
0
0
2
1
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
2
0
0
2
1
1
3
6
2
0
2
0
0
0
1
1
0
0
2
0
0
0
0
0
2
2
2
0
0
2
0
0
2
0
0
2
0
0
0
0
1
0
0
0
2
1
0
1
0
1
1
2
1
0
2
2
2
0
0
0
0
0
0
1
1
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
2
0
0
0
0
0
0
2
1
0
0
0
1
2
2
1
1
1
2
0
0
0
0
0
2
1
2
0
1
0
0
0
2
0
2
0
1
0
1
0
0
0
0
3
0
0
2
1
1
0
0
2
2
0
2
0
0
0
0
0
0
2
0
0
2
0
0
2
0
5
0
0
0
0
1
3
0
0
2
2
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
2
1
0
1
2
3
0
0
0
0
0
0
1
0
0
3
2
0
0
0
0
2
2
0
0
0
1
0
0
0
1
0
0
0
3
5
0
0
3
0
2
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
1
0
2
0
2
0
4
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
1
0
0
2
1
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
1
4
1
0
2
0
0
0
0
0
1
0
1
0
0
0
1
2
0
1
1
0
2
0
0
2
1
3
0
2
0
0
0
0
0
2
0
2
0
0
2
0
2
0
0
0
0
0
0
1
3
2
2
0
1
2
0
1
0
1
0
0
0
0
0
2
2
0
0
1
2
0
0
0
0
1
0
0
0
3
2
1
1
1
2
0
0
1
1
0
0
0
0
0
0
1
0
3
0
1
0
1
2
0
0
2
0
0
0
2
1
0
0
0
2
0
0
0
0
3
0
0
0
0
3
1
0
0
2
0
1
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
3
1
3
0
0
2
2
0
0
0
2
2
1
1
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
1
2
0
0
1
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
1
0
0
1
0
2
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
1
0
2
0
4
1
0
0
0
0
0
1
0
0
1
2
1
0
2
2
0
0
0
0
1
0
2
0
0
2
0
1
0
0
0
0
1
0
0
0
0
2
0
1
0
0
2
0
1
0
0
0
0
0
1
2
0
0
0
0
0
2
2
2
0
0
2
0
0
1
1
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
1
2
0
2
0
1
0
0
0
0
0
1
0
0
0
1
0
1
1
2
0
0
2
2
0
3
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
2
1
0
0
2
4
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
1
0
3
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
2
1
0
2
0
0
1
0
0
1
0
0
1
1
0
1
0
2
0
1
0
0
0
2
0
2
0
0
2
1
1
1
2
0
0
0
2
0
0
0
0
2
0
0
1
1
0
0
0
0
1
5
0
1
0
0
1
1
0
0
0
0
0
0
2
0
2
0
0
0
1
2
2
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
2
2
0
2
0
0
3
0
0
0
0
0
0
0
1
2
0
2
2
2
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
4
0
1
2
0
1
2
1
0
0
0
0
3
1
0
2
1
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
1
1
0
0
0
2
0
0
1
0
2
0
2
0
0
1
0
2
2
0
2
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
1
0
0
0
0
1
0
2
0
1
0
2
0
1
0
0
1
0
0
0
0
0
1
1
0
0
2
2
0
7
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
2
0
0
1
0
0
0
2
2
0
0
0
0
2
0
0
2
1
0
0
0
2
0
0
0
2
0
0
0
0
3
0
0
2
0
1
0
0
1
4
0
0
2
0
2
0
0
0
0
0
1
0
0
1
0
1
1
0
0
1
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
3
0
2
2
2
2
0
1
0
3
0
0
0
2
2
0
2
0
1
0
0
0
1
0
0
0
0
0
0
2
0
3
0
0
1
0
1
0
2
0
0
0
0
0
2
1
2
0
0
0
3
0
0
0
0
0
3
2
0
0
0
1
0
1
0
3
0
0
0
0
0
1
3
0
1
5
0
0
0
0
0
1
0
1
0
0
0
0
0
3
0
0
2
1
0
0
1
2
0
2
0
1
0
0
0
0
2
2
0
0
0
0
1
2
2
0
0
0
0
1
1
0
0
0
0
2
2
1
2
0
0
0
0
1
0
0
0
2
0
4
0
0
1
0
0
0
1
1
1
1
0
0
2
2
0
1
0
0
0
0
0
1
3
0
0
2
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
1
0
0
0
2
0
0
4
0
0
0
0
0
0
0
1
0
2
0
3
0
2
1
1
0
0
0
2
2
2
0
0
0
0
0
1
0
0
1
0
0
1
0
2
1
1
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
2
0
0
2
2
0
0
0
2
0
1
0
2
0
2
0
0
0
1
2
1
3
0
0
0
0
0
0
2
1
0
1
2
0
0
0
2
0
1
3
1
0
0
0
3
0
0
0
3
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
2
2
1
0
1
0
0
0
0
0
0
0
0
2
1
0
1
2
0
0
0
7
2
0
2
2
0
1
0
1
0
1
0
0
0
0
0
0
2
2
0
1
1
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
2
1
0
0
2
2
0
0
1
0
1
2
0
0
0
0
0
0
0
0
2
0
1
0
1
0
2
1
0
0
1
0
3
0
0
0
0
0
0
0
0
0
1
2
2
2
0
1
0
2
2
1
0
0
0
2
0
0
0
1
0
4
1
0
0
0
0
0
2
0
1
1
0
0
0
1
0
0
2
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
4
0
1
1
0
1
0
0
1
0
2
1
1
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
2
0
1
0
0
0
0
0
0
0
2
0
0
1
1
1
0
0
0
1
3
0
0
1
0
0
2
0
1
0
1
0
0
2
0
1
0
0
2
0
0
2
2
1
0
0
2
1
0
0
0
2
0
0
0
1
2
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
2
0
1
0
2
1
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
2
1
1
0
0
0
0
1
0
1
1
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
1
1
0
2
0
2
2
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
2
1
0
0
0
0
0
2
0
0
0
1
1
0
0
2
2
0
2
0
2
0
0
0
0
2
4
0
2
0
3
2
0
0
0
0
0
2
0
0
2
0
0
0
2
0
1
2
2
0
0
0
2
1
3
1
0
0
0
1
1
3
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
2
3
2
0
2
0
2
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
2
1
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
2
2
0
2
2
2
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
1
0
2
0
0
1
1
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
1
2
0
2
0
2
2
4
0
0
2
0
0
0
0
0
0
2
1
0
0
0
1
2
0
1
2
1
2
2
0
0
0
0
2
0
1
2
1
0
2
1
0
1
0
2
0
0
1
2
0
1
0
0
1
0
0
0
2
0
0
0
0
0
1
1
1
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
1
0
0
0
2
0
0
0
0
1
0
1
1
0
0
1
0
0
0
2
0
0
0
0
1
2
1
0
2
0
2
1
1
0
0
0
0
0
4
0
0
1
0
0
2
0
1
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
2
1
0
2
0
2
0
1
1
0
0
1
0
0
2
3
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
3
0
0
0
0
0
0
0
0
1
0
2
0
0
1
2
0
1
0
0
0
0
0
2
1
2
2
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
2
0
1
0
0
1
0
0
2
0
2
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
3
0
0
1
2
0
0
0
3
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
3
0
1
0
0
1
1
0
1
0
0
0
1
0
0
0
3
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
2
0
0
0
2
0
1
1
1
0
0
0
2
0
0
0
0
0
0
2
1
1
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
1
2
1
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
1
0
2
2
0
1
0
0
2
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
2
3
0
0
0
0
1
1
0
0
0
2
0
0
1
0
2
0
0
0
2
0
0
0
2
0
1
2
2
0
0
1
2
0
0
1
1
0
1
0
0
0
1
0
0
0
0
2
2
1
0
0
0
0
2
0
0
0
0
0
0
0
1
1
2
1
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
1
0
2
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
1
3
0
1
0
4
1
1
0
0
0
0
1
2
0
0
0
1
1
0
0
0
1
0
2
0
0
1
0
2
0
1
0
1
1
0
2
2
0
1
0
0
0
0
0
1
1
2
0
1
0
0
0
2
0
0
2
2
2
0
0
0
0
1
0
0
0
0
0
1
3
2
0
1
0
0
2
0
1
2
0
0
0
1
0
0
0
1
2
0
0
1
0
2
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
1
3
0
0
1
0
0
0
0
0
1
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
1
2
1
1
0
0
2
0
2
0
0
0
0
0
0
2
1
0
2
0
2
2
2
0
0
1
0
0
2
0
0
0
2
0
1
0
1
0
0
1
2
1
2
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
2
2
1
0
1
2
0
3
2
0
0
1
1
1
0
0
0
1
0
1
0
4
0
2
1
0
1
0
2
1
0
1
1
0
2
2
2
0
0
0
4
0
1
0
0
0
1
1
2
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
3
0
1
0
0
2
0
0
0
0
1
0
1
3
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
2
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
2
2
0
1
0
0
2
0
1
0
0
0
2
0
2
0
0
0
0
2
0
0
0
1
0
2
1
2
2
0
0
0
2
0
1
0
0
0
1
1
1
0
0
0
0
1
0
0
1
0
4
0
0
0
1
1
2
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
2
1
0
2
0
0
0
0
1
0
0
0
2
0
2
1
0
0
1
0
0
0
1
0
2
0
1
1
0
0
0
0
0
2
0
0
0
0
1
0
1
0
1
0
0
1
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
1
3
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
1
0
0
2
1
1
2
0
0
0
0
0
2
1
2
2
2
0
1
0
0
0
1
4
0
2
0
2
0
3
0
0
0
0
0
1
0
1
0
0
2
0
1
0
0
0
0
3
1
0
0
1
2
1
0
4
0
0
2
2
0
0
1
0
3
0
1
0
1
2
1
0
2
0
0
0
0
1
2
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
1
1
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
2
0
0
2
2
1
0
1
1
1
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
5
2
0
0
2
2
0
2
0
0
0
1
0
2
0
0
0
1
2
1
0
2
0
2
1
0
0
0
0
3
1
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
3
0
1
0
1
0
2
2
3
0
0
1
0
0
0
2
0
0
0
2
1
5
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
2
1
0
0
1
3
2
1
0
2
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
2
0
1
0
0
2
2
0
0
2
0
0
1
1
0
0
0
1
1
0
0
2
1
0
1
1
1
0
0
1
1
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
2
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
1
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
1
2
0
2
0
1
1
0
1
0
0
0
0
0
1
2
0
2
0
1
0
1
0
0
0
0
0
1
1
1
0
0
0
0
2
1
0
1
0
0
0
1
0
0
8
0
0
1
1
0
0
0
2
2
1
0
0
1
0
0
0
0
1
1
1
0
2
2
2
0
0
0
1
0
0
0
0
0
1
2
1
2
0
1
0
1
5
0
0
0
2
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
2
0
6
0
0
0
0
5
1
0
1
0
0
0
0
0
1
2
2
0
0
0
0
3
0
1
2
0
0
0
2
0
0
1
0
0
0
0
5
0
4
0
0
0
0
0
1
0
2
0
0
0
1
0
0
7
1
5
0
0
0
2
0
0
1
1
1
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
3
0
1
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
1
0
2
0
1
1
1
0
1
0
0
2
0
1
0
2
2
2
1
0
1
2
0
1
0
0
0
0
0
3
1
0
2
0
0
0
1
2
0
0
1
0
2
0
2
0
1
0
3
0
1
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
1
0
0
1
0
1
0
0
0
2
0
2
0
0
0
0
2
0
1
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
1
3
0
0
1
1
0
2
1
0
2
0
1
0
2
0
0
0
0
0
1
0
0
0
2
2
0
2
0
1
1
2
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
1
0
0
0
2
1
0
1
0
0
0
1
0
0
0
0
0
3
1
2
2
0
0
2
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
1
2
0
0
0
0
1
0
0
0
2
0
0
2
0
2
2
0
2
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
1
1
1
0
0
0
0
0
1
0
1
0
0
0
2
3
0
2
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
1
3
1
0
0
1
1
0
0
0
1
0
0
0
0
0
2
0
0
2
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
2
0
0
2
2
0
0
2
0
0
1
0
1
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
1
1
0
0
0
0
2
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
2
1
0
2
0
0
1
0
0
0
0
0
0
0
0
1
1
3
1
0
0
0
1
0
1
0
1
0
1
0
1
0
0
0
3
2
0
2
1
0
2
0
1
0
1
0
0
1
0
2
2
0
0
0
1
1
0
0
0
0
0
0
1
2
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
2
2
2
1
0
0
0
0
1
1
0
2
0
2
0
0
4
0
1
0
0
2
2
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
1
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
2
2
0
0
0
2
1
0
0
2
2
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
2
0
0
0
0
0
0
2
1
0
0
2
3
0
0
0
4
2
0
2
1
1
0
1
2
0
0
0
0
0
2
0
1
2
1
0
0
0
0
2
0
0
0
0
1
0
3
0
4
0
0
1
0
2
4
1
2
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
3
0
0
5
0
2
0
0
2
2
2
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
1
0
0
0
1
3
1
1
1
0
0
0
0
0
0
3
0
0
0
0
0
2
1
0
0
0
2
2
0
0
0
0
0
2
0
0
2
2
0
2
0
1
0
2
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
2
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
3
0
0
0
0
2
0
2
0
2
1
2
0
0
0
0
1
1
0
0
0
0
1
1
2
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
2
2
2
0
1
0
2
0
2
1
0
0
1
2
0
3
0
0
0
0
4
2
1
0
0
0
0
1
0
0
0
1
0
1
0
0
1
2
0
2
0
1
1
0
0
1
2
0
0
0
0
0
1
0
2
1
0
0
0
0
2
0
0
1
0
2
0
1
0
1
3
0
0
0
2
1
2
2
1
0
3
0
1
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
1
2
1
1
0
0
1
0
0
0
2
1
0
0
1
1
2
1
3
0
2
0
2
0
1
0
0
0
0
0
1
3
0
0
0
1
2
1
3
1
0
0
1
0
1
1
0
0
0
0
1
0
2
3
0
0
2
0
0
0
0
0
0
0
1
2
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
2
0
1
0
2
0
2
0
0
0
0
0
1
0
0
1
0
0
1
0
2
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
3
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
1
0
3
0
2
0
0
0
1
2
0
0
1
0
0
1
0
2
0
2
2
0
1
0
0
2
0
0
0
1
2
0
0
0
0
0
2
0
0
0
3
0
0
2
0
2
0
2
2
1
0
0
2
0
1
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
4
2
0
0
1
1
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
2
3
1
0
0
0
0
0
2
0
0
0
0
0
2
0
2
1
0
2
0
0
1
0
1
0
4
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
1
2
2
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
1
2
0
0
1
1
0
1
0
0
0
2
1
1
1
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
2
2
2
2
3
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
2
1
2
2
0
0
0
0
0
0
2
3
0
0
3
0
0
2
2
0
0
0
1
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
0
0
0
2
3
0
1
2
1
0
0
0
2
1
0
1
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
1
2
0
0
2
1
0
2
0
2
0
0
2
0
0
0
3
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
2
1
0
1
0
0
1
1
0
0
2
2
0
0
1
0
1
0
0
2
0
0
2
0
0
2
0
1
0
0
0
0
0
2
1
0
0
2
2
1
2
0
1
0
0
1
0
0
0
0
3
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
8
0
0
0
0
1
1
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
2
1
0
3
0
2
2
2
0
2
0
2
2
0
2
2
0
0
0
0
0
2
1
0
0
0
0
0
0
1
6
1
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
2
0
0
0
3
1
1
0
0
1
1
1
2
1
0
0
0
0
0
0
2
2
0
0
1
1
0
0
1
2
2
0
1
0
0
0
1
0
2
0
0
1
3
0
0
0
0
0
1
0
0
0
2
1
1
0
1
2
1
2
1
0
0
1
1
0
1
0
0
0
0
0
0
1
2
0
0
3
1
0
2
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
1
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
3
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
1
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
3
0
0
0
2
0
2
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
1
2
1
0
0
0
1
1
0
0
1
0
7
2
0
0
3
2
0
1
2
2
0
0
0
2
0
0
0
1
0
2
1
0
0
0
1
0
0
0
2
0
0
0
0
1
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
1
0
0
2
1
1
0
1
0
0
1
0
0
0
0
0
1
2
2
2
2
0
2
0
0
1
0
2
2
2
2
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
1
3
1
0
1
0
1
0
0
0
0
0
2
2
2
0
0
0
0
1
0
1
0
0
0
3
1
0
0
2
0
0
0
0
2
0
0
0
2
1
0
0
0
2
0
1
1
0
0
0
0
1
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
1
0
0
1
2
2
2
1
0
0
0
2
0
1
2
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
1
1
0
0
0
0
0
0
0
0
0
2
0
2
2
1
1
1
0
0
4
2
0
2
2
0
0
0
2
0
2
2
0
1
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
3
0
0
1
0
1
0
0
0
1
1
0
1
1
0
0
0
0
0
0
4
0
2
1
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
1
1
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
1
0
0
0
2
0
0
0
0
1
0
1
0
0
1
1
2
0
2
2
0
1
0
0
2
0
0
0
0
0
0
2
2
0
2
2
0
0
0
0
1
0
0
1
0
2
0
1
0
0
2
0
2
0
0
1
0
2
0
0
1
0
0
0
1
1
0
0
0
1
2
0
0
2
1
2
0
0
1
2
0
0
0
0
2
0
0
0
1
0
0
0
1
2
2
0
0
0
0
1
0
0
1
0
0
2
0
1
0
0
0
0
2
0
1
2
1
1
0
1
0
0
0
1
0
1
0
0
2
2
0
0
1
0
0
0
0
0
0
2
2
1
0
1
0
0
0
0
0
0
1
0
0
2
4
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
1
1
2
0
0
1
1
2
1
0
0
0
0
0
2
0
6
0
0
1
0
1
2
1
0
0
0
1
0
0
1
0
2
0
0
0
2
0
0
0
0
0
2
0
0
1
1
1
0
1
0
2
1
0
1
0
0
1
0
0
1
0
0
0
1
0
3
0
0
0
0
2
2
1
1
2
0
0
2
0
1
2
0
0
2
0
0
0
0
2
1
1
2
2
0
2
0
2
0
1
3
1
2
1
0
0
0
1
0
2
0
0
2
0
3
0
0
0
0
1
0
0
1
0
0
0
0
1
3
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
2
0
1
0
0
0
2
0
2
0
0
2
0
0
0
1
2
0
0
0
8
0
0
1
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
1
0
1
0
0
0
2
0
0
0
0
2
0
1
1
0
0
2
0
2
1
0
0
2
0
2
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
2
0
0
0
2
0
1
0
1
0
0
0
0
1
1
0
0
1
0
0
0
2
0
0
0
0
0
1
1
2
0
1
0
5
2
2
0
0
0
0
1
0
1
0
6
3
0
1
0
0
3
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
1
2
2
1
2
3
2
1
0
0
2
0
1
0
0
0
4
0
0
2
0
2
0
0
0
1
2
1
2
1
0
0
4
0
2
0
1
2
0
1
2
0
1
0
1
1
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
2
1
1
0
2
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
2
2
0
0
0
2
2
0
0
0
0
1
0
0
1
0
1
0
0
0
2
0
2
0
0
1
0
2
0
0
1
1
1
2
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
2
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
2
0
2
0
0
1
0
0
2
0
2
0
0
0
1
0
0
2
1
0
0
2
2
1
2
0
1
0
0
2
1
1
0
0
0
0
0
0
3
0
0
2
1
1
3
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
2
0
1
0
0
0
1
1
0
0
1
1
2
0
0
0
1
1
1
1
0
0
0
0
0
0
3
0
0
0
1
0
1
0
0
2
0
0
0
1
0
0
0
3
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
1
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
2
0
2
2
1
0
1
1
2
2
1
0
0
0
2
0
0
2
0
0
0
0
2
0
3
0
0
0
3
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
2
2
2
2
0
0
0
3
2
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
1
1
0
0
1
1
2
0
0
2
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
1
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
2
2
2
2
0
0
0
0
3
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
2
1
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
2
1
0
0
0
1
0
1
0
0
0
2
0
0
0
1
2
0
1
2
1
0
0
0
0
3
0
1
0
2
2
0
0
2
2
2
1
0
0
0
1
2
0
2
0
0
2
0
0
0
2
2
1
2
0
0
0
0
0
2
0
0
2
2
2
1
1
0
2
0
2
2
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
2
0
0
0
0
2
0
2
0
0
0
0
1
1
1
0
0
4
0
1
2
0
0
0
1
0
1
0
2
0
2
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
2
0
0
0
1
0
0
1
0
0
0
1
0
1
0
2
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
3
2
0
0
1
2
0
0
0
0
0
0
0
0
1
0
1
2
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
5
0
1
0
0
0
0
0
2
1
0
0
1
0
1
0
0
0
0
0
0
2
0
1
0
1
0
2
1
2
1
0
0
2
1
1
0
2
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
2
1
0
2
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
3
2
0
3
2
0
0
0
0
1
0
0
0
0
2
0
3
0
2
1
2
0
0
0
0
0
0
1
0
2
0
0
1
1
1
0
0
2
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
3
2
0
0
0
1
0
2
2
0
2
2
1
1
1
1
4
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
1
0
1
1
0
0
1
0
0
1
1
0
1
0
0
0
2
0
1
1
0
2
2
0
1
0
0
1
0
2
2
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
2
0
0
2
0
0
2
0
0
0
0
2
0
0
0
2
1
1
2
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
4
1
0
0
1
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
2
1
1
0
0
0
2
0
0
0
2
2
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
3
1
1
0
1
0
1
0
0
4
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
2
1
0
0
0
0
0
1
1
0
0
1
1
0
2
0
0
2
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
2
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
2
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
2
1
2
0
0
0
0
2
0
0
0
0
1
1
0
2
0
2
1
1
1
0
1
0
0
0
0
2
0
0
0
1
0
0
2
1
0
0
2
1
2
0
0
0
0
1
0
0
0
2
2
1
0
0
0
1
0
0
0
2
0
1
2
1
0
0
5
3
0
0
1
0
1
0
0
0
2
0
0
0
0
2
0
0
2
0
2
0
0
0
1
0
2
0
0
0
1
2
1
3
0
2
0
0
0
1
0
5
5
1
0
0
4
0
0
1
1
0
0
0
1
0
2
0
1
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
2
2
0
0
0
0
0
2
3
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
2
0
0
3
1
2
0
1
0
1
0
0
2
0
0
0
0
1
0
2
0
0
2
0
2
0
1
0
0
1
0
0
2
3
0
0
1
0
2
2
0
0
0
2
0
2
0
2
0
0
0
0
0
2
0
0
0
1
1
0
0
0
2
0
0
2
0
0
0
0
2
0
1
1
2
1
1
0
3
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
1
0
0
0
2
2
0
1
1
0
0
0
0
2
0
0
0
0
0
2
0
0
1
2
0
0
0
2
0
0
2
0
2
1
1
0
0
0
0
0
0
1
0
0
0
0
2
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
1
0
2
2
2
0
0
0
0
2
1
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
2
0
1
0
2
2
1
0
1
1
0
0
0
0
0
0
0
2
1
1
0
0
1
0
0
1
1
0
1
0
0
0
2
2
0
2
2
0
0
1
2
0
0
2
0
0
1
0
2
0
0
2
0
0
0
2
0
0
0
0
2
1
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
2
0
0
0
0
2
3
1
0
0
0
1
0
2
1
0
0
1
0
0
0
2
1
0
2
0
0
1
3
0
2
0
2
2
1
0
2
2
0
0
2
1
2
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
1
0
0
0
2
1
0
0
1
0
0
2
1
0
1
2
0
0
0
2
1
0
0
2
1
2
3
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
1
1
0
0
0
0
2
0
0
0
2
0
3
0
1
0
2
0
0
1
2
0
2
1
0
0
2
0
0
0
0
0
2
0
0
2
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
2
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
10
0
0
1
0
0
0
0
1
2
0
0
2
0
1
0
1
0
0
0
0
0
1
0
0
2
0
0
2
2
0
2
0
2
0
0
0
0
1
2
0
0
0
0
4
0
2
0
0
0
1
1
0
0
0
6
0
0
0
0
0
0
2
0
2
0
1
0
2
0
0
0
2
2
0
0
0
0
2
3
0
0
2
1
0
0
0
2
0
0
0
2
0
0
1
1
0
2
1
0
1
0
2
2
2
0
0
0
1
0
6
0
2
1
0
1
0
0
2
0
0
0
0
0
1
0
0
1
0
4
1
1
0
0
2
2
0
0
0
1
0
0
2
2
0
0
2
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
1
1
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
2
1
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
1
3
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
1
0
1
0
0
1
0
2
0
2
2
0
3
1
0
1
0
1
1
17
2
1
2
0
1
1
2
1
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
2
1
0
2
0
0
0
0
2
1
1
1
0
0
2
0
2
0
2
1
0
2
0
1
0
3
2
0
0
0
0
0
0
2
2
2
2
2
1
0
0
0
0
0
0
0
1
0
2
1
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
1
0
2
0
2
4
0
2
1
3
0
0
0
2
1
0
0
0
1
0
0
1
0
0
1
0
2
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
3
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
2
2
0
1
4
1
0
0
0
1
0
0
1
1
0
2
0
0
3
1
1
0
2
0
2
0
2
0
2
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
2
0
0
2
0
0
0
1
0
8
0
2
0
2
0
0
1
1
3
0
2
0
0
0
0
1
2
1
0
0
3
2
0
0
0
0
0
1
1
2
0
1
0
0
2
0
0
2
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
2
1
0
0
1
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
2
0
2
2
2
0
0
0
0
0
2
0
2
2
0
2
0
0
0
0
0
1
3
2
0
2
0
0
2
0
0
0
0
1
0
0
0
0
2
2
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
1
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
2
0
1
1
1
0
0
2
0
1
0
1
2
0
0
0
0
0
1
0
0
0
1
2
1
0
2
3
1
0
0
1
0
0
1
0
0
2
0
1
0
2
2
0
0
0
2
1
3
1
0
0
1
0
0
2
0
0
2
1
2
0
2
2
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
2
0
0
0
0
0
1
0
2
0
1
0
2
0
0
1
0
0
2
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
1
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
3
0
0
1
0
0
1
0
0
0
2
2
0
1
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
2
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
3
1
0
0
1
1
1
2
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
1
2
0
0
0
2
0
0
1
0
6
2
1
0
1
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
2
0
0
2
0
0
0
0
4
0
0
2
1
3
0
2
2
0
1
1
0
0
0
0
0
1
0
0
2
1
0
0
0
0
1
0
0
0
0
0
1
2
0
0
4
0
1
0
2
0
1
0
1
0
1
0
0
0
4
1
0
0
1
0
2
2
2
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
1
0
3
0
0
0
1
2
1
0
0
2
1
0
0
2
0
0
2
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
2
1
2
1
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
2
0
0
2
0
0
1
2
1
0
0
1
0
0
1
0
1
1
2
2
1
0
0
0
0
0
0
0
1
2
0
0
2
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
2
2
0
0
0
0
0
0
1
2
0
2
2
0
0
0
1
0
1
1
0
1
3
0
2
0
0
2
0
2
0
1
2
0
0
2
1
0
0
0
0
1
0
2
2
0
2
0
0
2
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
2
3
0
0
0
2
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
1
0
1
1
0
0
0
0
0
0
1
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
2
0
1
0
0
0
2
2
0
0
0
1
0
0
1
0
2
2
0
1
1
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
3
1
0
1
0
0
0
1
1
2
2
1
1
2
0
0
2
1
2
2
1
1
0
4
5
2
0
0
2
1
0
0
1
0
2
0
2
2
0
0
2
2
0
0
2
3
0
0
0
0
0
0
2
0
2
2
0
1
1
0
0
0
0
0
2
0
3
2
2
0
0
1
0
0
1
0
0
1
0
0
0
2
2
0
0
0
0
0
0
2
0
1
1
0
0
1
0
1
0
2
0
1
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
1
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
2
1
0
1
0
0
3
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
4
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
1
4
2
0
1
1
0
1
0
0
0
0
2
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
1
2
0
0
1
0
2
0
0
0
0
1
1
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
2
0
0
0
0
0
2
0
0
1
2
0
3
0
1
0
0
0
0
0
0
0
0
0
0
2
3
2
1
0
0
2
1
2
0
0
0
0
0
0
0
0
2
0
1
1
0
0
2
0
2
2
2
1
0
0
1
0
1
0
0
2
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
2
2
1
0
0
1
1
2
0
2
1
0
2
1
0
2
0
0
0
2
2
2
2
0
0
0
0
0
0
1
8
1
0
0
0
1
1
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
1
0
0
2
0
1
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
3
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
1
0
0
0
2
0
2
0
2
0
0
1
0
0
0
0
1
2
2
0
0
0
0
0
0
4
2
0
0
2
0
1
0
0
0
2
2
2
0
2
0
0
0
2
0
0
2
0
0
3
0
0
0
0
0
0
2
2
0
0
1
1
1
1
0
2
0
2
1
0
1
0
1
0
1
0
1
0
0
1
0
1
2
1
2
0
0
0
2
2
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
2
2
0
1
2
0
0
1
0
0
0
1
0
0
2
0
0
0
0
4
2
0
0
0
0
2
2
0
0
1
0
2
1
4
0
2
0
1
0
0
0
2
0
0
0
0
0
0
2
0
1
0
1
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
1
0
1
1
2
2
0
0
0
0
0
0
0
3
1
0
1
0
1
2
0
2
4
0
0
0
0
2
0
0
3
1
0
2
1
0
0
0
2
2
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
1
0
0
0
0
1
0
0
6
0
3
0
0
0
1
1
2
1
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
1
1
2
0
0
2
0
1
0
1
0
0
1
1
1
0
0
1
0
1
0
1
0
3
0
0
0
1
0
0
0
2
0
0
2
3
2
0
2
0
1
0
0
0
0
0
0
0
2
0
1
0
2
0
2
0
0
0
2
0
0
1
0
0
1
0
1
2
0
0
2
0
2
2
0
1
1
1
0
1
0
1
0
0
0
0
1
1
0
0
1
0
0
0
2
2
1
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
2
2
0
1
0
2
0
0
0
0
5
0
0
0
0
1
0
1
0
1
1
0
0
1
0
2
0
0
0
3
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
1
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
3
5
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
3
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
1
0
1
0
2
4
0
2
0
1
1
1
0
0
0
0
1
2
0
1
1
0
0
0
0
0
1
2
0
0
2
2
2
2
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
1
0
0
1
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
2
2
1
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
1
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
1
0
2
2
0
0
0
0
0
0
0
2
0
1
0
0
1
1
1
0
1
0
0
4
0
0
0
0
2
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
1
2
0
0
1
0
1
2
0
0
1
1
0
0
2
0
0
0
0
1
2
0
0
1
3
0
0
0
3
0
0
2
0
0
2
4
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
2
1
1
0
0
0
0
0
1
0
0
2
1
0
2
2
1
0
0
0
3
1
0
3
0
0
1
4
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
2
2
0
1
2
1
3
1
0
1
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
2
0
0
3
0
5
0
0
3
0
0
1
0
0
2
7
0
0
1
0
0
2
0
1
2
2
0
3
3
2
0
0
2
0
0
0
0
3
1
0
0
2
0
2
1
2
1
0
0
2
0
2
0
1
2
0
0
2
0
0
1
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
2
0
1
0
1
2
0
3
2
2
0
2
1
2
0
1
0
3
1
1
2
0
0
2
0
0
3
1
1
0
0
0
0
2
2
0
2
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
2
0
0
0
1
0
0
5
0
0
2
0
3
0
0
2
0
0
0
0
0
0
2
0
1
1
0
0
0
1
0
0
0
1
0
0
0
2
4
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
3
2
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
2
0
2
0
2
0
1
0
0
0
1
0
0
0
0
0
1
0
2
0
2
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
1
1
0
0
2
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
4
2
0
1
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
1
2
0
0
0
0
2
0
2
2
1
2
0
1
0
1
2
1
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
2
2
1
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
2
1
3
2
2
0
0
1
0
1
1
0
4
0
0
0
2
3
3
0
0
0
2
0
0
0
0
2
0
2
1
2
2
0
0
1
0
0
2
1
0
0
0
0
1
0
1
0
0
2
0
0
1
0
1
0
2
0
0
0
1
0
1
0
0
1
0
0
0
0
2
0
0
1
0
1
0
0
0
0
2
0
2
0
0
1
1
0
1
0
0
2
1
1
1
2
0
0
0
0
0
0
0
1
0
2
0
0
1
0
2
0
1
0
0
1
0
1
0
0
0
1
0
0
1
0
1
2
2
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
1
0
1
1
0
1
0
0
0
0
2
1
0
0
0
0
0
0
3
0
0
1
0
0
2
0
0
0
0
2
0
3
0
0
0
0
0
0
1
0
1
1
2
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
1
0
0
0
0
2
1
2
1
0
0
0
0
0
1
0
1
1
0
0
0
1
6
0
0
0
1
0
2
2
0
0
1
2
0
0
0
0
2
2
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
1
0
3
2
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
1
1
0
0
2
1
0
0
1
0
0
0
1
0
3
1
2
1
0
0
0
2
0
5
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
2
0
0
2
1
1
0
0
0
0
1
0
0
1
0
1
2
0
0
0
2
0
0
2
1
0
2
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
2
0
1
2
2
0
2
0
1
0
0
0
2
1
0
0
2
0
0
2
1
0
1
2
0
0
2
0
2
0
0
0
1
0
1
0
2
0
1
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
2
1
0
2
2
1
0
0
0
0
0
0
2
0
0
2
0
1
0
0
1
0
0
2
0
0
2
0
0
0
0
1
0
0
1
0
0
3
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
1
2
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
1
0
1
2
0
1
1
0
0
0
1
1
0
0
2
1
0
2
1
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
6
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
2
2
1
0
0
1
0
0
0
2
1
0
2
2
0
0
0
2
0
0
0
0
0
0
3
2
0
0
3
0
4
0
0
0
0
1
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
1
3
0
2
0
1
1
0
2
0
0
0
0
0
0
0
0
0
1
1
0
2
4
0
2
0
0
2
0
0
0
1
1
0
0
0
4
2
2
2
0
0
0
0
0
0
1
2
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
1
0
0
0
0
0
1
1
0
0
1
0
0
1
1
2
0
2
1
1
0
0
3
0
0
1
0
2
0
1
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
1
0
1
2
1
2
0
0
3
2
2
0
0
1
0
0
2
1
0
0
1
0
0
1
0
0
0
0
0
2
2
0
1
0
1
0
1
0
0
2
0
2
2
2
0
0
0
1
2
2
1
2
0
0
0
0
2
0
2
0
0
1
2
0
3
0
0
0
2
0
0
1
0
0
1
0
0
0
1
0
1
1
0
1
0
0
3
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
2
0
0
0
0
1
0
1
1
0
2
1
0
0
1
0
1
1
3
0
0
0
2
0
0
1
1
2
0
0
2
0
2
0
0
0
0
0
1
5
0
1
2
0
0
0
0
0
0
1
0
0
1
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
3
0
0
1
0
1
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
2
1
2
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
3
0
1
0
2
0
2
2
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
1
0
0
0
0
0
1
1
0
2
0
0
0
0
0
4
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
2
2
0
1
1
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
1
0
0
5
1
2
2
4
1
0
1
0
0
0
2
1
0
0
0
2
1
0
1
2
0
0
0
2
0
1
0
3
2
1
2
0
1
1
0
1
0
0
1
1
2
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
2
0
0
0
0
2
0
0
1
0
0
0
1
2
0
0
0
0
2
0
0
1
0
1
0
1
0
2
0
2
1
0
0
0
0
5
1
0
0
1
1
0
0
0
0
2
1
1
2
2
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
1
0
1
0
0
2
0
1
0
0
0
0
0
1
0
0
1
3
0
0
0
0
1
0
0
2
2
2
2
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
2
0
0
0
2
0
1
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
2
1
2
0
0
0
3
0
2
0
0
0
2
0
0
0
2
1
1
0
0
0
1
0
2
1
2
0
0
2
2
1
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
1
0
1
0
1
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
1
2
1
0
0
1
0
0
2
0
0
0
0
1
0
2
3
1
0
0
6
1
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
7
0
0
1
2
3
0
0
2
1
0
0
0
1
0
2
0
0
1
2
1
2
0
0
0
0
0
0
1
0
0
0
0
0
2
2
1
0
0
0
1
0
0
0
0
1
0
0
0
0
2
2
0
2
0
2
0
0
0
2
0
2
1
1
0
0
0
1
2
1
1
1
2
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
2
1
1
0
1
0
0
0
2
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
2
0
0
0
0
0
2
1
2
0
0
0
1
0
0
0
1
0
0
0
1
2
0
2
0
0
0
1
0
0
2
2
1
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
1
0
1
0
1
0
2
2
0
1
0
0
2
2
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
2
0
2
0
0
1
1
0
1
0
0
1
2
0
0
0
1
2
0
0
0
0
2
0
0
0
1
0
1
0
2
0
0
1
1
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
1
2
0
0
1
1
0
1
2
0
1
1
2
2
2
1
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
1
4
0
0
3
0
0
2
0
0
0
0
0
1
2
0
1
0
3
0
0
1
0
1
0
0
3
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
2
0
5
0
2
1
1
0
0
0
0
1
0
0
3
0
0
2
0
1
2
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
1
1
2
0
0
0
0
0
0
3
0
2
0
0
0
2
1
0
0
0
1
3
1
0
0
0
0
2
0
2
1
1
0
0
0
0
0
2
0
0
0
1
0
0
1
0
1
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
2
0
1
1
1
0
2
0
0
2
0
1
2
2
2
0
0
0
0
1
0
0
0
2
0
0
0
1
2
0
1
2
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
2
1
2
1
2
0
16
2
1
0
2
1
0
0
0
2
0
2
0
0
2
1
1
2
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
2
1
1
4
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
1
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
1
1
0
2
0
0
0
0
0
0
0
0
0
2
2
0
1
1
0
0
0
2
1
2
0
0
1
0
0
0
0
0
0
0
1
1
2
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
1
1
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
2
0
3
0
0
3
0
1
0
0
0
0
1
0
3
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
2
0
0
2
0
1
0
1
1
0
0
0
0
0
1
2
1
0
0
0
2
2
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
5
2
0
0
3
2
0
2
0
0
0
0
0
0
0
2
0
0
0
2
2
0
1
1
0
0
0
0
1
2
0
0
2
1
0
1
1
2
0
0
0
0
1
2
0
0
0
0
1
0
3
1
0
0
0
0
1
0
0
0
0
0
2
0
0
2
5
2
1
0
1
0
1
0
0
0
0
2
0
0
1
0
0
1
4
1
1
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
2
0
0
0
0
0
3
0
0
0
1
2
0
0
2
1
0
1
0
0
0
0
0
1
1
0
0
1
5
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
2
0
0
0
0
0
1
1
2
0
0
0
0
1
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
2
2
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
2
0
0
1
1
0
0
0
0
1
2
1
1
1
1
0
1
0
0
0
0
1
0
0
0
0
1
2
0
0
0
4
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
1
3
4
0
0
0
1
1
0
0
0
2
1
1
0
2
0
1
0
2
2
0
0
0
1
0
1
1
2
2
0
0
0
1
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
2
1
0
0
3
0
0
0
2
0
0
1
0
2
1
2
0
1
0
0
0
0
1
0
0
0
2
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
2
1
0
1
0
2
0
0
0
0
0
0
2
0
0
2
0
2
1
1
1
1
1
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
2
0
1
0
0
2
0
2
2
1
0
1
0
0
0
0
0
2
0
0
1
0
0
1
1
0
0
2
2
0
1
0
0
0
0
0
0
0
0
1
2
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
2
0
0
0
0
2
1
1
0
3
0
0
0
0
2
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
1
0
2
0
0
0
1
0
0
2
0
0
2
1
0
0
0
0
2
0
0
0
0
0
2
3
0
1
1
0
0
1
0
0
2
2
2
0
1
2
1
0
1
4
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
2
0
2
0
0
0
0
0
2
2
2
0
2
0
3
0
0
0
0
2
1
1
2
3
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
1
2
0
1
1
0
1
1
0
0
0
0
0
1
2
2
0
0
2
1
0
1
0
1
0
0
0
1
0
0
0
0
2
0
2
0
1
0
0
0
0
1
1
2
2
2
0
0
0
0
5
2
0
0
0
0
0
2
0
1
0
2
1
2
0
1
0
0
2
0
0
2
2
0
1
1
0
1
0
0
0
0
1
0
2
0
1
1
0
0
0
2
4
0
0
0
0
1
0
0
2
0
0
2
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
2
2
1
1
0
0
0
1
0
0
0
1
3
2
0
0
13
1
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
1
0
1
0
0
1
0
0
1
0
0
0
2
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
2
0
0
1
0
0
2
0
1
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
3
0
0
0
0
1
0
2
1
0
2
0
1
1
0
0
4
1
0
1
1
0
1
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
5
2
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
2
0
0
1
0
0
2
2
0
1
1
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
1
0
2
1
2
1
0
0
2
0
1
0
0
0
0
0
3
0
0
0
0
0
0
1
3
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
6
0
0
0
3
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
1
1
0
2
1
0
1
0
0
0
0
0
0
1
2
0
2
0
1
0
0
2
0
0
1
0
0
0
0
5
2
2
1
0
0
0
0
2
0
2
1
0
0
0
1
1
1
0
0
2
0
0
0
0
0
0
0
0
1
1
2
2
2
1
0
0
0
0
0
0
0
0
0
2
1
1
0
1
2
0
0
0
0
2
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
2
0
2
2
0
1
0
0
0
0
1
0
2
2
0
0
0
0
2
2
1
0
0
2
0
2
2
2
2
0
0
0
0
0
1
0
0
2
2
0
2
0
0
0
1
2
0
0
1
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
1
1
2
0
0
0
1
0
1
0
0
0
1
1
0
2
0
0
0
1
0
0
1
3
1
0
0
2
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
2
2
1
0
0
0
1
1
2
2
0
2
2
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
2
2
2
0
1
0
0
2
0
0
2
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
3
2
0
0
0
0
1
0
0
0
0
0
1
0
0
1
3
0
0
2
0
1
0
0
0
0
1
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
3
0
0
1
2
2
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
2
2
0
2
0
1
0
2
0
0
1
0
0
0
1
1
0
3
0
0
1
0
0
0
0
0
0
0
2
2
2
0
2
5
0
0
2
0
0
0
1
2
0
0
1
1
0
2
1
4
0
0
1
0
0
2
1
0
0
0
0
1
0
0
0
1
1
2
0
0
0
2
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
2
1
0
0
0
1
0
0
0
0
1
1
1
2
1
0
0
1
1
0
0
0
2
0
0
0
1
0
0
1
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
2
2
1
3
0
1
0
1
0
0
0
0
0
0
1
3
1
0
2
2
1
0
2
0
2
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
2
1
0
0
2
0
1
2
1
1
0
2
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
2
1
1
0
0
2
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
1
0
0
3
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
2
3
1
0
3
1
2
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
2
1
1
0
0
0
0
2
0
1
0
0
3
0
2
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
2
0
0
1
0
1
0
0
0
0
0
0
1
2
0
0
1
0
1
1
0
0
3
0
0
2
0
0
2
1
0
0
0
0
0
1
0
1
0
0
1
2
0
0
1
1
1
2
0
0
1
2
2
0
0
3
2
2
0
1
0
0
1
2
1
0
2
1
2
0
0
1
0
1
0
4
0
0
1
0
0
2
0
0
2
2
2
2
1
0
0
0
0
0
1
2
0
2
0
1
0
0
0
0
0
2
0
0
0
0
1
0
3
0
2
0
1
0
2
0
0
0
0
0
2
0
0
0
1
2
1
0
0
1
0
0
0
0
0
0
2
4
0
0
1
0
0
2
0
0
2
0
2
0
0
2
0
2
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
2
0
1
2
0
0
1
0
0
0
0
2
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
1
0
0
2
1
1
2
1
1
0
1
0
0
0
0
0
0
2
0
1
0
2
1
0
0
1
1
0
2
0
0
0
0
0
2
0
0
3
1
0
0
2
1
0
1
0
0
0
1
1
0
0
1
2
0
2
0
1
0
0
0
0
0
2
0
0
1
2
1
0
2
0
1
0
1
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
2
2
0
0
0
0
0
0
0
0
2
2
0
0
0
2
2
2
0
0
0
1
0
1
0
1
0
0
0
1
0
2
0
0
1
0
0
1
2
2
0
0
1
0
0
0
0
0
0
0
1
1
2
1
2
2
0
1
0
0
0
0
0
2
2
1
0
0
1
2
2
0
1
2
0
0
0
1
0
1
0
1
0
0
0
0
0
0
2
0
4
5
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
2
0
2
0
1
0
0
0
2
0
0
2
0
3
0
0
1
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
10
0
12
0
1
0
0
0
0
1
1
1
0
0
0
0
0
2
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
1
2
0
0
0
0
1
0
2
0
0
2
1
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
2
1
0
0
0
0
1
0
0
0
0
1
3
2
0
0
0
2
0
0
2
1
0
0
0
0
0
0
1
1
1
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
1
1
0
2
0
2
0
2
0
2
0
0
1
0
1
1
0
0
3
0
1
3
0
0
1
2
0
1
0
0
0
2
0
0
0
1
3
0
4
2
5
2
0
1
0
0
0
2
2
2
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
2
0
0
0
0
2
0
0
0
1
3
2
2
0
0
0
3
0
2
0
1
0
2
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
2
0
0
1
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
3
1
0
0
0
1
0
0
3
0
2
0
0
0
1
0
0
3
0
0
0
0
0
0
0
1
2
0
0
2
0
0
1
0
2
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
1
2
0
1
1
0
2
2
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
1
2
0
0
0
0
0
0
3
1
1
1
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
2
2
1
1
0
0
2
1
0
2
2
1
0
0
2
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
2
0
0
1
1
0
1
0
2
0
2
1
0
2
2
0
0
0
0
2
1
0
1
0
0
0
3
0
1
0
0
1
1
2
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
2
0
0
1
2
1
0
0
2
0
0
1
0
1
0
2
1
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
2
0
1
0
0
0
0
0
2
0
0
1
1
0
0
0
1
0
0
0
0
2
0
0
2
0
2
2
0
0
0
0
2
0
0
2
0
0
2
0
0
0
1
0
0
2
0
0
2
0
2
0
0
0
0
2
1
0
2
0
2
0
0
0
0
0
1
1
0
0
0
0
2
0
2
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
1
1
2
2
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
1
2
0
0
0
0
2
1
1
2
0
0
0
1
0
0
0
4
0
0
0
0
0
2
1
4
0
0
0
0
2
0
2
0
0
0
2
0
1
0
2
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
1
2
0
0
1
0
0
3
0
0
0
2
0
0
1
0
0
0
2
2
0
2
2
1
0
1
1
0
0
0
0
0
1
2
0
0
1
0
0
2
0
0
1
0
1
0
0
2
3
0
1
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
4
0
0
1
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
2
0
0
0
0
1
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
2
0
0
0
0
0
2
1
0
2
1
1
0
0
0
0
1
1
2
1
0
0
0
0
3
0
1
2
0
0
1
3
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
1
1
0
2
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
2
0
0
0
1
2
0
1
0
0
0
1
0
0
1
2
1
0
0
0
0
1
0
0
0
1
0
2
0
2
1
2
0
0
2
1
4
0
2
0
0
0
1
2
2
0
0
0
0
0
2
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
1
0
2
0
0
1
0
0
0
2
0
1
3
0
0
2
0
0
0
2
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
1
0
0
1
0
2
0
2
1
0
0
2
2
0
0
0
0
0
0
1
0
0
0
1
2
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
2
0
3
1
1
4
1
0
1
0
0
2
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
1
0
3
2
1
0
2
1
0
0
0
0
1
0
0
0
0
2
0
0
2
1
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
1
2
1
1
1
0
3
0
0
1
0
0
2
2
0
2
0
0
2
0
1
0
2
2
0
0
0
0
0
1
1
1
0
1
0
2
5
0
0
0
0
0
0
1
3
2
2
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
4
0
2
0
1
2
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
1
1
1
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
5
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
3
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
2
0
1
0
0
0
0
0
2
0
0
2
2
0
0
2
0
1
0
0
2
1
0
0
0
0
0
0
1
2
0
0
0
0
1
2
0
1
0
0
0
2
0
2
0
2
0
2
2
0
0
0
2
1
2
1
0
0
1
0
0
0
0
2
3
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
5
2
0
2
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
2
3
0
0
0
0
2
0
1
2
0
2
0
0
1
0
0
2
1
0
0
0
2
0
0
0
3
0
2
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
2
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
2
2
1
0
0
0
0
0
0
0
2
0
0
0
2
1
0
2
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
2
2
0
0
0
1
3
0
1
0
0
0
0
0
0
0
1
1
2
0
0
0
2
0
0
0
0
0
0
1
0
1
1
0
1
0
5
0
1
0
0
0
0
0
2
0
0
3
0
0
0
2
0
0
0
0
0
1
2
0
2
0
1
1
2
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
5
0
0
0
2
2
1
1
0
0
1
0
2
2
0
0
0
0
1
2
0
1
0
0
0
2
2
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
2
0
0
2
0
0
2
1
2
2
1
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
3
0
1
2
0
2
0
0
0
2
0
0
1
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
4
0
1
0
0
1
0
0
2
0
4
1
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
1
0
0
0
1
2
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
2
0
3
0
0
0
1
0
2
0
0
1
0
4
2
0
0
0
0
0
0
0
0
1
0
1
2
0
1
2
0
0
1
0
0
0
1
2
3
0
3
1
0
0
1
0
2
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
2
0
0
2
0
2
1
0
1
1
2
2
0
0
3
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
3
0
0
1
0
0
0
0
0
0
3
0
0
0
1
0
0
1
1
0
1
0
0
2
0
0
0
0
2
1
0
2
0
0
0
3
0
0
2
1
0
0
0
0
0
0
0
0
2
0
2
2
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
1
0
0
0
1
0
1
0
0
0
2
5
0
0
0
0
1
2
0
1
0
2
0
2
0
0
0
0
1
1
0
1
2
0
0
0
0
0
0
0
1
1
2
0
1
0
1
2
1
0
0
0
0
2
0
0
0
0
0
0
1
2
1
0
2
2
2
0
1
0
0
2
0
1
2
0
2
1
0
3
0
2
0
0
0
0
1
1
0
2
1
0
1
15
0
1
2
1
0
0
0
0
0
1
2
3
1
0
0
0
2
0
2
0
2
0
0
0
2
1
1
0
2
0
0
1
1
0
0
3
0
0
0
2
2
0
2
1
0
0
0
0
0
0
2
0
1
1
1
1
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
2
1
2
2
0
0
2
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
2
0
0
1
0
0
1
0
0
1
2
1
0
0
0
0
0
0
2
2
0
0
1
2
2
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
2
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
1
1
2
2
1
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
1
0
2
3
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
1
0
0
2
1
0
0
1
0
2
1
0
0
7
1
0
0
0
1
1
2
0
0
2
0
0
0
0
1
0
2
0
0
0
0
2
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
0
0
0
2
0
0
2
2
0
0
0
0
0
1
0
1
0
1
1
1
0
0
1
0
1
0
2
0
0
0
0
0
0
1
3
0
0
1
0
0
1
0
0
0
0
2
2
1
3
1
1
0
2
0
0
2
0
0
0
1
0
0
2
1
0
2
3
0
1
2
0
1
2
1
0
0
0
5
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
2
0
1
0
2
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
1
2
1
2
2
2
0
0
2
0
0
5
1
0
2
0
0
0
0
0
2
0
0
0
1
3
0
0
0
2
2
0
0
0
1
1
0
0
0
2
1
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
2
3
0
1
2
0
0
1
0
1
0
0
0
0
1
2
0
2
0
1
2
0
1
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
1
2
1
0
1
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
2
1
0
0
0
1
0
2
1
0
2
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
1
7
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
1
1
0
1
0
0
0
0
1
1
0
0
0
2
2
2
0
2
0
2
0
1
0
0
2
0
1
0
1
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
2
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
2
2
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
3
0
0
0
1
0
0
2
2
1
0
0
1
2
0
2
0
0
0
0
0
0
0
1
2
0
2
0
0
0
2
0
0
2
0
0
2
3
0
2
0
0
0
0
0
2
2
2
2
0
0
0
2
1
2
0
1
1
1
1
0
0
0
0
2
0
0
2
2
0
2
0
7
2
2
3
0
0
0
0
0
0
0
2
0
0
0
2
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
1
2
0
0
2
1
0
1
0
1
0
2
0
0
0
1
0
1
0
0
1
0
0
2
1
0
0
0
2
1
0
0
2
1
0
0
2
0
1
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
1
0
1
2
0
2
0
2
0
1
1
0
0
0
0
0
0
0
0
0
2
0
3
2
0
1
0
0
1
0
0
1
2
0
1
0
0
0
1
1
0
1
0
2
0
0
1
0
0
0
0
0
1
0
1
0
2
2
0
1
0
0
0
2
2
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
2
0
3
1
0
0
0
0
1
2
1
0
1
2
2
3
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
2
1
1
0
0
0
1
2
2
0
2
0
0
0
0
1
0
0
1
0
1
0
0
0
2
0
2
0
1
1
0
1
0
0
0
1
1
0
3
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
2
1
0
3
1
2
0
0
0
0
0
1
2
0
1
0
0
0
0
2
2
1
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
3
0
2
0
0
0
1
2
0
0
1
3
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
2
1
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
3
0
0
2
0
1
0
0
0
0
3
0
1
1
2
0
0
0
1
0
2
1
1
0
0
2
3
0
0
1
1
2
0
0
0
0
0
2
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
2
0
2
6
0
0
2
0
0
2
1
1
1
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
1
0
2
2
0
0
1
0
0
0
0
0
0
1
2
1
0
2
0
1
2
0
2
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
2
0
0
7
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
2
0
0
0
1
0
1
0
0
1
2
2
2
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
2
2
0
0
0
1
1
0
0
2
0
2
1
0
2
0
2
0
0
2
0
1
0
0
2
0
0
2
2
1
1
0
0
0
1
0
2
1
1
0
0
0
0
0
0
0
0
0
1
1
2
0
2
0
0
0
1
2
0
0
0
0
0
2
2
0
0
2
0
2
0
0
0
0
1
0
0
0
0
1
0
2
1
0
2
0
0
2
0
0
0
0
2
0
2
0
0
0
3
1
1
1
2
2
0
0
0
1
1
2
0
1
2
0
0
0
1
2
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
2
2
0
0
0
1
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
2
0
0
0
1
1
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
1
0
1
0
0
3
2
2
0
0
4
2
0
0
1
1
0
2
0
0
0
1
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
1
2
1
2
0
0
0
2
0
3
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
3
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
2
0
0
0
0
0
2
0
0
1
0
0
2
0
0
1
0
2
0
0
2
0
0
0
2
0
0
2
0
2
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
1
2
0
1
1
0
0
0
4
2
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
3
0
0
1
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
3
0
0
1
0
0
0
1
0
0
0
2
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
2
0
0
1
1
2
2
1
0
0
0
0
0
0
0
2
2
0
3
0
0
0
1
0
0
0
0
0
2
2
0
1
1
0
0
2
0
0
2
0
0
2
0
2
0
0
0
0
0
2
1
1
0
2
0
0
1
1
0
1
0
2
0
0
0
0
2
0
0
0
0
0
4
0
2
2
1
0
0
0
0
0
2
0
0
0
3
2
2
0
2
1
2
2
1
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
1
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
2
0
1
0
0
1
0
0
2
0
0
2
5
0
0
1
0
2
0
1
1
0
0
2
0
1
1
0
0
0
0
0
0
0
0
1
3
2
0
0
2
0
2
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
1
0
2
1
0
1
0
0
3
2
0
1
0
0
3
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
2
0
0
0
1
2
2
2
0
2
3
1
0
1
2
2
0
0
0
2
1
1
0
2
0
2
0
1
0
2
0
0
0
0
2
0
0
2
0
1
2
0
3
0
0
2
1
0
0
1
0
0
0
0
2
3
2
0
0
1
1
0
2
0
2
1
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
4
0
0
1
0
2
2
0
0
0
0
2
4
0
1
3
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
3
1
0
2
0
0
0
0
1
0
2
0
1
0
2
0
0
0
0
0
0
0
2
4
0
1
0
0
0
0
0
1
0
0
2
2
2
1
0
0
2
2
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
2
1
0
2
0
0
2
1
0
0
0
1
3
0
2
0
1
0
2
0
0
1
2
0
0
0
0
1
0
0
2
0
1
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
1
0
0
0
0
0
1
0
4
0
1
0
1
1
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
3
2
1
0
0
0
0
1
0
2
0
2
0
0
1
0
0
0
0
1
0
0
1
0
1
0
4
0
2
2
0
1
0
0
0
1
0
2
2
0
1
0
0
0
0
0
0
1
0
2
0
0
0
1
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
2
2
0
0
1
0
0
0
0
1
0
1
0
0
2
0
0
1
0
0
2
1
0
1
0
1
0
0
3
2
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
4
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
5
1
0
2
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
1
0
0
0
2
0
1
0
0
0
2
0
0
2
1
0
0
1
2
1
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
2
0
0
0
0
2
1
1
2
2
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
2
1
1
0
0
0
0
0
2
2
0
1
0
0
0
2
1
1
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
2
0
0
0
0
1
0
1
1
0
2
0
1
2
0
0
1
2
0
2
0
0
0
2
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
2
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
3
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
2
0
1
2
0
0
1
0
0
1
3
2
0
0
2
2
0
0
0
1
1
1
1
1
1
2
0
0
0
2
1
1
2
1
0
1
0
2
1
0
2
2
2
0
0
0
0
1
0
0
0
1
2
0
0
0
3
0
2
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
4
0
0
0
0
2
2
0
2
0
1
1
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
2
0
0
0
0
7
1
2
2
0
0
0
0
0
0
0
1
0
0
1
2
1
0
0
1
0
0
1
2
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
1
1
2
2
1
2
0
0
0
0
1
1
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
1
0
2
1
1
0
0
2
1
0
0
0
0
2
1
0
0
2
0
0
0
1
0
2
0
0
0
0
2
0
1
0
0
1
0
1
0
0
3
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
2
1
0
1
0
2
0
2
0
0
3
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
2
2
0
1
1
0
0
2
0
0
1
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
2
1
2
0
2
0
0
0
0
2
0
0
0
0
0
0
1
1
1
2
1
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
2
0
0
2
1
2
0
0
0
1
2
0
1
0
0
0
1
2
0
0
2
0
0
2
0
0
1
0
0
0
2
0
2
0
0
0
2
0
0
1
0
0
0
2
2
1
1
0
2
2
0
3
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
2
1
1
1
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
1
1
0
0
0
1
2
1
0
0
0
2
0
2
0
2
0
1
0
0
0
0
0
2
0
1
1
2
0
2
0
0
0
0
0
0
0
2
2
1
0
1
0
1
1
0
2
2
1
0
2
2
2
0
0
0
0
0
0
0
0
0
5
2
1
0
0
0
0
0
1
1
0
1
2
3
1
1
0
1
0
0
0
1
1
2
1
2
1
0
2
0
1
0
0
1
1
0
0
0
0
0
0
1
0
1
0
1
0
1
1
1
0
5
0
0
0
0
1
2
0
1
0
0
0
0
0
0
1
0
0
3
0
0
1
1
1
0
2
0
0
0
3
0
2
0
1
0
0
1
1
3
0
1
0
1
0
0
1
0
0
0
1
1
0
0
2
0
0
0
0
1
0
2
3
2
0
0
1
0
0
0
0
0
0
0
0
0
1
1
2
0
1
1
0
0
0
0
1
0
1
1
2
1
1
1
0
2
0
0
2
0
1
2
0
1
1
0
0
0
1
0
0
3
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
3
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
2
2
2
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
1
0
0
0
4
0
0
0
0
2
1
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
2
0
2
0
1
8
1
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
1
2
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
2
0
1
1
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
2
0
0
2
0
3
0
1
0
1
1
4
0
1
0
0
0
0
1
1
1
0
2
0
0
0
0
0
0
1
0
0
2
2
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
1
0
0
0
2
1
0
0
1
0
0
2
1
1
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
1
0
0
1
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
2
2
1
0
1
0
1
0
0
0
0
0
1
0
4
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
2
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
2
0
0
2
0
2
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
1
1
1
3
0
1
0
0
1
4
0
0
0
0
0
0
0
1
0
0
2
2
2
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
1
2
0
1
1
2
0
1
0
0
0
1
0
1
0
0
0
2
2
0
2
0
0
0
1
0
0
0
0
2
0
2
0
0
2
0
2
0
0
0
0
0
2
0
0
1
2
2
0
0
1
0
2
0
4
0
2
0
0
1
0
0
0
0
0
0
2
0
3
0
0
1
1
2
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
2
0
0
1
0
1
0
2
0
0
0
2
0
0
0
1
0
0
1
0
0
0
2
0
0
2
0
0
0
1
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
1
3
0
0
2
0
0
1
2
0
0
1
0
0
0
1
2
0
1
0
2
1
0
2
0
0
1
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
2
0
1
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
2
0
1
0
2
0
0
0
2
0
0
0
1
0
1
0
2
0
0
0
3
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
3
0
1
1
0
0
2
0
1
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
2
1
1
0
2
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
2
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
1
2
2
0
2
4
1
1
1
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
1
2
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
1
6
1
0
1
2
0
0
0
1
0
1
0
0
0
1
2
0
2
2
0
0
1
0
1
1
0
0
0
2
0
0
0
0
0
1
3
0
1
0
0
0
0
0
0
1
0
2
1
0
0
1
0
0
0
1
2
0
0
0
0
0
2
0
0
0
2
1
0
2
2
0
0
0
2
1
0
2
0
1
0
1
0
0
0
1
0
0
1
0
0
0
1
0
2
0
0
0
0
0
2
0
0
2
0
0
0
1
1
0
0
1
7
1
0
2
2
2
0
2
0
2
2
2
0
0
0
0
0
0
0
2
0
1
2
0
0
1
2
0
0
0
0
2
0
3
0
0
0
1
2
2
0
0
0
0
0
0
2
2
1
1
3
1
0
0
0
0
0
0
0
0
2
1
1
0
0
1
0
0
0
2
0
2
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
2
1
1
1
0
0
0
2
2
2
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
2
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
7
0
2
0
2
0
2
1
0
0
1
0
0
0
1
0
0
0
1
0
2
2
0
0
0
1
2
2
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
2
1
0
2
2
1
0
0
0
4
0
2
2
0
0
1
0
0
1
0
1
0
0
0
1
0
0
1
1
0
0
1
1
0
0
0
0
0
1
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
2
0
0
0
0
1
1
1
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
2
0
1
0
0
0
1
2
6
0
0
0
0
0
0
1
1
0
0
2
1
0
0
0
4
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
2
0
2
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
1
0
2
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
1
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
1
0
0
0
2
0
0
1
2
0
0
2
0
1
0
0
1
0
2
2
0
0
1
0
0
0
0
2
3
2
0
0
3
0
0
3
2
0
1
1
0
1
0
0
0
0
0
2
0
0
0
1
0
2
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
2
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
1
0
1
1
0
0
1
0
1
0
2
2
0
0
0
0
1
1
1
0
2
0
1
0
0
3
0
0
0
2
0
0
0
1
0
1
0
2
1
0
0
2
0
0
1
0
0
1
2
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
3
0
0
3
0
2
2
0
2
0
2
0
0
2
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
2
1
1
0
0
1
0
2
3
0
1
0
0
3
0
2
0
1
1
1
0
0
0
0
0
0
1
2
0
0
2
1
1
2
1
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
7
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
2
0
0
0
0
2
1
0
0
0
0
1
0
4
0
0
1
1
0
0
2
0
0
2
0
0
0
0
0
0
2
1
0
0
2
1
0
0
1
0
0
1
0
0
2
0
0
0
0
0
1
0
1
0
2
0
0
0
0
2
2
0
1
2
0
0
2
0
2
0
3
0
0
0
1
0
4
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
2
1
2
0
2
1
0
1
1
2
0
2
0
3
1
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
3
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
1
0
0
0
1
0
1
0
0
1
1
1
0
0
0
0
0
0
2
0
0
1
2
0
2
0
0
0
2
0
0
1
2
0
0
0
2
0
0
0
0
0
2
0
2
0
1
1
0
0
0
2
0
0
0
2
1
1
2
0
0
0
0
0
2
2
0
0
1
0
0
2
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
2
2
1
2
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
1
2
1
1
2
2
0
1
2
0
0
0
0
0
1
1
0
0
0
2
2
0
2
1
0
0
0
0
0
0
0
0
0
1
1
1
2
0
0
0
0
0
2
1
0
0
2
0
0
2
1
1
0
0
0
0
0
0
3
0
0
0
0
0
3
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
1
2
0
0
1
0
1
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
1
1
0
0
0
2
2
0
0
0
2
2
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
2
0
2
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
2
0
2
1
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
2
1
0
0
0
0
0
0
0
2
1
0
0
1
2
1
0
2
0
2
2
2
0
0
1
0
3
0
0
2
0
1
2
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
2
0
2
1
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
1
0
0
2
0
1
0
1
0
2
0
0
1
0
1
0
0
0
0
2
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
2
1
0
0
1
0
1
0
0
1
0
0
2
2
0
2
0
0
0
2
1
0
0
0
0
0
1
0
0
2
1
0
3
0
0
2
2
1
2
2
3
1
1
0
0
1
0
0
0
0
0
1
0
2
4
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
2
0
0
0
5
0
0
0
0
1
1
2
0
0
0
0
0
1
1
1
1
1
1
0
0
0
0
0
0
0
0
2
1
0
2
0
0
4
0
1
0
0
0
2
2
0
0
1
2
0
0
0
1
1
0
0
0
1
2
0
0
0
0
0
0
3
0
1
0
0
1
0
0
3
0
0
2
0
0
0
1
0
0
0
0
0
1
0
2
1
0
0
0
2
0
0
2
0
2
1
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
1
2
1
1
1
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
2
0
0
2
0
0
0
2
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
1
0
0
2
2
0
0
1
1
2
0
0
0
0
0
0
0
0
0
2
2
2
2
0
2
0
0
2
0
2
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
2
0
0
5
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
2
0
0
0
2
1
3
0
0
1
2
0
2
0
0
1
10
1
1
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
1
1
0
2
2
0
2
2
2
2
0
0
0
0
0
2
0
0
2
1
0
2
0
0
0
0
2
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
1
0
1
0
0
0
3
0
0
1
0
0
0
3
1
0
1
0
3
0
0
0
2
2
0
1
0
0
1
0
0
2
0
0
0
0
1
1
2
0
2
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
2
2
0
1
0
0
0
0
2
4
0
1
0
0
2
0
1
0
0
1
2
0
0
0
0
0
2
0
1
1
0
0
1
0
1
1
0
0
4
3
0
0
1
0
2
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
3
0
0
0
1
1
1
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
1
1
0
0
0
0
0
3
1
1
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
1
0
1
0
1
0
0
0
3
0
1
0
0
2
0
0
0
1
1
0
0
0
1
2
0
3
4
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
1
0
1
0
2
2
0
0
0
0
2
1
0
0
0
0
0
2
3
1
0
0
0
0
1
0
0
2
0
2
1
0
0
0
2
1
0
0
0
0
1
0
0
0
2
0
0
2
2
0
1
2
2
2
3
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
2
0
1
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
1
1
0
1
2
0
0
0
6
0
0
0
0
2
0
0
1
2
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
3
0
2
0
2
0
0
0
4
0
1
0
0
2
0
1
0
1
1
1
1
0
0
0
1
2
1
0
0
0
0
1
2
0
0
0
0
2
0
0
0
1
2
0
0
0
1
1
1
0
2
0
0
3
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
2
0
2
2
0
0
1
2
0
2
1
0
1
0
1
0
3
0
0
2
0
1
0
0
2
0
0
0
2
2
0
1
0
0
0
2
1
2
0
0
0
0
1
1
1
0
0
0
2
0
0
2
2
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
2
0
0
0
1
0
1
0
0
0
0
1
0
1
2
1
1
1
0
1
0
0
0
0
0
1
2
1
0
1
2
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
2
0
0
3
1
0
0
0
1
0
2
0
1
1
0
0
1
0
0
0
2
0
1
1
0
1
0
0
0
0
0
0
0
1
2
3
0
0
1
0
0
0
0
0
0
1
0
1
0
0
2
0
3
1
0
0
1
0
1
2
0
2
1
0
1
0
2
1
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
3
0
0
7
0
0
1
0
0
2
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
2
0
2
0
2
0
1
1
0
1
0
2
0
0
0
2
0
2
0
1
2
0
1
0
2
0
2
0
2
0
0
3
2
1
0
2
1
2
0
0
0
2
1
1
2
1
0
0
0
0
1
0
0
1
2
0
0
2
1
2
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
2
2
0
0
1
0
2
0
0
0
2
2
1
0
2
0
0
0
0
0
0
2
1
1
0
2
2
0
0
1
0
2
0
1
2
0
0
0
0
2
2
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
1
0
2
0
2
2
0
0
3
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
1
0
0
1
1
2
2
0
0
0
0
2
3
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
1
1
0
0
0
0
4
0
0
0
1
0
2
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
2
2
1
2
0
0
0
1
1
1
2
0
0
1
0
0
0
0
2
2
0
0
3
2
0
3
0
0
0
0
1
0
0
0
0
2
2
0
1
0
2
0
1
0
2
0
1
1
0
0
0
0
2
2
0
5
0
0
2
1
0
0
1
0
1
0
0
0
1
0
0
6
0
0
3
0
0
2
0
2
0
0
0
1
0
2
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
2
1
0
1
0
2
1
2
0
0
0
1
0
0
0
0
2
0
1
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
1
0
0
2
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
2
0
0
1
0
2
2
0
1
0
0
2
1
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
2
1
0
0
0
1
0
0
2
0
0
2
0
0
0
2
1
0
1
3
0
0
2
0
2
0
0
0
2
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
1
1
2
0
1
0
0
0
1
1
0
0
1
0
0
2
0
1
0
0
2
0
0
2
0
2
0
0
0
2
0
0
0
1
0
0
1
1
0
1
0
0
0
1
1
2
0
0
0
0
2
0
3
0
0
0
2
0
0
0
0
0
0
0
0
5
0
2
0
0
0
0
0
0
2
0
0
2
0
1
2
0
2
0
0
2
0
1
0
0
2
0
1
0
0
0
0
2
0
0
0
2
1
0
1
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
3
1
2
1
0
2
0
0
2
0
0
0
0
1
0
9
0
0
1
0
0
0
1
6
3
0
0
0
2
1
2
0
1
0
0
0
0
0
0
0
0
0
2
1
2
1
0
0
0
0
0
2
0
0
2
2
2
0
0
1
0
2
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
1
0
0
0
0
1
2
0
0
0
2
0
0
1
2
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
2
2
0
0
0
1
0
0
0
1
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
2
0
2
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
2
3
0
0
0
0
2
0
1
0
2
0
3
0
0
0
0
1
0
0
2
2
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
2
0
1
1
0
0
1
1
0
0
2
0
2
0
1
1
0
3
0
0
0
1
0
0
0
0
1
2
0
0
2
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
1
0
2
0
0
0
2
0
1
0
2
0
1
0
0
0
2
0
0
2
0
1
0
0
0
0
2
0
2
0
0
0
1
0
2
1
2
0
0
0
1
0
0
1
1
0
1
2
2
2
0
2
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
3
2
0
0
0
0
1
0
0
0
1
0
0
2
0
0
2
1
0
0
2
0
0
0
0
0
2
2
0
0
2
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
2
0
2
0
0
0
1
0
0
1
0
0
2
1
1
0
0
0
0
0
0
4
0
0
3
0
0
1
2
0
2
1
0
0
1
0
0
0
0
1
0
0
2
0
2
1
0
0
0
0
2
0
0
0
1
0
2
0
2
0
0
0
0
1
0
0
0
1
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
3
0
0
2
1
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
7
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
2
0
1
0
1
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
2
2
0
0
0
2
2
0
0
0
2
0
0
2
0
0
2
0
0
0
2
2
3
0
1
0
0
0
1
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
1
0
1
2
4
0
2
0
0
0
0
0
0
0
0
2
0
3
0
1
0
0
0
2
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
3
1
1
1
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
1
1
1
0
0
0
2
0
0
0
2
0
0
1
2
2
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
1
0
0
2
2
0
0
0
0
1
0
2
2
1
0
1
1
1
0
0
0
1
0
0
0
0
1
0
0
2
0
1
0
0
2
2
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
1
2
0
0
0
0
0
1
0
0
1
2
2
0
1
0
0
1
0
0
0
0
0
0
2
2
2
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
1
1
1
0
0
0
0
0
0
1
0
0
0
2
1
0
0
2
0
2
1
0
0
0
2
1
0
1
0
0
2
0
1
0
0
2
2
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
1
0
3
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
2
2
0
1
0
1
0
0
2
0
1
0
0
0
0
0
0
1
2
2
2
0
2
1
0
0
0
2
0
1
0
1
2
2
0
0
3
0
0
0
0
0
0
1
3
0
0
1
0
0
2
2
0
0
2
0
2
0
0
1
0
0
2
2
0
0
1
2
0
2
1
0
0
0
1
0
0
2
2
0
2
1
1
2
0
1
6
0
1
2
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
3
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
1
3
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
2
0
1
2
0
0
1
0
1
0
0
2
0
0
1
2
1
0
2
1
2
2
1
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
1
1
0
0
0
2
0
0
0
1
0
0
0
0
1
1
0
0
2
2
1
0
0
0
0
1
2
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
1
0
4
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
2
2
2
1
2
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
2
0
1
2
0
2
0
2
0
2
1
0
0
0
0
0
0
1
0
2
0
2
1
1
0
0
0
2
2
3
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
1
0
0
1
0
0
3
2
0
1
2
0
0
0
0
0
2
0
0
2
2
2
0
0
2
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
2
1
0
0
2
0
2
0
3
1
1
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
2
1
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
2
0
0
1
0
1
0
2
0
0
2
0
1
0
0
0
0
0
2
2
2
2
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
1
2
0
0
2
2
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
2
0
1
0
1
0
0
0
0
0
2
2
0
0
0
1
2
0
1
1
0
2
0
1
0
0
2
0
2
0
2
1
0
1
0
0
0
0
1
0
0
0
0
1
0
3
1
2
0
0
0
1
0
0
0
1
1
0
0
0
2
0
0
2
0
0
1
1
3
0
1
0
2
0
0
0
0
1
0
0
2
2
1
1
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
2
0
2
0
2
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
1
0
2
0
1
1
2
2
0
0
0
0
0
0
0
0
4
1
3
0
0
0
0
1
0
2
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
2
0
1
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
2
1
1
1
0
0
0
1
0
2
0
1
0
0
1
2
0
0
0
0
0
0
1
0
0
1
1
2
2
1
0
0
0
0
0
2
2
0
0
1
0
3
0
0
0
0
1
0
2
1
2
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
3
1
0
1
2
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
1
0
1
0
1
0
0
0
1
0
2
0
2
2
0
1
0
0
0
0
2
0
0
0
3
0
0
2
0
0
7
3
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
2
0
0
0
2
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
2
1
0
0
2
0
0
0
0
0
0
1
0
1
1
2
0
1
0
1
2
0
0
0
0
0
0
0
0
0
1
2
1
0
0
2
0
0
1
0
1
0
0
0
0
0
2
0
2
0
0
6
0
2
0
0
0
0
0
2
1
1
0
0
2
0
0
0
1
2
1
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
1
0
0
2
2
0
2
2
1
0
0
2
2
1
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
2
1
5
0
0
2
3
0
0
0
0
0
1
0
0
1
2
2
2
0
0
0
0
2
0
0
0
2
0
1
0
0
1
4
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
1
2
0
0
1
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
3
2
0
0
0
0
2
0
0
1
0
1
0
0
1
0
0
0
1
2
1
0
0
0
3
0
0
0
0
2
0
0
1
2
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
7
0
0
1
1
2
0
0
2
0
0
0
0
0
0
1
0
1
0
2
0
0
1
0
2
0
0
1
2
0
0
3
0
2
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
4
2
1
1
0
0
0
0
0
0
1
0
4
0
2
2
1
2
0
1
1
2
0
3
1
2
1
2
0
2
0
0
0
1
0
1
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
1
3
0
2
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
2
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
2
1
0
2
0
0
0
4
0
1
0
0
0
2
2
2
0
2
0
0
0
0
3
0
0
2
1
0
0
0
0
0
2
0
0
2
2
0
0
0
1
0
0
0
1
0
2
0
0
3
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
1
0
0
0
0
0
2
1
1
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
2
0
1
2
2
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
2
1
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
1
1
2
1
0
0
2
2
0
2
0
0
0
2
1
2
1
2
0
0
2
0
0
1
0
0
0
3
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
1
0
0
1
0
2
0
0
0
3
0
2
0
1
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
1
0
1
1
0
0
0
0
1
0
0
0
4
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
1
1
1
0
2
0
0
0
0
0
1
0
0
1
1
0
2
0
1
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
3
0
2
1
0
0
0
0
0
2
0
2
1
1
0
0
0
3
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
2
2
1
2
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
1
2
0
1
0
1
0
0
2
0
0
1
2
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
2
0
5
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
2
0
0
1
0
0
0
2
0
0
0
2
1
2
0
0
0
0
0
0
0
0
1
2
2
1
0
0
0
1
2
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
2
1
0
0
1
2
1
0
0
0
0
1
0
0
0
0
2
0
0
0
1
2
0
1
0
1
2
0
0
1
2
0
2
2
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
3
0
1
2
0
0
2
0
0
2
0
0
1
0
0
3
1
1
0
0
0
1
0
2
2
0
6
1
0
0
0
0
0
0
1
0
0
2
1
0
2
2
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
1
0
2
1
1
0
0
1
0
0
0
2
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
2
1
0
2
0
0
0
3
0
0
0
0
0
1
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
2
1
2
0
1
1
2
0
0
2
0
0
0
2
0
0
1
3
0
0
1
2
1
0
2
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
4
0
0
0
2
2
0
2
0
0
0
1
0
0
2
0
0
0
3
0
0
0
0
2
0
0
0
2
2
1
0
2
0
4
0
1
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
2
1
1
0
0
0
2
0
0
3
0
2
0
1
2
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
2
0
0
0
1
0
2
0
0
0
2
0
2
0
0
0
0
0
0
3
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
1
0
0
0
0
2
0
1
0
0
1
2
0
0
0
0
1
1
0
0
1
0
3
0
0
0
2
0
0
0
0
0
0
1
0
0
2
2
2
0
1
2
1
0
0
2
0
0
0
2
0
1
2
1
2
0
0
0
0
1
1
1
2
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
2
0
1
0
0
0
0
0
1
1
0
0
0
2
1
0
0
0
0
0
0
2
0
1
0
0
0
3
0
0
0
0
0
1
3
2
1
0
0
2
0
2
2
1
0
1
0
2
0
0
0
0
2
0
1
0
2
0
1
0
0
0
2
0
1
0
0
0
0
2
0
0
1
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
3
2
0
0
0
1
1
0
0
0
2
0
0
0
0
2
0
0
0
1
2
0
1
3
0
0
0
0
1
0
4
0
3
1
1
0
0
0
0
0
0
0
0
3
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
1
2
0
0
2
0
1
0
0
0
0
0
0
0
2
0
2
0
3
0
0
0
0
2
1
1
2
2
2
1
1
1
2
1
0
1
0
1
2
0
0
0
2
0
2
0
0
1
0
0
0
3
0
0
2
0
2
0
0
2
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
3
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
1
0
2
1
0
2
0
2
0
0
0
0
2
1
1
0
0
2
3
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
2
0
0
0
1
0
0
2
0
1
1
0
2
1
0
0
0
0
1
1
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
2
0
2
0
1
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
1
0
0
1
0
1
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
1
0
0
0
2
2
1
0
2
2
1
0
0
1
1
1
0
1
1
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
1
2
0
2
2
0
2
1
0
0
1
1
0
0
0
3
2
0
0
1
0
0
3
0
1
0
2
2
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
1
2
2
0
2
0
0
0
1
0
1
0
0
2
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
2
1
1
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
1
3
0
0
0
0
2
2
1
1
0
0
0
0
0
0
0
0
1
0
0
2
6
0
1
0
1
1
0
0
1
3
0
2
0
0
0
0
0
2
0
0
1
2
1
3
2
0
2
0
2
0
0
0
2
4
0
0
2
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
1
0
1
0
0
0
2
0
2
1
3
0
0
0
0
2
0
0
0
2
1
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
2
0
2
0
0
2
0
2
0
0
1
1
0
0
0
1
0
0
2
0
2
0
0
2
2
1
0
1
0
0
0
0
0
0
2
4
1
0
0
2
0
0
2
0
0
0
0
0
0
1
0
2
3
3
0
0
1
0
1
0
0
0
1
0
0
0
1
1
2
0
2
0
0
2
0
2
0
2
0
0
2
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
1
3
1
0
0
2
0
0
0
2
0
2
2
0
0
0
0
0
0
1
2
0
0
1
2
2
1
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
1
0
0
2
0
0
1
0
1
0
1
0
2
0
0
0
2
0
0
0
2
0
2
1
0
0
4
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
2
2
0
0
0
0
1
0
0
1
1
0
0
0
1
0
1
0
0
0
0
2
0
1
0
0
1
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
2
0
1
2
0
0
0
1
0
0
2
1
0
1
2
0
0
1
0
3
1
0
6
3
2
0
1
0
1
0
1
0
0
0
1
2
1
0
0
1
1
1
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
3
1
0
0
0
0
0
0
1
0
0
1
1
0
2
1
0
2
0
0
1
1
0
0
0
1
0
2
2
2
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
4
1
0
1
0
2
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
1
0
2
2
0
3
0
3
0
0
0
0
3
1
0
1
2
0
0
2
0
2
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
1
0
2
3
0
0
2
0
0
0
0
0
0
0
5
1
0
1
1
0
0
1
0
2
1
0
0
0
1
2
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
2
0
2
0
0
0
0
1
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
1
0
2
2
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
2
1
0
0
0
0
0
0
0
1
1
0
0
2
0
1
0
1
2
0
0
0
0
1
0
1
2
0
0
0
0
1
0
2
0
0
0
0
0
2
1
0
0
2
3
1
0
0
1
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
2
1
0
2
0
0
0
2
2
1
2
0
2
2
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
2
1
0
0
0
2
0
0
2
0
0
0
1
3
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
1
1
0
0
2
0
0
0
0
0
0
1
2
1
0
2
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
3
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
5
0
1
0
0
0
2
0
3
0
1
0
0
0
2
0
0
0
2
0
0
0
1
0
0
2
0
1
0
0
0
2
1
4
1
0
1
0
1
1
0
0
1
3
2
1
1
2
0
0
0
1
0
0
0
2
0
2
0
0
0
2
0
1
1
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
1
1
0
3
0
0
0
0
0
1
1
0
0
1
0
2
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
3
1
0
2
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
2
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
2
0
2
1
2
0
1
0
0
3
1
0
0
0
2
0
1
0
1
1
1
1
0
0
2
1
2
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
3
3
1
0
1
0
0
0
0
0
0
0
1
2
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
2
1
1
2
2
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
1
1
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
2
0
0
2
0
1
0
1
0
2
0
0
2
0
0
0
0
2
0
0
3
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
3
0
0
0
0
3
0
2
2
0
0
4
2
0
1
0
0
0
0
0
0
0
0
1
0
3
0
0
2
0
0
1
1
1
1
2
0
0
0
2
2
0
0
2
1
0
0
2
1
2
1
0
0
0
0
0
0
2
2
0
0
2
2
2
0
1
2
1
7
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
4
2
1
0
2
2
8
1
1
0
0
0
2
0
0
0
1
0
1
0
0
0
2
0
0
1
2
0
0
0
0
0
0
1
1
0
2
0
0
3
0
0
1
0
0
0
0
2
1
0
3
0
2
2
0
0
0
1
1
0
0
0
0
0
0
2
0
1
0
1
2
0
0
0
0
3
0
1
0
0
0
0
3
0
0
0
5
0
2
0
0
3
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
2
1
0
2
0
0
2
0
0
1
1
1
2
1
2
0
0
2
0
0
2
0
2
0
0
0
2
0
0
1
0
2
2
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
2
1
0
0
1
0
0
1
1
0
2
0
0
3
2
0
0
1
0
3
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
2
1
0
0
0
1
1
0
0
0
0
2
0
0
1
1
0
0
1
1
1
0
0
0
2
0
0
0
0
1
0
4
0
0
1
0
0
2
0
0
0
1
2
0
2
0
1
2
0
0
0
2
0
1
0
0
1
0
2
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
3
1
0
1
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
2
1
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
1
0
1
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
1
0
0
0
2
1
0
2
0
0
1
0
0
0
2
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
2
0
1
2
0
3
0
0
2
1
0
2
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
1
1
2
0
0
2
2
0
2
1
0
0
2
2
0
0
0
1
1
0
1
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
4
0
0
0
0
0
1
0
0
0
0
2
0
2
1
0
2
0
0
0
1
0
0
0
0
0
0
0
1
1
2
1
0
1
2
2
0
1
0
0
0
0
0
0
2
2
0
0
2
0
2
1
0
0
2
0
0
0
1
0
0
1
2
2
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
2
2
0
0
0
0
2
0
1
0
0
1
0
2
1
0
1
1
0
1
0
0
0
2
0
0
1
2
0
1
0
0
0
0
0
0
0
0
2
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
1
0
0
0
0
0
0
0
7
1
1
2
2
2
0
0
0
1
0
0
0
1
0
0
0
0
3
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
2
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
2
2
0
1
2
0
0
0
3
1
1
1
0
0
0
0
0
0
0
0
1
2
0
1
0
0
2
0
0
0
5
0
2
0
0
0
1
2
1
0
1
1
1
3
0
1
2
2
0
0
1
0
2
2
1
0
1
1
1
0
0
0
0
1
0
0
2
3
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
2
1
0
0
2
0
1
0
0
1
1
2
0
0
1
0
0
1
2
0
2
0
1
0
0
0
0
0
2
2
2
2
0
1
0
0
1
2
1
2
0
2
0
0
0
0
0
0
0
0
2
1
1
0
0
2
0
1
0
0
0
0
2
0
0
1
2
4
0
0
0
0
2
5
3
0
0
0
0
0
0
1
1
0
0
2
0
1
1
0
0
0
1
0
0
0
0
0
2
1
1
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
2
2
0
2
0
0
1
2
0
0
0
0
2
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
2
2
0
1
0
1
0
0
0
0
0
0
0
0
0
2
1
0
1
2
2
2
0
0
0
0
0
0
2
0
0
2
3
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
2
0
1
2
1
0
0
0
2
0
0
0
3
0
1
0
0
0
0
0
0
1
1
1
0
0
0
2
2
0
1
3
1
2
0
2
0
2
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
2
2
2
0
2
0
0
0
0
0
7
1
0
2
0
0
0
3
0
0
0
0
0
0
1
0
1
0
0
1
0
0
2
2
1
0
0
1
0
1
0
1
0
0
0
0
0
1
2
0
0
3
0
1
1
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
2
1
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
2
2
2
0
1
0
2
0
2
2
1
0
2
0
0
0
0
0
0
0
0
1
2
0
1
0
2
1
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
2
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
2
1
0
0
0
0
2
0
0
4
0
0
0
1
0
2
1
0
0
2
0
0
3
1
2
0
0
1
0
1
0
1
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
2
1
0
0
2
2
0
0
2
2
0
0
0
0
1
2
3
3
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
2
2
3
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
3
0
4
2
1
0
0
0
0
0
0
3
0
0
0
2
1
0
1
2
0
1
0
0
0
0
0
1
0
0
2
1
1
1
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
4
1
0
2
0
0
0
0
0
1
0
1
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
2
0
2
0
2
0
0
2
0
0
0
0
0
4
1
0
1
0
0
1
0
0
2
0
2
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
2
3
0
1
3
0
0
0
0
0
1
0
0
1
0
1
0
0
3
0
0
2
0
0
0
0
0
1
0
1
5
0
2
2
0
1
0
2
0
0
0
3
0
0
2
0
0
1
0
0
1
0
0
2
1
0
1
1
0
0
0
0
1
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
2
1
0
3
0
1
0
0
0
0
0
1
0
0
0
0
2
0
2
2
0
0
1
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
2
0
0
0
0
0
1
0
0
1
0
0
0
2
1
0
2
1
1
1
0
3
0
0
0
1
1
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
2
1
0
0
1
0
0
1
2
0
1
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
2
3
0
0
1
2
0
0
0
0
2
2
0
2
0
0
0
0
2
0
1
0
2
0
0
0
0
0
2
1
0
0
1
0
0
0
1
0
0
0
0
2
0
0
4
2
0
0
2
0
0
0
0
2
1
2
0
2
0
2
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
1
2
2
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
2
2
1
0
0
0
0
2
0
4
1
1
1
0
0
2
0
1
0
0
1
1
0
0
0
0
1
0
0
1
1
0
2
6
1
0
0
0
2
0
0
3
0
1
2
0
0
0
0
0
0
2
2
1
0
0
0
1
0
0
0
0
1
0
2
0
0
2
0
0
2
0
0
0
2
0
1
0
0
0
0
2
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
2
0
2
1
1
2
3
0
3
0
0
0
0
0
2
0
2
0
0
2
1
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
1
0
4
0
0
0
0
2
0
1
0
0
0
2
0
0
1
1
0
1
0
0
1
0
0
0
2
0
2
3
1
0
0
0
0
0
0
3
0
0
0
0
3
0
0
0
1
2
2
2
0
0
1
0
2
1
0
1
0
0
0
0
1
2
4
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
2
0
0
3
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
2
1
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
2
0
0
0
2
2
0
0
2
0
0
2
2
1
0
0
0
0
0
0
1
2
0
0
0
0
2
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
2
1
0
0
0
2
2
1
0
0
0
0
0
0
0
2
1
0
0
1
0
2
0
2
0
0
2
0
0
1
3
0
1
1
1
1
0
1
0
2
0
0
1
1
1
1
1
0
0
2
0
2
3
1
2
1
5
1
1
0
0
0
1
1
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
2
1
3
0
0
0
0
0
0
0
0
2
1
1
0
1
0
2
1
0
0
0
2
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
1
0
1
0
0
0
1
0
0
2
0
1
0
0
1
2
0
0
1
0
0
0
0
0
2
0
0
0
4
0
0
1
2
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
2
3
0
0
0
2
0
0
1
0
1
0
2
0
0
0
0
0
2
2
1
0
0
0
1
2
1
1
0
1
1
0
0
0
0
0
0
3
2
0
2
0
0
2
2
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
1
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
2
1
0
0
0
4
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
1
0
2
2
1
0
1
0
0
1
0
0
1
0
1
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
2
1
0
2
0
0
1
4
3
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
4
0
2
0
1
0
2
0
0
0
1
3
0
1
0
1
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
1
2
3
0
0
2
1
2
0
0
0
1
0
1
0
0
0
0
1
0
0
2
0
1
1
0
0
0
0
0
2
2
2
0
4
0
0
0
0
5
0
0
1
2
0
0
0
2
2
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
2
2
1
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
2
2
1
0
0
0
0
0
0
2
0
0
2
0
3
0
0
0
0
0
4
2
2
2
0
0
2
0
0
0
0
0
1
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
2
0
0
3
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
2
0
4
0
2
0
0
2
0
0
1
0
0
1
0
0
0
0
1
0
1
1
2
0
0
0
0
1
0
0
0
1
0
0
2
2
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
2
3
0
2
0
0
0
1
0
0
1
0
0
0
0
2
0
0
2
2
0
1
2
4
1
0
0
3
1
1
2
0
1
0
0
0
0
0
0
0
0
1
2
0
0
1
1
1
2
3
1
1
0
0
0
0
0
3
1
0
0
0
0
2
0
1
2
0
0
3
0
2
0
0
0
0
0
1
0
0
0
1
2
2
0
0
0
0
2
0
1
0
0
4
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
1
0
1
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
1
2
3
0
0
1
0
0
0
1
0
0
1
1
1
0
0
0
1
0
1
0
0
1
3
0
1
0
0
0
0
0
2
0
0
2
0
1
0
0
1
1
1
1
0
0
0
0
0
1
1
4
0
0
1
1
0
0
2
0
0
1
0
0
1
0
1
0
2
0
2
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
3
1
2
0
0
0
2
0
2
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
5
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
1
0
1
0
2
0
0
0
1
1
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
6
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
2
0
2
4
0
2
0
2
4
0
0
0
1
2
2
2
0
0
0
5
2
0
0
0
0
1
0
2
0
0
0
1
1
2
1
1
4
2
1
0
1
2
0
1
0
0
2
0
0
2
1
1
0
1
1
0
1
0
0
0
1
0
0
2
0
0
1
0
1
2
0
1
0
2
1
0
0
0
2
0
1
0
1
0
0
0
2
0
2
2
0
0
1
0
0
0
2
0
2
1
1
0
2
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
2
0
2
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
4
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
1
0
0
0
2
0
1
0
1
1
1
1
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
1
0
0
0
2
0
1
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
2
0
2
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
2
5
0
0
0
2
0
0
2
0
1
0
0
1
1
0
0
1
0
0
2
2
1
0
0
1
1
0
2
1
1
0
2
0
2
1
2
0
0
0
0
0
0
2
0
1
0
1
1
0
0
1
57
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
3
0
0
1
0
1
0
1
0
0
0
0
0
0
4
0
0
0
3
0
1
0
0
0
0
0
2
0
0
0
1
0
2
0
2
0
0
2
0
2
2
0
1
2
0
0
0
0
0
1
1
0
1
1
0
0
0
2
1
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
3
1
0
0
0
0
2
0
2
0
7
0
0
1
0
0
0
0
0
0
0
2
0
2
2
0
1
1
2
0
0
1
0
0
2
1
0
1
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
1
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
1
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
5
0
0
0
0
0
1
0
2
0
2
0
1
2
0
0
1
0
1
0
0
0
0
0
3
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
1
1
2
1
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
2
0
0
0
0
2
0
0
1
0
2
0
2
0
0
0
0
0
1
1
1
1
2
1
1
1
0
0
0
0
0
0
0
1
0
1
1
0
0
1
2
0
0
0
2
0
0
0
0
0
1
0
0
2
1
2
0
0
0
1
0
0
0
2
0
2
0
2
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
2
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
3
0
0
0
2
2
2
0
1
0
0
2
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
2
2
0
1
0
1
0
0
0
0
2
0
1
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
3
1
0
0
2
0
2
2
1
1
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
1
1
0
2
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
1
0
1
0
3
1
1
1
0
0
1
2
2
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
7
1
2
1
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
2
3
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
1
2
0
2
0
1
0
0
2
0
0
1
8
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
2
2
0
0
0
0
2
0
0
0
1
0
1
1
0
2
0
1
2
2
1
0
0
0
0
0
1
2
0
0
2
0
0
1
1
0
1
0
0
0
0
0
2
0
2
0
0
0
0
2
1
0
0
2
0
0
1
0
0
1
2
0
2
0
0
0
2
1
0
0
0
2
1
0
0
0
0
0
0
1
2
0
1
0
1
0
2
0
0
1
0
2
0
0
1
1
0
0
2
2
2
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
2
1
2
0
1
1
0
1
0
1
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
6
0
0
0
0
0
0
1
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
2
2
0
0
0
0
1
2
0
2
0
0
2
0
1
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
4
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
3
1
2
0
1
1
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
2
1
0
0
0
0
0
0
0
1
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
1
2
1
0
2
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
2
2
2
3
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
2
0
0
0
0
0
1
2
0
0
2
0
0
1
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
1
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
3
0
0
0
0
0
1
1
1
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
2
0
1
1
2
0
0
0
1
2
2
0
0
0
0
0
1
0
1
0
0
1
0
1
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
1
1
0
0
0
0
1
0
2
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
2
0
0
0
2
7
2
0
0
0
0
0
2
0
2
1
1
0
2
2
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
1
2
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
2
0
2
0
0
0
0
1
0
0
1
0
0
2
2
0
0
1
1
0
0
0
0
0
3
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
2
0
0
2
0
1
2
1
1
0
2
0
0
0
1
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
2
0
0
0
0
1
0
1
0
2
0
0
0
2
0
0
0
1
0
1
1
2
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
2
1
0
0
1
0
2
2
1
0
2
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
2
2
0
0
0
2
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
5
4
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
2
2
0
1
2
0
0
0
1
0
0
2
3
0
1
0
2
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
1
0
4
2
0
0
0
0
2
0
2
2
1
0
0
0
0
0
0
0
0
1
2
0
0
1
0
2
0
0
0
1
0
1
0
1
2
0
0
1
1
0
0
0
0
2
0
2
0
1
0
1
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
1
1
1
1
2
1
0
1
2
1
2
0
2
0
0
0
2
0
0
2
1
0
0
1
2
7
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
2
0
0
2
2
0
0
2
0
1
2
1
1
0
2
2
2
0
0
0
0
0
1
2
0
0
0
0
0
1
2
2
1
0
0
0
0
0
0
0
3
0
0
1
0
0
1
2
1
2
0
0
3
0
0
3
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
2
0
1
0
0
2
0
2
4
1
0
0
4
0
1
2
0
0
0
0
1
1
0
2
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
2
1
2
1
0
0
2
0
0
1
2
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
2
0
0
1
0
0
0
1
0
1
2
2
0
0
0
0
1
0
0
1
1
0
1
2
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
1
0
0
3
0
0
3
0
0
0
3
0
0
2
0
0
2
2
0
1
1
0
0
2
0
1
2
1
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
1
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
2
1
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
1
2
0
0
0
0
0
0
1
0
0
1
0
0
3
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
1
0
0
2
1
2
0
0
0
2
0
1
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
1
0
0
2
0
2
0
1
0
3
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
2
0
1
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
1
1
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
2
0
1
0
1
0
1
0
0
0
0
2
0
2
0
0
1
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
1
2
1
1
0
2
3
2
2
1
0
0
0
0
2
3
0
0
3
0
0
2
0
2
0
3
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
1
0
2
1
1
0
0
0
1
0
2
0
0
0
0
2
0
2
0
0
0
0
1
3
1
0
2
1
0
0
1
0
0
0
4
1
0
0
1
0
1
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
2
1
0
0
2
0
0
2
0
1
0
0
3
0
1
0
1
2
1
0
0
0
1
0
0
1
0
1
2
0
3
1
0
2
0
0
0
1
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
2
1
0
0
1
1
0
0
0
0
0
0
1
0
0
1
2
0
0
2
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
3
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
1
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
1
2
0
0
0
0
0
1
2
0
2
0
1
0
0
0
2
1
0
0
0
0
0
0
0
2
1
2
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
2
1
2
0
2
1
2
0
0
0
0
2
0
1
0
1
1
0
0
0
0
0
2
2
0
2
0
0
0
0
1
1
2
1
0
0
2
0
2
1
1
1
0
2
2
0
2
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
3
0
0
0
2
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
2
0
1
0
0
0
1
1
0
0
1
0
1
0
1
1
0
0
1
0
0
1
2
0
2
0
0
0
2
0
0
1
1
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
1
0
7
2
0
0
0
0
2
1
2
0
2
1
0
0
1
0
0
0
0
0
0
2
1
0
2
0
1
0
0
1
0
1
0
1
1
5
2
0
2
4
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
1
1
0
0
1
0
0
0
3
2
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
2
1
0
8
0
0
1
2
0
0
2
1
0
2
1
0
0
1
1
2
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
1
0
0
2
0
3
0
0
0
0
9
0
1
2
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
1
0
0
1
0
0
1
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
3
0
1
0
0
0
0
0
2
0
0
3
0
0
0
3
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
4
0
0
0
0
0
4
0
1
0
2
0
0
0
0
0
0
0
2
2
0
2
1
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
4
0
2
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
2
0
0
0
0
2
1
2
0
0
1
0
1
0
1
1
1
0
0
0
1
0
0
1
0
1
2
3
1
0
1
0
0
1
0
0
0
2
0
0
0
1
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
3
0
0
2
2
2
0
0
0
1
0
0
0
4
0
2
0
0
0
2
0
1
1
1
2
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
5
0
0
2
0
5
0
0
0
0
0
1
2
0
0
0
1
2
2
0
0
0
0
1
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
2
2
0
3
0
0
2
0
0
1
0
1
1
0
0
0
0
0
3
0
2
0
0
2
0
2
2
1
0
0
2
0
0
0
0
2
0
2
0
0
0
2
0
1
2
2
0
1
0
0
0
2
0
1
0
2
0
0
1
2
0
0
2
0
0
0
0
2
0
0
0
2
0
0
2
2
1
1
2
0
0
1
0
0
2
0
1
0
0
0
0
0
2
0
0
0
1
2
0
0
0
1
0
4
1
0
1
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
1
0
0
2
2
0
2
1
0
0
1
0
1
0
0
0
0
0
0
0
2
2
0
2
2
0
2
0
0
2
1
1
0
0
0
0
1
0
2
0
0
1
0
2
1
2
0
0
0
4
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
3
0
0
2
0
2
0
0
0
1
1
2
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
3
0
2
1
0
0
0
0
2
0
0
0
1
2
0
0
0
0
1
0
0
1
1
0
0
0
0
2
0
1
0
0
0
0
0
1
1
2
0
0
0
0
0
0
1
0
2
0
1
0
0
0
2
1
0
5
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
4
0
0
2
0
0
1
0
0
0
0
2
1
0
1
0
0
0
2
0
1
0
0
0
1
2
2
2
0
1
1
0
0
1
0
1
2
0
2
2
0
2
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
1
2
0
0
0
0
2
0
2
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
3
1
0
1
0
1
0
0
0
2
0
0
0
0
1
0
0
0
3
2
0
0
1
1
1
4
1
0
0
0
0
2
0
0
2
0
0
1
2
0
0
0
0
2
1
0
0
0
0
0
1
1
0
1
2
1
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
1
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
1
0
2
0
0
2
0
0
2
0
0
0
3
0
0
1
2
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
2
0
2
0
1
3
0
2
0
2
1
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
2
0
2
0
0
0
1
2
3
0
0
0
0
0
1
0
3
0
0
0
0
1
0
1
2
2
0
0
1
2
0
0
2
0
2
0
0
2
0
0
0
0
0
1
1
0
0
1
0
2
2
0
0
0
1
1
0
2
0
0
0
0
2
0
0
0
2
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
2
2
0
2
0
0
2
0
2
0
0
2
0
0
2
1
0
0
0
0
0
2
0
0
0
1
0
2
2
0
2
0
1
0
0
0
3
0
2
0
0
1
0
0
2
2
0
1
1
0
0
0
0
0
0
0
1
0
0
2
1
1
0
1
1
1
0
0
2
1
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
2
0
0
0
2
1
0
2
1
0
1
0
0
2
0
2
0
0
0
0
1
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
1
0
2
1
0
0
0
0
2
0
1
0
1
0
0
1
0
0
1
0
0
0
2
0
1
1
2
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
2
1
1
0
2
0
0
2
1
1
0
0
0
0
1
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
2
1
1
2
0
0
0
2
0
1
0
0
0
3
0
1
0
0
0
0
2
0
1
2
0
2
2
0
3
2
1
2
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
2
0
0
1
0
0
2
2
0
2
2
0
2
0
0
1
0
0
1
1
1
0
1
0
0
0
0
3
1
0
0
0
1
0
0
0
0
1
0
1
0
2
1
1
0
0
0
0
0
1
3
0
0
1
0
0
0
1
0
0
0
2
2
0
1
2
2
0
0
1
2
0
1
1
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
2
0
2
2
1
0
0
0
0
0
0
4
1
0
0
0
0
2
0
3
0
2
0
1
0
2
0
0
2
2
0
1
1
0
2
0
1
1
0
0
0
2
2
0
2
1
0
0
0
2
0
0
1
0
0
2
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
5
0
2
0
2
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
1
1
1
0
1
0
2
1
0
0
0
1
0
0
2
0
0
0
1
2
0
0
2
2
0
2
0
0
2
0
2
2
0
0
0
0
0
0
0
3
0
0
0
1
3
1
1
2
2
0
2
2
0
0
0
0
1
0
1
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
2
0
0
2
2
0
1
0
0
0
0
1
2
0
1
2
0
1
0
0
0
0
0
1
0
0
1
0
0
1
2
0
0
0
1
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
1
1
2
0
1
1
2
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
2
2
1
0
0
3
2
2
0
0
1
2
2
2
1
1
0
0
0
0
3
0
0
0
0
1
0
0
2
0
0
1
0
0
2
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
1
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
2
2
0
0
1
1
2
0
0
2
1
0
0
0
1
0
2
1
0
1
0
0
1
1
0
0
0
1
1
1
0
0
1
0
1
0
0
2
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
2
1
0
1
0
1
0
0
0
1
0
1
0
0
1
0
2
0
2
0
0
0
1
0
0
1
1
0
0
2
1
0
0
0
1
1
1
0
2
0
1
0
1
2
0
1
2
0
2
0
0
0
0
0
1
0
0
0
0
2
2
0
1
0
3
2
0
0
0
2
1
2
0
1
1
1
2
0
0
0
0
0
1
1
0
0
0
0
0
2
0
2
0
0
0
0
0
2
2
1
2
0
1
1
0
1
0
0
1
0
0
2
0
0
2
3
2
2
0
1
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
1
0
2
0
2
0
1
1
1
0
0
1
1
2
1
0
0
0
0
0
0
2
0
0
0
0
1
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
2
3
0
0
1
0
0
2
0
0
0
1
1
0
2
1
0
0
3
1
0
0
1
0
0
0
2
0
0
2
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
2
1
0
1
0
0
0
0
0
2
0
0
2
2
0
1
1
1
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
2
1
0
1
2
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
2
0
1
1
2
1
1
1
1
0
0
1
2
0
2
0
2
0
0
0
3
2
0
0
1
0
0
2
1
0
1
2
0
0
2
0
0
1
0
0
2
0
2
0
1
0
0
0
1
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
2
0
0
1
0
2
0
0
1
1
0
3
2
0
1
2
0
0
0
0
0
0
0
0
1
2
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
1
0
0
1
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
2
2
0
0
0
0
2
1
0
0
0
0
0
0
1
1
2
0
1
0
0
0
1
0
0
2
1
0
0
0
0
2
2
0
0
1
0
0
1
1
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
2
0
0
2
0
2
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
2
0
2
0
3
0
0
0
0
0
0
2
0
1
0
0
1
2
0
0
0
0
0
1
2
0
0
1
0
0
1
0
0
1
2
2
0
1
0
1
0
0
1
0
0
0
2
0
0
1
1
0
0
0
0
0
1
1
0
2
0
2
1
1
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
4
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
3
1
0
0
0
0
1
3
0
2
0
0
0
0
1
1
1
0
0
2
2
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
1
1
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
1
0
0
2
1
1
1
2
2
2
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
2
0
0
1
0
2
0
0
2
0
0
3
0
1
0
0
0
2
0
1
0
0
0
0
1
0
2
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
1
0
0
0
2
1
0
0
0
4
0
0
0
1
0
2
0
0
0
2
2
0
2
2
1
1
2
0
1
0
0
0
2
1
1
2
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
1
0
2
2
0
0
2
0
0
1
8
2
1
2
0
3
1
0
1
2
0
1
0
0
0
0
0
2
0
2
0
1
0
0
0
2
1
2
1
0
0
0
0
0
0
0
0
1
0
1
2
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
2
0
0
2
0
0
0
2
2
0
0
0
0
0
0
3
2
0
0
0
2
1
2
2
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
1
1
0
0
2
0
0
4
0
0
0
0
0
5
0
2
0
2
2
0
3
0
0
1
0
2
2
0
0
0
0
1
3
0
2
2
0
2
2
0
0
0
6
3
1
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
3
1
2
0
0
0
0
0
0
0
0
3
0
0
2
0
0
1
0
0
0
1
2
2
0
0
1
0
1
1
0
0
2
0
0
0
2
1
1
0
1
2
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
2
1
2
0
0
2
0
0
0
1
0
1
1
0
0
0
0
2
1
0
0
2
0
1
1
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
1
0
1
0
1
1
0
1
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
4
2
2
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
2
0
1
0
2
1
2
0
1
0
0
0
0
1
1
2
2
2
0
1
0
0
0
0
0
0
0
0
2
0
0
1
2
0
5
2
2
0
1
1
0
1
1
0
1
2
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
2
0
1
0
1
0
1
0
0
1
0
0
2
1
2
2
0
0
0
0
1
0
0
0
2
0
1
1
0
0
2
0
0
0
0
0
2
0
0
1
0
1
0
0
1
0
1
0
0
2
0
0
0
0
0
1
0
2
0
1
1
2
0
2
0
0
0
2
1
0
0
2
0
0
0
0
0
1
0
2
0
0
1
0
0
0
2
0
1
0
0
0
0
2
0
1
0
1
0
2
2
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
2
0
2
0
2
0
2
2
1
1
0
3
2
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
2
2
0
1
1
0
0
3
0
0
1
0
0
2
0
0
1
2
0
0
0
2
0
1
0
2
1
1
2
0
1
0
1
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
7
0
0
2
0
0
1
0
1
0
2
1
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
2
0
2
5
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
13
0
0
0
0
0
2
2
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
2
0
0
0
0
0
1
2
0
2
1
2
0
0
0
0
0
0
0
0
0
1
1
0
1
0
2
1
0
0
2
0
2
0
0
0
1
2
1
0
1
0
0
0
0
0
0
2
0
1
0
2
2
0
0
2
1
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
2
1
1
1
0
0
0
2
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
1
0
0
3
0
0
0
0
0
1
0
2
0
2
1
1
3
2
0
0
0
0
1
0
1
1
2
2
0
1
0
2
1
0
2
0
0
2
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
1
2
2
1
0
0
0
2
0
3
0
2
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
1
1
0
0
0
2
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
2
1
0
2
0
2
0
0
0
0
0
6
1
0
0
0
2
0
0
0
1
0
3
1
1
1
2
0
1
0
1
2
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
2
1
4
0
1
1
1
2
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
1
2
1
1
0
0
0
3
0
2
0
0
0
0
1
0
0
0
1
0
2
0
1
0
2
2
0
0
0
2
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
1
1
0
1
1
0
0
0
0
1
0
0
1
0
0
1
1
16
0
0
1
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
2
0
0
1
0
0
0
1
0
1
2
0
1
0
0
0
0
1
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
2
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
1
1
3
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
2
1
0
3
0
1
0
0
0
0
0
0
2
1
1
2
0
0
0
2
1
10
0
0
0
2
0
2
0
1
0
2
0
2
2
0
0
0
0
0
0
0
0
0
1
0
2
2
0
2
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
1
0
2
1
0
2
1
2
1
2
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
2
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
1
0
0
0
0
2
0
1
1
0
0
0
1
0
1
0
1
0
1
2
2
0
0
1
0
0
0
0
0
1
2
0
0
0
1
0
1
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
2
4
0
0
0
1
0
3
0
1
3
0
0
1
0
0
0
0
0
0
0
0
0
2
1
3
0
2
1
0
0
0
0
0
0
1
0
0
0
0
2
0
1
1
0
1
4
1
0
0
0
0
1
0
0
1
0
1
2
3
0
3
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
2
0
0
1
0
0
0
4
0
2
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
1
0
0
0
1
0
0
2
1
2
0
0
0
0
0
0
0
0
1
1
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
1
2
0
0
1
0
0
0
0
2
0
0
0
2
2
0
2
0
0
1
1
0
2
0
0
0
0
2
0
0
2
1
0
1
2
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
1
0
3
2
1
1
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
1
2
1
3
2
0
0
0
0
0
0
0
0
2
2
2
0
0
2
0
0
0
1
3
0
0
0
2
2
0
1
0
0
1
0
1
0
2
0
0
0
0
0
2
1
2
0
1
1
1
2
0
1
0
1
0
0
0
0
2
0
0
1
0
0
1
0
2
1
0
7
1
3
0
0
5
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
1
0
2
4
0
0
2
0
0
1
2
0
0
0
0
0
0
0
2
2
0
1
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
1
2
1
0
2
0
2
0
1
2
0
0
0
1
0
0
0
0
2
2
1
1
0
0
1
1
1
0
0
0
0
1
0
0
0
0
2
3
2
1
2
1
0
0
0
1
0
0
0
0
0
2
2
2
0
0
1
2
3
2
2
0
0
1
0
0
2
1
0
0
0
0
1
1
0
1
0
0
1
0
1
0
0
0
0
0
3
2
0
0
1
0
0
2
0
0
3
0
2
1
1
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
1
1
0
2
0
0
0
0
0
0
1
1
2
2
0
0
0
1
0
1
3
0
3
0
1
2
1
0
1
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
2
0
2
0
0
0
2
0
0
1
2
0
0
1
0
0
0
2
1
1
3
0
0
2
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
2
1
0
0
0
1
1
1
0
0
0
1
2
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
2
0
2
1
0
0
0
1
1
2
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
2
0
0
0
0
0
0
3
2
0
6
1
0
0
1
2
0
2
0
0
0
0
2
0
0
1
2
0
0
0
2
1
0
0
0
1
2
0
0
1
1
0
1
0
1
0
0
0
0
0
0
1
1
0
2
0
1
0
2
1
0
1
2
0
0
0
2
1
0
2
0
1
2
2
1
0
0
2
1
2
0
3
2
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
2
0
0
1
1
2
1
0
2
2
0
0
0
1
1
0
1
0
0
0
0
2
1
0
1
0
1
0
1
0
0
1
0
2
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
1
0
2
0
1
0
0
1
2
2
0
2
0
0
0
0
0
0
0
8
0
0
1
1
1
0
1
2
0
2
0
0
0
3
0
0
2
0
1
0
0
0
2
0
0
0
0
0
2
0
1
2
2
0
1
3
1
0
1
1
0
0
0
0
0
1
0
0
1
1
0
0
2
1
0
0
0
0
1
0
0
2
0
1
0
0
0
1
0
1
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
1
0
1
0
2
0
0
0
2
1
0
0
1
6
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
2
0
0
0
0
0
2
2
0
0
2
1
0
2
0
0
0
0
2
0
1
0
1
0
0
3
1
0
7
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
1
0
0
1
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
1
0
2
2
0
0
1
0
0
2
0
0
0
0
0
1
1
2
0
0
0
0
1
0
2
0
0
2
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
2
2
1
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
2
2
0
0
1
0
2
0
2
0
2
0
1
0
1
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
3
0
1
0
0
0
2
0
0
0
1
0
2
0
1
2
0
0
0
0
0
0
2
2
0
0
0
1
2
0
1
0
1
1
0
0
0
2
1
0
0
1
1
0
1
1
0
0
2
0
1
1
1
0
0
1
4
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
1
1
1
0
2
1
0
2
2
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
3
2
0
0
1
2
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
2
0
2
0
0
0
0
0
1
1
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
2
2
0
0
0
0
0
0
0
0
2
0
0
0
1
2
2
0
2
1
0
0
2
2
0
0
0
0
2
0
0
0
0
1
2
2
3
1
0
0
0
0
2
1
0
0
0
0
0
0
1
2
0
3
1
0
0
2
0
0
1
2
1
0
2
0
0
4
0
0
0
0
0
0
0
0
0
2
0
1
2
0
1
2
0
0
0
0
1
0
0
1
1
1
2
2
0
0
0
0
0
3
0
0
1
0
1
0
0
0
0
2
1
2
0
2
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
3
0
2
0
0
0
0
0
1
2
2
0
0
0
2
1
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
3
2
0
0
1
2
0
0
0
0
0
2
2
0
1
0
1
0
3
2
0
0
0
2
0
0
0
0
3
0
3
0
0
0
0
0
0
0
0
2
0
0
2
1
1
0
1
0
3
2
2
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
2
0
0
0
0
2
0
0
0
2
0
0
1
0
2
0
0
1
0
1
0
2
2
0
2
1
1
0
0
0
1
1
1
0
0
0
2
0
0
0
1
0
1
0
1
0
2
0
1
0
0
2
1
0
0
1
0
1
0
0
0
1
1
0
1
0
0
2
2
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
2
0
2
2
0
0
0
2
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
4
2
1
1
2
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
1
3
2
0
1
0
0
0
0
2
0
0
0
0
1
2
0
0
1
0
0
0
0
3
1
0
0
0
0
2
2
0
1
2
1
0
0
0
1
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
2
0
1
0
0
1
0
0
0
0
2
0
0
1
1
0
0
2
0
2
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
1
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
3
3
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
1
2
2
0
2
0
0
2
3
1
0
0
0
0
0
0
0
0
1
0
0
1
0
3
1
0
1
0
0
2
2
1
2
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
2
2
1
0
0
0
1
0
2
2
0
0
0
2
1
2
0
1
0
0
0
0
0
3
0
0
2
0
2
2
0
0
0
0
3
0
0
0
0
1
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
3
1
0
0
0
0
3
0
0
0
0
0
0
2
0
1
2
2
0
0
1
0
0
0
0
4
1
1
0
0
0
0
1
0
0
0
0
0
0
3
0
1
0
2
0
0
0
0
0
0
0
1
1
2
0
2
0
1
0
1
0
0
0
3
2
0
1
2
0
1
0
2
2
1
0
1
2
1
0
0
0
2
0
0
0
0
1
2
1
0
2
0
2
1
0
0
0
0
0
2
0
1
0
0
0
2
2
1
2
1
0
2
0
0
0
0
1
2
1
1
0
0
2
0
0
2
2
0
0
1
0
1
0
0
0
2
1
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
2
2
1
0
3
0
0
0
1
0
2
2
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
3
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
2
0
2
0
0
1
4
1
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
2
2
1
1
0
0
1
1
1
1
0
0
0
2
1
0
0
4
0
2
0
0
0
1
0
0
2
0
2
0
1
4
0
0
0
1
0
0
0
0
1
0
1
0
1
0
1
1
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
2
0
2
4
0
0
2
0
0
0
1
0
0
0
0
0
2
3
0
1
0
0
0
0
0
0
3
0
1
0
0
0
0
0
3
0
0
1
2
0
0
0
0
1
3
2
1
0
1
2
0
1
0
0
0
0
0
0
0
0
0
9
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
1
0
0
0
0
1
2
2
1
1
0
0
0
0
0
1
1
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
2
1
0
0
1
0
1
0
1
0
0
0
0
0
0
3
0
0
2
0
0
0
0
9
1
0
3
0
0
0
0
1
1
2
0
0
0
0
0
1
2
0
0
2
1
2
0
0
0
0
0
1
2
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
2
1
1
0
1
2
2
1
2
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
1
4
0
0
2
0
0
0
2
0
0
2
0
0
2
2
0
0
0
0
0
0
2
2
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
1
0
0
0
2
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
2
2
0
0
0
0
0
0
0
1
0
2
0
0
0
1
1
0
2
0
4
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
3
0
1
0
0
0
0
1
1
1
0
0
0
0
0
1
0
1
0
0
0
2
3
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
2
1
1
7
1
0
0
1
0
2
1
1
0
1
0
1
0
0
0
0
1
1
0
0
0
0
2
0
0
2
0
0
1
1
0
2
0
0
2
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
2
0
2
1
2
0
0
1
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
1
1
0
0
0
2
0
0
2
0
1
2
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
3
2
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
2
1
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
1
0
1
0
0
2
0
0
1
2
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
1
1
2
0
0
1
1
1
0
1
2
0
1
0
0
3
2
3
0
0
0
0
1
0
0
1
2
1
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
2
2
0
0
1
0
0
0
0
1
0
2
0
1
1
0
0
0
1
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
2
0
2
2
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
1
2
0
0
1
1
0
0
1
2
0
1
0
2
1
1
1
0
2
3
0
2
1
0
0
1
1
0
3
1
0
0
0
0
0
0
0
1
2
1
0
2
0
1
1
0
0
0
0
3
0
0
1
0
2
2
1
1
2
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
2
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
1
1
0
0
0
2
0
0
1
1
0
2
0
3
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
2
0
0
2
2
0
0
0
2
0
1
0
0
1
0
0
1
0
1
2
0
0
2
0
0
0
0
2
2
0
2
0
0
0
2
0
0
0
0
3
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
2
1
2
1
1
0
2
0
0
0
2
0
1
1
1
1
2
0
0
4
0
1
2
0
0
1
1
0
0
4
1
0
0
0
3
0
2
2
2
1
0
1
0
0
1
1
0
0
2
1
0
1
8
0
0
1
0
0
2
0
1
2
0
0
2
2
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
2
0
0
0
0
0
1
2
2
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
3
1
1
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
2
2
0
1
2
0
1
2
0
1
0
2
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
1
0
2
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
2
1
0
0
0
0
0
0
3
0
0
2
0
1
1
0
1
1
0
1
0
1
0
0
0
0
0
2
0
0
0
1
1
0
3
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
2
0
0
1
2
0
1
2
0
3
0
0
2
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
2
1
0
1
3
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
2
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
4
2
0
2
0
0
0
0
0
1
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
2
1
0
0
0
0
3
0
0
0
1
1
2
2
0
0
0
2
0
0
2
1
0
1
0
0
1
3
0
0
0
0
1
2
0
0
0
2
0
1
0
0
1
2
1
0
0
0
1
2
0
0
0
1
0
2
2
2
1
0
0
1
1
0
1
0
0
1
0
1
1
2
1
1
0
1
1
0
1
1
2
0
1
0
0
0
0
2
0
3
0
0
0
3
2
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
2
3
2
2
0
2
1
0
0
2
0
3
0
0
1
1
2
0
0
1
6
2
2
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
2
1
0
0
1
0
3
3
0
0
0
0
2
0
2
0
1
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
1
0
2
1
4
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
2
1
1
0
0
2
0
0
0
1
2
0
1
0
0
1
1
1
0
0
2
0
0
2
0
1
0
0
0
0
2
0
0
3
0
0
0
0
1
2
0
0
0
0
2
2
0
0
0
0
1
0
2
1
0
0
0
1
0
1
0
1
2
0
1
2
0
0
0
0
0
0
2
0
3
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
2
0
2
0
2
1
0
0
0
0
3
2
1
1
0
0
1
1
0
2
2
1
0
0
2
0
0
1
0
0
0
1
0
0
0
2
0
0
0
1
0
2
0
2
2
0
1
0
0
0
0
1
2
0
1
0
0
0
0
2
0
0
0
1
1
0
5
0
0
0
2
0
1
0
0
2
2
0
0
1
0
0
1
0
0
1
3
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
1
0
0
2
0
0
0
0
0
3
0
0
2
2
0
1
11
0
1
0
0
0
1
0
2
2
0
0
0
2
0
0
0
0
0
0
0
2
1
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
3
0
0
1
0
0
0
2
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
2
1
1
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
3
0
0
2
9
0
0
2
0
1
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
1
0
2
0
1
2
2
2
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
1
0
0
0
0
0
1
0
2
0
1
0
0
0
1
2
0
3
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
1
0
0
2
2
2
2
1
0
0
0
0
0
2
0
0
2
1
1
0
1
0
1
2
1
0
1
0
0
0
3
1
0
0
0
0
2
2
0
2
1
0
0
0
3
0
0
2
1
0
0
1
0
2
0
0
0
1
0
1
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
1
2
0
3
0
2
0
0
0
0
3
2
2
0
0
2
1
2
2
1
1
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
1
2
1
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
1
0
2
0
0
2
0
1
0
2
2
0
2
0
0
1
0
0
1
0
0
2
0
0
0
0
0
2
0
1
0
0
1
0
0
1
0
0
1
1
0
1
0
0
0
0
0
1
0
2
0
0
0
0
1
1
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
3
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
7
1
0
2
0
0
3
1
0
0
0
2
1
1
1
2
0
0
1
0
0
0
0
1
0
1
0
2
1
1
0
1
1
0
0
0
0
1
1
0
1
3
0
5
2
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
2
0
1
2
0
0
0
2
0
1
1
1
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
2
1
0
0
0
1
0
0
0
3
0
1
2
1
2
0
0
0
0
0
0
0
41
1
1
0
1
0
0
1
3
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
2
0
0
1
2
0
1
1
9
0
0
0
0
0
2
2
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
1
0
0
0
0
2
2
0
0
1
0
1
0
0
1
0
1
0
0
0
1
0
1
0
0
5
2
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
2
0
0
0
2
1
2
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
2
0
2
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
2
2
1
0
1
0
2
2
0
2
0
1
2
0
0
0
0
0
0
2
0
1
2
2
1
0
1
0
0
1
0
0
0
0
0
2
1
0
1
2
0
2
6
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
2
0
0
11
0
0
0
0
0
2
0
0
1
0
2
0
0
0
3
1
0
1
0
0
0
0
1
2
0
0
0
2
3
1
2
0
1
0
0
0
2
2
0
0
0
3
2
3
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
2
0
0
2
0
1
1
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
3
0
0
0
0
2
0
1
0
3
0
0
2
1
0
0
2
0
1
1
1
0
2
2
0
0
0
1
0
0
2
0
0
1
1
0
0
1
0
1
1
0
0
1
0
1
0
2
1
0
0
2
0
1
0
0
0
0
2
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
1
1
0
1
0
0
2
0
0
1
2
0
2
0
0
0
2
0
0
0
0
0
3
1
0
1
0
1
0
2
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
3
0
1
0
0
1
2
0
0
0
2
1
1
2
0
0
1
1
0
0
0
0
2
0
2
1
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
3
2
1
2
0
0
1
1
0
3
0
0
2
2
0
0
4
0
1
0
0
0
0
3
0
1
0
0
2
0
2
0
2
0
1
1
0
2
0
2
1
0
3
0
2
0
2
0
0
0
0
1
0
0
0
0
2
1
1
0
1
0
0
0
0
0
0
3
0
0
0
0
1
0
0
1
2
0
1
0
1
1
1
0
5
0
1
2
1
1
0
1
0
0
0
0
1
0
0
1
0
1
0
2
2
2
0
1
0
0
1
0
1
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
2
0
1
0
0
0
2
0
2
0
0
1
0
0
1
0
5
0
0
1
1
0
0
2
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
2
2
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
1
1
0
0
1
0
1
0
0
0
0
4
1
0
0
0
2
0
1
0
1
2
1
1
0
1
0
0
0
0
0
0
1
0
2
2
0
2
0
0
2
0
0
0
0
2
1
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
2
1
0
0
0
0
0
0
0
0
1
1
0
1
1
2
2
0
0
2
0
0
0
0
0
0
3
0
2
0
2
0
1
0
0
7
0
1
0
0
0
2
0
0
1
0
0
0
1
0
7
0
0
0
1
0
0
2
0
1
3
1
0
0
2
0
1
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
2
1
2
0
1
3
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
4
2
1
0
0
0
0
0
0
1
2
2
2
2
0
0
0
2
1
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
2
0
0
0
2
2
0
1
0
2
0
2
0
0
0
1
0
0
1
2
0
0
0
2
0
0
0
0
0
0
2
0
7
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
2
0
3
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
2
0
2
2
0
1
1
0
1
0
0
2
0
2
1
0
1
0
0
0
0
2
2
0
2
0
0
2
2
0
0
0
4
0
3
3
0
0
1
2
2
0
0
1
0
0
0
1
2
0
0
0
0
0
0
2
0
2
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
2
1
0
0
6
0
1
0
1
0
0
1
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
2
0
0
2
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
1
1
0
2
1
2
0
0
1
2
0
1
1
0
0
0
0
0
1
0
0
0
0
1
2
0
0
1
0
0
1
0
0
0
0
1
2
1
0
0
2
0
1
0
2
0
2
2
2
0
0
0
1
0
0
0
1
1
0
1
0
0
0
1
1
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
3
0
0
0
1
2
0
2
0
0
0
2
1
3
0
0
1
0
2
2
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
1
2
2
0
0
0
1
0
3
0
0
0
0
0
0
2
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
5
0
0
0
2
1
1
0
1
1
0
1
0
0
1
0
2
0
2
0
0
1
0
1
0
1
0
0
0
1
0
1
0
0
0
2
0
0
3
0
0
4
0
5
2
2
0
0
1
0
2
2
0
0
0
2
2
0
0
0
1
0
1
2
0
0
0
1
1
0
1
0
1
0
1
0
0
2
0
0
0
0
2
0
3
0
0
0
4
2
0
0
0
1
2
2
0
0
0
1
0
2
0
1
0
2
0
0
1
2
0
0
0
1
0
0
2
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
2
3
1
0
0
0
1
0
0
3
2
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
1
2
0
0
0
0
2
0
0
0
0
2
2
1
2
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
2
1
2
0
0
0
0
4
4
0
0
0
2
0
0
0
0
2
0
1
2
0
0
0
2
0
1
0
0
1
0
0
0
1
0
0
1
1
0
1
2
2
0
1
1
0
0
0
0
2
0
0
0
0
0
0
1
2
2
0
0
0
2
0
0
0
0
0
1
1
0
2
1
0
0
0
2
1
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
1
1
2
2
0
0
0
0
0
0
0
0
2
0
1
0
1
0
2
0
1
2
0
2
0
0
1
0
1
0
0
0
1
0
0
2
0
0
0
0
0
3
0
0
0
0
0
1
2
1
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
2
0
0
2
0
1
1
2
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
1
2
3
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
1
0
0
0
0
1
2
1
0
1
0
0
0
0
0
0
1
0
0
1
0
2
2
2
4
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
4
0
0
0
2
0
1
0
2
0
2
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
1
2
1
0
0
1
0
1
1
0
1
0
0
1
2
0
0
0
0
0
2
0
2
0
1
0
0
0
0
3
1
0
0
0
0
0
3
1
0
2
0
0
0
1
4
0
0
1
0
0
0
0
3
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
2
0
0
1
1
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
2
2
1
0
0
1
0
0
0
1
0
2
1
3
2
0
0
0
0
0
0
0
0
1
0
4
0
0
2
1
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
2
0
2
2
0
0
0
0
1
0
0
2
0
1
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
2
0
0
1
0
0
0
1
2
0
1
2
0
0
2
1
0
0
0
1
2
0
0
4
1
1
1
1
0
1
1
0
2
0
0
1
1
0
0
1
0
0
0
0
1
0
0
4
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
4
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
2
0
1
1
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
2
3
0
0
0
0
0
1
1
0
2
0
0
0
1
0
1
0
0
0
1
0
0
0
2
0
0
1
2
0
2
0
0
0
2
0
0
3
0
2
0
0
0
0
1
2
1
0
0
2
1
0
0
1
0
2
1
1
2
1
0
2
0
0
1
0
1
0
0
0
0
2
2
0
0
2
3
0
0
0
0
0
1
2
1
0
0
1
2
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
2
0
0
0
0
0
2
0
0
1
2
0
0
3
0
0
0
1
0
0
1
0
0
1
0
0
4
4
0
0
0
0
0
0
2
0
1
1
0
6
2
0
0
1
0
2
1
0
0
0
0
0
0
1
2
0
0
1
0
1
2
1
0
0
2
0
0
0
1
1
1
0
1
1
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
3
1
2
0
0
0
2
0
2
2
0
0
1
2
2
0
0
0
0
2
2
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
1
0
0
1
0
2
3
0
0
4
3
0
0
0
0
2
0
1
0
0
2
0
0
1
0
1
0
2
0
0
2
2
0
0
1
2
0
0
0
0
0
2
2
0
0
1
2
0
0
0
1
0
2
2
0
0
2
0
2
0
0
0
0
1
2
2
1
0
0
0
0
1
0
2
0
0
2
0
0
1
0
2
0
0
1
0
0
0
1
2
0
2
1
1
2
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
2
1
0
2
0
2
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
3
0
0
0
0
2
1
0
0
0
2
1
0
0
0
1
0
2
1
0
0
1
1
0
0
0
1
0
5
2
0
0
0
0
0
1
0
1
0
0
1
0
1
2
0
0
0
1
0
1
2
1
0
1
1
0
0
0
2
0
2
0
2
2
1
1
0
0
0
2
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
1
0
0
1
0
0
2
2
1
0
1
0
1
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
2
0
1
0
0
1
2
1
0
0
0
2
0
0
2
0
0
0
0
1
0
0
2
1
0
2
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
2
0
2
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
2
2
1
1
0
2
0
0
2
1
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
2
2
0
0
2
1
0
1
0
0
0
0
1
0
0
0
0
2
1
1
0
1
2
1
0
2
0
0
0
2
0
0
4
0
0
0
3
10
0
7
1
0
0
0
0
3
2
0
1
0
0
1
3
0
0
0
0
0
0
0
0
2
0
1
1
1
2
0
0
0
0
0
2
1
0
2
0
0
0
0
2
0
0
1
0
1
0
0
1
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
1
0
2
1
1
0
0
2
2
0
2
0
0
1
0
0
0
0
0
0
0
0
1
2
2
0
1
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
1
0
0
1
1
0
0
0
0
1
0
0
0
2
0
2
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
2
1
0
0
0
0
2
0
1
3
1
2
0
2
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
1
0
0
1
0
2
0
2
1
0
3
0
0
0
0
0
0
0
1
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
2
0
2
0
3
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
1
2
1
0
0
0
1
2
0
4
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
4
0
0
0
0
1
1
0
1
1
0
2
0
0
2
0
1
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
4
0
2
2
1
0
0
2
5
0
1
0
1
2
2
2
0
0
2
0
1
0
2
0
0
0
1
0
0
0
1
2
0
0
0
5
2
0
2
0
0
0
0
0
0
0
3
0
2
0
1
1
0
0
2
2
0
0
2
0
0
1
0
0
0
1
1
0
0
2
0
0
2
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
2
0
1
1
0
0
2
0
2
0
0
0
1
1
0
0
4
0
0
0
0
2
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
1
2
0
0
2
0
0
0
1
2
1
1
0
4
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
2
0
1
0
1
2
1
1
0
0
0
0
0
0
0
0
0
0
3
0
1
0
1
0
0
0
0
3
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
2
0
0
2
0
0
0
0
0
2
0
2
4
0
2
1
1
1
0
1
0
0
0
2
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
1
0
2
0
1
0
0
1
2
0
0
0
2
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
2
0
0
0
4
0
2
1
1
0
0
2
1
0
0
0
2
0
0
1
1
0
0
0
0
0
0
1
1
0
0
2
1
0
2
0
1
1
1
0
1
2
1
0
0
0
0
0
1
0
0
0
1
2
0
1
0
0
1
2
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
1
1
0
1
0
3
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
2
2
2
1
1
2
1
0
0
0
3
4
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
1
3
0
0
2
1
1
0
1
0
2
0
2
1
0
1
0
1
0
0
0
1
0
3
2
0
0
0
0
1
0
0
0
2
1
1
0
0
0
0
0
0
1
1
0
2
0
0
2
1
1
2
1
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
2
0
0
2
0
0
2
0
1
0
0
3
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
2
0
1
0
0
2
1
0
0
2
0
0
0
1
0
0
0
2
2
0
1
0
0
0
0
0
2
0
0
1
0
0
0
1
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
3
2
0
0
0
0
1
0
0
3
0
2
0
2
1
0
2
1
0
0
0
0
0
0
1
1
0
1
2
2
0
0
0
0
0
0
2
2
2
0
0
0
2
0
0
2
1
0
0
2
0
0
1
0
0
0
0
0
3
2
1
0
0
1
0
0
0
1
0
0
0
1
0
1
0
1
1
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
2
2
0
0
0
1
0
2
0
0
0
2
0
3
1
2
0
0
1
4
0
1
2
0
0
0
1
1
0
0
0
1
1
1
0
1
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
4
0
1
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
3
0
0
0
1
0
1
0
0
0
1
1
0
0
1
0
0
0
2
1
0
0
2
0
0
0
0
3
0
0
1
1
2
0
0
2
2
0
0
1
0
1
0
1
2
0
0
0
0
0
0
1
0
0
0
1
2
1
2
0
0
2
1
2
1
0
1
4
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
3
0
0
2
1
2
2
0
0
0
2
1
0
0
2
2
0
0
0
2
0
0
0
0
4
0
0
1
0
0
0
0
0
1
0
0
2
0
0
1
0
2
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
1
1
0
0
1
0
1
0
1
0
0
2
0
2
1
2
0
1
0
2
0
0
0
0
0
1
2
0
1
0
0
0
0
0
1
1
0
1
1
1
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
1
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
5
0
0
0
0
2
0
1
1
0
0
0
1
1
2
0
0
0
1
0
0
0
2
2
0
0
0
2
0
2
0
0
1
2
1
0
0
2
0
2
0
1
0
1
0
0
0
2
0
0
0
0
1
0
1
0
2
0
0
1
0
1
0
0
2
0
2
3
0
0
1
0
0
2
1
0
0
1
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
1
0
0
2
0
2
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
5
1
1
0
0
1
0
0
0
3
0
2
0
2
0
2
1
2
0
0
0
0
2
0
0
0
0
0
2
1
4
2
0
0
0
2
0
0
0
1
0
0
0
0
0
1
1
0
0
0
3
0
2
3
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
2
0
2
2
0
1
3
0
0
1
0
1
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
1
2
0
1
0
0
1
2
0
2
0
2
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
2
2
1
0
0
2
2
7
1
0
2
2
2
1
1
1
1
0
1
0
0
0
2
0
0
0
1
0
2
0
0
1
2
0
0
2
0
0
0
0
1
3
0
0
0
1
0
0
2
0
0
0
3
1
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
2
1
0
1
0
1
0
2
0
2
0
0
2
0
0
2
0
0
0
0
1
1
1
0
0
0
0
0
0
1
2
1
0
0
1
1
2
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
3
2
1
0
0
0
0
2
2
0
0
0
2
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
1
2
1
2
0
2
2
1
0
0
0
1
0
1
2
0
1
1
1
0
0
0
0
0
0
3
1
1
2
2
0
0
2
0
1
1
0
0
0
2
0
0
0
2
2
1
2
0
0
2
0
0
0
0
1
1
0
0
0
1
1
2
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
1
2
2
0
0
0
1
0
2
2
0
2
0
0
1
0
2
0
0
0
0
1
0
0
1
4
0
0
2
2
0
0
0
0
0
1
2
1
0
0
0
0
0
1
0
0
1
0
2
2
2
0
1
0
2
0
2
0
1
0
1
0
1
1
0
0
0
1
2
0
0
1
0
0
2
6
0
0
3
2
0
2
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
2
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
3
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
2
0
0
0
0
0
0
5
0
2
0
2
0
0
0
0
4
0
1
2
2
0
0
0
0
3
0
1
1
0
2
1
0
1
1
2
2
0
0
0
3
0
1
1
0
5
2
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
3
0
0
0
5
0
1
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
2
1
3
1
1
2
0
2
0
2
0
0
0
0
1
1
2
1
2
1
0
2
0
2
1
1
0
0
0
1
0
2
0
0
1
0
1
1
4
1
0
1
0
0
0
2
1
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
3
0
2
2
0
0
1
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
2
0
2
0
1
2
0
0
0
0
2
0
0
0
0
0
1
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
2
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
6
0
0
1
1
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
3
2
0
0
2
1
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
2
0
0
0
0
2
0
0
1
2
0
1
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
1
1
2
2
4
0
2
0
0
0
1
2
0
0
0
0
0
6
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
1
0
1
0
0
1
1
2
0
0
0
1
0
0
0
0
0
2
0
0
1
3
6
0
3
0
0
1
1
0
2
0
1
0
0
0
1
2
0
2
0
0
2
0
0
0
0
0
3
0
0
0
0
0
1
0
2
0
2
2
0
0
2
0
0
2
0
1
2
0
0
0
1
0
0
2
1
0
0
0
0
0
2
1
2
0
0
0
0
1
2
1
0
0
0
0
0
0
2
0
2
0
1
2
0
1
1
0
1
0
0
1
0
0
2
1
0
0
0
0
0
3
3
0
0
0
2
3
4
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
2
2
1
1
0
0
0
0
0
0
0
0
1
0
2
2
1
1
0
0
0
2
1
0
1
1
2
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
3
1
0
0
1
0
1
2
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
3
2
0
2
1
0
0
1
0
0
0
0
0
2
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
3
0
0
0
3
2
0
0
0
0
1
0
0
0
0
0
1
3
0
1
0
2
0
0
1
0
2
0
2
2
0
0
2
3
1
0
0
0
1
0
2
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
1
0
0
1
0
0
1
5
1
0
0
0
2
0
0
0
0
2
2
0
1
0
2
0
0
0
0
0
0
0
6
0
2
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
2
0
0
0
0
0
2
2
0
1
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
1
0
0
2
2
0
1
1
0
0
1
2
0
0
0
2
2
0
0
2
0
0
0
1
0
0
2
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
3
0
0
0
0
1
2
0
0
2
1
0
0
0
0
2
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
1
2
0
2
2
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
1
1
0
0
2
0
1
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
3
0
0
0
1
0
0
1
2
0
0
0
0
0
1
0
0
0
2
6
0
1
0
5
0
0
1
0
2
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
5
0
2
0
0
2
0
2
1
1
2
0
0
0
0
0
0
0
0
1
1
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
1
0
1
0
3
0
0
2
2
0
0
0
0
0
1
2
1
0
0
0
1
0
0
1
0
0
1
0
0
2
0
1
0
1
1
0
0
1
0
0
0
0
1
0
1
2
0
0
0
0
2
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
2
0
0
2
2
0
2
0
1
0
1
0
0
0
1
2
1
1
2
0
0
1
1
0
2
2
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
2
0
1
1
2
1
0
1
0
0
0
0
1
0
0
2
0
0
0
4
0
0
0
1
1
0
0
0
2
1
0
0
2
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
1
1
0
0
0
2
2
1
1
2
0
2
1
3
0
0
3
0
0
0
3
0
0
0
0
0
0
0
1
0
2
5
0
0
0
2
1
0
0
1
0
2
0
0
0
1
0
0
2
0
1
0
0
0
0
0
1
2
0
1
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
2
0
0
1
2
0
2
0
1
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
2
4
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
3
1
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
2
1
1
2
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
3
0
0
2
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
1
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
1
0
1
2
1
0
0
0
0
1
0
3
0
0
0
0
0
4
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
4
0
0
2
0
0
1
0
2
0
0
0
0
0
1
0
0
2
2
1
0
1
1
0
0
1
0
2
0
0
1
0
0
0
2
2
0
0
1
1
2
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
2
2
0
2
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
1
0
1
0
0
2
1
1
1
1
2
0
0
2
1
1
2
2
0
0
2
0
0
0
1
0
1
1
2
0
0
0
0
0
0
2
0
0
0
1
2
0
2
2
2
1
2
0
0
0
2
0
0
0
0
1
0
0
1
1
1
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
3
0
2
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
2
0
1
0
0
0
0
2
2
2
2
0
0
0
0
1
0
3
0
2
4
0
2
0
1
0
0
0
0
0
0
2
1
0
0
1
0
0
1
0
0
0
2
3
0
1
3
2
2
1
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
4
0
0
0
2
0
0
0
0
1
2
1
2
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
3
0
1
0
1
1
0
0
0
0
1
0
3
1
0
1
0
4
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
3
0
0
2
1
1
0
0
2
0
0
0
0
1
1
0
1
0
0
2
2
0
0
0
0
0
0
1
0
0
0
2
1
1
0
0
1
0
0
1
2
0
1
0
0
0
1
0
0
0
0
0
1
2
0
0
1
0
0
0
2
0
0
1
1
2
1
2
4
0
1
0
0
0
0
0
0
2
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
2
2
2
0
0
0
1
1
0
2
1
0
0
0
0
0
0
1
0
3
0
0
1
0
0
0
2
0
2
0
2
0
0
2
1
0
0
0
0
0
1
1
2
0
1
0
1
0
0
0
0
2
1
0
0
1
2
0
0
2
0
0
0
0
0
2
0
1
1
0
1
0
2
0
0
0
5
0
0
0
0
0
2
2
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
1
0
2
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
2
0
0
3
2
1
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
1
2
1
0
0
2
0
0
1
1
0
0
1
2
0
0
1
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
4
1
0
1
2
0
0
0
1
0
0
0
0
0
1
1
0
2
2
1
0
2
0
0
1
1
0
1
0
1
1
0
0
0
0
0
2
2
1
0
2
0
0
0
0
0
0
0
1
0
2
0
1
0
1
1
0
0
2
0
2
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
2
1
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
2
1
0
1
0
0
0
2
0
1
0
2
2
0
0
0
0
0
2
0
0
2
0
0
0
1
2
1
2
0
2
1
0
0
0
0
1
0
0
0
0
2
2
2
0
2
0
1
1
1
0
0
0
0
0
1
2
0
1
0
2
0
0
0
0
1
2
0
2
0
0
0
4
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
2
0
2
2
1
0
2
0
0
0
1
1
0
1
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
1
0
0
1
0
0
2
0
0
0
0
1
2
0
0
0
2
0
2
0
2
2
1
0
2
0
0
0
0
2
3
0
0
2
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
2
0
1
0
1
0
2
0
0
2
0
2
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
2
0
0
0
0
2
0
1
2
1
0
0
0
0
0
0
0
1
2
1
1
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
2
0
2
0
0
0
0
0
2
3
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
1
0
0
0
2
2
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
2
1
0
0
1
0
1
2
0
0
0
1
2
0
3
0
0
0
0
1
2
4
0
0
2
1
0
1
0
2
1
0
0
0
1
0
0
0
2
0
0
0
3
0
2
0
0
0
0
0
0
0
6
0
1
2
0
0
0
0
1
2
2
3
0
0
1
0
2
1
0
0
0
0
1
2
3
2
0
0
0
2
2
1
1
2
0
1
1
0
1
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
4
1
0
0
1
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
1
1
0
0
2
2
0
0
2
3
1
0
0
2
0
2
0
0
1
0
0
3
0
0
2
0
0
2
0
0
2
0
1
2
1
1
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
1
2
2
0
1
1
1
1
2
0
2
2
0
0
0
0
1
0
1
0
2
2
0
2
0
0
2
0
2
0
0
0
1
0
0
1
1
0
2
0
0
0
0
1
0
0
0
1
2
0
1
2
1
0
1
0
2
0
1
0
0
0
2
2
0
0
2
0
1
5
2
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
2
2
0
0
0
0
1
0
0
1
0
1
0
1
2
0
0
0
0
0
1
0
2
0
2
0
0
2
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
1
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
2
1
1
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
3
1
1
0
0
0
0
1
0
0
2
1
2
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
2
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
1
7
1
1
0
0
4
0
0
3
6
0
0
0
0
1
0
2
0
0
2
0
0
3
0
1
0
0
2
1
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
1
0
2
1
1
0
0
1
1
0
1
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
1
0
0
1
0
0
1
1
5
1
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
2
1
0
0
2
0
0
1
2
0
0
0
0
1
0
1
2
0
1
0
0
0
2
0
0
0
1
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
1
0
0
1
0
0
2
0
0
1
1
1
0
2
0
2
0
0
1
0
0
0
2
2
0
1
0
0
0
0
0
1
2
2
0
0
2
1
0
0
0
0
2
0
1
0
0
0
1
2
0
2
2
0
0
0
1
0
1
0
0
0
0
0
0
2
2
2
0
2
1
2
2
0
0
1
1
3
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
1
0
1
1
0
1
1
0
0
0
2
1
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
1
0
0
0
1
2
0
1
0
1
0
0
0
0
0
0
1
0
1
2
2
0
0
0
2
0
1
2
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
2
0
1
1
0
0
0
2
0
0
0
3
0
0
2
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
2
0
4
0
3
1
0
2
0
0
0
0
1
0
0
0
0
1
2
0
0
0
2
0
0
1
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
1
2
0
1
0
0
1
2
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
1
1
0
2
1
2
1
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
2
1
0
0
2
0
0
1
6
1
0
0
0
0
0
2
2
1
0
1
1
0
2
0
0
2
0
0
2
1
3
0
0
2
2
0
1
0
1
0
0
0
2
0
0
0
1
0
2
0
1
1
0
2
0
0
2
0
2
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
2
0
1
1
0
0
0
1
0
2
0
0
1
0
1
0
0
1
0
0
0
1
0
1
2
0
1
0
2
2
0
0
0
0
2
1
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
2
1
1
1
2
0
0
2
0
2
1
2
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
1
2
1
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
1
1
1
0
2
0
1
0
0
1
0
2
0
0
1
1
0
0
0
0
2
2
2
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
2
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
1
0
0
0
1
0
1
0
0
0
0
2
0
0
2
0
0
0
1
0
2
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
1
1
2
0
2
1
0
1
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
2
2
0
2
1
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
1
0
2
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
2
2
0
0
2
1
1
1
0
0
0
0
0
2
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
1
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
2
0
1
1
0
0
0
0
2
0
2
0
0
0
0
2
2
2
1
1
0
0
0
0
0
2
0
0
1
0
0
0
3
0
0
1
0
0
1
0
0
0
1
0
1
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
3
2
1
0
0
0
2
0
0
2
0
0
0
2
1
0
0
0
0
2
0
1
0
0
0
2
0
1
0
0
0
0
2
1
0
0
0
2
0
1
0
1
0
2
0
0
2
0
0
0
2
1
0
0
0
0
0
1
0
0
1
1
0
0
3
1
0
2
2
0
0
2
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
5
0
0
2
1
2
0
2
0
0
0
0
2
0
0
0
1
0
0
0
2
0
2
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
1
0
0
1
2
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
2
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
1
0
0
0
2
3
0
1
0
0
0
0
1
1
1
0
3
0
0
0
3
0
2
2
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
1
1
0
0
0
0
1
0
2
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
2
0
2
1
0
1
0
0
0
2
1
2
0
0
2
1
0
0
0
0
0
0
2
0
1
0
2
0
3
0
0
1
0
1
0
0
2
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
1
1
0
2
0
2
0
0
0
0
1
2
0
0
3
1
0
0
0
2
0
0
0
0
1
1
0
0
1
2
0
0
0
0
0
0
1
1
0
0
0
0
0
1
2
0
1
0
0
1
1
3
2
2
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
2
2
0
0
0
1
0
0
0
1
0
2
0
0
1
2
0
0
0
1
2
1
0
0
2
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
1
0
0
1
2
2
0
0
0
1
1
2
0
0
2
0
0
0
1
0
2
1
0
0
0
3
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
2
0
0
0
0
13
1
0
2
0
0
1
0
0
0
0
0
2
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
1
2
2
3
0
0
0
1
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
2
1
0
0
0
1
1
0
3
0
0
1
0
1
0
0
1
0
0
0
0
3
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
3
2
1
0
0
0
1
0
2
2
0
1
0
0
1
0
2
0
0
1
0
0
2
2
2
2
0
0
3
0
1
0
2
0
2
0
0
0
0
0
2
2
0
0
0
1
2
1
0
0
0
0
1
1
0
1
0
1
0
0
0
1
1
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
3
0
0
0
2
0
2
2
1
0
0
0
0
3
0
1
0
1
2
0
0
1
1
1
0
2
0
0
1
1
0
1
2
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
1
1
2
0
0
0
1
0
0
0
0
0
0
2
3
0
0
2
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
1
2
0
0
0
2
0
0
0
0
2
0
0
3
2
0
2
0
0
0
0
0
2
3
3
0
0
0
3
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
1
1
0
0
1
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
4
0
0
2
0
0
0
0
1
0
0
0
2
0
1
0
2
0
1
0
0
0
0
1
1
0
0
2
1
0
0
1
3
0
2
0
0
4
0
0
0
0
1
1
2
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
2
2
0
0
3
0
0
2
0
2
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
2
0
2
0
1
2
2
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
1
1
0
0
2
0
0
3
3
0
0
2
0
2
0
0
1
0
0
2
0
0
0
1
0
0
0
0
1
1
2
0
0
1
1
0
3
0
2
1
0
2
0
0
0
1
0
0
1
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
2
0
0
1
2
2
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
2
0
2
0
1
2
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
2
0
2
1
1
0
0
0
0
1
2
2
1
2
0
2
2
2
2
0
0
0
0
0
0
6
1
0
0
0
1
1
1
0
2
0
0
0
2
1
1
1
0
0
2
0
0
1
0
0
0
0
0
2
3
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
2
1
1
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
1
2
0
1
0
0
2
0
1
2
0
0
1
0
4
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
3
0
0
0
2
0
1
0
2
2
0
0
0
0
3
0
0
0
0
0
0
0
2
0
2
1
1
1
0
2
1
0
0
2
2
0
0
1
3
0
2
0
2
0
2
1
1
1
0
1
0
0
1
2
0
0
0
0
0
1
0
1
2
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
2
3
1
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
4
1
0
1
0
0
0
0
3
0
2
2
3
0
1
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
2
0
2
0
2
0
1
0
0
0
1
0
2
0
2
0
0
0
0
0
2
0
0
0
1
2
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
2
1
0
1
2
1
0
1
0
0
2
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
2
0
1
0
0
1
2
3
0
1
0
1
0
3
0
0
0
0
3
1
0
0
0
1
0
1
1
0
0
1
1
3
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
3
1
2
0
1
0
1
0
0
2
0
2
0
0
0
0
2
0
1
3
1
0
2
0
0
2
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
2
2
0
1
0
2
0
0
1
0
0
0
1
0
0
1
2
0
0
1
0
1
2
0
0
2
1
1
0
0
0
0
0
2
0
2
0
2
0
0
2
0
0
2
2
0
2
0
1
2
0
0
0
1
0
0
0
0
0
1
0
1
0
2
0
2
2
2
1
0
0
2
0
0
0
2
2
0
1
2
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
1
0
0
0
0
2
0
0
1
0
0
0
12
1
2
0
0
0
0
0
1
2
0
2
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
1
1
2
0
0
0
2
2
0
0
2
0
0
2
1
0
0
2
0
0
1
1
0
0
0
0
0
2
0
1
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
1
0
0
0
2
1
0
0
3
0
0
0
0
0
1
1
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
3
0
2
1
0
0
0
0
0
0
1
1
3
0
0
5
0
0
0
0
0
0
2
0
0
1
2
2
0
2
1
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
2
2
1
3
0
2
0
0
1
0
0
0
1
2
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
2
1
0
0
1
0
1
1
0
0
1
0
0
0
1
0
1
2
0
1
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
1
0
1
0
3
0
1
0
0
3
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
2
1
0
1
1
2
2
0
0
0
1
0
2
4
2
1
0
0
0
2
0
0
0
0
0
1
0
1
2
0
1
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
2
1
2
0
0
2
0
0
0
3
0
0
0
2
0
0
2
0
1
1
1
2
0
1
12
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
2
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
2
1
1
0
2
0
1
0
0
2
0
0
2
1
0
2
1
1
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
2
2
0
0
0
0
2
1
0
1
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
1
0
0
0
2
0
0
1
0
3
0
0
0
1
2
0
2
2
0
0
0
1
0
0
0
1
0
1
0
2
2
0
0
0
0
0
0
0
0
3
0
2
1
1
0
2
2
0
0
1
2
1
0
0
0
2
1
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
2
0
0
0
2
2
0
0
2
0
2
0
5
1
0
0
0
0
3
0
0
1
5
2
0
0
1
2
1
0
3
0
1
0
0
0
2
5
0
0
0
0
2
0
0
0
1
0
2
0
0
2
1
0
1
0
2
5
0
2
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
3
2
0
11
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
1
1
0
1
0
0
0
1
0
0
0
0
1
0
0
2
2
0
0
3
0
1
0
0
0
1
0
0
2
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
3
0
0
0
0
0
0
1
2
1
1
0
0
0
0
0
0
0
1
0
1
2
0
1
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
2
0
0
0
1
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
1
0
1
3
0
1
2
0
0
0
2
0
2
1
0
1
0
1
1
1
1
1
0
0
0
0
2
0
4
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
2
0
0
2
0
0
0
1
2
0
1
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
6
0
2
0
0
0
0
0
0
0
0
0
2
0
2
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
2
0
0
0
0
0
0
0
2
3
0
0
2
1
1
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
2
1
0
0
1
0
0
0
0
1
1
4
0
0
1
0
2
0
0
0
0
0
0
0
1
2
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
1
2
1
0
2
0
0
0
0
0
1
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
5
2
0
1
1
0
3
1
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
8
1
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
1
1
0
2
2
0
1
0
0
0
0
0
1
0
0
2
2
0
2
0
0
1
0
1
1
1
0
0
1
0
3
0
0
2
0
0
0
10
0
0
0
0
0
0
0
0
3
2
0
0
1
0
2
0
3
0
2
0
2
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
2
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
2
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
1
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
2
1
0
0
1
2
0
0
2
0
2
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
1
1
0
2
0
0
0
0
3
0
0
0
0
2
0
0
6
0
0
1
0
0
0
1
2
2
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
1
2
2
0
3
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
1
0
0
2
0
2
1
0
1
0
0
1
1
0
0
1
2
0
1
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
1
0
0
0
0
3
2
0
0
0
1
0
0
2
0
0
0
0
1
1
0
2
0
0
0
2
0
2
1
0
0
0
0
0
11
0
1
0
2
0
0
0
1
2
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
2
0
0
0
2
0
1
2
1
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
2
0
0
0
0
0
0
1
1
0
0
3
2
0
0
0
0
0
2
1
0
0
1
2
0
0
0
2
0
2
0
0
0
0
0
0
0
2
1
0
0
0
2
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
3
0
2
2
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
1
1
2
2
0
1
0
0
0
0
0
0
0
2
0
3
2
0
0
0
0
1
0
0
0
0
3
1
0
0
0
2
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
3
2
3
0
0
0
0
2
1
2
0
0
0
2
0
0
1
0
0
1
0
0
2
0
2
0
0
1
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
2
1
1
1
0
2
0
3
0
0
0
2
0
1
2
0
0
0
0
1
0
2
5
3
0
0
0
0
2
0
0
2
1
0
0
0
1
0
0
0
0
2
0
0
2
1
0
0
0
1
2
0
0
0
0
0
0
1
2
0
0
0
0
2
0
1
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
2
2
0
0
0
1
0
1
0
0
2
0
2
1
1
1
0
0
0
0
0
2
0
0
0
2
0
0
1
0
1
0
0
1
0
0
2
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
3
2
0
0
1
1
1
1
2
0
0
1
2
1
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
4
0
0
0
0
2
0
0
0
1
0
0
2
0
2
2
0
0
0
0
0
0
0
1
1
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
2
2
2
0
0
3
2
0
0
1
0
0
0
1
0
2
3
0
2
1
0
2
0
2
0
0
0
1
0
0
0
2
0
3
0
0
0
5
0
1
3
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
2
0
0
0
0
1
0
0
0
3
0
1
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
2
1
1
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
4
0
0
0
0
0
0
1
0
0
1
0
0
0
3
1
0
0
1
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
3
0
2
0
2
1
0
1
0
0
1
2
0
0
0
1
1
0
0
1
0
0
2
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
1
0
0
2
5
1
0
2
1
0
0
0
0
2
0
0
1
0
2
1
0
0
1
2
0
1
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
4
0
0
0
0
1
0
0
1
0
0
3
0
0
0
1
2
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
1
0
2
1
1
1
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
2
2
0
0
0
1
0
0
1
1
0
2
0
1
0
2
3
0
0
0
0
0
0
2
1
2
2
2
2
1
0
1
0
2
0
2
2
1
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
1
0
1
0
1
0
0
0
0
2
0
2
1
0
0
0
0
1
1
1
1
0
0
3
0
0
0
0
0
1
2
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
2
0
3
1
0
1
0
0
0
1
1
0
3
0
3
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
2
1
1
0
1
0
0
0
2
0
0
2
2
0
1
0
1
0
0
2
0
2
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
4
2
0
2
0
0
1
0
2
2
0
1
1
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
2
1
2
1
0
0
1
1
2
2
0
0
0
0
0
0
0
0
2
2
0
0
0
1
1
0
0
2
0
1
0
0
0
2
4
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
2
4
0
3
0
0
0
0
0
0
0
0
0
1
0
6
0
0
1
1
2
1
0
0
0
0
0
0
0
0
0
0
0
2
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
2
3
0
1
0
2
0
0
0
0
0
0
0
1
1
0
2
2
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
2
0
0
0
0
0
0
2
0
1
3
0
0
0
1
1
0
1
1
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
1
2
0
0
0
1
1
0
0
2
1
2
0
1
0
2
0
2
2
0
1
2
0
1
0
1
1
1
0
0
1
1
0
0
0
0
2
1
0
0
1
0
0
0
2
0
1
0
0
0
0
1
3
0
0
2
1
0
0
0
0
1
0
1
1
3
2
0
0
0
1
1
0
0
0
1
1
0
1
1
0
2
2
0
0
1
0
1
0
0
0
1
1
0
2
1
2
0
0
0
0
2
2
1
0
0
0
0
3
0
0
1
0
0
0
2
1
0
0
0
1
0
4
0
0
0
0
0
0
1
0
2
2
1
0
1
0
0
2
0
2
1
1
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
1
0
0
0
1
1
1
0
0
0
0
1
0
0
2
3
0
0
1
2
0
0
0
1
0
2
2
0
0
0
1
0
0
1
1
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
2
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
1
0
0
0
0
1
0
0
1
2
0
1
0
0
0
0
2
0
0
1
0
2
0
0
1
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
1
1
0
1
1
0
3
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
1
0
0
5
1
0
2
3
1
2
0
2
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
2
1
1
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
1
1
2
0
0
0
1
0
1
0
0
1
2
5
3
0
0
2
0
0
0
2
1
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
3
0
0
1
2
1
0
1
0
0
2
1
0
0
1
2
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
1
0
0
2
0
0
0
0
2
3
0
0
0
2
2
1
0
0
0
2
0
1
3
0
0
1
2
0
1
0
0
0
1
1
2
1
0
3
1
0
0
0
0
0
0
0
2
2
0
1
1
0
0
2
1
0
1
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
2
2
2
0
0
0
1
0
0
0
0
0
1
0
3
0
0
0
1
0
6
0
1
0
0
0
0
3
0
0
0
1
0
0
2
2
2
0
2
0
0
2
3
1
0
0
2
2
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
5
2
0
0
2
2
0
0
0
0
0
1
2
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
1
2
1
1
0
1
0
1
1
2
0
0
1
1
0
0
0
0
0
2
2
0
0
0
0
3
0
1
1
0
0
0
2
0
3
2
0
0
0
0
0
2
0
0
0
0
0
1
1
1
2
0
1
0
0
2
0
0
0
0
0
0
0
2
0
2
1
0
1
1
2
0
1
0
0
1
2
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
3
2
0
0
0
2
0
0
0
2
0
2
0
1
1
1
2
0
0
2
2
0
2
2
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
2
0
0
1
0
0
0
0
0
1
0
2
1
0
0
0
1
0
2
0
0
3
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
2
1
0
0
0
2
2
0
2
1
3
1
1
0
0
2
2
0
0
0
1
1
0
0
0
0
1
0
0
0
2
1
0
0
0
2
0
1
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
2
0
3
0
1
0
2
2
0
2
1
2
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
1
0
1
0
0
0
1
0
0
2
0
0
2
1
1
0
3
0
0
0
2
0
0
2
0
1
0
1
0
2
1
0
0
0
2
1
0
2
1
2
1
1
0
0
0
0
2
0
0
1
1
2
1
2
0
0
2
0
0
0
0
3
1
1
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
1
0
1
0
0
3
0
1
0
0
0
2
2
0
1
1
1
0
2
1
0
0
0
2
0
0
0
2
1
0
1
0
0
0
2
4
0
0
2
1
2
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
1
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
2
2
0
0
2
0
0
0
1
0
1
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
1
0
0
0
2
0
1
0
1
2
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
3
1
0
0
0
0
2
0
2
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
3
0
0
0
0
1
2
2
1
4
0
2
0
0
0
1
1
2
1
0
0
2
2
1
0
0
0
1
2
0
0
0
0
0
2
0
0
1
0
2
0
0
3
0
2
1
0
1
0
0
3
0
1
1
0
0
1
0
0
0
1
0
2
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
1
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
1
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
2
2
0
1
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
4
1
0
0
0
0
0
0
2
0
0
2
0
3
2
1
0
0
0
0
0
0
2
0
4
0
2
0
2
0
2
0
0
2
1
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
1
2
1
0
0
0
2
0
1
0
2
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
2
2
2
1
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
1
1
1
1
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
1
0
2
0
0
2
0
2
0
0
2
1
2
0
0
0
0
2
0
0
0
6
0
2
0
0
2
1
0
0
2
2
2
2
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
1
0
0
0
2
0
0
0
0
2
0
1
0
0
0
1
3
0
0
1
0
0
0
2
0
0
0
2
1
0
0
0
0
0
2
0
2
0
0
0
2
2
0
0
0
0
2
2
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
1
0
2
2
0
2
0
0
0
3
0
0
0
1
0
2
0
1
3
2
0
2
0
1
0
2
2
0
2
0
0
1
1
0
1
0
0
2
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
3
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
1
0
1
2
1
0
0
0
0
0
1
0
0
0
0
2
0
2
3
1
1
2
0
0
0
0
2
2
2
0
0
2
0
0
1
0
0
0
0
1
2
4
0
0
2
1
0
0
0
0
0
0
0
2
1
1
0
0
2
2
0
0
0
0
0
2
2
1
0
0
3
1
0
0
1
2
0
2
3
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
2
2
4
0
0
2
0
0
0
0
0
0
1
2
0
0
7
0
0
0
1
2
1
2
1
2
0
1
0
0
3
0
1
2
0
2
0
0
0
0
0
0
2
0
0
0
1
1
1
0
0
0
0
4
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
1
1
1
0
2
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
3
0
1
1
0
0
0
0
2
1
0
0
0
0
2
1
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
3
0
3
0
1
1
0
0
1
0
0
1
1
1
1
2
1
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
1
0
2
0
0
0
0
2
0
0
0
2
2
0
0
0
1
1
1
0
1
0
0
0
4
0
0
0
1
0
0
0
0
1
2
1
2
0
4
1
2
0
2
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
2
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
2
0
0
0
0
0
0
2
0
1
4
1
0
0
0
0
0
0
1
2
2
0
1
1
0
0
2
0
0
0
0
6
0
0
2
0
1
0
0
0
0
0
0
0
2
1
1
1
0
0
0
1
0
1
1
2
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
2
2
0
1
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
3
0
0
1
0
2
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
1
0
0
2
0
1
0
1
2
0
0
2
0
1
0
0
2
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
1
2
0
0
0
1
0
0
3
0
3
2
1
0
0
1
0
0
0
0
0
0
2
2
1
0
0
0
0
0
1
1
0
1
0
0
0
2
0
2
2
0
2
0
2
0
2
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
2
0
0
0
1
2
2
1
2
0
2
2
1
1
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
2
2
0
0
1
1
2
1
0
0
1
0
0
1
1
0
0
2
0
1
0
2
1
1
0
0
2
0
3
0
3
1
2
0
0
0
0
0
7
1
0
0
2
0
0
2
0
0
0
0
0
2
4
0
2
2
0
0
0
0
2
0
0
0
1
0
1
0
0
2
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
2
0
1
0
0
0
0
1
2
0
1
0
0
0
1
0
2
0
1
2
0
0
0
2
1
1
0
2
1
0
0
1
0
0
2
0
2
2
0
0
0
0
0
2
0
2
1
2
1
0
0
0
0
0
3
1
1
2
0
4
0
2
0
2
0
0
0
0
1
0
0
2
0
1
0
1
2
0
0
0
2
1
0
2
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
2
0
2
0
0
2
2
1
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
1
2
0
0
1
1
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
3
1
0
0
0
1
0
1
2
0
0
2
0
1
0
0
3
0
0
0
0
0
0
2
2
1
0
2
0
0
0
2
0
0
2
0
1
1
0
2
1
0
0
0
2
0
0
2
0
0
1
0
2
0
0
0
0
0
2
2
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
3
1
0
0
0
1
1
0
0
1
0
2
0
0
0
0
4
0
0
2
1
0
0
1
1
0
0
2
2
0
0
0
2
1
0
1
0
2
0
0
0
0
0
0
2
0
2
1
0
4
0
0
0
0
0
0
0
2
2
0
0
0
0
2
2
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
1
0
1
0
0
2
4
0
0
0
0
1
1
0
0
0
1
0
0
1
1
0
1
3
0
2
0
2
0
2
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
1
2
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
3
2
1
0
0
0
6
0
2
2
0
0
3
0
0
1
1
2
0
1
1
0
0
0
3
0
2
0
0
0
2
1
0
0
2
0
1
0
2
0
0
0
0
0
0
0
2
0
2
1
2
0
0
0
2
0
2
0
2
0
2
1
1
0
0
0
0
0
0
0
0
0
1
0
2
2
3
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
3
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
2
2
1
0
0
0
0
0
0
1
0
2
0
1
1
2
0
2
0
0
0
1
5
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
2
1
2
0
1
0
2
1
2
0
3
2
0
0
2
2
0
0
3
0
2
0
0
0
0
0
1
1
1
1
2
0
2
0
2
0
2
0
0
1
0
1
0
2
2
0
1
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
2
1
1
4
0
2
0
0
2
1
0
0
0
0
0
1
1
2
0
0
0
0
1
2
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
1
1
0
2
0
1
1
1
0
0
0
0
0
0
0
0
3
3
0
0
0
2
0
0
1
0
1
0
0
1
0
0
1
3
0
0
0
0
2
0
0
1
2
0
0
0
1
0
0
0
0
0
11
2
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
1
2
0
1
0
0
0
0
2
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
1
5
0
0
0
0
0
1
0
0
1
0
0
0
2
1
2
1
0
0
0
0
0
0
0
1
3
0
0
0
1
0
0
1
0
1
0
0
0
2
0
1
2
0
0
0
1
0
0
0
0
1
0
5
2
0
0
0
0
2
0
1
2
0
2
0
2
1
1
0
0
3
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
1
0
2
2
2
2
0
0
0
0
2
1
0
0
3
0
0
0
2
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
1
2
0
3
1
0
0
2
1
0
1
2
2
2
0
0
0
0
0
2
0
1
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
1
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
1
0
0
3
0
0
1
0
0
0
0
0
0
0
0
3
0
0
1
0
1
0
2
0
2
0
1
0
3
2
0
0
0
0
0
1
0
1
0
2
0
0
3
2
2
2
0
0
0
0
0
1
0
1
2
0
0
3
1
0
0
2
0
0
0
1
0
1
0
2
2
2
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
2
1
2
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
2
2
0
0
2
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
1
0
2
0
0
5
0
0
0
0
1
0
0
1
0
0
0
0
0
2
2
0
2
2
0
0
0
0
2
2
0
4
0
2
0
0
0
0
1
0
0
0
2
0
2
0
1
5
0
1
0
1
0
0
0
1
1
1
0
1
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
2
0
2
0
0
2
0
0
0
1
0
2
0
0
0
2
0
1
2
2
0
1
0
0
0
0
0
0
2
2
0
2
0
0
0
1
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
1
0
0
0
4
2
0
0
2
0
0
0
0
1
2
0
0
1
1
0
0
1
1
0
0
0
2
0
3
0
1
0
1
1
0
0
1
1
0
1
1
0
0
1
2
0
0
1
0
0
0
0
0
2
0
0
0
0
2
4
0
0
0
5
2
0
1
2
0
0
0
3
0
0
0
0
1
1
2
0
2
1
0
0
0
0
1
0
2
0
1
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
1
0
0
0
1
0
0
0
0
1
2
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
2
0
0
3
0
0
0
1
2
0
0
0
0
0
0
1
0
0
1
0
3
0
0
2
0
1
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
2
2
1
2
2
2
0
0
0
1
0
0
1
0
0
2
0
2
0
4
0
0
2
6
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
1
0
1
0
1
0
0
0
0
2
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
1
3
0
1
2
0
0
0
0
0
2
0
0
0
1
0
0
0
1
1
2
0
0
1
2
0
0
0
0
0
4
0
0
0
0
1
0
0
1
0
0
1
1
0
1
0
0
0
0
2
0
2
0
0
0
2
1
0
0
0
1
0
0
0
1
1
0
2
0
2
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
3
1
0
1
1
1
0
1
0
0
0
0
0
2
0
0
3
0
2
0
0
0
0
0
0
1
1
3
2
0
1
0
1
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
2
2
2
0
2
0
0
1
1
0
0
0
2
1
1
2
0
0
2
0
2
0
0
0
2
0
1
0
0
0
2
0
0
0
3
0
0
1
0
0
1
1
0
1
2
1
0
0
1
0
0
2
0
4
0
0
2
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
1
1
2
0
0
2
1
0
0
0
2
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
2
0
0
1
0
2
2
0
0
0
2
0
0
0
0
0
0
2
0
3
1
1
2
0
0
0
0
1
0
2
0
1
0
0
1
0
0
1
0
2
1
1
2
2
0
0
0
3
0
0
0
0
2
0
0
0
1
0
0
2
0
0
1
0
1
2
0
0
2
0
2
0
0
1
0
2
0
0
0
1
0
0
0
2
2
2
2
1
1
0
0
0
0
4
1
1
0
1
1
0
0
0
1
0
0
2
0
0
0
0
2
1
1
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
1
2
1
1
0
0
0
0
1
2
1
2
0
0
1
2
0
1
1
0
0
2
0
3
1
0
0
0
0
0
2
1
0
2
0
3
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
1
2
0
0
0
1
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
1
3
0
1
0
1
0
0
0
0
0
0
0
1
0
1
1
0
1
0
2
2
1
0
0
0
0
0
0
0
0
1
1
2
1
0
0
0
2
0
1
1
0
0
0
1
1
0
1
1
0
2
0
2
0
1
0
1
0
0
0
0
1
1
0
2
3
0
0
0
1
2
0
1
0
1
0
0
2
0
0
0
2
0
0
0
2
0
0
0
1
0
2
0
0
1
0
0
2
1
1
1
0
1
0
2
0
1
1
0
0
2
0
1
0
3
2
0
1
0
2
0
0
1
1
1
0
1
1
0
0
1
2
0
1
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
2
1
0
0
2
2
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
2
2
0
0
2
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
1
0
1
0
0
2
0
0
1
1
0
1
0
0
0
0
1
0
1
0
0
0
0
2
2
0
2
2
0
2
0
1
1
2
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
2
0
0
2
2
0
0
2
0
0
1
0
1
2
1
0
0
1
0
1
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
1
0
2
2
0
2
0
0
0
1
1
0
0
1
0
0
2
0
2
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
1
0
0
0
1
1
1
0
0
0
0
1
0
1
0
1
0
1
0
1
1
0
0
0
1
0
1
1
0
0
2
0
2
0
0
0
1
0
2
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
2
2
2
2
0
2
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
3
0
0
0
1
0
1
2
0
1
0
0
0
1
0
1
1
1
0
0
0
0
0
1
0
2
2
0
0
1
0
1
1
2
2
0
1
0
1
0
1
1
0
0
0
2
0
0
0
0
2
2
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
5
2
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
1
2
0
0
0
1
4
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
2
0
0
0
2
0
1
7
1
0
1
0
2
0
0
0
0
0
2
2
0
1
0
1
1
0
0
1
0
2
0
0
2
2
0
1
0
0
0
0
2
0
1
0
2
2
0
0
2
1
0
0
0
1
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
2
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
2
0
2
0
0
3
0
0
1
0
0
2
3
0
0
2
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
4
0
0
0
0
0
0
0
1
1
0
0
0
0
0
4
0
1
0
1
0
2
2
0
0
2
0
2
2
0
1
0
0
0
0
0
2
2
1
0
1
4
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
2
1
0
2
2
1
0
0
0
0
0
0
0
1
0
0
1
2
0
1
1
0
1
0
0
0
2
1
0
0
2
0
5
0
2
2
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
2
2
1
0
2
2
0
0
0
0
0
1
0
1
0
0
1
0
1
1
0
0
0
1
2
2
0
1
2
3
0
2
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
2
0
0
0
1
0
1
0
0
0
0
2
0
1
1
0
0
2
0
1
0
0
1
1
2
0
0
2
0
0
0
0
0
3
0
0
0
0
1
2
0
1
0
4
0
2
0
1
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
2
0
2
0
2
0
0
1
2
0
0
0
2
1
1
0
2
0
2
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
2
2
0
1
6
0
1
4
2
1
0
0
0
2
1
0
0
1
0
0
0
0
0
0
2
1
1
2
0
0
1
0
0
2
2
0
0
0
0
0
0
2
1
0
2
0
0
0
0
1
0
0
1
0
0
0
1
0
2
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
3
1
2
1
1
1
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
1
0
1
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
1
3
0
0
0
0
0
2
0
0
2
0
0
0
0
1
5
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
3
2
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
2
0
2
2
1
1
0
0
0
0
1
2
0
2
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
2
0
0
0
2
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
1
2
2
0
0
4
1
0
2
1
0
2
0
0
1
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
1
0
2
1
2
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
2
1
0
2
0
2
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
1
0
0
0
3
1
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
2
0
1
0
0
1
1
0
0
0
0
1
0
2
0
1
2
2
1
0
0
0
0
0
1
0
1
0
0
1
1
0
2
0
1
0
0
2
2
0
0
2
1
0
2
2
0
0
1
0
1
0
0
1
0
1
2
1
2
0
2
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
2
0
0
0
0
0
1
0
0
1
2
1
0
0
1
1
6
0
1
1
1
1
0
0
1
0
0
0
1
3
3
0
2
0
0
0
0
2
4
1
2
0
0
2
0
0
0
0
1
1
1
2
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
4
0
2
1
0
0
1
0
0
0
2
1
1
2
0
0
0
0
0
1
1
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
1
0
0
1
0
0
0
2
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
7
1
1
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
2
0
0
0
2
0
0
0
0
0
5
1
1
0
0
2
0
0
0
0
2
0
2
0
0
1
1
0
0
0
1
0
0
0
2
2
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
2
2
1
2
0
0
0
0
0
0
0
0
2
1
1
0
1
0
1
1
1
1
1
0
0
0
1
0
1
1
0
0
0
1
3
2
2
0
0
1
0
0
2
3
0
0
2
2
0
1
0
0
0
0
0
1
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
2
1
0
1
0
0
2
0
0
0
1
2
0
0
1
1
3
1
0
0
0
0
0
0
0
0
1
4
0
0
2
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
2
0
0
2
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
1
0
2
0
0
0
0
0
1
0
2
0
1
0
1
1
0
0
0
0
0
0
3
0
0
0
0
0
2
2
0
1
2
4
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
1
0
1
1
0
0
1
2
1
2
0
2
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
1
1
0
0
0
2
0
1
3
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
1
1
0
0
0
0
2
0
2
0
0
0
1
1
1
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
1
0
0
1
1
2
1
0
0
0
2
1
3
0
0
0
0
0
0
1
2
0
0
0
0
0
2
2
1
0
0
2
0
0
0
2
2
0
2
0
0
0
0
0
0
2
2
1
2
0
0
0
0
0
2
1
0
0
1
0
0
0
1
2
0
3
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
2
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
2
0
1
1
0
0
0
0
1
0
2
1
0
1
0
3
1
0
2
0
1
0
0
2
0
0
4
0
0
1
0
2
2
2
1
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
1
0
1
0
0
1
0
2
0
2
0
0
0
0
0
1
1
0
0
0
0
2
0
0
1
1
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
1
1
0
0
2
0
2
1
0
0
2
2
0
0
0
0
0
1
1
0
1
0
0
2
0
1
0
1
0
0
2
0
1
0
0
0
0
2
1
0
0
2
0
0
0
1
1
1
0
1
1
3
2
0
1
3
0
2
0
0
0
1
0
2
2
0
2
1
0
0
1
2
1
0
3
1
0
2
0
2
0
0
0
2
0
2
1
0
0
0
0
0
2
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
1
0
2
0
0
0
0
0
1
0
0
2
0
2
0
1
1
1
0
0
0
0
2
2
0
0
0
0
1
0
1
1
0
0
0
0
0
2
2
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
2
0
0
0
3
1
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
2
3
0
1
2
0
1
1
0
0
0
1
0
2
0
1
0
0
0
2
0
0
2
1
0
3
0
0
2
0
1
2
2
2
1
2
2
0
0
0
0
0
3
0
0
2
0
0
0
1
1
2
1
2
1
0
0
0
0
0
2
0
0
0
0
0
3
1
0
0
0
1
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
1
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
2
1
0
0
1
2
0
0
0
2
1
3
2
0
0
0
2
2
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
1
0
2
0
0
0
2
3
1
0
0
0
0
2
0
0
0
1
0
0
1
0
2
1
0
0
0
0
0
0
0
2
3
2
1
0
0
3
2
0
0
1
0
0
0
0
0
0
1
1
0
0
1
2
0
0
2
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
1
0
2
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
5
2
2
1
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
3
3
0
0
0
1
0
0
0
0
0
1
2
2
2
0
0
1
0
0
2
0
1
0
2
0
2
2
1
0
0
0
0
0
0
2
1
0
0
1
0
2
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
2
1
0
1
0
0
1
1
2
2
0
0
0
1
0
0
2
0
0
0
2
5
0
2
0
2
0
2
0
0
2
2
0
1
1
2
1
0
2
0
1
0
0
1
1
0
1
0
1
1
0
2
2
0
1
0
0
0
1
2
1
1
0
0
0
2
0
1
1
1
0
0
0
0
1
3
0
0
0
0
2
0
1
0
0
2
0
0
2
0
0
0
2
0
0
3
0
0
0
1
0
2
0
0
0
0
2
0
1
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
2
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
2
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
2
0
3
0
2
1
1
0
0
1
0
0
2
1
0
0
3
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
3
1
0
0
0
1
0
2
0
0
0
0
1
0
2
2
0
0
2
0
0
1
0
1
0
1
1
0
2
0
0
0
0
1
3
0
0
0
3
2
2
0
0
1
0
0
2
0
1
0
1
1
0
0
0
0
1
2
1
0
0
2
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
3
0
0
0
0
0
1
2
0
0
0
2
1
0
0
1
0
1
1
0
0
0
2
0
0
0
1
2
1
1
0
2
0
0
0
3
0
0
0
1
0
0
0
1
0
0
0
1
0
2
0
0
1
1
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
2
1
1
1
0
0
2
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
2
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
1
1
0
0
2
0
1
2
1
0
0
0
0
0
2
1
0
0
2
8
0
2
2
2
0
0
0
0
0
0
2
0
2
0
0
0
1
1
2
1
0
3
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
7
11
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
3
0
0
0
0
0
5
0
0
0
2
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
1
2
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
2
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
2
0
1
5
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
2
3
0
2
1
2
0
0
1
2
0
0
0
0
0
2
0
0
0
0
1
0
1
1
0
2
1
0
3
0
2
3
1
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
5
0
0
0
1
0
0
3
0
0
1
0
0
0
0
2
1
1
2
0
0
0
0
2
0
1
0
3
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
1
1
0
0
1
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
2
0
0
1
1
1
1
1
0
0
0
2
0
1
2
0
1
0
0
0
0
0
0
1
3
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
2
2
0
0
1
0
0
0
0
3
0
1
2
2
0
2
0
0
0
0
1
1
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
1
0
0
0
2
0
1
2
0
0
0
4
0
1
0
0
0
1
0
1
1
0
2
0
0
0
0
0
2
0
2
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
2
0
0
0
0
0
2
1
2
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
2
1
3
4
0
2
2
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
1
0
4
2
0
0
0
1
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
2
2
1
2
0
0
0
0
0
2
0
0
1
2
7
0
0
0
2
0
2
0
2
1
2
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
2
0
0
3
0
2
2
1
1
0
1
0
0
0
1
0
0
0
0
0
4
1
1
1
0
0
4
0
3
0
0
2
0
3
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
1
1
0
0
2
0
0
0
0
0
0
2
1
1
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
1
1
0
2
0
2
0
0
0
0
2
0
0
0
0
0
2
0
3
0
0
1
0
1
0
1
0
2
0
0
2
0
1
0
0
0
0
2
0
2
0
0
0
1
0
0
0
2
0
1
1
0
1
1
2
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
1
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
2
1
0
0
0
1
2
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
2
2
0
0
0
1
0
2
1
0
0
0
0
0
1
2
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
2
0
0
0
2
2
0
0
2
0
1
0
0
2
2
0
0
0
0
3
0
2
2
2
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
1
1
0
4
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
2
1
0
0
1
1
0
0
2
0
0
0
0
0
0
0
1
1
1
3
0
0
0
0
1
0
2
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
2
2
1
0
0
1
0
0
1
2
2
0
0
0
2
1
0
0
0
2
0
0
2
0
1
1
0
0
2
0
0
0
0
0
0
0
1
0
2
1
0
1
0
1
2
0
0
0
2
0
0
1
0
0
0
0
0
1
1
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
2
2
0
0
0
0
2
0
0
4
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
2
0
2
0
1
0
0
0
0
0
0
0
0
2
0
2
0
1
3
0
1
0
0
0
1
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
2
0
0
1
1
1
1
0
1
0
0
2
1
2
1
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
1
1
1
0
2
0
0
0
1
1
1
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
2
1
1
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
1
1
2
0
2
0
0
0
0
0
1
0
2
0
0
0
2
0
0
2
2
0
2
0
0
0
0
2
0
4
1
0
0
0
3
1
1
1
2
0
2
0
0
2
2
0
1
0
0
0
0
2
0
0
2
2
0
2
0
1
0
0
0
2
2
0
1
2
0
0
0
0
1
0
1
0
2
0
0
0
3
2
0
0
0
1
2
2
0
2
0
0
0
2
1
0
2
0
0
0
3
0
0
2
0
1
0
1
0
0
3
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
2
0
2
0
0
4
0
1
2
0
0
0
0
0
0
2
1
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
2
1
0
1
0
0
0
0
1
0
0
0
0
1
0
6
0
0
0
2
2
0
0
0
0
0
2
2
1
1
0
0
0
2
0
2
0
0
1
0
1
2
0
0
2
0
0
0
0
0
0
0
1
1
0
1
0
1
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
3
0
0
0
0
1
0
0
0
1
0
0
0
2
0
4
1
2
0
0
0
0
1
0
1
0
0
4
0
2
0
1
0
2
2
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
1
1
1
2
2
2
1
0
3
0
0
2
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
2
1
0
1
1
0
0
1
0
0
1
0
0
1
1
0
0
0
0
2
0
0
2
0
0
1
0
0
0
2
2
3
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
2
2
0
0
0
0
0
2
0
0
2
0
1
1
0
0
0
2
2
0
2
0
0
0
0
0
0
2
0
0
0
0
3
2
0
1
0
2
0
0
0
0
0
2
0
0
2
1
1
2
0
0
0
0
2
0
2
0
0
2
2
0
0
0
0
1
0
0
2
0
0
0
1
2
2
2
2
0
1
1
1
0
0
1
2
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
1
2
0
2
2
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
2
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
3
1
0
2
3
0
0
3
3
0
1
0
0
0
0
0
0
0
0
0
1
1
1
1
3
0
0
1
0
1
3
0
0
0
0
0
3
0
0
0
0
1
0
0
2
3
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
3
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
4
1
2
0
0
1
0
1
0
0
1
0
0
2
0
2
0
2
2
0
0
3
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
1
0
2
0
1
0
2
0
2
1
0
1
1
1
0
0
1
0
0
0
0
4
2
0
0
1
1
0
2
0
1
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
2
1
2
1
0
1
0
1
0
2
1
0
1
0
1
0
2
0
2
0
0
2
0
0
0
2
0
3
0
0
0
0
0
2
1
2
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
2
2
2
2
2
0
0
0
0
0
0
1
2
0
0
3
0
0
0
0
0
0
0
0
1
1
0
1
2
0
1
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
2
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
1
0
2
4
0
0
0
2
0
0
0
0
1
0
2
1
0
1
0
1
0
0
0
2
0
0
1
1
0
0
3
2
0
3
0
0
0
0
0
2
0
1
1
1
0
0
0
2
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
2
0
1
0
0
0
1
0
0
0
1
0
0
2
2
0
2
2
0
0
1
0
0
0
0
2
0
0
2
1
0
2
0
2
0
0
1
0
0
1
1
0
0
0
1
0
1
2
0
0
0
0
1
1
1
0
1
0
0
0
0
1
0
0
0
4
2
0
0
0
1
0
0
0
0
0
2
1
1
0
1
0
0
0
0
1
0
2
2
1
2
0
0
0
0
2
1
0
0
0
0
3
2
0
0
2
1
0
0
2
0
0
2
1
0
0
0
0
1
2
1
0
2
0
1
2
0
0
0
0
0
1
1
0
0
1
0
1
2
1
1
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
2
1
0
2
0
1
2
1
0
0
4
1
1
0
0
0
1
1
0
0
2
2
1
0
0
2
0
0
2
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
2
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
2
1
7
0
0
0
0
0
1
1
2
0
0
0
1
0
1
4
2
1
0
1
0
2
0
0
2
0
0
1
1
0
0
2
0
1
0
1
2
0
0
2
0
0
2
1
0
0
0
0
0
1
0
1
1
0
8
0
0
0
2
2
1
0
0
0
0
0
1
1
0
2
1
0
0
2
1
2
2
2
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
1
1
1
0
0
0
0
2
2
1
0
0
0
0
2
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
1
0
0
1
0
1
0
0
0
0
0
0
2
1
0
0
0
0
1
0
1
0
1
0
1
0
0
0
2
1
0
0
0
0
2
2
2
1
0
1
2
0
1
0
1
1
1
0
0
0
2
0
2
2
0
0
0
0
0
0
2
1
2
2
0
0
2
0
4
0
0
0
0
0
0
0
3
2
0
0
0
2
0
2
2
2
0
1
2
0
0
0
0
1
0
4
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
1
1
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
2
0
0
0
1
0
0
0
0
0
1
1
0
2
0
0
1
0
0
0
0
1
0
0
0
3
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
3
2
0
0
2
0
0
1
0
0
0
3
0
1
1
0
2
2
0
2
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
4
2
2
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
1
0
1
0
0
2
1
0
1
1
1
1
0
2
0
0
1
2
0
0
0
2
2
0
2
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
2
0
2
0
0
0
2
0
0
0
1
0
2
1
0
0
0
0
0
0
0
1
0
3
0
2
1
1
0
0
0
0
0
2
0
1
2
0
1
0
0
2
2
1
0
0
2
0
0
0
0
0
2
2
4
0
0
1
1
0
0
0
0
0
2
0
1
0
0
0
1
2
0
0
0
0
4
10
0
0
0
0
1
0
0
0
4
2
0
1
0
0
3
0
3
0
1
1
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
1
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
2
0
1
0
0
0
3
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
1
2
0
0
2
0
0
0
2
0
0
0
2
0
0
2
1
1
0
0
2
2
0
0
2
2
0
0
4
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
2
2
2
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
1
6
2
0
0
0
0
2
0
0
1
0
2
0
0
0
1
1
0
1
1
0
0
0
1
0
0
0
0
12
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
3
0
2
2
2
0
0
2
0
0
0
1
0
0
2
0
2
2
2
0
0
0
0
1
0
0
1
0
0
3
0
2
2
0
0
1
1
0
0
0
0
2
1
0
0
0
1
0
1
0
0
0
2
0
0
0
0
1
0
3
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
2
2
2
0
0
0
0
1
1
0
2
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
1
0
0
3
4
0
0
0
0
3
0
0
0
0
0
2
0
0
0
1
0
3
0
0
2
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
8
0
0
0
0
0
0
0
2
0
0
0
1
2
0
2
0
0
0
0
0
0
0
1
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
1
0
1
0
2
0
2
1
0
0
1
2
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
2
0
1
2
0
2
0
0
1
0
0
0
0
0
1
1
1
1
2
0
0
0
0
0
0
0
0
1
2
3
2
1
2
0
0
0
2
0
0
0
1
0
1
0
2
0
0
1
0
0
1
2
0
0
1
2
2
1
0
2
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
2
1
0
0
1
1
2
0
2
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
4
0
2
0
0
1
0
0
0
0
1
0
0
0
1
0
2
1
0
0
0
0
0
1
1
1
0
1
0
2
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
2
1
3
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
2
0
0
0
0
0
1
0
0
2
1
0
0
0
0
2
1
2
0
1
0
0
0
2
2
0
2
0
0
2
2
0
0
2
0
0
0
1
1
1
2
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
2
0
1
0
1
1
0
2
0
0
1
0
1
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
2
0
0
0
0
1
1
0
0
0
0
1
2
0
1
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
1
0
0
2
0
0
6
0
2
1
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
2
0
2
0
2
1
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
1
0
0
1
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
1
0
0
1
0
0
1
0
0
3
0
7
0
0
0
0
2
0
2
0
0
0
0
2
3
0
1
0
0
0
2
1
0
0
1
0
2
0
2
2
0
0
2
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
2
0
1
0
2
0
2
0
2
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
2
0
0
1
0
0
0
2
1
0
2
0
0
1
0
1
1
1
0
0
0
0
0
2
2
0
0
2
0
0
1
1
1
0
0
0
0
0
0
0
0
1
1
0
1
1
0
2
0
0
2
0
2
0
1
0
1
0
1
0
0
2
1
0
3
0
2
1
0
0
1
1
2
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
2
1
0
0
1
3
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
1
2
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
3
0
0
4
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
1
2
0
0
0
1
0
0
0
2
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
3
1
0
2
0
0
0
0
0
0
0
0
0
3
0
2
0
1
1
0
0
1
1
0
0
0
1
1
0
0
1
0
1
0
2
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
4
0
0
0
0
2
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
2
0
2
1
0
0
0
0
3
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
2
0
0
0
0
0
0
0
1
0
1
0
0
1
0
2
0
0
1
1
0
1
2
0
1
0
3
2
0
0
1
1
2
1
1
0
2
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
3
0
0
0
2
0
0
0
0
0
1
1
1
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
2
0
0
1
0
0
0
1
2
1
0
1
2
0
0
0
0
1
1
0
2
0
0
2
1
1
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
5
0
0
0
1
0
0
3
0
1
0
0
0
0
2
0
2
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
1
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
1
1
0
0
0
2
2
1
0
1
0
0
1
2
1
0
0
0
0
1
0
0
1
0
0
2
2
1
1
0
0
2
2
0
0
0
0
0
0
0
0
1
1
1
0
0
2
0
1
0
0
0
0
2
1
0
1
0
0
0
4
0
2
3
0
0
0
0
0
0
0
2
0
0
2
0
1
0
2
0
0
1
1
0
0
0
0
0
2
5
0
0
1
0
0
0
0
0
0
5
2
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
1
2
0
0
0
0
0
1
0
0
0
1
0
0
1
0
2
2
0
2
1
0
0
0
1
2
0
0
5
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
3
1
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
1
2
2
2
0
0
0
0
2
0
0
1
0
0
0
0
0
1
1
0
0
2
0
1
2
2
2
0
1
0
1
0
1
1
0
3
0
0
0
0
2
1
0
0
1
0
1
0
0
0
1
0
0
2
0
0
2
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
3
0
2
5
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
2
0
2
0
0
2
1
0
0
0
1
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
1
1
1
1
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
2
1
0
1
0
0
0
3
0
0
0
1
0
0
0
2
0
0
1
2
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
2
2
0
0
1
0
3
2
0
2
1
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
3
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
1
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
3
0
0
0
1
0
0
0
3
2
0
0
2
0
2
0
0
0
2
0
0
0
0
0
3
0
2
0
0
0
2
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
1
1
0
2
0
0
0
0
2
0
0
0
2
2
0
0
0
0
2
0
2
0
0
1
2
0
0
0
1
2
1
0
0
1
0
0
0
2
0
2
0
2
0
0
1
0
1
0
0
0
0
1
0
2
0
1
0
0
1
0
1
1
1
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
2
0
0
0
1
0
0
5
2
0
2
0
2
0
0
0
0
1
0
0
0
4
0
0
1
2
0
2
2
0
2
0
0
0
0
2
0
0
2
2
0
0
2
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
2
1
2
3
0
0
2
1
0
0
1
0
0
2
0
0
2
1
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
2
0
1
1
0
0
2
0
2
0
0
0
0
0
0
2
0
1
0
0
1
1
0
0
0
0
2
1
0
0
0
1
0
0
1
0
1
1
0
1
0
0
1
1
0
0
0
0
0
0
2
0
2
0
3
2
1
0
0
0
0
1
0
0
0
1
0
2
0
3
0
0
0
0
0
1
0
2
1
1
0
0
4
1
0
0
0
3
1
0
0
0
0
0
0
0
2
1
0
0
3
0
2
0
3
0
0
0
2
1
0
2
2
0
2
0
0
0
0
0
1
0
0
0
1
1
3
0
0
0
1
0
2
0
0
0
2
0
2
1
0
1
2
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
1
0
0
1
0
2
1
0
3
2
1
2
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
1
0
2
3
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
1
0
3
0
0
0
0
2
0
0
0
0
2
0
1
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
2
2
2
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
3
2
0
0
2
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
3
2
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
2
0
1
0
2
0
0
2
0
0
1
0
1
0
1
0
1
0
0
0
0
0
2
2
0
0
2
0
1
1
0
0
2
0
2
0
2
0
1
2
0
0
0
1
0
1
0
0
0
0
2
0
0
0
1
0
0
1
0
0
1
1
2
0
0
0
0
0
2
0
2
0
0
0
1
2
0
0
0
1
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
3
0
0
0
2
2
1
1
0
0
0
0
1
1
0
0
2
0
0
1
0
0
5
0
0
0
0
0
2
1
1
0
1
0
1
2
2
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
2
0
1
0
1
0
0
0
2
1
0
1
2
0
0
1
1
2
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
1
0
0
0
0
0
0
0
1
3
2
0
2
0
1
0
0
0
0
2
1
2
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
1
1
0
0
2
0
0
0
0
0
2
1
0
0
2
1
2
2
2
0
1
1
0
0
2
2
3
0
0
0
2
0
2
0
2
1
1
1
1
0
0
0
2
2
0
0
0
0
1
1
0
2
2
0
0
0
0
0
0
2
2
1
1
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
2
1
0
0
1
0
2
2
1
0
2
4
0
0
1
0
0
0
0
3
2
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
1
0
0
2
2
0
0
1
0
0
1
2
0
0
1
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
1
1
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
1
1
0
0
0
0
3
1
0
0
0
0
0
2
0
1
0
2
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
5
0
2
0
1
0
0
0
1
0
1
0
0
0
2
2
0
0
0
0
0
0
0
5
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
1
1
0
0
2
0
0
0
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
1
0
1
2
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
1
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
3
2
1
0
1
0
0
0
2
0
1
0
0
2
1
0
0
0
1
1
0
0
0
0
0
0
0
2
0
1
2
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
1
0
1
0
0
1
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
3
2
2
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
4
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
1
0
2
0
2
0
2
0
0
0
0
1
2
0
0
1
2
0
1
2
3
0
0
2
2
0
0
0
0
5
0
0
0
0
0
0
1
0
1
1
0
0
1
0
2
2
0
1
1
1
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
1
3
0
3
0
0
0
0
2
1
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
1
1
2
0
0
0
0
1
0
0
3
0
1
0
0
1
0
2
0
0
3
0
0
1
0
2
4
0
0
2
2
0
5
0
0
0
1
0
2
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
2
0
0
1
1
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
2
0
2
0
0
0
1
2
0
1
0
0
1
2
1
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
2
0
1
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
3
0
0
0
1
0
2
1
1
0
2
2
0
0
0
0
2
0
1
0
3
0
1
0
1
1
0
0
2
0
2
0
2
0
0
0
0
1
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
1
2
3
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
1
0
0
0
1
2
0
0
0
0
0
2
0
1
1
1
0
2
0
1
0
0
2
0
1
0
0
0
0
1
2
0
0
0
1
2
1
1
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
3
0
0
0
0
2
0
1
0
0
1
1
1
0
1
2
0
1
0
2
0
0
2
1
0
0
0
0
0
1
0
2
2
0
0
0
0
1
2
0
0
1
0
0
0
1
0
1
2
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
2
2
0
0
0
1
0
2
0
0
0
2
1
1
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
2
0
1
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
2
1
1
2
0
1
2
0
0
2
0
1
1
0
2
0
1
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
1
2
1
0
0
0
2
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
1
0
3
0
2
1
0
0
0
1
0
1
2
1
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
1
0
1
0
0
2
0
0
0
2
0
1
0
0
2
0
0
1
0
0
1
0
1
0
2
0
0
1
2
6
1
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
1
0
2
0
0
1
0
0
0
0
0
0
0
1
0
3
0
2
2
0
0
0
0
2
3
1
0
0
2
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
1
1
0
0
1
0
0
0
2
0
1
0
2
1
2
0
0
2
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
6
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
2
0
2
1
2
1
2
0
0
0
0
0
0
0
1
1
1
2
2
2
0
2
1
0
0
1
1
0
0
1
1
1
0
1
0
0
0
0
0
1
3
1
0
1
0
0
2
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
1
2
3
0
4
0
2
2
0
0
2
2
0
2
0
4
2
1
0
0
2
0
1
0
1
1
2
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
3
0
0
0
0
2
1
0
0
0
0
0
0
2
0
1
2
0
2
0
1
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
2
3
0
1
1
0
1
0
2
1
0
0
1
1
0
0
0
0
0
0
0
2
4
0
0
1
1
0
0
1
0
0
1
0
0
0
2
1
0
0
1
0
2
0
0
1
0
1
1
0
0
0
2
0
2
0
0
0
2
0
0
0
1
1
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
1
0
0
2
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
2
1
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
1
0
2
0
2
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
2
1
2
0
2
0
0
0
1
0
2
0
1
0
0
0
0
0
2
0
0
0
2
2
0
0
0
2
6
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
3
0
0
1
0
3
0
0
2
0
0
0
1
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
1
1
2
2
2
0
0
2
1
0
1
0
2
0
1
1
0
0
0
1
1
0
0
0
0
0
2
1
0
2
2
0
0
0
2
0
3
2
1
0
1
0
1
0
1
0
1
1
3
1
2
2
3
2
1
0
0
0
0
0
1
2
0
0
0
0
2
1
0
1
0
0
0
1
0
0
1
10
0
2
0
0
1
0
2
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
1
1
1
0
1
0
0
0
0
0
0
1
0
2
0
0
1
0
1
0
0
1
0
0
2
1
0
0
0
0
0
2
0
0
0
1
2
0
0
0
2
0
0
0
1
0
2
0
0
0
0
1
0
1
0
0
0
2
0
1
0
0
0
0
2
0
0
0
1
1
0
1
2
1
0
0
0
1
2
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
4
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
1
0
0
0
0
2
0
0
1
1
0
0
0
0
0
1
1
2
0
0
2
0
0
0
2
3
1
0
0
3
1
5
2
0
0
2
1
0
0
0
0
0
0
2
2
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
2
0
0
1
1
0
1
0
0
0
1
2
1
0
2
0
1
0
1
0
2
2
0
2
0
0
2
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
5
1
0
2
1
0
0
0
0
0
2
2
0
0
2
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
5
0
2
0
0
1
0
2
0
1
0
0
3
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
1
0
2
0
2
1
0
1
2
0
0
0
0
2
0
0
1
0
1
0
1
1
0
1
1
2
0
0
0
0
0
2
2
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
2
0
0
0
2
2
0
0
2
2
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
2
0
1
2
0
0
0
2
0
0
0
2
2
0
0
0
2
0
0
0
0
0
2
2
2
2
0
2
0
0
0
2
2
0
0
2
4
3
0
0
0
1
0
2
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
9
0
0
2
1
0
2
3
0
2
0
1
1
1
0
1
0
2
1
0
0
0
0
1
0
0
2
2
0
2
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
1
1
1
0
0
0
0
1
2
1
1
0
1
2
2
1
0
0
1
0
0
2
2
0
0
0
0
1
0
2
1
0
0
0
1
0
0
0
0
2
2
2
0
0
0
0
0
0
0
2
0
0
2
3
0
0
0
0
0
1
1
0
1
0
0
1
0
0
2
0
0
0
1
0
1
1
1
2
0
0
0
0
2
1
2
2
2
1
0
0
0
1
2
2
0
1
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
8
0
0
1
0
0
1
2
2
2
2
0
0
0
1
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
2
2
1
1
1
1
0
0
3
0
0
0
1
0
0
1
0
0
5
0
0
0
0
1
0
2
1
0
0
3
4
0
0
1
0
1
2
1
0
0
1
1
0
3
0
1
1
0
3
0
0
0
2
1
1
0
0
0
1
0
2
4
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
3
0
0
1
0
0
1
0
4
0
2
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
1
1
1
0
1
1
0
0
0
0
0
0
0
0
3
0
3
0
1
0
0
0
0
0
2
1
0
0
2
1
0
0
0
0
2
2
2
0
0
0
1
1
0
2
2
0
0
3
0
0
0
1
2
1
2
0
1
0
0
0
6
0
0
0
2
2
0
2
1
1
2
0
0
1
1
1
0
2
2
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
1
0
1
1
0
0
0
0
0
2
2
0
0
0
0
0
2
1
0
1
0
0
0
2
2
0
2
0
0
0
2
1
1
0
1
0
2
0
0
0
2
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
2
2
0
0
0
0
0
0
2
0
0
2
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
9
5
0
0
1
0
3
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
2
0
2
1
0
2
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
1
0
0
1
2
2
0
0
0
1
1
0
0
0
0
2
0
2
1
1
2
1
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
1
0
0
0
0
2
0
0
0
0
2
0
1
1
0
0
3
0
1
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
1
0
0
0
0
0
0
0
3
0
0
2
1
0
1
2
0
0
2
2
1
0
2
0
0
2
2
0
0
2
1
0
0
0
2
0
0
0
1
0
1
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
3
1
1
0
4
0
0
0
0
0
0
0
0
0
0
2
2
0
2
3
0
0
0
0
1
1
0
1
0
0
1
0
0
2
1
1
0
0
0
2
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
4
0
0
1
0
0
0
2
2
0
0
0
0
0
2
1
0
0
0
0
0
1
1
0
2
0
2
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
2
3
1
2
0
0
2
0
0
0
0
1
2
0
0
0
4
1
0
0
0
2
0
0
2
0
0
0
0
1
0
0
2
0
2
3
1
1
0
2
0
0
2
2
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
2
0
0
0
1
0
0
0
2
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
2
0
0
0
3
0
0
0
1
2
1
0
0
1
0
0
0
0
1
0
2
0
1
3
0
0
0
2
0
2
0
0
0
0
2
0
0
0
2
0
2
0
0
0
1
1
3
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
2
2
2
0
0
0
0
2
0
1
2
1
1
1
2
0
0
0
2
0
0
0
1
2
1
0
0
0
0
0
2
2
0
0
0
1
1
0
3
0
0
0
1
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
1
2
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
4
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
2
0
4
1
0
1
0
1
1
1
0
0
0
0
0
1
0
0
0
0
1
0
1
2
0
0
4
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
1
1
3
2
0
1
0
0
0
1
0
0
0
1
2
2
1
1
0
0
0
1
0
0
2
1
0
2
1
0
0
2
0
0
2
1
0
0
2
0
0
0
1
2
1
2
5
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
1
1
1
0
1
1
0
0
0
1
1
0
1
0
0
1
1
4
2
1
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
5
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
1
1
0
0
0
0
0
2
0
0
2
0
2
2
0
0
2
0
0
2
0
2
2
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
1
0
3
2
0
0
1
1
0
1
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
1
2
0
1
2
1
2
0
1
0
0
0
1
0
0
2
0
3
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
1
0
1
0
2
0
0
0
2
0
2
2
1
0
0
0
2
1
0
0
0
0
2
1
0
0
2
1
0
4
0
1
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
2
0
0
2
0
2
0
2
0
2
1
1
0
2
0
0
0
2
0
0
2
2
0
0
2
0
2
0
1
0
0
0
0
0
0
0
2
2
0
0
2
1
2
0
0
0
0
0
2
1
2
1
1
2
0
1
2
0
2
2
0
2
1
0
0
0
1
1
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
1
0
1
0
0
0
1
0
0
0
2
2
0
2
0
0
0
0
1
0
3
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
1
0
0
0
2
0
1
0
0
0
1
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
3
1
1
0
0
0
1
1
1
0
1
0
1
0
0
2
0
0
1
2
0
0
2
0
1
1
0
2
0
1
0
2
0
0
0
0
0
2
2
1
1
0
0
0
0
0
4
2
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
2
1
0
1
0
0
2
1
1
0
0
0
0
0
0
0
2
0
0
1
3
2
2
0
0
2
1
0
1
0
1
2
0
0
2
0
0
0
3
0
0
2
0
2
1
0
0
0
2
2
1
0
0
0
0
1
0
0
0
0
2
2
1
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
3
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
1
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
7
0
2
0
0
0
0
1
1
2
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
1
2
1
2
0
0
1
2
0
2
0
1
0
1
0
1
1
0
1
0
0
0
2
0
2
0
2
2
0
0
0
1
3
1
2
0
0
1
1
1
2
1
1
0
0
0
0
0
2
0
2
1
0
1
1
2
0
0
0
0
0
1
1
0
5
0
0
0
2
2
0
0
0
0
0
1
0
1
2
2
0
0
0
2
1
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
2
3
1
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
1
1
2
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
2
1
1
2
0
0
1
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
1
0
2
1
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
5
1
0
0
1
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
1
1
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
2
2
0
2
0
1
0
0
0
2
1
0
0
1
1
2
0
0
1
2
2
0
2
1
0
0
1
1
0
0
3
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
1
0
1
0
0
2
2
0
0
2
2
2
2
2
0
1
0
1
0
0
2
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
1
0
0
0
2
0
0
0
2
0
1
0
0
0
1
1
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
1
0
0
0
1
0
3
1
0
2
3
0
0
0
0
0
0
2
0
2
1
1
0
0
0
0
0
1
2
0
0
1
0
0
0
2
1
2
1
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
1
2
0
0
0
1
2
2
0
0
0
0
1
0
2
2
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
1
0
0
0
2
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
2
1
0
0
0
1
1
1
2
0
0
0
2
1
4
2
0
0
0
0
0
1
1
2
0
1
0
0
1
1
0
0
0
0
1
1
1
0
0
0
2
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
2
0
1
2
1
0
1
0
1
0
2
3
2
1
1
0
0
0
0
4
0
1
0
0
0
2
0
0
0
0
0
2
0
3
6
0
0
0
0
2
0
0
1
2
1
0
0
2
0
2
0
2
0
0
0
1
1
0
0
3
1
1
1
2
1
0
1
3
2
1
0
0
0
0
0
3
0
0
0
0
4
1
1
0
0
1
0
1
0
0
2
0
0
0
0
1
3
2
0
1
0
2
2
0
0
0
0
1
1
2
0
2
1
0
0
1
1
1
0
0
0
0
0
0
0
1
1
0
7
2
0
0
2
0
2
0
1
0
0
0
2
0
2
2
1
0
0
0
0
2
0
1
1
1
1
0
2
2
1
1
0
0
2
1
0
0
1
0
0
0
0
0
1
2
2
0
0
0
1
0
2
0
2
1
0
1
1
0
1
0
0
2
2
1
0
0
4
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
2
0
2
10
0
0
2
0
3
2
0
2
1
1
0
1
1
0
2
1
0
3
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
1
0
0
2
0
0
0
1
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
2
0
0
0
2
1
0
0
0
2
0
1
0
0
0
2
0
0
0
3
0
0
2
0
0
2
0
0
0
0
2
0
1
0
0
1
0
3
0
0
0
2
0
0
2
0
2
0
0
0
0
0
2
1
0
2
0
2
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
1
1
0
1
0
1
2
0
2
0
0
0
1
0
2
0
1
0
0
0
0
2
0
0
0
1
0
1
3
0
1
0
0
0
2
0
0
1
2
0
2
0
2
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
2
3
0
2
0
3
0
1
2
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
3
1
2
0
2
0
0
1
2
0
0
0
0
1
2
0
0
2
0
0
0
2
2
0
0
0
2
1
2
0
0
0
0
1
0
2
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
1
0
0
2
1
0
0
0
0
0
2
0
1
0
2
0
0
0
1
0
0
0
1
0
2
0
2
2
0
0
0
0
0
2
1
0
1
0
0
2
0
1
1
1
1
0
1
1
0
0
0
2
0
0
0
2
0
0
0
2
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
3
0
0
0
0
0
1
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
2
0
3
0
1
3
0
0
0
0
2
1
1
0
2
0
0
0
0
0
1
2
1
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
1
0
0
0
0
2
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
2
1
0
2
0
0
0
0
0
2
1
1
1
2
1
0
0
0
1
2
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
5
2
2
2
2
0
1
1
0
1
1
0
0
1
0
1
2
0
1
0
0
0
0
1
1
0
2
0
1
0
1
1
0
2
0
0
2
0
1
0
0
0
0
0
0
1
3
2
0
0
0
0
1
2
1
0
0
2
2
0
0
1
0
0
0
0
3
1
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
2
0
0
0
1
0
1
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
1
0
0
5
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
1
1
0
2
1
0
1
0
0
1
2
0
0
0
2
0
0
0
1
0
1
0
0
0
1
0
0
0
2
1
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
2
0
0
2
0
0
0
0
0
3
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
1
1
0
1
0
1
0
0
0
0
2
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
2
0
1
1
0
0
0
0
1
0
2
0
1
0
0
0
0
1
0
0
0
1
0
2
1
0
0
1
0
0
2
2
0
2
0
0
0
0
0
2
0
0
1
2
0
0
1
1
0
2
0
1
0
1
0
0
2
1
0
1
0
0
0
0
0
1
0
2
0
1
0
0
0
0
4
0
2
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
2
1
0
2
1
0
0
0
0
2
0
0
0
1
0
1
4
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
4
0
2
2
2
0
0
1
1
0
1
3
0
0
0
0
1
1
1
0
2
0
0
0
0
0
4
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
3
0
0
2
1
1
2
0
0
2
0
1
3
0
0
2
1
2
3
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
2
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
1
0
1
2
0
0
0
2
2
0
0
0
0
0
0
0
0
2
2
0
0
1
2
0
0
0
0
1
0
0
0
1
0
1
4
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
1
2
0
2
0
0
1
0
2
0
1
0
1
0
0
0
0
2
2
1
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
1
1
0
0
0
0
0
0
2
1
1
0
2
0
0
0
0
2
0
0
4
1
1
1
0
1
3
0
0
0
0
3
2
2
0
0
0
0
2
1
0
1
0
0
2
0
2
1
1
1
2
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
2
0
0
3
0
1
2
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
2
0
0
1
0
0
2
2
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
2
2
0
2
0
0
0
1
1
0
1
1
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
6
2
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
6
0
0
0
0
0
0
1
2
0
2
2
2
0
1
0
1
0
0
0
1
2
0
0
0
0
2
0
0
2
0
1
3
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
3
1
0
1
1
0
0
2
0
2
0
1
0
2
2
0
0
3
0
0
0
2
2
0
2
2
0
0
0
0
1
0
0
0
1
1
1
0
2
0
2
0
0
0
0
0
3
1
1
0
0
0
0
0
2
1
1
0
0
0
0
0
1
0
0
2
0
0
0
1
1
0
2
0
0
0
1
0
0
1
1
0
0
0
0
0
2
2
0
0
2
0
0
0
0
1
0
0
2
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
2
0
2
0
0
1
1
0
0
1
1
1
1
0
0
0
0
2
0
0
0
0
2
0
2
2
2
1
1
0
1
1
0
0
2
1
0
0
0
0
2
0
0
0
2
3
1
0
2
2
2
2
2
1
2
0
0
0
0
0
2
1
0
1
1
0
0
0
0
2
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
2
3
1
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
2
2
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
2
0
0
1
0
1
0
1
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
1
1
0
0
0
0
0
1
2
0
0
0
0
0
0
1
2
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
3
0
0
0
0
0
1
0
2
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
1
2
0
0
2
0
0
2
0
0
0
2
0
1
0
0
2
1
2
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
1
0
0
1
1
0
1
4
2
0
0
0
0
1
0
0
1
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
2
0
0
0
2
0
0
3
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
3
2
1
0
0
1
0
0
0
0
0
0
0
2
2
2
1
1
2
0
0
2
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
2
0
0
1
0
0
1
0
0
2
2
0
0
0
0
0
1
1
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
1
1
1
2
0
2
0
0
4
4
0
0
1
6
0
0
0
2
0
0
0
0
1
0
1
0
1
0
0
0
0
0
2
2
0
1
2
0
1
1
0
0
2
0
2
2
0
0
0
0
0
0
2
2
1
0
2
6
0
1
0
2
0
0
2
0
0
0
1
0
1
0
2
1
0
0
2
0
2
0
0
0
1
0
1
0
1
2
0
0
2
0
0
2
0
2
0
0
0
2
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
1
2
0
0
1
0
0
2
0
0
0
2
0
0
1
0
0
1
0
1
2
0
1
0
2
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
1
2
0
1
0
0
0
2
0
2
0
0
1
0
1
1
0
0
1
0
2
0
2
2
1
0
0
0
0
0
0
0
0
1
1
2
0
0
1
1
0
1
2
0
2
2
0
2
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
1
0
1
2
2
0
0
1
0
0
0
1
0
0
2
2
2
2
1
0
2
2
0
1
0
0
0
2
2
2
0
0
1
1
1
1
2
0
0
0
0
2
0
0
1
0
0
1
0
2
1
3
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
2
1
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
2
0
0
0
3
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
1
0
1
0
0
0
0
2
0
0
1
0
2
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
2
3
0
2
0
0
0
1
0
4
0
1
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
3
1
1
0
0
2
0
1
0
0
4
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
2
0
2
0
0
0
3
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
1
0
1
0
0
1
0
1
1
2
1
0
1
0
2
2
2
0
0
0
2
2
0
2
0
1
0
0
0
0
2
0
0
4
0
0
2
0
0
1
2
0
0
2
0
0
0
0
0
1
1
0
2
2
2
0
0
1
0
3
0
2
0
4
0
0
0
1
0
1
0
0
0
0
1
0
0
0
2
0
2
1
0
0
2
0
0
0
2
1
0
2
2
0
0
0
2
0
2
0
0
0
2
1
2
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
2
1
2
0
0
0
0
1
1
0
0
0
0
0
0
0
2
1
0
0
4
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
1
1
0
2
0
0
2
0
0
0
2
0
1
1
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
1
2
0
0
0
0
0
0
0
0
1
0
0
2
1
1
1
2
0
1
0
1
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
1
0
0
1
2
0
2
2
0
0
0
2
0
1
0
2
2
1
0
0
5
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
2
0
4
0
0
0
3
0
0
0
1
0
0
0
0
3
2
0
1
0
0
1
0
0
0
0
2
0
0
1
0
2
0
1
0
0
0
0
0
0
2
0
0
3
0
0
0
2
0
0
2
1
0
2
2
0
0
0
0
1
2
1
2
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
2
0
0
0
0
0
1
0
0
0
0
3
0
1
0
0
2
1
0
0
0
2
2
0
2
1
0
0
1
0
1
2
0
0
1
0
0
0
0
1
0
3
1
2
1
0
0
0
0
1
0
0
0
0
2
0
0
0
2
1
3
0
0
0
2
0
0
0
0
0
0
0
0
2
2
2
1
1
0
0
0
0
0
0
0
1
1
1
0
0
0
2
1
2
2
0
0
2
2
2
1
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
1
0
2
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
2
2
0
0
6
0
1
0
0
0
0
0
1
2
0
0
1
0
2
2
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
8
0
2
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
1
0
1
0
2
0
0
0
0
2
0
1
0
1
0
0
5
0
0
1
0
0
0
0
2
0
1
0
0
1
0
0
0
1
0
0
2
0
0
0
1
2
1
0
5
0
1
0
1
0
0
0
0
0
0
3
2
3
0
0
0
0
2
1
0
1
0
1
1
3
0
0
2
0
0
0
0
2
0
4
0
2
1
0
1
0
0
1
2
0
2
0
0
2
0
0
1
2
0
2
1
0
0
0
0
2
0
0
2
2
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
2
1
1
0
0
1
0
1
0
1
0
0
2
2
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
2
0
0
1
0
0
2
0
1
2
0
1
2
2
0
5
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
2
0
0
0
2
0
0
2
0
0
1
0
0
0
3
1
0
2
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
2
1
2
0
0
2
1
0
0
0
2
0
0
2
0
0
0
0
2
1
0
1
2
2
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
1
0
2
1
1
1
0
0
0
0
0
0
0
2
0
2
0
0
0
1
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
1
0
2
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
3
0
0
0
0
0
0
0
2
1
0
0
1
2
1
0
0
0
1
1
0
0
1
3
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
2
2
0
1
0
0
1
0
0
1
1
0
0
2
1
0
0
0
1
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
2
2
1
0
0
0
0
0
2
0
1
0
1
1
0
0
1
0
0
1
0
0
3
0
1
0
0
0
2
2
0
0
0
0
1
2
0
0
1
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
1
2
2
0
0
0
0
0
0
0
2
0
0
2
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
2
2
0
2
0
0
0
0
0
0
2
0
0
1
1
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
2
0
0
2
0
0
1
0
0
1
0
2
0
0
1
2
2
0
0
0
1
0
0
0
2
0
0
0
1
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
2
2
0
0
1
0
0
1
2
0
0
2
2
0
0
0
0
0
0
1
0
0
0
2
1
2
3
0
0
0
1
2
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
2
0
1
2
0
0
0
0
0
2
0
0
1
2
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
2
0
1
0
1
0
0
0
0
2
2
0
1
2
0
0
0
1
0
0
1
0
0
0
2
0
0
0
1
1
0
0
1
2
2
0
2
0
0
1
0
2
0
2
0
0
0
2
2
1
0
0
2
0
0
0
0
1
0
2
0
0
1
0
2
0
0
2
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
1
0
0
0
1
0
0
1
0
2
0
2
3
2
3
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
2
0
0
2
1
2
1
2
0
0
0
0
0
1
0
2
0
1
1
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
2
3
1
0
0
0
0
1
0
1
1
0
4
0
2
0
0
0
2
0
2
2
0
1
0
1
0
0
2
0
0
0
0
1
2
3
3
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
1
0
1
0
1
0
1
2
0
0
0
1
3
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
1
1
0
1
1
0
0
0
0
1
1
0
0
0
0
0
2
1
0
0
1
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
1
0
1
2
0
1
0
0
2
0
0
0
1
0
2
0
0
2
0
0
0
0
1
1
0
0
0
0
0
2
0
1
0
0
0
1
0
0
2
0
0
2
1
2
2
0
2
0
1
2
0
0
0
0
0
0
5
2
0
0
1
2
0
1
2
0
0
0
0
0
7
0
0
0
0
0
0
2
1
1
0
0
0
0
0
1
0
2
0
0
0
1
0
0
3
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
1
0
1
0
0
0
2
1
0
0
0
1
1
0
0
0
0
2
0
1
1
0
0
0
0
0
1
0
0
0
1
1
2
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
3
1
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
2
0
0
2
0
1
1
0
1
2
1
0
0
0
2
0
3
0
0
0
2
1
0
0
2
0
2
1
0
1
0
0
0
3
0
1
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
2
2
0
0
0
0
0
2
1
1
0
0
2
1
2
0
0
0
0
2
0
0
0
1
0
0
1
0
2
0
1
0
2
0
0
0
1
2
1
0
0
3
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
2
0
0
0
2
5
0
0
0
2
0
0
0
0
1
0
0
2
1
0
0
2
0
0
0
1
0
0
2
0
0
0
0
1
1
0
0
0
1
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
3
0
1
0
2
0
0
2
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
2
0
2
2
0
0
2
2
0
3
0
0
2
0
0
3
0
0
0
1
2
0
0
0
1
0
2
0
1
1
1
0
0
2
2
0
0
1
0
2
0
0
2
0
0
0
0
0
0
1
0
2
2
0
0
2
0
2
1
1
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
1
0
2
1
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
2
0
0
4
0
0
0
0
3
0
0
0
0
0
0
2
0
0
1
2
0
0
1
1
1
0
0
0
3
0
0
0
2
0
0
2
1
1
0
0
1
1
0
1
1
0
0
0
2
0
0
0
0
1
0
0
0
1
0
2
0
2
1
0
0
1
3
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
1
0
1
2
1
0
1
0
1
0
0
0
3
0
0
0
0
1
3
0
0
2
0
0
2
2
1
0
0
2
1
0
2
0
0
0
0
0
0
0
0
1
1
0
0
2
0
2
0
0
0
1
0
0
2
0
0
1
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
3
0
0
0
0
0
2
0
0
0
0
0
1
0
2
2
0
2
0
0
1
1
1
2
2
0
0
1
0
2
1
0
2
0
0
0
1
0
3
0
2
0
0
0
1
0
0
0
1
0
0
2
2
0
2
0
1
2
0
0
2
0
2
2
2
0
0
1
0
0
0
4
1
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
1
2
0
0
2
2
0
0
2
0
0
2
1
0
1
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
2
0
0
0
0
0
1
0
0
0
1
0
0
2
2
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
3
0
1
0
0
0
0
1
1
0
1
2
2
0
0
0
0
0
1
0
1
1
1
0
0
0
1
2
0
0
0
0
1
0
0
1
0
0
0
0
0
4
0
0
1
0
0
0
0
0
1
2
0
1
2
0
0
1
0
2
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
2
0
0
0
1
0
0
0
0
3
0
1
0
0
2
0
1
0
0
1
2
2
0
0
0
0
1
0
0
0
0
0
0
1
0
2
1
1
0
0
0
1
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
1
1
2
2
2
1
0
0
0
0
2
0
2
0
2
1
0
0
1
1
0
1
0
0
0
1
1
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
1
3
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
2
0
0
1
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
1
1
1
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
4
1
3
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
1
2
0
1
2
0
0
0
0
0
1
0
1
0
0
0
0
3
0
2
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
4
1
1
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
1
1
2
0
2
1
2
0
0
0
0
0
1
0
0
0
3
1
1
2
2
0
0
0
0
0
0
2
0
1
0
1
0
1
1
0
2
0
0
0
0
2
0
1
0
0
0
0
1
0
0
2
0
3
0
0
0
0
0
1
1
2
2
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
2
0
0
1
1
0
0
0
0
2
0
1
0
0
1
1
0
0
0
1
0
0
0
0
2
0
0
1
0
2
2
2
1
1
0
0
0
1
2
2
0
0
0
6
0
0
0
1
2
0
0
0
2
2
0
0
0
2
1
0
2
2
4
0
1
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
2
2
2
1
0
0
0
1
1
2
0
2
0
0
0
0
0
1
0
0
1
0
2
0
1
1
0
0
0
0
0
0
0
0
2
0
2
1
1
0
0
0
0
1
0
0
0
0
2
1
0
0
0
1
0
0
0
0
1
0
0
0
2
2
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
1
1
0
0
0
0
0
1
2
1
2
0
2
3
0
1
1
0
0
0
0
0
2
0
3
1
0
0
0
0
0
0
1
0
0
0
2
1
0
1
2
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
1
0
0
1
0
0
1
2
0
0
2
0
0
2
0
0
1
0
1
2
1
0
0
4
0
0
1
1
2
0
0
2
2
2
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
2
1
1
0
2
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
2
1
0
0
2
0
1
1
2
0
0
0
3
2
2
0
0
0
0
0
3
0
1
2
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
1
0
2
0
0
0
2
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
1
1
0
0
2
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
1
0
0
0
1
0
0
2
0
0
0
1
0
0
3
0
1
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
1
1
0
0
1
0
0
0
0
1
0
1
1
0
0
1
0
1
0
0
0
0
0
1
0
1
2
2
2
1
0
2
0
0
0
0
0
1
0
1
0
1
1
1
0
0
0
2
0
1
0
0
0
0
0
4
0
0
1
2
0
1
2
1
0
0
0
2
0
1
1
2
0
3
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
2
0
2
0
2
0
0
2
0
2
1
2
0
0
2
1
1
0
2
0
0
0
2
0
0
0
0
1
0
2
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
1
0
6
0
0
1
0
1
1
0
2
0
0
0
1
2
2
0
0
0
0
0
2
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
2
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
2
2
3
1
0
0
0
0
0
2
3
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
1
0
2
1
1
1
1
0
0
0
0
2
0
2
0
0
1
0
1
0
0
2
0
0
3
0
0
0
2
3
0
1
0
0
1
0
2
1
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
2
0
0
1
1
1
0
2
2
1
0
2
0
2
0
0
0
0
0
0
0
2
0
3
0
1
0
0
0
0
0
1
0
2
0
1
0
0
1
0
1
0
0
0
1
1
0
2
1
0
2
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
3
2
0
0
2
0
0
0
3
1
0
0
2
2
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
2
0
0
1
0
0
0
0
0
0
1
1
1
2
0
1
1
1
1
0
0
0
0
0
0
0
1
0
2
1
1
0
0
0
0
0
0
1
0
0
1
4
2
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
2
0
0
2
0
0
1
0
1
2
0
3
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
2
2
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
3
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
1
1
4
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
3
0
2
0
1
0
0
0
1
1
0
0
1
0
1
0
0
0
0
2
2
1
1
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
1
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
2
0
0
0
0
2
1
0
0
1
0
2
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
1
2
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
1
0
2
2
0
0
0
0
0
1
0
1
0
0
2
0
0
0
3
0
3
5
0
0
0
0
2
1
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
2
2
2
1
2
0
1
2
0
0
0
0
1
1
2
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
1
0
0
0
0
0
2
1
0
2
2
0
0
0
2
0
0
1
1
0
2
0
2
0
0
0
1
1
2
0
0
2
0
0
0
2
0
2
0
0
2
0
0
0
0
1
0
2
0
2
0
0
0
0
1
0
0
0
2
1
1
0
0
1
2
0
0
0
1
2
2
0
0
0
1
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
1
1
0
1
2
2
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
1
0
0
0
0
1
0
0
0
0
0
0
3
0
0
1
0
0
0
0
1
0
1
0
2
0
0
2
0
0
1
0
0
0
1
0
0
0
0
2
2
0
0
0
0
1
1
0
0
1
0
1
1
0
1
1
0
0
0
0
0
1
0
0
0
2
1
0
2
2
2
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
2
0
0
0
0
0
1
2
1
1
2
2
0
0
3
1
0
2
0
0
0
0
0
1
1
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
1
0
1
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
2
0
0
1
0
4
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
2
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
2
3
1
0
1
2
1
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
3
2
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
1
0
0
1
0
1
2
0
0
2
0
1
0
1
2
1
0
1
1
0
0
0
0
2
0
2
0
1
0
0
0
0
0
3
0
1
0
0
0
0
2
1
2
0
0
3
0
0
1
0
1
1
0
0
0
0
2
1
0
0
2
0
0
0
0
2
0
0
1
0
1
0
2
2
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
2
0
0
0
1
0
2
0
0
0
3
0
0
2
0
2
0
0
0
2
0
2
1
0
0
0
0
3
1
1
0
1
0
0
0
3
0
0
1
0
0
3
0
0
0
2
2
1
0
2
0
0
0
1
0
0
1
2
0
1
2
0
1
1
0
0
0
0
0
0
1
1
1
1
0
2
0
0
0
0
0
2
0
0
0
1
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
2
0
0
0
0
0
1
0
0
2
0
2
3
1
1
0
0
0
0
2
0
0
1
2
2
0
1
0
2
0
0
0
1
1
1
0
1
0
0
2
1
1
1
2
0
0
0
0
0
1
0
0
0
0
2
0
1
0
1
0
0
1
0
1
2
0
0
0
0
0
0
1
0
0
0
2
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
3
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
2
1
0
1
0
0
0
0
0
1
2
1
0
1
1
0
0
2
1
1
2
0
0
0
1
4
0
2
2
1
0
0
0
3
0
2
0
1
0
1
1
0
1
0
0
4
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
1
0
0
0
2
0
0
1
0
4
1
1
0
0
0
4
0
1
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
2
0
0
0
0
0
3
1
0
2
0
0
1
0
3
0
0
1
0
0
1
0
1
0
1
0
1
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
1
2
1
1
1
0
0
2
2
0
0
0
0
2
1
3
0
0
0
2
1
1
1
3
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
2
1
0
0
0
1
0
2
2
2
0
0
0
0
1
0
3
0
0
1
3
2
0
0
0
0
0
2
1
2
2
0
2
0
0
0
0
0
0
2
0
2
0
0
0
1
3
0
2
0
0
1
0
2
0
0
0
0
1
0
1
2
0
0
2
0
0
1
1
0
0
0
0
0
0
1
0
0
0
4
0
1
0
0
0
0
1
0
2
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
2
0
2
0
1
1
2
0
1
0
2
1
0
0
3
0
0
0
0
0
2
0
0
1
1
0
0
1
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
1
0
0
2
0
0
0
1
1
0
0
2
0
2
0
0
0
2
0
0
2
0
0
0
0
1
1
0
1
2
0
0
0
1
2
0
0
0
1
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
3
2
0
2
1
1
1
1
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
1
0
3
0
0
0
2
1
0
2
0
0
2
1
0
0
0
1
1
2
0
0
1
0
2
1
0
0
1
0
0
0
0
0
0
2
1
0
0
1
1
0
1
2
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
2
1
0
0
3
0
0
1
0
0
0
2
0
3
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
8
0
0
0
2
0
0
2
0
1
2
2
0
2
3
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
3
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
2
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
1
1
0
0
2
0
0
2
1
0
0
1
0
2
1
0
0
0
0
1
0
2
1
0
0
1
2
0
0
2
2
2
2
1
0
0
8
0
2
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
1
1
1
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
2
0
1
0
2
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
3
0
2
0
0
0
0
2
0
0
0
2
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
2
0
2
0
0
3
0
0
0
0
0
2
0
0
0
1
1
0
2
2
0
0
0
1
0
0
0
0
2
1
2
0
0
3
0
0
0
2
2
0
0
0
2
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
1
2
0
2
1
1
1
0
0
0
0
0
0
1
0
0
2
0
0
0
1
2
0
0
0
2
2
0
1
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
1
0
0
2
2
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
2
0
1
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
3
0
0
0
1
2
1
1
0
0
0
0
1
2
0
1
0
1
0
0
0
2
1
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
1
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
2
1
3
0
0
1
1
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
1
0
2
1
0
1
2
0
0
0
0
1
0
0
3
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
1
3
0
2
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
1
2
2
0
2
0
0
0
0
0
0
0
0
2
0
2
12
0
0
0
1
2
0
0
1
1
2
0
1
0
0
0
0
0
2
2
0
0
2
2
0
0
1
1
0
0
0
2
0
2
1
0
0
1
1
1
0
0
0
0
0
2
0
0
0
0
1
2
2
0
0
1
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
2
0
0
0
0
0
2
2
2
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
2
0
0
0
1
0
1
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
1
1
1
0
0
3
0
1
0
2
0
0
0
0
1
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
2
0
2
0
1
3
0
0
0
0
0
3
0
3
0
0
0
0
1
0
1
1
0
0
3
0
0
2
0
1
0
0
0
0
2
0
0
2
1
0
0
2
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
1
1
1
0
0
0
1
1
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
2
2
0
0
1
0
0
2
0
2
2
0
3
0
0
0
0
2
0
0
0
6
0
0
0
0
1
1
2
3
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
2
1
0
0
0
0
0
0
0
3
0
0
0
2
1
1
2
0
0
1
0
0
0
1
0
0
0
0
2
1
2
0
0
0
2
1
0
0
0
0
0
0
2
2
0
0
2
1
1
0
0
1
0
0
0
0
0
0
0
0
1
3
2
0
0
0
2
2
0
0
1
0
1
1
0
0
3
0
1
0
2
0
1
0
1
0
0
2
0
1
0
0
3
1
0
0
2
0
2
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
2
0
0
0
0
0
1
0
0
1
0
1
0
2
2
1
1
0
2
0
1
0
0
0
1
0
1
0
0
0
2
2
1
2
0
0
2
0
3
0
2
0
0
3
2
0
2
0
0
0
0
2
0
2
2
2
0
0
0
1
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
2
0
0
0
0
2
0
0
2
0
0
2
0
2
0
0
0
1
0
0
0
1
2
1
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
2
0
0
0
0
1
0
0
3
0
0
0
2
2
5
2
0
0
0
0
1
1
0
0
0
1
1
0
1
1
3
0
2
0
2
0
1
0
0
0
0
0
2
0
0
1
0
0
2
1
0
1
1
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
1
1
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
1
0
0
1
0
2
3
0
0
2
0
0
0
0
2
0
4
1
0
0
3
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
7
0
0
0
0
0
2
0
0
2
0
0
0
2
0
1
2
2
0
2
2
1
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
3
2
0
0
2
0
0
1
0
0
0
0
2
0
2
1
0
1
1
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
2
0
0
0
0
0
2
0
0
2
2
1
0
0
3
1
0
1
0
0
0
0
5
0
0
0
0
2
0
0
1
0
2
0
1
0
1
1
1
0
0
0
1
1
0
0
1
0
0
2
1
0
1
0
1
0
0
0
0
0
0
0
3
1
0
2
2
0
0
0
2
0
0
2
0
0
0
1
0
1
0
0
3
0
0
0
0
0
0
1
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
2
1
1
0
0
0
0
1
2
0
1
0
0
0
0
2
0
1
0
0
0
0
0
1
0
1
1
2
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
2
3
0
0
2
0
0
0
0
0
0
2
0
2
5
0
2
1
0
2
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
1
3
0
2
0
1
0
0
0
0
1
1
0
1
2
0
0
1
0
1
2
0
0
1
0
1
2
0
1
0
2
0
0
0
0
2
1
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
1
0
0
3
0
0
0
2
1
2
0
0
0
1
1
1
2
0
2
1
0
0
0
0
1
0
0
0
1
0
6
1
0
0
2
0
1
0
0
0
0
2
1
1
1
0
1
0
0
0
1
0
0
0
0
0
0
1
1
2
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
1
0
4
1
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
3
1
0
0
0
0
0
2
0
2
0
1
1
0
0
1
0
1
0
0
2
2
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
3
2
2
2
0
0
0
0
2
0
1
2
0
0
0
0
2
0
0
1
0
0
0
2
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
3
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
2
0
0
1
1
0
0
0
2
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
1
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
1
0
0
0
2
1
1
2
0
0
1
0
1
0
2
0
0
0
0
2
0
1
0
2
0
1
1
0
2
1
0
0
1
2
0
0
2
0
0
0
2
1
0
2
0
1
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
2
0
3
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
2
2
1
0
0
0
1
0
5
2
0
2
0
0
0
3
0
0
0
0
0
1
0
0
0
0
2
1
1
0
0
2
0
0
1
0
1
0
0
1
2
0
2
0
3
1
1
0
0
0
0
0
0
1
0
2
0
1
0
1
0
0
0
2
1
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
2
2
0
1
1
0
0
0
0
0
1
1
0
2
0
2
0
1
2
1
0
0
2
1
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
2
1
0
0
2
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
2
2
0
0
1
0
1
1
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
2
3
0
2
0
0
0
0
0
2
0
2
1
0
0
1
1
0
1
0
2
0
0
0
0
0
0
0
1
1
0
1
0
0
0
2
0
2
0
0
0
0
0
12
0
1
0
3
0
1
0
0
0
1
0
0
0
5
0
0
0
0
0
1
0
1
0
0
2
0
2
2
4
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
1
1
0
0
0
0
1
1
0
2
1
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
5
1
0
0
1
0
0
3
0
0
0
0
1
0
0
1
1
0
2
0
0
0
0
1
0
1
0
0
1
1
0
0
2
1
0
0
0
0
0
0
2
3
0
3
0
0
0
0
0
3
0
0
0
0
1
0
0
1
0
0
0
2
1
1
0
0
1
2
1
2
0
1
1
0
0
1
0
2
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
2
2
0
0
1
2
0
0
2
0
0
2
0
2
1
0
2
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
2
1
3
0
0
0
0
1
1
0
0
0
2
0
1
0
0
0
0
0
0
2
1
0
0
0
1
0
0
1
0
0
0
0
2
0
1
0
1
1
3
2
0
1
0
0
0
0
1
1
0
0
0
0
0
2
0
0
1
0
2
1
0
1
0
0
0
0
0
2
0
1
0
0
0
1
0
2
1
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
2
1
1
0
0
1
1
2
2
0
0
0
0
0
0
0
1
2
0
0
1
2
0
1
2
2
0
0
1
0
0
0
2
2
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
1
0
0
0
1
2
0
0
2
0
0
2
0
0
1
1
0
0
0
0
0
0
1
1
0
2
0
2
0
0
2
0
0
0
0
2
1
0
1
0
0
1
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
2
2
0
0
2
2
1
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
1
0
1
0
2
1
0
2
0
2
0
0
1
0
1
0
0
3
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
2
1
0
0
0
1
0
0
0
1
0
0
1
0
2
0
0
0
0
2
1
3
1
0
0
2
0
0
0
1
2
1
2
0
0
0
0
0
0
0
2
2
0
1
0
0
1
0
1
0
1
0
1
0
1
0
0
1
1
0
0
0
0
0
0
1
2
2
0
2
2
0
0
0
2
2
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
2
2
0
1
2
0
1
1
0
0
1
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
3
0
0
0
0
4
0
1
2
1
1
1
0
1
0
0
0
0
3
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
2
2
2
1
0
0
0
2
0
0
0
1
1
0
2
0
0
0
2
0
0
0
0
0
1
3
0
1
2
0
2
0
0
0
0
2
0
0
0
0
0
2
2
4
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
1
0
0
0
0
1
1
1
0
0
0
0
2
0
0
0
0
0
1
0
1
0
2
0
4
0
0
2
0
0
0
1
0
0
0
0
2
1
0
1
1
1
1
2
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
2
0
2
1
1
0
2
0
0
1
1
0
0
0
0
0
2
2
0
0
0
0
2
1
0
1
0
0
1
2
0
2
0
1
0
0
0
0
0
1
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
1
1
3
0
2
0
1
2
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
2
1
2
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
1
1
0
0
2
0
2
1
0
0
0
0
2
0
0
0
0
0
0
2
0
2
1
0
0
2
0
1
1
0
1
0
0
1
1
3
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
2
2
0
0
0
0
0
2
1
1
0
2
0
0
0
1
0
1
0
0
0
0
0
1
0
2
0
1
0
1
2
0
1
1
0
0
0
0
0
2
2
0
0
1
1
2
0
0
0
2
0
2
1
1
0
0
1
0
0
0
0
0
2
0
2
0
0
1
0
2
0
0
0
0
2
0
0
2
0
0
0
2
2
1
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
1
6
2
0
2
0
0
0
2
2
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
1
1
0
1
0
0
2
1
0
0
0
2
0
0
0
0
2
0
3
0
2
2
1
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
2
0
2
1
0
0
2
0
3
0
0
0
0
0
1
0
2
2
0
0
2
0
0
2
0
2
0
0
1
0
2
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
2
2
1
0
2
2
0
0
0
0
0
0
1
0
1
2
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
1
5
1
0
0
0
0
3
0
0
2
2
0
0
0
0
0
2
12
0
1
0
0
1
2
0
0
0
0
0
2
0
1
1
0
2
0
0
0
0
0
0
1
0
0
2
0
0
1
1
0
0
0
1
1
0
2
0
1
2
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
1
0
2
3
0
0
0
1
7
0
0
0
0
1
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
2
1
1
2
0
2
0
2
0
2
0
1
0
2
0
2
2
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
5
1
0
0
0
0
1
1
1
0
0
0
0
1
1
0
0
1
2
0
0
0
2
1
3
0
1
0
1
0
1
0
2
2
0
0
0
1
0
0
3
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
3
0
0
0
1
0
0
0
1
0
0
6
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
2
2
0
1
1
1
2
1
0
0
1
1
1
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
2
3
0
0
0
1
2
0
0
0
0
0
2
0
0
2
1
2
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
1
1
0
0
0
0
2
0
1
0
0
0
0
0
0
1
3
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
3
1
0
2
0
0
0
1
1
1
0
0
0
1
2
0
0
0
0
0
2
0
1
2
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
5
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
3
1
0
0
0
0
0
0
0
1
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
1
2
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
2
5
0
0
0
0
1
0
2
0
2
0
2
2
2
0
1
0
0
0
0
0
1
2
0
0
1
0
0
0
0
1
1
0
0
3
0
3
0
0
1
0
0
0
0
0
2
2
1
0
1
0
2
0
1
2
0
0
3
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
1
0
2
1
2
0
0
2
0
7
0
1
0
2
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
2
2
0
1
0
2
0
0
3
2
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
1
2
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
2
4
0
0
0
3
1
1
0
1
0
0
2
2
0
0
0
0
2
1
0
0
0
3
0
1
0
0
0
1
1
0
1
0
2
0
1
0
1
1
0
0
0
1
0
2
1
2
0
1
0
0
0
0
0
0
0
0
3
1
1
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
2
1
0
0
0
1
0
0
1
0
0
0
1
0
0
2
0
0
0
2
2
0
0
0
2
1
0
0
0
0
0
2
1
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
2
1
2
0
0
0
2
0
1
5
1
1
0
0
1
2
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
2
0
0
1
0
0
0
0
0
0
2
4
3
2
0
0
0
0
2
0
0
0
0
0
1
2
2
0
0
0
2
1
0
1
0
0
0
0
2
0
0
0
3
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
1
0
2
0
2
2
1
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
2
1
0
0
1
0
0
0
0
0
2
0
2
0
2
0
2
0
0
0
0
1
3
0
0
2
0
1
1
5
0
0
0
2
1
0
0
1
2
0
1
0
0
0
0
1
1
1
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
1
1
0
0
1
0
0
0
1
1
0
0
0
2
0
0
2
0
0
2
0
0
0
0
1
1
0
2
0
2
1
2
1
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
3
2
1
0
0
1
2
0
0
0
1
0
1
1
0
0
2
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
1
0
2
0
1
2
0
0
2
0
4
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
2
0
5
0
0
1
0
0
0
2
0
0
0
3
0
1
0
2
0
1
0
2
0
0
5
0
1
1
0
0
0
0
0
1
0
1
0
0
0
2
1
1
1
0
0
0
0
0
0
3
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
2
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
2
0
0
1
0
0
1
0
0
0
4
2
0
2
4
2
0
2
0
0
0
2
0
0
0
0
2
2
0
0
0
1
0
0
4
1
0
2
1
1
0
0
1
0
0
0
0
0
0
1
1
0
1
1
0
2
1
0
2
0
0
0
2
0
0
0
0
3
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
7
0
0
0
0
0
0
1
2
0
0
2
2
0
2
7
0
1
2
0
0
1
1
0
2
2
1
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
3
0
0
1
0
0
0
0
1
0
0
1
3
0
0
0
0
1
1
1
0
0
2
0
0
0
0
2
0
1
1
3
0
0
1
0
3
0
0
0
0
2
3
0
2
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
2
0
0
1
2
0
0
0
0
0
0
2
0
1
0
1
1
1
2
2
0
0
2
0
0
0
2
1
1
1
0
0
0
0
4
0
1
1
0
0
0
1
3
0
0
2
2
0
1
1
0
0
0
2
2
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
4
0
0
1
0
1
0
1
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
2
0
0
3
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
1
0
2
1
0
1
0
2
0
2
0
0
1
1
0
3
2
0
0
0
0
0
1
1
3
0
1
1
0
0
0
0
0
0
1
0
0
0
2
1
0
1
0
0
0
1
0
0
1
1
2
0
0
0
0
0
2
1
0
0
0
0
2
1
0
0
3
0
0
0
0
0
0
2
2
2
0
0
0
2
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
1
2
1
1
0
0
0
1
1
0
1
1
0
0
0
0
0
2
1
0
0
1
0
2
0
1
2
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
1
0
0
2
0
0
0
2
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
2
0
1
0
2
0
0
2
1
0
1
0
0
2
0
0
0
1
0
0
2
0
0
0
0
2
2
0
0
0
0
0
3
1
0
0
0
1
0
1
0
0
0
0
1
0
1
2
0
0
0
1
2
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
1
1
0
0
0
2
2
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
1
1
2
0
0
2
2
0
0
1
0
0
0
0
0
1
0
0
3
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
1
0
1
0
0
0
0
2
2
0
1
1
0
0
0
0
0
0
0
0
2
2
0
2
0
1
0
2
0
0
2
1
1
2
0
2
1
0
1
0
0
1
0
1
0
1
0
0
0
0
2
0
0
1
0
0
0
1
0
1
0
1
2
2
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
1
0
2
0
1
2
2
0
1
2
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
2
1
0
1
1
0
0
0
0
0
0
0
1
2
2
2
1
1
2
1
4
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
1
1
2
2
0
1
2
5
0
0
6
0
1
2
0
1
0
0
2
1
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
2
0
0
2
2
0
3
0
0
0
0
0
1
0
2
0
0
0
1
0
1
0
2
2
0
0
1
1
1
1
0
2
0
2
1
0
0
0
2
0
0
1
3
0
0
0
0
1
1
0
0
1
1
0
0
1
2
0
0
2
0
0
0
2
1
2
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
2
1
0
0
0
2
1
1
0
3
0
0
0
0
1
0
0
0
6
0
1
1
1
0
2
0
0
2
0
0
0
2
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
1
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
1
1
1
1
2
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
2
0
0
0
2
5
0
1
1
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
2
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
2
0
1
0
0
0
0
2
1
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
1
0
2
0
0
0
0
1
0
0
0
2
1
2
0
0
0
0
1
0
2
1
0
0
1
1
1
2
0
0
1
0
2
1
1
0
0
0
2
1
0
1
0
2
1
0
1
0
2
2
0
4
1
0
2
0
2
0
1
0
0
0
0
0
2
0
1
0
2
0
0
0
2
0
2
0
1
2
0
0
2
1
0
0
1
0
0
0
0
2
0
1
0
1
0
0
0
0
0
7
0
2
1
0
2
0
0
0
1
0
0
0
2
2
0
1
1
1
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
1
3
0
2
5
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
1
0
0
0
2
2
0
0
0
0
1
0
1
0
0
1
0
1
0
1
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
4
2
0
2
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
2
1
0
0
1
1
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
1
1
0
0
3
0
1
3
1
1
0
0
0
1
0
0
0
0
1
1
0
4
1
0
0
1
1
0
1
2
0
0
0
0
0
0
0
0
0
2
0
2
1
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
1
2
0
0
0
3
0
0
1
2
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
3
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
2
0
1
0
0
0
1
2
0
1
0
0
0
3
2
2
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
3
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
2
2
0
0
2
0
0
2
0
1
1
0
0
0
0
2
0
1
1
0
0
0
0
1
0
2
0
2
0
0
0
0
0
2
2
0
0
1
1
1
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
1
1
0
0
0
6
2
1
0
2
1
1
0
1
0
0
1
0
0
0
1
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
5
1
2
1
1
0
0
1
0
1
2
0
0
2
0
0
1
2
0
1
0
2
0
4
1
0
0
1
0
2
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
1
2
2
0
0
0
0
0
0
0
2
0
2
1
1
0
1
0
0
1
2
1
0
0
1
0
0
3
0
1
0
0
0
0
0
0
0
3
0
4
0
1
0
0
0
1
1
1
0
0
0
2
0
0
1
0
0
0
2
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
1
0
0
0
0
1
2
0
1
1
0
0
0
0
2
2
1
3
0
0
2
1
0
2
1
0
0
0
1
2
1
0
0
1
0
2
0
0
0
0
1
1
1
0
2
0
1
0
1
1
0
1
2
1
1
2
0
0
0
4
0
2
1
0
2
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
1
0
0
1
1
0
1
0
0
2
0
0
2
2
1
0
2
1
0
0
0
0
2
0
2
0
0
0
1
2
0
0
0
2
0
2
0
0
0
1
0
2
0
0
0
1
0
1
0
2
0
1
0
0
0
2
0
1
0
0
3
0
0
0
2
3
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
2
3
0
0
0
0
2
1
0
0
0
0
0
1
0
0
2
2
2
2
0
1
4
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
1
1
0
0
0
0
0
0
2
2
0
1
2
2
0
0
0
0
0
0
2
2
0
1
0
1
0
0
0
0
0
0
1
1
0
2
1
0
0
0
0
0
0
0
2
1
0
2
0
0
1
0
2
0
2
1
0
0
2
0
1
2
0
0
0
2
0
0
2
1
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
1
0
2
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
2
1
0
2
0
0
1
0
1
0
2
0
0
2
0
0
1
2
0
1
2
1
0
1
0
2
0
2
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
2
0
1
2
0
0
2
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
1
1
0
0
1
1
1
1
3
0
1
0
1
0
1
1
0
1
1
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
1
0
0
0
2
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
3
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
2
0
2
0
2
2
2
2
3
0
5
0
2
1
2
0
0
0
0
2
1
2
2
0
0
0
0
3
0
0
1
0
0
0
0
0
2
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
1
0
0
0
2
0
2
0
1
0
2
0
0
2
0
0
0
1
0
1
0
0
2
0
0
2
0
0
0
2
0
0
1
2
0
0
0
5
0
0
0
0
2
0
0
2
1
1
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
2
0
2
0
0
0
1
0
0
0
0
0
2
4
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
2
1
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
2
0
0
0
0
1
0
0
0
2
0
1
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
1
1
0
1
1
1
1
1
0
0
0
0
0
0
2
0
0
1
0
1
2
2
1
0
2
0
2
0
2
2
0
0
0
0
1
2
1
0
2
0
0
0
1
2
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
2
2
1
3
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
1
0
2
0
3
2
0
0
0
2
0
0
0
0
2
0
1
0
2
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
2
0
0
1
0
3
1
0
1
1
2
2
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
2
4
0
0
0
1
0
1
1
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
1
2
0
0
1
0
0
0
2
0
0
2
0
1
1
0
0
0
1
2
1
2
2
0
0
0
2
1
2
2
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
1
2
1
0
0
2
3
0
1
1
0
0
0
2
1
0
0
0
1
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
2
1
2
0
0
0
2
0
0
3
0
1
0
0
1
0
0
2
0
0
1
0
1
0
0
1
0
1
0
1
0
0
0
0
2
2
2
0
2
0
1
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
2
1
1
1
1
0
2
3
0
0
0
1
0
2
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
2
0
0
0
3
0
0
0
1
0
1
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
2
0
0
0
0
0
0
2
0
0
0
2
0
0
2
1
0
0
0
0
1
0
1
0
0
0
3
1
1
0
0
1
0
1
0
1
0
0
0
0
0
0
2
1
0
0
0
0
1
1
0
2
0
0
0
1
0
0
0
0
2
2
2
0
0
2
0
0
0
1
0
0
0
0
2
1
1
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
3
1
2
2
0
0
0
1
2
0
0
0
0
1
3
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
2
1
3
0
1
0
0
1
0
1
0
0
2
0
3
2
0
0
1
1
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
3
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
2
0
2
2
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
1
2
0
0
0
0
2
3
2
0
1
0
0
0
0
0
2
0
0
0
1
0
1
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
2
2
0
2
0
0
0
3
0
0
0
1
0
1
0
0
1
0
0
0
0
0
2
0
1
1
0
0
0
0
0
1
2
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
2
1
1
0
0
1
0
0
0
2
1
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
3
1
1
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
2
0
0
2
1
2
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
1
3
2
1
2
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
1
0
0
2
0
2
0
0
2
0
0
2
0
0
0
1
0
0
0
0
3
1
0
0
0
1
0
1
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
9
2
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
2
0
0
1
2
0
2
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
1
0
2
3
2
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
3
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
1
0
0
1
0
0
0
2
0
2
2
2
1
0
1
0
0
0
0
0
0
0
1
0
2
0
2
1
0
0
0
0
0
1
0
0
1
1
2
0
0
2
0
0
0
0
2
1
0
0
0
2
1
0
1
1
0
1
0
2
1
0
1
0
0
1
0
0
0
0
1
0
2
0
0
0
0
2
2
0
0
1
0
0
2
1
0
0
1
0
2
2
1
1
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
2
0
2
1
1
1
2
2
0
0
2
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
2
0
2
2
0
0
0
0
1
2
0
2
0
2
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
3
0
1
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
1
2
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
1
1
0
1
0
2
0
0
0
0
1
0
2
0
1
2
0
2
0
0
1
0
1
0
1
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
1
0
1
0
2
0
2
0
0
0
1
0
0
0
1
2
0
1
0
0
2
0
2
1
0
2
1
2
0
1
0
1
0
1
1
2
0
0
2
0
0
0
2
0
0
2
0
1
0
0
0
0
2
0
1
1
0
1
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
2
1
1
1
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
1
2
2
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
2
0
2
0
0
1
3
2
0
1
0
0
0
1
0
0
0
0
0
2
2
2
0
2
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
1
0
2
2
0
1
2
0
0
2
1
0
0
2
1
0
0
2
0
1
0
0
1
0
0
0
2
1
0
0
0
1
0
1
0
0
1
0
0
0
0
1
1
0
0
2
1
0
0
1
2
0
0
1
0
0
0
0
0
2
0
3
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
2
0
0
2
2
0
2
0
0
1
1
2
1
0
1
1
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
1
2
2
0
1
1
1
0
1
0
1
2
0
0
0
0
0
0
0
0
2
2
1
0
0
1
2
1
0
2
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
1
1
1
0
0
1
0
0
2
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
2
0
0
1
2
0
0
3
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
1
2
0
0
0
0
1
0
0
0
2
1
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
3
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
2
1
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
3
1
0
2
0
0
0
0
0
2
2
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
2
0
1
0
1
0
2
2
0
0
0
0
0
1
0
1
0
1
2
0
2
1
2
2
0
0
2
0
0
1
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
3
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
2
1
0
0
1
2
0
2
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
2
2
0
2
0
1
1
2
1
1
1
2
0
0
0
0
1
1
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
1
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
3
0
1
2
1
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
2
2
0
0
2
0
0
1
2
0
0
2
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
1
2
0
1
0
2
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
1
3
0
3
0
0
0
0
2
0
0
0
2
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
5
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
2
1
1
1
0
0
0
0
2
0
0
0
3
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
2
0
0
0
2
0
0
0
0
4
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
2
0
0
1
2
2
0
0
0
0
0
2
0
0
0
0
0
1
1
2
0
0
0
0
3
0
1
0
0
2
2
0
0
1
0
1
1
1
0
0
1
0
0
3
0
1
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
2
0
1
2
0
0
0
0
2
1
2
0
0
0
0
0
1
2
0
3
0
0
0
0
1
0
2
0
0
0
0
0
1
0
1
1
2
0
0
2
0
4
2
0
0
0
2
2
0
0
0
1
2
0
0
0
2
7
0
0
0
1
2
1
0
0
1
0
0
0
0
0
0
1
3
0
1
0
1
0
0
1
1
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
9
0
1
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
2
2
1
0
0
0
1
2
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
3
0
2
1
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
1
0
1
3
1
0
0
1
0
1
3
0
0
0
0
2
1
0
0
2
2
1
2
0
0
1
1
0
2
0
2
0
2
0
0
4
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
2
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
1
0
0
2
0
0
1
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
2
2
1
2
3
2
0
0
2
0
0
0
1
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
1
0
0
0
1
0
1
0
1
1
0
0
0
1
1
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
1
0
0
0
1
2
0
0
0
0
0
1
1
0
0
0
1
0
2
2
1
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
2
1
1
0
1
3
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
1
0
0
3
0
0
1
0
1
1
0
0
0
2
0
1
0
1
2
1
0
2
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
1
1
1
1
0
2
0
0
0
0
2
0
1
0
0
0
0
0
2
4
2
2
1
0
2
0
4
2
1
2
0
0
2
2
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
3
0
0
6
0
0
1
0
0
2
0
0
0
1
0
2
0
1
1
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
3
1
0
0
0
0
1
0
0
2
0
1
0
2
0
0
0
0
0
0
3
0
1
0
2
0
1
0
2
2
1
1
0
2
1
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
2
0
2
1
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
3
0
0
0
0
1
1
0
0
2
0
1
0
0
0
2
2
2
0
1
0
0
2
0
1
0
0
3
0
0
1
0
1
0
0
0
0
0
1
0
1
0
1
0
2
0
2
2
1
0
2
0
0
2
2
0
1
0
0
0
1
0
1
2
2
0
0
2
0
0
2
0
0
2
0
2
0
0
0
2
1
1
0
0
1
0
2
0
0
2
0
2
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
3
2
0
0
1
0
0
0
0
1
1
0
2
0
0
0
2
0
2
0
0
1
2
0
2
0
0
0
2
2
0
0
1
2
0
0
2
0
0
0
2
0
0
2
2
0
0
0
1
0
0
0
2
2
2
0
2
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
3
0
0
2
0
0
0
1
0
2
1
1
0
0
0
2
0
0
0
3
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
1
0
0
0
1
0
0
3
0
0
0
2
0
0
2
3
1
0
0
0
0
1
0
3
0
0
0
0
0
1
0
0
2
2
0
3
0
2
0
2
1
0
2
1
0
0
0
10
1
2
2
0
0
1
1
0
1
2
0
0
0
0
2
2
3
0
1
0
0
1
2
1
1
1
0
0
2
0
0
0
2
0
0
2
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
1
2
1
0
0
3
2
1
0
1
0
0
0
1
2
0
0
0
2
2
0
0
1
0
2
1
0
0
2
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
1
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
1
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
2
4
2
0
0
0
0
1
0
0
0
1
1
2
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
2
1
0
0
0
1
0
2
0
1
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
1
0
0
2
1
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
3
2
0
1
0
1
1
0
0
0
2
0
0
0
2
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
2
2
0
0
3
0
0
0
2
1
0
0
1
0
0
0
0
2
0
0
2
2
1
2
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
2
1
0
1
0
0
1
2
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
2
0
1
3
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
2
0
1
1
0
1
0
0
0
0
1
1
0
1
1
1
1
0
2
0
3
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
1
2
0
0
0
0
3
0
0
2
1
0
2
0
1
0
0
0
0
0
0
0
0
0
3
1
0
1
0
0
0
2
0
2
0
2
2
1
0
2
0
1
0
1
1
0
0
0
0
0
2
1
2
0
0
0
2
0
1
2
1
1
0
0
0
1
0
0
0
0
1
0
2
0
0
0
2
0
1
0
1
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
1
1
0
0
2
0
1
0
0
0
2
2
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
2
0
1
1
0
0
0
0
0
2
0
2
1
1
1
0
0
0
1
0
2
0
0
0
1
0
1
0
1
2
1
0
0
0
0
2
0
0
1
0
0
0
0
1
1
3
2
2
0
3
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
2
0
0
1
1
0
0
0
0
0
1
2
0
1
0
0
0
1
0
2
0
1
0
1
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
2
2
2
0
0
0
0
0
0
3
0
2
0
2
2
2
2
2
0
2
0
0
0
2
0
2
1
0
0
0
0
0
2
0
1
0
0
0
0
1
1
0
2
0
0
0
0
1
0
0
0
2
0
0
1
0
2
0
0
2
2
0
1
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
3
1
1
0
3
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
1
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
2
1
1
0
0
0
0
1
0
2
0
0
0
2
0
0
1
0
0
0
1
0
0
2
2
0
0
2
0
2
1
1
6
2
2
1
0
0
0
1
3
0
2
1
0
0
2
0
3
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
4
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
2
0
3
0
0
2
2
0
1
0
0
1
0
2
1
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
3
0
2
0
0
1
0
0
2
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
2
0
1
0
0
2
0
0
0
2
1
1
2
0
0
0
2
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
1
0
1
2
0
1
0
0
2
0
0
2
1
0
1
5
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
1
0
2
0
2
0
2
1
5
0
0
0
0
1
1
0
0
1
0
2
0
0
0
0
0
0
1
2
0
0
0
3
0
0
0
1
0
2
1
0
1
0
0
0
0
2
0
0
2
0
0
3
0
0
3
0
2
0
0
0
0
5
0
2
1
0
0
0
0
0
1
0
0
0
2
2
0
0
0
2
2
0
0
1
0
2
1
0
0
1
0
1
1
0
1
0
2
0
0
2
0
0
0
2
0
0
2
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
3
0
2
1
0
0
1
1
0
2
1
0
2
1
0
0
0
0
1
2
1
0
3
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
1
0
1
1
1
1
0
0
0
0
0
1
1
2
0
0
0
0
0
2
1
0
0
0
1
0
1
1
0
1
0
0
0
1
1
1
0
0
0
1
0
2
0
1
0
0
0
0
2
1
2
1
2
0
0
2
0
0
0
1
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
3
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
1
2
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
2
0
1
0
2
2
0
0
2
0
1
0
0
1
0
3
0
0
1
0
2
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
1
1
0
0
0
1
5
1
1
2
0
0
2
0
0
0
0
0
2
0
4
0
1
0
0
0
0
1
1
0
2
2
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
1
2
0
2
2
1
0
0
0
0
2
0
2
0
0
3
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
1
0
2
1
2
0
1
2
1
2
1
0
0
1
1
0
0
2
2
2
0
1
0
0
0
0
0
0
2
2
1
0
0
0
0
2
4
1
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
1
1
1
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
1
0
0
1
0
2
0
0
0
0
2
0
0
0
2
0
0
2
0
0
2
0
0
1
1
0
2
0
2
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
2
1
1
0
0
0
0
0
2
0
1
3
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
1
0
2
2
0
0
1
0
0
0
0
1
0
0
2
0
0
0
2
1
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
1
3
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
2
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
1
1
3
0
2
0
2
0
0
3
2
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
1
2
0
0
1
0
0
1
1
0
0
0
1
0
0
1
0
0
2
0
0
0
6
0
0
2
0
0
2
0
2
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
2
2
2
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
1
0
2
0
1
3
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
2
1
0
1
0
0
1
0
0
0
0
0
0
0
2
1
0
1
2
0
0
2
0
2
0
2
0
0
2
0
0
0
0
1
0
0
0
1
1
0
0
0
0
3
2
2
1
2
0
0
0
0
2
2
0
0
1
2
2
0
0
0
0
0
0
0
2
0
0
2
1
0
3
0
0
0
0
0
2
0
1
1
1
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
1
0
4
0
1
1
2
0
0
3
1
0
0
0
0
0
1
0
0
0
3
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
5
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
5
1
1
0
0
1
2
0
2
2
0
2
1
0
0
0
0
1
0
0
0
0
0
0
3
2
1
1
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
1
0
2
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
1
0
1
1
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
2
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
2
0
1
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
2
2
0
3
0
1
2
2
1
0
2
7
0
1
0
0
0
0
0
2
1
0
2
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
2
0
2
0
1
0
0
2
0
0
2
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
3
0
0
1
0
0
1
0
1
2
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
2
0
1
1
0
1
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
3
1
1
0
0
0
1
1
1
0
0
0
2
1
0
0
0
1
0
1
1
1
1
0
1
0
2
0
1
4
0
1
2
0
0
0
3
0
1
0
0
2
2
0
1
2
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
2
1
0
2
0
2
0
0
0
0
0
0
0
2
1
0
2
1
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
2
1
0
2
8
0
0
1
0
1
0
1
1
0
0
0
0
1
1
2
2
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
2
0
0
0
0
1
0
2
0
0
0
2
0
1
1
1
1
0
0
2
2
0
0
2
0
0
0
0
1
2
0
0
2
0
2
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
2
1
0
2
0
0
0
1
0
0
2
0
0
1
1
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
2
1
2
1
1
0
0
1
0
1
1
1
0
2
0
0
1
1
2
1
3
0
0
0
0
0
0
7
2
0
0
2
0
2
0
2
0
2
0
0
0
4
0
0
0
0
1
0
0
0
0
1
0
2
2
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
3
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
2
2
1
3
1
0
0
0
2
2
0
0
0
1
0
2
0
0
2
1
0
0
1
2
0
0
0
2
0
1
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
3
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
2
0
1
1
0
3
0
0
1
1
0
0
0
0
2
0
1
0
0
2
0
0
0
2
0
1
1
1
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
3
2
1
0
1
0
0
0
1
1
0
0
1
0
0
2
2
0
1
0
0
2
0
4
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
3
0
0
0
2
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
2
0
1
0
1
2
2
1
0
0
0
2
3
0
2
0
0
0
2
1
0
1
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
1
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
1
0
0
1
2
2
3
1
1
4
1
5
0
1
0
2
1
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
1
1
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
2
0
1
2
0
0
1
1
0
1
1
2
0
0
3
1
0
2
2
0
3
0
0
0
0
0
1
1
2
0
0
2
0
0
1
0
0
0
2
1
1
0
0
0
2
0
0
1
0
0
0
2
2
1
0
0
0
2
0
0
0
0
0
0
0
0
2
2
2
1
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
1
0
0
2
0
1
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
1
4
0
1
0
0
0
1
0
0
0
0
2
0
0
0
3
1
0
2
2
1
1
0
1
0
2
0
0
3
2
2
0
0
0
0
3
0
0
2
1
2
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
2
1
0
1
0
0
0
0
2
0
0
0
2
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
1
0
3
2
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
1
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
2
0
3
0
0
1
3
2
0
0
2
1
0
2
2
0
1
0
2
0
0
0
1
1
1
0
0
0
1
3
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
2
0
0
0
1
1
3
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
2
0
2
0
1
2
0
2
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
2
2
0
1
0
0
0
0
1
2
1
1
0
0
0
0
1
0
1
1
0
0
0
0
0
3
0
5
0
0
0
2
1
0
0
2
1
0
2
0
0
2
1
1
0
2
0
1
0
1
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
2
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
1
0
0
2
0
1
0
0
0
0
1
0
0
3
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
3
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
1
3
0
2
1
1
1
1
0
0
0
2
0
0
0
1
0
0
2
1
0
0
2
2
0
0
0
2
0
2
2
0
0
3
2
2
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
2
3
0
0
0
0
0
0
1
0
2
1
0
1
0
3
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
2
1
1
2
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
2
0
0
0
0
2
2
0
1
0
2
1
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
3
1
1
0
0
1
1
1
0
1
0
0
1
0
0
2
0
0
3
2
1
0
0
2
2
0
0
0
2
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
2
0
0
2
0
0
0
1
2
0
2
0
0
0
0
2
0
2
0
1
2
2
0
0
2
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
1
0
1
0
1
0
2
1
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
2
0
2
2
0
4
0
0
0
1
0
2
3
0
2
3
2
0
0
1
0
0
0
2
0
0
0
0
0
2
1
2
0
1
2
0
0
0
0
2
1
3
0
0
1
1
1
0
1
2
1
2
1
0
0
1
2
0
0
0
1
4
0
0
1
0
2
0
0
0
0
0
1
1
1
2
2
0
0
0
1
0
2
1
0
2
0
1
0
1
0
2
0
0
0
0
0
0
0
1
0
2
2
0
0
2
2
0
0
0
0
3
2
0
2
0
2
1
0
0
2
0
1
2
1
2
0
1
2
0
1
0
2
0
2
1
2
1
2
0
1
0
0
1
0
0
0
3
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
2
0
0
0
2
0
0
2
2
1
2
3
1
0
0
1
0
0
3
2
0
2
1
0
0
0
0
0
1
1
0
0
1
0
0
0
2
2
2
0
0
1
0
1
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
3
2
0
0
0
0
2
0
2
2
0
0
0
0
0
1
0
1
2
1
0
2
2
0
0
1
0
0
1
0
0
2
2
0
1
0
1
0
0
0
1
0
0
2
1
2
0
2
0
1
1
0
0
0
0
0
2
0
0
0
1
0
0
2
1
0
1
0
0
2
0
0
0
0
1
1
0
0
0
2
0
1
2
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
1
2
0
1
0
0
1
0
2
0
0
0
2
0
0
0
0
0
2
2
4
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
2
1
2
0
0
0
0
1
2
0
1
0
2
2
0
1
2
0
1
0
1
0
0
0
0
2
0
2
2
0
0
1
2
1
0
0
0
0
0
2
2
2
0
1
0
0
1
0
0
2
0
1
0
1
2
1
2
0
0
0
1
1
0
2
0
0
1
0
1
2
2
2
1
1
5
1
2
0
2
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
1
0
0
0
0
0
0
1
1
0
0
0
2
1
0
0
0
0
0
0
0
3
2
0
0
2
0
0
2
1
0
0
0
1
1
3
2
2
1
2
0
1
0
0
2
0
0
0
1
2
1
0
0
1
0
0
2
1
0
0
2
0
0
2
0
0
1
2
0
1
2
0
0
0
0
1
0
0
0
1
0
2
0
1
0
0
1
0
0
0
0
1
2
0
0
2
2
0
1
0
0
0
0
3
0
0
0
3
0
0
2
0
1
0
0
1
0
0
0
0
2
0
0
0
1
0
1
0
0
3
1
0
2
0
2
0
0
0
2
0
0
2
0
0
1
0
2
0
2
2
0
1
0
0
0
0
1
0
0
1
0
2
0
2
0
0
0
0
0
0
0
3
0
0
0
2
2
2
0
1
0
0
0
0
0
1
0
3
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
1
0
2
0
2
0
0
1
0
1
1
0
1
0
0
0
2
0
0
2
2
0
0
1
2
1
2
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
1
2
1
0
0
0
0
0
0
0
1
1
0
0
0
2
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
2
1
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
1
0
2
2
0
1
1
1
1
0
0
0
2
2
1
0
2
1
1
0
2
0
1
0
0
1
2
2
0
0
1
0
0
0
2
0
2
1
0
0
0
0
0
0
2
0
0
0
0
4
2
0
0
0
1
0
2
1
0
0
0
1
0
1
0
2
2
2
1
0
2
0
2
0
1
3
0
0
3
0
0
2
1
2
0
0
0
0
1
1
0
2
2
0
0
0
0
0
2
1
1
0
2
0
1
0
0
0
0
2
0
0
2
0
1
0
2
0
0
0
0
1
2
1
0
0
0
1
0
0
1
0
1
0
2
0
3
1
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
1
0
0
0
0
2
2
0
1
0
1
0
3
0
1
2
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
2
1
2
0
0
0
1
2
0
0
1
0
0
2
0
1
2
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
2
0
1
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
1
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
1
0
2
1
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
2
1
1
2
0
0
0
2
1
1
0
0
0
0
0
0
1
0
0
0
2
2
0
2
1
0
2
2
0
2
0
0
1
0
2
1
0
0
0
0
0
3
2
0
1
2
0
0
1
0
2
2
0
0
0
1
0
1
0
0
2
0
2
0
2
0
0
2
0
0
0
1
0
1
6
0
1
2
0
0
0
0
2
4
0
0
1
2
0
0
2
0
2
1
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
4
0
2
0
1
2
1
0
0
0
0
0
0
0
0
0
1
0
2
1
0
1
0
0
1
0
0
2
0
0
0
0
0
2
0
0
1
2
1
0
0
2
0
0
0
0
2
0
1
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
4
1
0
0
0
0
1
0
3
0
0
0
0
1
0
3
2
0
1
0
0
1
0
0
0
0
1
1
3
0
0
0
0
2
0
1
2
2
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
3
2
1
0
0
1
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
1
0
0
2
0
1
0
0
0
0
3
0
0
2
0
2
1
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
3
2
2
0
1
2
0
0
0
0
2
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
1
2
0
1
1
0
0
2
0
1
1
0
0
2
3
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
2
2
2
1
0
0
0
0
1
2
0
2
0
0
0
0
1
0
0
1
2
0
0
2
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
1
2
2
0
1
0
0
1
0
1
1
0
0
1
0
0
0
0
0
1
0
0
3
0
0
2
0
0
0
0
0
3
2
0
1
1
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
1
0
1
0
0
2
0
1
0
2
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
1
1
0
2
1
1
2
0
0
0
0
0
1
0
0
0
0
2
1
0
2
1
0
0
0
0
1
1
1
0
1
2
1
0
0
0
2
0
2
0
0
0
0
3
1
2
0
0
0
0
1
0
4
2
1
0
0
0
0
0
1
0
2
1
3
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
2
2
1
0
0
0
1
0
0
0
0
2
0
3
0
2
1
0
0
0
0
2
0
0
2
1
2
2
0
0
1
0
0
3
0
0
0
0
0
0
2
2
0
0
1
2
1
0
0
0
0
1
1
0
0
0
1
2
2
0
2
0
0
0
0
1
0
2
1
1
1
0
0
2
1
1
2
1
0
1
0
2
1
1
0
0
0
1
2
0
0
2
0
0
0
1
0
0
2
2
0
0
0
1
0
0
0
1
0
2
0
0
0
0
2
2
0
0
2
3
1
0
2
1
0
0
0
0
0
2
1
2
0
0
2
0
2
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
1
2
1
0
0
0
1
1
0
0
0
2
0
1
0
0
1
1
0
0
2
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
1
5
0
0
0
1
2
0
0
2
0
2
0
0
4
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
2
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
3
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
1
0
0
1
0
0
2
0
0
0
1
2
0
0
2
0
0
0
1
0
0
2
1
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
2
1
0
1
0
0
1
0
0
1
0
1
2
1
1
2
2
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
2
0
0
0
0
3
0
0
0
1
0
0
2
0
0
1
1
0
2
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
3
2
1
0
0
0
1
0
1
0
1
0
2
1
1
0
0
2
0
0
3
2
2
0
0
1
0
1
0
0
1
1
0
1
0
1
2
1
2
0
0
0
0
0
1
0
0
0
1
0
0
3
0
2
1
0
1
0
0
0
1
0
0
0
1
1
2
0
2
0
0
0
2
0
1
2
0
1
0
0
1
0
0
0
0
0
0
2
1
0
0
0
1
2
0
0
2
1
0
0
2
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
2
1
1
0
0
2
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
2
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
3
0
0
0
6
0
3
0
0
0
0
2
0
0
0
0
1
0
3
0
0
0
0
0
1
0
0
4
0
2
0
1
2
2
1
0
0
0
1
0
0
0
2
0
2
0
1
4
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
2
1
1
1
0
0
1
0
0
0
1
0
0
0
0
0
2
2
0
0
0
1
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
2
0
0
0
1
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
1
1
0
0
1
0
0
1
0
2
0
1
0
1
0
0
0
0
0
0
1
1
1
0
1
3
2
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
4
2
0
0
0
2
0
1
2
0
0
0
0
0
3
0
2
0
1
2
3
0
0
1
1
0
0
0
0
0
2
0
0
2
0
0
3
1
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
2
0
1
6
1
1
0
0
0
0
0
2
1
1
0
1
1
1
2
2
0
2
2
0
2
0
0
1
2
2
0
0
2
0
1
1
2
0
2
2
0
0
0
1
0
0
0
2
0
0
0
1
0
0
1
0
1
0
0
0
0
0
2
2
0
0
0
0
0
1
0
2
0
0
0
0
0
2
1
0
0
0
2
0
2
0
0
0
0
0
0
1
0
1
3
0
0
0
0
2
1
2
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
1
0
0
2
0
2
2
0
0
0
1
0
0
2
0
0
0
0
1
0
1
1
0
0
3
0
1
0
0
0
0
0
0
0
0
1
0
1
0
2
0
1
0
0
2
2
2
0
0
4
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
1
1
1
2
0
0
0
0
1
0
0
0
0
0
2
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
1
0
0
0
3
1
0
1
0
0
0
1
0
2
1
1
0
0
0
0
0
2
0
0
0
0
2
0
2
0
2
1
2
0
0
0
0
3
2
2
0
0
0
2
1
2
1
2
0
0
2
0
2
2
1
0
2
0
0
0
0
0
1
0
0
2
2
0
0
0
6
0
1
0
0
2
1
0
0
0
0
0
0
0
0
1
2
2
3
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
2
0
2
0
0
2
0
0
2
1
0
0
1
1
1
0
0
0
0
0
0
0
0
3
2
0
1
0
0
0
0
1
0
0
0
2
1
0
1
2
0
0
0
0
0
4
1
0
0
1
0
1
0
2
0
0
0
0
0
2
0
2
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
1
1
2
0
2
0
0
6
0
0
0
0
1
1
0
0
0
2
2
0
2
0
0
0
2
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
2
0
1
1
0
1
0
3
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
1
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
1
0
2
2
0
2
0
0
2
2
1
0
0
0
0
1
1
3
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
2
2
1
0
0
1
1
0
0
0
2
0
1
0
0
2
0
2
0
0
1
2
1
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
1
2
0
0
2
0
2
2
0
0
2
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
1
0
2
1
0
0
0
0
3
0
0
1
0
0
1
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
2
1
0
0
0
0
2
1
2
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
1
2
0
0
1
0
0
1
2
0
1
1
1
0
0
1
2
2
2
1
0
1
0
2
0
0
0
0
2
2
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
1
2
2
0
0
0
1
0
2
0
2
0
0
2
0
2
0
0
1
1
1
1
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
3
0
0
3
2
0
0
1
0
2
0
2
3
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
2
0
2
0
0
2
0
0
0
0
0
0
1
0
1
2
2
0
0
0
0
1
0
0
0
2
1
2
2
0
0
2
0
2
0
0
2
2
0
0
0
0
2
2
1
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
2
2
0
0
0
1
0
1
0
0
2
2
0
0
2
0
1
1
0
1
1
0
0
2
0
2
2
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
1
1
1
0
0
0
3
0
0
1
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
2
0
1
1
0
0
2
1
0
0
0
2
0
0
0
0
0
0
4
0
0
0
1
1
0
0
2
0
0
0
1
2
0
0
2
2
1
0
1
0
0
1
1
1
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
2
1
0
2
0
2
1
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
3
0
1
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
4
0
0
1
0
2
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
2
0
2
0
0
1
0
0
1
2
0
2
0
2
0
0
0
1
3
0
0
1
1
1
0
0
0
0
2
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
0
2
0
2
0
0
0
2
1
0
2
0
1
4
1
0
2
2
0
0
1
0
0
0
2
0
0
1
2
0
0
0
2
0
0
2
2
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
1
1
0
0
1
1
1
0
0
1
0
2
0
0
0
0
2
2
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
2
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
3
0
0
1
2
2
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
1
2
0
0
0
1
0
2
1
0
0
0
1
2
1
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
3
0
0
0
0
0
0
0
2
2
0
0
0
3
0
2
2
0
2
1
1
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
1
0
1
5
0
0
0
0
0
0
0
1
2
1
0
0
0
2
1
0
0
2
2
2
1
0
1
0
1
1
0
2
0
0
2
1
0
0
2
2
0
0
0
0
0
0
0
1
1
0
0
0
3
0
0
0
0
1
0
1
0
0
0
0
0
4
0
0
0
2
2
0
0
2
0
0
2
0
0
2
3
0
2
0
1
0
1
1
1
0
1
0
0
1
1
2
0
4
2
0
0
2
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
1
2
0
0
0
0
1
0
0
0
2
3
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
1
0
0
0
1
1
0
1
2
0
0
0
1
0
0
1
0
2
0
0
2
0
1
0
2
1
0
2
0
0
0
0
0
1
0
3
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
1
0
0
2
6
2
0
1
0
0
2
0
1
3
1
1
1
2
1
2
0
1
0
0
1
0
0
0
1
1
2
2
1
2
1
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
1
1
0
0
0
1
0
0
0
1
0
2
0
2
2
1
0
0
2
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
2
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
1
2
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
1
2
0
0
0
0
2
5
1
1
0
0
0
0
2
1
0
0
0
1
1
1
1
2
0
2
0
0
1
3
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
1
2
0
0
0
1
1
0
0
0
2
2
0
1
0
2
0
0
2
0
2
2
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
1
2
1
0
2
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
1
0
0
2
0
2
0
2
0
1
0
0
1
0
2
1
0
2
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
2
2
0
0
0
1
0
0
4
0
2
0
2
1
1
2
0
0
0
0
0
3
2
0
0
0
3
0
1
1
0
0
0
0
2
0
1
2
0
2
0
0
1
0
1
2
0
1
0
2
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
1
2
0
0
1
2
1
0
2
0
0
1
3
0
1
0
0
0
0
2
2
2
2
0
2
2
0
0
1
2
0
1
2
1
1
0
2
0
3
0
0
0
2
1
0
0
2
0
0
0
3
0
0
0
2
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
2
2
2
0
0
0
1
3
1
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
3
0
1
0
0
0
0
0
0
1
2
2
0
0
2
0
1
2
0
0
1
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
1
0
0
0
1
0
0
1
0
2
2
0
1
1
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
3
1
2
0
0
0
0
3
0
0
2
1
0
0
0
0
4
0
0
0
0
0
1
0
2
0
0
2
1
0
1
0
2
0
0
0
0
0
2
1
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
11
2
1
0
2
1
1
1
0
0
0
1
0
0
0
1
0
0
0
0
2
2
2
0
1
0
2
0
1
0
0
2
0
1
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
1
1
0
0
0
0
0
0
0
0
1
0
2
1
1
1
1
0
0
0
1
2
2
0
0
0
0
0
0
0
0
1
1
0
3
0
2
0
0
2
0
2
1
1
0
0
0
1
1
0
0
2
1
1
0
0
0
0
0
0
4
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
5
2
0
0
0
0
0
0
0
1
2
2
0
0
0
2
0
0
0
0
0
2
1
0
0
0
2
0
0
1
1
0
0
2
2
0
0
0
0
1
0
2
0
0
0
2
0
0
1
0
0
0
1
1
2
0
0
0
1
3
2
0
1
1
0
2
2
1
1
0
0
0
0
1
2
0
0
0
1
0
0
1
0
0
0
2
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
9
0
0
0
0
0
0
1
0
8
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
2
0
1
1
1
0
1
0
0
0
1
0
0
0
0
0
1
3
0
0
0
2
0
1
0
0
0
2
1
0
2
0
2
1
0
2
0
0
4
0
0
0
0
0
1
0
0
1
3
1
0
0
3
1
2
0
2
1
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
1
0
2
0
0
1
0
0
0
2
3
0
0
0
5
1
0
0
1
0
0
0
0
2
0
0
1
0
0
0
2
2
2
0
0
2
0
5
1
0
0
0
0
1
1
1
1
0
2
0
2
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
2
1
0
0
1
0
2
2
0
0
1
0
0
0
0
2
3
0
0
0
2
2
0
0
1
0
0
5
0
2
1
0
0
0
3
0
0
0
2
0
1
0
0
0
0
0
1
0
2
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
1
2
1
0
0
0
2
0
2
2
3
2
1
2
0
0
0
0
2
2
1
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
1
0
2
0
0
0
2
0
1
0
0
1
1
0
0
1
0
2
2
0
0
1
0
0
1
2
0
0
2
1
3
0
1
0
0
0
1
0
2
2
2
1
0
0
1
0
0
0
1
2
1
2
1
0
2
0
2
0
1
0
1
0
0
0
1
1
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
4
0
0
1
0
2
0
2
1
1
1
0
2
1
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
2
0
0
0
0
2
0
0
1
1
0
2
0
1
1
0
0
2
0
1
0
0
0
0
2
0
2
0
0
0
1
1
0
1
1
0
2
0
3
0
2
0
1
0
0
0
0
0
2
0
2
2
0
0
1
0
0
0
0
0
2
1
2
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
2
1
1
0
0
1
1
2
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
2
0
2
0
1
0
0
0
0
0
0
0
1
0
0
3
0
0
0
1
1
0
0
2
0
2
0
1
0
1
1
0
0
2
0
2
1
2
2
3
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
8
0
0
0
2
2
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
1
1
2
1
2
1
2
1
1
1
2
0
0
0
2
2
0
0
1
0
0
0
0
2
1
0
0
1
0
1
0
0
0
0
0
1
0
0
3
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
1
0
2
0
1
0
2
0
0
0
2
2
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
2
0
1
0
0
0
1
2
0
0
0
0
1
0
0
2
2
0
1
0
0
1
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
1
3
0
0
2
0
0
2
1
0
0
0
0
0
1
2
1
0
1
1
0
1
2
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
1
0
1
0
0
2
2
6
1
0
0
0
0
0
0
0
0
0
0
2
0
1
2
1
1
1
0
0
2
0
0
2
0
0
0
0
0
0
1
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
3
3
0
1
0
1
0
4
0
2
1
1
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
2
0
0
1
1
0
0
0
1
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
3
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
2
2
1
0
2
0
2
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
1
1
0
3
1
0
0
0
0
0
2
2
0
2
2
0
1
0
0
0
1
2
0
0
0
2
0
4
1
0
0
0
0
0
1
0
2
0
1
1
6
0
0
1
0
1
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
1
3
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
2
2
1
0
0
0
0
1
0
2
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
6
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
1
0
0
1
2
0
1
2
1
2
0
0
2
1
0
1
0
2
0
1
2
0
0
1
1
0
0
0
1
0
0
0
3
0
0
0
2
1
0
0
1
1
0
3
0
0
0
1
0
0
0
1
0
1
1
1
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
2
1
1
0
0
2
0
1
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
4
0
0
0
0
2
0
0
0
0
0
0
0
0
1
3
0
2
1
2
0
0
0
0
2
1
0
0
0
0
1
0
0
0
1
2
0
0
1
0
1
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
2
1
1
0
2
1
0
0
1
2
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
2
0
0
0
0
2
1
0
1
1
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
1
1
1
0
2
0
0
0
0
0
0
2
0
0
0
0
5
0
0
0
1
2
0
2
0
2
0
0
2
2
1
0
0
0
2
0
0
0
2
2
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
1
2
2
0
0
1
0
0
0
5
0
0
0
0
1
0
0
0
0
2
1
0
0
1
0
0
0
0
2
0
0
2
2
0
1
1
1
0
3
0
0
0
0
0
1
0
4
0
1
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
1
3
0
0
2
0
0
0
1
0
0
1
0
0
1
0
2
1
0
0
2
0
1
1
0
0
0
0
0
2
1
2
0
0
0
0
0
0
2
0
1
0
0
0
2
0
3
1
2
0
0
0
2
0
2
0
7
2
0
0
1
2
1
0
2
0
2
0
2
0
2
0
0
0
1
0
1
2
2
0
2
0
1
0
1
0
0
0
1
0
0
0
2
0
1
2
0
1
2
0
0
0
2
0
1
0
0
0
2
0
1
0
0
0
0
2
0
2
1
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
2
2
2
0
0
0
2
0
0
0
0
0
1
1
0
1
1
0
1
0
0
0
2
1
2
1
0
1
0
0
0
0
2
0
0
0
1
1
2
2
1
0
2
0
0
2
0
0
2
0
3
0
2
0
1
1
0
0
2
0
1
1
0
0
2
0
1
0
1
0
0
0
1
0
2
0
0
1
2
0
0
1
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
3
0
0
2
0
0
3
2
0
2
0
2
0
0
2
1
9
2
0
1
0
0
1
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
2
2
1
1
0
1
1
0
0
0
0
2
0
1
0
0
0
0
1
2
2
0
0
0
0
7
0
0
0
0
0
0
2
0
0
0
0
1
0
1
2
0
1
0
0
0
0
0
0
0
0
0
2
1
1
1
0
0
0
0
0
0
1
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
3
1
0
1
0
1
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
1
0
0
0
0
0
2
2
3
0
0
1
0
0
2
0
4
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
1
2
2
0
2
0
0
1
2
0
0
1
0
1
1
3
0
2
2
0
3
2
0
0
2
0
2
0
1
0
1
0
0
1
2
1
0
2
0
0
0
0
0
0
2
2
0
0
1
0
0
0
2
0
0
1
2
0
3
0
0
2
0
1
0
0
1
0
2
0
0
0
1
0
0
0
0
1
0
0
1
2
0
0
0
1
1
0
0
0
0
5
2
0
2
1
1
0
0
0
1
3
1
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
2
2
0
1
0
0
2
0
0
2
2
0
0
3
0
1
0
0
0
2
0
1
0
0
2
2
0
0
0
0
0
0
2
0
1
0
0
4
0
0
1
0
0
0
2
3
0
1
0
1
2
4
0
0
0
0
0
0
4
2
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
1
2
0
0
8
2
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
2
0
0
0
2
0
0
0
1
0
0
0
2
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
2
2
0
2
0
0
0
0
1
0
3
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
13
2
0
0
1
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
2
1
2
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
1
1
0
3
0
2
0
0
1
1
0
0
0
0
2
2
0
0
2
1
0
1
0
0
0
1
2
0
0
0
2
0
0
1
1
2
1
0
0
0
1
0
0
1
0
2
0
2
0
0
0
0
0
0
2
2
0
1
0
1
1
2
0
0
1
2
0
1
0
0
1
1
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
2
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
2
2
0
1
0
3
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
2
0
2
0
0
0
1
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
2
2
1
0
1
0
1
1
0
2
1
4
0
0
2
0
2
1
0
0
0
0
0
0
1
2
0
3
0
0
0
0
0
0
1
2
0
1
0
1
0
0
0
0
1
0
1
0
2
0
2
0
1
0
5
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
1
0
0
0
0
0
2
0
1
0
0
2
1
0
0
2
2
2
0
0
2
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
2
0
1
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
1
1
3
2
0
0
2
1
0
0
0
0
3
1
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
2
0
2
0
2
0
0
0
0
0
2
0
2
0
2
2
0
2
2
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
3
0
0
0
0
0
1
0
2
0
1
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
2
2
1
0
1
1
0
1
0
1
0
0
0
0
0
0
1
0
1
2
0
0
0
3
0
1
0
0
2
0
3
0
1
0
0
2
1
1
0
2
0
0
1
0
0
0
0
1
1
0
2
0
0
0
0
2
0
1
0
0
0
0
2
0
1
0
3
0
0
0
0
0
1
1
0
0
0
0
1
3
0
1
1
0
0
0
2
0
1
0
0
2
0
0
0
1
0
0
0
0
2
1
0
0
0
0
2
0
0
0
1
0
2
0
0
2
2
0
0
0
0
0
2
0
2
0
0
0
0
2
3
2
0
3
1
0
0
0
0
2
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
1
0
2
0
2
2
0
0
0
1
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
1
0
1
2
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
2
2
1
0
2
0
0
1
1
1
0
2
0
0
0
1
0
2
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
2
0
0
2
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
1
1
2
2
0
0
1
0
0
0
1
2
0
0
2
0
0
0
3
0
3
0
0
0
0
0
1
0
0
2
1
2
0
0
0
1
0
0
0
1
0
2
2
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
1
0
0
0
2
0
3
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
2
0
0
1
0
0
0
1
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
1
1
0
2
0
0
0
0
0
1
0
0
1
3
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
2
1
0
0
0
2
1
2
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
2
0
1
2
0
2
0
3
0
0
2
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
1
2
1
0
2
1
1
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
2
0
0
1
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
1
2
0
4
0
2
0
0
2
1
0
1
0
1
0
10
0
2
2
0
0
0
0
0
2
0
0
0
0
1
2
2
0
1
0
2
2
2
0
0
2
0
1
1
1
0
0
0
0
2
2
0
0
2
1
1
1
1
1
0
2
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
1
0
2
0
0
2
0
0
1
0
2
0
0
2
1
1
0
0
2
1
0
0
0
0
0
0
0
3
0
0
2
0
1
2
0
2
0
0
0
0
0
0
0
0
1
0
4
0
0
2
1
0
2
0
2
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
2
1
0
2
0
0
2
0
2
2
0
0
0
0
0
1
2
0
0
0
1
1
2
0
1
0
2
0
0
2
0
1
0
1
1
2
2
2
0
0
0
0
0
0
2
0
0
2
0
0
1
1
0
0
1
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
2
2
0
2
2
0
0
0
0
1
0
0
0
2
1
1
1
0
1
1
0
0
0
0
0
0
0
0
0
1
2
0
1
1
1
1
0
0
0
0
2
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
2
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
3
0
1
0
0
0
1
0
0
0
1
0
0
0
4
0
0
0
0
2
0
2
0
0
2
1
0
0
2
0
1
0
0
1
0
0
2
0
0
2
0
1
2
0
0
2
0
0
0
2
1
0
0
1
0
3
0
0
1
2
2
1
1
0
0
2
0
0
1
2
0
1
1
0
0
0
3
1
0
0
0
1
1
2
0
1
2
4
0
0
0
0
0
0
0
2
1
0
3
2
1
1
0
0
2
2
1
0
0
0
0
0
1
1
0
0
1
2
2
0
0
0
0
0
0
0
0
1
0
0
1
1
2
0
0
0
1
0
1
0
0
2
0
0
0
2
0
1
2
0
2
2
0
0
0
0
0
0
2
0
2
0
0
2
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
3
0
0
0
1
0
1
0
0
0
0
0
1
1
1
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
2
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
2
2
0
0
0
0
0
1
2
0
0
1
0
2
0
0
1
1
1
2
0
0
4
2
2
0
0
0
1
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
1
0
0
2
2
0
1
0
0
0
0
1
0
2
0
1
2
0
1
1
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
1
2
2
2
0
0
1
0
0
0
0
2
4
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
1
0
0
0
2
0
0
0
2
1
0
0
1
0
1
0
0
0
0
1
0
1
1
0
0
1
0
0
1
0
0
1
0
0
0
0
2
2
0
0
1
0
2
0
0
0
1
0
1
2
0
0
2
1
0
0
0
2
1
0
1
0
0
2
0
1
0
1
1
2
5
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
2
2
2
0
1
1
0
1
0
0
0
0
2
0
0
1
1
0
2
1
2
0
2
0
1
1
0
2
0
0
0
0
0
0
0
0
1
1
0
0
2
1
2
0
0
0
2
0
2
0
0
0
0
0
1
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
2
0
1
2
0
0
1
3
3
0
0
0
0
2
0
0
0
2
0
2
2
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
1
2
0
0
0
1
0
0
2
0
0
1
0
0
1
2
0
2
1
1
0
1
0
0
1
2
0
0
0
0
1
0
0
0
0
1
1
1
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
2
0
2
0
0
0
1
0
8
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
2
2
0
0
0
1
0
0
2
0
1
2
0
0
1
0
2
1
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
3
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
1
2
1
2
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
3
0
0
2
0
0
1
0
0
0
0
0
2
0
2
1
0
1
4
2
0
0
1
0
1
2
0
0
3
0
4
0
0
0
0
0
0
1
2
0
0
0
0
0
2
2
0
0
2
0
0
1
0
0
0
2
0
0
2
0
0
1
0
0
0
1
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
1
0
2
1
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
2
3
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
2
0
2
2
0
0
0
0
1
2
2
2
1
1
0
1
0
1
1
0
0
0
0
0
2
0
0
2
1
1
0
0
1
0
0
1
1
0
0
0
0
0
2
0
1
0
1
0
0
0
0
2
1
0
0
0
2
0
1
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
2
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
2
1
0
3
0
0
0
1
0
0
1
0
0
1
2
0
0
0
0
0
2
0
2
1
3
0
2
0
1
0
0
0
0
2
0
0
0
0
2
2
0
1
0
0
2
1
0
2
0
0
1
0
1
2
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
2
0
0
1
2
0
1
1
3
0
2
1
1
2
0
0
1
0
0
1
0
0
1
0
0
0
2
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
2
0
1
3
0
0
1
0
0
2
0
0
0
2
3
0
0
0
2
1
2
2
0
2
0
0
2
0
0
1
1
0
1
1
0
1
0
1
0
0
0
2
0
0
0
2
1
0
0
0
0
2
0
0
2
0
0
2
2
0
0
2
0
0
2
1
1
1
0
1
0
0
0
0
0
2
0
2
0
0
0
0
1
2
0
0
1
2
1
1
0
0
1
2
1
1
0
0
0
0
7
0
2
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
2
2
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
1
0
2
0
0
2
0
0
0
1
0
0
2
3
0
0
0
0
0
1
0
2
2
2
1
1
0
0
0
2
2
0
2
1
1
0
2
1
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
3
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
2
0
1
0
0
0
1
0
0
0
2
4
2
0
0
0
0
2
2
0
0
0
2
0
0
0
1
1
2
2
1
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
1
2
0
0
0
2
1
1
0
2
0
0
0
0
2
2
2
2
0
0
1
0
0
0
0
1
0
1
2
0
0
0
2
1
0
0
0
0
1
0
0
2
0
1
0
1
0
2
0
3
0
0
0
0
0
2
2
0
1
0
0
0
0
0
4
0
0
0
0
0
1
0
2
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
3
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
1
0
2
2
0
0
2
2
1
0
0
0
1
0
0
0
1
2
2
1
0
2
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
2
0
0
1
0
0
2
0
1
0
0
2
0
1
0
2
0
0
0
0
0
0
1
0
0
3
2
0
1
1
0
2
4
0
0
0
0
1
2
2
0
0
0
0
3
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
4
0
0
0
0
0
0
0
1
1
1
2
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
2
2
0
1
0
1
0
2
1
2
2
0
0
0
0
0
0
0
2
0
2
0
0
0
1
1
1
2
2
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
1
2
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
2
0
0
0
1
0
2
0
0
1
2
0
2
0
2
0
4
2
1
2
0
0
0
0
0
0
0
1
1
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
2
1
2
0
2
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
2
0
5
0
2
0
0
1
0
1
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
2
0
0
0
0
0
3
1
1
0
0
2
0
0
1
0
5
1
2
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
1
2
0
1
0
0
0
2
0
0
2
2
1
0
0
0
0
0
0
0
0
0
1
0
0
3
0
2
2
0
0
0
0
2
1
1
0
1
1
0
0
0
1
0
0
0
0
0
2
1
1
0
0
2
0
1
2
0
0
0
0
0
0
0
1
2
0
0
0
0
1
1
3
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
2
1
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
2
0
0
2
0
0
3
1
2
2
2
0
3
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
2
0
1
0
0
0
2
1
0
2
1
0
8
0
0
2
0
0
0
3
0
0
1
0
1
2
1
0
1
0
1
0
0
0
0
0
1
0
2
1
1
0
0
0
1
0
1
0
2
2
0
1
0
0
0
0
0
1
1
1
0
0
3
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
2
1
0
1
0
1
0
1
0
0
1
0
2
4
1
0
0
1
1
0
2
3
0
1
0
1
0
2
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
2
1
1
0
0
1
0
3
2
0
0
0
0
2
0
1
0
3
0
0
0
0
2
0
0
0
0
1
0
2
1
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
6
0
2
0
0
0
0
0
2
0
0
2
0
0
1
2
0
0
0
2
0
0
0
0
0
1
0
0
2
0
2
0
4
1
5
6
0
1
0
0
1
0
0
1
2
0
1
0
0
0
6
2
0
0
1
0
2
0
3
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
2
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
1
0
0
2
0
0
1
0
0
1
0
7
2
0
2
0
1
0
0
0
0
2
1
0
0
0
0
2
2
0
0
1
2
0
0
0
2
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
2
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
2
0
0
0
0
0
0
0
2
2
0
2
0
0
2
0
0
1
0
0
0
0
0
2
1
1
0
0
1
0
0
0
1
0
2
1
0
1
1
2
0
0
0
0
0
0
0
0
2
0
1
0
1
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
1
2
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
1
1
1
0
0
0
0
0
0
0
2
0
0
0
1
1
2
0
2
1
0
0
0
0
0
1
2
2
1
0
0
0
0
0
1
2
0
1
0
0
0
2
2
1
0
0
0
0
0
0
1
2
0
0
0
1
4
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
2
0
0
1
2
1
0
0
1
0
0
2
3
0
0
0
0
0
3
0
0
0
0
0
0
5
2
0
2
1
0
2
0
0
1
2
2
0
0
1
4
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
2
0
0
1
1
1
2
0
1
2
2
0
0
2
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
3
0
0
1
2
0
0
0
0
2
2
1
2
0
0
0
0
0
0
2
2
0
1
2
0
0
0
4
2
2
0
2
0
0
1
1
0
0
0
2
2
0
0
2
0
0
2
2
0
2
2
0
2
0
0
0
0
2
0
0
0
2
0
1
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
1
0
0
0
0
2
0
0
0
0
0
1
1
2
0
1
0
0
0
2
2
2
0
0
0
2
1
0
0
0
0
0
0
2
1
2
0
1
0
0
1
0
2
0
2
1
0
1
0
0
0
2
0
0
0
0
0
1
2
0
1
0
2
3
0
2
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
2
0
0
2
2
1
0
1
0
1
0
0
0
0
1
0
2
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
2
1
0
3
0
1
2
2
0
0
2
0
0
0
2
0
2
1
0
2
0
0
0
0
0
1
0
0
1
2
0
2
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
1
2
0
0
2
0
0
2
2
2
0
0
0
0
0
0
0
1
2
1
0
2
0
2
0
0
0
0
0
1
0
0
1
1
1
0
1
0
0
0
0
0
2
2
3
0
0
0
0
2
0
0
1
1
0
0
2
0
2
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
2
3
2
0
2
0
0
0
0
2
0
0
0
0
0
1
0
2
0
2
1
2
4
0
1
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
3
2
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
2
1
0
2
0
0
0
0
1
0
0
0
0
0
0
2
2
0
1
1
0
0
1
1
2
0
1
0
0
0
0
0
2
0
0
0
2
0
0
1
0
2
0
0
1
1
0
0
0
3
0
2
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
1
0
0
2
0
2
0
0
0
1
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
1
3
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
1
2
3
0
2
0
0
0
0
3
0
0
1
1
0
0
0
0
0
0
1
0
2
1
0
0
1
0
2
0
1
1
1
1
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
4
0
0
0
0
1
0
0
0
0
2
2
0
1
0
2
1
0
1
0
3
0
1
0
0
0
0
1
0
0
1
1
0
0
1
2
0
1
5
0
0
3
0
0
0
0
0
0
0
1
0
0
0
2
3
0
2
0
0
0
0
0
1
0
0
2
2
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
3
0
0
0
1
0
2
0
0
3
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
2
1
0
2
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
2
0
2
0
0
0
0
1
1
0
0
0
0
1
2
1
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
2
0
0
0
1
2
1
0
0
0
2
0
1
0
0
0
0
0
4
0
0
2
0
0
1
2
1
1
0
2
0
1
1
0
1
2
1
1
0
1
1
0
0
0
1
0
0
0
0
0
0
2
0
1
0
1
2
0
0
2
0
1
1
2
0
0
0
1
0
0
0
0
2
1
0
0
2
0
1
0
2
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
3
2
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
3
2
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
1
3
3
0
2
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
2
0
0
0
1
3
2
0
0
0
0
0
0
0
0
1
1
0
0
0
2
2
0
0
1
0
1
2
1
0
0
0
0
2
0
0
1
1
0
3
0
0
0
1
0
0
1
0
2
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
3
0
0
0
0
3
1
0
0
0
0
2
2
2
0
0
0
2
0
0
0
2
2
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
3
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
2
1
1
1
1
0
0
0
0
0
0
3
0
0
0
0
0
1
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
2
2
1
0
2
0
0
0
2
0
2
0
0
0
0
1
0
1
0
0
0
0
1
1
0
2
0
0
1
3
0
0
1
2
2
0
2
0
0
2
0
0
2
0
4
0
0
4
0
0
3
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
1
0
1
2
1
0
0
2
0
1
1
0
0
0
2
0
0
5
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
1
1
1
1
0
2
0
2
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
2
0
0
0
0
0
1
3
1
0
0
1
0
4
0
3
0
0
0
0
1
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
1
1
0
1
1
0
2
0
0
2
0
0
2
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
3
2
0
3
2
0
0
0
0
0
0
0
0
1
0
0
0
1
2
1
0
1
0
0
1
0
1
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
1
2
0
1
0
0
1
1
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
1
2
1
0
0
2
2
2
2
0
2
0
0
1
1
0
0
0
0
3
0
0
2
0
0
3
0
0
1
0
2
0
0
1
0
0
0
0
0
4
0
2
0
1
0
0
0
0
0
0
0
2
2
0
2
1
0
1
3
0
1
1
0
1
0
0
2
0
0
0
2
1
1
0
1
0
1
1
0
0
2
0
0
1
0
0
1
0
0
0
1
0
2
1
0
0
1
3
0
0
0
2
2
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
1
1
1
1
0
1
0
0
2
0
0
1
0
0
0
1
0
1
0
1
0
0
0
1
1
0
0
1
0
0
2
3
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
2
0
4
0
0
0
0
0
0
3
0
0
0
1
2
1
1
0
1
0
2
1
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
1
2
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
1
1
2
3
2
2
0
1
0
0
0
0
0
0
0
0
1
2
0
0
2
2
0
0
0
0
1
0
2
1
0
0
2
0
0
0
0
0
0
0
2
0
1
2
0
0
1
0
0
0
0
2
1
0
0
2
0
2
0
1
2
0
0
1
2
0
0
0
0
2
0
0
1
0
0
0
2
0
0
2
2
0
1
1
2
0
0
0
2
1
0
0
1
0
2
0
2
2
4
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
1
0
0
2
0
1
0
0
2
3
0
0
2
0
1
1
1
0
2
2
0
0
0
0
0
3
0
0
1
3
2
0
2
0
0
0
0
1
0
0
0
0
0
2
2
0
1
0
0
2
0
0
2
0
2
0
0
0
0
1
0
0
1
1
2
0
0
1
0
0
1
0
1
0
1
0
2
0
0
2
4
0
0
0
0
1
0
2
1
0
0
1
3
0
2
0
1
2
0
0
1
0
0
1
0
0
1
2
0
0
0
1
0
1
0
2
0
2
1
0
1
0
0
0
1
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
3
1
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
2
1
2
0
0
0
2
0
0
0
0
0
2
0
0
2
1
2
0
0
1
1
1
2
1
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
2
2
0
0
0
1
2
2
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
1
0
2
1
0
0
2
0
3
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
2
1
0
0
2
0
0
0
1
0
0
0
0
0
3
0
0
1
2
0
0
1
0
0
0
0
3
0
2
0
2
1
0
0
3
0
0
1
1
2
1
1
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
1
0
0
1
2
1
1
2
0
0
0
2
0
1
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
1
1
0
0
1
8
1
0
0
0
1
1
0
0
0
0
3
2
0
0
2
0
2
0
2
2
3
0
1
0
1
0
1
2
1
0
2
2
0
1
0
0
2
3
0
0
0
3
0
0
0
2
0
0
1
0
1
2
0
2
1
2
0
0
0
0
2
1
1
0
2
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
1
1
0
0
2
0
0
2
0
0
1
2
0
2
1
0
0
0
0
0
0
2
2
0
1
0
2
1
2
1
1
0
0
1
0
1
0
0
0
1
0
2
1
1
0
0
0
0
1
2
0
0
0
0
1
0
0
1
2
0
0
0
0
1
2
1
0
0
1
0
0
1
0
0
2
0
2
0
2
1
0
0
0
2
1
2
0
1
0
0
0
2
0
0
1
0
0
0
0
0
1
0
2
1
0
0
0
0
3
3
0
0
0
2
0
1
0
1
1
0
0
2
0
1
0
2
1
0
1
0
1
5
2
2
0
2
0
2
2
0
0
0
2
0
0
1
1
0
3
0
1
2
0
0
0
1
1
0
0
0
1
0
0
0
0
0
2
1
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
2
0
0
0
0
0
2
0
0
0
1
2
1
0
1
0
2
0
0
2
2
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
2
0
0
0
1
0
0
0
2
1
3
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
2
2
0
0
0
1
1
0
2
0
0
0
0
2
1
0
2
1
0
0
0
2
4
1
0
0
0
0
2
1
1
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
1
0
2
0
0
0
0
2
1
0
0
2
0
2
3
0
2
0
0
0
0
0
2
0
0
1
1
0
0
0
0
1
2
2
0
2
1
1
0
2
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
3
5
1
0
0
0
0
0
0
0
3
0
3
0
0
1
1
0
0
0
0
0
0
2
0
1
0
1
2
1
1
0
0
2
0
1
0
0
0
0
2
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
1
0
0
1
0
1
0
1
2
1
0
0
0
3
2
0
1
1
1
2
0
0
0
1
0
3
2
0
1
0
1
0
1
0
0
0
2
3
0
2
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
2
1
2
1
1
0
2
1
2
0
1
0
0
0
0
0
0
3
1
2
0
0
1
0
0
0
0
1
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
3
2
3
0
1
0
1
2
0
2
0
0
0
0
0
1
2
0
0
0
2
1
0
0
0
2
1
1
1
0
0
0
1
0
3
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
3
0
0
0
0
1
0
1
0
2
0
0
2
0
1
0
0
2
0
0
0
0
2
0
0
2
1
2
1
2
0
0
0
0
0
0
0
1
2
0
1
2
2
0
2
0
0
0
2
0
0
2
1
0
1
0
0
2
1
2
2
0
0
0
1
2
0
3
0
0
0
0
0
1
1
0
2
0
1
1
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
1
0
2
1
1
1
0
0
2
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
1
1
0
3
0
0
0
0
2
0
0
2
0
0
1
0
2
0
0
0
0
1
0
0
0
0
2
1
0
0
2
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
2
3
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
3
1
2
1
0
2
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
2
1
0
0
0
2
0
1
2
0
1
0
0
0
0
1
1
0
0
0
1
0
0
2
2
0
1
0
1
1
1
0
1
0
0
0
0
0
1
0
0
2
1
0
0
1
3
2
0
0
0
0
1
1
1
2
0
0
0
0
1
0
2
1
0
0
0
0
0
1
2
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
2
1
0
0
0
0
1
1
0
0
2
1
0
2
0
1
0
0
4
0
0
1
0
0
0
0
2
0
1
3
2
1
0
0
0
1
1
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
1
0
0
2
0
2
0
2
0
1
0
0
1
0
3
2
1
1
0
2
0
0
0
1
0
0
0
0
1
1
0
1
0
0
2
0
1
2
1
2
2
2
0
1
0
0
4
0
0
3
0
0
1
0
0
0
2
0
0
2
1
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
1
0
0
1
2
2
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
2
0
0
2
1
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
2
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
3
0
0
0
0
0
1
1
0
0
0
1
0
1
0
2
0
2
0
1
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
1
0
3
0
2
0
0
0
2
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
2
0
0
1
0
0
0
1
0
0
1
0
0
1
2
0
0
1
0
0
1
0
0
0
0
1
0
2
0
3
0
0
0
1
0
0
0
0
0
0
2
2
3
0
2
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
3
0
0
0
0
0
0
0
1
0
2
0
1
0
0
2
2
1
1
0
0
0
1
0
0
2
0
1
0
0
0
1
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
3
1
1
2
0
0
0
1
0
1
0
0
0
0
2
0
1
0
1
1
2
0
0
0
0
1
0
0
1
0
2
0
0
0
1
0
2
0
0
0
0
2
0
0
2
0
2
0
0
1
0
0
0
1
1
0
0
0
6
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
1
0
0
1
0
2
0
0
0
1
0
2
0
3
3
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
1
1
0
0
0
0
3
0
0
2
0
1
1
1
1
0
0
0
1
0
0
0
0
0
1
0
2
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
2
0
1
0
0
2
0
1
0
0
0
0
0
2
0
2
1
0
3
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
3
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
2
1
0
1
0
0
0
0
1
2
0
4
0
1
0
2
1
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
2
1
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
1
2
0
2
1
0
0
2
0
1
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
2
0
2
2
1
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
1
2
0
1
0
2
0
2
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
1
0
0
2
0
2
2
3
0
0
2
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
1
0
0
2
1
0
2
0
2
0
0
1
0
0
1
0
1
0
0
1
2
0
0
2
1
0
2
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
2
0
0
2
1
0
0
1
0
0
0
0
0
1
2
0
2
2
1
0
0
0
3
3
0
0
1
2
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
1
0
2
1
2
1
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
2
2
0
1
2
0
0
0
2
1
0
1
0
0
0
0
1
0
1
0
0
0
1
0
1
2
0
0
2
1
0
0
0
0
1
0
1
0
0
1
5
0
2
1
0
0
0
1
1
0
1
2
0
0
0
3
0
0
2
0
0
2
0
1
1
0
0
1
0
4
0
0
0
2
2
0
2
0
0
0
0
2
1
0
1
0
1
0
1
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
1
0
1
1
0
1
0
1
0
0
2
2
0
0
0
2
0
1
0
0
1
2
0
0
0
0
1
2
0
2
0
0
2
1
1
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
2
2
0
0
0
0
0
0
1
1
0
0
2
1
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
1
1
0
0
0
2
0
0
0
1
0
0
0
2
1
0
0
1
2
0
1
0
0
1
0
1
2
0
0
2
0
0
2
0
0
1
0
1
1
0
2
0
3
1
0
0
2
1
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
7
0
2
2
2
0
2
0
1
0
0
2
0
2
0
2
0
2
0
2
2
0
0
4
2
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
2
0
1
0
0
0
1
2
1
2
0
0
0
0
1
2
2
0
0
1
1
0
1
0
1
2
0
3
0
0
0
0
2
0
0
1
1
0
2
1
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
1
0
1
1
0
0
0
2
0
2
0
0
2
0
1
0
2
0
0
0
0
0
2
1
0
3
0
0
0
1
0
2
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
2
2
1
0
2
0
1
0
0
0
1
8
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
2
2
0
0
0
0
0
0
2
2
0
1
0
0
3
1
0
1
2
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
1
2
1
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
2
3
0
0
0
0
0
0
0
0
2
0
0
2
0
1
2
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
2
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
1
2
1
0
0
0
0
2
0
1
0
1
1
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
1
0
3
0
8
0
2
0
0
0
0
0
1
0
0
0
3
0
0
1
2
0
0
2
0
2
0
2
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
1
0
0
0
1
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
3
0
0
1
2
2
1
0
1
0
1
0
1
1
0
0
0
0
0
0
6
2
0
2
0
0
0
0
2
4
0
0
1
0
0
1
2
0
3
0
2
0
0
0
0
0
2
0
2
2
2
1
0
3
0
1
0
0
0
1
2
0
0
0
0
0
0
0
1
0
1
2
0
3
1
0
0
0
0
1
0
0
2
1
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
2
0
0
1
1
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
4
4
1
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
1
2
2
0
0
0
0
0
1
2
0
0
2
2
0
0
1
0
0
0
0
0
0
1
0
1
0
2
2
2
3
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
2
0
0
1
0
1
2
0
0
1
1
0
0
0
1
2
0
1
0
0
0
0
2
0
0
1
1
0
1
1
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
2
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
2
2
0
0
1
2
0
1
1
0
0
0
0
2
0
0
1
0
0
1
1
0
0
0
1
0
0
0
1
1
0
1
1
0
0
0
0
1
2
0
1
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
2
0
1
0
0
0
0
0
0
2
0
1
0
0
1
0
2
0
0
0
0
0
0
0
2
2
2
0
0
1
0
2
0
1
1
1
0
4
0
0
3
1
0
0
2
2
0
2
1
0
0
2
2
0
0
0
2
0
0
1
0
0
0
2
0
1
1
2
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
2
1
0
0
0
0
0
0
1
1
0
0
0
0
0
2
1
0
2
0
0
1
2
2
0
1
1
0
0
1
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
1
0
0
0
2
0
0
0
1
0
1
0
1
4
0
1
2
1
2
0
0
1
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
2
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
3
0
0
2
0
0
1
0
0
0
0
0
2
2
1
3
0
1
2
2
0
0
0
0
0
1
1
0
0
1
2
0
0
1
0
0
0
0
0
3
1
0
2
0
0
1
3
0
1
2
0
0
0
3
0
0
1
0
0
0
0
3
0
1
0
3
3
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
2
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
1
2
1
1
0
0
0
0
3
1
0
0
0
0
1
0
0
0
1
2
2
3
2
0
0
3
0
0
0
0
0
0
0
2
1
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
3
0
2
0
0
1
0
3
0
0
0
1
0
0
1
0
2
1
0
1
2
0
1
0
1
2
0
0
0
2
2
0
0
0
0
0
0
2
0
0
1
1
0
0
2
0
1
2
3
0
2
0
4
2
2
2
0
1
0
0
2
0
1
0
0
0
0
0
0
0
1
0
1
0
4
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
1
0
2
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
2
1
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
1
1
1
1
1
0
1
0
2
0
2
2
0
1
1
0
0
0
0
0
2
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
1
0
2
2
0
0
0
0
0
2
0
2
0
0
0
3
0
1
3
0
2
2
1
0
2
0
1
0
3
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
1
1
1
2
2
0
3
1
2
1
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
2
2
0
2
0
0
0
0
1
0
0
0
0
0
0
3
2
2
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
2
0
2
0
0
0
0
0
1
0
1
0
2
0
0
9
1
1
0
1
0
3
2
0
0
2
0
0
2
0
1
0
1
0
2
0
0
2
1
0
1
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
1
1
1
0
1
2
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
3
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
1
2
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
1
1
0
2
0
1
2
0
2
0
0
1
0
0
0
3
0
0
2
0
0
0
0
0
0
0
1
1
1
2
2
0
0
0
1
0
0
0
2
0
1
2
1
1
0
0
1
0
0
1
1
2
2
0
2
2
0
0
0
1
2
1
0
2
0
0
0
1
2
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
1
0
0
0
1
0
2
0
1
1
0
9
0
1
2
0
2
1
0
3
2
0
0
1
1
0
0
1
0
2
0
2
1
0
0
0
0
0
0
0
0
2
1
2
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
1
1
0
0
0
0
0
1
1
0
0
0
1
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
4
0
0
0
0
0
1
1
1
1
0
0
2
3
2
0
0
2
0
0
1
0
0
0
0
1
0
2
5
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
2
2
0
1
0
0
1
0
0
0
0
2
2
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
2
0
0
2
0
1
0
2
2
1
1
1
2
0
0
0
2
2
0
1
2
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
1
4
0
0
1
1
0
2
0
1
0
2
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
4
2
0
0
2
0
0
0
0
0
2
0
1
0
1
0
2
0
2
0
1
4
1
1
1
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
1
0
2
0
0
2
0
1
0
0
0
0
0
0
1
1
0
0
0
0
2
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
2
0
1
7
1
2
0
2
0
0
0
0
0
0
0
0
1
0
0
1
1
0
2
0
0
0
0
0
0
2
1
0
2
0
3
0
0
0
0
0
0
0
2
0
2
0
0
0
2
1
0
0
0
0
2
1
0
0
1
2
2
0
0
1
2
2
0
1
2
1
2
0
1
0
0
0
2
0
0
2
2
0
2
0
2
3
0
0
0
0
2
0
4
1
1
0
0
1
0
0
0
0
2
0
2
2
1
0
0
0
0
2
2
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
3
0
3
0
0
0
0
0
0
2
0
0
0
0
1
0
1
1
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
3
1
2
0
1
1
1
0
2
0
0
0
2
0
0
0
0
0
0
0
1
2
1
0
0
2
0
4
0
0
2
0
0
2
1
0
0
1
0
0
0
3
0
2
0
0
2
1
0
2
0
1
2
2
1
1
0
1
0
2
1
0
1
0
3
0
0
0
0
0
1
2
0
0
2
1
0
0
0
0
1
0
6
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
2
0
0
0
1
0
0
1
0
0
0
2
3
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
7
2
0
0
2
0
0
0
2
0
0
0
0
2
0
1
0
0
2
1
0
0
0
0
0
0
0
1
0
3
0
1
1
0
0
0
0
2
0
1
1
0
0
1
0
0
0
0
0
0
0
2
0
2
1
0
3
0
0
0
0
1
0
0
0
0
0
0
2
3
0
0
0
2
0
3
7
0
0
1
0
0
0
0
1
0
2
1
2
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
2
1
0
2
0
2
1
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
2
0
2
0
2
0
2
0
0
0
0
3
1
0
0
0
0
1
1
0
1
0
0
0
2
2
1
0
1
0
0
0
0
0
0
0
1
0
2
0
0
6
0
0
0
1
0
1
1
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
4
0
1
0
0
0
0
1
0
0
2
2
1
0
0
0
2
0
0
1
1
1
0
0
0
0
2
1
2
1
2
0
2
1
0
2
0
0
0
0
0
2
1
2
2
0
0
1
1
0
0
1
0
1
4
0
0
0
2
2
0
1
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
1
2
0
1
0
0
2
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
1
0
0
2
0
0
0
0
1
2
3
1
2
2
0
1
1
2
2
2
2
0
0
0
0
0
0
2
0
1
0
0
0
0
1
1
0
1
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
1
1
3
0
2
0
0
0
1
2
1
0
0
0
0
1
0
1
0
1
2
1
1
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
2
1
0
1
2
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
2
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
1
0
0
1
2
1
0
2
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
2
0
1
0
0
0
0
2
1
0
0
0
0
1
5
0
0
1
0
0
2
0
0
3
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
2
1
1
0
0
0
2
0
0
1
1
0
0
1
0
1
0
2
0
1
0
0
2
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
1
0
0
2
0
0
0
0
4
0
0
1
0
0
1
0
0
2
0
2
0
1
2
2
0
0
0
2
0
0
0
0
0
4
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
4
0
0
0
0
2
0
0
2
0
1
0
0
0
0
2
0
2
0
0
0
2
2
0
0
1
0
0
1
3
0
1
2
0
0
2
0
2
0
0
2
0
0
4
0
0
0
0
1
2
3
1
0
2
2
1
0
0
1
1
0
2
2
0
0
0
1
0
1
0
0
0
0
2
2
0
1
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
1
0
1
2
1
0
1
0
0
0
2
0
0
0
0
0
0
2
1
0
1
0
2
0
0
2
0
0
1
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
1
2
0
0
0
1
1
0
0
0
0
0
0
0
2
0
7
0
0
4
2
0
0
0
1
0
0
0
0
2
2
0
0
0
3
1
1
0
0
0
0
0
1
2
0
2
0
1
0
0
1
0
0
1
0
1
0
2
0
2
0
0
0
2
0
0
0
2
0
2
0
0
1
2
1
0
0
1
2
1
0
0
0
0
0
0
0
2
0
2
1
0
2
0
0
0
0
1
3
2
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
2
1
0
2
0
1
0
2
1
0
0
0
0
3
0
0
2
0
1
1
2
0
0
0
4
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
1
2
0
2
0
1
1
0
0
0
0
0
0
1
6
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
5
0
0
0
1
1
0
2
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
2
2
0
2
0
1
0
1
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
2
0
2
2
0
0
0
2
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
1
0
0
3
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
2
1
2
0
1
0
1
0
4
2
0
0
0
1
0
2
2
0
0
1
0
0
0
1
1
1
1
0
0
0
0
0
0
0
2
2
0
1
0
2
2
0
0
1
0
0
2
0
2
2
0
0
0
1
0
2
0
2
0
1
2
0
1
0
0
2
1
1
1
0
0
0
0
2
2
0
2
1
3
0
0
1
3
1
0
0
2
0
0
0
0
0
1
2
0
0
0
0
1
0
3
0
0
2
0
0
1
2
0
0
0
0
0
0
0
2
0
2
0
0
2
0
2
1
2
2
0
0
0
0
0
0
0
2
0
0
0
0
1
2
2
0
0
0
0
0
1
0
0
1
3
2
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
2
1
1
2
0
2
0
0
0
0
2
0
2
0
1
1
1
2
0
4
1
1
0
2
2
1
1
0
0
0
2
3
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
2
0
3
0
0
2
0
0
0
1
0
6
0
0
0
2
2
0
0
2
0
0
0
0
0
2
0
2
0
1
1
2
0
0
0
0
0
0
0
0
0
3
2
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
4
0
0
0
0
2
2
0
1
0
0
0
0
1
2
1
0
3
1
0
0
0
0
1
1
2
1
2
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
3
2
0
1
0
1
0
0
0
0
0
1
2
0
2
2
0
2
0
0
0
0
0
1
0
0
0
1
0
2
1
0
0
2
2
1
0
4
0
0
2
0
1
2
2
0
2
0
0
2
0
0
2
0
0
0
2
0
0
2
0
0
0
1
1
0
2
0
0
4
1
0
0
2
1
0
0
0
1
1
0
0
1
2
1
0
0
1
0
0
0
0
0
1
0
1
1
1
4
0
2
0
0
0
0
0
2
1
2
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
2
0
0
0
2
0
0
0
2
0
0
1
2
0
0
0
0
1
2
1
1
2
0
0
0
1
1
0
0
0
2
1
0
1
0
3
0
2
1
0
0
1
2
0
0
0
0
0
1
2
0
1
0
2
2
0
0
0
0
3
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
3
1
0
1
0
2
0
0
0
0
0
1
2
0
0
0
4
1
1
0
0
1
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
2
1
0
0
0
0
0
1
0
0
0
0
2
2
3
0
0
2
0
0
2
1
1
2
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
2
2
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
1
2
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
1
0
2
0
0
0
0
1
0
1
2
2
2
0
0
0
0
0
2
0
0
2
1
0
10
0
2
0
0
0
0
0
1
2
0
0
1
0
2
0
0
0
0
1
0
0
0
1
0
0
2
2
2
2
0
2
0
0
3
0
0
0
0
0
0
1
0
2
2
1
0
0
0
0
2
2
0
0
0
0
0
2
0
1
1
2
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
2
2
0
0
0
1
1
0
3
0
0
0
1
0
0
0
2
2
0
0
0
2
1
0
0
0
1
0
1
2
0
0
0
2
0
0
0
0
0
3
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
1
2
0
0
0
1
1
0
0
0
0
0
2
0
2
0
2
3
0
0
0
0
2
0
0
0
3
2
2
0
0
0
0
0
0
0
1
2
1
1
0
0
2
2
2
0
1
0
0
0
1
0
0
0
0
0
2
2
1
1
0
2
2
2
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
3
0
0
0
0
2
0
0
1
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
2
0
1
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
2
0
0
0
2
0
3
0
1
0
2
1
0
1
0
1
2
0
0
0
2
0
1
1
0
0
0
0
2
0
0
0
0
0
0
1
1
0
1
0
0
0
0
2
0
0
0
0
2
0
0
2
2
0
0
0
1
0
0
2
2
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
3
0
2
0
0
0
1
2
2
0
0
0
1
1
1
1
0
1
3
2
0
2
0
0
2
0
0
2
0
0
0
0
2
0
1
2
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
2
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
2
2
1
2
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
2
0
1
0
0
0
0
1
0
0
0
1
0
4
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
2
0
1
0
0
3
0
1
0
0
0
0
1
1
2
3
0
1
2
0
0
2
1
0
2
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
2
2
2
0
0
2
1
3
0
0
0
2
0
0
0
0
0
0
2
0
2
0
2
1
0
0
0
1
0
0
1
0
0
1
1
1
6
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
2
0
0
0
0
1
0
2
0
3
0
0
0
1
0
2
0
4
0
2
1
0
1
0
1
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
1
0
0
6
1
0
1
0
2
1
0
0
0
0
1
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
3
1
0
0
0
0
0
0
0
4
1
1
1
0
0
0
0
2
3
0
1
0
1
2
0
0
1
2
0
0
0
0
0
2
0
4
0
0
1
0
3
0
0
1
2
0
1
0
0
0
0
1
1
0
0
1
1
0
1
0
0
1
3
0
0
2
0
0
0
2
0
0
4
0
0
0
0
2
0
0
0
0
0
1
0
1
1
0
0
0
2
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
2
0
0
2
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
1
2
0
0
2
1
0
0
0
0
0
1
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
2
1
2
0
0
0
0
0
0
1
0
2
0
0
1
2
0
0
0
0
0
2
0
2
1
1
0
2
1
0
1
0
0
1
2
0
1
1
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
2
0
0
0
0
2
0
0
0
1
2
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
2
0
2
0
0
0
0
1
1
0
1
1
0
0
0
0
0
1
2
0
0
3
0
0
0
0
1
0
0
0
0
0
0
2
0
0
3
2
1
0
1
1
2
0
0
2
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
1
0
2
0
1
1
0
4
0
1
0
1
0
0
1
1
0
2
0
0
0
0
1
0
1
2
0
0
0
0
0
1
0
1
1
2
1
0
0
0
0
0
1
0
1
1
0
0
0
2
0
0
0
0
2
0
0
0
1
0
2
2
0
0
0
2
2
0
0
0
1
0
1
1
0
0
0
2
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
2
2
0
0
2
3
2
0
0
1
2
0
0
1
1
2
0
2
1
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
2
0
2
2
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
5
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
2
0
1
0
0
1
0
0
2
2
0
0
0
0
1
3
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
2
0
0
2
3
0
0
1
2
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
3
0
2
1
1
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
1
1
0
0
0
3
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
1
2
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
2
0
0
0
0
2
0
1
0
0
0
2
0
0
1
0
0
0
0
1
0
2
2
0
0
0
0
0
2
1
1
0
0
0
0
0
2
0
0
1
1
0
2
0
3
0
0
2
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
2
0
0
0
0
0
1
1
0
2
1
0
1
0
2
2
0
0
1
0
0
0
2
1
0
2
1
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
1
0
2
0
0
0
1
0
0
0
0
0
2
0
2
0
0
2
3
0
0
0
3
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
1
1
1
0
1
2
0
0
1
0
0
1
1
1
0
0
1
0
0
0
1
0
1
1
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
2
0
0
2
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
2
2
1
0
1
1
0
7
2
0
0
0
0
5
1
0
2
0
0
0
3
1
0
0
1
2
0
1
0
0
0
0
0
0
0
0
1
0
0
2
1
0
2
1
0
0
0
0
0
2
0
0
1
0
2
2
0
0
0
2
0
1
4
0
0
0
0
1
0
0
3
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
5
0
0
0
0
0
0
0
0
2
0
0
2
2
2
2
2
0
2
0
2
0
0
1
0
0
0
0
2
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
3
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
2
1
0
0
0
0
2
0
1
1
0
0
1
0
2
0
0
0
2
0
2
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
2
0
2
0
0
1
0
4
2
0
0
2
1
1
0
0
1
0
2
1
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
1
0
2
2
0
2
0
1
0
0
0
0
1
1
2
0
0
1
2
2
0
0
0
0
0
2
0
2
2
0
0
0
1
1
3
0
0
0
0
0
0
1
0
2
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
1
1
1
2
0
0
2
2
1
1
0
0
0
1
0
0
2
1
2
0
0
1
1
0
2
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
3
1
3
1
0
0
2
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
2
1
2
0
0
0
0
0
0
2
5
0
0
0
0
0
1
0
1
0
0
0
1
0
2
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
5
0
1
2
0
0
0
0
1
1
0
3
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
2
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
2
0
0
1
4
0
0
2
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
1
0
2
0
1
1
0
2
0
2
1
0
0
0
2
0
2
0
0
0
1
0
1
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
2
0
0
0
2
0
0
1
1
1
0
0
0
0
2
0
0
2
0
0
0
1
2
0
0
2
0
1
0
0
0
0
0
0
0
7
2
0
0
0
1
0
2
0
0
0
0
0
1
3
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
2
2
0
2
0
0
2
0
0
0
0
0
1
0
1
1
3
1
0
0
2
0
0
1
2
0
1
0
0
0
3
0
0
2
0
0
1
0
0
0
0
0
1
2
1
0
0
0
0
0
1
1
0
0
0
2
0
0
0
3
1
2
0
0
0
2
0
1
0
1
1
2
0
2
0
1
0
2
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
1
2
1
0
1
1
0
0
0
0
0
0
3
1
0
1
0
3
0
0
0
1
2
0
0
1
0
2
0
0
0
0
1
2
0
0
0
0
2
2
0
2
0
0
0
0
0
2
0
1
0
0
0
2
0
0
1
0
1
0
1
0
0
1
0
0
0
1
0
2
1
1
0
0
0
0
0
3
1
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
1
0
0
2
1
2
0
0
0
3
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
2
0
0
0
0
1
1
2
0
0
0
0
2
2
0
0
0
0
0
0
0
2
1
2
1
3
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
1
1
2
1
1
0
0
0
2
0
0
1
2
0
0
0
2
2
0
0
1
0
0
2
0
1
2
0
2
2
0
0
0
0
0
0
1
0
2
0
0
1
2
1
0
0
0
3
2
0
1
0
0
1
0
2
0
2
0
2
0
0
2
0
0
1
0
0
1
0
2
0
0
2
1
0
3
0
1
1
0
0
2
5
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
3
1
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
1
0
0
1
1
0
0
0
1
0
0
2
0
2
0
1
0
2
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
3
0
0
0
0
1
0
0
3
0
2
0
0
0
0
0
1
0
0
0
1
0
2
2
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
2
0
0
1
0
0
0
4
0
1
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
2
0
2
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
2
1
2
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
1
0
2
0
1
1
1
0
0
0
2
0
0
0
0
0
1
1
1
0
0
0
0
0
1
1
0
0
1
4
0
1
2
1
0
0
2
2
1
0
1
1
0
1
1
0
0
3
0
1
0
0
0
0
0
2
0
2
0
1
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
2
1
0
2
1
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
1
2
0
1
1
0
0
0
0
0
0
0
1
0
0
0
2
1
0
1
0
0
2
0
3
2
0
0
2
2
1
3
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
1
0
2
2
0
2
0
2
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
1
0
0
2
2
1
0
0
0
0
2
0
0
1
0
1
1
0
0
0
0
1
0
0
1
2
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
2
0
2
0
1
1
1
0
3
0
0
0
1
0
0
0
1
0
0
2
2
1
1
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
1
0
0
1
1
2
0
0
2
0
1
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
2
2
1
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
2
3
0
0
2
0
2
1
0
0
1
0
2
0
0
0
2
0
0
0
0
1
2
1
0
0
1
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
2
0
1
0
0
2
0
1
0
2
0
2
1
0
0
0
1
1
1
4
1
2
1
2
0
0
1
0
0
1
0
1
0
0
1
1
2
0
0
0
2
0
0
0
1
2
0
2
0
0
0
2
0
0
0
0
0
3
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
2
0
0
2
0
0
4
0
0
3
0
0
2
0
1
0
2
2
0
0
0
0
1
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
1
0
1
0
0
0
0
0
0
2
1
0
0
0
0
1
1
0
0
1
0
2
1
1
2
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
2
0
0
0
0
1
2
2
0
2
1
2
1
1
0
0
0
0
2
0
0
0
2
0
0
2
0
0
1
0
2
0
0
0
0
0
2
0
0
0
2
0
2
2
0
0
0
2
1
2
1
0
1
0
0
0
2
1
0
0
2
2
0
1
2
0
0
0
2
0
0
0
0
3
0
0
2
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
2
0
3
0
0
0
2
0
1
0
0
0
1
0
0
2
0
1
0
1
1
0
0
1
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
1
0
0
0
2
1
1
0
2
0
2
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
1
2
1
0
2
0
0
1
0
4
0
2
0
0
0
0
0
0
2
1
0
0
0
1
1
0
1
1
0
0
0
0
2
0
2
0
3
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
1
1
0
0
0
2
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
3
0
1
0
0
0
3
0
3
1
1
0
1
1
2
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
2
1
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
3
0
2
0
0
0
0
0
0
1
1
0
0
0
0
2
1
0
0
0
0
2
0
2
1
0
0
0
2
0
0
3
0
1
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
3
0
2
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
2
1
0
0
0
0
1
0
0
1
2
0
0
2
2
0
0
0
0
1
0
2
0
0
1
2
0
1
1
1
0
0
1
0
0
0
0
0
0
1
1
1
2
0
2
0
1
2
1
0
1
1
1
2
1
0
0
1
0
1
1
0
0
0
0
0
3
0
0
0
2
1
0
0
0
0
0
0
0
11
0
0
0
0
0
0
1
2
0
0
0
0
0
2
1
1
0
0
2
2
0
1
0
0
0
1
0
0
0
5
0
0
0
1
0
0
0
0
9
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
2
0
0
0
1
0
0
0
0
0
0
1
1
0
0
2
0
0
0
3
1
0
2
1
2
0
1
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
1
2
0
1
0
0
0
0
2
0
0
0
2
0
4
3
0
1
1
1
0
0
0
0
0
0
0
1
3
1
0
2
1
0
1
0
0
2
1
0
0
1
0
2
0
0
2
0
2
2
0
0
0
0
2
1
0
0
1
0
2
0
5
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
1
0
0
0
1
0
2
0
2
3
1
1
0
0
0
0
1
0
0
0
2
2
0
1
0
0
0
0
1
0
1
0
2
0
0
0
0
2
0
2
0
0
0
1
0
0
0
1
1
2
0
2
2
1
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
2
0
0
0
1
0
0
0
0
1
1
1
2
1
1
0
0
0
0
1
0
1
0
0
0
1
1
1
0
0
1
0
0
1
0
0
0
1
0
0
1
0
2
0
3
0
0
1
0
3
0
2
0
0
1
0
1
0
0
2
0
0
0
0
1
3
0
0
0
0
1
2
1
1
0
0
4
0
1
0
0
0
1
1
2
2
0
0
0
2
1
0
3
2
0
2
0
2
0
3
2
1
0
0
2
0
1
0
0
0
1
0
0
2
0
0
1
0
1
0
0
0
0
0
1
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
1
0
0
1
0
0
1
0
0
4
2
0
0
0
0
0
0
1
0
0
2
0
1
0
0
2
1
0
0
0
1
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
2
1
0
2
0
1
2
2
0
7
0
0
0
2
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
1
0
2
0
0
0
0
1
0
1
1
3
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
2
1
1
0
2
0
0
0
0
2
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
1
0
2
0
0
1
0
0
0
0
0
1
0
1
3
0
0
0
0
1
0
0
0
3
1
1
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
3
0
1
1
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
1
0
0
1
2
2
0
1
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
1
3
0
0
2
0
0
0
0
2
0
1
2
0
0
1
1
2
0
0
0
0
2
0
1
0
0
0
2
0
0
2
0
0
1
0
2
0
0
2
0
1
0
0
2
0
0
1
0
0
3
0
0
1
0
0
0
1
1
0
0
1
2
0
1
0
0
0
0
0
2
2
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
1
1
2
1
0
0
0
0
0
0
0
0
2
0
2
1
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
2
2
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
2
1
0
0
2
0
1
0
0
0
2
1
1
0
3
2
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
1
0
1
2
0
1
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
3
0
1
3
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
1
2
0
0
0
0
1
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
1
1
1
1
1
0
1
1
0
0
0
0
2
0
0
0
2
2
2
0
2
2
3
1
0
0
0
0
0
0
0
1
1
0
2
0
1
0
0
0
1
1
3
0
0
1
2
0
0
1
0
2
0
1
0
0
0
0
2
1
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
2
0
0
0
0
7
0
2
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
1
1
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
1
0
2
2
0
0
0
2
0
0
1
0
0
0
3
2
2
0
2
0
0
0
1
0
1
0
1
0
0
3
2
1
0
2
1
0
0
0
0
0
1
1
2
2
0
1
0
2
2
2
0
1
2
0
2
0
0
0
1
0
1
3
0
0
0
5
1
0
1
0
2
0
1
1
1
0
0
0
2
0
2
0
0
0
1
2
0
2
2
2
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
5
0
4
2
2
2
0
1
2
1
2
0
0
0
0
0
2
0
1
0
0
0
0
0
3
2
1
2
0
0
4
1
0
0
2
0
3
1
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
1
2
0
0
0
1
2
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
2
0
3
0
0
2
3
1
0
0
0
0
1
0
0
0
0
2
1
0
2
0
2
1
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
1
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
2
2
0
0
0
0
0
1
3
0
1
0
2
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
2
2
0
0
1
0
0
2
1
2
0
2
1
1
2
2
0
0
0
0
0
0
1
0
2
0
1
0
1
0
0
1
2
0
0
0
0
1
1
0
0
0
0
0
1
1
0
2
1
0
0
2
0
0
0
0
3
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
1
2
2
0
0
0
0
4
2
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
2
3
0
1
2
0
1
0
1
2
1
0
0
0
0
0
2
0
0
2
1
0
1
0
0
2
0
1
2
0
0
2
1
0
1
0
0
1
0
0
2
2
0
0
1
0
0
2
2
2
0
0
3
0
0
0
1
0
0
1
2
0
2
1
0
1
0
0
0
0
2
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
3
0
2
0
0
0
2
0
0
0
1
0
0
1
2
1
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
2
2
0
0
1
0
0
1
4
0
1
0
1
1
0
0
0
0
2
0
0
0
0
1
1
0
1
2
0
0
2
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
2
0
2
2
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
1
2
0
0
2
0
0
2
1
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
2
0
0
0
0
2
1
0
0
1
0
2
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
1
2
0
0
0
1
2
0
1
0
0
2
1
0
0
1
0
1
2
0
0
2
0
0
0
2
1
1
0
0
1
0
0
0
1
0
1
0
0
1
2
0
0
2
2
1
0
0
0
1
0
0
0
0
1
2
0
2
1
1
0
0
0
0
2
2
0
3
1
1
0
0
1
0
0
1
3
0
2
0
0
1
1
2
1
0
0
1
0
0
0
2
1
0
0
2
0
0
0
0
0
0
1
0
2
3
2
0
2
0
0
1
2
1
1
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
1
2
1
0
1
0
0
0
2
0
2
2
1
2
1
0
0
0
0
0
0
0
0
2
1
2
3
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
1
1
0
0
1
0
1
2
0
0
0
0
0
0
2
0
4
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
3
0
1
1
0
0
0
2
0
2
0
1
0
0
3
0
0
2
1
0
1
2
0
2
0
0
1
0
0
1
0
0
0
1
1
0
1
1
0
0
0
0
0
2
1
0
1
0
2
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
2
0
1
0
0
2
0
0
2
2
0
0
2
1
2
0
0
0
1
0
2
0
3
1
0
2
0
0
0
1
0
0
0
2
2
1
1
0
2
0
0
0
0
1
0
2
1
0
0
0
2
0
1
0
0
1
0
0
1
1
0
0
2
2
0
0
1
0
1
0
1
0
0
0
2
1
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
5
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
3
0
0
2
1
0
2
1
0
0
0
0
0
1
1
0
0
2
0
2
1
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
1
0
0
0
5
1
0
0
1
0
1
0
0
2
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
6
2
2
0
0
0
0
0
1
0
0
0
2
0
2
0
0
2
0
1
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
2
0
0
2
1
2
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
1
1
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
2
3
0
0
0
2
0
0
0
0
0
0
1
2
0
2
1
1
2
0
0
0
1
0
0
2
1
0
0
0
2
3
0
0
0
2
1
0
2
0
2
0
0
0
0
0
0
2
0
0
0
2
1
2
0
0
0
1
0
2
1
2
0
2
0
0
0
2
2
0
0
0
0
0
0
2
0
0
2
1
1
0
1
0
0
0
0
1
0
0
0
1
0
0
2
2
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
2
0
2
0
0
0
3
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
2
1
2
1
0
0
1
0
2
0
0
0
0
0
0
0
2
2
1
0
4
0
0
0
0
0
0
0
1
2
1
0
2
0
0
0
0
1
0
1
0
1
2
0
0
2
1
0
0
1
0
0
0
2
1
0
2
0
2
2
0
0
2
0
0
0
0
0
0
0
0
2
2
2
1
0
1
2
3
0
2
0
0
0
0
1
0
0
0
2
0
1
0
2
0
1
0
0
0
1
2
0
0
2
0
0
0
0
2
2
1
1
0
2
0
0
0
0
0
2
0
2
0
0
0
0
1
1
0
0
1
0
1
0
0
2
0
0
1
0
0
0
0
0
2
1
0
0
0
2
0
2
3
0
0
0
0
2
2
0
0
0
0
0
2
1
0
0
0
0
2
0
2
3
2
1
0
0
1
0
1
0
0
0
0
0
3
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
3
0
1
4
0
2
1
1
0
0
0
0
2
1
0
1
2
2
2
1
2
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
2
0
0
0
3
0
2
1
0
0
2
0
1
1
1
0
0
2
0
2
0
0
2
2
0
0
1
0
0
0
1
0
0
2
0
0
1
0
1
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
2
4
1
0
2
0
1
0
1
0
1
0
0
0
1
2
1
0
0
2
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
2
0
0
0
0
1
1
0
0
2
0
2
0
0
0
2
2
0
0
1
1
1
0
1
3
0
0
1
1
1
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
2
0
0
0
3
0
0
0
1
1
1
0
0
2
0
1
2
1
0
0
0
0
0
0
1
1
0
0
0
1
1
2
0
2
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
2
1
2
0
0
0
1
0
2
2
0
0
0
0
1
0
1
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
1
1
2
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
1
1
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
1
0
2
1
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
1
1
0
2
0
0
0
1
1
0
2
0
0
0
0
0
1
2
0
0
0
0
2
0
1
0
0
2
0
0
0
3
0
0
2
0
1
0
2
2
0
0
0
0
1
2
2
0
0
3
1
1
0
0
0
2
0
0
0
0
1
0
0
1
1
0
1
1
2
3
2
3
0
1
0
1
0
0
0
0
2
0
2
0
2
0
0
0
2
1
0
0
0
2
1
0
0
0
0
0
3
0
1
1
2
0
0
0
0
0
0
1
0
1
0
0
2
0
2
0
0
0
0
0
2
0
2
2
0
1
0
0
1
0
1
0
2
0
1
2
0
0
1
0
0
2
0
2
0
0
2
0
5
0
1
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
2
0
0
2
0
0
0
0
0
2
0
0
1
0
5
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
2
1
1
2
0
2
0
0
0
0
2
1
0
0
0
2
1
1
0
0
0
0
1
0
2
0
2
1
0
0
0
1
0
1
0
0
0
0
0
1
1
0
2
0
2
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
2
0
0
1
0
0
0
2
0
0
1
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
2
0
0
0
0
0
0
7
0
0
3
2
0
0
1
1
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
1
0
0
0
1
2
0
0
2
0
0
0
2
0
0
1
0
0
2
0
1
0
1
0
0
0
1
0
2
2
0
0
2
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
3
1
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
2
0
0
1
0
0
0
2
0
2
0
3
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
1
3
2
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
1
1
0
0
0
3
0
0
1
2
0
0
2
0
0
0
2
0
0
2
0
0
0
1
1
3
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
1
1
1
0
0
1
2
0
0
0
0
0
1
0
0
0
1
0
0
1
0
2
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
1
1
2
0
1
1
0
0
0
1
2
1
0
0
2
1
3
0
0
0
1
0
1
0
2
3
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
3
0
2
0
0
0
1
0
2
1
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
3
0
4
1
0
0
5
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
2
0
1
0
0
2
2
0
2
0
0
0
3
0
4
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
1
1
0
2
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
1
2
0
1
0
2
3
0
0
0
3
0
0
1
3
0
2
2
0
0
1
0
1
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
1
0
2
1
0
1
2
0
0
1
0
2
1
0
1
2
1
1
2
0
0
2
0
1
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
1
0
0
0
1
0
0
0
0
0
0
2
2
1
0
3
0
1
1
0
1
0
2
0
2
2
0
0
0
0
0
1
0
1
0
0
2
2
0
0
0
2
1
0
2
0
0
1
0
0
0
2
0
0
1
1
0
0
0
0
0
0
1
0
2
0
2
0
0
3
0
1
0
0
0
0
0
0
5
0
0
1
2
0
0
0
1
0
0
1
0
0
2
2
0
0
0
1
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
1
2
1
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
3
0
0
1
0
1
0
2
0
0
0
1
2
0
1
2
0
0
0
1
2
0
0
0
3
2
2
4
0
1
2
0
2
2
0
0
2
0
1
2
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
2
1
0
1
0
0
0
0
0
0
2
0
0
2
2
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
1
0
2
0
1
0
0
1
0
0
0
2
1
2
0
0
0
0
0
1
0
0
0
0
2
0
1
2
1
0
0
0
2
0
0
0
1
1
1
1
0
1
0
0
1
0
3
0
1
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
1
0
2
0
1
0
0
1
2
0
2
1
1
1
1
0
3
0
2
0
0
0
2
0
1
2
0
0
0
1
0
0
0
1
0
2
0
0
0
1
0
0
0
3
0
0
1
0
1
1
0
2
0
0
1
1
0
0
0
1
0
0
0
0
1
2
2
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
1
1
1
0
1
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
7
0
0
0
0
1
1
0
0
0
0
1
1
2
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
2
2
1
0
0
0
3
1
0
0
0
0
2
0
0
1
0
2
1
0
0
0
0
1
0
1
0
0
2
0
0
3
0
0
0
3
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
2
2
0
1
2
2
1
2
0
1
0
2
0
0
0
1
0
0
0
2
0
2
1
0
0
0
0
0
1
2
0
2
1
0
0
0
2
1
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
2
0
2
1
2
0
0
2
1
3
0
0
0
2
0
1
0
0
2
2
0
2
0
0
0
0
1
0
0
0
1
2
0
0
1
1
1
0
3
0
1
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
1
0
2
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
3
0
0
0
1
0
0
1
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
1
1
0
3
0
0
0
1
2
0
4
0
0
2
0
1
0
0
0
0
0
0
2
0
2
0
1
1
0
0
2
0
1
0
2
3
1
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
2
0
1
0
2
0
0
0
0
0
0
0
2
1
0
0
1
0
1
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
1
2
0
1
0
0
2
0
1
1
1
0
0
2
0
1
1
0
0
1
2
0
2
0
1
1
0
2
2
0
0
1
1
0
4
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
1
0
2
1
0
0
1
0
0
0
2
0
2
0
0
0
2
0
1
0
0
0
4
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
1
0
2
1
2
0
0
0
0
1
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
1
0
0
0
0
2
0
3
2
0
0
0
0
0
0
0
0
2
3
0
0
2
0
1
1
2
0
2
0
1
0
1
2
1
0
1
1
0
0
1
0
1
1
0
0
3
0
0
0
0
1
0
2
0
0
0
0
1
0
2
0
0
1
0
1
0
2
0
1
0
0
0
0
0
0
0
0
1
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
2
1
2
3
2
0
0
0
1
2
0
0
1
3
1
0
1
2
0
0
0
1
0
0
2
1
3
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
2
0
0
1
0
0
3
0
0
0
0
3
0
0
0
1
0
0
0
2
0
2
0
2
0
2
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
1
1
0
0
2
3
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
1
1
1
0
1
2
1
3
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
1
2
0
0
0
3
0
0
2
0
0
2
1
2
0
0
0
0
0
3
0
0
6
0
0
1
2
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
1
0
0
0
2
1
0
0
2
1
0
0
0
0
0
1
2
2
0
0
1
0
0
0
2
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
2
1
1
0
1
1
0
0
0
0
3
2
0
0
0
0
0
4
0
0
0
0
0
0
2
0
0
0
0
0
4
1
2
0
3
0
0
2
0
2
1
0
2
0
3
0
0
0
0
0
0
1
0
2
3
0
1
4
1
1
0
0
1
0
0
1
1
2
0
0
0
1
0
1
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
2
0
0
1
1
0
0
0
1
0
0
0
1
2
1
0
0
3
1
0
0
2
0
2
0
0
0
0
0
0
1
0
2
2
0
2
1
0
2
1
0
0
0
0
0
0
0
1
0
4
0
2
0
0
0
0
2
0
0
2
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
1
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
2
1
1
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
2
0
2
1
0
0
0
2
0
2
0
2
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
2
0
2
0
0
0
0
0
0
0
2
0
1
2
0
1
0
0
0
2
0
0
0
1
0
0
0
0
1
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
2
0
0
0
2
2
0
2
0
3
0
1
1
1
1
1
3
2
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
1
1
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
2
0
1
0
0
0
2
0
0
1
0
0
0
0
2
0
2
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
2
1
1
0
1
2
0
0
1
0
0
0
2
2
0
0
2
0
0
0
1
0
2
1
0
0
0
0
0
2
1
2
0
0
1
2
1
0
2
0
0
0
0
0
0
2
4
0
0
2
0
1
2
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
1
3
2
0
0
0
2
0
1
1
0
1
0
0
1
0
0
0
0
2
1
0
0
0
1
0
1
4
0
0
0
0
0
1
0
0
0
0
1
0
2
1
0
0
0
0
0
2
2
1
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
1
2
0
1
2
2
2
0
2
0
1
0
0
0
3
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
3
0
2
2
1
0
0
0
0
1
0
2
0
0
0
1
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
2
2
0
0
0
1
2
0
0
0
0
0
0
1
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
4
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
2
0
0
1
6
1
0
0
1
1
0
0
1
3
1
0
0
2
0
1
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
2
1
2
0
1
1
0
2
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
2
0
0
0
1
0
2
0
0
1
2
0
0
0
1
1
0
0
0
1
1
0
2
0
0
0
0
0
1
0
2
1
0
1
0
0
0
0
1
1
1
0
1
1
0
0
0
0
1
0
0
2
0
0
0
2
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
1
1
1
3
0
0
0
0
0
0
1
0
1
3
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
2
0
1
0
0
0
2
0
0
0
0
0
1
1
2
0
0
1
2
0
1
0
0
1
2
0
0
1
0
0
1
0
2
0
1
0
1
0
3
2
0
0
0
0
0
0
1
0
0
0
0
0
0
6
0
0
0
0
1
2
0
0
0
2
1
0
0
0
0
0
2
1
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
1
3
0
1
1
0
0
2
0
0
0
0
0
0
0
1
0
5
0
1
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
1
0
0
1
0
0
1
0
1
1
2
2
1
0
2
0
0
6
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
1
0
2
0
0
4
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
1
0
2
0
0
2
0
0
0
0
1
2
1
1
0
0
2
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
2
0
0
2
0
1
0
1
0
8
1
2
0
2
0
0
0
0
3
1
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
4
2
1
3
1
1
0
0
0
1
0
0
0
1
2
0
0
0
0
2
0
2
2
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
1
0
2
2
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
1
1
0
0
0
1
1
2
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
1
0
0
0
1
0
0
0
0
1
2
0
2
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
3
2
0
0
0
0
2
2
1
0
0
1
0
1
0
0
0
0
2
2
0
0
0
0
2
2
0
2
1
1
0
0
0
1
0
0
0
0
0
0
2
0
1
3
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
2
0
0
1
0
0
0
0
0
3
2
0
0
2
0
0
0
2
0
0
0
0
2
2
0
1
0
0
0
2
0
0
0
0
0
0
1
1
0
1
0
3
0
1
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
2
2
2
0
0
1
0
2
0
0
1
0
0
0
2
1
1
2
0
2
0
0
0
0
1
1
1
1
0
2
0
0
2
0
0
0
1
1
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
2
3
0
1
0
2
0
0
1
0
1
0
2
0
0
1
1
0
0
0
0
0
0
3
1
0
2
0
2
0
1
0
2
0
0
0
1
1
2
0
0
1
0
2
0
0
2
1
0
0
0
0
3
2
1
0
1
0
2
1
0
2
2
0
0
0
3
0
1
2
0
1
0
0
0
0
2
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
1
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
1
2
1
0
0
0
0
2
1
0
1
2
2
0
2
0
2
2
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
2
0
2
1
1
0
0
1
0
0
0
1
2
0
0
0
0
2
1
1
2
0
0
0
0
2
0
1
1
0
1
0
0
0
0
2
2
0
0
0
1
2
0
0
0
0
2
1
0
1
0
1
0
1
0
0
1
0
0
2
0
1
0
1
0
0
0
5
0
2
0
0
0
0
0
0
0
2
0
0
1
1
1
0
2
2
0
0
0
0
0
2
0
1
2
0
0
1
0
0
0
0
2
1
2
0
0
0
2
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
2
3
2
2
0
0
0
0
2
0
2
2
0
2
0
0
0
1
0
1
0
0
0
0
0
0
2
0
2
2
0
3
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
1
0
0
2
1
0
0
0
1
1
0
0
0
0
0
0
0
2
0
1
1
2
0
0
1
0
1
0
1
1
0
0
1
2
1
0
2
1
1
0
0
2
0
0
0
1
0
0
1
1
0
0
1
3
0
3
0
0
1
7
0
2
1
0
2
0
0
2
0
2
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
1
0
2
0
0
0
0
3
0
2
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
2
0
2
0
0
0
0
3
0
1
0
0
0
0
0
0
0
1
0
2
0
4
1
0
0
0
0
0
0
2
0
2
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
1
0
0
2
1
1
2
0
0
2
0
0
0
0
1
2
1
0
0
0
2
0
2
0
2
1
1
0
0
0
0
0
0
0
2
0
1
1
0
2
0
0
0
0
1
1
2
0
0
0
1
0
2
0
1
0
0
0
0
2
0
2
1
0
2
1
1
1
0
2
2
2
0
1
2
0
0
0
0
0
0
0
2
4
2
0
2
1
0
1
0
0
0
0
1
0
0
0
1
2
0
0
0
0
1
0
1
0
2
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
7
2
0
1
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
1
0
0
0
0
2
0
0
2
3
0
0
2
0
0
0
2
0
0
2
0
0
1
3
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
1
2
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
2
2
2
0
0
2
2
0
1
0
1
0
3
0
0
0
0
0
1
1
2
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
1
0
1
0
0
0
0
0
2
0
1
0
0
0
7
0
0
0
2
0
0
0
0
0
0
2
2
2
1
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
2
2
1
0
0
0
0
1
0
1
0
3
2
1
0
0
1
0
1
1
0
6
3
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
3
1
0
0
0
0
2
0
0
2
0
1
0
2
1
0
2
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
1
1
2
1
0
2
0
0
0
1
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
1
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
2
2
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
3
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
1
0
1
0
2
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
2
0
2
1
2
0
0
0
0
0
0
0
0
1
2
1
0
2
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
1
1
0
0
0
0
0
2
1
0
0
0
0
1
2
0
3
0
1
0
0
0
0
0
0
0
0
2
0
2
2
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
1
0
1
0
1
0
0
1
1
4
1
4
0
2
1
2
1
0
0
1
0
0
2
0
1
2
0
2
0
0
0
0
2
2
2
0
0
1
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
1
2
0
0
0
1
0
2
1
0
0
0
2
0
0
0
0
1
0
2
2
0
0
1
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
1
0
0
1
0
1
0
0
1
1
0
0
0
1
1
2
1
0
0
0
2
1
0
0
2
0
0
2
0
0
1
0
1
0
0
0
0
0
0
3
3
1
0
2
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
3
0
0
2
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
2
2
2
0
0
1
0
0
0
0
1
3
1
0
2
0
0
0
1
0
3
0
2
0
2
0
0
0
0
0
0
1
0
2
1
0
2
0
0
0
1
0
0
2
0
0
0
1
1
0
0
0
0
2
0
0
0
2
1
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
1
0
1
0
1
2
1
0
3
1
0
2
0
0
0
0
2
0
3
0
1
1
0
0
0
2
0
2
0
0
1
0
2
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
1
0
0
0
1
2
2
0
0
2
0
0
0
0
4
0
0
1
2
0
0
0
1
0
3
0
0
1
0
1
2
0
0
0
0
0
0
0
2
0
1
0
1
1
2
0
0
1
2
0
1
1
1
0
0
0
0
2
1
1
0
5
0
0
0
2
2
0
0
2
0
0
1
1
0
1
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
2
1
1
2
0
0
0
0
0
2
1
2
0
1
0
0
0
0
1
0
2
0
0
0
0
1
2
0
1
1
0
0
1
0
0
0
0
0
1
2
0
1
1
0
0
0
2
0
0
0
2
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
7
1
0
0
2
2
0
1
0
0
0
0
0
0
0
0
1
1
0
0
2
2
1
0
0
0
0
0
0
1
0
2
7
0
0
2
2
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
2
0
0
2
0
2
2
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
1
0
0
0
0
2
3
2
0
0
3
0
2
0
2
0
0
0
3
0
0
2
0
0
1
1
1
0
0
2
0
2
0
2
1
1
0
1
0
0
0
2
1
2
2
0
0
2
2
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
2
1
2
0
2
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
2
0
2
2
0
0
2
0
3
1
0
3
1
2
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
2
2
0
0
0
0
2
0
0
2
2
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
2
2
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
2
1
2
2
1
0
0
1
1
0
0
0
0
0
1
0
2
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
1
0
1
3
2
0
2
0
2
0
1
0
0
0
0
0
0
0
1
3
0
0
1
0
0
0
2
0
0
2
0
0
1
0
0
2
0
2
1
2
0
0
0
0
0
0
1
1
0
0
0
0
2
2
0
1
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
2
0
3
0
0
2
1
1
0
0
0
0
0
0
0
0
0
2
1
2
4
0
0
0
1
1
0
1
0
0
1
3
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
2
0
0
2
0
0
0
0
2
0
6
0
0
2
0
1
0
2
2
0
1
0
0
0
0
0
1
1
0
0
1
1
0
1
0
1
0
2
0
0
0
1
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
2
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
1
2
2
0
0
0
0
1
0
0
3
0
0
0
3
0
0
0
1
0
2
0
0
0
2
0
2
2
0
3
0
0
1
2
0
2
1
0
2
0
2
0
2
0
1
0
0
0
0
4
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
3
1
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
1
2
0
0
1
0
0
0
0
2
1
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
3
0
1
0
0
0
1
2
2
0
0
0
0
0
1
1
0
1
0
0
4
0
1
0
0
0
0
0
1
2
1
0
0
0
2
1
0
0
1
0
0
3
0
0
0
0
2
1
0
2
2
0
0
0
0
0
0
0
0
0
2
2
3
0
2
0
1
0
2
0
0
0
0
1
0
2
0
0
0
0
1
0
3
0
1
0
0
0
5
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
1
0
0
0
1
1
2
0
0
1
0
2
1
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
2
1
1
2
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
1
0
1
1
0
0
0
0
0
0
1
0
0
3
2
2
0
0
1
1
1
0
0
0
2
0
2
0
0
0
0
2
0
1
0
1
0
0
0
1
0
1
0
1
2
0
2
0
0
1
0
0
0
1
0
0
0
0
1
4
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
1
0
0
1
1
1
0
0
2
0
0
0
1
0
0
2
1
0
0
0
1
1
2
0
0
4
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
2
0
2
1
0
1
1
0
1
1
0
1
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
3
0
1
0
0
0
2
0
2
2
1
2
2
0
0
1
0
2
1
1
1
1
0
0
2
0
1
0
0
2
0
1
1
2
2
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
2
2
0
0
1
1
0
0
0
0
0
0
1
2
0
1
0
0
1
2
0
0
0
0
0
0
2
0
1
2
1
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
3
2
1
2
0
0
0
0
0
0
0
3
1
0
5
0
2
6
0
4
0
0
0
1
0
3
0
1
0
0
0
0
0
0
0
2
0
1
0
2
1
0
2
0
2
1
0
1
3
0
1
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
1
0
0
0
3
1
0
1
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
2
0
1
0
0
4
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
2
0
0
0
0
0
2
2
2
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
1
1
0
0
1
1
2
0
2
0
0
1
0
0
0
1
1
0
0
0
2
0
2
0
0
0
0
2
0
0
2
0
0
0
1
1
0
0
0
1
2
1
0
0
0
0
1
0
1
1
0
1
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
1
0
2
0
0
1
0
1
0
2
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
1
0
5
2
0
1
0
0
0
0
1
0
2
0
1
2
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
3
0
1
0
0
1
2
0
0
0
0
0
2
2
0
0
0
2
0
0
1
0
0
1
2
2
0
0
0
2
0
0
2
0
0
2
1
2
0
0
0
0
0
1
2
0
2
1
0
0
0
0
0
0
2
0
1
0
1
2
0
0
0
0
1
0
0
3
1
6
0
0
2
2
0
0
0
0
1
0
0
2
0
1
0
0
1
0
0
0
1
0
1
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
2
2
2
0
0
0
2
0
0
0
0
2
2
1
0
0
0
0
0
1
2
0
1
1
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
3
0
0
1
0
0
0
0
2
1
0
0
2
1
0
0
0
2
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
2
1
1
0
0
2
0
2
0
0
1
0
0
2
0
1
2
0
0
2
1
3
1
0
0
0
0
0
2
0
0
0
0
1
0
7
2
0
0
0
2
1
0
0
1
2
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
2
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
1
2
1
2
1
0
0
0
1
0
0
2
1
2
0
0
1
1
2
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
3
2
3
2
2
0
0
0
2
0
1
1
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
1
0
1
1
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
1
2
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
11
3
0
2
0
0
0
1
2
0
0
1
0
0
0
0
1
0
2
2
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
3
0
4
1
0
1
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
3
0
0
0
0
1
0
2
1
1
0
0
0
1
3
2
0
0
2
0
0
2
0
0
2
0
3
0
1
0
1
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
2
1
0
1
0
0
1
2
2
2
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
4
0
2
0
0
0
0
0
0
2
0
0
1
1
0
1
1
2
2
1
3
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
1
0
0
0
2
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
2
0
1
0
2
0
2
0
0
0
2
2
0
0
0
0
1
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
2
0
1
3
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
1
4
0
1
1
0
0
2
0
0
0
2
0
0
0
0
2
2
0
2
1
1
2
0
0
1
0
0
1
0
3
2
0
1
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
1
0
2
2
0
1
0
0
0
0
2
0
0
1
1
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
2
0
2
0
0
0
1
1
0
2
0
0
0
0
2
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
1
2
2
2
0
0
0
0
0
2
0
0
1
0
0
2
0
2
0
0
0
2
0
1
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
2
1
0
0
3
0
2
2
1
0
0
0
1
2
0
0
1
0
1
1
0
0
1
2
0
1
0
0
0
2
1
0
0
0
0
0
0
1
0
0
2
1
2
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
1
2
0
0
2
0
2
5
0
2
0
0
0
2
0
1
0
1
0
2
0
2
0
0
0
1
2
1
0
0
0
0
1
0
2
0
0
1
0
0
1
0
1
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
1
0
2
0
0
1
1
0
3
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
1
2
0
0
3
2
2
0
2
0
2
1
0
0
0
0
0
0
0
1
1
2
1
0
0
0
0
2
1
2
0
0
2
0
1
2
2
3
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
1
0
0
0
2
1
2
0
1
0
0
0
1
0
1
0
0
1
0
0
0
2
2
0
0
0
0
0
1
0
1
2
1
1
0
0
1
0
0
0
2
0
0
0
2
1
2
0
1
0
1
1
0
0
0
1
2
0
0
1
0
2
2
2
0
0
0
1
0
0
0
0
0
0
1
0
1
2
0
0
1
0
0
0
2
2
0
2
0
0
2
0
0
0
1
0
0
0
0
1
0
0
2
0
1
0
0
2
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
2
0
2
0
0
1
0
0
2
0
1
1
1
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
1
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
1
2
0
0
2
2
0
0
1
2
2
1
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
2
1
0
2
0
1
0
3
1
0
3
0
0
1
0
0
2
0
0
1
0
0
1
0
0
1
2
2
0
0
0
0
0
1
2
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
1
2
0
1
0
1
0
0
0
1
0
1
2
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
2
2
1
0
0
0
0
0
0
2
2
1
2
0
0
0
0
0
0
0
0
0
2
2
1
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
1
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
3
0
1
2
2
1
0
1
0
2
1
1
0
2
0
0
0
3
0
0
0
0
1
7
0
0
0
0
0
2
4
5
0
0
0
2
0
3
0
0
0
2
2
0
1
1
2
0
0
1
0
0
1
1
1
0
0
0
0
2
0
0
0
0
2
1
0
2
0
0
0
2
0
0
2
0
0
0
0
0
2
2
1
2
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
3
0
0
2
1
0
0
1
0
2
0
0
1
2
0
0
2
1
0
0
0
0
1
0
0
0
1
1
2
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
1
1
0
1
0
1
0
0
0
2
0
0
0
0
0
0
5
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
2
0
0
2
1
0
2
0
0
1
1
0
1
1
2
0
0
0
0
0
0
1
1
3
0
0
0
3
1
0
0
0
2
1
0
0
2
1
0
0
2
0
2
1
0
2
0
0
1
0
1
0
2
2
1
1
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
2
0
2
1
0
0
0
2
0
0
1
1
2
1
2
0
1
0
3
1
0
0
0
0
1
2
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
1
1
0
2
0
2
0
1
1
0
0
2
0
0
2
2
0
2
1
0
1
0
2
2
2
1
0
0
0
0
0
1
2
2
0
2
0
2
4
0
0
1
1
0
1
0
0
0
1
0
0
1
0
0
0
2
2
0
2
2
1
0
0
0
0
2
0
2
0
0
2
1
0
1
3
0
1
0
0
1
0
0
0
1
2
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
3
0
0
0
2
0
0
1
0
1
0
0
0
2
0
0
1
1
0
0
0
0
2
0
2
1
0
2
0
2
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
1
2
0
2
1
0
0
0
1
1
1
0
0
0
0
0
0
1
2
1
2
1
2
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
1
0
0
1
0
0
0
2
1
0
0
0
4
0
0
0
0
0
2
3
0
0
0
0
0
1
0
2
0
0
3
2
0
0
0
1
0
0
0
0
1
1
0
0
2
0
0
0
0
0
2
1
0
0
1
2
3
0
0
1
2
3
1
0
0
0
3
0
0
1
2
3
3
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
1
1
1
0
0
2
0
0
0
2
0
0
0
1
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
1
2
2
0
0
0
2
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
1
3
1
0
1
2
0
2
0
2
1
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
2
1
2
1
0
0
2
0
1
0
0
3
0
0
0
0
1
0
0
0
1
0
0
2
1
2
0
1
1
2
0
0
0
0
1
1
2
0
0
0
0
0
1
2
0
0
0
0
1
1
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
2
2
0
0
1
0
1
0
0
0
3
2
0
0
2
0
0
0
0
2
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
3
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
2
2
2
0
1
2
0
0
0
0
0
1
0
2
1
1
0
0
2
0
0
0
1
0
0
4
0
0
0
1
0
1
2
0
1
0
0
1
0
0
1
1
0
2
0
0
2
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
3
0
0
0
2
0
2
0
2
0
0
0
0
2
0
0
0
0
2
2
1
0
1
0
1
0
1
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
2
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
2
0
5
2
0
0
3
0
2
1
2
0
2
0
0
1
1
0
0
2
0
0
0
2
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
2
2
2
2
0
0
0
0
1
2
0
1
0
0
2
2
1
0
2
0
0
0
2
0
0
0
0
0
1
1
1
1
0
1
0
0
2
0
1
0
0
0
0
0
0
0
1
1
0
1
2
1
0
0
0
0
2
1
1
0
0
0
0
0
0
1
0
1
0
1
0
9
0
0
0
3
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
5
0
3
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
2
2
1
2
0
0
0
1
0
0
2
1
0
1
0
1
4
0
0
2
0
1
0
0
0
2
2
0
0
1
0
0
1
0
0
2
1
2
0
0
0
0
0
1
1
0
0
0
0
3
1
2
1
0
1
2
1
0
0
0
0
0
0
0
1
0
0
0
0
2
2
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
1
3
2
0
0
2
0
0
0
2
0
0
0
2
1
0
0
0
0
0
1
2
2
2
0
0
0
0
2
0
1
0
2
1
1
0
0
0
0
0
1
2
2
0
0
0
0
2
2
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
1
2
0
0
0
0
2
0
0
1
1
2
1
0
0
1
2
2
0
0
0
0
1
0
0
0
2
0
1
0
1
2
2
0
0
2
1
0
1
0
1
0
0
0
0
0
0
3
1
0
0
2
2
1
2
0
2
0
1
0
0
0
0
0
0
0
2
0
0
1
1
0
1
2
1
0
0
2
0
0
0
1
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
1
2
1
0
0
0
2
0
0
0
1
2
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
1
0
2
1
0
0
0
2
2
1
0
0
1
0
0
1
0
0
0
1
0
3
1
0
0
0
1
2
0
0
2
0
0
0
2
3
1
0
1
1
1
0
0
0
0
0
4
0
0
1
0
2
0
0
4
1
0
2
0
1
0
3
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
1
1
2
2
0
2
0
0
1
0
0
2
0
2
0
1
2
2
0
0
0
0
2
0
1
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
3
2
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
1
0
1
1
0
0
1
1
0
2
1
0
0
1
1
0
2
2
1
1
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
2
0
1
0
1
0
1
2
0
0
0
1
2
0
0
2
2
2
0
0
0
0
0
0
0
1
1
2
1
2
0
2
0
0
0
0
0
0
0
3
3
2
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
2
2
1
0
2
2
0
0
2
2
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
3
0
1
0
2
2
0
0
1
2
0
0
0
0
1
2
0
2
1
0
0
2
0
0
0
0
0
0
2
0
0
1
1
2
1
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
1
2
0
0
2
0
0
1
1
1
0
1
1
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
3
0
0
0
0
0
1
0
2
0
0
0
0
2
1
2
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
1
0
1
0
0
1
0
3
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
6
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
2
0
0
2
2
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
3
1
1
0
0
0
0
0
0
1
2
2
1
0
1
1
0
0
0
1
0
1
1
2
0
0
2
0
2
2
0
0
1
1
0
0
0
0
0
0
2
1
0
2
0
0
2
0
0
1
0
2
1
0
0
2
0
0
1
0
0
0
2
0
2
0
0
0
1
0
0
0
0
3
0
0
1
0
0
1
1
0
0
1
0
0
0
0
1
2
0
0
0
1
0
0
1
1
0
2
0
0
0
1
0
0
0
0
0
1
0
1
0
0
2
0
1
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
4
0
0
1
0
0
0
0
0
0
2
0
0
2
0
3
0
0
0
1
1
0
0
0
0
2
0
1
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
2
0
0
3
1
1
2
0
0
2
1
0
1
0
0
0
0
0
6
0
0
2
2
0
0
2
0
0
0
2
0
2
0
0
0
1
0
0
0
0
1
0
2
0
0
2
0
0
0
0
2
1
0
0
2
2
2
2
0
1
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
1
1
0
1
0
1
2
0
1
0
2
0
0
2
0
2
0
0
2
0
0
0
0
2
2
0
0
0
1
2
0
2
0
1
0
0
1
2
1
0
0
1
0
0
0
1
0
2
0
2
1
2
0
0
1
0
1
1
2
0
3
0
0
0
0
0
2
0
0
1
1
2
1
2
1
2
0
0
1
0
2
1
0
0
1
0
2
1
0
0
0
0
0
0
1
2
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
5
0
2
2
1
0
1
2
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
2
1
2
1
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
2
0
0
0
0
0
2
2
0
1
0
2
3
0
0
0
1
0
0
0
0
0
2
2
0
0
1
0
0
1
0
2
2
1
1
2
0
0
0
0
2
1
0
0
2
0
1
0
2
0
0
1
0
2
0
2
0
1
0
2
0
2
0
2
1
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
1
0
0
2
1
0
0
2
0
0
1
2
1
0
0
0
0
1
2
1
0
1
2
0
0
0
1
0
0
0
1
0
0
0
0
1
2
0
0
1
0
0
0
1
1
0
0
1
2
0
0
1
2
1
2
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
2
0
1
0
0
1
0
0
0
2
0
1
0
1
0
2
0
0
2
0
0
2
0
0
0
1
1
2
0
0
1
0
0
0
0
3
0
0
0
0
0
2
0
0
0
1
0
2
0
2
0
0
0
2
4
0
0
1
1
0
0
0
2
0
0
0
1
0
1
0
2
2
0
0
0
0
1
0
2
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
1
0
0
0
3
0
3
0
1
3
0
0
0
0
0
3
0
1
0
0
0
0
0
0
2
0
2
5
1
0
1
2
2
0
0
0
1
0
2
0
0
0
1
0
0
0
2
0
0
0
2
0
2
0
2
0
0
0
2
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
2
1
2
1
2
1
0
0
0
0
0
0
0
2
2
1
0
2
0
0
2
0
1
0
1
1
0
2
0
0
0
1
1
2
0
0
1
0
1
1
0
0
0
2
1
1
0
2
0
1
0
2
2
0
0
0
0
1
1
2
1
0
0
2
0
2
0
0
0
3
0
3
0
1
0
2
0
2
0
1
0
0
0
2
1
0
2
0
0
0
0
0
1
0
0
0
2
1
0
0
0
1
0
2
0
1
0
0
0
0
3
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
2
2
0
2
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
1
0
2
0
3
0
0
0
0
0
0
1
2
0
1
1
0
0
0
0
0
2
3
1
0
0
0
2
1
0
0
3
0
0
1
0
0
2
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
2
0
2
0
2
0
2
0
2
0
2
0
2
1
2
6
2
0
1
2
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
2
6
1
0
1
1
2
0
1
0
0
1
0
0
1
1
1
0
0
0
0
0
2
0
1
0
1
0
0
2
0
1
1
1
0
0
0
0
0
0
0
0
0
5
1
0
0
2
1
1
2
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
3
0
0
0
1
1
0
0
1
0
0
0
0
2
1
3
0
0
1
0
2
0
0
3
1
2
0
0
1
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
1
3
0
0
1
1
0
1
1
1
2
0
0
0
0
1
1
0
0
2
0
2
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
2
2
2
0
0
2
2
0
4
1
0
2
0
0
0
0
1
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
2
0
2
0
0
0
3
2
0
2
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
4
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
2
0
1
0
1
3
0
0
1
0
0
0
2
0
1
2
0
0
2
2
5
0
0
0
2
0
0
0
2
1
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
2
0
0
0
2
2
0
2
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
3
0
0
0
0
0
0
1
2
0
2
0
0
1
0
0
2
0
2
0
0
0
0
3
0
0
0
4
2
0
0
0
1
0
1
0
0
0
2
0
2
0
0
1
0
1
0
1
3
0
0
0
0
0
0
0
3
2
0
0
0
2
0
0
2
2
0
0
1
0
0
0
1
1
2
1
2
1
3
2
1
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
2
0
3
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
1
1
0
0
0
1
0
0
2
1
2
0
0
0
0
1
0
0
0
1
0
1
0
2
1
0
3
3
2
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
1
2
2
0
1
0
1
1
0
0
2
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
1
1
1
0
0
0
2
1
0
0
0
0
1
1
0
1
0
2
0
0
1
1
2
1
0
3
0
0
1
0
0
0
2
2
1
0
2
0
0
0
0
2
0
0
0
2
2
0
0
1
0
0
0
0
1
1
0
1
0
2
0
0
0
0
2
0
1
0
0
3
2
0
3
2
2
2
1
0
0
0
1
0
0
2
0
0
0
0
1
3
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
1
0
2
1
0
2
0
0
0
0
0
3
0
0
0
0
1
0
0
0
1
0
0
0
1
0
2
0
0
0
5
0
0
1
2
2
0
2
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
1
0
2
0
0
0
1
0
0
1
2
0
0
0
0
0
1
0
0
0
0
2
0
2
1
0
0
2
0
3
0
0
0
1
0
0
0
0
4
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
1
0
0
2
1
0
1
0
0
2
0
2
2
2
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
2
1
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
2
2
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
3
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
2
0
0
3
0
1
0
2
1
0
0
1
1
0
0
0
0
0
2
0
0
2
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
2
2
0
2
0
1
0
0
1
0
2
1
0
1
1
0
1
0
2
2
2
2
0
0
3
0
0
2
0
0
0
2
0
1
2
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
2
1
0
0
1
1
1
1
0
1
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
3
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
4
0
2
0
0
0
7
0
1
0
0
0
1
0
0
2
1
0
0
2
0
2
1
0
0
2
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
5
0
0
0
1
0
0
0
2
2
0
0
0
1
0
1
2
0
0
0
0
2
0
1
1
0
0
0
1
0
0
1
0
0
0
4
1
0
0
1
0
3
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
7
1
0
0
0
0
4
2
0
0
1
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
2
1
0
0
1
7
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
1
0
0
0
1
0
1
2
0
2
0
0
0
1
0
0
2
0
0
1
2
1
0
2
2
2
1
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
2
1
1
0
0
0
0
0
1
0
1
0
0
1
2
1
0
0
0
0
1
0
1
0
1
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
2
0
2
0
0
0
0
2
0
0
1
1
0
0
1
0
1
1
1
0
0
0
2
1
0
2
2
1
0
0
2
0
0
2
0
0
2
5
1
0
0
2
0
3
1
0
0
0
3
0
0
0
0
1
0
2
2
1
0
2
0
0
0
1
2
0
0
2
0
1
0
0
0
0
0
0
0
2
0
2
1
2
0
0
2
0
0
0
0
1
0
1
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
3
0
0
1
1
2
1
0
2
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
2
1
2
0
0
2
0
2
1
1
0
0
0
0
0
2
0
0
0
2
1
0
0
2
0
0
0
1
0
2
1
0
2
1
0
2
0
0
0
0
0
0
1
1
2
0
0
0
0
2
1
1
0
0
1
3
0
1
2
0
0
0
0
2
2
2
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
3
1
2
0
0
2
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
2
0
0
2
1
0
0
0
0
1
2
0
2
4
0
0
2
2
0
2
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
2
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
1
0
0
2
0
4
0
1
0
0
0
0
3
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
1
1
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
1
2
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
3
0
0
2
0
0
0
1
0
0
0
0
1
1
0
2
1
0
0
0
2
0
0
1
0
0
0
0
0
1
0
2
0
0
2
0
0
1
0
0
4
0
0
1
0
1
1
3
0
2
0
4
0
0
2
2
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
2
0
0
0
0
1
0
0
1
2
0
0
2
3
2
0
1
0
2
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
1
2
0
2
2
0
2
0
0
0
1
1
1
0
0
8
1
0
0
0
0
0
1
0
0
0
1
1
0
0
1
1
0
2
0
0
0
1
0
0
0
1
1
0
1
0
0
2
0
0
0
0
2
1
2
0
2
0
1
1
1
0
2
1
0
0
2
2
3
0
0
3
0
0
2
2
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
1
2
0
0
1
0
0
2
0
0
1
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
2
1
4
0
2
0
1
0
1
1
2
0
0
0
0
0
1
0
2
0
0
0
1
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
2
2
0
0
0
5
0
0
1
2
0
1
0
0
0
0
1
0
0
0
2
0
0
0
2
2
2
2
1
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
1
1
2
1
0
4
2
0
2
0
2
1
0
0
0
2
3
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
1
3
0
0
0
3
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
2
0
1
0
0
1
0
0
0
1
1
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
1
2
0
1
0
0
2
0
0
3
2
0
0
1
0
0
0
0
0
2
0
0
0
1
0
2
1
0
1
0
0
0
0
1
1
0
0
0
0
2
0
1
0
0
0
0
1
1
0
0
0
0
2
1
2
0
2
0
3
0
1
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
3
1
0
0
2
0
0
2
0
0
2
1
0
0
3
1
2
0
0
0
0
1
4
2
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
1
2
0
2
0
1
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
1
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
2
2
2
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
2
0
2
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
1
0
0
0
0
2
1
0
0
2
0
0
0
1
0
0
0
1
0
2
3
0
1
0
0
0
0
4
1
0
0
1
0
0
0
1
2
0
0
0
1
0
0
2
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
4
0
2
3
0
0
1
0
0
1
0
0
0
2
2
1
0
0
0
3
1
1
0
0
0
0
0
0
0
2
1
0
0
0
0
1
1
1
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
1
1
0
0
2
0
0
0
2
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
1
0
1
2
2
1
2
0
0
0
2
1
0
0
0
0
0
0
2
1
0
0
0
1
0
2
0
2
0
0
0
3
0
0
0
2
0
0
1
0
0
0
0
0
2
2
3
0
1
0
1
0
0
0
2
1
0
0
0
0
2
2
0
1
0
2
2
0
2
0
0
0
0
0
0
2
0
1
1
0
0
0
0
1
2
0
0
2
0
0
2
1
0
1
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
2
0
1
0
7
0
0
0
0
1
0
0
0
0
2
2
0
2
2
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
3
1
0
0
0
2
0
0
0
0
1
2
0
1
0
0
0
2
2
0
0
0
1
0
1
0
2
1
0
1
0
0
0
0
1
2
1
0
0
1
0
0
1
0
2
0
0
0
2
1
0
0
2
4
3
0
0
3
0
0
2
0
1
0
0
1
0
0
2
2
0
0
0
1
0
0
1
0
0
0
0
0
0
5
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
4
2
0
0
1
0
1
0
2
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
2
1
0
2
2
1
2
0
1
2
0
0
0
2
0
0
0
0
0
1
2
0
2
1
0
0
0
1
1
2
0
4
0
2
0
0
0
0
1
2
2
0
1
1
0
0
0
0
0
0
0
0
0
0
4
0
0
2
0
2
0
1
0
0
0
0
3
0
0
0
0
2
0
1
2
1
0
2
2
2
0
0
0
0
0
0
2
2
1
0
0
2
1
0
0
0
2
1
0
0
1
0
3
2
0
2
2
1
0
0
1
0
0
0
1
0
2
0
0
2
0
2
0
0
2
0
0
2
0
1
0
0
2
0
0
0
0
0
0
1
0
0
3
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
5
2
0
0
1
0
2
2
0
1
0
1
0
4
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
2
2
0
0
0
0
0
0
1
0
0
0
3
2
0
1
0
0
2
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
2
2
0
0
0
0
2
2
1
0
0
2
0
2
0
0
0
0
0
0
1
3
0
0
1
0
0
0
1
0
2
3
0
0
1
0
1
1
0
0
0
2
0
0
0
2
0
0
0
0
0
2
2
0
0
1
2
3
0
1
0
0
2
0
2
0
0
0
1
4
0
0
3
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
2
1
2
0
2
2
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
2
0
0
3
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
1
0
1
0
0
0
1
1
0
0
0
0
0
1
0
1
1
2
2
0
3
2
2
1
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
2
0
0
0
0
1
0
0
2
0
0
0
0
1
0
1
0
1
2
1
0
1
0
0
0
3
0
1
2
1
2
0
0
0
0
2
1
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
1
0
2
1
1
0
0
0
0
1
2
1
0
0
1
2
1
1
0
0
0
2
0
2
0
0
0
0
0
0
2
2
1
0
2
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
2
0
0
1
0
1
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
2
1
2
0
1
0
1
0
1
0
0
3
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
3
1
1
0
0
0
1
0
0
0
1
2
0
0
0
0
2
0
3
0
0
2
2
0
0
0
0
0
2
6
0
0
1
0
0
0
1
0
2
3
3
0
0
1
2
2
0
5
0
1
1
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
2
1
0
2
0
0
0
0
0
0
1
2
0
0
0
0
1
0
6
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
2
2
1
0
0
0
2
0
0
0
2
0
0
0
0
0
2
2
0
1
0
0
0
0
1
0
1
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
2
0
5
2
4
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
2
1
0
0
2
1
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
6
0
1
1
2
0
0
2
0
1
1
0
0
0
0
0
3
0
0
0
1
1
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
2
1
2
2
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
1
1
0
0
3
0
0
0
0
0
0
0
0
0
2
1
3
0
0
2
0
2
0
0
0
0
2
0
1
0
0
2
0
0
1
0
0
1
1
2
0
1
0
0
3
0
0
0
0
0
0
0
2
0
0
2
2
2
0
0
0
2
0
0
2
2
0
1
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
4
0
0
2
1
2
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
1
0
2
0
0
0
1
0
0
0
0
1
1
0
1
1
0
0
0
2
0
1
2
0
0
0
1
2
0
1
1
3
2
0
1
1
0
0
0
1
1
0
0
0
1
0
0
2
0
2
1
0
0
0
0
0
0
0
1
3
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
1
0
1
0
2
2
0
2
2
6
2
3
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
1
0
3
2
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
1
0
0
0
2
4
0
0
0
0
0
0
2
0
0
1
3
1
0
0
2
0
0
0
0
2
2
0
0
1
0
2
2
0
0
0
0
0
0
1
1
1
0
0
0
2
0
0
5
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
1
0
0
0
2
0
0
1
0
0
0
2
0
0
0
2
0
2
2
3
1
2
0
0
0
1
0
0
0
1
1
0
1
0
0
0
1
2
0
0
4
0
0
0
0
0
0
1
0
0
4
0
0
1
2
0
0
0
0
0
0
1
1
1
2
0
0
1
2
0
3
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
1
1
0
0
0
2
1
0
2
0
1
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
1
1
2
0
2
0
2
1
1
1
0
3
3
0
2
1
0
2
1
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
2
5
0
0
1
0
0
2
0
0
0
2
2
2
2
0
2
0
0
2
2
2
0
2
0
2
1
2
0
0
0
0
0
0
0
2
1
0
5
1
2
1
0
0
0
1
1
0
2
0
0
0
0
0
0
1
0
2
1
0
2
1
0
0
0
2
0
0
1
0
0
1
0
0
0
1
1
0
0
1
1
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
1
2
0
2
0
2
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
2
1
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
2
0
1
0
1
0
0
2
0
0
0
0
2
0
1
2
0
1
0
0
1
0
1
2
0
2
0
0
0
0
0
1
1
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
2
2
1
1
1
1
1
2
0
2
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
1
0
0
0
3
0
0
2
1
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
2
2
0
2
0
0
0
2
0
0
0
0
0
0
2
2
2
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
2
2
1
1
0
1
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
1
0
2
0
1
0
0
0
0
0
0
2
0
1
0
0
0
2
1
2
0
0
0
0
1
0
2
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
1
0
0
1
0
0
3
0
2
0
0
0
0
1
0
0
0
2
0
1
0
1
0
0
4
0
1
0
1
2
0
0
0
0
0
0
0
2
0
0
1
0
1
1
2
0
0
0
0
2
0
0
2
0
1
1
0
1
0
1
0
1
0
0
1
1
0
2
2
2
0
2
0
1
0
0
0
0
1
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
2
0
3
0
0
1
2
1
0
0
0
0
0
0
2
0
1
2
0
0
2
0
0
0
0
0
1
1
0
3
0
1
0
0
0
0
1
0
0
2
0
2
2
0
2
0
0
0
0
0
0
0
2
1
0
0
1
0
2
0
0
1
0
1
0
0
0
0
0
1
2
1
0
0
0
0
0
2
1
1
0
0
1
0
1
0
0
1
1
2
3
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
1
1
0
1
0
2
0
0
0
0
2
0
0
1
0
2
2
3
0
2
0
0
0
0
0
1
1
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
1
0
0
0
2
0
0
1
0
0
2
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
1
2
0
0
1
0
2
0
0
2
2
0
0
0
2
2
1
0
3
0
0
0
0
2
1
0
0
0
1
1
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
2
2
2
0
0
0
0
0
0
0
0
3
1
1
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
1
0
0
1
0
0
0
1
2
1
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
1
0
1
3
0
2
2
2
0
2
0
0
0
0
2
0
0
0
5
0
1
2
0
0
0
0
0
1
0
0
0
0
1
0
0
2
1
0
0
0
1
0
0
1
0
0
2
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
3
0
0
1
0
1
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
2
0
0
2
1
0
0
0
0
0
1
1
0
2
0
3
2
0
0
0
3
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
1
0
2
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
2
6
0
0
0
0
0
0
2
0
0
0
0
1
2
0
3
0
0
1
2
1
0
0
0
0
0
2
2
0
0
1
0
2
1
0
1
3
1
0
2
1
0
0
0
0
0
1
1
1
0
0
0
0
1
0
2
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
2
1
0
0
2
0
0
0
2
0
0
0
0
2
1
0
0
0
0
1
0
1
1
0
0
1
1
3
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
1
2
3
0
0
0
0
0
1
0
0
0
0
0
2
3
1
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
1
1
0
1
0
2
0
2
0
2
0
1
1
0
0
0
0
0
2
2
2
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
2
2
0
2
0
0
0
0
1
0
0
2
2
1
1
2
0
0
0
0
0
0
1
0
0
2
1
2
2
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
2
0
1
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
2
0
0
0
3
2
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
1
2
2
1
0
0
1
1
0
0
0
1
1
0
0
0
0
3
0
2
1
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
2
1
0
0
1
0
0
1
0
0
1
1
0
0
1
2
1
1
2
0
0
0
0
2
0
1
1
3
0
0
0
0
0
0
1
0
0
2
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
2
2
0
0
0
2
2
0
2
2
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
3
2
2
0
0
1
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
3
0
0
0
2
2
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
1
0
0
0
1
2
2
2
0
2
0
2
2
0
0
0
0
0
0
0
1
0
2
2
0
1
0
0
0
0
0
2
2
0
0
0
0
2
0
0
1
0
2
0
0
1
0
1
0
0
0
0
0
0
0
1
0
5
2
0
2
1
2
1
0
2
1
1
0
0
0
0
0
0
0
2
0
1
2
0
0
1
2
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
3
2
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
1
0
2
0
2
2
0
0
0
1
2
2
2
0
1
1
0
0
2
0
0
0
0
3
0
0
0
0
0
2
1
2
2
0
1
2
0
0
0
0
0
0
2
0
2
0
2
1
0
3
0
0
1
0
0
0
1
2
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
2
0
2
0
1
2
0
1
0
0
1
0
1
0
1
1
0
0
2
0
2
0
4
0
6
0
1
0
2
1
0
4
0
0
2
0
2
0
0
0
0
0
0
0
0
3
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
1
0
0
2
1
0
0
0
0
0
0
2
2
2
0
1
0
1
0
0
2
0
1
2
1
0
3
0
2
0
0
0
0
0
2
1
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
1
0
4
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
2
0
0
0
1
1
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
2
3
0
0
0
3
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
2
1
0
0
0
5
0
0
0
0
2
0
0
0
1
0
2
0
2
0
0
0
1
0
1
0
0
1
2
0
0
1
0
0
1
1
0
0
0
2
1
0
1
0
0
0
0
2
2
0
2
0
0
3
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
2
0
0
2
1
0
0
0
0
1
1
0
0
0
0
2
0
0
0
3
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
1
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
1
2
0
0
2
0
1
2
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
1
2
0
0
0
4
0
2
2
0
2
0
0
0
1
0
0
0
2
0
2
0
2
0
0
0
1
0
0
0
0
0
4
1
0
0
0
0
0
1
0
0
2
0
2
1
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
2
1
2
2
1
0
0
0
0
2
0
0
2
0
0
2
2
0
1
0
0
0
1
0
0
0
0
0
0
1
2
0
0
1
2
1
0
1
0
0
0
1
0
0
0
2
0
0
1
5
0
4
0
0
0
0
1
0
1
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
1
1
2
0
0
2
0
2
1
0
0
0
0
0
1
0
0
2
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
1
0
2
0
0
0
2
1
0
1
0
0
1
1
2
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
2
1
0
0
1
0
0
2
0
1
3
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
1
1
2
0
0
0
0
3
1
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
1
1
0
2
0
0
0
1
2
2
0
0
0
1
1
0
0
1
0
1
3
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
5
6
0
0
0
0
0
0
0
1
1
2
0
0
1
1
0
1
0
0
1
0
3
0
0
2
0
1
1
0
2
0
0
0
2
0
0
2
0
0
2
2
0
1
0
0
0
2
1
0
4
0
0
2
0
0
1
0
0
1
2
1
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
2
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
1
0
0
2
0
0
2
3
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
2
2
0
1
1
0
2
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
2
0
2
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
1
0
0
3
0
0
2
0
2
1
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
2
0
2
0
0
0
1
2
0
0
0
0
0
1
0
2
0
0
0
0
2
0
1
2
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
2
0
1
2
1
0
0
3
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
1
2
2
0
0
0
1
1
1
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
1
0
0
1
0
1
0
0
1
0
1
0
2
0
0
0
2
0
2
0
0
1
0
0
0
2
0
0
0
0
1
0
2
0
0
2
0
0
0
2
0
0
1
2
1
3
0
0
2
0
0
2
2
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
2
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
2
1
0
1
1
0
0
0
0
1
0
2
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
5
0
0
0
0
0
2
1
1
2
2
0
0
0
1
0
2
2
2
0
0
0
0
5
0
0
1
0
0
0
1
0
0
1
0
0
0
2
0
0
1
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
3
0
2
0
0
0
0
0
2
0
0
0
2
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
2
2
1
2
0
1
0
0
2
2
0
0
1
0
1
2
0
1
0
2
0
0
0
0
7
0
2
0
0
0
0
0
2
2
1
3
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
1
0
0
0
2
1
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
2
0
2
0
0
3
0
0
0
0
0
0
0
2
2
3
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
3
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
1
2
0
0
2
1
2
0
0
0
0
0
0
0
1
1
2
2
2
1
0
0
0
1
0
0
0
0
2
0
0
2
0
1
0
0
0
0
2
2
0
1
0
0
0
2
0
0
0
1
0
1
0
0
0
1
0
1
0
1
0
0
2
1
0
0
1
0
0
2
0
0
1
0
1
0
0
2
0
0
2
0
1
2
0
2
0
0
1
0
3
2
4
0
0
0
0
0
0
0
1
1
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
2
1
0
0
2
3
0
2
0
0
0
1
3
3
0
0
0
0
0
1
2
0
0
1
0
2
0
3
2
0
2
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
2
2
0
1
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
4
1
0
0
1
0
1
0
0
0
1
0
1
1
1
0
1
2
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
2
1
6
3
0
0
0
0
0
0
1
0
0
0
0
2
0
0
4
0
0
2
1
2
0
0
1
1
0
0
0
0
0
0
0
1
1
1
2
2
1
0
0
2
0
0
0
3
0
1
0
0
0
0
0
2
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
2
0
1
0
0
1
1
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
3
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
1
0
2
0
1
0
2
0
4
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
2
2
3
2
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
1
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
1
0
2
2
0
0
0
0
0
0
2
0
0
2
0
1
1
0
0
4
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
2
0
1
1
1
0
0
1
0
0
2
0
1
0
0
0
0
1
0
1
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
2
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
2
0
1
0
0
1
2
0
2
0
0
0
0
1
0
1
2
1
1
0
0
0
0
1
2
2
0
0
0
1
0
0
1
0
3
1
1
2
0
2
0
0
0
0
0
0
0
1
2
1
1
1
2
0
2
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
2
2
0
0
0
0
1
0
0
1
2
0
0
4
1
1
0
0
0
2
2
0
2
0
2
0
2
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
2
1
1
0
2
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
1
0
1
1
0
0
2
2
1
2
0
1
1
0
2
2
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
1
2
0
1
0
0
2
0
0
0
0
0
1
0
0
2
1
0
0
2
0
0
0
0
0
1
0
0
0
2
2
1
0
0
0
0
1
0
0
1
0
0
2
1
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
2
0
2
5
1
0
2
0
0
2
3
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
1
3
0
2
0
0
2
1
0
1
0
0
2
0
1
1
0
0
0
2
0
0
1
0
3
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
4
0
0
0
0
1
1
1
2
0
1
1
1
1
1
0
0
1
1
0
1
0
1
0
0
0
0
1
0
1
0
1
2
0
2
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
3
1
0
0
4
0
1
1
0
0
0
0
0
2
3
2
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
2
0
0
0
0
1
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
2
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
1
0
0
1
0
0
0
2
0
0
2
0
2
3
0
0
0
1
0
1
0
1
2
0
2
0
0
0
1
1
2
2
0
0
0
1
0
0
0
0
0
3
3
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
2
0
1
0
1
0
2
0
3
0
0
1
0
0
2
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
1
0
0
1
0
2
1
0
0
0
0
0
0
1
2
0
0
2
0
2
0
0
0
2
1
0
1
0
2
1
0
0
0
0
0
1
0
0
3
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
1
3
0
2
0
0
1
1
2
1
1
2
2
1
0
0
2
0
0
0
0
2
0
0
1
2
1
0
2
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
1
2
1
1
1
2
1
2
0
2
0
0
0
0
1
0
2
2
1
2
1
2
0
2
3
0
0
0
1
1
0
0
2
1
0
0
0
2
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
2
2
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
2
1
2
0
0
1
1
0
2
0
0
0
0
0
0
1
0
0
0
0
2
2
2
0
0
2
0
0
0
0
0
0
2
2
1
1
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
3
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
1
2
0
1
1
0
1
4
2
0
3
2
0
2
0
0
0
0
0
1
0
1
0
0
0
1
1
2
0
0
0
0
0
2
0
0
1
0
0
0
2
1
2
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
2
1
0
2
0
0
2
0
0
0
0
0
0
1
0
1
0
2
0
3
0
2
0
7
1
0
0
1
0
2
0
0
0
0
1
0
1
0
0
1
2
0
1
0
0
2
2
0
0
2
1
0
0
0
0
1
0
0
2
0
1
0
0
0
0
2
0
0
0
0
1
0
0
2
2
0
0
1
0
1
0
0
1
0
0
0
0
0
0
2
1
0
2
1
1
1
3
0
2
0
0
1
0
0
2
0
0
1
0
2
0
0
0
1
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
1
0
2
1
1
0
0
0
2
0
0
2
2
1
0
2
0
1
2
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
3
0
1
0
2
0
0
4
1
1
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
4
0
1
0
2
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
1
2
2
0
0
1
1
0
1
0
0
0
0
1
3
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
2
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
1
1
2
0
2
0
2
0
1
0
1
0
0
1
0
1
0
0
0
0
2
0
0
0
0
2
0
0
2
0
4
0
1
1
1
0
0
0
1
0
2
2
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
3
2
1
0
1
1
0
1
0
0
0
1
0
0
0
2
2
0
0
0
0
0
3
0
0
0
2
0
2
0
0
2
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
2
0
1
2
2
1
2
0
2
0
0
0
0
0
0
0
0
1
1
0
2
1
1
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
2
0
2
0
0
0
0
0
2
0
2
0
0
1
0
0
1
0
1
1
0
0
1
0
0
0
3
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
4
1
4
0
2
0
1
2
0
1
1
0
0
0
1
0
1
0
0
0
0
1
3
0
3
2
0
0
0
0
0
0
0
1
1
1
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
2
1
1
1
1
0
0
2
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
1
0
2
0
0
0
0
0
3
0
0
1
0
0
2
1
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
1
0
0
2
1
0
0
2
2
4
0
0
2
2
2
0
0
0
0
2
0
0
1
0
0
1
0
1
0
0
0
0
2
0
2
2
1
0
0
0
1
0
2
0
0
0
0
0
2
2
2
1
1
0
0
0
0
0
2
0
0
2
2
1
0
0
0
0
0
1
1
0
0
0
1
0
0
1
1
2
0
0
0
0
0
3
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
1
0
3
0
0
0
1
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
3
2
0
0
1
0
2
1
0
0
0
5
0
0
2
0
1
0
2
0
0
0
0
0
0
1
0
1
2
1
0
1
2
0
0
1
0
0
1
0
1
0
1
0
1
2
0
0
1
0
1
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
3
1
0
0
0
0
2
0
0
0
0
2
0
0
0
1
2
0
0
0
1
0
0
2
0
1
0
0
1
1
2
0
0
0
0
0
0
0
1
1
1
0
0
2
1
1
0
2
0
2
0
2
0
1
2
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
2
1
2
0
0
0
1
0
1
0
0
1
2
1
2
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
2
1
2
0
0
0
0
0
0
1
2
0
0
0
2
0
1
0
0
0
0
0
2
0
2
2
0
1
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
2
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
2
0
1
0
0
0
1
0
2
0
0
0
1
0
0
0
0
2
0
0
0
1
2
2
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
1
0
1
0
0
1
2
0
0
2
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
1
1
1
0
0
0
2
0
3
0
0
0
0
0
2
0
0
1
1
2
0
0
0
0
0
0
1
0
0
1
2
1
7
1
0
0
0
0
1
1
0
0
0
2
2
1
0
0
0
0
0
3
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
2
0
1
0
2
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
2
0
0
0
0
0
2
0
0
0
0
0
0
3
0
1
1
0
2
1
1
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
2
0
2
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
1
1
0
2
0
2
3
12
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
2
1
2
1
0
1
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
2
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
1
2
0
2
0
1
3
0
0
0
0
2
0
0
0
2
2
0
1
2
0
0
0
0
0
2
0
0
0
2
0
0
1
0
2
0
1
2
0
2
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
1
0
0
0
2
0
0
0
1
1
2
1
2
2
1
0
2
0
1
0
1
1
0
0
1
0
0
0
0
2
0
0
0
1
1
2
2
2
0
0
0
0
2
1
0
0
1
0
0
0
2
1
1
0
0
2
0
1
0
0
0
0
0
3
0
0
0
2
1
1
2
2
1
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
3
0
0
0
0
0
2
0
0
2
2
2
1
0
1
0
0
0
0
3
0
0
2
2
0
1
0
0
0
0
0
2
1
0
0
1
0
0
0
0
2
2
0
0
2
0
0
0
2
0
1
0
0
0
2
0
1
0
1
0
5
0
0
2
0
0
2
0
3
2
1
1
0
2
0
0
0
0
10
0
0
0
1
3
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
2
1
0
0
0
0
0
0
1
0
0
0
2
1
0
2
0
0
1
0
2
0
2
2
0
0
0
0
1
0
0
0
0
1
0
2
2
1
0
0
0
0
0
1
3
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
2
0
0
0
0
0
0
3
0
1
0
0
1
0
0
0
1
0
0
3
0
1
0
0
2
1
0
2
0
0
0
0
0
0
1
0
1
0
2
0
0
0
1
0
1
0
2
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
2
2
0
0
0
1
0
2
0
0
0
2
0
2
0
1
2
1
1
1
0
1
4
1
0
2
1
0
2
0
2
0
0
1
0
0
1
1
0
0
1
0
0
3
2
1
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
4
7
1
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
1
0
1
0
2
1
3
1
0
0
0
0
0
0
1
2
0
2
0
2
0
1
0
0
2
0
0
0
0
0
0
0
2
2
3
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
3
0
2
0
2
1
0
0
2
1
0
0
0
0
0
2
0
0
0
2
2
2
0
0
2
0
0
0
0
1
0
0
0
2
0
0
1
1
1
0
0
0
0
1
1
0
0
0
1
2
0
1
0
0
0
0
0
0
1
0
0
2
0
2
1
0
1
0
0
0
0
0
0
0
1
2
0
2
0
1
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
2
2
0
2
0
0
1
3
0
2
0
0
0
0
1
1
1
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
1
1
0
0
1
0
2
0
0
0
0
1
2
3
0
0
0
1
1
0
1
0
1
0
2
0
0
0
1
0
4
0
0
2
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
1
0
0
2
0
2
1
1
0
0
0
1
1
2
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
2
0
0
1
1
0
0
0
3
2
2
0
0
0
0
0
2
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
2
0
0
0
1
0
1
1
0
0
0
0
0
7
0
0
0
0
2
2
1
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
1
0
0
0
0
0
3
0
2
2
1
0
1
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
2
1
0
2
2
0
0
0
2
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
2
0
3
1
0
0
0
0
0
0
1
0
2
1
0
0
0
0
1
0
2
3
1
0
0
0
0
0
0
0
1
0
3
0
1
4
0
0
0
2
0
0
0
1
2
0
2
0
0
1
0
2
2
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
1
0
1
0
0
0
0
2
1
0
2
0
1
0
0
2
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
1
1
1
0
2
1
2
0
2
0
0
0
2
0
0
0
3
1
2
2
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
6
2
0
0
1
1
2
2
0
1
0
0
2
0
0
0
1
1
0
0
0
0
1
0
2
1
0
0
0
2
2
0
2
0
0
2
1
2
1
2
1
0
2
2
0
0
2
0
5
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
1
0
1
0
0
2
0
1
0
0
0
1
0
1
0
0
0
3
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
2
1
0
1
0
1
1
0
0
0
0
1
0
2
0
2
0
2
2
0
0
1
0
0
1
2
1
0
0
0
3
0
0
0
1
2
0
1
0
0
1
0
0
1
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
1
5
1
0
2
1
0
0
0
0
1
1
0
2
0
0
0
0
0
1
1
0
0
0
0
2
1
2
1
0
2
2
1
0
0
0
0
0
2
2
1
2
0
0
1
0
0
1
0
0
2
0
0
0
1
1
0
1
0
1
1
0
0
0
1
0
0
1
0
0
1
1
0
0
1
0
1
0
0
0
0
1
0
1
0
2
0
0
2
0
0
0
0
2
0
1
0
1
1
0
0
0
0
1
1
1
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
1
0
0
2
0
3
1
0
1
0
0
1
0
0
0
2
1
0
2
2
2
1
0
0
0
0
0
0
0
0
1
0
0
2
2
0
1
0
0
0
2
1
0
0
0
1
0
1
5
0
0
0
0
1
2
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
2
0
0
0
0
2
0
0
0
2
0
2
0
0
4
1
1
0
0
0
0
0
1
2
1
2
2
0
2
0
0
2
0
2
2
2
0
0
0
0
1
1
1
0
0
1
2
0
2
0
0
0
0
0
1
4
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
1
3
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
3
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
5
0
1
0
2
1
2
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
2
1
0
0
1
0
0
0
0
3
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
2
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
1
2
0
1
0
1
1
0
0
0
0
0
0
0
0
2
1
0
2
4
0
0
2
2
0
2
2
0
0
1
2
0
1
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
1
0
1
0
0
2
0
0
1
0
2
2
0
0
4
0
2
1
0
2
0
0
0
2
0
1
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
2
0
0
1
0
0
0
1
1
0
2
0
2
0
0
5
0
0
0
2
3
1
0
0
0
1
0
0
1
0
0
2
0
2
0
2
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
1
6
0
0
0
0
0
2
0
0
2
0
1
0
1
0
1
0
1
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
1
2
0
0
0
1
0
0
1
0
0
3
0
1
0
0
0
0
1
1
0
0
0
2
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
1
0
2
2
1
0
0
0
1
1
2
0
0
2
0
0
1
0
0
0
0
2
1
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
1
0
0
1
0
0
0
2
1
0
0
0
0
2
0
0
1
2
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
2
0
1
2
0
0
0
0
0
0
1
0
1
0
6
0
1
0
0
0
2
0
0
0
0
2
2
1
0
0
0
0
0
0
0
1
0
2
0
1
1
0
3
0
0
2
0
0
1
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
1
1
1
2
1
0
0
1
2
0
0
0
0
1
2
2
1
0
2
0
1
0
0
0
2
0
2
2
2
1
0
0
1
0
1
0
0
0
0
2
2
2
1
0
0
0
0
0
0
0
2
0
0
0
2
2
1
1
2
0
0
0
2
1
0
2
1
0
1
0
0
0
2
0
0
0
0
0
1
0
3
0
1
1
2
2
0
0
0
1
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
2
2
3
2
2
0
2
0
1
0
1
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
3
0
0
0
0
2
0
0
0
2
2
2
2
5
0
0
0
0
2
1
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
2
0
0
2
2
0
0
0
0
2
0
0
0
0
2
0
2
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
2
0
0
0
1
1
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
1
0
0
3
0
0
2
1
2
2
0
0
0
0
1
2
11
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
2
2
0
0
2
0
0
2
0
2
0
0
0
0
2
2
1
0
0
2
0
2
8
3
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
1
2
0
0
0
2
0
0
4
0
2
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
2
0
1
0
0
3
1
0
2
0
1
2
2
0
0
0
0
0
1
0
0
0
0
3
0
0
1
0
0
1
0
0
2
0
0
2
1
0
1
2
0
2
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
2
2
1
3
0
0
0
0
0
0
3
3
1
0
0
1
2
0
2
2
0
0
2
0
0
1
1
0
1
2
0
1
0
0
1
4
1
2
0
1
0
0
1
0
0
0
0
0
2
2
0
2
1
0
1
1
0
1
2
2
0
1
2
1
1
0
1
2
1
2
0
2
0
1
0
1
0
0
2
0
0
2
0
0
0
0
1
0
0
2
0
0
2
1
0
1
0
1
1
0
2
0
2
0
0
0
1
0
0
0
0
2
0
1
0
2
0
1
1
0
0
2
0
0
2
2
0
0
1
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
1
2
2
3
0
0
0
0
3
1
0
1
0
0
1
0
0
2
0
4
2
0
2
0
0
0
1
2
2
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
2
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
1
7
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
1
0
0
2
0
1
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
2
2
0
0
0
2
0
0
2
3
2
0
1
7
0
1
2
0
0
0
2
0
0
0
0
0
0
0
1
1
2
2
2
0
2
0
0
0
0
2
0
0
0
2
0
2
2
2
0
0
0
2
0
0
0
0
1
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
2
1
0
2
0
0
0
0
3
0
0
1
0
0
0
2
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
2
2
0
2
0
0
1
1
0
0
1
0
1
1
0
0
2
0
1
0
1
1
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
2
0
2
0
0
2
1
1
1
2
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
2
2
0
2
1
2
5
2
2
0
2
2
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
1
0
1
2
0
0
2
2
1
0
1
0
0
0
0
2
1
0
0
0
0
0
0
1
0
1
0
0
2
0
1
1
0
2
1
1
2
1
0
0
0
0
0
2
0
1
1
0
0
1
0
1
2
0
0
1
0
1
0
1
2
0
1
0
2
0
2
2
0
1
0
0
0
1
1
0
1
2
2
0
0
0
0
0
1
2
0
1
5
0
1
0
1
1
0
0
0
2
1
4
1
0
0
0
0
2
0
0
1
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
1
2
0
0
1
0
0
2
0
0
0
1
0
0
4
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
1
0
0
0
3
0
2
1
0
2
0
4
0
0
4
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
2
1
1
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
3
0
0
2
1
0
1
1
0
0
1
1
1
0
2
1
1
0
0
0
0
1
1
0
1
0
0
0
0
3
2
0
3
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
2
0
0
2
0
0
1
0
2
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
1
0
0
1
0
0
0
0
0
3
1
0
2
2
1
0
0
0
0
0
0
0
0
2
1
2
1
0
2
0
0
0
1
0
0
0
0
2
0
1
0
0
0
2
1
2
0
0
2
0
2
0
2
0
1
0
0
0
0
1
0
0
3
2
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
2
0
1
0
2
0
0
1
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
2
2
1
0
2
0
2
1
0
0
0
1
1
2
0
0
2
0
0
0
2
1
0
0
0
2
0
0
0
0
2
1
0
1
0
0
3
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
2
2
0
0
0
0
0
0
2
1
0
0
1
2
1
0
0
0
0
0
2
0
0
1
0
4
0
1
0
2
1
1
4
0
0
0
1
1
2
3
1
1
0
2
0
0
2
1
1
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
2
3
0
1
0
2
0
0
0
0
0
6
0
0
0
0
2
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
1
2
0
0
2
0
0
1
0
1
0
0
0
2
1
0
0
2
0
1
0
3
0
1
0
0
0
0
3
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
2
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
1
0
0
0
2
0
0
0
0
0
0
2
2
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
1
1
0
1
2
0
0
0
0
0
1
1
0
0
2
2
0
1
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
2
1
0
0
0
1
2
0
0
0
0
1
0
0
3
2
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
1
2
2
0
0
0
1
0
1
1
0
2
0
2
0
0
0
2
0
2
0
1
0
0
0
0
2
0
0
2
0
0
2
0
2
0
0
3
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
1
0
0
4
0
1
1
2
1
2
0
2
2
0
2
0
1
0
1
0
0
1
0
2
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
2
0
0
2
0
0
0
1
1
1
1
0
0
0
1
0
0
0
0
0
2
2
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
3
0
0
2
0
0
2
0
1
0
2
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
2
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
2
2
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
2
2
2
0
0
0
0
2
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
1
0
2
0
0
0
0
0
2
0
0
3
0
0
2
1
1
0
0
1
0
0
2
1
0
0
1
2
2
0
1
0
0
1
0
0
0
1
2
0
0
0
0
1
0
0
0
3
0
0
0
0
1
1
2
0
0
1
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
2
2
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
2
0
2
0
1
0
0
2
0
0
2
0
0
0
2
0
0
2
0
0
1
0
2
2
1
0
0
0
2
0
0
1
0
0
1
0
2
0
2
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
4
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
2
1
0
1
1
2
2
1
0
2
1
0
0
0
0
0
0
0
0
4
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
1
0
0
1
1
0
1
1
0
0
0
0
2
0
0
2
1
0
0
0
1
1
2
0
0
0
1
1
0
2
0
0
1
2
0
0
1
0
4
1
0
0
0
0
0
0
0
0
2
0
2
0
1
0
2
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
2
0
0
0
3
2
0
0
1
2
0
0
0
0
2
0
2
1
0
2
0
0
1
0
0
0
0
2
0
1
1
0
0
0
0
0
2
0
0
2
0
1
0
0
0
1
0
1
0
1
1
1
0
1
1
1
0
0
1
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
1
0
0
3
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
4
0
0
1
1
0
0
0
0
0
0
3
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
3
0
0
1
0
0
3
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
3
3
1
2
0
2
0
0
2
2
1
1
1
2
3
0
0
0
1
1
0
0
1
0
0
0
1
0
3
2
1
0
0
0
1
1
0
0
0
0
2
1
2
1
0
0
1
0
1
0
1
2
1
0
0
1
0
1
0
0
0
0
1
1
11
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
1
2
2
1
0
0
0
2
0
1
0
1
1
0
2
0
0
0
0
2
0
2
0
0
0
1
1
0
0
0
0
0
2
2
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
1
2
0
0
2
0
0
0
2
3
0
0
0
1
0
0
4
0
0
0
0
1
0
0
0
0
0
1
0
0
3
0
2
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
2
0
2
1
0
0
2
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
1
0
2
2
0
0
1
0
0
1
0
0
0
0
0
2
0
1
0
2
0
0
1
0
0
0
0
1
2
1
0
0
0
0
0
0
2
0
0
0
0
2
0
1
1
0
0
0
0
1
2
0
0
0
0
1
1
2
0
0
2
0
0
2
0
0
0
0
0
0
0
3
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
2
2
0
1
0
2
5
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
1
1
0
0
1
0
0
0
1
0
2
0
0
0
1
0
0
0
1
3
0
0
0
0
0
0
0
0
0
1
0
0
1
0
3
0
0
0
0
0
2
0
0
0
0
0
1
1
0
2
0
2
1
0
0
0
2
0
0
1
0
0
0
3
1
0
1
0
0
0
2
2
0
0
2
0
2
0
0
0
0
1
0
0
1
0
1
0
2
0
0
0
1
3
0
2
0
0
1
0
0
2
2
0
0
1
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
1
2
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
2
0
0
1
2
0
0
0
2
0
0
0
2
4
2
0
0
1
0
0
2
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
2
0
0
0
2
0
0
1
0
0
2
0
0
0
1
2
0
2
0
0
2
0
0
0
2
0
2
0
1
2
0
0
0
1
0
2
0
2
0
2
2
1
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
1
1
0
2
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
2
0
0
1
2
0
0
0
0
1
0
0
2
0
0
2
1
2
2
0
0
0
0
0
3
2
2
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
1
1
0
0
3
0
1
0
1
0
1
0
0
0
2
0
0
0
2
2
0
2
0
0
1
0
0
0
0
0
0
0
0
1
1
2
0
2
0
0
2
1
0
0
0
0
2
1
1
0
3
0
0
0
0
0
2
0
0
2
4
2
2
1
4
0
0
0
0
2
2
1
1
0
0
1
0
0
0
0
0
0
1
1
2
0
0
0
0
0
1
0
0
3
0
2
2
0
2
0
0
2
0
0
1
1
0
0
0
0
2
0
2
0
3
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
1
1
0
0
0
2
1
0
2
0
0
1
0
1
0
0
0
1
0
5
1
0
0
1
0
0
0
0
0
3
0
1
0
0
0
0
0
0
3
0
2
2
1
1
1
2
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
1
2
0
1
1
0
0
0
1
0
2
2
1
0
0
0
0
1
1
0
1
1
1
2
2
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
2
0
0
0
1
2
0
1
0
0
1
0
2
1
0
2
0
0
0
0
0
0
0
1
0
1
1
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
2
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
2
2
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
4
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
1
0
2
1
2
1
1
1
0
2
0
0
2
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
2
0
4
0
0
0
0
0
1
4
0
0
1
1
3
0
0
0
3
0
0
0
2
1
0
0
0
0
0
2
1
0
0
2
2
2
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
2
0
1
0
0
0
0
0
1
0
0
2
1
2
0
0
0
0
3
1
0
2
0
0
0
1
0
2
0
0
0
0
0
1
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
3
0
0
0
0
3
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
1
0
1
0
1
0
0
0
0
2
2
0
1
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
3
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
1
0
2
2
0
1
0
2
0
0
3
0
0
0
0
1
2
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
1
1
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
2
1
0
2
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
2
1
2
1
0
6
2
0
1
3
0
0
0
0
0
0
2
0
2
2
1
0
0
0
0
0
0
0
0
0
0
2
1
1
2
1
0
0
1
1
0
2
0
0
0
1
1
0
2
0
0
2
0
2
0
0
3
0
1
1
0
2
0
0
0
1
2
0
0
2
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
3
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
2
0
2
0
1
0
2
0
2
0
0
0
0
0
4
2
2
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
2
2
1
1
0
0
0
0
2
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
2
0
0
1
0
0
0
0
0
2
0
4
1
0
0
0
3
2
5
0
0
1
0
2
1
0
0
0
0
0
2
0
0
2
0
2
2
0
0
1
0
2
1
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
3
2
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
1
2
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
2
3
2
0
0
0
0
0
1
0
2
0
0
0
1
1
0
0
0
2
0
1
2
1
0
0
5
0
1
1
0
0
0
1
0
2
0
0
0
2
0
0
2
2
2
0
0
0
0
2
2
0
0
0
0
2
0
0
1
0
2
0
0
0
0
2
0
0
1
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
3
2
0
0
0
0
0
1
0
1
0
0
2
0
0
1
0
2
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
2
2
0
0
2
0
0
0
2
0
1
0
0
0
0
1
1
1
0
1
1
0
0
1
0
1
0
5
2
0
0
0
0
0
0
2
1
1
0
0
0
1
0
0
2
0
1
0
0
1
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
1
2
3
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
1
0
1
0
2
0
0
1
0
0
2
0
0
1
0
0
1
0
0
0
1
0
1
0
0
2
0
0
0
2
0
2
2
0
1
0
0
1
2
1
0
2
2
2
1
0
0
0
1
0
0
0
0
0
0
0
0
1
3
1
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
1
2
1
0
0
1
2
0
0
3
1
0
2
0
2
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
1
0
0
0
2
2
0
3
2
2
0
0
1
2
1
0
0
0
0
1
0
0
1
0
2
0
1
0
0
0
0
0
2
2
0
0
0
1
2
5
0
0
1
1
0
0
0
1
0
2
0
1
2
0
1
1
0
2
0
0
2
0
0
0
0
1
2
2
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
1
0
2
0
0
1
0
0
1
0
1
0
0
0
0
0
0
2
0
0
2
0
1
1
3
0
1
1
0
0
0
2
0
1
2
0
1
0
0
0
1
0
0
2
0
2
0
2
0
0
2
0
0
1
2
2
0
1
0
0
0
0
0
1
0
2
0
1
3
1
0
0
2
0
0
0
1
2
1
0
1
1
2
2
0
0
0
0
0
1
0
1
1
1
2
0
0
0
0
2
1
2
0
0
1
1
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
3
0
0
0
2
0
1
0
2
2
0
1
1
1
0
2
0
1
0
2
2
1
1
0
1
1
1
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
2
0
1
0
1
0
0
0
3
1
0
1
0
1
0
0
0
0
0
0
1
2
0
0
0
3
1
1
2
0
0
3
2
3
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
2
0
0
2
2
0
1
0
0
0
0
0
2
0
2
2
0
1
0
0
0
2
0
0
1
1
1
0
0
1
0
1
3
0
2
0
0
1
0
2
1
0
2
1
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
4
0
1
2
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
1
1
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
1
0
0
0
0
1
2
2
0
0
0
0
0
1
0
0
0
0
1
1
0
1
2
0
0
0
0
0
1
0
2
0
0
0
0
1
0
2
0
0
0
1
2
0
0
0
0
0
0
0
1
2
2
0
1
0
0
2
0
0
1
2
0
0
1
0
0
0
2
0
0
1
1
2
0
1
0
0
0
0
0
4
1
2
1
0
0
0
0
0
0
0
2
1
0
0
2
1
0
0
0
4
0
0
0
1
0
2
1
0
0
0
0
0
2
0
0
1
2
1
0
0
0
1
0
0
0
0
0
0
0
1
1
2
4
0
1
0
0
0
0
2
0
2
2
0
2
1
1
1
0
0
0
0
0
1
0
0
1
0
2
0
0
0
2
0
0
0
2
0
0
0
1
1
2
0
0
0
0
0
0
0
0
2
0
0
4
2
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
1
3
1
2
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
2
0
0
0
1
2
1
0
0
1
0
0
0
0
0
0
0
0
1
0
2
1
2
2
0
0
0
1
0
0
1
2
0
0
0
0
1
1
0
0
2
0
0
0
1
0
0
0
0
0
1
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
1
2
1
1
0
0
3
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
1
3
2
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
2
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
3
1
0
0
2
0
0
1
2
0
1
2
0
0
4
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
1
1
1
0
0
0
0
2
2
1
1
0
0
0
0
0
3
0
0
0
0
0
1
1
0
0
0
0
2
1
0
0
1
0
1
0
0
0
1
1
0
0
0
1
0
2
3
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
1
0
0
1
0
0
0
2
1
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
2
0
1
2
1
0
0
2
0
1
0
2
0
2
1
0
0
0
1
0
0
0
2
2
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
1
1
0
0
0
2
0
0
1
0
0
2
0
1
0
0
1
2
2
2
0
0
0
0
1
1
0
2
0
0
0
0
0
0
1
0
0
1
0
1
0
2
0
0
1
1
0
0
1
0
0
0
3
0
0
0
0
2
0
2
0
0
0
1
1
0
0
1
0
0
0
1
0
0
1
2
0
2
0
0
0
0
0
1
0
0
0
1
0
0
2
1
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
1
0
0
3
1
0
0
2
0
0
0
1
0
0
0
0
1
1
0
0
0
0
2
1
0
2
0
2
0
0
0
1
2
0
0
1
2
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
1
0
2
3
0
2
0
0
0
0
2
1
0
1
0
2
0
1
0
0
0
0
1
2
2
0
0
3
0
0
1
0
0
2
0
2
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
3
1
1
0
2
0
0
4
0
0
0
0
0
0
0
2
2
0
1
0
1
0
1
0
0
2
1
0
1
0
0
0
0
2
0
0
1
0
2
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
2
0
1
0
1
1
0
2
0
1
0
0
2
0
2
3
1
0
0
0
0
3
0
1
2
0
2
0
0
5
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
1
2
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
1
0
1
0
2
0
1
0
0
3
2
0
2
0
2
0
2
1
1
0
0
2
0
1
0
0
0
1
1
0
0
2
1
2
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
1
0
2
0
0
0
2
0
0
1
0
0
0
0
0
2
1
2
1
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
2
0
1
0
1
1
2
5
2
3
2
2
0
2
0
0
2
1
2
1
0
2
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
3
0
0
0
0
2
0
2
0
0
1
0
1
0
2
0
2
1
0
0
1
0
0
0
0
2
0
1
1
0
0
1
2
1
0
0
1
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
1
0
3
0
0
0
3
0
0
0
2
0
0
2
0
2
0
0
1
2
0
0
3
2
1
0
0
0
0
2
0
1
0
0
0
2
2
0
2
0
0
1
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
1
0
0
1
2
0
3
3
1
0
0
0
1
1
1
0
1
0
0
1
0
2
0
1
0
0
2
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
2
0
2
2
0
2
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
1
0
1
0
1
0
1
0
0
2
2
0
0
0
0
0
0
1
0
0
3
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
2
2
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
1
0
1
0
2
0
0
2
2
2
0
1
2
0
1
1
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
2
0
1
0
1
0
0
2
0
0
1
2
0
1
0
0
0
1
0
0
0
1
0
0
2
0
0
2
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
2
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
1
0
2
0
0
0
0
0
2
0
0
0
3
0
0
3
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
2
0
1
2
3
0
3
0
0
1
0
0
4
1
0
1
0
0
0
0
0
0
0
1
0
1
2
0
2
2
1
0
0
1
0
0
1
0
0
1
0
0
2
0
2
1
0
0
4
0
0
0
0
1
0
1
0
0
1
0
0
1
1
0
0
0
1
1
2
0
0
7
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
2
1
0
1
1
0
0
0
2
0
0
1
0
1
1
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
3
2
0
0
2
3
1
1
0
0
2
0
0
0
2
1
0
1
3
1
0
0
2
1
0
1
0
0
0
0
0
0
2
0
2
1
0
0
2
0
1
0
1
0
1
0
0
0
0
0
2
0
0
2
0
0
1
0
2
2
0
0
3
0
0
1
0
0
2
0
0
0
1
1
0
2
2
1
0
2
2
0
0
0
0
0
2
0
0
0
0
0
1
1
0
2
1
1
0
0
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
3
0
1
0
0
0
2
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
2
0
1
0
2
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
3
2
0
0
0
0
0
0
3
0
0
2
1
2
2
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
2
0
0
1
1
0
1
0
0
1
0
0
2
1
0
0
0
1
2
0
0
0
0
2
2
2
0
4
0
2
1
0
0
0
0
0
1
0
1
0
0
0
1
2
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
3
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
1
3
0
2
0
1
0
1
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
2
0
2
1
1
0
0
0
1
1
0
1
0
1
0
1
0
0
0
0
2
0
0
0
1
2
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
5
0
0
0
1
0
0
0
2
2
0
1
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
2
0
0
0
2
0
0
4
0
1
2
0
0
1
2
0
0
1
1
1
0
2
0
0
0
1
0
2
1
0
1
1
0
0
0
0
2
0
3
0
0
2
0
0
0
0
1
0
0
2
2
2
2
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
5
0
0
2
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
2
0
2
0
0
0
0
2
2
2
0
1
2
0
1
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
1
0
0
1
0
2
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
2
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
2
0
0
0
0
0
0
0
1
3
0
2
0
1
0
0
2
3
1
0
1
0
2
0
2
0
0
0
0
0
1
0
0
3
0
0
1
1
0
0
2
1
0
0
0
1
2
3
2
0
0
1
0
1
1
3
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
2
0
0
0
0
0
1
0
1
2
2
0
0
0
2
0
0
0
0
0
1
2
0
0
2
3
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
4
0
2
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
2
1
0
0
1
0
1
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
2
0
1
0
1
2
0
1
0
0
1
0
0
2
0
0
0
0
2
0
3
0
0
1
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
3
0
0
1
0
1
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
1
1
0
0
1
2
0
0
1
0
0
4
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
3
6
0
2
1
0
2
1
0
0
0
2
0
0
0
0
0
2
0
1
0
1
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
2
0
1
0
2
0
0
1
0
3
1
0
2
0
2
2
0
1
2
0
0
0
0
0
1
0
0
2
0
2
2
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
1
3
0
1
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
2
0
2
0
1
0
1
0
0
1
1
2
0
0
2
1
0
1
1
2
2
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
2
1
1
2
2
0
0
0
1
0
0
0
0
1
1
0
0
0
0
3
1
7
0
1
1
0
2
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
2
1
0
0
0
2
1
0
0
0
0
2
0
0
0
2
0
1
0
0
0
2
0
0
1
2
2
0
0
1
2
0
2
2
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
4
2
1
0
0
2
0
0
0
0
0
1
0
0
0
1
1
7
1
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
5
1
0
1
1
0
1
2
0
1
0
1
0
1
2
0
0
0
0
0
2
2
0
0
2
2
0
0
0
0
2
0
2
2
0
0
0
1
0
0
2
2
0
2
2
0
1
0
1
1
0
0
0
0
0
0
1
2
2
0
0
0
0
1
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
1
1
0
2
1
2
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
1
2
1
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
3
1
0
1
0
0
1
1
1
0
0
0
2
1
0
0
0
0
0
1
0
0
0
1
2
0
2
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
2
0
0
0
0
0
0
2
0
0
2
0
2
3
2
2
1
0
1
1
0
2
2
2
2
0
0
0
0
0
0
0
1
0
0
2
1
0
2
0
0
1
0
1
0
0
0
2
1
0
0
2
2
0
0
1
2
0
0
0
0
0
5
0
0
2
2
0
0
0
0
3
1
0
0
0
4
0
2
3
2
1
0
1
0
2
0
1
2
2
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
2
1
1
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
1
0
3
2
0
2
0
0
2
0
0
0
2
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
2
0
3
0
2
0
1
0
0
0
2
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
2
1
0
2
0
0
0
1
0
1
3
0
2
0
1
2
4
0
0
0
0
0
0
0
0
1
1
0
0
0
3
0
1
0
0
2
0
0
0
1
2
0
0
2
0
2
2
0
2
0
0
2
0
0
0
3
0
0
2
0
1
0
1
0
0
0
2
1
0
0
0
0
2
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
1
0
0
2
0
1
0
0
0
0
2
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
2
2
0
0
2
0
0
0
0
0
1
0
1
0
0
3
2
2
0
0
1
0
1
0
0
0
1
0
0
1
1
0
0
1
0
1
0
1
0
1
0
2
0
2
0
0
2
0
0
2
0
0
0
1
2
1
1
1
0
0
1
0
0
0
0
0
0
1
0
2
1
1
0
1
0
0
0
0
2
0
0
2
1
0
0
0
0
0
1
2
0
3
0
2
0
0
0
0
0
0
2
1
1
2
0
0
0
0
0
1
0
0
1
0
0
2
0
2
2
0
0
0
0
1
0
1
0
0
0
0
0
4
0
0
0
0
2
0
1
2
0
0
0
1
1
0
0
0
0
0
2
2
0
0
3
2
0
2
0
0
0
2
0
1
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
3
0
0
1
0
1
0
1
0
0
0
0
2
0
0
0
1
1
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
1
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
4
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
2
1
0
0
2
0
1
0
2
1
0
0
0
0
2
0
2
1
0
0
2
0
0
0
2
1
0
0
0
0
2
1
3
0
1
0
0
1
1
1
2
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
2
0
2
0
0
1
2
2
0
0
0
1
2
0
2
0
0
0
1
1
0
0
0
0
1
1
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
2
0
3
0
0
2
0
0
1
0
0
3
1
1
0
0
0
1
1
1
2
0
0
0
0
0
0
0
1
1
2
2
1
2
1
0
0
1
1
1
0
0
1
0
0
0
0
0
0
1
0
2
1
2
0
0
0
0
3
0
0
1
0
0
0
0
2
1
0
0
1
0
1
0
0
0
1
4
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
2
2
0
0
1
0
1
2
0
1
0
0
3
0
0
1
0
0
2
0
0
1
0
1
2
0
1
2
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
3
2
1
2
1
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
2
0
1
0
1
0
0
1
1
1
0
0
1
0
0
2
0
0
2
0
1
1
2
0
2
1
1
0
1
0
0
0
1
2
0
0
0
0
0
2
2
1
1
2
0
3
0
2
2
0
2
2
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
4
0
0
1
1
0
1
0
0
0
2
1
1
0
0
2
0
0
0
2
0
3
1
1
0
0
0
2
1
0
0
0
0
0
0
0
0
2
2
0
1
0
0
2
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
2
0
0
0
2
4
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
2
1
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
1
2
1
0
0
0
0
2
0
0
2
1
0
0
1
2
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
1
0
2
0
0
0
0
0
0
1
0
1
0
0
2
0
2
1
0
2
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
1
3
0
0
0
0
2
0
1
2
1
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
4
2
0
0
0
1
2
1
0
0
2
1
2
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
4
0
2
0
0
0
2
1
0
0
0
0
2
0
3
0
0
0
1
0
0
2
0
2
0
0
0
0
1
0
0
0
2
0
0
2
0
4
2
0
0
1
1
0
1
2
0
0
1
0
0
2
0
0
1
1
0
0
0
0
0
0
0
1
4
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
1
2
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
2
2
0
0
2
2
0
0
0
0
0
0
1
0
0
0
1
0
2
3
1
0
0
0
0
0
0
0
0
2
0
2
0
2
0
1
1
1
0
0
0
0
0
2
0
0
1
0
2
1
0
0
0
2
0
0
2
2
0
0
1
2
0
0
0
2
0
1
0
1
1
0
0
2
0
0
1
2
0
1
0
1
0
3
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
1
2
2
1
0
1
0
0
0
2
0
1
0
2
0
0
1
2
1
0
8
0
0
0
1
2
2
0
1
0
1
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
2
2
0
0
2
1
2
0
0
0
0
0
3
1
0
2
0
0
0
0
0
0
1
1
2
2
0
0
0
1
0
0
0
2
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
1
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
2
0
0
2
2
1
0
2
0
0
0
0
0
0
1
1
0
0
0
3
0
1
0
0
1
1
0
1
2
2
0
0
1
0
1
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
2
1
2
1
0
0
0
2
0
0
2
0
1
0
0
1
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
2
1
0
0
0
0
2
0
0
1
0
0
2
1
3
2
0
0
1
2
2
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
3
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
5
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
4
2
1
1
2
2
0
1
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
2
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
2
2
0
3
0
0
2
0
0
0
0
0
1
0
0
2
2
0
2
0
0
0
0
0
0
1
0
1
4
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
2
1
2
2
0
0
0
0
3
0
0
1
1
2
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
2
0
0
0
0
1
2
3
0
0
0
3
2
1
2
0
0
0
2
0
0
0
0
0
0
1
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
1
0
1
2
0
0
0
0
2
0
0
0
3
1
0
1
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
3
0
0
1
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
2
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
2
0
1
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
1
0
2
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
1
2
2
0
0
1
0
2
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
2
0
0
1
0
0
2
0
2
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
1
1
0
0
2
0
1
0
0
1
0
0
0
2
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
2
0
0
1
1
0
0
3
0
0
0
1
0
1
0
0
3
0
0
0
0
1
0
0
2
1
1
1
0
0
0
0
1
0
0
0
0
2
2
0
1
1
0
1
0
0
2
1
0
0
0
2
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
2
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
2
0
0
1
1
0
1
0
2
0
2
0
1
0
0
0
0
0
2
0
1
0
0
1
0
1
0
0
0
1
0
2
0
0
0
2
1
0
1
0
0
0
2
0
0
0
0
2
0
0
2
0
5
0
2
2
0
2
0
2
0
0
0
0
0
2
0
1
2
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
1
0
0
0
0
0
3
0
0
0
1
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
3
0
0
0
4
2
0
0
0
1
2
2
0
0
0
0
0
0
0
0
2
0
2
3
1
0
1
1
0
0
1
0
0
0
2
0
2
0
0
1
0
1
0
0
0
1
2
0
0
1
0
2
0
0
0
0
0
2
3
0
1
1
0
0
16
0
2
0
0
2
0
0
0
0
2
2
0
0
0
0
2
1
1
2
0
2
0
0
0
3
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
4
1
0
0
2
0
2
0
0
0
2
0
1
0
2
2
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
1
1
2
0
0
0
0
0
1
1
2
0
3
3
0
0
0
0
0
1
2
1
1
0
2
0
1
1
0
1
1
0
1
1
0
0
0
1
0
2
0
0
0
2
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
1
0
0
1
2
0
2
2
0
0
2
0
0
0
2
0
0
0
2
0
0
2
4
0
3
2
0
1
0
0
0
2
0
0
0
0
0
1
0
2
0
2
0
0
0
2
0
0
0
1
0
0
0
1
0
0
1
2
1
0
0
0
0
0
0
0
1
0
2
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
3
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
1
0
0
2
0
2
0
0
0
0
0
0
2
3
0
2
1
0
0
0
1
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
1
0
0
3
0
0
1
0
0
3
0
0
0
1
2
0
0
2
0
0
1
1
2
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
1
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
1
1
1
0
2
0
0
0
0
0
0
0
2
2
0
0
2
0
2
1
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
1
0
0
0
0
0
2
2
0
2
0
0
0
3
2
1
0
0
0
1
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
1
0
0
2
2
0
0
0
0
0
0
0
1
0
2
1
0
0
2
0
2
0
0
0
1
0
1
0
0
0
0
2
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
2
5
0
0
2
0
0
2
0
2
0
0
0
0
0
0
1
2
0
0
2
1
0
0
0
1
0
0
0
0
1
0
0
0
2
1
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
1
2
4
2
1
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
2
1
0
0
0
0
2
1
0
1
0
0
0
0
0
0
1
0
0
0
2
1
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
2
0
0
1
0
2
2
1
0
0
0
1
0
0
0
1
0
0
2
0
4
0
0
0
2
0
0
0
1
0
1
0
0
1
1
0
0
2
0
0
0
0
0
2
1
2
0
0
0
2
0
0
0
1
1
0
1
0
0
0
0
0
1
2
0
0
1
3
0
0
0
0
0
1
0
0
0
0
1
2
0
1
0
0
0
0
0
2
0
1
0
0
1
1
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
2
0
1
3
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
2
1
0
2
0
1
2
0
0
1
2
0
0
0
0
0
0
2
1
0
0
6
0
0
0
2
0
2
2
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
2
2
0
1
0
0
0
2
0
0
0
0
0
2
1
0
0
1
1
2
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
2
0
0
0
1
1
0
1
0
2
2
2
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
3
1
0
2
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
6
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
2
2
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
1
3
0
0
2
0
0
0
1
2
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
2
1
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
2
0
0
2
0
1
1
0
1
0
0
0
0
0
0
1
1
0
2
0
0
0
1
1
0
1
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
3
2
0
0
0
1
0
0
3
0
0
0
1
2
0
2
0
1
0
0
0
0
0
0
0
2
0
0
1
1
0
2
0
2
1
3
2
1
1
0
0
0
0
1
1
2
1
0
1
0
2
2
1
0
1
0
2
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
1
4
2
1
0
0
2
0
0
2
0
1
0
0
0
0
1
0
3
0
0
2
0
0
1
0
0
0
2
1
0
0
1
2
2
0
0
0
1
0
3
0
0
2
0
0
1
1
0
2
0
1
0
0
0
0
0
2
0
0
1
2
1
0
0
0
0
0
1
0
2
3
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
1
2
0
0
1
1
0
2
0
1
2
0
2
0
0
3
2
1
0
1
0
0
1
1
0
0
0
1
0
0
0
0
1
1
2
1
0
2
0
0
2
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
1
1
0
1
2
2
1
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
1
2
1
0
0
0
2
0
0
1
0
0
0
0
2
0
1
0
0
2
0
0
2
2
0
0
2
0
0
1
1
1
1
0
2
0
0
5
0
0
0
2
0
0
2
2
0
0
0
1
2
0
0
0
0
1
0
0
0
3
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
2
1
0
0
2
2
0
0
0
0
0
0
0
1
0
0
2
0
1
2
0
1
0
0
0
1
0
0
1
1
0
0
2
0
0
2
0
0
0
2
0
0
0
2
1
0
0
2
0
1
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
2
2
0
0
2
0
0
2
0
0
2
0
0
0
2
0
1
0
0
1
1
2
0
0
0
3
0
0
0
2
0
0
1
0
2
0
0
0
0
0
2
0
1
0
0
0
1
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
4
0
0
2
0
4
0
1
0
1
0
0
1
0
3
3
1
0
0
0
0
0
2
0
2
0
0
0
0
1
2
1
0
3
0
1
2
0
0
0
1
3
0
0
0
0
2
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
3
2
5
0
0
0
0
0
2
0
0
0
0
0
2
1
1
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
2
3
0
2
0
0
0
0
2
1
0
0
0
2
0
0
0
0
1
0
1
0
3
0
0
0
0
2
0
0
0
0
2
0
0
0
2
1
1
0
0
0
2
2
1
4
2
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
1
0
3
2
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
2
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
1
0
0
1
0
2
1
0
0
0
0
0
2
0
0
1
1
0
1
1
0
0
0
0
0
2
0
0
2
1
2
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
1
0
0
0
2
0
0
0
0
1
1
0
0
0
0
1
1
1
1
2
0
1
0
2
1
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
2
1
1
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
1
0
0
0
0
2
1
0
0
0
2
0
2
4
2
1
2
2
3
2
0
0
2
2
0
0
0
0
2
0
0
0
0
1
0
1
3
0
0
2
1
1
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
3
0
0
0
1
0
0
2
0
0
1
1
0
2
4
0
0
0
0
0
1
2
1
3
0
0
2
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
2
0
0
0
0
1
2
1
2
2
0
0
0
0
2
0
0
0
0
0
2
1
0
2
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
2
1
0
0
0
2
2
0
2
1
0
0
2
0
0
0
2
2
2
0
0
1
2
2
1
1
1
0
0
1
0
0
0
2
0
1
0
0
2
0
2
1
0
1
1
0
0
0
2
0
1
2
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
2
2
2
0
0
0
0
1
2
0
2
1
0
0
1
0
0
1
0
0
2
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
1
0
0
0
0
0
2
0
0
2
1
0
0
0
3
2
0
0
1
2
0
1
2
1
3
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
1
0
0
2
0
0
4
0
0
1
0
3
0
1
1
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
2
0
0
1
0
0
0
2
0
2
1
0
0
0
2
0
1
0
0
0
0
0
2
0
1
1
0
1
0
0
1
0
0
1
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
2
0
0
2
0
2
1
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
2
0
5
0
0
0
2
0
0
2
1
1
0
1
0
0
0
3
2
1
1
0
1
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
1
2
0
0
0
0
0
0
0
2
5
0
0
1
0
1
1
0
0
0
1
1
2
0
0
0
2
1
0
0
0
1
2
0
0
0
0
2
2
0
0
0
0
0
2
2
0
1
0
0
2
0
0
0
1
0
0
0
2
0
0
1
0
0
0
1
0
0
5
2
0
0
0
0
0
1
1
0
0
2
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
2
0
0
2
0
2
2
0
2
0
2
0
1
0
2
1
0
0
1
0
0
3
0
1
0
0
0
2
0
0
1
0
0
1
1
2
1
1
0
0
0
0
1
0
0
0
3
0
2
0
0
0
0
0
0
1
0
1
0
1
0
2
0
2
2
0
0
0
1
1
0
3
0
1
2
2
1
0
0
0
0
1
1
0
0
0
0
0
0
2
0
1
0
0
2
0
1
1
2
0
0
0
1
3
2
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
4
0
2
0
0
0
0
1
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
2
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
2
0
0
0
0
2
0
1
1
0
0
0
0
1
0
0
2
1
1
0
2
0
2
2
0
0
0
1
2
0
0
0
0
0
2
0
1
0
2
0
0
2
2
1
0
1
2
1
0
0
0
0
2
0
2
0
0
0
0
0
1
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
1
1
0
1
1
0
1
2
1
0
1
1
0
0
2
2
0
2
0
1
1
1
2
1
2
2
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
1
0
0
1
0
1
0
0
0
0
3
0
0
0
1
0
3
0
3
0
0
0
0
0
2
0
0
0
1
1
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
1
2
0
0
0
2
1
0
0
2
2
0
2
1
2
0
1
0
0
1
1
2
2
1
0
2
1
1
1
0
0
2
0
0
0
2
0
2
1
0
0
2
2
0
3
0
1
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
2
1
0
0
0
2
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
3
0
0
2
0
2
0
0
3
0
0
0
0
1
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
1
0
1
0
2
0
1
1
0
2
0
0
2
2
3
1
1
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
2
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
2
0
1
3
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
1
0
0
2
0
0
0
2
1
0
0
1
0
0
0
2
2
0
0
0
0
2
0
0
0
1
3
0
0
1
0
2
2
1
0
0
0
0
0
2
1
2
0
2
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
3
0
1
0
1
0
0
0
0
0
0
0
1
1
1
2
0
0
1
2
0
0
0
0
1
0
0
0
1
2
0
0
0
1
2
0
2
0
2
0
0
2
2
1
2
1
1
2
0
0
0
0
1
0
0
2
1
2
0
0
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
2
0
0
1
6
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
2
0
0
0
1
1
2
0
1
2
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
1
1
0
1
0
0
1
0
2
0
1
0
2
1
0
2
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
1
2
0
0
1
0
0
0
0
0
0
0
4
2
0
0
1
0
0
1
2
1
0
0
0
0
2
0
2
2
0
0
0
2
0
1
2
2
2
2
0
1
1
0
0
0
0
0
2
2
0
0
0
1
0
1
0
0
0
2
0
1
2
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
2
0
1
0
1
0
0
1
0
0
0
0
4
1
1
1
0
0
1
2
1
2
0
1
0
2
1
1
0
0
0
0
2
1
1
0
2
0
1
0
0
0
2
0
0
1
2
0
0
3
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
2
2
2
0
0
0
0
0
2
1
2
0
2
0
2
1
0
0
2
0
1
4
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
1
0
1
0
0
0
2
0
0
0
0
1
2
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
2
2
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
1
2
1
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
1
1
2
1
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
2
0
2
0
2
2
2
0
0
1
2
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
1
0
0
2
3
0
0
2
0
0
0
1
0
0
0
0
0
1
0
1
2
1
0
0
5
2
0
3
0
2
3
1
1
2
1
0
0
0
0
0
1
0
2
0
2
0
0
0
2
0
0
2
2
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
2
0
2
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
1
1
3
1
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
1
0
0
0
1
0
0
0
1
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
1
1
1
0
0
0
0
0
2
2
2
0
1
0
2
0
0
0
0
2
2
3
0
2
0
1
2
0
2
0
1
0
2
1
2
0
1
0
2
0
1
0
2
0
0
1
2
0
0
0
0
2
1
2
0
2
2
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
2
6
2
0
0
0
0
0
0
0
0
2
0
0
1
1
1
0
1
2
0
1
1
0
0
0
0
2
1
2
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
2
1
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
3
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
3
0
0
0
1
0
0
0
1
0
0
1
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
1
0
2
0
0
1
0
0
0
0
0
0
0
2
0
1
1
2
0
0
0
1
1
0
2
2
1
3
0
0
1
0
2
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
3
0
0
1
0
2
0
0
1
2
0
2
0
0
0
0
1
0
0
2
2
0
1
0
0
0
0
0
1
1
0
0
7
0
2
1
0
0
1
1
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
5
1
1
0
0
1
1
0
3
1
0
0
0
1
2
2
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
2
1
0
2
0
0
0
0
2
2
0
1
0
0
1
0
0
1
0
2
0
0
2
1
0
1
1
3
0
0
0
0
0
0
2
2
0
1
0
2
0
0
0
0
0
0
1
1
0
2
2
0
2
0
0
0
0
0
2
1
2
0
0
0
0
0
0
2
0
0
0
2
1
0
0
2
0
0
0
0
2
1
2
0
1
0
2
0
0
0
0
0
3
0
0
0
0
1
0
2
0
1
0
1
2
0
0
1
0
0
2
2
2
0
0
0
2
0
0
0
0
0
2
0
1
3
0
1
2
0
2
2
0
1
0
0
0
2
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
2
0
0
2
0
0
3
0
0
0
0
1
1
2
0
0
1
0
0
0
0
2
2
0
2
0
0
2
0
1
0
1
0
0
0
0
2
0
1
0
0
0
0
2
0
2
0
0
1
0
0
1
2
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
2
2
1
0
2
0
1
0
0
1
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
3
0
0
2
0
0
0
0
0
0
0
0
5
0
0
0
1
0
0
2
0
2
0
0
0
0
2
0
0
1
2
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
2
1
0
4
2
1
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
1
0
0
0
2
1
0
0
1
2
1
0
0
0
3
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
1
2
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
1
2
1
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
1
1
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
4
0
0
1
3
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
1
1
0
3
0
0
1
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
1
1
1
2
1
1
0
0
0
2
0
2
0
2
0
0
0
2
1
0
0
0
0
3
0
3
1
0
0
0
0
0
2
0
0
1
0
2
0
1
0
2
0
0
0
0
1
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
1
2
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
2
0
2
1
2
0
0
0
0
2
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
4
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
1
2
0
0
0
1
0
0
0
0
1
0
1
1
0
0
2
0
2
0
0
2
0
0
0
0
0
2
0
2
2
0
0
1
0
0
0
0
0
0
3
2
2
0
1
0
2
3
0
2
0
0
0
1
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
1
1
2
0
0
0
0
0
0
4
2
2
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
2
1
2
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
1
0
0
0
0
3
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
1
1
0
1
2
2
0
2
2
2
0
0
0
0
2
0
1
1
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
1
2
1
0
0
0
0
0
2
0
0
1
0
1
0
2
0
0
0
0
4
0
0
0
0
2
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
5
0
2
0
0
0
0
0
0
0
2
1
2
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
3
0
0
0
2
0
1
0
0
0
1
2
2
0
1
2
3
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
2
1
0
1
1
0
2
0
0
0
0
0
1
0
0
1
0
1
1
2
0
0
0
2
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
2
2
0
2
1
2
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
2
2
0
1
1
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
2
2
0
0
2
0
1
0
0
0
1
2
0
0
0
0
0
0
1
2
0
0
1
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
2
0
2
0
0
0
2
0
1
2
0
1
1
1
2
0
0
0
0
0
0
2
2
0
0
0
1
0
2
0
0
2
1
0
1
0
0
3
0
1
1
0
0
1
1
0
0
2
0
0
0
0
0
2
0
0
1
1
2
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
1
0
1
2
0
0
0
0
4
1
0
3
0
2
0
0
0
1
0
2
0
0
0
0
0
0
1
2
3
1
2
0
0
0
1
0
0
0
2
0
0
2
0
1
0
0
0
3
0
0
0
2
1
0
0
0
0
0
0
1
1
0
1
1
2
0
0
1
0
0
0
2
0
0
3
0
0
1
1
0
0
0
0
0
0
1
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
2
0
0
1
1
0
1
0
1
0
0
0
0
1
0
0
2
0
1
2
0
0
1
0
0
0
0
2
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
2
0
0
0
0
0
0
0
0
1
0
2
1
1
0
0
0
0
0
0
0
1
1
1
0
2
0
0
2
0
0
0
0
1
1
0
0
0
1
2
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
1
2
1
0
1
0
0
0
0
0
2
0
0
0
0
1
2
0
1
0
0
0
0
1
0
2
1
0
0
0
1
0
0
0
1
2
0
0
2
0
0
0
0
0
0
2
1
2
1
2
1
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
2
0
0
1
0
0
0
0
2
2
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
2
2
2
0
1
0
0
1
0
1
0
2
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
2
0
0
3
0
0
0
2
0
3
0
1
0
0
0
2
1
2
1
0
0
1
2
2
0
0
2
2
0
2
1
1
0
2
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
1
1
0
0
0
2
0
0
0
0
1
0
0
2
1
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
3
0
2
0
0
3
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
1
1
0
2
0
0
0
1
0
2
0
0
1
0
0
1
0
0
0
0
2
1
0
0
1
0
4
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
2
0
0
2
0
0
3
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
1
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
3
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
3
2
2
0
0
0
1
0
2
0
2
0
0
1
1
0
2
0
0
4
0
2
0
1
0
0
0
1
2
0
0
0
0
2
0
0
2
1
2
2
0
0
0
0
0
2
1
0
0
0
1
2
1
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
1
1
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
1
2
2
2
1
0
0
2
0
0
0
1
0
2
0
0
0
1
0
1
0
2
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
1
2
0
0
1
3
0
3
1
0
0
1
2
1
2
0
0
0
0
0
1
2
0
0
0
2
1
2
0
2
0
0
2
1
0
2
0
1
0
0
0
0
2
2
0
0
0
0
1
2
1
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
2
0
2
0
2
0
0
0
2
0
2
0
0
0
1
2
1
0
0
0
0
0
0
0
0
3
0
0
1
0
0
1
0
1
1
1
1
0
0
0
1
2
1
2
0
4
0
0
2
1
0
0
2
0
1
0
3
0
0
0
0
0
0
1
0
0
0
3
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
3
0
2
1
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
1
2
2
2
2
0
0
0
0
0
0
0
2
3
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
2
2
2
2
0
1
0
0
0
0
1
0
1
0
2
0
0
0
5
0
2
0
0
0
0
0
1
0
2
0
0
1
1
0
3
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
1
1
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
1
1
0
0
1
2
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
1
0
0
1
2
0
2
0
0
0
0
0
2
0
0
0
1
1
2
1
0
1
1
2
1
2
2
3
0
1
0
0
0
0
2
0
0
0
0
1
1
2
0
2
1
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
5
2
0
0
2
0
0
0
0
2
2
2
2
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
6
0
1
1
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
1
0
1
0
2
2
0
0
0
1
2
2
0
2
0
1
0
0
0
1
2
1
0
0
0
1
2
2
0
0
1
0
0
1
1
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
4
0
0
0
0
0
1
0
0
3
2
0
5
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
6
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
2
1
0
0
3
2
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
2
0
2
0
0
1
2
0
0
0
0
1
2
0
0
0
1
0
0
0
1
2
0
0
0
0
1
2
2
0
1
0
0
2
2
0
2
0
0
1
0
0
0
0
1
0
0
0
0
1
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
2
0
0
0
0
2
0
2
0
0
2
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
3
2
3
1
0
2
0
0
0
2
0
0
0
0
0
0
0
1
1
1
2
0
0
2
0
2
0
0
1
0
0
2
1
0
1
0
0
0
1
0
0
2
1
0
1
1
0
1
1
0
0
0
0
0
0
1
1
0
0
4
0
2
0
0
6
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
1
2
0
3
1
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
1
0
0
0
0
2
1
1
1
0
0
0
0
0
1
2
2
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
1
0
2
7
0
0
2
2
0
0
0
2
0
0
0
0
0
0
4
0
0
1
0
1
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
2
0
0
1
0
1
0
0
0
0
0
0
1
4
1
1
0
0
0
1
1
0
0
2
0
1
0
1
0
0
0
2
0
2
0
0
0
0
0
4
2
0
0
0
0
0
0
0
2
0
1
1
2
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
3
2
2
0
2
0
0
0
2
0
1
0
0
0
0
1
1
0
0
0
1
0
1
1
0
0
1
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
2
1
1
1
0
0
0
1
0
1
0
0
0
0
0
3
2
1
1
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
1
0
1
2
0
2
2
0
0
0
0
0
0
2
2
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
2
0
2
0
0
0
0
1
0
0
2
0
0
0
2
2
0
2
1
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
3
1
0
0
0
0
0
1
1
0
0
1
0
1
0
1
0
0
2
0
0
0
0
0
1
0
2
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
2
1
0
1
3
2
0
2
0
0
1
0
2
0
0
0
2
1
1
0
0
3
0
2
3
2
1
2
0
2
1
1
0
1
2
0
1
0
1
0
1
1
0
1
0
0
1
2
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
2
2
0
1
0
1
0
0
0
1
1
0
0
0
0
0
2
3
1
0
1
0
2
0
2
1
0
0
0
0
2
0
0
2
0
0
0
0
0
2
2
2
0
0
0
0
1
0
0
2
0
1
2
0
2
1
2
1
0
1
1
0
2
1
3
2
1
2
2
0
1
0
0
0
0
4
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
2
0
0
0
0
2
0
0
1
2
0
0
2
2
0
0
0
2
1
0
2
0
1
0
2
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
1
0
0
6
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
3
0
0
1
1
0
2
0
2
2
0
0
0
0
0
1
1
1
0
0
0
2
0
2
2
0
5
2
0
0
1
0
0
0
1
0
2
1
0
0
0
2
1
0
0
0
0
1
0
0
3
0
2
0
0
1
0
0
2
0
0
0
1
0
2
0
0
0
1
0
1
1
0
1
1
2
0
2
1
0
0
0
1
0
1
0
0
1
0
2
0
0
1
1
0
0
0
0
0
0
0
0
2
1
1
0
5
2
1
0
0
0
1
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
1
0
0
0
2
0
1
2
1
1
0
0
0
0
0
2
0
2
0
0
0
4
0
0
1
0
0
0
1
0
2
0
0
0
1
0
0
0
1
0
0
2
0
0
0
2
0
0
1
0
0
1
0
0
0
1
0
2
2
0
0
1
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
2
0
0
2
0
0
0
1
0
1
1
0
0
0
0
2
0
0
0
1
2
0
0
2
2
0
0
2
1
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
1
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
2
0
0
1
2
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
1
1
2
0
0
2
0
0
2
0
0
2
0
0
3
0
0
1
0
0
0
2
0
2
1
0
2
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
3
1
0
2
0
0
1
1
2
1
0
0
0
0
0
0
1
0
3
2
0
0
0
0
0
1
0
1
0
0
0
2
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
1
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
1
1
0
2
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
3
0
2
0
2
2
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
1
2
0
0
0
0
2
0
1
0
1
2
1
0
0
0
1
0
0
0
2
2
0
0
1
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
1
0
0
0
0
0
2
1
0
2
0
0
0
0
2
1
0
0
2
1
0
0
2
0
2
0
0
0
0
0
0
0
0
1
1
1
2
1
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
2
1
0
0
1
1
0
0
2
2
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
2
1
2
1
0
0
0
0
0
4
0
0
2
1
0
0
2
0
0
0
3
0
0
0
1
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
1
2
3
0
1
0
0
0
0
0
1
1
0
0
2
1
0
0
1
0
0
0
0
3
1
0
0
2
0
0
0
1
1
0
0
0
0
1
1
2
0
0
0
1
1
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
2
0
0
2
0
0
2
1
0
2
1
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
4
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
2
0
0
1
0
0
2
0
1
1
0
2
0
2
0
1
0
1
0
0
0
0
0
0
1
0
0
2
0
2
2
0
2
1
0
0
0
2
0
2
0
0
0
0
1
0
1
3
1
0
0
2
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
2
1
1
2
0
0
0
2
0
0
0
0
1
0
0
2
2
0
0
2
0
0
1
0
0
0
3
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
2
1
0
0
0
0
0
2
2
1
1
0
0
0
0
0
0
2
0
0
0
0
0
1
3
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
1
1
1
1
0
0
2
0
0
2
0
0
1
1
0
2
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
4
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
2
1
0
1
0
2
1
3
0
1
1
1
0
0
5
0
0
2
0
0
1
1
0
0
0
0
0
1
0
0
2
2
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
3
4
0
0
0
1
0
2
1
0
0
0
0
2
0
2
1
1
1
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
2
2
1
1
1
0
0
0
0
0
1
0
0
0
2
0
1
0
1
0
0
1
0
0
0
0
0
2
1
0
2
0
1
0
2
2
0
0
0
0
2
0
0
0
0
3
0
1
0
2
0
2
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
3
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
1
0
0
0
1
2
0
0
0
0
1
0
2
0
4
0
0
2
1
0
1
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
2
0
2
0
3
0
0
1
0
0
0
0
0
0
0
0
0
1
1
5
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
1
0
1
0
0
0
1
0
2
0
1
0
1
2
1
0
0
0
0
0
0
0
0
0
0
2
1
0
1
2
2
1
0
0
1
1
2
0
0
0
0
3
0
1
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
2
1
4
2
0
0
0
1
0
1
2
0
1
1
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
2
3
0
0
2
2
0
0
0
0
0
0
0
0
2
1
0
1
0
2
0
0
0
1
0
1
0
0
0
2
0
0
0
5
0
0
0
1
1
5
1
0
0
0
0
0
0
1
1
0
0
1
1
0
1
1
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
3
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
2
2
1
2
0
0
0
8
0
0
0
0
0
0
1
2
2
0
0
0
2
0
2
1
2
0
2
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
4
2
0
0
0
1
2
0
2
0
1
0
2
1
0
0
1
0
0
0
2
0
0
0
0
2
0
0
1
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
1
1
0
2
1
0
0
0
0
0
1
11
0
2
0
2
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
1
2
2
1
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
2
0
0
2
1
0
0
2
2
0
0
0
0
3
0
0
0
0
0
0
3
0
3
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
2
0
0
1
0
1
0
0
2
0
0
0
1
0
0
1
1
1
0
0
2
0
1
0
0
2
0
2
0
0
0
7
4
1
0
1
0
0
0
0
7
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
1
3
0
0
0
0
0
0
4
2
0
1
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
2
2
1
3
0
1
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
1
0
0
2
0
1
0
0
1
1
0
2
0
0
2
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
1
0
1
2
0
0
0
1
0
0
0
0
0
0
2
3
0
1
0
5
1
0
2
0
1
0
0
1
0
1
0
0
3
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
1
0
0
0
2
0
2
2
1
1
2
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
2
0
0
0
2
1
0
1
1
2
0
3
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
1
2
2
0
0
0
0
1
1
0
2
0
0
0
0
0
0
2
0
0
0
1
0
3
1
1
1
2
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
1
2
0
1
0
1
0
0
0
0
1
0
0
0
2
0
0
6
0
4
0
2
2
0
0
2
0
0
0
2
0
0
0
1
0
0
2
2
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
6
2
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
2
1
2
0
1
2
0
2
2
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
2
0
0
1
1
2
0
0
0
0
2
0
0
0
0
1
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
1
1
0
0
1
0
2
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
1
2
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
2
1
2
0
1
1
0
0
0
6
1
0
2
0
2
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
1
0
0
2
0
0
0
0
3
0
2
0
1
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
4
2
0
0
0
0
1
1
2
1
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
4
2
0
2
2
0
2
0
0
1
0
1
0
0
1
0
0
0
0
0
1
2
1
2
0
1
2
0
0
2
4
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
3
1
0
1
0
0
1
1
0
2
0
2
1
0
2
1
0
0
0
0
1
0
2
0
2
3
2
0
1
0
0
2
0
1
1
0
0
0
0
2
0
2
1
0
1
2
2
0
0
1
0
0
1
0
0
0
1
1
2
2
0
0
0
0
1
0
0
0
0
0
0
2
1
2
0
0
0
1
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
1
0
0
0
3
0
0
2
0
1
0
0
0
1
0
0
0
2
2
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
1
0
1
0
0
1
0
0
1
0
0
1
2
0
1
0
0
0
1
1
0
0
3
0
0
0
0
3
0
0
0
0
0
1
0
2
0
0
1
0
1
0
1
0
0
0
0
1
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
2
0
0
0
0
0
0
2
2
3
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
1
0
0
2
0
0
3
1
0
0
2
0
1
0
0
1
0
2
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
1
0
0
0
1
0
1
0
0
0
0
3
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
2
0
1
1
0
2
0
2
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
3
0
0
1
2
0
0
2
0
1
0
0
2
2
0
1
2
0
0
2
0
2
0
1
1
0
0
0
0
0
3
0
0
0
1
2
0
2
0
0
0
3
0
1
0
0
0
0
0
1
0
1
2
1
2
0
0
0
1
1
0
2
1
1
0
1
1
0
0
0
0
2
1
0
0
0
0
1
0
0
1
0
0
2
0
0
1
0
0
0
1
0
0
0
3
2
0
0
0
2
0
0
0
1
1
0
2
0
0
2
0
0
0
0
0
0
0
0
2
7
0
0
2
2
0
0
1
0
0
1
0
0
0
1
0
0
0
2
0
1
3
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
4
0
0
0
2
1
0
0
0
0
2
2
0
1
2
1
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
2
0
2
2
0
3
0
1
1
0
0
1
0
0
3
2
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
1
2
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
1
0
1
2
1
0
1
0
0
0
2
2
2
2
1
1
3
0
0
1
0
2
2
1
0
0
2
3
0
0
0
1
0
0
0
1
0
0
2
0
2
0
2
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
1
0
2
0
1
2
0
0
1
0
0
1
1
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
2
0
1
1
1
0
0
0
2
0
0
1
0
0
2
0
1
1
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
1
2
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
2
1
0
0
0
0
2
1
0
1
2
0
2
0
1
0
0
2
0
0
1
1
0
2
0
0
0
2
2
0
0
1
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
1
2
0
0
1
1
0
0
0
0
2
0
0
0
0
0
1
1
1
0
1
3
0
1
0
1
0
0
0
0
0
0
2
2
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
1
2
0
0
0
1
0
1
0
0
0
0
2
0
1
0
0
0
0
1
0
1
1
0
0
0
1
0
0
1
0
3
1
2
0
0
0
2
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
2
1
0
0
1
2
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
2
1
1
0
0
1
0
1
0
2
0
1
2
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
1
0
0
2
1
0
1
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
2
0
3
2
0
0
2
0
0
0
0
0
0
2
0
3
0
0
0
0
0
2
1
0
0
0
0
3
1
0
0
1
0
0
2
2
0
0
3
1
0
1
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
1
2
2
0
0
0
0
0
1
2
1
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
2
1
0
1
2
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
2
0
0
0
1
0
2
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
4
0
0
0
2
2
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
1
2
1
2
2
0
2
0
0
0
1
8
1
0
0
0
1
0
0
0
0
0
3
1
0
2
0
1
0
0
0
0
0
2
2
2
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
1
0
0
2
1
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
2
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
1
0
0
1
0
2
1
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
2
0
0
2
0
1
1
2
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
1
2
0
2
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
1
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
1
0
2
0
1
0
1
0
0
0
2
1
0
2
0
1
0
0
1
0
0
1
2
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
2
0
0
1
2
0
1
0
2
1
0
0
0
2
1
2
0
1
0
2
0
2
1
1
0
0
0
0
0
2
2
1
1
0
1
0
1
0
1
1
0
0
0
0
0
2
0
0
1
0
2
2
0
2
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
3
0
0
0
2
2
0
0
0
0
1
0
0
1
0
0
2
0
0
1
0
1
2
0
0
1
0
0
0
2
0
0
0
0
1
0
0
1
1
3
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
1
0
1
0
1
2
1
0
0
2
1
0
0
0
0
2
1
1
2
0
0
2
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
1
1
1
2
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
2
3
2
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
4
1
0
4
5
0
0
0
0
0
0
1
0
0
0
3
1
0
0
0
0
0
0
1
1
2
2
0
0
0
1
0
0
1
1
2
0
2
0
2
0
1
0
2
0
0
0
0
1
0
2
0
0
2
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
6
2
0
0
0
0
0
0
0
1
1
0
0
0
0
3
0
0
0
2
2
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
1
0
0
2
0
2
0
2
2
1
1
0
0
0
0
0
2
0
2
0
1
0
0
0
1
1
0
1
0
0
0
1
1
0
1
0
0
0
2
0
0
2
1
0
1
1
0
2
0
2
1
1
2
1
0
1
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
1
2
0
1
1
2
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
1
1
0
0
0
0
1
2
0
0
0
2
0
0
2
1
0
0
0
1
1
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
2
2
0
1
0
1
2
0
0
0
1
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
2
0
1
0
0
2
1
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
2
0
1
2
0
0
0
0
0
2
0
0
1
0
0
2
0
1
2
1
0
1
1
0
0
0
1
0
1
0
0
1
0
2
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
3
2
0
0
0
0
2
1
0
1
0
0
1
2
0
2
1
3
1
0
0
0
0
2
0
0
3
0
0
0
2
1
0
0
0
0
1
0
0
2
1
0
0
1
0
2
0
0
0
0
1
0
1
0
0
1
0
0
2
0
0
2
1
1
6
0
0
0
1
0
1
1
1
1
0
1
0
1
0
1
2
2
1
0
0
0
5
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
2
0
1
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
2
0
1
2
0
0
2
1
0
2
0
0
0
0
0
2
0
0
2
3
0
2
0
0
0
2
2
1
2
2
0
0
1
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
5
0
1
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
2
0
0
2
0
0
0
5
0
2
2
0
2
0
0
0
0
0
1
0
1
0
1
1
1
0
0
0
0
0
2
0
2
0
0
0
0
2
2
0
1
0
0
0
0
3
2
0
2
1
0
0
0
0
0
1
1
0
1
0
2
0
0
2
0
0
1
1
1
0
0
0
0
2
2
0
2
0
2
0
0
0
2
0
2
0
0
0
1
0
0
0
2
1
0
0
0
0
0
1
0
0
0
1
2
1
0
2
1
0
0
2
2
1
1
0
1
0
0
4
1
2
2
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
3
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
1
1
1
1
0
2
2
0
0
0
0
0
0
0
0
1
1
0
0
3
0
2
0
2
2
1
5
2
0
0
1
0
0
0
0
1
2
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
2
0
3
0
0
1
0
1
0
0
1
2
1
0
0
1
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
1
0
0
0
2
0
0
1
2
3
1
0
2
0
1
0
0
2
0
2
0
1
0
0
0
0
0
6
0
0
0
0
0
0
1
1
2
4
1
1
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
3
0
2
0
0
1
0
0
0
1
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
2
1
0
0
1
2
2
0
0
0
0
2
0
2
0
2
0
0
1
0
1
0
1
0
2
2
1
0
0
0
0
3
1
1
0
1
2
0
0
0
0
0
2
2
0
0
1
0
1
0
0
0
3
0
3
1
0
2
1
0
0
2
0
0
0
1
0
0
0
0
0
1
2
1
0
1
0
0
0
2
0
2
0
2
1
0
0
1
0
2
0
0
1
2
1
1
2
2
0
2
3
0
0
0
2
0
0
0
0
3
0
1
0
0
0
0
0
0
1
1
0
0
0
2
1
0
0
2
0
5
2
0
0
0
0
2
2
0
0
1
0
0
0
1
1
0
2
2
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
1
1
2
1
1
2
2
0
2
0
0
2
1
0
0
0
0
0
1
1
3
0
0
0
0
0
0
2
0
2
1
0
0
2
0
0
0
2
2
0
2
0
4
0
0
0
2
0
0
1
0
0
1
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
2
2
2
0
0
0
0
1
0
0
0
0
0
1
0
2
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
2
0
3
4
0
0
1
2
0
0
1
0
0
0
0
0
0
2
2
1
0
2
2
2
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
1
4
1
0
0
0
0
0
0
2
0
1
0
0
0
0
2
1
0
0
0
0
1
0
1
2
0
0
2
0
0
0
1
1
2
0
0
0
1
0
1
1
3
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
3
1
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
2
1
0
2
2
0
0
2
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
1
0
1
2
0
0
2
4
0
1
0
0
1
0
0
3
1
0
0
0
2
0
0
0
0
1
3
3
2
0
0
0
1
2
0
0
0
2
0
0
1
0
0
1
0
2
0
1
0
0
1
1
0
0
1
0
0
0
2
0
0
0
4
0
1
0
0
1
0
0
1
0
1
1
0
4
1
0
1
0
0
6
2
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
1
0
3
3
0
0
0
0
2
0
2
2
0
1
4
0
1
1
2
0
0
0
0
2
2
0
0
1
1
1
0
0
0
0
0
0
0
1
0
2
2
0
1
0
0
0
0
0
2
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
1
0
1
0
2
0
2
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
5
2
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
2
0
0
2
0
0
1
1
0
0
2
1
0
2
0
0
1
2
2
1
0
0
3
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
5
0
0
3
0
0
1
2
0
0
2
0
0
0
0
2
0
2
0
2
0
0
1
0
0
3
0
2
0
2
2
0
1
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
2
0
0
0
2
2
1
0
0
2
0
1
0
0
0
0
0
0
0
2
0
1
0
0
2
0
1
0
0
0
0
0
2
2
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
1
0
0
0
0
0
1
0
2
0
0
0
3
1
2
1
0
1
0
0
1
2
1
0
1
0
0
2
1
1
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
1
2
0
1
0
2
3
0
0
0
3
0
0
1
0
1
0
0
0
3
0
0
2
0
2
1
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
1
1
0
2
1
0
0
0
1
1
4
0
0
0
2
0
2
0
0
2
0
0
1
0
0
0
12
0
0
0
0
1
0
2
0
0
0
2
0
1
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
1
1
1
1
0
0
2
2
2
1
0
0
0
0
1
0
3
4
2
2
0
0
1
0
0
1
0
0
0
2
0
2
2
0
1
0
0
0
0
1
0
2
2
0
0
2
1
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
2
0
1
0
0
1
1
4
0
1
2
0
0
0
3
2
2
2
0
0
0
4
0
0
2
1
0
3
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
2
1
2
0
0
1
0
0
0
0
1
1
0
0
0
2
2
0
1
0
1
0
3
2
0
2
0
0
2
1
0
0
1
1
3
0
0
0
2
1
0
0
0
2
0
1
0
1
1
0
1
0
1
0
1
1
0
0
0
0
0
2
0
0
1
1
2
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
6
1
0
0
2
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
2
0
0
2
0
1
2
0
2
0
0
2
1
2
1
0
1
0
0
1
0
1
0
0
1
0
0
2
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
2
1
2
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
2
2
1
0
1
1
0
1
0
1
2
0
0
2
0
0
0
0
0
0
0
2
3
0
1
0
2
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
1
2
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
2
3
0
1
0
0
0
0
0
0
2
0
2
0
1
0
2
0
2
0
1
2
2
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
1
5
0
1
2
0
3
0
0
0
2
0
0
0
2
0
2
0
1
0
0
0
0
0
0
2
1
1
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
1
1
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
2
0
0
1
2
0
0
0
0
1
1
2
0
0
0
0
1
1
0
0
0
0
3
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
3
0
0
0
1
0
0
1
1
0
0
1
0
0
0
6
2
0
0
1
2
2
0
2
1
0
0
0
0
0
2
1
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
1
1
0
1
1
2
2
2
0
0
0
1
0
2
0
1
0
0
0
0
1
0
0
0
0
1
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
2
0
0
0
0
2
0
1
1
0
0
1
0
2
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
2
0
1
0
0
1
1
0
0
2
0
0
5
0
0
2
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
2
0
2
0
0
1
1
1
0
0
0
1
1
1
0
0
2
2
1
2
1
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
1
1
2
2
0
0
1
1
0
1
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
3
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
1
0
1
1
1
0
1
1
0
1
0
0
0
2
1
0
2
0
1
0
0
2
0
2
1
1
0
0
0
0
1
0
0
2
0
0
0
0
2
0
2
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
3
0
0
0
2
2
0
0
1
0
0
0
0
2
0
1
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
1
2
2
0
1
2
2
0
0
0
1
2
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
3
0
1
1
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
2
0
0
1
2
0
2
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
1
1
1
0
0
2
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
3
2
2
0
0
1
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
2
0
0
2
2
0
1
0
0
0
3
0
1
0
2
0
0
1
2
0
0
1
0
1
0
0
0
3
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
1
0
0
0
1
0
0
0
3
0
0
1
0
0
2
0
0
0
2
1
0
0
0
3
0
0
1
2
1
0
0
1
3
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
1
2
1
0
0
0
0
0
2
0
0
2
1
0
0
2
0
0
0
2
0
0
0
1
0
2
2
2
0
0
2
0
0
2
0
2
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
1
2
1
0
2
0
0
2
1
0
3
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
1
1
2
0
2
0
2
0
2
0
0
0
1
0
0
0
2
0
1
2
1
2
0
0
0
1
0
0
2
2
0
1
0
1
0
0
1
0
0
2
0
0
0
0
1
2
2
3
0
0
2
0
0
2
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
1
0
1
0
0
0
1
0
1
0
3
2
0
0
0
0
1
0
1
0
1
0
0
2
0
2
0
0
0
2
1
0
0
0
1
0
0
0
0
1
2
0
0
0
1
0
0
0
0
2
2
1
0
0
4
2
2
0
0
0
1
0
1
0
0
2
0
0
1
0
0
0
3
0
0
0
0
0
0
2
3
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
2
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
1
2
1
1
1
2
2
2
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
1
0
3
1
2
0
0
0
0
1
0
0
0
0
2
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
1
2
2
0
2
1
0
1
2
0
0
0
1
0
0
0
0
0
0
2
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
2
0
0
1
0
0
0
2
0
0
0
2
0
0
0
1
0
2
0
0
1
1
1
2
0
2
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
2
1
2
0
0
0
2
0
0
1
0
0
1
1
0
0
0
1
1
2
1
0
2
2
0
1
0
0
0
2
0
0
0
1
2
0
2
0
0
1
0
3
2
0
2
0
0
3
0
0
4
0
0
0
0
0
0
1
0
0
0
2
1
1
0
0
0
0
0
0
1
2
1
0
0
0
1
0
0
2
0
2
0
0
0
1
1
0
3
2
2
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
3
2
0
0
0
0
0
2
0
0
0
2
2
2
1
0
0
0
0
0
0
0
2
0
1
0
1
1
0
0
0
2
0
0
2
2
2
0
0
0
0
0
0
2
0
0
1
0
0
2
2
1
2
0
0
0
2
0
0
2
0
0
0
0
1
4
2
0
0
0
4
0
2
0
2
0
0
0
0
0
0
0
1
0
2
1
2
0
0
0
0
1
1
3
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
1
0
0
2
0
1
1
1
1
0
0
1
2
0
0
0
0
0
3
0
0
0
0
0
1
0
1
2
0
0
2
0
0
0
0
0
1
1
0
0
2
3
0
0
1
1
2
4
2
2
0
2
1
2
0
0
2
0
0
0
1
0
1
0
2
0
0
2
0
0
0
1
0
0
1
0
0
0
2
0
0
0
1
0
2
1
0
3
0
0
0
2
0
0
0
0
0
0
1
0
1
0
2
0
2
0
0
0
2
0
1
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
2
1
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
2
0
2
1
1
1
0
0
0
1
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
1
2
0
0
0
0
1
2
0
1
0
1
0
0
2
1
0
0
1
2
0
0
0
0
2
2
0
0
0
0
0
1
0
3
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
2
0
0
2
0
2
0
1
0
0
0
2
1
0
0
0
1
0
0
2
2
0
1
1
1
0
1
0
0
2
1
0
0
1
0
1
1
0
0
2
0
0
0
3
2
4
1
0
0
1
0
2
2
0
2
0
0
0
1
1
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
1
1
2
2
0
0
1
2
0
2
0
0
0
1
2
1
0
2
2
0
0
0
11
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
1
2
0
0
0
0
2
0
2
1
0
0
0
0
0
0
1
0
0
2
0
0
4
0
0
0
2
0
0
2
0
0
0
0
1
0
2
0
0
1
0
0
2
0
0
0
2
0
0
0
1
0
1
2
0
2
2
1
0
0
0
2
0
1
2
1
0
1
2
1
1
2
1
0
0
0
0
0
3
0
0
0
0
1
2
1
0
2
0
1
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
2
0
0
1
0
0
1
2
1
0
0
2
2
0
0
0
1
0
0
0
0
5
2
0
0
0
1
2
0
2
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
3
0
0
1
2
0
2
0
0
3
1
0
0
2
1
1
2
0
0
1
0
0
1
0
2
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
2
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
2
2
0
0
0
0
4
0
0
2
0
0
0
0
3
0
2
0
0
0
1
3
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
1
0
1
2
2
0
0
0
0
2
0
2
0
0
0
1
0
2
0
2
2
2
0
0
1
0
0
2
0
0
0
0
0
0
0
2
2
0
2
3
0
0
0
0
2
1
0
0
0
2
0
0
0
0
3
1
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
1
2
1
1
4
2
2
2
0
1
2
0
5
0
0
0
1
0
1
0
0
0
2
2
0
0
0
2
1
0
0
0
0
0
0
1
1
2
0
0
2
0
0
0
1
1
0
0
0
0
0
1
0
2
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
2
2
0
1
0
4
0
0
0
2
1
0
1
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
1
0
0
1
1
0
0
2
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
1
0
2
0
2
0
1
0
2
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
3
0
2
0
1
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
1
0
0
0
2
0
3
0
2
0
0
0
1
2
0
0
2
2
1
0
0
0
0
0
0
1
0
0
2
1
0
0
3
0
0
0
2
0
0
0
0
0
2
0
1
0
0
1
1
3
0
1
1
0
0
1
2
2
0
0
0
0
2
0
2
2
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
4
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
3
1
2
0
1
2
2
1
0
2
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
3
0
1
0
0
2
1
1
0
0
0
0
0
0
1
2
1
0
2
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
3
1
1
0
1
0
0
0
0
2
0
0
0
2
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
1
0
0
1
2
0
1
0
2
0
0
0
0
2
1
2
0
0
0
5
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
3
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
2
2
0
0
2
0
0
0
0
1
1
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
2
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
2
1
0
0
0
2
0
0
2
0
0
0
3
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
6
1
2
2
0
1
1
0
2
0
0
0
1
0
2
0
0
0
0
0
0
3
0
0
1
1
1
2
0
1
0
2
0
0
1
0
0
0
0
1
0
0
0
2
0
1
0
2
2
2
0
0
0
0
4
3
2
0
0
0
0
0
2
0
0
2
0
0
0
2
2
0
0
2
2
0
1
0
3
0
1
2
1
0
0
1
0
0
0
0
4
2
2
1
0
0
0
0
0
0
0
3
1
0
0
0
0
0
2
0
1
0
0
0
2
2
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
4
0
0
2
1
0
3
0
0
0
0
0
0
1
1
0
1
3
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
3
0
2
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
2
0
0
1
1
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
1
0
2
1
0
0
0
0
0
2
1
0
2
2
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
1
0
1
0
0
0
1
0
2
0
2
0
0
2
0
0
0
0
2
0
0
2
2
0
0
1
2
0
1
0
2
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
1
2
2
2
0
2
1
0
0
1
2
2
0
0
1
0
0
0
0
0
2
1
0
0
0
0
1
0
0
1
2
0
0
0
0
2
0
1
1
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
2
0
0
1
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
3
1
0
1
1
0
0
0
2
0
0
0
0
2
2
2
1
1
0
0
0
0
1
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
1
2
0
0
1
3
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
2
0
0
0
4
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
2
0
0
2
0
1
2
0
0
2
1
1
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
1
2
2
0
1
0
5
0
0
1
2
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
2
3
0
2
0
0
1
0
1
0
0
2
1
0
2
0
2
0
0
1
0
3
1
0
0
1
1
1
1
0
1
0
2
5
0
0
0
0
0
1
0
0
0
2
1
2
0
3
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
9
0
0
1
0
0
0
0
0
2
0
0
1
1
2
2
0
1
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
1
2
2
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
2
2
1
1
2
2
0
2
2
2
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
1
3
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
2
2
0
2
0
1
1
1
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
2
1
0
1
1
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
1
1
0
1
0
0
0
0
2
0
1
0
1
2
2
0
0
0
2
0
0
1
0
0
0
0
2
2
0
0
7
1
0
0
0
0
0
0
1
1
0
2
0
0
2
0
2
0
0
0
0
2
1
0
0
0
0
0
0
1
2
0
0
0
0
1
1
1
1
0
1
1
0
0
0
0
1
0
0
0
0
1
2
2
0
0
1
0
2
1
2
0
0
1
0
0
0
0
0
1
0
0
2
0
0
1
0
1
0
0
0
2
1
2
1
2
0
0
2
2
0
0
0
0
2
2
1
0
0
0
0
0
0
3
2
0
0
1
1
0
1
0
2
0
0
0
0
0
1
2
2
0
1
0
0
2
0
0
1
0
0
0
1
0
2
0
2
0
0
0
1
2
0
1
1
0
1
0
0
0
1
0
0
2
3
1
0
0
0
0
1
0
2
0
0
0
2
0
0
3
0
0
0
0
0
0
0
1
2
2
0
0
0
1
0
0
0
2
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
1
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
2
2
1
0
0
0
0
0
2
1
0
0
2
0
2
0
0
0
2
0
0
0
2
0
0
0
2
3
0
2
0
1
0
0
1
0
2
2
0
0
0
0
1
2
0
1
0
0
2
0
1
0
0
0
2
0
0
0
0
0
2
1
0
0
1
1
1
2
2
0
0
2
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
2
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
2
0
2
0
0
1
2
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
3
2
0
2
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
1
1
2
1
0
0
0
0
0
2
0
5
0
0
0
1
0
0
2
0
0
4
1
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
1
0
0
0
0
2
0
0
0
0
1
3
0
0
0
2
2
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
2
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
5
0
2
1
1
0
1
0
2
0
0
0
0
0
0
2
0
0
0
2
1
1
0
1
0
0
0
0
0
1
0
2
2
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
2
1
5
2
0
2
3
0
0
2
2
0
0
2
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
1
3
0
1
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
2
2
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
3
0
0
2
0
0
0
0
0
2
4
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
2
0
2
2
0
5
0
0
2
0
1
0
0
0
1
0
0
3
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
2
0
2
1
0
1
0
0
0
0
0
0
2
2
0
0
2
2
0
0
2
1
1
3
0
0
0
0
1
1
0
0
3
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
3
0
1
0
0
2
4
2
0
1
1
0
0
0
0
0
2
1
0
2
1
0
0
0
0
0
0
0
0
0
1
0
1
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
1
2
3
0
2
0
0
2
1
2
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
2
1
0
3
2
1
1
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
2
0
0
1
0
0
0
3
0
1
2
2
1
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
2
1
0
0
1
0
0
0
0
0
2
0
2
2
0
2
0
2
0
0
3
0
2
0
0
1
0
0
0
2
0
2
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
1
1
1
0
0
0
0
0
2
1
0
0
2
0
1
0
1
0
0
0
0
1
0
2
0
0
1
0
1
0
1
0
0
0
0
1
2
2
0
1
0
1
0
1
0
2
2
3
0
3
0
0
0
0
8
0
2
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
2
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
2
0
0
0
0
1
0
0
2
0
1
0
0
0
0
1
0
0
2
2
0
2
0
0
2
0
0
0
2
2
0
2
2
2
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
3
2
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
2
0
0
2
1
1
0
1
0
0
0
0
0
0
0
0
0
3
1
0
0
1
2
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
2
2
0
3
1
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
3
0
0
0
1
0
0
0
0
2
0
1
1
0
1
0
0
1
0
1
0
2
2
1
0
0
0
1
1
2
2
1
0
0
0
1
0
0
0
0
1
0
1
2
0
2
0
1
0
0
2
0
0
0
0
0
0
2
0
1
0
0
2
0
2
1
0
0
1
0
0
1
2
2
1
2
1
0
0
0
1
0
0
1
1
1
0
1
0
0
1
1
0
0
2
0
0
0
0
1
0
0
2
1
0
2
3
0
0
0
0
0
0
2
1
0
2
2
2
1
0
2
1
2
0
2
2
0
0
0
0
1
0
0
1
1
0
0
2
0
2
0
0
1
0
1
2
0
2
0
0
0
1
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
2
0
0
0
0
0
2
0
1
1
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
1
1
0
0
1
0
2
0
0
2
0
0
0
1
1
0
0
0
2
2
0
1
0
0
2
0
0
0
0
0
1
0
1
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
5
0
1
0
0
0
1
2
0
0
2
0
0
0
0
1
0
0
0
1
0
0
2
1
0
0
2
0
0
0
0
1
2
2
2
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
1
0
1
0
1
0
0
1
2
0
0
4
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
1
1
2
0
0
0
0
2
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
1
0
0
2
2
0
0
0
0
0
0
0
1
1
2
0
2
0
0
2
1
1
0
0
1
0
1
0
0
2
2
0
0
0
2
4
0
1
1
3
0
1
1
0
1
2
0
0
1
1
0
0
0
2
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
2
2
0
0
0
1
0
0
0
0
0
3
2
0
1
0
0
2
0
0
2
0
1
0
0
0
2
1
0
0
0
0
2
1
1
2
0
0
0
2
1
0
1
1
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
1
0
1
0
0
0
0
1
1
2
0
0
2
0
0
0
0
1
2
0
0
2
0
0
0
0
2
0
0
0
0
1
2
2
2
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
2
9
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
1
0
1
1
0
0
0
1
0
2
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
2
0
1
0
1
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
2
1
2
0
0
0
0
0
2
0
0
0
0
0
0
2
1
1
2
2
0
0
0
0
0
0
0
0
1
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
2
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
3
2
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
1
0
1
1
0
0
0
0
1
0
1
0
2
0
0
1
0
2
1
0
0
0
0
3
0
0
2
0
0
0
0
1
0
0
0
0
2
0
3
2
2
0
0
0
0
0
0
0
0
0
1
2
0
0
2
2
0
2
0
0
2
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
1
1
0
1
0
1
0
0
2
0
0
0
0
0
0
1
0
0
1
0
1
1
0
1
0
1
2
0
0
0
2
0
0
1
0
1
0
1
2
0
0
0
2
1
0
0
0
0
2
2
2
0
0
1
0
1
0
0
1
2
0
0
0
0
0
0
1
0
0
3
0
0
0
0
2
0
1
6
0
0
0
2
1
2
0
2
1
0
0
1
0
2
2
2
2
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
1
0
1
0
2
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
1
0
0
2
1
2
0
1
0
0
0
0
0
3
2
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
1
0
2
2
0
0
2
2
2
0
0
1
0
0
0
0
0
0
0
1
1
2
0
0
1
0
0
0
1
0
1
2
0
0
0
1
0
2
0
2
0
5
3
1
0
2
0
0
1
0
2
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
3
1
0
0
0
2
2
2
2
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
2
0
0
0
0
0
0
2
2
0
0
0
0
2
0
2
2
0
2
1
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
3
1
0
0
0
0
2
0
0
2
0
2
3
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
1
1
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
2
0
1
2
0
2
1
0
0
2
1
1
0
0
0
2
0
0
3
0
0
0
0
1
0
0
1
1
1
1
0
2
2
2
0
0
0
0
0
1
1
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
1
1
3
0
1
1
2
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
2
0
2
0
2
0
4
0
0
3
1
0
1
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
2
0
0
2
0
0
2
1
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
1
0
0
0
0
1
1
0
2
2
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
1
1
2
0
0
1
0
0
0
0
0
0
2
0
2
1
0
0
0
2
3
3
0
1
0
1
1
1
2
0
1
1
0
0
0
0
0
2
3
0
0
1
0
1
2
0
1
0
0
2
2
0
0
0
0
0
2
2
1
1
0
1
0
0
0
0
2
0
0
0
0
3
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
2
0
0
0
1
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
1
0
0
1
2
1
0
1
1
0
0
1
0
0
2
1
0
0
0
0
0
0
3
2
1
0
0
2
0
1
2
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
1
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
2
3
0
0
1
0
0
2
0
0
0
0
1
0
0
2
0
0
3
0
0
0
0
0
0
0
3
0
0
2
0
2
0
2
0
1
2
1
0
0
0
0
0
2
2
0
0
1
0
2
0
0
0
0
1
0
2
1
0
2
0
0
1
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
2
0
0
0
2
2
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
1
1
2
0
0
1
1
0
0
1
0
0
0
1
1
3
0
1
0
2
0
2
1
2
1
0
0
0
1
0
2
0
0
0
3
0
0
0
0
2
0
2
0
0
0
0
0
0
0
3
1
0
1
0
0
0
0
1
1
1
2
0
0
0
1
0
1
0
5
0
0
2
0
2
2
0
1
1
0
2
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
1
1
0
0
0
2
0
0
1
1
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
2
6
2
1
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
4
0
0
0
2
2
0
0
2
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
2
0
0
0
0
0
3
0
4
0
0
0
2
0
0
0
2
0
3
0
1
1
0
0
0
0
0
0
1
0
1
2
3
0
0
2
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
2
0
0
1
1
0
0
0
0
0
2
1
1
2
0
3
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
2
0
0
2
1
0
1
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
2
0
1
0
0
2
0
0
0
2
1
2
0
0
1
2
0
0
0
0
2
0
0
2
0
4
0
0
1
0
0
1
2
2
2
0
1
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
1
1
1
2
0
0
2
1
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
4
0
0
1
0
1
0
1
2
0
0
2
3
0
0
0
0
0
0
0
1
0
1
0
0
3
0
0
0
0
0
1
1
0
1
0
1
2
0
0
2
0
1
0
1
0
0
2
0
3
0
1
2
1
0
0
2
0
1
0
1
2
0
1
0
0
0
0
0
0
0
2
1
0
0
2
0
0
1
0
2
1
0
0
0
0
5
3
0
0
0
0
4
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
2
0
1
0
1
0
0
2
2
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
7
1
0
0
0
1
0
0
2
0
1
0
0
0
0
0
5
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
1
1
2
0
1
0
2
0
0
3
0
2
0
0
0
0
1
0
0
0
0
1
1
1
0
1
2
0
0
0
0
0
1
0
0
0
0
3
3
1
1
1
0
1
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
1
0
0
1
1
2
0
0
0
0
0
1
2
0
2
0
0
0
0
0
3
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
2
0
1
2
3
2
0
1
0
0
0
0
0
1
2
2
2
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
1
0
2
2
0
0
1
0
0
0
0
0
1
0
0
1
0
4
0
1
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
1
1
1
1
0
0
0
2
1
1
0
2
1
1
0
0
2
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
1
1
0
0
1
1
2
1
0
3
0
2
0
2
0
0
2
0
0
2
0
0
3
0
0
0
1
0
0
1
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
1
2
2
2
1
1
0
1
0
1
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
2
2
1
1
0
1
0
0
1
0
0
1
0
2
1
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
2
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
6
0
0
0
2
2
0
0
0
0
2
0
1
0
0
0
2
2
0
0
0
1
0
2
4
0
0
0
0
2
2
0
0
0
0
2
0
1
0
0
0
0
0
8
1
0
0
0
0
0
1
2
2
0
2
0
0
0
1
1
0
0
0
0
0
0
0
1
0
2
0
0
1
2
0
0
2
0
0
0
0
1
2
0
0
0
0
3
7
2
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
1
1
2
0
1
1
2
0
2
0
0
2
0
0
0
0
0
2
2
0
2
0
0
0
0
1
1
0
2
0
1
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
1
0
0
0
1
2
2
0
0
2
0
2
2
2
0
0
0
2
2
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
1
2
0
2
0
0
0
2
0
0
0
0
0
0
1
1
1
2
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
2
0
2
1
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
1
0
0
0
2
0
2
0
1
0
2
0
1
0
1
1
0
0
0
0
1
0
1
3
0
1
2
0
1
1
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
3
0
3
0
0
0
0
0
0
2
0
0
0
2
0
0
2
1
3
0
2
0
3
0
0
0
1
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
1
0
0
0
0
1
1
1
0
2
0
0
1
0
0
0
2
0
2
0
1
0
0
0
2
2
0
0
1
1
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
2
2
0
0
0
0
3
2
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
1
2
0
0
2
2
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
1
0
0
1
3
0
0
0
1
0
2
1
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
3
0
0
1
2
2
2
2
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
2
0
0
1
2
1
0
1
2
0
0
0
0
2
1
0
0
1
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
1
0
0
2
0
0
0
0
0
0
2
2
0
2
1
0
2
1
1
1
2
0
0
0
1
1
1
0
0
1
0
0
2
0
2
0
0
0
0
1
0
1
1
2
0
2
0
0
1
0
0
0
0
0
0
3
0
0
2
0
3
1
0
1
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
1
1
2
2
0
0
2
0
3
1
0
0
0
0
0
2
0
0
0
2
0
2
0
0
1
0
1
0
1
0
2
0
1
1
0
0
0
0
2
1
2
0
2
1
0
1
0
0
0
3
0
1
0
0
0
0
2
0
0
0
0
2
0
3
2
2
1
2
2
0
0
1
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
2
1
0
2
0
1
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
1
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
2
0
0
1
0
0
0
1
0
0
0
1
0
2
2
2
2
0
0
0
0
0
2
0
0
2
2
0
0
2
0
0
0
2
4
1
1
2
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
5
0
0
0
0
0
0
0
0
2
2
0
1
0
3
1
1
0
1
0
0
0
0
0
1
2
1
0
2
1
1
0
1
1
0
0
1
1
2
0
0
1
0
0
1
4
1
0
1
0
0
0
3
3
0
0
0
4
1
3
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
1
0
2
0
0
1
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
1
6
3
0
0
0
0
0
0
0
0
1
0
1
2
0
2
1
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
1
1
0
1
0
0
0
0
2
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
2
1
0
1
0
0
2
1
0
1
0
1
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
4
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
2
2
0
3
1
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
2
0
1
2
1
0
1
0
0
0
1
0
0
0
0
2
0
1
0
0
0
1
1
1
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
2
2
0
0
0
1
0
1
0
0
3
0
1
0
0
0
0
1
1
0
2
0
0
0
1
2
0
1
0
0
0
0
0
0
1
2
1
2
0
2
4
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
3
0
1
0
2
1
0
0
0
0
0
2
1
1
0
0
3
0
0
0
0
2
0
2
0
3
1
0
0
0
1
1
0
2
2
2
0
2
2
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
3
2
2
0
0
1
0
0
0
3
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
1
1
1
2
2
0
2
0
4
0
1
0
0
1
0
1
0
2
0
0
0
0
1
1
1
1
1
0
0
2
0
1
1
0
0
1
0
0
0
0
2
0
2
0
0
2
2
0
2
0
0
0
0
0
0
3
2
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
1
1
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
1
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
2
0
1
0
2
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
1
2
1
0
0
0
0
0
3
1
2
2
0
0
0
0
0
3
1
0
0
0
0
0
0
2
0
2
0
5
0
0
0
0
0
0
2
0
1
0
0
2
0
0
2
0
0
1
0
0
2
0
0
0
1
0
0
0
2
0
2
0
0
0
0
3
2
0
2
0
0
2
0
2
0
1
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
1
1
0
2
1
0
0
1
0
0
2
0
0
0
2
0
2
2
1
0
1
2
0
0
0
3
0
0
0
0
1
1
0
0
1
2
1
1
0
1
0
2
0
0
0
0
1
1
0
0
0
0
0
0
2
2
0
3
0
1
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
2
0
1
0
0
1
2
0
1
0
1
0
0
1
2
0
0
3
2
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
2
0
1
1
0
0
0
1
0
0
0
0
0
2
0
0
2
0
1
0
0
1
0
0
0
0
0
0
1
0
0
2
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
2
0
0
0
2
0
0
1
0
0
0
1
1
2
0
4
0
0
14
0
0
2
1
0
0
0
0
1
0
0
0
0
0
2
1
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
1
1
2
0
1
0
0
0
0
0
0
3
0
0
0
0
2
1
2
0
0
0
3
1
3
1
0
0
0
2
0
0
0
2
2
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
1
1
0
1
2
1
0
2
0
0
0
0
1
0
0
0
0
11
2
0
0
6
1
0
0
2
0
0
1
0
0
2
1
0
0
0
1
0
0
0
0
1
2
1
0
0
0
2
0
0
0
2
0
1
2
0
2
0
1
0
0
0
0
1
2
0
0
0
1
2
0
2
0
0
0
0
1
1
0
2
1
2
0
1
0
0
0
0
2
0
1
0
0
0
0
0
1
2
0
1
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
1
0
0
2
1
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
2
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
1
0
0
0
1
0
2
0
0
1
0
0
2
0
0
2
0
0
0
1
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
2
0
1
0
0
1
0
1
0
1
0
2
0
0
0
0
1
0
0
0
1
1
5
2
0
0
2
0
0
0
0
4
0
0
0
0
0
0
0
5
1
0
0
1
2
1
0
2
1
3
0
0
0
4
2
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
7
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
2
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
3
0
1
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
1
0
1
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
2
0
2
1
0
0
0
0
0
0
2
1
0
0
0
1
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
2
1
0
1
1
2
2
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
2
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
2
0
0
2
0
0
0
0
0
2
2
2
0
0
2
1
0
0
2
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
2
4
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
2
2
0
0
0
0
1
2
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
3
1
0
1
0
0
2
1
0
1
1
1
4
1
0
0
2
0
0
0
0
5
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
2
1
1
0
0
0
0
0
0
0
2
5
1
0
0
0
4
0
1
0
0
0
2
0
0
1
0
0
2
2
0
2
0
0
0
0
0
0
1
0
0
2
2
0
2
2
0
1
0
0
0
0
0
1
0
2
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
1
0
0
2
1
1
0
2
0
0
0
1
1
0
0
0
2
1
1
1
1
2
0
4
0
3
0
0
1
0
0
0
2
0
0
1
0
0
2
0
3
0
4
0
0
1
2
0
1
2
0
0
0
1
0
2
2
0
3
0
0
0
0
1
2
0
0
0
0
0
1
1
1
1
0
2
0
0
1
0
0
2
0
0
3
0
2
0
0
2
2
0
1
1
0
2
0
1
0
2
0
1
0
0
0
0
0
0
0
2
0
0
2
0
2
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
1
3
1
0
0
1
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
2
0
1
0
2
0
0
1
2
0
0
1
0
2
0
1
0
0
1
0
0
2
0
0
0
3
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
1
0
0
1
1
1
0
2
2
0
2
0
1
0
1
0
0
0
2
2
1
0
2
0
0
0
2
0
1
0
0
0
0
1
1
0
1
2
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
2
2
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
4
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
2
1
0
2
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
2
0
3
2
0
0
0
1
1
1
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
3
1
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
3
2
2
2
0
2
2
2
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
2
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
1
0
0
2
5
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
1
0
0
0
2
0
1
0
2
0
0
1
0
0
1
0
0
2
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
1
2
1
0
0
1
0
0
1
1
0
0
2
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
2
0
1
1
1
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
2
0
0
0
3
0
0
0
0
2
1
1
1
0
5
1
0
0
0
0
0
0
1
0
0
2
2
1
1
0
0
0
0
1
1
0
0
0
1
0
0
0
2
2
3
2
0
0
0
0
2
0
0
0
2
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
3
1
0
0
0
2
2
0
0
1
2
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
3
0
1
0
0
1
0
0
0
0
1
0
0
0
2
1
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
2
0
2
0
0
2
1
0
0
0
2
0
0
0
2
1
0
0
0
0
2
2
0
0
1
0
0
2
0
3
0
0
1
0
0
1
0
1
0
0
0
1
0
0
1
0
1
1
0
0
0
1
1
0
0
0
3
2
0
2
2
0
1
0
1
0
0
0
2
0
1
0
0
1
0
0
0
2
3
0
1
1
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
1
1
0
0
0
2
1
2
0
1
0
3
0
1
2
0
0
0
0
0
0
0
1
0
3
1
0
1
1
2
0
0
2
0
0
0
1
2
0
0
0
0
0
2
0
0
2
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
2
1
0
0
0
0
0
2
0
0
2
3
1
0
1
0
1
0
0
0
0
1
1
0
0
0
2
2
1
0
0
2
0
2
0
0
0
4
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
2
1
0
1
0
1
0
0
0
0
2
3
0
4
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
2
2
0
0
0
2
0
2
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
1
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
2
1
2
2
0
1
2
1
0
0
0
0
2
0
2
3
0
0
0
0
0
0
3
0
1
0
0
0
0
2
0
2
0
0
0
0
0
2
1
1
2
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
2
2
1
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
4
0
1
1
2
2
0
0
3
0
0
0
2
0
0
0
1
1
2
0
0
3
0
4
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
2
2
0
0
0
0
2
0
0
0
0
3
3
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
3
0
0
2
0
1
0
0
1
0
0
0
1
0
1
0
1
1
0
0
0
0
0
2
1
1
1
1
0
2
0
2
0
3
2
2
0
0
0
0
3
0
1
0
2
0
0
0
0
1
0
0
1
0
1
0
2
0
2
2
0
0
0
0
1
0
0
1
0
0
1
0
1
2
0
0
2
0
0
0
0
1
0
0
0
0
0
3
1
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
1
0
1
1
0
1
0
0
0
0
2
0
1
2
0
0
1
0
2
3
1
0
2
0
2
0
0
0
2
0
0
3
1
0
0
1
1
0
0
2
0
0
3
0
1
2
1
1
2
1
0
0
0
0
0
2
0
1
0
0
0
2
2
1
1
2
0
2
0
0
0
0
0
2
1
0
2
0
0
2
0
0
1
0
0
0
0
0
2
2
2
0
0
0
2
0
2
2
1
1
2
0
0
1
0
2
0
2
1
1
1
0
0
20
1
0
1
0
0
1
1
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
2
0
0
1
1
0
0
0
0
2
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
1
1
0
0
2
0
1
0
4
0
0
1
1
0
2
0
2
2
2
0
2
0
1
0
2
1
1
0
0
2
0
1
0
0
0
0
0
0
0
2
0
2
0
2
0
1
0
0
0
2
1
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
3
0
0
2
1
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
2
0
1
0
2
0
0
1
0
0
0
0
0
1
0
0
1
0
0
2
2
0
0
0
0
2
0
0
0
0
1
1
8
0
0
0
0
0
5
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
1
0
2
0
0
0
0
0
0
1
0
0
2
0
0
1
0
2
2
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
1
1
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
2
0
2
2
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
2
0
2
0
0
0
2
0
1
1
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
1
2
1
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
1
0
0
0
0
0
0
0
2
0
1
1
2
0
1
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
1
2
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
1
1
1
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
1
1
2
1
1
1
0
0
0
0
2
0
2
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
1
0
1
0
0
2
4
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
1
1
0
0
1
1
1
0
0
1
0
0
1
1
0
0
0
0
2
0
0
1
2
0
0
1
2
1
0
0
2
0
0
2
2
1
0
1
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
1
0
2
2
1
2
0
2
0
1
2
1
2
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
7
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
1
0
3
0
0
0
0
0
2
0
1
1
0
2
1
0
0
0
0
2
0
0
0
0
2
2
1
0
2
0
0
0
1
0
1
0
2
2
0
2
0
0
0
2
0
0
0
0
0
4
0
0
0
0
0
1
0
2
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
3
2
0
0
0
0
2
2
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
2
1
0
1
0
2
0
0
0
0
0
0
1
0
1
0
1
1
0
0
2
0
2
2
0
0
0
1
2
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
1
2
4
0
0
2
1
7
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
2
1
1
0
2
1
0
2
1
0
0
2
0
1
0
0
2
0
0
3
0
0
2
0
0
2
2
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
2
2
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
2
0
1
2
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
1
1
0
0
0
5
0
1
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
2
1
2
0
0
0
1
0
1
2
2
0
1
0
2
1
1
0
0
0
0
1
2
2
1
2
2
1
0
0
0
0
2
0
0
0
1
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
1
0
0
0
1
1
0
2
0
0
0
0
3
1
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
1
2
1
0
0
0
0
2
0
1
0
0
1
1
0
1
0
0
0
0
2
2
0
0
1
1
0
0
0
1
2
0
0
1
0
2
0
0
1
0
0
1
0
0
0
1
0
2
1
0
2
0
0
0
1
1
0
2
0
0
0
0
0
1
2
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
1
2
1
0
1
2
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
2
0
0
1
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
2
0
1
0
0
1
0
1
0
2
0
1
0
3
2
2
2
2
0
0
0
2
2
0
2
0
2
0
2
0
2
0
0
0
0
1
2
0
2
0
1
0
0
0
1
0
0
0
3
2
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
2
2
0
1
0
1
1
0
0
0
0
0
1
0
0
1
3
1
1
1
1
0
2
0
1
0
0
0
2
2
0
2
0
3
0
0
0
0
2
0
1
0
2
2
0
0
1
0
2
0
0
0
2
0
0
1
3
0
0
0
1
0
0
0
0
0
0
0
1
2
0
1
1
2
0
1
1
0
0
0
0
0
2
0
0
1
0
0
2
0
0
1
0
0
0
2
2
1
1
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
2
0
2
3
0
0
0
1
2
2
0
0
1
0
0
1
0
1
2
0
0
1
0
0
0
0
1
2
0
0
0
0
0
3
2
2
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
2
1
1
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
3
0
1
0
0
0
1
1
2
0
0
0
2
0
0
6
1
0
0
0
1
2
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
5
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
2
2
0
0
0
2
1
0
0
2
0
1
2
0
1
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
2
2
2
1
0
0
0
2
0
2
1
1
0
0
1
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
1
0
0
0
0
0
2
1
0
2
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
1
1
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
1
0
1
1
0
0
1
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
5
1
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
1
0
1
0
2
0
0
0
2
4
0
1
2
2
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
2
0
2
1
2
1
0
0
0
1
0
0
0
2
0
2
0
0
2
2
1
0
0
0
0
0
0
2
0
0
0
0
1
2
0
1
0
0
0
0
0
0
2
0
1
0
2
0
1
1
1
0
2
0
0
0
0
0
0
1
2
0
0
0
2
2
2
1
2
0
0
0
2
0
1
1
0
0
0
2
0
0
2
2
2
0
2
0
1
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
2
0
1
1
0
1
0
0
2
0
2
0
0
0
0
0
0
0
1
0
1
2
0
0
1
0
1
2
0
0
0
0
0
0
1
1
3
0
0
0
1
0
1
0
0
0
0
2
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
2
1
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
2
2
1
3
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
2
1
1
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
2
3
0
0
0
0
2
2
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
1
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
2
0
0
1
0
0
1
0
2
0
2
1
0
0
0
0
3
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
2
0
0
0
2
1
1
0
0
1
0
2
2
2
0
2
0
0
0
1
2
2
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
3
0
1
0
2
0
0
0
0
2
1
0
0
0
2
2
1
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
2
0
2
0
0
0
0
3
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
1
0
2
0
0
0
0
0
0
3
0
0
2
0
0
2
0
0
0
0
0
0
2
1
0
0
0
2
0
4
0
0
1
0
0
0
2
0
0
0
0
2
1
0
0
0
2
0
0
0
2
0
2
0
0
0
2
1
0
0
1
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
2
0
2
0
1
0
0
0
0
0
1
0
1
1
1
1
0
0
0
0
0
2
1
2
0
0
0
0
0
1
0
2
2
0
0
1
0
1
0
0
0
1
0
0
1
2
0
0
0
0
1
0
0
0
0
0
2
1
0
1
2
0
2
2
1
0
0
4
1
2
1
0
0
0
0
0
0
1
1
1
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
1
0
3
4
0
0
2
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
2
0
1
1
0
1
0
2
1
1
0
0
0
1
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
1
0
0
1
1
0
0
2
0
0
0
0
2
1
0
0
1
2
0
0
0
2
0
0
0
0
0
0
1
1
1
0
0
2
0
0
0
2
1
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
1
0
0
2
2
0
1
3
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
5
0
0
0
0
0
0
0
2
0
0
1
0
1
2
2
1
1
2
1
0
0
0
0
2
0
1
0
1
0
0
0
2
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
1
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
2
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
1
1
0
2
0
0
2
0
1
0
0
0
0
0
0
1
1
0
0
2
0
1
2
1
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
4
0
2
0
2
1
1
0
0
0
1
0
1
0
1
0
0
2
0
1
2
1
0
2
2
0
2
0
0
0
0
0
0
1
1
1
1
0
0
2
2
2
0
0
3
0
1
24
1
0
2
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
1
2
1
0
2
0
0
2
3
4
0
0
0
2
0
0
0
0
3
1
0
0
0
0
1
0
1
0
0
2
1
0
0
0
0
2
0
0
0
0
0
2
2
1
1
0
1
1
0
0
0
0
0
2
2
0
1
0
1
0
2
0
0
1
0
1
1
2
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
2
1
0
2
2
2
1
0
0
0
2
0
0
2
0
1
0
1
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
1
2
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
1
0
0
0
2
0
0
0
2
2
0
1
0
3
0
0
2
1
2
0
2
2
1
1
0
0
2
2
2
2
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
3
1
0
0
0
0
1
1
0
0
0
0
3
1
0
2
2
0
0
0
0
0
2
0
0
3
2
2
1
0
1
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
4
3
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
3
0
0
0
4
0
0
1
1
0
0
1
5
0
2
0
2
0
0
0
0
0
0
2
1
0
1
0
2
0
1
0
0
1
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
5
0
0
1
1
0
0
0
0
0
0
0
1
0
0
2
0
0
1
2
1
1
1
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
2
1
2
0
0
1
2
1
1
0
1
0
0
1
0
0
2
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
1
0
0
2
0
1
0
1
0
0
0
0
0
1
2
2
0
1
0
0
0
0
0
0
0
0
1
0
2
2
2
0
0
0
2
2
0
1
2
0
2
2
0
0
0
1
0
0
2
0
1
2
1
0
0
0
0
1
3
0
1
2
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
2
0
0
0
0
1
2
2
0
2
1
0
0
1
0
2
0
2
0
0
0
2
3
0
0
0
0
0
1
0
1
0
0
0
0
0
1
2
0
0
0
2
0
0
1
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
2
0
2
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
1
0
1
0
0
0
10
2
2
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
6
0
0
0
0
2
0
0
1
2
0
0
3
0
1
0
2
1
0
1
1
0
0
2
1
0
0
0
0
0
0
1
0
0
4
1
2
0
0
3
1
0
0
0
2
0
0
0
0
0
1
0
0
2
0
1
2
0
0
0
0
0
2
1
1
1
0
0
0
1
0
0
0
0
0
1
3
0
0
0
0
0
1
0
1
0
1
2
0
0
2
1
2
0
0
0
0
0
2
0
0
2
0
0
1
0
2
0
0
0
5
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
2
1
2
3
0
0
2
1
0
0
0
2
0
1
0
2
0
0
1
2
1
0
0
0
0
2
0
2
0
0
2
0
0
0
0
2
0
0
2
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
1
0
1
1
2
0
0
0
1
0
0
0
2
0
0
2
0
1
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
2
2
2
0
0
0
0
1
1
0
2
0
1
0
1
1
0
0
0
0
0
1
1
3
0
1
2
1
0
0
0
0
0
0
0
4
0
0
0
0
0
2
1
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
1
1
0
0
0
2
2
0
0
1
0
0
2
0
1
0
0
0
0
0
2
4
0
0
0
2
0
2
1
0
0
2
1
0
0
0
1
0
0
0
0
2
0
0
0
1
2
0
0
0
0
1
2
0
1
0
0
0
0
0
0
2
1
0
1
1
1
0
0
0
2
0
0
2
0
0
0
0
3
2
0
1
2
0
2
1
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
1
2
1
0
2
0
0
3
3
0
0
0
5
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
6
1
0
0
2
1
2
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
2
1
0
1
0
1
0
1
0
0
0
0
0
0
0
2
1
1
0
2
1
1
0
2
1
1
2
0
2
0
0
0
1
0
0
0
1
2
0
1
0
2
2
0
1
0
0
0
0
0
0
1
0
0
0
2
1
0
0
3
2
0
1
1
2
0
0
3
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
1
1
0
0
1
0
0
1
1
2
0
1
0
0
0
1
0
1
0
2
2
0
0
0
1
3
0
0
0
2
0
0
1
0
0
2
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
1
0
0
3
0
0
2
3
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
2
2
0
1
2
0
0
2
2
0
2
0
1
0
0
2
2
3
0
0
0
2
2
0
0
1
1
1
1
0
1
0
0
0
0
1
0
2
0
0
0
0
1
1
0
0
2
0
0
1
0
0
0
0
0
2
2
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
1
3
0
0
3
1
0
1
0
1
1
2
0
2
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
3
0
2
2
0
0
0
0
0
0
0
0
2
2
0
1
1
2
2
1
0
2
2
0
2
0
0
0
0
2
1
0
0
5
0
3
1
3
0
2
0
0
0
0
0
1
0
0
0
4
2
1
0
2
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
1
0
0
2
4
0
3
2
0
0
1
0
1
0
0
1
1
2
0
0
0
0
0
0
0
1
0
0
1
0
2
2
0
1
0
1
4
0
0
1
0
1
2
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
2
0
1
0
0
7
0
0
0
1
1
2
1
0
0
0
6
0
0
0
0
1
0
1
1
2
0
1
1
2
1
2
1
0
2
0
2
0
1
2
2
0
0
2
2
0
2
1
0
2
2
1
0
2
0
0
0
0
0
1
2
0
0
0
0
1
1
0
0
0
0
1
0
0
2
0
2
1
1
2
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
2
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
1
2
0
2
0
1
0
0
0
1
0
0
2
1
1
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
2
1
1
0
1
0
0
0
0
2
1
1
1
2
0
0
1
1
0
2
0
0
0
0
1
0
3
0
0
0
0
0
1
0
0
0
2
1
0
1
2
2
0
0
2
0
0
3
0
0
1
0
0
0
2
2
0
1
0
2
2
0
0
0
0
2
0
2
0
2
2
0
0
0
0
2
1
0
1
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
1
0
1
2
2
0
1
0
0
0
0
0
1
1
1
0
0
0
3
2
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
2
0
0
0
0
0
1
0
1
0
2
0
1
2
0
0
0
2
3
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
4
1
0
1
0
0
0
0
0
0
1
2
0
0
0
2
2
0
1
0
0
0
0
0
0
0
2
10
0
0
0
4
0
1
0
0
0
1
0
2
0
0
1
2
0
0
0
2
1
2
0
0
1
0
1
0
0
3
2
2
0
1
3
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
4
0
1
0
1
1
2
0
0
0
0
0
2
0
0
2
0
2
0
1
2
0
0
0
1
0
0
0
0
1
0
0
1
2
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
2
3
0
1
0
0
2
2
4
1
2
1
0
0
0
0
1
0
1
1
1
0
0
0
0
2
2
0
0
0
5
0
0
1
2
0
1
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
1
1
1
0
0
0
0
1
1
4
2
4
0
0
0
2
0
1
0
0
0
0
1
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
2
0
3
0
1
0
0
0
2
0
1
0
0
0
2
2
0
0
0
2
0
0
2
1
0
0
0
1
0
1
0
0
0
0
2
2
0
2
0
0
0
2
1
0
1
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
2
1
0
5
0
2
0
2
0
0
1
0
2
0
0
0
0
0
2
2
0
0
1
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
1
4
0
0
0
0
0
1
1
0
1
0
1
0
0
2
1
0
2
0
1
1
0
0
2
0
0
2
1
0
0
0
2
1
2
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
1
0
0
0
2
1
2
0
2
2
0
0
0
0
0
0
0
0
2
1
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
3
1
1
2
1
0
0
5
0
2
0
0
0
0
0
0
3
0
0
2
0
0
2
0
2
0
0
3
2
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
5
0
0
0
0
2
0
1
0
2
2
0
0
0
1
0
1
0
2
1
0
0
1
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
3
0
1
0
2
0
0
2
3
1
0
2
2
0
0
0
0
1
1
0
1
2
0
0
2
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
2
2
2
1
0
0
0
0
0
2
2
1
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
1
0
0
0
1
2
0
0
0
2
0
0
1
1
0
0
0
1
1
0
1
1
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
1
0
1
1
2
0
2
0
1
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
1
1
0
0
2
0
0
0
3
0
2
2
0
0
0
0
0
0
0
0
0
1
0
2
2
0
1
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
1
2
1
0
4
0
2
0
0
0
0
0
0
0
2
0
1
0
1
0
0
1
0
0
0
1
3
0
0
0
2
0
0
0
0
0
1
0
1
0
2
2
3
0
2
0
0
2
0
2
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
2
2
0
4
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
3
0
1
0
0
0
1
0
0
1
2
1
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
2
0
1
2
0
2
0
2
0
0
0
0
0
0
1
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
1
2
0
2
0
0
1
0
0
0
0
0
2
1
4
2
0
0
0
0
1
0
0
0
0
0
0
1
1
2
1
0
0
2
0
0
0
2
1
1
0
0
1
0
0
1
0
0
2
0
0
1
0
0
1
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
2
0
0
0
5
0
2
0
2
0
0
2
5
1
0
0
0
2
1
2
0
2
0
1
0
0
0
1
0
2
0
0
1
0
0
1
2
1
0
2
0
1
0
1
4
2
0
0
0
0
3
3
2
2
1
2
0
0
0
2
1
0
2
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
1
0
0
1
2
1
1
0
2
0
2
1
1
2
0
0
0
0
0
3
3
1
0
0
3
2
1
1
0
2
0
2
0
0
0
1
1
0
2
0
0
0
1
2
0
0
2
0
1
0
2
0
0
1
1
0
2
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
2
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
7
0
2
0
0
2
1
0
0
0
1
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
2
2
0
2
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
1
1
0
0
0
0
0
0
0
0
1
1
0
3
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
1
2
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
2
1
0
0
2
1
0
0
0
0
1
1
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
3
0
0
1
1
0
2
0
0
0
0
3
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
1
0
0
0
2
3
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
3
2
0
0
0
0
0
0
0
0
1
2
0
2
2
0
0
1
0
0
2
2
1
0
0
2
0
0
0
2
0
0
0
1
2
0
0
1
2
0
2
2
0
2
1
0
0
0
0
2
0
1
2
0
1
0
0
0
2
2
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
6
0
0
0
1
0
9
0
0
0
0
1
0
0
2
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
2
0
0
1
0
1
0
0
2
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
2
1
0
1
2
1
0
0
1
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
1
0
1
1
1
0
1
0
2
0
0
0
1
0
0
0
0
0
2
1
2
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
1
1
1
0
1
0
0
1
0
0
0
2
0
2
2
0
0
0
0
1
0
0
0
0
1
0
1
2
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
2
0
0
1
2
1
2
0
1
0
2
0
2
2
0
2
2
0
0
2
2
1
2
0
2
3
1
0
0
0
0
1
0
0
1
2
0
0
0
2
2
0
1
1
0
2
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
1
2
0
2
0
2
0
1
0
1
0
1
0
0
0
2
1
0
1
0
1
0
3
2
2
2
0
1
0
0
0
3
1
2
0
0
0
0
1
1
0
2
0
0
0
0
0
2
0
0
2
0
0
2
1
0
1
0
0
0
1
0
0
0
2
0
0
0
2
5
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
1
2
2
0
0
0
0
1
2
1
0
0
1
0
2
1
1
2
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
3
2
0
2
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
1
2
0
2
1
0
0
1
0
0
0
2
2
2
0
2
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
2
1
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
3
0
0
0
0
0
2
0
0
2
0
0
0
1
0
2
0
2
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
2
0
2
2
0
0
0
2
0
0
0
0
2
0
1
0
0
2
0
2
0
1
0
0
0
2
2
0
0
1
0
2
0
0
0
1
0
0
0
0
1
0
0
2
0
1
0
0
0
1
0
2
0
2
0
0
0
0
1
0
1
0
2
1
0
0
0
0
0
2
0
1
0
0
2
0
0
2
0
0
0
0
1
4
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
1
1
1
0
0
0
2
0
1
0
0
0
0
0
1
0
5
0
2
2
0
0
1
2
2
0
0
2
2
2
2
2
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
1
0
1
0
0
2
1
0
0
2
0
1
2
1
1
0
0
0
0
0
1
0
0
1
0
0
0
3
1
0
0
0
0
0
2
2
0
0
1
0
2
1
2
0
0
0
0
3
0
0
1
2
0
0
0
0
3
2
1
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
2
0
0
1
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
1
0
0
2
0
0
1
0
2
2
2
0
0
0
0
2
2
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
1
1
1
0
0
0
0
0
0
2
2
0
2
0
0
1
0
2
0
0
0
2
0
1
0
2
1
0
1
0
0
0
0
2
0
1
2
0
0
0
0
0
0
1
0
2
0
1
0
0
2
0
0
0
2
0
3
2
0
0
2
0
2
0
2
0
0
0
0
1
1
0
0
2
0
1
1
0
3
1
1
2
0
1
0
2
0
0
2
1
0
0
0
0
0
0
2
0
0
2
1
1
0
0
1
0
0
0
1
2
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
1
2
0
0
4
1
0
0
0
1
0
0
2
1
0
2
0
0
0
5
0
2
1
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
1
2
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
2
2
0
2
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
2
0
0
0
2
1
0
0
0
1
2
2
1
2
0
1
1
0
2
0
0
0
0
0
1
0
0
0
1
0
2
0
0
2
0
0
0
1
1
1
0
0
0
0
0
0
0
1
1
0
0
2
0
2
0
1
1
0
0
2
1
0
5
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
2
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
2
0
0
1
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
2
0
0
0
2
2
0
0
0
0
0
1
2
0
0
2
0
0
1
0
0
0
3
1
0
0
2
2
2
0
1
1
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
3
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
2
0
1
1
0
0
2
0
0
0
2
0
4
2
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
3
2
0
1
0
0
2
1
0
1
0
0
0
0
0
0
1
2
1
0
0
0
2
1
2
0
0
0
0
0
2
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
1
0
1
1
0
0
0
1
0
2
0
4
0
2
0
2
0
0
0
0
1
1
0
0
2
0
0
0
2
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
2
0
0
0
1
0
1
0
2
0
0
1
0
2
0
0
0
2
0
0
2
1
0
2
0
0
0
0
2
0
0
0
2
2
0
0
1
0
0
2
0
2
0
1
0
0
0
0
1
2
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
2
2
0
0
0
0
0
2
0
1
2
0
0
0
4
0
0
0
0
0
0
0
1
0
2
0
0
0
0
3
1
2
0
2
0
0
0
0
0
0
0
1
0
3
0
0
0
0
1
0
1
0
2
0
0
0
1
0
0
1
1
2
0
2
0
0
2
1
0
0
0
0
0
0
2
0
0
1
0
2
2
1
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
2
0
2
1
2
2
0
0
0
1
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
2
2
0
2
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
1
2
2
1
2
0
0
0
0
0
1
2
0
0
0
0
1
1
2
0
0
4
0
3
0
0
1
1
0
0
0
2
2
0
0
0
1
0
0
1
1
2
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
1
0
0
2
2
3
0
0
0
2
0
5
0
0
2
0
1
0
1
0
0
0
1
0
0
0
1
0
1
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
1
0
3
1
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
2
2
0
3
2
0
2
1
0
2
3
3
1
0
1
1
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
1
0
0
2
3
0
2
1
2
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
2
2
2
0
2
1
0
2
1
0
0
1
2
2
0
0
1
1
1
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
1
2
2
0
1
0
0
0
0
1
1
2
1
1
0
2
1
0
0
0
0
0
0
3
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
1
1
2
0
1
4
0
0
1
0
1
0
2
1
0
2
0
0
1
2
0
0
0
2
0
0
2
0
0
0
0
0
2
0
2
3
0
1
1
1
0
0
0
0
0
0
0
1
0
2
1
3
0
0
2
0
0
0
0
1
0
0
2
0
2
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
2
2
0
0
0
1
0
0
0
1
0
1
0
1
0
1
0
2
1
1
0
1
0
0
0
0
0
2
2
0
0
2
1
2
0
2
0
1
0
1
1
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
2
0
2
2
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
2
0
2
1
0
0
0
0
0
1
1
1
0
1
1
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
3
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
1
0
0
3
2
0
0
2
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
2
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
2
0
2
0
0
0
1
0
0
1
1
1
0
2
0
0
1
0
1
1
0
0
0
2
3
1
0
2
0
0
1
0
0
0
2
0
0
2
1
1
0
0
0
0
1
2
0
2
0
0
2
2
0
2
0
0
0
1
2
0
0
0
2
2
0
0
0
1
1
0
0
0
1
2
1
2
2
0
0
0
0
1
1
0
0
2
0
3
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
2
0
4
0
2
0
0
0
4
1
0
1
2
7
0
0
1
0
0
1
0
0
1
0
0
2
0
0
0
0
0
2
2
0
2
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
2
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
1
0
2
0
2
0
1
0
0
1
0
1
0
1
0
2
0
0
0
2
0
0
2
2
0
2
0
2
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
1
3
0
0
0
0
0
2
0
0
1
0
2
2
0
1
1
0
3
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
1
0
0
3
0
1
1
0
1
0
0
1
0
0
2
0
0
2
1
0
1
1
1
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
2
3
0
2
0
4
0
0
0
0
0
1
0
0
0
1
1
7
1
0
0
0
0
2
0
2
2
2
0
0
0
0
0
2
0
0
1
1
0
1
0
1
0
0
0
0
1
0
1
2
1
0
0
2
0
0
3
0
1
3
2
0
1
0
0
0
2
1
0
0
3
1
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
1
2
0
0
2
0
0
0
3
0
2
2
0
0
0
0
2
0
0
0
2
1
2
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
1
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
1
0
1
0
0
1
2
0
0
2
0
0
0
2
0
0
1
0
0
0
1
0
1
1
0
1
2
0
0
0
0
0
1
2
1
1
1
1
1
0
2
1
0
0
2
0
2
2
3
3
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
1
0
2
0
1
2
0
2
0
2
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
2
2
0
2
1
0
0
2
2
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
5
1
0
1
0
0
0
0
0
1
1
1
0
1
0
0
0
2
0
0
0
0
1
2
0
0
1
0
0
1
1
0
1
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
3
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
2
0
2
1
0
1
0
0
2
1
0
0
0
2
0
0
0
2
2
0
1
1
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
1
2
2
0
2
1
1
0
2
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
2
0
2
1
0
2
1
2
0
1
10
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
1
0
3
0
0
0
1
0
0
0
0
2
1
0
1
1
0
0
2
0
2
1
1
2
1
0
2
0
2
0
0
0
2
1
2
0
0
0
0
2
2
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
1
3
1
0
1
0
2
0
0
2
1
0
0
0
1
1
1
0
2
0
2
0
0
0
2
0
2
2
0
0
0
0
2
2
1
1
0
0
0
1
1
0
1
1
0
0
0
0
0
1
1
2
0
0
1
0
0
0
0
0
1
1
1
0
1
0
0
1
1
0
0
0
1
0
2
1
1
0
0
2
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
2
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
2
0
0
1
1
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
3
0
1
0
0
0
1
0
0
1
1
1
0
0
0
2
0
2
0
1
0
1
2
0
0
0
0
0
0
0
0
0
4
2
3
0
0
1
0
0
0
0
0
2
0
0
0
1
2
0
0
1
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
4
0
0
0
0
0
2
2
1
0
2
1
2
0
2
0
0
0
0
2
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
2
1
2
0
0
0
0
1
1
1
0
0
0
1
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
1
0
1
1
1
0
0
0
1
5
1
1
2
0
2
0
0
0
3
1
3
0
0
14
0
0
1
0
0
0
0
2
0
2
0
2
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
2
2
0
0
0
0
0
2
0
1
0
0
3
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
4
0
1
0
0
1
2
0
1
0
0
0
1
0
0
1
0
0
0
2
0
2
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
1
0
0
0
1
0
0
0
3
0
0
2
0
1
1
0
1
2
0
2
1
1
2
0
1
2
0
0
0
2
2
0
0
0
1
1
0
0
0
0
0
3
0
2
2
2
0
0
0
0
4
0
2
0
0
0
0
0
3
2
0
0
0
1
0
1
0
0
0
1
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
2
0
0
0
1
1
0
0
1
1
1
0
0
0
0
1
0
0
1
0
1
0
2
2
1
1
0
0
2
1
1
3
0
0
0
0
2
3
0
2
0
0
0
0
0
2
0
1
2
0
1
0
0
0
0
2
0
0
0
0
1
0
0
2
2
0
1
0
0
1
2
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
1
0
7
1
2
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
1
1
1
0
4
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
2
0
2
0
1
1
0
2
0
1
2
2
0
0
0
0
1
0
0
1
2
0
1
2
0
2
2
0
0
5
0
0
0
0
0
0
0
2
1
2
0
0
0
1
0
1
0
1
2
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
2
6
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
1
0
0
1
0
0
0
2
0
0
2
2
1
0
0
0
1
1
0
1
0
1
0
1
0
0
0
0
0
0
2
0
0
0
2
2
2
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
2
0
0
2
0
1
0
2
1
0
0
1
0
0
0
0
0
1
0
0
1
2
0
2
1
2
2
0
0
0
2
0
0
1
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
1
0
2
0
2
2
0
1
4
1
1
2
2
0
0
0
0
2
1
1
1
0
0
1
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
1
0
0
0
2
0
0
1
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
1
0
2
2
0
0
1
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
2
0
0
0
0
0
0
0
2
1
2
0
0
2
2
3
0
0
0
1
2
2
1
0
2
0
0
0
0
2
2
1
0
2
1
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
1
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
2
0
0
1
0
0
2
2
0
0
3
1
2
0
0
0
0
1
0
0
0
0
1
0
2
1
0
2
0
0
0
0
0
2
1
0
1
1
0
1
0
0
0
0
0
0
1
0
2
0
2
0
0
2
0
0
0
0
1
2
0
2
0
2
0
0
1
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
3
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
2
0
0
1
0
0
0
2
0
1
0
2
0
0
2
0
0
0
0
1
0
1
1
0
2
2
0
1
0
2
2
1
0
0
1
1
0
0
2
0
0
2
0
3
0
0
0
0
0
0
0
0
1
0
4
1
0
2
1
0
0
0
0
0
0
1
0
0
0
0
1
0
2
3
1
0
1
0
0
0
3
1
0
0
0
0
1
1
0
1
0
0
1
2
0
0
0
2
0
1
0
0
2
0
0
2
2
0
0
0
1
1
0
0
2
0
0
0
1
1
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
2
0
0
0
1
0
2
0
0
1
0
0
0
0
4
0
2
0
1
1
3
0
0
0
0
0
0
1
0
1
0
0
1
0
0
2
0
0
0
0
0
1
1
1
0
2
0
0
0
0
1
2
1
0
1
0
0
0
0
0
2
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
2
2
2
1
2
0
0
1
3
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
2
2
0
2
1
1
0
0
0
0
0
0
3
0
0
2
0
0
2
2
0
2
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
1
2
1
1
1
0
0
2
1
2
1
0
0
0
0
0
0
0
0
2
0
2
2
0
2
1
1
1
1
1
0
1
0
1
0
2
3
0
2
2
1
2
0
0
0
0
0
1
1
2
0
2
0
1
0
2
0
0
0
0
2
1
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
3
0
3
0
1
0
0
1
0
0
2
0
2
1
0
1
0
0
0
0
0
4
1
1
0
0
0
0
3
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
1
2
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
2
0
0
1
4
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
1
1
0
0
2
0
0
0
1
1
0
2
0
0
0
0
1
1
0
1
1
0
0
2
0
0
0
0
2
1
0
0
0
2
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
2
0
2
1
1
2
1
0
1
1
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
2
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
2
1
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
2
1
0
0
1
1
0
1
0
0
2
1
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
1
0
0
0
1
3
3
0
0
2
2
1
0
0
1
2
0
1
0
0
0
0
3
0
0
0
0
2
2
0
2
2
0
0
0
0
1
2
0
1
0
0
0
0
0
0
2
1
1
2
1
0
0
0
2
0
1
0
0
1
0
0
0
1
1
0
0
2
1
1
3
0
0
0
2
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
2
0
0
0
0
1
0
2
2
0
0
0
5
1
2
1
2
0
0
2
3
3
0
1
0
2
2
0
0
0
0
1
0
1
0
2
0
1
2
4
0
0
0
0
0
0
1
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
3
0
0
1
2
0
0
2
0
2
1
0
1
0
0
1
0
0
0
2
0
0
0
0
1
0
2
1
2
0
2
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
1
0
3
0
0
0
0
1
1
2
0
0
3
0
0
1
2
0
1
0
0
0
0
1
0
0
1
0
0
4
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
1
0
0
1
2
0
0
0
2
0
0
1
0
0
2
0
2
1
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
2
1
2
0
0
2
1
0
0
0
0
1
0
1
2
1
0
0
2
0
2
0
2
0
0
0
3
2
0
0
0
0
0
0
2
0
2
0
0
2
2
0
0
0
0
1
2
2
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
1
0
2
0
2
0
2
2
0
0
1
0
0
2
0
2
0
0
0
0
0
0
1
0
2
2
0
0
0
2
2
2
0
2
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
2
2
1
0
0
1
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
3
0
1
1
0
0
0
0
0
0
1
1
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
2
1
0
0
2
0
2
0
0
1
0
1
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
3
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
3
2
0
0
0
0
2
1
0
0
0
0
2
2
0
2
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
2
0
0
0
2
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
1
2
0
2
0
0
0
0
0
2
0
0
2
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
3
2
0
0
2
2
0
2
0
1
2
0
1
2
1
3
2
0
0
0
2
2
2
1
0
0
0
0
2
0
0
2
0
0
0
0
1
1
2
1
3
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
1
2
1
0
8
0
1
0
1
3
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
2
3
2
1
1
1
0
3
0
0
2
0
0
0
1
0
2
1
0
2
1
0
1
0
1
0
0
0
1
1
1
0
0
1
0
0
0
1
0
1
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
2
0
0
3
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
2
1
0
0
1
1
0
0
0
0
1
1
0
2
0
0
0
4
0
0
0
0
0
1
2
1
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
2
1
1
0
0
1
0
0
1
2
1
2
2
5
0
2
0
0
1
1
2
1
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
4
1
2
0
0
0
2
1
0
1
0
0
2
0
0
1
0
1
0
0
0
1
0
3
2
0
0
0
0
0
0
1
0
2
2
2
0
0
0
1
2
0
0
1
0
0
2
0
0
1
0
1
0
2
1
0
0
0
0
0
0
2
2
0
0
1
0
0
2
0
1
1
0
0
1
2
0
0
0
0
0
0
0
0
0
1
1
2
0
2
0
1
2
0
2
0
0
0
2
0
0
2
0
0
0
0
1
0
0
1
2
0
0
2
0
0
0
0
0
1
1
2
0
2
0
0
2
1
0
0
0
0
0
2
0
0
0
1
0
2
0
1
0
0
2
0
0
0
0
0
0
0
2
2
2
1
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
2
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
4
0
0
0
2
0
1
0
1
0
0
3
0
2
0
1
0
1
3
1
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
3
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
2
2
0
0
0
2
0
0
1
1
1
3
2
1
5
0
0
0
0
0
2
1
0
1
0
1
0
0
0
0
1
0
0
2
0
0
1
0
1
1
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
5
0
0
0
0
0
1
0
0
1
0
1
5
0
2
0
2
2
0
0
0
1
1
1
3
0
3
0
1
0
0
0
9
0
0
0
1
0
0
2
0
0
0
0
1
2
1
0
0
0
0
3
2
0
0
1
0
2
2
1
2
0
0
3
0
0
2
0
1
1
0
0
2
0
0
0
2
2
0
0
0
0
0
1
0
0
2
0
0
2
2
0
1
1
2
0
0
0
1
0
0
0
1
0
1
0
2
0
0
1
1
0
2
0
0
2
0
0
0
0
1
1
0
1
1
2
0
0
0
1
2
0
0
0
2
2
1
0
0
0
1
0
0
0
0
1
0
1
1
1
2
2
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
2
1
0
0
0
0
2
0
3
0
0
1
2
2
0
2
0
2
0
0
1
0
1
2
3
2
0
2
2
0
1
0
2
0
0
0
0
1
0
1
2
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
2
0
0
0
1
2
0
0
1
1
0
0
2
3
0
1
0
0
0
0
2
0
0
0
2
1
1
0
0
0
1
0
0
0
0
2
0
0
1
0
1
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
1
0
1
0
0
0
0
2
0
2
3
0
0
2
2
0
0
0
0
0
2
0
0
0
2
0
0
1
0
2
0
0
0
0
1
1
2
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
1
1
0
0
0
2
2
0
1
0
0
0
0
4
0
1
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
2
0
1
0
0
0
1
1
1
0
0
0
0
0
2
0
0
0
1
0
1
1
2
0
2
1
0
0
0
0
2
2
2
0
3
0
0
0
2
0
0
1
1
0
0
0
2
1
0
0
0
2
0
1
0
2
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
2
0
0
0
0
2
0
1
0
2
0
2
0
0
1
2
0
1
0
0
0
0
2
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
2
0
0
0
0
2
0
0
0
0
2
0
2
1
0
0
0
0
0
0
2
3
0
0
4
2
0
0
0
0
0
2
2
1
1
2
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
3
1
2
0
2
2
0
2
0
0
0
0
1
0
0
1
2
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
2
1
1
0
2
0
1
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
2
0
1
2
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
2
0
0
0
0
0
2
0
2
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
1
2
2
0
1
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
1
0
1
1
2
0
0
0
0
1
0
0
0
2
0
0
0
0
1
1
0
0
2
2
0
0
1
0
2
0
0
0
0
0
0
1
1
2
0
0
0
1
1
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
10
0
0
2
1
0
1
2
1
0
2
1
2
0
0
2
2
0
0
1
0
0
0
0
2
0
2
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
1
0
1
0
1
0
1
0
1
0
0
0
1
1
0
0
0
1
0
2
2
0
0
2
1
0
0
0
0
2
0
0
0
0
1
1
2
0
2
2
1
0
0
2
0
0
0
1
0
0
1
0
0
0
1
1
3
0
0
0
3
0
0
1
0
1
0
0
0
0
2
0
3
0
0
1
0
2
0
0
1
2
0
0
0
2
0
0
3
0
0
0
1
0
0
0
0
3
1
0
1
0
2
2
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
2
1
2
0
2
0
2
0
0
0
0
0
0
0
2
1
2
1
0
2
0
2
0
1
1
0
0
0
0
1
0
1
0
0
0
1
2
0
0
0
0
2
0
0
0
0
1
2
4
2
1
1
2
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
1
2
2
0
2
0
1
0
0
4
1
0
1
2
1
2
1
2
0
0
0
0
2
1
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
1
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
3
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
4
2
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
2
2
2
0
0
2
0
0
0
1
0
2
2
0
2
2
1
0
1
0
0
2
2
2
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
1
1
0
0
0
2
0
0
1
2
1
0
1
0
1
0
2
2
0
0
0
2
0
2
0
1
1
2
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
2
1
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
2
0
1
0
0
1
2
0
2
0
0
0
1
0
0
0
0
0
2
1
0
0
0
2
0
0
2
0
0
0
2
0
0
0
2
2
1
1
0
0
0
1
2
0
1
2
2
1
0
0
1
0
0
0
1
0
0
2
0
2
0
1
1
2
0
1
1
2
2
2
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
1
0
1
2
0
0
1
0
1
0
0
0
0
0
0
0
2
2
0
1
1
0
0
0
1
0
0
0
1
1
0
0
1
2
0
1
0
0
2
1
0
2
0
0
0
0
0
2
3
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
3
2
0
0
3
2
2
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
2
1
0
0
1
2
0
0
0
4
1
2
0
1
0
0
0
0
0
0
0
1
3
1
0
0
0
0
2
1
0
0
0
1
0
1
0
0
0
0
2
1
1
2
0
0
1
0
0
2
0
2
0
3
2
0
1
0
2
0
1
0
0
0
0
0
3
0
0
0
1
0
0
0
0
2
1
0
0
0
1
1
0
4
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
1
0
0
0
2
0
0
1
2
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
2
1
0
1
1
2
0
2
0
0
0
0
2
4
0
1
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
2
0
0
1
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
1
0
1
2
0
0
1
1
0
1
0
0
0
2
0
0
0
1
1
3
0
0
0
0
1
1
2
0
0
0
2
0
2
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
1
0
0
0
0
2
3
1
0
0
2
0
0
1
2
1
0
0
0
0
0
0
2
0
1
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
1
2
0
1
0
1
2
0
1
0
1
0
1
0
2
0
0
1
0
2
1
1
2
0
0
0
4
0
2
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
3
1
1
1
0
0
0
2
1
2
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
2
1
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
1
1
2
1
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
4
1
2
0
2
1
9
2
3
2
0
0
1
1
0
2
0
1
0
0
0
0
1
2
1
2
1
1
1
1
2
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
1
0
1
2
0
0
0
0
1
1
0
1
0
2
1
2
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
3
2
1
2
2
1
1
0
1
1
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
2
0
1
0
0
2
2
0
2
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
2
0
0
1
0
1
0
0
2
0
2
3
0
0
0
0
0
0
0
1
3
0
1
2
0
0
0
1
0
0
0
1
0
1
2
0
0
0
0
0
2
0
0
0
0
2
1
0
1
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
2
1
0
2
0
3
2
0
0
0
0
1
0
0
0
0
2
0
2
2
0
0
0
0
0
0
1
0
0
2
2
0
0
0
2
0
0
0
0
1
0
0
2
0
2
0
0
0
0
2
0
0
0
0
2
0
1
0
1
0
1
1
0
2
2
0
4
1
0
2
1
0
0
0
1
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
2
0
1
0
0
1
0
0
1
0
2
2
0
1
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
1
0
2
0
0
2
0
2
1
0
0
0
0
0
1
0
1
0
0
0
2
1
2
2
0
0
0
1
2
0
0
2
0
4
0
0
0
0
2
1
0
2
1
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
1
1
2
0
0
2
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
2
0
1
1
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
2
1
0
2
0
2
0
0
1
1
1
0
0
0
1
0
0
0
1
0
1
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
1
1
1
0
2
0
0
2
0
2
0
0
1
0
0
0
0
0
2
0
1
1
0
3
1
0
0
0
0
1
0
0
2
1
0
0
0
0
0
1
0
1
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
1
0
0
2
2
0
0
0
0
0
0
2
1
0
0
1
2
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
1
0
0
0
0
0
0
0
2
0
0
2
2
0
0
2
0
1
0
1
2
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
1
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
1
0
2
0
1
0
0
0
1
0
1
0
2
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
1
0
1
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
1
0
1
2
0
2
2
0
1
0
1
1
1
0
0
0
0
0
0
1
1
0
2
0
1
0
0
0
2
0
0
2
0
0
0
1
0
0
2
3
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
1
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
1
0
1
0
0
2
1
0
1
0
2
0
2
0
1
0
2
0
0
2
0
0
2
1
0
0
0
2
0
2
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
2
0
0
1
2
0
1
2
0
1
3
0
0
1
0
0
0
0
2
1
0
0
0
0
2
0
1
0
1
0
0
2
0
2
0
2
0
1
0
0
1
1
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
2
0
1
0
0
0
4
1
0
0
0
3
0
4
0
2
0
2
0
2
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
1
2
0
0
2
2
0
3
2
0
0
0
2
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
2
0
1
0
2
0
1
0
1
1
2
0
0
1
0
0
0
4
0
2
0
0
2
0
0
0
0
2
0
3
1
0
1
0
4
0
0
2
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
3
2
2
0
1
0
0
0
0
0
0
1
0
2
3
0
1
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
1
0
1
0
0
0
0
0
1
4
0
1
0
0
2
0
0
0
0
0
0
1
2
1
1
1
0
0
0
0
0
1
2
0
1
0
0
0
2
2
0
0
0
1
0
0
0
1
0
2
0
0
2
0
2
0
0
2
2
0
0
2
2
0
1
1
2
0
0
3
0
0
2
0
2
2
0
0
0
0
0
2
0
3
2
2
0
0
0
2
3
0
0
0
1
0
1
1
0
0
1
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
2
1
0
1
0
4
0
0
0
2
0
0
0
1
2
1
1
0
0
1
0
1
3
2
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
3
0
2
0
2
0
0
0
2
1
0
0
2
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
1
2
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
2
0
0
0
1
1
0
0
1
0
0
0
0
1
1
0
0
0
2
0
0
3
0
0
0
0
2
0
0
2
0
1
2
1
0
2
0
2
2
0
0
1
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
2
1
1
0
0
0
0
1
0
2
0
1
0
0
0
0
2
0
0
2
0
2
0
0
0
0
1
0
0
0
0
1
0
0
2
0
1
1
2
0
1
0
0
0
0
0
0
0
0
2
0
0
1
1
1
2
0
0
2
0
0
1
2
1
0
1
0
0
0
2
1
0
0
0
0
0
0
0
1
1
0
2
0
0
0
1
2
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
2
2
0
0
0
0
2
0
0
0
0
2
0
0
2
0
2
1
1
0
0
0
1
0
0
0
0
2
0
1
0
0
0
1
0
1
0
0
0
1
0
2
0
1
0
0
2
1
2
0
0
0
0
0
0
0
2
0
0
2
0
2
0
2
0
2
2
1
0
2
0
1
0
0
1
0
2
0
0
1
0
1
0
2
0
0
2
1
3
0
1
1
0
0
0
1
1
2
1
0
0
1
0
0
2
0
0
0
0
0
0
1
2
0
0
0
2
2
0
2
2
0
0
1
1
0
0
0
1
0
0
0
0
2
1
2
1
1
0
0
0
0
0
1
1
0
2
1
1
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
2
3
0
1
0
2
1
1
1
0
0
0
1
2
1
2
1
3
2
0
0
0
0
0
0
1
0
0
0
0
0
1
1
2
0
2
1
0
0
0
0
0
0
1
0
0
1
0
1
2
0
1
0
0
1
0
0
2
1
0
0
0
0
1
0
0
0
2
1
0
1
0
2
0
0
0
0
2
2
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
2
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
2
0
2
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
1
1
1
0
0
0
0
3
2
2
2
0
0
1
1
0
0
0
2
0
1
0
2
0
1
1
0
0
0
0
1
0
1
2
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
3
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
1
2
1
1
0
0
2
0
0
0
2
2
1
1
0
2
1
2
0
0
0
2
0
0
0
0
2
2
0
0
2
2
3
0
0
0
0
0
0
0
4
2
0
0
3
0
0
0
0
0
0
1
0
2
2
0
0
2
2
0
0
0
0
0
2
1
1
0
1
0
0
1
1
0
0
0
3
0
1
1
0
0
0
0
1
0
2
0
0
0
0
0
1
2
1
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
2
2
0
1
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
1
1
0
0
2
0
1
2
0
0
2
3
0
0
0
0
0
2
2
0
0
0
0
1
0
1
8
0
0
3
1
1
0
1
2
1
2
2
1
0
0
0
2
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
2
0
1
2
0
0
0
0
2
0
1
1
0
2
0
2
0
0
0
0
0
0
1
1
0
2
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
5
0
4
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
1
0
0
0
2
2
2
3
2
1
0
0
0
2
1
0
0
0
0
0
1
0
2
2
0
2
0
0
1
2
2
0
0
0
0
0
2
3
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
2
4
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
2
2
1
2
0
0
0
1
0
0
0
0
0
2
0
0
5
0
1
0
0
0
2
0
2
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
2
0
0
0
2
1
1
0
2
0
0
2
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
2
0
0
1
1
1
1
1
1
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
3
3
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
1
1
4
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
2
2
0
3
1
1
0
2
4
1
0
0
0
2
2
0
0
0
0
1
0
0
0
1
1
0
0
2
0
1
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
1
2
0
1
1
1
1
0
0
7
0
0
2
2
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
4
1
0
2
0
1
0
0
0
0
0
7
1
0
0
2
0
2
0
0
3
2
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
4
0
0
5
0
0
2
2
2
0
0
0
0
0
3
0
0
2
2
0
0
2
2
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
2
0
2
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
2
0
2
0
1
2
2
1
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
2
1
0
1
1
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
2
1
0
0
0
0
0
4
2
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
2
1
0
0
0
2
1
0
0
0
0
2
0
3
0
2
0
0
1
0
2
1
0
1
0
0
0
0
2
1
0
2
1
1
0
1
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
2
0
0
2
1
0
2
1
0
2
2
0
0
2
1
0
0
1
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
2
3
0
0
0
0
1
0
0
0
0
2
0
0
2
1
0
2
0
0
0
0
0
0
0
2
1
0
0
0
2
1
1
2
0
2
1
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
2
2
2
2
0
0
2
0
0
0
0
0
0
0
2
2
0
0
1
5
0
0
1
0
1
0
2
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
3
0
0
0
0
0
1
0
1
0
2
0
0
0
2
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
1
0
0
0
1
0
2
0
1
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
1
0
2
1
2
0
0
1
1
0
0
1
0
0
0
0
1
1
1
0
0
0
2
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
1
2
0
0
2
0
0
1
0
0
2
0
0
0
0
0
2
0
1
1
2
0
2
1
0
0
3
0
1
0
0
2
0
0
0
0
0
0
2
2
2
1
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
2
1
2
1
1
0
1
0
0
0
0
1
0
0
1
0
0
1
0
1
0
1
0
1
0
1
3
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
1
1
0
0
2
0
0
0
0
0
0
1
0
2
0
1
0
2
1
0
0
0
2
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
2
1
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
1
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
2
1
0
0
0
2
0
2
0
0
0
2
1
0
0
0
2
1
0
1
0
2
0
1
1
1
2
0
1
0
0
0
0
2
1
1
1
0
0
0
2
0
1
2
0
0
2
0
2
1
4
2
0
0
0
0
0
1
1
0
0
3
1
0
0
0
4
1
0
0
0
0
0
0
0
0
3
0
1
0
1
2
0
2
0
1
0
0
3
4
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
2
0
0
0
1
1
0
0
0
0
1
0
0
0
2
0
3
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
2
0
0
0
2
0
1
1
0
0
2
1
1
0
0
1
0
0
2
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
2
0
0
1
0
0
2
0
0
0
0
0
2
0
0
2
0
2
2
0
1
3
2
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
3
0
2
1
1
0
1
0
2
0
1
0
0
1
0
0
0
2
0
2
1
0
0
1
0
0
0
0
0
0
2
2
1
0
0
0
0
0
2
0
1
0
2
0
1
0
0
0
0
2
0
0
0
2
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
1
0
2
1
2
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
2
1
1
2
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
3
0
1
1
0
3
2
0
1
0
0
1
1
1
0
0
0
0
0
2
0
0
0
1
0
0
1
2
0
1
0
0
0
2
1
0
1
1
2
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
1
1
2
0
1
1
1
0
0
0
5
1
0
0
2
2
2
0
1
1
1
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
1
1
1
1
0
0
1
1
2
0
2
0
0
1
2
0
2
1
0
1
0
0
0
0
2
0
0
0
0
7
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
2
1
0
0
0
0
0
0
0
0
1
5
1
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
2
3
0
0
0
0
0
0
1
0
2
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
2
0
1
0
3
1
0
0
0
0
0
0
2
0
0
0
0
2
2
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
2
0
0
0
0
2
1
2
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
3
0
0
1
0
1
0
0
0
0
2
0
0
0
0
1
2
1
2
1
2
1
0
5
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
3
2
0
0
0
0
0
2
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
1
0
3
1
2
0
0
0
2
0
1
0
2
2
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
1
0
2
0
0
4
0
1
0
0
1
0
0
0
2
1
0
0
0
1
1
1
0
2
2
0
0
2
0
0
2
2
2
1
1
0
0
0
1
1
2
2
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
2
0
0
1
0
0
0
0
2
0
0
2
1
0
0
2
0
0
0
0
0
0
2
1
0
2
0
1
2
1
0
1
0
0
3
0
1
0
0
0
0
0
0
2
2
2
1
0
2
1
1
0
0
0
1
2
0
0
0
2
0
2
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
3
3
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
3
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
2
0
0
2
0
0
2
1
0
0
0
0
0
2
0
0
0
1
0
1
2
3
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
1
1
2
2
1
0
0
1
0
0
3
1
0
1
0
0
0
3
0
0
0
2
1
0
2
0
2
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
3
0
0
0
0
1
0
1
2
0
2
0
0
2
0
1
1
0
2
0
0
0
2
1
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
3
0
0
0
0
0
1
1
1
1
0
0
1
2
1
0
0
0
0
0
2
0
1
0
0
0
3
0
3
0
1
1
0
0
0
2
0
1
0
0
0
0
2
1
0
0
0
2
0
2
2
0
0
2
0
1
0
2
1
0
0
1
2
1
0
0
0
1
0
0
0
0
0
2
1
3
0
1
0
0
1
0
0
0
0
5
0
0
1
0
0
0
1
0
0
0
2
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
3
0
0
2
0
0
0
0
2
1
0
1
1
0
0
1
0
0
0
0
0
2
2
2
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
1
0
0
1
1
1
0
1
0
0
1
0
2
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
4
0
0
0
0
0
0
2
0
0
0
1
0
1
1
1
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
1
0
0
1
2
2
0
0
1
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
2
0
1
2
0
3
0
0
0
3
2
2
1
0
1
0
1
0
1
1
0
0
0
1
0
3
1
0
0
0
1
2
0
2
0
0
0
4
0
0
0
1
1
0
0
0
0
0
0
2
2
0
0
1
0
1
0
0
0
0
2
2
0
1
0
1
1
0
0
0
0
2
1
0
0
1
0
1
0
2
0
0
1
0
0
2
0
0
0
0
1
1
2
0
0
0
0
1
0
0
1
1
1
0
0
0
2
0
0
3
0
0
0
0
2
1
1
1
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
2
0
0
0
0
0
0
6
0
0
0
2
0
1
1
0
3
0
0
0
0
0
0
1
0
0
1
2
2
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
2
0
1
0
0
0
5
0
0
2
1
1
0
1
2
1
0
0
0
0
0
1
1
2
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
2
0
1
1
2
1
0
2
2
0
0
0
0
0
1
0
0
1
1
0
0
0
2
1
0
1
0
1
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
1
2
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
1
0
0
0
3
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
1
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
2
0
0
2
0
0
2
0
0
4
2
0
1
0
0
0
0
1
0
0
2
1
0
0
1
0
0
2
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
2
1
1
1
0
0
2
0
0
0
0
2
0
2
0
1
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
1
2
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
1
0
1
0
0
0
1
0
0
3
0
0
0
1
3
1
0
0
0
2
0
2
2
0
1
1
0
2
2
0
1
0
2
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
2
2
0
0
0
0
0
2
2
2
1
1
0
1
1
0
2
2
0
1
0
0
0
0
1
0
1
1
0
0
1
0
1
0
2
0
0
0
0
0
2
0
0
1
1
0
0
1
0
0
2
0
0
1
1
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
2
0
1
0
1
0
1
1
2
0
2
0
0
0
2
2
0
0
1
0
1
1
3
0
0
2
3
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
1
0
3
1
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
1
2
1
2
1
1
2
0
2
2
0
1
1
1
2
1
0
0
0
0
0
0
2
0
0
0
0
2
4
0
0
1
0
0
0
0
0
4
2
2
0
2
0
0
2
0
2
0
1
1
2
0
0
1
0
0
1
0
1
0
1
0
2
0
2
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
3
0
0
0
0
2
3
0
0
0
0
0
2
0
1
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
1
1
0
1
0
2
0
0
0
0
0
2
1
0
2
0
0
0
2
0
0
0
0
2
1
2
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
1
0
1
0
0
2
0
1
0
1
0
0
6
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
2
2
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
4
0
0
3
0
1
0
2
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
3
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
1
2
0
1
2
0
0
0
2
1
1
2
0
0
1
0
0
2
0
0
4
0
0
0
1
2
0
0
2
0
5
1
0
0
3
1
0
0
0
1
0
2
0
0
1
1
0
2
0
0
1
1
0
1
0
0
1
0
0
2
0
0
0
0
0
2
2
0
1
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
2
2
0
2
0
2
1
0
1
1
0
0
0
0
0
2
0
0
0
1
0
2
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
1
1
0
1
0
0
2
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
1
0
0
0
0
0
2
2
1
0
1
1
1
1
0
0
2
0
1
1
0
0
0
0
0
2
0
2
2
0
1
2
1
0
2
0
1
0
1
1
1
2
0
0
0
1
0
1
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
1
3
0
0
2
0
1
0
2
1
1
0
0
0
0
0
1
0
2
0
0
0
0
2
2
0
0
1
0
1
1
0
1
0
2
0
0
0
0
0
0
1
0
2
0
0
4
0
0
0
0
0
2
0
0
5
2
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
1
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
1
0
0
1
1
0
2
1
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
3
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
1
0
0
1
0
1
0
0
1
1
2
0
0
0
14
0
0
0
0
2
1
0
0
0
1
2
0
0
2
2
1
2
0
2
0
0
0
0
0
0
1
0
0
0
2
2
0
0
2
0
1
1
0
3
0
2
0
0
0
1
2
0
0
0
0
2
0
1
0
0
0
2
1
0
0
2
1
0
1
1
0
2
0
0
0
0
0
1
0
3
1
0
0
0
0
0
1
2
2
0
0
0
0
1
0
1
0
0
3
0
1
1
0
0
0
0
0
9
2
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
2
0
0
0
1
0
1
0
0
2
0
0
1
0
0
1
0
0
0
0
0
2
2
0
1
0
0
1
0
1
0
0
0
2
0
0
0
0
3
2
1
0
2
0
2
0
0
0
0
2
2
1
0
2
1
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
2
0
0
1
0
0
0
0
2
2
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
2
1
1
2
2
0
1
0
0
2
0
1
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
3
0
0
0
0
0
2
1
0
2
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
4
2
0
0
0
0
2
0
0
0
1
0
0
2
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
2
1
2
0
0
2
0
0
0
0
0
0
2
2
0
0
0
1
3
1
0
2
0
3
0
0
2
1
1
1
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
3
0
1
0
0
0
0
0
2
0
0
0
2
0
1
1
1
0
0
0
4
2
0
1
0
2
0
0
0
0
1
1
1
1
0
2
1
2
2
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
3
0
0
0
0
1
0
0
2
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
1
3
0
2
2
0
0
2
0
0
0
2
1
1
1
0
2
0
3
0
1
0
0
0
0
0
2
0
0
1
1
0
0
2
0
0
0
0
0
3
1
0
0
0
4
1
2
0
0
1
0
0
1
2
0
3
0
2
0
0
2
0
2
0
0
3
0
0
1
0
0
0
0
2
1
0
3
0
2
0
1
0
0
1
0
0
2
0
0
2
1
1
0
0
3
0
0
1
1
0
0
0
0
0
0
2
2
0
0
1
1
3
0
0
1
0
2
0
2
0
0
0
2
2
3
2
0
0
0
2
0
2
0
0
0
2
0
1
0
0
0
0
2
0
2
0
1
0
0
0
2
0
0
0
0
1
0
0
0
2
2
0
0
0
1
1
1
1
0
2
0
2
0
0
0
0
0
0
1
0
0
5
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
3
0
0
0
1
1
0
1
0
1
0
0
0
0
0
2
0
2
0
1
1
0
0
1
0
0
0
0
0
1
0
0
2
0
4
0
1
2
0
0
2
0
0
1
1
0
0
0
0
0
2
0
0
0
0
3
1
1
1
0
0
0
1
0
0
0
3
1
0
1
0
0
2
0
1
0
2
3
1
0
2
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
3
0
2
0
0
0
0
1
0
2
1
0
2
0
2
1
0
0
0
1
1
0
0
0
0
0
2
1
2
0
0
0
0
0
1
1
1
2
0
0
0
1
2
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
2
1
0
4
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
3
0
0
2
0
3
0
2
2
0
0
1
2
2
0
0
0
0
0
0
0
0
4
0
0
0
0
2
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
2
2
2
1
1
2
1
0
2
0
0
0
2
2
0
0
0
0
2
1
2
0
0
2
0
1
0
0
0
0
1
0
2
0
2
0
1
0
0
2
0
0
2
1
0
0
0
2
0
1
0
2
0
1
0
0
0
2
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
2
0
2
2
1
0
0
0
0
1
1
0
0
2
0
1
0
1
2
1
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
2
0
2
2
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
3
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
1
4
0
0
0
0
2
0
0
1
0
1
0
0
0
1
0
1
0
0
2
2
0
0
2
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
1
2
2
1
2
2
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
2
0
0
0
1
0
0
0
2
3
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
2
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
2
0
1
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
2
0
0
0
0
0
0
2
0
2
0
0
1
0
0
2
0
2
0
1
2
2
0
1
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
2
1
0
2
0
0
0
1
1
1
1
3
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
1
0
0
2
2
0
1
1
0
0
1
2
0
0
0
2
0
2
0
0
0
0
0
1
1
0
2
0
0
0
2
1
2
0
2
1
0
0
1
0
2
2
0
1
0
0
0
3
2
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
1
0
2
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
1
0
2
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
2
0
0
0
2
2
2
0
0
0
0
1
1
0
0
2
0
1
3
0
0
1
0
0
1
2
0
1
0
2
0
3
0
2
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
3
1
0
0
0
0
0
0
1
1
1
2
0
0
2
1
1
0
0
2
0
0
0
0
0
1
0
0
0
1
0
2
0
3
0
0
0
2
0
0
1
0
0
0
0
1
0
1
0
1
0
1
0
0
4
2
1
1
0
0
0
1
0
0
3
1
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
2
2
2
2
0
1
0
1
2
0
0
1
1
0
2
4
1
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
2
0
2
0
0
0
1
0
0
3
0
0
0
1
0
3
1
0
0
1
1
0
0
0
1
0
0
2
0
1
0
0
1
2
1
0
0
0
0
0
0
2
2
0
0
0
0
0
1
1
2
0
2
5
0
0
1
3
1
0
3
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
1
0
0
1
0
0
0
1
1
0
1
0
0
0
1
0
0
1
1
0
1
0
0
0
2
0
0
0
2
0
0
0
1
1
0
0
0
2
1
2
2
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
2
0
1
0
1
2
0
1
2
1
0
0
0
0
0
1
0
0
1
1
0
0
1
2
1
0
0
0
1
0
0
0
1
2
1
2
0
0
0
0
0
3
1
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
1
2
0
2
0
1
0
2
2
0
0
2
0
1
2
0
2
1
3
2
0
0
0
0
0
1
2
2
1
0
0
0
1
0
1
0
1
1
1
0
0
2
2
1
2
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
1
0
2
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
1
1
2
2
3
0
0
0
2
0
0
2
0
2
1
1
0
0
1
1
0
0
1
2
0
0
1
0
0
0
0
1
3
0
2
0
1
1
1
0
2
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
1
0
0
0
1
1
2
0
0
1
0
0
2
0
0
0
0
3
0
0
0
2
2
2
0
0
2
0
0
0
0
1
0
0
0
2
0
2
0
0
0
2
0
2
0
0
2
0
0
2
0
0
0
0
0
0
2
0
1
1
0
2
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
1
1
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
1
0
1
2
0
0
1
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
2
1
0
0
2
0
1
0
2
1
0
0
0
0
1
0
0
2
0
0
0
1
2
0
1
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
2
0
0
1
0
0
1
1
0
0
0
2
0
2
2
0
2
0
0
1
0
0
0
0
1
2
0
0
1
2
0
0
2
0
0
0
1
0
0
1
0
2
1
0
1
1
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
1
1
0
2
1
3
2
1
0
0
0
1
0
0
0
0
2
1
2
0
2
0
0
0
0
0
1
2
2
0
0
2
2
1
0
0
2
0
0
2
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
1
2
0
0
1
1
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
1
2
0
0
0
2
2
0
0
2
0
0
0
2
2
1
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
3
2
0
0
1
0
1
0
0
2
1
0
0
1
1
1
0
3
0
2
2
0
0
0
2
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
2
0
2
1
0
0
1
0
0
0
2
2
0
0
1
0
1
0
3
0
1
2
1
1
0
0
0
0
2
0
2
0
0
0
1
0
1
0
0
1
0
2
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
2
0
0
2
1
2
0
2
2
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
1
0
2
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
1
2
0
2
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
1
2
1
1
2
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
3
1
0
0
0
2
0
2
1
0
0
1
1
0
0
2
0
0
0
3
0
0
0
0
0
1
0
1
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
1
2
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
5
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
1
0
2
0
1
2
0
0
0
0
1
0
0
2
0
0
3
0
0
0
1
2
1
2
0
0
0
1
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
2
1
3
0
0
1
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
2
3
2
1
0
0
2
2
2
0
0
3
2
0
0
2
0
0
2
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
1
2
3
0
4
0
0
0
2
1
0
0
1
1
0
0
2
0
0
1
0
0
2
0
2
0
0
0
2
0
1
1
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
2
0
0
1
0
2
1
1
0
1
0
1
1
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
2
1
0
2
0
0
1
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
2
0
1
0
2
0
2
2
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
3
0
1
2
1
0
0
2
0
1
0
2
0
0
0
0
1
0
1
0
0
0
1
2
0
1
0
0
0
2
1
0
0
5
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
2
0
0
2
0
0
2
0
0
0
2
0
3
1
1
0
0
0
0
0
0
0
1
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
2
0
3
0
0
2
0
0
0
1
0
0
1
2
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
2
0
0
0
0
0
0
0
0
1
0
0
2
2
2
1
0
0
0
0
0
2
0
0
0
1
0
1
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
1
0
0
0
2
3
1
2
0
0
0
0
0
2
3
0
0
0
0
0
1
0
1
0
0
1
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
1
1
0
1
1
0
0
0
1
0
0
0
0
1
0
2
0
0
0
2
2
1
1
0
0
5
0
0
0
0
1
1
0
3
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
1
2
0
0
1
1
1
1
2
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
3
0
0
0
0
0
0
0
1
0
0
1
2
0
2
2
1
0
0
0
0
0
2
0
1
0
0
0
0
1
0
1
0
0
1
0
1
2
2
0
1
3
0
0
0
0
2
0
0
2
0
0
2
0
0
0
2
0
2
0
1
0
0
1
0
0
0
0
2
2
0
1
0
0
0
0
1
3
0
2
0
2
0
0
2
0
0
3
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
1
0
0
1
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
2
0
0
1
1
2
0
2
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
1
1
1
0
1
2
2
0
0
0
0
1
1
0
0
0
0
0
2
0
1
0
0
2
0
0
1
0
2
1
0
0
2
0
0
1
2
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
1
0
2
0
0
0
1
0
0
0
0
0
1
0
1
1
1
0
0
1
0
0
2
1
0
0
0
2
0
2
1
5
2
0
0
0
2
1
0
1
1
0
3
0
1
0
2
0
1
0
2
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
2
2
2
0
0
0
0
1
0
2
2
0
0
0
0
0
0
2
1
2
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
1
1
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
2
1
1
0
0
0
0
2
0
2
0
0
0
1
0
1
0
0
2
3
0
0
0
0
0
0
0
0
2
0
2
2
0
1
0
2
0
0
1
0
0
1
0
0
1
0
0
2
0
0
2
0
0
1
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
2
2
0
0
0
0
0
0
1
2
0
0
2
1
0
0
0
0
0
1
0
0
0
2
1
1
0
0
0
0
0
0
0
0
2
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
1
0
0
0
2
0
1
2
2
0
0
0
0
1
8
0
3
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
2
2
2
1
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
2
4
1
0
0
0
0
0
0
0
2
2
1
0
1
0
0
0
2
0
3
1
0
2
0
0
0
0
0
0
0
0
2
0
2
2
1
1
0
2
0
0
0
0
0
0
2
2
0
2
1
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
3
1
1
2
1
0
0
2
0
1
0
0
0
0
2
6
0
2
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
2
0
1
2
0
0
0
2
1
0
1
0
2
0
1
0
0
0
0
1
3
1
1
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
1
1
2
0
1
0
0
1
1
2
0
0
0
1
2
1
0
0
2
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
1
2
2
0
0
0
1
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
1
1
0
0
0
1
0
0
0
1
0
0
1
0
1
0
2
0
2
1
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
1
2
0
4
1
2
0
0
0
0
0
0
2
0
0
0
0
0
1
1
2
1
1
0
0
0
0
2
0
0
0
0
0
0
2
1
0
1
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
1
0
0
0
1
0
2
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
1
2
0
2
0
1
2
0
2
0
0
2
3
0
0
1
2
0
0
1
2
0
0
0
0
0
0
0
0
0
3
1
0
0
2
0
2
1
0
0
0
6
0
0
0
2
0
0
1
0
0
0
2
2
0
2
1
0
0
0
1
1
2
0
0
0
0
2
0
0
2
0
3
2
0
0
1
0
0
1
0
0
0
0
2
2
0
0
1
2
0
0
0
0
0
0
1
0
2
0
0
0
1
3
2
0
0
1
0
2
1
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
1
1
0
1
1
2
2
1
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
1
0
2
1
1
1
0
0
0
2
0
0
1
0
0
0
0
0
2
1
1
2
0
1
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
2
0
1
2
1
0
2
3
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
1
0
0
2
1
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
2
1
1
0
0
0
0
0
1
1
2
0
1
0
2
1
2
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
3
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
2
2
0
0
0
2
0
0
0
4
0
1
1
0
1
0
1
0
1
2
0
0
0
2
0
0
0
0
0
0
1
4
1
1
0
0
2
0
0
0
1
0
2
1
0
0
1
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
1
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
1
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
1
0
0
2
0
1
0
1
0
2
1
0
4
2
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
2
0
0
2
0
5
2
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
1
1
3
3
2
0
0
1
0
1
0
0
1
0
0
1
1
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
2
0
0
1
0
0
0
2
0
0
0
0
0
3
2
0
0
1
1
0
2
1
2
0
0
0
0
0
0
1
0
3
0
0
1
1
2
0
2
0
0
0
0
0
1
2
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
3
0
0
0
1
0
0
0
0
0
0
1
1
2
1
2
0
0
0
0
0
1
0
1
2
0
2
2
0
0
1
3
0
0
2
0
3
1
1
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
2
0
4
0
0
0
0
2
1
2
1
0
1
1
3
3
0
0
0
0
0
1
0
0
2
2
0
0
1
0
0
1
1
2
2
1
0
2
0
0
0
0
0
0
0
0
2
0
3
2
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
1
0
0
0
2
1
1
0
1
0
2
0
0
2
1
1
0
0
0
4
0
1
0
1
2
1
1
0
0
2
0
0
0
0
2
2
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
2
0
0
0
1
0
6
2
0
2
0
0
1
0
0
0
0
2
1
0
1
0
0
0
2
3
0
2
0
0
0
0
0
0
0
2
1
2
0
2
0
0
1
0
2
1
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
2
0
2
0
0
0
0
0
3
0
0
0
0
0
2
2
4
0
1
0
0
1
0
0
0
1
0
0
1
2
0
0
1
0
0
0
0
2
0
1
0
1
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
1
0
0
0
2
1
2
0
0
0
3
1
1
1
0
0
0
0
1
1
0
0
2
0
0
0
0
1
2
1
0
0
0
1
0
0
1
0
2
1
0
0
3
0
0
2
1
3
0
0
0
1
1
0
0
0
0
0
2
0
1
2
0
2
0
1
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
2
1
2
1
0
0
0
0
2
2
1
1
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
2
2
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
3
1
0
2
0
0
2
0
1
2
2
0
0
1
2
0
0
0
2
2
2
0
1
1
0
1
0
0
0
0
3
1
0
0
0
2
0
1
0
1
0
0
1
0
1
2
0
0
1
0
1
0
1
2
1
1
0
0
0
0
1
1
0
1
1
0
3
1
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
1
0
0
2
0
0
0
0
2
0
1
1
0
1
0
0
4
0
0
1
0
2
2
3
0
0
0
1
2
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
2
0
1
1
1
0
1
1
0
0
0
0
0
0
1
0
2
1
0
0
0
2
0
0
1
1
0
2
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
1
2
0
0
0
0
0
0
2
0
0
0
2
1
0
0
1
2
0
0
0
2
0
2
0
2
0
2
0
0
1
0
0
2
0
0
1
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
2
3
2
0
2
0
0
2
0
0
0
0
2
0
2
0
1
0
1
0
0
0
1
3
0
1
0
0
2
0
0
0
1
0
0
1
2
2
0
1
2
0
1
0
0
1
0
0
1
1
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
1
1
2
0
0
0
1
0
0
2
0
0
1
0
1
0
1
0
0
0
0
2
1
1
1
5
0
0
1
0
2
0
2
0
1
1
1
0
1
0
0
0
0
0
1
2
0
0
0
2
0
1
0
0
0
3
0
1
0
0
2
1
0
0
2
0
0
0
0
0
0
2
1
0
0
2
0
1
0
0
0
0
6
0
1
0
1
1
1
0
1
2
3
0
0
0
0
2
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
2
0
0
2
0
0
2
0
1
2
0
5
0
2
2
0
1
0
2
0
0
0
0
0
2
2
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
5
0
2
0
5
1
1
0
2
0
3
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
2
0
2
1
0
2
0
0
1
0
0
0
2
0
0
1
2
0
0
2
1
3
1
5
2
0
0
0
0
0
0
2
0
5
0
0
1
0
1
2
1
0
0
2
0
1
1
0
2
0
0
0
0
0
0
0
0
2
0
2
0
1
2
2
0
10
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
2
0
0
2
2
1
0
3
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
1
0
1
3
0
0
0
1
0
2
0
0
1
2
1
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
2
2
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
1
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
1
1
0
2
0
0
1
0
1
0
0
0
9
0
2
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
2
0
3
0
0
0
1
1
2
2
0
0
2
0
2
0
0
0
0
2
0
0
1
1
0
1
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
1
1
1
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
2
0
0
0
0
2
1
0
0
0
2
0
0
1
1
2
0
0
3
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
1
0
2
0
0
0
1
1
0
0
0
0
2
0
0
3
3
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
1
1
0
4
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
2
2
1
1
0
0
1
1
1
1
0
0
4
0
3
2
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
3
0
2
0
0
0
1
0
5
0
1
2
0
0
2
2
2
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
1
1
1
1
2
6
3
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
1
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
2
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
2
0
0
0
4
0
2
0
0
0
0
0
0
0
0
3
2
1
0
2
0
0
0
0
0
1
2
1
0
0
1
0
2
0
0
0
0
1
0
0
0
2
1
1
0
0
0
4
0
0
0
0
0
0
0
2
1
0
2
0
2
1
1
0
0
2
0
3
0
0
0
0
2
2
0
2
4
0
0
2
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
2
0
0
2
0
2
0
1
0
2
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
2
3
0
2
0
0
0
1
0
2
0
0
1
1
2
0
3
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
3
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
2
0
2
0
1
1
0
1
0
0
0
2
0
0
0
2
0
0
0
0
1
3
0
1
1
0
1
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
1
0
1
1
0
2
0
0
0
2
0
0
0
1
0
0
2
1
0
0
2
1
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
2
0
0
1
1
0
1
4
0
5
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
4
1
6
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
1
1
0
2
0
0
0
0
3
1
0
2
1
1
0
0
1
0
0
1
1
2
1
1
0
2
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
1
0
2
2
1
1
0
0
0
0
0
0
1
2
0
1
0
1
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
3
2
0
0
0
2
0
0
1
0
0
0
0
2
0
1
0
2
0
2
0
0
1
1
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
2
2
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
2
2
0
2
0
0
0
2
1
2
1
1
1
0
0
0
1
1
0
2
0
0
1
0
2
1
0
1
2
0
0
2
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
1
0
0
2
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
2
2
0
0
0
2
1
2
0
0
3
0
1
0
1
2
0
0
0
0
2
3
3
0
0
0
2
0
1
2
0
0
0
2
0
2
0
0
0
1
1
0
0
2
0
2
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
1
0
1
2
0
0
0
3
1
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
5
2
0
1
0
2
0
2
0
0
0
0
2
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
3
0
0
3
0
0
0
0
1
2
0
2
0
0
1
0
0
0
0
0
1
0
2
1
0
0
2
0
0
1
0
1
0
0
1
0
0
0
4
1
0
2
0
0
1
0
2
0
0
3
0
0
0
0
0
0
1
0
0
2
2
0
0
1
0
0
1
0
0
0
0
0
0
2
0
1
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
2
2
1
2
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
2
0
3
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
1
0
3
0
0
2
2
2
0
0
1
0
0
0
2
2
0
0
1
2
3
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
2
0
2
0
0
2
0
0
1
0
1
0
0
2
0
0
1
0
0
1
0
1
1
0
0
1
0
2
0
0
1
0
0
0
2
0
2
0
2
0
0
0
1
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
2
0
1
1
1
0
1
1
0
0
1
0
1
0
1
0
0
1
2
0
0
0
0
0
2
2
0
3
0
2
0
1
2
0
0
2
1
1
0
0
0
0
1
0
2
2
0
1
1
0
0
1
2
1
0
0
1
0
1
2
1
0
3
0
1
1
0
0
0
1
1
0
2
0
0
0
0
2
0
0
1
0
1
0
1
0
1
0
2
0
0
3
0
1
0
0
1
0
2
1
0
0
0
2
0
2
0
0
0
1
1
0
2
1
0
1
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
2
0
1
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
2
0
0
0
1
0
1
2
2
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
1
0
0
1
1
2
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
1
1
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
3
0
2
2
0
1
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
2
2
0
1
0
1
2
3
2
0
0
1
1
0
0
0
2
0
2
0
2
1
0
0
3
0
0
0
1
1
0
0
2
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
2
1
0
0
1
0
0
1
0
2
0
0
0
2
0
2
0
2
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
2
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
2
0
2
0
0
2
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
2
1
0
0
0
0
2
0
1
0
0
0
0
1
0
2
2
0
0
0
0
0
1
0
0
0
1
0
1
2
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
2
2
0
0
0
1
1
0
3
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
1
0
0
2
0
1
0
0
1
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
2
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
3
0
3
0
1
0
0
0
1
0
2
2
1
2
0
0
2
2
0
0
2
1
0
0
1
2
3
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
1
0
2
0
1
5
0
3
0
0
1
2
1
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
1
0
3
0
2
2
0
2
0
0
0
0
1
0
0
2
0
2
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
3
1
5
0
1
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
1
5
1
0
0
0
0
0
2
0
1
0
0
3
0
0
0
0
1
0
0
1
0
0
1
2
0
0
2
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
1
0
1
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
1
1
0
2
0
0
2
3
1
0
0
0
0
0
0
0
1
0
1
0
2
0
1
2
2
2
0
0
2
0
1
1
0
0
0
0
1
0
2
0
0
0
4
0
0
0
0
0
0
0
4
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
2
0
1
1
0
0
0
2
2
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
1
0
2
0
1
0
0
0
2
0
0
2
1
2
0
0
1
0
1
0
0
1
1
1
0
1
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
5
0
0
0
2
2
1
2
0
0
2
0
1
4
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
4
0
1
1
1
0
0
2
1
0
0
2
0
0
0
0
2
2
0
2
0
1
0
2
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
3
2
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
1
1
0
0
2
0
1
2
0
0
2
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
2
2
1
0
1
0
0
1
0
0
0
2
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
1
1
0
1
1
0
0
1
1
0
1
0
0
0
1
0
0
1
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
1
2
1
1
2
0
0
0
0
0
0
2
2
0
1
0
2
4
0
0
2
2
0
0
0
1
0
0
1
2
0
0
3
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
3
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
2
1
0
0
0
0
0
2
1
0
2
2
1
0
2
2
0
0
2
0
1
2
2
0
0
0
1
2
2
0
0
0
1
5
3
0
1
0
2
1
0
2
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
2
0
2
0
2
0
1
1
0
1
0
3
0
0
0
0
1
0
0
0
1
0
0
1
2
0
2
0
2
1
0
1
0
0
1
0
0
0
0
2
0
0
0
1
0
0
1
2
1
0
1
0
0
0
0
0
2
2
2
1
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
2
2
0
2
1
1
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
1
0
0
0
0
0
0
2
1
2
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
1
2
1
1
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
3
1
0
2
0
0
0
0
2
1
0
0
0
1
0
0
1
0
2
0
0
0
0
2
1
0
0
0
1
0
0
0
2
0
0
2
1
0
1
0
0
0
0
1
0
0
2
1
0
0
1
1
3
0
1
0
0
2
0
0
0
0
2
0
0
1
0
3
2
0
0
0
0
1
0
0
0
1
0
2
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
2
2
0
1
0
2
0
2
1
0
2
0
0
0
0
2
3
1
0
0
1
0
1
0
0
4
0
0
0
2
3
0
0
2
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
1
1
2
0
0
0
2
2
0
2
1
0
2
0
0
0
1
0
0
0
2
0
0
2
4
2
0
1
1
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
1
1
0
0
0
1
0
1
0
1
0
0
2
0
0
2
1
3
0
2
4
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
1
2
1
0
0
1
0
0
2
1
0
4
0
0
0
7
1
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
1
1
2
0
1
0
0
0
0
5
0
0
1
0
0
0
1
1
0
2
0
1
0
0
0
0
0
3
2
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
2
1
0
0
0
0
0
1
0
2
0
1
0
0
0
9
1
0
0
0
0
0
0
0
0
0
1
2
2
1
0
0
0
1
2
2
0
0
0
0
2
0
2
1
1
0
0
0
0
0
0
1
0
1
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
4
0
2
0
0
0
0
2
1
0
0
0
1
0
1
0
0
0
0
2
0
0
1
2
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
1
1
1
0
0
0
0
2
1
0
0
2
0
0
0
1
0
0
2
1
1
0
2
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
1
1
4
0
0
2
2
1
1
0
0
2
2
0
0
0
0
0
1
0
0
0
0
1
1
0
1
2
0
0
1
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
4
0
0
0
4
4
0
0
0
0
1
0
0
1
0
0
2
0
0
2
0
0
0
3
2
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
3
0
1
1
0
1
2
0
2
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
2
0
1
1
0
0
0
0
0
0
3
0
0
0
0
2
0
0
2
0
0
0
3
0
0
1
1
0
0
6
0
0
2
0
3
0
0
0
0
0
2
1
0
0
2
1
0
1
0
0
2
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
2
1
0
0
0
0
1
1
2
0
1
2
2
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
3
0
0
0
6
0
0
3
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
1
0
0
1
0
0
2
0
1
2
2
1
0
0
0
1
0
0
0
1
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
1
1
2
0
0
0
1
0
2
0
0
0
0
1
0
1
2
0
1
0
2
0
2
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
2
0
1
2
1
4
1
2
1
0
0
2
1
2
0
0
1
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
1
2
1
0
1
0
0
0
2
0
0
2
0
0
0
0
0
1
0
2
0
0
2
1
0
0
0
2
0
0
2
2
1
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
2
0
2
0
0
1
0
1
0
0
0
1
0
2
0
0
0
0
0
5
0
2
0
1
1
0
0
2
0
0
2
0
0
0
2
1
0
0
1
0
0
1
0
2
0
0
0
0
0
0
2
1
0
0
0
6
0
0
2
0
1
0
0
0
0
1
0
0
2
0
0
1
2
0
2
0
2
2
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
2
1
3
0
1
1
1
1
0
2
0
0
0
2
3
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
1
1
2
0
0
0
0
0
1
1
0
0
3
0
1
0
2
0
1
1
0
1
0
0
2
2
0
3
0
0
0
2
1
1
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
2
0
2
3
0
1
0
2
2
4
0
3
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
2
2
0
0
0
0
3
0
0
2
1
0
0
1
1
0
0
1
1
0
0
0
0
1
2
0
0
0
1
1
0
1
1
0
2
0
1
0
0
0
0
0
0
2
1
0
0
3
2
0
0
0
0
1
0
0
1
0
2
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
4
1
0
0
1
6
0
1
0
0
0
0
0
0
0
0
0
2
2
3
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
2
1
0
2
0
0
0
2
2
0
1
1
0
0
0
0
0
0
0
6
2
0
0
0
2
2
0
0
0
0
1
2
1
0
0
0
0
0
0
1
0
0
2
1
1
0
0
1
1
0
0
0
0
2
0
1
1
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
4
0
1
0
1
0
0
0
1
0
0
0
0
0
0
2
2
0
2
0
1
0
3
2
0
0
1
1
1
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
1
1
0
1
1
0
0
0
1
2
0
0
0
0
0
1
0
0
0
1
0
2
1
0
0
0
0
1
0
0
2
0
0
1
0
0
0
2
1
0
2
0
0
0
0
0
0
0
2
3
0
0
1
0
0
0
1
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
2
0
0
1
0
2
1
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
1
2
2
1
0
0
2
1
3
0
0
0
0
0
0
0
1
0
1
0
0
4
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
2
0
0
0
1
0
0
0
0
1
0
0
0
0
2
1
0
1
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
1
1
2
2
0
0
0
0
1
0
0
9
0
2
0
0
1
0
1
2
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
3
0
1
0
0
1
1
0
1
0
2
1
1
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
2
1
0
1
0
0
0
0
0
3
0
0
0
1
0
0
0
3
0
0
0
0
1
2
1
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
1
2
0
1
0
2
0
2
0
1
0
0
0
0
1
0
1
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
2
2
1
0
0
0
0
0
1
0
0
0
1
4
0
0
0
2
1
0
0
2
2
1
0
0
1
0
0
0
0
2
1
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
1
0
2
0
2
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
5
0
0
1
0
0
2
0
2
0
2
0
2
0
0
2
2
0
2
0
0
0
0
0
2
0
1
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
2
0
0
0
0
0
0
1
0
1
0
0
2
1
0
0
2
1
0
0
2
0
1
0
0
0
1
1
1
0
0
0
1
1
3
0
0
0
0
1
2
0
1
0
1
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
2
1
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
3
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
7
1
0
1
1
0
3
2
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
3
0
0
2
0
3
0
1
0
0
0
0
0
0
1
2
0
1
0
2
0
0
1
1
0
0
3
0
0
0
0
0
1
0
1
1
2
1
1
1
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
2
0
1
1
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
2
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
2
0
2
0
2
1
2
0
2
0
2
0
2
1
0
0
2
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
2
0
0
0
0
2
3
0
0
2
0
0
2
0
0
0
0
0
0
0
2
2
0
0
1
0
0
1
2
0
0
0
2
0
0
0
2
0
1
2
0
0
0
1
0
0
1
1
0
0
0
0
0
2
2
0
1
0
0
2
2
1
1
0
0
0
0
0
0
3
0
0
0
0
3
3
0
0
0
0
0
0
2
0
0
0
0
2
4
1
3
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
2
0
0
1
3
0
0
0
0
1
1
4
0
0
0
2
0
2
0
0
1
2
0
1
1
0
0
0
2
2
0
0
2
0
0
0
0
0
0
2
2
3
0
0
0
0
0
0
0
4
0
0
0
0
2
2
2
0
0
2
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
2
0
2
0
0
1
2
4
0
0
1
0
2
0
0
0
0
2
0
0
0
1
2
1
2
1
0
2
0
0
2
1
1
0
2
0
1
0
0
2
3
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
3
0
0
0
0
1
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
5
1
2
1
2
2
0
2
1
0
0
0
0
0
0
2
0
0
3
0
1
1
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
1
0
1
0
0
2
1
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
1
2
0
0
2
0
0
0
0
3
0
2
1
1
0
1
0
0
0
1
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
1
0
0
0
1
8
0
2
0
2
1
0
0
2
0
1
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
2
3
0
3
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
3
0
0
1
0
1
0
0
0
2
1
2
0
0
2
3
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
1
0
0
0
1
0
2
0
0
1
0
0
0
2
2
0
2
0
1
0
0
1
1
0
1
0
1
0
0
1
0
0
1
1
1
2
0
0
1
0
3
0
0
0
0
3
0
0
2
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
2
0
0
2
0
1
1
0
2
0
0
1
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
3
2
2
2
0
0
0
0
2
1
0
1
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
1
3
0
0
1
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
1
2
2
0
1
0
0
0
2
2
2
0
0
0
1
2
2
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
1
1
0
3
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
1
0
0
0
0
2
0
0
2
1
0
1
0
0
1
2
0
0
1
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
1
1
1
0
0
2
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
2
1
2
0
0
0
0
0
2
0
0
2
0
1
0
0
0
2
0
1
2
0
0
0
0
0
0
0
2
1
0
2
0
2
0
1
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
2
1
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
1
1
1
0
1
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
2
1
0
0
1
0
1
2
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
2
1
0
0
4
0
2
0
1
0
0
0
0
0
0
0
1
2
2
0
0
2
0
2
1
2
0
1
2
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
2
0
0
0
0
4
0
2
1
0
2
0
0
1
0
0
0
0
1
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
4
0
1
0
0
2
0
0
1
2
1
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
2
4
0
0
0
0
0
0
0
4
0
0
1
0
2
0
0
1
0
1
0
0
0
0
1
2
1
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
2
2
2
2
1
0
4
0
0
0
0
0
0
3
0
1
0
0
0
0
1
2
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
3
0
0
1
2
0
0
0
0
0
2
3
1
0
0
0
0
0
0
2
1
0
1
0
0
0
2
3
2
0
2
0
1
1
2
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
1
0
0
0
2
0
1
0
1
1
0
0
2
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
3
4
0
0
2
0
1
0
0
2
0
2
1
4
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
2
0
0
0
0
1
1
5
2
2
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
2
1
2
2
0
0
1
0
0
0
0
0
0
3
0
0
1
0
0
0
2
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
2
1
0
1
1
1
2
0
2
4
0
0
1
1
1
0
0
4
0
0
2
0
0
0
0
0
0
0
2
3
1
0
0
0
0
2
0
1
1
1
0
0
0
1
0
0
2
0
1
0
4
0
0
0
2
0
1
1
0
1
1
0
0
3
1
3
1
1
0
1
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
2
0
0
0
0
0
2
1
0
2
0
1
0
0
0
0
1
0
0
0
2
0
1
1
0
0
1
3
2
0
0
0
1
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
3
1
1
0
0
1
2
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
1
0
0
0
0
1
2
0
2
0
2
0
0
0
0
2
2
2
0
1
0
1
0
0
1
2
1
0
1
0
0
0
3
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
1
1
0
0
2
0
2
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
2
1
0
0
0
0
0
0
1
0
0
2
0
1
1
0
0
2
0
2
0
0
0
2
2
2
0
2
0
1
0
0
1
0
2
2
2
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
1
0
2
2
1
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
1
0
0
2
0
3
1
1
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
1
0
0
1
1
1
1
0
1
0
0
0
0
0
0
2
0
0
2
0
2
0
1
1
0
0
0
0
1
2
0
0
0
1
1
2
0
1
0
1
2
2
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
1
3
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
2
0
1
0
0
2
0
0
0
2
1
2
2
0
0
0
1
2
0
0
2
2
2
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
3
2
0
0
0
0
0
0
3
0
0
0
2
1
0
0
0
0
0
0
1
0
2
2
0
2
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
4
1
2
1
0
2
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
1
2
0
0
0
2
0
0
0
0
1
3
0
1
0
0
0
1
0
0
0
0
2
2
1
2
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
2
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
1
1
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
1
0
0
0
3
0
0
1
0
0
0
0
0
0
0
1
2
1
2
1
2
0
0
0
0
0
2
0
1
1
0
1
0
3
1
1
0
1
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
2
0
0
0
0
2
2
0
0
1
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
2
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
1
1
0
2
0
0
0
0
2
2
2
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
1
0
0
0
1
0
2
0
0
0
1
3
0
2
0
0
2
0
0
1
0
0
2
0
0
0
0
2
1
0
0
0
1
0
1
1
0
1
0
2
0
0
0
0
0
1
3
0
0
0
0
0
2
0
2
0
1
1
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
1
0
2
2
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
4
2
2
0
0
2
1
0
2
0
1
0
0
2
0
1
0
0
2
2
0
0
0
1
0
2
0
2
0
1
0
0
1
0
1
0
0
2
0
0
0
2
2
0
0
0
0
2
1
0
0
0
4
2
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
2
2
0
3
0
0
2
3
2
0
0
0
1
2
0
0
0
0
0
0
0
1
1
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
1
0
1
2
0
0
0
1
1
1
2
2
0
1
0
1
0
4
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
1
0
0
2
1
2
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
1
0
2
0
0
0
2
1
0
1
1
0
1
0
1
0
2
0
0
0
0
1
0
0
1
1
1
0
1
1
1
2
0
0
0
0
1
0
2
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
2
1
2
0
0
2
7
0
1
0
2
2
0
2
0
0
2
2
0
0
2
0
0
0
2
0
2
0
0
2
2
0
0
0
0
0
2
0
0
0
0
1
0
0
1
1
0
0
1
0
3
1
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
1
0
1
2
0
3
0
0
0
4
0
2
0
0
0
2
0
0
0
1
1
0
0
0
1
2
0
3
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
1
3
1
0
0
0
0
0
2
0
0
0
0
3
0
0
2
1
2
0
0
2
2
0
2
1
0
1
0
0
0
0
2
0
1
0
0
0
0
0
2
0
1
0
2
0
1
0
2
0
2
1
0
0
0
0
0
0
2
1
0
0
0
1
0
2
3
0
0
0
0
2
0
2
0
1
0
2
2
0
2
1
0
1
0
1
0
1
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
2
3
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
2
0
1
3
0
0
1
1
2
0
0
0
0
1
0
2
2
2
0
1
0
2
3
0
0
0
0
0
1
1
0
0
2
0
2
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
1
0
0
1
1
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
5
0
0
0
2
0
0
0
0
0
0
1
1
1
2
1
0
0
2
2
1
0
0
2
0
0
1
0
1
1
0
0
1
2
0
1
0
0
3
0
1
0
2
0
2
0
1
0
0
1
0
4
0
0
1
1
0
0
2
0
1
1
0
0
0
0
1
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
3
2
0
0
0
2
0
0
0
2
0
0
3
0
2
2
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
1
0
0
1
1
0
0
0
0
1
0
1
0
1
0
0
0
2
0
0
1
2
0
0
0
1
1
0
0
0
2
3
2
0
0
0
0
0
0
0
0
1
0
1
1
1
1
0
1
0
0
2
2
2
1
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
1
2
1
0
0
2
1
0
0
0
0
0
2
0
1
0
2
0
0
0
0
1
0
2
0
0
1
0
1
0
0
0
0
0
2
0
1
0
2
0
6
0
3
0
0
0
0
2
0
0
7
1
4
0
0
2
0
0
1
1
0
0
0
3
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
2
2
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
2
2
0
0
4
1
0
0
0
0
1
0
3
1
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
1
0
0
1
0
0
1
2
2
1
0
1
0
0
0
1
0
0
2
0
0
0
0
0
2
0
2
1
0
2
0
0
2
0
1
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
2
1
0
2
3
0
0
0
0
2
0
2
0
0
2
1
2
0
2
2
1
0
0
1
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
1
1
1
1
0
0
2
0
1
0
0
0
1
1
1
0
2
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
2
0
2
0
2
0
1
0
1
0
0
3
2
0
1
2
0
2
2
0
2
0
0
0
2
0
0
0
2
4
1
2
0
0
0
1
2
0
0
0
1
0
0
0
0
3
0
0
2
0
0
0
0
2
2
0
1
0
0
2
0
0
0
0
0
1
0
4
0
0
1
1
1
0
0
1
0
0
0
2
1
0
0
1
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
3
2
0
1
2
1
1
0
0
1
1
0
2
4
3
1
1
0
0
0
0
2
0
2
1
2
0
0
3
2
0
2
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
1
0
0
2
2
0
0
1
0
1
0
1
0
1
0
0
0
0
2
1
1
0
1
1
2
0
2
0
0
0
1
1
0
0
1
1
0
0
0
0
1
0
0
2
0
0
0
0
1
2
1
0
0
2
0
2
1
2
3
0
0
1
2
0
2
0
2
2
0
0
0
0
0
0
0
1
0
0
1
0
2
0
2
0
2
2
0
0
0
0
0
0
1
0
2
0
2
0
1
0
3
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
2
0
0
2
0
2
1
0
0
2
0
0
0
0
0
0
0
1
1
2
2
0
0
1
1
1
0
0
0
0
2
3
0
0
0
0
0
0
0
10
2
0
1
0
0
0
0
0
0
0
1
0
4
0
0
0
0
2
0
0
0
0
0
0
1
2
0
1
0
1
2
0
2
0
0
0
0
1
0
3
1
1
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
3
0
2
1
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
2
2
2
0
2
2
2
2
1
0
2
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
2
0
0
2
0
1
0
1
0
1
1
2
0
0
0
0
3
0
0
0
2
0
0
0
2
2
0
0
2
1
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
1
0
0
0
0
0
1
2
0
0
0
0
2
0
1
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
1
1
0
0
0
0
1
2
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
3
0
2
2
1
3
0
2
1
1
0
0
2
1
0
1
1
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
2
0
0
2
0
2
0
0
2
0
2
0
0
3
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
2
0
1
0
1
0
0
0
2
0
2
2
0
2
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
1
1
0
0
0
1
0
0
1
0
0
0
2
0
1
1
0
2
2
0
2
2
0
0
0
0
3
0
1
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
3
0
0
2
1
2
0
0
0
0
1
1
0
0
0
0
1
3
1
0
0
1
2
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
2
2
1
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
3
0
0
2
2
2
0
0
2
1
0
0
2
3
2
0
1
2
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
1
0
3
2
1
0
0
0
2
2
1
2
0
0
0
0
2
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
3
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
2
1
1
0
4
0
0
1
0
2
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
2
0
0
0
1
0
0
0
3
0
0
0
0
0
2
0
1
1
2
0
0
2
1
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
3
0
0
0
0
3
2
0
0
0
0
3
0
0
2
0
0
0
3
0
1
0
3
0
1
1
2
2
2
0
0
2
0
2
1
0
0
1
0
0
1
2
0
2
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
1
2
0
1
0
1
1
0
0
0
0
0
2
0
1
0
0
0
1
0
2
1
0
2
2
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
2
3
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
2
0
1
1
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
2
1
0
2
1
0
2
0
2
2
0
0
0
0
2
0
2
2
0
2
1
0
0
0
0
2
0
0
0
0
3
2
0
0
0
2
0
0
2
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
2
1
0
0
2
0
0
1
0
1
1
1
1
0
0
2
2
0
0
0
0
1
0
1
0
0
1
0
2
0
0
1
0
0
0
0
0
2
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
2
1
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
2
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
1
2
0
2
2
0
0
0
0
0
0
0
0
0
2
0
2
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
4
2
0
0
0
0
0
0
1
1
2
0
2
0
1
0
0
2
0
0
1
3
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
2
0
0
3
0
0
0
0
2
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
1
1
0
0
0
0
0
2
0
2
0
0
0
1
0
3
0
0
0
1
0
0
0
1
2
3
2
1
0
0
1
1
3
0
1
0
1
0
0
2
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
1
0
2
2
2
0
0
0
2
4
0
1
0
0
0
2
0
0
2
2
0
0
1
0
1
3
0
0
0
1
0
0
2
0
0
0
1
2
0
0
2
1
0
1
0
2
2
0
2
1
0
2
1
1
1
0
0
0
0
1
0
2
0
0
0
0
2
0
2
2
0
0
1
2
0
1
0
2
1
0
0
0
0
0
0
2
2
0
2
0
1
1
1
1
1
1
3
0
0
2
0
0
0
2
0
0
0
0
2
2
2
0
0
0
2
0
0
0
0
2
0
4
0
2
0
0
2
1
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
2
2
0
1
4
1
2
1
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
1
1
2
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
2
2
0
2
0
1
1
0
2
0
0
1
2
0
2
1
0
0
2
0
0
0
0
0
0
0
0
6
0
4
0
0
3
0
0
2
1
0
0
1
0
0
1
2
0
0
1
0
0
0
1
0
0
0
1
0
2
2
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
3
0
2
0
0
0
0
2
1
0
2
0
0
0
0
2
1
1
0
0
0
5
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
2
2
0
0
2
1
1
0
0
2
0
1
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
2
1
0
1
1
0
1
1
2
0
0
1
7
1
1
2
0
0
1
1
0
0
0
2
1
2
0
0
0
0
1
0
0
2
1
2
3
0
2
0
3
0
0
2
1
0
0
0
0
0
0
0
8
0
0
0
3
0
0
2
1
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
2
0
0
2
1
0
2
0
2
0
0
0
0
1
4
0
0
1
0
2
0
0
0
2
0
0
0
0
1
0
0
2
2
0
0
0
0
1
0
1
0
2
2
0
2
0
0
2
1
2
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
4
0
4
0
0
2
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
1
0
0
2
1
0
0
1
0
1
0
2
0
0
1
1
0
0
0
0
2
0
1
2
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
5
0
0
2
0
0
0
2
7
0
1
0
0
2
3
0
2
0
0
1
0
0
0
0
3
0
0
0
0
1
0
2
2
0
0
0
0
0
2
1
1
0
2
0
0
0
1
0
1
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
1
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
3
0
0
4
1
0
0
0
0
1
2
0
1
0
4
0
0
1
0
2
0
1
3
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
3
2
0
5
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
2
1
2
0
0
2
1
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
5
0
2
0
0
0
0
1
1
0
0
0
0
0
2
0
0
2
0
2
0
0
2
0
1
0
0
0
0
1
2
2
0
0
0
0
1
0
0
4
0
0
0
2
0
1
0
0
0
1
0
1
0
1
0
0
0
2
1
0
0
2
3
0
2
1
0
1
0
0
0
0
0
2
1
1
0
0
2
1
0
0
1
0
1
0
2
0
0
0
1
0
2
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
4
0
2
0
0
1
0
2
0
0
1
0
0
0
1
0
0
0
2
2
1
1
2
0
0
0
2
0
0
0
0
0
0
0
1
1
2
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
4
0
0
0
2
0
1
2
0
0
0
0
0
0
1
0
1
0
0
1
0
3
0
0
0
1
0
1
0
0
2
2
0
0
0
0
0
0
1
1
1
0
0
0
0
2
1
2
1
0
1
1
1
2
2
0
1
1
0
0
0
2
0
1
3
0
0
2
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
2
0
0
0
1
0
1
0
2
2
0
1
1
0
0
0
0
1
0
1
2
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
3
2
0
2
2
1
2
0
2
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
1
2
1
1
0
0
1
1
0
0
0
0
4
1
0
1
2
0
1
0
0
1
0
0
0
0
2
0
1
1
0
0
0
0
0
2
0
1
2
0
0
1
4
1
0
0
1
0
0
2
0
0
1
1
2
0
0
0
0
0
0
1
0
0
0
1
0
3
2
2
0
2
0
1
0
0
0
0
0
0
1
0
0
2
0
0
1
2
10
0
0
0
1
0
1
0
2
3
0
1
0
3
0
1
2
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
2
1
2
0
0
0
0
2
0
0
0
0
2
0
0
2
1
0
0
0
2
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
3
0
0
0
0
1
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
2
0
1
1
0
1
2
0
0
2
1
0
0
3
0
0
0
0
2
2
0
0
0
2
1
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
1
0
2
2
0
0
1
0
0
2
2
1
0
1
0
0
2
0
2
1
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
4
0
0
0
0
2
0
0
0
1
1
0
1
0
1
0
1
0
2
0
1
0
2
2
0
0
0
0
2
2
2
0
2
0
0
0
1
1
0
0
0
0
2
0
3
1
0
0
0
1
0
0
0
0
0
0
1
2
0
2
0
1
1
1
0
0
0
0
2
0
0
0
2
0
0
0
3
1
1
0
1
1
0
0
1
1
1
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
1
0
0
2
0
1
0
0
0
1
0
0
0
0
3
0
0
0
1
0
1
0
0
0
0
0
2
1
3
2
0
1
0
1
2
1
0
0
2
0
2
0
0
0
1
0
1
0
1
0
0
2
1
0
0
2
2
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
2
2
2
0
2
0
1
0
1
0
2
0
6
1
0
0
0
0
0
0
1
2
0
3
2
0
1
0
0
0
0
0
1
0
2
0
1
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
2
0
0
3
0
0
0
0
0
2
3
0
2
2
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
1
0
3
0
0
0
0
2
0
2
0
0
2
0
0
0
1
0
0
2
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
2
0
2
2
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
3
2
0
1
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
1
2
0
0
0
2
1
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
2
1
10
0
1
0
1
1
0
0
0
0
1
0
1
2
0
0
2
1
0
0
0
0
0
0
2
2
0
0
0
0
0
1
2
0
1
0
0
2
0
0
0
0
1
0
1
0
1
0
1
1
3
0
0
1
0
0
1
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
3
1
2
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
1
3
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
2
0
2
0
0
1
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
2
2
0
0
0
0
0
0
0
2
1
0
3
2
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
2
1
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
2
0
1
0
0
0
0
0
2
1
0
2
0
2
1
0
0
1
2
0
1
1
1
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
2
2
2
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
2
2
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
1
0
0
2
1
1
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
1
1
2
0
0
0
2
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
1
0
2
0
0
2
0
0
2
0
0
2
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
1
2
0
0
0
3
0
1
0
2
2
0
0
0
1
2
1
1
2
0
0
1
0
2
0
0
0
0
2
2
2
0
0
2
0
0
0
0
3
0
2
0
0
0
2
0
1
2
2
1
0
0
1
0
0
2
1
2
1
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
2
1
1
0
2
0
0
0
2
2
1
0
0
1
2
3
0
0
1
0
0
3
2
2
1
0
0
0
1
0
0
2
0
1
1
1
0
0
0
1
0
2
2
0
0
0
2
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
1
1
1
0
0
1
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
2
0
0
2
0
0
1
0
0
0
0
1
0
0
0
2
0
0
1
0
0
2
0
0
0
2
2
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
2
1
1
0
1
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
1
2
1
0
3
1
2
2
0
0
1
0
0
3
2
0
1
1
0
0
1
3
1
0
1
0
0
0
0
0
1
1
0
1
0
0
2
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
3
1
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
3
0
2
6
2
0
0
0
3
2
0
1
0
1
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
1
0
0
2
1
1
3
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
2
0
2
0
0
0
0
0
1
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
2
1
0
1
0
2
0
0
1
0
1
1
0
0
0
0
0
0
1
0
1
1
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
2
3
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
1
0
2
0
0
1
0
2
1
1
1
2
0
0
0
2
0
1
2
4
0
0
1
0
0
1
2
2
0
2
0
0
0
0
2
0
2
1
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
1
2
2
2
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
2
1
10
2
0
1
0
1
0
2
1
0
0
0
2
1
0
0
0
0
0
0
0
2
1
2
0
1
0
1
1
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
2
2
2
1
2
1
0
0
0
0
0
2
2
1
1
0
0
2
0
1
0
1
0
0
0
0
0
2
0
1
0
0
0
1
1
0
2
0
0
2
0
0
2
0
0
0
0
0
1
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
2
0
0
0
1
0
0
0
2
0
0
2
0
0
1
0
0
1
0
0
0
3
0
0
0
2
0
2
0
0
2
0
4
0
4
2
0
0
0
1
0
6
0
0
0
0
0
2
0
2
0
0
1
1
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
1
0
0
0
2
0
0
2
0
0
0
2
0
1
0
1
0
0
0
0
2
0
1
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
1
4
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
2
0
0
0
0
3
0
1
1
0
0
0
1
0
2
0
0
0
0
0
0
0
1
2
0
0
2
0
0
2
1
2
0
0
0
0
2
2
1
1
0
0
0
0
0
1
0
3
1
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
1
1
1
2
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
1
1
0
0
0
0
0
0
0
0
1
2
2
0
0
5
0
0
2
1
1
0
1
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
4
0
0
2
0
1
2
2
1
2
1
0
0
0
3
0
0
0
0
0
0
4
0
0
0
0
1
2
1
0
0
2
0
0
0
0
0
1
1
0
0
2
1
2
3
0
0
0
5
0
0
0
0
0
0
1
0
0
1
2
0
3
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
1
2
0
2
0
0
2
0
2
0
0
3
1
2
0
1
2
0
0
2
0
2
0
0
1
0
0
0
0
0
2
0
0
1
2
0
0
0
0
1
2
0
0
0
0
1
2
0
1
0
2
0
0
1
1
0
0
0
2
0
1
2
0
0
2
2
1
0
0
0
0
2
0
2
1
0
2
0
0
1
0
3
1
2
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
1
0
1
1
0
1
2
0
0
1
0
0
2
0
1
0
2
2
1
1
2
0
0
0
0
4
0
0
2
4
0
0
3
0
1
1
0
0
0
0
2
0
1
0
0
0
1
0
1
1
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
1
2
0
0
2
0
0
0
4
0
1
2
0
0
1
0
0
2
0
2
0
2
0
1
0
1
2
0
0
0
1
1
0
2
2
0
0
3
0
2
0
2
2
2
0
2
3
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
2
0
1
0
1
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
3
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
2
0
0
1
2
0
0
1
1
0
0
0
0
1
1
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
2
3
0
0
0
1
0
0
2
0
0
0
0
0
0
1
1
0
1
2
3
0
0
0
4
0
0
0
0
0
4
1
0
0
4
1
0
2
1
1
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
2
0
0
2
2
0
2
0
2
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
1
0
2
0
2
1
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
1
2
2
1
0
0
0
0
0
2
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
1
0
1
0
0
0
1
1
0
0
0
2
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
2
1
1
1
0
1
0
0
2
0
0
0
0
1
0
0
2
0
0
0
2
0
0
2
0
3
0
0
0
0
1
2
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
2
2
2
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
3
1
0
0
0
3
0
1
0
1
0
1
1
2
0
0
2
2
0
2
0
0
1
0
1
0
1
0
1
0
2
0
0
0
0
0
1
0
0
1
2
1
1
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
3
1
1
0
0
0
0
0
3
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
1
0
2
0
1
1
0
2
1
0
0
0
0
0
0
1
2
0
2
0
0
5
0
2
1
0
0
0
0
0
0
2
2
0
0
2
5
0
1
0
0
0
1
0
0
2
0
0
2
0
0
2
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
1
0
1
0
0
2
2
1
0
2
1
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
1
0
0
1
1
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
1
0
6
0
0
1
2
0
0
0
0
2
1
1
1
0
3
2
0
0
0
0
2
0
0
1
0
1
0
0
1
2
0
0
0
1
0
2
0
1
0
0
0
1
1
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
1
0
2
2
1
1
1
0
0
2
1
2
1
1
0
0
0
0
2
0
0
0
1
1
2
2
2
0
2
0
0
0
0
2
0
0
0
1
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
2
1
2
0
3
0
0
0
0
0
0
1
2
0
0
0
0
1
2
3
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
2
2
0
0
0
0
2
0
0
0
1
0
4
0
4
2
1
0
0
0
2
0
2
0
2
0
1
0
0
0
0
2
1
0
1
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
1
1
0
0
2
0
0
0
1
0
2
2
0
0
2
1
0
0
0
0
2
0
1
0
0
0
0
0
0
1
1
2
0
0
2
0
0
2
0
0
1
1
0
0
0
1
0
0
0
0
2
1
0
0
0
2
0
0
2
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
2
0
2
0
1
1
2
0
1
0
0
0
0
2
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
3
0
0
1
0
0
0
1
0
0
0
0
0
2
1
0
2
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
1
0
0
0
3
3
1
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
2
0
0
0
1
0
1
0
2
1
0
2
0
2
0
0
0
8
1
0
2
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
3
0
2
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
1
0
0
2
2
0
1
1
1
0
0
2
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
2
0
1
2
1
0
0
0
2
0
0
0
2
0
2
0
0
2
0
0
2
2
1
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
6
1
0
1
0
2
0
0
0
1
1
0
1
0
2
0
0
1
0
0
5
0
1
2
0
0
1
0
0
1
0
2
0
0
1
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
1
0
2
1
0
0
0
0
0
1
3
2
0
0
0
1
1
0
1
0
1
1
0
0
2
1
0
0
0
1
0
0
1
0
0
1
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
5
1
0
1
0
2
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
3
0
0
0
2
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
1
1
2
0
2
1
0
0
2
0
1
0
0
0
0
2
0
0
0
1
0
2
0
2
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
2
0
0
0
2
0
0
2
0
1
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
2
1
0
0
0
0
2
3
0
2
2
1
0
0
0
0
1
0
2
0
2
2
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
2
1
0
0
2
0
0
1
0
2
0
1
0
0
0
1
0
2
1
0
0
0
0
0
0
0
2
1
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
1
0
2
1
1
0
0
2
2
0
0
2
2
0
0
0
2
0
2
0
0
1
0
0
0
2
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
3
2
0
0
3
1
2
0
0
2
2
0
0
0
0
0
2
0
0
0
2
2
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
2
2
0
2
1
0
0
1
0
1
3
2
0
0
0
2
2
2
0
0
1
1
0
1
0
0
0
3
0
0
4
0
0
3
0
0
2
0
0
0
3
0
1
0
0
0
1
4
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
2
1
2
0
2
0
0
0
0
3
1
0
0
1
1
0
0
2
1
0
2
0
2
2
0
2
0
0
0
0
1
1
2
0
0
2
2
0
0
5
0
0
2
2
0
2
0
0
0
0
0
0
0
0
2
1
0
1
6
0
0
0
2
0
0
0
0
2
2
0
2
1
2
0
1
2
0
0
2
0
1
1
2
1
0
0
0
0
0
0
0
1
0
0
3
1
1
0
0
1
0
0
0
1
2
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
3
0
0
2
0
0
0
0
0
1
2
0
2
0
0
0
1
2
1
1
0
0
2
0
1
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
9
0
2
2
1
2
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
3
2
1
0
0
0
0
1
0
0
2
0
2
2
1
2
0
0
2
1
1
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
2
0
2
0
2
0
1
2
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
2
1
1
0
1
0
0
0
0
2
1
0
2
0
0
2
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
1
1
2
0
0
1
2
0
0
0
2
2
2
0
0
2
1
0
0
1
0
0
0
0
1
0
0
0
2
0
2
2
0
0
0
0
1
0
0
2
1
1
0
0
0
1
0
1
0
0
0
0
2
0
0
1
0
0
0
1
0
0
1
2
1
0
0
0
0
2
0
1
1
1
0
0
0
2
3
1
3
0
2
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
4
0
1
0
0
0
0
0
0
0
0
2
5
1
0
0
1
1
2
0
2
1
0
1
3
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
1
2
0
0
0
2
1
0
1
0
0
2
2
3
0
1
1
0
0
0
3
0
0
0
0
1
0
2
0
0
2
0
2
2
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
3
0
0
0
0
0
3
0
0
0
1
1
1
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
1
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
2
1
0
0
0
2
0
8
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
3
2
0
2
0
0
0
0
0
0
1
0
3
1
0
0
0
0
0
0
0
1
2
0
0
0
2
0
1
2
2
0
0
0
0
0
2
2
2
0
2
0
3
0
0
0
0
0
0
0
3
2
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
1
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
1
2
1
1
0
1
2
0
1
0
0
1
0
0
2
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
2
1
3
0
2
0
2
2
0
0
0
0
0
0
0
0
0
1
0
1
0
2
2
2
0
1
0
1
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
2
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
2
0
0
1
0
1
1
0
0
0
0
0
2
0
2
2
0
3
4
3
0
1
0
0
2
0
1
0
0
0
0
0
2
4
0
0
2
2
1
0
0
0
1
0
0
0
0
1
1
1
0
2
2
0
2
1
0
1
0
2
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
3
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
1
1
1
3
0
0
1
2
2
0
0
2
0
3
0
0
0
0
0
0
0
3
0
0
0
3
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
1
0
2
0
0
2
1
1
0
1
0
0
2
1
0
1
2
0
2
0
0
0
1
0
1
0
1
0
0
0
2
0
0
0
0
1
0
2
1
1
0
0
0
1
0
2
0
0
1
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
1
0
0
1
0
0
2
0
0
1
1
2
0
0
0
2
0
1
0
0
2
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
1
1
1
2
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
1
0
2
0
2
0
0
0
0
0
1
0
2
1
1
1
2
2
0
0
0
0
0
2
0
0
0
0
1
0
2
0
1
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
2
0
0
0
2
1
0
0
0
0
0
0
2
0
1
0
0
0
2
2
0
0
0
2
0
0
0
0
2
1
0
0
0
1
0
2
0
0
0
1
0
1
0
0
0
0
0
2
4
1
2
0
0
1
0
0
0
1
0
0
1
4
0
0
0
0
1
0
1
0
0
0
0
1
1
0
1
0
0
0
1
0
2
2
0
2
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
1
0
1
0
1
0
3
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
1
0
0
0
2
0
1
0
1
2
0
0
0
1
0
2
0
1
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
1
1
2
0
0
0
0
0
0
0
1
0
0
1
1
0
2
2
0
1
1
0
0
0
0
0
0
2
0
2
2
2
0
2
1
2
0
0
0
2
0
2
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
1
0
1
0
0
1
0
1
0
0
2
1
1
0
1
1
1
0
2
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
2
2
0
2
0
0
0
2
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
2
0
2
0
2
0
0
2
0
2
3
0
2
0
0
1
0
0
2
0
0
0
0
0
1
0
2
2
0
1
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
1
0
1
2
0
0
1
0
0
1
0
2
1
2
1
2
2
0
0
1
0
0
0
0
1
1
0
0
1
0
2
0
0
2
0
2
0
0
2
0
1
10
0
0
0
0
2
0
1
2
1
2
0
1
2
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
2
0
0
0
2
0
1
0
0
1
0
1
0
1
0
0
1
2
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
1
0
0
1
2
2
0
1
0
2
0
0
2
0
3
0
2
2
0
0
0
0
0
2
0
1
0
1
0
2
0
1
1
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
1
0
0
0
0
1
0
2
2
0
1
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
2
6
0
1
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
2
0
2
3
0
0
0
0
1
0
1
0
0
0
2
0
0
0
1
1
0
1
0
0
2
1
2
1
0
1
0
0
0
0
2
0
1
0
0
0
0
0
1
2
0
0
0
1
1
1
0
1
0
2
0
2
0
1
1
0
2
0
0
1
0
1
2
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
1
0
3
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
1
1
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
1
1
2
2
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
1
0
2
0
3
0
0
1
0
0
0
3
0
0
0
0
1
2
0
0
1
2
0
1
0
0
1
2
0
0
0
0
0
1
0
3
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
1
0
2
0
0
1
0
0
0
0
2
0
0
0
2
1
2
0
1
0
0
0
2
1
0
1
1
0
0
2
0
1
1
0
1
0
0
2
0
0
1
0
1
2
0
0
1
0
2
0
1
0
0
0
0
0
0
2
0
0
1
1
1
0
0
2
0
0
0
1
1
2
1
0
0
1
2
0
0
1
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
3
1
0
2
2
0
0
0
0
0
0
0
0
1
0
1
0
0
3
2
1
0
0
0
0
0
0
2
0
0
2
0
0
0
2
1
1
0
2
0
2
0
1
0
1
2
0
0
0
0
1
1
1
0
0
0
2
0
0
0
0
1
0
0
1
1
0
2
2
2
0
0
0
0
2
1
2
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
2
2
0
0
2
2
1
0
2
0
0
0
2
0
0
0
4
0
0
0
1
0
0
1
1
2
2
3
2
1
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
2
2
0
1
1
0
2
0
0
0
2
0
0
3
0
0
0
0
0
1
0
0
1
0
1
0
2
0
0
0
0
4
0
0
1
0
1
0
0
0
0
1
2
2
1
1
0
0
0
0
1
0
2
0
2
0
0
0
1
0
0
0
2
2
0
1
0
2
0
1
0
0
0
0
0
1
0
0
3
0
2
2
0
0
0
2
2
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
1
2
0
3
1
0
0
0
1
2
0
0
2
0
3
0
0
0
1
0
3
0
1
0
2
3
0
0
0
0
0
1
1
2
2
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
3
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
1
0
1
1
0
1
0
1
0
2
0
2
3
0
0
0
2
2
2
0
0
0
0
2
0
1
0
0
0
1
0
1
1
0
0
0
0
1
0
2
0
1
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
2
1
2
1
1
2
0
1
0
0
2
0
1
1
1
1
0
0
1
1
0
2
0
2
0
1
0
0
2
0
0
1
1
0
0
0
2
2
0
0
2
0
0
0
0
0
1
0
0
1
7
0
0
0
0
1
2
2
0
2
0
1
2
1
0
0
1
0
0
2
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
1
1
0
2
0
0
0
2
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
2
0
2
0
1
0
1
0
1
2
0
0
1
1
0
0
2
1
0
5
0
0
0
0
0
1
1
0
0
2
2
2
1
0
0
0
0
0
2
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
1
2
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
1
4
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
1
0
0
2
0
2
0
1
0
0
1
1
0
4
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
2
0
1
0
0
0
0
0
0
1
0
0
0
0
2
1
1
0
0
0
0
2
2
0
0
0
1
0
0
2
0
1
0
0
0
2
2
0
3
2
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
2
0
0
1
1
0
0
0
0
2
0
1
0
1
0
0
0
0
0
1
0
1
1
0
4
0
2
2
1
0
0
0
0
1
0
0
1
1
0
0
2
1
0
0
2
2
0
0
1
1
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
1
2
0
2
0
0
1
0
0
0
0
1
5
0
2
1
1
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
2
2
1
0
1
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
2
0
0
1
2
0
1
0
1
0
1
0
0
1
2
2
2
0
1
0
0
2
2
0
0
1
1
1
0
0
0
1
2
0
1
0
0
0
2
0
1
2
0
0
2
0
0
1
0
0
0
0
0
0
0
1
2
0
0
2
0
0
2
2
0
0
0
0
0
0
1
0
1
2
0
2
2
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
1
0
0
2
2
1
2
0
0
11
6
0
1
0
0
0
2
1
0
1
4
0
0
0
0
0
0
2
0
0
1
1
0
0
0
2
0
0
0
1
0
2
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
1
2
0
2
0
2
0
0
2
2
0
2
0
0
0
0
0
2
0
0
0
0
1
2
2
2
1
1
0
0
0
0
1
1
1
0
2
0
1
0
1
0
0
2
0
0
0
0
1
2
3
0
3
0
2
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
2
0
0
1
1
0
2
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
1
2
0
0
2
0
2
0
0
0
1
0
0
1
2
0
0
3
0
2
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
1
2
1
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
1
2
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
1
0
0
2
0
0
0
2
0
1
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
2
0
0
2
0
0
0
0
0
1
1
0
3
2
0
0
2
2
1
1
0
0
0
2
2
0
0
0
2
0
0
0
1
2
2
2
0
0
0
2
0
0
0
0
0
0
0
1
4
3
1
0
2
1
0
1
0
0
0
1
0
0
0
0
2
2
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
1
1
2
0
0
1
0
1
0
2
1
0
0
0
0
0
2
0
0
0
1
1
0
0
1
0
0
1
0
2
0
1
1
1
0
1
1
0
0
2
0
2
1
1
0
0
0
0
0
0
0
0
5
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
2
0
0
2
0
2
2
1
2
1
0
1
4
0
0
0
0
0
0
0
0
2
0
0
2
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
1
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
2
1
1
2
2
0
0
0
0
0
0
1
0
0
0
2
0
0
8
0
0
0
0
1
2
1
0
5
0
2
1
0
0
1
0
2
0
0
2
2
0
0
0
0
0
0
0
2
2
6
1
0
0
1
2
2
0
1
0
0
2
0
0
0
2
0
0
2
0
0
0
1
0
2
0
0
1
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
3
2
0
1
2
0
1
0
1
2
0
0
3
0
0
0
1
0
2
2
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
1
2
2
0
0
0
0
3
2
2
2
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
2
1
0
0
2
0
0
0
1
2
0
3
0
1
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
1
2
1
5
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
2
0
2
1
0
0
2
1
0
0
0
0
0
0
0
1
1
0
0
3
0
2
2
0
0
1
0
3
0
0
0
2
1
0
0
2
0
0
0
2
0
0
0
2
0
2
2
0
1
0
0
1
0
2
2
0
0
0
1
1
1
2
0
0
0
0
0
2
0
1
2
0
0
0
0
0
2
2
0
1
0
0
3
0
1
2
0
1
2
0
0
0
0
1
3
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
3
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
3
0
2
2
1
0
0
0
0
2
1
0
0
2
0
0
0
1
0
2
0
3
1
2
2
0
0
0
0
3
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
2
0
2
0
3
1
0
2
0
0
0
1
1
0
0
3
0
1
1
0
0
0
0
0
0
2
2
0
5
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
3
0
4
2
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
2
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
2
1
0
2
2
0
0
0
0
1
1
0
2
1
0
0
0
1
0
1
0
1
1
2
1
1
0
0
0
1
0
3
0
0
0
0
0
2
2
1
0
2
2
0
2
0
0
0
0
0
2
0
0
2
0
0
1
0
1
1
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
1
2
2
1
3
0
0
0
1
2
0
2
0
0
1
1
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
1
2
0
0
0
1
0
0
0
0
3
2
1
2
0
2
0
2
0
1
1
0
0
2
0
1
1
3
2
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
7
0
2
1
2
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
2
0
2
1
0
2
0
1
0
0
2
0
2
0
0
1
0
0
0
1
0
0
1
0
0
0
0
2
1
2
0
2
0
0
2
1
0
0
2
0
0
1
2
1
0
0
0
2
0
3
2
0
2
0
1
0
2
1
2
0
0
1
0
0
1
0
1
0
0
2
2
0
2
0
2
0
0
1
0
0
0
2
0
1
0
0
2
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
4
0
0
2
1
0
0
1
0
4
2
2
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
1
0
0
1
1
1
0
2
0
0
0
0
0
0
2
1
1
1
2
1
1
0
0
0
0
1
0
2
0
0
2
2
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
5
0
2
2
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
2
2
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
1
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
2
2
0
0
0
0
1
0
0
4
0
0
0
0
2
2
0
0
1
0
0
0
1
0
1
0
1
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
3
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
2
0
1
1
0
1
1
0
0
2
0
0
0
1
1
3
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
2
1
0
0
0
1
0
0
0
0
0
0
2
0
2
0
1
0
2
0
0
0
0
0
1
0
6
2
1
1
1
1
4
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
1
0
1
0
0
2
2
1
0
0
0
0
0
1
0
0
2
0
2
0
0
1
0
0
0
0
0
1
2
0
0
0
3
2
1
0
0
0
1
0
2
0
1
1
0
2
0
0
0
0
0
0
0
0
2
2
0
1
0
0
1
0
0
1
4
0
0
0
2
0
0
0
2
0
1
0
2
0
0
0
0
0
0
1
1
0
0
0
3
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
2
0
0
2
1
5
0
0
0
0
2
0
0
0
2
2
0
0
1
0
0
0
2
1
2
3
0
1
0
0
0
0
0
3
0
0
0
1
0
0
2
2
0
0
0
0
0
0
2
0
0
0
2
0
3
0
2
0
0
2
2
2
0
1
0
0
0
0
0
3
0
0
0
0
2
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
2
1
0
0
0
1
1
3
2
0
0
1
1
0
0
0
0
0
2
1
2
0
2
0
0
0
0
0
1
0
2
1
1
0
0
0
0
0
1
1
0
1
0
0
2
0
2
1
0
0
0
1
1
0
0
0
1
0
1
1
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
2
1
1
2
0
0
0
0
2
0
1
0
0
0
0
2
0
1
1
2
0
0
0
0
0
0
1
0
1
7
0
2
0
0
2
0
1
1
0
0
0
2
0
0
0
0
0
3
0
0
0
1
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
2
1
0
2
0
2
0
0
6
0
0
0
2
0
2
0
1
0
0
0
0
0
0
4
0
0
0
2
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
3
0
1
2
1
1
0
0
2
1
1
0
1
0
1
0
1
0
0
0
0
1
5
0
0
0
0
0
1
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
1
1
0
1
1
2
0
1
0
2
2
0
0
0
2
0
2
2
3
0
0
3
0
2
0
0
0
4
2
0
2
0
0
1
0
0
0
0
1
0
0
0
1
0
0
2
2
0
0
1
0
0
2
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
2
1
0
1
1
2
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
1
1
0
0
0
2
0
0
0
4
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
2
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
1
2
0
1
1
0
0
0
0
5
2
0
1
0
0
2
0
0
0
1
0
2
2
1
0
0
1
0
0
0
0
0
0
2
0
0
1
2
0
0
0
2
0
1
0
2
0
2
0
1
1
0
2
1
0
1
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
1
0
2
0
1
0
2
0
2
0
0
1
0
0
2
0
0
0
0
1
2
0
0
2
0
0
1
1
0
0
0
0
1
1
0
0
0
0
2
0
2
0
0
1
0
0
1
1
2
0
0
0
0
2
2
0
0
0
2
0
0
0
2
0
2
0
0
0
1
0
0
1
0
0
0
0
2
1
1
0
1
0
0
2
0
0
0
0
0
2
0
0
0
1
1
0
2
0
1
1
0
3
1
0
0
0
0
1
0
0
2
1
0
0
2
2
0
0
0
2
0
2
1
0
0
1
2
0
0
2
0
0
0
3
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
3
0
0
0
2
2
0
0
2
0
1
2
0
1
1
1
0
0
2
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
2
0
0
1
0
0
0
0
0
0
0
0
1
2
0
2
0
1
1
0
2
0
2
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
1
2
2
0
0
0
2
2
1
1
0
0
1
1
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
2
0
0
2
0
0
1
0
1
0
2
1
1
1
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
2
1
0
0
0
3
2
0
0
2
0
0
1
2
1
0
2
0
1
0
0
0
0
0
0
0
0
3
1
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
2
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
2
0
0
1
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
1
0
1
0
2
0
0
1
1
0
0
2
0
2
1
0
0
0
2
3
1
0
2
0
0
3
0
2
0
0
0
0
0
3
0
1
0
1
0
2
1
0
1
0
0
0
0
0
0
2
0
0
1
1
0
0
0
2
0
0
0
0
1
0
0
2
0
0
2
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
5
0
2
1
0
0
0
0
0
4
1
0
2
1
0
0
0
0
0
0
0
0
2
2
0
2
1
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
2
0
0
1
2
0
0
0
0
0
1
2
0
0
0
2
2
0
2
0
2
0
0
0
0
2
5
0
0
2
1
1
0
0
1
1
2
2
0
0
0
0
4
0
0
0
0
1
0
0
2
0
2
0
0
0
1
0
0
0
0
2
0
0
0
3
0
0
2
0
1
0
0
1
0
0
0
2
2
3
0
2
2
0
0
0
0
0
2
3
0
1
1
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
3
1
0
1
0
0
0
0
1
0
0
1
0
1
1
0
1
0
0
1
0
0
0
0
2
1
0
1
0
0
0
2
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
2
0
2
0
2
1
0
1
0
0
0
0
0
0
0
2
0
0
1
0
1
2
0
0
0
0
0
0
0
2
0
2
0
1
1
0
0
0
2
0
3
2
0
1
0
1
0
0
0
0
2
2
2
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
2
0
0
2
0
0
1
2
0
0
2
0
2
3
0
0
1
0
0
0
0
0
2
0
2
1
0
0
0
0
0
2
2
0
0
2
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
1
1
4
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
1
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
1
2
2
1
0
0
2
0
0
1
1
1
1
0
0
0
0
0
1
0
0
1
0
0
1
0
2
0
0
0
0
1
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
2
2
0
0
0
1
1
2
1
0
0
0
0
0
2
2
2
0
1
0
2
0
0
2
0
0
3
0
0
0
3
0
0
0
0
0
0
1
2
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
2
2
1
2
2
0
0
0
0
0
0
0
3
0
0
0
2
2
0
0
1
0
0
2
0
1
3
0
0
0
0
0
0
0
0
0
0
0
1
2
2
1
0
0
0
1
2
0
0
2
0
0
1
0
2
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
1
0
0
0
0
2
0
0
3
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
1
0
0
0
1
0
0
0
2
0
0
0
0
2
0
1
1
0
2
5
1
0
5
0
2
2
0
0
0
2
0
4
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
3
1
0
2
0
0
0
1
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
2
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
1
0
2
0
2
1
2
0
2
0
0
2
0
0
2
1
2
0
0
0
2
1
1
0
2
2
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
1
3
0
0
1
0
0
0
1
0
0
0
0
0
0
2
1
0
1
1
2
0
0
0
0
0
2
1
0
1
0
2
1
0
0
0
2
0
0
0
0
3
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
2
0
0
2
2
2
0
0
0
2
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
6
0
1
0
0
0
0
0
0
0
0
1
3
1
0
0
2
1
2
0
0
2
0
0
0
0
1
1
0
0
1
2
0
1
0
0
2
4
0
1
1
0
0
0
2
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
1
1
3
0
0
3
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
2
0
1
1
0
0
0
1
0
0
3
1
0
0
1
0
2
2
0
0
0
0
0
1
2
0
0
2
2
2
0
0
0
0
0
0
0
2
1
2
2
1
0
2
1
0
0
0
2
0
0
0
0
1
1
0
1
0
1
2
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
1
1
1
0
0
0
2
0
1
1
0
0
0
2
2
2
0
0
1
0
0
5
1
1
0
0
0
2
1
0
4
2
1
1
0
2
1
0
1
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
2
2
2
0
0
2
0
0
0
0
0
2
2
1
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
1
3
2
2
0
0
1
1
1
0
0
1
2
2
1
2
1
0
0
1
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
1
0
0
1
0
0
3
0
0
1
0
0
2
0
2
1
0
1
0
1
0
0
1
5
0
1
0
2
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
1
2
0
1
1
0
0
0
0
1
0
0
0
0
2
0
0
1
2
0
2
2
2
0
1
0
0
1
2
0
0
1
2
2
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
3
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
2
2
0
1
0
2
0
2
1
2
2
0
0
1
1
0
0
0
1
0
2
0
0
1
0
1
0
1
1
0
0
0
0
2
2
0
0
0
0
2
2
0
0
1
1
0
0
0
0
0
0
3
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
2
0
2
1
0
0
0
0
0
0
1
0
2
0
2
1
2
0
0
0
7
0
0
0
2
2
1
0
0
0
2
1
2
3
1
0
0
0
0
1
1
0
1
0
2
2
0
0
0
0
0
1
2
0
0
2
0
1
0
0
1
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
2
0
1
1
2
1
0
0
0
0
0
0
2
2
1
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
1
0
2
2
0
1
1
0
1
0
1
0
0
0
1
0
0
1
2
2
0
0
1
0
1
2
1
0
0
0
2
1
0
1
0
0
0
0
0
0
1
0
0
2
1
0
0
0
2
2
0
0
1
0
1
0
0
4
0
0
0
2
0
0
1
2
2
0
0
4
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
2
0
0
2
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
1
2
1
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
2
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
1
1
2
0
3
1
0
1
2
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
1
1
1
3
0
0
0
1
0
0
2
0
1
0
2
0
0
2
0
0
0
0
0
0
4
1
0
0
0
0
0
1
0
2
0
0
1
0
1
0
2
2
1
0
2
0
0
1
0
2
0
2
0
1
0
0
0
0
0
2
0
0
2
0
0
2
2
0
0
0
0
1
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
2
1
0
0
0
2
0
2
1
0
0
0
0
0
2
2
0
0
0
1
2
0
0
0
0
0
0
0
0
1
2
0
0
2
1
1
0
0
0
2
2
0
1
0
0
0
3
0
1
0
0
1
2
0
0
0
2
1
0
2
0
0
0
1
0
0
2
1
0
0
3
0
0
0
0
0
0
1
1
2
2
0
0
1
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
2
0
1
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
2
2
0
0
2
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
2
2
0
2
0
0
2
2
0
2
0
2
1
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
3
0
2
1
1
0
1
0
0
0
1
0
2
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
2
0
3
1
0
0
1
0
0
0
2
2
0
3
0
0
0
0
0
0
0
2
2
0
2
0
0
0
1
2
0
2
0
0
0
1
0
0
0
0
0
0
2
0
1
0
2
0
2
0
0
1
1
0
1
0
2
8
1
0
0
0
0
0
4
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
1
1
0
1
0
0
0
2
0
2
0
0
3
0
1
1
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
1
1
0
0
0
1
1
1
0
1
0
1
0
0
2
0
0
1
1
1
0
3
0
0
4
0
0
1
0
0
0
2
0
0
3
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
2
1
0
0
0
1
0
0
1
0
0
0
1
0
2
1
1
2
1
0
2
1
2
0
0
0
2
3
0
0
0
0
0
0
2
1
0
0
1
2
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
1
2
0
0
0
0
2
1
0
2
1
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
2
1
2
0
0
1
0
0
0
2
0
7
0
0
1
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
1
0
2
0
0
1
0
2
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
2
0
0
1
0
2
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
3
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
2
1
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
2
3
0
2
0
0
1
0
1
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
1
0
0
0
1
0
0
0
2
0
0
1
0
0
1
0
0
2
2
0
2
0
0
0
2
2
1
0
1
0
0
0
0
1
0
0
0
1
2
1
1
0
0
1
0
2
2
0
1
2
0
1
0
0
0
2
0
2
0
1
0
2
0
1
1
0
0
0
0
0
0
2
1
0
1
0
0
0
0
1
0
0
0
0
3
1
0
0
0
1
0
2
0
1
0
0
2
2
0
2
2
0
0
0
1
2
0
0
1
1
2
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
3
1
0
0
0
0
0
0
2
1
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
2
1
1
2
0
0
0
0
0
0
1
3
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
1
0
0
2
1
0
5
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
2
0
0
0
1
2
1
1
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
1
0
2
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
1
0
0
1
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
1
1
0
0
2
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
1
0
0
0
5
0
0
0
0
0
2
0
0
2
2
0
1
1
0
2
0
0
0
0
2
0
0
0
2
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
1
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
2
0
0
0
0
2
0
0
0
2
2
0
0
2
0
0
0
0
2
2
0
0
0
0
1
0
1
0
2
0
0
1
1
1
0
2
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
2
1
0
0
1
0
2
0
2
0
0
0
0
1
0
0
0
0
1
0
0
2
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
2
1
0
0
0
2
0
0
0
1
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
2
2
3
2
0
0
2
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
1
0
0
2
0
0
0
3
2
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
1
2
0
1
2
0
1
2
0
1
0
1
1
2
0
2
0
0
0
0
0
3
0
0
0
4
2
0
1
0
0
1
2
0
0
1
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
1
0
0
1
1
0
2
6
3
0
1
1
0
0
2
2
0
0
0
0
1
1
2
0
0
2
0
2
0
0
0
2
1
0
0
0
0
2
1
0
0
1
1
3
0
0
0
1
0
2
0
0
2
1
0
2
0
0
0
2
1
0
0
0
1
0
0
1
1
0
1
0
1
0
0
0
2
1
0
1
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
1
2
0
1
1
0
1
0
0
2
0
0
0
0
2
0
0
0
0
4
0
0
2
0
2
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
2
2
1
0
0
2
2
1
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
2
0
1
1
0
2
2
0
1
1
0
1
0
0
0
2
0
0
0
0
3
0
3
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
1
1
0
0
0
1
0
1
3
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
2
2
1
0
0
2
0
0
0
1
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
2
1
0
1
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
1
0
0
2
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
1
0
2
0
1
0
2
2
0
0
0
1
2
0
0
0
2
2
0
0
0
0
1
2
2
0
0
2
0
0
2
0
0
0
2
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
1
0
0
2
1
0
0
1
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
1
1
2
0
0
2
0
1
2
0
0
0
0
0
1
0
0
1
1
0
2
0
1
0
0
0
0
0
0
2
0
0
0
1
1
0
2
0
1
0
0
1
0
0
1
1
0
0
0
2
0
0
0
0
1
3
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
1
2
1
1
0
1
0
0
1
1
0
0
0
2
0
1
1
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
2
1
2
0
2
0
0
2
2
1
0
0
0
0
0
3
0
2
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
2
0
0
1
0
1
2
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
1
0
2
0
0
0
1
1
0
0
0
2
0
3
0
0
0
2
2
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
1
0
0
0
0
0
1
3
1
0
1
1
0
0
2
4
3
3
0
0
1
0
1
0
1
0
0
0
0
1
0
1
0
2
0
0
0
0
0
1
0
2
0
0
0
0
2
2
0
2
2
0
0
2
0
0
0
1
0
0
0
0
2
1
0
1
0
1
0
0
0
0
0
1
0
0
1
2
0
1
0
0
0
3
0
0
2
0
0
0
0
1
0
0
0
2
0
2
0
2
0
3
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
1
0
1
0
0
1
1
2
1
0
2
2
0
1
0
0
0
2
2
0
0
1
1
2
1
0
0
1
2
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
1
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
1
1
0
0
2
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
1
1
1
2
2
1
0
0
0
1
0
2
0
0
2
6
0
0
0
0
0
2
1
2
2
2
1
1
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
1
0
0
1
2
0
1
0
2
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
1
1
0
0
0
3
0
2
0
0
0
0
0
1
0
1
0
0
0
1
0
2
2
0
0
0
0
0
2
0
0
0
2
2
0
0
1
1
0
1
1
1
0
0
0
2
0
0
1
0
1
1
2
0
1
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
2
3
0
0
0
0
2
2
0
2
0
1
1
1
1
0
0
0
0
2
0
0
0
1
0
0
2
0
3
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
4
0
1
0
0
0
2
0
0
1
0
0
2
0
0
1
1
0
2
0
0
0
0
0
0
0
6
0
0
0
4
0
0
0
0
1
1
0
0
1
2
1
2
0
0
0
1
2
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
2
1
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
2
2
1
0
2
0
0
1
0
0
0
0
2
0
0
2
1
0
0
0
0
2
0
1
2
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
2
2
0
1
0
0
0
0
1
0
1
2
1
0
0
1
0
0
0
0
0
1
2
2
1
0
0
1
1
1
0
2
2
3
0
0
2
0
0
0
0
0
0
0
2
1
0
2
0
1
0
0
0
2
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
1
0
0
0
0
0
0
1
0
1
1
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
1
1
1
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
2
0
2
2
0
1
0
0
0
0
3
0
2
0
0
0
2
0
0
1
0
0
2
1
2
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
3
0
1
1
2
0
0
0
0
0
0
3
0
2
0
0
1
0
0
0
1
1
2
3
0
0
2
1
0
0
0
0
0
1
0
1
0
0
2
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
3
0
0
1
3
0
2
0
1
0
1
0
0
0
2
0
0
0
1
0
1
0
2
2
0
0
0
1
0
0
0
0
0
0
1
0
3
2
0
0
0
0
2
1
0
0
0
0
1
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
2
0
1
2
1
1
0
0
0
0
0
0
0
1
0
2
1
1
0
0
1
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
2
2
0
0
0
0
0
1
1
1
0
0
1
0
1
1
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
1
0
1
2
0
0
2
0
0
2
1
0
2
0
1
0
3
2
0
1
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
1
0
0
1
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
1
0
2
4
0
2
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
2
1
0
2
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
2
0
0
1
0
1
2
2
0
0
0
0
0
0
0
0
0
2
1
2
1
2
0
1
0
0
0
0
2
0
0
2
0
5
2
3
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
2
0
0
0
0
2
2
1
0
0
2
0
2
0
0
4
0
2
0
0
1
0
0
0
0
1
0
0
1
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
1
1
0
1
0
1
2
0
0
4
0
0
0
2
0
1
1
0
0
1
0
0
0
2
0
0
0
1
0
0
0
2
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
3
1
0
2
2
0
2
0
0
0
1
0
1
0
0
2
2
0
0
0
0
2
0
0
0
0
1
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
3
1
0
0
1
0
0
2
0
2
0
0
2
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
3
3
2
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
1
0
3
0
0
0
1
0
0
0
0
0
2
0
0
1
1
0
0
0
1
0
0
0
2
0
4
0
2
0
0
1
0
2
0
2
0
0
0
0
1
0
2
0
0
0
4
0
0
0
0
0
0
0
2
0
1
0
3
2
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
1
2
0
0
2
1
2
0
0
0
0
0
1
0
2
0
0
0
0
0
2
1
1
0
1
0
0
0
0
0
1
0
1
2
0
0
2
2
0
0
3
1
2
0
0
2
0
0
0
1
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
1
2
0
2
1
1
0
1
2
0
0
2
0
1
2
0
0
2
0
1
0
0
1
1
0
2
0
0
1
0
0
0
0
1
1
0
0
2
2
0
2
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
3
1
0
0
1
0
1
3
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
3
2
2
0
0
0
0
2
2
0
1
2
1
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
2
1
0
0
0
0
2
1
0
0
1
2
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
2
0
1
1
0
2
1
0
0
1
2
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
3
0
3
2
0
1
0
0
0
0
0
0
0
2
0
1
2
0
0
1
0
0
1
0
0
2
0
0
1
1
1
0
0
0
0
0
0
0
1
1
1
0
2
2
0
0
2
0
1
0
0
1
0
2
1
0
1
0
1
0
0
0
2
0
0
0
1
2
0
0
0
0
2
0
0
0
0
1
0
1
2
0
2
0
0
0
2
0
2
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
1
0
5
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
2
0
0
0
0
1
2
1
0
0
0
2
0
0
0
0
0
2
0
0
1
0
2
0
0
1
0
1
0
0
1
1
1
0
0
2
0
0
0
2
0
1
0
2
0
0
1
1
0
0
0
0
3
1
1
0
1
1
0
1
0
0
1
0
1
2
0
0
1
2
0
0
0
0
1
0
2
0
0
2
0
2
0
0
0
2
1
2
2
1
0
0
2
0
0
2
2
0
0
0
0
2
2
1
1
0
1
1
3
0
0
0
2
2
0
0
0
0
0
0
0
0
2
1
1
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
4
2
1
0
0
0
2
0
2
1
2
2
0
0
0
1
0
2
0
0
2
2
0
1
2
0
1
2
2
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
1
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
3
2
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
1
0
1
0
2
1
2
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
3
1
0
1
0
1
0
0
0
2
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
4
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
2
1
0
1
1
0
1
0
1
2
0
0
0
0
0
0
1
0
3
1
2
0
1
0
1
0
1
0
1
2
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
2
0
1
2
2
0
2
4
0
0
0
0
2
0
3
0
2
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
1
1
1
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
1
2
2
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
2
0
0
2
0
2
1
1
0
0
2
0
0
0
0
0
0
0
3
0
6
1
1
2
0
2
0
0
0
0
2
1
2
0
3
0
2
1
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
1
0
3
0
1
0
0
0
0
0
1
2
2
0
0
0
0
1
2
0
0
0
2
0
0
1
0
2
0
0
1
2
0
0
0
1
2
1
0
1
0
0
0
2
2
0
0
2
1
0
0
2
0
0
0
1
0
2
0
0
0
0
2
1
1
0
2
2
0
1
2
0
1
0
0
0
1
1
1
1
2
0
1
0
0
0
0
1
0
0
0
1
1
1
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
2
3
0
1
0
0
1
1
0
0
2
2
0
0
0
1
0
0
1
0
2
0
0
0
2
0
1
2
0
1
1
0
2
2
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
2
2
0
1
0
0
0
2
0
0
0
1
1
0
0
1
0
0
0
1
0
1
0
1
0
0
2
0
0
0
2
0
0
1
1
0
1
0
2
0
0
2
0
0
0
2
2
1
0
0
0
0
0
0
0
1
0
0
2
2
0
2
2
0
0
0
1
0
0
0
0
0
1
0
0
0
2
2
0
2
2
1
0
0
0
0
2
2
0
0
0
0
1
1
0
0
0
2
0
0
2
0
0
5
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
2
2
0
0
1
0
2
2
0
0
0
1
0
0
0
1
0
0
0
3
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
1
0
0
2
0
0
0
1
2
0
1
1
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
3
0
0
0
2
1
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
1
2
0
1
0
0
0
2
0
0
0
2
2
0
1
2
0
0
0
0
0
0
2
0
0
0
2
0
2
0
2
0
0
0
0
0
0
2
0
0
2
2
1
2
0
0
0
2
3
2
0
0
0
4
0
2
0
2
1
1
0
1
1
0
0
1
0
1
0
1
0
0
3
3
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
2
0
0
2
2
0
0
0
0
1
0
1
0
0
2
0
1
1
1
2
0
0
0
0
0
2
0
0
2
0
2
1
1
2
0
1
0
0
0
2
2
0
1
0
0
2
0
2
0
0
0
0
0
0
4
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
1
1
1
0
0
1
1
0
0
0
0
0
0
0
0
2
1
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
3
2
2
0
0
2
0
0
1
3
0
1
2
0
0
0
4
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
1
1
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
1
1
0
5
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
2
2
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
4
0
0
0
1
0
1
0
0
0
2
1
2
0
0
1
0
0
0
2
0
0
0
0
2
1
1
0
0
0
0
0
0
1
1
1
2
0
0
0
0
1
3
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
1
0
2
1
0
2
1
2
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
2
0
2
2
0
0
2
1
1
0
0
2
2
0
0
3
1
0
0
0
0
0
1
1
0
2
0
0
0
0
1
2
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
1
0
1
1
2
2
1
0
1
0
1
0
5
2
0
1
0
0
0
2
0
2
0
0
2
2
1
9
0
0
0
1
0
0
0
1
5
0
2
0
0
0
0
0
2
0
0
0
0
0
0
3
0
3
0
4
2
1
0
0
1
0
1
2
0
0
1
0
1
0
1
0
0
2
0
0
1
0
0
3
0
2
0
0
0
0
2
1
0
1
2
0
0
0
0
0
0
1
0
2
0
2
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
2
2
1
0
0
1
0
0
1
0
2
0
2
0
1
3
0
1
0
0
0
0
0
0
0
0
0
2
1
1
1
0
0
1
0
0
0
0
0
0
0
0
2
0
5
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
2
1
0
0
0
2
1
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
2
2
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
1
1
0
0
3
0
1
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
1
0
0
1
0
1
2
0
1
0
0
4
1
2
1
0
1
2
2
0
1
0
0
0
0
0
0
0
0
0
3
2
2
0
0
1
0
1
0
0
2
1
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
1
1
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
3
0
2
0
2
0
0
2
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
2
2
1
0
0
0
0
2
1
1
2
2
4
0
0
1
0
1
0
1
0
2
2
0
0
0
2
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
1
0
0
1
0
1
0
1
1
0
0
2
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
1
0
0
2
0
1
2
0
1
0
0
0
0
0
2
2
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
4
0
2
0
0
1
1
0
0
0
0
1
1
0
1
1
0
0
5
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
1
0
1
1
0
0
0
1
2
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
5
0
0
0
2
0
0
0
0
1
6
2
0
0
0
0
0
0
0
1
0
2
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
2
2
0
0
0
0
0
3
0
1
0
2
9
0
0
1
1
0
2
1
1
2
0
2
0
1
2
0
0
2
0
0
0
0
0
1
2
0
0
0
1
0
1
0
0
2
1
2
2
2
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
1
1
0
0
5
0
1
1
1
2
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
2
0
1
2
1
0
2
2
0
3
2
0
4
0
0
0
0
0
0
0
0
3
0
2
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
2
0
1
1
1
0
0
0
4
0
0
0
0
0
0
3
0
0
0
0
2
0
0
1
0
0
2
0
0
2
2
2
0
2
0
0
0
2
3
1
0
0
0
0
0
0
1
2
1
0
0
0
0
2
0
0
0
0
0
1
0
0
4
1
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
2
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
2
2
0
1
0
0
2
2
0
0
1
0
2
2
0
1
0
2
0
1
0
2
0
1
0
0
0
2
2
0
1
0
2
1
1
2
1
0
2
0
2
2
0
0
0
0
0
0
2
0
1
2
0
2
2
3
0
2
1
1
0
0
1
2
0
0
2
0
2
0
0
0
2
0
2
0
0
2
0
0
0
1
0
0
0
1
0
0
0
1
0
0
6
0
0
0
0
0
0
0
0
2
3
0
1
4
0
2
0
2
1
0
0
0
0
1
0
2
2
1
0
0
0
0
5
2
0
1
1
0
2
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
2
1
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
2
1
0
0
1
2
0
0
2
0
0
0
0
1
0
0
0
1
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
3
0
0
1
0
1
0
0
1
1
2
2
0
2
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
2
2
2
0
0
1
0
3
2
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
2
2
0
0
0
2
0
0
0
0
2
0
3
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
1
0
1
0
0
1
0
1
0
0
1
0
2
0
1
0
0
0
3
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
1
2
1
1
0
0
0
0
0
0
0
1
0
2
2
2
1
1
0
0
0
1
1
0
2
0
0
0
0
0
0
0
1
1
3
0
0
1
0
2
0
0
0
0
0
0
2
0
1
8
3
2
2
0
0
0
2
0
0
2
2
0
2
2
0
0
1
0
1
0
0
2
0
0
2
0
0
0
1
1
1
0
0
0
2
0
2
0
0
0
2
0
1
1
1
0
0
1
0
3
0
0
2
0
0
0
1
0
1
0
1
0
1
0
0
1
2
2
1
1
1
0
1
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
1
0
1
2
0
0
0
1
3
1
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
2
1
0
4
2
1
0
0
0
1
0
2
1
0
2
1
0
0
1
0
1
0
1
2
0
0
0
3
0
1
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
3
2
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
2
0
0
0
0
2
2
0
0
0
0
0
0
2
0
1
0
1
1
0
0
1
1
0
2
0
1
1
0
0
0
1
0
0
1
0
2
0
0
1
0
0
0
3
0
0
0
0
0
0
2
0
1
0
0
1
2
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
1
1
0
3
3
1
0
2
2
2
2
0
0
0
0
0
0
3
0
2
2
0
1
1
2
0
0
0
1
0
1
0
0
2
2
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
1
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
1
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
1
1
1
0
2
1
1
0
0
1
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
3
0
0
0
1
2
0
0
1
0
0
0
2
0
4
2
0
2
2
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
1
2
0
0
2
0
0
5
0
0
0
2
1
0
2
0
0
0
1
2
2
0
0
1
0
0
2
0
1
0
2
0
0
2
0
0
0
2
1
0
0
1
0
1
0
0
0
0
0
1
0
1
1
0
1
2
0
0
0
2
0
0
1
0
0
0
2
2
0
6
2
0
1
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
2
2
3
1
2
0
2
0
0
0
1
0
2
0
0
1
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
1
0
1
1
1
0
1
0
2
0
0
2
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
1
0
2
0
0
2
1
0
0
0
0
0
0
0
0
2
0
1
0
1
1
0
0
0
0
0
3
1
2
0
0
3
0
2
0
2
2
0
2
0
0
0
2
2
0
0
2
1
0
0
0
2
2
0
2
0
0
0
0
2
0
0
4
2
2
0
0
0
1
0
0
0
2
0
1
0
0
0
2
0
0
1
2
0
0
5
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
1
1
0
0
0
2
0
1
2
1
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
2
1
2
0
0
2
2
2
0
0
0
1
2
0
0
0
1
0
0
1
0
1
0
0
1
0
0
2
1
0
0
1
0
0
1
2
2
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
4
1
0
2
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
2
2
1
1
1
1
0
0
2
0
0
2
0
0
2
0
0
0
0
2
0
1
0
2
0
1
2
0
2
1
2
2
0
0
0
0
1
0
0
2
0
0
1
0
0
1
0
1
1
1
0
2
1
0
0
0
2
0
0
0
1
0
0
0
0
0
1
1
0
2
0
1
0
1
0
3
1
2
0
0
1
0
2
2
0
0
0
0
1
1
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
2
0
0
0
0
0
3
2
2
2
0
0
0
1
0
0
1
0
3
1
2
1
1
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
3
1
2
0
0
2
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
3
0
0
0
2
0
0
0
1
2
0
1
0
0
0
2
1
1
0
1
0
0
0
0
1
0
2
1
1
0
2
0
2
2
0
0
1
0
0
0
1
0
1
0
1
1
2
2
2
2
2
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
2
1
0
1
0
0
2
5
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
3
0
0
2
0
0
3
0
4
1
0
3
0
0
0
1
0
0
0
0
3
0
0
1
0
0
2
1
0
0
0
0
0
1
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
2
0
2
0
2
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
3
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
1
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
2
0
2
0
0
1
0
0
0
1
1
2
0
1
0
1
0
2
0
1
2
0
1
1
2
2
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
1
1
0
0
4
0
2
0
1
0
1
3
0
1
0
0
0
2
0
2
0
0
1
1
2
5
0
0
2
0
1
1
0
0
2
1
0
0
0
0
0
1
0
3
0
1
2
1
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
2
0
0
1
0
0
0
1
1
0
0
1
3
0
1
0
0
0
2
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
1
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
2
0
1
0
0
1
0
2
1
0
0
0
2
0
1
0
1
2
0
2
0
0
2
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
2
0
0
0
2
0
1
1
1
2
2
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
1
1
0
0
0
0
2
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
3
1
0
0
0
0
0
3
2
0
0
2
0
2
0
2
0
4
0
1
1
2
0
0
2
0
3
2
1
0
0
0
0
0
0
0
2
0
0
0
1
1
2
1
2
2
2
0
0
0
0
2
0
2
0
4
1
2
2
1
0
0
0
2
1
2
0
0
1
0
0
0
1
1
0
1
0
0
0
1
0
3
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
2
0
0
0
0
0
2
0
0
0
1
1
0
0
0
1
0
1
0
0
0
2
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
1
2
2
0
0
3
0
1
0
0
1
0
1
0
1
0
1
0
0
0
1
0
2
2
0
2
0
0
1
0
1
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
1
0
1
0
1
1
0
0
1
0
1
1
0
0
0
0
2
0
2
0
1
1
0
1
1
1
1
3
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
2
0
2
2
0
0
0
0
3
0
0
1
0
0
2
0
1
0
1
1
2
0
0
1
0
0
0
0
0
0
2
2
0
0
2
0
1
0
2
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
1
1
0
3
0
2
0
0
0
0
2
1
0
2
2
1
0
0
1
2
0
2
0
0
0
0
0
1
0
3
0
1
0
0
2
2
0
0
0
0
0
2
2
2
0
0
0
0
1
2
1
0
0
0
0
1
3
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
3
0
0
0
0
1
1
2
0
2
0
0
0
2
0
0
0
1
0
0
2
0
0
0
1
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
1
0
1
0
5
0
1
2
2
1
1
0
0
0
0
1
0
1
0
0
0
2
0
0
0
2
0
1
0
0
2
0
2
2
0
0
0
1
0
2
1
2
0
1
1
2
0
2
1
0
0
0
1
1
0
0
0
0
2
0
0
1
1
0
2
0
2
0
1
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
2
2
0
2
0
0
1
2
0
0
2
1
0
0
0
1
0
0
2
0
1
1
0
2
2
1
1
1
1
2
2
0
0
0
1
0
0
0
0
0
0
2
0
0
1
1
1
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
1
2
2
0
2
8
1
1
0
0
0
0
1
0
1
2
2
1
0
0
2
0
1
0
0
2
0
1
1
0
2
0
3
0
0
0
0
1
1
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
2
0
0
0
0
1
1
0
0
2
3
0
0
1
0
2
0
1
1
0
0
0
1
0
2
0
2
2
2
1
2
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
2
1
0
1
0
2
0
2
1
0
2
4
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
3
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
2
3
0
1
1
0
0
1
0
2
0
0
1
1
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
2
1
1
0
0
3
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
1
3
2
0
2
0
1
3
2
1
0
0
0
0
0
0
1
2
1
0
0
0
3
0
0
2
0
2
0
1
0
0
0
0
2
1
0
2
2
0
2
0
5
0
1
0
0
0
0
1
0
1
1
0
0
0
2
0
1
2
2
2
0
2
1
0
0
0
0
4
0
0
2
1
0
2
0
1
0
0
0
1
0
0
2
0
1
0
4
2
2
0
0
0
2
1
0
5
0
2
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
1
0
2
0
1
0
0
1
1
2
0
2
2
0
1
0
0
0
0
0
0
0
0
0
5
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
2
2
1
2
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
4
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
1
1
0
0
0
4
2
0
2
0
1
1
1
0
1
1
0
0
1
0
0
1
0
3
0
0
2
1
1
0
0
0
2
0
2
1
0
0
2
0
0
2
0
2
0
0
0
0
0
0
1
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
1
0
1
0
2
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
1
2
0
0
2
0
0
0
2
0
0
2
1
0
0
0
0
1
1
0
0
1
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
1
0
3
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
1
0
3
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
7
1
0
0
0
0
0
0
1
1
1
0
3
3
2
2
2
0
0
1
1
2
0
0
1
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
1
0
2
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
2
3
0
1
0
0
2
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
1
2
1
1
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
2
0
2
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
2
0
2
0
0
0
0
2
0
0
0
4
2
0
2
2
0
0
2
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
1
0
1
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
1
0
1
1
0
4
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
1
0
0
2
2
1
0
0
0
1
0
0
2
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
2
1
1
2
2
0
0
0
0
1
1
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
2
0
2
1
0
0
1
0
0
0
0
0
1
1
1
1
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
3
1
1
0
1
1
0
1
0
1
1
0
0
0
2
1
2
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
3
0
0
3
0
2
0
0
0
2
0
0
0
7
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
3
1
0
2
0
2
0
0
0
0
1
1
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
1
0
0
0
0
1
1
0
1
0
4
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
1
0
0
2
0
0
0
1
0
0
0
1
2
1
0
0
1
0
0
2
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
1
0
0
0
3
0
1
0
0
0
2
0
1
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
1
0
2
0
0
0
2
1
0
4
0
1
0
1
1
2
2
2
0
2
0
0
1
0
0
2
0
2
0
0
1
0
0
0
0
0
1
1
0
0
0
1
2
2
0
3
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
1
1
0
0
0
0
2
0
1
0
1
0
1
0
1
0
1
0
0
1
0
0
1
0
4
1
1
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
2
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
1
0
2
0
0
1
0
0
1
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
1
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
2
1
0
2
0
0
0
3
0
0
0
2
0
0
0
0
0
1
0
1
1
1
1
0
1
0
1
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
1
2
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
1
0
1
2
0
1
0
0
2
2
2
2
0
0
1
2
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
1
0
1
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
1
0
0
0
0
1
0
0
0
1
2
0
0
0
2
0
2
0
1
0
0
0
0
0
1
0
0
2
1
1
2
2
2
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
2
0
2
0
0
1
2
0
0
0
0
0
0
2
0
1
0
0
0
2
2
0
1
0
0
0
2
0
0
0
1
1
0
0
0
1
2
0
0
0
0
2
2
1
0
2
0
2
2
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
1
2
1
1
1
2
0
0
3
1
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
2
1
1
1
0
0
1
2
0
0
0
0
0
0
0
1
0
0
2
0
2
0
1
0
0
0
0
2
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
1
2
0
1
0
1
0
0
1
0
0
0
0
0
0
2
1
0
2
0
0
0
1
0
0
0
3
0
0
2
0
0
1
0
0
0
2
0
1
1
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
4
1
0
1
2
0
1
0
1
1
0
0
2
2
0
1
1
0
1
0
1
2
0
1
0
2
0
0
0
0
0
0
0
0
0
2
2
2
2
0
1
0
3
0
0
0
0
0
1
2
1
2
1
0
0
0
0
0
3
0
1
1
0
0
0
2
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
8
0
2
2
1
1
2
0
0
0
0
0
2
1
0
2
0
0
0
0
1
0
0
2
0
0
2
1
0
1
0
0
0
0
4
0
1
3
0
0
2
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
5
0
0
1
2
0
0
0
0
0
0
1
1
0
0
0
1
0
2
1
1
1
0
2
1
0
0
3
0
0
0
2
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
2
0
0
1
0
2
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
2
0
0
0
3
1
0
2
0
0
0
2
0
0
1
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
2
2
0
2
0
0
0
0
2
2
2
0
2
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
1
1
0
0
0
0
1
1
0
1
0
0
0
0
0
2
0
0
0
0
0
4
0
0
2
2
0
0
0
1
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
1
0
0
2
1
2
1
1
0
0
0
0
1
0
2
1
0
0
0
2
0
0
0
1
2
0
0
2
0
2
0
4
1
0
1
0
0
0
1
0
1
0
0
1
1
0
0
0
0
1
2
5
0
0
0
0
2
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
2
0
0
2
0
0
1
0
0
0
0
2
2
0
0
2
0
0
0
2
0
0
1
1
2
0
1
2
0
0
0
1
0
0
0
2
0
2
1
1
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
2
0
2
0
0
2
1
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
2
2
0
0
0
2
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
2
1
0
2
2
4
0
0
1
0
1
0
0
2
2
2
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
2
2
0
0
2
1
0
2
0
0
0
0
0
0
2
1
4
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
2
1
0
1
4
1
2
1
2
2
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
1
2
1
0
0
0
2
0
0
1
0
0
0
0
1
2
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
2
0
7
0
1
1
1
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
1
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
1
0
1
2
0
1
0
2
2
1
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
1
2
0
2
0
0
4
0
0
0
0
0
1
0
0
0
0
2
1
2
0
1
0
0
0
0
1
0
2
0
0
0
0
1
0
0
1
2
0
0
1
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
2
2
0
2
2
0
2
0
1
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
2
1
0
0
0
0
0
2
0
0
1
2
0
1
0
0
0
1
0
0
2
0
1
1
0
2
0
0
0
1
0
1
0
2
2
0
0
1
0
2
0
0
0
1
0
1
0
0
1
6
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
2
2
0
0
0
0
2
0
1
2
2
1
0
0
0
1
2
0
0
0
1
2
0
0
1
0
1
0
0
0
3
0
0
0
1
1
2
2
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
2
2
1
0
1
0
0
1
4
1
2
0
0
2
0
1
0
0
0
2
2
0
1
0
1
1
0
0
2
3
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
1
0
2
0
2
0
3
1
2
1
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
1
0
0
2
0
5
2
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
2
2
0
0
0
0
0
2
0
3
2
0
1
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
6
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
1
0
0
0
1
0
3
1
0
0
0
2
0
1
0
0
0
0
1
0
0
1
0
0
0
2
2
0
0
0
2
0
0
2
0
0
2
0
0
1
0
0
0
1
2
0
1
0
1
0
0
1
1
0
2
0
0
0
0
2
1
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
2
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
2
0
0
1
0
0
0
1
0
1
1
0
0
0
2
0
0
1
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
3
2
1
2
0
0
0
2
2
1
0
1
2
0
1
2
0
0
2
1
0
2
0
0
0
1
1
0
3
0
0
0
0
0
2
2
0
0
0
2
0
2
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
5
1
0
0
0
0
2
1
0
0
2
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
4
1
2
0
1
0
1
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
4
1
0
0
0
2
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
2
2
0
5
0
0
1
1
0
2
0
0
2
0
0
0
0
0
0
2
0
0
1
2
1
2
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
2
0
2
0
2
0
0
0
0
2
0
2
0
0
0
0
1
2
2
3
0
0
2
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
1
0
1
1
0
1
1
0
0
0
0
0
2
2
2
2
2
0
0
0
0
0
0
0
0
0
1
3
0
0
1
0
2
0
0
1
0
0
0
0
0
0
2
2
0
3
1
0
1
0
0
2
0
0
2
1
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
1
1
0
2
0
1
0
1
0
2
0
0
1
1
0
0
1
0
1
0
0
0
1
0
2
2
0
2
0
0
0
1
2
1
0
0
0
0
2
0
0
0
3
0
0
0
0
0
2
1
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
2
1
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
2
2
0
1
1
1
2
0
0
0
1
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
1
0
0
0
2
2
2
0
0
1
0
0
0
0
0
0
0
0
1
2
2
0
2
0
0
1
3
2
0
0
1
2
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
3
0
0
0
0
0
0
1
0
0
2
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
1
0
0
1
0
0
0
1
0
2
1
0
2
0
0
0
1
0
2
0
0
2
0
0
0
0
0
1
0
0
0
1
2
0
2
0
0
0
1
0
0
0
0
1
0
2
0
2
0
0
1
1
0
2
0
1
0
0
0
1
2
0
9
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
2
0
1
0
0
0
0
2
0
1
0
3
0
0
2
1
2
0
0
0
0
0
0
0
1
1
1
0
0
3
0
0
2
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
1
0
2
2
0
2
0
0
0
0
0
2
0
1
0
0
0
0
2
1
0
0
0
0
1
1
0
0
0
0
2
1
0
1
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
2
0
1
2
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
1
2
2
0
1
2
2
0
0
1
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
1
0
0
1
1
2
2
2
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
2
1
0
0
0
2
0
0
0
2
1
2
0
2
1
0
0
0
2
2
0
2
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
2
0
0
2
1
1
1
0
1
0
1
0
0
2
0
2
1
0
0
1
2
0
0
0
0
0
3
1
0
0
0
2
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
2
0
0
0
4
0
1
2
0
0
2
0
0
0
0
0
0
2
0
0
2
1
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
1
1
0
2
0
0
0
0
1
0
0
0
2
0
0
2
0
2
0
4
0
0
1
0
2
0
2
0
0
2
1
1
0
0
1
2
1
2
0
0
1
0
0
2
0
0
0
1
1
0
0
0
1
0
0
0
2
1
0
0
0
0
1
1
0
0
0
0
0
2
0
1
3
0
0
0
2
0
0
4
1
0
2
1
0
0
0
0
0
1
0
0
0
1
1
0
2
2
0
0
0
1
1
0
2
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
1
0
0
0
0
0
2
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
2
1
2
0
3
0
0
0
3
0
0
1
2
0
0
0
0
0
2
0
0
2
0
1
2
0
1
2
1
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
2
0
0
1
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
6
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
2
0
2
0
0
0
0
2
0
1
0
0
0
2
1
0
2
2
0
0
0
0
1
3
0
2
1
0
0
0
0
2
0
1
2
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
2
1
0
0
1
1
1
0
2
1
2
0
1
0
1
0
1
1
0
2
0
1
0
2
0
0
0
0
0
0
2
1
1
1
1
0
0
1
0
1
2
0
0
0
2
0
0
1
0
0
2
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
7
0
0
0
0
0
0
0
1
0
0
1
2
0
1
0
2
1
0
0
0
2
1
2
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
1
0
0
0
1
1
0
2
1
0
2
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
3
2
0
1
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
2
2
0
0
0
2
0
2
2
2
0
0
1
1
0
2
2
1
0
0
0
2
0
0
2
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
2
0
0
1
2
0
0
0
3
0
0
3
0
0
0
0
1
0
0
0
2
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
1
0
0
0
0
0
1
1
1
2
0
0
0
1
0
0
0
0
3
0
1
0
1
1
0
0
0
0
2
0
0
0
0
2
0
2
1
0
0
1
0
0
0
0
3
0
0
1
0
0
0
0
2
2
1
1
1
2
0
0
2
0
0
2
0
0
2
0
0
2
0
2
0
0
1
0
0
0
2
2
1
0
0
0
1
0
0
1
0
0
2
1
0
2
0
0
2
0
2
2
2
1
2
3
1
0
1
0
0
1
0
0
0
0
0
2
2
1
2
2
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
3
2
1
0
0
0
0
1
1
0
0
1
0
1
1
0
1
2
0
0
0
0
1
0
0
2
0
2
1
1
2
2
0
1
2
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
1
2
0
1
2
0
0
1
0
2
0
0
2
0
0
0
0
1
5
6
0
2
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
2
0
0
2
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
2
1
0
0
0
0
0
0
1
0
2
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
2
1
0
0
0
0
0
4
2
0
0
0
0
1
0
0
2
0
1
0
1
2
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
1
0
2
0
1
2
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
2
1
1
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
1
0
2
0
1
0
1
0
0
0
0
0
1
0
0
2
0
0
0
2
0
2
0
0
0
1
1
2
0
1
1
0
2
2
0
2
1
0
0
2
0
0
2
0
1
1
2
0
1
0
1
2
2
0
2
0
0
0
4
1
0
2
0
0
0
1
0
0
2
2
0
2
5
1
0
1
1
0
1
0
16
0
0
0
0
0
2
3
2
0
2
0
0
0
2
0
0
2
2
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
1
0
1
0
1
2
1
2
1
1
0
1
0
0
0
1
0
2
0
1
0
0
1
1
0
0
0
2
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
1
0
1
0
5
2
0
0
2
0
1
1
0
0
0
2
0
0
1
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
3
0
1
0
0
2
0
0
1
1
0
0
2
1
0
1
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
1
2
4
0
0
1
0
0
0
0
0
0
2
3
0
0
1
0
1
2
0
0
1
1
0
0
0
1
0
1
0
2
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
3
0
0
0
0
0
1
0
0
1
2
0
0
0
0
2
2
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
2
2
0
0
2
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
2
0
1
0
1
3
0
1
0
0
0
2
0
1
2
0
0
0
1
0
0
0
0
0
2
0
1
0
0
1
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
2
1
1
1
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
1
0
2
0
0
1
0
1
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
1
2
0
0
0
2
3
0
1
0
2
0
0
0
0
0
1
3
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
1
1
4
0
0
0
0
2
1
0
0
0
0
2
1
0
0
0
1
0
4
1
2
2
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
2
0
2
1
0
2
2
0
0
1
0
2
4
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
1
0
1
1
0
2
0
1
0
0
1
0
1
0
0
0
0
0
0
2
0
0
1
1
1
0
0
0
2
0
0
0
1
0
2
2
0
0
0
1
2
2
0
4
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
1
0
2
2
0
2
1
1
1
0
0
0
1
0
0
0
0
2
0
1
2
0
0
2
0
1
0
0
2
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
1
1
1
0
0
0
1
0
2
0
0
0
2
0
1
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
2
0
2
0
3
0
1
0
1
0
0
1
3
2
0
0
0
0
0
0
1
1
2
0
0
0
0
2
1
0
0
0
0
2
0
0
0
1
1
0
1
0
0
0
1
0
0
1
0
2
0
2
0
0
0
0
1
0
0
0
2
0
0
0
1
2
1
0
2
3
1
0
0
0
0
0
4
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
1
2
0
0
0
1
0
0
0
0
1
0
0
0
2
0
1
2
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
3
1
0
0
2
2
2
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
5
0
0
0
0
2
0
0
0
2
0
4
0
2
0
0
2
0
2
1
0
0
2
2
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
4
1
0
1
0
0
2
1
0
1
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
1
0
1
0
0
1
1
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
3
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
3
0
0
1
2
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
1
2
2
0
1
2
0
1
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
1
2
0
2
5
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
1
0
0
0
4
2
0
1
0
0
1
0
0
2
2
0
1
0
1
0
0
1
0
1
2
1
0
2
0
1
2
0
2
2
0
1
0
0
1
0
1
0
0
1
1
0
0
1
2
0
0
0
0
0
0
2
2
0
0
0
0
1
0
2
0
1
1
1
0
0
0
0
2
2
0
0
0
0
2
0
2
0
0
0
0
0
1
1
2
2
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
3
0
1
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
1
2
0
1
0
0
0
0
2
0
1
0
0
0
0
1
0
1
0
1
0
2
1
1
0
0
0
0
0
1
0
0
2
0
0
0
0
1
1
2
0
0
0
3
1
0
1
0
0
0
0
0
2
0
0
0
0
2
4
0
0
0
0
0
0
1
0
1
0
2
0
1
0
0
0
0
0
0
1
0
1
0
1
2
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
2
2
0
0
1
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
1
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
1
0
1
0
2
1
0
1
0
0
2
0
0
0
0
2
0
0
0
2
0
2
0
0
0
1
0
1
0
2
2
0
0
1
1
1
0
0
0
2
1
1
0
0
0
1
0
1
0
2
0
0
1
0
0
0
0
1
0
0
0
0
1
0
4
0
0
0
1
0
0
0
2
0
2
1
0
0
0
0
0
1
0
2
0
0
5
0
1
2
0
0
2
0
0
0
0
0
0
1
3
0
1
0
0
1
1
0
0
0
1
2
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
2
0
1
0
0
0
0
0
1
1
1
1
0
0
1
0
0
3
0
0
2
0
1
4
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
2
0
1
0
4
0
0
0
1
0
2
1
0
1
0
0
0
1
2
1
0
0
0
0
0
2
0
0
1
0
0
0
0
1
1
1
0
0
1
0
0
0
0
1
0
1
0
0
2
2
0
0
2
1
1
0
1
0
2
0
2
0
0
0
0
0
2
2
1
0
1
0
0
1
1
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
3
2
0
1
0
2
0
0
0
2
1
0
0
2
0
0
2
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
2
4
3
1
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
2
1
0
0
0
1
0
0
1
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
1
0
0
0
0
2
1
0
0
0
0
1
0
0
1
2
4
0
1
0
2
1
0
0
0
0
0
0
1
1
2
1
0
2
0
1
0
0
0
2
2
0
1
0
2
3
1
0
0
0
1
0
0
1
2
0
1
0
1
1
1
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
3
0
1
0
0
0
0
0
1
2
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
1
2
0
0
0
1
1
0
0
3
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
3
0
1
0
0
2
2
1
2
0
2
1
0
4
1
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
2
0
3
0
0
1
0
0
2
0
0
0
2
0
2
0
1
0
2
1
1
0
2
2
0
1
1
0
0
0
0
0
1
1
0
0
3
0
0
5
0
2
0
2
2
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
2
0
0
2
2
0
0
0
2
1
0
1
1
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
2
1
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
2
2
2
0
2
0
2
0
0
1
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
1
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
2
0
1
0
2
0
0
0
2
2
0
1
1
0
0
1
0
1
2
1
1
2
0
0
0
1
2
0
0
5
0
1
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
1
0
0
0
2
0
0
1
0
0
0
4
0
0
0
0
2
2
2
0
2
2
0
0
0
2
0
1
2
1
0
2
2
1
2
0
0
0
0
1
2
2
0
0
0
2
0
0
0
1
6
0
0
0
1
2
0
1
0
0
0
2
0
2
0
0
0
1
0
0
0
0
1
0
0
1
0
2
0
0
1
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
2
1
0
1
1
2
0
1
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
2
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
3
0
4
0
0
0
0
2
2
0
0
0
0
1
0
2
1
0
0
0
0
2
2
0
2
0
0
0
2
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
3
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
3
0
0
0
0
0
1
3
0
0
1
0
1
0
0
0
0
1
2
0
0
1
2
1
0
1
0
0
0
0
0
2
0
1
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
2
0
2
1
2
0
0
0
0
1
0
3
0
2
0
1
2
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
1
0
0
0
0
1
0
2
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
2
0
0
2
0
2
0
2
0
2
0
2
1
1
0
0
0
1
0
4
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
2
2
1
1
0
0
2
2
0
0
0
0
0
3
0
0
0
2
0
0
0
0
2
0
2
0
0
1
0
0
2
0
0
0
0
1
2
2
0
0
2
0
1
2
0
0
1
0
0
2
0
1
0
0
0
2
2
1
0
2
0
0
0
2
0
2
0
0
0
2
1
0
0
0
1
0
2
0
2
0
1
0
0
0
1
0
0
1
0
2
0
0
1
1
2
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
1
0
0
2
1
0
2
0
0
0
0
0
0
0
0
1
1
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
1
1
0
2
0
2
0
0
0
2
0
0
1
0
0
0
2
2
2
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
1
3
0
1
2
0
2
0
1
2
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
2
2
0
2
0
1
3
1
0
1
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
1
0
0
3
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
1
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
2
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
1
1
0
0
0
1
1
0
2
0
1
2
0
1
2
0
1
1
0
0
0
2
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
2
2
0
0
0
0
1
0
2
0
0
8
2
0
1
0
2
0
0
2
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
2
1
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
2
0
1
2
2
0
2
0
0
2
0
2
1
1
0
1
2
0
1
1
2
1
0
1
0
0
0
0
0
0
0
2
2
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
1
0
0
0
2
0
1
0
0
0
1
0
1
1
0
0
0
0
0
1
1
0
0
1
1
0
2
0
0
0
2
0
0
2
0
0
2
0
2
2
0
0
0
1
0
0
2
0
2
2
1
1
0
0
1
0
2
0
1
1
0
0
0
2
0
2
0
0
2
1
1
1
2
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
1
0
0
2
1
1
1
2
1
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
1
4
0
1
0
0
2
0
1
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
1
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
2
5
0
0
2
0
0
2
1
0
0
0
1
2
3
0
0
0
0
3
0
0
2
0
0
0
0
0
3
1
1
1
0
2
0
0
0
0
2
2
3
0
0
0
0
3
0
0
1
1
0
0
1
1
0
0
2
0
0
0
0
2
0
1
1
0
0
1
0
1
0
2
2
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
2
0
1
0
0
1
0
1
2
0
0
0
0
2
2
1
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
2
1
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
2
0
1
1
1
1
1
1
0
0
1
0
2
0
0
0
0
3
0
2
2
0
2
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
2
2
0
0
0
6
2
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
1
1
1
1
2
0
0
1
0
0
1
0
0
0
0
2
1
2
1
0
1
0
2
0
1
0
0
1
1
0
0
0
0
2
0
0
0
2
1
0
1
0
0
1
0
0
2
0
0
0
2
1
1
0
0
0
2
2
0
1
0
1
3
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
2
2
0
3
0
0
0
4
0
0
0
2
2
0
0
0
0
0
0
0
0
1
1
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
2
0
1
0
2
0
0
0
0
3
0
0
0
1
2
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
1
1
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
3
0
1
1
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
2
2
0
0
0
0
1
2
1
0
0
0
2
0
2
0
1
2
0
0
0
1
2
0
1
2
2
0
0
0
0
0
0
0
0
2
0
2
13
0
0
0
0
0
0
2
1
0
2
0
1
0
2
0
2
1
2
2
2
2
1
0
0
0
1
1
0
0
0
0
0
2
0
1
0
1
0
2
0
0
0
0
0
0
0
2
1
0
0
2
0
0
2
0
0
2
0
0
0
0
1
0
1
0
2
0
0
0
3
4
0
0
0
1
4
4
0
1
0
0
1
2
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
1
1
0
0
0
1
2
0
1
0
1
0
2
0
1
2
1
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
3
0
0
0
0
0
1
0
2
0
1
0
0
0
0
2
0
0
0
1
2
0
2
0
0
2
0
2
0
0
0
0
0
0
1
0
2
1
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
1
2
0
0
0
0
0
1
0
0
2
0
0
0
1
0
2
2
2
1
1
2
2
0
1
0
2
3
1
0
0
0
0
1
0
0
2
0
0
1
0
0
1
0
0
2
0
0
0
0
1
0
0
0
2
0
2
0
0
1
0
0
2
1
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
2
1
1
0
2
0
0
0
0
1
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
1
1
0
2
2
0
3
0
3
0
1
0
2
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
1
2
0
0
0
2
0
0
0
1
0
1
1
3
1
5
0
3
0
0
0
0
0
2
1
0
0
1
0
1
2
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
2
0
1
0
0
1
3
0
0
0
0
0
1
3
1
0
0
0
0
2
2
1
0
0
0
2
1
0
0
2
0
0
1
0
0
0
2
2
0
1
0
0
0
0
1
4
0
0
0
1
1
0
0
0
0
0
0
1
2
0
2
0
2
2
0
0
0
2
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
3
1
1
3
0
1
0
0
0
0
0
1
3
0
2
1
2
2
0
0
0
0
0
1
0
0
1
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
1
0
2
2
0
0
0
1
2
2
0
0
1
1
2
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
1
1
0
0
0
0
1
2
1
0
0
1
0
0
0
0
1
0
1
2
0
0
1
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
2
0
0
2
2
1
0
0
1
0
0
2
1
1
2
0
0
0
0
1
4
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
2
0
2
0
0
0
0
1
0
0
0
0
2
0
1
0
0
1
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
2
0
1
1
1
0
0
0
0
0
0
2
0
2
0
2
0
2
0
2
0
1
0
0
2
0
0
0
0
0
2
2
0
1
2
0
0
2
2
0
0
0
0
2
2
1
0
0
2
0
0
0
3
0
0
2
0
0
0
0
1
0
0
0
0
1
3
0
1
1
0
0
2
0
1
0
1
1
0
0
0
1
0
1
2
0
0
0
2
2
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
2
0
0
0
1
2
2
2
1
0
2
3
2
1
0
0
1
1
0
0
0
0
0
1
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
1
2
0
0
0
0
2
1
0
0
2
0
0
2
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
1
2
0
1
0
0
2
1
3
0
0
0
0
0
0
1
0
0
0
1
2
2
0
0
2
2
0
0
0
2
0
1
0
0
0
0
0
2
0
3
0
0
0
1
0
0
1
0
0
0
0
2
3
0
1
1
0
1
1
0
0
1
2
0
2
0
0
2
1
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
1
0
0
0
2
1
2
0
1
2
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
15
1
0
0
0
0
1
2
0
2
0
0
1
0
2
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
2
0
0
1
3
1
0
1
1
0
0
2
0
2
0
0
0
2
0
0
0
1
1
0
2
0
2
2
0
1
0
0
0
0
1
0
0
1
0
0
0
0
2
1
0
2
0
0
0
0
0
2
0
1
0
3
2
0
0
0
0
1
0
0
1
0
1
2
0
2
0
0
0
2
2
1
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
2
1
0
0
1
3
0
0
0
0
0
0
0
1
2
0
6
0
0
2
1
0
0
0
0
0
0
2
0
3
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
1
0
2
1
0
1
0
0
0
0
2
0
2
0
0
2
0
0
0
3
0
2
1
0
2
0
0
0
3
1
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
1
0
0
0
0
0
0
0
2
2
0
0
0
2
1
0
1
0
0
0
3
0
0
2
0
0
3
0
0
0
0
2
0
1
1
3
0
1
2
0
0
0
0
0
1
0
1
1
0
0
0
1
2
2
0
0
0
2
0
0
1
0
2
0
0
0
0
1
1
1
0
0
2
1
2
1
1
2
2
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
1
1
0
0
0
1
1
2
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
2
1
0
1
0
2
1
1
0
0
0
2
0
0
1
0
2
0
1
0
0
1
0
0
0
0
1
0
1
0
0
2
0
3
2
0
0
1
0
0
0
0
0
0
0
2
1
0
1
1
0
0
0
0
1
2
0
0
1
0
0
0
0
0
1
2
0
0
0
3
0
0
1
1
0
0
0
0
0
0
0
2
1
0
2
2
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
2
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
1
2
0
0
0
0
1
1
0
0
4
0
0
1
1
2
0
2
0
1
0
1
0
0
0
2
0
1
3
1
2
1
0
0
0
0
0
0
0
5
0
0
0
1
0
1
0
0
0
1
0
1
0
0
2
0
1
0
1
0
0
0
0
2
1
0
1
1
0
1
0
2
0
2
0
1
2
1
0
0
2
2
2
0
0
2
2
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
2
0
0
1
0
0
2
0
6
2
0
0
1
4
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
1
0
0
0
1
0
0
2
2
0
0
1
0
1
0
0
0
2
0
1
2
0
1
0
0
2
0
0
0
1
3
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
3
0
0
0
0
1
0
0
0
0
0
2
1
2
0
0
2
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
1
0
0
4
0
0
0
2
2
2
0
0
1
0
1
1
1
1
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
2
1
0
0
0
2
0
0
2
2
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
1
1
1
0
1
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
2
1
0
0
4
1
2
0
0
0
4
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
2
0
2
2
0
1
0
1
0
2
2
0
0
1
0
0
0
2
4
0
0
1
0
1
1
2
1
0
1
0
1
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
1
1
0
2
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
1
0
0
0
3
0
0
0
0
4
0
2
1
1
1
0
0
3
0
3
2
2
1
0
2
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
3
0
0
0
3
0
1
0
0
0
1
0
0
1
0
2
0
0
0
0
0
1
2
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
2
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
1
0
2
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
2
1
0
1
0
0
0
2
0
0
0
0
1
0
3
2
0
2
0
1
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
1
0
2
0
0
0
2
1
1
2
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
1
0
0
0
0
3
0
1
0
0
0
0
2
0
0
0
0
0
2
2
1
0
0
0
0
2
0
0
1
0
0
1
2
0
0
0
0
1
0
0
2
1
1
2
2
0
1
0
0
0
0
0
2
1
0
0
3
3
0
0
2
0
0
1
0
0
2
1
1
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
2
2
2
0
0
2
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
1
0
1
0
0
0
1
1
2
0
0
0
2
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
1
0
1
1
2
0
0
0
0
1
0
0
0
0
2
1
0
1
0
1
0
0
2
0
0
2
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
7
0
0
1
2
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
3
1
2
0
0
0
0
0
1
2
1
0
0
0
2
0
1
1
2
0
1
0
2
4
0
1
0
2
2
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
2
1
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
1
0
2
0
0
0
2
2
0
0
0
1
0
1
2
1
2
2
0
2
1
3
0
0
0
0
0
0
1
1
0
2
0
2
0
2
1
1
0
2
0
0
0
0
0
0
0
0
0
0
2
1
2
1
2
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
2
2
1
0
0
1
0
0
0
0
2
0
1
1
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
2
0
1
8
0
1
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
1
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
1
2
2
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
3
0
0
1
0
1
0
0
0
2
0
1
0
2
2
2
0
1
0
2
0
3
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
2
0
0
0
2
0
0
1
1
1
2
2
2
2
2
0
0
1
1
0
1
0
0
0
1
1
2
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
1
1
0
4
1
0
0
0
5
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
1
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
2
3
2
0
0
0
0
0
2
0
2
1
0
3
1
2
0
0
1
0
0
2
1
0
0
0
2
0
0
0
1
2
3
2
0
0
0
0
0
2
8
0
0
2
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
1
0
0
0
3
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
2
3
0
1
0
3
0
0
0
0
0
2
0
3
0
0
0
0
1
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
2
0
2
0
0
3
0
2
0
2
1
2
1
0
2
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
8
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
2
1
0
1
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
1
3
0
0
1
0
0
0
0
0
0
0
2
3
2
2
1
1
2
0
2
0
1
0
0
1
0
0
2
0
3
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
1
0
2
3
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
2
2
0
1
2
2
2
0
0
1
0
0
0
0
0
1
1
0
0
1
1
0
0
2
0
2
0
1
0
1
0
0
2
2
2
1
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
4
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
2
0
1
0
0
2
2
0
1
0
0
0
0
0
1
0
0
0
0
1
1
2
0
2
0
2
1
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
1
1
1
1
1
0
1
0
0
0
0
1
0
0
2
0
0
1
0
1
2
0
1
2
0
0
0
1
0
1
2
1
2
0
0
0
2
0
0
2
1
0
1
2
2
0
0
1
0
2
0
2
2
2
0
0
0
1
0
0
0
2
0
2
0
0
1
2
1
0
2
0
0
0
1
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
1
0
0
0
2
0
0
2
2
1
2
0
1
1
0
2
1
0
2
0
0
0
2
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
3
1
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
2
1
2
1
1
0
2
0
1
1
0
0
1
1
0
0
0
0
0
0
1
0
1
2
0
3
0
0
0
2
0
1
0
1
0
2
0
1
1
2
2
2
0
0
7
0
0
0
0
0
1
1
0
2
2
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
2
2
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
1
0
2
3
0
1
2
2
0
0
1
2
1
2
0
0
0
1
0
2
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
1
3
0
2
2
0
1
0
0
1
0
0
2
0
1
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
1
3
3
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
1
0
0
2
0
0
1
0
0
0
1
3
1
2
0
4
1
1
1
0
1
0
0
1
0
1
2
0
0
1
1
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
1
1
1
1
0
1
0
0
0
2
0
0
1
0
0
0
0
2
3
0
3
1
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
2
0
1
0
3
0
2
2
1
2
0
0
0
0
0
2
0
0
3
2
4
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
3
1
0
0
0
0
2
3
0
0
2
0
0
0
0
0
0
0
2
3
0
0
0
0
2
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
2
2
0
2
0
0
0
3
0
0
0
0
0
1
0
0
2
2
0
0
2
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
2
0
0
1
2
0
2
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
2
0
1
0
0
2
0
1
3
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
2
0
0
4
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
6
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
1
0
1
0
0
1
0
0
0
7
0
1
1
2
0
0
0
0
0
1
0
0
1
1
1
0
2
1
0
0
0
0
0
0
0
2
1
1
2
2
0
1
1
1
1
2
0
2
0
0
0
0
0
3
0
0
0
1
0
0
1
1
0
3
1
0
0
1
0
0
1
0
0
0
0
0
0
2
0
1
1
0
0
1
1
0
0
0
2
1
0
0
0
3
2
0
0
0
0
0
1
0
0
0
0
0
0
1
3
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
1
0
1
2
0
0
1
0
2
0
0
0
0
0
1
0
2
0
1
2
1
1
0
2
0
0
1
0
0
0
2
2
0
2
0
0
1
0
0
1
0
2
2
2
0
0
1
0
2
0
1
0
0
2
0
2
1
0
0
0
2
1
0
0
0
0
1
1
2
3
0
0
0
0
3
0
0
0
0
0
0
2
0
0
2
2
4
0
3
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
2
1
1
2
0
0
0
0
0
2
0
0
0
0
2
0
0
3
1
0
1
2
1
0
2
1
2
0
1
2
0
0
0
1
0
0
0
1
0
2
0
2
2
0
0
0
0
1
0
1
0
0
2
1
3
0
0
0
0
0
0
2
0
1
0
0
0
0
2
2
1
0
2
0
0
0
0
0
0
0
1
1
2
0
1
0
1
1
3
0
1
0
1
1
2
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
2
0
1
0
0
2
0
0
0
0
0
2
1
0
0
0
0
1
0
2
2
0
2
0
0
2
2
0
0
0
0
0
0
0
3
0
2
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
2
3
1
0
0
0
0
2
2
3
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
1
0
0
0
0
2
2
3
2
1
0
4
0
0
0
0
2
2
1
1
0
1
0
0
1
0
0
0
0
2
0
2
0
1
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
1
2
0
0
1
1
1
0
2
1
0
0
0
0
0
0
1
1
0
2
0
0
0
1
1
0
0
1
0
1
1
1
0
2
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
1
0
2
0
0
0
1
2
1
0
0
2
2
0
0
0
0
2
0
2
0
0
0
0
0
3
0
0
4
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
1
0
2
0
2
0
1
0
0
0
0
2
2
0
0
0
0
0
0
1
0
2
0
0
1
0
1
1
1
0
0
0
3
2
4
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
1
0
1
2
0
0
0
0
0
0
0
0
1
0
2
2
0
1
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
3
1
2
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
2
0
1
1
1
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
1
3
0
0
2
0
0
1
2
1
0
0
0
0
1
1
0
0
2
0
0
2
0
1
3
0
1
1
2
4
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
2
0
1
2
1
0
0
0
1
0
0
2
0
1
0
0
1
0
2
1
2
0
0
0
1
1
1
1
0
0
1
2
3
0
0
2
0
0
0
0
2
2
3
0
1
0
3
1
2
0
0
0
0
0
0
1
2
0
2
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
2
1
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
3
0
2
0
2
2
2
0
2
0
0
0
0
0
1
0
2
2
2
0
0
2
2
2
1
2
2
0
0
0
1
0
0
0
0
0
0
2
2
0
1
0
0
0
0
2
0
2
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
3
0
0
1
1
0
3
0
1
1
0
2
0
1
0
0
0
2
0
1
0
0
0
0
1
0
0
2
0
0
0
0
1
0
4
0
0
2
0
0
1
1
2
0
0
2
0
0
2
0
2
0
0
2
1
0
1
0
1
0
1
0
0
0
2
0
0
4
0
0
0
0
0
2
0
2
0
0
0
0
0
1
2
0
1
1
0
0
1
0
0
0
2
1
0
1
0
1
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
2
2
2
0
0
0
1
1
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
2
2
1
0
0
1
0
0
0
0
0
0
1
2
0
1
1
0
0
0
2
0
0
0
2
0
0
1
0
0
1
2
1
0
0
2
0
1
0
0
2
1
0
0
0
2
0
0
0
0
0
1
0
0
1
1
2
1
0
0
1
0
2
2
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
1
2
1
2
1
0
2
1
0
1
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
1
0
1
0
0
0
1
0
1
2
1
1
1
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
1
0
0
1
2
0
0
0
0
0
0
2
1
2
0
0
0
0
1
0
0
0
0
1
1
1
0
0
2
0
2
1
0
0
1
2
0
1
1
0
0
0
0
0
2
0
1
0
1
2
0
1
0
0
0
0
0
2
1
0
0
0
0
0
3
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
1
0
7
0
0
0
0
0
0
1
3
0
2
0
0
2
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
2
0
0
2
1
0
2
1
0
1
2
2
0
0
2
2
0
1
0
0
1
0
2
0
0
1
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
1
1
1
0
0
0
2
0
2
0
1
0
0
2
0
0
0
0
0
2
0
1
2
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
3
1
1
0
0
1
0
0
0
3
2
0
0
0
4
0
1
0
0
1
2
0
2
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
2
0
1
3
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
2
0
0
1
1
0
0
1
0
0
1
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
1
0
2
1
0
0
0
0
0
2
1
0
2
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
1
1
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
3
0
2
2
3
0
0
0
1
0
0
1
0
0
0
1
2
0
0
0
1
0
0
0
2
0
2
1
0
0
0
0
0
0
0
1
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
1
0
1
2
0
2
0
1
1
1
0
0
1
0
2
3
0
1
0
0
1
0
0
3
0
3
0
0
0
2
0
0
1
1
0
0
0
0
1
1
1
0
0
0
2
1
1
3
0
2
0
1
0
0
2
1
1
0
2
0
1
2
0
6
2
0
0
0
2
1
2
0
2
0
0
0
0
2
0
0
1
0
2
0
0
3
2
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
1
0
2
0
2
0
0
0
2
0
0
1
2
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
2
0
1
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
1
1
1
0
0
0
0
2
3
0
2
1
0
2
0
0
0
1
1
2
0
0
1
0
0
0
2
0
1
1
2
1
0
2
0
0
0
0
0
2
0
1
0
3
1
1
1
2
2
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
1
0
0
2
0
0
2
1
0
2
0
0
0
0
0
2
0
0
2
0
0
0
1
2
0
0
0
1
0
0
0
2
1
0
1
0
0
1
1
2
0
0
0
2
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
2
1
0
0
0
0
0
0
2
0
1
2
0
1
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
5
0
3
1
1
0
0
4
2
0
0
0
0
0
1
0
0
0
0
0
0
1
2
3
1
0
1
1
2
2
0
0
0
4
1
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
2
4
0
2
0
0
0
1
0
0
0
4
0
0
0
1
0
1
2
0
1
0
1
2
1
2
0
0
0
2
0
0
0
2
1
1
2
2
0
0
0
1
0
1
0
1
0
1
0
1
2
2
1
0
2
0
0
0
0
1
0
1
0
0
2
0
2
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
1
0
0
0
1
0
2
2
0
0
0
0
0
2
2
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
1
0
1
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
2
2
0
2
1
0
0
0
0
0
1
0
0
1
0
3
0
1
1
1
1
0
0
0
1
1
0
1
2
0
2
2
0
0
0
0
0
0
0
1
1
0
1
0
0
1
1
1
1
3
0
0
2
0
2
2
0
0
2
2
1
0
2
0
1
0
0
0
2
0
2
0
0
0
0
0
2
0
2
2
1
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
2
2
0
2
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
1
0
0
1
0
2
1
0
0
0
0
1
0
2
1
1
1
0
1
0
0
0
0
0
2
0
0
2
1
0
1
2
0
2
0
1
0
0
2
1
0
0
0
1
1
2
0
2
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
3
1
2
2
0
3
2
0
0
2
0
1
2
1
0
0
2
0
0
1
0
0
0
0
0
0
2
2
0
2
2
0
0
3
0
0
2
1
0
0
0
0
0
0
2
1
4
1
0
0
1
0
1
2
0
0
0
0
0
2
0
0
0
1
0
0
2
2
0
0
0
1
2
0
0
1
0
0
0
1
1
0
2
0
0
1
0
0
3
2
0
0
0
3
0
2
1
0
1
0
0
2
1
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
1
0
1
0
0
1
0
2
2
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
3
0
0
0
1
1
0
0
1
2
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
1
2
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
1
1
0
2
0
2
0
1
0
0
0
2
0
0
2
0
0
1
1
1
0
2
0
1
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
1
2
2
0
2
1
0
1
2
0
3
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
2
0
0
2
0
0
2
3
0
0
0
1
0
0
4
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
3
0
0
0
0
1
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
1
2
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
2
2
0
0
1
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
2
0
0
0
0
2
1
0
0
0
0
1
0
0
1
0
1
1
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
1
0
0
2
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
1
0
2
0
0
2
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
2
0
1
1
1
0
0
0
0
1
0
0
2
0
0
0
2
2
0
0
2
0
0
0
3
1
0
0
1
0
0
0
1
0
1
0
0
0
0
2
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
1
2
1
0
0
0
0
0
0
2
0
0
1
2
0
0
1
1
2
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
2
2
1
1
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
2
0
2
0
2
0
0
1
0
1
0
0
2
0
0
0
0
0
1
0
0
1
0
2
0
0
0
2
2
1
0
1
0
0
6
2
0
1
2
4
2
0
3
0
0
0
1
0
0
0
1
0
0
0
0
0
4
0
0
0
0
1
3
2
0
1
2
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
3
0
3
1
0
0
1
0
1
0
0
0
0
2
0
1
0
2
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
2
0
3
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
2
0
3
0
2
1
3
0
0
2
1
2
0
0
0
0
0
0
1
0
0
0
0
0
1
1
2
0
1
0
0
1
0
1
1
1
0
0
0
0
0
14
0
4
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
2
4
1
0
0
1
0
2
0
2
2
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
1
2
2
0
0
1
0
1
2
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
3
0
1
0
2
0
0
1
0
2
1
0
0
0
1
0
0
2
2
0
0
1
0
0
2
0
0
0
0
0
0
0
1
2
0
2
0
0
2
0
0
0
0
1
1
0
0
2
0
0
2
1
0
0
0
0
0
2
2
0
0
1
0
2
0
0
0
2
2
0
0
0
0
1
0
2
0
0
0
2
1
2
0
0
0
2
0
0
2
0
0
0
0
0
0
1
2
0
0
1
0
4
0
0
1
2
0
0
0
0
0
2
2
0
0
2
2
0
1
0
0
0
0
0
0
2
0
0
0
4
1
0
0
0
0
2
0
1
0
0
0
3
2
0
2
0
0
0
0
0
1
2
0
2
0
0
0
0
1
2
0
1
1
0
0
0
2
0
0
1
0
0
2
1
3
0
0
0
0
0
2
1
0
0
0
1
0
1
0
0
0
1
1
0
2
0
0
0
0
0
2
2
0
0
3
0
2
2
2
1
0
1
0
0
2
0
0
0
2
0
2
2
1
0
0
0
2
2
1
0
1
0
0
0
2
0
0
2
0
0
2
0
0
0
1
2
0
5
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
3
0
2
0
0
1
2
2
0
0
1
0
1
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
2
1
0
0
0
0
0
0
1
0
0
2
0
2
0
0
1
0
1
1
2
2
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
1
0
0
0
1
0
1
2
4
1
0
0
0
0
2
1
1
0
0
0
0
0
1
0
0
0
1
0
2
0
0
1
1
1
1
0
0
0
0
2
2
0
1
0
2
1
0
0
0
0
1
0
0
2
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
1
0
0
1
2
0
0
0
1
2
0
2
1
0
0
2
0
2
0
0
2
0
3
1
2
0
0
0
1
0
1
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
1
2
0
1
1
0
0
0
1
0
2
2
0
1
0
1
0
0
2
0
0
0
1
0
0
1
0
2
4
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
2
1
0
2
0
3
0
0
0
0
0
0
0
2
0
1
0
1
1
2
0
0
0
1
2
0
0
0
0
0
2
0
1
1
0
0
1
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
1
0
2
0
0
0
0
0
1
0
0
1
0
1
1
0
0
1
1
0
0
2
1
0
0
0
0
2
0
0
2
2
0
4
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
2
3
2
2
2
0
0
2
2
0
0
0
0
1
1
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
1
0
2
2
0
2
1
1
2
2
1
1
0
1
0
1
1
0
0
3
1
0
0
2
0
1
0
1
0
2
0
0
2
0
2
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
2
2
0
0
0
0
0
3
0
0
0
1
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
1
3
2
0
2
0
0
0
0
1
2
1
0
0
1
0
0
0
2
0
2
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
1
2
1
0
1
0
0
0
0
1
0
0
0
0
1
2
0
0
1
0
0
0
0
2
2
0
3
0
3
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
1
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
8
0
0
0
1
0
1
1
0
2
0
0
1
2
2
0
0
0
3
3
0
0
2
2
0
0
1
0
0
0
0
0
2
0
1
2
0
0
2
0
0
2
0
0
1
0
0
0
2
0
0
0
1
0
0
2
1
3
0
1
0
1
1
0
0
0
2
1
1
1
1
0
0
0
1
0
0
1
0
0
0
0
2
1
0
0
1
2
1
0
0
0
0
2
2
0
0
1
2
2
0
2
0
3
0
0
0
0
1
0
1
1
0
0
0
3
1
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
1
1
1
2
1
0
1
2
0
0
0
2
1
0
0
0
0
0
0
1
0
0
2
2
1
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
3
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
1
2
1
2
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
1
0
1
0
0
0
1
1
0
0
0
2
0
0
1
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
2
1
0
1
2
1
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
3
2
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
1
0
2
0
1
0
0
2
1
1
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
1
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
2
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
7
0
0
0
2
0
4
0
0
0
0
2
0
1
2
2
0
0
2
0
0
1
0
2
2
0
0
0
0
1
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
1
1
2
0
0
4
0
0
0
0
1
1
2
2
0
0
1
3
0
0
0
2
1
0
1
0
0
1
0
0
0
2
0
0
1
1
2
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
2
2
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
7
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
1
0
0
1
2
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
1
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
2
0
2
0
0
0
0
0
0
5
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
5
1
0
0
0
0
0
1
1
0
2
2
4
0
0
0
0
0
0
0
2
0
1
2
0
7
0
1
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
2
0
0
0
2
0
0
0
0
1
4
0
0
0
0
0
4
0
0
1
1
2
0
0
0
2
0
0
1
1
2
2
0
0
0
2
1
0
0
0
0
1
0
0
0
2
0
0
1
0
0
1
0
2
0
1
1
1
0
6
2
0
0
0
0
0
1
0
1
2
2
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
2
1
2
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
1
0
0
0
1
0
0
3
0
0
1
1
2
0
0
0
2
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
2
1
2
0
0
2
0
1
1
0
0
0
0
0
0
1
1
0
2
0
1
0
0
0
0
0
1
1
2
0
1
0
0
2
0
1
0
0
0
0
2
0
0
2
0
3
2
0
1
0
1
0
0
0
0
0
1
2
0
0
1
0
0
2
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
4
2
0
0
0
0
1
2
2
0
0
0
4
1
0
2
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
1
0
1
0
0
2
0
0
0
0
1
0
0
2
0
0
9
0
2
2
0
0
0
2
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
2
0
0
2
4
2
1
0
0
1
0
2
1
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
1
0
2
2
0
0
0
2
0
2
0
0
0
2
1
0
0
0
0
2
2
0
1
0
0
0
4
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
2
0
0
2
0
2
0
2
0
0
1
1
0
0
0
0
1
0
0
0
0
0
2
0
0
4
0
0
0
1
0
3
0
2
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
4
0
0
4
0
2
1
0
1
2
0
1
0
0
0
2
2
0
0
3
0
1
0
1
1
0
2
2
0
0
1
0
2
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
2
1
0
3
1
1
0
2
0
0
2
1
2
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
2
0
0
0
1
0
0
0
0
1
0
0
0
0
2
1
0
2
2
0
0
0
2
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
1
0
1
0
2
2
0
0
0
2
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
1
0
2
2
0
1
0
0
0
0
2
1
0
1
0
2
0
1
0
1
0
0
0
2
0
1
0
0
2
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
1
0
2
3
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
2
0
0
2
0
2
2
0
0
0
0
0
1
3
0
2
0
2
1
2
0
0
2
0
0
0
0
2
1
2
0
0
0
0
0
1
0
3
1
3
0
0
0
0
1
1
0
1
5
0
0
0
2
0
0
1
0
0
0
0
1
2
0
2
2
0
0
0
0
1
2
0
0
1
0
2
1
1
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
2
0
1
0
0
0
0
2
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
3
0
2
0
1
1
0
0
1
2
0
0
0
2
0
0
0
0
1
2
0
1
1
0
0
1
2
2
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
1
1
1
0
0
0
2
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
3
0
0
0
0
2
1
1
3
2
0
2
0
1
0
0
1
0
2
0
1
2
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
1
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
1
0
0
1
3
2
0
0
0
0
3
0
1
1
0
1
0
1
0
0
0
0
0
0
0
3
2
0
3
0
0
0
1
0
0
0
0
0
0
1
0
1
2
0
2
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
2
0
0
2
0
0
0
2
1
0
0
0
0
2
0
0
1
0
1
0
2
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
1
0
0
1
0
0
0
0
1
0
0
3
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
2
0
2
0
0
1
2
1
0
2
0
0
2
1
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
2
2
1
1
4
1
0
0
1
0
0
0
0
0
0
0
2
0
2
1
1
0
0
2
2
0
0
0
2
0
2
0
0
1
0
1
2
0
1
0
2
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
1
1
0
3
2
1
2
0
0
0
0
2
0
3
0
0
0
1
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
1
2
1
2
2
0
0
0
2
0
2
0
0
0
0
0
2
0
0
1
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
2
3
0
0
0
0
0
0
2
1
0
1
7
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
1
0
1
0
0
1
0
0
0
4
0
0
0
0
2
1
1
0
1
0
2
2
0
0
1
0
2
2
0
4
0
2
0
0
2
2
0
2
0
0
1
0
0
6
1
0
0
0
1
0
2
2
0
3
0
0
0
0
1
0
2
0
2
0
0
2
0
3
0
1
1
1
0
0
0
0
0
2
1
0
1
2
0
0
0
0
1
0
0
0
2
2
0
0
1
3
0
0
1
0
3
0
0
2
0
0
1
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
4
0
3
0
0
0
2
0
1
0
0
0
0
2
0
2
0
2
0
0
3
2
0
1
1
2
0
1
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
9
0
0
0
0
0
0
0
4
0
1
0
0
1
0
0
0
2
1
0
0
1
2
0
0
0
0
0
1
0
1
2
0
0
1
1
0
1
0
0
2
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
2
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
2
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
6
0
0
2
1
1
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
1
2
0
1
0
2
0
0
4
0
1
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
1
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
2
1
0
2
2
0
0
0
1
0
2
2
2
0
0
3
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
3
0
3
0
1
0
0
2
0
0
2
0
2
0
0
0
0
2
2
0
0
2
1
1
0
2
1
1
0
0
0
0
1
0
2
0
1
0
0
0
0
1
2
0
0
0
0
0
0
2
2
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
2
1
2
2
0
0
0
2
1
0
0
1
0
0
0
0
1
1
1
0
1
0
3
0
1
1
2
0
0
1
1
0
0
7
3
1
0
0
0
0
0
2
3
2
2
0
0
0
1
1
0
0
0
4
1
2
0
0
0
0
1
2
0
0
0
1
0
0
2
1
4
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
2
0
0
0
0
2
2
2
4
0
2
0
0
0
0
2
1
0
0
1
1
0
0
2
0
0
0
0
1
0
2
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
2
0
1
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
1
0
1
0
0
0
2
2
0
0
0
1
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
2
0
1
1
0
2
0
0
1
1
0
0
2
0
0
1
2
0
0
0
0
2
0
0
1
0
1
3
1
0
1
0
3
0
0
0
0
1
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
7
1
0
2
0
2
2
2
0
1
2
1
2
0
0
0
0
2
1
2
2
2
1
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
2
1
1
0
0
3
0
0
0
2
0
0
0
2
0
0
0
3
1
3
0
2
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
3
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
2
4
0
2
1
1
0
2
0
0
1
1
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
2
0
0
1
2
0
0
0
1
2
2
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
1
2
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
1
3
2
0
2
0
2
3
1
0
0
0
1
0
0
0
0
1
1
3
0
0
1
2
3
0
1
0
0
0
0
0
0
2
0
0
0
1
1
2
0
1
1
0
0
1
0
1
1
1
0
1
0
1
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
2
0
0
1
2
3
0
0
0
0
0
1
0
0
0
0
2
0
1
1
0
1
2
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
1
3
0
1
0
2
0
0
0
0
0
1
0
1
0
2
0
0
0
1
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
1
0
1
3
0
0
2
1
0
2
1
0
1
2
0
0
0
1
0
1
1
0
0
0
0
1
1
0
2
2
0
0
0
0
2
0
2
2
1
0
1
0
0
2
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
2
0
0
2
0
1
1
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
1
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
1
0
0
2
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
1
2
0
0
2
2
0
0
0
2
0
1
1
0
0
0
1
2
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
1
1
0
2
0
2
0
0
0
0
0
1
0
0
1
0
1
2
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
1
0
0
0
0
0
0
2
0
0
3
1
0
0
0
0
0
2
0
0
0
2
0
0
2
2
0
3
0
1
0
1
1
0
0
1
0
2
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
1
2
0
3
0
3
1
0
0
0
1
0
0
0
0
3
0
0
0
2
1
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
2
0
0
0
0
1
0
0
0
0
1
2
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
1
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
2
0
0
0
0
0
1
1
1
0
0
0
3
1
0
0
0
0
0
0
0
1
2
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
2
0
2
0
0
0
0
0
0
2
0
1
0
0
1
0
1
0
0
0
1
1
1
0
0
0
0
0
0
2
2
1
1
3
0
0
1
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
2
0
0
0
1
0
7
0
0
0
0
1
2
1
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
3
2
4
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
2
0
0
0
2
0
0
2
0
0
2
0
0
3
0
1
2
0
0
0
1
1
0
0
1
1
0
1
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
2
2
2
2
0
0
0
2
2
0
3
1
1
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
9
2
0
0
0
2
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
2
2
0
1
0
2
0
0
0
0
0
0
0
0
1
3
3
0
1
2
0
0
0
0
0
0
0
1
4
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
2
0
2
0
2
0
1
1
1
1
2
0
0
0
0
0
3
2
0
0
0
2
2
0
0
0
0
0
1
1
1
1
0
0
2
0
0
0
1
2
0
0
0
5
3
0
0
1
0
0
1
0
2
0
0
0
1
0
0
0
2
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
2
1
0
0
0
2
0
2
0
0
0
0
0
0
1
0
1
3
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
2
1
0
0
4
0
0
3
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
1
2
0
2
0
2
0
1
2
1
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
2
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
1
0
0
0
0
0
1
0
1
2
0
0
1
0
0
0
0
1
1
1
0
0
2
0
0
0
1
2
5
0
0
0
0
1
1
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
2
0
0
4
0
2
0
1
2
1
0
1
0
0
0
1
0
0
0
1
2
0
0
0
1
0
0
0
1
2
0
2
2
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
2
1
1
1
2
0
0
2
0
0
0
1
0
0
0
0
2
0
2
1
0
1
0
0
1
0
0
0
1
2
1
2
0
2
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
4
0
2
2
2
2
0
0
0
2
0
0
1
2
2
0
0
0
2
0
1
0
0
0
1
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
2
1
0
0
0
0
0
2
2
0
0
0
2
0
0
0
1
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
2
0
3
1
1
2
0
1
0
0
3
0
0
2
0
0
0
1
0
2
2
2
0
3
0
0
1
0
0
0
2
0
0
4
0
0
0
1
0
4
0
2
1
0
2
2
0
0
0
0
1
0
0
0
0
1
0
0
3
2
0
2
0
0
0
0
0
0
1
0
0
0
1
0
2
0
1
0
2
1
2
0
1
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
2
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
2
0
1
2
0
1
0
0
0
2
1
2
0
0
0
2
1
0
0
2
1
2
0
0
0
1
0
0
1
0
1
0
0
2
0
0
0
2
2
1
0
0
2
0
1
0
0
1
0
0
3
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
1
1
0
0
0
0
0
0
0
2
0
1
1
0
0
0
2
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
7
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
1
0
0
0
2
0
0
1
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
1
0
2
0
2
0
2
3
0
3
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
2
1
3
1
2
0
0
0
0
3
0
0
0
1
2
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
2
0
1
0
0
0
0
0
2
2
0
0
0
0
2
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
2
2
0
1
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
1
1
0
1
0
1
0
0
0
0
1
2
0
1
0
0
1
0
0
1
1
0
0
0
0
1
1
2
1
0
0
0
0
0
0
0
1
2
0
0
0
1
2
1
0
0
0
0
2
0
0
2
0
0
1
2
0
0
0
2
2
2
2
0
0
0
2
2
0
0
0
0
2
2
2
0
1
0
0
1
0
0
0
0
1
1
1
1
2
0
2
0
0
0
0
2
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
2
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
1
2
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
3
2
1
1
0
0
1
1
0
4
0
0
0
1
0
0
2
0
0
0
1
0
2
0
2
1
2
0
0
0
0
1
0
1
0
0
0
1
2
2
0
0
0
2
0
0
2
0
3
0
1
0
0
1
2
2
0
2
0
1
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
1
0
1
2
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
2
0
0
1
0
1
2
2
0
2
2
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
3
0
0
2
1
1
0
0
0
0
1
0
0
0
1
4
0
2
2
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
1
0
2
0
1
0
0
0
1
2
0
0
0
1
1
2
0
0
2
0
0
0
0
0
0
1
1
0
0
0
2
0
0
1
0
2
2
0
1
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
1
1
0
0
2
1
0
1
2
1
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
3
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
2
1
0
1
0
0
1
0
0
2
0
0
2
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
2
1
0
2
0
0
3
2
1
0
1
1
0
6
2
0
2
0
0
0
1
0
0
1
2
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
1
0
1
2
0
0
1
0
0
0
0
0
1
0
1
0
0
2
0
1
2
0
2
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
2
0
2
3
1
0
0
1
0
0
1
0
1
0
0
0
0
1
0
1
1
2
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
3
3
2
0
0
0
0
3
0
1
0
0
0
2
2
0
0
0
0
2
0
1
0
1
2
0
5
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
2
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
2
0
3
0
0
2
0
0
0
1
0
0
1
1
0
0
0
0
2
1
0
0
1
0
2
0
1
0
1
0
0
0
0
0
0
0
2
0
2
2
0
2
2
0
0
0
2
2
2
2
0
0
0
0
0
2
0
0
0
0
2
1
0
0
4
0
2
0
1
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
2
2
0
0
0
2
2
1
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
1
0
2
1
0
0
3
1
1
0
0
0
0
0
0
2
0
2
0
2
1
2
0
0
0
0
0
0
1
1
1
0
0
3
1
2
1
2
1
1
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
2
1
0
1
0
0
0
1
0
0
0
1
1
0
0
1
1
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
1
1
1
0
2
0
3
1
0
2
0
1
0
1
0
2
0
0
0
3
0
2
0
0
1
0
0
0
0
1
2
0
1
0
0
3
0
0
0
0
1
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
1
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
2
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
2
1
0
0
1
1
1
0
0
5
0
0
0
2
1
0
2
1
2
0
5
0
0
6
3
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
2
0
0
2
2
0
0
2
2
0
1
1
2
0
2
0
0
0
3
2
2
0
0
0
1
0
1
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
3
1
0
0
0
1
2
0
1
3
1
1
0
0
0
1
1
1
0
0
0
0
1
2
1
2
2
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
3
1
0
0
0
1
0
2
2
0
0
0
1
0
1
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
3
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
1
0
0
0
0
0
2
1
0
1
0
1
0
0
0
2
1
0
0
2
2
2
2
1
0
0
0
1
1
0
0
0
0
0
1
0
0
2
0
0
0
2
1
0
2
0
0
2
0
0
1
0
0
0
0
0
2
0
0
1
1
2
0
1
0
1
0
0
0
2
0
1
2
0
1
1
0
0
2
0
0
1
0
2
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
2
3
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
2
2
1
0
2
0
2
1
0
0
0
0
0
2
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
2
0
3
1
0
3
0
1
1
2
2
1
0
0
0
2
0
4
0
0
0
1
2
0
0
2
0
1
1
0
2
1
2
0
2
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
2
0
2
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
1
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
2
0
2
0
0
2
0
0
1
1
1
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
2
0
0
1
3
0
2
0
0
0
1
3
0
0
0
0
0
1
2
1
0
0
2
0
1
0
0
1
0
0
2
1
0
0
0
0
1
0
1
1
0
0
2
0
0
0
0
0
1
2
0
0
1
1
0
3
0
1
0
1
0
2
1
1
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
3
2
1
0
0
2
0
0
1
0
1
1
0
0
0
2
0
1
0
0
1
1
0
0
0
1
0
0
1
0
0
0
2
0
2
0
0
0
1
0
0
0
1
2
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
1
0
0
1
2
0
0
0
0
0
2
0
1
0
0
0
1
0
2
0
0
0
0
2
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
2
0
1
0
1
0
1
0
2
0
0
0
0
1
0
0
1
0
0
1
1
1
0
0
1
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
1
2
0
0
2
1
0
1
0
0
0
2
0
0
0
0
3
2
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
1
2
1
2
3
3
2
2
0
8
1
2
0
0
1
0
0
2
0
0
0
2
0
0
1
0
0
1
3
1
1
1
1
0
0
0
0
2
3
0
0
1
0
0
0
2
1
0
0
2
0
1
0
1
0
2
0
3
1
2
2
0
0
1
2
0
0
0
0
0
3
1
0
1
1
2
1
2
0
2
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
2
1
0
0
2
0
0
0
0
0
2
1
0
0
6
0
0
0
0
2
0
3
0
2
2
0
3
0
0
1
0
2
1
1
0
0
0
1
1
0
0
2
0
1
0
0
2
2
0
0
2
0
0
0
0
0
2
0
2
0
1
0
2
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
1
0
1
0
0
0
1
1
0
0
2
2
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
2
0
0
1
1
0
0
0
0
0
1
0
1
2
0
2
0
0
0
2
2
0
0
1
0
2
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
3
0
0
2
0
2
2
0
0
2
1
1
0
0
2
0
0
0
0
1
0
2
3
0
0
1
0
5
0
0
0
0
0
0
1
0
3
0
1
0
3
1
2
0
0
0
1
1
0
0
0
0
1
2
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
2
2
0
1
0
0
0
2
1
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
2
0
2
1
0
2
0
0
1
1
2
0
0
0
2
2
1
0
3
2
0
0
0
2
0
2
0
0
0
0
0
2
1
2
0
2
2
0
0
2
0
2
1
0
0
0
2
2
0
0
0
4
0
0
0
0
1
1
0
0
3
2
0
0
0
0
1
0
0
1
1
0
2
1
0
0
0
0
2
0
0
0
0
0
2
2
0
0
2
0
0
0
0
2
2
0
0
1
0
2
2
0
0
0
0
1
4
0
2
0
0
2
1
2
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
4
0
0
0
0
4
0
0
1
2
0
1
0
1
2
0
0
0
2
1
2
0
0
0
0
0
1
0
0
2
0
3
0
0
2
0
0
2
0
1
0
0
0
0
2
1
0
0
1
0
1
0
0
0
1
0
0
1
0
1
0
0
2
2
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
3
0
2
0
2
0
2
0
1
2
3
2
0
0
0
0
0
0
0
1
0
0
1
1
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
1
3
0
0
0
0
2
2
0
0
0
2
1
0
1
0
0
0
2
0
0
0
0
0
0
1
1
0
4
2
2
3
2
1
1
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
2
0
5
1
2
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
2
2
2
0
0
0
0
2
0
0
0
0
1
1
0
2
0
0
0
0
1
0
2
0
2
0
2
0
0
2
0
1
2
2
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
1
1
0
0
1
0
1
1
0
0
0
2
0
0
0
0
1
0
1
0
0
2
2
1
1
0
1
2
0
0
2
2
0
2
0
0
0
0
1
0
0
2
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
2
2
1
2
0
1
1
0
0
1
0
2
2
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
2
0
0
0
0
0
1
1
2
0
1
1
1
2
1
0
0
5
2
0
0
0
2
0
2
2
0
0
2
0
0
0
0
0
0
1
2
6
0
0
0
0
0
1
0
1
1
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
2
1
0
0
1
2
0
0
3
0
0
0
2
0
0
0
2
2
4
1
0
0
2
1
0
1
0
2
1
1
0
2
0
1
0
1
0
0
3
2
0
4
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
7
0
0
1
0
0
0
0
0
0
2
1
1
0
3
0
0
1
0
0
0
0
3
0
1
0
1
0
1
0
1
0
0
2
0
2
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
1
2
4
0
0
0
0
0
0
1
2
0
0
0
0
2
0
4
0
2
1
1
0
0
0
0
0
0
0
2
0
2
2
0
1
0
3
0
0
1
0
0
1
0
0
1
2
0
1
0
4
2
0
0
2
0
1
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
3
0
1
2
0
2
0
1
1
0
0
0
0
1
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
2
2
1
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
9
1
1
0
0
2
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
1
3
1
0
2
0
1
0
0
0
2
0
0
1
0
2
2
0
3
0
0
2
1
2
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
2
0
3
0
0
2
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
3
0
2
1
1
1
0
0
0
0
0
0
0
1
0
1
1
3
0
1
0
0
1
1
1
2
0
3
0
0
4
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
1
0
2
0
0
0
1
0
2
0
0
1
0
2
1
1
0
2
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
1
3
1
0
1
0
0
0
1
0
2
1
0
1
0
2
0
1
0
0
1
0
0
0
2
0
0
0
2
2
2
0
0
0
0
0
2
0
0
1
2
0
2
0
2
1
0
0
0
0
1
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
2
1
1
1
0
0
0
0
1
2
0
1
1
2
0
1
0
3
0
0
1
0
2
1
0
2
2
2
0
1
2
0
0
0
1
1
0
2
0
1
1
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
2
0
2
0
1
0
0
0
0
1
1
0
0
2
0
0
3
1
2
0
2
1
0
0
0
1
0
0
1
0
2
1
1
0
1
0
0
1
0
1
1
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
3
0
0
2
0
0
0
1
0
2
0
0
0
1
0
0
0
1
2
0
2
0
2
0
0
3
0
0
0
0
2
1
0
0
1
1
2
1
1
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
1
3
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
1
0
0
0
2
0
2
1
0
0
0
0
0
0
0
1
0
0
3
3
0
2
1
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
2
0
1
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
2
1
0
0
0
2
0
0
1
1
0
0
2
0
2
0
0
1
2
1
0
0
1
1
0
1
0
0
0
0
0
2
0
2
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
1
1
1
0
0
3
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
2
1
2
0
1
0
0
2
0
0
1
0
0
2
0
0
0
0
6
0
0
0
3
0
1
1
0
1
2
0
2
0
1
2
0
0
0
0
2
2
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
3
0
2
0
0
2
0
0
0
3
0
1
0
1
0
0
0
0
0
0
0
2
0
0
3
0
0
2
1
1
0
2
0
3
1
1
3
2
0
2
0
2
2
1
0
0
1
1
0
2
0
1
0
0
5
0
0
2
2
0
2
0
2
2
1
2
1
0
0
0
0
0
2
0
0
2
0
2
0
0
0
2
0
1
0
0
0
2
0
2
0
0
0
1
0
1
0
1
0
2
0
0
0
2
0
1
0
0
0
0
0
0
1
1
2
2
0
0
0
0
3
1
2
0
0
0
2
0
1
2
2
0
0
0
0
0
0
0
2
2
0
0
2
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
1
0
0
2
0
2
2
0
0
2
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
1
1
0
0
1
0
0
2
1
1
2
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
1
1
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
2
1
1
2
0
0
1
1
2
1
2
4
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
2
2
4
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
1
5
2
0
0
0
1
0
0
2
3
0
0
1
0
0
0
0
0
1
0
0
1
0
3
0
0
1
0
0
0
2
2
2
3
0
0
1
2
0
1
3
0
1
0
0
1
2
0
0
0
1
1
0
0
2
0
2
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
4
0
0
2
0
3
0
1
0
0
0
0
0
3
0
2
0
1
1
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
2
1
0
0
0
1
2
0
0
0
0
2
2
1
1
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
3
2
2
4
0
0
1
0
0
1
0
2
2
2
0
0
1
0
1
0
1
1
1
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
1
2
1
0
2
1
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
2
0
2
0
0
1
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
1
0
1
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
2
2
0
0
2
1
0
0
3
1
1
0
0
1
0
0
0
2
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
1
2
0
1
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
2
0
2
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
2
1
0
0
0
1
0
2
0
0
0
0
0
2
1
0
0
2
1
0
0
0
0
2
2
0
0
0
1
1
0
0
0
0
3
1
1
0
0
2
0
0
0
1
0
0
1
0
0
0
1
2
0
1
0
1
0
0
0
0
2
2
1
0
1
1
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
1
2
0
1
0
0
1
0
0
2
1
0
3
0
1
0
0
0
0
0
0
1
1
1
0
0
2
1
1
1
1
0
0
0
0
0
1
2
1
0
2
1
2
0
3
3
2
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
2
0
2
0
1
0
2
0
0
2
0
0
1
0
0
0
0
2
0
2
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
1
1
1
1
1
1
0
0
2
0
1
0
0
0
1
0
0
0
0
1
2
0
1
0
1
0
1
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
1
1
2
0
0
0
1
1
2
0
0
0
0
2
0
1
1
0
0
0
1
3
1
0
0
0
0
1
0
0
0
2
0
0
1
0
1
0
0
0
1
0
0
0
2
1
0
0
1
1
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
1
0
1
1
2
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
1
0
2
1
0
0
0
0
0
2
2
0
0
2
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
2
0
2
1
0
0
1
1
0
0
0
0
0
2
2
2
2
0
0
2
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
3
0
0
0
1
0
0
2
1
0
0
1
0
2
4
0
0
0
1
0
0
0
1
0
1
0
2
0
0
2
0
0
1
0
0
1
2
1
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
4
1
0
0
1
0
0
0
0
0
7
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
1
3
2
1
1
0
0
2
0
0
0
0
0
0
0
1
0
1
5
0
0
0
0
0
3
2
0
1
0
1
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
1
0
0
1
0
0
2
0
0
0
1
0
2
2
0
0
1
0
2
2
1
0
1
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
3
0
1
1
0
0
1
0
0
1
1
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
1
0
0
2
1
1
0
0
0
0
0
0
0
0
1
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
1
0
2
0
0
0
0
0
0
2
1
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
1
1
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
2
0
3
0
0
1
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
1
0
1
0
0
0
0
0
0
2
0
2
2
1
2
4
0
0
1
0
0
1
0
0
1
0
0
2
2
1
0
1
2
1
2
0
0
0
2
1
0
1
2
1
0
2
0
2
0
0
5
1
1
1
0
1
0
0
1
1
0
1
2
1
0
0
0
1
0
0
1
2
0
1
0
0
1
0
1
0
0
2
1
2
0
0
0
0
0
0
0
1
1
0
2
1
0
3
0
1
0
1
1
0
1
0
0
2
0
2
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
2
2
2
0
0
1
3
0
0
0
2
0
0
0
2
2
0
2
3
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
2
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
1
3
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
1
1
3
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
1
2
0
3
2
0
0
2
1
2
0
1
0
0
0
0
0
1
1
2
0
0
0
0
0
5
0
1
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
3
1
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
1
2
0
0
0
1
0
3
0
3
2
0
2
1
0
1
2
0
1
1
1
0
2
0
0
0
0
0
0
0
2
1
2
0
0
1
0
2
2
0
2
0
0
0
0
2
0
2
0
0
0
0
2
0
1
0
2
2
0
0
2
0
2
2
2
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
2
0
0
1
0
0
0
3
0
2
0
0
0
2
1
0
0
1
0
1
0
2
0
0
0
0
0
3
1
0
1
0
2
0
1
1
0
0
2
1
0
0
0
0
1
0
1
0
1
0
4
0
0
2
0
2
1
1
6
0
0
1
3
0
0
1
1
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
1
3
0
0
0
0
2
1
1
0
1
0
3
0
3
0
1
1
1
1
0
0
0
1
0
0
1
0
0
1
1
1
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
2
2
0
2
0
0
1
0
1
0
0
1
4
0
2
0
0
2
1
0
0
0
0
0
2
1
2
0
0
0
0
1
2
0
4
0
0
0
0
1
2
1
1
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
4
2
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
4
0
0
0
2
1
1
2
2
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
2
2
0
0
0
0
2
0
1
2
0
0
0
2
2
0
0
2
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
2
0
1
0
1
0
2
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
3
1
1
0
0
2
2
1
0
0
2
1
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
1
0
2
2
3
0
2
2
0
2
0
1
3
1
0
0
1
1
2
1
0
1
1
0
0
1
0
0
2
0
0
5
0
0
0
0
2
0
1
0
0
1
0
0
0
1
0
0
2
2
2
1
0
0
0
0
1
1
2
1
1
0
0
0
0
3
2
1
4
0
1
0
2
0
0
0
0
1
2
0
0
0
1
2
0
0
0
2
1
0
0
2
0
0
0
1
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
2
0
2
4
0
1
2
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
1
0
3
1
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
3
0
1
0
1
0
0
0
1
0
0
0
0
1
1
2
1
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
3
0
0
0
0
0
0
1
0
0
0
1
2
1
0
1
0
0
2
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
1
0
1
0
2
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
1
1
3
0
2
0
2
0
0
4
0
0
1
0
0
0
0
2
1
0
1
0
2
1
2
0
0
1
1
0
1
0
0
0
2
1
0
0
2
0
0
0
2
0
0
1
2
5
0
0
4
0
1
2
1
1
0
1
1
0
0
2
0
0
2
0
0
1
0
1
0
1
0
2
0
0
0
0
2
1
0
1
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
1
2
0
0
0
5
0
2
0
0
0
0
0
2
0
2
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
1
0
0
2
1
0
1
0
0
0
2
0
0
1
0
1
0
1
0
1
0
0
0
0
2
1
0
0
1
0
1
0
0
1
2
0
0
0
0
1
0
0
2
0
0
1
0
0
2
2
2
2
0
2
0
0
0
0
1
0
0
0
1
0
0
2
1
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
2
0
0
2
1
0
1
0
2
4
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
1
0
0
2
0
0
4
1
3
0
0
0
0
0
0
0
1
2
0
0
0
2
1
0
0
0
0
0
0
1
0
3
0
0
0
2
2
0
0
0
2
0
2
1
1
1
0
0
0
0
1
0
0
0
2
1
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
1
1
0
2
0
0
1
0
0
0
1
2
0
0
0
0
1
2
1
0
0
0
1
0
2
0
1
2
1
0
0
2
0
2
0
0
0
1
0
2
0
0
0
0
1
2
0
1
0
1
2
1
0
1
0
1
2
0
0
0
0
0
1
1
1
0
0
0
0
0
0
3
0
0
0
0
1
1
0
0
0
0
2
0
0
1
0
0
0
2
0
1
0
2
0
0
0
0
0
3
0
2
0
1
0
2
0
1
0
0
2
0
0
1
0
1
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
2
0
0
1
0
1
0
1
0
2
0
2
0
1
1
0
2
2
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
2
1
0
1
0
2
0
0
1
0
0
0
2
1
2
2
0
1
0
0
0
2
2
0
0
0
0
0
1
1
0
1
1
2
0
0
2
2
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
1
1
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
2
0
0
0
0
4
0
0
0
0
0
0
1
1
2
0
3
1
1
0
2
0
0
2
0
1
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
2
1
1
0
2
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
1
1
1
0
0
0
1
0
1
0
0
3
0
0
0
2
0
0
3
2
1
1
2
0
0
2
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
2
0
3
0
0
1
2
0
0
2
0
2
0
0
1
0
1
0
0
0
0
0
0
1
4
0
0
0
0
0
0
1
1
0
3
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
2
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
1
0
0
0
4
0
1
0
0
0
0
2
0
0
0
2
2
0
0
0
1
2
0
1
0
0
0
1
0
1
2
0
0
2
1
2
0
0
0
1
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
1
0
1
5
0
2
0
0
2
0
0
1
0
2
0
0
0
0
0
0
1
1
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
1
2
0
2
1
0
0
0
0
0
2
0
2
2
0
1
0
0
0
1
2
2
0
0
0
0
0
0
0
2
0
0
2
2
0
0
1
0
1
2
2
0
1
0
0
0
1
0
2
0
0
2
0
3
0
0
0
1
11
0
1
2
0
1
0
2
0
1
2
0
0
3
1
1
0
1
0
2
0
0
0
0
4
0
0
0
0
3
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
1
0
2
0
0
2
2
1
1
1
0
0
0
1
1
0
1
0
0
0
2
0
0
1
0
0
0
0
1
0
2
2
0
0
0
1
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
1
1
0
0
0
0
1
1
0
2
0
1
0
0
0
3
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
4
1
1
0
1
0
1
0
0
0
0
1
1
0
0
2
0
0
1
0
2
2
0
0
0
1
0
0
2
0
2
0
0
0
0
1
0
2
0
0
0
0
2
0
1
0
1
0
1
2
0
0
0
1
0
1
0
2
0
0
1
0
0
1
0
0
0
0
0
0
1
1
2
0
3
0
0
0
0
0
0
0
0
0
2
2
0
1
0
6
0
0
1
0
0
1
0
0
0
1
4
0
3
0
1
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
2
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
1
0
0
0
2
0
1
0
0
0
0
2
0
0
1
1
1
2
0
0
0
0
0
0
2
0
0
1
1
1
1
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
2
3
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
3
1
2
0
0
2
2
0
0
0
1
0
1
0
0
0
0
0
0
1
0
3
2
0
0
0
0
0
2
2
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
5
2
0
0
2
1
0
0
0
0
2
0
0
1
1
0
2
1
0
2
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
1
1
0
0
0
2
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
3
0
0
2
1
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
1
2
0
2
0
8
1
0
1
0
0
2
0
0
1
2
0
0
0
2
2
0
0
0
0
1
0
2
0
0
0
0
2
0
1
1
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
1
0
2
0
1
0
0
0
2
2
1
0
0
0
2
0
0
0
1
0
4
0
1
0
1
1
0
0
0
0
0
2
1
0
2
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
2
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
2
1
0
1
0
2
1
1
0
0
2
0
0
1
0
0
2
0
0
0
1
0
0
0
0
2
0
0
2
2
1
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
2
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
2
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
5
0
1
0
0
0
0
0
0
1
0
0
0
4
0
0
2
0
0
1
2
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
1
1
0
2
0
1
2
0
0
0
0
1
2
1
2
0
0
1
0
0
1
0
3
0
0
1
0
0
4
1
2
0
0
1
0
0
0
0
0
0
1
0
2
0
1
1
0
0
0
0
2
1
1
0
0
0
2
2
1
0
0
0
0
2
0
0
1
0
0
1
2
0
1
0
0
0
0
2
0
2
5
0
2
0
0
1
0
0
0
0
0
0
1
0
2
0
3
0
0
0
3
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
6
0
2
3
0
1
0
0
0
3
2
0
0
0
0
1
0
1
2
1
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
3
0
0
0
0
0
0
0
1
1
0
0
0
0
4
0
0
0
0
0
2
2
0
1
0
0
1
0
0
0
0
0
0
2
0
2
0
0
3
0
0
0
1
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
2
0
1
0
0
0
3
1
0
0
0
0
1
0
0
0
2
1
1
0
1
0
1
0
1
0
0
1
0
2
0
2
0
1
2
0
0
0
2
2
1
0
0
0
2
0
2
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
3
0
1
1
0
0
0
1
0
0
0
2
2
1
0
0
0
0
0
0
2
3
0
0
0
2
0
2
0
0
1
5
0
0
0
0
4
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
2
2
1
2
2
0
0
0
0
2
0
0
0
0
1
2
0
1
0
0
0
0
1
1
2
0
0
0
0
2
0
7
0
2
0
0
1
0
0
1
0
2
1
0
0
1
2
0
1
1
0
0
2
1
1
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
1
1
2
0
0
1
0
2
2
0
2
0
0
2
0
2
0
0
1
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
1
0
0
2
1
0
0
0
0
2
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
3
0
1
0
0
1
0
0
1
0
2
0
2
1
0
1
0
1
0
0
1
0
0
2
1
0
0
3
0
2
0
3
0
0
0
2
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
2
1
0
2
3
0
1
2
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
1
1
0
0
0
3
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
2
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
1
1
0
0
0
3
1
0
0
0
0
2
1
0
0
0
0
1
0
0
0
2
0
1
1
0
0
0
0
2
1
2
0
0
0
4
0
1
1
2
0
1
1
1
0
0
0
1
2
0
0
1
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
2
2
0
0
2
0
1
0
2
0
0
1
1
0
0
0
0
0
1
2
2
2
2
2
0
1
0
2
0
1
2
1
0
1
1
0
0
0
0
2
2
1
0
2
0
0
1
0
0
0
0
0
0
0
0
2
2
2
0
1
0
0
0
1
0
2
0
0
1
4
1
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
2
2
0
1
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
4
0
0
0
3
1
0
1
0
0
3
0
2
0
0
9
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
2
0
1
2
0
0
1
0
0
0
0
0
3
2
1
1
1
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
5
0
0
1
2
1
0
0
0
0
4
1
1
2
0
1
1
1
0
0
0
2
1
0
2
0
0
0
2
2
0
0
2
0
0
0
0
0
1
2
0
0
0
0
1
1
0
0
0
2
0
0
2
0
6
0
2
2
0
0
2
2
0
1
3
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
1
1
2
0
2
0
0
0
0
2
2
0
0
0
0
0
0
2
0
1
2
0
1
0
0
1
0
1
0
0
2
0
0
0
0
0
0
1
0
1
2
2
0
0
0
0
2
0
1
0
0
0
0
1
0
2
2
0
0
0
1
0
2
0
0
2
0
0
0
0
2
2
2
1
2
0
1
0
2
0
0
0
0
1
2
0
0
0
0
2
0
1
0
1
1
1
0
2
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
1
0
0
2
0
1
2
0
0
2
0
2
0
0
1
0
1
0
0
0
0
2
1
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
2
2
7
0
1
0
1
0
0
2
0
2
1
2
2
0
0
0
0
0
0
1
1
0
3
1
0
0
2
0
0
0
2
0
1
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
4
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
1
2
0
0
0
0
0
0
0
2
1
0
0
2
0
0
1
0
0
1
2
1
0
0
2
0
1
0
0
1
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
1
3
2
1
0
1
0
0
0
0
0
0
1
1
1
0
5
1
1
0
0
0
0
1
0
0
0
4
2
0
0
1
4
0
2
0
0
0
0
2
0
2
2
0
0
0
1
2
2
0
2
2
0
0
0
1
2
2
0
0
0
1
0
1
0
0
2
1
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
2
2
0
2
1
0
2
0
2
1
1
0
2
0
1
0
0
1
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
2
0
0
2
2
0
1
0
2
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
2
1
0
0
0
1
0
0
0
1
1
2
0
0
1
0
3
0
1
0
0
0
1
2
0
0
0
0
2
1
1
0
1
2
2
0
1
0
0
0
2
1
1
0
2
2
0
1
0
1
2
0
0
0
0
0
1
0
0
2
2
1
0
1
0
0
1
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
2
1
2
2
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
2
1
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
3
2
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
3
1
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
2
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
4
2
0
1
1
1
1
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
2
0
2
2
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
1
0
0
2
1
0
2
0
0
1
0
0
0
1
0
0
0
1
1
2
2
4
0
0
2
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
2
1
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
2
0
2
2
0
0
0
0
2
2
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
2
1
0
0
0
1
0
2
0
2
0
0
0
1
0
0
1
0
0
2
0
2
0
0
0
2
0
2
0
1
0
0
2
0
0
0
1
0
0
3
0
0
1
0
0
0
0
2
0
2
1
0
1
0
0
0
0
2
0
0
0
4
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
1
0
1
1
1
2
0
1
0
1
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
2
0
0
0
0
1
2
0
1
0
0
0
3
0
0
1
0
0
2
1
2
0
0
3
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
1
2
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
1
0
0
2
0
0
0
2
0
1
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
1
0
1
0
1
1
0
0
2
3
0
0
1
0
0
0
0
0
2
0
0
2
0
0
2
3
0
0
1
0
2
0
0
1
2
0
2
3
0
1
0
0
0
0
0
0
1
0
1
0
1
1
2
1
0
3
0
2
1
1
0
0
0
0
0
0
1
0
1
2
0
0
1
0
0
1
1
1
0
0
0
6
2
2
0
0
0
1
2
0
0
1
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
2
0
0
0
1
0
2
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
1
2
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
3
0
0
0
0
3
0
2
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
1
0
2
2
0
2
0
0
2
0
0
0
0
2
0
3
2
0
0
1
0
2
2
0
2
0
0
1
1
0
0
0
2
2
0
0
0
1
0
2
1
2
0
1
2
2
0
0
2
2
2
0
0
0
0
0
2
0
0
0
2
0
0
1
0
3
0
2
0
1
1
0
2
0
1
1
1
0
0
1
0
0
0
0
0
2
1
2
0
0
1
0
1
0
0
0
1
1
1
0
0
0
1
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
2
1
0
1
0
1
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
1
0
2
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
2
2
2
0
1
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
2
2
0
0
0
0
2
0
2
0
0
2
0
2
0
2
1
1
0
2
0
0
0
0
0
1
0
2
2
0
2
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
3
0
0
2
0
0
2
0
0
0
2
2
0
0
1
0
0
1
0
2
2
0
0
1
0
0
0
0
1
1
2
0
0
0
0
0
0
2
1
0
1
0
2
1
0
1
0
0
1
2
0
0
0
0
2
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
1
0
0
1
1
0
1
1
0
1
3
1
0
2
0
0
0
0
0
0
0
4
0
2
0
0
0
2
0
2
1
0
3
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
2
2
0
2
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
2
0
0
1
0
0
0
1
1
0
4
0
3
0
0
2
0
4
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
4
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
1
0
0
0
0
1
2
0
1
2
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
1
2
2
0
0
0
1
1
1
0
0
2
0
0
0
0
2
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
1
1
1
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
1
0
2
1
0
0
2
0
1
0
1
0
3
2
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
1
0
0
2
2
2
0
2
0
0
0
2
2
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
1
0
0
0
2
2
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
2
0
0
0
0
0
1
0
0
0
1
1
0
0
2
0
2
0
1
0
0
0
0
0
2
0
0
0
2
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
3
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
2
0
0
4
2
0
0
2
0
0
1
0
0
1
0
0
1
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
1
0
1
0
2
0
0
0
1
1
0
1
1
1
1
0
0
2
2
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
1
1
1
1
0
0
0
2
1
0
0
2
2
1
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
2
1
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
1
1
2
0
0
0
0
0
4
0
1
1
0
0
1
0
2
0
0
0
2
2
0
2
2
2
0
2
2
1
3
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
1
1
1
0
0
0
0
1
0
2
0
0
0
2
0
1
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
3
0
2
0
0
2
1
0
2
0
1
1
0
0
1
1
2
0
0
1
0
2
0
2
1
2
8
0
2
1
0
2
0
0
0
8
0
1
0
0
0
0
1
1
2
0
0
0
2
0
0
2
0
1
1
0
0
1
3
0
0
0
0
1
1
1
1
0
0
0
2
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
2
2
1
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
1
2
0
2
1
0
0
2
0
1
0
1
0
4
0
0
2
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
2
2
1
0
2
1
1
0
0
0
0
0
2
0
2
1
0
0
0
1
0
0
0
0
3
2
0
5
2
1
0
0
0
1
0
0
0
1
0
0
0
1
1
2
0
0
2
0
0
0
0
0
1
2
1
0
0
0
1
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
2
1
0
1
0
0
0
0
0
0
0
2
2
0
1
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
2
1
2
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
1
0
0
0
1
0
0
2
1
0
0
0
2
0
0
3
0
0
0
1
2
0
0
0
0
1
1
0
1
0
0
0
1
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
1
1
2
2
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
6
2
0
2
1
0
0
0
0
0
0
0
2
4
0
1
1
1
1
0
0
0
1
0
2
2
1
0
0
0
0
0
0
5
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
3
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
1
0
1
1
1
2
2
0
0
0
1
0
2
1
1
0
2
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
2
1
0
0
0
1
0
0
1
0
3
0
2
0
0
0
0
2
0
0
0
2
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
1
0
0
4
1
0
0
1
0
0
2
2
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
2
0
2
2
0
0
0
1
0
2
2
0
0
0
0
1
1
0
1
1
0
0
0
0
5
0
0
0
0
1
2
0
0
0
0
2
3
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
2
0
1
0
0
2
2
0
2
2
3
0
6
0
0
1
0
0
0
0
0
0
1
1
1
1
0
3
0
0
1
3
0
0
0
2
1
3
2
0
0
0
0
0
0
0
2
0
2
2
0
0
0
1
0
0
0
0
1
0
0
0
1
0
2
0
2
0
0
0
0
0
0
3
0
2
2
0
2
0
0
0
0
0
3
2
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
2
0
0
1
0
0
0
0
0
0
1
0
0
1
1
1
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
2
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
1
2
2
2
0
0
0
1
0
0
0
0
0
2
2
0
0
0
2
1
2
0
1
0
0
1
0
1
2
2
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
2
2
2
0
1
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
2
2
0
1
1
1
0
0
1
0
1
2
0
1
0
0
0
0
1
0
1
2
0
0
0
0
0
1
0
0
0
1
2
0
1
1
0
0
0
0
1
0
1
0
0
0
3
0
0
0
3
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
3
0
1
0
1
0
0
0
0
0
0
0
2
6
2
0
0
0
1
0
0
2
0
0
2
0
0
0
0
1
0
1
0
0
2
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
2
4
0
0
0
1
0
0
0
3
0
1
0
0
0
0
1
4
0
2
1
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
2
1
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
1
2
1
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
3
0
0
4
0
2
0
0
0
1
0
0
2
0
0
0
1
1
0
2
0
0
0
1
0
0
0
0
1
0
1
0
2
0
6
3
2
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
1
2
0
0
0
1
2
0
3
1
0
0
0
0
1
2
2
0
2
2
0
0
2
0
0
0
0
0
5
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
1
0
1
1
2
2
0
0
0
0
1
1
0
1
0
0
0
0
2
0
0
2
0
0
2
1
0
2
0
0
3
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
3
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
1
2
2
2
0
0
1
1
0
0
2
2
1
0
0
0
0
0
0
0
1
2
0
0
0
1
0
1
2
1
3
0
0
0
0
2
3
2
1
3
1
0
2
0
3
2
0
2
0
2
0
2
1
1
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
2
0
0
0
1
0
0
0
2
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
2
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
4
0
0
0
1
1
0
0
0
0
2
0
2
0
0
0
1
0
0
0
1
2
1
0
0
1
1
3
0
0
0
0
0
1
0
1
0
0
2
7
0
0
0
0
0
1
1
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
1
0
0
0
0
1
1
0
2
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
1
2
1
1
0
0
2
0
2
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
1
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
2
1
2
2
0
0
0
2
0
2
1
2
0
2
2
2
0
0
0
0
1
2
1
0
0
1
0
1
0
0
1
2
0
0
0
0
1
1
1
0
0
4
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
3
0
0
0
0
2
0
0
2
0
0
1
2
5
0
0
0
5
1
0
0
2
0
0
2
0
0
0
0
0
1
1
0
1
0
0
0
0
0
2
0
0
2
2
0
2
0
0
0
1
0
2
0
0
0
1
3
0
0
0
0
0
0
1
0
2
0
1
0
0
0
2
2
2
0
2
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
1
0
2
2
0
2
1
0
0
0
1
1
1
0
0
0
0
0
1
0
1
0
0
0
1
1
4
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
2
0
0
0
3
2
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
2
2
1
2
0
0
0
0
0
0
0
0
1
3
0
2
3
0
0
0
0
0
2
2
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
2
1
0
1
0
0
0
0
4
2
0
0
0
0
0
2
0
1
0
3
0
0
1
0
0
0
1
1
1
2
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
3
1
2
0
1
2
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
3
0
1
0
2
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
4
0
0
0
0
2
0
1
1
2
1
1
0
0
0
2
0
0
2
0
0
0
0
2
0
0
2
0
1
0
0
0
2
0
0
1
0
1
0
2
0
0
0
0
0
0
2
1
2
0
0
1
0
0
0
0
2
2
0
1
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
1
1
0
1
0
0
0
0
1
2
0
0
2
0
2
2
0
0
0
0
0
1
0
0
0
1
2
0
0
2
0
0
0
0
2
3
0
1
0
0
0
2
0
2
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
1
2
0
2
1
0
0
2
1
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
2
2
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
1
2
0
0
0
1
0
0
0
2
0
1
2
0
0
0
2
5
2
0
2
1
2
0
1
0
0
3
0
0
1
2
1
0
0
0
0
1
2
0
2
0
0
0
1
0
0
0
1
0
2
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
2
1
0
0
1
2
0
0
0
1
1
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
7
0
0
0
1
0
1
0
0
1
0
2
1
1
0
2
0
2
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
2
0
0
2
0
0
2
0
1
0
0
0
0
3
0
0
2
0
0
2
0
2
0
3
2
3
1
0
0
0
0
2
1
0
2
1
0
0
2
2
2
2
0
0
0
0
0
2
0
2
0
0
0
3
0
0
1
0
0
2
1
0
3
2
0
0
1
2
1
4
2
0
3
0
1
0
0
0
0
0
1
1
0
2
0
0
3
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
2
0
3
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
2
2
2
1
0
1
0
0
2
0
0
0
2
0
0
0
2
2
0
0
1
0
2
0
1
0
0
0
0
0
0
1
0
1
2
2
1
1
0
0
0
0
0
0
1
2
2
1
3
0
1
0
1
0
2
0
0
0
0
2
5
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
2
0
3
4
2
2
0
1
2
1
0
0
0
0
0
0
0
0
0
0
2
1
1
0
2
1
0
1
0
2
0
0
2
2
1
1
0
2
0
0
0
0
3
0
0
3
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
1
0
2
0
1
0
2
0
0
1
1
0
0
2
2
1
0
0
0
0
0
0
2
1
0
2
0
0
2
2
2
0
1
0
0
1
2
0
2
0
0
0
0
0
0
0
1
0
2
0
0
1
1
0
0
1
1
0
0
0
0
1
2
0
0
0
0
0
0
1
1
0
0
4
0
0
1
0
0
0
0
0
1
1
0
2
2
2
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
1
1
0
1
2
1
1
0
1
0
1
2
1
0
0
2
1
0
1
0
0
0
0
2
0
2
0
0
2
0
0
0
0
1
1
0
2
0
0
0
1
0
0
0
0
0
0
1
3
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
1
2
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
2
0
1
0
0
0
0
1
0
0
2
0
2
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
3
2
1
0
2
0
0
0
1
0
0
0
0
2
0
0
2
1
0
0
0
0
0
2
2
0
2
0
0
2
2
1
0
0
1
2
0
0
2
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
1
0
0
0
2
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
2
1
0
0
1
0
0
0
0
0
0
1
1
1
1
0
1
0
2
2
0
0
0
1
2
0
0
0
1
0
0
2
0
2
0
1
0
0
0
2
2
0
1
1
1
0
1
0
0
0
1
0
2
0
0
1
0
1
2
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
1
0
0
0
2
1
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
2
1
0
0
2
3
3
1
0
3
0
0
3
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
2
0
0
0
0
1
0
2
0
0
0
0
0
0
2
1
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
3
0
0
1
2
0
0
2
0
0
0
1
0
1
2
1
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
1
0
3
0
0
0
0
2
1
0
0
0
0
0
0
2
1
1
0
0
2
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
1
1
2
0
1
0
0
2
2
0
0
2
0
2
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
2
0
0
2
1
0
2
2
0
0
1
0
6
0
0
0
0
0
3
0
2
5
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
3
1
2
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
1
0
0
2
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
1
0
1
1
0
1
0
0
2
3
0
0
0
0
0
1
0
0
1
2
0
2
0
0
0
2
0
0
2
0
0
1
0
1
1
1
0
1
0
0
2
3
0
0
0
0
0
0
1
1
2
0
2
0
0
1
2
0
2
0
2
0
1
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
4
0
0
1
2
1
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
1
0
0
1
0
0
4
0
0
1
0
1
0
0
0
2
1
0
1
0
0
0
0
0
2
2
0
3
2
0
2
0
0
0
1
0
3
1
0
1
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
1
0
0
0
3
0
2
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
1
1
1
0
1
2
1
0
0
3
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
1
0
0
0
0
3
0
0
0
1
3
0
0
2
2
0
0
1
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
2
0
2
0
0
0
0
1
2
1
0
0
0
0
1
1
0
2
0
0
0
2
0
0
1
0
0
2
0
1
0
1
0
2
0
3
0
2
2
0
0
0
1
2
0
0
0
1
2
0
2
0
0
0
3
0
2
0
2
0
0
0
0
0
0
1
1
0
1
0
0
3
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
2
1
4
0
1
0
0
0
2
0
0
0
0
0
0
2
1
0
3
0
1
2
2
0
2
2
0
0
0
0
0
2
0
2
2
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
2
3
0
1
0
2
0
1
0
2
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
2
2
0
0
3
0
0
0
0
0
1
2
1
0
0
0
2
2
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
2
3
0
0
0
0
0
1
0
1
0
2
0
0
0
1
1
0
0
2
0
1
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
1
1
2
0
0
0
1
0
0
1
1
0
2
0
0
0
0
0
1
1
1
0
0
2
1
0
1
0
0
0
0
2
0
0
0
0
2
0
3
0
0
0
0
2
0
0
1
2
1
0
0
0
2
2
0
0
0
0
0
3
1
0
2
1
1
0
0
0
0
2
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
2
2
1
1
0
0
0
2
1
0
0
0
1
2
0
1
2
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
2
1
1
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
2
2
0
0
1
0
1
0
1
1
2
1
0
0
0
3
0
0
0
0
2
0
2
0
0
0
0
0
1
0
1
0
0
0
0
2
1
0
7
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
2
0
0
2
1
3
0
0
0
0
0
0
1
0
2
0
1
2
0
1
1
0
0
0
0
0
0
0
0
0
9
0
0
0
2
1
1
3
0
2
0
2
1
1
0
0
0
0
0
0
1
0
0
0
0
5
0
0
0
0
0
2
0
0
0
1
0
1
0
2
0
1
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
7
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
3
1
0
2
0
2
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
2
0
0
0
3
1
0
0
0
1
2
1
0
0
0
0
0
1
2
0
2
1
1
0
1
0
0
0
0
2
1
0
1
1
0
2
3
2
0
1
0
0
1
0
0
1
1
0
1
1
2
2
1
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
2
0
0
0
0
2
0
1
0
2
0
0
0
0
0
1
2
2
1
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
3
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
2
0
0
1
2
0
0
1
0
1
0
0
0
2
0
2
0
1
2
2
0
0
0
1
0
0
0
3
0
0
0
1
0
0
0
0
0
0
3
0
2
1
0
1
2
0
0
1
0
1
4
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
1
0
0
0
0
0
1
2
0
1
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
2
2
0
0
0
0
0
0
2
0
1
0
0
2
2
0
1
1
1
0
0
1
0
0
0
1
0
0
0
1
0
2
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
2
1
1
0
0
0
0
2
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
2
2
0
2
0
0
0
2
1
0
0
0
0
0
0
1
1
0
1
1
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
3
0
1
0
0
0
0
1
0
0
0
0
3
0
0
0
3
0
2
2
2
0
2
2
0
2
0
0
1
0
0
1
0
0
2
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
2
2
0
1
0
1
0
0
1
1
0
2
1
0
0
0
1
0
0
0
1
2
0
0
2
0
0
0
2
0
0
1
2
2
0
1
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
1
1
3
0
1
0
0
4
1
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
1
0
2
0
1
2
1
2
0
0
0
0
0
2
2
0
0
0
0
1
5
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
1
1
1
0
2
0
0
2
5
0
0
0
0
2
1
0
1
0
2
0
0
0
0
2
0
1
2
1
0
0
3
0
0
0
2
1
0
0
2
0
0
0
0
1
0
0
2
0
2
0
2
1
0
0
0
0
0
3
3
2
0
0
0
0
0
0
0
0
1
0
1
1
0
2
0
1
2
0
1
1
0
0
2
1
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
2
0
0
1
0
0
1
1
0
0
1
0
0
1
2
0
0
0
1
0
1
1
0
0
2
0
2
0
0
0
2
0
1
1
2
1
0
1
0
0
0
2
2
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
1
1
1
0
2
0
1
0
2
0
0
0
0
1
0
1
4
0
0
1
0
1
0
1
0
0
0
0
0
1
2
1
1
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
2
0
0
0
1
0
0
0
0
1
0
0
3
0
1
2
0
3
0
1
2
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
2
1
0
2
0
0
0
1
1
0
0
1
1
0
2
0
0
0
3
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
4
0
0
0
0
2
0
1
0
2
0
0
0
1
2
1
0
1
0
2
0
0
0
0
0
0
2
0
1
0
0
1
1
1
0
1
0
0
1
0
1
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
1
2
2
0
0
1
2
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
1
0
1
0
0
0
2
0
0
2
1
0
0
2
1
0
1
0
1
0
1
0
0
0
2
0
0
1
3
0
1
0
0
0
8
1
0
0
2
1
2
2
0
0
0
0
0
0
0
0
0
0
1
0
1
2
2
2
0
0
0
0
0
1
0
3
1
0
0
2
0
0
1
0
2
0
0
1
2
0
1
0
2
0
0
0
2
0
0
0
0
0
1
2
0
0
1
1
1
1
0
0
0
1
1
0
0
0
2
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
2
2
2
0
1
1
2
0
0
0
0
0
1
0
0
0
1
1
2
0
0
2
0
1
0
0
0
1
0
2
0
2
0
1
2
0
6
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
1
0
0
0
3
0
0
0
1
2
1
0
0
1
1
0
2
0
2
0
0
2
0
0
0
2
0
3
0
0
0
2
1
2
0
0
0
1
2
3
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
1
2
2
1
0
0
2
1
0
0
0
1
0
0
0
3
1
0
0
0
0
2
2
0
0
0
1
0
0
0
0
1
0
0
4
0
0
0
1
0
0
0
2
1
0
0
2
1
0
1
1
1
0
0
0
0
0
0
2
1
0
0
2
2
0
0
0
0
2
2
0
0
0
0
0
0
3
0
1
0
0
1
0
0
0
2
0
1
0
1
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
2
0
1
1
1
0
0
0
1
0
0
0
1
1
0
0
4
0
0
1
0
0
0
2
0
1
1
1
0
0
0
2
0
2
0
2
1
0
0
0
1
0
0
1
3
2
0
0
0
1
0
0
2
2
0
0
0
2
0
0
0
1
0
0
0
0
1
0
4
1
0
0
0
0
1
0
0
0
0
0
4
0
0
0
1
1
2
0
1
2
0
0
0
0
2
0
1
0
0
3
0
0
1
0
0
0
1
0
1
1
0
0
2
0
0
3
2
1
0
0
2
0
2
1
0
0
0
0
0
0
2
0
0
1
0
0
0
1
2
0
0
0
0
0
0
2
0
8
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
3
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
2
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
1
1
0
1
0
2
2
0
2
0
0
0
2
0
0
1
0
1
1
2
0
0
0
1
2
2
0
0
0
1
1
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
2
0
0
0
0
0
0
14
2
0
0
0
0
0
4
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
1
0
0
0
3
0
0
2
0
0
1
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
3
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
1
0
1
1
0
0
2
0
0
0
0
1
0
0
1
2
0
0
1
0
0
0
0
0
1
1
2
1
1
0
0
1
4
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
1
1
1
1
2
2
2
1
3
1
0
0
2
0
1
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
2
11
0
0
0
0
2
2
0
0
0
4
1
3
0
0
0
0
0
0
0
2
0
2
1
0
0
0
1
0
1
1
0
1
0
1
0
0
3
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
1
0
0
0
3
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
4
0
0
0
1
2
0
0
1
0
2
0
2
2
2
2
0
0
1
0
0
6
1
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
2
0
1
1
2
0
0
0
1
0
0
1
0
2
0
0
0
1
0
0
2
0
1
0
1
0
0
0
0
1
0
1
1
0
1
1
0
4
0
0
1
0
2
0
1
0
1
0
0
2
0
0
0
0
0
2
1
0
2
0
1
1
0
0
2
0
2
0
0
2
6
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
1
0
0
6
0
1
0
0
0
2
2
0
0
2
1
0
0
0
0
0
0
0
0
1
1
1
3
1
0
0
2
1
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
2
0
2
0
1
1
0
0
2
0
0
0
1
0
0
0
0
0
1
3
1
4
0
0
0
0
1
0
1
0
2
0
0
0
2
1
0
0
0
2
0
0
0
1
0
1
0
0
1
1
1
1
0
1
0
1
0
1
1
0
0
0
0
1
0
1
0
0
1
2
3
0
3
2
0
7
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
2
1
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
2
0
0
2
1
0
0
1
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
1
1
0
2
1
0
0
0
0
0
2
0
0
0
0
1
2
0
1
0
1
2
0
1
0
1
0
0
0
1
0
0
1
0
0
0
2
2
0
3
0
0
0
0
1
2
0
2
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
1
0
2
0
0
3
0
0
0
0
1
0
0
0
1
0
3
1
1
2
2
0
0
2
0
0
0
0
2
0
1
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
1
2
0
1
2
0
0
0
1
0
1
2
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
2
0
0
2
2
3
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
1
2
0
0
0
2
1
1
0
1
1
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
2
0
1
2
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
2
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
3
0
2
1
1
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
2
0
1
1
0
0
1
1
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
3
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
1
1
2
0
2
4
1
0
0
0
0
0
0
0
0
2
0
1
0
1
2
0
0
0
2
0
2
2
0
1
1
2
0
2
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
1
1
1
1
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
4
0
0
1
1
0
0
0
0
2
1
0
0
2
0
0
0
2
0
2
0
0
0
1
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
1
0
0
2
2
0
0
2
1
0
0
0
1
2
0
1
0
0
0
0
0
1
0
0
1
0
1
0
1
1
0
0
2
2
0
3
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
2
2
0
0
1
3
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
1
1
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
2
0
2
0
1
2
0
2
0
1
0
2
0
0
4
0
1
0
0
0
0
0
1
2
0
0
0
1
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
1
0
1
1
0
0
0
0
0
0
1
2
0
0
4
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
3
0
0
0
4
0
0
2
1
0
0
0
2
0
2
0
0
0
0
1
0
1
2
1
0
0
2
2
2
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
2
3
0
2
0
0
2
2
0
2
0
0
0
0
0
2
2
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
1
0
1
3
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
2
0
0
2
3
1
0
0
1
0
1
0
0
0
0
0
0
2
0
1
1
2
0
0
0
0
0
1
1
0
2
0
0
2
0
0
0
0
0
2
0
0
1
0
3
1
0
0
0
0
0
2
2
0
0
0
1
1
0
0
1
1
1
1
0
1
0
0
3
0
0
2
2
0
0
2
2
2
1
1
2
0
0
0
1
1
1
0
1
0
0
0
0
2
1
0
0
0
2
2
0
1
0
3
0
0
1
0
2
0
0
4
2
0
0
0
0
1
0
0
0
0
0
3
0
2
0
0
0
1
0
2
0
1
0
0
2
1
1
0
0
0
0
2
4
0
3
2
0
0
0
0
2
0
4
0
0
1
0
0
2
0
1
0
2
1
0
0
0
0
0
0
1
0
0
0
2
0
1
2
2
0
0
0
0
1
2
0
0
2
0
0
3
0
1
0
0
1
0
0
0
0
0
2
1
0
2
0
0
0
2
1
0
0
0
0
0
1
2
1
2
3
4
2
1
0
0
1
0
2
0
0
2
1
1
0
1
0
0
0
0
0
1
0
0
2
0
1
2
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
4
0
1
0
2
2
0
3
2
0
0
0
2
2
0
0
0
2
2
0
0
0
0
0
3
0
2
2
5
0
0
0
1
0
1
0
0
0
1
0
2
0
1
0
0
0
2
0
2
0
2
0
1
1
0
2
0
0
3
0
0
0
0
0
1
0
1
0
0
0
0
0
1
2
2
1
0
0
0
0
3
0
0
0
1
2
2
0
0
1
1
2
0
0
0
2
0
1
1
0
1
0
1
2
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
4
1
0
0
0
1
0
1
0
1
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
1
3
0
0
0
0
2
0
3
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
1
2
1
0
0
0
1
2
0
1
0
1
0
1
1
0
1
0
0
2
1
0
0
2
1
2
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
1
0
0
2
1
0
4
1
2
0
1
2
0
0
0
3
0
2
0
2
0
0
0
1
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
2
1
0
1
0
1
1
1
0
0
0
2
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
2
1
0
2
1
0
0
0
0
0
4
1
0
1
1
2
1
2
0
2
2
0
0
0
0
1
0
0
0
1
2
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
1
0
1
1
1
0
2
1
1
1
0
2
2
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
1
3
0
0
1
2
1
1
0
0
2
0
1
3
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
1
2
0
0
0
0
0
0
2
1
0
0
0
2
0
0
2
0
0
0
0
2
0
2
2
4
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
2
1
0
0
2
0
4
0
0
0
0
0
2
1
0
1
1
0
3
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
2
0
0
0
1
1
0
2
0
0
0
0
0
0
3
0
1
0
2
0
2
0
2
0
0
1
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
1
0
2
2
1
0
0
0
0
2
1
2
0
1
0
0
0
0
1
1
0
1
0
2
0
0
2
0
0
0
1
2
0
2
1
0
0
0
0
0
1
0
0
2
1
0
2
0
1
0
0
1
2
0
2
0
0
0
0
0
1
1
0
0
2
0
0
0
3
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
2
2
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
1
2
0
0
0
1
3
0
0
0
0
0
0
0
0
2
0
3
0
3
1
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
2
0
2
1
0
1
0
0
1
0
2
2
0
1
0
2
0
0
0
0
0
0
1
0
0
2
1
0
2
0
0
2
2
0
2
0
0
0
1
0
0
1
3
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
1
0
2
0
1
0
1
2
0
0
1
0
0
0
0
0
0
0
1
0
0
1
3
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
1
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
1
2
2
1
0
0
1
0
0
2
0
0
1
0
0
1
1
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
2
0
2
0
2
0
1
1
1
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
1
1
1
0
0
1
0
0
0
1
1
1
0
3
0
0
0
3
0
0
1
1
1
2
1
2
0
2
0
2
0
0
2
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
1
1
0
0
0
0
0
1
2
0
2
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
2
0
2
0
0
1
2
2
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
3
0
0
0
2
1
0
0
0
0
2
0
1
0
0
2
2
0
0
3
0
0
2
0
2
0
0
1
2
0
0
0
0
0
3
2
0
0
0
1
0
0
0
0
1
0
1
2
0
0
1
1
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
1
0
0
2
0
0
1
0
0
2
1
0
0
0
0
0
0
3
2
0
0
0
0
1
0
0
0
0
0
0
1
1
0
3
2
2
0
0
0
2
0
0
2
0
2
2
0
0
0
0
0
0
1
0
2
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
2
1
0
1
0
2
1
0
0
2
0
0
2
0
0
0
0
0
0
4
0
2
2
0
2
0
0
2
0
2
2
0
0
1
0
2
0
1
0
2
0
2
0
0
0
0
1
1
2
2
0
0
2
0
2
2
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
2
2
0
0
0
0
0
0
2
2
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
2
1
0
2
0
0
1
1
0
0
0
2
1
0
0
0
0
1
0
3
0
0
2
0
2
1
1
0
1
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
1
0
1
0
0
1
1
0
0
0
0
0
1
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
1
0
1
0
4
0
1
0
5
0
0
0
1
0
1
0
2
0
2
0
1
0
1
1
0
0
0
1
0
1
1
2
0
0
0
1
1
0
0
1
0
0
2
0
2
0
0
0
1
0
2
0
1
2
0
0
0
0
0
3
0
0
1
1
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
1
2
1
0
0
0
0
1
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
1
2
2
0
1
0
2
0
1
2
2
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
2
0
0
2
1
1
0
3
0
0
1
2
0
0
2
0
1
0
2
1
0
2
0
0
2
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
1
1
0
2
0
0
0
0
0
1
1
0
1
0
2
0
1
1
0
0
0
2
0
1
0
2
0
1
0
0
0
1
1
2
0
1
0
0
0
0
1
0
0
0
1
2
0
0
0
1
2
1
2
0
1
0
0
1
0
0
0
0
0
2
1
2
0
0
0
2
2
0
0
0
0
0
2
2
0
2
0
5
1
0
2
1
1
2
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
2
0
2
0
1
0
0
0
0
0
2
2
2
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
5
2
0
1
0
1
0
0
0
1
0
0
0
0
0
2
0
0
1
2
0
1
1
1
0
2
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
2
1
1
1
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
2
1
1
2
0
0
0
1
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
1
1
0
0
1
1
5
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
1
0
2
0
1
0
0
1
0
0
1
0
0
0
0
0
2
2
2
0
2
0
0
2
0
0
0
2
0
0
3
0
0
2
0
0
0
0
2
0
1
1
0
0
1
2
0
0
1
0
0
0
0
0
1
2
2
1
1
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
2
1
0
0
0
0
1
0
0
0
1
1
0
2
2
2
2
0
2
1
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
2
2
0
2
5
1
0
1
1
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
1
2
1
0
1
2
0
0
0
1
0
0
2
0
2
2
1
1
0
4
0
1
0
0
0
0
0
0
2
0
0
0
1
11
1
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
1
0
3
2
0
1
0
0
0
4
0
1
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
1
1
2
2
1
2
0
2
4
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
1
2
0
0
0
3
0
0
0
0
0
0
0
0
0
2
1
2
0
1
0
2
0
1
0
0
0
1
0
1
2
0
0
0
0
2
1
0
0
1
0
1
0
0
0
0
0
0
0
1
1
1
0
2
0
2
2
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
2
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
2
0
0
1
2
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
1
2
1
2
1
2
0
0
0
1
0
0
0
2
0
2
0
0
1
0
1
0
2
1
2
0
0
0
0
0
0
0
2
0
1
2
0
0
0
2
0
0
0
2
1
0
2
1
0
1
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
2
0
2
0
0
1
0
2
2
2
0
0
0
0
0
0
0
3
0
2
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
3
0
0
0
0
0
0
3
0
0
1
3
1
0
0
1
0
0
2
0
1
0
0
2
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
2
0
0
2
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
1
0
3
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
1
1
0
0
0
2
1
0
0
0
1
0
1
0
2
0
2
0
0
0
1
0
1
2
0
0
0
1
0
1
0
0
0
0
2
2
2
0
0
0
0
2
1
0
1
2
0
0
0
1
0
0
0
0
0
2
2
0
2
0
0
1
0
2
2
0
2
1
0
0
0
0
0
1
0
2
0
2
0
0
1
0
1
2
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
2
1
2
1
0
2
2
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
3
0
0
0
0
0
0
1
1
1
0
0
0
3
2
0
0
0
0
1
0
0
1
0
0
0
2
0
1
0
2
0
0
1
0
2
0
0
0
2
2
0
0
0
0
0
0
2
0
0
1
0
1
0
0
1
2
1
1
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
1
0
0
0
2
2
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
7
0
2
2
0
0
0
0
1
0
2
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
1
0
2
2
0
1
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
2
0
0
1
1
2
0
0
0
0
0
2
1
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
2
3
0
2
0
0
1
0
0
0
2
0
2
0
0
0
0
2
1
2
0
2
0
1
0
1
2
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
4
1
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
2
2
0
0
0
0
0
1
0
0
0
0
0
3
0
2
0
0
0
1
0
2
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
2
2
2
0
0
0
2
0
0
0
2
0
0
0
1
1
1
0
1
0
1
3
0
0
2
0
2
2
0
1
0
0
2
0
1
1
2
0
1
0
0
0
0
1
0
0
2
0
0
1
1
0
1
1
2
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
2
1
2
2
0
1
0
1
0
3
0
0
2
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
1
1
0
0
0
1
3
0
0
1
0
2
0
2
2
0
0
0
0
2
0
0
2
3
1
0
0
0
1
1
0
0
0
1
0
0
0
2
0
1
0
2
0
2
0
1
1
0
4
1
2
0
0
1
2
2
1
3
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
1
1
2
0
0
1
0
1
1
2
0
1
0
0
1
2
0
0
1
2
1
2
0
0
0
0
0
6
2
1
0
0
0
0
0
2
0
2
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
1
2
0
1
1
0
1
0
0
1
1
1
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
3
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
2
2
0
2
0
0
1
2
0
2
2
0
2
0
1
0
0
2
0
1
0
1
1
0
0
2
0
0
2
2
0
0
2
1
0
1
0
0
0
0
0
0
1
1
1
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
2
1
0
2
0
1
0
0
0
0
0
0
2
0
0
3
4
2
3
0
0
0
0
2
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
1
0
2
0
0
2
1
2
2
1
0
0
0
3
0
2
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
3
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
2
0
1
0
2
2
0
0
1
0
0
1
0
1
0
1
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
7
1
1
0
0
1
0
0
1
1
0
0
0
1
0
0
1
0
2
0
0
2
0
0
0
0
0
2
1
1
0
0
1
0
2
1
0
0
2
0
4
0
0
1
0
0
1
0
0
2
2
0
0
2
0
1
0
1
3
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
2
0
2
0
0
0
3
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
2
2
0
2
0
0
0
2
0
0
0
1
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
1
1
2
0
0
0
1
1
0
2
0
0
0
0
0
0
0
2
0
0
0
1
2
0
1
0
0
0
0
1
1
2
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
2
0
1
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
1
2
0
0
2
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
2
1
0
2
0
0
0
0
2
0
1
0
3
2
1
0
0
0
0
0
0
0
2
1
0
2
1
0
0
0
0
2
2
0
2
2
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
1
6
1
0
0
0
2
0
2
0
2
0
0
0
0
0
0
1
1
2
2
0
1
2
0
0
0
1
0
2
0
1
0
0
0
0
1
0
0
0
0
0
2
0
4
0
0
2
1
1
0
0
0
1
1
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
3
2
0
0
1
0
0
2
2
1
0
1
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
1
1
0
0
0
2
2
2
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
1
2
1
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
1
0
2
3
2
0
0
0
0
0
0
2
1
1
0
0
0
1
0
2
0
1
0
0
1
2
0
0
2
0
0
0
0
0
0
3
0
0
1
0
0
0
0
2
1
1
2
0
2
1
1
2
0
0
0
2
0
1
0
0
1
0
0
2
0
1
0
0
0
0
1
1
0
2
0
1
0
0
0
1
0
1
0
0
0
0
2
0
0
2
0
0
0
2
2
0
0
2
1
2
1
0
2
0
0
0
2
3
2
0
2
0
2
0
1
0
0
1
0
0
0
1
1
0
1
0
0
0
2
0
0
1
2
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
1
1
2
2
0
0
0
0
0
3
2
0
0
0
0
0
1
0
1
0
0
0
0
0
2
2
3
3
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
2
0
0
0
0
0
5
0
0
0
2
0
0
0
0
1
2
0
0
0
0
2
0
0
2
2
0
0
0
2
0
1
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
1
2
0
2
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
5
1
0
2
1
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
10
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
3
2
1
0
3
0
0
0
2
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
1
1
0
0
1
0
2
0
0
1
0
0
0
2
1
0
1
1
1
0
0
3
0
0
0
0
0
1
1
0
0
0
1
0
0
1
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
1
3
0
2
0
0
2
2
0
2
0
1
0
0
1
1
0
0
1
0
2
0
0
0
3
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
1
1
2
1
2
2
2
0
0
3
0
0
0
2
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
2
0
0
0
0
2
2
0
2
2
1
0
0
0
0
2
1
3
0
0
2
0
1
2
1
0
0
0
1
0
1
0
0
0
1
2
2
0
0
1
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
2
3
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
2
0
1
0
8
0
0
0
1
2
0
2
1
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
2
1
1
1
0
1
2
0
0
2
0
0
1
1
0
0
0
1
0
2
0
2
0
1
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
5
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
1
0
1
1
0
2
0
0
0
0
0
1
0
1
1
1
2
0
1
0
1
0
0
2
0
2
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
2
0
0
0
0
0
1
1
0
3
0
0
0
1
2
0
0
0
0
0
0
2
0
1
0
0
1
0
1
1
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
1
2
2
0
0
2
0
1
0
3
0
2
0
2
0
0
1
2
0
0
0
2
0
0
0
2
0
1
2
0
0
1
0
0
1
0
0
1
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
6
0
0
0
0
1
0
0
1
0
0
0
0
1
0
3
2
1
0
2
0
2
1
0
0
2
0
0
1
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
1
0
0
0
0
0
2
0
0
2
1
0
2
0
0
0
3
1
0
0
1
0
4
0
0
0
1
0
0
2
0
0
3
0
0
1
0
3
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
2
2
0
0
2
0
0
0
0
2
0
2
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
1
0
0
0
1
0
2
1
0
0
0
0
0
0
0
2
2
2
3
1
0
2
0
0
0
0
1
0
0
2
0
0
1
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
1
0
1
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
1
0
1
1
0
2
0
4
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
1
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
2
0
0
1
1
2
0
0
1
3
0
0
0
2
0
0
0
1
0
0
0
2
0
1
1
0
0
0
1
3
0
0
1
0
1
0
0
0
0
2
2
2
1
0
0
1
0
0
0
0
6
1
2
0
1
0
0
1
0
0
0
2
2
1
0
0
0
1
0
2
0
0
2
2
0
3
2
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
1
3
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
1
1
0
0
0
1
2
2
0
0
0
2
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
1
0
0
0
0
2
1
2
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
1
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
3
0
2
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
1
0
2
1
0
0
0
0
3
0
1
2
0
0
0
0
2
0
0
0
2
0
0
0
1
1
0
0
2
0
2
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
1
6
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
2
2
0
0
0
0
0
2
1
1
0
2
0
2
1
0
2
0
2
0
0
0
2
0
0
0
0
1
0
0
2
1
0
0
2
0
2
1
2
0
0
0
0
0
1
0
0
1
2
0
0
0
0
3
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
2
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
1
0
0
2
0
2
0
0
0
1
1
0
0
2
0
0
0
2
2
0
0
2
1
0
1
0
0
1
0
0
0
0
0
0
0
2
1
0
1
0
4
2
2
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
2
1
0
0
0
0
0
2
3
1
1
0
0
2
1
1
0
0
0
0
0
1
0
1
2
0
1
0
1
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
1
2
0
2
0
0
0
2
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
2
0
1
2
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
2
2
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
2
0
0
1
2
1
0
2
1
0
1
0
2
3
3
0
1
1
0
1
1
0
2
0
0
1
0
2
0
0
1
1
0
1
1
0
0
0
1
1
0
1
1
1
0
0
0
1
0
0
0
3
0
1
2
0
0
2
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
1
2
1
0
0
1
0
1
2
0
0
0
0
0
2
0
2
1
0
0
2
0
0
0
2
1
0
0
2
0
0
1
2
0
0
0
0
2
1
1
0
0
2
0
0
0
2
0
2
0
0
0
0
5
0
2
0
0
0
1
2
0
2
0
0
3
0
3
1
0
0
1
0
1
1
0
0
3
0
0
4
2
0
1
0
0
1
0
0
0
0
0
0
2
0
0
1
0
2
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
3
0
2
2
0
0
0
1
0
1
0
1
1
0
0
0
1
0
2
3
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
1
0
0
0
1
3
0
0
2
0
0
0
0
1
2
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
1
0
0
0
0
1
2
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
2
2
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
4
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
2
0
2
0
2
2
2
2
1
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
4
0
0
2
0
0
1
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
1
0
0
0
0
0
0
0
0
2
0
2
0
1
2
0
2
0
0
0
0
0
1
0
1
0
0
0
2
0
2
1
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
1
0
0
2
0
2
0
0
0
1
0
1
1
1
0
2
1
1
0
0
0
0
0
0
0
1
0
2
1
2
0
2
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
1
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
1
1
2
0
0
0
1
0
3
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
1
1
0
1
0
0
0
0
0
1
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
2
3
0
0
3
0
0
2
0
1
0
0
1
0
0
0
1
1
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
3
0
0
2
1
1
1
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
2
0
0
2
0
0
0
0
0
1
1
0
1
0
1
0
0
0
2
0
1
0
0
0
4
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
1
1
1
0
2
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
1
1
0
1
0
4
1
0
0
0
0
0
2
2
2
0
2
0
2
2
4
0
2
2
2
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
3
0
0
0
1
3
0
1
0
2
0
2
1
0
0
1
1
2
0
0
2
2
1
1
0
2
0
1
0
0
0
0
2
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
2
0
1
0
0
0
2
2
0
0
0
2
3
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
1
0
0
0
2
2
0
1
2
1
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
2
0
0
0
1
1
0
1
0
0
2
0
0
1
1
0
2
0
0
1
0
0
0
0
1
1
2
0
0
1
3
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
5
0
1
0
0
0
0
0
2
2
2
0
0
0
2
1
0
0
0
2
0
1
3
0
0
0
2
0
2
0
2
0
0
0
1
2
2
0
0
0
0
0
2
1
0
0
0
0
2
2
0
0
1
0
0
0
1
0
0
2
1
0
2
0
0
3
0
0
0
0
0
0
1
0
0
0
2
1
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
2
0
0
2
0
0
0
0
1
0
0
0
1
1
0
0
2
1
2
0
0
1
0
0
0
0
1
0
3
0
0
0
1
1
0
0
3
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
2
0
1
2
0
1
0
0
4
0
0
0
1
0
0
2
0
0
0
2
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
2
0
1
0
0
1
0
2
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
2
2
0
1
0
2
1
0
1
0
1
1
2
0
1
0
1
0
0
2
0
0
0
0
2
0
2
1
1
0
0
2
0
0
3
1
0
0
0
0
0
0
0
0
2
0
0
1
0
3
0
0
1
0
0
1
0
0
2
0
0
0
0
2
1
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
3
0
0
2
0
0
1
0
1
0
1
0
1
2
1
0
1
0
0
0
0
0
0
1
0
3
0
2
1
0
0
0
0
0
0
1
0
0
1
2
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
1
0
2
2
2
0
0
0
0
0
1
0
0
3
0
0
0
2
0
1
0
0
0
2
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
1
2
6
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
2
1
0
1
1
3
0
0
1
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
2
2
0
0
0
0
1
0
0
0
2
1
1
3
1
0
0
0
2
0
0
1
0
0
0
0
0
0
3
0
0
1
0
0
2
2
1
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
1
0
0
3
2
1
2
0
0
0
1
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
1
2
0
0
2
2
2
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
2
0
0
0
1
0
1
0
0
2
1
0
0
0
2
0
1
0
0
0
2
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
2
0
1
1
0
0
1
0
0
0
1
0
1
1
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
2
0
0
0
0
0
1
1
0
0
0
0
1
0
8
0
0
2
0
0
2
0
4
2
0
0
0
2
0
2
0
0
0
0
0
0
1
0
2
2
0
0
0
2
0
0
1
0
0
0
0
0
1
0
2
0
0
0
1
1
2
0
0
2
1
0
2
0
0
6
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
3
2
0
2
0
1
0
1
1
0
2
2
0
1
0
2
0
2
0
0
0
0
2
0
0
0
0
2
0
2
1
1
2
2
2
2
0
0
0
0
1
0
2
1
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
1
2
0
0
0
0
0
2
0
0
0
0
2
1
2
0
0
0
0
0
0
1
0
0
1
2
2
2
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
2
3
2
0
2
0
0
0
1
0
1
1
0
0
0
0
1
0
0
1
0
2
0
2
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
1
2
0
2
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
3
0
1
0
0
1
0
2
0
0
5
0
0
0
0
2
0
0
0
0
1
3
0
2
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
1
3
0
1
2
0
2
2
2
1
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
1
2
0
2
0
0
3
0
1
1
0
1
0
2
0
1
0
4
0
1
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
2
1
0
0
0
1
0
2
1
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
2
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
2
0
0
0
2
2
0
1
0
1
2
0
0
3
0
0
0
0
1
0
0
1
0
1
0
2
1
0
2
1
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
3
0
2
0
0
2
1
4
0
0
1
0
0
0
2
3
2
0
2
0
2
2
0
0
1
0
0
2
1
2
2
0
0
1
0
0
2
1
1
0
2
3
1
0
0
0
1
0
0
0
0
2
0
0
0
1
1
1
0
0
2
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
2
2
0
0
0
0
2
2
0
0
1
0
1
0
0
0
0
2
0
0
2
1
1
1
0
1
1
0
1
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
3
0
0
0
0
0
0
4
1
0
0
1
0
0
1
2
0
0
0
1
2
0
1
0
2
0
2
0
0
0
3
0
0
0
2
0
1
2
0
0
0
0
0
0
0
1
1
3
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
4
0
2
3
2
0
0
0
0
0
0
1
0
3
0
2
0
0
1
2
0
0
2
0
0
0
0
0
1
0
0
0
0
1
2
0
2
2
2
0
0
0
0
3
0
0
0
0
1
1
0
2
0
2
0
0
0
0
1
0
0
2
2
0
0
0
0
1
0
2
0
0
0
0
2
0
0
2
0
0
0
0
2
1
1
0
1
0
2
2
0
0
0
2
0
0
0
1
0
0
1
2
0
0
2
2
2
0
0
0
2
0
0
0
0
3
2
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
2
1
0
1
0
1
2
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
2
1
0
1
0
1
0
1
1
2
2
3
0
2
0
0
1
0
0
1
0
0
0
2
0
2
0
0
1
0
1
0
0
0
4
2
0
0
0
1
0
1
0
0
1
0
0
2
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
3
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
2
2
0
3
0
0
0
0
0
1
0
2
0
2
0
2
1
0
1
0
2
0
0
0
0
1
1
0
2
0
0
2
0
0
0
0
1
1
1
0
0
0
0
0
2
2
1
1
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
1
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
1
0
0
0
1
0
0
2
0
2
0
0
3
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
2
0
0
1
0
2
0
1
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
1
1
1
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
1
0
2
1
1
0
0
1
0
2
0
4
1
2
0
0
2
2
0
0
2
2
1
0
0
0
0
0
1
0
0
0
4
0
1
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
1
2
1
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
2
0
0
0
0
2
1
0
2
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
2
1
0
0
0
2
0
0
1
2
0
0
0
0
0
0
1
5
1
0
0
0
0
0
0
0
0
0
0
9
0
0
2
0
1
1
0
1
0
1
3
2
0
0
0
0
2
0
0
2
1
0
1
0
0
0
2
2
0
1
0
0
2
1
2
0
0
0
2
1
0
2
1
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
4
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
1
0
0
4
1
0
1
0
0
0
1
0
0
0
0
1
2
0
0
0
2
0
2
0
0
0
2
2
0
3
1
0
2
0
0
0
1
2
0
0
1
0
0
0
2
2
2
0
0
2
0
0
2
0
2
2
1
2
1
1
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
1
2
0
0
0
1
0
0
1
0
2
0
2
2
0
1
0
3
2
1
2
0
0
0
0
1
0
0
1
0
2
1
0
0
2
0
2
2
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
3
2
0
0
0
2
0
2
0
2
0
1
0
0
0
0
1
1
0
1
2
1
0
2
2
0
0
3
0
2
0
0
2
0
0
0
2
2
0
0
2
1
0
0
1
1
0
3
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
1
2
0
0
2
2
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
1
0
0
4
0
1
0
1
0
0
0
0
0
0
2
1
1
0
0
1
0
0
0
1
1
0
2
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
1
3
0
1
0
2
0
2
0
0
2
0
1
0
0
3
0
1
2
0
0
3
0
1
0
0
1
1
2
0
0
2
0
0
0
0
2
1
0
0
2
0
0
2
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
2
1
2
0
0
4
0
0
0
2
0
0
2
0
0
0
0
0
0
0
5
2
0
1
3
1
1
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
3
0
0
1
0
2
0
2
2
0
0
3
1
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
1
0
0
3
0
0
0
0
2
0
2
2
0
0
0
0
0
2
0
0
0
3
0
2
0
0
6
0
0
0
2
2
0
0
2
1
0
1
0
0
2
0
2
1
0
0
0
1
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
1
1
0
0
1
1
0
1
0
0
0
1
0
2
2
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
2
0
1
0
1
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
2
2
2
0
2
0
0
0
0
0
0
4
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
3
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
4
1
2
2
2
1
0
0
0
0
0
0
0
0
0
0
4
2
0
0
0
2
0
2
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
2
0
2
0
2
0
0
0
0
2
0
1
0
1
0
1
0
3
0
1
0
0
0
0
0
0
2
1
0
0
1
2
0
1
0
0
0
0
0
1
0
0
0
0
2
1
2
0
0
1
1
1
0
1
1
1
0
0
2
2
0
0
2
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
1
2
0
0
1
0
2
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
1
0
2
0
1
0
2
2
3
0
2
0
1
1
0
0
0
1
2
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
1
0
0
2
0
1
0
2
1
0
0
0
2
0
0
0
0
1
0
0
0
2
1
2
1
1
1
1
0
0
0
0
0
0
0
1
2
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
1
0
4
0
0
0
1
0
0
2
0
0
1
0
2
2
0
2
2
1
0
1
0
0
0
0
2
0
4
0
1
0
0
0
2
0
0
1
0
2
0
0
1
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
2
0
0
2
0
0
0
2
1
0
0
1
1
0
1
0
0
2
0
2
3
0
0
1
0
2
0
1
2
0
1
0
0
1
0
1
0
0
0
2
0
0
0
2
0
0
0
2
0
1
0
2
2
1
0
0
0
0
0
0
1
0
0
0
0
3
2
1
2
1
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
2
2
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
1
0
0
2
0
0
1
2
0
0
0
1
0
0
0
0
2
1
1
0
1
2
0
0
1
0
0
0
1
0
0
0
2
0
0
2
1
2
0
0
0
0
2
0
1
0
1
2
0
3
0
0
3
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
1
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
2
1
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
3
0
2
0
0
0
1
1
1
2
0
0
1
2
0
1
1
0
2
0
0
0
2
0
0
1
0
2
0
0
0
2
1
1
1
0
2
0
2
4
1
1
1
0
0
0
0
2
1
0
0
1
0
1
0
2
1
3
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
2
0
0
3
1
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
4
2
0
0
1
0
2
6
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
1
1
1
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
1
2
0
2
2
0
1
0
2
2
0
1
1
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
2
1
1
0
0
0
1
0
0
2
2
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
2
0
0
1
0
0
0
2
0
0
2
0
0
0
0
2
0
3
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
1
3
0
2
1
2
0
0
2
1
1
1
0
0
2
0
2
2
0
0
2
0
0
2
1
0
1
0
0
0
0
0
1
1
0
1
0
0
0
3
0
2
0
0
2
2
2
0
1
2
2
0
0
1
0
3
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
1
2
0
0
0
1
2
0
1
1
1
0
0
0
0
0
0
1
2
2
2
0
2
0
0
0
2
0
0
0
0
0
0
2
1
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
1
2
0
2
2
2
0
0
0
0
1
2
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
2
0
1
1
0
2
0
2
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
1
1
2
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
1
0
0
0
2
0
0
0
2
0
0
0
1
0
2
0
0
0
0
3
0
0
0
2
0
2
1
0
0
1
0
2
0
1
0
1
0
0
0
0
0
2
0
2
0
3
0
0
0
1
0
0
2
1
1
2
0
0
0
0
1
2
0
0
0
1
3
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
1
2
0
0
0
0
0
1
0
1
1
1
0
0
2
2
0
3
0
0
0
1
0
1
1
1
0
0
2
0
0
2
0
2
2
1
0
0
0
0
0
0
1
1
2
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
1
1
2
0
0
0
0
0
1
1
0
0
1
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
3
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
1
0
1
0
3
1
0
0
0
0
1
2
1
4
2
2
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
2
0
2
1
0
0
0
2
0
2
0
1
2
0
2
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
2
0
0
0
2
0
1
0
1
0
0
3
0
2
0
0
0
1
0
2
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
2
0
2
2
1
2
0
0
0
1
0
2
0
0
1
0
0
0
0
1
0
0
0
0
1
2
2
0
0
2
0
0
3
0
0
0
1
1
0
0
0
0
0
0
1
1
2
0
0
0
1
0
1
2
0
0
0
0
0
0
0
3
2
1
0
0
0
0
0
0
0
0
2
1
0
2
2
0
0
0
2
0
2
1
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
1
0
2
0
1
0
0
0
2
0
0
0
1
1
0
0
0
1
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
1
2
1
0
2
0
0
0
2
2
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
1
1
0
0
2
0
1
0
0
0
0
0
0
0
2
0
1
0
1
0
2
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
2
0
2
2
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
2
1
2
2
0
2
0
2
0
0
2
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
1
2
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
2
0
3
0
0
1
0
0
0
0
0
0
2
0
0
0
1
2
2
0
1
0
2
0
0
0
0
0
1
3
0
0
0
1
0
0
0
0
0
1
1
0
1
0
1
0
0
1
2
1
2
0
0
0
0
0
1
0
1
2
0
0
2
0
0
0
0
2
0
0
0
4
0
0
0
0
1
1
2
2
2
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
1
0
0
1
2
0
0
1
1
0
2
0
0
0
0
0
2
0
0
0
0
2
2
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
2
0
1
3
2
0
0
0
2
1
0
0
0
0
1
0
0
0
2
0
2
1
1
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
3
0
0
3
1
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
1
0
0
0
1
2
0
0
1
1
0
0
0
0
2
0
0
2
0
0
2
1
0
2
0
0
0
2
2
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
1
2
0
2
2
0
2
0
1
0
0
0
0
0
0
2
2
1
1
1
0
0
3
0
0
0
1
0
0
2
1
0
0
1
0
0
0
0
1
3
1
1
1
1
0
0
0
0
0
1
1
1
4
2
0
0
5
0
2
2
0
2
0
1
0
0
0
2
1
0
2
0
3
0
1
1
0
0
0
0
4
0
1
1
1
0
2
0
0
1
1
1
1
2
2
0
0
0
0
2
1
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
1
1
1
1
3
2
0
0
0
0
0
2
0
1
0
4
0
0
0
2
0
0
2
1
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
1
0
1
3
0
0
1
0
0
0
0
1
0
1
1
0
2
0
1
1
4
0
0
0
1
0
0
0
0
0
1
0
0
0
0
3
0
2
2
0
3
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
1
1
1
2
0
0
0
0
0
2
2
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
2
0
2
0
0
1
0
0
1
1
0
1
0
6
0
0
0
1
1
0
0
0
0
1
2
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
2
0
0
0
2
0
0
0
0
1
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
1
1
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
2
2
0
0
0
0
2
3
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
2
0
1
0
0
0
2
1
1
2
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
2
0
2
1
0
2
2
0
2
0
0
0
2
0
1
2
1
2
2
0
0
3
0
0
0
0
0
0
0
2
1
2
3
0
0
0
1
2
0
0
2
0
0
0
0
1
0
0
3
0
0
1
0
0
2
0
0
0
2
0
0
2
0
1
0
1
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
3
0
2
1
0
0
1
5
2
0
1
0
0
0
0
0
0
1
2
0
0
0
2
0
0
2
1
0
0
3
2
0
0
1
0
3
0
0
0
0
1
0
0
4
0
0
0
0
2
0
1
2
0
1
0
0
0
0
0
0
0
0
0
2
1
0
3
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
1
1
1
0
0
0
0
0
2
2
0
1
0
0
2
0
0
0
2
0
0
1
0
2
1
2
1
0
1
0
1
0
1
1
0
0
1
0
1
0
1
0
0
0
0
0
1
2
2
0
0
2
0
0
0
0
4
0
1
1
0
0
0
0
0
0
0
0
0
0
3
2
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
3
0
1
0
0
2
0
0
1
0
0
0
0
1
0
0
1
0
5
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
1
0
1
0
0
1
0
2
0
2
0
0
1
1
0
0
0
2
0
0
1
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
1
2
0
2
1
0
0
1
1
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
1
2
0
1
0
0
0
2
0
4
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
3
0
0
0
2
0
1
0
1
0
0
0
3
0
0
0
2
0
0
2
0
0
2
1
0
0
0
2
0
1
0
0
2
0
0
0
1
2
1
1
0
0
0
0
2
2
0
0
2
0
0
2
0
2
0
1
1
0
0
1
0
0
0
0
2
2
0
0
1
0
1
1
2
0
2
1
2
0
0
1
1
0
0
0
3
1
1
0
0
0
0
0
0
1
2
0
3
2
0
1
0
0
2
2
0
1
0
0
0
0
0
0
2
0
0
2
3
1
0
0
1
0
0
0
2
2
0
1
0
0
0
0
1
0
1
2
0
0
2
0
0
0
2
0
1
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
2
3
2
1
0
0
0
2
1
0
0
0
0
1
0
1
0
0
2
1
6
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
3
0
0
0
0
2
2
2
1
0
0
1
0
0
1
0
2
0
0
0
0
1
2
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
5
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
1
2
0
0
1
0
2
2
0
2
1
2
1
0
0
1
0
3
0
0
0
0
0
1
0
0
2
2
2
0
1
0
1
0
0
0
0
2
0
0
1
1
2
1
0
2
0
1
0
0
0
0
0
2
0
0
2
0
5
2
1
0
0
0
1
0
2
3
0
2
1
1
0
1
0
0
0
1
2
0
0
0
3
0
1
0
0
0
2
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
1
0
2
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
3
1
1
0
0
0
0
0
0
0
1
1
2
0
2
1
0
0
0
2
0
0
0
2
1
1
0
0
0
0
0
2
0
2
2
0
0
0
2
1
0
0
0
0
0
0
0
0
1
2
1
0
1
1
2
1
1
0
1
0
0
0
0
2
0
0
0
1
0
0
2
0
2
1
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
2
0
0
0
2
3
1
1
2
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
1
0
5
0
1
0
0
0
0
0
0
0
2
0
0
2
1
2
0
0
0
0
0
2
0
2
0
2
2
0
1
1
0
0
0
0
0
2
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
2
1
0
0
2
1
0
0
0
2
0
1
4
0
0
0
1
0
3
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
1
0
2
0
1
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
2
2
0
0
2
1
0
0
1
2
2
1
0
0
0
2
3
0
0
0
0
2
2
0
0
1
0
0
0
0
1
0
1
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
2
1
0
1
0
1
0
2
0
0
3
0
1
1
0
0
0
2
0
2
0
0
0
1
0
2
0
1
0
0
2
2
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
2
1
0
0
0
0
0
0
2
2
1
0
0
0
2
0
0
0
0
0
1
2
0
1
0
0
0
0
1
0
2
2
1
1
2
0
1
0
3
0
0
0
2
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
7
0
0
0
1
0
2
0
0
2
0
0
1
3
0
2
0
0
0
0
1
2
0
0
0
0
2
0
2
2
0
0
0
0
0
1
0
0
2
0
0
0
2
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
2
0
2
1
1
0
0
0
0
0
0
2
0
1
2
0
0
1
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
2
1
0
0
3
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
2
0
1
1
0
2
0
1
2
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
1
2
0
2
0
0
1
1
0
0
2
0
0
0
1
0
1
0
1
0
0
0
5
0
0
0
0
1
1
0
2
0
1
2
2
2
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
3
0
2
0
0
3
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
1
4
0
3
1
0
1
0
1
0
1
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
1
0
0
0
4
0
2
0
0
3
0
1
0
2
0
0
0
0
1
7
0
0
0
0
0
1
0
0
2
1
0
0
2
0
1
1
0
0
2
0
0
0
0
2
2
0
0
0
0
1
0
0
2
0
1
0
1
0
0
1
1
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
2
5
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
1
2
0
3
0
0
0
0
1
0
3
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
2
1
1
0
0
1
0
1
0
2
0
0
0
0
1
1
2
1
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
1
0
0
0
3
0
0
0
1
2
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
1
2
2
2
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
2
0
1
0
2
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
2
1
2
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
2
2
1
0
1
0
0
0
0
0
1
1
2
0
0
0
0
2
0
3
2
1
2
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
2
1
1
0
0
0
1
1
0
0
1
0
2
0
2
0
0
2
2
0
0
0
0
2
1
2
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
1
0
0
0
0
1
1
0
0
0
2
1
0
2
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
2
2
1
1
0
1
3
0
2
3
0
2
1
0
2
0
0
0
0
1
0
1
2
0
0
1
0
1
0
0
2
0
0
1
0
3
0
2
1
0
0
0
1
2
0
0
2
0
0
0
1
0
0
0
2
0
1
2
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
2
2
1
2
3
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
3
2
1
0
0
2
2
0
1
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
2
2
2
1
0
0
0
0
0
2
0
0
2
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
2
2
0
0
1
0
2
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
1
0
0
0
1
0
0
0
2
5
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
2
1
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
1
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
3
2
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
2
0
3
0
0
0
2
0
0
2
1
0
0
1
2
0
0
2
1
0
0
0
1
3
0
1
0
0
0
3
1
0
0
0
3
2
0
0
0
0
0
4
0
0
0
0
2
2
0
0
2
0
1
1
0
0
2
0
0
1
0
0
2
0
2
0
0
0
1
0
1
0
0
0
1
0
2
0
0
0
1
3
1
0
0
0
2
0
1
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
1
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
1
0
0
3
0
0
0
0
0
0
1
0
0
2
2
1
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
1
2
4
1
10
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
2
1
2
1
2
2
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
2
0
0
0
2
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
1
0
0
0
0
0
2
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
2
0
1
2
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
2
0
2
0
0
0
0
0
2
3
0
0
0
0
0
2
0
2
0
0
0
1
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
1
1
2
1
2
0
0
0
0
3
0
0
2
0
0
1
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
1
0
0
2
1
0
0
1
0
0
0
0
0
2
0
2
0
0
1
0
1
0
0
0
0
2
0
0
0
0
4
1
0
0
0
2
0
0
1
1
0
0
2
0
0
0
0
1
1
2
0
0
0
2
2
1
0
0
0
0
0
0
2
0
0
0
2
3
4
0
0
1
0
0
1
1
2
0
0
0
2
0
3
0
0
0
0
0
2
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
2
1
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
2
2
0
0
0
2
2
0
0
0
0
2
2
0
0
2
2
0
0
0
1
0
0
0
1
0
1
0
0
0
0
2
0
2
0
0
2
1
0
2
2
0
0
2
0
0
1
0
0
1
0
0
0
0
1
2
3
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
4
2
1
0
0
1
2
1
2
0
0
2
0
0
0
4
1
0
0
2
0
2
0
2
0
0
2
3
0
0
0
1
1
0
0
0
3
0
2
1
1
2
1
0
1
1
0
1
0
0
2
2
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
1
1
2
0
0
1
0
0
2
1
2
0
2
0
1
0
0
0
1
0
0
2
0
0
1
0
0
1
0
4
0
0
0
0
1
1
2
2
2
2
0
0
0
0
0
2
2
0
1
1
0
0
0
0
0
1
3
0
2
1
0
1
0
0
1
0
0
1
0
1
2
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
2
0
0
0
1
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
1
0
0
1
0
0
1
2
0
0
1
0
0
3
1
2
0
0
0
0
0
0
0
2
0
1
0
1
1
1
0
1
0
0
0
0
2
0
2
1
0
1
0
2
0
0
0
2
0
2
0
1
0
0
2
0
2
0
2
0
0
0
0
0
0
1
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
1
0
0
0
1
1
2
0
0
0
0
0
0
0
1
0
0
1
0
0
2
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
1
2
1
0
1
2
1
2
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
6
1
0
0
2
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
2
0
0
1
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
2
1
0
0
1
0
0
2
0
0
0
0
0
2
0
0
2
0
1
2
2
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
1
0
0
2
0
0
2
2
2
0
0
0
0
0
2
0
0
0
2
2
0
2
0
0
1
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
2
2
0
2
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
1
1
0
0
3
1
0
1
0
0
0
1
0
1
0
1
0
2
0
0
0
2
0
0
0
1
1
1
2
1
3
0
0
3
0
2
1
2
0
1
0
0
0
0
0
3
2
0
0
1
0
0
0
0
0
0
0
0
3
1
0
1
1
3
0
1
0
1
0
1
0
1
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
2
0
1
2
0
0
0
0
0
1
1
0
1
0
0
0
0
0
2
0
1
0
1
2
0
0
0
0
1
1
2
2
0
2
2
0
2
0
2
0
0
0
2
2
1
2
0
0
0
1
0
2
2
0
2
0
0
1
2
0
0
1
2
0
0
0
0
0
0
3
0
0
0
0
0
2
1
2
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
2
0
0
2
0
0
3
2
0
0
2
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
6
1
2
0
1
1
1
2
1
1
0
0
2
0
0
0
0
0
0
2
0
2
1
0
0
1
0
3
0
0
0
1
0
0
0
0
1
0
0
0
1
1
1
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
1
0
0
0
0
0
0
3
0
2
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
2
0
0
1
2
1
1
0
0
0
0
0
0
0
0
0
0
5
0
0
1
2
2
1
0
1
0
1
0
0
1
0
0
3
0
1
1
0
0
2
0
0
0
2
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
2
0
1
0
0
1
0
0
1
0
0
0
1
0
0
1
0
2
1
1
0
0
0
0
0
2
1
1
0
0
0
0
0
1
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
3
0
1
2
0
0
0
1
1
0
2
1
0
0
0
0
2
1
0
1
1
0
1
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
1
0
1
0
0
0
2
2
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
2
0
0
0
0
0
0
0
5
1
1
2
1
0
0
0
2
0
0
0
2
1
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
2
1
1
1
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
2
1
0
1
1
2
0
2
0
0
0
1
2
2
0
0
2
0
2
0
0
0
2
0
0
0
1
1
1
0
0
0
2
1
1
0
0
1
0
0
2
0
0
0
1
0
0
2
2
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
1
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
4
0
0
1
2
0
0
2
1
0
0
0
1
2
2
3
1
0
0
0
0
1
0
2
0
0
0
2
2
0
2
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
2
0
0
0
0
1
1
1
2
0
2
1
2
0
0
2
0
1
1
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
3
1
0
0
1
0
0
0
0
3
2
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
1
2
0
0
0
0
2
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
2
2
1
0
0
2
0
1
0
0
2
1
0
0
0
0
0
1
3
0
0
2
1
0
0
5
1
0
0
0
1
0
0
0
0
2
0
0
0
0
1
3
0
1
1
0
0
2
3
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
2
0
0
1
3
1
0
2
0
0
1
1
1
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
6
1
2
1
0
1
0
1
0
0
0
1
0
0
0
0
1
1
1
2
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
2
3
0
0
2
0
2
0
3
2
0
0
0
0
0
3
0
1
0
3
1
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
2
0
1
0
0
2
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
2
1
3
0
0
0
0
0
1
0
2
0
0
0
0
1
1
0
0
2
0
2
0
2
2
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
2
2
1
2
2
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
3
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
2
2
2
0
0
3
0
0
0
0
0
0
0
1
0
2
0
0
2
0
1
0
0
3
0
0
3
1
0
1
0
1
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
2
0
4
0
0
1
0
2
0
0
1
1
2
0
1
1
3
0
0
0
0
0
2
1
0
2
0
0
0
1
2
1
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
1
0
4
0
0
0
2
0
2
1
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
2
2
0
2
0
0
0
2
0
2
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
1
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
3
2
2
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
1
1
0
0
0
0
0
1
0
1
1
0
2
2
0
0
0
1
0
1
0
2
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
1
1
0
0
1
3
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
2
0
1
1
0
0
0
0
0
1
0
2
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
1
2
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
1
0
1
0
0
0
0
1
1
0
3
0
0
1
1
0
2
2
0
1
1
0
1
0
0
2
2
0
0
2
1
1
0
0
0
1
0
1
2
2
0
1
2
1
2
2
1
0
0
1
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
3
0
0
2
0
0
0
1
2
0
1
0
0
0
0
1
1
2
0
0
1
0
0
0
0
2
1
0
0
2
0
3
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
1
3
1
0
2
0
2
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
1
1
1
0
0
2
1
0
1
0
0
0
0
3
0
0
2
0
2
0
0
0
3
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
3
0
0
4
0
0
1
0
2
0
0
0
0
1
0
2
1
0
0
3
0
0
0
0
2
0
2
1
0
1
3
0
2
0
0
0
0
2
2
2
0
1
0
1
3
0
0
0
0
0
0
0
2
2
0
0
0
0
1
2
0
0
2
0
0
0
0
1
2
0
2
0
0
2
2
0
0
1
1
0
0
2
0
2
0
2
1
0
1
0
1
1
1
0
1
0
0
1
2
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
1
2
0
1
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
3
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
1
2
0
0
0
0
0
1
0
0
0
2
0
3
0
0
1
0
0
0
0
1
1
1
0
0
0
2
0
1
0
0
1
0
0
0
1
0
1
2
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
2
0
0
0
0
0
0
2
1
0
1
0
0
2
2
1
2
0
0
0
0
1
0
2
0
0
0
0
2
0
0
2
0
1
0
0
0
1
0
0
1
0
0
1
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
2
0
0
2
0
0
0
1
1
0
1
3
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
1
0
0
5
0
2
0
0
0
0
1
2
1
2
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
4
0
0
0
0
2
0
1
2
0
0
0
0
0
0
2
0
2
0
0
1
0
2
0
0
0
1
0
1
2
0
0
0
1
2
0
0
0
0
0
0
0
3
0
0
2
0
0
2
0
1
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
1
2
1
0
4
2
0
1
2
1
0
1
0
0
3
1
2
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
1
0
2
0
0
0
1
0
0
0
1
0
1
0
0
4
1
1
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
3
0
0
0
2
0
1
2
1
1
0
0
0
0
0
0
1
0
0
0
3
3
2
0
0
0
0
0
1
1
0
0
1
0
0
0
2
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
1
1
0
0
0
0
3
1
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
5
2
0
1
1
0
0
2
3
0
0
0
0
0
0
2
2
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
1
0
0
2
2
1
1
0
2
0
5
0
1
3
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
1
0
0
3
1
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
1
0
0
0
1
8
0
2
1
2
0
0
1
2
0
0
2
0
1
1
0
1
0
1
0
2
2
0
2
0
0
0
0
0
1
0
0
2
0
1
0
0
0
1
0
1
0
1
1
0
1
0
2
0
1
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
1
1
0
0
0
0
0
2
0
0
0
1
1
0
2
0
1
0
0
0
0
0
2
1
2
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
2
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
2
0
1
1
0
0
0
0
0
0
5
1
0
0
0
0
3
1
0
0
0
0
0
0
0
3
1
1
0
0
0
2
0
3
0
0
0
2
0
0
2
1
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
1
0
0
0
1
1
1
0
0
1
0
0
0
2
1
1
0
0
0
2
0
0
0
2
0
0
3
1
0
0
0
2
0
0
0
0
1
3
0
0
2
1
0
0
0
0
1
0
0
1
1
0
2
0
0
0
0
3
4
0
0
0
1
1
2
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
1
0
1
0
2
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
1
2
2
0
0
0
2
0
3
0
0
0
2
2
0
2
0
3
0
1
0
0
0
0
1
0
0
1
2
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
1
2
4
0
0
0
0
0
4
0
0
2
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
3
1
2
1
0
0
0
0
0
2
0
0
2
1
0
0
1
1
2
2
2
0
0
0
0
0
2
0
0
1
0
0
0
2
0
1
0
1
0
0
3
0
0
1
0
0
0
0
0
1
0
0
1
2
0
1
0
2
0
0
0
0
0
2
0
2
0
0
2
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
3
3
0
0
0
0
0
4
0
0
2
1
0
0
0
0
0
1
1
0
0
2
1
0
1
0
2
2
1
0
0
2
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
1
0
1
0
0
2
0
2
1
0
1
0
0
1
1
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
1
2
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
3
0
0
1
0
1
0
0
1
1
0
2
0
0
2
0
0
0
0
0
0
1
2
0
2
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
2
4
0
0
0
0
2
0
0
0
1
1
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
3
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
1
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
2
2
0
1
0
0
0
0
0
0
2
1
0
0
1
0
2
0
2
0
0
0
0
1
0
0
0
2
0
2
0
2
0
0
0
2
4
0
1
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
2
0
1
2
0
1
0
0
2
0
0
0
1
0
0
0
0
1
3
1
2
0
0
0
0
0
1
1
2
0
2
1
0
1
0
0
2
0
0
0
0
1
0
2
1
0
4
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
2
1
2
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
3
2
0
2
1
0
0
0
1
1
0
0
0
0
2
0
1
2
2
0
2
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
3
3
1
0
0
0
0
1
0
2
0
2
0
1
0
0
0
1
0
0
0
0
2
0
1
1
1
1
1
0
3
0
0
0
2
0
1
0
1
2
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
1
0
0
2
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
2
0
1
1
0
1
1
0
1
0
0
0
0
0
1
2
1
6
0
2
1
0
0
0
0
2
0
1
0
0
0
0
1
0
2
0
1
0
0
2
2
3
0
0
0
0
0
1
2
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
2
2
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
2
2
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
4
2
0
1
2
0
1
2
0
1
1
0
0
0
0
1
2
0
1
0
2
0
0
0
0
1
1
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
3
0
0
4
0
0
0
0
0
2
2
2
0
0
2
2
6
0
3
0
2
0
0
1
0
1
1
0
0
0
2
0
1
0
0
0
2
2
0
1
2
0
1
0
0
0
0
1
0
1
0
1
2
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
1
1
0
0
2
0
0
1
0
0
2
1
1
0
1
0
1
2
1
2
0
2
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
2
1
2
0
4
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
1
2
0
3
0
0
1
2
0
0
0
0
0
1
0
1
0
1
2
0
2
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
2
0
0
2
0
2
1
2
1
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
1
2
0
0
1
0
2
2
1
2
0
0
0
0
0
1
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
1
1
0
0
0
0
1
0
0
0
0
0
0
4
0
1
2
0
0
1
1
0
0
0
0
0
2
0
0
0
4
0
2
0
1
0
0
0
1
2
1
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
3
2
0
0
0
2
0
0
0
0
0
0
0
0
3
2
1
0
2
1
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
2
1
2
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
1
0
0
2
0
0
1
0
2
2
0
2
0
0
2
4
0
0
1
2
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
3
0
0
0
2
2
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
2
1
0
0
2
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
1
1
0
3
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
2
1
0
0
1
0
0
1
0
0
1
0
0
1
0
1
0
0
0
2
0
0
0
0
0
2
3
2
2
0
0
0
0
1
0
0
0
0
1
0
1
0
0
2
0
1
1
0
0
2
2
1
1
0
0
0
0
0
1
2
1
0
0
1
0
0
1
1
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
2
4
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
3
2
0
1
0
0
0
1
0
0
0
1
0
0
0
2
0
3
0
2
0
2
0
0
0
0
0
1
0
2
0
1
0
2
1
2
2
0
0
0
0
0
0
1
0
0
0
1
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
1
0
0
0
0
0
2
1
0
0
1
1
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
1
0
0
2
2
0
0
1
1
0
1
0
2
0
0
0
0
0
0
0
1
0
1
1
0
2
1
1
0
0
0
0
0
3
0
1
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
1
0
0
0
1
0
0
2
2
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
1
0
0
0
0
0
1
0
1
0
1
0
0
2
1
0
0
1
0
0
0
1
0
0
2
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
2
1
1
0
0
2
0
2
0
1
0
0
0
0
2
3
2
0
1
0
0
0
1
0
0
0
0
2
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
2
1
0
2
1
0
0
2
0
2
0
3
0
1
4
0
0
0
0
0
1
2
0
2
0
1
3
0
0
0
0
0
0
1
1
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
1
1
2
0
0
0
1
0
2
3
0
1
0
0
1
0
0
0
0
8
0
0
1
0
1
0
2
1
0
2
1
0
2
1
0
1
0
0
1
2
0
0
0
2
0
0
0
0
0
2
1
1
0
0
2
0
1
0
2
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
2
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
2
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
1
1
2
0
1
5
0
0
2
0
2
0
0
1
2
0
1
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
2
1
0
2
1
0
0
0
0
0
0
0
5
0
0
0
0
0
1
0
1
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
3
2
2
1
2
0
0
0
0
0
0
1
2
0
0
0
0
0
1
2
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
2
6
0
0
0
0
0
0
2
2
0
0
0
1
0
0
1
0
0
0
3
2
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
1
0
0
0
0
0
2
1
0
0
1
0
1
0
0
1
2
2
0
0
2
0
0
1
1
1
0
0
0
1
0
2
0
0
0
2
0
2
0
0
1
0
2
0
0
0
0
2
2
0
0
0
2
0
1
0
0
1
2
0
0
0
1
0
2
0
0
1
0
2
0
1
0
1
1
0
0
0
2
1
0
0
0
0
0
0
0
1
1
2
1
0
0
0
0
0
0
1
0
0
0
1
0
2
2
0
2
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
2
0
0
1
1
2
0
0
2
2
4
1
0
2
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
1
2
1
0
0
0
3
2
0
2
0
3
0
0
0
0
0
1
0
1
2
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
2
0
0
0
1
0
2
1
2
0
2
1
1
1
2
1
0
0
1
0
0
0
0
0
1
0
0
3
0
0
0
0
2
1
0
2
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
4
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
1
0
1
2
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
3
0
0
0
0
0
0
0
2
2
1
3
0
0
2
1
0
0
0
0
0
1
0
0
1
0
2
0
0
0
2
0
0
1
0
3
0
0
0
0
0
0
2
1
0
1
1
0
2
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
1
1
1
1
0
0
0
2
0
0
0
2
2
0
0
0
1
1
2
1
0
3
3
0
3
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
1
0
1
0
0
0
0
0
5
0
2
0
1
3
1
2
0
0
0
2
1
0
0
0
0
0
1
2
0
1
1
0
0
0
2
0
0
0
1
0
0
1
0
1
2
2
0
0
0
2
0
2
0
5
1
1
0
0
1
0
1
1
0
0
2
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
2
0
0
0
0
0
0
2
2
0
0
0
1
0
0
3
2
2
0
0
2
0
0
0
1
1
1
0
0
2
0
1
1
1
2
2
0
0
2
0
0
0
0
1
1
1
0
0
3
0
1
2
0
2
2
0
0
1
1
2
0
0
0
0
2
0
2
1
0
2
2
0
0
2
0
0
0
2
0
0
0
0
2
0
0
2
0
2
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
2
0
1
0
0
0
2
1
0
0
3
0
0
2
0
1
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
2
1
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
2
3
1
1
1
0
0
0
0
0
0
2
0
0
0
1
2
1
1
0
2
1
0
1
0
0
0
0
0
3
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
1
1
0
0
0
0
2
0
0
2
0
0
0
3
2
1
0
2
0
0
0
1
0
0
4
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
2
2
0
0
2
2
0
0
0
0
1
0
0
0
4
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
1
0
0
1
1
0
0
0
0
2
1
0
0
0
2
0
0
0
2
0
1
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
2
0
0
1
0
0
0
0
2
0
1
2
1
0
0
0
1
0
0
1
0
0
0
1
0
2
0
2
0
1
1
0
0
1
1
0
0
2
0
0
0
0
2
0
0
0
2
2
0
0
0
2
2
0
0
0
0
2
1
2
0
0
1
0
0
2
2
0
0
0
0
0
2
0
0
5
0
0
0
2
1
0
1
0
0
0
1
0
1
0
2
2
0
0
0
0
0
0
1
0
0
0
0
2
1
2
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
2
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
2
2
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
2
2
0
2
0
0
0
1
0
0
1
1
2
2
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
1
0
2
0
6
1
0
0
1
0
0
0
0
1
0
2
0
2
2
0
3
0
2
0
0
1
2
0
1
1
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
1
2
1
0
0
2
0
1
1
0
0
2
0
0
0
2
0
1
0
0
0
2
1
0
0
0
2
0
1
0
0
2
0
1
0
0
0
0
2
1
2
1
0
1
0
1
0
2
2
1
0
0
2
2
0
2
1
0
1
0
0
2
2
2
0
0
3
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
1
2
0
0
0
0
0
4
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
3
2
1
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
1
6
0
0
0
2
1
0
0
0
0
0
0
0
2
1
1
0
5
1
0
0
2
2
0
0
1
0
0
0
2
0
2
2
1
3
0
0
0
0
0
2
2
0
2
2
0
0
1
0
0
0
1
0
0
1
1
0
1
1
0
2
0
2
2
1
2
0
0
0
3
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
3
0
0
0
0
2
0
0
2
2
0
1
0
0
0
0
2
0
1
2
0
0
2
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
2
1
1
1
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
2
1
1
0
2
1
0
4
1
2
0
0
0
1
2
0
2
0
0
0
0
1
0
1
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
2
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
2
0
0
0
0
2
0
0
1
4
0
0
0
0
2
1
0
0
0
0
1
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
7
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
2
2
0
0
0
0
0
1
0
0
7
0
1
0
0
1
0
0
0
0
1
0
1
2
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
1
0
1
0
0
0
1
1
0
0
1
3
0
0
0
1
0
1
2
4
0
0
1
0
0
2
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
2
1
0
0
0
1
0
0
0
4
0
0
0
0
2
0
0
3
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
2
2
1
0
0
0
0
2
0
0
0
0
1
2
1
0
0
0
0
0
0
2
0
1
0
0
0
1
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
1
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
2
3
0
0
0
0
0
0
1
0
0
0
2
0
0
1
1
1
2
0
0
2
0
0
0
0
0
0
0
0
2
0
3
0
1
0
0
0
0
0
0
0
4
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
2
0
1
0
1
0
0
0
2
1
1
0
0
0
1
2
0
0
0
1
1
0
0
0
0
0
2
0
1
0
1
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
2
0
0
0
0
0
1
1
0
3
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
3
1
1
0
2
0
0
0
0
0
1
1
0
2
0
1
0
1
0
1
2
0
0
1
0
0
0
0
1
0
0
1
0
1
3
0
2
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
1
0
0
2
0
0
0
2
1
0
0
0
0
3
0
0
1
0
1
0
0
0
0
0
0
1
7
0
0
0
0
2
1
2
2
0
1
1
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
2
0
0
2
1
0
0
0
0
0
0
0
2
2
0
2
0
0
0
1
0
0
0
0
1
0
2
2
1
2
2
0
0
0
0
2
0
0
0
2
3
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
3
0
0
0
1
0
0
0
0
1
0
1
0
0
1
2
0
2
0
0
2
0
0
0
1
0
3
1
7
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
2
2
1
0
0
0
2
1
0
0
2
0
1
2
0
0
0
2
0
1
0
2
0
0
2
0
0
0
0
0
4
0
0
0
0
0
0
1
0
2
0
0
1
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
1
0
0
2
0
1
1
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
2
1
0
0
1
2
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
2
1
0
0
1
2
0
0
0
0
0
0
0
3
0
1
2
0
0
0
1
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
3
0
0
0
2
0
0
1
0
0
0
1
2
0
1
0
2
0
0
0
0
0
1
2
0
0
0
1
0
2
0
1
0
0
0
2
1
0
1
3
0
0
1
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
2
2
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
2
0
0
2
0
2
0
2
2
1
1
0
3
2
0
0
0
0
0
0
0
0
1
2
3
0
2
1
2
0
0
1
0
0
0
1
2
0
1
2
1
0
0
0
2
1
0
1
3
0
0
2
1
0
0
2
0
1
0
1
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
3
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
7
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
1
1
1
1
1
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
2
2
1
0
2
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
2
2
0
1
0
0
6
0
0
0
1
0
2
2
2
0
1
0
0
0
1
0
0
0
0
1
2
2
0
0
0
2
0
0
0
0
1
1
0
2
0
1
1
1
3
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
2
0
1
0
1
0
0
2
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
2
0
1
3
0
2
0
2
0
1
6
0
1
0
2
0
0
2
2
0
1
0
0
0
0
1
0
0
1
0
4
0
0
0
0
0
0
0
2
0
2
1
0
2
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
1
0
2
0
1
0
0
2
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
2
2
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
1
0
2
1
0
0
0
0
2
2
0
1
0
0
0
0
2
1
0
2
0
0
2
1
0
0
2
0
0
0
0
2
0
0
1
0
0
0
2
0
0
2
2
0
0
2
0
0
1
0
0
2
0
0
2
2
0
0
2
1
1
0
1
0
1
2
0
2
1
0
0
0
0
0
2
0
0
1
0
1
0
1
0
0
0
0
0
0
2
0
1
0
1
1
0
1
0
0
0
0
2
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
2
2
0
0
0
2
1
0
0
2
1
0
0
2
0
0
0
0
0
0
2
1
0
1
0
1
0
3
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
2
0
0
0
4
0
0
2
1
0
0
1
0
1
1
8
0
0
2
3
1
0
0
3
1
0
2
0
2
0
0
1
2
0
2
3
2
0
0
2
0
0
0
0
4
0
2
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
2
2
2
0
0
0
3
0
1
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
1
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
5
0
0
0
0
0
2
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
1
0
2
0
0
0
1
0
0
0
0
2
0
0
2
1
0
0
2
1
0
0
1
1
0
0
2
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
1
2
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
1
0
0
0
0
2
0
1
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
3
0
1
3
0
0
0
0
0
0
1
0
2
1
0
2
0
0
0
0
1
3
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
1
3
0
0
2
2
2
0
0
0
1
1
1
2
0
2
2
0
2
1
1
2
0
1
0
2
3
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
3
0
0
0
2
0
0
2
0
2
0
2
1
2
1
0
0
0
1
0
2
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
3
0
0
0
0
2
4
9
2
1
2
0
0
1
0
0
2
0
1
0
0
0
0
0
1
2
0
0
0
1
0
1
0
2
2
1
2
0
1
1
0
0
2
0
0
1
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
1
0
1
3
1
2
0
2
1
0
0
0
0
1
0
0
0
2
0
1
2
0
2
2
1
1
0
2
1
1
0
1
0
0
1
0
0
2
0
0
0
1
0
0
0
0
1
1
0
4
1
1
0
2
0
0
0
0
2
0
0
2
1
2
2
0
0
0
0
0
0
2
0
1
0
2
0
1
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
2
0
0
1
1
0
0
1
0
0
2
1
0
1
0
0
0
0
0
0
1
2
1
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
2
4
0
2
0
0
0
0
0
2
0
2
0
1
0
2
0
0
0
2
0
0
0
0
0
0
5
0
0
0
0
1
0
0
0
0
3
0
0
0
0
2
0
2
0
0
1
2
0
2
0
0
0
1
0
2
0
2
0
1
0
2
0
2
2
0
0
0
0
0
1
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
1
0
2
0
0
1
0
0
1
0
1
0
2
3
1
0
0
0
1
0
2
1
2
0
2
2
0
0
2
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
2
1
0
2
2
2
0
0
1
0
1
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
1
1
0
0
0
0
0
1
2
0
2
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
1
0
0
0
2
2
0
0
0
1
0
2
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
3
1
0
0
0
0
2
0
3
0
1
0
0
0
0
0
2
0
0
2
0
2
1
0
0
0
2
1
0
0
0
1
0
0
0
1
2
0
0
0
1
0
0
1
0
0
2
0
1
0
0
0
0
3
1
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
4
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
1
0
0
0
8
1
0
0
0
0
2
1
0
0
0
2
0
1
1
1
0
2
4
0
0
0
2
0
1
1
0
1
0
1
1
0
0
0
1
0
2
1
2
0
2
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
1
0
0
0
2
0
0
1
2
1
0
2
0
2
0
0
0
1
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
2
0
0
0
0
0
1
0
0
2
0
1
0
0
1
1
1
0
1
0
0
2
0
1
0
0
0
0
0
1
2
0
0
0
0
3
2
0
1
2
0
2
1
0
0
0
2
1
3
0
0
0
1
0
0
2
0
0
0
1
0
4
0
0
0
0
0
0
0
0
1
0
1
0
3
0
0
0
0
0
2
0
1
0
0
0
0
2
0
1
0
0
2
1
0
0
0
0
0
2
0
0
1
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
2
0
1
2
1
0
0
0
0
0
0
1
0
1
4
0
0
1
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
2
0
0
2
0
0
0
0
1
2
2
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
2
1
0
0
1
0
0
2
0
0
0
1
0
0
0
1
0
2
0
0
2
0
2
3
0
0
0
0
2
2
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
3
1
0
2
1
0
2
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
1
0
2
0
0
2
1
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
2
0
2
0
2
0
0
1
8
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
1
0
3
0
2
0
0
2
0
0
1
1
0
0
2
1
1
3
2
0
0
1
1
2
0
0
2
0
0
0
0
0
1
2
0
1
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
1
3
0
1
0
0
1
0
0
0
0
2
0
1
0
0
2
0
2
0
2
0
2
1
0
1
0
2
0
0
1
1
0
0
0
2
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
2
2
1
1
0
0
1
2
1
0
1
0
0
1
2
0
0
1
1
3
0
0
1
0
0
2
0
0
0
1
0
0
0
4
1
0
2
0
0
2
0
3
2
0
0
2
1
0
0
0
1
0
0
0
3
2
1
2
0
0
0
2
0
0
0
0
0
0
3
1
0
1
0
1
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
6
1
2
0
0
0
0
3
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
2
0
0
2
0
3
0
1
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
1
1
0
0
0
0
2
1
0
1
1
0
3
0
1
0
0
0
0
2
0
0
2
0
1
1
0
2
0
2
0
0
2
0
0
1
0
0
0
0
2
1
0
1
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
1
0
0
0
0
0
2
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
2
0
1
1
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
2
1
1
1
0
1
3
0
1
0
1
0
0
1
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
6
1
0
2
0
0
0
2
3
0
0
0
0
0
0
0
1
0
0
0
2
2
0
1
2
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
1
1
0
0
1
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
2
0
0
0
3
0
2
1
0
0
0
0
1
0
0
0
1
0
2
0
0
2
1
0
0
2
0
0
0
0
0
0
0
3
2
0
0
0
0
2
1
1
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
1
0
0
1
1
2
0
0
0
0
0
0
1
1
0
0
1
2
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
3
2
4
1
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
2
0
2
0
0
1
2
0
6
0
0
0
0
0
0
0
2
0
2
1
1
1
2
2
0
0
1
3
1
3
2
1
1
0
0
0
0
2
1
1
0
1
0
0
0
2
0
0
0
1
1
0
0
2
2
2
0
2
0
1
1
1
0
0
0
0
2
2
0
0
0
0
2
0
0
0
1
0
0
1
0
0
2
0
2
0
1
0
2
1
3
0
0
2
0
0
0
0
2
1
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
2
2
0
0
2
1
0
0
2
0
0
2
0
0
0
0
2
0
0
0
2
0
1
1
0
2
0
0
2
2
2
2
2
0
0
1
0
0
0
1
0
2
1
1
2
1
0
0
0
2
0
2
2
1
0
0
2
0
2
0
0
0
0
0
7
6
0
0
0
0
0
2
0
2
1
0
0
1
0
2
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
1
0
2
0
1
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
1
0
0
2
0
0
1
0
2
0
0
0
0
0
1
2
0
0
0
0
4
0
0
0
2
1
2
1
2
0
0
0
1
0
0
0
1
2
0
2
0
0
2
0
1
2
0
1
0
0
0
1
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
3
1
3
0
0
1
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
2
0
2
1
0
2
0
0
0
1
2
0
0
2
0
0
0
1
1
0
2
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
2
0
0
0
1
0
0
2
0
1
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
2
0
0
0
3
0
0
2
2
3
0
2
1
0
0
1
2
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
1
2
2
0
0
0
1
0
0
0
0
1
0
0
0
0
2
1
0
2
1
0
0
0
0
1
0
3
0
0
3
4
2
1
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
2
0
1
0
2
0
1
2
0
0
0
1
0
0
3
1
2
0
0
1
2
0
0
0
2
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
2
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
1
2
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
1
1
0
1
2
0
2
1
0
0
0
0
1
0
2
1
2
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
2
0
1
0
0
2
2
2
0
0
1
0
0
0
1
0
3
0
0
0
0
1
0
0
0
2
1
0
1
0
0
1
0
1
0
2
2
0
0
0
0
1
1
3
2
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
1
0
1
0
0
0
1
2
0
2
0
1
1
0
2
2
0
0
0
0
1
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
1
0
1
0
0
0
0
2
1
2
0
0
0
0
1
0
0
2
0
1
0
2
0
0
2
1
0
0
0
2
0
1
2
0
1
0
0
2
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
3
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
4
2
0
0
0
2
2
0
0
0
0
1
0
1
0
0
0
2
0
2
2
0
0
0
1
1
0
3
1
0
0
0
1
1
0
0
0
0
0
1
0
2
1
1
1
0
2
0
0
1
0
2
0
0
5
4
0
0
1
0
0
1
0
0
2
1
0
0
1
0
2
0
1
4
0
0
0
2
0
0
0
0
2
2
0
1
0
0
0
0
2
2
1
1
0
0
0
0
1
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
1
0
0
0
0
1
0
2
1
0
1
0
0
0
0
0
0
0
1
2
2
1
0
0
2
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
1
1
0
0
2
0
0
0
2
0
0
0
0
0
1
1
2
10
1
0
1
0
3
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
7
0
1
2
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
1
0
0
2
1
0
0
1
0
0
0
1
0
1
0
2
0
0
0
0
0
1
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
1
1
0
0
2
0
0
0
2
0
1
0
0
0
0
2
2
0
0
0
1
0
1
0
2
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
1
0
4
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
3
0
1
0
2
0
0
0
0
2
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
2
0
2
0
1
1
2
0
3
0
0
3
0
0
0
0
1
0
2
0
0
0
0
0
2
1
0
2
2
2
1
0
2
0
1
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
2
1
0
0
2
0
1
1
0
0
1
0
0
0
2
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
2
2
0
0
0
1
0
2
0
0
0
1
0
2
0
2
2
0
0
1
2
0
1
0
0
0
1
2
2
0
0
2
0
0
0
0
4
0
0
0
1
0
1
1
0
2
0
0
2
0
0
0
0
0
0
2
1
0
2
0
3
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
1
0
1
0
0
1
0
1
1
2
1
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
2
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
1
0
0
1
3
0
0
0
0
0
0
2
2
0
2
0
1
0
0
0
0
0
4
0
2
0
0
1
0
0
1
0
1
3
0
1
0
0
0
1
0
4
0
0
1
0
1
0
2
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
1
0
0
2
0
1
0
0
2
2
2
2
1
0
1
0
0
0
3
1
0
0
1
0
2
0
0
2
2
2
2
1
0
1
1
1
0
0
0
2
0
2
2
0
0
0
0
0
1
1
0
0
1
1
1
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
1
0
2
0
0
0
0
2
2
1
1
0
0
0
0
0
0
2
2
0
0
0
1
2
0
0
0
1
0
0
0
4
0
0
0
2
0
2
1
0
0
0
2
0
0
0
1
1
0
0
0
0
1
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
1
2
0
2
0
2
2
0
2
0
0
0
1
0
2
0
2
2
1
0
0
2
0
0
0
1
0
0
0
0
0
2
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
2
0
4
0
2
1
3
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
2
0
1
2
2
1
2
1
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
2
0
2
0
2
0
2
0
0
1
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
4
0
0
1
0
0
0
2
1
1
0
0
2
0
1
2
0
0
0
0
0
0
0
2
1
0
1
0
1
3
0
0
2
0
0
0
4
1
0
3
0
0
5
3
1
1
0
0
2
0
0
0
1
2
0
0
0
1
1
1
1
0
1
0
0
0
0
2
2
0
0
0
0
2
1
0
1
1
0
1
1
0
2
1
0
2
0
2
0
1
0
0
0
0
0
1
0
3
0
2
0
0
1
0
0
2
0
0
0
1
0
1
0
0
0
2
1
0
2
0
0
0
2
0
0
0
0
2
1
0
0
0
3
0
1
0
1
0
0
6
0
0
0
0
0
1
1
0
0
8
2
0
0
0
1
0
1
1
1
0
0
0
2
0
1
0
3
0
1
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
1
0
0
2
2
0
2
0
0
0
0
0
1
0
1
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
1
1
0
0
1
2
0
2
2
0
0
2
0
0
1
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
1
0
2
0
2
0
2
0
6
0
2
0
1
0
0
1
0
1
0
0
0
0
3
1
0
0
1
2
2
0
0
1
0
1
0
0
2
1
0
1
0
0
0
0
1
1
2
0
0
1
0
0
1
0
0
0
0
0
2
0
2
0
0
1
0
0
2
0
2
0
0
1
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
1
0
2
0
0
2
0
3
1
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
2
0
2
2
0
1
0
1
0
1
2
2
0
0
0
0
0
0
2
2
0
0
2
1
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
1
2
0
1
2
0
0
0
1
3
0
0
0
2
0
0
1
0
0
0
0
0
0
0
3
1
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
1
0
2
0
2
0
1
0
0
0
0
2
1
1
1
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
1
1
2
1
0
1
0
0
2
0
0
1
0
0
0
0
2
1
2
0
1
1
0
0
1
0
1
2
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
3
0
0
2
3
2
0
0
0
0
1
1
0
4
0
2
1
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
1
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
1
0
1
0
1
0
0
1
1
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
4
2
0
2
2
0
0
0
0
3
0
0
3
0
2
0
1
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
1
0
0
2
0
0
2
0
0
1
1
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
2
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
2
0
0
0
2
0
7
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
1
0
1
0
0
0
0
0
1
4
0
0
1
0
1
0
0
0
0
0
1
1
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
1
1
1
4
0
2
0
0
0
0
0
0
1
0
1
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
1
0
0
1
2
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
2
0
1
0
0
1
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
2
0
0
2
0
0
0
1
0
0
0
0
1
0
3
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
2
1
0
3
0
0
2
0
1
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
2
0
2
0
1
1
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
2
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
2
0
0
1
1
0
0
1
1
1
0
0
2
0
2
1
2
1
1
0
0
1
2
0
2
1
0
0
1
1
0
0
0
0
12
2
1
0
0
3
2
1
0
1
1
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
2
0
0
2
0
0
3
0
0
1
0
1
1
2
0
0
0
0
0
1
0
2
0
1
2
0
1
0
0
0
1
1
0
1
2
1
0
1
0
0
0
0
1
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
1
1
0
2
2
0
0
0
1
2
0
0
0
0
0
2
0
2
0
0
0
0
2
2
4
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
2
0
1
0
0
0
0
2
3
0
0
0
0
2
4
0
0
0
0
1
1
0
0
2
0
0
3
2
0
0
0
2
0
0
0
1
2
2
0
0
2
2
0
1
0
0
3
1
0
1
0
0
2
1
0
0
0
0
0
2
0
0
0
1
2
3
0
1
0
0
0
0
0
1
1
2
0
2
2
2
9
0
0
0
0
1
0
0
0
2
2
0
2
0
0
2
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
1
2
0
1
1
0
2
1
0
1
0
0
0
1
0
0
0
0
0
0
2
0
2
1
0
0
1
1
0
0
1
0
0
1
0
2
0
0
1
0
2
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
2
0
1
0
1
0
0
0
0
1
0
2
2
1
0
2
0
2
1
0
0
0
1
0
2
1
2
1
0
0
0
1
0
0
2
0
1
0
0
4
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
1
0
0
1
0
0
0
1
2
0
0
3
0
0
0
0
1
0
0
2
0
0
0
2
0
2
0
0
2
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
1
0
1
0
2
0
1
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
2
2
1
3
0
0
1
0
3
1
2
0
2
2
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
2
0
0
1
0
2
0
2
0
0
0
0
2
0
0
1
2
0
0
2
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
2
2
0
1
0
1
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
2
2
0
1
0
1
0
0
1
0
1
0
0
0
2
1
0
0
0
2
1
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
4
1
3
1
0
2
1
0
0
2
0
1
0
0
0
0
0
0
0
2
2
0
2
0
2
0
1
2
1
0
1
0
0
0
0
1
1
2
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
2
1
1
0
0
0
3
0
0
0
0
0
1
3
0
1
2
0
0
2
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
1
3
0
0
2
2
0
0
0
2
0
2
0
0
0
1
0
1
2
0
0
0
0
2
0
0
1
1
0
0
1
1
0
1
0
1
0
1
0
0
0
2
0
0
2
0
1
2
0
0
0
0
0
0
1
0
2
1
2
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
1
0
0
1
0
1
2
1
1
1
0
0
0
2
0
0
0
0
3
2
0
0
0
0
0
0
0
0
2
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
1
1
0
0
0
0
0
1
2
0
0
1
2
0
1
0
2
0
0
0
0
0
2
1
2
0
2
0
2
1
1
2
0
1
3
0
0
0
1
2
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
2
0
3
0
1
1
0
2
0
0
0
3
1
0
0
0
2
1
2
1
1
0
0
4
0
0
0
0
0
0
0
2
1
0
1
0
1
1
2
1
1
1
0
0
0
0
0
0
0
0
3
0
0
0
1
2
0
1
0
2
1
0
0
2
1
0
0
0
0
0
2
2
0
2
0
0
3
0
0
0
2
0
2
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
1
0
1
3
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
2
0
2
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
2
1
0
1
3
2
0
0
1
0
0
0
2
0
1
0
1
9
0
2
0
0
0
0
0
2
0
0
1
2
0
0
0
2
1
0
0
0
0
0
2
2
1
0
2
1
0
0
0
2
0
1
0
0
0
2
0
1
0
0
0
1
2
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
2
2
0
0
1
0
0
1
0
0
0
0
0
2
1
0
0
0
0
1
1
0
0
3
0
0
0
2
0
1
0
0
0
0
0
1
1
2
0
1
0
0
2
1
0
1
0
2
0
0
0
2
1
0
2
1
0
1
1
0
1
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
2
0
1
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
1
1
0
1
3
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
3
0
1
0
0
0
0
0
2
0
1
2
1
2
1
1
1
0
0
0
0
1
0
0
0
2
0
2
1
2
0
0
0
2
0
2
0
2
0
1
0
1
0
0
0
1
0
0
0
1
0
2
1
0
0
2
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
1
2
2
0
0
0
0
0
1
0
0
3
0
0
1
2
0
1
0
0
0
0
2
0
1
1
0
0
0
0
2
0
0
2
0
0
0
1
0
0
1
2
0
0
2
0
2
1
0
0
0
0
2
2
0
0
0
0
0
1
0
0
2
1
0
1
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
2
1
0
0
0
0
0
2
0
1
0
0
0
2
0
2
2
0
1
2
1
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
1
2
1
0
1
0
0
0
0
0
0
2
0
0
2
1
1
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
1
0
2
3
1
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
1
1
0
2
2
0
1
0
0
0
0
0
2
0
0
2
0
1
0
1
1
0
0
0
0
2
0
0
2
0
0
1
0
0
0
1
0
0
2
4
0
1
1
0
1
2
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
1
0
4
2
0
3
1
0
0
0
0
0
0
1
0
0
0
0
0
3
3
2
1
2
2
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
2
2
0
0
0
2
1
1
1
2
2
2
0
1
0
0
0
0
0
0
2
0
0
2
2
0
0
2
0
0
0
2
0
0
2
2
2
2
0
0
1
0
0
0
1
0
0
1
0
1
2
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
2
2
1
0
2
0
0
1
0
1
1
0
0
0
0
2
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
1
2
2
0
0
0
2
0
1
0
0
1
0
0
0
2
2
0
0
0
2
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
2
2
0
0
0
1
2
0
0
4
0
0
0
1
1
0
0
0
0
0
3
0
2
0
0
1
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
2
1
0
0
0
2
3
3
0
0
0
0
2
0
2
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
1
1
1
0
0
2
0
0
0
0
0
3
1
0
1
0
0
0
2
0
2
0
0
1
2
1
0
0
4
0
0
0
3
0
0
0
2
0
1
3
2
0
0
2
1
0
0
2
0
1
0
0
0
0
1
0
1
2
0
2
0
0
1
1
1
0
1
0
1
0
0
2
3
2
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
2
0
0
0
3
0
0
4
1
0
0
2
0
0
0
1
0
0
1
0
0
0
0
1
2
0
0
0
0
1
0
0
0
1
0
5
0
0
0
1
0
0
0
2
3
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
1
2
0
0
0
1
0
0
0
0
0
0
2
0
3
0
0
2
0
0
1
0
2
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
2
1
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
2
0
1
0
0
0
3
1
2
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
2
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
3
2
0
0
1
0
1
0
0
1
0
0
1
2
0
2
0
0
1
0
0
1
2
0
0
2
0
1
0
1
0
1
0
0
0
3
1
2
0
1
0
1
1
2
0
2
1
0
0
0
0
2
2
1
0
0
0
0
2
0
1
0
0
1
0
0
2
2
0
5
4
0
0
0
1
0
2
2
0
0
0
3
1
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
3
0
0
0
3
2
0
0
1
0
0
0
2
0
0
0
2
1
0
0
0
0
0
1
0
2
0
0
0
2
0
1
0
0
0
0
4
1
0
0
10
0
0
1
0
0
1
0
1
0
0
0
1
1
0
2
1
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
1
2
0
1
0
0
1
1
2
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
1
1
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
2
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
2
0
1
1
0
0
0
0
1
1
1
0
2
0
1
0
0
0
1
0
0
0
0
0
2
1
1
0
2
0
0
0
1
0
1
0
1
1
0
0
1
2
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
2
0
0
0
2
1
0
1
0
1
0
0
1
0
1
1
0
2
0
0
0
0
0
2
0
0
0
2
2
1
5
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
3
2
0
0
2
0
1
0
0
0
2
2
0
1
0
2
1
0
0
0
0
3
0
0
0
0
0
0
2
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
2
0
2
2
0
0
0
2
2
0
2
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
2
1
1
1
0
2
1
1
0
2
0
1
0
0
1
0
2
0
0
2
1
0
1
0
0
1
0
0
2
1
1
0
0
0
1
1
1
2
2
0
1
0
0
0
0
0
0
6
0
0
2
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
2
0
0
2
0
0
0
1
2
2
1
0
1
0
0
1
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
3
2
0
0
2
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
1
0
2
0
0
0
2
0
0
4
1
2
0
0
0
2
2
1
0
0
1
0
2
0
0
3
0
0
1
1
0
2
0
0
0
2
2
0
0
0
0
1
0
2
0
0
0
2
1
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
2
1
0
5
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
2
0
0
0
2
0
0
2
1
0
5
0
0
0
2
0
0
3
0
0
0
1
0
1
1
2
0
0
2
1
0
0
0
4
0
1
0
0
3
0
1
0
0
0
0
0
2
2
0
0
2
0
0
2
1
2
0
2
0
0
0
0
0
2
2
0
1
3
0
2
0
1
0
2
0
1
1
0
2
2
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
1
1
1
0
2
4
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
5
0
1
0
1
2
0
0
4
0
0
1
0
0
1
3
0
0
0
0
0
1
7
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
1
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
2
2
0
1
1
1
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
1
0
0
0
1
2
0
3
0
0
2
0
2
1
0
2
0
1
2
2
1
2
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
1
1
1
2
0
0
0
2
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
1
1
1
0
0
3
0
2
0
2
0
0
2
1
0
0
0
0
0
2
0
1
0
0
1
1
0
0
0
2
1
0
1
0
0
2
3
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
2
2
0
0
0
2
0
0
2
1
0
0
1
0
0
2
1
0
0
0
2
2
0
2
0
0
2
1
0
0
1
1
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
2
0
0
0
1
0
2
3
2
2
0
1
0
0
0
0
1
0
1
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
3
0
2
0
3
0
3
0
0
0
1
2
0
0
1
0
2
2
0
1
2
0
0
1
0
0
2
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
1
2
0
0
0
1
2
0
0
2
0
1
0
0
0
1
4
0
0
1
2
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
1
1
0
0
0
0
0
1
2
0
3
0
1
0
1
3
0
0
0
2
0
0
1
2
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
2
3
0
0
3
0
0
2
0
0
0
0
0
2
1
0
0
0
2
0
1
1
0
0
0
0
0
1
3
1
0
2
0
1
1
0
0
0
2
1
0
0
2
0
0
1
3
1
0
1
0
2
2
1
0
2
1
0
0
0
0
1
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
3
1
0
1
0
0
0
2
0
0
2
0
0
0
2
0
2
1
4
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
2
0
0
0
1
0
0
2
0
0
1
2
2
0
2
0
1
0
2
0
1
0
0
0
0
0
0
1
2
2
1
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
2
3
0
0
0
0
0
1
0
1
2
0
0
0
1
2
0
1
0
1
0
1
0
0
0
2
0
2
1
0
0
0
0
0
1
0
0
0
0
0
2
0
2
1
0
1
0
0
0
0
0
2
0
3
0
0
0
0
0
0
2
0
0
0
2
2
1
0
0
0
0
2
0
2
0
0
0
0
1
0
0
2
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
9
0
0
0
3
1
2
0
0
0
1
2
0
2
2
1
1
2
3
0
1
0
0
0
2
1
0
2
0
0
0
4
0
0
2
0
2
0
2
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
1
1
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
4
0
2
0
0
3
1
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
1
1
0
0
2
1
0
1
0
2
0
1
2
0
1
0
1
0
1
0
0
1
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
1
0
1
0
0
0
1
2
0
0
1
0
0
0
0
1
2
0
2
0
1
0
0
1
2
0
1
2
0
0
0
0
0
2
2
0
0
0
1
0
0
2
2
0
2
3
2
2
2
0
0
0
1
1
0
0
4
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
1
2
0
2
0
0
3
1
1
1
0
0
1
1
0
0
2
2
2
2
0
0
0
0
2
2
0
0
3
0
0
1
0
0
0
0
0
2
0
1
0
0
1
2
0
0
1
0
0
2
1
0
1
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
3
0
2
0
0
0
2
0
0
0
1
0
0
1
2
0
0
1
2
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
1
1
1
2
1
0
1
2
2
0
0
1
0
1
2
0
2
0
0
2
0
2
1
0
1
0
0
2
0
0
0
2
2
2
0
0
2
0
0
2
0
1
2
0
1
1
0
2
0
0
1
0
0
3
0
0
0
0
3
0
1
0
0
1
1
0
0
0
2
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
7
0
0
0
0
0
0
0
2
0
3
0
0
1
0
0
0
0
2
0
0
2
0
1
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
2
3
1
0
0
1
0
0
0
1
0
0
0
2
0
1
1
0
0
0
2
0
0
0
0
2
0
2
0
1
2
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
2
0
0
2
1
2
0
0
0
0
1
2
1
0
0
0
0
0
2
0
0
0
2
1
0
0
1
4
0
1
0
2
0
0
0
1
0
0
2
1
0
1
2
0
0
1
1
0
0
0
1
0
0
0
1
2
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
3
0
1
0
2
0
0
0
0
0
0
0
1
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
1
0
1
0
5
1
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
2
5
1
0
0
1
2
0
0
0
2
0
1
2
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
2
0
1
0
2
2
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
1
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
3
0
1
0
2
1
0
1
2
0
3
0
2
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
3
0
3
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
2
0
1
0
2
0
1
1
2
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
2
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
1
1
1
0
0
3
0
0
0
0
2
0
0
0
0
0
0
1
0
0
3
0
0
1
0
0
0
2
0
0
0
0
2
0
2
1
0
2
0
1
0
2
0
2
0
0
0
0
0
0
1
8
2
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
5
1
0
0
3
0
1
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
1
0
0
2
0
1
0
1
1
0
0
0
2
0
0
0
2
0
1
2
0
0
0
1
0
0
0
0
0
0
4
1
1
0
0
0
1
1
1
0
1
2
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
2
0
0
0
3
2
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
1
0
1
0
0
2
0
4
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
3
0
2
0
0
0
2
0
1
1
1
0
2
0
0
2
1
0
1
1
2
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
2
1
1
1
0
2
0
6
2
0
1
0
0
1
2
0
1
0
0
0
2
1
5
2
0
1
0
0
0
2
5
2
0
0
1
0
0
2
0
0
1
0
1
0
0
1
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
1
3
0
1
1
0
0
0
0
0
2
6
0
0
0
0
0
2
0
0
2
2
2
0
2
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
1
0
0
0
1
0
0
0
0
1
0
0
2
0
1
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
1
1
2
2
0
0
2
0
2
2
0
2
2
0
1
0
0
0
1
2
3
0
2
0
5
0
1
0
1
0
0
0
0
0
0
1
1
0
2
1
0
1
0
0
0
1
0
0
0
0
0
0
5
2
0
0
0
0
1
10
4
1
1
0
2
2
0
1
0
1
2
2
0
0
0
2
3
0
0
0
1
0
0
1
0
0
0
1
1
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
4
1
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
1
0
2
1
1
1
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
3
1
0
2
0
1
2
0
0
0
1
2
0
0
1
2
4
0
0
0
1
1
0
0
1
2
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
3
2
0
0
1
1
0
1
2
0
1
1
0
0
0
1
2
0
0
0
2
0
0
0
0
2
2
1
0
0
2
3
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
2
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
2
0
0
0
1
1
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
1
0
0
0
1
0
2
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
1
0
0
0
0
0
0
1
0
2
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
1
0
0
3
2
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
1
1
3
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
3
1
0
2
1
0
0
2
0
0
1
1
2
2
0
0
0
2
1
1
2
0
0
0
0
0
1
3
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
2
2
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
2
0
1
0
0
1
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
2
1
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
4
2
0
0
2
2
0
2
0
0
0
2
2
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
3
0
2
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
2
1
2
0
0
0
2
2
1
0
2
0
0
0
0
0
0
2
0
0
0
1
1
0
0
1
0
2
1
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
2
1
0
2
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
2
0
1
0
0
0
3
1
0
2
0
2
2
1
0
0
0
2
1
0
0
0
2
0
1
0
0
0
0
1
2
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
2
1
2
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
2
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
1
1
0
2
0
0
2
0
0
0
0
2
2
0
0
0
2
0
2
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
2
1
2
0
0
0
0
0
0
2
0
1
0
2
1
0
0
0
1
0
0
0
0
1
0
1
2
0
3
0
0
1
1
2
2
0
0
0
2
2
3
0
3
0
1
0
0
1
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
1
0
2
0
0
1
0
1
0
0
0
0
2
1
0
0
0
2
0
3
1
1
0
1
0
0
2
2
1
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
1
2
1
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
1
2
1
1
0
0
2
0
0
1
1
1
0
1
0
1
2
1
0
0
1
2
1
0
0
1
0
0
0
0
0
2
1
0
0
0
0
2
1
2
0
1
2
0
0
0
0
7
1
4
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
2
0
2
0
1
0
1
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
2
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
1
0
1
0
0
0
0
2
1
0
0
0
2
0
0
1
1
1
0
0
0
0
0
0
2
2
4
2
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
9
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
2
0
1
0
0
0
0
0
1
1
0
0
1
1
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
2
2
2
1
0
1
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
2
2
0
0
1
1
0
0
0
0
0
2
0
0
0
2
0
6
2
0
1
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
2
2
0
0
2
1
0
0
2
0
0
0
0
0
0
0
1
2
1
0
0
2
0
0
1
0
2
2
0
0
0
2
0
0
0
0
1
0
2
1
0
1
0
0
4
1
0
0
0
2
2
1
0
0
2
2
0
0
0
0
0
1
0
0
0
2
0
0
3
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
2
2
0
0
1
0
0
0
1
1
0
2
0
2
0
0
0
0
0
0
1
3
0
0
4
0
2
0
0
0
2
1
3
0
3
0
0
0
1
0
0
0
0
1
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
2
0
2
0
0
0
0
0
0
2
1
0
2
0
0
0
1
0
2
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
2
0
0
2
1
0
0
2
0
0
0
0
0
0
1
2
2
0
2
2
0
0
1
0
2
1
0
2
3
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
2
0
1
1
0
0
2
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
1
0
0
0
9
0
0
0
2
0
0
2
0
0
0
2
1
0
0
3
0
2
0
1
0
0
0
1
0
0
5
0
0
0
0
1
1
2
0
0
0
0
1
0
0
0
0
0
2
2
0
5
0
0
0
0
0
0
1
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
2
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
1
1
0
1
1
0
1
1
0
2
0
1
0
0
2
0
0
0
0
2
1
0
1
1
1
0
0
2
6
0
0
1
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
5
0
0
0
0
0
1
0
0
0
0
0
0
1
1
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
2
2
0
0
0
0
2
2
0
0
0
2
1
2
0
2
1
2
0
0
0
0
2
0
0
2
0
2
2
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
1
2
0
0
2
0
1
0
0
0
0
1
0
2
0
2
1
0
1
0
0
0
0
0
2
2
1
2
4
0
2
3
1
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
2
3
0
2
0
0
1
0
0
0
0
1
0
2
0
0
2
0
0
0
3
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
3
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
3
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
2
2
0
0
1
0
1
0
0
2
0
0
1
1
0
0
0
1
0
2
1
0
0
0
0
1
0
1
0
0
1
2
0
1
2
2
2
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
2
0
0
0
1
3
0
0
1
0
0
2
2
0
0
0
0
2
2
0
0
0
0
0
0
1
0
3
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
2
0
1
2
0
0
0
0
0
2
1
2
3
0
1
0
0
0
1
0
2
0
0
2
2
0
1
0
1
1
0
2
0
2
1
1
0
0
0
2
0
0
0
0
2
0
2
0
1
0
0
1
1
3
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
5
0
1
1
0
0
0
0
1
0
3
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
1
0
0
1
0
0
0
0
0
0
3
1
0
0
0
0
0
7
1
0
0
2
0
0
0
1
0
0
0
0
1
1
2
3
2
2
0
0
0
0
2
4
1
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
2
2
2
0
3
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
4
0
0
0
0
0
0
2
0
1
0
1
1
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
4
3
0
0
0
0
2
2
0
0
1
2
0
0
0
3
0
2
0
0
0
0
0
0
0
1
0
3
0
2
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
2
0
1
0
0
0
0
2
0
2
0
0
2
0
2
0
0
0
0
0
1
1
0
1
0
0
2
0
1
2
0
1
1
2
0
0
0
1
0
0
0
0
0
0
1
2
1
1
1
0
1
1
1
0
1
0
0
0
2
1
0
0
2
0
0
0
0
0
0
2
1
1
0
1
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
1
0
1
2
0
0
0
0
0
0
1
2
3
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
2
1
2
0
0
0
0
2
0
0
1
1
0
0
0
1
1
1
0
0
0
0
0
0
0
2
0
0
1
0
0
2
3
2
0
0
2
0
2
1
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
2
1
2
1
0
2
0
0
0
2
2
0
0
0
2
0
1
2
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
2
0
0
1
0
0
0
0
1
0
0
2
0
0
0
3
1
0
0
2
0
0
0
0
1
0
0
2
1
0
0
2
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
2
0
0
0
2
2
1
0
1
1
2
3
2
0
2
1
0
1
2
0
0
0
2
1
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
1
5
0
0
1
0
2
2
0
1
2
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
4
1
0
0
0
0
1
0
0
2
0
0
0
1
1
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
4
0
0
2
0
0
1
0
0
0
2
1
2
2
1
0
6
1
0
0
2
1
1
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
2
3
0
0
0
0
0
0
0
0
0
1
0
1
0
3
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
2
0
1
2
2
3
1
1
0
0
0
1
0
0
0
1
3
1
2
0
0
0
0
0
2
0
1
2
0
0
0
0
2
1
0
0
0
0
1
0
0
5
0
0
0
0
0
0
2
2
2
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
2
2
1
0
3
0
1
1
2
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
5
0
2
0
1
0
0
0
0
0
1
0
2
2
0
2
0
0
0
0
2
0
0
0
2
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
1
0
2
0
0
0
1
0
1
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
2
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
2
0
0
1
0
0
1
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
2
2
0
0
0
0
0
2
0
2
1
0
0
0
1
3
1
0
2
1
1
2
0
0
1
0
0
0
1
0
1
2
0
0
1
0
0
0
0
0
2
1
0
0
0
2
1
2
0
0
2
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
2
0
0
0
0
0
1
0
0
2
0
2
1
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
2
4
0
1
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
1
3
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
1
0
1
1
0
0
4
0
0
1
0
0
0
2
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
2
0
0
0
1
2
0
0
0
0
0
2
1
1
1
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
2
2
1
0
0
0
0
4
2
0
0
1
0
0
1
0
0
0
0
1
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
1
2
0
0
0
0
6
0
0
0
1
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
2
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
2
2
2
0
2
1
0
1
0
1
0
2
2
0
1
0
1
0
0
0
0
0
0
0
1
0
2
2
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
2
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
1
0
2
1
0
0
2
0
0
0
1
0
1
1
0
1
0
3
0
0
1
1
0
2
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
2
0
2
0
0
0
0
1
1
2
0
0
1
0
0
0
1
0
1
0
1
0
0
1
0
2
0
1
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
1
0
1
0
0
0
2
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
2
0
0
0
0
0
1
3
0
2
0
0
5
0
0
0
0
2
0
1
0
0
2
0
2
0
2
0
0
2
0
1
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
2
1
0
0
0
0
2
1
0
0
0
0
2
2
1
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
3
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
1
0
1
0
0
2
0
2
0
1
2
0
2
0
1
0
1
1
0
0
0
0
0
0
1
1
1
0
1
1
0
0
0
0
0
3
0
2
2
0
0
0
0
0
2
1
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
1
0
0
1
0
0
0
1
0
2
0
0
1
0
0
0
0
1
0
2
2
0
2
0
1
1
2
0
0
0
0
0
2
2
1
0
2
2
0
0
0
2
0
3
0
0
0
2
0
0
2
0
2
1
0
1
0
0
2
0
1
0
0
1
1
1
0
0
0
0
1
2
0
0
0
1
2
1
0
2
4
2
0
4
0
0
1
0
2
0
0
1
0
0
0
2
0
0
0
2
0
0
0
2
1
0
1
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
4
0
0
0
4
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
1
0
2
0
0
1
1
0
0
1
2
2
0
1
1
1
2
0
0
0
0
2
2
0
0
1
0
1
2
1
0
0
0
1
0
0
2
2
2
1
0
2
1
0
1
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
2
1
1
0
1
2
0
0
1
2
1
2
1
2
0
0
3
2
0
0
0
0
0
2
3
0
0
2
2
0
0
0
0
0
2
0
0
2
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
3
0
2
0
1
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
2
0
1
0
0
1
2
0
1
0
0
0
0
0
0
0
1
0
2
1
0
0
2
0
1
1
2
0
0
0
0
2
1
0
0
2
1
2
1
0
2
3
0
1
2
2
0
2
0
0
0
0
2
0
0
1
0
1
0
2
1
0
1
3
1
0
1
1
0
1
0
0
0
1
0
2
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
2
1
1
2
0
0
0
0
0
0
2
0
0
0
0
1
0
3
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
1
0
0
1
0
2
2
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
2
0
1
0
4
1
0
1
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
2
2
0
0
2
0
2
2
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
2
0
0
3
2
3
1
0
2
0
0
0
1
1
9
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
2
0
3
0
3
0
0
0
0
0
1
0
0
1
2
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
2
0
1
0
1
1
0
0
0
0
10
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
1
0
2
0
6
0
0
2
1
2
2
1
0
1
0
0
0
0
1
2
0
0
0
3
0
2
0
2
0
0
0
3
0
1
0
0
0
0
0
0
2
1
0
0
2
0
1
0
0
1
0
2
2
1
0
1
1
3
0
0
1
2
0
0
2
0
1
0
0
1
0
1
0
0
0
0
1
0
2
4
0
0
1
0
0
0
0
1
0
1
1
0
0
1
2
2
0
1
0
0
2
0
0
0
9
0
0
1
3
0
2
0
0
0
1
0
1
1
0
2
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
2
0
1
0
2
0
2
0
0
1
0
2
0
0
0
0
0
0
1
2
0
0
0
2
2
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
1
0
1
2
4
0
1
0
1
2
0
0
0
1
0
1
2
1
0
0
0
0
2
0
1
0
1
1
0
0
2
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
2
4
1
0
2
0
0
1
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
22
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
1
1
2
0
0
1
1
0
1
0
0
2
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
2
1
1
0
0
1
1
0
2
0
2
2
0
0
0
0
0
1
0
2
0
0
0
2
0
1
0
0
0
2
0
1
1
0
0
0
2
0
1
2
2
2
0
0
2
0
0
0
0
0
0
1
0
2
1
0
2
0
1
0
0
0
0
0
1
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
3
0
2
0
0
0
1
0
0
2
0
0
0
2
0
0
0
2
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
1
0
1
0
0
1
0
2
2
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
6
0
2
0
0
0
0
1
0
2
0
2
0
0
2
0
2
0
0
1
0
2
0
1
2
0
2
1
0
0
1
0
1
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
3
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
2
2
0
0
1
0
0
2
2
0
0
0
2
0
2
1
0
0
0
0
0
0
2
2
0
0
0
0
2
2
0
0
0
3
6
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
5
2
2
0
0
0
0
0
2
0
0
2
1
2
0
2
0
1
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
2
0
0
1
3
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
3
1
2
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
1
2
0
0
0
0
0
3
2
0
2
0
3
1
1
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
2
1
0
2
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
3
2
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
2
0
0
1
2
0
1
0
0
1
0
0
0
2
0
2
0
1
2
1
1
0
0
1
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
1
0
2
0
0
3
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
2
0
0
0
0
1
0
3
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
2
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
2
0
0
0
0
0
0
2
2
0
2
0
2
1
0
0
2
1
1
0
3
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
2
1
0
1
0
0
0
1
0
0
2
0
0
2
0
0
2
2
0
0
2
0
0
2
0
0
1
1
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
3
0
0
2
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
3
0
0
0
0
1
2
0
1
0
0
0
2
0
0
0
2
0
2
0
0
2
0
0
0
2
0
0
0
0
0
2
2
2
0
0
0
1
2
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
2
0
2
2
1
0
0
0
1
0
1
0
1
2
2
0
0
0
2
0
0
2
1
0
0
0
1
0
0
2
0
0
0
2
0
0
2
0
0
2
0
2
2
0
0
0
2
0
0
2
0
0
0
2
1
2
0
0
2
2
0
0
0
0
2
0
0
2
1
1
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
1
0
1
1
0
0
1
0
0
0
0
0
0
3
0
0
1
0
0
4
0
0
2
2
2
0
0
0
0
1
1
0
0
2
0
1
1
2
0
0
0
2
1
1
3
0
1
0
0
0
3
0
0
0
2
1
2
0
0
1
2
1
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
1
0
1
0
2
0
2
2
0
0
0
0
2
6
1
0
1
0
1
0
0
0
2
0
0
0
0
0
1
0
1
0
2
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
2
2
1
0
1
2
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
2
0
0
0
1
1
0
0
0
0
1
0
0
1
1
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
1
0
2
2
0
0
0
2
0
1
4
0
1
0
1
2
0
0
3
1
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
2
0
0
0
0
3
1
2
0
1
0
0
0
0
0
2
0
0
1
1
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
2
0
0
1
0
1
0
2
0
0
1
1
2
0
0
0
1
1
0
0
1
0
1
0
1
0
0
0
1
3
0
0
0
0
0
0
0
2
2
0
0
2
0
1
0
2
1
0
0
0
1
2
0
0
0
0
1
0
8
0
2
0
1
0
0
1
0
2
1
0
0
0
0
0
0
0
0
1
0
2
0
1
1
0
1
1
0
1
0
2
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
2
2
1
0
0
0
1
1
0
0
0
4
1
0
0
2
1
1
0
1
2
0
2
2
0
0
1
2
0
0
3
0
0
0
0
2
1
0
0
2
2
0
0
2
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
1
0
0
1
1
2
2
1
0
0
0
0
1
0
0
0
3
0
0
0
0
0
2
0
0
0
0
2
0
0
1
1
0
0
0
0
1
1
0
1
1
0
0
2
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
1
2
2
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
1
2
0
3
0
0
1
0
5
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
1
0
0
2
0
0
1
1
1
0
0
0
2
0
2
1
1
3
0
1
1
1
0
0
0
1
0
0
0
0
0
4
0
0
0
0
2
2
2
0
0
2
0
2
1
1
0
0
1
0
0
0
2
2
0
0
0
0
0
1
2
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
2
0
1
0
0
0
1
0
0
3
0
1
0
5
0
2
0
0
2
1
0
2
0
1
0
0
0
1
0
0
0
2
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
2
0
0
2
4
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
2
2
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
2
0
0
1
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
1
1
0
2
0
2
0
1
0
0
0
2
0
0
0
0
0
2
0
1
0
1
1
0
0
3
0
0
0
0
1
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
1
2
0
2
1
1
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
2
0
1
0
0
3
1
0
2
1
1
2
0
0
0
0
0
2
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
1
1
2
0
0
0
1
1
1
2
1
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
3
0
0
0
0
1
1
0
2
0
2
1
0
0
1
2
0
0
1
2
1
0
5
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
2
0
1
0
2
7
0
0
0
2
1
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
2
0
1
1
1
2
2
0
0
0
0
0
0
0
0
1
0
2
1
0
1
2
0
0
0
0
0
0
0
1
0
0
0
1
2
4
0
3
1
2
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
1
0
2
0
2
0
2
2
0
0
1
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
2
1
0
2
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
2
0
1
0
0
1
1
0
0
2
0
1
0
0
1
0
1
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
1
0
2
0
0
0
3
1
0
0
0
0
2
0
2
0
1
0
2
0
0
2
2
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
1
0
2
0
4
0
2
2
0
0
1
2
1
1
2
0
1
3
2
0
1
0
0
0
0
0
2
2
0
1
2
2
0
0
0
0
0
0
2
0
0
1
0
0
0
3
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
1
0
2
0
1
0
1
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
2
0
0
3
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
1
1
2
0
0
0
0
1
0
0
2
0
0
1
1
0
1
0
2
2
0
2
0
0
0
2
0
2
2
1
0
2
2
0
2
2
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
4
0
0
4
0
0
0
1
0
0
0
2
0
0
0
0
2
0
1
2
3
3
0
6
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
2
2
0
0
2
0
0
1
0
0
0
0
3
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
3
0
0
2
0
1
1
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
1
3
1
1
0
0
2
0
0
0
2
0
2
0
0
0
0
4
0
0
2
0
2
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
1
2
2
0
0
1
2
0
0
0
0
2
0
1
2
1
0
0
2
1
1
0
0
1
0
0
0
3
0
1
0
0
0
2
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
2
0
0
1
1
0
2
1
0
2
0
0
0
0
2
1
2
0
0
0
2
0
0
0
0
2
0
1
0
0
0
2
1
2
1
2
0
2
4
2
0
0
1
2
0
0
0
0
2
1
1
1
0
0
0
2
0
1
2
0
2
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
2
2
0
0
2
2
0
4
0
0
0
0
0
1
1
0
0
1
0
2
0
0
0
2
2
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
2
2
0
0
0
0
1
0
2
1
3
0
0
2
0
1
0
1
0
0
2
0
1
2
0
0
2
0
0
2
6
2
0
3
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
1
2
3
3
1
0
0
0
2
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
3
0
0
1
0
1
0
2
2
0
1
0
2
2
0
1
1
2
0
0
2
1
0
0
0
0
2
2
0
0
0
1
0
0
2
0
0
0
4
2
0
0
0
0
1
0
0
0
1
0
2
0
0
0
1
0
2
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
3
1
0
1
0
0
0
0
2
0
1
0
0
1
0
1
0
0
0
2
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
3
0
0
0
2
1
0
1
1
2
0
0
0
1
1
0
4
0
2
1
0
0
2
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
1
2
0
0
0
0
0
2
2
0
0
2
0
0
0
0
2
0
0
0
0
0
2
2
1
0
0
2
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
2
2
0
0
0
0
0
1
1
0
0
2
1
5
3
0
2
0
4
0
0
0
0
1
1
0
0
0
0
0
0
0
2
1
0
0
0
0
2
2
0
6
0
0
0
0
0
1
0
0
1
0
0
0
0
1
2
2
0
0
0
0
0
0
0
2
0
0
1
0
2
2
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
1
1
0
0
0
0
0
3
0
3
0
0
0
1
1
0
2
0
2
0
0
0
0
0
0
0
1
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
2
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
2
0
3
0
0
0
1
0
0
0
0
1
2
0
2
0
0
0
1
0
0
0
0
0
2
2
0
0
2
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
2
0
0
0
2
4
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
1
1
0
0
2
6
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
1
0
0
0
2
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
1
0
4
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
8
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
2
2
0
1
3
0
2
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
2
1
2
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
1
0
1
2
0
0
1
0
0
0
2
0
1
0
1
2
1
1
0
0
0
2
0
0
0
0
0
1
0
0
1
2
1
0
0
0
0
0
2
0
0
2
3
0
0
0
0
0
2
0
1
0
0
2
2
1
2
0
0
0
2
0
0
1
1
0
0
1
3
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
1
0
1
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
2
0
0
2
1
0
2
0
1
0
0
0
5
2
2
0
0
2
0
0
0
1
0
1
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
1
0
0
0
1
0
2
0
0
0
0
0
0
1
1
1
0
0
1
0
2
0
1
0
1
0
0
2
0
0
3
0
0
0
3
0
0
1
0
0
0
0
0
2
0
0
1
2
0
2
2
0
0
0
1
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
1
0
1
2
2
3
0
2
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
2
2
2
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
2
0
2
0
0
0
0
0
2
2
0
0
1
0
0
2
2
1
0
0
0
2
0
0
2
0
1
0
1
1
1
1
1
0
0
2
0
0
0
1
0
2
1
1
0
0
2
0
0
0
0
0
1
0
2
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
1
1
0
1
0
0
0
0
2
0
1
0
2
0
1
0
2
0
1
0
0
0
1
2
0
0
0
0
1
0
0
3
2
0
2
0
1
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
1
1
0
0
0
2
0
0
1
1
3
1
1
2
0
0
1
0
0
0
1
2
0
2
1
0
0
2
2
2
0
0
0
0
0
2
0
1
2
0
0
0
2
0
0
0
1
0
0
0
0
2
1
0
0
1
0
3
2
1
2
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
2
2
0
0
2
0
0
2
0
1
0
0
2
0
0
2
0
0
1
3
0
0
0
0
1
0
2
0
0
0
0
0
0
1
2
1
0
0
1
0
1
0
2
1
1
1
0
1
0
0
1
0
2
2
0
2
0
0
0
2
0
0
2
2
0
0
0
2
0
0
1
0
1
0
0
1
0
1
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
2
2
1
0
2
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
1
3
0
0
0
1
1
2
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
4
0
0
2
0
0
0
2
1
3
0
1
0
0
0
1
0
0
0
0
0
2
2
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
1
0
1
2
0
1
2
1
0
1
1
0
0
0
0
3
0
1
0
0
1
2
1
2
1
0
2
3
0
2
2
1
0
0
1
1
0
1
0
1
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
1
0
0
2
0
0
0
2
0
0
0
0
2
2
0
2
2
1
0
0
0
0
0
0
2
0
0
0
1
0
1
0
1
2
0
1
0
0
0
2
0
2
0
0
0
2
0
1
0
2
0
0
0
0
1
2
0
2
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
1
0
0
1
2
0
2
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
1
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
2
0
2
1
0
0
0
1
0
2
0
0
1
0
0
1
1
0
1
0
0
1
1
0
0
1
3
0
1
0
0
2
0
0
0
4
0
0
1
2
2
0
0
0
1
0
1
1
2
0
0
0
1
0
0
2
0
0
2
2
0
1
0
0
0
1
0
0
2
1
0
0
0
3
1
2
1
0
0
0
0
0
1
0
1
0
2
3
2
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
2
0
3
0
2
5
1
0
0
0
1
0
0
0
0
0
2
0
1
1
0
0
1
1
2
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
2
2
0
0
1
1
0
0
0
0
0
0
3
0
0
0
0
0
0
3
0
2
0
0
2
0
0
1
0
1
0
2
1
0
0
1
2
0
1
0
2
2
0
0
0
4
0
1
0
4
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
2
0
0
2
4
0
0
1
0
1
0
0
0
0
7
1
2
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
2
0
0
0
2
1
0
0
0
1
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
1
2
0
2
0
1
1
2
2
0
1
0
2
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
2
2
2
0
0
0
0
1
3
2
0
3
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
1
0
2
0
0
1
0
0
0
2
2
1
0
0
1
2
0
0
3
0
0
0
0
1
0
1
2
2
1
2
0
0
0
1
1
2
0
1
0
1
4
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
4
1
0
0
0
0
0
0
0
3
1
0
2
0
2
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
1
0
2
0
1
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
3
1
1
0
0
0
0
0
2
0
0
1
2
2
1
2
0
0
1
2
0
1
1
1
0
0
2
0
0
1
0
0
0
1
1
0
0
0
2
0
2
0
1
2
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
1
0
1
2
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
1
3
0
0
0
0
2
0
0
0
0
0
1
2
0
2
2
0
0
0
0
1
0
2
2
0
0
3
0
2
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
2
3
0
0
3
0
8
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
2
0
2
0
0
2
0
3
0
0
0
3
0
1
4
1
0
0
1
0
0
0
0
0
0
1
0
2
0
1
0
0
2
2
1
2
0
0
2
2
0
3
2
0
0
0
0
0
0
2
0
0
3
0
0
2
3
0
0
0
2
0
0
0
0
0
0
1
0
2
0
1
0
0
1
0
2
3
0
0
2
2
2
2
0
0
0
0
1
1
0
0
2
0
1
1
0
1
0
2
2
0
2
1
0
0
0
0
2
0
0
3
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
5
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
1
0
2
1
0
0
0
0
2
0
0
0
0
0
2
2
0
0
1
0
0
2
0
1
0
0
0
2
4
0
0
0
1
1
0
0
0
0
0
0
2
1
0
0
2
0
0
0
2
3
0
2
0
1
0
2
0
1
0
0
0
2
0
1
1
0
0
0
0
1
0
2
0
0
1
2
0
1
0
0
2
1
0
2
2
2
0
2
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
2
2
0
2
1
0
0
0
1
1
0
0
0
1
0
0
2
1
0
2
2
0
2
0
0
0
2
0
0
0
0
1
1
0
1
0
2
1
0
2
1
1
0
1
0
0
2
0
0
0
2
2
0
2
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
1
0
0
1
0
2
0
0
2
0
0
2
0
3
1
1
14
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
2
0
1
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
3
0
0
2
0
2
3
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
3
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
1
0
1
0
3
0
0
0
1
2
0
0
0
1
1
0
0
1
1
0
1
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
1
0
2
0
0
2
0
2
0
0
0
2
1
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
2
0
0
0
1
2
0
1
2
0
0
0
2
0
0
1
0
0
0
2
2
0
1
0
4
0
0
1
0
2
0
0
0
0
0
0
2
2
2
0
0
0
0
2
2
0
0
0
0
0
0
2
1
0
0
0
0
0
1
2
1
1
0
0
2
0
0
1
0
0
2
1
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
2
0
0
0
1
0
0
1
0
1
1
1
0
2
0
0
0
0
0
0
2
2
2
2
0
2
3
0
0
0
0
0
1
0
1
0
0
2
0
2
3
0
0
0
0
1
0
2
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
2
1
1
1
0
0
0
0
0
2
0
3
0
0
1
0
0
0
1
0
1
0
0
0
0
2
1
1
0
2
0
0
0
0
1
1
0
2
2
0
1
1
1
2
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
3
1
0
1
0
3
1
2
2
0
0
0
0
3
0
0
1
0
2
0
1
1
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
2
2
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
2
1
1
0
0
0
2
0
1
0
2
1
0
2
0
0
0
2
0
2
2
1
0
0
0
0
0
2
0
0
0
0
2
1
2
0
4
0
0
0
1
0
0
2
2
2
1
3
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
1
0
0
0
1
1
1
0
3
1
1
2
2
2
0
0
2
0
0
2
2
0
0
2
0
0
0
0
0
0
1
2
1
1
1
0
0
0
0
1
2
0
0
2
0
0
1
1
3
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
2
0
2
0
0
1
0
0
1
0
0
0
1
0
2
0
1
1
0
0
0
0
3
0
0
1
0
0
0
4
0
0
0
1
1
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
3
0
0
2
0
0
0
0
0
1
0
0
3
0
0
0
2
1
0
2
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
1
1
2
1
0
0
2
1
0
1
0
0
0
2
0
2
0
1
2
0
2
0
0
0
4
0
0
1
1
1
0
0
0
0
1
2
0
0
1
0
0
0
0
1
0
1
1
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
1
2
0
0
0
2
2
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
1
0
0
0
0
0
0
3
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
2
0
1
0
0
0
2
0
2
0
1
2
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
2
2
0
0
1
0
1
0
1
1
2
0
0
0
2
0
1
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
2
2
1
0
0
0
1
0
0
0
1
0
0
0
4
0
2
1
1
2
0
0
0
0
0
1
0
0
0
1
2
0
1
0
0
1
0
0
0
1
2
2
0
0
0
0
1
2
2
0
1
0
2
0
0
0
1
1
0
0
1
2
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
2
2
0
0
2
1
1
2
0
1
0
2
0
0
0
1
0
0
0
0
0
0
4
0
0
0
2
1
4
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
3
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
2
0
0
0
3
3
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
2
1
0
0
1
1
1
1
0
1
0
3
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
1
0
1
0
2
0
2
0
0
0
0
0
0
0
1
0
1
0
0
6
0
0
0
0
2
0
1
2
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
1
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
2
0
0
0
0
2
0
2
1
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
2
2
0
0
0
2
0
0
0
0
1
0
0
2
0
1
2
2
1
0
0
1
0
0
0
0
0
0
0
1
2
0
3
0
0
2
0
0
2
0
0
0
0
3
0
0
3
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
2
0
1
0
1
0
1
0
0
0
1
1
0
0
0
2
1
1
0
0
0
0
0
3
1
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
2
2
2
0
0
0
2
0
0
0
1
2
0
0
0
1
0
0
2
0
2
1
0
0
0
0
2
0
0
0
0
1
1
1
0
0
1
0
0
1
1
0
0
0
0
0
2
0
0
0
2
0
2
1
0
0
0
0
0
2
2
0
2
0
2
0
0
0
1
2
0
0
1
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
1
1
1
0
0
0
0
3
0
0
1
2
0
2
0
1
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
1
0
2
0
0
0
0
2
2
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
2
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
2
2
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
12
2
0
2
1
2
0
2
1
0
0
2
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
3
0
2
0
4
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
3
0
0
3
1
0
0
2
0
4
0
0
0
0
1
0
0
0
0
0
0
0
3
0
2
2
0
1
2
0
0
1
2
1
1
2
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
3
0
2
0
1
0
0
1
0
0
0
1
0
1
0
2
2
5
0
1
1
1
0
2
0
1
0
0
0
0
0
0
0
0
0
2
1
1
0
1
0
0
0
0
2
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
3
0
0
0
1
1
0
0
1
0
2
0
0
2
0
3
0
2
1
0
3
0
0
2
0
1
0
0
0
2
0
0
1
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
2
0
2
2
0
1
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
2
0
0
0
0
0
3
0
0
2
0
0
1
0
1
0
1
0
0
2
1
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
1
0
1
0
0
2
1
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
1
0
0
0
0
1
1
0
0
0
0
0
0
2
1
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
2
1
0
0
0
0
0
0
0
0
1
0
2
0
1
0
2
0
0
1
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
1
1
0
2
0
2
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
2
0
2
0
1
0
0
1
0
0
1
1
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
1
0
0
2
1
0
0
0
2
0
0
0
1
0
0
0
0
1
2
1
0
1
0
0
0
0
0
0
0
0
1
2
0
0
3
1
0
0
0
0
1
0
0
1
2
2
1
0
0
0
0
0
0
1
0
0
0
2
0
1
3
2
0
0
1
3
1
0
0
0
2
0
0
0
0
0
5
0
0
0
1
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
2
0
0
0
0
0
2
0
0
1
1
0
1
0
0
0
2
3
0
0
0
0
0
0
0
3
2
0
1
0
0
0
0
0
2
0
2
1
3
0
3
4
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
1
0
2
0
1
0
0
0
2
3
1
0
2
0
0
1
0
1
1
1
1
0
0
1
0
0
0
0
0
0
0
2
0
1
0
1
1
0
2
0
0
0
0
0
1
2
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
1
8
2
0
0
1
0
0
0
0
0
0
1
0
2
2
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
2
0
1
0
0
1
0
0
0
0
1
0
0
1
0
2
0
0
2
1
0
0
0
0
0
1
1
0
1
0
0
0
2
1
0
2
2
0
0
0
2
2
2
0
0
7
2
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
1
2
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
2
0
0
1
0
0
2
1
2
2
1
0
3
1
1
0
1
0
0
1
2
0
0
2
2
0
0
2
1
1
1
2
0
0
0
2
3
0
0
2
0
0
2
0
0
0
1
1
0
2
0
0
3
2
0
2
1
0
0
0
0
2
2
0
4
0
0
1
0
1
1
0
0
0
2
0
1
0
1
1
0
0
0
2
0
0
1
0
4
0
1
0
0
0
0
2
0
0
0
1
1
2
1
0
0
0
0
1
0
2
0
0
0
0
0
2
2
0
0
1
0
2
0
2
0
0
1
0
0
0
0
2
0
1
0
0
0
1
1
0
0
0
0
0
0
0
2
0
1
1
0
2
2
0
1
1
2
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
2
0
3
2
1
2
0
0
0
1
1
0
0
2
1
2
1
2
3
3
2
2
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
3
0
0
2
2
0
1
1
0
0
0
1
0
0
0
2
0
0
0
1
0
3
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
1
0
2
1
0
0
2
0
0
0
1
1
0
0
0
0
2
0
0
2
0
2
0
2
2
0
0
0
1
0
1
1
1
0
0
0
2
1
0
1
0
1
0
1
0
2
0
0
0
0
2
0
0
0
0
2
0
2
0
0
1
0
1
0
0
1
0
2
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
2
2
0
2
1
0
2
0
0
0
0
0
0
2
0
0
2
1
2
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
1
1
0
0
2
1
0
0
0
1
2
0
0
0
2
0
0
2
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
1
0
5
2
0
0
0
0
2
1
2
0
0
1
0
0
0
2
1
2
3
0
1
0
0
0
0
0
0
1
0
1
0
2
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
1
0
0
0
0
1
0
0
2
0
0
0
3
2
2
0
0
2
0
0
6
2
0
0
1
1
0
0
2
0
0
0
3
0
0
3
0
1
2
1
0
0
1
0
1
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
2
0
0
1
1
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
1
0
2
0
0
0
0
3
0
3
0
1
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
3
0
0
0
0
0
2
1
0
0
1
1
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
1
0
1
0
1
1
0
2
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
2
0
1
2
0
4
0
2
2
1
0
0
2
0
0
3
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
2
0
0
0
2
0
1
2
0
0
0
0
0
1
1
1
0
1
0
0
0
2
2
3
2
0
0
0
1
0
0
2
0
1
2
0
0
1
1
1
0
0
0
0
0
0
2
0
2
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
2
0
2
0
1
0
1
2
0
0
1
0
0
0
2
0
1
0
2
2
0
0
0
1
0
0
0
1
0
0
0
0
0
2
2
0
1
1
0
0
0
0
0
0
0
0
2
0
2
1
2
0
0
0
2
0
1
0
0
1
0
1
0
3
1
0
0
0
0
1
0
1
1
0
2
0
0
0
0
0
0
2
1
0
0
1
0
0
1
1
0
2
0
0
0
0
0
1
2
0
1
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
1
0
0
0
0
1
1
0
0
0
2
2
0
1
0
0
3
0
0
0
0
0
1
0
0
0
2
0
0
0
3
0
0
0
1
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
1
0
2
2
0
3
1
0
0
0
2
0
4
0
0
1
0
1
2
0
0
0
2
2
2
0
2
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
3
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
1
0
0
2
2
0
0
2
1
0
0
0
0
0
2
0
1
0
2
0
1
0
0
0
2
2
0
0
0
0
2
1
2
2
0
5
0
0
0
0
0
1
2
1
0
0
0
0
2
2
0
0
4
0
0
0
1
0
2
0
1
2
1
1
0
0
3
0
0
0
1
0
0
0
0
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
1
0
0
0
1
2
1
1
1
0
0
0
1
0
0
0
0
2
0
0
0
2
0
1
0
0
1
0
0
0
2
0
0
2
2
0
2
0
1
0
2
0
0
0
1
0
1
2
1
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
1
0
1
1
2
0
2
0
0
0
0
1
2
1
0
1
0
2
0
0
0
1
0
0
0
1
0
0
2
3
2
0
1
8
1
0
0
0
2
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
2
0
3
2
0
0
1
0
0
3
0
2
2
0
2
0
0
2
0
0
1
0
0
2
0
0
0
2
0
0
1
0
0
2
0
1
0
2
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
1
0
2
0
0
2
2
1
0
0
0
0
2
1
0
0
1
0
0
2
2
2
3
2
5
1
0
2
0
1
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
1
0
1
0
2
1
1
0
1
0
0
3
1
0
2
0
0
0
0
0
0
0
2
2
0
0
3
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
2
0
1
2
2
0
0
0
6
2
0
2
1
1
1
0
1
0
2
2
0
1
2
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
1
0
0
3
0
0
0
1
0
0
1
1
1
0
1
0
0
0
1
0
0
1
1
0
0
0
2
1
0
0
0
0
2
0
0
1
0
1
0
0
1
0
0
0
0
0
2
0
0
1
0
1
0
0
1
0
0
1
2
0
0
1
0
0
2
1
0
0
0
1
0
1
2
1
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
1
0
2
1
0
2
0
2
0
0
0
0
2
0
2
2
0
1
2
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
1
0
2
0
2
0
0
0
0
0
2
0
0
0
1
0
1
2
0
1
0
0
0
0
1
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
1
0
0
1
0
1
0
0
1
1
3
1
1
0
0
0
0
1
0
1
2
0
0
0
0
1
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
2
1
0
2
0
2
0
1
0
0
2
0
0
5
0
0
2
0
0
0
2
2
0
0
2
0
0
1
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
2
0
2
0
2
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
2
0
3
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
1
0
1
2
1
0
0
0
1
0
1
4
0
0
2
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
2
0
0
2
1
0
2
0
2
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
2
0
0
0
2
0
0
1
0
0
0
0
0
2
0
3
3
0
0
3
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
1
2
0
0
0
4
2
3
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
1
0
1
0
2
0
0
1
0
0
1
0
2
0
0
2
2
0
1
2
0
0
1
2
0
2
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
1
0
0
2
1
0
0
0
0
0
0
0
1
2
0
0
2
0
0
2
0
0
2
1
0
0
1
2
0
0
5
0
0
2
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
2
1
1
2
2
1
0
0
1
0
2
0
0
0
2
0
0
0
2
0
0
2
1
2
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
4
0
2
0
1
0
0
2
1
2
2
0
0
0
3
0
1
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
3
0
1
0
0
2
1
0
0
0
0
0
2
2
0
1
2
0
1
0
0
0
0
1
0
0
2
1
0
0
0
2
2
2
0
1
0
2
0
0
0
2
0
2
0
0
0
0
2
1
2
2
2
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
1
2
2
1
0
0
2
0
0
0
0
0
0
2
0
0
2
0
1
0
2
3
0
0
2
0
0
0
1
0
0
2
1
0
0
0
0
1
3
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
1
1
2
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
1
0
3
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
1
0
6
0
0
1
3
0
2
1
2
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
2
1
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
4
0
1
0
0
4
0
2
2
0
1
0
0
0
0
2
1
0
0
1
0
1
1
0
0
1
2
0
0
2
1
2
2
0
0
1
0
0
0
2
2
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
2
0
2
3
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
3
0
0
2
0
0
0
1
1
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
1
0
1
0
1
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
1
0
0
0
1
2
0
1
8
0
0
1
1
0
1
0
0
0
2
2
2
0
0
0
1
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
1
0
0
2
3
0
1
4
0
0
0
0
0
0
0
0
0
0
2
0
1
3
0
0
0
0
0
0
0
1
0
0
0
2
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
2
1
0
1
2
0
1
2
0
2
0
0
1
0
0
0
2
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
2
1
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
1
0
8
0
0
0
1
0
1
1
1
0
0
0
2
2
0
1
0
0
0
0
1
0
0
2
5
0
0
0
0
2
0
0
4
2
0
1
0
0
1
3
2
3
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
2
0
0
1
0
2
0
1
1
0
1
2
2
0
0
1
0
2
0
0
1
0
0
0
0
0
0
1
2
0
0
2
0
1
0
3
0
1
0
1
0
0
4
0
1
2
2
1
0
1
2
0
0
0
2
0
0
0
0
0
0
1
0
0
1
3
0
0
0
1
2
0
0
0
2
1
1
2
1
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
2
0
0
2
1
0
0
1
0
0
0
0
2
0
2
0
0
2
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
2
1
2
0
0
0
0
2
0
3
0
1
0
0
2
0
0
2
3
1
0
0
2
0
2
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
1
0
0
0
0
1
0
2
0
0
0
0
2
0
1
0
2
0
1
0
0
0
0
1
0
0
0
2
2
2
0
2
0
2
0
1
2
2
1
0
1
0
0
1
1
0
2
2
0
1
0
0
0
0
0
1
1
1
0
0
1
1
0
0
1
0
0
2
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
2
2
0
1
2
0
0
0
1
1
1
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
2
0
1
0
0
0
2
2
1
0
1
0
1
0
0
0
1
0
2
0
0
0
2
1
0
2
0
0
2
0
0
0
2
0
0
0
1
1
0
2
2
2
1
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
2
1
1
1
0
0
1
1
5
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
2
0
1
0
1
0
1
0
0
1
2
1
0
2
0
2
0
2
0
1
0
0
0
0
2
0
2
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
1
2
2
0
0
1
0
0
0
2
2
0
0
0
0
2
0
1
0
0
0
0
4
2
0
2
0
0
0
0
0
1
0
1
4
3
0
0
0
1
0
0
0
0
0
1
1
0
1
2
1
0
2
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
2
2
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
1
1
0
0
0
2
0
0
0
2
1
0
0
2
0
1
1
2
2
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
3
0
0
0
0
1
0
0
1
0
0
0
0
2
1
2
5
0
0
0
0
1
1
0
1
1
1
0
0
1
1
0
1
0
2
2
0
0
0
0
0
0
0
1
2
1
0
0
0
0
2
0
0
0
0
2
0
0
0
10
0
1
0
1
0
0
0
0
0
0
1
2
0
2
0
0
1
0
1
2
1
2
0
0
0
1
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
4
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
1
0
1
1
2
4
0
0
0
2
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
2
1
2
2
0
0
0
0
1
0
1
2
2
0
2
0
0
0
2
0
0
0
0
0
1
0
1
0
0
2
0
2
2
0
0
0
0
1
1
1
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
1
2
0
2
1
0
0
0
0
0
1
0
0
0
1
0
2
0
0
1
0
1
0
0
0
0
2
0
0
1
0
0
2
2
0
2
0
0
0
0
0
1
0
0
0
5
0
0
1
0
0
2
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
2
1
1
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
1
1
0
0
0
0
2
0
1
0
0
2
0
0
0
1
0
1
0
0
0
0
1
1
1
0
0
0
1
2
2
0
0
0
0
0
0
2
2
1
1
1
0
0
0
1
2
2
0
2
0
1
2
2
1
1
1
1
0
2
0
0
0
0
2
1
1
2
0
0
1
1
0
0
2
0
2
0
0
2
0
0
1
2
0
0
0
0
0
0
2
2
2
0
0
0
3
1
1
0
0
0
0
2
2
0
0
0
0
1
1
2
0
0
2
0
2
0
0
0
0
1
0
2
2
2
0
1
1
0
0
2
0
0
2
2
2
0
0
0
1
1
0
2
0
0
2
0
0
2
0
0
0
0
1
0
0
0
1
2
0
0
0
3
0
0
0
0
5
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
2
0
2
0
1
0
1
0
1
1
0
0
0
0
0
1
0
0
3
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
2
0
0
0
2
0
1
1
0
0
2
0
1
2
0
0
0
0
1
2
2
0
0
2
0
5
0
0
0
0
2
0
0
0
1
2
2
0
2
0
0
0
0
2
0
0
2
2
2
2
0
0
1
0
0
1
1
1
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
3
2
0
1
0
0
1
0
1
0
1
1
1
1
3
0
3
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
4
2
0
0
0
2
0
1
0
0
0
0
0
0
2
2
2
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
2
1
0
0
0
2
0
2
1
0
0
2
0
0
3
0
2
0
2
1
1
0
1
0
0
0
0
1
2
0
0
0
0
0
1
2
1
2
0
2
2
0
0
0
1
0
0
2
0
0
2
0
1
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
2
3
0
1
0
0
2
0
0
0
0
0
0
0
1
1
0
2
0
2
1
0
0
1
0
0
0
0
1
1
2
0
0
0
0
2
0
0
0
0
0
7
0
0
0
3
0
2
0
0
0
0
2
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
1
2
0
0
0
3
0
0
1
1
0
0
0
1
0
2
3
0
2
0
2
2
0
2
1
0
0
0
0
0
2
1
1
1
0
0
2
0
0
1
1
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
1
0
4
1
0
1
0
0
0
3
0
0
2
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
1
1
2
0
0
1
0
0
2
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
2
1
2
0
0
0
0
0
0
2
2
2
0
2
0
0
0
0
0
2
0
0
1
0
0
2
2
0
0
0
0
0
2
0
0
0
0
1
1
2
2
0
2
0
1
0
1
2
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
2
0
2
0
0
0
0
2
0
0
2
0
2
0
1
0
0
2
1
1
0
0
3
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
2
2
0
0
2
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
3
0
1
0
2
2
0
0
0
2
2
0
2
1
3
0
0
2
2
0
0
0
0
0
0
1
0
0
0
2
0
2
0
1
1
1
1
0
2
1
3
0
0
0
0
0
2
1
0
2
0
0
1
1
0
1
0
1
1
0
2
0
2
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
2
1
2
0
1
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
1
3
0
1
0
0
0
2
0
0
0
2
0
1
0
2
0
0
1
0
2
0
0
0
1
2
0
0
0
0
1
0
0
5
0
2
2
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
2
0
1
0
1
0
1
0
0
2
0
1
0
1
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
3
2
0
0
2
0
0
0
0
0
1
0
1
1
2
2
0
1
2
0
0
0
1
0
0
2
0
2
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
2
1
0
0
0
4
1
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
1
2
2
0
1
0
1
0
0
2
0
1
0
0
0
0
1
0
1
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
2
0
1
3
1
0
1
0
1
1
0
0
0
0
2
0
2
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
1
0
2
0
2
0
1
2
0
0
2
1
0
0
0
2
3
0
2
0
0
2
0
0
0
0
1
1
0
0
2
2
1
2
0
2
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
1
1
2
0
0
1
0
0
0
2
0
2
0
1
0
0
0
0
0
2
1
1
0
0
1
1
0
0
0
0
0
0
0
0
2
1
2
2
0
0
2
0
2
0
0
4
1
0
0
1
0
1
0
0
1
0
1
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
1
1
2
0
0
0
2
1
1
2
0
1
0
0
1
0
2
2
1
0
0
0
0
1
2
1
1
2
0
2
2
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
2
0
0
0
2
0
0
0
3
0
2
3
2
0
1
2
1
0
2
0
1
0
0
0
0
0
0
0
0
0
2
1
2
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
2
0
1
0
0
0
0
0
0
2
0
0
2
0
0
1
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
5
0
0
0
2
2
2
0
0
0
1
0
0
0
0
1
0
2
1
2
0
0
0
0
0
2
2
4
0
2
1
0
0
0
0
0
0
0
2
0
0
0
1
0
1
1
0
0
1
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
2
2
3
0
0
2
0
4
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
2
1
1
1
1
0
0
1
0
2
1
0
0
0
1
1
0
2
0
1
0
1
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
1
0
0
1
0
0
0
1
0
2
0
1
1
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
2
0
1
0
0
0
1
0
2
3
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
2
2
2
0
0
2
0
2
2
0
2
0
1
1
0
0
2
0
0
2
4
0
0
0
0
0
0
1
0
1
0
1
2
1
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
3
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
2
0
1
1
0
0
0
1
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
2
0
1
0
0
0
2
0
3
0
0
0
0
1
0
2
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
2
0
2
1
0
2
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
1
0
0
1
0
0
0
1
0
2
0
1
0
0
1
0
2
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
1
0
0
0
1
2
0
2
2
0
1
0
0
0
0
0
1
8
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
2
2
0
2
0
2
0
2
0
0
1
0
2
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
1
0
0
2
0
0
0
0
0
1
2
1
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
3
0
0
2
0
0
0
0
0
0
1
2
0
0
0
2
2
0
2
1
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
2
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
1
2
0
1
1
1
0
0
1
0
0
2
3
0
0
0
1
1
0
0
0
2
0
0
3
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
2
0
2
1
0
2
0
2
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
2
0
2
1
0
0
4
5
3
0
0
0
0
0
1
0
0
1
3
1
0
0
0
0
0
2
1
1
0
0
0
0
1
0
1
0
1
0
2
0
2
0
0
0
0
0
0
0
0
1
2
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
1
0
1
0
0
1
0
0
2
2
2
0
0
0
2
0
3
0
0
2
0
0
2
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
1
1
2
0
13
0
0
2
0
0
1
0
1
0
0
1
2
1
2
0
1
0
2
0
2
1
0
0
1
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
1
0
2
0
0
0
0
0
1
2
0
0
2
0
0
1
0
0
0
2
2
0
1
3
0
0
3
1
1
0
2
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
2
0
0
0
1
0
1
1
2
0
0
0
1
0
0
0
4
2
0
3
2
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
1
1
0
2
2
1
0
1
2
0
2
0
1
0
2
0
1
1
2
0
0
0
1
3
0
1
1
0
2
0
2
0
2
2
0
0
0
1
0
0
0
2
2
0
1
0
2
0
2
0
0
0
1
1
3
0
0
0
0
0
0
2
2
0
0
0
2
0
2
0
2
2
2
1
0
0
2
1
0
0
0
0
1
0
0
5
2
0
0
1
2
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
1
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
1
2
0
0
0
0
0
0
1
1
1
0
1
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
2
0
0
0
1
2
1
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
3
0
0
0
0
0
2
2
0
2
0
0
0
0
0
1
0
4
0
2
1
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
4
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
2
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
2
1
0
2
2
1
2
2
0
0
0
0
0
2
1
0
0
0
2
1
0
0
0
0
2
2
2
0
2
0
0
1
0
0
0
1
0
0
1
0
2
2
2
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
2
2
1
0
0
1
0
0
0
2
2
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
1
1
0
0
0
0
0
2
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
1
0
0
0
1
0
1
0
0
1
1
1
0
0
0
0
0
2
1
0
0
0
0
2
0
0
3
2
1
2
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
3
0
1
0
1
0
2
0
2
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
1
0
2
0
0
0
0
0
2
0
2
1
0
1
2
0
0
0
0
5
0
0
0
1
1
0
0
2
2
0
0
0
0
1
0
0
4
0
1
0
1
1
0
1
0
0
0
0
0
0
0
2
2
1
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
2
0
0
2
0
0
1
0
1
0
2
0
0
1
0
0
2
0
2
2
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
1
0
0
0
1
2
0
0
1
0
1
0
0
2
1
1
2
0
0
0
0
0
0
0
1
2
0
1
1
2
1
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
2
0
0
0
0
3
0
0
1
2
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
2
2
0
2
0
1
1
3
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
1
1
0
1
0
0
0
1
0
0
1
0
2
0
1
0
0
1
2
1
0
0
0
0
0
0
0
3
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
2
2
0
0
2
0
1
0
0
0
0
0
2
0
1
0
0
0
2
0
2
1
1
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
1
0
3
0
1
1
0
0
0
0
2
0
1
1
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
2
1
0
0
0
0
0
2
0
0
0
2
2
0
0
1
1
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
1
0
1
2
0
2
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
1
2
2
0
1
0
0
0
0
0
0
0
2
1
0
0
1
0
3
0
0
0
0
0
0
0
0
0
3
2
1
2
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
2
0
2
0
0
1
0
2
0
0
0
0
0
1
0
2
1
0
1
0
2
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
1
1
0
0
1
0
2
1
0
0
1
1
0
1
0
2
0
1
0
0
1
0
0
0
0
2
0
0
0
1
0
2
0
1
0
1
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
5
1
0
0
3
0
0
0
0
2
0
0
1
0
2
1
2
0
1
0
0
1
0
2
0
2
3
0
0
0
0
2
0
1
2
0
3
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
3
1
2
2
0
0
1
1
2
0
1
0
2
0
1
0
0
2
2
2
0
1
1
0
0
1
0
2
0
0
1
1
1
0
0
1
0
1
0
0
2
0
0
1
1
1
2
0
0
1
1
0
0
2
0
0
1
0
0
2
2
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
3
2
0
2
0
1
1
0
0
2
0
1
0
0
1
0
0
0
1
2
0
0
0
0
0
2
0
0
0
1
0
0
0
1
2
1
0
0
0
0
0
2
0
2
2
0
0
1
2
1
3
0
1
1
0
0
0
0
0
0
2
0
0
2
4
0
1
1
0
1
0
0
1
0
0
0
0
0
8
1
0
0
0
1
1
0
2
0
0
1
0
1
1
0
0
0
0
0
2
1
0
1
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
2
2
3
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
5
2
0
2
2
0
2
1
0
0
1
1
1
0
0
2
0
0
0
2
1
0
2
7
0
2
0
1
0
0
1
0
0
0
1
0
1
3
1
0
1
1
0
0
2
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
1
0
0
0
0
1
0
0
1
0
0
0
2
0
2
0
0
0
0
0
2
0
3
1
0
0
2
2
0
0
1
0
0
2
1
0
0
0
3
0
2
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
2
5
2
1
0
0
0
0
2
0
0
0
0
3
0
0
2
0
3
1
1
1
1
3
0
1
1
0
0
0
0
3
0
2
0
0
2
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
2
0
3
0
0
1
0
0
2
0
0
0
1
0
0
3
2
0
0
0
2
0
0
0
0
0
8
0
0
1
2
0
0
2
0
5
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
1
0
1
1
0
0
1
0
0
2
0
0
0
2
1
0
0
0
0
1
3
0
0
0
0
0
2
0
1
0
2
0
2
2
5
0
2
0
0
1
1
2
2
1
0
0
1
0
2
0
0
0
2
0
2
2
2
0
0
0
2
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
1
2
1
0
0
0
0
0
1
2
1
2
0
0
2
0
1
0
0
0
1
1
0
1
2
0
0
1
0
0
0
2
2
0
2
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
6
1
0
0
1
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
1
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
1
1
1
0
1
2
0
4
0
0
0
0
0
0
1
2
0
0
1
0
2
0
1
0
0
0
2
2
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
1
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
1
0
1
0
0
2
2
0
2
0
5
0
1
1
0
0
0
1
0
2
0
1
0
0
0
0
2
0
1
0
1
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
2
2
1
1
0
1
2
0
3
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
5
2
0
1
2
1
2
4
2
0
0
3
0
0
1
0
1
1
1
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
1
0
0
0
2
0
0
1
2
0
0
0
1
0
0
0
0
2
0
0
1
0
2
0
0
0
3
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
2
2
0
0
1
1
7
0
0
0
0
0
3
0
2
2
0
0
1
0
0
0
2
1
1
2
1
0
1
0
0
2
0
5
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
3
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
1
2
2
0
0
0
0
0
0
0
0
2
0
2
0
2
1
0
0
0
0
1
0
2
0
2
0
0
0
2
0
0
0
2
1
2
0
0
3
0
2
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
1
1
0
2
2
0
2
1
0
0
0
0
0
0
0
1
0
0
2
1
0
2
0
0
0
1
2
2
1
2
4
1
1
0
0
0
1
1
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
1
2
0
1
2
0
0
2
1
0
0
1
1
3
1
0
3
0
1
0
0
0
1
2
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
2
0
2
0
0
2
1
4
0
0
0
1
2
0
1
0
2
1
2
1
0
0
0
1
1
2
0
1
0
0
2
1
0
2
0
0
0
5
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
2
1
0
0
0
2
0
2
1
2
1
0
0
0
0
0
2
0
0
0
0
0
0
3
0
1
0
1
1
0
1
1
0
1
0
0
1
1
0
1
2
1
0
0
2
0
0
3
0
2
0
2
0
0
0
0
1
2
0
0
2
0
0
0
0
0
5
0
0
1
2
0
0
0
1
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
3
0
2
0
0
0
2
3
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
2
0
0
1
0
1
1
0
2
2
2
0
0
0
0
1
0
0
1
1
0
0
0
3
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
2
1
0
0
4
0
2
1
0
1
0
0
0
0
1
0
0
2
0
0
1
0
0
2
0
1
0
1
0
0
1
0
0
0
0
1
1
1
0
2
0
0
0
0
3
2
0
0
2
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
2
1
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
2
0
1
2
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
3
1
1
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
2
0
0
1
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
1
0
4
0
0
1
2
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
1
0
0
2
0
1
0
3
1
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
2
1
2
1
0
3
0
0
0
0
0
0
0
0
4
0
0
1
2
2
0
0
0
1
1
0
1
2
0
1
0
0
0
2
0
0
2
0
2
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
1
1
0
2
0
0
0
2
1
0
0
0
0
0
0
1
0
2
1
2
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
2
1
0
2
0
0
0
2
2
2
0
0
2
0
0
0
2
0
1
0
0
0
2
1
0
1
0
0
0
3
1
1
3
0
2
0
0
0
0
3
0
0
0
2
3
1
2
2
0
0
0
2
0
0
0
0
0
2
1
0
0
2
2
0
2
1
1
2
0
3
1
2
0
2
0
0
0
2
2
2
1
2
2
2
0
2
0
1
0
0
1
0
0
1
0
3
2
1
0
0
2
1
1
0
0
2
0
1
0
2
0
0
2
2
0
1
0
0
0
0
2
3
0
2
2
0
2
0
0
0
0
0
2
0
0
1
2
0
0
0
2
0
0
1
0
0
2
0
1
2
1
0
0
3
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
1
1
2
0
2
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
1
1
2
0
1
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
2
0
2
0
2
2
1
0
0
0
0
2
0
0
0
0
1
2
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
2
2
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
3
0
2
1
0
0
2
2
0
0
2
1
0
2
0
0
0
2
3
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
1
1
0
0
2
0
1
0
2
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
3
0
0
0
0
1
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
2
1
0
0
1
0
0
0
1
0
2
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
4
0
0
0
0
0
2
2
0
0
3
2
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
1
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
1
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
1
1
0
0
1
0
2
0
0
1
0
0
0
1
3
0
0
1
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
3
3
1
0
0
1
1
0
1
0
0
1
0
2
1
1
1
1
0
0
0
1
0
0
0
0
0
0
0
1
2
1
2
0
1
0
0
0
1
2
1
0
1
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
1
1
2
0
1
2
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
1
1
0
0
0
0
1
2
1
0
0
1
0
0
3
1
1
0
0
2
0
2
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
2
0
2
0
1
0
0
0
0
0
1
2
1
0
2
2
0
0
0
0
0
1
0
2
2
0
0
2
0
0
0
2
0
0
0
1
0
0
2
0
0
0
1
0
1
0
2
0
3
0
1
0
0
0
0
1
0
0
0
2
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
1
1
3
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
2
0
1
1
0
0
1
2
2
2
2
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
1
0
2
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
1
2
1
2
0
0
1
0
1
0
0
0
1
0
3
1
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
1
1
2
1
0
1
2
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
2
2
1
0
0
2
2
0
1
10
0
0
1
1
2
0
0
0
0
2
0
1
1
0
0
0
0
2
0
2
0
1
0
0
1
0
3
0
0
0
0
0
1
0
3
0
0
2
0
0
1
1
0
0
1
0
0
2
2
1
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
3
2
0
0
1
0
2
0
0
0
4
0
2
0
0
0
0
0
0
2
1
0
0
1
1
0
2
0
0
0
0
0
1
0
4
0
1
1
0
0
1
0
0
2
2
0
0
2
0
2
0
2
2
0
2
0
0
3
2
0
0
0
0
1
2
0
0
0
1
2
0
2
0
2
2
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
1
0
0
2
0
2
0
0
0
0
1
0
1
0
0
2
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
3
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
2
0
0
0
3
0
0
0
0
0
2
0
0
1
0
2
1
0
0
0
0
0
0
0
1
0
0
3
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
2
0
2
0
1
0
0
0
0
2
2
4
2
0
3
1
0
0
0
1
0
0
1
0
2
2
2
0
3
0
1
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
2
3
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
1
0
3
0
0
0
2
0
1
0
0
0
1
0
0
0
2
0
0
2
0
0
1
0
0
1
0
1
1
0
0
0
0
2
0
0
2
0
1
0
0
1
0
0
0
2
1
1
2
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
1
0
2
1
1
0
0
0
0
0
2
2
1
2
0
1
0
1
0
0
0
0
0
1
1
2
0
2
0
1
2
0
0
0
2
0
1
0
2
1
1
0
0
0
0
0
0
0
2
1
2
1
0
0
0
0
0
2
0
0
0
0
0
3
1
0
0
0
2
0
0
0
0
2
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
1
0
1
3
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
2
0
2
1
0
1
0
0
0
0
1
0
0
0
2
1
0
1
0
2
0
0
0
0
0
1
2
1
0
0
0
2
1
0
0
1
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
2
1
0
0
0
0
1
2
0
1
0
0
2
0
1
2
0
0
0
0
0
0
2
0
1
1
0
2
0
2
0
3
0
0
0
0
2
1
0
1
0
0
3
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
2
0
1
0
1
0
0
1
2
1
0
0
0
2
0
1
0
1
1
0
1
0
2
0
0
0
0
0
0
2
0
1
0
0
0
2
0
2
1
2
0
0
0
0
1
1
2
2
0
2
2
0
0
3
0
2
0
0
2
0
0
0
0
0
1
1
1
2
0
0
0
2
2
2
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
2
1
0
0
1
2
0
0
1
0
0
0
2
0
0
1
1
2
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
2
1
2
0
0
0
0
0
0
1
2
0
0
1
0
0
0
2
0
2
0
0
0
0
0
2
0
0
1
2
0
2
2
2
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
2
2
1
0
3
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
2
1
0
2
0
0
3
0
2
0
0
0
0
0
3
1
1
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
1
0
1
1
0
0
0
1
1
0
4
0
0
0
1
0
2
0
2
1
0
0
0
1
0
0
0
0
2
0
0
1
0
2
0
1
0
2
2
0
0
2
1
0
0
2
1
1
0
0
0
2
0
0
1
1
0
0
0
1
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
1
0
0
0
2
1
0
0
0
0
2
2
2
0
0
2
0
0
2
0
2
0
0
0
2
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
1
0
0
0
1
0
1
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
2
0
1
2
2
0
0
2
0
2
1
2
1
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
3
1
1
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
2
1
0
0
1
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
1
0
0
1
1
0
2
0
1
2
0
0
1
2
1
0
2
0
2
0
0
1
0
1
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
2
3
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
2
1
0
1
0
1
2
0
2
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
3
2
1
1
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
1
1
2
0
0
2
2
0
1
0
2
0
0
0
0
0
0
0
0
0
3
2
0
0
1
0
1
0
1
0
2
2
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
1
2
2
2
1
1
0
0
0
0
0
2
1
0
0
1
0
0
0
0
2
0
0
1
0
0
2
0
0
1
0
0
0
0
24
1
0
0
0
2
1
1
0
1
2
0
2
2
0
0
0
0
2
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
2
0
0
1
2
0
0
0
0
1
1
0
0
0
0
0
2
1
1
0
1
1
0
2
0
0
0
0
1
0
0
1
0
1
0
0
1
2
2
1
0
0
1
0
0
3
1
0
0
2
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
3
0
2
2
1
1
0
0
0
0
0
2
0
3
0
0
1
0
1
0
0
0
1
0
0
0
1
1
0
0
1
0
2
1
2
0
0
0
0
0
1
0
0
1
0
2
0
2
0
0
0
0
0
0
1
0
1
2
1
2
1
0
2
2
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
3
0
0
0
3
1
0
2
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
2
0
1
2
2
0
2
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
2
0
0
2
0
0
0
0
2
0
2
0
0
1
0
0
0
2
0
2
1
0
2
0
0
0
0
0
0
1
3
0
2
1
2
0
0
0
0
0
0
4
0
0
0
1
1
2
1
0
0
0
0
2
0
0
0
2
1
0
0
1
0
0
1
1
0
0
0
0
1
1
2
0
1
0
0
1
0
0
1
1
0
2
0
0
0
1
0
0
2
5
1
0
0
1
2
0
0
0
0
1
0
0
2
0
0
0
0
1
2
6
0
3
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
2
1
2
2
1
0
0
2
0
0
2
0
0
0
0
0
0
0
2
2
4
0
0
1
0
2
4
0
3
0
0
0
0
0
0
1
2
0
5
2
0
0
0
0
0
4
3
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
2
0
1
0
0
1
0
2
0
1
0
1
1
0
0
0
0
0
0
2
0
2
1
0
0
0
0
1
0
0
1
0
0
2
1
2
2
1
2
0
0
0
0
2
1
0
2
0
0
1
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
2
0
0
1
1
0
0
0
0
1
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
1
1
1
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
1
2
4
0
0
0
0
1
1
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
1
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
1
0
2
0
0
0
2
0
2
1
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
1
0
1
1
0
2
2
0
0
0
0
1
0
1
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
1
0
2
0
0
1
0
0
0
3
1
0
0
0
1
0
2
0
1
0
0
1
0
2
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
1
1
0
1
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
2
1
0
2
0
1
1
2
0
0
1
0
0
3
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
4
0
1
2
0
0
0
1
0
0
0
2
0
0
2
1
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
1
0
1
2
2
1
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
1
1
0
1
0
2
0
0
2
0
0
1
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
4
1
1
0
0
0
0
0
0
1
2
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
6
2
3
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
2
0
1
0
1
0
3
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
2
2
1
1
0
0
3
0
0
2
0
0
0
0
0
0
2
0
0
0
0
3
0
2
0
0
1
0
1
0
0
2
0
0
0
4
0
0
2
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
2
0
0
1
1
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
2
1
0
0
0
0
2
0
0
0
2
0
2
2
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
2
0
1
2
0
0
1
0
3
0
0
0
0
0
0
1
0
0
0
0
1
1
1
2
1
0
0
1
0
0
2
0
0
2
1
0
1
2
1
0
2
0
2
2
0
0
2
0
0
0
0
2
2
2
0
2
0
1
1
0
0
0
0
1
0
2
0
0
0
0
0
1
0
2
0
1
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
4
1
0
0
0
0
2
0
0
1
0
0
2
0
2
0
1
1
0
2
0
0
1
0
0
0
2
0
0
0
0
0
3
1
1
0
0
0
1
1
0
0
2
2
0
2
1
0
2
2
2
0
0
1
2
0
0
0
0
0
0
0
1
3
0
2
0
1
1
0
0
0
6
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
1
0
2
2
0
0
0
0
0
0
0
2
2
1
0
0
1
0
2
0
0
0
0
0
0
2
1
0
0
0
0
1
0
3
0
1
0
1
2
2
1
4
2
1
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
1
1
0
0
3
1
0
0
0
0
0
2
2
0
0
0
1
1
2
0
0
0
0
1
0
0
0
0
2
2
1
0
0
1
1
0
2
0
0
1
3
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
1
0
2
0
2
0
0
0
2
0
0
0
2
2
0
0
0
0
2
0
1
0
0
0
0
1
2
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
2
3
1
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
1
1
0
1
0
0
0
0
2
0
1
0
0
0
0
2
0
0
2
1
0
0
0
2
2
0
2
0
0
0
0
0
0
1
1
0
1
4
0
0
1
0
0
1
2
0
0
1
2
0
0
0
0
2
0
1
0
0
2
0
0
0
2
0
0
2
0
0
2
1
0
1
0
1
1
0
0
0
0
1
0
0
0
1
2
0
2
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
1
2
0
2
1
0
0
1
2
0
1
2
0
0
1
0
0
0
2
0
2
0
0
2
0
0
0
0
3
2
0
1
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
2
0
0
1
0
0
0
1
0
2
2
0
0
0
1
1
0
0
1
1
0
0
3
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
2
2
0
0
2
2
0
0
0
0
0
0
2
1
0
0
0
1
0
0
2
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
2
1
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
2
1
1
1
1
0
0
1
0
0
0
0
0
0
1
0
1
2
0
0
1
2
0
2
0
0
0
1
0
2
0
0
0
2
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
2
0
5
0
0
0
0
0
1
0
0
0
2
0
0
3
1
2
2
0
0
0
1
0
1
0
0
2
0
1
0
0
0
0
1
3
0
0
0
2
2
2
0
3
2
2
2
0
0
2
2
0
0
0
0
0
1
0
0
2
0
2
0
3
2
0
2
0
3
2
0
0
0
0
2
1
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
3
0
3
2
0
0
0
1
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
2
1
0
2
1
0
0
0
2
0
2
0
0
0
0
0
2
3
2
0
1
3
0
2
1
0
0
0
0
0
2
0
1
2
1
2
2
0
0
0
1
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
1
1
0
1
0
1
2
0
1
0
0
1
0
0
0
0
0
1
0
0
2
2
0
2
0
2
0
2
1
0
0
2
2
2
1
0
0
2
0
0
0
0
0
0
0
1
0
2
0
1
0
3
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
2
2
0
1
1
0
0
0
2
1
0
2
1
0
0
0
0
2
0
1
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
2
2
0
1
2
0
0
0
0
1
0
1
0
0
0
1
0
2
0
0
0
0
1
0
0
2
0
0
1
0
0
0
3
3
1
0
2
2
0
0
0
0
0
1
0
2
0
5
2
1
0
2
0
2
0
0
0
1
0
2
0
1
0
0
0
2
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
2
2
0
0
0
0
0
1
0
0
0
1
6
0
0
0
0
1
0
2
2
2
0
0
0
2
0
1
0
1
0
0
2
2
2
0
3
0
0
0
0
2
1
1
0
0
0
1
0
0
0
1
2
0
2
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
4
0
2
0
1
0
1
0
0
3
0
0
2
1
0
1
2
0
0
0
0
1
2
0
0
0
0
0
1
0
0
2
0
2
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
1
1
0
0
1
0
0
3
0
0
0
0
0
0
1
0
0
6
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
2
0
0
1
1
2
0
0
0
0
3
1
2
0
1
0
2
1
0
0
0
1
0
1
0
2
0
2
2
0
0
0
2
0
0
1
0
1
0
0
2
1
1
1
0
0
2
0
1
2
3
2
0
0
0
3
1
0
1
0
0
0
0
2
0
1
0
0
0
2
1
1
0
0
0
0
2
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
2
2
3
2
2
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
1
1
0
4
1
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
2
1
1
0
0
0
1
2
0
0
2
1
0
0
1
2
2
0
0
2
0
2
1
0
0
2
0
1
2
0
1
1
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
2
0
0
1
3
0
1
2
0
0
0
0
1
0
0
0
0
2
2
0
3
3
1
1
6
0
1
0
0
2
1
0
2
1
0
0
0
0
0
0
0
0
0
0
2
1
0
1
2
0
0
0
2
0
0
0
1
0
0
4
0
0
0
0
0
0
2
3
2
0
1
1
0
1
0
1
2
1
2
0
1
0
1
1
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
1
0
1
1
1
0
0
0
0
2
1
2
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
2
2
0
1
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
2
1
0
0
0
1
1
0
0
0
0
0
0
2
0
0
1
0
0
2
0
2
2
0
0
0
1
1
0
2
0
0
0
0
0
2
1
1
1
1
0
0
3
0
0
0
2
0
0
0
0
2
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
2
2
0
0
0
0
0
1
2
0
0
2
0
1
2
0
2
0
0
0
2
0
2
2
1
1
2
2
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
1
0
2
0
1
5
1
0
0
0
1
0
0
2
0
2
0
0
1
2
0
0
2
0
1
0
0
0
0
0
1
0
2
1
1
0
0
0
1
2
0
1
1
0
0
0
2
1
0
0
1
1
8
0
2
2
0
0
0
1
0
0
2
0
0
1
1
2
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
1
0
0
0
1
1
0
1
0
0
0
0
0
2
0
0
2
2
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
1
0
0
2
0
0
0
0
2
0
1
0
0
2
0
0
0
1
0
0
1
2
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
3
0
1
1
0
0
1
1
1
0
0
0
0
0
1
3
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
3
0
2
0
1
1
1
1
1
0
1
0
2
1
2
0
2
3
1
0
1
0
3
0
2
0
0
2
0
0
0
0
0
1
0
1
2
0
0
2
0
0
2
1
0
0
1
0
2
1
1
0
1
0
2
1
0
1
0
2
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
1
0
2
0
0
0
0
0
2
1
1
0
3
0
2
0
0
1
0
0
2
2
0
2
0
0
0
1
0
0
0
0
0
0
1
0
2
0
2
2
0
0
2
0
1
0
3
0
2
2
0
0
1
3
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
3
2
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
1
2
0
0
2
2
0
0
0
1
0
0
1
0
0
0
2
2
0
1
1
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
2
2
1
0
0
1
0
0
0
3
0
0
1
0
1
0
0
0
0
0
1
2
1
0
1
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
1
1
0
1
0
2
0
0
1
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
3
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
1
2
0
0
1
0
2
0
0
0
0
2
0
1
1
2
0
0
1
0
0
0
0
0
0
2
2
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
2
1
0
0
1
0
1
2
0
0
1
0
0
0
0
0
0
0
0
2
2
2
1
2
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
1
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
1
5
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
1
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
1
1
0
1
0
2
0
0
0
0
0
0
0
0
0
3
1
0
1
0
0
0
2
0
0
0
1
0
2
1
1
0
2
1
0
0
1
0
0
1
1
0
0
0
0
1
0
2
1
0
2
0
1
1
0
0
0
1
0
2
0
0
0
0
0
0
2
1
0
1
0
2
0
0
0
2
0
2
1
0
0
0
1
0
1
0
0
0
1
0
5
0
0
0
2
0
2
0
0
0
1
0
2
1
2
1
0
0
0
0
0
1
0
3
0
1
0
1
2
0
2
0
1
0
0
0
0
0
0
2
2
0
1
0
0
1
0
0
3
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
2
0
0
2
2
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
2
0
0
2
0
0
0
1
1
0
0
0
6
3
2
0
2
2
1
2
2
0
0
0
0
1
0
2
1
0
0
0
2
1
0
2
1
2
0
2
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
1
0
1
0
0
1
1
2
1
1
2
2
0
0
0
0
0
1
0
0
0
1
0
0
0
1
2
0
1
0
0
0
1
0
1
0
1
2
0
0
0
0
0
2
1
0
0
2
0
1
0
0
0
0
2
1
0
3
2
0
0
2
0
0
0
0
1
2
0
0
0
2
0
0
0
1
0
0
0
1
2
0
1
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
2
0
0
0
2
0
1
0
1
2
3
2
0
0
1
1
2
2
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
1
0
1
0
0
1
2
0
0
2
3
0
2
0
0
0
1
1
0
2
0
0
1
0
1
2
0
0
2
0
2
0
2
0
0
0
0
1
0
1
1
0
0
0
0
0
2
0
0
0
2
0
0
1
0
1
2
0
0
1
1
1
0
3
2
0
0
0
0
4
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
1
1
3
0
0
0
3
0
2
1
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
2
1
1
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
1
1
0
0
0
1
11
0
1
2
0
0
2
0
2
0
2
4
0
0
0
0
6
0
0
0
1
2
0
0
0
1
1
3
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
3
0
1
1
0
0
1
0
2
0
2
0
0
1
1
0
1
0
1
1
2
1
0
0
0
1
1
0
0
2
0
0
0
0
1
0
0
2
0
2
0
2
0
0
1
2
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
3
0
0
3
2
2
2
0
1
1
0
0
2
0
0
0
2
13
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
2
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
3
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
1
1
0
3
0
0
2
0
0
1
0
0
8
2
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
1
0
2
1
0
0
0
0
1
1
0
0
2
3
0
1
0
0
4
1
2
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
1
0
1
0
0
0
1
2
0
0
4
1
0
0
0
0
1
0
2
0
1
4
0
0
0
0
2
0
0
0
0
0
0
2
1
2
0
1
0
0
0
0
1
2
0
0
1
0
0
2
0
1
0
2
0
0
2
1
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
1
0
0
2
0
0
2
0
0
2
0
0
2
2
2
0
0
3
0
2
0
0
0
2
0
0
2
0
1
0
0
2
0
0
0
0
1
0
1
1
0
1
0
1
0
1
0
0
0
2
2
0
2
0
0
0
0
0
0
0
2
0
0
5
0
0
0
2
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
2
0
4
3
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
1
0
1
0
0
0
1
0
2
0
0
2
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
2
1
0
2
0
2
2
0
0
0
2
0
2
1
0
2
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
1
0
0
0
0
1
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
2
1
0
2
2
0
0
0
0
2
1
0
0
0
1
3
0
0
0
2
2
0
1
0
0
0
0
0
0
2
0
0
0
0
5
0
2
0
0
0
0
0
0
0
2
0
1
2
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
2
2
1
0
1
0
2
0
0
2
0
0
0
2
0
1
1
0
0
0
2
0
0
0
4
1
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
2
0
0
0
0
3
1
0
0
0
2
0
0
0
1
0
1
0
1
1
0
0
1
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
1
1
0
0
1
0
0
0
2
0
0
0
0
1
0
0
2
0
5
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
2
0
1
0
0
1
0
2
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
5
1
0
1
1
0
0
4
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
1
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
3
0
0
1
2
0
0
2
0
0
1
0
0
2
0
0
0
0
0
1
2
2
1
0
1
0
0
2
0
2
0
0
0
0
2
0
2
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
1
0
2
2
2
0
0
0
0
0
0
0
1
2
2
0
0
0
0
2
0
1
2
2
2
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
2
0
0
2
0
1
0
1
0
1
0
0
0
0
1
2
0
1
0
0
3
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
2
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
5
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
1
2
1
0
1
0
0
1
0
0
0
0
0
0
0
1
2
1
1
0
0
0
0
1
3
0
0
0
1
3
0
0
0
0
2
1
0
1
0
0
0
2
2
2
0
0
0
0
0
0
5
0
1
0
0
1
0
0
0
1
0
3
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
2
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
3
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
4
0
2
0
0
2
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
1
0
2
0
1
0
0
1
1
1
0
0
0
2
0
0
2
0
9
0
1
0
0
0
2
0
0
2
2
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
1
1
0
1
2
0
2
1
0
0
1
0
0
2
0
0
0
2
2
0
0
0
2
5
2
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
2
0
0
0
0
0
2
0
0
1
2
0
0
2
0
2
1
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
2
2
0
0
1
0
0
0
1
2
0
0
3
1
1
2
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
2
2
0
0
1
2
0
0
0
0
0
0
4
2
0
0
3
1
0
0
0
0
0
0
5
0
0
2
0
0
0
0
0
0
0
1
0
0
1
1
3
0
0
0
0
2
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
3
0
0
0
0
0
2
0
0
0
0
2
2
1
0
0
0
0
0
2
2
2
0
0
6
1
0
1
0
3
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
1
0
1
1
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
1
0
2
0
3
0
1
2
3
0
1
0
2
0
0
0
1
0
1
0
0
3
0
0
0
2
0
1
2
2
0
0
0
0
0
0
0
0
2
2
2
0
0
0
1
0
0
2
2
0
1
0
0
0
1
0
0
0
2
0
2
1
0
0
0
0
0
0
1
1
1
0
0
0
0
1
2
2
0
0
0
0
0
0
2
0
3
0
0
0
1
1
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
1
2
0
0
1
0
2
0
1
1
1
0
0
2
0
0
0
1
0
0
0
2
1
1
0
2
0
0
2
0
0
1
0
1
0
2
0
0
2
2
0
1
1
0
2
0
1
2
0
0
0
0
0
0
0
1
0
0
2
1
0
3
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
1
2
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
1
0
0
2
2
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
2
0
0
0
0
1
2
2
0
0
2
2
1
0
0
0
0
5
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
1
0
2
2
1
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
2
2
0
0
1
0
1
0
0
0
0
0
0
2
1
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
3
0
0
2
2
1
0
1
0
10
1
2
1
1
0
0
2
1
1
0
0
0
4
0
0
0
1
0
0
2
1
0
1
1
1
0
1
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
2
1
1
0
0
1
2
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
2
1
0
2
3
2
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
1
0
0
1
0
2
0
1
0
0
0
2
1
0
0
0
1
0
1
0
0
2
0
2
0
0
0
0
0
0
1
0
1
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
2
2
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
5
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
1
0
0
0
0
1
0
0
1
1
0
3
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
2
1
0
1
1
0
0
0
0
0
2
0
2
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
1
1
3
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
3
1
1
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
3
0
0
0
0
2
1
0
0
1
0
2
0
0
2
0
0
1
0
0
0
2
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
2
1
0
1
0
2
1
0
0
2
0
2
0
0
1
0
0
2
0
0
1
2
0
1
2
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
5
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
2
1
0
0
0
0
1
0
3
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
2
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
1
0
0
2
0
0
1
0
1
0
0
2
0
2
0
0
0
0
2
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
2
1
0
1
1
1
0
0
0
1
0
0
0
0
2
0
2
2
1
1
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
3
0
1
2
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
2
1
0
0
0
0
1
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
1
0
0
0
0
0
4
0
0
0
0
2
2
0
1
0
3
0
2
2
0
0
1
0
0
1
0
2
1
0
2
3
0
0
1
0
2
1
0
2
2
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
2
2
0
0
1
0
4
0
1
0
0
0
1
1
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
1
2
1
2
0
0
0
0
0
0
1
1
2
1
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
2
1
0
1
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
5
0
0
1
0
0
2
2
6
4
0
0
1
0
2
0
0
0
0
0
1
1
0
0
0
2
1
0
0
0
1
1
0
0
0
0
0
1
0
1
0
2
0
0
0
3
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
2
0
0
2
0
0
0
0
1
2
2
0
0
1
2
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
2
4
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
2
3
0
0
1
0
2
1
0
0
2
2
1
2
1
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
2
2
0
0
3
1
2
0
0
0
2
1
2
1
2
0
0
0
0
0
0
1
1
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
1
0
3
2
0
0
1
0
0
0
2
0
0
0
0
2
3
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
5
0
1
0
0
0
0
0
1
1
2
2
0
0
1
0
1
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
2
0
0
2
0
0
0
1
1
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
2
1
0
0
0
2
2
0
0
0
0
2
1
0
0
0
0
1
0
2
2
0
0
0
0
2
1
0
0
0
0
0
1
0
2
2
2
2
0
0
1
9
1
2
0
2
0
2
0
1
2
0
2
0
0
0
1
0
0
0
2
0
1
0
3
0
0
0
0
1
0
0
0
2
0
0
2
0
0
1
0
1
1
0
0
2
0
1
0
0
0
1
1
0
0
0
0
3
2
0
0
1
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
2
1
0
0
0
0
0
0
0
1
0
0
1
3
2
1
0
0
0
1
1
2
0
0
1
0
1
0
0
0
0
0
2
0
0
0
2
0
2
1
0
0
0
1
0
0
0
1
0
0
2
0
0
0
2
1
2
0
1
1
0
0
0
0
2
1
0
0
0
0
0
1
2
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
1
1
0
1
0
0
0
1
2
0
0
0
0
1
0
1
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
2
0
1
1
1
0
2
2
1
0
0
0
0
1
0
0
1
2
2
1
2
0
0
0
0
1
1
1
0
0
0
0
0
2
0
1
0
1
0
2
2
0
1
3
0
0
0
1
0
0
0
0
2
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
1
0
0
0
3
0
0
0
2
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
1
0
0
2
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
2
0
0
0
2
1
0
0
0
0
2
0
0
0
2
0
1
1
0
0
0
0
2
2
0
0
0
2
1
1
0
2
1
0
0
6
0
0
2
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
1
1
2
0
0
1
0
0
2
0
0
0
2
0
0
0
0
2
1
0
2
0
0
0
0
0
0
1
1
0
2
1
0
1
0
1
0
0
0
0
2
1
0
0
0
0
0
2
0
0
1
2
1
2
0
0
0
0
2
0
0
1
0
0
0
2
0
0
2
0
2
0
4
1
0
1
0
0
0
0
0
2
0
0
2
2
2
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
3
0
0
0
1
1
1
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
2
2
1
0
0
2
0
0
0
0
2
0
0
0
0
0
2
1
0
0
1
0
1
1
0
0
2
2
1
1
3
1
2
1
1
0
1
1
2
2
0
0
0
1
0
1
0
0
1
2
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
1
0
2
1
0
2
0
0
2
0
0
1
0
2
1
0
5
0
0
0
1
0
0
0
2
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
1
2
1
0
0
2
1
3
2
0
1
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
2
0
2
0
0
0
0
1
0
2
0
0
2
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
3
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
1
0
0
3
0
0
2
1
0
1
2
0
0
1
0
0
0
1
1
0
0
0
1
0
0
1
2
1
1
0
1
0
1
0
0
2
1
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
2
0
1
0
1
0
0
2
0
0
0
2
1
0
0
0
1
0
0
0
0
0
3
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
2
0
0
3
2
1
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
2
0
2
2
0
0
0
2
0
2
0
0
0
2
0
2
0
0
1
1
0
1
2
1
3
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
1
1
0
2
1
0
2
0
0
1
2
0
0
0
1
2
0
2
0
0
2
0
3
0
0
1
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
2
0
0
1
0
0
1
1
0
1
0
0
1
2
0
0
0
0
0
3
2
0
2
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
3
1
1
2
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
2
1
0
0
1
0
0
0
0
0
2
0
1
0
1
0
2
0
1
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
2
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
1
0
1
1
1
2
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
2
0
0
0
0
3
0
0
0
1
1
2
0
1
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
3
0
0
0
2
0
1
1
0
0
0
0
0
0
2
1
2
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
2
1
0
1
5
0
0
1
2
0
0
0
0
0
2
0
1
0
1
2
1
0
2
0
1
0
1
1
0
2
2
0
2
0
0
0
3
1
0
1
0
2
0
0
1
0
0
4
1
0
0
1
0
0
1
0
0
2
1
0
0
2
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
2
1
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
1
0
2
1
1
0
1
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
3
0
0
0
0
0
2
0
2
0
1
0
0
1
0
0
1
1
1
0
0
0
2
0
1
1
1
0
0
2
0
0
0
1
0
1
0
1
1
0
4
0
0
0
1
1
1
2
2
0
0
1
1
0
0
7
0
2
1
0
1
0
1
2
2
0
0
0
1
1
0
2
0
0
0
1
1
0
0
0
1
0
0
0
0
0
3
0
1
0
1
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
1
1
4
1
0
0
0
0
0
0
1
1
0
5
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
4
0
2
0
4
0
0
2
0
0
0
0
1
3
0
0
0
0
1
1
0
1
1
0
0
0
0
1
1
0
2
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
2
0
2
1
0
0
0
0
1
0
0
0
1
2
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
2
0
1
0
0
0
2
2
2
1
0
2
0
2
0
0
0
0
0
0
1
0
0
0
2
2
2
1
0
1
0
0
0
0
0
0
2
1
0
1
1
1
0
1
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
2
3
2
1
0
0
0
2
0
0
1
1
0
1
1
0
1
2
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
2
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
1
2
1
0
2
2
0
0
0
0
0
1
4
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
2
0
0
0
0
0
0
0
2
0
1
0
0
1
1
0
0
0
0
0
0
1
1
2
0
2
0
4
3
0
1
1
0
0
1
1
0
0
1
0
0
0
1
2
2
0
0
1
0
2
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
1
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
2
0
0
0
0
1
2
0
4
0
4
2
0
0
1
1
0
0
2
0
0
5
1
1
0
2
1
0
0
0
2
1
1
0
1
3
2
1
0
0
0
0
2
3
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
2
1
2
0
1
0
0
0
0
1
0
1
1
1
0
0
1
0
0
1
2
0
0
2
0
0
0
0
2
0
0
0
0
1
2
0
0
0
2
0
1
0
2
2
0
0
0
2
0
1
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
2
3
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
2
0
0
1
2
0
0
1
0
0
0
1
2
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
2
2
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
1
0
2
0
2
1
0
2
0
0
2
1
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
2
1
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
1
2
0
2
0
2
0
1
1
0
1
1
0
0
0
0
0
0
2
0
0
0
2
1
1
1
0
0
0
0
0
2
0
0
0
1
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
2
0
0
0
1
2
2
2
0
2
0
0
1
1
0
2
0
2
0
0
0
0
2
2
0
2
0
2
0
0
0
0
1
1
1
2
0
1
0
0
2
1
1
0
1
0
2
0
0
0
1
1
0
0
1
1
1
0
2
2
1
2
0
0
0
0
0
1
0
0
0
0
2
1
0
1
2
0
1
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
2
1
1
3
1
1
0
0
1
2
0
2
1
0
0
1
1
2
2
0
1
1
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
1
2
0
0
0
0
0
2
0
0
0
2
0
0
2
0
1
0
0
0
1
0
2
0
1
1
2
0
0
2
0
0
1
0
1
0
1
1
0
1
0
2
0
0
1
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
2
0
1
0
1
0
1
0
0
2
1
3
0
1
1
0
0
2
0
0
0
0
1
1
0
2
0
2
0
1
2
0
0
0
0
0
0
0
0
2
0
0
1
2
0
2
0
0
0
4
0
1
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
2
1
0
0
2
1
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
3
0
0
0
0
1
2
0
0
0
1
0
0
1
0
0
1
2
0
0
0
2
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
3
1
2
1
0
0
0
0
2
1
2
1
1
0
0
1
0
0
2
0
2
0
1
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
1
2
0
0
2
0
0
1
4
0
0
5
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
1
0
0
2
1
0
2
0
1
0
0
0
0
0
2
2
0
0
0
2
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
1
2
0
2
0
0
0
0
0
3
0
2
2
1
5
1
0
2
0
0
1
2
0
0
0
1
2
0
0
0
1
4
0
0
0
1
0
2
0
5
2
1
4
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
1
1
0
1
0
0
0
0
0
0
1
0
1
0
0
2
0
0
2
2
2
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
1
1
2
0
0
6
0
0
2
1
0
2
1
2
1
0
0
0
1
0
0
1
1
0
0
1
1
0
0
0
2
1
0
1
2
0
0
0
1
1
0
1
2
0
0
1
2
0
3
0
0
0
0
1
0
1
0
0
0
2
2
0
1
0
1
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
3
0
2
0
0
0
0
1
3
2
0
2
0
2
2
0
2
1
2
0
0
0
1
3
0
1
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
1
1
0
0
0
1
0
1
1
2
0
1
3
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
1
2
2
1
1
2
0
0
0
1
0
0
0
0
2
0
1
1
2
1
2
1
0
2
0
0
0
1
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
2
0
2
0
0
1
0
0
0
0
1
0
1
2
0
0
0
2
0
0
0
2
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
1
2
2
2
0
0
1
0
0
0
1
0
0
1
0
0
0
0
2
0
0
1
0
1
0
1
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
5
3
0
1
0
0
0
0
0
0
1
0
2
0
2
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
1
1
2
1
0
0
0
2
0
2
0
4
0
0
1
0
0
1
2
1
7
1
2
0
0
0
0
0
1
0
3
0
0
2
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
2
0
2
2
3
2
0
1
0
0
0
0
0
0
2
0
2
2
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
1
1
1
0
1
2
0
0
0
0
1
0
0
0
2
1
0
0
0
2
0
0
0
1
0
1
2
2
0
0
1
0
0
0
1
0
3
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
3
0
0
2
0
2
2
0
0
0
2
5
1
1
0
0
2
0
1
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
2
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
2
0
2
1
0
2
2
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
3
2
0
1
0
2
0
0
0
1
0
1
0
0
0
1
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
3
1
0
0
0
0
1
0
0
1
0
2
0
3
0
2
2
0
0
0
1
2
0
0
0
0
2
0
1
0
0
0
0
2
0
2
2
1
2
1
0
0
0
0
2
0
0
0
2
2
1
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
1
0
2
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
2
0
1
2
0
2
0
0
1
0
0
0
1
0
0
0
0
2
0
2
0
0
0
2
0
0
2
1
0
1
0
0
0
0
0
0
1
1
0
0
0
1
2
3
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
3
1
0
1
2
2
0
0
2
0
2
0
1
0
0
0
1
1
0
1
0
0
0
2
1
0
0
1
0
0
0
0
1
1
5
0
0
2
0
2
0
0
1
3
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
2
0
2
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
2
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
1
2
0
1
0
0
0
0
1
2
0
1
2
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
2
3
1
0
2
0
0
0
1
0
0
0
0
2
2
1
1
2
2
0
3
2
2
2
0
1
0
0
1
0
2
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
3
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
2
0
2
5
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
2
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
2
0
3
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
2
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
2
1
0
2
2
0
0
0
0
0
1
0
1
1
0
0
1
1
0
2
1
0
0
0
0
7
2
0
2
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
2
2
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
1
0
0
2
2
0
0
0
0
0
0
0
2
0
2
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
2
0
1
1
2
0
0
0
0
0
2
0
0
2
0
0
2
0
1
1
0
0
1
2
0
0
0
3
0
0
0
2
2
0
0
0
1
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
6
0
0
0
0
0
0
2
0
0
0
1
0
1
0
1
2
0
0
0
0
2
0
1
2
0
0
0
0
2
2
0
2
2
2
1
2
1
0
0
0
0
0
0
0
0
0
2
2
0
1
2
2
2
0
2
1
0
1
0
0
0
0
0
2
0
0
3
1
1
3
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
2
0
1
0
0
0
0
4
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
2
4
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
2
1
2
0
0
0
0
2
1
0
0
0
1
0
0
0
1
1
0
2
0
0
0
2
1
0
1
0
0
0
2
2
0
2
2
0
0
1
0
2
0
0
1
1
3
0
0
1
1
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
2
1
0
2
0
0
2
0
3
2
0
1
0
2
0
0
1
2
2
0
1
0
0
0
0
0
0
2
0
1
0
1
0
0
0
1
1
1
0
0
0
0
1
2
0
0
0
2
0
0
0
0
2
0
5
4
0
1
0
0
0
1
0
0
1
1
1
1
0
0
2
1
2
0
0
0
0
0
1
0
0
2
1
2
0
0
0
0
0
1
0
1
0
0
1
7
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
3
0
2
3
0
2
0
0
0
0
0
1
1
2
1
0
0
0
2
0
0
0
0
1
0
0
0
1
1
1
1
2
2
0
0
0
1
0
0
0
1
1
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
1
2
0
0
0
2
2
0
0
0
2
0
0
1
0
0
0
0
0
2
0
3
0
0
0
0
1
0
1
0
0
0
2
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
1
0
0
0
1
0
0
2
0
0
2
1
2
0
0
0
0
1
0
2
0
0
2
1
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
1
0
0
2
2
0
2
0
0
0
2
2
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
1
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
2
2
0
0
0
3
1
0
0
0
2
2
1
0
0
2
2
1
0
0
0
2
0
0
2
1
1
0
2
0
0
2
2
0
0
0
0
0
2
1
0
2
2
2
0
0
0
1
0
0
1
0
1
1
1
0
0
0
1
0
1
0
2
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
2
0
2
0
0
0
1
2
0
2
2
0
0
0
0
2
0
0
0
1
0
0
1
1
0
0
3
1
0
0
0
0
0
3
0
0
0
6
0
0
0
0
0
0
2
0
1
0
1
1
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
1
2
0
3
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
2
0
1
1
0
0
0
0
0
0
2
1
1
0
0
0
2
0
1
0
0
2
5
0
0
1
0
1
2
0
1
0
1
1
0
1
1
2
1
1
0
0
0
0
1
2
0
2
1
0
0
2
0
0
0
0
1
0
1
2
1
0
0
3
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
2
0
0
0
3
4
2
0
1
1
0
0
0
3
3
2
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
2
1
1
0
0
0
1
0
0
0
0
2
3
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
2
0
0
1
0
0
0
0
1
2
2
1
1
3
0
2
0
4
1
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
6
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
3
0
0
0
0
0
1
0
0
0
1
1
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
2
0
4
0
1
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
1
0
1
0
0
1
0
1
2
0
2
0
0
2
1
1
0
0
3
0
0
0
3
2
0
1
0
0
0
2
3
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
1
1
0
0
1
0
0
0
1
0
4
6
0
0
0
0
0
0
0
1
0
0
1
0
1
3
1
0
0
2
2
0
0
0
2
0
0
2
0
2
0
0
0
2
0
0
0
1
0
3
0
2
1
0
3
2
2
0
0
0
0
0
1
1
0
0
0
2
0
0
2
0
1
0
0
0
5
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
2
0
0
2
1
0
0
0
2
2
0
1
0
0
2
0
14
1
0
1
0
0
1
1
0
0
2
1
0
1
2
0
2
0
0
0
1
2
1
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
2
2
2
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
1
0
0
0
2
1
1
2
1
0
1
0
0
0
0
0
2
0
0
1
0
1
0
0
1
1
0
0
0
0
2
2
0
1
1
2
0
0
0
0
1
0
2
0
1
0
0
0
0
0
1
1
2
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
1
0
0
0
1
0
2
0
0
0
0
0
2
1
0
0
0
0
0
2
0
1
0
0
1
0
2
0
1
0
0
0
0
1
0
2
0
0
0
3
0
0
1
0
0
0
0
0
2
0
0
1
0
1
0
0
2
0
1
0
2
0
0
1
1
0
0
0
0
0
2
2
0
1
0
1
0
0
0
0
0
0
0
0
0
5
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
1
2
0
3
0
0
0
0
0
1
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
3
0
2
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
2
1
0
0
0
0
0
0
3
0
0
0
0
2
0
0
2
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
2
1
0
0
0
0
1
0
0
0
0
1
0
2
0
0
1
1
0
0
1
0
1
0
0
0
0
2
1
0
0
1
0
1
0
1
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
2
0
0
3
0
0
1
0
1
1
0
0
2
2
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
2
0
2
0
0
2
0
0
0
1
0
1
0
0
0
0
2
0
2
2
1
0
0
0
1
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
2
3
0
2
2
2
0
1
5
1
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
1
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
2
0
0
2
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
2
1
0
0
0
2
2
2
2
4
0
1
0
0
1
2
0
0
0
2
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
1
2
1
0
0
2
0
8
0
0
0
0
0
0
0
0
0
0
0
6
1
0
0
0
1
0
1
0
0
0
1
0
0
1
3
1
2
4
0
0
3
0
0
1
1
0
0
0
4
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
1
0
2
1
0
0
0
2
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
2
2
0
0
1
4
0
0
0
1
0
0
2
1
0
0
0
2
0
0
0
3
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
2
1
0
0
0
0
0
2
3
2
0
0
2
2
3
0
2
0
0
0
1
0
0
0
0
0
0
1
0
2
0
2
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
1
0
1
1
2
0
0
0
0
0
0
0
1
0
2
2
0
1
0
0
0
0
0
3
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
2
0
0
0
16
0
0
2
0
0
0
0
2
0
0
2
0
0
1
0
0
0
1
0
0
4
0
0
0
0
0
1
0
0
0
4
0
2
0
0
0
1
0
0
0
2
0
0
0
0
2
3
0
0
0
2
1
2
1
0
0
0
1
1
0
2
0
1
0
0
0
2
0
0
1
0
2
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
2
1
2
1
1
0
1
0
0
0
1
2
0
3
0
2
0
2
2
1
0
4
1
1
0
0
2
0
0
2
0
2
2
3
1
2
1
2
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
4
0
0
1
0
2
1
2
0
0
0
2
0
1
1
0
0
0
5
0
0
0
2
0
1
0
2
0
0
1
0
0
0
0
0
2
1
2
1
2
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
6
0
0
0
0
0
2
0
0
2
1
0
0
1
1
0
0
0
0
0
2
2
3
0
0
0
0
0
2
0
2
1
0
0
0
0
0
1
0
1
0
0
0
2
2
0
2
0
0
0
1
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
1
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
2
0
0
0
1
0
0
0
1
0
1
1
0
0
2
3
2
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
1
1
0
2
0
0
1
0
0
0
0
0
0
1
2
0
0
1
0
0
1
0
0
1
2
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
3
0
0
1
0
2
0
1
1
4
2
0
0
2
0
2
0
4
0
2
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
3
0
0
5
0
0
0
3
2
2
1
0
0
2
1
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
3
1
0
0
0
0
0
0
0
2
5
0
1
1
0
1
0
0
0
2
0
0
0
2
0
0
0
1
3
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
2
3
2
2
2
0
0
0
1
1
1
1
0
2
1
2
0
0
0
2
2
1
0
1
0
1
0
2
1
2
0
1
0
0
0
1
2
0
0
0
0
0
2
0
1
0
0
2
2
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
2
2
2
0
2
1
3
0
2
0
1
0
2
0
0
0
2
1
2
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
1
1
0
0
1
0
1
0
2
0
0
1
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
2
0
0
1
2
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
1
1
0
0
0
1
0
0
1
2
0
0
0
0
1
0
2
0
2
0
0
0
3
3
0
0
0
1
0
1
0
0
2
0
0
0
0
1
0
0
0
1
2
1
0
0
1
2
0
0
1
0
1
2
0
0
0
2
0
2
0
2
0
0
1
0
0
0
0
2
0
0
1
2
2
0
0
0
0
0
0
0
1
1
2
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
3
0
0
0
0
0
0
0
2
0
0
1
1
2
2
2
1
0
0
0
2
2
0
0
0
0
4
0
1
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
1
0
0
1
0
1
0
0
2
0
1
0
0
0
1
0
0
0
2
1
0
1
2
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
2
0
0
0
0
1
0
2
2
0
0
0
1
0
0
2
0
1
0
1
0
2
0
0
0
1
0
4
0
0
1
2
0
0
0
0
1
0
2
2
1
0
3
1
0
2
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
2
0
2
0
0
2
2
0
2
0
0
0
1
0
2
0
0
0
2
0
0
0
0
2
0
0
0
2
0
2
2
4
1
0
0
2
2
2
2
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
1
1
0
0
0
2
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
2
2
0
1
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
1
0
2
1
0
0
2
0
0
0
0
1
1
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
1
0
1
0
0
3
0
2
0
1
2
1
0
0
1
0
2
1
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
1
0
0
0
3
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
1
1
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
2
1
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
1
1
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
3
1
2
2
0
2
0
2
1
0
0
3
0
1
0
2
0
0
0
2
0
3
1
0
1
0
0
2
1
0
0
1
0
0
0
2
0
0
1
0
0
1
2
0
0
0
0
0
1
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
1
0
2
0
0
0
0
0
0
1
1
2
0
1
0
1
0
1
1
0
0
0
0
0
1
1
0
1
0
2
0
2
0
1
0
1
0
1
0
0
2
1
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
1
0
2
2
1
0
0
1
1
0
0
0
2
0
2
0
0
1
1
0
0
0
0
2
0
1
2
0
0
0
2
2
1
0
0
0
1
0
0
1
0
1
1
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
3
0
0
0
0
2
0
0
1
2
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
1
2
2
0
0
1
0
0
3
1
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
2
0
1
2
1
0
1
0
0
1
0
0
0
0
0
0
0
0
4
1
1
2
3
0
0
0
0
2
0
0
0
2
0
1
0
0
0
3
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
2
0
2
0
1
1
0
0
0
1
0
2
0
1
3
2
1
0
1
0
1
0
0
0
1
0
0
2
0
2
0
2
3
1
0
2
0
0
0
1
0
0
0
0
0
1
0
3
2
0
1
0
0
0
0
2
1
1
0
0
0
2
0
0
0
4
1
0
0
1
0
1
0
0
0
2
0
2
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
2
1
2
0
0
2
0
0
0
0
1
2
0
0
2
0
0
0
0
3
0
2
0
0
0
2
0
1
0
0
1
0
1
2
0
0
2
1
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
1
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
2
0
2
1
2
0
0
2
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
1
0
13
0
2
1
0
1
0
1
2
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
1
0
0
3
0
0
1
1
0
1
0
1
0
1
1
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
2
1
0
1
3
0
1
1
0
0
0
2
1
0
0
0
0
0
2
0
2
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
2
0
2
0
2
0
0
0
0
2
0
0
2
1
0
1
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
1
1
0
0
4
0
0
0
1
1
2
1
0
0
0
1
0
1
0
2
0
1
0
2
2
0
0
0
1
1
2
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
2
2
1
2
0
0
3
0
0
0
0
2
0
0
2
3
1
0
0
0
2
1
0
0
2
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
2
0
3
0
0
0
0
0
2
2
0
1
2
0
0
1
1
0
0
0
1
0
2
0
1
2
0
0
0
0
0
0
0
2
0
0
0
2
1
2
0
0
0
1
1
1
0
2
0
0
1
0
3
0
1
1
0
0
0
0
1
0
0
0
1
1
1
0
2
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
1
0
0
1
0
0
0
0
0
2
1
0
0
0
2
2
0
0
0
0
4
2
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
1
2
0
2
0
0
0
0
1
1
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
2
0
0
2
1
0
1
0
2
0
0
0
1
0
0
2
2
0
0
6
2
0
2
1
0
1
0
1
2
0
5
0
0
2
1
0
1
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
1
0
0
0
1
2
1
0
0
0
1
1
2
0
0
2
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
3
0
2
2
1
0
0
1
1
0
0
0
1
0
0
1
0
0
2
0
0
0
1
0
2
0
1
2
3
0
2
0
1
1
1
0
1
2
0
0
1
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
2
0
2
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
1
1
5
0
2
1
2
0
0
0
0
2
0
2
0
1
0
0
1
0
0
0
0
1
0
0
0
0
2
1
2
1
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
2
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
1
1
6
1
0
0
0
0
3
1
0
0
0
1
2
1
1
0
1
2
0
0
1
0
0
2
2
1
1
0
1
1
0
0
1
0
2
1
1
0
1
0
0
2
0
1
0
0
2
1
0
1
0
2
0
0
1
0
0
0
0
0
1
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
1
0
0
2
1
0
0
0
2
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
2
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
2
2
0
0
1
2
2
0
0
2
0
0
1
0
1
2
2
0
0
0
0
0
0
0
1
0
0
1
2
1
1
2
0
0
0
2
0
0
0
0
0
0
1
3
0
1
0
0
1
1
0
0
2
0
0
0
3
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
4
0
1
0
0
0
2
0
0
0
2
2
0
2
1
0
0
1
1
2
0
0
0
1
2
3
2
0
0
2
0
0
2
0
2
0
2
0
0
0
2
2
2
2
2
1
0
1
0
3
0
2
0
2
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
3
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
3
1
0
0
0
2
0
1
2
0
0
2
2
0
1
2
0
0
0
1
0
2
0
0
0
0
2
0
0
3
0
0
0
0
2
0
1
0
0
0
0
0
2
0
1
0
0
1
0
0
4
1
0
0
0
1
0
0
0
1
1
2
1
1
0
0
1
2
0
3
2
0
0
1
0
1
2
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
2
0
0
0
1
4
0
0
0
0
2
2
0
0
1
0
0
0
0
2
0
1
0
0
1
1
0
0
4
2
0
0
0
2
11
1
0
0
0
0
0
0
0
2
0
2
0
5
0
0
0
0
2
0
1
2
0
1
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
2
0
3
0
0
1
0
0
1
0
2
0
0
0
0
0
0
3
0
1
2
0
1
0
0
1
2
0
2
0
0
0
0
2
0
0
0
0
1
0
2
1
0
2
1
0
3
0
2
0
1
0
1
0
0
1
0
0
0
2
0
2
0
1
1
0
0
0
0
0
0
0
0
1
1
0
2
0
0
1
2
0
0
2
2
0
0
0
1
0
2
0
0
0
2
0
0
2
2
2
0
2
0
2
0
0
0
0
0
0
2
1
1
0
2
1
1
0
0
1
0
0
1
0
0
1
0
2
0
0
0
0
1
0
0
1
0
0
1
0
1
0
1
0
0
1
0
0
2
0
1
2
1
0
1
0
0
0
0
0
1
0
2
0
2
1
0
2
1
1
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
1
2
2
2
0
2
2
2
0
1
0
2
2
0
0
0
3
0
0
0
2
1
1
2
1
0
2
1
0
0
0
0
1
0
1
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
1
0
1
0
1
0
2
1
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
2
1
1
1
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
2
0
1
0
0
0
0
0
0
1
2
1
1
0
0
0
0
1
1
0
0
0
0
1
2
0
2
0
0
0
3
0
0
0
0
2
0
0
1
2
1
0
0
0
2
0
0
2
2
0
0
0
0
0
1
1
0
1
0
0
2
1
2
0
0
0
2
0
1
0
0
2
0
0
2
0
1
0
0
2
0
3
0
0
0
2
0
0
1
0
1
0
0
0
0
1
0
1
0
2
1
0
1
0
3
1
0
1
0
0
1
1
0
0
2
0
0
0
0
0
3
1
0
0
0
2
0
0
0
1
1
0
0
2
0
1
2
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
2
2
1
0
0
0
0
1
0
0
0
2
2
0
0
0
0
2
2
0
0
0
0
2
2
1
2
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
2
2
1
0
0
2
1
0
2
2
2
0
2
2
2
0
0
3
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
1
0
0
0
0
0
1
1
1
0
1
1
0
2
1
3
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
2
2
4
0
0
0
0
0
0
0
1
0
0
0
2
2
1
0
4
1
0
1
0
1
0
0
2
0
2
0
1
0
0
0
0
1
1
0
0
0
0
2
1
0
2
2
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
4
1
0
0
0
1
1
0
0
1
2
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
3
0
0
0
2
0
1
0
0
0
3
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
3
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
2
1
0
1
2
0
1
0
1
1
0
5
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
2
0
2
2
0
0
0
0
3
1
0
2
0
0
2
0
0
1
0
0
1
0
0
0
1
0
0
1
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
1
1
0
6
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
1
0
0
0
2
0
2
0
0
0
0
0
1
0
2
2
1
0
0
3
2
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
2
1
0
0
0
1
0
0
0
3
0
3
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
2
0
1
0
0
0
0
2
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
2
3
2
0
1
0
0
2
2
0
0
2
1
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
2
0
0
4
0
1
1
0
2
1
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
1
0
0
1
0
1
0
0
2
0
2
0
0
1
0
0
0
2
3
1
2
1
2
1
2
0
2
0
0
0
0
2
0
1
2
0
0
0
2
0
1
0
2
1
1
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
2
2
0
0
0
1
3
0
0
0
2
2
1
0
0
0
2
0
0
0
0
0
2
0
2
0
0
1
2
1
1
0
0
0
0
0
0
1
0
0
2
0
1
1
4
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
2
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
2
0
0
2
0
0
1
0
2
1
0
2
2
2
0
1
0
0
0
1
0
1
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
1
0
0
1
0
1
0
0
0
5
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
5
0
0
0
0
1
0
0
4
1
0
5
0
1
1
2
2
0
2
1
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
2
0
2
1
0
0
0
2
2
0
1
1
0
0
0
0
2
2
0
0
1
0
0
0
0
2
2
0
1
0
0
1
0
0
1
2
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
2
0
0
2
0
0
0
0
2
7
0
0
0
0
0
2
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
2
0
1
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
2
2
0
4
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
1
0
1
3
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
3
0
0
0
0
0
0
1
3
0
0
0
1
1
0
2
2
0
0
1
2
1
1
2
1
0
0
1
2
0
0
1
2
2
0
0
0
1
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
4
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
1
0
0
0
0
1
2
0
0
2
2
0
0
0
0
2
0
0
0
0
1
0
0
1
0
2
0
0
2
1
0
1
0
0
0
0
2
0
1
0
2
0
2
0
1
1
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
2
0
2
0
2
0
0
0
0
0
0
2
0
2
0
0
0
2
1
0
1
0
1
0
0
2
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
1
3
0
0
1
2
0
0
1
1
0
0
0
0
3
0
2
1
2
0
0
0
2
0
0
1
0
0
2
4
1
2
0
1
1
0
0
0
2
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
1
1
2
3
0
0
0
0
2
0
0
0
0
2
2
0
0
2
0
0
0
0
1
0
0
0
0
0
2
2
2
0
1
0
1
0
0
0
0
4
0
1
0
1
1
0
3
4
0
0
0
0
2
0
0
0
0
3
0
2
0
3
0
0
0
2
0
0
1
0
0
0
0
2
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
1
0
3
1
0
0
1
0
0
0
1
0
1
1
1
0
0
1
1
1
0
0
1
0
0
2
0
0
1
0
2
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
1
2
0
0
0
0
0
0
1
0
0
1
0
5
1
0
0
2
0
0
0
0
0
0
0
0
3
2
2
2
0
0
0
0
2
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
2
0
3
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
3
0
0
1
0
3
0
0
0
1
0
1
0
0
0
0
4
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
2
2
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
1
0
5
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
1
1
1
0
2
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
3
0
2
0
2
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
1
0
0
0
0
2
1
0
4
1
2
2
0
0
0
1
2
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
2
0
2
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
2
0
1
2
0
0
0
0
2
1
0
0
1
0
0
1
1
0
0
0
2
0
2
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
2
0
0
0
0
2
0
1
0
0
1
0
0
3
0
0
0
0
2
1
0
0
2
1
0
0
0
1
2
1
0
0
0
2
1
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
1
0
0
1
0
0
2
0
1
1
0
0
1
1
0
1
0
2
1
0
0
0
0
2
0
0
1
2
0
1
0
0
2
0
0
1
0
1
0
1
0
0
0
0
2
0
0
1
2
0
2
0
0
1
0
0
0
0
0
0
1
0
5
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
3
0
0
2
0
0
0
0
0
0
1
2
0
0
3
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
2
0
1
0
0
0
2
1
1
0
0
0
2
0
1
0
2
0
0
0
0
1
0
2
0
0
0
1
1
0
2
1
0
1
1
2
0
1
0
0
0
0
2
0
0
0
1
0
1
0
0
0
2
2
0
0
1
0
1
0
2
1
1
1
2
0
0
2
0
1
1
2
0
0
0
0
0
0
0
0
0
0
1
0
3
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
2
1
0
2
2
0
2
0
1
0
2
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
3
2
0
2
2
0
0
3
2
0
0
0
2
0
2
0
1
0
1
2
0
0
0
2
2
0
0
0
1
0
1
2
0
2
0
1
1
2
1
0
0
0
2
2
2
1
3
0
0
2
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
2
0
0
0
0
0
1
2
1
0
1
0
2
1
0
2
0
2
0
0
0
0
0
1
0
0
2
2
0
0
0
0
2
0
1
2
0
0
0
2
0
0
0
0
0
1
2
0
0
2
1
0
2
0
0
2
1
2
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
2
0
1
0
0
0
2
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
2
1
0
0
1
1
0
3
1
2
0
0
0
1
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
2
2
0
0
2
0
0
0
2
1
0
2
2
0
1
0
0
1
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
2
0
0
2
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
2
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
2
2
0
0
1
1
0
2
0
0
1
1
1
1
1
0
3
0
0
0
1
2
0
0
1
1
2
0
0
0
1
1
0
0
1
0
0
2
0
0
1
0
0
2
0
1
1
0
0
2
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
2
0
0
2
1
0
0
0
1
0
0
0
1
0
0
3
0
4
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
2
0
0
1
0
5
0
1
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
2
1
2
2
0
2
0
2
2
0
0
0
0
1
1
0
2
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
2
1
0
0
0
0
1
1
2
2
2
0
0
0
0
0
1
0
0
1
0
0
0
3
0
0
2
0
0
1
0
0
3
2
1
0
2
0
0
2
1
3
3
1
2
0
0
0
0
0
3
2
0
3
2
0
0
2
1
1
0
0
0
0
0
0
1
0
2
0
0
0
2
1
1
0
1
0
0
0
0
1
0
0
0
1
0
2
0
1
0
3
0
0
0
0
0
0
1
2
0
0
2
2
1
1
0
1
0
0
0
2
0
0
0
0
1
1
0
1
0
0
2
0
1
0
0
0
0
0
4
1
0
0
0
0
2
0
0
1
0
0
0
0
0
4
0
0
0
1
3
0
1
1
2
0
0
0
2
0
2
2
0
0
0
0
0
3
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
3
0
2
0
1
0
1
2
0
0
0
2
0
2
0
0
0
0
0
0
0
1
2
0
0
0
1
0
1
0
2
0
0
1
0
0
1
0
1
0
0
0
2
1
0
0
0
1
0
1
0
0
1
0
0
0
2
1
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
1
0
0
0
2
1
0
0
8
0
2
2
0
3
0
0
1
1
0
0
1
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
2
0
3
0
0
0
0
2
0
0
0
1
0
0
0
10
0
0
0
0
0
2
1
0
0
1
0
0
0
2
1
1
0
0
0
0
0
0
1
2
0
2
1
0
1
0
2
0
2
1
2
0
0
0
0
0
0
0
0
2
2
1
0
0
2
0
2
1
0
3
2
2
3
0
0
1
0
2
0
0
1
0
1
0
0
0
0
2
2
0
0
0
3
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
2
0
1
2
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
1
0
0
1
2
2
1
0
1
0
0
0
0
2
0
2
2
0
0
0
0
0
0
1
2
0
2
0
0
0
2
0
0
2
2
0
2
0
0
0
0
3
0
0
0
0
2
0
1
2
1
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
2
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
1
0
1
0
0
0
2
0
0
1
2
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
3
0
0
1
1
0
1
0
1
0
0
0
1
0
0
0
1
1
8
1
2
0
3
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
2
0
0
2
2
0
2
1
0
2
3
0
0
0
0
2
1
0
1
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
2
1
0
1
0
3
0
1
0
0
0
2
0
1
0
0
0
0
0
2
0
0
1
2
1
2
0
0
0
1
0
0
0
3
0
0
0
2
0
0
1
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
2
1
0
2
1
0
0
2
0
3
1
0
2
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
1
1
0
0
2
0
2
2
2
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
1
0
1
0
0
2
1
1
1
0
1
0
0
0
2
2
0
0
0
0
1
0
0
0
2
0
2
1
0
0
2
2
0
0
0
0
2
0
0
0
2
0
0
0
2
1
0
2
2
1
0
0
0
0
2
0
0
0
0
0
1
3
1
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
2
1
1
0
2
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
2
2
1
0
0
2
0
0
0
1
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
2
3
0
2
0
2
0
0
0
0
0
0
2
0
2
0
3
0
2
0
0
1
1
1
0
0
0
0
0
2
0
1
0
0
0
2
0
1
0
2
0
0
0
0
2
0
0
0
2
1
0
1
0
1
2
2
1
1
2
0
1
0
0
0
0
1
2
0
1
1
1
2
1
1
0
0
1
0
0
1
0
0
0
0
2
2
0
0
1
0
1
0
0
0
2
0
2
0
0
2
0
0
1
0
0
1
0
0
0
0
0
1
0
0
2
0
0
1
2
0
1
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
2
2
0
0
1
1
0
0
2
2
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
1
0
0
0
2
2
3
1
0
3
0
0
2
0
0
0
1
1
0
0
1
0
0
0
0
2
0
0
0
0
2
1
2
0
2
0
2
3
0
0
1
0
1
0
0
0
0
1
1
0
0
2
2
0
1
2
0
0
0
1
0
0
2
0
1
1
0
0
3
0
0
2
0
0
0
0
2
2
0
0
0
2
0
1
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
1
1
1
1
0
0
1
0
1
2
0
2
1
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
1
6
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
2
0
1
0
2
0
0
0
0
1
1
1
2
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
2
0
2
1
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
1
0
2
0
1
0
0
0
2
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
3
0
0
0
1
0
0
2
5
0
0
0
1
0
0
3
4
1
0
0
2
0
2
0
0
0
1
1
2
2
1
0
1
0
0
2
6
1
5
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
2
1
1
0
0
0
0
0
1
0
0
1
0
0
2
3
0
0
0
0
0
0
0
0
0
1
1
1
0
2
2
1
0
0
0
2
0
0
0
2
2
1
2
1
1
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
2
1
1
0
0
0
0
1
0
0
0
2
0
0
2
1
0
0
0
2
0
2
2
0
0
0
2
3
0
1
0
1
2
0
0
2
2
0
1
0
0
0
1
0
1
0
2
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
2
0
4
0
0
0
0
0
2
2
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
2
0
0
2
1
4
2
0
2
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
1
1
2
0
0
0
0
2
2
0
0
0
2
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
1
0
0
1
2
0
1
0
0
0
0
0
0
0
2
2
0
0
0
2
0
1
2
1
0
2
1
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
2
0
4
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
2
0
1
0
0
0
0
0
2
1
2
2
2
0
1
2
1
1
2
0
0
0
1
0
1
1
0
0
2
0
2
1
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
1
2
0
0
0
2
1
0
0
0
0
0
0
0
1
3
0
0
1
0
2
0
0
0
0
0
1
0
0
1
2
1
0
2
1
0
0
0
0
0
0
2
1
0
0
0
0
1
6
1
0
0
0
2
0
1
0
1
2
2
0
0
0
2
0
2
0
0
2
1
0
0
0
0
0
1
0
2
1
0
0
0
0
1
0
2
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
2
0
0
1
2
0
0
0
1
0
0
0
0
0
1
1
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
1
0
1
0
1
1
2
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
2
1
0
0
0
2
0
0
0
0
2
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
1
1
0
0
0
1
0
1
0
0
1
3
0
0
2
0
0
1
2
0
0
0
3
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
2
1
0
0
0
0
0
1
1
0
2
0
1
1
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
1
3
0
0
0
0
0
0
0
1
0
0
0
0
0
1
3
0
1
0
2
0
1
0
0
0
0
0
0
0
0
3
0
0
0
2
3
0
0
1
1
2
0
0
1
1
0
0
1
0
1
0
0
2
0
2
2
2
1
0
3
0
0
1
2
0
0
0
2
1
0
0
0
0
0
2
0
0
0
1
0
0
0
1
2
1
4
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
3
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
3
1
0
0
1
2
0
1
0
2
0
0
2
2
0
0
0
0
2
0
1
0
0
1
1
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
5
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
2
2
1
0
3
0
0
0
0
0
2
2
0
0
0
0
0
1
2
0
2
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
1
1
0
2
0
0
0
1
0
0
0
2
1
0
0
0
0
0
2
1
2
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
2
1
2
0
0
0
0
1
0
0
2
0
0
0
0
0
2
1
1
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
2
0
0
0
0
0
1
2
0
0
1
2
0
0
0
0
1
0
0
0
0
0
1
2
0
1
0
0
1
0
0
0
0
0
1
0
2
1
0
0
0
0
1
0
0
1
2
0
2
2
1
0
2
0
0
0
0
1
2
2
0
2
0
0
2
0
1
0
1
0
0
0
1
1
0
0
0
0
0
1
1
0
0
2
0
0
1
0
2
0
0
2
0
0
2
1
1
0
0
0
1
1
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
2
2
0
0
2
2
1
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
3
0
2
0
1
0
2
0
0
2
0
0
0
0
0
1
2
0
2
0
1
0
0
0
0
2
0
2
0
1
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
2
0
2
0
1
1
0
2
2
0
5
0
0
0
1
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
2
1
1
2
0
0
3
0
0
0
0
0
0
0
1
1
0
1
0
1
0
1
0
0
0
2
0
3
0
0
0
0
1
0
2
0
0
1
2
0
0
0
2
0
1
0
0
0
1
2
0
1
0
0
0
3
2
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
1
1
1
0
1
0
0
0
1
0
0
2
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
3
2
0
1
0
0
2
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
2
0
0
0
2
0
2
1
1
0
1
0
0
0
2
2
0
2
0
0
0
0
1
0
0
2
0
0
0
2
1
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
3
1
0
1
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
1
2
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
1
0
0
0
0
0
1
1
1
0
2
0
0
1
0
0
0
0
1
1
0
0
0
1
0
2
0
1
2
2
1
2
0
0
0
0
0
0
2
2
0
0
1
0
0
0
2
1
2
1
0
0
2
0
2
0
0
2
0
2
0
0
2
1
0
0
1
0
0
2
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
2
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
1
1
0
1
0
2
0
0
0
0
0
2
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
2
1
0
2
0
2
0
0
0
0
0
4
0
1
0
0
2
0
2
0
0
0
2
2
0
0
0
0
0
2
2
0
1
0
0
1
0
0
1
0
0
0
0
2
1
1
0
2
1
0
1
2
2
0
0
0
0
1
0
3
3
0
0
0
1
1
0
2
0
0
1
0
0
0
0
0
4
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
1
1
0
0
0
1
1
2
0
0
2
0
0
0
4
1
0
1
0
1
0
0
0
0
1
0
1
1
1
2
2
0
0
0
0
2
1
0
0
2
0
1
0
0
0
0
0
1
1
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
1
2
2
0
2
0
2
0
1
0
0
1
1
1
0
0
0
0
2
0
0
0
2
0
1
0
0
2
0
0
1
0
1
1
0
0
0
1
0
3
0
0
1
0
3
0
0
0
0
1
0
0
0
2
0
3
3
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
3
0
0
0
2
2
1
0
0
0
0
0
2
0
2
1
3
0
0
0
2
0
0
0
1
1
0
2
0
0
0
1
2
0
0
0
1
1
0
1
0
1
1
0
0
2
2
2
2
1
2
0
5
1
1
0
0
0
0
0
0
0
1
1
1
0
2
2
0
0
0
2
0
0
0
0
0
0
0
2
0
3
0
2
0
0
0
0
0
0
0
0
0
3
2
1
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
1
2
0
2
0
0
2
0
1
1
0
0
0
1
0
0
3
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
2
0
2
1
2
1
0
0
2
1
0
2
0
0
0
2
0
2
0
3
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
2
2
0
1
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
1
0
1
0
0
0
0
0
2
1
0
2
0
2
0
1
2
0
1
1
0
1
2
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
2
0
0
0
2
0
0
0
1
0
0
1
2
0
0
0
0
2
0
2
0
0
1
0
0
0
0
1
0
0
0
1
0
0
2
2
0
1
0
2
0
0
0
0
0
0
0
2
1
0
1
0
0
1
0
1
1
1
1
0
0
0
0
0
0
0
0
0
1
2
1
3
0
0
0
0
2
0
1
0
0
0
0
0
0
2
1
0
2
4
0
0
0
0
1
1
0
1
2
0
2
0
3
1
1
0
0
0
0
0
0
0
0
0
2
2
2
0
2
0
1
0
0
0
2
0
0
0
2
0
0
2
1
1
0
0
0
0
2
2
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
4
0
0
1
2
0
0
1
0
1
0
1
2
0
2
0
0
2
0
0
0
0
1
1
0
3
1
0
0
0
1
0
0
0
1
0
2
2
1
0
0
0
0
0
2
0
2
0
0
0
2
2
0
0
1
0
2
3
0
0
2
2
0
1
0
1
1
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
5
0
1
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
1
2
2
0
0
0
0
0
2
0
1
0
0
1
5
0
0
0
0
0
0
2
1
0
0
1
7
0
0
1
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
2
2
2
0
0
1
0
0
2
1
0
0
0
0
3
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
1
0
2
0
0
0
1
0
1
0
0
1
1
0
0
1
0
0
2
0
0
0
2
0
0
0
1
0
1
0
1
0
0
1
0
0
0
1
0
0
1
0
2
0
0
0
0
1
0
2
0
1
3
0
0
0
0
0
0
1
0
0
0
0
2
1
2
0
0
3
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
1
1
0
2
1
0
0
0
2
0
0
0
0
0
0
2
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
1
0
1
1
0
0
2
1
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
1
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
2
0
1
0
0
0
0
1
0
0
4
0
1
0
0
2
2
0
1
0
2
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
3
0
0
0
1
1
0
0
0
0
1
0
0
0
0
2
0
0
1
0
2
2
3
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
1
0
0
0
0
3
0
0
0
2
0
1
0
2
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
2
0
0
0
0
0
0
2
1
0
0
0
2
0
0
2
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
2
1
0
0
2
1
2
2
0
2
2
0
2
0
0
0
0
1
3
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
1
0
0
0
0
1
0
0
0
1
0
1
2
0
0
0
1
0
1
0
0
1
0
1
0
0
1
0
2
0
2
0
0
0
0
1
1
0
2
1
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
3
3
0
2
0
0
1
1
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
1
0
1
1
0
3
1
1
1
0
0
0
2
1
0
5
0
0
0
0
0
0
1
1
0
3
2
1
0
1
0
0
0
0
1
2
2
2
1
1
1
0
2
1
0
0
1
0
1
2
0
0
0
2
1
0
0
0
0
3
2
2
0
4
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
2
1
1
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
2
0
2
0
0
0
1
1
3
2
4
0
0
0
0
0
2
0
0
0
0
0
0
3
0
1
1
1
0
0
0
0
0
0
0
2
0
2
0
2
0
2
0
0
1
1
0
2
0
1
0
0
0
0
3
0
1
0
0
1
5
2
1
0
1
0
0
0
0
0
1
0
0
1
0
2
2
1
0
3
0
2
0
0
0
1
0
1
1
1
0
2
1
1
1
0
1
0
0
1
0
2
2
0
1
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
3
0
0
3
0
0
0
0
0
1
1
0
0
2
0
2
0
0
1
0
2
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
2
0
1
1
0
1
2
0
0
0
0
0
0
2
1
0
2
0
2
0
2
1
0
2
2
0
1
1
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
1
0
1
0
0
0
0
2
0
0
2
0
0
2
0
0
0
1
2
0
1
0
0
0
3
0
0
0
0
1
1
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
1
0
0
1
0
2
0
0
0
1
1
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
1
0
1
0
1
0
1
2
0
0
0
3
1
1
3
0
1
0
2
0
2
2
0
2
0
1
3
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
4
1
0
0
1
1
0
0
0
0
0
0
0
2
0
1
2
1
0
0
0
3
0
0
0
0
0
0
0
1
0
2
0
1
0
2
0
0
2
0
1
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
4
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
1
1
1
0
0
1
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
2
0
2
0
0
0
0
0
1
2
0
2
1
0
0
1
2
0
1
2
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
1
1
1
2
0
0
2
0
0
0
1
2
0
0
0
1
0
2
0
0
1
0
1
2
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
1
0
2
2
0
0
2
2
0
2
2
1
0
0
2
0
0
0
0
0
1
2
2
0
0
2
0
1
2
1
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
1
1
0
0
1
1
2
0
0
0
0
0
0
0
1
0
0
0
1
3
0
0
0
0
0
1
0
0
2
0
0
1
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
5
0
0
2
0
0
2
1
3
2
0
0
0
0
0
1
1
2
2
0
0
0
1
2
0
1
0
0
0
0
1
0
0
2
0
0
0
1
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
2
1
2
0
0
0
0
1
2
2
0
4
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
2
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
2
0
0
2
2
3
0
0
2
0
2
0
0
2
0
1
0
1
2
0
0
0
0
2
0
1
0
0
0
0
0
1
1
0
2
0
0
0
0
0
1
0
0
2
0
0
5
0
0
0
1
0
0
2
0
0
2
2
1
2
1
0
0
0
0
0
2
2
0
0
0
1
2
0
0
2
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
4
0
0
0
0
2
0
0
0
0
0
0
3
2
1
0
0
2
1
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
1
1
2
2
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
1
1
1
1
2
0
0
1
0
0
1
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
1
2
0
0
0
1
0
0
0
0
0
0
0
0
2
2
1
0
0
0
1
1
0
0
0
1
0
0
1
1
2
0
1
0
0
0
1
0
1
2
0
0
0
2
2
0
0
0
0
1
0
2
1
2
0
0
1
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
1
0
3
0
2
0
2
0
2
0
0
0
0
4
2
2
4
1
2
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
2
1
1
2
0
0
0
0
0
0
0
3
0
1
0
1
1
2
2
1
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
2
2
0
0
0
0
0
1
0
2
2
0
0
1
2
1
1
0
0
2
0
1
0
1
1
4
0
0
2
0
0
0
0
2
1
3
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
2
1
2
1
2
0
1
0
0
0
2
0
0
0
0
2
2
1
0
0
0
0
2
0
1
1
2
1
0
2
1
1
1
2
1
0
0
0
0
2
2
0
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
4
0
0
2
0
3
0
0
0
2
0
0
2
0
0
0
0
0
0
4
0
3
0
2
0
1
0
1
0
2
1
1
0
0
0
2
0
1
1
2
0
0
0
0
0
3
0
1
0
0
0
0
1
3
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
2
1
0
0
0
0
0
0
2
2
2
3
2
0
3
0
2
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
2
1
2
0
2
1
0
0
0
0
2
0
0
0
2
0
0
1
0
1
1
1
0
0
0
1
2
2
1
0
0
2
0
1
2
1
0
2
1
0
1
2
0
0
0
0
0
0
0
2
0
2
2
0
0
0
1
0
0
0
0
0
2
2
2
2
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
3
2
0
2
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
2
2
0
0
1
2
0
2
0
0
2
0
2
2
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
2
0
0
0
0
3
0
2
0
0
0
1
0
0
0
0
2
0
0
0
1
2
0
1
0
2
0
2
2
0
2
0
2
1
0
0
3
2
0
0
2
0
0
0
0
0
2
0
0
1
1
1
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
3
0
0
1
1
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
1
1
0
0
0
0
2
0
1
4
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
3
1
2
0
0
0
0
0
0
0
0
2
1
1
1
0
0
0
0
1
3
0
0
1
0
0
0
1
0
2
0
2
0
0
3
0
1
0
0
1
1
0
0
0
1
0
0
2
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
2
1
0
0
2
0
0
0
0
1
0
0
1
0
0
0
3
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
3
0
1
2
0
0
0
0
1
0
0
0
0
2
1
0
2
0
1
0
0
1
0
2
0
1
1
0
0
7
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
2
2
0
0
0
0
0
1
2
1
2
0
2
2
0
0
0
0
0
1
0
0
1
0
0
0
1
0
2
0
0
2
0
0
2
4
0
0
1
0
2
0
0
0
0
0
0
2
1
2
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
2
1
1
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
2
1
2
0
0
2
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
2
0
1
0
0
0
0
2
0
0
0
1
0
2
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
1
0
0
1
0
0
2
0
0
2
1
0
0
0
0
0
2
0
0
3
0
2
1
2
0
2
0
0
0
1
2
1
1
0
2
0
0
0
0
1
0
2
0
2
0
0
2
2
2
1
1
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
2
0
1
0
1
2
0
0
0
0
0
0
1
1
2
0
4
0
2
0
3
0
0
2
0
0
1
0
1
0
0
1
0
0
0
0
2
1
0
2
0
0
0
0
1
0
2
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
2
1
0
0
0
0
1
0
1
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
2
0
2
1
1
0
0
0
0
2
0
2
1
2
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
1
0
2
0
0
2
1
0
0
1
0
0
0
2
0
1
0
2
0
2
0
0
0
0
1
4
0
0
1
0
0
0
2
1
0
1
0
0
1
3
0
0
0
0
0
0
0
1
2
2
1
0
0
0
0
0
0
0
3
0
0
2
1
0
0
0
2
1
0
1
0
0
1
0
0
0
0
0
1
0
1
0
1
0
2
1
2
3
0
0
0
2
0
0
2
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
2
1
0
0
0
3
1
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
2
1
1
0
1
2
0
0
0
1
0
2
1
0
3
1
0
0
0
0
2
2
1
0
0
0
2
0
0
1
0
1
0
1
0
0
0
1
0
1
0
2
0
1
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
2
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
2
0
0
0
0
0
0
1
0
0
1
1
0
2
0
1
0
0
0
0
7
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
1
2
1
0
0
0
0
0
2
1
0
0
0
0
2
2
0
1
1
0
0
0
0
0
2
0
1
2
2
0
11
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
3
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
2
0
0
0
0
2
2
1
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
3
0
0
2
0
0
0
2
2
0
1
1
0
0
2
0
0
1
0
0
2
0
0
0
1
0
1
0
0
2
0
0
0
0
2
0
1
0
2
0
0
1
0
3
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
2
0
1
2
0
1
2
0
2
0
0
0
0
0
0
0
0
2
0
2
1
1
0
2
2
0
0
0
0
1
0
1
1
1
1
1
0
0
2
1
0
1
2
1
2
1
1
0
2
0
0
0
2
0
0
1
0
0
0
0
0
2
2
1
1
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
2
0
2
0
2
1
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
2
0
0
2
1
0
0
2
0
2
0
0
0
3
2
2
0
0
1
0
0
0
2
1
0
0
2
0
2
0
1
0
2
1
0
2
0
0
1
1
0
0
0
1
0
2
0
0
0
2
2
0
0
0
2
0
0
0
0
1
2
0
1
2
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
1
0
7
0
1
0
0
0
1
2
0
0
0
0
1
0
0
0
0
1
1
0
2
2
0
1
1
0
0
0
0
2
0
1
0
1
2
0
1
2
0
0
0
1
0
2
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
1
1
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
1
0
0
2
0
0
2
5
0
1
0
0
1
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
3
0
0
1
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
2
1
2
0
0
0
0
0
4
0
0
2
1
1
1
0
0
0
0
1
1
0
0
0
2
2
0
2
1
0
2
0
0
0
0
2
2
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
1
0
2
5
0
1
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
3
0
2
0
0
1
0
2
0
0
0
0
0
2
1
0
0
0
0
0
1
1
0
0
1
0
0
2
0
0
0
1
2
2
0
1
0
1
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
2
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
3
1
0
1
0
1
1
2
0
0
0
0
0
2
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
2
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
2
0
2
0
6
0
2
2
1
0
0
0
0
0
0
1
2
3
0
0
2
0
1
2
0
0
0
0
3
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
1
0
2
0
0
0
0
0
1
2
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
3
0
0
1
0
0
0
0
1
0
0
2
1
0
0
1
1
1
1
1
0
0
0
0
2
0
0
2
2
0
0
2
0
1
0
0
1
2
0
2
0
1
0
2
0
1
0
1
0
1
0
2
0
0
0
0
0
2
0
0
0
2
0
0
1
2
0
0
0
0
3
0
2
0
2
0
0
0
1
0
1
0
0
0
0
0
0
2
0
2
0
1
0
2
0
1
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
2
0
2
0
0
2
2
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
1
4
0
0
0
0
0
0
0
1
2
0
3
1
0
0
0
0
0
3
0
1
2
2
0
0
1
0
0
0
2
0
0
0
0
0
2
0
2
0
1
0
0
0
0
2
0
0
2
1
0
1
0
0
0
0
0
1
1
0
0
2
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
1
1
0
2
0
0
1
1
1
1
0
1
0
0
0
1
1
2
0
1
2
1
2
0
0
1
2
1
0
2
0
0
1
2
0
0
0
0
5
2
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
1
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
1
2
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
3
2
1
0
0
1
0
0
0
0
0
2
3
1
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
1
2
0
0
0
0
0
0
2
0
1
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
2
2
0
1
2
1
0
1
0
1
0
0
0
2
2
1
1
1
1
0
0
0
0
0
1
2
2
0
0
0
0
0
0
1
0
2
1
0
0
0
0
2
2
0
1
0
0
4
0
0
2
0
0
0
0
1
0
0
0
2
1
0
2
1
0
2
0
0
3
1
3
0
0
0
0
2
0
0
1
0
0
0
2
0
2
2
0
2
0
2
0
2
0
0
1
2
0
2
0
2
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
2
1
0
0
0
0
0
1
10
0
2
0
0
0
1
0
0
1
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
2
0
2
0
2
0
0
0
2
0
0
2
0
0
0
2
1
0
0
2
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
2
0
1
0
0
0
1
0
2
2
0
0
0
0
2
0
0
0
2
1
1
0
1
0
0
0
0
0
0
0
2
0
0
2
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
5
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
1
3
0
2
0
0
1
3
0
2
0
0
0
3
1
0
0
0
1
1
0
2
0
0
2
0
0
0
1
1
0
1
0
1
2
3
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
2
2
2
2
0
0
2
2
1
1
0
0
0
0
2
2
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
2
0
0
1
1
1
0
0
1
0
2
0
2
1
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
2
1
0
2
2
0
0
0
0
1
0
0
0
2
0
0
0
0
3
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
2
0
0
2
0
0
0
0
2
1
0
0
2
2
0
0
0
1
0
2
0
2
0
2
0
0
0
0
1
2
1
0
0
0
1
3
0
0
5
0
0
0
0
0
1
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
3
1
0
3
2
2
0
0
0
0
1
0
0
1
1
1
0
0
1
0
2
0
0
2
2
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
2
2
0
0
0
4
0
0
0
0
4
2
1
0
0
0
2
0
0
2
0
0
1
0
1
0
0
2
4
0
1
2
2
0
0
2
0
0
0
1
1
1
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
1
0
3
2
0
0
0
0
1
0
2
0
0
1
0
0
0
1
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
1
1
0
2
1
1
0
0
1
0
0
0
2
1
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
1
0
2
2
0
0
0
2
0
0
0
1
0
0
2
0
0
1
0
1
0
0
0
0
1
0
1
0
0
2
0
1
0
2
0
2
0
0
1
0
0
1
1
0
0
0
2
0
0
0
0
0
1
0
0
2
1
1
0
0
2
0
0
0
0
0
0
0
0
3
0
1
0
1
1
2
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
2
2
0
0
1
0
0
0
0
0
2
1
2
1
1
2
1
0
5
0
0
0
3
0
0
0
0
0
2
1
2
1
0
0
0
1
0
0
0
0
2
1
0
0
1
0
1
1
0
0
1
0
0
0
0
1
0
0
2
1
0
0
0
0
0
2
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
1
2
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
2
0
0
0
2
2
0
1
1
0
0
0
0
0
0
0
0
0
1
0
13
0
0
0
0
1
2
0
2
1
0
0
0
0
1
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
2
0
0
2
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
1
3
2
1
0
1
0
0
0
0
2
0
0
0
0
0
1
0
2
2
0
0
0
0
1
0
1
2
2
0
3
0
2
0
0
0
1
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
2
0
2
0
0
1
0
0
0
2
1
0
1
0
0
2
0
0
0
0
2
1
0
0
3
0
0
1
0
0
2
0
2
2
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
1
2
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
1
2
2
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
2
0
0
2
0
1
0
0
2
1
0
0
2
1
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
1
0
2
0
0
0
1
2
0
2
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
5
0
4
0
1
0
3
0
1
0
0
2
0
2
0
0
0
3
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
2
1
1
1
1
0
0
0
1
0
1
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
1
0
2
0
2
0
1
2
1
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
2
0
1
1
0
2
0
0
0
1
0
0
0
0
2
1
0
0
0
0
2
2
0
1
0
1
0
0
0
0
1
1
0
1
0
0
2
1
0
1
0
5
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
5
0
1
0
0
2
0
0
1
0
1
1
0
0
1
4
1
0
0
0
0
1
2
0
0
2
1
2
2
0
0
0
0
0
0
0
2
0
1
0
4
0
0
0
3
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
1
1
2
0
0
1
0
2
2
0
0
0
1
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
1
0
0
2
2
0
0
0
1
1
13
0
2
0
0
0
0
0
0
0
2
1
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
2
2
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
1
2
0
1
0
1
1
1
0
0
0
1
0
0
1
0
2
1
1
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
2
0
2
0
0
1
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
1
1
0
0
0
0
2
3
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
1
0
0
1
0
2
0
0
0
0
2
0
1
0
0
2
0
0
0
1
1
0
0
0
0
0
2
3
0
0
0
2
0
0
1
1
0
0
2
0
1
0
0
3
2
1
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
2
0
0
1
0
2
0
0
0
1
1
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
2
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
1
2
0
1
0
0
0
0
0
3
1
0
0
0
0
0
0
1
2
0
0
2
1
0
0
0
1
0
0
0
0
1
0
2
2
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
3
0
0
0
1
0
0
0
0
3
0
1
2
1
0
0
0
0
1
0
2
1
2
0
0
2
0
0
2
0
2
0
2
0
0
0
1
0
0
2
1
1
0
0
3
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
1
0
2
0
0
0
2
1
0
1
2
0
0
0
0
2
1
1
0
1
0
0
0
1
0
0
0
2
1
0
0
0
0
2
1
0
2
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
2
2
1
2
1
1
1
0
0
2
1
1
0
0
2
0
0
0
0
0
0
2
1
0
0
0
2
1
0
0
2
2
0
1
2
0
0
0
0
1
1
0
2
2
0
0
1
0
2
1
0
1
0
0
0
0
0
0
0
1
2
1
1
1
0
0
0
0
0
0
1
0
1
9
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
1
0
3
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
1
1
0
1
0
0
1
2
1
2
0
0
0
0
0
0
1
0
2
0
1
1
0
0
0
0
2
0
1
3
0
1
1
0
2
0
0
2
0
2
0
0
1
0
2
0
0
2
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
2
0
0
0
1
2
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
3
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
2
0
0
0
7
0
0
1
0
2
0
0
0
0
2
0
2
0
1
0
0
0
2
0
0
0
0
0
1
0
2
2
0
1
2
0
1
0
1
0
0
0
0
1
0
1
2
6
1
1
0
1
0
0
0
1
1
0
0
0
0
0
2
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
1
1
1
0
0
3
2
0
0
1
2
1
0
2
0
0
0
0
0
0
2
0
2
0
1
2
0
2
1
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
1
2
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
3
2
0
0
0
2
0
2
0
2
0
0
0
0
0
0
1
0
0
0
3
2
0
0
2
0
0
0
0
0
0
2
1
2
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
2
2
0
2
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
2
0
1
1
0
0
0
1
0
0
2
1
0
0
1
0
1
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
1
3
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
2
1
0
0
1
0
0
0
0
2
3
1
0
0
1
2
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
2
0
0
0
1
1
0
0
0
2
1
0
0
0
2
0
0
0
0
0
4
0
0
0
0
2
0
0
1
0
1
0
0
0
1
0
2
0
0
0
0
1
1
0
0
0
0
2
0
1
3
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
2
2
0
1
0
0
2
0
1
2
2
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
1
2
0
0
0
2
1
0
0
0
0
2
0
0
0
2
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
3
0
0
0
0
6
1
0
0
1
0
1
2
2
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
3
1
1
0
1
0
0
0
0
0
0
0
0
0
2
1
0
3
1
0
0
1
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
1
0
1
1
0
1
0
0
1
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
2
0
1
0
0
0
1
1
0
2
0
0
0
0
3
0
1
0
0
1
0
0
0
0
0
0
0
1
2
1
0
2
1
0
2
0
1
0
0
2
0
1
0
0
2
0
0
0
0
0
2
0
1
1
0
0
0
3
2
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
3
0
1
1
0
0
0
2
0
2
2
0
0
3
0
0
1
0
0
2
0
1
0
0
0
1
0
0
1
2
0
0
0
1
0
2
2
1
0
2
1
0
2
2
0
0
0
3
1
2
2
0
0
0
2
0
0
0
0
0
1
0
2
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
1
0
0
1
0
1
1
0
2
0
0
2
0
0
0
2
0
2
0
0
0
0
0
2
1
0
5
0
0
0
2
0
0
0
0
0
2
0
1
3
1
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
3
0
0
0
2
0
1
0
0
1
0
0
0
3
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
2
1
0
1
0
0
1
0
1
0
0
3
0
0
0
0
0
0
2
0
1
0
2
0
2
0
2
0
0
0
2
2
0
0
0
2
1
0
1
0
0
1
1
0
1
0
0
0
2
0
3
2
2
0
0
2
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
2
1
0
3
2
0
0
0
2
2
0
0
0
1
1
0
0
0
0
2
2
0
0
1
0
0
0
1
0
0
1
1
3
2
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
1
0
1
0
2
0
0
0
0
0
0
1
0
1
0
2
0
0
2
0
2
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
3
0
0
1
0
1
0
0
0
2
0
0
0
0
0
1
0
1
3
2
2
0
0
0
2
3
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
2
2
3
0
0
0
0
1
1
2
2
0
0
0
0
0
0
2
0
2
1
0
0
1
2
0
0
0
0
3
1
0
0
0
1
0
2
2
0
0
0
2
0
2
0
0
1
0
0
1
0
0
1
0
1
0
1
1
1
0
0
0
0
0
0
2
0
3
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
2
0
0
2
0
0
1
2
0
0
0
1
0
0
0
1
0
0
2
0
4
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
1
1
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
1
2
1
1
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
2
2
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
2
0
0
0
1
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
2
1
0
0
0
1
7
0
1
0
1
1
1
0
0
0
0
0
2
2
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
3
0
0
0
2
2
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
1
1
0
0
0
0
2
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
1
0
0
1
0
1
2
2
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
2
0
0
4
0
0
0
1
0
0
0
1
2
0
1
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
1
2
1
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
2
0
3
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
2
1
2
2
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
2
1
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
2
0
1
1
1
0
2
2
2
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
2
1
2
0
0
0
0
0
2
0
3
0
0
1
0
2
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
2
0
1
0
2
2
0
0
0
2
0
2
2
0
0
0
0
0
0
0
1
0
0
0
3
0
1
2
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
1
2
2
0
0
1
1
0
2
0
2
0
0
0
0
0
2
0
0
0
0
2
0
2
1
0
2
0
0
1
0
0
3
0
0
0
0
2
0
0
1
1
0
2
0
0
0
0
1
2
0
0
0
1
1
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
2
0
1
2
0
2
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
2
0
0
2
2
0
0
0
0
3
0
0
0
2
3
1
1
0
0
0
2
0
1
3
0
1
2
0
1
0
0
1
0
0
2
0
2
0
0
1
0
2
2
2
0
0
2
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
2
0
1
1
0
0
0
0
0
0
0
1
2
2
1
1
2
1
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
1
1
0
1
2
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
1
2
2
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
1
2
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
2
0
7
1
2
0
1
3
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
2
4
2
0
1
0
1
0
1
0
2
2
5
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
2
1
2
2
6
0
0
1
1
0
0
0
2
1
0
1
1
1
0
1
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
2
1
0
0
3
2
2
2
2
1
0
0
2
0
1
0
0
0
2
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
3
0
2
1
2
0
1
0
6
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
2
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
1
0
2
0
0
2
0
3
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
1
3
0
0
2
1
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
2
2
2
0
2
1
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
2
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
1
0
0
1
2
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
2
2
2
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
1
0
0
1
0
0
1
2
0
0
0
2
2
0
0
1
0
0
2
2
0
0
0
0
2
0
1
1
0
2
0
2
0
0
0
2
0
0
0
0
0
0
1
1
1
1
0
0
1
2
0
0
3
0
0
0
0
0
3
2
1
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
2
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
1
0
0
0
0
0
1
2
0
2
0
0
0
2
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
1
0
2
0
2
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
2
0
0
1
1
0
2
2
3
0
0
0
0
0
1
0
0
2
0
2
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
2
2
0
0
0
3
0
0
0
1
0
0
1
0
0
0
2
0
1
0
0
0
0
1
0
0
0
1
0
0
1
2
0
1
1
0
0
0
0
7
2
0
0
0
0
0
2
0
1
2
0
0
1
0
1
0
0
2
0
0
0
0
0
2
2
0
2
0
0
2
0
0
0
1
1
2
1
0
1
0
2
2
0
0
0
2
0
1
0
0
0
2
0
0
1
0
2
1
0
2
0
0
2
0
0
0
0
0
0
2
3
2
0
1
0
1
0
2
1
0
0
2
0
0
2
2
0
1
1
0
1
1
0
0
0
1
4
0
1
0
1
1
0
1
0
2
0
3
0
2
2
0
0
0
0
2
2
0
2
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
2
2
0
2
1
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
2
0
0
0
0
0
0
2
0
0
2
0
0
1
0
2
1
3
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
3
0
1
2
0
0
1
0
0
0
0
3
2
0
0
1
3
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
2
2
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
1
0
0
0
0
2
0
0
0
1
2
2
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
3
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
2
2
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
2
0
0
2
0
2
2
0
0
0
0
0
2
0
0
0
0
1
1
1
1
0
0
0
0
2
1
0
4
1
0
0
2
0
2
0
1
0
0
0
0
0
0
2
1
0
0
1
0
1
0
2
1
0
0
1
0
0
2
0
0
0
2
0
3
0
0
0
0
0
2
1
2
2
0
1
0
2
0
0
0
0
2
0
0
2
2
0
2
1
0
0
0
0
2
0
1
0
0
0
1
1
0
2
0
0
0
1
0
0
0
0
0
2
0
2
1
0
0
0
1
1
2
0
1
0
0
0
0
0
2
0
0
0
0
0
1
2
1
0
1
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
2
0
1
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
2
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
1
0
0
0
0
1
2
2
0
0
0
0
1
1
0
2
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
2
2
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
3
2
3
0
0
0
2
2
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
6
5
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
5
0
0
0
2
0
1
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
1
1
0
0
0
2
0
2
1
0
1
0
1
0
2
0
0
1
0
0
0
1
0
0
0
1
1
2
1
4
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
1
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
3
1
0
1
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
2
0
2
0
2
0
0
0
1
0
0
0
0
1
1
1
1
1
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
2
1
1
0
2
0
0
0
2
0
0
0
1
0
0
0
0
2
0
2
0
0
0
2
0
0
0
1
0
2
0
1
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
2
1
0
2
0
1
2
0
2
0
0
1
1
0
0
0
0
0
2
1
2
0
1
0
0
0
0
0
2
0
0
0
2
0
2
2
0
0
0
2
0
0
0
1
0
2
0
0
0
0
1
2
0
2
0
0
0
1
0
1
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
2
3
4
1
0
0
0
2
1
0
0
2
2
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
3
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
2
1
1
0
0
2
1
2
1
2
2
0
0
0
2
2
2
0
0
0
1
3
1
0
0
0
2
0
1
0
0
2
0
0
1
0
0
0
0
1
1
0
0
0
0
1
4
0
0
0
0
2
1
2
2
0
0
0
0
1
0
0
2
0
1
1
0
2
2
5
2
1
0
0
0
0
0
0
2
2
1
1
0
2
0
0
0
1
0
0
0
0
2
0
1
2
0
0
0
0
2
1
0
0
0
1
1
0
0
4
0
0
0
0
0
2
0
2
0
0
0
0
2
0
1
2
0
0
0
4
0
1
0
0
2
0
0
0
0
1
0
1
2
0
0
2
0
2
0
0
2
0
0
0
2
0
1
2
0
0
0
0
0
1
0
0
0
2
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
1
2
1
0
3
0
0
1
0
0
1
0
0
0
0
0
3
0
2
2
0
2
0
0
0
1
0
0
1
1
0
0
2
0
0
2
1
0
0
0
0
1
0
0
0
0
0
2
1
1
0
0
1
0
0
1
0
0
1
0
2
0
0
0
0
2
0
2
0
0
2
2
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
2
0
1
2
2
1
0
0
1
0
0
0
1
2
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
1
0
0
2
0
0
0
0
3
1
2
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
3
0
2
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
3
0
0
0
2
0
0
0
3
1
0
8
0
0
0
0
2
1
1
2
0
0
0
1
0
1
0
0
1
2
1
0
0
0
2
1
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
3
1
0
0
0
0
0
0
0
3
2
0
0
0
0
2
2
0
1
0
1
0
0
2
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
1
0
2
0
7
1
1
0
0
0
1
9
0
0
0
0
0
3
2
0
0
3
0
0
1
0
0
0
0
3
2
0
0
0
0
2
1
0
0
2
0
2
3
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
2
0
2
0
0
0
0
0
2
0
2
5
0
0
0
1
0
0
2
0
5
0
0
0
0
1
0
1
3
0
0
0
1
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
1
0
0
0
0
1
2
0
0
2
0
0
2
0
0
0
0
0
2
2
2
1
0
1
0
1
0
0
0
2
2
1
0
2
0
0
0
0
1
2
15
0
0
0
3
1
0
0
2
0
0
0
0
1
0
2
0
0
0
0
3
2
1
0
0
0
0
0
2
0
0
0
0
1
1
1
2
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
3
0
0
0
0
2
0
1
0
1
2
1
0
2
0
0
0
1
1
0
2
2
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
2
4
2
2
0
0
0
2
0
0
1
1
0
0
0
2
0
1
2
1
0
0
1
2
0
1
1
0
0
1
0
0
2
0
0
2
1
2
1
0
0
0
0
0
2
2
0
0
0
0
2
1
1
0
0
0
0
0
0
1
1
0
0
2
2
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
3
3
0
0
3
2
0
1
2
0
0
0
2
0
0
1
1
0
1
0
0
0
0
2
3
0
0
2
0
0
0
0
1
0
1
0
3
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
4
0
0
1
0
2
0
0
2
0
0
0
0
0
0
2
1
2
0
2
1
0
2
0
2
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
2
2
1
0
0
0
0
2
1
0
0
2
0
0
0
0
2
0
2
0
3
0
2
2
0
0
0
0
0
0
2
0
0
2
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
3
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
5
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
1
2
0
1
1
0
2
2
1
0
3
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
2
0
1
1
1
0
1
0
3
1
0
0
0
2
0
0
0
2
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
3
2
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
5
0
0
0
2
2
0
2
0
2
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
1
0
2
2
0
0
0
1
0
1
1
0
2
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
2
1
3
8
2
0
0
2
0
0
0
2
0
0
2
1
2
1
0
0
0
0
0
3
0
0
1
3
1
1
0
1
0
0
2
0
0
0
0
2
0
0
1
0
0
0
1
0
0
2
0
1
0
0
0
0
2
0
1
3
0
0
2
1
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
5
1
0
1
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
1
1
2
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
1
0
0
2
2
2
0
0
0
0
0
0
0
1
1
3
1
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
1
0
1
0
1
0
0
2
0
0
0
0
0
1
0
1
0
0
1
2
0
0
0
0
0
3
0
0
0
1
0
0
0
2
1
0
0
0
1
0
0
1
0
1
0
1
0
1
0
0
2
0
2
0
1
0
0
0
1
0
3
0
0
0
0
1
0
2
0
0
0
0
3
2
0
1
0
2
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
1
2
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
2
0
0
2
1
0
0
2
2
0
0
0
0
1
2
1
0
2
2
1
2
1
1
0
1
1
0
0
0
2
0
1
0
0
1
0
0
2
0
0
1
0
2
0
2
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
3
0
0
0
1
2
2
0
2
0
2
0
0
0
0
1
0
0
0
0
1
2
2
2
2
1
0
0
1
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
1
0
0
1
2
0
0
0
0
0
0
1
1
0
1
1
1
2
0
1
0
2
2
0
0
0
2
0
0
0
1
3
1
0
1
3
0
0
2
0
0
2
0
0
1
1
0
1
1
1
1
2
1
1
0
0
0
0
0
0
0
0
0
0
1
0
5
0
0
2
2
0
0
0
1
0
1
0
0
0
0
2
1
0
2
0
0
1
2
0
0
1
2
0
0
1
0
1
7
0
0
0
0
1
0
0
0
2
2
2
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
1
0
0
2
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
2
2
0
3
0
0
0
1
0
2
0
0
1
0
1
0
0
0
2
0
2
0
2
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
2
1
0
0
0
0
2
2
2
0
0
0
0
0
1
0
1
0
0
0
0
2
2
1
0
2
1
1
1
1
0
0
0
0
2
0
0
0
0
2
0
1
1
0
0
0
0
0
2
0
1
0
0
1
0
0
1
0
0
0
2
0
0
0
1
1
0
0
0
0
1
3
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
1
0
0
0
2
1
0
0
2
0
1
0
2
1
0
3
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
3
0
1
1
0
0
2
0
0
0
1
2
0
1
0
0
0
1
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
2
0
2
0
1
2
0
2
1
0
2
3
0
1
0
1
0
0
2
0
1
0
0
0
1
0
1
2
0
0
0
0
1
0
2
2
0
0
1
0
1
0
0
1
2
0
0
0
1
0
8
0
4
2
0
0
0
0
0
2
0
0
2
2
1
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
2
2
2
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
1
2
1
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
3
2
2
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
2
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
4
1
0
0
3
0
0
0
1
0
0
3
1
0
1
1
1
1
2
3
2
0
2
0
0
0
1
1
0
3
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
2
0
0
0
0
1
0
0
3
0
2
2
0
0
0
1
0
0
0
0
2
1
0
2
0
0
2
1
0
2
1
0
0
0
0
0
0
0
1
1
0
1
2
0
0
0
0
0
0
0
3
0
3
2
1
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
2
2
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
2
0
2
0
0
0
0
0
0
3
0
1
0
0
0
0
2
2
2
2
1
1
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
1
0
0
0
2
0
1
0
0
0
0
0
1
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
1
1
0
0
1
1
0
2
9
0
0
0
0
1
0
1
1
0
0
3
0
1
0
0
0
0
0
0
1
0
2
3
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
1
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
1
0
1
1
0
0
0
0
0
4
2
2
2
0
2
0
0
0
0
2
0
1
0
1
0
2
2
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
2
0
2
2
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
2
0
0
2
0
4
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
2
2
0
0
1
0
0
0
2
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
1
0
0
1
0
1
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
2
1
0
1
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
3
1
0
3
0
2
0
0
1
0
2
0
1
0
0
0
0
0
3
0
2
0
0
2
1
0
0
0
0
2
0
0
1
0
1
1
0
0
0
2
1
1
0
0
0
1
0
0
0
0
0
0
1
0
2
1
0
1
2
0
2
0
0
0
1
0
0
0
0
0
0
3
1
0
0
5
0
2
0
0
1
0
0
2
2
2
0
1
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
1
1
2
1
0
0
0
1
2
0
0
0
0
1
2
0
0
0
4
0
0
0
2
1
0
0
1
2
0
0
0
2
0
0
1
3
2
0
0
2
0
1
0
0
1
0
1
3
0
0
0
1
0
0
4
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
2
0
0
1
1
0
1
0
0
0
0
0
2
0
1
0
1
2
0
0
0
0
0
1
1
1
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
2
0
1
0
0
0
0
1
0
1
0
2
0
2
0
0
1
0
2
0
0
1
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
2
1
0
1
0
2
0
1
0
2
1
0
2
2
0
2
0
1
1
0
3
2
0
2
0
0
4
0
2
1
0
3
0
0
1
0
0
1
1
0
0
2
0
0
0
0
1
0
0
0
2
0
0
2
1
1
0
1
0
0
0
3
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
3
1
0
0
2
1
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
2
0
0
0
0
1
1
2
2
0
0
1
0
1
0
0
0
0
0
0
2
0
0
3
0
2
0
2
0
2
3
0
0
0
2
0
1
0
0
1
1
1
0
0
2
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
2
0
0
0
1
1
2
1
0
3
2
0
0
1
2
1
0
0
0
1
2
0
0
2
0
0
1
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
3
0
2
0
2
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
1
3
0
1
0
0
0
0
0
2
2
0
0
2
0
0
3
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
3
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
3
0
0
1
2
0
2
0
0
0
0
0
1
0
0
0
2
1
0
0
1
1
0
2
1
2
0
0
2
0
0
1
0
1
0
0
0
0
1
2
0
0
3
2
0
0
0
2
0
1
0
0
1
0
0
1
0
1
0
0
0
1
0
0
2
1
0
1
0
0
0
2
2
0
0
0
2
0
0
0
0
0
3
0
0
0
1
1
0
2
1
0
0
0
0
0
0
0
2
0
3
0
0
2
0
5
0
32
0
0
0
0
0
1
2
1
1
0
0
2
0
0
1
0
1
0
1
0
7
0
0
0
1
0
2
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
1
0
0
1
1
0
3
2
1
1
0
2
0
0
0
2
0
0
0
0
2
0
1
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
2
0
0
1
1
0
2
0
0
0
0
0
0
2
1
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
1
0
1
0
0
1
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
1
0
1
1
0
0
0
2
0
1
1
0
0
0
2
1
2
1
1
0
0
0
0
2
1
0
0
0
2
0
0
1
1
0
0
0
3
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
2
1
0
1
1
0
0
2
0
0
0
0
0
1
1
2
0
2
0
1
0
2
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
1
1
0
0
1
0
0
0
1
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
2
0
0
0
1
1
0
0
0
0
1
0
3
0
2
0
0
0
0
0
2
1
0
2
0
2
0
2
1
0
0
0
0
2
0
0
1
0
1
2
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
1
0
2
1
0
0
0
2
1
0
0
0
2
0
0
0
0
0
1
0
2
0
0
2
0
0
0
2
2
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
1
1
0
0
1
0
0
0
0
2
1
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
3
0
1
0
1
0
2
0
0
0
2
0
0
0
0
2
2
2
0
0
2
2
2
0
0
0
2
2
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
2
1
3
0
1
0
0
1
0
2
0
0
0
0
1
0
0
2
1
0
0
0
0
2
0
2
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
6
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
1
0
0
1
0
3
0
0
2
0
2
0
1
1
0
0
0
0
1
2
0
0
2
0
1
0
1
0
0
0
1
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
1
0
1
0
1
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
2
1
0
1
0
2
1
0
0
2
0
2
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
3
1
0
0
1
0
0
2
1
0
0
1
0
2
0
2
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
2
2
0
0
0
0
2
0
2
1
0
2
1
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
1
1
1
0
1
0
0
2
0
0
2
1
1
2
2
0
0
0
1
0
0
0
0
3
0
1
1
0
0
0
1
1
1
1
0
1
0
0
0
0
0
1
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
1
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
2
0
0
2
0
2
0
0
2
1
0
3
2
0
1
0
0
0
0
2
0
1
0
1
1
0
0
2
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
2
0
0
1
0
0
1
0
0
2
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
4
0
0
0
0
0
0
0
0
1
1
0
1
2
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
1
0
3
2
2
0
0
0
0
0
1
0
1
0
2
2
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
2
0
0
0
2
0
0
0
1
0
0
0
1
0
0
1
1
1
1
0
2
2
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
1
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
1
0
0
3
0
0
1
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
4
2
0
0
1
0
0
1
0
1
2
2
0
0
1
0
0
0
0
0
1
0
0
1
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
2
1
0
0
0
2
0
1
0
1
0
0
0
0
0
0
1
2
2
0
1
0
0
0
1
0
0
0
1
3
0
1
1
1
5
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
1
1
2
1
0
1
0
2
1
0
0
1
0
0
0
0
0
2
2
0
2
0
2
0
1
0
0
0
0
0
1
1
0
2
2
0
1
0
0
0
0
0
2
0
0
2
0
0
1
1
0
0
0
1
0
0
1
3
2
0
0
0
0
0
1
2
2
0
0
0
2
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
3
0
1
0
1
3
1
2
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
2
2
0
2
0
0
0
0
0
0
2
2
2
1
0
0
1
0
4
2
1
2
1
1
1
1
0
0
0
1
0
0
0
2
0
0
3
0
0
1
2
2
0
0
0
2
1
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
3
0
0
1
0
0
1
2
0
1
1
0
2
1
0
1
0
0
2
0
1
0
0
1
0
1
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
2
0
2
0
0
2
0
0
0
0
2
2
1
0
0
1
3
2
0
0
1
0
1
0
1
2
1
0
1
1
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
3
0
1
0
0
2
2
1
0
1
0
1
0
0
2
0
1
1
0
1
0
1
1
0
0
0
0
0
0
0
1
0
2
0
4
0
1
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
1
0
0
1
0
0
1
0
1
1
1
1
1
0
1
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
1
0
0
0
0
0
1
0
2
2
0
0
2
0
2
0
1
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
1
1
0
1
0
2
0
0
0
0
0
1
1
0
1
0
0
0
0
2
0
1
0
0
0
0
1
1
1
0
0
1
2
0
1
0
3
0
0
0
0
3
1
0
0
0
1
0
2
1
0
1
0
2
0
0
5
0
0
1
0
2
2
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
3
1
0
1
3
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
2
1
0
1
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
2
2
2
0
2
2
0
1
2
1
0
2
0
1
0
1
0
0
0
0
2
0
0
0
0
3
2
0
1
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
1
0
0
0
0
2
0
0
1
0
0
0
2
1
0
2
0
0
0
4
2
0
2
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
1
1
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
1
0
1
0
1
2
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
2
0
1
1
1
2
0
0
0
1
0
0
0
0
3
1
3
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
1
1
0
2
0
1
1
0
0
3
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
3
2
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
1
0
1
0
0
2
0
1
0
2
2
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
5
2
0
0
1
0
0
0
0
1
2
0
0
0
1
0
0
2
1
0
0
0
1
0
0
0
1
0
2
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
1
0
2
0
0
0
0
2
2
0
1
2
0
0
0
0
0
0
2
2
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
1
0
1
2
0
0
0
0
2
2
2
0
0
2
0
0
0
1
0
0
0
0
0
2
0
1
0
2
0
0
0
3
0
0
0
0
1
2
0
1
1
0
1
0
2
0
1
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
1
2
0
0
0
1
3
1
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
1
0
0
0
1
0
0
0
3
0
0
0
0
2
0
0
0
0
0
2
0
1
0
2
0
0
0
0
1
0
0
1
0
4
0
1
0
2
1
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
2
0
0
0
2
1
0
0
0
1
1
2
0
1
0
2
0
2
0
0
1
0
1
2
0
0
0
0
2
0
2
1
0
0
0
5
0
0
0
1
0
3
0
1
0
0
0
3
0
0
0
1
2
0
0
0
1
2
0
2
1
1
1
1
0
0
0
0
1
0
0
0
2
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
1
2
0
1
0
1
0
0
2
0
0
2
0
0
1
0
1
0
2
0
1
0
1
0
1
0
0
1
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
2
0
1
0
0
2
0
0
2
0
1
0
0
0
0
0
2
1
2
0
0
0
0
3
0
0
0
0
2
0
1
0
0
5
0
0
0
0
2
0
1
3
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
1
2
0
0
2
2
0
0
1
0
0
0
0
0
1
2
0
0
1
0
1
0
0
1
1
0
0
2
2
1
1
0
0
0
0
2
0
0
2
0
0
2
0
0
0
3
2
0
0
1
0
1
0
2
0
2
0
0
0
0
2
1
2
0
0
5
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
1
0
0
0
0
0
2
1
2
0
1
0
2
2
2
0
2
0
1
0
0
0
0
0
0
5
0
0
1
0
1
1
0
0
2
0
0
1
1
0
1
0
3
1
0
0
0
2
1
0
0
0
1
0
2
0
2
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
2
0
0
1
2
1
0
0
2
4
0
1
0
0
0
0
0
0
1
1
2
1
1
0
2
0
0
2
2
0
0
0
1
0
0
0
1
2
1
0
0
1
2
0
0
1
2
3
0
0
2
0
0
0
0
1
0
0
0
0
0
6
0
0
2
0
1
0
0
2
0
2
1
0
2
2
0
0
0
1
2
0
0
0
0
0
2
4
2
0
0
5
0
0
0
0
0
1
0
2
0
2
0
2
2
0
0
0
0
0
0
3
2
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
8
0
1
0
0
0
1
2
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
2
2
0
2
0
2
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
4
0
0
0
2
0
2
2
0
0
2
0
0
2
0
0
2
2
2
2
1
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
2
0
1
1
0
1
0
1
0
0
2
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
2
0
0
2
2
0
2
2
0
2
0
0
2
2
0
0
0
1
3
1
0
2
0
1
2
1
2
0
0
0
0
0
2
1
0
0
1
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
3
0
0
0
0
0
1
0
0
2
0
1
0
2
0
0
0
0
2
0
0
0
3
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
1
0
1
0
2
1
0
2
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
2
1
0
2
2
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
1
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
2
3
0
3
0
1
3
0
0
1
3
0
2
1
2
0
1
3
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
1
0
3
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
2
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
2
1
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
2
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
2
0
0
0
1
2
1
2
0
0
0
1
2
0
0
0
0
0
0
0
1
0
2
2
1
1
0
0
0
1
0
0
0
0
2
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
2
0
0
6
0
0
0
2
0
2
0
0
2
0
0
0
0
2
2
1
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
2
0
2
0
1
1
2
0
0
2
6
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
2
0
2
0
1
2
0
1
0
2
0
2
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
3
0
1
2
0
1
1
0
2
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
2
0
1
1
2
0
1
0
0
0
1
2
1
0
0
0
0
0
2
0
0
0
2
0
2
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
2
2
0
0
2
2
1
0
0
1
2
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
2
2
0
0
0
2
2
0
1
0
0
0
1
2
0
1
0
2
2
0
2
0
0
2
0
1
0
0
0
0
0
2
0
2
1
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
2
0
1
1
0
0
0
2
0
0
3
0
1
0
2
0
1
0
0
4
0
0
0
1
0
2
0
0
1
0
2
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
1
0
0
1
0
0
1
0
1
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
2
0
0
0
0
2
0
1
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
2
0
2
0
0
1
1
2
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
1
0
0
3
1
0
0
0
0
0
2
0
1
0
2
0
1
0
14
1
0
7
2
0
0
1
0
1
0
0
0
0
1
2
0
1
2
1
1
0
0
0
0
0
0
0
1
0
2
0
0
1
0
1
0
2
0
0
2
0
2
0
0
0
1
1
0
2
0
0
0
2
0
2
4
0
0
1
2
0
1
2
1
0
0
1
0
0
0
2
0
2
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
2
1
1
2
2
0
0
1
1
0
0
2
0
0
0
0
0
2
0
0
1
0
0
1
0
0
2
1
0
0
0
1
2
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
8
1
2
2
1
0
1
1
1
0
0
0
2
0
1
0
1
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
1
0
1
0
0
0
2
1
0
0
0
1
0
2
1
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
2
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
2
1
0
0
2
2
1
1
0
0
2
2
0
0
1
2
2
0
1
2
0
2
2
0
0
4
2
1
0
2
0
4
1
0
0
0
0
0
0
1
0
0
2
0
0
0
1
1
1
0
1
2
2
0
0
0
1
0
1
1
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
2
1
0
1
0
0
0
1
0
2
2
2
0
2
1
0
1
1
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
2
0
1
0
1
2
0
0
2
0
2
2
2
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
3
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
1
3
2
1
1
0
0
1
0
0
2
4
2
0
2
0
1
1
1
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
1
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
2
1
0
0
2
0
2
0
0
0
0
0
0
0
1
0
2
0
1
2
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
3
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
1
0
2
2
2
0
0
0
1
0
3
0
5
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
2
0
1
1
2
0
0
0
0
0
0
1
0
2
1
0
0
1
0
0
2
1
1
0
0
1
0
0
2
0
0
0
1
1
0
0
0
0
1
4
0
0
2
0
0
1
1
0
1
0
0
1
0
1
0
0
0
2
2
0
2
1
0
2
0
0
0
0
2
0
0
0
3
2
2
2
0
2
1
0
0
0
1
2
0
2
0
0
2
1
0
1
0
0
2
2
0
1
0
5
0
2
2
0
0
0
3
0
0
2
2
2
0
0
0
1
1
0
0
1
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
2
2
2
0
2
0
0
1
1
1
2
2
2
0
2
0
2
1
1
0
1
0
0
1
0
0
0
0
1
0
0
2
0
0
0
1
0
2
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
1
2
0
2
0
0
2
0
0
1
0
1
0
1
0
0
0
0
0
3
0
0
0
1
0
0
0
1
2
0
2
2
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
1
0
1
2
0
0
2
2
0
0
0
0
0
0
0
0
1
0
1
2
0
0
2
1
0
1
2
0
0
0
0
1
1
0
0
8
3
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
3
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
2
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
2
0
2
0
0
1
0
2
0
1
0
1
0
0
0
0
0
0
1
0
1
2
2
1
0
1
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
1
4
0
0
1
0
1
2
0
0
0
1
1
0
0
0
1
0
0
2
1
0
4
0
2
2
1
0
1
0
0
0
0
0
1
0
0
1
2
0
0
1
0
1
0
0
0
0
0
0
0
1
2
0
1
0
0
2
1
0
0
0
2
0
0
0
0
0
0
1
0
2
0
1
0
1
1
0
1
0
0
0
0
0
3
1
1
2
1
0
0
0
0
0
0
9
0
1
0
1
0
1
2
2
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
3
0
3
0
0
0
0
0
3
1
0
2
1
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
2
0
0
0
2
2
0
1
0
0
1
0
0
2
0
0
0
1
1
0
1
0
0
1
0
2
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
3
2
2
0
1
0
0
0
2
0
0
0
1
2
6
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
3
0
0
0
0
1
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
2
3
0
0
1
0
0
0
0
0
2
0
1
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
5
2
0
0
0
3
0
2
0
0
0
6
0
2
0
0
1
0
2
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
3
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
1
0
0
1
0
0
0
8
0
0
0
0
0
1
0
0
2
0
2
0
0
0
1
0
0
0
0
0
4
4
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
1
1
4
0
0
0
1
0
2
0
1
0
0
0
0
0
0
2
2
0
0
0
3
0
1
0
2
0
0
1
2
2
0
0
1
1
0
2
2
0
1
0
2
0
0
2
0
1
0
0
2
0
3
0
0
1
0
0
0
0
2
0
2
1
0
1
1
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
2
0
0
2
2
0
0
2
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
2
0
0
3
2
1
0
1
0
1
0
0
2
1
0
0
0
0
0
1
0
0
1
2
0
0
0
2
1
2
1
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
2
0
0
0
2
1
2
2
0
0
0
2
0
0
3
1
0
0
1
2
0
1
0
2
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
1
2
0
2
1
0
0
2
0
1
0
0
0
0
4
0
1
1
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
1
1
0
2
0
0
0
0
2
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
2
0
2
2
0
2
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
2
0
2
0
1
0
0
0
0
1
0
3
0
2
0
1
0
0
0
0
0
0
1
1
1
0
0
1
0
0
2
0
0
0
1
0
0
1
2
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
2
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
1
0
0
1
1
0
2
2
1
0
0
0
0
0
0
2
2
0
0
2
0
2
0
0
0
0
2
0
0
2
0
2
2
0
1
0
0
0
1
1
1
0
1
0
0
0
0
2
0
3
0
0
0
2
0
1
1
0
0
2
1
0
0
0
0
0
0
0
0
0
1
2
0
1
0
1
0
1
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
2
2
2
2
1
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
5
0
0
0
0
2
0
0
0
0
0
0
1
1
1
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
1
0
2
2
1
0
0
2
2
0
0
3
0
0
1
0
0
0
1
0
1
0
0
0
0
0
2
3
0
0
0
0
0
0
1
0
0
1
1
1
2
0
0
1
1
0
2
2
2
0
0
2
0
0
1
1
0
2
2
0
1
0
0
0
0
0
1
0
2
0
0
2
0
3
0
0
0
0
0
0
0
2
2
0
2
2
0
0
2
0
0
0
2
0
0
0
2
3
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
2
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
1
2
0
3
0
2
0
0
0
0
0
2
0
0
2
0
5
1
1
2
0
0
1
0
0
0
0
1
1
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
1
2
0
1
0
0
1
0
1
2
0
2
0
1
0
1
0
0
0
0
2
0
0
0
2
0
0
1
0
1
0
1
1
0
0
2
0
0
2
0
2
0
0
0
3
1
0
0
0
0
0
2
1
0
1
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
1
2
0
2
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
2
0
0
1
0
0
0
1
1
0
0
1
0
0
1
1
0
1
2
2
0
0
0
0
2
0
0
0
0
3
0
0
0
2
0
2
0
1
0
1
0
2
0
0
0
3
0
1
1
0
0
0
0
2
0
0
1
1
1
0
0
0
0
1
1
2
0
1
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
7
0
0
0
2
0
0
2
3
0
1
0
2
1
2
1
1
0
1
2
0
0
1
2
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
3
0
0
0
0
0
2
1
0
0
1
0
0
0
1
0
2
0
1
0
1
0
1
2
0
0
0
0
2
3
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
2
0
0
1
4
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
3
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
3
0
0
0
2
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
1
2
0
1
0
0
1
0
4
2
0
0
0
1
2
0
1
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
2
0
2
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
2
2
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
1
1
1
2
0
0
0
0
0
2
0
0
2
1
0
0
0
0
2
0
0
2
2
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
2
0
0
0
0
3
1
0
2
0
0
0
1
0
0
0
0
2
2
0
0
0
1
1
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
1
0
0
0
3
0
0
0
0
2
0
0
0
0
0
1
1
1
2
0
0
0
2
2
0
1
0
2
0
0
1
2
0
2
0
1
0
0
7
1
1
2
0
0
1
0
6
2
0
0
1
2
0
0
0
0
1
1
0
2
1
0
0
0
0
0
2
4
0
0
0
0
0
2
4
0
2
0
2
0
4
1
0
0
0
1
0
0
0
3
2
0
1
0
0
0
0
0
0
0
0
0
2
2
0
2
1
0
0
0
0
2
0
2
0
0
1
1
1
2
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
4
0
0
2
0
0
2
0
0
0
0
2
0
0
3
2
0
0
1
0
0
0
0
0
2
0
0
2
0
0
1
1
0
0
0
2
0
1
0
0
1
0
0
2
1
0
0
0
0
1
0
1
0
2
1
0
0
0
0
2
0
0
2
1
1
1
0
1
0
0
0
0
0
0
1
2
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
1
1
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
2
2
0
1
0
0
2
0
0
1
0
0
1
1
0
0
2
1
0
2
0
2
0
2
0
0
0
1
3
0
1
0
0
0
0
0
0
0
1
0
0
2
1
0
1
2
1
0
0
0
0
0
2
2
3
0
1
1
2
0
0
2
0
0
0
0
1
3
0
2
2
0
0
1
0
0
2
0
3
3
0
0
0
2
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
2
1
2
0
1
0
0
2
0
2
2
0
0
0
0
1
0
0
1
0
1
1
1
2
1
0
1
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
1
0
1
0
0
0
2
0
0
1
1
0
1
2
1
5
2
2
0
0
1
1
16
0
0
0
2
1
0
0
1
0
2
0
0
1
0
0
1
0
1
0
2
0
0
1
0
0
0
1
1
0
2
0
0
0
0
2
3
1
1
1
2
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
2
0
0
4
2
1
0
0
1
0
0
2
0
0
0
0
1
2
0
0
0
1
2
0
0
2
0
1
2
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
2
1
0
0
2
2
0
0
0
0
0
7
0
0
0
0
0
2
2
2
1
0
0
0
2
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
9
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
2
0
1
0
0
3
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
2
0
0
3
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
3
2
0
0
1
0
2
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
2
0
2
0
2
2
0
0
0
0
4
0
0
0
2
1
0
1
0
0
0
0
4
0
0
0
0
2
1
1
0
0
3
2
1
0
2
0
0
0
0
2
0
1
0
0
0
0
0
2
0
2
0
3
1
2
0
4
1
0
0
0
0
0
2
2
2
0
2
0
0
0
0
0
2
0
0
0
1
2
0
0
0
2
0
2
1
0
0
0
3
0
1
1
0
0
0
0
1
0
3
1
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
1
0
0
1
0
0
0
2
0
1
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
2
2
0
0
0
2
1
0
0
0
2
0
0
2
0
0
0
0
0
2
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
1
0
0
0
2
1
0
0
0
1
2
0
0
2
1
0
0
2
5
2
1
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
2
2
0
3
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
2
1
2
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
1
0
1
2
0
2
0
0
1
1
0
0
0
0
0
0
0
0
2
0
2
0
2
0
1
0
0
0
0
0
1
2
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
1
0
1
3
0
0
0
1
0
0
0
0
0
0
2
2
2
0
1
1
0
0
0
0
0
0
1
1
1
1
2
2
0
1
1
0
1
0
0
1
0
2
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
1
2
0
2
0
0
0
0
0
1
0
0
0
1
2
2
1
0
0
0
1
2
0
1
0
0
0
1
0
0
1
0
0
0
1
1
0
1
0
0
7
0
1
2
0
1
2
1
0
0
1
2
0
2
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
4
1
0
0
0
0
2
0
1
0
0
2
0
0
3
1
0
2
2
0
0
0
2
1
0
2
0
0
0
0
0
0
0
1
0
1
0
0
2
1
0
3
2
1
0
1
5
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
3
0
0
0
0
0
3
0
2
1
0
0
0
1
3
0
0
0
0
0
0
2
0
2
2
0
1
0
0
0
0
0
1
4
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
2
2
0
2
0
2
0
0
1
2
0
1
0
0
0
1
2
0
3
1
0
0
0
1
0
0
2
2
0
1
2
0
0
1
0
1
1
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
2
1
0
0
0
2
0
0
0
0
2
0
2
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
2
0
0
0
0
3
1
0
0
0
2
1
0
0
0
0
0
0
0
3
0
0
0
0
0
2
1
2
1
0
1
0
2
1
0
1
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
1
1
0
0
0
0
2
1
0
0
0
2
0
0
0
2
0
0
0
2
1
0
2
0
0
0
0
1
0
0
0
2
0
2
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
2
0
1
1
0
0
0
1
0
2
0
4
2
0
0
2
0
0
0
2
0
2
0
0
0
0
1
0
3
1
0
0
1
0
0
0
2
0
2
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
2
2
1
0
0
0
1
1
2
1
2
1
0
0
1
0
1
2
0
1
0
0
0
2
0
0
1
0
0
1
0
0
0
3
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
1
4
0
0
0
2
4
0
1
0
1
0
0
0
0
2
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
1
0
0
0
2
0
1
0
0
0
0
2
1
1
1
0
0
1
1
1
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
2
0
2
1
2
0
0
1
1
0
0
3
0
0
0
5
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
2
1
0
0
4
0
0
0
0
2
1
1
0
0
0
2
0
0
2
0
0
0
1
2
2
1
0
2
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
2
0
1
2
0
2
0
1
1
0
0
0
2
0
0
0
0
1
1
0
1
0
0
0
0
0
2
0
0
0
0
2
1
0
2
0
0
1
2
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
3
1
2
0
0
2
0
0
1
0
2
0
0
1
1
0
0
0
0
0
2
0
2
0
1
1
0
0
0
0
0
0
2
1
2
2
0
2
0
0
2
2
0
0
1
0
2
0
0
0
2
1
0
0
0
0
1
0
1
1
2
0
4
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
2
2
2
0
1
1
0
0
0
1
0
0
0
0
2
2
0
0
1
1
0
3
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
2
0
1
0
0
0
0
1
2
0
0
4
0
0
1
1
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
1
1
0
0
0
1
0
0
2
0
0
2
0
0
0
1
0
1
0
2
0
0
0
0
1
0
0
2
0
0
1
0
0
0
2
0
1
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
2
2
1
0
0
0
2
2
2
0
1
0
2
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
3
0
2
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
3
2
0
0
4
0
0
0
1
0
0
0
1
0
0
0
4
0
0
4
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
1
0
2
1
2
1
0
0
1
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
1
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
2
0
0
0
0
2
1
1
2
2
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
2
1
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
2
0
2
2
0
2
0
1
0
1
2
0
0
1
0
0
1
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
2
2
1
0
2
0
0
1
0
0
2
1
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
1
0
3
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
1
2
1
0
0
2
1
0
0
0
0
0
0
0
0
0
1
2
0
1
0
1
0
2
0
2
1
0
0
2
0
0
2
0
0
1
0
1
0
0
2
0
0
0
1
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
2
2
0
2
1
1
1
0
0
1
0
0
2
0
0
0
0
2
2
3
2
0
0
0
1
0
2
0
0
0
2
0
0
0
1
0
1
0
0
0
0
2
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
2
0
0
0
0
1
0
0
0
0
2
2
0
0
0
1
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
1
2
0
1
1
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
2
2
0
0
2
0
2
0
0
0
1
0
1
0
2
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
2
1
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
4
1
1
1
0
1
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
2
0
0
0
0
1
0
0
0
1
2
2
0
0
2
0
0
0
2
0
0
2
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
2
2
1
1
0
0
0
1
0
1
2
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
3
0
0
0
2
0
0
0
0
1
0
1
0
0
2
1
0
0
0
1
0
1
0
1
0
0
2
0
0
0
0
0
0
1
2
1
0
1
0
0
1
0
2
0
0
2
1
0
0
0
1
1
1
0
0
2
1
0
0
0
1
0
0
0
2
0
1
0
0
0
0
2
2
2
0
0
1
0
2
5
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
1
0
0
0
0
2
0
1
0
1
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
1
2
0
0
0
2
0
2
1
1
0
0
3
2
1
1
0
0
2
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
2
0
1
0
0
1
0
2
0
1
0
2
2
3
2
1
0
1
2
2
0
0
1
0
0
2
0
1
0
1
1
0
0
1
0
2
0
0
0
0
0
0
0
2
2
0
1
0
1
0
0
0
2
0
0
0
1
2
1
2
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
2
1
0
1
0
0
0
1
2
0
0
2
1
1
0
1
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
2
0
0
0
2
0
0
2
2
0
0
0
0
2
1
0
0
0
3
2
1
2
0
2
1
1
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
1
0
1
2
0
0
0
0
0
2
2
4
0
0
0
0
1
0
1
0
2
1
1
0
0
0
2
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
2
2
2
0
2
0
1
0
0
3
0
0
0
2
0
1
2
0
0
0
2
0
0
1
0
0
2
0
1
0
0
0
2
1
2
0
0
0
0
0
2
0
1
2
0
0
0
2
3
0
1
1
2
2
0
0
2
0
1
0
0
0
0
2
2
1
2
0
0
1
0
0
0
0
0
1
1
2
5
0
0
2
2
2
1
0
2
0
0
1
1
1
0
0
0
2
1
0
1
1
0
0
2
0
1
0
0
0
1
0
0
0
0
0
2
1
2
2
1
0
0
0
3
0
2
2
0
1
1
4
0
0
0
2
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
3
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
1
1
0
0
2
2
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
2
1
1
1
1
0
0
0
0
0
0
0
0
0
2
0
0
2
1
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
1
1
0
1
0
0
2
0
0
0
2
2
0
2
2
1
1
0
1
3
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
2
1
0
0
1
0
0
2
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
1
0
2
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
1
0
0
2
0
0
1
1
1
1
1
0
1
0
0
1
0
0
0
2
1
0
0
0
0
2
2
0
1
0
0
0
1
0
2
1
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
1
2
0
0
2
0
0
3
0
2
0
0
2
0
1
1
2
0
0
2
0
2
2
0
1
0
0
0
0
2
2
1
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
2
13
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
3
0
0
3
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
3
2
0
1
2
0
0
0
0
0
1
0
2
3
0
0
0
0
0
1
0
1
0
0
1
3
0
1
1
0
2
0
2
1
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
2
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
2
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
3
0
0
0
1
0
0
1
0
0
1
2
1
0
0
0
1
2
0
2
0
0
3
0
0
2
2
0
2
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
3
0
0
2
2
0
0
1
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
1
0
1
1
0
0
1
0
0
0
0
2
2
0
0
0
1
0
0
0
1
0
3
2
0
1
0
2
0
3
2
0
0
1
0
0
0
1
0
0
2
0
1
4
2
0
0
0
0
1
0
0
2
0
1
0
1
0
0
0
0
0
0
1
0
1
3
0
2
0
0
0
2
0
0
2
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
3
2
1
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
15
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
1
1
1
0
0
0
2
0
2
0
0
0
1
1
0
1
2
0
1
0
0
0
0
1
2
0
0
0
1
0
0
1
0
0
0
2
0
1
0
0
2
0
0
0
1
1
3
1
0
1
0
3
2
1
0
0
0
0
3
3
0
2
2
0
3
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
2
0
1
0
2
0
2
0
0
0
2
0
0
2
0
2
0
3
0
2
0
0
0
0
0
0
2
0
0
2
0
1
1
0
2
0
1
0
0
2
0
1
0
0
0
0
0
0
1
1
2
0
2
0
0
1
0
2
3
0
0
1
1
0
2
1
2
0
2
0
0
0
0
0
1
2
0
0
2
0
2
0
0
0
0
0
2
0
1
0
2
0
1
0
1
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
3
0
0
2
1
0
0
0
0
0
0
0
2
2
0
0
1
2
2
0
0
0
0
0
0
2
0
0
0
0
2
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
4
0
0
2
0
1
2
1
0
0
0
1
0
0
0
0
2
0
1
0
1
0
0
0
0
0
2
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
3
2
2
2
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
1
0
2
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
2
0
1
0
2
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
2
0
2
2
2
0
0
0
2
0
2
2
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
3
3
0
1
1
1
2
0
1
0
0
1
0
2
3
0
2
0
1
0
1
1
0
0
0
0
0
0
0
0
0
5
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
3
0
2
1
0
0
2
0
0
3
2
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
2
0
0
1
1
0
0
0
0
0
0
2
1
0
2
2
0
0
0
1
0
1
0
0
1
0
0
0
0
2
0
0
1
0
2
0
0
0
3
1
0
0
0
0
0
1
0
1
1
0
0
2
0
2
3
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
1
0
0
0
0
1
0
0
2
0
0
1
0
0
1
1
1
2
1
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
1
0
2
0
0
0
1
0
0
1
1
1
2
0
0
0
0
1
2
2
1
1
2
0
1
1
1
0
0
0
0
0
0
0
0
0
2
0
0
2
1
2
2
0
0
0
1
0
3
0
0
2
0
0
0
2
1
1
0
0
3
0
0
0
0
0
0
1
0
0
0
1
0
3
1
0
0
0
0
0
2
3
0
0
1
4
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
2
0
0
2
0
1
0
1
1
0
1
0
0
2
0
1
0
0
2
0
2
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
2
0
2
2
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
3
0
0
2
2
0
1
2
1
1
1
0
0
2
1
2
0
0
0
1
2
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
1
0
2
0
0
2
1
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
2
0
2
2
2
0
0
0
2
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
8
0
1
1
0
0
0
1
0
0
0
0
2
2
2
2
0
0
0
0
0
0
2
2
0
2
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
1
0
3
0
1
1
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
2
0
2
0
2
0
0
1
0
0
2
2
0
1
0
0
0
1
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
2
0
2
0
1
0
2
0
0
0
0
0
2
2
1
0
0
1
2
2
1
1
2
3
0
0
2
1
0
0
1
1
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
1
1
4
2
0
0
1
0
0
0
1
0
1
0
1
0
0
2
0
0
0
0
1
1
0
2
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
1
0
1
2
1
2
1
0
0
0
0
0
1
2
0
0
1
0
0
0
2
0
1
0
1
3
0
1
0
1
0
2
1
2
0
2
0
0
2
2
4
1
1
0
1
0
1
0
1
2
0
1
1
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
3
1
0
1
1
0
0
1
0
1
3
2
0
0
2
1
0
2
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
1
0
1
2
2
0
2
0
0
0
0
0
1
0
1
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
2
0
0
0
1
0
1
1
0
2
1
0
1
0
0
0
0
0
0
0
0
1
1
2
6
0
1
0
2
0
2
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
3
0
0
0
2
0
3
0
1
0
2
0
2
0
1
1
2
0
0
0
3
0
0
0
0
0
2
2
1
0
3
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
1
0
0
0
0
0
4
0
0
0
0
1
0
4
1
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
2
2
0
0
1
2
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
2
0
0
2
2
0
0
0
1
2
1
2
3
0
0
2
0
0
2
1
0
0
0
0
1
2
0
0
2
0
0
2
1
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
1
0
0
3
2
0
0
4
0
1
0
1
0
0
0
2
1
0
1
2
0
0
2
2
1
0
1
2
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
2
1
0
0
0
0
0
0
1
1
0
0
0
1
1
0
2
0
0
0
0
0
2
0
0
1
0
0
0
2
0
2
0
0
2
0
0
0
2
2
0
4
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
2
5
2
0
2
0
0
1
2
2
0
1
2
0
0
0
1
0
0
0
0
1
0
0
6
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
2
1
0
1
0
0
3
0
2
0
0
0
0
2
1
1
0
0
0
0
2
1
0
2
0
1
2
0
0
0
1
0
2
0
4
1
0
0
1
0
1
3
0
0
2
0
0
2
0
1
1
0
0
0
0
1
0
0
1
1
1
1
0
0
0
1
1
0
0
2
1
1
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
2
0
0
1
1
0
2
0
0
0
0
0
2
2
1
0
1
1
0
0
1
0
5
1
0
0
2
2
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
1
0
3
2
0
1
2
1
0
0
2
1
2
0
2
2
0
0
0
0
2
0
1
2
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
4
1
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
3
0
1
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
1
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
2
0
1
2
0
0
2
0
0
0
1
0
0
1
3
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
1
0
0
3
0
0
1
0
1
0
10
0
1
2
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
3
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
2
2
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
1
1
0
1
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
1
1
2
0
0
1
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
3
0
0
1
0
0
0
1
0
0
0
1
1
0
2
0
3
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
2
0
3
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
2
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
2
1
1
0
3
0
8
2
1
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
1
2
0
0
1
0
2
0
0
2
0
0
3
0
0
2
0
4
1
0
0
0
1
0
1
5
1
0
0
0
2
0
1
0
2
3
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
2
0
2
1
0
0
2
1
0
0
0
3
0
0
0
0
0
0
0
0
0
1
1
1
1
0
2
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
2
0
0
0
0
0
3
0
1
0
0
0
0
0
0
1
0
2
1
0
0
0
3
0
0
0
0
1
0
0
0
0
0
1
1
2
0
0
0
0
2
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
2
1
2
0
1
0
0
1
0
0
2
0
1
2
2
0
0
0
0
0
1
1
0
0
0
1
0
2
0
0
0
1
2
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
2
0
0
1
1
2
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
3
1
0
0
2
1
2
1
0
0
1
0
0
0
5
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
2
0
2
1
0
1
0
0
0
1
1
1
0
0
2
2
2
0
0
1
0
0
0
0
2
0
2
0
2
0
2
0
0
0
0
2
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
2
0
2
0
3
2
0
0
0
1
0
2
0
1
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
3
3
0
0
1
0
2
0
2
0
1
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
2
0
1
0
0
0
2
2
0
0
0
0
2
0
0
3
0
0
1
0
0
10
1
0
1
0
0
0
0
0
2
2
0
0
1
0
3
1
0
0
0
0
0
1
3
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
2
1
3
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
2
0
0
0
2
1
2
0
1
1
1
0
0
0
0
0
1
0
0
1
0
0
0
3
0
0
0
0
0
0
2
2
0
0
2
0
0
1
0
0
0
2
0
0
0
1
0
2
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
2
0
1
0
0
0
1
0
1
0
1
2
2
1
0
2
2
0
0
0
1
1
0
2
0
1
1
0
1
2
0
1
0
0
1
0
0
0
0
0
0
1
0
3
1
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
1
0
1
0
2
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
1
0
2
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
1
3
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
1
2
3
0
0
0
2
0
0
0
0
0
0
0
1
0
1
2
0
2
0
0
0
0
0
1
0
0
2
0
0
1
2
1
0
0
0
1
0
0
0
1
1
0
0
1
0
1
0
0
2
0
1
2
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
1
2
0
2
0
3
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
2
0
1
3
2
0
0
2
0
0
2
0
2
0
2
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
1
0
2
0
2
1
0
0
2
2
0
0
2
3
1
0
0
0
1
1
2
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
1
2
0
2
0
0
0
7
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
2
0
2
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
1
0
0
0
1
2
0
0
2
0
0
0
0
1
0
1
2
1
1
1
0
1
0
2
2
0
0
0
0
2
1
0
1
2
1
0
1
2
0
0
0
0
0
1
1
2
0
0
2
0
2
1
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
1
1
0
2
1
0
0
0
0
0
2
1
0
0
0
1
1
0
1
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
2
0
0
1
0
0
1
1
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
3
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
2
1
0
0
2
0
2
1
0
1
1
0
1
0
1
0
2
0
0
0
0
0
1
1
0
0
3
2
0
0
2
0
0
0
0
0
0
2
0
0
1
1
1
0
0
0
1
0
6
0
0
1
1
0
0
0
0
2
0
0
2
0
1
1
1
0
2
2
0
1
1
1
1
3
0
0
1
1
2
0
0
0
1
0
1
0
2
0
0
0
0
3
0
0
1
0
0
2
0
1
0
2
0
2
1
0
1
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
2
1
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
1
2
0
0
0
0
0
1
0
2
1
0
0
2
0
0
1
2
2
0
0
0
2
1
1
0
2
1
0
0
3
1
0
0
0
0
3
1
0
2
0
2
0
2
1
0
0
0
0
2
0
3
0
0
0
0
1
2
0
2
1
3
0
2
0
0
0
0
1
0
0
0
3
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
1
1
0
0
0
0
2
3
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
3
0
0
0
0
0
2
0
1
1
2
0
1
0
0
0
2
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
1
0
0
2
0
0
0
2
0
1
0
1
0
1
0
0
0
0
0
1
2
3
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
2
0
1
0
0
0
0
1
1
0
2
0
0
0
0
2
0
0
0
0
1
0
2
0
2
0
2
0
2
0
0
0
2
1
0
0
2
0
0
7
0
0
2
0
0
1
1
0
2
0
1
0
0
0
0
0
0
3
0
1
1
2
2
0
0
2
2
0
0
0
2
0
0
1
0
1
1
0
0
3
0
0
0
1
1
0
0
0
2
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
2
3
1
0
0
0
2
2
2
0
0
1
0
0
0
0
2
0
0
0
2
1
2
2
0
0
2
2
2
0
0
0
2
1
0
0
0
1
0
2
0
0
1
0
0
1
2
0
0
0
0
0
2
3
0
2
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
1
0
0
2
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
2
0
0
1
0
1
6
0
0
2
0
0
0
0
2
1
0
0
0
0
1
0
2
0
2
1
0
0
0
0
0
2
2
2
0
1
0
0
0
1
2
0
0
0
0
0
1
0
0
2
1
0
3
0
0
0
0
1
0
0
0
1
2
0
0
1
0
0
2
0
2
0
2
0
0
0
0
1
0
6
1
0
0
0
0
1
1
1
1
2
0
1
2
0
1
0
1
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
2
2
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
4
0
0
0
0
5
0
0
0
0
0
2
0
1
0
2
1
2
0
2
1
4
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
2
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
1
4
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
2
1
0
1
0
0
1
1
2
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
2
2
1
0
2
2
0
1
1
0
0
0
1
0
0
1
2
1
0
0
2
2
0
2
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
2
0
1
1
1
1
0
1
0
0
0
0
0
0
1
2
2
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
2
0
1
2
2
0
1
0
0
2
0
0
0
0
0
3
0
0
0
1
2
2
0
1
0
2
0
0
0
1
0
0
1
1
1
2
2
0
0
0
0
0
0
0
1
0
1
0
0
0
3
0
1
2
1
0
0
9
0
0
2
1
1
2
2
0
0
1
0
0
2
1
0
4
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
2
0
1
0
0
0
2
1
0
0
3
1
0
0
1
2
0
1
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
1
2
1
0
2
1
0
0
0
0
0
0
0
0
1
0
0
1
0
2
2
3
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
2
2
0
0
0
0
1
2
0
3
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
2
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
2
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
2
0
2
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
2
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
1
0
2
0
2
1
2
0
0
1
1
0
2
0
0
1
0
1
1
0
0
0
0
1
2
0
2
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
8
0
1
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
8
0
2
1
0
0
0
2
1
2
1
0
2
2
0
1
0
0
0
2
1
0
0
1
2
1
1
2
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
3
0
0
0
1
0
1
0
3
0
0
0
0
0
0
3
0
2
0
0
0
0
1
0
0
0
0
2
2
0
0
0
2
0
0
0
2
2
0
1
1
1
1
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
2
1
0
0
2
1
0
0
0
0
0
3
0
1
2
0
0
1
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
3
0
1
1
2
2
0
1
0
0
0
1
0
0
0
0
2
0
1
1
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
4
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
5
0
0
2
0
0
2
0
1
0
0
0
1
1
2
0
0
0
0
1
0
0
0
2
0
2
2
0
0
2
2
0
0
0
0
0
0
1
0
2
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
2
0
2
2
0
0
1
2
0
0
1
0
0
1
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
2
2
0
0
0
0
0
1
0
0
1
0
0
2
0
1
0
0
0
0
0
2
2
0
0
2
2
0
1
3
0
1
2
3
3
2
2
0
2
2
0
0
1
0
2
2
0
0
1
2
0
0
0
0
2
0
2
0
0
0
1
0
0
5
0
0
1
0
1
0
0
0
1
3
0
0
0
0
0
0
0
1
0
1
3
0
0
1
0
2
0
0
1
3
1
0
2
0
2
0
0
2
1
0
0
0
0
0
1
0
2
0
1
0
2
0
4
2
0
0
1
1
0
2
0
0
2
1
0
0
2
0
0
2
0
0
2
0
0
0
0
1
2
0
0
0
0
1
0
0
2
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
2
1
0
0
1
0
2
0
1
0
0
0
2
1
2
0
1
0
1
2
0
0
1
0
1
1
0
0
0
0
1
2
0
0
1
2
1
0
1
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
2
1
1
2
2
0
2
0
1
0
0
0
0
2
0
0
1
2
0
0
0
0
0
2
1
0
2
0
2
1
0
0
0
0
0
0
1
0
0
1
1
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
2
0
4
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
2
3
0
0
0
0
1
0
0
0
0
1
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
2
0
1
0
0
0
2
2
2
0
2
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
1
2
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
3
0
0
0
1
0
0
1
0
0
0
0
0
2
1
2
0
0
0
0
0
5
0
2
0
0
0
2
0
1
0
1
0
0
0
1
1
3
2
0
3
0
1
1
2
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
2
2
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
1
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
2
2
2
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
1
1
0
1
2
0
1
0
0
2
1
0
0
2
0
0
1
0
0
2
1
1
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
5
0
0
0
0
0
0
1
0
0
1
0
2
2
0
0
1
1
0
2
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
2
0
3
1
1
0
0
2
0
0
0
0
0
1
1
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
2
0
0
2
2
0
0
0
0
0
2
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
3
1
0
0
0
1
0
0
0
0
1
0
0
2
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
3
0
1
0
2
0
0
2
0
0
0
0
0
0
0
1
2
0
0
2
2
0
2
0
0
0
2
0
0
1
0
2
0
2
0
0
2
2
2
2
2
0
3
0
1
1
0
0
2
0
0
0
2
0
2
0
0
2
2
2
0
0
2
0
0
2
1
0
1
0
0
0
0
0
0
1
3
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
4
2
0
0
3
1
0
0
2
2
0
0
0
0
3
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
2
0
2
0
1
0
1
0
0
0
1
1
0
2
0
0
0
0
1
0
1
1
0
0
0
0
2
2
0
0
1
0
1
0
1
1
2
2
0
1
0
2
0
0
1
1
2
2
0
0
0
0
0
0
0
1
0
0
1
0
0
2
2
4
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
2
0
0
1
1
0
1
2
0
0
1
2
2
2
0
1
0
1
0
0
1
0
1
0
0
0
0
1
0
2
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
2
0
1
0
2
0
1
1
0
0
1
2
0
0
1
0
0
1
0
1
0
0
0
2
0
1
1
0
2
0
0
0
0
2
0
3
1
1
0
2
0
0
1
1
3
0
3
0
0
0
1
1
0
0
3
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
2
0
0
0
2
2
0
0
4
0
0
2
0
0
3
2
0
0
0
0
0
1
0
2
0
0
0
1
1
1
1
0
1
2
1
5
0
1
2
0
0
0
0
0
1
0
0
1
0
2
0
0
2
0
0
0
0
1
2
0
0
0
0
1
0
0
2
0
2
7
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
1
3
0
2
0
2
0
0
1
0
0
2
1
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
1
0
2
1
0
0
0
0
1
0
2
1
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
2
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
2
1
0
1
0
0
2
0
0
0
3
1
0
1
0
2
0
1
0
2
0
0
0
0
0
2
0
2
1
0
0
0
2
0
2
0
0
2
0
1
0
0
1
1
0
0
0
2
2
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
2
3
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
2
0
0
1
1
1
0
2
0
0
0
0
1
2
0
0
1
0
2
0
0
1
0
0
2
0
0
3
0
1
1
0
0
2
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
2
1
2
2
0
0
0
2
0
0
1
1
1
0
0
3
0
0
0
1
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
2
0
2
0
0
1
2
0
0
2
0
1
1
0
0
1
2
0
2
0
0
0
0
2
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
2
0
0
0
0
0
2
0
0
1
0
0
2
2
0
0
0
0
0
0
0
2
1
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
2
0
1
0
0
2
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
2
0
0
0
0
1
2
2
2
0
0
2
2
0
0
0
0
0
1
3
0
1
0
1
0
0
0
0
1
2
2
0
0
2
0
2
0
0
2
0
0
1
0
1
0
0
0
2
0
2
0
0
0
0
0
0
1
0
2
0
0
1
0
2
1
1
2
0
0
0
0
2
0
1
1
1
2
0
0
2
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
3
0
0
0
0
0
0
0
0
1
1
2
2
0
0
2
0
2
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
10
1
0
0
0
0
0
2
0
1
1
0
1
0
0
0
0
2
0
0
0
2
1
0
0
0
0
1
0
0
2
0
1
2
1
1
2
1
4
1
0
1
0
1
1
1
2
2
1
2
0
0
0
0
0
0
2
0
0
0
2
1
1
0
3
0
0
0
4
0
0
0
0
1
0
1
0
0
2
0
0
0
2
0
0
1
2
0
0
2
0
0
2
2
0
0
1
0
1
0
1
0
1
2
0
1
0
0
3
2
0
1
0
2
0
0
2
2
2
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
3
1
0
0
2
0
2
0
0
2
0
1
2
2
1
1
0
1
1
1
1
0
1
0
2
1
0
0
0
1
0
0
1
2
0
3
1
4
1
0
5
1
0
0
0
0
0
2
0
3
1
1
0
0
7
0
0
1
0
2
0
0
0
0
0
0
2
0
0
3
0
0
0
2
0
2
0
0
3
0
0
1
2
1
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
1
0
0
0
2
2
0
2
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
1
0
0
0
2
0
0
0
1
0
1
0
3
0
2
3
0
0
1
0
0
0
0
0
0
0
1
0
0
2
2
3
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
1
0
0
0
0
2
3
0
0
0
3
2
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
5
0
0
0
0
2
1
0
2
0
0
0
1
1
1
0
0
0
0
0
0
0
2
0
0
2
0
3
0
0
0
0
2
2
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
1
2
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
1
0
2
1
0
0
0
2
0
2
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
2
3
1
1
0
0
0
0
0
1
0
4
0
2
3
2
0
1
2
0
0
0
0
0
1
1
0
2
1
0
0
0
3
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
2
1
0
2
0
0
2
2
0
2
0
0
1
0
1
0
1
0
2
0
5
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
2
0
2
2
0
0
0
0
0
2
2
0
0
0
0
0
3
1
0
2
0
0
1
0
1
2
0
2
1
0
0
2
0
0
0
1
2
0
0
3
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
2
1
2
1
0
1
1
0
0
0
0
1
0
0
0
0
0
2
0
0
2
1
1
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
1
0
1
0
2
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
2
2
0
0
0
1
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
3
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
3
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
2
0
1
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
3
0
1
0
0
1
2
0
1
1
0
1
0
0
0
0
0
0
2
0
0
3
6
1
1
0
2
2
1
1
0
1
0
2
1
0
0
0
1
0
0
2
0
0
1
2
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
1
0
1
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
1
0
0
2
1
0
0
0
2
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
2
0
4
1
0
0
0
2
0
0
2
0
0
0
2
0
0
6
1
0
2
1
0
0
0
0
15
0
0
1
2
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
3
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
7
0
1
0
0
0
0
2
0
0
0
1
2
0
1
2
0
0
2
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
1
0
3
1
1
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
2
0
0
0
1
0
0
0
1
0
0
0
2
1
0
0
2
2
0
1
0
0
0
1
1
0
2
1
0
2
0
1
0
1
2
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
1
0
0
4
0
0
0
0
2
1
0
0
0
0
2
0
1
0
0
0
0
1
0
2
0
2
1
0
0
0
0
0
0
2
0
0
2
0
1
2
2
2
0
0
0
1
0
1
2
0
1
0
0
3
0
0
0
2
0
0
2
0
3
0
0
0
0
0
0
0
2
0
0
0
2
1
1
0
0
1
1
0
1
1
0
2
0
0
0
0
1
0
0
1
2
0
0
2
0
2
3
1
0
0
0
0
0
0
2
0
0
0
6
0
2
2
1
0
1
0
0
0
0
0
0
1
1
0
1
0
0
2
0
0
0
0
0
0
1
2
0
0
0
2
1
1
2
0
0
2
0
0
1
0
0
0
1
0
2
0
1
1
0
0
0
1
0
0
2
2
0
1
0
0
0
0
2
1
0
0
2
1
1
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
5
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
1
1
0
1
1
0
1
0
1
0
0
0
1
0
0
0
2
0
0
0
1
3
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
1
2
0
0
0
1
3
0
0
0
1
0
3
0
2
0
1
0
3
0
1
0
0
0
1
1
0
0
0
0
1
1
2
3
0
0
0
0
2
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
1
1
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
2
1
1
0
0
0
1
0
1
0
0
0
2
4
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
2
2
0
0
2
0
0
0
0
1
2
2
6
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
2
2
2
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
2
2
1
2
0
2
0
0
1
1
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
2
0
0
2
0
3
0
2
0
2
0
0
0
0
1
0
0
1
0
0
0
4
0
3
5
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
1
0
2
0
0
0
2
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
1
0
0
2
0
0
0
1
2
1
0
0
2
1
0
1
0
0
0
0
1
0
0
0
2
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
1
0
0
0
0
1
2
3
0
2
4
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
1
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
4
0
0
0
2
1
0
2
2
2
0
0
0
2
0
2
2
2
1
0
0
0
1
2
1
0
2
3
0
0
0
0
2
0
0
0
2
2
0
5
0
0
0
1
2
1
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
1
0
2
0
2
0
0
1
2
0
0
1
0
0
0
0
0
2
4
1
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
1
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
2
0
0
0
1
1
0
0
0
0
2
1
1
1
0
0
0
1
0
0
0
1
2
0
1
0
0
0
0
0
0
2
0
0
3
0
0
0
0
1
0
0
0
1
0
2
2
3
0
1
1
0
2
1
0
1
0
0
1
1
0
1
0
1
0
0
1
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
1
1
0
0
0
0
2
2
0
2
0
2
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
1
0
3
0
0
0
0
3
0
0
0
1
0
0
1
0
0
0
2
1
2
0
0
2
0
1
1
2
2
0
1
0
0
0
1
2
0
0
0
3
0
2
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
1
1
0
0
1
0
1
0
1
0
0
2
0
0
0
0
0
0
1
2
0
2
0
0
2
0
0
2
2
0
0
3
0
0
0
1
1
2
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
2
1
2
2
0
2
0
0
2
0
0
3
0
0
5
2
1
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
3
0
0
0
0
1
0
2
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
1
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
1
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
2
0
0
0
0
0
0
2
1
0
0
3
0
2
0
1
0
2
0
1
0
0
0
0
2
0
2
2
2
2
0
0
0
2
0
0
0
0
3
2
0
2
2
0
0
1
1
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
2
1
0
1
0
0
0
2
0
0
0
0
2
2
0
2
0
1
2
0
1
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
1
0
0
0
2
2
0
0
1
0
2
0
0
1
0
1
0
1
0
2
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
1
0
2
2
0
3
0
0
2
0
1
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
3
1
2
0
0
0
0
0
2
0
1
2
0
0
2
0
0
0
2
0
0
0
2
0
2
0
2
1
0
0
0
2
0
0
1
1
1
2
0
0
0
1
0
0
0
0
2
0
2
0
0
0
2
3
0
0
0
2
1
1
0
0
0
1
2
0
0
0
0
0
1
2
0
2
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
1
0
2
2
0
2
0
2
0
0
0
1
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
1
2
0
1
2
0
0
1
0
0
2
2
0
0
0
1
0
0
0
2
0
0
2
0
1
1
1
0
2
0
2
0
3
0
2
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
2
2
0
0
3
0
0
2
3
0
0
1
0
0
0
0
0
0
2
1
0
0
0
1
2
2
0
0
2
0
0
0
0
1
0
0
2
2
2
0
2
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
3
0
0
2
0
1
3
0
1
0
0
0
0
1
0
0
0
0
0
0
4
0
3
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
3
2
0
0
0
0
1
0
0
0
0
2
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
2
2
1
0
0
0
0
0
0
0
0
4
0
2
0
2
0
4
0
0
0
0
0
3
0
0
0
1
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
2
0
0
2
0
0
0
2
0
0
1
2
1
2
0
0
1
1
0
0
0
0
0
0
1
2
0
0
2
1
0
1
0
0
0
0
0
1
0
0
0
0
2
1
0
1
0
1
0
0
0
1
0
2
1
0
1
0
0
0
0
0
2
0
1
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
2
4
0
0
2
0
0
1
0
2
0
0
0
1
2
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
1
0
1
0
0
1
1
0
1
2
1
1
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
2
1
0
0
0
1
0
2
0
0
2
0
2
1
0
0
1
2
0
0
2
0
1
0
0
1
0
0
0
0
1
0
2
0
1
3
0
1
0
0
0
0
0
0
1
2
0
2
0
0
1
0
2
0
0
0
1
2
0
2
1
1
1
0
0
2
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
2
0
0
0
0
0
0
0
1
0
0
4
2
1
0
0
0
1
0
0
0
0
2
2
0
0
2
2
0
0
0
0
0
0
0
1
0
4
1
0
0
0
1
1
0
0
2
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
1
0
0
0
1
0
1
3
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
3
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
2
0
0
2
0
2
0
0
2
2
0
1
0
1
2
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
1
0
0
0
0
1
2
1
0
1
0
0
0
1
2
0
1
0
2
0
2
0
2
0
3
0
2
1
2
1
1
0
0
2
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
1
0
0
0
1
0
1
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
3
0
0
0
1
3
0
0
2
0
0
0
0
0
0
0
2
1
0
0
2
0
0
2
0
0
2
0
0
0
1
2
0
2
0
2
1
0
0
0
2
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
1
0
2
0
0
2
0
0
0
1
0
1
0
2
0
0
2
0
2
0
1
0
2
1
0
1
0
0
0
0
0
0
2
3
1
0
2
0
0
0
0
0
3
0
0
0
2
0
0
0
1
1
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
1
0
1
4
1
0
1
1
1
0
1
2
3
1
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
2
1
0
1
0
3
0
0
0
3
0
3
0
0
2
0
0
0
0
0
0
1
0
1
2
0
2
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
2
2
5
1
0
2
0
1
0
2
0
0
2
0
3
0
2
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
3
2
1
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
2
0
0
0
2
2
1
1
0
2
0
0
4
1
0
0
2
1
0
0
0
1
1
0
0
1
0
1
0
1
0
0
2
2
0
0
0
0
3
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
2
2
0
2
1
1
9
0
0
0
0
0
0
0
0
2
1
2
0
0
1
0
1
2
0
4
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
3
0
1
0
0
1
0
1
0
0
0
4
0
0
0
0
1
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
3
1
0
2
0
2
2
1
0
0
1
0
1
0
2
0
0
0
1
2
0
2
0
2
0
2
0
2
2
0
1
0
0
0
2
0
2
0
2
0
1
0
1
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
1
0
0
2
0
0
0
1
0
1
0
1
0
2
1
2
0
2
0
2
0
0
3
0
0
1
0
0
1
0
0
1
0
0
0
1
0
1
1
2
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
2
0
0
2
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
2
0
0
0
1
1
1
0
0
0
1
1
0
1
1
1
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
2
1
2
0
0
0
0
0
0
0
2
0
0
2
1
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
3
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
2
0
2
1
1
0
0
2
0
0
1
1
0
1
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
1
0
1
1
1
0
0
0
2
0
0
1
0
0
1
1
0
1
0
1
1
0
0
0
0
2
1
0
0
1
1
0
0
1
1
0
0
0
2
0
1
1
2
0
2
2
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
1
0
0
0
2
0
0
0
2
1
0
1
0
0
0
0
0
0
2
2
2
1
0
1
1
0
0
1
0
0
2
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
1
2
2
0
0
2
1
1
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
2
0
0
0
0
2
1
0
0
3
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
1
0
2
0
0
1
2
0
2
1
0
0
0
0
0
0
2
0
0
0
0
1
1
1
0
2
0
0
0
2
0
0
0
0
0
0
0
2
1
0
1
2
0
0
0
0
0
2
1
0
1
1
0
0
0
0
0
1
0
2
0
3
2
1
0
0
0
1
0
0
0
1
2
0
4
0
2
0
1
1
0
0
0
0
0
2
0
0
1
0
0
0
3
0
0
1
2
1
1
0
0
1
0
0
2
0
1
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
1
2
0
2
0
0
5
0
1
1
2
0
2
0
1
0
0
1
0
2
0
2
4
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
1
1
0
0
0
0
0
0
0
1
0
0
1
1
2
0
0
1
2
0
1
0
0
0
1
0
0
2
0
1
1
2
1
1
0
0
0
0
0
1
1
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
1
0
0
0
1
0
0
0
0
0
3
3
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
3
0
3
1
0
2
0
0
2
0
2
0
1
2
2
5
0
0
0
0
0
0
1
1
1
0
0
0
1
2
0
0
1
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
1
3
0
0
0
1
1
2
2
0
2
0
1
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
2
4
1
0
1
2
2
0
1
1
1
1
1
0
0
2
1
1
1
0
2
0
0
0
0
0
0
0
1
1
0
0
2
3
0
1
0
0
4
0
0
1
1
1
0
0
1
0
0
0
1
1
2
0
2
0
2
2
1
1
2
2
0
0
2
2
0
0
0
0
1
0
0
2
2
0
2
2
2
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
2
0
0
0
0
2
2
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
2
0
2
0
0
0
2
0
0
1
2
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
1
0
0
0
0
2
0
2
1
0
0
2
0
0
0
1
0
0
0
0
0
1
1
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
2
0
2
0
6
0
0
0
0
0
2
0
1
1
1
0
0
0
0
0
2
0
0
0
3
2
0
0
2
1
0
2
0
0
2
2
0
0
0
0
0
0
2
0
0
0
1
2
1
0
0
0
1
4
0
0
0
0
0
1
1
1
2
0
1
0
2
1
0
0
0
1
2
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
2
0
0
0
2
0
0
2
0
5
0
0
0
0
0
0
0
2
0
3
1
0
1
2
0
0
2
0
1
1
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
2
2
0
0
0
2
0
2
0
2
0
4
0
0
2
0
0
0
0
0
0
0
1
1
0
0
2
0
2
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
2
2
0
0
1
0
0
2
1
0
0
0
2
0
2
0
0
0
0
2
1
0
0
0
0
3
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
1
2
0
1
2
2
1
1
1
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
1
2
0
2
0
0
0
1
1
0
0
1
0
0
0
0
0
2
3
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
1
3
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
2
2
0
0
2
0
1
0
0
1
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
2
1
2
2
1
1
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
2
0
0
2
3
1
2
0
0
0
0
0
1
0
0
0
0
1
0
2
0
2
2
0
2
2
0
0
1
1
2
0
0
0
0
0
1
0
0
0
1
0
0
1
2
1
2
2
2
2
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
2
0
0
0
1
2
0
0
0
1
0
1
0
0
1
0
1
1
0
0
0
2
0
0
0
0
0
2
2
2
1
0
0
0
0
1
1
0
1
0
2
0
2
0
0
0
0
2
0
1
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
2
1
0
1
2
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
2
0
2
0
0
2
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
2
0
2
1
0
0
0
0
1
1
1
0
1
2
2
1
0
0
2
5
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
1
0
0
2
0
0
0
1
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
2
2
0
0
3
0
2
0
1
3
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
2
0
1
0
0
0
2
1
1
0
1
2
2
0
0
0
0
0
1
0
0
2
2
0
0
1
0
2
2
2
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
1
0
1
0
0
1
2
1
0
0
1
0
0
0
0
0
2
0
0
2
1
0
2
1
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
3
3
1
0
0
0
0
1
0
0
0
0
2
0
1
0
4
2
0
2
1
0
3
0
2
0
2
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
3
0
0
0
2
0
1
0
0
2
0
0
0
0
0
2
1
2
1
0
4
1
0
2
0
0
1
0
0
2
1
0
0
0
1
0
0
1
0
0
1
0
2
0
1
0
1
0
1
1
0
0
2
1
1
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
1
0
0
2
1
0
2
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
2
2
0
0
1
0
0
0
0
2
0
2
2
0
0
0
1
2
0
0
2
2
0
2
1
1
0
0
2
0
1
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
2
2
0
2
2
0
0
0
0
0
5
0
1
2
0
0
1
6
0
0
1
0
1
0
0
1
0
0
0
0
2
2
0
0
0
2
1
0
0
1
0
0
0
1
0
2
0
0
0
0
1
0
2
0
3
0
0
0
2
4
1
3
1
0
0
0
0
2
0
1
0
2
0
2
2
2
0
0
1
0
0
0
0
0
0
2
3
0
2
0
0
0
2
0
0
0
1
1
0
2
0
1
2
0
1
0
0
2
4
0
0
0
1
0
0
7
0
2
0
1
2
0
1
1
0
0
0
0
1
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
1
0
0
2
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
2
2
1
0
0
0
1
0
1
0
9
0
0
4
1
0
0
0
0
1
3
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
2
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
2
2
0
1
0
2
0
0
0
1
0
0
1
0
0
0
0
1
2
0
0
0
2
1
0
0
0
1
0
0
0
0
1
0
2
2
1
0
0
2
0
3
0
0
0
0
1
2
0
1
1
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
2
1
0
0
0
0
1
0
0
2
2
2
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
1
0
1
0
1
0
3
1
1
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
1
2
0
0
0
0
1
0
1
0
3
0
0
0
0
2
0
0
3
0
1
0
0
0
0
0
0
0
2
0
2
2
0
2
0
0
0
2
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
1
2
0
1
0
0
0
0
2
2
0
0
2
1
2
0
2
0
1
2
0
0
2
0
0
1
0
0
1
0
0
0
1
0
2
0
0
0
0
0
2
1
1
0
2
0
0
1
2
0
2
0
0
2
1
0
2
0
0
0
2
0
2
0
2
0
0
2
2
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
1
2
1
2
1
0
1
0
2
1
0
0
2
2
0
0
0
0
0
1
2
0
0
0
0
2
2
0
0
1
0
0
1
2
0
2
0
1
0
2
0
0
0
1
0
0
0
0
1
1
0
1
0
1
3
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
1
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
3
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
1
0
0
1
1
0
0
1
0
2
0
1
0
0
0
0
0
2
0
0
0
0
2
0
1
0
1
0
0
0
0
1
1
0
0
0
0
3
0
2
1
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
2
0
0
2
2
0
2
0
0
2
0
1
0
0
2
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
1
1
0
0
0
0
0
1
2
0
1
2
0
0
0
0
0
2
0
2
0
2
0
0
1
0
0
0
2
0
4
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
2
1
3
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
2
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
1
0
2
0
6
2
0
1
1
0
1
2
0
2
1
1
2
0
0
0
1
1
0
1
0
1
0
0
0
0
2
1
0
0
2
4
0
0
0
1
0
0
0
0
2
0
0
1
1
0
2
0
2
0
0
0
0
1
0
0
0
0
1
0
2
0
0
1
0
0
2
0
2
0
2
0
0
0
1
0
1
0
0
0
0
0
1
0
0
2
3
0
0
0
0
1
0
1
0
1
0
2
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
3
0
0
0
4
1
0
0
2
0
1
2
0
0
0
2
1
4
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
3
2
0
2
0
1
0
0
0
0
1
0
2
1
0
0
0
0
0
1
0
0
0
0
1
2
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
1
0
0
1
0
5
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
1
4
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
1
0
0
0
3
0
0
0
2
0
2
0
0
0
0
0
0
2
2
3
7
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
3
0
0
1
5
0
2
1
2
0
0
0
0
0
1
2
0
2
0
0
1
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
6
1
0
0
0
0
0
1
1
0
1
0
2
0
0
1
0
0
0
0
2
0
1
0
2
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
3
0
1
0
0
2
2
0
2
2
2
0
2
2
0
2
0
2
1
1
0
1
2
0
0
0
2
0
0
1
1
0
0
1
0
1
3
0
1
0
0
4
0
0
0
0
1
0
0
1
1
0
0
0
2
3
2
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
7
0
0
0
0
1
2
2
0
0
0
2
0
0
1
0
1
2
2
1
0
0
0
2
0
0
1
1
0
0
0
2
0
0
2
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
1
1
0
2
0
0
0
1
0
2
2
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
2
3
2
1
0
0
1
0
1
1
3
2
2
1
0
1
0
0
0
0
0
1
0
2
0
0
0
1
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
1
0
2
2
2
2
0
0
0
0
0
1
1
0
0
2
0
0
0
0
3
2
1
0
2
0
2
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
5
1
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
2
0
3
4
0
2
4
0
0
3
0
0
2
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
1
2
0
1
0
3
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
1
0
2
1
2
2
0
0
2
2
2
2
2
0
0
0
0
0
2
2
0
0
0
0
1
0
0
2
0
0
2
1
0
1
0
0
0
1
1
1
1
0
0
1
0
0
2
1
3
0
1
0
0
2
0
0
1
0
0
0
0
0
1
1
0
0
2
1
1
0
0
0
1
2
0
1
1
0
0
1
0
3
2
0
0
0
0
2
0
0
0
0
0
0
1
0
4
2
0
0
0
0
2
0
0
1
0
1
0
3
0
0
1
0
0
0
2
1
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
1
6
0
0
1
2
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
2
1
2
0
2
1
0
0
2
0
0
1
2
2
0
0
0
1
0
2
0
2
2
0
0
3
0
1
0
0
0
0
1
0
0
0
2
0
0
1
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
2
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
2
0
0
1
2
2
0
0
0
0
0
0
1
1
0
0
2
0
0
1
0
0
2
2
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
2
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
1
0
0
0
0
0
1
1
0
1
1
2
0
0
2
0
3
0
2
0
1
2
2
0
0
0
0
2
5
1
2
0
0
2
0
2
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
3
0
1
2
0
1
2
3
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
3
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
2
0
2
0
1
1
0
0
0
0
0
1
2
2
0
0
1
2
0
0
0
0
0
1
2
0
0
0
0
0
1
1
0
1
1
1
0
0
0
0
0
0
1
1
0
1
2
0
0
0
0
0
1
0
0
2
0
1
0
2
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
2
1
0
0
0
1
0
0
0
2
2
0
2
0
0
0
4
0
1
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
1
0
2
0
1
0
1
0
0
0
0
1
0
0
0
3
0
0
0
0
0
2
2
2
0
1
0
0
0
0
1
3
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
1
0
0
2
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
1
2
1
0
0
0
1
0
2
0
0
1
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
1
1
0
0
0
0
2
2
0
0
0
1
0
0
0
1
0
0
3
3
1
0
0
0
1
0
1
1
1
0
3
2
0
0
1
2
0
2
0
2
6
1
0
0
0
0
2
0
1
0
0
0
0
2
0
0
1
1
0
0
1
1
0
2
3
0
1
0
1
0
0
0
0
2
0
2
1
0
0
0
2
2
1
0
2
0
0
0
2
2
0
0
0
0
8
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
1
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
2
2
3
0
1
0
0
0
1
1
1
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
1
0
2
4
0
1
0
2
0
3
0
0
0
1
1
0
0
0
0
1
0
2
0
0
0
1
0
3
0
0
0
2
0
0
2
0
1
0
1
0
0
0
0
1
1
0
0
0
2
0
0
0
0
2
0
0
2
1
2
0
0
0
1
0
1
0
0
2
0
0
5
1
3
0
1
1
1
0
0
0
1
0
0
0
2
1
0
2
2
0
0
0
0
1
0
1
0
0
2
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
1
3
1
1
2
0
1
1
2
0
1
0
0
0
0
2
1
0
2
0
3
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
2
2
0
0
0
2
0
2
1
0
1
0
0
2
0
0
0
0
0
0
1
0
2
2
3
2
0
0
1
0
3
0
0
2
1
1
3
0
0
0
0
0
1
0
0
0
0
3
0
0
1
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
3
0
2
3
0
2
0
2
2
5
0
0
4
1
0
0
4
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
4
0
0
2
0
0
1
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
2
2
2
1
0
1
1
0
0
0
2
0
0
0
0
0
0
1
3
1
1
0
0
0
0
0
0
2
0
1
1
2
4
0
0
0
0
0
0
0
1
1
2
1
0
1
0
2
0
1
0
0
0
0
0
1
0
1
1
0
1
1
1
2
0
0
0
0
0
0
2
0
1
0
0
0
2
0
2
0
0
0
1
0
0
2
0
1
1
2
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
2
3
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
2
2
0
2
1
0
0
0
3
0
0
0
0
2
0
2
0
0
2
1
0
0
2
2
0
0
0
1
2
1
2
2
0
2
0
0
1
0
0
1
0
2
0
0
0
0
1
0
0
1
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
2
0
2
0
0
0
2
0
0
0
4
1
2
1
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
3
0
0
1
0
2
1
0
0
1
0
3
0
0
0
0
0
2
0
0
1
1
0
1
0
2
0
0
2
0
0
0
1
0
1
0
1
0
0
0
2
0
1
1
0
0
0
2
2
0
0
0
1
0
1
6
0
1
2
2
0
2
2
0
0
0
0
0
1
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
3
2
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
2
0
0
2
0
2
2
0
0
1
0
1
0
1
0
0
0
0
0
1
0
1
0
1
0
0
2
0
0
0
3
0
0
0
0
0
0
0
1
1
0
3
0
0
1
0
0
0
1
2
0
0
1
0
0
1
0
2
0
0
0
0
2
0
0
2
1
1
1
0
0
0
2
0
0
1
0
1
0
2
0
6
0
0
0
0
0
2
1
0
2
1
1
0
0
1
0
0
1
1
0
0
0
1
0
0
0
2
2
0
0
0
0
2
1
0
2
0
0
0
0
1
0
2
0
2
0
0
2
0
0
0
0
0
0
1
1
0
0
0
1
0
0
2
2
0
0
3
1
0
0
0
1
0
0
1
2
2
1
0
0
0
0
0
0
0
2
2
2
2
0
0
2
0
0
1
0
2
0
2
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
1
0
0
0
2
1
0
2
0
0
1
0
0
0
1
2
2
2
0
1
1
0
1
0
2
1
0
2
2
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
2
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
2
2
0
0
0
0
2
0
0
1
1
0
3
1
2
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
3
2
0
0
0
3
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
1
1
0
0
1
2
2
0
0
0
2
0
0
0
0
0
0
2
1
0
3
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
2
0
0
2
2
0
1
0
1
0
0
3
0
0
1
1
1
0
2
2
1
1
0
0
2
1
2
2
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
2
2
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
1
0
0
0
2
2
0
0
0
0
0
2
0
2
0
3
2
0
0
0
3
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
3
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
1
0
2
2
0
0
0
0
0
2
0
2
2
0
0
0
0
0
4
0
0
0
0
2
0
3
1
0
2
1
0
1
0
0
0
1
1
2
0
0
0
0
1
0
0
2
1
1
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
2
0
0
2
0
2
1
1
0
0
3
0
0
0
0
0
0
1
0
2
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
3
2
0
0
3
1
2
2
0
0
0
0
0
0
2
0
2
0
0
2
0
1
1
1
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
2
0
2
2
2
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
15
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
2
5
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
2
1
0
0
0
0
1
3
1
1
0
1
1
0
0
1
1
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
2
2
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
2
1
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
2
0
2
0
0
3
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
7
1
0
0
0
1
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
2
1
1
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
1
1
2
0
1
1
0
0
0
0
0
1
0
0
1
0
3
0
2
0
1
0
0
0
0
1
0
2
0
0
0
0
0
3
1
2
0
2
0
0
0
0
1
1
0
1
0
2
0
0
1
0
0
0
3
0
0
0
1
2
0
1
1
3
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
2
0
2
0
0
1
2
1
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
2
0
0
1
0
2
1
0
0
0
0
0
3
0
0
0
1
0
0
1
0
0
0
2
0
2
0
0
0
0
0
2
0
0
2
0
1
0
1
0
0
2
0
0
0
0
0
0
1
0
2
2
0
0
0
0
2
0
0
1
0
1
0
2
0
2
1
1
0
0
0
1
0
0
0
0
0
0
1
2
2
0
1
2
1
0
2
0
0
1
2
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
1
0
0
3
2
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
1
1
0
0
0
0
1
2
0
1
2
0
0
1
0
0
2
0
0
0
1
1
0
1
0
2
2
0
0
1
0
1
0
1
2
0
0
1
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
2
0
0
0
2
2
0
0
0
0
1
0
1
0
2
0
2
2
0
2
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
2
0
0
5
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
3
1
0
1
0
0
2
0
2
0
3
1
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
2
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
1
0
2
1
1
0
0
0
0
1
2
0
0
1
0
0
0
0
0
1
3
2
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
1
4
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
1
4
0
0
0
1
0
0
0
0
0
1
0
2
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
2
0
0
0
0
0
0
2
2
0
0
1
0
0
0
2
0
0
0
0
2
2
1
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
2
0
0
2
0
0
1
0
1
0
0
0
0
0
1
0
1
2
2
0
0
2
0
1
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
1
1
2
1
0
0
0
0
0
0
2
0
1
1
0
0
0
2
2
2
0
0
0
1
0
0
0
1
2
2
0
0
1
0
0
0
2
0
0
3
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
1
0
1
1
3
0
0
0
0
0
3
2
2
0
0
1
0
0
0
1
0
0
0
2
0
0
1
0
2
0
0
4
2
3
0
0
0
1
0
1
0
0
0
4
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
1
0
2
2
3
1
2
0
0
0
3
0
0
0
0
0
0
3
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
2
1
6
0
0
0
0
0
1
2
0
0
2
0
0
0
2
2
2
1
2
0
1
0
0
0
2
0
6
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
2
1
1
1
0
0
1
0
0
0
0
2
0
0
2
1
0
0
0
0
1
0
2
0
0
0
1
0
0
2
2
0
0
0
0
2
0
2
0
0
1
1
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
2
1
1
0
1
0
1
0
0
1
0
0
2
0
0
2
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
1
0
1
0
1
1
0
2
0
1
0
0
1
2
0
2
0
0
4
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
2
1
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
2
2
0
0
2
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
2
0
1
4
0
0
0
0
0
0
0
1
0
1
1
5
0
0
3
2
0
0
0
0
0
0
2
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
2
0
1
0
1
0
0
1
2
0
0
0
0
0
2
0
0
1
2
0
1
0
0
0
0
1
0
0
0
0
2
2
1
0
2
0
0
0
1
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
3
0
2
0
0
0
1
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
8
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
2
1
0
1
0
0
1
1
0
0
1
2
0
0
1
0
0
2
1
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
2
1
0
2
3
0
0
2
0
2
0
0
0
3
0
0
0
0
0
3
0
0
1
0
0
0
3
0
0
0
2
1
1
0
0
0
2
0
0
2
2
2
0
0
0
1
0
0
0
0
2
2
2
0
0
1
0
2
0
0
0
1
0
0
0
0
0
1
1
0
2
1
0
1
0
0
2
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
1
0
2
0
0
0
0
1
0
2
2
0
2
1
3
0
0
1
1
1
2
0
2
0
0
1
0
0
1
0
0
0
0
0
1
2
0
0
0
2
1
0
0
2
0
0
0
0
2
0
0
1
1
0
0
1
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
1
1
1
0
1
0
0
5
0
0
1
0
2
0
0
0
0
1
0
0
1
1
0
0
2
2
0
0
2
0
0
0
1
0
0
2
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
2
2
0
0
1
1
0
0
0
2
1
0
0
0
1
0
1
0
1
0
3
0
2
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
2
0
0
1
0
0
0
0
2
0
2
2
2
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
2
0
1
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
2
2
1
0
0
2
0
1
0
0
0
2
0
0
0
2
2
1
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
1
0
2
0
0
1
0
2
0
3
2
1
0
1
0
2
0
0
0
0
2
2
0
2
0
0
0
2
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
3
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
2
0
0
0
2
0
0
0
0
0
1
0
0
2
1
1
0
1
0
0
0
3
0
0
0
1
2
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
2
0
0
0
2
0
0
3
1
2
0
0
1
0
2
2
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
3
0
0
0
0
0
2
0
1
0
0
0
2
0
0
2
0
2
0
0
1
0
0
1
0
0
0
0
2
0
0
0
2
0
2
0
4
0
1
0
0
0
0
0
1
2
0
2
0
0
0
0
0
1
1
0
2
0
0
1
0
0
2
0
0
0
0
2
1
0
1
2
0
0
1
1
1
2
0
0
0
0
0
0
0
0
2
0
0
0
1
1
2
2
0
2
2
2
2
1
0
2
0
0
0
2
0
0
0
2
0
1
0
0
2
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
4
0
0
0
0
0
0
0
0
1
3
1
0
5
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
1
1
0
0
0
2
3
0
0
0
0
1
0
1
0
0
1
0
0
2
0
0
0
2
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
1
0
0
1
1
2
3
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
1
3
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
2
0
2
0
1
1
0
0
0
0
0
1
0
1
0
1
2
3
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
2
0
0
0
2
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
2
2
0
2
0
2
0
0
0
0
2
1
0
0
0
0
0
0
1
0
2
0
1
0
0
0
1
0
0
0
6
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
5
2
2
0
0
2
0
0
0
2
0
0
1
0
2
1
0
1
2
1
0
2
1
0
1
2
0
0
0
1
2
0
0
0
0
1
2
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
1
1
0
0
2
0
1
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
3
1
2
0
0
1
2
4
0
0
0
2
0
0
0
0
3
0
0
3
0
1
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
2
2
1
0
0
2
1
3
0
2
0
0
1
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
2
2
0
0
0
0
0
0
2
2
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
3
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
2
0
1
0
0
0
1
0
0
0
1
0
4
2
0
1
0
0
1
1
1
2
2
0
3
0
0
0
1
1
2
0
1
2
0
2
2
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
1
0
3
0
0
0
1
0
0
0
0
2
2
1
0
1
0
0
3
1
1
0
2
2
0
2
0
0
1
0
1
0
0
0
0
1
0
0
0
1
2
0
0
1
0
0
2
0
3
0
1
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
5
2
0
2
0
0
0
2
1
2
0
0
0
2
0
3
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
2
1
2
0
0
0
1
0
0
1
0
0
2
0
0
2
0
0
0
0
4
0
0
1
2
1
0
0
2
0
1
2
2
0
0
0
0
0
0
4
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
8
0
0
0
2
0
0
0
0
0
1
2
0
0
0
2
0
0
0
2
1
1
1
1
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
3
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
1
0
0
0
0
0
0
1
2
0
1
0
4
0
2
0
0
0
0
0
1
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
1
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
2
1
1
1
0
1
3
0
1
0
0
1
1
0
2
0
2
0
0
0
1
0
2
0
2
0
1
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
1
0
1
0
3
0
0
2
0
2
0
0
0
2
0
1
3
0
0
0
1
0
2
0
0
1
0
1
4
0
0
0
0
0
0
0
0
0
1
0
2
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
1
0
0
2
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
2
1
0
2
1
0
0
0
0
1
2
0
1
1
0
1
0
1
1
0
0
0
2
0
1
0
0
6
0
2
2
0
1
1
0
2
2
2
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
1
2
0
0
0
0
1
1
2
0
0
2
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
2
0
0
2
0
2
0
2
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
3
2
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
1
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
1
1
0
0
0
0
0
7
0
0
0
0
1
0
2
2
0
0
4
2
0
2
2
0
0
0
0
2
1
0
3
0
0
1
0
2
0
0
2
2
0
1
0
1
4
0
0
0
0
0
2
0
0
1
0
2
2
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
2
0
3
1
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
1
1
1
1
1
0
0
0
2
0
0
0
0
0
1
2
1
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
2
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
2
6
0
0
1
1
1
2
0
1
2
0
0
0
0
1
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
1
3
1
0
2
2
1
0
2
0
1
0
0
0
2
0
0
0
1
3
0
1
1
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
1
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
2
2
0
0
0
0
0
0
0
2
1
0
0
2
0
2
2
1
1
0
0
1
0
0
2
1
0
0
0
0
1
1
2
0
1
1
0
0
0
0
1
0
2
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
2
2
1
0
0
0
0
5
0
1
0
0
2
0
0
0
0
0
0
4
1
2
1
0
2
1
0
0
1
0
2
0
0
0
0
0
3
0
0
2
0
2
0
1
0
0
0
0
0
3
0
0
0
1
0
2
0
1
2
2
2
1
0
1
2
2
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
1
0
2
1
0
0
0
2
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
2
2
0
0
3
2
0
1
1
0
0
2
0
0
0
0
0
0
2
1
1
0
0
2
0
1
0
0
1
0
0
4
1
2
2
2
0
0
0
0
0
2
0
0
0
0
2
2
0
1
0
0
0
1
0
0
2
0
0
2
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
2
1
0
2
2
0
4
0
0
1
0
0
0
0
0
2
4
2
2
0
0
1
1
0
0
1
0
0
1
2
9
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
2
1
0
0
0
0
0
0
0
0
1
0
2
2
1
1
0
1
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
2
2
0
1
2
0
0
1
0
0
2
3
1
2
0
0
2
1
2
2
1
2
2
2
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
3
0
4
0
0
0
0
1
2
1
0
1
0
0
0
0
0
0
1
1
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
2
0
2
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
2
2
0
2
0
0
2
0
1
0
0
0
1
1
0
1
1
1
1
0
0
0
2
0
2
1
0
0
0
0
2
0
0
3
0
0
0
0
2
2
0
0
0
3
1
0
0
1
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
2
1
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
2
0
0
1
0
0
0
1
1
0
1
0
2
1
1
2
0
0
0
1
0
0
1
0
0
1
1
0
3
0
0
0
0
0
0
1
0
2
2
0
0
0
1
0
0
2
0
0
2
0
0
1
0
0
0
0
0
1
1
1
0
1
0
0
2
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
2
1
1
0
0
0
0
0
4
0
0
2
1
0
2
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
2
3
0
0
1
0
0
2
0
0
0
0
0
1
0
0
2
2
0
0
5
0
0
0
0
1
0
2
2
3
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
1
2
0
0
2
0
1
0
0
0
0
0
0
0
2
2
0
0
2
0
0
2
0
0
1
0
0
0
0
1
2
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
3
1
0
1
1
0
0
0
2
0
2
0
1
0
0
0
1
0
2
0
0
0
0
0
1
1
2
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
3
0
1
1
0
0
1
1
0
2
2
2
2
0
1
1
0
0
0
0
2
0
0
1
0
1
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
1
0
2
2
0
0
0
0
2
0
0
0
0
1
0
0
1
3
0
0
0
1
0
1
2
1
2
0
1
0
0
0
0
0
2
4
0
1
0
0
0
0
2
0
2
3
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
2
3
5
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
2
0
0
0
2
1
1
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
2
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
2
1
1
0
0
0
0
2
0
0
1
2
1
0
0
0
0
0
1
0
4
0
2
1
0
0
0
2
0
1
2
0
0
0
1
0
0
2
1
2
2
0
1
0
1
0
0
1
2
2
0
0
0
0
2
2
0
2
0
0
3
3
2
2
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
2
4
1
0
0
0
2
1
0
0
0
1
0
0
0
0
2
0
0
3
0
2
0
0
1
0
0
1
1
0
0
0
2
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
3
0
0
2
0
0
0
0
0
2
0
0
1
2
0
0
1
0
1
0
0
0
2
0
0
0
0
0
1
6
0
0
0
0
0
0
1
2
1
0
0
0
2
0
0
0
3
0
1
0
0
1
0
0
0
2
0
1
1
0
0
0
0
2
0
0
0
0
2
1
0
1
2
0
1
0
0
0
0
0
2
2
0
0
0
0
0
1
0
1
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
3
0
1
0
0
0
0
2
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
1
1
0
2
2
0
0
2
3
0
0
2
0
0
0
0
0
1
2
0
0
0
1
0
0
1
0
2
1
0
0
2
2
0
0
2
2
1
0
0
0
2
2
1
0
0
0
0
1
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
2
1
0
0
1
0
0
0
0
0
1
0
1
0
0
2
0
2
0
2
2
0
0
0
1
0
0
0
0
0
0
2
2
0
2
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
4
0
0
0
2
1
0
0
0
2
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
3
2
0
0
0
2
2
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
2
3
1
0
0
2
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
2
0
3
0
1
2
2
2
1
0
0
1
1
2
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
1
0
0
1
0
0
0
0
1
2
0
2
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
2
0
2
0
0
1
0
2
0
0
1
2
0
1
0
0
0
0
0
0
0
1
2
2
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
2
0
0
2
1
0
0
1
0
0
0
2
0
0
1
1
0
0
2
0
1
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
4
0
0
0
0
2
2
1
0
0
2
0
1
2
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
2
0
2
0
0
0
0
0
2
2
0
2
0
1
0
0
0
0
2
0
2
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
2
0
1
0
1
1
1
0
0
0
0
0
0
1
0
0
0
2
0
1
2
0
1
0
0
0
0
2
1
2
0
2
0
1
1
2
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
1
0
1
1
0
0
0
6
2
1
0
3
1
0
1
0
1
0
2
0
0
0
0
0
0
0
3
0
0
2
0
1
0
0
1
1
0
1
0
1
0
0
2
0
1
1
0
1
0
3
0
0
2
2
0
2
2
0
0
0
0
2
0
0
0
1
0
2
0
1
1
0
0
0
1
0
1
3
0
0
1
2
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
2
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
2
0
1
2
2
1
1
0
0
3
0
0
3
0
2
0
0
1
0
0
0
0
1
2
1
0
0
2
0
0
1
0
0
0
1
0
0
0
2
2
1
0
2
0
0
2
2
0
0
0
0
1
0
2
0
0
0
2
2
0
0
0
0
1
0
2
0
0
0
3
2
1
1
0
0
4
0
0
0
6
0
2
2
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
2
1
0
0
0
0
2
0
1
2
0
1
2
3
0
1
0
0
2
1
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
2
5
0
0
2
2
0
1
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
1
0
0
1
1
1
0
1
0
0
0
0
0
0
3
0
0
1
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
1
1
0
1
0
1
0
1
2
1
4
0
1
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
1
1
1
0
0
1
0
0
2
1
1
0
2
2
1
0
3
0
3
0
1
0
0
0
5
0
2
0
0
1
0
0
0
2
2
2
1
0
0
0
0
0
1
1
1
1
1
0
0
2
0
0
1
0
0
2
0
1
0
0
2
2
0
0
0
1
0
0
2
1
0
0
2
4
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
1
2
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
2
0
2
0
0
0
0
0
0
2
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
1
0
2
0
0
1
2
0
0
4
2
0
1
0
0
2
2
0
2
0
2
0
0
2
0
0
0
1
0
2
0
2
0
0
0
0
0
0
3
2
0
0
2
0
0
0
0
2
0
0
2
1
1
2
0
0
2
0
0
1
2
0
0
0
1
0
0
0
2
0
0
0
2
0
0
2
0
1
0
1
0
0
2
0
0
0
0
0
0
2
1
0
0
0
3
0
1
0
0
0
0
0
0
1
0
1
0
0
0
2
2
0
0
0
0
1
1
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
2
0
0
2
1
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
1
0
2
0
1
0
1
0
0
0
0
2
0
1
0
0
0
2
0
2
0
1
0
0
0
1
2
0
2
0
0
1
0
0
0
2
0
0
1
0
1
0
2
1
2
2
0
1
0
0
0
0
0
0
0
0
3
0
1
2
0
2
0
0
0
0
1
2
1
0
0
0
0
1
0
0
0
0
0
1
0
1
1
2
0
2
2
1
2
1
0
1
0
0
1
0
5
1
2
0
0
0
2
1
0
1
0
0
0
2
1
0
0
2
0
0
0
2
0
2
0
1
0
0
0
2
0
0
1
0
0
2
2
0
0
0
1
0
1
0
2
0
2
0
0
1
2
0
0
0
0
1
0
1
0
0
2
1
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
3
1
0
0
1
0
0
0
0
2
0
0
0
2
0
0
1
2
1
2
0
0
3
0
2
0
0
1
0
1
0
2
0
0
0
0
0
2
0
0
1
0
0
2
2
1
1
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
1
1
0
0
0
2
0
0
2
0
0
1
1
0
3
2
2
0
2
0
0
0
0
2
0
2
0
0
0
1
0
1
3
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
3
0
0
0
0
1
1
2
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
1
2
3
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
2
0
0
0
0
1
0
2
0
2
1
1
2
0
0
0
0
1
0
0
0
1
2
0
2
0
0
0
0
1
0
1
0
0
2
1
1
3
2
2
1
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
2
0
3
0
0
1
0
2
0
0
0
0
2
0
0
1
0
2
0
1
0
0
2
0
0
0
1
1
1
2
2
0
0
0
0
0
0
1
2
0
2
0
1
0
0
0
0
2
0
2
3
0
6
1
2
1
0
2
0
3
0
2
1
0
0
1
0
2
0
0
0
0
2
0
1
2
0
0
2
0
1
1
2
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
4
0
2
0
0
1
2
0
0
1
1
0
0
1
0
1
0
0
0
0
2
2
2
0
0
0
1
0
0
0
0
1
1
0
1
0
2
1
0
1
2
0
1
0
1
0
3
0
0
0
0
0
0
0
0
1
1
4
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
2
0
0
1
0
1
0
1
0
0
1
0
0
0
0
1
1
0
0
2
2
0
0
1
1
2
1
0
2
2
1
1
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
1
0
0
0
0
0
1
0
2
0
2
1
0
0
0
1
0
0
0
0
1
0
0
2
2
0
1
1
1
2
0
3
1
1
1
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
2
0
0
0
0
1
0
2
0
1
0
0
0
0
0
2
1
7
1
1
2
1
0
0
0
0
2
0
0
2
0
2
0
0
1
2
0
2
0
0
2
0
0
1
0
1
2
0
0
2
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
2
0
0
0
0
1
2
0
2
0
1
2
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
2
2
0
0
0
4
1
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
2
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
1
0
3
1
0
1
0
1
0
1
2
0
0
1
0
0
2
2
2
1
0
2
1
0
2
0
0
1
0
0
0
1
1
2
2
0
0
0
0
0
1
2
0
1
0
0
1
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
2
2
2
0
0
2
0
2
0
0
0
4
2
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
1
0
1
0
0
1
0
3
0
1
1
1
0
0
0
2
2
0
0
0
1
2
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
3
0
0
1
0
2
0
0
1
0
0
2
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
1
0
2
3
3
4
1
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
2
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
2
1
0
0
0
2
0
0
0
1
0
0
4
1
0
0
0
2
0
0
0
0
0
0
2
1
0
2
2
0
0
1
2
1
0
0
1
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
3
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
2
1
2
1
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
3
0
0
4
0
0
3
2
0
5
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
2
2
0
1
2
0
0
1
0
2
2
0
1
0
0
0
0
0
0
0
0
0
1
2
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
2
1
0
2
2
2
2
0
0
1
1
0
0
2
1
0
1
0
0
2
0
2
0
3
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
4
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
1
0
2
3
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
2
0
2
0
1
1
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
1
0
0
2
0
1
2
0
1
0
0
0
0
0
2
5
0
0
1
2
0
0
2
0
1
0
0
0
0
5
2
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
1
2
0
2
0
0
0
2
0
0
0
2
2
0
0
2
0
0
2
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
1
2
1
0
0
0
0
0
1
0
0
0
0
2
0
1
1
1
2
0
0
0
5
0
2
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
4
0
0
2
0
0
0
2
0
0
0
0
1
0
1
0
0
0
1
0
0
0
2
1
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
1
0
3
0
0
0
2
0
1
0
0
0
0
0
1
3
1
0
0
0
0
1
0
0
1
0
2
2
2
1
2
0
1
1
0
0
0
0
0
5
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
2
0
0
0
2
1
0
0
1
0
0
0
0
2
3
1
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
3
0
0
0
1
0
2
2
0
0
0
0
0
0
5
1
0
2
1
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
4
0
1
0
2
2
0
0
0
0
1
2
1
1
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
2
0
0
0
1
0
0
1
2
1
0
1
0
3
0
0
2
0
0
2
0
0
1
0
1
0
0
2
0
0
0
0
1
1
0
0
2
2
0
0
0
0
2
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
2
0
0
2
0
2
2
2
1
0
1
1
0
0
2
0
0
0
0
0
2
2
2
0
0
1
0
0
0
0
1
0
4
0
0
4
0
0
1
0
0
0
0
2
1
0
0
0
0
0
2
0
2
0
2
0
2
2
0
0
2
0
0
0
0
2
2
0
0
0
0
0
2
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
1
0
0
1
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
2
1
0
0
0
0
0
0
2
0
0
2
0
1
2
0
0
0
0
0
0
0
2
3
0
0
0
2
1
0
3
0
1
0
0
1
2
0
2
0
0
3
0
0
0
0
0
3
0
0
2
0
0
2
3
2
0
0
0
1
3
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
4
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
1
0
1
2
0
0
2
0
1
3
3
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
1
0
0
0
3
0
2
0
0
0
0
0
0
0
1
0
2
0
2
1
0
2
0
0
1
1
0
0
0
1
0
1
2
0
3
2
0
0
0
0
2
0
0
0
0
0
0
2
2
3
1
1
0
2
1
0
1
1
0
0
0
0
2
1
0
0
0
1
0
0
0
0
2
0
0
1
1
1
0
0
0
2
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
3
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
1
0
0
2
0
1
0
2
1
0
0
0
0
1
0
2
1
2
0
0
1
0
2
0
0
2
0
0
2
0
1
0
4
0
0
1
0
0
0
0
2
2
0
2
0
2
0
4
0
0
0
0
0
3
0
1
1
0
0
0
2
0
1
1
2
1
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
2
2
0
1
2
0
0
0
0
2
1
1
0
0
1
1
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
2
0
0
2
1
0
2
1
0
0
0
2
0
2
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
2
2
0
0
1
0
0
0
0
2
0
0
1
0
1
0
1
0
0
0
3
0
0
0
0
2
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
2
2
0
0
0
0
2
0
0
2
0
0
3
2
2
2
2
0
0
1
1
0
2
1
3
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
3
2
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
2
0
2
0
0
0
0
1
2
0
0
0
0
0
0
2
2
0
0
0
0
2
2
0
0
0
1
0
0
2
2
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
1
2
0
0
1
2
0
0
0
0
1
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
2
1
1
0
0
0
1
0
1
0
1
2
2
2
0
0
2
0
0
1
0
0
0
0
0
0
0
1
2
0
1
0
0
0
2
0
0
1
0
2
2
0
0
0
2
0
2
0
0
2
0
2
2
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
2
1
0
0
0
0
1
0
1
0
0
1
2
0
2
2
0
2
0
0
0
2
2
0
0
1
0
0
1
0
1
0
2
0
1
0
0
0
0
0
1
0
1
0
1
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
2
0
3
0
0
0
0
0
0
0
1
3
2
2
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
1
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
2
0
0
2
0
0
0
1
0
2
0
0
1
0
2
1
0
0
0
0
0
3
0
1
0
2
0
1
0
0
3
0
0
0
1
0
1
0
0
0
0
0
0
1
2
2
1
0
0
0
0
1
0
2
2
1
0
1
0
0
0
7
0
1
2
2
0
0
0
2
0
1
1
0
0
0
0
1
0
1
1
0
0
0
0
0
3
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
1
0
1
0
0
0
0
2
2
1
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
1
0
0
8
0
4
0
0
0
0
1
0
2
0
2
0
0
2
0
2
0
0
0
0
1
1
0
1
0
1
1
1
0
0
2
1
2
0
3
0
0
1
2
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
2
0
1
0
0
0
0
1
2
2
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
1
2
0
0
0
0
0
0
2
2
0
0
0
2
4
0
1
0
0
0
0
1
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
1
0
1
2
1
3
1
0
0
0
0
0
0
1
1
0
2
1
1
3
2
2
1
0
0
2
1
1
1
0
0
0
0
1
0
1
2
0
2
0
0
0
0
0
0
0
1
2
0
0
3
0
0
0
1
1
0
1
1
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
1
0
1
0
1
0
0
0
1
1
3
0
0
0
0
2
1
0
0
2
1
1
0
0
0
7
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
2
0
2
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
1
1
0
0
2
0
2
0
3
2
0
0
1
0
0
0
0
3
0
0
0
0
1
2
1
0
0
1
0
2
0
0
0
1
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
2
1
0
2
0
0
0
0
0
0
2
0
1
0
0
2
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
3
2
0
0
0
0
1
0
1
2
0
2
1
0
0
0
1
2
2
0
0
2
1
0
0
2
1
0
0
0
5
2
0
0
0
2
0
0
0
0
1
1
1
0
0
0
1
2
1
1
0
2
0
2
0
0
1
0
0
1
0
0
0
1
0
0
0
1
2
0
1
1
0
2
1
2
0
0
2
0
2
0
1
1
0
1
0
0
0
0
0
0
1
0
2
4
0
2
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
1
0
1
2
0
2
2
0
2
0
1
0
0
0
0
0
0
0
2
1
1
1
0
0
1
0
0
0
0
2
2
2
0
0
0
1
2
0
0
0
0
1
2
0
1
1
0
0
0
0
2
0
0
0
0
2
0
2
1
0
0
2
0
2
2
3
0
0
0
0
0
3
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
2
2
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
1
1
0
0
6
1
1
0
2
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
3
0
0
1
0
0
0
1
2
0
0
0
0
2
0
0
0
1
0
0
2
0
1
0
0
2
0
0
2
0
1
0
0
1
1
1
0
2
0
1
0
2
2
2
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
1
1
2
0
0
0
1
2
0
0
2
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
3
0
0
0
1
0
0
0
0
1
1
0
2
6
2
2
4
0
0
0
0
1
0
2
0
0
0
2
0
1
0
0
0
0
0
2
2
3
0
0
0
0
2
0
1
3
0
0
0
0
0
1
1
0
1
0
0
0
3
1
0
1
0
1
0
2
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
2
1
2
0
1
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
2
3
0
2
2
0
0
2
2
1
0
0
1
1
0
0
1
2
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
3
0
0
0
0
1
0
2
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
2
0
0
2
0
0
0
2
0
0
0
0
0
2
0
1
0
1
0
0
2
2
0
1
0
1
0
0
0
0
1
0
1
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
4
0
1
1
0
0
0
0
3
1
0
1
2
2
2
2
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
1
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
2
0
2
0
2
0
0
0
0
1
0
0
1
0
0
5
2
1
0
1
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
2
0
1
0
1
0
0
2
1
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
1
0
0
0
1
2
0
2
0
0
1
2
0
0
2
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
1
0
2
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
1
0
0
1
0
0
1
0
0
0
1
1
0
0
0
3
0
0
0
0
0
0
0
1
1
2
2
0
2
3
0
2
2
1
0
1
1
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
1
3
2
0
3
1
1
0
1
0
0
2
0
0
2
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
3
0
0
0
1
0
1
0
1
0
0
0
1
2
0
0
0
2
2
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
1
2
0
1
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
2
0
1
0
0
0
1
2
1
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
4
0
1
0
0
0
1
3
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
3
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
3
0
0
1
0
2
0
3
0
1
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
2
0
0
3
0
2
1
0
2
2
2
0
0
0
0
0
0
1
0
0
0
2
0
0
9
1
0
0
0
0
2
0
2
1
0
0
0
1
0
3
1
2
0
0
0
0
2
2
0
2
0
2
0
1
0
0
0
2
1
1
0
0
2
3
0
0
0
0
0
0
1
2
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
2
0
3
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
1
0
0
1
0
2
0
0
1
0
0
0
0
1
0
0
0
1
0
2
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
1
0
0
0
1
0
2
0
2
0
2
2
0
0
2
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
1
2
3
0
0
0
0
1
0
2
0
0
1
2
0
0
0
0
0
0
0
0
2
5
0
0
0
0
0
0
0
1
0
1
2
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
1
3
0
2
2
1
0
0
0
0
1
2
1
0
0
0
0
2
0
0
0
0
0
1
0
2
0
2
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
2
1
0
0
2
1
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
2
0
0
2
1
0
4
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
2
0
0
1
0
0
0
0
1
0
2
2
0
0
2
1
1
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
9
0
0
0
1
2
2
0
0
2
0
0
1
0
0
2
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
3
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
3
0
0
2
0
0
4
0
0
2
2
0
0
0
0
0
0
2
1
0
0
1
1
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
4
0
2
0
0
2
0
0
2
0
2
1
0
2
1
0
0
0
0
2
1
2
0
2
2
0
0
0
0
2
1
0
2
2
0
0
0
1
4
0
0
0
0
2
0
0
2
0
0
2
3
0
0
0
1
0
0
0
0
1
2
2
2
0
0
0
0
0
0
1
0
2
0
0
0
1
1
2
0
0
2
0
0
2
1
0
2
0
0
1
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
1
0
1
0
0
0
1
0
1
1
0
0
0
2
1
0
1
2
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
2
0
0
0
1
1
0
0
0
0
2
1
0
2
3
0
0
0
0
1
0
1
1
0
0
2
0
0
0
1
1
0
0
0
0
0
1
0
2
1
1
2
0
2
1
0
0
0
0
1
2
1
1
1
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
1
0
2
0
0
2
0
0
1
0
0
0
0
0
1
0
0
2
1
1
3
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
2
2
2
0
0
0
0
2
3
2
0
0
0
1
0
4
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
1
0
2
2
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
4
0
0
2
0
1
0
0
0
0
0
2
0
0
2
1
0
2
2
0
0
0
2
1
0
0
0
0
0
0
1
2
0
0
1
0
0
2
2
0
0
0
2
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
2
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
3
0
0
0
3
0
1
0
0
2
2
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
1
2
0
1
0
0
0
2
0
0
2
0
1
0
0
2
0
1
1
2
0
2
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
2
1
0
0
0
2
2
2
0
0
0
1
0
1
1
2
1
2
0
0
1
0
1
2
1
0
0
2
0
2
0
0
0
1
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
1
0
1
1
1
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
3
1
0
0
0
0
1
0
0
3
0
0
0
1
1
1
0
0
0
2
0
2
0
0
1
3
0
0
1
0
0
0
2
0
0
1
0
0
1
0
0
0
0
2
1
2
0
2
0
0
2
0
0
0
0
0
2
2
0
1
0
0
0
1
0
0
0
3
1
1
0
1
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
2
0
2
1
0
0
0
0
0
0
0
1
0
1
0
0
1
2
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
2
0
0
0
0
1
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
3
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
2
1
3
1
2
0
2
0
0
0
2
1
0
0
0
0
0
2
0
0
2
0
0
0
0
3
0
0
2
0
0
0
1
0
5
0
0
0
0
0
0
0
1
0
1
0
2
0
2
0
0
0
1
0
0
0
1
2
2
1
0
0
8
0
1
2
1
1
1
0
0
0
2
0
0
1
0
0
2
2
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
2
2
0
0
1
0
0
2
0
0
1
2
1
0
0
0
0
2
1
0
0
2
0
0
1
0
0
0
1
1
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
1
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
1
2
0
2
0
0
0
1
2
1
2
0
2
0
0
0
2
0
0
0
0
0
1
0
2
2
2
0
4
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
3
2
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
2
2
0
1
0
1
2
0
1
0
0
0
0
0
1
0
0
0
0
2
2
2
0
0
0
1
1
2
1
0
0
1
1
2
0
0
1
0
2
0
2
0
1
0
0
0
2
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
4
1
0
0
1
0
2
0
0
2
3
0
2
1
0
0
0
0
0
1
1
0
0
1
1
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
1
2
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
1
0
0
1
0
0
0
1
3
0
0
0
2
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
1
2
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
2
2
2
0
2
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
3
2
0
0
2
0
2
0
1
0
1
0
0
1
1
0
1
2
0
0
1
0
0
0
2
0
0
0
0
2
0
0
2
0
0
1
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
1
0
2
1
0
0
0
0
0
0
1
0
0
1
0
0
2
0
1
2
0
0
2
1
2
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
2
0
2
2
0
0
0
1
0
0
0
0
0
0
2
1
2
2
0
1
0
0
0
0
2
0
1
1
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
1
0
0
2
0
0
2
2
0
1
0
0
0
0
2
2
2
0
1
1
1
2
2
0
0
0
0
2
0
2
1
0
0
0
0
3
0
0
1
2
0
4
1
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
1
1
0
0
0
1
0
3
0
2
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
1
2
8
0
0
0
0
2
0
0
3
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
3
1
0
0
0
1
0
3
2
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
1
1
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
2
1
0
1
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
1
1
0
1
2
0
1
0
1
2
0
0
0
0
0
1
2
2
1
2
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
2
0
2
0
1
1
0
0
2
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
12
1
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
4
0
2
0
0
4
1
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
3
1
2
0
0
0
2
0
0
0
0
0
2
2
2
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
3
2
3
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
1
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
2
0
0
2
1
0
0
0
0
2
1
0
0
1
0
0
0
1
2
0
0
0
1
0
2
2
0
0
1
0
0
0
0
1
0
0
2
1
0
0
2
2
0
0
0
1
0
0
1
0
0
1
0
0
1
0
1
0
2
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
1
3
0
0
0
0
3
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
2
0
1
0
0
2
2
0
0
0
1
0
1
1
0
2
0
1
1
2
0
0
0
2
0
1
0
2
0
0
0
0
0
4
0
0
0
0
0
0
2
1
2
0
0
1
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
1
2
3
0
0
0
3
0
0
0
0
0
2
0
2
0
0
0
1
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
2
0
0
1
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
1
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
1
2
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
1
1
0
2
0
0
0
0
0
2
1
0
2
0
0
0
0
0
3
0
2
0
2
0
0
0
0
0
1
0
1
1
0
0
0
2
2
0
3
0
0
0
0
1
1
0
0
1
2
2
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
2
1
0
0
0
0
0
3
0
2
4
0
2
0
0
1
1
0
0
2
0
0
0
1
0
1
0
1
0
0
0
1
0
1
0
0
0
0
2
2
0
1
1
0
0
0
0
2
1
1
0
1
2
2
1
2
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
2
1
1
0
0
1
0
0
0
0
2
0
0
3
0
1
2
1
0
0
0
0
1
2
0
1
0
2
1
0
0
1
0
0
0
1
0
0
3
0
0
0
1
1
2
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
1
0
0
0
2
1
1
1
3
1
0
1
0
0
0
2
0
0
1
1
2
0
0
2
0
0
0
1
2
0
0
2
0
1
0
1
1
0
0
0
0
1
0
2
0
2
0
1
2
1
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
2
3
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
7
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
2
0
0
0
0
2
0
0
1
0
0
1
0
2
0
2
1
0
2
0
0
0
1
2
0
1
0
0
1
0
0
1
0
2
0
0
0
2
0
2
0
1
0
2
0
1
1
0
0
0
1
2
0
0
0
0
0
2
2
0
0
0
2
2
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
2
1
0
0
0
0
1
1
0
0
1
0
1
1
2
0
0
1
2
2
1
2
2
0
1
0
1
0
0
2
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
3
0
1
0
0
0
1
1
2
0
0
1
0
0
0
6
0
1
0
1
0
0
1
0
0
2
0
0
0
1
0
0
4
0
0
0
1
0
0
0
0
2
2
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
2
0
0
1
2
2
0
2
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
2
1
2
0
0
0
1
0
0
0
2
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
3
2
2
2
2
2
0
0
1
0
0
0
0
0
0
0
2
2
1
0
0
2
0
0
1
0
0
1
2
0
1
2
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
1
0
1
0
0
0
0
1
0
0
0
1
2
0
1
0
0
2
0
0
0
0
1
2
0
0
0
0
2
0
0
2
5
0
0
0
1
0
0
1
1
0
0
0
0
0
0
2
1
0
2
0
0
0
0
2
0
0
2
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
1
0
2
2
0
2
1
0
0
0
3
0
2
0
2
0
0
0
2
0
1
2
2
1
0
0
1
0
0
2
1
0
0
1
0
0
0
2
0
0
2
0
0
0
2
1
2
0
0
3
0
1
0
0
0
2
0
1
0
0
0
0
0
1
0
0
2
3
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
2
1
0
0
0
0
2
2
0
1
0
0
1
0
2
0
2
0
0
0
1
0
1
2
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
2
0
0
1
0
2
0
0
0
0
1
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
2
3
0
1
1
0
0
0
0
1
2
0
0
0
0
0
1
4
2
0
0
0
2
3
2
3
2
0
0
1
0
0
0
0
1
2
1
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
6
0
0
0
0
0
0
1
1
1
0
2
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
2
2
0
0
2
0
1
0
0
2
2
3
0
2
0
3
0
1
0
1
2
0
1
0
4
0
1
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
1
0
0
0
2
0
1
0
2
0
0
0
2
0
0
0
1
0
1
1
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
3
1
0
0
3
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
3
0
0
2
1
0
1
0
2
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
1
2
0
0
1
0
2
0
0
1
0
0
0
0
1
1
2
0
1
0
1
0
0
0
1
2
1
0
0
0
2
1
1
0
0
1
0
1
0
2
0
0
0
2
2
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
2
1
0
0
0
0
0
6
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
1
2
0
2
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
1
0
0
1
1
2
0
0
2
0
0
2
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
2
2
0
0
2
0
0
0
2
2
0
0
0
1
1
0
2
0
0
2
1
0
0
0
0
2
1
0
0
0
1
0
0
2
0
0
1
0
1
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
1
3
0
2
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
2
2
0
0
0
0
2
0
0
2
0
2
0
2
1
1
0
1
0
0
0
0
3
0
0
0
0
2
2
2
2
0
0
0
2
0
2
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
4
0
4
0
1
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
2
0
0
2
0
0
0
2
1
0
1
2
3
0
2
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
2
0
1
2
0
1
1
0
0
2
2
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
2
1
4
0
1
0
0
1
0
1
0
1
0
0
2
0
0
0
0
0
0
2
0
3
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
2
2
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
1
1
0
1
0
0
0
3
2
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
1
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
2
0
2
0
2
0
1
0
0
1
0
2
0
1
0
3
0
0
1
0
0
2
0
1
0
2
0
0
0
0
0
2
3
0
0
0
0
1
0
0
0
2
0
0
0
1
2
1
0
0
1
0
3
0
0
0
0
0
0
1
0
2
0
0
1
0
1
2
2
0
0
0
0
0
0
0
0
1
2
1
0
2
0
0
1
1
2
0
0
2
0
0
0
6
1
0
0
2
0
1
2
1
0
0
0
0
1
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
1
1
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
5
2
0
0
0
0
2
1
2
0
0
0
0
9
0
0
1
1
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
1
0
0
0
0
2
3
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
2
1
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
1
2
0
1
0
0
1
0
0
6
0
2
0
1
0
0
0
2
0
1
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
2
0
0
1
0
1
1
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
1
0
2
0
0
0
0
2
1
0
0
1
0
0
0
0
1
0
0
2
0
0
3
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
2
0
0
3
0
0
1
1
1
1
0
0
1
1
0
0
0
2
2
0
1
0
2
2
0
0
1
0
1
0
1
0
2
2
0
2
0
1
0
1
0
0
1
0
0
2
0
0
0
1
1
0
0
0
0
2
2
1
0
0
0
0
0
0
0
2
1
0
0
0
2
2
0
0
0
0
0
3
0
0
0
2
0
2
0
2
0
1
1
1
0
0
0
0
0
1
0
2
1
1
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
4
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
1
2
2
0
0
0
3
0
0
0
2
0
1
1
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
2
0
1
0
0
1
0
1
2
0
0
2
1
0
0
0
0
0
0
0
2
0
0
1
0
1
2
0
0
0
0
1
0
2
2
0
0
0
1
1
0
0
0
0
0
0
2
0
0
2
0
0
3
1
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
3
0
0
1
0
2
1
2
0
0
1
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
1
0
1
0
1
1
0
1
1
2
1
0
0
0
0
0
0
0
2
0
0
2
2
0
1
0
1
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
1
1
0
1
0
2
0
0
2
0
0
0
2
1
0
0
0
0
1
3
0
0
0
0
0
0
1
2
2
2
1
1
2
0
5
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
5
0
0
2
0
0
1
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
1
2
0
1
0
0
0
1
0
1
2
1
0
0
0
0
1
1
0
0
0
0
1
0
1
0
1
0
1
0
2
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
1
0
1
1
0
2
0
0
2
0
0
2
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
2
0
0
0
0
1
0
1
1
0
0
0
1
1
1
0
0
0
0
2
2
1
0
1
0
0
0
0
0
2
0
1
0
0
2
0
2
0
0
2
2
0
0
0
1
0
0
0
1
1
0
0
0
1
1
0
0
0
0
1
0
1
1
0
0
3
0
2
2
0
2
0
0
2
0
0
0
1
1
0
3
0
3
0
0
0
0
1
0
1
3
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
2
0
0
1
0
0
0
2
0
2
0
0
0
0
1
0
0
0
2
0
3
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
1
2
0
1
0
2
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
14
0
1
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
2
0
2
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
3
0
1
1
0
1
2
0
0
0
2
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
7
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
1
2
0
0
2
1
0
0
1
1
1
0
0
2
0
4
4
0
0
5
0
3
0
0
0
1
2
2
0
1
1
1
0
1
1
1
1
1
0
1
0
0
0
2
0
1
0
1
0
0
1
2
0
1
0
0
1
2
0
0
2
0
2
0
0
0
0
0
0
1
2
2
1
0
0
0
1
0
2
0
2
2
2
2
4
0
0
1
0
0
0
0
3
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
2
0
4
0
0
0
0
1
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
3
0
1
0
0
2
0
0
0
0
0
2
2
0
0
0
3
0
1
2
1
1
0
2
0
2
0
0
0
0
2
2
2
0
0
0
0
0
0
0
2
0
1
3
0
0
0
0
0
2
0
2
1
0
1
1
0
2
0
0
0
0
0
0
1
0
0
0
2
2
0
2
3
0
2
1
0
0
2
2
0
0
0
0
4
0
0
1
0
1
3
1
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
2
0
1
7
1
0
0
1
3
3
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
6
1
0
0
0
0
0
0
2
0
2
0
3
1
1
0
0
0
0
0
2
0
0
0
1
0
2
0
2
0
0
1
1
1
2
0
0
0
0
1
1
0
0
0
0
0
1
0
2
0
0
2
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
3
3
0
0
0
0
0
0
0
1
2
0
1
1
2
2
0
0
0
1
2
0
0
0
0
0
0
0
1
0
1
1
0
2
3
3
0
0
2
0
1
3
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
2
2
0
0
2
0
1
1
0
0
0
1
0
0
1
0
0
1
0
3
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
2
0
1
0
0
2
0
1
0
0
0
0
0
2
1
2
0
1
0
2
0
0
0
2
0
2
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
2
1
0
0
1
0
2
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
2
1
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
1
2
0
1
0
0
1
1
0
1
2
0
0
1
0
0
0
0
0
2
0
0
0
0
2
1
3
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
1
0
2
0
3
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
5
0
0
0
1
0
1
0
0
0
1
4
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
6
3
1
1
0
1
0
0
1
0
0
3
2
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
1
2
0
0
0
3
0
0
0
3
2
2
0
0
1
0
0
1
2
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
1
2
0
3
0
0
0
0
1
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
1
0
3
0
2
0
2
0
2
1
2
0
0
0
1
0
2
0
2
2
0
2
0
2
2
2
0
1
1
2
1
0
0
1
2
2
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
2
1
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
2
0
2
0
0
3
0
1
0
0
0
0
0
1
2
2
0
0
0
0
1
0
1
1
1
0
0
2
0
0
0
0
0
0
0
0
0
1
4
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
3
0
2
0
0
0
1
0
0
0
0
1
1
2
0
0
0
0
1
1
0
0
0
0
2
2
1
0
2
0
0
0
4
0
1
1
0
0
2
1
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
2
1
0
0
0
1
0
2
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
1
2
2
0
0
0
1
2
0
0
2
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
3
2
2
1
2
1
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
2
0
1
0
0
0
1
0
2
0
0
0
4
0
1
2
0
0
1
0
0
1
0
0
0
2
2
2
0
2
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
2
1
0
2
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
1
0
1
1
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
1
1
2
2
1
0
0
2
0
2
0
0
1
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
1
0
2
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
1
1
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
1
1
0
0
0
0
1
0
1
0
0
2
0
0
1
0
0
0
1
1
0
0
2
0
1
1
1
0
3
0
0
1
1
1
0
0
2
0
0
0
2
0
0
0
1
0
0
2
0
0
1
0
1
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
2
0
0
2
0
1
2
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
2
2
0
0
2
2
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
1
2
0
0
0
1
0
0
0
0
0
1
0
2
0
0
2
2
0
2
0
1
1
2
0
0
0
0
0
0
0
2
0
7
1
1
0
1
2
0
0
1
0
0
1
2
0
1
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
2
0
1
3
0
0
2
2
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
2
0
0
1
0
1
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
1
0
2
1
1
1
0
0
1
0
0
0
1
0
0
2
0
0
2
0
0
0
1
1
1
0
0
0
0
2
0
0
0
1
0
0
0
2
0
2
0
3
0
0
0
0
0
0
2
0
0
1
2
0
0
2
2
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
2
1
3
0
0
2
0
2
1
2
1
3
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
1
0
1
0
0
0
2
0
2
0
0
1
0
0
1
0
0
0
2
1
1
0
0
1
0
1
0
0
2
0
1
1
1
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
1
2
0
0
0
1
1
2
0
0
2
0
0
2
3
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
3
0
0
2
0
2
1
0
2
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
2
1
0
0
1
0
2
0
0
2
1
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
1
2
0
0
0
0
0
0
2
0
1
2
2
1
0
2
0
2
0
2
2
0
0
1
1
0
0
0
0
0
1
1
2
2
0
0
2
0
1
10
0
0
1
0
0
0
0
2
1
1
0
0
0
0
2
0
2
1
0
0
2
0
2
0
1
0
3
2
0
0
0
0
0
2
0
0
1
1
0
2
3
0
1
1
0
2
1
0
1
0
0
0
0
0
2
1
2
1
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
2
1
0
2
0
0
0
1
1
0
0
0
2
0
1
2
0
0
0
0
0
2
0
0
1
0
2
0
2
1
0
0
0
0
0
2
0
0
0
2
0
1
0
1
2
2
1
0
0
0
0
2
2
1
2
0
2
0
0
0
2
0
2
0
1
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
2
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
1
0
1
2
0
1
2
0
0
2
0
0
2
0
1
1
0
0
0
1
0
0
0
0
1
0
1
0
2
1
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
2
2
0
0
0
1
0
3
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
1
3
1
0
1
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
1
0
2
0
3
2
0
1
1
1
0
0
0
2
0
0
0
0
2
1
0
2
0
0
1
2
2
0
0
0
2
0
0
1
0
0
0
2
2
0
2
0
0
0
1
1
0
0
0
2
2
2
0
1
0
1
2
1
0
0
0
0
0
0
0
0
1
1
2
0
1
1
0
0
1
0
1
0
2
0
0
1
4
0
2
2
0
0
0
0
1
1
0
0
2
2
2
0
1
2
1
1
0
1
2
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
3
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
2
2
1
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
1
2
0
2
0
2
1
2
0
2
2
2
1
0
0
0
1
1
1
2
0
0
3
0
2
1
0
0
0
0
1
0
0
2
0
0
1
0
2
0
0
2
1
2
5
2
0
0
0
0
0
0
0
0
1
0
2
1
0
1
1
0
0
0
0
1
0
2
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
2
2
0
1
2
1
3
2
0
0
2
2
0
0
0
0
0
0
0
0
2
2
0
0
2
1
2
2
0
0
0
0
0
3
0
2
0
0
1
1
0
1
0
0
0
2
2
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
3
2
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
2
0
0
2
2
0
0
1
0
0
2
4
0
0
0
0
1
0
0
2
0
4
0
0
0
0
2
0
0
1
0
1
0
0
0
0
2
0
0
0
0
2
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
1
0
0
0
0
1
1
0
1
2
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
1
0
0
1
2
0
1
2
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
1
1
0
1
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
2
2
2
1
0
2
0
1
2
0
2
2
1
1
0
1
0
0
0
0
0
2
0
1
1
0
2
0
0
0
0
0
2
0
3
1
0
1
0
2
0
0
0
1
0
1
0
0
2
0
0
0
0
0
1
0
0
3
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
2
1
0
0
1
0
0
0
2
1
0
1
0
2
1
1
0
0
0
0
1
1
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
2
0
2
0
0
0
3
0
0
0
2
2
0
2
0
0
2
0
0
0
0
1
1
1
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
2
1
2
1
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
4
1
0
0
0
1
0
0
0
1
0
0
2
0
1
0
0
0
0
1
0
3
1
0
0
0
0
2
0
0
0
2
2
0
0
1
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
3
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
1
0
2
1
0
1
2
0
1
2
0
2
0
2
2
0
0
0
0
0
0
0
1
0
0
1
2
0
2
0
1
0
1
0
2
0
0
2
0
2
0
0
0
0
0
0
1
1
1
0
1
1
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
1
0
0
0
1
0
1
0
2
1
1
1
0
0
0
1
2
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
4
0
0
2
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
2
0
2
0
0
0
0
0
0
1
0
1
0
1
0
0
2
0
0
0
0
1
0
1
0
0
0
2
1
0
0
0
0
2
2
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
1
0
0
0
2
0
2
2
0
1
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
3
0
2
2
0
0
3
1
0
0
0
0
0
0
2
0
0
3
2
0
0
0
1
0
6
0
1
0
1
0
0
1
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
1
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
1
1
0
2
1
1
0
2
1
0
0
0
0
0
0
0
2
2
2
0
0
0
1
2
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
2
0
2
0
1
0
2
0
0
0
0
2
1
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
1
1
1
2
0
2
0
0
1
1
0
1
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
1
3
2
0
2
0
0
1
0
2
0
1
0
4
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
2
1
1
0
0
2
0
1
0
0
1
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
2
0
1
1
0
1
0
0
2
0
6
1
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
2
2
0
0
0
2
0
0
1
0
0
1
3
0
0
0
2
2
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
2
2
0
0
1
2
0
2
1
0
2
0
0
1
1
0
0
0
2
0
2
0
0
2
2
0
0
0
0
0
0
1
0
0
0
2
1
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
1
2
0
0
0
2
2
0
0
0
0
0
1
0
6
0
0
0
1
2
0
1
0
2
0
0
0
2
0
1
1
0
0
0
0
0
0
0
2
0
2
1
0
0
1
2
0
0
0
1
2
0
1
0
0
2
0
1
0
1
0
1
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
8
0
0
2
0
3
0
0
0
1
0
0
1
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
4
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
3
1
0
1
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
1
0
1
3
1
0
0
0
1
0
0
0
2
0
0
1
0
2
1
0
0
0
1
2
1
0
0
2
2
2
0
0
1
0
0
0
2
2
0
3
0
0
0
0
2
0
0
0
0
1
1
0
0
2
1
0
2
0
0
2
0
0
2
0
0
0
0
2
0
2
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
2
2
0
3
1
1
0
2
1
3
0
2
0
0
0
1
0
2
0
0
0
0
2
0
1
0
2
2
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
2
2
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
2
1
1
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
4
0
2
0
2
2
1
2
2
1
0
0
0
0
0
1
1
0
2
1
0
0
0
0
0
1
0
0
0
0
2
0
2
1
2
0
2
0
0
0
1
0
2
0
1
2
2
0
0
0
0
0
2
2
0
2
0
1
0
0
0
1
0
2
6
1
0
2
0
0
1
0
2
2
0
0
0
2
2
2
1
0
0
1
0
0
0
1
0
0
1
0
0
1
1
0
0
1
2
0
0
0
0
0
2
1
1
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
2
1
1
1
0
0
0
0
0
2
1
2
0
3
0
0
0
0
0
0
1
1
2
1
2
0
4
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
2
2
0
0
0
2
0
0
2
2
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
3
0
0
0
0
1
1
1
0
0
2
2
0
0
0
0
2
1
0
0
0
0
1
0
0
2
0
0
1
2
0
0
2
2
0
0
0
2
2
0
0
0
0
7
1
1
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
2
0
0
0
0
1
2
0
0
0
1
0
0
0
2
1
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
2
2
0
0
2
0
1
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
2
1
0
0
2
0
2
1
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
2
1
1
0
1
0
0
1
0
0
2
0
0
0
0
0
2
2
0
0
0
0
2
0
2
1
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
4
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
3
0
1
0
1
2
0
0
0
0
2
1
3
0
0
0
0
1
0
2
0
0
0
0
2
3
0
0
3
0
0
2
0
0
2
0
0
0
2
0
2
0
4
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
2
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
3
1
0
2
0
0
0
0
2
0
0
1
1
0
1
1
1
2
0
2
1
1
0
2
0
0
2
2
0
0
1
1
0
1
0
2
1
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
1
2
1
1
0
0
1
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
1
1
3
0
0
0
0
0
0
0
0
1
0
0
1
0
4
1
0
2
0
1
4
0
2
0
1
2
0
0
5
2
0
0
1
3
1
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
3
0
0
0
0
0
2
0
0
0
2
0
0
1
0
2
0
2
0
2
1
0
0
0
3
0
0
0
2
0
2
1
0
0
0
2
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
3
0
2
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
2
0
2
0
2
2
1
1
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
3
0
3
0
1
0
2
0
2
0
1
6
2
0
2
1
2
2
0
1
1
0
1
1
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
1
1
0
0
0
0
0
0
1
2
0
1
0
0
1
0
1
0
1
0
0
0
2
1
2
0
0
2
0
0
3
0
2
2
1
2
1
0
2
2
0
2
0
1
1
0
0
0
0
0
0
0
3
0
0
0
1
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
2
2
0
0
2
1
2
0
0
0
1
0
0
1
0
0
0
0
2
0
3
0
0
0
1
0
0
0
2
0
0
2
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
2
0
1
2
0
1
0
2
2
2
0
0
0
0
0
0
2
2
0
1
0
0
2
0
0
0
0
1
2
0
0
2
2
0
2
2
0
1
2
0
0
0
0
1
1
2
1
0
0
0
0
0
0
0
1
1
1
0
2
3
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
1
0
0
7
1
0
0
1
0
1
0
1
2
0
0
0
1
0
0
2
0
2
0
1
0
0
0
1
3
0
2
2
2
1
0
0
1
0
0
0
1
2
0
0
0
1
0
0
0
4
0
2
0
0
1
0
2
1
0
0
1
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
1
0
0
0
2
1
1
0
1
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
6
0
0
0
0
2
0
1
0
0
0
1
0
2
0
0
0
0
3
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
2
0
2
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
1
2
0
0
1
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
5
0
0
1
1
2
0
0
0
1
0
1
0
0
2
0
1
0
0
2
0
0
1
0
1
1
1
0
0
1
3
0
0
2
1
0
1
1
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
4
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
2
1
0
2
2
0
0
0
0
0
0
0
0
1
2
0
0
3
2
2
3
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
2
2
2
0
0
0
0
1
1
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
2
2
1
3
0
0
0
2
0
0
2
0
0
0
2
2
0
1
0
0
1
0
1
1
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
1
0
0
0
3
2
0
7
0
2
0
2
0
0
2
2
0
2
1
0
0
2
2
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
2
0
0
0
2
2
1
0
0
2
0
0
1
2
1
0
0
0
2
3
1
0
1
0
2
1
0
1
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
2
0
0
9
0
0
0
0
0
0
0
1
2
11
1
0
0
0
1
2
0
2
0
1
0
3
3
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
3
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
2
2
2
0
0
0
2
0
0
2
0
0
0
0
0
2
1
0
1
0
2
0
0
0
0
2
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
1
2
0
1
0
1
2
1
1
6
0
0
1
1
0
2
0
0
0
0
1
2
0
7
0
0
1
0
0
2
4
0
0
1
0
0
1
1
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
1
0
2
0
2
0
0
0
0
0
0
1
2
1
0
1
0
2
0
2
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
2
0
1
0
0
1
2
1
0
0
1
1
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
2
2
0
0
0
2
0
0
0
0
3
0
0
2
0
0
9
0
0
0
1
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
1
2
0
2
0
1
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
2
1
0
0
0
0
0
2
0
1
0
2
0
0
0
1
0
1
0
2
0
1
0
0
1
0
1
1
2
0
0
0
1
2
1
0
1
1
0
2
0
0
0
2
0
0
1
0
0
0
0
0
2
2
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
1
0
1
0
0
1
1
1
1
2
0
0
0
0
0
0
2
1
0
0
0
1
0
0
1
2
2
1
2
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
4
1
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
1
2
1
2
2
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
2
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
2
2
0
0
2
2
1
0
0
0
0
1
1
0
1
0
1
0
0
0
0
2
0
2
0
0
0
1
1
1
0
0
0
0
0
2
3
0
0
1
0
0
0
2
0
1
0
0
2
1
0
0
0
0
0
1
1
1
2
1
0
0
0
0
0
2
1
0
1
0
0
2
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
2
2
0
2
0
0
0
0
0
2
2
2
1
0
0
3
0
1
1
0
0
0
2
0
0
0
0
0
1
2
0
0
2
0
1
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
1
2
0
1
0
0
0
0
1
0
0
0
2
0
1
0
1
0
1
1
0
2
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
1
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
2
0
2
2
0
0
2
0
1
1
0
1
0
2
0
1
0
1
0
2
0
0
0
0
0
0
0
1
2
2
2
1
0
1
0
0
1
0
1
0
2
0
0
2
0
0
0
3
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
2
2
2
0
0
0
1
2
1
0
0
0
0
0
1
2
1
1
0
0
0
0
2
0
1
0
0
0
2
1
0
2
1
2
0
0
0
0
1
0
1
1
0
0
0
1
1
0
0
0
2
0
0
1
0
0
0
1
0
1
1
0
0
2
0
1
0
0
0
0
0
0
2
2
0
2
1
4
0
0
1
1
0
2
1
2
0
0
1
0
0
1
0
2
2
0
0
0
0
1
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
2
2
0
1
2
0
0
1
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
1
1
1
2
1
0
2
2
0
0
0
0
0
0
1
0
0
1
0
2
0
1
0
1
0
0
0
0
2
0
2
0
0
0
2
3
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
3
1
0
2
1
0
0
0
1
0
0
0
0
0
0
0
2
1
0
1
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
1
0
4
1
0
2
0
0
0
0
2
1
0
0
2
0
1
0
2
1
0
0
0
0
1
1
0
3
0
0
1
2
0
0
0
0
2
0
2
0
0
0
0
1
0
3
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
1
2
0
0
2
1
0
1
2
0
0
0
2
0
2
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
1
2
0
2
2
0
0
0
0
0
0
3
1
2
0
0
2
2
0
0
0
0
2
0
0
0
0
0
1
4
2
0
0
0
0
1
0
1
2
0
0
3
0
0
3
0
1
2
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
2
1
2
1
0
0
1
0
1
0
2
0
0
1
0
0
1
0
0
2
0
0
2
0
0
1
0
0
0
2
1
2
0
0
0
2
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
2
0
2
1
1
2
0
1
2
0
0
0
2
1
0
0
1
0
1
1
0
1
0
0
0
0
1
1
0
0
3
1
0
0
0
2
1
0
0
0
1
0
0
2
1
2
0
0
0
2
0
0
0
2
0
0
0
2
2
0
5
1
0
0
0
2
0
2
2
0
1
0
0
2
1
0
0
0
1
0
2
1
0
3
0
0
1
1
2
0
0
1
1
0
0
0
2
1
1
0
0
2
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
1
2
2
0
0
0
2
0
0
0
0
1
2
2
0
0
8
0
0
1
0
2
1
0
0
0
0
1
2
0
0
0
0
2
1
1
2
2
0
2
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
1
4
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
2
2
0
0
0
1
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
2
0
2
0
0
2
0
0
1
3
0
0
1
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
2
0
0
4
0
0
0
0
1
0
0
3
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
2
0
1
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
4
1
2
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
1
2
0
0
0
0
0
0
0
1
0
0
2
0
3
0
0
1
0
3
0
3
2
0
0
1
2
0
0
1
0
0
0
0
2
0
0
0
1
1
2
1
0
2
0
1
0
1
0
2
2
0
1
0
0
2
2
1
2
2
0
0
0
0
1
2
0
1
0
0
0
1
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
5
0
2
1
0
0
3
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
2
0
2
4
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
1
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
4
0
0
0
0
0
0
1
0
0
0
0
1
0
2
2
0
1
0
2
0
2
0
0
0
0
0
0
0
1
0
1
0
1
2
0
0
0
0
2
0
0
0
2
2
0
2
0
2
0
1
2
2
0
0
3
0
0
0
0
0
0
0
2
0
1
0
0
0
1
2
0
0
0
0
0
0
2
1
2
2
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
1
1
0
2
1
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
4
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
2
0
2
1
2
0
0
0
0
0
0
2
1
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
2
0
0
0
2
1
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
2
2
0
1
2
1
0
0
0
2
1
2
0
2
0
1
1
0
1
2
2
0
1
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
5
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
3
0
0
0
2
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
1
2
2
0
2
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
1
0
0
0
0
1
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
1
0
0
0
0
2
0
0
1
0
0
2
1
2
2
1
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
2
1
0
0
2
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
2
0
0
1
1
1
1
0
0
1
4
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
1
2
0
0
1
0
2
0
0
0
0
4
0
1
0
0
0
2
2
0
0
0
0
2
0
0
1
0
2
1
1
1
1
0
2
2
0
0
0
0
0
1
1
2
0
0
2
1
1
0
0
0
0
0
0
2
2
0
0
0
1
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
5
0
3
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
1
0
3
1
0
0
1
0
0
0
0
0
0
0
2
0
0
2
1
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
3
2
0
0
1
0
0
0
2
2
0
2
0
0
1
0
1
1
0
2
2
2
2
0
0
1
1
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
1
0
1
0
2
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
2
0
0
2
1
0
2
0
0
2
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
2
0
6
2
2
0
0
0
0
2
2
0
0
0
0
2
1
0
0
2
0
3
0
2
1
0
2
1
0
0
0
0
3
2
0
2
2
1
0
0
1
0
0
0
1
0
2
3
0
0
0
1
0
1
1
0
1
0
0
1
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
2
2
0
1
0
2
0
0
1
0
2
1
1
0
0
0
1
0
0
2
1
0
2
0
1
1
0
0
0
1
0
0
1
2
0
2
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
1
0
2
0
0
0
0
0
2
0
1
2
2
1
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
1
2
0
0
0
0
0
1
0
2
2
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
3
0
3
0
0
3
0
0
2
0
0
0
1
0
0
2
0
0
0
0
2
1
0
2
0
0
2
0
1
1
0
2
0
0
0
1
0
0
1
0
0
0
0
2
1
4
2
0
0
0
0
0
0
0
3
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
3
0
1
0
1
0
2
0
0
0
2
0
0
6
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
1
1
0
0
0
1
0
2
0
0
1
1
0
2
0
1
0
2
0
0
0
0
0
0
0
1
0
2
2
0
0
0
1
1
0
2
0
2
0
2
2
0
2
0
0
0
0
0
1
1
1
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
6
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
2
2
0
1
2
0
1
0
0
1
2
2
0
2
0
0
0
0
0
0
0
2
1
1
0
2
0
0
0
1
0
0
0
1
0
1
0
0
0
1
1
0
0
0
2
2
0
0
2
1
0
0
0
0
2
2
0
1
0
4
0
0
0
0
0
0
2
2
1
0
0
2
1
0
1
0
2
2
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
1
0
0
0
0
1
0
1
0
0
2
0
0
0
1
0
2
0
0
2
2
0
0
2
2
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
1
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
1
0
3
2
0
0
0
0
0
0
2
0
0
1
3
0
1
0
3
2
0
1
0
2
0
1
3
0
0
2
3
2
1
0
0
0
0
1
2
0
0
1
2
2
0
0
0
0
2
1
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
2
2
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
2
1
2
0
1
0
5
1
0
0
0
0
4
0
0
0
2
0
1
0
2
2
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
2
2
2
0
2
0
1
2
1
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
2
0
2
0
0
0
2
0
1
0
2
1
0
0
2
2
0
0
2
0
0
2
0
0
0
2
4
0
2
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
2
2
2
0
2
0
0
1
0
1
0
1
0
1
0
1
0
0
0
2
2
2
2
0
1
0
2
1
0
0
0
0
0
0
0
0
2
1
2
1
1
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
2
2
0
1
2
0
2
0
0
1
1
0
1
0
0
2
2
0
0
1
2
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
2
1
0
1
4
1
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
1
0
0
0
0
3
0
0
0
2
1
0
0
0
0
1
0
1
1
0
0
0
0
2
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
1
0
0
0
2
0
1
0
3
0
0
2
1
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
2
1
0
0
0
1
0
2
0
0
0
0
0
0
2
0
1
0
0
1
1
5
0
2
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
2
0
1
2
0
2
0
2
0
1
0
5
0
0
0
0
1
2
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
1
1
0
2
0
2
0
2
1
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
1
0
2
0
0
2
0
1
1
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
1
1
0
2
0
0
4
0
0
1
0
0
0
0
0
1
0
3
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
2
0
0
2
1
0
0
0
0
0
0
0
0
2
2
0
2
0
1
0
0
1
2
1
0
0
0
0
0
0
0
0
1
0
0
0
2
1
1
0
2
2
1
0
0
0
0
0
0
1
0
0
1
1
0
2
0
0
1
1
0
0
0
0
0
2
0
0
0
4
1
1
0
0
0
0
2
0
0
0
1
0
0
2
0
2
1
0
0
0
0
1
0
2
0
2
1
1
1
2
2
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
2
1
0
0
2
2
1
0
0
1
2
1
2
2
0
1
0
0
0
0
1
0
0
1
6
1
2
0
1
2
1
0
0
5
1
0
0
1
0
1
1
2
0
0
0
0
1
0
1
0
0
0
2
0
2
0
1
2
0
1
0
0
2
2
0
0
0
0
1
1
0
0
1
0
7
2
2
0
1
0
0
3
1
0
0
2
0
0
1
2
0
1
1
1
0
0
2
0
0
1
0
2
1
0
0
0
0
1
1
2
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
2
0
2
0
2
0
1
0
0
1
1
0
0
0
0
1
0
0
2
0
2
0
1
0
1
0
0
0
0
3
1
1
0
0
0
0
0
0
1
2
1
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
1
0
0
0
2
0
0
0
0
1
0
0
0
2
1
0
1
0
0
0
2
0
0
2
0
0
2
3
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
2
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
1
2
0
0
0
3
0
0
0
0
0
0
0
1
1
2
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
2
2
0
0
0
0
2
2
2
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
3
0
0
0
3
0
2
0
0
0
0
2
2
0
0
5
1
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
3
0
0
1
0
0
0
0
0
0
3
2
0
1
0
2
0
0
0
1
1
0
0
1
0
0
2
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
1
0
2
2
0
0
0
3
0
0
0
0
1
0
1
0
2
1
0
0
0
0
0
2
0
0
1
2
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
4
2
0
2
2
0
1
1
1
0
0
0
0
1
0
2
0
2
0
0
1
1
0
3
4
2
1
2
0
0
0
0
1
2
0
2
0
0
0
2
0
3
0
0
0
0
0
1
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
1
0
0
0
0
1
2
0
0
0
1
2
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
3
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
1
0
1
1
2
0
0
0
3
1
2
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
4
0
0
1
2
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
2
0
2
2
2
0
1
2
2
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
1
1
1
0
0
0
2
0
0
0
0
1
1
1
0
0
2
0
0
3
0
0
2
0
3
0
0
0
0
0
2
1
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
2
0
1
0
1
0
0
1
0
2
0
0
0
1
0
0
0
1
2
0
0
1
1
1
0
2
1
0
0
0
0
0
0
1
2
2
2
0
2
0
2
0
0
2
1
4
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
2
9
2
0
2
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
2
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
1
2
0
1
2
1
0
3
0
2
0
0
2
0
4
1
0
0
4
0
2
0
2
0
0
1
0
0
0
0
0
0
2
2
1
0
1
0
0
0
1
0
1
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
1
1
1
3
2
0
0
0
2
1
0
0
2
1
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
3
1
0
1
0
1
0
0
2
0
0
0
0
0
0
0
2
0
2
2
0
2
0
0
1
0
0
2
0
2
0
0
0
0
1
1
0
1
2
1
2
2
1
1
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
2
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
1
2
1
0
0
2
0
0
3
0
2
0
0
0
1
1
2
3
2
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
2
0
0
2
1
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
2
1
2
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
3
1
0
2
1
0
0
2
0
3
0
2
1
0
0
1
0
0
1
2
0
0
0
0
0
2
2
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
2
1
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
2
0
1
0
0
0
0
1
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
1
1
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
2
0
1
0
2
1
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
3
1
2
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
2
0
0
0
2
0
0
0
0
0
1
0
2
0
0
1
0
0
2
1
0
2
0
0
2
0
0
1
0
0
2
0
0
1
0
2
0
1
1
1
1
0
2
0
2
0
3
0
0
0
1
1
2
0
0
1
0
0
0
0
0
2
1
0
2
0
1
0
0
0
0
0
0
4
0
0
3
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
2
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
1
1
2
1
2
2
2
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
2
1
2
0
0
0
0
2
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
2
0
0
2
0
0
1
0
0
0
0
0
2
0
1
2
3
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
1
2
0
0
0
0
5
2
0
0
0
0
1
0
2
2
0
2
0
0
2
2
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
2
1
0
0
0
0
0
0
0
2
0
1
2
0
2
1
2
0
1
0
0
1
0
2
1
1
1
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
2
1
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
2
2
0
2
0
0
1
0
0
1
1
0
1
0
0
2
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
3
0
2
0
1
0
0
0
2
0
0
0
0
0
1
1
1
0
2
1
1
0
0
0
1
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
3
0
2
2
0
0
0
0
0
0
0
0
3
2
0
0
0
1
1
0
2
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
2
1
0
1
0
0
0
0
2
0
2
1
1
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
1
2
2
0
0
0
0
0
0
1
1
0
2
0
2
1
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
3
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
2
3
0
1
0
1
0
0
0
0
0
0
2
0
0
1
1
3
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
2
1
0
0
1
3
0
0
0
2
0
0
0
1
0
0
0
0
1
0
1
0
0
0
3
0
0
0
1
0
0
1
0
0
0
2
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
3
0
0
0
0
0
1
0
1
1
0
0
2
0
1
1
0
1
1
0
0
1
0
0
0
1
0
0
2
0
2
0
0
2
0
0
2
0
0
0
0
0
0
1
2
1
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
2
2
0
0
0
0
1
0
0
1
1
0
0
1
0
0
1
0
0
0
0
1
0
2
0
2
0
0
1
0
3
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
2
1
0
0
1
0
4
0
1
0
0
0
0
0
0
0
0
2
0
1
2
2
0
0
0
2
0
1
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
2
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
2
1
2
0
0
0
2
3
0
0
1
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
1
0
0
1
0
0
2
0
0
2
0
0
0
2
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
1
1
0
1
2
0
0
0
0
1
1
2
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
2
0
2
0
0
1
2
0
0
3
1
0
0
0
2
0
0
2
0
1
0
2
0
0
0
0
0
0
1
1
1
2
0
0
0
1
0
0
1
0
0
0
3
1
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
2
0
2
2
0
0
0
0
0
3
0
1
2
4
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
3
0
2
2
0
0
0
2
0
0
0
0
0
0
2
0
3
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
2
0
0
0
1
2
0
2
0
1
0
0
6
0
1
0
0
1
1
0
2
0
0
1
1
2
0
0
0
1
0
1
2
0
1
2
0
0
1
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
1
0
0
2
2
2
0
2
0
2
0
2
2
0
0
2
0
0
0
0
2
1
0
5
0
0
1
2
0
1
0
4
0
0
2
1
2
2
1
0
0
0
3
0
0
1
0
0
0
0
0
0
3
0
1
2
2
2
1
0
0
0
2
1
0
0
0
0
0
0
2
0
1
0
1
2
0
1
3
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
1
3
0
0
0
0
0
0
2
0
1
2
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
1
2
0
0
2
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
4
0
1
3
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
1
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
2
1
1
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
2
0
0
1
1
2
1
2
1
0
0
0
2
0
1
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
1
0
0
0
0
0
3
1
0
2
0
0
1
2
0
0
2
1
3
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
1
0
0
2
0
1
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
1
1
1
1
1
1
0
1
0
0
1
2
0
0
0
1
0
0
0
0
0
1
1
0
0
0
2
0
0
2
0
1
0
0
0
2
0
1
0
0
0
0
2
2
2
1
0
0
0
0
0
0
1
2
0
0
1
3
0
0
0
0
1
1
0
0
2
0
0
0
1
3
2
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
1
2
0
1
0
0
1
0
0
0
0
1
0
0
0
2
0
1
0
2
2
0
0
0
0
0
2
0
0
1
0
2
0
0
2
2
1
0
0
0
1
1
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
2
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
1
2
2
0
0
0
2
0
0
0
1
1
0
1
0
0
0
0
3
1
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
1
0
0
2
0
2
0
0
1
0
0
1
1
0
0
1
0
0
0
2
0
1
0
2
0
1
0
0
1
1
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
3
0
1
4
0
0
2
0
2
0
2
1
0
0
0
0
1
0
0
0
2
2
1
0
0
2
0
1
0
0
0
2
1
0
0
0
1
2
0
7
0
2
2
0
0
2
1
0
2
1
0
1
0
0
0
0
0
2
0
2
0
1
0
0
3
0
0
0
2
0
0
0
0
2
1
2
0
0
2
1
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
2
2
1
0
0
0
1
0
0
1
0
2
0
0
2
0
0
2
0
2
0
2
0
0
0
2
1
0
0
0
0
2
1
2
0
0
0
1
2
0
0
0
0
2
0
1
0
0
0
2
0
1
0
1
0
0
0
0
2
0
1
0
0
0
3
3
0
0
0
0
1
0
1
0
0
1
1
3
0
0
0
0
0
3
0
2
0
0
1
0
0
3
0
0
0
1
1
0
2
2
0
2
2
2
0
2
0
2
2
0
0
1
0
0
0
0
0
0
1
0
0
1
3
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
1
2
0
0
0
0
1
1
1
0
0
1
1
0
1
1
1
0
0
0
2
5
0
0
2
1
0
0
0
3
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
3
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
2
2
0
0
2
0
2
0
0
1
3
0
1
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
2
3
1
2
0
1
0
2
0
0
0
3
0
0
2
0
1
0
2
0
0
4
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
1
1
0
0
1
0
0
1
0
0
1
0
1
0
0
1
0
2
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
1
0
0
0
0
1
0
1
2
1
0
0
3
2
1
2
2
2
0
0
0
0
2
0
0
2
2
1
0
0
0
1
0
0
0
2
1
0
0
2
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
3
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
2
2
2
1
2
2
1
3
0
0
0
2
0
0
0
3
2
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
1
0
1
1
0
2
0
0
0
0
0
0
0
2
2
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
2
1
2
0
1
0
1
1
0
0
1
0
0
0
0
2
0
1
1
0
0
0
0
2
0
1
0
0
0
3
1
0
0
1
3
0
2
0
0
0
0
1
0
0
4
2
0
0
1
1
2
2
0
0
0
0
1
0
2
0
2
1
1
0
0
1
1
2
0
0
2
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
2
1
0
8
2
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
3
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
2
2
0
2
0
2
0
2
0
1
0
0
0
1
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
1
1
1
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
3
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
2
0
1
2
1
0
1
0
0
0
0
0
1
0
1
2
0
0
0
2
2
0
0
1
4
0
0
0
0
1
0
2
2
0
0
0
0
1
2
0
0
0
0
1
0
0
0
1
0
2
1
0
0
0
2
2
0
0
1
0
3
0
0
0
1
0
2
1
2
0
0
0
7
0
1
0
0
0
1
0
0
0
0
2
1
0
0
2
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
2
1
1
0
2
0
0
0
2
0
0
1
0
0
0
0
0
2
0
2
0
0
2
0
0
2
0
0
0
0
3
0
0
2
0
1
0
0
0
1
0
0
0
1
1
0
0
0
2
0
0
1
2
1
0
0
0
3
0
2
1
0
0
0
0
2
0
2
0
1
0
0
0
0
3
2
0
0
2
2
0
1
0
0
0
1
0
0
0
0
2
0
2
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
3
0
0
1
0
0
1
0
2
0
1
0
0
1
1
1
0
0
3
0
0
0
0
0
1
1
0
3
0
2
0
3
0
1
0
0
0
2
0
0
2
0
0
3
0
2
0
0
0
2
0
0
0
1
1
2
2
0
0
0
2
0
0
0
1
0
0
1
0
0
2
0
1
0
2
0
0
2
2
0
0
1
0
0
0
2
1
1
0
0
2
0
0
1
0
0
0
0
2
1
0
2
0
0
0
2
1
0
0
1
0
0
0
0
0
6
0
2
0
0
1
2
0
4
2
0
0
0
0
0
0
0
0
1
2
1
0
1
1
0
1
1
2
0
0
2
0
2
0
1
0
3
1
2
0
2
0
0
0
0
1
0
3
0
0
1
0
0
0
1
0
1
2
0
0
0
0
2
0
0
0
0
0
0
3
0
1
0
0
0
1
0
1
1
2
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
2
0
0
1
0
1
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
1
0
1
0
0
0
3
6
0
0
0
2
1
1
0
0
0
3
3
0
0
0
3
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
1
0
0
1
2
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
2
0
0
3
2
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
2
1
1
0
0
2
0
0
0
0
2
0
0
0
0
0
1
1
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
1
2
0
1
1
1
0
2
1
0
0
0
2
0
0
1
0
0
0
0
0
1
0
1
0
2
0
0
1
0
2
0
2
1
0
0
0
0
1
0
0
0
0
0
0
3
3
0
0
3
2
2
0
0
0
2
0
1
0
1
1
0
0
2
0
2
0
0
0
2
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
1
0
0
1
0
1
0
0
2
0
3
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
1
1
1
0
0
0
0
0
0
0
1
1
0
0
1
2
0
0
0
0
1
0
0
1
2
0
0
1
0
0
1
0
0
0
0
0
0
1
0
2
2
1
0
0
2
3
0
0
1
1
5
1
0
2
0
0
0
0
0
0
1
0
0
0
2
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
2
0
1
0
0
1
1
0
2
0
0
1
0
0
0
2
0
0
1
2
0
1
0
0
0
2
0
0
2
4
0
0
0
1
2
2
0
0
1
1
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
1
1
0
1
0
2
0
0
0
2
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
4
2
1
2
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
1
0
1
1
0
0
2
2
0
2
0
0
2
0
1
4
0
0
1
0
0
1
0
3
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
2
0
2
0
0
1
0
0
0
0
0
0
1
1
0
0
5
0
2
0
0
1
0
0
2
0
1
0
1
2
2
0
2
0
0
0
0
1
2
0
2
1
0
0
0
0
0
0
0
0
0
1
0
2
2
3
0
2
2
0
0
0
1
0
2
0
0
1
1
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
2
1
2
0
0
0
2
0
1
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
1
2
0
0
0
0
1
0
1
0
0
2
0
0
2
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
1
0
0
2
2
0
0
0
0
0
0
1
2
1
0
1
0
0
1
2
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
2
0
3
1
2
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
2
0
0
1
0
2
0
0
4
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
1
0
0
3
0
2
3
0
2
0
1
0
0
0
1
0
1
2
2
1
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
1
0
0
2
0
0
0
0
0
0
2
2
0
3
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
2
1
1
0
1
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
1
3
0
2
2
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
4
0
2
2
1
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
3
2
1
0
0
0
1
0
1
0
2
0
1
0
2
0
3
0
0
2
0
0
0
0
1
0
0
0
0
2
1
0
0
1
0
0
2
0
2
2
0
0
0
1
0
0
0
0
2
0
5
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
2
1
0
2
0
2
0
1
0
0
0
2
0
0
0
0
2
2
0
0
0
1
0
2
0
0
0
2
2
0
6
0
0
0
2
0
0
2
1
0
0
0
0
0
0
2
0
1
1
2
0
4
2
0
1
2
1
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
4
0
0
0
0
2
0
0
1
1
0
2
0
2
1
0
1
0
1
1
0
0
0
0
0
0
1
1
0
1
1
1
0
1
0
1
0
2
8
0
0
2
1
1
1
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
4
0
0
0
3
0
1
0
0
0
0
1
2
0
1
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
4
0
0
0
2
1
1
0
0
0
1
2
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
3
0
2
0
0
0
1
1
2
2
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
1
2
0
1
0
0
0
2
0
0
0
0
1
0
0
0
1
1
0
0
1
1
0
0
0
0
2
0
0
0
2
0
2
2
0
0
2
1
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
2
0
0
0
1
0
2
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
2
0
1
0
1
0
1
0
2
0
0
0
3
1
0
1
4
0
0
1
0
2
0
0
2
1
0
0
0
2
2
1
0
0
0
0
1
0
2
0
2
0
1
0
0
0
0
2
1
0
0
2
0
0
0
0
0
3
1
0
0
5
1
1
0
2
0
0
0
2
0
1
1
0
1
0
0
1
2
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
1
0
0
0
2
2
0
0
0
1
0
1
0
1
0
2
1
2
0
2
0
0
0
0
2
0
0
1
2
0
0
2
0
0
0
0
0
1
2
0
0
1
0
1
0
1
2
0
0
2
1
0
0
0
2
1
0
0
0
5
2
1
1
1
2
0
0
0
0
1
0
2
1
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
1
2
0
0
0
1
0
1
0
0
1
4
0
0
0
2
3
2
1
0
0
0
0
0
1
1
0
0
0
0
0
1
2
0
3
0
0
0
1
0
0
2
1
0
0
0
1
0
1
0
2
0
0
0
0
0
7
0
0
0
0
0
0
0
2
1
0
0
0
2
2
1
0
0
0
0
0
0
1
2
1
0
0
1
0
0
0
0
0
4
2
2
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
6
2
4
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
2
0
0
0
0
1
0
1
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
1
3
0
0
0
0
3
0
0
0
2
1
0
1
0
2
1
2
0
1
0
0
1
0
0
0
2
0
2
1
1
2
0
1
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
2
2
0
0
2
2
1
2
0
3
1
0
0
2
2
1
0
0
0
1
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
1
2
0
3
0
0
2
1
0
0
2
2
2
0
0
0
0
3
0
0
0
1
0
0
0
2
0
0
0
0
3
1
0
0
0
2
0
2
2
0
0
0
2
0
0
1
0
0
0
1
0
1
0
2
0
1
1
0
0
0
1
0
0
0
2
2
2
1
1
0
0
0
0
0
0
2
0
0
2
1
0
1
0
0
0
0
1
3
0
0
0
1
2
0
1
0
0
0
1
4
2
2
0
1
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
2
0
1
0
1
0
0
2
0
2
1
1
2
0
0
2
2
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
3
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
1
0
0
0
1
0
0
0
0
2
1
1
2
0
0
0
0
0
0
0
0
0
2
0
1
3
0
0
0
1
0
0
1
2
1
1
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
2
2
1
1
2
2
2
0
1
0
0
0
1
1
0
3
2
2
2
0
0
2
0
0
2
0
1
0
2
0
0
2
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
1
2
4
2
0
1
0
0
2
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
2
2
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
1
0
1
2
0
0
0
1
0
0
0
2
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
1
3
0
0
2
0
0
0
0
1
0
0
2
1
0
0
1
0
0
1
0
2
1
0
0
0
2
1
0
0
2
0
0
1
0
0
1
1
0
0
0
1
0
0
2
1
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
2
0
1
0
0
0
0
0
1
0
0
0
2
0
1
0
0
3
0
0
0
0
2
0
0
1
0
0
1
0
4
1
0
0
0
0
0
0
2
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
1
0
2
0
0
0
0
2
0
0
0
1
1
0
0
1
0
0
3
4
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
2
0
1
1
0
0
0
1
0
0
2
0
0
0
2
2
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
3
2
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
2
0
0
0
0
1
0
1
2
1
1
0
0
0
0
0
0
1
0
0
2
0
0
1
0
1
2
0
2
4
2
0
0
0
0
3
0
0
0
0
1
1
0
2
2
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
1
3
0
1
1
0
0
4
0
0
0
2
0
1
2
1
2
1
1
0
0
0
0
2
3
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
2
2
0
1
0
1
1
0
3
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
2
2
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
2
3
0
2
0
0
1
1
0
0
0
0
0
0
2
1
3
1
1
1
1
0
1
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
1
2
0
0
0
2
1
2
0
0
5
0
1
0
0
0
0
1
0
0
0
0
0
1
2
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
2
1
2
0
0
1
1
1
0
2
2
2
0
0
2
0
0
3
0
0
1
0
1
2
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
3
0
0
2
0
2
2
2
0
0
2
0
1
0
0
0
0
2
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
1
0
4
0
0
2
0
2
2
0
1
1
1
0
2
0
1
1
0
0
0
1
3
0
0
2
0
1
2
0
1
0
0
0
2
0
0
0
0
2
1
0
2
0
2
1
0
0
0
1
0
0
2
1
1
0
2
3
2
1
0
1
0
1
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
1
0
0
2
0
1
0
0
2
0
2
1
0
2
0
1
0
3
0
2
0
0
0
0
0
0
2
2
0
2
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
1
1
0
2
1
0
0
3
1
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
1
0
5
1
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
1
1
0
1
0
0
1
0
1
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
2
2
1
5
1
3
0
0
0
0
1
0
2
2
1
0
0
0
1
0
0
0
0
0
0
1
1
1
0
1
0
0
1
0
0
4
1
2
0
0
0
1
2
2
0
0
0
0
0
2
3
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
1
0
0
0
1
2
1
0
0
2
2
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
3
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
2
2
0
0
1
0
0
0
2
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
2
2
2
0
0
2
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
1
0
0
2
2
0
0
1
1
0
2
0
2
0
0
0
0
0
0
1
2
0
0
0
2
0
0
2
3
2
0
0
0
1
1
1
0
2
0
2
0
0
0
1
0
2
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
3
2
0
0
0
0
2
0
1
0
0
2
1
0
0
2
0
1
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
1
4
0
0
0
1
0
2
0
1
2
0
2
1
0
0
0
0
0
0
0
3
1
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
2
1
0
2
0
0
0
1
0
1
1
0
2
5
0
0
0
0
1
0
2
2
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
1
0
0
0
2
0
0
0
1
0
0
0
1
3
0
0
0
0
0
2
2
0
0
0
1
0
2
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
1
1
2
0
0
2
0
2
1
0
0
1
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
2
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
1
0
0
1
0
0
0
0
0
2
1
1
0
2
2
1
2
0
0
0
1
0
0
1
0
0
1
0
2
1
0
2
1
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
1
2
0
0
2
1
1
0
1
0
3
0
2
1
1
1
0
1
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
1
1
1
0
0
2
0
0
0
3
0
3
0
0
0
5
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
3
0
0
0
0
0
2
1
2
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
2
1
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
2
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
1
0
2
0
0
0
2
1
0
0
0
0
0
0
1
0
2
1
2
0
0
1
0
0
0
0
3
0
1
0
2
0
1
1
2
0
0
1
0
0
2
0
0
0
1
0
1
0
2
1
0
0
0
0
0
1
1
0
0
3
0
0
0
1
0
0
0
0
1
0
2
0
0
1
0
0
0
1
0
1
2
3
0
0
0
0
1
0
1
2
0
0
1
0
1
1
1
0
0
0
1
2
0
2
0
1
1
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
2
0
2
0
0
0
1
0
2
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
1
0
0
0
2
2
0
2
0
0
0
1
0
0
2
0
0
2
0
0
0
0
1
3
0
2
2
0
0
0
0
0
1
0
0
1
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
1
2
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
1
2
1
2
4
0
0
1
2
0
0
1
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
2
0
0
2
0
0
1
0
0
0
0
0
0
2
2
1
0
0
0
0
2
1
0
0
0
0
0
1
3
0
2
0
0
0
0
0
0
1
6
0
2
2
1
1
2
0
0
0
2
0
0
0
0
1
2
0
0
1
0
0
0
0
2
2
0
1
0
0
0
1
0
2
2
0
0
0
0
2
0
2
2
0
0
0
0
1
2
0
1
0
0
2
1
2
0
1
0
0
3
0
0
0
0
0
0
0
0
0
3
0
0
2
1
1
1
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
2
6
0
1
0
1
0
0
0
1
0
0
0
1
0
0
1
1
0
0
2
1
0
1
0
2
3
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
2
2
0
0
0
0
3
0
0
0
0
0
0
0
3
0
1
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
1
0
0
0
0
0
2
0
0
0
1
2
2
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
2
1
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
2
2
0
0
2
0
0
0
2
0
0
2
0
2
0
2
0
0
0
1
0
0
2
0
0
1
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
1
0
1
3
0
1
1
0
1
2
0
0
2
0
2
1
2
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
1
1
0
0
2
0
1
0
0
1
0
2
0
1
0
0
0
0
0
0
0
2
1
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
2
0
0
0
2
0
1
0
1
1
3
0
2
0
1
0
0
2
0
1
0
0
2
0
0
0
2
0
0
2
3
0
2
0
0
1
1
0
1
1
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
3
0
2
0
0
0
1
2
2
1
2
2
0
0
0
0
1
0
3
0
0
1
0
3
2
0
2
2
0
0
0
1
0
0
2
2
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
2
0
0
2
0
0
1
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
3
0
0
0
0
0
2
0
1
1
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
3
0
0
4
2
0
2
1
2
2
1
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
2
2
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
1
1
2
0
0
2
0
0
0
0
2
0
0
2
1
0
0
0
0
1
0
0
2
0
0
0
0
2
0
2
0
0
0
1
0
2
1
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
0
2
2
0
4
0
0
1
0
0
1
0
0
0
2
1
0
0
1
1
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
2
2
0
0
0
1
2
0
0
2
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
2
0
2
0
0
1
0
0
0
0
1
0
3
0
1
0
2
2
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
3
1
0
1
0
0
0
2
0
0
0
0
0
0
1
0
3
0
0
1
0
1
2
0
0
0
0
1
0
1
0
0
0
2
0
1
1
1
0
0
1
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
2
0
1
0
0
0
0
0
0
1
0
1
2
0
3
1
1
2
0
2
0
0
0
0
0
0
0
0
2
2
0
1
0
0
2
0
0
1
0
0
1
0
2
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
3
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
3
0
1
1
2
0
2
0
1
0
0
0
0
2
2
0
2
0
0
0
0
1
0
0
1
1
1
2
0
1
0
0
0
1
0
2
0
2
2
2
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
1
2
0
2
0
0
0
0
0
3
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
2
2
0
0
0
1
3
0
2
0
0
2
0
0
2
0
0
0
0
2
0
2
0
2
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
2
0
0
2
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
1
0
2
2
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
2
2
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
1
1
5
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
5
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
2
2
0
0
1
0
1
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
4
1
0
1
0
0
0
0
1
0
1
2
0
0
2
2
0
0
1
0
1
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
2
0
2
0
0
0
3
0
0
0
0
0
2
1
2
1
0
0
2
0
1
0
2
1
0
0
0
0
0
0
0
1
0
1
1
2
1
0
0
0
0
0
1
0
0
1
1
0
2
2
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
3
3
1
0
0
0
0
0
2
0
0
0
1
0
0
0
3
2
0
0
0
3
0
5
0
0
2
2
0
0
0
0
0
2
0
0
1
1
3
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
3
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
2
0
0
1
2
0
0
0
0
2
2
2
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
2
1
2
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
2
2
1
1
1
0
2
1
0
2
0
1
0
1
1
0
0
3
2
0
2
0
0
2
0
2
0
0
1
2
2
0
0
0
0
0
1
3
0
0
0
1
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
2
1
2
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
1
2
0
1
0
0
1
2
0
1
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
3
0
2
0
0
2
0
0
4
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
1
0
2
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
3
2
0
0
0
0
0
0
1
0
0
0
1
0
0
1
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
1
2
0
0
3
0
1
0
1
1
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
3
0
0
0
1
0
0
0
0
2
2
0
0
2
0
0
0
0
0
1
0
1
0
0
1
2
0
0
0
0
0
0
2
1
1
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
1
0
1
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
2
0
0
1
0
0
0
2
2
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
3
1
2
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
1
0
0
0
1
0
2
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
2
1
2
0
3
0
0
1
1
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
1
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
2
0
0
0
0
1
4
0
0
0
0
0
0
0
2
2
0
0
3
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
2
5
0
2
1
1
2
2
0
0
0
1
2
0
0
0
1
0
0
0
0
0
1
3
0
0
2
0
0
0
0
0
0
0
1
1
0
1
1
0
1
1
0
2
0
0
2
2
0
1
0
0
0
0
2
0
0
0
0
0
0
2
1
0
2
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
2
4
1
2
0
6
1
0
0
0
0
0
3
1
2
4
0
1
0
2
0
0
0
0
0
0
0
0
0
1
3
0
0
0
1
0
0
0
0
2
2
3
2
2
0
1
0
0
0
1
0
2
0
0
1
0
0
0
0
0
2
1
0
0
2
0
2
1
1
0
0
0
2
2
3
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
3
2
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
2
2
2
1
1
0
0
0
0
1
2
0
1
0
0
1
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
1
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
2
0
0
0
2
1
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
2
0
0
1
0
0
1
0
2
1
2
0
0
3
0
0
0
0
0
0
7
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
2
1
2
0
0
0
0
0
1
0
0
1
0
1
3
0
0
0
0
0
0
1
0
3
1
0
0
1
0
0
2
1
0
0
2
0
0
0
1
1
1
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
3
1
0
0
0
3
2
1
0
1
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
2
1
0
1
2
0
1
0
1
1
0
0
0
0
1
0
1
1
0
2
0
1
3
2
2
0
0
0
2
0
3
0
0
1
0
1
0
0
5
0
2
0
2
2
2
1
0
0
0
2
0
1
4
2
0
2
0
0
0
2
0
0
0
0
2
0
2
2
0
0
0
0
2
0
0
0
0
1
1
0
0
1
0
0
0
1
2
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
1
0
0
0
1
2
1
0
0
0
0
0
0
1
0
2
0
2
0
0
1
0
0
0
0
0
2
1
0
1
1
1
2
0
1
0
0
0
1
0
0
2
0
2
0
2
0
2
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
1
1
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
1
1
1
1
1
2
0
0
2
0
0
3
0
0
3
2
0
1
2
0
0
0
0
1
2
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
2
0
0
2
0
0
0
1
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
1
0
0
2
1
0
0
1
0
0
0
0
0
2
0
1
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
2
1
0
0
4
0
0
0
1
2
0
0
0
0
1
0
0
1
1
0
1
1
1
0
1
2
0
0
0
1
1
1
5
0
1
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
1
0
0
0
1
2
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
1
1
1
1
2
0
0
1
0
2
0
1
0
0
3
0
2
2
0
1
0
2
0
0
0
0
0
2
0
2
0
0
1
1
2
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
2
1
0
1
0
2
0
1
0
0
3
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
1
0
2
3
0
1
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
2
1
0
0
2
0
0
0
1
0
0
2
0
0
0
0
1
2
3
0
2
0
5
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
2
0
1
0
0
1
2
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
3
1
2
1
0
1
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
1
2
1
2
0
0
1
0
1
2
0
2
0
0
2
2
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
2
0
2
1
0
0
0
0
0
0
2
2
0
0
0
2
1
0
1
0
0
3
2
0
2
1
2
0
0
0
1
0
1
0
0
0
0
1
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
2
0
0
0
1
0
0
2
0
0
0
2
2
2
0
0
0
0
0
0
1
2
0
0
2
0
0
2
0
0
0
0
0
0
2
0
2
0
2
0
0
1
1
0
0
0
0
2
0
2
0
0
0
2
0
2
1
0
0
0
0
0
1
0
0
0
0
1
0
2
1
0
1
0
2
0
0
1
0
7
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
1
2
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
2
1
0
1
2
1
1
1
2
0
1
1
1
0
0
0
2
0
2
2
0
1
2
2
2
0
0
1
1
0
0
0
0
0
0
2
1
0
0
0
3
0
0
0
1
2
0
0
0
0
0
0
2
0
2
0
5
0
0
0
0
1
2
3
0
0
1
3
0
1
0
0
0
0
0
2
1
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
1
1
2
2
0
1
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
2
2
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
2
0
1
1
1
2
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
2
2
2
2
0
0
0
2
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
1
0
0
0
0
0
1
1
0
1
2
0
3
0
0
2
0
0
0
0
0
0
1
0
1
0
0
2
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
2
0
2
2
0
0
1
1
0
0
2
2
0
1
1
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
2
1
0
2
0
2
1
0
0
0
0
0
0
0
1
0
0
0
1
1
2
2
0
0
2
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
2
0
1
1
0
1
0
0
1
0
3
0
0
1
0
0
0
0
0
0
0
0
1
0
3
0
0
0
1
1
0
0
2
0
0
0
2
0
1
1
1
2
0
0
0
0
2
0
0
0
1
0
3
0
1
0
1
2
0
1
0
0
0
0
0
0
0
0
2
1
1
0
1
0
1
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
1
1
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
1
0
0
0
1
0
1
2
0
0
0
1
1
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
1
1
3
0
1
0
0
2
1
1
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
1
3
2
2
1
0
0
0
0
0
1
0
0
0
0
0
2
1
0
2
1
0
0
1
0
0
1
1
0
1
0
0
2
0
2
2
0
0
0
0
6
0
0
0
0
2
1
1
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
1
0
1
2
0
0
0
2
0
1
1
0
1
0
2
1
0
1
0
0
0
2
1
0
0
1
1
0
0
1
0
0
1
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
5
0
0
0
0
0
0
0
1
0
2
1
1
0
0
3
0
0
0
0
2
0
1
1
0
2
0
0
0
0
2
2
0
1
1
0
0
2
0
2
0
0
0
1
0
0
2
1
0
0
0
0
0
1
2
2
0
0
1
0
0
0
1
3
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
3
0
0
2
2
0
0
1
0
0
0
1
1
0
0
0
2
2
0
1
0
0
0
0
2
0
0
0
0
2
0
2
0
2
0
0
0
0
1
0
0
0
2
2
2
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
1
0
2
0
2
0
0
2
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
1
2
0
0
0
0
1
2
0
2
0
0
0
0
3
0
0
0
0
0
1
0
1
0
0
0
1
0
1
2
0
2
0
0
0
1
2
1
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
2
1
0
0
1
1
0
0
0
2
0
0
2
0
0
2
0
0
1
2
0
1
0
2
0
2
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
2
0
1
0
2
1
0
3
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
3
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
1
2
0
1
0
1
0
2
1
0
0
2
0
0
2
0
1
0
0
1
0
0
0
0
0
2
2
0
0
2
0
0
0
0
1
0
0
2
0
2
4
0
0
1
0
0
0
0
2
2
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
1
0
0
3
0
0
0
2
0
0
2
3
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
2
1
0
0
0
0
2
1
0
0
0
2
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
1
0
2
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
2
2
2
0
1
0
0
1
0
0
2
0
0
1
0
4
1
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
2
0
0
0
2
0
1
3
1
0
1
0
0
0
1
2
0
0
0
0
1
0
1
0
1
1
2
0
0
0
0
0
0
0
1
2
2
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
1
0
1
0
2
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
2
0
2
0
0
0
1
1
1
2
0
0
0
1
0
0
0
1
2
1
1
0
0
2
0
0
0
2
0
0
0
0
2
0
2
0
1
0
2
2
3
1
1
0
0
0
0
0
0
1
0
0
0
2
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
1
3
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
2
0
1
1
0
0
2
0
0
0
0
1
2
0
0
0
0
2
1
0
0
0
0
0
1
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
2
0
2
0
2
0
0
0
2
0
1
2
2
0
0
0
0
0
0
2
0
0
0
0
1
1
0
2
1
0
2
0
6
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
2
1
0
0
0
1
3
2
0
0
2
0
0
1
1
0
1
1
0
0
2
0
0
1
0
0
0
0
1
0
0
2
0
1
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
3
0
0
1
1
0
0
1
0
2
0
1
0
0
1
0
0
2
0
0
1
0
2
0
0
2
1
0
1
0
0
0
0
2
2
1
0
0
0
0
3
1
0
0
2
2
0
0
1
1
2
0
0
1
0
0
2
1
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
1
2
0
0
0
1
0
2
2
0
0
0
0
3
1
0
0
0
1
0
0
1
6
0
0
2
0
0
1
2
0
1
0
0
0
0
1
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
1
0
2
0
2
0
2
0
0
0
1
0
1
0
2
0
1
2
2
3
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
2
1
0
0
0
1
2
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
1
0
0
2
0
1
2
1
1
0
0
0
2
0
0
0
0
1
0
1
1
0
0
0
0
2
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
3
2
0
0
2
1
0
0
0
1
3
0
0
0
0
1
0
1
0
6
0
0
0
0
0
3
1
0
0
0
0
2
0
0
0
2
1
0
2
0
1
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
2
0
0
0
0
0
6
0
0
0
0
0
1
0
0
0
1
2
1
0
1
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
2
1
0
0
0
1
1
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
1
0
3
0
0
0
3
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
3
0
0
2
0
0
2
0
0
0
0
0
0
1
1
0
1
1
0
1
2
0
2
0
0
0
3
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
1
0
1
0
0
0
0
0
0
1
3
0
0
0
2
0
1
2
1
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
5
0
2
0
1
3
2
0
2
0
0
2
1
0
0
0
0
0
1
1
2
0
0
0
0
1
0
2
0
0
0
1
2
0
0
2
0
0
0
0
2
0
0
2
1
0
1
1
0
0
1
1
0
0
0
2
2
0
0
0
2
3
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
1
0
1
2
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
2
0
0
2
0
0
1
0
1
0
0
0
2
0
0
2
0
1
0
1
0
0
0
2
0
2
2
1
2
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
2
1
0
2
0
2
0
0
2
0
0
1
0
0
0
0
0
1
2
0
1
0
0
1
1
0
0
0
2
2
0
0
0
0
2
1
0
0
0
2
1
0
0
0
2
0
0
2
0
0
0
0
0
4
2
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
2
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
3
2
3
0
0
1
0
2
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
2
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
1
2
0
1
0
0
0
2
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
2
1
0
1
1
0
1
2
2
7
0
2
0
4
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
1
2
0
0
2
1
1
0
0
0
3
0
2
0
0
0
0
0
1
0
1
0
0
1
2
0
0
2
11
0
0
0
0
0
0
0
2
1
0
0
3
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
1
2
1
2
0
0
1
2
0
0
0
0
2
0
2
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
2
0
0
1
1
0
0
0
0
0
0
0
0
2
1
1
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
1
0
1
2
0
1
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
2
0
0
0
0
0
2
0
0
1
0
2
2
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
2
0
0
2
0
2
0
1
1
0
1
0
2
2
0
1
0
0
0
1
0
0
3
0
2
0
2
1
1
2
0
1
1
2
0
0
2
1
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
2
2
0
2
2
0
4
1
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
2
0
2
0
0
0
2
0
0
0
0
1
2
0
2
0
1
2
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
1
1
0
0
0
0
0
0
5
0
0
0
0
2
0
0
0
0
0
2
1
0
2
2
2
0
0
0
0
0
2
2
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
2
1
0
0
0
0
0
2
3
1
0
0
1
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
3
0
0
4
0
2
2
3
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
2
0
2
1
0
4
0
5
0
0
1
1
0
4
0
1
2
0
0
0
0
0
3
0
1
1
0
1
0
2
0
2
2
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
1
0
1
9
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
2
0
2
0
1
0
2
0
2
1
1
1
0
0
1
0
0
0
0
1
1
1
0
0
0
1
1
0
1
1
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
4
0
2
0
0
0
0
0
1
0
2
2
1
1
0
0
3
0
0
0
0
0
1
0
0
0
1
0
0
1
2
0
1
0
0
1
2
0
0
1
4
0
0
3
0
1
4
2
0
1
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
1
1
1
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
3
2
0
0
0
1
0
0
2
0
0
2
1
0
0
0
0
1
1
0
3
0
2
0
0
0
1
0
4
1
1
0
0
2
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
4
0
1
1
1
2
0
0
0
0
2
0
2
2
0
0
0
3
0
1
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
1
0
1
2
0
0
1
0
0
0
0
1
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
1
2
2
0
0
0
1
0
0
2
0
1
0
0
0
1
0
0
0
0
3
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
1
1
0
0
0
0
0
0
1
1
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
1
0
0
0
2
1
0
2
0
2
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
2
0
1
0
1
0
0
2
0
1
2
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
2
0
0
0
0
2
2
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
2
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
2
2
1
0
2
2
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
3
0
0
1
2
0
0
2
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
1
0
2
0
0
1
0
0
1
0
1
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
2
3
0
0
0
1
1
2
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
3
2
2
0
0
0
1
1
0
2
0
1
0
0
0
0
1
1
1
0
0
0
2
0
0
0
0
0
2
0
1
2
2
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
2
2
0
2
1
2
1
0
0
2
0
2
0
0
0
2
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
2
0
3
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
1
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
6
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
2
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
3
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
2
2
1
0
0
0
2
0
0
2
1
1
0
2
0
2
0
0
2
0
0
1
0
1
0
1
2
0
3
0
2
0
0
0
0
0
2
0
0
2
0
3
1
0
2
0
0
0
0
0
0
2
0
0
2
1
0
2
0
0
0
0
0
2
0
1
0
0
0
2
3
0
1
0
0
1
2
0
10
0
1
0
0
1
2
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
1
0
2
0
0
2
2
0
0
2
0
0
2
2
1
0
0
1
1
0
0
0
2
1
1
0
0
1
0
0
1
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
9
1
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
1
2
0
0
2
0
0
1
0
2
0
1
2
1
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
1
0
0
0
1
2
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
1
1
2
0
1
0
1
0
0
0
0
1
0
0
1
0
3
1
0
2
0
1
2
0
2
0
0
0
3
0
0
0
2
0
2
0
1
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
3
0
0
1
0
0
0
3
0
3
1
0
0
0
0
2
1
0
0
2
1
2
1
0
1
0
1
2
1
0
0
2
0
0
0
1
0
0
1
1
1
0
0
2
0
0
1
1
0
0
2
1
1
0
1
0
0
2
0
0
0
0
2
1
0
0
1
0
0
1
0
0
0
2
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
2
0
0
2
0
1
0
2
0
0
1
0
0
1
2
0
0
0
0
0
0
1
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
1
2
1
0
0
0
2
0
3
0
0
1
1
2
1
0
0
0
0
0
0
0
0
1
0
2
2
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
1
0
2
0
3
1
0
0
0
0
0
0
0
2
2
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
1
0
0
1
0
0
0
2
0
2
0
0
0
1
0
0
0
2
0
1
0
0
0
2
0
1
0
0
0
2
0
0
2
2
0
0
2
2
1
0
1
0
0
1
0
1
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
1
0
0
2
0
0
2
1
0
0
0
0
0
0
1
0
0
4
0
1
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
1
2
0
0
2
0
0
0
2
1
0
0
1
2
1
2
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
2
0
0
2
2
0
0
0
0
2
2
0
1
1
2
0
0
0
0
0
0
1
2
2
0
1
0
0
1
0
0
0
2
1
0
0
0
0
2
2
2
2
0
0
0
2
2
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
1
0
2
2
2
2
1
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
2
0
0
0
2
1
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
1
2
0
3
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
1
2
0
2
0
0
0
0
1
1
2
0
1
0
1
1
1
0
1
0
2
1
0
1
0
1
1
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
1
0
2
2
0
1
0
3
0
0
1
3
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
2
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
2
1
0
0
0
2
0
2
2
0
0
2
2
0
0
2
0
1
1
0
2
2
0
0
0
1
0
0
0
2
1
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
1
2
2
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
1
1
1
0
0
0
0
2
1
3
1
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
3
0
0
2
3
2
2
1
0
0
1
0
2
0
1
2
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
3
0
0
0
0
0
1
2
0
1
0
1
0
2
3
0
0
1
0
0
1
0
0
1
0
1
1
0
0
0
0
1
0
2
0
0
2
0
0
0
2
0
1
1
0
2
0
0
0
0
1
0
1
1
0
0
2
1
0
0
3
0
0
1
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
1
0
2
1
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
1
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
3
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
2
1
0
0
0
0
0
0
0
0
1
2
2
0
0
0
2
1
2
1
1
2
1
0
1
3
0
1
2
0
0
2
1
1
0
1
0
2
2
0
0
0
1
2
0
0
2
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
10
0
0
0
1
1
0
0
2
0
0
1
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
3
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
3
1
0
0
0
0
1
0
0
1
0
0
0
2
1
0
0
0
0
0
4
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
2
1
0
2
0
0
0
0
0
0
0
3
0
0
0
2
0
3
2
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
2
0
2
0
1
0
0
0
2
0
1
1
0
0
3
1
0
0
0
0
0
1
1
2
0
1
0
0
1
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
2
0
1
4
2
0
0
0
0
0
0
0
4
0
2
0
0
2
0
0
0
1
0
1
0
2
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
3
2
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
1
0
1
1
0
0
0
0
0
1
2
0
0
1
2
0
0
0
0
0
2
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
2
0
1
0
0
0
0
0
0
2
2
1
0
2
0
2
0
2
2
0
2
2
0
2
0
0
2
0
2
0
0
0
0
0
0
1
1
2
0
0
0
1
0
0
0
2
1
0
0
2
2
0
0
3
0
2
0
1
0
2
0
2
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
6
0
2
1
0
1
0
0
0
2
0
0
0
1
0
0
0
2
2
0
0
1
2
0
0
2
0
0
0
1
0
0
2
2
0
1
3
0
2
0
0
2
0
1
0
0
2
0
2
1
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
1
0
0
0
0
0
1
3
0
0
1
0
0
0
0
1
0
0
0
0
0
1
3
0
0
0
0
2
0
1
1
0
1
0
0
0
0
0
1
0
0
0
2
2
1
2
2
2
2
1
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
1
0
1
2
2
0
0
1
0
0
0
0
0
1
0
2
0
0
3
0
2
1
0
0
0
0
0
0
0
1
0
0
3
2
0
1
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
2
1
0
0
0
0
2
0
1
1
1
1
0
2
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
0
2
0
2
0
0
1
1
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
2
1
0
0
0
0
0
2
0
6
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
2
2
0
0
2
0
2
0
2
0
2
0
0
2
2
1
0
0
0
0
0
2
1
0
1
0
2
0
1
0
0
0
0
0
2
0
2
0
2
2
0
1
2
1
0
0
0
0
1
0
0
0
0
2
0
1
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
6
0
2
2
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
1
1
0
0
2
0
0
0
0
3
0
2
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
2
0
0
2
0
6
0
0
0
0
1
3
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
1
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
1
0
0
0
1
0
1
0
1
0
1
0
0
0
0
2
1
0
3
1
2
0
1
2
0
0
0
0
4
0
1
0
0
0
0
1
0
0
1
0
0
0
2
0
2
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
1
0
0
1
2
0
0
2
1
0
2
0
2
2
0
2
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
2
2
1
0
1
0
0
0
0
0
1
0
0
0
0
2
2
2
0
4
2
0
3
0
1
2
2
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
1
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
2
0
2
0
0
0
1
3
0
0
0
1
2
0
0
2
0
0
0
0
0
2
2
0
0
1
2
0
1
1
2
0
0
0
0
1
0
2
2
0
0
0
1
0
2
1
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
1
0
0
1
2
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
1
2
2
0
6
2
0
2
0
0
0
0
0
3
0
1
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
2
1
1
0
0
0
0
0
1
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
2
0
2
2
0
0
0
0
0
0
0
3
0
0
0
0
0
2
1
0
0
0
1
2
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
2
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
2
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
3
0
0
0
0
1
0
0
1
0
3
0
2
0
0
0
0
1
1
0
0
0
1
0
0
1
2
0
1
0
0
0
0
1
1
1
0
0
0
0
3
0
0
0
0
1
0
2
0
0
0
0
0
1
0
1
2
1
0
0
2
0
1
1
0
0
2
0
0
2
1
2
0
3
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
1
2
0
0
2
1
1
0
2
0
1
0
0
0
0
0
1
0
1
0
0
2
2
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
4
1
0
1
1
2
2
2
0
1
1
0
0
2
0
0
3
0
0
1
0
0
0
0
0
0
7
0
2
0
0
0
0
4
0
0
0
2
0
0
0
2
0
1
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
2
1
0
0
1
0
0
2
2
0
1
0
0
0
2
0
0
5
1
0
0
1
1
0
0
0
1
0
0
0
2
0
2
1
0
0
0
0
0
0
1
0
1
0
1
0
0
2
0
2
0
0
0
0
0
0
0
1
1
0
0
0
1
0
2
0
2
0
1
0
0
1
0
0
0
3
0
0
0
0
0
2
0
1
1
2
1
2
0
2
2
1
1
0
3
0
0
0
0
0
2
2
0
3
0
2
1
0
0
1
0
0
1
2
0
0
2
0
1
0
0
0
0
0
1
0
2
1
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
1
0
1
0
1
1
0
5
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
1
1
0
0
0
5
1
2
0
2
1
0
0
0
0
0
0
2
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
1
0
0
0
1
2
0
0
2
1
0
0
0
0
0
0
0
1
1
0
0
2
0
1
4
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
2
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
2
0
1
0
0
1
0
2
0
0
0
1
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
2
0
7
1
0
2
2
0
0
0
2
0
2
2
0
2
0
0
0
0
1
0
0
0
1
0
1
2
0
1
2
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
5
1
3
0
0
1
0
0
1
1
2
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
2
0
1
1
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
2
0
0
1
0
0
2
0
0
0
0
0
2
0
0
2
2
0
0
1
1
0
0
0
2
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
1
0
0
1
0
0
2
0
2
0
1
0
1
0
0
0
3
1
0
2
1
2
0
1
0
0
0
2
1
2
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
2
1
1
2
3
0
1
0
0
0
0
0
0
0
1
0
0
3
0
1
2
0
0
1
0
0
0
0
0
0
0
0
2
0
2
2
4
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
3
1
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
2
0
1
1
1
1
0
0
0
0
1
0
0
0
0
2
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
2
0
0
1
2
0
1
0
0
2
0
2
3
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
1
2
0
0
0
0
0
2
0
0
2
0
0
2
0
0
2
1
3
0
0
3
0
0
0
2
0
0
1
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
4
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
1
0
1
0
0
2
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
3
1
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
3
0
0
0
4
1
0
0
2
0
4
0
0
0
0
1
1
0
0
0
1
1
2
0
4
1
1
0
1
0
0
3
1
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
2
2
0
0
0
0
0
1
2
0
0
1
0
1
0
0
0
2
0
0
0
0
0
2
1
0
1
0
0
0
1
0
1
1
2
2
2
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
1
1
2
3
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
1
0
1
2
0
0
0
1
1
0
0
1
0
0
0
1
2
0
2
0
0
0
0
0
0
1
2
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
3
0
0
1
1
2
0
0
0
0
0
1
2
0
0
1
1
0
0
0
2
0
1
1
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
1
0
0
0
1
1
0
2
0
1
0
0
0
0
0
0
1
2
0
0
2
3
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
2
0
0
2
0
0
0
0
0
0
0
1
1
1
0
2
0
0
0
0
1
0
0
2
0
1
0
0
1
0
0
1
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
3
0
2
0
1
0
2
0
1
0
1
0
2
0
2
0
1
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
1
0
0
0
0
0
1
0
0
2
1
0
0
0
2
0
0
0
1
0
1
1
0
0
7
0
1
0
2
1
0
4
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
2
0
2
0
2
1
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
1
1
1
2
0
0
0
0
0
1
2
9
0
1
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
3
0
0
0
1
0
0
0
0
1
0
2
0
2
0
0
0
0
0
1
2
0
0
0
0
3
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
3
0
1
0
2
1
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
1
3
2
0
0
1
1
0
0
1
2
0
2
0
0
0
1
0
0
0
2
0
1
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
1
1
2
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
2
1
4
0
0
0
0
2
0
0
0
0
1
5
0
1
0
0
0
0
6
0
0
0
0
3
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
1
0
2
2
1
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
2
2
0
0
0
0
0
0
1
1
0
0
3
0
0
1
2
0
0
0
0
1
0
1
2
0
0
2
0
2
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
2
2
0
2
0
2
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
2
1
1
1
0
0
1
0
3
0
0
2
0
0
0
0
2
1
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
1
0
0
1
0
0
3
1
0
2
0
0
1
0
0
0
0
0
0
2
0
2
2
0
0
0
2
1
0
2
1
0
0
0
0
0
0
2
0
1
2
0
1
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
2
3
0
1
0
2
0
3
0
2
0
2
0
4
2
2
0
1
0
0
1
0
0
2
0
0
0
1
0
2
0
0
0
0
2
1
0
0
0
0
1
0
2
1
0
2
0
0
0
2
2
1
2
0
0
0
1
1
0
1
0
0
2
1
0
0
0
0
0
0
2
0
2
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
1
0
1
0
2
0
1
2
0
1
1
0
0
1
0
2
0
2
0
0
1
0
0
0
0
0
0
2
2
1
0
0
2
0
1
0
2
0
0
1
1
0
0
0
0
0
1
0
0
0
2
2
0
0
1
0
1
2
0
0
0
2
0
0
0
2
2
0
0
0
0
1
1
0
0
2
0
0
1
1
0
0
0
1
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
5
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
1
0
1
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
4
0
0
0
2
0
0
0
1
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
1
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
1
2
2
0
1
0
0
1
0
0
2
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
2
0
0
1
0
1
0
0
1
0
0
3
0
0
0
2
0
0
0
1
0
0
1
0
2
0
1
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
2
1
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
6
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
2
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
2
0
1
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
2
2
0
2
0
0
1
1
0
0
1
0
0
0
2
0
0
2
0
0
0
0
2
2
2
1
1
1
0
2
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
2
2
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
1
0
2
0
1
0
0
0
0
2
0
2
0
0
2
0
0
0
2
0
1
0
0
1
0
1
1
0
0
0
0
2
1
0
0
0
0
0
2
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
1
0
0
0
0
1
1
1
0
1
0
0
0
0
1
0
1
0
2
3
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
2
0
0
1
1
0
0
3
3
0
0
1
2
1
0
0
2
0
2
1
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
1
0
3
2
0
1
0
0
0
1
0
0
2
0
0
2
1
0
0
2
0
2
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
2
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
2
1
0
1
0
0
1
0
2
0
0
1
0
3
0
2
0
0
0
0
1
2
2
0
1
1
0
0
0
0
0
0
1
2
0
0
1
0
2
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
2
0
1
2
0
0
0
0
0
1
0
0
2
0
2
0
0
0
2
2
0
0
1
0
2
0
0
0
0
1
1
0
1
0
0
0
0
1
2
0
0
1
1
0
0
0
0
2
0
0
0
0
2
0
0
1
1
0
0
1
2
1
0
0
0
0
2
0
1
0
1
1
2
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
1
1
0
1
1
0
1
0
2
0
0
1
0
2
0
2
0
1
2
0
2
0
1
0
0
2
1
1
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
1
2
0
0
2
0
0
0
0
0
0
0
0
2
3
1
3
2
2
2
0
3
1
0
0
0
2
2
2
1
1
0
0
1
0
0
0
1
0
2
0
2
0
2
0
3
1
0
0
0
0
0
0
0
2
2
0
2
2
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
1
3
0
1
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
1
0
1
1
1
2
0
1
0
2
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
2
2
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
1
0
2
0
0
0
1
2
0
0
0
0
2
1
0
4
0
1
2
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
1
0
1
0
3
2
1
0
2
0
2
0
0
2
2
0
2
0
0
3
0
0
1
2
0
0
0
2
2
1
0
0
2
0
0
0
0
3
3
1
0
0
2
1
0
0
0
1
0
2
0
1
2
3
0
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
1
0
2
1
0
0
0
2
1
0
0
0
0
0
1
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
1
2
0
0
1
2
4
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
2
2
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
4
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
1
0
0
0
2
0
0
2
2
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
3
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
1
2
0
0
4
0
0
0
1
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
2
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
2
0
5
1
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
1
0
0
2
1
0
1
0
2
0
0
2
1
2
1
0
0
2
0
2
2
2
1
0
0
0
2
1
0
2
0
1
0
2
0
1
0
0
1
1
0
0
1
2
2
0
0
2
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
1
2
1
0
2
2
0
2
1
1
0
1
0
1
0
0
2
0
0
1
0
0
0
0
2
0
1
0
0
0
0
2
0
0
2
3
2
1
1
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
4
0
0
0
0
0
2
1
0
2
0
0
1
0
1
0
0
1
2
0
0
0
0
0
0
1
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
3
0
0
2
0
0
0
1
0
2
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
1
1
0
2
0
0
0
0
2
1
2
0
1
0
0
2
0
0
2
0
1
0
3
0
2
0
0
0
2
0
0
1
1
0
0
3
1
0
1
0
2
0
0
2
0
0
0
2
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
1
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
1
2
0
2
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
1
0
2
0
0
0
0
1
2
0
2
0
0
2
0
2
2
2
0
0
0
1
0
2
0
0
2
0
1
0
1
0
0
1
0
2
1
0
0
0
0
0
2
2
0
2
2
0
0
1
0
0
1
1
0
1
1
0
1
4
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
2
2
2
1
0
1
0
2
0
1
0
0
0
0
2
1
2
2
0
1
0
0
2
0
0
0
0
0
0
2
0
1
2
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
2
0
2
2
0
1
2
2
0
0
2
0
0
0
0
0
1
0
0
0
2
0
1
0
1
1
2
0
0
1
0
0
0
0
0
1
0
2
0
0
0
1
0
0
2
0
0
2
0
3
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
2
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
2
0
1
0
0
2
0
1
3
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
3
3
0
0
0
2
0
0
0
0
0
3
0
0
1
0
0
1
2
0
2
0
0
0
0
2
0
1
2
1
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
3
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
5
0
0
0
1
1
0
0
1
0
2
1
0
1
0
0
0
0
0
0
5
0
0
0
2
0
0
2
0
0
2
0
0
0
0
2
2
0
2
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
1
0
2
2
0
1
0
0
2
0
0
0
0
1
0
1
0
0
2
2
2
1
0
0
1
0
1
0
1
1
1
2
0
0
1
2
0
0
0
0
0
0
0
1
1
0
2
2
1
0
0
0
2
1
2
0
0
3
0
0
0
0
1
1
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
4
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
2
2
1
0
0
0
0
0
1
3
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
3
0
1
0
0
0
0
2
0
1
1
0
0
2
2
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
2
1
1
0
0
2
0
2
0
0
0
3
0
0
0
1
2
0
0
0
0
0
4
2
2
0
2
0
0
0
1
1
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
2
0
0
0
0
1
0
0
2
2
2
1
0
2
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
6
0
0
0
0
1
0
0
0
0
0
1
0
0
2
2
2
1
0
3
2
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
2
0
0
2
0
1
0
1
1
1
0
0
2
1
0
0
0
2
0
0
1
1
0
1
1
1
0
0
0
2
0
0
1
2
0
0
1
0
2
2
0
0
0
0
0
2
1
1
2
1
0
3
0
0
0
0
0
0
0
0
0
2
0
0
1
1
2
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
2
1
2
0
0
1
2
0
0
0
1
0
13
0
2
0
1
0
2
2
0
2
1
0
0
1
2
1
0
2
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
2
0
0
1
2
0
0
1
0
4
0
0
0
0
0
2
1
2
0
2
0
0
0
0
0
2
4
1
0
0
0
0
1
0
2
2
2
1
0
0
2
0
0
1
2
0
0
0
0
0
2
1
1
0
1
0
0
2
0
0
0
1
0
0
0
0
1
1
0
0
0
2
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
1
2
1
0
0
1
0
1
0
0
1
1
2
1
2
2
1
1
0
0
0
1
0
1
0
2
2
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
2
0
2
0
1
1
0
0
0
0
2
0
0
2
2
0
1
1
0
2
1
0
1
1
0
1
2
1
0
1
0
1
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
1
0
0
0
0
1
0
0
0
2
3
0
3
0
2
0
0
0
0
0
1
1
2
0
0
0
0
0
0
1
2
0
2
0
9
0
0
2
0
0
0
1
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
3
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
1
0
1
2
0
0
0
0
3
0
2
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
4
0
0
3
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
3
1
1
0
2
0
0
0
1
1
0
1
0
0
0
0
3
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
2
0
0
2
0
1
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
1
2
0
2
2
0
0
2
0
0
2
2
2
0
2
0
1
0
0
0
2
2
1
0
1
1
2
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
2
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
3
0
1
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
2
0
0
0
0
0
0
2
0
6
0
0
0
1
0
0
0
1
0
2
0
0
0
3
0
0
0
0
0
2
0
0
0
1
0
0
1
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
3
1
2
0
1
2
2
2
0
1
0
0
1
0
2
1
0
0
3
0
1
2
0
1
0
2
0
0
2
0
0
0
1
2
0
0
0
0
1
1
2
0
2
1
2
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
1
3
2
1
1
0
4
1
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
4
0
1
0
2
0
0
1
0
0
2
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
2
0
0
0
1
2
0
2
0
1
2
0
0
0
0
0
0
2
0
0
1
11
2
0
1
1
0
0
2
1
0
0
2
0
0
0
3
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
3
1
0
0
2
0
1
0
0
1
2
0
0
2
1
0
0
0
1
0
2
0
0
2
1
0
2
0
3
1
2
0
2
0
3
0
0
3
3
2
0
2
1
1
1
0
0
1
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
2
0
1
0
1
0
0
1
0
0
1
0
1
0
0
0
1
0
1
2
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
3
0
0
0
2
0
0
0
1
1
0
0
2
2
0
1
2
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
1
0
1
0
2
0
0
0
0
2
3
0
0
0
0
0
2
6
0
0
0
0
1
0
1
0
1
1
0
1
2
0
0
2
0
0
0
2
2
0
0
0
1
0
0
1
0
0
1
0
2
0
1
0
0
0
0
0
1
0
2
0
0
0
2
0
2
0
1
0
1
2
0
2
0
1
1
1
0
2
0
2
1
0
2
0
2
2
2
2
2
2
0
2
0
2
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
1
0
1
2
1
2
0
0
0
0
2
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
2
2
0
2
1
2
1
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
3
0
1
1
0
0
0
1
0
1
1
0
1
0
1
1
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
1
0
2
0
0
0
1
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
1
0
1
0
0
1
0
2
2
0
0
0
2
2
2
2
0
0
0
1
0
0
0
0
1
2
1
0
0
1
0
0
0
0
0
1
0
2
1
0
0
1
0
0
0
1
1
1
0
1
0
0
1
0
2
0
2
0
1
0
0
1
0
0
0
2
1
0
1
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
2
1
0
0
0
1
0
0
1
2
1
0
3
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
1
0
2
2
0
0
1
0
2
2
1
0
0
0
0
0
0
0
2
1
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
1
0
4
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
1
2
0
1
0
0
1
0
0
0
0
1
0
2
1
1
0
0
0
0
0
0
2
0
0
1
0
9
0
1
1
2
0
2
0
0
0
1
5
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
2
0
1
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
1
1
0
4
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
3
0
2
0
1
0
1
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
3
0
0
0
2
0
0
5
2
1
3
0
0
0
1
2
0
0
0
1
2
0
0
3
1
1
2
0
0
0
1
1
0
0
1
1
0
2
0
0
0
2
0
4
0
0
0
0
0
1
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
2
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
1
2
0
1
1
1
0
0
3
0
2
0
0
0
0
0
0
1
2
2
0
0
0
0
0
2
2
0
2
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
3
0
1
2
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
2
2
0
2
2
0
1
0
0
2
0
0
0
1
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
2
0
0
1
0
1
0
1
0
0
2
0
1
0
0
0
2
0
1
1
1
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
1
2
1
0
0
0
0
0
1
2
1
0
0
0
1
1
0
0
2
0
0
0
0
2
0
2
0
0
2
0
1
0
2
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
2
0
0
0
1
1
0
1
0
0
2
1
0
0
0
2
0
0
1
0
1
3
0
0
0
0
0
0
1
0
2
3
0
0
2
1
0
3
0
0
2
0
1
0
1
0
0
0
0
2
2
2
0
1
0
1
0
2
0
0
0
1
0
0
1
0
0
0
0
0
3
1
0
0
1
0
1
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
1
0
1
2
0
2
2
0
0
0
0
0
0
2
2
0
0
0
0
2
0
1
0
1
0
1
0
1
1
0
0
0
0
3
0
0
0
0
1
1
0
2
1
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
2
2
1
0
0
0
2
0
1
0
0
0
2
0
0
0
1
0
2
1
0
1
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
2
3
0
1
2
0
0
0
0
2
2
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
2
0
0
2
2
2
0
1
0
0
0
0
2
1
2
1
2
1
0
0
1
0
0
1
0
1
1
0
0
2
0
0
0
0
0
2
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
2
0
0
2
0
0
0
2
1
3
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
1
2
0
0
0
2
1
0
0
0
0
0
0
0
2
1
0
2
2
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
1
1
0
0
0
1
2
0
2
0
1
1
0
2
0
0
1
3
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
2
1
1
0
2
2
2
0
1
2
0
0
1
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
1
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
1
1
2
0
2
0
0
0
0
2
0
0
2
0
0
1
0
0
2
0
0
2
2
1
1
1
0
1
0
0
0
0
1
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
2
0
1
3
0
0
0
0
2
1
0
0
1
0
0
0
0
3
2
2
0
2
0
2
0
0
0
2
0
0
0
0
2
0
0
1
1
0
0
0
1
0
0
0
0
0
3
1
0
1
1
0
2
0
0
0
0
0
2
0
0
0
0
2
2
0
2
0
3
0
1
1
1
0
0
1
0
3
0
0
0
1
0
2
0
0
1
0
1
0
0
0
0
1
2
0
2
1
0
0
0
1
2
0
0
0
0
0
0
0
4
2
0
0
0
2
0
1
2
2
6
2
2
0
0
1
1
3
0
1
0
0
1
0
0
0
2
0
0
0
2
1
0
0
1
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
2
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
2
2
2
1
0
0
0
2
2
1
1
0
1
0
0
2
2
2
0
2
0
2
0
0
0
0
0
0
0
0
5
2
1
1
3
0
0
1
0
0
0
1
1
1
0
1
2
0
1
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
1
0
2
0
0
2
1
7
1
0
2
0
0
0
1
0
0
1
3
1
1
0
0
2
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
1
1
1
2
0
1
1
1
0
0
2
2
0
2
0
0
1
2
2
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
2
1
0
0
1
2
0
0
2
1
0
0
2
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
1
0
2
0
2
0
1
2
0
0
0
0
0
0
0
0
1
0
0
4
1
0
5
2
0
1
2
2
0
2
1
0
1
1
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
1
0
1
0
2
0
0
1
1
0
0
3
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
2
0
0
0
2
3
0
0
0
0
0
0
0
1
2
1
0
0
2
0
1
2
0
0
0
1
2
0
2
0
0
0
0
0
1
0
2
2
1
1
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
1
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
2
0
1
2
0
1
0
0
1
2
0
0
0
0
1
2
2
0
0
0
0
2
0
1
2
2
0
0
0
0
2
0
2
0
3
0
1
0
2
2
0
0
0
2
1
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
2
2
0
2
2
0
3
0
0
0
0
3
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
7
0
0
0
0
0
0
0
0
0
1
0
5
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
2
2
2
0
0
0
0
0
1
0
0
1
0
1
1
1
0
0
0
1
2
1
0
1
0
1
0
0
0
0
2
1
2
0
0
0
0
2
2
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
2
0
0
0
2
0
0
1
0
0
2
0
0
3
0
0
0
2
2
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
2
1
1
0
1
0
1
0
0
0
0
2
0
0
2
0
1
0
2
0
1
0
1
0
2
0
0
2
0
2
1
1
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
1
3
0
0
0
1
0
0
0
2
2
0
3
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
2
2
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
2
0
0
0
0
0
0
1
1
0
2
2
0
0
0
0
0
0
2
0
0
0
3
0
2
0
0
0
1
0
0
0
1
0
0
2
2
0
1
0
0
2
2
1
0
0
0
1
0
0
2
0
0
1
2
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
1
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
1
0
2
0
1
0
0
2
0
0
0
0
1
0
0
0
0
2
0
1
0
0
1
0
0
2
2
0
2
1
0
0
1
1
0
0
0
0
0
2
0
0
0
0
2
0
1
1
0
0
1
1
0
0
1
2
0
0
0
0
0
2
0
3
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
2
0
2
1
0
1
0
0
0
0
0
2
0
0
2
0
0
0
1
1
0
0
1
0
2
1
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
2
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
2
0
1
0
0
0
2
0
2
0
1
0
0
2
0
1
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
1
1
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
2
1
0
0
0
1
0
1
0
0
2
0
2
2
0
0
1
2
0
1
0
0
2
0
2
1
2
1
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
1
1
0
1
0
1
1
0
0
1
2
2
0
0
0
0
0
0
2
1
2
0
4
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
8
0
0
0
2
0
0
2
0
2
0
0
0
0
1
0
2
0
0
0
1
0
0
0
2
2
0
0
2
0
0
5
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
1
0
0
0
2
1
0
2
2
0
1
1
0
0
0
0
0
0
0
0
2
0
0
1
0
1
3
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
3
0
1
0
2
1
0
0
0
0
0
2
0
0
0
0
0
1
0
4
1
0
0
0
0
1
0
0
1
1
0
1
0
4
0
2
0
0
0
0
0
2
2
0
2
0
2
1
0
2
0
1
1
0
2
2
2
0
0
1
0
0
0
2
0
0
2
1
0
0
0
2
2
0
0
0
0
2
1
0
0
2
0
1
2
0
1
1
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
2
0
0
0
0
2
0
0
0
1
1
0
0
1
0
2
0
2
0
3
1
0
0
0
2
2
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
3
1
0
0
2
0
0
3
3
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
2
0
2
1
1
1
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
2
0
3
2
0
2
0
2
0
0
0
1
0
1
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
2
6
2
0
0
0
0
0
1
0
1
1
1
2
2
2
1
0
2
0
0
0
0
0
1
2
0
0
1
0
2
0
0
1
0
1
0
0
1
2
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
2
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
3
1
0
0
1
0
0
2
2
0
0
2
1
0
1
2
0
0
3
1
2
0
0
1
0
1
2
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
1
2
1
1
2
0
0
0
0
2
2
0
2
0
0
0
2
1
0
1
0
1
0
0
0
1
0
1
1
0
0
0
1
0
0
0
1
1
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
1
0
0
0
4
1
0
0
0
1
0
0
0
0
0
0
2
4
0
1
2
2
0
0
3
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
4
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
2
5
2
1
0
1
2
0
0
1
2
1
0
0
0
0
1
1
0
2
0
0
0
0
0
1
0
1
2
1
1
0
1
0
0
2
4
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
1
0
0
0
0
0
1
1
0
4
0
0
0
2
0
0
0
1
0
0
1
0
0
1
0
2
2
1
0
0
0
1
0
0
2
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
3
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
2
1
0
0
0
2
0
2
1
2
2
0
0
0
0
0
0
1
1
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
2
2
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
1
2
2
0
0
0
0
1
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
1
2
0
0
2
0
0
0
0
1
1
0
0
3
0
0
1
0
4
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
1
0
2
0
0
5
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
1
1
0
0
1
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
1
0
0
0
0
1
1
0
0
1
2
0
0
0
0
0
0
0
1
2
0
1
0
0
0
2
0
0
2
7
0
0
0
0
0
1
0
3
0
0
1
0
0
3
1
2
0
0
0
2
0
0
2
0
0
0
0
0
2
0
3
1
0
0
0
0
1
0
0
0
1
1
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
3
0
0
2
0
2
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
2
0
0
2
2
1
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
1
2
3
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
1
0
0
0
1
1
0
1
1
0
0
0
4
1
0
0
2
0
0
2
0
0
0
0
0
2
0
2
2
3
0
0
0
0
0
0
2
0
0
1
0
0
2
0
1
0
1
2
2
2
0
0
2
0
1
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
2
2
0
3
0
0
2
0
1
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
1
3
1
2
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
1
0
2
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
2
2
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
2
0
2
0
1
0
2
0
1
4
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
2
1
2
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
2
2
0
0
2
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
2
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
3
2
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
2
1
5
0
1
0
2
2
1
4
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
1
0
2
0
0
0
2
0
0
0
0
0
2
0
1
1
1
1
1
0
1
0
1
0
0
1
0
0
0
0
0
2
1
0
0
0
1
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
3
1
0
0
1
1
0
0
1
0
0
2
0
0
0
0
0
0
1
2
1
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
2
1
1
2
0
2
2
0
0
1
1
2
0
1
1
1
0
0
2
0
5
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
2
2
0
2
1
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
2
0
0
0
0
1
0
3
2
0
1
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
3
2
0
2
0
0
0
0
0
1
0
0
0
0
1
1
1
1
3
4
0
2
1
0
0
0
2
0
1
0
0
0
2
2
2
0
0
2
0
0
1
0
0
1
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
1
0
0
1
1
0
1
0
0
0
0
2
3
2
2
2
0
0
0
0
0
0
1
1
0
0
0
2
2
2
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
1
0
1
0
1
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
1
1
1
0
2
1
2
0
0
2
0
0
0
0
0
2
0
0
1
2
0
0
1
1
1
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
2
1
0
1
0
2
0
1
0
0
0
3
1
1
0
2
2
0
2
1
0
0
2
1
1
0
1
2
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
3
0
0
0
1
2
2
0
0
0
0
2
0
0
0
0
0
1
0
1
0
2
0
0
1
0
2
1
0
0
2
0
0
0
0
0
1
0
2
2
0
1
0
2
2
0
8
0
0
0
1
2
0
0
0
1
0
0
1
2
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
1
2
0
2
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
2
2
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
1
1
0
0
4
0
0
0
2
0
0
0
0
0
0
1
2
1
0
1
1
2
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
1
0
2
0
0
2
0
3
2
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
3
0
0
0
2
1
0
0
0
0
0
0
0
2
2
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
2
1
0
1
0
0
2
0
1
0
2
1
0
0
0
0
1
0
1
2
0
0
0
0
0
1
0
0
0
1
0
0
0
1
2
2
0
0
0
2
1
1
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
1
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
2
0
0
1
0
1
0
0
0
0
2
0
2
0
4
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
1
0
3
0
0
2
0
0
2
3
4
0
0
2
0
0
0
0
2
1
0
0
0
1
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
3
1
0
1
0
0
0
1
0
0
0
0
2
0
0
2
0
1
1
2
1
0
1
1
0
2
0
0
0
2
0
3
0
0
2
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
2
4
1
0
0
0
0
0
0
0
1
2
0
0
2
0
1
0
2
1
2
0
0
2
0
0
0
0
2
1
0
3
2
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
2
1
0
1
1
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
2
0
1
0
0
1
0
0
0
0
1
2
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
1
2
0
0
0
1
0
1
0
0
2
0
0
0
0
1
0
1
0
1
0
0
0
0
2
0
0
0
1
8
1
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
2
1
2
1
0
1
2
0
2
0
0
0
0
0
1
0
2
2
0
3
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
1
0
0
0
0
2
0
0
0
0
0
2
1
0
3
0
0
1
0
0
2
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
2
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
1
2
0
2
1
0
2
1
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
1
2
0
0
1
0
1
0
1
0
2
2
0
1
1
0
0
0
0
0
2
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
4
2
0
0
0
1
0
0
0
0
0
2
1
0
0
1
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
1
2
0
0
0
6
1
2
3
0
1
0
0
0
0
2
0
0
0
1
0
1
0
2
3
2
0
0
0
0
1
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
1
1
2
0
0
0
0
0
2
2
0
0
2
0
1
0
0
0
0
1
0
0
0
2
0
0
1
2
0
1
2
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
5
0
0
0
2
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
2
2
0
3
0
0
0
0
3
2
0
0
4
4
0
1
0
0
2
0
2
0
0
0
0
0
1
0
2
0
0
0
1
2
0
1
0
0
0
2
2
0
3
0
0
0
4
0
0
0
0
0
3
1
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
1
0
0
1
1
2
0
2
0
3
0
0
0
0
3
0
2
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
2
2
1
7
2
0
0
1
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
1
0
3
0
2
0
0
0
0
0
2
2
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
1
2
0
1
0
0
1
2
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
2
0
0
1
0
0
0
5
0
2
1
2
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
2
2
0
2
0
0
1
0
0
0
0
1
0
0
0
1
0
2
1
0
0
2
0
0
2
0
1
0
1
1
1
0
2
1
0
0
0
0
2
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
1
1
0
0
0
1
0
0
0
0
1
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
1
0
0
0
1
1
0
1
1
1
0
1
0
0
0
2
1
0
0
0
0
1
2
2
0
0
0
0
0
0
2
1
0
0
2
0
0
1
0
0
0
0
0
2
0
2
0
0
0
1
0
2
2
0
1
4
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
2
0
2
2
0
0
1
0
0
0
0
0
0
1
2
2
2
3
0
0
0
0
0
0
0
1
0
1
0
0
0
2
1
0
2
1
2
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
2
0
2
1
0
2
0
0
0
0
0
2
1
0
1
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
4
1
0
2
0
0
1
1
0
0
0
0
2
0
0
0
5
0
0
0
1
0
0
0
0
2
0
0
0
3
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
2
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
2
0
2
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
2
2
2
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
1
2
0
2
0
2
1
0
0
2
2
0
1
0
0
1
2
2
0
0
1
0
0
0
0
0
0
0
1
0
2
0
2
0
2
0
0
0
1
2
0
0
0
0
1
0
0
2
0
2
2
0
0
0
0
1
1
4
0
0
2
1
0
1
0
0
0
0
1
1
0
0
2
1
2
1
0
0
2
0
1
0
0
0
0
1
0
0
1
1
1
0
0
0
2
0
2
0
1
0
1
0
0
0
2
0
1
0
0
0
1
0
2
2
1
1
0
2
0
0
0
2
0
0
0
1
2
1
0
0
2
0
0
0
0
1
0
0
0
0
1
2
2
0
1
0
2
0
0
2
0
1
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
2
1
1
0
1
0
0
1
0
1
0
0
0
2
1
2
0
0
0
1
0
0
1
0
0
0
1
0
2
0
1
1
0
0
0
1
5
0
2
2
0
2
0
2
0
0
0
1
0
1
0
3
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
1
1
0
1
0
2
0
0
0
1
0
1
2
0
0
0
0
0
0
1
0
3
2
0
0
0
0
0
0
0
0
1
0
2
0
3
1
0
0
0
0
1
0
0
1
1
0
1
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
1
0
3
1
0
0
0
0
2
0
2
0
0
1
2
0
0
0
1
0
2
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
1
1
0
2
1
1
1
0
0
0
2
1
0
0
2
0
2
0
0
2
3
0
1
0
0
0
3
2
0
0
0
1
2
0
1
0
0
0
2
2
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
1
0
2
1
0
0
1
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
3
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
1
0
2
2
0
0
0
3
0
0
0
2
0
0
1
0
0
0
0
0
3
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
1
0
2
0
0
2
0
2
0
1
0
1
0
0
1
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
1
2
0
2
1
1
2
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
3
0
0
1
2
0
1
0
1
0
1
1
2
0
0
2
0
0
2
0
0
0
0
1
0
0
0
2
0
2
1
0
0
0
0
0
3
1
1
2
0
2
1
2
0
1
1
0
0
1
0
1
0
0
0
0
0
2
2
0
0
0
0
1
1
0
2
1
0
0
1
0
0
2
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
2
0
0
1
2
2
1
0
1
0
0
0
3
1
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
1
2
0
0
1
1
0
0
1
0
2
0
0
0
0
1
2
0
0
2
2
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
9
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
1
0
0
2
2
0
0
0
1
0
1
2
3
1
2
2
0
0
2
0
0
2
0
0
2
2
0
0
0
1
0
0
1
2
0
0
0
1
0
0
0
2
0
0
0
1
0
0
2
2
0
0
0
2
2
0
0
0
0
1
0
2
1
4
0
0
1
0
1
0
0
0
0
1
0
2
0
0
2
2
0
0
1
0
0
0
2
0
0
1
0
0
2
0
2
0
0
0
0
0
1
2
0
1
1
0
0
0
1
1
2
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
2
2
2
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
5
1
2
2
0
0
0
1
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
1
0
2
2
0
2
0
0
2
1
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
1
1
0
1
2
0
1
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
2
0
0
0
1
0
1
1
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
1
3
2
0
0
0
2
0
2
0
0
0
0
0
2
0
0
2
0
0
1
2
2
0
1
0
0
1
0
1
0
0
0
1
0
0
3
2
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
2
2
3
0
0
0
0
0
0
2
2
0
2
0
0
0
1
0
0
0
2
1
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
2
1
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
1
0
0
3
3
0
0
1
0
0
1
0
0
2
0
0
0
2
0
0
0
1
2
0
0
0
2
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
2
2
0
0
1
2
2
1
0
1
0
0
0
1
0
0
2
3
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
1
2
1
0
0
4
0
0
0
0
0
0
0
0
0
1
2
2
0
1
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
1
1
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
2
0
3
0
1
2
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
2
0
1
2
0
0
1
0
0
0
2
2
10
1
0
3
2
0
0
0
0
1
0
0
2
0
0
2
0
2
0
0
0
2
1
0
3
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
2
0
1
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
2
0
1
0
1
0
0
1
2
0
2
0
1
1
0
0
0
0
1
2
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
2
1
0
2
0
0
0
3
3
2
0
2
2
1
1
0
0
0
0
0
0
3
2
0
1
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
1
0
2
2
2
0
2
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
1
0
2
1
2
0
1
0
2
0
0
0
1
0
0
1
0
1
2
0
0
0
5
1
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
2
0
1
2
0
5
1
0
1
0
1
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
1
4
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
1
1
0
2
0
0
0
3
0
0
1
0
1
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
1
1
0
0
0
0
0
2
0
2
1
0
0
1
2
1
1
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
1
0
0
0
0
0
0
1
0
2
0
0
0
3
1
0
1
1
0
0
1
1
0
0
0
0
0
0
2
0
1
0
2
1
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
1
1
0
1
0
2
1
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
5
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
2
0
0
1
2
0
0
0
0
1
2
0
1
0
0
1
0
0
0
2
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
2
0
0
0
1
0
0
1
0
0
1
0
2
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
2
3
0
0
2
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
3
1
0
0
0
2
2
0
0
2
0
0
2
0
3
3
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
4
0
0
0
1
0
0
1
0
0
2
1
2
0
0
0
0
2
1
0
0
2
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
1
0
0
0
1
1
0
2
0
2
0
2
0
2
1
3
1
0
0
1
0
0
3
1
2
1
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
3
0
0
0
0
2
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
1
1
0
1
1
0
0
1
0
0
0
0
1
1
0
1
0
6
0
2
4
0
2
2
0
0
0
0
0
1
0
2
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
2
2
0
1
0
1
0
1
0
1
7
0
0
1
2
1
1
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
5
0
0
2
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
3
0
1
0
2
0
0
0
0
0
2
1
0
2
0
0
1
0
2
0
6
3
0
0
3
0
1
0
0
0
0
0
1
0
0
0
0
0
0
3
1
0
1
1
0
0
0
0
0
1
0
1
0
0
2
1
0
1
2
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
1
2
1
1
2
1
0
0
2
0
1
1
0
1
1
2
0
0
0
0
2
0
0
1
0
0
0
1
2
0
0
0
1
0
2
1
0
0
0
0
2
0
0
3
2
1
0
1
0
0
2
2
0
2
0
0
0
0
2
2
0
0
2
0
0
0
1
0
0
2
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
1
1
0
0
0
1
0
0
0
1
0
0
2
0
0
0
1
1
0
0
0
0
2
0
0
1
0
2
2
0
2
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
2
0
1
0
1
0
0
0
2
0
0
2
0
0
0
1
0
2
0
1
0
2
0
2
0
0
1
2
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
2
0
2
0
0
0
2
0
0
1
2
2
3
1
0
0
0
2
1
0
2
0
2
1
0
1
0
0
0
0
0
0
0
0
1
2
0
1
0
0
2
0
0
0
2
0
0
1
1
2
0
0
1
0
0
0
0
2
1
0
0
0
1
0
2
1
0
0
0
1
0
0
1
1
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
3
0
0
0
2
2
0
0
0
1
1
1
2
0
1
0
0
0
0
0
1
2
1
1
0
2
1
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
2
0
1
1
0
0
3
2
0
3
0
0
0
0
1
2
1
0
0
0
2
2
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
1
0
2
2
0
0
1
1
1
0
0
0
0
0
0
0
0
0
2
0
2
0
2
1
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
1
0
1
2
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
3
0
0
0
0
2
1
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
2
0
2
0
1
0
2
1
2
0
2
0
7
0
2
0
1
1
0
1
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
1
0
0
1
2
2
1
0
1
0
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
2
4
0
2
0
0
2
0
0
0
0
0
2
0
0
2
2
0
0
0
0
2
1
0
0
2
0
1
1
2
0
1
0
0
3
1
1
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
2
0
0
2
0
2
2
0
1
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
3
0
1
1
2
0
0
0
1
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
2
0
0
2
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
2
2
2
0
0
1
2
0
0
0
0
1
2
0
1
0
2
0
2
0
0
1
0
0
2
1
1
0
0
0
1
1
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
3
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
1
1
0
2
2
1
2
0
2
0
0
1
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
3
0
1
2
0
0
1
1
0
0
0
0
0
0
1
4
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
1
0
0
2
3
0
0
0
0
1
1
0
2
2
3
3
2
0
0
0
2
0
0
0
0
2
0
0
0
1
2
2
0
2
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
2
2
2
0
0
1
1
0
1
1
0
1
0
0
2
1
2
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
1
2
0
0
0
3
0
2
0
0
0
1
1
0
3
2
2
0
2
1
2
0
0
0
0
1
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
1
0
2
2
2
2
2
0
0
0
0
0
0
0
0
1
2
1
0
0
0
1
1
3
0
1
0
0
1
2
0
0
0
0
2
0
0
0
0
1
0
2
0
0
1
0
0
1
2
2
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
2
0
2
0
0
0
2
0
0
2
2
2
0
0
2
0
0
0
0
0
0
3
2
2
0
0
2
0
2
1
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
1
2
0
1
1
0
1
0
0
1
0
0
1
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
1
1
0
0
1
0
0
1
0
0
0
1
2
0
0
0
0
0
0
1
0
0
2
0
1
1
2
0
1
0
0
1
0
0
0
1
1
0
0
0
2
2
0
2
0
0
0
0
2
0
2
0
0
0
0
3
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
1
1
1
0
0
0
0
2
0
0
2
0
0
0
0
2
0
1
0
0
0
2
0
1
0
1
0
0
0
1
3
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
3
0
1
1
2
0
0
0
2
0
0
0
0
0
0
0
0
1
1
1
0
2
0
1
2
0
0
0
2
0
0
0
0
1
1
0
0
0
3
0
0
0
0
0
0
2
0
1
1
0
0
1
0
3
2
1
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
1
0
2
0
0
0
0
0
3
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
2
0
3
0
0
0
1
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
2
3
0
0
0
2
4
0
0
0
0
0
0
1
0
2
2
0
0
2
0
0
0
0
1
1
2
0
0
2
0
0
0
0
0
0
2
0
1
0
0
2
0
2
2
0
8
1
0
1
0
3
1
0
0
1
0
0
2
0
2
0
0
0
0
0
3
0
0
2
0
0
0
0
1
1
0
1
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
1
2
0
0
0
0
1
0
2
0
0
0
2
2
2
0
0
0
3
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
3
0
1
2
0
1
1
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
3
0
0
1
0
0
1
1
0
0
0
2
0
0
0
1
1
1
0
0
0
2
0
0
1
0
0
1
2
0
2
1
1
2
2
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
1
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
2
0
0
1
0
0
1
0
1
0
0
0
0
1
3
2
2
0
5
2
0
0
2
0
1
0
2
2
0
0
2
0
1
0
0
1
0
0
0
0
2
0
1
3
0
0
2
0
0
0
0
0
0
0
1
0
0
2
2
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
1
0
0
0
3
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
2
1
0
2
0
0
0
0
3
0
1
1
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
6
0
2
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
1
2
0
2
0
0
2
1
0
2
0
0
0
2
0
0
0
0
0
0
1
0
2
0
2
2
0
0
0
0
0
2
2
0
0
0
2
2
0
1
0
0
2
0
0
0
0
2
0
1
0
1
1
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
2
4
0
1
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
2
3
0
0
2
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
4
0
0
2
2
0
0
0
0
2
1
0
0
0
0
0
2
0
2
0
0
2
0
0
2
0
0
1
0
0
7
0
2
0
0
1
0
1
1
2
0
0
0
2
0
1
1
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
2
2
2
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
1
0
0
1
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
3
2
0
0
2
0
0
0
0
2
0
1
0
0
0
1
1
2
2
0
2
0
0
0
0
1
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
2
0
2
0
0
0
2
0
1
0
1
0
0
0
0
2
0
1
0
0
0
1
1
2
0
1
0
1
1
0
0
0
1
1
1
2
0
0
0
0
0
1
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
1
1
0
2
0
1
2
0
1
2
0
2
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
4
0
1
0
0
0
0
0
0
3
0
1
0
0
0
1
0
2
2
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
2
1
2
1
0
0
0
2
1
0
0
2
3
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
1
0
1
0
1
0
1
1
0
0
0
0
2
1
2
1
2
0
0
2
0
0
1
0
1
0
0
1
2
0
0
1
0
0
1
3
0
1
0
2
0
2
0
0
0
0
1
0
0
4
0
0
0
0
2
2
0
0
0
3
1
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
2
0
1
3
2
0
0
2
0
1
0
3
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
2
0
0
0
0
0
2
2
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
1
0
0
0
0
1
1
0
1
0
0
0
1
2
0
0
0
2
0
2
4
0
2
1
1
1
0
2
0
2
0
1
0
0
2
2
0
0
0
1
2
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
2
0
0
0
1
0
2
0
0
1
0
0
2
0
0
1
1
2
0
1
1
0
0
0
0
0
0
0
0
2
0
0
11
0
2
0
0
0
1
0
2
0
1
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
1
0
3
1
0
0
1
0
1
1
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
2
0
3
1
0
2
0
2
1
0
0
0
0
0
1
0
0
2
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
1
1
0
0
0
2
2
0
1
2
1
0
0
2
0
2
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
2
0
1
0
2
1
1
3
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
2
0
2
0
0
0
0
1
0
0
1
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
4
8
0
0
0
0
0
2
0
1
0
2
0
0
0
2
0
2
0
2
0
1
2
2
0
0
0
1
0
1
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
1
0
1
3
0
0
0
1
0
0
0
2
0
3
3
0
1
0
1
0
0
1
2
1
0
1
0
2
1
2
0
2
1
3
0
0
0
1
2
2
3
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
1
2
0
0
0
0
1
0
1
2
0
0
0
2
1
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
2
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
2
1
0
0
0
2
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
3
1
0
1
0
1
0
1
0
2
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
2
0
0
2
2
1
0
0
0
1
0
0
2
0
2
0
1
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
3
0
0
1
0
0
0
0
2
2
2
1
0
2
0
0
1
1
1
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
1
3
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
2
4
1
3
0
0
1
0
1
0
0
0
2
0
0
0
1
2
3
0
0
0
2
0
1
1
2
0
2
1
0
1
1
0
2
1
1
1
0
0
0
0
4
0
0
1
0
0
2
1
1
0
0
2
0
0
2
0
0
0
2
0
1
0
1
0
0
0
0
0
1
1
0
1
2
1
2
1
2
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
2
0
1
0
2
1
0
0
2
0
1
0
0
1
2
1
0
0
0
0
0
2
1
0
1
0
0
0
0
2
2
0
3
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
3
0
2
0
1
0
0
0
1
0
0
2
0
6
0
0
0
0
3
0
0
0
0
0
0
2
1
0
3
0
0
2
0
0
1
0
0
3
2
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
2
4
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
1
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
1
0
2
0
1
1
0
2
0
0
2
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
2
4
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
2
0
0
2
0
2
0
1
0
1
0
0
0
2
0
1
0
2
0
4
2
0
0
0
2
0
1
1
4
1
0
0
0
1
1
0
0
0
0
1
0
1
0
0
1
2
1
0
0
0
0
0
0
0
0
1
0
1
0
1
2
0
0
0
0
2
0
2
1
2
1
0
0
0
0
0
1
0
0
0
1
0
1
2
0
1
0
1
0
0
0
0
0
2
0
0
0
4
2
0
0
2
1
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
2
0
0
0
0
1
0
5
0
2
1
0
1
1
0
0
2
0
1
3
1
1
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
2
0
0
0
1
0
0
1
0
0
0
0
1
0
1
2
0
1
2
0
1
0
0
1
0
1
1
0
0
0
2
0
0
1
2
1
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
1
1
1
1
4
0
0
0
0
0
2
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
3
0
1
0
0
0
2
2
0
0
0
0
5
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
2
0
0
0
0
2
0
2
2
1
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
1
2
0
0
1
0
0
0
0
3
0
0
2
0
0
0
0
0
0
2
0
0
0
2
3
0
2
1
0
0
0
0
1
0
1
0
0
0
0
0
2
0
2
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
1
1
0
0
0
0
0
0
0
0
3
0
0
2
1
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
1
2
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
2
0
0
0
2
1
1
11
0
0
0
0
0
0
1
0
1
0
1
0
2
2
2
0
0
0
0
0
0
1
0
2
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
2
0
0
0
0
1
0
0
2
2
0
2
2
0
0
1
0
3
0
0
0
2
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
1
2
0
0
0
0
0
8
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
1
0
1
1
0
2
0
0
0
0
1
0
2
0
2
1
0
1
2
0
1
2
0
0
0
0
0
0
1
0
0
0
2
2
2
0
0
0
0
1
0
0
1
0
0
2
0
2
2
0
0
0
0
2
2
2
0
0
1
2
1
0
0
0
1
1
0
0
0
0
0
3
0
1
1
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
2
0
0
1
0
0
2
0
0
0
0
0
1
0
1
0
0
1
0
1
0
1
0
0
2
2
0
0
3
3
1
2
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
2
0
1
2
2
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
3
2
0
1
0
0
0
0
2
0
0
0
1
3
1
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
1
1
0
0
2
0
0
3
0
2
0
0
1
0
2
0
0
0
0
0
0
1
1
1
0
0
1
0
0
1
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
1
0
2
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
2
1
1
0
0
0
0
3
1
0
3
0
0
0
0
0
0
1
1
2
0
0
1
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
2
0
2
0
0
0
0
0
0
0
1
3
0
2
2
0
3
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
2
0
2
1
0
0
2
0
0
0
0
0
2
1
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
1
2
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
1
0
0
1
0
0
0
1
1
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
1
1
0
0
1
0
1
0
0
1
0
2
1
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
8
0
0
2
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
2
0
0
1
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
2
1
0
0
1
0
0
2
4
0
0
1
0
0
2
0
0
0
0
1
0
2
0
0
0
0
1
0
1
0
2
0
0
1
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
3
0
0
2
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
1
1
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
1
0
3
2
0
0
0
0
0
2
0
1
0
0
0
0
1
1
0
0
1
0
0
0
6
2
0
1
2
1
0
0
2
0
2
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
3
2
2
1
3
1
1
2
2
2
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
1
0
0
0
0
1
2
0
0
1
1
0
1
0
0
0
1
1
0
0
0
0
0
1
2
1
0
0
2
0
0
2
2
1
2
0
0
0
0
1
2
0
1
2
2
2
0
0
2
0
0
0
2
0
0
1
0
0
1
0
0
2
0
3
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
4
1
0
2
1
0
0
0
0
0
0
2
1
0
0
0
0
2
2
1
0
0
0
0
0
2
0
1
0
0
3
0
2
2
0
0
3
0
0
0
1
0
0
0
1
0
3
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
2
1
2
1
0
0
0
1
1
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
1
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
2
1
0
0
0
0
2
2
1
2
0
2
0
1
0
0
0
1
0
1
0
2
0
1
2
0
2
0
0
0
1
0
0
1
0
0
2
0
0
2
2
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
1
1
1
0
2
1
0
1
1
0
0
0
0
2
1
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
1
1
0
0
0
0
2
0
2
0
1
1
0
0
0
2
1
2
1
0
0
1
3
2
0
0
3
0
0
2
0
0
0
0
0
1
4
0
0
2
2
0
0
1
0
2
0
0
0
1
0
3
2
2
2
0
0
0
0
0
1
2
2
1
2
0
2
0
2
1
2
0
0
0
0
1
2
0
0
0
2
1
0
0
0
0
0
1
1
0
0
1
2
1
0
0
0
0
0
0
1
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
1
1
0
1
2
0
3
2
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
3
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
1
0
2
0
1
0
0
1
0
0
1
1
2
0
0
1
0
1
0
1
0
3
0
0
2
3
1
2
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
3
1
0
0
0
0
1
1
0
0
0
0
2
1
0
0
0
0
0
3
0
0
2
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
1
0
2
0
2
1
0
1
0
0
0
0
0
1
1
0
0
4
0
0
0
2
0
0
0
1
0
2
2
0
2
0
0
1
0
0
1
0
0
2
0
1
0
0
0
1
0
1
0
0
0
2
1
0
1
0
0
0
0
4
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
1
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
1
0
0
2
1
0
0
0
0
0
1
2
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
3
2
2
1
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
1
0
1
1
1
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
2
1
0
0
0
1
0
0
0
1
2
0
0
0
0
1
1
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
2
2
2
2
0
1
0
0
0
1
0
0
0
1
0
0
2
0
2
0
1
0
1
0
0
0
0
0
0
0
2
1
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
3
1
1
0
0
0
0
2
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
3
1
0
0
0
0
0
0
0
2
0
0
2
2
4
0
1
2
0
0
0
1
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
4
0
0
1
0
0
2
2
2
0
0
0
0
1
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
1
2
0
1
0
1
2
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
2
2
0
0
1
0
2
2
1
2
0
0
0
0
0
0
0
3
0
0
2
2
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
1
2
2
0
1
0
1
0
0
0
1
0
0
0
0
1
2
0
0
0
0
1
0
0
1
0
0
3
0
1
0
1
0
0
0
2
3
0
1
0
3
0
0
0
0
1
3
2
2
1
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
1
0
2
0
1
0
2
0
0
0
0
0
0
2
0
0
1
2
2
0
2
2
0
0
0
0
0
2
1
0
0
2
1
0
0
1
1
1
0
0
0
0
1
1
2
0
0
2
0
0
1
0
0
1
2
2
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
2
0
0
0
2
1
2
1
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
2
1
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
3
0
0
0
0
1
0
0
2
1
0
0
2
1
0
2
2
1
2
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
2
0
1
0
0
0
3
0
2
3
0
0
0
0
0
0
0
0
0
1
2
1
1
0
0
0
0
0
2
0
1
0
0
0
2
1
0
1
0
0
1
0
1
1
1
0
1
0
2
2
0
0
0
0
2
0
0
0
1
1
0
0
0
0
1
2
0
1
2
0
2
0
2
0
0
0
0
2
0
1
0
0
1
0
3
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
2
3
1
0
1
0
0
0
0
0
2
0
0
0
1
2
2
1
0
3
0
0
0
2
0
0
0
0
1
0
0
1
0
0
2
1
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
2
0
2
0
0
0
0
2
1
1
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
2
1
0
0
2
0
2
0
0
1
0
0
0
2
0
0
1
1
0
0
1
0
1
0
3
0
1
0
1
0
0
0
1
2
2
1
0
2
0
0
0
0
2
0
0
1
0
2
2
0
1
0
1
0
0
0
2
0
2
0
0
0
0
3
0
0
1
0
0
0
4
0
0
0
0
1
0
0
2
0
1
0
0
0
1
0
0
0
2
1
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
7
1
2
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
2
0
1
0
1
3
1
2
2
0
2
2
1
0
4
2
2
1
2
2
0
0
0
0
2
1
0
0
1
2
0
0
1
0
2
0
0
0
0
0
0
0
3
2
1
0
0
0
0
0
2
2
0
1
0
0
0
0
2
1
0
1
0
2
0
0
0
0
3
1
0
1
2
2
1
0
2
0
0
0
0
1
0
1
1
0
1
1
0
0
0
0
0
0
2
0
1
0
0
2
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
1
0
0
2
1
0
0
1
0
2
0
1
1
0
0
0
1
1
2
0
1
0
0
0
0
0
3
0
0
2
2
0
1
1
0
0
0
0
1
2
2
2
0
0
0
0
2
0
0
0
1
3
0
0
0
0
0
0
3
0
0
2
0
0
0
1
0
1
1
0
0
0
2
1
0
0
0
1
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
1
1
0
0
2
0
0
0
1
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
1
2
1
0
2
0
0
0
0
0
2
0
1
0
1
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
2
1
0
1
0
2
1
1
2
1
0
0
0
0
2
0
2
0
0
2
0
0
0
0
1
1
0
0
1
1
4
0
0
3
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
1
2
0
1
3
1
1
1
4
0
0
1
0
2
1
0
1
2
1
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
2
0
2
0
0
1
0
1
0
0
0
3
0
0
3
2
0
2
2
0
2
0
0
0
0
0
0
0
0
1
1
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
4
1
1
0
1
0
2
0
1
0
1
0
0
0
0
0
0
1
3
0
0
1
1
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
1
0
0
1
2
1
1
0
0
2
0
1
0
0
0
0
0
3
0
0
1
0
1
0
1
0
2
0
0
0
1
0
0
0
1
1
2
0
0
2
0
2
0
0
0
0
0
0
0
5
1
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
2
0
0
2
2
1
0
0
2
0
0
1
2
1
0
1
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
3
0
1
0
0
0
1
2
0
0
0
0
1
0
2
0
2
1
0
1
0
0
0
0
0
0
0
0
1
0
0
2
1
1
2
0
0
0
2
0
0
0
0
0
2
1
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
2
1
2
0
1
0
0
1
0
0
0
0
1
0
4
0
0
1
0
1
0
0
1
0
2
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
1
3
0
2
0
0
0
0
4
0
1
0
0
0
2
0
0
0
1
0
2
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
2
0
0
2
0
2
1
0
0
0
0
1
0
0
1
2
0
1
2
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
1
0
0
2
2
0
1
4
2
0
0
1
0
0
2
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
2
0
0
0
1
0
0
1
0
1
1
2
2
0
0
2
0
0
0
3
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
1
1
1
2
0
1
0
2
1
1
0
2
0
0
1
0
0
0
1
1
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
2
0
0
0
0
2
1
2
0
0
2
1
2
2
0
0
2
0
2
1
0
0
1
2
1
2
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
2
3
0
0
0
1
0
2
1
1
0
2
0
2
0
0
0
0
1
0
1
0
0
0
0
0
2
1
0
2
0
0
1
0
0
2
1
1
1
1
1
0
0
1
0
0
0
2
2
0
1
0
0
0
0
0
2
0
2
0
0
1
0
2
2
2
2
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
1
2
0
1
1
0
0
0
1
0
2
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
2
0
0
1
2
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
1
0
2
4
0
4
3
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
2
2
2
0
0
1
2
1
0
0
1
1
0
2
2
0
0
0
1
0
0
0
1
1
0
2
0
1
0
0
2
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
2
0
0
2
0
1
0
4
2
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
2
0
1
2
0
0
0
0
2
1
0
0
0
1
0
2
1
1
0
3
2
0
0
0
0
2
2
0
0
0
1
0
0
0
1
0
0
1
0
2
1
0
1
2
1
1
4
0
1
2
1
2
0
0
0
0
0
2
0
0
1
0
0
4
0
0
2
0
0
0
0
0
2
1
2
0
0
2
1
0
2
0
0
2
0
1
0
2
0
0
0
3
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
1
0
0
2
2
0
0
0
1
0
0
0
0
1
0
2
0
1
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
2
0
0
2
2
2
0
2
1
0
0
0
0
0
0
3
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
2
0
1
0
2
0
3
0
0
2
0
0
0
2
2
0
1
0
2
0
0
1
0
1
2
0
0
0
1
1
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
1
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
1
1
0
3
0
0
0
2
0
0
0
2
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
4
0
1
0
1
0
2
0
0
2
1
1
2
0
0
1
0
1
0
0
0
2
2
1
0
1
1
0
0
0
1
0
0
1
2
0
0
0
0
0
1
0
2
0
0
0
0
3
0
0
1
2
1
1
0
0
0
0
0
0
0
0
0
0
1
1
2
2
0
0
1
0
0
0
1
1
2
0
0
2
0
0
2
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
1
0
0
1
1
2
2
1
3
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
3
0
2
2
2
2
0
0
0
1
0
1
0
0
1
0
1
0
0
0
2
0
0
1
0
2
0
0
0
1
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
2
0
2
3
0
1
0
0
0
0
0
2
0
4
2
1
1
4
0
2
0
0
0
0
0
1
0
2
0
0
2
0
1
0
0
1
0
2
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
2
2
2
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
2
0
0
0
1
2
0
0
2
1
0
1
2
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
2
2
1
0
1
1
0
1
0
1
0
2
0
2
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
4
0
0
1
0
1
0
0
0
5
0
0
2
2
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
1
0
4
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
2
2
0
0
0
1
1
2
0
0
0
0
0
1
0
0
2
0
1
1
0
0
2
0
0
0
2
0
0
0
0
0
0
1
1
2
0
0
1
2
1
1
0
1
0
1
0
0
2
0
1
1
0
3
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
2
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
3
3
0
0
0
0
0
1
0
0
0
2
0
1
2
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
1
0
0
0
2
2
0
0
0
5
3
1
1
0
0
0
0
0
0
1
0
1
2
1
0
0
2
0
0
1
0
0
1
0
0
2
0
0
1
2
0
1
0
0
1
0
0
2
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
1
1
0
0
1
2
1
0
0
0
1
0
1
0
0
0
1
0
0
2
2
0
0
2
0
1
0
0
0
0
2
0
0
0
0
7
2
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
2
1
0
1
0
2
0
0
1
1
0
0
0
0
0
0
0
1
2
0
0
2
0
0
1
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
2
2
1
0
0
0
2
0
1
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
3
0
0
0
2
2
0
0
0
0
0
1
0
0
2
0
3
0
0
0
2
0
1
0
2
2
0
0
1
0
0
1
1
2
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
1
2
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
2
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
2
0
2
2
0
0
0
0
2
0
0
1
2
0
1
0
0
0
0
0
0
2
1
1
0
0
0
1
0
2
0
0
2
0
0
0
0
1
1
2
2
0
0
1
0
2
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
2
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
2
2
0
9
0
0
0
1
0
0
0
2
0
1
0
0
1
2
0
1
2
0
0
1
1
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
2
1
0
1
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
1
0
0
0
0
2
1
0
1
1
2
1
1
1
1
0
2
0
0
0
0
0
2
0
1
0
0
1
0
0
1
0
1
2
3
0
0
0
0
0
0
0
1
0
1
0
2
2
0
0
0
0
2
2
2
0
0
0
0
0
1
1
1
1
2
2
1
0
1
2
0
0
2
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
2
1
1
0
0
0
3
2
0
0
0
2
1
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
1
2
2
0
1
2
1
1
0
0
0
0
2
1
0
0
2
0
2
0
0
2
3
0
0
0
0
3
1
0
2
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
2
1
0
0
1
0
0
0
1
1
0
0
0
0
3
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
1
0
0
2
0
0
0
0
3
0
0
1
0
0
1
2
0
0
1
2
0
0
2
1
1
0
0
0
2
1
0
1
2
0
1
0
2
3
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
2
1
0
0
2
0
0
1
1
0
0
0
2
0
0
0
0
1
0
0
5
0
0
0
2
1
0
1
0
0
1
0
0
1
0
0
0
0
2
0
2
1
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
2
2
0
1
0
0
1
0
2
0
1
0
0
2
0
0
0
0
0
2
0
0
1
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
1
2
0
2
2
0
2
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
2
2
0
0
0
2
2
2
0
2
0
0
0
2
1
0
1
1
0
1
0
0
0
1
0
0
1
1
0
0
2
3
0
1
1
2
0
0
1
1
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
3
1
2
0
1
0
0
0
1
0
0
0
1
1
0
2
0
2
1
0
0
0
0
0
1
0
0
0
0
2
2
0
2
0
0
2
1
0
1
0
0
0
1
1
0
0
1
0
2
1
0
1
1
0
1
0
0
1
0
0
2
2
0
2
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
2
0
0
0
0
1
6
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
2
0
0
2
0
2
2
0
0
1
0
0
0
0
0
1
1
0
0
0
0
2
0
1
0
0
0
1
0
0
6
0
0
0
3
0
0
0
0
0
0
0
0
2
0
2
1
2
0
0
0
0
2
0
2
0
0
0
1
1
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
1
2
1
0
1
0
1
0
0
0
0
2
1
0
3
0
1
1
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
1
0
0
3
0
2
0
2
0
2
0
2
0
0
0
1
2
1
0
2
0
1
0
0
1
2
0
0
1
0
2
0
0
0
0
0
1
0
0
0
1
2
2
0
2
0
2
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
1
2
0
0
2
0
0
0
0
0
1
0
0
1
0
1
0
0
2
0
2
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
1
2
2
1
2
0
2
0
0
0
4
2
0
0
1
3
5
1
1
1
12
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
3
2
0
2
0
2
0
0
4
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
2
0
0
2
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
1
0
2
3
1
2
0
0
0
0
0
2
2
2
2
1
0
2
0
0
2
0
0
0
2
0
2
2
0
1
0
1
0
3
2
1
0
0
0
0
0
0
0
1
2
0
0
2
0
0
1
0
0
0
0
0
0
1
3
0
0
1
0
0
0
2
0
1
0
0
0
3
0
1
0
0
2
1
2
0
2
0
2
1
1
0
0
1
1
0
1
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
2
0
1
1
0
2
0
0
3
0
2
0
1
5
0
1
2
0
1
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
3
0
0
0
2
0
3
0
0
0
0
0
0
1
2
0
2
0
1
0
0
0
0
2
0
1
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
1
0
0
1
2
1
1
2
0
0
0
0
0
0
2
1
0
1
0
0
1
0
0
0
0
1
1
1
1
0
2
0
0
0
1
1
2
0
0
0
0
1
0
0
0
0
1
0
1
3
0
0
2
0
0
2
0
1
1
0
0
0
2
0
0
2
0
1
2
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
1
2
0
0
0
2
2
0
0
2
0
1
0
0
0
0
0
1
2
2
0
0
0
1
0
1
0
0
0
2
0
0
2
2
1
0
0
1
0
1
0
1
0
0
4
0
0
0
0
0
2
0
0
0
1
2
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
2
2
0
0
1
0
0
0
0
1
1
0
1
0
1
0
2
1
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
2
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
1
0
0
1
1
1
2
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
5
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
1
0
0
0
0
0
0
2
4
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
3
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
1
1
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
1
0
2
2
2
1
0
2
0
1
2
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
2
1
0
0
2
0
0
0
0
1
0
2
0
2
2
0
0
0
0
2
1
0
0
0
0
2
0
2
0
1
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
1
0
0
0
0
1
2
1
0
0
1
1
2
2
1
0
0
0
0
0
3
1
0
1
0
0
2
2
2
0
0
1
0
0
1
2
1
0
0
0
2
0
1
0
1
0
3
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
2
0
1
0
0
1
0
0
0
0
0
2
0
0
0
1
1
0
0
0
2
0
2
1
1
0
2
0
1
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
6
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
3
0
1
0
0
1
0
1
0
0
1
2
1
0
0
2
0
1
0
0
0
1
0
2
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
1
0
2
0
0
2
2
0
1
0
2
2
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
2
1
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
2
0
1
1
1
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
2
1
2
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
3
0
1
1
1
2
0
0
0
1
0
1
0
0
0
4
0
0
0
2
0
0
2
1
0
0
1
2
0
1
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
9
0
0
1
0
0
0
2
1
0
3
0
0
0
1
0
0
0
1
0
2
2
0
2
2
0
1
0
0
0
0
2
0
0
0
1
1
0
0
1
0
1
2
0
1
0
0
0
0
1
0
0
2
0
0
0
2
0
2
1
1
2
3
2
0
0
0
0
0
2
1
0
2
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
1
1
0
0
0
0
1
1
1
0
0
0
0
0
1
2
3
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
2
0
0
0
2
0
3
1
0
0
1
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
2
3
0
0
0
0
0
0
3
2
2
0
1
0
0
2
2
0
0
0
2
0
0
2
0
0
4
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
1
0
2
1
0
0
0
1
1
0
3
0
5
2
1
1
0
0
0
0
0
1
1
0
0
1
0
2
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
1
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
2
0
3
0
0
0
0
0
2
1
2
0
0
0
2
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
2
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
8
0
0
1
0
1
0
0
0
0
2
1
0
0
0
2
0
0
8
0
1
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
2
0
0
4
1
0
0
1
0
0
1
0
0
0
2
0
1
0
0
0
1
0
1
0
1
2
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
2
0
0
0
2
3
0
0
1
4
1
1
0
1
0
3
0
2
1
1
0
0
0
1
0
0
0
3
2
0
0
1
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
1
1
0
3
0
0
0
2
0
1
2
0
2
0
1
2
0
0
1
0
1
1
0
0
0
0
1
0
0
0
2
1
0
2
1
0
0
0
1
1
0
0
1
0
2
0
1
2
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
2
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
1
0
0
0
1
2
0
0
1
0
0
0
2
1
0
0
0
0
2
1
1
0
0
0
0
0
3
0
2
6
1
2
1
0
3
0
3
0
0
0
3
1
2
0
0
2
0
0
0
2
3
0
0
1
0
1
0
2
2
0
5
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
1
0
0
0
0
1
0
0
1
2
0
0
0
3
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
1
1
1
0
2
0
0
0
0
2
0
2
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
2
0
2
2
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
3
0
0
2
0
0
2
2
0
2
0
0
1
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
1
2
0
1
2
0
0
0
0
1
1
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
2
0
0
1
2
1
0
0
3
2
0
2
0
0
2
0
1
0
1
0
0
0
2
0
1
0
0
0
0
2
0
0
2
1
1
0
0
0
0
0
0
2
0
0
0
0
1
10
0
1
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
1
2
0
0
1
0
0
0
0
0
2
0
0
2
0
1
0
0
1
2
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
4
0
0
1
0
2
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
2
2
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
1
2
0
0
0
0
2
1
1
2
0
1
2
0
2
0
2
0
0
2
2
0
0
0
0
0
1
0
1
0
0
1
2
0
1
0
2
0
2
0
0
1
0
2
2
2
0
0
0
0
0
0
1
2
1
2
0
0
1
0
0
1
2
1
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
2
1
0
2
0
1
1
0
2
0
0
0
1
0
1
0
0
1
0
1
2
0
0
0
0
0
1
0
2
0
2
0
2
0
0
0
2
1
0
0
0
1
0
0
2
1
0
2
0
0
1
0
2
0
0
0
1
1
0
0
0
0
1
0
0
0
2
0
0
0
0
1
2
0
2
0
0
0
0
0
4
0
0
0
0
1
2
0
0
2
0
1
0
0
0
2
0
0
2
0
0
2
0
1
0
0
2
2
3
0
0
2
0
1
0
0
0
1
0
0
2
0
6
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
2
0
1
0
0
0
0
2
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
2
1
0
1
4
0
0
0
1
0
0
0
0
0
4
0
4
0
2
0
1
0
0
1
0
0
1
2
5
0
2
0
1
0
1
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
1
0
0
0
0
1
0
0
0
1
1
3
0
1
0
2
2
0
0
0
1
0
0
2
2
0
1
1
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
1
0
2
0
0
4
0
0
0
0
1
2
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
1
1
2
0
2
0
2
0
2
0
1
0
0
0
0
0
0
0
0
2
0
2
1
0
0
1
0
2
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
1
1
1
1
0
0
2
0
1
0
1
0
2
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
2
1
0
0
1
0
0
2
0
1
0
1
2
0
0
0
0
2
2
0
0
0
2
0
2
0
0
0
0
2
0
1
4
0
0
0
0
3
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
1
0
0
2
1
0
3
0
0
0
0
0
1
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
3
0
2
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
2
0
1
0
0
0
0
3
0
0
0
0
0
1
2
0
0
0
2
2
0
1
0
0
2
0
2
1
1
1
1
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
2
0
1
0
0
0
2
1
0
0
0
0
2
0
0
0
2
1
2
0
0
0
2
0
0
2
0
0
1
2
0
0
2
0
0
2
0
0
0
1
0
1
1
2
0
2
0
2
0
0
0
0
0
0
0
2
0
2
0
0
1
2
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
1
1
0
0
0
0
0
0
2
0
1
0
2
0
0
1
1
0
1
0
0
1
1
0
0
0
0
2
0
0
0
0
1
1
1
0
0
1
0
1
0
0
0
2
0
0
0
1
0
0
1
0
1
0
0
1
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
2
0
0
2
0
0
0
0
0
1
1
0
0
2
0
2
0
0
0
0
0
0
0
1
1
0
1
0
3
0
0
0
0
3
1
0
1
0
0
2
2
0
0
0
3
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
2
1
0
0
2
0
0
0
0
0
0
0
2
2
2
0
0
0
0
2
1
0
2
0
0
0
0
0
1
0
1
0
1
0
0
2
0
0
0
1
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
3
0
2
0
0
3
0
2
0
1
0
0
5
0
0
2
0
1
0
1
0
1
0
0
2
2
1
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
2
2
0
0
1
0
0
2
2
0
2
2
2
1
0
0
2
0
0
0
0
1
2
2
2
1
1
0
0
0
0
2
1
4
0
0
0
2
0
2
0
0
0
0
2
0
0
1
1
1
0
0
1
0
1
0
2
0
0
0
2
0
0
0
2
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
2
2
2
0
0
2
1
1
0
0
0
3
2
0
2
0
0
0
0
2
1
0
0
0
0
0
1
0
2
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
1
0
2
0
0
0
2
2
0
0
2
0
0
2
2
0
1
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
2
0
0
2
0
2
0
2
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
2
2
1
1
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
3
0
1
0
1
0
0
0
1
0
0
0
2
0
0
2
1
0
0
2
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
2
2
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
1
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
2
0
0
0
2
0
0
2
0
0
2
1
0
1
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
3
0
1
0
0
3
0
1
0
0
0
1
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
2
0
1
1
2
0
0
0
2
0
1
1
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
2
2
0
2
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
1
1
0
1
0
0
2
0
0
0
2
0
0
2
0
2
2
2
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
2
2
0
1
0
0
1
0
0
1
1
0
0
1
0
0
0
2
0
1
0
2
1
0
0
1
0
0
0
0
1
1
0
0
2
2
0
1
0
2
0
0
2
1
0
1
2
0
0
0
0
2
3
0
0
0
1
0
2
0
0
0
0
0
0
2
0
2
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
1
0
1
0
0
0
0
0
1
0
0
0
0
2
1
2
0
2
0
0
2
0
2
0
0
2
0
0
0
0
1
0
0
1
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
1
0
2
0
0
0
2
0
1
0
2
0
1
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
1
2
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
1
0
0
0
1
0
0
0
2
1
1
1
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
1
2
0
2
1
2
2
1
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
3
0
1
0
0
0
0
0
0
1
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
3
0
2
0
0
0
0
0
0
0
0
2
2
1
0
0
0
1
2
3
0
0
0
2
3
0
0
1
2
1
0
1
0
2
0
4
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
2
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
1
2
0
0
2
0
0
8
2
1
2
0
0
0
0
2
2
1
0
1
2
0
1
2
0
0
0
0
1
0
2
1
0
0
2
0
0
0
0
0
0
4
1
0
2
2
0
1
0
0
0
0
0
0
0
1
2
2
3
0
0
2
1
2
1
0
0
3
0
0
0
2
0
0
0
0
0
2
0
0
3
0
1
0
2
0
2
0
2
0
1
0
2
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
1
1
0
1
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
1
2
2
2
0
0
1
1
0
0
1
0
0
0
1
0
0
0
1
0
0
1
3
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
1
0
0
0
1
0
1
0
1
0
0
3
0
0
1
0
2
0
0
0
1
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
1
2
1
1
1
1
0
0
0
0
1
2
0
2
0
0
0
0
0
2
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
1
1
0
1
2
0
0
0
1
1
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
2
1
1
2
0
0
3
0
0
0
2
1
0
3
0
0
0
0
0
1
1
2
0
1
0
0
1
0
0
0
0
1
0
0
1
2
0
2
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
1
0
1
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
2
0
2
0
0
0
1
2
0
0
2
0
1
0
2
0
0
1
1
1
0
2
0
2
0
0
2
0
0
1
1
1
0
0
1
1
0
0
0
1
0
0
0
1
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
1
0
0
1
0
0
0
0
2
2
1
1
1
1
1
0
1
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
2
0
0
0
1
0
0
0
0
1
1
0
0
0
0
2
0
1
2
0
0
0
0
2
2
3
2
0
2
2
2
0
0
2
2
1
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
2
0
0
1
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
2
6
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
2
0
0
0
0
0
1
1
2
0
1
0
1
0
1
2
0
0
0
0
0
2
1
2
0
0
1
0
0
2
0
2
1
2
1
0
2
2
1
2
0
0
0
0
0
0
0
1
0
0
2
2
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
1
0
0
1
0
1
0
0
2
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
1
2
2
1
1
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
2
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
2
0
2
0
1
2
0
0
0
2
1
2
0
0
4
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
2
1
0
0
2
1
0
0
0
0
3
0
0
0
1
2
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
1
0
1
0
1
0
0
0
2
0
0
1
0
0
2
2
0
2
0
0
0
1
1
0
2
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
1
1
0
0
0
0
1
2
1
0
1
2
1
0
2
0
1
0
1
0
0
0
2
0
1
2
0
0
0
0
0
2
0
1
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
2
0
0
0
2
0
1
0
0
0
0
1
0
2
0
0
0
0
2
1
0
0
0
1
1
0
2
0
2
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
2
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
1
0
0
2
4
0
0
0
0
2
0
0
0
2
0
0
0
0
2
2
0
2
3
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
2
0
0
0
1
2
0
1
2
0
0
1
0
2
2
0
0
0
1
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
1
2
2
0
0
2
0
2
7
1
0
2
0
2
0
0
0
0
1
2
0
2
0
2
0
0
0
0
1
0
0
2
1
0
1
0
0
0
2
0
0
1
1
0
1
1
2
1
0
2
0
0
0
0
2
2
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
2
0
0
1
0
0
1
0
0
0
2
0
1
0
0
0
0
1
0
0
1
2
1
1
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
2
0
0
0
2
0
1
1
1
0
0
0
1
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
1
0
0
2
2
1
0
0
0
0
2
0
0
0
0
3
2
0
0
0
0
0
0
0
2
1
0
1
0
0
0
1
0
0
0
0
2
0
0
1
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
8
1
2
0
0
2
2
0
1
0
2
0
1
0
0
1
0
1
1
0
1
0
0
3
2
1
0
1
0
2
2
0
0
0
0
0
0
0
0
1
1
0
0
1
0
2
0
2
1
2
0
1
0
0
0
0
0
2
0
0
2
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
1
0
0
1
1
0
1
0
0
0
1
3
0
2
0
2
1
0
0
0
0
0
4
0
0
2
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
1
0
4
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
2
1
3
1
0
0
0
0
0
0
0
0
0
0
0
5
3
0
3
1
0
1
0
0
1
2
0
0
0
0
0
2
2
2
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
1
0
1
0
0
1
0
0
0
1
10
3
2
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
5
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
2
0
2
2
0
1
0
1
2
1
0
0
0
0
0
2
2
0
0
0
2
0
2
0
0
0
0
1
2
2
2
1
0
0
1
0
1
2
0
0
2
1
1
0
0
0
0
2
0
0
0
1
0
0
0
2
2
0
3
0
2
2
0
1
1
2
1
0
1
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
2
1
2
0
0
0
2
0
2
0
0
0
0
0
1
2
0
0
1
1
9
0
0
0
0
0
0
0
1
0
1
2
0
0
2
1
0
0
1
1
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
1
2
2
0
0
3
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
2
0
0
2
0
0
0
1
0
2
1
0
0
0
1
1
0
2
0
0
0
0
0
0
1
0
2
1
0
1
1
0
0
0
0
0
0
1
2
0
1
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
4
1
0
0
0
0
2
0
0
0
2
0
0
0
1
2
0
3
0
2
0
0
0
2
2
2
0
1
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
1
3
3
0
2
1
2
2
2
2
1
0
1
1
0
0
2
0
0
0
1
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
2
0
2
0
0
0
1
0
3
2
0
0
2
0
0
0
1
0
2
1
2
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
2
2
0
2
1
1
0
0
0
0
0
2
2
0
0
2
0
2
0
0
2
2
0
2
0
2
2
0
2
3
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
2
1
2
0
0
2
0
1
0
0
1
0
0
0
0
3
0
0
0
2
1
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
1
0
4
2
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
2
0
0
0
1
0
1
1
2
2
2
0
0
0
2
1
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
1
2
2
0
2
0
2
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
2
1
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
10
1
1
2
0
1
2
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
1
0
0
0
0
1
2
0
0
2
0
0
1
0
0
0
0
1
0
1
0
2
0
0
2
1
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
3
0
2
0
0
1
1
0
0
0
0
0
2
0
0
0
0
3
0
0
1
0
3
0
3
0
0
0
0
0
0
1
0
3
0
1
0
4
1
0
0
0
0
0
0
1
0
0
2
2
0
0
0
1
0
1
2
0
0
0
2
0
2
3
0
0
0
1
0
0
0
1
0
0
0
2
4
0
1
2
1
0
0
1
1
0
0
0
2
1
0
2
0
0
0
2
0
2
0
0
0
0
2
0
0
0
1
0
1
0
0
4
0
0
0
1
0
0
0
0
2
0
2
0
0
0
1
0
1
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
1
0
0
0
0
0
1
0
2
1
1
0
1
0
0
2
2
0
2
3
0
0
0
1
1
0
1
1
0
4
2
0
1
0
2
2
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
3
0
0
0
2
3
0
1
0
2
0
0
0
1
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
2
0
0
1
1
0
0
0
2
1
0
0
2
1
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
1
1
1
0
0
0
0
2
1
0
0
0
0
1
0
1
0
2
1
0
0
1
0
0
0
2
0
1
0
0
0
2
1
0
0
1
2
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
2
0
2
1
0
2
2
2
0
2
0
0
0
0
2
1
0
1
0
0
1
0
1
0
2
0
2
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
5
2
0
0
0
0
1
0
0
0
1
1
0
0
2
0
2
0
0
0
2
1
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
1
0
0
0
2
0
0
0
0
4
0
2
0
2
2
0
1
0
0
2
0
0
1
1
1
0
0
0
0
0
1
1
0
0
0
0
2
0
1
0
1
0
0
1
2
0
2
0
0
0
0
0
0
1
0
2
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
1
0
0
3
0
6
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
1
0
0
1
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
2
2
1
0
2
0
0
1
0
2
0
2
2
0
0
1
1
2
0
2
0
0
0
0
2
1
1
1
1
0
0
1
0
0
0
0
2
2
0
1
7
0
0
2
0
0
0
0
11
0
0
0
0
1
0
0
1
0
2
0
0
0
2
0
1
2
1
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
4
2
0
1
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
2
0
2
2
0
0
0
1
0
0
1
2
2
0
0
0
0
0
0
0
2
1
0
3
0
0
2
0
8
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
2
0
0
2
0
0
1
0
1
1
0
5
0
0
0
1
1
0
0
2
0
0
2
0
2
0
0
1
0
0
0
1
2
0
1
1
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
1
1
0
1
1
2
0
1
0
0
2
1
0
0
2
0
0
0
2
0
0
2
1
0
1
0
1
3
0
3
0
0
2
2
1
0
0
2
2
0
1
2
0
0
0
0
1
1
2
0
0
0
1
2
2
0
0
0
0
1
2
0
0
2
1
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
1
0
0
1
0
2
0
0
0
0
0
0
1
1
0
0
1
2
2
2
1
0
0
0
1
0
0
0
1
0
2
0
0
0
2
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
1
1
1
2
0
0
0
1
0
0
0
0
1
0
3
0
0
0
0
0
0
1
2
0
3
2
2
1
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
2
2
1
2
0
0
0
1
0
2
2
0
0
2
2
0
0
0
0
0
2
2
0
2
0
1
0
0
0
0
0
2
1
2
0
0
0
4
0
1
0
2
0
1
0
1
2
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
1
2
0
1
0
0
2
1
0
2
2
0
0
0
2
0
0
0
1
0
0
2
1
2
0
0
0
0
0
1
1
0
2
1
0
0
0
0
0
2
0
3
2
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
3
2
2
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
4
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
2
0
1
0
1
2
0
0
0
1
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
2
1
0
2
1
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
2
0
0
3
0
1
0
2
0
2
0
0
0
1
0
0
1
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
6
1
1
0
0
0
0
0
0
2
1
0
0
1
1
0
1
0
0
0
1
0
0
0
0
2
4
2
0
0
0
0
2
0
2
0
1
0
0
2
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
2
0
4
0
0
0
0
0
0
2
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
2
0
0
0
0
1
0
0
1
1
1
1
0
1
3
1
0
0
0
0
0
0
0
2
1
2
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
2
1
1
0
0
2
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
3
0
0
0
2
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
3
0
0
0
0
0
1
0
0
0
0
0
2
1
1
1
0
0
0
2
0
0
1
0
3
0
2
0
0
1
2
3
2
0
0
1
2
0
0
0
1
0
2
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
1
0
0
1
1
0
2
0
0
2
2
0
0
0
1
2
2
0
3
4
2
0
0
0
0
2
1
0
1
0
0
0
0
1
0
0
2
2
0
0
1
0
0
1
0
0
2
0
1
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
1
0
2
0
0
0
0
0
0
1
0
0
0
2
1
0
1
0
3
0
2
0
0
2
2
0
0
0
2
1
1
2
0
1
1
2
2
2
2
0
2
0
0
0
2
0
1
2
0
1
0
0
0
1
0
2
0
0
1
0
0
2
2
0
1
0
0
0
0
0
1
2
3
0
0
3
2
1
0
0
0
0
0
0
2
0
0
0
0
3
1
0
0
1
1
0
1
0
0
2
0
0
0
0
0
2
1
0
0
0
0
2
0
0
2
2
1
2
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
1
1
2
1
0
1
3
0
0
1
0
0
1
0
0
0
0
3
1
0
1
0
1
1
0
0
0
1
0
2
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
2
0
1
0
1
2
2
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
3
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
3
2
0
3
0
3
0
0
2
0
0
2
1
2
0
1
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
1
1
0
2
3
0
2
0
2
0
0
2
0
1
0
0
1
1
0
0
0
0
0
0
1
2
6
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
1
0
1
2
0
0
0
0
2
1
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
2
0
2
2
0
0
0
0
0
1
0
1
1
1
1
0
0
1
2
0
0
0
1
2
1
0
0
2
0
1
0
0
3
2
2
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
3
2
0
0
0
1
0
2
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
2
0
0
0
0
0
0
1
0
0
2
0
0
2
0
2
0
2
0
0
0
0
1
2
1
3
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
3
2
2
0
0
2
1
0
0
0
0
2
2
0
0
0
0
0
0
1
3
0
1
2
1
1
0
1
0
2
0
0
2
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
1
0
0
0
0
0
1
1
1
0
0
0
0
0
1
1
0
1
1
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
2
0
3
0
0
0
2
0
1
0
1
0
1
2
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
1
0
1
1
0
2
0
3
0
1
0
0
0
0
0
0
2
1
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
3
0
0
0
1
1
1
0
0
0
0
1
0
2
0
0
1
2
2
0
0
0
0
0
1
2
4
1
2
0
0
0
0
1
2
2
0
2
1
0
0
0
1
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
2
0
0
2
0
1
0
0
1
0
0
0
0
0
2
0
2
2
2
0
0
1
4
0
1
0
0
0
0
0
7
0
0
1
0
0
0
2
0
2
0
2
1
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
1
0
0
0
0
0
0
0
1
0
0
0
2
0
1
1
2
0
3
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
2
1
0
1
0
0
2
0
1
0
2
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
1
0
1
0
2
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
2
0
0
1
2
2
1
0
0
0
0
1
2
1
2
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
2
2
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
2
1
0
0
2
0
0
0
0
1
0
1
0
2
0
0
2
0
0
0
0
1
2
0
1
0
1
0
2
0
0
5
0
0
0
0
0
1
1
0
0
0
1
0
0
0
2
1
1
0
1
0
1
1
0
2
0
0
0
1
0
2
1
1
0
1
1
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
1
2
0
0
2
0
2
0
2
0
0
0
0
1
2
0
1
1
0
0
0
2
0
2
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
2
0
0
1
0
0
2
0
0
1
0
1
0
0
1
0
0
0
1
3
0
0
0
0
1
0
2
0
0
0
1
0
0
0
2
1
0
0
1
0
0
0
0
2
0
0
0
1
1
1
2
2
8
0
1
1
1
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
2
0
2
2
0
3
1
1
1
0
0
0
0
0
0
1
5
0
0
0
0
0
1
0
1
0
0
2
1
2
0
0
0
0
0
0
0
0
0
2
0
3
2
1
0
0
1
0
0
2
0
0
0
0
2
4
0
0
0
0
0
0
0
2
0
9
0
0
1
0
0
1
0
0
0
3
0
1
0
0
1
2
0
1
0
0
0
0
0
0
0
4
0
0
2
0
0
1
2
2
0
0
1
2
0
0
2
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
2
2
0
1
0
0
0
0
0
0
2
0
1
1
0
0
2
0
1
0
0
2
0
0
0
0
1
0
1
0
0
2
1
0
1
1
1
2
0
1
1
0
0
0
0
1
2
0
1
0
1
1
0
0
0
0
1
0
2
0
0
0
1
0
0
1
0
2
0
0
1
0
1
0
0
1
0
0
0
0
0
0
2
0
0
2
3
0
0
0
2
0
2
1
0
0
2
1
0
0
0
0
0
2
0
2
0
2
0
2
0
1
0
0
2
2
0
3
0
1
0
1
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
2
2
0
0
1
6
0
0
1
0
0
0
1
0
0
0
2
0
2
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
2
0
1
1
0
0
0
0
2
0
0
1
0
0
0
2
0
1
0
0
0
0
0
1
0
1
2
2
0
1
0
0
0
0
0
4
0
0
0
1
0
0
0
0
2
0
3
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
3
0
0
0
2
1
0
1
1
2
0
0
0
0
1
2
0
1
0
2
0
0
1
0
1
0
4
0
2
0
0
0
0
2
0
0
2
0
0
2
1
0
4
0
0
3
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
2
2
0
0
1
0
2
1
0
0
2
0
0
1
2
0
0
0
0
0
0
4
0
0
0
1
0
0
2
0
0
2
2
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
2
1
0
0
1
3
2
0
0
2
0
0
1
0
0
0
0
0
4
1
0
0
0
0
1
2
3
0
0
0
0
0
0
0
0
0
0
0
2
3
1
2
2
0
0
1
3
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
4
0
1
2
0
1
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
2
2
0
2
0
0
1
0
2
2
0
2
0
1
0
2
0
1
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
2
0
1
0
0
0
2
1
0
1
0
0
0
0
2
2
0
2
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
1
0
2
2
2
2
1
0
0
0
2
0
0
0
0
0
1
1
0
0
0
1
1
0
0
1
1
2
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
2
0
1
2
0
1
0
0
1
0
0
1
4
1
2
0
0
1
3
0
1
1
0
2
0
2
0
1
0
0
2
0
1
0
0
1
2
0
2
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
2
0
1
0
1
0
2
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
4
0
1
0
0
2
0
0
0
1
0
2
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
2
1
1
0
1
0
0
0
0
0
2
0
0
0
0
2
1
2
0
0
1
0
0
0
0
0
1
4
0
3
0
1
0
1
0
0
1
0
0
1
0
1
0
2
1
0
0
0
0
6
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
2
0
3
0
1
0
0
0
1
1
0
2
0
2
0
0
0
0
0
2
1
2
0
2
1
0
0
0
0
1
1
0
1
2
0
1
0
2
0
0
0
0
2
2
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
2
0
1
0
0
0
0
0
0
2
1
0
0
0
0
2
0
1
0
2
1
0
1
0
1
0
3
0
0
1
1
0
1
0
0
1
0
2
0
0
0
2
0
1
0
0
1
0
0
0
1
2
2
2
0
0
0
0
0
0
0
2
2
2
0
0
2
1
0
0
0
0
0
2
0
0
7
0
0
0
0
1
1
3
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
1
0
2
0
0
2
2
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
3
0
1
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
1
0
0
0
1
1
0
2
0
0
2
0
0
1
0
0
0
0
2
4
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
1
2
0
2
0
2
2
0
0
1
0
0
0
1
2
0
0
1
0
2
4
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
2
0
0
2
1
1
0
0
0
0
1
0
2
4
2
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
1
0
2
1
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
4
1
3
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
1
3
0
0
0
0
0
2
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
2
2
1
0
0
1
0
0
0
1
0
1
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
1
1
0
0
0
1
4
0
2
0
0
0
0
0
2
0
0
2
0
0
2
2
0
3
1
0
0
2
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
2
0
0
0
1
1
0
1
0
0
0
1
0
1
0
1
3
2
0
1
2
0
0
0
1
0
2
1
0
1
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
2
2
1
1
1
0
1
0
0
0
0
0
0
2
1
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
2
0
1
2
0
0
1
1
1
0
0
2
0
1
0
0
1
0
0
2
0
0
1
1
9
1
0
0
0
0
0
1
2
0
0
0
1
0
0
1
2
2
0
0
2
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
1
1
0
0
1
0
0
0
1
0
2
0
0
1
0
0
0
0
0
2
1
2
1
2
2
0
3
2
0
0
0
0
3
2
2
0
0
1
0
2
0
1
0
0
0
1
0
2
0
3
0
0
0
2
1
0
0
0
0
2
0
0
0
1
2
1
1
0
1
2
0
0
0
0
1
0
2
0
2
0
0
0
2
0
0
0
2
0
2
0
1
0
0
2
0
0
0
0
2
1
0
0
0
2
0
2
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
5
1
3
0
0
0
1
2
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
1
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
2
0
4
0
2
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
2
0
1
1
2
0
2
0
2
0
1
0
1
0
0
0
0
1
2
0
0
2
2
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
4
0
0
3
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
3
1
2
3
0
0
0
0
0
0
2
1
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
4
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
1
1
0
0
2
0
1
0
1
4
0
0
0
0
0
0
2
0
0
0
0
3
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
1
2
0
2
0
0
0
2
0
0
1
0
0
3
0
2
2
2
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
1
1
2
1
0
3
2
2
1
0
0
2
0
1
2
0
0
2
1
2
0
1
2
0
0
0
1
0
0
3
0
1
0
0
0
0
0
1
0
0
1
0
0
2
2
2
2
2
0
1
0
0
2
2
2
0
0
1
1
0
0
0
0
4
0
0
0
0
2
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
2
3
1
0
0
0
0
0
0
2
5
0
2
0
0
0
0
0
2
0
0
1
1
0
1
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
1
2
0
0
0
1
3
2
0
2
0
0
3
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
2
1
0
0
1
1
0
0
0
1
0
1
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
2
0
0
1
2
2
0
0
0
1
1
0
1
2
0
0
2
2
0
1
2
0
0
1
1
2
1
0
3
0
0
1
2
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
2
0
2
0
0
0
1
2
0
0
2
2
0
0
0
0
2
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
1
0
1
0
1
1
0
2
1
0
0
1
0
0
0
1
0
0
1
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
2
0
1
0
2
0
1
1
2
2
2
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
4
0
2
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
1
3
0
0
0
1
3
0
0
2
2
0
0
0
0
0
2
2
0
0
2
0
0
0
0
4
0
0
0
1
1
1
0
1
0
0
0
2
2
2
2
0
1
2
0
1
0
1
0
0
0
0
0
0
1
0
0
3
0
0
0
2
0
5
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
2
0
0
0
3
0
3
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
2
1
0
0
2
2
2
0
2
0
0
2
2
0
1
0
0
1
0
0
2
0
0
0
2
2
0
1
0
2
0
0
2
2
2
0
0
0
0
0
2
2
0
0
0
3
0
0
2
0
0
0
0
0
2
0
0
0
2
1
3
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
4
2
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
2
2
1
2
1
2
0
2
0
0
0
0
0
1
0
1
0
0
0
2
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
1
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
1
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
3
0
0
0
0
0
1
0
0
2
0
2
2
0
0
0
2
0
0
2
1
0
1
0
0
2
0
1
1
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
1
2
0
1
1
0
1
2
0
0
0
0
0
0
0
0
0
2
1
1
0
0
1
0
1
0
0
1
0
0
0
0
2
1
0
2
0
2
3
0
1
0
0
0
0
0
2
2
2
0
0
1
0
3
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
3
1
0
1
2
0
0
3
0
1
0
0
2
1
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
1
0
0
0
2
1
2
2
1
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
2
2
0
1
1
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
8
0
0
0
0
0
0
0
1
1
0
0
1
0
0
2
0
0
0
3
0
0
0
1
0
0
0
0
1
1
2
0
1
2
4
2
2
0
0
0
2
0
2
1
0
2
0
1
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
1
0
2
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
5
1
0
0
1
1
2
0
5
0
1
2
0
1
0
2
2
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
3
1
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
2
2
0
0
1
0
0
0
1
0
1
0
0
0
0
0
2
0
0
4
0
0
1
0
0
0
0
1
1
0
1
0
0
0
4
0
0
0
0
5
0
0
2
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
2
0
1
0
2
0
0
2
2
0
1
1
1
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
2
3
1
2
0
1
0
2
1
0
3
1
0
0
1
2
0
1
0
0
1
1
1
0
1
0
0
0
0
2
0
0
3
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
2
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
1
1
0
0
0
1
2
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
2
0
1
0
0
1
3
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
2
0
0
0
0
1
2
0
0
1
0
0
0
2
1
0
0
1
0
1
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
4
1
2
1
0
1
0
0
2
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
1
0
0
3
0
1
0
0
1
3
1
1
0
0
0
1
0
2
0
0
0
0
5
0
0
5
0
0
1
0
2
1
2
1
0
5
0
3
0
1
0
3
0
0
0
1
0
0
0
0
2
3
2
2
0
1
3
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
2
0
2
1
0
0
0
0
0
0
1
0
0
1
2
1
0
3
1
0
2
0
0
0
0
1
0
0
0
0
2
2
0
0
1
0
0
0
0
0
2
0
2
0
0
1
2
4
2
0
3
0
0
1
1
0
0
0
2
0
0
0
2
2
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
6
1
0
2
0
1
0
0
0
0
0
0
0
1
2
1
0
1
1
2
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
2
0
0
0
0
0
0
2
0
2
0
2
0
0
0
2
0
1
0
0
0
2
1
2
1
3
0
0
0
3
2
0
1
1
0
0
0
0
1
3
2
3
0
0
0
0
2
0
2
2
0
1
1
0
0
2
2
0
0
0
0
0
1
2
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
2
0
1
2
1
0
0
2
2
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
1
1
0
1
0
2
0
0
1
2
0
0
0
2
0
0
0
0
0
0
2
0
2
0
1
4
0
0
1
2
0
0
1
0
0
1
1
2
3
0
0
0
0
0
0
1
0
0
2
0
1
0
0
2
1
0
2
0
0
0
0
0
1
0
2
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
2
0
1
1
0
0
2
0
2
0
0
1
0
1
0
0
0
0
2
0
0
0
1
2
4
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
2
1
2
0
0
0
1
0
1
1
0
0
0
1
1
2
0
2
0
1
0
0
1
2
2
1
1
0
0
1
2
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
1
1
0
1
1
2
1
0
5
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
3
0
0
2
0
0
0
2
1
0
2
0
1
2
1
0
0
0
0
4
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
2
2
0
0
1
0
0
0
0
0
2
0
2
0
0
1
2
0
1
1
1
1
0
0
0
0
0
0
0
0
0
2
0
0
2
1
1
0
1
0
0
1
0
0
3
1
1
0
1
2
4
1
2
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
3
0
1
2
0
0
2
0
2
0
0
0
0
1
0
0
2
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
1
0
0
0
1
0
0
0
0
0
1
1
0
1
1
0
0
2
0
3
1
0
0
1
4
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
2
0
2
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
1
0
0
0
0
1
0
2
0
1
0
0
0
0
2
1
0
0
1
1
0
0
0
0
0
1
1
1
0
2
0
0
0
2
3
0
2
0
0
0
0
0
0
0
0
0
0
0
2
4
0
0
1
0
0
0
0
1
2
0
1
1
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
1
3
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
1
0
1
4
1
1
2
0
0
0
0
1
0
0
0
2
2
2
0
1
0
3
0
2
3
1
0
1
1
0
0
1
0
3
0
0
0
1
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
2
1
0
0
1
0
0
0
0
1
0
3
0
0
2
0
0
1
0
0
1
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
1
0
0
0
3
0
1
0
0
0
1
2
1
0
2
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
2
2
0
0
0
2
0
0
2
0
0
0
2
0
2
2
1
0
0
6
0
2
1
0
0
3
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
3
3
2
1
1
2
0
0
1
1
2
0
0
0
0
0
0
0
0
2
0
1
0
1
2
0
1
0
0
1
0
2
2
0
0
0
2
2
1
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
1
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
3
2
4
1
2
1
1
2
1
0
0
1
0
0
2
2
0
0
0
2
2
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
2
1
0
0
1
2
0
2
2
0
0
0
0
0
2
2
1
0
0
0
0
1
0
1
0
2
2
2
0
2
0
0
0
0
0
0
3
0
0
0
1
0
1
0
1
0
0
0
3
0
2
2
0
1
2
0
2
0
0
0
0
2
0
2
2
2
1
0
1
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
3
2
0
0
0
2
0
1
3
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
2
1
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
2
1
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
2
1
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
1
0
0
0
0
1
1
1
2
1
0
2
0
2
1
0
0
0
0
0
0
2
3
1
1
0
1
0
0
2
0
1
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
6
1
0
2
2
3
0
0
2
2
1
0
1
1
2
3
0
0
0
2
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
1
1
0
2
1
2
0
0
0
0
1
0
1
0
0
2
0
2
0
1
0
0
0
0
0
3
0
2
0
0
2
0
1
0
0
0
0
0
1
0
0
1
3
0
0
0
0
0
1
0
0
2
2
1
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
2
0
0
1
0
0
0
1
0
2
0
2
0
2
0
0
3
0
2
0
0
0
0
1
1
0
0
0
1
2
0
0
0
0
0
0
6
2
2
0
1
0
2
0
1
0
1
2
0
0
2
2
0
0
0
0
3
0
0
1
2
1
0
2
2
2
0
1
0
0
1
0
2
1
0
0
0
0
1
2
0
2
2
0
0
0
0
1
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
1
2
0
0
0
0
2
0
1
2
0
0
0
0
0
1
0
1
0
0
0
1
0
2
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
3
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
5
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
1
0
3
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
2
2
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
2
2
0
0
2
2
0
1
2
0
0
0
0
1
0
1
1
0
1
1
0
0
2
1
0
1
0
2
0
0
0
4
0
0
0
0
0
0
0
2
0
2
2
0
1
0
2
0
0
1
0
0
2
0
1
0
0
0
0
2
1
1
1
0
0
0
0
0
2
1
0
0
1
0
0
2
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
3
0
0
0
2
5
0
1
0
0
0
0
1
0
2
0
0
0
2
1
1
0
1
0
2
0
1
1
0
1
0
0
2
3
0
0
0
1
1
0
0
0
0
2
2
0
1
0
0
0
2
1
0
0
0
0
1
0
0
1
0
0
2
1
0
0
0
0
0
2
0
0
1
2
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
1
1
0
0
1
2
0
0
0
1
0
0
2
0
0
0
0
2
1
2
0
1
1
0
1
2
1
1
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
1
0
1
2
0
2
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
1
0
0
2
0
0
0
1
1
0
0
0
2
1
0
0
0
0
0
0
0
2
1
2
0
0
0
0
1
0
1
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
2
0
2
0
0
1
2
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
2
1
0
2
1
0
0
2
0
0
0
0
2
0
1
2
1
0
3
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
6
0
2
0
2
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
2
0
2
1
0
1
0
1
1
2
2
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
2
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
1
2
1
0
0
0
0
0
0
1
0
0
0
0
2
3
2
2
0
0
2
0
0
0
0
2
1
0
0
0
0
0
1
0
2
0
0
2
2
0
2
0
0
2
0
1
1
0
1
0
0
0
2
2
0
1
0
0
0
2
0
2
0
2
0
2
0
2
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
1
6
0
0
0
0
3
2
0
0
1
0
0
0
0
0
2
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
1
0
2
2
0
1
0
1
0
0
0
0
2
2
1
0
0
0
0
0
0
0
1
2
0
1
1
0
0
2
2
0
0
1
2
0
0
5
0
0
0
2
1
0
0
0
1
0
0
2
2
0
0
2
0
1
2
0
0
0
0
0
2
0
1
1
0
0
0
0
2
2
3
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
2
0
3
0
1
1
2
0
0
0
0
0
3
2
0
1
0
0
0
2
1
1
0
1
0
0
0
0
2
0
0
2
1
0
0
1
0
1
2
0
1
2
1
3
0
1
1
1
0
0
0
0
0
0
0
0
1
2
2
0
0
0
1
0
0
0
1
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
1
1
1
0
0
0
1
0
0
1
0
1
0
0
0
0
2
0
2
0
0
1
1
0
0
2
0
0
0
0
0
1
2
3
0
0
0
0
2
0
1
0
0
0
1
1
0
1
0
0
0
0
0
1
2
0
1
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
2
0
0
0
2
1
1
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
2
3
2
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
2
1
1
0
0
0
2
0
0
0
1
1
0
0
0
0
1
0
0
0
2
0
1
0
1
0
1
0
0
2
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
2
0
0
0
0
2
2
1
0
1
2
1
0
0
0
2
0
0
2
0
0
1
1
0
2
0
1
0
0
2
0
1
1
0
1
2
0
2
0
0
3
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
2
0
0
2
0
1
0
0
0
1
1
0
0
0
2
0
1
2
0
0
0
0
0
0
3
2
0
0
5
2
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
4
0
0
0
0
0
3
0
0
0
0
0
2
1
0
3
0
0
0
0
2
2
0
0
0
0
0
1
1
0
0
1
2
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
2
1
0
2
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
2
1
0
0
1
0
0
1
1
0
0
2
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
2
0
1
1
0
2
2
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
1
1
0
1
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
2
0
1
0
0
1
0
0
0
2
2
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
2
2
0
0
0
1
2
0
0
2
0
0
0
0
0
1
0
3
0
0
1
0
1
1
5
2
0
0
0
0
0
1
1
0
2
0
2
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
2
2
0
0
2
0
1
2
1
0
0
3
2
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
1
0
2
2
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
4
2
0
0
1
0
0
0
1
2
2
2
2
0
0
1
0
0
1
0
1
0
0
1
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
2
2
0
0
2
1
0
0
0
2
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
1
0
0
0
1
0
1
0
0
0
0
2
2
0
1
3
1
0
0
0
0
0
3
1
0
1
0
0
0
0
1
0
0
0
1
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
2
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
2
2
0
4
0
0
2
0
0
0
0
2
0
0
2
0
0
0
1
0
0
1
2
0
1
0
0
0
1
0
0
1
0
2
1
0
0
1
0
0
0
2
0
2
0
0
2
0
1
0
2
0
0
0
0
0
0
2
0
1
0
0
1
1
0
2
0
0
1
0
0
2
0
0
5
0
0
0
1
2
1
0
0
0
0
0
0
2
0
0
0
0
2
0
2
1
1
2
0
0
0
4
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
1
0
2
1
2
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
1
0
1
0
2
1
1
1
0
0
0
0
0
0
0
1
2
0
0
0
2
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
4
1
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
2
1
0
1
0
0
0
1
2
0
0
0
2
1
0
0
0
2
0
0
1
0
1
3
0
0
0
0
2
0
0
0
2
1
0
0
1
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
2
0
0
1
0
0
0
1
1
0
1
0
0
2
0
0
0
0
0
0
0
3
0
2
2
0
0
0
0
0
0
0
0
2
3
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
2
1
2
1
2
2
1
2
2
0
1
0
0
0
0
0
0
1
0
1
0
1
0
2
0
0
1
2
3
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
3
0
2
1
2
1
0
0
0
0
2
0
2
0
2
0
1
0
1
0
3
0
0
0
1
0
2
0
0
0
2
0
1
0
2
1
0
0
0
1
0
0
0
0
2
1
0
1
0
3
0
0
0
0
2
0
0
0
2
0
2
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
2
0
2
0
0
1
0
0
0
3
2
0
1
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
1
0
1
0
1
0
1
0
0
2
0
0
0
0
3
0
0
2
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
1
1
0
0
0
0
0
2
0
2
0
0
1
0
2
0
1
0
0
3
2
0
0
0
2
1
0
0
0
0
2
0
0
1
0
2
4
0
0
1
2
1
0
0
1
0
3
0
0
0
0
1
0
0
0
1
3
2
2
0
2
2
0
0
2
1
0
2
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
2
0
2
1
0
0
0
0
0
2
1
0
1
0
0
1
0
2
2
0
1
0
0
2
0
1
1
0
1
0
2
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
1
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
4
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
2
0
0
0
1
2
2
2
0
1
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
1
1
2
2
2
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
7
1
2
2
0
0
1
0
0
0
2
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
1
1
1
2
0
0
2
1
2
0
0
2
1
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
2
1
4
2
3
0
0
2
0
0
0
1
1
2
0
0
0
2
3
0
0
1
0
0
1
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
5
2
2
1
0
1
0
0
1
0
0
0
1
1
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
1
2
0
1
3
3
0
1
1
0
1
0
0
0
0
0
0
2
1
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
1
3
0
0
0
2
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
2
1
0
1
0
1
1
1
2
2
1
0
2
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
2
2
0
0
1
2
0
1
1
2
2
0
1
1
0
0
0
1
1
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
1
0
2
0
0
0
0
0
2
0
2
0
1
1
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
1
2
0
1
0
1
0
2
0
0
2
0
0
0
0
0
1
1
0
1
0
1
0
0
0
1
0
0
0
0
2
2
1
2
1
0
0
2
0
1
0
0
2
0
1
0
0
0
0
2
2
1
0
0
0
2
2
0
1
1
2
0
1
1
1
2
2
0
2
2
0
0
0
0
2
0
0
0
2
0
0
0
0
1
1
0
0
1
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
3
0
0
0
0
0
3
0
0
0
0
1
0
0
0
1
2
0
1
0
0
0
2
0
2
2
0
2
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
4
2
4
0
0
0
0
0
2
0
0
0
2
0
0
2
2
0
0
1
0
0
0
3
0
2
1
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
3
0
2
1
0
3
0
0
1
0
0
1
0
0
1
0
0
0
2
0
2
0
0
0
0
1
0
2
0
0
0
0
1
0
0
2
0
0
2
0
0
1
0
1
1
2
1
0
0
0
0
1
0
0
0
2
1
0
1
0
0
0
1
1
1
0
0
0
0
0
0
4
1
0
0
0
3
0
0
1
0
1
0
0
0
0
2
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
2
1
2
0
0
0
0
0
1
0
0
0
0
0
5
2
1
1
0
2
0
3
0
1
0
0
1
0
2
0
0
0
0
1
0
0
0
2
0
1
1
0
2
0
3
0
0
0
1
0
4
2
1
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
12
2
0
0
0
2
1
0
1
1
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
2
0
2
1
1
0
0
1
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
2
1
0
0
1
1
0
0
0
0
2
0
1
0
0
0
0
0
0
2
1
0
0
0
0
1
2
0
0
1
2
2
1
0
0
0
0
2
0
1
0
2
0
1
0
2
1
0
0
12
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
1
0
0
0
3
2
19
2
0
2
0
4
0
1
2
0
0
0
1
0
0
0
4
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
4
0
0
0
0
1
0
1
0
0
1
0
2
0
0
2
3
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
1
0
3
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
1
2
0
1
0
0
0
3
0
0
2
1
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
2
0
0
3
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
1
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
1
1
0
0
0
2
0
2
2
0
0
1
0
2
0
1
0
2
1
0
1
0
0
0
0
1
0
2
0
0
1
1
0
2
2
0
4
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
1
0
2
2
0
1
3
0
7
0
2
0
2
0
0
0
3
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
2
2
0
1
1
0
0
2
0
0
3
1
0
0
2
0
4
0
2
0
2
1
0
1
2
0
0
0
0
0
0
1
0
2
1
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
1
0
0
0
2
2
0
0
0
2
0
0
0
0
1
2
0
2
2
0
0
1
1
0
0
2
0
0
3
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
1
0
0
0
1
0
1
2
0
0
0
1
0
0
2
0
2
0
1
1
1
0
2
0
0
0
0
0
0
3
2
0
0
0
1
2
1
0
0
2
0
0
2
0
0
0
0
2
0
0
2
1
0
2
0
1
1
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
2
2
1
0
1
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
2
0
2
0
0
2
0
0
0
0
1
0
0
0
4
0
0
0
1
0
1
1
0
0
1
0
0
1
0
0
0
3
0
1
1
1
0
0
1
2
0
0
3
0
2
2
0
2
2
2
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
3
0
0
0
2
0
1
0
0
0
0
0
2
1
0
0
0
1
0
0
1
1
0
2
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
1
1
2
0
0
0
2
0
0
0
1
0
0
0
2
0
2
1
1
0
0
0
0
0
1
0
0
0
2
1
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
3
1
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
2
1
0
0
1
0
0
0
1
1
2
0
2
0
2
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
1
4
0
2
0
0
2
0
0
0
3
0
0
1
0
0
2
0
0
0
1
0
10
1
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
2
0
2
2
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
2
1
0
2
0
4
0
2
1
0
2
1
0
1
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
2
0
0
0
1
1
1
1
0
0
1
0
0
0
0
0
0
2
1
0
0
2
1
0
0
0
0
0
0
1
0
0
2
2
0
1
2
0
0
0
0
0
1
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
2
1
0
2
2
2
0
0
0
0
2
0
0
4
0
2
0
0
0
2
2
0
0
1
0
0
2
0
1
1
0
1
0
0
1
0
0
2
0
0
1
0
0
0
2
0
0
5
2
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
2
0
2
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
1
0
0
2
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
1
1
0
0
1
2
0
0
2
0
1
0
0
2
0
0
0
0
1
0
1
1
0
0
0
2
0
1
2
0
0
0
0
3
1
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
2
0
0
0
1
0
2
2
0
0
0
0
0
1
0
1
0
1
0
2
0
0
0
0
1
0
0
0
0
3
0
0
0
0
1
2
3
2
0
0
0
0
0
0
0
0
0
0
1
0
5
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
1
0
1
2
2
2
2
0
1
0
0
0
1
0
1
0
1
0
1
1
2
0
0
0
1
2
0
1
1
0
0
1
0
0
2
0
0
0
0
0
1
0
0
2
1
0
1
0
0
0
0
0
2
0
0
0
1
1
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
4
0
0
0
1
0
0
3
0
3
0
0
0
2
2
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
2
0
0
1
2
2
0
0
0
0
3
2
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
7
0
1
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
2
1
0
1
0
1
0
2
0
0
0
1
0
0
2
0
0
3
0
1
1
1
0
0
0
2
0
1
1
1
1
2
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
4
0
0
0
1
0
0
2
1
0
1
0
0
0
0
3
2
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
1
1
0
2
1
0
0
1
0
0
1
0
0
0
0
0
0
1
2
0
2
0
0
0
0
1
0
0
0
4
3
2
0
1
0
0
1
0
0
0
3
0
0
0
0
0
0
0
1
0
1
1
0
1
1
0
0
0
0
0
3
0
2
1
2
1
1
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
1
0
2
1
1
2
2
0
3
0
0
0
0
0
0
0
0
4
0
0
3
0
0
1
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
2
0
0
2
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
1
0
0
0
1
2
0
0
1
2
1
0
1
0
0
2
1
0
1
0
0
0
1
1
0
0
1
1
0
1
2
0
1
2
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
3
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
1
0
0
0
1
0
2
0
0
0
2
2
1
0
0
2
2
1
0
1
0
0
0
2
0
0
2
2
1
0
0
2
2
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
2
0
3
0
0
0
0
0
0
0
2
2
0
0
0
0
2
1
4
2
4
1
2
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
3
0
0
3
0
0
0
2
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
1
2
0
0
0
0
1
0
0
1
2
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
3
2
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
2
3
0
0
0
2
0
2
0
0
0
2
1
2
2
0
0
2
0
0
0
1
0
0
0
1
0
0
2
2
0
0
0
2
0
0
0
1
2
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
1
1
0
0
0
2
2
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
2
0
0
0
0
0
1
2
2
0
0
0
2
0
0
2
2
0
0
1
0
0
2
1
0
7
0
0
2
0
2
0
0
1
2
0
0
0
0
0
0
0
0
1
1
1
0
1
0
1
1
1
0
0
2
0
0
1
0
0
1
0
0
2
0
0
0
0
0
3
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
2
1
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
3
0
2
1
1
0
2
0
0
0
2
0
1
0
0
0
0
0
1
1
0
0
1
2
0
0
2
0
3
2
2
0
1
2
0
0
0
0
2
0
2
2
0
1
2
0
0
2
0
0
0
0
0
0
0
0
3
0
1
1
0
0
0
0
0
0
0
0
0
2
0
1
1
0
1
1
0
0
1
0
0
6
0
0
0
2
0
2
0
1
0
0
2
2
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
2
0
0
1
1
3
2
1
0
0
3
0
0
2
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
2
1
1
0
0
1
0
0
1
0
0
2
0
1
2
0
0
2
0
2
2
1
0
1
0
2
0
4
0
0
0
0
0
1
2
1
0
0
0
1
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
7
1
0
1
0
3
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
1
3
0
2
2
0
0
1
0
0
0
0
2
0
2
2
0
0
0
2
1
1
1
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
2
0
0
2
0
0
2
0
2
0
2
0
0
0
0
0
0
0
1
0
2
2
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
2
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
2
0
0
0
0
0
2
1
1
2
2
0
1
1
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
2
1
0
1
0
1
2
1
4
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
1
1
0
0
0
0
0
1
0
0
0
4
2
2
2
1
0
0
0
0
0
1
0
2
0
1
0
0
0
0
4
3
0
1
0
2
2
2
0
2
1
0
0
0
0
1
1
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
3
2
2
0
0
0
1
1
3
0
1
0
1
4
2
0
0
2
0
0
0
1
0
1
2
0
2
0
0
0
2
0
1
2
0
1
0
1
0
0
10
1
0
0
0
1
2
0
0
1
0
1
0
0
0
2
0
0
1
0
0
1
0
0
0
2
2
0
0
2
0
0
0
0
0
2
0
0
0
0
3
0
0
2
0
0
1
0
0
2
0
0
0
2
0
1
2
0
0
0
2
0
0
0
0
2
0
0
2
5
0
0
2
0
3
0
0
0
0
0
2
0
2
0
2
2
1
0
0
1
0
1
0
1
0
0
0
2
0
0
4
1
2
2
0
2
0
0
0
0
1
0
0
1
2
0
0
0
0
0
2
0
0
1
1
1
1
0
0
1
0
0
0
2
1
0
2
0
0
0
1
0
1
0
1
0
2
2
0
1
0
4
2
1
0
0
0
2
0
1
1
0
1
1
1
0
1
2
1
0
0
0
1
0
0
0
1
7
0
0
0
3
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
1
2
0
0
0
2
0
2
0
2
1
0
0
0
0
1
0
0
1
1
0
1
0
2
2
0
1
2
0
1
2
0
0
0
2
0
0
3
1
0
0
1
0
0
0
0
0
0
0
1
2
1
0
2
1
0
0
0
2
2
2
3
0
2
1
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
3
1
1
0
2
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
1
0
2
0
0
3
0
0
2
1
0
2
1
0
0
0
0
0
2
0
0
1
2
0
0
0
0
2
2
0
2
2
0
1
2
0
0
2
4
0
0
0
0
0
0
2
0
1
0
2
0
0
2
2
0
0
0
2
0
0
1
1
2
0
2
1
0
2
1
0
0
0
1
0
2
0
2
1
0
0
1
0
0
2
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
3
0
0
2
2
2
0
0
0
0
0
0
0
2
0
1
0
0
0
1
2
2
0
1
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
5
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
4
0
2
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
1
2
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
1
1
0
0
0
0
0
0
2
1
1
0
0
2
0
0
0
0
0
0
2
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
3
1
0
0
1
2
0
2
1
2
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
2
2
3
1
0
0
1
1
0
0
0
0
0
2
0
2
0
0
0
1
0
2
2
0
0
0
1
2
1
0
2
0
0
0
0
0
0
2
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
1
0
0
0
2
3
2
1
0
0
0
0
0
0
2
0
1
0
0
2
0
0
4
0
0
2
1
2
0
1
0
0
1
3
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
2
2
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
2
4
0
2
2
0
0
4
2
0
0
6
0
0
2
0
0
1
0
0
0
1
2
0
0
1
1
1
0
0
2
1
0
0
0
0
1
0
1
1
0
0
1
2
0
2
2
0
0
0
1
2
0
2
0
2
0
1
1
0
1
0
2
1
1
0
0
1
0
2
0
0
0
0
2
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
3
1
2
0
1
0
0
0
0
1
0
0
1
0
0
0
0
2
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
1
0
0
2
1
0
0
0
0
0
2
0
0
1
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
2
0
0
1
3
0
1
0
0
0
0
0
1
0
2
2
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
1
0
0
0
0
0
2
2
0
2
2
0
1
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
1
0
0
0
1
2
1
3
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
2
0
3
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
1
2
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
1
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
1
2
0
1
2
1
2
1
2
0
2
0
1
0
0
1
2
0
0
0
0
0
2
0
0
1
1
0
1
0
0
0
0
2
0
0
0
0
1
0
0
2
1
0
1
0
0
0
0
2
1
0
2
2
0
0
0
1
0
0
1
0
0
1
0
0
0
2
0
0
1
0
0
2
0
0
1
1
0
0
0
2
1
0
1
0
0
0
0
0
0
1
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
2
2
0
1
1
0
0
0
0
2
0
0
2
2
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
1
0
0
3
0
0
0
0
3
0
1
1
0
1
0
0
0
1
1
0
0
0
0
0
0
2
0
0
2
1
1
0
0
0
1
1
0
1
0
2
1
0
0
0
0
0
1
0
0
1
0
0
4
0
0
0
0
0
0
1
2
0
1
0
0
0
2
0
0
0
1
3
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
2
3
0
0
0
0
0
1
1
0
2
2
0
0
0
4
0
0
1
0
0
1
0
0
3
0
2
0
1
2
0
0
0
0
0
0
0
2
2
0
0
8
0
0
0
0
0
3
0
0
0
0
2
1
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
4
0
0
1
2
0
2
1
1
1
1
2
1
0
0
0
0
0
0
0
1
0
0
1
0
3
0
1
0
2
2
0
1
2
0
0
0
0
0
0
1
3
0
1
0
1
0
0
0
1
0
1
2
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
3
0
1
1
0
2
1
0
0
1
0
0
0
0
0
0
0
2
1
1
1
1
0
0
0
2
2
0
2
0
1
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
1
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
3
0
6
0
1
0
0
0
0
0
2
0
4
0
0
1
0
1
1
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
1
0
0
2
1
0
2
1
0
0
2
2
2
1
2
0
0
0
1
0
0
3
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
1
0
1
1
0
0
0
1
0
1
0
1
0
0
1
3
0
0
2
1
2
0
0
0
3
0
0
1
0
0
0
2
0
0
1
2
1
1
0
3
0
0
2
2
0
0
0
2
2
2
0
0
1
1
0
0
0
0
0
1
0
0
0
0
4
0
0
0
2
1
1
1
0
0
0
0
0
1
0
6
0
0
0
2
2
0
0
4
0
1
0
0
0
3
0
1
0
2
0
1
0
1
0
0
2
0
0
0
2
0
0
2
0
2
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
2
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
2
1
1
0
4
0
0
0
0
1
0
1
0
1
0
0
0
0
1
3
1
2
0
0
0
1
0
2
1
1
0
0
0
0
2
1
1
0
0
0
0
0
0
1
0
1
0
1
1
2
1
2
0
1
1
0
0
2
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
1
0
3
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
1
2
1
0
0
4
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
2
0
2
0
0
1
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
1
2
2
1
1
2
1
1
2
0
0
0
2
0
0
2
1
0
1
0
0
0
0
0
1
0
0
3
0
0
0
1
0
0
0
0
3
0
0
0
3
0
0
0
1
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
3
2
0
2
0
0
0
0
4
2
0
3
1
0
0
1
0
0
0
2
0
0
0
0
2
0
2
2
2
0
0
0
0
0
0
2
0
0
0
2
0
2
1
1
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
2
2
0
0
0
0
2
1
0
4
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
1
0
2
2
1
2
1
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
2
0
1
0
0
1
1
0
0
2
0
0
0
3
0
0
0
0
0
1
1
0
2
1
2
0
2
0
1
2
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
3
0
0
0
1
0
0
0
2
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
2
0
1
0
0
0
0
0
3
2
0
1
0
0
0
0
0
3
0
0
0
0
0
2
1
1
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
2
0
0
0
4
2
2
2
0
2
1
1
0
0
0
0
2
6
1
3
0
0
1
0
0
0
0
0
1
0
2
0
0
1
0
0
2
0
1
0
0
1
2
0
1
0
0
0
0
2
0
0
0
0
0
0
1
2
0
2
2
0
0
0
0
2
1
2
0
1
0
0
0
2
1
2
0
0
0
2
0
3
0
0
0
0
0
3
0
0
0
0
0
1
0
1
0
0
0
0
0
2
2
1
0
0
0
0
0
2
0
1
0
0
0
1
0
0
2
0
1
3
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
4
0
2
0
0
1
2
1
0
0
0
1
4
0
1
0
1
0
0
0
0
0
1
0
0
1
0
1
1
0
0
2
2
0
2
1
1
1
0
0
0
0
2
1
0
2
0
1
1
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
1
0
2
0
0
0
2
0
0
0
0
0
1
1
1
0
3
0
2
1
1
0
0
0
2
0
2
0
2
1
0
0
1
0
0
1
0
0
0
0
0
1
6
0
0
2
0
1
0
1
0
0
0
0
2
1
1
1
0
0
1
0
2
0
2
0
0
2
0
0
0
0
0
1
0
1
2
2
2
0
1
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
1
0
0
0
1
1
0
0
0
1
1
0
0
0
2
0
0
0
2
2
0
2
0
0
2
0
2
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
2
2
1
2
2
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
2
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
4
0
2
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
2
0
1
0
2
0
2
0
0
3
1
0
0
0
0
2
7
0
0
2
2
1
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
2
2
0
0
0
0
0
0
1
0
0
1
0
0
2
2
1
0
0
0
0
1
0
0
0
0
0
2
2
0
1
2
1
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
6
0
1
2
0
0
2
2
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
1
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
2
0
2
3
1
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
2
0
0
1
1
2
2
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
1
0
1
1
1
0
0
0
1
0
0
2
1
0
0
0
1
1
0
2
2
1
1
0
1
3
0
0
1
0
0
0
0
1
0
0
2
1
3
0
1
1
2
0
0
0
0
1
2
0
0
0
2
0
0
0
0
3
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
2
0
1
1
0
0
0
0
2
1
0
1
0
2
2
0
0
1
2
0
0
2
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
2
2
0
1
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
1
0
0
2
2
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
1
1
0
0
0
0
4
2
0
1
0
0
1
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
3
2
2
0
0
0
0
2
1
0
0
0
2
0
0
1
0
0
0
1
1
0
0
1
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
1
0
1
0
0
3
0
0
1
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
2
0
0
0
1
1
0
2
1
0
1
0
0
0
0
1
0
0
1
1
0
0
0
2
0
1
0
2
1
2
0
1
0
1
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
2
0
1
0
2
5
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
3
3
0
1
0
7
1
0
0
2
1
0
2
0
0
0
0
0
1
0
0
1
0
0
1
0
1
1
0
0
1
0
0
1
1
0
2
1
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
3
0
2
0
1
1
2
0
0
0
0
2
0
2
0
2
0
0
0
0
2
2
2
2
2
2
1
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
2
2
0
0
0
0
2
2
0
0
0
0
0
0
3
2
0
2
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
1
1
0
0
0
0
2
1
0
2
0
2
1
1
2
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
1
0
0
5
0
0
1
0
0
0
1
0
1
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
2
2
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
2
1
0
2
0
0
2
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
1
0
1
1
1
4
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
2
2
2
0
2
3
1
0
0
2
0
0
0
0
2
1
0
0
1
0
1
3
3
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
1
2
1
0
0
0
0
0
1
0
0
1
2
1
0
3
0
0
1
0
2
0
1
1
0
0
1
1
0
0
1
0
0
2
0
0
1
1
4
0
0
4
0
0
0
0
0
2
0
0
1
0
0
1
0
2
1
0
0
0
1
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
1
1
0
0
0
0
0
3
0
0
2
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
2
1
0
1
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
3
0
1
0
0
1
1
0
2
0
0
0
1
0
0
1
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
1
1
1
6
0
0
0
2
0
0
0
0
2
2
2
0
1
0
0
0
0
1
0
1
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
1
1
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
3
1
2
1
0
0
0
0
0
1
0
0
1
1
1
2
0
0
0
1
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
2
2
0
2
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
1
2
0
0
0
0
2
2
0
0
0
2
0
0
2
1
0
0
0
2
0
0
2
0
0
0
2
0
2
0
2
0
0
2
2
1
0
0
0
0
1
0
0
0
2
1
0
0
1
0
0
0
4
0
1
1
0
0
1
0
0
0
0
0
1
2
0
5
0
2
0
0
2
2
0
0
0
0
2
2
0
1
1
0
0
0
2
0
1
0
0
0
2
2
2
0
0
2
0
0
0
0
0
2
0
1
1
0
0
1
0
2
0
0
0
0
0
0
7
0
0
0
1
1
0
0
0
3
0
2
0
0
0
0
2
2
0
1
0
1
2
0
2
0
1
2
0
1
0
0
1
5
0
2
1
0
0
0
0
0
0
2
0
0
0
3
0
0
1
0
2
0
0
4
0
0
2
2
0
1
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
1
1
1
2
2
1
0
1
0
2
0
2
1
0
0
0
0
0
2
0
0
3
0
1
0
2
0
0
0
0
2
0
1
0
0
2
0
0
2
0
0
2
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
2
0
2
1
2
0
0
0
0
1
0
0
0
1
0
0
2
2
3
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
1
2
1
0
0
0
0
2
0
0
1
3
1
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
2
0
0
1
0
0
3
0
2
1
1
0
0
1
2
0
1
0
1
6
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
1
0
2
4
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
2
1
1
0
0
0
0
0
2
0
0
0
2
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
2
0
2
1
1
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
5
0
0
0
0
0
0
2
0
0
2
0
0
0
2
2
0
1
2
0
1
0
0
0
2
1
1
1
0
0
0
4
0
1
0
2
0
2
0
3
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
2
0
0
0
2
2
1
0
0
1
0
0
0
2
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
1
2
0
0
2
0
0
0
0
0
1
1
0
0
0
3
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
2
1
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
1
0
1
1
0
0
1
0
1
2
0
0
1
0
1
0
4
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
2
0
0
2
0
1
2
0
0
2
1
0
0
0
2
0
0
0
0
0
1
2
0
2
0
2
1
2
0
0
0
2
2
0
1
2
0
0
2
0
1
0
2
0
0
2
0
2
2
0
0
0
2
0
2
1
2
0
0
0
0
1
1
0
1
1
0
0
1
0
0
0
1
2
0
0
0
0
0
0
4
0
0
1
2
1
0
2
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
3
0
0
0
2
0
0
0
1
2
0
0
0
2
0
1
0
0
0
1
0
0
1
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
1
1
0
1
2
1
2
2
0
0
0
2
1
3
1
0
0
0
0
0
2
1
0
1
0
2
0
0
0
0
0
2
2
2
0
0
0
1
0
0
0
1
1
2
0
0
2
0
0
1
0
4
0
0
1
0
0
0
1
0
0
1
1
2
0
0
2
0
0
2
2
0
1
2
1
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
12
0
0
1
0
0
0
2
0
2
2
1
2
0
3
0
1
2
0
1
3
0
0
1
0
2
0
4
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
2
0
0
0
0
0
2
0
1
1
1
0
2
0
0
0
0
1
2
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
1
0
1
0
0
0
2
1
0
0
2
2
2
1
2
0
0
0
0
1
0
2
4
0
3
0
0
2
2
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
5
0
0
0
2
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
2
0
1
2
2
0
2
0
2
1
2
2
0
0
0
0
1
0
0
2
0
1
3
0
0
2
0
0
0
0
1
0
0
0
1
0
2
1
0
0
0
2
0
1
0
0
2
0
0
2
1
2
0
0
0
0
0
0
3
0
0
2
0
0
2
0
1
0
0
0
0
1
0
2
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
1
0
1
0
0
2
0
1
2
0
1
1
2
3
0
1
0
3
0
0
2
0
1
0
3
0
0
0
0
4
1
0
1
0
0
0
2
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
1
0
0
1
0
1
2
0
0
1
0
1
1
0
0
0
2
0
0
0
0
0
0
4
2
2
1
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
3
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
2
1
0
3
1
1
8
0
0
0
0
0
2
1
1
0
0
4
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
3
2
0
2
6
1
0
0
1
0
1
0
1
0
0
0
2
0
0
1
0
0
1
1
1
0
0
1
1
2
0
0
0
0
1
1
0
0
1
0
0
0
2
0
0
0
6
0
1
2
0
0
0
0
1
0
0
0
0
0
0
1
2
2
2
0
0
0
0
2
0
0
0
0
2
2
2
0
0
0
1
1
0
0
0
2
0
2
2
0
3
0
0
1
0
1
0
0
1
1
0
0
1
2
0
1
0
0
2
1
0
0
0
1
0
0
1
0
1
2
0
1
0
2
0
1
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
1
2
2
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
5
0
0
0
1
0
2
0
0
1
0
3
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
7
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
1
0
3
0
1
1
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
2
0
2
0
4
1
0
0
0
0
0
0
0
1
0
0
2
2
0
1
1
0
2
0
2
0
0
0
0
0
1
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
2
0
0
2
0
1
1
0
1
0
1
2
0
0
0
0
2
0
1
3
1
1
1
0
0
0
0
1
2
0
0
2
0
0
0
1
0
0
0
1
2
0
2
0
0
0
0
1
0
0
1
0
0
0
2
0
1
0
1
0
0
1
0
1
0
0
2
0
1
1
0
2
0
1
0
0
0
0
2
1
1
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
2
1
1
0
0
0
1
0
0
0
0
3
1
0
1
1
0
2
1
0
0
0
0
2
0
1
2
1
0
0
5
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
2
0
1
2
0
0
0
1
0
1
3
0
0
1
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
2
0
0
1
0
3
0
0
0
0
2
1
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
2
1
0
1
0
0
2
0
0
0
1
0
0
0
3
0
0
0
0
1
2
2
1
1
0
0
0
2
0
2
2
1
1
0
0
2
0
1
0
0
2
1
1
0
0
2
2
1
2
0
0
0
2
0
0
0
0
0
0
1
1
0
0
2
0
3
0
0
0
4
1
0
1
0
0
2
0
0
0
0
1
1
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
1
0
1
0
2
0
0
0
0
0
0
2
1
0
0
1
0
0
0
1
0
0
0
3
1
0
0
0
0
0
2
0
0
5
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
2
0
0
2
1
2
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
3
0
0
2
0
0
0
2
1
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
1
1
2
0
0
0
0
1
2
3
0
0
0
0
1
2
0
0
0
2
0
0
0
2
1
0
0
0
0
0
1
0
1
1
2
1
0
2
0
0
1
0
0
0
0
0
2
0
2
0
0
2
2
0
0
1
0
0
1
2
0
0
4
0
0
2
2
0
2
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
1
0
0
0
2
0
0
2
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
2
1
1
0
0
2
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
1
2
0
1
0
2
0
1
0
1
0
0
2
0
2
0
1
1
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
3
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
1
1
1
0
0
0
0
2
0
2
0
2
1
0
1
0
0
0
0
2
0
0
1
0
1
0
2
0
0
2
3
0
0
0
0
0
1
0
3
1
2
0
0
0
0
0
2
3
0
2
2
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
2
2
1
2
1
1
2
0
1
1
0
0
0
0
1
0
0
0
1
2
0
0
0
0
1
1
0
3
0
0
0
2
1
1
0
0
0
1
0
0
1
0
0
1
0
2
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
2
2
0
1
0
0
1
0
0
2
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
1
0
2
0
3
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
2
2
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
3
2
2
0
0
0
0
0
0
1
1
2
0
1
0
0
0
4
1
0
2
2
1
0
0
0
1
2
1
0
0
0
0
0
0
0
3
0
0
2
0
2
0
0
1
2
1
2
0
0
0
0
0
0
0
2
1
1
0
0
0
2
0
0
0
2
0
0
0
0
1
1
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
3
0
0
1
1
1
0
1
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
1
1
2
1
0
0
0
3
1
0
0
0
0
1
1
0
0
1
2
0
0
0
0
2
0
1
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
2
2
1
2
0
2
1
2
0
0
0
0
0
0
1
0
0
0
0
5
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
1
2
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
2
0
0
1
0
0
0
2
1
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
2
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
1
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
1
1
0
1
0
0
0
0
0
0
2
0
3
1
0
0
0
0
1
1
0
3
2
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
2
2
1
2
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
1
0
0
2
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
3
1
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
2
0
1
1
1
2
0
0
0
1
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
2
0
1
0
1
0
2
0
0
0
1
1
0
0
0
3
1
0
1
0
0
1
1
0
1
0
0
0
0
2
0
3
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
5
0
7
0
0
0
2
0
0
5
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
2
0
1
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
5
0
0
0
0
0
3
1
2
2
0
0
0
0
0
1
1
0
2
0
0
0
1
2
0
1
2
0
2
0
2
0
2
0
0
0
2
0
0
0
0
0
0
3
3
2
0
1
0
1
2
0
0
0
0
1
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
2
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
4
0
0
0
0
2
0
2
2
0
2
1
2
0
3
2
1
0
0
2
0
2
0
2
1
0
4
2
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
2
1
1
0
2
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
2
2
1
0
2
0
0
0
0
0
0
0
0
0
0
1
1
2
1
0
1
0
0
2
1
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
1
0
1
0
0
0
0
0
0
2
2
0
2
0
0
1
0
1
0
0
0
1
2
0
0
1
0
2
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
2
0
0
2
1
1
0
0
0
0
0
0
0
2
2
0
2
0
1
4
0
1
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
1
0
0
2
2
1
2
0
0
4
1
1
0
0
0
0
2
0
0
2
0
3
1
0
0
0
2
0
1
1
0
0
0
0
0
1
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
2
5
0
1
0
0
1
1
0
0
0
0
2
0
0
0
3
0
2
1
0
1
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
1
4
0
0
0
0
0
1
2
0
18
3
2
2
0
0
0
1
0
0
0
0
2
0
1
0
2
0
1
0
2
2
1
0
1
1
0
0
1
0
0
0
2
1
1
0
0
0
0
0
2
1
0
0
0
1
0
0
1
0
1
1
2
0
0
1
0
0
1
0
1
0
0
0
0
0
2
3
2
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
1
2
0
1
0
0
0
0
1
0
2
0
2
0
0
0
0
2
0
0
2
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
1
0
2
0
0
0
3
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
1
1
0
1
2
0
2
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
1
0
2
1
0
0
0
2
0
0
2
0
0
0
0
0
1
1
2
0
0
0
0
0
2
0
2
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
3
0
1
0
0
0
1
0
0
1
0
3
0
1
0
0
0
2
1
2
3
0
0
0
2
0
0
3
2
0
0
0
1
0
0
2
0
1
0
1
0
2
0
1
0
0
0
2
0
0
0
0
0
0
2
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
3
0
0
0
0
1
0
0
0
0
0
1
0
2
0
2
0
2
1
0
0
2
0
0
3
0
0
1
0
2
2
0
0
0
6
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
1
0
0
0
2
1
0
0
1
3
0
0
0
2
2
2
1
1
0
2
2
0
1
0
2
0
0
0
0
0
1
0
3
2
0
0
1
1
0
0
0
0
1
0
0
0
0
0
2
0
2
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
2
0
2
1
0
2
0
0
3
0
0
0
0
1
0
0
0
0
0
4
0
0
0
2
0
1
1
0
1
1
0
0
2
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
1
0
2
1
0
0
1
1
0
1
0
2
0
5
0
0
2
1
2
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
1
0
0
0
0
2
1
1
0
0
0
0
0
0
1
1
0
0
2
2
1
0
0
0
0
0
0
0
1
2
0
2
2
1
0
0
0
2
0
1
0
0
2
2
2
0
2
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
3
0
1
0
1
1
1
2
2
0
2
0
0
2
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
2
0
1
1
2
1
0
0
4
0
2
0
0
2
2
3
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
2
1
0
0
1
0
3
0
0
0
0
0
1
2
0
2
0
1
0
0
1
0
4
1
0
0
0
1
1
2
0
1
0
0
2
0
0
4
0
0
0
2
0
2
0
0
0
1
0
0
2
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
1
0
0
0
1
0
2
2
2
0
0
1
2
0
0
0
0
0
0
0
0
1
1
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
1
2
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
2
2
0
0
2
0
0
0
0
1
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
1
1
0
0
0
0
0
1
2
1
0
0
0
0
0
2
0
0
2
0
0
1
2
0
0
1
0
0
1
0
0
0
2
0
0
1
0
0
0
1
0
2
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
1
3
1
0
2
0
0
0
0
0
2
2
2
0
0
1
2
0
2
0
0
0
0
3
0
3
0
0
0
2
1
0
1
1
1
1
0
2
0
0
0
0
0
0
0
2
0
0
0
2
1
3
2
0
0
0
2
1
2
1
0
0
0
0
1
0
0
0
1
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
2
0
2
0
1
0
0
0
0
0
0
2
0
1
1
3
1
3
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
3
4
7
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
2
0
0
1
0
1
0
2
0
0
1
0
0
3
3
0
1
0
0
1
2
1
1
3
0
0
0
0
1
0
1
0
0
0
0
4
2
2
0
0
1
0
0
0
1
0
0
2
0
0
2
0
4
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
2
1
1
0
0
0
2
0
0
1
2
0
0
0
2
0
1
1
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
1
1
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
1
2
1
0
2
0
0
0
0
0
1
0
2
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
2
2
0
1
1
0
0
0
1
1
2
1
1
0
0
0
0
0
2
0
2
0
2
0
1
0
1
1
0
2
0
1
2
1
1
0
0
0
1
1
0
1
2
0
0
0
0
2
0
1
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
1
0
0
1
1
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
1
1
0
1
2
2
1
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
1
0
1
1
1
1
0
0
2
0
0
0
0
0
0
0
1
1
0
3
2
1
1
0
0
2
0
0
0
2
0
2
0
0
1
2
2
0
0
0
1
0
0
1
1
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
2
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
1
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
1
2
0
0
1
2
0
1
0
0
0
0
1
1
1
3
0
0
0
1
0
0
0
2
0
0
2
1
0
0
1
1
0
0
0
0
0
0
3
0
2
1
0
1
1
2
1
0
1
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
1
1
0
0
2
0
1
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
2
1
1
0
3
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
2
0
0
1
2
0
0
0
0
2
2
2
2
1
1
0
0
2
0
1
0
0
2
2
2
0
5
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
1
0
0
2
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
4
0
0
0
1
0
0
2
0
0
1
2
0
0
0
0
0
2
0
1
0
0
0
1
0
0
2
1
2
0
2
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
1
2
2
2
0
0
1
0
0
0
0
0
0
1
1
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
2
2
0
2
0
1
0
3
2
0
2
0
0
1
0
0
2
0
2
0
0
1
1
3
1
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
2
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
2
6
0
1
0
2
0
1
1
2
2
0
0
0
0
0
2
0
0
0
2
0
0
2
1
1
2
0
0
0
2
0
0
0
0
2
2
0
0
2
0
2
0
1
0
0
2
0
2
0
0
1
1
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
2
2
1
1
0
2
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
1
0
0
2
0
1
1
0
1
0
1
0
1
0
0
0
2
0
0
0
0
1
1
2
1
0
0
0
1
0
2
0
2
0
2
1
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
1
0
2
2
0
0
0
1
0
0
1
0
0
0
1
2
2
0
0
2
0
0
1
0
1
2
0
2
0
0
0
0
0
0
0
0
0
1
0
2
2
2
0
0
1
0
0
2
1
0
2
1
0
0
0
0
0
2
2
1
0
0
2
2
1
2
0
0
0
0
2
0
0
2
2
2
2
0
0
0
0
0
1
0
0
2
10
2
1
2
0
0
0
0
1
0
2
2
0
3
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
1
3
2
0
1
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
2
0
0
2
1
2
0
2
0
2
0
1
2
3
0
0
0
0
0
0
0
0
1
2
0
1
1
0
0
0
0
2
0
2
0
1
0
0
0
0
1
0
0
2
1
2
0
2
0
0
0
2
0
0
0
1
0
2
2
0
1
0
0
2
2
0
0
0
3
1
0
0
2
0
2
2
2
7
0
0
0
0
0
2
0
2
1
0
0
2
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
1
1
1
1
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
2
2
1
2
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
2
0
0
1
3
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
4
0
1
2
1
0
0
0
1
0
0
0
1
2
0
0
2
0
0
0
0
1
1
0
2
3
0
0
2
2
1
0
1
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
1
0
0
0
2
0
0
0
1
2
0
0
2
0
2
0
0
1
2
0
2
1
0
0
0
0
0
1
0
0
1
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
1
0
0
0
2
0
0
0
0
0
2
2
1
0
0
0
1
1
0
0
0
1
0
0
0
2
0
0
2
2
0
0
0
2
0
0
0
3
1
0
0
1
0
1
1
1
2
1
0
0
1
0
1
0
1
1
2
0
1
1
2
1
0
0
0
1
1
1
0
2
0
0
0
0
0
0
1
0
0
0
2
2
1
1
2
0
0
0
0
2
0
0
0
1
2
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
1
0
1
2
1
1
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
2
2
0
0
0
0
0
0
0
0
2
2
2
1
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
3
2
0
0
0
0
1
1
1
0
0
1
2
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
2
0
0
1
0
0
1
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
3
0
0
0
0
2
0
0
0
0
0
2
2
0
0
3
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
2
0
0
0
1
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
1
0
0
2
0
2
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
2
1
2
2
1
0
2
1
0
0
3
3
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
2
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
5
1
0
0
0
2
0
2
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
3
0
2
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
1
2
0
2
0
1
0
1
2
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
4
0
1
1
0
2
1
1
0
0
1
1
1
0
1
0
1
0
0
2
0
4
0
0
1
0
2
0
0
0
0
2
1
3
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
1
2
2
0
0
0
0
1
0
2
0
0
1
0
1
0
0
0
0
0
0
2
0
0
1
2
3
0
0
2
0
0
0
0
0
0
0
0
2
0
2
3
0
1
2
0
0
0
0
0
2
3
0
0
0
0
2
0
0
0
0
2
0
0
1
2
0
2
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
4
2
2
0
0
0
0
0
2
3
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
3
2
2
0
0
0
1
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
2
0
0
0
0
1
2
0
0
0
0
1
0
2
1
0
0
2
2
0
0
0
0
1
2
1
0
0
2
1
0
0
1
0
2
3
2
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
2
1
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
1
0
3
0
0
0
2
1
0
0
1
2
1
2
0
0
0
1
0
0
2
0
0
2
2
0
2
0
0
0
2
0
2
1
1
0
0
0
0
0
0
0
2
0
4
2
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
1
0
0
0
1
2
4
0
2
0
0
0
2
0
0
0
0
1
0
0
2
2
0
0
0
1
0
0
0
1
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
4
0
0
0
0
0
1
2
0
1
0
2
0
0
0
0
0
1
0
0
0
3
0
1
2
0
0
0
0
0
4
1
0
0
0
0
0
0
0
1
2
0
1
0
3
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
3
0
2
3
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
2
0
1
0
0
0
2
0
2
1
0
0
0
0
4
0
0
1
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
2
1
0
1
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
2
0
2
0
0
2
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
1
0
1
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
2
0
0
7
1
0
0
0
3
0
0
0
0
0
1
0
0
3
2
0
0
0
0
2
0
2
2
0
0
2
2
1
2
0
2
0
1
0
1
0
0
0
1
0
0
0
0
0
3
2
0
1
1
2
0
2
0
0
0
0
0
0
2
2
2
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
3
1
0
0
0
0
0
2
0
3
0
0
0
2
1
2
0
2
1
0
0
0
0
2
0
3
2
0
1
1
0
0
1
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
3
0
0
0
0
3
1
2
0
0
0
1
0
1
2
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
2
1
0
0
1
2
0
3
1
0
2
3
0
1
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
2
1
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
1
2
1
0
0
0
0
0
0
1
0
0
0
0
1
2
1
0
0
2
2
2
1
0
0
0
1
2
0
1
1
1
1
0
0
0
1
4
3
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
2
0
0
2
2
0
0
0
0
2
0
0
0
4
2
0
1
0
0
0
0
0
2
1
0
0
1
0
0
2
0
1
0
1
1
0
1
0
0
0
0
2
4
0
0
4
0
0
0
2
2
2
0
0
0
1
0
1
0
1
0
0
0
0
2
2
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
2
0
0
2
0
0
1
1
0
2
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
2
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
2
0
1
0
0
1
0
2
1
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
1
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
1
0
0
0
2
0
2
2
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
2
0
2
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
1
0
2
1
1
0
0
2
0
0
0
1
2
0
1
0
0
0
1
1
0
1
2
0
0
2
1
0
0
0
0
1
3
2
0
0
0
1
1
0
0
2
0
1
1
0
1
0
2
0
0
0
0
2
0
3
0
0
0
0
1
0
2
0
1
0
0
0
8
0
0
0
0
0
0
2
0
1
2
0
1
0
0
2
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
1
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
2
0
2
0
2
0
0
2
1
0
1
0
0
2
0
2
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
3
0
0
0
0
2
0
2
0
0
1
1
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
3
0
2
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
2
0
0
0
2
0
2
2
0
0
0
2
0
1
0
0
1
0
0
0
2
0
0
0
1
0
3
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
2
0
2
0
2
0
2
1
2
0
0
0
1
0
2
0
0
0
1
1
1
2
1
0
0
0
0
1
0
0
2
0
2
0
1
0
1
2
0
0
0
0
1
1
0
0
0
0
1
0
0
1
1
0
2
2
0
0
0
0
1
0
1
0
0
1
0
1
0
0
1
0
0
1
0
2
2
0
0
0
0
0
1
0
1
0
0
2
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
2
0
1
0
0
2
2
2
2
0
1
0
2
0
0
0
0
0
2
2
0
0
3
2
1
0
0
0
0
0
2
1
0
0
0
0
0
5
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
1
1
2
0
0
0
2
0
0
0
2
0
0
0
3
0
0
0
1
0
1
3
1
0
0
0
2
0
2
0
1
2
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
5
0
0
2
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
7
2
4
0
2
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
1
0
1
2
0
0
0
0
0
0
2
0
0
0
2
2
1
2
3
1
0
2
0
0
2
0
0
0
0
2
1
0
2
0
1
0
0
0
0
0
2
0
2
1
1
0
1
2
1
2
2
0
0
0
0
0
0
0
0
0
1
0
2
1
2
0
0
2
0
2
2
0
0
0
0
2
1
0
0
0
1
1
2
0
0
1
0
0
0
2
0
2
1
0
0
0
1
0
0
0
0
3
0
0
0
2
0
0
0
1
0
2
1
0
0
1
0
0
2
0
0
0
0
0
2
2
0
1
2
0
2
0
2
0
0
0
0
0
0
0
1
2
1
0
0
0
0
2
1
2
2
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
2
1
0
0
0
1
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
1
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
2
1
0
1
2
0
2
0
0
0
0
2
0
0
1
2
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
1
1
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
2
3
0
0
0
0
0
0
0
1
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
1
2
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
2
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
1
0
5
0
0
2
0
0
0
0
2
0
0
0
0
2
0
2
0
1
1
0
2
0
1
0
0
0
2
1
0
1
1
0
0
0
0
0
2
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
1
0
0
2
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
2
0
2
0
0
0
0
2
0
0
4
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
2
0
0
0
0
2
1
0
3
0
0
0
0
2
2
1
0
2
0
0
3
0
0
2
0
0
1
1
0
0
2
0
2
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
2
0
2
0
2
2
0
0
0
0
2
1
0
0
0
0
0
2
0
2
0
0
0
1
1
0
0
0
0
1
0
2
3
0
2
0
0
1
0
2
0
2
1
0
1
1
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
1
2
0
0
2
0
0
0
1
0
2
0
1
0
0
0
0
1
5
7
0
0
1
0
2
0
0
0
2
1
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
1
2
1
1
0
1
0
2
2
1
1
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
2
2
0
0
0
2
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
2
0
2
2
1
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
1
1
0
0
1
1
2
0
0
0
2
0
0
0
0
0
0
0
1
2
1
1
0
0
0
2
1
1
0
1
0
5
2
0
0
0
2
2
1
0
1
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
1
2
0
0
0
2
0
1
2
0
0
1
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
1
1
0
0
2
1
0
1
2
3
0
0
2
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
1
3
0
2
0
0
0
2
0
2
2
0
0
0
0
0
2
1
1
0
2
0
0
2
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
2
0
0
2
2
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
3
2
2
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
2
0
0
0
0
0
2
2
0
0
0
1
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
2
1
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
2
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
2
1
2
0
0
3
0
0
1
0
2
0
0
2
0
0
0
0
0
2
0
0
0
1
3
0
0
0
1
0
10
0
2
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
4
1
0
1
1
0
1
0
2
0
2
0
2
0
0
0
2
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
1
4
1
2
0
0
0
2
3
0
0
1
0
1
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
6
0
0
0
0
1
0
0
1
2
2
0
1
0
1
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
1
2
0
1
0
0
4
2
0
1
0
2
0
0
0
0
0
0
1
0
3
0
0
2
0
0
2
1
0
0
0
0
0
0
2
2
0
0
0
0
2
1
2
0
0
0
0
0
0
1
0
0
1
0
0
1
2
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
1
0
0
0
2
2
2
1
2
0
0
1
0
0
0
2
2
0
0
1
2
0
0
1
0
1
0
0
0
0
0
2
0
2
0
2
0
0
0
2
1
1
0
2
0
0
0
0
3
1
2
2
1
1
0
0
0
0
2
2
1
2
0
0
1
2
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
1
5
0
1
0
0
1
1
0
0
0
0
2
1
2
2
2
2
2
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
1
1
2
0
0
2
2
0
0
1
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
1
1
2
0
0
0
0
0
0
2
1
2
2
1
0
0
0
0
0
1
0
0
1
0
3
0
2
1
0
0
0
3
1
2
1
0
2
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
2
0
0
1
0
0
0
0
2
0
2
0
0
0
0
2
0
0
1
0
0
2
0
0
1
0
0
0
2
2
0
1
0
0
2
2
0
0
1
0
1
2
4
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
2
1
0
0
0
2
2
1
0
0
0
1
2
2
0
1
0
1
0
1
0
0
0
0
1
2
0
0
1
2
0
0
0
0
0
0
0
0
0
4
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
2
1
0
0
0
0
0
0
0
1
0
1
0
0
1
1
1
0
3
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
2
0
0
1
1
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
2
2
0
2
0
4
0
0
2
0
0
1
0
0
2
1
0
2
0
1
2
0
0
2
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
3
2
2
0
0
2
0
1
2
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
2
2
0
0
0
0
0
1
0
3
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
4
1
1
0
0
0
0
0
2
0
0
3
0
1
2
0
1
1
0
1
0
0
0
2
2
1
0
0
0
0
0
2
0
0
0
0
0
3
1
0
1
2
2
3
0
2
0
0
0
1
0
0
2
3
1
1
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
2
1
0
0
0
0
0
0
0
2
2
1
2
0
2
0
1
0
0
1
0
0
1
1
0
2
0
0
2
2
0
0
0
1
0
0
1
2
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
2
0
0
0
0
2
0
2
1
0
1
0
0
1
0
0
2
0
0
0
2
0
0
0
2
0
2
2
0
0
1
0
0
0
0
0
0
0
1
2
2
0
2
1
0
0
0
0
0
1
0
3
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
2
1
0
2
1
1
5
0
0
2
2
0
2
0
0
0
0
0
0
0
1
0
1
2
2
0
0
2
1
0
0
0
2
1
0
0
0
4
0
1
0
1
2
0
1
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
1
2
0
0
0
1
0
1
0
0
0
0
0
0
1
2
0
2
0
1
0
4
0
2
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
2
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
1
0
0
0
0
3
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
1
0
2
0
3
0
0
0
0
0
0
1
0
1
0
2
0
1
2
0
2
0
0
0
0
0
0
0
0
1
1
2
1
0
0
2
0
0
0
1
0
1
0
2
0
1
2
0
0
0
0
0
0
0
0
1
0
2
0
1
0
1
3
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
1
1
1
3
0
0
1
0
0
0
2
0
0
1
1
0
0
0
0
1
0
1
2
0
0
2
0
0
2
0
0
3
0
0
2
0
0
0
0
0
1
0
1
2
2
0
1
2
2
0
1
0
3
0
0
0
0
2
1
2
0
0
0
0
0
0
0
2
1
0
0
2
1
0
4
0
1
0
2
0
2
0
0
2
0
2
0
0
1
1
1
2
0
0
2
0
1
0
0
0
0
1
0
1
0
1
0
0
0
1
0
2
1
0
0
1
0
0
2
1
0
0
2
0
0
0
2
0
2
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
2
1
0
0
1
1
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
1
2
0
1
1
0
0
0
1
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
2
2
2
2
0
0
0
0
0
1
0
0
2
2
4
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
2
0
2
0
1
0
0
0
0
0
1
0
2
2
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
1
0
0
2
0
2
0
1
0
1
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
2
0
0
2
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
1
0
2
0
2
0
2
5
1
1
0
0
0
1
0
1
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
2
0
0
2
0
0
1
2
0
1
0
0
0
0
2
0
2
0
0
0
2
2
1
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
3
0
2
2
2
2
0
1
1
0
1
2
0
0
1
2
1
1
0
2
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
1
0
0
0
2
2
0
0
1
3
3
0
2
2
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
1
1
1
1
0
1
0
0
0
0
0
2
0
1
0
0
0
2
0
0
2
0
0
0
0
1
1
0
0
0
0
0
5
0
2
0
0
3
0
1
0
0
0
0
0
1
2
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
1
0
0
2
0
0
0
2
0
0
1
0
0
1
2
1
2
0
0
0
1
2
1
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
1
0
1
2
0
0
1
0
0
2
3
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
2
0
1
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
2
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
2
3
2
1
4
0
2
1
0
0
2
0
2
0
0
1
0
0
0
1
0
0
0
0
1
2
2
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
2
0
1
0
1
2
0
1
2
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
1
1
0
0
0
0
2
0
2
0
0
0
2
0
2
0
0
0
0
0
0
1
2
0
4
0
1
0
1
0
2
0
0
0
2
0
0
1
0
0
0
0
2
0
1
1
0
0
1
2
0
0
2
0
0
0
3
0
0
3
0
1
0
0
1
1
0
1
0
8
0
1
0
0
0
0
1
1
1
0
1
0
0
2
0
0
1
0
2
0
2
0
0
0
1
0
0
1
0
0
0
1
0
0
0
2
1
3
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
3
1
0
0
0
0
0
0
0
2
1
0
0
1
1
0
0
0
2
0
0
1
0
1
0
2
2
0
2
0
0
0
0
1
0
0
0
1
2
0
3
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
2
0
0
0
0
1
1
2
0
0
0
1
2
0
0
2
0
2
0
2
0
0
0
1
2
1
2
0
0
0
0
2
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
1
1
0
0
0
1
0
1
0
0
2
0
0
0
2
2
0
0
0
2
0
1
0
0
1
0
2
0
1
0
1
0
0
0
0
0
1
0
0
0
2
0
1
0
0
1
0
0
0
1
0
0
0
0
2
0
0
2
2
0
2
0
3
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
1
0
2
1
2
0
0
0
0
0
0
2
0
0
0
2
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
3
0
0
0
1
0
1
0
2
2
0
0
2
0
0
0
0
2
1
0
0
1
1
0
0
0
0
2
2
1
2
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
2
0
0
0
0
0
2
1
0
0
2
0
0
0
0
3
2
0
0
0
2
0
2
0
2
0
0
1
0
0
0
2
0
0
0
2
0
0
2
2
0
0
2
0
0
0
1
0
0
2
0
0
3
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
5
0
0
3
1
0
0
0
2
2
0
0
0
0
1
1
0
1
3
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
3
0
0
0
0
0
2
1
0
0
1
2
2
0
0
1
0
2
0
2
0
0
1
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
1
1
0
0
0
0
0
1
0
2
0
1
0
0
0
1
0
0
2
2
2
0
1
0
0
3
0
0
0
1
0
0
0
0
1
0
0
0
1
2
1
0
0
1
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
2
2
2
0
2
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
1
2
0
0
0
0
0
0
1
3
2
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
4
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
2
1
0
0
0
1
1
0
0
2
0
0
2
0
0
0
0
0
2
2
0
1
1
0
1
0
0
1
0
1
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
3
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
4
1
0
0
0
3
2
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
3
0
5
1
0
0
0
1
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
2
3
1
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
2
0
0
0
0
1
1
0
2
0
0
1
0
2
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
1
2
0
0
0
1
0
0
0
0
1
0
1
1
0
2
1
0
0
0
0
1
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
2
0
0
1
0
0
2
1
1
0
2
2
0
0
0
0
2
0
0
1
0
4
3
0
0
2
1
3
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
1
0
2
1
0
2
0
1
2
0
1
0
0
0
0
0
0
0
2
4
2
0
1
0
0
0
1
2
0
0
0
1
0
0
2
2
1
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
2
0
0
2
2
2
0
0
0
2
0
0
0
0
1
1
0
0
2
4
0
4
2
0
3
0
2
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
1
1
0
0
1
1
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
1
1
0
0
1
0
2
2
0
0
0
0
1
0
0
3
0
0
0
3
0
0
0
0
5
1
0
2
0
0
1
0
3
2
1
0
0
0
0
1
0
0
2
3
0
0
1
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
1
0
0
0
1
2
1
0
0
0
0
0
0
1
0
0
1
0
2
2
1
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
2
0
1
2
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
1
0
1
0
2
0
0
0
0
0
1
1
0
0
2
2
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
1
2
2
0
1
0
1
0
0
0
2
2
0
1
0
2
0
0
0
0
1
0
1
0
3
2
0
1
0
0
1
2
0
1
2
1
0
1
0
1
0
2
1
2
1
2
0
1
2
3
1
3
1
0
1
1
0
0
0
1
0
0
0
0
0
2
0
3
0
0
2
0
0
0
0
1
0
2
1
0
2
2
2
0
0
0
1
3
2
0
0
0
1
2
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
1
0
1
2
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
2
1
2
2
0
0
0
0
0
0
1
0
0
0
0
2
2
0
1
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
1
3
1
1
2
0
2
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
1
1
0
1
0
0
1
0
2
2
0
1
1
2
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
1
2
0
0
0
2
0
3
1
2
2
0
1
1
2
0
0
2
2
0
0
1
1
0
2
0
0
0
0
0
0
2
2
0
2
3
0
0
0
0
0
2
0
0
6
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
2
2
0
0
0
1
1
2
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
3
0
2
1
0
1
2
0
2
0
0
0
0
1
2
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
3
0
0
2
0
0
4
2
0
0
0
1
0
2
0
0
0
2
0
0
0
3
0
0
0
0
2
1
0
0
2
0
1
1
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
2
0
0
0
0
0
2
2
0
1
0
0
0
1
2
0
0
1
1
2
0
1
1
0
0
1
0
0
0
0
0
0
2
0
0
0
1
2
0
2
3
0
0
2
0
0
1
1
0
1
0
0
0
1
1
0
2
3
2
0
1
1
0
0
0
0
0
0
0
0
0
5
0
1
0
0
1
1
0
2
0
2
0
1
1
2
0
0
1
2
0
1
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
2
2
0
2
2
0
0
0
0
2
1
0
0
1
0
0
0
2
1
0
1
0
0
0
0
0
2
0
2
0
0
0
3
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
1
0
0
0
0
3
0
0
0
0
0
2
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
3
0
0
0
0
2
0
0
0
2
1
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
1
1
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
1
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
1
0
0
0
0
1
0
0
0
2
0
0
1
1
2
0
0
0
0
2
1
1
0
0
0
1
0
0
0
2
2
0
0
1
0
0
2
2
0
0
0
0
0
0
0
2
2
2
1
0
1
0
0
0
0
2
1
1
2
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
1
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
2
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
1
0
0
0
2
0
0
0
0
1
0
0
6
2
2
8
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
3
2
0
2
0
2
1
2
0
0
2
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
1
1
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
2
0
0
0
2
1
1
0
0
0
0
2
0
2
1
0
0
4
0
0
0
2
1
1
0
2
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
2
1
2
0
2
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
1
1
0
1
0
0
1
0
0
2
2
0
1
0
0
0
0
0
0
2
1
0
0
1
1
0
2
2
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
2
0
1
0
0
0
1
0
0
3
0
0
2
0
1
0
0
1
3
0
0
0
2
3
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
1
0
2
0
0
1
2
0
0
0
0
1
0
1
1
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
1
0
2
0
5
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
1
0
1
0
0
2
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
1
1
2
0
2
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
1
0
0
3
0
0
0
1
2
0
0
0
0
2
0
0
0
0
2
0
1
2
0
2
0
2
0
1
0
1
0
0
0
0
2
2
0
2
0
0
0
0
1
0
0
1
1
0
0
0
0
2
0
0
0
2
1
0
2
0
0
2
2
0
2
2
0
1
0
0
0
2
2
0
0
1
0
2
0
2
0
0
1
1
0
0
2
0
2
0
1
0
0
0
1
2
2
0
0
1
0
1
2
0
0
0
3
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
2
0
0
3
2
2
0
0
0
0
2
0
0
1
1
0
0
1
1
0
1
1
1
1
0
2
1
3
0
0
3
2
2
3
0
2
1
1
0
2
2
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
4
0
0
0
0
1
1
0
0
0
0
2
0
0
0
3
0
2
1
0
0
3
0
2
1
16
1
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
1
0
0
2
0
1
1
2
2
1
0
2
2
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
2
0
1
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
3
0
0
0
0
1
1
0
2
1
0
0
0
0
0
2
0
2
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
1
1
0
1
0
0
0
2
2
0
0
1
2
0
0
0
0
1
0
0
0
1
0
0
1
2
0
0
0
0
2
2
1
0
2
0
0
0
0
0
2
0
0
2
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
2
2
0
1
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
1
2
1
0
0
0
1
0
0
0
0
1
0
2
1
0
0
0
0
2
2
0
2
0
0
0
0
2
0
0
0
0
6
0
0
0
0
0
2
2
0
0
0
0
2
1
0
0
2
2
0
0
0
0
1
2
0
1
0
1
0
1
0
0
0
2
0
0
0
2
0
3
2
0
0
1
1
2
0
1
2
0
0
0
3
0
0
0
2
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
2
1
0
4
0
0
0
1
0
0
1
0
1
2
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
2
0
0
0
0
1
1
2
2
0
0
1
0
2
0
0
2
0
0
3
0
1
1
0
0
0
1
0
2
2
0
0
2
0
0
2
0
0
0
2
0
0
0
0
2
5
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
3
0
0
0
1
0
1
0
1
0
0
1
0
2
2
1
2
0
0
1
0
1
0
1
0
1
0
1
2
0
2
0
0
1
1
0
0
0
0
0
0
2
0
1
1
2
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
1
2
1
0
2
0
0
1
0
0
0
0
0
2
1
2
1
0
1
2
2
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
2
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
1
0
0
1
1
0
2
0
0
2
0
1
0
0
1
2
2
0
1
0
0
0
0
0
1
0
0
1
1
0
2
0
3
0
2
1
1
2
0
0
0
0
0
0
2
0
1
0
0
2
0
0
1
0
0
2
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
2
0
3
0
0
0
1
0
0
0
0
0
1
0
0
2
2
2
2
0
0
0
0
1
0
2
2
3
3
0
0
0
0
0
0
1
0
0
1
2
2
0
1
0
1
1
0
4
0
2
0
2
2
2
1
1
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
2
2
0
2
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
2
0
0
0
1
2
0
1
0
1
0
0
2
0
0
0
2
0
0
1
0
2
0
1
0
0
0
0
2
2
1
1
0
2
2
1
0
0
0
0
0
0
1
2
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
3
1
1
0
0
0
0
0
2
2
1
1
0
0
0
0
4
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
2
0
2
0
1
0
0
0
3
0
0
0
0
0
1
1
2
0
2
0
1
0
0
2
2
0
0
0
0
0
0
1
0
1
1
0
0
0
2
0
0
0
0
0
1
0
2
1
0
0
2
0
2
2
2
0
1
3
0
3
1
2
0
0
0
2
0
0
2
2
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
2
0
1
0
4
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
2
2
0
0
2
0
0
0
1
1
1
2
0
0
0
2
0
1
0
0
0
1
0
2
1
0
0
0
0
2
0
0
1
0
0
0
0
2
0
2
0
1
0
0
0
0
2
0
1
1
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
2
0
1
1
0
0
0
0
0
1
0
0
0
1
0
3
0
0
0
0
0
2
0
2
2
0
2
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
2
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
1
0
0
0
2
2
0
2
0
0
0
0
0
2
2
0
1
1
0
3
0
2
0
0
0
0
0
0
0
1
2
0
2
2
0
0
1
2
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
2
0
0
2
3
2
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
4
0
1
0
2
0
1
0
1
2
1
2
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
2
0
1
2
1
0
1
0
0
2
0
0
0
0
1
3
0
0
0
0
0
0
0
0
2
1
0
0
1
2
0
1
0
1
1
1
2
0
0
0
0
0
1
0
0
3
0
0
0
0
1
0
1
1
0
1
0
0
1
2
2
0
0
0
1
2
0
0
2
1
0
2
2
2
0
0
0
0
0
0
2
2
0
0
1
1
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
1
0
0
0
0
0
0
1
2
1
0
1
0
1
1
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
1
0
1
0
2
0
2
2
0
2
0
0
2
0
0
0
0
2
0
1
0
0
1
1
0
0
0
0
0
0
1
2
0
0
1
0
2
0
1
0
1
0
0
2
2
0
0
2
0
1
0
1
3
3
0
0
0
1
0
2
2
0
1
0
0
0
2
2
0
0
2
0
0
1
0
0
2
3
2
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
1
0
0
2
0
0
0
3
0
0
4
0
0
2
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
1
0
0
1
0
1
1
0
0
0
0
2
0
1
0
0
0
0
4
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
1
0
0
1
0
0
0
2
0
0
1
1
0
0
1
2
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
3
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
2
1
0
2
0
0
0
1
2
2
0
0
0
1
0
2
2
0
0
0
1
2
1
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
1
2
0
2
0
0
1
2
0
0
0
0
0
0
2
2
0
1
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
2
0
3
0
2
2
2
0
2
0
0
0
2
2
1
0
1
1
0
0
0
0
2
0
0
0
2
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
2
1
0
0
2
0
3
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
2
0
0
1
0
0
2
1
0
2
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
1
1
0
0
0
0
1
2
0
2
2
0
0
0
0
2
0
2
0
0
2
0
1
2
0
2
0
2
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
2
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
1
2
2
1
0
0
0
0
0
0
0
2
2
0
0
0
0
2
1
2
1
0
0
0
1
0
0
1
1
0
0
0
0
1
1
0
1
0
0
0
2
13
2
0
0
1
0
2
1
0
2
0
0
0
2
0
0
2
0
2
0
0
0
0
2
0
1
2
2
0
0
1
0
1
0
0
0
0
2
0
0
1
0
2
0
0
1
2
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
3
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
2
1
0
0
2
0
0
2
0
0
1
0
1
0
0
1
0
0
0
0
0
2
0
2
0
0
1
0
0
0
2
1
2
1
0
1
0
2
0
0
0
0
1
2
0
0
2
0
0
0
2
2
0
1
0
4
0
0
2
0
0
0
0
0
1
0
0
0
2
0
1
2
2
0
2
0
0
0
0
2
2
0
0
2
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
2
0
1
0
3
2
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
2
0
0
0
0
1
0
0
2
2
2
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
4
0
5
0
0
1
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
1
0
0
0
1
0
2
2
0
0
0
2
1
1
0
1
1
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
2
0
0
2
0
1
1
0
0
1
0
0
1
0
0
2
0
1
0
1
1
2
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
2
1
0
0
1
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
1
2
0
0
0
0
2
2
0
0
2
3
0
0
0
0
0
1
0
1
0
0
0
0
1
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
3
0
2
1
1
2
0
0
1
0
0
0
0
0
3
0
0
0
0
1
0
0
1
0
0
2
0
0
0
1
1
0
2
1
1
0
1
0
4
0
1
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
3
1
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
2
0
0
2
0
0
1
0
0
1
2
1
2
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
2
1
0
0
0
2
2
0
2
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
2
1
1
0
0
1
0
0
0
2
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
2
0
0
0
2
0
2
1
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
1
0
0
1
0
1
0
0
0
1
1
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
2
1
0
2
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
1
0
2
0
0
2
1
0
2
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
1
1
0
0
0
0
2
0
1
0
1
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
2
0
2
0
0
1
2
0
0
0
1
3
0
0
0
2
0
0
0
0
3
0
2
0
2
1
0
0
0
1
0
1
0
0
2
0
2
1
1
0
2
0
2
4
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
2
0
2
1
1
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
3
2
1
1
0
2
0
1
2
3
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
7
0
0
0
0
1
0
0
1
0
0
1
0
2
0
0
0
1
2
1
1
0
0
0
1
0
1
1
0
0
0
3
0
2
0
0
0
0
2
0
0
0
0
1
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
1
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
2
1
2
0
0
0
0
0
1
2
0
2
1
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
2
1
0
2
0
0
0
2
1
0
1
1
0
2
1
1
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
1
1
1
2
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
2
3
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
2
2
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
2
0
0
2
0
0
0
1
2
0
2
0
0
2
1
0
0
0
1
0
0
0
0
2
1
1
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
2
1
2
1
1
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
3
0
1
0
3
0
0
2
1
0
2
0
1
2
0
0
0
1
0
0
0
2
0
1
0
0
3
1
1
0
0
0
0
0
1
0
2
0
0
0
1
0
0
1
2
1
0
0
3
2
0
2
0
0
1
0
2
0
2
1
0
1
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
1
2
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
1
1
0
2
1
1
0
0
0
0
0
1
0
0
0
1
1
0
1
1
0
0
0
2
0
0
0
1
1
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
2
1
2
0
2
0
0
1
2
0
0
0
2
0
0
1
1
0
0
0
0
1
0
0
1
0
0
2
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
2
1
0
0
0
0
0
1
1
0
1
1
0
0
3
0
0
0
0
0
0
2
0
0
0
1
1
0
1
1
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
2
1
1
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
1
0
0
1
2
0
0
2
1
1
0
0
1
0
0
1
0
1
2
2
0
0
2
1
0
0
2
0
0
2
1
1
0
2
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
1
0
1
0
0
1
0
0
0
0
1
0
1
1
1
0
0
0
0
0
1
0
2
0
0
2
0
0
2
1
0
0
0
0
1
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
3
2
0
0
0
0
0
1
1
2
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
2
2
1
0
0
0
1
3
1
2
0
0
0
1
0
1
0
2
0
0
0
1
0
0
2
2
2
1
1
0
0
0
0
2
3
0
2
0
1
0
0
0
2
0
0
0
1
2
2
0
0
2
2
1
1
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
1
1
0
0
2
0
2
0
0
1
3
1
2
2
0
0
0
0
1
1
0
0
0
1
0
0
1
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
3
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
2
0
2
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
2
0
2
0
0
0
1
2
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
2
1
0
1
2
1
1
0
0
1
0
0
2
0
1
0
3
0
1
0
0
1
0
2
0
0
0
2
1
1
0
2
2
1
0
2
2
1
0
2
2
2
1
0
2
4
0
2
0
0
1
2
0
0
2
1
0
0
0
0
5
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
2
5
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
3
0
0
0
0
0
0
2
1
0
2
0
0
0
0
1
3
2
0
0
2
0
1
0
0
0
0
2
2
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
1
0
1
1
2
0
0
0
0
2
3
1
1
0
2
1
0
1
0
0
1
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
2
0
2
0
0
2
2
2
0
2
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
2
2
1
0
3
0
0
0
0
0
0
0
2
0
1
0
1
0
1
2
0
0
2
0
0
0
1
0
0
0
3
0
0
2
1
0
0
2
0
0
0
2
0
2
0
0
0
1
1
1
0
0
0
2
0
2
2
0
0
0
2
2
0
2
0
0
2
0
0
3
0
0
1
2
0
0
0
0
0
2
0
0
0
3
1
0
0
0
1
1
1
2
0
0
0
0
2
0
0
1
3
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
3
2
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
3
0
0
0
2
0
1
0
0
1
0
0
2
0
0
2
0
2
2
2
1
0
0
2
2
0
0
0
0
1
3
0
0
0
0
0
0
0
2
0
1
0
2
0
0
1
0
0
3
1
0
0
0
0
0
0
1
0
2
1
1
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
2
1
0
0
0
0
0
0
1
2
1
2
0
2
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
2
0
0
2
0
2
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
2
0
2
4
0
2
0
0
0
2
1
2
0
0
0
0
2
0
0
2
1
0
0
0
2
1
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
1
0
0
0
3
3
0
0
0
0
0
2
1
0
0
0
2
0
0
1
0
3
0
0
0
0
0
0
0
0
3
0
2
0
0
2
0
0
3
1
0
2
0
0
2
2
1
0
0
2
1
0
1
0
0
0
1
1
0
2
0
1
2
0
3
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
1
0
2
2
1
0
0
0
0
0
0
0
1
0
2
0
0
2
0
2
0
1
0
0
1
0
2
1
1
0
0
2
2
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
1
0
0
0
1
0
0
0
2
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
1
1
0
0
0
0
2
0
2
0
0
0
0
0
2
2
0
0
1
2
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
2
2
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
1
0
1
0
2
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
4
0
0
0
1
0
0
3
2
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
3
2
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
1
2
0
0
0
1
2
2
0
0
2
3
0
0
2
2
0
0
0
2
0
2
1
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
2
0
1
0
0
0
0
0
0
2
0
2
0
0
1
0
2
1
0
0
1
0
1
1
2
1
2
0
0
0
0
0
2
0
0
0
1
0
0
1
1
0
1
0
0
1
0
0
1
0
0
2
2
3
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
2
2
0
2
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
1
1
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
1
1
2
1
0
3
2
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
1
0
0
1
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
2
2
1
2
0
1
2
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
2
0
0
0
1
4
0
0
1
0
2
0
0
0
0
2
1
1
1
1
0
0
0
0
0
0
1
1
0
0
2
0
1
1
0
0
0
0
0
2
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
1
1
1
0
0
1
1
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
1
1
2
2
0
0
0
2
0
0
2
0
0
1
2
0
0
0
0
1
2
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
2
3
0
2
1
2
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
2
0
2
1
0
0
0
0
0
1
0
1
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
1
2
2
0
0
1
0
2
1
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
2
2
0
0
0
2
1
1
0
1
2
0
2
0
2
2
1
0
0
0
0
0
0
0
1
0
1
1
0
0
7
0
0
0
1
0
2
0
0
1
1
0
3
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
1
1
0
0
0
0
1
1
2
0
3
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
1
2
1
2
0
0
1
1
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
1
0
0
0
0
0
0
2
1
0
1
0
0
0
2
0
1
2
4
0
0
0
0
2
1
0
0
0
1
0
2
0
2
2
1
0
0
8
2
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
2
0
0
1
1
0
1
2
0
0
0
1
0
1
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
2
1
0
2
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
1
1
0
0
0
0
1
2
2
0
1
0
2
1
0
0
0
0
1
0
2
0
0
0
0
3
2
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
2
0
2
0
0
2
2
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
3
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
2
2
0
0
1
0
0
0
0
0
1
3
2
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
2
0
0
3
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
2
1
0
2
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
3
0
0
0
0
0
0
1
2
0
0
2
0
2
2
0
0
3
0
3
0
1
0
0
1
0
0
1
0
0
0
2
1
0
0
1
0
0
2
0
2
0
1
2
0
2
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
1
2
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
1
0
1
2
1
0
2
0
0
0
2
0
1
1
2
1
0
0
3
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
2
0
0
0
1
0
1
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
2
1
1
1
0
3
2
1
1
1
0
5
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
2
1
1
2
2
0
0
2
0
0
0
0
0
0
4
0
2
1
1
2
0
1
0
0
0
0
2
1
2
0
2
0
1
0
3
1
3
2
0
0
1
1
0
0
3
2
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
1
1
2
2
1
2
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
2
3
0
0
1
3
0
2
1
0
0
0
0
2
0
0
0
1
2
0
1
1
0
0
0
2
0
0
2
0
0
0
1
2
0
0
0
2
0
0
1
1
0
2
1
0
0
2
0
0
0
0
0
2
2
2
1
0
0
1
0
0
0
0
0
0
2
1
3
2
0
0
0
0
2
1
0
0
2
0
0
0
0
0
1
1
1
4
0
0
0
0
3
0
2
0
0
2
2
3
0
3
2
2
0
2
0
0
0
0
0
0
0
0
2
1
2
0
0
1
2
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
2
0
1
2
0
0
0
1
0
0
2
1
0
1
1
1
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
2
1
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
2
0
1
0
0
2
0
1
0
1
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
2
1
0
0
2
0
0
0
1
1
0
0
0
2
0
2
0
1
0
0
0
2
0
0
1
0
0
0
1
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
2
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
2
2
2
1
1
0
2
0
0
0
1
0
0
0
0
1
0
0
2
0
1
0
1
0
1
0
1
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
1
0
1
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
3
0
0
0
0
0
2
0
2
0
2
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
2
2
0
2
1
3
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
2
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
6
0
0
1
0
0
0
2
0
1
0
1
0
1
0
0
1
1
1
1
0
0
1
0
0
0
4
0
0
0
0
0
1
0
1
0
2
0
0
1
0
0
2
0
0
1
1
0
2
0
0
0
2
0
0
0
2
2
0
2
0
0
0
0
1
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
4
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
2
2
1
0
1
1
0
1
0
1
0
1
1
0
0
1
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
1
0
0
1
0
2
0
0
2
0
0
0
2
0
0
0
1
2
1
1
0
0
0
1
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
3
1
2
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
1
2
1
2
2
2
0
0
0
0
0
2
0
0
0
1
0
1
0
1
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
1
2
2
0
1
0
0
2
0
1
0
1
2
0
0
0
0
0
1
3
0
0
1
0
0
2
0
2
0
0
0
0
1
0
1
2
0
1
0
0
1
0
0
0
0
2
0
1
1
1
2
0
1
0
1
0
0
0
1
2
1
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
1
0
0
2
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
2
0
1
0
0
0
1
2
0
0
0
2
0
2
0
1
0
1
0
1
1
0
0
1
2
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
2
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
2
2
2
0
0
1
1
0
1
1
0
0
2
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
1
1
2
0
1
0
0
1
0
0
0
0
1
0
1
0
7
0
2
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
2
1
0
0
0
0
0
3
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
3
1
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
2
0
0
0
0
1
0
1
2
0
1
0
0
0
1
0
2
0
1
0
2
0
0
0
2
2
0
2
0
2
0
0
2
0
0
0
0
0
0
1
0
2
2
0
0
0
0
2
0
0
0
0
1
0
0
2
8
0
0
0
2
1
0
2
0
0
0
0
0
0
2
1
1
0
1
0
2
2
1
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
1
1
0
2
0
0
2
0
2
1
2
0
2
0
0
0
1
0
0
0
0
0
2
7
0
2
0
2
0
0
0
0
1
0
0
1
2
0
1
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
2
1
1
0
2
1
2
0
2
0
0
1
1
2
1
0
1
0
2
2
1
0
0
0
0
1
2
0
1
2
0
0
0
1
0
0
0
0
1
0
0
1
0
1
2
1
4
1
0
0
0
0
1
0
0
0
0
1
0
1
1
2
0
0
0
0
4
0
0
0
0
0
2
0
2
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
1
2
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
4
0
0
0
2
1
1
0
2
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
2
2
3
1
1
0
0
0
1
0
2
2
4
0
0
0
1
0
2
0
0
2
1
0
2
0
0
0
0
2
1
0
0
0
0
1
2
0
1
2
0
0
2
2
1
0
0
2
0
0
0
2
1
0
0
0
0
3
0
1
0
0
2
0
1
2
0
0
0
0
2
1
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
1
2
1
0
2
0
2
1
0
0
0
1
0
0
0
0
2
2
1
1
2
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
1
0
0
2
1
0
0
0
1
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
2
3
0
1
1
0
2
0
0
2
0
3
0
0
0
0
0
0
0
0
1
1
2
0
1
0
0
1
0
0
3
0
1
0
0
0
0
1
0
1
2
0
0
3
0
1
1
2
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
1
0
0
2
0
0
0
2
1
2
2
0
0
0
1
0
0
0
1
0
0
2
0
0
2
0
0
0
2
0
0
2
0
0
1
0
0
3
2
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
1
0
2
0
1
0
0
0
1
1
0
0
1
2
0
0
0
2
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
2
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
1
2
0
0
0
0
1
2
3
0
0
0
1
0
0
0
0
0
2
1
2
0
0
0
0
0
0
1
1
0
1
0
0
1
2
2
0
2
0
1
3
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
2
0
2
1
0
0
2
0
0
2
0
0
2
0
0
0
0
1
2
0
0
1
0
0
0
6
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
1
1
0
0
0
2
0
1
0
0
2
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
2
0
1
0
2
0
0
0
0
0
2
2
0
0
1
2
0
1
0
1
2
2
0
1
0
1
0
1
4
2
1
0
0
0
1
2
0
0
0
0
2
0
1
0
1
0
0
0
2
2
0
0
0
0
0
1
1
0
8
2
0
0
0
2
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
3
0
0
2
1
0
0
0
0
0
0
2
0
2
0
0
1
0
1
2
2
0
0
2
0
0
2
1
0
0
0
2
0
0
2
2
2
0
0
0
1
0
0
0
1
1
2
0
1
1
0
1
1
0
2
0
0
0
0
0
2
1
0
0
2
1
0
3
3
0
0
0
2
0
1
0
1
0
1
1
0
2
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
4
0
1
0
0
0
1
2
0
2
0
0
2
0
2
0
0
1
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
2
0
2
0
0
0
0
2
0
2
1
0
1
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
2
2
0
0
2
2
0
0
0
4
2
0
0
2
2
1
1
0
2
1
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
1
0
0
2
2
0
0
0
1
0
1
1
0
0
2
2
0
0
0
2
2
1
0
0
0
1
2
0
0
2
0
1
2
0
0
2
0
0
0
1
0
1
0
1
0
0
3
0
0
2
0
2
0
0
3
0
0
1
0
0
0
0
0
3
2
0
0
0
1
0
1
0
3
1
0
0
0
0
0
1
2
0
0
1
9
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
2
0
0
1
0
2
0
0
0
0
0
1
0
0
3
1
3
0
0
2
0
0
1
0
1
0
0
1
2
1
1
0
0
2
1
0
1
1
0
2
0
2
4
0
1
0
0
2
2
2
0
0
0
0
1
0
2
0
0
0
2
0
2
0
0
1
0
0
1
1
0
2
0
0
0
2
0
3
0
0
0
0
0
1
0
2
1
0
0
0
2
0
0
0
0
0
0
1
0
0
2
2
0
0
1
0
1
2
0
1
0
0
1
1
0
1
1
3
2
0
0
0
0
0
0
0
0
0
2
1
1
0
2
0
0
1
1
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
1
2
0
1
2
0
0
0
1
2
1
2
0
2
0
2
0
2
0
0
4
0
0
0
1
3
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
2
1
1
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
1
1
0
1
0
0
2
2
2
1
0
0
0
0
0
0
2
0
5
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
3
2
3
0
0
0
0
2
1
0
0
2
0
0
2
0
3
2
2
2
0
1
0
0
0
2
1
0
0
0
1
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
1
0
1
0
1
0
0
0
0
0
2
2
0
3
1
1
0
0
1
1
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
2
2
0
0
0
2
3
0
0
0
2
0
2
0
0
1
6
0
0
0
1
2
0
2
2
1
1
1
0
2
2
2
1
0
0
0
0
2
0
0
0
0
2
2
0
4
0
1
0
0
2
2
1
0
0
1
0
0
0
2
1
3
0
1
0
0
0
1
0
2
1
0
1
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
2
1
0
2
0
0
0
1
2
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
4
1
1
0
0
0
0
0
0
0
0
2
0
1
0
1
2
0
0
0
2
0
0
2
1
0
0
1
2
0
2
1
0
2
0
0
0
2
0
1
2
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
2
2
0
0
2
2
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
1
0
0
1
1
0
2
1
0
0
0
1
0
2
0
2
0
0
1
1
0
1
2
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
5
0
0
2
0
2
0
0
2
0
0
1
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
4
1
0
0
0
1
1
0
1
0
1
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
3
0
0
0
0
2
0
0
0
0
0
1
2
1
2
0
1
0
0
0
0
1
2
2
0
1
0
0
4
1
0
1
0
0
1
0
2
0
1
0
1
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
1
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
3
2
2
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
2
1
2
0
0
1
1
0
1
0
0
0
1
0
0
0
2
0
0
0
3
0
0
2
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
2
0
2
1
0
0
0
0
0
1
2
0
0
0
0
3
0
0
0
1
0
1
0
0
2
0
0
2
2
2
0
3
0
2
2
0
0
2
2
1
0
1
0
2
0
2
0
2
0
0
1
0
1
0
1
0
0
2
2
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
2
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
2
0
0
0
0
0
3
0
0
0
2
0
1
0
0
2
0
1
0
0
0
1
1
1
2
2
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
2
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
1
0
1
0
0
2
0
0
1
0
1
2
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
1
0
3
0
1
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
2
0
0
0
0
0
6
0
0
3
2
0
0
0
0
1
0
0
1
0
0
0
3
0
0
0
0
0
0
1
0
0
1
2
0
1
0
3
0
0
0
0
0
0
2
5
0
0
0
2
0
2
0
1
1
0
3
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
2
6
0
1
0
1
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
1
0
0
2
0
1
0
0
1
1
2
2
1
0
0
2
1
0
0
0
2
1
0
0
0
1
0
0
2
1
3
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
1
0
2
2
2
0
2
0
1
0
1
1
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
3
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
2
0
0
1
0
1
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
1
0
0
1
2
0
0
0
0
1
0
0
0
0
1
2
0
1
0
2
0
0
3
0
1
0
1
0
1
2
0
0
0
2
0
0
0
1
0
1
0
0
2
5
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
2
0
0
2
2
0
1
0
2
1
2
0
0
0
1
0
0
2
0
2
0
1
2
1
2
0
2
0
0
0
0
2
2
3
0
0
0
0
0
0
1
1
0
3
0
1
2
1
2
0
2
2
0
0
0
0
2
0
2
1
0
2
0
10
0
0
0
1
0
0
0
1
0
0
2
1
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
1
0
0
1
1
0
0
0
1
3
0
0
0
0
0
0
1
0
1
0
0
0
1
2
0
1
0
1
0
0
0
0
0
0
1
0
0
0
2
2
2
1
0
1
0
0
0
0
1
2
2
1
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
1
0
0
0
1
0
0
2
2
0
1
2
0
1
0
0
2
0
1
2
1
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
2
1
0
0
0
0
0
1
0
1
2
0
0
1
0
0
0
2
1
0
0
1
0
2
2
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
2
0
0
2
0
1
1
0
0
0
0
1
2
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
2
0
2
1
2
1
1
3
0
0
0
0
2
0
1
0
0
0
0
2
0
2
0
1
0
0
2
2
1
0
0
3
1
0
1
0
0
1
1
0
0
1
2
0
2
0
0
0
2
0
0
1
0
1
0
2
0
0
0
2
0
2
0
0
0
0
0
1
1
1
2
1
0
0
1
0
0
2
2
0
0
0
0
2
0
2
0
0
0
1
0
2
0
2
0
0
0
1
2
0
0
1
1
2
1
0
1
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
4
1
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
2
2
1
0
0
0
0
0
0
1
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
1
0
1
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
3
0
1
2
0
0
0
4
2
2
0
6
0
1
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
1
3
1
2
0
1
0
0
0
0
0
1
0
0
2
1
0
0
1
0
1
0
1
0
0
0
2
0
0
1
0
0
0
1
2
0
2
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
2
0
0
0
0
1
1
1
0
0
0
3
1
0
0
0
0
0
0
0
0
3
0
0
0
1
2
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
1
0
2
2
1
1
0
0
2
0
1
0
0
0
0
2
1
1
0
0
1
0
0
0
0
1
6
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
2
2
1
0
0
2
0
2
0
0
0
0
0
2
2
1
2
0
1
2
0
2
0
0
0
0
0
0
2
1
0
2
2
0
1
0
2
1
1
0
0
0
2
2
0
4
0
0
1
5
0
3
1
0
0
2
0
0
0
1
1
2
1
0
1
1
1
0
0
0
2
2
1
1
2
2
0
0
1
2
0
1
0
1
0
0
0
0
0
0
2
0
0
1
0
0
4
1
0
0
1
2
2
2
0
0
0
0
1
0
0
1
2
1
0
2
1
0
0
2
2
1
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
3
0
2
0
2
0
2
0
0
0
1
1
0
0
0
1
2
0
0
2
0
0
1
0
0
1
0
1
0
2
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
1
1
5
2
1
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
1
0
1
2
2
0
2
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
3
0
0
0
0
0
1
1
0
0
0
3
1
0
0
0
0
2
0
2
0
0
0
1
1
0
0
0
0
0
0
1
1
2
0
0
0
2
0
1
0
0
0
2
2
1
4
0
0
0
0
0
0
3
1
0
0
0
0
5
0
0
0
0
2
0
0
0
1
1
1
1
2
0
0
1
0
0
0
2
3
1
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
2
0
0
0
2
1
0
0
0
1
0
2
1
2
0
2
1
0
0
0
0
0
1
0
0
2
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
1
0
0
2
1
1
0
2
0
2
0
1
0
0
0
2
0
1
2
0
2
2
1
0
0
0
0
0
0
1
0
1
0
1
2
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
1
0
1
2
0
1
1
0
1
0
0
0
0
0
0
2
0
0
2
2
3
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
1
0
5
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
2
0
1
0
1
0
2
2
0
0
1
1
0
0
0
2
0
1
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
2
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
2
0
1
1
0
0
0
0
2
1
1
1
0
1
0
1
0
2
0
1
2
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
2
2
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
1
2
2
0
0
0
0
2
0
1
2
0
2
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
3
1
0
1
0
2
1
2
0
0
1
0
0
2
2
0
0
1
1
0
2
0
1
0
1
0
0
1
1
0
0
0
1
0
2
0
2
2
0
0
0
0
0
0
0
0
2
1
0
2
0
1
0
0
0
1
0
0
1
0
0
0
2
0
1
0
1
0
3
3
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
3
2
0
0
0
0
0
3
0
1
2
0
0
2
1
1
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
2
2
0
0
0
1
1
0
0
0
1
1
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
1
0
0
1
2
0
0
0
0
2
0
0
1
1
1
2
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
3
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
2
2
0
2
0
1
0
0
0
1
2
0
0
0
2
2
0
1
0
0
1
2
1
1
0
0
0
0
0
2
0
0
0
2
2
1
2
1
0
0
0
1
0
0
0
1
1
2
1
0
0
1
0
2
0
0
0
0
2
2
2
0
0
2
0
4
0
0
1
1
0
0
2
0
0
2
1
3
2
0
2
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
2
0
0
0
3
2
0
2
0
0
0
0
1
1
0
0
0
1
1
0
1
2
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
1
0
2
0
2
0
2
0
0
1
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
2
1
0
2
0
1
0
0
3
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
2
0
0
2
3
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
4
0
2
0
0
0
0
2
0
0
0
2
2
2
0
0
0
1
0
2
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
1
0
3
0
2
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
2
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
1
0
0
0
2
1
0
0
1
0
0
0
0
2
0
0
0
1
2
0
0
0
10
0
1
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
3
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
2
0
2
0
0
0
0
0
7
2
0
0
2
0
0
0
1
3
1
0
2
2
2
0
1
0
0
1
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
2
0
0
0
1
1
2
0
0
2
0
1
0
1
0
0
2
0
0
2
0
0
2
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
1
1
0
1
1
0
1
0
4
0
0
1
1
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
4
0
1
0
0
1
1
0
0
3
1
1
2
0
0
1
0
2
2
2
0
0
2
0
0
1
2
0
1
0
0
0
0
0
0
1
2
0
0
1
0
1
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
1
0
4
1
0
0
0
2
0
0
1
0
2
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
9
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
2
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
2
0
1
1
2
2
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
2
2
0
0
0
1
1
0
0
0
0
1
1
0
2
0
0
0
0
0
0
1
0
0
1
0
2
0
0
1
0
2
2
0
0
0
3
0
2
2
0
0
2
0
2
2
0
2
0
0
1
2
0
0
0
2
0
0
1
2
0
2
1
0
1
0
0
0
2
2
0
0
1
0
0
2
2
0
0
0
1
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
1
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
2
0
1
1
0
1
1
0
0
0
2
0
0
0
1
1
0
0
2
0
4
0
1
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
2
1
2
1
2
0
0
0
0
0
0
2
2
1
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
2
2
0
0
0
0
6
0
3
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
2
0
2
1
3
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
2
0
0
1
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
3
0
0
1
1
0
0
0
2
0
1
1
0
0
0
0
0
2
0
4
0
0
0
0
2
2
0
1
1
2
0
2
1
0
0
1
0
0
1
0
0
2
0
0
2
2
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
2
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
1
0
0
0
2
0
1
0
0
0
2
0
2
3
0
0
2
2
0
0
1
0
0
0
0
0
1
0
0
0
0
2
2
0
1
2
0
0
0
0
1
3
3
1
2
0
1
1
3
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
2
1
2
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
1
0
2
2
0
0
0
0
0
1
0
2
0
0
1
0
1
0
0
0
0
0
2
0
3
0
1
0
0
1
2
1
1
0
0
0
0
4
2
0
0
1
2
0
0
0
0
0
1
1
0
0
0
0
4
1
0
0
0
1
0
0
1
3
1
0
0
0
0
2
0
0
0
0
2
0
2
1
0
0
0
0
2
0
0
2
2
1
0
1
2
0
0
0
0
1
0
0
1
0
0
0
2
0
0
1
1
0
0
2
2
2
0
0
2
1
0
3
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
2
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
2
0
0
4
1
1
0
0
0
0
0
3
3
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
2
3
0
0
0
0
1
0
0
0
1
3
2
1
1
0
0
1
0
0
0
0
0
2
2
2
0
2
0
0
3
2
2
0
0
0
1
0
0
2
0
0
0
0
1
2
0
1
0
1
0
0
0
0
2
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
1
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
2
0
0
0
1
1
0
0
2
0
2
0
0
0
0
0
0
0
0
1
1
1
0
0
1
1
0
0
2
0
3
0
0
0
3
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
2
2
2
10
0
0
0
0
0
2
1
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
2
0
0
1
0
0
0
0
0
0
1
2
1
0
0
0
0
2
6
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
2
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
2
2
1
2
0
2
0
0
3
0
0
0
0
9
1
2
0
3
0
0
1
1
4
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
2
1
0
1
0
2
0
0
2
1
0
2
0
1
2
2
1
2
0
1
0
0
0
1
1
0
0
0
0
1
0
2
0
0
0
1
0
0
8
1
2
1
0
0
0
2
2
0
1
0
6
0
0
0
8
1
2
0
2
0
0
0
0
0
1
2
1
0
0
2
0
0
0
0
1
2
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
3
1
0
0
1
0
0
0
0
0
0
2
1
0
2
2
2
1
2
2
0
0
1
1
1
0
2
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
1
1
1
1
2
0
0
0
0
1
0
0
1
0
3
0
1
2
0
0
0
0
0
2
0
0
0
0
0
3
0
1
2
0
0
0
0
2
0
0
2
0
0
0
1
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
2
1
0
6
0
1
0
2
1
0
3
1
0
2
0
0
0
0
0
0
3
1
2
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
1
0
0
2
0
0
4
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
2
0
0
0
0
1
0
0
2
3
0
0
0
0
1
0
2
1
2
0
1
0
0
0
2
2
2
0
0
2
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
2
0
1
0
5
0
0
0
6
0
2
2
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
1
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
2
0
2
2
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
2
2
1
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
2
0
0
0
0
0
1
2
0
1
0
0
0
4
0
0
0
1
0
0
2
4
0
1
2
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
1
4
1
0
0
0
0
0
2
1
1
0
0
2
0
3
0
3
3
0
0
1
1
0
2
0
0
0
0
2
0
0
0
2
2
0
0
0
1
2
1
0
0
0
0
0
0
1
0
0
1
1
2
0
2
0
0
0
1
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
2
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
1
2
0
0
0
1
0
0
1
0
0
0
2
3
0
0
0
0
1
1
0
2
1
3
2
0
0
0
2
2
0
0
5
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
1
2
0
0
0
0
0
0
1
0
3
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
3
1
0
0
2
0
1
1
0
0
0
0
2
2
0
2
2
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
3
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
1
0
2
2
1
0
2
1
2
2
1
0
0
2
0
0
3
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
1
1
0
1
1
0
1
1
0
2
2
0
1
0
0
1
0
2
2
1
0
0
0
0
0
0
0
1
0
0
1
0
2
1
1
1
0
0
0
2
2
0
0
0
0
2
0
2
1
0
2
0
0
0
0
0
0
0
1
2
1
0
2
0
0
0
0
1
3
0
0
3
0
0
2
1
0
0
2
1
1
0
0
2
0
2
1
5
1
0
0
0
1
1
4
1
0
2
0
0
1
0
0
4
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
1
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
1
1
2
3
0
0
0
1
0
0
0
0
1
0
1
0
1
0
3
0
0
0
2
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
2
0
3
2
0
2
1
0
0
1
0
0
1
0
0
0
0
0
1
1
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
1
0
0
2
0
1
0
0
2
0
0
1
2
0
0
3
2
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
2
2
0
0
2
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
2
2
1
0
0
0
2
0
2
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
1
0
1
0
1
0
2
2
1
2
0
0
1
2
0
1
0
2
1
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
2
2
0
1
0
0
0
0
2
1
1
0
0
0
0
2
0
0
0
1
0
0
2
0
2
0
0
0
1
3
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
1
2
4
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
1
0
0
1
1
0
3
2
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
1
1
1
2
0
0
2
2
0
0
2
1
0
0
2
0
0
0
0
0
0
1
0
1
1
2
1
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
2
1
2
2
1
0
0
1
0
3
1
1
0
0
0
0
0
2
0
3
0
0
0
1
0
0
0
1
4
0
0
2
0
0
0
2
0
2
0
0
0
1
1
0
0
0
1
0
1
2
2
0
2
0
0
0
0
0
0
1
2
0
0
1
0
0
0
1
0
1
0
2
0
0
0
1
0
0
2
2
0
0
1
0
2
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
2
0
0
0
1
2
0
0
0
2
0
2
2
0
0
1
2
0
3
2
0
2
0
0
2
0
0
0
1
0
0
2
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
1
2
3
1
0
0
0
0
0
1
0
3
4
0
2
0
0
0
0
0
0
3
0
0
2
2
0
0
0
1
2
0
1
0
0
2
1
0
0
0
0
2
2
0
0
1
0
1
0
1
0
0
2
1
0
1
1
0
1
0
0
2
0
2
1
0
3
0
2
0
0
0
1
0
0
1
1
1
1
0
0
1
1
0
0
0
1
0
0
0
2
2
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
2
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
3
2
1
1
0
0
0
0
1
0
0
0
1
0
1
2
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
3
0
0
2
0
1
2
0
1
2
0
2
0
0
2
2
0
1
1
0
0
0
0
2
0
1
2
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
2
0
0
1
2
0
2
0
2
1
1
0
2
0
0
0
1
0
0
0
1
1
0
1
0
0
0
2
0
0
0
1
0
2
1
0
0
0
0
0
0
2
0
0
0
0
2
1
0
2
1
0
2
0
1
4
0
2
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
1
3
1
0
0
1
0
1
0
1
0
0
0
0
2
2
0
1
0
0
0
0
1
0
0
1
0
2
0
0
0
2
0
1
1
0
0
0
3
0
2
0
0
0
2
0
0
2
0
2
2
0
0
0
2
0
0
1
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
1
0
0
1
1
0
2
0
1
0
0
2
5
0
0
1
1
1
1
0
2
0
0
1
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
1
0
1
2
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
2
2
3
0
1
0
0
0
5
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
2
0
2
0
1
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
3
1
2
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
1
0
0
2
0
4
0
0
0
1
0
2
1
0
1
0
0
1
4
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
4
2
0
0
1
0
0
0
0
2
0
0
2
1
2
0
1
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
2
1
0
1
0
0
0
0
0
0
0
1
2
1
1
0
0
0
1
0
0
2
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
3
0
1
0
1
2
2
0
2
0
3
0
0
0
0
0
2
4
0
0
2
2
0
0
1
2
0
2
0
2
0
0
0
1
0
0
1
0
0
1
0
0
0
0
2
0
0
2
1
2
0
2
0
0
3
0
0
0
1
0
0
2
0
1
0
0
1
0
0
1
3
1
0
1
0
0
0
2
0
0
2
0
2
2
0
1
0
0
0
0
0
0
0
2
0
0
1
0
2
1
1
0
0
0
2
0
1
0
0
2
0
0
2
1
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
2
1
0
0
2
2
0
2
2
0
0
0
1
0
0
2
1
1
0
0
0
0
0
2
0
0
0
0
0
0
1
2
2
0
0
2
0
2
1
2
0
2
3
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
1
2
2
0
0
2
0
0
0
1
0
0
2
2
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
2
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
3
1
2
0
0
0
0
0
0
0
2
2
0
0
2
1
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
1
0
2
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
2
0
0
3
0
0
0
0
0
0
0
2
1
0
2
3
0
0
1
0
1
2
1
0
2
1
0
0
0
2
2
0
0
1
0
6
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
2
0
1
2
0
0
0
2
2
0
0
1
0
2
0
0
1
1
2
0
0
0
0
0
1
1
0
2
1
2
0
1
0
0
0
0
2
0
0
1
0
2
1
3
1
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
2
0
2
0
1
1
0
1
2
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
1
1
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
2
2
1
1
0
1
0
0
0
0
1
2
1
0
0
0
0
0
1
0
2
2
0
1
1
0
0
0
0
1
1
0
0
0
0
2
0
2
0
0
2
2
0
0
3
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
1
2
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
2
0
1
2
1
0
0
0
2
0
0
1
2
0
2
0
0
0
0
0
1
1
2
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
2
0
0
0
0
0
0
6
0
0
1
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
1
0
1
0
2
2
0
0
0
2
1
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
2
1
0
0
0
1
0
0
2
0
0
1
0
2
1
0
0
0
2
0
1
1
2
0
0
0
0
0
0
0
0
1
0
2
1
0
0
1
0
0
0
0
0
0
2
2
0
1
1
2
2
0
0
0
0
0
0
0
1
0
1
3
3
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
1
0
0
0
1
0
1
0
1
0
1
0
2
0
2
2
1
0
0
0
0
2
0
0
2
2
0
0
0
0
0
1
0
0
2
2
0
0
0
0
1
0
2
2
0
0
1
0
0
0
0
0
1
0
0
2
0
0
2
0
1
0
2
1
2
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
2
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
1
2
1
2
0
0
0
0
0
0
0
0
3
2
0
2
1
1
2
2
0
0
0
0
0
2
2
0
1
2
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
2
1
2
0
0
2
0
0
1
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
2
2
1
0
0
0
0
2
2
0
0
0
0
1
0
0
4
2
2
0
0
1
1
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
1
0
0
2
0
0
1
0
0
1
0
0
2
0
0
0
3
2
0
2
0
1
0
0
0
2
1
0
1
0
0
1
1
0
2
0
1
0
0
2
2
0
0
0
0
0
2
0
0
0
1
0
3
1
0
0
1
0
2
0
0
0
3
0
0
0
3
0
0
0
1
1
1
0
0
1
0
0
1
0
0
0
0
0
1
1
0
2
0
0
0
2
0
1
0
2
1
2
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
2
0
0
2
1
0
0
0
1
1
0
1
0
2
2
0
0
0
0
0
0
3
2
2
0
0
0
1
0
2
0
0
0
0
1
1
0
1
0
0
0
0
1
2
0
0
0
0
2
1
2
0
1
3
0
0
0
2
0
0
2
0
1
0
0
0
0
1
0
0
1
0
0
2
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
2
1
1
0
3
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
2
0
0
0
2
0
0
1
1
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
1
0
2
0
0
0
0
0
1
2
0
1
0
2
0
0
0
0
2
0
2
0
1
0
0
0
1
0
5
1
0
2
1
0
0
1
2
0
0
2
1
0
0
1
0
0
0
0
1
0
0
0
3
0
0
1
2
0
1
0
0
2
1
0
0
0
0
0
0
5
1
0
0
0
8
0
0
0
0
2
1
0
1
1
1
2
0
1
1
0
0
0
1
2
0
2
0
0
0
0
2
0
0
0
0
1
2
0
1
0
2
1
0
0
1
0
0
2
3
1
0
2
0
3
0
0
2
0
2
0
0
0
0
0
1
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
1
0
0
2
0
0
2
1
0
2
0
0
1
1
0
0
2
0
0
2
0
1
0
0
0
0
1
0
0
1
2
0
0
0
0
2
0
0
0
0
2
1
0
0
2
0
1
0
1
0
2
2
2
0
1
1
0
0
1
1
0
2
0
2
2
2
0
1
2
0
1
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
2
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
1
0
0
3
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
2
0
2
0
2
0
0
0
2
1
0
2
1
0
1
0
0
0
2
0
0
0
1
0
0
2
0
2
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
1
1
2
2
0
0
0
3
1
1
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
1
0
1
0
1
2
0
0
2
0
0
0
0
1
0
2
0
0
0
2
1
2
0
0
0
0
0
1
0
0
2
2
1
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
2
0
2
1
1
0
0
2
1
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
3
1
0
1
3
0
0
2
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
1
0
1
1
0
0
1
0
0
2
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
1
0
2
0
0
3
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
4
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
3
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
3
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
1
0
0
1
2
0
1
0
0
1
0
1
0
0
0
0
1
1
0
0
2
0
0
2
0
0
0
0
0
0
2
1
2
2
0
0
0
2
1
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
4
0
0
0
0
0
0
3
2
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
1
0
1
1
2
1
0
1
0
1
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
1
0
2
1
0
0
2
0
0
0
1
0
0
2
0
1
0
0
0
2
2
0
0
0
0
0
1
0
0
0
2
2
0
1
1
0
0
0
0
2
0
0
2
0
0
2
0
1
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
1
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
2
0
0
1
0
0
0
0
0
0
1
2
0
0
0
1
2
0
0
0
0
0
1
1
0
0
1
0
0
0
2
0
0
2
1
2
0
0
0
0
0
2
2
1
0
1
0
2
0
2
0
0
0
8
0
0
0
4
0
0
0
0
0
0
2
0
0
1
0
1
0
0
2
0
0
0
1
1
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
1
2
2
0
0
1
0
0
0
0
0
0
2
4
0
0
0
0
1
1
1
0
0
0
0
2
2
1
0
0
0
1
1
1
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
8
7
0
0
0
0
0
2
0
0
2
1
2
0
0
0
2
0
0
1
0
0
0
1
0
2
1
0
0
0
0
2
2
2
0
2
2
0
2
0
0
0
2
0
2
0
0
0
0
2
1
0
2
3
2
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
2
2
0
2
0
0
0
2
0
0
1
0
0
0
0
1
1
2
1
0
0
0
0
0
0
0
0
0
0
1
0
2
1
1
3
0
0
1
2
2
0
0
0
2
0
0
1
6
0
0
1
0
0
2
0
0
0
1
0
1
2
0
0
1
0
0
1
2
0
0
1
1
0
2
0
0
0
2
0
1
2
1
0
0
1
0
0
0
3
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
2
0
0
2
1
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
2
2
1
2
0
0
0
0
0
0
1
1
0
0
1
0
1
0
2
1
0
2
2
0
1
0
0
0
0
0
1
0
0
0
0
0
5
0
2
2
2
0
0
0
0
0
2
1
0
2
0
1
0
0
0
0
1
1
1
0
0
0
0
2
0
2
1
1
1
0
0
1
2
0
0
1
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
2
1
2
0
0
0
4
0
0
0
1
0
0
0
0
0
1
2
0
2
1
4
0
0
0
0
0
0
1
2
0
0
3
0
0
1
1
0
2
1
1
1
0
0
0
0
0
1
1
0
1
0
0
1
0
1
0
2
2
1
0
3
0
1
0
0
0
0
0
0
0
0
0
2
1
0
1
2
0
0
2
0
2
0
0
1
0
3
0
0
0
0
3
1
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
2
2
1
0
1
0
1
1
2
2
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
2
1
0
2
0
0
2
0
0
0
1
0
0
0
4
0
0
1
0
0
2
0
1
2
3
0
1
0
0
1
0
2
0
0
1
2
0
1
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
1
0
0
2
0
0
0
2
1
0
1
0
1
0
0
0
0
2
0
0
0
3
0
2
0
0
2
0
1
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
1
0
2
0
1
0
0
0
1
0
0
0
3
1
0
1
0
0
3
0
2
0
0
0
2
1
0
2
0
2
3
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
4
0
1
1
0
0
2
1
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
1
0
1
1
0
0
0
2
0
0
0
0
2
1
0
1
0
0
0
1
2
0
0
2
0
1
0
0
0
0
0
0
0
0
1
2
1
0
0
1
0
0
0
0
0
0
2
1
0
0
2
2
0
0
0
2
0
3
2
0
1
2
2
0
0
0
2
0
2
1
0
1
2
0
0
1
0
2
1
0
0
2
0
0
2
1
2
2
2
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
2
0
0
0
0
0
1
0
4
0
1
0
2
1
0
0
2
1
1
2
2
2
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
2
0
0
0
3
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
1
1
2
0
0
2
0
1
0
1
0
1
0
0
1
0
1
0
0
0
2
2
0
0
3
0
0
0
4
0
0
3
0
1
0
0
1
0
2
2
0
0
0
0
0
1
0
2
2
2
0
0
1
4
0
0
0
1
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
2
0
0
0
0
2
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
1
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
6
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
1
1
0
2
0
1
7
0
2
1
0
2
1
0
0
0
0
1
0
1
2
0
0
0
2
3
0
0
1
2
0
0
0
0
2
2
0
1
0
0
2
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
2
0
3
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
3
0
0
0
0
1
0
0
0
0
0
3
0
2
0
0
1
0
0
3
1
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
3
0
0
1
0
0
0
2
1
0
0
1
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
3
0
0
1
0
2
0
0
2
0
0
1
1
0
0
1
0
0
1
4
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
2
0
0
0
0
1
0
0
1
0
0
2
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
2
0
0
0
0
0
2
0
2
1
0
0
0
0
0
1
0
3
1
0
0
1
2
1
0
0
0
0
0
0
2
0
6
0
0
1
2
0
1
0
3
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
1
2
0
1
0
0
0
0
1
0
2
0
0
0
2
0
0
2
0
0
1
0
0
0
0
2
0
2
0
0
1
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
1
0
0
1
0
2
1
0
1
0
1
2
0
2
3
2
0
0
0
0
0
2
1
0
2
0
1
0
3
0
3
2
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
1
2
0
2
1
0
0
0
2
0
0
0
2
2
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
2
1
2
2
0
2
0
1
0
0
0
0
0
1
1
0
0
2
0
0
2
0
1
0
1
2
2
1
0
2
1
0
0
0
0
0
0
0
0
0
2
2
1
1
0
0
0
0
0
0
0
1
3
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
3
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
2
1
0
2
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
1
1
0
0
2
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
1
0
0
4
0
0
0
0
0
0
1
2
0
0
1
1
0
0
3
0
2
0
2
0
0
1
0
0
2
2
1
0
0
0
0
2
0
4
2
0
0
0
0
0
0
2
0
0
2
2
0
2
0
2
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
3
0
1
1
0
2
2
0
1
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
2
0
0
0
1
0
2
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
2
6
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
2
0
1
1
1
0
0
0
0
0
3
4
0
2
0
2
1
0
1
0
0
2
1
1
0
0
2
0
0
1
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
3
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
5
2
0
0
0
0
1
1
1
0
0
0
0
1
0
2
0
0
0
0
0
0
1
1
0
0
2
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
2
1
0
1
0
0
0
1
0
0
0
1
1
0
1
0
0
2
0
1
0
0
0
2
0
0
1
2
2
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
1
0
1
2
0
0
2
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
4
2
0
0
0
0
1
0
0
3
1
2
2
0
0
2
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
5
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
2
1
0
1
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
2
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
3
0
1
1
2
0
0
0
0
2
2
0
0
0
0
2
0
0
1
1
2
0
0
0
1
0
0
2
0
0
1
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
2
0
1
0
0
0
8
0
1
0
1
0
3
0
0
1
1
0
0
2
0
0
1
0
0
0
2
0
0
1
0
0
0
0
2
0
2
0
0
2
2
0
2
0
0
0
0
1
2
1
2
0
0
2
2
1
2
0
0
0
0
0
0
0
0
1
3
0
1
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
1
0
0
0
0
0
1
0
0
0
2
0
0
1
1
0
1
0
1
2
1
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
1
1
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
1
1
1
2
0
2
0
1
2
1
0
0
0
2
0
0
0
0
0
3
2
2
1
0
0
0
0
1
2
0
1
2
1
0
2
0
2
0
2
0
0
2
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
3
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
1
0
0
3
0
0
0
0
0
1
2
0
2
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
3
2
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
1
0
0
0
2
0
0
2
0
0
0
2
2
0
0
2
0
0
0
2
0
1
0
0
0
0
2
0
0
3
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
1
0
1
0
0
0
5
1
1
2
0
0
1
0
0
2
0
1
3
0
0
0
0
0
1
0
1
0
1
0
1
0
0
2
0
0
0
0
0
0
1
0
1
1
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
2
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
2
1
0
2
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
2
2
0
0
0
0
0
0
1
0
1
0
3
0
0
1
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
3
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
2
0
2
1
0
0
0
0
2
1
2
1
2
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
2
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
2
0
2
0
0
0
1
0
1
1
0
2
0
0
0
0
0
0
1
1
0
0
2
0
0
0
1
2
0
1
2
1
0
0
0
2
0
0
0
0
1
2
0
3
2
0
0
2
0
1
2
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
2
2
0
0
0
0
1
0
0
0
0
0
2
0
1
1
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
2
0
1
1
0
2
0
1
1
0
1
1
1
1
0
0
2
0
0
0
2
1
0
2
0
1
0
0
2
0
1
0
0
2
0
0
1
2
0
0
0
1
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
1
1
0
0
1
4
0
2
0
0
2
5
0
1
2
2
1
1
0
0
0
2
1
0
0
0
0
0
4
0
0
0
1
2
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
2
1
0
0
1
0
0
1
0
0
0
0
1
0
0
2
2
0
0
0
0
2
0
0
0
0
3
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
3
1
1
0
0
1
1
0
0
0
1
0
0
2
2
2
1
0
0
0
0
0
3
2
0
0
0
0
0
1
0
1
0
1
11
0
2
0
1
0
1
1
0
0
0
1
0
0
0
0
2
0
1
0
2
0
1
0
2
0
0
0
3
0
2
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
3
0
2
0
0
1
0
0
0
0
0
0
2
0
1
2
1
0
0
0
2
0
0
2
0
0
2
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
1
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
1
0
0
2
1
0
0
0
2
0
0
1
2
2
2
0
1
2
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
1
1
0
0
0
0
5
0
0
0
0
2
0
0
0
0
0
0
2
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
3
2
1
0
1
2
0
1
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
1
0
1
0
1
1
1
0
0
0
0
0
0
0
1
0
2
0
0
3
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
1
2
0
0
1
0
1
2
2
2
0
0
0
1
2
0
0
2
1
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
2
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
1
0
1
0
1
1
1
0
1
0
0
0
0
0
2
0
1
0
2
1
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
2
0
0
2
1
2
0
1
2
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
2
0
2
1
0
2
0
0
0
0
0
0
0
2
0
2
1
2
2
0
1
0
0
0
1
0
0
0
1
2
1
1
2
0
0
0
0
1
0
0
2
0
0
0
0
1
1
0
1
0
0
2
0
2
0
0
1
0
0
1
0
4
0
0
2
0
0
0
0
1
2
1
0
0
1
0
1
0
3
0
2
0
0
1
0
1
0
0
2
0
0
2
0
2
0
0
0
0
0
3
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
2
3
0
0
3
0
1
1
1
0
0
1
2
1
0
2
0
0
2
2
0
0
1
0
0
0
1
0
1
0
0
1
0
2
1
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
1
2
0
2
0
0
1
0
0
2
0
2
0
0
0
2
0
0
0
1
0
0
0
1
0
2
1
0
0
2
1
3
0
0
0
1
0
1
0
0
0
2
0
1
0
0
0
0
1
0
2
2
0
0
1
0
0
0
2
4
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
2
0
0
1
0
1
0
1
0
0
0
1
1
1
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
2
2
1
1
0
0
0
1
0
0
0
0
2
1
1
2
1
0
2
0
1
0
0
1
0
1
0
0
2
1
0
1
2
0
0
0
0
0
0
0
2
2
0
0
2
0
1
0
1
2
0
1
0
0
2
2
0
0
3
0
0
1
1
0
0
0
0
1
0
2
0
0
0
2
1
0
0
2
0
3
0
0
1
0
1
0
1
0
0
5
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
1
0
1
1
0
0
0
2
0
0
1
1
3
0
0
0
0
1
0
1
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
2
0
1
0
1
0
1
0
0
0
0
1
1
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
5
1
1
0
2
0
0
1
0
0
2
0
0
2
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
2
2
0
1
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
5
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
2
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
3
1
0
1
0
1
2
0
1
0
0
0
0
1
2
0
2
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
2
1
0
3
0
0
0
0
0
1
3
0
0
2
0
0
0
1
0
2
0
2
0
2
0
1
1
0
0
0
0
0
1
2
1
1
0
3
0
0
1
3
0
0
0
2
0
3
0
0
1
1
1
0
0
0
0
0
2
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
2
1
2
0
0
1
0
2
1
0
1
0
0
0
2
0
0
0
1
2
0
0
1
2
3
1
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
1
0
1
0
0
2
1
0
2
1
0
0
0
2
0
0
2
0
0
1
1
2
0
0
0
0
0
1
2
0
0
0
2
0
1
0
0
0
0
0
0
0
2
2
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
4
1
0
0
4
1
2
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
2
2
0
1
0
8
2
0
0
0
0
0
2
0
2
0
2
0
0
0
2
2
0
0
0
1
0
1
2
1
0
0
2
2
0
1
0
0
0
1
2
0
1
0
0
2
0
1
0
0
0
0
0
1
0
2
0
2
0
0
1
1
2
0
0
1
0
1
3
0
1
0
0
2
1
0
0
1
0
0
4
2
0
0
1
0
0
0
1
2
0
1
0
0
2
0
0
0
0
1
0
1
0
1
0
0
0
1
0
1
1
0
2
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
2
0
0
1
0
1
0
0
2
0
0
1
0
0
0
2
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
1
0
0
0
0
3
0
0
3
0
0
2
0
0
2
1
0
2
2
1
0
0
1
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
2
0
0
0
0
0
1
0
1
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
1
5
0
2
0
0
1
1
0
0
0
1
1
0
0
1
0
2
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
1
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
1
0
1
2
0
0
0
0
0
0
0
3
0
2
2
0
1
0
2
0
0
0
0
4
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
1
3
0
1
0
1
0
0
3
2
0
0
0
1
0
0
2
2
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
2
1
1
2
0
0
0
2
0
0
0
0
0
0
0
1
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
8
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
1
2
1
0
0
1
2
0
0
0
1
0
0
2
2
0
0
1
0
1
2
0
3
0
0
2
0
0
2
0
1
0
1
0
0
0
0
0
3
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
1
1
0
2
0
0
1
0
0
0
1
2
2
0
2
0
2
2
2
0
4
0
2
0
0
2
0
2
0
0
1
1
0
0
0
1
0
1
2
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
1
1
2
0
0
1
1
1
0
0
0
0
0
0
2
0
2
0
2
0
1
0
0
0
2
2
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
2
2
0
1
0
0
0
2
1
1
0
0
2
1
0
1
0
0
3
0
0
1
1
0
2
0
2
1
1
2
0
2
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
1
1
0
0
1
1
3
0
0
1
0
2
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
1
3
0
0
1
0
3
0
2
0
1
0
0
0
2
2
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
2
5
1
0
0
0
2
1
0
3
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
2
0
0
0
1
0
0
1
0
0
0
0
2
0
1
2
2
1
0
0
0
0
0
0
0
0
2
2
0
3
2
0
0
0
1
0
1
1
0
0
0
0
0
1
1
0
2
0
0
2
1
1
1
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
2
1
0
0
1
2
0
3
0
0
0
2
0
0
0
2
1
2
2
0
0
2
0
2
0
1
2
1
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
1
0
2
0
2
0
0
2
0
0
0
1
2
0
1
1
0
0
2
1
2
2
0
1
1
2
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
2
0
1
0
1
0
3
0
1
0
2
0
1
0
0
0
2
0
3
2
0
0
0
0
0
1
0
3
1
0
0
0
1
1
0
2
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
3
0
0
2
0
0
2
0
0
0
0
1
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
3
2
1
5
0
5
0
0
0
0
0
1
0
0
0
4
1
2
0
2
1
1
0
0
0
0
2
0
2
2
2
0
0
1
0
0
0
1
1
1
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
4
0
0
0
0
0
1
0
2
1
0
2
0
0
0
0
0
1
1
0
0
0
1
1
0
3
2
2
3
0
0
0
0
1
1
0
1
0
2
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
2
0
3
1
0
0
1
0
0
0
0
3
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
1
1
2
0
2
0
2
2
5
0
2
1
0
2
0
2
0
0
2
0
0
0
1
1
1
0
0
0
0
0
0
2
0
0
0
0
2
2
2
2
1
0
0
1
0
0
2
0
1
1
0
2
0
0
0
2
0
0
0
0
0
1
2
0
4
0
0
0
1
0
0
0
1
0
1
0
1
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
2
0
1
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
3
0
1
0
1
1
0
0
2
2
0
0
0
0
1
1
2
0
2
2
2
0
0
0
0
0
1
2
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
2
1
2
0
0
0
0
0
1
2
0
1
0
0
3
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
2
0
0
0
0
2
1
0
2
3
0
0
2
0
0
0
1
0
2
0
0
2
1
0
0
1
1
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
1
3
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
2
2
0
1
0
0
0
0
1
0
1
0
1
0
0
2
0
0
0
0
1
0
2
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
2
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
1
2
0
2
0
1
1
0
0
1
2
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
2
0
3
0
1
0
0
0
0
0
1
0
1
0
0
2
0
0
0
1
0
2
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
1
1
0
2
1
0
1
0
0
0
0
0
1
0
2
0
0
2
0
0
1
0
2
1
2
0
0
2
0
2
0
0
1
1
0
2
0
0
1
0
0
1
0
0
0
1
1
1
1
0
2
0
0
2
1
2
0
0
0
3
2
0
2
0
1
0
0
2
0
0
0
0
0
2
0
0
2
0
0
2
0
1
0
0
1
0
2
0
1
0
2
0
0
0
0
4
0
0
0
0
0
2
0
0
4
0
0
2
0
0
0
1
0
0
0
0
1
0
1
0
1
2
0
1
0
0
0
1
2
1
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
1
1
0
0
2
0
0
0
1
2
0
0
0
0
0
0
1
0
0
2
1
1
0
0
0
0
0
0
3
0
2
0
2
0
1
0
0
0
0
0
0
2
1
0
2
2
2
1
1
0
0
2
0
0
0
2
0
0
0
1
2
0
2
1
0
1
0
0
0
0
0
2
2
1
1
0
1
2
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
2
0
0
1
0
0
0
0
0
0
0
2
0
2
0
1
3
0
0
2
0
0
0
0
0
2
1
0
2
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
1
0
2
2
0
1
2
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
1
1
0
2
1
0
1
3
3
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
4
0
1
0
0
1
0
0
0
0
1
2
0
0
0
0
1
0
0
0
1
2
0
0
1
0
0
0
0
0
0
1
2
1
0
1
0
0
5
1
2
0
0
0
1
0
0
2
1
1
2
2
1
0
0
2
0
0
1
0
0
0
0
2
1
2
0
2
2
0
0
2
0
2
1
0
2
2
0
0
0
0
0
2
0
3
0
0
0
1
0
2
1
1
0
1
8
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
2
0
0
0
1
0
0
0
0
1
3
1
2
0
0
0
3
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
1
0
0
1
0
2
2
0
1
0
4
0
2
2
2
0
0
0
0
0
0
0
0
1
0
2
1
0
0
1
0
0
0
0
3
1
2
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
1
2
0
0
2
1
0
0
1
3
0
1
1
0
2
0
0
0
1
2
1
4
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
2
0
0
1
0
2
0
1
1
2
0
0
0
0
0
0
0
3
1
1
0
0
1
2
3
1
0
1
1
1
0
0
1
1
0
2
0
0
0
0
2
0
0
0
0
0
3
1
0
0
0
2
0
0
0
0
0
2
2
2
0
2
0
0
0
0
0
1
0
0
1
0
0
2
2
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
2
0
0
0
1
0
0
0
0
0
1
0
0
1
2
2
0
2
2
1
0
0
0
2
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
2
2
0
0
0
1
0
1
0
2
2
0
0
0
0
0
0
0
3
0
0
1
0
0
0
2
2
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
7
2
0
0
0
0
0
0
2
1
2
0
2
1
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
1
1
0
0
0
1
0
1
0
0
0
1
0
0
0
2
0
0
0
0
2
1
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
2
0
0
2
0
0
0
3
0
0
2
2
0
2
2
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
5
0
0
1
1
0
0
0
1
0
1
0
0
2
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
2
0
0
2
0
0
2
0
1
0
0
2
0
0
0
1
2
0
0
0
1
2
0
0
1
0
0
0
0
1
0
0
0
1
2
0
0
3
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
2
0
0
0
0
2
0
1
2
0
1
0
2
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
1
0
0
5
2
1
3
0
2
0
1
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
3
0
2
0
0
0
2
0
0
0
0
1
2
0
2
0
2
2
0
0
0
0
1
0
0
0
1
0
9
0
0
0
2
0
0
0
2
0
1
0
0
0
2
2
0
0
0
0
0
1
2
0
0
1
0
0
1
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
1
2
2
2
0
2
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
2
3
0
0
0
0
0
2
2
3
1
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
1
2
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
3
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
1
0
0
1
1
4
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
2
2
0
0
0
0
0
0
0
3
0
1
1
0
2
0
0
2
0
0
0
3
0
1
0
2
0
1
0
0
0
1
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
1
0
0
0
0
0
0
0
2
1
0
1
0
3
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
2
0
0
1
0
0
0
1
2
1
0
0
0
0
1
0
0
0
1
0
0
3
0
2
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
2
0
2
0
0
0
2
0
0
0
0
0
2
4
3
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
2
2
1
0
2
2
0
0
0
0
0
2
0
0
1
0
2
1
1
0
0
0
2
1
2
0
1
0
0
1
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
1
1
0
1
0
0
1
0
0
0
0
0
0
1
0
2
1
0
0
1
0
0
0
2
0
1
0
1
3
0
0
0
0
0
2
2
0
2
0
0
0
2
0
4
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
2
0
0
0
0
0
1
0
1
0
2
0
0
1
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
2
0
4
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
2
1
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
2
1
2
1
0
2
2
0
0
0
0
0
1
2
0
0
0
0
1
8
0
0
0
2
2
0
1
0
0
0
0
0
1
0
2
0
2
0
1
0
0
0
2
6
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
2
0
2
1
0
0
0
0
1
0
0
0
2
1
0
0
0
0
2
2
0
0
0
1
1
2
0
0
0
1
2
0
2
0
0
0
2
0
1
0
0
0
1
2
0
0
0
0
1
0
2
0
0
0
0
0
1
1
0
0
2
1
0
2
4
0
0
0
0
0
1
2
0
2
2
0
1
1
0
2
0
0
0
1
0
1
2
1
0
4
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
4
2
0
1
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
3
0
0
2
1
1
0
1
1
0
0
0
0
3
0
2
0
0
0
0
0
0
2
2
0
3
0
0
0
0
0
2
1
0
0
2
0
1
2
1
2
0
0
1
1
0
0
0
1
0
0
0
0
0
2
0
0
6
0
0
0
2
0
0
0
3
0
0
0
1
0
1
3
0
0
0
0
2
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
2
2
3
0
1
0
0
0
1
0
4
1
0
0
2
1
2
1
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
2
0
0
1
0
0
0
0
3
0
0
0
1
0
0
1
0
0
0
2
3
0
1
0
0
2
2
0
0
1
0
0
2
1
0
0
0
0
2
0
1
1
0
3
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
2
2
1
0
2
0
0
2
1
1
0
1
4
0
0
2
1
1
2
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
2
1
0
2
0
2
0
0
0
0
0
2
2
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
2
0
2
0
5
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
3
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
2
2
0
0
0
1
0
0
2
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
4
6
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
1
0
0
0
1
0
0
0
1
0
0
0
0
4
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
1
0
0
0
1
5
2
0
0
1
0
2
2
0
1
0
0
1
1
0
2
0
0
0
0
0
1
0
1
2
0
2
1
0
0
0
2
0
1
0
0
0
0
1
0
2
2
0
0
0
0
2
0
0
2
2
0
0
0
0
1
1
0
0
1
0
1
0
0
1
1
0
2
2
1
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
2
1
0
1
1
0
0
0
0
0
1
0
0
2
1
0
2
0
0
0
1
0
0
2
0
1
0
1
2
0
2
1
0
1
0
0
0
1
0
0
0
0
0
0
4
1
2
1
0
1
0
2
0
1
0
0
1
0
1
0
0
0
0
0
0
0
2
2
2
2
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
2
0
2
2
0
0
0
0
2
1
1
0
0
2
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
2
0
2
2
0
0
0
0
2
0
1
0
0
0
0
1
3
2
0
0
0
0
1
3
0
0
0
0
0
0
1
0
0
0
1
1
2
2
2
0
1
1
1
0
1
0
2
1
0
0
0
0
0
2
1
2
1
0
2
0
0
0
1
0
0
2
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
1
6
0
0
3
0
0
1
0
0
1
0
0
0
1
0
3
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
1
2
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
2
1
0
0
0
2
0
0
0
1
1
2
2
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
1
0
1
1
0
0
0
1
0
4
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
1
0
3
2
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
2
8
0
2
0
0
0
0
2
2
1
0
0
2
0
1
2
0
0
0
0
1
0
1
0
0
0
2
1
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
2
0
1
0
2
0
0
2
1
0
0
2
2
2
1
0
0
0
2
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
2
0
2
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
2
0
2
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
1
3
0
0
0
0
0
1
0
1
0
1
0
0
0
2
0
2
2
0
1
0
0
1
0
0
0
0
1
1
1
2
1
0
2
0
0
2
0
3
0
0
1
1
2
0
0
0
0
1
1
1
2
0
0
0
2
1
0
1
0
1
0
0
0
2
0
0
0
1
0
0
2
2
0
1
2
0
0
0
0
0
3
2
1
0
0
0
0
0
2
0
0
0
1
2
1
1
1
0
1
1
1
3
0
2
2
0
0
1
0
1
0
2
0
0
0
0
2
0
2
0
0
3
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
1
1
2
1
2
1
0
1
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
3
0
2
2
0
0
0
0
0
0
2
0
0
0
1
2
2
0
0
2
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
1
0
0
1
0
0
0
1
0
0
5
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
2
1
1
2
0
0
2
0
0
10
0
0
0
1
0
0
1
0
0
2
1
1
1
0
0
0
2
0
3
0
0
0
0
0
2
2
1
1
0
3
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
2
1
0
2
0
0
0
0
1
0
0
0
0
0
0
3
1
0
0
1
0
0
3
0
0
0
0
0
2
1
0
0
0
0
2
1
0
0
0
0
0
2
2
0
0
2
2
0
0
1
1
0
0
0
0
2
2
2
0
2
0
0
0
1
2
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
3
1
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
4
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
2
1
0
0
4
0
0
0
0
0
0
1
2
2
0
0
0
0
1
1
0
0
0
0
0
0
0
1
2
0
0
1
0
0
2
0
0
0
2
2
0
1
2
2
1
0
0
0
1
1
0
0
0
0
1
1
2
0
0
0
0
1
0
0
0
1
1
0
0
0
3
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
2
2
2
1
1
0
2
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
2
0
2
0
2
0
2
2
0
0
0
1
0
1
1
2
0
0
0
0
0
2
0
0
1
0
2
2
0
0
0
0
1
6
2
0
0
1
1
0
0
1
3
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
2
0
1
1
0
1
1
0
0
0
0
1
0
0
0
1
0
0
1
5
0
0
0
0
0
0
2
0
0
3
2
0
2
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
4
2
0
2
0
0
0
0
0
1
2
0
0
3
2
0
1
0
3
2
0
1
1
2
0
1
0
0
0
0
0
1
0
1
0
0
5
0
3
0
0
0
0
2
0
1
2
0
0
0
1
0
0
0
0
0
1
2
0
0
2
0
2
0
0
1
2
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
2
0
1
1
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
2
0
1
0
0
2
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
3
0
2
0
1
1
0
0
0
2
1
0
0
0
1
1
0
0
0
2
0
0
0
0
2
1
0
1
0
1
0
0
0
0
2
0
0
0
0
0
1
1
0
2
2
0
2
1
0
0
0
0
2
0
2
1
0
2
0
0
1
0
0
1
0
0
2
0
0
2
0
2
0
0
0
0
2
0
0
2
2
0
0
0
1
0
2
1
0
0
0
1
2
0
0
0
1
0
2
0
1
0
1
1
0
0
0
0
2
1
1
0
0
0
1
2
0
0
0
0
0
0
1
1
1
2
2
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
1
1
3
0
0
0
2
1
0
1
0
1
0
0
0
1
0
2
2
0
3
0
0
0
0
1
4
0
1
0
3
0
2
0
0
2
0
2
0
1
2
0
1
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
1
2
0
1
0
1
0
0
2
0
0
0
0
0
0
0
1
2
1
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
2
0
1
0
0
0
3
0
0
0
0
6
0
0
2
2
0
0
1
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
2
2
2
3
0
0
0
1
0
0
0
1
0
0
1
0
0
1
2
1
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
1
1
1
0
0
0
0
1
0
0
2
0
0
1
5
0
0
0
0
0
2
3
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
2
1
0
0
0
1
0
1
2
1
0
2
0
0
0
0
0
1
1
2
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
2
0
0
1
0
0
0
0
1
0
0
1
2
0
0
0
1
2
0
0
2
0
0
0
1
1
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
2
0
3
0
0
0
2
0
2
3
1
0
1
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
1
2
1
1
0
0
0
0
0
2
1
0
1
0
1
0
6
0
0
0
0
0
0
1
0
2
2
0
0
0
1
2
0
0
0
0
0
0
0
2
1
0
0
1
2
2
0
1
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
1
0
0
0
0
2
0
0
1
0
0
0
2
0
0
2
0
1
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
2
0
0
1
2
1
2
0
0
2
0
0
0
0
0
0
3
2
1
2
0
0
1
1
2
0
0
2
0
0
3
0
1
0
0
0
0
0
1
0
1
2
0
0
0
2
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
6
0
1
0
0
0
2
0
0
1
1
1
1
0
0
2
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
2
0
0
0
0
0
1
0
0
0
0
2
0
2
0
1
2
0
0
2
1
0
0
2
0
4
0
0
1
0
0
2
1
0
0
0
0
0
0
2
1
0
1
1
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
5
0
0
1
0
0
2
1
0
0
0
0
0
0
3
0
0
0
2
2
2
0
0
0
0
0
1
1
0
2
0
0
0
0
0
1
0
1
1
0
2
0
2
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
2
0
1
2
0
0
0
2
0
0
1
0
0
1
0
1
0
0
2
0
0
2
0
2
0
0
1
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
2
0
2
0
0
0
0
0
0
2
2
0
3
0
0
2
1
0
1
0
1
1
0
0
0
0
0
1
2
0
0
1
2
0
0
1
0
0
2
2
2
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
2
2
0
0
0
0
1
0
2
1
2
0
0
0
0
0
2
0
1
1
1
0
1
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
1
0
0
1
1
0
0
0
2
2
2
1
1
1
0
1
0
0
0
1
0
1
2
0
2
0
0
3
0
1
0
0
1
1
1
0
0
0
0
1
0
0
0
2
0
0
1
1
0
0
0
0
0
0
2
2
3
0
0
0
0
0
1
0
2
0
2
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
2
1
1
0
0
1
0
0
2
0
0
0
1
0
2
2
0
2
0
0
0
0
0
0
2
1
0
2
0
1
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
1
0
2
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
2
1
1
0
0
0
0
0
1
0
0
1
0
0
2
1
2
1
2
0
0
0
2
0
0
1
2
0
2
2
2
0
0
2
0
3
0
0
1
0
2
0
0
1
0
1
0
0
4
1
0
0
0
0
0
0
4
0
2
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
2
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
1
1
0
0
2
2
0
0
3
0
0
1
0
0
0
0
0
0
0
2
1
2
1
0
0
2
1
0
0
0
2
0
2
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
3
0
1
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
2
1
0
0
1
0
2
0
0
2
0
3
0
0
0
2
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
1
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
3
0
0
1
0
1
1
0
0
0
1
2
0
0
2
0
0
0
1
0
2
1
0
0
0
0
2
0
0
0
1
0
0
1
2
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
2
0
0
2
0
1
0
0
1
0
3
0
1
0
2
2
0
1
0
0
0
2
0
1
0
1
1
2
2
0
2
0
3
0
0
0
0
0
0
3
0
0
0
1
0
0
0
1
0
0
0
1
4
2
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
1
0
1
2
1
0
1
0
2
0
0
0
0
2
0
3
0
2
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
2
2
0
0
0
1
1
1
0
0
1
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
1
1
1
0
1
1
0
0
0
1
0
0
0
0
2
1
0
0
0
2
0
0
1
2
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
1
0
0
1
0
0
0
2
0
1
1
3
0
2
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
2
2
2
0
0
0
0
2
0
0
1
0
0
2
2
0
0
0
2
0
0
0
1
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
2
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
2
0
0
3
0
0
0
2
0
0
2
0
0
2
2
0
0
0
0
0
1
2
0
0
3
0
0
3
0
0
0
0
0
0
0
1
1
1
0
0
0
2
0
1
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
2
1
0
0
0
0
0
1
0
1
0
0
2
1
0
1
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
2
2
0
0
0
2
0
2
0
3
0
0
0
0
0
1
1
0
0
1
2
0
0
2
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
2
0
2
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
5
0
2
1
0
0
0
1
0
0
2
1
2
0
0
0
0
0
0
2
1
2
2
0
2
1
0
2
0
0
0
2
0
0
2
0
0
3
1
0
3
0
0
0
2
0
0
1
0
0
0
0
1
2
0
1
0
0
0
0
1
0
1
2
0
0
1
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
2
2
0
0
2
0
0
2
0
0
0
2
0
0
0
3
1
0
0
3
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
1
1
1
0
2
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
1
0
0
2
1
2
1
4
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
2
1
0
0
0
1
1
0
0
0
2
2
3
1
0
0
0
1
2
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
2
1
0
0
1
0
1
1
1
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
3
0
0
0
0
5
0
0
0
0
2
2
1
0
1
1
1
0
0
0
2
0
2
0
0
5
0
0
0
0
0
0
0
0
1
2
1
1
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
3
0
1
0
1
0
2
0
0
0
0
1
0
0
1
2
0
1
0
0
2
1
2
0
0
0
2
4
1
2
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
2
0
2
0
2
0
0
0
0
0
0
1
1
0
2
0
0
0
0
2
0
0
1
2
0
0
0
1
2
0
0
0
2
0
2
1
0
1
1
0
0
0
0
0
0
0
0
1
2
1
2
2
0
0
0
0
2
0
1
2
0
1
0
0
1
0
0
0
0
0
1
2
0
1
2
1
1
0
0
0
0
1
0
0
2
0
1
2
2
2
0
0
0
0
1
1
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
2
2
1
0
2
0
1
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
1
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
3
3
0
0
0
0
0
0
0
2
1
0
2
0
1
2
0
0
0
1
0
2
2
0
0
0
0
1
0
2
0
1
1
0
0
0
0
0
0
0
0
0
2
0
2
2
1
1
0
1
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
2
2
0
0
1
0
0
0
2
0
0
2
5
0
0
1
2
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
2
0
2
0
0
2
1
2
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
1
2
2
0
0
0
0
0
2
0
0
2
0
2
0
0
1
0
0
0
0
0
1
1
0
0
1
0
2
0
0
1
2
1
2
0
2
0
0
0
0
1
2
1
1
2
1
0
0
0
0
0
2
0
0
1
1
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
1
0
2
0
5
0
1
2
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
1
0
0
1
0
0
1
0
2
0
2
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
4
1
4
0
0
0
0
0
3
0
3
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
1
0
1
0
0
0
2
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
2
0
0
0
1
0
0
2
0
2
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
1
0
0
0
2
0
1
0
0
1
1
1
0
0
0
0
0
2
0
2
1
0
4
0
1
0
1
2
0
0
0
0
1
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
2
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
2
1
2
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
1
2
0
1
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
1
0
2
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
3
2
0
0
0
1
0
0
0
0
0
0
2
2
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
4
1
0
1
0
2
2
0
0
0
16
2
3
0
0
2
1
0
3
2
2
0
0
2
2
1
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
2
2
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
5
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
3
2
3
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
4
7
1
2
0
0
0
0
0
0
0
0
0
2
2
0
0
1
1
0
0
0
0
2
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
1
2
2
0
2
0
2
0
0
0
2
0
1
0
2
0
2
0
0
0
0
0
0
0
1
3
0
0
0
0
2
2
0
0
3
0
0
0
0
0
0
0
0
2
2
0
0
1
0
2
2
0
0
0
1
0
0
1
1
1
0
0
0
0
1
0
0
1
0
1
0
1
0
2
1
2
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
1
0
2
2
2
0
1
0
0
0
2
0
2
0
4
0
2
0
2
2
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
3
0
1
4
2
1
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
2
0
2
0
0
0
0
1
0
2
0
1
0
0
2
0
5
0
0
1
0
0
0
2
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
1
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
2
0
0
0
0
0
2
1
1
0
1
4
0
0
1
2
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
1
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
1
1
0
0
0
0
1
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
1
0
0
2
1
2
0
0
0
1
1
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
2
0
0
0
1
0
1
2
0
1
0
1
0
0
0
0
0
1
1
1
1
0
0
2
0
5
2
1
0
0
0
0
0
0
0
2
1
0
0
2
2
0
0
2
1
0
0
0
0
0
1
1
0
0
0
2
0
2
0
0
1
0
0
1
2
0
0
0
2
2
0
0
0
0
1
1
4
0
2
1
1
2
0
0
0
0
0
2
0
0
0
2
0
1
0
2
0
0
2
0
1
0
0
1
0
1
0
0
1
0
1
2
0
0
1
0
0
8
0
0
1
0
2
0
0
1
0
0
0
2
2
1
0
0
1
1
2
0
1
0
2
4
0
0
0
0
0
0
1
0
0
0
2
2
2
0
2
0
0
0
0
2
0
1
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
1
2
0
2
0
0
0
0
1
0
1
2
0
2
0
0
0
1
1
0
1
0
0
1
1
0
0
0
0
2
3
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
2
0
2
0
1
1
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
2
3
1
0
2
2
0
2
1
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
2
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
2
1
2
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
2
0
0
2
0
0
0
0
0
1
0
1
0
0
2
0
1
0
0
2
0
2
0
0
0
1
2
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
1
0
1
0
0
0
0
0
0
1
0
1
1
2
0
0
0
0
1
2
1
2
0
0
2
0
1
3
1
0
0
0
1
0
0
0
0
0
1
0
1
0
2
0
0
5
2
0
0
0
0
2
2
0
1
0
0
1
2
0
1
1
0
0
0
2
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
3
0
2
0
0
0
2
0
2
0
0
1
0
2
1
2
2
0
0
0
0
0
2
0
1
1
1
0
0
2
2
2
0
0
0
2
0
0
0
0
0
0
2
0
1
2
0
0
1
0
2
3
2
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
1
0
0
2
0
0
0
0
1
2
0
0
2
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
2
1
1
2
0
0
0
0
2
0
0
1
0
0
0
0
0
3
0
3
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
3
0
0
0
0
1
0
1
0
2
4
0
2
2
0
0
0
1
0
2
2
0
0
0
1
0
0
2
1
0
0
0
2
1
0
1
0
2
0
1
1
0
0
1
0
0
0
4
0
0
0
1
0
0
2
1
0
0
1
0
2
2
2
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
1
0
0
1
2
0
0
0
0
3
0
2
0
0
0
2
0
0
1
0
0
1
4
0
2
0
1
0
1
0
0
0
0
3
0
0
1
0
0
0
3
0
0
2
2
1
1
1
0
0
0
0
0
0
0
1
1
0
0
1
1
2
0
0
2
0
0
0
1
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
2
0
1
0
0
0
1
0
0
0
1
0
2
0
0
1
2
0
0
1
0
1
0
0
0
2
0
4
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
2
2
0
0
1
2
0
0
0
0
0
0
2
0
0
1
0
0
0
1
1
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
1
2
0
0
2
0
0
0
0
0
2
2
0
0
3
2
0
0
0
1
0
2
3
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
1
0
1
1
2
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
2
0
0
4
0
0
2
0
0
0
0
0
2
0
0
0
1
2
0
0
0
1
0
1
0
2
1
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
2
2
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
1
0
1
2
1
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
1
0
2
1
0
0
0
0
0
2
0
1
0
0
0
0
1
2
0
2
0
0
3
2
0
0
0
0
1
2
0
1
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
3
2
1
0
2
1
0
0
3
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
2
2
0
0
3
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
1
1
0
0
0
2
0
0
0
3
2
0
1
0
0
3
1
0
2
0
0
0
4
0
0
0
2
0
1
2
0
1
0
1
0
1
0
0
0
2
1
0
0
2
0
3
0
0
2
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
2
1
0
2
0
0
0
1
0
0
0
2
2
0
1
1
1
0
0
0
0
0
1
1
0
0
0
2
2
1
1
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
3
0
2
0
2
0
0
0
0
0
1
0
1
1
1
1
0
0
0
0
1
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
1
2
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
1
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
2
1
0
0
1
1
0
0
2
0
0
0
4
0
0
0
3
0
2
0
0
0
3
0
1
0
0
2
0
0
0
2
2
0
0
0
0
0
1
0
2
1
0
2
0
2
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
1
5
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
2
1
2
0
0
0
1
1
2
0
0
0
0
2
0
4
1
0
2
1
0
0
0
0
0
0
1
0
2
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
1
0
2
0
0
1
0
0
0
0
2
1
2
0
1
0
1
0
0
0
1
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
2
3
2
0
2
5
0
1
0
1
0
2
0
0
0
0
0
0
1
1
0
2
1
0
2
0
0
0
3
0
0
0
0
0
1
0
4
2
2
0
2
0
0
2
0
0
1
0
0
0
0
2
1
3
0
1
0
0
7
2
2
1
1
1
0
0
0
1
2
0
1
0
0
0
5
2
0
1
1
0
1
0
1
0
3
2
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
2
4
5
0
2
1
0
1
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
2
0
0
1
3
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
2
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
1
0
0
0
0
1
0
1
2
0
0
4
0
0
0
5
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
2
1
1
0
1
0
0
0
0
0
2
2
0
1
1
2
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
1
0
2
0
2
0
0
1
0
0
0
0
4
0
1
0
0
0
2
0
0
1
0
2
2
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
2
0
0
0
1
0
0
0
0
0
2
0
2
2
1
0
0
0
0
1
0
1
1
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
1
1
0
0
2
0
2
0
0
0
1
2
2
0
0
0
0
0
0
0
0
2
0
1
2
1
0
1
0
2
2
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
3
0
0
0
0
0
0
1
1
1
0
1
0
0
0
1
1
0
1
1
2
0
0
0
0
0
0
0
1
2
1
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
1
0
1
0
0
0
1
0
0
0
2
1
0
0
0
2
0
0
0
0
1
0
3
0
0
2
0
0
2
0
0
0
1
0
0
0
3
0
1
0
1
1
2
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
8
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
1
0
0
1
1
0
2
0
2
3
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
2
0
1
1
0
0
1
2
0
1
1
0
3
0
0
1
0
0
1
0
0
0
0
0
1
1
2
0
0
0
2
0
0
0
0
0
3
0
2
0
1
1
0
1
2
0
3
0
0
0
0
2
2
3
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
4
1
0
0
1
0
0
1
1
0
0
0
0
2
2
1
1
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
3
1
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
2
0
0
1
2
0
0
0
0
1
1
0
0
1
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
2
1
2
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
2
0
1
0
0
0
2
1
1
0
0
2
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
1
0
0
0
1
0
0
1
0
0
2
0
0
2
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
2
0
0
0
0
0
2
0
1
2
0
0
0
3
1
0
0
1
0
1
0
1
2
0
0
1
0
3
0
2
2
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
2
2
1
0
1
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
3
0
0
0
1
0
0
0
0
2
0
0
2
0
2
0
0
2
0
0
0
2
0
0
0
0
1
2
0
1
1
0
0
0
1
0
0
1
1
1
0
1
1
1
0
0
0
0
2
1
0
1
2
0
0
0
1
0
1
1
5
2
0
2
2
0
0
1
2
0
1
0
0
1
0
1
1
0
0
0
0
1
0
2
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
2
1
0
0
1
0
0
0
2
2
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
2
0
0
0
2
0
6
2
0
1
0
1
2
0
1
0
2
0
0
1
2
1
0
0
0
1
0
1
0
0
0
2
0
1
2
1
0
0
0
0
1
0
0
2
0
0
0
1
0
1
1
2
0
0
0
2
2
2
0
2
1
0
0
1
0
1
2
0
0
0
0
0
1
0
1
1
0
0
0
2
0
1
0
0
2
0
0
0
3
0
2
2
0
0
0
0
0
0
1
0
0
1
3
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
2
1
0
0
1
0
1
0
0
0
0
1
0
2
0
1
0
0
2
1
0
0
1
0
2
1
1
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
4
2
3
0
0
2
0
2
0
0
0
0
0
0
2
2
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
2
1
0
0
0
4
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
1
2
0
0
1
0
0
0
2
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
2
0
0
3
0
1
1
0
0
0
1
0
0
0
1
1
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
2
0
2
0
1
1
1
0
1
0
1
0
1
0
2
3
3
0
2
0
0
0
2
0
1
2
0
0
0
2
2
2
1
1
2
0
0
2
0
0
1
0
0
2
0
0
0
0
0
1
0
1
0
0
2
0
1
0
1
0
0
2
2
0
0
2
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
3
2
2
2
0
8
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
3
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
2
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
1
2
0
0
0
2
0
1
0
1
0
0
0
0
0
0
2
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
2
0
1
1
0
0
2
2
0
1
1
1
1
0
0
1
1
1
2
3
0
0
0
0
1
1
0
0
3
0
1
1
0
0
2
0
2
1
0
0
0
0
0
0
2
0
0
0
1
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
4
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
2
3
0
0
2
1
1
0
0
0
2
1
2
1
0
0
1
0
4
3
1
0
0
0
0
0
1
1
0
1
1
0
0
2
1
0
0
0
0
0
0
1
0
2
1
2
0
2
2
0
0
1
0
0
2
0
0
0
1
0
1
0
2
1
0
1
0
0
2
0
0
4
1
0
0
0
0
0
0
0
2
2
0
1
0
0
1
0
5
0
0
0
1
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
2
2
0
1
1
0
1
0
0
0
0
0
0
1
0
0
3
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
2
0
0
0
2
0
1
0
0
0
1
0
0
1
0
1
0
0
1
0
2
0
2
0
0
0
1
2
2
2
2
0
0
0
0
0
0
2
0
1
0
1
0
0
0
2
0
2
1
0
0
1
0
0
0
2
0
2
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
3
0
1
0
2
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
1
3
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
2
0
0
0
2
1
0
0
0
2
0
0
0
3
0
0
0
0
1
0
0
0
0
2
0
1
1
0
0
0
2
0
0
0
0
3
0
0
0
2
0
2
0
0
0
1
0
2
1
0
0
0
1
2
0
1
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
2
0
3
1
0
1
0
2
0
2
0
0
0
2
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
2
0
2
0
2
1
0
1
0
0
0
0
0
0
0
1
2
1
0
2
1
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
6
0
2
0
4
0
0
0
2
1
4
0
0
2
2
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
2
0
0
1
0
1
0
0
1
1
0
1
0
0
0
1
1
3
0
0
0
0
1
1
1
1
2
1
0
0
0
0
3
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
2
0
0
0
0
0
1
1
1
0
0
2
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
4
0
0
0
2
0
2
0
0
4
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
2
2
0
0
0
2
0
2
0
0
2
2
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
3
1
0
0
0
0
2
0
2
0
0
0
2
2
1
2
0
0
2
0
0
0
1
0
0
0
0
2
2
0
2
1
0
1
0
0
2
0
1
1
2
0
0
2
1
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
1
0
0
2
1
0
2
0
0
1
1
1
0
0
1
0
1
0
1
0
0
0
2
1
0
0
2
2
0
0
2
0
1
3
1
0
1
2
1
0
1
1
0
0
0
0
2
1
1
2
0
3
1
0
0
0
0
0
0
0
2
1
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
3
2
2
0
0
0
0
1
0
0
0
2
0
0
1
2
0
2
0
0
0
0
2
2
1
0
0
0
0
0
0
0
1
0
0
1
0
3
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
3
4
1
0
0
0
0
0
0
0
0
1
1
1
2
0
2
2
0
3
1
2
1
0
0
0
0
0
2
2
0
0
0
1
2
0
1
0
0
0
0
0
0
2
1
0
0
0
1
1
0
0
0
2
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
1
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
2
0
1
0
0
0
2
0
2
1
0
1
1
0
0
0
0
0
0
0
2
0
0
0
1
0
4
1
0
1
0
0
1
2
1
2
0
1
0
2
5
0
3
0
0
0
0
0
0
0
0
1
0
2
2
2
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
3
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
1
0
0
1
0
0
1
0
1
0
1
1
0
1
2
0
0
1
0
3
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
1
0
0
2
0
2
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
4
0
0
1
0
0
1
2
1
0
0
1
0
0
0
0
0
1
0
2
0
0
1
0
2
2
2
3
0
0
1
0
2
0
0
0
1
0
0
0
2
0
6
2
1
1
0
0
2
1
0
0
0
1
0
0
2
1
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
1
0
2
0
0
1
0
0
0
0
0
1
0
2
0
0
0
4
0
2
0
0
1
1
2
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
5
0
0
0
2
1
2
0
1
1
1
2
0
0
0
0
1
0
1
0
0
2
2
0
2
1
0
0
1
0
1
0
2
0
0
2
0
0
0
2
0
2
0
0
1
2
0
1
1
0
0
0
0
0
0
0
3
1
1
1
0
0
0
1
0
1
2
1
0
0
0
1
2
0
2
1
0
0
0
4
0
0
1
1
0
1
1
0
0
2
1
0
1
0
0
0
1
0
0
1
1
0
0
0
1
1
0
0
0
0
2
1
0
3
2
0
1
0
3
0
0
0
0
0
2
0
2
0
1
0
0
2
0
1
0
3
1
0
0
0
0
0
2
1
2
0
2
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
1
2
0
0
0
0
0
1
2
1
0
0
0
0
0
0
1
0
1
2
0
2
0
1
0
0
0
0
0
1
0
1
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
1
2
0
2
1
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
2
0
0
0
2
0
0
0
0
2
3
0
0
1
1
0
1
0
0
1
3
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
2
2
0
0
3
0
0
0
0
0
1
2
1
0
1
0
0
2
2
0
0
2
0
2
0
0
1
1
3
0
2
0
0
0
1
0
2
0
0
0
1
0
0
2
0
1
0
0
0
1
0
0
0
0
0
1
0
0
2
2
2
0
2
2
0
0
0
0
1
0
4
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
4
0
2
0
0
0
2
2
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
1
0
3
0
0
1
3
0
0
0
2
1
0
1
0
1
1
0
0
1
2
0
1
0
0
0
0
2
2
0
2
0
0
1
0
1
0
0
1
2
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
2
0
3
0
0
0
2
3
0
0
0
0
0
2
2
0
0
0
0
2
2
0
0
0
0
0
0
1
2
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
2
1
2
2
0
1
2
2
1
2
0
0
0
1
2
0
0
1
1
1
0
0
1
0
0
1
0
1
0
1
2
0
1
1
0
0
3
0
0
0
1
0
2
0
1
0
1
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
2
0
1
2
2
1
0
0
1
0
0
0
0
0
0
2
2
0
0
0
1
1
2
0
1
0
0
0
5
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
1
0
5
1
2
0
1
2
0
0
0
0
0
2
2
1
0
0
0
0
2
1
0
0
0
0
0
0
1
1
0
2
0
0
3
0
0
0
0
0
0
0
1
0
0
3
4
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
2
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
2
0
0
0
0
0
2
0
2
0
0
1
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
4
0
0
2
0
0
2
4
5
0
0
0
0
0
0
0
2
2
1
0
0
0
0
1
3
0
0
0
2
1
0
0
1
0
1
0
2
1
0
1
0
0
0
1
0
2
0
0
2
0
2
0
1
0
0
0
2
0
0
2
0
2
0
1
2
0
0
0
2
1
0
0
0
2
1
0
0
1
0
0
0
3
0
2
0
0
0
0
1
4
3
0
0
0
0
0
3
0
0
0
0
2
0
1
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
3
0
0
0
0
5
1
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
6
0
0
0
0
1
1
2
0
1
1
0
1
0
1
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
1
1
0
0
0
2
4
0
2
0
0
4
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
4
0
0
1
0
2
0
0
2
1
0
0
2
2
0
0
0
1
5
2
0
1
0
2
0
0
0
0
0
1
0
0
1
1
0
0
2
0
0
0
1
2
2
1
0
0
0
0
1
0
1
0
1
0
1
0
0
0
3
0
0
0
0
0
2
0
1
0
0
0
1
1
0
0
0
2
1
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
2
2
0
2
0
0
2
1
3
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
2
0
0
0
2
0
0
0
0
0
1
0
0
2
2
1
0
0
0
1
2
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
2
0
2
0
0
0
2
1
0
0
0
0
1
0
2
0
2
1
0
0
2
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
1
4
0
2
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
1
1
2
0
2
0
2
1
0
0
0
0
0
0
1
0
2
0
1
0
2
0
0
1
0
0
1
0
0
0
2
0
2
1
0
0
2
2
0
2
2
0
2
0
0
1
0
2
0
1
2
0
2
0
0
0
0
1
2
2
0
2
0
0
0
0
3
2
0
1
0
3
0
0
0
0
0
5
0
0
1
2
2
0
2
2
2
0
2
0
0
0
1
0
0
0
0
2
0
1
2
0
2
0
2
2
0
0
0
1
0
1
0
2
2
2
0
0
1
0
0
1
2
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
2
2
0
2
1
0
0
0
0
1
0
0
1
0
0
0
0
4
0
2
2
0
0
0
0
0
1
0
0
0
3
0
20
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
4
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
2
0
0
0
0
5
0
0
3
2
0
3
1
3
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
3
0
1
1
2
0
1
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
2
0
1
0
0
0
0
2
2
0
1
0
0
1
0
0
2
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
3
2
0
0
0
2
1
0
2
0
0
1
0
1
1
0
1
0
0
0
2
1
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
1
1
0
0
2
0
0
0
1
0
2
2
2
0
0
4
0
2
0
0
3
2
0
0
0
0
0
0
0
0
2
2
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
2
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
1
2
0
0
2
0
0
2
0
0
0
2
2
1
2
2
0
1
1
1
0
0
0
1
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
1
2
0
0
0
1
0
0
0
0
2
0
0
2
0
0
1
0
0
0
2
2
0
1
1
1
0
0
0
1
0
0
2
5
0
0
0
0
0
2
2
0
0
1
0
2
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
3
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
2
0
0
0
1
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
1
2
1
1
0
0
1
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
2
1
2
2
0
1
1
0
0
0
0
0
2
0
0
0
2
0
1
0
0
2
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
1
1
0
0
0
0
0
0
1
0
1
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
1
1
0
0
2
1
0
1
0
0
0
0
1
0
0
2
2
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
7
0
0
2
0
0
1
2
1
0
1
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
1
2
0
0
0
0
2
0
0
0
1
1
0
2
1
0
0
0
2
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
11
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
2
2
0
1
0
0
0
0
0
1
0
0
2
0
1
1
0
0
0
1
0
2
0
0
0
0
2
0
1
0
0
2
1
0
0
1
0
1
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
1
0
0
1
1
2
0
0
0
0
0
0
0
2
0
2
0
1
1
1
1
0
0
4
0
2
2
0
2
0
2
1
0
0
1
0
0
3
0
1
0
1
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
1
1
1
0
0
0
2
0
0
0
0
1
1
3
0
0
0
0
0
2
2
0
2
0
0
2
0
0
2
0
0
0
0
2
0
2
2
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
2
0
0
0
1
1
2
0
2
0
0
0
0
2
1
0
0
0
2
0
2
0
0
1
2
0
3
0
0
0
1
0
2
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
2
0
1
0
0
2
0
1
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
1
1
0
0
1
0
2
1
0
2
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
1
0
3
0
0
2
0
0
1
0
1
1
1
0
0
1
0
0
1
0
1
0
2
1
0
0
2
2
2
0
0
0
0
0
1
0
1
0
0
0
2
5
0
0
0
2
1
0
0
0
0
2
0
2
0
0
1
0
2
2
0
0
0
0
3
1
1
0
0
0
2
1
1
0
0
0
0
0
0
0
2
0
0
2
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
2
0
0
1
2
0
0
2
0
2
2
1
0
2
0
1
0
0
3
0
2
0
0
0
0
0
0
2
0
2
1
0
0
1
0
0
2
1
0
1
0
2
0
0
2
0
4
0
2
2
0
0
14
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
2
2
0
0
2
0
0
0
0
2
0
1
0
0
2
0
0
0
0
1
0
2
0
0
2
1
0
0
1
0
1
0
0
0
0
1
1
0
2
0
0
0
0
1
1
1
0
1
0
0
0
1
1
0
1
0
2
2
0
0
1
0
0
0
1
1
2
0
0
0
1
1
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
1
0
1
3
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
2
0
1
0
0
0
2
0
0
2
1
0
0
2
0
0
0
3
1
0
2
0
0
0
0
1
3
2
0
1
1
0
2
1
2
0
1
0
1
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
5
0
1
0
0
1
2
2
2
0
2
0
0
0
2
0
0
0
1
0
0
3
0
1
0
0
1
2
2
0
0
0
2
0
0
2
1
0
2
0
1
0
2
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
2
1
0
3
0
1
1
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
1
0
2
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
2
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
1
2
0
2
0
1
0
0
0
2
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
1
0
0
2
0
2
0
0
1
1
2
0
6
0
0
2
2
0
0
1
1
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
1
0
2
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
1
0
0
0
0
1
0
0
1
0
2
1
0
0
1
0
0
0
0
0
0
0
2
0
0
1
3
0
0
1
2
0
0
1
0
0
1
0
0
0
0
2
1
0
0
0
1
0
2
1
0
0
0
0
2
0
0
1
0
2
0
0
1
1
0
1
1
0
0
1
1
1
0
0
0
1
2
0
2
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
3
1
1
0
2
0
2
0
2
0
0
0
2
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
2
0
2
0
1
2
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
1
0
0
0
0
0
0
0
1
1
2
0
2
1
0
0
0
3
0
0
2
0
1
0
0
1
0
0
0
0
0
0
3
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
1
0
1
1
2
2
1
0
0
1
0
1
1
1
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
4
0
1
2
0
0
2
0
0
2
0
2
0
0
0
0
1
0
0
2
1
0
0
0
0
0
2
0
0
0
0
2
0
2
2
0
2
1
0
0
0
0
0
0
2
0
1
2
1
0
0
0
3
0
0
0
0
0
1
0
0
2
1
1
1
0
0
0
0
2
0
2
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
1
2
0
1
0
2
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
1
0
1
0
1
3
1
0
0
1
2
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
2
3
0
0
0
1
0
0
0
0
2
0
0
2
1
1
2
0
0
1
0
0
3
3
0
1
0
0
0
0
0
0
5
0
0
0
0
1
0
0
2
2
0
0
2
0
0
1
1
0
2
0
0
2
0
0
0
3
0
0
0
0
0
1
0
2
2
2
0
1
0
0
0
1
0
2
1
0
0
0
1
0
3
0
0
0
0
0
1
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
2
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
2
3
0
0
0
0
1
1
1
2
0
1
1
0
0
0
0
2
0
0
0
1
2
2
0
0
0
0
3
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
6
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
2
2
1
0
0
0
0
0
0
1
0
0
1
0
2
0
2
1
0
2
0
0
2
3
0
0
0
0
0
1
0
0
0
0
0
0
3
0
1
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
2
2
0
0
0
0
1
0
0
2
2
0
0
0
0
0
1
2
0
2
0
0
1
0
1
0
0
0
0
0
1
0
2
0
3
0
1
0
3
0
0
0
0
0
0
0
2
1
1
0
0
1
1
1
2
0
0
1
0
0
2
0
1
3
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
1
0
0
2
1
0
2
0
1
2
0
0
0
2
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
2
1
0
0
2
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
2
2
1
0
0
0
0
1
0
0
0
0
2
3
1
0
0
0
0
0
1
2
0
2
0
0
0
0
1
4
0
1
1
2
0
0
1
0
0
1
0
0
0
3
0
1
1
2
0
0
0
1
3
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
1
0
0
1
0
0
2
2
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
5
0
0
2
0
2
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
1
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
2
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
1
0
1
0
0
0
0
0
0
0
2
0
0
2
1
1
0
1
2
2
0
0
0
0
2
0
0
1
0
0
0
0
2
0
1
0
0
0
2
0
0
4
0
0
1
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
1
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
1
0
0
0
4
0
0
0
0
0
0
2
1
1
0
0
0
0
0
2
0
2
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
2
1
0
0
0
3
2
1
0
0
2
2
2
0
1
0
2
1
0
0
1
0
1
0
0
0
1
0
0
0
1
2
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
2
0
2
3
0
0
0
2
0
0
0
0
2
0
0
0
1
2
1
0
3
1
1
1
1
0
0
0
0
2
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
2
1
0
0
0
0
0
2
0
1
0
2
0
2
0
0
0
0
0
0
1
0
0
0
1
0
1
1
1
1
0
1
2
1
0
0
0
1
0
1
1
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
1
2
0
0
0
1
2
0
0
2
1
0
0
0
1
4
0
0
0
0
0
1
0
1
0
1
0
3
3
0
0
2
0
0
2
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
1
0
2
1
0
0
0
0
0
0
0
1
0
2
2
1
0
4
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
2
0
0
0
2
0
0
0
0
1
1
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
1
2
0
2
5
0
0
1
2
0
1
0
2
4
0
0
0
2
3
0
0
0
3
1
0
0
0
0
1
1
0
2
3
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
5
1
2
2
1
0
1
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
2
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
3
0
0
0
0
1
3
2
1
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
3
0
0
0
0
1
0
0
0
1
1
0
2
0
2
2
0
2
0
0
0
1
0
1
0
1
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
2
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
2
1
2
0
0
0
0
2
2
1
0
1
1
3
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
1
0
2
1
0
1
0
0
0
1
0
1
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
1
2
0
1
0
0
2
0
1
0
0
0
0
0
0
6
0
1
0
0
0
0
0
0
0
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
1
2
0
0
0
0
1
1
0
0
0
0
0
2
2
0
1
0
2
0
0
9
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
2
0
0
0
1
0
0
0
0
1
1
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
3
1
2
0
0
0
1
1
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
2
2
0
1
0
2
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
3
2
1
1
3
0
1
0
0
0
0
2
2
0
0
1
1
0
0
0
2
0
0
0
0
1
2
0
1
0
1
1
0
2
0
0
0
1
0
1
0
0
0
0
0
2
0
1
0
2
0
2
2
1
0
0
0
1
1
1
0
0
2
0
1
2
0
0
0
0
2
0
1
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
2
0
2
0
0
0
0
0
0
0
2
0
2
0
2
0
1
0
0
0
0
0
0
0
1
0
0
2
1
0
0
1
1
2
0
0
1
1
1
0
3
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
3
0
2
1
0
0
0
2
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
2
1
0
0
1
2
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
2
2
0
0
0
0
0
2
0
2
1
1
0
1
1
2
0
0
4
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
2
3
0
1
2
0
1
2
0
0
1
0
1
0
1
2
1
0
0
0
0
1
2
0
1
0
0
1
0
2
0
0
1
0
0
1
0
0
1
1
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
3
1
1
0
1
2
0
0
0
0
2
0
1
0
1
0
0
2
1
0
1
1
0
1
0
0
0
0
1
0
0
0
2
0
0
2
1
0
2
0
1
0
2
0
1
2
1
0
0
1
2
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
1
0
2
0
0
2
0
0
3
0
2
1
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
2
0
0
0
1
0
0
0
0
2
1
0
0
0
1
1
0
0
0
1
2
0
2
0
1
5
0
0
1
0
1
2
2
3
0
0
4
0
1
2
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
2
0
0
2
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
3
0
1
2
0
0
1
1
0
1
0
0
0
2
0
2
0
1
0
0
0
1
0
0
0
0
0
0
1
2
1
1
1
4
0
2
1
0
0
0
0
0
1
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
2
0
0
2
0
0
2
1
0
0
0
0
5
2
0
2
0
1
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
1
0
1
2
0
0
0
0
0
2
0
0
0
1
1
0
2
0
0
0
0
2
0
1
0
0
1
2
0
0
0
1
0
2
0
0
0
2
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
3
0
0
0
0
0
2
0
0
1
0
0
0
0
1
1
0
0
2
0
0
0
0
2
0
1
1
1
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
3
1
1
2
0
0
0
0
1
0
2
0
0
2
0
0
2
0
0
0
0
0
2
0
0
1
2
0
0
0
2
1
2
0
2
0
2
1
1
0
2
1
1
2
0
2
2
0
1
0
0
0
0
2
0
0
1
1
0
1
2
0
2
0
2
0
0
0
0
1
0
0
2
1
2
0
2
0
0
0
1
1
0
0
0
0
0
2
0
2
1
2
1
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
3
0
0
2
0
0
0
3
1
0
1
2
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
4
0
0
0
2
3
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
1
1
0
0
0
0
8
0
0
0
0
2
0
0
0
0
0
3
0
0
0
1
1
0
1
1
0
0
1
0
0
1
0
0
2
0
1
2
0
0
0
2
1
0
0
2
0
0
1
2
0
2
1
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
1
1
1
0
0
2
0
2
3
1
0
1
0
0
0
0
0
1
1
0
0
0
1
0
1
0
1
0
1
0
0
0
0
2
1
1
0
0
1
0
0
0
2
1
0
0
0
0
1
1
2
1
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
2
0
1
1
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
1
2
0
1
1
0
3
1
2
0
0
0
0
0
2
0
1
1
2
0
0
0
0
1
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
2
1
2
1
0
0
1
0
0
0
0
1
0
0
0
2
1
0
1
0
1
0
0
0
2
0
0
0
2
2
0
3
0
0
0
2
1
0
0
0
0
0
0
0
2
0
1
0
2
2
1
3
0
0
0
0
0
1
0
0
2
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
2
0
2
2
1
0
0
0
1
1
1
0
0
1
0
2
2
2
0
1
0
0
0
7
0
0
0
1
0
0
4
1
2
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
2
2
1
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
2
0
0
0
2
2
0
2
2
0
1
0
0
1
1
1
1
2
0
1
1
0
2
0
0
1
1
0
0
0
2
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
4
0
2
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
2
2
1
2
0
0
0
2
0
0
0
0
2
1
0
2
0
0
0
0
0
3
0
2
0
1
0
0
0
1
0
1
0
0
0
0
0
1
2
0
1
2
0
1
0
0
0
2
0
1
1
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
1
0
2
1
0
2
1
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
3
0
1
2
0
1
0
0
0
0
2
0
1
1
1
0
0
0
0
0
1
1
0
0
2
0
0
0
1
0
0
1
0
2
1
0
0
0
0
1
0
0
0
1
0
0
0
0
2
2
1
0
1
1
0
0
2
1
3
2
0
0
2
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
2
2
0
0
2
2
0
0
1
0
0
1
0
0
2
0
1
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
2
0
0
0
1
2
0
0
0
0
1
0
0
1
1
0
0
2
1
0
0
0
0
2
0
0
0
3
2
0
1
0
2
0
0
0
0
0
1
0
0
2
0
1
0
0
1
2
0
4
0
0
0
0
1
2
0
2
0
0
2
0
0
1
1
0
1
1
0
0
2
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
2
0
0
10
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
3
0
0
2
2
0
1
0
1
0
0
0
1
0
2
0
0
0
2
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
1
3
0
2
0
0
0
0
0
0
0
2
1
1
0
2
0
0
0
1
2
2
2
0
2
0
0
0
1
0
1
0
1
2
1
1
0
0
0
0
0
0
0
0
1
0
0
1
3
0
0
1
0
0
0
1
3
0
2
2
0
0
3
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
2
6
0
0
0
2
0
2
2
1
3
0
2
0
0
0
2
2
0
0
0
0
0
0
0
2
2
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
2
2
0
1
0
0
1
0
0
0
2
0
0
1
0
2
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
2
1
0
0
2
0
0
1
0
0
1
2
0
0
0
2
1
0
1
0
1
1
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
1
2
0
2
0
0
2
0
3
0
2
0
0
1
0
0
1
0
0
0
2
1
0
0
0
4
0
0
0
0
0
0
0
0
3
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
1
1
0
0
2
0
3
1
1
2
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
1
0
2
1
0
0
0
2
0
0
2
0
0
0
1
0
0
2
0
0
0
0
2
2
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
2
0
2
0
0
2
0
0
0
2
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
1
0
2
1
2
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
2
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
1
2
0
0
2
1
1
0
0
2
0
0
0
2
2
3
0
8
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
2
4
1
2
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
2
1
1
2
0
0
2
0
1
0
1
0
0
0
2
0
1
0
2
0
0
0
0
0
0
2
2
2
0
2
1
1
2
0
1
0
0
0
0
1
1
0
0
0
1
2
0
1
2
0
0
0
2
0
0
0
0
1
2
0
0
2
0
0
2
1
1
1
2
1
0
0
0
2
0
2
0
0
2
0
2
0
0
0
0
0
0
1
0
1
0
4
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
1
0
3
0
1
1
0
0
2
0
2
0
2
2
1
2
0
0
0
0
0
0
2
0
1
0
0
2
1
1
1
2
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
3
2
2
2
1
0
2
2
1
1
1
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
1
2
0
0
2
1
1
0
0
0
0
1
0
1
0
0
2
0
0
1
4
0
0
2
0
0
0
1
0
1
0
1
0
4
0
2
0
0
1
2
0
1
0
0
0
2
1
1
2
0
0
0
1
0
0
0
0
0
2
1
0
0
1
2
0
2
0
0
1
1
1
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
2
0
1
2
1
2
1
0
0
2
0
0
0
0
0
4
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
2
1
0
0
0
0
3
0
0
0
0
3
0
2
0
0
2
2
0
0
0
0
2
2
1
0
0
2
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
2
0
1
0
0
2
0
2
0
0
1
0
1
0
0
0
0
1
0
1
0
0
2
0
1
1
0
2
0
0
0
2
0
2
0
1
0
1
0
1
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
2
0
1
1
0
3
0
1
1
1
0
0
0
1
0
0
0
1
1
0
2
2
1
0
2
0
3
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
1
2
0
0
0
1
0
3
0
0
0
3
0
0
1
2
4
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
2
1
0
0
2
0
1
0
0
0
0
0
0
0
1
3
2
0
0
0
1
0
0
0
2
0
2
0
0
0
1
0
0
1
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
2
2
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
2
1
0
0
0
0
0
2
0
2
1
1
1
2
2
0
2
1
0
0
1
1
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
1
2
0
0
0
1
0
11
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
2
0
2
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
2
0
0
2
0
0
2
1
1
0
0
0
0
0
0
0
2
0
0
3
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
2
1
0
1
0
2
1
0
0
1
0
0
0
0
1
2
7
0
0
1
0
0
2
0
0
0
5
0
0
0
2
0
0
0
0
0
0
0
0
1
2
1
0
2
0
0
2
0
2
0
0
0
0
1
1
0
0
0
0
0
1
0
2
0
3
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
7
0
0
0
0
2
0
1
0
3
0
0
0
0
0
0
0
1
0
2
0
1
2
0
2
2
0
0
0
2
2
0
0
2
0
0
1
0
0
0
1
1
0
0
2
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
2
2
0
7
0
1
0
0
0
1
0
0
2
0
0
0
0
1
0
1
0
0
2
0
1
0
0
1
0
2
1
0
0
0
2
1
2
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
2
0
0
1
0
2
0
4
0
1
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
2
0
2
0
0
0
1
1
2
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
3
1
2
0
0
2
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
1
0
0
0
0
2
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
2
1
0
1
0
2
0
0
1
0
2
0
0
1
0
0
0
1
2
0
0
1
0
1
0
0
2
0
1
0
1
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
2
1
1
0
1
2
0
2
0
1
0
0
0
0
0
0
2
0
0
2
2
1
0
0
0
1
2
0
0
1
1
1
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
2
0
1
1
0
2
0
0
1
0
0
0
0
0
2
4
0
1
0
1
0
0
2
0
0
0
2
0
0
1
0
0
1
1
3
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
2
1
0
1
0
0
0
0
3
0
0
0
0
0
1
2
0
2
0
0
0
1
1
0
0
2
0
0
0
0
2
2
1
2
0
1
0
1
0
0
0
2
1
0
0
0
1
0
0
1
0
0
0
0
0
3
1
1
2
0
0
0
0
0
0
6
0
2
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
2
1
0
0
2
0
3
1
1
0
0
0
0
2
0
0
1
2
5
1
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
4
0
0
1
1
0
2
2
1
2
0
0
0
0
2
1
0
1
0
3
0
2
0
0
0
0
0
0
0
4
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
3
0
1
1
0
1
1
0
1
1
0
0
0
0
5
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
2
0
0
1
1
1
0
1
0
1
0
0
0
0
1
0
0
0
2
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
1
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
4
7
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
2
2
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
3
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
2
0
0
0
0
1
0
2
1
1
0
0
1
0
0
0
1
0
2
0
2
0
1
2
0
0
0
0
0
2
0
2
0
1
1
0
2
3
0
0
0
0
3
0
1
0
0
0
0
0
2
0
0
1
0
0
1
2
2
0
1
0
2
0
0
0
0
0
0
0
1
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
4
0
2
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
2
0
0
1
0
0
2
0
1
0
2
1
0
0
1
2
0
0
0
0
0
0
0
2
0
1
0
0
1
0
2
0
0
1
1
0
8
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
2
0
1
0
0
1
1
0
0
1
0
0
0
0
1
2
1
1
2
0
0
0
1
0
0
0
1
0
2
0
0
2
0
1
0
1
0
0
2
0
0
0
0
2
2
0
0
0
2
1
1
0
1
0
0
0
0
1
2
1
0
1
0
1
0
0
0
0
0
0
1
1
0
2
0
0
2
2
0
1
0
0
1
2
0
2
0
0
0
0
1
0
0
3
0
2
0
0
0
2
0
0
0
3
0
0
0
0
0
2
0
0
2
0
1
0
0
2
2
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
2
1
0
1
0
0
3
2
3
0
0
0
0
0
2
0
0
3
0
2
2
1
0
0
0
1
0
0
0
0
0
1
1
0
0
1
1
0
0
1
0
2
0
0
0
0
1
0
0
1
0
0
0
0
1
0
2
0
2
0
1
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
4
0
1
0
0
1
0
0
2
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
2
0
0
0
2
0
1
2
0
2
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
2
0
0
0
2
0
2
0
2
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
1
1
0
0
1
0
0
1
0
0
1
0
2
0
1
0
0
0
0
0
2
0
0
2
1
0
0
1
0
0
2
0
0
2
1
1
5
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
1
2
0
2
0
0
0
0
2
0
2
1
0
0
0
1
0
1
0
1
0
0
0
2
2
1
0
0
2
0
3
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
3
2
0
0
0
0
0
1
0
1
0
0
1
1
0
2
1
0
1
0
2
1
0
2
0
0
0
0
0
2
0
0
0
0
2
0
2
0
2
0
0
0
1
0
2
0
1
0
0
3
0
0
0
0
0
0
1
0
0
1
2
1
0
0
2
1
1
0
0
0
0
0
0
0
1
1
1
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
2
2
2
1
0
0
2
2
0
0
0
0
0
1
0
2
2
2
0
2
0
0
0
1
1
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
2
0
0
1
0
0
3
1
1
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
3
0
1
1
0
1
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
2
1
0
0
0
2
0
2
2
0
0
1
0
1
0
0
2
2
2
0
0
1
0
0
1
1
0
2
0
0
0
0
0
0
0
0
2
0
0
2
1
1
1
0
0
0
1
0
1
1
0
0
1
0
0
0
0
2
1
2
0
1
0
0
0
2
2
0
2
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
3
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
2
1
0
0
0
0
0
0
0
0
1
1
3
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
3
2
0
0
0
1
0
2
0
0
2
2
1
2
2
3
0
0
3
1
0
2
0
4
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
2
0
0
0
0
1
0
2
0
0
2
1
1
0
2
1
2
0
0
0
2
0
1
0
2
0
0
0
2
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
2
0
0
0
0
2
0
0
2
0
0
1
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
2
1
1
2
0
0
0
0
0
0
0
0
2
0
2
1
1
1
0
0
0
0
0
0
3
1
1
0
1
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
1
3
1
4
1
0
0
0
1
2
1
2
0
0
0
0
1
3
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
2
0
1
0
1
0
0
0
1
0
0
1
0
1
2
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
2
0
0
1
0
1
2
0
1
0
0
0
0
0
0
0
0
2
1
0
0
3
2
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
1
0
2
0
0
0
2
0
1
0
1
0
2
1
0
0
0
0
0
2
0
0
0
2
2
2
0
1
1
0
2
0
1
0
0
0
0
0
0
0
1
2
1
0
0
0
1
0
0
0
1
1
0
0
0
0
2
2
0
0
2
0
0
1
2
0
0
1
2
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
4
0
2
0
0
0
0
0
0
3
1
0
1
2
0
0
0
0
0
0
1
0
1
1
2
0
1
2
0
0
2
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
2
2
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
2
2
1
2
2
0
0
1
2
0
0
2
0
0
0
0
1
2
0
0
0
2
0
1
0
0
2
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
3
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
2
2
1
0
0
0
0
0
2
0
0
1
2
1
2
0
0
0
0
1
0
2
0
2
1
1
2
0
0
0
2
0
1
5
0
0
0
2
0
0
2
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
1
2
1
0
0
0
0
1
0
0
1
0
2
1
2
0
0
0
2
0
0
0
0
0
0
0
0
3
1
1
0
0
0
0
0
1
1
0
0
0
1
0
2
2
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
4
1
0
0
1
1
2
0
0
2
2
0
0
1
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
4
0
0
0
0
0
0
1
0
0
0
0
3
2
2
0
0
3
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
1
2
0
0
1
1
1
0
2
1
1
0
0
0
0
0
0
0
0
0
1
1
0
3
2
0
0
0
2
0
0
0
0
2
2
0
3
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
2
0
2
2
0
0
2
3
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
2
0
0
2
2
2
0
1
0
0
2
2
0
0
0
2
2
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
2
1
1
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
2
0
2
2
0
0
0
0
0
2
0
0
0
1
1
1
0
4
2
0
1
0
1
3
0
2
0
8
2
0
0
2
0
0
0
1
1
0
0
2
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
1
0
1
0
0
3
0
2
0
0
0
0
0
0
1
0
2
0
0
2
0
0
2
1
0
2
2
0
0
3
0
0
0
2
0
5
0
1
0
1
0
1
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
1
1
0
1
1
1
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
2
2
0
0
2
1
2
1
2
2
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
2
1
0
0
2
0
1
0
0
0
0
2
2
1
0
1
0
0
0
0
0
0
2
0
2
2
3
0
1
0
0
1
2
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
1
1
0
1
0
0
0
6
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
1
0
2
0
0
0
0
0
1
4
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
2
0
2
0
0
1
1
0
2
0
0
0
0
0
0
2
3
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
1
0
2
1
1
2
0
3
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
2
1
0
0
0
4
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
1
2
0
0
0
1
0
0
2
0
0
0
0
4
2
0
0
0
2
2
0
1
1
0
2
1
0
0
0
0
0
0
0
0
1
0
1
2
0
0
1
0
0
0
0
1
0
0
2
0
1
2
1
0
2
0
0
0
0
1
2
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
3
0
0
0
0
0
0
2
1
0
1
0
0
2
1
0
0
1
0
0
0
1
0
0
1
3
0
0
0
2
1
0
3
1
2
0
1
0
0
0
2
0
0
0
2
0
0
4
0
1
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
2
2
0
2
0
0
0
2
1
0
0
0
0
0
0
1
2
0
0
1
0
4
0
0
0
0
1
0
1
0
2
0
2
0
0
0
0
1
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
2
2
0
2
2
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
5
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
2
2
1
3
0
0
2
1
2
0
0
1
2
1
0
2
0
2
0
0
0
1
0
0
1
0
0
0
0
2
0
0
2
1
0
0
0
0
2
2
0
0
0
1
1
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
1
2
1
0
0
1
0
3
1
0
2
0
1
0
1
0
3
0
1
0
0
1
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
4
0
0
1
0
1
1
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
6
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
1
0
2
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
3
0
0
2
1
1
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
2
2
0
1
0
0
0
1
1
0
0
0
0
2
0
0
2
0
3
0
0
1
0
0
3
0
0
2
0
2
1
1
2
0
0
0
2
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
2
1
3
0
2
2
2
0
1
0
0
1
0
2
0
1
2
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
2
0
0
1
1
2
1
0
0
4
1
1
2
2
1
0
1
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
2
1
0
0
2
0
1
0
2
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
1
0
1
0
0
0
0
1
2
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
1
0
3
1
2
2
0
0
3
0
0
0
1
1
1
0
0
0
0
2
2
0
0
0
0
0
0
1
1
0
2
1
0
1
0
1
0
0
0
0
2
2
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
3
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
1
0
0
0
1
1
0
0
2
0
2
0
2
1
0
2
0
1
2
0
0
0
2
0
0
0
2
0
2
0
0
2
1
1
0
0
1
2
0
0
0
1
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
1
0
2
2
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
2
2
0
0
2
1
0
0
2
0
1
0
2
0
3
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
2
0
2
2
1
0
2
0
0
0
0
5
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
3
0
0
9
4
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
4
0
0
1
0
0
3
0
2
0
2
1
0
0
0
0
0
1
1
0
0
0
2
0
0
0
1
0
0
0
0
0
1
1
0
1
0
2
2
0
2
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
2
6
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
1
1
1
0
0
1
2
0
2
1
2
0
0
0
0
2
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
2
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
4
2
0
2
0
1
0
0
0
2
0
0
0
0
2
0
1
0
0
2
0
3
0
0
0
0
1
0
0
0
0
0
0
1
2
0
2
0
0
0
1
0
2
1
0
0
0
0
0
2
0
1
0
0
0
2
2
0
0
1
1
2
0
0
2
1
0
2
0
2
0
0
2
1
2
0
0
0
0
0
2
0
0
1
0
3
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
1
2
2
1
1
0
1
0
2
0
2
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
1
3
0
0
0
2
0
0
1
0
0
2
2
0
0
0
1
2
1
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
3
0
0
1
0
0
0
2
0
0
2
0
0
0
2
0
0
2
0
0
1
2
0
2
0
0
0
1
1
0
0
0
0
0
0
2
2
0
2
0
1
0
0
0
2
0
0
0
2
0
0
1
2
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
3
2
0
1
2
0
1
0
0
1
0
0
0
0
0
0
2
0
0
1
0
2
1
0
0
2
0
1
1
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
1
0
0
0
3
0
1
0
2
0
0
1
1
0
2
1
2
0
0
0
1
0
0
0
0
2
2
2
0
0
0
0
0
1
2
0
1
0
1
2
2
2
0
0
0
0
2
3
2
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
1
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
7
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
2
0
5
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
1
0
0
0
2
0
0
1
2
2
0
0
0
1
2
0
0
1
1
2
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
3
0
3
2
0
0
0
0
0
0
0
0
2
1
0
0
2
2
0
0
0
0
1
0
2
2
0
0
0
0
0
1
2
2
0
0
0
1
1
0
0
0
1
0
0
0
0
0
3
0
0
2
2
0
2
0
0
0
0
0
0
0
2
0
2
0
1
0
0
3
1
1
0
0
0
0
0
0
0
4
0
0
0
0
2
2
0
0
0
0
0
1
3
0
0
0
1
2
0
0
0
2
1
2
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
1
1
0
0
1
0
2
0
2
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
2
0
0
2
3
0
0
0
0
0
1
1
2
0
0
0
0
0
2
0
1
1
0
2
0
1
0
0
0
0
1
0
1
0
2
1
0
0
0
1
1
0
0
1
2
1
1
0
0
3
0
0
0
0
1
0
2
0
1
0
1
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
2
0
0
2
1
0
0
0
0
0
0
0
2
0
0
1
2
0
0
1
0
1
2
1
0
0
0
0
0
1
1
1
3
0
0
0
2
1
2
1
1
0
0
0
0
0
2
0
2
2
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
1
2
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
2
0
2
0
0
1
2
0
0
1
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
2
1
0
0
0
0
2
2
0
0
0
0
2
0
1
0
2
0
1
0
0
2
0
1
0
0
0
2
0
0
0
2
0
2
1
1
0
0
1
0
1
0
0
0
0
0
1
0
0
1
2
1
0
1
0
0
1
0
1
0
1
0
0
0
1
0
2
1
1
0
0
0
1
1
0
2
0
0
0
0
1
2
0
2
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
3
0
2
0
0
0
2
2
0
0
0
0
2
1
0
2
0
2
0
2
2
0
2
2
0
0
0
1
0
0
0
2
0
1
0
0
0
2
0
0
2
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
1
1
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
2
0
0
0
0
0
1
0
0
0
0
1
1
0
0
2
0
0
2
0
0
2
0
1
0
1
1
0
0
2
2
0
2
0
1
0
0
0
0
0
0
0
2
2
0
2
0
0
4
0
2
2
1
0
0
2
3
2
0
1
0
2
2
0
2
0
2
1
0
0
2
0
0
3
2
2
1
0
2
0
2
0
0
1
1
0
0
0
0
0
0
1
3
0
1
2
0
1
0
2
0
0
0
0
0
1
2
1
1
1
0
0
0
0
1
3
1
0
1
2
0
0
1
0
0
0
0
0
0
2
3
0
0
0
1
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
6
0
2
0
0
0
1
2
0
0
1
0
2
2
0
1
0
2
0
1
0
0
0
2
1
2
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
4
2
0
0
0
0
0
0
0
1
0
0
1
0
3
1
0
0
1
0
0
2
0
0
1
0
2
1
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
1
0
2
0
2
2
0
1
1
0
1
0
1
2
1
2
0
0
3
1
2
0
1
0
0
2
0
0
0
1
1
0
1
0
1
0
3
0
0
1
2
2
2
0
1
0
0
0
0
0
1
1
2
0
0
0
0
1
0
1
0
0
1
0
1
2
1
2
0
0
0
0
0
0
1
1
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
2
2
2
2
0
0
0
0
1
0
0
1
0
0
0
2
1
2
4
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
1
3
0
0
2
0
2
1
2
1
1
2
2
1
0
0
1
2
0
0
2
0
0
1
0
1
0
2
0
0
2
0
1
0
0
0
1
0
0
2
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
3
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
1
2
0
1
0
2
2
0
2
0
0
0
1
2
2
0
0
0
0
2
0
1
0
0
0
0
2
0
2
1
1
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
2
0
0
2
2
0
0
2
2
2
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
1
0
2
1
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
2
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
2
0
0
0
2
2
0
1
2
0
1
0
0
1
0
0
0
0
0
1
1
0
0
2
0
0
0
1
0
2
0
0
0
0
3
0
0
1
2
0
4
2
0
1
1
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
1
2
2
0
0
2
0
0
0
1
1
2
0
0
0
2
0
2
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
2
2
1
1
2
2
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
1
2
0
0
0
0
0
2
2
0
0
2
0
0
0
2
0
0
0
0
2
0
2
1
0
0
0
0
0
0
2
1
0
0
1
1
2
1
1
3
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
3
0
0
1
0
1
0
2
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
2
0
1
0
2
2
1
0
2
1
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
1
0
1
0
0
2
1
0
0
0
0
1
1
0
0
2
0
0
2
0
0
0
0
1
0
0
0
2
2
0
0
0
3
0
0
0
0
0
0
1
0
2
0
0
1
0
3
0
0
1
2
0
1
1
0
0
0
0
0
0
0
0
0
1
2
2
2
0
0
2
0
0
0
2
0
0
2
0
1
1
5
2
0
0
0
0
2
2
2
0
2
1
1
0
0
5
2
1
0
0
1
0
1
0
3
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
7
3
0
0
0
0
1
0
0
0
2
0
1
1
0
0
0
1
0
3
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
2
0
0
2
2
0
1
3
0
0
0
0
0
0
2
0
0
2
0
2
2
1
2
0
0
0
0
0
1
0
2
1
0
0
2
0
0
0
2
0
0
0
1
0
2
0
0
2
2
2
0
1
0
1
0
2
1
0
0
0
0
2
0
2
2
0
0
0
0
0
0
1
0
0
2
2
0
0
2
0
0
2
1
0
0
0
3
0
1
1
2
2
1
0
0
2
1
0
1
2
0
2
0
0
2
0
0
2
0
0
0
1
0
2
1
1
1
0
0
1
2
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
3
0
0
0
0
0
2
0
1
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
2
0
1
0
3
0
2
0
0
0
0
1
1
1
0
2
0
0
0
1
0
0
0
0
2
0
1
0
1
0
0
0
0
0
1
0
0
0
2
2
0
0
1
0
1
0
2
0
2
4
0
2
1
3
0
0
0
0
0
3
0
1
0
2
0
0
2
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
1
0
0
1
0
5
0
2
0
0
0
1
0
0
1
0
0
1
0
0
2
1
1
1
2
0
0
3
1
0
0
3
2
0
2
0
2
1
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
2
2
2
0
0
0
2
2
0
0
0
0
1
2
2
0
0
0
0
1
0
2
0
2
0
0
0
4
0
1
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
1
0
2
1
0
0
1
0
1
0
0
1
0
1
0
1
0
0
0
0
0
2
2
0
2
2
0
0
0
1
2
1
0
0
2
2
0
0
0
1
0
1
1
1
1
0
0
2
0
0
2
0
0
0
0
2
2
0
0
1
2
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
10
1
1
0
0
0
0
0
1
2
0
1
1
0
0
2
1
0
2
2
0
3
0
2
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
2
0
2
0
0
1
0
0
2
0
1
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
2
2
0
0
0
1
2
0
0
2
0
0
0
2
0
0
1
4
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
1
0
1
2
0
3
0
0
2
1
1
0
0
0
1
7
0
0
0
0
0
0
2
1
0
0
0
0
1
3
0
1
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
1
0
1
0
2
0
1
0
1
5
0
3
0
0
0
1
0
2
1
0
0
0
0
0
1
0
2
1
2
0
0
1
2
0
1
0
0
0
0
0
0
1
0
0
0
2
0
3
1
2
2
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
4
2
0
0
0
0
0
1
0
0
2
1
1
2
2
0
0
0
0
0
0
0
2
2
0
1
0
1
0
0
1
0
0
1
0
2
0
0
2
0
1
1
0
0
2
1
0
2
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
2
2
0
0
0
2
0
0
3
0
2
0
0
6
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
1
1
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
2
0
1
1
1
0
1
1
0
2
0
0
0
2
3
0
0
0
1
2
1
0
0
0
2
0
0
1
1
0
1
1
0
3
1
2
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
2
1
0
1
0
0
1
0
0
0
3
0
2
0
0
0
0
0
0
1
4
2
0
0
2
0
0
0
0
2
2
0
1
0
0
2
2
2
0
0
0
0
0
1
0
2
0
2
0
0
1
0
1
1
0
0
2
0
0
1
1
2
0
3
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
1
1
2
2
2
2
0
0
1
1
3
0
0
1
2
1
0
1
0
2
0
0
0
1
2
0
0
0
0
2
3
2
0
2
0
0
0
1
0
0
0
1
0
2
1
0
1
3
0
0
0
2
2
0
0
2
0
1
0
1
2
0
2
0
0
2
1
0
0
1
2
2
0
0
3
0
2
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
3
1
1
0
4
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
2
0
0
0
3
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
1
0
1
0
0
1
0
2
0
0
2
0
0
0
1
1
0
0
3
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
1
0
2
0
2
0
0
2
2
0
2
0
0
0
0
2
0
0
0
0
0
4
0
0
0
0
2
0
0
1
0
0
1
3
1
2
0
0
0
2
0
7
2
4
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
2
0
1
3
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
3
0
2
2
0
0
0
0
0
0
1
0
1
0
2
0
0
5
0
0
2
1
0
2
0
0
0
0
2
0
1
1
0
1
1
1
0
0
1
2
1
1
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
1
0
0
3
0
2
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
2
0
2
0
2
0
2
2
0
0
0
0
5
0
0
0
0
2
0
2
1
1
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
2
2
2
0
0
1
1
2
0
0
0
4
0
1
0
2
0
1
1
0
1
1
1
0
0
0
2
2
1
0
0
0
1
0
0
1
0
1
2
0
0
1
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
2
2
0
1
0
2
0
2
0
0
0
0
0
2
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
2
3
0
0
0
2
1
2
0
0
0
0
2
3
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
3
0
0
1
1
0
0
0
2
0
2
2
0
0
1
2
1
0
1
1
0
0
0
0
0
0
1
1
6
0
1
0
0
0
0
0
1
0
2
0
3
2
0
2
0
0
0
2
4
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
1
2
0
1
0
0
0
1
0
0
2
0
0
0
1
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
2
0
2
0
0
2
3
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
2
1
0
2
0
1
0
0
2
0
0
0
0
1
0
1
0
1
0
4
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
2
2
0
0
6
0
0
0
0
1
0
0
0
1
0
0
1
0
2
2
0
0
0
1
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
2
2
0
1
0
1
0
0
0
0
0
1
0
1
1
0
1
2
2
1
1
0
1
0
2
0
3
0
2
0
3
0
0
1
0
0
0
0
0
0
2
1
0
0
2
0
0
2
0
1
0
0
1
0
0
0
2
1
0
0
2
1
1
1
2
0
0
2
0
1
0
0
1
0
0
2
0
0
0
0
0
0
1
0
2
0
1
0
2
0
1
0
0
0
0
2
0
2
2
0
0
0
0
2
3
0
1
0
0
0
0
2
2
0
0
0
2
0
0
0
2
0
0
0
1
0
0
1
0
0
2
0
0
2
0
2
1
0
0
2
0
0
1
2
0
0
2
0
2
0
0
1
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
2
0
0
0
1
1
2
2
0
0
0
0
2
1
0
0
0
0
0
2
1
3
1
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
2
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
2
2
2
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
2
3
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
1
2
0
1
1
0
0
0
0
0
0
2
0
2
2
0
0
0
0
2
2
0
0
1
0
2
1
0
0
0
2
2
0
1
0
0
2
0
0
0
0
0
1
0
2
2
1
0
0
2
0
0
0
0
0
1
3
0
0
2
0
0
0
0
0
1
0
1
1
1
0
0
0
2
2
0
0
1
1
1
0
0
0
2
0
1
2
0
0
0
1
1
0
0
0
1
3
2
0
0
1
1
0
0
0
2
1
1
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
1
2
1
0
0
0
0
3
1
2
0
1
0
2
0
1
0
0
0
0
1
0
0
0
0
1
0
1
2
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
2
0
1
0
1
0
0
0
0
1
0
1
1
0
0
2
2
0
2
0
0
1
3
0
2
0
2
2
0
0
0
0
0
0
1
0
0
2
0
1
1
0
1
0
0
1
0
1
2
1
0
0
2
2
0
0
0
0
1
0
0
0
0
2
1
0
0
2
2
2
0
0
0
0
0
1
0
0
2
1
2
2
0
0
1
0
0
0
2
0
0
1
0
2
2
1
0
0
0
1
0
0
0
0
0
0
5
0
1
0
0
0
0
0
0
0
0
1
0
1
2
0
2
0
0
0
1
1
0
1
2
2
0
0
0
0
0
2
1
0
1
2
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
8
0
1
2
2
2
0
0
1
0
1
0
0
0
0
1
1
2
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
4
0
2
2
2
0
0
3
0
0
1
0
0
0
0
0
1
0
0
1
0
0
4
0
0
1
2
0
0
3
0
0
0
0
0
0
0
0
0
1
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
2
0
2
0
0
3
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
1
0
3
1
0
0
0
0
0
2
1
0
1
0
0
0
1
0
0
0
2
2
0
2
1
1
0
0
2
1
2
0
2
0
0
0
0
2
1
1
0
0
0
2
2
0
0
0
0
0
0
0
0
1
2
1
3
0
0
1
0
2
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
1
0
0
1
0
0
2
0
2
0
1
0
0
1
2
0
1
1
0
0
0
2
0
2
2
0
0
2
0
2
1
1
0
2
1
2
0
1
0
0
0
0
1
0
0
3
0
0
0
0
1
0
0
0
0
2
2
0
0
1
0
0
2
0
0
0
0
0
2
0
2
0
0
2
2
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
4
0
0
1
0
1
1
0
3
0
0
0
0
1
2
0
0
2
0
0
1
0
0
1
0
2
0
0
0
2
2
2
0
1
0
0
0
0
0
2
2
0
0
0
0
2
0
2
2
5
2
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
2
0
1
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
2
1
0
0
0
0
1
0
0
1
2
1
0
2
2
2
1
0
0
3
1
0
1
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
2
0
2
0
0
1
0
0
2
0
2
1
0
2
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
2
3
0
2
1
1
1
0
0
0
0
2
1
2
2
1
2
0
0
0
2
0
0
0
2
2
1
1
0
0
1
0
0
2
0
0
0
0
0
1
0
4
0
0
0
0
0
0
2
0
1
0
0
2
0
0
2
0
0
1
2
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
2
0
0
2
1
0
3
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
1
1
0
0
0
0
0
1
0
1
0
0
2
0
1
0
1
1
1
2
0
2
1
0
1
4
0
0
0
0
0
0
2
0
1
2
0
1
0
2
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
2
0
0
0
2
0
0
1
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
3
0
2
0
0
1
0
0
0
0
2
0
1
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
2
1
1
0
0
0
0
0
2
0
2
1
3
1
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
1
0
0
0
2
0
2
0
0
2
0
1
2
0
3
1
0
2
0
2
0
2
0
0
0
2
0
0
2
2
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
1
0
3
1
0
0
0
2
1
0
0
1
0
0
0
3
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
4
0
0
1
0
0
0
0
1
1
0
0
0
0
6
1
0
0
1
0
0
0
2
3
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
7
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
2
2
0
0
0
0
0
2
0
2
2
0
1
2
2
4
0
0
3
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
2
0
1
2
0
0
0
1
0
0
0
0
2
0
3
1
1
0
0
0
0
2
1
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
7
0
0
0
2
0
0
2
0
2
0
0
0
0
1
0
0
0
2
2
0
2
0
0
0
0
0
2
0
0
2
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
2
2
2
0
0
1
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
1
0
0
2
1
2
0
3
0
0
0
0
0
1
0
0
2
0
3
0
0
1
0
0
3
0
0
0
0
0
3
0
0
0
0
3
0
0
0
2
2
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
1
2
0
2
2
0
0
0
2
0
0
1
0
0
2
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
5
2
0
0
0
0
0
3
0
2
2
0
2
0
0
0
0
0
0
0
1
3
1
0
0
0
0
0
2
0
0
2
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
3
0
1
0
0
0
0
2
0
0
0
1
0
2
0
0
1
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
2
0
0
0
1
0
0
0
2
0
0
1
3
0
1
0
0
0
3
0
2
0
0
2
0
0
0
1
0
0
2
2
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
2
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
2
0
0
1
1
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
4
0
0
0
0
1
0
0
2
0
0
2
2
0
1
0
1
0
1
1
0
0
0
0
2
0
0
0
0
0
1
3
1
0
0
0
0
0
1
0
0
0
1
0
1
0
1
2
0
0
0
0
2
0
2
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
1
0
1
0
1
0
0
2
1
1
0
0
0
0
1
0
0
0
0
0
1
0
1
2
0
1
0
0
0
2
1
0
0
2
0
1
0
0
2
2
1
0
0
0
0
0
0
1
1
1
0
3
0
2
0
1
2
2
0
0
0
0
0
0
0
2
1
0
0
0
2
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
2
2
0
2
1
0
0
0
0
0
0
0
2
0
0
2
2
0
3
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
2
0
0
2
0
0
1
0
2
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
1
2
1
1
0
0
0
2
0
1
1
0
0
0
1
2
0
0
2
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
2
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
1
0
1
0
0
1
2
0
0
0
0
1
0
0
1
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
2
0
1
0
2
0
0
0
0
3
0
0
1
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
1
0
0
1
0
0
2
1
0
1
0
0
0
1
2
0
0
2
2
2
0
0
0
0
0
0
3
3
0
2
0
1
0
0
3
0
2
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
2
0
0
2
0
0
1
0
2
0
0
0
0
0
2
1
1
0
0
0
2
0
1
1
0
0
2
0
1
1
0
0
0
1
0
0
2
0
0
4
0
0
1
0
0
1
1
0
3
0
0
0
0
1
0
1
0
0
0
2
0
2
4
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
1
0
1
0
1
1
2
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
2
2
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
2
1
0
1
2
0
0
0
0
1
0
0
0
0
0
0
1
2
2
2
0
0
0
0
0
0
0
1
2
1
0
0
0
0
2
0
2
0
1
2
1
1
2
0
0
2
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
1
0
1
1
0
1
0
1
0
0
1
0
0
2
2
0
0
0
0
0
0
3
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
1
0
0
1
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
1
2
0
1
0
0
3
0
2
0
0
0
0
1
1
0
0
1
0
0
1
1
1
0
1
0
0
1
0
1
0
0
2
2
0
0
0
0
0
0
1
2
0
4
0
0
0
0
0
0
3
0
0
0
2
0
1
2
1
0
0
0
2
2
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
2
0
3
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
3
1
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
1
0
1
0
0
2
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
1
1
0
0
0
2
1
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
2
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
1
0
1
0
2
0
1
0
0
0
1
0
0
0
0
0
2
0
0
2
1
1
1
1
1
0
0
1
0
0
0
0
0
3
0
0
2
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
1
1
0
1
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
2
0
1
0
2
0
0
0
1
2
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
2
0
0
1
0
0
1
1
0
0
2
2
2
2
0
0
2
0
0
2
1
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
1
0
0
0
2
1
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
6
1
3
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
1
2
0
2
0
0
2
2
0
0
1
0
0
1
0
2
0
1
0
2
0
0
1
0
0
0
0
0
2
1
1
0
2
1
0
0
0
0
0
1
0
0
2
0
2
0
2
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
1
0
0
1
0
0
0
2
0
2
0
2
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
1
0
2
2
1
1
1
2
0
0
0
0
1
0
0
0
2
0
2
0
1
2
2
2
0
1
0
0
0
4
2
0
1
0
1
0
2
2
0
0
1
2
1
1
0
0
1
0
0
1
0
0
0
0
2
1
2
4
2
0
0
0
0
2
0
0
2
0
1
0
3
0
0
0
1
0
2
2
0
0
0
1
0
5
2
0
0
0
1
0
0
0
1
2
0
0
0
0
0
2
0
2
0
1
0
1
0
0
0
0
1
0
0
1
0
1
3
0
0
2
0
2
0
0
0
1
0
0
1
0
0
1
0
0
0
1
2
3
0
0
0
1
0
0
1
0
0
1
0
1
2
0
1
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
3
0
0
2
1
0
2
1
0
2
0
0
2
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
1
0
0
1
0
1
0
0
1
0
0
2
1
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
1
0
0
0
2
1
0
0
2
0
3
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
15
0
5
1
0
0
1
0
0
0
0
0
3
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
5
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
2
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
2
0
2
2
2
2
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
1
0
2
0
0
2
0
0
0
2
1
0
2
0
0
2
0
2
0
1
0
0
0
0
2
0
1
2
0
2
0
0
2
0
0
1
1
1
1
0
2
0
0
0
0
0
2
1
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
1
1
0
0
1
2
2
1
0
0
0
2
2
0
0
0
0
0
2
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
3
1
0
0
0
0
2
1
0
3
0
1
1
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
1
1
0
2
1
2
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
3
0
2
1
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
1
1
0
1
1
0
0
0
0
4
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
1
0
0
0
1
1
0
0
0
0
0
3
1
0
0
1
0
0
0
2
0
2
2
3
0
1
0
0
0
2
0
2
1
2
3
0
0
2
0
2
0
0
0
2
0
2
2
2
0
0
2
2
0
0
0
0
0
1
0
2
0
1
0
1
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
2
0
2
0
1
3
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
3
2
0
2
0
0
2
0
0
0
2
0
2
0
1
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
2
0
0
0
0
0
0
3
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
2
0
1
0
0
0
0
0
2
1
0
0
0
0
0
2
0
2
0
0
0
0
2
0
1
0
2
0
2
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
2
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
1
0
2
1
1
0
0
1
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
1
0
0
1
1
0
0
1
0
0
2
0
1
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
5
0
3
0
2
2
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
1
2
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
1
0
1
2
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
2
0
0
1
0
1
1
0
0
1
0
2
0
2
0
0
1
0
2
0
1
0
1
0
0
0
0
0
1
1
0
0
2
0
0
1
1
3
1
2
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
6
0
0
2
2
0
0
0
0
1
0
2
2
0
4
0
2
0
0
0
0
0
1
0
1
0
0
0
0
1
1
2
0
0
2
1
0
0
0
2
1
1
0
0
2
2
0
0
2
1
2
0
1
0
0
0
2
0
1
0
0
0
2
0
0
0
2
0
2
0
0
1
0
1
0
0
1
0
0
0
1
0
2
1
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
1
2
0
0
0
2
0
0
0
2
0
0
1
0
0
2
0
0
0
1
0
0
4
0
0
1
0
1
0
0
0
0
2
1
4
0
0
2
0
0
0
1
2
1
2
2
0
0
0
0
1
2
1
0
1
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
2
1
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
4
0
2
0
0
2
1
0
0
0
0
0
1
0
2
0
1
0
2
0
1
0
2
2
1
0
1
0
0
0
0
0
2
0
0
2
2
0
0
0
2
0
0
2
0
0
2
0
0
1
0
0
0
0
1
0
0
0
2
1
0
0
2
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
2
0
0
0
0
0
1
0
1
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
2
2
0
0
0
0
0
0
2
0
0
0
2
3
0
0
1
0
2
0
0
3
2
3
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
1
2
0
0
0
0
2
1
0
0
1
0
2
0
0
0
2
1
2
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
2
0
0
0
0
2
0
0
1
0
0
1
0
1
1
2
0
2
2
0
1
2
0
0
0
0
1
1
1
0
1
1
2
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
3
0
0
2
0
0
0
1
1
2
0
0
0
0
0
0
0
1
0
0
0
1
2
2
0
1
0
2
0
2
0
0
4
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
2
2
0
0
0
1
1
0
0
0
0
2
1
0
0
0
0
2
1
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
3
0
1
2
0
1
0
0
0
0
0
1
0
2
0
2
0
0
1
0
0
1
1
0
0
0
1
0
1
2
0
2
0
1
0
0
0
0
0
0
0
2
0
1
1
0
2
0
2
0
3
0
1
0
0
1
0
2
2
0
2
2
3
3
0
1
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
1
0
0
0
0
0
2
1
0
0
0
0
0
1
1
0
1
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
1
0
0
3
0
0
1
0
0
0
0
0
1
2
0
0
2
2
0
1
0
0
0
0
0
0
0
1
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
2
1
2
0
0
1
1
0
0
0
0
2
1
0
0
3
1
3
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
9
2
0
0
0
0
2
1
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
3
1
0
2
2
0
2
2
0
0
0
0
0
1
0
0
2
2
0
2
2
0
2
0
0
0
0
0
0
1
0
0
1
2
0
0
1
0
2
2
0
0
0
1
0
0
0
1
2
0
0
0
0
1
0
0
0
3
0
1
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
7
2
0
0
0
0
2
0
0
0
1
1
0
2
0
0
2
2
1
0
0
0
0
2
2
2
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
3
0
0
1
1
0
2
0
1
2
0
0
0
2
0
0
3
0
0
1
2
2
1
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
3
0
0
1
3
0
0
0
2
4
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
2
1
2
1
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
2
1
2
1
0
2
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
2
5
1
0
1
1
1
0
0
0
0
1
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
2
2
0
0
2
1
0
0
0
0
1
0
0
1
0
0
1
0
0
2
0
1
1
2
2
0
1
0
2
0
2
2
0
0
0
0
1
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
1
1
0
0
0
3
1
0
2
0
1
1
1
0
0
0
0
0
2
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
2
0
2
1
0
0
0
0
0
0
0
2
0
0
2
0
0
10
0
0
0
0
0
0
0
1
0
0
0
2
2
0
2
0
0
0
2
0
2
0
0
2
1
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
2
0
1
0
0
1
0
0
3
0
2
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
1
0
2
0
0
0
2
1
0
1
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
1
0
1
1
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
1
0
2
0
0
2
0
0
2
2
0
0
7
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
2
1
0
2
1
0
0
0
0
0
0
0
0
0
4
0
1
0
1
0
2
0
0
1
1
0
0
0
2
1
0
1
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
1
0
0
0
2
2
0
2
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
2
1
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
2
0
1
2
0
0
0
0
2
0
0
1
1
1
0
0
0
2
0
3
1
0
2
0
0
0
2
0
0
0
1
3
2
0
1
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
1
0
2
2
0
0
2
0
1
0
0
0
0
2
0
0
0
2
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
1
0
0
1
2
0
0
2
0
0
1
2
0
0
0
1
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
1
2
1
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
2
1
0
2
1
0
0
3
0
1
0
0
0
1
1
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
2
0
0
0
0
0
0
2
0
2
2
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
1
2
0
1
0
0
2
0
0
2
0
1
1
0
1
1
0
1
2
2
0
0
2
0
2
1
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
2
0
0
2
1
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
2
0
2
0
2
0
1
0
0
0
0
0
2
0
0
0
0
5
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
2
0
1
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
1
0
0
3
0
0
0
0
2
0
0
1
0
0
0
0
2
0
2
0
2
0
1
1
0
1
0
0
0
2
0
0
0
0
1
2
2
0
3
0
1
0
0
0
0
0
2
0
1
2
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
1
0
0
1
0
0
1
1
0
8
1
2
0
1
0
2
0
4
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
1
0
0
1
0
0
0
0
0
0
2
0
0
0
3
2
0
0
2
0
0
1
0
2
0
2
1
1
0
2
1
0
5
0
0
0
1
0
2
0
0
0
1
2
1
0
0
2
2
1
0
0
0
1
0
0
2
0
0
0
1
1
2
0
1
2
1
2
2
0
0
0
1
0
3
0
0
0
0
2
0
0
0
1
2
0
0
2
0
2
0
0
3
0
0
0
0
0
0
2
0
1
2
0
1
0
0
1
4
0
0
0
0
1
0
2
0
0
0
1
3
2
0
2
2
2
2
0
4
0
0
0
0
1
2
3
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
1
1
0
0
2
2
0
1
2
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
5
0
0
0
0
0
1
0
0
0
0
0
0
3
0
2
1
2
0
0
2
0
0
0
0
0
4
0
0
1
0
0
2
2
0
0
1
0
0
1
0
0
0
1
0
2
0
0
3
1
2
1
0
0
0
1
0
0
1
2
0
0
0
2
2
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
3
0
0
0
1
0
0
1
0
2
1
0
0
0
1
2
0
0
0
0
0
3
1
0
0
0
1
0
0
0
1
2
3
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
1
3
0
4
2
0
1
0
2
0
0
1
2
2
0
0
0
0
0
0
0
1
2
0
2
0
1
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
1
0
0
3
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
1
3
0
0
2
0
0
0
1
2
1
0
0
0
0
0
2
1
0
2
1
2
0
0
2
0
0
3
0
1
0
2
0
0
2
0
2
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
6
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
1
1
2
0
1
1
2
2
0
0
0
0
1
0
2
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
2
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
3
1
0
2
0
0
1
0
0
0
0
0
2
0
2
1
0
0
2
0
0
0
0
2
0
2
2
0
6
0
0
0
0
0
1
0
2
0
0
0
2
0
2
2
0
1
0
0
1
2
1
0
0
1
0
1
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
1
1
1
2
5
0
1
2
0
2
0
1
0
0
0
0
1
1
0
0
0
2
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
2
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
2
3
0
0
0
0
0
3
0
0
0
0
0
2
1
0
3
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
3
0
0
1
2
0
2
0
0
0
2
0
1
0
2
2
0
1
0
0
2
0
0
1
2
0
0
1
2
0
1
0
0
1
0
0
2
0
0
0
0
1
0
0
2
1
2
0
0
0
0
1
0
0
1
0
0
1
0
2
3
1
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
1
2
0
0
0
1
0
1
0
0
1
0
2
1
0
0
0
2
2
1
0
0
2
1
2
1
0
2
0
0
3
0
2
1
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
2
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
2
1
2
0
0
0
1
0
0
1
0
1
2
0
0
0
1
0
0
0
0
0
0
3
0
2
3
0
0
0
0
0
0
3
2
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
1
0
1
0
0
1
1
2
0
0
2
2
0
1
0
0
2
0
0
1
0
0
1
1
1
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
2
2
1
2
0
0
2
0
1
0
0
0
0
0
0
0
2
2
3
0
0
2
0
0
1
1
2
0
0
2
2
0
3
0
2
2
2
2
1
0
0
0
0
1
0
0
0
1
0
0
2
0
2
0
1
0
0
3
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
3
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
1
0
0
0
0
2
1
0
2
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
2
0
1
0
3
0
1
0
0
0
0
4
0
2
0
0
0
0
2
0
0
1
1
0
2
0
1
1
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
1
0
2
0
1
3
0
0
1
1
1
0
0
0
2
0
2
0
2
0
0
0
0
0
2
2
2
0
1
0
0
0
0
2
0
0
2
1
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
2
2
2
2
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
1
5
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
2
1
0
0
0
0
0
0
0
0
1
1
0
0
2
0
2
3
1
0
0
2
0
2
0
0
0
0
0
0
2
0
0
1
0
2
0
2
1
0
2
1
1
0
2
0
0
0
0
0
0
1
0
1
2
0
0
1
0
0
0
2
1
0
0
1
2
0
1
3
1
1
1
0
2
0
0
1
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
2
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
3
0
0
1
0
1
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
2
0
2
0
0
2
0
0
0
1
0
1
0
0
2
0
0
1
0
0
0
0
0
1
0
1
2
1
1
0
0
0
0
0
1
0
0
0
0
0
2
0
1
2
0
5
2
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
2
2
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
5
0
2
2
1
4
0
2
2
0
0
0
0
0
0
1
2
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
2
0
1
0
0
1
0
0
1
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
2
2
1
0
0
1
6
0
3
1
2
0
0
0
0
0
0
0
0
2
1
0
0
1
1
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
10
0
0
3
0
0
0
0
0
0
3
3
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
2
2
0
0
1
3
0
2
5
2
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
2
2
1
0
0
5
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
3
0
0
1
2
0
0
0
0
0
1
0
1
0
0
0
0
0
2
1
0
1
0
0
0
1
2
2
1
0
0
0
0
1
2
1
4
0
0
2
1
0
0
2
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
1
0
0
0
1
0
0
2
2
1
0
3
2
0
0
0
0
0
2
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
1
0
0
1
2
0
0
0
2
0
0
1
0
0
0
1
1
0
0
0
1
0
3
2
0
0
0
2
0
4
2
1
1
0
0
2
0
2
0
1
0
0
1
2
0
1
0
2
0
3
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
3
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
2
0
0
0
0
2
0
1
1
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
2
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
2
0
2
0
3
1
2
0
0
2
0
1
2
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
2
1
0
0
0
1
1
0
2
1
0
0
0
0
0
2
1
0
0
1
0
2
0
1
0
0
0
0
2
1
0
3
0
1
2
0
0
2
0
0
0
0
2
0
2
0
0
0
0
2
3
2
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
2
0
0
2
2
1
3
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
2
2
1
0
2
0
0
0
1
0
1
0
0
0
0
1
2
0
3
0
4
0
2
0
0
0
0
1
0
2
0
1
0
1
0
0
0
2
0
2
0
1
0
0
0
0
2
1
2
2
1
0
2
2
2
1
0
0
3
0
1
0
0
2
0
0
2
0
0
0
1
0
2
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
2
2
0
1
0
1
0
1
0
0
0
0
2
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
3
0
0
0
0
1
0
1
2
1
2
0
1
1
0
2
0
0
0
0
0
1
0
7
0
0
2
0
0
0
0
0
0
0
2
0
0
1
4
0
0
2
2
0
0
0
0
0
2
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
2
0
0
0
0
0
2
0
0
0
1
1
0
4
1
1
1
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
1
0
2
0
0
2
0
2
0
0
0
0
1
0
2
2
0
0
1
1
0
0
1
4
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
2
0
1
0
0
1
0
1
0
0
0
0
2
0
2
0
0
4
0
0
1
1
0
0
0
0
2
0
0
3
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
3
1
0
0
0
0
0
1
0
1
0
2
0
0
1
1
0
0
0
0
2
1
0
3
0
2
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
2
3
0
0
0
0
0
0
1
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
2
0
1
0
2
0
0
0
2
0
0
0
1
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
1
1
0
0
0
0
2
0
0
7
0
1
1
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
2
0
2
0
1
1
2
0
2
2
0
1
2
0
0
0
1
0
1
2
3
0
0
1
0
0
0
2
0
2
0
0
0
2
2
0
0
0
0
0
0
2
0
2
0
1
0
2
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
3
0
0
2
2
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
5
0
0
0
3
0
0
0
0
0
0
2
2
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
2
0
1
2
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
2
2
0
0
1
0
2
0
1
0
0
1
0
0
0
0
1
0
2
1
3
0
0
0
0
0
2
0
1
0
0
3
1
0
1
6
2
0
0
2
0
0
2
0
0
1
2
0
2
0
2
0
0
0
1
0
2
0
0
0
0
0
2
2
0
0
0
0
1
1
0
0
2
2
0
0
0
0
1
0
0
0
1
0
2
0
2
0
0
2
2
0
2
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
3
2
1
2
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
1
4
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
4
0
0
2
0
1
2
2
0
0
0
0
0
2
0
0
0
0
2
2
0
0
2
2
0
1
0
0
0
2
0
2
0
2
1
0
1
1
0
0
0
2
0
0
1
0
0
2
1
1
0
1
0
0
1
0
3
0
1
1
0
0
0
1
0
2
0
1
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
3
2
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
1
0
2
2
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
12
2
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
2
2
1
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
2
1
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
5
0
1
0
0
2
2
1
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
1
1
0
1
0
0
0
1
0
5
1
0
3
0
0
0
1
0
2
1
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
5
0
0
0
1
1
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
1
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
2
0
0
0
2
0
2
0
0
5
2
0
1
0
0
0
0
0
1
0
0
1
0
0
2
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
3
0
2
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
2
2
0
0
0
0
1
0
2
0
1
0
0
0
1
1
0
0
1
1
1
0
0
1
1
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
3
1
0
0
0
1
0
1
1
1
0
0
2
0
2
0
1
2
0
0
2
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
3
0
0
0
1
1
0
0
0
1
0
2
0
0
0
4
1
0
0
1
1
1
0
0
0
0
0
1
0
3
0
2
0
2
0
1
0
1
2
2
0
0
2
0
2
0
0
0
1
0
0
2
2
0
0
0
2
0
0
0
2
1
1
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
1
1
0
0
0
2
1
1
0
0
2
0
1
0
2
2
1
0
0
0
0
1
2
1
0
0
1
0
1
2
0
2
1
0
2
0
0
1
2
2
1
0
1
0
0
2
0
0
0
2
1
0
1
1
0
2
1
1
3
1
0
0
0
0
0
2
0
2
0
0
2
2
0
0
0
0
1
2
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
2
0
1
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
2
1
0
3
0
0
0
2
1
0
2
0
6
0
0
0
0
2
0
0
2
1
0
1
0
0
0
1
2
1
0
0
0
1
0
0
3
0
0
0
0
2
1
2
0
0
2
0
0
1
0
0
0
0
1
0
1
0
0
0
0
2
2
0
1
0
0
0
0
1
0
0
0
2
0
2
0
0
0
3
0
2
0
1
0
0
0
2
3
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
3
1
0
0
2
0
0
2
0
0
0
1
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
1
0
0
0
0
1
0
0
0
0
1
0
1
4
0
1
0
2
1
0
3
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
3
2
0
0
2
0
1
0
0
2
0
1
2
0
2
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
2
0
0
1
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
1
0
2
0
0
0
0
2
0
0
0
2
2
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
1
0
1
1
1
1
0
0
1
0
0
0
3
0
1
1
1
0
0
1
0
0
1
1
1
0
0
0
1
2
0
0
0
2
0
0
2
0
0
2
0
2
0
0
1
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
2
0
0
3
2
0
1
2
0
2
0
2
2
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
2
0
0
1
1
0
0
2
1
0
1
2
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
2
2
2
1
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
1
0
2
1
0
0
1
0
0
2
2
1
0
1
1
0
0
2
0
0
3
0
1
1
1
2
0
0
1
0
2
0
0
4
1
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
2
1
0
1
0
1
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
4
0
0
1
0
1
0
0
1
0
2
0
2
2
0
2
0
2
0
0
1
1
0
0
2
2
1
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
1
2
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
1
2
0
1
3
0
2
1
0
0
0
0
0
0
1
0
0
2
0
0
2
0
2
2
0
2
0
0
0
2
0
2
0
0
2
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
2
2
1
0
0
0
0
2
0
0
2
1
0
2
0
0
0
2
0
0
0
0
1
2
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
1
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
3
1
0
0
0
2
2
2
1
1
0
0
0
0
2
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
2
1
0
2
0
0
3
1
0
0
2
1
0
2
1
0
0
0
2
1
2
0
0
1
0
2
0
1
2
1
0
2
0
0
0
2
0
0
0
0
0
0
2
2
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
2
1
0
2
0
0
0
0
2
1
0
0
0
2
0
2
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
2
0
1
1
0
0
2
1
2
2
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
2
2
1
1
2
0
2
1
0
0
0
0
1
0
1
1
0
0
2
0
0
0
1
3
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
1
1
3
0
1
0
0
0
0
0
0
2
1
0
0
0
0
2
5
0
0
0
0
0
0
0
0
5
0
0
2
0
0
0
0
1
0
0
0
0
0
1
2
0
1
0
0
1
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
3
1
0
0
0
2
0
0
1
3
0
0
2
0
0
0
0
0
1
2
0
0
2
1
0
3
1
0
1
0
0
0
0
0
2
0
0
3
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
3
2
0
0
0
0
2
0
0
0
3
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
4
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
1
2
0
1
0
0
2
2
0
2
2
0
0
1
0
2
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
5
0
1
3
0
0
1
0
0
0
0
1
0
0
0
0
2
1
0
1
0
0
0
0
0
0
2
0
1
1
1
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
4
1
0
2
0
2
0
0
0
0
2
0
2
0
0
1
0
2
0
0
0
2
0
0
1
0
0
2
0
3
3
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
1
2
0
1
0
0
0
2
0
1
1
0
1
0
2
0
0
0
1
4
0
0
0
0
3
0
2
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
1
0
0
0
0
0
1
1
0
2
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
2
0
0
0
2
0
1
0
0
2
0
1
1
0
3
0
0
2
0
0
3
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
2
0
1
0
0
0
1
0
0
0
1
2
0
0
0
2
0
0
0
1
2
0
0
2
0
0
0
2
3
0
1
0
0
1
0
0
0
0
0
2
0
0
1
0
2
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
2
0
0
2
0
2
0
0
0
1
2
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
2
0
1
2
1
0
0
0
1
0
2
0
0
0
2
1
0
2
0
1
0
0
1
0
1
0
0
2
1
0
0
0
2
0
2
0
2
0
0
0
3
1
0
1
0
0
0
0
0
2
1
2
0
0
2
0
0
0
2
1
0
0
1
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
1
2
2
2
0
2
2
0
0
2
2
0
0
0
2
0
0
0
0
1
0
0
0
1
0
1
2
1
0
0
3
0
0
1
0
2
0
2
2
3
0
0
0
1
0
0
0
2
2
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
2
1
2
1
0
0
2
0
0
2
0
0
0
1
0
2
0
0
3
0
2
0
0
1
0
0
0
1
0
0
1
0
0
1
1
1
0
2
2
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
2
0
0
1
1
0
3
0
0
0
1
0
0
2
0
2
0
2
2
0
0
0
2
0
0
0
0
3
0
2
2
1
0
0
0
0
0
7
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
2
1
2
0
1
1
0
0
0
0
9
0
0
1
0
0
0
0
0
1
1
2
0
1
0
0
0
0
2
0
2
0
0
1
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
2
0
3
3
1
0
1
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
1
1
0
0
2
2
1
0
2
0
2
0
0
0
2
0
0
3
2
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
1
0
1
1
1
0
0
2
4
0
0
0
0
2
1
0
1
0
0
1
1
1
0
0
0
0
0
0
0
2
1
0
1
1
0
2
0
1
1
1
1
1
0
1
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
1
0
1
2
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
2
2
0
0
0
2
0
2
1
1
0
0
2
1
1
0
0
1
0
0
3
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
1
2
0
2
0
2
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
2
0
0
2
0
0
1
0
2
2
0
2
4
2
0
0
0
0
1
0
3
0
2
2
0
0
0
0
0
0
2
0
1
0
0
1
0
0
1
0
1
0
2
0
0
0
1
0
1
3
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
2
0
0
2
0
2
2
1
1
1
2
0
1
1
0
1
0
0
1
1
0
2
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
1
0
1
2
1
0
0
2
1
1
2
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
1
0
2
0
1
2
1
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
1
0
2
0
4
0
0
0
0
0
0
0
3
0
1
1
0
0
0
0
0
0
2
0
0
0
0
2
2
0
1
2
0
0
0
0
2
0
0
0
1
1
0
0
0
0
2
0
0
3
0
0
0
0
2
0
3
0
0
2
0
0
0
0
0
1
0
0
1
2
2
0
2
1
0
0
0
0
2
0
1
2
2
0
2
1
0
0
0
0
0
2
0
1
0
1
0
2
0
0
0
0
0
0
2
0
1
1
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
1
0
2
1
0
0
0
0
0
1
2
1
0
0
0
0
2
2
0
0
1
0
3
1
1
0
1
0
0
0
1
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
3
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
2
1
1
0
0
0
0
0
1
2
1
0
2
3
0
3
2
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
2
0
0
0
3
0
3
0
1
0
2
1
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
2
0
1
0
0
0
2
0
1
0
0
2
0
0
0
2
0
0
2
0
0
2
1
0
0
0
2
2
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
1
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
1
0
0
2
0
0
1
0
0
0
0
0
0
0
2
2
0
0
2
1
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
3
1
2
0
0
0
0
2
1
2
2
0
0
2
0
2
0
2
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
2
0
1
1
1
1
2
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
1
0
1
0
0
0
0
2
2
0
0
2
2
1
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
7
0
2
2
2
0
1
1
1
2
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
2
0
1
2
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
1
1
2
1
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
2
0
1
4
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
1
1
0
1
1
0
2
2
3
2
1
2
2
2
1
1
1
2
0
0
0
0
0
0
0
0
0
3
2
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
2
0
0
2
0
0
0
0
0
1
0
0
2
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
2
1
0
0
3
0
0
2
1
0
1
0
1
8
0
0
0
3
0
0
2
0
1
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
1
2
0
1
2
0
0
0
1
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
2
0
2
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
1
0
2
0
1
1
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
2
1
2
0
2
1
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
1
1
0
3
0
0
0
1
0
0
1
0
0
0
1
0
0
2
1
2
0
2
0
0
2
0
0
0
0
1
0
2
0
1
0
0
1
0
0
0
2
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
2
0
2
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
2
2
0
1
0
0
0
2
0
2
0
0
0
1
0
2
0
0
0
2
0
0
0
0
2
1
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
2
2
0
1
1
0
0
1
3
1
0
1
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
2
1
0
2
1
0
3
0
0
3
0
0
0
0
0
0
0
4
2
2
2
1
0
0
1
2
0
0
0
0
1
0
2
0
0
0
2
0
2
2
1
0
2
1
0
0
1
0
2
0
0
1
0
0
2
0
1
0
1
0
2
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
4
0
0
2
0
1
1
0
0
0
0
2
0
2
0
0
0
0
0
2
1
0
1
0
0
1
0
1
0
0
0
0
0
1
4
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
5
1
1
0
0
2
0
5
0
1
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
1
0
0
0
0
0
0
2
1
0
0
3
0
1
0
0
1
0
2
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
2
0
0
0
0
2
0
1
0
0
2
0
1
0
0
0
2
1
0
0
2
1
2
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
1
0
0
0
0
0
2
1
0
1
0
0
1
0
0
0
0
1
2
2
2
0
0
0
2
2
1
0
0
1
1
2
0
1
0
2
1
0
0
0
0
0
0
1
0
1
0
1
1
0
1
5
1
0
0
0
1
2
0
0
2
0
0
0
1
1
2
0
2
0
0
0
2
0
0
1
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
2
0
0
2
2
0
3
2
0
0
0
0
0
0
0
0
0
0
1
0
2
2
2
0
0
0
2
1
0
0
0
0
0
0
0
2
0
1
0
0
1
0
2
0
2
0
0
0
1
0
0
0
2
2
3
0
2
0
0
0
1
0
0
1
0
0
0
2
0
1
1
0
2
0
0
1
2
1
0
2
0
0
0
1
1
1
0
0
1
0
1
2
0
0
0
2
0
0
2
0
2
0
0
0
1
2
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
2
0
0
2
2
2
0
0
1
0
0
0
0
0
0
1
2
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
1
0
2
2
1
0
2
0
1
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
3
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
2
0
1
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
2
0
0
2
2
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
2
2
0
2
0
0
1
5
0
0
3
0
1
0
1
1
2
0
0
3
1
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
1
4
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
2
2
0
0
1
0
1
0
0
2
0
1
1
2
2
3
0
2
0
0
0
1
0
0
0
2
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
2
1
0
0
0
0
0
1
0
1
0
1
1
2
0
0
1
1
1
0
0
0
6
0
0
0
1
2
0
0
0
0
0
0
0
2
1
0
0
0
2
2
2
0
3
1
0
0
2
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
0
0
0
0
0
1
2
0
0
1
1
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
1
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
1
0
0
2
0
1
0
1
1
0
1
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
2
2
2
4
0
0
0
1
0
2
0
0
1
2
0
2
0
0
2
2
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
2
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
2
0
0
1
0
0
2
0
1
0
0
0
0
0
0
3
0
0
1
1
4
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
1
0
2
0
2
1
1
1
0
2
4
4
1
0
0
0
0
0
2
2
2
0
0
1
0
0
3
0
0
0
0
0
0
0
3
2
0
1
0
0
0
0
1
2
1
0
0
2
4
0
0
1
0
0
0
0
0
2
0
0
1
0
1
2
2
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
2
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
3
0
2
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
2
0
0
1
2
0
1
2
0
2
0
0
0
0
1
3
2
0
1
0
2
0
0
1
0
0
0
0
0
0
2
1
0
1
1
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
3
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
1
2
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
1
2
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
2
2
0
0
1
2
0
2
0
1
2
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
1
0
1
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
5
0
0
2
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
6
1
2
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
3
0
2
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
2
0
1
0
0
1
0
2
0
2
0
0
0
0
0
0
1
1
1
2
0
1
0
0
0
0
2
1
0
1
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
1
0
1
1
0
0
2
0
0
2
2
2
0
1
1
2
0
1
1
2
0
1
0
2
0
0
2
0
0
2
2
0
0
0
0
0
0
1
0
3
0
2
0
2
0
1
1
3
1
2
0
1
0
2
0
0
1
1
0
0
2
1
0
0
0
0
0
0
2
0
3
1
0
1
2
0
0
0
2
0
1
0
0
1
2
0
3
0
1
0
0
0
0
2
0
5
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
13
0
0
0
0
3
0
0
0
1
0
0
1
0
1
2
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
2
2
0
0
2
0
0
1
0
0
1
1
2
1
1
0
0
3
1
3
0
2
0
0
0
0
0
0
2
0
0
0
1
1
0
2
2
0
0
0
0
0
2
0
1
1
0
2
2
2
1
0
0
2
0
0
1
2
2
2
0
0
0
0
0
0
2
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
4
0
0
0
0
0
0
1
0
0
0
0
2
2
0
1
2
2
1
0
0
0
0
0
2
2
2
1
0
2
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
4
2
1
0
0
0
1
0
2
0
0
0
2
0
0
0
1
0
1
0
1
2
0
0
2
2
0
1
0
0
3
0
1
0
2
0
0
0
0
2
0
1
0
2
0
0
0
2
0
2
0
0
1
0
0
1
0
0
0
0
0
2
0
0
2
1
0
0
2
1
2
1
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
2
2
2
0
0
2
0
2
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
2
6
0
2
0
1
0
2
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
1
0
0
0
0
0
2
0
3
0
0
0
0
0
0
1
0
0
2
1
1
0
2
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
4
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
1
0
2
0
2
4
0
0
0
1
0
0
1
2
2
2
4
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
3
0
1
1
0
0
0
1
0
0
1
0
0
0
1
0
1
1
1
1
0
0
0
0
2
0
0
2
2
1
0
0
1
0
1
2
0
2
0
0
1
0
0
0
0
0
1
4
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
1
1
0
0
2
0
2
0
0
0
2
1
0
0
0
0
3
2
0
1
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
2
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
1
0
0
0
1
0
0
1
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
1
0
0
2
1
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
1
1
2
1
0
2
0
1
2
1
1
0
0
0
0
1
0
0
0
0
2
0
2
2
1
0
0
0
0
0
0
2
1
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
1
0
0
2
0
0
0
0
0
1
0
0
0
2
3
0
1
1
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
2
1
4
2
0
3
0
3
0
0
2
1
0
0
1
0
1
0
0
0
2
0
1
0
0
2
0
0
1
1
0
0
0
0
0
1
1
0
0
2
0
0
2
0
1
1
7
0
0
0
0
2
0
0
0
2
0
1
2
1
0
1
0
0
0
0
0
0
2
2
0
2
0
1
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
2
0
0
0
0
0
0
0
1
0
2
0
2
1
0
0
1
2
1
3
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
8
1
0
1
2
1
2
0
0
0
0
3
0
2
0
0
0
0
0
0
1
1
0
0
0
2
1
0
1
0
0
1
0
0
0
2
2
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
2
0
3
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
2
2
0
0
1
0
0
0
2
0
0
0
0
2
2
2
2
0
1
0
0
0
0
1
0
1
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
2
2
2
0
2
2
0
0
3
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
1
0
1
0
1
0
0
0
0
0
2
0
0
0
3
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
2
0
0
0
1
0
0
2
1
2
0
2
0
0
0
3
0
0
0
0
0
2
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
2
0
0
0
2
0
0
1
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
2
1
2
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
2
1
0
0
0
0
3
0
1
3
0
2
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
9
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
2
0
4
0
0
1
0
0
0
0
1
0
0
0
2
0
1
0
2
1
2
2
0
0
0
0
2
1
0
0
0
0
2
1
0
3
2
0
0
0
0
2
0
2
2
0
0
0
0
0
0
1
1
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
2
0
5
0
2
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
2
1
1
0
0
0
0
0
2
2
0
3
2
0
0
0
0
2
0
0
0
1
0
1
0
0
0
2
0
2
0
1
0
4
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
2
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
1
0
1
2
1
0
1
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
1
3
2
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
3
1
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
3
0
0
2
0
0
2
2
2
0
0
1
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
1
0
1
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
2
2
0
0
0
1
3
0
0
2
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
1
0
1
0
0
0
2
2
0
0
2
2
1
2
0
0
2
0
0
0
2
0
0
0
1
0
1
2
0
0
0
0
1
2
2
0
0
2
0
2
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
1
2
2
0
0
0
0
1
0
0
0
0
0
2
0
1
1
0
2
0
2
2
0
1
0
1
0
3
0
0
0
0
0
0
0
0
2
0
0
1
0
1
2
0
0
0
0
2
0
3
1
1
1
0
1
0
0
2
1
0
1
1
0
0
0
2
0
0
2
0
1
2
1
1
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
2
1
0
1
0
0
0
0
3
1
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
1
0
2
2
0
0
1
0
1
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
2
2
0
2
0
3
0
3
0
0
1
0
0
6
0
0
2
0
0
1
1
0
0
2
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
3
0
0
1
0
0
0
1
0
2
2
1
3
0
1
0
2
1
0
0
1
0
1
0
0
0
1
1
0
0
2
0
0
2
1
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
1
0
0
2
1
2
0
0
2
2
0
0
0
0
2
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
1
2
1
0
0
0
0
0
1
0
0
0
0
0
1
0
2
2
2
1
0
0
0
1
0
3
1
2
0
2
0
0
2
0
0
2
0
0
1
0
0
1
1
0
0
0
0
2
0
0
0
2
0
1
1
0
0
1
2
2
0
1
0
0
0
1
1
1
1
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
1
0
0
2
1
2
0
5
0
3
0
0
0
3
0
0
0
0
1
3
2
0
0
0
2
0
1
0
0
2
0
0
0
0
2
1
0
0
1
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
3
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
2
0
7
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
2
0
1
0
0
1
0
2
0
1
0
1
0
0
0
2
0
1
0
0
0
1
1
0
1
2
1
0
0
0
0
2
0
1
2
1
2
0
2
0
1
0
0
0
2
1
0
0
0
0
3
0
2
2
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
2
2
0
2
0
0
0
1
1
0
0
1
0
2
0
0
1
2
0
0
0
0
2
0
0
1
2
0
0
2
0
1
0
0
0
3
0
0
0
0
0
1
2
0
1
0
2
0
0
0
5
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
1
1
1
0
4
0
0
0
0
0
1
0
2
1
0
0
0
1
0
0
0
9
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
1
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
1
0
0
2
0
0
0
0
1
0
0
1
0
0
1
1
1
0
0
1
0
0
0
0
1
0
0
0
1
2
0
0
2
0
2
0
0
2
0
0
1
0
1
0
0
2
3
2
0
0
0
0
0
2
0
0
2
0
0
0
2
0
2
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
10
0
0
1
0
0
0
0
0
0
2
0
0
2
3
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
1
0
0
2
1
0
0
2
0
0
0
2
1
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
3
0
0
0
1
2
0
2
0
2
0
0
1
1
2
1
0
0
0
1
0
0
0
2
2
0
1
0
0
0
0
1
2
0
0
1
0
0
0
2
1
5
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
3
1
2
2
0
0
1
2
0
1
0
0
3
1
2
0
2
3
0
0
0
1
0
0
2
0
0
0
0
0
2
1
0
1
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
2
1
0
0
0
0
0
1
4
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
2
0
0
1
0
4
0
0
1
0
0
2
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
2
3
2
0
0
2
0
1
2
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
3
0
0
3
3
0
1
0
2
0
0
1
1
2
2
2
0
0
0
2
0
2
0
2
0
0
2
0
0
0
1
0
0
1
0
0
2
0
1
0
0
0
2
0
1
0
0
0
2
0
4
2
0
0
2
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
1
1
0
1
2
1
1
2
2
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
1
1
0
1
0
1
0
0
0
0
0
1
2
0
0
0
0
1
2
0
3
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
2
0
2
0
0
1
0
0
1
0
0
0
0
0
1
0
0
2
2
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
2
2
1
0
0
0
0
0
0
0
1
1
3
2
0
1
0
0
2
0
0
0
2
2
0
2
0
3
0
1
3
0
1
2
0
0
0
0
0
0
0
0
2
0
2
0
1
0
1
0
0
0
0
0
1
0
0
0
1
2
0
2
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
2
0
3
0
0
2
0
0
0
2
0
0
0
4
0
1
0
0
1
2
0
0
2
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
1
3
0
0
0
1
3
0
0
0
1
1
0
0
0
0
4
0
0
0
0
0
0
2
0
0
0
3
1
1
2
1
0
2
0
2
0
0
0
1
2
0
0
0
0
0
2
2
2
0
0
2
0
0
0
0
0
2
0
0
2
1
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
2
1
0
0
1
1
1
2
0
0
0
1
2
0
0
1
0
0
1
0
1
0
1
1
1
1
1
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
2
0
1
0
0
0
1
0
0
1
2
0
1
2
0
0
0
0
2
0
1
1
2
0
0
0
0
0
0
0
1
1
0
2
0
2
1
0
4
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
1
0
0
2
1
0
0
0
2
2
2
0
2
0
2
1
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
4
0
0
0
1
4
0
2
2
0
0
2
0
2
0
0
0
0
0
0
2
0
1
1
0
0
1
0
2
0
0
2
2
1
0
0
0
2
0
0
0
0
0
2
0
1
1
1
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
2
2
0
0
4
2
0
0
0
0
2
0
2
0
0
0
0
1
2
0
1
0
0
2
0
1
4
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
3
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
2
1
0
0
0
0
0
0
0
3
1
2
3
0
2
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
2
1
1
0
0
1
0
0
1
0
0
0
0
0
2
1
0
2
2
0
0
0
1
0
0
2
0
0
0
2
0
0
1
0
2
0
0
1
0
1
0
2
0
1
1
0
0
0
0
2
2
0
5
0
0
0
0
0
2
0
1
0
2
0
0
1
1
0
1
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
1
2
0
2
0
0
2
0
1
2
0
0
0
2
0
0
2
2
2
0
0
0
1
2
1
0
0
1
0
0
0
2
3
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
1
2
0
1
0
0
0
0
0
0
1
0
1
1
0
2
3
1
0
1
0
0
1
0
0
0
1
1
1
0
0
2
0
2
1
0
0
1
1
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
1
0
0
0
2
1
0
1
2
0
0
0
0
0
1
0
1
7
0
0
0
1
0
0
0
0
2
1
2
0
0
0
1
1
0
0
1
2
0
1
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
1
1
1
0
0
1
0
0
1
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
3
2
0
0
0
0
0
2
0
0
4
0
2
2
1
0
0
1
0
2
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
2
0
2
0
1
1
0
0
1
2
0
1
0
4
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
1
0
2
0
3
0
0
0
0
2
0
1
0
0
0
2
3
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
2
2
0
0
0
0
0
1
0
1
0
0
0
2
1
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
2
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
1
0
4
2
0
0
2
2
0
1
0
1
1
2
1
1
0
0
0
0
0
0
0
0
2
0
2
0
2
0
6
1
1
0
0
0
4
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
2
1
0
0
2
2
0
1
0
1
0
0
0
2
1
1
2
0
0
0
1
0
2
0
0
0
0
1
0
1
0
0
3
1
0
0
0
2
2
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
1
0
0
1
0
1
2
0
0
1
0
0
0
2
0
0
1
0
0
4
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
2
2
0
2
2
0
0
0
3
0
0
1
2
0
0
0
1
0
0
0
0
0
0
2
2
1
2
1
2
0
2
2
0
0
0
0
0
0
2
0
1
1
1
0
1
0
1
2
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
1
0
0
2
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
2
0
1
0
0
2
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
1
2
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
1
0
1
0
0
2
1
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
2
0
1
0
0
0
1
0
0
3
1
0
0
0
0
0
0
2
0
0
0
3
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
2
2
0
0
0
1
2
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
2
2
0
1
0
0
0
0
2
1
0
0
1
0
0
2
2
1
0
0
0
0
0
2
0
2
0
2
0
2
2
4
0
0
0
1
0
2
1
2
0
0
1
2
2
0
0
1
1
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
2
2
0
0
2
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
2
0
0
0
1
0
1
0
0
0
0
2
0
1
0
0
1
0
2
0
1
0
2
0
0
0
0
0
1
0
3
0
0
1
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
2
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
2
0
0
0
0
1
0
0
0
1
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
3
0
0
0
1
3
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
2
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
1
1
0
2
0
2
0
0
0
0
0
1
2
0
1
2
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
4
0
2
0
0
0
0
0
0
0
1
0
2
0
0
1
2
2
0
0
1
0
2
1
0
0
0
0
0
0
0
0
1
3
1
0
3
0
2
0
1
0
1
0
0
1
2
0
0
0
1
0
0
0
0
1
2
0
1
2
0
0
0
0
2
0
2
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
2
0
0
0
0
1
0
0
0
2
1
2
0
0
2
0
0
1
0
2
0
2
1
0
0
2
1
1
0
0
1
0
1
0
0
0
1
1
0
0
5
1
2
0
0
0
1
2
2
1
1
0
0
2
0
0
2
1
0
1
0
0
0
0
0
2
1
2
1
0
0
1
0
0
0
1
1
0
0
0
0
0
1
1
0
2
1
0
2
0
2
0
0
0
0
0
0
1
0
2
0
0
2
1
0
0
0
0
0
6
0
0
3
0
0
1
2
0
2
2
0
1
1
0
1
0
1
2
0
1
0
2
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
2
2
0
0
0
0
0
1
0
2
2
0
0
2
0
0
0
2
2
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
1
2
0
2
2
1
0
2
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
1
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
4
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
2
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
3
0
1
6
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
1
1
0
0
2
0
0
0
2
1
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
2
1
1
0
0
0
2
0
0
2
0
2
0
0
0
2
1
0
0
0
2
0
0
0
5
0
1
0
0
0
0
0
0
2
2
1
0
0
2
0
1
0
0
0
0
0
2
0
0
0
2
1
1
0
0
0
3
0
0
0
0
0
0
0
2
0
1
0
0
1
1
0
1
0
0
0
0
0
2
0
2
2
0
1
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
2
1
0
1
1
0
2
0
0
0
0
0
2
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
1
1
2
0
0
1
0
2
0
0
1
0
0
0
0
2
2
2
2
0
0
0
0
0
1
2
0
1
1
0
0
0
0
0
0
0
1
0
2
0
0
1
2
2
0
0
2
2
1
1
0
0
2
1
0
0
2
0
0
0
0
0
0
0
2
2
0
2
0
2
0
2
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
3
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
2
2
0
3
0
2
1
1
2
2
2
0
0
1
0
1
5
0
1
0
0
0
1
0
3
0
1
0
1
1
1
0
0
0
1
0
1
0
0
0
0
0
2
1
0
2
0
0
0
1
0
2
0
0
1
0
2
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
3
0
0
2
3
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
2
1
0
1
0
2
0
0
0
2
0
1
0
0
0
0
0
2
0
2
0
0
2
0
0
4
0
0
0
0
1
3
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
1
2
1
1
0
0
2
2
0
0
0
0
2
1
0
0
1
2
1
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
2
2
0
1
0
1
0
2
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
3
1
0
0
1
0
0
1
2
1
0
0
0
1
0
1
4
0
1
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
1
0
0
2
2
0
0
0
0
1
0
1
0
2
0
0
2
0
0
1
0
0
1
0
0
1
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
1
0
0
1
0
0
0
0
0
2
2
2
0
0
0
0
0
0
2
1
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
2
0
1
2
2
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
2
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
2
2
1
1
1
2
1
3
0
0
0
0
0
0
2
0
0
2
1
2
1
0
0
0
3
0
1
2
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
1
0
2
0
0
0
1
0
1
0
0
0
0
0
2
2
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
1
0
2
0
1
1
2
0
1
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
1
1
0
2
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
5
0
2
0
0
2
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
2
0
1
3
0
0
0
1
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
2
1
0
5
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
6
0
1
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
2
2
1
0
0
2
0
1
2
0
0
0
0
0
0
0
2
2
1
0
0
2
0
2
0
0
2
1
0
1
0
0
0
0
0
2
1
2
2
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
1
2
2
0
0
2
4
0
2
0
0
1
0
0
0
0
1
0
0
2
0
2
2
1
1
0
1
1
0
0
0
0
0
2
4
1
0
0
0
0
0
0
1
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
3
0
2
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
1
0
0
0
3
2
0
0
0
0
2
0
0
0
0
2
0
0
2
0
1
2
3
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
2
2
0
0
0
2
0
2
2
0
0
0
0
2
0
0
2
0
0
2
0
0
1
1
0
2
0
1
0
0
1
0
1
2
0
0
0
0
2
1
2
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
1
4
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
4
2
2
1
0
2
0
0
2
0
2
2
0
2
0
2
1
2
0
2
2
1
2
2
1
2
0
0
1
0
1
1
2
0
2
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
1
0
3
0
1
0
0
0
0
0
0
0
3
0
2
2
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
2
1
1
0
2
0
0
2
1
0
0
2
2
1
0
0
0
0
0
1
0
1
0
2
2
0
0
0
1
0
0
0
2
2
0
1
0
0
0
0
0
0
2
0
1
2
1
1
2
1
1
2
0
2
0
1
0
2
0
1
0
0
2
0
0
0
2
0
0
0
2
0
2
0
0
0
1
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
2
1
0
0
6
0
0
2
1
0
1
1
0
0
2
0
2
0
3
0
0
0
2
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
1
0
0
0
0
2
1
0
1
2
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
2
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
2
0
0
2
0
0
0
0
2
1
0
0
0
0
0
2
2
1
0
0
0
0
0
1
3
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
2
0
2
0
0
2
0
1
0
0
0
0
0
0
2
4
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
3
2
0
0
1
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
2
1
3
2
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
1
1
1
0
1
0
0
1
0
0
2
0
0
2
1
0
0
0
1
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
4
1
0
0
1
1
2
1
2
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
1
2
1
0
2
0
0
1
2
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
2
0
1
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
1
0
2
0
1
0
0
0
1
0
2
0
2
2
0
0
0
0
0
0
2
1
0
0
0
1
1
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
7
0
1
0
0
1
1
4
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
2
1
0
0
0
0
0
0
2
1
2
0
0
2
2
0
1
0
3
1
2
0
0
2
0
0
1
0
0
2
0
2
2
0
0
2
0
0
0
0
0
0
4
1
0
1
0
2
0
2
1
1
0
1
0
0
2
1
0
3
0
0
0
0
2
0
0
0
0
2
1
0
1
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
1
2
0
0
0
0
1
0
2
1
1
2
0
0
0
1
5
0
0
0
0
1
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
1
0
0
3
0
1
0
0
0
0
0
0
2
5
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
2
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
2
0
0
3
0
0
0
1
0
0
1
0
2
0
1
3
0
0
0
2
0
1
1
1
0
0
0
1
0
3
0
0
0
0
0
2
0
0
0
0
1
2
3
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
1
0
1
1
5
2
0
0
1
0
2
1
2
0
1
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
2
4
0
0
0
1
3
4
0
2
0
0
2
1
0
1
1
0
0
0
0
6
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
2
4
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
1
1
0
0
2
0
0
2
0
1
0
0
0
0
1
2
0
0
1
4
0
0
0
0
1
0
2
2
0
0
0
0
2
0
0
0
0
0
1
1
2
0
1
1
1
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
1
0
4
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
2
2
2
0
0
0
0
4
0
0
2
0
0
0
1
1
0
1
0
0
0
0
1
1
1
1
1
1
2
2
2
0
0
0
2
0
0
0
0
0
0
0
1
0
2
2
0
1
0
0
2
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
2
0
3
0
0
3
0
5
2
0
0
3
0
0
2
0
2
2
0
0
0
0
0
0
0
1
0
0
3
0
0
0
2
0
2
2
0
0
4
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
1
0
0
1
0
2
0
1
4
2
1
0
0
0
0
2
2
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
2
0
0
1
0
1
0
0
0
2
0
0
1
0
1
0
2
0
2
2
0
0
0
0
0
0
0
1
0
0
2
0
2
0
1
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
1
0
0
1
2
1
1
0
0
1
2
1
0
0
2
0
2
0
1
0
0
1
4
0
2
0
1
1
1
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
1
1
0
1
0
0
2
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
3
0
0
1
2
0
0
4
0
1
1
0
0
0
2
0
0
0
1
0
0
0
3
2
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
1
2
2
0
0
0
0
0
2
0
0
2
0
2
0
0
2
1
0
0
2
0
2
0
0
0
0
1
1
0
0
2
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
2
2
3
1
0
0
0
0
3
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
3
0
1
2
0
0
0
0
0
0
0
0
1
2
1
0
1
0
1
2
0
2
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
2
2
1
0
0
0
0
0
0
2
0
1
0
1
3
0
0
0
0
0
1
0
2
1
0
1
0
0
0
0
0
0
1
3
2
0
0
0
1
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
2
0
1
0
2
0
0
0
0
2
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
2
5
0
1
0
1
0
0
5
0
1
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
1
0
0
2
1
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
1
0
0
0
1
0
2
1
0
0
2
0
2
0
0
0
0
0
2
2
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
2
1
1
2
2
0
4
0
0
1
1
0
1
0
0
0
0
0
2
2
0
0
0
1
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
1
1
0
1
0
0
0
0
2
0
2
0
0
0
0
1
1
0
2
1
0
0
0
0
2
0
0
0
0
0
1
2
0
1
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
2
0
1
2
1
0
1
0
0
2
1
2
0
0
0
1
2
0
0
0
0
2
0
0
4
2
0
2
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
2
1
1
0
1
0
2
0
0
1
0
1
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
2
0
0
0
0
0
1
1
0
1
0
0
0
2
0
1
1
0
0
2
0
0
0
0
0
2
2
0
0
0
0
1
1
0
0
0
2
0
1
0
0
0
0
0
2
1
0
2
0
0
2
1
0
2
0
2
2
0
0
1
2
2
0
1
2
1
2
0
0
1
0
0
2
0
0
1
0
0
0
3
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
1
0
0
0
2
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
2
1
1
2
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
1
1
0
0
1
2
0
2
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
9
0
0
0
0
0
1
0
1
0
0
1
2
2
2
0
0
2
0
0
0
0
0
0
0
2
0
2
1
2
1
4
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
1
0
0
1
3
1
0
2
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
6
0
0
0
0
1
0
0
1
1
2
2
0
0
0
1
1
2
0
1
1
0
0
0
1
0
0
0
0
0
0
0
2
2
2
0
0
1
0
1
0
0
0
1
0
2
0
0
0
0
0
2
0
1
2
0
2
0
0
0
0
0
0
1
0
2
0
2
0
0
0
2
0
0
2
0
0
0
0
0
1
1
0
0
0
2
2
0
2
0
0
0
0
0
1
0
0
0
0
3
0
1
0
0
0
0
0
0
3
0
1
0
2
2
0
0
0
0
0
0
0
0
0
1
0
2
2
0
1
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
2
0
2
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
2
0
0
1
2
1
0
0
0
0
4
0
0
0
0
2
1
0
1
1
0
0
0
3
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
2
0
1
0
0
0
0
2
2
1
1
0
0
0
0
0
0
1
1
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
1
0
4
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
2
2
1
0
2
0
1
2
0
0
0
1
0
1
0
2
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
2
2
0
0
0
0
2
0
2
1
2
0
0
0
0
0
2
1
0
0
0
2
0
0
0
5
0
3
0
1
0
0
3
1
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
1
0
0
0
2
2
0
0
0
0
1
0
0
0
1
0
0
0
1
1
1
0
0
0
0
2
0
2
0
0
0
2
2
0
0
0
2
2
0
0
0
1
0
0
0
0
0
1
0
2
2
0
0
0
1
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
1
0
0
2
0
2
0
0
1
0
2
2
1
0
0
1
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
3
0
1
2
1
2
0
0
2
0
0
1
0
0
0
0
1
1
4
1
0
0
2
2
2
0
0
0
0
0
2
0
0
2
1
0
1
1
1
0
1
0
0
0
0
0
1
0
1
2
0
0
0
2
2
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
2
1
0
0
2
0
0
2
0
0
1
1
1
1
0
0
0
0
0
0
1
1
2
2
0
0
1
0
0
0
0
0
2
0
1
0
3
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
5
0
0
0
0
1
0
2
1
0
0
2
0
0
0
0
0
2
1
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
7
0
0
0
0
2
0
0
0
2
0
1
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
2
1
0
0
1
1
1
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
2
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
9
1
0
0
1
0
1
1
1
0
2
2
0
0
1
0
0
0
0
0
1
0
1
0
0
2
1
0
0
0
0
0
1
0
0
0
0
3
0
0
0
2
1
0
2
2
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
2
0
6
0
2
1
0
0
0
0
0
2
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
1
0
1
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
2
2
0
0
2
3
0
0
0
0
1
0
2
0
1
1
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
2
1
1
0
0
0
2
0
0
0
2
0
2
0
2
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
4
0
1
2
3
0
2
0
5
3
1
0
1
0
0
1
0
0
0
2
2
0
0
0
0
2
0
0
3
1
0
0
1
0
0
0
0
1
3
1
0
0
0
0
3
2
1
2
0
1
0
2
1
0
0
0
0
0
0
1
0
0
1
3
0
0
2
0
1
2
0
2
1
0
1
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
2
1
0
0
0
0
0
2
0
2
0
0
2
0
0
0
3
0
1
0
1
2
2
1
0
0
0
0
2
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
2
0
3
0
0
2
1
0
0
2
2
1
0
1
0
0
1
0
2
0
0
0
1
1
0
0
2
2
0
0
0
0
2
1
1
0
1
0
5
2
3
2
2
0
0
0
0
0
3
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
1
0
2
0
0
0
0
0
0
4
0
2
0
0
2
1
0
0
1
0
2
0
1
1
2
0
0
1
1
0
0
2
0
0
0
1
0
0
0
1
0
0
0
2
1
0
0
1
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
2
1
0
0
0
1
0
0
7
0
0
0
2
0
0
0
3
0
1
1
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
1
0
2
0
0
0
0
2
0
0
2
1
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
1
2
1
2
0
0
0
2
0
0
0
1
1
1
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
2
2
0
0
0
1
0
0
2
0
0
1
0
0
1
0
0
1
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
2
1
2
1
2
2
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
3
0
0
0
2
0
2
0
0
2
0
2
0
0
0
0
2
0
0
0
1
1
2
2
0
0
2
0
0
2
1
0
0
2
0
0
0
0
2
0
0
0
0
2
2
0
2
0
0
1
0
2
0
1
0
2
1
2
0
3
0
0
0
0
0
0
0
1
0
0
1
2
2
2
0
0
1
3
0
0
0
0
1
3
2
0
1
2
1
1
0
1
0
2
2
0
1
0
0
0
2
0
0
0
1
0
0
0
2
2
1
2
0
1
2
0
0
0
0
1
2
0
0
2
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
2
1
2
1
1
0
0
0
0
0
7
0
1
0
2
0
0
1
1
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
1
1
3
0
0
0
1
0
2
0
0
1
0
2
0
0
1
0
0
0
1
0
0
0
0
0
1
2
0
0
2
2
2
0
0
0
1
1
1
0
1
0
0
0
2
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
1
0
0
2
0
2
2
0
2
0
0
0
1
0
0
1
0
2
0
0
0
0
3
0
0
0
1
3
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
2
3
1
0
0
3
0
0
1
0
0
1
0
0
0
1
0
0
10
0
0
2
0
0
0
1
0
0
1
2
0
1
0
0
2
0
4
0
1
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
1
3
0
2
0
0
2
0
0
2
1
0
0
0
0
1
0
2
2
0
1
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
1
0
0
0
2
2
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
1
0
2
2
1
0
0
2
1
2
2
0
0
4
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
2
2
0
0
1
0
2
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
2
1
2
0
0
2
1
0
0
1
1
1
3
0
0
2
0
0
0
2
0
0
0
2
1
0
3
2
0
0
0
0
1
0
1
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
3
0
1
0
2
0
0
1
1
0
3
0
1
0
0
2
2
0
0
0
0
0
3
0
0
2
0
1
0
1
0
2
0
0
0
1
1
0
1
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
1
0
0
0
0
1
2
1
0
1
0
1
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
1
0
1
0
2
0
0
0
1
0
0
2
2
0
0
0
1
2
0
0
1
2
0
0
2
0
1
0
2
0
0
0
0
0
0
2
1
2
0
0
1
0
1
1
0
0
1
0
0
0
0
2
0
0
1
0
0
1
0
2
2
1
0
1
0
0
0
3
0
0
1
2
0
3
0
0
0
2
1
0
0
0
2
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
2
1
3
2
0
0
2
0
1
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
3
2
0
0
0
0
0
0
0
2
1
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
2
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
2
2
0
0
0
0
1
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
4
0
2
0
1
0
1
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
3
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
1
0
1
2
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
1
0
0
0
0
1
1
1
1
0
1
0
2
0
0
2
0
0
1
0
1
0
2
1
0
0
0
1
0
2
0
0
2
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
2
1
0
1
0
0
1
0
0
0
0
0
2
0
1
2
0
2
2
2
0
0
0
0
1
2
0
0
0
0
0
1
0
1
2
1
0
1
0
0
0
0
1
1
7
0
0
0
2
1
0
0
0
0
0
1
0
0
1
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
3
0
1
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
1
0
1
3
0
1
2
0
1
0
2
2
0
0
1
0
0
0
0
0
2
0
3
0
2
0
0
2
1
0
0
1
0
0
0
0
0
2
0
0
1
1
0
0
1
0
0
0
0
0
2
1
2
0
7
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
2
1
0
0
1
2
0
0
0
1
0
0
0
0
0
3
2
0
0
2
0
1
0
3
1
1
0
0
2
0
0
3
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
1
4
0
0
2
1
1
0
1
2
0
0
0
3
1
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
1
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
1
0
0
0
0
4
1
0
2
0
1
4
0
0
0
3
0
0
1
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
1
2
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
1
0
0
1
4
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
1
1
0
1
0
0
1
0
2
0
2
1
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
1
2
1
3
1
0
1
0
0
0
0
0
2
0
0
0
1
0
2
0
3
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
2
2
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
2
4
1
0
0
1
0
2
2
2
0
0
0
1
0
1
0
0
0
3
2
0
1
0
1
0
2
0
3
1
2
0
2
0
0
0
2
1
1
1
0
0
0
0
0
0
1
0
3
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
1
0
1
1
1
2
0
0
0
0
0
0
0
3
1
0
1
0
0
2
1
1
1
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
1
0
2
1
0
0
0
1
0
2
0
1
0
1
0
2
1
2
0
4
0
2
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
2
2
0
1
0
0
0
1
2
0
0
1
0
0
7
2
1
0
2
1
1
2
2
1
1
2
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
1
2
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
2
0
0
0
0
0
2
0
2
2
1
0
0
0
0
1
0
2
2
0
0
2
0
0
0
0
0
2
0
1
2
0
1
0
0
2
0
0
1
0
2
2
0
0
1
1
0
2
0
0
0
0
0
1
3
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
2
0
0
2
2
1
1
0
0
2
0
5
0
1
0
0
0
2
0
1
0
2
0
2
0
0
1
2
0
0
0
2
0
0
0
0
0
2
3
2
0
2
2
1
0
0
0
0
0
0
1
0
0
2
0
2
0
0
2
2
1
0
0
0
0
0
4
0
1
0
1
1
1
1
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
2
0
1
1
0
0
0
0
0
0
0
2
1
0
0
0
3
0
0
0
0
0
1
0
1
0
0
0
2
2
0
0
1
0
0
0
1
0
0
2
1
0
2
2
0
0
1
0
0
0
0
0
0
2
2
0
0
1
0
2
2
1
2
1
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
2
0
3
0
0
2
2
2
0
0
1
1
0
0
0
2
0
0
0
0
1
0
0
0
2
1
2
0
4
1
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
1
0
2
1
0
0
1
1
0
0
2
2
0
0
2
0
0
0
1
0
2
0
0
0
1
1
0
0
1
0
0
0
2
1
0
0
0
0
2
0
2
2
2
1
0
0
0
0
0
0
0
0
2
2
0
1
1
0
0
0
0
1
2
0
0
1
0
0
0
2
2
1
0
2
0
0
2
1
1
0
0
2
2
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
2
1
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
1
0
1
1
0
1
1
0
0
1
1
0
1
0
2
0
0
1
0
0
2
0
0
0
1
3
1
1
2
1
0
0
0
0
0
0
1
0
1
0
1
2
2
0
0
2
0
1
1
0
0
2
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
4
2
0
2
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
2
0
0
1
0
2
0
0
0
0
0
1
2
0
2
0
2
0
0
2
1
2
1
1
3
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
2
0
0
1
0
0
0
3
1
2
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
3
1
1
0
0
0
0
1
0
1
1
0
0
1
0
2
0
0
0
0
1
1
0
4
0
0
1
0
2
0
0
0
0
1
0
0
0
1
2
0
3
0
0
1
0
2
0
2
0
0
0
0
0
2
1
0
0
0
0
1
1
2
0
0
1
2
2
0
1
0
0
2
1
0
0
0
1
0
2
0
1
2
0
1
0
0
0
0
0
0
0
2
0
0
0
3
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
2
0
1
1
2
0
0
1
2
0
1
0
2
0
0
0
3
0
2
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
3
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
3
2
1
2
1
1
2
0
0
0
1
0
0
0
0
0
3
2
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
1
1
0
0
3
0
1
2
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
1
0
0
2
0
2
0
2
0
3
0
0
2
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
3
0
1
1
1
0
1
0
1
0
1
0
2
0
4
0
1
0
0
0
3
0
0
5
0
1
2
0
0
0
0
0
0
0
2
0
1
2
0
1
1
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
1
2
0
0
0
0
0
1
1
0
3
2
0
1
1
2
0
1
0
1
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
1
0
0
0
1
2
2
0
1
0
0
1
0
0
0
0
1
0
1
0
0
1
2
0
0
2
2
0
0
2
2
1
1
0
0
0
1
0
3
1
0
1
0
0
0
0
2
1
0
1
0
1
0
0
0
0
3
0
0
1
1
0
1
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
1
0
2
1
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
2
0
1
0
2
0
0
0
2
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
3
0
0
0
0
1
2
0
0
2
0
0
0
2
1
0
1
0
1
2
0
0
1
2
0
2
0
0
0
2
2
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
2
0
2
0
0
0
1
0
0
1
1
1
2
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
1
0
0
0
0
1
1
0
0
0
0
1
2
2
0
0
1
2
0
0
0
2
0
1
0
0
0
2
1
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
2
0
1
0
0
0
0
0
0
1
0
0
1
2
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
2
0
6
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
2
1
0
1
0
1
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
2
1
0
0
2
0
0
0
0
1
0
2
0
1
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
2
0
2
0
2
0
0
0
2
0
0
1
1
2
0
0
0
0
0
1
0
1
2
0
1
1
1
0
2
0
2
1
0
0
0
0
0
0
2
0
5
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
1
0
1
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
2
0
2
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
1
1
0
2
2
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
2
0
2
0
0
0
2
1
0
0
1
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
2
0
0
1
0
1
0
2
1
0
1
0
2
2
0
0
0
0
3
2
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
2
0
2
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
3
2
0
0
2
4
2
0
2
2
0
2
0
0
2
0
2
0
0
0
0
0
1
0
2
1
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
2
1
2
1
1
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
2
2
0
0
2
0
0
0
1
0
0
0
2
0
0
0
2
2
1
0
0
0
2
0
0
1
0
2
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
2
0
0
1
0
1
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
5
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
6
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
2
2
0
1
0
2
1
0
2
2
1
1
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
3
0
0
1
0
1
0
1
0
0
0
2
0
0
2
1
2
0
0
0
2
2
0
0
2
0
0
2
0
2
0
0
2
0
0
2
0
1
0
0
2
0
0
0
0
1
1
1
0
2
0
0
2
2
0
0
1
2
2
1
0
3
0
0
0
2
1
0
0
0
0
0
0
1
2
1
0
3
0
0
0
0
1
0
2
0
0
0
0
0
1
1
1
0
1
0
0
0
1
2
1
1
1
1
0
1
0
0
0
1
0
2
1
0
0
0
2
0
2
1
0
0
0
1
1
0
1
2
0
1
0
2
3
0
1
0
0
1
0
1
0
2
0
0
0
1
0
1
0
0
2
0
2
1
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
2
0
0
1
2
1
1
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
1
0
2
1
0
0
0
2
0
2
0
0
2
0
0
0
0
1
2
0
0
0
2
0
1
1
2
0
0
0
0
0
1
4
1
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
1
2
0
1
2
0
0
2
0
0
0
0
0
6
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
2
2
0
0
0
1
0
0
1
0
0
0
0
1
1
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
1
1
1
0
1
0
3
0
0
0
2
0
0
0
2
0
0
1
0
2
0
0
2
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
1
1
2
0
2
0
0
0
0
0
6
2
0
0
0
0
0
0
2
1
0
0
0
2
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
1
0
0
0
0
3
0
2
0
0
1
0
0
0
0
2
1
1
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
2
1
0
1
0
2
0
0
0
0
1
0
0
0
0
1
1
0
0
2
0
1
0
2
0
2
0
0
2
0
0
0
1
2
1
0
1
0
0
0
2
0
2
1
2
1
1
0
0
0
1
3
1
0
0
1
2
3
2
0
0
0
1
0
0
1
2
0
5
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
4
0
2
0
2
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
2
2
4
0
0
0
2
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
3
0
0
0
1
0
1
0
0
2
2
2
2
0
0
0
0
0
0
0
0
1
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
1
0
0
1
0
3
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
2
0
0
0
0
0
0
1
2
2
2
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
2
1
0
0
0
2
1
1
0
1
0
0
0
0
0
2
2
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
2
2
0
1
2
0
0
0
2
0
6
2
0
0
1
1
1
0
0
1
0
0
1
3
0
0
1
0
0
0
4
0
0
1
0
1
0
0
4
0
0
0
0
0
0
1
0
1
2
1
0
1
1
0
0
0
0
2
0
2
0
0
1
0
1
2
2
1
0
0
2
0
0
0
0
0
1
0
1
1
0
1
0
0
1
2
2
0
0
1
0
1
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
2
0
4
0
0
0
0
1
0
0
0
2
2
0
0
0
1
1
0
1
0
2
0
1
0
0
0
2
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
2
0
0
0
1
1
2
0
0
0
0
1
0
2
0
2
3
0
1
2
0
0
0
0
1
0
2
0
1
0
1
0
0
0
0
0
0
0
2
0
2
3
0
1
0
2
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
9
0
0
0
1
2
0
0
0
2
0
1
0
0
2
2
0
0
0
1
0
0
2
0
2
1
0
0
2
0
8
0
0
0
1
0
0
1
0
0
1
1
2
0
1
0
1
0
1
0
0
0
1
0
1
0
0
0
0
1
2
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
2
0
1
0
1
2
2
1
1
0
0
0
0
2
0
0
0
2
1
1
1
2
2
0
5
0
0
0
0
0
0
2
2
0
1
0
0
1
1
7
0
2
1
0
0
0
0
0
2
0
0
0
0
1
2
2
0
2
1
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
3
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
2
1
0
4
0
0
0
1
0
2
0
2
2
0
2
0
2
1
0
0
0
0
0
0
2
1
0
0
2
1
0
4
0
0
2
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
1
0
0
0
2
0
2
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
4
0
0
2
0
0
0
0
2
0
1
1
0
1
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
2
0
0
1
0
1
0
2
1
1
0
0
2
0
0
1
2
1
0
0
0
1
1
0
1
0
0
0
2
5
0
0
0
2
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
2
0
1
1
0
0
1
0
1
2
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
1
2
2
0
0
2
2
1
3
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
1
1
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
2
2
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
1
2
2
0
0
0
0
1
0
0
1
1
0
3
1
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
1
0
0
2
3
0
1
0
0
0
1
0
0
1
3
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
2
1
0
0
0
1
2
1
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
3
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
2
0
0
2
2
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
2
0
0
1
0
0
0
2
0
0
1
0
0
0
2
2
0
0
0
0
3
0
2
0
0
1
2
2
0
0
0
0
0
1
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
2
1
0
0
1
0
0
1
0
0
0
2
2
2
0
0
0
1
2
2
0
2
0
2
0
0
0
0
2
1
0
2
0
0
5
0
2
2
2
0
0
0
0
0
0
2
1
0
0
2
0
0
2
0
2
2
3
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
2
2
0
1
0
0
0
2
0
3
0
0
0
2
3
0
0
0
0
0
1
2
0
2
0
0
1
0
2
0
2
0
1
0
1
0
0
1
0
1
0
0
1
2
5
0
1
1
1
0
0
2
0
0
0
3
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
1
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
2
2
0
0
1
2
0
0
2
2
0
2
0
0
0
0
0
2
2
1
0
0
0
0
1
0
0
2
0
2
0
0
2
0
0
0
0
0
2
0
1
2
0
0
0
1
0
1
2
1
0
0
0
0
2
1
0
2
0
0
2
0
2
0
0
0
0
0
0
0
2
3
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
2
1
1
0
0
0
2
1
0
2
0
0
0
1
0
0
0
1
4
1
0
0
0
2
0
2
1
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
2
2
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
2
0
0
2
0
1
0
0
0
2
0
0
2
2
1
0
0
0
0
0
1
0
0
2
0
0
1
1
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
1
2
3
0
0
0
0
0
2
0
0
0
2
0
1
2
1
0
0
0
0
3
0
2
0
0
1
0
0
2
2
2
1
0
0
1
1
0
0
0
1
0
1
0
3
0
0
1
0
0
0
1
1
2
0
0
0
0
0
0
1
1
1
8
0
0
0
2
0
0
0
0
1
0
1
0
3
1
0
0
1
0
3
0
0
0
0
0
0
0
2
1
2
0
2
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
2
1
2
0
0
0
0
2
0
0
0
1
0
2
0
0
2
1
1
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
3
0
1
1
0
0
2
0
2
0
2
0
0
0
1
0
0
0
1
1
1
0
2
2
2
2
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
1
0
1
2
0
0
0
1
0
0
2
0
1
0
4
0
0
2
0
1
1
0
2
0
0
1
2
0
0
0
1
0
0
0
1
2
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
3
3
0
2
0
0
2
0
2
0
1
0
0
0
15
0
1
2
0
0
0
0
0
1
1
0
0
0
2
3
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
2
0
2
0
1
1
0
0
0
0
0
2
0
2
0
0
1
0
1
0
0
0
0
2
1
0
1
0
0
0
0
2
0
1
2
2
0
0
1
0
1
1
2
0
2
1
1
0
2
0
1
0
0
0
0
2
0
3
2
0
0
0
0
0
0
2
0
0
1
0
0
1
0
2
0
0
0
1
2
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
1
2
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
2
0
0
0
2
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
1
0
0
2
0
2
2
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
2
0
0
0
0
3
2
0
0
0
1
0
0
3
0
1
2
0
3
0
2
0
1
0
0
2
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
1
0
1
1
3
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
1
2
1
0
2
1
0
0
0
0
2
0
1
0
0
0
0
0
2
2
1
1
0
0
0
2
0
0
0
0
1
2
0
0
0
0
1
1
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
2
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
3
2
0
2
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
2
0
1
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
2
2
2
2
2
0
0
0
2
0
0
0
0
0
0
0
1
0
2
1
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
2
1
0
1
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
2
0
1
0
0
1
2
0
0
2
0
0
3
1
0
0
2
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
2
1
2
1
2
1
0
2
0
0
2
0
1
0
1
0
0
0
0
7
2
0
1
1
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
2
0
3
0
2
2
0
2
0
0
1
0
2
1
1
0
0
0
0
0
2
0
0
0
0
2
0
2
1
2
0
0
0
0
0
0
0
0
1
0
0
0
1
1
2
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
2
1
0
1
1
1
0
0
2
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
2
2
0
1
0
0
1
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
1
0
1
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
1
2
0
1
0
2
1
2
1
0
0
2
2
0
3
0
0
1
0
0
1
0
0
0
0
0
0
0
1
4
1
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
1
0
0
2
0
1
0
1
2
2
0
0
0
0
0
4
0
2
2
2
0
0
0
2
2
0
0
0
2
0
0
0
1
2
0
2
0
0
0
0
0
0
1
0
1
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
2
0
0
0
0
2
0
2
1
2
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
1
1
1
0
1
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
2
2
2
0
0
0
0
0
0
1
0
0
1
2
2
2
0
0
0
0
1
1
0
0
2
2
1
0
0
0
1
0
0
1
2
2
0
0
0
0
0
0
1
0
0
1
0
1
2
0
0
2
2
0
0
0
0
0
0
2
2
1
0
0
0
1
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
2
0
0
0
0
1
0
2
1
2
0
0
2
0
0
0
0
2
2
1
1
0
0
1
2
0
0
0
2
1
0
0
0
0
3
0
0
1
0
3
0
0
2
1
1
2
0
1
0
0
2
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
2
0
1
1
2
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
1
0
1
0
1
0
1
0
0
2
1
0
1
1
0
2
1
0
0
4
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
1
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
2
0
2
1
0
0
0
0
0
0
2
1
0
1
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
2
0
0
0
3
2
0
2
1
0
1
1
2
0
0
0
0
0
0
2
0
1
2
1
1
2
1
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
2
0
2
1
0
0
0
0
1
0
0
2
0
1
0
2
1
2
1
1
0
2
0
0
2
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
1
0
0
2
1
0
0
0
2
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
1
2
0
1
0
2
0
0
0
0
0
1
0
0
1
0
0
1
2
0
2
0
0
2
0
0
0
0
1
0
1
0
0
2
1
0
0
0
0
1
2
0
0
0
1
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
2
1
2
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
1
0
0
2
2
0
0
2
0
0
0
2
2
1
1
1
1
0
1
1
0
0
0
0
0
1
1
0
0
1
2
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
2
1
0
2
2
0
0
0
0
0
0
0
0
1
0
0
1
3
0
0
0
0
1
2
2
0
1
1
0
1
0
0
0
0
0
0
0
0
3
1
1
2
0
1
2
0
0
0
0
1
0
1
1
2
2
0
1
1
8
0
0
0
3
0
0
1
0
2
0
0
0
0
2
0
0
0
2
0
2
2
0
1
2
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
1
1
0
1
0
2
0
0
0
1
2
2
0
0
2
0
6
2
0
0
1
0
2
0
2
0
1
0
0
2
0
1
0
0
0
2
0
0
0
1
1
0
3
1
0
0
0
0
0
3
0
1
0
1
0
0
0
2
0
0
0
0
0
2
0
2
1
0
0
0
1
1
1
0
0
0
2
0
0
0
0
0
0
0
2
0
1
1
1
0
0
0
0
0
1
0
2
1
1
0
1
0
2
1
2
0
0
1
0
0
0
0
2
3
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
2
0
0
2
0
0
0
0
0
0
0
0
2
1
1
0
0
2
2
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
1
0
0
1
0
0
2
0
0
0
0
0
11
2
1
0
0
0
2
3
0
0
1
0
2
0
1
1
0
0
0
1
1
2
0
1
0
4
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
2
0
1
0
0
0
0
0
2
0
2
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
1
0
0
1
0
2
2
0
0
0
1
2
1
1
0
1
0
1
0
2
0
2
2
1
6
0
0
0
2
0
0
0
0
2
1
0
2
0
2
2
1
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
3
1
2
2
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
2
0
2
0
0
1
1
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
2
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
5
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
1
1
1
2
2
0
0
0
0
1
1
1
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
4
0
1
0
1
0
0
1
0
0
0
0
5
0
2
0
2
0
1
0
0
2
2
0
0
2
0
2
5
1
0
0
0
0
0
1
0
5
4
0
0
0
0
2
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
2
1
1
1
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
2
2
0
1
0
0
1
0
0
2
0
0
1
2
1
0
0
0
0
0
0
0
0
1
4
0
0
0
0
1
1
0
1
0
1
2
0
0
0
0
0
1
0
0
2
1
2
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
1
0
0
1
0
0
2
0
2
0
0
0
0
2
2
2
0
0
0
0
0
0
2
1
2
0
1
0
1
0
0
0
1
1
5
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
1
0
3
0
0
0
0
0
2
1
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
2
2
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
3
1
2
1
0
2
2
3
2
1
0
5
0
0
3
0
0
0
1
0
2
0
1
0
2
0
0
0
1
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
3
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
3
0
1
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
4
0
0
1
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
2
2
3
0
0
0
0
0
1
0
0
0
3
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
2
1
0
1
0
0
0
0
2
2
0
0
0
0
2
0
1
2
1
2
0
0
0
2
1
1
0
0
0
0
0
3
0
0
0
3
2
0
0
0
0
4
0
0
0
0
0
1
0
0
1
0
0
0
3
0
0
0
2
0
1
1
1
0
0
2
1
2
2
0
0
1
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
2
0
2
0
0
1
2
0
0
0
1
2
0
0
0
0
0
2
0
0
2
1
0
0
0
1
0
0
2
0
0
0
3
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
2
0
0
2
0
0
0
0
2
0
2
1
0
0
2
2
1
0
2
0
1
0
0
0
0
0
2
1
0
2
0
2
1
1
0
2
0
1
1
0
0
0
1
0
0
1
2
2
0
0
5
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
4
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
3
1
0
0
0
0
2
2
2
0
2
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
1
2
1
0
1
0
2
0
1
5
0
0
1
0
0
1
0
0
0
0
0
2
1
2
2
2
0
2
3
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
1
0
2
0
0
1
2
2
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
1
0
0
0
0
0
1
0
2
0
0
0
0
1
2
2
0
0
3
0
0
0
2
0
1
1
2
0
5
0
0
1
0
0
1
0
1
2
2
0
0
0
1
0
1
3
0
0
0
0
0
1
0
0
0
3
0
0
0
2
1
3
0
5
0
0
0
0
0
2
1
1
0
2
1
0
0
0
0
2
0
0
4
0
1
0
0
1
0
0
1
1
0
0
0
2
2
0
2
2
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
2
1
0
1
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
6
0
0
5
1
0
0
0
1
1
2
0
0
0
2
0
0
0
0
1
0
2
1
0
0
2
0
0
2
2
1
0
0
7
0
0
1
0
0
0
2
0
0
0
1
0
1
2
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
1
0
0
0
0
0
4
0
3
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
1
2
3
0
0
0
2
1
0
0
2
1
0
1
0
0
0
2
0
0
0
0
1
1
2
2
0
2
0
0
2
0
0
0
1
0
0
1
0
0
0
1
0
2
0
0
0
1
1
0
3
0
0
0
1
0
1
0
1
0
0
0
0
2
0
0
0
1
0
1
0
2
0
0
1
0
1
2
0
1
2
0
0
0
1
0
0
0
0
2
1
0
0
0
0
2
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
2
0
0
1
0
0
2
2
0
2
0
3
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
2
0
2
0
1
0
1
1
0
1
0
3
1
0
0
2
1
3
0
1
0
0
1
2
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
2
0
0
2
2
2
1
2
0
0
0
0
2
1
0
2
0
1
0
2
0
0
0
0
0
1
0
0
5
0
1
1
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
2
0
0
0
0
1
1
0
0
7
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
2
1
0
2
0
0
0
3
1
2
0
1
0
0
1
0
2
0
2
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
2
0
1
0
0
1
2
1
2
0
0
2
0
0
2
0
0
0
1
2
2
0
0
0
0
0
0
0
1
1
2
1
3
0
0
2
0
1
0
1
1
0
2
2
2
1
0
0
0
1
1
1
0
0
2
2
2
1
0
0
0
0
1
0
0
1
2
0
2
0
1
0
0
0
0
2
0
3
1
0
0
1
0
0
0
0
0
2
1
1
2
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
2
0
0
1
0
2
0
0
0
0
0
1
1
0
0
2
2
0
2
2
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
2
1
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
1
1
0
2
0
0
0
0
2
0
0
0
2
1
0
0
1
1
0
0
2
0
0
0
1
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
2
0
2
1
0
1
0
0
2
0
0
0
1
0
1
1
0
1
1
0
0
0
0
0
2
3
0
3
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
2
0
0
2
3
0
0
0
1
2
0
0
0
0
2
0
0
2
1
0
0
1
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
1
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
1
0
0
1
2
3
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
2
0
1
0
1
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
2
1
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
2
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
2
5
0
0
2
0
0
0
0
3
1
1
0
0
3
2
0
2
2
0
2
0
3
0
1
0
2
2
0
1
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
2
2
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
6
0
0
1
1
2
0
0
0
0
2
1
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
5
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
1
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
2
1
1
0
0
0
1
2
0
0
0
0
2
0
1
0
0
2
0
0
0
2
0
2
0
0
0
1
0
1
3
2
0
2
0
4
2
0
1
0
1
0
0
2
3
0
0
0
1
0
0
1
1
1
0
0
0
1
0
0
2
0
2
0
0
2
2
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
3
1
0
2
2
0
2
0
0
0
1
2
0
0
2
0
1
0
1
2
2
1
0
0
1
1
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
2
2
0
1
0
1
0
2
0
2
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
2
0
1
1
0
2
1
2
0
0
2
0
0
0
2
0
3
0
0
0
0
0
1
0
0
2
0
0
0
1
1
0
2
2
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
1
2
0
0
2
0
0
2
1
0
2
0
0
2
0
0
1
2
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
2
2
1
0
1
0
2
1
0
0
2
0
0
0
0
2
0
2
0
0
2
0
1
2
0
1
1
2
2
2
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
2
0
1
0
0
1
1
2
0
0
0
1
0
0
1
2
0
2
0
0
2
0
0
0
1
2
0
0
0
1
2
0
2
0
1
1
0
2
0
3
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
2
0
0
0
1
1
0
0
2
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
2
2
0
1
0
1
0
1
1
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
3
3
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
1
1
2
0
0
0
2
0
0
0
0
0
6
2
2
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
6
0
0
1
0
0
2
2
0
0
0
1
0
2
4
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
1
3
1
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
1
2
1
0
0
1
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
6
0
1
2
3
2
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
3
0
0
0
1
0
0
2
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
2
0
1
1
0
0
0
0
2
1
0
0
2
0
2
0
3
0
1
1
0
0
0
0
0
1
1
0
2
0
0
0
4
0
3
3
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
2
0
0
0
1
0
1
0
0
0
0
0
1
0
2
2
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
2
1
0
0
0
0
1
0
2
1
1
1
2
0
1
0
0
0
4
0
3
0
1
0
2
0
0
1
1
1
0
0
0
0
0
0
2
0
1
1
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
2
0
2
1
1
0
2
1
4
2
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
1
0
1
0
2
1
0
0
0
0
2
0
0
0
0
2
0
0
1
0
6
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
1
2
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
2
0
0
1
2
0
0
0
0
0
0
1
0
1
0
1
0
0
0
2
0
1
0
1
0
1
0
0
2
0
0
0
0
0
0
1
1
0
0
1
2
0
0
2
0
2
0
0
0
2
0
1
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
1
2
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
2
0
3
0
2
0
2
0
0
0
3
0
0
1
0
1
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
5
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
2
0
1
1
0
0
2
0
2
0
0
0
2
0
1
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
2
3
2
0
0
0
0
2
3
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
2
2
0
0
0
2
1
1
0
2
0
0
2
0
0
0
3
2
0
1
0
1
0
1
0
1
0
2
0
0
0
0
0
0
0
0
2
0
1
0
1
0
2
0
0
3
0
2
1
1
0
0
1
0
0
2
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
3
0
1
2
0
0
1
2
3
0
1
1
1
0
2
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
2
2
1
0
0
0
2
1
1
2
1
1
1
0
1
3
0
0
0
1
3
0
0
1
0
2
1
1
0
0
0
2
0
2
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
2
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
3
0
2
1
0
0
0
0
2
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
1
1
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
1
1
0
2
2
0
1
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
1
0
0
0
0
2
3
0
1
1
0
1
0
2
2
0
1
2
0
0
0
0
1
0
4
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
3
0
2
0
0
0
1
0
1
0
0
1
0
3
0
0
0
2
2
0
0
2
0
0
0
0
1
0
2
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
1
2
2
0
2
0
0
0
0
1
1
0
0
1
0
0
2
0
0
0
2
0
0
1
0
2
0
0
2
2
0
0
1
0
1
0
0
2
1
0
1
2
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
2
2
0
1
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
2
0
0
2
1
0
0
0
0
4
1
2
0
1
0
2
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
2
2
2
0
2
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
2
3
0
2
2
0
0
0
1
0
0
2
2
0
0
0
2
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
2
2
2
1
2
0
0
1
0
0
2
0
0
0
1
0
1
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
2
1
0
0
2
2
2
1
1
0
0
0
0
1
1
0
1
5
0
0
0
1
2
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
2
0
1
2
0
0
1
0
0
0
2
0
0
0
2
4
0
2
2
0
0
0
1
0
1
0
2
0
2
0
0
1
1
2
0
0
0
1
0
0
2
0
0
3
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
2
1
0
2
1
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
2
5
1
2
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
2
1
3
0
1
0
0
1
0
3
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
1
2
2
2
0
0
0
1
1
1
0
1
2
0
0
0
1
1
0
0
0
0
3
2
1
1
0
1
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
11
0
0
2
0
1
1
0
1
0
2
0
0
1
3
0
0
2
0
1
0
0
0
0
3
0
0
0
0
0
1
2
0
0
0
0
0
9
2
1
0
0
2
1
0
2
0
0
0
0
1
0
0
1
0
0
0
0
2
2
1
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
2
0
1
0
2
0
0
1
0
0
0
0
0
2
0
0
0
1
0
3
0
3
0
1
0
0
0
0
0
0
0
2
1
0
1
0
1
1
1
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
2
0
1
1
0
0
2
0
0
1
0
2
0
0
0
5
0
2
0
0
0
0
0
0
0
1
0
1
2
2
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
1
0
0
1
1
0
0
0
0
0
2
0
1
0
2
2
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
2
2
1
0
0
0
1
1
0
0
0
0
2
1
0
1
0
0
2
0
0
0
1
1
0
2
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
3
2
2
0
0
0
4
0
1
0
0
0
2
0
0
0
0
2
0
0
0
1
1
0
0
0
1
0
0
3
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
3
0
0
1
0
0
0
0
0
0
2
0
0
1
1
1
1
2
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
1
0
0
0
2
2
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
2
0
2
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
1
2
0
0
0
1
2
0
0
2
0
1
0
2
0
1
1
2
0
0
1
1
2
1
0
0
0
0
2
1
0
1
0
3
1
0
0
1
0
1
0
0
0
1
0
0
0
3
0
0
0
1
0
1
2
0
0
2
2
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
4
1
0
0
0
0
1
1
5
1
2
2
2
2
1
0
1
1
1
2
2
0
0
0
0
2
1
2
0
0
0
0
0
1
0
0
2
0
0
0
1
0
2
0
0
0
0
1
0
0
2
0
0
0
0
3
0
1
1
2
1
0
0
0
1
1
0
0
0
0
0
2
2
0
3
1
0
0
0
0
2
0
0
2
1
0
1
0
3
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
2
0
1
2
0
1
0
0
0
0
0
1
0
0
0
1
2
0
0
0
1
2
0
0
0
0
1
1
0
1
0
3
0
0
2
0
0
2
0
0
2
2
2
1
0
0
2
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
1
0
0
2
0
1
1
0
0
0
0
0
0
3
0
2
0
0
2
0
1
0
2
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
1
2
2
0
1
0
0
0
0
1
1
2
0
0
0
1
0
2
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
1
0
1
0
2
1
0
0
0
0
0
0
0
1
2
0
0
2
1
1
1
2
0
1
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
2
4
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
3
2
0
1
1
2
2
0
2
2
0
1
2
0
5
0
1
0
2
0
0
0
0
2
1
0
0
3
2
0
0
1
0
0
2
2
3
1
0
0
0
1
0
0
2
0
2
0
2
0
0
0
0
0
1
0
0
3
2
0
2
0
2
0
0
0
2
0
0
2
0
2
0
0
0
0
0
4
0
2
0
0
0
0
1
1
1
0
0
1
1
0
2
0
1
0
0
2
1
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
4
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
2
0
0
0
2
0
1
0
2
2
1
0
1
0
0
1
1
0
1
0
0
2
1
0
0
0
0
0
0
0
2
0
0
2
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
3
0
1
0
2
1
0
0
2
0
0
0
0
0
2
1
0
0
2
0
2
0
1
0
1
1
0
0
2
1
0
2
0
0
2
1
1
0
1
2
0
1
2
0
0
1
2
1
0
0
1
1
0
0
0
2
0
0
0
2
0
3
5
0
0
0
0
0
2
0
0
0
0
0
1
0
2
1
1
2
1
1
0
0
0
0
0
2
1
0
0
0
0
1
0
1
1
0
3
1
0
1
0
0
0
2
3
0
0
1
0
1
0
0
1
2
0
0
1
0
0
0
0
2
0
0
4
2
10
2
1
2
0
2
1
2
0
0
0
2
0
3
2
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
1
0
1
0
0
1
1
1
2
0
0
0
0
1
0
0
2
0
2
0
1
2
1
0
4
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
2
1
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
4
2
0
2
1
0
0
0
0
0
2
2
0
0
0
0
2
1
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
1
2
1
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
2
0
0
1
1
0
0
3
0
0
0
0
3
0
2
2
0
3
0
0
0
2
2
2
0
0
0
0
1
0
1
0
0
1
0
0
0
1
2
3
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
6
0
0
2
0
1
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
4
0
2
1
0
0
2
0
0
2
0
0
0
1
0
1
1
0
2
0
2
0
2
0
2
0
0
0
0
2
0
0
0
0
2
0
4
0
0
0
0
0
0
2
0
2
0
0
1
0
0
2
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
1
1
3
1
0
2
0
0
2
0
0
0
0
1
2
0
2
1
1
0
0
0
2
2
0
2
0
2
0
0
0
0
0
0
2
0
2
0
1
1
0
3
0
0
0
0
1
0
0
0
1
1
0
0
0
1
2
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
2
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
3
0
0
0
0
0
1
0
0
2
1
0
2
0
0
1
1
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
2
0
0
2
0
2
0
1
2
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
2
0
1
0
0
1
0
2
0
1
0
2
2
0
0
4
2
0
2
4
0
1
2
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
1
0
0
0
0
2
1
0
0
0
0
0
3
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
2
1
0
0
4
0
1
0
3
0
2
1
0
4
0
2
0
0
0
1
1
0
0
0
1
0
2
0
0
1
1
1
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
3
2
0
0
0
0
4
1
0
0
0
0
0
0
2
2
0
0
0
0
2
1
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
1
2
0
0
2
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
2
0
0
0
2
0
2
5
2
0
0
0
2
2
0
0
2
0
0
1
0
1
0
0
0
0
0
1
2
0
2
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
1
0
2
0
1
0
2
2
2
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
1
0
0
1
0
1
0
2
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
1
0
0
0
2
1
0
1
2
0
2
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
1
0
0
0
4
0
0
0
0
1
2
1
0
2
2
0
0
0
0
0
0
2
1
0
1
2
0
0
0
1
0
0
0
2
0
2
2
0
0
0
1
0
1
0
2
1
1
2
2
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
2
2
1
0
2
2
0
3
1
2
0
0
2
2
0
0
0
1
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
2
0
0
1
0
2
0
2
0
1
1
2
2
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
2
2
1
0
0
1
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
1
1
2
1
0
1
0
2
0
1
1
2
1
2
1
0
1
1
0
1
0
2
3
3
0
2
0
0
0
0
0
0
0
1
0
0
2
1
0
2
2
0
0
1
0
0
0
2
0
2
0
0
0
2
0
0
0
2
1
2
1
0
2
0
1
2
0
0
0
2
1
1
1
0
0
0
0
2
1
0
0
0
0
0
0
2
4
0
0
2
0
2
0
0
0
1
3
1
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
2
0
0
1
0
1
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
3
0
0
2
0
0
1
0
2
0
0
0
2
0
2
0
0
0
0
1
0
0
0
2
0
0
2
2
0
4
2
1
0
0
0
3
0
0
0
0
1
2
0
2
1
0
0
1
1
2
0
1
3
1
1
1
0
2
0
0
0
1
2
1
3
2
0
0
1
0
2
2
1
0
0
1
0
2
1
0
0
0
0
1
0
0
1
0
0
1
2
2
2
0
0
2
0
2
0
0
2
2
2
0
0
0
2
0
0
1
0
0
1
0
2
0
1
0
0
2
0
0
0
2
1
0
0
1
0
2
0
0
0
0
2
1
1
0
0
0
0
3
1
1
0
0
0
2
0
6
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
1
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
2
2
3
0
0
0
0
2
0
0
1
0
1
1
2
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
2
0
1
0
2
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
1
2
2
0
0
0
2
0
0
0
0
0
0
1
0
0
5
0
2
0
1
1
0
0
0
1
2
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
2
4
0
0
0
0
0
1
0
0
1
1
1
0
0
0
1
0
3
0
1
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
3
1
0
0
0
2
1
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
1
0
1
1
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
4
0
0
1
1
0
4
0
0
0
0
2
0
2
0
0
0
2
0
0
1
2
0
1
0
2
0
0
2
2
0
0
0
0
0
0
0
2
0
0
1
0
3
0
0
1
0
1
0
2
0
1
4
1
2
2
0
2
0
0
0
0
1
0
0
0
0
2
0
1
0
2
0
0
1
0
0
0
0
0
0
2
2
2
1
2
0
2
2
0
1
2
0
0
0
0
0
2
1
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
3
3
1
0
1
0
1
0
0
0
0
0
0
2
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
3
0
2
2
0
0
0
0
3
0
0
0
2
0
0
0
0
2
2
0
0
0
2
0
1
1
0
0
0
1
1
0
2
0
0
0
0
1
0
0
0
3
0
0
1
1
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
2
0
0
1
1
0
0
0
0
1
0
0
2
2
1
0
0
1
0
0
3
0
0
0
1
0
0
0
0
2
0
2
0
1
1
2
0
0
1
1
2
0
0
0
0
0
4
0
0
0
0
2
0
1
1
0
1
0
3
2
3
0
4
0
1
0
0
2
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
2
2
0
0
0
2
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
3
0
0
2
0
0
11
2
0
0
1
2
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
3
0
1
0
0
2
1
2
0
0
1
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
3
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
2
0
0
2
0
0
0
1
1
0
0
2
0
0
1
0
0
1
0
1
1
0
0
0
2
1
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
1
2
0
1
0
1
1
0
0
4
0
0
0
0
1
0
2
2
0
0
0
0
0
1
0
2
3
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
3
0
0
2
0
0
0
3
3
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
3
0
1
0
0
1
0
1
2
0
0
0
0
1
0
2
0
1
0
0
1
0
0
0
0
0
2
0
1
0
0
1
2
0
0
0
0
2
2
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
2
0
1
0
2
0
0
0
0
0
2
1
0
0
0
2
0
0
0
2
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
1
1
0
0
2
2
1
0
1
1
0
1
1
2
0
5
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
2
2
1
0
2
1
0
2
0
0
0
0
1
0
1
2
0
1
2
1
0
0
1
0
2
0
0
1
2
0
0
0
2
3
0
2
0
0
0
1
0
2
3
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
2
0
0
2
2
2
0
0
0
0
2
2
1
0
0
0
0
0
0
1
1
2
1
1
6
1
0
1
1
0
0
1
1
0
0
0
2
2
2
1
0
2
0
2
0
1
0
0
0
0
0
1
2
2
3
0
0
1
0
1
0
0
1
0
0
1
0
0
0
4
2
2
0
0
0
1
0
2
0
0
2
1
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
1
1
0
0
6
0
1
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
1
0
1
0
0
0
4
0
2
2
0
0
0
0
3
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
1
1
0
0
3
2
0
2
0
1
0
2
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
5
2
0
0
1
0
1
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
3
0
0
0
1
0
0
2
2
2
0
0
2
2
0
0
0
0
0
1
1
0
2
0
1
2
1
1
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
1
0
1
2
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
2
0
0
0
0
1
0
1
1
0
2
0
0
0
2
1
2
2
0
0
0
1
0
2
0
1
0
0
0
0
0
1
1
2
0
2
2
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
2
2
1
2
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
3
0
0
1
0
0
0
0
4
1
0
0
0
0
1
0
0
0
4
0
0
0
0
0
2
0
1
1
1
0
2
0
1
1
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
2
2
2
0
0
2
2
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
2
0
0
2
2
0
0
0
0
2
0
0
0
0
2
0
0
2
2
2
1
2
0
2
0
0
0
3
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
1
1
0
0
1
1
0
2
0
0
0
0
2
0
0
0
0
2
2
0
2
0
0
0
0
0
4
0
0
0
0
1
1
2
1
0
1
0
0
0
1
0
0
0
0
2
2
1
0
0
0
0
1
0
0
1
2
0
2
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
2
2
2
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
1
0
2
1
0
0
2
0
1
2
1
1
0
1
2
2
1
0
1
0
0
4
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
1
1
0
0
0
6
1
0
0
0
3
0
0
0
0
3
2
0
0
2
2
2
0
2
0
0
0
2
2
3
0
0
1
0
0
0
0
0
0
2
2
0
1
1
1
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
2
1
0
1
0
0
0
0
0
1
0
2
2
0
1
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
2
0
0
0
1
1
0
0
0
0
2
2
1
0
0
0
0
2
1
0
0
0
2
0
1
1
0
0
1
1
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
2
0
2
1
0
0
0
0
2
0
0
0
0
0
0
2
3
0
0
2
2
0
1
0
0
1
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
2
0
0
2
2
0
0
1
0
2
1
1
4
0
0
1
0
1
1
0
0
0
0
0
2
0
0
0
2
0
1
0
0
2
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
1
1
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
1
0
2
3
0
1
1
1
1
0
0
0
2
0
0
0
0
0
0
2
2
0
0
3
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
2
0
0
2
0
1
4
1
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
1
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
1
0
1
0
0
0
2
0
2
2
0
1
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
1
1
1
0
0
0
0
1
0
0
1
2
2
0
0
0
0
1
1
0
1
2
2
0
0
0
0
0
2
0
2
0
0
0
1
0
0
2
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
1
2
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
2
0
0
0
2
0
3
2
0
0
0
0
0
0
1
0
2
2
0
0
2
2
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
1
1
0
0
2
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
2
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
1
2
0
0
0
2
0
0
0
0
0
1
0
0
0
1
1
2
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
1
0
0
0
2
2
2
0
2
0
0
0
0
0
0
0
0
1
1
0
3
2
0
0
1
0
0
2
0
1
1
0
0
0
0
2
0
2
0
0
0
2
0
0
2
0
0
0
0
3
0
3
0
0
0
0
3
0
2
0
0
1
2
1
2
0
2
0
0
0
0
0
0
1
0
1
3
0
1
0
2
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
1
0
0
2
0
0
0
0
2
1
3
1
0
1
0
0
1
0
0
0
1
0
0
0
0
1
1
0
2
0
2
0
2
0
0
2
0
0
0
0
0
0
2
2
2
0
1
0
0
0
0
1
1
0
1
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
2
1
0
0
1
1
1
0
2
0
1
0
2
0
1
1
2
1
2
0
0
3
0
2
0
2
0
1
0
0
2
0
0
0
0
1
0
0
0
1
0
2
0
0
2
0
0
0
0
1
2
1
0
0
0
1
0
1
0
0
2
0
0
0
3
0
0
2
0
0
0
2
1
1
0
2
0
2
0
2
2
1
0
0
0
2
1
0
0
0
1
0
0
0
0
1
0
0
0
2
0
1
1
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
2
0
2
0
1
0
2
0
0
0
2
2
0
0
0
1
1
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
2
0
1
0
2
2
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
1
0
4
0
0
0
0
2
0
0
0
1
0
0
0
2
2
0
1
0
1
2
0
0
1
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
1
1
0
0
0
2
0
0
1
0
1
0
0
0
3
1
1
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
1
2
0
10
0
0
0
2
0
0
2
1
2
0
1
2
2
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
1
1
0
2
0
0
0
2
0
1
0
0
2
2
0
0
0
1
0
2
0
0
0
3
0
0
0
0
0
3
3
1
1
1
0
1
1
1
0
1
0
0
0
3
2
0
2
0
0
0
0
0
1
0
2
2
0
0
2
0
0
2
1
3
1
2
0
2
1
0
0
0
2
0
0
0
1
0
0
0
2
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
2
0
0
2
1
1
2
2
0
0
1
0
1
1
0
0
0
0
2
1
0
0
1
0
0
2
0
0
0
0
1
0
4
2
0
0
0
0
1
0
0
0
1
2
2
2
0
1
2
2
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
1
1
2
0
0
1
0
0
7
0
0
0
2
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
2
2
0
1
2
0
1
0
2
0
1
1
0
0
1
2
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
1
0
1
0
0
1
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
4
2
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
1
0
0
0
1
2
2
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
1
0
0
0
1
1
1
0
0
0
1
0
1
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
2
0
2
0
0
0
1
2
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
4
1
0
1
3
1
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
3
0
0
0
1
0
2
0
2
1
0
0
2
0
1
2
0
0
0
0
0
0
0
0
1
0
1
1
0
0
2
1
1
2
0
0
0
1
0
2
0
0
1
0
0
1
2
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
2
0
0
0
1
0
2
1
0
0
0
4
2
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
3
1
0
2
2
0
0
0
1
0
7
2
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
2
0
0
0
1
0
1
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
3
0
0
1
1
1
3
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
2
1
0
2
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
2
2
0
0
2
1
2
0
0
0
0
0
0
0
2
2
0
1
2
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
1
1
0
2
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
2
0
1
0
1
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
2
0
2
0
0
1
1
1
0
0
0
0
0
0
0
2
2
0
2
1
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
2
0
0
2
1
0
0
2
1
0
0
0
0
1
0
0
1
0
0
0
4
5
0
0
0
2
0
0
1
0
2
0
0
2
0
1
0
0
1
0
0
3
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
1
0
1
0
2
0
0
0
2
0
0
0
0
0
2
2
0
2
0
1
0
0
0
1
0
2
3
0
1
1
0
0
0
0
2
0
2
0
0
0
0
2
0
0
2
0
0
1
0
1
0
1
2
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
2
0
1
0
1
1
0
0
2
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
5
0
1
3
2
0
1
0
1
1
1
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
1
1
0
3
2
0
2
0
1
1
1
2
1
0
1
0
2
0
0
0
0
1
0
0
0
0
1
2
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
1
3
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
1
0
1
0
0
2
1
0
2
0
0
0
3
0
0
0
0
0
0
0
0
1
0
2
2
0
1
3
0
0
0
0
2
0
2
3
0
1
0
0
0
0
0
0
0
0
0
1
2
0
1
1
2
0
0
2
0
2
0
1
1
0
0
3
0
1
0
0
1
0
0
0
2
1
0
2
0
1
0
0
2
2
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
1
2
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
1
2
0
1
0
1
1
0
2
0
1
2
2
2
0
0
1
2
2
0
0
2
2
0
1
1
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
2
1
0
1
0
0
0
2
0
0
2
0
0
1
0
0
2
0
2
0
0
0
0
0
1
2
0
0
3
0
0
1
2
2
2
1
0
0
0
0
0
1
0
0
0
0
1
0
1
1
2
1
0
0
3
0
1
0
0
0
0
1
0
1
1
0
2
2
0
0
0
4
0
0
1
2
0
1
0
0
2
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
2
1
2
0
0
1
0
0
1
0
2
1
0
0
0
2
0
0
2
0
0
1
0
1
0
2
1
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
2
1
0
0
2
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
1
0
1
0
0
0
2
0
0
0
2
0
2
0
2
0
1
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
2
0
0
1
1
0
0
0
0
2
0
2
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
2
2
3
0
2
0
2
0
2
0
0
2
0
1
1
1
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
2
2
1
0
0
0
2
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
2
2
0
2
0
1
0
1
0
0
0
0
1
4
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
2
1
2
1
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
2
0
1
3
1
0
0
1
1
2
0
2
0
1
2
0
0
1
0
0
0
0
0
1
2
0
3
0
0
1
0
0
0
0
0
0
0
0
0
1
2
3
0
0
0
0
0
1
0
2
0
0
2
2
0
1
1
1
1
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
2
0
2
0
6
0
0
0
2
0
0
0
1
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
1
1
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
3
0
1
0
1
2
0
3
0
0
0
0
0
0
0
0
2
1
0
1
0
2
0
0
2
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
3
2
0
2
0
2
2
1
0
0
0
2
0
0
0
0
0
0
0
1
0
1
1
0
2
0
0
0
0
0
1
3
0
0
0
0
0
0
1
0
1
0
3
0
0
0
0
0
0
0
0
0
2
2
0
1
0
1
1
2
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
2
0
1
0
2
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
4
1
1
0
0
2
0
0
0
0
0
2
0
0
0
2
0
1
1
0
0
0
2
0
2
0
1
2
1
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
3
0
2
1
2
0
2
2
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
2
1
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
2
1
0
1
0
0
0
0
0
2
0
0
1
0
1
2
0
0
1
0
2
0
2
0
1
2
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
2
1
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
1
0
3
2
1
0
2
1
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
1
0
4
0
1
1
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
1
0
1
0
1
2
2
1
0
2
0
0
0
0
0
5
0
0
1
0
1
0
0
2
1
0
0
0
1
1
0
1
1
1
0
0
0
0
0
2
0
0
3
1
2
0
0
2
0
0
0
0
0
3
1
0
0
2
0
0
0
0
3
1
0
1
1
2
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
1
0
0
2
0
1
1
1
0
0
2
0
1
0
2
1
0
0
0
0
2
1
0
1
0
0
0
0
1
2
2
0
0
2
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
1
2
0
1
0
0
0
2
0
1
0
1
0
0
1
1
0
0
2
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
1
0
2
3
0
3
0
0
0
0
1
0
1
0
0
0
0
0
0
1
2
0
0
1
0
2
2
0
1
0
0
0
0
0
0
1
0
0
2
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
2
2
0
1
0
1
1
7
0
2
2
2
0
0
0
1
0
1
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
5
0
2
1
0
0
2
1
0
0
0
1
0
1
1
0
0
0
0
2
1
1
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
2
0
0
0
2
0
2
2
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
3
0
0
0
0
0
1
2
0
0
0
0
1
0
0
1
0
2
1
0
0
0
1
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
1
2
1
0
0
0
0
2
0
0
0
1
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
2
0
1
2
2
1
0
2
0
0
2
0
0
0
0
2
0
3
0
1
2
0
0
0
0
0
0
2
0
0
0
1
3
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
3
2
1
0
2
0
1
6
0
0
0
1
0
0
1
0
2
0
1
0
0
1
1
0
1
0
1
0
0
0
0
0
3
0
0
0
2
0
0
0
0
1
0
0
1
0
2
0
0
0
0
2
0
0
2
0
1
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
1
2
1
0
3
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
2
2
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
2
1
0
2
1
1
2
0
0
0
2
0
2
0
0
0
1
0
0
1
0
0
0
0
0
1
2
2
2
2
0
1
0
1
0
2
0
1
2
0
1
0
0
0
2
2
1
1
2
0
0
2
0
1
0
0
0
0
0
1
0
0
2
0
2
3
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
6
1
1
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
2
2
0
3
0
2
1
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
2
0
1
0
0
1
0
0
0
2
0
2
0
0
0
1
0
2
0
1
1
2
0
0
3
2
0
2
0
1
1
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
1
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
1
0
1
0
1
0
0
2
0
0
0
0
0
2
0
0
1
1
2
0
1
2
0
2
0
2
0
0
0
0
2
0
0
0
1
2
1
0
1
0
5
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
2
0
4
0
0
1
0
0
1
2
0
4
0
0
1
0
0
0
0
0
2
1
2
2
0
0
1
0
0
0
2
0
1
0
0
0
0
1
1
1
1
2
0
1
0
0
0
2
3
0
0
0
2
2
0
1
1
2
2
3
2
0
1
0
1
1
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
2
1
0
1
0
3
2
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
3
1
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
1
0
2
0
2
2
0
0
0
2
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
1
0
2
1
0
0
0
2
0
2
1
0
0
0
2
0
2
2
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
1
2
4
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
1
1
6
0
0
0
0
0
2
1
0
0
0
0
1
2
0
7
1
0
0
2
1
0
0
2
2
0
0
1
0
0
1
0
0
2
1
1
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
4
0
0
0
0
2
0
2
0
2
0
0
1
0
1
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
1
0
0
0
2
0
0
0
1
1
1
0
0
0
0
1
2
0
0
2
0
0
0
0
0
1
2
0
2
0
1
0
0
0
0
1
0
1
1
3
2
1
2
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
2
1
0
0
1
2
0
2
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
2
0
2
0
0
0
2
0
0
5
0
2
0
0
2
0
0
0
2
3
0
0
2
1
0
0
0
1
1
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
3
0
0
0
1
0
1
0
0
1
0
0
0
2
0
0
0
2
0
1
0
0
0
3
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
1
2
0
1
0
0
1
2
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
1
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
1
1
0
1
2
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
5
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
2
3
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
1
2
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
3
0
1
0
0
0
1
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
2
1
0
0
1
1
0
1
0
1
0
2
2
2
0
2
0
2
2
0
2
0
0
0
2
2
0
0
2
4
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
3
2
0
1
0
2
0
0
1
2
0
0
0
0
3
2
2
0
0
1
0
2
0
2
0
0
0
0
1
0
0
2
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
1
0
1
1
0
4
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
1
2
0
1
2
0
0
0
0
2
1
0
0
0
0
0
2
0
0
1
0
0
1
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
2
0
0
2
0
2
1
1
0
0
2
1
0
0
4
0
0
0
1
0
0
0
2
1
0
0
0
1
0
0
0
1
0
0
0
0
1
2
1
5
1
1
2
2
0
0
0
2
3
0
2
0
0
0
2
2
1
1
0
1
2
0
0
0
0
0
1
0
2
2
0
0
2
1
2
0
0
1
2
2
0
2
3
0
0
1
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
2
3
1
0
0
0
0
0
0
1
0
2
0
0
0
2
1
2
0
2
0
1
0
0
2
1
2
1
0
0
0
0
1
0
0
2
1
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
1
0
0
2
0
0
0
0
2
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
4
2
0
1
0
0
1
0
0
3
2
2
0
2
2
1
0
0
2
0
1
2
3
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
1
1
1
2
0
0
0
1
0
2
0
0
2
0
0
0
1
0
2
0
2
1
0
0
0
0
4
0
0
2
0
0
0
2
0
0
1
0
1
0
1
0
0
2
0
2
2
0
0
3
0
0
2
0
1
2
0
0
0
2
2
0
1
0
0
0
0
0
2
3
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
1
0
0
0
0
0
3
0
2
1
0
1
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
1
0
0
2
0
1
0
3
1
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
2
1
1
1
1
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
2
1
1
0
0
0
3
2
1
2
0
0
0
2
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
2
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
2
0
1
1
0
0
2
0
2
0
2
2
0
1
0
0
0
1
1
1
0
2
0
0
2
0
0
0
1
1
0
1
0
0
0
0
2
0
2
0
0
0
0
0
2
1
0
0
3
0
0
1
2
0
0
1
0
0
0
0
0
1
0
0
2
0
0
2
0
0
4
3
0
1
0
0
0
0
0
0
2
0
1
1
0
3
0
0
0
1
0
2
0
1
0
2
1
0
0
1
0
0
2
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
1
2
0
0
1
2
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
2
0
0
1
2
0
0
0
2
0
1
0
0
1
1
4
3
0
2
0
0
0
2
0
0
1
1
0
1
0
0
2
0
4
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
2
3
0
2
0
2
0
2
0
2
0
0
0
0
0
0
2
2
0
0
2
2
0
0
1
0
1
0
2
0
0
1
0
1
1
0
1
0
0
0
1
1
0
0
1
0
0
0
0
2
0
2
1
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
3
2
0
0
0
1
0
4
0
2
2
0
0
1
0
0
0
0
0
2
2
0
1
1
0
2
0
0
0
2
1
0
0
1
1
0
0
2
0
2
2
1
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
1
1
0
0
2
2
0
0
0
0
0
0
2
0
2
0
2
1
0
0
0
0
0
0
0
2
3
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
1
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
3
1
2
0
0
0
0
0
2
2
1
1
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
2
0
1
2
0
0
2
4
0
0
2
0
1
0
2
1
2
0
1
0
1
0
0
0
0
1
0
0
1
0
2
0
1
0
0
0
1
0
1
2
0
0
1
2
1
2
2
0
2
0
0
0
1
0
0
0
0
0
0
2
0
1
2
1
0
0
1
0
2
0
0
0
2
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
2
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
1
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
1
1
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
4
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
3
1
1
0
0
0
0
0
0
2
0
0
0
2
0
0
1
2
0
2
0
1
0
0
1
0
0
0
2
2
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
4
2
0
0
0
1
0
2
1
1
0
2
0
2
3
0
2
1
0
0
0
4
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
2
0
0
1
1
0
0
2
1
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
1
1
0
0
0
1
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
2
2
1
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
2
0
0
1
0
1
0
2
0
3
1
2
0
2
2
0
0
0
1
0
0
0
1
0
0
0
3
0
2
2
3
2
0
0
0
2
0
0
0
2
2
1
0
1
0
0
2
2
2
0
0
1
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
1
0
2
1
2
0
0
0
0
1
2
1
1
2
0
1
0
0
2
1
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
1
4
1
0
1
1
0
0
2
1
0
1
0
2
0
0
1
0
0
2
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
3
2
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
2
0
2
1
0
0
0
1
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
2
1
0
1
2
1
0
3
0
1
0
0
0
0
2
0
2
0
0
1
2
0
0
0
0
3
0
1
0
0
0
0
1
0
0
0
0
0
3
0
0
0
2
0
0
0
1
0
0
0
0
0
0
4
0
0
0
2
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
2
0
1
1
1
1
2
0
0
2
0
0
0
1
0
2
1
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
2
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
2
0
1
0
1
0
0
1
0
0
1
0
2
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
2
1
2
0
0
0
0
0
0
2
2
1
0
1
0
0
0
0
1
2
1
0
0
0
2
0
0
1
0
0
2
1
0
3
3
0
0
2
3
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
1
1
0
0
0
0
1
0
1
0
0
0
0
1
0
1
1
0
1
0
0
2
0
0
1
0
0
2
0
0
1
0
0
2
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
2
1
1
0
0
0
0
0
0
3
2
0
2
0
2
0
0
0
0
1
2
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
1
2
0
1
1
1
0
1
0
0
2
2
2
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
1
2
1
2
0
1
1
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
1
1
0
2
2
0
0
0
1
0
0
0
1
2
0
0
1
2
0
1
2
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
1
1
2
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
1
2
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
2
2
0
0
1
0
1
2
0
2
1
0
1
0
1
0
1
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
1
1
1
0
0
0
0
3
1
0
0
1
0
2
0
0
1
3
0
0
0
0
2
1
2
0
0
0
3
0
0
2
1
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
1
1
2
0
1
2
2
0
0
1
0
0
2
1
0
0
0
2
0
0
0
0
1
0
0
2
0
2
1
0
0
0
2
0
2
0
0
0
0
1
0
0
0
1
0
0
4
2
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
1
0
0
2
0
1
1
2
1
0
0
0
0
3
0
0
0
0
2
1
0
3
1
0
2
0
0
0
0
0
0
2
0
0
2
2
2
1
0
0
2
0
0
0
0
0
0
1
1
1
0
2
0
2
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
2
1
0
0
0
2
1
0
0
1
1
0
1
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
1
2
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
1
3
0
2
0
0
2
0
0
0
0
2
1
0
0
0
1
0
0
2
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
2
0
0
1
0
1
4
1
0
0
0
0
2
2
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
3
0
0
0
1
0
0
0
0
1
0
0
3
0
1
0
0
0
0
0
0
2
0
0
0
2
0
2
1
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
1
2
0
0
0
1
1
1
0
0
0
0
3
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
3
2
1
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
2
1
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
1
2
2
0
0
0
1
2
0
1
0
0
0
0
0
2
0
1
0
0
1
1
6
0
2
0
0
1
0
0
2
0
0
0
1
2
0
0
2
2
1
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
2
1
0
0
0
0
1
0
1
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
1
0
0
2
0
0
2
0
0
0
0
4
0
2
0
3
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
2
2
0
0
0
0
2
0
2
0
0
1
1
0
0
2
0
2
0
0
0
0
0
0
2
2
0
0
0
0
2
2
2
0
1
2
0
0
0
0
1
0
0
1
0
1
0
0
2
0
2
1
2
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
1
0
2
0
0
0
0
1
0
0
1
0
0
0
0
2
1
0
0
0
2
1
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
1
1
1
0
0
1
0
0
0
6
0
0
0
2
0
1
0
0
0
0
0
0
2
2
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
1
0
2
1
0
1
0
3
0
3
2
0
0
0
0
1
0
1
0
2
0
0
3
0
2
0
1
1
1
0
1
2
0
1
1
0
1
0
0
1
1
1
1
2
0
0
2
1
0
0
2
0
1
0
0
0
0
0
0
0
1
1
1
2
0
0
0
0
1
0
0
0
0
0
4
0
0
1
1
1
0
1
0
2
0
1
0
1
0
0
2
1
2
1
0
0
0
0
0
2
2
0
0
1
1
1
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
1
2
1
0
0
0
0
0
0
2
0
0
0
1
3
0
0
2
0
2
0
0
2
1
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
1
3
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
1
1
0
1
0
0
0
3
0
0
1
1
0
0
0
0
1
0
1
2
0
0
0
2
3
2
0
0
2
1
0
0
0
0
1
0
2
0
2
0
0
0
1
0
1
0
0
0
1
1
2
2
3
1
0
2
0
0
2
1
0
0
0
2
1
0
2
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
2
1
0
1
0
2
0
0
2
0
1
1
1
0
0
1
0
1
0
0
1
4
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
1
0
0
0
0
2
0
0
2
0
1
0
2
0
0
0
3
0
1
0
1
3
0
0
1
2
1
0
0
0
0
0
0
1
1
2
1
0
2
2
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
1
0
0
0
0
0
1
2
1
1
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
1
0
0
0
1
1
0
1
1
2
2
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
2
2
2
0
0
0
2
0
0
4
1
0
1
0
5
0
2
1
0
0
0
1
4
2
1
2
0
1
2
2
0
1
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
3
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
2
0
2
2
0
0
0
0
0
0
0
2
2
2
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
2
2
2
0
0
1
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
1
0
0
0
1
2
0
1
2
2
0
1
0
2
2
0
0
0
1
0
0
2
0
1
1
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
1
0
1
2
0
1
1
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
1
1
1
0
3
0
2
1
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
2
1
0
1
1
8
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
3
0
1
0
1
3
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
2
1
3
0
0
2
0
0
0
1
2
0
0
0
0
0
1
0
0
1
0
0
0
0
2
1
1
0
1
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
3
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
1
0
3
0
1
0
2
0
1
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
1
2
2
0
0
0
0
0
0
0
2
0
0
0
3
2
1
2
0
1
0
0
0
2
1
0
2
0
0
0
2
1
0
0
0
0
1
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
3
0
0
0
1
0
2
2
0
0
0
0
2
1
1
0
1
4
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
2
0
0
0
2
6
0
0
0
1
0
0
0
1
1
0
0
2
0
1
0
1
0
0
0
0
0
0
0
2
1
0
2
1
0
0
0
1
0
0
0
0
0
0
0
3
0
0
2
0
0
1
1
0
2
0
2
1
1
2
0
1
2
2
1
1
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
1
1
2
0
0
0
2
0
1
0
2
0
1
2
0
2
2
0
3
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
1
0
0
3
0
0
0
0
2
1
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
2
0
0
0
2
1
0
0
1
0
1
2
3
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
1
0
1
0
0
2
1
0
0
2
0
1
0
2
0
2
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
1
0
0
0
0
1
0
2
0
0
0
0
3
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
1
2
0
0
0
0
1
2
0
2
0
2
2
0
1
0
0
2
0
1
0
0
1
1
1
0
0
2
2
2
0
1
2
0
0
0
0
0
1
1
0
0
3
2
0
0
1
0
1
0
0
2
1
2
3
0
0
1
1
0
1
2
2
0
0
2
2
1
0
3
2
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
1
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
2
3
2
1
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
1
1
0
0
1
0
2
0
0
1
0
0
2
1
0
0
0
0
0
0
0
2
0
1
1
1
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
2
0
2
2
0
0
0
2
2
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
1
0
1
2
0
1
0
1
0
0
1
0
0
4
0
0
0
1
0
0
0
1
0
0
3
0
0
0
1
2
2
1
0
0
2
1
0
0
0
0
1
0
0
1
0
0
2
0
0
2
0
2
1
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
2
0
1
0
0
0
2
0
0
0
0
0
1
2
2
0
2
2
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
5
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
2
1
0
0
1
0
2
0
0
2
0
3
0
0
0
1
0
0
0
1
1
0
1
0
0
2
1
0
0
0
1
2
2
2
1
0
0
2
0
2
2
2
0
0
0
2
0
0
1
2
0
0
1
0
0
0
0
1
2
0
1
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
2
0
0
1
0
0
1
1
1
2
0
0
2
0
0
0
0
0
0
0
2
2
1
2
1
0
0
0
0
0
0
2
0
1
1
0
2
0
0
2
0
1
0
0
0
1
0
0
0
0
3
0
1
1
0
0
1
1
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
3
0
1
0
0
0
2
0
3
1
2
0
1
0
1
0
1
1
2
0
0
0
0
0
2
0
0
2
1
0
0
0
2
0
0
2
2
0
0
0
3
0
0
1
0
0
0
2
1
2
0
0
2
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
4
0
0
0
0
0
2
0
0
0
1
0
0
0
1
1
0
0
0
0
2
0
1
2
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
2
0
0
1
1
0
0
0
1
1
1
0
2
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
1
0
1
0
1
1
0
2
2
1
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
2
2
0
0
0
0
0
2
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
1
2
0
0
0
0
2
0
2
0
0
0
2
1
0
0
0
0
1
1
2
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
2
0
3
1
2
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
1
2
0
0
1
0
0
0
0
0
0
2
1
0
2
2
1
1
0
0
0
0
4
0
0
1
0
0
0
1
0
0
2
0
2
1
0
0
0
1
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
1
1
0
0
2
2
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
3
0
0
0
2
0
1
0
1
2
0
2
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
1
1
0
0
2
2
2
0
0
2
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
2
1
2
2
0
0
2
0
2
0
0
0
0
0
0
1
1
2
0
2
2
2
0
0
1
0
0
2
0
0
1
0
0
0
1
0
0
2
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
2
0
4
0
0
0
1
0
2
0
0
0
0
2
0
2
0
2
0
1
0
0
0
0
0
0
4
0
0
2
0
2
0
0
0
2
0
0
0
1
1
0
1
0
2
0
0
2
0
0
0
0
4
1
0
1
2
0
2
2
1
2
0
0
0
0
0
1
0
1
1
2
0
0
1
0
0
2
0
0
4
1
0
1
0
0
0
0
2
1
0
0
0
0
0
2
0
2
1
0
0
2
2
0
0
3
2
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
1
0
0
0
2
1
0
2
1
2
1
0
0
0
0
1
2
0
0
2
0
1
2
0
0
0
0
1
0
0
0
0
0
0
4
2
0
0
1
0
2
0
2
0
0
0
0
0
1
1
1
2
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
2
0
0
1
2
0
0
2
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
4
0
3
0
0
0
0
1
0
0
0
2
0
0
2
0
2
0
0
0
0
3
0
0
0
0
1
0
3
0
2
1
0
0
1
0
0
0
1
0
1
2
0
0
1
0
0
1
0
2
0
2
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
2
1
2
1
0
2
0
0
0
0
4
0
1
0
1
1
0
0
1
8
2
0
0
0
0
2
0
0
0
1
0
0
1
1
3
0
1
0
0
2
0
0
0
0
0
2
2
2
1
0
1
0
1
2
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
1
0
0
2
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
2
1
0
2
0
0
0
3
0
1
1
2
0
0
0
0
0
0
0
1
0
0
2
2
0
2
1
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
2
1
0
2
2
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
2
3
0
1
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
2
0
0
2
2
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
4
0
1
1
0
1
0
0
0
0
1
1
0
2
3
2
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
1
2
1
0
0
3
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
2
0
0
1
0
1
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
2
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
1
0
0
2
1
0
1
0
0
1
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
2
1
0
2
0
0
0
0
1
0
0
1
0
1
0
0
2
1
0
1
0
0
0
4
0
0
0
0
0
0
1
3
0
0
1
0
0
0
1
1
0
0
2
0
0
1
0
1
2
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
2
0
1
0
2
0
2
2
0
0
0
2
0
0
0
0
0
2
0
0
0
3
2
0
0
0
0
0
2
2
0
0
1
1
2
1
0
0
0
0
0
1
1
0
0
3
1
2
2
1
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
3
0
2
0
0
0
1
0
2
0
2
0
0
2
0
0
0
0
0
2
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7
1
0
2
0
2
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
1
2
1
0
2
0
0
1
0
0
1
0
0
3
0
1
1
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
1
1
2
1
2
0
1
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
1
1
2
0
0
0
0
0
2
0
1
2
0
2
2
2
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
1
2
0
0
0
1
0
2
0
0
0
0
1
0
1
0
0
2
2
0
0
0
1
1
1
0
1
0
2
2
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
1
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
1
0
0
0
0
3
0
1
2
0
0
2
2
0
0
0
0
0
0
1
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
2
0
1
0
1
2
0
1
0
0
0
0
0
1
0
0
0
1
0
2
1
0
0
1
0
0
0
0
0
2
2
0
0
1
0
0
1
0
2
1
0
0
0
0
0
0
2
2
2
2
1
0
0
0
1
0
1
1
0
2
0
0
1
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
1
0
0
0
0
0
1
2
0
2
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
1
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
3
2
0
2
1
0
1
1
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
2
0
0
1
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
1
2
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
1
2
6
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
1
0
0
0
0
0
0
1
1
1
2
1
0
1
0
0
0
2
0
3
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
2
1
1
0
0
2
2
1
3
0
0
0
0
0
2
0
2
0
0
0
0
0
1
2
2
0
0
0
0
1
0
1
0
0
1
2
0
0
2
1
0
2
0
1
0
0
3
0
1
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
2
1
0
2
0
0
1
1
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
2
0
1
2
1
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
1
0
1
0
2
0
0
0
0
0
2
0
0
4
2
0
0
2
0
0
2
2
0
2
0
0
0
0
1
0
0
1
2
0
0
2
0
0
1
0
2
2
0
0
0
0
0
2
1
0
0
2
1
0
0
1
1
0
1
0
2
0
0
0
0
1
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
2
2
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
2
0
2
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
2
1
1
1
2
0
1
0
0
0
0
2
0
1
0
0
0
0
0
2
1
0
0
0
0
2
2
1
0
0
1
1
0
0
0
2
0
0
0
1
1
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
3
0
0
0
2
0
0
3
2
0
2
0
0
2
2
2
0
0
1
2
2
1
1
0
0
2
0
0
2
0
3
0
0
2
1
0
3
0
0
0
2
0
0
0
0
1
1
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
1
0
0
0
0
0
3
0
1
2
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
1
0
2
0
0
0
0
0
1
2
0
0
0
1
0
4
0
0
0
0
2
0
0
2
0
0
1
0
1
1
0
0
0
2
2
2
0
3
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
1
2
0
2
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
2
2
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
2
0
1
2
0
0
1
0
2
0
0
0
0
0
0
0
3
1
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
1
1
0
2
1
1
0
0
0
0
2
0
0
0
0
3
0
0
1
0
0
0
0
1
2
0
2
0
0
0
0
0
1
0
0
0
2
0
2
0
0
2
0
0
2
0
2
0
0
2
0
2
0
0
0
0
0
3
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
1
0
0
1
0
0
0
0
0
0
1
0
2
3
1
0
1
2
0
0
0
0
1
0
2
1
0
0
0
1
0
1
0
0
0
0
2
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
2
3
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
3
1
0
0
0
0
0
0
1
1
0
2
2
2
2
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
1
0
1
2
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
2
0
0
2
0
0
3
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
2
0
2
0
0
0
0
0
0
3
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
5
0
0
3
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
2
1
0
0
2
0
0
0
1
0
0
0
0
0
2
2
1
0
0
1
1
2
0
0
0
0
0
0
0
0
2
2
0
2
0
2
1
0
0
0
0
1
2
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
2
2
1
0
1
2
1
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
1
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
1
2
2
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
1
2
3
0
0
0
1
0
0
0
0
0
0
2
1
1
0
0
0
0
0
1
2
1
0
2
0
0
0
0
0
0
0
3
0
2
0
1
0
1
0
0
2
4
0
0
0
2
0
0
2
1
0
1
1
0
2
0
0
2
2
0
0
0
1
2
0
0
0
0
2
0
0
0
1
0
0
0
0
1
1
0
0
2
2
0
2
1
0
1
0
2
0
0
0
0
0
0
1
2
2
0
2
0
0
0
0
1
2
0
1
0
0
0
0
3
0
2
0
0
1
0
2
1
1
0
0
1
0
2
1
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
2
0
2
2
0
0
0
0
0
0
3
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
1
1
2
0
0
0
0
0
2
0
0
0
1
0
1
2
5
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
1
0
0
0
0
3
1
0
1
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
2
2
1
0
0
1
0
0
0
2
0
0
1
1
0
2
0
1
0
2
2
2
0
0
0
0
0
0
1
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
2
0
0
3
0
0
2
1
0
0
2
0
0
2
0
0
0
1
0
1
2
0
0
0
0
1
1
0
1
2
0
0
2
2
1
2
2
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
3
1
1
1
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
2
0
0
0
0
0
1
0
1
0
0
1
2
0
0
0
2
0
0
0
0
2
0
0
2
3
2
0
0
0
0
1
2
0
1
0
0
2
2
0
0
2
1
0
0
0
0
0
0
1
0
0
2
1
0
0
2
0
2
0
2
0
0
0
0
2
1
0
0
0
0
1
0
2
2
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
1
2
1
0
0
1
0
0
1
0
2
2
0
2
2
0
0
0
2
0
1
0
0
0
0
3
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
1
0
1
0
1
0
2
0
2
2
0
0
0
0
0
1
0
0
0
1
0
0
10
0
0
0
0
2
0
2
0
3
1
1
2
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
1
0
1
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
1
0
1
0
1
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
1
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
1
0
0
0
0
1
2
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
1
0
2
0
3
1
0
0
2
0
1
0
1
1
3
0
0
1
1
1
0
0
0
2
3
0
0
0
0
0
0
1
2
0
0
0
1
0
0
2
0
0
1
0
1
0
1
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
2
2
2
1
0
0
1
0
1
2
0
2
1
0
2
1
2
1
0
0
0
1
1
0
0
0
0
0
0
2
2
1
2
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
1
0
2
0
0
1
0
0
0
1
0
3
0
0
0
0
2
2
3
0
0
0
2
0
0
1
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
1
2
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
1
0
0
2
0
0
0
2
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
2
1
0
0
1
0
1
0
2
2
2
0
6
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
1
1
1
0
0
0
0
2
0
1
2
0
1
0
1
0
2
0
1
3
0
2
0
0
0
1
2
2
0
2
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
2
0
0
1
0
1
6
0
0
0
1
0
0
0
1
1
0
1
1
0
1
0
0
0
0
1
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
2
2
1
2
0
0
2
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
6
2
2
0
1
2
0
1
2
0
1
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
2
0
0
0
1
5
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
2
1
0
1
2
0
0
0
0
0
2
1
0
2
3
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
1
3
2
0
0
0
0
2
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
2
0
0
0
0
2
2
2
0
0
0
0
1
0
0
2
2
4
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
1
0
0
0
2
0
0
1
0
0
1
0
2
1
0
1
0
0
0
0
1
1
1
0
2
0
0
1
6
1
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
2
0
0
2
1
0
0
0
0
0
3
0
1
0
0
1
2
1
2
0
1
1
1
0
0
0
2
3
2
2
0
2
0
1
1
4
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
1
1
0
0
1
0
0
1
2
0
0
2
2
1
0
4
1
1
0
0
2
1
0
2
0
0
1
2
1
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
2
0
0
0
0
0
2
2
2
2
1
0
2
2
0
0
2
0
0
0
0
0
0
2
2
1
1
0
0
0
1
0
1
1
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
1
0
0
2
0
2
1
0
0
2
2
0
0
0
0
0
2
0
3
2
0
0
1
0
0
0
1
0
2
0
0
1
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
1
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
1
2
2
2
0
0
0
0
1
0
0
0
1
0
0
2
0
0
2
2
1
0
0
0
0
2
0
2
1
0
0
1
0
0
0
0
0
1
0
2
0
0
3
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
3
0
0
2
0
0
0
0
2
0
0
2
2
1
0
0
1
0
0
1
2
0
0
0
0
0
2
0
0
0
0
2
1
0
1
0
1
2
2
0
0
0
2
0
0
1
0
1
1
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
3
0
0
4
0
2
0
0
0
0
1
0
2
2
0
0
1
1
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
2
1
1
2
0
1
0
0
0
0
0
2
1
0
0
0
1
2
1
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
3
0
0
1
0
1
1
1
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
1
0
0
0
2
0
2
1
0
1
1
0
0
1
0
3
0
0
0
0
0
0
2
2
0
1
0
2
3
0
0
0
2
1
0
0
2
0
1
0
0
2
2
0
0
0
0
0
0
0
1
2
0
0
0
3
0
0
0
2
2
0
1
0
0
0
1
0
2
0
0
1
0
0
2
0
0
3
0
2
3
2
0
0
0
0
0
0
2
0
1
0
0
1
0
0
2
0
0
0
0
0
2
2
0
0
0
3
0
0
1
0
0
0
0
2
0
0
0
1
1
2
1
0
1
2
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
2
0
1
0
2
2
0
0
0
0
0
0
1
0
0
0
1
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
2
2
2
0
1
0
0
2
0
0
1
0
0
1
0
0
0
3
1
0
0
0
2
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
3
0
2
2
3
0
0
0
0
0
0
0
0
0
1
1
1
0
2
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
2
1
2
0
0
1
0
2
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
2
0
2
0
1
0
0
1
0
0
1
0
0
0
0
3
0
0
0
0
0
0
2
0
1
2
0
0
1
0
2
2
2
0
0
2
0
1
0
1
0
2
0
0
1
0
0
0
2
0
0
0
1
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
1
1
0
0
2
0
0
0
0
0
0
0
2
2
0
2
1
0
2
0
0
2
1
0
0
0
0
0
2
0
1
0
1
0
0
1
2
0
0
0
0
0
0
0
1
2
0
0
2
0
1
0
0
0
1
1
1
1
1
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
1
0
2
2
0
1
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
1
0
1
2
0
0
0
1
2
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
1
0
2
0
2
0
0
1
2
1
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
2
2
2
0
2
0
2
0
0
2
1
0
2
0
0
2
2
0
1
2
0
2
0
0
0
2
0
0
2
0
0
1
0
0
0
1
0
0
1
0
0
1
2
0
0
0
1
0
0
1
0
0
0
2
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
2
2
0
0
0
0
1
0
1
1
1
2
0
0
0
0
0
1
1
0
0
0
2
0
1
0
0
4
0
3
1
2
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
3
2
2
2
0
0
2
0
0
4
0
1
0
0
0
1
0
2
2
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
1
0
2
3
0
1
2
0
0
0
1
0
1
0
0
0
0
2
0
0
0
2
1
2
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
4
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
1
0
0
1
1
0
1
0
1
2
0
0
0
1
0
0
1
0
2
0
0
0
2
0
3
0
1
2
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
1
0
1
3
0
0
0
1
1
1
0
0
3
0
0
1
0
2
2
1
1
0
0
0
0
0
0
0
2
1
0
1
2
1
0
2
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
1
0
1
0
0
1
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
1
2
0
0
0
1
0
2
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
1
0
0
0
0
1
0
0
0
1
0
0
2
2
0
0
0
0
0
2
2
0
2
1
0
1
1
2
0
0
0
1
0
1
2
0
2
2
1
0
0
1
0
2
0
0
0
0
0
0
0
3
2
1
0
0
0
0
1
0
0
2
0
0
0
1
1
1
0
0
0
0
0
0
0
2
6
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
1
0
0
1
1
0
0
0
0
0
1
0
2
2
0
1
0
0
0
1
2
0
0
0
0
0
0
0
1
0
2
2
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
1
0
2
0
2
2
2
0
0
1
0
0
0
0
0
2
0
0
0
1
0
1
2
2
3
4
0
0
0
2
2
1
0
0
2
0
1
1
1
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
2
0
2
1
2
0
2
0
0
0
0
0
2
0
0
0
0
2
2
1
0
0
0
4
2
0
0
0
0
0
0
0
2
0
0
0
2
2
0
1
0
1
1
2
0
0
0
0
1
0
0
1
1
0
2
0
1
0
0
0
0
0
0
0
0
4
2
0
1
2
0
0
2
0
1
0
0
2
0
0
2
0
0
0
0
2
0
2
2
2
1
0
2
0
1
0
0
0
0
2
1
0
1
0
2
0
0
1
1
0
0
0
0
0
0
1
1
2
1
0
1
0
0
0
0
0
0
1
1
0
3
2
0
0
0
1
2
0
0
0
1
0
1
1
3
2
2
0
2
0
3
2
0
1
0
0
1
1
2
0
0
2
2
0
0
1
0
0
0
0
0
2
0
0
2
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
2
2
0
2
2
1
0
0
0
0
1
0
0
2
0
2
0
0
0
3
2
2
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
1
0
2
1
0
1
0
2
1
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
4
3
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
1
0
1
2
0
0
0
0
0
0
0
1
1
0
1
0
0
1
2
0
0
2
0
0
0
0
1
0
2
0
0
2
0
2
2
4
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
1
1
2
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
2
2
2
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
1
0
0
0
0
0
3
0
0
0
0
2
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
3
2
2
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
1
0
0
0
2
2
0
2
0
0
2
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
3
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
1
1
0
0
0
0
0
1
1
2
0
0
0
1
0
0
0
0
2
3
1
0
2
0
0
2
0
9
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
1
0
0
0
1
0
1
0
0
0
1
3
2
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
2
0
0
0
2
0
2
2
1
0
2
0
0
2
0
0
1
2
0
0
0
0
0
2
0
1
0
0
0
0
0
2
1
1
0
1
0
0
1
0
0
3
2
2
0
0
2
0
0
0
2
0
2
2
0
2
0
0
0
3
2
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
1
0
2
0
0
0
0
0
2
1
0
0
0
0
2
0
2
1
2
1
2
0
1
0
0
0
2
0
0
0
1
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
4
2
1
0
2
2
1
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
1
2
1
0
0
1
0
0
0
0
1
2
0
3
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
1
6
0
1
0
0
0
2
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
1
0
1
0
2
0
0
1
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
2
1
0
2
3
0
1
1
0
0
0
1
2
0
0
0
2
1
0
5
0
2
2
0
2
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
2
0
0
1
2
0
0
0
0
0
0
2
1
1
1
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
2
0
4
1
0
0
3
0
0
2
1
2
0
1
0
0
0
1
3
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
1
2
2
1
0
1
0
2
0
1
3
2
1
1
2
0
0
1
0
0
3
0
1
1
0
0
1
0
1
0
4
2
0
0
1
1
2
0
0
1
0
2
1
0
2
1
0
0
0
2
2
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
1
0
4
0
2
2
0
1
0
2
0
0
0
0
0
0
1
2
2
0
0
0
1
0
1
0
1
0
1
2
0
1
0
0
0
1
2
1
2
0
2
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
2
0
0
0
1
0
1
0
0
2
0
2
0
0
0
1
0
0
16
0
0
2
3
0
0
0
0
1
0
2
0
2
0
0
2
0
0
0
0
1
2
0
0
0
0
0
2
0
2
1
2
1
1
2
0
1
2
0
1
0
0
0
0
2
0
0
0
0
0
1
0
1
2
0
0
1
2
1
0
2
0
0
0
3
0
0
0
2
0
1
2
0
2
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
2
0
2
2
0
0
1
1
2
1
0
1
0
1
0
0
1
0
2
2
1
0
0
2
3
1
0
0
0
0
1
0
0
1
0
0
2
0
0
1
2
0
0
0
0
1
0
1
1
0
3
0
2
0
0
0
1
0
0
1
0
2
2
2
0
0
0
0
2
1
2
2
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
2
2
0
0
1
2
0
0
0
0
1
0
1
1
0
2
1
1
0
0
0
2
0
0
0
0
0
0
2
1
0
0
2
0
2
2
1
1
0
2
2
0
0
0
1
1
2
2
2
2
0
0
0
0
1
0
2
2
0
0
0
2
1
0
0
0
0
0
0
1
0
2
0
0
2
0
2
5
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
2
3
0
2
0
3
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
2
0
1
2
3
0
0
0
2
0
3
0
2
0
0
0
0
0
2
1
0
0
0
2
0
1
1
0
0
1
2
2
1
0
0
0
3
1
8
1
2
1
0
0
2
2
0
1
0
1
1
0
0
0
0
1
0
1
0
0
2
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
1
2
0
0
0
0
0
0
1
0
1
2
0
0
2
0
1
2
0
0
0
1
0
0
0
0
0
0
1
0
1
0
2
0
1
2
0
0
1
0
0
0
0
0
1
1
2
0
0
1
0
0
1
0
0
0
0
1
0
2
0
1
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
3
0
0
0
0
2
0
0
2
0
6
0
0
1
0
4
0
0
0
0
0
1
2
2
3
1
3
0
0
0
0
1
1
0
3
0
0
0
0
0
0
2
0
0
0
2
3
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
2
0
0
0
2
0
0
0
2
2
0
1
2
2
0
0
1
2
1
2
1
1
2
1
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
1
1
0
0
1
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
1
3
0
0
1
0
2
0
0
0
0
0
0
1
1
0
1
2
1
1
0
0
2
0
0
0
1
0
2
0
0
1
0
0
0
0
0
4
0
0
0
2
1
2
3
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
2
0
1
0
1
2
2
0
1
0
0
1
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
3
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
2
1
0
0
3
0
0
0
1
1
2
0
1
1
0
1
0
0
2
0
0
0
0
1
0
0
2
0
2
0
1
1
0
2
2
1
1
0
0
2
0
0
0
0
1
0
0
0
1
2
1
0
5
0
0
1
0
1
0
0
1
0
2
2
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
2
0
1
0
1
3
0
2
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
1
0
2
1
0
2
2
0
1
1
0
0
0
2
1
0
1
0
1
1
2
1
0
0
0
0
2
2
3
2
0
0
0
2
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
2
2
2
0
0
2
1
0
1
0
0
0
2
0
0
0
0
0
2
0
1
1
2
0
0
0
2
0
0
3
0
3
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
1
1
2
0
0
1
0
2
0
1
3
1
0
0
0
0
0
1
0
0
2
0
1
1
0
0
1
0
0
2
2
0
1
1
0
0
1
0
1
0
0
2
3
0
0
1
0
0
0
2
0
0
0
3
0
2
0
3
0
2
0
2
0
2
2
0
0
0
0
0
0
0
0
0
6
0
0
3
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
2
0
0
2
0
0
0
1
2
0
0
1
4
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
4
1
1
0
0
2
0
2
0
2
1
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
4
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
2
0
0
0
1
2
0
0
0
2
2
0
0
0
1
0
0
0
2
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
3
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
2
0
1
1
0
1
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
2
1
0
1
0
0
2
0
0
0
0
0
0
0
0
3
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
1
1
0
1
2
1
0
0
0
1
0
2
0
0
1
2
1
2
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
2
1
1
0
1
2
0
0
0
0
2
0
0
2
0
1
0
0
1
0
2
0
0
2
0
1
1
0
1
1
0
1
1
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
2
1
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
1
2
1
0
0
2
1
1
0
3
2
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
2
2
0
0
2
2
1
0
2
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
2
0
0
1
0
2
0
2
0
0
0
0
0
2
0
1
0
0
1
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
1
0
0
0
1
0
2
0
0
0
2
0
0
0
0
2
0
0
1
1
2
2
0
1
0
1
0
0
0
2
0
0
1
1
2
2
1
1
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
3
2
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
2
2
2
0
1
2
0
1
1
1
0
1
1
2
0
0
2
0
0
0
0
2
0
0
0
0
0
1
1
1
0
0
0
0
1
2
1
1
0
2
0
0
1
0
0
0
1
0
0
0
2
0
0
2
1
2
0
2
0
0
0
0
2
0
0
2
1
0
1
0
0
0
2
0
0
0
2
0
0
0
2
2
0
0
0
0
0
2
0
2
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
2
2
0
0
0
2
0
0
2
0
0
2
1
0
0
2
1
0
1
1
0
0
0
0
2
1
0
2
2
0
1
2
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
1
0
0
0
1
0
0
0
2
0
1
2
2
0
0
3
0
1
0
1
1
1
1
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
1
1
0
0
2
0
2
0
1
0
1
1
3
2
0
0
0
2
0
0
2
1
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
2
2
0
0
0
1
1
0
0
2
2
0
1
1
0
0
2
0
1
1
0
0
2
1
0
1
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
2
0
1
0
0
0
0
0
2
2
0
0
2
0
0
1
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
2
0
1
0
1
0
1
0
1
0
4
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
2
2
0
0
0
0
0
1
2
1
0
0
2
2
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
2
0
0
1
0
2
0
1
0
0
0
0
0
0
1
0
0
1
2
1
0
1
2
0
0
2
2
0
0
0
0
1
2
1
0
0
0
0
0
0
1
0
0
2
2
1
3
0
1
0
1
1
0
0
0
0
1
0
1
0
1
0
0
2
0
0
0
2
0
0
0
0
0
1
1
1
1
0
0
0
2
0
2
0
2
0
0
0
2
1
2
1
0
1
0
1
0
1
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
3
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
3
2
1
0
2
0
1
1
0
2
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
3
0
0
2
0
0
1
1
1
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
4
0
1
0
0
1
0
0
2
2
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
1
2
0
0
0
2
4
6
0
0
1
0
2
0
0
2
0
0
0
0
2
0
2
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
3
2
0
0
1
0
0
0
1
0
0
2
1
0
2
0
0
0
0
1
2
1
2
1
0
0
0
0
0
1
0
0
2
0
1
0
0
2
2
0
0
0
2
1
0
2
2
0
0
0
0
1
0
0
1
0
2
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
2
0
1
0
2
0
2
1
1
0
0
1
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
2
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
2
0
2
1
2
0
0
2
0
0
2
0
0
2
0
0
0
3
0
1
0
1
0
0
1
1
0
0
0
2
0
1
0
0
1
2
0
0
1
0
0
2
1
0
0
3
0
0
0
0
0
1
0
0
2
2
2
0
0
0
0
0
3
0
5
0
0
1
2
0
2
0
0
0
3
0
0
0
1
0
0
2
0
0
0
0
0
1
2
0
0
1
0
0
1
2
1
1
0
0
0
0
1
0
0
1
0
0
2
0
0
0
1
2
2
2
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
2
1
0
0
1
2
0
1
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
1
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
1
0
0
3
0
0
0
1
0
1
0
0
2
2
0
2
2
0
1
0
2
0
0
0
0
0
2
1
2
1
2
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
1
0
0
1
0
2
3
0
2
2
0
0
1
0
1
0
1
0
0
0
0
0
0
2
0
0
2
3
0
0
0
0
0
1
0
0
2
0
0
0
0
1
2
0
2
0
0
0
1
0
2
0
0
0
0
1
0
0
2
1
0
0
0
0
1
0
3
1
0
1
0
0
1
0
0
0
2
1
0
0
0
1
0
0
0
0
2
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
4
0
2
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
2
0
1
0
3
0
2
0
2
1
0
2
0
0
0
0
0
0
4
0
0
0
0
2
1
0
2
0
2
0
2
0
0
1
0
0
1
0
0
0
2
2
1
0
0
0
1
0
0
1
2
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
2
0
0
0
0
3
0
1
0
2
0
0
1
0
1
2
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
1
2
0
3
0
0
0
2
1
0
2
2
2
0
0
0
0
0
0
0
0
1
1
0
0
1
0
2
0
0
0
0
2
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
2
1
0
0
1
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
2
1
2
2
0
2
0
0
3
0
0
0
3
0
0
0
2
2
0
2
0
0
0
0
0
0
0
1
1
2
1
0
2
0
2
1
2
0
0
4
0
0
2
0
0
0
0
0
0
0
0
0
0
4
0
1
0
2
2
1
0
0
2
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
1
2
2
0
0
0
0
1
0
0
0
2
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
1
2
1
0
2
1
2
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
2
0
2
0
0
0
2
0
0
0
2
0
0
1
1
1
0
8
0
2
0
0
0
0
2
1
0
0
1
0
2
0
1
2
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
2
2
0
1
0
5
2
0
0
0
0
2
2
0
1
0
2
0
0
2
0
0
0
0
0
0
0
2
0
1
2
0
1
2
0
0
0
0
0
0
1
0
0
0
2
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
2
1
0
2
0
0
2
1
0
2
1
0
0
0
1
0
0
1
0
2
0
1
1
1
2
0
2
0
0
0
0
1
0
2
0
2
0
0
0
1
0
0
2
0
1
0
0
2
3
0
1
0
1
0
0
0
1
0
0
1
0
0
0
2
2
0
1
0
0
1
0
1
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
1
0
1
0
2
0
1
0
0
1
0
0
2
0
0
0
1
0
1
0
0
1
0
2
2
2
1
0
1
0
1
0
0
0
0
0
0
2
1
0
1
0
0
1
0
0
0
2
1
0
2
2
2
0
0
0
0
1
0
1
0
0
2
0
0
2
2
3
1
0
0
0
2
1
1
0
2
0
0
1
0
0
2
2
0
0
0
0
3
0
1
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
2
0
2
0
5
0
1
0
0
0
0
1
0
0
0
0
0
3
0
2
1
1
0
1
0
0
0
0
0
0
0
2
2
1
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
1
2
2
0
0
0
1
0
1
1
0
2
1
0
0
0
0
1
1
0
2
2
0
0
0
0
1
1
3
0
0
0
2
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
1
2
1
2
0
1
2
2
2
0
0
2
0
3
1
0
0
0
0
0
0
0
0
1
0
1
2
1
0
0
0
1
0
0
0
1
3
0
2
1
0
0
0
2
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
2
2
3
1
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
2
3
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
2
0
0
2
0
0
0
1
0
0
0
0
2
0
4
0
0
0
0
1
0
1
0
2
0
0
2
0
2
1
1
0
0
0
1
0
0
3
1
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
1
2
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
1
0
0
0
1
0
0
1
2
0
0
0
1
1
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
2
0
0
1
2
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
2
0
0
0
1
0
0
2
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
2
0
0
2
0
0
0
2
2
0
0
1
0
2
1
0
9
0
0
2
1
0
0
0
1
0
2
0
3
0
0
0
0
1
0
1
0
0
1
2
1
1
0
0
0
1
4
0
0
1
0
1
2
2
1
1
0
0
0
2
0
0
0
1
0
0
0
0
2
1
1
0
0
0
0
0
0
2
0
0
2
1
2
1
2
0
0
0
0
0
0
0
0
2
1
0
2
0
0
2
0
2
0
0
0
0
1
0
0
0
2
0
1
2
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
3
0
0
0
0
0
0
0
0
0
3
2
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
2
1
0
0
0
0
0
1
2
0
1
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
2
2
0
0
0
0
0
1
0
0
1
1
0
0
0
2
4
0
0
0
2
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
1
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
2
2
0
0
0
1
0
0
0
0
1
0
2
2
0
2
0
0
1
2
0
0
0
2
2
0
0
1
2
2
0
1
0
0
0
2
0
1
0
0
1
1
1
2
2
0
1
2
0
2
0
1
0
0
1
1
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
1
1
0
2
0
0
0
0
1
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
2
1
2
1
0
0
0
0
1
0
0
3
0
1
1
0
0
0
1
0
0
1
0
0
0
1
2
0
0
1
0
0
0
2
0
0
1
0
1
0
1
0
2
0
0
0
1
1
0
3
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
2
0
1
0
3
0
0
0
0
0
0
0
3
1
2
0
0
2
1
1
0
1
0
0
0
0
0
1
2
2
0
1
2
2
0
2
2
0
0
0
2
0
1
0
0
2
0
2
0
1
1
1
0
8
0
1
0
1
0
0
0
1
0
2
2
2
1
0
2
0
0
0
2
0
0
1
0
1
4
2
0
0
2
0
1
0
0
3
0
0
0
0
2
0
2
0
0
0
0
0
3
1
0
0
0
2
1
0
0
1
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
2
4
0
0
0
0
0
0
0
0
1
0
3
0
2
2
0
1
0
0
0
1
1
2
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
7
1
0
2
1
2
0
1
2
0
0
0
1
2
0
2
1
1
2
1
0
0
0
1
0
2
0
0
0
0
0
2
0
0
3
0
2
0
0
2
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
1
0
0
1
3
1
1
1
2
1
0
0
1
0
0
2
2
3
2
0
1
2
0
1
0
2
0
0
0
0
1
1
0
0
1
0
0
0
2
1
2
0
0
0
2
0
1
0
2
2
0
2
0
0
0
0
1
1
0
1
0
0
3
2
1
0
2
0
0
0
0
1
0
0
2
2
0
1
2
0
1
1
0
0
0
0
1
1
1
2
0
2
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
2
0
1
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
1
1
0
0
0
1
2
0
3
0
0
0
0
0
2
1
1
0
1
1
0
1
3
0
0
4
0
0
0
0
0
0
0
2
1
0
2
2
1
0
0
2
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
2
1
0
1
0
0
0
0
2
0
0
2
0
2
0
0
0
0
2
2
1
0
0
0
1
0
1
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
4
0
0
0
1
0
3
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
6
1
1
0
0
0
0
2
2
0
2
0
0
1
1
0
1
0
1
0
0
0
0
2
0
0
1
0
0
0
2
0
1
0
0
2
2
1
0
1
1
0
1
0
2
1
0
1
0
0
3
0
1
2
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
2
0
0
0
6
0
0
2
2
1
0
0
0
1
1
2
0
1
1
1
1
0
1
2
0
0
1
1
0
1
2
2
0
0
0
0
2
2
2
1
0
2
0
2
0
0
1
0
0
2
2
2
1
3
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
1
1
0
0
0
0
0
0
1
2
0
0
1
2
0
3
1
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
2
2
1
2
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
2
0
1
0
0
1
0
1
0
0
0
0
0
0
0
2
1
0
0
2
0
0
2
0
2
0
0
0
0
0
2
0
2
0
2
1
3
0
0
0
1
1
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
2
2
2
0
2
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
1
0
1
0
0
0
2
0
0
2
0
0
2
0
0
0
2
0
0
0
1
2
2
0
0
1
0
0
0
0
1
0
1
0
0
0
2
1
0
3
2
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
1
0
0
0
2
0
0
0
3
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
3
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
2
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
5
0
1
1
2
0
1
0
1
0
0
0
0
2
0
0
0
2
0
0
1
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
2
1
0
0
2
0
2
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
2
0
0
2
0
2
1
0
2
2
2
1
1
0
0
0
1
0
1
0
2
2
0
3
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
1
0
1
0
1
0
0
0
2
0
1
1
0
0
0
1
1
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
2
1
0
0
0
3
0
1
1
2
0
0
0
1
0
0
0
1
1
0
1
0
0
2
1
0
3
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
2
1
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
2
0
1
0
2
1
13
0
0
2
0
0
0
1
0
2
2
0
1
2
0
0
1
0
0
2
0
1
2
0
2
0
2
0
3
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
2
1
0
0
0
2
0
0
3
0
0
0
2
2
0
0
1
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
2
0
0
0
0
1
0
0
0
0
0
1
2
2
0
1
0
1
2
0
2
0
2
0
0
0
0
0
0
1
1
0
0
0
0
3
0
2
0
2
0
0
1
0
2
0
2
0
0
2
3
0
0
2
1
2
0
0
0
1
0
2
0
1
0
1
1
1
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
2
2
0
0
0
0
1
1
0
1
1
0
0
0
1
0
1
2
1
0
0
0
2
0
0
2
0
0
0
2
1
0
0
1
0
0
1
2
0
0
0
1
0
0
0
2
0
1
0
2
1
0
5
2
0
0
0
2
0
0
0
0
0
2
0
2
3
1
1
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
1
0
0
2
0
1
0
0
0
0
0
0
2
0
1
1
0
0
1
1
0
0
2
1
4
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
2
1
2
0
0
1
0
0
0
1
0
0
0
0
0
1
1
3
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
2
4
2
0
1
0
0
2
0
1
1
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
1
2
3
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
2
0
0
0
2
0
2
0
0
0
2
0
0
1
0
0
1
1
0
0
0
0
0
0
2
0
0
0
2
0
1
1
2
0
0
1
0
0
1
0
0
1
1
1
2
3
1
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
2
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
1
0
1
0
1
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
1
0
0
3
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
2
0
0
0
1
0
1
2
2
2
0
0
0
1
0
0
1
2
1
0
0
0
1
1
0
1
1
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
1
1
2
0
0
2
0
3
1
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
1
2
0
0
0
1
2
1
2
0
0
0
0
0
0
0
1
0
0
0
1
0
2
2
1
0
0
0
1
0
0
2
2
2
0
0
1
0
1
0
1
2
0
1
0
0
0
0
2
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
1
2
0
3
1
0
0
0
0
3
0
2
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
2
1
3
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
2
2
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
2
0
0
2
1
0
0
4
0
1
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
2
0
1
2
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
2
0
0
0
2
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
3
0
0
2
2
0
1
0
0
2
0
2
1
1
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
2
2
1
0
0
1
1
2
0
0
0
0
0
1
2
3
0
1
0
0
0
0
0
0
0
0
0
1
2
0
2
1
0
0
0
0
1
0
0
0
0
0
1
0
2
0
2
0
0
0
0
2
0
0
0
1
1
2
0
1
0
1
0
0
1
2
2
1
1
1
0
1
2
1
1
1
0
0
2
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
1
2
0
3
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
2
2
0
0
1
0
3
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
2
0
4
0
2
0
1
0
1
2
0
2
2
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
1
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
1
0
0
0
1
1
2
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
1
0
0
0
2
2
0
0
3
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
2
0
1
0
1
0
0
1
0
1
0
1
2
2
0
2
0
1
0
1
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
2
0
2
2
0
1
0
2
0
1
0
0
0
1
0
3
1
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
1
2
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
3
0
2
1
0
1
1
1
0
2
1
0
0
0
0
0
2
1
2
1
2
2
0
0
0
0
2
0
1
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
6
1
2
0
0
2
2
2
2
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
1
0
1
0
1
0
0
0
1
1
1
0
0
2
2
2
0
0
2
0
3
0
0
1
3
0
0
0
3
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
2
0
0
0
0
0
0
2
2
0
0
0
0
1
1
0
0
0
1
1
0
0
0
3
2
0
1
0
2
0
0
2
0
0
0
2
1
2
1
0
0
0
0
0
0
0
0
1
0
0
2
1
0
2
0
2
3
0
0
0
2
0
0
0
1
0
0
0
0
4
1
0
0
0
0
5
2
0
1
1
0
3
0
0
1
1
0
0
1
0
0
0
0
1
3
0
2
0
2
2
0
0
2
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
2
0
1
1
0
0
0
1
0
0
0
2
1
0
3
0
0
0
1
0
0
2
0
2
0
1
0
1
0
0
0
0
2
0
0
0
0
0
1
2
2
1
2
2
0
0
0
0
0
0
0
0
0
0
17
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
1
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
3
2
0
0
1
0
2
0
0
1
3
0
2
1
0
0
0
0
3
2
0
0
0
0
0
0
0
0
1
1
0
0
1
2
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
2
4
0
1
0
2
0
1
0
0
2
0
0
1
1
0
0
0
2
0
2
0
0
0
1
0
0
0
0
2
0
0
1
2
0
2
0
1
0
1
1
2
0
0
1
0
0
0
2
1
2
0
0
0
2
0
0
1
2
1
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
1
1
2
0
0
0
1
0
2
0
1
0
0
0
0
0
2
0
2
0
1
0
3
0
0
2
1
0
0
2
0
0
1
0
0
0
0
2
2
0
0
0
0
0
2
0
0
2
0
1
2
0
1
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
2
0
2
1
1
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
6
1
0
0
0
0
4
0
2
1
0
1
1
1
0
0
0
1
0
0
1
2
0
0
0
1
2
1
1
0
0
0
0
2
0
0
0
0
0
2
1
2
0
2
0
0
0
0
1
2
0
0
1
0
0
0
3
0
0
0
2
0
0
0
2
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
1
1
0
1
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
2
0
2
0
0
4
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
1
2
1
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
2
0
0
0
0
2
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
2
1
2
0
0
2
2
2
0
0
2
0
2
0
0
0
0
1
1
0
2
0
2
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
1
0
1
0
1
1
0
1
2
2
0
1
3
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
1
1
1
0
1
2
2
0
1
3
0
2
0
0
1
1
0
0
2
0
0
0
0
0
1
2
1
0
0
0
1
1
0
1
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
2
0
0
0
2
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
3
0
0
0
3
0
1
1
0
0
0
0
2
0
0
2
0
2
0
0
0
1
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
2
1
0
0
0
2
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
2
2
0
1
0
0
0
1
0
1
2
2
0
0
0
2
2
0
0
1
0
0
1
0
0
2
0
1
0
0
1
0
2
2
1
1
0
3
2
0
0
4
0
0
0
1
1
2
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
1
1
0
0
2
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
2
1
0
0
0
1
0
0
2
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
2
3
0
0
0
0
1
0
1
0
2
2
0
2
0
0
2
0
0
0
1
1
0
0
0
1
0
0
1
1
2
0
0
0
1
1
0
0
0
2
2
0
0
0
1
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
2
1
1
3
1
2
1
0
2
2
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
1
0
0
2
0
0
0
1
0
0
2
0
0
0
2
1
2
0
1
0
2
0
0
0
2
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
1
1
1
1
6
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
1
0
0
1
2
0
1
1
0
0
2
2
0
0
0
1
0
2
0
0
2
0
0
0
0
2
0
2
3
2
1
0
1
2
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
1
1
0
0
5
1
0
1
0
2
2
0
2
5
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
1
2
2
0
2
1
2
5
2
2
0
2
0
0
1
0
0
0
0
1
0
0
2
2
2
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
1
1
1
0
0
1
0
0
0
0
0
1
2
2
2
0
0
0
0
0
0
0
0
1
0
0
3
2
0
2
0
0
0
0
2
1
0
0
2
0
2
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
2
0
0
0
2
2
0
2
0
0
0
1
0
0
1
0
0
1
0
2
2
0
0
0
2
2
1
0
0
1
0
3
0
0
2
0
0
0
0
0
1
2
0
0
0
1
0
3
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
1
1
1
0
0
0
1
0
0
0
1
0
0
0
0
2
1
0
0
1
0
0
0
2
2
0
0
0
1
2
1
0
2
2
0
0
1
0
0
0
0
0
0
0
0
2
1
1
7
2
0
0
1
1
0
1
2
0
1
1
0
0
1
2
2
0
1
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
4
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
2
1
0
1
1
0
2
2
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
2
1
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
2
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
2
1
0
1
0
0
2
0
0
0
1
1
0
0
2
2
0
1
0
0
1
0
1
0
0
0
2
0
0
1
2
0
0
0
0
0
0
2
0
0
0
1
0
1
1
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
6
0
2
0
0
0
0
2
1
1
8
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
2
0
0
0
2
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
1
0
1
0
1
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
2
2
0
1
0
0
0
0
0
2
2
2
0
1
0
0
0
2
0
1
0
0
0
0
2
0
1
0
0
0
2
0
1
2
1
0
1
0
0
0
0
0
0
2
0
3
0
2
0
0
0
2
0
1
0
1
1
1
0
0
0
2
0
0
3
0
1
0
1
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
2
0
1
0
1
1
0
1
0
2
1
0
0
2
2
2
2
0
2
2
0
1
1
0
1
1
0
1
3
0
0
0
0
3
0
0
0
1
0
2
0
0
2
0
0
0
1
2
3
0
0
2
2
0
0
1
2
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
1
1
1
0
0
2
2
0
0
0
0
0
0
1
1
2
0
0
1
1
0
1
0
1
1
2
1
2
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
1
0
1
0
0
0
2
0
0
2
1
0
1
0
0
0
0
0
0
2
0
0
0
2
0
2
2
0
1
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
2
0
1
0
2
0
1
1
0
2
0
2
0
0
2
1
0
0
2
1
0
0
0
0
2
0
0
0
2
0
1
0
0
1
0
0
1
2
0
0
2
0
1
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
2
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
2
0
0
0
1
0
0
0
2
2
0
0
0
1
2
0
1
1
0
1
0
0
0
1
0
2
2
0
0
1
0
2
0
0
1
1
1
0
0
0
0
1
0
1
1
0
0
0
1
0
2
0
0
1
2
1
0
1
0
0
0
1
1
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
2
0
0
2
2
0
1
0
0
1
0
0
0
1
2
0
0
1
0
1
0
0
2
2
0
1
0
2
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
3
0
0
2
1
0
0
0
2
3
0
0
0
0
0
2
0
0
2
2
0
1
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
2
0
0
0
0
2
0
0
3
2
0
0
0
1
0
0
2
5
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
1
2
0
0
1
0
0
1
1
0
1
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
2
0
1
1
0
1
1
0
0
0
1
2
0
2
0
0
0
0
0
0
2
1
1
0
1
1
0
2
0
0
0
0
0
2
0
1
0
2
1
2
1
2
3
2
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
2
2
1
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
2
2
1
0
0
0
2
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
5
0
0
0
0
1
2
0
0
1
0
0
0
0
1
0
0
1
1
1
0
0
0
0
4
0
2
1
0
1
2
1
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
3
0
0
0
2
1
0
0
0
1
6
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
4
2
0
0
0
2
3
0
0
1
2
1
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
1
0
2
0
0
1
0
1
0
0
0
0
1
1
0
1
0
0
1
0
1
0
0
0
0
1
2
0
0
2
0
0
2
2
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
2
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
1
2
2
0
0
0
0
1
2
0
2
0
0
0
0
0
2
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
2
1
0
0
0
1
0
1
1
2
2
1
0
0
0
0
1
0
3
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
2
0
0
1
0
0
1
0
0
2
0
0
0
0
1
1
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
2
0
2
0
0
2
1
0
2
0
0
1
0
0
0
1
2
0
0
0
2
0
0
2
0
1
0
0
0
2
1
2
0
0
0
0
0
0
0
2
5
0
0
2
0
2
1
2
0
2
0
0
0
2
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
1
1
0
1
2
0
0
0
0
2
0
0
0
0
0
0
1
0
3
2
0
0
2
0
2
0
1
0
0
0
0
0
1
0
1
0
2
2
0
0
0
0
1
0
2
0
0
2
0
0
2
2
2
0
0
0
0
2
0
0
0
0
3
0
0
0
0
1
8
0
0
2
4
0
0
0
0
1
0
0
1
0
0
0
5
0
0
1
1
0
0
1
0
0
2
0
0
2
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
1
1
2
0
0
0
0
0
0
1
0
1
2
1
1
0
0
1
0
0
0
0
2
2
1
1
0
1
1
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
2
1
0
0
3
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
2
2
0
1
0
1
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
2
0
0
2
0
1
0
0
3
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
7
0
2
0
0
0
1
3
0
3
0
2
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
2
0
2
1
0
0
1
0
0
2
0
0
0
0
1
0
2
0
0
1
0
0
1
3
1
0
0
0
1
0
2
0
1
0
0
0
2
0
0
2
0
0
0
0
0
2
0
1
0
1
0
0
2
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
2
1
0
0
1
0
2
0
0
2
1
1
0
0
0
0
0
0
0
0
2
0
0
3
2
1
0
1
0
0
1
1
2
1
0
0
1
0
0
2
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
2
2
0
0
2
1
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
2
0
0
1
1
0
0
0
0
0
1
0
3
0
0
0
2
0
0
1
0
0
0
2
0
2
0
2
0
8
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
2
0
2
0
2
0
1
2
0
1
0
0
1
0
2
0
0
0
0
0
0
2
2
0
0
1
0
2
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
1
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
3
0
1
2
0
1
2
0
2
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
2
0
2
0
2
1
0
0
0
0
1
1
0
2
0
6
0
0
1
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
2
1
0
0
0
0
0
1
0
2
0
0
2
0
1
0
0
0
0
0
0
0
1
1
2
0
2
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
2
1
0
1
0
2
0
0
1
0
0
1
0
0
0
0
0
2
1
0
0
2
0
0
1
1
9
0
0
2
0
0
2
0
0
2
2
0
0
1
1
1
2
0
3
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
2
0
2
0
2
3
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
2
1
0
2
2
0
1
0
0
0
0
1
0
0
1
0
0
0
1
1
2
1
3
0
0
0
0
1
0
2
0
0
2
0
0
2
0
1
1
2
0
2
0
0
0
0
0
3
0
2
0
0
0
0
2
0
0
0
1
0
2
0
0
2
0
0
1
4
0
0
1
0
2
1
0
0
3
0
0
0
1
1
1
0
0
0
0
0
0
1
0
2
0
0
0
1
1
0
2
1
3
1
0
0
0
0
0
0
3
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
3
2
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
3
0
2
0
0
1
0
0
2
0
0
2
1
0
1
0
0
0
0
1
2
0
1
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
2
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
2
1
1
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
1
0
2
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
2
0
0
0
1
2
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
3
2
0
2
0
0
0
0
4
0
1
2
0
0
0
0
0
0
1
2
0
1
0
2
2
1
2
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
2
2
1
1
0
2
0
2
0
1
1
1
0
1
0
0
1
2
0
0
0
3
0
0
0
0
0
0
2
0
2
0
0
0
2
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
2
0
0
0
0
0
2
1
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
1
0
2
0
0
0
2
0
2
0
2
0
1
2
1
2
1
0
2
0
0
0
0
0
0
0
0
1
0
2
2
0
1
0
1
0
0
0
0
1
1
0
1
2
0
0
0
0
0
0
1
0
0
0
0
1
1
0
2
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
1
0
0
0
0
1
2
0
1
0
0
0
1
0
0
0
0
0
1
0
2
0
0
2
0
0
2
0
0
1
0
2
0
2
0
1
0
0
0
2
0
0
2
1
2
0
0
0
1
0
1
0
2
2
2
0
2
0
1
2
0
2
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
1
1
0
3
1
1
0
0
0
0
0
0
2
0
1
0
1
2
1
0
2
2
0
0
1
2
0
0
2
0
0
0
2
0
1
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
2
3
2
0
0
3
1
3
2
0
0
0
2
4
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
2
2
0
0
1
0
2
2
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
9
0
1
0
0
0
2
2
2
0
1
2
0
2
0
0
0
0
0
1
0
0
1
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
2
1
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
3
1
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
1
0
2
0
0
0
1
0
1
0
0
0
1
1
0
0
1
3
2
2
3
1
0
1
1
0
0
0
0
3
1
0
0
1
0
0
4
0
0
2
0
1
1
2
0
1
3
2
2
0
1
0
1
1
1
2
1
2
1
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
2
2
0
0
0
1
0
0
2
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
1
2
1
2
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
1
2
2
1
0
0
1
0
2
0
0
0
0
2
2
0
0
0
2
4
0
0
0
0
0
0
1
0
0
3
1
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
2
1
1
0
0
0
0
1
2
2
0
0
2
0
0
2
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
1
0
0
3
2
3
0
0
0
1
1
0
2
0
0
0
1
0
14
1
0
1
0
0
1
0
0
0
0
2
0
1
1
0
2
0
2
0
0
2
1
0
0
2
2
0
2
0
1
0
0
0
1
4
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
1
2
0
0
0
1
0
0
0
0
2
0
0
0
2
2
0
2
0
0
1
3
1
1
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
3
0
2
0
1
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
1
0
1
1
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
1
1
0
1
2
0
0
1
0
0
1
0
0
0
2
0
1
2
0
0
0
1
0
0
0
0
0
2
1
1
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
1
1
0
0
0
0
2
0
2
0
2
1
3
0
0
0
0
0
0
2
2
0
1
2
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
3
0
0
0
2
0
1
1
0
0
0
1
0
0
0
2
0
0
0
0
1
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
2
0
0
5
0
0
0
0
1
0
0
2
3
0
0
1
0
1
2
0
1
0
0
2
0
2
1
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
1
0
0
0
0
0
0
2
0
1
0
1
0
0
2
0
0
3
0
1
0
0
0
0
0
2
1
0
0
1
0
0
1
1
1
1
0
0
0
0
0
0
2
0
0
1
0
1
1
1
0
0
0
4
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
1
2
0
0
0
0
1
0
2
0
1
0
0
0
4
2
1
0
0
2
1
2
1
0
0
0
0
2
0
1
1
0
0
0
0
0
0
4
2
0
2
0
0
2
0
0
0
0
0
0
3
2
0
0
0
0
1
0
1
2
0
0
0
2
0
2
2
0
1
0
2
2
1
0
0
0
0
2
0
0
2
1
0
0
3
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
3
2
0
0
1
0
0
0
3
1
0
0
0
0
0
0
0
1
1
0
0
0
2
1
0
0
0
0
0
0
0
1
0
1
1
0
0
3
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
2
2
0
0
1
0
1
0
0
0
2
0
0
0
0
2
1
2
0
1
2
1
1
2
0
0
0
0
0
0
0
1
0
0
0
0
3
2
0
1
0
0
1
0
2
0
0
0
1
0
0
1
0
0
0
0
2
0
3
0
0
0
0
2
0
0
2
0
1
1
0
0
3
0
0
0
0
2
0
0
1
0
2
0
0
0
0
1
0
0
0
4
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
2
2
0
2
0
0
0
0
0
1
1
0
0
2
0
0
0
0
2
0
2
0
0
0
1
0
0
2
1
0
0
0
0
0
2
0
0
0
0
4
0
0
0
0
0
0
3
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
1
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
3
0
0
1
2
1
1
2
0
0
0
1
1
0
2
0
3
0
0
1
0
0
2
1
0
0
0
1
0
0
0
1
2
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
2
0
1
0
2
0
1
0
0
0
1
2
0
0
0
1
2
0
0
0
0
2
2
1
3
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
2
2
0
0
0
1
3
0
0
0
0
0
1
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
1
5
2
1
2
0
0
0
1
0
0
2
0
1
0
0
0
4
0
2
1
2
0
0
0
1
0
0
0
0
0
0
0
0
2
2
4
0
2
0
2
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
1
2
0
2
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
1
2
1
0
1
2
1
0
2
0
2
2
0
0
0
0
0
0
0
1
0
0
0
1
1
0
2
6
0
0
4
0
2
0
0
0
2
0
1
0
0
0
2
0
2
2
0
0
0
2
0
0
2
0
1
0
0
1
0
0
1
0
0
0
0
2
0
3
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
2
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
1
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
1
0
0
0
2
0
2
1
0
0
1
0
0
0
0
0
2
0
1
0
0
2
0
2
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
2
0
0
0
0
0
0
1
0
0
2
1
0
0
0
1
0
0
4
0
0
1
1
0
1
2
2
3
0
2
0
1
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
2
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
2
0
0
1
0
0
1
2
1
0
1
0
2
0
0
0
0
0
0
0
2
0
2
2
1
0
0
0
1
1
0
2
0
1
0
0
0
0
3
1
2
0
0
0
2
0
2
0
2
0
0
1
2
0
0
0
0
0
0
2
0
0
2
1
1
0
0
0
0
1
2
2
3
0
2
0
0
0
2
2
0
3
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
5
0
0
3
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
2
1
0
1
0
1
0
0
0
0
0
0
0
2
4
0
1
0
0
0
1
0
0
0
1
0
1
0
2
0
0
0
0
0
3
2
0
0
1
0
0
0
2
0
3
0
2
0
0
0
0
1
2
0
0
2
1
5
0
0
0
0
0
0
0
1
0
2
1
0
0
3
0
2
1
0
0
0
1
2
0
0
0
0
1
0
3
0
0
0
0
3
0
0
0
1
1
2
2
1
0
0
3
0
1
0
1
1
0
2
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
3
2
0
1
1
7
1
2
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
2
0
0
0
2
1
0
1
1
2
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
3
1
2
0
1
0
0
0
0
0
1
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
1
0
2
1
1
0
0
0
1
0
0
0
0
2
2
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
2
0
0
1
0
0
1
1
3
1
0
3
0
0
2
2
0
0
0
0
1
0
0
0
2
0
0
1
2
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
2
1
0
0
0
2
1
2
0
0
0
0
1
0
0
0
0
0
1
0
2
1
0
0
1
0
1
0
0
0
3
0
0
0
0
0
0
2
0
2
0
1
1
0
0
0
0
0
1
2
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
2
0
1
0
0
2
0
0
0
0
0
0
0
0
2
2
0
1
2
2
0
2
0
1
0
0
0
1
3
0
0
1
1
0
2
2
0
2
0
0
4
0
0
1
0
1
0
0
0
1
1
1
0
2
0
1
0
2
2
0
0
0
0
0
0
1
0
0
2
0
0
3
0
2
0
0
2
0
0
0
3
1
0
0
0
1
0
0
1
0
1
0
0
0
2
0
0
0
0
1
4
0
2
0
1
1
1
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
2
0
1
2
0
1
0
0
0
0
0
1
2
0
1
0
0
1
0
2
2
1
2
0
3
0
0
1
0
0
0
4
2
0
2
0
2
0
1
1
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
1
2
0
2
0
0
1
0
0
0
3
0
1
2
1
0
1
0
0
2
1
0
0
0
1
0
0
0
1
0
2
0
0
1
3
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
3
0
0
1
0
2
0
1
0
0
0
0
2
0
1
0
0
1
0
0
1
0
0
2
2
2
0
0
0
0
1
0
2
0
0
0
0
0
2
0
1
0
1
1
0
2
2
0
0
1
3
0
0
0
2
0
1
2
1
1
0
0
0
0
0
0
4
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
3
2
0
0
2
0
0
1
0
0
2
0
0
0
3
2
2
0
0
0
2
0
0
0
0
0
0
10
1
0
0
0
0
0
0
2
2
0
1
0
0
0
1
0
0
0
0
2
0
1
3
1
1
0
0
0
0
0
2
1
1
0
0
0
0
1
2
0
0
2
0
3
1
0
3
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
3
1
0
1
0
0
0
2
0
1
0
5
1
0
0
0
2
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
2
1
0
1
0
0
0
1
1
1
0
1
0
2
0
0
1
1
2
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
2
0
2
1
0
0
2
0
2
0
1
0
0
0
0
0
0
0
1
0
0
1
1
1
0
2
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
3
0
1
2
0
1
0
0
0
0
2
0
0
2
1
1
0
0
0
0
0
0
1
0
2
3
0
2
2
0
2
1
0
2
0
0
1
3
0
0
1
0
0
1
2
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
1
0
0
2
1
0
2
2
1
0
1
0
0
0
0
0
2
0
0
0
2
3
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
1
0
0
0
1
2
0
0
2
0
0
1
0
1
1
0
0
0
1
0
0
1
0
0
0
0
3
0
2
0
2
0
0
0
0
0
0
0
0
2
0
2
1
0
4
0
0
0
1
0
0
2
0
1
1
0
0
0
0
0
2
1
0
0
0
0
1
0
1
0
0
2
0
0
1
2
1
2
2
0
0
2
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
5
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
1
2
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
1
2
0
0
0
0
0
0
1
1
1
0
2
2
1
0
0
0
0
2
2
1
0
0
2
1
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
5
1
1
1
0
1
1
3
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
1
2
2
0
0
0
2
0
0
0
1
2
1
0
1
0
0
0
0
2
1
1
0
0
0
2
0
1
3
0
0
0
0
1
0
1
1
0
1
1
0
0
1
2
0
0
0
0
1
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
2
2
0
0
0
1
0
0
0
1
2
2
2
0
0
0
1
1
4
0
0
1
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
2
0
0
2
0
1
0
1
0
1
0
0
1
0
1
2
1
1
1
0
0
1
0
0
0
0
7
0
0
0
0
0
0
0
0
2
1
0
1
1
2
0
0
4
0
0
0
0
0
0
0
1
0
2
0
1
0
0
3
0
1
2
2
0
0
0
2
2
0
1
0
2
0
0
0
1
0
1
0
0
2
0
0
2
0
2
2
0
0
0
0
0
0
0
0
2
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
2
1
3
0
0
0
0
1
0
0
1
1
2
2
0
0
0
1
2
1
0
2
0
0
0
1
0
1
0
0
0
1
2
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
2
2
2
2
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
2
3
0
2
1
2
2
0
0
1
1
2
1
0
0
1
0
0
0
2
0
0
1
0
2
0
0
0
0
0
2
0
3
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
1
0
0
0
1
0
2
0
1
0
0
0
1
0
0
1
4
2
1
0
0
1
0
2
3
0
3
1
0
1
0
1
0
0
1
1
0
0
0
2
0
2
1
0
2
0
0
1
0
0
4
0
2
0
1
1
0
1
0
2
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
4
2
1
0
0
0
0
0
1
1
0
0
1
0
0
1
2
0
0
0
2
1
0
3
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
1
2
0
2
0
1
0
0
2
0
1
0
1
1
1
1
2
0
0
2
2
1
2
1
0
2
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
2
1
2
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
1
0
0
0
2
1
0
1
0
2
0
0
1
0
0
0
1
0
0
1
2
1
0
2
0
0
0
2
1
1
2
0
0
0
0
2
0
2
0
0
1
1
0
2
2
3
1
0
2
0
0
0
1
2
0
0
0
0
3
0
2
0
0
0
0
0
0
1
1
0
1
0
0
0
0
2
0
0
0
0
1
0
0
1
1
0
0
8
0
1
2
0
0
0
0
0
0
2
1
0
1
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
1
1
0
4
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
4
0
2
0
0
2
2
1
2
0
0
0
0
3
1
2
1
1
0
0
0
0
0
2
0
0
4
0
0
0
0
0
0
1
0
2
1
2
0
0
0
4
0
0
0
2
1
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
2
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
2
0
1
2
0
0
1
0
3
0
0
0
0
2
0
2
0
2
0
1
0
0
0
0
0
0
0
0
1
0
3
2
0
0
0
2
0
0
1
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
2
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
1
1
0
2
1
0
0
2
0
0
0
2
1
0
0
2
0
0
0
1
0
2
2
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
1
0
2
0
0
0
0
2
0
2
0
0
2
0
1
0
0
2
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
2
1
2
0
0
0
0
2
0
2
1
0
2
2
1
0
4
2
0
0
0
0
0
0
2
0
1
0
0
0
3
0
0
0
2
0
1
1
2
2
2
0
3
1
1
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
2
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
2
0
0
2
0
0
0
2
1
0
1
0
0
1
0
2
0
1
0
0
2
1
1
0
0
1
0
0
2
1
0
0
1
0
1
2
0
1
0
0
0
0
0
1
0
0
0
1
0
2
1
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
1
0
0
0
1
0
0
0
0
0
2
1
0
0
1
1
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
2
0
0
1
1
2
2
0
0
1
0
0
2
0
0
1
1
1
0
2
1
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
2
0
1
0
0
0
0
0
4
0
1
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
1
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
2
0
2
0
2
0
0
1
0
0
2
0
0
0
2
1
0
0
1
0
0
2
0
0
0
0
0
2
2
0
2
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
2
0
2
0
0
0
1
1
0
0
0
0
2
0
2
1
0
0
0
0
3
0
0
2
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
2
1
0
1
0
2
0
0
1
0
1
0
0
0
0
1
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
2
1
0
1
0
0
0
0
1
0
0
0
0
0
2
0
1
1
0
0
0
1
0
0
1
1
0
1
0
1
0
2
0
0
1
0
1
0
1
0
0
3
0
0
1
1
2
2
0
0
0
0
0
0
2
0
1
0
1
2
2
1
1
0
0
0
0
2
2
0
0
2
0
0
2
2
1
2
1
2
1
0
0
2
2
0
0
0
0
2
2
0
0
0
1
2
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
2
2
0
0
0
0
1
0
1
0
0
0
1
0
0
0
2
0
1
0
2
1
0
0
0
0
2
0
0
2
1
0
2
0
0
2
0
2
0
0
1
0
0
0
1
0
0
2
0
2
0
0
2
0
0
0
0
0
1
0
0
2
1
0
0
0
0
2
0
0
2
0
0
1
1
1
2
0
2
0
0
0
1
1
0
3
0
0
0
0
0
0
2
2
0
0
2
1
0
0
0
0
0
0
0
2
0
0
2
0
2
0
2
1
2
1
0
2
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
2
0
0
2
0
1
1
0
0
1
0
0
0
0
1
0
0
1
0
0
1
1
2
2
0
0
0
0
1
0
1
0
0
1
0
2
1
0
4
0
0
0
0
0
3
0
1
2
2
0
0
0
0
2
0
0
1
1
2
2
0
0
4
0
0
0
2
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
1
0
2
2
0
1
2
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
2
0
0
2
1
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
2
0
1
0
0
3
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
1
1
0
1
0
0
2
1
0
2
1
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
3
0
1
0
0
0
0
0
0
2
1
0
2
0
2
0
0
0
0
2
1
1
0
1
0
0
2
2
0
0
0
2
2
1
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
3
0
0
0
0
2
1
1
2
4
0
0
0
2
0
1
0
1
1
0
0
0
0
0
0
2
0
0
0
2
0
1
2
0
4
0
1
0
0
2
1
0
0
0
2
0
1
0
0
1
0
0
0
0
1
1
0
0
2
0
1
0
0
0
0
0
1
1
1
0
0
0
2
0
0
0
2
0
1
0
0
0
1
2
1
2
0
0
2
0
0
0
0
1
2
0
1
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
2
2
0
0
0
0
0
1
0
1
0
0
1
0
0
0
2
2
1
0
2
2
0
0
0
0
1
0
0
2
1
0
0
1
1
2
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
2
0
3
0
1
0
0
0
1
0
0
0
0
2
0
0
0
2
0
2
0
0
2
0
2
0
0
0
0
0
2
0
0
1
0
0
1
0
1
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
2
2
1
0
0
0
0
0
2
2
0
1
2
0
0
0
1
0
9
0
0
2
0
0
0
0
0
0
0
2
2
1
0
1
0
0
0
0
0
1
1
2
1
2
0
1
1
2
0
0
1
1
0
0
1
0
0
2
1
2
0
0
1
1
3
1
0
0
2
1
0
0
1
1
0
0
0
1
0
1
2
2
1
0
0
0
0
2
0
0
0
0
0
0
0
4
1
0
0
2
0
1
0
0
2
1
1
0
0
0
0
2
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
1
3
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
1
3
0
2
4
0
0
0
0
0
0
0
0
2
0
0
0
3
0
2
0
0
0
0
2
0
1
0
0
0
0
2
1
0
2
0
0
2
0
1
2
1
0
2
0
0
1
0
0
0
1
0
2
0
1
2
0
1
0
0
0
2
0
0
1
0
2
0
2
0
1
2
0
0
0
0
15
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
1
2
0
0
0
1
2
0
0
0
0
0
3
0
1
2
0
0
1
0
0
0
0
0
1
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
5
0
2
0
0
0
0
1
0
1
2
0
0
0
2
0
1
3
2
2
0
5
1
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
1
2
0
2
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
2
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
2
2
0
0
1
1
1
0
2
2
0
2
1
0
1
0
0
0
0
0
2
0
0
0
1
0
0
2
0
2
0
1
0
2
0
0
2
2
0
0
0
2
2
1
0
1
1
0
0
0
1
0
0
1
0
0
2
0
0
1
0
0
2
0
0
0
1
0
0
2
1
0
0
2
2
0
2
1
0
1
2
0
0
0
0
0
1
0
2
0
1
0
1
0
1
0
0
0
1
2
2
2
2
1
2
0
0
0
0
0
0
0
1
0
0
1
3
0
1
1
0
0
1
0
0
2
0
2
1
0
1
1
0
0
1
1
2
1
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
4
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
3
1
1
1
0
2
0
2
0
0
0
2
2
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
1
1
0
1
0
0
2
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
1
0
1
0
2
1
0
0
1
0
0
1
0
0
1
0
2
1
2
0
0
1
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
3
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
4
0
0
0
0
1
2
0
0
0
0
0
0
0
2
2
0
0
2
0
0
1
0
0
4
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
1
3
1
0
0
2
1
0
0
0
1
1
0
0
3
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
2
0
1
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
1
2
0
0
0
0
0
1
1
2
0
2
0
0
2
1
0
0
0
0
0
2
0
1
2
1
0
0
1
0
2
0
0
0
0
0
2
0
0
1
0
2
2
0
3
2
0
0
0
0
1
2
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
1
4
1
0
0
1
1
0
0
0
3
0
0
0
0
2
2
2
0
0
1
0
2
0
1
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
1
0
2
0
0
2
2
0
0
0
2
1
0
0
0
0
2
1
2
0
1
1
2
0
3
0
2
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
2
0
0
0
1
0
0
0
1
3
2
0
0
2
1
0
2
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
1
1
0
0
0
0
3
0
0
1
1
4
2
0
0
0
0
0
2
0
0
2
0
1
0
0
2
1
0
1
1
0
2
2
1
0
0
0
1
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
1
0
2
0
0
3
0
1
0
1
0
0
2
0
0
0
0
1
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
4
0
0
0
2
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
1
0
0
0
1
0
1
0
0
0
4
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
2
1
1
1
0
0
0
0
0
0
0
0
0
0
3
2
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
3
0
0
1
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
1
2
0
0
0
2
0
0
0
0
0
0
0
1
0
1
1
1
0
1
0
0
1
0
0
1
0
2
1
0
0
0
0
0
0
0
1
2
2
0
0
0
0
1
1
0
2
0
0
0
2
0
0
2
0
2
0
0
0
2
2
0
0
2
0
0
0
1
0
0
2
1
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
2
2
1
1
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
2
0
0
0
0
1
0
0
0
2
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
3
0
0
4
0
0
0
0
1
1
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
1
1
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
1
1
0
0
0
0
2
2
0
2
0
0
1
0
0
1
0
1
1
0
1
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
1
1
4
1
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
2
4
0
0
2
0
0
2
0
6
5
0
0
0
0
1
0
1
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
2
2
1
0
0
1
0
0
0
0
0
2
0
1
0
1
0
0
0
1
2
2
0
0
0
0
0
0
1
2
0
0
1
0
0
0
2
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
2
1
1
1
0
0
0
0
0
1
0
2
0
0
2
1
3
0
0
0
2
1
0
0
0
3
1
0
0
0
0
0
0
0
1
2
0
0
0
0
3
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
2
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
2
0
0
0
0
1
0
2
0
0
0
0
0
2
0
2
0
1
0
2
0
0
2
1
0
0
4
2
1
0
0
0
0
2
1
0
0
0
0
0
0
2
0
3
3
2
1
1
0
0
0
2
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
1
2
1
1
0
0
1
1
2
0
0
2
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
3
0
0
1
0
1
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
2
1
0
1
0
1
0
0
0
1
0
0
0
2
0
2
0
0
0
1
0
0
0
2
0
2
1
0
2
0
0
0
0
2
0
0
0
1
0
0
0
1
2
0
1
0
0
1
1
0
2
3
0
0
0
0
0
0
1
1
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
1
3
0
1
0
0
3
0
1
1
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
1
0
0
2
2
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
1
1
2
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
4
0
1
2
0
3
0
0
1
2
1
0
0
1
0
1
1
1
2
0
2
1
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
1
0
1
0
1
2
0
1
1
1
0
1
2
2
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
1
0
2
0
0
0
0
1
1
0
0
0
1
0
2
0
0
0
0
0
1
1
0
2
0
0
0
0
0
1
0
0
0
2
1
3
1
1
0
0
0
0
2
2
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
2
0
1
2
0
0
1
0
0
0
1
0
2
0
0
0
0
2
1
0
0
1
1
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
1
0
1
0
1
3
0
2
2
1
2
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
2
0
0
0
0
1
1
0
0
1
0
1
1
1
2
3
2
1
0
0
0
0
0
0
2
1
1
3
0
0
2
0
0
1
0
0
1
0
0
2
0
0
1
2
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
2
0
1
0
0
0
2
2
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
2
0
1
0
0
0
2
0
5
2
1
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
1
2
1
0
0
2
0
0
1
2
3
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
2
2
2
0
0
1
1
0
1
1
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
1
0
2
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
1
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
3
0
0
0
0
0
0
0
0
0
2
6
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
1
0
2
0
0
0
0
1
0
0
0
1
0
2
0
0
2
2
0
0
0
2
3
1
2
0
0
0
0
2
2
2
2
0
0
3
0
0
0
0
0
0
0
1
0
3
0
0
1
2
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
1
2
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
2
0
0
1
2
2
1
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
3
2
0
1
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
1
2
2
0
0
0
0
0
0
1
0
0
4
2
2
0
0
0
0
0
3
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
1
0
2
0
0
0
1
0
0
1
0
0
0
1
0
2
0
1
2
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
5
0
1
0
1
0
4
0
2
1
0
0
0
2
0
0
0
0
0
2
0
0
1
2
1
0
1
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
3
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
2
0
2
0
2
2
0
0
2
0
0
2
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
1
2
0
0
2
2
0
0
0
2
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
4
1
1
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
2
0
6
0
1
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
2
1
0
0
0
0
0
0
1
0
5
0
2
0
1
0
2
0
0
0
0
0
0
0
1
0
1
0
0
1
2
0
0
2
1
0
2
0
2
0
0
1
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
3
2
0
6
1
0
2
0
0
0
0
1
0
0
0
0
1
1
0
0
0
2
0
0
1
1
2
0
2
0
2
0
0
0
0
3
2
1
0
0
0
0
0
0
2
0
2
0
0
1
0
0
2
2
2
2
2
0
0
0
0
1
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
3
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
3
0
0
1
2
7
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
2
2
0
2
2
0
0
0
0
1
1
0
4
2
0
2
0
0
0
1
0
0
0
1
0
2
2
2
3
0
1
0
0
1
0
0
1
0
1
0
0
4
1
0
2
1
0
2
1
2
0
0
1
0
1
0
2
0
0
0
0
0
1
0
2
1
0
1
0
0
0
0
1
0
0
0
0
2
2
2
2
0
0
2
2
0
1
0
0
1
0
0
0
0
1
0
2
2
0
8
0
2
0
0
0
0
5
0
0
0
0
0
0
0
0
4
0
0
0
2
2
0
2
0
0
2
2
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
1
2
1
0
0
2
2
0
0
1
0
0
0
2
1
0
0
0
2
2
1
0
2
2
0
0
0
4
2
0
0
0
3
2
0
0
0
1
0
0
0
2
1
2
2
0
0
3
0
1
1
2
0
1
3
0
0
0
0
0
2
0
0
0
1
0
3
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
1
0
0
0
2
0
0
1
2
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
3
1
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
1
2
1
0
1
1
0
2
1
0
1
3
0
0
0
0
0
0
1
0
0
9
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
2
1
0
2
0
3
3
0
2
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
2
2
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
1
2
0
0
0
2
0
3
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
2
0
2
0
0
0
0
0
1
1
0
2
2
1
0
2
1
2
0
2
0
0
2
2
0
1
0
0
0
1
0
0
0
0
1
0
0
1
3
0
0
0
2
2
0
0
2
0
0
0
0
0
0
2
1
0
0
0
1
0
2
0
3
2
0
0
2
1
1
0
0
2
1
0
3
1
0
0
0
1
2
2
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
2
2
1
1
0
2
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
1
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
2
0
1
0
0
0
1
1
2
0
1
1
0
0
0
1
0
1
0
0
0
1
0
0
2
0
1
1
0
0
0
0
0
0
0
1
2
2
0
0
0
1
0
1
0
2
0
0
0
0
1
0
0
0
2
0
0
1
0
2
0
0
0
0
0
3
0
1
0
2
2
0
1
2
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
2
2
0
2
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
1
2
0
2
2
0
0
2
1
0
0
0
1
2
1
0
0
0
1
0
2
0
2
0
1
1
3
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
2
1
0
0
1
3
0
1
0
1
1
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
2
0
2
0
2
0
0
0
0
0
2
2
2
4
2
0
2
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
2
0
1
0
1
0
0
0
0
0
0
0
2
3
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
1
1
0
1
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
1
0
1
0
0
0
0
1
0
0
0
0
2
0
2
1
1
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
1
0
1
5
1
0
2
0
1
1
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
1
1
0
0
0
1
0
0
0
2
1
0
2
0
0
2
0
0
1
0
0
1
0
1
0
2
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
2
2
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
1
0
4
2
0
1
0
0
0
0
0
4
0
2
0
0
2
1
2
0
0
1
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
3
2
0
0
1
0
1
0
0
2
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
2
0
0
2
2
0
0
0
1
0
2
0
2
0
3
0
2
0
0
0
0
2
2
2
0
2
1
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
1
0
5
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
1
0
0
0
2
0
0
0
1
1
1
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
3
0
0
0
0
0
2
0
0
0
2
2
0
0
2
0
0
0
1
1
0
0
0
0
0
2
2
0
2
0
0
0
2
0
0
0
1
2
2
0
0
0
1
3
0
0
1
0
0
0
2
0
0
0
2
0
1
0
2
0
0
0
1
0
2
2
0
2
0
0
2
0
0
0
0
0
0
2
0
1
2
0
0
0
0
1
0
0
1
0
0
2
1
0
2
1
1
0
0
4
2
0
0
0
1
0
1
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
2
0
0
0
1
1
1
0
0
2
3
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
1
1
1
0
0
0
1
4
0
2
0
0
0
1
0
0
0
0
0
2
0
0
1
1
0
0
2
0
0
0
0
0
2
0
0
0
2
1
3
0
0
2
1
1
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
2
0
1
0
0
1
0
2
0
0
0
0
0
0
0
1
2
1
0
1
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
2
2
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
2
0
2
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
3
0
0
2
0
2
2
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
3
1
0
0
0
2
0
2
0
1
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
1
1
0
0
0
1
0
1
0
2
0
1
2
0
0
1
2
1
2
0
0
4
0
0
0
2
2
0
2
0
0
0
0
0
1
1
0
2
2
0
2
0
0
1
0
1
0
1
0
0
1
0
2
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
3
0
0
2
0
0
0
2
2
0
2
0
0
1
2
0
0
0
0
1
0
0
0
2
0
0
1
2
0
0
1
2
0
2
2
0
2
0
2
0
0
0
0
0
0
0
1
1
0
0
0
1
0
2
0
0
0
0
0
0
1
0
1
0
2
0
2
0
0
0
0
0
1
2
0
2
1
0
2
2
0
1
0
0
0
0
0
2
0
0
0
3
1
0
2
0
0
0
2
0
0
0
0
0
3
0
0
2
0
2
0
2
1
2
0
2
1
0
2
0
0
1
1
2
1
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
3
0
1
0
0
0
0
3
0
0
0
2
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
1
0
0
2
0
2
0
2
0
1
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
2
0
2
2
0
0
0
2
0
3
0
0
0
0
0
0
2
1
1
0
0
0
0
1
1
0
0
2
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
1
0
1
0
0
1
1
2
0
2
0
2
0
2
0
1
0
1
0
0
2
1
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
1
1
3
4
0
2
1
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
2
0
0
2
0
0
3
2
0
0
0
2
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
2
1
1
0
0
0
3
0
0
2
0
1
1
0
0
1
0
0
0
0
1
0
0
0
2
1
0
1
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
2
0
0
0
0
1
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
1
0
2
0
0
1
0
0
0
0
1
0
0
0
0
1
1
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
2
2
0
2
0
3
2
0
0
5
0
0
2
1
0
0
0
1
0
0
0
2
1
0
0
0
2
0
2
0
2
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
1
1
0
0
0
2
0
2
0
0
0
0
0
2
0
1
0
0
0
1
1
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
1
0
2
0
1
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
1
1
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
1
2
2
1
0
0
0
0
0
0
0
2
0
0
0
0
1
2
1
0
0
3
0
0
0
0
1
0
1
0
3
0
2
0
1
0
0
0
0
2
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
1
0
1
2
0
2
0
0
0
0
1
0
1
3
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
3
2
0
2
2
0
0
0
0
1
1
0
3
0
0
0
0
1
0
0
0
1
1
0
0
0
2
2
0
2
0
2
1
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
1
0
2
2
0
0
0
0
2
0
0
0
0
0
1
1
0
2
0
1
0
0
0
2
2
1
0
2
1
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
2
0
2
1
0
0
2
0
0
0
0
2
0
2
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
2
0
1
0
0
1
0
0
0
3
0
0
0
0
1
1
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
2
2
2
1
2
2
0
1
0
0
1
0
0
0
0
0
2
0
0
0
2
2
1
2
0
2
0
1
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
4
0
1
3
0
2
0
0
0
2
0
2
0
0
1
2
0
0
2
1
1
0
0
1
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
11
1
0
0
0
1
0
0
1
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
2
0
0
3
3
0
0
0
1
2
0
0
2
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
1
0
0
1
0
2
0
2
0
1
2
0
0
0
1
0
1
0
0
2
0
0
0
0
3
2
0
0
2
1
3
0
1
0
0
0
1
0
1
0
2
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
2
0
0
0
0
2
1
1
1
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
1
0
0
2
1
0
1
2
0
0
0
0
0
2
2
0
0
1
0
2
0
2
2
1
2
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
2
0
1
0
0
0
0
1
2
0
2
0
0
0
0
3
2
0
2
0
1
2
0
2
0
0
1
2
0
0
1
0
0
0
0
1
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
1
0
2
1
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
2
0
1
0
3
0
1
2
2
0
0
0
0
0
0
0
0
3
0
3
0
1
0
0
0
0
0
0
2
0
2
1
2
0
0
0
2
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
1
2
1
0
0
2
0
0
0
1
2
1
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
1
2
2
0
0
0
0
0
0
0
0
2
2
2
1
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
1
0
1
1
0
0
2
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
2
3
0
2
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
1
2
1
3
0
2
1
3
0
1
0
2
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
1
0
1
0
2
1
0
0
0
0
0
1
0
0
1
0
0
2
3
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
1
0
1
1
0
1
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
1
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
2
0
2
0
2
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
2
2
0
2
1
2
0
0
2
0
0
0
0
8
0
0
0
0
0
2
1
0
0
0
2
2
0
0
0
0
0
1
0
2
0
0
0
3
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
2
0
0
2
0
0
2
2
0
0
2
1
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
1
0
2
0
0
0
0
0
0
2
1
0
1
0
1
0
1
0
2
1
0
1
0
2
2
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
5
0
3
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
3
0
0
0
1
0
2
0
1
2
0
0
0
0
0
4
2
1
0
0
1
2
0
0
2
0
1
0
0
2
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
3
0
2
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
2
0
2
0
0
1
0
4
3
0
2
1
0
0
0
0
0
0
1
0
0
3
0
0
0
2
0
1
0
2
2
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
2
0
0
0
0
1
0
0
2
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
1
0
0
0
2
0
0
1
0
0
1
0
1
1
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
1
0
2
0
0
0
0
0
1
3
0
0
1
1
3
0
0
0
2
0
0
0
2
2
0
0
1
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
1
2
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
2
2
1
0
0
1
0
1
1
0
0
0
0
0
4
0
1
0
0
0
3
2
2
0
1
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
2
0
0
0
1
0
2
4
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
2
0
2
0
2
0
0
0
0
2
0
0
0
0
0
2
0
1
2
0
1
0
0
2
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
2
0
2
1
2
0
2
0
0
0
2
0
2
2
0
1
0
0
0
1
0
0
0
0
0
2
0
1
0
1
0
0
2
0
0
0
1
0
0
1
2
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
3
0
1
0
1
0
1
0
2
1
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
2
0
0
1
1
0
1
1
0
0
1
1
0
2
1
0
0
0
1
0
2
0
0
0
0
3
0
0
1
0
0
6
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
1
2
1
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
3
0
2
0
0
1
0
1
0
0
0
0
0
2
2
0
1
0
1
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
2
2
0
0
0
0
2
2
0
0
0
0
0
2
0
5
0
0
0
0
0
0
0
1
0
0
3
1
2
1
0
5
2
2
0
0
2
11
0
0
2
1
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
2
1
0
0
1
0
1
0
0
0
0
0
0
1
2
0
1
2
1
0
0
0
0
1
0
2
0
2
1
2
0
0
0
1
0
0
0
0
0
1
0
2
0
5
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
3
2
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
1
0
2
0
2
3
0
0
0
0
0
0
2
1
2
0
0
1
0
0
3
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
2
1
1
0
0
1
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
1
1
0
0
0
1
2
0
1
2
1
0
1
3
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
2
3
0
1
0
0
0
1
0
1
1
0
0
2
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
1
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
2
1
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
1
2
2
3
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
2
0
2
0
2
0
2
0
0
2
2
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
3
0
0
0
2
1
0
0
0
3
0
2
0
0
0
0
1
0
0
0
0
2
1
0
0
1
0
1
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
2
0
0
0
1
0
1
0
0
0
2
0
0
1
0
0
1
3
0
1
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
2
0
2
1
1
0
1
0
0
1
1
0
0
0
0
0
0
2
2
1
2
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
3
1
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
2
2
1
0
2
1
0
0
2
1
2
1
2
2
2
2
0
1
0
0
0
0
2
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
1
0
1
0
0
0
0
0
5
0
0
0
1
0
3
0
0
0
0
3
0
2
0
2
1
0
0
2
0
0
3
1
1
0
0
2
0
3
2
0
1
0
0
0
2
0
0
2
0
2
0
2
0
0
0
4
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
2
0
0
1
5
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
5
2
0
2
0
0
0
0
2
0
4
0
0
0
3
3
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
4
0
0
0
0
0
0
1
0
0
0
1
3
2
0
0
0
0
3
0
0
0
1
2
0
0
0
1
1
2
2
0
0
2
0
0
0
0
0
0
0
2
0
0
2
1
1
0
0
0
0
1
3
1
2
0
0
0
1
0
2
0
0
1
0
0
0
0
0
2
1
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
3
0
0
2
2
1
0
0
2
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
1
0
2
0
0
0
2
0
2
0
0
2
0
0
0
0
1
1
0
0
1
1
0
0
1
1
1
0
0
0
0
0
0
2
0
0
1
0
1
0
1
0
2
0
1
2
0
0
2
0
1
1
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
2
0
2
0
1
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
2
1
0
2
0
0
0
1
0
0
0
2
0
0
1
2
0
0
0
2
2
1
0
1
0
0
0
0
2
2
0
0
0
1
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
2
1
2
2
2
0
0
1
0
0
0
1
2
0
1
2
0
0
1
1
0
1
2
3
0
1
0
1
0
0
0
2
1
1
0
0
0
2
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
2
0
1
2
2
3
0
0
0
0
2
2
8
0
0
0
2
2
0
0
0
2
0
0
0
2
0
2
0
0
0
0
2
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
2
0
2
0
3
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
8
0
0
0
0
0
1
2
0
0
0
1
0
2
2
0
0
0
2
2
0
2
0
0
2
0
0
0
1
0
0
0
0
2
0
7
0
0
0
2
0
0
0
0
1
1
0
0
0
0
2
2
2
0
0
1
0
0
2
0
0
1
0
0
7
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
2
0
1
2
0
3
0
1
0
0
2
0
0
0
1
0
0
3
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
4
2
0
2
0
2
3
0
1
1
0
2
2
1
0
2
5
0
0
2
2
0
0
1
2
0
0
2
2
0
1
0
1
0
0
0
0
1
0
2
2
0
0
2
1
0
2
1
0
0
2
0
0
2
0
0
1
1
0
6
0
0
0
1
0
0
1
2
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
1
1
0
0
2
0
0
2
0
0
0
1
0
0
0
1
0
0
1
0
0
1
1
1
0
0
0
0
0
2
0
2
0
0
0
0
0
1
5
0
0
0
2
2
2
0
2
0
2
0
0
0
0
0
2
0
0
2
0
0
1
1
0
2
2
0
1
0
0
1
0
1
0
0
3
2
2
0
0
0
2
0
0
0
0
0
2
2
2
0
0
0
2
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
2
2
1
0
0
0
5
0
0
0
0
2
2
1
2
0
0
0
2
0
0
1
0
0
2
2
0
0
2
0
2
2
0
0
0
0
0
0
0
8
2
0
0
0
0
2
0
0
0
0
1
3
0
0
0
1
0
2
0
4
0
0
0
0
1
1
1
2
0
2
0
0
3
2
0
0
0
1
2
1
0
1
0
0
0
0
0
2
2
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
2
0
3
0
0
0
5
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
1
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
1
1
0
0
0
0
0
2
2
0
0
2
0
0
1
0
0
0
0
0
2
0
1
2
0
0
1
3
0
0
0
1
0
2
2
1
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
1
2
1
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
1
0
0
0
0
0
1
0
0
2
2
2
1
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
2
2
1
0
0
0
0
0
0
2
0
2
1
3
0
1
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
2
2
1
2
1
0
1
1
0
0
2
1
2
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
2
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
3
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
2
0
0
0
1
0
2
0
0
2
0
0
2
0
1
0
0
2
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
1
0
1
0
1
3
4
0
3
0
2
0
0
0
0
2
0
2
0
1
0
0
0
0
0
2
0
1
1
0
1
0
10
0
0
0
0
0
0
1
1
0
2
0
0
1
0
0
0
3
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
1
0
0
1
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
2
1
2
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
2
0
0
1
1
0
0
2
2
2
0
2
0
0
0
1
0
1
0
2
0
1
0
0
1
0
1
0
2
1
1
0
0
0
0
1
0
1
2
2
2
0
0
0
2
0
1
0
0
0
2
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
1
0
2
0
3
2
0
1
0
0
0
0
2
0
1
2
0
2
0
2
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
4
0
1
1
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
2
1
0
3
0
0
0
1
0
1
3
0
0
1
1
6
1
0
1
1
2
0
0
0
0
2
0
1
0
1
0
3
2
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
1
0
0
0
2
0
4
0
0
0
0
0
1
0
0
0
0
1
2
1
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
3
2
1
0
2
2
2
1
1
0
0
0
2
1
0
0
0
0
0
1
0
0
0
3
0
0
0
0
1
1
0
0
0
2
0
3
1
0
0
0
2
2
2
1
0
2
1
0
1
3
0
0
2
0
0
2
2
0
0
2
1
0
0
0
0
0
1
0
1
2
2
2
0
2
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
1
0
4
2
0
0
0
1
0
0
2
0
2
1
1
0
0
0
1
0
1
0
0
0
0
0
2
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
2
0
1
1
1
1
2
1
1
0
2
0
0
0
0
0
0
0
0
1
2
0
0
2
2
0
1
2
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
2
1
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
1
1
2
0
1
2
0
0
1
3
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
2
1
0
0
0
0
0
1
0
1
2
0
2
0
0
0
0
1
0
0
1
1
1
0
1
23
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
2
0
0
0
2
2
0
0
2
0
0
0
3
2
0
0
2
0
1
0
0
1
0
2
2
3
2
2
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
2
0
0
2
0
0
0
0
0
0
2
0
0
1
2
0
0
2
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
2
0
1
0
1
0
0
1
0
2
1
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
1
0
0
2
0
0
0
2
0
0
0
2
2
2
0
1
0
4
0
1
0
0
0
0
1
2
4
0
1
0
2
2
2
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
2
0
0
0
0
3
0
1
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
1
1
0
0
1
0
0
4
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
2
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
2
0
2
0
2
0
0
1
1
2
2
0
2
0
0
0
0
0
0
3
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
2
0
0
0
1
0
1
2
1
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
1
0
0
1
0
1
2
4
0
0
2
2
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
2
1
0
2
0
1
2
1
1
0
2
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
2
0
2
0
2
1
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
2
0
2
1
0
1
1
0
0
2
1
1
0
0
0
0
0
0
0
3
1
0
0
1
2
0
0
0
2
0
0
1
0
3
1
0
1
0
0
0
0
4
2
0
1
0
2
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
5
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
2
1
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
2
1
2
0
0
0
0
1
2
0
0
1
2
0
0
0
0
0
2
0
0
0
1
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
4
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
2
2
2
0
0
0
0
0
3
0
0
0
0
1
0
0
0
2
1
0
0
4
0
2
0
1
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
2
1
2
0
0
2
1
0
1
0
1
0
2
1
3
0
1
0
1
0
0
0
0
0
0
2
2
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
2
1
1
2
1
0
0
0
1
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
2
2
0
2
0
2
0
0
2
1
0
1
2
0
0
0
1
0
0
0
0
1
0
2
0
1
1
0
0
2
1
0
0
0
0
0
1
0
1
0
0
0
1
1
0
1
0
1
0
0
2
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
2
0
0
0
0
0
1
0
2
1
0
0
0
0
1
2
0
2
0
2
1
2
0
1
2
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
2
0
0
0
2
0
2
1
3
1
1
0
0
0
0
0
0
1
2
1
6
1
0
0
0
8
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
4
0
2
0
0
0
2
0
0
2
0
0
0
0
0
3
0
1
0
0
2
0
0
0
0
1
0
2
0
1
0
3
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
4
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
2
0
0
1
0
0
1
2
0
1
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
2
0
2
0
8
1
2
2
0
1
0
1
0
1
2
0
0
0
0
0
1
0
0
1
0
0
0
2
0
1
0
4
2
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
1
2
1
0
2
2
0
1
0
0
0
1
0
1
0
0
1
2
0
0
0
1
0
0
0
0
2
1
0
2
0
1
2
0
0
1
1
2
1
0
0
0
0
0
0
0
1
2
0
1
2
0
0
0
2
0
0
0
2
0
0
2
0
1
0
1
2
0
0
0
0
0
0
2
2
2
1
2
1
0
0
0
0
2
2
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
1
0
2
1
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
2
0
0
2
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
2
2
0
4
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
1
2
2
0
1
0
1
0
2
0
1
1
0
1
2
0
0
0
1
0
0
0
0
4
0
2
0
0
2
2
0
0
0
0
1
0
1
0
2
0
0
2
0
0
0
0
1
0
1
0
0
0
0
2
0
2
0
2
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
1
1
1
0
0
0
2
0
0
0
2
4
0
2
1
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
3
0
0
2
0
0
0
0
1
2
0
1
0
0
0
0
3
0
0
2
0
0
0
0
1
2
0
1
1
0
2
0
1
0
0
0
6
1
2
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
1
2
2
0
0
0
1
0
0
0
2
0
2
2
2
1
0
2
1
0
0
2
0
0
2
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
0
2
0
2
2
2
0
0
0
1
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
2
0
2
0
0
1
0
1
0
1
0
0
2
0
3
0
1
0
1
0
1
0
2
0
1
0
0
0
0
0
2
2
0
2
2
2
0
0
0
0
0
0
0
0
0
2
1
0
2
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
2
0
0
1
0
0
0
1
0
2
0
0
1
0
1
1
1
2
1
1
0
4
0
1
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
2
2
0
0
2
0
6
1
2
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
2
0
1
0
2
0
1
0
0
1
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
1
0
2
0
0
0
1
0
0
0
0
0
1
0
1
0
2
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
1
0
2
0
1
0
0
0
0
0
0
0
2
1
1
0
1
1
2
0
1
0
0
1
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
3
0
0
0
0
0
6
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
3
2
0
0
0
2
0
0
1
0
0
0
3
0
0
0
0
1
0
2
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
2
1
0
0
0
3
0
0
0
2
0
0
0
1
2
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
1
0
0
2
0
1
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
2
0
2
1
0
1
0
0
2
0
0
1
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
1
0
1
1
0
2
0
0
0
1
2
0
1
3
0
0
0
0
2
0
1
0
2
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
1
1
0
0
1
1
0
0
2
0
1
0
0
0
2
0
0
0
0
7
2
0
1
1
2
1
2
3
0
0
0
3
0
0
1
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
3
0
1
0
2
0
0
2
1
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
2
0
2
0
0
4
0
0
0
2
0
0
0
2
0
0
0
1
0
3
0
0
0
0
0
1
0
1
1
0
0
3
1
0
0
0
0
2
0
1
2
2
0
0
1
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
2
0
0
1
0
2
0
2
3
0
2
1
0
0
2
2
0
0
0
0
0
2
0
0
2
1
0
4
0
0
0
0
1
1
2
2
0
1
2
1
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
2
0
1
0
0
2
0
1
0
0
1
3
0
0
1
0
0
0
0
0
2
0
0
1
1
2
0
0
0
1
0
0
0
1
1
0
0
0
2
0
1
1
1
2
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
4
1
0
0
2
0
0
0
2
0
2
1
1
0
2
1
0
0
0
2
2
0
0
2
1
0
1
1
0
0
1
1
2
0
0
3
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
1
0
2
0
1
2
1
1
0
2
0
0
0
0
1
2
0
1
2
1
0
3
2
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
2
0
0
1
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
2
1
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
3
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
1
0
1
7
1
2
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
1
0
0
4
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
1
2
0
0
2
9
0
0
0
0
0
0
2
1
1
0
2
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
2
0
3
0
0
0
0
0
0
1
0
0
1
2
0
2
0
1
1
0
0
1
0
0
2
1
2
1
0
0
1
0
3
0
0
1
3
1
1
0
1
0
0
0
1
0
2
2
0
1
1
2
0
0
1
2
1
1
1
2
0
1
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
2
2
0
0
1
0
0
0
1
0
0
2
1
2
0
0
2
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
3
0
0
4
2
0
0
0
1
2
2
0
0
0
0
0
1
2
0
0
0
1
2
0
0
2
0
0
2
6
0
1
4
0
0
0
0
0
0
0
0
0
0
0
6
0
1
1
0
0
0
0
1
0
0
2
2
0
3
1
1
0
2
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
1
1
0
1
0
3
2
0
0
2
0
2
0
0
1
0
0
0
0
2
0
0
2
0
2
0
0
0
0
1
1
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
2
0
2
1
0
2
2
0
0
0
2
1
0
0
0
1
1
1
2
0
0
2
1
0
1
1
0
0
0
0
2
0
0
0
0
2
2
1
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
1
0
1
0
0
0
2
0
0
2
2
0
1
0
0
2
0
0
0
2
2
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
2
2
0
0
1
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
1
1
2
2
1
0
2
3
1
0
0
0
0
1
0
0
2
1
0
1
0
0
0
0
2
0
0
0
2
1
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
2
2
1
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
2
1
0
0
0
0
1
0
0
0
2
0
0
0
0
1
2
0
0
0
0
1
0
0
0
3
0
1
0
2
0
0
1
1
2
0
2
1
1
1
0
0
0
0
1
0
4
0
1
0
2
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
2
0
0
1
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
1
0
0
1
0
0
2
0
0
2
0
0
0
0
0
4
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
1
2
2
0
0
0
0
1
0
2
0
2
2
1
0
1
1
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
2
0
2
0
1
0
0
0
1
0
2
2
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
2
2
0
0
0
2
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
1
0
1
0
2
2
2
1
1
1
0
3
1
0
0
0
0
4
0
0
0
2
1
2
0
0
0
2
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
2
1
0
1
2
2
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
2
3
0
0
0
0
1
2
0
0
0
0
0
0
1
0
1
2
1
1
0
0
0
4
0
0
0
2
0
1
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
2
1
0
2
0
1
2
4
0
0
0
3
1
0
1
2
0
0
4
1
0
0
0
1
0
0
0
1
0
0
2
0
0
2
0
1
4
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
1
1
0
1
0
0
1
1
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
4
0
1
0
2
1
0
0
2
1
0
2
3
0
0
2
2
0
4
2
2
0
0
2
2
0
0
0
2
0
0
0
1
2
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
1
0
2
0
1
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
2
1
0
3
0
0
1
1
2
2
0
0
0
2
1
0
0
2
0
1
0
0
2
0
0
0
0
0
2
3
0
1
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
2
0
4
1
0
0
1
0
0
0
1
0
2
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
2
2
0
0
0
0
0
2
0
1
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
2
0
0
0
7
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
2
0
0
0
0
0
1
0
0
3
2
2
0
0
0
0
2
0
0
0
2
0
2
0
0
2
1
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
2
1
0
1
0
0
0
0
0
1
1
2
1
3
3
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
2
2
1
0
2
2
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
2
1
0
0
2
2
1
0
2
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
2
0
0
0
1
0
0
0
3
0
0
0
0
2
0
0
0
2
2
0
0
0
0
2
3
1
0
1
0
0
0
2
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
1
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
3
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
3
1
1
1
2
2
1
1
0
2
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
3
0
0
1
0
0
0
1
0
2
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
1
0
1
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
2
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
3
1
1
0
0
0
0
0
0
0
2
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
3
0
1
2
0
2
2
0
1
0
0
1
2
2
0
2
0
2
2
0
0
1
0
1
2
0
3
0
0
2
2
1
0
0
3
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
2
0
0
2
0
0
0
2
0
0
0
0
1
1
1
0
2
1
1
0
2
1
0
1
0
0
0
2
0
0
0
4
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
2
1
0
0
1
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
2
0
2
0
0
0
3
0
0
2
2
2
2
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
4
1
0
1
0
1
1
0
0
0
2
0
2
1
1
0
1
0
0
1
2
2
2
0
2
0
1
0
0
1
0
1
1
0
0
0
2
0
0
0
6
0
0
0
2
2
1
1
0
0
3
1
0
0
0
2
1
0
2
2
0
0
0
0
0
2
2
2
1
1
2
0
0
2
0
1
0
0
0
0
0
0
0
1
2
0
2
0
2
0
1
0
0
0
0
1
0
0
0
2
0
2
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
3
3
2
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
2
0
0
0
0
2
0
2
2
0
0
2
0
0
2
2
0
1
1
0
0
0
0
2
0
0
1
1
1
2
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
3
0
0
3
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
4
1
2
2
2
0
0
2
2
0
0
0
2
0
2
0
0
0
0
1
2
2
1
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
3
1
0
0
0
0
0
0
0
2
2
0
0
2
0
0
2
0
2
0
0
0
6
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
3
0
0
2
0
2
0
0
0
0
0
2
2
0
0
1
2
2
0
0
4
0
2
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
4
0
1
1
0
0
1
1
0
1
0
0
2
2
2
1
0
1
0
1
0
0
0
1
2
3
0
0
3
0
1
0
1
0
0
0
2
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
1
0
0
0
2
1
0
2
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
2
0
6
2
2
2
0
0
0
0
0
2
0
0
2
1
0
0
1
1
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
1
1
0
0
0
2
0
0
0
1
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
2
1
2
0
0
0
0
3
0
1
0
2
0
2
2
0
0
0
2
2
0
2
0
0
0
1
0
2
0
2
0
0
2
0
3
0
2
0
0
0
2
2
0
2
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
3
2
2
2
3
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
1
0
0
0
2
0
3
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
2
0
0
0
2
2
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
1
3
0
0
0
0
2
1
2
0
0
0
0
2
2
0
1
0
0
0
2
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
2
0
0
0
1
0
1
0
0
0
1
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
2
0
0
2
2
1
0
0
1
0
3
0
0
2
1
0
0
2
0
1
0
2
0
0
1
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
2
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
3
0
0
3
0
0
0
0
0
0
1
0
1
0
1
0
0
0
2
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
9
0
1
0
0
0
1
1
0
1
2
0
0
0
0
0
0
1
0
2
0
1
2
0
2
0
2
2
0
0
1
0
1
2
0
0
0
2
0
0
0
0
7
0
2
1
2
2
0
0
2
0
0
0
1
1
2
2
1
0
0
2
2
0
0
2
0
2
0
1
0
0
0
0
0
0
3
0
0
1
1
1
1
0
0
0
2
2
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
2
0
1
0
3
0
0
1
1
0
0
0
0
1
2
0
0
3
0
0
0
1
0
1
1
0
2
1
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
1
1
2
0
0
1
1
1
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
3
0
2
1
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
1
0
1
0
2
4
0
1
0
0
0
0
2
1
1
0
1
0
0
1
2
0
0
1
1
0
0
2
0
0
0
1
0
1
1
2
0
1
3
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
2
0
1
0
0
0
2
0
2
0
1
0
0
0
1
0
2
0
1
0
0
0
2
0
0
0
1
0
0
0
0
2
6
3
2
0
2
3
0
0
0
0
1
4
1
0
0
0
0
0
0
1
0
2
0
1
0
2
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
2
0
2
0
0
0
2
1
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
2
1
1
0
0
0
3
0
0
1
0
0
0
2
1
0
2
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
2
0
2
1
0
1
1
1
0
0
2
0
0
2
0
1
0
0
0
2
1
0
1
0
1
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
2
6
0
2
0
2
2
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
3
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
3
0
0
0
0
2
1
0
2
0
0
0
0
0
0
2
1
1
1
0
1
0
1
0
0
2
0
1
0
2
0
0
0
4
0
0
1
0
1
0
0
0
0
0
2
1
0
3
0
0
1
2
2
1
2
0
0
0
4
2
2
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
2
0
1
2
1
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
3
3
0
0
0
0
1
0
2
0
2
0
0
1
0
2
2
1
0
0
0
2
1
2
0
1
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
1
0
5
0
0
0
2
0
0
0
0
0
0
3
0
3
2
1
2
1
0
1
2
1
0
3
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
2
1
0
1
1
0
0
2
0
2
0
0
0
0
0
0
0
2
2
0
0
1
0
0
1
0
0
0
0
2
0
0
3
1
1
0
0
1
0
0
0
0
0
0
2
0
1
0
0
2
3
2
0
0
2
2
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
1
0
0
0
2
0
1
0
2
1
0
0
0
2
0
0
1
2
2
1
0
0
2
1
0
0
1
2
0
1
1
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
2
1
0
0
2
0
0
2
0
0
1
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
2
2
0
0
0
0
0
0
1
1
0
1
2
0
1
0
0
0
2
2
1
0
0
0
1
0
0
2
0
0
0
1
0
2
0
0
0
0
1
1
1
0
0
0
2
0
0
0
0
0
0
1
0
1
1
1
1
0
0
0
0
2
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
1
1
0
0
0
0
1
1
0
2
0
0
1
0
0
1
3
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
2
1
1
0
0
1
2
2
0
0
0
1
0
0
0
2
0
2
0
2
2
1
0
0
0
0
0
2
0
1
0
2
0
1
2
0
1
0
0
0
0
0
0
2
1
2
0
1
2
0
0
0
1
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
2
2
1
0
2
0
2
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
2
0
0
0
0
2
2
1
2
2
0
0
0
0
0
0
1
0
0
2
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
2
2
0
2
0
1
0
0
0
2
2
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
1
1
0
2
2
0
0
2
0
1
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
3
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
2
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
1
1
0
0
0
1
2
0
0
0
3
0
1
1
1
0
0
0
2
0
0
0
4
0
0
1
0
1
0
0
0
0
2
0
0
1
4
0
1
1
1
0
1
0
0
0
0
1
0
0
0
2
0
0
2
1
0
0
0
0
2
0
0
0
0
0
1
2
1
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
2
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
2
1
0
0
0
0
2
1
0
0
0
0
0
0
0
2
1
0
0
1
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
2
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
1
0
0
0
2
3
0
2
0
2
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
2
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
2
1
0
0
2
2
1
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
2
0
0
1
1
1
1
0
0
0
0
2
0
0
0
2
0
0
0
0
1
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
2
2
0
1
0
2
0
0
1
0
0
0
1
0
2
0
0
0
0
0
2
0
1
1
0
0
0
0
0
3
0
1
2
0
0
0
0
0
0
0
0
0
1
0
1
3
0
0
0
2
2
0
0
0
2
1
1
2
2
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
2
0
0
0
2
0
1
1
0
0
0
0
2
0
0
2
0
2
0
1
0
1
1
2
0
0
0
0
2
0
1
0
0
0
0
0
0
2
2
2
0
0
0
1
0
0
2
2
0
0
2
2
0
0
1
0
1
2
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
2
1
0
2
0
0
3
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
3
2
2
0
2
1
0
0
0
0
2
1
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
2
1
0
1
0
2
0
0
2
0
0
0
0
2
0
2
0
2
0
0
1
0
1
0
0
0
2
2
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
1
3
0
0
2
2
0
1
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
3
2
1
1
1
2
1
1
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
2
0
1
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
3
0
0
2
0
0
0
2
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
1
2
2
0
0
3
0
1
2
0
0
0
0
0
0
1
0
0
2
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
1
2
0
1
0
0
1
0
1
2
0
0
0
3
2
1
0
1
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
1
0
1
0
0
2
2
1
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
1
0
2
1
0
0
0
0
0
1
0
0
0
0
0
2
1
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
2
2
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
2
0
3
0
0
0
1
0
0
0
1
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
2
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
2
0
2
1
2
0
2
0
0
0
0
0
0
1
1
2
0
0
1
1
1
0
1
0
1
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
2
0
0
2
0
1
0
0
0
1
1
0
0
3
3
0
1
0
0
1
2
2
0
0
0
0
4
0
0
4
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
3
3
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
3
2
0
0
1
0
0
0
0
0
2
0
3
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
2
0
2
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
2
0
3
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
2
2
0
0
1
1
1
0
1
2
0
1
2
0
1
0
0
0
0
2
1
0
0
1
0
1
2
1
0
2
0
0
0
0
2
0
0
0
2
0
0
2
2
0
0
0
1
0
0
0
1
0
0
2
2
0
1
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
1
0
2
1
2
0
0
2
0
0
1
0
0
0
2
2
0
2
0
2
1
2
2
1
0
0
0
1
3
1
0
2
0
2
0
0
1
0
1
2
0
0
0
2
0
0
0
1
0
2
0
0
0
1
1
0
0
0
0
0
2
2
0
3
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
3
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
2
1
0
1
0
0
3
2
2
0
0
0
0
0
0
1
1
6
1
0
2
0
0
0
0
0
1
0
2
0
1
0
3
0
0
2
1
1
0
1
7
0
0
2
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
2
0
0
0
0
5
0
0
0
0
0
0
2
0
0
0
1
3
0
0
0
2
2
0
0
1
0
1
0
0
0
0
1
1
2
0
0
1
1
0
1
2
0
0
0
2
0
0
2
0
0
1
0
1
0
0
2
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
2
0
0
0
0
0
0
3
2
0
0
1
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
1
0
1
3
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
1
0
2
1
0
0
2
0
2
0
0
0
0
3
0
1
1
0
0
3
0
7
0
0
1
2
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
2
0
2
1
1
0
1
0
0
1
1
1
0
2
2
0
0
1
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
2
0
0
2
1
0
0
0
0
0
0
1
2
0
0
0
0
1
0
1
0
0
2
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
1
2
0
0
0
0
1
0
0
0
0
2
0
1
0
2
0
0
0
0
0
2
0
0
1
1
1
1
1
0
1
1
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
3
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
2
1
0
1
0
2
0
0
0
1
0
0
2
0
1
2
0
0
2
0
0
0
4
0
0
0
0
0
0
1
2
1
0
2
0
2
0
0
1
0
0
1
0
2
2
0
0
1
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
1
2
2
0
0
0
0
0
1
0
2
0
0
0
0
1
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
3
0
2
0
0
0
0
0
2
0
0
0
3
0
0
2
0
0
0
0
0
0
2
0
0
2
2
0
0
2
0
0
0
1
1
0
0
0
0
0
0
2
1
0
1
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
1
2
0
0
1
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
3
1
0
1
0
1
2
0
0
0
0
1
1
1
0
1
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
1
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
2
0
0
0
0
2
0
1
0
2
0
0
0
0
2
0
1
0
2
0
0
1
1
2
0
0
0
0
0
0
0
2
0
0
2
0
2
1
1
0
0
0
0
0
1
0
0
2
2
0
0
0
3
1
0
1
0
0
0
0
0
0
0
0
1
0
0
2
1
1
2
1
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
1
2
0
1
0
0
0
2
0
0
0
0
1
2
2
0
0
0
0
0
1
0
3
0
0
0
2
0
0
0
0
0
0
2
2
0
2
0
0
0
2
1
0
2
0
0
3
0
0
0
2
2
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
1
1
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
2
1
0
0
0
1
2
1
0
0
0
1
1
0
0
1
1
2
1
2
1
0
0
0
0
0
1
1
2
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
2
2
0
2
2
0
0
2
0
2
0
0
0
1
2
0
0
1
0
0
2
0
0
1
0
1
3
1
0
0
0
2
0
2
0
1
1
1
3
0
0
3
5
2
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
2
0
0
2
0
0
2
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
1
1
0
0
0
0
2
0
0
2
1
2
0
2
0
0
0
0
1
1
1
1
1
0
0
2
2
1
2
1
0
1
1
0
0
1
1
0
0
0
0
0
2
0
0
3
1
2
0
1
0
2
0
0
1
0
0
2
0
0
0
0
0
1
2
0
2
0
1
0
1
0
2
2
2
0
0
0
2
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
2
0
0
1
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
6
3
0
1
3
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
1
0
1
0
0
1
1
0
1
1
0
0
2
1
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
1
3
2
0
0
0
0
0
0
4
0
2
0
0
0
0
0
1
0
2
1
0
2
1
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
2
0
2
0
0
0
0
0
2
0
1
2
0
0
0
0
0
1
0
0
0
3
2
0
0
4
0
1
0
0
2
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
1
2
0
0
0
1
0
2
1
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
2
0
0
1
1
0
2
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
4
0
4
1
2
0
2
0
0
0
0
1
0
0
1
0
2
3
1
2
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
2
2
1
0
0
1
0
0
1
0
0
0
1
0
0
1
2
0
0
0
2
0
1
2
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
2
1
2
0
0
3
0
0
0
0
0
0
1
0
5
0
0
0
0
0
0
2
2
1
0
1
1
2
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
3
1
0
0
0
0
1
0
0
1
0
0
0
1
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
1
1
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
2
0
0
2
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
1
0
2
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
2
1
0
1
0
1
0
0
2
0
0
1
1
2
2
1
0
1
0
0
0
2
1
0
2
0
0
1
0
1
0
0
2
1
1
2
0
0
2
0
1
2
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
1
1
2
0
1
0
0
2
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
3
0
0
0
2
0
0
0
2
0
0
2
0
0
1
0
1
0
1
0
0
0
0
2
2
1
0
0
0
0
1
2
0
2
0
1
0
2
1
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
1
1
2
0
2
0
0
2
2
0
0
0
0
0
0
0
1
0
2
0
0
2
1
1
1
0
2
1
0
2
1
0
2
0
2
0
0
0
0
3
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
2
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
1
0
0
2
1
1
0
0
1
0
1
0
0
1
0
1
2
0
2
2
0
1
0
0
0
0
0
2
0
2
2
0
0
0
3
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
2
1
0
0
2
0
0
0
1
0
0
2
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
1
0
0
0
4
1
0
0
2
0
0
0
1
0
2
2
0
0
0
1
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
2
0
0
0
0
2
0
1
0
0
1
2
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
1
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
3
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
2
3
2
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
1
2
0
3
0
2
0
0
0
2
0
0
2
0
2
2
2
0
0
1
0
1
0
0
0
1
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
2
0
1
1
1
0
0
0
0
0
3
0
3
2
0
1
0
0
6
0
0
0
1
1
0
1
0
2
0
0
1
1
0
1
0
0
2
1
1
0
0
2
1
0
2
0
2
0
2
0
2
1
0
0
1
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
2
1
0
1
0
0
0
0
0
0
0
2
0
0
1
1
1
0
1
2
0
0
0
0
1
2
0
1
2
2
1
0
0
0
2
1
0
2
0
0
0
0
2
5
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
13
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
1
1
0
2
0
0
0
0
2
1
2
2
1
0
0
0
1
0
2
0
0
1
1
0
0
0
0
1
1
0
0
0
2
0
1
2
0
0
0
1
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
2
0
0
0
1
2
1
3
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
1
0
1
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
2
0
0
1
3
2
2
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
1
3
0
0
1
0
0
0
5
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
1
0
0
2
0
0
1
0
0
0
2
2
0
0
0
0
7
1
2
1
1
2
2
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
2
0
1
1
0
2
0
0
0
0
2
2
0
3
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
1
2
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
2
0
1
0
0
0
0
3
0
0
4
0
2
1
0
0
0
0
2
0
1
0
1
1
0
0
0
0
2
0
0
2
0
3
0
0
0
0
0
0
0
2
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
2
0
1
1
2
1
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
2
2
0
0
0
0
1
0
1
1
1
0
0
1
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
1
0
0
0
0
2
0
2
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
2
3
0
2
0
2
0
0
0
0
0
0
0
0
0
2
2
2
2
0
0
0
1
0
1
0
0
2
0
0
1
2
0
0
1
1
0
0
0
0
0
1
0
2
0
1
0
2
0
2
1
2
0
0
1
1
2
0
2
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
2
1
0
0
2
1
1
0
0
0
1
2
0
0
1
0
0
0
2
0
0
0
2
0
2
2
0
0
2
2
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
1
1
2
1
0
1
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
3
0
1
2
3
0
0
0
0
0
0
2
0
2
2
1
0
0
0
0
2
0
0
0
0
2
0
0
1
1
1
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
2
0
1
0
1
1
0
2
0
0
0
0
1
1
0
0
1
0
1
1
3
0
0
2
0
2
1
2
0
2
2
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
2
0
1
0
1
2
2
0
2
0
2
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
1
2
0
0
0
2
1
0
2
0
1
0
0
0
0
1
1
0
1
0
0
0
1
0
2
0
0
1
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
1
2
2
2
1
0
0
2
0
2
1
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
2
0
0
3
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
2
2
0
1
2
0
0
3
0
0
0
0
1
0
0
0
0
0
1
0
0
0
4
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
3
0
0
0
0
1
2
2
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
1
2
0
0
0
0
0
2
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
1
1
2
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
5
0
0
0
0
0
1
0
0
3
1
1
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
2
1
0
1
1
1
0
0
0
0
0
0
0
3
0
2
2
2
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
4
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
2
3
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
3
0
0
1
0
0
3
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
2
0
0
2
1
2
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
2
1
1
0
2
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
2
0
0
0
1
2
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
2
12
0
2
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
1
0
1
0
0
1
0
2
1
1
0
0
2
2
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
2
0
2
1
2
0
0
0
0
2
2
0
0
0
1
0
0
2
0
1
1
1
1
0
0
0
0
0
1
0
2
0
0
0
2
1
0
1
2
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
2
1
0
0
0
0
0
2
2
1
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
4
0
2
0
1
0
0
2
0
2
0
0
2
0
0
1
0
0
0
0
0
2
0
2
0
0
1
0
2
1
1
0
0
0
1
2
0
0
2
0
1
0
0
2
1
2
0
1
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
4
0
0
0
2
2
0
0
0
1
0
0
1
0
0
0
2
0
2
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
3
0
2
2
0
2
1
0
2
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
3
0
1
0
0
0
3
2
0
0
0
2
0
0
0
0
0
0
1
2
0
2
0
2
0
0
2
0
2
0
0
0
3
2
0
1
0
0
0
2
2
0
0
2
1
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
1
2
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
3
0
0
0
0
1
0
2
0
2
0
1
0
1
1
0
0
0
0
5
0
0
0
1
0
3
0
0
0
1
2
2
0
0
1
2
0
0
1
2
0
0
4
1
2
1
2
0
0
0
0
1
0
0
2
0
0
2
0
2
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
1
0
0
1
0
0
0
2
1
0
1
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
1
1
0
2
2
2
0
0
0
2
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
2
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
12
0
0
0
0
3
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
1
1
1
2
0
0
1
0
0
2
0
0
0
0
0
1
2
0
0
0
1
0
0
1
2
0
0
0
1
2
0
0
0
2
1
0
2
1
0
0
0
2
0
0
0
2
2
0
0
0
2
0
2
0
2
0
0
1
0
0
0
0
0
0
1
0
2
1
2
1
1
0
0
0
0
0
2
0
0
0
1
5
0
0
0
0
2
0
0
0
0
1
0
2
0
2
0
2
0
0
2
0
0
0
2
1
0
0
2
2
0
2
0
0
2
0
0
0
1
0
0
1
0
1
0
1
0
1
0
1
0
1
0
0
1
0
0
0
2
1
0
0
0
3
0
0
1
1
0
1
1
0
3
2
1
7
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
2
1
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
2
1
0
0
0
1
2
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
5
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
2
0
2
2
2
0
0
0
0
2
2
0
1
1
0
1
0
0
0
3
0
0
2
0
0
0
0
0
3
0
0
0
0
0
2
0
0
3
0
2
1
0
0
0
1
0
1
0
0
0
1
2
2
1
0
1
0
0
1
2
0
0
0
2
0
0
0
2
0
1
0
2
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
2
1
0
0
1
0
0
0
2
2
0
2
0
2
1
2
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
1
1
1
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
2
1
0
0
2
1
0
1
0
0
0
0
0
0
2
0
1
2
0
0
0
0
1
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
1
1
0
0
2
0
0
0
2
0
1
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
1
2
0
2
0
0
0
0
1
0
1
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
2
0
0
0
0
0
0
2
1
1
1
2
0
0
0
1
2
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
1
2
0
2
0
0
2
1
0
2
1
0
0
1
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
1
0
0
0
1
2
0
0
3
0
0
0
0
1
2
0
1
0
0
0
0
0
2
2
2
0
2
0
0
0
0
0
2
2
0
0
2
0
1
0
1
1
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
8
0
0
0
0
0
0
0
2
0
0
2
1
1
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
1
1
0
0
0
2
2
0
0
2
0
0
1
0
0
1
1
0
1
0
0
0
0
0
2
0
0
3
0
2
0
0
0
0
1
2
1
0
3
0
2
0
0
0
2
0
0
0
2
1
0
2
1
0
0
2
0
1
1
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
1
0
0
2
2
0
2
0
1
1
2
0
0
0
1
0
0
2
0
1
0
0
0
1
1
0
0
0
0
0
3
0
0
0
0
1
0
1
1
2
0
0
1
0
1
1
0
0
1
2
0
1
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
2
0
0
0
1
0
2
0
1
0
2
0
0
0
0
1
2
0
0
2
1
0
3
1
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
2
0
0
2
1
0
0
0
2
3
0
0
1
2
0
0
0
0
0
2
1
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
2
0
0
0
0
0
0
2
1
0
2
0
0
1
0
2
0
2
0
2
0
1
0
0
0
2
2
0
0
0
0
0
0
1
0
2
2
0
0
0
3
2
0
0
0
3
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
1
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
2
0
0
1
1
0
1
0
1
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
1
0
0
0
0
2
2
0
1
0
0
0
0
2
0
0
4
1
0
2
4
0
1
0
2
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
2
1
4
0
1
0
0
0
0
0
2
0
1
0
1
0
1
0
1
0
1
1
1
2
2
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
2
1
1
0
1
0
0
1
3
0
0
0
0
0
1
0
1
0
0
0
0
0
1
2
0
4
0
0
1
2
0
2
0
0
0
0
0
0
0
1
2
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
1
0
0
2
0
2
2
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
3
1
0
0
0
0
0
1
0
0
0
0
0
2
0
3
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
2
0
0
1
2
0
0
0
1
0
2
0
0
1
0
1
0
0
0
2
0
0
0
1
0
3
0
0
1
4
2
2
0
0
1
1
0
2
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
3
0
0
1
0
0
2
0
0
0
2
0
0
1
2
1
0
0
1
0
1
0
2
1
4
0
0
0
0
0
0
3
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
1
2
0
0
0
0
1
0
1
0
2
2
0
2
0
0
3
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
2
0
2
1
0
0
0
1
2
1
3
0
1
0
0
0
0
2
0
0
0
2
2
0
0
0
1
0
0
0
2
0
2
0
0
0
0
1
1
0
0
1
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
1
1
0
2
0
1
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
2
0
2
1
0
0
0
0
0
3
2
1
2
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
1
3
0
0
2
0
0
0
0
2
2
2
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
2
1
0
0
2
0
0
2
1
2
2
1
3
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
2
0
1
2
1
0
2
0
0
1
0
0
0
0
3
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
3
1
2
2
2
1
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
2
0
2
0
0
2
1
0
0
0
0
0
0
2
0
2
0
0
2
1
6
2
2
0
0
0
0
2
2
1
0
1
1
0
0
0
0
0
0
0
3
2
0
1
0
0
1
0
2
0
0
0
0
0
1
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
3
2
0
2
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
2
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
2
0
2
0
1
0
1
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
2
1
1
0
2
1
0
0
0
2
0
1
6
2
0
0
0
3
0
0
0
2
0
1
0
0
2
0
0
0
1
0
2
0
0
0
0
0
2
2
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
1
0
0
3
0
0
0
0
0
3
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
1
0
0
2
2
1
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
2
2
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
1
2
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
1
1
0
1
4
0
0
0
0
2
2
2
0
0
2
0
1
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
2
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
2
1
3
2
2
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
2
0
0
0
0
3
1
0
2
0
0
1
2
0
0
1
0
1
0
0
0
2
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
2
0
0
1
0
0
3
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
8
3
0
0
0
1
0
0
2
0
2
1
2
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
2
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
3
2
1
2
3
0
0
2
0
0
0
0
0
5
1
0
1
0
1
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
2
0
2
1
1
0
0
1
0
2
0
0
0
2
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
1
2
0
0
0
2
0
0
1
0
0
0
0
2
1
1
0
1
0
0
2
0
2
2
2
2
2
0
1
0
1
0
1
1
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
2
0
0
0
1
0
1
0
0
2
2
1
0
2
0
0
1
2
0
0
0
1
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
2
0
0
2
1
0
0
0
1
0
1
0
0
2
0
2
0
0
0
2
0
0
0
0
0
6
2
1
0
0
2
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
3
0
0
0
0
0
0
1
2
0
0
2
0
2
0
0
0
1
1
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
2
0
2
2
0
0
0
2
0
0
1
0
0
0
0
3
0
0
0
2
0
1
0
1
2
0
1
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
3
0
0
2
1
0
0
0
0
0
0
3
0
1
1
0
2
4
0
1
1
1
0
0
1
1
0
0
0
0
2
0
0
1
0
2
2
2
2
2
0
0
2
0
0
0
0
0
1
0
2
1
0
0
0
2
1
0
1
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
1
0
0
0
1
2
0
0
2
2
0
2
0
2
4
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
1
3
0
0
0
3
0
0
2
0
1
2
0
0
0
0
0
0
3
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
1
0
0
0
0
1
0
2
0
1
0
1
0
0
1
2
0
1
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
2
2
1
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
1
1
2
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
1
2
0
0
0
0
0
2
0
0
2
3
0
0
0
0
0
1
0
3
0
0
0
2
0
0
0
0
0
1
1
1
0
0
1
1
0
0
0
0
2
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
3
2
0
1
1
0
3
2
0
0
0
1
0
0
1
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
2
0
1
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
2
0
0
4
1
0
0
1
1
1
2
2
1
1
2
0
1
0
0
0
1
0
3
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
2
0
0
0
3
0
0
1
2
0
1
1
0
0
0
0
0
0
0
1
1
1
0
1
2
1
0
0
0
0
0
1
0
1
0
0
0
2
0
1
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
2
0
0
1
2
0
2
0
0
0
2
0
0
0
2
0
0
0
1
1
0
2
0
1
0
1
2
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
2
2
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
4
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
2
0
0
1
0
0
2
2
0
0
0
0
0
0
2
0
0
0
1
0
1
0
1
2
0
0
1
1
0
1
1
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
1
1
1
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
2
0
0
0
3
0
0
0
0
0
1
0
0
0
2
2
2
0
3
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
2
1
0
0
2
0
1
0
0
0
3
0
0
0
2
0
1
0
0
1
1
1
0
5
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
3
2
1
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
1
4
0
0
0
1
2
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
2
1
0
0
2
1
0
0
0
2
1
0
2
0
0
0
0
0
2
1
0
0
0
0
2
2
0
2
0
3
1
0
1
2
0
2
2
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
1
0
0
3
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
1
2
0
0
0
2
0
2
1
0
0
1
0
0
0
1
0
0
0
0
0
0
2
1
0
0
2
0
1
0
0
0
0
0
0
0
0
2
1
1
1
0
0
0
0
1
1
0
3
0
1
2
2
0
0
0
0
0
1
0
0
1
1
2
0
3
0
0
0
0
2
2
0
0
0
0
0
1
0
1
2
2
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
2
0
1
0
0
0
0
0
2
2
0
2
2
2
0
0
0
2
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
1
2
2
0
0
0
0
0
2
0
0
1
2
0
2
0
0
0
0
0
0
1
0
0
0
1
2
0
0
3
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
1
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
1
0
0
3
0
0
0
3
0
0
2
2
2
2
0
0
0
0
1
0
0
0
0
1
0
1
0
2
1
0
0
0
1
0
2
0
0
1
0
1
0
1
0
3
2
0
2
0
0
0
0
0
0
1
0
0
0
0
2
1
1
1
0
2
2
1
0
2
1
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
2
2
2
0
0
0
2
0
3
2
0
2
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
1
0
1
1
2
2
0
0
0
0
0
0
0
0
0
4
2
0
0
2
0
0
0
0
0
1
0
11
0
1
0
0
1
1
1
2
0
1
2
0
2
0
0
0
0
0
0
1
3
0
0
2
0
0
0
1
0
0
0
0
0
1
0
2
2
2
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
1
2
0
0
1
0
0
1
0
0
0
0
2
0
2
0
0
0
0
4
0
0
2
0
1
2
2
1
0
1
0
0
0
0
0
1
2
1
0
0
1
0
0
1
2
0
0
0
0
2
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
2
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
1
0
1
1
2
0
0
2
0
2
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
3
0
1
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
2
0
1
0
0
1
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
6
2
0
0
0
0
1
0
3
2
0
0
0
0
1
0
1
0
0
0
0
1
1
0
2
0
1
3
0
0
0
1
0
0
0
3
0
0
0
0
0
0
2
1
0
1
0
2
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
2
2
4
0
1
0
1
0
0
1
0
0
1
0
0
0
2
2
0
0
1
0
0
0
2
2
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
2
0
2
1
2
2
0
0
0
2
0
2
0
0
2
0
2
1
0
0
0
2
0
0
0
0
2
0
0
0
2
2
0
0
0
1
0
0
0
0
2
3
0
2
0
1
0
0
0
0
2
0
2
1
1
0
2
0
0
0
2
0
1
2
0
0
1
1
0
0
1
0
0
0
0
2
1
0
1
0
1
0
2
1
0
0
0
2
2
0
0
1
0
0
1
1
2
0
2
1
0
0
0
0
1
0
3
2
0
0
0
1
0
0
0
2
2
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
1
1
6
0
2
0
1
0
0
0
0
0
2
0
0
0
0
2
1
1
0
0
1
0
0
2
1
0
0
1
0
0
0
0
1
2
0
0
2
0
0
1
1
0
0
0
2
0
0
0
1
1
0
0
0
2
1
2
0
0
0
0
0
2
0
1
0
1
0
0
2
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
3
1
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
2
0
2
0
0
1
1
0
0
0
0
0
1
2
2
1
0
0
1
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
2
7
0
0
0
2
0
0
0
0
0
1
1
1
2
0
0
0
2
0
0
1
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
1
1
0
1
0
0
1
0
0
0
0
2
1
1
0
2
0
0
0
0
1
2
1
1
1
0
1
0
0
0
0
2
4
0
2
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
2
1
0
1
0
1
2
0
0
1
0
0
0
0
2
0
0
0
3
0
0
0
2
0
2
0
0
2
0
0
2
1
1
0
0
1
1
0
0
1
0
2
0
1
0
0
0
0
1
2
4
1
0
2
0
0
0
0
1
1
2
1
0
0
0
1
0
0
1
0
1
0
0
1
0
0
2
0
3
0
0
0
0
2
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
3
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
2
0
0
0
0
0
2
1
0
0
1
0
0
1
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
2
1
0
0
0
0
0
1
0
2
2
1
3
2
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
2
1
2
1
0
0
0
0
0
0
2
0
1
1
1
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
1
1
1
4
0
0
0
0
3
0
2
0
2
1
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
1
1
2
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
2
3
1
0
1
0
0
0
2
2
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
1
3
1
0
2
0
4
0
2
0
2
0
0
0
0
0
1
1
1
1
2
0
0
0
0
2
0
0
2
0
0
0
0
5
0
0
0
0
0
0
1
0
0
2
0
2
2
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
1
2
2
0
0
2
0
0
0
1
0
2
0
1
2
0
0
0
0
2
1
0
0
0
2
3
0
0
0
1
1
2
0
0
0
1
0
0
0
0
1
0
0
0
1
0
7
0
0
0
1
0
1
1
1
0
0
0
1
1
0
2
0
0
0
2
2
0
1
0
2
0
1
0
2
0
0
0
0
1
2
1
1
4
0
0
0
0
3
0
1
2
0
2
0
0
2
0
1
3
0
0
0
0
3
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
1
2
2
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
2
0
0
9
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
3
0
0
0
1
0
2
0
0
1
0
0
1
0
3
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
1
3
3
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
1
0
0
1
2
0
1
0
0
3
0
1
0
0
0
0
0
1
1
0
1
2
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
1
2
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
2
0
0
2
0
0
2
0
2
0
0
2
0
0
0
2
0
2
1
0
0
0
0
1
2
0
2
2
0
0
1
4
1
0
0
2
1
2
1
0
0
1
2
1
0
0
0
2
0
2
0
0
1
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
1
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
2
2
0
2
2
1
2
2
2
0
0
2
0
0
0
2
2
0
1
0
0
0
2
0
0
0
1
0
0
1
0
0
0
1
0
1
0
2
0
1
1
0
2
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
2
2
1
0
0
0
2
1
0
0
1
0
0
1
0
2
2
1
0
0
0
0
0
1
0
0
0
1
1
3
0
0
2
0
0
1
0
0
0
3
1
3
0
0
0
0
0
0
1
2
0
0
2
0
2
0
2
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
1
0
0
1
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
1
1
0
1
2
3
1
0
0
2
0
0
0
0
0
1
0
1
0
0
0
2
0
0
2
2
1
1
0
0
2
0
1
0
0
0
1
0
0
0
1
0
0
2
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
4
2
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
1
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
2
0
1
0
0
0
2
1
0
2
1
0
0
3
0
0
1
0
2
0
1
2
0
0
1
0
3
0
0
0
0
0
0
0
1
1
0
0
2
0
0
2
1
0
0
0
2
0
2
0
3
0
1
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
2
0
0
1
0
0
1
2
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
3
0
0
0
0
0
2
0
0
0
1
0
2
2
1
0
0
0
0
0
1
0
0
2
1
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
1
0
2
1
2
0
0
0
0
0
0
4
0
1
0
1
0
0
1
2
2
0
2
0
0
0
2
0
1
0
1
1
0
0
0
1
0
1
0
1
0
0
0
1
1
0
3
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
6
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
1
1
1
1
0
0
2
0
6
0
0
2
2
0
0
0
2
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
2
3
0
0
4
2
2
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
5
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
1
2
0
0
0
3
1
0
3
0
0
0
0
1
0
2
0
1
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
1
0
1
0
1
0
2
1
0
0
0
0
0
0
0
2
1
0
2
2
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
2
0
0
0
0
0
0
5
0
1
2
1
0
2
0
0
1
2
0
2
0
0
1
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
2
2
0
0
0
0
0
0
2
1
0
2
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
2
0
1
1
0
0
0
2
0
0
1
0
2
2
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
2
0
2
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
8
2
3
2
0
2
0
2
2
2
2
0
0
0
2
0
2
0
1
0
1
0
0
0
1
1
2
0
1
1
2
0
0
1
2
0
1
0
0
0
0
0
2
0
1
2
0
0
0
0
0
2
0
0
2
2
2
1
2
0
0
1
1
2
1
0
0
0
0
0
1
1
0
2
2
0
2
1
0
0
1
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
3
0
1
0
0
1
2
0
2
0
0
1
0
1
0
0
0
3
0
2
0
0
2
0
0
1
1
0
0
1
0
0
2
1
4
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
2
1
2
1
0
0
0
2
1
1
0
0
0
0
1
0
0
1
1
0
1
2
1
0
0
0
0
0
0
2
2
0
0
0
0
1
1
1
1
1
4
0
0
0
0
0
2
2
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
1
1
0
0
2
1
1
0
1
1
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
2
0
0
1
2
0
0
1
2
0
0
0
0
0
1
0
1
1
3
0
0
0
0
0
0
0
0
1
1
0
2
0
0
1
0
0
1
4
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
2
0
0
0
2
0
0
1
0
1
0
1
0
0
0
2
1
1
1
2
0
0
3
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
2
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
3
0
0
0
2
0
1
0
2
0
0
1
0
0
0
2
0
0
2
2
0
1
0
1
0
2
7
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
1
2
0
0
1
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
2
0
0
2
2
2
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
3
0
0
0
0
2
1
2
0
2
0
1
0
1
1
2
0
0
0
0
2
1
0
1
0
0
0
2
0
0
0
1
0
0
0
2
1
0
0
1
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
1
0
0
0
0
2
0
0
0
1
3
0
0
2
0
0
0
3
0
0
3
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
1
2
0
1
0
0
0
2
1
0
0
0
0
1
2
0
0
0
0
2
0
2
2
0
0
0
1
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
2
2
3
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
2
2
2
0
2
0
0
1
0
1
0
2
0
2
0
1
1
0
2
0
2
4
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
2
3
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
1
0
2
0
1
0
0
0
1
0
0
0
1
2
0
0
2
0
0
0
0
1
2
0
0
2
0
1
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
1
0
2
1
1
1
0
1
0
2
0
2
1
0
1
1
1
1
0
0
0
0
0
0
0
1
0
0
2
2
2
2
0
2
0
1
2
0
2
1
1
0
0
0
0
0
0
1
2
0
0
0
0
2
0
1
1
0
1
0
1
2
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
2
0
2
0
3
0
0
1
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
2
2
0
0
2
2
0
1
2
1
1
0
0
0
0
1
2
0
0
0
0
2
1
0
0
0
0
0
0
0
5
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
1
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
4
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
1
0
1
0
0
1
0
0
0
2
0
2
2
0
0
2
0
0
1
0
0
2
2
0
0
3
0
0
0
0
1
0
0
1
0
0
2
0
3
1
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
2
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
1
1
1
2
1
2
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
2
0
1
0
2
0
1
2
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
2
0
0
0
2
0
0
1
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
2
1
0
0
0
0
1
1
0
0
0
2
0
0
0
0
1
0
3
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
2
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
6
0
0
0
2
1
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
1
1
0
0
0
0
0
1
2
2
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
3
1
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
3
0
0
0
0
0
0
1
0
4
2
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
3
0
2
0
2
0
0
1
0
1
0
1
1
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
2
5
1
1
0
0
0
2
2
2
0
0
1
0
0
0
2
0
0
1
3
2
0
0
2
0
0
0
2
0
0
1
1
2
1
0
2
0
0
0
2
2
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
3
0
0
0
1
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
2
0
0
2
0
1
1
0
2
0
1
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
2
2
0
0
1
0
0
2
1
1
1
0
0
0
1
0
2
2
1
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
3
1
2
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
1
0
0
0
3
1
0
0
0
2
2
0
2
0
0
0
0
0
3
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
1
0
2
1
2
0
0
0
0
1
0
0
0
2
0
0
0
0
1
1
0
0
0
1
2
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
2
0
1
0
1
0
1
1
0
0
2
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
2
0
1
0
2
2
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
1
2
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
1
1
2
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
1
0
0
1
2
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
1
0
2
0
0
0
0
0
0
0
1
1
0
1
0
0
1
2
0
0
0
0
0
3
0
0
0
1
0
0
1
0
2
1
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
2
0
0
1
0
0
0
2
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
1
0
0
0
0
0
1
0
1
0
2
0
0
2
1
0
0
0
0
0
0
3
1
2
0
0
0
0
2
0
0
1
0
2
0
2
2
0
0
0
0
0
0
2
0
0
0
2
0
0
2
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
2
0
3
0
0
1
2
0
0
0
0
0
0
0
0
1
7
3
0
2
2
0
2
1
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
3
1
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
2
0
0
1
1
0
2
2
0
2
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
1
1
0
1
0
1
0
1
0
0
1
0
2
0
1
0
0
0
2
0
0
2
0
1
0
2
1
0
0
2
0
0
0
0
0
0
2
0
1
0
2
4
0
2
0
1
2
1
0
0
2
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
1
1
0
0
0
2
0
0
0
0
1
0
0
2
2
0
1
0
0
0
1
1
2
0
0
0
0
0
3
2
4
0
0
0
0
2
0
0
1
0
2
0
2
0
1
0
0
0
0
0
0
2
0
1
1
2
0
0
1
0
0
2
0
0
2
0
3
0
0
0
0
0
1
0
1
2
0
2
1
2
1
1
1
0
1
0
1
0
2
0
1
0
0
1
1
2
2
1
0
0
2
0
0
0
1
0
0
0
2
3
1
0
0
0
0
0
0
2
2
0
2
0
0
0
0
2
0
1
1
2
2
0
0
0
0
0
2
1
2
0
2
0
0
0
0
0
0
0
0
3
1
0
1
0
1
0
0
0
1
1
0
0
0
0
2
1
0
0
1
0
2
0
1
1
2
0
1
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
1
0
1
0
2
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
2
0
0
2
0
0
2
1
0
4
0
1
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
1
0
0
0
0
1
0
1
0
1
2
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
1
2
0
1
0
0
0
0
0
0
0
1
1
0
2
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
2
5
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
2
2
0
0
1
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
1
1
0
1
1
2
0
0
1
2
3
0
0
0
1
3
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
2
0
0
0
0
1
0
3
0
2
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
1
0
2
1
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
2
0
1
1
0
2
2
0
0
0
0
2
0
2
0
0
0
0
0
2
0
2
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
1
1
1
0
2
2
0
0
0
2
1
0
0
2
0
0
1
2
0
0
0
0
0
2
2
0
2
2
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
3
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
1
1
0
0
1
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
1
1
2
0
0
2
2
0
0
1
1
2
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
2
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
2
3
1
1
0
0
0
2
1
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
1
1
0
0
1
0
1
0
0
0
2
0
0
0
3
1
0
0
1
0
0
2
0
0
2
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
3
1
2
0
2
1
0
5
0
2
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
3
0
0
0
1
2
1
2
0
0
1
2
1
0
0
3
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
2
0
2
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
2
0
2
0
0
2
0
0
0
2
0
0
1
0
2
2
1
0
0
0
0
3
0
0
0
0
1
0
2
1
0
1
0
1
1
1
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
1
1
0
1
2
2
2
0
2
1
1
0
0
1
2
0
2
0
1
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
1
2
0
0
1
2
1
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
2
0
4
2
2
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
2
0
2
0
0
2
0
3
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
2
0
2
2
2
3
1
0
1
0
0
0
1
0
3
0
2
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
1
2
0
0
1
0
1
0
0
2
1
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
2
0
0
3
1
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
2
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
1
1
0
1
0
1
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
2
0
1
0
1
2
0
0
0
0
1
1
0
1
0
0
0
2
0
0
0
1
0
2
0
2
1
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
1
0
2
0
0
0
0
0
0
1
0
2
0
1
0
0
0
2
0
0
2
0
0
1
1
2
1
0
0
0
0
0
1
2
2
0
0
1
0
2
0
1
0
0
0
2
1
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
2
3
1
0
0
0
0
0
2
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
1
2
1
1
2
0
1
0
1
2
2
0
0
0
0
0
2
2
2
1
2
1
0
0
0
0
0
0
2
0
0
2
0
0
2
2
1
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
1
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
2
0
0
0
0
2
2
1
0
2
0
0
0
2
0
0
1
0
0
0
0
1
2
0
0
0
0
1
2
0
0
2
0
2
0
0
0
0
2
0
0
2
1
0
2
1
0
2
0
0
0
2
1
2
0
0
0
0
0
0
0
2
1
0
0
0
0
2
2
1
0
1
2
0
0
15
1
0
2
0
0
2
0
0
0
0
0
1
1
0
1
0
0
0
2
0
1
0
2
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
1
1
0
0
2
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
2
1
1
1
0
0
0
3
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
2
0
2
0
0
1
0
2
0
0
0
2
0
2
0
3
2
1
2
0
0
2
0
0
0
0
0
0
3
2
0
1
0
2
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
2
2
0
1
0
2
0
0
0
2
0
2
0
0
2
0
0
0
1
0
0
0
0
2
2
0
2
0
0
2
1
2
2
2
1
3
2
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
3
0
0
0
0
2
1
0
2
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
4
0
0
0
2
0
2
3
0
0
2
2
0
1
2
0
0
1
1
1
0
0
0
2
2
0
0
1
0
0
1
0
0
1
0
2
0
0
3
0
0
0
0
2
0
0
1
0
2
0
0
1
0
0
2
0
1
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
4
0
0
0
3
0
2
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
1
1
0
1
2
1
0
4
0
1
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
3
0
0
0
1
2
0
1
1
2
0
0
0
0
0
0
0
0
2
3
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
2
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
2
0
2
0
0
2
1
0
0
0
1
2
1
1
0
0
0
0
0
1
1
1
1
0
2
0
1
0
0
0
2
2
0
0
0
2
0
2
0
0
0
2
2
0
0
0
0
0
1
1
0
0
2
2
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
1
0
0
2
2
2
0
0
6
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
2
2
0
0
0
2
1
0
2
1
0
0
0
0
0
0
0
0
2
2
2
2
2
0
0
0
1
0
2
0
0
0
2
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
2
2
2
1
0
0
0
0
0
2
0
0
0
0
2
0
0
1
4
1
0
1
0
1
1
0
0
2
0
1
1
2
3
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
3
0
0
1
0
2
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
2
0
0
0
0
1
0
0
0
1
1
0
2
1
0
3
1
0
0
2
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
2
0
1
0
5
0
0
0
2
0
1
0
0
0
0
4
0
2
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
2
2
1
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
2
0
0
0
0
2
2
0
0
0
2
2
1
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
1
2
0
0
2
0
0
0
0
0
1
0
0
0
4
0
0
2
1
0
0
0
0
2
0
0
2
1
2
0
1
0
0
0
1
2
0
0
0
0
1
0
0
0
1
0
2
0
2
0
0
0
1
2
0
0
2
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
14
0
0
0
0
0
0
0
1
0
2
0
1
2
0
0
0
2
1
0
0
2
0
0
2
0
0
0
0
0
2
0
2
1
0
2
1
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
3
2
0
0
0
0
0
0
0
0
1
0
5
0
0
0
0
0
1
0
1
2
2
1
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
2
4
0
0
0
1
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
2
2
3
0
2
0
0
0
0
0
0
0
0
0
4
0
1
0
2
1
1
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
1
0
0
1
0
2
1
0
0
0
0
3
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
1
2
2
0
2
0
0
0
0
1
0
1
1
1
0
2
0
2
1
0
2
0
0
0
1
2
1
0
0
2
1
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
1
1
0
0
1
0
0
0
1
0
0
2
2
0
0
1
1
1
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
2
2
0
0
0
1
0
0
2
3
0
0
1
0
0
2
0
0
0
2
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
1
1
2
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
7
0
0
0
0
2
2
0
0
0
3
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
3
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
1
0
2
2
0
1
0
0
0
0
1
2
0
2
4
0
0
0
0
0
0
1
0
2
0
1
1
1
0
2
0
0
0
2
0
2
0
0
0
0
6
0
0
2
23
2
3
0
1
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
5
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
1
1
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
1
1
0
1
1
0
0
0
0
0
1
2
1
0
2
1
0
0
0
0
2
3
0
2
0
2
0
2
1
0
1
0
0
0
0
0
0
2
2
0
0
2
0
0
0
3
0
2
0
0
0
1
2
1
0
0
0
1
1
1
0
0
0
0
1
2
0
2
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
1
1
0
1
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
4
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
4
1
0
0
0
0
2
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
2
2
3
0
0
0
1
2
0
2
0
0
3
0
2
2
2
0
0
0
5
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
2
0
0
2
0
0
0
0
0
0
0
1
0
1
2
0
0
1
1
1
1
1
0
0
1
0
2
1
1
0
1
2
0
0
1
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
2
0
0
2
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
1
0
0
1
3
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
1
1
0
0
0
0
0
3
2
2
2
0
0
0
0
0
0
0
0
2
0
2
2
1
2
2
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
1
1
1
0
0
0
0
0
0
2
0
1
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
1
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
2
2
1
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
1
0
0
2
0
0
2
0
0
1
0
1
1
1
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
1
1
0
0
0
2
1
0
0
3
0
0
0
0
1
1
2
1
1
3
1
0
1
1
2
1
2
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
3
1
0
1
0
0
0
0
2
2
0
0
0
0
0
3
0
2
0
0
0
0
0
2
0
0
2
0
3
0
0
0
1
0
0
2
0
0
0
2
1
0
0
1
0
0
0
0
1
0
0
2
0
0
0
1
0
2
0
1
0
2
0
0
0
0
3
2
1
0
0
0
1
0
1
2
2
3
0
2
0
0
0
0
0
2
0
7
2
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
2
1
1
1
0
0
0
0
2
2
1
1
1
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
1
2
0
0
0
0
1
1
0
1
1
3
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
1
2
0
2
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
2
0
0
1
0
1
1
1
0
0
0
0
1
2
0
2
0
0
0
1
1
0
0
0
1
1
0
0
0
2
0
0
0
1
0
0
1
0
0
0
1
1
2
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
2
0
0
2
1
2
0
0
0
0
2
0
2
0
0
0
2
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
1
2
1
1
0
2
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
1
3
0
0
0
1
1
1
2
0
1
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
1
0
1
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
3
0
2
0
6
1
1
1
0
0
0
0
0
0
2
0
0
0
2
2
0
1
0
0
0
0
0
0
2
0
0
2
2
0
0
2
2
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
2
1
0
0
1
0
0
0
2
0
0
0
2
1
0
0
0
0
3
0
0
1
2
1
2
0
0
0
0
0
0
1
2
0
1
0
0
0
1
0
2
1
0
0
0
0
1
0
0
0
3
0
1
1
1
2
0
2
1
0
0
0
1
0
0
2
0
0
2
0
0
1
0
2
0
0
1
2
0
0
1
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
2
0
0
0
1
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
2
1
0
0
0
0
0
3
0
0
0
2
1
2
3
1
2
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
2
0
1
0
1
0
0
0
0
1
0
1
2
1
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
1
0
0
1
0
2
0
1
0
0
0
2
0
0
0
0
0
1
0
3
1
1
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
3
0
2
0
0
5
0
0
0
0
0
3
0
0
0
0
1
1
2
1
0
2
0
6
0
0
0
2
2
0
0
1
0
1
2
1
0
0
0
0
0
0
2
0
1
0
2
2
0
0
0
0
0
0
1
0
0
0
0
1
4
1
1
0
0
2
0
2
1
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
2
1
0
2
0
0
0
0
0
1
6
0
0
0
1
2
0
2
0
1
0
2
0
2
0
1
0
1
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
1
0
0
0
2
0
1
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
1
0
0
0
2
0
0
1
1
0
0
0
0
2
0
0
2
2
2
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
2
0
2
2
0
2
0
2
0
0
0
1
0
0
2
1
0
0
1
0
3
1
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
3
0
2
0
2
0
2
0
0
0
2
0
2
2
0
0
2
0
2
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
1
0
2
2
0
0
0
1
2
1
0
2
0
2
0
0
0
0
0
0
0
2
0
2
1
1
2
0
0
1
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
2
0
1
1
0
0
0
0
0
0
1
0
1
0
1
0
0
1
1
0
1
0
0
0
0
1
2
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
1
3
3
0
2
2
1
1
0
0
1
0
0
0
0
0
0
3
0
0
3
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
8
0
0
0
0
0
1
1
0
1
0
0
0
1
2
0
0
0
1
1
0
1
0
0
6
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
2
1
2
2
0
0
0
0
0
0
2
2
1
3
0
0
3
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
2
1
0
2
0
0
1
0
1
0
2
0
2
0
0
0
0
4
1
0
0
0
0
0
2
2
2
0
1
1
0
0
0
2
0
2
2
2
0
0
0
0
0
0
0
1
0
2
0
2
2
0
0
1
0
1
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
3
1
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
1
2
0
0
0
0
0
0
0
2
0
0
2
0
0
2
2
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
1
0
0
1
0
0
0
0
1
0
0
2
0
0
4
3
2
0
4
0
4
1
0
0
0
0
0
1
0
2
0
0
0
0
1
1
2
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
3
0
0
0
0
0
1
0
0
0
2
1
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
1
0
1
0
2
0
2
0
0
0
0
1
2
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
2
1
0
0
2
1
0
1
0
0
1
0
0
2
2
2
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
2
0
2
0
2
0
1
4
1
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
1
3
0
1
2
0
0
2
2
0
0
0
0
0
0
3
0
2
2
0
3
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
2
0
0
6
0
0
2
1
0
2
1
0
0
0
2
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
1
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
2
0
0
0
3
0
0
2
1
0
0
0
0
0
1
0
1
2
0
0
0
1
0
0
0
1
1
0
1
0
0
8
1
0
0
1
2
2
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
1
0
2
2
1
2
1
0
1
0
0
1
0
1
2
0
0
0
0
0
0
2
2
0
0
1
2
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
1
1
0
0
0
0
0
0
0
1
1
1
2
0
0
1
0
0
0
2
0
0
0
1
0
2
0
1
0
2
0
2
2
0
0
5
0
2
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
1
0
2
1
1
1
0
2
2
0
0
0
0
0
0
0
0
0
2
2
2
2
0
0
1
0
0
2
0
0
1
1
1
3
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
6
1
0
0
0
0
2
2
2
0
0
0
3
0
0
0
0
0
1
2
2
0
0
2
0
2
0
0
0
0
1
2
1
0
1
1
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
3
4
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
2
0
2
0
0
0
2
0
2
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
1
0
1
0
0
4
0
2
0
2
0
7
1
0
2
0
0
0
1
0
0
0
3
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
2
0
1
0
0
2
0
2
1
1
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
1
0
0
0
3
0
0
2
0
0
0
0
2
1
0
0
0
0
1
0
0
2
0
0
0
0
2
1
2
0
0
1
0
0
0
2
0
0
2
0
0
1
0
1
6
1
0
1
0
0
2
1
0
0
1
2
2
0
0
0
1
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
1
1
0
0
2
0
3
0
0
0
1
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
1
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
3
1
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
2
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
4
2
0
0
0
2
2
0
2
0
0
0
0
0
0
2
0
0
2
0
0
1
1
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
5
0
2
0
1
0
0
0
2
0
0
0
0
2
0
0
3
1
0
0
0
0
0
0
0
2
6
0
0
0
1
2
0
1
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
2
0
0
3
0
0
1
0
2
0
0
0
0
0
0
2
1
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
1
2
1
0
0
0
0
0
5
0
1
0
2
0
1
1
0
0
0
0
1
2
0
0
2
0
0
1
0
0
1
0
2
0
1
0
1
1
0
1
0
0
1
2
0
2
0
0
0
2
0
0
1
0
1
1
2
0
1
1
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
4
0
2
0
2
2
0
2
2
0
0
0
2
0
0
0
0
2
2
0
1
0
0
0
0
0
1
0
1
0
0
0
2
1
0
1
0
2
0
0
0
3
0
0
0
1
0
0
2
1
0
0
0
0
0
2
0
0
0
0
2
0
1
3
1
0
2
0
0
0
0
3
0
0
0
0
2
2
0
0
0
2
0
0
2
0
1
1
0
2
0
0
0
1
0
1
0
0
0
1
0
2
0
0
1
0
0
0
3
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
6
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
2
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
2
0
0
0
2
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
1
1
0
0
2
1
2
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
3
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
2
2
0
0
0
0
2
1
0
0
3
0
0
0
2
2
0
2
2
0
1
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
2
0
1
2
1
0
0
2
1
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
2
3
1
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
1
2
0
0
2
2
0
0
3
0
0
1
0
1
0
1
2
2
0
0
1
2
0
0
1
1
2
0
0
0
0
1
1
0
2
1
0
0
0
1
0
0
2
2
0
0
0
2
2
0
0
0
2
2
1
0
2
2
0
0
0
0
0
1
0
0
1
0
0
0
0
1
2
2
0
1
0
0
2
0
0
1
0
0
2
2
0
1
0
0
0
1
1
0
0
1
0
2
0
0
0
2
0
0
0
0
1
2
1
0
1
0
0
1
1
1
1
0
0
2
0
0
0
0
0
2
1
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
1
0
0
2
0
0
2
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
2
1
0
2
0
4
0
0
0
0
2
0
1
0
0
0
1
0
1
0
0
0
0
2
0
1
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
2
2
2
0
3
0
0
1
0
0
0
1
1
3
2
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
2
2
0
0
0
1
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
2
3
0
2
0
0
0
0
2
2
2
0
0
0
0
2
1
0
0
0
1
0
0
0
2
0
0
0
2
0
2
0
1
0
1
0
1
2
0
2
0
1
1
3
0
2
0
1
0
0
0
0
0
3
0
0
0
1
1
0
0
1
0
0
1
1
0
2
0
1
0
0
0
1
2
0
0
0
0
0
1
0
2
2
1
1
0
2
2
2
2
0
0
0
0
0
0
2
0
2
2
0
1
0
1
0
0
1
2
1
1
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
2
0
2
0
4
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
1
0
1
0
0
1
2
0
1
0
1
0
2
0
2
0
0
0
2
0
0
1
0
0
2
2
0
2
1
0
0
0
1
1
2
2
0
1
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
2
0
1
0
0
3
0
2
0
0
3
2
0
2
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
2
0
1
0
1
0
1
2
0
0
1
0
0
0
0
2
2
2
0
3
1
0
0
0
0
0
0
2
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
3
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
1
0
1
0
1
2
0
0
0
1
0
0
0
0
1
2
0
1
0
1
0
2
0
0
0
3
0
2
2
0
0
2
0
0
1
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
2
0
0
0
1
0
0
0
1
0
2
0
1
0
2
0
2
0
0
2
0
0
0
0
0
1
3
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
2
3
0
1
2
0
0
0
0
1
0
2
0
0
0
0
0
1
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
3
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
2
0
0
0
0
2
0
0
0
1
0
0
0
2
15
1
0
0
0
0
1
0
0
2
1
0
0
2
0
0
1
0
0
0
3
1
2
0
1
0
1
0
0
0
1
0
3
0
0
2
1
2
1
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
1
0
2
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
1
0
0
1
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
2
0
0
0
0
0
1
1
0
0
1
1
0
0
1
0
0
0
0
1
0
1
2
0
1
0
1
0
6
0
0
0
2
2
0
1
0
0
0
1
3
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
2
1
0
1
0
1
1
0
1
0
0
0
0
2
0
0
1
0
2
0
0
0
0
2
2
0
1
1
0
2
1
0
2
1
0
0
0
0
0
0
1
0
2
2
0
2
2
2
2
2
0
0
0
0
0
0
0
0
2
2
0
0
0
1
1
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
2
1
2
0
0
0
0
0
2
2
0
1
0
0
1
0
0
0
0
2
2
3
2
0
2
2
2
2
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
2
0
0
2
2
0
0
0
0
0
0
0
2
1
0
0
1
0
3
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
1
3
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
2
0
1
0
0
0
1
2
0
2
0
0
0
0
1
1
0
2
0
0
2
1
0
0
0
2
0
3
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
1
1
0
2
2
2
0
0
3
0
2
0
1
0
0
1
0
0
0
2
0
2
2
0
0
0
2
0
1
0
0
1
0
1
2
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
3
0
1
2
1
0
0
0
0
0
0
1
0
1
0
0
1
0
2
0
1
2
2
0
1
1
3
1
0
1
1
0
2
0
1
0
0
2
0
1
1
2
0
0
0
0
1
0
0
0
0
2
0
2
2
0
1
0
0
0
2
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
1
1
2
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
2
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
2
1
0
0
0
2
0
1
0
0
0
1
0
0
2
2
0
0
0
2
2
1
1
2
0
0
2
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
2
0
4
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
2
2
2
0
1
0
1
0
0
1
0
0
1
0
0
0
2
0
1
2
0
0
0
2
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
2
0
0
0
0
1
1
2
2
0
0
0
5
0
0
2
2
0
0
0
0
0
3
0
0
3
0
0
0
0
0
2
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
1
0
1
0
0
0
1
2
0
0
0
2
0
0
0
0
0
1
0
0
1
2
0
0
2
0
2
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
2
0
2
0
0
2
0
0
0
0
0
2
0
0
0
1
1
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
2
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
3
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
2
0
4
0
1
2
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
4
0
0
1
0
1
1
0
1
0
2
1
0
3
0
0
2
0
0
0
2
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
2
0
0
0
0
1
0
1
0
0
0
1
2
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
3
0
1
0
0
0
0
0
2
2
1
1
0
0
1
0
0
2
1
1
0
0
0
0
2
0
0
1
0
1
0
2
0
7
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
1
0
0
1
2
0
2
2
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
2
3
2
0
1
0
2
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
2
2
2
0
0
1
0
1
1
1
1
0
0
0
2
0
0
0
0
0
0
1
1
2
0
4
2
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
1
2
5
0
0
0
1
1
0
0
0
0
0
0
0
2
7
0
0
0
1
0
2
1
2
1
0
0
2
0
0
0
0
2
1
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
1
0
0
1
0
0
2
0
2
0
0
1
2
0
0
0
0
0
0
1
1
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
4
1
0
0
2
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
2
2
0
0
0
0
1
1
0
0
0
1
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
1
2
0
0
0
0
0
2
0
0
1
0
0
1
1
1
0
2
1
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
5
1
0
0
1
0
0
0
0
0
0
2
1
1
0
1
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
1
0
0
2
0
0
1
0
1
0
0
0
0
0
1
0
2
0
0
0
2
0
2
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
1
1
1
1
2
0
0
0
0
0
0
1
0
2
0
2
0
0
2
0
0
0
0
1
0
0
2
2
0
2
0
2
0
1
0
4
0
0
2
0
0
0
2
0
0
0
0
0
0
2
1
0
0
2
1
0
2
0
0
0
0
2
0
0
2
0
2
0
0
0
1
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
2
0
0
0
0
1
1
0
0
2
1
1
2
2
0
0
1
0
0
0
1
1
0
1
2
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
1
0
0
0
0
1
3
0
0
1
2
0
0
0
0
1
2
0
1
0
0
2
0
2
2
0
1
0
0
0
0
0
0
0
2
0
0
2
1
2
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
2
0
3
0
0
1
1
1
0
0
2
2
1
0
0
0
0
2
1
0
0
3
0
0
0
0
0
0
0
2
3
2
0
0
1
2
2
0
0
0
0
0
2
0
0
0
1
1
1
3
0
0
2
0
0
0
2
0
1
0
1
0
0
1
8
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
6
0
1
0
0
1
0
0
0
0
0
1
1
1
0
0
4
0
2
0
0
0
0
2
0
0
0
0
1
1
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
3
1
0
0
0
0
0
1
0
2
0
3
2
0
0
0
0
0
0
0
1
2
0
5
1
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
2
2
2
1
1
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
2
0
0
0
2
0
1
0
0
0
2
0
4
2
0
0
0
0
0
0
1
0
2
1
1
1
0
0
0
0
0
0
0
0
1
2
1
2
1
0
0
2
0
1
0
0
0
0
0
3
1
2
1
0
0
0
0
0
2
1
5
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
3
0
0
0
1
0
0
0
0
5
0
2
0
1
0
0
2
0
0
0
0
2
1
0
0
1
0
0
0
0
0
2
0
0
2
0
1
0
0
0
1
0
0
0
0
3
2
0
0
0
0
0
0
0
3
2
0
1
0
0
0
0
1
2
0
1
1
0
0
2
0
0
0
0
0
0
2
0
0
0
3
0
0
4
2
0
0
0
0
0
0
0
2
1
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
3
1
1
1
2
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
2
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
2
2
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
5
2
0
3
1
2
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
2
1
0
0
0
0
2
1
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
1
0
0
0
0
1
0
1
0
0
1
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
2
2
0
1
0
0
3
1
2
2
0
0
2
0
0
1
0
2
0
2
0
0
0
1
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
2
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
1
2
0
0
0
0
0
0
4
0
1
0
1
0
0
0
0
0
0
1
2
1
0
0
2
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
1
1
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
4
1
0
0
0
7
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
2
0
0
1
0
1
0
1
0
0
0
1
2
0
0
2
0
3
2
0
0
0
2
2
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
4
0
0
0
0
2
3
0
0
0
0
0
3
1
3
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
2
2
2
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
1
0
2
1
1
2
1
0
1
0
1
0
0
0
1
2
2
0
0
0
0
1
0
3
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
1
2
0
0
2
0
0
1
3
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
3
2
1
0
2
0
1
0
0
0
0
1
0
0
3
0
0
0
0
0
1
1
2
0
0
0
0
0
0
1
2
0
0
0
2
0
0
2
1
2
0
1
1
0
1
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
3
0
1
0
2
1
0
0
0
0
0
0
0
0
0
5
0
0
0
1
3
0
0
2
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
1
2
1
0
0
2
2
0
0
0
2
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
1
0
2
2
0
0
0
0
1
0
0
2
0
0
0
0
1
2
2
0
0
0
0
3
0
0
0
0
0
0
0
1
3
1
0
2
0
2
0
1
0
2
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
4
0
1
0
1
0
0
1
0
1
0
1
0
1
0
0
0
1
0
3
0
0
2
1
0
0
2
0
0
0
0
2
0
0
2
4
4
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
1
0
0
0
1
1
0
0
0
0
0
0
3
0
0
1
0
0
2
0
1
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
3
1
1
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
2
1
1
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
1
0
1
0
1
2
2
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
1
1
2
0
0
0
0
0
0
0
1
2
1
2
0
0
0
0
6
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
1
0
2
0
2
0
0
3
0
2
1
2
0
0
0
7
0
0
1
0
0
2
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
3
2
1
0
0
0
1
0
2
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
2
2
0
0
3
0
0
2
0
3
0
1
4
2
2
0
2
1
0
1
0
0
2
1
0
1
1
0
2
0
0
0
0
2
2
0
0
0
2
3
1
0
1
0
2
1
0
0
0
0
0
1
1
2
0
0
0
0
2
0
0
0
0
0
1
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
1
0
0
1
0
2
1
2
0
3
0
0
0
1
0
0
3
0
10
1
0
1
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
2
2
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
1
1
0
2
2
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
1
1
2
0
0
1
0
0
2
0
2
0
0
0
1
1
0
0
1
0
0
0
0
0
0
3
0
1
0
0
0
0
0
2
2
3
2
0
2
0
0
0
0
2
1
0
1
0
0
0
0
0
0
1
0
3
0
0
3
2
0
0
0
0
1
0
0
2
0
0
2
1
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
1
2
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
1
0
1
0
1
1
0
0
0
0
0
0
0
2
0
0
0
1
2
1
1
0
0
1
1
0
1
0
0
1
1
1
0
0
0
0
0
0
0
1
3
2
0
0
0
1
0
2
0
1
2
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
1
0
1
0
0
0
1
1
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
1
0
0
0
0
2
0
0
0
0
2
1
2
0
0
0
3
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
3
3
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
1
0
1
0
2
1
0
1
0
0
2
2
0
0
0
1
2
1
0
1
0
2
0
2
0
0
2
2
0
3
3
1
0
1
2
0
0
2
0
0
2
0
3
0
0
0
0
0
4
0
2
0
0
0
3
3
0
1
0
0
0
0
0
1
0
1
0
0
0
0
2
2
1
0
0
0
1
2
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
1
1
1
1
1
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
3
0
0
0
0
0
2
0
0
2
0
0
2
0
0
2
0
0
0
2
0
0
2
0
0
1
0
1
0
2
0
2
0
1
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
1
1
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
2
0
0
2
2
0
0
2
0
0
0
0
1
0
0
0
1
2
0
1
2
2
1
2
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
1
0
1
0
9
1
0
2
1
2
1
2
2
2
0
1
0
0
2
0
2
0
0
0
2
0
0
2
0
2
0
0
0
1
0
0
0
2
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
1
0
1
1
1
0
3
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
2
1
0
2
1
7
1
0
1
0
2
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
1
0
0
0
0
0
0
2
2
0
0
0
3
1
2
1
0
0
2
1
0
0
1
0
2
1
0
0
0
2
2
2
0
1
0
2
0
0
0
0
0
0
0
3
1
2
0
0
0
1
0
0
0
2
0
0
1
0
0
3
0
0
1
0
0
0
0
2
0
0
1
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
2
2
0
1
0
0
0
2
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
2
0
1
2
0
0
0
2
1
0
0
1
0
0
0
1
0
1
2
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
1
3
0
0
0
1
0
0
1
1
2
7
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
1
2
0
2
0
0
0
2
0
0
2
0
0
0
4
0
1
0
2
0
0
1
0
1
2
0
4
0
2
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
1
1
0
0
2
0
0
0
0
2
0
0
1
0
2
2
2
0
0
0
0
0
0
0
0
0
0
2
1
2
1
0
1
1
0
2
2
0
0
1
1
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
2
2
1
0
2
0
0
1
2
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
2
1
0
0
0
0
0
0
3
1
0
2
0
0
0
0
0
0
2
1
1
9
1
0
1
2
0
0
0
1
0
0
0
0
0
2
0
1
0
6
0
0
1
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
2
2
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
1
1
0
0
2
1
0
0
2
0
3
1
0
0
0
0
0
0
0
0
0
1
0
2
1
4
0
1
0
0
0
2
0
2
0
0
0
0
0
1
2
4
0
2
2
0
0
1
0
0
5
0
0
2
1
0
0
0
1
1
0
2
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
1
0
1
0
1
1
3
1
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
2
0
2
2
0
0
0
2
0
2
1
0
2
1
3
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
1
1
1
0
0
0
1
3
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
1
2
0
1
0
0
1
0
1
0
1
0
0
1
0
2
0
0
2
0
2
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
4
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
1
0
1
2
0
0
0
2
0
0
1
0
0
0
2
1
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
2
1
0
0
0
1
0
0
0
1
0
0
2
0
2
0
0
1
2
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
1
0
2
2
0
0
0
2
0
0
4
0
0
0
0
0
0
2
0
0
2
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
1
0
3
0
2
0
2
0
3
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
1
1
2
0
0
2
1
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
1
0
0
0
1
0
2
0
0
1
0
1
0
2
0
1
0
0
2
2
0
2
1
1
0
0
1
0
1
1
2
3
0
0
4
0
0
0
0
3
2
2
1
1
0
0
0
2
3
3
0
0
0
0
2
0
0
2
1
0
0
0
0
0
2
0
2
1
0
0
1
1
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
1
0
0
0
0
4
0
0
2
0
0
1
0
1
0
0
1
1
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
1
1
2
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
2
0
1
0
2
1
0
0
1
2
1
1
0
0
0
0
0
1
0
2
1
0
0
3
0
0
1
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
1
3
2
2
0
3
0
1
0
3
0
0
1
0
2
0
1
2
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
2
2
0
1
0
0
1
0
1
1
0
0
3
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
2
3
0
0
1
1
2
0
1
1
0
2
0
0
0
1
3
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
2
1
0
2
3
1
2
2
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
2
1
2
2
1
1
0
1
0
1
0
0
0
0
1
0
0
2
0
2
0
0
0
0
1
0
1
0
0
0
2
0
1
4
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
1
0
0
1
0
0
1
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
1
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
1
4
0
0
0
1
0
0
0
2
1
1
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
2
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
1
1
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
2
1
0
0
0
0
0
2
2
2
0
1
0
0
0
0
1
3
1
1
0
0
2
2
2
0
0
0
1
2
0
0
0
0
2
2
2
0
0
0
0
0
2
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
2
0
2
0
0
0
2
2
0
1
0
2
0
0
0
2
0
0
0
0
0
0
3
2
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
2
3
0
0
0
0
2
0
0
0
0
3
0
0
1
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
4
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
2
0
1
2
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
1
1
0
0
0
0
2
0
0
2
0
2
0
2
2
0
2
0
0
0
0
1
0
0
0
0
0
1
1
0
2
2
0
0
0
0
0
0
0
0
5
2
1
0
2
1
1
0
0
1
15
1
2
0
8
2
1
0
1
1
2
2
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
2
1
0
2
0
0
1
0
0
0
2
0
2
0
0
2
0
0
0
0
3
0
2
0
1
1
0
3
0
2
1
0
0
0
0
0
2
1
0
1
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
1
1
0
0
2
0
1
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
2
1
1
3
0
0
0
0
0
1
0
0
0
1
2
2
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
1
1
0
0
2
1
0
0
2
2
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
2
0
2
0
1
0
0
0
2
0
1
0
0
0
1
2
0
0
0
0
0
2
2
1
1
1
0
0
1
0
0
0
2
3
2
2
0
2
0
1
3
0
1
1
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
3
0
0
1
0
1
0
2
1
1
0
0
1
0
2
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
3
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
1
0
2
0
1
1
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
1
0
2
2
2
0
0
0
0
0
0
0
0
0
3
2
0
1
1
1
1
0
3
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
1
1
4
0
0
0
0
0
2
0
1
0
1
0
1
1
2
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
1
1
0
2
0
0
1
1
1
0
0
0
0
0
0
1
0
4
0
2
0
1
0
0
0
0
1
0
1
0
0
2
0
0
1
1
0
2
1
1
0
0
0
2
0
0
0
0
0
0
1
2
0
0
1
0
1
0
1
0
0
0
1
0
0
0
2
0
0
0
2
0
0
1
0
2
0
1
0
0
2
0
1
0
2
0
0
1
0
0
0
0
0
1
2
2
3
0
0
2
2
0
2
0
2
0
0
1
0
0
2
0
2
0
0
0
2
2
0
2
0
0
0
0
0
2
0
2
2
1
0
2
0
1
0
1
2
0
0
2
0
1
1
2
0
0
1
0
0
0
0
0
2
0
1
0
0
0
1
2
0
4
0
0
0
0
1
1
2
0
0
0
0
1
0
0
0
0
0
0
0
4
2
0
0
0
0
4
1
0
2
1
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
1
1
0
0
1
2
0
0
0
2
2
2
2
0
1
0
3
0
2
2
1
0
1
2
0
0
0
0
3
1
1
0
1
0
2
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
2
3
1
0
0
0
1
0
0
2
0
0
0
0
2
0
1
0
2
0
2
1
1
0
0
0
0
1
0
2
0
2
3
0
1
0
0
0
0
2
2
0
0
0
2
0
0
1
0
0
0
2
0
0
2
0
0
2
0
0
1
0
0
2
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
2
0
1
0
0
1
0
0
0
0
1
0
2
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
1
3
0
0
0
0
6
2
1
1
0
0
1
0
2
0
0
0
4
0
0
4
1
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
1
0
0
2
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
2
1
0
0
1
0
1
0
0
1
0
1
0
2
4
1
0
0
0
2
1
0
1
0
0
0
0
0
2
0
2
0
0
0
1
0
1
2
2
1
0
2
0
0
0
0
2
1
0
0
0
1
0
0
1
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
2
0
2
0
0
0
0
0
3
2
1
1
0
2
0
0
0
1
0
1
0
2
1
0
1
2
0
0
0
0
0
1
2
2
0
0
0
0
2
1
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
2
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
1
0
0
1
2
0
2
0
0
0
2
3
1
0
0
0
0
0
1
1
0
0
2
1
0
0
2
0
0
0
2
0
0
0
0
0
0
1
6
1
2
0
2
1
0
0
0
0
0
2
2
0
0
2
2
0
0
0
0
0
0
1
2
0
1
0
1
0
0
2
2
0
1
0
0
0
0
0
1
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
1
1
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
1
1
2
0
0
0
0
1
0
0
1
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
2
0
0
1
1
3
1
2
1
1
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
1
0
1
2
0
0
2
0
0
0
0
0
2
0
0
2
0
0
1
0
1
1
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
2
0
0
2
0
1
2
2
0
0
0
1
0
0
1
0
0
0
2
1
0
0
0
0
0
0
1
0
3
0
3
0
4
2
1
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
2
2
1
0
0
2
0
0
0
0
0
2
2
2
2
0
2
1
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
2
1
0
0
0
1
1
0
0
0
0
0
1
0
0
3
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
2
0
0
0
2
2
0
2
0
0
2
1
0
1
0
0
2
1
2
2
0
0
2
0
0
0
0
2
1
2
0
0
0
0
0
0
2
0
0
0
0
1
1
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
1
2
0
0
0
0
1
2
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
2
0
2
3
0
0
0
0
0
0
0
0
1
2
3
1
0
0
1
2
0
0
1
2
0
0
0
0
1
0
0
2
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
2
2
3
0
2
1
0
0
0
1
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
1
1
0
0
0
0
0
2
1
2
0
1
0
1
0
0
1
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
3
0
1
1
1
2
2
1
0
0
0
0
0
0
0
0
0
3
2
0
0
1
0
0
2
0
2
1
0
0
0
0
0
0
0
1
0
0
2
0
0
3
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
2
0
1
1
0
0
0
1
1
0
0
0
1
2
0
0
1
0
0
2
0
0
1
0
2
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
2
2
2
0
0
2
1
1
0
0
1
0
1
1
0
1
2
1
1
1
0
1
0
0
0
2
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
2
0
1
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
2
1
0
0
2
2
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
2
4
2
0
1
1
0
0
2
2
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
2
1
1
2
2
0
0
0
0
0
0
0
0
2
4
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
1
0
0
0
3
0
2
1
0
0
0
0
2
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
1
0
2
1
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
2
0
2
0
0
1
2
0
2
0
0
1
0
1
0
0
0
0
0
1
2
0
2
0
0
0
1
0
0
1
1
0
2
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
4
2
2
0
0
0
0
0
2
2
2
0
1
1
2
0
0
2
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
2
0
0
2
1
0
0
1
2
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
1
2
0
1
1
1
0
0
0
0
2
0
0
0
0
4
1
2
0
3
2
0
0
0
2
0
0
0
3
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
2
0
1
0
1
1
1
0
0
0
4
0
0
1
0
0
0
2
0
0
0
2
1
1
0
2
0
0
0
0
0
1
0
0
0
1
1
2
0
0
0
0
0
0
0
2
0
0
3
1
0
1
0
0
2
1
0
4
0
0
0
2
1
0
0
1
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
1
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
3
0
1
2
2
0
1
1
0
1
0
2
0
0
0
1
0
2
0
2
0
0
2
1
2
0
0
0
0
2
0
0
0
2
0
3
0
2
3
0
0
2
0
0
0
1
0
1
0
0
0
0
1
0
0
2
0
2
0
1
2
0
0
1
1
0
2
1
0
0
1
0
0
0
2
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
2
0
0
1
0
2
2
0
0
1
2
0
0
0
2
0
0
1
0
0
0
1
0
1
2
0
1
2
0
0
0
0
0
1
1
2
0
0
0
1
0
1
4
5
0
2
0
0
0
0
1
2
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
1
0
2
0
0
2
0
2
1
0
2
1
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
2
0
0
4
0
0
1
1
1
0
2
0
0
1
4
0
1
0
1
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
1
1
0
0
0
0
2
1
0
0
0
0
0
0
1
1
0
0
4
2
0
0
1
1
0
1
0
0
1
0
0
1
0
1
1
1
0
0
0
0
0
2
2
1
0
0
0
0
1
0
0
0
2
2
0
2
0
0
1
2
0
0
0
2
0
0
0
2
1
1
0
0
0
1
1
1
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
2
1
0
0
0
0
1
1
2
0
2
0
0
2
0
2
0
5
0
0
0
0
0
0
1
0
0
0
2
1
0
0
2
1
0
0
0
2
0
2
0
1
0
0
1
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
1
1
0
0
0
0
0
1
0
2
2
0
0
2
3
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
1
1
2
0
0
0
1
0
2
0
2
2
1
0
0
0
1
0
2
1
1
0
3
2
0
1
0
0
0
0
0
0
2
0
3
2
0
0
0
0
2
0
0
2
0
0
2
0
0
1
2
0
2
0
0
0
2
1
1
0
4
2
0
2
2
0
0
0
0
0
0
2
1
1
0
2
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
2
2
2
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
1
1
0
2
0
5
0
0
0
1
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
2
0
0
1
2
2
0
2
2
0
0
0
2
2
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
2
1
0
1
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
1
2
0
0
1
0
0
0
0
1
1
2
5
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
1
2
0
0
0
0
1
1
1
0
2
0
0
2
0
2
0
0
2
2
2
0
0
0
1
2
0
2
1
0
0
0
0
0
1
1
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
1
1
0
0
0
0
3
0
0
0
0
1
0
0
2
1
2
2
0
0
2
0
0
3
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
1
2
2
0
0
0
1
2
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
2
0
0
0
2
0
0
1
0
0
1
1
1
2
1
0
2
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
2
0
0
0
0
1
3
2
2
0
0
0
0
0
0
0
0
0
1
2
1
0
0
2
0
1
0
2
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
2
0
2
1
0
2
0
2
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
2
0
1
0
0
2
2
1
2
1
0
0
2
0
0
1
1
0
0
0
0
0
0
2
2
2
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
2
1
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
3
2
0
0
0
1
0
1
0
0
0
0
0
1
0
0
2
2
2
0
1
0
1
0
0
0
0
0
0
0
2
0
2
0
2
2
1
2
0
0
0
2
2
0
0
0
0
0
0
0
2
1
1
0
1
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
2
1
0
1
0
0
2
0
0
0
0
2
2
2
0
0
0
1
1
1
1
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
1
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
6
0
2
0
1
1
0
0
2
2
0
0
1
1
0
0
2
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
1
0
0
0
2
0
2
1
2
0
1
0
2
0
0
2
2
0
0
1
0
0
0
1
2
1
0
2
2
0
0
0
1
2
2
1
0
0
1
0
0
1
6
3
1
0
0
2
0
0
0
2
2
1
0
1
0
2
0
2
0
0
0
0
0
2
0
0
1
0
0
0
1
1
1
0
1
0
0
0
0
2
2
0
1
1
1
1
0
1
0
2
3
0
0
0
1
0
2
0
0
2
0
2
2
1
0
2
0
0
1
2
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
8
0
2
1
0
0
0
1
2
0
1
0
0
1
0
2
0
2
1
0
2
2
0
0
2
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
2
0
1
3
1
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
2
0
0
0
1
2
1
0
0
0
0
0
0
2
0
0
0
0
0
4
0
0
0
0
2
0
1
2
3
0
0
0
1
0
0
2
0
0
0
1
0
1
0
2
0
0
1
1
0
0
2
0
1
0
0
0
0
2
1
0
0
0
0
2
2
0
2
0
3
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
2
2
0
0
0
0
0
0
2
0
0
0
1
1
0
2
1
2
0
0
0
0
0
0
0
0
0
6
0
0
1
1
0
0
0
0
0
0
1
2
3
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
1
0
0
1
2
1
1
1
0
1
0
1
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
3
0
0
2
1
0
0
0
1
2
0
0
0
2
0
0
1
0
0
0
2
1
1
0
0
4
0
0
0
0
0
0
0
0
1
0
3
0
1
5
0
1
0
5
0
1
0
0
0
0
0
2
0
2
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
2
0
0
0
0
2
0
1
1
0
0
1
0
1
0
0
2
0
0
0
0
2
2
0
0
0
0
1
0
1
1
1
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
1
0
0
1
0
0
2
0
1
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
1
0
0
0
2
0
1
2
2
0
0
0
0
0
2
2
0
0
0
0
1
0
4
0
0
0
3
0
0
0
0
0
0
1
2
0
0
0
2
0
1
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
3
0
0
0
0
0
0
1
0
1
2
0
0
0
2
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
3
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
2
2
0
0
0
0
1
0
0
0
0
1
2
0
2
0
0
1
2
1
0
0
0
0
1
0
1
0
0
0
0
0
2
2
0
0
0
0
0
2
1
0
1
0
0
0
3
0
0
2
4
0
0
0
1
0
0
0
1
1
2
0
2
2
2
0
2
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
2
2
0
1
2
0
0
0
0
2
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
2
1
2
2
2
2
5
0
1
1
2
0
0
0
1
0
0
0
0
0
3
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
1
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
1
0
0
0
0
0
2
0
1
0
0
0
2
3
0
0
0
0
0
0
0
1
1
0
2
0
1
0
1
0
1
0
0
0
1
1
0
0
3
0
1
0
0
0
2
0
0
2
1
2
2
0
2
3
3
0
0
2
0
2
0
0
0
0
2
0
1
1
1
1
0
2
0
0
0
0
0
1
0
0
0
0
0
1
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
6
2
1
1
2
1
0
0
0
2
2
0
0
0
0
2
0
1
0
0
1
0
0
5
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
2
2
0
0
2
0
1
2
2
1
0
2
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
1
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
2
0
3
2
0
0
0
2
0
0
0
2
0
0
0
0
0
1
2
0
1
0
0
0
1
1
1
0
4
4
2
0
0
0
1
0
2
2
0
1
2
1
0
0
5
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
6
0
1
1
0
1
0
0
0
1
2
0
1
2
2
0
0
1
0
0
0
0
2
0
1
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
1
0
1
2
0
2
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
1
0
0
0
2
1
0
0
1
0
1
0
1
0
0
2
2
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
1
1
1
0
0
2
0
1
1
0
0
1
1
0
0
0
1
0
0
0
2
0
1
2
0
0
3
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
1
2
1
0
0
2
0
9
2
0
0
1
0
2
0
0
1
1
0
1
1
0
0
0
0
1
0
1
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
1
0
0
0
2
1
0
0
0
0
1
1
0
0
0
1
1
0
2
0
0
1
0
0
0
0
2
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
1
1
0
0
1
0
0
0
1
2
3
0
1
2
2
0
0
2
2
2
0
1
0
1
1
2
0
0
2
1
0
0
0
0
0
0
0
1
0
2
3
1
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
7
0
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
1
0
1
4
1
0
2
0
0
2
0
0
0
2
0
0
0
0
2
0
4
0
2
1
0
0
1
0
0
1
0
0
0
0
2
1
2
1
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
1
0
0
0
2
2
1
0
2
0
0
2
0
0
0
0
4
0
1
2
0
3
0
2
0
0
1
0
0
0
1
2
0
0
1
2
0
1
0
0
2
0
1
0
0
0
1
3
0
0
0
0
1
3
1
0
0
0
0
0
0
0
1
0
1
0
1
2
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
2
2
1
0
0
0
2
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
1
1
0
0
3
2
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
2
2
1
2
0
0
0
0
2
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
3
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
1
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
2
0
0
2
0
1
0
1
0
0
0
0
1
3
0
0
1
2
0
1
0
1
0
0
0
0
2
6
1
2
0
2
0
2
1
2
2
1
2
0
1
0
0
0
2
2
0
1
0
1
1
0
1
0
0
0
0
1
0
2
0
0
0
0
2
1
0
0
0
0
0
2
1
0
0
1
3
1
1
0
0
0
0
0
1
2
1
0
0
1
1
0
0
0
1
0
0
0
2
1
0
1
1
0
0
1
1
1
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
2
0
1
0
0
0
0
1
0
0
0
1
0
2
0
2
3
0
1
0
0
1
2
2
0
0
0
0
0
0
1
2
0
2
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
3
2
1
1
1
0
0
0
1
0
2
0
0
0
0
1
0
0
2
0
0
3
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
1
2
0
0
1
2
0
0
0
0
0
0
0
0
1
2
0
1
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
2
2
0
0
0
0
0
0
2
0
2
0
0
0
0
2
2
0
0
1
0
0
1
0
2
2
0
0
1
0
0
0
0
0
1
0
0
0
1
2
1
1
0
0
0
0
3
2
2
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
1
1
0
0
2
0
0
0
1
0
0
0
1
0
2
0
0
0
0
1
0
1
2
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
2
3
0
0
0
0
2
0
2
0
0
0
0
0
3
0
2
0
0
2
0
2
1
2
3
0
2
0
0
0
0
1
0
3
1
1
0
0
0
2
0
1
1
0
0
1
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
7
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
2
0
1
0
2
1
1
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
3
0
0
2
2
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
2
2
0
0
0
1
0
1
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
1
2
0
0
1
0
2
0
0
1
0
0
1
0
2
0
0
2
2
0
0
0
0
9
0
0
0
0
0
1
0
1
2
0
0
0
1
1
2
1
1
2
0
0
0
2
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
1
1
0
0
0
1
0
0
2
1
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
1
2
0
0
1
2
0
0
0
1
0
1
1
0
1
0
2
0
0
0
0
0
3
0
0
2
0
1
0
0
2
0
0
0
0
0
1
1
0
1
0
0
2
1
0
0
0
0
0
0
0
0
3
1
0
1
2
3
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
2
2
0
1
0
0
2
0
0
0
2
1
0
2
0
0
2
0
0
1
1
2
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
3
0
1
1
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
1
1
3
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
2
1
3
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
2
0
0
0
2
1
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
3
2
0
0
1
0
0
0
0
0
0
1
2
2
0
0
0
1
0
0
1
2
0
2
0
1
2
0
1
0
0
1
0
0
1
0
2
0
1
1
0
2
1
0
0
0
0
2
0
0
2
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
2
1
1
1
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
2
1
0
0
0
2
2
0
0
1
1
0
0
0
0
0
2
0
0
1
0
1
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
1
3
0
0
0
2
0
0
0
0
0
0
4
1
0
0
0
2
0
0
1
3
0
1
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
1
1
0
1
1
1
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
2
0
0
1
0
0
1
0
2
1
0
0
0
1
1
1
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
4
0
2
0
2
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
1
1
0
0
1
1
0
1
2
1
0
1
1
0
2
0
1
0
2
0
0
0
0
1
0
0
1
2
2
1
0
0
4
1
0
0
0
1
0
0
1
0
1
0
1
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
2
0
0
0
0
2
3
2
3
2
1
0
2
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
2
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
3
0
0
0
0
2
2
2
0
0
1
2
1
1
0
1
3
1
0
0
3
0
2
2
1
0
2
1
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
2
1
1
1
2
2
0
2
2
1
0
0
2
0
2
3
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
2
2
0
0
0
0
0
1
1
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
2
0
1
0
0
0
0
0
2
2
0
0
0
2
0
2
0
1
0
0
0
2
0
1
1
0
0
0
0
1
3
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
4
0
2
1
0
0
1
0
0
1
0
0
2
2
0
6
0
0
0
0
1
4
0
0
0
0
0
0
0
1
0
2
0
2
2
2
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
2
0
0
0
2
1
2
0
2
0
0
0
0
0
3
0
2
0
0
0
1
0
1
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
2
0
0
0
5
0
1
0
2
0
2
2
0
1
2
3
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
2
0
1
0
1
0
0
0
1
0
3
0
1
2
0
0
0
0
0
0
0
1
0
0
6
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
3
0
0
0
0
0
1
3
1
1
2
0
0
0
0
0
1
0
0
0
0
0
4
4
0
0
0
0
0
3
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
4
1
2
0
0
0
3
0
0
0
0
1
0
2
0
0
0
2
0
2
0
0
0
2
0
0
0
2
0
2
2
0
1
0
0
0
2
1
0
1
1
0
2
2
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
3
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
2
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
2
2
0
0
1
2
2
0
2
2
2
0
0
0
0
0
1
1
1
2
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
6
0
0
0
1
2
0
0
0
0
0
0
2
0
1
2
1
0
1
0
0
0
2
1
1
0
0
0
0
0
1
0
2
0
4
0
14
0
0
0
0
0
0
0
2
4
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
1
1
2
0
0
0
2
2
2
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
2
1
0
0
0
1
0
2
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
2
1
0
2
0
1
0
2
1
1
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
1
0
0
0
1
0
0
2
0
0
2
0
0
2
0
0
0
0
0
5
0
3
1
1
0
0
0
0
0
0
2
0
0
1
0
0
0
1
2
0
0
7
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
1
4
1
2
0
0
0
0
0
0
0
1
2
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
1
0
1
2
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
1
0
0
0
2
0
1
2
0
0
0
0
1
3
0
0
3
0
0
1
0
1
1
0
0
0
2
0
2
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
3
0
0
2
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
1
2
0
1
1
0
0
0
0
0
1
0
1
0
0
0
2
2
0
0
3
2
0
2
2
1
0
1
0
2
0
0
0
0
1
1
2
2
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
3
0
0
0
0
2
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
2
0
2
0
1
0
1
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
2
0
0
1
3
1
0
0
0
0
0
0
2
0
0
3
1
0
2
1
0
0
0
1
0
1
0
0
2
2
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
2
1
0
0
1
0
0
1
0
0
0
2
2
2
0
2
0
0
0
0
2
0
1
2
0
0
2
0
0
2
1
0
1
0
0
0
0
0
0
0
0
2
1
0
2
1
0
0
0
0
1
2
0
0
0
1
1
0
1
0
0
0
0
0
2
0
0
3
0
1
0
1
1
0
0
0
0
0
1
2
0
0
0
0
0
3
1
0
0
2
0
0
0
0
0
2
1
2
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
2
0
0
0
2
1
0
2
1
2
0
4
1
1
2
2
2
2
0
0
1
0
0
2
0
2
0
0
1
2
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
5
0
2
0
0
0
1
0
2
1
0
0
2
0
0
3
0
0
0
0
1
0
0
1
2
0
5
1
2
1
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
1
7
2
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
2
0
0
0
1
1
0
2
1
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
2
1
1
2
0
2
0
0
0
0
2
0
0
1
0
1
4
0
0
1
0
0
0
0
1
1
3
0
0
1
1
0
0
2
1
0
2
0
0
2
2
1
0
0
2
2
2
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
2
1
2
2
2
0
1
0
0
2
2
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
1
2
0
0
2
0
1
0
2
0
0
1
1
0
0
0
1
0
0
0
2
1
1
0
0
0
1
0
2
0
3
6
0
0
2
0
0
0
0
1
1
2
0
0
0
0
0
1
1
0
0
0
0
2
0
0
1
2
0
0
2
1
2
0
0
0
0
2
2
1
0
2
0
3
0
1
1
1
0
1
2
1
2
0
0
0
0
0
0
2
0
0
2
2
0
2
0
0
2
2
0
0
1
0
0
0
2
1
0
0
0
1
0
0
2
0
0
0
0
2
2
0
2
0
2
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
1
0
5
0
0
0
0
1
3
2
0
1
0
0
0
2
0
0
1
0
2
0
0
2
0
0
0
2
0
2
1
0
3
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
2
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
1
1
1
2
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
2
0
2
0
1
2
0
2
0
0
0
0
0
0
0
2
0
2
2
1
1
0
2
0
0
0
0
0
0
1
2
1
2
0
1
0
0
0
3
0
2
0
2
0
0
2
2
1
0
1
0
2
0
3
0
5
2
1
1
1
0
2
1
2
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
2
0
0
2
2
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
2
1
0
0
2
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
1
2
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
1
3
0
2
1
5
2
0
1
3
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
1
1
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
1
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
3
0
0
0
0
2
1
2
5
0
1
0
0
0
1
0
0
0
0
0
0
1
1
1
0
2
0
2
0
0
2
1
0
0
0
0
0
0
2
3
0
2
0
0
0
1
0
2
0
0
1
0
0
0
2
0
3
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
1
0
2
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
1
0
0
0
0
0
3
1
0
2
0
0
0
0
0
2
1
2
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
5
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
1
1
0
3
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
1
0
0
1
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
1
0
1
0
0
0
1
0
0
0
0
2
2
1
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
3
1
0
1
0
2
0
0
0
0
2
0
2
1
2
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
2
0
0
0
2
0
0
0
0
1
0
2
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
2
1
0
2
1
1
1
0
2
0
1
2
0
0
0
0
1
0
2
0
0
1
0
0
0
0
3
3
0
0
2
0
0
0
0
1
2
1
0
1
0
3
0
1
0
0
0
0
0
2
0
1
0
0
1
0
0
0
2
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
5
0
0
0
0
1
0
0
0
0
0
1
0
0
3
0
0
0
2
0
2
0
0
1
1
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
3
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
2
2
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
2
0
0
1
0
0
0
2
3
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
1
0
1
2
0
0
0
1
0
0
8
2
2
1
0
0
0
0
0
1
1
0
1
0
0
0
2
0
0
2
0
1
1
0
1
0
0
0
1
0
0
0
0
0
2
1
0
0
2
0
2
1
1
0
0
1
0
0
0
0
0
1
2
0
0
1
1
2
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
2
1
0
0
1
2
0
0
0
2
0
1
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
2
0
0
2
2
0
0
0
0
2
0
2
1
2
0
2
2
0
0
0
1
2
0
0
0
2
0
2
0
3
0
0
0
3
0
0
3
0
0
1
0
0
0
0
0
2
1
0
0
2
1
2
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
2
0
0
0
2
0
0
2
0
0
0
2
1
0
0
0
1
0
0
0
0
2
0
1
0
0
1
1
0
2
0
2
0
0
0
0
0
0
1
4
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
2
0
0
3
0
0
0
2
0
0
0
0
0
0
2
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
1
0
2
3
2
1
0
2
2
2
0
0
0
2
1
0
0
0
0
1
1
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
2
2
0
2
0
0
1
0
0
1
0
1
0
2
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
1
0
4
0
1
2
0
0
1
0
0
0
0
0
0
1
0
1
2
0
1
2
0
0
0
0
0
0
0
0
1
1
1
0
0
0
2
0
5
0
2
2
2
0
0
1
1
2
0
0
0
0
0
4
2
1
0
0
0
0
0
0
2
0
1
0
1
2
0
1
1
0
2
0
0
0
0
0
0
2
0
2
1
0
2
0
3
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
2
0
2
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
1
2
1
0
1
0
0
0
1
0
1
2
0
0
0
0
1
2
0
0
0
1
1
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
2
0
0
0
2
0
0
2
0
2
2
2
0
0
0
0
0
0
0
2
2
1
1
0
2
0
0
0
2
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
1
2
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
3
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
1
2
0
0
2
0
4
2
2
0
1
1
0
0
0
0
1
1
0
0
1
1
1
0
0
0
0
0
1
0
0
2
3
2
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
2
0
0
0
0
2
0
1
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
1
0
0
1
1
0
0
0
1
1
0
0
0
0
2
0
1
0
0
2
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
1
1
0
2
2
1
1
1
0
1
0
2
2
0
1
0
2
0
0
0
0
0
1
1
0
0
0
0
2
0
2
0
0
0
0
1
2
0
1
2
0
2
0
0
0
0
0
0
0
1
0
1
0
2
2
2
1
0
0
0
1
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
1
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
2
0
2
0
0
1
1
2
2
0
2
0
0
2
0
0
1
2
0
2
1
1
0
0
1
1
2
0
1
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
1
1
1
0
1
0
2
0
0
2
0
1
1
1
0
0
1
2
1
0
0
0
0
1
0
0
0
0
1
1
1
2
2
0
0
2
0
0
0
0
0
2
0
1
0
2
0
0
0
0
1
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
1
1
0
0
0
2
1
0
2
2
0
2
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
1
1
1
0
0
0
0
1
0
2
2
0
0
0
1
0
1
2
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
2
0
1
0
5
1
1
0
0
0
0
1
1
0
0
0
1
0
1
2
0
0
2
0
0
0
2
0
2
2
0
0
0
0
0
0
0
3
0
0
1
1
0
0
2
0
0
0
1
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
1
0
1
2
1
0
0
0
1
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
2
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
1
2
0
1
0
2
0
1
3
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
1
0
2
0
4
0
2
0
2
0
0
3
1
0
0
0
0
2
1
0
0
0
0
1
0
0
0
1
2
0
0
0
1
1
0
2
0
0
1
0
1
0
1
0
0
0
1
0
1
0
1
0
0
0
1
0
1
0
0
2
2
0
0
3
1
0
0
0
0
2
0
1
2
0
0
0
0
2
0
0
1
1
2
0
0
1
0
0
0
0
2
2
0
0
0
0
2
1
2
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
1
0
1
0
0
0
0
0
0
2
0
0
1
1
0
1
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
2
0
0
0
0
3
4
0
0
2
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
2
1
1
0
0
0
2
2
0
0
1
1
0
0
5
0
1
2
0
0
1
0
0
0
1
1
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
2
2
2
0
0
1
0
1
0
2
0
0
0
1
0
0
1
0
2
0
1
0
0
0
0
0
0
0
4
1
0
1
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
2
1
0
2
0
2
0
2
2
0
0
0
0
0
0
1
0
0
1
1
0
1
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
1
0
1
1
2
0
0
0
0
3
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
1
1
1
2
1
0
2
2
1
0
1
0
1
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
1
0
1
0
0
1
1
2
0
0
0
1
0
0
0
1
1
0
0
1
1
2
0
2
2
0
0
0
0
2
0
0
0
0
0
1
0
0
5
1
1
2
2
0
0
1
0
0
0
0
2
0
0
0
2
0
1
0
2
1
0
0
0
3
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
2
0
2
2
0
2
0
2
2
0
0
0
1
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
2
1
0
2
0
2
1
0
0
0
1
0
0
0
0
2
0
2
1
0
1
0
1
1
0
0
0
1
0
0
0
0
1
0
2
4
0
1
0
2
0
0
0
0
1
2
1
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
2
1
0
2
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
2
0
0
0
0
1
0
0
0
1
1
0
0
0
1
2
1
1
0
0
0
1
2
1
2
0
0
0
0
2
0
0
2
0
0
0
0
2
2
1
0
1
0
0
1
0
1
1
2
1
0
0
0
1
0
0
1
2
0
0
0
1
0
0
1
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
2
0
2
1
0
1
0
4
1
0
0
0
1
0
2
0
1
2
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
2
0
0
2
0
5
1
2
2
0
0
0
0
0
0
2
2
0
0
0
1
2
0
2
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
1
0
2
0
0
0
0
2
0
2
0
0
0
2
0
1
0
2
0
0
2
0
0
0
2
0
0
0
0
1
2
0
0
2
2
0
0
0
0
1
1
4
1
0
1
0
3
0
2
2
0
2
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
2
2
0
0
0
0
2
0
0
2
0
1
0
0
1
0
1
1
0
0
0
0
0
2
3
0
3
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
2
1
1
1
0
2
0
0
0
2
1
1
0
2
0
0
1
0
2
0
0
0
0
2
0
1
4
0
2
0
1
0
0
0
0
0
0
0
0
1
2
2
0
0
2
2
1
0
0
0
0
0
1
0
0
0
0
0
2
2
1
1
0
1
0
0
0
0
1
3
0
1
1
0
0
1
2
0
0
0
1
0
1
0
0
0
0
0
1
0
2
1
1
0
0
0
0
2
1
1
2
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
1
1
0
1
0
1
0
2
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
1
3
2
2
0
0
0
0
2
0
2
2
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
2
0
0
0
1
0
0
0
0
0
0
1
2
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
3
2
0
0
2
0
0
2
1
0
1
0
2
1
1
1
0
1
0
0
0
2
0
1
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
2
0
2
0
0
0
0
0
1
0
4
2
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
1
0
1
0
1
2
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
1
2
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
2
0
0
1
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
1
0
0
1
0
1
2
1
0
2
2
0
0
1
0
0
1
0
1
0
1
1
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
1
0
1
2
2
0
0
2
1
0
0
0
0
0
1
0
0
0
0
2
0
0
3
3
0
0
0
0
2
0
1
0
0
0
0
1
2
1
0
2
1
1
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
1
0
0
2
0
0
1
0
0
0
0
1
0
4
0
0
0
2
2
2
0
0
0
0
0
0
2
2
0
0
1
2
2
1
0
0
0
0
2
2
0
0
0
0
4
0
2
2
0
0
3
0
3
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
1
1
2
0
4
0
0
0
2
2
0
0
2
1
0
0
0
0
1
0
1
1
2
0
0
3
0
2
0
0
1
0
0
1
0
0
0
0
1
0
2
2
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
1
2
2
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
2
0
1
1
0
0
0
0
0
2
0
0
0
2
0
2
2
0
0
0
1
2
0
1
0
2
0
2
1
0
0
2
0
0
0
1
1
0
0
0
2
0
0
0
1
0
0
3
0
2
0
2
0
0
0
0
2
0
1
0
0
2
1
0
2
0
0
3
0
0
2
0
0
0
2
0
4
0
0
1
0
1
0
0
0
2
0
2
0
0
0
0
0
0
2
0
2
0
2
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
3
1
0
1
0
0
2
1
0
0
0
0
1
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
2
0
0
2
0
2
2
0
2
0
5
1
0
0
0
2
2
0
0
1
0
0
2
0
0
0
2
2
0
2
0
3
0
2
3
0
0
0
0
2
0
0
0
2
2
0
0
2
2
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
1
0
2
0
2
0
1
1
0
1
0
3
0
0
1
1
2
0
2
0
0
0
2
2
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
2
0
1
0
0
0
1
0
0
1
2
2
2
0
1
2
0
0
0
2
0
2
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
2
1
1
0
0
1
0
2
1
0
0
0
2
1
0
1
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
4
0
0
0
2
0
1
0
3
0
2
1
0
0
0
0
1
0
1
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
1
0
0
2
0
0
1
1
0
0
0
1
0
2
0
0
1
0
0
0
0
1
1
0
1
0
0
0
2
2
0
2
0
0
2
2
2
0
3
2
0
1
0
0
0
2
0
1
2
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
2
2
2
1
0
1
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
2
1
0
0
2
0
0
0
0
0
1
0
0
0
3
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
1
0
0
1
2
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
1
2
2
0
2
0
1
1
0
0
1
0
0
1
0
0
0
0
2
2
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
2
1
0
3
0
0
2
0
0
0
0
0
1
0
1
0
0
0
1
2
1
1
0
2
0
0
1
0
0
0
2
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
1
1
3
0
3
0
0
0
0
1
2
0
2
0
2
1
1
0
1
1
0
2
2
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
4
1
0
0
0
0
0
0
2
0
0
1
1
1
1
0
0
0
0
2
0
2
0
0
0
0
3
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
3
0
0
0
0
0
0
0
1
3
0
5
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
2
0
0
0
0
0
1
0
0
1
0
1
0
2
1
0
0
0
0
2
2
0
1
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
2
1
0
3
2
0
1
0
2
0
2
2
2
1
3
0
0
1
2
2
3
0
1
0
2
1
0
1
0
0
2
0
1
0
12
1
0
0
2
0
0
1
0
2
0
0
1
0
0
0
0
1
2
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
3
1
0
0
0
0
1
2
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
2
4
0
0
2
2
2
0
0
1
0
1
0
1
0
1
0
0
0
3
2
0
0
0
1
2
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
1
1
0
0
0
0
0
0
4
1
0
0
0
2
2
0
0
0
0
2
1
2
2
0
1
0
0
1
0
0
1
0
0
1
0
0
0
2
0
0
0
1
0
2
0
0
0
0
1
0
1
2
1
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
1
0
0
0
2
0
0
0
0
1
0
0
2
1
1
1
0
1
2
0
0
0
1
0
0
0
0
4
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
1
0
0
0
4
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
3
3
3
3
2
0
0
2
1
0
1
2
0
0
1
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
2
0
1
2
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
2
0
2
0
0
0
0
0
1
4
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
2
2
1
0
1
0
1
1
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
4
0
0
3
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
2
1
1
0
0
0
1
0
0
0
2
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
2
0
1
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
2
0
0
2
0
0
1
0
0
0
1
1
0
2
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
2
2
1
0
0
0
0
2
1
0
0
0
0
0
0
0
1
2
2
0
0
1
0
0
2
0
1
0
0
0
0
0
2
3
0
0
0
2
0
2
1
0
1
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
1
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
2
0
2
2
0
1
0
0
0
2
0
2
0
1
0
0
1
0
1
0
1
0
0
0
1
0
1
0
2
0
0
0
3
0
0
1
0
0
0
0
1
2
0
0
0
0
0
2
0
0
1
2
0
2
2
0
1
0
0
1
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
1
2
0
0
0
0
0
0
0
0
3
2
1
0
0
0
1
0
1
0
0
3
0
0
2
0
1
0
2
0
0
1
7
2
0
2
2
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
1
1
0
0
0
0
1
0
0
3
0
0
0
0
1
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
2
0
1
1
0
2
0
0
0
1
1
0
0
1
0
0
0
0
0
0
2
4
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
2
1
2
2
7
0
0
2
1
1
0
0
1
1
1
1
0
0
2
2
0
2
0
0
0
1
1
3
0
1
0
0
0
2
0
0
0
0
2
0
2
0
0
2
0
0
3
1
2
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
2
2
2
1
0
0
0
2
0
2
0
2
1
2
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
1
0
0
1
0
0
3
3
1
3
2
0
0
1
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
4
1
0
0
1
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
7
3
0
3
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
2
0
3
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
1
0
0
0
1
0
0
3
2
0
2
0
1
0
0
0
0
2
1
0
0
0
1
0
1
0
0
0
1
2
0
1
0
0
0
1
0
0
1
4
0
3
0
0
0
2
0
0
2
0
0
0
0
0
0
0
5
1
1
2
1
1
0
0
0
0
0
1
2
0
2
1
1
0
1
0
2
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
2
2
2
2
0
0
0
0
0
2
2
0
0
0
0
2
0
1
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
2
0
0
0
0
0
1
0
1
3
0
4
2
0
0
0
0
1
2
0
0
1
0
0
2
0
2
0
0
0
0
2
0
1
0
2
0
0
0
1
1
0
0
2
2
0
0
0
1
0
2
1
0
2
0
0
0
0
0
1
2
1
0
0
2
0
0
0
2
1
0
0
0
1
1
1
0
2
2
1
1
5
1
0
0
0
0
0
1
0
1
3
0
1
0
0
0
3
0
0
0
0
1
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
3
0
1
1
0
2
0
2
0
0
0
0
0
0
2
0
0
1
0
2
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
7
0
0
0
0
1
0
0
1
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
1
0
2
2
0
0
2
0
0
0
1
0
1
0
2
1
2
0
0
1
0
0
0
2
0
1
0
1
1
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
2
3
2
1
0
0
1
0
1
0
1
1
0
0
0
1
1
0
0
0
0
2
0
0
0
0
2
0
1
1
2
0
0
2
0
0
0
0
0
1
0
2
0
2
2
7
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
1
2
1
0
0
2
0
0
0
2
0
0
1
1
0
0
0
2
0
0
2
3
0
0
0
0
1
0
1
1
0
0
2
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
2
2
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
1
0
0
0
0
0
0
2
1
0
0
1
0
1
0
0
2
1
0
1
1
2
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
2
7
0
1
0
0
0
0
0
0
0
3
2
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
2
0
0
1
0
3
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
2
0
0
0
2
0
0
0
2
0
0
0
1
0
1
0
0
2
1
0
2
2
1
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
1
2
0
0
0
0
2
2
0
0
2
0
0
1
1
0
0
0
0
2
0
0
0
4
0
2
0
0
0
2
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
1
1
2
1
0
0
0
0
0
2
0
0
2
1
0
0
3
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
2
2
2
0
1
1
2
2
0
0
1
0
1
2
0
1
1
2
0
0
0
0
1
3
1
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
1
0
2
0
0
3
0
0
0
0
2
0
2
0
0
0
2
0
1
4
1
0
0
0
0
2
1
0
0
0
0
2
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
1
2
2
0
0
0
1
1
3
4
1
0
0
0
1
0
0
0
0
2
0
2
0
0
2
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
1
0
1
2
2
0
0
1
0
0
0
0
0
0
0
0
2
0
2
1
1
0
0
1
0
0
0
0
2
0
0
0
2
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
1
0
0
1
0
1
2
2
0
2
0
0
0
0
0
0
0
0
2
1
0
2
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
1
1
2
2
0
1
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
2
0
0
0
0
0
0
2
2
0
0
2
0
2
0
1
2
0
1
1
0
0
1
0
1
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
2
0
0
1
1
2
0
0
1
0
0
0
0
0
0
0
0
2
0
3
3
1
0
0
2
0
0
0
0
2
2
0
0
0
1
0
2
1
1
2
0
0
0
1
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
4
2
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
2
2
0
2
0
0
2
0
0
1
2
0
0
2
0
0
0
2
0
0
1
0
0
0
2
0
0
0
3
2
0
0
0
1
1
1
0
0
0
0
0
0
1
2
2
2
0
3
0
2
0
0
1
0
0
0
2
0
3
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
2
0
1
0
1
0
0
1
0
0
2
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
2
2
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
2
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
3
2
0
0
1
0
1
0
4
0
0
0
0
0
0
2
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
1
2
0
0
1
0
1
0
1
0
0
1
0
2
0
1
1
0
0
0
0
2
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
2
0
1
1
4
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
1
1
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
1
0
1
1
1
0
0
2
0
2
0
0
1
0
0
0
0
2
2
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
2
1
0
2
0
2
0
2
2
0
0
1
2
0
0
0
0
1
0
0
0
1
0
2
0
1
0
0
2
0
2
2
0
1
1
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
3
1
1
0
0
0
1
0
0
0
2
0
0
1
0
3
0
0
0
1
0
1
0
1
0
0
1
1
2
3
2
2
2
2
0
0
0
0
2
0
0
0
0
0
0
1
1
0
2
0
0
0
1
0
2
0
2
0
2
0
0
0
2
0
0
0
0
1
0
0
1
3
0
0
1
0
2
0
0
0
2
2
0
0
2
3
1
0
0
1
0
2
1
0
0
0
0
3
0
0
0
1
0
1
0
0
1
0
5
1
1
0
0
1
2
0
1
0
2
2
2
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
2
1
1
1
0
0
1
0
0
1
2
0
0
0
0
0
0
1
0
1
0
4
0
0
0
0
0
0
2
0
0
2
1
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
1
0
0
0
1
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
2
2
0
2
0
0
0
1
1
1
0
0
0
1
1
1
1
1
0
2
0
0
1
0
0
0
3
2
0
0
0
0
2
0
2
1
0
1
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
3
0
2
0
0
0
1
0
2
0
2
0
0
2
0
0
1
0
0
0
0
1
2
0
0
2
0
0
0
5
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
1
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
2
0
1
2
2
2
1
2
2
0
1
0
1
0
0
1
1
2
0
2
0
0
0
2
0
1
1
2
0
0
1
0
0
2
3
1
0
2
2
1
1
0
0
0
1
1
0
0
0
1
0
0
2
1
0
2
0
0
0
0
1
2
2
0
0
0
3
2
0
3
2
1
0
0
2
5
0
0
1
2
0
0
0
0
0
3
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
5
2
1
0
1
0
2
0
1
2
1
0
0
0
0
0
2
0
0
3
0
0
0
0
0
2
0
2
0
0
0
1
2
1
0
0
2
0
0
1
0
2
2
2
0
0
1
2
3
1
0
0
0
0
2
0
0
0
3
0
2
0
1
2
3
0
0
0
1
1
0
0
0
0
0
1
1
0
2
0
0
0
0
0
2
1
2
1
0
2
0
0
2
1
0
0
0
0
3
2
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
2
0
0
0
2
3
0
0
1
0
0
1
2
2
0
0
1
0
0
0
1
1
2
0
1
1
0
0
0
2
0
0
0
0
2
2
0
0
1
0
0
0
2
0
0
0
0
1
3
0
2
0
1
2
0
0
0
0
2
2
0
0
1
2
0
0
0
0
1
0
2
0
0
1
1
0
0
0
1
2
0
2
0
0
0
0
0
0
1
2
0
1
0
0
0
2
0
0
2
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
3
0
0
0
0
1
2
1
0
2
0
0
1
0
0
0
1
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
2
0
1
1
0
0
5
2
0
0
1
0
2
0
0
1
0
2
0
0
0
0
1
0
2
0
0
0
2
0
0
1
0
1
0
2
5
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
5
0
1
0
0
0
2
0
0
1
0
0
0
2
2
0
1
2
0
0
0
2
0
0
3
0
0
1
0
0
0
0
1
2
1
4
2
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
1
0
0
1
2
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
2
0
0
0
0
0
0
1
0
1
0
0
0
1
3
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
1
0
2
2
2
0
0
0
0
1
2
0
2
1
0
0
2
0
3
3
0
0
0
2
1
0
1
0
0
0
1
0
0
2
0
0
1
0
0
2
0
1
0
3
0
0
0
0
0
0
0
1
2
0
0
2
2
0
0
0
2
1
0
0
2
0
3
0
0
2
0
1
0
0
2
0
2
0
0
0
0
0
0
2
0
1
0
1
0
0
2
0
0
0
0
0
2
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
1
2
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
4
2
0
0
5
0
0
1
0
0
1
1
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
1
2
1
1
0
0
1
0
2
1
0
0
0
0
0
3
0
0
0
0
2
0
5
0
0
0
0
0
0
1
0
2
2
1
4
0
0
1
2
0
0
0
2
0
0
2
0
0
1
0
2
0
2
0
0
1
0
1
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
1
0
9
0
2
0
0
0
1
0
0
0
2
2
0
0
0
0
1
0
0
1
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
2
1
0
0
1
0
2
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
1
1
2
0
0
0
0
0
0
2
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
3
3
1
2
0
0
2
0
3
2
0
0
0
2
0
2
0
0
0
0
0
1
0
0
2
0
3
0
0
0
0
4
0
0
0
2
0
2
0
0
0
2
0
0
3
0
0
1
2
0
4
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
2
1
1
2
0
1
2
1
1
0
0
0
0
0
2
0
0
1
0
2
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
2
2
2
0
0
0
0
1
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
1
3
1
0
0
0
0
0
2
0
2
1
0
2
0
1
0
0
0
0
0
2
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
2
1
0
3
0
0
0
0
1
0
1
2
0
0
2
0
0
0
1
2
2
2
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
2
1
0
1
0
0
0
0
2
0
1
2
0
1
2
1
0
0
0
1
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
2
2
1
2
1
0
0
2
0
0
0
0
0
0
0
0
5
1
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
1
0
1
0
0
2
0
2
0
0
0
0
0
0
3
0
0
4
2
1
2
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
2
2
2
0
3
0
0
1
0
0
0
2
0
2
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
1
1
0
2
2
1
0
2
0
0
0
0
0
2
0
0
0
0
1
2
0
1
2
0
0
2
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
3
1
2
0
0
1
3
0
0
0
0
0
1
0
0
0
1
2
3
0
0
0
0
0
2
0
0
0
0
0
2
2
3
1
1
2
4
1
2
3
2
0
0
2
2
2
0
0
0
0
0
0
0
1
2
0
0
3
0
2
0
0
0
0
2
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
3
2
0
0
3
1
0
2
0
2
2
1
2
0
4
0
0
0
0
0
2
3
0
0
0
0
1
2
1
1
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
2
0
2
0
0
2
2
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
2
2
0
0
0
0
0
2
0
0
0
1
1
2
0
0
1
2
0
0
0
1
2
0
1
1
0
0
0
2
1
1
0
1
1
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
1
0
0
2
1
0
0
0
2
0
0
1
0
2
2
0
0
1
2
0
0
15
0
0
1
0
0
1
0
0
0
2
0
1
0
0
0
2
0
1
0
2
0
3
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
1
3
0
0
0
0
2
1
2
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
2
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
3
0
0
1
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
2
0
1
1
0
0
2
2
2
0
0
0
0
2
1
1
2
0
0
1
0
2
2
1
0
0
1
0
0
0
0
0
0
1
0
2
2
0
0
0
0
2
0
2
1
1
0
0
0
0
0
6
0
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
2
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
2
0
2
0
0
0
0
2
0
0
3
0
2
1
0
0
4
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
2
0
0
2
2
0
0
0
0
0
0
0
2
5
0
2
1
0
1
0
0
0
0
0
0
0
2
1
2
2
1
0
2
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
4
0
1
1
0
0
0
2
0
0
0
1
1
0
1
0
1
0
0
1
0
0
0
0
0
1
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
1
0
0
2
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
1
2
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
1
0
3
0
0
1
3
0
0
2
0
1
0
1
0
1
2
2
0
1
0
0
0
1
0
2
1
0
0
0
0
0
2
0
0
0
1
1
2
0
0
0
2
0
1
2
1
2
4
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
1
0
2
1
0
1
0
1
0
0
0
0
2
0
0
2
1
0
0
2
0
1
0
2
0
0
0
0
2
0
1
0
0
0
0
2
0
2
0
0
1
2
0
0
1
0
0
1
1
1
0
2
0
0
0
2
0
0
2
0
0
0
0
2
1
1
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
4
0
1
2
1
0
0
1
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
1
1
0
2
0
2
0
0
1
0
1
1
1
0
0
1
0
2
0
0
2
2
0
0
0
0
1
0
0
0
1
1
0
2
0
0
0
1
0
0
0
2
1
1
0
0
0
0
0
0
1
0
0
1
0
1
0
1
2
1
4
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
2
1
0
1
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
2
2
0
0
0
1
2
0
0
2
2
0
0
0
2
1
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
1
2
0
2
2
0
0
0
1
0
0
0
2
4
0
1
1
0
0
1
0
0
1
0
2
0
1
0
0
0
2
0
1
0
1
0
0
2
1
0
0
0
0
1
16
0
1
0
2
2
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
1
2
0
0
2
1
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
2
1
1
1
0
1
0
1
0
2
1
0
0
0
0
2
0
0
0
0
8
0
1
0
0
2
1
1
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
1
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
1
2
1
0
0
0
2
2
1
3
0
0
1
1
1
0
0
1
0
0
0
0
1
0
2
2
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
1
0
0
2
2
3
0
0
4
0
0
0
2
2
0
0
0
0
1
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
4
1
0
0
0
2
0
1
1
0
0
2
2
0
0
1
0
0
0
0
0
2
0
0
0
1
0
1
2
0
2
1
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
2
2
0
1
0
0
0
1
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
3
0
0
0
0
2
0
0
0
0
0
0
0
1
1
1
2
0
0
0
1
3
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
1
1
4
0
0
0
1
0
1
0
2
1
2
2
1
0
2
1
2
0
0
1
3
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
1
2
0
1
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
3
1
0
0
0
0
1
1
0
2
0
1
2
0
0
1
1
0
0
0
1
1
2
0
1
1
0
2
1
0
1
1
0
0
0
2
0
0
0
1
0
0
1
0
2
4
0
0
0
0
0
2
0
1
0
0
1
1
2
2
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
1
1
0
0
0
0
0
0
2
3
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
1
1
2
0
1
1
0
1
0
0
3
0
2
0
1
2
0
0
0
0
0
0
1
0
1
0
0
3
1
0
0
0
0
0
0
1
2
1
0
0
1
2
0
0
1
0
0
1
0
0
0
0
0
2
0
2
1
1
1
1
1
2
2
2
0
2
0
0
2
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
2
0
1
0
0
2
0
1
0
1
1
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
2
2
2
0
0
2
0
0
0
0
0
0
1
1
1
0
1
2
0
2
1
2
0
2
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
2
0
1
0
0
0
0
2
1
0
0
0
0
4
2
0
3
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
2
1
0
2
0
0
0
1
0
0
0
0
1
0
1
0
0
0
2
0
0
0
2
2
4
0
2
0
0
1
0
0
0
0
4
0
1
0
0
0
0
0
2
0
2
0
0
0
2
0
2
0
0
0
0
0
2
0
0
1
2
2
0
0
1
0
0
2
0
0
2
0
1
2
1
0
0
0
0
1
0
0
1
0
2
3
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
3
1
0
0
0
1
0
0
0
0
0
0
1
0
1
3
0
2
1
0
0
0
1
0
2
0
0
2
0
1
0
0
1
0
1
0
1
0
0
0
1
1
0
0
5
3
0
0
0
1
2
0
0
0
2
0
0
2
0
2
2
2
0
0
0
2
1
0
3
0
0
1
0
0
0
0
2
1
0
2
1
2
0
2
0
0
0
3
0
0
1
0
0
0
0
0
0
1
2
1
0
0
2
2
1
0
0
0
1
0
0
3
2
0
0
0
1
2
0
2
0
0
1
0
3
0
0
1
0
2
0
2
1
0
0
2
2
0
2
1
0
2
1
0
0
0
0
1
1
0
2
1
0
0
0
0
2
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
2
1
1
0
0
1
0
1
0
4
0
12
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
2
0
2
0
0
0
2
0
0
0
0
0
1
0
3
1
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
1
0
2
1
0
0
0
0
0
0
0
2
0
1
2
1
0
0
1
0
0
0
0
1
1
1
1
0
1
0
0
0
1
2
2
0
0
0
0
0
0
2
0
0
2
1
0
0
0
2
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
2
2
2
0
0
0
0
4
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
1
0
1
0
0
2
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
2
0
0
0
0
0
0
1
2
0
2
1
0
0
0
0
0
0
1
2
0
0
4
2
0
2
0
2
0
0
0
2
2
0
1
0
0
0
2
0
1
1
0
1
0
3
0
0
0
0
4
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
1
0
0
1
1
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
1
1
0
1
0
1
0
0
0
1
1
2
1
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
2
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
1
1
1
2
2
0
0
2
0
0
1
1
0
0
1
0
0
0
0
1
0
1
1
0
0
1
0
1
0
4
1
0
1
0
0
0
0
0
1
2
1
0
2
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
1
0
0
1
0
0
2
0
0
0
0
1
1
0
0
2
2
0
0
1
0
1
0
0
1
0
0
3
0
0
1
1
0
0
0
0
0
2
2
0
1
1
1
0
0
2
0
2
0
1
2
0
0
2
0
0
1
1
0
2
1
0
2
2
0
0
1
2
0
2
0
0
1
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
1
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
1
0
2
2
2
0
1
0
2
0
0
1
2
0
0
2
0
5
0
0
0
0
0
0
2
0
0
0
2
1
1
0
0
1
0
1
2
0
2
0
0
0
2
0
1
0
2
0
0
1
0
2
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
2
3
0
0
0
0
2
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
1
0
1
0
0
1
0
0
2
0
2
2
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
1
0
1
0
2
2
0
0
1
1
2
0
0
2
1
0
2
0
0
0
2
0
1
0
0
2
0
2
2
0
2
1
1
1
0
1
3
0
0
2
1
0
1
0
0
0
2
0
0
0
0
2
0
0
2
1
1
2
0
2
2
0
1
0
0
2
1
0
0
2
0
1
0
0
0
2
1
2
2
1
0
0
0
0
0
2
0
0
0
0
1
1
0
0
2
0
2
0
0
1
0
0
0
0
0
1
0
0
0
2
0
2
2
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
1
2
2
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
2
0
0
1
1
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
3
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
3
0
1
0
2
2
1
2
0
0
0
2
1
2
0
0
0
2
0
1
1
1
1
2
0
1
0
2
0
2
1
0
0
0
2
1
0
2
0
0
1
0
0
0
0
3
0
2
0
1
2
1
1
0
0
0
0
0
0
1
2
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
2
1
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
2
0
2
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
1
2
1
1
0
0
0
0
1
0
0
4
0
0
0
0
0
3
2
0
2
0
2
0
0
1
0
0
4
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
2
4
0
1
0
0
0
1
1
0
0
0
2
0
1
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
1
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
2
0
0
0
2
2
1
0
0
0
3
0
0
0
0
1
0
0
0
1
0
1
0
2
0
0
0
2
0
2
0
0
0
1
0
0
0
1
0
1
2
0
1
0
0
2
0
0
0
0
1
0
0
2
0
2
1
2
0
1
0
0
0
0
0
0
0
0
0
0
1
2
1
3
2
1
0
0
1
0
2
1
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
4
0
1
0
0
0
2
1
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
3
2
0
0
2
0
0
1
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
1
2
0
0
0
0
1
0
1
0
2
0
2
0
2
2
0
0
1
2
0
0
2
2
1
1
0
0
2
0
0
0
0
1
1
0
0
0
0
4
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
3
0
0
2
0
0
0
0
2
0
0
0
1
0
1
1
0
0
0
0
1
0
0
2
1
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
3
0
1
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
1
1
2
0
0
1
2
0
0
1
1
0
0
1
0
1
0
0
2
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
1
1
0
1
0
3
1
1
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
1
0
0
1
2
0
0
2
2
2
0
1
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
2
0
0
2
3
0
0
0
2
2
1
0
1
0
2
0
1
0
1
2
0
0
2
0
0
2
0
0
0
0
0
1
2
0
1
1
0
0
0
0
1
0
0
2
1
1
1
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
1
0
0
2
2
0
0
0
0
1
1
0
0
0
0
2
0
2
3
2
1
1
0
0
0
0
1
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
1
0
0
0
0
2
1
0
0
1
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
2
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
1
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
2
0
1
2
0
0
1
2
1
1
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
2
0
0
1
0
1
0
0
1
0
0
1
0
1
1
0
1
0
0
0
2
3
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
1
0
0
1
1
2
1
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
1
0
0
0
1
1
0
0
0
1
1
0
1
0
0
0
0
0
5
0
0
0
1
0
0
0
0
1
2
1
2
0
1
0
0
0
0
1
2
0
0
1
1
0
2
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
1
2
0
2
0
1
0
0
2
0
0
0
1
0
2
0
0
1
0
0
0
0
1
0
1
3
0
2
0
0
0
0
0
0
0
3
0
0
0
1
0
2
0
2
3
0
0
0
0
2
0
0
0
1
1
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
1
2
0
0
2
1
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
1
1
0
2
0
0
1
0
1
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
2
2
0
1
1
3
0
2
0
0
2
0
1
0
0
2
0
0
1
2
0
0
0
3
2
0
0
0
2
0
1
0
0
1
0
0
0
1
0
0
2
0
0
1
0
0
0
2
0
2
0
0
0
1
0
0
0
3
0
2
0
2
0
0
0
2
0
2
0
1
0
2
1
0
1
0
0
1
0
0
0
0
0
0
0
3
2
0
0
0
1
1
2
0
2
1
0
1
0
0
0
1
0
2
3
0
1
0
1
2
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
1
0
1
0
0
0
0
0
2
0
0
0
1
3
2
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
2
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
4
0
0
1
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
4
0
2
1
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
1
0
0
0
0
2
0
1
0
0
0
2
0
0
1
1
2
0
1
0
0
1
0
0
0
0
0
2
2
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
2
2
2
2
0
0
2
0
0
0
0
0
0
0
0
10
0
0
0
0
1
1
1
0
2
0
0
1
0
0
0
2
1
1
0
0
0
2
1
0
0
1
1
0
0
0
1
0
2
2
0
1
1
0
1
1
0
2
2
0
2
2
0
0
1
0
0
0
2
0
3
0
0
2
0
2
2
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
2
0
0
0
1
1
1
1
1
2
1
1
0
0
0
0
2
2
0
0
2
0
7
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
2
2
0
1
0
1
0
2
0
1
0
0
0
0
0
0
0
1
3
2
2
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
2
0
1
0
0
0
0
2
0
2
1
4
0
0
1
0
2
2
0
0
0
0
0
1
0
1
2
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
3
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
2
1
1
2
0
2
0
0
0
1
0
2
3
0
0
0
2
0
0
2
0
0
3
0
0
0
2
0
1
0
0
2
2
1
1
0
1
0
0
0
0
1
0
0
1
2
1
0
1
2
1
0
0
0
1
3
2
0
1
2
2
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
2
0
1
1
0
0
2
2
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
1
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
2
1
0
0
3
0
0
2
0
0
1
1
2
0
0
1
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
3
0
2
0
0
0
2
2
0
0
0
0
2
0
4
0
0
0
0
0
0
0
2
1
2
0
1
1
0
2
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
7
0
0
0
0
2
0
1
0
2
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
2
1
2
1
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
2
2
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
2
1
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
3
1
0
2
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
1
2
0
2
0
2
0
1
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
1
0
0
0
2
0
2
0
0
2
0
2
2
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
1
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
1
0
2
0
0
0
0
0
1
0
2
0
0
0
0
5
0
0
0
1
1
1
0
0
2
1
0
1
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
3
0
0
0
2
1
0
0
1
1
0
0
0
0
0
0
1
0
0
1
7
0
0
0
0
0
0
0
1
2
0
0
3
1
2
3
0
1
1
0
1
0
0
0
0
2
2
0
2
0
0
0
0
1
1
0
0
1
0
2
0
2
2
0
3
0
1
2
0
0
2
0
0
0
1
2
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
2
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
1
2
0
0
2
0
2
0
2
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
1
1
0
0
2
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
3
1
2
0
0
0
2
2
2
1
0
2
0
0
1
0
0
0
0
0
0
2
2
1
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
2
0
2
0
1
0
0
1
0
0
1
0
0
1
0
1
1
0
1
0
2
1
0
2
2
1
0
0
2
0
0
0
0
0
0
0
0
1
0
2
5
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
1
2
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
2
2
0
0
2
0
0
0
0
0
1
0
2
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
2
0
2
0
1
1
0
2
0
0
0
0
0
1
0
0
1
2
2
0
2
2
2
0
1
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
1
3
0
2
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
2
1
0
2
0
0
0
0
2
0
1
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
1
0
3
0
1
1
0
0
0
1
0
0
1
0
0
0
1
1
2
0
0
0
0
0
1
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
2
0
2
0
0
2
2
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
1
0
5
0
0
0
0
0
3
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
2
0
0
2
1
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
1
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
1
1
1
0
1
0
0
1
0
0
0
1
0
0
3
1
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
1
0
0
0
0
0
1
0
2
0
0
0
1
0
1
0
0
1
2
1
0
0
0
0
0
0
1
2
0
2
1
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
3
1
1
0
0
0
1
0
2
2
2
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
2
0
1
1
1
0
0
0
0
0
2
1
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
1
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
2
0
0
0
1
0
2
0
0
0
0
0
0
2
0
2
1
1
0
1
0
0
0
0
0
0
2
1
3
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
2
0
2
0
3
0
1
0
0
2
1
1
0
1
0
0
0
2
2
2
0
1
0
0
0
0
0
0
1
1
0
2
0
1
1
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
1
2
0
1
1
0
0
0
0
0
2
3
0
0
0
1
0
0
4
0
1
2
0
0
0
1
0
2
0
0
4
0
2
2
0
1
0
0
0
1
0
0
0
0
0
1
2
0
0
0
2
0
0
2
3
2
2
1
0
0
0
0
0
1
0
0
2
0
2
3
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
2
0
0
0
0
1
0
0
0
0
0
3
1
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
1
0
1
0
2
0
2
0
0
0
0
0
2
0
0
0
3
0
0
2
2
2
2
0
0
3
0
1
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
2
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
2
2
0
2
0
0
1
0
0
1
2
0
0
0
2
0
1
0
0
0
1
2
0
2
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
2
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
3
1
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
2
0
2
0
1
2
0
1
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
5
2
1
0
0
0
0
0
0
1
0
0
1
2
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
1
1
0
2
0
0
0
0
0
2
0
0
3
2
0
1
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
2
0
1
1
0
0
2
1
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
2
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
2
2
1
1
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
2
2
0
0
1
0
1
0
0
0
0
0
0
1
0
2
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
2
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
2
0
0
0
0
1
0
2
0
2
0
1
2
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
2
1
0
0
5
0
0
0
2
0
0
0
2
3
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
2
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
1
2
2
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
2
2
0
0
1
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
2
0
2
2
0
1
0
0
1
1
2
0
0
2
0
0
2
0
0
0
0
0
0
0
1
2
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
1
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
1
3
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
1
0
0
1
0
2
0
0
0
2
0
0
0
0
1
1
0
1
2
0
0
0
0
0
0
0
0
2
1
0
0
2
0
1
0
0
0
2
1
0
0
0
1
2
0
1
0
2
0
1
0
0
2
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
7
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
2
0
0
0
1
2
1
0
0
0
0
0
2
2
0
2
0
2
1
0
0
1
0
0
2
1
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
1
1
2
1
1
1
0
1
0
2
1
0
2
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
2
0
0
2
1
0
0
5
0
0
0
0
1
0
0
0
0
1
0
2
2
0
0
0
0
0
2
0
2
0
0
2
1
1
1
3
0
3
1
0
2
0
0
0
0
0
1
1
2
0
0
1
1
1
0
2
0
0
1
0
2
0
0
2
3
0
0
1
2
0
0
0
0
2
1
0
2
0
0
1
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
3
2
0
0
0
0
1
0
0
0
1
0
0
2
2
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
3
0
1
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
1
1
0
0
0
1
2
0
2
0
2
0
0
0
2
0
0
2
1
2
0
0
0
3
3
1
2
0
0
1
0
1
0
0
1
0
0
0
0
0
1
2
0
2
1
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
2
0
1
1
1
0
1
0
0
2
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
1
0
2
0
0
0
0
0
0
1
2
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
3
0
2
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
1
0
1
0
0
0
1
0
1
1
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
2
1
0
0
2
0
0
0
0
0
1
0
1
1
1
1
0
0
0
2
2
0
0
1
0
0
1
0
1
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
2
2
1
0
0
0
0
3
0
1
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
5
0
2
0
0
1
2
0
0
1
2
0
0
0
1
4
0
0
0
0
0
0
0
2
1
0
3
0
2
2
1
1
0
2
0
1
0
0
0
2
0
2
0
0
1
2
0
1
0
0
2
2
3
0
1
0
0
0
0
0
0
0
1
0
0
0
3
0
0
2
0
2
0
1
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
2
0
2
0
0
3
0
1
2
2
0
0
0
1
1
0
1
0
0
0
2
0
1
0
2
0
1
0
1
0
0
1
0
0
0
2
2
0
1
0
0
0
0
0
0
1
1
2
0
0
1
0
0
1
0
0
0
3
1
0
0
0
0
2
0
0
0
2
0
0
1
0
0
2
0
0
1
1
0
2
0
1
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
6
0
0
0
0
1
0
0
0
1
0
0
1
2
0
0
0
1
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
1
0
0
0
6
3
2
1
0
0
0
2
0
2
0
1
0
2
1
0
0
0
0
0
0
2
0
1
1
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
1
2
2
1
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
1
2
0
0
1
0
1
1
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
3
0
1
0
0
0
1
1
0
2
0
1
0
0
3
0
0
0
0
0
0
0
0
0
2
3
0
2
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
4
0
0
0
2
0
1
0
0
0
0
0
1
2
0
2
0
0
1
0
0
1
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
2
0
2
2
0
0
0
1
0
0
3
0
0
0
0
0
1
0
3
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
3
0
0
3
3
0
0
1
0
1
0
1
2
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
2
2
1
0
2
2
0
0
0
0
0
1
0
0
2
2
0
0
1
0
2
2
0
4
0
0
2
3
0
0
0
0
1
0
0
2
0
2
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
2
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
2
1
0
0
2
0
0
0
2
1
0
2
0
0
0
0
0
2
0
0
0
1
0
2
2
3
0
1
1
0
0
0
0
2
0
0
0
1
2
3
0
2
0
2
0
0
0
0
0
0
0
1
0
2
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
1
2
1
2
0
2
5
1
1
0
0
0
2
0
2
0
0
0
2
0
1
1
0
0
0
0
2
0
0
2
0
0
2
1
4
1
0
1
0
0
2
2
0
1
0
0
0
2
2
2
2
0
1
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
1
0
2
0
1
0
0
1
2
0
2
0
0
1
0
0
3
0
2
0
0
1
0
0
0
0
1
1
0
2
2
2
0
2
1
0
0
0
2
2
2
0
0
3
0
1
2
0
0
0
2
1
0
0
2
2
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
3
2
1
0
2
0
0
0
1
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
6
2
0
0
1
0
0
0
0
1
2
0
2
0
0
0
0
2
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
4
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
2
0
2
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
4
1
1
0
0
0
0
2
0
1
3
0
3
1
2
0
1
3
0
0
0
0
0
0
2
0
0
0
1
0
2
0
2
1
0
0
1
3
1
0
0
0
2
0
7
0
0
0
2
0
0
0
1
3
1
0
0
2
0
0
0
0
0
0
1
0
0
3
0
0
0
0
2
0
1
0
2
0
2
0
2
0
0
1
0
0
1
0
2
0
2
0
0
2
1
2
0
0
0
0
0
0
0
3
2
0
2
0
2
2
0
2
2
0
0
0
1
0
0
0
0
0
2
0
2
0
2
2
0
2
2
0
0
2
0
0
2
0
1
0
1
2
0
2
0
0
0
0
0
2
2
3
2
1
2
0
0
0
1
1
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
1
0
0
0
0
2
1
0
0
0
2
0
2
0
0
0
2
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
10
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
2
0
1
1
0
2
1
0
0
0
0
1
0
1
0
0
0
0
1
2
0
0
2
2
0
1
0
0
1
1
0
2
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
2
2
1
0
0
0
0
2
0
0
0
1
1
0
4
0
1
0
2
0
0
1
4
1
0
0
0
0
0
1
0
2
0
1
0
0
0
4
0
1
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
1
0
3
1
0
0
2
0
0
0
3
0
0
2
0
1
3
0
1
2
0
2
0
2
0
0
0
0
2
0
1
0
0
0
2
0
3
0
0
0
0
2
1
0
2
0
0
1
0
1
2
0
0
0
1
2
0
0
0
1
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
1
1
0
0
1
0
0
1
2
0
0
1
2
2
0
0
0
1
0
1
2
0
0
2
0
0
0
0
2
1
0
0
0
2
1
2
0
2
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
1
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
2
0
2
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
2
0
2
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
2
0
0
0
1
2
1
1
2
1
0
0
0
1
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
1
0
3
0
2
0
0
0
0
1
2
2
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
4
0
1
3
1
3
0
1
2
0
1
0
2
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
3
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
2
0
2
1
0
0
1
2
0
0
0
0
0
2
0
2
4
0
1
0
0
1
2
0
2
0
0
2
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
1
0
2
2
0
0
2
0
0
0
0
0
1
0
2
1
0
0
1
0
0
0
2
1
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
1
2
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
1
1
0
1
0
0
1
2
1
0
0
0
0
0
2
0
1
0
1
1
2
1
0
0
0
1
0
2
0
0
0
3
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
2
2
6
2
1
0
3
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
1
0
2
0
0
0
0
1
0
0
6
2
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
1
0
3
2
0
1
3
0
3
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
2
2
0
2
0
0
0
2
2
1
1
0
2
5
0
2
0
1
1
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
1
0
2
0
0
1
1
0
2
1
0
0
0
1
0
2
1
0
1
0
1
0
0
0
0
1
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
1
0
0
1
0
0
1
2
0
0
1
1
0
1
0
0
0
0
0
0
1
2
0
2
2
2
0
0
2
0
0
2
2
0
1
2
2
0
0
0
3
0
0
2
1
2
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
2
0
2
0
0
2
0
2
1
1
1
0
0
0
0
0
0
0
2
1
2
0
2
0
0
1
2
1
0
0
1
1
0
1
1
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
1
2
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
1
2
0
4
0
2
0
0
2
2
0
1
1
1
0
0
0
0
0
1
1
2
1
0
0
1
0
1
0
2
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
3
0
1
0
0
0
2
0
0
2
1
0
2
1
0
2
0
0
1
2
2
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
1
0
0
2
1
0
0
0
0
2
0
0
2
2
0
0
0
0
0
2
2
0
0
0
2
0
0
1
2
2
0
0
0
0
0
0
0
0
1
1
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
1
0
1
0
0
0
2
0
1
2
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
1
2
0
1
0
0
1
1
0
1
0
0
1
1
1
2
0
0
4
1
2
0
0
2
0
0
0
0
2
2
0
1
3
0
0
0
2
2
4
2
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
2
2
0
0
1
2
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
2
0
2
0
2
3
2
0
0
0
1
2
0
2
0
0
2
0
1
0
0
0
2
1
2
1
0
0
0
0
1
1
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
1
1
0
2
0
2
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
2
0
1
2
1
1
0
0
0
0
1
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
2
0
2
0
0
0
0
2
1
3
0
0
1
2
0
0
1
0
0
0
0
1
0
0
0
2
2
1
0
0
0
0
2
0
0
1
0
0
0
1
2
0
0
2
0
0
1
0
0
0
1
1
0
0
0
0
2
2
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
2
0
2
1
0
0
1
0
0
0
2
1
0
1
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
1
0
1
0
0
0
1
0
1
0
1
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
3
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
2
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
2
1
1
0
2
0
1
0
0
0
0
0
3
0
0
0
0
0
0
2
2
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
1
0
0
1
1
0
1
0
1
0
1
0
1
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
1
1
0
1
0
1
1
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
2
1
0
1
0
0
0
0
2
0
0
2
0
0
0
2
1
0
0
2
0
1
0
1
2
0
2
0
1
0
2
0
0
0
1
1
1
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
1
0
0
2
1
0
2
1
2
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
2
1
0
0
0
0
2
0
2
0
0
0
1
0
0
2
0
2
1
0
0
0
0
2
0
0
0
0
3
0
0
0
0
2
0
0
0
0
3
17
0
0
2
0
0
0
0
2
0
0
0
1
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
2
0
2
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
1
1
0
1
0
2
3
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
6
0
2
0
0
2
0
0
1
0
0
0
1
2
2
2
0
2
0
0
0
1
3
1
0
2
0
0
0
0
0
0
2
0
1
0
0
2
2
2
0
0
0
2
2
0
2
0
0
0
1
1
0
1
2
3
0
0
0
0
0
0
0
0
0
2
0
2
1
0
3
1
1
2
1
0
0
0
2
2
4
0
1
0
0
2
0
2
1
1
0
2
0
0
0
1
0
0
0
0
1
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
1
2
2
0
0
0
1
0
1
0
0
1
0
0
0
0
0
2
2
1
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
7
0
0
1
1
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
1
3
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
1
0
0
2
2
2
0
1
1
0
2
1
0
1
1
0
1
0
0
0
1
2
0
1
2
2
0
0
0
1
1
1
3
0
2
0
1
0
0
3
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
1
0
1
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
1
1
0
0
0
2
0
1
2
1
0
2
0
2
0
0
2
0
0
0
1
0
1
0
7
2
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
1
0
0
2
0
0
0
2
0
1
1
0
0
1
0
3
0
0
0
0
0
0
0
0
1
1
0
0
2
2
0
1
0
1
0
0
0
0
0
0
0
0
0
1
7
0
0
1
2
0
2
0
1
1
0
0
0
1
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
1
0
0
0
1
0
0
1
0
2
1
0
0
1
0
0
0
1
1
0
0
0
0
0
2
1
0
0
1
1
0
2
0
0
0
0
1
0
2
1
1
2
0
0
1
1
0
0
0
0
1
0
0
0
0
2
1
0
2
0
1
0
1
0
2
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
2
0
0
3
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
4
1
0
0
2
0
0
0
2
0
0
0
2
1
1
0
0
0
0
0
0
2
2
1
2
0
2
0
1
0
0
0
1
2
3
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
2
0
0
2
0
2
2
0
0
2
0
0
2
0
1
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
2
1
0
0
0
1
0
0
2
1
2
1
0
2
0
0
0
1
0
0
0
2
1
0
0
0
1
0
0
1
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
3
0
0
0
0
1
0
0
0
0
0
2
2
0
0
1
0
2
2
1
2
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
3
1
0
1
0
2
0
0
0
2
1
1
1
0
1
1
0
0
0
1
2
0
2
0
0
0
1
0
0
0
0
0
0
2
0
1
0
2
0
2
0
0
0
2
0
0
2
0
2
0
0
0
2
0
0
2
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
2
0
0
2
0
0
0
0
1
0
0
0
4
0
2
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
2
1
0
0
1
2
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
4
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
2
1
0
1
0
0
0
1
0
0
1
0
0
0
2
0
0
0
2
1
0
2
1
0
0
1
0
0
2
1
0
0
0
3
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
1
4
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
4
0
2
0
0
0
2
0
1
0
5
0
0
0
0
2
0
0
2
2
1
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
1
0
1
1
1
1
0
1
1
2
0
0
0
0
0
2
0
0
0
2
2
2
0
1
0
0
2
0
1
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
1
0
1
1
0
0
0
0
2
1
1
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
1
0
0
0
0
0
0
2
2
0
2
0
1
2
1
2
0
0
0
0
0
2
3
0
0
0
1
0
0
2
2
1
0
1
0
1
2
1
0
2
0
0
0
1
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
1
0
0
2
4
2
1
0
2
2
0
0
0
0
0
1
0
0
0
2
0
1
0
1
0
0
2
2
0
0
0
2
1
1
0
0
1
3
1
0
0
0
0
0
2
0
4
2
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
2
0
0
2
0
0
1
0
0
0
0
0
1
0
1
0
3
0
0
2
2
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
1
0
1
3
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
3
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
8
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
6
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
1
0
0
2
0
1
0
0
0
0
1
0
0
2
1
0
2
0
1
2
0
0
0
1
0
1
3
0
0
0
0
1
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
2
0
2
2
1
0
0
0
4
2
0
0
3
1
0
1
1
6
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
2
2
0
2
2
2
5
1
2
0
0
2
0
0
0
0
1
0
0
2
0
0
0
2
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
3
2
0
2
0
1
2
2
0
0
1
0
2
0
0
0
0
0
3
0
1
0
2
3
0
0
0
0
2
1
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
3
2
0
0
1
11
1
2
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
3
1
0
1
0
2
0
1
1
1
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
3
0
0
0
0
1
0
2
1
4
1
2
1
1
0
0
0
0
0
2
1
0
0
0
0
0
3
0
6
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
2
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
1
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
1
0
5
0
2
0
0
2
0
0
0
0
0
2
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
1
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
1
0
1
0
0
2
0
1
0
0
1
1
0
0
1
0
0
2
1
0
2
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
3
0
3
0
0
0
1
0
0
0
1
0
0
0
0
1
1
1
1
1
0
0
1
0
1
0
2
0
0
2
0
1
0
0
0
0
2
2
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
2
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
2
1
0
7
0
0
2
0
2
0
1
1
0
0
1
1
0
0
0
0
0
1
0
5
0
0
0
0
0
0
1
0
1
0
0
1
0
0
2
0
1
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
2
1
7
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
2
2
0
2
0
0
1
0
1
2
0
1
0
0
0
0
0
1
0
0
3
2
1
1
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
2
2
2
0
0
0
1
0
0
1
2
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
1
2
3
0
0
0
1
1
1
0
1
0
2
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
1
0
0
1
0
0
0
0
0
2
0
2
0
1
3
2
1
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
1
0
0
0
1
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
2
1
0
0
0
2
2
0
8
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
2
0
0
0
2
1
0
1
0
0
0
0
0
0
1
0
1
0
2
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
2
1
0
0
1
0
2
0
1
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
1
2
0
0
0
0
0
2
0
1
0
1
0
1
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
1
2
0
1
0
2
2
0
2
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
1
0
1
1
0
0
0
0
1
1
1
0
0
0
9
2
0
0
0
0
2
2
0
1
0
0
0
1
0
3
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
1
0
0
1
1
2
0
0
0
2
0
0
2
0
2
1
0
2
2
0
0
0
0
1
1
0
2
0
2
0
0
0
0
0
0
1
0
1
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
4
3
0
0
0
1
2
0
0
0
0
2
1
1
0
0
2
0
0
1
2
1
0
0
0
1
0
2
1
0
0
0
0
2
0
2
0
0
2
0
0
0
0
3
0
0
0
2
1
0
0
2
0
0
2
3
0
0
0
0
2
0
0
1
2
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
1
0
1
2
2
1
1
0
0
0
2
2
0
0
2
2
0
0
0
0
1
0
0
0
0
1
0
3
1
3
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
2
0
1
0
0
0
2
0
2
0
0
1
0
1
2
0
0
0
1
1
2
0
1
2
2
1
0
0
2
2
0
2
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
1
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
5
1
0
0
1
0
0
2
0
2
0
2
2
0
0
2
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
2
1
1
0
0
1
2
0
0
0
0
2
0
0
3
0
0
0
0
0
0
3
2
2
0
2
2
1
0
0
0
1
1
0
2
0
0
0
1
1
1
0
0
1
0
0
2
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
2
0
1
0
0
2
2
0
2
0
0
0
0
0
0
0
0
2
1
2
0
0
1
0
0
0
0
0
0
13
0
0
6
2
2
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
1
0
0
0
0
2
0
0
1
0
2
1
0
2
0
0
0
0
1
1
0
0
0
2
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
2
1
0
0
2
0
0
1
2
0
0
0
0
2
0
0
0
2
1
2
0
1
0
0
3
2
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
1
0
5
0
3
0
0
2
2
0
0
0
0
0
0
3
0
1
0
0
2
3
1
2
0
1
0
0
0
2
0
0
2
0
1
1
2
0
0
1
0
0
0
0
0
1
0
5
0
0
0
0
0
0
2
2
1
0
0
2
1
1
2
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
2
0
2
0
2
0
1
0
1
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
1
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
1
1
0
0
2
0
1
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
3
0
0
0
1
1
1
0
0
0
0
1
0
1
0
0
2
0
0
0
1
0
0
2
0
0
0
2
1
1
1
0
0
4
1
0
0
1
0
0
0
0
0
1
0
0
2
0
2
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
2
0
0
0
0
3
0
0
1
0
0
1
0
0
1
0
0
1
1
2
0
2
0
0
2
2
0
1
0
0
1
0
3
1
2
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
1
2
0
2
0
1
0
0
0
3
0
2
1
0
1
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
2
0
1
0
0
0
2
1
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
2
0
1
0
1
0
0
0
2
0
1
1
1
4
2
0
4
2
0
1
0
1
0
0
0
0
0
0
0
1
1
2
0
0
0
1
0
0
0
0
1
2
0
1
2
0
0
1
0
0
0
2
0
1
2
0
0
3
2
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
1
0
1
0
0
0
1
0
4
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
3
0
2
0
2
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
3
0
0
2
0
0
1
0
0
0
0
0
3
0
0
3
2
0
1
2
2
0
0
0
0
0
2
0
0
0
2
1
0
11
1
1
1
0
1
1
0
0
2
0
0
3
1
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
1
1
0
0
2
1
0
2
1
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
1
0
1
0
0
2
1
2
2
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
2
0
7
2
0
0
2
0
1
1
0
0
0
0
0
0
0
1
0
2
0
1
0
1
0
3
0
0
1
2
1
1
0
2
0
0
2
0
0
0
4
0
2
2
0
1
0
0
1
0
0
0
0
0
0
2
0
2
0
0
2
2
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
3
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
2
2
2
0
0
0
0
0
2
1
3
1
2
0
1
1
2
0
1
0
2
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
2
0
0
1
4
1
0
1
1
2
5
1
0
1
0
0
0
2
0
0
0
0
5
0
0
1
2
2
1
2
2
3
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
1
0
1
2
0
0
0
3
2
0
0
0
0
0
0
0
0
1
0
4
1
0
1
2
0
0
1
1
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
4
6
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
2
1
1
0
0
1
1
0
2
1
0
2
2
2
0
1
1
1
0
0
5
0
0
0
0
0
2
0
0
0
0
0
2
1
1
2
0
0
0
0
0
0
2
2
2
1
2
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
2
2
0
0
2
2
3
0
0
0
0
0
0
2
1
0
0
0
1
1
0
2
0
1
0
0
0
0
0
3
0
0
0
0
1
0
1
1
2
0
0
1
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
3
0
0
0
2
3
0
0
0
2
0
0
0
0
0
2
0
1
0
1
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
3
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
2
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
2
0
1
0
0
3
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
2
2
1
0
0
2
2
0
0
3
2
2
0
3
0
0
2
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
3
0
0
2
2
0
0
0
0
0
3
0
0
2
0
2
2
0
0
2
0
0
1
0
2
0
0
2
0
0
2
0
0
1
0
2
0
0
0
2
0
2
0
3
1
0
1
0
2
1
0
0
0
2
1
3
0
0
0
1
0
1
0
0
2
2
0
0
0
1
0
2
0
0
2
2
0
0
2
1
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
2
1
0
1
0
2
0
0
0
0
2
0
2
1
0
0
3
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
1
0
1
2
2
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
2
2
1
0
2
0
0
0
1
0
2
0
1
0
2
2
0
1
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
1
1
0
0
2
2
0
0
0
0
0
0
1
0
2
2
4
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
1
1
0
0
0
0
2
0
0
0
2
0
0
0
2
0
2
0
1
0
0
0
1
0
0
0
0
0
0
2
0
1
1
0
0
2
0
0
0
0
2
0
0
0
2
1
0
1
2
0
1
2
0
0
2
0
0
0
0
0
0
0
0
1
0
2
1
0
0
1
1
0
2
0
0
0
0
2
0
0
1
0
0
0
2
0
2
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
3
0
0
0
0
0
1
0
2
3
2
1
0
0
2
2
0
0
1
1
2
2
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
2
2
0
0
1
0
1
0
0
1
0
2
1
0
0
0
0
0
2
2
0
2
0
0
1
0
0
0
0
0
0
2
0
2
0
0
2
0
2
0
1
2
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
1
0
3
0
0
0
0
0
0
2
0
1
2
0
3
0
1
1
0
0
1
2
0
0
0
0
1
3
0
1
1
3
2
0
0
0
1
1
0
1
2
2
0
2
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
3
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
5
0
0
0
2
0
1
2
1
0
0
2
0
3
0
1
1
1
2
0
2
0
3
0
0
2
0
0
0
0
0
0
0
1
1
2
0
0
0
4
0
0
2
0
0
2
0
2
1
2
2
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
2
0
0
0
1
3
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
1
1
0
0
0
0
0
0
2
0
0
0
0
2
3
0
0
0
1
0
1
0
0
1
0
1
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
2
0
3
0
3
0
0
0
1
0
0
0
1
2
0
0
2
0
0
0
2
1
0
0
0
2
0
1
2
0
0
0
0
2
0
0
0
0
2
1
0
2
0
1
0
2
0
0
1
0
1
1
1
1
2
1
0
1
1
0
0
0
0
3
0
2
0
0
0
1
2
1
1
2
1
0
0
0
2
0
0
1
0
0
3
0
0
0
0
0
2
2
0
3
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
2
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
1
0
2
1
2
1
0
0
0
0
2
0
2
0
1
2
0
3
1
0
1
1
0
0
1
0
0
1
2
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
2
0
0
0
2
0
0
1
1
0
1
0
1
2
0
2
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
2
0
0
1
0
1
0
0
1
0
0
2
2
0
0
0
0
0
1
0
0
0
1
2
0
0
2
0
0
1
0
1
0
0
0
2
0
0
0
0
0
1
0
1
0
0
1
0
0
3
1
0
2
1
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
1
0
0
1
0
0
0
2
2
0
0
0
2
0
0
2
1
0
2
1
1
0
1
0
0
1
1
0
0
0
0
0
0
4
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
1
2
2
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
1
0
0
2
0
0
0
0
2
2
1
0
0
0
2
0
0
0
0
1
2
1
1
0
0
0
0
0
2
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
3
0
2
2
0
0
0
1
0
0
0
2
0
1
0
0
1
1
0
0
2
2
0
2
0
1
0
2
2
0
0
0
2
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
2
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
2
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
1
4
0
0
0
2
1
0
2
2
0
0
3
2
0
0
0
1
1
0
0
0
1
0
1
0
0
0
1
0
2
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
3
0
4
0
0
2
0
0
2
1
0
0
0
0
0
0
2
1
1
0
0
0
1
0
2
0
0
2
0
0
2
2
0
2
1
2
0
1
2
0
0
0
3
0
3
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
1
1
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
2
3
0
0
1
0
2
3
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
3
1
2
0
0
1
1
2
0
4
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
3
0
1
1
1
1
0
1
0
1
1
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
1
1
1
0
0
2
2
1
0
0
2
2
0
1
1
3
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
2
2
4
0
0
0
1
1
2
0
0
2
2
0
0
0
1
0
2
3
0
0
0
0
2
0
3
0
1
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
1
0
1
1
1
1
0
1
1
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
2
2
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
2
0
0
0
1
0
0
1
0
0
0
0
2
0
0
2
7
0
2
3
0
0
0
0
0
16
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
1
0
0
1
0
0
2
0
0
1
2
0
2
5
2
0
0
0
0
0
0
1
0
1
0
0
2
1
0
1
0
1
0
1
3
0
0
0
0
0
2
0
3
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
4
0
1
0
4
0
1
0
0
1
1
1
0
0
0
2
1
0
0
1
2
1
0
0
0
0
0
0
0
2
2
2
2
0
1
0
0
1
0
0
0
0
1
0
0
0
0
2
0
1
0
1
0
0
2
1
0
3
0
1
0
0
0
1
0
0
1
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
2
2
2
2
1
0
1
1
1
0
0
1
0
0
1
1
1
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
3
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
1
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
1
2
0
0
2
1
0
2
0
1
0
0
0
1
2
0
1
2
0
1
2
0
0
1
1
1
0
0
1
0
2
0
1
0
0
2
0
1
2
2
0
2
0
0
0
0
1
2
1
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
2
1
0
1
0
0
2
0
0
0
0
1
0
1
1
0
0
0
0
0
0
3
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
3
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
2
0
0
0
0
1
0
0
0
2
0
0
2
0
2
0
0
0
2
0
2
0
0
2
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
2
1
1
0
0
0
1
1
2
1
1
0
0
0
1
0
0
0
1
3
0
0
0
0
0
2
2
0
1
1
1
0
0
1
2
2
0
2
0
0
0
4
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
1
2
0
3
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
1
0
2
3
0
2
2
0
0
2
3
0
1
0
0
0
0
0
1
0
0
1
2
1
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
2
0
0
0
2
2
2
0
0
0
0
1
1
1
1
0
0
0
0
0
1
1
0
0
0
2
2
2
0
0
1
0
0
2
0
0
0
1
0
0
0
2
0
2
0
1
1
0
2
1
0
1
2
1
0
1
0
0
0
2
0
0
0
0
1
0
0
1
2
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
2
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
3
1
0
1
0
0
0
0
0
1
0
1
0
2
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
5
0
1
0
1
1
0
3
0
0
0
0
1
0
2
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
2
0
1
2
1
0
3
3
0
0
1
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
1
1
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
1
2
0
0
0
2
0
2
2
0
1
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
1
0
0
0
0
0
2
1
0
0
1
0
0
0
4
0
0
0
0
2
0
1
2
0
0
0
0
0
2
2
1
0
1
0
1
0
1
0
0
0
0
2
0
2
0
0
0
2
0
0
0
2
2
2
2
0
0
0
2
0
1
0
2
0
1
1
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
3
1
2
0
0
0
1
2
0
0
2
0
1
2
0
1
0
0
5
0
1
0
0
0
0
1
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
2
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
1
1
0
0
2
0
0
2
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
1
4
0
0
1
2
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
1
0
0
0
1
1
0
2
1
0
0
2
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
1
0
1
0
1
1
0
1
0
0
2
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
1
1
0
0
0
1
1
0
0
0
1
0
0
1
0
2
1
0
0
0
0
0
2
0
1
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
2
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
1
0
1
0
2
0
0
1
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
1
0
0
1
0
0
2
0
1
0
4
2
2
1
0
1
0
2
2
0
1
0
1
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
1
0
1
0
3
2
0
1
0
1
1
0
0
0
1
0
0
2
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
1
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
2
1
0
0
1
0
0
0
1
2
0
0
1
1
0
0
1
0
0
0
2
0
1
0
0
0
4
1
0
0
2
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
2
0
0
1
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
1
0
0
1
1
0
2
0
0
0
0
1
1
2
0
4
0
1
0
0
0
0
0
0
1
0
0
0
3
0
0
0
1
0
1
0
2
0
0
0
1
0
1
0
1
2
0
0
0
1
0
1
2
0
2
0
0
0
1
0
0
0
0
0
1
0
3
1
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
1
1
0
0
2
0
0
1
0
0
1
1
0
0
0
0
0
0
1
2
0
2
0
0
2
0
0
0
1
0
0
0
0
0
2
0
1
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
3
0
0
1
0
1
0
0
2
2
0
0
0
2
0
1
0
0
0
0
0
0
2
0
2
1
1
0
1
1
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
3
0
0
0
0
0
0
0
3
1
0
1
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
1
0
2
0
0
1
0
2
2
0
1
2
0
0
2
1
0
0
1
0
0
2
2
0
2
1
0
2
0
1
1
0
2
0
1
0
0
0
0
0
6
1
0
1
1
0
2
1
0
1
0
0
1
0
0
0
0
1
0
0
3
0
0
0
0
0
0
2
0
1
0
1
0
0
0
1
0
2
2
0
1
0
1
1
2
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
1
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
2
4
0
1
0
0
0
0
0
0
1
0
2
1
0
0
0
0
1
2
0
0
0
1
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
3
1
0
2
1
0
0
0
0
1
0
0
2
0
1
3
0
0
0
1
0
2
1
0
0
0
0
0
1
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
1
0
0
1
0
1
0
1
0
1
0
0
0
2
1
2
1
0
0
0
0
1
0
0
0
1
0
1
2
1
0
0
2
0
0
0
0
0
0
0
2
0
2
2
2
1
1
2
1
0
0
0
0
0
0
1
2
0
0
0
1
2
1
0
0
2
1
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
2
1
0
0
0
0
3
1
0
2
1
0
0
2
0
0
2
0
2
1
0
1
0
1
0
0
0
0
0
1
0
0
2
2
2
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
3
1
2
0
0
2
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
2
5
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7
0
0
0
1
0
2
0
0
0
0
1
0
1
0
1
1
0
2
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
2
0
2
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
2
0
1
0
2
1
2
1
0
0
0
1
2
2
0
0
0
2
2
0
1
0
0
0
2
2
1
0
1
1
0
2
2
2
0
0
2
2
3
0
0
0
2
0
2
1
0
1
1
0
3
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
1
2
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
2
0
2
1
1
0
2
1
0
1
2
0
2
1
0
0
0
0
0
0
0
3
0
1
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
1
0
0
0
0
0
1
0
2
0
0
1
0
1
0
0
1
0
0
3
2
0
2
0
2
0
0
0
2
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
2
0
0
0
2
0
0
0
2
1
0
0
0
2
1
2
2
0
0
0
0
0
2
2
0
0
1
0
0
2
1
0
0
0
0
0
1
2
0
0
0
3
0
2
0
0
0
1
0
2
0
0
1
1
2
0
0
0
0
0
0
1
0
1
0
1
0
1
1
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
1
1
0
2
1
2
1
0
0
0
0
0
1
2
0
0
0
2
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
2
0
0
0
0
2
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
6
1
0
1
2
2
2
0
0
2
1
0
0
1
2
2
0
0
0
0
0
1
2
0
0
0
1
1
0
2
0
0
0
0
2
2
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
1
2
0
1
1
1
0
0
1
0
0
0
1
0
0
1
0
0
2
0
0
0
0
1
1
0
2
0
1
0
2
0
2
0
0
0
0
2
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
19
2
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
1
1
1
2
2
0
0
4
0
0
1
4
0
1
0
0
0
0
0
1
0
2
1
2
0
1
0
2
0
0
0
0
2
3
1
0
0
0
1
0
2
1
0
0
1
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
1
2
2
0
1
0
0
0
0
0
3
0
0
1
2
1
0
0
0
2
2
0
0
0
2
3
0
0
0
1
0
1
0
1
0
0
0
0
1
2
1
0
0
3
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
2
0
0
0
0
3
1
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
1
1
0
0
0
1
0
1
0
1
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
1
1
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
7
0
2
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
1
0
0
0
0
2
0
1
0
2
0
0
1
2
3
0
0
0
0
0
1
0
2
0
0
0
2
3
0
0
0
1
0
0
4
0
2
0
0
1
0
2
0
0
1
0
0
0
2
0
0
0
0
0
1
1
0
1
0
0
0
1
2
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
2
2
0
1
2
0
3
3
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
2
1
0
0
0
2
1
2
0
1
2
0
2
0
1
2
0
0
0
1
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
2
0
0
0
2
0
1
0
1
0
0
2
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
1
0
0
2
2
0
1
1
0
0
0
1
0
3
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
2
1
1
0
1
0
0
2
0
0
0
0
2
1
2
0
1
0
0
1
0
0
6
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
2
2
2
1
0
0
0
3
2
1
2
3
2
1
0
0
2
0
0
2
0
0
2
0
0
0
0
1
0
2
0
0
0
2
0
0
2
2
2
0
6
0
0
4
0
0
0
2
1
0
0
0
2
0
0
0
0
5
0
0
0
1
1
0
1
0
1
0
0
0
1
0
2
0
1
0
2
0
0
0
0
0
0
2
2
0
0
0
1
0
1
0
1
0
2
0
0
1
0
0
0
0
0
0
2
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
8
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
2
0
0
0
1
1
1
1
0
0
5
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
1
0
0
0
1
0
1
0
0
0
0
1
2
1
2
0
1
0
2
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
1
2
0
0
0
0
0
2
0
1
2
0
0
0
0
0
2
0
2
0
2
0
0
0
0
2
4
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
1
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
2
0
0
0
0
0
2
0
0
1
0
0
1
2
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
2
0
2
0
0
0
2
3
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
3
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
1
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
2
0
1
0
2
2
0
1
0
0
0
0
0
0
0
0
2
2
3
0
1
0
0
0
2
1
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
1
0
2
1
0
0
0
0
0
1
0
2
1
0
2
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
2
3
0
0
1
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
2
2
1
1
2
3
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
2
2
0
1
2
0
2
0
0
0
0
0
3
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
1
2
0
0
0
1
1
1
0
0
0
2
1
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
3
0
2
0
0
2
0
0
0
0
1
2
0
1
1
0
0
0
2
1
2
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
1
0
1
0
0
0
0
0
0
2
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
1
0
2
0
2
0
3
0
0
1
1
0
2
0
0
0
2
0
2
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
3
0
1
2
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
2
0
0
1
0
0
0
2
1
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
6
0
2
0
0
0
1
0
0
0
0
0
0
0
2
1
1
0
0
0
0
1
0
0
0
0
0
2
0
1
0
1
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
1
2
0
0
0
0
2
0
0
2
0
0
1
0
0
0
2
0
0
2
2
2
0
0
2
1
0
1
0
1
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
2
0
1
0
1
0
1
0
0
0
0
2
2
1
0
0
0
0
0
1
2
1
0
2
1
0
3
2
0
0
0
0
0
2
1
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
1
0
0
1
0
3
0
4
0
0
2
0
0
0
0
0
0
0
1
0
2
2
2
2
0
0
0
0
0
0
2
0
1
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
2
2
0
2
2
1
1
1
0
0
0
0
0
1
0
0
0
0
0
2
5
0
1
0
2
0
0
1
1
2
1
1
2
0
1
0
0
0
2
2
0
2
0
2
2
0
0
0
2
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
2
1
4
0
0
0
5
1
0
0
0
0
0
0
0
2
1
0
7
1
2
1
0
0
0
1
0
2
1
1
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
1
1
1
7
2
0
0
1
1
0
0
2
0
0
0
1
2
0
1
0
0
5
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
3
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
2
1
0
2
2
1
2
0
2
1
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
4
0
0
1
0
4
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
1
1
0
0
0
0
1
0
0
0
2
0
0
0
0
1
1
0
1
0
2
0
1
0
0
0
0
1
1
0
2
0
0
4
1
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
2
0
1
0
0
2
0
1
2
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
2
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
2
0
2
2
1
0
0
0
0
0
3
0
0
0
0
2
1
0
1
1
0
1
0
2
0
1
1
0
2
0
1
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
2
0
1
0
0
0
0
1
0
1
1
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
2
0
0
1
0
1
0
2
2
0
0
2
0
2
0
0
0
0
0
0
2
0
1
0
0
0
1
0
2
0
2
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
2
0
0
2
1
1
0
1
0
0
0
3
0
1
0
0
2
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
2
3
0
1
0
1
0
0
2
0
4
2
0
3
2
0
2
0
1
0
1
1
3
3
0
0
2
0
2
2
0
0
2
0
0
0
0
2
1
0
0
1
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
1
0
4
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
1
1
0
15
1
2
0
1
0
0
0
2
1
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
2
2
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
2
0
0
1
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
2
1
2
0
1
0
1
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
2
2
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
3
0
0
0
0
2
0
0
0
0
0
0
3
0
1
2
0
1
0
0
0
2
2
0
0
2
0
0
2
0
0
2
0
2
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
1
1
3
0
3
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
1
2
1
0
0
0
0
0
1
0
2
1
0
1
0
3
0
0
0
0
0
2
1
0
0
0
0
0
1
1
0
0
1
2
0
0
0
0
0
3
0
0
0
2
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
3
0
1
0
0
0
0
0
2
1
0
2
2
0
0
0
1
0
0
2
0
1
2
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
1
0
0
1
0
3
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
2
0
0
0
0
2
0
0
1
0
2
0
0
0
2
2
1
0
1
1
3
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
2
1
0
0
1
0
2
0
1
0
0
0
0
1
0
2
0
0
0
2
0
2
0
0
1
1
0
3
1
3
2
1
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
1
0
0
0
0
1
0
2
2
2
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
1
3
2
1
1
0
0
0
0
0
1
1
2
0
0
2
1
2
0
0
2
0
0
0
2
1
1
0
2
1
0
0
0
0
1
3
1
0
2
2
0
0
2
1
0
0
1
1
2
0
0
1
0
0
0
5
2
0
0
0
0
0
1
0
1
1
2
0
1
0
0
0
0
2
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
1
2
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
2
0
0
2
0
1
1
1
0
0
0
2
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
1
2
0
0
1
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
1
1
0
3
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
2
0
0
1
1
0
1
0
2
0
0
2
0
0
0
0
0
0
1
1
2
0
0
0
2
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
1
0
3
0
0
2
0
0
0
0
0
0
0
2
0
1
2
0
2
0
1
1
0
0
0
1
2
0
1
0
0
2
0
2
2
0
0
0
0
2
1
0
1
0
2
2
2
0
0
0
0
0
0
0
0
0
0
2
6
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
4
0
0
2
0
2
0
0
0
0
2
0
0
0
1
0
0
1
0
1
2
0
1
0
2
1
3
0
0
0
0
0
2
0
1
2
1
2
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
11
2
1
0
0
0
1
0
2
2
0
2
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
1
0
0
1
2
0
0
2
0
0
1
0
1
0
0
1
0
0
2
0
0
0
0
1
2
1
1
0
0
0
0
1
1
0
1
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
4
0
2
0
0
0
1
1
0
0
3
2
0
2
0
0
0
0
2
0
1
0
0
0
0
2
2
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
2
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
2
2
0
2
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
1
0
0
0
3
0
5
0
0
0
0
2
1
0
2
0
0
3
2
0
0
3
2
0
1
2
0
0
0
2
4
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
3
0
2
1
0
2
0
1
1
0
0
1
1
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
2
2
2
2
0
1
0
0
1
1
0
1
2
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
1
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
1
1
2
1
1
1
0
0
0
0
0
0
0
2
0
1
0
2
3
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
1
0
1
1
0
1
0
0
3
0
2
0
2
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
2
0
0
1
0
0
0
0
1
3
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
2
1
1
0
0
0
0
2
1
1
2
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
3
0
2
0
10
1
0
0
1
0
5
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
1
0
2
1
0
0
0
2
1
0
1
2
0
3
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
2
0
2
2
0
0
0
2
0
0
0
2
2
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
2
2
1
0
0
0
0
0
1
1
1
0
0
0
1
2
0
4
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
2
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
3
0
1
0
2
0
1
1
1
0
0
0
0
0
1
0
0
0
0
1
2
2
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
2
1
0
0
0
2
0
1
0
2
0
1
3
0
0
1
1
0
0
0
2
0
0
1
0
0
0
2
1
2
0
0
1
0
0
1
0
4
0
0
2
2
0
0
0
1
0
1
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
2
1
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
3
1
0
1
0
0
1
0
0
0
2
2
1
0
0
0
0
0
4
0
2
0
1
1
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
2
0
1
1
0
0
0
0
0
2
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
3
0
2
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
2
0
0
2
0
0
1
2
0
0
0
0
1
0
0
1
0
3
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
1
0
2
2
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
1
0
0
2
0
0
0
0
0
5
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
1
2
0
0
0
1
1
0
0
1
0
0
2
2
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
1
3
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
2
1
0
0
0
1
0
0
0
1
1
1
0
0
0
1
0
0
1
1
0
0
1
0
0
1
0
0
1
0
0
0
2
2
0
0
1
0
2
0
0
0
0
1
0
1
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
2
2
0
0
2
0
0
0
2
0
2
0
2
2
0
0
0
0
0
2
0
0
0
0
1
2
2
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
1
0
0
5
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
2
0
0
1
2
0
0
0
0
1
0
0
2
2
0
2
2
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
2
2
0
1
0
0
1
1
1
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
1
2
0
0
0
2
0
2
0
1
0
0
0
0
0
0
1
1
0
2
0
0
1
0
2
1
0
0
1
0
1
0
0
1
2
1
0
0
2
0
0
1
0
2
0
1
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
1
0
2
0
2
1
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
1
1
2
0
0
0
0
0
2
1
0
0
0
2
0
0
1
1
0
0
0
1
0
2
0
1
0
0
0
0
0
1
3
0
0
1
3
1
2
0
1
0
1
3
0
1
0
0
0
0
2
1
0
1
0
0
0
1
1
0
0
2
0
0
0
2
1
0
0
2
0
0
2
1
0
2
0
3
0
0
1
0
0
0
0
1
0
2
0
2
0
0
0
2
1
1
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
2
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
1
3
2
0
1
1
1
0
2
0
0
0
2
0
0
0
2
0
1
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
1
0
0
2
0
2
2
0
0
0
1
0
0
0
0
1
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
2
2
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
1
3
3
0
0
0
2
0
2
3
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
2
0
0
0
0
2
0
2
0
1
1
0
0
0
0
0
0
2
2
2
1
0
1
2
2
1
1
1
0
0
0
0
2
2
0
2
2
0
2
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
1
0
0
1
0
0
2
2
0
0
0
2
1
0
1
0
0
0
1
0
2
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
2
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
1
0
0
0
0
0
0
3
0
0
0
1
0
2
1
0
1
0
0
1
1
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
2
2
0
0
1
0
1
3
0
0
1
0
3
1
0
2
1
0
1
0
1
0
2
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
2
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
1
0
1
1
0
3
1
2
1
0
3
0
2
0
0
0
3
0
1
1
0
0
0
0
1
1
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
4
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
2
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
2
0
0
0
2
0
0
0
2
0
1
0
2
0
5
0
0
0
0
0
0
1
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
1
0
1
0
2
1
0
0
2
1
0
0
2
0
1
0
1
0
2
0
0
0
1
0
1
2
1
1
0
0
0
0
1
0
1
0
0
2
4
0
1
1
2
0
2
0
1
1
2
0
2
2
14
3
0
0
0
1
0
1
1
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
2
2
1
1
0
2
0
0
1
0
0
1
1
1
0
1
2
1
0
2
0
1
0
0
0
2
0
3
3
0
0
3
0
0
0
0
2
2
0
2
1
2
0
0
0
0
2
0
1
0
1
1
0
1
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
1
0
0
0
0
2
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
2
1
2
2
0
0
1
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
1
1
0
0
2
0
0
1
0
0
0
1
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
1
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
2
1
0
2
2
1
0
0
1
0
2
0
0
0
0
0
1
0
1
2
0
0
0
0
1
0
4
2
1
0
1
0
0
0
0
0
2
1
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
3
1
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
2
2
2
0
0
2
2
0
0
0
2
0
0
0
1
2
1
1
2
0
1
0
0
0
2
0
0
0
0
1
1
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
1
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
1
2
1
1
1
3
0
1
0
0
1
0
0
1
0
0
1
0
0
0
2
0
0
2
0
0
0
2
1
2
1
0
0
0
0
1
0
0
0
0
2
0
0
3
0
2
0
0
4
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
2
0
0
0
0
1
0
1
2
0
2
2
0
0
1
0
0
0
2
2
0
0
0
1
0
0
0
1
0
0
2
0
0
1
3
2
0
0
0
0
0
2
0
0
0
1
2
0
1
0
2
1
0
0
0
0
0
0
2
0
0
0
2
0
3
0
0
1
0
0
2
1
0
0
0
0
0
1
1
3
0
0
2
2
0
0
0
2
1
2
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
2
0
1
1
1
1
0
1
2
0
0
0
1
0
0
2
2
1
1
0
1
1
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
2
0
1
1
3
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
2
0
2
0
0
3
0
0
0
0
2
0
2
0
0
0
0
2
0
2
0
2
2
0
0
6
0
1
0
0
0
0
0
0
0
0
2
0
4
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
3
0
2
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
9
0
1
1
0
1
0
0
2
2
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
1
0
2
0
0
0
2
0
1
0
1
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
1
2
0
0
0
1
0
0
0
0
0
2
1
0
0
1
1
3
1
2
0
1
0
0
0
2
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
1
0
1
3
0
1
1
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
2
2
0
0
0
0
0
1
1
1
0
0
2
0
0
1
2
0
0
0
0
1
2
0
0
0
2
1
0
0
1
0
0
2
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
4
1
0
0
2
0
2
0
0
2
1
0
2
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
1
0
0
4
0
0
1
0
0
1
0
1
0
0
1
0
1
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
2
0
0
2
1
0
2
0
0
0
0
0
1
0
2
2
0
1
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
2
0
0
0
2
0
0
0
2
0
1
0
1
0
2
0
0
0
1
2
0
3
0
0
1
1
1
2
0
1
1
0
0
0
0
1
2
0
0
1
1
0
1
0
0
1
1
0
1
0
0
0
4
0
0
1
0
1
0
2
0
0
1
1
0
0
0
0
0
2
1
2
1
1
1
0
0
0
1
0
0
0
1
1
1
2
0
1
1
0
0
0
0
1
0
0
2
2
0
0
0
2
0
0
1
0
0
0
1
0
0
0
2
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
2
0
1
0
1
0
2
2
0
2
2
2
0
0
1
0
0
0
0
0
0
4
0
0
0
1
0
0
1
0
0
2
3
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
3
0
1
0
2
0
0
0
0
3
0
0
3
0
0
0
0
0
0
1
3
0
0
0
1
1
1
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
1
1
1
1
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
2
2
0
1
0
1
0
2
2
0
1
1
0
2
0
0
0
0
0
2
1
2
0
1
0
0
1
0
2
2
0
2
2
0
0
2
0
1
0
0
1
0
2
1
2
0
0
0
0
1
2
0
2
1
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
2
0
0
0
2
0
1
1
0
0
0
0
2
2
0
1
0
0
0
2
0
1
1
0
0
2
0
2
2
1
1
0
0
2
0
0
2
1
3
1
0
0
1
2
2
0
3
2
2
4
0
2
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
2
0
0
1
0
2
2
0
1
1
2
0
0
0
0
0
0
0
1
5
1
0
0
1
0
0
0
0
1
0
1
2
1
0
0
2
1
0
2
2
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
1
3
0
2
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
2
1
2
0
4
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
2
0
0
0
0
2
0
0
2
2
2
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
1
0
0
1
1
0
1
0
2
0
2
2
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
2
2
0
8
1
1
0
2
1
0
0
3
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
2
0
0
2
1
0
0
0
0
0
0
0
2
0
1
2
0
0
1
0
4
0
1
1
0
0
0
0
0
1
0
0
1
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
2
1
2
0
0
1
0
0
0
0
2
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
6
0
2
1
1
1
0
1
0
0
1
1
1
0
7
0
0
0
2
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
2
0
1
0
3
0
1
1
0
0
2
0
1
0
0
0
0
0
0
0
2
1
0
0
0
4
0
0
2
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
2
0
0
0
0
1
2
0
2
0
2
0
0
0
2
0
2
0
0
0
1
2
0
0
1
4
0
1
0
1
2
0
0
1
0
0
0
2
0
2
0
0
0
1
1
3
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
3
0
1
0
0
1
1
0
0
0
2
0
0
4
0
1
0
0
0
0
0
2
1
0
2
1
0
0
2
0
1
1
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
1
0
0
0
0
0
0
2
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
2
1
1
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
1
0
0
0
1
2
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
6
0
0
0
0
0
2
0
0
2
0
1
1
0
0
0
2
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
2
0
1
1
1
2
2
0
2
0
0
0
0
0
0
0
0
0
0
2
2
2
2
0
0
0
1
2
1
2
1
3
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
1
2
0
3
0
0
0
0
0
1
0
0
1
0
2
0
2
2
0
1
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
4
0
1
1
0
2
0
0
1
0
1
0
0
0
0
3
2
1
2
3
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
3
0
2
0
2
0
2
2
0
0
0
0
1
0
0
0
2
0
0
1
2
0
1
5
2
0
0
0
0
2
2
0
0
1
0
0
0
0
0
1
1
0
2
0
2
1
0
0
2
0
0
2
0
2
2
3
2
1
0
1
2
0
0
0
3
0
0
0
1
1
1
1
1
0
0
0
0
0
2
0
1
0
1
0
0
0
0
2
0
1
0
2
3
0
0
0
0
2
2
2
0
0
2
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
2
0
8
1
0
0
0
0
1
0
0
2
0
0
0
1
1
1
1
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
2
0
0
1
2
1
1
1
0
0
2
0
0
0
3
3
0
0
0
1
0
2
0
1
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
3
2
4
2
2
2
0
0
0
0
0
0
1
0
3
1
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
1
0
0
3
0
0
0
1
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
2
2
1
0
3
0
0
1
0
0
1
0
2
0
2
0
0
0
1
2
2
0
3
0
3
0
0
1
0
0
0
0
2
0
0
0
1
1
0
0
1
0
1
0
0
0
0
2
0
0
0
2
0
0
2
2
1
0
0
1
0
0
0
0
0
0
0
2
0
3
0
0
1
0
2
2
1
1
2
0
0
1
2
0
0
0
0
0
1
1
0
1
0
2
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
1
1
0
1
0
3
0
2
0
1
0
0
0
2
2
0
0
1
0
0
0
0
1
0
0
0
2
0
1
0
3
2
0
0
0
0
1
0
0
0
0
0
2
1
0
0
1
0
0
1
0
0
0
0
0
0
2
2
0
1
0
0
0
1
0
0
0
0
1
2
1
0
0
0
0
2
0
1
0
1
1
0
0
3
0
0
1
0
1
0
2
0
2
2
1
0
0
0
1
0
0
1
2
0
0
0
0
0
0
2
0
1
0
1
0
2
0
2
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
3
1
0
0
0
2
0
1
0
0
0
1
2
2
0
0
0
0
2
0
0
1
1
2
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
2
0
0
2
1
0
0
1
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
2
3
0
1
2
0
1
2
0
0
1
1
0
0
2
0
1
0
0
0
1
0
2
1
0
0
0
2
0
0
3
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
1
0
0
2
1
2
0
0
0
1
0
0
0
2
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
2
2
0
2
0
2
0
0
0
0
2
1
0
0
2
0
0
0
2
0
0
0
0
0
1
0
2
2
1
0
2
0
2
0
1
0
0
0
0
0
0
0
0
3
0
1
0
0
2
0
2
0
1
0
0
0
3
0
0
1
0
0
2
1
1
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
2
0
0
0
2
0
3
0
1
2
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
1
0
2
0
1
0
3
0
0
2
2
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
1
4
0
0
2
0
0
0
0
0
0
1
2
0
1
0
0
0
1
0
0
0
0
2
0
0
6
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
1
2
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
2
0
0
2
0
1
0
1
4
1
1
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
2
0
1
0
1
0
2
0
0
0
1
1
0
1
0
1
0
0
0
0
0
3
0
0
0
2
1
0
2
0
0
0
0
1
0
0
1
1
0
1
2
5
0
0
0
2
0
0
2
0
1
0
2
0
1
0
0
2
0
1
1
1
2
3
2
0
2
1
0
2
0
2
0
0
1
0
0
0
0
2
0
0
1
0
2
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
1
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
4
0
0
0
0
2
0
0
0
2
0
1
1
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
2
0
0
0
1
0
0
2
0
1
0
0
0
2
1
0
0
1
1
1
0
0
0
0
1
3
0
0
0
0
0
2
1
2
0
0
0
0
1
0
0
1
2
2
0
1
0
2
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
2
1
0
1
3
2
0
2
0
0
0
1
0
3
0
2
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
1
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
2
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
11
0
1
0
0
0
1
0
0
1
4
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
3
1
0
0
1
1
0
0
0
1
0
2
2
0
0
0
1
1
0
0
3
0
0
0
0
13
0
0
0
0
0
0
0
1
0
1
0
2
1
1
1
2
1
0
0
0
2
0
0
1
4
0
0
0
2
1
2
0
1
0
2
1
0
0
0
1
0
1
0
2
0
0
0
0
1
0
0
0
2
0
3
0
3
3
0
2
2
0
0
1
0
2
1
1
0
2
0
0
0
0
0
0
0
1
1
2
0
2
1
0
0
1
0
1
0
0
0
0
0
2
0
0
1
2
0
2
1
1
0
0
0
0
0
3
0
1
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
2
1
0
3
0
0
0
0
0
0
0
3
0
0
2
0
1
0
0
0
0
3
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
1
0
0
2
0
1
0
0
0
0
0
1
3
2
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
2
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
2
0
2
0
0
1
1
2
0
0
0
0
0
0
0
4
0
2
0
1
0
2
0
0
0
0
0
2
1
0
2
0
0
0
0
1
1
0
2
0
1
0
2
1
0
1
0
0
0
0
0
0
2
1
0
0
0
0
1
3
0
0
0
0
7
3
2
2
1
0
0
0
0
2
0
1
0
0
0
0
3
1
0
0
0
1
0
2
4
0
0
0
1
1
1
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
2
2
0
0
0
0
1
0
0
0
0
1
0
0
1
2
0
0
3
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
2
0
0
0
1
0
0
1
0
2
0
0
0
1
1
0
2
0
0
0
1
0
0
0
2
0
2
0
0
0
1
0
0
0
1
1
0
0
0
0
0
2
0
0
2
1
1
0
2
1
0
1
0
0
0
1
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
2
1
0
0
2
0
0
0
0
0
0
1
1
2
0
1
0
1
0
0
2
0
0
1
0
0
6
2
0
0
1
0
0
0
2
3
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
2
0
2
2
0
2
0
0
0
0
0
2
3
0
0
1
3
0
0
2
0
0
1
0
1
0
0
0
0
2
0
1
0
0
0
3
0
1
0
2
1
2
1
0
0
0
0
0
0
0
0
1
1
1
1
0
0
1
0
0
0
1
0
1
0
1
0
2
0
2
0
0
0
0
0
1
2
2
0
0
0
2
0
0
1
0
0
1
0
0
2
0
0
0
0
1
1
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
2
0
0
0
2
0
0
0
3
0
0
0
2
1
1
1
0
0
0
0
0
1
0
0
2
0
1
0
0
1
0
0
0
0
1
0
1
1
1
1
1
2
0
3
0
2
0
0
0
3
0
0
0
0
0
1
1
0
2
0
0
0
0
1
1
0
2
0
2
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
3
0
2
2
0
0
0
1
0
2
2
4
0
0
1
0
0
2
1
0
0
0
0
1
0
0
2
0
0
0
1
0
1
0
0
0
0
1
1
0
1
0
2
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
2
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
2
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
7
2
0
0
1
2
0
0
0
0
0
0
2
1
0
0
0
2
0
1
0
0
1
0
2
1
2
1
1
2
0
0
0
0
0
1
0
1
2
0
0
0
0
2
1
0
2
0
1
0
0
2
0
0
0
1
0
0
1
0
0
1
0
0
3
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
2
0
1
0
1
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
2
1
0
1
0
0
0
2
0
0
0
0
0
0
0
3
0
1
0
0
1
2
2
0
1
2
2
0
1
2
1
0
0
0
0
0
0
0
0
1
0
1
0
2
0
1
0
2
1
0
0
0
1
0
0
2
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
1
1
2
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
1
2
0
0
2
0
1
0
0
1
0
0
0
0
0
2
2
0
2
0
2
2
1
0
0
0
2
0
0
2
1
0
1
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
2
1
0
2
2
2
0
0
0
0
0
1
0
0
0
2
0
1
2
1
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
2
1
0
0
0
1
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
1
0
0
0
0
1
0
3
2
2
0
5
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
1
0
0
0
3
1
0
0
0
0
0
1
0
2
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
2
2
0
0
0
2
2
0
0
0
0
0
1
2
0
0
2
0
0
3
2
2
0
0
0
0
0
0
0
2
0
0
2
0
0
2
1
0
2
3
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
2
1
1
0
2
1
0
1
2
0
2
0
1
0
0
0
1
1
0
0
0
1
0
0
1
2
0
0
1
0
0
0
1
1
1
2
0
0
0
0
3
1
0
2
0
0
0
0
0
0
0
0
0
1
1
0
1
2
0
1
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
1
0
1
0
1
0
0
0
0
0
0
1
2
0
2
0
0
2
0
0
0
2
1
0
0
0
0
2
3
2
0
0
0
0
0
3
1
2
2
0
0
0
0
0
0
2
0
1
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
2
0
2
0
0
0
0
2
0
2
0
2
1
2
0
1
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
1
0
0
2
2
1
0
0
0
0
0
0
0
1
0
2
2
0
0
0
2
0
0
0
1
1
2
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
3
0
0
2
1
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
4
0
1
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
2
0
2
0
0
2
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
5
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
2
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
2
2
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
2
2
0
2
0
1
0
0
0
2
0
0
0
2
0
0
0
2
0
1
1
0
0
1
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
3
0
1
1
0
0
0
0
4
0
0
2
0
0
2
3
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
2
1
1
0
2
0
2
0
0
0
1
0
6
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
2
0
2
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
2
1
0
0
0
0
0
0
1
0
0
1
0
1
0
1
1
0
1
0
0
2
1
0
2
0
0
3
0
1
0
1
0
2
0
2
0
1
0
0
0
0
2
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
3
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
1
0
0
2
0
0
1
0
2
0
0
1
0
2
0
1
0
0
0
0
1
3
1
0
2
1
0
1
0
0
1
0
0
0
1
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
1
0
1
0
1
0
0
0
0
0
0
2
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
3
1
0
2
1
1
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
1
0
2
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
2
0
1
1
0
2
2
2
1
0
0
1
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
3
2
0
1
0
0
1
1
1
0
0
2
0
0
0
0
2
2
1
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
3
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
2
0
2
2
0
2
1
1
2
0
0
1
0
2
0
0
0
0
0
3
0
1
0
0
0
0
1
0
1
0
0
2
1
0
0
0
0
0
2
0
1
2
0
0
0
0
0
1
0
1
0
0
0
0
1
0
2
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
2
0
1
0
0
0
0
2
1
0
0
0
0
1
2
0
3
1
1
0
0
3
0
0
1
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
2
2
0
2
0
1
0
1
0
2
4
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
2
0
1
0
0
1
0
0
2
1
0
1
1
0
0
0
1
2
0
1
0
0
0
2
0
0
0
0
1
0
2
2
0
0
2
0
0
2
0
2
0
0
0
2
0
0
1
2
0
0
0
1
6
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
2
2
0
1
0
0
0
2
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
1
3
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
2
2
1
1
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
7
2
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
5
0
0
1
1
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
2
0
1
2
0
2
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
1
1
1
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
3
0
4
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
1
0
0
0
1
0
2
0
1
2
1
0
0
0
0
0
2
1
0
0
1
2
0
1
1
1
0
0
0
0
0
1
0
1
2
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
2
2
0
0
0
0
2
2
1
2
2
1
0
0
0
0
2
1
2
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
1
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
2
0
0
2
0
2
0
0
2
0
7
0
1
1
0
1
0
2
2
0
0
1
0
0
2
0
2
2
0
4
0
0
0
0
1
1
0
1
2
0
1
0
2
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
2
0
3
1
0
1
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
4
0
0
0
0
0
1
0
3
0
1
0
0
0
0
1
0
0
2
3
1
0
2
2
1
0
0
0
2
1
0
3
0
1
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
4
1
1
0
0
2
0
0
0
0
0
1
2
0
2
0
0
0
0
0
2
2
0
0
2
0
3
1
0
0
1
0
0
0
5
1
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
2
1
1
1
4
0
1
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
1
1
3
0
2
0
1
0
0
1
0
0
0
0
2
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
2
0
1
0
1
2
2
1
0
1
0
0
2
0
0
0
2
0
0
0
1
0
1
0
0
2
1
0
0
2
0
0
0
4
0
0
0
1
0
0
2
0
0
0
0
1
1
2
0
0
2
0
2
0
0
0
2
0
0
2
0
1
0
1
0
1
0
0
2
0
0
0
0
0
2
0
0
1
2
1
1
0
0
0
0
0
3
0
0
1
1
0
0
0
0
0
0
2
1
2
0
0
0
0
2
0
1
0
1
3
0
0
0
0
2
6
0
1
0
0
2
0
0
0
1
1
1
0
0
0
0
0
0
1
1
1
0
0
0
1
1
0
0
0
1
0
0
0
2
0
0
1
2
1
0
0
0
1
0
0
0
0
4
1
0
0
0
0
2
0
2
1
1
0
0
0
0
0
0
0
2
2
2
0
0
0
2
0
0
3
0
0
1
0
0
2
0
1
0
0
2
0
0
0
1
1
1
0
0
0
0
0
0
1
2
0
1
0
0
0
1
0
0
2
0
3
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
2
1
0
0
2
2
1
2
1
0
2
0
0
0
1
0
0
2
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
1
0
1
0
3
0
0
0
1
0
0
1
2
1
0
0
0
1
1
2
2
0
0
0
0
0
0
0
1
0
1
0
4
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
1
0
0
2
0
0
0
2
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
1
0
2
2
0
0
0
0
0
0
2
1
2
1
1
1
2
2
2
0
0
2
0
1
1
2
0
0
2
0
0
0
0
0
2
1
1
0
2
0
1
1
1
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
2
2
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
3
3
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
2
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
3
1
0
0
0
0
2
0
2
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
2
0
0
1
2
0
1
1
0
0
0
0
0
3
0
0
0
0
1
1
1
0
0
0
4
0
0
0
1
0
3
1
0
0
2
1
0
0
1
1
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
2
0
1
0
2
0
0
1
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
1
0
1
0
0
1
0
2
0
2
1
2
2
1
0
0
0
0
2
0
0
2
1
2
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
1
2
0
2
2
0
0
0
0
1
0
1
0
0
0
3
0
0
0
1
0
0
2
0
0
2
0
2
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
0
1
1
0
0
0
0
1
2
3
0
2
0
0
0
0
1
0
0
2
3
0
0
1
0
0
0
0
1
0
1
2
1
0
0
0
0
2
1
0
1
3
0
1
0
1
3
0
1
2
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
3
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
2
2
0
0
0
0
0
0
1
1
3
2
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
4
0
2
0
0
0
2
0
0
0
2
0
3
0
4
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
2
0
0
1
0
0
1
3
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
1
0
0
2
0
1
4
0
0
0
0
0
0
2
0
0
0
2
1
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
1
2
1
2
1
0
0
0
0
0
1
0
0
2
0
1
1
0
0
2
2
0
2
0
2
0
2
2
0
0
0
2
0
1
1
0
0
0
0
0
2
0
0
0
1
2
0
1
2
0
0
0
1
0
0
0
1
1
0
0
0
2
2
0
2
0
0
0
0
1
0
0
0
2
0
1
0
2
2
0
1
0
0
0
0
2
0
2
1
0
0
0
0
0
2
0
0
0
0
1
1
0
2
0
0
0
1
0
0
1
0
2
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
3
0
3
0
0
0
0
0
0
2
0
3
3
1
2
0
1
0
1
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
2
0
2
2
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
4
0
1
2
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
1
1
0
1
1
1
2
0
2
1
1
1
0
1
0
0
2
0
0
0
0
0
0
0
0
5
0
0
1
0
1
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
2
1
0
2
0
0
0
0
0
3
1
0
0
2
0
2
2
0
0
0
0
2
0
1
0
1
0
0
0
0
1
0
1
0
0
0
1
2
0
0
1
1
1
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
3
1
0
2
0
0
0
1
1
0
1
0
0
2
0
2
1
0
0
0
0
0
0
1
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
2
0
2
1
2
0
0
2
0
0
0
3
0
0
0
1
0
2
0
0
0
1
0
2
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
2
0
0
1
1
0
2
0
2
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
2
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
1
0
1
4
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
2
2
0
0
0
2
1
0
2
2
0
1
0
0
1
2
0
2
0
4
0
0
1
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
2
2
1
2
0
2
0
0
1
0
0
0
2
2
0
1
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
1
0
0
2
0
1
2
1
1
0
1
0
0
2
0
0
0
0
0
1
0
0
2
1
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
2
0
0
2
1
1
1
0
0
2
0
0
1
0
2
0
1
0
2
2
2
2
1
0
0
0
1
0
2
2
0
0
0
1
0
0
0
2
0
0
1
0
2
0
2
0
2
0
0
0
0
0
3
0
0
0
0
2
2
2
1
0
2
0
0
2
0
0
0
3
0
2
0
2
2
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
1
2
0
1
0
0
0
1
0
0
3
0
0
0
0
0
1
1
0
2
2
0
0
0
1
0
2
0
0
0
1
0
0
3
2
2
0
1
0
0
0
1
1
2
0
1
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
1
1
1
1
1
3
0
0
0
0
1
0
0
0
1
0
2
1
1
3
0
0
0
1
0
0
1
0
2
0
0
0
2
0
0
0
3
3
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
1
0
2
0
1
0
0
0
0
0
0
1
1
0
1
3
2
0
0
0
0
1
2
0
0
0
1
3
0
2
0
0
0
5
0
0
0
1
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
1
0
1
0
0
0
2
1
0
2
0
1
1
0
0
0
0
2
2
0
0
2
0
0
2
0
0
1
0
0
0
0
0
3
1
0
2
1
0
2
0
0
0
0
3
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
4
0
1
1
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
1
0
1
1
1
0
0
0
0
1
0
0
1
1
0
0
1
1
2
0
0
0
2
1
0
0
1
1
1
0
2
0
2
0
0
2
0
2
0
0
1
0
2
0
0
0
0
3
2
1
0
1
0
0
0
0
2
0
0
0
2
0
1
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
1
2
0
4
2
0
1
2
0
1
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
1
1
0
0
0
0
0
1
2
0
0
2
3
0
0
1
0
0
1
0
0
3
0
0
0
1
0
1
2
1
0
1
0
0
1
0
0
0
0
2
0
2
0
2
0
2
0
0
2
0
2
0
1
1
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
2
2
0
0
0
2
1
1
0
0
2
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
1
4
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
2
0
1
0
0
3
0
0
0
1
0
0
1
1
2
0
1
0
0
3
0
1
1
0
0
1
0
0
2
0
0
0
0
1
1
0
1
1
1
2
0
0
1
0
0
0
0
1
0
2
0
1
2
2
6
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
1
1
2
0
0
1
0
0
1
0
0
0
2
3
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
2
2
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
3
0
0
0
2
1
0
1
0
2
0
1
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
2
2
0
0
0
0
0
0
0
0
3
0
0
0
1
2
0
1
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
1
1
0
0
2
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
1
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
2
1
0
0
4
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
2
1
2
2
6
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
1
0
3
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
2
0
0
1
0
1
2
0
0
0
1
2
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
2
0
1
0
0
2
0
0
1
0
0
0
1
0
2
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
1
3
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
1
1
0
2
1
1
0
0
0
0
1
1
2
0
0
0
0
2
0
2
1
1
2
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
2
0
0
1
2
1
0
0
1
2
0
0
1
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
3
0
2
0
2
0
2
0
0
0
0
4
0
0
1
2
0
0
0
1
2
2
2
0
3
5
0
0
0
0
2
2
0
1
0
0
1
0
0
0
0
1
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
2
4
1
2
0
2
0
0
3
0
0
0
0
1
0
0
0
1
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
2
0
0
1
0
0
0
1
0
1
2
2
0
0
0
0
2
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
2
0
0
3
0
0
0
0
0
0
1
2
0
1
0
2
2
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
2
1
1
0
2
2
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
1
0
0
2
0
2
0
0
2
0
2
3
0
0
1
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
2
0
1
1
0
1
0
0
2
4
0
2
2
0
0
0
0
0
2
0
3
1
0
0
0
1
0
0
0
0
0
1
0
0
1
1
1
1
2
0
0
0
0
0
0
0
1
3
2
0
0
2
1
2
3
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
2
0
0
1
0
5
0
1
1
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
1
0
0
0
1
0
0
1
0
1
0
2
0
0
0
2
0
0
0
0
2
0
0
0
1
1
1
0
0
0
1
0
1
3
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
2
0
1
0
0
0
0
0
1
0
2
0
0
1
2
0
2
0
0
0
5
0
0
0
2
2
0
2
0
0
3
0
0
1
2
2
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
11
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
2
0
0
2
0
0
1
1
0
0
0
0
3
0
0
0
1
0
0
0
2
0
0
1
0
0
1
2
0
2
0
0
0
1
1
0
1
2
0
0
0
0
0
0
3
0
0
2
1
1
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
1
1
0
0
1
1
0
0
4
2
2
3
0
2
0
1
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
2
0
0
1
0
0
0
1
1
0
2
0
2
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
2
2
0
2
1
0
0
2
0
0
1
1
2
1
1
1
1
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
3
0
0
2
2
2
4
1
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
3
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
3
0
0
0
2
2
0
0
0
1
0
1
0
1
0
2
0
0
2
2
0
0
0
0
0
0
0
2
0
2
0
0
2
1
0
0
1
1
0
0
2
0
0
1
0
0
2
0
1
0
2
0
0
3
0
0
0
0
1
1
0
0
1
1
0
0
0
0
1
0
0
0
1
2
1
1
0
0
1
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
2
0
0
2
0
0
0
0
1
0
0
1
0
2
2
2
0
0
0
0
0
2
2
2
0
0
0
1
0
0
2
0
0
0
2
1
2
2
0
0
0
2
2
0
0
0
0
2
2
0
2
2
1
0
2
1
0
0
1
0
4
2
0
0
0
0
0
0
0
0
2
0
0
0
5
0
0
0
0
0
0
0
1
0
0
0
0
4
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
4
1
0
2
1
1
2
0
1
0
2
2
2
0
0
1
0
0
0
0
0
0
0
0
0
1
1
2
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
2
1
6
1
1
0
2
0
1
2
0
0
0
0
0
0
0
0
2
0
2
1
1
0
0
0
1
0
0
1
0
0
2
2
0
1
2
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
1
1
0
0
2
0
2
2
0
0
2
0
0
1
2
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
2
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
1
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
1
2
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
2
0
1
0
1
1
0
0
0
0
1
0
2
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
3
0
2
1
2
0
1
0
1
1
0
2
0
0
1
0
0
0
1
0
2
2
1
0
0
0
0
0
2
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
1
2
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
2
1
2
0
0
0
0
0
0
0
10
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
2
0
1
0
0
2
1
0
0
0
0
0
0
0
1
2
0
0
1
2
0
2
0
0
0
0
2
3
1
2
0
1
1
0
0
0
1
0
2
0
0
2
0
2
0
0
0
1
1
0
2
1
0
2
0
0
0
0
0
0
0
1
0
1
2
2
0
0
3
0
1
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
1
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
2
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
2
0
1
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
2
1
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
2
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
1
3
0
0
1
0
0
0
0
2
1
1
1
1
0
0
1
0
0
3
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
1
1
0
0
0
0
0
1
0
2
0
0
1
1
1
1
1
2
1
2
1
0
0
2
0
0
1
2
1
0
0
1
0
1
2
1
2
0
0
1
0
0
0
0
0
0
0
2
2
2
1
0
2
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
2
0
0
1
2
1
2
2
1
2
0
0
0
0
0
2
2
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
6
1
2
1
0
0
0
1
1
2
1
0
1
0
3
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
1
0
2
0
0
0
3
0
2
2
0
0
0
0
1
0
1
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
1
2
1
0
0
0
0
0
0
0
2
0
1
3
2
0
0
0
2
0
0
0
1
2
0
0
3
0
1
2
0
0
0
0
2
0
0
1
0
0
0
0
1
2
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
3
0
0
1
2
2
0
2
0
0
0
0
0
0
0
2
0
0
0
3
0
1
0
2
0
1
3
0
3
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
2
1
2
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
2
0
2
0
0
1
2
0
0
0
0
0
0
0
1
1
2
1
0
3
0
1
0
0
0
1
0
0
0
0
1
0
0
0
2
1
0
0
0
1
1
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
1
3
0
0
2
3
0
0
0
0
2
0
0
1
0
0
0
2
0
1
1
0
0
0
0
0
0
0
1
0
0
2
0
0
2
3
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
2
1
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
2
0
2
0
0
0
1
1
0
2
0
0
0
0
4
0
2
3
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
2
2
0
0
2
0
0
2
0
0
0
1
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
1
1
0
1
0
0
0
0
0
0
2
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
2
1
0
0
1
0
0
0
0
2
1
1
0
0
1
1
0
1
3
1
0
0
0
0
0
0
1
0
0
0
0
2
2
2
3
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
1
2
0
0
0
0
0
0
2
2
0
0
1
2
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
2
4
1
2
0
0
2
0
0
1
0
1
0
3
0
0
1
0
2
0
0
1
2
0
0
2
2
0
0
6
0
2
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
2
0
1
2
1
0
0
0
0
0
0
2
0
1
0
0
1
1
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
1
0
0
0
0
2
2
2
0
0
1
0
0
0
0
2
1
0
2
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
6
2
2
0
0
0
1
0
0
0
2
1
3
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
2
1
2
0
1
1
0
0
0
1
2
1
1
2
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
1
0
0
2
1
2
0
0
1
0
2
0
0
0
0
2
0
2
0
1
0
1
0
0
0
1
0
0
2
1
2
0
0
0
0
0
2
1
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
2
2
2
0
0
0
1
0
0
1
0
1
0
2
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
4
0
1
1
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
2
0
3
2
0
2
0
0
1
0
2
1
0
3
0
0
0
1
2
1
1
0
0
0
0
1
2
0
0
0
4
1
0
0
0
0
3
2
3
0
0
1
0
2
0
0
0
2
2
0
0
0
0
3
1
0
0
0
2
1
3
2
0
1
0
0
1
0
0
2
0
0
2
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
1
0
0
1
1
2
0
2
2
0
2
0
0
0
2
1
0
2
1
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
1
4
0
0
0
0
0
0
2
0
1
1
0
0
1
0
0
0
0
0
2
2
0
0
3
0
0
0
2
1
1
0
4
1
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
1
0
1
0
1
2
2
2
0
1
2
2
2
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
2
3
2
0
1
0
2
0
0
1
2
0
0
0
1
0
1
2
0
0
1
2
1
0
0
0
0
2
1
0
0
2
0
0
2
0
0
2
0
2
0
0
0
1
0
0
2
0
0
1
0
1
0
0
0
2
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
2
0
2
0
2
0
3
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
2
1
0
1
0
0
1
1
2
0
0
0
0
1
3
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
3
0
2
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
2
2
2
0
2
1
0
0
1
0
2
2
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
3
2
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
2
1
0
2
0
0
0
0
0
0
1
0
0
0
7
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
1
3
0
1
1
0
2
0
0
1
0
1
2
1
2
1
0
0
0
0
2
2
1
0
0
0
2
0
0
0
2
0
0
2
0
2
0
0
0
2
2
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
1
0
1
0
1
0
0
2
2
0
2
0
0
2
2
1
2
2
0
0
0
0
0
0
1
1
3
0
0
0
2
1
0
0
2
0
0
0
0
0
1
0
0
0
0
2
1
0
1
0
2
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
4
0
0
0
0
2
0
1
0
0
2
0
0
1
3
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
1
0
0
2
0
0
0
3
0
0
0
2
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
1
0
2
0
0
2
0
2
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
2
0
0
1
1
0
0
0
2
0
0
0
1
2
0
2
0
1
2
0
0
0
6
0
0
1
0
0
0
0
0
1
1
0
0
0
1
1
4
0
0
0
4
0
0
1
0
0
2
2
0
0
0
2
0
1
2
0
0
0
2
0
0
1
0
0
0
1
0
2
0
0
2
0
0
0
2
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
2
0
14
0
1
0
0
1
0
3
0
0
0
2
3
0
0
1
0
0
4
2
0
0
0
4
0
0
2
0
2
0
0
0
0
0
0
1
0
1
0
1
0
2
0
0
2
0
0
2
0
0
0
1
0
2
0
0
1
3
2
1
0
0
0
0
0
2
3
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
1
1
0
2
1
2
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
1
1
0
2
2
0
0
0
0
0
0
0
3
0
1
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
2
2
2
0
1
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
1
0
3
2
0
0
1
0
0
1
0
0
2
1
0
1
2
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
2
0
2
0
0
2
0
3
3
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
1
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
1
1
2
0
1
0
1
0
0
0
1
0
0
1
0
2
3
0
1
0
1
0
1
0
2
0
0
0
2
0
2
1
0
0
3
0
0
2
1
0
2
1
0
2
3
1
1
2
4
3
0
2
0
1
0
1
0
0
0
2
1
0
1
1
3
0
0
0
10
0
2
0
1
2
0
9
0
0
0
0
2
1
0
2
2
0
2
0
2
1
0
0
0
2
1
0
0
0
1
1
1
0
2
0
0
2
2
0
2
0
1
1
0
5
0
1
0
0
0
0
1
0
0
2
0
1
0
0
0
2
0
0
0
2
0
0
3
0
0
2
0
2
0
2
0
0
0
0
1
2
0
0
1
0
0
6
0
0
0
2
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
1
1
0
0
1
0
0
2
2
0
0
0
1
0
1
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
1
0
0
0
0
1
1
2
0
0
1
0
0
3
0
0
0
2
0
2
0
0
3
0
0
0
2
0
2
2
0
0
2
0
2
0
2
0
0
1
0
0
0
2
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
3
2
0
0
0
0
1
0
0
0
2
2
0
1
0
0
0
0
0
0
0
3
0
0
1
0
3
1
1
0
0
0
0
0
0
0
0
0
2
0
0
1
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
8
0
0
0
0
0
3
2
0
2
0
7
0
0
0
2
0
0
0
0
2
0
1
2
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
1
1
2
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
2
0
0
1
0
0
2
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
1
1
0
0
0
1
0
1
1
0
0
3
0
0
0
2
0
0
0
0
0
1
0
2
0
1
2
0
1
0
1
0
0
0
1
0
2
0
1
1
0
0
3
0
0
0
0
0
0
1
2
0
0
0
0
1
0
2
0
1
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
1
2
0
1
0
0
2
0
0
0
1
2
2
2
0
0
1
2
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
2
2
0
0
0
2
0
1
2
0
1
1
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
1
4
0
0
0
2
0
0
0
0
1
1
0
2
1
1
2
0
0
0
0
3
2
0
1
0
2
0
0
1
0
0
0
1
2
0
0
2
1
2
0
0
0
0
2
0
1
0
1
0
1
0
0
0
1
4
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
2
0
1
0
0
0
1
0
1
0
2
0
2
0
0
1
0
0
0
0
1
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
2
0
0
0
1
0
7
0
0
2
2
0
2
1
2
0
0
2
1
1
1
1
0
2
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
1
1
0
1
2
1
0
0
0
0
0
1
1
2
0
1
1
1
0
2
1
0
0
1
0
0
0
0
0
0
2
1
2
1
0
0
0
0
2
1
0
1
0
5
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
2
0
2
0
0
0
0
0
2
1
0
0
0
4
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
2
2
2
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
4
0
0
0
1
3
0
0
0
1
0
0
0
0
3
0
2
0
0
1
0
0
1
0
0
0
1
2
0
0
1
1
0
0
0
1
0
0
0
0
0
1
1
1
1
0
2
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
1
3
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
1
0
0
0
1
0
0
0
0
0
1
2
0
2
0
0
1
0
0
2
0
2
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
1
0
1
0
0
1
0
0
0
1
0
2
2
0
0
2
2
0
2
0
0
3
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
4
4
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
2
1
0
0
0
0
0
0
1
0
0
2
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
1
0
2
0
0
0
1
0
1
0
0
1
1
0
0
0
1
2
0
2
0
0
1
2
0
1
0
0
0
0
2
0
1
0
0
1
1
1
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
1
1
0
0
1
0
0
0
0
1
0
0
2
1
0
0
1
0
3
2
2
2
0
0
0
0
0
0
0
2
2
0
1
1
1
0
0
0
3
0
0
0
0
2
1
0
2
0
0
0
0
0
1
2
0
2
0
0
0
2
0
2
0
1
0
2
1
0
0
0
0
0
0
0
3
0
0
0
3
0
0
0
0
0
1
0
0
2
1
0
0
1
0
2
0
0
0
1
2
0
0
2
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
1
0
0
1
0
2
0
0
2
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
2
2
0
0
2
0
0
0
3
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
4
1
1
0
0
0
1
0
3
0
2
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
1
0
2
2
1
0
0
0
0
0
1
0
0
0
0
1
1
2
0
0
1
1
4
0
0
0
2
0
0
0
1
0
1
2
2
0
2
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
1
2
1
0
2
0
0
1
0
0
2
0
2
0
0
0
0
0
0
2
0
2
0
1
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
2
1
0
1
0
0
3
1
1
0
8
1
0
0
0
0
0
0
0
2
0
2
0
0
1
0
2
2
2
0
2
0
2
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
2
1
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
2
0
1
0
2
2
1
0
0
0
3
2
1
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
1
0
0
1
0
0
1
2
0
1
0
0
0
1
1
0
0
1
1
0
0
0
0
1
1
0
2
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
3
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
3
0
0
4
0
0
0
2
1
0
1
0
2
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
2
2
0
2
1
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
2
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
1
0
0
1
2
0
1
1
0
2
0
0
0
0
0
0
1
0
1
1
0
0
0
2
0
1
2
0
0
3
0
0
0
1
2
2
2
0
0
1
0
0
2
1
2
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
2
0
0
0
2
2
1
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
5
0
2
0
2
0
0
0
0
0
1
0
0
0
2
2
0
0
1
0
0
0
1
0
0
2
0
0
1
1
0
1
0
0
0
2
3
0
2
0
0
2
0
0
0
2
2
1
2
0
0
0
0
1
0
0
3
0
1
0
0
0
0
0
0
1
0
2
1
0
0
1
1
2
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
1
2
0
0
2
0
0
1
0
0
0
1
0
0
1
0
0
1
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
5
2
0
0
1
0
1
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
5
0
0
0
0
2
0
0
0
1
3
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
2
2
0
0
0
0
0
2
2
1
0
1
1
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
2
0
0
1
0
2
0
0
0
0
1
0
0
0
0
3
0
2
1
0
0
0
0
0
2
0
1
0
0
0
1
0
0
2
1
0
1
1
0
1
0
0
0
0
1
0
1
1
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
1
1
2
0
1
2
0
0
0
0
2
1
0
1
0
0
0
0
2
2
0
0
1
0
0
2
0
0
0
0
2
0
0
0
1
1
0
0
1
0
1
1
0
2
0
1
0
1
0
0
0
0
5
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
3
3
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
1
1
0
2
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
2
1
1
1
2
0
0
1
1
1
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
3
0
2
0
0
0
2
0
0
2
0
0
0
0
0
2
1
1
0
0
1
0
0
0
0
0
2
0
0
1
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
2
0
2
0
1
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
2
0
0
2
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
2
2
0
0
1
6
0
0
0
0
0
1
0
0
0
0
0
2
2
0
1
1
0
0
0
2
1
0
1
0
0
1
2
0
0
0
0
0
2
2
0
0
0
2
1
1
2
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
3
1
0
0
0
0
0
1
2
0
0
0
0
2
0
1
0
0
2
0
1
0
3
0
0
2
0
0
1
0
0
0
0
1
0
0
1
0
0
0
2
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
2
3
1
1
3
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
1
0
0
5
1
1
0
0
0
0
1
0
1
0
0
2
2
4
0
1
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
2
1
0
0
1
0
0
0
2
0
2
1
0
0
0
0
0
4
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
1
4
0
0
2
0
0
0
2
0
0
0
2
1
0
0
0
0
0
2
0
0
0
2
0
1
1
1
0
0
0
2
0
8
0
1
1
0
0
1
0
0
3
6
0
0
2
0
2
0
0
0
0
0
2
0
1
1
1
0
0
2
0
2
0
2
1
0
1
1
0
0
1
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
2
0
2
2
2
2
1
0
3
0
1
0
2
0
0
0
1
0
0
0
1
2
0
0
2
0
0
0
2
2
0
1
1
0
1
0
2
0
2
0
0
0
0
1
0
0
0
1
0
0
0
1
1
1
1
2
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
2
3
1
0
0
0
0
1
2
0
0
1
0
0
0
0
0
1
1
0
1
0
1
0
0
1
1
0
0
2
0
1
0
0
0
0
1
1
0
2
0
0
1
0
2
0
0
0
2
0
1
2
0
1
0
0
1
0
0
0
1
0
2
0
0
0
2
1
0
1
4
0
0
0
0
0
0
0
2
0
1
1
0
0
0
2
0
0
0
2
0
0
0
0
1
1
0
0
0
1
0
2
0
1
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
2
0
0
2
1
2
0
0
0
0
0
3
0
0
1
0
0
0
0
0
1
1
2
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
1
1
0
0
0
0
0
2
1
0
2
0
1
2
0
0
0
1
0
0
0
0
0
0
1
0
1
0
2
0
0
1
0
0
0
0
1
0
1
2
0
0
0
2
0
0
1
0
0
2
0
1
0
2
0
0
0
1
0
2
0
0
0
0
2
1
0
0
0
0
0
1
0
1
0
0
2
0
0
1
1
2
1
2
2
0
2
2
4
1
0
0
0
0
0
0
4
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
1
0
0
2
2
0
0
0
2
1
0
0
0
1
0
0
1
0
0
2
0
0
0
2
0
0
0
2
0
1
0
0
1
0
0
2
0
0
0
1
2
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
1
3
0
2
2
1
0
0
2
2
0
2
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
3
1
0
2
1
1
0
2
0
0
3
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
2
0
0
1
0
3
0
0
1
0
0
0
2
0
0
2
2
0
2
2
2
0
2
2
2
0
0
0
1
0
0
0
2
0
0
1
0
0
1
1
1
1
2
0
0
0
0
2
2
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
3
0
0
1
2
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
1
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
1
1
1
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
1
1
0
2
0
0
2
0
0
1
0
2
2
0
0
2
0
0
1
8
1
0
0
0
0
0
1
0
0
4
0
0
0
3
0
0
1
0
2
0
2
0
0
0
0
0
0
0
2
0
1
0
0
1
2
1
6
0
0
1
0
0
0
0
1
0
2
0
0
0
3
0
1
1
0
0
0
2
0
1
0
0
0
0
0
0
0
2
1
0
0
1
0
1
0
0
0
0
0
0
0
0
2
1
0
0
2
2
0
0
0
2
0
0
0
0
1
0
1
0
0
0
3
1
0
0
0
2
1
0
0
0
1
1
1
0
0
2
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
1
2
0
0
2
0
0
2
0
0
1
2
1
0
0
1
1
0
2
0
1
0
1
2
0
0
0
0
2
0
2
0
2
2
0
1
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
1
0
2
1
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
3
1
0
0
1
0
0
0
0
1
0
0
0
1
1
2
7
1
0
1
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
3
2
3
0
2
0
0
3
0
3
0
0
0
1
1
0
2
2
2
0
0
3
0
0
0
0
2
0
0
0
2
0
1
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
3
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
1
5
1
0
2
0
0
2
0
1
0
0
0
0
0
0
2
0
1
0
2
2
1
0
0
0
0
0
0
1
0
2
2
0
0
0
0
2
0
2
0
2
2
1
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
1
2
0
0
2
0
2
0
1
0
3
4
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
2
2
1
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
2
2
0
2
0
0
0
0
0
2
1
2
2
0
2
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
2
1
1
4
0
2
0
1
2
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
2
0
0
0
2
1
1
2
0
1
1
0
2
0
3
2
0
0
0
2
1
2
0
0
0
0
0
0
2
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
1
0
2
0
0
5
1
0
0
2
0
0
0
0
3
1
0
0
0
2
0
0
0
2
0
1
0
0
0
1
1
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
2
1
2
0
0
0
0
0
0
1
3
0
1
0
0
2
0
0
0
2
1
0
0
0
0
0
0
5
0
1
0
2
0
1
0
0
1
2
2
1
1
2
0
0
2
0
0
0
1
2
2
0
2
0
2
0
0
0
0
5
0
0
2
2
0
0
1
1
0
0
0
0
1
1
0
2
0
0
0
0
0
0
1
0
1
2
3
0
0
1
2
2
2
0
2
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
3
2
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
1
1
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
4
0
0
2
1
0
2
2
2
1
0
0
0
0
0
1
2
0
0
0
2
0
2
3
0
1
1
0
0
1
3
2
2
0
1
2
1
0
2
0
0
0
0
0
1
6
2
0
0
1
0
1
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
1
0
1
1
1
0
2
0
1
0
1
0
0
0
0
2
0
0
0
4
0
2
4
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
1
1
2
1
0
0
2
1
1
0
0
0
0
1
0
0
1
0
3
0
0
0
0
3
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
4
0
1
0
1
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
3
0
0
0
3
2
3
0
0
0
0
2
0
0
0
1
2
1
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
2
0
2
1
0
0
0
0
2
2
0
2
0
0
3
0
0
0
0
0
0
2
0
1
0
0
0
0
1
1
0
0
3
0
1
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
1
2
2
1
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
1
1
1
0
0
0
1
0
2
2
0
2
1
0
0
0
0
1
0
0
2
0
0
0
2
1
0
0
2
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
1
0
4
1
0
3
0
2
0
0
0
2
2
2
1
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
2
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
1
1
2
1
2
0
1
0
0
2
0
2
0
0
1
1
1
2
0
0
0
0
2
0
1
0
0
0
0
0
0
2
2
0
1
0
0
2
1
1
2
0
2
0
3
1
0
0
1
0
0
0
1
0
0
0
0
2
0
2
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
3
0
0
2
0
0
2
0
0
0
3
2
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
1
0
0
1
2
0
0
0
0
0
0
0
0
1
0
3
0
2
2
1
0
2
0
3
0
3
0
2
2
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
1
0
0
0
0
0
2
2
1
0
0
0
2
1
0
1
0
2
0
1
0
1
0
2
1
1
2
3
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
2
0
0
1
0
0
0
4
0
0
2
1
0
0
1
0
1
0
1
0
0
2
1
0
0
0
0
2
0
0
1
2
2
1
0
2
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
1
0
1
0
2
0
0
1
1
0
0
1
1
0
0
2
2
1
2
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
2
0
0
1
0
2
0
1
0
2
0
0
0
0
0
0
0
3
0
0
2
2
1
0
0
0
1
0
0
1
0
0
2
2
0
0
0
2
1
0
0
0
0
0
1
1
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
2
0
0
0
3
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
1
2
2
0
2
0
2
1
0
0
0
0
1
0
1
0
3
0
0
0
1
1
2
2
1
0
0
0
2
0
2
0
0
1
0
2
0
2
1
2
0
1
0
0
2
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
2
0
0
1
0
1
0
1
0
0
1
0
0
0
0
1
1
0
2
0
0
0
0
0
4
0
1
0
0
1
0
0
0
7
0
0
0
0
2
2
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
2
0
2
2
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
1
0
0
3
0
0
0
0
1
0
1
0
0
3
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
2
2
1
1
2
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
1
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
4
0
0
1
2
0
2
0
0
2
1
2
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
3
13
0
0
0
0
0
0
1
0
1
0
1
1
0
0
2
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
1
2
1
0
0
0
0
1
1
0
5
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
1
0
1
2
2
2
1
0
0
0
0
4
0
2
0
0
0
2
2
0
2
0
0
2
1
2
1
3
0
0
1
0
0
0
3
1
0
1
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
2
1
1
2
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
4
0
0
1
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
2
0
2
2
0
0
0
0
0
0
1
1
0
0
0
2
0
2
0
1
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
1
1
0
0
1
0
1
0
0
1
2
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
1
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
2
2
0
1
2
0
0
0
2
0
2
0
0
0
0
2
0
1
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
2
0
0
1
1
0
0
1
0
0
2
0
1
0
0
0
1
0
0
0
0
1
1
0
2
1
0
0
0
0
1
0
3
1
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
1
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
1
1
1
0
2
2
2
0
0
2
1
0
2
0
0
0
2
2
0
2
0
1
0
2
2
5
0
2
0
1
2
0
2
0
0
2
0
0
0
3
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
1
2
0
0
0
1
2
0
0
0
0
1
0
0
0
2
2
0
1
1
0
0
1
2
1
0
1
0
0
0
0
0
2
0
1
5
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
2
0
0
0
0
0
0
0
2
0
2
1
0
2
0
0
0
0
0
0
0
1
0
2
0
0
1
0
1
1
0
1
1
2
1
0
0
2
0
0
3
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
2
2
2
0
2
0
0
2
0
2
0
0
1
1
0
1
1
0
0
3
0
0
0
0
0
2
0
0
2
0
0
0
0
1
2
0
0
2
2
2
0
1
0
2
0
2
0
2
0
0
0
0
0
0
1
2
1
0
2
2
0
1
0
0
2
0
0
0
0
0
2
0
2
0
1
2
0
2
0
0
2
0
0
0
3
2
0
4
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
1
1
0
0
0
0
2
0
0
0
1
2
0
0
0
1
1
1
1
2
2
0
0
0
2
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
2
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
2
1
0
0
1
1
1
1
0
2
0
0
0
0
0
2
2
1
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
2
0
2
0
2
0
0
0
0
0
1
0
2
0
2
0
2
0
0
0
1
0
0
0
0
0
0
2
0
1
0
3
0
0
1
0
0
0
2
0
0
0
0
3
0
0
0
0
0
2
2
0
0
0
1
0
0
0
1
0
0
0
1
2
0
0
0
0
2
1
0
0
0
0
0
0
0
2
2
1
1
1
0
1
0
1
0
0
0
1
0
0
1
0
4
1
2
0
0
1
0
1
3
1
1
2
0
0
1
0
2
0
2
5
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
1
2
0
0
0
0
2
1
0
0
0
1
0
1
0
1
1
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
2
0
0
0
2
2
0
1
3
0
0
0
2
1
0
0
0
0
1
0
2
1
0
1
2
1
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
1
6
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
3
0
1
0
0
1
0
0
0
2
2
0
0
0
0
2
0
0
0
0
2
1
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
1
0
0
2
0
1
0
1
1
0
0
0
1
0
1
1
1
0
1
2
0
0
1
0
2
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
2
0
0
0
0
0
1
0
1
0
2
0
1
0
2
0
0
1
1
1
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
3
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
2
1
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
1
1
0
0
3
0
2
1
2
0
1
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
2
0
2
0
0
1
2
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
4
0
1
0
1
1
0
1
0
1
2
0
0
0
1
1
0
2
0
0
0
0
2
0
1
0
0
0
2
1
0
2
0
0
0
0
0
2
0
0
1
1
0
2
2
3
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
2
2
0
7
0
0
0
1
0
1
0
0
1
0
7
0
1
3
0
0
0
0
0
0
0
0
1
0
1
2
1
0
2
0
1
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
2
0
0
0
0
0
1
1
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
3
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
1
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
2
0
2
1
0
2
0
0
1
0
2
0
0
0
0
0
1
2
0
0
0
0
0
1
1
1
0
1
0
0
2
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
2
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
2
0
0
3
0
0
0
1
0
0
0
0
2
0
2
0
0
1
0
0
1
0
0
1
0
1
1
1
0
0
0
0
2
1
0
2
0
0
4
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
1
1
1
0
0
2
1
0
0
0
0
2
2
0
0
2
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
1
1
1
1
1
1
1
0
1
3
0
0
0
2
0
0
0
2
0
0
2
0
1
0
0
0
0
1
2
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
1
2
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
2
2
1
1
0
0
1
0
0
0
0
2
1
0
0
0
0
1
1
0
0
1
3
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
2
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
1
0
0
1
1
1
0
0
2
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
4
0
0
0
0
2
0
0
3
0
1
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
1
2
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
9
0
0
0
0
1
0
0
0
0
1
2
2
0
0
0
2
0
0
0
0
2
0
0
0
2
3
0
0
0
0
0
0
1
0
1
1
1
2
0
2
1
0
1
0
0
0
0
0
0
1
2
0
0
1
2
0
0
2
2
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
1
2
2
2
0
3
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
2
0
0
0
0
2
0
2
0
0
0
0
2
0
0
2
3
0
1
0
0
1
0
0
2
2
1
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
2
0
2
2
0
3
1
0
1
1
2
0
0
0
0
1
0
0
1
0
0
6
0
1
2
0
0
0
0
1
2
1
0
1
0
0
0
0
1
0
0
0
0
2
0
0
2
2
0
3
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
2
0
1
2
0
0
0
0
0
0
2
1
4
2
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
3
0
2
0
1
0
0
2
1
0
0
0
0
1
2
0
0
0
0
0
0
2
2
1
3
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
2
0
3
3
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
1
1
0
0
0
0
1
2
0
0
0
0
0
0
2
0
1
0
2
1
0
2
0
0
0
0
1
1
1
0
4
0
0
0
1
0
0
0
0
3
2
0
0
2
0
1
1
0
2
0
2
0
0
2
2
1
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
1
3
1
1
0
0
0
0
2
0
1
0
0
2
0
0
0
0
3
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
1
3
1
0
2
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
2
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
1
1
2
2
0
2
0
0
2
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
1
0
0
0
2
0
0
0
0
0
1
0
1
0
2
0
0
0
0
2
0
1
0
1
2
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
2
0
1
0
0
1
1
0
2
2
0
2
1
0
0
0
0
1
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
1
0
2
0
0
0
2
0
0
2
0
3
0
1
0
0
0
0
0
0
0
0
1
0
2
2
1
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
3
0
1
0
1
0
0
0
0
1
1
0
3
2
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
3
0
1
0
0
1
1
1
1
0
0
0
0
0
0
0
2
2
0
0
2
0
0
1
0
0
0
5
0
0
0
1
0
0
1
3
0
0
0
2
0
0
2
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
2
2
1
1
1
0
0
0
0
1
1
10
0
0
2
0
0
2
0
3
0
0
0
0
0
0
0
2
0
1
0
1
0
2
0
0
0
0
1
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
1
0
0
0
0
2
1
0
0
2
0
0
1
2
0
1
0
0
0
0
0
1
0
2
0
0
0
3
0
0
0
0
2
2
0
0
3
0
2
0
0
0
0
0
0
2
0
1
0
0
1
2
0
0
0
2
0
3
0
0
1
0
1
0
0
1
0
1
0
0
2
1
2
0
0
0
0
0
0
0
0
2
5
1
0
2
2
2
0
0
0
1
0
3
1
1
0
0
1
0
0
2
0
0
0
2
0
0
1
1
0
0
0
0
2
0
0
0
1
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
1
2
1
0
0
0
0
1
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
3
0
1
2
1
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
2
0
0
0
0
1
0
1
0
0
0
0
0
0
5
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
1
0
1
2
2
0
0
4
0
0
3
0
0
1
0
0
2
1
1
0
0
0
2
1
0
0
0
0
0
1
0
2
1
0
0
3
0
0
0
0
0
0
0
0
2
1
0
1
2
1
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
2
2
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
2
0
1
3
3
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
2
1
0
0
0
0
0
0
1
1
0
0
2
0
2
2
0
0
0
1
0
0
0
2
0
0
2
2
2
0
1
2
0
1
1
0
3
0
0
0
0
0
3
2
0
0
1
1
0
0
2
0
1
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
1
2
0
1
0
2
0
1
0
0
0
0
0
1
0
1
1
0
0
0
2
0
0
0
4
0
0
2
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
1
3
0
1
0
0
1
0
2
0
2
2
2
2
0
1
2
0
1
0
0
1
0
0
2
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
1
0
0
1
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
1
0
0
1
0
2
0
0
1
4
0
0
0
0
1
0
0
0
1
2
0
0
1
1
0
2
0
0
0
4
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
1
2
0
2
1
1
0
1
2
0
0
1
0
0
0
2
0
2
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
1
2
1
0
8
1
0
1
1
0
0
1
0
0
0
0
1
0
1
2
3
0
0
1
0
2
3
0
0
0
1
0
1
0
0
2
0
1
2
0
2
2
1
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
1
0
0
0
1
1
0
0
2
1
0
2
0
1
2
0
0
0
0
2
0
2
1
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
1
0
0
0
1
1
1
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
4
0
0
0
0
1
0
0
0
0
1
0
0
3
0
1
0
1
0
0
1
0
0
0
1
1
0
0
2
1
0
0
0
0
0
0
0
2
0
1
0
4
0
2
0
0
1
0
1
0
1
2
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
2
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
3
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
1
3
0
0
0
3
0
1
3
0
2
3
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
1
0
1
2
1
1
0
2
0
0
3
2
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
2
1
0
0
0
0
1
0
13
0
1
0
2
0
0
1
1
0
0
0
0
2
1
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
3
0
1
1
2
0
1
0
0
0
0
2
0
1
0
0
2
2
0
0
1
0
0
0
2
0
0
0
0
1
0
0
3
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
1
1
0
1
1
1
0
2
0
2
0
0
0
0
0
0
2
0
1
0
1
0
0
3
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
2
0
0
0
0
0
2
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
1
1
0
1
0
0
1
2
0
1
2
0
2
2
1
0
1
0
1
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
1
2
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
2
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
2
2
0
3
1
0
0
0
0
0
1
0
1
2
2
1
2
0
0
0
0
11
1
0
0
0
1
2
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
2
0
2
2
2
2
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
2
0
0
3
0
2
0
0
2
0
0
1
1
2
1
0
0
2
0
1
1
0
0
0
2
0
0
0
3
0
2
0
1
2
0
0
0
0
1
0
2
0
0
2
0
0
1
0
1
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
2
0
2
2
0
1
0
0
1
0
0
0
3
0
0
0
0
0
0
1
1
0
0
0
2
0
0
1
0
2
0
2
1
0
0
2
1
0
0
0
0
0
0
0
1
0
0
3
0
1
0
0
3
0
2
1
2
0
0
0
0
0
1
0
2
1
0
0
1
0
3
1
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
2
1
0
0
0
0
1
2
0
2
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
2
1
0
2
0
1
0
2
0
2
0
0
0
0
0
0
1
0
1
0
2
2
0
0
0
0
0
1
0
2
2
0
0
0
1
0
1
0
0
0
4
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
3
1
0
0
2
0
0
0
2
0
1
0
0
0
0
2
2
0
0
0
2
0
0
0
2
0
0
2
0
2
0
0
0
0
1
0
1
0
0
2
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
3
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
3
0
0
1
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
2
1
0
2
0
2
0
1
0
1
0
3
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
2
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
1
2
0
1
0
0
0
3
1
1
1
0
0
1
0
0
0
0
0
0
1
0
1
1
3
1
3
0
0
2
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
2
0
2
1
0
0
1
0
0
0
0
2
1
1
0
0
0
0
0
0
2
0
0
1
1
0
3
0
0
0
2
1
0
2
0
0
1
0
1
2
1
0
0
0
1
3
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
3
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
1
0
4
0
0
0
1
0
0
2
1
0
0
0
0
2
1
0
2
0
0
2
0
2
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
2
0
1
0
2
0
0
0
1
1
0
0
0
0
2
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
2
0
2
0
2
0
3
1
0
1
0
0
0
0
3
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
4
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
1
0
0
2
0
0
2
0
3
0
0
1
0
0
3
0
0
0
0
0
0
1
2
0
3
0
0
0
2
0
0
3
1
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
2
0
0
3
1
2
0
1
1
2
1
0
0
1
1
0
2
0
0
0
0
2
0
0
0
0
1
0
1
2
0
0
0
0
0
4
0
0
0
0
0
2
0
0
1
0
0
7
2
0
3
1
0
1
2
2
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
3
0
1
1
0
0
0
0
2
2
0
2
0
0
0
0
0
0
2
0
0
0
0
2
1
0
1
2
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
3
0
1
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
1
0
2
0
2
0
0
0
1
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
1
0
0
0
0
0
1
2
1
0
1
0
0
1
0
7
0
0
0
0
1
4
0
0
0
2
1
3
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
2
2
0
2
0
0
2
0
0
1
1
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
1
0
0
0
2
2
1
0
0
0
0
0
0
2
0
1
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
1
2
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
1
1
0
0
2
0
0
1
4
2
1
1
0
0
1
0
1
0
0
0
0
0
1
1
2
2
0
2
0
1
1
0
1
0
0
0
2
1
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
13
2
2
0
1
2
0
3
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
2
2
2
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
1
0
2
0
0
0
0
1
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
1
0
0
0
1
2
0
0
0
2
0
0
1
3
0
0
2
0
0
0
0
0
0
0
0
2
0
9
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
2
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
2
0
0
0
1
0
2
1
0
0
0
0
0
2
0
0
0
2
1
1
0
1
2
0
1
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
1
0
2
0
1
0
0
1
2
2
0
1
2
0
0
5
0
0
0
1
0
2
0
1
0
0
1
0
1
0
3
0
2
0
0
2
1
0
0
1
1
0
0
1
1
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
2
0
0
1
0
0
0
1
2
0
0
2
0
0
0
2
1
0
1
0
2
0
0
0
0
3
0
2
0
2
2
2
2
0
2
0
1
0
0
1
2
1
2
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
4
0
2
0
0
2
2
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
1
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
2
0
0
1
0
1
0
2
0
2
0
2
2
0
0
1
3
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
2
0
0
0
0
0
0
0
1
1
4
4
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
3
2
3
0
2
0
0
2
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
2
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
3
2
0
2
0
0
2
4
1
0
0
0
2
3
0
0
2
0
0
0
0
1
2
0
1
0
0
0
1
0
2
0
1
0
0
0
0
1
0
0
2
1
2
2
0
0
0
0
2
2
1
0
2
0
0
0
0
0
0
0
1
0
0
2
0
1
1
0
0
0
0
1
2
0
3
0
1
0
0
1
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
1
1
3
0
0
0
2
2
0
0
0
0
2
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
2
0
2
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
1
0
1
0
0
2
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
2
0
2
2
0
2
0
0
0
2
2
1
2
2
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
4
0
0
0
1
2
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
2
2
0
1
0
1
0
2
2
0
1
0
4
0
0
0
0
0
0
0
2
3
0
1
1
0
0
0
1
0
0
0
0
0
0
0
2
3
2
0
2
2
1
0
0
1
1
2
0
0
2
0
1
0
0
0
0
0
2
0
0
1
2
1
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
1
0
1
0
2
2
1
0
2
1
0
2
0
2
0
0
3
1
0
0
2
1
0
0
0
2
1
2
0
1
1
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
2
2
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
1
2
0
0
0
1
1
0
0
0
0
0
0
1
3
0
0
0
1
1
0
0
2
0
0
2
1
1
1
0
3
1
0
2
6
1
1
0
1
0
0
2
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
2
0
2
0
0
2
1
0
0
0
1
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
2
2
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
3
1
0
0
0
0
0
1
0
2
2
0
0
1
0
0
1
2
0
1
0
0
0
2
0
1
1
0
0
1
3
0
0
0
1
0
0
1
2
0
0
0
0
0
5
0
0
1
0
1
0
2
1
0
0
0
0
2
0
0
0
1
0
0
1
0
3
0
2
2
1
0
0
2
3
0
1
2
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
1
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
2
0
2
0
0
2
1
2
0
0
0
2
0
0
0
0
0
0
0
0
3
0
1
2
0
1
0
0
0
2
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
2
0
1
0
0
0
1
3
0
0
2
0
0
2
0
0
0
2
3
1
0
0
0
2
0
2
1
0
0
2
2
1
1
0
0
0
0
0
1
0
3
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
2
2
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
1
0
2
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
6
2
0
0
0
2
0
1
0
0
0
0
0
3
0
0
1
0
0
1
0
0
1
0
0
1
1
0
1
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
3
1
0
1
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
2
0
0
0
0
0
3
2
2
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
2
1
0
0
0
2
0
0
1
1
1
0
1
2
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
2
1
1
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
3
1
0
0
0
0
0
1
1
1
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
1
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
1
0
2
0
0
1
1
0
2
0
0
0
0
2
2
3
1
2
0
0
0
0
0
0
0
1
1
2
1
0
2
0
0
0
0
1
0
2
0
0
1
0
1
0
0
0
2
2
0
2
0
0
0
0
1
0
0
0
0
1
0
3
0
0
0
2
0
0
0
0
2
1
1
0
0
1
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
2
1
0
0
0
0
0
1
1
2
0
1
0
0
3
0
0
2
0
0
0
0
0
1
1
0
0
0
0
2
0
0
2
0
0
0
1
0
1
0
2
1
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
2
0
0
0
1
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
2
0
2
0
0
1
1
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
1
2
2
2
0
2
4
2
0
2
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
4
0
0
1
0
3
0
2
1
0
2
1
0
1
2
1
2
1
0
0
2
1
1
0
0
2
0
0
1
2
2
0
0
0
3
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
5
1
2
0
2
0
0
0
0
1
0
2
3
0
0
0
1
0
2
2
0
0
2
0
0
0
2
1
2
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
2
0
0
0
12
2
1
0
0
0
0
1
0
0
5
1
0
0
2
0
0
2
3
2
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
3
1
6
0
1
2
0
0
0
2
1
0
0
1
1
0
2
0
0
1
0
0
0
6
0
1
2
1
0
0
2
0
0
0
0
1
0
0
0
5
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
2
0
3
3
0
0
0
2
0
1
0
0
1
1
0
2
0
0
0
0
1
0
0
0
1
1
0
0
2
2
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
3
2
0
4
0
2
0
2
0
0
0
0
1
2
0
0
0
0
2
0
1
0
0
0
3
0
2
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
2
1
0
0
0
0
2
0
0
0
2
1
0
0
0
2
2
0
2
0
3
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
2
0
1
2
2
1
0
0
0
1
0
1
0
0
1
0
2
0
0
0
0
2
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
2
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
1
2
1
0
2
0
1
1
0
0
0
2
0
0
0
1
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
3
1
0
1
1
0
1
0
0
1
1
0
2
2
0
0
0
0
1
0
0
0
3
2
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
1
0
2
0
2
0
2
0
2
0
3
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
1
2
1
1
0
1
2
0
0
4
0
1
0
1
0
0
0
1
0
0
0
0
2
0
2
0
2
2
2
0
1
0
0
0
0
0
0
0
0
0
0
5
2
0
0
0
0
1
1
0
2
0
1
0
0
0
2
2
2
0
0
0
2
0
0
2
2
0
1
0
0
1
0
1
1
0
1
0
0
0
2
1
2
0
0
0
2
0
0
0
1
0
2
4
2
2
0
0
2
0
0
1
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
2
0
1
0
0
0
1
0
0
0
2
2
0
0
0
1
0
0
0
2
0
0
0
2
0
2
0
1
2
0
0
0
1
1
2
0
1
4
1
0
0
2
1
0
3
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
2
3
0
2
0
0
2
0
1
0
0
0
0
2
2
0
0
0
2
1
1
0
1
1
0
0
0
0
0
0
0
1
2
0
2
0
3
0
2
0
0
0
0
0
1
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
2
0
0
0
2
1
0
0
1
0
0
0
1
2
1
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
2
1
0
1
2
0
2
1
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
2
2
0
0
2
0
0
0
0
2
0
0
2
0
0
1
2
0
5
0
0
0
1
0
0
0
0
3
0
0
3
1
2
0
3
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
2
1
2
2
0
0
2
2
0
0
0
0
0
3
0
0
2
0
0
0
2
0
2
1
1
0
2
0
1
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
2
0
5
0
0
2
3
2
0
2
0
0
0
0
2
1
0
1
2
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
2
1
0
0
2
0
0
0
0
0
0
1
1
0
0
2
0
2
0
0
0
1
0
0
1
0
1
2
1
0
0
0
0
0
0
1
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
2
0
2
0
0
0
0
3
0
1
0
0
1
0
0
0
2
0
0
0
2
0
0
2
1
2
2
0
0
0
0
2
0
2
3
2
0
0
0
1
0
0
0
0
0
0
2
0
1
1
0
0
0
2
1
0
1
0
2
0
0
0
2
0
0
0
2
2
0
0
0
0
0
1
0
1
0
1
1
1
0
0
0
0
2
0
0
0
1
0
1
0
2
0
1
0
1
3
0
0
0
0
0
1
0
0
0
1
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
1
2
0
1
0
0
2
3
0
1
0
1
0
2
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
1
1
1
0
0
0
0
0
0
2
0
0
0
2
1
0
2
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
1
2
0
0
2
0
2
1
2
0
0
0
0
0
2
2
2
0
3
0
0
0
0
2
2
2
0
0
0
2
2
2
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
2
0
0
2
0
0
2
0
0
0
1
0
4
0
0
0
0
2
1
0
0
0
2
0
2
1
0
0
0
0
2
0
2
2
0
0
0
0
1
2
1
0
0
1
0
1
0
0
2
0
2
0
0
0
1
0
0
1
2
0
0
0
0
0
0
1
0
2
2
0
0
1
0
0
0
0
0
0
1
0
0
2
3
0
0
1
1
2
0
0
1
0
0
0
2
0
0
1
0
0
1
0
0
2
0
0
0
0
2
2
0
0
1
0
0
1
0
2
2
1
0
1
0
0
1
0
1
0
3
5
0
0
0
1
0
2
0
1
0
0
0
2
0
2
0
1
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
1
1
0
0
2
0
0
0
0
0
0
1
0
2
0
2
0
1
0
0
2
0
0
0
0
0
1
3
0
0
0
2
0
0
1
1
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
2
0
0
1
1
0
0
0
0
2
0
0
0
0
0
2
2
1
0
2
0
0
0
3
0
0
1
0
1
2
0
0
0
0
1
2
1
2
0
3
0
0
1
0
0
0
0
2
0
0
0
2
0
0
1
0
0
1
1
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
2
0
0
0
0
2
0
0
1
2
0
0
0
2
0
0
0
0
1
0
0
2
2
0
1
0
0
0
0
0
0
2
1
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
1
1
0
2
2
0
0
0
0
1
0
1
0
0
1
2
0
0
2
0
0
1
0
0
0
0
0
0
1
2
1
0
0
0
0
2
0
0
0
0
5
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
1
0
0
1
0
0
0
2
2
2
2
0
0
1
2
0
0
0
0
0
0
1
2
0
2
0
1
1
0
0
2
0
1
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
2
0
2
0
1
0
2
0
0
0
1
1
1
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
2
3
1
2
0
2
2
1
2
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
2
0
0
1
1
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
2
1
2
0
0
0
0
1
0
0
0
0
4
3
1
0
0
2
3
0
0
0
0
1
0
0
0
2
1
0
2
0
2
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
2
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
2
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
3
1
0
0
0
2
0
1
1
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
2
5
1
0
0
0
0
0
2
1
0
0
0
2
0
0
2
0
1
0
0
2
0
0
0
0
0
1
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
3
0
0
0
0
0
1
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
3
0
1
0
0
1
0
3
0
0
0
0
1
1
1
2
0
0
0
0
0
0
1
0
2
2
0
2
0
2
0
0
2
0
0
2
1
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
1
0
1
0
0
1
1
0
0
0
2
5
0
0
0
0
0
2
0
1
1
0
0
0
0
0
1
0
0
2
4
0
0
2
0
0
0
0
0
0
1
1
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
2
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
1
0
1
1
1
0
2
1
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
2
0
1
0
0
0
1
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
3
0
0
0
0
2
0
1
0
0
1
1
3
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
2
0
0
1
0
1
1
0
0
0
0
0
0
1
2
0
2
2
0
0
0
0
3
0
0
0
1
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
1
2
0
1
0
0
1
0
0
0
0
2
2
0
2
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
1
1
3
1
0
0
2
2
0
0
2
2
0
0
0
0
1
1
1
0
0
2
0
0
0
0
0
0
2
0
0
2
0
1
2
0
2
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
1
1
1
2
0
1
2
0
10
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
1
2
1
2
2
0
1
2
1
2
1
0
0
1
0
0
0
2
2
1
0
2
0
0
2
0
0
0
2
0
1
0
0
0
1
0
2
0
0
2
1
0
0
0
7
0
0
3
0
0
0
1
2
1
0
2
0
0
0
0
0
2
0
0
2
4
2
0
2
0
0
0
2
0
0
2
0
0
0
1
0
0
0
1
0
1
0
1
1
0
0
0
6
0
0
3
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
2
1
0
0
1
2
1
0
0
0
0
0
0
0
0
1
1
1
2
8
0
0
0
1
1
0
1
0
0
0
1
1
2
0
0
0
0
0
0
0
1
1
2
1
0
1
0
0
0
0
0
0
0
2
1
2
0
2
0
0
0
0
0
2
1
0
1
1
0
0
1
0
0
0
0
2
1
0
0
0
2
0
0
2
1
1
0
2
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
3
1
1
0
1
0
0
1
0
0
0
1
0
2
0
0
2
0
0
2
0
2
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
2
0
1
2
0
0
2
0
0
0
1
0
1
2
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
1
2
0
0
0
0
1
2
0
2
0
1
1
2
2
0
0
2
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
2
0
0
2
2
1
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
9
0
2
0
2
0
0
0
2
0
1
0
1
0
1
0
0
0
0
0
0
0
2
2
0
1
0
1
1
0
2
0
0
0
2
0
1
0
0
0
0
2
2
2
0
0
1
0
1
2
0
1
0
0
0
1
1
0
0
0
2
1
0
2
0
2
0
0
2
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
1
2
0
0
0
2
0
2
0
0
0
0
0
0
2
1
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
5
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
1
1
2
2
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
1
0
0
2
0
1
0
0
0
0
2
1
0
0
1
0
1
0
2
0
0
0
0
0
1
0
2
0
2
0
0
1
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
2
3
1
0
0
0
1
0
2
4
0
1
0
0
0
0
2
0
0
1
2
0
0
0
0
0
1
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
2
2
2
0
1
0
0
2
2
0
0
0
3
3
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
1
1
0
1
0
0
0
0
0
0
1
1
2
0
1
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
1
1
0
0
1
3
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
2
3
0
2
0
1
0
2
1
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
4
0
0
0
0
0
0
0
2
2
1
0
2
0
1
2
0
1
2
0
0
0
0
1
2
0
2
0
0
2
0
2
1
0
0
2
0
0
0
0
2
1
0
1
2
2
0
0
0
1
2
0
0
0
0
1
0
0
0
0
2
0
0
5
2
0
2
2
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
1
2
0
0
1
2
0
2
1
2
2
0
0
3
1
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
2
0
2
0
2
1
2
0
0
2
2
0
0
0
2
0
1
2
0
0
2
0
0
0
0
0
1
0
1
0
0
1
3
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
1
0
2
0
1
0
0
0
0
0
2
0
2
0
0
0
1
0
1
0
0
1
0
0
0
0
2
1
0
0
0
2
0
1
0
2
0
1
2
0
0
0
2
0
2
0
0
3
0
0
0
0
1
2
0
1
0
0
0
0
1
0
0
0
0
1
0
0
2
1
0
2
0
0
2
5
0
0
0
2
0
1
0
1
0
0
0
2
0
1
0
1
0
2
0
0
2
0
0
0
1
0
0
0
1
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
2
0
3
2
0
0
0
1
0
1
0
0
0
0
2
2
2
1
1
2
0
0
0
0
0
0
0
0
1
2
0
1
0
2
2
2
0
0
0
1
0
0
0
1
2
2
0
0
0
3
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
3
0
2
2
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
2
0
0
2
2
0
0
1
0
1
0
0
1
2
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
4
1
1
0
2
1
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
2
2
0
7
0
0
0
0
1
0
2
0
0
3
0
1
2
0
0
0
1
0
3
0
2
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
2
0
6
0
0
0
2
1
0
3
0
0
0
0
0
1
1
1
2
0
0
0
0
0
2
2
0
0
1
1
0
0
0
0
0
2
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
2
0
1
0
1
1
0
0
0
2
0
0
2
0
1
1
0
2
0
2
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
2
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
1
0
0
0
1
0
2
0
0
2
1
1
0
0
2
0
0
2
0
0
0
0
0
2
2
2
1
0
0
0
0
0
0
0
2
4
0
0
0
1
1
2
0
0
0
0
2
0
3
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
3
2
0
0
2
0
1
0
1
0
0
0
3
2
0
2
0
1
0
0
1
1
0
0
2
0
0
0
2
0
2
1
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
2
1
0
2
2
0
0
0
0
2
0
2
3
0
0
0
0
0
0
1
0
2
0
0
2
0
2
0
0
0
2
1
1
0
0
0
0
0
0
2
1
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
1
2
0
0
0
0
0
0
2
0
0
2
0
2
2
0
0
0
0
0
0
1
0
0
2
2
0
4
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
2
2
0
1
0
1
0
0
1
0
1
0
1
0
0
2
2
0
0
0
0
0
0
1
2
0
0
1
0
1
0
0
2
0
0
0
0
0
0
2
2
0
0
0
2
1
2
2
0
0
2
0
0
1
2
0
0
1
0
0
0
1
2
0
0
0
0
1
2
2
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
3
2
0
0
1
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
1
0
1
0
0
2
1
1
2
0
0
0
1
2
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
4
1
0
1
0
0
1
0
0
0
0
1
4
0
0
2
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
1
2
1
2
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
3
1
0
0
2
0
2
1
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
1
0
1
0
0
3
0
0
0
0
0
1
1
1
0
0
0
2
1
0
0
0
3
0
2
0
0
0
0
2
1
0
0
4
0
2
0
0
0
2
0
1
1
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
2
1
1
0
0
0
0
1
0
0
0
0
0
0
11
2
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
2
0
0
0
1
0
1
0
3
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
2
0
0
2
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
2
0
2
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
2
0
0
1
0
2
2
0
2
2
0
0
7
0
1
0
0
0
0
1
1
0
1
0
0
0
2
2
1
0
1
0
0
0
0
0
1
0
0
2
0
1
2
0
0
2
0
0
0
0
2
0
0
0
1
1
0
0
3
0
0
2
1
1
1
0
0
2
0
0
2
0
9
0
1
1
0
0
0
0
0
0
0
3
0
0
0
0
2
0
1
0
1
1
0
1
0
2
0
1
1
0
0
1
1
0
0
0
0
0
0
0
1
1
2
0
1
0
0
1
1
0
0
2
0
0
0
0
0
1
1
2
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
1
2
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
1
2
1
1
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
2
1
2
1
1
2
1
2
0
1
3
1
0
1
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
2
2
1
1
0
0
2
0
1
0
3
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
2
0
0
1
0
0
1
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
2
2
0
3
2
1
1
1
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
1
0
2
0
3
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
1
0
2
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
2
0
0
0
1
0
2
1
0
1
0
0
0
0
2
2
0
0
1
0
2
0
0
1
0
0
0
0
1
2
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
8
0
2
0
0
0
0
0
3
1
1
2
0
0
1
0
2
0
0
0
1
0
1
0
2
2
3
0
0
3
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
2
0
0
0
2
0
2
3
0
0
0
0
0
0
0
1
3
0
0
0
3
0
0
0
0
2
0
0
0
0
1
0
0
2
0
2
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
3
0
0
0
2
1
0
1
4
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
1
0
0
2
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
2
0
2
1
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
2
2
1
0
0
3
0
0
2
0
1
0
1
2
0
1
0
0
0
0
2
0
1
0
1
0
0
0
0
0
1
2
1
2
0
0
0
0
0
1
0
1
1
0
0
1
0
2
0
0
0
1
0
0
1
2
0
0
0
2
0
0
0
0
1
0
8
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
2
3
0
2
0
1
0
2
0
1
1
0
1
0
0
0
0
3
0
1
1
1
1
0
0
0
0
0
0
0
2
0
1
0
1
1
0
0
1
0
0
0
14
1
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
2
1
0
0
0
1
1
0
0
0
0
1
2
1
0
1
2
2
0
0
2
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
2
0
0
1
1
0
0
1
0
3
0
0
0
0
0
2
0
0
2
1
0
0
0
2
7
0
2
0
0
1
0
2
0
0
0
1
0
2
1
2
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
1
1
0
0
3
0
2
1
0
3
0
0
1
2
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
2
1
0
3
2
0
1
0
0
1
1
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
3
0
0
0
0
0
2
1
1
2
0
0
1
0
0
1
0
0
0
0
0
2
1
2
0
0
0
1
0
0
2
0
0
0
0
1
1
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
3
0
0
2
0
1
1
0
0
0
0
4
2
0
1
1
0
0
0
0
2
0
3
2
0
0
0
3
0
2
0
0
0
0
3
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
1
1
2
0
1
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
2
2
2
2
0
0
1
1
1
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
1
1
2
0
0
1
1
0
2
0
0
0
2
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
2
0
0
1
1
2
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
1
2
2
0
0
0
0
0
1
0
1
0
6
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
1
0
2
0
0
0
2
0
2
0
1
0
1
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
2
1
0
1
0
0
1
0
0
0
2
0
2
0
0
0
0
1
2
2
0
1
0
0
0
5
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
1
0
1
0
2
1
0
0
2
0
0
1
1
0
0
0
1
0
0
2
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
1
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
1
0
1
0
1
0
0
0
1
0
2
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
2
1
2
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
1
1
0
1
2
1
0
1
0
0
0
0
0
0
1
1
2
0
2
1
0
0
2
0
1
0
0
0
2
0
0
0
0
0
1
2
0
0
2
0
2
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
2
1
0
0
2
0
0
0
0
1
1
0
0
0
1
1
2
1
0
2
0
0
1
0
1
0
1
1
1
0
0
0
0
1
2
0
0
2
2
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
3
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
3
0
0
0
0
1
1
1
1
2
2
0
2
0
2
0
0
1
0
1
0
1
0
0
1
0
3
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
3
0
0
1
0
1
1
2
0
0
1
1
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
1
1
1
0
0
2
0
1
0
2
2
0
2
2
1
0
0
0
1
1
0
0
0
2
0
0
0
1
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
2
2
0
0
0
0
2
1
0
0
0
0
0
2
3
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
1
1
0
0
0
1
1
0
0
2
2
0
0
0
0
9
2
1
0
2
1
0
0
0
2
1
0
0
0
2
0
0
0
1
0
1
0
2
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
2
0
0
0
0
1
0
0
2
4
0
2
0
0
0
3
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
2
1
0
1
1
2
0
0
2
0
0
0
0
0
2
1
0
1
0
1
1
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
3
2
0
1
1
0
1
2
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
2
0
0
1
1
0
1
2
0
1
0
2
2
0
0
2
0
1
0
3
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
1
0
0
1
0
2
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
1
2
2
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
2
2
0
0
0
1
2
0
0
0
2
0
2
1
1
0
2
3
0
1
2
0
0
1
0
0
0
1
1
0
0
3
1
0
3
1
2
0
0
0
3
0
0
0
0
0
2
0
0
3
2
0
0
2
0
0
1
3
0
2
0
1
1
2
1
0
0
0
0
0
2
3
1
0
0
0
0
1
0
3
0
0
2
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
2
1
0
0
2
0
0
0
0
1
0
0
0
4
0
0
0
1
0
0
0
2
1
1
0
2
1
0
0
0
0
0
0
0
2
2
1
0
0
0
1
0
0
0
2
2
0
0
0
0
0
2
0
1
0
0
2
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
1
2
2
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
1
3
0
1
0
0
2
0
1
0
2
2
0
1
0
0
0
0
1
2
0
1
0
0
0
0
3
0
0
0
0
0
0
2
0
2
0
1
0
1
1
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
1
7
4
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
3
1
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
2
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
2
0
0
1
0
0
2
0
2
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
3
1
1
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
2
0
0
0
2
0
0
0
2
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
4
2
0
3
0
0
0
1
0
0
2
0
1
0
0
0
0
1
0
0
4
0
0
0
0
2
0
2
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
1
0
2
0
0
0
1
0
0
0
1
1
2
0
0
1
1
0
0
0
0
3
2
0
0
1
0
5
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
2
0
2
0
0
1
2
0
0
0
2
2
1
0
2
2
0
0
0
0
0
3
2
0
0
0
2
0
0
2
0
2
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
2
0
2
0
0
0
0
2
1
0
0
1
1
2
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
1
0
1
0
0
1
0
2
2
1
1
0
2
0
2
0
1
1
0
0
0
5
2
0
0
0
2
0
0
1
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
2
0
0
0
1
1
1
2
0
0
0
0
0
2
0
0
0
0
1
0
1
1
0
0
0
2
0
0
0
0
0
0
1
1
0
4
0
0
1
1
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
2
0
0
0
0
0
1
0
0
2
0
0
4
0
2
2
3
0
0
0
0
0
1
0
1
0
4
0
1
0
0
1
0
0
2
2
0
0
2
1
2
0
0
0
2
0
1
0
0
0
1
0
0
1
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
2
2
0
0
1
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
2
0
2
2
0
1
0
0
1
1
1
2
0
0
0
1
1
1
3
0
0
3
1
2
0
0
0
0
0
1
0
0
0
0
0
2
2
0
1
0
0
0
2
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
1
2
1
1
2
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
2
1
2
1
0
0
0
1
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
1
0
0
0
2
0
2
0
0
0
2
1
0
1
0
0
0
0
4
0
1
1
2
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
2
1
0
0
0
1
2
0
1
1
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
1
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
1
0
1
0
0
0
0
1
0
0
1
1
0
2
0
0
0
0
0
3
0
0
0
2
0
0
0
1
0
2
0
0
0
1
0
0
1
0
2
0
2
1
0
0
1
1
0
0
0
2
0
0
1
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
1
3
0
2
2
1
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
1
1
0
0
2
0
0
0
3
0
1
0
1
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
1
2
0
0
1
0
0
2
2
0
0
2
0
0
0
0
1
2
0
0
0
0
3
2
0
0
0
0
1
0
2
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
12
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
4
0
0
2
1
0
0
0
1
0
0
0
1
0
2
0
0
2
0
3
0
1
0
0
0
0
2
0
0
1
0
0
0
1
1
0
2
0
0
0
0
1
2
2
0
0
1
0
4
3
2
0
0
0
1
0
0
0
0
2
1
1
2
0
0
0
0
0
0
0
0
2
2
2
1
0
0
0
0
2
0
1
0
0
1
2
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
1
2
0
1
1
0
1
1
0
0
1
1
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
3
0
0
0
1
0
0
2
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
8
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
1
1
2
0
0
2
1
0
0
1
0
0
0
0
0
3
0
0
0
1
2
0
0
0
1
4
0
1
0
0
0
0
2
0
0
1
0
0
0
0
2
0
1
0
0
0
1
0
0
0
1
2
0
2
2
2
2
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
1
2
0
1
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
1
0
4
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
2
1
1
0
0
0
1
0
2
1
2
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
4
2
0
2
1
0
0
0
2
1
2
0
2
0
0
1
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
2
0
0
0
1
0
2
2
0
1
0
1
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
1
0
1
2
1
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
3
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
1
0
0
2
0
0
0
2
0
0
0
0
2
1
1
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
2
0
0
0
0
0
1
0
1
2
2
1
0
0
2
0
0
0
0
0
2
0
0
0
0
3
2
0
0
0
1
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
1
0
0
0
1
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
1
0
2
2
0
1
0
0
2
1
0
2
0
3
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
1
1
2
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
2
2
0
2
0
1
0
0
0
2
0
4
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
1
2
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
2
0
1
0
0
1
0
0
2
0
1
0
0
2
0
0
0
3
0
1
1
0
0
1
1
0
0
1
0
1
1
1
0
0
0
0
0
2
0
2
1
1
0
0
0
0
0
2
0
2
0
2
0
2
0
0
0
0
0
2
2
0
0
0
3
5
0
0
3
0
0
0
0
0
2
0
0
3
2
1
2
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
1
1
0
0
0
1
0
0
0
1
0
0
3
2
3
0
0
0
0
2
0
2
0
0
0
2
0
2
1
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
2
0
2
1
0
0
1
0
0
0
2
0
0
1
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
1
0
2
0
0
0
0
0
1
0
2
1
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
1
0
1
1
0
1
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
11
2
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
2
1
0
0
0
0
0
0
2
1
2
0
0
0
1
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
1
2
1
1
1
0
2
0
2
0
0
0
0
2
1
0
0
0
1
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
2
0
4
0
0
1
0
0
0
0
0
1
2
2
2
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
2
0
0
2
1
0
2
0
0
0
1
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
2
1
0
0
2
0
0
0
0
0
1
0
1
0
0
2
1
0
0
0
2
0
0
0
0
0
1
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
1
1
0
1
2
0
0
0
2
0
0
1
0
0
0
0
1
0
0
2
2
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
2
0
0
0
0
1
2
1
0
0
0
3
0
2
2
2
0
0
1
2
2
0
1
0
0
0
4
0
2
1
1
0
0
0
0
0
0
0
2
2
0
0
2
1
2
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
3
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
3
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
1
1
0
0
0
1
0
1
0
0
2
0
0
1
0
8
2
2
1
0
1
2
7
0
0
0
0
2
0
1
0
0
2
2
2
0
1
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
2
0
3
0
0
0
0
1
0
1
1
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
5
1
0
0
0
2
2
2
1
0
1
0
2
0
0
1
0
0
0
3
0
0
2
0
0
2
0
2
0
2
1
0
0
0
1
0
0
2
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
1
0
2
3
2
3
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
3
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
1
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
3
1
0
0
0
0
0
0
2
0
0
1
0
0
1
0
3
0
0
1
0
0
0
2
0
0
0
2
1
0
0
1
0
0
0
6
0
1
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
1
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
1
2
1
1
0
2
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
1
2
1
0
0
0
1
1
0
1
0
1
1
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
1
0
0
0
1
0
2
0
1
0
2
1
0
0
2
1
0
0
0
1
1
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
2
2
0
2
2
0
0
0
2
1
3
0
1
2
1
0
2
1
0
0
2
0
4
0
0
2
0
0
3
0
0
0
0
0
0
1
0
1
0
2
1
0
0
0
0
0
1
0
0
0
0
3
1
2
1
1
0
0
2
2
2
0
0
2
0
1
2
0
0
2
5
2
2
1
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
1
2
0
0
0
0
1
1
0
0
0
2
0
0
0
1
0
1
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
2
0
2
0
0
2
1
0
0
0
0
0
2
0
0
2
0
1
3
2
0
0
1
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
2
0
1
2
0
0
2
2
2
0
0
1
0
1
0
0
1
2
0
0
8
3
2
0
0
0
1
0
2
0
0
1
0
0
1
0
2
0
0
2
0
0
0
0
4
0
0
1
0
2
2
0
1
1
0
0
0
2
0
0
4
0
2
2
0
0
0
1
1
1
0
0
2
2
1
0
1
1
0
0
0
1
2
0
1
0
0
2
0
1
0
0
0
0
0
0
3
2
0
1
1
0
0
1
2
0
2
0
0
1
0
1
0
0
0
0
0
1
1
1
2
0
0
0
0
2
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
2
2
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
2
2
0
0
1
0
1
1
4
0
0
2
0
0
0
0
2
0
1
0
0
3
2
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
2
0
0
0
0
0
2
0
0
1
0
1
2
0
0
2
2
1
1
0
0
0
0
0
0
3
2
2
0
1
0
0
0
2
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
2
0
1
3
0
1
1
0
5
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
3
0
2
2
0
0
1
0
2
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
2
0
2
1
2
0
0
0
2
2
0
0
1
0
0
0
0
0
0
1
1
1
1
1
0
2
0
0
3
1
0
2
0
2
0
0
0
2
1
2
1
0
2
0
1
3
0
2
0
1
0
1
0
1
0
1
0
0
1
2
1
0
0
1
0
2
1
1
0
0
0
1
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
2
0
0
2
0
0
0
0
1
1
2
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
1
2
1
0
0
0
0
0
1
0
1
0
1
0
0
2
1
1
0
2
0
2
1
1
0
2
0
2
0
0
2
0
2
2
1
0
2
1
1
0
2
2
0
0
1
0
1
2
0
0
1
0
1
0
0
2
0
1
0
0
1
8
0
0
0
3
0
0
0
0
1
2
0
0
1
0
1
0
0
0
3
0
0
1
0
1
0
1
0
0
0
0
0
0
1
2
2
0
0
0
1
0
1
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
1
1
0
0
0
0
0
2
0
2
0
0
0
2
0
1
0
1
1
2
2
0
0
0
0
0
0
3
0
0
0
1
2
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
5
0
0
2
0
0
2
0
3
2
0
0
0
2
0
0
0
0
0
1
2
0
0
0
1
2
0
0
2
0
0
7
0
0
0
0
5
0
0
0
1
0
2
0
2
0
0
1
0
0
0
2
0
0
0
0
2
2
1
0
2
0
0
0
0
0
2
1
0
2
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
1
0
2
1
0
2
0
0
0
0
1
2
0
0
2
0
0
0
1
0
2
0
0
1
0
0
0
1
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
1
2
1
2
0
0
0
0
0
3
0
0
2
0
1
0
0
2
2
2
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
1
2
0
0
0
2
1
0
2
2
0
0
0
2
0
2
0
0
0
0
2
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
2
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
1
0
1
0
0
0
2
0
2
0
2
2
1
0
0
0
0
1
0
2
1
0
0
0
0
1
0
0
0
0
2
8
0
0
0
1
2
0
2
0
0
0
0
1
2
2
2
2
0
1
0
1
0
0
2
2
1
2
2
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
1
0
2
0
1
0
0
0
0
0
2
3
0
1
0
0
0
0
3
0
2
0
0
0
0
0
0
1
2
0
0
1
1
0
0
1
0
0
0
0
1
0
0
1
2
0
1
0
1
0
0
1
2
0
0
0
1
0
1
0
1
0
2
1
0
5
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
5
1
2
0
0
0
1
1
0
0
0
0
3
0
0
1
0
0
0
1
0
0
2
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
1
0
0
2
2
0
2
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
2
1
0
0
0
2
1
0
0
0
2
1
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
2
0
3
0
3
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
2
0
1
1
2
1
0
2
1
2
0
0
0
0
0
2
2
2
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
1
0
0
0
1
2
0
0
2
0
0
1
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
1
1
0
0
2
0
0
0
0
0
1
0
2
1
0
2
1
0
0
0
0
0
0
0
1
1
0
0
1
2
1
0
0
1
0
0
4
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
2
0
0
0
0
1
1
0
2
0
0
1
0
2
2
0
1
0
2
0
0
0
2
0
1
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
1
2
0
0
0
1
0
0
1
1
1
0
0
0
0
0
2
1
0
0
2
2
0
0
2
1
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
2
0
2
0
2
1
2
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
2
0
1
2
0
2
1
1
0
3
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
3
1
1
0
0
0
2
0
3
0
0
2
1
1
0
1
0
0
2
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
1
0
1
1
0
0
1
0
1
0
1
0
0
0
0
1
1
0
1
0
0
0
2
0
2
2
0
0
0
0
0
0
2
0
0
1
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
1
2
1
0
0
5
2
0
0
1
0
0
2
2
2
0
0
1
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
2
2
1
0
2
0
1
0
0
2
0
1
1
0
1
1
1
0
0
0
4
0
0
0
1
2
0
2
2
0
0
0
1
2
2
0
0
2
0
0
0
2
2
1
1
2
2
3
0
0
0
2
0
0
1
0
0
1
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
1
1
2
1
2
0
0
0
3
2
0
0
0
0
1
1
0
0
0
0
0
0
2
1
0
2
0
0
2
0
3
0
0
1
0
0
0
0
0
0
1
0
0
2
0
2
1
1
0
0
2
0
0
2
3
0
1
0
0
1
1
0
0
2
0
0
0
0
0
0
2
2
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
2
0
0
0
0
0
0
0
1
2
18
0
0
2
0
2
0
2
0
2
0
2
0
0
1
0
0
0
1
0
0
1
1
0
1
0
0
1
1
2
0
2
2
0
0
2
0
0
2
0
0
2
2
2
0
1
2
2
0
1
0
0
0
0
2
0
0
0
3
1
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
2
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
1
0
2
1
0
0
0
0
0
2
1
1
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
2
0
0
0
0
1
0
0
0
0
0
2
2
3
0
0
3
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
2
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
2
2
0
2
1
1
1
0
0
0
0
2
2
2
0
0
0
0
0
0
0
1
0
2
0
0
1
0
2
0
0
2
0
0
0
2
2
0
0
1
2
2
0
2
0
0
1
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
1
0
3
0
0
0
0
1
0
0
7
0
2
0
0
1
0
0
0
0
1
0
0
3
0
0
0
1
0
0
0
0
2
0
0
0
3
0
0
1
0
2
1
0
7
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
1
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
3
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
2
0
1
0
0
0
2
0
0
0
0
1
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
2
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
1
0
0
0
2
1
3
0
0
0
2
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
2
0
0
0
0
0
1
1
0
0
1
0
1
1
2
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
2
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
2
0
1
0
3
1
0
1
2
0
2
0
2
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
2
0
0
0
1
0
6
0
0
0
0
0
0
1
1
1
0
0
1
0
1
2
1
0
2
0
0
0
0
0
0
0
1
2
0
1
1
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
5
0
1
0
0
1
0
0
0
1
3
0
1
0
0
1
0
0
0
0
2
0
2
2
0
0
0
3
0
0
1
1
1
1
2
0
2
0
0
2
1
2
0
0
0
0
1
2
0
0
0
0
1
0
2
2
0
0
0
0
0
1
0
1
0
0
0
0
2
1
0
0
0
0
1
0
0
3
2
0
1
0
2
0
0
4
0
1
0
0
0
1
0
1
1
0
1
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
2
1
0
0
0
1
2
0
1
2
0
1
0
1
0
0
2
0
1
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
2
1
2
0
0
1
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
2
4
0
3
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
4
1
0
2
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
2
0
0
2
0
0
0
0
0
1
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
2
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
2
0
2
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
2
0
0
0
1
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
5
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
2
0
1
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
2
3
2
0
2
0
0
2
0
3
0
0
1
0
0
0
2
2
1
2
0
0
0
0
1
0
0
0
0
0
2
1
1
0
1
0
1
0
1
0
0
0
0
0
2
2
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
2
2
0
0
1
0
2
2
1
0
3
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
1
2
2
0
2
0
2
2
0
1
1
0
0
0
0
0
0
0
1
1
2
1
0
2
0
0
0
2
0
0
2
0
1
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
1
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
2
2
1
0
4
7
0
0
2
0
0
0
0
2
0
9
0
0
0
0
2
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
2
0
0
0
1
1
0
2
0
0
1
0
2
2
0
1
0
0
0
0
0
1
2
0
2
0
0
0
0
1
0
2
1
2
0
0
2
1
0
0
0
2
2
3
0
0
1
2
0
2
0
1
0
1
2
0
0
2
2
0
0
0
0
0
8
2
0
1
1
0
0
0
2
0
0
0
0
1
0
0
2
2
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
1
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
1
2
0
2
0
0
2
0
0
1
2
1
0
2
0
1
1
0
2
0
0
2
0
1
0
1
0
0
0
0
0
0
2
1
0
0
1
1
0
1
0
0
0
1
1
0
2
0
0
0
3
3
0
2
0
1
2
2
0
0
1
0
0
2
0
0
0
0
1
2
1
0
0
1
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
3
0
0
2
1
0
2
0
2
0
2
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
1
0
2
1
0
0
0
1
0
0
0
0
6
0
0
2
0
2
2
0
2
0
1
1
1
2
0
2
0
0
0
2
1
0
0
0
2
0
0
1
2
2
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
1
2
0
0
0
2
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
3
2
2
0
0
0
0
0
0
0
2
1
4
0
0
1
0
0
0
0
0
3
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
1
2
0
0
0
0
2
0
1
2
0
0
0
4
0
1
1
0
0
1
0
0
1
0
0
1
2
1
0
10
0
2
2
0
0
0
0
2
2
2
0
0
2
0
2
0
7
0
0
0
0
1
0
0
0
0
0
0
2
0
2
4
0
0
0
2
0
2
0
0
0
0
0
2
1
3
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
2
0
0
1
1
0
1
0
0
1
2
2
1
2
2
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
2
2
0
0
0
0
2
1
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
1
0
3
1
0
0
0
0
2
0
1
0
3
0
0
0
2
0
0
0
0
0
2
0
1
0
2
0
2
0
0
2
0
0
0
0
0
0
0
3
0
0
0
1
0
1
0
0
0
2
0
0
2
0
0
0
1
0
0
0
1
1
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
2
2
0
0
0
0
0
1
2
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
2
0
0
1
3
0
0
0
1
2
1
0
0
0
0
0
0
0
1
0
0
0
2
0
2
2
0
1
0
1
1
0
1
2
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
1
0
2
0
1
0
0
0
0
0
2
2
0
0
1
0
0
2
2
3
1
1
2
0
0
1
0
0
0
0
0
1
0
0
1
1
2
0
2
1
0
2
1
0
0
0
0
0
0
0
2
0
3
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
2
0
2
0
0
1
0
0
0
1
0
0
1
0
0
3
0
0
0
0
2
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
5
0
0
3
1
0
0
0
1
0
1
0
2
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
6
2
0
2
0
0
1
0
0
0
2
0
0
2
0
0
3
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
1
0
0
0
0
0
2
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
2
0
1
2
0
0
2
0
0
0
0
3
0
0
0
1
1
0
2
1
0
2
0
0
0
0
0
1
0
2
1
2
0
0
0
0
2
1
0
0
0
3
2
0
0
0
0
0
0
0
0
2
5
2
2
0
0
0
2
1
0
0
0
0
0
1
0
0
3
0
2
0
2
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
3
0
5
0
1
0
0
1
0
0
1
1
0
1
0
2
0
1
0
0
2
0
0
0
0
0
1
0
0
2
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
1
2
0
0
2
1
0
0
1
0
1
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
1
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
2
0
0
0
2
2
1
0
0
0
0
0
0
1
2
0
2
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
1
1
0
2
0
0
0
2
0
0
0
0
1
2
0
1
0
1
1
2
0
0
0
0
2
0
0
1
0
0
0
2
1
0
0
1
2
0
0
1
0
0
1
0
0
0
3
0
0
0
2
0
0
0
0
0
0
2
2
1
0
2
1
0
2
2
0
1
0
2
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
1
2
0
0
1
0
1
0
0
1
0
1
3
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
1
0
2
2
0
0
0
2
0
0
0
1
0
0
2
0
2
2
0
0
0
0
0
0
3
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
2
1
1
2
0
0
2
1
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
3
0
1
1
0
2
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
2
2
1
0
0
1
0
0
1
0
0
0
1
0
0
2
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
8
1
0
2
1
0
0
1
0
0
0
0
0
3
0
1
0
0
0
1
6
0
0
0
0
2
1
0
1
0
2
0
2
0
0
0
0
2
0
0
0
1
0
1
1
0
2
1
2
0
2
1
0
0
0
0
2
2
2
0
0
0
2
0
1
1
0
1
4
2
0
0
0
2
1
0
1
0
0
0
0
1
0
1
0
1
3
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
1
0
1
0
0
0
1
0
0
3
1
0
0
1
0
0
2
0
1
0
2
1
0
0
0
0
0
1
2
0
0
2
2
0
0
0
1
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
2
2
1
0
0
2
1
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
3
0
0
0
0
1
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
1
2
2
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
7
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
2
4
0
1
0
0
1
0
1
0
0
0
0
2
0
0
5
0
0
0
0
1
2
1
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
2
2
0
0
0
2
2
0
1
0
0
0
0
1
2
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
2
0
1
5
0
0
0
1
0
2
1
3
1
0
0
0
1
0
1
0
1
0
0
2
1
0
0
0
1
1
0
0
0
1
0
0
2
0
0
2
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
1
0
0
3
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
2
0
0
0
0
0
4
0
1
0
0
0
3
0
0
1
0
0
0
1
0
0
0
0
1
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
2
0
0
2
0
2
0
1
0
0
0
1
0
0
0
0
0
0
2
0
1
1
0
0
3
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
1
0
2
1
0
0
0
0
0
2
0
1
0
2
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
9
1
1
3
0
2
1
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
2
3
0
0
0
1
0
0
0
0
0
1
0
2
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
1
0
2
1
1
0
0
2
0
0
2
0
0
0
0
0
0
0
2
1
0
0
1
1
0
1
0
1
0
1
0
1
1
1
1
2
0
1
0
0
2
0
2
0
0
2
0
0
0
0
0
1
0
0
0
1
3
0
2
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
1
2
2
1
0
0
0
0
2
2
0
0
1
1
0
0
3
0
0
2
2
2
0
1
0
0
0
0
0
0
1
1
2
0
0
0
0
0
4
0
2
1
1
0
3
0
0
1
0
1
0
0
0
0
0
2
0
2
2
2
0
2
2
0
0
0
2
1
0
0
1
0
0
0
0
1
0
0
1
1
0
2
0
1
1
0
2
2
2
0
0
1
1
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
1
0
3
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
2
1
0
0
0
3
0
0
1
2
0
0
0
0
0
0
2
0
0
2
2
0
0
2
0
0
1
2
1
0
0
2
0
0
0
0
0
1
2
0
2
0
1
0
1
0
0
0
1
0
0
2
0
0
1
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
1
0
0
2
4
0
2
0
0
0
1
1
0
0
0
0
2
1
0
1
0
1
0
1
0
0
0
3
0
0
0
0
2
2
0
1
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
2
0
0
2
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
2
0
0
0
2
1
0
1
0
0
2
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
1
0
1
1
0
2
2
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
2
0
1
1
0
0
0
3
2
0
0
1
0
2
0
0
1
0
0
2
0
1
1
0
0
0
1
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
2
0
2
1
2
2
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
3
0
3
1
0
1
2
2
0
0
1
2
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
3
1
1
1
1
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
2
0
0
1
2
1
0
0
0
1
0
0
1
0
1
0
0
0
0
2
0
1
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
1
0
2
0
2
1
0
1
1
2
1
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
2
0
1
0
0
1
0
1
0
1
0
0
2
0
2
0
0
0
2
0
2
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
1
0
0
0
1
1
2
1
0
0
1
1
0
1
0
1
0
1
2
0
0
0
2
1
2
0
0
0
1
1
1
1
1
0
1
0
2
0
0
0
0
2
0
2
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
2
2
0
0
2
2
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
2
2
0
0
0
0
1
2
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
2
0
2
0
0
2
1
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
1
2
1
0
0
2
0
0
0
0
1
1
1
1
1
0
1
0
2
0
2
0
0
0
1
1
0
2
0
0
1
1
0
2
2
0
2
1
0
0
0
0
0
0
2
2
0
0
2
0
1
0
0
0
1
0
0
0
2
1
0
0
0
0
1
1
1
0
1
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
2
1
2
0
1
0
0
1
0
2
0
0
2
0
0
2
1
0
1
0
0
1
2
0
0
1
2
0
2
2
0
1
0
0
5
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
3
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
2
0
2
0
1
0
0
1
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
2
1
0
0
7
0
0
1
0
0
0
0
0
1
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
1
0
1
0
0
2
2
0
2
0
0
0
0
0
0
0
1
0
0
2
1
0
0
1
0
0
0
0
2
0
0
1
0
0
1
0
1
2
0
0
2
0
1
1
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
3
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
1
0
2
2
1
0
0
0
1
0
0
0
0
2
0
0
0
1
2
0
1
0
1
2
1
2
0
0
2
0
0
0
1
0
3
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
1
0
0
0
3
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
1
1
0
2
1
0
2
1
0
2
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
2
0
0
1
0
0
0
2
0
1
0
0
0
0
0
2
2
0
3
0
0
0
0
0
0
0
0
3
1
0
1
2
0
0
0
2
0
0
0
2
2
1
0
2
0
0
0
1
0
0
0
0
0
0
1
4
2
0
1
0
0
0
1
0
3
2
0
0
0
3
1
0
0
1
1
2
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
2
1
1
0
0
0
0
0
2
0
1
2
0
0
0
0
0
2
2
0
0
0
0
1
0
3
1
0
0
2
2
0
0
3
0
0
0
0
0
1
0
0
0
1
0
3
0
0
2
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
1
0
0
1
2
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
2
1
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
2
0
0
0
0
2
0
0
2
1
4
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
1
1
0
1
0
1
0
2
0
2
2
0
1
2
0
0
0
1
2
0
2
0
0
0
1
0
0
2
0
1
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
1
1
0
2
0
0
0
1
1
0
0
0
2
0
0
0
0
2
0
0
0
2
1
0
1
1
0
1
1
0
0
2
2
0
0
0
1
1
0
0
0
1
1
1
0
0
2
0
2
0
0
0
0
1
0
0
0
2
0
0
2
1
2
0
0
0
0
2
0
2
1
0
1
2
0
2
0
0
0
0
0
0
0
3
2
0
0
4
2
0
0
0
2
0
0
1
0
0
0
2
0
0
2
1
0
0
1
1
0
2
0
0
0
0
0
0
0
0
2
0
1
1
1
0
2
0
0
0
0
0
0
0
0
2
2
4
0
2
0
0
0
1
2
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
1
3
0
0
2
0
0
0
1
1
2
0
0
0
0
0
2
0
1
1
0
2
1
0
0
0
3
0
0
0
0
2
0
0
0
2
0
1
0
0
0
2
0
1
2
2
0
1
0
1
0
0
0
2
0
0
2
2
2
0
1
1
0
0
0
2
3
0
0
0
1
0
0
3
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
2
1
0
1
0
0
2
0
1
1
0
0
0
0
1
2
0
0
0
1
0
0
2
1
0
0
0
0
0
2
0
0
0
3
2
2
0
3
0
1
0
0
1
1
0
1
1
0
1
0
0
0
0
2
0
2
2
2
0
0
0
1
1
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
1
1
0
2
2
0
0
0
0
0
2
0
2
0
1
2
2
2
4
0
2
0
0
3
0
0
1
0
0
0
1
2
0
0
0
3
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
3
0
1
0
0
0
1
0
2
0
2
0
0
1
0
0
2
2
0
3
2
3
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
2
0
3
2
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
3
0
0
2
0
1
0
0
4
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
3
0
1
2
2
0
1
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
3
2
2
2
0
0
0
1
5
2
0
2
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
3
2
7
1
2
0
2
0
1
1
0
1
1
2
0
1
0
0
2
0
0
1
0
0
3
0
0
0
0
2
2
0
0
0
0
0
3
2
1
0
0
0
1
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
2
2
0
0
1
0
1
0
0
0
0
0
0
2
1
2
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
2
1
1
0
0
2
0
0
1
2
0
1
0
1
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
1
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
3
2
3
0
0
0
0
0
0
2
1
0
0
2
0
2
1
1
0
1
0
0
2
0
0
0
1
1
1
2
1
0
0
0
0
0
2
2
0
2
0
0
1
1
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
1
0
0
2
0
0
0
0
2
0
1
2
0
0
2
0
1
2
1
0
0
2
0
2
0
0
2
0
0
0
3
0
0
1
0
0
0
0
0
0
0
2
0
1
2
0
2
0
0
0
0
0
1
0
1
2
1
0
1
1
1
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
1
0
1
1
0
2
0
0
2
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
1
0
1
0
1
0
0
0
0
0
0
0
2
0
1
2
0
0
0
1
0
0
0
0
0
1
0
1
0
0
2
0
0
0
2
0
0
0
0
0
1
2
2
1
1
0
2
0
0
0
2
0
0
0
0
1
0
0
1
0
3
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
1
2
0
0
2
0
1
0
0
0
1
0
2
0
1
0
0
2
2
0
1
0
0
2
1
0
3
1
0
2
0
0
0
0
1
0
1
0
0
0
0
1
0
0
3
1
0
0
0
0
1
0
1
0
2
0
0
0
0
1
1
0
1
1
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
2
1
2
2
0
0
0
0
0
2
0
0
1
2
2
0
0
0
0
2
1
0
0
1
0
0
0
1
3
0
0
0
0
1
2
0
2
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
2
2
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
1
0
1
2
0
0
0
1
0
1
0
1
0
0
0
5
0
0
0
0
2
0
2
2
2
0
2
4
0
1
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
1
2
1
0
0
2
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
1
0
0
0
1
2
1
2
1
1
0
0
2
1
0
2
2
0
1
1
0
0
0
2
0
0
1
1
0
0
0
0
0
2
0
1
2
0
0
0
1
0
1
0
0
2
1
0
2
2
0
0
0
0
3
0
2
1
0
0
0
2
0
1
0
2
0
0
0
1
0
0
2
0
0
0
0
1
0
2
3
0
0
2
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
2
0
0
0
1
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
2
1
1
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
2
0
0
3
0
0
0
0
0
0
2
1
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
2
0
1
1
1
2
0
1
0
0
1
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
2
0
2
2
2
0
0
0
0
0
0
0
2
0
1
0
0
0
2
1
0
0
0
0
1
0
0
0
1
0
0
3
0
2
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
2
0
2
0
1
1
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
1
1
0
3
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
7
2
2
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
1
0
2
1
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
1
0
0
2
0
0
0
2
2
0
0
0
1
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
2
0
1
0
0
0
0
0
2
0
2
0
0
2
1
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
1
2
2
3
1
0
1
0
2
2
0
4
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
2
1
2
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
1
2
2
0
0
0
1
0
1
3
0
1
2
0
0
0
1
0
0
0
0
2
1
0
1
0
0
0
2
2
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
1
1
0
2
0
1
0
1
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
1
0
2
0
1
0
0
0
1
2
0
0
1
0
0
1
0
2
0
0
0
1
3
0
1
0
0
2
0
0
2
0
0
1
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
2
0
0
2
0
0
2
1
1
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
3
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
1
2
2
2
0
1
0
2
0
0
0
2
0
0
2
0
0
2
1
0
0
0
1
1
0
2
0
0
0
0
1
0
1
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
1
2
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
1
1
1
2
2
2
0
0
1
2
2
0
0
1
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
2
0
2
0
0
0
0
1
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
3
0
2
2
0
0
2
0
1
0
0
0
0
2
2
0
0
0
0
0
3
0
1
0
2
0
0
0
0
0
2
0
0
0
0
1
0
1
2
0
0
2
2
2
0
0
0
0
1
0
1
2
1
0
1
1
0
0
0
0
0
0
1
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
2
0
0
0
1
0
1
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
2
0
4
0
1
0
0
0
0
1
2
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
1
0
0
0
2
2
0
1
0
1
2
0
1
3
0
0
3
1
0
0
4
2
0
0
1
2
1
1
0
0
1
0
0
0
2
2
0
0
1
2
7
0
0
2
0
0
0
1
1
0
1
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
1
1
1
0
0
3
0
0
2
2
0
2
1
1
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
1
0
0
0
0
2
0
2
1
0
1
0
0
1
1
0
0
2
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
1
1
0
0
0
2
0
3
1
0
1
0
0
1
2
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
2
2
2
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
2
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
1
0
0
1
0
0
0
0
2
1
2
2
1
0
1
1
0
0
0
0
0
0
2
1
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
3
2
0
1
0
0
0
2
1
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
1
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
2
0
2
0
0
0
1
0
0
1
0
1
0
0
0
0
2
0
0
0
2
1
2
0
0
0
0
0
2
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
2
3
0
0
0
2
0
0
0
2
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
3
0
0
0
1
0
2
1
1
2
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
2
0
0
0
1
0
0
1
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
1
2
0
2
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
1
1
0
0
2
1
2
0
0
0
0
2
0
1
1
0
0
2
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
1
1
0
3
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
2
4
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
3
0
0
0
1
6
0
0
1
0
2
0
0
0
3
1
0
0
0
0
0
0
0
0
2
1
0
0
0
2
8
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
1
0
2
1
0
2
0
2
1
2
2
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
2
1
0
0
0
0
0
2
0
0
0
2
2
0
2
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
1
1
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
2
2
0
0
2
2
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
1
4
0
0
1
2
0
0
1
0
0
0
2
0
1
2
2
0
6
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
2
2
0
1
0
0
0
3
0
0
0
1
1
0
1
2
2
3
0
0
0
0
0
0
1
2
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
3
1
1
0
0
3
0
2
0
0
2
0
0
0
0
1
0
2
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
2
0
1
0
1
0
0
2
0
0
0
1
0
0
2
0
1
1
1
1
0
0
2
0
0
0
0
2
0
2
0
2
0
0
0
2
0
2
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
1
1
2
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
2
0
1
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
2
2
0
0
2
1
0
0
0
0
1
6
1
2
2
0
2
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
2
1
2
0
0
2
0
3
2
0
2
2
0
2
0
0
2
0
1
0
1
0
0
0
0
1
3
1
0
0
0
0
1
0
2
0
0
0
0
2
0
0
1
0
1
0
0
0
2
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
2
2
2
0
0
1
0
0
0
2
1
0
2
0
2
0
0
0
1
2
1
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
2
0
1
0
2
2
0
1
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
4
0
0
1
1
0
2
1
0
0
1
1
0
0
2
1
1
1
1
2
2
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
2
1
1
0
1
2
0
0
1
0
1
1
0
0
0
0
0
1
1
0
0
1
0
3
2
1
3
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
1
0
0
0
2
3
0
0
1
0
0
0
4
2
1
2
2
0
2
0
0
1
1
1
0
0
0
1
0
2
0
0
0
2
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
2
2
1
0
0
0
0
0
0
1
3
4
0
0
0
0
1
1
0
1
0
0
2
2
0
1
2
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
1
2
1
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
1
1
0
0
0
2
0
0
0
0
1
0
0
4
2
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
1
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
1
2
0
1
0
0
0
1
1
1
3
2
1
0
0
2
0
0
0
2
0
0
0
3
0
0
1
0
1
0
3
2
2
0
0
0
2
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
2
0
1
0
0
2
2
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
1
1
0
1
0
0
0
1
0
0
2
1
0
2
0
0
0
2
2
1
0
0
2
0
1
2
0
0
1
2
0
0
1
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
1
2
0
0
0
2
0
2
0
0
0
0
1
2
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
2
2
0
0
0
0
0
0
0
1
1
0
1
2
0
0
1
0
0
0
4
0
0
0
0
1
1
0
0
2
0
0
0
2
1
0
1
1
0
1
0
0
0
1
1
0
0
2
2
0
0
2
0
1
1
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
1
3
0
0
0
0
2
1
1
0
1
0
0
1
0
0
1
0
0
2
0
0
2
3
0
1
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
1
5
0
2
0
0
1
0
1
1
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
3
0
1
4
2
2
0
0
0
1
0
4
0
0
1
0
0
2
1
0
0
0
0
1
0
1
0
2
0
1
0
1
1
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
1
1
1
0
0
0
0
1
0
0
2
2
0
2
0
1
0
0
1
0
2
2
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
4
1
2
1
1
2
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
14
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
3
2
0
0
4
1
0
0
0
0
2
0
0
1
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
2
2
0
0
0
0
0
3
2
3
2
1
0
0
0
3
2
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
2
2
0
0
1
0
2
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
2
0
0
1
1
2
0
0
0
2
0
2
2
0
0
0
1
0
1
1
3
0
2
2
0
2
2
0
2
1
2
0
1
0
0
0
0
1
2
0
0
2
2
1
0
0
0
0
0
2
2
1
0
0
0
0
0
0
1
0
0
0
0
2
0
1
4
2
0
0
1
0
0
0
1
0
0
0
1
0
1
2
0
0
2
0
2
2
2
0
0
0
2
0
0
0
0
1
1
0
0
0
0
1
0
1
0
1
0
0
0
0
1
2
0
0
0
0
0
1
2
0
0
0
1
0
2
0
0
0
2
2
0
2
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
1
1
3
2
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
3
0
2
2
1
1
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
2
0
2
5
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
1
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
2
0
2
1
0
0
0
2
0
0
0
0
1
1
0
1
2
0
1
3
0
1
0
2
0
0
1
1
1
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
1
1
0
0
0
1
0
2
0
2
1
2
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
2
0
0
0
1
0
2
0
0
1
2
0
1
2
0
0
0
2
0
2
2
0
1
0
0
0
0
0
3
0
0
0
2
2
0
2
0
1
0
0
0
0
4
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
3
1
1
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
2
1
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
5
0
1
1
2
0
0
0
0
2
2
0
0
0
0
3
1
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
2
0
1
0
0
2
0
2
2
4
1
0
0
0
0
0
0
2
0
1
0
1
2
0
0
0
0
0
2
0
0
1
1
0
0
0
2
0
0
1
0
0
1
0
0
2
0
2
0
0
1
0
0
0
2
1
0
0
0
0
1
0
0
0
0
2
0
0
2
1
3
0
2
0
0
0
0
0
2
0
2
0
0
1
0
0
0
2
0
1
1
0
2
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
1
0
1
0
1
0
2
0
0
1
0
0
0
0
2
0
2
2
1
0
2
0
2
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
1
0
1
2
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
4
0
2
2
2
0
0
0
2
0
0
0
4
1
1
1
2
0
0
0
1
0
0
0
0
0
2
2
0
0
2
0
0
1
0
0
6
0
0
2
2
0
0
1
1
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
2
2
1
0
0
0
2
2
0
0
0
0
2
0
0
0
3
0
1
1
0
0
2
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
1
1
1
0
2
0
0
2
0
0
2
0
1
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
1
1
4
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
3
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
2
2
2
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
2
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
3
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
3
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
5
0
2
1
0
1
1
2
3
1
0
6
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
3
0
0
0
0
0
1
0
2
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
5
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
2
1
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
1
0
1
0
1
0
0
1
0
1
0
0
0
2
0
0
2
0
0
0
0
0
1
0
1
1
0
0
0
0
0
2
0
1
0
1
3
0
0
1
0
0
0
1
3
0
0
0
1
2
0
0
0
2
0
1
0
0
0
0
0
2
0
0
2
0
0
0
1
1
2
0
0
0
0
0
2
2
3
0
2
0
0
3
3
2
0
2
1
0
0
2
0
2
1
0
0
2
0
2
0
0
1
0
0
1
0
0
0
0
2
1
0
1
1
0
0
2
0
0
1
0
0
2
1
0
2
0
0
1
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
2
1
0
0
0
1
0
2
0
0
0
0
1
0
2
0
1
0
0
0
0
0
2
0
2
1
1
0
0
1
0
2
0
0
0
0
0
1
0
0
1
0
1
0
0
2
2
3
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
2
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
1
0
1
0
0
2
0
0
1
0
0
0
0
1
2
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
2
0
0
2
2
1
1
0
1
0
0
0
2
0
2
2
0
0
0
0
0
3
0
0
1
0
0
0
0
2
0
0
0
2
0
0
2
0
0
1
0
2
2
0
0
2
0
0
0
0
1
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
2
0
0
1
0
0
0
2
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
1
2
2
0
0
1
0
2
0
2
0
0
0
0
0
1
2
2
0
0
2
1
1
0
0
0
2
0
0
0
2
0
0
0
2
0
1
0
0
1
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
2
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
1
0
2
0
0
0
2
1
3
2
0
0
0
0
1
0
1
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
1
1
0
0
0
2
0
0
2
0
0
1
0
0
0
0
1
0
2
0
2
0
1
0
0
2
0
0
1
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
2
0
2
2
0
0
0
0
0
0
1
1
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
3
0
2
2
1
0
0
0
0
0
0
2
0
0
0
0
1
1
1
0
0
0
0
2
2
1
2
0
0
0
0
2
2
0
0
0
0
0
0
1
2
0
0
0
2
2
1
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
3
1
2
1
0
1
3
0
3
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
1
0
0
6
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
4
0
0
0
0
2
2
2
0
1
1
0
3
0
0
2
0
0
0
0
1
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
2
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
1
0
1
0
1
1
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
2
1
0
4
1
0
0
0
0
0
0
0
0
2
0
2
1
1
1
1
0
2
0
0
0
0
0
1
1
0
3
3
0
0
0
1
1
1
0
0
0
0
0
1
0
0
2
1
0
0
1
0
0
0
2
2
0
2
0
0
0
0
0
0
2
1
0
0
0
2
0
4
0
1
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
3
0
0
0
0
0
0
2
0
1
1
0
0
0
0
2
0
0
0
1
0
1
2
0
0
1
1
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
4
2
0
0
2
2
0
0
2
0
3
2
0
0
2
0
0
0
0
1
0
1
2
2
1
1
1
0
2
0
0
0
2
0
1
0
2
1
0
0
1
0
0
1
0
1
0
0
2
2
1
0
0
1
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
2
0
0
2
0
0
1
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
1
2
1
0
0
3
0
0
1
0
0
0
2
1
0
0
0
0
2
2
0
2
0
0
2
2
0
0
2
0
0
1
0
0
1
2
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
1
2
1
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
2
2
1
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
2
0
0
0
0
1
1
2
0
0
2
1
0
1
2
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
2
0
0
1
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
1
2
0
0
0
2
0
0
0
0
1
0
2
3
2
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
2
5
0
0
0
2
2
0
0
2
0
0
0
0
0
0
2
1
1
1
0
0
1
0
0
1
0
0
2
0
1
1
0
2
0
1
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
2
0
2
0
2
0
1
1
1
2
0
0
0
0
0
1
2
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
2
2
2
2
0
0
0
0
0
1
1
2
4
0
0
0
0
0
0
3
0
2
1
0
1
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
1
0
0
0
0
1
0
1
0
0
0
2
0
1
2
4
0
0
2
1
0
1
1
0
0
1
0
0
1
2
0
1
0
2
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
1
0
0
0
2
0
0
0
1
0
4
1
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
3
0
1
1
2
1
0
2
2
0
1
1
2
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
2
2
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
6
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
3
0
2
0
1
0
0
1
1
0
0
0
0
0
2
1
2
0
0
1
0
2
4
0
0
0
0
0
3
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
2
0
1
2
1
1
1
0
2
1
0
0
0
0
0
1
0
1
0
0
0
0
2
1
0
4
0
0
2
0
0
0
1
0
0
2
0
1
0
0
1
1
0
1
0
0
0
1
2
0
3
1
2
0
0
0
0
1
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
3
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
2
0
1
0
2
0
2
0
0
1
0
0
2
2
0
0
0
0
0
0
1
0
0
1
1
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
4
1
0
0
0
1
0
0
0
1
1
0
0
0
1
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
2
2
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
1
2
0
0
2
2
2
1
0
0
1
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
1
1
1
1
0
0
1
2
1
0
0
0
1
0
2
4
0
0
2
0
0
2
1
0
0
1
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
1
1
0
0
1
3
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
2
1
1
0
0
0
1
0
2
1
0
0
0
2
1
0
0
0
2
0
1
0
0
0
1
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
2
0
0
2
0
0
1
0
1
2
1
1
0
1
0
1
0
1
1
0
0
1
0
0
2
1
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
2
0
1
0
1
1
0
1
12
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
1
2
0
0
0
1
0
0
0
3
0
0
1
0
0
1
2
0
3
0
1
0
0
0
1
0
2
1
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
2
0
0
0
0
0
2
1
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
2
0
0
1
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
2
0
0
2
1
0
0
0
0
2
0
1
0
1
2
0
0
2
1
0
0
0
0
0
2
0
1
0
0
0
2
0
2
2
0
0
2
0
0
0
0
0
0
0
0
2
2
0
1
0
2
2
0
0
1
0
2
0
0
0
2
0
3
0
2
2
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
1
0
0
1
0
0
2
0
0
0
0
2
0
2
1
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
3
0
0
1
0
1
0
0
1
2
2
2
0
0
2
0
2
0
1
0
1
1
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
1
2
0
2
2
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
1
1
2
0
0
0
0
2
0
0
0
0
1
0
1
1
0
3
0
1
2
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
3
1
2
0
0
0
1
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
4
2
0
0
2
4
0
1
0
0
0
0
0
1
0
0
0
2
0
1
1
2
0
0
2
2
2
0
0
1
0
0
2
4
0
0
0
0
2
2
0
0
0
4
0
1
0
0
2
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
1
1
1
2
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
2
0
0
1
3
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
2
2
0
0
1
1
1
1
1
2
0
0
2
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
2
1
1
1
0
0
0
0
0
0
0
2
0
0
0
4
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
2
1
0
0
2
2
0
1
3
0
2
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
3
1
0
0
1
2
0
2
0
0
4
0
0
0
0
0
0
0
0
0
1
0
2
2
1
1
0
3
0
2
1
0
0
0
2
0
1
0
0
1
2
2
0
1
1
0
2
0
0
0
0
1
1
0
1
1
0
0
0
2
0
1
1
0
2
0
2
0
1
0
0
2
0
1
2
0
0
2
2
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
1
2
1
1
1
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
2
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
2
1
2
0
0
2
2
0
0
0
1
1
0
1
0
3
0
1
0
0
0
1
0
0
0
0
1
0
1
1
2
1
0
1
2
0
0
1
0
0
0
0
0
1
2
0
0
1
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
3
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
3
0
0
0
0
0
0
0
0
1
1
2
1
2
0
0
0
0
0
2
2
0
2
1
1
0
2
0
0
1
2
1
0
1
2
2
0
0
2
0
0
2
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
3
2
2
0
0
1
2
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
1
1
0
0
0
0
1
1
2
0
0
0
0
2
3
0
1
0
0
2
1
2
1
2
1
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
2
2
0
2
0
0
0
1
0
0
1
0
2
2
0
0
0
5
0
0
1
0
1
0
0
0
0
0
2
0
0
2
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
1
0
2
1
0
2
0
2
0
0
2
2
2
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
3
0
0
2
0
0
0
0
0
3
0
1
2
0
0
0
0
0
0
2
0
0
2
0
0
1
2
0
2
0
0
0
0
2
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
1
0
0
1
2
0
0
3
1
0
0
0
8
2
0
2
2
0
0
1
2
2
0
1
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
1
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
1
0
0
1
2
0
2
0
2
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
3
0
1
0
2
0
0
2
0
0
1
2
1
2
2
0
0
0
1
0
0
1
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
3
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
1
0
0
0
1
0
0
0
0
1
1
1
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
2
3
0
0
1
3
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
2
0
1
0
2
2
2
1
0
2
3
1
2
3
1
0
0
0
2
0
0
0
1
0
1
0
2
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
2
0
1
0
1
1
2
1
0
0
1
1
0
1
0
0
0
1
0
0
1
1
0
2
0
2
0
2
0
2
2
0
0
0
2
3
3
1
0
0
3
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
3
0
0
3
1
0
0
0
2
0
0
0
0
0
1
2
2
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
3
0
0
1
0
2
0
0
1
0
4
0
0
4
0
2
0
0
0
1
1
0
0
0
1
1
2
0
0
0
0
0
0
0
3
2
0
0
0
0
1
1
1
1
0
0
2
2
0
0
0
1
0
2
0
1
1
0
0
0
0
1
0
0
1
0
1
2
0
1
2
0
1
2
1
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
1
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
2
0
4
0
0
1
0
0
0
0
0
0
0
1
1
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
1
1
0
1
0
2
0
2
0
0
2
0
0
1
0
0
0
1
0
0
1
0
0
0
1
2
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
2
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
1
0
0
1
1
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
1
2
1
0
0
0
0
2
0
0
0
0
1
2
1
0
2
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
3
0
0
0
2
0
2
3
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
1
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
2
1
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
4
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
1
0
2
0
2
0
0
0
0
1
2
0
0
1
4
0
0
0
0
0
1
0
1
0
0
2
0
0
2
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
1
0
0
0
1
0
0
0
1
2
0
0
0
2
0
3
0
0
0
1
0
2
1
1
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
1
0
1
2
1
2
0
2
2
0
0
0
2
0
0
2
0
0
2
2
0
0
2
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
1
0
1
0
0
1
2
1
0
0
0
0
0
0
2
0
0
0
1
1
2
0
2
1
0
2
3
0
0
1
0
1
2
2
0
0
0
0
0
0
1
2
0
0
5
0
0
0
2
1
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
1
2
0
1
0
1
1
1
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
1
0
0
2
0
0
4
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
1
0
2
0
0
2
1
0
0
1
2
0
2
0
1
0
2
0
0
2
0
3
0
0
0
0
1
0
1
0
0
2
2
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
6
1
1
1
0
0
2
2
0
2
1
1
0
0
0
2
1
1
0
4
0
0
1
1
0
3
0
0
0
0
0
2
0
0
0
0
3
1
0
0
0
0
0
0
0
2
2
2
0
2
0
0
0
0
0
2
0
1
1
2
0
2
1
0
1
0
0
1
0
0
0
1
0
0
1
0
0
1
0
1
1
0
1
0
0
2
0
1
0
0
0
2
3
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
2
2
0
2
2
0
0
0
2
2
2
3
0
0
0
2
0
2
0
2
1
0
0
2
1
0
1
0
0
0
0
1
0
2
0
0
0
1
0
0
2
0
0
1
1
0
2
2
0
0
2
0
1
0
2
1
0
1
0
2
0
0
0
1
0
0
2
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
3
1
0
0
1
0
2
1
2
2
0
0
0
2
0
1
0
0
1
1
0
0
1
2
0
1
1
0
1
3
0
0
2
2
2
0
0
0
0
0
2
2
1
1
1
2
0
0
0
0
0
2
0
0
0
0
1
1
2
0
0
0
2
0
2
1
0
2
0
0
1
2
2
0
2
1
0
0
0
0
2
2
0
1
3
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
1
0
2
0
0
0
1
0
0
0
1
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
2
0
1
4
0
0
2
0
0
0
0
0
2
0
4
0
2
0
0
2
1
0
2
0
0
1
0
0
0
1
2
2
0
0
2
0
2
2
0
0
1
0
0
2
0
0
0
0
2
0
4
1
0
0
1
0
0
0
4
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
4
0
0
0
1
0
2
0
0
1
0
2
0
1
2
1
0
2
0
0
2
0
0
0
0
0
4
0
0
0
2
1
2
0
1
0
0
0
0
2
1
0
0
0
2
0
0
0
0
1
1
0
2
1
2
5
1
0
1
0
0
0
2
0
2
0
0
1
0
2
1
0
0
1
2
2
1
2
0
0
0
2
1
0
2
2
0
0
0
2
0
2
1
0
2
0
0
1
1
1
0
0
0
2
0
2
0
0
1
1
0
0
0
0
2
2
0
0
0
0
0
0
2
1
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
1
0
0
0
3
1
1
0
2
0
0
2
0
0
0
0
1
1
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
1
2
2
2
1
0
2
0
0
1
0
0
0
0
0
1
1
2
2
0
0
0
2
0
0
0
3
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
2
1
1
1
1
0
0
1
0
2
0
0
0
2
1
2
1
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
1
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
1
0
1
0
0
1
1
0
0
2
0
1
1
0
0
1
1
0
0
0
1
0
0
0
0
1
2
1
0
2
0
0
0
1
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
2
0
2
0
4
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
3
1
0
0
1
4
0
1
0
2
1
0
0
0
0
0
2
0
0
2
0
2
0
2
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
1
0
0
0
2
0
0
0
2
2
1
3
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
3
0
1
4
1
0
2
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
2
1
0
2
0
0
1
0
0
1
0
0
4
0
1
0
0
0
2
0
0
0
0
0
0
0
4
1
2
0
0
1
2
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
1
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
1
0
0
1
1
0
2
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
1
2
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
2
1
0
3
0
0
0
1
2
1
1
2
0
2
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
4
2
4
0
0
0
0
1
0
1
0
1
1
2
0
0
1
0
0
0
1
0
0
1
0
0
2
1
0
2
0
1
0
1
0
0
2
0
0
0
1
2
0
2
0
1
0
0
0
0
1
2
0
2
0
0
1
0
2
0
0
0
0
1
0
0
0
0
1
1
0
2
0
0
0
0
1
1
1
0
0
1
0
0
0
0
1
2
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
2
1
1
0
0
0
0
0
0
0
1
1
0
0
1
1
2
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
1
0
1
0
2
0
0
2
1
0
0
0
0
2
0
1
1
0
0
1
2
0
0
0
0
0
2
2
0
0
0
2
0
2
0
0
2
0
1
0
2
0
2
0
2
1
1
0
2
5
0
0
0
3
3
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
2
0
0
0
1
1
0
2
0
2
1
0
2
0
0
0
0
2
0
1
0
0
2
6
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
2
0
0
0
1
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
2
0
0
1
0
0
1
1
0
0
0
0
0
2
2
2
1
1
0
2
0
2
1
0
1
0
2
0
0
2
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
1
2
2
0
1
0
0
0
2
0
0
0
1
0
0
0
0
3
2
0
2
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
3
2
0
0
3
1
2
2
0
0
0
5
2
0
1
1
1
1
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
2
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
2
2
2
0
3
0
0
4
0
0
0
0
1
0
0
0
0
1
0
1
2
1
2
2
0
0
2
1
2
0
0
2
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
2
3
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
1
0
1
0
0
1
2
1
0
0
0
0
0
2
0
1
0
2
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
2
2
0
0
0
0
4
6
0
0
0
0
2
1
0
0
0
2
1
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
2
1
1
3
0
0
0
0
0
0
0
3
0
0
3
0
0
0
1
2
0
0
0
0
2
1
1
1
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
8
0
2
0
0
0
0
0
0
0
0
1
0
1
2
2
2
0
0
0
0
0
1
2
2
0
0
0
0
7
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
2
0
0
0
2
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
1
0
2
0
2
0
0
1
0
1
2
2
0
2
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
1
0
2
2
0
3
1
0
0
0
0
1
1
2
0
0
0
1
1
0
0
0
2
0
1
2
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
2
2
2
0
0
1
0
0
0
0
0
1
0
4
0
0
0
1
1
2
0
0
2
0
0
0
0
0
2
0
0
0
4
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
1
2
0
0
0
0
0
0
0
2
1
0
2
0
1
0
0
1
0
2
0
0
0
0
0
1
0
0
2
2
0
1
0
0
0
0
0
1
2
2
0
0
1
0
0
0
0
0
0
1
0
2
0
2
2
0
1
2
0
0
2
2
1
0
0
1
0
2
0
2
0
0
0
2
2
0
2
0
0
0
0
3
0
1
1
0
2
0
0
0
0
1
2
0
1
1
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
1
0
2
0
0
0
1
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
4
0
3
0
1
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
3
0
0
1
2
2
0
2
0
0
1
1
2
0
0
0
3
1
0
0
2
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
2
0
1
0
1
0
0
2
0
2
0
0
0
2
0
0
0
1
0
1
0
0
0
0
2
0
0
0
5
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
3
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
1
0
2
0
1
0
0
0
1
0
0
2
0
0
0
0
0
1
1
0
2
0
1
0
0
0
0
2
0
0
2
0
1
0
2
0
0
0
0
1
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
2
2
1
0
2
0
2
0
0
1
1
1
0
0
0
0
0
0
0
0
2
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
2
2
0
2
0
1
0
0
2
2
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
2
2
1
0
2
0
0
2
0
0
2
0
0
0
0
0
3
1
0
0
2
0
0
0
0
0
0
2
3
0
1
0
2
0
3
1
0
2
2
1
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
9
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
10
0
0
0
0
0
2
1
0
0
0
0
1
0
2
1
2
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
5
2
0
0
2
2
0
0
0
0
0
4
0
0
0
0
0
0
2
1
2
1
0
2
2
2
1
0
0
2
0
0
2
0
0
0
0
1
0
3
0
0
0
0
0
1
0
2
1
0
3
0
1
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
2
0
0
1
0
1
0
0
2
0
1
1
0
0
0
0
0
1
1
0
3
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
7
0
0
2
0
0
1
0
0
2
0
0
2
2
0
2
0
0
1
1
0
1
1
0
2
1
0
2
1
0
0
0
0
0
0
0
2
0
0
2
0
0
1
1
0
5
0
0
1
0
2
0
0
0
0
0
1
0
1
1
3
2
0
1
0
2
1
0
0
0
0
0
0
1
5
0
0
2
1
0
1
0
0
2
0
0
5
0
1
1
1
0
1
2
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
1
2
0
0
0
0
1
1
0
0
0
0
2
0
0
0
1
0
1
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
3
0
0
2
0
0
1
1
1
0
7
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
2
0
2
0
2
0
3
0
1
1
1
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
3
0
0
2
0
0
0
2
0
0
0
1
1
1
0
1
0
0
2
2
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
2
3
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
2
0
1
0
2
2
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
2
1
0
0
1
2
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
3
0
0
0
0
0
0
0
0
0
0
1
1
4
0
0
0
0
0
0
2
2
0
0
0
1
3
1
2
1
0
1
2
0
1
1
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
1
2
0
2
0
0
0
1
2
1
1
0
0
0
2
0
1
3
0
0
0
1
0
0
0
1
2
0
2
2
0
2
0
0
2
0
2
1
3
1
0
0
0
1
0
0
1
2
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
1
0
0
0
2
0
1
2
2
1
0
0
0
0
0
2
2
0
1
1
1
0
0
0
0
0
1
2
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
1
0
0
3
2
0
1
1
1
0
2
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
2
0
0
0
2
0
0
1
1
0
0
0
2
0
0
0
0
1
0
0
0
1
0
2
0
0
3
0
0
1
2
0
0
0
1
2
1
0
0
0
2
0
0
2
0
0
0
1
0
1
1
0
0
1
0
0
0
1
0
1
0
2
0
0
1
1
2
2
0
0
0
0
2
0
1
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
2
1
1
1
0
0
2
2
0
0
2
0
0
2
0
0
0
1
0
2
0
1
2
0
1
1
0
0
2
1
1
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
3
0
0
0
2
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
1
1
2
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
1
0
0
0
0
1
1
0
0
2
2
3
0
1
0
0
2
0
0
0
0
0
0
0
2
0
3
2
1
0
0
0
2
0
1
2
2
4
2
0
0
0
0
1
0
1
3
0
0
0
0
0
2
2
0
3
0
2
2
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
2
1
2
0
0
0
0
2
2
0
1
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
4
0
0
1
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
1
0
1
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
2
1
2
0
2
1
0
2
1
0
0
1
1
1
1
0
2
1
0
0
0
1
0
2
1
0
2
0
1
0
0
0
0
0
0
1
0
1
2
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
1
1
0
2
0
1
0
0
2
0
0
0
0
1
0
0
0
0
3
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
2
2
0
1
0
0
0
0
0
1
0
2
1
0
0
0
1
0
0
1
2
0
0
3
3
0
0
0
2
3
0
0
0
1
0
1
0
0
1
1
0
1
0
0
0
2
2
2
0
2
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
3
0
1
0
2
2
1
1
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
1
1
0
0
2
0
0
1
0
2
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
1
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
1
0
0
2
0
1
0
1
0
2
0
0
2
1
1
0
2
0
0
1
0
0
2
1
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
1
2
0
0
1
0
1
0
0
0
0
1
0
0
2
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
2
0
0
3
0
1
0
0
2
1
0
0
0
0
0
1
0
1
0
1
1
0
2
2
0
0
0
0
0
0
0
2
2
1
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
1
2
0
1
1
2
0
0
0
2
2
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
2
4
1
0
2
0
1
0
2
1
0
0
2
0
0
0
0
2
1
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
2
0
0
0
1
1
2
2
0
0
1
0
2
3
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
2
0
0
1
1
0
0
1
0
2
1
0
0
2
2
1
0
2
0
0
0
0
0
0
0
0
2
3
2
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
1
0
0
2
2
0
0
2
1
0
2
0
0
0
0
1
0
1
2
0
0
1
0
0
0
0
0
1
1
1
0
0
0
2
0
0
0
0
2
0
0
1
2
2
3
1
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
2
1
0
0
1
2
0
0
2
0
5
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
2
1
0
1
0
0
0
0
0
0
1
0
0
2
2
4
0
2
1
0
1
1
0
0
0
0
0
0
0
0
1
0
1
2
0
1
2
2
2
0
0
1
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
1
2
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
1
3
2
1
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
2
2
0
3
4
1
0
2
2
0
0
1
0
1
4
0
1
2
1
1
0
0
2
2
0
1
0
1
0
0
2
0
0
3
0
0
0
2
0
0
0
0
1
2
0
1
0
0
2
1
0
0
0
2
1
0
0
0
0
1
0
0
0
0
2
1
1
0
3
0
0
1
0
0
1
0
1
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
1
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
2
0
2
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
2
0
0
2
0
0
0
0
1
0
0
3
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
2
2
2
0
0
0
0
0
0
2
0
2
1
1
0
0
0
0
0
2
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
2
2
0
1
0
0
0
2
1
0
0
0
1
0
0
0
2
0
0
1
0
2
0
0
0
0
2
1
0
0
0
0
0
1
1
0
2
0
1
1
1
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
3
0
0
0
2
2
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
2
0
4
0
0
1
0
8
0
0
0
2
0
0
3
2
2
0
0
0
0
0
1
0
0
0
0
1
0
4
1
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
3
2
1
0
0
1
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
3
1
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
2
0
2
0
0
2
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
2
2
0
1
0
1
2
0
0
0
1
0
0
0
2
0
2
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
3
2
0
0
1
0
0
0
0
0
2
2
0
1
0
0
2
1
2
0
0
1
0
0
2
0
1
0
0
1
0
0
0
2
0
1
0
0
0
2
2
0
0
1
2
0
2
1
0
0
0
3
0
1
1
0
2
0
2
0
5
2
1
2
2
1
2
0
2
0
1
0
2
1
2
1
0
1
2
0
2
0
0
2
2
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
2
0
3
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
1
2
0
0
3
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
2
2
0
0
1
0
0
3
0
2
0
0
2
1
0
2
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
3
0
0
0
3
0
1
0
2
1
2
0
1
2
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
1
0
2
0
0
0
1
0
2
0
2
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
2
2
0
1
0
1
2
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
3
0
2
1
0
0
2
0
1
0
0
0
0
2
0
2
1
0
0
0
0
0
0
1
0
1
0
0
0
2
1
0
0
2
0
0
0
1
0
0
2
1
0
2
0
0
2
1
0
1
1
0
1
2
1
2
0
0
0
0
2
1
0
0
0
3
0
0
0
0
0
0
0
1
1
2
1
0
0
1
0
0
4
0
0
0
1
0
0
3
0
0
2
2
2
2
0
2
0
0
2
0
0
0
0
2
0
0
5
2
1
1
0
0
0
2
0
6
0
0
0
0
0
0
0
3
2
0
0
3
2
0
1
0
3
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
2
1
1
0
0
1
3
0
0
2
1
2
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
2
0
1
2
0
2
0
0
0
0
0
1
0
0
1
0
0
0
1
0
2
1
0
2
0
0
0
1
0
2
0
6
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
2
2
0
1
0
0
0
2
0
2
1
0
0
0
0
0
0
2
0
2
2
0
0
2
3
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
2
0
2
0
2
1
0
0
2
2
0
0
1
0
2
0
2
0
1
0
0
2
1
1
1
1
0
1
0
2
0
2
0
1
0
2
0
0
0
0
1
1
2
0
0
1
2
1
0
2
0
0
4
2
0
2
2
0
0
1
0
0
0
0
0
0
0
2
2
1
0
0
0
0
1
1
0
0
2
0
2
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
3
0
1
0
1
0
2
1
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
6
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
1
0
2
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
1
2
0
0
1
0
2
0
1
1
0
1
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
2
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
1
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
1
1
0
0
0
0
0
0
0
2
2
1
0
0
0
4
0
0
0
2
2
1
0
0
0
0
0
0
0
0
2
2
0
0
1
0
2
0
0
2
0
2
0
0
0
2
0
0
0
0
1
1
0
0
0
0
2
0
0
0
2
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
2
3
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
1
1
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
2
0
2
1
0
1
0
1
1
0
0
0
0
1
0
0
2
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
3
0
0
0
1
0
0
0
0
2
0
1
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
1
2
2
2
0
0
1
0
0
2
1
0
1
2
5
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
2
1
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
2
2
0
1
2
1
2
0
1
0
0
0
2
2
0
0
2
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
2
0
2
0
0
1
2
0
0
1
3
0
0
0
0
2
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
1
1
0
0
0
0
0
0
1
0
2
1
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
2
1
1
0
0
0
0
1
0
1
0
1
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
2
2
0
2
0
2
0
1
1
0
0
2
0
0
1
0
1
0
1
1
0
0
0
0
4
3
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
1
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
1
1
0
0
0
2
0
0
0
0
0
1
0
2
0
2
0
0
0
3
0
0
3
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
1
0
1
0
0
1
1
0
1
0
2
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
1
0
0
0
0
0
2
0
2
1
0
0
2
2
0
1
0
1
1
0
0
0
1
0
0
0
0
1
1
0
0
1
1
0
0
2
2
1
2
0
1
2
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
1
1
0
0
0
0
2
0
0
2
0
2
2
0
1
2
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
4
1
0
1
0
0
0
2
0
2
0
0
1
1
1
0
1
0
1
0
0
0
0
2
0
0
2
1
0
2
1
2
2
2
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
1
1
0
0
0
1
0
3
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
2
0
0
0
0
3
2
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
2
6
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
2
0
0
0
0
2
0
2
0
0
1
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
3
1
0
0
0
1
2
0
0
1
1
2
1
0
0
0
0
1
0
0
0
1
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
1
1
0
1
2
0
0
2
0
1
0
0
0
0
0
1
1
0
0
0
2
0
1
0
0
0
0
2
3
0
0
0
1
2
1
0
0
0
0
2
0
0
0
0
3
0
2
4
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
2
0
2
1
0
2
0
0
0
2
2
0
0
0
0
2
2
0
0
0
0
0
0
1
1
0
0
0
1
2
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
1
1
0
2
0
0
0
0
0
1
2
0
0
0
1
0
2
2
1
1
0
0
1
2
0
0
0
1
0
0
0
0
0
7
0
0
0
0
0
2
0
7
0
1
1
0
2
0
3
0
0
1
1
1
2
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
2
0
0
2
0
0
0
0
0
1
2
2
0
3
0
0
0
0
2
0
0
1
1
0
2
1
0
1
0
0
0
0
1
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
2
2
0
2
2
0
0
0
0
7
0
0
0
0
0
2
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
1
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
1
0
0
2
0
0
1
0
0
0
1
0
0
0
0
2
0
2
2
1
1
2
0
0
2
0
0
0
0
2
0
0
0
1
2
0
0
0
1
0
0
1
0
0
0
0
1
2
0
1
0
0
0
0
0
2
0
0
0
0
0
1
1
1
0
1
0
0
1
1
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
1
2
2
0
0
1
0
0
0
0
1
1
2
0
0
0
0
0
0
0
2
1
0
0
3
0
0
3
0
0
0
0
0
0
2
2
2
0
0
0
3
0
0
2
0
1
2
0
0
2
0
2
0
0
0
0
0
2
1
0
0
7
0
2
2
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
2
0
0
0
2
0
2
0
2
1
0
2
1
0
0
0
0
1
1
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
2
1
0
1
0
2
2
0
3
1
1
2
0
0
0
0
0
0
0
0
0
1
2
1
1
0
3
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
2
0
2
0
2
1
1
0
1
0
2
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
2
0
0
1
1
2
0
2
1
2
1
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
2
0
1
0
1
1
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
1
1
0
0
0
1
1
0
1
3
0
1
0
2
0
0
2
1
0
0
2
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
4
0
0
0
0
1
0
2
0
0
0
1
0
0
0
2
0
0
2
1
0
3
1
0
0
0
2
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
2
0
0
0
0
1
0
0
2
2
0
0
2
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
1
0
2
0
0
2
1
0
2
0
2
2
1
0
2
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
2
2
0
0
1
0
0
2
0
0
2
1
0
0
2
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
2
0
0
2
2
2
0
0
2
0
0
5
1
1
1
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
2
0
2
2
0
0
1
2
0
0
0
0
0
0
4
0
0
0
2
2
2
0
2
2
4
1
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
2
2
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
3
0
0
2
1
0
2
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
2
2
0
0
1
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
2
0
0
0
0
0
4
0
0
2
2
1
0
1
0
0
0
0
0
0
0
0
1
3
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
3
0
0
1
0
0
1
0
1
0
0
0
0
1
2
0
0
1
0
1
2
2
0
5
2
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
1
1
0
2
0
0
0
1
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
7
1
0
2
1
0
1
2
0
0
0
2
1
1
2
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
2
0
0
0
1
0
1
0
2
0
0
1
0
0
0
0
1
6
2
0
2
0
0
0
0
0
0
1
0
0
0
3
4
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
3
0
2
1
0
0
0
0
1
1
0
1
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
2
1
0
3
0
1
1
0
2
0
1
0
0
0
0
0
2
1
0
0
1
0
0
0
3
0
0
0
0
2
0
0
0
0
1
9
0
0
1
0
0
0
1
0
1
0
2
4
0
0
2
0
2
0
1
0
1
2
1
0
1
0
1
1
0
0
0
2
0
0
0
0
0
2
2
0
3
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
2
3
0
0
0
2
0
0
0
0
0
1
2
2
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
1
0
2
0
0
0
0
2
1
0
1
1
1
0
0
2
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
1
0
0
3
2
2
0
0
2
2
1
0
2
0
0
2
0
3
2
2
2
0
0
1
2
2
0
0
3
2
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
4
0
0
0
0
3
4
2
0
0
0
2
0
1
2
0
0
1
0
0
0
2
0
0
0
1
0
1
0
0
2
1
1
0
1
0
0
0
0
1
2
1
0
1
0
0
1
0
0
2
2
0
2
0
0
0
0
0
0
2
0
1
0
1
2
0
0
0
0
0
0
2
1
0
0
1
1
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
1
1
1
1
0
0
0
0
1
1
1
0
1
2
0
0
0
0
1
0
0
0
2
0
2
1
2
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
2
0
0
0
0
1
0
1
0
0
0
0
0
1
2
0
0
0
3
0
2
0
0
0
1
0
2
1
0
3
0
0
0
0
3
0
0
0
2
1
0
1
2
0
0
2
0
0
3
0
1
0
0
0
2
1
1
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
2
0
5
2
1
0
2
0
0
0
0
0
2
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
3
0
0
1
0
0
1
1
1
0
1
0
0
1
1
0
0
2
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
3
1
2
0
0
0
0
0
2
0
2
0
0
0
0
2
2
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
2
1
6
0
0
0
0
0
0
1
1
1
2
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
1
1
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
4
2
1
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
1
0
0
2
0
0
0
0
0
0
0
2
2
1
0
0
1
2
2
0
1
0
0
1
0
1
0
2
0
0
1
0
0
0
2
0
0
0
2
1
0
2
0
1
2
1
0
0
0
0
0
0
1
0
0
0
2
0
1
2
2
0
0
0
0
1
0
0
1
2
0
1
1
0
0
0
0
0
0
2
0
0
0
1
0
1
0
1
0
0
1
0
0
0
2
1
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
1
0
0
1
2
2
2
4
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
2
0
0
0
1
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
1
2
0
2
0
0
0
2
0
2
0
0
0
0
0
0
2
2
0
0
4
2
0
0
2
0
0
0
1
1
0
0
0
1
1
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
2
1
0
0
0
0
0
1
1
5
1
0
2
0
0
0
1
0
2
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
7
0
2
1
0
0
0
0
0
0
0
2
0
2
0
2
0
0
2
0
0
0
1
1
0
0
0
0
2
1
1
5
0
1
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
1
2
0
0
0
2
0
0
0
0
0
0
2
2
2
0
0
1
0
1
0
0
2
2
1
0
0
1
0
0
4
6
2
0
0
1
0
0
0
1
0
0
4
0
0
0
1
0
1
3
0
1
0
0
0
0
0
1
1
0
1
0
0
0
3
0
0
2
0
1
0
0
0
0
0
0
1
0
0
2
2
1
0
2
2
0
0
2
0
0
0
0
0
0
0
1
0
1
1
0
1
0
2
0
0
0
0
0
0
0
0
0
2
1
1
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
11
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
1
0
0
2
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
2
0
0
0
2
0
1
0
0
0
3
0
0
0
4
1
0
0
0
2
0
0
2
0
0
1
0
2
0
1
0
0
0
0
3
0
0
0
0
0
0
0
2
2
0
1
0
2
0
0
0
1
0
1
1
0
0
2
0
0
1
2
0
0
1
0
1
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
2
1
1
0
1
1
0
2
0
1
0
0
0
2
0
0
2
2
2
0
0
0
0
0
4
0
1
1
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
2
0
0
2
0
0
0
0
2
2
1
1
0
2
0
0
1
0
2
0
0
0
0
0
0
2
0
2
2
2
0
0
1
0
1
0
0
1
2
0
2
0
4
0
0
1
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
1
0
0
1
0
0
2
0
0
0
3
0
2
0
1
0
0
0
0
7
0
0
0
0
3
1
0
2
1
1
0
0
2
0
2
0
1
1
0
0
1
0
0
0
0
0
3
2
2
0
1
0
0
0
0
1
2
0
0
0
1
0
2
0
0
0
0
2
0
1
0
0
0
2
1
2
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
1
0
1
1
0
1
2
2
0
0
1
1
0
3
1
0
3
0
1
0
2
2
0
0
0
0
0
1
1
0
0
0
1
2
1
2
1
0
0
0
0
0
0
0
0
1
2
2
0
1
0
2
0
2
0
0
0
2
0
1
2
1
0
0
0
1
0
0
0
0
0
0
1
0
1
2
0
0
0
1
1
2
0
0
0
2
0
2
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
1
0
1
0
0
2
5
0
0
0
2
0
0
1
0
2
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
1
2
0
2
0
0
0
3
0
0
0
1
0
2
1
0
1
0
0
1
0
2
0
0
0
2
0
0
0
1
0
0
1
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
2
0
2
0
1
1
0
0
0
1
1
1
0
1
0
0
1
1
2
0
1
0
1
0
1
0
0
0
3
5
0
0
0
1
2
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
4
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
1
0
2
0
0
1
0
1
1
1
0
0
0
2
0
2
0
0
1
0
2
1
2
0
0
1
0
0
1
0
0
0
0
0
0
0
2
2
0
2
0
1
0
0
0
0
2
0
2
0
0
0
2
3
0
0
0
1
0
2
0
2
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
1
0
0
1
2
1
0
1
0
0
0
0
1
1
0
1
0
0
1
1
0
1
0
0
3
0
0
2
0
0
0
2
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
1
0
2
1
0
2
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
1
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
4
0
2
0
0
0
6
0
2
0
2
2
0
1
1
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
1
1
0
0
0
0
0
2
0
2
2
1
0
1
0
1
0
1
1
0
0
2
0
0
0
0
0
1
0
1
2
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
1
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
6
3
0
2
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
1
2
0
0
1
2
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
1
0
0
2
2
0
0
2
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
1
0
2
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
2
0
0
1
0
0
0
0
0
2
0
2
0
2
0
2
1
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
1
5
0
4
1
0
0
1
0
0
0
1
0
1
0
3
0
0
3
0
1
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
2
3
0
0
0
2
1
0
0
0
3
0
1
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
1
0
2
0
2
0
0
0
0
1
0
0
0
2
2
0
1
0
0
0
0
2
1
0
2
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
1
2
0
0
0
0
2
2
0
0
3
0
0
2
0
1
2
1
3
2
1
1
0
0
2
0
1
0
0
0
0
1
2
1
0
2
1
2
1
0
2
2
0
0
0
2
0
1
0
1
1
0
0
1
0
0
1
0
2
2
2
0
0
0
0
0
4
1
0
0
1
0
0
0
2
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
1
2
0
0
0
1
0
0
1
2
0
0
0
2
0
0
0
1
0
2
0
0
2
0
2
0
1
0
0
0
1
0
0
2
1
1
0
0
1
4
2
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
3
0
0
2
0
0
0
0
0
0
0
0
1
5
2
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
2
0
0
2
2
0
1
0
1
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
1
1
0
0
1
0
1
0
2
0
0
0
0
1
1
1
0
1
0
1
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
3
1
1
0
0
1
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
2
2
0
0
0
1
3
0
0
0
0
2
1
1
0
0
1
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
3
0
0
2
0
0
0
1
1
1
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
1
0
2
1
1
0
1
0
0
2
0
2
2
0
2
0
0
0
0
1
0
0
0
0
2
2
2
0
0
0
1
1
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
4
0
0
2
0
0
0
1
0
0
2
0
0
0
1
0
1
0
0
2
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
2
1
2
0
0
2
0
2
0
0
0
1
0
1
0
0
0
2
0
0
1
0
2
0
0
1
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
1
1
0
0
0
0
2
0
0
0
1
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
2
5
1
0
2
0
0
0
0
5
0
2
0
1
0
0
0
2
2
0
0
2
1
0
0
0
0
5
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
1
0
6
0
0
0
3
1
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
1
0
2
0
0
0
2
1
2
0
0
0
1
0
1
1
2
0
1
0
2
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
1
0
3
0
1
0
0
0
1
8
0
0
0
0
0
0
1
1
0
0
1
1
0
2
1
0
1
0
0
0
1
1
0
0
0
1
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
1
2
0
2
0
1
0
0
1
2
0
1
0
0
1
1
1
0
0
0
0
0
1
0
0
2
1
0
2
0
2
0
0
2
0
1
0
0
0
2
2
1
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
2
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
1
2
1
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
1
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
2
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
2
0
0
0
0
1
0
2
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
2
0
2
0
2
0
1
0
0
3
0
0
2
1
1
0
0
2
1
0
0
0
0
0
0
1
2
0
2
2
0
2
8
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
2
2
0
1
1
0
2
0
0
0
0
0
2
0
1
0
0
1
0
0
2
0
0
2
3
2
3
0
0
1
2
0
1
1
1
0
0
0
0
0
2
0
2
0
0
2
2
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
2
3
0
0
0
2
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
1
3
0
0
0
0
3
0
1
0
0
2
3
0
1
0
2
0
1
1
0
0
0
2
1
0
1
2
0
2
0
2
0
0
0
0
0
1
0
0
0
0
3
1
1
0
0
0
0
0
0
0
4
2
1
0
0
2
0
0
0
1
2
2
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
2
0
0
0
2
0
2
2
0
0
1
0
1
0
2
0
3
2
3
2
0
0
0
1
1
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
1
1
2
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
2
2
0
0
0
1
0
0
0
2
0
0
0
0
3
0
0
0
1
0
0
3
0
2
0
0
0
0
0
0
6
2
0
2
0
0
0
1
0
0
0
2
0
2
0
1
0
1
0
0
0
2
2
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
3
0
0
0
1
2
0
0
1
0
1
0
0
1
0
0
1
0
0
0
1
2
1
1
1
0
0
0
0
0
0
1
0
0
0
1
0
3
0
1
1
0
0
0
0
0
1
0
0
0
2
1
0
2
0
0
2
0
0
0
0
0
0
0
0
3
0
3
2
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
3
0
1
3
0
0
0
0
0
2
0
0
0
1
1
0
0
2
4
0
2
0
0
0
0
0
0
1
0
2
0
0
0
3
2
0
2
0
1
0
0
0
0
0
2
0
0
0
0
2
2
2
1
0
2
0
0
0
3
2
0
0
0
1
0
0
0
2
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
1
0
2
0
0
1
0
0
0
0
1
0
2
0
1
0
1
1
0
1
1
2
0
1
0
0
0
0
2
0
0
0
0
1
0
1
2
2
0
0
1
0
0
2
0
1
0
1
0
0
0
0
1
2
2
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
1
2
0
0
0
2
0
3
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
3
0
0
0
1
0
0
0
0
1
1
1
2
0
3
0
0
1
0
2
0
2
0
0
3
0
2
0
1
0
0
0
1
0
2
0
0
1
0
0
2
0
0
0
0
4
0
0
0
2
0
0
2
1
0
0
2
0
1
0
0
0
0
1
0
0
2
0
3
0
0
0
2
0
2
0
0
0
2
2
0
0
2
0
0
1
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
1
2
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
3
1
0
0
0
2
2
0
0
2
2
0
0
1
1
0
0
0
3
1
1
0
0
2
0
1
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
1
0
3
0
0
3
1
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
2
2
1
2
0
1
0
0
0
0
0
2
1
0
1
0
2
0
0
0
0
0
2
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
1
0
2
1
1
2
1
0
2
0
0
0
0
0
0
0
0
0
2
0
3
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
1
1
0
2
1
0
0
2
1
2
0
0
2
0
2
0
0
1
0
1
0
0
1
1
0
0
0
2
1
1
0
2
2
0
0
1
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
1
1
0
1
0
0
2
0
2
0
0
0
2
0
2
0
3
0
0
2
2
2
0
0
1
2
2
0
0
2
2
0
0
1
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
2
4
1
6
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
1
0
2
0
0
1
2
0
3
0
0
0
0
0
1
0
0
0
1
0
2
0
1
0
0
0
1
0
2
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
2
0
0
0
1
1
0
0
1
0
0
2
1
0
0
2
0
1
0
0
0
0
1
0
1
2
2
0
0
0
0
0
2
0
1
5
0
0
0
1
1
2
0
0
0
0
0
4
2
0
0
0
0
0
2
2
0
2
0
1
1
2
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
3
0
0
3
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
2
0
0
0
2
2
2
1
2
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
1
2
0
1
0
0
0
0
0
0
0
1
0
0
2
1
0
2
1
1
0
0
0
1
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
2
1
1
1
0
0
0
2
0
2
0
0
0
0
1
0
0
0
1
0
1
0
1
0
4
2
2
1
1
2
2
0
0
2
0
2
0
1
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
2
3
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
2
0
0
0
0
0
0
0
1
0
1
0
1
2
0
0
0
2
0
1
0
2
0
0
1
0
1
2
0
2
1
0
2
0
0
1
2
0
0
0
2
0
2
0
0
0
0
2
1
2
1
0
5
1
1
0
1
1
0
0
1
0
0
0
1
0
1
2
1
0
1
1
0
0
0
0
1
2
2
1
0
0
0
0
0
0
0
1
2
2
0
1
0
2
0
0
0
1
0
6
0
0
3
2
1
0
1
0
0
0
1
0
1
2
2
1
1
0
0
0
0
0
0
0
3
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
4
0
0
0
0
5
0
2
0
1
0
1
0
2
0
0
2
1
0
0
1
0
2
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
2
0
0
0
0
2
0
1
1
1
0
2
0
0
0
0
0
0
0
2
2
1
3
0
0
0
0
0
2
0
1
1
0
0
0
0
1
2
2
0
0
2
2
0
0
0
2
0
1
0
0
1
0
0
5
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
3
0
0
0
1
1
3
0
0
1
0
0
0
0
0
0
0
1
0
2
1
0
1
0
0
1
2
0
0
0
0
1
0
0
0
1
2
0
1
2
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
1
2
0
0
3
3
0
0
0
1
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
2
0
0
2
0
0
2
1
0
3
0
1
0
0
0
0
0
1
1
1
0
0
0
2
2
3
2
0
0
1
1
2
0
1
0
1
2
0
0
2
1
1
1
0
0
1
0
0
0
1
0
1
0
1
1
0
0
2
2
2
0
0
0
0
0
0
0
2
1
1
0
0
2
2
0
0
2
0
0
2
0
2
0
2
0
1
0
0
0
2
0
0
2
1
0
0
0
0
0
1
1
0
3
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
1
0
2
2
3
2
1
0
1
0
0
2
1
0
0
0
1
1
0
2
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
2
2
0
0
1
0
0
0
0
0
1
1
0
0
1
1
2
0
1
2
0
0
0
1
0
0
2
3
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
1
4
0
1
0
0
0
0
0
2
0
0
2
1
0
0
0
0
2
0
0
2
3
0
1
0
0
0
0
0
2
2
0
0
0
4
0
2
0
1
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
2
2
0
0
13
0
0
0
2
2
1
0
0
2
1
0
0
2
0
0
0
0
2
0
0
2
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
1
0
0
1
0
0
2
0
0
0
1
0
1
0
2
2
0
0
1
0
2
3
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
2
0
1
0
0
2
0
1
2
0
0
0
2
0
1
0
0
0
0
2
0
2
1
1
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
2
0
0
1
0
2
0
1
0
1
0
1
0
0
0
0
0
1
0
1
0
1
2
0
0
0
2
0
1
1
1
0
0
0
2
0
0
0
0
5
0
2
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
3
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
2
3
5
0
0
2
0
0
2
0
2
2
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
2
0
0
0
1
2
4
0
0
0
0
1
2
1
0
0
0
4
0
1
0
1
0
0
1
1
2
0
0
3
0
1
0
0
1
0
0
0
0
1
1
0
2
0
2
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
1
0
0
1
0
1
0
0
0
1
0
2
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
1
2
0
0
1
0
1
1
1
1
2
3
0
2
0
0
0
1
2
0
1
0
0
0
0
0
0
3
2
3
0
2
1
2
1
1
0
0
0
2
1
2
0
1
0
1
0
2
2
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
2
1
1
0
2
2
0
2
0
0
0
3
1
1
0
2
0
0
0
0
1
2
0
2
2
0
0
0
1
0
0
0
0
2
2
0
1
1
2
2
0
0
1
1
0
1
0
0
0
0
0
0
0
2
2
0
0
0
1
1
0
0
2
2
1
3
0
2
2
0
0
0
0
1
2
0
0
0
0
2
1
0
1
0
0
6
1
0
4
0
0
1
1
2
0
1
0
2
0
1
1
2
0
0
1
0
0
2
2
2
0
0
0
1
0
0
0
1
0
1
0
0
2
0
0
0
1
0
0
0
2
3
0
0
0
0
0
1
0
2
0
0
0
0
2
1
2
0
0
0
1
0
0
1
0
0
2
0
5
0
0
2
1
1
4
0
0
0
1
0
0
2
0
0
6
2
1
2
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
3
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
1
2
0
2
0
0
1
0
1
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
2
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
2
2
0
0
0
0
0
0
2
1
0
2
2
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
1
0
2
2
2
0
2
0
2
0
0
0
0
1
2
1
0
0
0
0
0
0
1
0
2
3
0
2
0
0
0
2
0
0
3
2
2
0
0
1
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
4
0
0
0
1
2
0
0
0
0
0
0
2
1
0
0
0
1
0
0
1
2
0
0
0
0
2
0
0
0
0
3
4
0
0
0
2
0
0
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
3
0
0
0
2
2
2
0
0
0
0
0
1
2
0
0
0
0
5
1
0
1
0
1
0
0
2
0
1
2
3
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
1
0
1
0
2
1
0
0
0
0
0
1
0
0
2
0
0
1
0
2
0
2
1
2
0
0
0
0
0
0
3
0
0
1
0
2
0
2
0
2
1
0
0
1
2
0
1
0
0
0
0
1
0
0
0
0
4
0
0
2
0
2
0
0
0
0
1
1
3
2
2
1
2
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
1
0
1
1
0
0
1
0
0
0
2
0
0
0
0
0
3
0
0
5
0
0
1
2
0
0
0
2
0
0
0
0
1
1
0
2
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
3
0
2
1
0
0
0
0
0
2
1
3
0
1
1
0
1
1
0
1
1
0
0
0
1
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
3
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
3
2
0
0
0
0
0
0
1
1
1
1
0
0
0
0
2
0
0
0
2
2
2
0
2
0
0
2
0
0
0
0
2
0
2
1
1
1
2
0
0
0
6
1
0
0
0
0
2
0
0
2
1
0
2
2
0
2
2
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
2
0
2
0
0
0
0
0
2
0
0
4
0
1
2
1
0
2
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
1
0
0
2
0
0
0
2
2
0
2
2
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
1
0
0
0
0
0
2
0
1
0
2
0
0
2
0
0
2
0
1
0
0
2
0
1
1
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
1
0
0
1
0
0
0
3
0
2
0
0
2
2
0
2
0
0
1
0
0
0
0
1
3
4
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
1
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
2
1
0
0
0
2
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
1
0
2
0
1
1
0
1
0
1
1
0
0
0
0
2
1
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
1
0
0
0
0
1
2
0
1
0
0
0
2
0
0
2
2
0
0
1
0
0
1
2
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
1
0
0
0
2
0
0
1
0
0
0
2
1
0
4
1
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
3
0
1
0
5
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
2
2
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
2
0
2
0
3
0
0
0
0
0
0
0
0
1
0
2
3
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
2
0
0
2
0
0
0
0
2
0
1
0
1
0
2
1
2
1
0
2
2
0
2
0
1
0
0
0
2
0
4
1
0
2
0
0
1
0
2
2
0
0
3
0
0
0
0
0
0
0
1
0
1
2
0
2
0
1
3
0
0
1
0
0
0
1
1
0
1
0
0
2
1
0
0
0
0
0
0
2
0
0
2
3
1
0
2
0
0
0
0
0
0
0
2
1
1
0
0
0
2
0
0
6
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
2
2
1
0
0
0
1
1
1
0
0
0
1
2
0
1
0
7
0
2
0
1
0
2
0
0
0
2
1
0
0
1
2
0
0
2
0
0
0
0
1
0
1
1
2
0
1
0
0
0
0
0
2
2
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
4
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
2
0
0
0
4
0
2
0
1
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
2
0
0
1
0
0
1
0
0
2
0
0
0
0
1
2
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
2
2
0
2
0
1
0
2
1
1
2
0
2
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
1
1
0
1
0
4
0
0
2
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
1
0
0
2
0
1
0
1
0
3
0
0
1
0
0
0
2
0
1
1
2
0
0
2
2
0
0
0
0
0
2
0
0
0
1
0
0
1
1
0
2
0
0
2
0
0
0
0
1
0
0
0
1
2
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
3
0
0
1
2
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
2
4
0
2
0
0
0
0
2
0
0
0
3
1
0
0
1
0
0
2
0
0
2
0
0
2
0
0
0
0
0
2
0
0
4
0
0
0
1
0
0
0
0
1
3
0
2
1
0
0
0
1
0
0
2
0
0
0
0
2
1
1
1
0
2
0
0
2
0
1
2
0
2
2
0
0
0
2
0
0
0
1
1
2
0
0
3
2
1
0
0
0
1
2
0
0
0
1
2
0
0
1
1
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
1
0
1
2
0
0
0
1
0
2
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
2
0
0
1
2
0
0
1
0
0
0
0
0
2
0
2
0
1
2
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
3
1
2
0
0
0
0
3
0
0
2
0
0
0
3
0
0
1
0
0
1
0
1
0
2
0
0
0
1
0
0
1
0
2
0
1
0
0
0
2
0
1
0
2
1
0
0
0
0
2
1
1
1
0
2
1
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
3
0
0
0
0
2
1
0
0
0
1
0
0
0
0
4
1
1
2
0
0
0
0
0
2
0
0
0
0
0
2
0
2
1
1
0
0
0
0
0
1
0
2
1
0
0
0
1
1
0
1
1
1
2
2
2
2
1
1
0
1
1
0
1
0
0
0
0
1
0
2
0
0
0
1
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
2
2
2
3
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
2
0
0
2
2
0
0
1
0
1
2
2
0
0
2
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
2
0
2
2
1
0
0
0
0
2
1
1
1
0
1
0
0
0
0
2
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
2
0
2
0
1
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
2
0
1
2
1
0
0
3
0
0
0
1
0
1
2
0
2
2
0
0
0
1
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
2
1
2
1
0
2
0
2
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
2
8
0
1
0
2
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
1
0
1
0
0
0
0
0
0
0
1
4
0
2
0
1
0
0
1
0
0
0
1
0
0
2
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
2
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
2
1
0
0
0
1
2
3
0
0
0
1
2
1
1
0
2
2
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
1
0
0
0
3
0
0
0
2
0
0
3
0
2
1
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
1
6
0
0
0
2
0
0
1
2
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
1
0
1
3
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
2
2
1
0
2
0
0
2
3
0
0
3
1
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
2
0
1
0
1
0
0
0
0
0
2
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
2
5
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
2
0
1
2
0
2
0
0
0
1
0
1
0
0
1
0
0
0
3
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
3
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
2
1
2
0
0
1
0
0
0
0
0
1
0
2
0
0
1
2
1
0
2
0
1
1
0
2
0
0
0
1
0
0
0
3
2
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
4
2
0
1
0
2
0
0
2
2
0
0
2
0
0
2
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
3
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
1
1
0
2
0
0
0
2
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
1
3
1
1
0
2
0
0
0
0
0
2
1
0
0
0
2
0
2
0
0
3
2
1
0
0
0
0
0
1
1
0
0
0
0
5
0
1
0
1
0
2
1
2
0
0
0
0
2
0
0
2
0
0
0
2
1
1
2
2
0
2
0
0
0
0
0
0
1
0
0
0
3
0
1
0
0
0
1
0
0
0
1
1
1
0
2
0
0
0
2
0
2
0
0
2
0
0
1
0
0
2
0
3
0
1
0
0
2
1
0
1
0
0
0
0
0
1
0
2
0
0
4
0
0
0
1
3
1
0
0
1
0
1
2
1
2
0
0
1
0
0
0
0
0
2
0
2
0
0
1
1
2
0
1
0
2
0
0
2
0
3
1
1
0
0
1
0
0
0
2
0
1
3
0
0
0
3
1
2
0
1
1
0
1
0
2
0
2
0
1
1
0
0
1
0
0
0
0
1
2
0
0
2
1
0
0
2
3
0
0
0
0
0
0
0
3
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
1
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
1
2
1
0
1
1
1
0
0
1
0
1
2
0
2
0
0
0
0
3
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
1
3
1
0
0
1
0
2
1
1
0
1
0
2
0
0
0
0
2
0
2
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
2
2
0
1
1
0
1
2
0
0
0
0
1
1
0
1
0
1
0
2
0
0
0
0
1
0
1
0
1
0
0
2
1
0
0
0
0
2
0
1
0
0
0
2
0
2
0
1
1
0
3
0
0
0
2
0
1
0
1
0
0
1
0
0
0
0
0
1
1
3
0
1
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
3
0
0
1
0
0
1
2
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
3
0
0
2
3
4
2
0
0
0
0
0
2
1
0
0
2
2
0
0
2
0
0
0
1
0
0
0
0
2
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
4
0
2
1
0
0
1
0
0
2
0
3
0
2
2
0
0
0
0
1
0
0
2
1
2
0
0
0
0
1
1
0
0
0
0
0
0
1
2
0
0
2
0
0
0
2
0
1
1
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
3
0
0
0
1
1
0
0
0
1
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
1
1
0
0
1
2
0
1
0
0
0
0
1
0
0
0
2
0
1
0
1
0
1
0
0
1
0
0
0
1
0
0
0
3
0
0
0
0
0
1
0
1
0
1
0
1
0
0
1
0
2
0
0
0
0
2
2
2
0
0
0
1
0
1
0
0
2
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
6
0
2
0
0
0
0
0
1
0
2
2
2
2
0
0
0
0
0
0
1
1
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
4
0
2
1
0
0
0
0
2
1
1
0
0
1
2
2
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
3
3
0
2
0
0
0
0
1
0
0
2
0
0
0
2
0
1
0
1
0
0
0
0
1
0
2
0
0
0
0
1
2
0
2
0
0
0
0
0
1
0
0
0
0
5
0
0
3
2
0
1
0
0
1
0
0
2
0
0
0
0
2
0
3
1
0
0
2
0
0
2
1
1
1
0
0
1
1
1
0
2
1
0
1
2
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
4
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
1
0
2
0
0
0
2
0
0
0
0
2
1
0
0
6
2
2
3
2
0
1
0
0
1
0
0
2
1
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
2
0
2
0
0
1
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
1
1
0
2
0
2
0
0
2
0
0
2
0
2
2
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
5
0
1
3
0
0
0
0
0
1
2
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
2
0
2
1
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
3
2
2
0
0
0
1
0
0
2
0
0
1
3
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
1
0
1
0
1
2
2
0
0
1
0
2
0
1
0
0
0
2
0
0
0
1
1
0
1
0
1
1
0
0
0
2
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
2
0
2
0
0
2
0
0
0
2
0
0
0
2
0
0
1
0
1
0
1
2
2
0
0
1
2
2
0
0
0
0
0
0
0
2
2
0
1
2
0
1
0
1
0
0
0
3
2
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
1
0
1
1
1
1
0
0
0
3
0
1
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
4
1
1
3
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
2
2
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
1
0
1
1
0
0
1
1
0
0
0
2
0
2
0
2
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
1
2
0
2
1
0
0
2
0
0
1
0
0
0
0
1
2
0
0
0
2
2
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
1
2
0
0
0
2
0
0
0
3
0
2
1
2
0
2
0
0
0
0
1
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
3
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
2
0
2
0
0
0
2
0
0
0
1
0
1
0
0
0
0
2
1
0
1
0
0
0
2
0
2
0
0
0
0
2
0
1
2
0
3
0
0
0
0
0
0
0
4
0
0
0
1
2
1
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
1
2
0
0
1
1
2
1
1
0
1
0
1
2
1
3
0
0
5
1
2
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
3
0
0
0
0
2
0
0
0
0
2
0
2
2
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
2
1
0
1
0
1
0
0
0
2
0
1
2
2
0
1
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
1
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
2
0
1
0
0
0
0
1
0
2
1
0
0
0
3
0
0
0
0
0
0
0
1
0
0
1
1
2
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
2
2
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
1
1
0
2
0
0
2
1
2
1
1
1
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
2
0
1
1
2
0
1
2
0
1
0
2
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
2
0
0
2
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
2
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
2
0
1
0
0
3
0
0
0
3
0
1
0
0
0
2
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
1
0
0
0
5
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
6
0
0
0
0
1
0
2
0
0
1
2
0
0
0
2
0
0
0
2
1
0
0
0
4
2
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
2
0
0
0
2
0
0
1
0
0
2
1
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
1
0
1
2
1
2
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
3
0
0
2
0
2
0
0
0
2
2
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
1
0
0
0
2
0
0
1
0
0
0
2
0
1
0
0
1
2
0
0
1
0
0
1
0
0
1
0
0
0
2
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
1
5
0
0
0
1
1
2
0
2
2
0
0
0
1
0
1
0
0
0
0
0
2
3
2
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
2
0
2
0
2
0
1
0
2
1
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
2
0
0
0
0
0
1
5
0
0
0
1
1
11
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
2
0
2
1
0
2
0
2
0
0
0
0
0
2
0
0
2
0
1
0
2
1
0
2
0
0
0
1
2
0
0
2
0
0
0
2
1
2
0
0
0
0
1
0
0
0
1
0
2
2
0
2
0
2
0
2
2
0
0
0
0
0
0
0
0
1
2
0
0
2
1
1
0
0
0
0
0
2
2
1
2
3
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
2
0
0
0
0
0
0
1
2
1
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
1
1
1
0
0
2
1
0
0
1
0
2
0
0
0
0
0
2
0
0
2
1
1
0
0
0
0
0
0
1
2
0
1
0
0
0
0
2
0
0
0
1
2
0
0
0
1
0
0
2
1
0
0
0
1
0
1
0
0
0
1
0
0
2
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
2
0
0
0
0
2
0
0
0
2
0
0
0
2
1
0
0
0
1
0
2
1
0
1
0
0
0
0
2
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
1
2
0
0
1
1
2
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
2
1
0
0
0
3
0
0
0
0
1
1
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
2
0
1
0
0
0
1
0
0
3
0
1
2
0
0
0
0
2
2
0
0
0
1
0
2
2
0
2
0
1
2
1
1
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
3
0
1
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
2
2
0
2
2
0
0
0
0
0
0
3
1
0
2
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
6
1
0
0
0
0
1
1
1
2
1
1
0
1
0
0
1
2
1
1
0
0
2
3
1
0
0
0
0
2
1
1
0
0
0
1
0
2
2
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
2
0
1
0
0
0
0
2
0
0
0
1
0
1
0
2
0
0
0
0
0
0
2
1
5
2
0
0
0
0
2
0
2
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
1
3
1
0
0
2
0
1
0
0
0
0
0
0
0
0
1
2
0
1
0
0
2
1
2
1
0
1
1
0
1
1
0
1
0
0
2
0
0
2
0
0
0
1
0
2
0
0
2
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
2
1
1
0
3
0
0
2
0
1
1
1
0
0
0
0
2
1
0
0
0
2
2
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
1
2
0
1
0
3
1
2
0
1
0
2
2
2
0
2
1
0
1
0
2
1
1
0
0
0
2
2
1
2
0
0
0
2
2
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
2
0
0
2
4
0
1
1
0
1
2
0
2
5
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
2
0
0
1
0
0
2
1
0
0
0
2
2
0
1
0
0
3
0
1
0
0
0
0
0
3
0
0
1
1
0
2
0
2
2
1
1
2
0
0
0
2
0
0
0
2
0
2
1
1
0
3
1
0
0
0
0
0
0
0
1
0
0
1
2
2
0
1
2
1
0
0
0
0
1
0
0
0
2
1
1
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
1
1
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
2
0
0
0
0
2
2
0
1
0
0
0
0
0
0
2
0
0
2
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
2
0
1
0
0
0
1
2
0
2
0
1
2
0
0
1
1
0
1
1
1
0
1
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
2
1
0
1
2
0
2
0
1
4
2
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
1
2
0
4
0
0
3
1
0
1
2
1
0
2
0
0
0
0
0
1
0
0
1
0
0
1
2
0
0
2
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
2
1
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
2
0
1
0
0
0
1
0
0
0
2
0
1
0
2
0
0
1
2
0
0
2
0
0
1
0
0
0
0
2
0
1
1
2
3
7
0
0
0
0
0
0
0
1
0
1
0
0
2
2
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
1
0
1
1
0
1
0
0
1
0
1
1
1
0
0
0
2
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
1
0
1
3
0
2
2
0
0
0
0
0
2
0
2
2
0
2
0
2
1
0
3
0
0
1
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
4
0
0
2
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
2
1
1
0
2
3
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
2
2
2
2
0
0
0
0
0
0
1
0
0
0
4
0
0
2
0
1
0
5
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
3
0
1
0
1
0
0
0
0
0
1
2
0
0
0
0
3
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
1
0
2
0
0
2
2
1
0
0
2
2
1
0
2
0
0
2
0
0
0
2
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
2
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
3
1
1
0
1
0
0
2
0
1
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
2
0
2
2
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
3
0
0
1
1
0
2
0
0
1
0
1
0
1
0
0
4
0
0
0
1
0
0
1
1
0
2
0
0
0
0
1
1
1
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
1
0
0
2
1
0
1
0
2
0
2
0
0
0
2
0
0
2
0
1
0
0
1
0
3
0
0
0
1
1
2
0
0
3
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
3
0
0
0
0
1
2
0
0
1
3
1
0
5
3
0
0
0
0
0
0
5
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
2
1
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
1
0
1
0
0
2
1
0
2
0
3
1
0
0
0
0
0
0
0
4
1
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
2
1
1
0
0
0
0
0
2
0
0
0
0
0
2
0
2
1
1
0
0
1
3
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
2
1
0
2
2
0
2
0
0
0
1
2
2
0
0
2
0
0
0
0
0
1
3
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
1
1
0
0
1
0
1
0
2
0
0
2
1
0
5
0
1
2
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
2
0
0
1
0
2
0
1
0
0
2
0
0
2
0
0
0
1
0
1
0
0
2
0
2
1
0
0
0
0
0
0
0
0
1
2
2
0
2
1
0
0
0
0
2
0
0
0
1
2
0
0
1
0
0
6
0
0
0
0
1
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
3
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
1
1
0
1
2
0
0
0
0
0
1
0
2
1
1
0
0
1
2
0
0
1
0
0
2
0
1
0
0
1
0
0
0
1
2
0
2
1
1
0
3
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
1
1
0
1
0
2
0
0
2
0
0
0
0
0
1
2
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
3
0
0
2
0
1
0
0
0
0
2
0
0
0
1
0
4
0
0
1
0
0
1
0
2
0
0
2
1
1
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
1
2
0
0
1
0
1
2
0
1
0
0
0
0
0
3
0
0
0
3
0
2
2
0
2
2
1
2
1
1
0
4
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
2
0
0
1
0
1
0
0
0
0
5
2
0
0
0
0
0
2
3
0
1
0
2
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
2
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
1
0
2
1
0
0
0
0
0
1
2
0
0
0
0
2
0
1
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
2
0
1
0
0
2
1
0
2
0
0
0
0
0
3
0
0
0
0
2
0
0
2
2
1
0
0
0
0
2
2
0
2
1
0
0
0
0
0
0
0
0
1
2
0
0
0
3
0
2
0
1
1
0
0
1
0
0
2
3
1
3
1
0
4
0
1
1
0
1
2
1
0
0
0
0
0
0
0
0
0
3
1
0
0
0
3
0
0
1
1
2
2
0
0
0
0
0
1
3
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
1
0
0
1
0
0
0
1
1
2
0
0
1
1
0
0
0
0
1
0
0
0
2
2
0
1
0
1
0
0
0
0
0
0
0
0
1
0
2
0
2
0
1
0
4
0
1
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
1
0
2
0
0
2
0
2
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
3
2
0
0
0
1
0
1
1
0
0
1
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
1
0
5
1
1
1
1
1
1
0
1
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
1
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
1
0
1
0
2
2
0
0
0
0
2
1
1
0
0
0
0
0
0
2
1
0
0
0
0
0
3
0
0
0
0
3
0
2
0
0
0
1
0
2
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
1
2
0
1
1
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
2
0
0
1
0
3
2
2
0
0
1
1
1
0
0
3
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
2
1
0
0
0
1
2
0
0
2
0
2
1
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
2
0
0
0
1
0
1
0
2
1
0
3
0
2
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
2
0
3
1
0
0
0
1
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
1
0
0
0
2
0
1
1
1
0
1
0
3
2
0
2
1
0
0
0
0
2
0
0
1
0
0
0
2
0
0
2
2
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
1
0
0
5
0
0
2
2
0
0
1
4
0
0
0
0
0
0
1
3
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
2
2
2
0
1
0
0
0
0
1
2
3
2
0
0
0
1
1
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
2
0
1
2
0
0
0
0
0
4
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
2
2
0
0
2
0
0
0
1
0
2
1
0
3
2
0
1
1
2
2
0
1
2
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
1
2
0
0
0
0
1
2
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
3
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
3
0
1
1
2
0
0
2
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
2
0
1
1
0
0
0
0
0
0
0
0
2
2
0
1
1
2
0
0
0
0
0
2
0
0
0
2
0
4
1
1
2
0
0
0
0
2
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
2
1
0
0
1
0
2
1
0
0
2
1
0
0
1
0
0
1
0
0
1
0
0
2
1
0
0
0
0
2
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
2
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
1
0
3
0
1
2
1
0
2
0
2
0
2
1
0
2
1
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
3
0
2
0
1
0
0
0
0
1
0
2
0
1
0
1
2
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
1
0
0
2
0
0
0
0
0
2
1
0
0
1
2
0
0
1
1
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
3
0
0
0
0
0
2
0
1
1
0
1
0
0
0
0
2
0
2
2
2
0
0
0
0
0
0
3
0
1
0
0
0
1
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
1
0
0
2
0
0
1
2
0
0
0
0
0
1
0
0
0
1
1
0
2
0
0
0
0
0
0
0
2
0
1
2
0
1
1
2
0
0
0
0
0
0
3
1
3
0
3
0
0
0
0
1
0
0
2
0
0
0
2
1
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
1
0
0
2
2
0
0
0
2
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
3
2
0
1
0
0
0
0
1
1
0
2
0
1
1
1
0
0
0
1
0
0
0
1
1
0
0
2
0
0
1
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
1
0
2
0
2
2
0
0
1
0
1
0
0
0
2
0
0
2
2
0
2
1
0
0
2
0
0
0
0
2
0
1
2
0
2
3
1
0
1
1
0
0
0
0
0
2
2
1
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
2
0
2
0
0
1
1
0
0
0
2
0
2
0
0
0
0
0
0
1
2
0
0
2
0
1
2
0
2
0
0
0
0
0
1
1
0
0
0
2
1
1
0
1
4
0
1
0
2
2
1
2
0
0
0
1
0
1
2
1
1
0
0
0
0
0
2
0
0
1
2
0
0
2
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
1
0
0
0
0
2
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
4
0
1
0
0
0
0
0
0
0
0
0
4
2
1
0
0
0
0
1
0
0
0
0
2
1
0
0
0
1
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
2
1
0
0
1
0
2
0
0
0
1
2
0
2
0
3
1
0
0
1
0
2
0
0
2
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
2
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
2
0
0
0
1
0
2
0
2
2
0
1
0
0
2
2
0
0
1
0
1
0
0
0
1
2
2
3
2
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
8
1
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
1
0
2
0
0
2
2
1
2
1
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
2
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
2
2
0
0
2
0
2
1
0
1
1
0
0
0
1
1
4
0
0
1
0
0
4
1
1
0
0
2
0
1
0
0
1
1
0
0
2
0
0
0
0
0
0
2
1
2
0
2
3
1
1
0
1
4
0
2
4
0
1
0
2
2
0
0
0
1
1
0
0
0
0
2
1
0
0
0
1
0
0
2
1
2
0
0
0
1
0
0
0
0
2
1
0
0
2
0
1
0
0
2
1
0
0
2
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
2
0
1
1
1
0
0
0
0
0
1
0
0
1
4
0
2
1
0
1
0
2
1
1
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
1
0
1
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
1
0
2
0
2
2
1
0
0
0
1
0
1
0
1
2
1
2
0
0
0
0
0
0
0
1
1
1
2
0
0
0
1
2
1
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
2
0
0
0
0
2
1
0
1
0
2
2
0
1
1
0
0
0
3
0
0
1
0
1
1
3
1
1
0
0
1
0
1
1
0
3
0
0
0
0
2
2
0
0
0
1
0
0
2
2
1
0
0
0
0
0
2
0
0
1
8
0
0
0
0
2
0
0
2
1
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
2
1
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
1
3
0
0
0
0
0
2
0
0
1
2
0
0
1
0
0
0
0
2
0
0
0
3
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
2
0
0
0
0
7
0
2
1
0
4
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
1
2
1
1
1
0
0
0
0
0
1
4
0
4
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
4
2
0
0
0
0
0
0
1
0
2
0
0
1
1
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
7
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
2
2
0
2
2
0
4
2
0
2
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
1
1
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
3
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
1
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
2
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
13
1
2
2
0
0
1
2
0
0
2
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
1
2
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
2
1
0
0
0
0
0
0
4
0
0
0
0
1
0
1
1
5
1
1
1
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
1
1
0
1
2
1
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
2
1
0
2
1
0
1
2
0
0
0
2
2
0
1
0
0
0
2
0
2
3
0
2
0
0
0
0
3
1
0
0
1
0
0
0
1
0
0
0
0
0
2
1
0
1
0
2
1
0
0
0
2
1
2
0
0
0
0
0
0
2
2
2
0
0
1
1
0
0
0
1
0
0
0
1
2
2
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
2
0
0
2
1
2
0
0
2
0
0
0
0
1
0
2
2
4
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
3
2
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
2
1
0
1
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
2
0
1
0
2
0
0
2
3
0
1
0
0
0
1
0
1
0
1
1
0
1
2
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
3
2
0
0
2
0
1
0
0
1
0
0
2
2
1
1
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
2
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
2
0
0
1
0
1
2
0
0
0
1
2
0
0
0
0
1
1
0
0
1
2
1
0
0
0
0
1
3
0
0
0
0
0
3
2
0
1
0
0
2
1
0
0
0
0
0
0
0
0
1
1
0
0
1
2
0
0
0
2
0
0
1
3
0
0
0
2
2
0
1
1
0
0
0
2
0
0
1
0
2
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
3
1
1
0
0
0
0
0
2
2
0
0
2
2
0
0
0
1
6
0
0
0
0
1
0
1
0
0
2
0
1
1
0
0
2
0
0
1
0
0
1
2
1
2
0
1
2
1
2
3
0
0
0
0
0
2
0
1
0
1
1
0
0
1
0
0
0
0
0
0
2
0
0
2
1
1
0
0
0
0
1
0
0
0
0
2
0
0
2
2
1
0
2
1
0
2
0
0
0
1
0
1
0
0
0
1
2
0
0
1
1
0
0
0
0
0
0
0
1
2
0
1
0
2
2
2
0
0
0
0
0
0
0
4
0
0
0
1
0
1
0
0
2
0
0
0
0
0
1
1
1
0
1
2
2
0
1
0
0
0
0
2
0
2
0
0
0
0
2
2
0
0
0
0
0
2
2
2
10
0
0
2
2
0
0
1
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
1
0
1
0
0
0
0
2
0
0
1
2
1
0
3
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
1
2
0
0
0
0
1
0
1
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
1
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
4
0
2
1
1
0
2
0
1
1
0
2
0
1
0
0
0
1
2
0
0
0
2
0
2
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
3
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
2
0
0
2
0
0
0
1
0
2
0
0
2
0
1
0
0
0
0
1
0
1
1
0
0
1
0
0
0
2
0
0
0
1
0
1
0
1
0
2
1
0
0
2
4
0
2
0
3
2
0
0
1
0
0
3
2
1
0
0
1
2
0
0
0
0
0
0
0
0
2
1
1
1
0
2
0
0
2
0
0
0
1
1
3
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
1
0
1
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
2
0
0
0
1
0
2
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
1
1
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
1
0
0
2
0
2
0
0
2
0
3
0
1
0
0
0
0
1
1
2
0
0
0
2
1
0
2
0
1
2
1
1
0
1
0
0
2
0
0
1
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
1
0
1
0
1
0
1
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
1
2
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
1
2
0
1
0
2
0
0
0
1
2
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
1
2
0
0
0
1
0
0
2
0
0
0
2
2
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
1
1
0
0
0
0
2
0
0
1
2
2
0
8
1
0
1
2
2
0
1
2
0
2
0
0
0
2
1
2
0
0
0
1
3
0
2
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
2
1
0
0
0
2
1
0
0
0
1
0
0
0
1
0
1
0
1
0
0
1
0
0
3
2
1
3
0
0
1
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
3
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
2
1
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
1
0
1
1
0
2
1
0
0
0
0
4
0
0
2
1
0
2
0
0
3
1
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
1
2
0
0
0
0
0
0
2
0
0
0
0
2
0
1
2
2
0
0
1
1
0
0
0
0
0
0
0
0
2
1
0
0
2
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
2
0
2
0
1
1
0
0
1
0
1
2
2
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
1
0
0
0
0
0
2
2
1
0
0
1
1
1
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
2
1
0
0
0
1
0
0
0
0
0
3
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
1
0
0
2
0
1
0
2
0
0
0
1
0
0
0
2
2
0
4
2
1
0
0
2
2
0
0
0
0
0
2
1
0
0
0
0
3
0
0
0
0
1
1
0
2
0
2
1
1
0
0
1
0
0
2
2
0
2
0
0
0
0
0
2
0
0
1
0
0
2
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
1
1
2
2
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
1
0
1
0
2
0
0
0
0
0
2
2
0
0
0
0
0
1
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
2
0
0
0
0
3
2
0
0
0
1
2
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
2
0
1
1
0
0
3
2
3
0
2
0
0
0
2
0
0
0
0
2
0
0
1
0
1
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
2
0
1
1
3
1
0
0
0
0
0
0
0
0
1
2
1
0
0
3
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
2
0
0
0
0
2
2
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
1
1
0
0
0
1
0
0
5
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
2
2
3
0
0
0
0
0
0
1
1
0
0
0
2
0
1
0
0
0
0
0
0
0
1
4
0
1
2
0
2
3
0
0
0
2
0
1
0
2
2
0
0
0
0
1
0
2
0
0
1
1
0
0
2
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
2
0
0
0
2
0
2
0
2
2
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
1
0
0
1
0
2
0
0
2
0
1
2
2
0
2
0
0
1
3
0
2
1
1
0
0
0
0
0
4
1
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
1
0
0
0
2
1
2
2
0
1
0
0
2
0
0
0
0
0
1
1
2
0
2
1
0
0
0
1
0
1
2
0
0
0
2
0
0
3
2
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
2
0
2
0
0
2
0
0
0
0
1
1
4
0
1
0
1
0
0
0
1
0
0
2
1
1
1
0
1
0
2
2
1
0
0
3
0
9
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
2
2
0
1
2
0
0
1
0
0
0
1
0
1
2
0
0
1
0
1
1
0
0
0
2
0
4
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
2
0
0
0
0
2
1
0
0
0
0
0
0
1
1
1
0
4
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
2
0
3
1
2
0
0
0
0
0
3
0
2
1
0
0
0
0
0
0
0
0
0
0
0
5
2
1
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
2
0
0
0
0
2
1
1
1
1
0
0
2
0
0
1
0
0
5
0
0
0
0
0
0
3
0
0
0
0
1
0
0
2
0
1
0
0
0
2
0
0
1
0
1
2
2
2
0
1
0
0
1
1
0
0
3
2
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
1
1
0
0
1
4
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
2
1
1
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
2
2
1
1
0
1
0
2
2
0
0
0
1
0
2
3
0
0
0
0
0
1
1
1
0
0
2
0
0
0
0
0
1
0
1
0
0
2
0
0
1
1
1
4
0
0
0
0
0
0
3
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
1
2
1
2
0
0
0
0
0
0
2
0
2
0
3
2
2
2
1
2
1
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
3
1
0
0
0
0
2
0
0
2
1
0
1
0
0
0
0
0
0
0
0
2
0
0
3
0
0
1
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
2
0
0
2
2
0
0
2
0
1
2
0
2
0
0
1
0
2
0
2
0
0
0
0
1
2
0
0
0
0
0
0
2
4
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
3
0
0
1
2
0
0
1
1
0
0
0
0
0
0
2
1
2
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
1
2
0
0
1
0
0
2
0
0
10
0
2
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
1
3
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
1
0
0
0
1
0
2
1
0
0
1
0
0
0
0
1
0
1
2
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
2
2
2
0
0
0
2
0
2
0
2
0
0
0
0
0
0
2
1
1
0
0
2
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
1
1
3
1
0
0
2
0
0
3
0
0
0
0
0
0
1
0
1
1
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
3
0
1
0
1
0
2
2
0
0
0
0
0
0
3
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
1
2
0
0
0
0
0
0
2
1
0
0
1
0
0
0
3
0
1
0
0
2
2
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
1
0
1
1
1
1
0
0
0
2
0
0
2
0
0
2
2
0
2
2
0
0
0
1
0
2
2
0
0
0
0
0
2
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
1
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
1
0
0
2
0
2
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
2
0
1
0
0
0
0
0
2
2
2
2
0
0
1
0
0
0
0
0
2
2
0
0
1
2
1
1
0
0
1
1
1
0
4
2
2
0
0
2
0
0
1
0
0
9
2
0
0
0
3
0
0
0
1
2
0
0
0
1
2
0
2
3
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
5
0
0
1
0
2
0
0
0
2
2
0
1
1
1
2
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
2
0
0
0
2
0
1
0
1
0
0
0
1
0
0
0
1
0
1
0
0
1
2
0
1
0
2
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
11
0
0
0
0
0
4
1
1
0
0
2
0
1
0
1
0
1
0
0
0
0
0
2
1
0
2
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
3
0
1
2
2
0
2
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
1
0
0
1
2
1
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
1
1
1
0
2
2
2
0
1
0
1
0
0
2
1
2
1
1
0
0
0
2
2
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
2
1
0
0
0
0
0
1
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
1
1
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
1
1
0
0
0
1
0
2
0
0
0
1
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
2
0
0
0
0
2
1
3
2
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
2
1
1
1
0
2
0
0
2
0
0
0
0
0
0
2
0
0
2
2
1
2
1
0
1
0
0
0
0
0
0
1
0
2
2
0
1
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
2
1
1
2
1
1
0
0
2
0
0
0
0
1
2
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
2
0
0
1
2
0
0
0
0
2
0
2
0
0
0
0
1
2
0
0
0
1
0
2
2
0
1
0
0
1
3
0
0
0
0
1
0
0
0
1
0
2
0
0
0
2
0
1
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
2
2
0
2
0
0
0
0
0
0
1
1
0
2
2
1
1
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
1
2
0
6
0
1
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
1
0
1
0
0
2
0
0
0
0
2
0
2
0
0
2
0
0
0
2
2
0
3
2
0
0
1
2
0
1
0
0
1
0
0
1
2
1
1
0
3
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
1
2
0
2
0
1
1
0
2
0
1
0
0
2
0
0
2
1
2
0
0
2
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
1
2
2
0
1
0
0
0
0
1
0
2
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
2
1
1
2
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
1
0
0
2
1
0
2
0
1
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
2
0
0
0
0
2
0
0
2
1
2
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
2
2
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
2
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
2
0
2
3
0
0
0
0
0
2
0
0
1
3
0
0
0
14
0
0
0
1
0
0
1
0
0
1
2
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
1
2
2
0
0
0
0
0
1
2
1
0
2
2
2
1
0
3
0
2
1
0
0
1
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
2
0
1
0
0
0
2
1
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
5
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
3
0
2
1
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
1
1
2
0
0
1
0
0
0
0
0
1
0
1
0
0
2
0
0
1
1
0
1
0
0
0
0
0
0
2
2
1
0
0
3
0
0
0
1
1
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
2
0
0
1
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
1
3
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
2
0
1
0
0
0
0
0
2
0
2
0
5
0
0
2
0
0
0
0
0
0
2
0
0
2
1
0
1
1
1
1
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
1
1
0
3
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
1
0
1
2
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
3
0
0
2
0
0
0
0
1
2
2
0
1
0
1
0
2
0
2
1
1
2
0
0
1
0
0
0
0
1
0
3
0
0
0
0
1
1
4
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
2
2
0
2
0
0
0
0
0
1
0
0
2
0
0
0
1
1
1
0
2
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
2
0
0
0
0
2
0
1
0
1
0
2
1
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
2
0
3
1
0
0
0
0
1
2
0
2
1
0
0
0
0
0
0
1
1
0
1
0
0
2
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
2
0
0
1
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
2
1
0
0
0
0
1
1
2
0
2
0
2
0
0
0
0
0
0
1
0
1
0
0
0
3
0
0
3
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
1
0
0
1
0
0
0
2
0
1
1
2
0
0
2
0
0
0
1
0
0
1
0
1
1
0
0
0
1
0
1
0
1
2
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
4
0
0
0
2
0
0
0
0
1
0
0
0
0
2
2
2
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
2
0
0
0
0
2
0
2
2
0
0
0
2
0
0
0
1
2
0
0
0
0
0
2
2
0
0
0
0
1
0
0
2
0
0
0
2
2
0
1
0
0
0
1
2
0
0
0
1
0
2
1
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
6
1
0
0
0
0
0
0
0
3
0
0
2
2
0
0
2
0
0
0
2
0
1
2
1
0
0
0
0
1
1
0
0
2
2
0
2
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
1
2
2
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
3
0
0
2
2
2
0
0
2
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
2
1
1
0
0
0
0
0
1
0
2
0
1
2
1
0
1
0
0
5
0
2
2
3
0
0
1
2
1
1
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
3
2
1
2
0
0
2
0
0
0
0
0
1
2
0
1
0
0
1
2
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
1
0
1
0
0
2
0
0
0
2
2
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
2
0
2
1
1
0
0
0
0
1
0
0
0
0
0
2
1
1
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
2
1
2
1
0
0
0
1
0
1
0
0
1
1
1
0
0
0
0
2
0
0
0
2
2
0
2
2
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
1
2
2
0
0
1
0
0
2
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
2
4
2
2
2
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
2
0
0
0
0
0
0
1
1
0
0
2
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
3
1
0
0
0
2
1
0
0
0
0
1
2
2
1
1
0
2
1
3
1
0
2
0
0
1
0
0
2
0
1
1
0
1
5
0
0
0
0
0
0
0
0
1
0
2
0
2
2
0
0
0
0
3
0
0
1
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
1
1
0
4
0
0
1
1
0
0
0
1
0
0
2
0
0
0
1
2
0
0
1
0
2
1
0
3
0
3
0
0
0
0
1
0
0
0
1
0
0
0
1
0
4
0
1
0
1
1
2
0
1
0
1
4
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
2
1
0
2
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
1
0
1
1
3
0
2
2
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
1
1
2
0
0
1
0
2
2
1
0
0
0
0
0
1
0
1
1
0
0
1
0
0
1
1
0
0
3
0
1
0
3
0
1
2
2
0
0
2
0
0
1
0
1
0
0
6
0
0
0
1
0
2
0
2
0
1
0
0
0
0
0
0
1
0
0
0
1
2
0
0
2
1
0
2
1
1
0
3
0
0
2
0
2
1
0
0
1
2
0
0
0
0
0
0
3
0
0
1
0
1
0
1
0
1
1
2
0
1
0
1
0
0
2
0
0
0
0
1
0
0
1
0
0
2
0
1
0
0
0
0
0
0
2
0
0
1
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
1
0
0
0
0
1
0
2
0
2
1
1
1
0
0
2
2
0
0
0
0
0
0
2
0
2
0
2
0
0
2
0
0
0
0
1
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
1
2
0
0
1
0
0
0
0
0
2
0
0
0
1
2
0
0
1
0
2
0
0
2
0
0
0
0
0
1
0
0
2
1
1
0
0
0
0
2
0
0
2
1
1
2
2
0
0
0
0
1
0
2
2
0
1
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
2
3
0
0
0
0
1
2
0
0
0
3
2
0
1
0
0
0
1
2
2
0
0
2
1
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
1
3
1
2
0
2
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
1
0
0
2
0
1
0
2
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
1
2
0
3
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
1
0
4
1
0
2
0
0
0
1
0
0
0
2
0
1
0
0
1
0
1
0
0
1
0
2
0
2
0
0
0
1
1
1
2
0
0
1
2
2
0
0
1
0
0
1
2
0
0
3
0
0
0
1
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
1
3
0
0
0
2
0
1
0
4
0
0
1
1
0
3
0
1
0
3
0
2
1
0
1
0
0
0
0
1
0
0
0
1
0
1
2
0
0
0
0
0
0
0
2
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
3
1
1
2
0
0
0
0
1
1
2
0
0
2
0
0
1
3
2
0
0
0
1
1
0
1
0
0
1
0
2
0
2
0
2
0
0
0
1
1
0
0
0
0
0
0
0
3
0
0
1
0
0
0
2
3
1
0
0
0
0
0
0
0
0
1
0
1
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
2
2
1
1
0
0
0
0
0
0
0
2
0
0
0
1
2
0
2
0
2
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
2
0
0
2
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
1
0
0
0
1
0
0
0
1
2
0
0
0
1
0
0
0
0
2
0
2
0
0
1
2
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
2
0
0
1
0
1
0
0
2
0
0
1
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
1
0
0
2
4
1
2
0
0
0
0
0
2
0
0
0
2
0
0
0
2
1
0
2
1
4
2
0
0
0
1
0
0
1
2
0
0
2
0
0
2
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
2
0
1
0
0
1
0
2
0
3
13
0
0
0
0
2
0
2
0
2
0
0
2
1
1
0
0
0
0
0
0
0
0
1
0
0
1
3
1
0
0
1
0
0
0
1
0
2
0
0
0
0
1
0
0
0
1
0
0
2
1
2
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
3
1
0
0
2
0
1
0
1
6
0
0
1
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
2
0
0
1
0
0
1
0
0
0
0
0
0
2
1
1
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
2
3
0
0
0
0
2
0
0
0
3
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
2
4
2
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
2
1
0
0
2
1
2
3
0
1
0
0
0
0
0
0
1
2
0
0
4
2
1
0
2
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
2
1
2
2
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
2
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
2
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
2
1
1
1
1
0
2
0
0
1
0
0
0
0
0
0
2
0
0
2
3
0
0
1
0
1
0
0
0
0
2
0
1
1
1
0
1
0
0
1
0
1
2
0
0
3
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
2
2
0
0
0
0
1
0
0
0
2
0
2
0
0
1
0
1
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
17
0
2
0
2
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
1
2
0
0
1
0
3
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
2
2
1
0
0
2
0
1
2
1
0
0
2
0
2
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
2
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
1
0
2
0
1
0
0
0
2
2
1
2
0
0
1
1
1
0
3
0
0
0
0
0
5
2
1
0
1
2
1
2
0
1
0
0
2
0
0
0
0
1
0
0
3
1
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
2
1
0
1
2
2
2
0
0
1
0
0
3
0
0
0
0
2
1
2
0
0
0
0
1
0
3
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
2
2
0
0
0
3
1
2
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
1
0
0
2
0
2
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
1
0
0
1
0
0
2
0
1
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
3
0
0
2
2
0
0
1
0
0
0
0
0
0
0
1
0
2
2
2
2
0
1
1
0
2
0
0
0
0
1
0
2
0
0
0
0
2
3
0
1
0
0
0
0
1
0
2
0
0
1
0
1
0
1
1
0
1
1
0
0
0
0
2
1
2
0
3
0
1
0
2
2
1
0
1
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
2
1
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
2
1
1
0
0
0
0
0
2
0
0
0
3
2
0
0
2
0
0
0
0
0
0
2
2
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
3
0
2
1
2
0
0
0
0
0
3
2
0
1
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
3
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
2
1
0
0
0
0
0
0
3
0
3
2
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
2
0
0
2
1
0
0
0
0
2
0
0
0
1
0
0
1
0
0
2
4
0
0
0
0
0
0
0
2
1
2
1
0
2
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
2
1
0
1
0
1
1
0
0
2
0
0
0
0
0
0
0
0
4
1
0
0
2
0
1
0
1
0
0
0
0
0
0
1
2
0
2
0
1
0
2
1
0
0
0
3
2
0
0
0
3
0
0
2
0
1
0
2
0
0
2
0
1
0
2
0
0
2
0
0
2
0
1
0
0
2
0
1
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
2
1
0
2
3
1
1
0
0
1
0
1
2
0
0
1
1
2
2
1
0
0
2
0
1
1
2
0
0
1
1
0
0
0
2
2
0
2
0
0
0
0
0
1
0
0
1
4
0
0
0
2
0
0
1
0
0
0
0
0
1
0
2
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
2
2
1
0
2
0
0
0
0
0
4
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
2
2
0
1
0
1
0
0
0
0
0
2
0
4
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
3
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
2
0
0
0
0
3
0
0
2
0
0
0
0
1
2
0
1
0
0
0
0
4
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
2
1
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
2
0
1
0
0
0
1
0
1
0
0
2
0
4
0
0
0
2
0
0
0
0
0
2
2
0
2
0
1
1
0
0
0
2
0
0
0
1
2
3
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
3
0
0
1
0
0
0
0
1
1
2
1
1
0
0
0
2
3
1
1
0
1
0
0
0
0
1
0
0
0
2
0
0
1
2
2
2
0
1
0
0
2
0
0
2
2
0
0
0
0
0
3
1
0
1
3
0
1
1
2
2
2
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
2
0
1
2
2
0
0
1
0
0
1
0
2
1
0
1
0
1
0
0
0
0
1
0
2
0
0
0
0
1
0
0
2
2
0
0
0
0
0
1
0
2
1
2
2
0
0
0
1
0
2
0
2
0
2
0
2
0
4
0
1
1
0
0
0
6
0
0
2
0
0
2
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
4
1
1
0
1
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
3
0
0
0
0
4
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
1
2
0
0
0
2
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
2
1
0
0
0
0
2
0
0
0
0
0
4
0
0
0
0
1
3
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
3
0
0
2
0
0
2
0
2
2
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
2
2
2
0
1
1
2
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
2
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
1
1
2
0
0
5
0
0
0
0
0
0
0
4
1
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
1
0
2
0
0
0
2
0
0
0
0
1
0
0
1
1
0
1
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
1
0
0
0
1
1
0
0
2
2
0
0
2
0
2
2
0
0
0
0
3
1
0
1
0
0
0
0
0
0
2
0
2
1
0
0
1
0
0
0
2
10
2
1
0
4
0
2
0
3
2
2
0
0
0
0
2
2
1
0
0
1
2
0
0
3
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
1
1
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
1
0
0
2
0
0
0
4
1
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
2
0
0
0
1
0
2
2
1
0
0
0
0
2
1
1
0
1
0
0
1
1
2
1
0
3
1
2
0
1
0
0
0
0
2
0
0
1
0
2
0
2
0
2
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
2
0
0
1
0
0
0
0
1
1
0
0
0
0
0
2
1
3
1
2
1
0
0
3
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
1
1
0
0
2
0
0
0
2
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
2
2
3
1
2
0
1
1
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
2
1
0
0
0
1
0
0
0
1
0
2
0
0
0
2
0
1
0
0
0
2
2
0
0
0
1
0
0
0
1
0
0
1
0
0
0
2
0
0
0
2
0
0
0
1
1
2
0
1
0
0
2
2
1
0
0
2
0
0
0
2
0
2
0
0
2
0
2
5
2
0
0
0
2
2
2
1
0
0
0
3
1
0
2
0
0
0
1
0
0
0
1
1
1
2
2
0
0
0
0
2
0
0
2
2
0
0
2
1
2
0
0
0
0
0
0
1
0
0
0
0
0
1
2
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
2
0
2
0
2
0
0
0
2
0
0
1
2
0
0
2
2
2
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
2
0
2
0
1
4
0
0
1
1
0
1
0
0
0
2
0
2
1
5
0
0
2
0
0
0
0
3
3
1
3
1
0
0
0
0
1
0
0
0
0
0
0
2
0
2
1
2
2
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
3
0
1
1
1
0
1
2
0
1
0
2
2
0
1
0
1
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
3
0
2
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
1
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
1
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
1
3
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
1
2
0
2
0
0
0
1
2
0
2
1
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
1
1
0
0
0
2
0
0
0
1
1
2
1
0
0
0
4
0
1
0
0
0
0
2
0
0
2
5
2
0
0
0
2
0
0
0
0
0
3
0
2
0
2
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
4
1
0
0
0
0
1
0
2
0
1
2
2
2
2
0
3
0
0
0
1
1
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
2
0
2
1
0
0
0
0
1
0
0
0
0
1
0
2
1
0
0
0
0
0
1
1
1
1
0
2
0
2
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
2
3
0
0
2
0
2
0
0
1
0
2
0
2
2
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
1
0
2
0
2
2
1
1
0
0
0
0
2
2
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
2
0
2
1
0
0
0
1
2
0
2
0
0
0
1
2
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
2
2
2
2
2
0
0
0
0
4
1
0
0
0
0
1
0
0
0
0
1
0
0
2
0
2
0
1
0
0
1
1
0
1
0
0
0
0
2
0
2
0
2
0
0
0
0
2
0
0
2
1
0
2
2
0
0
0
3
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
1
1
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
1
2
0
0
0
2
0
0
3
0
1
0
0
1
0
1
0
0
0
2
0
0
1
0
0
0
1
0
0
2
1
0
0
1
0
0
2
0
0
1
0
0
0
1
0
0
0
0
3
0
2
0
3
1
0
0
0
0
0
0
0
0
0
0
1
1
2
0
1
0
0
0
0
3
0
0
0
1
0
0
1
2
2
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
3
2
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
2
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
2
1
0
0
0
2
0
0
2
1
0
2
0
2
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
3
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
1
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
3
0
0
0
2
2
0
2
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
1
0
1
0
0
0
0
5
0
1
0
0
0
0
1
3
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
2
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
4
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
3
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
2
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
1
0
3
0
1
0
0
1
3
0
0
0
0
2
2
0
2
1
0
0
0
0
0
0
0
1
3
1
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
2
2
0
1
0
1
1
1
0
0
0
0
0
1
1
0
2
0
2
2
0
0
0
2
0
0
0
2
3
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
2
0
0
1
2
1
0
0
0
2
2
4
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
2
0
0
0
1
0
0
2
2
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
1
2
0
2
0
1
0
0
0
0
1
0
2
2
0
0
0
0
0
2
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
2
0
1
2
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
2
1
0
0
0
0
1
0
1
2
1
0
0
2
0
0
0
3
1
0
2
0
2
0
1
2
0
1
2
0
2
0
0
0
2
0
0
3
0
0
0
2
0
0
2
3
1
0
2
1
0
1
0
0
2
1
2
2
0
1
0
0
0
0
0
2
2
1
2
1
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
2
0
0
0
2
0
0
2
1
0
1
2
0
1
2
2
2
2
2
0
1
1
1
0
0
0
0
0
1
2
1
0
0
0
0
2
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
2
2
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
1
1
4
2
0
1
2
4
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
1
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
1
0
1
0
1
0
0
0
0
2
0
0
1
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
2
3
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
1
3
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
1
0
1
2
1
1
0
0
0
2
0
0
1
0
0
2
1
0
1
1
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
2
0
0
6
0
0
0
2
1
0
0
0
0
1
2
0
0
0
0
0
1
0
1
1
2
1
0
0
2
0
0
0
1
1
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
1
2
0
1
0
0
0
1
2
0
0
0
0
3
1
0
3
1
0
2
0
2
2
0
0
0
0
1
0
0
0
1
1
0
0
2
0
0
0
1
2
0
0
0
1
0
1
0
2
0
1
0
2
0
1
0
3
0
2
1
0
0
0
1
0
0
0
1
2
0
1
0
0
0
1
0
0
1
0
1
2
1
3
1
0
0
0
0
3
0
0
1
0
0
0
3
2
1
0
2
0
2
0
2
2
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
1
0
2
0
0
0
0
0
4
0
0
0
0
2
0
3
1
0
1
0
3
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
2
0
2
2
0
0
0
0
0
0
0
2
0
0
1
1
1
1
0
1
0
0
0
0
1
0
0
1
1
0
0
0
2
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
2
1
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
1
1
3
2
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
2
0
2
1
0
0
1
0
2
0
0
0
0
0
0
1
0
2
1
0
2
0
0
0
0
0
2
1
1
0
0
0
0
3
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
1
2
2
0
0
0
1
0
3
0
0
0
0
0
2
0
0
0
0
0
1
2
0
2
0
0
0
0
0
2
1
1
0
0
0
2
2
0
0
0
0
1
0
1
0
2
0
1
0
0
2
0
0
0
0
3
0
1
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
1
1
0
2
0
0
0
0
1
1
3
0
3
2
0
1
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
1
1
0
0
1
2
0
0
2
1
3
0
0
0
0
0
1
2
2
0
1
0
0
0
1
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
1
2
2
0
2
1
0
1
0
2
2
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
2
2
0
0
0
2
0
2
1
0
0
0
2
2
1
0
0
0
0
0
1
0
2
0
3
1
2
0
0
0
0
2
0
0
0
2
1
0
0
0
1
0
0
0
2
0
0
1
1
2
0
0
0
1
0
0
0
0
4
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
3
2
0
1
0
0
1
0
0
0
2
1
0
0
0
1
2
0
0
0
0
2
2
1
1
0
0
0
2
0
0
1
0
0
0
2
0
0
0
2
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
2
0
0
2
1
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
2
0
2
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
4
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
2
0
0
2
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
3
0
0
0
2
1
0
0
0
2
0
0
1
1
0
0
2
1
0
0
1
1
0
2
0
1
0
2
0
0
0
0
1
0
1
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
2
0
0
2
0
1
2
0
0
0
0
0
1
1
2
0
6
0
1
2
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
3
0
0
0
1
0
1
0
2
2
0
0
0
0
0
0
1
2
0
2
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
6
1
1
0
0
1
1
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
2
0
2
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
4
0
0
0
0
2
1
2
1
0
0
0
2
2
0
0
0
0
0
1
0
3
0
2
0
0
1
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
1
12
0
1
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
2
0
2
0
3
2
1
0
0
0
2
0
3
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
2
1
1
1
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
2
0
0
2
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
1
0
2
0
0
0
0
0
1
1
2
0
1
0
0
0
0
2
0
1
1
1
0
0
2
1
0
0
1
2
0
2
0
0
2
0
0
0
2
0
0
1
0
0
1
2
0
2
0
1
0
2
0
0
0
0
0
1
2
2
0
0
0
0
2
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
4
0
0
0
1
2
0
1
0
0
1
0
0
0
1
0
0
0
0
0
3
0
2
2
0
0
1
0
1
0
0
1
0
0
0
1
0
4
0
0
1
0
0
0
1
0
0
1
1
1
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
2
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
3
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
1
0
0
0
1
11
0
2
1
1
0
1
0
0
0
0
0
2
0
2
2
0
1
2
1
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
2
0
3
1
2
0
2
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
1
1
0
0
2
0
0
1
0
1
0
1
0
2
2
0
0
0
0
2
1
2
0
0
1
0
4
2
0
0
0
0
0
2
0
0
0
1
2
1
1
0
2
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
1
0
2
0
0
0
1
1
0
2
0
0
0
0
0
2
0
2
1
2
0
1
2
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
1
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
1
0
2
0
0
2
1
1
2
0
2
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
1
2
0
0
2
4
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
1
0
0
1
0
2
1
0
0
0
0
1
0
2
3
0
0
0
0
1
0
0
0
2
0
0
0
0
1
1
0
0
2
0
2
0
0
0
1
2
0
2
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
2
0
1
0
2
0
0
0
0
2
0
1
1
0
1
2
2
1
0
1
0
0
0
0
2
1
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
1
1
0
1
2
0
0
0
0
0
0
0
2
2
2
0
1
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
1
0
2
0
0
0
1
0
0
1
0
0
0
2
2
2
0
0
0
0
0
1
0
1
0
0
0
2
0
0
2
0
0
1
2
2
0
1
0
0
0
3
0
0
0
1
2
0
0
1
0
0
0
0
1
1
0
0
6
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
2
0
0
0
1
2
0
1
0
0
0
2
0
0
1
1
0
0
1
0
0
2
0
0
0
0
5
0
1
0
0
0
2
0
2
1
0
0
0
0
1
2
0
0
2
1
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
2
2
1
0
1
0
1
0
0
0
0
0
0
3
0
0
2
0
0
0
1
0
0
0
0
0
1
2
0
2
2
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
2
1
1
0
0
0
0
2
3
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
5
2
0
2
2
0
0
0
0
0
0
2
0
0
0
0
2
1
2
0
0
2
0
7
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
3
0
0
1
1
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
1
0
0
0
0
2
0
1
1
0
0
1
0
1
0
1
0
0
2
0
2
0
1
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
2
0
1
1
0
1
0
2
0
0
0
3
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
2
0
2
0
1
2
0
0
0
2
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
2
0
1
0
1
2
0
0
0
0
0
1
0
4
0
2
1
0
0
3
0
0
2
0
2
0
1
1
0
2
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
4
1
1
1
2
0
0
2
2
0
0
5
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
4
0
0
0
1
1
2
0
0
1
1
0
0
0
0
0
0
0
2
2
0
2
0
0
2
0
0
0
0
0
1
0
0
1
2
1
0
1
0
0
2
0
0
1
0
0
0
2
0
1
1
0
3
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
2
0
0
0
0
0
0
1
1
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
1
3
0
2
0
0
0
1
2
0
4
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
2
1
1
0
0
2
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
1
2
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
2
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
1
1
2
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
2
1
3
0
0
5
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
1
0
2
0
0
0
1
0
1
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
1
1
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
1
1
0
0
0
0
2
1
0
1
0
3
0
1
2
2
0
0
0
1
2
3
0
0
1
2
3
0
2
0
0
2
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
2
1
2
0
0
0
2
0
1
0
0
0
3
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
1
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
2
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
2
0
1
0
0
0
1
0
0
0
0
0
0
2
2
0
1
1
1
0
0
1
0
1
0
2
2
2
0
2
10
0
0
0
2
1
0
2
0
0
2
0
0
2
2
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
1
2
0
0
2
0
0
1
2
2
2
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
1
0
2
0
1
0
2
0
1
0
1
0
1
1
0
0
0
0
2
0
0
1
2
0
2
0
0
0
0
1
2
0
0
0
1
0
1
0
0
2
2
3
1
0
0
0
0
0
0
0
2
0
0
1
2
1
0
2
0
0
2
0
0
0
0
0
0
1
1
0
0
2
1
1
0
2
2
0
0
1
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
1
2
2
0
2
0
0
3
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
2
2
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
2
0
0
3
0
0
0
0
2
2
0
0
0
0
2
1
0
0
0
2
0
1
1
2
1
0
1
0
1
0
2
0
1
0
0
0
1
0
0
1
2
3
2
0
0
0
0
1
0
0
5
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
3
0
0
0
2
1
0
1
1
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
2
0
0
0
1
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
2
2
0
3
1
0
0
0
1
0
1
0
0
0
0
0
2
1
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
4
0
0
1
0
0
1
0
1
0
0
0
1
1
0
0
0
0
1
0
0
2
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
1
0
0
0
1
0
1
1
0
0
1
0
1
2
0
0
2
2
0
2
2
0
1
0
0
0
0
2
0
0
2
0
0
0
0
2
2
0
0
1
0
0
2
0
2
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
1
0
0
0
2
0
2
1
0
2
0
1
2
2
0
0
0
0
0
0
0
1
0
2
1
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
2
0
0
1
0
0
2
0
0
0
3
0
0
2
0
0
0
0
1
0
0
0
0
0
4
2
0
0
0
0
1
0
2
0
0
2
0
1
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
2
1
2
2
2
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
2
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
2
0
2
2
2
0
0
0
0
0
3
0
0
1
4
1
0
0
0
0
2
2
0
1
1
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
1
2
0
0
1
0
0
0
1
0
0
1
0
0
2
0
2
2
0
2
0
1
3
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
2
0
4
2
0
0
0
1
3
0
2
0
0
0
1
0
1
1
1
0
2
1
0
1
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
2
2
0
1
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
1
2
1
0
0
0
1
0
0
2
1
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
3
0
1
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
2
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
5
0
0
0
0
0
2
3
1
0
0
0
0
0
2
0
1
2
0
0
1
0
2
1
0
0
0
2
0
0
0
0
0
0
1
0
2
0
2
2
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
5
0
0
0
0
3
0
0
0
1
1
1
0
0
0
0
2
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
3
2
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
2
0
0
0
1
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
1
2
0
0
0
0
0
0
0
2
1
0
0
1
1
0
1
0
2
1
0
0
0
2
2
0
1
3
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
2
1
2
2
0
2
0
3
0
2
2
0
0
0
0
0
1
0
0
0
2
0
1
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
1
0
1
2
2
0
0
0
2
0
0
0
0
0
1
0
0
2
1
3
0
1
2
0
2
0
0
0
1
0
0
0
2
1
1
2
0
1
0
0
0
0
0
0
0
0
1
2
2
0
0
2
0
1
0
0
0
1
3
0
0
0
0
0
0
0
0
0
1
1
0
3
0
0
2
0
2
1
0
0
0
0
0
2
0
0
0
1
0
1
0
2
2
1
0
2
1
1
0
2
0
0
0
0
1
3
0
0
0
0
3
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
3
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
2
0
0
0
2
0
0
2
0
0
0
0
0
4
2
2
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
1
0
0
2
1
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
4
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
2
0
2
1
0
0
1
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
3
2
0
0
2
1
0
2
0
2
2
0
1
2
0
0
3
2
0
0
2
0
0
0
0
0
0
2
0
1
0
1
0
0
3
2
2
1
2
2
0
2
0
0
1
0
1
1
0
1
2
0
2
0
2
2
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
1
2
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
2
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
2
0
1
2
0
1
0
1
0
1
2
0
0
0
1
0
0
1
0
0
2
2
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
1
1
0
0
2
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
1
0
0
0
0
0
3
0
0
1
2
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
4
2
0
0
0
0
3
1
0
2
1
0
0
0
0
0
0
0
0
1
2
0
2
2
2
0
0
2
0
1
0
0
4
2
1
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
1
1
2
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
3
0
2
1
1
0
1
0
2
0
1
1
0
0
1
0
0
0
0
1
0
0
0
1
4
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
3
0
0
0
1
1
0
0
0
1
0
1
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
1
1
0
3
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
1
1
0
0
0
1
2
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
1
2
2
1
0
0
0
1
0
0
1
0
1
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
1
1
0
0
0
3
0
0
2
3
0
1
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
2
0
0
2
0
0
2
2
2
0
1
0
0
2
1
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
2
0
3
2
1
3
2
3
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
4
0
2
0
1
1
0
0
0
0
0
0
1
0
0
0
7
3
0
0
1
0
2
0
0
0
0
0
2
0
0
1
0
0
0
4
0
0
2
1
2
1
2
1
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
1
1
2
2
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
2
1
2
0
0
3
2
1
0
1
0
1
0
1
0
0
2
0
1
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
2
1
2
2
1
1
0
1
0
0
0
0
0
2
2
0
1
0
2
0
2
0
1
2
0
1
0
0
1
0
0
0
0
0
1
0
2
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
1
1
3
0
0
0
1
0
1
0
0
1
1
0
3
0
0
0
1
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
2
0
2
0
1
0
0
2
1
0
0
1
1
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
2
2
0
0
0
2
0
0
0
0
2
0
2
2
1
0
0
1
0
0
0
2
0
0
1
0
1
0
2
0
0
0
0
0
2
0
2
0
0
1
1
1
0
1
0
2
1
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
2
1
2
0
2
1
0
1
0
2
0
0
0
0
0
0
1
1
1
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
2
0
0
2
0
2
2
2
0
0
0
0
0
3
0
0
2
2
0
0
1
0
0
1
0
2
0
0
0
0
0
0
3
0
0
0
0
0
2
1
2
0
0
0
1
0
0
0
2
0
0
0
4
1
0
0
2
0
0
0
0
0
0
0
0
2
0
1
1
1
0
0
0
0
1
2
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
2
1
0
0
1
1
0
1
0
2
1
0
2
2
5
2
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
1
2
1
0
0
1
2
2
3
0
0
1
0
0
2
0
1
0
2
0
0
0
0
0
2
2
0
0
0
0
0
1
2
0
2
0
1
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
1
2
3
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
2
1
2
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
1
0
0
0
5
2
0
0
2
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
2
0
0
0
1
0
1
2
0
0
0
0
0
4
1
0
2
0
0
1
2
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
1
1
0
3
0
2
0
0
2
0
0
0
0
0
0
5
1
0
1
4
0
0
1
0
2
0
2
0
1
2
1
0
2
2
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
1
0
2
0
2
1
2
0
1
0
0
1
0
0
0
0
0
0
1
3
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
5
0
0
0
0
2
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
1
0
2
2
2
0
2
0
0
0
1
2
2
0
1
0
3
0
0
4
1
1
0
0
0
0
0
2
0
0
1
1
0
0
2
2
1
0
1
0
0
2
1
0
1
0
0
2
0
3
0
0
0
0
0
0
2
2
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
2
0
1
0
1
0
0
0
7
0
1
0
1
0
2
1
0
1
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
4
2
0
0
0
0
2
2
0
0
0
2
0
0
0
2
2
0
0
1
0
0
1
2
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
3
0
0
2
2
0
0
1
1
0
0
0
4
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
1
0
0
0
0
0
0
0
1
1
2
0
0
0
0
2
0
0
0
0
0
0
3
0
2
0
0
0
0
5
0
0
0
0
0
2
0
0
0
0
1
2
1
0
0
0
2
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
1
0
2
0
1
0
0
5
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
1
0
0
0
0
1
0
0
2
0
0
2
0
1
0
0
0
0
1
1
0
1
1
1
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
1
0
0
1
1
1
3
0
0
1
1
1
0
1
2
0
4
3
0
0
0
0
2
1
1
0
0
0
1
0
0
0
1
1
1
2
1
0
0
0
0
1
1
2
0
1
0
2
0
2
1
0
0
2
1
2
0
1
1
0
1
2
1
0
0
0
0
0
0
1
1
2
1
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
2
0
0
0
1
0
1
2
0
1
1
0
1
0
0
2
0
0
0
1
0
0
1
0
0
2
1
0
0
3
0
0
0
2
0
2
0
0
2
1
1
0
0
3
1
1
0
0
2
1
1
0
0
1
0
0
0
1
1
1
1
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
2
1
1
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
2
1
1
4
0
2
0
0
1
0
0
0
5
0
1
0
0
0
0
2
1
1
1
0
1
0
0
0
0
0
1
1
0
2
0
1
2
0
0
0
1
0
2
0
0
2
0
5
0
1
2
0
2
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
1
0
1
0
4
2
1
0
1
0
0
0
0
2
1
2
0
0
0
0
0
0
1
0
3
0
0
1
0
0
1
2
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
1
0
2
0
0
0
2
0
0
1
0
0
1
0
2
0
0
1
0
1
3
0
2
0
0
0
0
0
0
0
0
0
0
0
2
4
0
0
1
0
0
1
0
1
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
3
1
0
0
3
0
0
0
0
1
2
0
0
0
0
0
1
0
0
2
2
0
0
0
2
0
1
0
0
0
0
2
0
0
2
1
0
1
0
0
0
1
0
2
0
0
2
1
1
2
0
0
1
1
0
0
0
0
3
1
0
1
0
0
0
1
3
0
0
0
0
2
1
0
0
0
0
1
0
1
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
2
2
2
2
0
0
0
4
0
1
1
0
0
2
0
0
0
2
0
0
0
0
0
1
5
0
0
0
0
3
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
2
1
0
0
2
0
0
2
0
0
0
0
0
0
0
1
2
0
0
1
2
0
2
0
2
1
0
1
0
0
0
0
0
0
0
2
0
0
1
1
0
2
2
1
4
0
2
2
2
0
0
2
0
0
2
0
1
2
0
2
0
0
1
1
0
1
0
0
1
0
2
0
0
2
2
0
0
0
0
0
1
2
2
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
3
0
1
0
2
0
1
0
0
2
0
2
0
0
1
0
0
1
2
1
2
0
1
0
0
2
0
0
0
1
1
1
0
1
1
1
0
0
0
0
0
0
2
0
2
2
0
3
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
3
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
2
0
2
0
0
2
0
1
1
0
2
0
0
0
0
0
0
0
0
2
1
0
2
0
2
1
3
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
2
0
2
0
1
1
2
0
2
2
0
0
0
2
1
0
0
0
0
0
3
0
1
0
0
0
1
0
0
0
1
2
1
0
0
1
0
0
1
0
2
0
0
1
1
0
0
0
0
0
0
0
0
3
2
0
1
0
0
1
0
0
0
0
0
1
0
0
0
2
0
1
0
1
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
2
1
0
0
0
0
1
1
0
2
0
1
2
1
4
0
0
0
0
0
1
0
0
1
1
0
1
0
1
0
0
2
1
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
2
0
3
0
2
0
1
0
1
0
0
2
0
0
1
1
2
1
1
0
2
0
0
3
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
1
0
1
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
1
2
1
2
3
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
2
0
0
3
0
0
0
0
3
2
0
0
0
0
0
0
1
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
1
0
0
0
0
1
0
3
1
0
0
2
1
0
0
2
0
1
1
2
0
0
0
0
0
0
0
1
1
0
3
0
2
2
0
0
0
0
0
2
0
0
0
0
1
1
1
0
2
0
2
0
2
0
0
0
0
0
0
0
1
2
1
0
2
2
0
3
0
2
3
4
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
2
2
2
0
0
0
2
0
0
2
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
4
0
2
0
0
0
0
0
1
2
4
2
0
0
2
0
0
0
2
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
1
0
2
0
0
3
0
0
0
0
0
0
0
1
0
2
0
2
0
2
2
1
0
0
1
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
1
0
1
2
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
1
1
0
1
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
1
0
0
2
0
0
0
0
0
4
0
0
0
2
1
0
2
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
2
2
0
0
0
0
2
0
1
0
1
0
0
1
0
2
2
0
0
0
0
2
1
1
1
1
0
0
0
0
0
2
1
0
2
0
2
2
0
2
0
1
0
0
0
1
0
0
0
1
0
2
4
2
0
0
0
2
0
0
2
0
2
0
0
0
0
1
2
0
0
2
0
0
1
0
2
1
0
0
0
0
1
1
0
2
1
0
1
1
0
4
1
1
1
1
1
2
0
1
0
2
0
6
0
6
2
0
4
0
0
0
0
0
1
4
0
0
1
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
2
1
1
1
0
1
0
3
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
1
1
0
0
0
1
2
5
0
0
0
0
0
0
0
2
2
0
2
0
1
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
1
1
5
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
1
0
0
1
0
2
0
0
2
1
2
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
1
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
1
2
4
0
0
1
1
2
1
1
4
0
0
0
1
1
0
0
0
0
1
0
2
0
0
2
0
1
2
2
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
3
0
2
0
0
2
0
1
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
1
1
1
0
0
0
0
0
3
0
0
0
1
0
0
2
2
0
0
0
2
0
0
0
1
3
0
2
0
0
2
0
0
0
2
1
2
2
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
2
1
0
1
0
2
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
1
0
0
0
0
4
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
4
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
1
1
0
3
0
0
1
0
2
0
0
1
2
0
1
3
1
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
3
0
0
1
0
1
0
0
0
2
0
0
0
1
0
1
1
0
0
8
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
2
0
1
1
3
0
0
0
1
0
0
0
0
0
2
0
2
0
0
1
0
2
0
0
5
0
0
0
0
0
0
2
0
2
2
2
0
2
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
3
2
0
0
1
0
1
1
0
0
1
1
0
2
0
0
0
0
2
0
1
0
0
0
2
2
0
0
1
1
0
0
0
2
0
0
0
1
0
0
0
1
0
0
2
0
0
1
0
2
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
1
0
0
0
1
0
1
1
0
1
0
0
0
2
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
3
0
13
1
1
0
1
0
0
2
0
0
0
0
1
2
0
1
0
0
0
2
0
0
1
0
0
0
0
2
2
0
2
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
1
2
1
0
0
0
0
0
0
3
0
1
0
0
2
1
0
0
5
0
0
0
0
1
0
0
1
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
1
2
0
0
2
0
0
2
2
0
0
2
0
2
1
0
2
0
0
0
0
2
0
0
0
0
0
1
1
3
3
0
1
0
0
3
0
1
3
0
2
1
2
0
0
0
0
0
0
0
0
1
3
0
1
0
0
1
0
1
0
0
0
1
0
1
0
2
0
0
2
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
1
0
0
0
2
0
0
1
1
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
2
1
0
1
0
0
1
0
2
0
0
0
2
0
0
0
4
2
0
0
0
0
3
0
3
0
0
0
2
1
1
2
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
3
0
1
0
0
0
0
1
2
0
0
0
0
2
0
1
0
0
0
2
0
0
0
1
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
2
0
1
1
2
1
2
1
0
2
0
2
1
2
0
0
2
0
0
0
2
0
0
0
1
2
0
0
0
1
2
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
4
1
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
1
1
0
0
0
0
1
2
0
1
2
2
0
2
0
0
1
1
3
0
3
0
1
0
0
0
0
0
1
0
0
1
3
0
1
1
1
0
0
1
0
1
2
0
0
2
0
0
0
0
0
0
2
1
0
0
2
0
1
1
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
2
0
1
2
0
1
2
0
0
2
0
0
0
1
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
1
1
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
1
0
2
0
2
0
0
2
2
0
0
1
2
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
2
0
1
0
2
1
0
2
2
2
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
1
2
0
0
0
0
0
0
0
1
1
0
0
0
0
1
2
0
0
0
0
0
1
2
2
0
2
0
0
1
2
0
0
2
0
0
0
0
1
0
0
2
1
0
0
0
0
2
3
0
0
0
2
0
2
0
0
0
0
0
2
1
3
0
0
1
1
0
0
0
1
1
0
2
0
0
0
1
1
0
0
0
3
0
1
2
0
0
4
2
1
0
2
0
0
0
3
0
3
2
0
0
1
0
0
1
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
1
1
1
0
0
2
0
0
0
2
0
0
1
0
0
0
0
1
0
1
2
2
1
1
1
1
2
1
0
1
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
1
0
0
1
0
0
0
4
0
2
0
0
0
0
1
0
1
2
0
0
0
0
1
1
2
1
1
1
2
2
2
2
0
1
0
0
0
1
2
0
1
0
0
0
2
0
0
0
2
0
0
1
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
2
0
0
0
0
1
3
1
0
1
0
0
3
2
0
1
0
0
0
0
2
1
0
0
2
1
2
0
0
0
0
2
0
0
0
2
1
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
1
0
0
1
4
1
0
2
0
1
2
0
0
1
0
0
0
0
0
1
0
2
0
0
1
2
0
2
1
1
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
3
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
1
0
0
0
0
2
0
1
0
0
0
0
1
0
2
1
0
2
0
2
0
0
1
1
0
0
2
0
0
0
0
0
1
0
0
0
1
0
1
0
2
2
1
1
0
0
5
1
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
3
0
2
1
2
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
1
0
0
0
0
4
1
2
1
2
1
0
0
2
0
0
1
0
0
2
2
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
2
1
0
0
1
0
0
2
0
0
0
1
2
0
0
0
1
1
0
0
0
2
2
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
2
2
0
2
0
1
0
0
2
0
0
2
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
1
1
2
0
2
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
1
0
0
0
2
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
1
1
2
1
0
0
1
0
3
0
0
1
0
0
0
0
4
0
0
1
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
1
0
1
0
2
0
3
0
0
2
0
2
1
2
1
0
0
1
0
1
2
0
0
7
0
1
0
0
0
0
0
0
1
0
1
2
2
1
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
3
0
1
0
2
0
0
1
0
2
0
2
0
1
1
0
1
0
0
4
0
0
1
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
2
0
0
2
1
1
0
0
2
0
1
0
0
0
0
0
4
2
0
0
1
0
0
0
0
1
2
0
0
3
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
3
2
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
4
0
0
0
3
1
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
1
0
0
1
1
0
0
1
1
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
1
0
2
0
1
0
2
1
1
0
2
0
0
1
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
1
0
2
0
0
2
0
0
2
2
0
1
2
0
0
0
0
0
0
0
0
1
0
1
1
0
0
3
1
3
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
1
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
2
1
0
1
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
1
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
1
0
0
0
1
3
0
2
2
0
1
5
2
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
3
2
0
1
1
0
1
0
1
0
1
2
0
0
0
0
0
0
2
2
0
0
1
0
2
1
0
0
1
0
0
0
0
0
0
0
1
2
2
0
2
0
0
2
0
1
0
0
2
2
0
1
0
0
3
0
2
0
0
0
0
0
1
2
0
0
1
2
0
0
0
0
1
0
0
0
2
0
0
1
0
0
2
0
2
0
0
5
2
2
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
1
2
1
1
0
0
0
2
2
2
1
0
2
1
0
0
0
0
0
0
1
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
1
0
2
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
1
1
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
2
2
0
1
0
1
2
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
2
0
1
0
1
0
2
2
0
0
0
0
1
0
0
1
2
0
0
2
2
0
0
2
1
2
0
0
0
0
0
1
1
2
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
1
1
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
2
1
0
0
0
0
2
3
2
0
1
0
0
0
2
3
0
0
2
0
0
0
0
2
0
0
3
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
6
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
2
0
1
1
0
1
2
0
0
0
1
0
2
0
2
1
2
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
6
0
0
0
1
0
0
0
2
0
0
0
0
0
1
1
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
2
0
0
2
2
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
1
1
1
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
2
2
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
1
1
1
0
1
0
0
0
1
0
0
0
0
0
2
0
1
0
4
0
1
0
1
0
0
0
0
1
1
1
2
0
2
1
1
2
0
0
0
0
0
0
2
2
0
1
0
1
1
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
2
1
0
3
0
0
0
1
0
0
1
0
2
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
1
0
0
0
2
2
0
0
1
2
2
0
0
0
0
2
2
0
0
0
3
0
0
2
0
1
0
0
1
0
0
1
2
0
0
0
0
0
0
0
4
0
0
0
1
1
1
1
2
0
0
0
0
0
1
0
0
0
0
2
1
0
1
0
1
0
0
2
1
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
5
2
0
0
1
2
0
0
1
0
0
2
0
0
2
1
1
0
0
2
1
0
0
0
0
0
0
2
2
3
0
0
0
1
2
0
0
1
0
0
2
0
2
0
0
0
0
2
1
1
0
1
0
0
0
2
0
1
0
0
1
1
0
0
0
2
0
0
0
2
1
0
0
0
0
2
0
1
0
1
0
2
1
2
2
0
0
0
0
2
2
0
0
0
0
0
1
0
0
2
2
1
2
0
0
2
0
0
2
0
0
1
0
2
0
0
2
1
0
0
0
0
0
2
1
0
0
0
0
2
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
4
0
4
1
1
2
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
1
0
2
1
1
2
0
0
0
0
2
2
2
0
0
0
0
2
0
0
2
0
0
1
2
0
0
2
0
1
0
1
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
2
0
1
8
0
2
0
0
2
0
0
0
0
0
3
0
0
1
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
1
2
0
0
0
2
0
0
0
1
0
0
0
0
3
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
1
0
1
2
2
1
0
0
2
0
1
0
0
0
0
2
2
0
1
0
1
0
1
0
0
0
0
0
2
0
0
2
1
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
2
1
0
0
0
0
0
2
2
0
0
0
1
0
3
0
2
2
1
2
0
1
2
0
0
1
0
0
0
0
2
0
2
0
0
0
2
1
0
1
2
1
0
2
1
0
0
0
0
0
1
0
0
0
4
1
0
2
0
0
1
0
0
1
0
2
0
0
1
3
0
1
0
0
0
2
0
2
0
3
2
1
0
1
0
0
2
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
1
0
0
0
0
2
0
2
0
3
0
0
2
1
0
4
1
0
0
0
0
0
1
0
0
1
3
0
0
0
2
0
0
0
5
3
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
2
2
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
1
0
0
0
2
0
0
1
0
1
1
2
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
3
2
2
0
0
1
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
1
0
0
0
1
0
0
2
1
3
1
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
2
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
7
0
2
0
1
0
0
0
0
3
1
0
2
3
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
1
0
0
0
0
1
2
0
1
0
2
0
2
0
0
1
0
0
0
0
0
0
0
2
0
1
0
1
2
2
0
1
0
0
4
3
1
0
2
1
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
2
1
0
0
0
1
1
0
1
0
0
0
2
1
0
0
2
0
0
2
0
0
2
0
0
0
1
0
0
0
0
2
0
1
2
0
0
1
0
2
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
1
0
0
0
2
2
2
2
0
1
0
0
0
2
0
0
0
0
0
4
1
0
0
0
0
0
0
0
1
2
0
1
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
5
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
2
0
3
1
0
0
0
0
2
0
1
0
1
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
2
0
0
0
0
2
1
1
1
1
0
2
0
0
0
0
2
1
1
0
0
0
1
0
0
2
0
0
0
1
1
0
2
0
0
0
1
1
0
0
1
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
2
2
0
0
2
1
0
0
2
0
0
1
2
0
1
0
1
1
0
0
1
2
0
0
0
0
0
0
3
0
0
1
0
2
0
0
0
2
2
4
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
1
2
0
0
2
1
0
0
2
2
0
0
0
0
2
1
2
0
1
2
0
0
0
0
0
0
1
0
0
0
8
1
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
2
2
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
1
2
0
0
3
0
1
1
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
2
0
2
2
0
0
1
0
1
2
2
0
2
0
1
0
1
0
0
1
2
0
0
0
0
2
0
0
1
0
2
2
0
2
0
0
1
0
1
0
3
3
0
0
0
0
0
1
0
0
0
0
0
1
2
0
1
0
1
1
2
0
0
1
0
2
0
1
1
0
2
2
0
3
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
1
0
1
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
1
4
0
2
0
2
1
0
2
1
1
1
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
1
0
0
0
1
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
2
0
1
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
2
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
1
2
0
1
1
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
1
0
4
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
3
2
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
2
2
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
1
0
0
1
1
0
2
0
0
1
0
0
1
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
2
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
5
0
0
0
0
0
1
1
0
2
2
0
3
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
1
2
3
1
1
1
0
1
0
1
3
0
2
0
2
0
1
0
0
1
0
0
2
0
0
0
1
2
0
0
0
0
0
2
0
3
1
0
1
0
0
2
1
0
1
1
0
0
1
0
0
0
0
0
0
2
5
2
2
2
2
0
0
0
0
0
0
0
2
0
2
2
2
0
2
3
2
2
0
0
0
2
4
2
0
0
0
1
0
2
0
1
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
1
1
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
2
0
0
0
0
5
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
2
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
1
1
0
0
0
0
2
0
0
0
3
1
0
1
3
1
0
0
1
0
0
1
5
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
2
0
1
0
0
0
0
0
1
1
3
2
0
2
0
2
0
1
0
0
3
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
1
2
0
2
1
0
1
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
2
2
0
0
1
0
1
0
1
0
0
0
6
0
2
0
1
0
0
2
1
2
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
5
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
2
0
1
0
1
0
2
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
1
0
2
1
2
0
0
2
0
1
1
0
1
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
2
0
0
1
0
0
0
0
0
1
0
0
0
1
0
2
0
2
1
0
0
0
1
0
1
0
0
2
1
1
1
0
0
0
1
0
0
0
0
1
3
0
0
2
1
0
0
0
1
1
0
0
5
2
0
2
0
0
2
0
0
2
2
2
0
0
0
0
0
0
1
1
0
0
0
2
1
1
0
0
0
0
0
1
0
1
2
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
2
0
1
0
1
0
0
0
3
2
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
1
2
0
1
0
0
2
1
1
0
0
2
3
0
2
0
1
0
2
1
2
0
2
0
1
0
0
0
3
0
2
1
3
2
0
0
1
2
0
1
2
0
0
0
0
1
2
1
0
0
1
0
0
0
0
3
1
0
0
0
0
1
1
1
0
0
0
0
1
1
1
1
0
0
0
2
0
0
3
0
2
1
1
1
0
0
0
2
2
0
1
0
1
1
0
2
1
2
1
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
5
2
0
1
0
0
2
0
1
0
0
2
0
0
0
0
0
1
1
1
0
0
0
2
0
1
0
0
0
2
0
1
0
0
0
2
0
1
1
0
0
1
0
0
0
0
2
0
1
0
0
0
2
0
0
0
2
0
2
1
0
2
0
0
0
0
0
2
6
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
1
3
0
2
2
1
0
0
0
0
0
0
0
4
2
0
0
0
2
0
0
2
0
2
2
0
1
0
0
0
2
2
2
0
0
0
0
1
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
5
1
2
1
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
2
2
4
0
0
0
3
1
1
0
2
0
0
4
0
0
0
0
0
1
0
0
0
0
2
1
2
0
1
0
0
0
2
0
0
0
0
0
3
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
2
1
0
2
1
0
0
0
0
2
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
2
1
0
0
1
0
0
0
0
0
2
0
0
1
2
0
0
1
0
2
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
1
0
0
0
0
4
2
3
0
0
1
0
0
0
2
0
1
2
0
0
0
2
1
0
0
0
1
1
2
2
2
0
0
1
2
1
0
0
0
0
2
3
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
3
1
1
0
0
2
0
0
0
0
0
0
0
1
2
1
0
0
2
0
0
0
0
2
0
0
2
0
0
1
2
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
3
0
0
2
0
2
0
0
0
0
0
1
0
3
0
0
0
0
0
3
0
2
2
0
1
0
1
0
1
0
2
0
0
0
0
0
1
0
1
1
0
2
1
0
2
1
0
2
0
0
2
0
0
1
2
0
0
0
0
1
2
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
1
1
2
2
0
4
0
0
1
2
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
5
2
1
2
0
0
1
0
2
1
0
1
2
0
1
0
0
2
0
0
1
0
1
1
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
4
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
1
0
2
0
0
3
0
1
0
0
2
1
1
0
0
0
1
2
0
1
0
2
2
0
0
0
0
2
0
1
2
0
2
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
2
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
2
0
0
2
0
0
3
0
1
1
0
0
1
0
1
1
2
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
2
4
0
1
0
0
0
2
0
1
1
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
1
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
1
2
3
0
0
5
0
0
0
0
0
0
2
0
0
0
1
2
0
0
5
3
0
1
0
2
1
1
0
0
1
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
1
1
2
1
0
0
0
1
0
0
1
1
1
0
1
2
0
0
1
0
0
1
0
1
0
0
0
0
2
0
2
0
3
0
2
0
0
0
0
1
0
0
1
2
0
0
0
1
0
0
0
2
0
2
0
1
0
2
0
0
0
0
0
0
2
1
0
2
5
0
0
0
0
0
0
0
1
1
0
0
0
2
2
0
0
0
0
0
0
0
2
0
2
1
0
0
0
2
1
0
1
0
2
0
0
0
0
0
0
1
1
0
0
0
1
2
2
0
1
0
2
0
0
0
1
1
1
3
0
0
1
2
0
0
1
1
0
1
1
0
0
0
0
1
2
0
0
2
1
0
0
0
0
3
0
7
0
1
1
0
2
2
0
1
0
2
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
1
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
1
1
2
2
3
2
1
1
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
1
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
1
0
1
0
0
0
0
0
1
1
2
0
0
0
0
0
1
0
0
0
0
0
2
1
1
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
1
2
0
0
0
1
0
0
0
0
1
3
0
3
0
0
0
2
0
2
0
0
2
0
3
1
0
1
0
0
1
3
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
6
0
0
0
0
2
2
0
0
5
0
1
2
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
3
1
2
0
0
0
1
0
1
2
2
0
0
0
0
0
0
1
0
0
5
1
0
0
0
1
1
2
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
2
1
0
0
1
2
0
0
2
0
0
0
0
0
2
1
0
1
2
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
2
2
1
0
0
1
0
0
0
0
0
2
2
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
1
0
0
3
0
0
2
2
1
0
0
2
0
0
0
1
1
0
2
0
1
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
4
0
0
1
0
1
0
0
0
1
0
0
1
0
0
1
0
1
0
0
2
1
0
0
0
2
0
0
0
0
2
0
1
0
3
0
0
0
0
1
2
0
0
1
1
0
0
0
0
0
1
1
2
0
2
0
1
0
2
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
6
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
1
1
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
1
0
0
0
0
0
0
2
3
0
0
0
1
0
0
3
0
0
0
1
2
2
2
0
2
0
2
0
2
2
2
0
1
0
1
2
0
0
1
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
2
0
0
1
0
0
2
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
3
0
2
0
1
0
2
0
0
0
0
0
4
2
0
0
1
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
2
0
1
1
0
0
0
2
0
1
0
1
1
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
3
0
0
0
2
0
0
1
1
1
0
0
0
0
0
0
1
1
2
0
0
2
0
0
0
0
0
0
1
1
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
1
0
2
0
0
0
2
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
4
0
2
0
0
0
0
0
2
0
0
2
0
0
0
2
0
2
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
1
2
0
1
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
1
0
0
0
2
1
2
0
0
0
0
0
2
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
2
0
0
1
1
0
1
1
0
2
0
0
1
0
2
0
1
0
0
1
0
2
2
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
2
0
0
0
0
0
0
2
0
0
1
2
1
4
2
0
0
0
2
0
0
0
0
0
0
3
2
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
1
0
2
1
0
0
0
0
0
0
10
0
0
2
0
0
2
0
3
0
0
0
1
0
0
1
0
0
0
2
2
1
0
0
0
0
0
0
0
0
2
0
1
0
1
2
0
0
3
0
1
0
0
2
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
3
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
2
2
0
0
0
0
0
0
1
0
1
0
0
0
3
1
1
2
0
0
2
0
2
1
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
3
0
1
0
0
0
0
0
0
0
0
2
2
2
0
0
1
0
3
0
0
0
0
2
0
1
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
1
2
0
2
0
3
1
0
0
0
0
0
2
0
2
0
2
0
1
0
2
0
0
0
0
0
0
1
2
1
0
1
0
0
0
0
0
2
1
1
0
0
1
0
0
0
0
0
3
0
3
0
1
0
0
0
0
0
0
1
0
0
1
0
2
1
2
0
0
3
0
0
0
2
0
0
2
0
2
0
0
0
1
0
0
1
0
3
2
0
0
0
0
0
1
2
2
0
0
2
1
0
0
0
0
0
0
4
2
0
0
0
1
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
1
1
2
0
1
1
1
0
0
0
1
0
1
2
0
0
0
2
0
0
0
0
0
1
2
0
2
0
0
0
2
0
0
5
0
2
1
0
3
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
1
0
0
1
0
0
2
2
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
3
0
0
2
0
0
0
0
2
0
0
2
0
0
1
0
1
0
2
2
0
1
1
2
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
1
1
2
1
2
2
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
2
1
0
2
0
0
0
0
0
0
0
3
0
0
1
1
2
1
0
1
1
0
0
0
0
0
1
2
0
1
0
0
2
0
1
0
1
0
0
1
0
0
3
0
0
1
0
0
1
2
0
0
4
0
0
0
0
1
0
0
3
0
1
0
2
2
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
2
2
0
0
0
2
1
2
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
1
1
1
0
0
0
0
2
2
0
0
0
0
1
1
0
0
2
0
2
0
0
0
0
0
0
0
0
3
0
0
1
0
2
2
2
2
0
2
0
1
1
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
3
2
0
1
0
1
1
0
0
0
2
2
0
0
1
1
0
3
0
0
1
1
3
0
0
0
0
0
1
0
0
2
1
0
0
2
1
1
1
0
1
0
0
2
0
0
0
1
0
1
2
0
0
0
2
2
1
0
0
0
0
0
0
2
1
0
1
0
2
0
0
0
0
0
1
0
0
0
2
0
0
1
0
2
0
0
0
0
3
3
1
0
0
2
2
0
0
0
2
0
0
0
0
0
0
2
5
0
2
0
0
2
1
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
2
0
0
1
0
2
0
2
2
0
0
0
0
0
0
0
1
0
1
1
0
2
0
0
0
0
0
1
0
2
2
0
0
0
0
0
1
1
0
0
3
0
0
8
0
0
2
0
1
0
0
0
0
0
0
2
1
0
1
0
0
1
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
1
2
0
2
0
0
2
0
0
0
0
1
0
1
2
0
0
0
3
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
3
2
1
1
1
0
0
0
2
0
0
1
1
0
0
1
2
0
1
0
1
2
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
3
0
0
3
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
3
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
2
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
3
0
2
2
0
1
0
1
0
2
1
1
0
2
0
0
0
1
2
0
0
2
0
3
2
0
1
0
0
0
0
0
4
0
0
0
0
2
0
2
0
0
2
0
2
1
0
0
2
2
1
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
1
0
0
0
0
3
0
0
1
0
1
1
1
0
0
2
3
2
2
2
1
0
0
2
0
0
0
1
0
0
1
3
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
1
0
0
0
2
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
2
0
2
0
2
0
4
0
2
0
0
1
2
1
0
2
1
0
0
0
0
0
2
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
3
2
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
2
1
1
0
2
0
0
1
0
0
2
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
3
1
3
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
2
2
1
2
2
0
1
0
0
0
0
2
2
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
2
0
0
5
0
0
0
2
3
0
0
0
0
0
2
1
1
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
4
5
0
0
2
0
0
0
0
2
0
1
0
1
0
0
0
0
2
0
6
0
1
0
0
0
0
0
0
0
0
0
1
2
0
2
0
2
0
0
0
0
0
0
2
0
2
0
0
1
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
1
0
1
0
1
1
0
0
0
2
0
2
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
3
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
2
2
0
0
1
0
0
1
0
0
3
0
0
0
0
2
0
0
0
0
0
1
2
0
0
2
0
2
2
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
1
1
0
0
0
0
0
0
7
2
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
1
0
1
0
0
0
0
0
3
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
1
0
1
0
2
2
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
1
1
2
0
0
0
2
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
1
0
0
1
2
0
0
1
0
0
0
0
0
0
0
1
2
0
0
1
0
0
2
1
0
0
0
2
0
1
0
2
1
0
1
1
2
0
1
1
0
0
0
2
0
0
0
2
1
0
2
0
2
1
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
1
0
0
0
3
2
2
0
2
2
0
0
0
2
1
2
0
0
0
1
0
0
0
0
3
0
0
0
2
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
2
0
0
2
0
4
3
0
0
1
0
0
0
2
0
2
0
1
0
0
0
0
0
2
0
0
1
0
2
1
0
0
2
0
3
0
0
1
0
3
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
3
2
1
2
0
2
0
0
1
0
1
2
0
2
0
0
4
0
0
0
0
1
0
1
0
0
2
0
0
0
1
0
2
0
0
0
0
1
0
0
2
0
1
1
0
1
2
0
2
2
1
0
0
0
0
1
2
0
0
0
0
2
2
0
0
0
1
0
1
0
0
1
0
2
1
1
0
1
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
2
1
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
1
1
0
3
0
2
2
1
0
1
0
0
0
3
1
2
0
0
0
0
2
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
1
0
2
2
2
0
0
1
0
0
0
0
0
3
2
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
2
2
0
0
1
1
0
3
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
1
0
1
2
0
0
0
0
0
2
1
0
0
1
1
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
1
1
2
1
2
1
0
0
0
0
0
0
2
2
1
1
3
0
0
0
1
0
1
2
0
1
1
0
0
0
2
0
0
0
0
1
2
0
1
0
2
0
1
0
0
2
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
0
3
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
2
0
0
1
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
3
0
1
0
0
0
0
2
0
0
2
0
1
2
0
0
0
2
0
0
2
0
0
0
0
0
1
1
0
1
2
0
0
1
0
1
1
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
2
2
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
2
0
1
0
3
1
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
2
0
2
0
2
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
2
0
2
9
0
2
1
0
0
0
0
3
0
1
1
2
0
2
1
0
2
0
0
2
2
0
0
0
0
0
0
2
1
1
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
3
1
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
1
2
0
0
7
0
0
0
0
0
0
0
1
1
0
0
0
0
2
2
0
0
0
2
1
1
0
0
0
2
2
1
1
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
2
0
0
0
0
1
0
2
0
0
0
1
0
3
0
0
1
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
2
1
0
2
1
0
2
1
2
0
0
2
2
0
0
0
1
0
0
1
1
0
0
0
2
2
0
2
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
3
0
0
0
0
0
0
4
3
0
1
1
0
0
0
1
2
2
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
2
0
0
2
3
2
0
1
2
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
1
0
2
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
3
3
0
0
0
0
0
0
2
0
0
1
1
1
0
0
0
1
1
2
0
0
2
1
0
0
0
0
0
0
1
3
1
0
0
0
0
0
0
4
1
1
1
0
0
0
1
0
0
2
0
0
2
1
0
0
1
0
0
2
0
0
0
1
1
0
2
2
0
0
1
1
0
1
0
2
1
0
2
0
0
0
0
2
0
1
2
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
1
1
2
0
2
0
1
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
2
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
2
0
2
1
0
0
1
2
0
0
0
0
0
2
0
3
1
1
0
0
0
0
1
0
0
0
2
1
1
1
2
0
3
1
0
2
0
0
0
0
0
0
5
0
0
0
0
3
0
3
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
2
0
1
1
0
0
0
1
0
0
0
3
0
0
2
0
0
0
2
1
0
1
0
2
0
2
0
0
0
0
0
0
4
1
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
4
0
0
0
2
0
0
5
0
1
0
2
0
0
0
0
1
0
0
0
1
0
1
2
2
2
1
1
0
0
0
0
0
1
0
0
1
1
1
0
0
1
0
1
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
1
1
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
1
0
1
0
2
2
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
2
0
0
0
0
3
1
0
2
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
7
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
2
0
2
0
0
1
2
0
0
2
0
0
0
2
5
1
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
3
1
0
0
0
0
2
0
1
2
0
1
0
0
0
0
2
0
1
2
1
0
2
0
2
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
2
0
0
0
4
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
2
0
0
0
0
0
2
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
6
0
3
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
2
2
0
2
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
4
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
2
2
0
1
2
0
0
0
2
1
3
0
0
0
0
0
4
0
1
0
0
2
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
1
2
0
0
2
0
0
2
0
2
0
0
0
0
1
0
1
1
0
0
0
1
2
0
0
1
0
0
0
2
0
2
0
0
0
0
1
2
2
0
0
1
0
0
0
0
0
2
0
2
1
2
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
1
0
0
0
0
0
1
0
2
1
0
0
0
0
3
1
2
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
1
0
2
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
2
1
0
0
0
0
0
6
0
0
1
2
0
0
0
0
2
0
0
1
1
0
0
3
0
0
1
0
0
2
1
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
3
2
1
2
0
0
0
2
0
0
0
2
0
0
1
0
1
0
0
0
0
1
1
1
0
0
0
0
2
0
0
1
0
1
2
1
0
1
0
0
1
3
2
0
0
0
1
2
3
1
0
3
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
1
1
0
2
2
0
0
0
2
1
0
2
2
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
3
0
1
0
0
0
0
2
0
1
1
0
0
0
1
2
0
0
1
1
0
0
0
1
3
1
0
0
0
1
0
0
0
0
0
2
1
0
1
2
2
1
0
0
0
0
0
0
3
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
3
2
0
0
6
1
2
2
2
1
0
0
2
0
1
1
0
1
2
2
1
0
0
2
1
0
0
2
1
2
0
0
2
0
1
1
0
0
1
4
1
0
2
2
0
0
1
1
1
0
0
0
1
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
1
0
0
0
1
0
1
0
1
0
2
0
1
1
0
0
0
0
1
1
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
1
2
1
0
1
0
0
2
1
1
0
0
0
0
0
0
0
0
2
0
2
2
0
2
0
1
2
0
0
0
1
2
0
0
0
0
2
1
2
2
0
1
0
0
3
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
2
0
2
0
2
0
1
0
2
0
2
0
0
1
0
1
0
0
0
1
0
0
0
3
2
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
2
0
1
0
0
2
0
0
0
2
0
1
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
2
1
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
2
1
0
2
0
0
0
0
3
0
0
1
0
1
1
0
0
0
0
2
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
1
0
2
0
0
2
0
0
1
0
0
1
1
1
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
3
2
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
2
2
0
0
0
0
0
1
1
0
0
2
2
0
0
0
0
0
2
0
1
1
2
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
8
0
1
0
0
0
0
0
1
0
0
0
0
2
0
1
0
1
1
1
0
2
3
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
1
0
1
1
2
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
1
0
0
1
0
0
0
2
1
2
0
0
0
0
2
0
0
0
0
2
0
1
0
0
1
0
0
0
1
0
2
1
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
2
2
2
2
2
0
2
0
0
3
1
0
0
0
1
0
1
0
1
0
0
1
0
0
1
2
0
0
0
1
1
3
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
2
2
2
2
0
1
1
0
0
2
0
2
0
0
0
0
2
0
3
0
2
1
1
1
0
0
2
1
0
0
1
0
1
2
0
2
2
2
0
0
2
0
0
2
0
1
1
0
0
0
0
1
3
0
0
0
0
5
0
0
1
1
2
0
2
0
1
2
0
0
0
0
0
0
2
2
0
0
2
1
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
2
0
0
2
6
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
2
0
0
0
0
0
3
0
1
2
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
2
0
0
2
0
2
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
1
2
0
1
0
0
1
0
0
0
2
0
2
0
0
2
2
0
0
0
1
0
1
0
4
0
0
1
1
0
0
0
0
0
0
0
0
2
0
4
0
2
0
0
2
1
1
0
0
2
1
2
0
0
0
0
1
2
0
0
0
0
1
1
2
0
0
2
0
2
0
0
1
0
0
0
0
2
1
0
2
2
0
0
0
2
1
0
0
0
1
0
0
0
3
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
1
2
0
2
0
1
2
0
0
0
3
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
2
0
1
0
0
0
1
0
0
0
3
2
0
4
1
2
2
0
0
0
0
0
0
0
0
0
1
0
1
2
0
2
0
0
0
0
0
2
0
0
3
0
2
0
0
0
0
1
1
0
0
0
1
0
0
1
1
1
0
1
0
0
0
0
1
2
0
2
0
0
2
1
0
2
0
0
3
0
1
0
0
0
1
0
0
0
0
1
2
2
2
2
0
0
1
2
0
2
0
2
0
2
1
0
0
0
0
0
0
0
3
1
0
0
1
0
2
0
0
0
1
0
0
0
4
2
0
1
2
1
1
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
2
1
1
0
2
0
0
0
0
2
2
1
1
0
2
0
0
0
1
1
2
3
0
0
0
2
1
1
2
0
1
0
0
0
2
0
0
0
1
2
1
1
0
0
0
1
0
2
0
0
0
0
0
0
2
0
2
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
2
0
2
1
1
0
2
0
1
0
1
2
2
0
0
0
2
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
2
0
2
3
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
2
2
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
1
0
0
1
0
1
4
0
0
0
2
2
0
0
0
0
0
0
2
0
0
2
1
0
0
0
2
0
1
0
2
1
2
0
2
0
2
1
0
1
0
0
2
3
0
0
1
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
4
3
0
0
0
2
0
2
0
0
0
2
1
0
0
0
6
2
0
1
0
1
2
2
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
1
1
1
0
0
0
0
0
0
0
1
2
0
0
1
1
1
0
2
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
1
0
2
0
2
2
0
1
2
1
2
2
1
1
0
1
0
0
0
0
0
0
2
0
0
1
0
1
2
0
0
1
0
3
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
1
0
1
0
0
0
0
0
2
0
1
0
0
1
0
2
0
0
3
0
0
0
0
2
0
0
5
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
1
0
0
2
0
0
0
1
1
1
0
0
0
0
2
0
0
0
0
0
0
2
0
6
0
2
0
1
0
2
0
0
0
0
0
0
0
0
2
0
1
0
1
0
1
0
2
0
1
0
0
0
0
0
0
1
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
8
0
0
1
0
0
0
1
2
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
2
0
0
2
0
1
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
3
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
2
0
0
0
2
0
1
2
0
1
0
3
2
2
1
0
0
1
0
0
2
0
0
2
2
2
1
1
2
0
1
0
0
0
0
0
0
2
1
2
0
0
1
0
0
0
0
0
2
2
2
1
2
0
1
2
1
1
1
0
0
0
1
0
0
0
1
0
1
5
0
0
2
0
1
0
0
2
0
0
0
2
2
0
2
1
0
3
0
0
0
0
0
1
3
1
0
1
0
1
0
0
1
1
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
8
2
0
0
2
0
1
2
0
0
0
1
0
2
0
0
0
2
1
2
0
3
0
2
2
0
0
0
0
2
0
0
2
0
1
0
0
2
0
0
0
0
2
0
1
2
0
0
1
1
0
0
2
0
0
0
0
3
2
0
0
0
0
0
0
0
0
1
0
1
2
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
2
0
0
0
3
0
1
1
0
0
0
0
2
2
0
1
1
0
0
2
0
2
0
0
0
1
0
0
0
0
0
2
0
0
1
0
1
2
0
1
0
0
2
2
0
0
0
0
0
1
0
0
2
0
0
0
0
2
1
2
0
0
2
0
0
0
0
0
1
2
2
2
2
0
0
0
0
2
1
0
0
2
0
0
0
3
1
2
0
0
0
0
0
2
2
2
4
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
1
5
2
0
0
0
0
1
5
1
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
1
0
0
0
1
1
0
1
0
1
0
0
0
2
0
0
0
1
2
0
0
2
1
0
0
4
0
0
1
1
2
0
0
3
0
0
1
0
0
0
0
1
0
1
0
3
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
3
2
0
2
0
0
0
0
0
2
1
2
0
1
0
0
0
0
0
2
2
0
1
1
1
0
1
2
0
1
1
0
0
0
2
2
0
0
1
0
1
2
0
0
0
1
0
2
0
0
2
1
0
3
0
2
2
0
0
2
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
2
1
0
2
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
1
2
2
2
0
0
2
0
0
1
0
2
0
2
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
2
3
0
0
0
0
1
1
1
0
0
0
0
1
0
2
0
0
0
0
1
1
1
0
2
0
0
0
2
0
0
1
2
0
2
2
0
0
2
1
1
0
2
0
2
0
0
1
0
0
0
0
4
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
2
2
0
2
0
0
1
2
0
0
0
1
1
0
2
1
1
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
1
0
0
1
2
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
2
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
2
2
0
0
0
0
1
0
4
0
0
1
2
3
2
2
0
0
1
0
2
3
0
0
0
0
2
1
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
1
1
0
0
2
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
3
0
0
0
0
1
0
0
0
2
2
0
0
0
0
1
0
0
2
0
1
1
1
0
0
0
0
0
0
0
1
1
1
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
2
1
2
0
0
0
2
0
0
1
1
0
0
1
0
0
2
0
2
0
1
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
1
0
1
1
0
0
3
0
1
2
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
2
2
1
0
1
1
0
0
0
0
0
2
0
0
4
0
0
0
0
0
2
3
1
2
0
1
0
2
2
0
1
0
1
0
0
1
0
1
2
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
1
2
0
2
0
2
3
0
0
0
0
1
2
0
1
1
0
0
0
0
1
3
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
2
0
0
0
1
1
1
0
0
2
0
0
0
0
0
2
1
0
2
1
0
0
0
3
3
2
1
0
0
2
2
2
0
0
0
0
1
4
0
0
1
0
0
1
0
2
1
2
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
2
0
1
1
0
0
1
0
3
0
1
1
0
1
0
0
1
1
0
1
2
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
1
0
0
1
2
0
2
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
1
0
0
2
0
0
2
1
2
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
3
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
1
0
1
3
2
0
0
3
2
1
0
2
0
0
1
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
3
1
0
0
0
2
0
4
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
1
0
0
2
0
3
0
1
2
0
1
0
2
0
2
0
1
0
0
0
0
1
0
0
1
4
2
2
0
1
1
0
0
0
0
1
0
0
0
2
2
2
0
0
0
0
1
0
2
0
0
0
0
2
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
1
1
0
2
0
0
1
2
0
1
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
1
2
0
1
0
0
0
0
0
2
0
1
0
0
2
2
0
2
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
2
0
0
0
0
1
4
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
1
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
1
0
0
2
0
2
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
2
0
1
2
0
0
2
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
1
2
0
2
0
2
1
2
0
0
1
0
1
0
0
0
0
0
0
2
2
0
0
2
0
1
3
0
0
0
0
0
3
1
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
2
4
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
1
2
2
0
2
0
2
0
1
1
0
1
2
0
0
0
0
0
0
0
0
0
3
0
3
1
1
1
2
0
0
1
0
4
0
2
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
2
1
0
1
0
0
2
2
0
0
2
0
0
0
0
3
0
1
0
0
2
1
1
1
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
1
3
0
1
0
2
0
2
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
1
0
0
0
0
3
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
1
2
0
1
3
0
0
0
0
2
0
0
0
2
0
0
1
0
0
2
1
1
0
0
0
0
0
0
2
0
2
0
2
1
2
0
1
0
2
0
0
2
2
0
1
0
0
0
0
0
1
2
1
0
0
0
0
0
0
2
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
5
0
2
0
0
0
0
2
2
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
2
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
1
0
0
0
0
0
0
2
2
0
0
0
0
2
1
2
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
1
0
2
2
2
1
1
2
0
1
0
0
1
0
0
0
2
0
1
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
4
0
0
0
1
1
2
0
2
0
0
1
0
1
2
1
2
0
1
1
2
0
0
0
0
2
1
0
0
1
1
0
0
0
0
2
0
1
0
0
0
2
0
1
2
2
2
0
0
0
0
0
0
1
0
1
0
2
1
0
0
0
0
1
0
0
0
0
0
2
2
1
0
1
0
0
2
4
0
0
0
0
2
0
0
0
1
0
1
0
1
0
0
0
2
1
0
0
0
0
1
3
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
1
0
2
0
2
0
0
0
0
0
0
0
2
2
0
1
1
2
2
0
0
1
0
0
0
2
0
2
1
0
0
1
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
3
0
0
0
0
2
1
2
1
2
0
0
0
0
0
2
0
0
0
0
0
1
0
2
1
0
2
0
1
0
10
0
0
0
0
2
0
0
2
0
0
0
1
1
0
1
0
0
0
0
0
2
0
0
3
0
1
0
2
0
0
0
0
2
2
1
0
1
0
0
0
3
2
1
5
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
2
0
0
0
2
1
0
2
2
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
2
0
1
0
0
0
1
0
0
2
2
1
2
0
1
0
0
0
2
1
0
0
1
0
0
1
2
0
2
0
0
3
2
0
2
0
0
0
0
2
0
0
0
1
1
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
2
0
1
0
0
0
0
2
0
2
2
2
1
1
0
1
0
0
0
2
0
1
3
3
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
3
1
1
1
1
1
0
0
0
0
0
1
1
0
2
0
0
0
2
1
1
9
0
0
2
0
0
0
0
1
2
1
0
2
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
3
2
0
0
1
1
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
2
0
0
2
0
2
1
1
0
0
0
1
0
0
0
1
0
2
1
0
0
1
1
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
2
1
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
1
4
1
0
2
0
1
0
2
0
0
1
0
2
1
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
1
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
1
0
1
2
0
0
0
2
0
0
2
2
2
0
0
0
0
1
0
0
0
0
0
0
2
0
2
1
0
0
3
1
0
0
0
1
2
0
0
0
2
2
0
0
0
0
0
0
0
0
3
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
2
0
0
2
12
0
3
1
0
1
0
0
2
0
0
0
2
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
2
0
1
0
2
0
0
0
3
0
0
2
1
2
0
0
1
1
0
3
0
0
0
2
0
1
2
0
1
0
0
0
0
0
1
0
1
0
0
1
2
1
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
3
0
0
0
0
4
0
0
2
1
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
1
0
0
0
2
0
0
0
1
2
0
1
2
2
0
2
3
0
2
2
0
2
1
0
0
3
0
0
0
0
4
0
0
1
0
2
0
0
0
0
0
0
1
2
1
2
2
1
0
0
2
0
0
0
1
2
0
2
0
2
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
1
0
2
0
0
1
0
1
0
0
0
2
0
0
0
2
0
2
2
0
3
2
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
1
1
0
2
0
0
0
0
0
0
1
2
1
2
0
0
1
0
2
0
0
1
3
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
1
0
2
0
2
2
3
0
0
0
0
0
0
2
0
0
1
0
0
2
0
1
0
0
0
0
2
0
1
1
1
3
0
0
1
2
0
1
4
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
1
0
0
1
1
0
0
1
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
1
0
2
0
2
0
0
0
6
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
2
1
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
1
0
2
1
1
5
0
3
0
0
0
1
0
1
0
0
1
2
0
0
0
1
1
0
2
0
0
0
1
0
2
1
0
0
0
0
0
0
5
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
2
0
1
0
0
0
0
0
0
1
2
0
2
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
1
1
1
0
2
2
0
1
0
0
1
1
0
0
0
0
2
0
0
2
0
1
3
0
0
0
0
1
0
0
0
0
0
1
0
2
0
1
2
3
0
2
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
1
0
0
0
3
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
4
0
0
2
2
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
1
1
2
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
2
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
1
1
1
0
0
0
2
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
1
1
0
3
0
0
0
1
2
0
0
0
0
0
0
0
3
0
1
1
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
1
1
1
1
0
0
1
2
1
1
0
0
0
0
3
0
0
0
0
2
1
1
0
2
0
0
0
0
1
2
0
0
2
0
1
1
2
0
0
0
0
1
2
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
1
1
0
0
0
1
1
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
2
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
2
2
0
2
0
2
2
4
0
0
3
0
0
1
2
2
2
0
1
1
2
0
2
0
2
0
2
0
0
0
0
0
0
2
2
0
0
2
2
0
0
1
0
0
0
0
0
1
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
2
0
0
0
1
2
0
0
2
0
2
0
1
2
1
1
2
0
0
0
0
0
0
0
0
0
2
1
3
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
1
2
0
1
0
1
0
2
0
0
1
0
0
0
2
0
1
0
0
0
0
1
0
0
2
2
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
2
1
1
1
1
0
2
0
0
0
0
1
0
1
0
2
0
0
2
0
0
1
2
1
2
0
2
0
0
0
0
2
1
0
0
3
2
0
0
1
0
0
0
0
0
0
1
1
0
0
2
0
2
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
2
0
0
0
0
0
0
0
1
4
1
3
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
1
1
2
0
2
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
2
0
2
0
0
1
0
0
0
2
1
0
0
3
2
0
0
0
0
2
0
0
0
0
1
1
2
0
3
0
0
2
2
1
1
2
0
1
0
0
0
0
0
4
0
0
0
0
2
0
1
0
0
2
0
1
0
1
0
1
0
1
0
0
0
0
0
0
1
2
0
0
0
2
0
0
2
2
0
0
2
3
2
0
0
0
2
2
0
3
2
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
1
2
2
0
0
3
1
0
1
0
0
1
1
0
0
0
1
0
0
2
0
1
0
0
0
2
0
1
0
1
0
0
0
0
0
1
1
1
0
2
0
0
2
2
0
1
0
2
0
0
0
2
0
2
0
1
0
1
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
2
0
1
0
0
1
0
2
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
3
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
1
0
0
1
3
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
3
0
0
0
2
0
0
0
1
2
0
2
1
2
1
0
0
2
2
2
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
2
2
0
0
0
0
0
0
0
1
1
0
2
0
2
0
2
2
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
2
1
0
0
2
3
8
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
3
2
0
2
2
0
0
3
2
0
2
0
0
1
0
4
0
0
0
0
0
2
0
2
1
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
2
0
2
3
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
2
2
0
0
1
0
1
0
0
0
0
2
0
0
3
1
0
0
0
0
0
0
2
2
0
2
1
0
0
2
2
0
0
2
0
0
1
0
0
0
2
0
0
0
1
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
3
0
0
1
2
1
0
0
0
0
0
2
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
2
0
0
1
0
0
0
2
0
3
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
3
2
0
2
2
0
1
2
0
1
0
0
1
0
1
0
0
0
2
2
1
0
0
1
0
1
1
2
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
3
2
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
3
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
1
4
0
0
0
1
0
1
0
0
0
1
2
0
0
0
2
0
0
3
0
0
0
2
0
0
2
0
2
0
0
2
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
2
2
0
0
0
1
0
0
0
0
0
2
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
1
0
0
2
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
2
1
0
0
0
1
1
0
0
0
1
1
0
0
1
2
0
0
0
1
1
0
0
2
0
2
2
1
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
3
0
0
1
0
2
0
0
0
0
0
1
0
2
2
1
2
1
0
0
0
2
1
0
0
2
0
1
2
0
0
0
0
2
0
0
1
0
2
0
1
2
0
2
0
2
1
2
2
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
2
2
0
2
3
0
2
1
2
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
1
0
0
2
2
2
0
2
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
2
0
2
2
2
1
0
0
0
1
0
2
0
0
0
0
0
0
0
2
2
0
0
0
1
0
1
0
0
2
1
0
2
1
0
2
0
0
1
0
0
0
0
0
1
1
0
2
1
0
0
0
2
0
0
0
0
1
2
0
0
2
2
0
3
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
2
1
0
1
0
0
0
0
0
1
0
2
0
4
0
3
0
6
1
3
0
0
3
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
1
2
0
0
0
2
2
2
1
1
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
2
0
1
0
1
0
1
0
1
0
0
0
1
1
1
0
2
0
0
2
1
0
3
1
1
0
0
1
2
1
0
0
1
0
4
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
2
0
1
2
0
2
1
0
0
3
1
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
1
0
2
2
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
2
2
1
0
0
3
1
0
2
3
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
1
0
2
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
4
0
0
0
0
0
2
2
0
0
0
1
0
2
1
0
1
0
0
0
2
0
0
0
2
0
1
0
0
2
1
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
2
2
0
0
0
3
0
3
0
2
2
0
1
2
0
0
0
0
0
1
0
1
0
3
0
0
0
0
0
1
1
2
1
1
2
0
0
0
0
0
0
0
1
0
1
0
0
3
0
1
0
1
0
0
1
3
2
0
0
1
1
0
0
0
0
0
1
1
0
2
1
0
0
0
0
0
0
0
0
3
0
0
0
1
0
1
2
0
0
1
0
1
2
2
0
0
3
1
1
2
0
0
0
1
2
2
0
1
0
1
1
3
2
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
2
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
1
0
4
0
1
0
0
1
1
0
0
0
2
0
1
0
1
0
2
0
0
3
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
2
2
0
2
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
1
0
2
0
1
0
2
1
2
0
0
0
0
2
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
2
2
0
0
0
0
2
1
2
1
0
0
0
1
0
0
0
0
0
4
2
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
2
0
1
0
0
1
2
0
0
0
0
0
0
0
2
3
0
1
0
0
0
0
1
0
0
0
0
2
0
0
2
0
2
2
0
0
2
1
2
3
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
2
0
2
1
0
2
2
0
0
0
0
0
2
0
0
2
0
0
0
2
1
0
0
0
0
0
2
0
1
1
1
2
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
2
1
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
2
2
0
1
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
1
2
0
0
1
0
0
0
1
0
2
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
1
0
1
0
0
0
1
2
0
0
0
0
2
0
0
0
1
2
0
0
0
1
0
0
1
0
0
1
4
0
0
0
0
2
0
2
0
0
0
0
1
1
0
0
2
0
2
0
1
1
1
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
2
1
0
0
0
0
0
1
0
1
1
0
2
1
2
1
2
0
0
1
2
2
0
1
0
0
1
2
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
2
0
0
1
0
0
1
0
2
0
2
0
0
1
0
0
2
0
1
0
3
1
0
2
0
0
0
2
2
0
0
0
0
3
0
0
0
0
1
0
2
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
2
3
0
0
0
0
1
1
0
0
0
2
0
0
0
2
2
0
2
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
1
0
0
0
2
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
2
0
2
0
0
1
2
0
0
0
1
0
2
0
0
0
0
0
1
2
2
2
0
0
2
0
0
2
0
2
0
0
0
1
2
0
0
0
5
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
2
0
2
0
0
0
1
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
2
2
2
0
0
0
0
1
2
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
3
1
0
2
0
3
2
0
0
0
0
1
0
2
1
0
0
1
0
0
1
0
0
2
0
0
0
2
2
2
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
1
0
0
0
1
0
2
2
1
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
2
2
7
0
0
0
1
0
0
2
0
0
2
0
0
1
0
1
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
1
0
0
3
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
2
1
0
2
0
0
0
1
0
0
2
0
0
1
0
0
0
2
2
0
0
1
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
2
2
0
0
2
1
0
0
0
0
0
0
0
0
0
1
1
2
0
1
0
2
0
0
2
1
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
1
2
0
0
1
0
0
0
0
2
7
0
0
0
2
0
0
0
2
1
0
0
2
2
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
5
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
2
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
2
1
1
0
0
0
0
0
1
0
2
0
2
2
0
1
1
0
1
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
2
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
2
0
1
4
1
0
0
0
2
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
3
1
0
0
1
0
0
0
0
0
2
0
4
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
2
0
1
1
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
2
3
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
1
1
1
0
1
1
0
0
2
2
0
0
0
2
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
2
2
0
0
0
0
0
0
1
2
0
1
0
2
2
0
0
0
0
2
0
0
0
2
1
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
2
2
0
0
0
0
0
0
0
0
0
0
1
2
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
2
1
2
0
0
2
3
0
0
1
2
2
1
0
0
0
3
0
0
2
8
0
3
0
0
0
0
0
1
0
1
1
0
0
2
1
0
1
2
0
2
1
2
0
0
0
1
4
2
0
0
2
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
2
2
0
0
0
2
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
3
3
0
0
0
0
0
1
0
2
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
1
2
2
1
0
2
2
0
0
0
1
0
4
0
1
0
0
0
1
3
1
0
0
1
0
0
5
0
0
0
0
0
1
3
0
0
1
2
0
0
2
0
2
3
3
2
2
0
0
0
0
0
0
2
1
0
0
1
0
3
0
1
2
0
0
2
0
0
0
0
0
0
2
2
2
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
1
1
2
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
1
0
1
1
1
3
0
0
4
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
4
0
2
2
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
2
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
2
2
0
0
0
0
0
1
0
0
0
2
0
0
0
1
1
0
0
1
0
2
2
0
0
0
0
1
1
0
0
0
0
1
1
0
0
4
0
0
0
0
0
11
1
0
2
0
0
3
0
2
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
2
0
0
0
5
0
0
0
0
0
2
0
0
1
2
1
2
0
1
1
0
2
0
0
0
0
2
2
1
3
0
0
1
0
1
0
0
0
0
0
1
0
1
0
2
1
2
1
0
3
0
2
0
1
1
0
0
4
0
0
0
1
0
0
0
1
2
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
1
0
1
0
1
1
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
1
0
0
2
0
2
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
2
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
1
1
0
1
0
4
2
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
2
0
1
0
0
2
0
0
0
0
3
0
0
1
1
2
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
2
0
0
2
0
1
1
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
4
0
1
0
1
0
0
0
0
1
0
0
2
0
1
0
2
2
0
0
0
0
0
2
1
1
0
0
2
0
1
0
0
0
0
0
0
1
2
0
1
1
2
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
2
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
2
0
2
0
0
0
0
2
0
0
0
1
0
1
0
1
0
0
0
0
0
2
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
3
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
1
2
0
1
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
2
0
0
0
2
0
2
2
1
0
1
0
0
1
0
0
0
0
0
2
2
0
2
1
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
1
2
0
0
0
1
0
0
0
1
0
0
0
1
0
1
2
1
0
1
0
0
2
2
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
2
0
2
3
0
1
0
1
0
0
3
0
0
0
0
0
0
1
0
2
2
1
2
4
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
1
2
2
2
0
0
2
0
2
3
0
0
1
2
0
2
0
0
0
1
2
2
0
1
0
1
1
0
0
0
3
2
0
1
2
0
1
0
0
0
2
0
1
0
0
1
0
2
1
2
0
0
0
0
0
0
2
0
0
2
2
0
0
1
0
2
0
0
0
0
0
2
0
0
0
2
0
0
4
0
1
0
0
0
2
1
0
2
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
8
2
0
1
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
4
2
0
0
0
2
1
0
0
0
0
1
2
0
0
0
1
0
1
0
0
1
1
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
2
2
0
0
0
0
0
2
0
1
1
0
2
0
0
1
0
0
2
2
0
0
1
0
1
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
2
1
1
0
0
0
0
0
1
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
1
0
0
0
2
0
0
1
0
0
2
0
1
0
2
0
0
2
0
0
0
0
1
3
0
1
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
1
0
1
1
0
2
1
1
0
1
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
2
0
1
3
2
3
0
0
0
1
0
0
3
0
0
0
2
0
0
2
2
0
2
0
0
3
0
0
0
0
2
0
0
1
0
0
1
2
0
2
0
0
0
1
0
0
0
1
0
2
0
0
0
2
0
0
0
0
1
0
0
3
2
0
0
0
0
1
0
0
0
0
0
1
2
4
0
2
0
2
0
0
0
0
2
0
0
0
1
0
1
2
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
2
2
2
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
2
3
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
2
0
1
0
2
0
0
2
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
1
2
2
1
0
1
1
0
0
0
0
0
2
2
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
2
0
0
1
0
0
2
1
0
0
2
3
2
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
1
2
0
2
0
2
0
0
0
1
0
1
2
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
1
1
0
0
2
0
0
2
1
1
2
0
1
3
0
0
0
1
1
0
0
1
1
1
0
0
0
0
0
2
0
0
2
0
0
2
0
2
0
0
0
0
0
0
2
0
0
2
1
2
0
2
0
0
1
0
0
0
0
0
1
0
4
0
0
1
1
0
0
0
2
0
1
0
0
0
0
2
2
0
0
0
2
0
0
0
0
3
0
1
0
0
0
0
0
5
0
0
0
2
0
0
3
0
0
0
0
0
1
0
0
0
1
0
0
0
1
2
0
0
2
2
0
1
2
1
2
1
1
2
2
0
1
2
0
0
0
0
0
0
1
0
1
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
8
0
0
0
1
2
0
3
0
0
1
0
2
0
1
2
0
0
1
0
0
0
0
2
0
0
1
0
0
0
2
0
3
0
1
1
1
0
0
0
0
0
0
0
1
2
0
3
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
1
1
0
0
0
0
0
2
0
1
0
1
0
1
0
0
0
5
0
0
1
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
2
2
0
0
0
0
2
0
0
1
0
1
0
2
0
3
1
2
0
2
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
2
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
3
0
0
1
1
0
1
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
2
0
2
0
0
0
1
1
0
0
2
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
1
2
0
0
0
0
1
2
2
0
1
1
0
2
2
1
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
2
0
2
0
0
0
0
0
1
0
0
0
0
1
2
0
2
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
1
2
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
2
0
0
1
2
0
0
2
0
0
0
1
0
4
0
1
0
0
1
2
2
0
1
2
0
0
1
0
0
0
0
0
0
1
1
1
2
0
0
0
0
1
1
0
0
2
0
0
4
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
1
1
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
1
1
0
1
0
0
0
0
2
0
1
2
0
2
2
0
2
0
0
1
0
1
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
1
1
1
2
0
5
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
2
2
0
0
2
1
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
2
0
3
0
0
0
2
0
0
0
1
1
1
1
0
1
9
0
1
0
0
0
0
0
1
3
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
3
0
2
0
1
0
2
0
1
1
0
0
0
1
2
0
1
0
2
0
0
1
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
1
0
0
0
0
5
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
1
1
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
2
0
0
2
2
0
1
2
0
0
0
2
4
1
0
0
1
2
0
0
0
0
2
0
1
1
0
1
0
1
2
0
0
0
1
0
0
0
1
0
0
2
2
1
0
0
1
0
0
2
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
1
0
1
0
0
0
0
2
0
2
2
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
1
0
2
2
1
1
0
0
1
2
0
2
0
0
2
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
4
0
0
1
0
0
2
0
0
1
0
0
2
0
0
1
1
0
0
0
1
1
1
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
1
2
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
2
0
0
0
2
0
2
1
5
1
0
1
2
0
0
0
1
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
3
2
0
2
2
0
0
0
0
0
0
0
0
1
2
0
0
0
1
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
1
0
2
1
1
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
2
3
1
1
0
0
2
1
0
0
1
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
1
1
1
1
0
0
2
0
0
2
2
1
0
0
0
4
0
0
0
0
0
0
0
1
0
1
2
2
0
0
0
0
1
1
0
0
2
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
1
2
0
0
0
2
0
4
0
0
1
0
0
0
0
0
2
0
0
0
0
2
1
1
0
0
0
0
3
2
0
0
0
0
2
0
2
2
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
2
2
2
0
0
0
0
2
1
2
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
1
0
2
0
1
0
0
0
0
0
0
1
1
1
3
0
0
2
1
0
2
0
2
1
2
0
0
1
1
0
1
0
0
1
1
0
0
0
1
1
0
0
0
2
0
3
0
1
2
1
0
0
3
2
0
0
2
1
0
2
0
0
2
2
2
0
1
0
0
1
1
0
0
0
0
0
0
0
2
2
1
2
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
2
2
0
0
0
0
2
2
0
0
1
1
0
1
0
0
1
1
0
0
0
0
2
0
0
0
4
0
2
2
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
2
0
0
2
0
0
1
0
0
0
0
2
0
0
1
1
2
0
0
1
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
1
1
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
3
0
2
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
2
0
0
0
0
0
0
2
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
2
0
0
2
0
0
0
0
0
0
2
0
0
3
0
0
1
0
0
0
2
1
0
0
0
0
0
0
1
0
1
1
2
0
1
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
1
0
1
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
4
0
0
0
0
0
1
1
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
1
0
2
2
0
0
1
1
0
2
0
2
0
0
0
0
0
1
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
1
0
0
0
2
1
2
0
2
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
4
0
0
1
1
1
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
2
0
0
12
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
2
0
2
0
2
0
0
0
2
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
2
0
3
0
0
0
0
0
2
0
1
1
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
5
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
2
2
0
1
0
0
2
0
0
0
0
0
1
1
0
0
0
0
1
1
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
1
2
0
0
0
0
2
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
1
1
0
0
0
0
2
1
0
1
0
2
0
0
0
0
1
1
0
0
0
0
2
2
2
0
0
2
0
0
0
0
1
3
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
1
2
0
3
0
0
2
0
0
0
2
0
1
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
2
3
0
2
2
4
0
0
0
0
0
0
3
1
1
1
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
2
0
0
4
0
2
0
0
0
0
0
0
3
1
0
0
1
2
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
1
0
0
1
2
1
0
0
0
1
1
0
0
2
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
2
1
1
2
0
2
0
1
0
0
0
1
0
0
0
2
0
0
0
1
0
1
1
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
4
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
2
2
2
0
3
0
1
0
0
2
0
0
0
0
0
0
2
5
0
2
1
0
0
2
2
2
0
0
0
0
3
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
2
1
0
0
2
0
1
0
3
0
10
0
1
0
1
1
1
0
2
0
0
0
1
0
2
0
2
0
0
0
1
0
0
1
0
0
0
2
1
1
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
1
0
1
3
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
3
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
1
2
0
0
0
1
0
0
0
1
0
2
1
2
0
0
0
1
0
0
2
1
2
1
0
1
0
0
0
0
1
0
2
0
0
1
0
0
0
2
1
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
2
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
2
0
2
2
0
2
0
0
1
1
0
0
0
0
1
0
0
1
0
0
2
0
0
0
2
0
4
0
0
1
1
0
0
0
0
0
2
0
2
1
0
0
0
2
0
0
1
3
0
0
0
2
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
1
1
0
0
1
2
2
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
2
1
0
7
0
0
0
0
2
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
2
2
0
0
0
0
1
0
0
0
2
1
1
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
2
2
0
0
1
1
0
2
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
2
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
2
0
0
1
0
2
1
0
1
2
2
1
0
0
0
2
2
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
1
3
1
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
2
2
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
2
4
0
1
1
1
1
0
0
0
0
0
1
0
1
1
0
0
0
0
7
2
0
0
0
2
0
0
0
4
0
0
1
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
4
0
2
0
0
0
1
0
2
0
1
0
0
0
1
0
0
0
0
0
2
0
2
2
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
5
1
1
0
0
0
1
0
0
0
0
0
0
4
1
0
0
0
1
0
0
0
0
2
1
0
1
0
2
5
0
1
1
0
0
0
0
0
0
1
3
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
1
0
0
0
1
2
0
0
0
1
0
6
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
4
0
2
0
1
0
0
9
2
0
1
0
2
2
2
0
0
0
0
1
2
4
2
0
0
1
0
0
0
0
1
0
0
2
2
0
0
0
0
1
2
0
0
0
1
0
0
1
2
0
0
3
0
0
0
0
1
1
0
1
0
2
0
0
0
0
0
0
2
1
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
4
1
0
0
1
0
2
3
0
2
0
1
0
0
2
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
1
2
1
0
2
0
2
4
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
2
1
0
0
1
0
2
0
0
0
1
1
0
0
0
1
0
2
0
2
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
2
0
0
1
2
0
2
0
0
1
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
2
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
2
1
1
4
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
2
0
0
0
0
2
0
0
2
2
1
0
0
1
4
2
0
0
0
0
0
1
0
0
0
2
2
0
1
0
0
0
0
0
0
0
2
0
8
2
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
1
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
2
0
0
0
2
0
1
3
0
0
1
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
2
2
0
0
2
2
6
2
0
0
0
5
0
0
0
1
0
1
2
1
0
0
0
0
0
0
1
0
1
0
1
0
0
2
0
0
0
0
1
0
1
1
0
2
0
1
2
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
1
1
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
2
1
0
0
1
1
0
0
0
0
1
2
3
0
0
0
0
1
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
2
0
0
2
2
0
0
1
0
1
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
2
0
1
0
0
0
2
2
0
2
0
0
0
0
1
0
0
1
2
0
0
3
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
2
0
1
0
0
0
6
0
0
1
2
1
0
0
2
0
0
1
1
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
2
0
2
35
0
0
1
0
1
0
2
0
0
0
0
2
0
0
1
1
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
5
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
2
2
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
3
0
0
0
2
1
0
0
0
0
0
0
2
0
0
2
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
2
0
0
1
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
2
0
0
0
1
2
1
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
2
2
0
1
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
1
0
0
1
0
0
0
2
0
1
0
0
2
2
1
0
1
0
0
2
0
0
2
2
2
0
0
2
0
0
2
2
0
1
0
0
4
0
1
2
0
1
2
0
2
0
0
0
0
0
0
1
2
0
1
0
2
0
3
1
0
0
2
0
1
2
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
2
0
2
2
2
0
0
0
0
0
3
0
0
2
0
0
0
2
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
2
2
0
1
1
0
2
1
0
0
0
1
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
1
1
0
1
0
1
2
0
0
0
3
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
1
0
2
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
1
1
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
2
0
1
0
0
0
1
1
0
1
2
0
0
1
0
0
0
0
1
1
1
1
0
1
2
1
0
2
2
2
2
0
0
1
0
2
2
0
0
0
1
2
1
0
0
1
0
0
0
3
1
0
0
0
2
1
0
0
1
0
1
1
0
0
1
0
2
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
1
0
1
0
0
3
0
0
2
1
0
0
0
0
0
2
0
0
1
0
2
0
1
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
1
1
0
0
1
0
0
1
2
0
0
0
0
0
0
1
0
2
3
0
0
1
9
1
0
0
0
0
0
2
0
1
0
0
2
0
0
4
0
1
0
2
1
0
0
0
1
1
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
2
3
0
0
0
0
2
0
0
2
4
1
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
2
0
0
0
0
2
0
0
1
1
2
1
1
0
0
2
0
0
0
2
2
2
0
2
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
9
0
2
0
2
0
2
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
2
2
1
0
0
0
0
0
2
1
0
0
0
0
2
0
2
0
0
1
0
2
0
0
0
0
0
0
2
0
1
1
1
0
0
0
0
0
0
0
1
0
1
2
2
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
1
2
0
0
1
0
2
0
0
1
0
3
0
0
2
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
2
0
0
0
0
1
0
0
1
0
0
0
1
0
2
2
3
1
0
0
1
0
0
0
0
2
1
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
1
1
0
2
0
2
1
2
2
0
3
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
2
0
2
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
1
0
0
0
2
1
2
3
2
0
1
0
2
0
0
0
0
0
0
2
1
0
2
2
0
0
0
0
2
0
0
0
0
0
2
0
2
0
1
1
0
1
3
0
0
0
1
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
2
0
0
3
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
1
0
0
0
0
1
0
0
2
2
0
2
0
1
0
0
3
0
1
1
2
1
0
0
2
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
2
2
1
0
2
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
1
2
0
0
0
1
0
0
0
1
1
0
2
3
0
0
2
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
1
0
0
2
3
0
0
0
0
0
0
0
4
0
2
2
0
2
0
0
1
0
0
1
0
0
0
0
0
1
0
2
0
1
1
1
2
0
0
0
0
3
0
0
0
2
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
2
0
0
2
0
1
0
1
0
1
0
0
1
0
0
0
0
1
1
2
0
0
0
0
1
0
2
0
0
0
2
1
3
1
0
3
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
2
1
0
1
2
0
0
1
0
0
2
0
2
0
0
2
1
2
0
0
1
0
2
1
1
0
0
0
0
0
0
2
0
3
2
0
0
0
0
2
0
2
2
0
2
0
0
0
0
2
2
1
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
1
1
0
1
0
2
0
2
0
0
1
1
2
2
0
1
1
1
2
1
0
0
0
1
0
1
1
0
0
0
1
0
2
1
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
1
0
1
0
0
2
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
2
0
2
0
2
1
0
2
0
1
2
0
0
0
1
0
1
2
0
0
0
2
0
0
3
2
0
1
0
2
0
0
0
0
0
2
0
1
1
2
2
0
0
0
0
1
0
0
1
0
0
0
0
3
1
0
0
2
0
2
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
1
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
3
1
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
1
1
0
0
1
0
2
0
0
1
1
0
1
1
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
3
0
1
0
0
0
1
0
2
0
0
0
0
0
2
0
0
1
0
1
0
1
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
1
0
0
0
1
0
0
0
0
2
1
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
3
0
0
0
0
0
1
0
0
1
1
1
2
2
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
3
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
1
2
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
2
2
0
0
1
0
0
0
0
0
0
2
0
2
2
0
2
2
0
1
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
1
1
0
1
2
0
0
1
2
2
2
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
1
0
1
1
0
0
0
0
1
0
0
2
1
2
1
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
2
1
0
0
0
0
2
0
0
0
1
0
0
2
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
2
2
0
0
1
0
2
0
1
0
0
0
1
2
0
2
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
2
0
1
0
0
0
0
2
0
2
1
0
0
1
2
1
0
0
0
0
0
0
1
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
1
0
0
1
3
2
0
0
0
0
0
2
1
1
0
0
0
0
0
0
2
2
0
1
2
2
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
3
0
0
0
2
0
0
1
2
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
2
0
1
0
2
2
2
2
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
2
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
2
2
1
0
4
0
0
0
0
0
0
2
0
1
1
2
0
0
2
0
0
2
0
1
2
1
0
1
2
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
1
0
0
0
0
0
1
2
1
0
0
0
1
1
0
0
0
1
1
0
0
0
0
1
0
0
1
3
1
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
5
2
1
1
0
0
1
2
0
2
0
0
1
0
0
0
1
0
0
0
2
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
2
3
0
1
0
0
0
0
0
3
1
0
0
0
3
1
2
2
0
2
1
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
1
0
1
0
1
2
0
0
0
0
0
0
0
0
2
3
0
1
1
0
1
0
0
1
0
0
0
0
1
0
0
2
2
1
2
0
1
0
2
0
0
0
0
1
2
0
0
2
1
4
1
0
1
0
0
0
2
0
0
1
1
2
0
0
2
0
1
0
0
0
0
0
0
0
0
1
3
0
0
2
1
1
0
0
0
1
2
0
0
0
0
2
0
0
1
2
3
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
1
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
2
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
2
2
0
1
0
2
0
0
0
0
1
0
0
0
1
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
6
0
2
0
0
1
0
0
0
1
0
0
2
2
0
0
2
0
0
0
1
0
0
2
2
1
0
0
0
1
0
3
0
2
0
0
0
0
0
0
2
0
2
2
0
0
1
1
0
2
0
0
0
0
1
0
2
0
0
2
0
0
0
2
0
0
0
1
0
0
0
3
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
2
0
0
1
0
1
0
1
3
0
1
1
0
1
2
0
2
2
0
0
0
4
0
0
0
1
2
0
0
0
0
0
0
3
0
0
2
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
2
1
0
0
3
0
0
0
0
2
2
1
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
2
1
0
2
0
2
1
1
0
0
0
0
0
0
4
0
0
1
1
1
0
2
2
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
1
0
0
1
0
2
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
2
0
1
1
0
0
2
0
1
0
1
1
0
1
7
1
0
0
0
1
2
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
1
2
0
0
0
0
1
0
2
0
1
0
0
0
0
0
2
1
2
0
0
0
0
0
0
3
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
2
0
0
1
0
2
0
0
1
0
0
1
0
1
0
0
0
0
2
2
2
0
0
0
2
2
1
2
0
1
2
1
0
1
1
2
0
2
1
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
2
0
2
2
0
0
2
0
0
0
0
5
0
2
0
2
0
0
1
1
0
0
0
2
0
2
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
5
0
0
3
0
2
0
0
0
0
2
0
3
0
0
0
0
1
1
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
1
0
2
0
1
1
0
2
0
0
1
0
0
3
1
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
2
0
0
0
0
1
0
1
2
0
1
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
4
0
0
1
0
0
0
0
1
0
0
0
2
2
0
0
1
2
1
0
0
2
0
0
0
0
2
0
2
1
1
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
2
3
0
0
0
1
0
0
2
0
1
1
2
1
0
0
0
1
0
1
0
1
0
1
4
2
0
0
0
2
1
1
2
0
0
2
0
1
0
0
5
2
0
0
1
1
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
3
0
0
0
0
0
2
0
0
1
0
0
0
1
2
3
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
2
0
2
1
2
2
0
1
0
0
0
2
1
1
0
2
0
0
0
1
0
4
0
1
0
0
1
0
0
0
0
0
0
0
2
0
1
2
2
0
6
0
0
0
0
0
0
2
0
0
2
0
0
2
2
2
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
2
0
1
0
2
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
1
1
4
0
0
0
0
0
2
0
1
2
2
0
0
1
2
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
3
0
0
2
0
0
0
2
1
2
2
0
1
2
3
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
2
0
0
0
1
0
2
0
1
0
0
0
0
1
0
2
0
2
2
2
0
1
0
0
0
2
3
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
1
0
1
0
0
0
0
0
1
0
0
0
3
0
0
0
0
1
0
3
0
1
2
2
1
0
0
0
2
0
2
1
0
1
1
2
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
2
1
0
0
1
0
1
0
2
3
0
0
0
0
0
4
2
2
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
4
4
1
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
1
2
0
0
2
2
0
1
0
0
3
0
0
0
0
2
0
0
0
0
0
0
2
0
2
2
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
1
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
2
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
2
0
0
0
2
2
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
2
0
1
2
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
2
1
0
0
0
1
0
1
0
6
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
6
2
1
0
1
0
0
0
0
0
0
2
1
0
1
0
0
1
2
0
0
1
1
0
0
1
0
0
2
3
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
3
0
0
0
0
1
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
1
1
4
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
1
2
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
2
1
0
0
3
0
0
0
1
1
0
0
0
0
0
1
1
0
2
0
2
0
0
2
0
0
2
0
0
5
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
3
0
2
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
1
2
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
2
1
0
0
0
0
4
2
0
2
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
2
2
0
0
0
0
1
0
1
0
0
0
1
2
0
2
0
2
0
2
2
0
0
3
2
0
0
3
2
0
1
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
2
1
2
0
0
1
0
2
0
0
0
5
0
1
2
0
2
1
0
0
0
0
0
0
0
1
0
0
0
3
0
0
2
0
0
0
2
0
1
0
0
0
2
2
0
1
1
0
0
2
2
2
2
0
0
0
0
1
0
0
2
0
8
0
0
0
1
2
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
2
1
0
0
0
0
2
0
0
0
2
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
1
0
2
0
0
2
2
0
1
1
0
0
0
0
3
0
0
0
0
0
0
1
0
2
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
2
2
0
1
3
0
0
0
0
2
0
1
0
0
2
0
2
0
2
0
0
3
3
0
1
0
0
2
0
1
3
0
2
0
1
0
0
0
0
0
1
0
0
2
3
0
1
0
0
0
0
0
0
0
1
2
0
0
1
1
2
0
0
0
0
0
2
2
1
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
2
4
0
0
0
0
1
3
0
0
2
2
0
2
1
2
0
0
0
1
0
1
1
1
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
3
0
0
0
0
1
0
1
0
0
2
0
0
0
2
0
0
1
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
1
2
3
0
2
0
0
0
1
1
0
1
0
1
0
0
1
0
0
2
0
0
2
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
1
0
2
1
0
3
1
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
9
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
2
0
6
1
2
1
0
0
1
0
1
3
0
1
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
3
0
1
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
2
0
0
2
0
0
1
0
1
2
2
0
0
0
0
2
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
2
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
3
2
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
2
0
1
2
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
2
0
3
0
2
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
1
1
0
2
0
1
2
0
2
0
1
0
0
0
0
2
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
1
2
2
0
0
0
0
2
0
2
0
2
0
0
1
2
0
0
0
0
1
0
2
0
0
2
0
0
0
0
2
0
0
0
0
9
0
1
2
0
0
3
0
0
0
0
0
0
1
0
0
1
0
2
0
1
0
0
0
0
2
0
0
0
1
0
0
2
0
1
1
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
2
2
0
0
0
4
1
3
0
0
2
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
1
0
0
1
0
0
1
0
0
1
2
0
0
2
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
2
1
2
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
2
2
0
1
0
3
0
0
0
2
0
0
0
0
2
2
0
0
0
2
2
0
1
0
1
0
1
2
0
1
0
2
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
1
2
0
0
0
1
1
0
2
0
1
1
1
0
2
0
0
0
0
2
0
0
3
0
2
1
1
0
1
1
1
0
2
1
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
3
0
0
0
1
0
0
0
0
0
0
0
0
2
1
1
0
2
0
0
0
1
1
0
3
0
0
0
0
2
2
0
1
2
2
0
2
0
1
1
0
0
0
2
1
0
0
0
1
0
0
0
1
0
3
0
1
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
1
0
0
0
1
1
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
1
0
0
2
0
0
2
0
0
0
2
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
1
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
2
1
2
0
0
2
0
0
0
0
1
0
1
0
3
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
2
1
0
2
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
1
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
2
3
0
0
0
1
0
0
0
2
0
0
1
0
0
0
2
0
2
3
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
1
2
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
1
1
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
4
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
1
1
2
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
2
0
2
0
1
1
0
0
1
0
0
2
0
0
0
2
2
0
0
2
0
0
1
1
0
0
2
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
1
0
0
0
1
0
0
0
1
1
0
1
0
0
2
2
2
0
0
0
0
0
1
0
2
0
0
1
1
0
1
0
0
2
1
0
1
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
2
0
0
1
0
0
0
0
0
2
1
0
1
2
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
1
0
0
2
1
2
2
1
2
0
2
0
0
0
0
0
0
3
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
3
0
0
0
2
2
0
0
0
0
2
0
0
0
0
3
0
2
1
0
0
0
2
0
0
0
0
1
0
2
2
2
0
0
0
0
0
1
0
1
3
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
1
1
2
0
0
1
0
0
2
2
0
1
0
0
0
2
0
1
0
1
1
0
1
0
1
1
1
0
1
0
0
0
1
0
1
2
0
2
0
1
1
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
1
0
1
2
0
1
2
0
0
0
0
2
0
0
2
1
1
1
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
1
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
5
0
2
0
0
2
2
1
2
0
0
0
0
2
0
1
3
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
1
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
1
2
2
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
2
0
2
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
1
0
0
1
1
0
0
1
0
2
0
0
1
0
0
0
0
0
2
0
0
1
4
1
0
1
0
2
0
0
2
0
0
0
0
0
2
0
1
0
4
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
1
2
0
0
1
0
0
0
1
1
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
3
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
2
0
0
2
2
7
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
2
2
2
0
0
1
0
0
3
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
1
0
1
1
0
2
0
0
0
1
0
2
0
1
1
0
0
1
0
0
0
0
1
2
0
0
0
2
0
1
0
0
1
0
2
2
2
0
1
2
0
0
0
0
1
0
0
0
2
0
1
2
0
1
0
1
0
0
0
0
0
0
2
0
2
0
2
0
0
0
1
1
0
1
2
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
2
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
2
2
0
1
3
2
1
1
0
0
0
0
0
0
0
2
0
0
0
6
0
0
1
1
1
0
2
1
2
0
2
2
1
0
1
1
0
0
0
2
1
0
0
0
2
2
0
0
1
0
0
1
1
0
1
1
2
1
0
2
2
2
1
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
2
0
0
0
2
0
2
0
0
0
0
2
0
0
1
0
0
0
1
2
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
2
0
0
0
3
0
3
0
0
1
1
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
1
2
0
2
0
0
0
1
0
0
0
0
1
2
0
2
0
4
0
2
1
1
1
0
0
1
2
0
0
0
0
1
0
1
0
0
2
1
0
0
0
0
0
0
2
0
1
1
0
1
1
1
0
0
3
0
0
1
0
2
0
0
0
1
0
2
0
0
1
2
0
0
0
0
0
3
0
1
0
2
0
2
1
2
1
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
2
2
2
1
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
1
4
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
3
1
0
0
1
1
0
1
0
0
2
2
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
2
0
1
0
0
0
2
0
1
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
10
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
2
0
0
0
1
0
0
0
1
1
3
0
1
2
1
0
0
2
1
0
3
0
0
0
0
3
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
1
0
5
3
0
0
0
2
2
0
0
0
2
1
3
2
1
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
2
0
2
0
3
1
1
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
2
2
1
1
0
1
0
0
0
0
0
0
2
0
1
1
0
0
2
0
3
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
1
0
1
1
0
1
0
2
0
0
0
1
0
2
0
0
1
0
1
0
0
0
0
2
0
0
2
0
0
0
2
1
0
0
0
0
0
2
0
0
0
3
0
0
2
1
0
0
2
0
0
0
0
7
0
0
0
1
1
0
0
1
0
1
0
2
1
2
1
0
0
0
0
1
4
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
2
1
0
0
0
0
0
1
0
0
2
1
4
4
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
3
2
2
2
0
0
2
2
2
0
0
0
0
0
0
0
3
2
0
0
0
0
0
1
0
0
0
0
2
7
0
0
0
0
0
2
0
1
1
0
1
0
1
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
2
0
0
2
1
0
0
1
2
0
1
0
0
0
0
0
0
0
1
1
0
0
0
2
1
1
0
0
1
1
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
1
0
1
0
0
2
0
2
0
0
0
0
2
1
0
0
0
1
1
0
0
1
1
0
1
2
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
2
3
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
1
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
1
0
0
0
0
0
0
1
3
0
1
2
2
0
0
0
2
0
1
0
0
0
1
0
0
0
3
0
0
0
0
0
1
0
1
3
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
2
1
0
0
8
0
0
0
0
0
1
2
2
0
0
0
0
3
0
0
2
0
1
0
2
0
1
2
1
2
0
0
0
1
1
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
1
0
0
1
0
0
0
0
3
0
2
2
0
0
0
0
0
1
2
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
3
2
0
0
1
0
0
0
0
0
1
0
0
2
0
2
0
2
3
0
0
2
0
2
0
0
2
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
2
0
0
0
0
3
1
0
0
1
1
0
0
0
0
0
0
1
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
3
2
0
1
0
0
0
1
1
0
0
0
2
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
2
2
1
0
2
0
1
0
1
0
0
0
0
2
1
0
3
0
0
2
0
3
0
1
2
0
0
0
0
0
0
2
0
2
0
0
0
1
0
1
2
1
0
0
0
2
1
0
2
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
1
0
0
2
0
2
1
0
0
0
2
0
2
0
0
2
2
0
0
0
0
0
1
1
3
0
0
0
0
0
0
1
0
2
0
0
0
1
1
2
3
0
0
0
0
0
0
1
0
2
0
3
0
0
0
0
0
1
0
1
0
0
0
2
3
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
2
2
0
0
0
2
0
3
2
0
0
1
0
1
0
2
3
2
0
3
0
1
0
2
3
0
1
2
0
0
0
2
1
0
2
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
3
2
1
0
0
1
0
0
1
0
1
0
0
3
3
0
2
1
3
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
2
0
0
0
1
0
1
0
2
0
0
0
0
0
1
1
0
0
1
0
1
1
0
2
2
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
2
0
0
0
0
8
0
0
0
0
0
0
0
1
0
0
1
0
2
0
1
0
0
0
0
0
0
0
2
2
2
0
2
0
0
0
0
0
0
0
0
0
0
4
2
1
0
0
0
2
0
2
0
2
0
2
2
5
0
2
2
0
0
0
0
0
1
0
2
0
0
1
0
2
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
3
0
1
0
0
0
0
0
2
0
0
0
0
1
2
0
0
2
1
0
0
0
1
0
2
1
0
1
0
0
0
2
0
2
0
3
1
0
3
0
1
1
0
0
0
0
1
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
4
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
3
0
1
1
0
1
0
0
0
0
0
0
0
0
2
3
1
0
1
0
0
0
0
0
2
0
2
0
0
2
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
1
0
2
1
0
1
1
0
4
0
0
1
0
2
0
0
0
0
2
1
2
0
1
0
0
0
0
1
0
0
0
2
1
0
1
1
1
0
0
0
0
1
0
4
0
1
1
0
0
2
2
0
0
0
1
2
5
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
2
0
0
1
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
2
0
3
1
0
1
0
1
2
0
1
0
0
1
1
0
0
0
0
0
0
1
2
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
3
0
0
0
0
2
1
2
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
3
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
2
0
4
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
8
0
0
0
0
0
2
1
3
0
0
1
0
0
3
0
2
0
0
0
3
0
1
0
0
1
0
1
1
1
3
0
0
1
0
0
1
0
0
1
2
1
0
0
2
0
0
0
2
0
0
0
1
0
4
0
1
0
2
0
0
1
0
0
2
1
2
0
0
0
0
1
1
0
0
2
0
0
0
2
0
0
0
1
1
0
0
0
0
0
2
2
1
0
0
2
0
0
1
1
0
0
2
2
1
0
0
0
0
0
0
1
2
0
0
0
2
0
1
0
0
1
0
0
0
2
0
0
0
0
0
1
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
1
1
0
1
0
0
2
0
2
0
0
2
0
0
1
1
0
0
1
0
0
2
0
0
0
0
1
2
1
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
1
2
0
1
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
11
0
0
0
0
0
0
0
3
2
1
1
1
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
1
1
0
0
2
2
1
3
2
1
0
0
0
2
0
2
0
0
0
0
0
0
2
2
1
0
0
0
0
1
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
3
0
1
2
3
0
0
0
0
0
3
0
0
0
0
2
0
0
1
0
0
2
0
0
1
2
0
2
0
2
0
0
4
1
0
0
2
2
2
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
1
1
0
0
8
1
0
1
0
0
0
0
0
0
1
0
2
0
1
1
1
0
2
0
1
0
1
0
0
6
0
0
0
0
0
1
0
0
1
1
2
0
0
3
0
0
0
0
0
0
2
2
1
0
2
1
0
2
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
2
0
0
0
1
0
0
1
1
2
0
4
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
1
0
0
7
0
5
0
0
1
0
1
0
0
0
0
3
0
0
0
1
1
0
4
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
2
3
0
0
0
2
0
1
0
4
0
1
1
0
0
2
0
0
0
1
2
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
3
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
1
0
2
0
0
0
1
1
0
2
0
2
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
4
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
2
1
1
0
1
0
0
2
0
2
0
2
0
0
0
1
0
0
2
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
2
0
0
0
1
0
1
1
1
2
1
2
0
4
2
0
1
0
2
2
0
0
0
0
1
2
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
2
0
0
0
2
0
0
2
0
0
1
0
0
0
2
0
2
2
2
0
2
0
0
0
0
1
0
1
0
0
0
2
1
0
2
1
0
0
0
0
2
1
0
0
0
1
1
2
0
0
0
1
2
4
0
0
1
2
1
0
0
1
0
0
1
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
1
2
0
2
0
0
0
0
0
1
0
1
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
4
0
0
0
1
0
2
2
0
0
0
0
0
0
3
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
1
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
2
1
2
0
0
0
0
0
0
0
2
0
1
1
2
0
0
0
0
0
0
0
5
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
3
0
0
0
0
0
0
0
1
2
0
2
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
1
0
0
1
0
1
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
5
0
0
1
0
1
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
2
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
4
0
0
1
0
3
0
0
1
0
0
2
2
0
3
0
0
2
0
0
0
0
1
1
2
0
0
0
0
3
0
0
0
0
0
0
3
0
0
2
0
0
1
2
0
1
0
0
0
3
0
0
1
1
0
0
0
0
0
0
2
1
0
0
0
1
0
1
2
1
2
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
2
3
0
0
0
0
2
1
1
0
0
1
2
2
0
2
2
1
0
1
2
0
2
0
0
1
3
1
0
2
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
2
0
2
1
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
7
1
0
0
2
0
0
0
2
3
0
2
0
0
0
0
4
0
1
0
0
0
0
1
0
1
0
0
0
2
0
0
0
1
0
0
0
2
0
1
2
0
0
0
1
0
0
1
1
6
2
2
0
0
0
1
0
0
0
0
2
1
1
2
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
2
0
0
1
2
0
1
2
0
0
0
2
2
1
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
3
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
11
0
0
0
0
0
2
0
1
2
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
2
0
2
1
0
2
1
1
0
2
1
0
0
5
0
0
3
2
0
0
0
1
0
0
0
2
2
1
0
2
0
2
2
0
0
2
1
0
2
2
0
0
0
1
0
0
0
0
1
0
0
0
2
0
2
2
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
2
0
0
0
2
0
0
5
0
2
2
0
0
1
0
1
0
0
0
0
0
2
1
0
0
0
3
0
0
0
0
0
1
1
0
0
0
2
2
0
0
2
2
1
0
0
0
2
2
1
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
1
0
0
1
0
0
0
2
0
0
0
0
0
0
5
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
2
0
1
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
2
1
1
0
0
1
1
0
1
2
0
0
0
2
0
0
1
2
0
1
0
0
2
0
0
2
3
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
5
2
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
1
2
0
2
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
2
0
1
1
2
2
0
1
3
1
0
0
2
0
0
0
0
0
0
0
0
2
2
2
0
0
2
1
0
0
1
0
2
0
0
0
2
0
0
0
2
0
0
2
0
0
1
0
0
0
0
1
2
2
0
0
1
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
2
1
1
2
0
1
2
2
0
0
0
2
0
1
0
0
0
0
0
0
0
2
1
2
3
2
2
0
2
0
0
0
0
2
0
0
0
2
0
0
0
1
0
1
1
0
1
2
2
0
1
0
0
0
2
0
0
1
1
0
0
0
0
2
0
1
0
1
1
0
2
0
0
1
0
1
2
0
0
0
0
0
1
0
0
0
1
0
2
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
3
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
2
0
0
0
2
0
2
0
2
1
0
1
0
0
0
0
1
2
0
0
1
4
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
1
0
0
1
2
2
0
0
0
0
0
0
0
0
0
2
0
2
2
1
2
0
1
0
0
1
0
0
0
2
3
2
0
0
2
0
1
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
2
1
1
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
2
1
0
1
0
2
4
2
0
0
0
0
0
0
0
1
3
0
0
1
0
0
3
1
1
0
0
2
0
2
0
0
0
0
1
2
0
0
0
0
0
1
1
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
2
0
0
0
0
1
0
0
0
0
1
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
1
0
0
1
1
0
0
2
2
0
3
0
0
1
0
2
1
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
2
0
0
0
1
2
0
0
1
0
5
0
1
1
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
2
1
0
0
0
0
0
3
0
0
0
0
2
0
0
2
1
0
1
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
2
1
0
0
1
0
0
1
2
0
0
2
1
0
0
0
0
2
0
2
0
1
0
0
0
2
2
1
1
2
2
0
0
4
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
1
0
0
0
2
0
0
0
2
3
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
1
2
2
0
0
0
0
1
0
2
0
0
2
1
1
0
0
4
2
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
1
0
2
0
0
0
1
2
3
0
0
0
2
0
0
2
1
0
0
0
1
1
0
2
0
1
0
0
0
0
2
1
1
1
0
0
0
0
1
0
1
0
0
2
1
1
0
0
0
0
2
0
0
0
1
2
2
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
2
0
0
0
2
1
0
1
0
0
0
0
0
1
0
1
2
0
0
2
1
1
2
0
0
1
0
1
0
0
1
0
0
1
0
1
0
2
0
0
0
0
0
0
1
2
2
2
1
0
0
0
0
0
0
0
2
0
1
1
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
2
0
0
0
0
0
0
2
1
1
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
2
1
1
0
0
0
0
3
0
0
0
0
2
1
2
1
2
2
0
0
0
0
0
0
2
2
0
2
0
0
0
2
2
4
0
2
4
0
0
0
0
0
0
0
4
1
0
2
0
1
0
0
1
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
1
1
0
0
0
0
5
2
1
0
0
0
0
0
1
0
2
1
0
3
0
1
0
0
0
0
0
1
2
0
0
0
0
2
1
0
4
0
0
0
0
0
1
0
0
0
1
0
0
3
0
0
0
0
0
1
3
1
0
2
0
0
1
2
0
1
0
0
0
1
2
0
1
1
0
0
0
0
1
2
0
0
1
0
0
1
1
2
2
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
2
0
0
0
1
0
0
1
2
0
1
0
0
0
0
2
0
2
1
0
0
0
2
0
1
0
0
0
0
2
0
2
0
1
0
1
0
0
0
0
0
2
2
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
1
2
0
0
0
2
2
0
0
0
1
1
1
0
2
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
2
0
3
1
0
0
0
0
1
0
2
1
2
0
0
0
0
2
0
0
1
0
0
2
1
0
2
1
0
1
2
2
0
0
0
2
0
0
3
0
2
1
0
0
2
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
1
0
1
0
1
1
0
1
4
1
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
1
0
0
0
0
0
2
2
1
1
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
2
0
0
2
2
2
2
3
0
0
0
0
0
0
3
0
0
2
0
0
2
0
0
0
0
0
2
0
5
1
0
0
1
0
0
0
1
0
1
2
2
3
2
0
0
0
2
1
0
0
0
1
0
2
2
0
1
0
0
2
2
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
2
0
1
0
0
1
2
0
1
1
0
0
2
0
0
0
0
3
0
2
0
0
1
0
2
0
0
0
2
0
0
0
1
0
0
2
2
0
0
0
0
3
0
1
0
2
1
0
1
0
0
1
2
1
0
1
0
0
0
0
1
2
0
2
1
0
0
1
0
0
2
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
1
0
2
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
2
3
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
2
0
2
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
1
0
1
0
1
1
0
2
2
0
0
0
1
0
2
0
0
0
0
1
0
0
1
2
0
1
0
2
0
0
0
0
0
1
1
2
0
0
0
1
0
0
0
1
0
0
0
0
2
0
2
0
0
2
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
1
2
1
0
0
0
0
0
0
0
0
0
1
1
2
2
0
2
0
0
0
0
0
2
1
0
0
0
0
1
0
0
1
1
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
3
0
2
0
2
0
0
1
1
0
0
0
0
0
0
0
1
0
2
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
2
1
0
0
2
1
0
0
0
0
0
0
3
2
2
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
1
1
0
2
0
0
2
0
0
2
0
0
1
0
0
2
1
0
0
0
1
1
1
1
1
0
2
8
0
1
0
0
2
0
3
0
0
0
1
0
0
0
0
0
2
1
0
1
2
0
0
2
0
0
1
0
0
0
3
0
0
0
0
0
0
0
2
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
1
0
1
0
2
0
0
1
2
3
1
0
1
2
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
1
2
1
1
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
2
2
0
1
0
2
2
0
0
0
0
1
0
0
3
2
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
1
0
0
0
1
1
1
2
1
3
1
2
1
0
0
0
0
0
0
1
1
1
1
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
2
3
0
0
0
2
0
0
0
0
2
1
0
0
0
0
3
0
0
2
0
0
0
0
2
0
0
0
3
0
3
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
1
0
0
2
2
1
0
0
0
0
1
2
1
0
0
0
0
1
3
0
0
2
0
0
1
1
0
1
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
2
0
0
0
0
2
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
2
0
0
2
0
0
1
0
0
0
0
2
2
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
2
2
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
1
2
0
0
1
0
0
0
0
1
0
0
0
0
5
0
2
1
1
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
1
0
1
0
0
0
1
0
0
2
2
0
0
0
0
2
0
0
0
1
0
0
1
0
1
0
1
0
2
2
0
0
2
0
0
0
0
0
2
0
1
1
1
2
0
0
0
0
0
0
5
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
2
0
2
1
0
2
0
0
0
1
0
0
2
1
0
0
0
0
1
1
0
0
0
2
0
0
0
1
0
0
1
2
0
5
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
2
0
1
2
0
1
0
1
0
0
0
2
0
0
0
1
1
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
2
0
0
1
1
0
0
0
0
1
0
0
0
3
0
1
0
0
0
0
0
2
0
0
0
2
0
0
1
0
2
0
1
2
0
1
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
1
1
0
0
0
2
0
2
2
0
1
1
0
0
0
0
0
0
0
2
0
1
0
0
2
0
6
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
2
0
0
0
1
2
0
2
0
0
2
1
1
2
2
0
1
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
2
0
0
2
0
1
0
1
0
0
0
2
2
1
0
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
2
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
3
2
2
2
0
0
1
2
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
2
0
0
0
2
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
1
0
2
1
1
1
0
2
2
0
2
2
0
0
0
0
0
1
0
2
0
1
0
2
0
1
1
1
0
1
0
2
0
0
1
1
0
0
0
2
2
1
0
1
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
1
0
0
0
0
0
2
0
2
2
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
2
2
0
0
1
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
1
2
1
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
2
1
1
0
1
0
0
0
3
1
0
0
2
2
2
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
2
0
0
0
0
0
3
1
1
0
1
0
0
1
0
2
0
3
0
0
0
0
0
1
2
1
0
0
0
0
2
0
2
1
2
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
1
0
0
1
0
0
0
0
0
0
1
2
0
1
0
0
0
5
0
0
0
1
1
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
2
2
2
2
0
1
0
0
0
0
1
0
0
0
0
3
1
0
0
0
0
0
1
0
0
1
1
1
0
0
0
2
0
1
0
0
3
1
2
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
2
1
2
2
0
1
1
0
0
0
1
0
0
0
0
0
0
0
2
1
2
0
0
0
1
0
0
0
0
0
1
2
1
0
0
2
0
0
2
0
2
1
0
2
2
2
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
1
1
0
0
0
1
2
0
0
0
1
2
0
1
0
0
0
0
1
1
0
0
0
1
1
0
0
0
1
2
2
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
2
2
1
0
2
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
2
3
1
1
0
1
0
0
0
0
0
1
0
6
1
0
1
0
0
2
2
0
0
1
2
0
0
0
2
0
0
1
0
0
1
0
2
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
2
3
0
0
3
1
2
1
0
0
0
1
0
2
1
0
1
0
2
1
1
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
2
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
2
1
0
2
1
2
3
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
1
0
0
2
0
0
2
0
0
2
0
0
0
1
1
0
0
3
0
0
1
1
0
0
2
0
1
2
0
1
0
0
0
2
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
2
1
0
2
0
2
0
2
0
0
0
0
2
0
1
2
0
1
1
0
2
0
3
0
0
0
0
1
0
2
2
1
2
0
0
2
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
1
0
0
1
0
2
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
3
0
1
0
5
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
4
0
0
2
0
3
1
0
0
0
0
2
0
2
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
1
0
1
0
0
1
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
3
0
0
1
1
0
2
0
0
0
1
0
0
1
1
2
0
0
0
0
0
2
0
1
1
0
0
0
0
1
1
0
0
0
1
0
0
0
2
0
0
2
0
0
2
0
0
1
0
0
1
0
0
0
1
0
0
1
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
3
1
1
1
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
2
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
2
2
0
0
0
0
0
0
0
2
0
0
0
1
1
1
3
3
0
1
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
1
1
0
0
2
0
0
0
0
2
2
0
0
0
1
1
0
1
0
1
0
0
2
1
1
0
1
0
0
0
0
2
1
0
0
0
0
0
1
1
0
0
0
2
0
0
2
0
3
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
5
0
2
2
2
1
1
0
0
1
1
0
0
0
0
0
0
0
2
1
0
2
1
0
0
0
1
0
0
0
1
0
0
2
0
0
7
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
1
0
0
0
0
1
0
0
2
2
1
0
0
0
2
0
3
0
0
0
0
1
0
0
0
0
0
0
0
2
1
2
0
2
0
1
0
0
2
2
0
0
1
0
0
0
1
2
0
0
0
0
1
0
2
0
0
2
0
0
1
0
0
0
0
0
0
5
2
0
1
1
3
0
0
0
0
1
0
1
0
0
0
2
2
0
0
0
2
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
1
0
0
7
0
2
0
1
1
0
2
0
0
0
0
6
0
2
0
0
1
1
1
0
0
0
0
0
0
1
0
2
2
0
0
0
0
2
0
0
3
2
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
2
3
2
0
0
0
2
0
2
0
0
1
0
0
0
1
1
0
0
0
0
0
2
1
0
0
1
0
0
0
2
0
0
0
5
0
0
0
0
0
0
0
2
1
0
0
0
0
2
2
0
0
1
0
1
0
2
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
2
0
0
0
4
2
0
0
0
0
1
1
0
0
2
0
2
0
0
0
0
1
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
2
0
0
0
1
2
0
0
0
1
0
2
1
0
0
0
0
0
1
2
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
2
0
2
1
2
0
1
0
0
4
2
0
1
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
3
1
0
0
1
0
0
2
2
0
0
0
2
0
3
1
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
2
0
0
0
0
1
0
3
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
2
0
0
3
0
1
2
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
2
2
0
2
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
2
0
2
0
0
2
1
1
0
2
0
0
2
1
0
0
0
1
1
0
0
1
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
3
0
0
0
1
0
0
1
0
0
0
0
0
0
0
3
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
1
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
1
1
0
0
1
1
0
0
0
1
0
0
1
1
2
3
0
1
0
0
0
1
2
2
2
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
3
0
0
0
0
0
2
0
0
0
2
0
2
0
0
1
0
1
0
2
0
0
0
0
0
0
2
0
0
0
2
2
1
2
0
1
1
2
0
0
1
1
1
0
0
1
0
2
0
2
2
0
2
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
2
1
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
2
0
0
1
0
0
0
0
3
1
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
1
2
0
0
2
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
2
0
0
0
0
0
2
0
2
0
3
0
0
1
0
0
0
1
0
1
0
0
0
1
0
2
0
0
0
2
2
0
1
2
0
1
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
1
2
0
0
1
0
0
0
3
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
2
1
1
1
0
3
0
0
2
0
1
0
1
2
2
1
1
0
0
0
0
0
0
1
2
0
2
2
0
0
0
0
2
0
0
0
0
1
0
1
0
0
1
0
1
1
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
1
2
0
0
0
0
0
2
2
1
0
0
0
0
2
0
0
0
0
1
0
0
1
0
2
0
0
1
0
0
1
0
0
0
0
1
2
0
1
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
1
1
2
0
1
1
1
0
0
1
0
0
0
0
1
1
0
1
0
0
2
1
0
0
2
0
0
1
1
2
2
0
0
1
2
0
0
0
0
1
1
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
2
2
0
0
2
0
0
2
0
0
1
0
2
0
0
0
0
1
0
0
1
0
0
0
0
3
2
2
2
0
0
0
0
0
2
2
1
1
1
0
2
0
0
0
8
0
0
0
1
0
2
2
0
2
0
0
0
0
0
1
0
0
2
0
0
1
0
0
1
0
0
1
2
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
2
1
2
2
0
1
0
0
0
0
0
0
1
1
0
3
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
2
0
3
1
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
2
0
3
0
0
0
0
1
1
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
2
0
1
1
0
0
2
0
0
1
3
0
0
1
0
0
0
2
0
0
1
1
1
0
0
1
3
0
0
2
0
2
0
0
1
0
1
1
1
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
1
0
2
0
0
0
0
0
0
2
2
0
1
0
2
0
0
0
0
0
0
0
0
14
0
2
0
0
0
0
1
1
1
0
2
1
2
0
1
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
3
1
0
0
1
0
0
0
0
0
0
1
3
3
2
0
1
0
0
1
0
0
0
2
0
0
0
0
0
2
1
2
0
0
0
0
1
2
2
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
3
1
1
0
3
2
1
0
0
0
0
2
3
0
0
0
1
1
2
0
0
0
2
2
0
2
0
0
0
0
1
1
0
0
2
2
1
0
0
0
0
0
0
0
0
0
1
3
2
0
0
0
2
0
0
2
0
0
0
2
1
1
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
2
0
2
0
0
2
5
1
0
0
0
0
1
0
2
1
0
0
1
0
0
2
1
0
1
0
1
0
0
0
0
0
0
1
2
0
0
1
3
3
0
1
2
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
1
0
1
0
2
0
0
3
0
0
0
0
1
0
0
0
0
1
0
2
0
3
2
0
3
0
2
2
0
2
0
0
0
2
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
1
0
1
0
1
1
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
2
0
1
0
0
0
2
0
0
0
0
0
0
1
2
2
0
2
0
0
0
1
0
0
2
0
0
0
0
1
0
2
0
0
0
0
2
0
0
4
1
0
0
1
0
1
0
2
3
0
2
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
1
0
0
2
0
2
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
3
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
1
0
1
2
0
2
0
0
0
0
1
2
0
0
2
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
3
0
0
2
2
2
0
1
0
1
1
0
0
2
2
4
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
1
5
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
1
1
3
1
0
0
2
0
0
1
0
0
0
0
2
0
0
0
7
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
2
1
0
0
1
0
0
0
2
2
1
0
2
0
0
0
0
0
3
0
0
2
0
0
0
2
1
0
0
0
2
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
1
2
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
2
1
0
2
2
0
4
0
0
0
1
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
1
1
1
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
1
1
1
1
0
0
0
0
2
0
0
1
0
2
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
1
0
1
0
0
0
0
0
2
0
0
4
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
3
1
0
0
2
0
1
6
0
0
1
0
0
0
0
0
1
0
2
2
0
2
2
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
3
0
0
0
0
1
0
0
2
0
0
1
2
0
1
1
0
3
0
2
3
0
0
0
1
0
0
0
0
0
1
0
0
1
0
4
0
2
0
2
2
0
0
1
0
0
3
0
1
0
1
2
2
0
1
1
2
0
0
0
0
0
1
1
2
0
0
2
0
1
2
0
0
1
0
0
0
1
3
0
0
1
2
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
2
2
0
0
2
0
2
2
0
1
0
0
1
0
2
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
2
2
0
1
0
0
2
0
2
0
0
0
0
0
1
1
0
0
2
1
0
0
3
0
0
0
1
1
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
3
0
0
0
1
2
1
1
0
0
2
1
0
3
0
0
2
0
0
0
0
0
4
0
0
2
1
0
0
0
0
1
0
0
0
2
0
0
5
0
2
1
0
0
0
2
5
0
0
0
2
0
0
1
0
1
0
0
0
2
1
2
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
2
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
6
0
2
0
0
0
0
0
0
2
1
1
0
0
4
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
1
0
0
2
1
0
0
1
0
2
4
3
2
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
1
1
1
1
0
2
2
1
0
0
1
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
1
1
0
0
2
2
1
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
1
0
2
0
0
0
1
0
2
0
0
1
2
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
1
1
2
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
1
2
0
0
2
2
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
2
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
3
0
1
0
1
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
2
0
1
0
0
0
2
1
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
2
2
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
2
0
2
0
1
2
0
2
0
0
0
1
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
2
0
1
2
1
2
1
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
2
0
0
2
0
0
0
0
3
0
0
0
1
1
0
0
0
1
0
0
1
1
0
0
0
1
2
2
0
1
1
0
0
0
1
0
1
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
1
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
2
3
0
0
6
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
4
0
1
0
0
0
0
0
0
0
2
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
2
1
0
0
0
2
0
0
1
2
0
1
0
0
0
0
0
0
0
0
2
0
2
0
2
1
2
0
0
0
2
0
0
0
2
0
2
2
0
2
0
0
2
0
1
1
0
0
1
0
1
1
0
0
0
0
0
2
2
2
1
0
2
2
0
0
0
0
0
2
2
0
0
2
1
0
2
0
0
1
1
0
1
0
2
0
0
0
0
0
1
1
1
0
1
0
0
0
0
2
0
2
0
0
1
1
3
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
2
0
0
1
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
3
0
2
0
0
0
2
0
0
0
2
0
0
2
2
0
0
0
3
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
1
0
0
0
1
1
0
2
1
1
0
2
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
3
1
0
0
1
0
0
1
2
0
1
1
1
1
0
2
1
1
0
0
0
0
0
2
1
0
0
0
0
2
1
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
2
0
2
0
1
2
0
0
0
2
1
0
1
1
0
0
2
0
1
0
0
1
0
6
2
0
0
0
0
0
0
0
0
1
0
1
3
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
2
1
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
2
1
0
0
0
0
0
0
0
1
1
2
2
0
0
2
0
1
2
0
2
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
1
2
2
0
2
0
0
1
0
0
0
0
0
1
0
0
1
2
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
1
0
0
2
0
0
1
0
0
0
2
0
1
0
0
0
2
0
0
0
1
0
2
0
0
0
2
1
0
0
1
0
0
0
1
2
1
0
2
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
2
1
0
0
0
0
3
0
0
0
0
0
0
2
0
2
1
0
0
2
0
2
0
0
0
1
0
1
0
2
0
2
2
0
0
0
0
1
0
3
0
1
0
0
2
1
0
0
1
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
2
0
0
2
0
0
2
2
2
1
1
2
0
0
0
0
1
2
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
1
2
0
0
0
0
0
2
1
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
1
0
0
0
2
1
3
0
0
0
0
0
0
0
0
0
0
1
0
1
0
3
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
1
4
0
0
2
0
2
0
0
0
0
0
0
0
2
1
1
2
3
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
1
1
0
0
2
0
0
1
0
2
2
0
2
0
0
1
0
0
2
0
0
2
2
0
0
1
2
2
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
2
0
2
0
1
0
1
1
0
0
1
1
2
0
0
0
1
2
2
0
1
0
2
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
2
0
2
0
2
3
0
0
0
0
1
0
0
2
0
2
0
0
2
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
2
0
0
0
1
1
0
0
0
0
0
0
0
2
0
2
2
0
0
0
1
0
0
0
2
3
0
0
0
0
0
0
2
0
1
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
2
0
2
0
0
0
1
0
0
3
1
0
0
0
2
0
1
1
1
0
0
4
0
0
0
0
1
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
1
0
2
2
1
1
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
6
0
0
2
0
0
0
0
0
3
0
0
1
0
0
2
1
1
0
3
2
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
3
0
1
0
0
0
0
0
1
0
1
2
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
2
2
0
0
1
2
1
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
1
2
0
0
2
2
0
1
2
1
2
1
0
2
1
0
0
0
0
1
1
0
0
0
0
0
0
2
2
0
1
0
2
0
0
0
2
0
1
1
5
0
0
1
0
0
0
0
0
0
0
0
4
1
0
0
0
1
0
3
2
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
1
3
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
1
1
0
1
1
1
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
2
1
0
1
0
0
0
1
2
0
1
0
0
0
0
0
0
0
1
4
0
2
1
0
0
1
1
0
1
0
0
0
1
1
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
1
0
0
0
1
0
4
0
0
0
0
0
0
0
0
2
0
2
0
0
4
0
2
0
0
0
0
2
0
0
0
0
0
1
3
0
0
0
3
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
3
2
2
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
7
3
1
0
0
0
0
0
0
0
0
0
0
3
2
0
0
2
0
0
0
3
1
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
1
0
0
2
0
2
0
0
2
0
1
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
2
0
0
3
0
0
0
1
0
0
2
1
0
4
2
0
0
1
0
2
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
3
0
0
2
1
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
2
0
1
1
0
3
0
0
0
2
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
2
0
1
1
0
0
2
0
0
2
3
0
0
6
0
0
0
2
0
0
2
0
0
0
1
0
0
2
0
1
0
2
0
0
1
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
1
1
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
2
3
0
0
0
1
0
1
3
2
0
2
0
0
2
0
1
1
1
1
2
0
1
1
0
0
0
4
0
2
2
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
1
1
0
0
1
0
2
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
2
1
0
0
2
0
1
0
0
0
1
0
0
0
0
3
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
2
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
2
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
2
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
2
0
0
0
1
0
1
1
0
0
1
0
2
0
1
1
0
0
0
1
2
0
0
0
2
2
2
0
0
1
0
0
1
0
2
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
3
2
4
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
7
0
0
1
0
0
1
1
2
0
0
0
0
0
2
0
0
0
0
1
0
2
0
1
1
0
0
0
1
0
0
1
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
1
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
1
2
2
0
1
0
0
0
1
0
0
0
0
0
2
1
0
4
2
1
0
0
1
0
0
0
0
0
0
0
1
0
2
1
0
0
3
0
0
1
0
1
0
0
1
0
2
0
1
0
1
1
0
2
0
2
0
0
0
0
0
0
0
1
1
0
0
2
0
1
0
0
0
0
0
2
2
1
1
0
0
0
2
0
0
1
0
0
4
0
5
2
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
3
0
0
0
0
1
0
0
2
0
0
3
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
2
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
1
0
0
0
2
1
0
1
1
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
2
0
0
1
1
0
0
0
0
1
0
2
2
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
1
0
0
1
2
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
2
0
2
0
0
0
0
0
4
0
4
0
2
0
0
0
2
4
0
0
0
0
0
1
1
0
0
0
3
0
0
4
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
2
0
0
0
2
1
1
0
1
0
0
0
2
2
0
0
1
2
2
0
0
0
0
2
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
2
1
0
1
0
1
0
0
0
1
2
0
0
0
2
0
0
0
0
0
2
2
0
0
0
3
2
0
2
0
0
0
0
3
0
0
2
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
2
4
2
0
0
1
3
0
2
0
0
2
0
0
0
0
0
2
0
0
2
2
0
1
0
2
1
0
0
0
0
0
2
2
0
0
0
1
0
1
2
0
2
0
0
0
0
2
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
2
0
0
1
0
0
2
0
2
1
1
1
0
1
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
2
0
1
3
0
0
2
1
0
0
0
0
1
2
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
1
1
1
1
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
2
0
0
1
0
1
0
0
0
4
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
2
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
2
0
2
2
2
3
0
1
4
0
0
1
2
0
1
0
2
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
2
0
2
0
0
0
0
1
0
2
0
0
0
0
0
1
3
0
0
4
0
1
0
2
0
0
0
0
2
1
0
2
1
1
0
0
0
0
2
1
0
0
0
1
0
0
1
0
1
1
1
0
2
1
0
0
3
0
0
0
2
2
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
1
0
0
0
0
2
1
1
0
2
0
2
0
0
0
2
0
0
0
0
2
3
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
3
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
2
2
1
2
1
0
1
1
0
1
1
0
0
0
0
2
0
2
0
2
2
1
0
1
0
0
0
0
0
0
0
2
0
0
1
1
1
2
0
0
0
0
0
2
0
0
2
0
1
1
1
0
2
2
0
1
1
1
0
0
1
0
0
0
2
0
0
0
0
0
1
2
0
0
0
2
2
1
2
0
2
3
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
3
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
2
2
0
0
0
0
0
0
1
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
3
0
2
0
0
0
0
1
0
0
1
1
0
0
1
0
0
1
0
0
0
2
2
0
0
1
0
2
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
1
0
0
0
2
2
2
0
0
2
2
0
1
1
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
4
0
0
2
1
1
0
0
0
0
2
1
1
0
0
0
0
2
1
0
0
0
2
0
2
0
2
0
1
0
0
2
0
0
2
2
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
3
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
2
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
2
0
5
0
0
0
1
7
0
1
0
2
0
0
0
6
0
0
0
0
3
0
2
3
0
0
0
0
0
0
1
0
1
0
1
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
2
0
0
0
2
2
0
0
0
0
0
1
2
3
0
0
0
0
8
0
0
0
1
1
0
0
2
0
2
1
2
0
0
0
2
2
0
1
1
1
0
1
0
0
0
2
1
0
0
0
0
0
4
3
0
4
0
0
1
0
0
0
1
0
0
0
0
1
2
5
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
1
1
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
1
0
2
1
0
0
0
0
2
0
0
1
0
0
1
2
0
0
0
0
0
2
2
0
2
0
0
0
11
1
1
0
0
0
1
0
0
0
2
0
2
0
0
0
2
2
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
1
0
0
1
0
1
0
0
0
0
2
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
1
1
0
0
2
0
0
1
0
2
1
0
0
0
0
0
2
1
0
2
0
1
1
0
0
2
0
1
0
2
0
0
1
1
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
2
0
2
1
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
2
1
0
0
0
1
2
0
0
0
1
0
0
0
0
2
0
0
0
3
2
1
0
0
0
0
2
1
0
3
0
0
0
1
3
2
0
2
0
0
0
0
1
0
0
0
0
3
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
2
1
0
0
0
3
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
1
0
0
1
2
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
1
2
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
2
0
0
0
0
1
0
0
2
0
1
0
0
1
2
0
0
0
1
0
0
2
0
2
0
0
0
0
0
2
1
0
0
0
2
0
1
2
0
0
0
1
0
0
0
2
0
2
0
0
2
0
1
0
0
0
0
0
2
0
0
1
2
0
4
0
0
0
0
0
0
1
0
0
1
0
0
0
2
2
0
0
0
1
1
0
0
1
0
2
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
1
0
1
0
0
0
0
4
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
1
0
3
0
0
0
0
0
0
1
2
1
1
2
0
0
1
0
1
0
1
0
4
2
0
0
2
2
2
0
0
7
0
0
2
0
0
2
0
1
1
1
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
1
2
0
0
2
0
1
0
0
1
0
0
1
0
2
0
0
1
0
0
4
0
0
0
0
0
1
0
1
1
2
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
2
0
0
0
2
0
1
0
2
0
1
1
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
1
0
0
2
0
2
0
1
0
2
0
2
2
1
0
0
0
9
0
2
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
3
0
2
0
2
0
0
2
0
0
2
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
1
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
1
0
2
0
1
0
0
2
0
2
0
0
0
1
0
2
2
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
2
2
2
4
0
1
0
2
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
1
1
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
2
0
1
0
1
0
0
0
0
0
0
2
1
2
0
0
1
1
0
2
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
2
0
2
1
0
0
2
0
1
0
1
1
3
0
0
0
0
1
0
0
2
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
2
0
0
3
2
1
2
3
2
1
0
1
0
0
1
1
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
2
2
0
0
0
0
4
1
0
1
2
0
0
3
0
2
0
0
0
0
0
0
0
0
2
1
1
1
0
3
0
1
0
0
2
0
1
0
0
0
0
2
0
0
0
5
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
1
0
2
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
2
2
1
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
2
2
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
1
2
4
2
1
2
0
0
0
0
0
2
3
0
0
0
0
0
2
0
0
0
0
3
2
0
0
2
0
2
0
1
2
0
1
0
1
0
1
0
1
2
0
2
0
2
0
0
3
16
2
0
0
0
2
0
1
1
2
0
0
0
0
0
7
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
2
0
0
0
0
2
1
0
0
0
0
1
1
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
2
0
0
0
2
1
0
1
1
1
3
0
1
1
0
0
2
0
0
0
0
1
0
0
0
2
0
1
2
2
2
1
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
2
0
2
0
0
1
0
0
0
2
2
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
2
0
2
3
1
0
0
0
2
0
0
0
0
2
0
1
1
0
1
0
1
0
0
0
2
0
0
3
2
0
0
0
2
0
2
2
0
1
4
0
0
0
0
0
0
0
1
2
1
0
0
1
2
0
1
1
0
0
2
0
1
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
1
1
0
3
0
0
0
1
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
2
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
2
2
0
3
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
1
1
0
0
2
0
2
0
2
0
0
0
0
1
0
2
1
0
0
0
2
0
0
0
0
0
0
1
1
1
2
0
0
1
0
2
0
0
0
1
0
1
0
1
0
8
0
2
0
0
2
0
0
0
0
4
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
2
2
0
0
0
0
0
1
1
1
0
0
0
0
2
0
1
1
0
2
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
3
0
0
3
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
2
1
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
4
0
0
1
0
1
0
1
0
2
2
1
1
0
2
0
0
2
0
0
1
0
1
1
1
1
0
0
0
0
2
0
0
1
0
0
3
2
0
1
1
0
2
1
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
1
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
3
0
1
1
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
2
1
0
0
1
0
2
0
0
0
0
0
0
0
0
2
2
3
1
1
0
0
1
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
1
2
2
0
0
0
2
1
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
1
0
0
0
0
0
3
0
2
0
1
0
1
3
0
2
0
1
0
0
0
3
0
0
2
0
0
0
0
1
2
0
0
0
0
2
0
1
0
2
0
0
0
0
0
2
0
0
0
0
2
2
0
1
0
0
0
0
0
0
2
0
2
2
1
0
1
0
0
2
2
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
1
1
2
2
1
0
4
0
0
0
0
3
0
0
2
1
2
2
0
0
0
0
0
1
0
0
0
0
1
2
0
0
1
0
1
0
0
0
1
0
2
1
1
0
0
0
0
1
1
1
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
2
0
1
1
0
0
1
2
1
3
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
1
1
1
0
0
1
0
0
2
0
1
0
1
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
4
4
0
0
0
1
2
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
2
0
0
0
2
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
1
2
3
2
0
2
2
0
2
0
2
0
0
2
0
0
0
0
1
2
0
0
0
0
2
0
0
1
2
0
2
2
0
2
2
2
4
0
1
0
0
0
0
0
2
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
1
1
1
0
3
1
0
2
0
0
0
1
0
0
2
1
1
0
2
0
0
1
3
1
0
0
0
1
2
1
0
1
0
2
0
0
2
0
0
1
0
0
0
0
0
1
2
2
1
0
0
0
0
0
3
0
0
0
0
0
1
0
2
0
0
3
1
0
0
1
0
0
2
0
0
0
1
0
3
0
0
0
1
1
0
2
0
0
0
1
0
0
0
0
2
0
1
0
0
0
2
2
0
0
0
3
2
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
1
2
0
0
0
0
0
1
3
1
1
1
0
3
2
0
2
0
0
0
1
0
0
2
0
3
1
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
1
0
3
3
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
1
0
3
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
1
1
0
0
2
2
0
2
0
0
1
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
5
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
3
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
2
3
0
0
0
2
0
0
0
2
0
0
0
0
2
3
0
0
1
0
1
0
0
2
0
0
0
0
2
0
0
1
1
1
0
0
0
0
2
0
0
0
0
0
3
0
1
1
0
0
0
0
0
1
0
0
1
2
1
1
0
2
0
0
1
0
0
1
0
2
2
0
0
2
0
0
2
2
0
0
1
1
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
1
0
8
0
0
0
0
3
0
0
0
1
0
1
0
0
0
0
1
2
0
2
2
1
0
2
0
2
0
0
0
0
2
0
1
0
2
2
0
0
2
0
0
2
2
0
0
0
0
1
0
0
3
0
2
0
0
1
2
2
0
2
0
0
0
0
0
0
0
2
0
1
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
1
1
1
0
1
0
0
0
0
0
0
2
0
2
0
2
2
1
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
1
0
0
0
0
2
2
1
1
0
3
0
0
0
0
3
0
0
2
2
0
0
0
1
1
2
0
1
2
1
2
1
2
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
2
0
0
0
0
10
0
0
0
2
0
3
1
1
0
1
0
1
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
1
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
1
3
1
1
0
2
0
0
0
1
0
1
2
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
3
2
2
0
0
0
0
2
2
0
0
2
3
1
1
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
4
2
2
0
2
2
2
0
0
0
0
1
0
0
3
1
0
0
1
0
2
0
2
0
0
0
0
0
3
2
1
1
0
1
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
2
2
0
1
0
0
0
0
3
0
0
0
2
0
0
1
0
2
1
0
0
1
2
0
0
0
0
0
0
0
1
0
0
1
2
2
0
1
2
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
2
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
2
0
0
0
0
2
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
5
0
0
2
1
0
0
2
0
0
0
0
0
0
1
5
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
1
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
2
2
2
0
1
2
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
1
0
2
1
0
1
2
0
0
0
3
0
0
0
0
1
0
0
1
0
0
0
2
1
0
0
0
0
0
2
2
2
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
3
0
0
0
2
2
1
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
2
1
3
0
0
0
0
2
0
0
0
0
0
0
0
0
1
3
0
1
1
0
2
1
3
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
2
1
0
2
0
0
0
0
0
0
2
2
0
2
2
2
2
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
2
2
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
2
1
1
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
2
0
2
0
2
0
1
0
1
2
0
2
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
2
1
0
0
2
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
1
0
2
2
0
2
0
0
2
0
1
1
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
2
0
0
2
1
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
2
0
0
0
0
0
3
0
0
2
1
0
2
0
1
0
0
4
0
0
0
0
0
2
1
1
1
1
1
0
1
0
0
1
1
0
2
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
2
0
1
2
0
0
0
0
2
2
1
0
0
1
0
0
1
0
0
0
0
0
2
2
1
1
0
2
2
1
1
0
0
0
0
0
0
2
2
0
1
0
0
2
0
0
0
0
0
0
0
2
1
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
2
0
0
0
0
2
2
3
0
1
1
0
2
0
0
1
1
1
0
1
1
2
0
0
1
1
1
2
0
0
0
0
0
1
1
0
0
1
2
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
2
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
2
1
0
0
6
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
2
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
3
1
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
1
0
0
1
1
0
2
0
0
0
1
0
2
0
0
0
2
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
1
1
0
0
1
2
0
0
0
0
2
1
0
0
1
1
1
0
0
0
0
1
0
0
2
1
0
2
1
0
1
0
2
0
0
0
2
1
0
0
0
2
0
0
0
0
0
1
0
2
1
2
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
2
1
0
0
1
0
0
0
1
0
2
1
0
0
0
2
0
2
2
0
0
1
0
0
0
0
1
0
2
0
2
2
0
0
0
0
0
0
1
1
0
0
1
0
0
2
1
0
0
2
0
1
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
2
2
0
0
0
1
0
2
0
0
1
0
0
0
2
0
0
0
0
1
1
0
2
2
0
0
0
0
0
1
0
0
0
1
0
0
1
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
1
0
2
0
0
0
0
0
1
0
0
1
1
0
0
1
1
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
1
0
0
1
0
0
0
1
1
2
3
2
2
0
1
0
1
8
0
0
2
0
0
1
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
2
0
2
0
0
0
0
2
1
0
0
0
0
1
2
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
2
0
0
0
0
4
0
1
0
1
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
1
2
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
4
0
0
1
0
0
0
0
1
0
1
1
0
2
0
0
0
1
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
2
0
1
0
0
1
0
1
2
0
2
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
2
0
0
0
1
0
1
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
1
0
3
0
0
0
0
2
0
0
1
0
0
2
0
2
1
0
0
0
2
0
3
0
0
0
1
1
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
3
0
1
1
0
2
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
1
1
0
0
0
1
0
2
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
2
0
0
0
0
0
1
0
1
1
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
1
2
0
0
0
0
1
0
2
1
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
1
2
0
0
1
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
2
1
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
1
1
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
2
3
2
2
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
1
1
0
0
1
1
2
0
0
2
1
0
2
0
2
0
0
3
0
0
0
0
0
0
0
3
0
1
0
0
2
3
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
4
1
0
2
0
0
3
0
0
1
0
0
1
0
0
0
1
2
0
2
0
0
0
0
0
1
0
1
1
0
0
1
1
0
0
2
0
1
1
0
0
1
0
0
0
0
2
1
0
0
0
1
1
1
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
2
2
0
2
1
1
0
0
2
0
0
0
0
0
0
1
1
2
0
0
1
1
2
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
1
0
0
2
0
3
0
0
0
1
0
1
0
0
3
0
0
0
0
0
2
0
1
0
0
0
0
2
0
2
0
1
0
7
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
1
1
2
0
0
2
0
0
0
0
0
1
2
0
2
0
1
0
0
2
1
0
2
2
1
0
1
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
1
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
2
1
0
0
0
0
3
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
1
0
0
2
1
0
1
1
2
2
4
0
0
0
1
2
0
0
0
1
3
2
0
1
0
1
1
2
1
0
2
3
0
0
0
0
1
0
0
1
0
0
2
0
0
2
0
0
0
0
1
0
0
2
0
0
0
2
0
0
2
2
2
0
0
0
0
0
0
1
0
2
3
0
0
0
0
0
0
0
0
1
0
2
0
2
0
3
0
0
1
0
2
0
0
0
0
2
0
2
0
0
0
0
1
0
1
1
0
0
2
0
0
1
0
2
0
1
0
0
0
0
0
2
0
2
2
0
0
1
0
0
6
1
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
5
0
0
1
0
0
0
2
3
0
0
2
0
0
2
0
0
0
2
0
0
0
1
0
1
2
0
2
0
0
0
0
2
0
0
2
0
2
2
3
0
0
1
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
1
1
2
1
0
2
1
0
1
0
1
0
0
0
0
0
1
2
2
0
1
1
1
2
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
1
1
0
1
2
0
0
0
0
0
2
0
0
0
2
0
1
0
1
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
3
1
0
2
1
0
1
0
1
0
0
1
0
1
0
0
0
2
0
2
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
2
0
2
1
0
0
2
2
1
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
1
1
0
4
1
0
1
1
0
1
0
2
0
1
0
0
0
0
0
0
0
3
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
1
2
0
0
2
1
2
0
1
0
1
1
0
0
0
2
1
0
0
0
0
1
0
0
1
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
2
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
1
1
2
1
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
1
1
0
0
1
2
0
0
2
1
2
1
0
1
0
0
0
0
5
1
0
2
0
0
0
0
2
0
0
2
1
0
0
4
0
0
2
4
0
0
2
4
1
1
0
0
2
0
2
0
0
0
0
1
0
0
0
0
3
0
1
0
0
0
2
1
0
0
1
1
0
1
2
0
0
1
0
4
0
0
2
0
0
0
2
0
1
2
0
0
0
1
0
1
2
0
0
3
0
0
1
0
0
1
0
0
1
0
0
0
0
2
1
2
0
0
0
0
0
0
2
0
0
0
0
2
2
2
0
0
0
2
0
0
0
1
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
1
4
2
0
2
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
7
0
2
0
0
1
0
0
1
2
0
1
0
0
0
0
0
1
3
1
0
0
2
0
0
0
0
2
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
1
0
2
0
0
0
2
0
1
0
0
0
0
0
2
2
0
0
0
0
1
1
0
0
1
2
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
2
1
0
0
0
0
2
0
0
0
0
1
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
1
2
1
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
1
1
0
0
0
3
2
2
0
0
0
2
0
3
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
1
0
2
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
2
2
0
1
0
0
0
1
0
1
0
2
0
0
0
0
0
3
0
1
1
1
0
2
0
2
2
1
0
2
0
0
2
0
0
0
5
1
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
1
0
1
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
3
0
1
1
0
0
2
0
0
1
0
0
0
2
1
0
0
0
0
0
2
0
2
2
0
0
0
0
1
0
1
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
1
0
2
1
1
1
0
0
0
1
0
2
0
0
3
0
0
1
0
3
4
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
1
1
1
0
0
0
2
0
0
0
0
0
0
3
0
0
1
0
0
1
0
0
0
0
0
2
2
1
0
0
0
0
0
2
0
2
0
1
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
2
0
0
0
2
0
0
2
0
0
0
1
2
0
0
1
0
1
0
1
2
0
2
1
0
1
0
0
1
0
0
0
2
0
1
1
0
3
0
0
0
0
2
0
0
3
0
0
2
0
0
2
1
0
0
0
0
2
1
0
0
1
0
1
1
0
0
0
2
0
0
1
1
1
0
0
0
0
0
0
1
0
0
2
0
1
0
2
1
2
0
0
0
0
0
0
2
2
3
0
0
0
0
1
1
0
0
0
0
1
0
0
2
1
2
0
0
0
2
1
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
1
0
0
1
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
2
2
0
1
2
0
2
2
2
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
1
0
1
0
2
0
0
0
2
2
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
2
0
2
0
2
3
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
4
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
9
0
0
2
1
0
0
3
2
0
0
0
0
1
0
0
0
2
0
1
1
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
3
0
1
0
0
1
0
0
2
0
0
1
0
1
0
0
2
0
1
0
2
1
0
1
0
0
0
1
0
0
0
0
0
2
0
1
3
2
3
0
1
0
0
0
0
3
2
0
0
1
0
1
0
0
0
0
3
0
2
1
1
1
0
0
0
0
2
0
0
0
2
0
0
0
0
1
1
1
0
0
3
0
0
2
2
0
0
2
3
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
2
0
2
0
3
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
1
2
0
0
2
0
1
2
1
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
3
3
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
1
0
3
1
0
0
0
0
0
0
0
2
0
0
1
0
0
3
0
0
1
0
2
0
0
0
0
0
3
0
0
2
0
1
0
0
1
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
1
0
1
3
2
0
0
1
0
0
0
3
0
0
0
0
2
0
0
2
2
0
0
0
5
0
0
2
2
1
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
1
0
0
0
0
1
1
0
0
2
0
0
1
2
1
2
1
0
0
2
2
0
1
0
0
1
1
1
1
0
0
0
0
0
1
3
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
2
0
2
0
0
0
0
0
2
0
1
0
1
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
2
0
2
0
0
0
0
1
2
2
1
2
1
1
0
0
1
2
0
0
1
1
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
2
0
1
0
0
0
0
0
2
5
1
2
0
2
2
2
0
0
2
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
2
0
0
0
1
2
1
1
0
1
0
0
2
0
1
2
0
1
0
1
0
1
0
2
0
0
2
1
0
0
1
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
1
1
0
1
2
0
1
0
0
2
1
0
0
0
2
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
1
2
2
2
0
0
0
0
2
0
0
4
1
0
1
0
1
0
1
2
0
0
0
0
0
2
0
1
1
0
0
0
2
2
0
1
0
0
3
0
0
0
1
0
0
3
1
0
0
0
4
0
0
0
0
0
0
0
0
2
0
2
0
1
2
0
0
0
1
0
0
0
0
1
0
0
1
0
0
2
1
0
0
1
0
1
1
0
0
0
2
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
1
0
0
0
0
3
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
2
1
0
0
2
1
2
0
1
0
0
0
2
0
0
0
2
0
0
0
1
2
0
0
1
0
3
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
4
0
2
0
0
2
0
0
0
0
1
0
2
2
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
2
0
1
0
0
1
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
2
1
0
0
1
2
1
2
2
0
0
0
0
0
0
2
1
0
1
0
1
0
0
1
0
2
0
2
0
0
0
0
0
0
0
2
4
0
2
0
0
0
0
1
2
1
0
0
0
1
1
0
1
2
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
1
2
0
1
0
0
2
0
1
0
0
0
2
1
1
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
2
0
2
1
0
0
0
3
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
1
0
1
4
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
2
0
3
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
2
0
0
2
0
1
1
1
3
2
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
1
2
0
0
1
1
0
0
0
0
0
2
0
1
0
1
2
0
0
3
0
0
0
0
1
1
0
0
0
1
0
1
0
2
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
1
0
0
4
0
0
3
2
1
0
3
0
0
0
1
0
3
0
1
3
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
1
0
0
5
0
0
1
0
0
1
0
0
1
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
2
2
0
1
0
0
0
0
0
0
2
0
0
2
0
2
0
1
1
0
1
1
0
1
1
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
2
0
2
0
0
1
2
0
0
0
0
0
0
2
0
0
0
1
1
0
1
0
0
0
2
0
3
0
0
0
0
0
2
1
0
0
2
1
0
3
0
0
0
0
1
1
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
1
3
3
0
0
0
0
0
1
0
0
0
2
0
0
1
2
1
0
2
1
0
0
0
0
0
1
0
0
0
1
0
1
0
2
0
2
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
4
2
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
4
0
0
0
0
1
0
0
2
0
0
0
2
2
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
1
0
2
0
0
1
0
0
0
2
1
1
0
0
0
0
0
1
1
0
0
2
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
2
2
0
0
0
1
0
1
0
1
2
1
0
0
1
0
1
0
0
2
0
0
0
1
0
0
0
0
3
0
0
0
3
0
0
0
0
1
0
1
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
1
0
0
4
0
0
2
0
0
0
2
0
0
1
2
0
0
2
2
0
0
0
1
3
0
1
0
0
0
0
2
3
0
0
1
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
1
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
1
1
0
0
0
1
0
1
1
0
0
2
0
1
2
0
1
0
1
2
0
0
2
1
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
1
2
0
0
0
0
2
0
0
1
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
2
0
1
0
0
0
0
3
2
0
0
0
0
4
2
0
0
0
2
1
0
0
0
1
1
2
2
0
0
0
0
0
1
2
0
0
1
1
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
2
0
1
1
1
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
2
0
2
0
0
4
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
1
2
2
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
1
0
1
0
0
0
2
0
0
0
0
1
0
2
0
1
0
0
0
0
1
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
2
0
0
2
0
0
0
2
1
0
0
0
0
0
0
2
0
1
0
0
2
0
0
2
2
2
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
2
0
1
0
0
0
1
1
3
0
1
0
0
0
0
1
0
0
0
2
0
2
1
2
0
0
1
0
0
0
1
1
1
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
1
1
0
2
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
4
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
1
0
1
0
0
0
1
0
2
0
2
0
0
0
1
0
1
1
0
0
0
0
1
1
2
2
0
0
0
1
0
0
0
3
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
1
0
0
1
0
2
0
0
1
1
0
1
0
1
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
1
0
2
0
0
1
0
0
1
0
2
2
2
2
0
0
0
0
0
0
0
2
0
1
2
2
0
2
1
0
0
2
0
0
0
0
0
0
2
0
1
0
0
4
0
0
5
0
2
1
0
2
0
1
1
0
0
0
2
2
0
1
0
1
0
2
1
1
0
2
1
0
0
0
2
0
0
0
0
2
2
1
0
0
0
1
0
0
2
0
0
2
1
0
0
0
0
0
2
0
1
2
0
2
0
0
0
0
1
0
1
2
0
2
0
0
1
1
0
3
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
2
0
2
0
0
1
1
0
2
0
0
0
0
0
2
0
0
2
0
0
1
1
1
1
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
7
1
0
0
0
1
0
1
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
1
0
2
0
2
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
2
2
0
0
0
0
0
0
1
1
0
0
2
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
1
1
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
1
1
2
0
0
1
3
1
2
0
1
0
2
1
0
0
0
2
0
2
2
1
0
0
0
2
0
0
0
0
0
2
1
2
0
0
1
0
1
1
1
0
0
0
0
1
0
1
0
0
1
1
2
0
0
0
3
2
0
0
2
2
2
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
1
1
2
2
0
0
0
0
0
0
0
2
1
0
1
1
0
1
4
0
0
0
2
0
0
2
2
0
2
0
0
0
1
0
0
0
2
0
1
2
0
2
2
2
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
1
0
2
0
3
1
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
2
2
0
1
0
1
0
1
0
0
0
0
1
2
0
0
1
1
1
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
2
0
0
5
0
0
0
0
1
0
0
0
0
0
1
1
0
0
2
0
0
0
1
0
0
2
1
0
2
0
0
0
0
0
3
0
1
1
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
1
1
0
0
1
0
1
1
0
0
2
0
2
2
0
0
0
0
2
0
0
0
4
2
0
0
1
0
0
0
0
3
0
1
0
0
0
2
0
1
1
1
0
0
0
0
1
0
0
2
0
1
1
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
2
0
2
1
0
0
0
1
0
7
1
1
0
1
0
0
1
1
0
0
1
0
2
0
0
0
1
0
3
0
2
0
0
2
1
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
1
0
0
0
2
1
0
0
1
2
0
0
0
2
2
0
0
2
0
0
0
0
1
3
2
0
0
0
1
0
0
0
3
0
0
0
0
2
0
1
2
1
0
0
0
1
0
2
0
1
0
1
0
1
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
2
0
1
1
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
1
0
2
0
0
0
0
2
2
1
0
2
1
1
1
0
1
2
5
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
3
0
1
3
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
1
0
0
1
0
2
0
0
2
0
0
0
0
0
0
2
0
0
2
1
2
0
1
0
2
0
0
0
1
0
0
2
2
0
2
1
1
0
0
8
2
2
1
2
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
1
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
2
0
1
2
0
4
0
0
0
0
0
0
0
1
2
0
0
0
3
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
2
0
0
0
1
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
1
2
1
2
0
0
3
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
5
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
1
0
1
0
2
1
2
1
0
1
0
1
0
0
0
2
0
0
0
0
2
1
1
0
1
2
0
0
0
1
1
4
2
0
0
1
0
2
1
0
2
0
0
0
1
0
0
0
5
0
2
0
2
0
0
1
1
0
0
2
1
0
2
0
0
0
0
1
0
3
0
2
0
0
0
0
2
2
3
0
0
2
2
1
1
0
1
0
1
1
0
0
0
0
0
3
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
2
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
2
2
0
1
1
0
1
0
0
5
2
3
0
2
1
0
1
0
0
1
1
2
2
0
0
0
0
1
0
1
2
0
2
2
0
0
1
0
1
1
1
0
2
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
5
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
2
2
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
3
0
0
0
0
0
0
0
0
2
1
0
0
1
5
0
0
0
0
0
0
0
0
1
0
2
1
0
2
0
0
0
1
0
0
0
2
0
0
0
2
2
1
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
2
1
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
2
0
0
2
0
2
0
1
2
0
0
2
0
0
0
1
0
1
0
1
0
0
0
0
2
0
1
0
0
0
1
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
1
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
2
2
0
1
0
1
0
0
1
0
1
0
1
2
0
1
0
0
1
0
0
1
0
1
0
0
0
2
0
0
1
0
2
0
0
1
0
0
0
0
0
2
0
2
1
0
0
0
1
0
0
0
2
1
2
0
0
1
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
3
1
0
0
2
0
0
0
1
0
0
2
0
0
1
1
1
1
1
2
6
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
1
0
1
1
0
2
1
0
0
0
2
0
0
0
2
0
1
1
2
0
0
0
2
0
0
1
0
0
2
0
0
1
2
2
0
0
0
0
0
2
0
17
2
1
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
1
2
0
1
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
2
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
1
0
0
0
2
2
1
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
2
2
0
1
0
2
0
0
3
0
2
0
0
2
0
0
1
2
0
0
1
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
2
2
0
2
0
0
1
0
2
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
2
3
0
0
1
1
0
0
0
0
3
0
1
2
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
2
2
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
3
1
0
0
0
1
0
1
2
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
2
2
1
0
2
0
2
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
2
0
0
0
2
2
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
2
0
3
3
0
1
0
0
2
1
0
0
0
0
0
0
1
0
0
0
1
1
0
2
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
2
2
1
0
0
1
0
0
2
0
0
1
2
0
0
0
0
1
1
2
0
0
0
0
1
1
0
1
1
0
0
2
0
1
0
2
2
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
2
0
1
0
0
2
0
1
0
0
1
0
0
0
2
1
2
2
0
2
0
0
0
0
1
1
0
1
4
0
0
2
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
3
1
2
1
0
0
0
0
2
0
1
0
0
2
0
0
0
0
2
1
0
2
2
2
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
1
2
1
1
0
2
0
0
1
2
0
0
0
0
0
0
2
0
0
2
0
0
2
4
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
1
0
2
0
0
1
0
0
2
2
0
0
3
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
1
0
0
0
1
0
0
0
0
0
0
1
2
0
0
2
0
0
0
1
0
1
0
0
1
3
1
0
0
0
2
0
1
1
0
0
0
0
0
0
1
0
1
0
2
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
2
1
2
1
1
2
0
0
0
0
0
1
0
0
0
0
0
3
0
1
0
0
1
1
0
1
0
2
0
2
2
1
0
0
2
0
1
1
2
1
1
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
2
1
2
0
0
0
0
1
0
1
0
0
0
2
1
0
0
0
1
1
0
0
1
0
1
0
0
0
2
0
8
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
2
1
0
2
1
0
3
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
2
2
2
2
2
0
2
0
5
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
1
1
0
1
0
0
2
2
1
1
0
0
0
1
0
0
2
0
0
0
0
2
1
0
0
0
0
2
1
0
0
0
1
1
0
1
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
1
1
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
1
1
0
0
0
0
1
2
0
0
0
0
0
2
1
1
0
1
2
0
1
0
0
0
0
0
1
0
6
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
3
0
1
0
0
0
0
0
0
0
0
3
0
2
0
0
0
2
0
0
0
2
0
0
0
0
3
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
1
0
2
1
0
0
0
2
1
0
0
0
0
0
2
3
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
2
2
0
1
0
0
2
0
0
1
1
0
1
0
0
0
0
0
1
2
1
0
1
0
0
0
1
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
1
0
0
2
0
0
1
0
0
0
1
0
0
0
1
2
0
0
0
1
2
2
2
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
5
1
0
2
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
1
0
0
0
0
0
1
0
2
0
0
1
0
1
0
2
0
0
2
2
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
2
0
2
0
0
2
0
0
0
1
1
2
0
0
0
2
0
0
0
1
0
0
2
2
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
1
1
1
0
1
0
0
1
2
1
2
0
0
0
0
1
0
2
0
0
3
0
0
1
0
2
0
0
0
1
0
1
0
0
1
0
0
2
1
0
0
1
2
1
0
2
0
0
0
0
0
0
1
2
0
0
1
2
0
0
0
0
2
2
0
0
0
0
1
1
0
0
0
0
0
2
0
2
2
4
0
0
0
1
2
0
2
1
2
0
3
0
0
0
1
1
0
2
1
0
2
0
0
2
0
3
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
2
0
0
0
0
0
0
1
0
2
1
0
0
0
1
0
2
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
2
0
1
0
1
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
3
1
0
0
4
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
2
2
0
1
0
1
0
0
0
1
1
1
0
1
0
0
1
1
0
0
0
1
0
1
0
1
0
0
1
0
0
2
2
2
0
0
11
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
3
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
2
2
0
0
0
0
1
1
0
1
0
2
0
0
0
0
0
0
0
2
2
0
2
0
0
0
1
2
0
0
2
0
0
0
1
0
0
2
0
0
0
1
0
1
1
1
0
0
2
0
2
0
0
0
0
2
0
2
0
0
0
2
1
0
2
0
0
0
0
1
0
0
1
1
1
1
2
0
0
2
0
0
0
0
2
0
0
0
0
1
1
2
0
2
1
2
2
0
0
0
2
0
0
1
0
3
2
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
2
2
1
3
1
0
1
0
0
0
0
0
1
0
1
0
0
2
1
0
0
1
0
1
0
0
2
1
0
0
0
0
1
0
2
0
2
0
3
0
1
2
0
1
1
7
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
4
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
2
0
0
0
2
0
1
0
2
0
0
2
0
1
0
0
0
2
2
0
2
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
1
0
1
0
2
0
0
1
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
2
0
0
0
3
0
1
1
0
1
0
0
0
0
2
1
0
0
0
1
4
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
2
0
0
0
0
2
1
1
0
0
2
0
0
2
2
0
0
1
3
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
2
1
2
0
1
1
0
0
3
0
3
0
1
0
1
0
2
2
0
1
0
0
0
1
0
0
0
0
2
2
0
1
2
0
0
3
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
4
1
1
1
0
0
3
1
0
0
1
0
0
0
0
1
2
0
0
0
0
1
2
0
1
0
0
0
1
1
3
0
2
0
2
0
0
0
1
0
3
2
0
3
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
2
0
1
2
1
2
0
1
1
0
0
2
2
0
0
1
0
2
0
0
0
0
0
0
3
0
2
0
0
0
1
0
0
2
1
0
0
0
2
2
0
1
0
0
0
2
0
3
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
5
0
0
0
2
0
0
0
1
0
0
1
0
2
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
3
0
2
0
0
1
0
1
0
0
1
0
0
1
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
2
3
2
0
2
0
0
2
2
2
0
0
1
0
0
0
2
0
0
1
0
0
0
1
0
0
2
0
0
1
0
2
0
2
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
4
2
1
2
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
3
0
3
0
2
1
2
0
0
0
0
1
1
0
0
1
0
0
0
2
1
0
2
2
0
0
0
3
2
0
0
1
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
2
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
4
1
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
2
1
1
0
0
2
2
0
2
1
0
0
0
1
0
2
0
0
0
0
0
0
0
1
2
1
0
1
0
0
0
0
1
0
1
0
0
2
0
2
0
1
0
1
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
2
0
0
0
0
2
2
0
0
0
0
2
1
0
0
5
0
0
0
0
0
2
2
0
0
0
0
0
0
1
4
0
0
2
0
3
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
1
0
1
2
0
2
1
0
1
1
0
1
0
0
2
0
0
0
1
2
0
0
0
0
0
1
0
0
2
1
2
0
0
0
2
0
0
0
0
2
1
1
0
0
0
0
0
0
2
0
2
0
2
0
0
1
0
3
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
7
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
1
0
1
5
0
2
0
0
2
0
2
0
1
0
6
0
2
0
0
0
0
2
2
2
2
0
2
0
0
0
1
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
2
2
0
0
2
0
0
2
1
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
1
0
1
0
0
0
1
3
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
6
0
2
0
2
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
2
2
0
1
1
0
0
2
0
0
1
1
2
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
1
0
2
0
0
2
1
0
1
5
2
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
1
1
0
0
1
2
0
0
0
0
2
0
1
0
2
3
0
0
0
0
0
0
0
1
1
3
0
0
0
0
0
1
2
4
2
0
0
2
0
0
0
0
0
1
1
0
1
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
2
2
0
1
1
0
0
0
0
0
0
2
0
0
0
1
0
2
0
1
0
2
0
1
1
1
2
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
1
2
1
0
0
0
1
0
3
1
0
1
1
1
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
3
0
2
0
0
2
0
0
0
0
0
0
3
0
2
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
1
0
3
0
2
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
1
0
0
2
0
0
2
1
0
0
0
0
1
2
1
0
0
1
0
1
0
1
1
0
0
0
2
0
0
0
0
0
0
2
1
2
0
2
1
0
0
0
0
1
0
2
2
2
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
1
2
1
0
0
1
0
2
2
0
0
2
1
2
1
0
0
0
0
2
0
3
0
1
0
0
0
0
1
2
3
0
0
2
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
2
0
1
0
0
0
1
0
0
1
0
3
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
2
1
0
2
3
0
3
0
0
0
1
1
1
2
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
1
0
1
0
2
0
0
2
0
0
2
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
2
1
1
0
0
0
1
1
2
1
0
2
2
0
0
0
0
2
0
1
0
0
0
2
1
1
1
0
1
0
4
0
0
0
0
0
0
1
0
0
1
0
2
1
0
0
0
0
0
0
1
0
0
2
0
1
2
1
1
0
0
3
3
0
2
2
0
0
2
0
0
0
0
2
0
0
2
0
0
0
2
2
2
1
3
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
1
0
0
0
2
0
1
0
3
0
2
1
2
4
0
1
0
0
0
0
0
0
1
0
0
0
1
1
2
0
2
0
0
0
0
0
2
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
2
0
0
0
0
0
0
2
1
1
3
0
2
0
1
0
0
0
1
11
0
1
4
1
2
3
0
0
0
0
0
0
2
0
0
0
0
0
1
2
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
3
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
2
0
0
2
1
1
0
0
0
3
1
0
0
2
0
1
0
1
1
2
0
2
0
0
1
0
0
2
0
0
0
1
0
0
2
0
3
2
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
1
2
0
0
1
2
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
3
2
1
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
2
0
2
2
2
0
1
2
0
0
0
0
0
2
2
0
0
0
1
2
2
2
0
2
0
1
0
0
2
2
0
1
3
0
2
0
0
0
3
0
0
0
0
0
0
1
0
1
0
0
0
1
0
2
1
0
6
2
0
0
1
1
1
1
0
2
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
1
0
2
0
0
0
0
2
1
0
0
0
2
0
0
1
0
0
2
1
1
0
0
0
2
1
0
0
0
0
2
0
3
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
2
1
1
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
2
1
1
0
2
2
0
0
1
1
2
0
0
2
0
1
0
0
0
0
0
2
1
0
1
1
0
3
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
4
1
0
0
0
1
0
0
1
2
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
2
0
0
0
0
1
0
0
2
0
0
0
1
0
0
2
0
2
0
0
0
2
0
0
0
2
0
2
2
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
2
1
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
2
2
2
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
1
0
1
0
0
2
0
0
0
2
0
0
2
0
2
0
0
2
0
2
0
0
1
2
0
0
0
0
0
2
0
0
1
1
0
3
0
2
0
2
0
1
0
0
0
0
0
0
0
4
1
0
0
0
0
1
1
0
0
0
1
0
0
2
2
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
4
0
1
0
0
0
1
0
0
0
2
2
2
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
1
1
0
0
1
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
1
1
0
0
0
1
1
1
0
2
2
1
1
3
2
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
2
2
0
2
0
0
0
2
0
0
1
2
0
0
1
0
0
2
0
0
0
0
4
1
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
1
2
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
1
0
2
1
0
3
0
2
0
0
0
0
1
0
0
0
0
2
1
2
1
0
0
1
2
0
0
2
2
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
2
0
0
0
5
1
0
0
0
1
1
1
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
2
1
0
0
0
3
0
0
0
0
0
0
0
0
2
0
3
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
1
2
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
4
0
2
1
1
1
2
0
1
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
1
1
0
0
0
1
0
0
2
2
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
2
0
0
1
2
1
0
0
0
0
0
2
0
0
2
0
0
1
2
0
0
0
0
0
1
2
0
0
0
0
0
0
2
2
0
0
0
2
2
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
1
0
0
2
1
0
0
0
0
1
1
1
0
0
1
0
0
0
3
0
2
1
0
0
2
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
2
0
1
0
1
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
2
1
0
1
0
0
0
2
0
0
2
0
1
0
2
0
0
0
2
2
1
1
0
0
0
0
1
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
2
2
3
1
0
1
3
0
0
0
2
1
1
0
0
0
1
0
0
0
1
0
2
0
1
0
1
0
0
1
0
0
1
0
1
1
0
0
1
0
1
2
0
2
2
2
0
0
0
0
0
2
1
0
2
0
1
0
0
1
0
0
0
0
1
2
1
1
2
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
2
2
1
1
0
2
0
0
0
3
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
3
2
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
1
2
0
1
0
0
0
0
1
0
0
1
6
1
0
3
0
0
2
0
0
0
2
0
2
0
2
0
2
0
1
1
1
2
0
0
0
4
0
1
0
1
0
1
1
0
0
2
1
0
2
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
3
2
2
3
2
0
2
0
0
0
2
0
1
0
0
0
1
0
0
2
0
1
0
0
1
0
0
0
0
0
2
0
0
0
2
2
0
1
0
0
0
2
0
0
2
1
2
0
2
0
0
1
0
0
2
0
0
0
1
0
1
0
0
0
1
0
0
0
2
0
0
0
0
6
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
3
0
0
0
2
0
0
2
0
0
0
1
1
1
0
0
0
1
0
1
0
0
2
0
0
1
0
2
1
1
0
0
0
0
0
0
2
0
1
0
0
1
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
2
2
2
0
1
0
0
0
0
0
0
0
1
2
1
1
0
1
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
1
3
2
3
0
0
0
0
0
0
0
2
1
1
0
0
0
4
1
0
0
0
1
0
0
0
0
0
1
1
1
0
2
0
0
0
2
0
1
0
0
0
2
0
2
0
2
2
0
0
0
0
0
0
0
0
3
2
0
2
1
0
0
1
0
5
1
0
0
0
4
0
0
1
0
3
0
0
0
0
1
0
0
0
1
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
1
0
0
0
1
2
1
0
1
1
0
0
0
2
0
0
0
3
0
0
0
0
0
0
2
0
0
1
2
0
1
1
2
0
0
0
0
1
0
2
1
2
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
2
1
1
2
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
12
1
0
0
0
0
2
0
0
0
2
0
0
1
2
3
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
1
0
0
2
1
3
0
2
0
0
0
0
2
2
1
0
1
2
0
0
0
1
0
0
0
0
0
3
0
0
3
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
1
0
0
2
0
2
0
0
2
0
2
1
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
1
2
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
1
1
0
1
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
1
0
1
0
0
0
1
0
3
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
2
3
2
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
2
2
1
0
0
0
0
1
0
0
0
1
2
0
0
0
1
1
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
1
1
0
2
1
0
0
2
1
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
2
0
2
2
0
0
1
0
1
2
1
5
0
0
0
0
0
0
1
2
1
2
0
2
0
2
1
0
0
2
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
2
0
1
1
1
0
0
0
2
0
0
0
1
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
4
0
0
0
2
1
0
0
2
0
1
1
0
0
4
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
2
2
0
0
3
0
0
0
1
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
2
0
2
2
1
0
1
0
0
0
0
0
2
1
0
1
0
0
2
1
0
2
0
0
0
0
1
0
2
2
2
0
1
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
2
0
0
0
0
4
1
2
0
0
0
0
2
0
0
0
0
1
0
0
0
1
2
2
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
4
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
2
0
0
1
1
0
1
0
2
0
1
0
0
2
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
1
1
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
1
2
2
1
2
2
0
0
0
0
0
1
0
0
1
2
1
2
0
1
0
0
0
0
0
1
0
2
2
1
0
2
2
0
0
0
2
0
1
1
0
0
2
1
0
1
0
0
0
2
0
0
0
1
0
1
0
2
0
0
2
2
0
1
1
0
1
2
0
0
1
0
2
0
2
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
3
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
1
2
0
0
0
2
2
2
0
1
1
0
0
0
1
0
0
0
0
2
2
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
8
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
2
0
1
0
1
1
0
0
2
0
0
2
2
0
2
1
3
0
0
0
1
0
2
0
0
1
0
0
0
0
0
2
0
2
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
2
0
1
0
0
3
0
3
0
2
0
1
0
0
0
0
0
0
0
0
0
2
2
1
0
0
2
0
1
0
0
2
1
0
1
0
0
0
0
1
0
0
0
2
0
1
2
0
0
3
0
1
0
0
0
0
0
0
1
1
2
2
0
1
0
1
0
0
1
0
0
2
0
0
0
1
1
0
1
2
0
0
1
0
0
2
0
0
2
2
0
0
1
0
0
0
0
0
0
0
1
0
0
1
4
0
0
0
0
0
2
0
0
0
0
2
2
1
0
2
0
0
2
0
0
0
1
1
0
0
2
1
0
16
2
2
0
2
0
0
0
0
1
0
1
2
0
0
0
4
0
0
2
0
0
0
2
0
0
2
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
1
2
2
0
0
1
0
0
2
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
2
1
0
1
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
1
0
1
0
1
0
2
0
0
0
0
0
0
7
0
0
1
0
0
0
0
0
1
1
0
0
3
0
1
0
0
0
2
0
0
0
0
0
0
0
3
0
0
1
0
0
1
1
0
0
2
0
2
1
2
0
0
2
2
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
2
0
0
0
2
0
1
4
0
0
0
0
0
1
2
1
0
0
0
1
1
2
0
0
0
0
2
4
1
0
0
2
1
1
1
0
2
0
0
0
1
1
0
0
3
0
1
0
2
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
2
0
2
2
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
2
2
2
2
0
0
0
0
4
0
0
0
2
0
0
0
3
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
2
0
0
2
1
0
0
1
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
2
1
0
1
0
0
0
0
0
0
0
4
1
0
1
0
0
3
1
0
0
1
2
0
1
0
0
0
2
0
0
1
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
2
0
0
2
1
0
0
0
0
0
2
2
0
1
0
0
0
1
0
1
1
1
0
0
2
0
1
1
0
0
2
0
0
0
2
0
0
2
2
0
1
0
1
0
0
2
2
0
2
0
0
0
2
1
2
0
2
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
2
1
1
2
1
0
0
0
2
0
0
1
0
0
0
0
2
0
1
0
0
0
0
2
1
2
1
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
2
2
0
0
2
0
2
0
1
0
0
1
0
0
0
1
1
0
1
0
0
0
0
2
0
0
3
0
2
0
0
0
2
0
0
1
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
2
1
2
2
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
13
0
0
2
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
1
2
1
2
2
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
1
1
2
3
0
2
0
0
0
0
2
0
1
0
0
0
2
1
0
0
0
2
1
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
5
1
0
0
1
0
0
0
1
0
1
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
1
4
2
0
0
1
0
2
0
2
0
0
0
0
2
1
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
2
3
0
2
0
0
1
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
1
2
0
0
0
1
5
2
1
2
1
0
0
2
0
0
0
2
2
1
0
1
2
1
0
0
0
2
0
0
0
0
0
1
0
1
0
2
1
2
2
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
1
0
0
1
0
0
0
0
1
1
0
1
0
0
0
1
2
0
1
0
0
2
0
0
1
4
0
2
1
2
0
1
0
0
0
1
2
0
1
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
2
0
0
0
1
0
0
2
0
1
0
0
2
2
0
0
0
0
0
0
4
0
1
0
0
0
0
0
2
0
2
0
0
0
0
1
1
2
0
0
0
0
0
2
1
0
0
0
1
1
1
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
2
1
0
1
1
1
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
2
2
0
1
0
0
0
2
1
1
0
1
1
0
0
2
0
0
1
1
0
0
1
2
0
0
0
2
1
0
2
0
0
0
1
0
0
2
0
0
0
0
2
0
1
2
1
0
0
1
0
0
0
0
0
1
2
1
0
0
0
0
0
1
1
2
1
0
0
0
1
2
2
0
0
4
0
0
1
0
0
0
1
0
0
2
1
0
2
1
1
0
1
0
1
2
0
1
0
1
0
0
0
0
0
1
0
1
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
5
0
2
0
0
0
0
1
1
0
2
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
1
2
0
1
2
0
0
2
2
1
0
0
2
0
0
1
0
2
0
2
0
1
1
0
2
0
0
0
0
1
0
0
0
0
1
0
1
1
2
0
0
0
0
0
1
1
0
0
0
0
1
0
0
4
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
1
3
2
0
0
1
0
0
2
0
2
2
2
0
2
0
0
0
0
0
1
0
4
0
0
1
0
0
0
2
0
1
0
0
0
2
0
3
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
2
0
0
0
0
0
2
1
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
2
2
1
0
0
0
0
0
0
1
2
1
0
0
1
0
1
0
0
0
0
0
0
1
2
0
2
2
2
0
2
0
0
1
0
0
2
0
0
0
0
0
2
2
2
0
0
0
0
4
2
2
2
0
0
0
0
0
1
0
0
0
2
0
2
1
0
0
0
1
0
2
1
0
1
2
1
0
0
1
0
0
0
0
2
0
1
0
2
0
3
2
0
0
0
2
1
0
0
1
2
1
0
1
0
0
0
1
2
0
0
1
1
0
0
0
0
0
2
0
1
0
1
0
0
1
1
0
1
1
0
0
1
1
0
1
1
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
1
0
0
3
0
0
0
0
2
0
0
3
0
0
0
0
2
0
0
2
0
0
0
2
2
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
2
0
0
0
2
0
0
0
0
1
0
0
3
1
0
0
1
5
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
2
1
0
0
1
0
0
0
0
0
1
1
5
0
1
0
0
0
0
0
0
0
0
1
0
0
2
1
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
1
0
0
1
3
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
1
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
1
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
1
2
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
2
0
2
0
0
0
1
0
0
0
0
2
3
0
0
0
1
0
0
0
2
0
0
0
0
1
1
1
1
0
1
0
0
0
0
2
0
1
0
0
0
2
1
1
0
0
1
2
0
0
0
2
0
0
0
0
0
2
0
2
0
1
2
1
0
0
0
1
2
0
1
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
1
1
0
2
2
0
0
0
1
0
0
0
0
0
4
2
0
0
0
2
0
0
0
1
2
1
0
2
0
0
2
0
2
2
1
0
0
0
0
2
2
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
2
5
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
3
0
1
2
2
0
0
2
1
0
0
0
0
0
2
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
2
1
0
1
0
0
0
1
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
1
3
1
0
0
0
0
1
0
1
0
0
0
0
2
0
0
3
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
1
2
0
2
0
1
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
1
0
0
1
0
1
0
0
2
1
1
2
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
1
0
0
0
1
0
0
1
2
0
2
2
0
0
2
0
0
1
1
0
0
1
0
0
3
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
1
0
0
2
2
2
0
1
6
0
0
6
0
0
0
0
2
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
1
0
0
2
1
1
0
0
0
0
3
2
2
0
1
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
2
1
2
2
1
2
0
0
0
2
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
2
1
2
0
0
0
1
0
0
0
0
2
1
0
0
1
1
0
1
0
1
0
0
0
2
1
0
2
0
2
0
0
0
2
1
0
0
1
0
2
0
0
2
0
0
1
1
0
1
1
0
0
1
2
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
2
0
0
0
2
1
0
2
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
2
3
2
1
1
0
0
0
0
2
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
1
0
0
0
2
0
0
0
0
2
1
2
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
1
1
1
2
0
0
2
0
0
0
0
1
2
1
1
0
0
0
0
3
0
1
0
0
0
0
0
0
0
1
0
0
3
1
0
0
1
1
0
0
0
0
0
0
0
0
0
3
1
0
0
1
2
0
2
0
0
2
1
3
0
1
0
0
2
1
0
1
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
2
0
0
1
0
0
0
1
10
0
0
0
1
0
1
0
0
1
0
1
0
2
0
0
0
0
3
1
0
1
0
1
1
0
0
0
2
0
0
1
1
1
0
0
3
0
0
2
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
6
0
1
0
0
0
0
0
1
2
0
0
0
1
1
0
1
0
2
0
0
0
0
2
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
2
1
0
0
2
2
0
0
0
0
0
0
0
3
0
1
0
0
0
0
1
1
0
0
2
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
2
1
1
5
0
0
3
0
2
0
0
0
0
1
1
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
2
1
1
1
1
0
2
0
0
0
3
0
0
0
0
0
2
1
1
0
0
2
1
1
1
1
0
0
2
0
0
2
0
1
0
2
0
1
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
6
2
0
0
0
1
0
0
0
0
0
2
0
1
0
0
2
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
1
0
2
0
0
0
1
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
3
0
2
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
3
3
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
1
0
1
4
0
0
0
1
2
2
0
0
2
0
1
0
1
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
1
3
0
0
0
1
2
2
0
0
2
0
1
1
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
1
5
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
2
0
0
2
0
0
1
2
2
2
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
3
2
1
0
0
0
0
0
1
0
2
0
0
0
2
2
0
2
0
0
2
2
0
1
0
0
2
2
1
2
0
1
4
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
2
0
3
1
0
0
2
0
0
0
0
0
0
0
2
2
0
0
1
0
6
0
1
2
0
0
0
2
0
0
0
0
1
2
0
2
2
1
2
1
0
0
0
0
3
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
3
2
1
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
1
1
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
2
0
3
1
1
0
0
1
0
0
2
0
0
2
0
0
0
1
0
2
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
2
0
2
0
0
0
2
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
2
2
1
0
1
3
0
2
1
1
2
0
0
1
0
2
0
1
1
2
0
0
0
1
1
0
1
0
1
1
0
0
0
0
0
0
0
2
2
2
0
0
3
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
3
2
0
0
2
0
0
0
1
0
0
1
2
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
1
0
2
0
0
1
0
0
0
2
1
0
0
0
0
0
1
2
1
2
2
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
7
0
0
1
0
0
0
1
1
0
1
3
0
0
0
0
0
2
1
0
0
0
1
1
0
0
1
0
0
0
2
0
0
2
0
0
0
1
0
0
0
2
1
2
0
0
0
0
0
0
0
1
0
1
0
0
3
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
2
2
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
3
1
2
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
2
3
0
2
2
0
2
2
0
2
0
2
0
0
2
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
2
2
1
0
0
0
2
0
0
2
2
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
1
0
0
1
0
3
0
0
2
0
2
0
0
0
1
2
0
0
0
1
0
0
1
2
0
3
1
0
0
0
0
1
0
0
0
3
0
1
0
0
0
1
2
0
0
0
0
2
0
1
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
2
0
0
0
0
0
0
0
1
0
2
1
2
0
2
0
0
2
0
1
0
2
1
2
1
2
1
2
0
0
1
0
2
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
1
0
0
2
0
0
3
1
2
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
3
0
2
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
3
2
1
0
0
0
0
1
0
0
0
2
2
0
0
2
0
0
1
0
1
0
2
0
2
0
3
1
0
1
0
0
2
0
0
1
1
1
0
0
0
2
0
0
0
0
0
0
0
2
3
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
1
2
0
0
1
1
0
0
0
0
0
0
0
0
2
3
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
2
0
2
0
2
2
0
0
0
2
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
1
0
1
0
2
0
1
1
0
1
0
1
0
2
0
2
1
0
3
2
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
3
1
1
1
0
2
0
2
0
2
1
2
4
0
0
1
0
1
0
0
0
0
2
0
1
1
1
0
1
0
0
0
1
0
0
2
2
1
0
2
0
1
0
0
1
0
0
0
0
2
0
0
0
2
3
0
0
2
1
3
0
0
0
2
0
0
0
1
0
1
0
0
0
1
0
0
3
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
3
2
2
1
0
0
2
0
0
1
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
6
0
1
2
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
1
0
2
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
1
0
0
0
1
1
2
2
1
4
1
1
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
2
2
1
2
0
1
0
0
2
0
1
0
0
1
0
0
0
0
1
0
0
4
0
0
0
1
0
1
1
1
0
0
0
2
0
2
1
0
1
0
0
2
2
0
0
1
0
0
1
3
0
2
0
0
0
0
0
0
0
0
1
1
0
0
2
2
0
3
0
0
0
0
1
0
1
0
0
2
0
1
2
4
1
2
2
3
0
0
1
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
1
0
2
2
2
2
1
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
1
0
0
0
2
0
4
0
0
0
0
2
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
1
1
0
0
0
1
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
4
1
1
0
0
0
0
2
2
0
1
2
0
0
0
0
1
2
0
2
1
2
0
0
0
0
0
0
1
0
0
0
2
4
2
1
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
2
3
2
1
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
3
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
2
2
0
0
0
3
2
1
0
0
2
2
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
1
2
0
2
0
0
0
2
0
1
0
0
1
0
1
0
0
0
2
1
0
0
0
1
1
0
0
0
0
2
0
0
2
1
0
2
2
0
0
1
2
0
0
1
0
2
0
1
0
0
0
1
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
1
2
0
0
1
2
0
3
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
2
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
1
0
0
2
2
1
1
4
0
0
0
1
0
0
1
3
0
2
0
0
0
2
0
2
1
0
0
0
0
4
2
0
0
2
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
1
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
1
1
0
0
0
2
1
0
3
0
0
0
2
0
2
0
1
1
1
0
2
0
0
2
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
2
1
0
0
1
0
2
1
0
2
0
1
0
0
0
0
0
0
4
3
0
1
2
0
0
0
2
0
0
0
1
0
0
1
2
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
2
2
0
2
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
2
0
0
0
0
1
2
0
0
2
0
1
0
0
0
0
0
2
2
0
0
1
0
1
0
0
2
0
3
1
2
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
2
0
0
0
5
0
0
1
2
0
0
0
0
2
0
0
1
6
1
0
0
0
0
0
2
11
2
0
0
0
0
0
0
0
3
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
2
0
0
0
0
2
2
0
0
0
0
0
0
1
2
0
0
2
1
0
0
0
0
0
0
0
2
0
1
2
0
2
1
0
2
0
3
0
2
1
0
0
5
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
1
0
1
0
0
0
1
0
0
0
0
2
0
1
1
2
0
3
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
2
2
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
2
2
1
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
1
2
0
0
1
0
0
0
0
0
2
0
0
1
4
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
1
0
0
2
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
1
0
2
2
0
0
0
0
0
1
0
0
1
2
1
1
0
2
1
0
2
0
0
2
2
0
1
0
2
1
2
0
1
1
0
0
1
1
1
2
0
0
1
2
0
0
1
0
0
2
0
2
1
0
1
0
0
0
0
0
0
2
0
0
0
0
1
1
1
0
0
0
1
0
0
1
3
0
0
0
0
1
0
0
0
2
0
0
3
0
2
1
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
2
0
0
2
1
0
0
0
2
2
1
0
0
2
0
0
0
0
1
0
0
2
0
0
1
0
1
0
0
0
1
0
0
2
1
0
2
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
2
2
0
0
0
1
6
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
2
1
0
0
0
0
0
0
0
1
0
0
1
2
0
2
2
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
2
1
2
1
2
0
2
2
1
0
0
0
2
2
0
0
1
1
0
0
1
0
0
1
0
0
1
0
0
2
1
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
2
0
1
0
1
1
2
0
0
0
2
0
0
0
1
0
0
0
0
1
0
1
0
0
2
2
2
0
0
1
2
2
1
2
0
1
1
0
0
0
0
3
0
0
0
2
0
0
0
1
2
2
2
0
0
0
1
1
1
0
0
3
2
0
1
0
3
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
1
2
0
0
0
0
1
2
2
1
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
3
1
0
0
0
0
1
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
1
0
10
0
2
0
1
0
0
1
0
0
2
0
1
0
1
0
3
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
1
0
0
2
2
0
0
1
1
0
1
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
2
0
2
1
0
0
0
0
2
0
0
2
0
1
2
0
2
3
0
0
1
0
0
1
1
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
1
2
1
2
1
0
0
0
0
0
0
0
0
0
2
0
1
1
0
2
2
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
1
0
0
0
2
2
2
0
0
3
0
2
0
0
0
1
2
0
1
0
0
0
2
3
0
2
1
1
0
0
0
2
0
1
1
0
2
1
2
1
0
0
0
0
0
0
0
0
2
1
0
1
2
2
0
0
1
0
0
0
2
1
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
1
0
0
1
1
2
5
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
2
2
0
1
1
4
0
2
0
0
2
0
1
0
0
0
0
2
2
2
1
0
1
0
0
1
0
0
0
4
4
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
2
0
0
2
0
0
1
0
0
0
1
0
0
1
0
1
0
1
0
0
1
0
1
2
2
0
0
1
0
2
0
1
1
0
1
0
0
0
2
0
0
2
0
0
0
2
1
0
0
0
0
0
2
1
0
0
1
0
1
0
2
4
0
0
0
2
0
0
0
2
0
0
0
0
0
3
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
9
0
1
1
2
0
0
1
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
3
2
0
2
0
0
0
0
0
0
1
1
0
0
2
1
0
2
0
0
1
0
0
2
0
1
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
2
2
0
3
1
1
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
1
1
5
2
0
0
0
0
2
0
0
2
0
2
0
1
0
0
0
2
0
1
0
0
0
1
0
0
1
2
0
0
2
2
0
1
1
0
2
1
0
0
0
0
2
0
0
1
2
0
2
0
2
0
0
0
2
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
3
0
0
2
0
0
0
2
0
2
2
0
1
1
0
3
0
0
0
0
2
0
0
0
2
0
0
0
0
1
2
0
0
0
0
1
2
0
0
0
0
2
0
0
0
1
0
1
2
0
1
0
0
0
6
2
0
0
0
0
0
2
0
3
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
1
0
0
0
0
2
3
0
0
2
1
0
2
0
1
0
1
0
1
0
0
0
2
0
2
0
2
2
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
1
0
0
0
0
1
2
1
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
1
1
0
0
5
5
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
1
0
0
0
1
2
0
0
0
2
0
0
2
2
0
0
0
2
1
0
0
0
0
0
1
1
2
1
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
1
0
0
0
1
0
2
0
0
1
2
0
1
3
0
3
1
2
0
1
0
0
0
0
0
2
0
2
2
0
0
0
2
1
0
0
0
0
0
2
3
0
0
0
0
2
1
0
0
0
2
0
0
0
2
0
2
1
3
1
0
1
1
0
0
1
0
1
1
0
1
0
0
0
1
0
0
0
5
1
0
1
0
0
2
2
0
0
0
0
1
0
1
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
1
0
0
0
2
0
1
0
0
1
0
1
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
2
0
0
2
0
0
0
1
0
3
2
0
0
2
2
0
0
2
0
0
1
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
2
0
1
0
3
0
0
0
1
0
0
1
0
0
1
0
0
0
1
1
0
0
2
0
0
1
0
0
0
0
2
0
1
0
0
0
1
1
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
2
2
2
1
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
2
0
0
0
3
1
0
0
0
0
3
0
0
0
0
0
0
2
1
0
2
1
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
2
0
1
2
0
1
0
0
0
0
0
1
0
0
1
1
0
2
0
3
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
1
0
1
1
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
2
0
0
0
0
2
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
3
1
1
0
1
2
1
0
0
0
0
2
2
0
2
0
0
0
5
1
0
2
0
0
0
1
0
0
0
0
1
0
0
2
0
1
2
0
4
0
0
0
0
0
0
2
1
0
1
0
0
0
0
2
2
0
0
1
0
2
3
1
2
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
1
0
1
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
2
1
0
2
2
0
0
2
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
1
0
0
2
1
0
0
0
2
1
1
1
0
0
0
0
0
2
2
2
0
0
0
0
0
0
2
2
0
1
0
1
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
2
0
0
1
1
0
0
0
2
1
0
0
0
0
0
0
3
0
0
1
0
1
1
0
0
0
4
0
0
0
1
1
0
3
0
2
0
0
0
0
2
2
1
0
0
0
2
0
1
0
0
0
2
3
3
0
0
1
1
0
0
0
0
1
3
0
1
0
0
0
0
0
2
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
1
0
0
2
0
0
0
0
0
2
0
2
1
1
1
0
0
0
0
0
0
0
0
0
0
2
2
0
1
2
0
2
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
2
1
0
2
1
0
0
1
0
0
2
0
1
0
0
0
1
0
0
0
2
0
0
0
0
1
0
2
4
2
0
0
2
0
0
2
2
2
0
1
0
0
0
0
1
0
1
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
2
3
0
0
2
2
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
7
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
2
0
3
0
0
0
0
0
0
2
0
0
0
1
1
0
1
0
0
1
0
0
1
0
0
0
0
1
0
2
0
0
0
2
0
0
2
1
1
0
0
0
0
0
0
0
2
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
1
2
0
2
0
2
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
3
2
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
4
0
2
0
1
1
0
1
0
0
0
0
0
0
2
0
1
0
1
2
0
0
0
2
0
1
0
3
1
0
3
0
1
0
0
0
0
0
0
4
0
2
0
2
0
1
1
0
0
0
0
0
0
1
1
0
2
2
3
0
0
0
1
0
2
0
0
1
0
0
1
0
2
2
0
0
0
0
0
0
0
1
0
1
0
0
1
2
0
2
0
2
1
0
0
0
0
0
1
0
2
0
0
1
4
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
2
0
1
1
0
0
0
0
0
1
0
0
0
0
0
3
2
1
0
0
0
2
0
2
0
0
0
2
0
0
2
0
1
0
0
2
1
2
0
0
3
0
1
2
0
2
0
0
1
1
0
0
0
3
1
1
0
0
0
2
2
0
2
0
2
0
0
0
0
1
0
0
0
2
2
2
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
2
0
0
2
0
4
2
2
0
2
0
1
0
1
1
0
0
1
2
1
0
0
0
2
1
0
0
0
2
0
0
0
1
2
2
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
2
1
0
0
0
1
0
2
1
0
0
0
0
1
1
0
1
1
1
0
1
0
2
0
1
0
1
0
0
1
0
2
0
2
0
0
2
0
2
0
1
0
1
0
1
0
0
0
0
0
0
1
2
0
1
0
0
0
1
0
0
0
2
0
0
1
0
1
2
9
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
2
2
0
0
0
0
1
0
1
0
1
0
1
2
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
7
2
0
0
0
0
0
0
0
2
0
2
1
0
0
2
3
0
0
0
0
0
2
2
0
3
2
1
1
0
0
0
3
0
0
0
1
0
0
2
0
0
0
2
0
1
0
1
3
2
1
0
2
4
2
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
2
2
0
0
0
0
3
0
1
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
1
1
0
2
0
0
0
1
2
0
0
0
2
0
0
0
2
0
0
0
0
0
2
1
2
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
1
2
1
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
2
0
1
0
2
1
0
0
1
0
1
0
0
0
1
0
2
2
1
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
1
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
1
1
0
0
2
0
0
0
0
0
0
1
3
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
2
2
1
0
2
1
1
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
3
1
1
1
2
0
0
1
0
0
1
2
1
0
0
1
2
0
1
0
0
2
3
0
0
0
3
0
0
0
0
1
1
0
0
0
0
0
3
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
2
2
0
1
0
0
0
0
0
0
1
1
0
1
0
0
2
2
0
1
0
0
0
0
1
0
1
0
0
2
0
2
0
2
0
0
2
0
1
2
0
0
2
1
0
0
0
0
0
0
5
0
1
0
6
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
1
0
3
2
2
0
0
0
1
2
0
0
0
0
0
0
1
1
0
1
1
0
0
0
2
0
5
0
0
0
0
2
0
0
2
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
2
4
3
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
1
0
0
2
3
2
0
2
0
2
0
0
0
2
0
0
2
0
0
0
0
1
0
0
3
0
0
0
0
2
0
0
4
0
0
2
0
2
0
0
0
1
0
0
0
0
2
2
0
0
0
0
1
2
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
1
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
2
1
0
1
2
0
1
0
0
2
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
1
2
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
1
1
0
0
3
2
0
1
2
1
0
0
2
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
5
1
1
0
1
0
0
0
2
0
0
1
0
2
0
0
2
0
0
0
0
1
0
2
2
0
3
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
4
2
0
0
0
0
1
2
0
2
2
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
1
0
0
1
3
2
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
2
0
2
2
0
2
1
2
0
0
1
0
0
0
0
0
0
0
0
1
2
1
0
2
1
0
2
1
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
1
0
0
0
5
0
2
0
3
2
2
0
0
1
0
0
1
3
1
0
2
0
0
0
2
0
2
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
2
1
0
0
0
1
2
0
0
1
2
1
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
3
2
2
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
2
1
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
2
0
1
0
0
1
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
1
1
0
2
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
2
0
0
0
0
0
0
0
3
0
1
1
0
0
0
1
0
1
0
0
1
2
1
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
2
0
1
1
1
2
0
0
0
0
1
2
0
0
0
0
1
1
0
0
0
2
0
2
0
2
0
2
0
2
0
0
0
1
2
0
0
2
2
0
0
0
0
1
1
1
1
0
0
0
1
0
1
0
0
2
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
1
0
0
0
2
1
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
2
0
0
0
2
1
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
1
4
3
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
1
2
0
0
1
0
1
0
0
0
2
0
2
0
2
0
0
0
0
1
0
0
0
2
1
1
0
1
0
0
0
2
1
1
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
2
1
2
1
0
0
0
2
2
0
2
0
1
0
1
0
1
1
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
1
1
0
0
0
0
2
0
0
0
0
2
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
2
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
1
1
1
0
1
0
0
0
0
1
2
1
0
0
0
1
1
1
1
2
2
1
0
2
0
1
1
0
0
0
0
0
1
3
0
0
1
0
0
1
3
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
1
0
0
0
2
0
1
2
2
0
0
0
2
0
0
1
1
0
1
2
2
0
0
0
0
0
0
2
0
2
0
0
0
1
0
2
1
0
0
2
0
2
0
0
0
0
0
1
0
0
2
0
0
1
1
0
1
1
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
2
0
3
0
0
2
0
0
2
1
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
1
1
2
0
0
0
0
0
1
0
0
1
1
2
2
1
0
2
2
1
0
0
0
1
0
1
0
0
1
0
2
3
0
0
0
1
0
0
0
2
0
1
1
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
3
0
0
2
1
2
2
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
2
0
2
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
2
2
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
1
0
2
1
1
0
0
2
1
0
0
1
0
0
1
0
2
0
0
0
0
0
0
3
0
2
1
1
1
0
2
2
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
1
2
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
1
0
2
0
2
0
0
0
0
2
2
1
0
1
2
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
2
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
1
1
1
0
1
0
2
3
0
0
2
0
1
2
3
1
0
0
0
2
0
0
2
1
2
0
0
1
0
2
0
0
0
1
0
0
0
1
0
2
2
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
2
2
0
0
0
1
1
0
0
0
0
0
1
1
0
0
1
0
1
0
3
1
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
1
0
2
1
0
0
4
1
0
1
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
7
0
0
0
1
3
2
1
0
2
1
0
0
2
0
1
0
0
2
0
0
0
0
2
0
0
2
0
1
2
1
0
1
0
0
1
0
0
0
0
1
0
2
2
5
0
0
0
0
0
2
0
2
0
2
0
1
2
0
0
0
2
1
3
0
1
0
0
1
0
1
2
1
0
0
0
0
0
0
2
1
2
0
1
1
0
0
2
2
0
0
0
0
2
0
0
0
0
0
2
1
0
0
3
0
0
1
1
0
0
0
0
0
0
0
1
2
0
2
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
1
1
0
0
0
0
0
2
0
0
0
0
0
1
1
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
3
0
0
1
2
1
0
1
0
0
1
0
1
0
0
0
3
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
3
1
0
1
1
0
0
1
1
0
2
2
0
3
0
2
2
0
0
0
0
0
1
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
5
0
0
1
0
3
2
2
1
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
2
0
3
0
1
1
0
1
0
0
0
1
3
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
1
1
0
2
0
1
0
0
1
0
2
1
1
0
0
2
1
1
0
0
1
0
0
2
0
0
0
0
3
0
2
1
0
0
1
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
2
0
0
1
0
0
0
2
0
2
0
0
0
2
3
0
0
1
2
0
2
0
1
1
0
1
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
1
0
1
0
0
2
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
4
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
3
0
2
1
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
1
1
0
0
0
1
2
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
2
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
3
1
0
0
1
1
0
0
2
1
0
2
0
0
0
0
3
1
1
0
0
0
0
0
0
2
2
1
0
1
1
0
1
3
0
1
1
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
2
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
3
0
0
2
0
2
2
0
4
0
2
0
0
2
0
2
1
0
2
0
0
1
0
0
0
1
2
0
0
0
0
1
2
1
0
0
2
2
0
0
0
1
0
0
0
0
1
0
1
0
1
2
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
2
1
2
0
1
0
5
0
0
0
0
0
0
0
1
0
0
1
2
0
0
1
0
2
1
3
2
0
1
2
1
0
0
0
0
0
2
0
0
0
0
0
0
1
2
2
1
0
2
0
0
2
0
0
0
1
0
2
0
1
0
1
0
0
1
0
0
0
2
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
3
0
2
0
2
0
2
0
0
0
0
0
1
2
1
1
0
0
0
0
0
0
0
0
0
0
0
4
4
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
2
2
1
0
0
0
2
0
1
0
2
3
0
0
1
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
1
0
2
1
0
0
0
4
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
1
0
0
1
0
1
2
0
1
2
0
0
0
0
0
0
1
0
0
3
0
0
1
2
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
2
0
3
2
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
2
1
0
0
2
7
1
0
1
0
0
0
2
0
2
1
0
2
0
0
2
2
1
0
2
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
4
2
0
0
0
0
2
1
0
2
1
0
0
1
2
0
2
0
0
0
0
0
2
2
0
1
2
0
0
0
0
0
1
2
0
0
0
0
2
1
0
0
2
0
2
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
3
1
1
1
0
2
1
2
1
0
1
0
2
0
2
1
0
0
1
2
0
1
0
0
1
0
2
2
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
1
0
1
2
1
0
0
0
2
0
4
2
0
0
0
1
0
0
2
0
0
0
1
0
0
0
1
0
0
1
2
0
0
0
0
0
2
0
2
0
0
0
2
0
5
0
1
0
0
0
1
0
2
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
3
2
0
0
0
0
0
2
1
0
2
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
3
1
3
0
0
0
2
2
1
0
0
0
1
0
0
2
0
1
2
1
2
0
0
0
1
0
0
1
1
2
0
2
2
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
2
0
0
1
2
2
1
2
1
2
0
0
0
0
1
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
2
0
1
1
0
0
0
2
1
2
0
0
1
0
1
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
2
0
0
1
1
0
0
0
2
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
6
1
0
0
1
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
2
1
0
0
2
0
0
1
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
2
0
0
0
0
0
0
1
0
0
2
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
2
2
1
1
1
1
0
0
0
0
1
2
0
0
0
0
0
1
1
0
0
0
2
2
1
0
0
0
0
2
0
0
1
1
1
0
2
0
0
1
1
0
1
2
0
0
0
0
0
1
2
0
0
2
1
0
0
0
1
2
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
2
0
2
0
0
1
0
0
2
0
0
0
1
0
2
0
0
0
2
3
2
0
0
0
0
0
2
2
0
1
2
0
0
1
0
2
1
0
2
0
0
0
0
0
2
0
2
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
1
1
0
2
1
1
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
2
1
0
0
0
3
0
2
0
2
0
0
0
2
0
0
1
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
1
1
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
2
1
1
0
0
0
0
0
3
0
0
0
0
0
0
3
1
1
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
1
0
2
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
4
0
2
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
3
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
2
0
1
2
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
2
2
2
1
1
0
0
0
0
2
0
0
1
0
0
0
1
0
2
0
1
1
1
1
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
0
0
1
2
0
1
0
0
0
2
0
1
1
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
6
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
3
0
0
0
1
1
0
1
0
1
0
2
1
0
2
0
0
0
2
0
0
1
1
0
1
0
2
0
0
1
1
0
1
0
0
0
3
0
0
0
1
0
1
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
2
1
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
3
0
2
0
0
1
0
0
1
2
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
1
0
0
0
1
3
0
3
1
0
0
0
2
0
0
0
2
0
2
3
0
0
0
0
2
2
0
0
1
0
0
0
0
2
1
2
0
0
0
0
0
1
0
0
1
1
0
0
2
0
0
2
1
0
0
2
3
2
1
0
0
0
0
0
2
0
0
0
0
0
1
4
0
0
1
1
1
1
0
1
2
0
4
1
0
0
0
0
0
0
0
0
2
1
0
0
1
0
1
0
2
0
0
0
6
0
2
0
0
2
0
1
0
0
1
0
0
1
0
0
0
0
0
4
2
2
0
2
0
0
0
2
2
0
1
0
0
0
2
0
0
0
0
2
0
0
1
1
2
1
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
1
2
0
0
0
1
0
1
2
0
0
0
1
1
0
0
0
0
2
0
0
0
1
0
1
0
0
1
0
0
0
5
3
0
0
2
3
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
2
2
2
0
1
0
0
2
0
0
1
0
0
0
0
1
0
2
0
0
0
2
0
2
2
0
3
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
2
2
0
2
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
1
1
1
0
2
2
0
0
0
1
0
0
0
0
1
2
0
0
1
1
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
1
2
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
1
1
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
2
0
0
2
2
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
3
1
1
1
0
0
0
1
0
0
0
0
1
1
0
2
2
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
1
1
1
0
2
2
0
0
0
0
1
0
0
2
2
0
0
1
1
0
0
2
0
0
1
0
0
0
2
0
3
0
0
0
0
0
0
2
0
0
1
1
1
0
0
2
1
0
0
0
2
1
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
2
2
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
6
0
3
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
2
0
0
0
2
0
0
3
0
0
0
0
0
0
1
1
2
2
0
0
0
0
0
0
0
1
2
1
0
0
0
0
1
0
10
0
2
2
0
0
1
0
0
0
0
2
0
1
0
1
1
2
4
0
0
0
0
0
0
0
1
1
0
1
2
0
2
0
0
1
1
0
1
0
0
0
1
0
2
0
0
0
2
0
0
1
0
0
0
2
0
2
0
0
1
0
0
0
0
0
1
1
0
2
0
0
0
0
0
1
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
2
2
1
3
0
0
0
0
8
0
1
1
0
6
0
0
0
1
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
2
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
4
1
0
0
1
1
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
4
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
4
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
3
2
0
1
0
3
0
0
0
0
0
2
1
0
0
1
0
0
0
0
1
0
0
2
0
1
0
2
0
1
0
0
0
2
0
1
1
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
2
1
0
0
1
0
0
0
0
0
2
0
0
1
1
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
1
4
1
2
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
1
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
2
1
0
2
0
2
2
0
0
0
0
1
0
0
0
1
3
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
1
0
1
0
0
0
0
0
1
2
1
2
0
0
1
0
0
2
2
0
0
2
0
0
0
2
2
2
0
0
1
2
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
1
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
10
0
0
0
0
2
1
0
0
1
0
0
2
1
0
2
2
0
2
0
0
0
0
1
0
0
0
2
0
0
0
1
0
1
0
0
1
1
0
2
0
0
0
1
0
0
0
1
2
2
0
0
1
0
0
1
0
0
0
1
1
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
2
1
0
0
1
1
0
0
0
0
0
0
0
2
3
0
0
0
0
1
0
0
1
0
1
0
2
1
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
4
1
1
2
0
0
1
2
0
2
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
6
0
0
2
0
2
1
1
0
1
0
0
2
0
1
0
0
2
2
0
0
0
1
0
0
1
1
2
0
0
0
0
2
0
1
0
2
2
3
0
2
0
0
2
0
1
0
2
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
1
0
0
1
2
0
1
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
2
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
2
0
2
1
0
0
0
5
1
2
4
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
4
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
1
0
0
0
2
0
0
1
2
0
0
1
0
1
0
1
0
0
0
2
1
2
0
3
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
5
2
0
0
0
0
4
0
2
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
1
0
1
0
0
2
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
3
2
0
0
1
1
0
0
0
0
2
0
0
0
2
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
2
0
0
5
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
1
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
2
0
0
0
2
0
2
1
1
0
0
1
0
1
0
0
1
2
0
0
1
0
0
0
0
1
0
2
0
0
0
2
0
0
2
0
0
1
0
0
0
0
1
1
1
0
2
1
0
3
2
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
2
0
1
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
1
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
2
0
0
0
0
1
0
0
3
0
2
0
0
0
0
1
0
0
3
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
2
1
0
1
0
1
1
1
1
1
1
1
0
0
3
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
2
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
1
3
2
0
1
0
0
0
2
1
0
0
0
4
0
1
1
0
1
1
1
1
1
1
0
0
0
0
0
1
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
3
0
0
2
0
0
1
0
1
0
0
1
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
1
0
0
0
2
2
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
2
1
2
0
0
0
0
0
0
0
0
1
3
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
1
0
1
0
1
1
1
0
1
0
0
0
1
0
0
1
2
0
0
0
1
2
0
0
0
2
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
1
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
1
1
0
0
0
0
2
0
1
0
0
0
0
0
2
0
3
0
1
0
1
0
0
5
0
2
2
0
0
0
0
1
0
0
2
2
1
0
0
1
0
0
1
0
2
1
0
1
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
1
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
5
0
0
0
0
0
0
0
0
0
0
0
3
1
1
1
1
1
2
0
0
0
1
1
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
2
0
1
2
0
0
0
0
0
1
2
1
0
0
0
0
2
0
0
2
0
1
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
2
0
1
1
0
1
0
0
0
0
0
2
2
1
0
1
2
0
0
0
0
0
1
3
0
2
0
0
1
1
2
0
1
0
2
0
0
2
0
0
1
0
0
1
0
2
2
2
0
0
0
1
1
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
2
1
1
0
0
0
1
0
0
0
1
0
0
0
1
2
0
2
0
0
0
0
2
0
3
2
2
0
2
0
2
0
1
0
1
2
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
1
0
0
1
0
2
2
0
0
0
1
0
0
0
0
1
1
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
1
1
0
0
0
3
0
5
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
2
1
0
0
0
1
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
2
1
1
0
0
2
1
0
0
0
1
0
0
1
0
0
2
0
0
2
0
0
0
1
0
0
0
1
0
0
2
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
3
0
2
0
0
1
1
0
8
2
0
2
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
2
0
1
2
1
0
2
2
0
0
0
0
0
0
0
1
1
0
0
2
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
3
0
0
1
0
0
0
2
7
0
0
0
1
0
0
0
5
0
0
0
2
1
1
0
0
2
0
2
1
0
1
1
1
0
0
1
0
2
0
0
0
0
0
1
0
1
0
2
0
0
0
2
1
0
0
0
1
1
1
0
0
0
0
1
2
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
2
0
3
0
0
1
0
4
0
0
0
2
0
0
1
4
1
0
0
0
1
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
3
0
0
0
2
0
0
1
1
0
0
1
1
0
0
1
0
0
0
0
0
0
2
1
1
1
0
1
2
13
0
2
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
2
1
0
0
0
0
1
0
0
0
0
2
0
1
1
2
2
0
1
1
0
0
0
1
0
0
2
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
1
1
0
2
1
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
6
0
0
0
2
0
1
0
0
0
2
0
3
1
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
1
0
0
1
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
2
2
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
2
2
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
1
3
0
0
0
0
2
2
0
2
0
0
1
0
2
0
0
0
0
0
0
1
0
1
0
2
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
1
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
2
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
1
2
0
0
0
0
0
0
2
2
0
2
0
0
7
0
0
0
0
0
0
0
1
1
0
0
1
2
0
3
0
0
0
0
0
2
0
2
1
0
0
2
0
0
0
0
0
2
2
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
2
0
2
0
0
1
0
2
0
0
0
2
0
0
1
2
1
2
1
1
1
0
0
0
0
0
2
0
2
2
2
1
0
0
0
0
1
0
0
3
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
1
0
1
0
0
0
0
2
1
1
0
0
1
1
2
0
2
0
0
0
0
1
1
3
2
2
1
0
1
2
0
2
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
2
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
3
2
1
2
2
0
0
2
0
0
1
1
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
1
0
2
1
0
0
0
1
1
0
0
0
3
0
0
2
0
0
3
1
0
0
0
0
0
0
0
0
2
0
0
2
4
1
0
0
0
2
0
1
2
2
0
0
1
4
0
0
0
2
0
1
2
0
0
1
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
1
2
0
1
0
2
1
1
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
1
2
1
0
0
0
0
0
2
0
0
3
0
2
0
0
0
0
0
0
2
0
2
0
1
1
0
2
0
2
0
0
1
0
0
0
1
0
0
2
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
2
1
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
2
2
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
2
1
0
1
0
2
1
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
2
1
0
0
0
0
0
1
0
0
2
0
1
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
4
0
0
2
0
0
0
2
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
1
4
2
0
0
0
2
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
1
0
0
2
0
1
2
0
1
0
0
1
1
0
2
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
1
1
2
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
2
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
2
3
0
2
2
1
1
1
0
0
0
0
0
0
1
2
0
2
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
2
1
3
0
0
2
2
0
0
1
0
2
0
0
1
0
1
1
0
0
0
0
0
0
2
0
0
0
0
11
0
0
2
0
2
0
1
1
0
0
2
0
0
1
0
0
0
0
1
2
0
0
2
2
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
4
0
1
0
2
3
0
0
0
1
0
2
0
0
0
0
1
2
2
1
0
0
0
2
0
2
2
0
0
1
0
1
2
1
0
2
0
0
0
1
0
3
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
2
0
2
0
1
2
1
0
1
2
0
0
1
0
0
0
3
0
0
2
1
0
2
0
1
1
2
1
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
1
2
0
0
0
1
1
4
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
4
0
0
0
0
0
0
1
0
2
2
0
0
0
1
1
0
0
0
0
0
3
0
2
0
1
0
2
0
0
0
0
2
0
0
0
1
0
0
0
1
0
2
0
0
2
2
0
0
2
0
1
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
2
0
0
1
1
0
3
0
1
0
2
1
0
0
0
5
1
0
0
0
1
0
0
0
0
2
0
1
1
1
2
0
0
0
4
0
0
0
0
0
2
1
1
0
1
0
1
0
0
0
0
0
2
1
0
0
3
0
0
1
0
0
0
2
0
2
1
1
0
0
0
1
1
2
0
0
3
0
0
2
0
1
2
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
2
1
0
0
1
1
1
2
0
1
0
0
2
0
2
0
1
2
0
0
2
0
0
1
0
0
3
2
0
2
3
0
0
0
1
2
2
0
1
1
0
0
0
0
2
0
1
6
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
3
0
1
1
2
0
0
1
0
0
1
0
0
0
4
0
0
0
4
1
2
1
0
0
1
0
2
1
0
0
0
1
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
1
0
3
1
1
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
1
1
2
2
0
0
1
0
2
2
0
5
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
5
0
0
0
0
0
1
0
0
0
0
1
2
2
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
1
3
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
1
3
0
0
1
0
0
0
0
1
0
0
2
0
1
0
4
2
2
0
0
1
2
0
0
2
0
1
0
2
2
0
1
0
0
1
0
0
1
0
0
1
0
2
0
0
0
1
0
2
0
0
0
0
0
2
0
1
1
0
0
2
2
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
2
1
0
0
0
0
2
0
1
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
3
0
0
1
4
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
1
2
2
0
2
1
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
2
0
2
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
1
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
3
0
0
0
1
0
1
2
0
5
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
2
0
3
1
0
1
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
1
1
0
0
1
0
0
0
3
0
1
1
1
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
2
1
0
1
4
0
0
1
0
0
2
2
0
2
0
1
1
0
0
0
0
0
0
0
0
1
0
0
2
0
1
1
0
2
0
1
0
1
0
0
0
0
6
0
2
0
0
2
0
2
0
2
4
0
3
0
2
4
0
0
0
1
0
2
0
2
0
0
0
0
0
0
1
2
2
0
1
1
0
0
0
0
1
0
0
0
3
9
3
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
1
2
2
0
0
0
0
1
0
1
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
4
1
0
0
0
0
1
0
1
0
2
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
2
3
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
2
1
0
0
1
0
2
0
2
2
0
3
0
0
1
0
1
0
0
0
0
0
1
1
0
2
0
0
0
0
2
0
0
0
1
2
0
0
0
0
1
1
0
0
1
0
1
0
6
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
1
2
0
4
1
0
0
2
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
2
2
1
1
2
1
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
3
0
0
0
1
1
0
0
0
0
0
3
2
0
1
0
0
1
2
2
1
0
0
2
0
1
2
0
2
0
1
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
2
1
4
0
2
0
0
0
0
0
1
2
0
2
0
2
0
0
0
0
1
1
2
0
0
1
1
0
0
0
1
0
0
1
0
0
0
1
1
0
0
1
2
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
3
0
0
2
1
0
2
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
1
0
1
0
2
0
0
1
0
0
2
0
2
1
0
2
0
0
0
0
1
0
2
0
2
0
0
1
0
1
1
0
0
0
2
1
1
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
2
1
2
5
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
1
1
1
2
0
1
1
0
2
2
0
0
0
1
3
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
2
0
0
0
0
0
0
0
2
2
1
0
0
0
1
0
0
1
0
0
1
0
0
0
1
1
2
0
0
1
0
0
0
0
0
1
0
2
1
0
0
0
2
1
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
2
1
2
2
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
1
0
0
0
2
0
4
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
1
0
0
1
2
0
0
1
0
0
3
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
2
0
2
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
2
0
0
0
0
1
1
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
2
1
0
1
2
0
0
0
0
0
0
2
0
0
0
0
1
3
0
2
0
0
1
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
3
1
2
0
0
2
0
0
0
1
1
0
0
0
0
0
2
0
0
2
2
2
1
0
1
0
0
2
0
2
1
1
0
0
0
1
0
0
2
2
0
3
0
0
0
2
0
4
1
0
0
0
1
0
0
0
0
1
2
0
0
2
0
0
5
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
3
2
0
0
0
0
0
1
0
1
1
0
2
0
0
0
0
1
0
1
4
0
1
0
0
2
0
0
1
2
0
0
1
0
1
0
0
0
1
0
1
2
0
0
0
2
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
1
2
0
2
0
0
2
0
0
0
2
0
0
0
3
0
0
0
2
0
0
1
1
1
0
0
0
0
0
0
0
2
1
0
1
0
1
0
2
2
0
2
0
0
0
0
0
0
0
2
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
1
2
0
4
0
0
0
0
0
0
2
0
1
0
0
2
0
1
2
1
1
0
0
0
3
0
1
1
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
1
2
0
1
1
0
1
3
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
1
0
0
3
2
0
0
0
1
0
1
1
1
0
0
1
0
2
0
1
0
1
0
0
0
0
1
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
1
0
0
2
0
0
0
1
1
2
1
2
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
1
0
2
0
2
1
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
2
4
2
0
0
0
0
2
1
2
0
2
0
0
0
0
0
1
0
2
0
2
2
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
1
7
1
0
0
4
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
1
1
0
2
0
0
0
1
0
0
0
0
0
1
0
0
1
0
4
1
0
2
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
2
1
2
2
0
0
0
2
2
0
0
2
2
0
1
1
1
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
1
1
0
2
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
1
0
1
2
0
0
0
0
0
0
1
0
0
2
2
0
0
2
1
1
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
3
1
0
0
0
0
0
1
0
0
0
1
0
0
2
0
1
1
0
0
0
0
0
1
2
0
1
0
1
0
0
0
0
1
0
0
0
1
2
1
0
2
0
0
1
0
0
1
1
0
1
0
1
0
2
0
0
3
0
0
0
0
2
0
1
0
0
1
1
0
0
4
0
0
5
2
0
1
0
0
0
0
0
0
0
2
4
3
2
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
1
0
2
2
1
0
0
0
0
1
0
0
0
0
0
2
0
0
3
2
1
1
0
2
2
1
0
0
1
0
2
2
0
1
0
0
0
1
0
0
2
0
1
0
0
0
0
2
1
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
2
0
0
0
0
0
1
0
2
1
1
0
0
0
2
1
2
0
0
0
0
0
0
1
2
0
1
0
0
0
0
1
1
0
0
2
0
1
0
1
1
0
4
2
1
0
0
1
0
0
2
0
1
0
1
0
0
0
0
0
0
0
4
0
0
0
0
2
2
2
2
0
2
0
0
2
0
5
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
2
1
0
1
0
2
0
0
0
1
2
0
0
0
2
0
1
1
0
0
2
0
1
1
0
0
0
0
1
0
4
1
2
0
0
0
2
1
1
0
1
2
2
0
1
0
0
0
1
0
2
2
0
0
3
0
2
1
2
0
3
2
0
0
1
0
2
0
0
0
0
0
0
0
2
1
0
0
0
2
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
2
0
1
0
0
1
1
2
1
2
1
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
2
2
1
0
1
1
0
0
3
0
0
2
0
2
1
2
5
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
2
0
1
0
1
0
0
2
1
0
0
0
0
1
4
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
1
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
1
0
2
0
0
0
0
0
0
0
0
2
1
1
0
0
1
0
0
2
0
0
1
0
0
2
1
0
2
2
0
0
2
0
1
0
0
2
0
0
0
2
0
3
0
0
0
0
0
0
0
0
2
0
2
1
0
0
2
0
0
4
0
1
0
0
0
5
0
0
0
0
1
1
2
0
0
0
1
1
3
0
0
0
2
1
3
0
0
0
0
2
0
0
2
0
0
0
2
0
2
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
1
0
1
0
3
1
0
2
0
1
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
2
0
0
0
2
0
0
2
0
0
0
2
2
0
0
0
1
0
0
0
0
0
1
2
1
2
0
2
0
5
0
2
1
2
0
1
0
1
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
2
1
5
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
2
0
2
2
2
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
1
2
1
0
0
0
0
0
0
0
2
1
0
2
0
0
7
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
2
0
0
0
1
0
0
2
0
2
0
0
2
1
2
0
0
1
0
2
0
0
0
3
0
1
0
0
0
0
0
2
2
0
0
0
0
2
0
2
0
0
2
1
0
0
0
0
0
2
2
0
0
0
0
1
1
3
3
0
0
0
0
0
0
2
2
0
1
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
3
0
0
2
1
1
1
2
0
1
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
2
0
1
0
2
2
3
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
3
0
0
2
0
2
0
2
2
0
1
0
0
0
0
0
2
2
0
0
0
3
0
1
0
0
0
0
2
0
0
0
0
0
1
0
3
1
0
0
0
1
0
0
1
0
3
0
0
0
1
1
0
0
1
2
0
0
0
0
0
1
0
2
0
2
0
2
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
2
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
2
3
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
2
0
0
0
0
0
0
0
0
1
2
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
2
0
0
3
0
2
0
0
2
1
0
1
0
2
0
1
1
0
0
0
3
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
1
0
0
2
0
2
0
2
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
2
0
0
0
0
1
1
2
0
0
0
0
0
0
1
0
1
4
2
0
0
0
0
1
0
0
0
0
0
0
1
1
0
2
0
0
0
1
0
0
0
0
0
2
0
0
2
0
6
0
1
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
3
0
1
0
0
2
0
0
1
0
0
0
0
0
1
1
0
2
1
2
3
1
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
3
0
0
0
0
3
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
2
1
0
0
2
0
1
0
0
0
0
0
2
0
1
0
0
0
2
0
0
2
0
0
1
0
0
2
5
0
0
0
2
0
0
0
2
0
2
1
2
2
0
0
0
0
1
0
0
4
0
2
0
0
0
0
0
0
4
0
1
2
1
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
1
2
2
0
0
0
0
0
0
2
1
0
3
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
2
1
0
2
0
0
1
2
0
3
0
3
0
0
1
1
2
0
0
1
1
0
1
0
2
2
0
0
0
4
0
1
2
0
0
2
0
2
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
2
1
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
2
0
1
2
2
1
0
1
0
0
3
0
1
1
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
1
0
0
0
0
2
1
0
2
3
2
2
0
0
2
0
0
2
0
0
0
0
1
2
6
0
0
0
2
2
0
0
3
0
0
0
1
0
0
0
1
0
1
2
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
2
0
0
0
1
0
0
0
0
2
1
2
0
2
0
0
0
0
0
0
1
0
1
1
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
2
0
0
1
1
0
1
3
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
1
1
0
0
0
0
0
1
2
3
0
0
2
0
0
2
1
2
0
1
0
2
1
0
1
1
0
1
0
2
0
0
2
2
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
1
1
0
0
3
0
0
0
2
2
0
2
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
2
0
1
0
0
2
1
0
0
2
0
0
0
1
0
0
2
2
1
0
1
0
0
0
0
0
0
0
1
0
0
0
2
2
1
0
0
0
0
1
1
0
1
0
0
2
0
3
0
0
0
2
0
0
0
0
1
0
2
0
2
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
5
0
2
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
2
2
0
0
0
0
1
0
0
2
0
0
0
0
1
1
2
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
1
0
3
3
0
1
2
0
0
2
0
0
0
0
1
1
0
0
2
0
0
0
0
1
0
4
1
2
0
2
0
0
0
1
1
0
0
0
0
1
0
0
2
0
3
0
0
3
0
2
0
0
0
0
0
3
0
2
0
1
0
0
0
0
0
0
0
0
0
5
2
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
2
1
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
1
1
0
0
0
0
2
0
1
0
0
0
0
2
2
0
0
2
0
0
2
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
3
1
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
1
0
0
1
0
1
2
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
4
0
0
0
1
1
2
2
0
2
1
0
0
0
2
0
0
2
0
0
0
0
1
1
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
2
2
1
0
0
0
0
1
0
1
1
1
0
2
0
2
2
1
0
2
0
1
0
0
0
1
2
0
0
1
0
4
1
1
0
2
1
0
0
1
1
2
1
0
0
2
0
0
2
0
0
0
1
2
2
0
2
0
0
1
0
2
0
1
2
5
2
1
3
0
1
1
0
2
1
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
2
0
0
1
0
0
0
1
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
1
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
2
1
0
0
0
0
0
0
1
1
0
0
2
0
2
0
2
0
0
2
0
3
0
0
0
0
3
4
0
0
0
0
0
1
2
1
1
0
2
0
0
1
2
1
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
3
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
4
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
3
1
0
0
0
1
1
2
0
2
1
0
0
3
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
5
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
1
1
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
1
3
0
0
2
0
1
3
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
2
0
0
0
0
1
0
1
0
3
0
0
0
0
0
2
2
0
0
0
0
1
0
1
2
2
0
0
0
1
1
2
0
0
0
0
2
2
0
0
0
0
0
2
0
1
0
2
2
0
0
0
1
0
2
0
0
1
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
2
1
0
0
0
0
1
1
0
0
0
1
1
1
0
2
0
2
1
2
0
0
1
2
0
0
2
2
0
1
3
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
2
2
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
1
1
0
0
1
1
0
0
0
0
2
2
0
0
0
1
0
0
1
0
0
0
0
0
1
1
2
0
0
0
2
1
1
0
0
2
0
0
2
2
1
3
0
1
0
2
1
1
1
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
2
2
1
0
0
0
2
0
1
0
0
2
1
0
0
0
2
0
2
0
3
1
2
0
1
0
0
2
0
2
2
0
2
1
0
2
0
2
2
0
0
2
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
3
0
2
0
0
0
0
0
2
0
0
0
3
0
0
0
1
0
0
3
2
0
2
2
0
1
0
1
0
1
2
0
2
1
2
0
2
1
2
0
1
2
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
2
2
0
0
2
0
0
2
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
1
1
2
3
2
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
2
0
0
0
2
0
0
2
0
1
2
0
1
0
0
0
2
0
0
0
0
0
0
3
0
1
2
0
2
1
0
2
0
2
1
0
0
0
2
0
0
0
0
2
1
0
0
0
0
1
0
0
1
1
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
1
0
2
0
2
0
1
0
0
0
0
0
1
1
2
0
0
0
0
2
0
0
0
0
1
0
2
1
0
2
0
0
0
0
2
1
3
1
2
0
2
1
0
2
0
0
1
2
1
2
0
0
0
2
0
0
0
0
2
1
2
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
1
0
2
1
0
2
1
2
2
0
1
0
3
0
0
0
2
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
6
1
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
2
0
0
0
2
0
0
1
0
0
2
0
1
1
0
4
0
0
3
2
0
2
0
0
1
0
2
0
1
0
0
0
1
0
0
2
1
0
0
2
0
0
0
2
0
0
0
0
0
3
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
3
0
2
2
0
0
0
2
0
2
2
0
0
0
1
4
0
0
1
0
0
0
0
2
0
0
0
2
4
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
2
0
0
0
0
0
0
2
3
0
1
4
2
0
1
1
2
2
1
2
1
0
2
0
0
1
1
0
0
0
0
0
0
2
1
1
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
2
2
0
2
0
0
0
0
2
0
0
0
2
2
2
0
2
3
1
0
0
0
0
1
0
0
1
4
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
1
2
0
0
0
1
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
4
2
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
2
2
0
1
0
1
0
1
1
1
0
1
0
3
0
1
0
0
0
2
0
0
1
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
1
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
2
2
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
1
3
3
0
2
6
0
0
0
0
1
2
1
0
1
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
1
0
3
2
0
2
0
0
0
0
0
0
0
2
1
3
0
2
0
2
0
0
0
0
2
0
0
0
1
0
0
0
1
2
0
0
1
0
0
0
0
2
0
0
1
0
0
0
1
0
2
1
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
1
2
1
0
0
0
1
1
0
0
2
0
0
0
0
2
0
4
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
3
1
3
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
6
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
1
0
0
0
0
2
2
0
0
0
1
0
1
0
0
1
0
2
1
0
2
0
5
1
1
0
0
1
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
2
1
1
0
0
0
1
1
2
1
1
1
0
0
0
2
0
0
2
0
1
0
1
0
0
0
0
0
0
0
1
2
1
0
0
0
1
1
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
2
0
2
3
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
1
0
1
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
2
1
3
0
0
0
0
0
0
0
0
3
0
1
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
2
1
0
2
0
0
2
1
0
0
0
0
0
5
1
1
2
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
2
2
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
1
2
0
0
1
0
0
2
0
2
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
2
0
0
0
0
1
0
2
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
1
3
1
0
0
0
1
1
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
1
0
1
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
1
0
2
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
4
2
1
0
0
0
1
0
2
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
1
5
2
0
0
0
2
0
2
0
0
1
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
1
0
1
1
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
3
0
1
0
0
0
0
1
4
0
0
0
2
0
1
1
0
0
0
0
0
0
1
0
2
3
0
1
0
2
2
0
0
1
0
0
2
0
0
2
0
0
0
1
0
2
1
0
1
1
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
10
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
1
0
0
0
2
0
9
2
0
0
1
2
0
0
0
0
0
0
5
0
0
1
1
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
2
2
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
2
0
1
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
1
4
0
0
0
0
0
1
0
0
0
0
0
1
3
2
0
0
1
0
0
0
0
1
2
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
5
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
2
2
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
1
3
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
7
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
2
1
1
1
1
0
2
0
0
0
0
0
0
2
0
0
1
0
1
0
1
0
0
2
0
1
0
0
0
0
2
1
0
1
0
2
0
1
1
2
0
2
0
0
1
0
1
2
5
0
4
2
2
1
0
0
3
0
2
2
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
2
0
0
0
1
1
0
0
0
0
0
0
0
2
0
3
0
0
1
0
0
0
1
0
0
1
1
3
1
0
0
0
1
0
1
2
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
2
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
2
0
0
0
2
0
1
0
0
1
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
2
0
0
0
1
0
0
0
1
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
1
3
0
0
0
1
0
0
0
0
0
2
0
2
2
0
0
0
0
0
1
0
3
0
3
0
0
3
5
1
0
0
0
0
0
0
2
5
2
0
1
0
0
0
1
0
0
1
0
0
0
2
2
0
0
0
1
3
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
2
0
1
2
0
0
2
0
0
1
2
1
0
0
0
0
1
1
1
0
0
0
0
0
0
2
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
1
2
0
0
0
0
0
3
0
0
0
2
1
1
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
2
1
0
1
0
0
1
0
0
2
0
0
0
1
0
0
0
0
2
0
0
2
1
1
2
0
0
0
1
2
0
2
0
0
0
0
1
0
1
0
1
1
0
0
0
1
0
2
0
0
0
1
1
0
0
0
0
0
1
2
0
1
0
0
1
2
0
2
0
0
0
1
0
0
0
2
0
1
0
0
0
2
3
0
1
1
0
1
1
0
0
0
0
0
1
0
2
0
0
0
2
0
0
2
0
0
0
2
1
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
1
0
2
0
0
0
0
0
0
0
2
1
0
2
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
3
1
2
0
0
0
1
0
0
0
2
2
1
0
0
3
0
2
1
2
0
0
1
0
1
1
2
0
1
0
0
0
0
0
1
1
1
1
2
0
0
0
1
0
0
1
0
0
0
1
0
3
1
2
0
0
0
1
0
0
0
2
5
1
1
0
2
0
0
1
2
0
2
2
1
0
1
1
0
0
0
0
0
0
0
0
0
0
3
1
0
1
2
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
2
0
0
2
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
2
0
3
0
0
2
0
0
0
0
0
1
0
2
1
1
3
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
1
0
0
0
1
2
1
0
2
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
2
0
2
1
2
2
0
1
3
0
0
0
1
0
0
0
1
0
1
2
0
1
0
2
0
0
0
0
0
0
0
0
0
1
2
4
1
1
1
0
0
3
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
2
0
0
0
1
0
0
2
0
0
0
1
0
0
2
1
2
0
0
2
1
0
1
2
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
2
0
2
1
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
1
0
1
2
0
0
0
2
1
0
2
1
4
0
0
0
0
2
0
0
0
0
0
0
0
1
1
2
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
4
0
3
0
0
0
1
1
2
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
2
0
2
1
0
0
0
2
0
1
3
0
0
1
1
0
2
0
1
1
1
0
0
2
0
2
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
2
2
0
0
2
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
2
1
0
0
0
0
1
2
1
2
0
0
0
0
0
0
2
2
0
0
0
0
1
1
0
0
2
1
0
2
0
1
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
2
0
0
1
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
1
0
0
0
0
4
0
0
0
0
0
0
1
0
1
0
2
0
0
0
1
0
2
0
0
0
0
2
0
0
3
2
0
3
0
0
3
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
4
0
0
0
1
2
0
0
0
2
2
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
1
1
2
1
2
0
0
1
0
0
1
0
0
2
0
0
1
2
0
0
2
0
0
0
2
1
0
0
0
2
0
2
0
0
1
1
0
0
0
0
0
0
0
4
2
0
0
0
1
1
0
0
2
0
0
2
1
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
1
0
1
0
2
0
2
0
0
0
1
0
2
0
1
0
0
0
1
0
0
0
0
2
0
1
1
0
3
0
0
1
2
0
1
0
0
2
0
0
2
0
2
0
0
0
1
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
2
0
0
0
3
1
2
1
0
0
1
0
1
2
0
0
0
0
0
1
0
1
1
0
2
1
0
0
0
0
0
2
0
0
2
0
0
0
0
1
2
3
0
0
0
0
0
1
0
3
0
0
0
0
0
2
0
0
0
1
3
3
0
0
0
1
3
1
1
0
2
0
1
0
0
0
0
2
1
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
4
0
2
0
0
1
1
0
0
2
2
2
0
0
0
0
0
0
2
0
0
0
1
2
1
1
2
1
2
0
0
0
0
0
0
2
0
2
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
2
0
0
1
1
0
1
0
0
1
1
0
0
0
0
1
0
0
2
1
1
0
2
1
0
0
0
0
0
2
2
0
1
0
0
0
2
0
1
0
1
1
0
2
0
0
0
0
3
0
0
0
2
0
1
2
1
0
0
1
0
1
0
0
4
0
0
0
0
0
0
2
1
0
0
6
3
0
1
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
5
0
0
0
2
0
0
2
0
0
0
0
0
0
2
1
2
2
0
0
0
1
0
2
0
0
2
2
0
0
3
0
0
0
2
0
0
0
0
0
2
0
2
2
2
1
2
2
1
0
0
0
2
1
0
0
0
0
0
0
0
1
1
1
2
0
0
0
0
0
0
1
0
2
0
0
0
0
3
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
3
0
2
0
2
0
0
0
0
0
0
2
0
0
7
1
0
0
0
0
2
0
0
0
0
0
1
2
1
0
3
1
0
0
0
1
0
2
0
2
2
0
1
2
2
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
2
2
0
0
3
0
2
0
0
0
1
0
2
0
0
2
1
0
3
1
0
0
0
0
0
0
0
0
0
2
0
1
0
3
0
0
0
2
2
0
0
1
1
2
0
2
2
1
1
0
1
1
0
0
0
0
0
2
0
1
0
0
0
1
2
1
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
2
2
0
2
1
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
2
1
2
1
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
2
2
4
0
0
0
0
0
2
0
0
0
0
2
0
1
1
0
2
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
1
1
3
0
2
0
0
0
0
1
3
0
0
1
0
1
2
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
1
1
0
0
2
0
0
1
0
0
0
0
0
1
1
2
0
2
0
3
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
1
2
0
0
0
0
0
0
1
2
1
0
2
0
4
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
2
0
1
2
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
3
0
0
2
0
0
1
1
0
1
2
0
2
0
0
0
0
2
3
0
2
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
2
2
1
0
2
2
0
3
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
1
0
2
2
0
0
0
2
0
0
0
0
1
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
3
0
0
0
0
0
0
1
2
2
0
0
1
1
0
0
0
0
2
0
0
0
5
0
0
0
2
2
0
0
2
0
0
2
0
0
0
0
2
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
2
1
1
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
1
1
0
0
2
0
2
0
1
0
1
1
0
2
0
0
2
3
2
0
0
0
0
0
1
1
0
3
2
0
2
1
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
3
0
2
2
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
1
0
2
3
1
0
1
0
0
2
1
2
0
0
2
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
2
1
1
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
1
0
2
1
1
0
1
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
4
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
1
0
2
0
0
1
0
0
2
0
2
0
2
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
2
0
2
0
0
2
1
2
1
2
3
3
0
0
0
0
2
2
2
0
1
0
2
0
1
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
2
0
2
0
0
1
1
0
0
0
1
0
0
1
2
0
0
0
4
1
3
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
3
0
2
1
0
0
0
0
0
0
0
0
2
4
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
1
0
1
0
0
0
0
0
1
0
2
0
3
0
0
2
0
2
2
0
0
1
0
0
0
0
0
0
0
2
0
2
2
0
0
0
1
2
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
2
0
0
4
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
1
2
0
6
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
3
3
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
8
2
0
4
0
1
0
0
0
0
0
0
2
2
1
0
3
2
0
1
0
2
0
2
0
0
1
1
1
0
0
0
0
0
0
0
1
0
2
0
0
3
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
2
0
2
0
1
2
2
0
0
2
2
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
2
2
0
1
0
0
0
1
0
0
3
1
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
2
0
2
0
0
2
0
1
2
0
1
2
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
1
0
2
0
1
0
1
1
0
0
0
0
0
1
1
0
2
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
1
0
0
0
2
0
0
0
0
2
0
1
2
2
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
2
1
1
0
1
1
0
0
2
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
1
0
0
2
0
0
0
1
1
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
3
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
2
1
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
1
1
1
1
2
0
1
0
0
0
0
0
0
0
2
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
1
1
1
0
2
1
0
1
1
0
0
0
0
1
1
0
0
0
3
0
0
1
1
0
0
0
0
0
3
5
2
0
2
0
0
0
2
0
1
0
0
0
0
2
1
0
0
2
0
2
0
0
7
0
0
0
2
0
2
1
0
0
0
2
0
0
0
1
0
0
0
2
1
1
0
0
0
1
0
0
0
2
0
0
2
1
1
1
2
0
1
2
0
1
1
2
0
0
0
1
1
2
0
1
1
0
2
0
0
1
1
1
0
0
2
0
0
1
0
0
0
0
1
0
0
0
1
0
2
0
3
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
1
0
2
1
0
0
0
1
2
0
2
0
0
2
0
0
2
0
3
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
2
0
0
2
0
0
0
0
2
0
0
1
1
2
1
1
0
0
0
0
2
0
0
2
0
4
0
0
2
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
2
2
0
1
0
0
0
1
0
0
0
0
0
2
0
1
2
0
3
2
0
0
0
2
0
2
0
0
2
1
0
0
0
0
0
1
0
0
0
0
1
2
3
0
0
0
0
3
0
1
2
0
0
0
1
1
0
2
1
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
1
0
1
2
0
0
1
2
0
1
0
0
1
3
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
2
2
2
1
0
0
0
1
2
0
0
0
1
0
1
0
0
1
0
0
0
2
0
0
1
0
3
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
2
2
0
1
0
0
0
0
0
1
1
2
0
0
0
2
1
1
2
0
0
0
0
0
0
2
0
0
1
2
2
2
0
2
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
3
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
4
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
2
0
0
0
0
2
0
0
1
3
0
3
0
2
2
0
0
0
0
0
0
1
0
1
2
0
1
1
0
0
0
2
2
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
3
0
0
0
1
3
2
0
0
1
2
2
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
10
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
1
1
0
2
0
1
1
0
1
0
2
1
1
1
0
0
0
1
2
0
2
0
0
0
1
0
0
0
0
0
0
0
1
2
2
0
1
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
2
0
2
0
0
0
1
0
0
0
0
0
3
0
0
1
0
0
1
1
2
1
0
0
0
0
2
0
4
0
0
1
0
0
0
0
0
1
0
0
0
2
1
4
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
1
2
0
1
0
2
1
1
1
0
0
0
0
0
2
1
0
0
1
0
0
1
0
2
0
0
2
2
0
2
0
0
0
1
0
0
0
1
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
2
0
0
0
1
1
1
7
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
1
1
0
0
1
0
0
2
0
0
6
0
0
0
0
2
0
0
0
0
0
1
2
2
2
0
3
3
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
2
2
2
2
0
0
1
0
0
0
1
0
2
1
3
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
1
0
1
2
0
0
0
0
0
2
0
0
10
2
1
0
1
2
0
2
0
0
0
0
0
0
0
2
1
2
0
2
0
0
0
0
2
2
0
0
2
0
0
2
2
0
0
0
0
1
0
1
2
0
0
1
4
0
1
0
0
1
0
0
0
0
0
0
3
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
2
0
0
0
1
0
1
0
0
0
0
0
1
4
1
3
1
0
1
1
1
0
1
0
1
0
1
0
0
0
0
0
1
2
0
7
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
1
0
0
0
2
0
0
0
0
2
3
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
2
1
0
0
0
0
0
2
4
0
0
0
0
1
3
2
0
0
0
0
1
2
0
2
0
0
0
3
0
0
0
1
0
0
3
0
1
0
2
3
0
2
0
0
2
2
1
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
2
0
1
1
0
0
1
2
0
0
0
1
2
1
0
0
0
0
0
1
2
0
2
0
1
0
1
0
1
3
1
0
0
1
0
0
0
0
0
0
1
1
2
0
0
1
2
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
1
2
0
0
2
2
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
4
0
0
0
2
2
1
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
1
3
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
4
0
1
0
0
0
0
2
0
2
0
0
0
2
3
0
0
0
2
2
0
2
0
0
3
1
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
2
0
2
2
0
0
0
0
0
2
1
0
1
1
2
0
0
3
1
2
0
2
0
0
0
9
1
2
1
1
2
0
0
1
0
2
5
0
1
0
3
0
0
0
1
2
1
2
0
0
0
1
2
0
3
0
2
0
0
0
0
0
0
1
2
0
0
0
3
0
2
0
0
0
0
5
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
2
2
0
0
0
1
0
0
0
1
1
0
2
0
1
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
1
1
3
0
0
0
0
0
0
0
3
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
2
1
0
0
0
1
2
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
2
0
0
3
0
0
0
1
0
0
0
0
1
0
1
1
2
0
1
0
1
0
0
0
0
3
4
0
0
0
2
0
3
0
0
1
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
2
0
1
0
0
1
0
0
0
0
2
0
2
0
2
1
1
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
2
0
2
2
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
2
2
2
0
0
1
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
2
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
2
0
0
0
1
2
3
0
0
1
0
0
0
0
0
0
0
1
0
0
2
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
1
0
2
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
1
0
2
0
0
0
1
1
0
2
2
0
0
0
0
3
0
0
2
0
0
1
1
2
0
1
0
0
2
0
0
0
0
0
1
1
0
1
0
3
1
2
0
0
1
1
0
3
0
0
2
1
1
0
1
1
2
2
0
2
2
0
1
0
0
0
3
0
0
2
1
0
0
2
1
1
1
0
0
0
2
1
0
2
0
0
2
0
0
0
1
0
1
0
0
2
2
1
2
0
0
0
0
2
0
1
0
0
0
0
2
0
0
1
0
2
0
2
1
1
2
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
1
0
0
1
0
0
0
0
1
9
0
0
0
0
1
0
0
2
0
1
0
0
0
1
0
0
0
2
1
0
1
1
0
3
0
0
0
2
0
0
1
2
1
0
2
2
0
0
0
7
1
0
0
2
1
0
2
2
1
0
0
2
0
0
0
2
2
0
0
0
0
1
1
0
0
1
1
0
2
1
0
0
0
0
2
1
0
2
1
2
2
0
0
1
0
0
0
0
0
2
1
0
2
2
1
0
0
3
3
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
4
0
2
0
2
2
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
2
1
1
0
0
0
1
0
0
0
1
0
0
1
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
2
3
0
0
1
0
0
0
0
0
1
1
0
0
0
0
2
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
1
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
2
2
0
0
2
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
2
2
0
0
0
0
0
0
0
1
0
4
0
1
0
0
0
2
2
0
0
2
0
0
0
0
1
1
0
2
1
0
0
0
0
1
0
0
1
2
2
0
2
0
0
0
0
1
0
1
1
0
0
2
2
0
3
0
0
0
2
0
0
1
0
0
0
1
0
1
0
2
0
0
1
0
0
0
0
0
0
0
1
1
2
1
0
1
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
4
1
0
2
1
0
0
2
0
2
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
1
0
0
1
2
0
0
0
0
0
1
1
0
0
0
1
4
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
1
0
2
0
0
2
1
1
2
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
5
2
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
2
1
0
0
0
2
2
0
0
0
2
1
0
2
2
0
0
0
0
2
0
0
2
3
2
0
0
0
0
0
0
0
1
2
0
1
1
0
0
0
1
5
0
0
3
1
0
1
0
0
0
0
2
2
2
0
0
0
1
0
0
0
2
0
0
0
1
0
2
0
1
0
0
1
0
3
0
0
1
2
3
0
0
1
0
1
0
0
1
1
0
0
2
1
0
2
0
0
0
0
1
0
3
0
3
0
0
2
0
2
0
1
2
0
0
0
0
1
4
0
0
1
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
1
0
1
0
2
0
1
0
0
0
1
0
0
0
2
0
0
0
2
2
0
1
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
2
2
1
2
0
1
1
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
2
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
2
1
0
0
2
0
2
2
0
5
0
0
0
2
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
1
1
2
0
0
0
2
0
2
0
0
2
1
0
0
1
2
2
0
2
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
1
0
0
2
0
0
0
0
2
1
0
2
0
6
2
0
0
1
3
0
2
2
1
0
0
0
0
3
0
0
2
0
1
0
0
0
1
2
2
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
2
2
0
0
0
0
0
0
4
1
0
0
1
0
1
1
0
0
1
0
0
2
0
0
2
1
1
2
0
0
0
1
2
0
2
0
1
1
0
1
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
1
1
0
0
0
0
1
2
0
0
2
2
0
0
0
0
0
1
0
0
3
0
0
1
0
0
0
0
0
0
4
0
0
0
0
2
2
0
0
0
1
0
0
0
1
0
0
1
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
1
0
0
0
2
3
1
0
1
1
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
1
0
0
3
0
0
1
2
2
0
0
1
0
1
2
0
0
0
1
1
0
2
0
2
0
0
0
0
0
0
0
0
0
2
1
1
2
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
5
1
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
2
2
0
1
0
1
0
0
0
0
1
0
2
0
0
0
1
0
0
2
1
1
0
0
1
2
0
0
0
0
2
0
1
0
2
0
0
1
2
0
0
0
1
2
0
2
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
1
0
2
1
0
2
0
1
0
0
0
1
1
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
1
2
1
0
2
2
0
0
2
0
2
1
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
1
0
0
0
0
0
0
1
2
0
1
0
0
2
0
0
0
0
0
2
1
2
0
1
1
0
0
2
0
2
0
0
0
0
0
2
2
1
2
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
2
2
0
1
0
0
0
1
1
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
6
0
0
0
0
0
0
2
0
0
1
0
0
1
0
2
2
0
1
2
1
2
0
0
1
4
1
0
0
0
1
0
0
0
0
2
1
2
2
1
0
1
0
3
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
1
0
12
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
1
0
1
1
0
0
5
2
0
0
0
1
1
0
3
0
2
1
2
0
0
0
1
0
2
0
0
1
0
0
0
1
0
0
2
0
1
0
0
0
3
2
0
0
0
2
0
0
0
1
0
0
1
1
0
0
1
0
0
0
2
0
2
1
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
1
1
0
0
2
0
0
0
0
1
0
2
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
1
0
1
2
0
1
2
0
4
0
0
0
2
2
0
0
4
0
0
1
2
1
4
0
0
0
0
1
2
0
0
0
0
1
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
1
1
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
2
1
0
0
1
0
0
0
0
2
0
0
1
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
2
0
2
0
0
2
0
0
0
1
2
0
2
0
0
0
0
0
0
1
0
2
0
2
1
0
1
2
0
2
0
0
2
2
2
0
0
0
2
0
0
0
0
2
1
0
2
0
0
1
0
1
2
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
1
0
0
1
0
0
1
2
0
2
0
0
1
2
0
0
0
2
0
1
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
1
2
2
2
0
0
0
0
0
0
2
0
0
1
0
4
2
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
1
2
1
2
0
0
0
0
0
1
0
1
0
0
2
2
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
2
0
0
2
0
2
0
0
2
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
1
0
2
0
0
2
0
1
1
2
0
0
0
0
0
0
0
2
4
2
0
0
0
2
0
1
0
0
0
0
2
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
2
0
0
2
0
0
2
0
3
0
0
0
0
0
0
1
0
0
2
0
1
1
0
0
2
4
0
1
1
1
2
0
0
0
0
0
0
1
2
2
1
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
1
0
2
2
1
2
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
6
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
1
1
0
0
1
0
5
0
2
0
0
2
0
0
2
4
1
0
2
2
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
1
1
0
0
0
0
0
0
1
0
0
0
0
3
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
2
1
0
0
0
0
1
0
0
1
0
2
2
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
2
3
1
0
1
0
2
0
3
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
1
0
1
1
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
3
0
2
1
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
1
1
1
0
1
0
2
2
0
1
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
1
0
1
5
0
1
0
1
0
2
0
0
0
2
0
2
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
1
0
0
0
2
2
0
2
0
0
0
2
0
0
4
0
0
0
0
2
0
0
2
0
0
3
0
1
1
1
0
1
0
1
0
0
0
0
0
0
1
0
0
2
2
1
0
1
0
1
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
1
0
2
0
1
4
3
0
1
1
2
0
1
0
1
2
0
0
0
0
0
2
0
1
0
0
1
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
2
0
0
0
0
0
0
0
2
0
2
2
2
0
2
2
0
0
0
0
0
1
2
0
2
2
1
0
0
0
0
0
0
0
0
2
0
2
2
0
1
1
0
0
0
2
2
0
1
1
2
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
2
2
0
0
1
0
0
0
2
1
1
1
0
0
0
0
1
3
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
2
1
1
0
0
0
1
1
0
0
0
1
1
0
0
2
2
0
0
0
1
0
5
0
2
0
1
2
0
3
0
2
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
1
1
0
1
0
0
0
2
1
2
0
2
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
2
0
2
0
0
0
2
0
0
0
0
2
0
0
1
0
1
0
1
0
2
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
2
2
2
3
0
0
0
1
0
1
0
1
0
1
2
5
0
2
2
2
0
2
0
0
0
0
2
1
0
0
1
2
2
0
1
1
0
0
2
2
0
0
0
2
1
1
1
0
1
2
0
3
2
0
1
1
0
0
0
0
1
0
2
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
2
0
2
1
0
3
0
0
3
0
0
0
1
0
0
3
0
0
0
0
2
1
1
1
0
0
0
0
0
0
0
2
2
2
0
0
2
1
2
0
3
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
1
0
0
1
0
0
0
2
3
0
0
0
1
2
1
0
1
0
0
0
1
0
1
2
3
0
0
0
4
0
0
0
0
0
3
2
0
2
1
2
0
2
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
1
1
0
0
0
0
0
1
0
0
0
1
0
0
2
3
0
2
0
1
0
0
1
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
2
0
1
0
1
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
2
2
0
2
2
0
0
0
1
0
1
1
2
0
1
0
2
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
1
3
0
2
0
0
0
0
0
0
3
0
0
2
1
2
0
1
0
0
0
0
0
0
2
1
0
0
0
2
3
1
0
1
0
1
0
0
0
0
1
2
0
1
1
0
0
0
0
0
0
0
0
2
1
0
0
1
2
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
3
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
2
2
0
0
0
2
0
4
2
0
0
0
0
0
1
5
0
0
2
0
0
0
0
0
0
3
0
1
0
0
1
0
2
0
2
1
0
0
0
1
0
2
0
1
0
0
1
0
0
0
0
2
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
1
4
1
0
2
0
0
0
0
0
1
0
2
4
2
0
0
0
0
1
2
0
0
0
2
2
1
0
0
2
1
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
2
0
1
1
0
2
0
0
0
0
0
0
2
2
0
1
2
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
1
0
0
1
0
2
1
0
1
0
3
4
1
2
0
0
2
0
1
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
3
1
0
0
0
0
0
2
0
0
0
1
1
0
0
3
0
2
0
3
1
0
0
0
2
1
0
0
0
0
0
0
1
1
0
2
0
1
0
1
0
0
3
0
1
0
1
0
0
1
1
1
0
0
0
0
0
0
2
0
0
6
0
1
2
0
2
0
0
0
0
0
1
1
2
0
0
2
0
0
0
1
0
2
0
0
0
0
0
1
2
2
0
0
1
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
1
1
0
1
0
0
0
0
0
1
0
3
1
2
0
0
1
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
1
0
0
1
2
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
2
0
1
2
1
0
0
2
0
1
0
0
1
1
0
0
2
1
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
3
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
2
0
0
0
2
0
0
0
1
0
1
0
0
1
0
1
32
1
1
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
1
3
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
1
0
0
0
0
2
0
0
0
1
0
0
1
0
2
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
2
2
0
0
0
0
0
2
0
0
0
0
1
2
0
0
2
2
2
2
2
0
0
2
0
2
0
1
0
0
2
0
1
1
0
1
0
1
0
2
0
1
2
0
2
1
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
1
0
1
2
0
0
2
0
1
0
0
2
2
0
0
0
2
1
0
1
1
0
0
1
0
0
2
0
0
0
0
0
1
2
0
0
0
0
1
0
0
1
0
0
0
2
0
1
1
1
0
2
0
1
0
0
1
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
2
2
2
0
2
2
0
0
0
0
1
0
0
4
1
0
0
0
0
3
1
2
0
3
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
2
2
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
1
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
2
0
2
0
0
0
0
0
0
4
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
2
0
0
1
0
0
1
0
0
1
2
1
0
1
0
2
0
0
0
1
1
0
2
0
0
0
0
0
2
0
2
0
2
0
0
0
0
1
1
1
0
0
2
0
0
0
2
0
2
0
1
0
0
2
1
1
0
1
1
0
0
3
1
0
1
2
1
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
3
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
2
1
0
0
0
2
0
2
1
0
2
0
0
2
0
0
4
1
0
0
0
1
1
2
2
3
2
0
0
0
0
0
0
1
0
0
3
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
1
0
0
0
2
0
0
1
0
1
2
1
0
1
0
2
1
2
0
2
0
0
0
0
2
3
0
1
0
0
1
0
0
0
1
0
2
0
0
4
0
0
1
0
0
0
0
0
0
0
2
1
1
0
0
2
0
2
0
0
0
0
0
0
0
0
3
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
3
0
2
2
0
2
1
0
0
2
0
0
7
2
0
2
0
0
0
0
1
2
0
2
2
0
2
0
2
1
2
0
1
1
0
1
0
0
0
0
2
3
0
0
0
0
0
0
1
1
2
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
1
0
0
0
0
1
0
0
2
2
0
2
0
1
0
1
0
0
0
0
1
0
2
1
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
2
2
0
0
1
3
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
6
1
0
0
0
0
0
0
0
0
0
1
0
2
1
0
2
1
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
1
0
3
2
0
1
0
0
1
0
1
2
0
2
1
2
2
1
2
2
1
0
3
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
2
1
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
1
3
0
0
0
0
0
1
0
3
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
3
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
4
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
2
3
1
1
0
0
1
1
0
0
0
0
1
2
0
1
0
0
2
0
0
0
2
1
0
6
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
2
0
2
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
2
0
2
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
2
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
2
0
0
3
0
1
0
0
0
0
2
0
0
2
0
0
0
1
3
2
0
0
0
1
0
0
0
2
1
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
2
0
0
3
0
0
2
0
0
0
0
1
1
0
3
0
0
0
1
0
1
2
2
1
1
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
2
3
0
0
2
1
0
2
0
0
0
2
1
0
2
0
0
2
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
3
2
0
1
0
0
0
2
0
0
0
0
1
0
2
1
1
1
1
0
0
1
0
0
2
0
0
0
0
0
0
0
2
1
2
0
0
1
2
0
0
0
0
1
0
0
0
0
1
2
1
0
0
2
1
2
1
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
2
1
0
0
0
1
1
2
1
0
0
0
0
1
0
0
0
2
1
0
0
0
1
0
0
2
0
2
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
2
0
0
0
0
2
0
0
0
1
2
1
0
0
2
0
1
0
0
1
2
1
0
0
0
0
0
2
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
2
0
0
0
0
2
2
0
0
4
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
3
0
0
0
1
0
2
1
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
2
2
0
0
0
2
0
0
1
0
2
0
1
0
0
0
0
0
0
2
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
2
0
1
1
0
0
0
2
2
0
0
0
2
0
0
1
0
1
1
0
0
1
0
0
0
2
1
2
2
0
0
0
1
0
1
1
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
2
0
2
2
0
0
0
0
1
2
2
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
2
2
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
2
0
3
2
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
3
2
3
1
2
1
1
0
0
0
0
3
0
0
2
0
0
1
2
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
1
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
2
1
0
0
0
0
0
0
0
1
0
0
1
1
2
1
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
3
2
2
1
2
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
1
0
0
1
0
0
1
0
0
0
0
3
2
0
1
0
0
2
2
0
1
1
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
1
0
2
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
3
2
1
2
0
2
0
2
1
0
0
0
2
0
0
1
0
1
0
0
1
0
0
2
0
2
3
0
2
0
0
0
1
0
1
1
2
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
3
1
0
0
0
0
0
0
1
2
0
0
0
0
1
0
1
0
2
1
0
1
0
2
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
2
0
1
2
0
2
0
0
1
0
0
0
0
1
2
0
2
0
0
0
0
0
2
0
0
1
0
1
0
1
1
0
0
0
0
0
1
0
1
0
2
0
1
0
2
0
0
1
0
0
3
1
2
2
0
1
2
0
0
0
4
0
0
3
1
2
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
3
0
1
0
2
0
0
1
0
0
0
0
0
2
0
1
1
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
1
1
2
0
0
0
1
0
0
2
0
0
7
0
0
0
0
0
0
2
0
0
0
0
0
1
0
3
2
0
1
0
0
0
1
0
1
2
1
3
0
0
0
0
2
2
1
2
2
0
0
0
1
0
0
0
0
2
1
2
0
0
1
0
0
0
0
1
0
0
2
2
0
0
0
1
1
0
1
0
0
0
0
0
1
2
2
1
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
2
1
1
0
2
3
0
1
1
0
0
2
0
0
0
0
3
0
1
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
6
0
0
0
0
0
0
0
2
0
3
0
2
0
2
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
3
0
1
0
1
2
4
0
0
2
0
1
0
0
0
1
2
0
2
0
0
1
4
0
2
0
1
0
2
1
1
2
1
0
0
0
0
0
0
2
2
1
2
0
1
1
2
1
1
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
1
1
0
0
2
0
1
1
0
2
2
2
0
0
0
2
0
1
1
0
7
2
4
2
1
1
2
0
0
0
0
0
0
0
1
1
0
0
1
4
0
0
0
0
0
0
0
0
1
2
0
0
0
3
0
2
0
0
0
0
0
1
1
0
1
0
0
0
0
0
2
0
0
0
2
2
0
0
1
0
2
2
0
0
2
1
2
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
1
1
0
1
0
0
2
2
0
2
2
0
0
0
1
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
1
0
0
1
2
0
0
0
0
2
0
0
0
1
1
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
1
0
0
1
1
2
0
0
0
0
1
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
2
2
0
0
1
0
0
0
0
0
0
1
0
3
2
0
0
0
0
0
0
0
0
0
1
0
2
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
1
0
0
1
0
0
0
2
0
2
3
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
2
2
0
0
1
0
2
0
0
0
1
0
0
2
0
0
0
1
0
1
2
0
0
2
2
0
0
3
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
2
0
2
0
1
2
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
2
0
2
0
1
2
0
0
0
3
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
3
2
0
0
0
0
1
1
0
0
1
0
0
2
0
0
0
0
6
0
1
0
0
1
0
0
0
0
0
0
2
0
0
2
0
2
1
2
2
0
2
0
0
0
0
0
0
0
0
2
0
2
1
0
0
1
0
1
0
2
2
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
2
3
2
2
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
4
2
0
0
1
0
0
0
0
0
0
2
1
2
1
0
0
1
1
0
2
2
0
0
2
0
0
0
0
0
0
0
4
1
1
1
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
2
1
2
0
1
0
0
2
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
1
0
5
2
0
2
0
0
1
0
0
0
1
0
1
0
0
0
1
1
1
0
1
2
0
1
0
0
1
0
1
1
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
2
0
0
6
0
0
2
0
1
0
1
0
3
0
0
0
0
0
0
0
1
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
1
1
0
0
0
2
0
1
0
0
0
0
1
0
1
0
0
2
1
1
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
2
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
1
0
0
1
0
0
0
2
2
1
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
2
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
2
0
2
1
2
0
2
1
0
0
0
0
0
1
0
1
3
0
0
0
0
0
0
1
5
0
2
1
0
0
1
1
0
1
3
0
0
0
0
0
0
0
0
0
1
1
1
0
2
0
0
2
1
2
0
0
1
0
4
0
0
0
0
0
0
0
2
1
0
2
0
2
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
2
1
0
0
0
0
2
0
0
1
0
2
2
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
2
0
0
0
0
3
0
1
0
2
0
0
0
0
2
0
0
0
1
0
0
2
2
0
0
0
0
0
0
2
2
1
1
0
0
2
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
2
0
3
0
0
0
3
1
0
0
2
0
0
0
0
5
0
0
2
0
2
0
1
0
0
0
2
1
0
0
2
1
1
0
1
0
0
0
0
0
2
2
2
0
0
0
0
1
3
0
1
0
0
0
0
1
0
2
1
0
2
0
2
0
4
0
1
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
1
2
0
0
1
1
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
3
0
0
1
0
1
0
2
0
0
0
1
0
1
1
1
0
0
0
3
1
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
2
0
0
0
2
1
2
0
0
2
0
0
1
2
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
2
0
2
0
0
1
0
2
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
5
3
1
0
2
0
1
0
0
0
0
0
1
0
2
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
2
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
1
0
1
0
2
0
1
0
0
3
4
0
1
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
3
0
2
1
0
0
0
2
0
0
2
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
2
2
0
1
3
0
0
0
0
0
0
2
3
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
2
0
1
2
0
0
1
0
0
1
0
0
0
3
0
1
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
2
0
0
0
1
0
0
0
1
0
0
2
0
0
0
2
1
2
0
0
0
2
1
2
0
4
0
0
0
0
1
2
0
0
0
0
2
0
2
1
0
0
1
0
1
2
1
1
2
0
1
0
0
0
2
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
2
1
0
0
2
0
1
0
0
0
1
2
1
2
0
0
0
0
0
0
0
2
2
0
0
2
0
2
1
2
0
0
0
0
0
0
1
0
0
2
0
0
0
1
2
0
2
0
2
0
1
0
1
2
0
0
0
0
1
0
1
0
0
0
0
0
2
0
2
0
1
0
2
0
2
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
1
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
3
3
0
0
0
0
1
0
0
2
0
0
1
1
1
0
2
0
2
0
0
0
0
1
0
0
0
0
1
0
1
2
0
2
0
0
1
2
1
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
1
0
0
1
0
2
1
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
1
0
1
0
1
0
0
2
0
1
0
1
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
2
0
0
2
0
2
0
0
0
0
0
0
0
1
0
3
0
0
0
0
1
2
0
1
0
0
1
0
2
2
0
0
0
0
2
3
0
0
1
0
2
1
0
2
1
0
0
3
0
0
0
2
2
1
0
0
0
0
0
2
2
0
0
2
0
1
0
2
0
2
0
1
0
2
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
2
0
0
2
2
0
2
1
0
0
0
2
1
3
0
0
0
1
2
2
0
0
0
2
4
2
0
0
2
0
0
1
2
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
2
0
0
1
0
0
1
1
0
2
0
2
2
0
1
0
0
0
0
0
0
0
3
0
0
2
1
0
1
2
2
1
1
0
0
0
0
0
0
0
0
0
5
0
0
0
1
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
2
1
1
0
0
1
0
0
1
0
0
0
1
1
1
0
0
2
0
0
0
1
0
1
0
0
0
1
2
1
1
2
0
2
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
1
1
1
0
1
2
0
0
0
0
1
1
2
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
2
0
2
3
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
2
0
0
0
2
0
1
1
0
0
0
0
0
2
0
2
1
0
0
0
2
2
1
0
0
0
2
0
0
0
0
1
1
0
0
0
1
1
1
0
0
0
0
0
0
0
2
2
2
1
2
0
0
1
0
0
0
1
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
2
0
0
0
1
0
0
1
0
2
2
1
0
3
0
0
2
1
0
1
3
0
0
1
0
0
0
0
0
1
0
0
1
0
1
4
0
0
0
1
0
2
0
0
3
2
0
2
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
2
1
1
2
0
2
0
2
2
1
0
0
0
1
0
0
2
2
1
1
0
0
0
0
1
0
2
3
1
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
2
2
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
3
2
2
0
0
2
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
2
1
0
2
0
1
1
0
1
0
0
0
3
0
2
1
2
0
0
0
0
0
3
0
0
2
0
0
1
1
0
0
0
0
0
0
1
0
0
0
2
0
3
0
1
2
2
0
2
0
0
0
2
2
0
0
0
0
2
1
0
0
2
1
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
1
2
2
0
3
0
1
0
0
0
1
1
1
1
0
0
0
0
1
1
1
1
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
1
0
0
2
0
0
1
0
0
0
0
1
0
1
0
2
0
0
2
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
1
0
2
0
0
0
2
0
1
2
0
0
0
0
0
0
0
1
0
1
3
0
0
1
2
0
2
1
2
2
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
2
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
1
0
0
2
2
0
0
2
0
2
0
0
1
0
1
0
2
2
2
0
1
0
0
0
0
0
1
0
2
1
0
2
2
2
0
1
0
0
1
0
0
1
0
0
0
2
0
0
1
1
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
3
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
1
0
0
0
1
1
2
0
0
0
0
2
0
2
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
4
0
0
0
0
1
0
0
0
0
2
0
0
1
2
0
0
2
0
0
1
3
1
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
2
0
1
0
0
0
0
0
0
1
0
2
2
1
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
2
2
0
0
0
0
1
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
1
0
2
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
2
0
0
0
3
1
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
2
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
1
2
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
1
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
1
0
1
1
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
1
3
2
0
0
0
0
1
0
1
0
1
2
0
0
2
1
0
1
1
0
0
0
0
0
0
0
0
2
1
5
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
3
2
0
0
1
0
0
1
2
0
0
0
0
2
1
0
0
2
0
0
0
1
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
2
0
0
3
2
0
0
0
0
1
2
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
1
3
0
1
0
2
0
1
15
0
1
0
2
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
2
0
1
0
0
1
0
0
2
0
0
2
2
0
0
1
0
0
0
1
5
2
0
0
0
1
0
0
0
2
1
2
0
0
0
0
0
3
0
0
0
0
2
1
0
1
0
0
0
1
0
2
0
0
0
0
1
0
1
0
0
0
0
0
2
0
1
1
0
0
1
0
1
1
0
1
1
2
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
2
0
0
0
0
1
0
0
0
0
2
0
2
0
0
2
0
1
1
2
0
0
0
0
1
0
0
0
0
0
0
0
5
1
0
1
2
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
2
0
2
1
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
2
0
1
0
2
0
0
0
1
0
0
0
0
0
2
2
0
1
0
0
2
0
0
2
0
1
0
0
0
0
3
5
0
0
0
0
0
0
2
1
0
0
0
4
3
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
2
1
0
0
0
0
0
1
1
0
0
2
0
0
1
2
0
0
2
0
0
2
0
0
0
0
2
0
0
2
2
2
0
0
0
0
2
0
0
0
0
0
0
0
3
0
1
1
1
1
0
0
1
3
5
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
2
2
0
1
0
1
0
2
0
1
0
1
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
2
0
1
1
3
0
2
0
0
0
0
1
0
1
2
1
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
1
2
0
0
1
0
0
2
0
1
1
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
2
1
0
0
1
0
2
2
0
0
0
0
0
2
1
0
1
0
2
0
0
0
1
0
2
0
2
2
0
3
2
2
0
4
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
4
0
1
0
2
0
0
0
0
0
0
0
0
0
0
3
1
2
0
3
0
0
0
2
7
0
1
2
1
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
3
2
2
0
0
0
0
3
4
1
0
0
0
0
0
1
1
0
0
1
0
2
1
1
0
1
1
1
1
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
1
0
0
2
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
1
1
1
0
4
1
0
0
0
1
0
0
0
0
0
3
0
1
0
2
1
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
2
1
2
0
0
0
0
0
0
0
0
0
3
0
2
0
2
1
0
0
1
2
0
0
0
0
2
2
8
1
2
2
1
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
2
0
0
0
0
0
0
2
1
1
0
2
1
0
0
0
0
0
0
0
2
0
1
0
2
3
0
2
0
2
0
0
0
2
2
0
0
2
1
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
3
3
2
0
0
0
0
0
0
2
0
1
0
1
1
0
0
0
3
0
2
0
0
0
0
0
0
2
0
0
1
0
0
1
0
3
0
0
0
1
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
1
2
1
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
4
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
2
2
0
0
0
0
1
0
0
0
0
1
0
0
3
0
0
0
0
1
0
0
0
2
0
0
2
0
1
0
1
0
0
0
0
1
0
1
0
0
0
1
1
0
1
1
2
0
0
0
2
0
0
0
0
0
1
1
0
0
0
1
0
0
0
2
2
1
1
0
0
4
0
0
2
0
0
2
0
1
0
0
0
0
2
0
0
0
2
0
3
0
0
0
0
2
0
1
0
0
2
0
0
4
0
0
0
0
0
0
4
0
1
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
1
2
1
0
1
0
2
0
0
0
0
0
0
0
1
0
2
1
2
0
0
1
2
0
1
0
0
1
1
0
1
1
0
0
1
1
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
1
0
1
1
1
2
2
0
2
2
2
1
2
0
1
1
0
0
1
0
0
0
1
0
1
0
0
1
3
2
0
2
1
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
1
3
0
1
1
1
1
0
1
0
2
2
0
1
0
1
0
2
0
0
1
0
2
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
1
1
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
2
0
5
0
0
0
1
0
0
0
1
0
2
0
0
0
0
3
2
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
2
0
0
1
2
0
3
2
0
0
2
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
2
2
0
1
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
2
2
2
3
0
0
1
0
0
0
0
2
0
2
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
1
1
0
0
0
0
2
0
0
0
2
0
2
1
0
2
3
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
3
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
2
0
0
0
0
0
0
0
1
0
0
2
0
2
1
2
0
0
0
0
1
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
2
1
0
2
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
2
2
0
2
0
2
0
0
0
0
1
2
2
0
0
1
0
2
0
0
2
1
2
1
2
0
0
2
0
0
0
1
1
0
0
0
0
0
3
0
1
2
0
0
0
0
0
0
1
3
0
2
2
0
0
0
0
0
1
0
0
3
1
0
0
0
0
0
0
4
0
0
1
3
0
1
0
0
0
0
0
0
0
0
0
1
2
2
0
2
0
0
0
0
0
0
3
2
1
0
0
2
0
0
2
0
2
0
0
0
0
0
2
0
1
0
1
0
0
0
0
1
0
3
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
2
0
2
0
0
0
0
0
1
1
2
0
0
0
0
2
0
1
2
0
0
0
0
1
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
2
4
0
0
0
0
0
3
0
0
2
0
1
1
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
2
0
2
1
1
0
2
0
0
2
0
0
0
0
0
1
0
0
1
0
1
0
1
2
0
0
0
2
0
0
0
1
1
0
1
1
0
0
2
1
0
1
0
2
0
2
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
1
0
2
0
0
4
0
0
1
2
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
1
0
0
2
2
1
0
0
2
0
0
0
2
0
0
1
0
0
2
0
3
1
1
1
1
0
0
0
0
1
2
1
0
0
0
0
2
0
2
2
2
1
0
0
0
0
0
0
0
0
0
2
0
1
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
1
0
0
0
0
2
1
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
2
0
2
0
1
0
0
2
2
0
1
0
0
0
0
2
0
2
0
0
1
0
0
0
1
2
0
0
1
1
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
1
1
1
0
4
2
3
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
2
2
0
0
0
0
3
1
2
0
3
0
1
0
1
0
0
0
0
0
1
1
2
1
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
3
1
0
0
2
0
0
1
0
0
0
2
0
0
0
1
1
2
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
2
0
2
0
0
0
1
1
0
0
0
0
2
0
0
0
1
0
1
0
4
0
1
0
0
0
1
0
0
1
0
2
2
1
0
0
2
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
3
0
0
0
1
0
2
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
2
2
0
1
1
1
0
2
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
1
0
0
0
2
0
2
1
0
0
2
0
0
2
2
0
0
1
0
2
0
1
0
2
2
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
2
0
1
2
0
0
1
0
2
0
0
2
1
0
1
2
0
0
0
0
0
0
2
1
2
0
2
0
0
0
0
0
0
1
2
0
0
0
1
3
1
0
0
0
0
1
2
0
0
1
0
0
0
0
3
0
0
1
2
0
0
0
0
0
0
1
0
3
1
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
2
1
0
0
1
1
0
0
2
0
1
0
0
0
2
0
2
0
2
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
4
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
1
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
4
0
1
0
0
0
2
2
0
0
0
0
1
0
0
2
0
0
2
2
0
0
0
2
0
0
1
0
2
2
1
2
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
1
0
0
0
1
0
1
0
0
2
0
0
0
0
2
0
0
0
0
1
1
1
1
2
0
0
1
1
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
0
1
1
0
0
2
0
2
0
0
0
1
0
0
0
1
1
0
0
0
0
3
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
1
1
0
2
2
0
1
2
0
0
0
0
0
0
0
0
0
1
0
2
2
1
0
1
0
1
1
2
0
2
0
0
0
2
0
0
0
0
0
0
0
2
2
1
0
0
0
4
0
0
0
0
0
0
0
2
0
0
0
2
0
0
3
0
2
0
0
1
0
0
0
4
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
3
0
0
0
0
0
0
1
1
0
0
0
1
2
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
3
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
3
0
2
1
1
0
1
0
3
0
0
5
2
0
2
0
0
0
0
0
0
0
0
0
0
0
3
2
2
0
1
0
0
1
0
0
0
2
0
1
0
0
2
1
2
0
2
0
1
0
0
0
1
0
0
0
1
0
2
4
0
0
0
0
0
0
0
0
3
1
0
2
0
2
0
1
0
2
0
0
1
0
0
0
0
2
2
0
0
2
0
0
3
1
2
0
1
0
0
2
0
1
0
0
0
2
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
2
0
7
1
0
3
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
1
0
2
1
0
0
1
0
2
0
0
1
4
0
0
0
0
2
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
2
2
2
0
0
2
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
2
2
1
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
3
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
1
0
1
0
0
0
0
0
0
0
0
0
0
2
2
2
1
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
2
0
0
1
2
0
1
0
0
0
0
1
0
0
2
0
2
0
0
3
2
0
0
0
0
0
2
0
1
0
1
0
1
0
2
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
2
2
0
0
0
0
0
2
0
2
0
1
1
1
0
1
0
1
0
0
0
0
2
0
0
1
0
2
1
1
0
0
2
0
0
2
0
4
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
2
0
0
0
1
2
0
0
2
1
0
0
0
0
0
2
0
0
0
3
1
2
0
0
2
3
0
2
2
0
0
0
0
1
0
2
1
2
1
1
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
1
1
0
0
2
2
0
0
0
0
0
0
0
2
2
0
0
1
0
1
1
0
0
0
0
2
0
0
0
1
0
2
0
0
1
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
1
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
2
0
2
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
3
0
2
0
0
1
0
1
0
4
0
1
1
1
0
0
0
0
0
0
2
1
2
0
0
1
3
0
1
0
0
0
0
2
2
0
0
1
0
0
0
0
2
0
2
0
2
0
0
0
0
2
3
0
0
0
0
0
2
1
1
1
0
1
0
0
0
0
2
3
0
2
0
0
1
0
0
1
0
2
0
0
2
1
0
1
0
0
2
2
0
0
0
1
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
2
0
0
0
0
0
0
1
1
0
0
2
0
1
1
0
2
0
3
2
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
2
0
2
0
0
0
0
0
0
1
0
0
2
1
0
0
0
1
0
0
0
2
0
0
2
1
0
2
1
2
0
0
2
0
2
0
1
3
0
0
0
0
2
2
2
1
0
0
0
5
0
2
1
0
0
2
1
0
0
2
0
0
0
0
2
0
1
0
1
2
0
0
0
0
1
1
0
2
2
0
0
2
4
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
2
1
0
0
2
1
0
1
0
0
0
2
1
0
1
0
0
1
1
0
2
1
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
2
0
0
0
2
0
0
1
0
0
0
0
0
2
2
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
2
1
0
2
0
2
0
4
1
0
0
0
0
2
0
2
0
0
0
1
0
1
4
0
0
0
0
2
0
0
1
0
0
0
0
1
2
0
0
1
1
1
0
0
1
2
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
1
0
0
0
2
0
0
3
1
1
0
0
2
1
0
0
1
2
1
0
0
2
0
2
0
1
2
1
1
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
2
0
0
0
1
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
2
0
0
0
0
0
1
3
0
2
0
0
0
0
2
2
1
0
0
0
2
0
1
0
0
1
0
0
1
0
3
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
3
0
0
0
0
6
0
1
2
0
2
1
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
11
0
0
0
0
0
0
0
1
0
1
1
0
2
0
0
0
1
3
0
0
0
2
1
3
0
2
0
0
2
0
2
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
1
5
2
0
0
1
0
0
0
0
6
1
0
0
0
1
0
0
2
3
0
0
0
0
0
0
1
0
0
0
1
0
1
0
2
1
2
6
0
0
0
1
0
2
0
1
0
2
0
0
0
0
2
0
0
0
1
2
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
4
1
0
1
0
2
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
1
0
0
0
2
1
2
1
1
2
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
1
0
0
3
2
0
2
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
3
0
0
1
2
0
0
0
1
1
1
0
2
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
2
0
1
0
0
2
0
0
0
0
0
0
0
2
1
0
0
1
0
0
1
1
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
1
0
0
2
3
1
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
2
0
0
0
0
0
2
0
2
0
6
2
2
0
2
0
0
0
0
0
0
0
1
1
0
0
1
2
0
2
0
0
0
2
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
2
2
0
2
0
0
0
0
6
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
3
1
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
2
1
1
1
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
4
1
0
0
0
0
2
0
1
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
4
2
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
3
0
2
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
1
1
1
1
0
2
1
0
2
0
0
2
0
0
0
1
0
1
0
0
0
0
0
1
0
2
0
0
2
0
1
0
1
0
3
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
5
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
2
0
0
1
0
0
2
0
1
0
0
1
2
0
0
0
0
2
0
2
0
2
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
2
2
2
1
2
0
1
0
3
0
3
0
0
0
0
0
0
0
0
2
0
1
2
0
0
2
0
0
0
0
0
2
0
0
0
1
2
0
0
3
0
0
0
1
0
0
1
2
0
1
0
0
1
2
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
1
2
0
0
0
0
0
5
0
1
1
0
1
0
0
0
1
0
3
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
1
1
0
0
2
4
0
0
1
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
5
0
2
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
2
3
0
0
0
0
0
0
0
13
1
0
1
1
0
0
2
2
2
0
0
1
0
2
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
4
3
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
2
0
2
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
1
2
0
0
4
2
1
3
2
1
1
0
2
0
1
1
0
3
0
2
0
2
0
2
2
1
1
0
1
2
2
0
0
1
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
3
2
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
1
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
2
0
0
1
2
0
0
2
1
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
2
0
0
2
0
0
2
0
0
1
1
1
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
2
0
0
3
0
0
1
1
0
0
2
0
1
0
0
0
2
0
1
3
1
1
0
0
0
0
2
0
0
0
0
0
2
2
0
1
0
0
0
1
0
0
0
0
0
0
1
1
5
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
7
0
1
0
1
0
0
0
1
0
0
0
2
0
2
1
2
0
0
2
0
0
0
0
0
0
0
1
0
2
1
0
4
2
0
0
1
2
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
2
0
2
0
2
0
1
0
0
2
0
0
2
1
1
2
1
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
2
0
2
0
2
2
2
0
0
2
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
1
0
0
0
0
1
0
0
1
0
0
0
0
3
0
2
0
0
0
4
0
1
0
1
0
0
0
1
0
1
1
0
2
0
2
2
0
2
0
0
1
0
0
1
0
1
0
0
0
2
0
2
0
0
1
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
1
1
2
2
0
0
0
0
0
1
0
0
2
0
1
0
2
1
0
0
0
0
0
0
3
1
0
0
1
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
2
1
2
0
0
0
0
1
2
2
2
0
3
2
0
0
1
0
1
0
0
2
2
0
0
0
3
0
2
0
1
0
0
2
0
0
0
0
1
0
1
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
2
2
1
0
0
2
2
4
1
0
0
0
2
0
2
1
2
0
0
0
0
1
2
2
0
3
0
0
0
0
1
1
1
0
2
1
0
0
2
0
0
0
0
0
0
0
0
4
1
7
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
1
0
1
2
0
0
0
0
1
1
2
0
0
0
2
0
3
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
1
0
0
1
0
2
2
0
0
0
0
2
1
0
0
0
1
0
1
0
0
0
1
0
2
1
3
2
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
3
0
0
0
0
2
0
0
0
0
0
1
2
0
0
1
0
2
0
2
0
0
0
0
0
2
2
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
2
0
2
0
0
2
0
1
0
0
2
0
1
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
2
1
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
3
2
1
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
2
1
0
2
0
0
1
0
0
0
1
0
2
0
2
0
1
0
0
0
2
0
1
0
1
1
2
0
0
0
0
2
1
0
0
2
0
2
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
2
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
3
0
0
1
0
0
1
0
2
0
2
2
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
2
0
1
2
0
2
1
0
0
0
1
0
1
2
0
0
5
0
2
0
0
0
1
0
0
0
0
0
0
1
1
0
2
1
0
0
1
0
0
0
0
0
0
1
0
0
1
2
1
1
0
2
0
2
0
0
0
3
0
0
2
2
2
0
0
0
0
2
2
0
0
2
1
2
3
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
1
0
0
0
0
0
0
0
0
2
0
0
1
1
2
0
0
1
0
1
0
2
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
1
2
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
1
0
0
0
0
1
2
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
1
1
1
0
1
0
1
0
0
0
0
0
2
1
0
0
1
2
0
0
0
3
1
0
1
0
0
0
1
2
0
1
1
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
2
1
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
1
1
0
0
0
1
2
0
0
0
1
1
0
0
0
2
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
2
2
1
0
0
0
2
0
0
0
0
2
3
2
1
0
0
0
0
1
2
2
0
3
2
1
0
2
1
2
1
1
3
0
0
1
0
2
0
0
0
2
0
0
3
0
1
2
0
0
0
2
0
1
1
0
0
0
1
0
1
0
0
0
0
1
1
2
1
0
2
0
0
0
2
2
0
0
1
0
2
2
1
0
0
0
1
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
2
1
0
2
0
2
1
0
0
1
0
0
0
2
2
1
2
0
2
2
1
1
0
1
1
0
2
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
2
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
2
2
1
0
0
0
1
0
3
0
0
0
0
3
0
0
0
1
0
0
1
0
0
0
2
0
0
3
0
0
2
0
1
0
1
2
0
3
2
1
0
0
0
2
2
0
0
0
0
1
0
1
1
0
1
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
2
1
0
0
3
0
3
0
1
0
0
1
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
1
2
0
0
1
0
0
0
1
0
2
0
0
3
1
0
2
2
1
0
0
0
1
0
2
0
1
0
1
2
2
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
1
0
1
0
1
0
0
2
0
1
0
0
3
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
1
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
2
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
2
0
0
1
0
2
2
0
3
1
0
0
2
0
0
0
0
0
1
0
0
2
0
1
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
9
0
1
0
0
0
0
1
0
2
2
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
1
1
0
0
0
0
5
0
1
0
0
0
2
1
0
1
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
2
1
1
0
0
0
2
0
0
4
0
1
2
0
1
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
1
0
1
0
2
0
0
0
3
2
0
0
0
2
0
0
2
1
0
0
2
3
0
0
1
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
2
2
0
1
2
0
0
0
0
2
0
1
0
1
1
5
0
0
0
2
0
0
0
2
1
1
0
0
0
2
1
0
0
0
4
0
2
1
0
2
1
1
0
0
3
0
0
2
0
1
0
0
1
0
0
1
1
0
2
2
2
1
0
1
0
0
0
2
1
0
0
2
3
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
2
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
1
2
2
2
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
1
0
0
1
1
0
0
0
1
0
0
0
0
1
2
0
0
0
0
3
0
1
2
1
0
2
0
0
1
1
0
2
0
1
0
0
2
0
0
0
1
0
0
2
1
0
0
0
2
1
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
3
0
2
0
1
0
0
2
0
2
0
0
0
0
0
1
2
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
1
0
0
1
0
0
0
3
0
0
2
0
2
1
0
1
0
1
0
0
2
0
0
0
0
1
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
1
3
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
1
1
1
0
2
0
2
0
0
1
2
1
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
2
1
0
0
2
2
1
2
1
0
0
1
2
0
0
0
0
0
0
1
2
0
1
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
4
2
1
2
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
1
3
2
1
0
3
0
0
0
1
1
1
0
0
1
2
2
0
2
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
2
3
0
0
0
0
2
1
0
3
1
0
0
0
0
0
0
1
1
2
0
2
0
0
1
0
1
0
0
0
0
2
0
2
0
0
1
1
0
2
0
2
1
0
0
2
0
2
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
2
0
0
1
1
0
0
1
1
2
0
0
0
0
0
1
1
1
0
2
0
0
0
0
3
0
0
0
0
0
2
0
0
2
0
0
2
1
0
1
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
3
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
1
0
2
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
2
1
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
3
0
1
0
0
1
2
0
0
0
1
0
2
2
0
1
0
2
0
0
2
0
1
0
1
2
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
5
0
1
1
0
2
0
0
0
1
0
0
1
0
1
0
0
2
1
0
0
0
0
0
0
2
0
0
1
0
1
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
2
2
0
0
0
0
0
1
0
0
2
2
1
0
2
0
0
0
0
2
1
0
2
0
1
2
2
0
0
0
1
2
1
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
1
0
1
0
0
2
1
1
1
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
2
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
2
0
0
0
2
0
0
1
1
0
1
0
1
0
0
1
0
0
0
1
0
0
4
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
0
2
0
0
1
0
0
0
1
0
0
0
0
0
1
2
2
0
2
0
0
0
0
1
1
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
1
0
2
0
2
0
0
1
2
0
1
2
1
1
2
0
0
0
0
0
2
0
0
0
0
2
0
1
2
0
0
2
0
1
0
3
1
1
0
2
0
0
1
0
0
1
0
0
2
0
0
1
0
1
1
1
0
0
0
2
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
2
1
0
1
1
0
0
0
0
0
1
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
2
0
0
2
1
1
0
1
2
0
0
0
2
3
0
1
1
0
2
0
1
0
0
0
0
1
1
0
0
0
0
2
1
2
1
0
1
1
0
0
2
2
0
1
1
0
0
2
0
0
0
0
0
1
0
2
0
1
2
0
0
0
3
2
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
2
0
1
1
0
0
0
0
1
0
0
2
0
0
0
2
0
2
0
3
0
2
0
7
0
1
0
0
2
0
0
0
1
0
0
2
0
2
1
1
2
0
0
2
0
1
0
1
3
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
3
0
1
0
1
1
0
1
0
0
2
0
0
0
0
0
0
0
1
0
2
1
0
0
1
2
1
0
1
0
2
0
2
0
2
2
1
2
0
0
1
2
1
0
1
0
2
2
1
1
2
0
0
0
0
1
1
0
0
0
1
0
0
1
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
2
1
0
0
1
0
0
2
0
1
2
2
2
0
0
0
1
0
0
4
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
1
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
2
2
0
1
2
2
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
3
0
0
2
0
0
1
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
2
0
1
0
0
3
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
1
2
1
0
0
3
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
2
1
0
2
1
2
0
0
0
0
1
1
0
0
0
0
3
0
4
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
2
4
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
2
1
0
0
2
1
0
0
1
1
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
1
0
2
0
0
3
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
1
0
1
0
0
0
0
0
0
2
0
0
0
4
2
2
2
0
0
1
0
0
1
2
2
0
0
1
0
1
1
0
0
1
0
1
0
0
0
0
0
1
0
1
2
1
0
0
2
1
0
0
0
0
2
0
1
0
1
0
2
0
0
0
2
0
2
0
3
2
0
0
0
0
2
0
0
1
0
0
0
1
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
2
0
1
1
0
1
1
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
2
0
2
0
1
0
0
0
1
0
0
1
0
0
0
1
2
0
0
2
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
2
0
0
0
2
0
0
0
0
0
1
1
2
0
0
0
3
0
0
0
0
0
1
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
2
2
0
0
0
1
0
2
0
0
0
2
1
0
0
0
3
0
1
0
0
2
0
0
0
1
0
0
1
0
1
0
2
1
0
3
0
0
2
1
0
4
0
0
0
0
2
1
1
0
0
1
1
2
0
1
0
0
0
0
2
0
1
3
2
0
0
1
2
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
1
0
0
0
0
2
1
0
1
0
0
1
0
0
2
0
2
0
0
0
2
0
0
0
2
1
3
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
2
0
0
0
1
0
1
0
0
1
1
0
0
1
1
1
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
1
0
1
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
2
1
0
0
0
0
0
0
1
1
1
0
0
0
1
0
2
1
2
0
1
0
0
0
1
0
1
0
0
2
0
0
1
0
2
0
1
2
0
0
0
0
0
0
4
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
3
1
0
0
2
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
3
1
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
3
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
2
2
1
0
3
0
0
0
0
0
0
0
1
0
1
0
2
2
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
1
1
2
3
0
0
1
0
0
0
0
1
0
0
0
1
3
0
1
2
2
1
2
0
0
1
0
0
2
0
0
0
0
0
0
3
4
0
2
2
0
0
0
1
0
0
2
0
2
0
0
2
4
2
0
0
0
0
1
1
2
0
0
2
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
2
0
0
0
0
1
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
3
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
1
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
2
0
0
0
2
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
2
0
0
0
0
2
2
4
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
1
2
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
3
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
1
2
0
0
2
2
0
0
0
0
0
2
0
0
0
0
3
0
0
1
0
2
0
0
0
0
0
0
1
0
2
0
0
1
0
0
3
2
0
1
0
0
0
0
0
2
1
0
1
1
0
0
0
0
1
0
0
0
2
0
1
1
1
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
2
1
0
0
0
1
0
0
0
0
0
0
2
0
2
0
1
0
0
1
5
2
0
0
1
1
1
0
0
0
3
0
0
2
0
0
0
0
3
1
0
0
0
0
0
1
0
0
0
2
0
1
0
0
1
0
1
3
1
0
0
0
1
1
0
2
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
2
0
1
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
5
0
1
1
1
0
0
3
0
2
0
2
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
2
2
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
1
1
0
2
0
2
0
2
1
0
0
0
0
0
0
2
3
0
1
0
0
1
1
1
0
0
1
2
0
0
2
0
1
0
0
2
3
0
0
1
2
1
1
0
2
0
2
0
2
0
0
0
0
0
0
2
0
0
0
3
0
1
1
2
0
0
2
0
0
0
2
1
0
0
0
0
3
1
0
0
0
0
0
0
0
0
2
1
0
2
1
2
0
0
0
0
2
0
2
1
0
2
0
0
0
2
0
0
2
0
2
0
0
1
0
0
0
0
0
0
2
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
1
2
2
0
1
2
0
1
2
1
2
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
1
1
2
0
1
0
1
0
0
0
0
2
0
0
0
0
0
1
0
2
1
0
0
0
1
0
0
0
0
0
0
0
2
3
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
2
0
0
0
0
1
0
1
0
0
1
2
0
0
0
0
0
3
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
4
2
0
1
0
1
0
0
0
0
0
0
0
0
0
3
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
1
1
3
2
0
0
0
0
1
1
1
1
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
3
0
2
0
3
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
1
1
0
1
0
0
2
0
0
1
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
3
2
0
0
0
1
0
0
0
2
0
0
1
1
0
0
0
0
0
0
2
1
0
1
1
0
1
2
0
0
0
2
0
0
0
2
0
3
2
2
0
2
0
0
0
1
0
2
0
2
0
3
0
0
0
0
0
0
0
2
3
0
0
0
2
2
0
0
1
2
1
0
0
0
2
0
0
0
1
0
2
0
0
1
0
0
3
0
0
0
0
2
0
2
1
2
0
2
1
0
0
1
0
0
0
2
0
0
0
0
0
0
1
1
1
0
0
1
4
1
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
3
0
2
0
0
0
0
2
0
0
1
0
0
0
2
2
0
0
1
1
0
1
0
1
0
0
0
0
0
0
2
0
0
0
1
2
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
1
0
2
0
0
0
0
2
0
2
1
0
1
3
0
1
0
1
6
1
0
0
1
0
0
0
0
2
0
4
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
5
0
0
2
0
1
0
0
0
1
0
0
0
1
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
1
2
0
0
0
0
2
0
4
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
2
0
1
0
0
2
0
0
0
2
0
0
1
1
2
0
0
0
0
0
1
0
2
0
2
0
1
2
0
0
5
2
1
0
2
0
0
0
0
1
2
1
0
1
0
0
1
0
2
2
2
0
2
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
2
0
0
1
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
1
2
0
2
0
1
0
0
1
1
2
0
1
0
0
1
0
2
0
0
0
0
2
0
0
0
0
4
0
2
0
0
0
0
0
1
0
0
2
0
1
0
1
2
0
2
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
2
0
0
1
1
0
0
0
0
0
2
2
2
0
2
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
3
0
1
0
2
0
0
0
2
4
0
1
2
0
0
0
0
0
0
0
3
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
5
1
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
6
0
0
0
0
0
1
0
0
1
1
0
2
0
0
3
0
0
0
2
0
2
0
0
1
2
0
3
0
0
3
2
0
0
0
1
1
0
0
2
0
0
0
1
0
0
0
0
1
1
2
0
0
0
0
0
3
0
2
0
2
2
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
1
0
1
0
0
0
1
0
0
0
0
0
2
0
0
1
2
0
0
0
2
0
0
0
1
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
1
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
1
1
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
1
2
2
0
0
0
0
2
0
0
2
1
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
3
0
0
2
0
0
1
2
2
1
2
0
0
1
0
0
0
0
1
1
0
2
0
0
0
0
0
0
1
0
1
0
0
1
0
0
2
4
0
1
1
1
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
1
5
1
0
0
0
1
0
0
2
0
1
2
0
0
2
0
0
5
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
2
1
0
1
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
1
2
0
0
0
1
0
1
0
1
0
0
2
2
0
0
2
0
1
1
0
2
1
0
0
0
0
0
0
0
0
2
1
1
0
2
0
0
2
2
0
0
0
0
1
0
0
2
1
0
2
2
0
0
1
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
2
2
2
2
1
0
2
0
0
1
0
2
2
1
0
0
0
1
0
0
0
0
2
0
0
1
4
2
0
0
0
2
1
0
1
0
0
0
0
0
1
0
0
1
0
0
2
1
0
0
1
0
0
1
2
0
0
2
0
3
3
0
0
0
1
0
0
2
0
0
1
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
2
1
1
1
2
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
1
1
1
0
0
0
1
1
1
0
2
2
1
0
0
0
0
0
0
0
1
1
1
1
0
0
3
0
0
0
0
0
0
1
0
1
1
0
3
2
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
1
0
0
0
0
0
0
3
2
0
0
1
1
1
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
2
0
1
0
0
0
0
2
0
0
1
0
1
0
0
0
2
1
0
0
0
1
0
2
0
0
1
0
0
0
2
0
0
2
0
2
0
0
1
1
0
0
0
1
1
0
0
2
1
2
0
2
0
2
0
1
0
2
2
0
0
0
0
0
2
0
2
0
0
0
1
0
2
0
0
1
0
0
0
0
1
2
3
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
8
1
0
0
0
1
2
0
0
2
0
1
1
0
3
2
0
0
1
0
0
0
3
0
1
1
1
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
1
3
2
2
0
1
0
0
1
0
0
0
0
0
0
0
0
2
5
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
2
1
0
1
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
2
1
0
0
1
3
0
1
2
0
0
0
1
0
0
2
1
0
0
1
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
2
1
1
1
0
0
2
2
1
0
2
1
0
1
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
4
2
1
0
0
1
0
1
0
2
0
1
0
4
2
0
0
4
3
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
1
2
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
2
0
2
0
1
1
1
0
1
0
0
0
0
2
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
3
0
1
0
0
0
0
1
1
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
2
0
1
2
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
2
2
1
2
0
0
0
0
0
0
0
0
1
0
2
0
3
0
1
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
4
0
0
0
1
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
1
1
0
0
2
0
0
0
1
0
0
2
1
1
0
1
0
1
0
0
0
2
1
0
0
0
2
0
0
3
1
0
0
2
0
0
0
0
0
2
0
0
0
1
2
0
0
0
1
0
1
2
0
0
0
0
2
2
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
2
2
0
0
0
0
0
1
0
0
2
0
0
0
0
3
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
1
1
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
2
2
0
2
1
0
0
0
1
1
1
1
2
0
0
0
1
0
0
0
1
0
3
1
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
1
6
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
1
2
1
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
2
0
0
2
1
0
2
0
0
2
0
0
1
0
0
2
2
0
0
2
1
0
1
0
0
6
0
2
1
0
0
0
0
1
0
1
2
1
2
0
0
0
0
0
2
1
0
0
0
2
2
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
2
3
0
2
0
0
0
3
6
0
1
0
2
0
0
1
0
0
0
1
5
1
0
0
0
0
0
2
1
0
3
0
0
0
0
2
0
1
0
0
0
0
0
0
1
2
1
0
0
0
1
0
0
0
0
0
1
1
0
1
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
3
2
2
0
0
0
0
0
0
2
1
0
1
2
0
0
0
0
2
0
1
1
2
0
0
2
1
0
0
0
1
8
0
0
0
0
2
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
1
0
1
0
0
1
0
2
0
1
0
1
0
0
0
0
1
1
0
3
0
1
0
0
0
1
0
0
0
0
1
0
0
1
2
2
0
0
0
0
0
1
2
1
0
0
0
0
1
1
0
0
0
2
0
2
0
2
0
1
3
0
1
0
0
1
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
1
0
0
1
0
2
0
0
1
0
0
1
0
0
0
0
1
0
1
2
1
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
1
1
1
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
6
0
1
0
0
0
0
0
1
2
0
1
2
0
1
2
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
2
1
0
0
1
0
1
0
0
0
0
2
0
3
0
2
0
0
0
0
0
2
1
2
0
0
0
0
1
1
1
0
0
0
0
2
2
2
0
0
0
0
2
1
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
2
1
0
2
0
0
0
0
2
3
0
0
0
1
0
0
0
0
0
0
2
1
2
2
0
0
0
0
0
1
2
0
0
1
3
3
1
1
2
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
2
0
1
0
0
1
0
0
0
1
0
2
0
0
0
0
0
1
0
2
1
0
0
0
0
0
2
0
0
0
1
1
0
0
2
2
1
0
2
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
2
0
0
1
0
0
0
3
0
2
0
0
1
0
0
0
1
0
0
1
0
3
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
1
1
0
0
4
1
0
1
2
0
0
0
0
0
2
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
2
1
0
1
0
0
0
2
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
1
1
2
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
2
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
2
0
1
2
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
2
0
2
0
0
0
0
0
2
2
2
0
0
1
1
1
0
0
2
0
0
3
0
0
1
0
1
0
0
0
0
2
1
2
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
1
2
0
2
2
1
0
0
1
0
1
0
2
0
2
0
1
1
1
0
1
0
1
0
2
0
2
0
0
0
2
0
0
2
0
0
0
1
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
2
0
0
0
1
0
0
2
0
2
0
2
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
2
0
0
1
0
0
1
0
0
1
0
0
0
0
2
1
0
0
1
1
1
0
0
0
1
1
1
2
0
0
0
2
2
1
0
1
1
2
0
2
1
1
0
0
1
0
6
2
0
1
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
2
2
1
2
0
0
0
2
3
0
0
1
0
2
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
1
2
0
0
3
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
2
0
1
0
0
0
2
0
0
0
2
0
2
0
1
3
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
4
3
0
0
0
0
2
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
4
0
0
2
2
0
0
0
2
0
0
2
2
0
0
0
0
2
3
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
1
0
0
2
2
0
0
0
0
0
0
2
0
2
2
3
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
2
0
1
0
1
0
0
0
0
1
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
3
1
1
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
5
2
2
0
0
0
1
2
2
1
1
0
0
2
0
1
0
0
0
0
2
0
0
3
2
0
0
0
0
0
0
0
1
2
0
1
1
0
0
1
0
0
2
0
1
0
2
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
1
2
0
0
0
1
0
0
0
1
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
1
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
2
2
2
0
0
0
1
0
0
20
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
1
0
0
0
2
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
3
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
2
2
0
0
0
1
2
1
0
0
0
0
2
0
2
0
1
1
0
1
1
0
0
0
1
0
0
2
3
0
0
0
0
1
0
0
0
3
1
0
0
4
1
0
1
0
0
0
0
1
0
0
0
2
1
1
0
0
2
0
0
1
0
0
0
3
1
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
1
0
0
1
0
1
3
1
0
0
2
1
0
0
0
0
1
0
0
1
2
0
1
0
1
4
0
0
1
0
0
0
0
2
0
0
2
0
3
1
1
2
0
0
0
3
0
1
0
4
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
1
2
1
2
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
2
1
1
0
1
1
3
0
0
2
0
0
0
3
2
1
0
0
0
0
0
0
2
0
2
0
2
0
0
1
2
0
2
0
0
0
2
2
0
0
1
0
1
0
2
1
0
2
0
0
0
0
0
3
0
0
2
0
2
1
0
0
1
0
0
0
0
0
5
0
0
1
0
2
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
2
0
0
0
0
2
4
0
0
0
0
0
2
0
4
1
0
0
0
1
2
1
0
2
3
1
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
2
2
0
1
2
0
0
2
5
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
1
2
0
0
1
0
0
2
3
0
0
1
1
2
1
0
2
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
2
0
0
2
0
0
0
2
0
3
0
1
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
2
0
0
2
0
0
0
1
0
0
1
0
1
2
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
2
1
0
2
0
0
0
2
0
0
0
0
1
0
1
0
0
2
1
0
0
2
0
2
2
2
1
2
0
1
1
1
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
3
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
1
1
2
2
2
0
0
0
0
0
4
0
0
0
1
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
2
1
0
2
0
0
0
0
0
1
1
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
2
2
0
2
1
0
1
1
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
1
8
0
0
0
0
0
2
1
0
0
0
0
2
0
2
2
0
0
2
0
2
0
2
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
7
2
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
3
0
2
0
1
0
0
2
2
3
1
0
4
2
0
0
0
0
0
0
0
1
0
0
2
1
0
0
4
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
2
2
1
0
0
0
0
0
0
2
0
0
0
2
1
0
1
0
0
0
0
1
1
1
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
1
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
2
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
3
2
0
0
2
0
1
0
0
1
1
0
0
0
0
0
0
2
2
0
2
0
1
0
0
2
1
1
0
1
0
0
0
1
0
0
1
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
3
0
0
2
0
2
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
5
0
0
6
1
0
0
1
0
1
2
2
0
1
0
2
1
0
0
2
1
0
0
2
2
0
0
0
2
2
2
1
0
0
0
2
0
2
0
1
2
2
5
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
2
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
11
0
2
4
0
1
2
0
1
1
0
0
0
5
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
7
1
0
2
0
0
1
2
1
1
0
0
0
0
1
0
0
0
0
0
2
1
3
2
0
4
0
0
0
0
1
0
0
0
3
0
3
0
2
0
1
3
2
0
2
0
0
0
0
2
0
0
0
2
2
0
0
1
2
0
1
2
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
2
1
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
1
0
1
0
0
0
1
0
2
1
1
0
0
0
2
0
0
2
2
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
4
0
0
1
0
0
0
0
0
1
2
0
0
1
0
0
3
0
0
2
0
1
2
0
2
0
1
0
0
0
0
0
2
0
0
1
2
0
1
0
0
2
0
0
2
0
0
1
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
1
0
1
1
8
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
1
0
0
0
1
0
2
0
2
3
2
0
0
2
0
0
0
0
0
0
1
0
1
2
1
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
2
2
1
2
2
0
0
0
0
0
1
3
0
0
0
3
0
0
0
2
0
3
0
0
0
0
0
0
0
2
0
0
1
0
0
3
0
0
1
1
0
1
1
0
0
0
0
0
1
0
0
2
1
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
2
0
0
2
0
0
1
0
0
1
1
0
1
0
0
0
2
2
2
1
1
1
0
1
1
0
1
0
0
0
0
1
0
2
1
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
1
1
0
1
0
1
0
0
2
0
0
1
2
0
3
2
2
0
0
3
2
0
0
0
0
2
2
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
2
0
3
0
0
2
0
0
1
3
0
8
0
1
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
2
0
0
1
2
2
0
2
0
0
0
0
0
2
0
2
1
1
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
2
0
1
0
0
0
3
2
0
0
0
3
0
4
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
1
1
0
1
2
2
0
2
0
3
0
2
0
0
0
0
0
2
0
2
2
0
1
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
1
0
0
0
2
0
1
1
2
1
0
0
0
2
0
0
0
0
2
0
2
0
2
0
0
0
0
3
1
0
1
0
0
0
1
0
1
0
1
0
0
2
1
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
5
2
0
2
0
1
1
0
0
1
0
0
2
0
0
0
0
0
0
0
7
0
0
0
2
0
0
0
0
1
0
0
1
0
2
0
0
0
2
0
2
0
2
0
0
2
1
0
3
0
0
0
0
2
0
0
2
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
2
0
0
0
0
0
0
1
2
1
2
0
1
0
0
0
0
0
0
0
0
1
2
2
1
0
2
1
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
2
0
2
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
2
2
0
0
0
0
0
0
3
2
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
1
0
2
0
3
2
1
1
0
0
0
0
0
2
0
4
2
2
1
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
2
1
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
3
0
0
0
1
0
0
1
2
0
0
3
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
1
3
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
2
0
2
1
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
1
0
2
1
0
0
0
2
0
4
2
0
0
4
0
0
1
2
2
0
0
0
0
0
0
0
0
0
3
0
2
0
1
2
0
0
1
2
1
2
1
0
0
2
4
1
0
0
0
0
2
0
0
0
3
0
0
0
1
0
0
1
0
0
0
1
2
0
0
2
0
0
2
0
0
0
0
1
1
1
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
2
2
1
1
2
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
2
0
2
1
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
2
0
2
0
2
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
2
1
0
1
1
0
0
2
2
2
0
0
0
0
0
3
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
2
2
4
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
2
2
0
1
0
0
1
0
0
0
0
2
0
0
0
2
2
0
1
0
0
0
2
0
1
0
0
0
0
1
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
3
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
4
0
0
0
0
0
0
2
2
0
3
0
2
2
2
0
0
1
1
3
0
0
2
0
0
1
0
3
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
2
2
0
1
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
3
0
1
0
5
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
2
2
0
1
1
1
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
2
0
0
1
0
3
4
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
4
1
0
0
0
1
2
2
3
0
0
0
0
0
1
0
0
0
2
1
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
4
2
1
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
1
0
0
2
0
0
0
2
1
0
0
2
0
2
0
0
0
0
0
1
0
0
2
0
1
0
2
0
1
0
0
0
0
0
1
1
0
0
2
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
2
2
1
1
0
2
0
2
0
0
1
0
1
1
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
2
2
0
1
0
0
0
1
0
1
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
5
3
1
2
0
0
2
0
2
1
0
4
0
0
0
2
3
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
1
1
1
1
3
0
0
2
0
0
0
1
2
1
0
0
2
1
1
0
1
0
1
0
0
0
2
0
1
0
1
1
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
2
2
1
1
0
0
0
8
2
2
0
0
0
1
2
0
0
0
0
0
1
1
2
0
1
0
0
0
0
3
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
2
0
0
0
0
2
0
0
2
0
2
0
1
0
0
1
1
2
6
2
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
2
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
1
1
1
0
1
1
0
0
1
0
0
0
0
1
2
0
0
0
0
1
1
0
3
0
0
0
2
2
2
2
0
1
0
0
1
0
0
0
0
1
0
0
2
0
0
1
0
0
0
1
0
0
0
2
2
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
3
0
0
1
1
0
2
0
0
1
1
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
3
2
0
2
0
0
2
0
0
0
0
0
0
1
0
2
9
2
0
0
1
0
1
0
4
0
0
0
0
0
0
2
0
0
0
2
2
1
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
2
0
1
0
0
0
0
0
1
0
0
1
1
1
0
1
0
0
0
0
0
0
1
2
0
0
0
3
0
2
0
0
2
0
0
0
0
0
1
0
3
1
0
2
0
0
0
1
2
0
0
2
2
1
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
2
3
1
0
0
3
3
1
0
1
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
1
1
0
0
0
0
0
0
2
0
0
0
4
2
0
0
0
0
0
0
0
0
0
4
0
3
0
0
2
0
0
0
1
0
0
2
1
0
0
0
0
2
0
0
2
0
0
2
2
0
0
0
4
0
0
1
2
0
0
7
1
0
2
0
0
0
0
0
0
1
0
0
3
1
1
2
3
1
2
0
1
0
0
1
1
0
3
0
0
0
0
0
0
2
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
1
2
2
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
1
0
0
0
1
1
0
0
1
1
0
2
0
2
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
3
0
2
0
0
0
2
0
0
2
1
0
2
2
1
2
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
1
0
0
0
0
1
2
2
0
2
2
0
1
0
0
0
0
1
0
0
1
0
2
1
0
0
2
0
0
0
0
2
0
0
0
0
2
1
0
0
0
1
0
0
0
1
1
2
1
0
1
0
0
0
0
1
0
0
0
2
2
0
1
0
0
0
0
2
2
0
0
1
2
0
0
1
1
0
0
2
0
0
0
0
2
0
1
0
0
0
1
1
0
1
0
9
0
0
0
1
4
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
1
0
2
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
1
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
2
1
0
1
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
1
0
0
1
3
0
2
0
0
0
0
0
1
1
0
0
2
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
1
0
2
1
1
1
0
1
2
1
0
0
0
2
0
1
1
0
0
0
1
0
0
0
2
1
0
0
0
2
0
3
2
1
0
0
0
0
0
0
0
2
0
0
0
2
1
3
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
8
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
2
1
2
0
0
0
0
4
0
0
0
0
0
2
0
2
1
2
0
0
2
0
1
0
0
0
0
0
1
0
0
2
1
0
1
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
1
0
0
1
1
0
1
0
2
0
1
0
0
0
3
0
0
4
0
3
0
0
1
0
0
0
0
0
0
0
1
0
0
0
3
0
0
2
0
0
0
1
0
0
0
1
1
0
2
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
2
0
2
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
2
1
0
0
2
0
0
0
0
1
0
1
0
0
0
0
2
2
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
1
2
0
2
1
0
0
1
0
0
1
2
0
0
1
1
0
2
2
0
1
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
1
0
2
0
2
0
1
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
2
0
3
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
3
0
0
1
2
0
0
0
0
0
0
2
1
0
0
1
0
2
2
0
2
0
0
0
2
0
0
1
0
0
1
0
2
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
1
0
0
0
0
0
2
0
0
1
2
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
1
1
0
1
0
0
3
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
1
0
1
1
0
0
1
0
2
0
2
0
0
0
1
0
0
0
0
2
0
0
0
3
0
1
0
1
2
0
0
2
2
2
0
0
1
0
1
0
0
0
0
4
0
1
2
0
0
0
2
0
2
1
0
0
0
0
0
0
0
1
2
2
0
0
0
1
1
0
0
1
0
0
0
2
0
2
0
0
2
2
0
0
0
0
0
0
0
0
1
0
1
4
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
1
0
0
1
0
1
2
2
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
2
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
1
1
1
0
1
0
1
1
0
2
1
0
0
0
0
1
0
1
1
1
0
2
0
3
0
1
1
3
1
0
0
0
1
2
0
0
2
0
2
2
0
2
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
1
0
1
1
0
0
0
0
0
1
0
2
0
0
2
0
0
2
1
2
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
4
0
2
0
1
0
0
2
0
0
0
0
3
0
2
0
2
0
0
0
1
0
0
3
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
2
0
2
2
0
0
0
2
0
0
0
0
2
0
0
1
0
2
1
0
2
2
2
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
5
0
1
2
0
0
3
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
2
0
1
0
0
0
0
0
2
1
0
1
0
0
3
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
4
0
1
0
0
1
0
3
0
0
2
0
0
0
0
0
2
0
2
0
2
1
0
0
0
0
0
0
0
2
1
1
0
1
1
1
0
0
0
2
0
1
0
1
1
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
3
2
0
0
1
1
0
0
0
1
0
0
0
0
3
0
0
0
2
0
2
2
0
0
0
0
0
2
0
1
1
1
0
1
0
0
0
0
1
2
0
0
0
5
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
2
1
2
0
0
0
2
2
0
0
0
0
6
2
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
2
0
1
0
0
0
2
1
2
1
1
0
0
2
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
3
1
0
1
0
3
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
1
0
0
0
1
3
1
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
1
2
0
0
0
0
0
1
0
0
2
0
2
1
1
1
0
0
0
0
1
0
0
0
0
1
2
0
0
2
0
0
1
2
2
2
2
0
0
1
0
0
0
2
2
0
0
0
0
1
0
1
0
2
2
0
0
0
0
0
1
0
0
2
1
0
1
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
1
1
0
0
3
0
0
0
0
0
0
2
2
1
0
0
0
0
1
0
3
0
0
2
0
1
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
3
1
0
1
0
0
1
0
2
1
0
0
0
1
0
2
1
2
1
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
2
1
0
0
0
2
0
2
0
0
0
2
0
1
2
2
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
1
0
0
1
0
1
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
6
0
0
1
0
0
2
0
0
0
1
0
1
0
2
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
2
2
0
2
0
2
0
1
0
0
0
0
0
0
0
1
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
1
0
1
2
2
1
0
0
0
2
0
0
0
1
0
3
1
1
0
0
0
3
1
1
0
0
1
0
1
1
1
0
0
0
0
0
1
2
0
2
0
0
2
1
0
3
1
3
0
0
3
0
1
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
2
0
1
2
1
2
1
0
1
1
1
0
2
2
1
2
0
1
0
2
0
1
2
2
2
2
2
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
2
1
1
0
0
0
1
0
1
0
0
0
2
2
0
0
1
2
0
1
0
1
2
0
0
0
1
0
0
0
0
0
1
2
0
0
1
0
2
0
1
0
0
3
0
0
0
0
0
3
0
2
2
1
2
0
0
0
2
1
2
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
2
0
0
0
2
0
0
0
2
0
1
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
1
0
1
0
2
0
0
0
0
1
2
0
3
1
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
1
1
2
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
1
0
0
0
0
1
0
1
0
1
2
0
0
0
0
0
0
2
0
0
1
0
3
0
5
2
0
0
0
1
0
2
0
1
2
0
0
0
0
1
2
2
2
0
0
0
0
2
0
0
0
0
2
1
4
3
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
3
0
0
0
0
1
1
0
0
0
1
1
2
0
0
2
1
2
2
0
0
0
0
0
4
0
0
2
0
0
1
0
0
0
2
1
0
1
0
0
2
0
0
0
1
2
2
0
0
2
1
0
0
0
0
1
0
2
3
0
0
0
2
0
2
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
2
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
1
0
1
2
0
3
1
1
2
1
0
0
2
1
0
0
3
0
2
1
4
0
2
1
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
2
0
0
1
3
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
2
0
0
1
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
6
1
0
0
1
0
2
0
0
2
0
0
0
0
0
0
1
1
6
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
1
1
0
0
0
2
0
0
2
1
0
2
1
0
2
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
1
1
0
1
0
1
2
0
0
0
0
0
2
0
0
2
2
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
3
0
1
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
1
1
2
3
0
0
0
0
0
0
0
0
0
1
0
0
2
0
4
0
2
1
0
0
0
1
2
0
0
0
2
1
0
0
0
0
2
0
0
1
1
0
1
1
1
1
0
2
2
0
0
1
0
0
1
0
0
1
2
0
0
3
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
1
3
2
2
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
1
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
1
2
1
2
2
1
2
1
0
4
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
2
0
2
0
2
0
1
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
2
8
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
2
0
2
0
0
2
1
1
0
3
1
0
0
0
0
0
2
1
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
2
0
0
0
0
3
1
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
2
1
1
2
1
0
0
0
0
1
4
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
1
1
1
0
1
2
0
0
1
2
0
0
0
0
0
1
0
0
1
2
2
0
0
1
0
0
0
0
1
0
2
0
0
2
0
2
1
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
2
0
2
0
1
0
0
0
1
0
2
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
2
0
2
3
0
0
0
1
0
0
2
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
1
0
3
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
2
2
1
2
5
0
0
1
1
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
3
1
0
2
1
0
2
1
2
0
1
3
1
0
3
0
1
0
0
1
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
3
1
0
0
2
2
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
2
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
1
1
0
2
1
0
0
0
0
0
0
1
0
1
2
0
0
1
0
1
1
0
0
0
0
3
0
1
2
0
1
2
0
1
1
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
1
0
2
1
1
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
1
1
0
0
0
2
2
0
0
2
0
2
0
0
0
0
0
2
0
2
1
0
0
0
1
0
1
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
2
2
0
0
0
6
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
3
2
3
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
2
2
0
2
0
0
4
0
3
3
0
0
0
0
1
2
1
3
2
1
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
3
0
0
2
0
0
1
0
0
0
0
2
1
0
0
1
0
1
0
0
1
0
1
0
0
2
1
1
2
2
0
0
0
2
0
0
0
2
0
0
0
0
1
1
1
0
0
0
0
1
1
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
2
0
2
0
0
0
1
0
0
1
0
1
0
9
1
0
1
2
2
0
0
0
0
0
2
2
0
2
3
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
3
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
1
0
1
2
0
1
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
2
0
0
0
4
0
2
1
1
3
1
0
0
1
0
0
1
3
2
0
0
1
1
0
0
2
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
1
1
2
0
0
1
0
0
0
1
3
2
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
2
1
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
2
0
0
2
2
0
3
1
2
2
0
0
2
2
1
0
2
1
0
0
0
0
0
0
0
0
0
2
2
2
0
1
0
2
0
0
0
1
0
0
0
2
1
0
2
1
0
0
0
0
0
0
2
0
0
3
0
1
2
0
1
0
0
1
1
0
2
0
0
0
0
0
0
2
7
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
4
2
2
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
1
0
2
0
0
0
0
1
0
0
2
1
2
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
2
1
0
2
0
0
0
0
0
0
1
0
1
0
2
0
2
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
4
2
2
0
0
0
1
0
1
1
1
0
1
0
2
0
1
0
3
0
0
0
0
0
0
0
2
2
0
2
0
0
2
0
1
1
0
0
1
0
2
0
0
1
0
1
2
3
0
0
2
0
1
2
0
0
2
1
0
1
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
1
0
1
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
1
1
1
2
0
0
0
0
0
0
0
3
0
0
0
0
2
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
1
0
1
0
0
0
0
0
0
0
0
2
2
1
0
0
2
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
2
0
0
0
2
1
1
0
1
0
0
0
4
0
1
0
2
2
0
1
0
0
0
0
2
0
2
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
2
2
1
2
2
0
0
0
0
1
2
0
7
1
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
1
1
0
1
0
2
0
0
0
1
0
0
0
1
2
0
0
0
0
0
1
0
2
0
2
1
0
1
0
1
2
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
3
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
1
0
0
0
1
2
3
0
0
0
1
2
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
2
0
1
1
1
0
0
0
1
2
2
0
1
0
0
0
0
0
0
0
1
1
0
2
1
2
0
0
2
0
2
0
0
0
0
2
0
2
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
2
1
1
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
2
0
2
1
3
0
1
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
2
0
1
0
1
0
0
0
1
0
0
1
0
0
3
0
0
2
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
1
2
2
0
0
1
0
0
0
0
2
1
0
0
0
2
0
0
1
1
0
0
0
0
2
1
0
0
0
2
0
5
0
0
0
0
2
1
3
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
3
0
0
0
0
0
0
2
0
1
0
1
2
0
0
0
0
0
0
0
0
3
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
2
0
0
1
0
0
0
0
2
0
2
0
2
0
2
1
0
4
0
0
0
0
0
0
0
0
3
0
0
0
2
0
2
0
1
0
1
0
0
0
0
3
0
1
0
2
2
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
1
0
1
0
2
0
0
1
1
0
2
0
0
0
0
0
1
0
0
2
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
1
0
2
0
0
2
0
0
0
0
0
2
1
0
1
0
1
0
0
2
0
0
3
1
3
0
0
7
0
1
0
0
0
0
2
0
0
0
1
2
0
0
0
0
2
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
2
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
2
0
2
0
0
0
0
1
0
1
4
0
0
2
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
1
2
0
0
2
1
1
0
0
0
1
2
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
1
2
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
1
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
3
0
2
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
2
0
0
0
1
1
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
1
0
0
1
0
0
1
1
0
2
2
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
2
0
0
0
3
0
0
1
1
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
2
0
0
0
2
0
0
0
0
0
1
1
0
0
0
1
0
2
2
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
2
3
2
0
0
2
0
0
0
0
0
0
1
2
1
0
0
0
2
0
0
1
3
0
0
2
0
2
0
1
0
0
0
0
0
2
0
2
0
0
0
0
2
0
2
0
0
0
1
1
0
0
0
0
0
0
0
2
0
1
2
0
1
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
1
2
1
0
0
1
6
0
1
0
0
0
0
1
0
2
2
0
0
2
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
2
0
0
2
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
2
2
1
0
0
2
2
0
0
1
2
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
1
0
1
0
0
0
0
2
0
0
2
0
0
1
0
1
1
1
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
1
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
2
1
0
2
2
2
1
0
1
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
2
0
0
1
8
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
2
0
0
0
1
2
1
0
2
1
0
0
2
1
0
2
2
0
3
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
1
4
0
2
0
0
0
0
1
2
0
0
0
0
0
0
1
1
0
0
3
0
0
0
0
0
0
2
1
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
1
2
0
0
0
0
2
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
4
0
2
0
0
0
2
2
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
4
1
2
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
2
0
0
0
0
1
0
0
2
0
0
1
2
0
1
0
0
0
0
0
0
0
1
0
0
1
0
3
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
4
1
1
0
1
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
1
8
0
0
0
0
1
1
0
8
0
0
0
0
0
0
0
0
0
3
1
0
0
2
1
2
0
0
0
0
1
2
0
0
2
3
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
1
1
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
1
0
0
1
1
2
0
0
4
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
3
0
0
1
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
1
0
3
0
0
1
0
1
0
1
0
0
1
0
2
0
2
0
0
0
1
2
1
0
1
0
0
2
1
0
0
0
1
0
3
0
0
0
0
0
0
2
0
0
3
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
2
0
1
3
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
1
0
2
0
1
0
0
0
0
1
3
0
2
2
0
0
0
0
0
1
2
0
0
0
0
1
2
1
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
2
2
1
0
2
3
0
0
2
1
0
2
2
2
0
0
2
0
0
2
0
0
0
1
0
1
0
3
0
1
0
0
0
0
2
0
0
0
0
0
1
0
1
1
0
0
2
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
1
1
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
1
1
0
1
2
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
2
0
2
0
0
0
3
0
0
0
0
0
0
2
0
1
0
0
1
0
0
2
0
0
0
1
0
1
0
1
0
1
0
0
0
0
1
0
1
0
2
0
0
2
0
1
0
0
1
1
2
0
2
1
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
1
1
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
4
2
0
0
0
0
0
2
0
0
2
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
2
2
0
0
0
0
0
1
0
1
0
2
0
0
0
2
2
2
2
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
1
0
0
1
0
2
0
2
1
0
1
2
0
0
2
0
0
0
2
0
0
2
2
0
1
0
3
2
0
1
1
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
2
1
0
0
0
2
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
2
0
1
2
0
0
1
0
0
0
2
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
2
6
0
1
0
0
3
1
0
0
0
2
1
0
0
2
0
0
0
2
0
0
0
1
2
0
0
2
0
1
0
0
0
0
2
2
0
0
3
0
2
0
0
2
0
0
1
0
1
2
0
2
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
2
2
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
3
2
0
0
0
1
1
0
3
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
1
2
0
0
1
0
0
2
0
1
2
2
0
0
0
0
0
1
0
1
0
2
0
0
1
2
3
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
1
0
2
2
2
1
2
0
0
2
0
0
0
0
0
0
4
2
0
1
0
2
0
0
1
0
0
2
0
0
0
0
0
1
7
2
0
0
1
0
0
0
1
2
1
0
0
0
0
0
1
0
0
9
2
0
0
1
0
2
0
0
0
0
0
0
1
0
1
0
1
1
0
0
1
2
0
0
2
0
0
2
0
0
0
0
0
2
0
1
0
1
2
1
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
2
2
1
0
0
0
1
0
2
0
0
1
0
0
0
2
0
0
0
2
1
0
0
0
0
0
3
0
1
0
1
0
0
2
0
0
1
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
1
0
0
0
2
1
0
0
0
0
2
0
1
3
2
0
2
1
0
3
0
1
1
0
0
0
0
3
0
0
0
0
1
0
2
0
0
0
5
0
2
0
2
0
0
2
0
1
1
2
0
2
1
0
0
0
0
0
0
0
0
3
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
2
1
1
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
1
1
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
6
0
0
0
2
0
1
2
0
0
0
0
0
2
2
0
4
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
1
0
2
0
0
3
1
0
2
0
1
1
0
0
0
0
0
1
1
2
2
0
0
0
0
0
4
0
0
0
0
0
0
2
1
3
0
0
2
0
0
1
0
0
2
0
2
1
0
0
1
0
1
2
2
0
1
2
0
0
0
0
1
0
2
0
0
0
1
0
2
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
1
0
3
2
0
0
0
1
5
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
2
3
1
0
0
0
0
0
3
1
0
0
0
0
0
1
0
0
1
0
0
2
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
3
0
0
0
0
2
2
1
0
0
0
0
2
1
0
0
1
0
2
0
0
0
0
1
1
2
1
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
2
0
0
0
2
2
0
0
0
0
1
1
0
0
1
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
4
0
0
0
0
1
0
0
0
0
0
2
0
0
1
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
3
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
2
1
0
0
0
2
2
0
0
0
2
3
0
0
2
0
0
0
0
1
2
0
1
0
2
1
2
1
0
0
0
0
0
0
0
0
1
2
1
0
2
0
0
1
0
0
0
0
3
0
0
1
0
0
0
0
0
2
0
2
2
0
0
2
1
0
1
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
1
1
0
0
0
0
2
1
0
1
0
1
0
1
2
2
0
2
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
2
2
0
0
1
0
0
0
1
2
1
0
0
0
0
1
0
1
0
2
0
2
0
1
0
0
2
0
1
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
1
0
2
0
2
1
1
1
0
2
0
0
1
0
0
3
1
2
0
0
1
1
0
0
0
1
1
0
0
0
1
1
0
0
0
1
1
1
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
2
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
1
1
2
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
1
2
0
0
0
0
2
0
0
2
3
2
1
0
2
4
3
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
2
1
2
1
0
7
1
0
0
2
0
0
1
0
1
2
1
0
0
0
0
1
0
0
0
0
0
0
0
2
1
1
2
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
2
2
0
2
0
0
2
1
0
2
0
0
1
0
2
0
0
2
0
2
1
1
1
3
1
0
0
0
0
0
0
0
2
0
2
0
0
0
1
2
0
0
0
0
7
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
1
0
0
1
2
0
0
1
0
1
0
0
2
0
4
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
2
1
0
2
0
0
2
1
0
0
0
0
0
0
0
1
3
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
2
1
2
1
0
2
0
1
0
0
0
2
0
1
1
0
0
3
0
3
2
2
0
0
0
0
0
0
1
0
1
2
0
0
0
1
0
1
2
0
0
0
2
0
1
0
0
2
0
0
0
3
0
0
1
1
0
0
0
2
1
4
0
2
1
2
1
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
2
0
0
0
1
0
0
1
0
0
1
2
2
2
2
2
1
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
2
1
2
3
0
1
1
0
0
0
2
0
0
0
1
1
0
0
1
3
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
2
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
2
3
2
2
0
2
0
0
1
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
2
1
1
0
2
2
0
2
0
0
1
0
3
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
1
0
0
0
2
0
0
0
2
0
1
1
0
0
0
1
2
0
0
3
3
0
0
0
1
2
2
0
0
0
2
0
0
1
2
0
0
1
1
2
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
2
2
0
2
1
0
0
1
2
0
2
0
5
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
2
2
0
0
1
2
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
1
2
0
0
2
0
2
0
0
0
2
0
0
1
2
0
0
0
0
2
2
0
0
0
1
0
1
0
0
2
1
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
3
1
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
2
2
0
0
2
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
2
0
0
0
2
2
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
2
0
0
0
0
1
0
0
0
0
1
2
0
0
0
1
0
1
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
2
0
0
1
2
2
0
0
0
0
0
2
2
0
0
1
4
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
3
0
2
0
0
2
1
0
1
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
2
4
0
0
0
0
1
1
1
0
0
3
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
2
0
6
2
3
0
0
0
0
2
0
0
2
1
0
0
0
0
0
3
1
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
1
0
0
1
0
0
5
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
1
0
0
0
4
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
2
0
2
1
1
2
1
0
0
1
0
2
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
3
2
2
0
0
0
0
1
0
0
1
2
1
1
0
0
0
0
0
0
0
0
0
4
0
4
0
0
1
0
1
0
0
0
0
0
2
0
2
0
0
2
0
0
0
1
1
2
0
0
1
1
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
3
1
1
0
2
0
0
0
0
0
0
2
1
0
0
1
2
2
0
0
0
1
0
0
2
0
0
0
0
2
0
0
1
2
0
1
0
0
0
0
4
0
0
0
0
1
1
1
0
0
0
0
0
1
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
2
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
2
0
0
0
1
1
0
0
1
3
0
0
2
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
1
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
1
0
2
0
0
0
0
0
4
0
2
1
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
4
2
0
0
0
0
0
0
1
0
2
1
0
0
0
0
3
0
1
1
0
0
0
2
0
2
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
7
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
1
0
1
2
0
1
1
0
0
0
3
1
2
2
2
0
0
0
1
0
2
1
0
2
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
3
1
0
0
0
0
0
0
2
2
1
0
1
0
0
4
0
0
1
0
1
0
0
1
0
2
1
2
0
0
1
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
3
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
3
0
1
2
1
0
4
2
0
3
3
0
0
0
0
0
0
2
1
0
0
0
2
2
0
0
0
0
0
2
1
0
0
0
2
0
1
1
1
0
0
1
2
0
1
1
0
0
0
0
4
0
0
2
0
3
1
1
1
2
0
0
0
0
0
0
2
0
0
0
0
0
3
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
1
0
0
0
3
1
0
1
1
0
0
0
0
1
0
0
0
2
2
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
2
0
0
1
0
2
0
0
1
0
0
2
0
0
0
4
2
1
1
1
0
1
0
0
0
1
0
0
0
0
1
3
0
0
0
1
2
1
0
0
2
1
2
0
0
3
0
1
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
1
0
1
2
0
0
1
2
0
0
2
2
0
0
0
2
0
0
0
2
2
5
0
1
2
3
0
0
0
2
1
0
1
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
1
2
0
0
0
2
0
2
0
0
4
0
0
1
3
2
0
0
0
0
2
0
0
0
0
2
2
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
1
2
1
0
0
0
0
0
0
0
2
0
2
0
1
1
0
1
0
0
1
1
0
0
1
1
0
0
3
2
0
0
0
0
2
0
1
4
0
1
1
1
1
0
0
1
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
2
0
0
0
0
0
1
0
1
2
2
0
1
0
0
0
2
0
2
0
3
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
5
0
1
0
0
0
0
0
1
0
0
0
0
0
3
2
2
0
0
1
2
0
0
2
0
2
0
1
1
0
0
0
3
0
0
2
0
0
0
1
0
0
0
0
3
2
0
0
2
1
0
0
0
0
0
0
2
0
1
0
1
0
1
0
0
0
0
1
0
0
0
1
3
0
3
1
2
0
2
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
1
2
1
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
1
0
3
1
2
0
0
1
1
0
0
0
0
2
0
0
0
0
0
3
1
0
0
0
1
1
0
0
2
2
0
0
0
0
0
1
0
1
2
1
0
0
0
0
0
2
0
0
0
0
0
0
3
0
2
0
0
0
1
0
1
0
0
5
2
0
1
0
1
0
0
0
0
1
1
0
1
0
2
0
0
0
0
1
2
0
3
2
0
0
2
0
2
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
1
0
0
1
0
0
1
1
0
2
2
0
0
0
0
2
0
0
0
2
0
1
0
1
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
1
3
0
0
2
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
2
0
1
1
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
1
0
0
2
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
2
3
0
0
1
2
0
0
0
0
0
2
2
1
0
0
1
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
2
0
0
0
0
1
0
1
0
0
1
1
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
1
0
0
1
2
2
0
2
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
3
1
2
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
2
0
0
2
0
0
1
0
0
0
0
5
0
0
1
0
0
2
0
5
0
0
0
0
0
1
0
1
0
1
0
0
0
1
2
0
0
0
0
1
2
0
0
0
1
0
0
0
2
0
0
0
2
0
0
1
0
1
0
2
1
0
1
0
2
0
2
0
0
0
2
0
0
2
1
0
0
1
0
0
0
1
0
0
0
1
1
0
2
0
0
0
0
0
0
2
2
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
2
3
2
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
1
1
2
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
1
2
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
1
0
1
0
3
1
2
2
0
0
0
0
2
0
0
0
0
1
0
2
2
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
1
2
3
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
2
1
2
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
7
0
0
2
0
0
0
2
0
0
0
0
1
0
3
0
2
1
2
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
3
0
1
0
0
4
0
1
0
0
0
0
0
1
0
1
0
2
0
0
0
1
2
0
1
0
0
0
0
0
2
0
0
0
0
1
1
0
1
0
0
0
0
0
2
0
0
1
0
1
2
0
2
0
0
1
2
0
0
0
1
1
1
0
0
0
0
0
0
2
0
0
0
0
1
2
0
2
1
2
0
0
2
1
1
0
0
2
0
1
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
3
1
0
0
0
0
0
1
0
0
0
1
0
0
1
2
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
2
0
3
1
1
0
1
0
0
0
0
1
3
0
0
1
0
0
0
2
0
0
0
1
2
0
1
1
0
0
1
0
0
0
1
0
2
0
0
0
2
0
1
1
0
0
2
0
0
0
0
0
0
1
0
0
2
0
1
0
1
0
2
0
1
0
0
1
0
1
0
0
0
1
0
0
0
1
1
0
0
1
2
1
0
0
0
2
0
0
1
2
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
1
2
1
2
0
2
0
0
0
0
2
1
3
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
2
1
0
2
0
0
0
0
2
2
2
0
0
0
0
0
0
0
1
1
0
3
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
6
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
2
0
0
1
0
0
2
0
2
0
0
1
0
0
0
2
0
0
0
0
2
0
2
0
0
4
0
3
0
2
0
0
1
0
2
0
2
1
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
3
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
1
2
0
2
0
1
2
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
1
1
0
1
1
0
0
0
0
0
0
0
0
1
3
0
0
1
0
2
0
2
1
1
1
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
2
1
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
1
0
0
0
2
1
0
2
0
0
2
0
2
0
0
0
2
0
1
3
0
0
0
0
0
0
0
2
1
0
0
0
0
1
2
3
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
3
0
0
0
2
0
1
0
0
0
1
0
2
0
0
0
1
0
0
1
3
0
0
2
1
0
0
0
2
2
0
0
0
0
1
1
1
0
0
3
0
6
1
2
2
0
0
0
1
0
2
0
0
2
2
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
1
2
1
0
0
2
0
0
2
2
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
3
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
4
0
2
1
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
1
0
0
0
2
2
1
0
1
0
2
1
1
0
0
0
0
1
1
2
0
3
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
3
0
0
0
0
0
1
1
0
0
0
4
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
1
1
3
1
0
0
0
0
0
0
0
0
1
0
1
3
0
0
0
2
0
0
0
3
2
0
2
0
2
0
0
0
2
1
0
0
0
2
0
1
0
2
2
0
2
0
0
1
1
2
1
1
0
0
1
1
1
0
0
1
1
0
0
0
0
1
0
1
2
0
0
1
0
0
0
0
0
2
0
0
0
0
1
2
0
2
1
1
4
0
0
0
0
0
2
1
1
0
3
0
0
0
0
0
1
2
0
0
1
1
0
1
2
0
0
0
1
1
0
0
2
0
0
0
0
0
0
2
0
3
0
1
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
1
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
2
0
2
0
0
0
0
2
1
0
2
1
0
0
0
1
0
0
1
0
2
0
0
0
3
0
0
0
0
0
0
0
4
0
0
2
0
2
2
0
2
3
1
0
0
0
0
0
2
0
0
4
1
0
3
1
0
0
2
4
0
0
1
0
0
0
0
2
0
0
0
1
0
1
0
0
0
1
0
1
0
1
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
2
1
1
2
0
0
0
4
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
2
1
0
2
1
2
0
0
0
1
0
0
1
0
1
0
1
0
0
1
1
2
0
2
1
4
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
1
2
0
0
0
1
0
0
2
0
1
0
0
2
0
0
1
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
2
2
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
4
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
3
2
2
0
2
1
0
0
0
0
1
0
1
1
0
2
0
1
0
0
2
0
0
0
0
0
3
0
0
1
0
0
0
1
0
0
0
0
1
2
0
1
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
2
0
0
1
0
2
1
1
2
0
0
1
2
3
0
2
0
1
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
2
0
1
1
0
0
5
1
5
2
0
0
0
0
0
2
1
4
0
0
1
0
0
0
1
0
1
3
0
0
2
2
0
0
0
2
0
0
0
2
0
2
1
0
3
0
0
1
1
0
0
1
0
0
1
1
1
1
0
0
1
0
0
0
0
1
0
4
0
0
0
0
0
1
1
1
0
0
0
0
3
0
2
0
0
0
2
1
1
3
0
0
0
1
0
0
1
1
1
0
1
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
2
1
0
2
2
2
1
0
0
2
0
0
0
2
0
0
0
0
0
1
2
0
0
0
2
0
1
0
0
0
1
1
3
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
1
2
3
0
1
0
1
0
1
2
0
0
0
2
1
0
0
0
1
0
3
0
0
2
2
0
0
2
0
0
0
0
2
1
0
2
2
0
0
1
0
0
1
0
0
0
2
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
1
0
0
1
2
0
0
0
1
0
0
0
0
0
2
0
0
3
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
1
1
0
2
0
0
2
0
0
0
3
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
2
0
0
0
0
2
0
0
2
2
1
0
2
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
2
2
1
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
2
0
0
1
1
0
1
0
2
1
0
0
1
2
2
0
0
0
0
5
2
1
0
0
2
2
0
2
0
0
1
1
0
0
0
0
0
4
1
0
0
0
0
0
0
0
5
3
0
0
0
0
0
3
2
0
2
2
0
0
0
0
3
2
1
0
0
0
1
0
0
0
0
0
2
2
0
0
2
1
0
0
0
0
0
0
1
0
1
2
1
0
0
0
0
0
0
2
0
0
2
1
1
1
0
0
1
0
0
1
0
2
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
3
0
2
2
0
1
1
3
1
0
0
2
1
0
0
0
2
0
0
0
0
1
0
3
1
2
2
0
1
2
4
0
0
0
0
2
0
2
2
0
2
1
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
2
0
0
0
1
2
0
1
2
3
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
2
0
0
1
0
2
0
3
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
1
2
0
0
0
0
1
0
2
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
1
1
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
1
0
1
1
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
3
0
2
1
0
0
0
0
0
0
12
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
1
0
1
2
0
0
0
0
1
0
0
0
0
2
0
1
0
0
1
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
2
2
2
0
0
1
0
0
0
1
1
2
0
2
1
1
2
1
0
0
1
0
0
2
1
0
0
0
0
3
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
1
0
0
3
0
0
0
0
0
0
0
1
0
0
1
1
0
0
2
0
2
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
3
0
0
0
0
0
1
2
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
2
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
2
1
0
0
0
1
5
0
2
0
2
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
2
2
1
1
0
2
0
0
1
1
0
0
0
1
0
0
2
2
1
0
0
1
0
0
0
0
0
3
0
2
0
1
0
0
0
1
0
0
2
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
2
6
0
0
2
0
2
2
0
0
0
1
0
0
0
0
3
1
1
1
2
0
0
2
0
1
0
0
5
0
3
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
6
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
2
0
0
0
2
0
0
2
0
3
0
0
2
0
2
1
0
0
1
0
1
0
0
0
5
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
2
1
0
0
2
0
2
0
1
1
0
1
3
2
0
0
2
0
2
1
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
2
2
2
0
1
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
1
0
2
0
0
0
3
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
1
0
0
0
0
0
2
2
1
0
1
0
0
0
0
0
3
0
0
0
0
1
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
2
0
2
0
1
1
1
0
0
2
4
1
0
0
0
0
0
2
1
0
2
0
0
2
0
0
1
1
1
0
0
2
0
0
0
2
0
0
0
1
0
0
2
0
0
9
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
1
0
0
0
0
1
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
1
0
2
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
2
1
1
1
0
0
1
0
0
1
1
1
1
1
0
0
0
0
0
0
1
2
2
2
0
0
0
1
1
1
0
0
0
2
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
4
0
2
2
0
0
0
0
1
0
0
0
0
1
0
2
0
1
0
0
2
1
0
0
0
0
3
0
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
2
1
0
0
2
2
1
2
0
2
0
1
0
0
2
0
0
2
0
0
0
0
1
6
1
3
0
0
1
2
0
2
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
3
0
0
0
1
2
0
0
0
3
2
0
0
0
0
1
0
0
0
3
2
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
1
3
0
0
2
0
1
0
0
2
0
0
2
0
0
0
2
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
4
0
1
0
2
0
2
0
1
0
0
0
0
0
2
0
0
1
2
2
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
1
0
1
0
0
0
0
1
0
1
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
2
0
0
0
1
1
0
1
5
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
1
0
0
0
0
0
1
1
0
0
2
1
2
2
0
2
1
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
2
0
1
0
0
0
0
1
0
2
1
0
2
0
0
0
1
1
0
0
2
0
1
3
0
0
0
0
1
0
2
0
3
0
0
1
1
0
1
0
0
0
0
0
2
1
2
0
0
0
0
0
0
2
1
1
0
0
0
0
2
2
2
0
2
1
0
0
2
0
2
1
0
2
1
0
0
0
2
2
0
1
0
0
1
0
0
0
2
1
0
0
1
0
0
1
2
1
0
0
0
0
2
1
0
1
0
0
1
1
0
0
0
2
0
1
1
0
2
2
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
3
1
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
1
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
2
1
2
2
0
1
0
2
0
1
1
0
2
2
1
0
2
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
1
0
0
1
2
2
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
2
0
0
0
0
3
2
1
0
0
2
0
2
1
2
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
1
1
0
2
0
1
1
0
2
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
4
0
0
0
2
0
0
2
1
2
0
1
1
2
0
0
1
0
1
1
2
0
1
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
1
2
0
0
1
1
0
0
0
1
1
0
0
2
1
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
3
2
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
2
0
0
0
2
2
1
0
0
0
1
1
0
0
0
0
0
0
0
3
0
1
0
0
1
0
0
0
0
0
1
4
0
0
2
0
1
1
2
0
1
1
1
0
0
0
2
0
2
0
0
2
0
2
1
2
2
12
2
0
2
1
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
1
0
0
2
0
1
0
0
2
0
0
0
0
0
1
0
0
1
2
0
0
0
2
3
1
0
0
0
0
1
1
1
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
1
4
0
1
1
2
0
2
0
0
0
4
0
0
0
0
0
3
1
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
2
0
0
0
0
1
1
0
1
1
1
0
1
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
2
0
0
2
0
0
0
2
0
2
1
0
1
0
0
0
0
0
1
0
0
0
3
1
0
0
0
1
1
0
0
0
1
0
1
0
1
0
2
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
1
2
0
0
1
2
1
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
2
0
1
1
0
2
0
0
4
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
1
0
0
1
0
0
0
0
0
1
0
2
0
0
1
0
1
1
0
0
2
0
1
0
1
0
0
1
2
0
1
0
1
0
1
0
0
0
2
1
0
0
0
0
0
0
0
1
0
2
1
1
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
2
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
2
2
0
1
2
0
0
0
1
1
0
0
2
3
0
0
0
0
0
2
0
2
0
0
0
0
2
0
1
0
1
0
0
3
1
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
2
2
0
0
1
1
1
0
0
0
0
0
2
7
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
1
1
1
0
1
2
2
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
2
0
2
0
0
1
0
2
2
3
1
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
4
0
2
0
0
1
0
0
2
0
1
0
0
1
0
1
2
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
2
0
0
3
2
0
0
1
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
5
0
2
2
0
0
0
2
0
0
0
2
0
2
0
3
0
0
0
0
1
1
0
1
2
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
1
2
0
2
0
0
0
1
0
1
1
0
1
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
6
0
1
0
2
0
0
0
0
0
1
1
0
2
0
0
1
0
1
0
0
0
0
1
0
0
1
0
2
1
0
0
2
0
0
2
0
0
1
2
0
0
0
1
1
0
0
3
2
3
0
2
3
2
1
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
2
0
2
0
0
2
0
2
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
1
2
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
2
2
2
2
0
0
0
2
1
0
1
0
0
1
0
0
2
1
2
1
0
0
0
1
0
0
1
0
0
0
2
1
0
0
2
0
0
0
2
4
0
0
1
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
2
0
2
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
2
2
0
0
12
0
0
0
0
0
0
0
0
0
1
2
1
2
1
0
0
0
3
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
5
2
3
1
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
1
0
0
0
0
2
0
0
1
4
3
1
0
0
2
0
3
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
2
0
1
2
0
2
0
2
0
2
0
0
0
1
0
5
0
1
0
1
0
0
1
0
0
1
0
0
0
2
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
1
2
2
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
1
2
0
1
2
0
0
3
0
2
0
1
0
0
0
0
2
0
0
2
0
1
0
0
0
1
0
2
0
0
0
0
1
0
0
1
0
1
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
1
1
1
1
0
1
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
1
0
2
0
2
2
0
0
0
0
2
0
1
0
4
1
0
2
0
0
0
1
4
0
1
1
0
0
0
0
1
3
1
0
0
0
3
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
2
0
0
0
1
0
1
0
0
0
3
1
0
1
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
2
0
2
0
0
0
0
1
1
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
4
0
1
1
1
2
2
1
2
0
0
1
0
0
0
1
1
0
2
1
0
0
2
0
0
0
0
2
3
0
0
0
1
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
1
0
0
0
2
0
1
0
1
0
1
1
0
2
0
0
0
0
0
1
0
0
0
0
2
2
1
0
0
0
0
1
2
0
0
0
0
1
0
0
2
0
0
2
0
2
0
0
1
2
0
1
0
3
0
1
0
0
2
3
1
2
1
0
2
0
0
0
0
0
3
0
0
0
2
0
2
2
2
0
2
0
0
2
0
2
1
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
2
0
0
0
2
2
0
1
3
0
0
1
0
0
2
1
0
1
2
1
0
0
0
2
0
0
1
0
0
0
0
2
0
2
0
0
0
2
1
0
0
0
0
2
0
0
2
0
0
2
2
0
0
0
0
0
0
2
0
2
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
4
4
0
1
1
0
1
0
0
0
1
0
0
0
1
0
2
2
0
1
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
2
0
1
0
1
0
0
0
0
0
2
2
1
0
0
0
2
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
1
1
0
3
0
0
0
1
1
0
0
0
1
0
2
2
0
2
0
0
0
0
0
0
0
1
0
2
1
2
0
0
0
0
2
0
1
1
0
0
2
0
1
0
0
0
0
0
2
2
1
0
0
0
0
1
0
2
0
0
0
1
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
3
0
0
2
0
0
0
2
0
0
0
0
0
0
3
0
2
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
1
1
4
0
0
1
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
1
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
2
0
0
1
1
1
0
0
0
0
0
1
1
0
2
0
0
0
0
2
0
0
1
0
0
3
0
0
0
0
0
1
0
2
0
0
0
1
9
1
3
0
1
0
0
0
0
2
0
0
0
2
0
2
0
0
0
2
1
0
0
1
0
0
2
2
0
0
2
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
2
1
0
0
1
2
0
3
2
2
0
0
0
0
0
2
0
0
0
0
0
2
1
2
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
1
0
0
2
0
2
2
0
2
0
2
1
1
1
0
1
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
1
1
4
1
0
0
0
2
0
0
0
1
2
3
1
2
2
0
2
0
0
0
0
0
0
2
0
1
1
1
0
2
0
0
0
1
0
0
1
0
0
5
2
0
2
1
2
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
1
0
1
0
0
0
2
0
0
0
3
1
2
0
2
0
0
0
3
0
0
0
0
0
1
0
3
0
0
2
0
0
2
0
0
0
0
2
4
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
2
0
0
0
1
0
1
0
0
0
2
0
0
2
2
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
1
0
2
1
0
1
2
0
0
3
0
0
0
0
2
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
3
0
0
1
0
2
0
2
0
0
1
0
2
2
0
0
0
0
2
0
2
0
1
1
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
2
2
0
0
0
1
2
0
2
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
2
2
0
1
0
0
6
0
0
0
1
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
1
0
1
0
0
1
2
0
0
0
0
0
0
3
0
0
0
2
0
1
1
0
2
1
1
1
0
2
0
0
0
0
1
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
2
0
0
1
2
5
0
0
1
2
0
0
0
0
0
0
1
0
0
1
0
5
1
0
1
2
0
2
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
1
0
0
3
0
0
5
2
2
0
1
0
0
0
1
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
1
1
2
0
0
0
0
3
2
0
0
1
0
0
0
2
1
1
0
1
0
2
0
1
0
2
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
1
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
2
1
0
1
2
2
0
0
0
0
0
0
1
1
0
2
0
1
0
0
0
2
2
1
0
0
0
1
0
2
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
1
3
2
0
0
0
1
0
2
2
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
1
0
0
1
1
1
0
2
0
0
0
0
1
0
0
2
1
0
0
1
0
1
0
1
0
1
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
2
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
3
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
2
1
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
1
0
0
0
0
0
0
1
0
3
1
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
2
0
0
0
1
0
0
0
1
0
2
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
2
0
2
0
0
1
2
1
0
2
0
1
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
1
2
2
2
2
0
1
0
0
0
0
0
0
1
1
2
0
0
0
1
2
0
0
1
0
3
0
0
0
0
0
0
0
2
2
0
0
1
0
2
1
1
0
0
0
0
0
0
0
2
0
0
0
0
4
0
0
0
1
0
2
0
0
9
0
1
0
1
1
1
2
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
2
1
1
2
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
1
0
0
2
0
2
6
0
2
0
1
0
0
0
1
2
0
0
0
1
3
0
0
1
2
2
0
1
0
1
0
2
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
2
1
0
0
0
1
1
0
1
0
0
0
0
0
1
0
2
0
1
0
0
1
2
0
0
1
2
0
0
0
2
0
0
1
2
0
6
0
0
1
0
0
0
1
0
0
2
0
2
0
0
0
1
0
2
0
0
0
0
1
1
3
0
0
0
1
0
2
4
3
0
2
0
2
0
2
0
2
2
1
0
0
0
0
0
0
0
1
2
0
2
0
0
1
1
0
0
0
1
0
0
0
0
1
1
2
1
0
0
0
0
2
3
0
0
2
0
4
0
0
0
2
1
0
0
0
0
1
3
0
0
0
0
1
0
2
0
0
0
0
1
0
1
2
0
0
1
0
0
1
3
0
2
2
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
1
1
0
2
0
1
0
0
0
0
3
0
0
1
0
0
2
0
0
0
2
0
0
1
0
0
1
0
3
0
1
0
1
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
1
2
0
0
1
3
2
1
0
0
0
1
6
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
2
1
0
3
0
0
1
0
2
0
1
0
1
0
0
0
0
0
0
2
0
1
0
0
2
0
2
0
0
0
1
0
0
0
0
1
0
3
0
0
0
0
0
2
0
0
0
1
3
0
0
0
1
0
0
0
1
0
0
1
0
0
2
0
0
2
0
1
0
0
0
0
2
1
0
0
2
1
0
0
1
0
0
0
2
0
1
0
0
0
2
1
0
0
1
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
1
0
0
0
0
2
0
0
0
2
0
0
0
1
2
4
0
2
0
1
2
2
0
0
0
0
0
0
0
3
0
2
1
1
0
1
0
0
0
0
0
0
2
1
0
1
2
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
2
0
2
1
1
1
1
2
1
0
2
0
1
2
1
0
0
0
0
1
1
0
2
0
2
2
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
3
6
0
0
0
0
1
0
0
3
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
1
0
3
0
0
0
0
2
0
0
1
2
0
0
0
0
1
0
0
1
0
0
2
0
3
1
2
0
0
3
1
2
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
2
2
1
2
0
0
0
0
0
1
0
0
0
0
2
0
2
2
0
0
2
2
0
0
2
0
2
0
1
1
2
0
0
0
0
0
0
0
0
1
2
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
3
0
2
0
1
2
0
0
0
2
0
0
0
1
0
0
0
0
0
2
2
0
0
1
1
2
0
0
0
0
0
4
1
0
0
1
0
1
0
0
2
1
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
2
2
0
0
0
0
0
3
0
0
3
0
1
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
1
2
1
0
0
2
4
1
4
0
0
1
3
1
1
0
0
0
3
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
1
3
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
3
1
0
0
1
0
1
0
0
0
2
0
0
0
0
0
1
1
0
0
0
1
0
0
2
0
1
0
0
0
1
0
0
0
2
0
0
0
1
0
1
2
0
2
0
1
0
1
0
0
0
1
2
2
0
0
1
2
0
2
1
0
3
0
1
1
0
1
1
0
0
0
0
2
0
1
0
2
1
0
2
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
1
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
4
0
2
0
0
0
1
2
0
1
0
0
0
2
0
0
0
0
0
2
0
2
2
0
2
1
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
1
2
1
0
1
1
2
2
0
1
2
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
2
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
3
0
2
0
0
5
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
3
1
1
0
0
0
0
2
2
0
0
0
0
5
0
1
0
0
1
0
0
0
0
0
0
1
2
0
2
2
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
2
2
1
0
0
0
2
0
1
0
0
1
0
1
0
1
2
0
0
2
0
0
0
0
2
1
0
1
0
2
0
2
0
0
0
1
0
0
1
2
0
0
1
1
0
2
0
0
1
0
0
0
2
0
0
2
0
3
0
0
0
2
0
2
0
0
0
0
0
2
2
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
2
3
0
0
0
0
0
1
0
2
2
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
1
0
0
1
0
1
2
0
0
1
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
1
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
1
0
2
0
2
0
2
0
0
0
1
3
1
0
0
0
0
0
1
1
0
0
0
0
1
2
1
0
0
2
0
0
2
0
0
1
0
2
2
0
0
1
2
0
2
0
0
1
2
0
0
0
0
2
0
0
0
1
0
0
0
2
1
0
0
2
0
0
0
0
0
0
2
0
0
0
1
2
2
1
2
0
0
1
0
0
1
0
0
0
2
0
0
0
1
2
0
0
2
0
1
2
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
1
2
0
0
0
0
1
2
0
1
0
0
0
2
2
2
0
2
0
2
0
3
0
0
0
1
0
0
3
1
1
2
0
0
2
0
0
0
3
1
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
1
2
0
0
1
0
0
0
0
7
0
0
2
0
1
0
0
2
0
1
0
0
0
0
0
0
2
0
1
0
0
2
1
2
0
1
0
1
0
1
1
0
1
0
0
2
0
2
0
1
0
1
0
0
2
1
0
1
1
0
0
1
0
3
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
1
1
0
0
0
1
2
0
2
0
0
0
0
0
0
2
0
0
0
5
2
2
4
0
1
0
3
1
0
0
0
0
0
1
0
0
0
0
0
0
3
0
1
2
2
1
0
0
0
0
1
0
1
0
0
1
1
3
3
0
0
0
2
0
0
1
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
2
2
0
0
0
0
0
1
0
0
2
0
0
2
1
2
1
2
0
0
0
0
0
0
0
0
1
1
0
2
0
3
0
0
0
2
1
2
0
2
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
2
0
3
3
0
0
0
1
2
1
1
0
0
0
0
1
2
2
0
0
1
1
0
1
2
0
0
0
0
0
2
0
0
2
2
0
2
2
0
0
2
1
1
0
0
0
2
1
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
2
0
1
0
2
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
2
0
1
0
0
2
0
2
0
0
0
0
0
0
1
0
1
0
2
0
0
0
1
1
0
1
0
0
0
2
0
2
0
0
2
0
0
0
1
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
2
0
0
0
0
0
0
0
1
2
2
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
1
0
3
0
0
2
1
0
0
0
0
0
0
1
0
0
2
2
0
2
2
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
3
0
0
0
0
2
3
0
1
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
1
1
2
0
1
0
2
1
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
2
0
2
0
0
0
1
2
2
2
1
2
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
3
2
1
0
2
1
0
0
0
3
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
2
0
0
1
2
4
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
2
1
0
0
2
0
0
0
0
3
0
0
1
0
3
0
0
0
0
0
2
1
2
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
4
0
0
0
0
0
1
0
1
0
0
0
0
2
1
0
0
2
1
0
2
1
0
0
1
2
1
0
0
1
0
0
0
0
0
1
0
1
0
0
1
2
0
2
0
1
0
0
10
1
0
1
2
2
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
1
1
0
0
2
2
2
0
2
0
1
0
0
0
0
2
0
0
1
1
0
1
0
2
1
0
0
1
0
0
0
1
1
0
0
2
0
0
0
0
0
2
0
0
3
2
4
2
0
0
0
0
0
2
2
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
2
2
1
0
0
0
0
2
2
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
4
0
0
1
1
0
1
0
0
0
2
0
2
0
1
1
0
0
2
0
2
2
0
0
0
0
0
0
0
2
1
0
0
0
0
1
2
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
1
1
0
1
0
1
0
0
1
3
0
0
0
0
0
0
0
0
1
0
0
0
0
1
3
0
0
0
0
2
0
2
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
1
1
0
3
2
0
0
2
0
0
1
0
2
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
1
0
1
0
2
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
2
0
0
0
1
0
1
1
0
0
1
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
2
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
2
0
3
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
2
0
0
3
0
0
0
1
2
1
0
0
0
0
0
2
0
0
2
0
0
2
0
2
0
0
1
1
2
2
0
1
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
3
1
2
1
0
1
1
2
0
0
0
1
0
0
0
0
2
1
2
0
0
0
2
0
2
1
0
0
2
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
2
0
0
2
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
1
2
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
3
0
0
0
1
1
0
2
0
0
5
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
2
0
0
2
0
2
0
8
0
0
1
0
1
2
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
2
2
1
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
2
0
2
0
0
0
2
0
2
0
0
2
2
0
0
2
1
0
0
0
0
0
2
0
2
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
2
0
2
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
7
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
2
2
1
0
1
2
2
1
2
0
0
0
2
0
0
0
3
2
3
0
2
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
2
1
1
2
0
0
0
0
1
0
1
0
2
0
2
0
0
0
0
1
2
0
0
0
1
1
2
2
0
1
1
0
3
0
5
0
0
0
2
2
1
1
0
0
2
0
0
0
0
0
1
0
1
2
1
1
0
1
0
1
2
2
0
0
0
2
1
0
0
0
0
0
2
7
0
2
0
0
2
0
1
1
2
1
0
0
0
0
0
2
2
1
1
0
0
0
0
2
0
0
0
0
1
1
2
0
4
0
1
0
0
0
0
0
0
0
3
2
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
2
0
1
0
0
2
0
2
0
2
0
0
0
0
2
1
2
2
0
2
2
2
0
2
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
2
0
2
0
0
2
0
1
0
0
0
0
1
1
0
1
2
0
0
0
0
2
0
2
0
0
1
0
0
0
2
0
0
2
0
1
0
0
0
0
1
0
0
2
2
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
2
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
4
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
2
0
0
0
0
2
2
0
0
0
2
1
0
0
0
1
0
0
0
0
0
1
0
1
0
2
1
2
0
0
0
4
0
0
2
0
0
2
2
0
0
0
0
0
2
1
0
2
2
0
0
0
1
0
0
0
1
0
0
0
1
0
2
2
2
0
1
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
3
0
0
2
0
0
2
2
0
0
0
0
0
0
2
0
0
2
0
0
0
2
1
1
0
1
1
0
0
0
2
2
1
0
0
1
1
2
1
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
1
0
2
2
2
0
0
2
1
0
0
1
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
1
0
2
0
1
1
1
0
0
0
0
2
0
0
0
0
1
2
0
1
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
2
0
0
1
0
0
0
0
0
0
1
2
1
0
0
0
7
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
2
0
2
1
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
1
2
0
2
0
0
0
1
0
1
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
2
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
2
0
0
1
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
1
1
1
0
0
0
1
3
0
0
0
0
2
0
0
0
3
2
0
1
0
1
2
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
1
0
1
0
0
2
2
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
1
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
2
2
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
1
2
0
1
0
0
1
0
0
0
0
1
0
1
0
0
3
0
0
2
0
0
0
0
1
0
2
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
2
0
2
0
0
0
0
0
0
0
2
0
2
0
2
0
2
0
13
0
0
1
0
0
0
2
3
2
0
0
0
1
0
0
2
0
1
0
0
1
1
1
1
0
0
0
0
0
0
0
2
2
0
0
0
0
2
1
0
0
2
1
0
1
0
1
0
2
0
0
0
0
0
2
2
0
0
0
0
0
2
0
2
2
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
1
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
2
0
1
2
1
0
0
1
0
0
0
2
0
0
1
0
0
1
2
1
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
2
0
1
0
2
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
8
1
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
2
0
1
0
0
0
0
3
1
0
0
0
1
2
0
2
0
1
0
0
2
2
0
0
2
2
0
1
0
0
2
0
1
0
0
1
0
2
0
0
0
0
3
1
1
0
0
2
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
1
1
0
0
0
0
0
1
0
0
2
1
0
0
0
2
0
0
0
1
0
0
0
2
0
2
0
0
2
0
0
0
0
1
1
0
10
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
2
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
1
0
0
2
0
0
1
0
0
0
0
1
1
0
1
1
0
2
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
1
0
2
1
0
0
0
0
0
3
0
0
1
0
0
0
1
1
0
0
0
2
0
0
2
0
2
1
0
0
1
2
0
1
0
0
0
0
0
0
0
0
2
0
2
2
1
0
0
0
2
0
0
1
0
0
1
0
2
0
2
0
2
0
0
1
0
0
1
0
0
1
0
0
2
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
1
1
0
0
0
2
0
0
0
2
0
0
1
0
0
2
0
0
1
0
0
0
2
0
1
0
2
0
0
0
0
0
1
0
0
1
0
0
0
4
0
0
0
1
0
0
1
2
1
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
2
0
2
0
2
0
0
0
0
0
2
1
0
2
0
0
0
2
0
0
0
1
2
0
0
2
0
0
0
0
1
0
0
0
1
2
0
2
0
0
1
0
1
0
2
2
0
0
0
2
1
2
0
0
0
0
0
0
0
2
1
0
2
0
1
0
0
0
0
0
2
2
1
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
1
1
0
0
4
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
4
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
1
2
2
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
3
2
0
0
0
5
2
0
0
1
0
1
2
0
0
0
0
1
0
0
1
4
0
0
0
2
0
1
0
0
0
1
0
2
0
0
1
0
1
2
0
2
0
1
1
2
0
0
0
0
2
1
0
0
1
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
1
1
0
0
0
0
2
1
1
1
0
0
0
0
0
0
3
1
0
2
1
0
0
2
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
1
1
0
1
2
0
2
2
0
0
2
0
0
0
0
0
0
2
0
0
0
1
2
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
2
2
0
0
0
1
0
0
2
0
3
0
0
1
0
0
2
2
0
0
1
1
1
0
1
0
1
2
0
5
2
0
1
1
0
0
2
1
0
0
2
1
0
2
1
0
0
0
0
0
3
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
1
2
0
1
0
0
4
1
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
2
2
2
0
2
1
0
2
4
0
1
0
2
1
0
0
0
0
0
5
2
2
0
0
0
2
0
0
2
1
0
0
0
0
0
2
0
1
0
1
0
0
1
0
0
0
0
1
0
1
0
1
0
0
1
0
2
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
2
1
0
1
0
0
0
0
0
2
0
1
0
0
0
1
1
0
0
0
0
0
0
2
0
1
0
0
2
0
1
1
0
0
0
0
0
0
0
1
0
1
1
2
0
0
0
0
2
3
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
2
0
1
2
0
0
0
1
2
1
0
0
1
0
0
2
0
0
0
2
1
0
0
1
0
1
0
2
0
1
1
0
1
1
2
0
0
1
1
0
1
2
0
0
2
1
1
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
2
0
0
0
2
0
1
0
1
0
1
0
1
2
0
0
2
2
1
0
0
0
1
0
0
2
0
0
0
1
0
1
0
0
0
0
0
1
0
1
2
0
0
0
0
0
2
0
0
2
1
1
1
0
0
1
0
2
2
2
0
2
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
2
1
0
2
0
0
2
0
0
0
1
0
1
0
1
0
0
0
0
0
1
1
0
0
1
2
0
2
0
1
0
1
1
0
0
0
1
0
0
1
3
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
1
0
0
2
0
0
2
0
2
0
0
0
2
0
0
0
1
1
0
0
2
2
0
0
2
0
0
0
2
0
0
0
0
0
1
1
2
2
2
0
1
1
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
3
1
3
1
1
0
0
0
1
0
0
0
2
1
0
2
0
0
1
0
1
0
1
1
0
0
0
2
0
2
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
1
2
0
1
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
1
1
0
0
0
0
0
0
2
2
0
1
0
0
2
0
0
0
1
1
0
0
0
0
2
1
0
0
0
1
2
0
0
1
0
0
0
2
2
0
1
2
1
0
2
0
0
0
0
0
2
1
0
0
0
0
4
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
2
2
2
0
2
1
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
1
2
0
0
0
1
1
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
2
2
15
0
0
0
3
2
0
1
0
2
0
0
0
0
0
0
0
2
0
0
2
2
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
2
0
0
2
1
0
0
0
4
2
1
6
2
0
2
0
1
0
0
0
0
0
2
0
0
0
1
2
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
2
2
0
0
1
0
0
0
0
0
0
1
0
0
2
1
0
0
1
0
2
0
0
0
0
0
0
1
1
2
2
1
2
0
2
0
0
0
0
0
0
0
1
1
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
6
0
1
0
0
1
2
2
0
0
0
1
2
1
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
2
2
0
1
0
0
1
0
2
0
0
0
1
0
1
1
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
2
3
2
0
0
0
0
0
0
2
1
0
0
1
4
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
1
3
2
0
0
2
0
0
0
2
0
0
0
2
0
1
0
0
0
0
1
2
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
2
1
0
0
2
0
1
1
0
0
0
0
0
2
1
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
1
2
1
0
1
0
1
1
0
0
0
0
4
0
1
0
2
0
0
0
0
1
0
0
0
2
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
1
0
1
0
1
2
2
2
1
2
0
0
0
0
0
1
4
0
1
0
0
0
1
0
2
1
1
0
0
1
0
0
0
1
0
0
0
0
0
2
2
0
2
0
0
0
2
0
2
0
1
0
0
0
0
0
2
0
2
1
0
2
0
0
0
0
1
0
0
0
1
2
0
1
0
0
0
0
2
0
1
2
0
0
0
1
0
0
1
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
1
2
2
0
0
0
0
2
1
0
0
3
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
1
2
2
2
0
1
0
1
0
0
0
2
0
0
0
0
1
1
0
0
0
2
2
1
0
1
0
0
1
0
2
0
1
1
0
1
0
0
2
1
0
0
0
2
1
0
2
0
0
0
0
0
1
2
0
0
1
2
4
0
0
0
2
0
2
0
0
0
1
0
1
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
3
2
1
1
0
0
2
0
0
0
0
2
0
0
2
0
2
0
0
0
3
0
0
2
0
0
2
0
0
1
0
1
0
1
0
0
2
0
2
0
0
0
1
2
1
0
2
1
0
2
0
2
0
3
1
2
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
2
2
2
0
2
0
0
1
0
0
2
3
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
2
0
1
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
1
0
0
2
1
0
0
0
2
0
0
1
0
3
0
2
2
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
3
0
2
0
0
2
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
1
2
0
0
0
1
0
0
1
0
0
2
0
0
0
0
1
2
1
0
0
0
2
0
2
0
0
1
0
0
0
0
2
0
2
2
0
0
1
3
0
0
0
2
0
2
1
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
1
0
0
1
2
0
0
0
2
0
2
2
0
0
0
0
2
0
0
1
2
0
2
0
1
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
2
1
0
1
0
0
1
2
0
0
2
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
1
1
0
1
0
0
0
2
0
0
2
0
0
1
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
1
2
0
1
0
2
0
0
0
0
2
0
0
1
0
0
1
2
0
2
0
2
1
2
0
0
0
2
0
0
0
0
1
0
1
2
1
7
0
2
2
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
2
0
2
1
0
0
0
0
2
0
1
0
1
1
1
0
0
2
1
0
0
1
0
0
0
1
2
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
1
2
0
1
2
2
0
1
0
3
0
0
1
0
0
0
0
0
0
1
0
3
0
0
0
3
0
1
0
0
1
2
0
0
0
0
1
2
2
0
1
1
0
1
1
0
1
0
2
2
0
2
0
0
0
0
0
0
0
1
0
0
0
2
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
3
0
0
0
0
0
0
2
0
0
2
0
2
0
0
1
1
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
1
0
2
2
0
2
0
1
0
0
0
0
0
3
0
0
1
2
5
1
0
0
0
0
0
0
3
1
0
2
0
1
0
0
0
0
0
3
0
1
2
2
0
0
0
1
0
1
0
0
0
0
0
0
2
2
1
2
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
2
2
4
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
2
2
0
0
1
1
4
1
1
0
0
0
0
2
0
2
2
0
0
0
1
0
2
0
0
2
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
2
0
2
0
2
0
0
0
0
0
0
0
0
0
2
2
2
0
2
2
0
2
0
0
0
0
2
2
0
0
0
0
0
3
0
0
0
0
2
0
2
0
0
0
2
0
0
1
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
2
2
1
0
1
0
0
0
1
0
2
0
1
0
2
0
0
0
2
1
0
0
0
0
3
1
1
0
0
0
1
0
0
0
0
1
0
2
0
0
2
0
0
0
0
3
0
1
0
1
1
0
0
1
0
2
0
1
0
0
0
0
0
1
3
0
0
0
0
0
2
0
0
1
0
0
0
1
1
0
0
1
0
0
0
2
1
0
0
1
2
0
2
0
0
0
1
0
0
0
3
3
0
1
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
2
0
0
1
0
0
0
0
6
1
3
0
2
1
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
3
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
2
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
1
1
0
2
1
0
2
0
0
0
1
0
0
2
0
0
0
2
0
1
1
0
0
0
1
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
2
0
0
0
0
2
2
3
0
0
0
2
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
11
3
0
2
0
0
0
0
3
0
1
0
0
0
2
2
1
0
4
2
0
2
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
1
2
2
1
2
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
2
0
0
0
0
0
1
2
1
0
0
1
0
0
0
2
2
1
0
0
0
0
0
1
0
0
0
3
0
0
0
1
0
0
2
2
2
2
0
2
0
0
0
0
1
0
0
1
2
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
1
1
0
0
0
1
0
1
0
0
0
0
0
3
2
3
0
0
1
0
2
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
1
0
0
1
2
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
1
0
2
0
0
0
1
0
2
0
0
0
2
0
0
0
2
0
0
1
0
3
1
0
0
0
0
0
0
0
1
0
0
0
0
3
0
1
0
0
7
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
1
2
1
1
0
0
2
1
0
0
0
0
1
0
0
0
0
3
0
0
0
0
1
0
0
1
2
1
2
0
0
0
2
2
0
0
2
2
0
0
2
5
0
0
0
0
0
1
1
2
1
1
1
0
0
2
0
1
0
0
0
0
0
1
0
1
0
0
0
1
1
1
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
2
1
0
2
0
5
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
2
0
1
2
3
0
1
2
2
0
0
0
0
0
0
0
0
1
0
1
0
0
2
1
0
2
0
2
2
0
0
0
0
2
1
0
1
0
0
2
0
0
2
1
0
0
1
0
1
0
0
1
0
0
2
2
0
0
2
2
0
0
2
1
0
1
0
2
0
2
0
0
2
0
0
0
1
0
3
1
0
0
1
0
0
0
0
0
0
4
2
5
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
2
2
3
0
1
0
2
0
0
0
0
0
3
2
1
0
0
0
0
0
0
0
0
0
0
2
0
10
0
0
0
1
0
2
0
0
1
2
0
0
0
0
0
0
2
2
0
0
1
0
0
2
0
0
0
0
2
1
1
3
0
0
0
0
0
1
0
5
1
0
2
1
0
0
1
1
1
0
0
0
1
0
0
1
0
1
0
0
2
0
0
1
0
2
1
0
0
0
0
0
5
0
0
0
0
0
0
1
0
1
3
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
2
0
1
0
1
0
0
0
0
1
0
2
0
1
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
1
1
2
0
0
3
0
0
0
1
0
1
2
0
0
0
0
1
0
0
2
3
0
2
2
2
1
0
2
0
0
0
0
0
2
2
2
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
2
0
0
0
1
3
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
3
0
2
2
0
0
0
0
0
0
2
0
0
0
0
2
0
1
2
0
3
0
0
0
1
2
1
0
0
0
0
0
0
2
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
1
0
2
1
0
0
0
2
0
2
2
0
2
2
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
3
0
1
1
0
0
0
0
1
3
0
0
0
0
0
0
1
3
0
2
2
0
0
0
0
1
0
0
2
1
1
0
2
0
0
4
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
1
1
0
0
0
1
0
0
1
0
2
0
2
1
0
0
2
2
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
1
1
2
1
1
0
2
0
2
0
0
0
0
2
0
2
0
2
2
1
0
0
0
0
0
2
0
3
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
2
1
0
0
2
0
1
0
0
0
2
2
8
1
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
2
1
1
0
0
0
1
0
1
1
2
2
0
0
0
2
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
4
0
0
2
3
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
2
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
1
2
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
1
2
2
0
0
0
1
2
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
1
2
0
0
0
0
2
0
0
1
0
1
0
0
0
0
2
1
0
3
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
2
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
3
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
2
2
0
0
0
2
0
0
0
0
0
4
1
2
0
0
1
0
1
0
0
0
0
0
1
1
1
0
2
0
0
0
0
0
3
0
1
0
0
0
1
0
1
0
2
0
1
0
0
0
2
0
2
2
3
0
0
0
0
2
2
0
2
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
3
0
3
0
0
3
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
1
0
1
3
0
0
0
0
2
0
0
0
0
2
2
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
2
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
1
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
1
0
2
3
5
0
0
0
0
1
1
2
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
2
2
2
0
0
1
0
0
0
2
2
1
2
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
3
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
4
0
0
0
0
0
0
0
2
0
2
0
2
0
2
0
3
0
0
0
0
0
1
2
0
2
1
0
1
1
1
0
0
4
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
2
1
0
2
2
0
0
0
0
0
0
2
0
2
0
1
1
0
0
0
2
0
0
0
1
0
0
2
1
0
0
0
0
0
2
1
0
0
1
3
1
1
0
0
0
2
5
1
0
0
0
0
4
1
0
0
2
0
0
1
0
0
2
2
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
2
0
0
0
0
2
2
2
0
0
0
3
1
0
0
1
3
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
1
0
2
0
0
2
0
1
2
0
0
0
0
2
2
0
1
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
4
2
0
0
0
0
0
0
0
2
5
0
0
1
0
0
0
0
0
0
0
4
0
1
0
2
0
0
0
2
2
0
0
2
0
0
0
0
0
1
0
0
1
0
0
2
0
0
1
0
0
0
0
0
1
0
0
2
2
0
1
0
2
2
0
0
0
0
0
0
1
0
0
3
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
1
1
0
0
1
0
2
0
0
0
2
0
0
1
0
0
0
1
0
0
1
0
0
0
0
2
0
0
4
0
0
0
0
1
2
1
0
2
0
2
1
2
1
0
2
0
0
0
0
0
0
0
0
2
2
1
0
0
0
2
0
0
1
1
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
2
2
0
1
1
1
0
2
2
2
0
0
1
2
0
0
0
0
3
0
0
0
2
0
0
0
0
2
2
2
0
3
0
1
0
0
0
0
1
2
1
0
2
2
0
0
2
0
0
0
4
1
0
0
0
1
0
2
0
1
0
1
3
2
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
2
0
0
2
2
0
1
2
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
2
2
0
0
2
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
3
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
1
1
0
1
0
2
0
0
0
1
0
2
0
2
0
0
1
0
0
0
1
1
2
0
1
0
0
0
0
0
1
0
2
2
0
1
0
0
0
0
2
0
0
0
2
1
0
4
0
1
0
0
0
2
0
0
1
0
0
1
1
0
0
0
0
2
2
0
0
2
1
1
2
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
2
1
0
2
1
0
0
2
4
0
0
0
1
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
1
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
1
0
0
0
1
0
0
0
2
0
1
0
0
0
1
0
0
2
3
0
0
0
2
0
0
2
1
0
0
0
1
1
3
1
1
4
3
2
2
0
2
0
2
0
0
2
0
0
0
0
0
0
0
5
0
2
1
1
1
0
2
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
1
2
1
1
0
0
0
0
0
2
0
2
0
2
0
1
1
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
2
0
1
2
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
2
0
0
2
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
5
0
1
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
2
2
0
0
2
1
0
0
1
0
0
0
1
1
0
0
0
1
2
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
2
2
2
0
0
0
0
2
0
0
0
2
2
1
0
0
1
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
1
2
2
2
0
1
0
0
1
1
1
0
1
0
1
0
2
2
1
0
0
2
0
0
0
0
2
0
2
0
1
2
1
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
2
3
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
3
0
2
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
2
2
0
1
2
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
1
0
1
0
1
0
2
1
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
2
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
2
0
0
0
4
0
0
0
1
2
1
0
2
0
1
1
0
0
0
1
2
0
0
0
2
0
0
0
1
1
0
3
0
2
0
0
0
0
2
6
0
0
0
0
0
0
0
1
2
3
0
0
0
0
0
3
0
3
2
0
1
0
0
1
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
3
0
0
1
2
0
0
2
1
0
0
2
0
2
0
1
0
1
0
0
1
0
0
0
0
6
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
2
0
2
2
0
2
2
0
2
0
1
0
0
3
2
2
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
2
0
1
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
2
1
0
0
0
1
1
1
1
0
0
0
0
1
0
0
2
0
3
0
0
3
0
2
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
2
1
0
0
0
2
0
1
0
1
0
0
2
0
1
0
0
1
1
0
2
0
2
2
0
0
0
0
2
0
0
1
1
0
3
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
1
0
2
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
1
0
0
1
2
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
2
0
1
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
2
1
0
0
0
1
0
2
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
2
1
1
0
0
2
0
0
3
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
2
0
0
0
0
2
1
1
2
0
1
0
0
0
0
3
1
3
1
0
2
1
0
0
0
0
2
0
0
0
0
2
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
1
2
3
1
1
0
0
1
1
0
0
1
0
0
1
1
2
1
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
1
0
2
2
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
3
0
0
0
0
0
0
1
1
2
1
0
0
1
0
1
0
0
0
0
2
0
1
0
0
0
2
4
0
0
1
0
0
3
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
1
0
0
1
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
2
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
2
1
0
2
1
0
0
0
0
0
1
0
0
2
0
0
0
0
1
1
0
1
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
1
0
3
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
3
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
7
0
1
0
1
0
0
1
1
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
1
1
0
0
2
0
2
0
1
0
1
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
1
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
1
0
0
2
0
1
2
0
0
1
1
0
2
1
0
0
0
0
1
2
0
1
1
0
1
2
1
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
1
1
1
1
0
1
0
1
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
1
1
0
2
0
1
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
2
0
1
1
0
0
0
1
1
0
2
2
1
0
4
2
0
0
2
0
2
0
2
0
2
0
0
2
0
1
0
0
2
0
2
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
2
1
2
0
2
3
0
0
1
0
3
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
2
1
0
2
2
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
2
2
0
2
0
2
2
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
2
0
1
0
0
0
0
1
0
0
0
1
0
0
2
0
1
2
1
0
0
0
2
0
0
1
1
0
0
1
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
3
1
2
0
0
0
0
0
0
0
1
1
1
0
0
4
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
3
0
1
1
1
0
0
0
0
0
0
0
0
2
0
0
1
2
2
0
2
0
1
1
0
0
0
0
1
0
1
2
0
0
0
0
2
0
1
0
2
2
0
2
0
0
2
1
0
2
2
0
3
0
3
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
2
1
0
0
1
1
1
3
0
1
0
0
3
0
0
0
0
0
3
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
2
0
0
2
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
1
2
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
1
3
1
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
1
0
1
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
1
0
1
0
1
2
0
1
0
0
2
0
1
0
1
2
2
1
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
1
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
4
0
2
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
1
0
0
3
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
3
0
0
0
1
0
0
0
1
1
0
1
1
0
0
0
0
0
1
1
1
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
3
0
0
0
0
0
2
1
1
1
0
2
2
3
2
2
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
2
0
1
1
0
1
1
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
3
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
2
4
2
0
2
1
0
0
0
0
0
0
0
2
0
2
0
1
0
2
0
0
0
0
0
0
2
0
0
0
3
2
2
0
1
0
4
0
0
0
0
0
0
0
0
1
0
2
2
1
1
0
0
0
0
1
0
0
1
0
0
0
1
0
2
0
0
0
0
1
1
2
1
2
1
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
1
9
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
1
2
0
1
0
0
0
1
0
0
0
0
0
2
0
1
0
0
2
1
0
0
2
0
2
1
0
0
0
0
3
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
1
2
2
0
1
0
0
2
0
0
0
1
0
0
0
0
2
0
1
0
0
0
3
0
0
0
2
0
0
2
0
0
0
0
0
0
1
1
2
0
0
2
0
2
0
0
0
2
0
0
0
1
0
0
2
0
1
2
0
0
2
0
0
0
0
0
1
0
2
0
0
0
3
0
1
2
0
0
1
0
0
1
2
0
0
2
0
2
1
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
2
1
3
0
0
2
0
0
0
2
0
1
0
0
0
0
2
0
0
1
0
1
0
1
0
2
1
0
0
1
0
1
0
2
0
0
1
0
0
0
2
0
0
3
2
2
1
0
0
1
2
0
0
0
1
2
1
2
0
0
1
0
0
2
1
0
1
2
0
0
0
0
0
2
0
0
0
0
2
2
1
0
0
0
2
2
1
1
1
1
1
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
2
2
0
2
0
1
0
1
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
2
2
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
4
0
0
1
2
1
0
0
1
2
0
1
0
0
1
0
0
0
2
0
1
0
2
0
1
2
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
2
2
0
0
0
2
2
1
0
1
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
2
2
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
3
4
0
0
0
2
1
3
0
0
2
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
2
0
0
0
2
0
0
0
2
1
0
0
1
0
0
0
0
3
2
0
1
0
2
0
1
1
0
0
1
0
1
0
0
1
2
0
1
1
2
0
0
1
0
0
0
0
1
1
2
0
0
0
2
0
0
1
1
1
1
0
0
1
0
0
0
0
0
2
0
2
0
1
0
1
0
0
0
2
0
1
0
1
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
2
0
0
2
0
1
1
1
0
1
0
2
1
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
5
1
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
1
0
0
2
1
2
0
0
0
2
2
0
0
4
0
0
0
2
0
1
0
0
1
0
2
1
0
1
0
0
2
0
0
0
2
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
1
0
2
0
0
0
0
1
0
0
0
2
0
2
0
0
2
2
0
0
0
0
1
1
4
1
0
0
0
0
1
0
0
0
0
1
0
0
2
1
0
2
0
1
0
0
0
0
0
0
0
1
5
2
1
0
1
0
1
0
2
1
1
0
1
0
1
1
1
0
0
1
0
1
1
0
1
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
2
1
1
0
0
0
0
2
0
0
1
0
1
1
0
0
1
0
0
0
0
0
1
0
3
0
0
0
1
0
0
0
1
0
0
3
2
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
2
0
0
2
0
0
1
1
0
1
1
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
2
0
0
1
0
0
0
0
2
0
2
2
0
1
0
0
2
2
0
0
0
0
1
2
0
3
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
3
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
2
0
0
2
0
0
2
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
2
2
1
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
2
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
1
0
2
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
2
1
1
2
0
0
1
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
2
0
1
0
0
0
0
6
0
0
0
2
0
0
0
1
2
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
7
0
0
0
0
0
0
0
1
0
0
1
0
2
2
0
2
2
0
1
0
0
2
0
0
0
2
2
0
0
0
2
3
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
1
2
1
0
0
4
2
0
0
0
0
0
2
0
0
0
0
2
1
1
0
1
0
1
3
0
0
1
2
2
0
3
2
0
1
0
0
2
2
1
0
0
0
0
0
0
1
1
0
0
0
2
0
0
1
0
1
0
2
1
2
0
5
0
0
1
0
1
0
0
2
0
0
0
0
0
3
0
1
2
0
0
1
2
0
0
0
2
2
0
0
0
0
0
0
2
2
1
0
0
0
0
2
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
5
0
2
0
0
3
1
0
0
2
2
0
2
0
1
1
0
0
0
0
1
0
2
2
0
2
1
0
0
0
0
3
0
1
1
0
1
1
0
0
0
0
1
0
0
0
1
0
2
0
0
1
0
0
0
0
1
2
0
0
0
0
2
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
1
1
0
0
2
2
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
3
1
1
0
0
0
1
1
2
0
0
0
3
0
0
1
2
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
2
0
1
0
0
2
0
0
0
2
0
1
0
0
2
0
4
0
1
0
0
0
0
0
0
1
0
0
1
2
2
0
0
1
1
2
2
0
1
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
2
2
0
1
2
0
0
0
0
1
0
0
2
1
0
0
0
0
1
2
0
0
0
2
0
2
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
1
1
1
0
0
1
1
0
0
2
3
0
0
0
2
0
0
2
1
0
0
1
1
0
0
0
0
1
2
3
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
2
2
0
0
2
0
1
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
1
0
0
0
3
0
1
0
0
0
1
3
0
0
0
0
3
2
0
0
0
2
0
2
2
1
0
0
2
2
1
0
0
1
1
2
1
1
0
0
0
0
0
0
2
1
2
2
0
0
0
0
0
0
1
1
1
0
0
0
2
0
0
0
1
3
0
2
2
0
1
1
0
0
0
0
0
0
1
0
0
2
1
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
2
0
1
0
0
0
0
1
3
2
0
0
0
1
1
0
1
0
0
2
1
0
1
0
2
0
1
0
1
0
1
0
0
0
2
3
3
0
0
2
0
0
1
0
0
0
0
1
1
0
0
1
0
0
4
0
0
0
0
0
2
0
1
0
0
2
2
1
0
0
2
2
2
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
1
0
1
0
2
0
0
0
0
2
2
0
0
0
2
0
0
0
4
0
0
2
0
0
0
1
1
1
0
0
0
1
0
0
1
0
1
0
0
0
2
0
0
1
0
0
5
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
4
2
0
1
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
4
0
2
0
0
0
2
0
1
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
1
2
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
2
2
1
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
1
0
0
0
0
0
0
3
0
3
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
2
1
0
0
0
0
0
0
0
2
0
0
1
0
2
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
2
2
2
0
1
2
2
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
1
0
1
0
1
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
2
0
2
2
0
1
0
0
0
1
0
2
2
2
0
0
0
0
0
3
0
0
0
0
0
1
0
1
2
0
3
0
0
0
0
0
2
0
1
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
3
0
1
0
2
0
0
1
0
1
2
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
2
1
1
0
0
0
0
1
1
0
1
0
0
0
0
0
2
4
1
0
0
0
0
2
2
1
0
0
0
0
1
0
0
0
0
0
0
2
1
0
2
2
0
0
2
2
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
3
1
2
0
1
0
0
0
1
0
2
1
0
1
2
0
1
1
2
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
1
0
3
0
0
1
1
0
0
0
2
1
0
0
0
0
3
0
3
2
2
2
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
2
1
0
1
0
0
0
0
1
0
1
1
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
3
1
0
2
0
0
1
0
0
0
2
0
2
0
0
0
0
0
2
0
4
5
2
0
0
0
2
1
0
0
1
2
0
0
0
2
0
2
0
0
0
0
4
0
0
2
2
3
1
0
3
2
0
0
0
0
0
1
0
0
0
0
0
2
2
2
0
0
2
0
2
1
0
0
1
0
2
0
1
2
0
1
0
0
0
0
0
0
0
2
0
1
2
2
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
1
1
0
0
0
2
0
0
1
2
0
0
1
0
3
1
0
2
0
0
0
0
0
5
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
3
0
0
4
0
4
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
3
0
0
2
0
0
0
0
1
2
0
1
1
2
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
2
1
2
0
2
2
0
0
1
0
0
0
1
0
2
1
0
0
0
2
0
1
2
1
0
2
0
2
0
0
0
2
0
0
2
1
2
1
1
1
2
2
0
0
0
0
0
1
0
0
0
1
2
0
1
0
0
1
0
2
2
0
0
0
0
2
0
0
0
0
2
2
2
1
0
1
0
0
3
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
2
2
1
0
0
0
2
2
1
0
2
1
2
0
0
2
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
2
2
2
1
0
0
0
0
4
0
0
2
0
1
0
0
4
3
2
0
1
0
2
2
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
1
0
0
0
1
2
0
0
1
0
0
2
0
0
2
0
1
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
1
0
0
0
1
0
1
0
2
3
0
0
0
2
2
0
0
1
0
0
0
2
0
0
2
1
1
3
0
0
0
0
0
0
2
1
1
0
0
1
0
0
0
0
1
0
0
0
3
0
0
0
2
0
0
2
0
0
2
0
1
0
2
0
2
0
0
0
0
0
3
0
0
0
0
3
2
2
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
1
0
0
1
0
0
1
0
0
1
1
2
0
0
0
0
0
0
1
0
1
0
2
0
1
1
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
2
0
0
4
1
0
2
2
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
3
0
0
1
0
2
0
0
1
0
0
1
0
3
0
0
1
0
0
2
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
2
0
2
0
0
0
0
0
2
1
0
2
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
1
2
1
0
3
1
0
2
0
0
0
1
2
0
0
0
1
1
1
0
0
0
2
2
0
0
0
0
0
0
0
5
0
1
0
0
2
0
2
0
1
0
0
0
2
0
0
2
1
0
2
0
0
0
0
0
0
1
0
0
0
0
1
2
1
0
2
0
0
0
0
2
0
2
1
0
3
1
0
1
1
1
0
2
1
0
0
0
0
1
1
3
0
0
2
1
0
0
1
0
0
0
0
1
0
0
1
1
0
6
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
2
2
2
0
2
0
0
2
0
0
0
0
2
1
0
2
0
0
0
1
2
1
0
0
1
0
2
0
0
1
0
0
1
1
0
0
0
0
0
0
1
2
1
0
0
1
3
2
0
0
0
0
0
0
0
0
0
1
1
0
3
2
1
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
1
3
0
0
0
0
0
0
1
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
4
2
1
2
0
0
2
0
2
0
0
0
0
1
2
0
0
0
0
0
1
1
0
0
0
1
1
0
2
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
2
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
1
2
0
0
0
0
0
1
2
1
0
0
1
0
1
0
1
0
2
0
2
2
0
2
0
0
2
0
0
0
0
0
2
1
0
0
0
2
2
1
0
0
1
0
2
0
0
1
0
2
0
0
0
0
1
0
0
1
0
0
2
0
0
2
0
0
0
0
0
2
0
1
2
2
0
0
0
2
1
0
0
0
0
1
2
2
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
1
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
3
1
0
1
0
5
0
0
1
0
0
1
0
1
2
0
0
0
1
1
0
0
0
1
0
1
0
1
0
0
1
3
2
0
0
0
0
1
0
0
2
0
2
0
0
0
1
1
1
0
0
0
1
0
2
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
2
0
0
2
2
1
0
2
0
3
0
0
1
1
3
2
0
2
0
3
1
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
1
0
4
2
0
0
0
2
0
0
3
2
1
0
0
0
0
0
1
3
0
0
0
0
0
0
3
1
0
0
0
2
0
1
0
0
2
2
2
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
2
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
1
0
0
2
2
2
0
1
0
0
1
0
0
2
0
2
1
0
0
0
0
1
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
2
2
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
2
0
2
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
2
0
1
2
0
0
2
0
0
0
1
0
0
2
0
2
0
0
0
1
1
0
0
0
3
0
0
2
0
1
2
0
0
0
1
1
0
2
2
0
1
0
0
2
0
0
1
3
0
0
2
0
0
3
0
0
0
0
0
0
0
0
2
0
2
0
1
2
0
2
0
0
2
2
0
0
1
0
2
2
0
2
0
0
1
2
1
0
1
0
0
0
0
0
0
0
0
0
0
3
1
0
0
1
2
2
1
0
0
1
0
0
0
0
0
0
0
2
0
1
1
2
0
0
0
0
2
0
0
1
0
1
0
0
1
2
0
0
0
0
1
0
1
0
2
0
0
1
0
1
0
2
0
0
2
1
0
2
0
1
0
0
0
0
3
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
2
0
0
0
1
0
0
0
1
1
0
0
0
1
1
0
2
0
0
0
1
2
2
0
0
0
2
1
1
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
1
0
1
2
0
1
0
0
2
0
0
0
0
0
0
1
1
1
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
2
1
0
0
0
0
2
0
0
2
1
1
0
2
0
2
0
2
0
0
0
1
0
0
1
0
0
2
2
0
0
0
2
2
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
7
0
0
0
0
2
0
1
0
2
0
0
2
0
2
0
1
0
1
0
0
2
0
0
2
0
0
0
2
0
0
0
2
0
1
0
0
0
0
1
0
0
3
1
1
0
0
2
0
0
0
2
1
0
4
0
2
0
0
1
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
2
1
2
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
1
0
0
1
0
2
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
2
0
1
0
0
1
2
0
0
0
3
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
2
4
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
2
0
0
0
0
2
0
0
1
2
1
1
2
2
0
1
0
0
3
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
2
0
2
0
2
0
0
11
1
0
0
0
0
0
0
2
2
1
0
0
0
0
1
0
0
0
0
3
0
0
4
0
2
0
2
0
1
0
1
0
0
0
1
0
0
0
0
0
3
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
2
1
2
0
2
0
0
3
0
2
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
1
0
2
0
0
0
0
0
0
1
0
0
0
2
0
2
1
1
0
0
0
0
1
1
0
0
0
0
0
2
0
0
2
2
1
0
0
1
0
0
1
0
0
0
0
0
0
2
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
1
1
1
0
2
1
0
0
0
0
0
1
0
2
0
1
0
0
0
2
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
1
0
2
0
1
0
2
0
1
0
2
3
0
0
0
2
0
0
0
2
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
2
0
1
2
5
0
0
0
0
2
0
2
0
2
3
0
0
0
0
0
0
0
2
0
1
0
1
2
0
0
0
0
1
0
1
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
3
0
0
1
0
1
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
2
0
0
0
0
0
2
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
5
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
3
0
0
1
0
0
1
0
2
0
0
0
2
2
3
0
0
0
0
0
0
0
0
2
1
0
1
2
0
2
0
0
1
0
0
1
0
7
1
0
1
2
0
0
0
0
2
1
0
0
0
2
0
1
2
0
0
2
1
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
1
2
2
0
0
2
1
0
0
1
1
0
1
0
1
0
2
0
0
0
0
0
0
2
2
0
2
0
1
0
0
0
2
0
0
0
2
0
1
0
0
1
0
2
0
0
0
2
0
0
0
2
0
3
0
1
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
1
2
2
0
0
0
1
0
2
0
2
2
0
0
2
0
0
0
0
0
0
3
0
2
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
2
0
1
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
6
2
2
0
0
1
0
0
0
3
0
0
0
0
1
1
1
2
3
0
0
1
1
0
1
1
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
2
0
0
0
0
3
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
2
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
4
0
0
2
0
2
0
3
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
10
1
3
0
0
0
0
0
1
0
0
4
1
0
0
0
1
0
1
0
2
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
2
0
2
0
0
5
1
0
1
1
0
0
1
2
0
0
1
0
2
3
1
0
2
0
0
0
0
0
1
4
2
0
0
1
0
0
0
1
0
0
2
0
0
0
0
1
0
2
0
2
0
0
0
0
0
2
0
0
1
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
1
2
3
2
0
0
0
0
1
0
0
1
0
0
3
0
2
0
0
0
0
2
0
0
1
0
0
0
0
2
1
2
0
0
2
0
1
1
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
4
2
1
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
3
0
1
2
0
0
0
0
0
1
0
0
0
1
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
8
1
1
0
1
0
0
0
0
0
0
2
0
1
1
0
2
0
2
2
0
0
0
1
0
1
0
0
2
2
0
2
3
0
0
1
0
0
3
2
0
1
0
0
0
2
0
0
1
0
0
1
2
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
1
1
0
0
0
2
0
0
0
1
0
2
0
0
0
2
0
0
3
2
4
0
0
0
0
1
2
0
0
0
2
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
2
0
0
1
0
2
0
0
1
2
2
1
0
0
0
2
2
0
0
0
0
0
2
1
2
0
0
1
0
2
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
2
1
2
2
0
0
0
0
0
1
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
2
2
1
2
0
2
0
0
0
1
0
0
0
1
3
0
0
0
1
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
2
0
3
0
0
0
0
0
1
2
0
1
0
2
0
0
0
1
0
0
2
0
0
0
0
2
0
2
0
5
0
1
1
0
0
0
0
0
0
3
0
0
0
2
0
0
1
1
0
0
2
0
8
2
0
0
0
2
0
0
0
1
0
0
0
0
0
4
2
0
0
0
1
2
0
0
0
0
3
0
0
2
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
1
2
1
2
0
2
3
0
0
0
0
1
0
0
2
1
2
1
1
0
2
0
2
1
0
0
1
2
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
2
0
0
1
0
0
0
0
0
1
0
2
1
2
0
1
0
0
2
0
0
1
1
0
0
0
0
1
0
0
2
2
2
0
0
1
0
2
1
2
1
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
2
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
1
0
2
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
3
1
1
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
1
2
0
1
0
0
0
3
0
0
0
0
0
2
2
2
2
2
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
2
0
0
2
0
1
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
1
1
0
12
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
3
1
0
0
0
0
0
1
0
2
0
0
0
0
0
1
2
0
1
0
4
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
3
0
2
1
0
1
0
0
0
0
0
0
1
3
2
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
2
0
2
4
2
0
1
0
0
2
1
2
1
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
1
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
3
0
0
2
2
1
0
0
0
1
0
2
1
0
0
4
0
0
0
1
1
1
0
2
3
0
0
2
0
0
1
1
0
0
0
0
1
0
1
0
0
1
0
0
2
0
0
0
0
0
2
2
0
0
0
1
2
0
1
0
2
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
2
2
2
0
2
1
0
0
1
0
0
1
1
0
2
2
0
1
1
0
0
0
2
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
2
1
3
0
3
2
0
0
0
0
2
0
2
0
0
0
0
0
0
2
1
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
2
2
2
2
0
2
0
2
0
0
1
1
0
0
1
1
0
1
0
0
1
3
0
0
2
0
0
2
1
0
0
1
0
0
0
2
0
0
1
1
2
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
2
0
0
0
2
0
0
0
3
0
0
0
0
0
2
1
1
0
0
0
0
1
1
0
0
0
0
2
3
0
1
0
1
0
0
1
0
1
0
0
0
0
1
1
0
0
2
0
1
0
1
0
2
0
0
0
2
2
1
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
2
2
2
0
1
2
2
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
1
1
0
0
0
1
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
2
3
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
2
0
1
0
0
3
0
1
0
0
0
2
1
0
0
1
1
2
0
1
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
1
0
0
3
0
2
0
0
2
0
0
2
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
2
1
0
0
4
0
0
2
2
0
0
0
0
0
0
1
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
1
0
2
0
0
2
0
0
0
0
0
0
0
0
4
2
0
0
0
2
0
1
1
1
0
1
0
0
1
0
0
0
0
3
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
1
1
0
3
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
3
1
0
1
0
2
0
3
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
1
0
0
0
2
0
1
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
2
2
0
1
2
1
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
2
5
0
1
2
0
0
0
0
1
5
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
1
2
0
1
0
0
1
0
0
1
2
0
2
0
0
0
0
0
2
0
2
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
1
0
0
2
2
0
0
0
1
1
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
2
2
0
1
0
2
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
2
0
0
2
1
0
1
0
0
2
0
0
2
0
3
2
1
0
0
0
0
2
0
1
0
0
2
0
0
0
0
1
0
0
2
0
0
1
0
0
6
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
4
0
0
1
0
2
1
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
1
2
0
0
3
8
0
2
2
0
0
1
3
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
1
0
2
0
2
0
0
0
2
0
0
0
0
0
1
0
2
1
0
0
0
2
0
1
3
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
6
0
0
1
0
2
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
1
1
2
2
1
0
0
2
1
0
1
0
0
0
0
2
0
0
0
0
1
0
1
1
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
2
2
2
0
0
1
0
0
0
0
0
1
1
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
2
0
0
2
0
1
2
0
0
1
0
0
0
0
0
0
0
0
5
0
0
2
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
3
0
2
0
0
1
0
0
1
2
0
0
0
0
1
0
1
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
1
1
0
0
2
2
2
0
0
0
2
2
0
0
0
0
0
0
1
0
0
10
1
2
0
0
0
0
1
1
0
2
0
2
1
0
2
0
0
1
0
2
3
0
1
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
2
0
3
2
0
1
0
0
0
0
2
0
0
0
0
2
2
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
1
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
2
0
0
2
0
0
0
0
0
4
4
2
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
2
1
0
1
0
0
0
0
1
2
2
0
1
0
0
1
0
2
0
1
0
0
0
0
0
0
1
2
0
1
0
1
1
1
2
0
0
0
0
0
0
2
0
0
1
1
0
1
1
2
0
1
2
1
1
0
1
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
2
0
0
0
2
0
0
1
2
0
0
0
0
0
0
1
3
0
0
2
0
0
1
0
0
1
2
0
0
0
0
2
2
1
2
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
1
1
0
2
1
0
0
2
0
2
0
2
1
0
0
3
3
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
4
2
2
0
2
0
0
0
1
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
2
2
0
0
1
0
1
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
5
0
0
0
1
1
2
2
0
0
2
0
0
0
0
0
2
0
1
2
0
2
2
0
0
0
0
2
1
0
2
0
0
1
0
0
0
0
2
0
0
0
2
1
0
0
0
1
2
0
0
1
0
1
2
0
1
2
1
2
0
0
3
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
2
0
3
5
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
1
3
0
0
0
0
0
0
0
1
0
0
0
2
3
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
3
0
1
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
2
1
1
2
0
0
0
1
0
0
1
0
0
0
1
1
2
0
1
0
0
0
1
1
1
0
0
1
0
1
1
0
0
0
0
2
2
1
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
1
4
0
0
0
0
2
0
0
0
1
0
2
1
0
2
0
0
0
1
0
0
2
0
0
0
0
1
0
2
1
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
2
1
0
0
0
1
0
0
1
1
1
0
0
0
0
0
2
1
0
0
0
0
0
1
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
1
0
0
0
0
0
0
2
2
0
1
0
0
7
0
1
0
4
0
0
0
0
0
0
0
3
0
0
0
0
2
1
2
0
0
2
0
5
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
1
0
1
0
0
2
0
2
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
2
1
1
2
3
0
2
0
0
1
2
2
0
0
2
1
2
0
1
0
0
0
0
0
0
1
0
1
0
2
2
0
0
0
0
2
2
2
0
0
0
0
0
2
1
0
1
1
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
1
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
1
7
0
1
0
1
0
2
2
0
0
0
2
0
0
2
0
1
0
1
0
0
0
0
3
2
0
0
1
0
0
0
0
0
0
2
0
0
3
0
0
0
3
0
2
0
0
3
0
3
2
0
0
0
1
0
0
0
0
3
0
0
0
3
0
0
0
0
0
1
0
2
0
0
0
0
2
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
2
1
0
0
2
1
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
2
2
0
1
0
1
1
0
0
2
0
3
0
0
0
0
2
0
0
0
0
2
0
1
2
1
0
0
2
0
0
0
0
0
0
1
1
1
0
0
0
1
0
2
0
1
1
0
0
0
2
0
3
3
0
0
0
0
2
2
2
0
3
0
0
0
1
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
2
1
0
0
0
0
0
0
0
0
2
3
0
0
0
2
0
1
1
0
0
2
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
1
0
0
2
0
0
2
0
2
0
0
2
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
1
0
0
0
2
2
1
2
0
0
0
0
0
0
0
0
0
2
2
1
0
0
7
2
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
2
4
0
1
0
0
0
1
0
0
2
1
2
0
0
0
0
2
0
0
1
0
0
0
1
3
0
1
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
5
2
0
0
0
3
1
2
0
2
0
2
1
0
1
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
2
0
2
2
0
1
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
2
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
1
0
2
2
0
0
1
0
2
0
0
2
0
3
2
0
0
0
0
0
0
1
2
0
0
0
0
2
1
0
0
0
0
4
2
1
1
1
1
4
2
0
0
0
0
0
0
2
2
0
0
1
0
2
0
0
0
1
0
2
0
1
0
2
0
0
1
2
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
1
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
2
6
2
2
0
2
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
2
0
0
2
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
2
0
0
3
1
0
0
0
0
0
0
1
2
0
3
2
2
1
0
0
0
2
0
0
0
2
0
1
0
0
2
0
0
1
1
0
0
1
2
1
0
0
0
0
2
2
0
0
0
0
1
0
0
0
1
0
0
2
2
2
0
0
1
2
1
0
0
0
2
0
2
0
0
0
0
2
1
1
1
0
1
4
2
3
0
0
0
0
1
1
2
0
1
1
0
2
1
0
0
0
0
2
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
1
0
2
2
0
0
0
1
0
0
0
0
1
0
0
0
1
2
0
0
0
2
0
0
1
0
1
0
1
1
2
0
2
1
0
2
0
1
0
0
0
0
2
0
0
0
0
2
0
2
0
5
0
2
1
2
0
0
0
0
0
0
0
0
2
0
1
1
1
0
0
1
0
0
0
1
0
0
1
0
1
0
2
0
1
0
1
0
0
1
3
0
0
2
3
3
0
0
0
0
3
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
1
0
0
0
1
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
2
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
2
0
0
0
0
2
3
0
1
0
0
0
0
2
0
2
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
3
0
11
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
2
0
0
0
0
0
2
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
1
2
0
0
0
1
0
0
0
2
1
2
0
0
1
0
1
1
0
0
1
1
0
1
0
0
0
0
0
0
2
1
0
1
1
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
2
0
0
0
0
1
0
2
2
0
1
0
0
1
0
0
1
1
0
0
0
2
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
2
2
0
1
1
0
0
2
0
1
0
1
0
0
0
0
2
0
1
2
1
0
0
0
1
0
0
1
0
0
0
2
0
1
0
1
2
5
0
0
3
0
0
2
0
1
0
2
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
1
0
2
1
0
0
1
0
2
1
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
1
0
0
0
1
0
1
0
3
0
1
0
0
2
0
0
0
0
0
1
2
0
0
1
2
0
1
2
0
0
1
1
2
0
0
2
2
1
0
0
0
0
0
0
1
0
0
2
1
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
1
0
2
3
0
0
0
0
2
2
0
1
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
2
0
0
2
0
1
1
1
0
0
2
0
0
0
1
0
1
2
0
1
2
0
1
0
2
0
1
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
1
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
2
1
0
1
1
0
1
0
2
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
2
2
2
1
0
0
1
0
0
2
0
0
0
0
0
4
0
2
0
0
0
0
2
0
0
0
2
2
1
0
1
0
1
0
2
0
2
2
2
0
2
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
1
0
0
0
0
0
0
3
2
1
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
2
0
2
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
2
2
0
1
0
0
0
5
0
0
2
2
0
0
0
1
0
1
0
1
1
1
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
2
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
2
0
0
1
2
0
0
1
0
0
0
0
2
1
1
1
0
0
0
0
3
0
0
0
0
0
1
2
0
4
0
0
0
0
2
2
0
0
0
1
1
0
0
0
2
2
2
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
2
0
1
2
0
0
0
1
2
0
1
2
2
1
0
1
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
1
1
0
3
0
0
0
2
0
0
0
3
1
0
0
1
0
2
2
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
1
0
1
1
0
2
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
1
0
0
0
0
0
2
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
2
0
0
0
2
0
0
2
0
2
1
0
0
0
0
1
0
0
0
0
3
1
0
2
0
1
2
0
1
0
0
0
0
0
1
0
0
4
1
0
0
1
2
0
1
2
2
0
1
2
1
1
0
0
0
0
1
2
0
0
0
1
1
0
2
0
0
0
0
1
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
2
0
3
0
1
0
0
0
0
1
0
1
1
0
2
1
0
0
0
2
4
2
0
1
0
0
0
1
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
2
0
3
2
0
2
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
2
0
1
2
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
2
0
0
2
0
1
1
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
1
0
0
2
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
2
2
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
2
0
2
0
2
2
0
0
0
0
3
0
0
0
2
0
0
3
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
2
0
0
4
0
0
2
0
2
0
1
1
0
0
0
4
0
0
0
0
0
0
2
0
1
0
3
0
0
1
2
0
0
0
0
1
0
0
0
1
0
1
1
2
1
0
2
1
1
2
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
2
0
0
0
0
0
2
0
0
0
1
1
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
1
1
2
0
2
0
2
0
0
0
0
2
2
2
2
0
0
1
0
0
0
1
0
0
0
0
1
0
2
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
7
4
1
0
1
0
1
0
0
1
0
0
1
1
0
0
0
1
2
0
1
2
1
2
0
2
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
2
1
2
0
0
0
0
0
0
0
1
0
1
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
2
2
0
1
0
0
0
1
0
2
0
0
2
1
0
2
1
0
1
0
2
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
2
1
0
1
0
0
0
1
1
1
0
2
0
1
1
0
0
2
0
1
0
2
0
0
0
0
0
2
0
0
0
0
1
1
0
0
1
2
0
0
0
1
2
0
1
1
2
0
2
1
2
1
0
1
0
1
0
0
0
1
1
0
0
0
2
0
2
1
4
0
2
2
0
1
0
2
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
1
0
4
1
0
1
1
2
1
1
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
1
0
0
0
0
1
0
0
0
0
2
2
0
1
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
6
0
0
0
2
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
2
2
2
1
2
0
2
0
0
0
2
3
0
0
0
0
0
0
2
0
1
0
0
0
0
2
2
0
0
3
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
2
3
0
2
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
2
0
2
2
0
0
0
0
2
1
1
0
1
0
2
0
0
1
1
0
0
0
2
2
0
0
0
0
3
2
0
0
0
0
0
0
1
1
2
2
0
0
0
0
0
0
2
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
3
0
0
1
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
6
2
0
0
0
0
1
0
0
0
0
1
1
0
2
2
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
2
0
0
0
0
1
1
0
2
2
2
0
0
0
0
1
1
3
0
0
1
2
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
1
0
0
0
2
2
0
1
0
1
0
0
0
0
0
0
0
1
0
1
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
1
2
0
1
1
0
0
0
2
0
0
1
0
0
0
2
0
2
1
0
1
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
4
0
0
2
0
1
0
0
1
0
0
3
2
1
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
2
1
0
1
3
0
0
0
1
2
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
1
2
0
0
2
1
0
0
0
2
2
0
2
1
0
0
2
0
1
1
0
0
0
0
0
0
0
2
0
2
1
0
1
3
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
2
2
0
1
0
1
2
11
1
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
2
0
1
2
2
0
0
0
0
0
0
0
0
0
0
2
1
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
1
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
3
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
1
1
4
0
0
0
0
0
0
0
0
0
2
2
0
2
0
1
2
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
4
0
1
0
0
2
0
0
2
3
2
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
1
0
1
0
0
0
2
0
0
2
1
0
2
0
0
2
0
1
0
1
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
2
1
0
0
3
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
1
0
1
0
0
0
1
2
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
1
1
1
0
1
0
0
4
0
0
0
0
1
0
1
2
2
3
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
1
0
0
0
1
0
3
2
2
0
0
0
0
0
0
1
3
0
0
0
1
0
0
0
2
0
1
1
0
1
0
0
0
0
4
0
0
0
1
0
2
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
1
2
0
0
1
2
0
0
0
0
1
0
0
2
0
1
0
0
0
0
1
0
1
0
0
2
2
0
0
0
0
1
1
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
2
5
1
0
2
0
0
0
2
2
1
0
0
3
0
0
3
0
0
0
0
1
0
4
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
1
0
2
0
2
0
0
0
2
1
0
2
0
0
0
0
1
0
0
0
2
2
0
0
0
0
1
0
2
0
0
0
2
0
1
0
0
0
0
0
2
0
0
1
2
0
2
0
0
1
0
0
0
0
0
1
0
2
0
2
2
1
0
1
0
0
0
2
0
3
0
0
0
2
0
0
1
0
0
2
0
0
0
2
0
1
0
0
0
0
1
0
0
2
2
0
1
0
0
0
1
0
2
0
0
0
0
2
1
0
0
0
0
0
2
0
2
0
0
0
0
0
1
2
0
0
2
0
0
1
0
0
2
2
2
2
0
0
0
2
0
2
0
1
0
2
0
2
2
0
0
0
2
0
0
0
0
1
0
0
0
0
1
1
2
0
2
0
0
2
0
3
0
1
1
0
3
0
0
0
1
2
2
1
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
4
0
1
2
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
1
2
1
2
2
0
0
1
1
2
1
4
0
1
0
0
0
0
2
0
0
1
1
0
0
1
2
2
2
0
0
1
0
0
0
1
2
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
2
0
0
0
0
2
0
0
2
0
0
0
1
2
0
2
1
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
1
0
2
2
1
0
0
1
0
2
0
0
0
2
2
2
0
0
0
0
0
2
0
3
2
2
2
0
2
0
2
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
1
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
3
2
0
2
1
1
0
0
2
0
0
2
0
0
1
0
1
0
0
1
0
0
2
2
0
2
1
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
2
0
0
1
0
1
2
0
1
1
0
1
0
0
1
0
0
4
0
0
1
0
0
2
0
2
0
0
0
1
2
0
0
2
0
0
2
0
2
1
1
1
0
2
3
0
0
0
0
0
1
1
0
0
1
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
1
2
0
0
0
0
0
0
1
0
3
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
2
0
0
1
1
0
0
4
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
6
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
2
0
3
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
2
0
0
0
3
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
1
0
3
1
0
0
1
0
2
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
3
0
0
0
0
0
0
0
0
1
0
5
1
0
1
0
2
2
2
2
0
2
0
0
0
0
0
3
0
2
3
2
2
0
0
1
2
0
0
0
2
1
1
0
0
2
1
0
0
1
0
0
0
2
2
0
1
0
0
1
2
1
2
1
0
0
2
0
0
2
0
0
0
1
0
0
2
1
0
0
2
0
0
2
0
0
0
0
0
0
1
1
0
1
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
2
2
2
0
2
1
4
2
1
1
0
1
0
0
4
0
3
0
2
2
0
0
0
2
0
0
2
2
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
3
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
2
0
1
0
0
0
0
0
0
2
1
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
2
2
2
0
0
2
0
0
0
1
2
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
8
2
0
0
1
1
3
0
0
1
0
2
0
0
1
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
3
0
0
0
0
0
2
0
0
2
0
0
2
0
0
2
0
0
0
0
1
2
0
0
2
0
2
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
4
0
1
0
1
0
1
1
0
0
0
0
0
0
0
1
0
2
0
0
0
2
1
0
0
2
1
0
0
0
0
0
2
0
2
0
1
2
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
1
0
4
1
0
1
0
0
0
0
0
0
1
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
2
0
2
2
1
0
0
2
0
2
2
2
0
1
0
2
0
0
0
0
0
1
0
0
1
2
1
0
2
0
0
1
0
0
1
1
2
0
0
0
0
0
2
0
3
0
0
0
0
3
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
1
2
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
6
0
1
0
0
2
0
0
2
0
1
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
2
2
0
0
0
0
0
2
2
0
0
0
1
1
1
0
2
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
3
0
1
1
0
0
0
0
0
1
0
1
0
0
3
1
0
0
1
0
1
0
0
1
1
0
2
0
1
0
0
2
0
0
0
2
0
0
0
1
2
0
0
1
1
0
0
1
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
5
0
2
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
2
2
0
1
0
0
0
0
0
0
0
0
0
2
1
1
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
2
0
2
0
1
1
0
0
0
0
0
0
2
0
3
2
0
2
0
0
0
0
2
0
2
0
2
0
1
0
2
3
0
0
0
1
0
0
0
1
1
0
0
0
0
2
1
0
0
0
0
0
1
0
2
0
0
0
1
2
0
2
2
2
0
0
0
2
2
2
0
0
1
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
2
2
2
2
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
2
0
0
0
0
1
0
0
0
1
1
0
0
2
0
0
1
2
1
2
0
0
1
2
0
0
0
2
2
0
0
2
0
1
1
0
1
0
0
0
0
0
1
0
0
1
1
2
2
0
0
1
0
0
1
0
2
0
0
1
1
0
0
3
0
0
0
0
0
0
0
3
0
0
0
1
0
2
2
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
1
1
0
0
0
0
0
0
0
2
1
0
1
0
0
3
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
2
1
0
2
2
0
0
0
0
2
0
1
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
1
0
0
0
3
2
0
0
0
0
0
1
0
0
2
0
1
0
1
0
1
2
0
0
2
0
2
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
1
4
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
2
1
1
0
2
0
0
0
0
0
2
0
0
1
0
1
1
0
0
2
1
2
0
0
0
0
0
2
2
0
0
0
0
0
2
2
2
1
1
2
0
1
0
0
2
0
0
1
0
0
0
0
0
0
2
0
2
1
0
0
0
1
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
2
1
0
1
1
2
0
0
0
1
0
1
2
3
1
0
0
3
1
1
0
0
2
0
0
1
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
1
1
0
0
0
0
0
0
2
0
0
2
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
3
0
0
1
2
2
0
2
0
0
2
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
2
2
0
0
2
1
2
1
2
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
2
0
2
1
2
5
0
1
0
0
0
0
1
0
0
0
2
0
0
1
1
0
1
0
1
0
0
0
1
0
0
0
2
0
0
3
8
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
2
0
2
0
0
0
0
1
1
0
0
1
1
1
0
0
2
0
2
1
1
0
1
0
2
0
0
0
0
0
1
0
1
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
2
0
1
0
0
3
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
1
1
2
2
0
0
1
1
2
0
0
0
0
0
1
0
0
0
2
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
6
0
0
0
0
2
0
2
0
0
0
0
2
1
0
0
0
0
0
0
3
0
0
0
0
2
0
2
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
2
0
0
2
0
0
1
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
1
1
2
0
0
0
1
2
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
2
0
2
2
1
3
0
2
0
1
0
0
0
1
0
0
1
0
0
0
1
2
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
1
0
0
3
0
0
2
0
0
0
0
0
0
0
2
1
0
1
1
2
0
0
0
0
0
1
2
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
1
1
0
2
0
2
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
1
0
2
0
0
0
3
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
2
1
0
0
2
0
0
0
2
2
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
2
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
1
3
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
2
1
1
0
0
1
0
0
2
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
2
0
1
1
0
0
0
0
2
0
1
0
0
0
2
0
0
2
0
0
0
3
2
1
0
0
0
2
0
0
0
0
2
2
0
0
0
1
0
2
1
0
0
2
1
0
0
1
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
3
0
1
0
0
0
0
0
0
0
0
1
2
0
0
1
0
2
0
0
0
0
0
1
0
1
0
2
0
0
0
0
2
0
0
1
1
0
2
0
0
0
1
1
0
1
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
3
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
1
1
0
1
0
0
0
0
1
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
1
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
4
2
1
2
1
0
1
1
3
0
1
0
0
0
0
0
0
0
0
0
1
2
0
1
1
1
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
1
0
0
0
2
2
0
1
0
0
0
0
1
0
1
0
0
0
0
2
0
2
0
3
3
1
1
0
0
0
1
0
0
0
1
1
6
3
3
1
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
1
2
1
0
0
0
2
1
0
2
2
0
0
0
0
0
0
1
1
0
0
1
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
2
0
0
0
0
0
1
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
2
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
3
2
1
0
0
0
1
1
0
2
2
0
0
0
2
0
0
0
1
2
0
1
0
2
2
0
3
0
2
0
0
2
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
1
1
2
2
7
0
0
2
0
3
0
0
2
0
0
2
1
0
2
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
2
2
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
3
0
0
0
0
0
0
0
0
0
0
0
2
1
0
3
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
1
3
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
3
2
0
0
2
0
0
0
0
0
1
1
0
3
0
0
2
1
1
0
0
3
0
0
2
0
0
1
1
0
2
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
1
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
1
0
1
2
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
2
2
0
0
0
0
2
0
0
0
0
0
1
2
0
0
1
1
2
0
0
2
2
0
0
0
2
0
0
0
0
0
2
2
2
1
1
0
0
0
2
0
2
2
3
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
2
1
4
1
2
0
0
1
1
0
0
1
0
0
1
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
4
0
0
2
0
1
1
0
0
0
0
0
0
1
2
2
0
3
0
0
2
1
0
0
0
0
0
0
1
0
1
1
0
1
0
1
2
0
1
0
1
0
1
1
0
0
2
0
0
2
0
1
1
0
2
0
0
1
0
1
4
2
0
0
0
1
2
0
0
1
0
0
0
0
7
2
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
1
0
0
1
0
0
0
0
0
0
0
1
2
0
0
1
1
2
2
0
2
2
0
0
0
0
2
1
0
0
0
2
0
0
2
2
0
1
0
1
0
4
0
0
0
0
0
0
0
3
2
1
1
0
1
0
0
0
1
1
3
2
0
0
0
2
0
0
0
0
3
1
1
0
0
0
0
0
0
1
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
2
0
3
0
2
0
0
2
0
0
0
1
0
0
0
1
0
1
2
0
1
0
0
0
0
2
0
0
1
0
0
1
1
0
1
2
0
2
0
0
1
0
0
2
1
0
2
0
0
0
1
1
3
0
0
0
0
1
1
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
1
0
1
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
1
2
2
0
0
0
0
1
1
0
0
0
1
0
2
2
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
3
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
2
3
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
3
1
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
3
1
1
2
1
0
2
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
2
1
0
1
0
2
0
2
0
0
0
2
1
0
2
0
2
0
1
0
0
0
2
0
1
0
2
0
2
0
1
1
0
0
0
0
0
0
0
2
2
0
2
0
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
2
0
0
1
0
2
2
1
0
0
1
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
1
0
0
2
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
2
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
1
2
3
0
1
1
0
2
1
0
0
1
0
0
2
2
0
0
1
0
0
1
1
1
0
1
2
2
0
0
0
0
1
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
1
0
0
0
2
1
0
1
0
0
1
0
1
0
0
0
2
0
1
0
2
0
0
1
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
2
0
1
1
0
2
0
0
2
2
0
0
0
1
1
0
0
0
0
3
0
0
1
2
0
3
0
0
0
0
2
3
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
2
0
0
1
1
0
0
0
0
4
2
0
0
1
0
0
0
0
2
0
2
0
0
0
1
0
3
0
0
1
0
1
1
0
0
0
1
0
0
1
0
0
3
0
0
3
2
0
0
0
0
0
0
2
0
3
0
0
2
0
0
0
0
0
1
0
0
0
2
0
2
7
1
0
0
0
1
2
0
0
0
2
0
0
1
0
0
1
0
1
2
0
0
1
0
1
0
0
0
2
0
0
1
0
2
0
0
0
0
0
1
2
0
0
1
0
1
1
0
4
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
2
0
2
0
0
0
1
0
0
0
2
0
0
1
0
2
2
0
2
1
0
0
1
0
2
0
2
0
1
0
0
0
0
1
0
0
0
0
2
0
3
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
1
1
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
2
2
0
0
0
0
0
1
0
0
1
1
1
2
0
1
1
0
0
0
1
1
1
1
6
0
0
0
0
1
0
1
0
0
0
2
0
0
1
1
0
0
0
3
0
2
2
0
1
2
0
1
0
2
0
0
1
0
0
0
0
0
0
0
1
2
2
0
2
1
0
0
0
1
0
2
1
1
0
0
0
0
0
0
1
0
0
4
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
1
0
1
0
6
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
2
0
0
0
2
2
0
0
1
0
0
1
0
0
0
1
0
0
2
2
2
0
0
0
0
0
0
0
0
2
1
1
0
2
2
0
0
0
0
0
0
0
1
1
0
0
0
1
0
2
0
2
1
0
2
3
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
1
0
0
1
1
0
4
0
0
2
1
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
1
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
2
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
3
1
0
0
2
2
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
1
1
0
1
1
2
0
0
1
0
0
2
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
2
0
3
0
3
0
3
2
1
2
2
2
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
1
1
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
2
0
0
0
0
1
0
1
2
0
1
2
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
6
0
0
1
1
1
0
0
1
2
0
0
0
0
0
2
1
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
3
2
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
1
0
0
1
0
2
0
2
0
0
2
2
0
1
5
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
1
2
1
0
1
0
1
1
0
0
0
2
0
1
0
2
0
1
1
2
0
0
1
0
0
2
1
0
0
0
0
0
1
0
0
1
4
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
1
1
0
2
2
0
0
0
0
2
0
2
0
0
0
2
2
0
0
0
1
0
2
0
0
2
0
0
0
3
0
0
0
0
2
0
1
0
1
0
1
0
0
0
3
0
0
1
0
0
1
2
0
1
0
0
0
0
0
1
0
0
1
0
0
4
1
0
1
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
1
2
0
0
2
0
2
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
2
0
1
0
0
0
0
2
0
0
1
0
0
1
1
0
0
0
2
0
1
1
0
0
0
0
0
0
2
1
0
1
1
1
0
0
0
1
2
0
2
0
0
5
0
2
2
0
0
2
0
1
0
0
0
2
0
0
0
1
2
0
1
0
2
2
3
0
0
0
1
1
2
0
0
2
0
2
0
1
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
2
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
3
0
0
0
0
2
0
1
0
0
0
0
2
2
0
0
0
1
0
0
0
1
1
0
0
1
1
0
0
0
0
2
0
1
1
0
0
0
0
0
1
0
2
2
2
1
1
0
1
0
1
0
2
2
2
2
0
0
0
0
0
0
0
0
2
1
2
0
0
2
2
1
0
0
1
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
2
0
0
0
1
0
1
0
1
0
0
2
0
1
0
0
0
0
0
1
0
0
0
2
2
2
0
0
2
0
0
2
0
0
1
0
0
1
0
0
0
2
1
0
2
2
1
0
0
1
2
0
0
0
2
0
0
2
2
0
0
0
0
2
0
0
0
0
0
4
1
2
1
0
0
0
0
0
1
2
0
2
0
0
0
2
0
0
1
0
2
0
0
0
3
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
2
0
2
0
0
0
1
1
2
0
2
1
1
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
2
0
1
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
2
1
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
6
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
1
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
1
1
0
1
0
2
2
1
1
0
2
0
0
2
0
1
0
0
0
0
0
1
0
2
0
0
0
0
1
0
1
0
2
0
0
0
0
0
2
0
0
1
0
1
1
0
1
1
3
0
2
0
1
2
0
0
1
0
0
0
2
2
1
0
0
0
0
0
0
2
0
0
0
1
1
1
2
0
2
1
1
0
0
0
3
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
1
0
2
0
3
0
1
0
0
0
0
0
0
2
0
1
3
0
0
1
0
0
0
1
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
2
0
1
0
5
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
2
0
2
0
0
3
1
0
0
1
1
0
0
1
1
0
2
0
0
0
1
0
1
1
3
1
0
2
0
1
1
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
3
0
2
0
0
1
0
0
1
1
1
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
2
2
2
0
0
0
0
0
0
1
0
0
0
1
3
1
2
0
0
0
0
2
0
0
1
0
0
1
0
0
0
1
0
0
4
0
0
4
1
0
1
0
0
2
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
3
0
0
0
0
0
0
1
0
1
0
1
0
0
4
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
1
0
2
0
0
2
0
0
0
3
1
2
0
0
0
0
0
1
3
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
1
0
0
2
0
0
2
2
0
2
0
0
2
0
0
0
2
3
4
0
0
0
0
0
0
2
1
2
0
2
2
2
0
2
0
0
0
0
0
0
1
0
0
1
2
0
1
0
0
0
0
0
2
0
1
0
2
0
0
1
0
0
1
0
0
1
2
0
0
0
0
0
2
0
2
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
2
0
0
0
0
1
0
2
0
2
2
0
0
2
0
1
0
0
1
2
0
0
0
0
0
0
2
0
0
1
1
1
1
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
1
2
0
2
1
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
4
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
3
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
1
1
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
3
1
0
0
0
0
0
0
2
1
0
2
0
0
1
0
0
0
2
1
1
0
1
0
3
0
0
0
0
0
1
0
0
0
0
2
1
0
2
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
2
2
0
0
0
2
1
0
0
2
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
2
1
2
1
0
1
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
2
0
0
2
0
2
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
1
0
0
0
0
1
0
0
1
0
1
1
0
0
8
1
0
0
0
2
2
2
0
0
0
0
1
0
0
2
0
0
0
0
1
0
2
3
0
0
0
1
2
0
2
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
1
1
0
1
0
1
1
0
1
0
0
2
0
0
0
1
1
0
2
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
2
1
0
0
0
2
0
0
0
0
0
1
2
0
0
2
1
0
0
2
0
1
0
3
0
0
0
1
0
0
1
0
2
0
3
0
0
0
0
0
0
2
0
2
0
0
2
1
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
2
2
0
0
1
3
2
0
0
2
0
0
0
1
0
1
0
0
2
1
0
2
0
0
2
0
0
3
1
0
0
0
0
0
2
0
0
0
2
0
1
0
2
0
0
2
0
0
1
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
1
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
7
2
0
0
0
6
0
2
0
0
6
0
3
1
0
0
2
0
1
3
0
0
0
0
0
1
1
0
0
0
0
2
2
2
0
2
0
0
0
2
1
3
0
2
2
0
2
0
0
0
0
1
0
0
0
2
0
1
0
2
1
0
0
0
0
0
0
2
1
2
3
2
1
2
0
0
1
1
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
1
0
2
2
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
2
2
0
0
0
2
0
3
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
3
1
0
2
1
0
2
3
0
2
0
2
0
0
2
0
0
0
2
0
0
2
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
4
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
1
0
0
3
0
0
0
0
0
0
0
2
2
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
1
0
1
2
0
0
1
0
2
0
5
0
0
0
2
0
1
0
0
0
0
4
2
0
0
1
0
0
2
0
0
0
0
1
2
1
0
0
0
2
2
2
0
0
0
0
1
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
2
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
1
2
0
0
0
0
0
1
0
0
0
1
0
1
0
2
0
0
2
0
0
3
0
0
0
0
0
2
0
0
0
2
2
1
0
0
0
0
2
1
0
1
0
0
0
0
1
2
0
0
2
0
0
0
2
0
0
0
2
2
3
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
2
0
0
1
3
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
3
2
2
0
1
0
0
1
1
1
0
0
0
2
0
1
0
0
0
0
0
1
0
2
1
0
1
1
1
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
3
0
0
0
0
1
0
1
1
0
0
1
0
1
0
0
0
0
0
4
0
0
0
0
2
3
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
3
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
3
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
1
0
2
1
1
0
0
0
0
1
0
0
2
2
0
2
1
0
0
0
0
0
0
1
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
1
1
0
1
0
0
0
0
0
0
2
0
0
0
2
0
4
0
1
0
0
0
2
1
2
0
0
1
0
2
0
1
0
2
0
0
0
0
9
0
0
0
0
0
0
1
0
0
0
1
0
2
5
0
2
0
3
0
2
0
2
2
2
0
1
0
0
0
0
0
2
2
1
1
0
0
0
0
0
0
6
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
5
2
0
1
0
0
1
0
0
1
0
2
0
0
0
0
0
2
1
0
2
0
1
1
2
0
0
0
0
0
1
0
0
2
1
3
2
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
1
0
1
0
0
1
0
1
1
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
2
0
1
0
0
1
2
0
0
2
1
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
2
4
2
0
0
0
0
2
0
0
2
0
2
0
0
3
0
0
1
0
0
1
0
0
1
1
1
0
0
0
1
0
0
0
2
0
2
2
1
0
0
0
2
1
1
1
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
2
2
0
0
2
0
0
0
0
3
0
1
0
2
1
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
1
0
2
0
0
0
0
0
2
1
0
0
1
1
0
0
1
2
0
0
0
1
0
0
1
0
2
2
0
0
0
1
0
0
0
0
0
1
1
0
2
0
2
1
0
2
1
7
0
0
1
0
1
2
0
0
1
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
1
1
2
0
0
2
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
2
0
1
0
1
2
0
2
2
0
0
0
0
1
2
0
0
0
0
4
0
0
0
0
1
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
3
1
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
1
0
0
1
1
0
0
0
0
2
1
0
0
0
0
0
1
0
1
1
0
0
0
2
0
0
0
0
1
0
0
1
0
1
0
0
1
0
2
0
0
0
0
2
1
1
0
1
0
0
3
0
2
0
1
0
0
0
0
2
0
0
0
0
0
1
1
2
0
1
2
1
0
0
1
0
0
2
2
1
0
2
2
0
0
0
2
0
3
0
1
0
0
2
0
3
0
0
1
0
0
0
0
2
1
0
0
2
1
0
0
1
0
0
0
0
1
0
0
2
0
0
3
1
0
0
0
0
2
0
5
1
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
1
0
3
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
2
0
0
2
2
0
0
0
0
0
1
0
2
1
1
0
0
1
2
0
0
1
1
0
0
0
0
1
0
1
0
2
0
0
0
0
0
2
1
0
0
2
0
2
1
0
0
4
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
1
0
1
1
0
1
2
0
0
1
0
1
0
0
0
0
0
0
2
0
0
2
0
1
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
1
0
0
3
0
1
0
1
0
2
0
2
0
1
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
2
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
1
0
0
1
1
0
2
0
0
1
0
2
1
0
0
3
2
2
0
0
1
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
5
0
0
1
2
0
0
2
0
4
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
2
2
1
0
1
0
1
0
2
0
2
1
1
2
2
0
1
0
0
1
0
0
0
2
0
0
2
0
0
1
0
0
0
0
2
1
2
1
2
1
0
0
1
1
0
0
3
0
0
1
1
0
1
0
1
2
0
2
1
0
0
0
0
2
2
0
0
2
0
0
1
2
2
0
0
0
2
0
0
2
1
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
6
0
0
3
0
2
0
0
2
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
2
2
0
0
1
0
0
2
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
2
0
0
0
3
1
1
2
0
1
1
0
1
0
2
0
0
0
1
0
0
0
0
1
0
2
1
1
2
0
0
2
1
2
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
1
0
0
0
0
2
0
0
2
0
1
0
2
0
0
0
1
2
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
2
0
0
2
0
1
2
1
1
0
1
1
0
0
2
0
2
0
0
1
1
0
2
0
0
2
0
0
2
0
1
0
1
0
2
2
0
0
0
2
0
1
1
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
3
0
0
0
0
0
0
1
2
0
1
1
1
0
0
0
0
0
0
0
2
1
1
0
0
0
1
2
0
4
0
1
2
1
1
0
2
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
5
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
2
0
1
0
1
0
1
1
0
0
0
0
2
0
0
0
0
0
2
0
1
0
1
1
1
0
0
0
0
1
2
0
0
0
0
2
0
2
1
1
0
3
0
0
0
1
0
2
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
1
1
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
2
0
2
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
2
1
0
3
0
0
0
0
0
1
1
0
1
0
0
1
0
1
0
0
0
0
2
0
2
0
0
2
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
2
0
2
2
1
2
3
0
0
0
1
1
0
2
2
0
0
0
2
0
0
2
1
3
1
2
0
0
0
0
0
0
0
2
1
0
0
0
2
3
0
0
2
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
1
0
0
1
0
0
0
0
0
3
2
2
1
0
0
0
0
0
0
2
0
2
2
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
1
3
2
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
1
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
1
1
0
0
1
0
2
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
2
1
2
0
0
1
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
2
0
0
0
0
1
1
1
2
2
1
2
1
0
0
0
0
2
2
0
2
2
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
1
1
2
0
1
2
0
0
4
0
0
1
0
0
0
2
0
0
0
0
0
1
2
0
0
0
2
2
0
1
0
2
0
0
2
0
0
0
0
2
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
2
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
4
1
0
0
0
2
0
2
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
1
4
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
3
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
2
2
0
0
1
0
2
0
0
0
0
0
0
1
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
2
1
1
0
0
2
1
0
1
0
2
1
0
2
2
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
2
2
4
0
0
0
2
0
2
0
2
0
0
0
1
0
0
0
0
0
0
1
0
1
0
2
0
1
0
2
0
0
0
0
1
3
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
4
0
0
1
0
1
0
1
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
1
0
0
1
2
0
0
0
0
1
0
2
0
2
0
2
0
1
0
0
1
1
0
0
0
0
2
0
1
0
0
1
0
1
0
0
3
0
0
0
0
0
1
1
0
1
2
0
1
0
1
0
0
5
1
0
0
0
2
0
2
1
1
0
0
1
0
0
1
0
0
0
0
1
1
0
3
0
0
0
2
0
1
0
0
2
0
2
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
2
3
0
0
0
0
0
0
1
1
0
2
1
0
2
2
4
4
2
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
2
1
1
0
0
2
1
1
0
3
0
0
0
3
0
0
2
0
2
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
3
0
0
1
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
2
0
2
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
1
1
0
1
1
0
0
1
0
1
0
0
0
0
0
2
0
1
0
0
0
1
1
0
2
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
3
2
0
0
0
1
0
0
2
0
1
0
1
1
0
2
1
0
0
0
2
0
0
0
0
0
2
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
2
0
0
0
0
0
2
0
1
1
1
0
0
2
0
1
0
0
2
0
0
2
0
0
0
2
0
2
2
0
0
0
0
2
2
1
1
0
0
2
0
1
0
1
0
0
2
0
0
1
0
0
2
1
0
0
1
1
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
2
2
1
0
0
0
0
0
1
0
1
3
0
0
1
0
2
1
0
1
0
0
2
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
3
2
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
1
2
2
0
0
0
1
0
0
0
2
2
0
2
0
0
0
2
0
0
1
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
2
0
2
0
1
0
0
2
0
0
0
0
0
0
0
1
0
1
0
1
0
2
0
0
0
0
4
0
2
0
0
2
1
1
2
2
1
0
1
0
2
0
0
0
0
1
0
0
0
2
0
0
1
0
1
1
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
1
0
0
2
0
1
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
2
0
1
0
1
1
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
2
2
0
0
0
0
2
2
4
1
2
0
1
1
1
1
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
2
2
0
0
0
0
2
0
2
0
1
0
1
1
0
0
0
0
0
1
1
0
0
1
1
1
0
0
0
2
0
1
0
0
0
2
0
0
1
0
0
2
0
0
2
1
0
0
0
1
0
0
2
0
0
3
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
1
0
0
2
0
2
0
5
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
4
2
0
0
6
0
0
0
0
1
0
0
3
2
0
0
0
0
0
1
0
0
2
3
0
0
0
0
0
0
0
1
0
2
1
0
1
0
0
0
0
2
1
2
0
0
2
1
0
0
2
0
2
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
4
0
0
0
3
0
0
7
0
1
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
2
0
0
2
1
0
0
0
1
1
1
2
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
2
1
2
2
0
0
0
0
2
1
0
0
0
0
0
1
2
1
0
0
0
0
1
1
0
0
1
0
2
0
2
0
2
0
2
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
2
0
0
0
0
2
1
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
3
2
0
0
0
1
2
0
0
0
1
2
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
2
2
0
0
4
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
2
0
0
2
0
2
2
2
0
0
0
1
2
0
2
1
0
2
0
0
1
2
0
3
4
0
1
0
0
1
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
2
1
2
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
2
1
0
0
2
0
0
0
1
2
1
0
2
0
2
0
1
1
0
0
1
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
1
1
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
2
2
1
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
1
0
0
1
3
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
2
2
0
2
0
2
0
0
2
3
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
1
2
0
2
2
0
0
2
0
2
1
2
1
2
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
2
0
0
1
2
3
1
3
1
2
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
2
2
0
1
0
0
0
1
1
4
0
0
0
0
1
0
0
0
2
0
1
0
0
2
2
0
0
1
0
0
0
2
1
0
2
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
2
2
0
0
0
1
0
1
2
2
1
0
0
2
1
1
0
0
0
0
0
0
0
0
2
0
2
0
0
2
2
0
0
1
0
0
2
0
0
1
0
0
2
1
0
0
1
0
0
0
1
0
1
1
2
1
0
0
1
0
0
2
0
0
1
2
3
0
1
1
1
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
5
0
1
0
0
1
0
2
2
0
3
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
4
0
0
0
1
1
0
0
0
0
0
0
0
0
2
2
1
1
0
0
0
0
0
0
0
0
0
2
1
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
4
0
1
6
1
0
0
0
0
0
3
1
0
1
0
0
2
0
0
0
2
0
0
0
1
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
1
0
0
0
0
1
0
0
5
0
0
2
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
3
3
1
0
0
0
0
2
0
0
0
0
0
1
1
1
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
1
0
0
0
2
3
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
3
1
0
1
1
0
0
0
3
1
0
0
1
0
0
1
2
0
0
0
2
0
0
1
2
0
0
0
1
1
0
0
0
2
1
2
0
0
0
1
1
2
2
0
1
1
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
1
1
0
0
2
0
0
1
0
0
0
0
1
1
2
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
1
0
2
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
1
0
2
1
4
3
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
2
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
1
0
0
0
2
1
0
2
0
0
0
2
0
0
0
0
3
3
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
1
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
1
0
2
0
2
0
2
1
0
0
0
1
2
1
0
0
0
0
0
1
0
0
1
1
0
0
1
1
0
1
0
1
1
0
2
0
0
0
2
0
3
2
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
2
1
1
0
2
1
0
1
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
2
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
1
0
0
0
0
0
1
0
2
0
0
2
0
2
2
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
2
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
3
2
0
3
0
0
1
0
1
1
0
0
0
3
0
2
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
2
1
0
0
2
0
0
0
0
1
0
3
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
2
2
0
1
2
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
3
0
0
0
1
0
2
0
1
2
0
0
0
1
0
2
1
0
1
1
0
0
2
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
2
0
1
0
1
1
1
2
3
2
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
2
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
1
0
0
2
0
1
2
1
1
1
1
0
0
1
7
0
1
4
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
1
0
2
0
2
1
0
0
0
0
1
2
0
0
1
1
0
1
0
0
0
0
0
0
1
2
0
0
0
1
0
2
0
1
1
0
0
0
0
0
0
2
2
0
0
0
1
0
0
2
0
0
2
0
0
1
0
0
0
1
2
0
2
1
0
0
0
0
0
0
1
3
0
0
0
0
3
0
0
0
0
2
0
1
0
1
2
1
0
0
0
0
2
0
0
0
1
0
1
2
0
0
0
0
0
0
0
1
1
2
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
3
1
0
0
0
1
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
2
3
0
0
1
3
0
0
0
0
0
2
1
0
2
1
1
0
0
0
1
0
0
2
0
2
1
0
0
0
2
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
1
0
1
0
0
3
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
1
0
1
1
0
0
0
0
2
2
1
0
0
1
0
0
0
0
0
1
0
0
2
0
0
1
0
1
0
1
0
2
0
0
1
0
2
1
0
0
2
2
0
1
0
0
1
2
2
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
1
2
1
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
1
0
0
2
0
0
2
1
0
0
2
4
0
0
1
1
0
0
2
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
1
1
1
0
0
0
2
0
0
2
1
0
0
1
0
1
0
0
1
3
0
0
0
2
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
5
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
1
0
0
1
0
0
0
2
2
2
3
2
1
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
2
0
0
2
0
1
0
2
0
0
0
2
0
1
3
0
1
0
0
1
2
0
1
0
2
2
0
2
1
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
2
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
2
2
0
0
2
0
0
1
0
1
4
0
0
1
0
3
0
0
0
2
0
1
0
2
0
4
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
2
1
0
0
1
0
0
1
0
2
1
0
0
1
0
0
3
0
0
2
1
0
0
2
0
2
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
1
0
0
0
1
0
0
0
1
0
2
0
0
0
0
1
0
0
1
0
0
1
0
1
0
2
2
1
1
0
1
0
1
0
0
2
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
1
2
0
0
1
0
2
0
1
0
2
0
2
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
1
1
0
0
0
0
1
2
0
0
1
1
3
1
2
1
0
2
0
0
0
0
1
0
0
2
1
0
0
1
0
0
2
0
2
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
2
1
0
0
3
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
2
0
5
0
0
0
3
0
0
0
1
1
0
0
0
0
0
2
0
1
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
4
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
1
0
0
4
0
0
0
0
0
0
2
0
2
5
1
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
1
3
0
0
0
1
2
1
0
0
2
0
0
2
0
1
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
2
0
1
0
1
1
0
0
2
0
0
0
0
3
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
1
0
0
0
2
2
1
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
2
2
1
0
0
0
1
0
1
0
0
0
1
1
0
1
0
0
3
0
0
4
0
0
0
0
0
0
0
0
2
0
3
2
2
0
0
1
0
1
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
1
0
0
1
1
0
0
1
2
1
0
2
1
1
0
0
0
0
2
1
0
0
2
1
0
2
1
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
3
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
2
2
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
1
0
0
3
3
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
1
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
3
2
1
0
0
1
0
0
2
0
2
1
0
4
2
0
0
1
0
0
2
0
1
0
0
0
0
0
0
1
0
0
1
2
1
0
2
0
2
0
0
3
0
0
1
0
0
2
0
3
0
0
0
0
2
1
0
0
0
0
0
0
3
0
0
0
1
0
0
2
0
0
0
2
2
0
2
0
1
0
0
0
0
1
0
0
2
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
3
0
0
2
0
0
1
0
2
0
1
0
1
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
2
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
2
0
0
3
0
0
0
1
0
0
0
2
3
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
2
0
0
0
3
2
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
1
0
0
1
0
1
1
0
0
0
6
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
3
0
0
0
0
0
2
7
2
1
0
0
1
3
0
0
0
0
0
1
0
0
2
2
1
0
2
0
0
1
1
0
0
1
0
0
2
0
1
0
0
1
0
2
0
0
0
0
0
2
2
0
0
2
2
1
0
0
0
0
1
1
0
0
0
0
2
0
1
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
1
0
0
1
0
2
0
3
1
1
0
0
0
0
1
2
0
2
2
2
1
1
0
0
0
0
1
4
0
1
0
2
2
0
2
8
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
2
0
0
0
1
0
1
0
0
0
1
0
2
0
2
0
0
2
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
3
0
2
0
1
0
2
0
1
1
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
1
2
0
0
0
0
0
4
0
0
0
0
0
1
1
2
0
0
1
0
1
0
1
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
1
0
1
0
0
0
2
0
0
2
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
1
2
2
1
0
0
0
1
1
0
2
0
0
0
0
2
1
0
0
1
0
3
0
0
3
0
3
0
1
0
0
0
0
2
1
0
1
0
2
0
0
2
0
0
0
1
1
0
0
0
2
0
2
0
0
2
2
0
0
2
0
0
2
1
0
0
0
0
2
0
0
0
2
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
2
2
0
0
2
0
0
0
1
2
0
0
2
2
0
1
0
1
0
2
1
0
0
1
0
1
0
0
2
0
0
1
1
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
1
0
0
1
0
0
0
9
0
1
2
0
2
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
2
0
0
2
2
0
1
1
0
0
2
1
0
0
0
6
0
0
1
0
1
0
0
0
2
0
0
0
0
0
2
0
0
2
0
1
1
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
2
0
2
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
2
0
1
0
0
1
0
0
0
2
1
0
0
0
0
0
2
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
2
0
0
0
2
0
3
2
0
2
0
1
0
1
1
0
0
2
0
0
2
1
0
0
0
2
0
0
0
0
2
0
2
1
0
1
1
0
0
0
0
0
1
0
0
2
2
0
1
0
0
0
0
0
0
3
0
0
0
0
2
3
1
0
0
0
1
0
3
1
1
1
0
2
0
0
0
2
1
0
0
0
1
2
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
3
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
2
0
0
1
0
2
2
0
0
1
0
1
0
2
0
2
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
2
1
0
0
0
0
2
1
0
0
0
0
0
1
0
2
1
0
0
0
0
3
0
0
2
1
0
2
0
2
2
0
0
1
0
1
0
0
0
0
2
0
0
1
0
0
2
0
0
2
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
3
0
0
0
1
1
0
1
0
0
2
0
0
2
0
2
2
0
3
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
2
1
1
0
0
2
1
2
0
1
0
0
0
0
2
1
0
2
0
1
1
0
3
0
2
0
0
0
1
0
1
0
2
0
1
1
3
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
2
0
1
0
7
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
5
0
3
1
1
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
3
0
0
0
0
0
1
0
1
2
0
0
2
0
0
0
2
0
0
1
2
2
0
0
2
1
0
0
1
1
0
2
1
0
2
0
2
0
1
0
0
0
0
0
0
2
1
2
0
0
1
0
1
0
0
1
2
0
1
2
0
0
2
0
1
0
0
1
2
0
2
0
0
1
0
2
0
0
0
1
0
1
0
2
2
1
1
0
2
0
0
0
0
0
0
0
0
2
2
2
0
0
2
1
0
2
2
2
0
1
0
0
0
2
0
0
1
0
0
0
0
1
0
0
1
0
3
0
0
0
0
2
1
0
2
0
1
0
0
2
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
1
0
0
0
7
0
0
0
0
0
0
0
0
1
0
0
2
2
0
2
2
0
2
0
0
0
0
3
0
1
0
0
2
3
2
0
0
1
1
0
0
0
0
0
2
1
0
0
2
2
0
0
0
0
0
0
0
1
1
0
0
1
1
0
1
1
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
1
2
0
0
1
0
0
0
0
1
0
3
0
0
0
1
2
0
1
0
0
1
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
2
0
0
1
0
0
2
0
0
0
0
0
0
1
0
9
1
1
2
1
1
1
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
2
3
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
1
2
0
1
0
0
0
0
0
0
0
0
2
0
0
6
0
1
0
0
0
2
0
2
0
0
2
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
1
0
0
0
0
2
1
0
0
0
0
2
1
0
0
0
0
0
1
0
0
2
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
2
0
0
2
1
1
0
0
0
1
0
0
4
0
0
0
0
0
2
0
1
2
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
1
1
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
1
0
0
1
2
1
0
0
0
2
1
0
2
1
0
2
4
1
1
0
0
1
0
0
0
2
3
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
1
3
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
2
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
2
1
0
1
0
0
0
0
2
0
0
0
0
0
0
10
2
1
1
0
1
2
0
1
0
0
0
0
0
0
1
2
0
0
2
0
1
0
0
0
0
0
0
2
1
0
0
0
2
2
0
1
0
0
1
1
0
1
1
1
2
0
0
0
0
3
0
0
0
0
0
2
2
1
0
0
0
2
0
1
0
0
0
0
1
0
0
0
2
2
1
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
2
0
0
1
0
1
0
0
0
0
1
1
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
2
0
0
0
0
1
0
0
1
2
0
0
0
3
0
2
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
1
0
2
0
2
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
2
0
0
0
0
2
0
1
0
0
1
2
2
0
1
0
0
1
2
0
0
0
2
1
0
0
0
2
2
0
0
1
0
2
0
1
0
0
0
0
3
1
0
0
1
2
2
1
0
0
0
5
0
2
1
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
2
0
0
2
0
1
0
0
1
0
2
0
0
0
2
0
0
0
0
1
2
1
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
2
0
2
0
1
1
0
1
3
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
2
1
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
2
2
0
0
0
0
1
0
0
1
0
0
2
0
0
1
1
2
1
1
0
0
0
2
0
2
0
0
2
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
2
3
0
0
0
0
0
1
2
0
1
0
0
0
1
1
0
2
0
1
0
0
0
1
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
2
0
0
1
0
2
0
0
0
0
0
0
2
0
1
2
2
0
0
0
2
0
1
0
0
2
2
2
0
0
0
0
1
0
3
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
2
0
0
1
1
0
0
1
0
0
2
2
0
0
1
0
0
2
0
0
0
0
0
2
1
1
2
0
0
0
1
0
2
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
2
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
1
1
0
0
3
0
1
0
1
1
0
0
2
0
1
0
1
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
2
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
1
1
0
0
1
1
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
3
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
2
0
0
0
1
2
1
2
0
0
0
1
0
0
2
1
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
1
2
1
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
3
1
1
0
0
0
2
0
1
0
0
0
0
1
1
0
2
1
0
0
2
0
0
0
0
2
2
1
0
0
0
2
0
0
1
2
2
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
3
2
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
1
0
0
2
0
1
0
1
0
2
1
0
0
0
2
0
1
0
0
0
0
1
0
2
2
0
1
0
1
2
1
1
0
1
0
0
1
0
0
0
0
4
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
1
2
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
1
2
0
0
1
0
1
0
0
1
0
1
2
0
0
0
0
0
0
0
2
2
1
0
2
1
2
0
1
2
0
2
0
2
1
0
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
2
1
1
0
0
0
0
0
1
3
0
2
0
0
2
3
1
0
0
2
0
2
1
0
0
0
0
1
0
2
1
0
0
0
0
3
0
0
0
0
0
1
0
0
1
2
0
1
0
1
0
1
0
2
0
2
0
0
2
1
0
0
0
0
0
2
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
3
1
0
0
2
0
2
0
0
1
2
1
1
1
1
0
0
2
0
0
0
0
0
2
0
2
0
0
2
0
2
0
0
0
1
0
1
0
0
0
3
0
0
1
0
1
2
1
0
0
0
0
0
2
0
0
0
1
0
0
2
0
2
1
2
1
0
0
0
3
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
1
0
0
2
0
2
0
2
2
2
0
3
0
0
0
0
0
1
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
1
3
0
1
1
1
2
0
2
0
2
0
0
0
2
0
0
1
0
1
0
0
0
0
1
0
0
0
2
2
0
2
0
2
2
0
0
1
0
1
0
2
1
0
0
0
0
3
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
2
0
2
3
0
0
0
3
0
0
3
0
1
1
3
0
1
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
3
3
0
1
1
0
0
0
1
0
2
0
0
3
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
1
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
5
0
0
0
2
0
0
0
0
0
0
1
1
0
0
2
1
0
0
1
0
0
0
0
0
0
1
2
3
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
1
3
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
2
0
0
2
0
1
1
1
0
0
0
0
3
2
1
0
1
0
0
2
1
0
0
0
0
1
0
1
0
1
0
5
0
0
2
0
0
1
1
0
1
0
0
2
1
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
4
0
0
1
0
0
0
0
1
0
0
5
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
2
0
1
0
1
0
0
0
0
1
0
0
0
1
0
3
0
1
2
0
0
2
0
0
0
0
0
1
0
2
0
0
2
2
0
0
1
1
1
0
3
0
0
0
0
0
1
0
1
0
1
0
2
0
1
0
0
1
1
0
2
2
0
0
2
1
0
1
0
0
1
1
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
1
1
0
2
0
0
2
0
2
0
0
0
0
0
0
2
1
0
2
0
1
1
0
0
0
0
0
0
2
0
1
0
1
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
4
0
0
0
1
0
0
0
0
2
2
0
1
1
1
0
2
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
2
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
11
0
0
0
0
0
2
0
0
1
0
1
0
0
2
0
0
0
1
0
2
0
2
0
2
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
1
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
1
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
2
0
1
1
2
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
2
0
2
0
0
0
0
3
0
2
0
2
2
0
1
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
1
1
0
2
0
0
2
1
0
0
0
0
0
1
0
2
0
3
0
1
1
0
1
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
2
2
0
0
2
0
2
0
0
0
2
3
1
1
2
0
0
2
0
2
0
0
2
0
0
1
0
1
0
1
0
1
0
1
1
0
1
0
1
0
0
1
0
0
2
2
0
0
2
0
0
0
0
2
2
1
1
3
0
1
0
2
0
1
0
2
2
1
1
0
0
0
0
0
2
0
3
0
0
2
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
2
1
1
0
0
0
2
0
0
0
0
1
1
2
1
0
0
0
0
0
0
0
0
0
3
1
1
2
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
2
0
2
0
1
5
0
1
2
4
0
0
0
0
0
1
0
0
2
1
2
0
0
0
0
0
2
0
0
0
0
1
8
1
0
0
0
0
4
1
2
1
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
2
2
0
0
1
0
0
0
0
0
0
0
2
4
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
1
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
1
0
1
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
2
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
2
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
2
1
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
1
0
0
0
1
0
1
0
0
1
0
1
0
1
0
0
0
3
0
0
2
0
2
0
1
0
0
1
2
2
2
0
2
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
1
1
3
0
0
0
0
1
0
0
0
3
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
1
0
0
0
0
0
1
0
2
0
1
2
2
0
0
1
0
0
1
0
0
0
2
0
0
0
2
0
2
2
1
2
1
0
0
1
1
0
0
0
0
0
0
7
2
0
0
3
1
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
1
0
0
1
0
2
2
0
2
2
0
0
0
0
0
1
2
0
2
0
2
0
0
2
0
1
0
0
1
1
0
0
2
0
1
0
1
1
0
1
0
1
1
8
1
0
1
2
0
0
0
0
1
0
2
0
0
0
1
0
0
0
1
1
1
0
0
0
2
0
2
0
0
0
0
1
1
0
0
0
3
0
0
2
0
2
1
2
2
1
0
1
1
1
0
0
0
0
1
2
2
0
0
0
0
0
2
0
0
1
0
0
0
2
0
1
0
0
2
1
0
0
2
0
2
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
1
0
4
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
7
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
3
0
0
2
0
0
0
0
0
1
1
0
1
0
0
0
0
0
2
0
0
1
0
1
0
0
2
0
0
0
1
0
0
0
0
3
0
0
0
2
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
1
0
2
2
1
0
1
2
1
0
0
2
0
2
0
1
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
2
0
2
0
0
1
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
1
0
2
0
2
0
0
0
3
3
0
2
2
0
0
0
0
0
3
0
1
1
1
0
1
0
1
0
0
1
0
0
0
1
0
0
1
0
2
0
0
0
3
2
2
0
0
0
1
0
0
0
1
0
1
2
0
0
0
0
2
3
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
2
0
0
1
5
3
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
2
0
2
1
0
1
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
6
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
1
0
0
2
0
0
0
1
0
0
3
2
1
0
2
0
0
1
2
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
4
0
2
0
2
1
0
0
0
0
2
0
0
1
1
0
0
0
0
2
1
1
0
1
0
0
0
2
0
0
0
0
2
2
0
0
1
1
2
0
0
0
1
0
0
0
2
1
0
2
0
0
2
0
0
0
0
2
0
0
3
0
0
0
0
0
2
2
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
2
0
2
0
0
1
0
0
2
0
1
0
0
0
0
1
0
0
0
1
1
0
0
2
1
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
2
0
0
2
0
0
0
1
0
0
0
2
0
2
2
0
0
8
2
0
2
0
0
2
1
1
2
0
0
0
0
0
0
1
0
0
0
2
0
2
2
0
0
1
0
2
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
2
0
0
2
0
2
2
2
0
0
1
0
0
0
1
0
1
0
3
0
1
0
2
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
3
0
1
0
0
2
0
0
2
0
2
2
0
2
1
0
1
0
0
0
0
0
0
1
2
1
0
3
1
0
1
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
2
0
1
0
1
0
0
2
0
1
0
0
0
2
0
0
1
3
0
0
0
0
2
0
0
0
0
0
0
2
0
4
0
0
0
2
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
1
1
2
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
2
2
0
1
0
0
0
2
0
0
0
0
0
2
0
2
2
2
0
0
0
0
1
1
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
2
0
1
2
0
0
0
0
0
0
2
0
0
0
1
2
2
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
3
0
1
0
1
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
1
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
1
0
1
0
0
0
0
2
0
0
0
1
5
1
2
0
0
0
0
2
2
3
0
1
2
0
0
1
0
0
0
0
2
0
2
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
1
0
0
0
1
2
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
2
0
1
0
0
2
0
0
3
0
0
0
1
1
0
2
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
3
0
0
0
0
1
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
1
1
0
0
2
0
2
0
0
1
0
0
2
0
0
1
0
0
3
0
0
1
2
1
8
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
5
0
0
0
0
0
0
0
15
0
4
0
0
0
0
0
0
1
0
0
0
0
0
2
2
2
0
0
0
0
0
0
1
1
0
0
2
0
0
1
0
1
2
0
0
1
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
4
2
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
1
0
0
2
0
0
1
2
0
0
0
0
0
1
1
0
3
0
0
0
1
0
0
2
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
2
0
1
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
2
2
0
0
0
2
0
0
2
1
0
1
0
0
0
0
1
0
0
2
0
0
0
1
1
2
1
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
2
0
2
0
1
0
0
1
0
2
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
2
0
0
0
0
1
0
0
2
0
0
0
1
2
0
0
0
0
3
1
0
3
3
0
1
0
1
0
0
2
1
0
2
0
0
0
0
0
0
0
0
2
0
1
7
0
0
0
0
0
2
1
0
0
0
0
1
0
0
2
2
0
1
0
0
0
0
0
2
0
1
0
0
0
2
2
1
0
0
0
0
1
0
2
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
1
0
0
0
2
0
2
1
1
0
2
0
2
0
1
1
1
1
0
2
1
2
0
0
0
2
1
1
0
0
1
1
0
2
0
0
0
0
0
1
0
2
0
0
0
2
0
0
2
2
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
1
2
0
2
0
0
0
0
2
0
0
0
0
0
1
2
0
0
1
0
0
1
0
1
0
0
0
2
0
3
1
0
0
1
1
1
0
1
0
1
2
0
0
0
0
1
2
0
0
1
0
2
1
0
1
1
2
1
2
1
2
0
0
1
0
0
2
0
1
1
2
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
2
1
0
1
1
0
0
0
0
0
0
1
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
3
0
3
1
0
0
1
0
0
0
0
1
2
1
2
0
0
0
1
0
2
0
1
0
2
2
0
0
0
0
0
2
0
1
1
0
0
0
2
0
0
1
0
1
2
0
0
0
1
0
4
0
1
0
4
2
0
0
1
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
3
2
0
0
0
1
0
0
1
2
1
1
1
0
3
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
1
2
0
1
2
0
0
2
0
0
0
0
0
1
0
0
2
1
0
2
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
2
0
1
0
0
0
0
3
0
2
0
2
1
0
0
0
0
0
1
0
1
1
0
0
0
4
1
0
0
2
0
1
0
1
0
0
0
2
2
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
1
3
0
0
0
0
0
1
0
1
0
0
1
1
1
2
0
0
1
0
0
0
1
1
0
1
0
0
2
2
4
0
2
0
1
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
3
0
0
0
0
2
0
1
0
2
0
0
2
2
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
1
0
2
1
0
0
2
0
1
0
0
0
5
0
0
0
0
0
0
0
3
1
2
0
0
0
0
0
0
0
0
1
0
1
0
0
3
1
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
1
0
3
1
1
1
1
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
1
0
1
0
2
0
0
0
2
2
0
0
0
0
1
1
0
2
2
1
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
3
2
0
0
1
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
2
2
0
0
2
0
0
4
2
0
0
0
2
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
1
0
1
1
0
0
1
2
0
0
0
1
2
0
1
2
1
1
0
0
1
1
0
1
0
0
0
0
2
0
1
1
2
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
1
0
1
2
0
0
0
2
1
0
0
2
1
1
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
1
2
1
0
1
0
0
1
0
1
0
2
2
0
0
0
1
0
0
0
2
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
2
0
0
2
1
0
1
0
2
0
0
0
0
0
0
0
0
2
2
1
0
1
0
2
0
2
0
2
1
0
1
3
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
1
0
1
3
0
0
0
0
2
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
3
0
1
1
1
2
1
0
0
0
0
2
0
0
2
2
0
2
0
0
0
1
0
2
1
0
0
1
0
0
0
1
0
1
3
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
1
0
0
2
0
1
0
0
0
0
0
1
0
1
4
0
0
0
0
0
0
1
0
0
4
0
1
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
1
1
0
0
0
2
3
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
1
0
2
2
2
0
0
0
0
0
2
0
0
2
0
2
0
2
1
0
0
2
1
2
1
1
0
1
0
0
2
0
0
0
2
1
3
1
3
0
0
1
2
1
0
2
0
0
2
0
2
0
2
0
0
2
2
2
0
0
1
0
1
0
2
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
2
2
0
0
2
0
2
0
1
2
1
1
2
2
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
2
0
1
0
0
0
0
0
2
1
0
0
0
2
2
0
0
1
0
0
2
0
0
0
0
0
0
0
3
2
1
2
1
2
0
0
1
2
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
4
0
1
0
2
2
0
0
1
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
1
3
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
3
0
2
0
2
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
2
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
1
0
0
2
0
0
7
0
0
2
0
0
0
0
1
0
3
0
0
2
0
2
0
1
0
1
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
2
0
2
1
0
2
0
0
2
0
0
1
0
1
0
0
0
1
0
0
0
2
2
2
2
0
0
1
0
0
2
0
0
0
2
1
0
0
2
3
0
0
0
2
0
2
2
1
0
2
0
1
0
0
0
0
1
2
0
0
1
0
0
1
0
1
1
0
2
0
0
0
0
0
0
2
1
0
2
0
3
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
2
0
0
0
1
12
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
1
2
2
2
0
2
0
0
1
2
1
0
1
1
0
0
0
0
0
3
0
0
0
0
1
0
1
0
0
0
2
0
0
2
2
1
0
0
0
1
0
0
0
0
1
1
2
0
1
0
0
2
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
2
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
3
0
0
0
1
2
0
1
2
2
2
0
1
0
1
0
0
1
0
1
0
1
2
1
0
2
0
0
0
0
0
1
4
2
0
0
1
0
2
0
2
0
1
0
0
0
2
0
1
0
3
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
3
0
0
0
2
1
2
0
0
0
2
0
2
1
2
0
0
2
4
0
0
0
0
0
1
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
1
2
2
0
0
2
2
0
0
0
0
1
2
0
4
0
2
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
4
1
0
1
0
1
1
0
0
1
2
0
0
1
0
1
1
0
0
0
0
0
0
0
3
1
0
0
0
2
0
1
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
3
0
1
1
1
0
1
2
0
0
0
3
0
0
2
0
0
1
0
2
2
0
0
0
0
0
0
1
2
0
0
2
1
0
0
2
0
0
0
0
0
0
1
0
2
2
0
0
3
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
1
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
1
0
0
0
0
0
1
0
1
0
0
0
3
2
0
0
1
0
1
0
2
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
6
0
2
0
1
1
0
0
0
1
0
2
0
2
1
0
1
0
0
0
1
1
1
0
1
0
2
0
2
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
1
1
2
0
2
0
2
0
0
0
1
0
2
2
1
0
0
0
1
0
0
0
0
1
0
0
2
2
0
2
0
0
1
0
0
0
1
0
0
2
3
0
1
0
0
1
2
2
1
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
1
0
3
2
0
1
0
1
0
0
2
2
0
0
0
1
0
0
1
0
1
0
0
0
1
1
0
0
1
0
1
1
0
0
0
0
0
1
0
0
1
0
2
0
1
0
1
0
2
0
0
4
0
2
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
3
0
1
0
0
0
0
0
2
0
1
0
0
1
0
0
0
1
0
0
0
2
1
0
0
0
0
0
1
2
4
0
0
0
0
3
0
0
0
0
1
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
1
0
2
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
2
0
1
0
0
4
0
0
0
0
0
0
2
1
0
1
0
0
1
2
0
0
1
1
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
2
1
0
0
1
2
0
0
0
0
1
1
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
2
0
1
2
0
0
0
1
1
0
2
0
0
1
1
3
0
0
0
0
1
1
3
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
2
3
1
0
0
2
2
2
2
2
0
0
0
2
1
0
0
1
0
1
0
1
0
2
2
0
1
0
0
0
0
1
0
2
1
2
2
1
0
0
0
2
0
1
0
1
0
0
0
1
0
0
0
2
1
1
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
2
2
0
2
2
0
1
0
0
0
1
0
0
0
0
0
0
1
2
0
1
1
0
0
0
2
2
0
2
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
1
0
0
0
2
0
0
2
0
3
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
1
2
0
2
2
1
2
0
0
0
0
2
0
0
0
0
1
1
0
0
2
0
0
0
0
1
2
1
2
0
2
0
0
0
2
2
0
0
0
2
2
0
0
1
0
1
0
2
0
0
1
2
0
0
0
2
2
0
0
1
0
2
1
0
0
0
2
2
0
0
1
1
0
0
0
0
2
0
1
0
2
0
2
0
2
0
1
0
0
1
2
1
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
2
2
1
2
2
0
1
0
0
0
0
2
1
1
0
2
0
0
1
2
2
0
3
0
0
1
0
5
1
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
1
1
2
2
0
0
0
1
1
0
1
3
1
2
0
0
1
0
0
0
1
0
0
0
1
0
1
2
0
0
2
0
0
0
1
0
0
2
0
0
0
1
1
0
0
0
0
1
0
0
1
0
2
0
1
0
0
0
0
1
0
0
2
0
2
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
1
0
2
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
2
0
1
0
0
0
0
0
0
2
2
0
2
0
0
2
0
0
0
0
0
0
3
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
1
1
0
1
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
3
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
3
0
1
2
1
0
0
2
0
2
2
2
0
0
2
1
2
1
2
0
0
0
0
0
0
0
2
0
2
0
4
0
0
1
2
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
1
2
2
0
1
2
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
2
1
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
2
0
6
1
2
0
1
0
1
0
1
2
0
0
0
1
0
0
0
0
0
2
0
0
2
1
2
0
0
0
0
0
0
0
0
1
1
0
0
3
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
1
0
0
1
0
0
0
0
0
1
2
2
0
1
0
0
0
0
0
1
1
1
0
0
0
0
1
0
2
1
1
0
0
0
0
1
0
0
3
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
2
0
0
2
0
0
0
1
0
1
1
0
0
0
0
0
1
0
2
0
5
0
1
0
0
0
0
0
2
0
1
3
0
0
0
0
2
0
0
0
2
0
1
0
0
2
0
0
0
0
2
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
2
0
2
1
0
0
1
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
1
0
2
0
2
2
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
1
0
1
0
1
2
3
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
2
1
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
2
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
1
0
1
0
1
1
0
0
1
1
0
0
0
0
0
1
0
0
2
1
1
0
0
1
0
0
0
0
1
1
0
3
0
0
0
2
0
0
1
0
0
1
0
0
1
2
0
0
2
0
2
0
0
2
0
0
2
1
0
0
1
0
1
0
2
0
0
2
1
0
1
0
2
0
0
0
0
1
0
0
3
2
2
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
1
1
0
0
0
1
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
2
0
1
0
0
2
0
1
0
2
0
2
0
0
0
0
1
0
2
2
0
1
1
0
1
2
1
0
0
2
2
0
1
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
2
1
0
2
2
0
0
0
0
0
0
1
1
0
0
0
1
2
1
2
0
0
0
0
3
2
0
0
1
0
2
1
0
1
0
0
0
0
0
2
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
2
2
0
0
1
0
0
1
0
4
0
1
0
0
0
0
0
0
1
0
1
0
2
2
1
2
0
1
0
1
0
0
2
0
0
0
0
0
2
2
0
0
1
1
0
0
0
0
0
0
1
1
1
1
1
0
0
0
0
0
0
0
2
0
1
0
3
0
0
2
2
2
2
1
0
0
0
1
0
2
0
2
0
2
0
0
0
2
2
0
0
2
2
2
0
3
0
0
0
0
0
0
0
0
0
1
0
1
3
3
2
1
2
2
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
2
0
2
0
1
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
2
0
0
0
0
0
1
1
0
2
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
2
1
1
2
0
0
0
2
0
0
0
1
1
0
2
0
0
0
1
1
0
0
0
2
0
0
0
0
0
1
0
0
3
2
0
1
0
0
1
0
0
0
0
0
1
0
0
0
2
0
2
0
1
0
0
0
1
1
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
4
1
1
1
0
0
1
0
0
0
0
0
2
1
0
0
0
0
1
2
2
0
2
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
3
2
0
0
2
2
0
1
0
1
2
0
0
0
0
0
0
0
0
4
0
0
1
0
2
0
2
0
0
2
2
2
0
0
0
0
0
3
1
0
0
2
0
0
0
0
0
1
0
0
3
0
0
1
2
1
2
1
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
2
0
0
0
2
0
0
2
2
0
1
2
0
2
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
5
2
0
0
1
2
2
3
0
0
1
0
0
0
0
0
4
1
0
1
0
0
0
0
1
1
0
0
1
2
1
2
0
0
0
0
0
0
0
1
1
2
1
0
1
0
2
2
0
1
2
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
2
0
1
1
0
0
1
1
2
0
1
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
3
0
2
1
0
1
0
1
1
1
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
2
0
0
1
2
0
0
1
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
1
2
0
0
0
0
0
0
0
4
0
0
2
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
5
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
1
0
3
1
0
1
2
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
2
0
0
2
2
0
2
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
2
2
2
0
0
0
0
0
0
0
0
1
0
2
1
1
0
0
2
0
1
1
0
0
0
0
0
1
2
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
1
2
0
2
0
0
3
0
4
0
0
0
0
0
1
1
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
1
2
0
0
2
0
0
0
1
0
0
1
0
1
2
0
1
3
0
0
0
1
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
2
1
2
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
2
3
1
0
2
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
2
0
2
3
1
0
2
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
2
0
0
1
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
2
0
0
2
1
2
0
1
0
2
0
2
0
0
0
0
0
2
1
0
2
0
0
1
0
0
0
0
3
0
0
1
1
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
2
0
0
0
0
0
0
2
0
1
2
0
0
2
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
1
0
2
0
1
1
0
1
0
3
2
0
0
1
0
0
0
1
0
2
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
1
0
1
1
2
2
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
2
0
0
2
1
0
0
2
0
0
1
0
0
2
2
1
0
0
2
1
0
0
2
0
1
0
0
1
0
0
1
0
0
1
0
1
0
1
0
0
0
1
0
0
1
1
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
1
2
0
1
2
2
2
0
0
0
2
0
2
1
2
2
1
1
0
0
0
0
2
0
0
2
0
0
2
0
2
1
0
0
0
0
0
1
1
0
0
0
0
0
2
1
1
0
0
0
0
2
0
2
1
0
2
1
0
1
0
2
2
0
0
4
0
0
0
1
0
0
0
2
2
0
0
0
0
2
0
1
1
0
0
0
0
0
0
2
0
0
1
0
1
0
0
1
1
3
0
0
0
2
0
0
0
0
1
0
0
0
1
2
2
0
2
2
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
1
0
1
0
0
1
2
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
2
1
0
0
0
0
1
0
0
2
0
0
0
1
1
0
0
0
1
2
0
2
2
1
1
0
1
0
1
0
0
2
1
0
0
0
2
6
0
0
0
1
0
1
0
0
0
0
0
3
1
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
2
0
1
0
1
0
0
2
1
0
2
2
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
4
0
0
2
1
0
0
0
2
0
0
1
0
1
0
0
2
0
0
2
0
0
0
1
0
2
0
0
0
0
0
1
2
0
1
0
0
0
1
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
1
1
0
0
1
0
0
0
2
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
2
1
5
0
3
1
2
0
0
1
0
1
0
2
1
0
1
0
0
1
0
2
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
5
0
0
0
0
1
0
0
0
0
2
0
1
1
0
0
1
0
0
0
0
0
0
0
2
0
1
0
1
1
1
3
0
3
0
0
2
0
0
0
1
2
2
0
0
0
0
0
1
2
0
2
1
1
0
0
0
2
0
0
0
0
1
0
2
0
2
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
2
2
0
2
0
0
0
1
2
0
0
1
0
2
2
0
0
0
2
0
1
0
2
0
0
1
0
2
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
3
2
0
0
0
2
9
1
0
0
2
1
1
2
0
0
2
1
0
0
1
1
0
1
0
0
0
0
0
1
0
4
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
1
0
0
4
0
0
0
0
2
3
0
0
0
0
2
0
2
0
2
0
0
2
0
0
1
3
3
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
1
0
0
2
0
0
0
0
1
1
0
0
2
1
0
0
0
0
0
2
3
2
0
0
0
1
0
0
0
0
0
0
0
2
2
0
2
0
1
0
0
0
0
1
0
0
3
1
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
2
0
1
0
0
0
1
1
2
0
0
0
0
1
2
1
0
2
0
0
0
2
0
1
0
0
0
0
2
1
0
2
0
0
0
1
2
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
2
0
3
0
1
1
1
0
0
0
2
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
1
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
1
1
0
1
0
2
2
0
1
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
2
0
2
0
3
0
2
2
1
0
0
1
6
0
1
2
3
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
1
4
1
0
0
0
0
0
0
1
3
0
0
1
1
0
0
0
0
0
2
2
0
2
0
0
0
0
2
2
0
1
0
0
2
2
0
0
1
0
0
0
0
0
1
0
0
1
3
3
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
1
0
1
0
0
2
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
2
0
0
0
0
1
0
0
0
0
2
2
0
0
2
0
2
1
0
0
0
0
0
0
0
2
1
0
0
1
1
1
0
4
0
0
0
2
3
0
7
0
2
2
0
1
0
0
0
2
2
1
0
0
3
0
2
0
0
0
2
0
0
2
0
3
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
1
0
0
3
0
1
2
0
0
0
0
0
0
0
0
2
2
2
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
2
2
0
2
1
0
0
1
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
2
1
0
1
0
0
0
0
0
2
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
2
2
0
3
0
0
0
1
1
2
2
0
2
1
3
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
2
2
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
1
2
1
1
1
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
2
0
0
1
0
0
0
2
0
0
0
1
2
2
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
1
2
1
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
2
0
2
1
0
0
2
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
2
1
3
2
5
0
1
2
0
0
2
0
0
0
0
0
1
0
2
1
2
1
3
0
0
1
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
2
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
5
2
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
3
0
1
2
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
5
2
10
0
0
2
6
2
0
0
0
0
0
0
1
0
3
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
1
0
0
0
1
2
2
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
2
0
1
1
0
2
1
0
0
0
2
0
2
0
1
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
1
0
0
2
0
0
1
0
2
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
1
0
0
0
2
0
0
0
1
2
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
1
0
0
0
1
0
1
0
0
2
1
0
0
0
0
1
0
1
2
0
0
0
0
1
2
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
1
0
0
0
0
1
0
0
1
2
2
0
2
1
0
0
1
2
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
1
0
1
0
2
0
2
2
2
2
0
0
0
0
1
0
0
0
3
0
2
3
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
2
0
0
0
3
1
0
1
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
2
2
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
4
0
1
0
0
0
1
0
2
0
0
1
0
0
0
0
3
0
0
2
1
2
0
0
0
0
0
0
1
0
0
1
2
2
0
0
0
1
1
0
1
2
0
0
0
0
2
0
0
2
4
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
2
1
0
0
1
4
0
0
1
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
3
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
3
1
1
0
0
1
0
0
0
0
0
2
2
0
0
0
0
1
1
0
0
1
0
1
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
1
0
0
2
0
1
0
1
0
0
2
1
0
0
0
0
1
0
1
0
2
0
2
0
2
1
0
0
0
1
2
0
2
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
2
0
2
0
1
1
0
0
0
0
2
0
0
0
1
0
0
0
2
0
2
4
0
5
0
0
0
1
2
0
1
1
0
2
0
0
0
0
2
0
0
1
1
1
2
0
2
0
0
0
0
1
1
0
0
2
2
0
2
0
2
0
0
1
0
0
1
1
2
0
0
0
0
1
0
0
2
0
0
1
0
3
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
2
0
3
2
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
2
0
2
1
0
0
0
1
0
2
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
1
3
2
0
2
2
0
2
2
0
0
0
0
1
2
2
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
1
0
2
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
5
0
0
0
2
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
3
2
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
2
0
2
1
0
0
1
0
0
4
0
2
0
0
2
0
1
2
1
0
2
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
2
2
0
0
2
0
1
1
0
2
2
0
0
1
1
0
2
3
0
3
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
1
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
5
0
1
1
0
2
1
2
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
2
2
0
1
2
2
0
2
0
0
0
4
0
0
0
0
1
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
1
0
0
3
0
0
0
0
2
0
1
0
1
3
0
0
0
0
2
0
1
1
1
2
0
0
1
0
2
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
1
0
0
1
2
2
0
0
0
2
1
0
0
0
2
0
5
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
2
0
3
0
1
0
0
1
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
1
0
0
2
2
2
1
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
2
0
0
0
1
2
1
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
3
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
2
1
2
3
0
0
2
0
0
2
0
0
0
0
2
0
0
2
0
2
0
0
0
0
2
0
0
0
1
0
2
0
1
0
0
0
2
0
2
0
0
2
1
0
0
0
2
0
2
0
0
0
2
2
0
0
1
2
0
0
0
0
1
0
0
2
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
1
1
0
1
0
1
0
2
0
0
0
1
0
0
2
1
1
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
2
1
1
0
0
0
1
1
0
0
1
1
1
0
0
0
0
1
2
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
8
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
2
0
0
0
2
3
0
1
0
1
0
1
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
4
2
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
2
0
0
3
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
1
0
0
1
2
0
0
2
0
2
1
1
2
1
0
0
1
1
2
3
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
3
0
0
0
4
2
0
1
0
1
0
1
1
0
0
0
0
0
0
0
2
0
0
0
2
0
4
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
2
1
0
0
2
1
0
0
1
0
3
0
2
2
0
1
1
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
1
1
0
0
0
2
0
0
2
0
0
2
0
1
0
0
0
0
0
2
0
2
0
1
0
0
0
2
3
3
1
1
0
0
0
2
0
8
0
2
1
0
2
0
0
0
0
0
0
0
0
0
2
1
1
0
2
0
1
2
1
0
0
3
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
3
0
0
1
2
0
0
0
0
1
1
1
0
0
0
3
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
2
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
2
2
0
1
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
1
0
2
0
2
0
0
2
0
0
1
0
2
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
2
2
0
2
0
3
1
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
1
0
0
1
3
2
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
1
1
1
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
1
3
0
0
0
2
0
0
2
2
0
1
2
0
0
0
0
1
2
0
0
0
1
0
0
2
0
0
2
0
0
2
0
0
0
2
0
1
0
0
2
1
0
2
0
0
1
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
1
0
0
2
0
0
0
0
1
0
2
5
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
2
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
1
1
0
6
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
2
2
2
2
0
0
4
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
1
0
2
0
0
0
1
0
2
0
0
0
2
0
0
1
0
0
2
1
0
1
0
1
1
2
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
2
1
0
1
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
3
0
0
0
0
2
0
1
0
0
0
2
1
0
0
1
0
2
0
0
1
3
0
0
0
0
0
0
1
0
0
1
1
2
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
1
0
5
0
0
0
0
1
1
1
0
0
2
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
2
0
2
0
0
0
0
2
0
1
1
0
0
0
0
0
2
0
3
1
0
0
1
1
2
0
0
0
0
0
0
2
0
1
0
1
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
2
1
1
5
0
0
0
1
0
0
1
0
0
0
0
1
1
0
1
0
0
1
0
2
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
1
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
1
0
1
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
1
2
0
0
0
2
0
0
2
0
0
0
0
4
1
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
1
0
0
0
0
0
0
0
1
1
0
0
0
2
2
2
0
1
0
1
1
0
0
0
1
0
0
2
0
0
0
0
1
0
2
0
2
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
3
2
2
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
1
2
1
0
0
0
2
0
2
0
0
2
0
0
1
1
1
2
0
1
0
0
0
0
2
0
0
0
2
0
2
1
0
0
1
2
0
0
0
0
0
2
2
2
0
0
0
0
1
0
2
0
2
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
1
0
0
0
0
0
0
1
1
2
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
1
2
2
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
2
0
0
0
1
0
0
3
0
0
0
2
0
0
0
0
2
0
2
2
0
0
0
0
0
2
0
0
2
2
0
0
1
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
2
0
2
0
0
2
0
0
2
2
0
0
0
0
0
0
0
1
0
1
0
1
2
0
0
0
2
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
2
0
2
2
0
2
2
0
0
0
2
0
0
0
2
0
1
2
0
0
0
0
3
0
0
0
1
0
0
0
0
0
3
1
2
0
2
2
0
1
2
0
0
0
5
0
0
0
0
0
6
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
1
2
0
1
0
0
0
0
0
3
1
0
0
3
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
3
0
1
2
1
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
2
2
2
0
0
0
2
0
2
1
1
0
0
2
0
0
2
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
3
2
0
0
2
1
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
2
1
0
2
1
0
0
0
0
0
1
0
0
0
0
0
2
2
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
2
1
0
0
2
1
0
0
0
1
0
1
0
2
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
3
0
0
4
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
3
2
1
1
2
1
0
0
0
3
0
2
0
0
1
2
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
2
0
0
3
1
0
1
1
2
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
1
2
0
0
0
0
1
2
0
0
0
0
0
0
4
1
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
1
0
2
0
0
3
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
1
0
0
0
0
1
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
2
2
2
0
1
0
0
0
1
0
0
0
2
0
0
0
2
2
0
2
0
0
0
0
2
2
2
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
2
1
2
0
1
0
0
1
0
0
0
1
2
1
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
1
0
0
0
3
2
0
2
0
2
0
0
1
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
1
2
0
0
4
2
0
1
0
2
0
0
0
2
0
0
0
0
2
0
0
1
0
0
2
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
2
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
2
0
0
1
0
0
2
0
0
1
0
0
0
2
0
0
2
1
0
2
2
2
0
0
1
0
2
0
4
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
2
0
1
0
0
0
0
1
0
0
2
0
1
0
0
0
1
0
0
2
0
0
0
2
0
0
1
2
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
3
0
2
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
1
0
0
0
0
2
0
0
0
0
1
0
2
0
1
1
0
0
3
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
1
1
0
1
1
0
5
0
0
0
0
0
0
1
0
0
0
0
2
1
5
0
4
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
2
0
0
1
0
2
0
0
0
2
0
3
0
0
0
1
0
2
1
0
1
1
2
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
3
0
0
2
0
1
2
0
0
0
4
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
2
0
1
0
2
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
2
0
0
2
0
0
1
0
0
2
0
0
0
1
1
0
0
2
0
0
0
2
2
0
0
0
0
0
2
0
0
2
0
0
1
0
1
0
0
1
2
0
3
0
1
0
0
0
0
2
3
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
2
2
0
0
0
0
2
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
1
2
0
0
0
0
1
2
0
0
0
2
0
2
0
0
0
2
0
1
1
0
2
1
0
1
0
0
2
0
0
0
0
2
0
3
1
0
3
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
1
1
0
0
2
0
4
0
0
1
1
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
2
2
1
0
0
0
0
1
0
0
0
2
0
0
1
2
2
2
1
0
0
1
0
0
0
0
2
2
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
1
0
2
0
0
0
0
0
0
2
1
0
2
0
0
0
2
0
1
1
0
0
3
0
0
2
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
2
1
0
0
1
1
0
0
0
0
0
1
0
0
1
1
0
0
2
0
2
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
1
0
1
0
2
1
0
0
1
0
1
0
0
1
1
1
2
0
0
0
0
0
0
0
0
2
1
2
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
2
2
0
2
0
2
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
2
0
1
0
0
0
3
0
0
0
2
3
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
1
2
0
0
0
0
2
2
0
0
0
1
0
0
0
0
2
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
3
0
0
0
0
0
1
1
0
0
0
2
0
1
1
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
1
0
0
2
0
1
0
1
1
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
4
2
0
2
0
0
0
0
0
0
0
1
2
1
0
0
2
0
0
0
0
0
1
1
0
0
0
1
2
0
0
0
0
2
0
0
1
0
4
0
0
0
2
0
0
0
0
2
5
0
0
0
1
0
2
0
0
1
0
0
2
0
0
0
0
2
1
2
0
1
0
0
0
0
0
2
0
0
1
0
1
0
0
0
1
0
0
2
1
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
1
2
0
2
0
1
2
0
0
0
0
2
0
1
1
0
0
2
2
1
0
0
0
0
0
1
0
0
3
2
0
0
0
0
0
0
2
0
1
1
0
0
1
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
1
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
1
0
2
0
0
1
1
2
0
0
4
2
0
0
1
3
0
1
0
0
0
0
1
0
0
2
0
0
1
0
0
1
0
1
0
1
0
0
0
1
0
1
0
3
1
1
0
0
0
0
0
0
2
0
0
0
1
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
2
1
0
0
0
0
0
0
2
1
0
0
0
1
2
0
1
0
0
0
0
0
0
1
0
0
1
2
0
0
0
2
0
0
0
0
2
2
1
0
0
0
0
0
0
1
0
1
0
2
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
2
2
0
0
2
0
2
0
0
2
0
0
3
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
1
3
0
0
0
0
0
0
0
0
2
1
2
2
0
0
0
1
0
0
0
2
2
0
0
2
0
0
2
0
2
0
0
1
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
1
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
1
2
6
1
1
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
1
0
1
2
0
0
0
0
0
2
0
0
1
1
2
2
1
0
0
0
0
0
2
1
2
0
3
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
4
0
0
0
2
1
0
3
0
0
0
0
1
0
1
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
2
0
2
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
1
0
2
0
0
2
1
0
5
0
1
2
1
0
1
0
0
0
1
2
0
0
1
0
0
2
2
0
0
0
0
0
2
0
1
0
0
0
0
2
0
2
0
2
1
0
2
2
0
0
4
0
0
1
2
0
0
1
0
0
0
2
1
1
0
0
1
0
6
0
1
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
1
1
0
0
0
0
3
1
0
0
0
0
1
0
0
3
2
0
2
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
2
0
2
2
0
1
0
0
0
0
2
1
0
0
0
2
0
0
0
1
1
0
1
0
2
0
0
0
0
0
0
0
1
0
3
0
0
0
1
0
0
0
1
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
2
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
3
0
0
0
0
2
0
0
1
0
0
2
0
1
0
1
1
1
0
0
0
2
0
1
0
1
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
1
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
5
0
1
0
0
2
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
2
0
0
2
1
1
0
0
3
1
2
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
3
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
5
0
0
0
0
0
0
0
1
0
0
0
1
2
1
0
0
0
0
1
0
0
2
0
0
0
2
0
1
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
5
0
0
1
1
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
2
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
2
2
2
0
3
0
0
0
0
0
1
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
1
0
0
1
1
0
0
0
1
0
2
1
1
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
1
0
0
2
0
0
0
0
1
0
3
0
0
0
0
1
0
0
0
0
2
0
0
4
0
2
0
0
0
1
0
4
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
2
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
2
2
0
0
0
0
1
3
0
0
0
3
0
2
2
1
1
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
2
0
0
7
0
0
2
0
0
3
0
0
0
0
0
1
2
2
2
0
2
0
2
2
0
1
0
0
0
1
0
0
2
1
2
0
0
0
2
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
2
1
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
2
0
1
0
0
0
1
2
0
1
0
1
0
0
0
0
3
0
0
0
5
0
1
1
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
1
1
0
1
1
0
0
0
2
2
0
1
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
2
0
0
0
0
1
0
0
0
1
0
0
0
1
2
0
2
1
0
0
1
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
2
1
2
0
0
0
0
0
1
0
0
2
1
0
0
1
0
1
0
2
0
0
0
0
1
0
0
1
0
0
0
2
0
2
1
2
1
2
0
0
0
0
0
0
0
1
0
0
0
1
0
1
2
0
1
0
1
0
2
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
1
2
0
2
0
0
0
2
0
2
0
0
0
0
0
1
0
2
2
1
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
1
2
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
2
2
0
0
0
1
0
1
0
0
2
0
0
0
2
1
2
0
0
0
2
2
0
0
0
1
0
0
1
1
0
0
0
2
0
2
0
0
0
0
0
2
1
1
0
0
0
0
1
1
3
1
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
1
0
1
2
0
0
0
1
0
0
2
0
1
1
0
2
0
0
0
0
0
0
1
0
0
1
0
3
0
0
1
0
0
0
0
0
1
0
2
0
1
1
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
1
0
2
0
2
0
0
0
0
0
2
0
1
0
2
0
2
2
0
1
1
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
2
1
0
1
0
0
0
1
2
0
2
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
3
0
2
0
0
0
0
0
1
0
2
0
1
0
0
0
1
0
0
2
1
2
0
2
7
1
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
1
2
0
2
0
1
0
0
0
0
0
0
0
0
0
1
1
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
3
2
0
0
0
2
1
0
0
3
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
1
0
1
2
0
0
0
0
0
2
2
0
0
1
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
2
0
2
1
1
0
0
2
2
0
0
0
0
0
0
2
2
0
1
0
2
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
2
1
0
0
0
1
0
2
0
0
1
1
5
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
1
1
1
0
1
0
0
0
0
5
1
0
1
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
5
0
1
1
2
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
3
0
2
8
0
0
0
0
0
1
2
5
2
0
2
1
0
0
2
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
2
2
0
0
0
0
0
1
0
0
0
0
2
0
0
1
2
2
2
2
0
0
2
0
2
0
0
0
1
2
0
1
0
0
0
0
0
0
6
0
0
0
1
0
1
1
1
0
0
0
0
0
2
0
0
1
0
0
1
0
0
1
4
0
1
0
0
3
1
2
0
0
2
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
1
0
0
0
0
0
0
0
2
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
1
0
3
1
2
2
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
2
0
0
0
0
2
2
0
2
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
1
0
3
2
1
0
4
0
0
0
0
0
3
0
1
0
0
0
0
2
0
3
0
1
1
0
0
1
0
0
2
0
0
0
2
0
4
0
3
1
0
0
0
0
0
2
2
0
1
0
2
0
0
1
0
0
1
2
0
2
8
1
0
0
0
2
0
0
0
0
5
0
2
0
0
0
1
3
0
0
0
0
2
0
0
1
2
0
1
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
1
1
0
2
0
0
0
0
0
3
0
1
0
0
3
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
1
1
2
0
0
0
1
0
0
0
3
0
1
0
2
2
1
1
2
0
2
1
0
0
0
3
2
2
0
1
2
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
1
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
5
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
3
0
3
0
0
1
0
2
1
1
1
0
0
3
0
0
0
0
0
1
0
0
1
0
0
0
1
1
1
0
0
1
0
2
0
1
0
0
1
3
1
0
0
0
2
1
0
0
1
0
0
1
0
0
1
0
0
0
1
2
0
1
3
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
2
2
0
0
0
0
0
0
1
0
0
2
1
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
2
1
1
0
1
1
0
1
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
1
1
0
1
1
0
0
0
0
0
0
0
0
1
2
0
4
1
2
2
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
1
0
0
0
2
0
3
1
0
0
2
3
0
0
0
0
2
3
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
2
0
2
1
1
2
0
0
0
0
0
1
2
0
1
0
1
0
0
1
1
0
2
5
0
1
0
2
3
3
0
0
0
0
0
0
1
2
0
5
1
0
0
1
0
1
0
0
3
0
1
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
1
1
1
1
0
2
0
0
2
0
2
2
0
2
0
1
0
0
1
0
1
2
0
2
1
0
1
0
0
2
1
0
0
0
0
0
0
0
1
1
1
0
2
0
0
0
1
2
0
1
0
2
1
0
1
0
0
1
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
3
0
0
2
4
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
3
1
0
0
0
1
0
0
3
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
3
0
0
0
0
1
4
1
0
1
1
0
0
3
0
0
0
2
1
1
1
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
1
1
0
1
2
0
0
4
1
2
1
0
1
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
2
2
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
3
0
0
1
0
0
0
0
4
2
2
0
1
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
1
0
0
0
2
0
0
2
0
0
1
0
3
2
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
2
1
0
0
0
0
2
2
0
0
0
0
2
1
0
0
0
0
1
1
0
1
1
0
0
0
0
1
1
0
0
0
0
1
2
2
0
0
0
0
3
0
1
0
0
0
0
1
2
2
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
2
0
0
3
0
0
2
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
1
0
1
2
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
2
2
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
1
2
2
0
0
0
0
2
0
0
2
0
1
0
3
0
3
0
0
2
0
0
2
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
3
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
3
2
0
0
0
0
0
2
0
0
0
0
2
4
3
0
0
0
1
0
0
1
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
2
1
0
2
1
1
3
0
1
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
4
1
0
2
3
0
0
0
0
5
0
0
1
0
0
0
3
0
0
0
2
0
1
0
1
0
0
0
0
0
3
2
3
0
2
3
2
0
0
0
2
0
0
0
0
2
0
0
5
0
2
0
0
0
2
2
0
0
0
2
1
2
2
0
2
0
1
0
0
0
0
0
0
0
2
2
0
0
1
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
2
0
1
0
2
1
0
0
0
0
0
2
1
0
1
1
0
2
2
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
1
1
4
1
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
1
2
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
3
1
0
0
3
0
0
1
0
0
0
0
0
1
0
1
0
0
2
0
1
0
12
0
1
1
2
0
0
2
0
1
0
0
0
0
2
4
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
2
0
2
0
0
0
0
0
1
0
0
1
0
0
0
2
2
0
2
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
2
1
0
0
1
2
0
0
1
0
1
2
4
0
0
0
2
0
1
1
2
1
0
1
3
0
0
0
0
1
2
0
0
0
3
1
1
2
2
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
5
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
2
0
2
1
0
0
0
1
0
0
0
0
1
2
0
0
1
2
2
0
2
2
0
2
1
1
0
0
1
1
0
1
0
0
2
0
1
1
0
0
0
0
1
0
5
0
1
2
0
3
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
4
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
3
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
2
2
1
0
0
1
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
2
0
0
0
2
2
1
0
0
0
0
7
0
0
1
0
0
0
1
0
0
0
3
2
2
2
2
0
0
0
1
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
2
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
1
0
3
0
0
0
1
0
2
2
0
2
0
2
0
0
0
1
0
0
1
2
0
0
0
0
0
1
0
2
0
0
1
1
3
0
0
2
0
2
1
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
2
0
2
2
0
0
0
0
2
0
0
1
0
1
0
0
2
0
0
0
0
0
1
1
0
0
0
0
2
1
0
5
1
0
0
0
0
0
0
0
1
1
0
0
2
2
0
0
0
1
2
0
0
2
0
0
0
0
2
0
3
3
0
1
1
0
0
1
5
1
2
0
1
0
1
2
3
0
0
2
1
0
2
0
0
0
0
2
2
0
0
0
0
0
2
0
0
1
0
0
2
1
0
0
0
0
0
0
2
8
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
1
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
2
0
0
0
1
2
1
0
2
0
0
1
0
0
0
0
1
1
0
3
0
2
0
0
0
0
1
2
0
1
2
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
4
0
1
0
0
0
0
0
0
2
0
1
0
2
0
0
2
0
0
0
0
3
2
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
2
1
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
2
1
0
1
0
2
0
3
0
2
0
2
0
2
2
1
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
2
0
0
2
1
0
1
2
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
5
2
0
0
0
2
2
1
0
0
1
2
0
1
1
0
2
0
0
1
0
0
1
1
0
0
2
0
1
2
0
0
2
0
2
0
1
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
1
0
2
1
0
0
2
0
0
0
1
0
1
0
0
1
0
0
0
2
0
1
0
2
1
1
1
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
3
0
0
10
2
0
2
3
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
3
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
1
0
0
0
0
0
1
1
1
0
0
5
0
0
2
0
0
0
0
2
2
0
0
0
0
1
0
0
1
0
1
0
3
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
3
0
1
0
0
0
4
0
0
2
0
0
1
2
2
0
2
2
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
1
0
2
0
0
0
1
1
0
0
0
0
2
0
0
0
0
1
2
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
2
0
0
0
0
2
1
0
1
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
1
0
0
1
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
1
0
2
1
1
0
1
0
2
3
0
1
0
1
1
0
0
0
5
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
2
0
0
1
0
0
1
0
1
0
2
2
0
2
1
0
0
0
0
2
0
0
0
2
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
2
0
1
1
0
1
2
0
2
0
1
0
2
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
1
0
2
4
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
3
2
0
0
0
0
0
0
0
2
0
2
1
0
1
0
3
2
0
0
0
0
0
0
1
1
0
2
1
2
0
0
0
0
0
0
0
0
0
1
1
0
2
1
3
2
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
1
1
2
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
1
0
0
1
2
0
0
0
0
2
0
0
1
2
0
0
0
1
0
0
0
0
1
1
0
0
0
0
6
0
2
0
0
3
0
2
0
0
0
0
2
0
0
0
0
0
0
2
4
1
1
1
0
2
0
0
0
2
1
0
2
1
1
0
1
0
0
0
0
2
0
0
3
0
2
0
3
0
1
0
0
0
2
2
0
0
0
0
0
0
3
0
0
0
0
0
2
1
0
2
1
0
0
0
2
0
0
0
0
3
1
1
0
2
0
1
0
0
0
0
0
1
2
0
2
0
1
0
0
2
0
0
2
1
0
0
0
2
1
2
1
0
0
0
0
0
0
2
1
0
0
2
1
2
0
0
0
2
1
0
2
1
1
0
1
0
1
0
0
4
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
2
1
0
1
0
2
1
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
2
1
0
2
2
2
2
0
0
0
0
1
0
0
2
0
0
0
0
0
3
2
0
0
0
1
2
0
0
1
0
1
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
3
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
2
0
2
0
0
1
1
0
1
0
0
2
0
0
1
2
0
0
0
0
0
0
0
1
0
1
0
0
2
0
1
0
0
0
1
0
0
1
2
0
2
0
0
1
3
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
1
0
0
2
2
1
0
1
0
2
0
0
2
1
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
1
0
1
0
0
0
1
0
1
1
1
0
0
2
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
2
0
0
2
0
0
0
0
0
1
3
0
0
2
0
0
0
0
0
2
0
2
1
2
0
0
1
0
0
0
1
1
1
1
0
0
0
0
0
1
0
0
0
0
4
1
0
0
2
1
0
0
0
1
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
1
0
2
0
0
0
0
1
3
0
2
0
0
1
0
0
0
0
2
1
2
1
2
0
0
0
0
1
2
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
1
1
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
2
0
2
2
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
3
0
0
1
0
0
1
0
0
0
0
2
4
0
2
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
1
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
2
2
0
1
0
1
0
1
1
1
2
0
1
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
2
1
0
1
3
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
2
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
2
0
1
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
4
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
2
0
0
0
1
1
0
0
0
0
0
2
2
0
1
2
0
0
0
0
1
0
3
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
1
0
2
1
1
1
1
0
1
3
0
0
0
0
0
3
0
0
0
2
0
1
1
3
0
2
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
2
2
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
1
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
3
0
1
0
0
4
1
0
0
2
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
2
0
1
0
2
0
1
1
1
0
0
0
0
3
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
1
0
2
0
0
0
0
2
0
0
0
0
0
1
2
0
1
0
0
0
1
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
2
4
1
0
0
0
0
2
0
0
2
0
1
0
0
3
2
0
0
0
0
2
0
0
1
0
1
2
0
0
0
0
1
2
2
0
0
1
0
0
0
0
0
2
1
2
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
1
0
0
1
0
0
0
0
2
2
0
0
4
0
0
0
0
0
2
3
1
0
0
0
0
1
2
0
0
0
0
2
0
2
0
1
0
0
0
1
0
1
0
1
0
0
1
0
2
0
2
2
1
0
0
0
0
0
1
2
2
2
1
0
0
0
0
0
2
2
0
2
0
1
3
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
2
0
1
0
0
2
0
0
0
1
1
3
2
1
1
0
0
0
2
0
0
1
2
0
0
1
0
2
0
0
2
2
0
0
0
0
1
2
0
0
4
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
3
3
0
1
0
0
0
2
0
1
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
2
2
0
1
0
2
0
0
2
0
2
0
0
0
0
1
0
2
0
0
2
0
0
1
1
0
0
1
2
2
0
1
1
0
0
0
0
0
2
4
3
4
0
0
2
2
1
0
0
2
1
0
0
0
1
2
1
0
0
0
2
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
2
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
1
0
0
0
0
3
1
0
0
0
0
0
0
0
0
2
0
1
4
3
0
1
2
0
2
1
0
0
0
0
1
1
0
0
2
0
0
1
0
2
0
2
1
3
2
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
2
0
0
3
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
1
0
0
1
2
1
0
0
0
0
1
2
1
0
0
0
0
0
3
2
1
0
1
1
0
0
0
0
0
0
0
2
0
0
0
1
0
2
2
1
0
2
0
0
0
0
0
2
0
2
1
0
0
0
0
1
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
1
0
1
1
2
0
0
1
0
1
0
0
2
0
0
0
0
1
1
0
0
1
0
0
1
2
0
1
1
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
2
2
4
0
0
0
4
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
2
0
1
0
0
0
1
2
0
1
1
2
0
1
0
0
2
2
0
0
0
1
0
2
0
0
0
0
2
3
1
0
0
0
2
2
2
0
0
0
0
2
0
0
1
0
0
0
0
0
2
1
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
4
1
2
0
0
0
0
0
1
2
1
2
0
2
0
0
0
0
0
1
0
0
1
2
1
0
0
0
1
0
2
0
0
0
2
0
0
1
1
0
0
2
0
0
0
0
0
1
2
0
0
0
0
2
2
3
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
2
1
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
3
0
0
0
0
0
0
1
0
2
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
2
2
1
1
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
2
1
2
0
0
0
0
1
0
0
3
2
1
0
2
0
0
0
2
2
0
1
2
2
0
0
1
0
0
0
0
0
1
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
1
1
0
0
0
0
0
0
0
0
0
2
0
1
0
2
2
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
2
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
2
1
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
2
0
2
0
0
0
0
1
2
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
2
0
0
0
2
0
0
0
0
2
0
3
0
2
0
0
1
1
0
2
0
0
2
0
1
0
1
2
0
0
0
2
1
1
0
0
0
2
1
0
0
2
0
0
0
0
1
0
0
4
0
0
1
0
0
1
0
0
0
0
0
2
0
0
2
2
0
0
2
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
5
1
3
2
0
0
1
2
0
1
0
2
1
2
0
1
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
2
0
3
2
0
0
2
0
0
0
0
0
9
0
2
0
0
1
3
0
0
0
0
4
0
0
0
0
0
0
1
2
1
0
1
0
1
0
1
1
0
2
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
2
0
0
0
0
0
1
0
1
1
1
1
1
0
4
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
1
0
0
0
0
1
0
1
0
0
0
1
2
0
2
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
2
0
1
1
1
0
0
3
2
0
1
0
0
2
0
0
0
0
1
2
0
0
2
2
0
5
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
1
2
0
1
0
0
0
6
0
0
0
0
1
0
0
0
0
1
1
2
2
0
0
0
0
0
0
0
0
0
0
4
2
0
0
0
0
2
0
0
0
0
0
0
5
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
4
1
0
3
0
0
3
5
1
0
0
0
0
0
1
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
3
0
5
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
1
0
0
3
5
1
1
1
1
0
2
0
0
1
0
1
0
1
5
2
1
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
6
0
0
0
2
0
2
2
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
2
2
1
0
2
0
0
0
2
1
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
1
0
3
1
0
1
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
1
0
2
2
0
0
1
0
0
0
2
0
0
2
2
0
0
2
0
0
2
0
0
1
0
1
1
0
1
0
2
0
0
1
1
0
1
1
0
0
0
1
1
0
2
0
0
2
1
1
0
0
0
0
0
0
0
2
0
1
2
0
2
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
3
0
0
0
0
0
0
2
0
0
1
0
0
1
0
1
0
0
0
3
0
0
0
1
0
0
0
0
3
0
0
0
1
0
0
0
2
0
0
0
0
1
0
4
1
1
4
0
0
2
0
0
1
0
0
2
1
2
0
2
1
2
0
0
0
1
2
2
3
0
0
0
1
0
7
2
0
0
0
0
2
0
1
0
2
2
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
5
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
1
0
2
0
0
1
0
1
0
3
1
1
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
2
2
0
0
0
0
0
0
2
2
0
2
0
0
2
2
2
0
0
0
1
0
1
0
0
1
0
0
2
0
1
0
0
0
0
0
2
1
0
6
2
0
0
1
0
1
0
4
0
1
0
0
0
0
0
2
1
5
2
2
0
0
0
0
2
0
0
0
3
0
0
2
0
0
0
0
0
0
0
1
0
1
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
3
0
2
0
0
2
0
0
0
1
2
0
2
2
0
1
0
1
0
0
2
0
0
0
0
0
3
2
3
0
2
1
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
2
0
0
1
0
0
0
2
1
0
1
1
0
0
1
2
0
0
0
0
0
0
0
1
0
1
1
0
1
0
1
0
0
1
1
3
0
0
0
0
2
2
0
0
1
0
1
2
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
3
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
2
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
3
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
2
0
2
0
0
1
0
0
2
0
0
1
0
2
0
1
5
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
1
0
1
2
0
0
0
0
0
2
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
2
0
0
1
1
0
0
0
0
2
0
0
0
1
0
1
0
0
0
2
1
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
1
2
0
0
0
0
1
2
1
1
0
1
0
0
0
0
1
0
1
2
0
0
2
0
0
0
2
1
0
3
2
0
2
1
0
0
0
0
0
0
2
0
1
0
2
3
0
0
0
2
2
0
0
0
1
2
0
1
0
1
0
1
0
1
0
0
1
0
0
0
0
3
3
0
2
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
1
1
0
0
0
0
1
0
2
1
0
2
1
2
4
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
2
0
0
1
0
0
0
1
0
1
0
0
0
1
0
2
2
0
2
0
2
0
2
0
0
2
2
2
0
0
1
3
0
3
2
0
0
0
1
1
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
1
3
0
0
1
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
2
0
1
0
0
2
0
1
0
0
1
0
0
0
1
0
1
2
1
0
4
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
8
2
0
1
0
0
0
1
0
0
2
1
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
3
0
0
0
1
0
3
2
2
0
0
0
1
1
0
0
2
3
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
1
0
4
0
0
1
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
4
1
2
2
0
0
0
3
2
2
0
2
2
0
0
1
0
0
0
0
1
2
2
0
1
1
0
0
2
2
0
3
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
4
0
0
0
0
2
2
1
0
0
2
2
0
0
0
0
2
0
0
2
0
3
0
0
0
0
0
1
0
1
0
0
1
1
0
1
1
2
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
1
0
0
0
2
0
0
0
2
2
0
0
0
0
0
1
0
2
0
0
0
4
1
0
0
0
0
3
0
0
0
0
0
1
0
0
1
1
0
0
2
1
0
1
0
2
0
3
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
1
0
1
0
0
0
2
4
0
3
2
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
2
1
0
2
0
0
1
3
0
0
1
0
2
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
1
2
0
1
0
0
1
0
1
1
3
0
1
3
0
2
0
0
2
1
0
0
0
3
0
0
0
0
1
1
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
1
0
0
1
4
0
2
0
0
0
1
2
3
0
0
0
2
1
2
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
2
1
0
2
0
0
2
0
0
0
0
0
0
2
1
1
0
0
0
1
0
2
0
0
2
2
0
0
0
3
0
0
1
0
2
0
1
0
0
3
0
0
0
0
2
0
0
1
1
0
2
2
0
0
2
1
0
0
0
0
0
2
0
0
1
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
4
1
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
2
2
0
0
2
0
0
0
0
0
0
0
1
0
0
1
3
0
0
2
0
0
4
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
3
0
3
0
0
0
0
2
1
2
0
0
2
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
4
0
0
0
1
0
0
0
0
3
2
0
0
1
0
2
2
2
1
0
1
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
1
0
0
0
0
3
1
1
1
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
1
2
1
2
0
0
0
0
0
1
2
3
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
4
0
0
0
0
0
1
0
2
2
0
0
1
1
0
0
2
0
2
0
1
0
2
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
5
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
2
1
0
0
0
0
0
3
0
0
1
1
0
0
1
0
2
1
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
1
0
2
0
2
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
2
2
3
0
1
2
0
0
0
2
0
0
0
1
0
1
0
0
0
0
1
0
1
3
0
1
0
0
0
1
0
0
0
2
1
0
2
0
0
0
0
0
1
0
6
0
0
2
2
0
0
0
0
0
2
2
0
3
1
2
0
0
2
0
0
0
0
0
0
1
0
1
2
2
0
0
0
0
0
0
0
0
0
1
2
0
2
0
1
1
0
0
0
1
0
2
0
0
2
1
0
0
0
0
3
0
0
1
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
1
1
1
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
2
2
0
0
0
0
0
0
2
1
0
1
1
0
0
0
0
0
1
0
0
2
0
0
2
1
0
1
0
0
2
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
4
0
0
0
2
0
2
2
0
0
0
3
1
1
0
2
3
0
0
1
1
0
1
0
0
1
2
0
2
0
0
0
0
0
0
0
1
0
2
0
0
1
0
1
0
0
1
0
2
0
0
0
1
1
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
2
2
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
3
0
0
1
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
2
0
1
0
2
1
0
0
0
2
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
1
0
0
1
0
1
0
0
0
0
0
1
0
1
0
2
1
0
0
1
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
2
2
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
3
0
0
1
2
0
4
1
0
0
0
1
1
4
0
1
0
2
0
2
1
0
0
1
1
0
0
0
2
1
1
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
1
0
0
0
2
1
0
0
2
0
0
0
0
0
0
2
2
0
1
2
2
1
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
2
2
2
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
0
0
1
0
1
1
2
0
0
0
0
5
0
0
0
0
0
0
0
0
0
2
2
0
0
3
1
1
2
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
3
0
2
0
1
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
1
0
0
0
0
2
0
0
1
1
2
0
1
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
1
1
2
2
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
5
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
4
0
0
0
0
1
0
0
2
1
1
0
0
0
0
0
0
1
0
1
1
2
0
1
1
1
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
2
0
1
0
1
1
2
1
0
0
0
2
0
1
0
0
0
0
0
0
0
2
1
1
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
1
0
0
1
0
2
0
2
1
1
0
0
0
0
0
1
0
0
0
3
2
4
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
1
1
1
0
0
2
0
0
0
0
0
1
0
2
0
0
2
0
0
2
2
0
0
0
0
1
0
0
2
0
0
1
1
2
0
2
3
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
2
0
0
0
2
2
1
1
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
1
1
0
0
0
2
2
1
0
0
0
0
1
0
0
0
0
0
0
1
2
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
3
2
0
2
2
0
0
0
0
1
0
0
0
1
2
0
3
0
2
0
1
1
0
1
0
0
0
0
1
1
0
0
0
0
2
0
0
0
2
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
2
0
1
0
0
0
3
0
0
0
0
1
0
2
0
0
0
2
0
4
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
1
2
0
0
1
0
0
2
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
2
1
0
2
0
0
0
0
3
1
0
0
0
1
0
1
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
3
1
0
2
1
2
2
0
0
0
2
0
0
0
0
0
2
1
2
0
0
0
1
0
1
0
0
0
0
0
0
2
3
0
0
1
0
0
2
1
1
0
0
0
0
0
2
2
2
2
2
3
0
1
0
0
0
0
1
2
0
0
2
1
0
0
1
0
0
0
0
0
0
2
0
1
1
0
2
0
0
0
2
0
0
1
0
1
0
1
0
2
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
2
0
0
1
2
0
0
0
0
2
0
2
0
0
1
1
3
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
2
1
0
0
3
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
3
0
1
0
0
0
0
0
1
0
1
0
0
2
0
0
1
0
0
0
0
1
2
0
0
0
0
1
2
0
2
0
0
0
0
5
2
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
1
2
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
1
0
2
0
0
2
0
0
0
0
2
0
2
0
0
0
2
2
0
1
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
1
0
3
0
0
0
0
0
0
0
2
0
0
1
1
0
2
0
0
0
1
0
2
0
0
1
3
1
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
2
0
0
1
2
2
0
0
0
2
0
0
0
0
0
0
1
1
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
1
0
0
2
1
0
2
0
0
1
3
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
2
0
0
0
0
4
4
0
2
1
0
0
2
2
0
0
1
0
1
0
1
0
2
0
0
1
1
0
0
1
0
0
0
1
2
1
0
0
0
2
2
0
0
0
0
1
2
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
2
1
0
0
0
0
1
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
2
1
0
0
0
0
0
0
1
2
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
1
0
2
2
0
0
0
0
1
0
0
0
0
0
2
4
2
1
0
1
2
0
0
0
0
3
0
0
0
0
0
0
0
0
2
2
0
0
0
3
2
0
0
0
0
1
0
0
0
0
0
0
0
6
0
1
0
2
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
1
1
0
2
0
0
1
0
2
1
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
2
0
1
0
1
0
3
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
2
1
0
0
0
0
2
0
0
0
1
0
0
0
0
2
2
0
0
2
8
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
2
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
2
0
2
1
0
0
0
2
2
0
0
0
2
0
1
0
1
0
0
0
0
0
1
0
0
2
2
3
0
0
4
1
0
0
0
0
0
0
1
0
1
2
1
0
0
0
1
0
2
0
2
0
0
0
0
1
0
1
0
2
0
0
1
2
1
2
0
0
0
2
0
2
0
1
1
2
0
0
2
1
0
0
0
0
0
0
0
1
0
0
3
0
0
0
1
2
1
2
0
0
0
0
0
2
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
2
2
0
1
0
0
0
0
1
0
2
0
0
0
0
9
2
1
1
1
0
1
2
1
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
1
2
1
0
0
0
0
0
1
0
2
0
0
1
0
0
1
0
0
0
0
0
0
3
0
0
0
0
2
2
0
0
0
0
3
0
0
1
0
1
0
0
2
0
0
0
0
0
2
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
3
1
0
0
2
0
0
0
2
0
0
2
0
2
0
0
0
0
1
0
0
2
2
3
0
0
0
0
1
0
1
0
1
2
1
0
1
0
0
2
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
1
1
0
2
1
2
2
0
1
0
0
0
0
2
2
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
2
5
0
0
0
0
1
0
0
2
0
0
3
2
2
0
1
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
1
1
0
2
1
0
0
2
0
0
2
0
0
2
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
1
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
2
1
0
0
0
0
0
2
0
0
1
0
2
0
0
0
1
0
0
0
2
0
2
0
0
0
2
0
1
0
0
0
0
1
1
5
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
1
2
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
1
0
0
0
2
0
0
2
0
0
2
0
0
0
2
0
2
0
0
2
0
2
0
0
1
0
0
0
0
1
1
0
0
2
0
1
1
4
0
0
1
1
2
0
1
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
1
0
2
0
0
0
1
0
0
1
0
2
6
2
1
0
0
0
0
0
1
0
1
0
0
1
0
2
0
0
2
0
2
2
1
0
0
0
1
1
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
1
0
1
1
1
0
2
2
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
1
0
0
0
3
2
1
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
1
2
0
0
0
1
2
0
0
0
0
0
3
0
3
0
0
1
0
2
0
0
1
0
0
2
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
1
0
1
0
0
1
0
0
2
0
1
2
2
2
0
0
0
0
0
0
1
0
0
0
0
3
1
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
1
2
0
1
0
2
1
1
0
2
0
0
0
0
0
0
0
0
0
1
1
2
2
2
0
0
2
4
0
1
1
0
0
1
0
0
2
0
0
0
3
0
0
5
1
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
3
1
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
2
1
1
1
0
0
2
0
0
0
0
2
0
0
0
0
0
3
0
0
1
2
0
0
1
3
0
0
1
0
1
0
0
3
0
0
0
0
1
1
0
1
0
0
2
1
0
0
2
0
0
0
0
0
1
1
0
1
0
0
0
2
0
2
2
0
1
1
0
0
0
3
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
1
0
3
1
0
0
2
2
2
0
0
3
1
2
0
0
0
0
2
0
0
0
0
0
0
1
1
2
0
1
0
1
0
2
1
0
0
0
0
0
0
0
2
3
2
0
2
0
0
0
0
0
0
2
0
2
1
1
0
0
0
2
0
0
0
1
0
0
2
0
2
3
2
2
0
0
0
5
0
0
0
0
0
0
2
0
0
1
0
0
2
1
0
0
0
1
1
0
0
0
0
0
1
0
2
0
0
3
0
0
0
0
0
0
2
0
0
0
2
1
2
1
0
1
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
2
0
2
1
2
0
1
0
2
1
0
1
1
2
2
0
0
0
1
0
2
0
2
2
0
1
0
2
3
3
0
0
0
2
1
0
2
0
0
2
1
1
0
1
2
1
0
0
2
0
0
0
1
1
0
0
2
0
0
0
2
0
1
0
2
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
2
2
4
0
1
0
2
2
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
2
1
0
0
0
0
3
2
0
0
0
2
0
1
1
2
0
0
2
0
2
2
0
2
1
2
1
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
2
0
1
0
0
2
0
2
2
0
0
0
0
0
2
2
1
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
1
0
0
1
0
0
0
1
0
0
2
0
0
2
1
0
0
1
2
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
2
1
0
1
0
0
0
0
2
1
1
0
1
2
0
1
1
2
0
1
1
0
1
0
1
0
0
0
0
3
2
0
0
2
0
0
0
0
1
0
2
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
2
0
2
0
1
2
0
0
4
2
0
2
1
2
0
0
0
2
0
1
0
0
1
1
0
1
0
1
0
0
0
2
0
1
0
0
2
2
0
0
0
0
0
0
2
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
1
2
0
1
0
0
1
0
0
0
0
1
0
2
0
1
1
0
0
0
0
0
0
0
0
6
0
2
0
0
0
1
0
0
0
1
0
3
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
2
0
2
0
1
0
1
1
0
1
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
1
0
1
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
4
1
1
0
0
1
1
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
3
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
1
0
0
0
0
2
0
0
0
0
1
1
0
2
0
1
0
0
1
0
0
0
2
1
0
0
1
0
0
0
1
1
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
2
2
2
1
0
0
0
1
0
2
0
0
0
3
0
2
0
1
0
2
0
0
2
0
1
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
1
2
0
0
2
1
0
0
0
0
1
0
2
0
2
3
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
1
2
0
0
1
0
0
0
1
2
2
0
2
0
2
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
1
0
2
0
0
1
1
0
0
1
0
0
0
0
0
0
2
0
0
1
2
2
0
1
4
0
2
2
0
0
0
1
0
2
0
0
0
0
1
0
0
1
0
4
2
0
0
0
0
1
0
2
0
1
0
2
0
2
2
0
1
1
0
0
0
1
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
4
0
1
0
0
0
0
2
0
2
0
1
0
0
0
0
0
1
0
0
2
2
0
2
0
0
0
1
0
1
0
2
0
0
0
0
1
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
1
1
3
0
0
1
0
1
1
0
0
2
2
0
1
0
0
0
3
0
1
2
2
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
2
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
1
0
0
1
2
0
2
0
2
2
0
0
0
0
0
0
0
0
1
0
2
1
4
2
1
0
0
2
0
1
0
0
0
0
0
1
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
2
0
0
2
0
0
0
1
0
0
0
0
1
0
0
2
2
0
0
0
1
2
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
4
2
0
2
2
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
1
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
1
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
2
0
1
0
1
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
2
0
1
0
0
2
0
1
1
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
2
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
1
4
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
3
2
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
2
1
1
0
2
0
1
0
2
0
0
0
2
0
1
2
2
0
1
1
0
2
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
8
2
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
1
0
2
0
0
0
2
0
2
2
2
2
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
12
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
1
2
0
0
0
0
0
2
0
0
2
0
1
1
2
0
0
0
0
0
0
2
1
0
0
2
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
1
1
1
1
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
2
0
0
1
0
2
0
0
0
2
0
0
0
1
2
0
0
0
1
1
1
2
0
2
0
0
1
0
1
2
1
1
0
1
0
1
0
2
0
1
1
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
2
1
0
2
0
1
1
1
1
0
0
0
2
0
8
0
2
0
0
0
0
0
1
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
1
0
0
0
0
0
2
0
0
0
1
0
1
0
0
5
0
2
1
0
0
0
0
2
0
0
2
1
1
2
0
0
1
0
2
0
0
0
0
0
0
1
1
1
1
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
2
0
0
0
2
0
2
1
3
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
2
0
1
1
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
1
0
1
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
1
2
1
0
0
9
1
0
1
1
0
0
0
0
0
2
0
1
1
0
0
1
1
1
1
1
0
3
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
2
1
0
0
1
0
0
0
0
1
1
0
0
2
0
0
0
2
0
0
2
0
0
0
0
2
0
1
2
2
0
0
1
0
0
0
2
1
3
1
2
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
1
0
0
2
2
0
2
0
2
0
0
0
1
2
0
1
0
2
0
0
2
0
0
0
1
0
0
0
1
0
0
2
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
5
0
0
2
2
0
1
0
0
2
1
0
0
0
3
0
0
1
0
0
0
0
0
1
2
0
1
0
1
0
0
0
0
2
0
0
2
0
0
1
0
1
2
1
0
0
2
0
0
0
0
0
2
0
0
1
0
2
1
3
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
2
2
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
2
0
0
0
1
2
0
1
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
2
0
1
1
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
3
0
2
0
1
0
0
0
3
1
0
0
0
0
0
0
1
0
1
0
3
1
0
1
0
0
0
0
4
0
0
6
2
2
0
1
0
0
0
0
0
4
2
1
1
5
0
2
0
1
0
0
0
0
0
2
1
0
0
0
0
2
0
1
0
2
0
2
0
1
0
0
1
0
0
2
0
0
0
1
1
0
0
0
0
0
1
1
0
0
2
0
0
0
0
1
0
3
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
2
1
0
0
0
1
2
0
1
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
1
1
1
0
0
0
0
0
1
0
3
5
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
1
0
0
1
0
2
1
0
0
2
0
0
2
0
0
0
0
0
3
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
2
0
2
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
4
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
1
1
3
0
0
0
3
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
1
2
0
0
0
2
1
1
0
0
0
0
0
2
0
2
0
0
2
0
0
2
0
2
0
0
0
1
0
0
2
0
0
0
0
0
1
1
0
0
1
0
1
0
0
1
2
0
2
0
0
0
0
0
0
1
0
0
0
2
0
1
1
0
2
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
1
3
1
0
0
0
0
2
1
0
0
2
0
2
0
2
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
1
0
2
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
1
2
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
3
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
3
1
0
1
0
1
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
2
3
0
0
2
1
2
2
2
0
0
0
0
2
1
2
2
0
2
0
0
1
0
0
2
0
2
1
1
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
1
3
3
2
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
2
0
0
0
0
0
1
0
0
0
3
0
0
0
2
3
0
0
2
0
2
0
1
0
0
2
1
1
0
2
0
0
0
2
0
0
0
3
4
0
2
0
0
0
0
1
2
1
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
2
1
1
0
0
0
1
0
0
1
0
0
0
1
0
3
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
1
2
1
0
1
0
0
1
0
1
2
2
0
2
0
0
0
0
0
1
2
0
0
0
0
2
0
0
1
1
0
0
0
0
1
2
0
0
1
2
0
1
2
0
4
2
1
0
0
0
0
0
0
2
0
0
0
2
0
1
0
2
0
1
0
0
0
1
0
2
1
0
0
0
1
1
0
0
1
0
2
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
3
0
1
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
1
1
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
2
0
0
3
2
0
2
0
0
0
0
1
2
0
2
0
0
0
1
0
2
1
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
4
1
0
0
1
1
0
0
0
0
0
0
1
0
0
2
2
2
2
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
2
0
1
2
2
0
2
0
1
0
0
0
2
0
0
0
1
0
2
0
0
0
0
2
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
1
0
2
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
2
1
2
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
1
0
0
0
1
2
1
0
1
1
0
1
2
0
2
0
2
1
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
1
1
0
0
1
0
1
0
0
0
1
0
0
0
0
3
0
2
0
0
0
0
2
0
0
0
2
0
1
0
2
0
0
0
0
0
1
1
0
0
3
1
0
0
0
1
0
2
0
3
0
0
1
0
1
0
0
0
0
1
0
1
1
0
0
0
2
0
1
0
0
0
0
1
0
3
0
0
2
2
0
0
0
2
0
1
0
0
0
0
1
0
1
2
3
0
1
0
0
0
2
2
0
0
0
2
0
2
0
0
1
0
0
2
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
1
0
1
2
3
4
1
0
0
1
2
0
0
0
1
1
2
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
1
2
0
0
0
2
0
0
0
2
0
0
2
0
2
1
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
2
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
2
2
0
6
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
3
0
1
2
0
2
3
0
1
1
2
0
0
0
3
0
0
2
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
2
1
0
0
0
1
1
0
0
1
0
2
0
0
0
2
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
2
2
0
2
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
3
1
0
0
0
3
0
0
1
0
0
0
0
2
2
0
2
0
0
0
0
1
3
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
2
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
2
3
0
0
2
1
0
0
0
0
2
0
0
0
0
1
1
1
0
1
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
2
1
0
0
2
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
2
0
0
1
0
0
0
0
0
2
0
2
1
0
0
0
0
2
0
1
0
1
1
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
2
1
2
0
2
0
2
0
0
0
0
1
0
0
2
1
0
0
3
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
1
1
2
1
0
0
1
0
0
1
2
0
0
0
0
2
0
1
1
0
0
0
0
1
0
0
0
2
1
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
2
0
0
0
2
2
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
7
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
1
0
1
0
0
1
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
2
0
2
3
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
1
0
0
0
4
0
1
1
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
2
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
2
2
1
0
0
0
0
1
0
0
0
2
0
0
1
1
0
0
1
0
0
2
0
1
0
2
0
0
1
0
0
2
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
2
1
2
2
0
0
0
2
0
1
0
0
1
2
1
0
0
0
2
0
1
0
0
0
1
1
0
0
2
1
0
0
0
0
0
1
0
2
1
0
0
2
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
2
0
3
0
1
2
1
2
1
1
0
0
2
0
1
0
1
0
2
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
3
0
0
0
0
3
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
2
2
0
2
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
2
4
2
0
1
0
0
0
1
0
0
0
3
2
0
2
0
0
2
2
1
0
1
0
1
2
0
0
0
0
0
1
2
0
1
0
2
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
2
1
0
1
0
0
1
0
0
1
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
3
0
0
1
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
1
2
1
2
0
3
0
1
1
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
1
0
0
2
0
0
0
0
1
0
0
0
2
0
2
1
0
0
1
0
0
1
0
0
1
2
0
0
2
0
0
0
3
1
0
0
0
1
0
0
0
0
0
2
1
0
1
0
0
0
2
1
0
3
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
1
2
0
0
0
0
1
0
0
0
2
0
1
1
0
0
1
0
2
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
2
1
0
0
0
0
0
0
2
1
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
2
1
1
6
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
2
1
0
0
2
0
0
2
4
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
2
1
0
2
1
0
2
0
0
0
2
0
0
0
1
0
2
0
0
2
0
0
0
0
0
1
0
3
0
0
0
2
1
0
2
0
2
0
1
0
1
2
0
0
0
1
0
1
0
0
2
0
3
1
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
5
1
1
2
2
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
1
2
0
0
0
0
1
2
1
2
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
1
2
0
1
19
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
2
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
2
2
0
0
0
0
2
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
2
0
0
1
0
2
2
1
0
0
0
2
0
0
0
5
2
0
0
1
0
0
0
0
5
0
0
2
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
1
0
0
6
0
0
0
1
0
0
0
2
3
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
2
1
2
2
0
0
0
2
5
1
1
0
0
2
2
3
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
1
0
0
2
0
0
0
1
2
0
0
0
0
0
2
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
4
0
2
2
2
2
0
0
1
1
0
0
0
0
0
0
2
0
2
0
0
0
2
2
1
0
0
0
1
2
0
0
2
2
0
0
0
1
6
0
0
1
2
1
3
0
0
0
0
2
1
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
1
3
0
0
2
0
0
1
0
0
2
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
6
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
2
1
0
2
0
0
0
3
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
2
0
0
0
0
0
1
1
1
2
1
3
0
0
0
0
0
1
0
0
1
1
2
1
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
1
2
0
0
0
2
0
0
2
0
0
0
2
0
0
0
1
2
0
1
0
0
1
1
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
1
1
2
2
0
2
0
1
2
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
5
2
2
1
2
0
0
0
0
0
1
1
2
0
0
0
2
2
1
1
0
0
0
1
0
2
1
0
0
0
0
2
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
2
0
0
0
0
1
2
0
0
1
0
2
0
2
0
0
1
1
0
2
1
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
2
0
2
1
0
0
0
0
0
0
3
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
2
2
2
0
0
0
2
0
0
0
0
0
2
0
1
2
0
0
1
0
1
1
1
0
0
0
1
0
7
0
2
0
2
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
1
0
0
2
0
0
0
0
0
2
0
2
0
0
2
2
2
0
0
1
1
1
2
0
0
0
0
1
2
2
0
1
0
0
2
0
2
1
0
0
0
0
0
2
0
2
2
0
0
1
0
0
0
2
0
0
0
1
2
0
0
0
0
3
1
0
2
0
0
0
1
0
1
0
0
0
0
1
1
0
1
1
2
0
0
0
3
0
2
0
0
0
0
1
0
0
0
0
2
0
4
0
0
0
0
0
2
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
1
0
0
0
0
2
2
0
1
1
1
0
1
1
2
0
0
2
0
1
2
0
0
1
0
2
3
0
1
3
0
0
0
0
0
1
2
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
1
0
2
0
0
0
0
1
0
0
0
2
1
1
2
0
1
0
2
0
1
0
0
1
1
0
1
0
0
2
2
0
0
0
0
0
0
2
1
0
1
1
1
2
0
0
0
0
0
1
0
2
1
0
1
2
2
0
0
0
0
0
0
0
1
1
0
2
0
0
0
1
0
0
0
2
1
3
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
3
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
1
0
0
0
2
1
0
0
0
2
0
0
0
2
2
2
1
0
1
3
0
1
2
1
0
0
0
0
0
0
2
0
0
0
0
0
2
2
3
1
0
0
3
0
0
0
0
0
1
0
0
1
0
2
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
2
2
2
1
0
0
0
0
0
0
2
3
0
1
0
0
1
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
1
0
1
1
1
0
1
1
2
0
0
0
0
0
2
0
1
0
2
2
0
0
0
0
1
0
0
0
4
2
0
0
0
0
0
1
1
0
0
2
0
0
2
0
0
1
1
2
1
0
0
1
0
0
1
3
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
2
0
0
2
0
0
0
0
0
1
2
1
2
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
1
0
0
0
1
0
2
1
0
0
2
0
3
1
0
0
1
0
0
0
0
0
1
2
0
0
3
0
0
0
0
1
0
1
0
0
0
0
1
1
5
2
0
0
0
0
0
0
3
2
0
0
0
0
2
0
1
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
1
4
0
0
0
0
0
2
0
3
0
0
0
0
0
1
1
4
0
2
2
0
0
0
1
2
0
1
0
1
2
1
1
0
1
2
0
0
0
2
2
0
0
2
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
1
0
1
2
0
0
1
0
0
0
0
2
0
3
2
0
0
0
1
0
2
0
0
2
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
1
2
0
0
3
0
2
0
0
0
0
0
0
0
3
1
1
0
1
1
2
0
0
3
0
0
1
0
0
1
1
1
2
0
2
0
0
0
0
0
0
2
1
2
2
0
1
1
1
0
1
0
0
0
0
0
2
0
2
2
0
2
2
0
0
0
1
1
1
0
2
2
0
1
0
2
2
3
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
1
1
0
0
0
0
2
0
1
0
0
0
0
0
1
0
1
0
0
1
0
2
0
0
0
0
0
0
2
1
1
2
0
2
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
2
0
2
0
0
1
1
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
2
0
1
0
1
2
0
2
1
0
3
0
2
1
2
0
1
0
2
0
0
1
3
0
0
2
0
1
1
0
2
2
1
3
0
0
0
0
2
0
0
0
2
0
3
6
2
3
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
2
2
2
1
1
0
0
0
0
1
2
0
2
1
1
1
1
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
1
2
0
4
0
2
1
0
2
0
1
0
2
2
0
0
1
0
1
1
0
1
0
0
2
2
0
0
2
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
1
2
3
0
1
0
0
0
2
1
0
2
0
0
2
0
1
4
1
1
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
2
2
2
0
2
0
1
0
0
3
0
2
0
0
3
0
1
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
2
2
1
0
0
0
0
1
0
0
1
3
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
2
1
0
0
0
2
0
0
0
0
2
0
1
0
2
0
0
0
0
1
1
1
1
0
2
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
1
5
1
0
0
0
0
0
0
0
2
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
2
6
0
1
3
2
1
1
2
0
0
0
2
0
0
0
0
1
2
0
2
0
1
2
2
2
0
2
1
0
0
0
0
0
0
1
2
0
2
0
0
0
2
3
0
1
0
0
0
1
3
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
1
0
2
2
0
0
0
0
1
2
2
0
0
2
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
1
0
0
2
3
4
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
2
0
0
1
0
0
4
1
1
0
0
0
0
1
0
2
0
0
1
0
0
1
0
1
2
0
4
0
0
0
2
0
0
0
2
0
1
1
1
1
0
0
0
2
0
1
0
0
0
2
0
1
2
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
2
0
2
1
0
4
0
0
0
0
3
2
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
1
0
0
0
0
1
0
2
1
0
1
0
2
0
1
2
0
0
1
0
0
2
1
0
0
0
2
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
2
0
0
0
2
2
1
0
0
0
3
3
0
0
0
2
1
0
2
0
0
0
1
0
0
1
0
2
1
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
2
1
0
0
0
0
2
2
0
0
0
1
2
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
2
1
3
0
1
0
0
0
0
0
2
2
0
2
1
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
1
0
2
0
0
1
2
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
2
0
1
0
2
0
0
0
0
0
2
2
0
1
0
1
0
0
0
2
1
2
0
1
2
2
0
0
0
0
0
0
0
2
0
2
0
0
3
1
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
2
2
2
0
2
0
0
2
2
3
0
1
0
1
0
0
0
1
1
2
0
0
0
0
2
0
0
0
1
0
0
0
1
2
1
0
0
0
0
2
0
2
0
0
0
1
0
0
1
0
2
0
1
0
2
1
1
0
1
0
2
0
2
0
0
1
0
1
1
2
1
1
1
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
1
2
0
1
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
1
1
0
2
0
0
0
2
0
0
2
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
3
1
1
0
0
0
0
1
1
0
0
1
0
0
0
0
2
0
0
0
1
0
0
2
2
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
1
0
0
0
4
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
3
2
0
1
2
0
0
0
1
3
1
1
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
2
0
0
0
3
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
1
0
2
0
0
0
1
0
0
1
2
2
0
2
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
3
1
0
0
0
0
0
2
0
2
0
2
0
0
0
2
3
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
4
2
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
2
2
1
0
2
0
2
2
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
3
0
0
0
0
0
2
0
0
2
0
0
7
1
2
0
0
0
0
0
0
2
2
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
3
0
2
0
0
1
1
0
0
1
0
0
1
1
0
2
0
1
0
2
1
0
1
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
1
0
0
0
0
1
0
0
2
0
0
0
0
1
1
0
1
0
1
2
0
1
0
2
1
0
0
2
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
3
0
2
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
1
0
0
0
0
0
1
2
1
0
1
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
2
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
3
3
0
0
1
0
2
0
0
2
0
0
0
1
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
3
0
0
1
1
0
1
0
0
1
2
0
1
0
0
0
0
3
0
0
1
1
0
0
2
0
0
0
1
0
1
1
1
0
0
0
1
2
3
0
1
0
0
0
0
0
0
0
3
0
2
0
1
0
1
0
0
0
2
0
0
0
0
0
1
0
0
1
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
1
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
4
1
0
0
0
0
0
0
2
0
0
0
2
2
0
1
0
0
0
1
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
1
0
0
2
0
1
0
0
1
1
0
1
0
0
0
2
0
1
0
0
2
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
2
0
0
0
2
2
1
4
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
2
2
0
1
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
1
0
0
1
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
3
0
0
0
1
2
1
1
0
2
2
2
0
0
2
2
2
1
0
0
0
0
1
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
1
1
0
1
0
0
3
1
0
2
1
0
0
0
2
0
0
1
0
0
0
2
0
0
0
2
0
1
2
0
0
1
0
0
0
0
0
0
0
2
0
1
0
1
1
1
1
0
1
0
0
0
0
0
0
0
0
1
2
2
2
0
0
0
0
0
0
1
0
0
1
0
2
0
0
2
0
2
0
0
0
2
0
0
0
1
2
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
1
2
0
1
0
1
0
0
0
0
2
0
0
2
0
0
0
0
4
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
1
1
1
0
0
0
0
1
0
0
1
2
0
2
0
2
0
1
0
0
0
0
3
0
0
0
0
1
1
0
2
2
0
1
0
1
0
1
1
2
0
0
1
2
1
0
1
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
1
1
0
2
1
0
1
0
0
0
2
0
0
1
0
2
2
0
0
0
0
1
1
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
3
1
0
0
0
0
1
0
0
0
0
0
1
0
0
2
2
0
0
0
1
1
3
0
0
1
0
0
2
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
1
0
0
1
2
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
2
0
1
0
0
0
0
0
0
0
4
0
0
0
1
2
2
1
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
1
3
0
0
1
0
0
0
0
0
0
0
0
0
1
3
2
0
0
0
0
2
0
0
1
0
0
1
0
0
4
2
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
1
2
0
2
1
0
0
0
0
0
0
0
2
1
0
3
0
1
1
0
0
0
0
3
0
0
1
0
0
1
2
0
0
0
2
1
1
0
2
1
0
0
1
0
0
0
0
0
0
1
2
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
2
1
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
2
0
1
2
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
2
2
0
0
0
2
0
1
0
0
0
1
2
0
0
1
0
2
5
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
1
2
0
2
0
0
2
1
0
3
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
1
1
0
0
1
0
0
0
2
0
1
0
2
1
0
2
0
2
0
0
0
1
2
0
0
1
0
0
0
0
1
0
0
0
0
0
1
2
1
0
0
1
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
2
0
0
0
1
1
0
0
0
1
4
2
0
0
0
2
0
1
2
1
0
0
0
1
0
2
1
1
5
4
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
2
2
0
0
2
2
2
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
2
1
0
1
1
0
0
0
0
2
0
2
0
0
0
0
0
0
3
0
1
0
1
2
2
0
0
2
2
1
0
1
0
0
0
1
0
0
0
1
0
0
0
1
3
0
1
2
0
1
1
1
0
0
3
0
2
0
0
2
1
0
0
1
1
0
2
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
1
0
2
0
0
2
0
0
2
1
1
2
1
0
0
0
0
0
1
0
0
2
0
0
1
0
0
2
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
3
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
2
0
0
2
0
1
0
2
0
0
0
0
0
0
1
2
1
1
0
0
0
1
3
0
1
1
0
0
0
1
0
0
2
0
0
0
2
0
0
0
1
0
2
0
0
2
2
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
2
0
0
0
0
1
1
0
2
0
0
2
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
3
1
0
0
2
1
0
1
1
0
0
1
0
2
1
0
0
3
0
2
0
0
0
0
2
0
0
0
2
0
1
0
0
1
2
1
1
0
2
1
0
1
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
2
1
1
0
0
2
0
0
0
0
1
0
1
2
1
1
0
0
1
0
0
1
0
0
2
0
0
0
0
1
0
1
0
2
1
0
0
0
0
0
0
3
0
1
1
0
0
0
2
0
1
0
1
0
1
0
1
2
0
0
1
0
1
2
0
0
1
2
2
0
2
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
2
2
0
1
1
0
3
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
2
0
1
0
0
0
1
4
2
1
0
2
0
0
0
0
0
0
1
0
2
0
1
0
0
0
1
0
1
0
3
0
0
2
0
0
0
2
1
0
0
3
0
2
0
0
0
0
0
3
1
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
2
1
1
0
0
0
0
0
0
1
2
0
1
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
1
2
0
0
1
3
1
2
0
1
0
2
0
0
0
0
1
1
0
2
3
0
1
0
0
2
2
1
0
3
1
0
2
2
0
0
1
0
0
2
2
3
1
0
0
2
0
3
0
1
0
0
0
0
2
1
1
2
0
0
0
1
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
3
2
0
0
0
1
0
0
0
0
2
2
0
2
3
1
0
0
0
1
1
0
0
1
2
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
1
1
2
2
1
0
0
0
0
0
2
1
0
0
0
1
1
0
0
0
0
0
2
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
2
0
0
1
0
0
2
0
0
1
2
1
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
3
0
1
1
2
0
1
0
2
0
0
0
0
2
0
1
2
0
0
2
0
0
1
0
2
0
0
0
2
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
3
1
0
0
0
0
1
0
0
1
2
3
0
2
0
2
2
2
1
0
0
1
1
2
0
1
0
0
1
0
0
0
0
2
0
0
0
0
1
0
1
2
0
0
0
0
0
2
1
0
0
0
1
0
1
2
0
0
2
1
2
0
0
0
0
0
0
0
0
1
1
4
0
0
0
2
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
2
0
2
0
0
1
0
0
2
0
0
0
0
0
0
4
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
2
1
0
0
0
0
0
2
1
0
1
2
0
0
2
2
0
1
1
0
0
0
0
0
2
3
2
0
0
1
2
0
0
0
0
2
0
0
0
0
2
1
1
2
0
0
0
0
0
2
0
1
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
1
1
2
0
0
0
1
2
2
0
0
0
0
0
1
1
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
1
2
2
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
2
0
1
2
1
0
1
0
0
2
2
4
1
0
1
2
0
0
0
0
0
0
0
0
2
0
0
2
2
0
2
0
0
0
0
1
0
0
0
3
0
3
0
1
1
0
0
2
1
0
2
0
1
0
0
1
2
0
0
0
0
0
0
0
2
1
1
2
1
0
1
0
2
2
2
0
0
0
1
3
0
0
0
0
0
0
1
0
2
2
1
1
3
7
1
0
1
2
0
0
0
0
0
0
0
0
0
2
1
0
1
0
1
1
0
0
2
0
0
5
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
3
0
2
0
2
4
2
0
2
2
0
0
0
0
0
0
0
2
0
0
1
1
0
0
2
0
0
0
1
0
1
0
0
0
3
0
2
0
0
0
0
1
2
2
2
0
0
2
0
0
0
0
1
0
0
2
2
0
0
2
0
1
0
0
0
1
0
0
0
0
2
0
0
1
2
0
2
0
0
0
0
1
2
0
2
0
1
1
0
0
0
0
2
0
0
0
0
2
2
2
0
0
0
0
0
0
2
0
0
1
0
2
1
2
0
2
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
1
0
0
0
1
1
0
0
0
0
1
0
2
4
0
1
0
1
1
0
0
2
0
0
0
1
0
1
0
0
2
1
2
0
0
0
2
0
0
0
1
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
2
0
2
1
1
0
1
0
0
2
0
2
0
2
0
0
0
2
0
1
0
0
0
0
3
2
0
0
0
2
1
0
0
0
0
1
2
0
1
0
2
2
1
0
0
0
0
1
0
0
0
0
1
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
2
0
2
2
0
0
3
0
0
0
1
2
0
0
0
1
1
1
0
2
0
0
0
1
2
2
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
2
0
0
1
2
2
0
0
0
0
1
0
0
3
2
0
2
2
3
1
1
0
0
2
2
1
0
1
0
0
1
0
1
1
3
0
0
0
0
2
1
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
2
1
1
0
2
0
0
0
1
0
1
0
0
0
2
0
0
1
2
0
0
0
1
1
2
0
0
0
3
1
2
0
1
0
2
1
0
0
0
2
0
2
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
2
3
0
0
2
2
2
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
3
1
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
2
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
3
1
2
1
0
0
2
0
0
0
1
0
0
1
0
0
1
2
0
0
0
0
0
0
1
1
0
0
3
0
0
0
1
2
0
0
0
0
1
2
0
0
0
0
0
0
2
2
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
1
2
0
1
0
0
1
0
2
1
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
2
0
2
3
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
2
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
2
0
1
1
0
0
2
1
0
0
0
1
3
0
2
0
2
0
1
0
0
0
1
0
0
1
1
1
0
2
2
3
0
0
0
2
1
1
0
0
2
0
0
1
2
0
0
1
0
0
2
0
1
0
2
0
1
0
0
0
1
0
1
2
0
0
0
0
0
0
0
3
2
0
2
0
0
0
0
1
0
0
0
0
2
1
0
0
2
1
0
0
0
1
0
0
0
0
2
0
0
0
0
1
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
2
1
0
2
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
2
0
0
2
3
1
0
1
0
0
0
1
0
2
0
0
1
2
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
3
1
0
0
0
3
2
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
1
0
0
0
2
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
3
0
2
1
0
1
0
2
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
2
1
0
0
0
0
2
2
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
3
1
0
0
0
2
0
2
1
2
1
0
0
0
2
0
0
0
2
0
0
0
0
1
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
2
0
0
0
0
3
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
3
0
2
0
0
2
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
1
0
2
1
0
2
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
1
3
0
0
0
0
0
0
0
0
2
0
0
2
1
0
3
0
2
0
2
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
2
3
1
2
2
0
1
1
0
1
0
2
0
0
0
0
2
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
2
0
2
0
0
0
2
1
0
0
2
0
0
0
0
2
0
0
0
2
0
0
2
2
1
0
0
0
2
0
0
2
3
0
0
1
0
0
0
0
3
2
0
0
0
0
1
0
4
0
0
2
0
0
0
0
0
0
0
0
1
1
3
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
1
2
2
0
0
0
0
1
2
0
0
0
0
0
0
1
1
1
0
0
2
0
0
2
2
1
1
0
0
0
0
0
1
0
0
0
2
0
0
0
1
2
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
1
1
0
0
0
1
0
0
1
0
0
3
2
0
2
2
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
3
1
0
0
0
0
0
2
1
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
2
2
0
2
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
2
0
0
0
1
1
0
0
2
0
5
1
0
1
1
1
0
2
0
0
0
4
0
0
0
0
0
2
2
0
1
0
0
0
1
4
0
1
0
2
0
0
0
0
0
0
0
0
0
2
1
2
0
2
0
0
0
0
1
0
0
1
0
0
0
1
0
0
3
0
2
2
0
1
0
7
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
2
0
0
0
2
1
0
2
1
0
2
0
2
0
0
0
0
1
0
2
0
2
0
1
3
1
0
0
0
3
0
2
0
0
1
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
3
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
1
0
0
0
0
2
2
1
0
0
0
0
0
1
0
0
1
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
3
0
0
1
0
0
0
1
0
0
2
0
0
0
1
0
2
0
1
0
0
0
0
1
2
0
0
1
1
0
0
2
2
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
2
0
1
0
0
2
2
2
0
1
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
1
0
0
2
1
0
0
1
0
0
2
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
3
0
2
1
0
0
0
0
0
2
0
2
0
1
1
0
0
1
2
0
0
1
0
0
0
0
0
2
0
0
2
1
0
0
1
3
2
2
0
1
2
2
1
0
4
1
0
0
0
3
1
2
0
0
0
0
0
2
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
1
2
0
0
3
0
3
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
2
1
0
0
1
0
0
2
0
0
1
0
2
1
1
0
0
2
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
1
2
5
0
0
0
0
0
0
2
2
3
0
0
0
1
1
0
0
0
0
0
0
1
2
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
1
0
2
0
2
0
2
1
0
0
2
2
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
2
1
2
0
0
0
1
1
1
2
2
1
0
1
0
2
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
3
0
0
0
0
1
1
1
0
0
0
0
0
0
2
0
0
0
0
2
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
1
1
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
2
0
1
0
1
0
0
0
1
2
0
0
2
0
2
0
0
0
1
1
0
0
0
2
0
1
0
0
2
0
0
0
1
1
3
0
0
1
0
1
0
0
0
0
0
0
0
1
1
2
2
0
0
2
2
1
0
2
0
0
2
0
0
0
0
0
2
2
0
0
1
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
1
1
0
2
0
1
0
1
0
0
3
0
2
0
0
1
1
0
0
0
1
5
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
1
1
0
1
0
0
2
0
0
0
0
0
1
1
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
3
2
2
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
1
0
2
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
1
1
0
0
0
0
1
1
1
1
0
0
1
1
2
1
0
0
0
0
0
0
0
0
2
0
1
3
2
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
1
1
0
0
0
2
2
2
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
1
1
2
1
2
1
1
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
1
2
2
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
1
0
3
2
0
0
2
2
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
1
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
1
1
1
1
1
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
2
2
1
0
0
0
1
0
2
0
1
0
0
2
0
0
1
1
0
0
0
0
2
0
0
1
0
0
2
0
2
0
0
3
0
1
0
0
2
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
2
0
0
1
1
1
2
1
0
0
0
0
0
0
0
4
2
0
2
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
1
2
0
0
0
1
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
1
0
0
2
0
1
0
2
0
0
0
0
3
2
0
0
0
0
2
0
2
3
0
2
1
0
2
0
0
0
2
0
1
0
3
0
0
0
1
2
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
3
2
0
0
0
1
0
0
2
2
0
0
0
3
0
0
2
0
1
3
0
0
1
1
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
1
0
2
3
1
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
4
0
0
2
0
0
0
0
1
0
0
0
2
1
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
2
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
3
0
2
0
0
3
2
0
0
0
2
0
0
1
0
0
0
2
0
0
1
0
0
0
2
0
0
1
2
0
2
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
2
0
0
0
1
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
2
1
3
3
2
2
3
0
0
2
0
0
0
2
0
0
2
0
0
2
2
2
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
2
1
0
0
0
2
1
0
0
0
0
0
2
1
2
1
1
0
0
0
0
1
2
1
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
2
1
0
2
2
0
0
0
2
0
2
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
2
1
0
0
1
2
1
1
1
0
0
0
2
2
0
0
0
0
0
0
0
0
3
0
0
0
6
0
0
0
3
2
3
0
0
0
2
0
1
0
1
9
0
0
1
2
0
4
0
2
0
0
0
0
1
1
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
1
0
2
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
2
0
1
4
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
2
1
0
2
0
0
0
0
0
2
2
0
0
2
1
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
1
2
0
0
0
0
0
2
2
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
1
0
3
0
2
1
0
0
1
0
2
1
0
2
0
2
1
1
0
3
1
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
2
0
0
0
2
0
0
0
1
0
0
0
1
1
0
1
2
0
2
0
0
0
2
0
0
0
0
1
1
2
0
1
1
0
1
0
1
0
1
0
0
0
0
0
0
3
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
1
0
0
0
0
0
0
2
0
2
2
0
0
0
1
0
0
1
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
1
0
1
1
0
0
2
2
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
1
0
2
0
2
0
0
2
0
1
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
1
1
1
0
0
0
0
2
0
2
2
0
0
2
0
0
3
0
0
0
0
0
2
1
0
2
2
4
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
1
2
0
0
0
1
1
0
0
0
3
2
0
0
1
1
0
0
0
2
0
0
1
0
1
1
0
0
0
2
0
0
0
0
2
0
0
0
2
0
1
0
0
0
2
0
2
2
1
0
0
1
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
4
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
2
0
2
3
2
0
2
0
0
0
0
0
0
1
0
3
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
2
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
6
0
0
0
1
1
0
0
0
1
2
1
0
2
2
0
2
1
1
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
3
0
0
2
0
2
0
2
0
0
0
0
0
4
2
0
1
1
0
0
1
2
2
0
0
0
2
2
0
0
0
0
1
5
0
0
0
0
2
1
2
0
0
0
0
0
0
2
1
0
0
0
1
0
1
0
1
0
0
0
0
2
1
1
1
0
2
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
1
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
1
0
0
1
0
0
0
0
2
0
2
0
0
2
1
0
0
0
2
0
1
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
1
0
0
0
2
0
0
1
2
0
1
0
0
0
0
2
0
0
0
2
0
0
0
4
0
0
1
2
0
2
0
0
0
3
0
0
0
0
0
1
2
2
2
1
0
1
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
4
1
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
2
0
0
1
0
1
2
0
0
0
1
0
1
2
0
2
0
3
0
0
0
2
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
1
0
0
1
1
3
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
1
0
1
2
0
0
0
0
0
1
1
2
0
0
1
0
1
0
0
1
0
2
0
0
1
0
0
2
2
1
0
0
2
2
0
0
0
0
0
1
1
0
1
2
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
4
1
0
0
0
0
0
0
1
2
0
0
2
0
0
0
1
0
2
0
2
2
2
0
0
0
0
0
2
1
0
0
0
1
0
0
0
1
1
0
2
1
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
2
3
0
2
0
0
0
1
1
2
1
2
0
0
0
2
1
0
0
0
0
0
1
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
2
0
5
0
0
0
0
0
0
1
0
0
0
1
0
2
0
2
1
3
1
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
2
0
2
2
0
0
0
0
1
0
0
0
2
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
2
0
0
1
0
0
0
0
3
0
0
0
0
0
0
1
0
2
0
1
0
0
0
1
2
2
0
1
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
2
0
0
2
0
0
0
0
2
1
0
0
2
0
1
0
0
1
0
0
0
1
0
0
2
2
0
0
2
0
0
2
2
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
2
0
0
6
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
1
0
2
0
0
0
0
0
2
1
0
1
2
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
2
0
3
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
3
1
1
0
0
0
0
0
2
0
0
1
1
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
2
0
1
1
2
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
1
2
2
0
0
0
1
0
3
0
0
1
0
2
2
0
0
1
1
0
1
1
2
0
0
2
0
2
0
2
2
1
0
0
0
0
0
0
1
1
2
2
0
0
0
2
2
1
2
0
1
1
0
0
1
0
0
0
0
1
2
0
2
1
0
3
0
4
1
1
0
0
0
0
0
1
1
1
0
0
0
1
0
2
2
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
2
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
3
1
0
0
0
0
1
1
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
1
0
2
2
0
2
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
2
2
0
1
0
0
0
0
0
0
0
1
1
0
3
0
0
2
1
1
2
0
0
0
2
0
2
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
1
0
0
0
0
2
0
1
2
0
1
0
1
0
2
2
0
0
0
0
2
0
0
0
2
1
0
0
1
2
0
0
2
2
0
0
0
1
0
0
1
0
0
1
2
0
3
0
1
0
2
2
2
0
2
0
0
0
2
2
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
1
2
3
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
1
2
3
1
0
0
0
0
0
1
2
1
0
0
0
1
0
4
1
0
0
1
0
0
0
0
2
2
2
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
6
3
2
0
0
2
0
3
1
1
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
1
0
1
2
0
1
0
0
1
0
0
0
0
2
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
1
2
1
0
2
0
2
2
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
1
2
0
0
2
1
0
0
3
1
1
0
0
2
1
2
0
1
0
2
1
0
0
2
0
1
0
0
0
4
0
1
0
2
2
2
0
0
0
1
0
0
3
2
1
0
0
0
3
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
2
0
4
0
0
0
1
0
0
2
1
0
0
3
0
0
2
3
0
1
0
0
0
0
0
2
2
0
0
2
1
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
3
0
0
1
0
0
2
0
0
2
0
1
2
0
1
0
2
0
0
2
0
0
1
0
0
0
0
2
0
1
3
0
0
1
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
2
0
1
1
0
2
1
1
0
1
0
1
1
2
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
2
1
1
2
0
0
0
1
0
0
3
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
3
0
1
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
1
1
0
0
0
0
0
0
2
0
2
1
1
0
0
2
0
0
1
0
0
2
0
1
1
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
3
1
0
0
0
3
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
2
0
0
2
2
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
1
0
1
0
2
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
1
2
2
0
0
1
0
0
1
0
1
0
1
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
1
2
2
0
2
0
0
1
0
0
2
1
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
1
0
1
4
0
1
1
0
1
0
2
0
2
1
0
2
1
2
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
2
0
3
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
4
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
1
0
2
0
1
1
0
0
0
0
0
0
1
0
0
1
1
0
2
2
1
1
0
2
1
0
2
0
1
0
1
0
0
1
0
3
2
0
1
2
0
0
0
0
0
0
1
2
0
1
0
2
1
2
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
1
0
0
0
2
0
2
0
2
0
0
0
0
1
1
0
0
1
1
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
2
1
0
2
2
0
0
0
2
0
0
1
0
2
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
3
3
0
3
1
0
0
0
2
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
1
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
2
0
5
1
0
0
0
0
2
0
1
0
0
2
1
0
0
2
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
1
0
0
2
1
0
0
0
0
1
1
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
1
2
0
0
0
2
0
2
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
3
0
0
0
0
2
0
0
0
2
0
2
0
0
0
1
0
3
2
0
0
0
1
1
2
1
2
0
1
2
1
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
2
2
0
1
0
0
0
0
0
0
0
6
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
2
0
0
0
0
3
0
1
1
1
0
2
0
0
0
0
0
2
1
2
2
0
0
0
0
3
0
1
2
0
0
1
0
0
0
0
2
1
0
0
0
1
0
0
1
0
0
2
2
0
2
2
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
2
0
0
1
0
1
0
1
1
0
2
0
1
3
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
2
0
2
0
1
0
0
1
1
3
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
2
0
1
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
2
0
1
0
0
1
0
0
0
2
0
2
0
5
0
0
1
1
0
0
0
1
1
1
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
1
0
2
1
0
0
0
0
0
0
1
0
1
0
0
0
2
0
3
1
1
0
1
0
0
3
1
0
0
0
4
0
0
2
0
0
1
0
2
0
0
3
0
0
2
2
1
0
2
0
0
2
0
0
0
0
2
0
0
1
0
0
1
2
0
0
2
0
1
2
2
1
4
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
3
0
0
2
3
3
0
0
0
0
0
0
4
0
0
0
2
0
1
0
0
0
0
0
2
0
1
0
2
0
0
0
0
2
0
0
1
0
0
2
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
2
0
2
0
0
2
0
0
3
0
0
0
3
1
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
2
0
1
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
2
1
2
0
0
0
1
0
0
2
0
0
0
2
0
1
5
1
1
0
2
1
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
5
1
2
0
0
5
0
0
0
2
1
1
0
1
1
1
2
0
0
0
0
0
3
0
0
0
0
0
0
0
2
1
0
5
2
0
0
0
2
2
0
0
2
1
0
0
1
1
0
0
0
1
2
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
2
0
0
0
0
0
2
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
2
0
2
4
0
1
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
2
1
3
0
0
1
0
1
0
1
0
1
0
0
0
1
0
0
0
2
2
1
0
0
0
1
1
0
0
1
0
1
2
2
1
2
4
0
0
0
1
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
2
2
1
0
0
1
0
0
0
1
1
0
0
2
0
0
0
1
0
0
2
1
2
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
2
0
1
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
2
0
1
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
2
0
0
0
0
0
1
0
2
2
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
1
1
1
0
0
1
0
1
0
0
0
0
0
2
2
0
2
1
0
0
0
0
2
0
2
1
1
0
3
2
0
0
1
0
2
0
1
0
0
0
0
0
1
1
0
0
1
2
1
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
1
0
2
1
0
2
0
0
0
0
3
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
1
1
2
3
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
2
0
1
2
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
1
0
2
3
0
0
2
0
0
0
0
2
0
0
0
1
0
0
1
2
0
0
0
0
2
0
0
0
0
0
1
0
0
2
2
0
2
0
0
0
2
0
3
1
0
0
3
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
2
3
1
0
0
0
0
1
0
1
0
0
1
0
2
0
2
0
0
0
2
2
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
1
0
1
2
1
0
2
1
2
0
0
0
0
0
0
2
1
0
1
0
0
2
1
0
0
0
0
1
0
0
3
0
1
0
0
0
0
0
0
0
0
0
2
1
2
0
1
1
0
0
0
0
2
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
2
1
1
0
1
0
0
2
1
1
1
0
2
0
0
2
0
0
0
0
1
0
0
1
2
2
0
0
2
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
2
0
2
2
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
1
7
2
3
4
0
4
0
1
0
2
1
2
1
0
1
0
2
0
0
0
0
2
0
0
1
1
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
1
0
0
0
1
0
0
2
0
0
0
1
0
1
0
1
0
2
0
2
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
1
1
4
2
0
2
0
0
0
0
2
0
0
0
2
0
0
1
3
0
0
0
0
0
0
2
0
1
1
0
1
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
2
2
0
1
1
0
1
0
0
0
1
2
1
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
2
0
1
0
0
0
0
0
1
0
1
3
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
1
2
0
0
2
0
3
0
2
1
0
0
0
0
2
0
0
1
0
1
0
0
0
0
2
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
2
0
2
1
0
1
0
0
1
2
0
2
0
2
1
0
0
1
0
0
0
2
0
1
2
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
1
0
1
0
0
0
0
0
1
2
0
0
1
0
0
0
2
0
1
2
0
2
3
0
1
0
2
0
6
0
0
0
0
0
0
1
1
1
2
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
2
2
0
2
2
0
1
0
0
2
0
0
0
0
0
1
0
2
0
3
1
0
0
2
0
0
0
1
0
2
2
0
0
0
1
2
2
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
1
0
1
2
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
2
0
3
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
2
0
1
0
2
2
0
0
0
2
0
0
0
2
0
0
1
1
1
0
0
0
0
2
0
0
1
1
0
2
0
0
1
0
0
0
0
2
0
2
0
2
0
2
2
2
2
0
1
2
1
0
0
0
0
0
2
0
1
0
0
0
0
1
2
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
2
1
2
0
2
0
0
1
0
0
0
0
0
1
0
0
2
0
0
2
0
2
0
0
2
0
0
1
0
0
1
0
2
0
0
2
2
0
0
0
1
1
1
1
0
0
0
0
0
0
0
1
0
4
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
1
0
0
0
0
1
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
2
1
0
1
1
0
3
0
1
1
1
0
0
0
0
1
0
0
0
2
2
0
0
1
0
2
3
0
0
0
1
0
0
2
0
0
0
2
2
0
0
2
0
0
2
0
1
4
0
0
2
0
2
0
1
0
0
0
0
1
0
0
2
0
0
0
1
0
2
0
0
0
2
0
2
2
1
0
0
2
0
0
2
0
0
4
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
2
2
0
0
0
2
1
0
1
1
0
2
3
0
0
0
3
0
0
0
0
0
1
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
1
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
1
2
0
3
2
0
0
0
0
3
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
2
2
0
0
0
2
1
0
0
0
0
0
2
0
1
2
0
0
0
0
0
5
0
1
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
1
0
0
0
0
0
1
2
0
1
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
3
1
2
1
0
0
0
0
0
0
0
0
3
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
2
2
1
0
0
0
0
2
1
0
0
0
1
0
1
0
0
2
1
0
0
2
0
0
0
3
1
1
0
0
2
0
0
0
0
0
0
1
1
1
1
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
1
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
1
1
0
0
0
1
1
0
0
0
2
0
2
0
1
0
0
0
1
0
1
0
0
0
3
0
2
1
0
0
0
2
2
0
2
0
0
2
0
3
0
0
0
0
0
0
0
4
2
2
0
0
1
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
3
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
2
1
0
2
1
2
0
0
0
0
2
0
1
0
0
1
0
0
0
1
0
0
1
0
0
2
0
0
0
2
0
2
0
1
0
0
0
0
0
2
2
1
0
0
0
0
0
1
2
1
1
0
1
0
1
0
1
1
0
0
0
0
2
1
0
1
0
2
0
1
0
0
0
1
1
1
1
0
4
0
3
1
0
0
2
0
0
0
2
0
0
1
1
2
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
2
2
3
0
0
0
2
2
0
0
0
0
4
0
2
0
0
3
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
1
0
0
0
2
2
0
1
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
2
0
1
0
0
2
1
0
0
1
0
0
2
0
0
0
0
2
0
0
2
0
0
3
0
0
1
0
0
0
0
0
0
1
1
0
1
0
2
0
0
2
0
2
0
2
0
0
2
0
0
0
2
0
1
0
1
0
1
2
0
0
2
0
2
0
1
0
0
0
0
0
1
2
2
1
1
0
0
0
0
0
0
2
0
0
0
1
0
3
0
0
0
0
0
0
2
0
0
1
2
1
0
0
1
1
0
2
0
2
1
0
0
0
0
0
0
0
2
0
2
0
2
0
1
0
0
0
0
0
4
1
0
0
0
0
2
1
0
0
0
0
1
2
0
2
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
2
0
1
0
0
2
2
1
0
1
1
2
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
1
2
0
0
0
1
1
2
0
0
1
0
0
0
1
2
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
1
1
0
0
2
0
0
0
2
0
0
1
1
0
0
0
0
1
0
0
0
0
2
2
0
0
0
2
0
0
0
1
1
4
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
2
2
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
2
0
0
1
0
0
0
1
2
0
0
0
0
0
2
1
0
1
1
2
1
0
0
0
1
1
3
0
0
2
1
1
1
0
0
1
0
0
0
0
2
0
0
2
0
0
2
1
2
0
0
0
0
0
0
2
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
3
0
0
0
4
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
2
0
0
0
1
0
0
0
1
1
0
1
4
1
0
0
2
0
0
0
1
0
1
1
0
0
1
1
0
0
0
2
0
0
1
1
0
0
2
3
0
0
1
0
2
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
1
0
2
0
1
0
1
0
1
2
1
2
0
1
0
0
0
1
0
0
0
1
4
2
0
1
2
0
2
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
3
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
1
0
0
0
1
0
0
2
0
2
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
3
1
0
0
2
2
2
0
1
0
0
0
1
0
0
0
0
1
0
6
1
0
2
0
0
2
0
0
2
0
2
1
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
2
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
2
2
0
0
2
0
1
1
0
0
2
1
2
0
0
2
0
3
0
0
0
1
0
3
0
0
1
1
0
0
1
0
3
0
0
1
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
1
0
0
1
2
0
0
0
0
0
0
2
2
1
2
0
1
0
0
1
0
0
3
0
0
2
1
1
0
0
0
0
0
2
1
0
0
0
1
2
1
0
0
0
0
1
0
2
2
2
0
1
1
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
1
0
2
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
1
0
1
2
0
0
0
0
0
2
2
1
0
3
3
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
2
2
0
0
3
2
0
0
1
0
1
0
0
2
0
0
0
0
1
1
2
0
4
0
0
1
1
0
0
0
0
2
1
2
8
1
0
0
2
0
0
1
3
1
3
0
0
1
1
0
2
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
2
0
0
2
0
2
0
0
2
1
1
2
0
0
0
0
0
0
1
1
0
0
1
2
2
2
2
0
0
2
0
0
2
0
2
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
2
1
0
2
0
1
0
0
1
2
1
2
1
0
0
1
1
2
0
1
2
0
2
0
1
0
2
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
1
1
2
0
1
1
2
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
1
1
2
0
4
0
0
0
1
1
0
3
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
2
1
0
1
1
0
0
0
0
2
2
2
1
0
0
1
2
0
3
0
0
2
2
0
0
0
0
1
2
0
1
2
0
0
0
1
1
0
1
2
0
0
2
0
0
0
0
1
0
0
1
1
2
0
1
2
0
0
0
2
4
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
3
2
2
2
0
1
0
0
0
2
0
0
2
1
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
2
0
2
0
0
0
2
0
0
1
2
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
1
0
0
1
0
0
2
1
0
2
0
0
0
0
0
0
2
0
1
2
0
0
2
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
1
1
0
2
0
0
0
1
0
1
0
0
1
0
2
2
0
0
1
2
0
2
0
0
0
2
2
1
1
0
0
2
0
0
0
0
1
2
0
2
1
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
2
0
1
1
0
1
0
0
2
1
1
0
0
2
0
0
0
1
2
0
2
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
3
0
0
0
0
3
2
0
1
0
1
0
0
0
0
0
1
2
0
2
2
0
2
1
0
1
0
0
0
2
0
0
1
0
0
4
0
2
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
1
0
0
2
2
0
0
0
1
1
0
1
2
0
2
2
2
0
0
1
0
0
1
0
1
1
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
2
0
0
1
0
1
0
0
0
0
0
0
0
0
2
2
0
0
1
0
2
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
5
2
2
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
1
2
0
0
2
2
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
3
0
0
0
2
0
0
0
3
0
0
0
1
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
2
0
0
1
0
0
1
0
0
2
0
0
0
1
0
0
2
0
0
0
2
0
0
2
0
0
2
0
1
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
1
0
2
1
0
0
0
0
2
0
1
1
0
0
1
0
1
0
1
0
1
0
0
0
1
1
0
2
2
0
2
2
0
0
0
1
1
0
0
0
0
0
0
2
0
1
1
1
0
0
1
0
0
0
0
0
1
3
0
0
0
0
1
1
2
0
1
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
1
2
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
2
0
2
0
0
0
1
0
0
0
1
0
2
2
0
0
0
0
0
1
1
0
1
2
0
0
0
1
0
0
0
1
0
0
0
2
2
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
2
1
3
0
2
0
0
0
0
0
1
2
1
0
0
0
0
1
3
2
0
0
0
0
0
0
0
1
0
1
1
2
0
0
0
0
0
2
1
0
1
0
0
1
0
0
1
0
0
1
1
1
1
0
0
1
0
0
2
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
5
0
2
0
0
0
0
0
1
0
0
0
3
2
0
0
0
0
2
0
1
0
3
0
1
1
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
1
1
1
0
2
1
0
1
0
0
0
0
0
0
0
0
1
0
2
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
2
0
1
0
1
0
1
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
2
0
2
0
0
0
1
1
1
2
1
0
1
0
1
1
2
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
2
0
0
0
0
3
1
0
0
0
0
0
2
0
1
1
0
0
1
0
0
2
0
1
0
2
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
3
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
2
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
1
0
1
0
0
0
0
1
0
0
0
2
2
1
1
0
1
0
2
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
2
0
0
0
4
2
0
0
0
0
0
1
2
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
2
0
0
0
0
0
2
0
0
1
2
1
1
2
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
1
0
1
0
0
2
0
1
1
0
0
2
0
0
2
2
1
0
0
0
0
0
0
0
0
2
1
0
0
3
0
0
2
0
0
2
0
1
1
1
1
0
2
0
0
2
1
0
0
1
0
2
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
1
0
2
0
1
0
0
0
1
0
0
0
1
0
0
1
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
1
1
0
0
1
1
0
2
0
0
0
2
0
0
0
0
0
2
0
1
1
0
2
0
0
0
0
2
0
0
2
1
0
2
0
2
0
2
2
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
1
0
0
2
1
0
0
2
0
0
2
0
1
0
2
0
1
1
2
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
2
0
2
2
0
0
0
0
1
2
1
0
0
2
4
2
2
0
0
0
0
0
0
0
1
0
1
0
2
0
2
0
0
1
2
2
0
0
0
0
0
5
0
2
1
0
0
0
0
0
0
2
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
1
0
1
0
0
2
0
0
0
0
0
1
2
2
0
0
1
2
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
2
0
0
1
1
0
1
0
0
0
0
5
1
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
1
0
1
1
1
1
0
2
4
1
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
3
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
1
0
0
0
2
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
1
3
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
2
2
1
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
1
2
3
0
1
0
0
2
1
0
0
0
0
1
1
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
2
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
2
5
0
2
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
1
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
1
2
0
2
0
0
0
1
0
7
0
2
0
2
0
2
0
4
0
0
0
0
0
0
0
1
2
0
2
3
0
0
0
0
0
1
0
0
0
2
0
0
2
0
1
0
1
0
0
0
0
1
0
0
0
2
1
1
1
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
1
1
2
0
0
2
0
0
0
0
0
1
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
1
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
1
1
0
0
1
2
2
1
0
0
1
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
1
0
2
2
0
0
0
1
2
0
0
1
0
0
0
3
0
2
1
0
0
0
1
0
0
0
0
1
1
1
0
2
1
2
0
0
0
0
1
0
1
3
0
0
0
0
0
1
0
0
2
0
1
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
1
1
0
0
0
0
0
1
0
1
0
2
2
1
0
1
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
3
0
0
0
0
1
0
2
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
1
2
0
2
0
1
0
0
1
0
0
0
0
2
0
2
0
0
9
0
0
1
0
2
1
0
0
0
2
0
2
0
1
1
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
2
2
0
0
0
0
1
0
0
2
2
0
2
0
1
0
0
2
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
2
0
0
2
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
2
0
0
1
0
0
2
0
0
0
2
0
0
0
1
2
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
2
1
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
5
0
0
0
0
3
2
0
1
0
0
0
1
2
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
2
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
2
1
0
0
1
2
0
0
2
0
0
1
0
0
2
2
0
2
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
1
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
2
2
3
0
0
0
2
1
0
0
0
1
0
2
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
2
2
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
1
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
2
1
0
1
0
0
0
2
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
1
1
3
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
2
0
0
0
2
1
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
7
0
0
0
1
0
0
3
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
2
0
0
2
1
1
0
0
0
0
0
0
3
1
0
1
1
0
2
0
0
0
0
2
1
1
2
0
0
2
0
0
1
3
0
0
0
0
0
0
0
0
0
0
6
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
2
0
2
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
2
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
1
1
2
0
0
2
0
0
1
0
0
0
2
1
0
0
0
2
1
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
4
0
0
2
1
0
1
0
2
0
0
0
0
0
1
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
3
0
0
0
2
0
0
0
0
2
0
0
0
1
1
2
0
0
0
0
0
2
0
2
0
0
0
1
1
0
0
1
0
2
3
0
2
1
2
1
0
1
0
2
0
0
2
0
2
0
3
0
1
0
0
2
2
2
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
4
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
1
0
2
0
0
2
4
0
0
2
0
0
2
2
0
0
1
0
0
2
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
3
1
1
0
0
0
0
0
0
2
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
2
0
0
0
1
1
0
0
1
0
0
2
1
0
0
0
0
0
2
1
2
0
2
0
2
1
3
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
2
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
2
0
1
2
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
1
1
1
0
1
1
1
1
2
0
3
2
0
1
2
0
0
0
1
0
2
1
0
0
0
0
0
0
1
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
1
2
0
1
0
0
0
0
0
0
1
0
2
0
0
1
0
1
1
0
2
2
0
0
0
0
2
0
0
0
0
2
0
1
1
1
2
2
2
0
0
0
1
0
1
0
0
2
0
0
2
0
0
0
0
1
1
0
0
2
0
0
0
0
1
0
0
2
0
0
1
2
2
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
3
1
2
0
2
0
0
1
2
0
1
0
0
2
0
0
0
1
2
2
0
0
1
2
0
0
0
0
0
1
2
6
2
2
0
0
0
2
0
2
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
1
1
0
0
2
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
2
1
1
0
0
0
0
1
1
0
0
0
2
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
2
0
0
2
0
1
2
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
2
1
0
2
0
0
0
0
2
0
0
1
0
0
1
2
0
0
2
0
2
0
0
0
0
0
0
2
2
0
0
2
0
0
2
0
0
2
0
1
0
0
1
0
0
0
3
1
2
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
2
0
0
0
2
0
0
0
2
2
0
1
1
0
0
1
0
0
0
1
2
2
0
1
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
2
2
0
0
0
0
2
2
2
2
0
0
0
2
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
1
0
1
0
2
0
1
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
7
0
1
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
1
0
1
0
1
2
0
0
0
1
0
2
0
0
0
0
2
0
2
2
0
2
0
1
0
0
1
1
0
0
1
0
0
3
1
2
0
0
0
0
2
0
0
1
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
1
1
2
0
0
0
2
1
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
1
0
0
2
1
0
0
2
0
0
0
0
2
1
2
0
0
2
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
2
1
0
0
0
1
2
0
0
1
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
3
1
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
1
2
2
0
2
0
0
0
0
0
2
0
2
1
2
0
2
1
0
0
0
0
0
1
0
0
2
1
2
0
2
0
1
1
0
1
1
0
1
4
0
2
0
0
0
2
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
2
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
3
1
4
4
0
1
0
0
0
0
0
0
2
0
6
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
1
1
2
2
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
1
3
0
0
0
0
0
0
5
0
0
0
0
0
2
0
0
3
0
1
0
0
0
0
0
0
0
0
2
0
2
1
0
2
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
5
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
2
0
1
1
2
1
1
0
0
0
2
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
2
0
0
0
1
2
0
4
0
0
2
0
2
0
1
0
0
1
0
0
2
2
2
0
0
2
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
1
1
1
0
0
1
2
1
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
2
0
1
1
0
0
0
1
0
0
0
2
2
0
2
1
0
1
1
0
0
2
1
1
0
1
2
0
0
3
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
1
0
2
1
0
0
0
2
0
0
0
0
1
0
0
2
0
1
2
0
0
2
0
0
0
1
0
0
2
0
0
2
2
0
2
1
4
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
3
0
2
2
0
0
0
0
0
0
0
3
0
1
0
0
0
1
0
2
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
1
2
0
3
1
0
0
2
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
2
0
2
5
1
1
0
2
2
1
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
2
0
2
0
0
0
2
3
3
1
0
0
2
0
1
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
2
2
0
0
0
0
2
1
0
3
0
1
0
0
0
1
2
0
0
0
0
1
1
0
0
0
0
1
2
1
0
0
1
0
0
0
1
0
0
0
3
0
2
1
1
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
3
0
0
1
0
1
0
2
2
2
0
2
4
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
2
0
1
2
0
0
1
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
2
3
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
3
0
0
0
1
0
0
2
1
2
0
2
0
1
2
2
0
0
2
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
2
3
0
0
0
2
0
0
0
0
2
0
2
0
0
0
3
0
0
0
0
0
0
1
2
1
0
0
0
2
0
2
0
3
1
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
2
1
0
0
0
1
0
0
0
0
3
0
0
0
0
0
2
0
0
0
7
0
1
0
3
4
0
5
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
2
0
0
0
5
0
2
0
2
6
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
2
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
3
2
0
0
1
0
11
0
0
1
1
0
0
0
2
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
3
0
1
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
2
0
0
2
0
0
3
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
1
1
0
0
3
1
0
0
1
0
0
0
0
1
0
3
2
0
0
1
2
0
1
0
0
0
1
1
0
0
0
2
0
2
0
0
4
0
0
0
2
2
0
2
0
0
2
0
0
0
1
0
1
2
0
4
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
1
1
0
0
1
0
0
1
0
0
0
2
0
0
2
0
0
0
2
1
2
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
2
1
0
0
2
0
0
1
2
0
1
3
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
1
0
5
3
0
0
0
1
0
0
0
2
0
1
0
1
0
1
2
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
1
0
0
0
0
2
1
1
0
2
0
4
0
2
1
0
2
0
0
2
0
1
0
0
0
2
4
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
2
1
0
1
0
0
2
0
2
1
0
0
0
0
2
1
0
0
0
2
0
1
1
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
1
0
0
2
0
0
0
0
2
0
1
0
0
1
2
0
0
0
2
2
0
0
0
2
0
0
5
1
0
0
0
2
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
2
2
0
2
0
2
0
0
0
1
1
2
0
1
2
4
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
1
0
2
1
2
0
0
0
0
0
0
1
2
0
2
0
0
1
0
2
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
1
2
0
0
0
1
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
2
2
0
0
3
0
0
2
0
2
0
1
0
2
0
2
0
0
0
0
0
2
0
0
0
0
1
3
2
2
1
2
0
2
0
2
0
0
2
4
0
7
0
1
0
0
0
0
4
1
1
0
0
0
2
1
0
0
0
0
3
2
0
2
2
0
0
0
0
0
0
1
0
2
0
0
2
1
0
1
0
0
0
2
1
0
0
0
2
0
0
0
1
2
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
3
0
0
0
0
0
0
2
0
0
8
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
1
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
2
0
0
0
0
3
2
0
1
0
1
2
0
2
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
3
0
1
0
1
0
1
0
2
2
3
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
5
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
1
1
0
0
1
1
0
2
0
1
0
0
1
0
0
1
1
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
2
0
0
0
2
3
2
0
0
0
2
0
0
0
1
0
1
2
1
0
1
3
0
0
2
0
0
2
0
1
3
0
0
2
0
1
1
0
0
2
0
2
1
1
1
0
3
0
0
0
0
0
0
1
1
0
0
1
0
2
1
0
0
1
1
0
0
0
3
0
0
2
0
2
0
0
0
0
0
3
0
0
2
0
0
1
0
0
0
1
0
2
1
0
0
1
4
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
4
1
1
0
0
0
0
0
0
0
1
0
1
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
1
0
1
0
0
2
0
1
0
1
4
0
0
1
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
2
0
1
0
0
1
0
3
1
1
0
0
0
1
2
1
0
2
1
0
1
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
2
1
0
1
1
0
0
1
0
0
0
0
2
0
0
0
2
3
0
1
0
0
1
0
0
0
1
1
0
1
0
1
1
0
0
2
0
0
0
1
0
0
1
0
0
0
0
1
0
2
0
2
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
2
2
2
0
0
0
1
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
1
6
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
2
0
1
0
0
0
0
2
0
0
0
0
0
1
2
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
2
2
2
1
0
1
1
1
0
0
2
0
0
2
2
0
0
0
0
2
0
0
0
0
2
0
0
0
1
1
1
0
0
0
0
0
2
0
0
1
5
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
5
0
0
1
0
0
1
2
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
3
0
0
0
2
0
2
0
0
3
0
1
0
0
0
2
0
0
2
1
0
0
0
0
0
2
0
2
2
1
0
0
0
0
0
1
3
0
1
0
2
0
0
2
1
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
1
0
1
0
0
0
0
1
0
1
0
0
2
2
0
2
1
1
0
0
1
0
0
0
1
1
1
1
0
3
0
0
2
0
0
0
0
0
0
2
0
6
0
0
0
2
0
1
0
0
1
2
1
1
0
0
0
2
0
0
2
0
1
0
0
0
0
0
1
0
0
2
0
0
1
0
2
0
0
2
0
0
5
0
0
0
2
0
2
0
0
0
0
0
1
2
1
2
1
0
2
0
0
1
0
2
0
1
2
2
0
2
0
1
1
0
0
3
0
0
1
0
0
0
0
0
1
0
2
0
0
1
0
0
0
1
1
0
0
0
1
0
1
0
0
1
0
0
1
1
0
2
2
1
0
0
3
0
2
1
0
0
0
0
0
0
3
0
0
0
2
0
2
2
2
2
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
2
0
0
0
2
2
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
2
2
1
1
1
0
0
0
0
0
2
2
0
1
0
0
0
1
0
0
2
1
0
0
0
3
2
0
0
0
3
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
2
0
1
0
0
0
0
0
0
10
0
0
0
0
2
0
1
1
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
2
4
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
1
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
1
5
0
0
0
0
0
1
1
0
2
1
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
1
2
2
1
0
0
0
0
0
0
0
1
0
0
2
0
2
0
4
0
0
0
0
0
0
1
0
2
0
1
0
2
0
1
2
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
3
0
0
0
3
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
1
0
0
2
3
0
0
1
0
0
0
1
4
0
0
1
0
0
2
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
2
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
2
0
0
0
0
2
0
0
2
1
0
2
0
1
0
0
2
2
0
2
1
0
1
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
1
0
3
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
1
0
2
1
2
0
3
1
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
2
2
0
0
0
2
0
1
0
0
0
1
0
2
0
0
0
0
0
0
1
1
1
2
0
0
0
0
2
0
2
0
0
1
0
0
2
0
0
0
0
0
1
3
0
0
0
0
2
2
1
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
3
0
0
2
2
0
0
0
0
0
1
0
1
0
0
1
0
2
0
0
0
1
0
1
2
0
0
2
1
0
0
1
0
0
2
0
0
2
0
3
0
1
1
1
0
0
2
0
0
0
1
0
1
2
0
1
2
0
1
2
0
0
1
0
2
0
0
2
1
0
0
0
0
0
7
0
0
0
1
0
0
0
2
0
1
0
1
0
0
0
0
1
0
2
0
2
0
1
0
2
0
0
2
0
0
1
0
2
2
1
0
1
2
0
1
0
0
0
0
1
0
0
1
0
2
2
2
0
0
0
0
0
0
0
0
0
1
0
4
0
2
0
0
1
0
0
0
0
1
0
1
2
0
0
4
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
1
2
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
1
0
0
0
0
2
2
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
2
2
1
2
2
0
0
0
0
1
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
1
0
0
0
0
0
4
0
1
2
1
1
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
1
0
4
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
1
0
0
1
0
0
0
1
1
0
0
0
2
0
1
0
0
2
2
0
0
0
0
0
0
0
1
2
0
0
3
0
2
2
2
2
2
0
2
0
0
0
1
1
1
1
2
0
0
0
0
2
2
1
0
2
0
1
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
2
0
0
0
0
1
0
2
0
1
0
0
2
0
1
1
0
2
0
2
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
5
0
1
2
1
2
2
0
0
0
0
0
3
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
2
2
0
2
0
1
0
2
0
0
1
0
0
2
0
0
1
0
0
1
0
0
0
2
0
2
0
2
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
2
0
1
0
3
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
2
0
0
2
0
3
0
2
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
6
2
0
1
0
0
0
0
0
1
1
0
0
0
1
0
2
0
1
0
2
0
2
0
0
1
1
0
0
2
0
1
0
0
0
0
0
0
0
1
1
0
3
0
0
0
0
2
0
2
2
0
0
1
0
1
0
1
0
2
2
0
1
2
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
1
0
1
1
0
0
0
0
0
1
0
2
0
2
0
2
1
2
1
0
0
2
6
1
2
0
3
0
0
1
0
0
0
1
0
1
1
1
1
2
0
0
1
0
0
0
1
0
0
0
3
2
2
0
2
0
0
0
2
1
0
0
0
1
0
2
0
0
1
2
2
0
0
0
0
2
0
2
2
0
1
1
0
0
0
0
1
2
0
0
0
0
0
2
0
1
2
0
1
0
0
0
0
0
0
0
1
2
2
0
0
0
0
4
0
1
0
0
0
4
0
0
1
0
1
1
3
2
0
0
0
3
0
0
0
1
2
0
0
0
0
0
1
1
2
2
0
2
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
2
0
0
0
0
6
0
1
1
0
0
1
0
2
1
0
0
0
0
0
0
1
0
0
0
1
0
1
2
0
2
0
1
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
2
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
2
0
1
0
0
0
0
0
2
1
2
0
0
2
0
0
0
2
0
0
0
1
0
2
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
6
2
0
0
1
1
0
0
2
0
0
0
1
1
0
2
0
0
0
0
2
0
0
0
1
0
4
2
1
2
1
1
0
0
0
1
0
0
0
0
0
2
2
0
1
1
2
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
1
2
0
0
1
3
0
0
0
0
2
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
1
1
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
2
0
1
0
0
1
0
1
1
0
5
0
0
0
0
0
0
0
2
2
1
0
0
0
2
0
0
1
0
0
1
2
1
0
2
0
0
0
0
0
1
0
0
2
2
0
4
0
2
0
0
0
1
0
0
0
2
1
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
2
0
2
1
0
0
2
2
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
1
2
1
0
1
0
0
1
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
1
2
1
0
1
0
1
0
0
0
0
2
2
0
0
0
0
0
0
2
2
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
1
1
0
0
2
2
1
3
0
0
0
0
1
1
0
1
2
2
0
1
0
0
2
0
0
0
0
2
1
1
0
0
0
0
0
0
1
0
0
1
2
2
0
2
0
1
2
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
2
3
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
1
0
0
0
2
0
0
0
1
2
1
0
0
2
0
1
0
1
0
2
0
0
1
1
2
0
0
1
0
0
1
0
0
1
0
2
0
0
2
0
1
0
0
0
0
0
3
0
0
0
0
2
1
0
0
0
0
0
2
0
0
2
1
0
0
0
0
1
0
1
0
0
0
0
0
1
1
2
1
0
2
1
2
0
0
1
3
0
0
2
0
1
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
1
0
0
2
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
2
1
0
0
1
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
3
1
0
1
0
0
1
2
2
0
0
0
2
0
2
0
1
0
0
0
0
0
0
2
0
1
1
2
0
0
0
0
0
0
0
2
0
4
0
1
2
1
0
0
0
0
2
0
0
0
1
0
2
2
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
1
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
3
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
0
0
2
2
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
1
0
1
0
0
0
0
1
3
0
1
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
2
2
2
0
0
0
1
0
0
0
0
1
0
0
0
3
0
10
0
2
0
0
0
0
0
2
2
0
3
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
2
0
0
0
2
0
0
1
0
0
0
3
0
2
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
3
2
2
0
0
2
0
0
0
2
0
0
2
1
1
1
0
4
6
2
3
2
2
0
0
0
2
0
0
2
0
2
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
1
0
1
0
0
0
3
2
0
0
1
0
0
0
0
0
2
2
0
0
0
1
0
0
0
2
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
2
1
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
2
2
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
2
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
1
2
0
0
1
0
0
0
1
0
0
0
0
2
2
0
1
0
1
2
0
0
0
2
2
0
0
0
2
1
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
1
0
0
0
1
1
1
2
0
0
2
1
0
2
0
0
0
2
1
0
0
0
0
1
1
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
2
0
0
2
0
0
2
1
0
0
2
0
1
0
2
1
0
1
0
2
0
0
0
3
2
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
2
0
0
5
0
0
2
0
1
0
0
0
1
1
0
2
0
2
0
0
3
0
2
4
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
2
2
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
2
0
0
0
0
0
18
1
0
2
0
2
0
1
1
0
2
0
0
0
2
3
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
2
1
1
0
2
0
2
0
2
1
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
2
2
1
2
0
0
0
0
0
1
0
1
2
0
0
0
1
1
2
0
1
0
1
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
4
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
1
1
1
0
1
1
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
2
2
0
0
0
0
2
0
0
0
2
0
2
1
1
0
0
2
0
0
2
1
0
0
0
1
0
0
2
0
1
1
0
0
1
0
0
1
0
1
0
0
0
0
1
2
0
3
1
3
0
2
0
0
0
0
0
1
0
2
1
0
1
0
2
0
2
2
1
0
1
2
2
1
0
2
1
1
2
0
0
0
0
0
0
0
2
0
2
0
0
0
1
1
0
1
0
0
0
4
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
1
0
2
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
1
1
2
2
0
0
3
1
0
0
0
0
2
0
0
1
0
0
2
0
1
0
1
0
0
1
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
2
0
0
0
0
0
1
2
0
0
0
2
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
2
0
0
1
0
1
4
0
0
5
0
1
0
0
0
1
0
0
1
1
0
0
2
2
0
0
2
0
0
1
0
0
0
2
1
0
0
2
2
2
1
1
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
2
0
0
1
2
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
1
2
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
2
1
1
0
2
2
1
1
1
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
1
1
2
2
1
2
1
0
1
0
0
1
1
0
2
2
0
2
0
1
1
0
0
0
2
2
0
2
1
0
1
0
0
1
0
1
2
0
0
0
0
0
0
0
2
0
1
1
2
2
0
0
3
0
3
0
0
0
1
3
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
1
0
1
0
2
0
0
1
0
0
0
0
2
0
0
0
0
3
0
1
0
0
0
0
1
0
2
0
0
2
0
2
3
2
0
0
0
0
0
0
2
0
0
1
0
1
2
1
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
1
0
0
2
2
0
0
0
3
2
0
0
0
3
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
2
0
1
1
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
2
0
1
0
0
2
0
0
0
0
1
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
4
0
1
1
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
1
1
1
2
0
0
2
0
1
9
0
0
0
1
2
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
2
3
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
2
1
2
0
2
0
0
0
0
1
1
0
0
0
0
0
0
1
5
1
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
1
2
0
0
0
1
2
0
0
0
2
0
0
2
0
2
0
1
0
2
0
0
0
0
0
0
0
2
2
2
0
1
0
1
1
2
0
2
0
0
0
0
0
0
0
2
1
2
2
0
2
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
4
0
1
0
0
0
0
0
1
1
0
2
0
0
0
0
2
1
1
1
2
0
0
0
2
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
1
2
0
0
1
0
1
3
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
2
2
1
0
0
1
0
0
0
0
7
0
2
0
0
0
1
3
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
1
2
1
2
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
3
2
0
0
0
0
1
2
0
2
0
0
2
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
2
0
1
2
0
0
0
0
0
0
0
0
2
1
0
1
2
1
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
2
1
0
0
0
0
2
1
2
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
3
4
2
0
0
1
0
2
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
1
0
1
1
0
2
0
2
1
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
2
0
0
0
0
0
1
0
0
0
2
2
0
0
4
0
0
1
3
1
0
0
0
0
0
0
0
0
0
2
1
0
1
2
0
0
1
2
0
2
0
0
2
0
0
0
0
0
0
0
0
3
1
0
2
1
0
0
0
0
2
2
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
1
1
1
2
0
1
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
3
0
0
1
0
2
1
0
2
0
0
0
1
0
0
0
1
1
0
0
2
1
0
0
1
0
2
2
0
2
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
2
0
2
0
1
0
2
0
2
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
2
0
1
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
2
0
2
1
0
0
0
2
0
0
2
2
0
0
1
1
2
0
0
0
0
0
0
0
0
1
1
1
0
0
2
0
2
0
0
1
0
0
3
0
2
0
0
0
0
0
2
2
1
0
0
0
4
1
2
0
1
0
0
1
0
0
1
0
1
0
0
2
0
0
0
2
0
0
1
0
2
0
3
0
8
2
0
0
2
0
1
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
2
1
0
1
1
2
0
0
0
3
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
2
2
0
0
0
0
0
2
0
0
0
2
0
0
1
0
2
0
0
0
1
0
1
0
0
1
0
0
0
1
2
0
0
1
0
1
1
0
0
1
0
0
0
0
4
0
1
0
1
2
2
1
1
0
2
0
0
0
2
2
1
0
0
0
0
2
2
0
0
0
1
0
1
0
0
0
2
1
2
1
0
2
0
2
1
0
0
0
0
0
1
0
0
0
3
0
2
0
0
1
0
0
0
2
1
1
2
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
2
0
1
0
2
2
0
1
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
2
0
0
2
0
1
0
0
0
0
0
1
0
1
0
0
1
1
1
0
0
0
0
1
0
1
0
0
0
2
2
0
3
2
0
0
0
2
2
0
2
0
0
0
0
2
0
0
2
0
0
2
2
1
0
1
0
1
0
1
0
2
0
1
1
0
0
0
2
0
0
2
0
2
0
0
0
1
2
3
0
0
1
0
0
1
1
2
0
0
1
2
0
0
4
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
4
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
3
0
0
0
0
0
0
0
0
0
2
0
3
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
1
2
3
0
1
0
1
0
3
2
1
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
1
1
0
0
0
0
2
0
0
0
0
1
0
1
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
1
0
4
0
0
0
1
2
2
0
0
1
0
0
2
0
2
0
2
0
0
0
1
0
0
1
1
2
0
1
1
0
2
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
1
0
0
0
2
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
1
0
1
0
1
0
0
0
0
0
1
1
2
0
0
0
0
0
0
2
2
0
0
1
0
2
0
0
0
2
0
2
1
2
0
2
0
0
0
1
3
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
1
1
0
1
2
2
2
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
2
0
1
0
0
1
0
1
2
0
0
4
0
0
0
0
0
2
0
0
2
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
2
2
1
1
2
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
1
0
2
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
2
0
0
1
0
2
2
0
2
0
0
0
0
2
2
2
0
1
2
1
0
0
0
2
0
0
0
1
0
0
1
1
1
0
0
2
0
0
0
0
0
0
1
1
2
1
0
2
0
0
0
1
0
0
2
0
0
2
1
3
0
1
2
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
3
0
1
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
1
1
1
1
1
2
2
0
0
2
0
1
3
2
0
0
1
0
1
0
2
2
0
0
0
2
0
0
0
0
0
1
0
2
0
1
1
0
0
1
0
0
0
2
2
1
0
1
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
2
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
3
1
2
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
1
1
0
0
0
0
1
0
2
0
0
0
0
0
2
1
1
0
0
0
3
2
0
3
0
1
2
0
0
0
0
2
1
2
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
3
20
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
2
0
0
0
1
0
0
0
0
2
3
2
0
0
2
0
0
0
1
2
0
0
0
1
0
2
0
0
2
0
0
0
1
2
1
1
0
0
0
0
1
2
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
1
0
2
5
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
2
0
0
0
3
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
2
0
1
0
0
0
1
2
0
0
2
0
0
0
0
1
6
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
4
0
0
1
0
0
0
1
0
1
0
2
0
0
1
1
0
0
0
1
0
0
1
1
0
0
2
0
0
2
0
1
0
0
0
1
0
0
2
1
2
1
0
3
1
2
2
0
0
0
1
1
2
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
2
0
2
0
0
2
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
2
2
0
0
0
1
0
0
0
1
0
0
1
1
0
1
1
0
0
0
1
0
1
0
2
1
1
0
0
0
1
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
2
0
1
2
0
0
0
2
0
0
0
2
2
0
0
1
2
0
0
2
2
2
0
0
1
3
1
0
0
0
0
1
0
0
0
0
3
0
0
0
1
0
0
0
1
2
1
0
0
1
2
0
0
0
2
0
2
0
0
0
0
2
0
0
1
2
1
1
2
2
1
1
0
2
1
0
0
1
2
1
0
0
1
0
0
0
1
0
1
0
2
2
1
0
1
0
2
0
0
1
0
0
0
1
0
0
0
1
1
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
2
2
0
1
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
1
1
0
0
0
2
3
0
0
0
2
0
0
0
0
1
2
0
2
0
0
0
2
1
2
0
2
0
2
2
0
0
2
0
0
0
1
2
0
0
0
0
2
0
0
0
2
0
0
1
2
1
2
0
2
0
1
1
1
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
1
0
1
0
0
0
0
0
0
0
2
1
0
1
3
0
2
0
1
0
4
2
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
1
0
1
0
3
0
2
0
1
0
0
0
4
0
1
3
1
2
0
0
2
0
0
0
0
0
0
0
2
0
2
1
0
1
2
2
0
0
0
1
0
2
0
1
4
2
0
0
0
2
0
0
2
0
0
0
0
1
1
1
4
0
1
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
2
0
2
1
1
0
3
2
2
0
0
0
0
2
0
1
0
1
0
0
0
2
6
0
0
1
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
3
1
0
0
0
0
0
0
0
2
0
1
3
2
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
2
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
2
0
0
0
0
0
0
2
2
0
1
0
0
1
1
5
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
1
2
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
1
2
2
0
2
1
0
2
0
0
0
0
0
0
3
0
0
0
0
1
0
0
1
1
2
0
0
0
0
1
0
1
0
2
0
2
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
1
0
3
3
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
2
0
1
0
2
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
1
2
0
3
0
0
0
2
0
1
1
1
1
2
1
0
1
0
0
0
0
0
0
0
0
3
0
0
2
0
1
0
0
0
0
0
1
1
0
1
0
0
3
0
0
2
0
0
0
2
0
0
0
0
2
1
0
4
0
0
0
0
1
0
0
0
0
1
0
0
1
0
2
0
0
0
3
0
3
0
0
1
0
0
0
0
0
0
1
0
0
1
4
1
0
0
0
1
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
1
1
0
0
0
1
1
4
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
3
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
1
0
3
0
0
0
0
1
0
0
0
0
0
1
1
1
1
2
1
0
0
2
0
0
1
8
0
0
0
0
0
0
2
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
2
0
0
1
2
0
0
2
0
0
0
0
0
2
0
0
1
2
0
2
0
0
0
0
0
1
2
0
0
1
2
0
2
1
0
0
0
1
3
1
2
1
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
1
0
3
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
1
0
0
0
2
0
2
0
1
0
0
0
2
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
1
1
0
0
2
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
2
0
0
0
0
0
2
0
0
0
2
0
0
2
5
0
2
0
1
0
3
1
0
1
2
0
2
0
0
1
2
1
0
0
0
1
1
0
0
0
1
0
1
0
2
0
0
0
0
0
2
1
0
0
2
0
0
0
2
0
0
3
0
0
2
1
0
0
0
0
1
1
0
2
0
0
0
0
1
0
0
1
0
0
2
0
1
0
2
0
1
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
3
3
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
1
2
2
1
1
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
2
2
0
2
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
1
2
0
0
2
3
0
0
0
1
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
2
1
0
2
0
1
0
0
0
0
1
2
0
2
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
1
2
0
0
0
2
2
0
0
1
0
0
0
0
1
0
1
0
0
2
0
0
0
1
2
0
2
1
0
0
2
0
0
3
0
0
0
2
0
1
0
0
0
2
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
2
0
0
0
2
0
0
0
1
2
0
1
0
0
0
0
0
0
0
2
0
2
0
1
1
0
0
0
2
1
2
1
2
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
1
2
1
2
0
0
2
0
2
0
1
0
3
2
0
0
1
1
0
0
2
0
2
0
0
0
1
0
0
1
1
0
3
0
0
0
1
0
0
2
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
3
0
1
3
0
0
1
0
2
2
0
2
0
0
0
0
1
0
1
0
0
0
0
3
0
0
1
0
0
0
0
1
0
2
1
2
0
0
0
1
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
6
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
1
3
2
2
0
2
0
2
0
1
0
0
0
0
2
2
0
0
0
2
1
0
0
0
0
1
1
0
0
2
0
0
2
0
2
0
0
0
1
0
0
2
0
2
2
0
2
1
2
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
1
1
3
1
0
1
0
0
0
2
0
0
0
0
2
3
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
1
0
0
0
0
0
0
2
0
1
0
0
1
0
1
0
0
1
0
0
0
4
0
0
0
1
0
1
0
2
0
1
4
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
2
0
1
0
0
2
0
2
0
0
0
2
2
1
2
0
0
0
2
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
3
0
1
0
1
0
0
0
1
0
0
2
0
1
0
0
3
0
0
2
0
0
0
0
0
1
2
0
0
0
1
2
0
0
0
0
1
1
1
0
2
1
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
2
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
2
0
2
0
1
0
0
0
0
2
0
2
0
1
9
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
7
0
0
1
0
2
2
0
1
2
1
0
0
0
0
0
2
0
0
0
2
0
0
2
1
0
0
0
0
1
0
2
2
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
2
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
2
1
0
0
0
1
0
0
0
7
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
2
0
0
0
4
2
1
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
2
3
3
0
0
0
1
0
4
0
0
0
0
2
1
0
0
1
0
0
0
2
1
2
0
1
0
0
2
0
0
2
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
4
0
0
0
2
3
0
0
3
0
0
1
0
2
0
1
0
0
1
1
0
0
1
2
0
0
1
0
2
1
0
0
1
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
3
0
0
2
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
2
0
2
0
1
0
0
0
0
0
1
2
0
0
0
1
0
0
2
0
0
0
1
0
4
0
0
1
0
1
0
1
1
2
0
2
0
0
0
1
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
8
2
2
0
0
0
0
1
1
0
1
2
0
0
2
0
0
2
4
1
0
1
3
0
0
1
2
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
1
0
2
2
2
2
0
1
0
2
0
0
0
2
0
2
0
2
3
2
0
2
0
1
0
1
0
1
1
2
2
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
2
0
1
0
2
1
3
0
0
2
0
0
0
0
0
2
0
8
2
0
0
0
1
0
1
0
0
0
0
0
0
2
1
0
2
0
1
0
1
0
0
1
0
0
0
2
0
0
0
0
2
2
0
0
1
1
2
1
0
1
1
0
2
0
1
0
0
0
0
0
1
2
0
1
0
0
0
0
3
0
1
0
0
0
0
0
0
0
1
4
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
3
0
0
2
1
1
0
1
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
1
0
3
0
1
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
2
4
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
2
1
0
1
0
2
0
1
0
0
0
0
0
2
0
0
4
0
0
0
0
0
3
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
2
0
7
4
0
0
0
0
1
0
0
1
2
1
0
1
0
2
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
2
1
0
0
0
2
1
1
0
0
0
0
0
0
1
0
0
4
1
0
2
0
0
1
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
2
4
0
0
3
1
0
2
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
1
1
0
1
2
0
0
0
2
0
0
0
0
3
2
2
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
5
0
0
3
2
0
1
1
0
0
0
2
1
1
0
0
0
0
4
2
0
0
1
0
1
0
0
0
0
1
0
0
0
1
2
1
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
1
1
2
0
0
0
0
2
1
0
1
2
0
1
0
0
1
1
0
0
0
1
0
0
0
1
1
0
0
1
0
2
1
1
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
1
2
1
0
0
0
0
0
0
2
3
1
0
0
0
1
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
1
0
0
2
2
0
1
1
1
1
2
0
0
2
1
1
0
0
0
0
2
0
3
2
0
2
0
0
1
1
1
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
2
0
0
1
0
2
0
1
2
0
0
0
1
0
0
0
1
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
2
0
2
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
2
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
3
0
0
1
0
0
0
0
0
1
2
0
3
0
2
0
0
2
0
0
0
2
2
5
0
0
0
2
2
0
0
2
0
0
0
0
0
1
0
0
2
0
2
3
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
2
0
1
0
0
0
2
1
0
0
0
0
2
0
1
3
2
0
2
0
0
0
2
2
3
0
1
1
0
0
0
2
1
2
0
1
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
1
0
2
11
0
0
0
2
0
1
3
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
2
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
2
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
2
1
0
4
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
2
0
2
1
1
0
0
0
1
0
0
0
3
0
0
0
0
0
2
2
0
2
1
0
1
0
2
2
0
1
0
0
0
0
0
0
0
0
2
1
0
0
2
0
1
0
2
0
1
2
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
9
0
0
0
1
2
0
0
1
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
2
1
3
0
2
2
0
2
0
0
2
0
1
0
1
5
0
0
0
1
0
0
2
0
0
0
2
2
0
1
0
0
0
2
0
0
1
1
1
0
0
0
0
4
0
0
0
0
0
0
4
0
1
0
2
0
1
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
2
0
0
0
1
0
1
0
2
0
0
0
0
0
0
2
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
1
1
0
0
0
2
0
0
0
0
1
0
1
1
0
1
0
0
1
1
0
0
1
0
0
0
1
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
2
1
0
1
2
0
1
4
0
0
0
0
1
0
1
0
2
0
2
0
0
1
1
0
0
0
0
0
2
0
0
0
2
0
0
1
2
1
0
0
0
1
0
0
2
2
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
3
1
1
1
0
2
2
0
0
2
0
0
0
0
0
0
1
0
1
0
0
2
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
2
0
7
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
2
1
1
2
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
1
0
0
0
2
1
0
1
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
2
1
1
3
1
3
0
0
0
1
2
3
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
4
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
1
1
0
5
0
11
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
2
0
1
0
2
2
0
0
1
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
1
0
4
0
0
0
2
0
0
0
0
0
0
0
1
3
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
3
0
2
0
0
2
0
4
2
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
2
0
0
0
2
0
1
1
0
0
0
0
1
2
2
1
0
0
1
2
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
1
0
0
0
0
3
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
4
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
2
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
2
0
0
1
3
0
0
1
2
0
1
0
0
2
0
2
0
0
0
0
0
0
0
1
2
0
2
0
1
0
0
0
0
3
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
1
0
2
2
1
0
2
2
0
0
8
3
0
2
0
3
3
0
0
0
2
2
0
1
2
0
1
0
0
0
0
2
0
2
1
4
2
1
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
1
1
1
1
0
0
0
2
0
0
0
2
0
1
0
0
0
1
0
0
2
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
1
2
0
1
0
0
0
0
0
0
0
0
1
1
0
1
2
0
0
1
2
0
0
0
0
0
0
3
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
3
0
0
2
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
2
0
2
2
0
0
0
0
0
0
2
0
0
0
1
1
0
1
0
0
0
1
1
0
1
1
0
0
1
0
0
0
0
0
0
2
1
0
2
0
2
2
1
1
0
3
0
0
0
0
0
0
0
0
0
0
0
3
1
2
1
1
1
1
0
0
0
0
1
0
0
2
0
0
0
0
1
1
0
2
2
0
0
2
0
0
0
0
3
1
1
2
1
0
0
0
0
0
0
1
0
1
0
0
2
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
1
0
0
3
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
1
0
1
0
2
0
2
0
0
2
2
2
0
0
7
1
2
0
0
2
2
1
1
0
1
0
3
0
2
0
0
0
3
0
0
0
0
1
1
1
0
0
0
0
0
0
0
3
1
0
0
1
2
2
0
0
1
1
0
3
0
2
0
0
1
1
0
4
4
1
0
2
1
1
0
0
0
0
0
0
1
2
0
2
0
0
2
0
0
0
3
0
0
0
2
0
0
2
0
2
1
0
0
0
2
1
1
0
2
0
0
0
0
0
0
5
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
2
0
0
0
2
2
1
0
0
0
1
2
0
0
0
0
0
0
1
1
2
0
2
0
0
1
0
0
0
1
0
1
3
1
3
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
2
2
0
3
0
0
0
0
0
1
0
0
2
0
2
1
1
3
1
1
0
0
0
1
1
0
2
0
0
1
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
3
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
3
0
0
0
0
0
2
1
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
1
0
3
1
2
0
0
2
2
0
0
2
0
0
0
1
2
0
2
2
0
1
1
0
1
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
2
0
2
0
0
1
0
1
0
0
0
0
2
0
0
0
0
1
2
0
0
1
2
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
1
1
0
0
0
0
0
2
0
2
1
0
0
0
0
2
1
1
0
1
0
0
2
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
1
4
1
0
0
1
0
1
0
1
2
0
1
0
0
2
3
0
2
1
0
0
0
2
0
2
0
1
1
0
2
0
0
0
0
0
2
2
0
0
1
0
1
0
0
0
0
1
0
0
3
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
1
2
2
0
0
0
1
0
0
0
2
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
1
0
0
0
0
2
0
0
0
2
0
1
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
1
0
0
2
0
0
3
0
1
2
1
0
0
0
0
0
2
0
2
1
1
0
1
3
0
0
0
0
1
0
0
2
0
2
0
2
0
0
0
0
2
0
2
2
0
0
0
2
0
0
0
0
0
0
0
1
0
5
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
2
0
0
1
0
2
1
0
0
1
0
2
0
2
1
0
3
3
0
2
0
0
0
0
0
0
2
3
1
0
0
0
0
1
0
0
0
0
0
2
0
0
1
2
2
2
0
0
0
3
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
8
1
0
0
0
0
0
0
2
1
0
0
0
1
3
3
0
0
1
0
0
0
2
2
1
0
1
0
0
2
0
0
4
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
1
0
0
0
1
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
2
1
0
0
2
1
2
0
0
0
0
1
0
0
2
0
0
2
0
1
0
2
0
0
0
7
0
2
2
0
1
2
1
0
2
0
0
0
0
1
0
4
2
0
0
2
0
4
0
0
0
0
0
2
1
0
2
0
0
0
0
0
4
3
0
0
0
2
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
1
0
0
1
2
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
2
0
1
0
0
0
0
2
0
0
1
0
1
1
0
0
0
0
0
3
0
0
1
0
0
2
1
1
0
1
1
0
3
0
0
0
0
0
1
0
2
0
0
0
1
0
1
0
0
1
0
0
0
2
0
1
0
2
0
1
0
1
2
0
0
1
0
1
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
1
0
3
1
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
2
2
0
1
0
1
0
0
0
0
2
0
0
0
0
2
2
0
0
0
1
0
0
0
1
0
0
0
1
0
2
1
0
0
2
0
0
0
0
2
2
2
0
2
0
0
2
2
0
2
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
2
0
0
2
0
0
0
0
1
0
0
1
0
0
0
2
1
0
2
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
1
3
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
2
3
1
1
0
2
0
0
0
1
2
0
0
2
0
0
2
2
2
0
1
0
0
1
0
1
0
1
0
0
0
0
0
2
0
2
2
2
0
0
0
0
0
5
2
2
1
4
0
0
2
1
0
2
2
1
1
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
2
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
4
2
1
7
2
2
0
1
2
0
0
2
0
0
0
0
0
1
0
0
0
2
2
1
0
0
2
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
1
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
1
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
4
2
0
0
3
0
0
0
2
1
1
1
2
0
0
1
0
0
0
0
2
2
0
1
0
2
0
2
0
0
1
0
2
1
0
0
0
0
1
2
0
1
0
1
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
1
2
0
0
0
0
0
1
0
0
5
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
3
3
0
1
0
0
0
0
0
0
1
3
0
0
0
0
1
1
2
0
0
1
0
1
1
0
0
2
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
3
0
0
1
1
2
1
0
0
0
0
0
0
1
3
1
1
0
0
0
0
0
0
0
2
0
0
2
1
0
1
2
1
0
0
2
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
2
0
1
3
1
0
1
0
2
1
2
1
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
1
1
0
0
0
0
2
0
0
1
2
2
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
2
1
2
0
0
0
0
0
0
1
1
1
2
0
0
0
3
0
1
1
0
0
0
0
2
2
1
1
0
0
0
2
0
0
0
1
0
0
0
1
0
0
3
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
2
2
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
2
0
0
0
0
2
2
2
2
0
0
1
1
0
1
0
0
0
0
0
3
0
0
0
3
0
0
1
0
0
0
1
1
0
0
0
1
1
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
1
0
0
0
0
2
0
0
1
1
0
0
0
0
0
1
2
0
0
0
0
0
1
2
0
0
0
0
2
1
1
0
0
0
0
0
2
0
1
0
0
1
1
0
2
0
0
2
0
0
0
0
0
2
2
0
2
1
0
0
12
1
4
1
0
1
0
2
0
0
0
0
0
0
2
3
0
0
1
0
0
0
0
1
0
1
0
2
2
0
0
2
0
0
0
0
1
2
0
0
1
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
3
1
0
0
2
0
0
1
0
1
1
0
0
2
0
0
1
1
0
2
0
0
0
0
0
0
1
1
1
0
1
1
0
3
1
4
0
0
2
2
2
0
2
0
0
0
0
0
0
0
2
0
0
0
3
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
2
0
3
2
0
0
2
0
0
0
0
1
0
0
2
0
3
1
4
0
0
2
1
0
1
1
0
0
3
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
2
0
0
2
2
1
0
0
3
0
2
2
0
0
1
2
0
1
0
1
0
0
0
1
0
0
2
0
0
0
0
2
0
2
1
0
0
0
0
1
0
2
0
1
0
2
0
0
0
0
2
1
0
2
0
2
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
1
0
2
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
2
0
2
0
0
1
0
2
0
0
1
2
2
0
0
0
1
0
0
1
2
1
0
0
1
2
0
0
0
0
0
2
2
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
1
1
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
3
2
0
0
0
0
2
0
1
2
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
3
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
1
0
0
0
3
2
0
0
0
1
0
0
2
2
0
2
0
0
2
0
4
0
0
1
1
0
0
5
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
2
2
0
0
0
2
1
0
1
2
0
0
2
0
0
0
1
2
2
0
2
3
0
0
1
0
0
1
0
0
0
0
0
0
1
0
2
12
1
0
0
0
0
0
0
0
1
0
1
0
0
1
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
2
2
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
1
0
0
2
0
0
0
2
2
1
0
0
1
1
0
0
0
0
0
1
1
2
1
1
0
0
0
0
2
4
0
0
0
2
1
0
0
0
0
1
2
2
0
0
3
0
0
0
0
0
2
0
1
0
0
0
1
2
0
2
2
0
2
2
0
2
1
0
0
0
2
0
1
0
0
2
1
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
2
0
0
0
0
0
3
0
2
0
2
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
1
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
2
0
0
6
0
0
1
0
0
0
0
0
2
0
2
2
0
1
0
0
0
0
0
2
0
1
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
1
0
1
1
1
0
0
3
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
1
2
0
0
2
0
0
1
0
0
0
0
1
2
0
0
3
0
0
2
2
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
1
0
0
2
0
2
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
2
1
0
0
0
0
1
3
0
0
0
1
1
0
0
0
1
0
0
3
0
0
0
0
0
1
0
0
0
2
0
1
0
0
2
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
2
0
1
0
2
2
2
0
2
0
1
0
0
0
0
0
0
1
0
4
0
0
0
2
1
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
1
2
1
0
0
1
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
1
0
2
0
0
2
1
0
1
1
0
1
1
1
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
1
0
0
2
1
1
0
0
0
0
0
1
0
0
0
2
0
2
0
1
0
1
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
2
2
2
0
0
0
0
20
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
1
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
1
0
0
1
2
0
0
0
1
0
2
0
0
0
0
0
0
1
1
0
2
0
1
1
1
1
0
0
2
0
0
2
0
0
1
0
1
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
1
0
0
1
0
1
0
5
3
4
0
3
0
0
1
0
1
0
0
2
0
0
2
0
0
2
0
0
0
2
0
0
0
0
1
2
0
2
0
0
0
2
0
0
1
0
1
1
0
0
6
2
0
0
0
0
2
1
4
0
2
0
0
1
0
1
0
2
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
2
0
0
2
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
2
0
2
0
0
1
0
0
0
0
2
0
0
0
2
0
0
1
0
1
0
1
0
3
0
2
0
0
1
0
2
0
2
0
0
0
0
0
0
2
0
1
0
0
1
0
0
2
0
0
1
2
0
2
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
2
0
2
1
1
1
0
0
0
2
0
0
1
0
0
2
0
0
0
1
0
1
0
0
0
0
0
1
0
2
1
0
0
0
0
2
0
1
0
1
0
0
0
0
0
1
0
1
2
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
1
0
1
1
0
0
0
2
0
2
0
0
2
2
0
0
2
0
0
2
0
0
0
0
0
2
0
0
1
2
2
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
1
1
2
1
2
0
2
0
0
6
0
0
5
0
0
2
2
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
2
0
1
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
2
2
2
2
2
0
0
0
0
2
0
2
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
2
0
2
0
0
1
0
0
0
2
0
1
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
4
1
2
1
2
0
0
0
0
0
0
0
2
0
0
1
0
3
0
0
2
1
0
2
2
0
0
0
0
2
0
0
4
0
1
0
0
1
0
0
0
0
0
1
2
0
0
0
1
2
0
0
0
1
0
0
0
1
2
2
0
2
0
0
0
0
3
2
0
1
0
0
0
0
2
0
1
0
0
0
0
0
3
0
2
0
1
0
0
2
0
4
0
2
0
1
2
1
0
0
1
3
0
0
0
0
0
0
0
5
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
1
2
3
0
1
0
0
0
1
0
0
1
0
0
2
0
0
0
2
0
1
4
2
0
1
0
0
0
0
2
2
0
1
0
0
0
1
0
3
0
2
0
0
2
1
0
0
0
0
0
0
0
2
0
0
2
0
3
1
1
1
1
0
0
2
2
0
3
0
0
2
0
1
0
0
2
1
0
0
2
0
0
0
0
2
1
0
2
1
0
0
0
0
0
1
0
0
2
0
0
2
0
3
0
1
2
0
0
2
0
1
0
0
0
0
2
0
0
2
1
0
1
0
0
0
0
0
2
0
2
2
2
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
1
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
1
0
1
0
0
2
0
0
1
0
2
2
1
0
0
1
0
2
1
0
0
0
0
0
2
2
0
1
1
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
1
2
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
1
2
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
1
0
2
1
0
2
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
1
0
0
2
0
0
2
0
0
2
0
0
2
0
0
0
0
0
2
2
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
2
2
2
2
1
1
0
0
2
0
0
1
0
0
0
0
2
1
0
0
0
2
0
1
0
0
2
2
0
0
2
0
2
0
0
0
1
2
0
0
2
2
0
1
0
2
0
0
0
2
0
0
0
0
2
0
2
1
0
0
1
2
0
1
2
0
0
1
0
0
0
2
0
0
2
0
2
0
1
0
2
0
0
1
0
1
0
0
24
0
1
2
0
0
0
1
0
3
2
0
1
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
3
0
0
1
0
0
1
0
2
2
0
0
1
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
1
0
0
0
1
0
1
2
0
1
0
0
1
0
0
2
0
0
0
0
2
0
8
2
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
2
1
1
2
2
1
1
2
2
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
1
1
1
1
0
2
0
0
0
2
0
0
1
0
1
3
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
1
1
2
0
0
1
0
2
0
0
0
2
0
2
1
0
0
0
0
2
0
0
0
2
2
0
2
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
1
0
2
2
0
2
0
0
0
0
5
0
1
2
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
6
2
1
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
2
0
1
1
2
2
0
0
1
0
0
1
2
0
0
0
1
0
0
1
2
0
1
0
1
0
0
0
1
3
0
2
0
0
1
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
4
2
0
0
1
0
0
0
1
0
0
2
0
0
1
2
2
0
2
2
0
0
2
0
0
0
0
0
0
1
2
0
1
0
0
0
2
0
0
0
0
1
0
1
1
0
1
2
0
0
0
1
1
0
2
0
1
1
3
1
0
0
0
1
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
3
1
0
0
0
1
0
0
0
0
0
0
4
0
0
1
0
2
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
2
0
2
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
1
0
1
0
2
0
0
0
0
0
0
0
3
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
1
3
0
0
2
1
0
0
2
0
0
0
0
0
1
0
0
0
1
2
1
0
1
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
1
2
0
0
0
1
0
2
2
0
0
0
0
1
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
2
0
1
0
0
0
1
0
0
1
0
0
0
3
1
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
1
2
0
0
0
3
0
0
1
0
0
0
0
1
0
1
0
1
1
0
0
0
1
0
1
0
0
0
1
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
1
3
1
0
1
0
1
0
1
0
0
1
1
1
0
0
2
2
0
0
0
2
1
1
0
0
1
0
1
0
0
1
0
0
0
0
2
0
2
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
1
0
1
1
0
0
0
1
1
1
2
0
0
0
0
0
0
1
1
0
0
1
0
1
2
0
1
0
1
1
0
0
0
1
3
1
0
0
2
2
2
0
0
0
1
1
0
0
2
0
0
0
1
0
0
0
0
0
1
0
2
0
0
1
2
0
2
0
0
4
0
1
0
0
2
1
0
1
1
0
0
0
1
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
2
2
1
0
0
0
0
1
0
1
0
0
2
0
1
2
1
0
0
2
2
0
2
0
0
0
0
0
2
0
0
0
0
0
1
2
0
1
0
0
0
0
1
0
0
0
2
0
0
0
2
2
2
0
0
0
0
0
1
0
0
1
0
0
0
1
2
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
2
1
1
0
1
2
0
0
0
0
0
1
0
0
0
3
0
0
0
1
0
1
1
0
0
1
1
0
0
0
0
1
0
0
0
2
0
0
2
0
2
0
1
0
0
0
2
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
1
4
1
0
0
0
0
1
0
3
0
1
0
0
1
0
0
0
0
1
0
0
0
2
0
0
2
0
0
2
0
1
4
1
0
0
1
2
0
0
0
2
0
2
2
0
0
0
0
1
0
1
0
1
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
2
2
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
1
0
0
2
0
2
2
0
0
0
0
1
1
0
0
2
0
0
0
2
0
0
0
2
3
7
0
1
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
1
1
0
0
1
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
2
1
0
3
0
1
0
2
0
2
0
0
3
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
1
0
0
1
0
0
2
2
0
2
0
0
0
0
0
2
4
0
0
0
2
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
4
0
0
0
1
0
1
0
0
0
0
5
0
0
0
0
0
0
0
0
0
5
0
2
3
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
3
2
0
0
0
0
0
0
2
0
0
1
1
0
2
2
1
2
0
0
0
0
0
2
0
0
0
0
0
2
2
0
1
0
0
0
0
1
1
2
1
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
1
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
3
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
1
2
0
0
2
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
3
0
0
0
2
0
0
0
1
2
0
1
2
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
1
1
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
1
4
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
2
0
2
0
2
1
0
0
0
1
0
0
2
0
1
0
0
1
2
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
1
2
2
1
0
2
0
1
0
0
0
1
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
3
0
0
1
0
1
0
0
0
0
0
3
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
2
0
1
2
0
0
0
1
0
0
2
0
1
2
0
0
2
2
0
0
0
1
0
2
0
1
1
1
2
0
2
0
2
0
0
0
0
0
0
0
1
0
1
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
2
1
0
1
2
0
0
0
0
2
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
6
0
1
0
1
0
0
0
0
0
1
1
0
1
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
2
0
1
0
2
0
0
0
2
0
3
0
0
0
2
0
0
1
2
1
0
0
1
0
0
0
4
0
0
0
0
2
3
0
1
0
0
0
0
0
1
0
2
1
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
2
0
0
0
1
1
2
0
1
0
0
2
1
0
2
0
2
0
0
0
0
3
3
0
0
2
0
0
1
0
1
0
4
0
13
0
0
0
1
3
1
0
0
2
0
0
2
0
0
1
1
0
2
0
0
0
0
1
2
0
2
0
0
3
0
0
0
1
0
1
0
3
1
0
0
0
0
0
0
0
1
2
2
2
0
0
2
1
0
0
0
0
0
0
1
0
0
0
2
4
1
0
0
0
0
0
2
1
0
0
0
0
2
1
2
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
1
2
0
1
0
0
1
3
0
0
0
2
0
2
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
2
2
0
2
1
0
1
1
2
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
3
0
0
0
0
3
1
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
1
0
1
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
1
1
0
2
0
0
0
0
0
0
3
2
0
0
0
1
1
0
0
0
0
2
0
0
0
1
0
0
0
0
2
1
2
0
0
1
0
1
1
0
2
0
0
0
1
0
1
0
0
0
0
3
0
0
2
2
2
1
0
0
1
0
0
0
0
0
0
2
0
1
1
0
1
2
0
0
1
0
0
2
0
0
2
1
1
2
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
1
0
0
1
0
2
0
0
0
1
0
0
0
2
0
1
2
0
0
0
2
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
1
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
1
1
2
1
0
0
0
0
2
2
0
0
2
2
0
4
2
0
0
2
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
1
0
1
0
0
2
0
0
1
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
1
1
2
0
0
3
1
0
0
0
0
0
1
1
0
2
0
0
2
1
0
1
1
0
4
2
0
0
0
1
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
1
0
0
3
0
4
1
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
3
0
2
1
0
0
0
1
0
0
0
1
0
0
0
2
2
1
1
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
4
1
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
1
0
2
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
1
1
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
1
0
1
1
0
0
0
1
0
2
1
1
0
0
3
0
0
2
0
0
0
2
2
0
2
1
1
1
2
0
0
2
1
0
0
2
0
0
2
0
0
0
1
0
2
2
1
0
1
0
0
0
0
2
2
2
2
2
1
0
0
0
1
0
0
0
0
0
4
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
2
0
2
0
1
0
0
0
0
1
0
0
0
0
0
1
2
0
1
0
0
0
0
2
1
2
2
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
1
0
1
3
0
0
1
2
0
0
0
1
0
1
0
1
1
0
1
0
0
2
0
0
0
0
0
0
0
2
0
1
0
2
0
1
1
0
0
0
1
0
0
0
0
1
2
0
2
1
0
0
0
0
1
1
0
1
1
0
0
2
0
0
0
1
0
0
0
0
0
3
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
1
0
2
1
1
4
1
0
0
0
1
0
1
2
2
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
2
0
2
1
0
1
0
0
0
0
2
0
0
0
0
1
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
1
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
2
1
0
1
0
0
0
2
2
0
1
0
0
2
1
0
1
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
2
3
0
2
0
3
5
0
2
0
0
2
0
0
2
0
0
0
0
0
2
1
0
1
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
2
0
3
1
0
2
1
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
1
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
3
0
0
1
0
0
2
1
0
1
0
0
0
0
2
0
0
2
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
1
2
0
1
6
5
0
0
2
0
0
0
2
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
11
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
1
1
0
1
0
1
2
0
2
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
2
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
1
0
0
0
0
1
2
1
1
1
0
1
3
0
0
2
0
2
0
0
2
1
0
0
0
2
0
0
1
2
0
0
1
0
0
0
1
1
1
0
0
2
0
1
0
0
1
1
0
1
0
1
0
0
2
1
0
1
0
0
0
0
0
1
0
1
2
0
0
2
0
3
1
0
2
0
0
0
0
1
2
0
0
1
0
1
0
1
0
0
0
0
2
0
2
0
2
0
0
1
0
0
0
1
0
0
0
1
1
0
2
0
0
1
0
1
0
0
0
0
0
0
5
0
0
2
0
2
1
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
1
2
0
1
1
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
2
2
2
1
0
1
0
0
0
2
1
1
0
0
1
0
2
0
1
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
2
0
0
0
0
0
2
0
1
1
1
2
0
0
0
1
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
1
0
0
0
0
3
0
0
1
0
2
0
0
3
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
3
1
0
0
2
0
0
0
2
0
1
0
0
0
0
0
1
2
0
0
0
2
2
0
0
0
0
1
0
4
4
2
0
0
0
0
0
0
2
0
0
0
0
1
0
1
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
1
4
1
2
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
2
2
1
0
1
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
1
0
2
0
0
1
0
1
0
1
1
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
2
0
0
1
0
1
2
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
2
0
1
0
0
0
0
0
3
0
0
0
0
2
0
1
1
0
0
1
0
0
0
2
2
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
2
0
0
1
2
0
0
0
1
1
0
3
2
0
2
1
0
2
0
2
1
2
1
0
2
1
0
9
1
1
0
0
0
0
1
0
0
2
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
1
0
1
0
2
2
0
2
0
2
0
0
0
2
0
1
0
1
0
1
0
1
2
0
2
0
0
0
2
0
0
0
1
0
0
2
0
0
1
0
3
2
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
2
0
0
0
0
3
0
0
0
0
1
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
1
0
1
0
0
1
0
0
3
0
2
0
0
1
2
0
0
1
2
2
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
1
0
2
1
0
1
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
2
2
0
0
1
0
1
0
2
0
0
2
0
2
0
0
0
2
1
0
1
2
0
0
1
1
0
4
0
0
2
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
2
0
2
1
0
1
0
2
1
1
0
0
1
0
0
0
2
2
1
4
0
0
0
1
0
0
1
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
5
0
2
1
2
2
2
0
0
0
0
0
0
2
1
0
0
0
0
1
2
0
2
0
2
0
0
1
2
0
0
2
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
2
0
0
1
0
0
0
1
0
0
0
2
3
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
1
0
0
0
3
0
2
0
1
0
0
2
0
2
1
0
0
0
0
0
1
0
2
0
3
2
0
1
0
0
0
2
2
2
2
1
0
1
1
0
1
0
0
0
0
0
0
0
4
0
1
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
1
0
0
1
2
0
3
2
0
0
1
0
0
0
0
0
0
0
0
0
2
1
1
1
1
2
0
0
0
1
2
0
0
0
3
0
2
1
0
0
1
0
2
0
0
0
1
1
2
0
0
0
0
0
2
0
0
0
0
1
1
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
1
0
0
0
1
0
0
3
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
2
1
0
2
0
2
1
0
0
0
0
0
0
1
2
0
0
0
0
2
0
1
0
3
0
2
0
0
1
1
1
0
0
0
2
0
0
2
1
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
1
1
2
0
0
0
2
0
0
0
0
0
1
0
1
0
0
2
1
2
0
2
2
2
5
1
1
2
0
0
0
4
0
0
0
0
0
0
0
2
3
0
1
2
1
2
0
0
0
0
2
2
0
0
2
2
0
0
2
1
2
1
0
2
0
1
1
0
1
0
3
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
2
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
2
0
1
0
0
1
0
0
2
0
0
0
1
0
0
0
2
0
0
2
0
1
0
1
0
0
0
0
2
1
0
1
0
2
2
0
2
0
0
0
0
3
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
4
0
0
1
0
0
1
3
0
0
0
2
0
0
1
0
3
0
1
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
3
1
0
1
0
0
0
0
0
0
2
1
1
2
0
0
0
0
2
0
1
2
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
2
2
0
0
0
0
0
0
2
2
2
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
2
0
0
2
0
0
0
1
0
2
0
0
0
0
0
3
1
2
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
3
1
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
2
0
0
0
0
2
2
0
2
0
0
1
2
0
1
0
0
0
0
0
0
0
1
1
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
2
0
1
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
2
1
0
1
0
0
1
0
1
1
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
2
1
2
1
0
0
0
2
1
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
2
2
0
0
1
0
1
0
1
0
1
1
2
1
0
2
0
0
0
3
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
4
0
0
3
1
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
2
0
0
0
0
0
2
1
2
0
1
0
0
1
0
0
0
1
1
0
0
0
0
2
0
0
0
0
2
2
0
0
0
2
0
2
2
2
0
0
0
0
0
2
0
0
0
2
1
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
3
1
2
0
0
2
0
1
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
2
0
1
0
0
0
1
0
1
2
0
4
6
0
0
1
0
0
1
1
1
0
0
3
0
0
2
0
0
2
2
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
2
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
1
2
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
1
0
2
0
2
2
1
0
0
0
0
0
0
1
0
3
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
2
0
2
2
0
1
2
0
0
1
2
1
2
3
2
0
2
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
2
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
1
0
3
2
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
3
0
0
0
1
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
2
1
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
1
2
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
1
0
0
1
1
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
1
1
0
3
0
1
5
0
0
0
1
3
0
0
2
0
3
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
2
1
3
0
2
0
1
0
2
1
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
1
1
0
1
0
0
1
0
2
0
0
2
0
0
0
1
3
3
2
1
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
3
0
1
0
0
0
2
1
0
0
0
1
1
0
0
0
1
2
0
3
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
2
0
1
0
2
1
0
0
0
0
0
0
1
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
2
0
0
0
1
0
0
0
0
0
1
2
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
2
3
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
2
1
1
0
1
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
2
0
1
1
0
0
0
0
0
0
1
0
2
2
0
2
0
0
0
4
0
0
2
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
2
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
2
2
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
2
1
0
0
0
0
1
0
2
2
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
1
1
1
0
0
2
2
1
1
0
0
0
0
1
2
0
0
0
1
2
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
4
0
0
0
1
0
3
0
0
2
2
0
0
0
1
0
0
0
2
0
0
5
0
0
0
0
2
0
0
0
3
0
1
0
0
0
1
1
0
2
0
1
0
2
0
0
0
0
1
0
0
0
1
2
1
0
0
1
2
0
2
2
0
2
0
1
0
0
2
0
0
1
2
0
2
0
0
1
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
2
0
1
1
2
0
2
0
0
0
1
0
2
1
0
0
0
0
0
1
2
1
0
1
1
0
2
0
0
0
0
0
1
0
1
2
1
1
0
0
2
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
2
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
3
2
0
1
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
3
1
1
0
0
0
2
0
0
2
0
1
0
1
0
2
2
1
0
0
0
0
2
2
0
0
0
0
0
1
2
0
1
0
0
0
0
0
2
0
1
0
2
0
0
1
0
1
0
3
1
0
0
1
0
2
1
0
0
0
0
0
2
0
1
2
1
0
1
0
0
1
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
3
1
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
2
0
1
0
2
0
0
3
0
2
0
0
1
2
0
2
0
1
2
0
0
2
1
0
0
1
1
1
0
0
3
0
0
0
1
1
2
0
0
1
2
1
0
0
0
1
1
0
0
0
0
0
3
0
2
0
1
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
2
0
0
2
0
2
0
0
2
1
0
1
1
0
1
0
0
0
0
0
2
0
0
1
2
0
1
0
0
5
0
0
2
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
2
1
0
2
2
2
2
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
1
1
2
0
0
0
2
0
7
0
0
2
0
1
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
1
2
2
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
2
2
0
0
2
0
0
0
1
0
0
0
1
1
0
0
0
3
0
0
0
2
0
2
2
0
0
0
0
0
2
2
1
2
0
0
2
0
2
1
0
1
0
0
2
1
1
0
0
0
0
0
0
1
0
0
1
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
2
0
0
2
0
3
0
1
0
0
0
2
0
0
1
1
0
2
0
0
0
3
0
0
0
1
2
1
0
2
0
0
0
0
2
1
0
0
1
1
0
2
2
0
0
0
3
1
0
0
0
1
2
0
0
2
0
0
0
0
0
0
2
0
0
0
3
0
2
0
2
2
1
0
0
0
1
1
0
0
0
0
2
0
2
0
0
3
1
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
2
0
1
0
1
0
0
3
0
2
1
0
0
0
0
10
0
0
2
2
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
2
0
2
2
2
1
0
1
0
2
0
0
0
0
1
2
2
1
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
1
1
0
0
2
0
0
2
0
2
1
0
0
0
0
0
2
0
1
0
0
0
0
1
1
2
0
0
0
0
0
0
0
1
0
0
0
0
2
2
2
0
2
0
0
0
0
0
0
0
0
2
2
0
1
2
0
0
2
1
1
2
2
0
0
0
1
0
0
0
0
2
1
0
2
0
0
0
0
2
0
0
2
0
0
3
1
0
0
1
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
2
0
0
0
2
0
2
1
0
2
0
0
1
0
2
2
1
3
2
2
2
2
0
0
0
0
1
2
1
2
0
0
0
2
0
2
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
2
2
2
0
0
0
3
0
0
0
2
0
2
1
0
1
0
0
2
0
0
0
0
1
2
0
0
3
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
2
0
2
0
0
1
1
1
0
0
0
0
0
0
2
0
1
1
2
0
0
2
0
2
0
1
1
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
3
2
1
0
2
0
0
2
0
0
0
2
0
2
0
0
0
1
0
1
0
0
0
1
0
2
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
1
2
0
1
0
0
0
0
1
0
0
0
3
1
0
1
2
0
0
1
0
0
0
1
0
0
2
0
1
2
2
0
0
0
1
0
0
2
0
0
2
2
0
0
0
0
0
0
1
0
2
1
0
1
0
2
0
2
0
0
2
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
2
2
2
1
0
0
0
1
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
1
0
0
1
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
2
2
2
0
1
0
0
1
0
0
0
0
1
7
0
0
0
2
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
1
0
2
1
0
2
2
1
0
5
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
2
1
1
1
0
1
0
1
0
2
1
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
2
0
0
0
0
2
0
0
1
0
1
0
1
3
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
2
2
0
2
0
1
1
0
0
2
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
2
2
1
2
1
0
0
0
0
0
0
3
0
1
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
2
0
1
1
0
0
0
0
1
1
0
0
0
0
2
1
0
1
0
0
0
0
2
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
2
3
0
0
1
0
0
2
0
2
0
0
0
2
0
0
1
0
1
0
0
1
4
0
0
1
0
2
2
0
0
2
0
3
0
0
0
0
0
2
1
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
6
4
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
3
2
0
0
0
0
1
0
0
0
0
2
2
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
1
4
0
2
0
0
0
0
0
0
0
1
2
0
0
2
0
1
0
0
0
1
0
0
0
0
2
1
2
0
0
1
0
2
0
0
0
0
2
3
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
1
0
0
0
1
1
0
0
0
0
0
2
0
1
0
2
1
1
2
2
0
1
0
2
1
0
0
1
1
0
0
1
0
0
1
0
0
1
1
1
0
0
1
0
0
2
0
0
2
4
0
1
0
0
0
2
0
0
1
0
2
0
2
0
0
2
0
0
0
1
2
0
0
2
2
0
2
0
0
0
1
0
2
1
1
0
1
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
3
2
0
0
0
0
0
1
0
0
0
0
0
1
0
2
2
0
0
1
0
0
0
1
0
0
6
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
1
1
1
2
0
1
0
0
0
0
2
2
0
0
1
0
0
5
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
1
0
0
2
0
0
2
0
0
0
1
0
3
1
0
0
0
0
0
1
3
2
0
0
0
0
1
3
1
0
0
0
0
0
5
0
0
0
0
0
0
0
1
5
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
2
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
2
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
2
0
1
2
0
0
2
0
0
2
0
2
0
0
0
0
0
2
0
0
0
1
2
2
0
0
1
0
2
0
0
1
0
0
0
1
2
2
1
1
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
3
0
0
2
1
2
2
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
2
3
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
2
1
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
2
0
0
0
3
1
0
0
0
0
0
0
1
2
1
0
0
1
1
0
3
0
2
0
0
0
0
1
0
1
0
2
0
1
0
0
0
2
0
1
1
0
0
0
1
2
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
3
1
0
2
0
1
1
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
1
2
2
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
16
0
0
2
0
0
3
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
3
0
0
0
1
4
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
2
4
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
1
0
0
3
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
2
2
1
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
1
1
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
1
0
0
4
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
1
0
0
0
0
2
2
2
0
0
0
0
1
0
0
2
0
0
0
1
0
2
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
4
0
0
2
0
0
5
3
0
4
0
2
0
1
0
0
3
0
0
0
0
0
0
1
0
2
0
4
4
0
0
0
0
2
3
0
5
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
2
0
2
0
0
0
2
0
0
0
0
1
1
1
0
0
2
0
1
0
1
0
0
0
8
2
0
0
0
0
0
0
1
0
0
0
3
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
2
2
0
0
3
2
0
1
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
2
0
0
0
0
1
2
2
0
0
0
0
0
3
0
0
2
0
2
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
1
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
3
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
5
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
5
0
0
2
0
2
0
0
2
0
3
1
0
0
2
3
0
0
2
2
0
0
0
0
3
0
0
1
1
2
0
0
0
0
0
2
0
0
2
0
2
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
3
2
0
2
1
1
1
1
0
1
2
1
0
0
0
2
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
2
1
2
0
0
0
0
1
2
1
1
0
1
0
0
2
2
1
3
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
2
1
0
2
2
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
3
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
3
2
0
0
0
1
0
0
4
0
4
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
1
2
0
0
0
0
5
0
2
0
0
0
2
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
1
0
2
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
1
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
3
1
2
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
2
0
0
3
1
0
1
0
0
2
1
0
0
0
1
2
1
0
3
0
3
0
0
1
1
0
3
0
3
0
2
1
1
0
0
0
1
0
0
0
0
0
1
2
0
0
0
2
1
2
0
0
0
1
0
2
0
0
0
0
2
0
0
2
0
1
0
0
1
0
2
1
0
0
1
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
3
1
0
0
1
0
1
0
0
2
2
0
0
0
0
1
0
0
1
0
0
0
0
2
2
0
0
0
0
1
0
0
1
0
1
2
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
2
1
0
1
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
2
1
0
1
2
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
2
0
1
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
1
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
3
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
1
0
2
1
0
0
0
0
1
0
0
2
0
0
2
2
0
0
1
1
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
1
2
0
0
2
0
0
0
0
1
0
1
1
0
0
1
1
1
0
0
0
0
0
1
0
2
0
2
1
0
0
2
0
1
0
0
0
1
1
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
2
2
0
0
2
1
1
3
0
0
0
0
2
0
0
2
0
1
0
0
0
0
1
1
0
0
0
2
0
0
1
1
0
0
2
0
0
4
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
1
0
0
1
0
2
2
0
0
0
0
0
1
0
1
0
0
0
0
1
2
1
2
0
0
0
1
0
0
0
0
2
0
0
1
0
1
0
0
2
0
0
0
1
2
0
2
0
0
0
0
1
1
1
0
1
1
0
0
1
0
3
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
2
1
0
0
1
0
0
2
0
2
0
0
2
2
0
2
0
0
2
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
2
0
3
2
0
2
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
2
0
0
2
0
1
2
0
1
1
1
0
0
2
0
0
1
0
0
0
2
2
0
0
0
0
2
2
0
0
0
0
0
0
0
1
3
0
0
1
0
0
0
1
2
0
1
0
1
2
1
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
1
0
0
0
1
0
1
0
0
0
2
0
2
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
1
0
1
0
0
0
2
0
0
0
1
3
0
0
2
3
0
0
0
0
0
0
2
0
0
0
1
1
2
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
2
2
0
0
0
2
2
0
0
3
2
0
0
0
1
0
0
2
1
2
0
0
0
0
0
2
0
0
2
0
0
0
1
1
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
2
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
2
0
0
1
0
1
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
2
0
1
0
0
0
1
0
0
15
0
0
0
0
3
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
3
1
1
0
0
0
2
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
2
0
3
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
3
1
0
0
0
0
1
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
6
0
0
0
0
0
1
0
1
2
0
0
1
0
0
0
0
0
0
2
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
4
0
2
0
0
0
0
0
1
3
2
2
0
0
2
0
0
3
0
0
2
0
0
0
1
1
0
0
0
2
0
1
1
0
0
1
0
0
0
0
2
0
2
0
0
1
0
2
2
0
0
0
2
0
2
0
1
0
1
0
0
0
3
0
0
0
0
1
2
0
2
1
0
2
1
0
0
0
1
0
1
0
0
0
2
1
2
2
0
1
2
0
0
0
0
0
0
0
0
0
2
3
0
0
1
1
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
5
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
1
1
0
0
1
1
0
0
0
1
3
0
1
0
0
1
3
0
0
0
0
2
1
0
1
0
1
2
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
4
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
3
0
0
0
2
0
0
0
0
3
1
0
0
1
0
2
0
1
0
0
1
2
0
2
1
0
0
0
2
1
2
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
2
1
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
1
2
0
0
0
1
0
0
2
3
2
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
2
2
0
0
0
2
1
2
0
1
0
0
0
0
0
2
0
0
0
2
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
3
0
0
2
0
2
0
0
0
0
2
0
0
4
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
1
0
0
0
2
0
0
0
2
0
0
0
2
0
1
1
0
0
0
0
1
0
1
0
2
0
0
0
0
1
0
0
0
1
0
4
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
1
0
1
0
0
1
3
0
0
0
0
2
1
0
0
0
2
1
0
0
1
0
2
2
0
0
0
0
3
0
0
1
0
2
2
0
2
0
0
0
0
0
1
0
2
0
1
1
1
0
0
0
1
2
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
3
1
2
0
0
0
1
2
3
1
0
0
0
1
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
1
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
2
0
0
0
1
0
0
0
0
0
2
1
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
3
1
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
1
1
0
0
0
1
0
2
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
2
1
0
1
0
0
0
2
0
2
0
2
0
3
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
4
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
1
0
1
0
0
0
0
2
0
0
2
2
0
0
0
0
0
1
0
11
1
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
1
2
1
2
0
0
0
2
0
0
1
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
1
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
1
4
2
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
5
0
0
0
1
1
0
0
2
2
0
0
0
0
0
0
1
0
0
1
2
1
2
0
0
2
1
1
1
0
0
0
1
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
2
0
1
0
2
2
0
0
0
0
0
0
2
1
0
1
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
1
0
1
4
0
0
0
0
0
0
0
0
0
2
2
1
0
1
1
1
0
1
3
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
2
0
0
1
0
0
0
1
0
1
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
3
0
2
1
1
1
1
0
1
2
1
1
1
0
0
0
0
0
0
1
2
2
1
2
0
2
0
0
1
0
0
0
0
0
1
2
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
5
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
2
2
0
0
0
0
0
0
2
1
0
0
0
2
0
0
2
1
2
0
0
0
0
2
1
2
0
1
0
0
0
2
0
0
0
1
0
0
1
0
0
3
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
3
1
0
2
0
1
0
0
0
0
2
0
0
1
0
1
2
0
1
3
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
1
2
2
3
2
0
0
0
0
0
1
2
0
2
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
2
2
2
0
0
2
2
0
0
0
0
0
1
1
0
0
1
2
0
0
3
1
0
1
0
2
1
1
0
7
2
0
1
0
2
1
1
0
3
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
2
1
0
2
0
1
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
2
5
0
0
0
0
0
0
0
0
1
0
0
2
0
0
3
0
0
0
0
3
1
0
2
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
2
0
0
1
1
2
1
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
1
0
1
0
1
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
2
1
0
0
0
2
1
0
4
0
0
0
0
2
0
0
0
0
2
1
0
0
1
3
0
0
0
0
0
0
1
0
0
0
2
0
2
0
1
0
0
0
2
2
1
0
0
0
0
1
0
2
0
0
0
0
0
1
0
4
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
2
1
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
2
0
2
2
1
0
2
2
0
1
1
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
1
1
0
0
2
0
1
0
2
0
0
2
0
0
0
0
3
0
1
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
1
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
1
1
0
0
0
3
1
2
3
2
0
1
0
0
0
1
2
0
2
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
2
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
3
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
1
1
1
0
0
0
0
1
0
0
0
2
2
3
4
1
1
2
1
0
3
0
1
0
0
2
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
2
0
0
2
3
2
0
3
0
0
0
0
0
1
0
3
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
1
0
2
0
1
2
0
0
0
0
0
1
0
0
0
0
0
2
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
1
0
1
0
0
0
0
1
1
0
0
0
2
0
0
0
0
2
1
2
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
5
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
2
0
1
0
0
1
2
3
0
2
0
0
0
0
0
1
0
2
0
1
0
0
1
0
0
2
2
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
1
0
0
2
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
4
2
0
0
1
0
0
2
0
0
0
0
0
2
0
0
3
0
0
1
0
0
2
2
0
0
2
0
0
1
2
0
1
0
0
2
0
0
1
0
1
0
2
0
0
1
0
2
2
2
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
4
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
1
2
0
0
1
0
0
0
2
0
1
1
1
0
0
2
0
0
0
0
0
0
0
2
2
0
1
0
0
1
0
1
2
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
2
2
1
2
0
0
2
2
2
1
0
0
0
1
2
1
0
1
1
0
0
0
2
0
1
0
1
2
4
2
1
0
0
0
2
0
0
0
0
0
2
3
0
1
2
0
0
1
1
0
0
0
2
2
1
0
2
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
2
0
0
1
0
1
0
0
1
0
0
2
0
2
2
2
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
2
1
1
2
0
0
0
1
2
0
2
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
1
2
0
1
0
2
0
0
0
0
0
2
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
1
2
1
1
0
0
0
1
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
1
2
2
0
0
1
0
0
2
0
1
2
1
0
0
2
0
2
0
0
0
0
0
0
0
2
0
1
1
0
0
4
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
2
0
1
0
1
0
2
0
0
0
2
2
0
0
0
0
0
0
4
2
0
3
1
0
2
3
1
0
2
0
0
1
0
0
0
3
0
0
0
2
0
2
1
0
2
0
0
0
1
0
0
0
0
0
1
2
0
0
1
1
0
0
0
0
0
0
1
0
2
0
0
2
0
2
0
0
0
1
1
0
2
0
1
0
0
1
0
0
0
2
2
1
1
0
0
0
1
0
4
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
2
0
0
0
0
1
2
2
0
0
0
0
2
0
0
1
0
2
1
0
0
0
1
1
0
0
0
0
2
0
1
0
2
0
0
1
0
0
1
0
0
1
0
2
0
0
2
0
0
1
3
0
1
0
2
0
2
2
0
0
0
0
0
2
0
0
0
0
4
0
2
1
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
2
0
0
0
0
1
0
0
0
0
2
1
1
2
0
0
2
0
2
0
1
1
0
0
0
1
1
0
0
0
0
0
0
1
2
0
0
2
0
0
2
0
2
0
0
0
0
2
0
2
0
0
0
0
0
2
2
0
2
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
1
0
0
3
0
2
0
0
2
1
0
3
0
0
0
2
0
2
0
2
0
0
0
0
0
1
0
0
2
0
0
1
2
0
2
0
0
0
0
0
1
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
2
1
3
2
0
1
0
1
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
2
2
0
0
0
0
0
0
2
0
2
1
2
0
0
1
3
0
0
0
0
0
0
1
0
1
0
5
2
0
0
0
2
1
2
2
0
1
2
0
2
0
0
0
0
0
0
0
0
2
0
0
2
9
0
0
2
0
0
2
1
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
5
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
2
0
0
1
1
0
1
0
0
0
1
6
0
2
0
0
0
0
1
3
0
0
0
2
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
1
3
3
0
1
0
0
2
1
0
0
0
1
0
2
1
0
0
0
0
2
0
1
0
0
2
4
2
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
3
0
1
0
0
1
2
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
1
0
2
0
4
2
0
2
0
2
0
4
0
0
0
0
0
2
0
0
0
0
0
1
1
3
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
2
0
2
0
1
2
2
0
0
1
0
0
0
2
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
1
1
0
2
2
0
2
0
0
1
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
1
0
1
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
2
2
0
0
0
3
0
0
0
0
1
2
0
1
0
2
1
1
0
1
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
2
0
0
1
0
0
2
0
0
1
1
0
0
0
1
2
0
0
0
2
0
1
0
2
1
0
1
0
0
0
0
0
1
0
1
0
1
0
2
1
2
0
2
0
2
0
2
0
0
2
0
0
1
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
2
0
1
1
0
0
2
0
0
1
0
4
0
0
0
0
2
1
0
0
0
0
0
1
1
2
0
1
0
0
0
0
1
0
0
0
1
1
0
0
2
0
2
1
0
0
0
0
2
2
0
5
0
1
0
0
0
2
0
0
1
2
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
2
2
2
2
0
0
0
2
0
0
0
0
1
0
1
1
2
0
1
0
0
0
0
1
3
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
1
0
2
0
1
0
0
0
2
0
0
0
0
1
0
0
1
0
2
0
0
3
0
2
0
0
1
2
0
2
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
6
0
0
0
0
0
0
0
2
0
1
0
0
2
2
0
0
0
2
0
0
0
1
0
0
0
2
0
0
4
1
0
0
1
0
0
1
0
2
0
2
0
0
0
2
1
1
0
0
9
0
0
0
0
1
0
0
2
0
0
0
2
2
0
1
0
0
0
1
3
1
0
0
0
0
0
1
0
1
0
2
0
3
0
0
0
0
0
1
2
4
2
4
1
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
2
1
1
2
1
0
2
0
1
0
0
0
2
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
3
0
0
0
1
1
0
1
0
0
1
2
0
2
2
0
0
0
0
0
0
0
0
1
0
0
5
0
1
0
0
2
0
0
2
0
0
1
0
0
0
2
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
2
0
0
0
0
2
2
0
0
2
0
1
1
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
1
2
0
0
0
2
0
1
0
1
0
0
0
2
2
2
1
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
3
0
0
2
2
1
2
2
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
2
0
1
0
2
2
0
1
2
0
0
2
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
2
0
2
2
2
1
1
0
0
0
0
0
0
2
2
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
1
0
1
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
1
0
0
0
2
1
2
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
3
3
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
1
0
2
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
1
0
0
0
2
3
0
2
1
0
0
1
0
1
0
1
0
4
1
0
1
0
0
1
0
2
0
2
0
0
0
0
2
2
0
0
1
0
2
0
2
0
2
1
0
1
1
0
0
0
0
0
1
2
0
1
0
0
0
0
3
0
0
0
1
0
0
2
0
0
2
2
0
2
0
0
0
2
0
0
0
0
1
0
0
0
2
1
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
2
0
0
0
0
0
0
2
0
0
5
0
0
0
2
0
2
1
0
4
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
1
0
0
0
0
2
0
1
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
1
1
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
1
0
0
3
0
0
0
0
0
2
1
0
2
1
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
2
0
2
4
2
0
0
0
1
2
0
1
0
0
0
0
1
2
0
1
2
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
1
2
0
0
0
0
0
2
2
1
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
2
0
0
1
0
2
2
0
0
2
2
3
0
0
1
0
2
0
2
2
1
2
0
0
0
1
0
0
0
0
2
0
2
1
1
0
0
0
0
0
0
1
2
0
1
1
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
2
0
1
0
0
1
0
1
0
1
0
0
2
0
0
0
0
2
0
0
2
2
2
1
2
0
0
0
0
2
0
2
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
2
3
0
2
0
2
0
0
2
1
1
0
1
0
1
2
2
0
2
1
2
0
0
0
3
1
0
1
0
0
0
0
0
0
0
2
1
1
0
0
3
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
2
2
0
1
0
0
0
0
0
0
0
2
0
2
0
0
6
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
2
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
2
3
0
0
1
0
1
1
0
2
2
0
0
1
0
0
0
0
3
1
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
2
0
0
1
2
0
0
2
0
0
2
0
0
2
0
1
5
1
0
0
0
2
1
0
0
0
1
0
2
0
0
4
0
1
0
0
0
2
0
2
0
0
2
1
0
2
0
0
3
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
2
0
0
0
2
0
0
0
1
0
3
0
0
1
0
0
0
1
3
0
2
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
1
0
2
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
2
1
0
2
0
0
0
2
0
1
0
1
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
1
0
1
0
0
2
0
0
0
0
1
0
1
1
2
0
2
2
1
1
1
3
1
0
0
2
3
2
0
0
1
0
0
0
0
0
0
2
0
0
1
0
2
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
2
1
0
0
0
0
1
0
2
0
3
1
0
1
0
0
1
1
1
0
0
2
0
0
0
3
0
1
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
1
0
0
1
0
1
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
2
0
0
1
0
0
0
1
0
0
2
0
0
2
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
2
0
0
2
2
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
2
2
0
1
0
0
0
0
2
1
0
0
0
1
0
0
0
0
2
2
0
2
2
0
3
0
0
0
2
1
0
0
2
0
0
0
1
0
0
0
0
0
0
1
2
1
1
0
0
1
0
2
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
2
0
1
0
0
1
2
0
0
0
0
0
1
0
0
3
1
2
0
0
2
0
0
2
0
0
2
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
2
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
1
0
0
0
2
0
2
0
2
1
2
2
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
1
2
1
0
1
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
1
0
2
2
1
0
0
0
0
0
0
2
1
0
0
0
2
1
2
0
1
0
1
0
0
2
1
1
0
0
1
0
2
0
0
1
0
2
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
2
0
0
2
0
0
2
0
2
0
2
1
1
0
1
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
3
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
3
1
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
2
0
0
2
1
2
1
0
3
0
0
0
1
0
0
4
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
1
1
0
1
1
1
3
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
1
0
1
0
0
0
1
1
2
0
0
1
1
0
0
2
0
0
4
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
1
0
0
0
1
2
0
0
2
0
0
1
0
0
1
0
0
1
0
0
0
1
0
1
1
2
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
2
0
0
0
2
0
2
2
1
0
0
1
0
1
0
0
0
2
0
2
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
1
2
0
0
0
1
3
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
2
0
1
1
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
1
0
0
2
0
0
2
0
0
1
0
1
0
1
0
0
0
2
0
0
0
2
0
0
2
1
2
0
1
2
0
0
1
0
0
0
2
0
0
0
0
1
1
0
0
0
2
0
0
2
0
0
0
0
2
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
2
3
0
0
0
2
0
0
2
1
0
1
0
0
0
2
0
0
1
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
1
1
0
0
2
0
1
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
2
1
1
2
1
1
1
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
2
0
2
1
0
0
1
0
2
0
0
1
2
0
0
0
0
0
0
1
2
2
2
0
0
1
2
0
1
1
0
0
0
0
0
0
0
0
2
2
2
1
0
1
0
1
2
0
2
0
2
0
2
2
0
0
0
1
2
1
0
1
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
2
1
0
2
1
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
1
0
0
2
1
1
0
3
0
0
2
0
2
0
0
2
0
1
1
0
0
0
2
0
0
1
0
0
2
0
0
0
0
3
0
0
0
0
2
0
0
1
0
1
0
2
0
0
0
0
1
0
1
2
1
0
2
1
1
0
0
0
0
1
0
0
2
0
2
0
0
1
0
2
0
1
0
0
1
0
1
1
0
0
1
2
3
0
1
0
0
0
0
1
0
0
2
0
0
0
0
1
1
4
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
2
3
0
0
0
1
0
1
1
2
2
0
0
0
2
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
2
0
0
1
1
2
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
1
2
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
1
0
3
0
0
0
0
1
0
1
0
2
0
0
1
3
2
1
1
1
0
0
0
2
0
0
0
0
1
0
0
0
1
0
1
0
2
0
2
0
0
0
1
0
0
2
1
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
1
0
0
1
1
1
1
2
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
2
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
1
1
2
0
0
0
2
0
2
7
1
0
0
0
0
1
0
0
4
2
1
0
0
2
0
0
0
0
0
1
0
0
2
2
2
1
0
4
0
0
0
0
0
2
1
0
0
0
1
0
0
1
6
0
0
2
0
0
2
0
1
3
3
2
0
0
0
2
2
0
1
0
1
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
1
0
1
5
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
3
2
0
0
0
2
0
2
1
1
0
1
0
2
0
0
0
0
2
1
1
2
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
1
1
0
2
0
6
0
0
1
0
2
2
1
1
0
0
0
1
0
3
1
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
2
0
2
0
2
2
2
0
0
1
13
0
2
0
2
0
1
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
4
0
2
0
1
0
0
0
0
2
0
2
0
0
1
2
0
2
0
2
0
0
1
0
0
1
2
2
0
0
0
2
1
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
2
0
0
2
0
0
0
1
0
0
2
0
0
0
0
1
0
0
3
0
0
1
0
0
0
0
0
0
0
2
2
1
0
0
3
1
2
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
2
1
0
0
0
1
1
0
2
1
0
0
0
0
1
3
0
0
0
0
0
0
0
1
1
0
5
0
0
0
4
3
0
0
2
0
1
1
0
0
1
2
1
0
0
0
0
1
2
0
0
2
0
0
2
0
0
1
0
2
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
1
1
1
2
2
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
1
2
0
2
0
0
0
2
1
0
1
1
1
0
2
0
1
1
1
0
0
0
3
0
3
1
0
0
2
0
0
0
0
0
2
1
0
1
0
0
2
0
0
0
0
2
0
2
0
0
0
2
2
0
0
0
4
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
1
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
1
0
1
1
0
2
3
0
0
0
0
0
1
0
0
0
0
0
1
1
0
2
3
1
2
1
0
0
0
2
1
2
0
0
2
1
0
0
0
1
1
3
0
0
2
1
2
2
0
2
0
2
2
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
2
1
0
2
2
0
0
2
2
1
2
0
0
1
0
0
1
0
0
3
0
0
0
0
2
1
0
1
0
0
3
1
0
0
0
0
0
0
1
0
1
2
0
0
1
2
0
0
0
1
2
0
2
0
0
0
2
0
1
2
0
0
2
0
1
0
0
0
0
2
2
0
2
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
2
0
0
2
0
0
1
2
1
0
0
0
1
0
0
2
0
0
0
2
2
0
3
1
0
1
1
0
0
2
2
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
2
0
0
1
0
0
0
0
0
2
0
0
0
2
1
0
0
1
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
2
1
1
0
0
0
1
0
2
0
2
0
1
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
2
2
0
2
1
0
2
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
2
0
1
0
2
0
0
0
0
1
1
3
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
3
3
0
0
0
1
2
0
0
1
0
1
0
2
1
1
0
2
0
0
0
0
0
1
0
2
0
1
3
0
0
0
0
0
0
2
0
2
1
0
0
0
2
0
1
2
0
2
0
0
0
2
0
1
0
2
0
0
2
0
2
2
1
0
0
0
0
1
0
0
1
0
0
2
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
1
1
0
2
0
2
3
1
0
0
1
2
0
2
2
0
2
0
1
2
2
0
0
0
0
2
0
0
0
0
0
1
2
1
0
0
0
1
1
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
1
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
1
0
0
1
1
0
2
2
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
3
0
0
1
2
0
0
1
4
5
0
2
0
2
0
0
0
1
2
0
0
0
2
0
3
2
4
0
2
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
2
2
0
1
0
1
2
0
0
0
0
1
0
1
0
0
1
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
1
2
1
2
1
0
2
1
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
2
1
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
1
0
0
0
0
3
2
0
1
0
0
2
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
2
0
0
2
0
0
0
0
1
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
2
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
2
0
1
2
0
0
1
0
0
0
0
2
1
0
0
1
2
1
0
2
1
1
0
0
0
2
1
0
0
0
2
0
0
2
0
0
0
0
1
2
4
1
0
0
0
2
0
0
0
1
0
1
0
0
1
2
0
0
0
2
1
1
1
0
2
0
0
0
0
2
0
0
0
0
1
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
2
2
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
1
1
0
0
4
0
2
0
1
0
0
1
1
1
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
1
0
1
0
1
0
2
0
0
0
1
0
0
1
0
0
0
2
0
1
0
0
2
2
0
0
1
0
0
0
2
0
2
2
0
0
2
0
0
0
2
0
0
0
0
0
1
0
1
1
0
0
0
0
0
3
0
1
1
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
2
2
0
0
0
0
2
1
0
0
0
0
0
0
1
2
0
2
0
0
0
0
2
1
0
2
2
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
1
0
2
2
0
2
0
0
0
1
1
2
0
0
1
3
2
1
0
0
2
0
1
0
0
2
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
4
1
0
0
0
0
2
2
1
0
0
1
0
0
0
0
0
2
2
0
0
1
2
0
0
1
0
2
2
0
0
2
0
0
2
0
0
2
0
0
0
0
2
0
2
0
2
2
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
2
1
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
1
2
2
0
0
0
0
0
0
0
1
0
0
2
2
0
0
2
1
2
0
2
1
2
1
0
3
0
0
2
1
0
0
0
1
2
0
0
0
0
1
0
0
0
1
0
0
0
0
2
1
0
1
0
0
0
0
0
1
0
0
0
2
0
0
1
0
2
0
0
2
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
2
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
1
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
2
1
0
1
0
3
0
0
0
1
2
0
1
2
0
0
0
2
0
1
2
0
0
0
1
0
1
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
2
0
0
4
3
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
4
1
1
0
1
0
0
6
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
1
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
2
2
0
0
0
0
1
2
1
0
0
0
0
0
0
0
2
0
2
1
0
0
2
1
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
2
0
1
2
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
1
0
2
2
2
2
1
1
0
2
0
0
0
1
0
1
0
0
0
2
0
0
0
0
1
1
0
2
2
0
2
0
0
0
1
2
0
0
0
0
0
0
2
0
2
0
0
0
0
2
1
0
3
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
1
1
0
1
2
0
0
0
0
1
0
2
0
1
1
0
0
0
1
2
0
0
2
1
0
0
1
0
0
0
0
2
1
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
2
0
2
0
0
1
0
2
0
1
1
0
0
1
0
3
6
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
2
0
2
0
0
2
0
1
0
0
0
1
2
0
1
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
1
2
1
0
2
0
0
2
0
0
0
2
1
0
1
0
0
0
1
1
0
1
0
2
0
0
0
0
1
2
2
2
0
2
1
0
1
0
1
2
0
0
0
1
0
2
2
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
1
1
0
0
1
0
1
0
1
1
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
1
0
0
1
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
1
0
0
1
0
0
2
0
0
0
2
1
2
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
2
2
0
1
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
3
0
1
0
2
0
0
0
2
0
2
2
1
0
0
3
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
2
0
1
0
0
0
2
0
0
0
2
0
2
1
2
0
2
0
0
2
2
1
1
2
0
0
0
0
2
2
0
0
0
1
1
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
1
0
0
0
1
0
1
2
0
0
0
2
0
1
0
0
0
1
0
2
1
0
0
0
1
0
1
0
2
0
0
0
0
1
0
0
0
0
2
0
0
2
1
1
0
1
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
2
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
1
0
0
0
2
0
2
2
0
1
0
0
0
2
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
1
1
1
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
2
1
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
1
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
2
1
0
0
1
2
2
1
1
1
2
2
0
2
0
0
0
2
1
0
0
3
0
2
0
2
0
0
2
0
0
1
0
0
1
2
2
0
0
0
1
0
0
2
0
0
0
0
0
2
2
0
3
0
0
0
0
0
0
0
1
2
0
0
0
0
1
1
2
1
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
1
1
2
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
2
0
0
0
2
0
0
1
4
2
0
0
0
1
0
0
1
0
5
1
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
2
1
0
0
0
0
0
0
2
1
4
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
2
2
0
0
2
0
0
0
0
3
0
1
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
2
0
0
0
6
0
2
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
1
1
0
0
2
0
0
1
0
2
0
0
0
1
1
0
0
0
2
0
1
0
0
0
0
1
0
0
0
1
2
0
0
1
0
1
0
0
0
0
0
0
0
2
0
2
1
0
1
0
0
2
1
0
0
1
0
0
0
1
1
0
0
0
2
0
0
0
2
1
0
0
0
0
2
0
2
2
2
2
0
0
1
0
0
1
1
2
0
0
2
2
1
0
0
0
0
0
2
2
2
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
2
1
0
3
2
0
0
2
0
1
0
0
2
0
0
0
0
3
1
1
2
0
2
2
1
1
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
2
2
2
0
0
0
0
0
0
3
1
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
4
0
0
0
0
2
2
2
0
0
0
0
1
0
1
0
0
2
2
0
0
1
1
0
2
2
0
1
0
2
0
0
0
0
0
0
1
1
2
0
2
1
0
0
0
1
1
0
0
0
1
0
0
2
0
0
1
0
1
0
1
0
0
0
0
3
0
0
2
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
2
4
0
0
0
0
0
0
3
0
0
1
1
0
0
0
0
2
2
0
1
2
0
0
0
1
0
0
0
0
1
0
2
2
0
1
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
1
1
2
6
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
2
1
5
0
2
1
0
0
0
1
0
0
0
0
1
0
1
2
0
1
0
0
2
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
1
2
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
1
0
2
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
2
1
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
2
2
3
0
0
1
0
1
0
4
3
0
1
0
0
1
2
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
1
2
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
3
1
0
0
1
1
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
2
0
2
1
0
0
1
0
0
2
1
0
0
2
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
4
1
0
0
2
1
0
0
0
0
1
2
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
2
0
0
3
2
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
2
0
0
0
1
0
0
2
0
0
2
0
1
1
0
0
2
0
0
1
1
2
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
2
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
2
1
0
1
1
0
2
0
2
2
0
0
0
0
0
1
2
0
5
0
0
1
0
1
2
0
0
2
2
2
1
0
0
1
0
1
0
0
0
0
2
0
2
0
2
2
0
1
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
1
1
2
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
1
1
1
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
3
0
2
1
0
0
0
0
0
1
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
1
0
2
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
4
1
0
1
0
0
1
0
1
0
0
2
0
0
0
2
2
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
2
0
1
1
2
0
0
0
0
0
2
0
2
0
1
0
0
2
0
2
2
0
0
0
0
3
5
1
1
1
0
0
0
0
0
0
0
1
2
0
0
1
0
0
1
0
1
1
2
0
1
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
1
0
0
1
2
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
1
2
0
0
1
0
1
0
3
0
0
1
0
0
2
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
2
0
3
2
0
1
1
0
3
0
0
0
0
0
0
1
1
0
3
0
7
2
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
1
1
2
0
0
1
0
0
0
0
2
2
0
2
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
1
4
0
0
0
1
0
4
1
0
0
0
0
0
0
0
1
1
0
0
0
2
0
1
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
3
2
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
1
2
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
1
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
1
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
2
0
2
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
1
0
2
2
0
1
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
2
2
0
0
2
0
1
1
1
0
0
0
0
0
2
0
1
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
1
2
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
1
0
0
2
0
0
2
0
0
2
0
0
0
1
0
1
0
2
0
0
0
1
0
1
2
0
0
0
2
1
0
0
0
0
1
0
0
0
0
1
7
0
0
0
0
2
0
0
0
1
0
2
0
0
0
2
0
1
0
0
0
1
0
0
0
0
1
0
0
0
2
2
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
2
0
1
0
0
0
2
0
0
1
1
0
0
0
2
2
2
0
0
3
0
1
0
4
0
0
1
0
0
0
0
0
0
0
0
3
1
1
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
3
0
2
1
2
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
3
0
0
1
0
0
0
1
1
0
0
2
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
2
0
2
1
2
1
0
0
0
0
0
5
2
0
2
0
0
0
1
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
2
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
2
2
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
2
0
0
0
0
3
0
0
0
0
0
2
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
4
0
0
0
0
0
1
0
1
0
1
0
6
1
1
0
3
1
1
0
0
0
1
0
0
1
0
1
1
0
0
0
2
0
2
2
1
0
1
0
0
0
0
0
0
0
0
1
0
2
2
1
0
0
0
0
0
0
2
0
0
0
1
0
1
0
1
0
1
0
1
2
0
0
1
2
0
0
0
0
0
0
0
2
1
1
0
2
0
2
0
0
0
1
2
2
0
0
0
0
0
0
0
2
1
2
2
0
0
4
0
0
1
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
1
1
0
0
0
4
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
7
1
0
1
0
0
0
0
0
11
2
1
0
0
0
0
0
0
0
1
0
0
0
3
7
1
0
0
0
0
0
2
0
0
1
1
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
2
2
0
0
2
0
0
0
0
2
2
0
2
1
0
0
2
1
0
2
0
2
2
2
0
0
0
0
2
0
2
0
0
2
0
2
0
1
0
0
2
0
1
2
0
0
1
1
3
1
1
0
1
0
0
0
1
0
0
0
0
2
0
2
0
2
1
1
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
2
1
0
0
2
0
1
0
0
0
1
0
0
1
0
1
0
1
1
2
0
0
2
0
2
2
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
1
2
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
1
2
0
2
2
0
0
0
0
1
0
0
1
0
2
2
0
0
0
1
0
0
1
3
0
0
0
0
0
0
1
0
0
0
1
0
0
2
2
0
0
0
0
0
0
1
0
0
0
1
2
0
1
1
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
3
0
0
2
0
2
0
0
0
1
0
2
1
0
2
0
0
1
2
0
0
2
0
2
2
1
1
2
0
0
0
0
0
2
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
2
0
0
1
0
0
1
2
0
0
0
1
1
0
2
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
2
0
1
0
3
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
3
0
0
0
1
0
0
1
0
1
0
0
1
0
0
2
0
0
1
1
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
1
0
2
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
1
0
1
2
0
0
1
2
0
3
0
0
0
2
0
1
0
0
0
3
0
0
0
0
2
0
0
0
0
0
2
2
0
0
1
1
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
1
0
2
0
2
0
0
0
2
0
2
1
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
2
2
1
2
0
0
0
0
1
1
1
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
1
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
2
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
3
2
2
0
0
1
0
2
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
2
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
1
0
0
0
5
0
0
0
0
0
2
2
0
0
0
2
2
1
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
6
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
4
4
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
2
0
1
0
0
2
0
0
2
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
1
2
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
2
3
0
1
1
0
0
0
1
1
0
2
2
0
0
2
0
0
2
0
2
1
2
2
1
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
4
1
1
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
1
2
2
0
0
0
0
1
0
0
2
0
2
0
1
0
0
0
4
0
0
1
0
0
0
1
2
0
2
0
1
1
0
2
2
0
0
0
1
0
2
0
0
1
0
1
0
0
1
0
0
0
0
4
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
2
0
1
2
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
1
1
0
0
2
0
0
0
0
0
0
1
1
0
0
0
1
2
0
0
3
1
1
0
0
0
1
2
0
0
2
1
0
0
3
2
0
0
0
2
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
2
0
0
2
5
0
0
2
0
0
1
0
1
2
0
0
0
1
0
0
2
0
2
2
0
0
1
1
0
0
0
0
0
0
1
0
0
0
3
2
0
2
2
0
1
0
0
0
2
1
0
0
0
2
0
2
0
2
0
0
1
1
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
2
2
0
0
0
0
1
1
0
0
1
1
4
1
3
0
0
0
0
0
1
0
0
2
0
0
1
2
0
0
0
0
2
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
1
0
2
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
1
0
0
1
1
1
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
4
0
0
0
0
3
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
2
0
0
0
4
0
0
0
0
2
2
3
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
2
1
0
1
0
0
0
2
0
2
0
1
0
1
0
1
0
0
0
0
0
2
1
0
2
0
0
0
0
0
1
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
2
0
1
0
0
0
1
0
0
1
0
0
0
2
1
3
0
0
0
0
0
0
2
0
0
0
2
2
2
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
2
0
0
1
0
0
0
2
2
1
2
0
0
1
0
0
2
1
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
2
0
4
1
2
0
1
0
0
0
1
0
0
4
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
3
1
2
1
0
1
0
1
2
0
1
0
1
0
0
1
0
0
0
1
0
0
2
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
1
2
0
1
0
0
1
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
6
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
2
0
1
0
2
1
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
1
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
1
1
1
1
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
2
0
0
0
0
0
1
0
0
1
0
2
0
1
0
0
1
1
3
0
1
0
0
2
0
2
1
0
1
3
0
1
0
2
1
0
0
1
1
1
1
0
0
0
1
0
0
0
0
1
1
0
3
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
5
2
0
1
0
0
7
0
2
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
3
1
0
0
1
0
0
1
0
0
0
0
2
1
0
0
0
4
2
1
0
0
0
0
0
0
0
0
0
1
0
0
8
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
2
0
0
0
0
2
2
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
3
1
0
2
0
2
0
2
3
0
2
2
2
3
0
0
1
2
2
0
0
0
0
2
0
1
2
0
1
2
0
0
0
0
2
0
1
2
1
1
0
0
1
0
0
0
0
2
0
0
0
1
0
0
2
1
0
0
0
0
1
2
1
0
1
0
3
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
1
1
1
0
0
1
0
1
0
0
0
0
3
0
0
1
0
2
0
1
3
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
2
0
0
0
0
2
2
1
0
0
0
0
2
0
0
0
0
0
1
1
0
1
0
0
0
0
2
2
0
1
0
0
0
0
0
0
1
1
0
1
0
0
6
0
0
4
0
2
0
0
0
0
2
0
1
0
0
1
1
0
0
2
0
2
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
1
0
0
1
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
1
2
0
0
0
0
0
0
0
1
2
1
0
0
2
1
0
2
2
0
1
0
0
2
2
0
2
1
1
2
0
1
2
0
0
0
0
0
0
0
1
0
0
2
0
1
2
2
0
2
0
0
0
0
0
2
2
0
0
2
1
0
1
2
1
0
0
2
2
0
0
2
0
0
0
2
1
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
1
0
0
0
2
0
0
2
4
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
4
2
2
0
0
1
0
2
0
0
0
1
0
2
0
0
0
0
3
1
0
0
0
2
0
2
0
1
1
0
1
1
0
0
0
2
0
0
2
2
0
0
1
2
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
3
3
0
0
2
0
0
0
1
0
0
2
3
0
1
0
1
1
2
2
0
0
2
0
0
0
1
0
2
1
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
1
0
0
0
1
0
0
0
0
0
0
1
3
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
2
0
4
0
0
0
0
0
2
0
0
0
0
0
1
1
0
1
0
3
0
2
2
0
1
0
3
3
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
2
4
2
1
1
0
0
0
0
0
0
2
1
0
2
0
0
0
0
2
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
3
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
3
0
0
0
0
1
0
0
1
0
1
0
2
2
2
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
2
1
0
0
1
0
1
0
0
1
1
0
1
2
0
0
0
0
1
0
0
0
0
1
0
1
0
0
3
2
2
0
0
0
0
0
0
2
1
0
1
1
2
0
0
0
0
2
0
0
0
0
0
2
1
2
3
0
2
1
0
0
0
4
2
1
0
0
0
0
0
1
3
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
2
1
0
2
3
0
1
4
0
6
0
0
2
0
1
0
0
1
0
4
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
1
2
0
0
2
0
2
2
0
4
1
0
0
1
0
2
0
0
1
1
0
1
1
2
1
1
0
0
0
2
1
0
0
0
1
1
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
4
0
0
1
0
0
2
0
0
0
0
1
2
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
1
0
0
1
0
0
1
0
0
1
0
1
0
0
0
1
0
0
1
0
2
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
2
2
0
0
0
1
1
0
1
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
1
2
2
2
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
2
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
1
1
2
0
1
1
0
0
0
2
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
3
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
2
1
1
0
3
0
0
0
2
0
0
0
2
2
0
2
0
0
0
0
1
2
0
1
2
0
0
0
0
1
0
3
1
3
0
1
0
0
2
0
0
2
0
2
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
2
1
3
0
0
0
2
2
0
0
0
0
0
0
1
1
2
0
1
1
1
0
1
0
0
0
0
0
1
0
0
0
2
2
0
0
1
2
0
1
0
0
0
0
1
0
0
1
1
0
0
2
0
0
2
1
0
0
2
0
2
0
1
0
2
2
1
2
0
0
0
2
0
0
0
0
0
2
0
2
1
0
1
0
2
1
2
0
0
2
0
0
0
0
2
0
0
1
2
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
2
0
2
0
2
2
0
0
0
0
1
1
0
1
3
1
0
0
1
0
2
0
2
0
0
0
0
3
0
1
0
2
2
0
2
1
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
3
2
1
2
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
2
0
2
0
0
0
3
0
0
0
0
0
0
2
0
0
0
2
0
2
0
1
0
1
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
1
1
0
0
0
0
2
0
2
2
0
1
0
1
0
1
0
0
0
1
2
0
0
0
0
0
0
0
2
0
2
1
1
2
1
1
0
0
0
0
1
0
1
0
0
0
0
3
2
0
1
1
0
2
2
0
0
2
0
0
0
7
0
0
0
1
2
0
0
2
1
1
1
0
0
0
0
0
2
0
0
0
0
0
4
0
1
0
0
0
0
3
0
0
1
0
0
0
1
0
1
0
0
0
2
0
0
0
0
2
0
2
0
2
0
2
0
0
0
0
4
4
0
0
2
0
0
0
0
1
0
1
0
0
2
0
0
2
2
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
2
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
3
0
1
1
0
1
0
1
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
1
0
1
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
1
0
1
0
1
2
2
0
1
1
1
0
1
1
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
2
1
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
2
1
0
2
2
1
0
0
0
0
1
0
0
1
2
1
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
4
0
3
4
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
4
2
0
0
2
2
0
1
1
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
1
0
0
0
0
2
0
1
2
0
0
2
1
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
2
0
1
1
0
0
0
2
0
2
0
1
0
0
1
0
0
0
0
2
1
0
2
1
0
2
0
0
0
0
1
0
0
0
2
1
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
2
0
0
1
1
1
0
0
0
1
0
0
1
0
1
0
3
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
1
0
1
0
0
1
0
0
1
0
0
2
0
1
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
3
3
2
0
0
2
2
3
0
0
2
0
0
0
1
2
1
1
0
2
0
0
1
0
0
2
0
0
0
1
2
1
0
0
1
1
0
0
0
0
0
0
2
0
0
2
1
1
0
1
0
2
0
1
0
0
1
0
0
0
0
0
4
2
0
2
1
2
1
0
0
2
0
2
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
1
2
0
2
0
0
1
0
1
1
0
0
0
0
1
2
0
0
1
0
2
0
0
0
0
0
0
0
0
1
2
0
2
2
0
0
0
0
1
0
0
2
0
0
0
1
0
1
2
0
1
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
3
0
0
0
0
0
0
2
0
0
2
0
1
2
0
0
0
0
0
2
0
3
1
0
0
0
0
2
0
1
0
0
0
0
2
1
0
0
2
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
1
0
0
2
0
0
2
0
1
1
0
2
0
1
0
1
0
2
0
1
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
1
2
1
1
1
0
1
0
0
2
0
0
0
1
1
2
0
0
0
0
0
0
0
2
1
1
1
0
2
1
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
2
2
0
1
0
0
0
0
1
0
1
1
0
2
0
2
0
2
0
0
0
0
0
0
2
2
0
1
0
0
1
1
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
2
2
1
3
0
0
1
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
1
0
1
0
0
1
0
2
0
0
0
0
1
1
0
1
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
1
1
0
2
0
0
0
1
0
1
0
0
0
0
1
0
0
2
1
0
0
0
1
0
0
1
0
0
2
2
0
0
0
2
1
1
0
0
0
0
0
3
0
0
0
1
2
0
2
0
0
0
1
1
0
2
0
1
0
0
2
0
1
0
0
0
0
1
2
0
0
2
0
1
0
0
0
1
0
1
1
2
1
0
0
2
0
0
1
2
1
0
2
0
1
1
0
0
0
0
0
3
0
0
1
2
0
0
1
2
0
1
0
0
1
2
0
0
3
1
0
1
0
2
0
2
0
2
0
1
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
2
0
2
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
1
0
2
0
2
2
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
2
3
2
0
1
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
2
1
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
1
0
1
0
1
1
0
0
0
0
1
2
0
1
3
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
2
1
1
0
2
0
2
0
0
1
1
0
3
1
0
2
1
2
2
0
0
0
1
0
0
1
0
2
2
0
0
1
0
3
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
3
0
2
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
2
0
0
0
0
2
0
1
1
0
3
0
0
0
2
2
0
0
0
0
0
0
0
1
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
1
0
0
0
0
0
0
0
1
2
5
2
2
2
1
0
0
0
0
1
0
0
0
0
0
1
2
8
0
1
0
0
0
0
1
0
0
1
0
0
2
1
0
0
1
0
0
0
0
2
0
2
1
0
0
0
1
2
0
5
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
1
0
0
0
2
1
1
2
0
2
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
1
0
0
2
2
0
0
0
3
0
1
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
2
0
0
0
0
0
2
1
0
0
0
2
0
2
1
0
0
2
0
0
2
0
0
0
0
2
0
1
0
0
0
1
0
2
0
0
0
0
0
0
1
0
2
0
0
0
2
2
0
0
11
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
2
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
2
2
0
0
0
0
1
1
0
0
1
0
0
1
1
0
1
0
0
0
0
3
0
0
0
0
0
4
0
4
0
0
1
1
1
0
1
1
1
0
0
0
1
0
0
0
2
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
2
2
1
0
0
1
0
0
2
0
1
0
0
0
0
0
0
2
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
1
2
2
1
0
2
0
1
1
1
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
1
1
1
1
0
0
0
0
1
0
1
1
1
1
0
0
0
0
0
2
0
0
0
1
0
0
2
1
0
0
0
2
1
0
0
2
0
2
0
1
2
0
0
0
2
2
0
1
2
0
1
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
3
1
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
2
0
2
0
0
0
1
1
0
0
0
1
0
0
1
1
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
1
0
0
1
0
0
0
0
0
0
2
0
0
1
3
1
0
2
1
0
0
0
1
0
0
0
2
0
3
0
2
2
0
0
0
0
2
0
0
0
1
2
0
0
0
3
0
1
1
0
0
0
2
0
0
0
0
1
0
0
0
1
1
1
0
0
0
2
2
0
2
1
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
1
0
0
1
0
1
1
0
3
1
0
0
0
0
0
2
0
0
0
0
0
2
0
1
2
0
0
1
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
2
0
0
0
0
1
0
0
3
0
2
1
2
0
0
0
0
2
0
0
0
1
2
0
0
1
2
0
1
1
2
0
2
0
1
0
2
0
2
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
2
0
0
1
3
1
1
0
1
0
0
1
0
0
3
0
2
0
0
0
3
0
3
1
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
2
0
2
0
0
4
1
0
0
0
0
0
0
1
0
2
0
4
3
0
0
2
1
0
4
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
1
6
0
0
0
0
1
0
1
2
5
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
1
2
0
0
0
2
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
4
2
2
0
0
1
0
2
0
0
1
2
2
0
1
0
0
0
0
0
0
2
0
2
0
0
1
0
1
2
2
0
0
2
0
1
0
1
0
1
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
1
2
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
2
3
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
1
2
0
1
0
0
0
1
1
0
0
0
0
1
1
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
1
0
1
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
5
0
0
1
1
0
1
0
0
0
0
2
2
1
1
0
0
0
1
2
0
2
2
0
1
1
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
2
1
4
0
0
0
0
0
1
1
0
1
2
0
0
0
0
0
0
0
0
1
0
2
0
1
2
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
2
0
1
1
1
0
2
1
0
0
0
1
2
0
0
3
0
0
0
1
0
0
0
2
0
0
1
0
0
1
1
3
0
0
4
0
2
1
0
0
0
0
2
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
2
0
2
1
1
1
1
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
2
3
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
1
1
0
4
0
0
0
0
0
2
1
0
1
0
1
0
1
0
1
0
0
0
0
0
1
4
0
0
1
1
0
0
2
0
2
3
1
0
1
1
1
0
1
0
0
0
0
3
0
0
0
0
0
0
0
2
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
4
2
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
3
0
0
0
1
0
1
0
0
0
1
0
0
1
5
0
0
2
0
0
0
0
2
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
3
2
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
2
3
1
0
1
0
2
0
0
0
1
2
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
2
0
2
1
0
2
0
0
2
0
0
0
0
0
3
0
0
0
0
1
0
2
0
2
1
0
0
0
2
0
0
0
0
2
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
2
0
2
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
1
2
1
2
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
2
1
0
0
0
1
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
1
0
0
2
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
1
3
2
0
0
0
0
0
1
1
1
0
0
0
3
0
0
0
0
8
0
2
0
1
0
1
1
0
0
1
2
0
0
0
1
1
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
2
0
2
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
3
0
0
0
0
4
1
0
0
0
1
0
0
0
0
0
0
0
4
0
0
2
0
0
0
1
2
0
0
1
0
0
0
1
0
1
0
2
0
0
1
2
0
0
0
2
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
1
0
0
2
0
0
0
2
1
2
0
0
0
1
0
0
0
1
2
0
1
2
0
1
2
0
2
3
0
0
0
0
0
1
0
2
1
1
0
2
0
0
2
2
0
0
3
2
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
2
0
1
0
0
1
0
1
0
0
0
1
2
1
0
4
0
0
0
0
0
0
1
0
0
1
1
0
2
1
1
1
0
0
2
0
1
0
0
0
1
0
0
0
0
1
1
0
2
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
2
0
2
2
0
1
0
0
0
0
0
0
1
0
2
0
0
1
2
0
0
1
1
2
0
1
0
0
1
2
1
2
1
0
0
0
2
1
0
2
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
5
0
0
0
0
1
0
3
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
1
2
0
0
0
1
0
3
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
3
1
2
2
0
0
0
4
0
1
2
2
2
1
2
0
2
0
0
2
2
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
1
0
0
0
3
0
0
0
0
2
1
2
0
0
0
0
2
1
0
2
1
0
1
0
1
2
0
0
1
0
0
0
2
0
1
0
0
1
1
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
6
2
0
0
0
0
0
3
2
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
3
0
0
0
0
2
4
0
0
1
0
0
0
0
2
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
1
2
2
0
0
2
0
0
0
2
2
0
2
0
0
0
0
0
1
1
0
1
0
0
0
0
2
2
5
1
0
0
1
0
2
2
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
1
0
2
0
1
2
0
2
2
1
0
0
0
2
0
0
0
0
1
0
0
2
0
0
1
2
0
2
1
2
1
0
0
0
2
2
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
2
0
2
2
0
0
1
0
0
0
2
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
2
1
1
2
0
0
1
0
0
2
0
1
0
0
0
2
4
0
1
0
0
2
0
2
0
1
2
1
0
2
0
0
1
1
0
1
0
0
2
1
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
1
0
2
2
1
0
0
0
0
0
0
0
2
1
0
0
1
0
1
0
0
0
1
0
0
1
0
2
0
0
2
0
0
0
1
0
0
2
0
0
1
0
1
0
2
1
0
2
0
1
1
2
1
0
2
2
0
2
0
0
0
0
0
0
0
1
2
2
0
1
0
0
1
1
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
3
0
1
0
2
1
0
2
2
0
2
1
2
0
0
2
1
0
1
0
0
0
0
0
0
0
2
0
2
0
2
1
0
0
2
0
0
0
0
1
2
0
0
1
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
10
1
2
0
0
0
0
0
2
0
1
1
0
1
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
2
1
0
2
0
1
0
1
1
0
0
0
0
1
0
5
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
1
1
0
0
0
1
0
0
2
0
3
2
0
2
3
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
1
0
2
2
0
0
0
0
0
1
0
0
3
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
1
2
0
0
0
0
0
0
2
1
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
2
0
1
2
0
2
0
0
0
1
1
0
0
4
0
1
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
2
0
1
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
2
0
0
1
0
0
2
0
0
0
0
2
2
0
0
0
1
0
0
0
1
1
1
1
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
2
1
0
0
0
2
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
2
2
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
1
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
2
2
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
2
0
1
0
0
0
1
1
0
0
0
1
0
0
2
1
0
1
2
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
2
0
0
0
0
2
1
1
0
3
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
1
2
2
0
0
0
0
1
0
0
0
0
1
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
2
1
0
0
0
2
1
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
1
1
0
0
0
1
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
1
4
2
0
2
0
0
0
0
2
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
2
1
0
0
0
0
1
2
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
1
0
1
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
1
1
0
0
0
1
2
2
0
0
0
3
0
0
0
0
1
0
0
1
0
1
0
6
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
1
0
0
2
0
2
2
0
0
2
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
2
0
2
0
1
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
1
5
1
0
2
0
3
0
2
0
2
0
3
0
1
0
0
0
0
2
4
0
0
1
0
0
0
4
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
2
2
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
3
0
0
0
0
0
2
0
2
1
0
0
1
2
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
2
0
3
0
2
1
1
0
1
0
0
0
1
0
3
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
2
2
0
1
2
2
0
0
1
0
0
0
0
1
3
0
0
0
0
0
1
0
1
0
0
2
2
2
0
0
1
1
2
1
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
2
0
0
0
2
0
0
1
1
0
2
0
2
2
0
0
3
1
0
1
0
1
0
1
1
0
0
0
0
1
2
1
0
2
2
0
0
2
0
2
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
1
1
1
0
0
0
0
1
1
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
2
2
2
0
3
0
0
0
0
0
2
0
0
0
1
1
0
0
2
0
1
0
0
6
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
2
1
0
0
0
0
3
2
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
2
0
0
1
0
2
0
2
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
1
0
0
0
2
2
1
1
0
0
3
1
1
4
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
1
1
0
0
0
2
0
0
0
2
0
1
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
2
0
0
2
0
1
0
0
0
2
0
2
2
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
5
2
1
2
1
0
0
1
0
0
1
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
1
0
5
0
0
1
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
3
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
4
0
0
0
0
0
0
0
3
0
0
2
0
0
2
0
1
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
2
2
0
2
1
0
0
1
1
0
0
0
0
10
0
0
1
0
0
0
0
1
1
0
0
0
2
0
1
1
0
0
0
1
0
0
0
2
2
2
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
6
1
0
2
0
0
1
2
2
1
0
1
1
2
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
1
2
0
1
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
1
2
0
0
2
2
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
1
0
0
0
1
2
0
3
1
0
2
1
0
0
0
2
0
0
1
0
0
1
0
0
1
0
0
0
2
2
0
0
0
1
2
2
0
0
2
1
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
1
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
1
0
3
1
0
2
0
0
1
1
0
0
1
0
0
0
1
0
2
0
0
1
0
0
0
0
2
0
0
0
2
0
2
0
0
1
0
0
0
0
2
0
1
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
2
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
4
0
0
2
2
2
0
0
0
0
1
2
0
2
2
0
0
0
0
6
0
0
1
0
2
1
0
1
0
2
0
1
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
2
2
2
3
3
1
0
1
2
2
2
0
0
0
0
0
2
1
1
2
2
0
1
2
1
0
1
0
0
1
2
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
1
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
1
0
0
1
0
3
0
1
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
1
0
2
2
0
2
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
2
2
1
0
0
0
0
0
0
1
2
2
1
0
0
0
0
0
1
2
1
0
0
0
0
1
2
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
2
1
0
2
2
0
1
0
0
1
1
0
0
0
0
2
1
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
2
0
2
1
2
5
0
1
4
1
0
1
0
0
2
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
1
0
0
0
0
0
2
5
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
2
2
1
0
0
7
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
2
0
3
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
1
0
1
0
0
0
0
2
2
0
1
0
0
2
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
2
2
1
1
0
0
1
0
0
0
0
0
0
3
0
0
0
0
1
1
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
3
1
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
2
1
0
2
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
6
2
0
0
0
2
0
0
0
0
0
1
1
0
2
1
0
2
2
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
2
2
0
1
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
1
0
0
0
1
0
1
1
2
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
3
1
0
1
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
3
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
1
1
2
5
0
0
1
2
1
0
2
0
1
0
2
0
0
0
0
0
1
0
0
0
1
1
1
3
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
2
1
0
0
1
1
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
1
0
0
0
1
2
1
0
2
2
0
1
1
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
2
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
3
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
1
1
2
0
0
1
0
0
0
1
0
1
0
2
0
0
0
0
0
0
2
2
1
1
0
1
0
1
0
2
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
1
0
1
0
0
2
0
0
1
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
2
1
1
0
0
0
2
0
0
0
0
2
0
0
2
2
0
2
1
0
0
1
0
0
1
0
0
0
0
0
0
2
2
1
0
1
0
1
0
3
0
0
0
0
0
1
2
1
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
1
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
2
0
0
0
1
0
0
0
2
2
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
6
0
0
1
1
1
0
2
0
0
1
1
0
0
0
0
1
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
1
0
0
1
1
0
0
2
2
1
0
0
0
0
0
0
0
0
1
18
1
0
0
0
1
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
1
0
1
1
2
1
1
0
0
0
0
1
0
0
0
0
2
6
0
0
0
0
1
0
0
2
2
2
0
0
0
0
0
1
0
1
2
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
2
2
2
4
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
3
0
2
0
0
1
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
2
0
2
1
2
0
0
0
0
2
1
0
0
4
0
0
0
2
4
0
0
0
1
2
0
3
0
0
0
0
0
1
0
0
0
2
0
3
0
0
0
2
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
2
2
0
2
0
2
0
0
1
0
0
0
3
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
2
2
1
2
0
0
1
1
2
2
0
2
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
1
0
0
2
2
1
0
2
0
0
1
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
2
0
1
2
0
0
0
0
1
0
2
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
4
2
1
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
1
0
0
2
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
4
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
1
0
2
0
0
2
2
1
0
0
0
0
0
0
0
7
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
3
0
0
1
0
0
3
0
0
0
0
1
0
0
2
1
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
1
1
0
2
0
0
0
2
1
0
0
2
1
0
0
0
2
0
0
0
2
3
4
0
0
0
2
0
0
0
0
0
0
2
0
4
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
2
1
0
0
1
0
0
3
0
1
3
1
0
0
2
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
2
0
2
0
1
0
0
0
2
2
1
0
0
0
0
0
0
0
1
0
0
2
0
0
2
2
0
0
0
1
1
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
2
0
1
0
1
0
0
2
0
1
0
3
0
0
1
1
0
0
0
1
1
0
1
0
0
0
0
2
2
2
0
0
0
2
0
2
0
0
0
2
2
0
2
0
0
0
1
1
1
0
0
2
0
0
3
2
0
2
1
0
0
1
0
0
2
0
3
1
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
1
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
2
1
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
6
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
2
2
1
0
0
0
0
1
2
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
4
0
0
0
1
0
1
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
2
1
0
0
2
0
0
2
0
0
0
1
2
0
2
2
0
1
0
1
1
0
0
4
0
1
0
0
1
1
1
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
1
1
1
0
0
1
0
1
1
0
0
0
1
0
2
0
0
0
1
0
4
1
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
2
0
1
0
0
0
1
0
0
2
0
1
0
0
2
0
0
1
2
0
0
0
0
0
2
1
1
0
0
0
0
1
0
0
0
0
2
0
1
2
0
0
0
3
0
0
0
0
0
0
0
3
0
5
0
0
0
0
2
0
2
0
0
0
0
1
0
0
2
3
0
0
0
0
2
2
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
3
0
0
1
1
2
0
2
0
0
0
1
1
0
0
0
2
2
0
1
0
0
1
0
2
0
0
0
0
2
0
1
0
0
1
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
1
2
0
2
0
1
1
0
0
0
0
1
1
1
0
1
0
0
1
0
2
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
2
1
0
1
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
1
0
1
1
2
0
0
2
2
0
2
0
2
0
0
0
0
2
3
0
0
0
0
0
0
0
2
0
0
0
1
2
2
0
0
2
0
0
0
0
0
0
4
1
0
0
0
0
0
0
2
0
1
0
1
0
0
0
2
2
0
2
1
0
0
2
0
0
0
0
0
3
0
2
2
0
2
1
0
2
0
1
0
0
1
2
0
0
0
0
1
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
2
2
2
0
0
0
0
0
0
3
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
1
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
2
2
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
3
2
0
2
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
2
0
0
0
1
1
0
0
2
0
0
0
1
2
2
0
0
0
0
2
0
0
1
0
2
0
0
0
2
0
1
0
0
2
0
0
0
1
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
2
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
2
1
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
1
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
3
0
2
0
0
1
2
0
1
0
0
0
0
2
0
2
0
0
0
0
1
1
0
0
0
0
1
0
0
0
2
0
0
1
0
0
2
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
1
0
0
0
2
2
0
1
0
2
1
0
0
1
0
0
0
1
1
0
0
0
2
1
4
2
0
0
0
1
2
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
2
3
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
2
0
0
0
0
2
0
3
2
0
2
0
0
1
2
0
0
3
0
2
0
0
0
1
2
0
0
0
3
2
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
1
0
1
0
2
0
4
1
0
1
0
0
2
0
1
0
0
0
0
0
0
1
0
0
2
1
0
0
0
3
1
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
2
1
0
0
2
0
0
1
1
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
2
1
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
3
0
0
0
1
1
0
0
2
0
0
0
1
0
0
0
0
2
0
1
0
0
1
0
1
0
0
2
0
0
4
0
0
0
2
0
0
0
0
2
0
2
0
1
2
0
0
2
0
2
0
0
0
0
0
0
3
0
2
0
1
1
0
2
0
1
0
0
1
0
0
0
0
0
1
1
0
0
2
0
0
0
2
0
1
0
0
0
0
1
0
1
0
1
0
1
0
0
0
2
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
1
6
0
0
2
0
0
0
0
0
1
0
0
0
0
2
2
1
0
0
1
1
0
0
0
0
2
0
0
2
1
0
0
0
4
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
1
1
0
1
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
2
0
1
3
1
0
1
0
2
2
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
5
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
2
0
0
0
0
1
0
0
0
2
0
0
0
3
0
0
0
0
2
0
0
0
0
2
0
2
2
0
0
0
2
3
0
0
0
0
0
2
0
0
0
2
2
2
0
0
0
0
1
2
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
2
1
2
0
0
1
0
0
2
0
1
0
0
2
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
3
0
0
0
0
2
2
0
0
2
0
0
1
0
1
0
1
0
0
0
0
2
1
0
0
0
0
1
2
0
2
0
2
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
1
2
1
0
0
1
1
0
0
0
0
0
0
0
2
3
0
0
0
0
1
0
2
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
1
0
2
0
4
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
2
1
2
0
2
0
2
0
0
1
2
1
0
0
0
0
0
0
2
3
1
0
0
2
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
1
0
0
0
0
3
0
0
0
2
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
2
0
0
2
0
0
0
0
3
1
0
1
0
2
0
0
0
2
0
4
0
0
0
0
0
0
0
0
2
1
0
1
0
0
1
0
0
0
0
3
3
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
2
1
2
0
1
2
2
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
2
1
0
0
0
0
0
1
0
0
0
0
2
0
1
0
1
2
0
0
0
0
2
0
0
1
0
0
0
0
1
0
1
3
0
0
0
0
0
0
1
0
2
1
0
1
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
1
3
1
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
4
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
3
0
0
1
0
0
2
8
0
0
0
1
0
2
1
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
1
0
0
0
2
0
0
1
2
1
10
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
2
0
0
1
0
0
0
0
0
0
2
0
0
0
1
1
1
0
0
1
0
0
1
2
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
1
0
2
1
4
1
0
0
0
0
1
0
2
1
0
0
1
0
0
0
0
0
3
1
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
1
0
1
0
0
1
0
0
1
2
0
2
0
0
0
0
0
0
1
2
1
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
2
0
2
2
2
2
0
0
0
2
0
0
1
0
5
0
0
0
0
3
0
0
0
1
0
0
2
0
0
3
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
1
1
1
0
0
2
1
0
1
0
0
0
0
2
2
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
2
0
0
1
0
1
0
0
0
1
0
0
2
0
3
0
0
0
0
2
0
0
1
0
0
1
2
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
1
1
2
1
0
2
1
0
0
0
2
0
1
0
0
3
0
2
0
0
0
0
0
0
2
0
1
0
0
1
0
2
0
0
2
0
0
0
3
0
0
1
2
0
0
1
0
0
0
2
0
0
2
0
0
0
0
3
0
2
0
2
0
0
1
0
1
0
0
1
0
2
2
1
0
3
1
1
1
2
0
1
0
1
2
1
0
0
1
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
1
0
4
2
1
1
0
2
0
2
0
0
0
0
0
1
0
0
2
0
2
1
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
3
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
1
0
0
2
0
0
0
0
2
2
5
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
2
0
2
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
3
1
2
1
0
1
1
2
1
1
0
0
1
0
0
1
0
0
0
2
1
2
1
0
0
1
0
0
0
0
0
1
2
0
0
0
2
0
0
3
0
1
0
2
0
0
0
0
2
0
0
0
2
0
1
0
1
0
0
0
0
0
1
0
2
1
2
1
0
2
2
0
0
0
0
0
0
0
0
0
2
2
0
1
0
1
0
0
1
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
2
0
2
0
0
2
0
2
0
0
1
0
3
1
0
2
2
0
2
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
1
2
0
1
0
0
0
1
1
0
0
2
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
2
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
1
3
0
1
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
1
0
0
0
2
1
0
1
0
1
1
0
1
2
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
2
0
0
0
1
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
1
1
1
0
0
0
0
0
1
0
0
1
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
1
0
2
0
0
1
2
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
1
0
0
1
2
0
2
0
2
0
0
0
3
0
0
0
1
0
0
2
1
2
0
0
0
0
0
3
1
1
0
0
0
0
0
1
2
0
1
2
4
2
2
2
0
0
0
0
2
0
0
0
2
1
2
1
0
0
0
0
1
1
0
0
0
5
1
0
2
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
3
0
0
0
1
0
0
2
0
1
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
2
1
2
0
0
1
0
0
0
0
0
2
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
1
0
0
0
2
0
1
0
0
0
0
2
2
0
0
1
2
2
0
0
1
2
2
2
0
2
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
2
1
1
2
0
1
0
0
2
0
2
2
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
1
0
2
1
3
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
1
1
0
0
1
1
0
2
0
2
0
0
0
0
1
0
2
0
1
0
1
0
0
0
0
1
1
0
2
1
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
4
1
0
0
0
0
1
0
1
0
0
0
2
3
2
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
3
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
3
2
0
0
0
0
0
1
0
2
0
0
1
0
0
0
2
0
0
0
1
1
0
1
1
0
0
2
0
0
0
0
0
1
0
2
1
0
2
0
0
2
0
0
1
2
0
1
1
0
2
0
0
0
1
2
0
1
0
2
0
0
0
0
1
1
1
0
2
0
1
2
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
6
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
2
1
1
0
2
2
1
0
0
0
0
0
1
0
2
0
1
2
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
2
2
0
1
1
0
1
0
1
0
1
0
1
2
2
0
1
2
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
1
0
0
2
1
0
1
0
2
0
0
0
2
0
0
1
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
1
0
2
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
3
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
1
1
2
0
1
0
2
0
1
0
0
0
0
1
0
1
0
2
2
0
0
0
0
0
1
2
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
3
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
1
0
1
1
0
0
0
0
0
1
0
2
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
3
2
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
2
0
0
0
0
0
2
2
2
0
2
0
0
0
0
0
0
0
0
3
0
1
0
1
2
1
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
1
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
2
0
1
0
0
2
1
2
0
0
0
0
2
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
1
1
1
2
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
2
0
1
0
0
2
0
0
0
0
0
2
1
0
0
1
0
1
0
0
0
3
0
1
0
0
0
2
2
1
0
0
0
0
0
0
2
2
0
0
1
2
0
1
0
0
0
0
2
0
0
0
0
0
2
1
0
0
2
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
1
1
0
2
1
0
1
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
2
1
1
0
0
0
1
2
1
0
1
0
3
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
1
1
2
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
3
0
0
1
2
2
0
0
2
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
2
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
8
1
0
0
1
0
0
3
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
1
0
1
0
2
0
0
0
2
2
1
0
1
0
3
0
1
0
0
0
1
0
0
2
0
3
0
1
0
0
2
1
1
3
0
2
0
3
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
1
1
0
0
2
1
1
0
0
0
0
0
0
0
2
2
2
2
0
0
0
0
0
0
2
1
2
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
1
0
0
2
0
0
0
0
5
2
2
0
1
2
0
0
0
0
0
0
0
1
0
1
0
0
3
1
0
0
0
0
0
1
0
0
1
0
2
2
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
1
1
0
0
2
0
0
0
2
0
2
1
0
1
0
0
0
0
1
0
1
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
2
0
0
0
0
0
0
0
1
0
1
1
0
0
0
2
2
0
0
0
1
0
1
0
0
0
0
1
1
0
0
2
0
1
0
2
0
3
0
2
0
2
0
0
2
0
2
0
0
0
0
1
2
0
2
2
0
1
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
1
1
0
2
2
0
1
0
0
2
0
1
1
1
0
1
2
1
0
1
1
1
0
0
1
0
0
1
0
1
0
2
0
0
0
0
1
0
2
0
0
2
0
0
0
1
0
0
2
1
1
0
1
0
0
2
0
2
3
0
0
0
1
1
2
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
8
2
2
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
4
2
0
1
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
2
2
0
3
2
0
0
1
1
2
0
1
0
2
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
2
0
0
0
1
0
1
2
0
0
1
0
0
0
4
0
0
0
0
0
2
2
0
2
1
2
2
0
1
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
3
0
1
0
0
0
2
0
0
0
2
1
0
0
0
1
0
0
0
0
1
3
0
2
0
1
0
2
2
0
0
1
1
0
0
0
2
2
0
0
2
0
0
0
1
0
1
0
1
0
0
0
1
0
2
2
0
0
0
0
0
2
0
0
0
0
2
2
0
1
4
0
0
0
1
0
0
2
0
2
3
0
0
0
2
1
1
1
0
0
1
2
0
2
2
2
0
0
1
2
1
0
1
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
1
0
1
1
0
2
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
1
0
0
0
1
0
1
0
1
0
0
0
0
0
2
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
3
0
0
2
0
2
0
2
1
0
0
3
0
3
0
0
0
0
1
0
1
0
0
0
0
3
0
0
1
0
0
0
1
0
0
2
1
1
0
3
1
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
2
1
2
1
0
0
2
0
0
2
2
2
0
1
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
1
0
0
2
0
0
0
2
1
0
0
0
0
0
1
0
0
2
2
2
2
0
1
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
1
0
3
2
2
0
2
0
0
1
0
0
0
0
1
0
1
0
0
0
3
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
1
2
1
0
1
0
1
0
1
0
0
0
1
0
2
0
2
2
0
1
1
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
2
1
0
0
0
2
2
0
0
0
0
2
1
3
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
1
2
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
1
3
2
0
2
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
2
2
0
2
0
0
0
1
0
1
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
2
8
0
1
0
0
2
1
1
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
1
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
1
0
0
0
0
0
1
0
2
1
0
2
2
1
0
0
1
3
0
1
0
0
1
0
0
0
3
1
0
1
0
1
0
2
3
0
0
1
0
0
2
0
2
0
1
0
0
3
0
0
0
0
0
0
2
0
0
0
2
0
0
5
0
0
0
0
0
1
0
0
1
1
0
1
0
2
1
0
1
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
1
0
0
0
2
2
1
2
3
0
0
1
0
0
2
1
0
0
0
0
3
0
0
0
1
0
1
0
0
2
0
1
0
0
0
2
2
0
0
0
0
0
1
0
0
2
1
0
1
2
0
2
0
0
4
2
0
0
3
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
2
0
0
1
0
0
2
1
0
1
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
1
1
2
0
0
1
0
0
2
0
0
0
2
0
1
2
1
0
0
0
1
0
0
0
0
4
2
1
0
0
0
1
0
0
0
0
2
0
0
0
0
2
2
1
0
0
1
0
0
0
0
0
2
0
1
4
1
0
0
0
1
2
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
2
1
1
0
1
0
0
2
0
2
2
0
1
0
0
0
0
2
0
0
0
0
2
0
2
1
0
0
0
0
1
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
2
0
0
0
0
0
1
2
0
0
0
0
2
1
0
1
0
2
2
0
2
1
0
0
3
0
1
0
0
0
2
1
3
0
1
0
0
0
0
1
1
1
0
0
0
0
1
2
0
0
0
0
0
0
2
0
2
0
0
1
2
0
0
0
0
0
0
0
0
2
2
2
0
0
1
0
3
0
2
1
0
0
0
1
0
1
0
1
2
0
1
0
1
2
0
0
0
2
0
0
1
2
0
1
2
0
0
0
0
1
2
1
0
0
1
0
1
0
0
0
0
1
0
3
0
1
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
3
0
0
1
0
0
0
0
0
2
3
0
0
0
0
2
2
0
0
2
0
2
0
0
0
1
0
0
0
1
0
2
1
0
0
2
0
2
3
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
4
1
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
3
0
0
1
0
1
0
0
0
0
2
1
0
0
0
2
0
1
0
0
2
2
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
1
0
0
0
2
0
1
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
2
0
2
4
1
0
0
2
0
0
1
2
0
1
0
0
2
0
2
0
1
0
2
0
0
2
2
1
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
3
2
0
2
1
0
0
0
0
0
0
0
1
1
0
0
0
2
2
0
0
2
0
1
2
2
0
0
0
0
0
2
2
0
0
1
0
0
0
0
2
0
0
0
1
0
0
2
1
0
0
0
3
1
0
0
0
0
1
1
1
2
2
0
2
2
0
2
0
2
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
3
2
0
0
1
3
1
0
1
0
2
0
1
0
0
2
0
0
0
0
1
3
0
0
0
2
2
1
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
2
0
2
0
0
0
0
1
0
0
2
2
2
0
0
0
0
2
2
1
0
0
0
0
1
3
0
0
1
0
3
2
0
1
0
0
0
0
0
0
0
2
0
1
1
0
1
0
0
2
0
0
2
0
0
0
0
1
2
0
0
1
0
0
2
0
1
0
2
0
0
0
1
1
1
2
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
1
0
0
2
2
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
1
2
0
2
0
2
4
0
0
0
2
0
1
1
1
0
0
0
0
0
3
0
0
1
0
0
1
0
0
1
2
0
0
0
0
0
0
0
1
0
2
3
0
0
0
0
2
0
0
2
2
0
0
1
0
0
0
1
0
1
1
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
2
0
2
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
2
0
1
2
2
2
0
0
1
2
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
1
2
0
0
0
2
0
0
0
0
1
0
2
0
0
0
3
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
2
0
0
0
0
0
2
1
2
0
2
0
0
0
0
0
0
0
1
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
3
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
2
0
0
1
0
0
1
2
0
1
1
0
1
1
0
0
0
0
0
2
0
3
0
2
0
0
1
0
0
2
1
0
0
0
2
0
0
1
9
2
0
0
0
0
0
0
0
2
1
1
0
1
0
1
0
0
0
2
0
0
0
0
1
1
0
0
1
0
0
0
3
0
1
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
2
0
2
0
1
0
0
2
1
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
1
2
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
3
0
0
0
1
0
2
0
0
2
0
3
0
1
1
0
2
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
2
0
0
0
3
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
2
1
1
0
4
0
0
0
0
0
1
2
0
2
1
3
0
0
0
2
1
0
0
5
0
0
0
0
0
0
1
0
0
2
0
0
2
0
1
2
0
0
0
0
0
3
0
1
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
2
1
0
0
0
1
1
0
0
1
0
0
0
1
0
2
2
0
2
0
0
2
1
0
1
0
0
0
1
0
2
0
2
0
0
0
0
0
6
0
2
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
3
2
0
2
1
0
0
2
4
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
3
0
0
0
5
0
0
1
0
0
0
0
0
0
1
2
2
1
0
2
0
1
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
3
0
0
4
0
0
0
2
2
2
0
3
0
1
0
1
0
0
0
2
0
0
0
0
2
1
2
0
0
0
1
0
0
2
2
0
1
2
0
0
2
2
0
0
0
0
0
0
0
0
1
2
2
0
0
2
1
2
0
1
0
2
0
0
1
0
0
0
0
0
2
0
0
0
2
2
1
0
0
1
0
0
0
0
1
0
1
1
0
2
0
0
0
0
0
1
3
0
0
0
0
1
0
1
2
0
0
0
0
0
2
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
2
1
0
0
2
0
0
0
0
0
0
2
1
0
0
2
2
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
2
0
2
0
0
1
0
0
0
0
2
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
2
0
0
2
0
0
0
0
0
2
2
0
0
0
0
2
0
2
1
0
0
0
0
0
3
1
2
0
0
0
0
3
0
0
1
1
1
2
0
1
0
0
0
0
0
0
0
1
0
1
0
2
2
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
3
3
0
1
1
0
1
1
0
0
2
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
1
0
2
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
2
2
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
1
2
1
0
1
0
0
1
2
0
1
2
0
0
0
2
1
0
2
2
0
0
0
0
0
1
0
1
1
0
0
2
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
2
0
2
2
2
0
2
1
0
1
0
0
0
0
0
0
2
1
2
0
0
1
0
0
0
0
2
0
0
1
2
0
0
0
1
0
0
1
2
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
2
1
0
0
2
0
0
0
0
1
2
0
3
4
0
3
1
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
3
0
0
2
0
1
0
1
2
2
0
0
0
0
2
2
0
0
0
1
0
0
2
1
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
2
1
0
0
0
0
0
5
0
0
0
1
0
0
0
0
0
5
3
2
1
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
6
0
2
1
2
0
0
0
3
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
3
0
1
0
4
1
0
0
0
0
1
0
2
0
0
2
0
0
0
2
1
0
0
0
0
0
0
1
2
2
0
0
2
0
1
0
0
0
2
0
2
4
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
1
0
1
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
2
0
0
0
2
0
0
0
1
3
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
1
0
0
0
2
0
2
0
0
0
2
2
0
0
1
0
0
1
0
0
1
0
0
2
0
0
1
0
0
5
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
2
0
1
0
0
2
1
0
0
0
2
0
5
0
0
1
0
1
0
1
0
0
1
1
0
0
0
0
1
0
2
0
0
0
1
0
2
1
1
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
2
0
1
0
0
0
0
1
0
0
0
4
0
1
0
0
1
2
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
1
1
0
0
1
2
1
0
1
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
1
0
0
1
1
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
1
0
2
0
1
3
0
2
0
2
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
2
3
2
2
0
0
1
0
1
0
0
0
0
2
0
1
2
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
1
0
0
0
2
0
0
0
0
0
0
1
2
2
1
0
0
1
0
0
3
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
1
2
0
1
1
1
1
2
0
2
0
1
0
0
2
0
0
0
1
2
0
0
1
0
3
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
2
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
2
0
1
0
2
2
2
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
1
0
2
2
0
0
0
0
0
1
1
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
2
0
1
0
0
0
1
2
0
2
0
4
0
0
0
2
0
0
0
0
0
1
1
2
2
0
0
0
2
1
1
0
0
0
0
0
5
1
0
0
0
0
0
0
0
0
0
0
2
2
3
1
1
1
0
2
0
1
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
2
0
0
0
2
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
3
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
2
3
1
0
1
0
0
0
0
0
0
2
1
0
1
0
0
0
1
1
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
2
0
1
0
2
0
0
2
2
0
0
0
1
0
0
1
0
0
1
2
0
2
2
0
0
2
2
2
0
0
0
1
1
0
2
0
2
0
0
0
0
1
0
2
0
2
2
0
1
0
0
0
0
0
1
3
2
2
0
0
0
0
0
0
2
2
0
1
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
3
0
0
0
2
0
0
0
0
0
2
1
2
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
1
0
1
0
0
0
0
1
7
0
1
0
0
0
1
0
1
0
2
2
0
0
2
0
2
0
0
0
0
0
2
0
0
0
2
0
4
0
0
0
1
0
0
1
2
1
1
0
2
2
1
1
0
1
0
1
0
0
1
0
0
2
0
0
0
0
0
6
0
1
0
2
0
0
2
0
2
2
0
2
2
0
1
0
1
0
0
1
0
0
0
0
1
0
2
0
1
0
0
2
0
0
0
0
0
1
0
2
0
0
1
0
1
0
0
0
0
1
0
2
0
0
0
1
1
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
3
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
1
2
0
0
0
0
0
1
0
0
0
2
0
0
3
0
3
0
0
0
1
0
0
2
0
2
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
2
0
0
0
2
1
1
0
1
2
2
0
0
2
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
2
0
1
0
1
0
0
2
2
0
1
0
0
2
0
0
2
0
0
2
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
1
0
0
2
1
0
0
1
0
1
1
0
0
0
2
0
2
1
2
0
0
2
0
0
1
2
0
0
2
0
0
0
2
0
2
2
0
0
0
0
0
0
0
1
2
1
1
0
0
0
2
0
0
0
1
0
2
0
0
1
0
1
0
0
0
0
0
1
0
0
0
2
0
1
2
0
1
0
4
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
2
2
4
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
2
0
2
1
0
0
0
0
1
0
0
1
0
0
1
0
1
0
2
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
2
0
2
0
0
1
0
0
0
0
1
0
0
0
2
0
2
2
1
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
4
1
2
1
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
2
2
0
2
1
0
2
2
0
0
2
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
1
0
0
3
0
2
0
2
1
0
2
0
0
0
0
0
0
0
1
0
2
2
0
1
0
0
0
0
0
0
2
0
0
0
2
1
0
0
2
2
0
0
0
3
0
1
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
1
0
0
2
0
1
1
2
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
2
2
1
2
0
0
0
0
0
2
3
0
0
0
0
1
1
0
2
1
0
0
0
0
0
0
0
0
0
2
0
1
0
1
1
0
0
0
1
2
0
1
2
1
1
2
0
0
2
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
2
0
0
0
1
3
0
0
0
0
2
3
4
0
1
0
2
0
1
0
0
0
1
1
0
0
0
0
0
2
0
0
0
2
3
0
0
0
0
0
0
1
1
0
1
0
0
0
2
0
0
0
0
0
0
0
1
1
0
2
0
0
0
3
0
2
0
0
0
2
0
0
0
2
2
0
0
6
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
1
0
3
0
2
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
3
3
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
2
2
1
1
0
0
0
2
1
0
2
2
0
0
0
0
0
0
0
2
0
0
0
1
2
1
0
0
2
0
0
0
0
0
0
0
2
1
0
2
0
0
1
2
1
1
1
0
0
0
1
0
0
0
0
0
2
2
0
1
0
1
0
0
2
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
2
2
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
2
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
2
0
0
0
1
2
0
0
2
0
1
0
1
0
0
0
0
1
1
2
0
0
0
2
0
1
0
1
0
0
0
1
1
0
2
0
1
0
0
2
0
0
1
0
0
1
2
0
0
2
1
2
0
1
2
0
0
0
2
1
3
0
0
0
0
0
1
1
0
0
0
0
0
0
1
2
0
3
0
0
1
0
0
1
1
1
2
1
2
0
1
3
2
0
3
0
0
2
0
0
0
0
3
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
1
1
0
1
0
2
0
2
0
0
0
0
3
0
2
1
0
0
0
0
0
0
5
0
0
1
0
2
0
2
2
0
0
0
1
0
0
0
1
0
1
1
0
0
0
1
1
0
1
0
0
2
2
5
2
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
1
1
0
0
2
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
2
0
2
6
2
0
2
2
1
1
0
1
2
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
2
2
0
0
2
0
0
1
0
0
0
0
0
1
0
0
2
1
0
1
0
0
1
2
0
0
0
0
0
0
1
0
1
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
2
2
0
0
0
0
2
0
1
2
1
1
1
1
2
0
2
0
0
1
0
0
2
0
1
0
1
0
1
1
0
0
0
2
0
0
0
0
0
0
0
1
0
2
1
1
0
0
0
1
0
0
1
2
0
0
0
0
0
1
0
0
0
0
1
0
2
0
1
0
0
1
0
0
2
1
0
0
2
0
0
0
0
0
1
1
0
2
0
2
0
0
0
0
0
2
2
3
0
0
0
0
0
2
2
0
0
1
0
2
1
0
0
0
0
0
1
1
0
1
1
1
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
1
2
2
0
0
0
2
2
0
0
0
2
4
0
0
1
0
0
0
3
2
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
3
3
1
1
1
0
1
0
2
2
0
0
1
0
0
0
1
2
1
0
0
2
2
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
3
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
2
0
0
0
0
6
0
0
0
2
0
0
1
0
1
1
2
0
0
0
0
0
2
0
2
0
3
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
2
0
2
0
1
1
0
0
0
2
2
0
0
0
1
0
1
0
0
2
0
0
0
0
2
0
0
2
1
0
0
0
2
0
0
0
1
0
0
0
2
0
2
1
2
0
0
0
2
0
0
0
0
0
0
3
1
2
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
2
1
0
2
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
2
1
0
0
0
0
0
2
2
0
0
0
0
2
1
2
2
1
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
2
1
1
0
0
0
1
0
0
0
0
1
2
1
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
2
0
3
0
0
0
0
0
1
0
2
2
0
1
2
1
0
0
1
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
1
2
0
1
1
2
2
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
3
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
2
2
1
0
0
2
0
0
1
0
0
0
2
0
0
0
2
3
0
0
1
0
0
0
0
0
1
4
0
2
0
2
2
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
2
1
0
0
0
0
1
1
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
1
1
1
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
1
1
1
0
0
0
0
1
2
2
0
0
0
0
0
1
2
0
2
1
0
0
0
0
2
0
0
1
3
0
5
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
2
2
0
0
0
0
1
0
0
1
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
2
0
1
5
1
2
0
2
0
0
0
3
2
1
2
2
1
1
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
2
1
1
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
2
1
0
0
1
1
2
0
0
0
1
0
2
0
1
2
1
1
0
0
0
0
0
0
0
4
0
0
0
0
6
2
2
0
0
0
1
1
0
2
2
0
2
0
0
0
0
0
1
0
2
0
0
3
0
0
2
0
1
1
1
0
0
0
1
0
1
3
0
0
0
2
0
0
0
1
2
0
0
0
2
0
0
0
5
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
2
2
1
0
0
0
0
8
0
0
0
2
0
0
0
0
0
0
2
2
1
1
0
0
2
0
3
0
2
2
0
2
0
1
0
0
0
2
2
0
2
1
3
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
2
0
2
0
2
0
0
0
0
1
0
2
0
0
1
0
2
0
0
2
1
0
0
2
0
0
1
2
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
2
0
1
0
7
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
1
0
1
0
2
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
1
0
1
1
0
0
2
0
2
0
2
0
0
0
0
0
2
0
2
0
1
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
3
1
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
6
0
0
0
2
1
3
1
0
2
4
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
3
0
0
2
2
0
0
2
2
0
1
0
0
2
2
0
3
0
0
0
0
0
0
0
0
1
1
0
0
0
3
0
0
1
0
0
2
0
0
0
0
1
2
1
0
0
0
2
3
1
2
0
1
0
0
0
0
2
0
0
0
0
0
2
0
1
0
2
0
2
0
0
2
0
0
0
0
0
2
2
0
1
1
0
0
0
0
2
0
1
1
1
0
1
0
0
2
0
0
0
1
0
1
1
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
3
0
2
1
0
0
1
2
1
0
0
2
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
2
2
0
2
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
1
0
1
1
0
0
0
2
2
0
1
2
0
0
0
1
0
4
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
2
0
0
1
1
2
0
0
2
3
0
1
0
0
0
0
0
0
0
2
2
1
0
2
0
0
3
0
0
0
0
1
1
0
0
1
1
0
1
2
0
1
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
2
1
3
1
0
0
2
1
5
0
0
0
0
0
2
0
0
0
0
1
2
0
2
2
0
0
0
0
1
0
0
1
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
2
2
2
0
2
0
3
2
0
0
0
0
1
1
0
1
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
1
2
1
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
2
3
0
0
0
0
2
0
0
2
0
0
2
0
0
0
2
1
1
0
1
0
0
1
0
0
2
2
1
0
0
1
1
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
3
0
2
0
0
3
0
0
0
0
2
0
0
4
0
0
0
0
1
0
0
2
0
0
0
0
0
1
2
0
2
0
2
0
0
0
0
1
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
1
0
2
0
0
0
0
2
1
0
1
1
2
0
0
0
1
0
0
1
0
2
0
2
2
0
0
2
1
0
0
2
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
1
0
2
0
1
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
2
2
0
1
1
0
0
2
0
5
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
1
0
1
0
0
0
0
1
4
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
3
0
0
0
0
0
0
1
0
0
2
2
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
3
0
2
0
0
0
0
2
0
2
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
2
0
1
0
0
0
1
0
0
0
0
0
2
0
2
0
1
0
0
0
1
0
0
2
1
2
0
0
2
1
0
0
0
0
1
3
0
1
0
0
2
0
0
0
1
0
2
3
0
0
0
1
0
2
0
0
0
1
0
0
0
2
0
0
1
0
1
2
0
0
2
0
2
0
0
1
2
0
0
2
2
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
2
2
2
0
0
2
0
0
0
2
1
2
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
1
1
4
0
0
3
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
3
1
2
4
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
2
0
0
4
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
2
1
0
0
5
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
1
0
0
2
0
0
1
0
0
0
0
2
0
0
1
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
2
2
2
1
2
0
0
0
1
0
0
0
1
2
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
2
1
0
1
2
1
0
0
0
0
2
2
1
1
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
1
0
2
1
0
1
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
1
0
0
2
0
1
0
2
0
1
0
0
0
0
0
1
1
2
1
0
0
2
0
0
0
2
1
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
5
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
2
0
0
0
0
2
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
4
0
0
1
0
1
0
6
0
0
0
0
0
0
0
1
0
1
1
0
3
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
2
0
2
4
0
1
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
1
2
0
2
0
3
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
1
2
1
2
2
1
2
1
1
0
1
0
0
0
0
0
0
0
1
0
1
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
1
0
0
1
2
2
0
0
0
0
0
4
0
0
1
2
0
2
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
1
0
3
0
0
0
0
0
3
0
0
2
2
1
0
0
0
2
0
0
0
0
1
0
2
0
2
0
3
0
0
0
0
0
1
0
2
0
2
0
0
2
2
1
0
1
0
0
2
0
1
1
0
0
0
1
0
3
0
0
2
1
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
1
1
0
0
0
0
1
0
0
2
0
2
0
0
1
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
1
0
2
0
0
0
0
1
0
0
1
0
3
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
2
0
0
1
2
0
2
2
1
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
1
1
0
1
0
1
0
0
2
0
2
0
0
3
0
0
2
0
0
0
0
0
2
0
0
1
2
0
0
1
0
0
0
0
0
2
2
2
0
0
0
0
2
0
0
1
1
1
0
2
0
0
0
1
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
3
0
0
0
3
0
0
0
0
0
1
3
0
2
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
1
0
0
2
0
1
0
0
0
2
0
0
0
1
2
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
2
1
1
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
1
0
0
0
0
2
2
1
0
0
11
2
0
0
0
0
1
0
2
0
2
0
0
2
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
5
0
1
0
0
0
0
1
1
1
0
1
0
0
0
0
3
0
0
0
0
0
0
1
1
0
1
1
0
2
0
0
0
0
0
0
1
2
0
3
0
0
2
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
6
0
0
0
0
0
2
0
2
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
2
0
1
0
0
0
1
2
1
0
0
2
1
1
0
0
0
0
2
1
1
0
0
2
2
0
0
3
0
0
0
0
1
0
1
0
0
0
0
0
2
0
2
0
0
2
0
0
0
2
0
2
0
0
0
0
1
0
0
0
1
0
1
0
1
2
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
2
0
0
2
0
2
1
3
1
0
3
3
0
1
1
0
1
0
0
0
1
2
0
0
0
0
0
2
2
0
0
2
2
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
1
1
2
0
2
2
2
1
0
2
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
7
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
1
2
0
0
0
2
3
2
0
0
0
2
0
0
3
0
1
0
0
0
2
1
0
5
2
0
3
0
1
0
0
2
1
0
1
0
0
2
2
1
0
1
1
0
0
0
2
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
2
0
1
0
1
1
0
2
0
0
0
2
0
0
0
2
2
1
0
1
1
2
0
0
0
1
0
0
1
2
0
0
0
1
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
2
0
0
0
0
1
2
0
0
0
0
1
0
0
0
1
2
2
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
2
1
0
0
2
0
0
1
0
0
3
1
3
0
0
0
0
0
0
2
0
0
0
2
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
1
1
1
0
0
1
1
0
1
0
0
2
0
2
0
0
2
0
0
1
1
0
0
1
2
0
0
0
2
0
0
0
0
0
2
0
0
0
2
2
0
2
2
0
2
0
0
2
0
2
0
0
0
0
2
0
0
0
0
2
2
0
1
0
0
0
1
0
0
1
3
0
0
0
0
0
3
0
0
1
0
1
0
0
1
0
2
0
2
2
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
2
2
0
0
0
0
0
0
4
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
1
0
2
0
2
0
9
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
1
1
2
2
1
0
0
0
0
1
0
0
0
0
2
0
2
0
2
1
0
2
0
0
0
0
2
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
2
0
0
3
0
1
0
0
0
2
0
2
0
1
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
3
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
2
0
1
2
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
1
3
0
0
0
2
0
0
2
0
1
1
0
1
0
0
0
1
0
2
3
1
0
0
0
0
0
0
2
0
3
0
0
0
0
0
2
2
0
1
0
2
0
0
2
0
0
1
2
0
0
1
0
1
2
0
0
1
3
0
0
0
2
2
1
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
2
2
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
6
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
3
0
1
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
3
0
6
1
0
3
3
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
2
2
0
2
0
0
0
0
0
2
0
0
0
0
0
1
2
0
2
0
0
0
1
0
0
2
0
2
0
0
0
0
4
1
2
0
0
0
2
0
2
1
0
0
0
1
2
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
2
0
0
1
0
3
0
0
0
0
0
0
2
2
0
3
0
0
0
0
0
2
1
0
1
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
2
0
0
0
0
3
0
2
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
1
1
0
0
1
2
0
0
0
0
0
1
2
1
0
0
0
0
0
1
0
0
3
0
1
0
0
2
0
0
3
0
0
0
0
0
2
0
2
1
0
2
0
0
1
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
3
1
1
1
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
1
0
0
2
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
4
0
0
0
0
3
0
1
2
1
0
1
0
0
1
0
0
0
0
0
2
2
0
0
2
1
0
1
4
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
2
1
0
0
0
0
0
1
0
0
1
1
1
0
0
0
1
0
0
0
0
2
0
0
0
1
2
2
0
0
1
0
1
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
2
1
0
1
0
0
0
1
0
3
1
1
2
0
0
0
0
1
0
2
0
0
0
0
0
0
1
1
0
2
0
0
0
0
1
0
1
0
2
0
2
2
0
0
0
0
0
2
1
2
0
2
0
0
0
0
1
2
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
3
0
2
0
2
1
0
0
0
2
0
0
0
1
0
0
0
4
0
2
0
2
0
0
1
0
0
1
8
0
0
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
2
1
0
1
1
1
2
0
0
0
0
0
2
3
1
0
0
1
0
3
0
0
0
1
0
0
1
2
0
0
1
0
2
2
0
1
3
0
1
0
0
0
1
0
2
0
0
1
0
0
3
0
0
2
2
0
0
0
0
0
0
0
0
0
2
1
2
2
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
2
1
0
1
0
2
0
0
0
1
0
0
2
1
0
0
0
1
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
2
1
0
0
0
0
0
0
1
3
0
0
0
0
0
0
2
0
0
2
1
1
0
0
0
1
0
0
1
1
0
2
0
0
0
0
0
0
1
0
0
2
0
3
1
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
2
2
0
4
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
3
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
2
0
0
0
1
0
0
1
1
0
0
0
2
3
0
0
0
0
0
0
0
0
0
1
2
0
0
3
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
3
0
1
0
2
0
2
0
0
2
1
1
0
0
2
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
1
0
0
2
0
0
0
0
2
0
0
1
0
0
0
1
2
0
3
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
1
0
1
0
2
3
0
1
0
0
0
2
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
2
2
2
1
0
0
0
0
1
1
1
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
1
0
0
4
0
0
1
1
0
0
0
1
0
1
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
2
0
1
0
0
0
2
1
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
1
3
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
2
0
0
0
0
0
2
0
1
2
0
0
1
0
0
1
0
3
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
2
6
2
1
0
0
0
1
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
2
1
1
1
1
2
0
1
0
1
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
2
0
2
1
0
1
0
1
2
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
1
1
0
0
1
1
0
2
0
0
0
0
0
0
2
0
1
1
0
2
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
1
2
0
1
0
0
0
0
0
0
0
1
2
0
0
0
1
0
1
2
0
0
0
0
0
1
0
1
0
2
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
2
0
0
1
1
5
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
3
0
2
0
0
0
1
1
0
1
0
1
0
1
1
2
0
1
1
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
2
2
0
0
0
3
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
1
0
3
0
0
2
0
0
0
0
0
1
0
0
2
0
0
2
2
0
3
4
1
1
1
0
0
0
3
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
2
0
0
2
0
1
1
2
0
0
0
1
2
1
0
2
1
1
0
1
0
0
1
0
2
0
0
1
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
4
0
0
0
2
0
0
0
1
0
0
0
0
2
1
2
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
1
0
1
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
1
5
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
2
0
2
0
2
2
0
0
0
0
1
0
2
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
2
2
0
1
0
0
0
4
0
0
0
1
1
0
1
0
1
2
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
3
2
2
0
2
0
2
3
1
0
0
0
0
2
1
0
0
0
0
0
2
1
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
2
1
1
1
1
0
0
1
0
0
0
2
0
1
0
1
1
0
0
0
1
0
0
2
1
0
0
0
2
0
0
0
2
2
0
2
0
0
2
0
0
2
0
2
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
1
0
0
0
2
0
2
0
0
0
2
0
1
1
0
0
2
0
0
0
0
1
0
0
0
1
2
0
0
2
0
1
0
2
0
1
0
2
0
0
0
0
0
0
1
0
0
1
0
2
2
0
1
0
0
0
2
2
2
2
1
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
2
1
0
3
0
2
1
0
2
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
1
2
0
2
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
1
0
0
0
0
2
0
2
1
0
1
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
2
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
2
0
1
0
0
0
0
0
2
0
1
0
0
2
0
1
3
0
1
0
0
0
2
0
0
0
2
3
0
0
1
0
0
0
2
0
0
0
0
1
0
1
2
0
0
2
0
3
0
1
0
2
0
0
2
0
2
0
0
0
1
0
0
1
2
1
1
1
2
1
2
0
0
2
0
2
1
0
0
0
0
2
0
0
0
0
0
2
2
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
3
2
0
2
0
2
0
1
0
3
5
1
0
0
0
5
0
0
0
0
0
0
2
2
1
0
0
2
1
2
1
0
0
0
0
0
2
0
1
3
1
0
4
0
0
0
0
0
1
0
0
0
1
2
0
2
0
0
2
2
0
2
1
0
0
1
2
0
0
1
2
1
1
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
2
0
1
0
1
2
0
0
1
2
1
0
0
0
0
0
0
2
0
0
0
2
2
0
0
1
0
2
0
1
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
1
2
0
2
4
0
0
0
0
0
4
0
0
1
0
1
0
0
1
1
0
2
1
2
0
0
2
1
0
0
2
0
1
2
0
0
0
0
1
0
0
0
0
1
1
2
0
0
1
0
0
0
1
0
0
0
3
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
1
1
1
0
0
2
0
2
0
0
0
0
0
0
1
3
0
1
0
1
3
2
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
2
2
0
0
0
0
2
0
0
0
1
2
2
1
0
2
0
2
2
1
0
0
0
0
2
0
1
1
1
1
2
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
3
0
1
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
2
0
0
2
2
1
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
1
0
0
2
2
0
0
0
3
0
0
1
2
0
0
0
0
0
0
2
0
1
0
2
1
2
0
1
0
0
2
0
1
0
0
0
0
0
1
0
0
0
2
2
0
0
0
5
1
0
0
0
0
0
1
0
1
1
0
0
1
1
2
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
1
0
0
2
2
0
0
2
2
0
2
0
0
0
0
0
0
1
0
0
1
0
0
2
0
1
3
0
0
0
0
0
1
2
0
2
0
0
1
1
0
0
1
0
1
0
1
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
2
0
0
2
0
3
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
2
0
0
1
0
0
0
1
1
2
0
0
2
2
2
0
0
0
1
1
0
0
0
2
0
0
0
0
1
1
0
0
0
1
2
1
1
0
1
0
0
0
0
2
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
1
1
0
0
0
1
2
0
2
0
0
0
0
1
0
1
1
0
0
1
0
0
2
2
0
2
2
0
0
2
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
1
1
0
0
2
0
0
0
1
2
2
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
1
2
0
2
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
1
0
2
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
6
1
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
3
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
2
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
3
0
0
0
1
0
0
0
0
2
2
1
2
0
2
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
2
0
1
2
0
0
1
0
2
2
0
0
2
5
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
3
1
0
1
1
0
0
5
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
1
2
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
1
0
1
2
1
2
0
0
0
0
2
1
1
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
2
2
1
1
1
0
1
1
0
0
1
0
0
0
1
3
2
0
0
0
0
0
2
1
0
0
0
1
0
1
2
1
1
1
0
1
0
1
2
2
0
2
0
3
0
0
4
0
0
0
0
2
0
0
0
1
2
0
2
1
0
0
0
0
1
1
4
3
0
0
1
0
2
1
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
1
0
0
2
0
1
0
0
0
0
1
2
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
2
2
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
2
1
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
2
1
0
0
2
0
0
0
2
0
0
2
0
1
3
3
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
1
1
2
0
2
0
2
0
0
0
0
1
0
0
0
1
2
0
0
0
3
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
2
2
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
2
1
0
1
2
0
2
0
0
2
1
2
2
2
1
1
1
0
0
0
0
6
0
1
0
0
0
0
1
0
0
1
2
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
1
1
0
0
1
0
0
2
0
1
0
0
0
0
2
1
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
2
0
3
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
1
4
0
0
0
0
0
2
0
3
0
0
1
0
0
0
0
0
2
0
2
0
2
1
0
1
0
0
0
2
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
1
0
0
1
0
1
0
1
1
2
0
0
1
1
0
0
3
1
0
2
0
1
0
2
0
0
1
1
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
1
2
0
0
0
2
1
0
1
2
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
1
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
5
1
1
0
0
3
2
2
0
0
0
1
2
2
1
2
2
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
1
0
2
0
0
2
0
3
0
1
0
0
0
3
0
1
1
0
2
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
2
0
2
2
0
0
1
0
2
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
13
2
0
0
1
2
0
3
0
1
1
0
0
0
0
0
0
0
1
0
1
2
0
0
2
0
0
0
0
2
2
2
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
1
0
0
0
1
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
4
2
0
1
0
4
0
0
0
2
0
2
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
1
2
0
1
0
0
1
2
0
1
0
1
2
0
0
2
1
1
3
0
1
1
2
0
0
2
0
1
1
2
0
0
0
0
2
1
2
0
0
0
0
0
1
3
1
1
0
0
2
0
0
1
2
1
0
1
0
1
2
1
0
1
3
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
2
0
0
0
2
0
2
0
2
0
0
0
1
1
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
13
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
2
0
0
1
1
0
1
0
1
0
0
0
1
0
1
0
0
2
0
0
0
1
0
1
1
2
0
0
2
0
0
2
2
3
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
2
0
2
2
2
2
0
1
0
0
0
1
0
0
2
0
0
3
1
1
0
1
0
0
0
0
2
0
0
0
2
0
0
0
2
1
0
2
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
3
1
0
0
1
0
0
0
0
0
0
0
1
0
2
0
3
0
1
0
0
1
0
0
6
0
1
0
0
2
0
0
0
1
0
2
0
0
2
0
0
3
0
2
0
1
0
2
0
0
0
0
0
0
2
1
0
4
1
0
1
2
2
0
0
1
0
2
0
1
0
0
3
0
2
0
2
2
2
1
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
2
2
1
1
2
0
1
0
0
1
0
4
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
2
0
0
0
2
1
2
0
2
0
0
0
0
1
1
0
3
1
0
0
1
0
2
0
0
2
0
0
1
2
1
0
1
2
2
0
0
0
0
6
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
1
0
1
0
2
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
2
2
1
0
0
0
0
1
2
0
1
1
2
1
0
0
2
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
2
0
0
1
0
0
1
1
0
0
0
2
0
0
4
3
0
0
0
3
0
0
0
0
3
0
2
0
1
1
1
0
2
0
0
0
0
2
0
0
0
2
0
0
1
2
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
3
0
2
0
0
1
0
0
0
3
0
1
2
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
2
1
1
2
0
2
0
0
2
2
0
0
0
0
0
0
2
0
4
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
2
0
0
3
0
1
0
0
2
0
0
6
0
0
0
2
0
0
2
3
0
1
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
1
1
2
0
0
0
0
0
2
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
2
1
0
2
1
0
1
1
0
2
0
0
1
0
0
1
0
0
1
0
2
0
0
2
0
0
0
0
0
1
2
1
2
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
3
2
0
0
0
1
5
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
2
2
2
3
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
1
2
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
2
2
2
5
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
1
0
0
2
0
0
0
2
1
0
0
2
0
0
0
0
0
0
4
1
1
1
2
0
0
0
1
0
0
1
2
0
1
1
2
0
0
0
2
0
0
1
0
1
0
0
2
0
3
0
1
0
0
1
2
0
0
0
1
2
1
0
1
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
3
1
1
0
0
0
2
2
0
2
2
2
4
0
0
2
0
0
0
0
2
0
1
0
0
2
1
1
0
0
2
0
0
0
0
0
1
2
0
0
2
1
0
0
0
2
0
1
0
0
0
2
0
0
0
2
0
0
2
1
2
0
0
1
0
0
0
1
0
0
0
5
0
0
9
0
1
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
1
0
0
1
0
0
0
0
0
2
2
0
0
0
1
0
1
0
0
0
0
1
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
2
0
2
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
2
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
3
3
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
2
1
2
1
2
0
0
1
0
1
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
1
0
2
1
1
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
1
0
2
3
1
0
0
2
0
0
0
2
0
1
0
0
0
0
2
0
0
2
1
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
1
1
2
1
0
0
0
0
1
2
2
2
0
0
0
0
1
0
1
0
0
2
0
0
0
2
2
2
1
0
1
1
0
1
2
2
1
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
2
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
1
0
0
2
2
0
1
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
2
0
2
0
0
0
1
0
0
0
0
0
0
2
1
3
2
0
0
0
0
0
1
2
1
0
0
0
1
3
2
0
0
0
1
0
0
0
0
2
0
0
0
0
1
2
2
0
0
2
0
0
0
2
1
1
0
0
0
0
1
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
2
2
0
0
2
1
0
0
0
0
2
0
0
0
3
0
8
0
0
0
0
0
0
2
0
1
0
0
2
0
2
0
1
0
0
0
0
0
2
1
0
1
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
2
2
0
0
0
1
0
0
0
1
0
0
0
2
0
2
0
0
1
0
1
1
0
0
1
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
1
0
2
1
0
0
0
0
0
0
2
1
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
2
1
0
0
0
0
1
0
2
1
0
0
2
0
0
0
0
0
1
1
0
0
0
0
2
1
0
0
3
0
0
0
1
2
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
2
1
2
1
0
0
0
0
0
0
3
1
1
2
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
4
0
0
2
0
0
0
1
2
0
0
0
2
0
2
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
1
1
2
0
0
0
0
2
0
0
0
0
1
0
0
2
0
1
2
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
1
0
2
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
5
0
0
0
3
2
2
3
0
2
2
0
0
0
1
1
0
2
0
1
1
0
2
2
2
0
0
0
0
0
2
0
0
2
0
0
1
0
0
1
0
1
2
0
0
0
0
0
1
0
1
3
1
2
0
2
1
0
2
1
1
0
3
0
1
0
0
1
4
0
0
5
0
0
1
0
0
1
0
1
0
0
0
0
0
1
2
5
0
2
1
1
0
0
2
2
1
0
2
1
0
0
1
1
1
1
0
0
0
1
0
0
0
2
2
2
1
0
0
0
1
0
2
1
0
0
0
0
0
2
2
0
0
0
0
4
0
0
2
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
3
2
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
2
0
0
3
2
1
2
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
1
3
1
0
2
2
1
1
0
0
0
0
0
1
0
0
2
0
0
2
2
1
0
2
0
2
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
2
0
5
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
1
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
1
1
2
1
0
2
0
0
0
0
0
2
1
2
2
0
0
0
0
0
1
0
0
0
0
0
2
2
1
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
2
2
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
3
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
1
0
1
1
0
0
2
0
0
2
0
2
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
1
0
0
0
2
0
0
0
0
0
1
1
0
0
2
0
1
0
0
1
1
2
0
1
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
2
0
0
1
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
1
1
2
0
0
0
1
1
1
2
0
1
0
0
0
0
0
2
2
2
0
1
1
2
0
0
3
2
2
0
1
0
1
0
0
0
1
0
0
0
0
1
2
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
1
0
2
0
0
0
0
2
0
1
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
1
0
2
0
1
0
0
0
0
1
3
0
3
0
2
0
2
0
0
1
0
1
0
2
1
0
0
0
1
0
1
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
2
0
0
1
0
2
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
2
2
1
0
0
0
3
1
0
0
0
0
1
0
1
1
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
2
1
0
1
0
0
0
2
2
1
0
2
0
2
0
0
2
0
2
0
1
0
1
0
0
0
2
1
0
0
3
1
2
0
0
0
0
1
0
0
2
5
0
0
0
0
2
0
1
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
1
0
0
0
0
2
0
2
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
1
2
0
1
0
0
1
4
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
1
2
1
2
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
1
2
2
0
0
2
0
2
2
2
0
0
1
3
1
0
0
2
0
0
0
2
0
0
2
0
2
0
0
2
0
0
3
1
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
1
0
2
2
1
0
1
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
3
0
2
0
0
1
1
0
2
0
0
0
2
1
0
1
0
2
3
0
1
2
0
0
0
0
1
0
1
0
0
2
0
0
1
2
0
3
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
1
3
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
2
0
1
1
0
0
0
2
0
1
1
1
0
1
1
0
1
2
1
1
0
1
2
0
0
2
0
1
1
2
0
1
0
0
0
2
0
1
0
2
0
1
0
0
0
2
0
0
1
0
1
0
0
1
0
3
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
3
0
1
0
2
0
0
0
0
2
0
0
0
0
2
1
0
1
0
0
2
0
3
0
0
2
0
0
2
0
0
2
0
1
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
2
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
1
0
1
0
0
2
0
1
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
4
1
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
2
2
2
2
2
1
0
2
0
2
0
1
0
0
0
0
1
0
0
0
2
0
2
0
1
0
0
2
0
0
1
0
2
0
1
0
2
1
1
0
1
0
2
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
1
0
2
1
0
0
0
0
0
0
1
2
0
2
0
0
0
2
0
1
3
0
1
0
0
0
3
1
0
0
0
0
0
0
0
0
1
2
0
2
0
0
2
2
0
0
2
2
1
0
0
2
2
0
0
0
2
1
1
0
0
0
1
0
1
0
1
0
0
0
2
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
1
2
2
0
0
0
0
1
0
2
0
0
2
2
2
0
0
0
0
2
0
2
2
0
0
0
0
2
1
1
2
2
0
2
1
0
1
2
0
0
0
0
2
0
0
0
1
0
0
1
2
0
1
0
0
1
1
1
0
1
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
2
0
1
0
1
1
0
0
2
2
2
2
0
2
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
2
1
0
0
2
2
0
2
4
0
0
0
2
0
0
0
0
0
0
2
2
0
0
1
2
0
0
0
0
0
2
0
0
0
0
2
0
1
1
0
0
0
0
2
1
5
0
2
0
1
0
2
0
1
0
1
2
1
0
0
1
0
0
0
2
0
1
0
0
1
0
1
0
0
0
0
0
1
1
2
1
0
0
2
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
2
0
2
2
3
2
0
0
0
0
0
1
0
0
0
1
0
2
0
2
0
0
0
1
0
2
3
1
1
0
3
2
0
1
0
2
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
3
0
0
0
1
0
1
0
0
0
0
0
0
1
3
0
0
0
2
1
1
0
0
0
0
0
2
1
2
0
1
0
0
0
0
0
2
0
0
0
1
0
0
1
1
2
0
2
0
1
3
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
1
2
2
2
0
0
0
0
4
4
2
1
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
10
2
0
0
2
0
0
1
0
2
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
2
1
0
0
3
0
1
0
0
1
2
0
0
0
2
2
0
0
0
0
3
0
2
1
0
0
2
0
2
2
0
0
0
0
2
2
0
2
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
2
1
2
0
0
2
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
1
1
1
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
3
0
1
2
0
0
0
0
2
0
0
0
0
0
2
2
0
0
2
1
0
0
0
2
0
2
2
2
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
1
0
4
2
0
0
0
1
0
1
0
0
0
1
4
0
0
0
1
2
0
2
0
0
0
0
2
0
0
1
2
1
1
0
0
2
0
0
1
0
1
2
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
2
2
0
0
0
0
2
2
0
0
1
2
2
2
2
0
0
1
0
1
0
0
0
0
3
1
0
1
1
0
1
0
1
2
2
0
0
0
0
0
0
0
1
1
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
2
0
0
0
0
1
0
3
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
2
2
0
1
2
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
1
0
1
1
1
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
3
1
1
0
0
0
1
0
0
0
2
1
0
0
0
0
0
1
2
0
0
0
0
0
2
0
1
0
1
2
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
3
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
2
1
0
1
2
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
3
1
1
1
0
1
0
0
0
1
1
0
2
0
0
1
0
0
2
0
0
0
3
0
2
0
0
0
0
2
2
2
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
1
0
1
0
1
0
0
0
0
0
1
1
1
1
0
3
0
0
0
0
2
2
1
0
1
1
1
0
0
2
0
0
0
1
0
2
0
0
0
0
2
2
0
2
0
2
0
0
1
2
0
0
1
2
0
0
2
2
1
0
1
0
0
0
0
1
0
1
0
1
0
0
0
1
1
0
1
2
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
1
1
2
2
0
2
0
0
2
0
2
0
0
3
0
2
1
0
0
2
2
0
1
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
1
0
3
2
1
1
0
0
1
0
0
0
0
3
0
4
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
2
0
0
1
0
2
0
1
2
0
1
0
0
0
0
1
1
2
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
7
2
0
0
2
2
0
0
1
0
4
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
2
0
1
2
0
0
0
0
0
0
1
1
0
0
0
2
0
2
0
0
0
2
3
0
0
0
2
0
0
0
1
1
0
0
0
1
0
0
0
1
1
1
0
1
0
0
2
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
2
2
0
1
0
1
1
0
0
2
0
0
1
0
2
0
0
1
0
1
0
0
1
1
2
0
0
1
0
2
0
2
0
0
0
3
0
0
0
2
0
0
0
0
0
2
0
2
0
1
2
0
0
2
0
1
0
2
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
5
1
0
2
0
5
2
2
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
2
1
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
1
1
0
0
0
2
0
0
0
1
2
0
1
0
0
0
0
0
0
2
0
2
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
2
0
1
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
3
0
0
1
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
2
1
0
0
0
1
0
2
0
0
1
0
1
2
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
4
1
0
0
2
0
1
0
0
0
0
0
0
2
1
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
1
2
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
2
3
1
0
2
1
1
0
0
1
0
0
2
0
1
0
2
2
0
0
0
0
2
1
3
0
0
0
0
0
0
0
3
0
0
1
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
2
1
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
1
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
1
2
2
1
3
0
3
0
0
1
0
2
0
0
0
1
0
2
0
2
0
2
3
0
1
0
2
0
1
0
0
2
0
0
1
0
0
0
1
0
2
0
0
2
1
0
0
3
0
3
0
2
1
1
0
2
0
2
0
0
0
0
0
0
2
0
2
2
0
0
0
0
2
0
2
2
0
1
1
0
0
2
0
0
1
0
0
0
1
0
2
2
2
1
0
0
0
0
0
0
1
0
1
0
0
0
2
2
1
1
1
0
1
0
0
0
0
0
0
2
1
0
1
0
0
1
0
0
3
1
1
0
0
3
0
2
2
0
0
0
2
0
3
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
1
2
0
2
0
0
0
1
1
0
1
0
1
1
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
3
0
0
0
3
0
0
1
0
0
0
1
2
0
0
0
0
0
1
0
0
1
0
0
1
5
0
0
0
0
0
4
0
1
0
2
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
2
3
1
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
8
0
0
0
0
0
0
1
3
0
0
7
2
0
1
1
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
1
0
0
1
0
1
0
0
2
2
0
2
0
0
0
0
0
0
0
1
2
0
0
0
2
5
0
1
0
0
0
1
0
0
2
0
0
1
1
2
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
2
2
0
3
0
2
0
1
2
0
0
0
0
0
0
0
0
2
3
0
0
0
0
2
0
1
0
1
0
0
0
1
0
0
2
0
0
0
1
2
1
0
0
0
0
0
0
2
0
1
2
0
0
1
0
0
0
1
1
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
3
2
0
0
1
2
0
1
1
0
2
0
1
0
0
0
0
0
0
2
0
0
1
0
2
0
1
2
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
1
0
2
0
1
0
0
1
0
3
0
0
0
0
0
1
1
2
1
0
1
0
0
0
1
2
2
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
8
0
0
0
1
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
1
2
0
0
2
0
2
0
0
0
0
1
2
2
2
2
0
2
0
1
0
2
0
2
0
0
0
0
1
2
2
3
0
0
0
0
0
0
2
1
2
0
0
0
0
0
5
1
0
0
0
0
1
0
0
3
0
7
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
3
2
0
0
0
1
2
2
3
0
2
0
1
0
2
1
3
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
1
0
2
2
0
0
1
0
2
0
0
0
1
0
0
1
0
0
1
0
1
0
0
2
2
0
0
1
0
2
0
1
0
2
0
0
2
0
1
0
0
1
0
2
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
2
0
2
2
0
2
1
0
0
0
1
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
2
3
0
0
0
0
0
0
2
0
0
0
2
1
0
0
3
2
0
2
0
1
2
1
2
0
0
0
1
2
0
2
0
1
2
0
2
0
0
0
0
0
2
1
0
2
1
0
0
0
1
0
0
0
2
2
0
2
0
2
0
0
0
1
0
0
0
0
0
1
0
0
2
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
1
3
1
3
2
2
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
4
2
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
1
0
0
2
2
0
0
1
0
2
0
0
2
4
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
2
1
1
0
0
1
1
0
0
0
0
0
0
1
1
2
0
0
0
0
0
1
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
2
0
1
1
0
0
2
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
1
0
3
0
0
0
1
0
1
4
0
0
0
0
0
0
0
0
1
0
3
0
0
0
1
0
0
0
0
0
1
5
1
0
2
1
0
0
1
2
0
2
0
0
2
3
0
0
1
0
1
0
0
0
2
0
0
2
0
0
2
0
0
2
1
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
1
0
0
0
0
2
2
0
2
0
1
0
5
0
0
1
2
0
2
1
0
0
2
0
0
0
0
10
1
2
0
0
0
1
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
1
0
0
1
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
2
1
0
1
0
3
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
1
2
2
0
2
2
0
0
1
0
3
0
0
0
2
2
1
0
2
3
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
3
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
2
1
0
1
2
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
2
2
1
1
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
4
1
2
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
1
1
0
2
5
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
1
0
1
3
1
0
0
0
0
0
2
1
1
0
1
0
2
0
1
0
0
0
3
1
0
0
0
10
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
1
0
0
1
2
1
0
1
0
0
2
0
0
1
4
0
0
0
0
0
0
1
0
0
1
0
1
2
0
0
0
1
0
1
1
1
1
2
0
0
0
4
0
1
4
0
0
1
0
0
1
0
0
1
0
0
2
0
0
0
0
3
0
2
0
5
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
6
0
0
0
0
0
1
0
0
0
1
0
2
0
1
3
0
0
0
0
0
1
0
1
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
2
0
0
0
0
2
0
0
0
2
0
0
0
1
1
2
0
0
0
0
1
0
2
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
1
0
0
2
0
1
0
0
0
0
3
0
0
0
0
1
0
3
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
4
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
2
0
0
3
2
0
0
0
0
1
3
0
0
1
1
2
2
0
1
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
6
0
0
0
1
1
0
0
0
0
5
0
0
0
1
2
0
1
0
0
0
0
0
0
1
0
2
0
0
1
0
2
1
1
0
0
0
1
0
2
2
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
2
1
2
3
1
0
1
2
0
1
0
2
2
1
0
1
1
2
1
1
0
0
2
1
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
2
1
0
0
2
0
1
2
0
1
0
2
2
0
0
0
2
0
0
0
2
0
1
1
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
2
0
2
2
0
0
1
1
1
1
3
0
0
1
1
0
1
1
0
0
0
2
1
0
1
0
2
0
0
2
0
0
0
0
1
1
3
0
0
0
0
2
1
2
0
1
0
0
0
1
1
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
1
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
2
0
0
0
2
0
0
2
0
0
2
0
0
1
1
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
1
0
0
2
1
1
0
0
2
2
0
2
1
3
0
0
0
2
0
0
2
0
0
0
0
0
1
2
0
0
1
0
0
1
0
3
0
0
0
2
0
0
5
0
1
0
2
0
2
0
0
4
0
1
0
0
2
0
1
0
2
2
3
1
0
0
0
1
0
0
0
0
0
1
1
2
0
0
1
0
0
2
1
0
2
1
0
0
0
2
1
0
2
0
4
1
0
1
0
3
0
2
0
2
0
0
0
0
0
1
0
0
2
2
0
1
1
0
0
1
1
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
1
0
0
1
1
2
1
0
0
0
0
0
1
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
2
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
2
2
2
0
0
2
0
0
0
0
3
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
2
1
0
0
2
2
1
0
0
1
1
1
0
4
2
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
2
2
1
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
2
3
0
1
0
0
1
2
0
0
0
0
0
0
1
1
4
0
0
0
0
2
0
1
2
0
1
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
1
2
1
1
0
0
0
0
0
1
1
1
0
0
0
0
9
0
0
0
0
0
2
0
2
1
0
0
1
0
1
0
0
0
2
2
0
1
3
0
2
0
2
2
2
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
1
0
0
3
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
1
4
0
0
0
1
0
2
0
2
1
2
1
0
0
1
0
0
0
0
2
0
3
0
0
0
1
3
1
0
0
0
1
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
1
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
1
0
1
2
0
2
1
0
0
0
3
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
4
0
2
0
0
1
0
0
2
0
0
0
1
4
3
0
3
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
1
1
0
1
1
0
2
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
2
0
0
1
2
0
0
1
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
2
2
1
0
1
0
0
0
1
0
1
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
1
1
0
0
4
0
5
1
0
0
2
0
2
1
0
1
0
0
0
5
0
1
0
0
2
0
0
2
0
1
0
0
0
2
0
0
1
0
0
1
0
2
0
0
0
1
1
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
2
1
0
0
1
0
0
2
0
0
1
0
1
3
0
0
0
0
0
0
2
0
0
2
2
2
2
2
1
0
3
1
1
0
0
0
0
0
0
0
0
2
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
2
0
0
0
1
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
2
2
2
0
0
2
1
0
0
2
0
0
0
0
0
1
1
2
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
2
1
1
0
0
0
2
0
0
0
1
1
2
1
0
0
0
0
1
3
1
0
0
2
0
0
0
1
0
1
0
1
0
0
0
1
0
1
0
0
0
2
1
0
1
0
0
0
1
0
2
1
0
2
1
3
0
0
0
1
0
1
0
0
3
0
0
0
0
7
2
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
1
1
0
0
0
0
0
2
1
0
0
3
2
1
0
0
1
2
0
3
2
1
0
0
2
1
0
0
0
0
1
0
1
2
0
0
1
1
0
1
0
1
2
1
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
2
4
0
2
2
0
2
3
2
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
2
0
0
3
0
1
0
0
0
0
1
0
2
0
0
1
0
0
0
1
0
2
2
0
0
2
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
2
0
0
0
0
2
0
2
0
0
1
1
2
0
0
1
1
0
0
1
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
2
0
1
0
0
1
0
0
1
1
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
1
1
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
1
1
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
2
2
2
0
0
2
1
1
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
3
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
2
2
0
0
2
2
0
0
0
1
0
0
0
0
1
0
2
0
1
0
5
0
1
0
0
0
0
0
0
0
1
0
0
0
2
1
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
6
3
0
0
1
1
2
2
1
0
2
2
1
1
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
4
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
1
2
0
2
0
0
2
0
0
2
0
2
0
1
7
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
2
2
2
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
3
0
0
1
0
3
1
0
0
2
0
0
1
2
1
3
0
2
0
0
0
0
2
0
1
0
1
0
2
0
0
1
0
4
1
2
1
1
1
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
0
1
0
2
3
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
2
0
1
2
0
0
0
0
1
2
0
0
1
1
2
2
0
0
0
0
0
0
0
2
0
2
2
0
0
2
0
2
0
0
0
0
0
1
0
0
1
1
0
0
0
2
0
2
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
2
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
3
0
0
0
0
0
0
3
0
0
0
0
1
0
0
1
1
1
2
0
0
2
0
3
0
1
1
0
1
0
0
0
2
1
0
1
4
2
0
1
0
0
1
0
0
3
2
3
0
0
0
0
0
0
1
0
0
0
0
1
2
2
1
0
0
0
0
0
2
0
0
2
5
0
0
1
0
0
2
0
1
1
0
0
2
0
0
0
0
1
1
1
0
1
0
0
2
0
0
0
0
1
1
0
0
0
0
3
0
1
0
1
0
0
3
1
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
2
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
2
0
1
0
2
0
0
0
2
0
0
2
0
0
2
2
1
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
1
0
1
1
1
2
0
1
0
1
1
2
0
1
1
0
1
0
2
0
0
0
0
0
0
0
1
2
0
0
1
0
2
0
1
0
1
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
1
9
2
0
1
0
0
2
2
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
1
0
0
2
2
0
1
2
1
2
0
0
1
0
0
0
0
0
2
2
0
2
0
0
2
0
0
0
3
0
0
0
2
0
0
0
0
1
3
0
1
0
1
0
0
2
1
2
0
0
3
0
0
2
2
0
1
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
2
2
1
0
2
0
2
0
0
0
0
0
0
1
0
0
0
1
2
0
0
1
0
2
2
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
3
1
2
0
0
0
0
0
1
0
0
2
0
0
0
0
7
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
1
0
0
2
1
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
6
2
0
1
0
0
0
0
3
0
0
0
0
0
0
1
1
0
0
0
0
6
2
2
0
0
0
0
1
2
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
1
1
1
2
0
0
0
0
0
1
1
1
2
0
0
2
0
0
0
1
2
1
0
2
0
0
2
0
1
0
0
0
2
1
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
1
2
0
0
2
2
0
1
0
0
0
0
0
3
0
0
2
0
0
1
0
0
1
0
0
1
0
5
4
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
2
1
0
2
0
0
2
1
0
0
0
0
1
2
0
2
0
2
1
0
0
0
2
0
0
1
0
2
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
2
2
0
0
1
0
0
5
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
7
0
0
0
2
5
0
0
0
0
2
1
0
0
0
0
0
0
2
2
2
0
0
0
0
0
2
0
2
1
2
0
2
2
0
1
1
0
1
0
0
1
2
0
1
0
1
0
2
0
3
2
1
0
0
0
1
1
0
1
0
1
0
0
2
0
0
1
0
0
0
1
0
0
0
0
2
0
0
1
2
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
3
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
1
0
0
1
1
0
0
0
1
2
1
0
2
0
1
2
0
5
1
0
2
0
0
0
0
0
0
0
1
0
2
0
0
1
0
1
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
1
1
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
1
2
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
2
2
0
1
2
0
2
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
2
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
2
1
0
0
0
2
1
0
2
1
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
2
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
2
2
0
0
0
1
0
0
0
0
0
1
0
1
2
0
2
0
0
2
0
0
2
0
1
0
0
1
0
0
0
5
1
0
1
0
0
0
0
0
0
2
2
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
2
0
1
0
0
1
0
0
0
1
0
1
0
2
0
1
0
0
2
0
0
0
1
0
0
2
0
0
1
2
0
0
0
0
0
3
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
3
0
1
1
1
0
0
0
1
0
2
0
1
0
0
0
1
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
1
0
0
3
0
0
0
0
2
4
2
0
1
0
0
0
0
0
4
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
2
1
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
1
0
1
1
0
0
0
0
1
0
1
1
3
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
5
0
0
0
0
0
2
0
2
1
0
2
0
0
1
3
0
0
0
0
2
0
2
0
1
0
0
0
1
0
0
2
0
0
0
0
1
2
1
0
2
0
2
0
1
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
2
1
0
1
0
1
0
0
1
1
0
2
2
0
0
0
0
0
2
0
2
2
1
1
2
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
2
1
1
1
2
1
2
0
1
1
0
0
0
2
3
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
2
2
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
2
1
1
2
0
0
0
0
1
0
2
1
1
0
0
0
0
0
0
0
1
0
1
2
0
0
1
1
0
0
0
1
0
0
3
0
3
0
1
0
7
0
1
2
0
0
2
0
2
0
2
2
0
0
0
1
2
0
0
2
2
0
2
0
1
0
0
0
0
0
0
3
0
2
0
2
0
0
3
1
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
1
1
0
2
0
0
0
0
2
0
0
0
1
0
0
2
1
0
0
1
1
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
3
1
0
2
0
0
2
0
2
1
0
1
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
2
0
1
2
0
2
0
0
1
0
0
0
0
2
0
0
2
0
1
0
0
2
1
0
0
2
0
2
2
2
0
0
0
2
0
0
0
0
1
0
1
0
1
2
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
3
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
4
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
1
1
0
0
2
0
0
0
0
0
2
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
2
0
2
0
1
2
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
2
2
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
2
0
1
1
3
0
2
0
0
1
2
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
1
0
0
2
1
2
2
0
1
3
0
0
4
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
2
2
2
0
0
0
0
2
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
1
0
0
2
0
1
0
0
0
1
6
0
2
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
1
0
1
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
4
0
0
2
0
4
0
0
0
0
1
0
0
0
0
3
2
0
1
0
1
0
0
1
0
0
2
2
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
1
0
0
1
0
3
0
0
0
1
0
0
1
0
2
0
2
0
0
1
2
2
3
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
2
2
0
0
0
2
2
0
1
0
0
2
0
2
1
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
2
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
3
0
1
1
1
0
1
0
2
2
0
0
0
0
1
1
0
1
0
0
2
0
1
0
0
0
0
2
0
0
0
1
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
1
0
0
0
0
1
1
2
0
0
5
2
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
2
0
0
2
1
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
2
3
0
0
0
0
1
0
0
3
0
0
0
1
0
0
0
2
2
0
0
0
2
1
1
1
1
1
0
0
2
0
0
0
1
3
1
1
0
0
0
2
2
1
0
0
2
0
2
0
0
0
0
1
2
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
2
0
0
2
1
1
1
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
2
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
2
1
0
1
0
2
0
0
0
1
0
0
2
0
0
0
0
2
1
2
0
2
1
0
0
0
2
0
1
0
0
0
0
0
2
0
2
2
0
2
0
1
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
1
2
1
2
0
0
0
2
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
3
0
0
0
1
2
0
0
0
1
0
4
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
7
3
0
0
0
0
1
0
2
2
1
0
2
0
2
2
0
0
0
1
0
0
2
0
2
0
0
0
1
1
0
0
1
3
0
0
2
0
0
0
0
0
0
0
0
2
0
3
1
2
0
0
1
0
0
0
0
1
2
2
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
1
0
2
1
0
0
0
0
0
0
0
2
2
0
0
0
1
1
0
0
0
0
0
1
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
1
0
0
0
1
0
0
2
2
0
0
0
2
0
0
2
0
0
2
0
0
2
2
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
2
0
2
2
0
2
1
0
0
0
1
0
0
0
0
1
0
2
0
2
0
1
0
0
1
0
0
1
0
0
0
0
3
0
0
2
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
3
0
1
0
2
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
1
0
0
2
0
2
0
1
0
0
0
3
0
0
0
0
0
2
1
0
0
0
1
2
0
0
1
2
0
1
2
0
0
0
2
1
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
1
0
2
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
2
0
2
4
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
2
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
1
0
1
2
0
0
0
1
2
1
1
0
1
1
0
1
0
1
0
0
0
0
1
1
2
0
0
0
0
0
0
0
2
1
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
2
2
1
0
0
1
0
0
1
0
1
1
0
2
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
1
3
0
1
0
0
1
0
0
2
0
0
2
0
2
0
0
0
0
3
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
1
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
3
0
2
0
0
0
0
2
2
0
2
0
0
0
0
0
1
1
0
0
1
1
0
0
5
0
1
0
2
0
10
0
0
0
2
0
1
0
0
0
0
0
0
0
2
1
1
1
4
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
1
2
1
0
0
1
0
0
0
0
0
1
2
0
1
0
1
1
0
0
0
0
1
2
1
2
0
0
0
2
0
0
0
2
0
0
1
0
0
0
1
0
2
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
2
2
2
0
0
0
0
2
0
0
1
0
2
2
1
1
1
0
0
0
2
0
0
2
0
2
1
1
1
0
0
0
0
0
1
0
0
3
0
0
0
1
0
1
0
2
0
0
0
3
2
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
5
0
1
3
1
0
0
0
1
0
0
4
0
0
0
0
3
0
1
1
0
0
1
0
0
1
0
0
0
1
1
1
1
1
0
1
1
2
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
4
1
0
0
0
0
2
0
1
0
0
2
1
0
2
2
1
2
0
0
1
0
1
2
0
0
2
0
1
0
2
0
2
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
3
2
1
0
1
1
2
0
2
3
0
2
2
1
1
0
0
2
0
0
1
0
2
1
0
0
0
2
2
0
0
0
2
2
0
2
1
0
2
0
1
0
0
0
1
0
0
0
1
0
0
0
0
2
0
2
3
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
2
0
0
0
0
2
0
1
0
0
2
1
2
0
0
0
0
0
0
2
1
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
1
0
0
2
1
0
2
2
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
2
1
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
2
1
0
1
0
1
1
3
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
2
0
2
1
0
0
0
3
2
2
0
2
0
0
0
1
0
0
0
0
2
0
0
1
1
0
0
0
1
0
1
0
0
1
1
0
0
0
2
0
1
1
0
2
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
2
0
0
0
0
0
0
2
1
1
0
0
5
0
0
0
0
1
2
0
2
0
0
0
0
0
1
2
0
2
2
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
1
0
0
0
2
0
2
0
1
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
1
1
2
0
0
0
0
2
0
1
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
3
0
0
3
0
0
0
1
0
1
0
1
0
2
2
0
1
0
0
0
0
0
0
2
0
0
0
2
3
2
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
1
0
0
0
0
2
0
0
2
1
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
2
0
0
0
1
0
0
0
0
3
0
0
2
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
1
0
0
0
1
2
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
1
2
0
0
1
0
2
0
0
0
2
1
1
0
2
0
2
0
0
0
2
0
0
4
0
0
0
0
0
0
1
1
1
4
0
0
0
4
0
0
0
0
0
1
0
0
2
1
1
1
0
1
0
1
2
0
0
0
0
2
0
1
0
2
1
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
2
1
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
12
0
2
1
0
0
1
1
0
0
0
0
0
2
0
3
1
0
0
0
1
0
0
0
0
3
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
1
0
0
1
0
2
0
3
2
0
2
1
0
0
2
0
1
1
0
0
0
1
2
1
2
2
2
1
0
0
3
0
1
0
0
2
0
0
0
1
0
0
0
1
0
2
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
2
0
0
1
0
0
0
0
4
0
0
0
0
2
2
0
0
0
1
0
0
1
0
1
0
2
0
0
0
3
0
0
0
0
0
0
1
0
2
0
0
1
2
0
0
1
0
0
0
0
0
2
0
4
0
0
0
5
0
2
0
3
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
4
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
2
2
0
0
0
0
2
1
0
0
0
0
2
1
1
2
2
0
0
0
1
0
0
0
2
2
0
4
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
2
0
0
0
0
2
3
0
0
3
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
3
0
0
2
0
0
0
0
1
2
0
0
2
3
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
1
0
3
0
0
2
2
0
2
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
1
0
0
0
2
1
7
0
0
2
0
0
0
3
0
1
0
2
2
0
0
1
0
0
0
3
0
0
1
0
1
0
1
0
0
0
2
0
0
2
0
1
0
0
2
0
1
0
0
0
0
0
1
2
0
0
2
2
1
1
0
0
2
0
0
0
1
1
0
0
1
0
1
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
2
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
1
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
1
0
0
1
0
4
7
0
2
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
7
0
1
1
1
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
2
0
2
0
2
0
2
0
2
0
3
0
0
0
2
3
1
0
1
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
2
0
0
0
0
2
0
2
0
0
0
0
1
2
0
1
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
2
0
0
0
3
0
0
0
0
1
4
2
0
0
0
0
0
1
1
1
0
2
2
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
2
1
1
0
0
1
0
0
2
0
2
0
0
0
0
0
1
0
1
0
0
2
0
0
0
1
0
1
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
3
2
0
0
2
0
0
0
1
0
0
1
2
3
0
3
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
2
0
2
0
0
0
0
1
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
2
0
2
3
1
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
1
2
0
3
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
2
2
1
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
2
0
0
1
1
1
3
0
0
0
2
0
0
1
0
2
2
1
0
1
1
0
0
0
0
0
1
0
1
3
1
0
0
0
2
1
0
0
2
1
0
1
0
0
2
0
0
2
2
0
0
0
1
0
1
0
2
0
0
0
0
1
1
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
1
0
0
1
0
0
2
0
0
0
0
0
0
1
1
1
0
0
1
1
0
0
0
1
0
0
0
1
1
0
2
0
0
0
0
0
0
3
0
1
0
0
0
0
0
1
0
0
2
3
2
3
0
2
0
0
2
0
0
2
1
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
2
2
1
1
0
0
0
0
0
2
0
0
0
2
0
2
1
0
0
0
2
0
0
0
0
0
0
2
2
0
0
1
0
0
1
2
1
2
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
1
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
1
0
2
1
0
0
0
0
0
1
2
1
0
0
0
0
0
1
0
1
0
0
2
2
0
0
0
0
0
0
1
0
2
0
2
2
1
0
1
0
0
0
1
0
0
2
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
1
1
0
0
1
0
2
0
1
0
0
0
0
0
1
0
0
2
2
0
0
0
1
0
2
1
0
0
1
2
0
0
1
1
0
0
0
0
1
0
0
2
1
1
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
2
0
0
1
3
0
1
2
0
1
2
0
1
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
1
3
0
0
0
0
2
1
0
0
1
0
0
0
0
0
1
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
1
2
0
0
0
2
0
0
2
0
2
1
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
3
2
0
0
0
0
1
0
1
1
1
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
7
2
0
0
2
0
2
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
5
1
2
1
1
0
0
0
0
2
3
2
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
2
0
1
2
0
1
1
1
1
3
1
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
1
0
0
0
3
0
1
0
0
0
2
1
0
1
1
0
1
0
0
0
0
0
1
1
2
0
0
1
2
0
0
2
0
1
0
2
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
2
0
1
0
1
0
1
0
0
0
0
0
0
0
2
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
3
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
2
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
2
0
1
2
1
1
0
0
0
0
0
2
5
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
1
2
2
0
0
0
0
0
0
0
2
2
1
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
2
1
0
2
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
1
1
1
0
0
0
1
0
0
0
0
0
0
2
0
1
1
0
0
0
1
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
7
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
2
2
2
0
8
0
0
0
1
0
3
1
0
0
1
1
0
0
0
2
0
0
1
0
1
2
0
0
2
2
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
1
1
0
0
2
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
1
0
0
0
1
1
0
0
0
2
2
0
0
0
1
0
0
0
1
1
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
1
0
0
2
1
0
1
0
0
0
0
1
2
0
0
0
0
2
2
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
1
0
1
0
0
0
2
0
2
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
2
0
0
0
2
0
0
0
0
1
3
0
0
1
1
3
1
0
1
1
0
0
1
0
2
1
0
0
0
2
0
0
0
1
2
0
0
2
0
2
0
1
0
0
3
0
2
0
0
2
3
0
0
0
1
1
0
0
0
0
2
0
0
0
0
3
0
2
0
0
0
0
0
1
1
0
0
0
0
0
1
2
0
0
1
2
1
0
1
2
0
0
1
0
0
1
0
0
0
0
1
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
2
1
2
0
0
1
0
0
0
2
0
0
1
4
0
2
1
1
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
3
2
0
0
2
0
1
0
1
1
1
0
0
0
0
0
2
1
0
0
0
0
0
1
3
2
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
3
2
0
2
1
0
0
0
0
0
0
1
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
2
0
0
0
0
0
2
0
0
0
0
2
0
2
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
2
1
0
2
0
0
2
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
2
0
0
0
0
0
2
1
1
0
6
1
0
0
0
0
2
1
0
0
0
0
2
0
0
1
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
4
0
0
0
0
1
3
1
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
1
0
1
1
2
0
2
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
1
0
2
0
1
1
0
0
0
1
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
2
0
2
0
0
0
0
2
0
0
1
0
1
2
0
0
0
0
0
2
0
1
0
0
0
0
1
0
1
0
1
1
2
2
1
0
0
0
0
0
0
0
0
2
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
1
1
0
0
0
0
0
0
1
1
2
0
0
0
1
0
0
0
1
0
0
0
0
0
9
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
2
0
0
0
3
1
1
0
0
2
1
0
1
0
1
0
0
0
0
2
0
0
0
2
0
1
3
1
2
0
0
0
0
1
0
0
0
1
0
0
3
0
0
2
0
0
0
1
0
0
0
0
0
1
2
1
0
0
0
0
1
0
3
0
0
1
2
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
2
2
0
1
2
0
0
0
3
0
1
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
2
2
0
0
0
1
0
2
0
0
1
0
0
0
0
2
4
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
2
0
0
1
0
0
0
0
1
0
1
1
2
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
1
2
0
0
1
1
0
1
2
2
0
2
0
0
0
0
0
0
0
2
0
2
0
1
0
1
0
0
1
1
0
1
0
2
0
2
0
0
2
1
1
2
0
0
0
0
2
4
0
0
0
2
0
1
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
1
1
0
0
0
1
0
1
0
0
1
2
1
0
0
2
1
2
1
0
4
1
0
0
2
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
2
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
3
0
0
0
0
2
0
1
1
1
0
0
1
1
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
3
0
0
0
0
0
0
1
0
2
0
1
0
1
1
0
0
2
0
0
1
0
0
1
0
6
2
0
2
0
2
0
1
0
1
2
0
1
0
0
0
2
2
0
0
0
0
0
0
0
3
1
0
0
2
0
2
0
0
0
0
1
3
0
0
1
0
0
0
2
1
0
0
0
0
0
0
2
0
0
1
2
0
0
0
1
0
0
3
0
0
0
0
1
1
0
0
0
2
0
2
0
1
0
0
1
1
3
2
1
0
1
0
1
2
0
0
0
1
0
2
0
0
0
0
2
2
0
3
2
0
2
0
0
0
0
0
2
0
0
2
2
0
0
1
0
1
0
0
1
0
2
0
0
0
0
1
0
2
0
0
0
0
0
2
2
1
0
2
0
0
1
0
0
2
1
0
0
1
0
0
0
2
0
0
1
0
0
0
3
0
0
0
0
0
1
0
0
2
2
0
2
1
4
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
1
0
2
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
2
2
0
0
0
2
0
0
0
0
2
1
1
0
0
1
0
0
0
2
0
3
0
0
0
0
3
0
0
0
2
0
2
0
3
0
0
0
2
0
0
2
0
3
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
2
0
1
0
2
1
3
0
2
0
1
0
1
2
0
0
0
1
0
2
2
2
2
0
0
0
1
1
2
1
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
1
2
2
1
2
1
0
1
0
0
2
2
0
2
0
0
2
0
0
0
3
0
0
0
1
0
0
2
0
0
0
1
0
0
2
0
2
0
2
0
0
0
0
0
2
1
0
0
0
1
0
0
0
1
0
0
0
0
2
1
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
1
0
4
0
0
0
1
0
0
2
2
1
0
0
2
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
2
1
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
1
2
0
2
0
0
1
0
0
2
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
3
0
0
0
1
0
0
1
0
1
0
2
0
0
0
0
0
0
0
3
1
1
0
0
0
3
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
3
0
0
0
6
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
1
0
0
2
1
1
0
0
0
0
2
0
1
0
2
2
0
3
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
2
1
1
2
1
0
1
1
0
0
0
1
3
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
1
0
2
0
2
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
2
2
0
0
0
0
0
0
2
0
1
0
1
2
0
0
0
0
2
0
0
0
0
0
2
1
0
0
2
0
1
0
0
0
0
1
0
1
2
2
0
0
0
0
0
0
2
0
0
2
1
2
0
0
0
2
1
2
0
0
0
1
1
0
1
2
0
0
0
0
0
0
0
0
0
2
2
2
1
0
1
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
3
0
2
0
0
0
0
0
0
0
1
0
0
1
0
1
0
2
2
1
0
0
0
0
0
1
0
2
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
1
1
1
0
0
1
0
0
1
0
1
0
0
0
0
1
0
1
1
1
0
0
0
0
0
2
0
0
0
0
0
0
14
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
2
4
0
0
0
1
0
2
0
0
0
0
1
0
0
2
0
0
0
2
2
2
0
4
1
0
0
1
1
0
0
3
0
0
2
0
2
2
0
1
0
1
0
2
2
0
3
1
3
0
0
0
2
0
0
0
0
0
0
2
0
1
2
0
0
1
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
2
0
0
0
1
0
0
0
1
0
0
3
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
1
0
0
3
0
2
1
0
0
1
2
2
0
0
0
0
0
0
3
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
2
2
1
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
3
0
2
0
0
4
2
1
0
0
1
0
0
0
2
0
0
0
0
1
1
1
1
2
0
0
0
1
0
2
2
0
1
2
0
3
0
0
2
0
0
0
0
0
0
0
1
1
4
0
1
0
0
0
1
2
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
2
0
0
0
0
1
0
2
1
1
0
2
1
0
0
0
0
2
2
2
1
1
0
0
0
2
1
0
0
0
2
1
0
0
1
0
2
3
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
2
2
2
0
0
2
0
0
0
2
2
2
0
0
1
0
2
0
2
0
0
4
0
2
0
0
2
0
6
1
1
2
0
2
1
0
0
0
2
0
2
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
2
0
0
2
2
0
2
0
1
1
0
0
2
0
0
0
0
0
1
2
4
0
2
0
0
0
1
1
0
0
1
0
0
4
0
0
0
2
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
2
0
0
0
0
0
1
1
2
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
1
0
0
2
0
2
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
1
1
2
2
0
0
0
0
0
0
0
0
0
1
0
0
2
1
2
2
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
2
0
1
0
0
0
1
1
2
2
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
2
0
1
0
2
2
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
2
0
3
1
0
2
4
2
1
0
0
0
2
2
1
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
2
3
2
1
2
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
2
2
1
2
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
1
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
3
0
0
1
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
1
0
1
0
2
0
0
1
0
0
0
1
0
0
2
0
2
2
0
2
0
0
1
0
2
1
0
0
0
0
1
0
3
0
1
1
0
0
0
0
0
0
0
0
0
0
0
3
1
2
2
0
2
0
0
0
2
0
0
1
0
0
1
0
0
2
2
0
1
2
0
0
0
0
0
0
0
1
1
1
0
0
0
0
2
1
0
0
0
2
0
2
3
0
0
0
0
2
0
2
0
0
0
0
1
0
2
1
1
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
1
1
0
0
0
0
0
0
1
0
1
1
0
0
1
4
0
0
2
0
0
2
0
4
2
1
0
1
0
0
1
2
0
2
0
0
1
0
0
2
0
0
0
2
0
0
1
0
0
0
1
2
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
3
0
3
0
0
0
0
0
2
1
0
0
0
1
0
0
1
0
0
2
1
1
0
0
0
0
0
0
0
0
2
0
0
0
3
0
1
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
2
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
2
1
2
2
0
2
0
1
2
2
0
0
0
0
0
1
0
1
0
0
3
0
0
0
2
0
0
0
2
0
0
1
0
1
2
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
1
0
0
0
0
0
1
2
4
2
3
0
2
2
0
1
0
0
0
1
0
0
0
0
0
2
2
0
0
0
2
1
1
0
1
4
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
1
1
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
2
0
0
0
0
2
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
1
0
0
2
0
0
0
1
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
1
2
0
0
2
0
0
0
5
0
1
0
2
1
0
0
2
0
0
0
0
2
0
1
2
2
0
1
1
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
4
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
2
0
2
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
2
1
0
2
0
0
0
0
0
2
1
1
1
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
2
0
2
1
0
0
0
0
1
0
2
0
1
0
0
0
1
3
3
0
0
0
0
0
2
3
0
0
2
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
1
2
1
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
1
0
2
2
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
2
2
2
1
0
2
0
0
2
0
0
0
0
0
3
0
1
0
0
0
0
2
0
0
0
0
2
2
0
0
3
2
1
0
0
0
0
0
0
0
0
1
2
0
1
2
0
2
0
0
0
1
1
0
1
1
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
2
1
0
0
0
1
1
1
0
0
0
1
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
8
1
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
2
0
1
1
0
1
3
0
2
0
0
1
1
2
1
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
2
1
0
0
2
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
2
0
0
0
2
0
0
2
0
2
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
2
0
0
0
0
0
0
3
2
1
1
0
0
0
0
2
1
0
3
0
0
0
4
0
0
1
0
2
0
0
2
0
0
2
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
6
1
2
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
4
2
0
0
0
0
2
0
0
1
0
0
2
0
1
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
2
0
0
1
1
2
0
0
1
0
2
1
0
0
0
1
0
0
0
0
1
1
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
1
0
0
2
1
1
0
1
0
1
0
3
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
3
0
2
0
2
0
0
0
0
1
1
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
1
1
0
2
0
0
0
2
1
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
2
0
2
4
0
1
0
0
1
0
1
0
0
0
0
1
0
3
0
0
1
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
2
1
0
0
3
0
0
2
0
0
0
0
1
0
0
0
0
2
1
2
0
0
0
0
1
0
0
0
2
0
0
2
1
0
1
0
0
0
0
0
0
0
0
1
0
2
1
3
3
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
3
0
0
0
0
2
0
0
0
0
2
2
1
0
1
0
0
0
0
1
2
0
1
2
0
0
0
0
0
2
2
0
2
1
0
0
0
0
0
0
2
0
1
0
0
1
1
0
0
0
0
0
1
0
0
1
1
2
0
0
1
0
0
2
0
1
0
0
1
0
2
1
2
1
0
0
0
0
0
0
0
2
0
0
2
2
1
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
1
2
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
1
0
2
2
1
0
0
0
0
0
0
2
0
3
2
0
0
0
0
0
0
2
0
0
2
0
3
1
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
1
1
0
2
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
1
2
0
2
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
1
2
0
4
0
2
0
0
1
0
0
2
0
0
0
2
0
1
1
1
0
1
2
2
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
2
1
0
0
0
0
2
0
2
0
0
1
0
0
1
1
0
0
2
2
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
1
0
2
0
0
2
0
3
1
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
1
0
1
0
0
0
0
2
0
0
0
2
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
2
0
1
2
1
0
0
0
1
1
0
3
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
1
2
0
1
0
2
1
0
1
0
0
0
0
0
0
5
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
4
1
2
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
1
0
0
0
3
2
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
3
1
2
0
1
0
0
0
0
2
1
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
2
1
0
1
1
2
2
0
0
0
0
1
0
0
0
2
1
0
0
0
0
1
0
0
0
0
2
0
0
1
0
3
1
2
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
1
0
0
2
0
1
1
0
1
0
0
1
2
3
2
0
0
1
0
2
2
1
0
1
0
0
10
1
0
0
0
2
0
0
0
0
2
0
0
0
1
0
1
2
0
2
2
0
3
0
0
2
0
2
2
1
2
2
1
2
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
1
0
0
1
0
1
1
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
2
0
0
0
0
1
0
0
0
3
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
2
2
0
1
0
2
0
0
2
0
2
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
1
0
0
2
2
0
0
1
2
0
1
0
0
0
0
2
2
2
0
0
0
1
2
0
2
0
0
0
0
7
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
2
1
2
1
1
0
0
0
2
0
2
0
0
2
0
2
0
0
0
0
2
2
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
2
0
1
0
2
1
0
2
0
2
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
2
1
2
3
2
2
0
0
0
0
1
0
2
0
1
1
0
2
0
0
0
2
1
0
0
0
0
0
0
1
1
2
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
2
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
1
1
0
0
0
0
0
2
1
0
0
0
2
0
2
1
1
2
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
1
0
2
0
2
0
0
1
0
1
2
0
0
1
0
0
1
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
1
0
0
2
0
2
0
1
2
0
2
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
1
0
0
4
0
1
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
1
2
0
0
1
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
1
2
0
0
0
0
0
1
0
2
0
0
0
2
1
1
0
0
2
0
0
0
1
0
0
0
2
2
0
0
1
1
0
1
1
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
1
1
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
1
0
0
2
0
0
2
1
0
0
2
0
0
0
0
2
0
0
1
0
0
2
0
3
0
0
0
0
0
0
0
1
2
3
0
2
0
2
2
0
0
0
2
0
0
0
0
1
1
1
0
4
0
0
0
2
1
0
0
0
4
1
0
0
2
0
0
0
1
2
0
0
0
3
2
0
2
0
0
2
2
2
0
0
1
0
0
0
0
2
1
0
0
1
2
0
3
0
0
0
0
0
0
0
0
1
0
1
0
1
2
0
0
0
0
0
0
0
1
0
0
2
1
0
2
0
2
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
1
1
0
0
2
3
0
0
0
2
0
2
0
0
0
0
1
1
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
2
1
0
0
2
0
0
2
0
2
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
2
0
0
0
0
0
0
2
0
2
0
1
1
0
0
2
0
0
0
1
0
0
2
0
0
3
0
2
0
0
0
0
0
2
3
4
0
0
0
0
12
0
0
0
0
3
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
2
0
3
0
2
1
2
1
0
0
2
2
2
0
0
0
1
0
0
2
1
0
2
0
0
0
2
0
0
0
0
2
2
0
0
0
5
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
1
2
0
1
1
0
2
0
0
1
1
1
0
0
2
0
0
0
0
0
2
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
1
2
0
0
2
2
0
0
1
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
1
0
2
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
2
1
1
2
0
0
0
0
0
2
2
0
1
0
0
0
0
0
2
0
1
1
0
0
1
2
0
0
2
3
1
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
1
1
0
1
0
0
0
1
1
0
1
0
0
0
0
2
0
2
0
0
2
0
2
0
1
1
1
0
1
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
1
0
2
0
0
0
1
0
2
2
0
0
0
1
0
0
0
1
0
0
0
1
1
1
2
0
3
2
0
3
2
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
1
0
4
1
0
0
2
0
1
0
1
2
0
2
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
2
3
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
2
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
4
0
0
0
1
0
0
2
3
1
2
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
3
0
0
0
0
0
2
0
1
2
0
0
0
0
2
1
0
0
0
2
2
0
0
1
1
1
0
2
2
0
1
0
0
0
0
2
1
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
2
0
2
0
2
0
0
4
1
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
4
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
1
0
2
2
0
1
0
1
0
1
2
0
0
0
2
0
2
2
2
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
2
2
1
1
0
0
3
0
0
3
0
2
0
0
2
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
2
0
0
0
0
0
1
0
1
0
2
0
1
2
0
0
3
0
0
2
1
0
1
0
0
0
0
0
0
1
1
2
2
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
2
0
2
0
0
0
0
0
0
2
0
2
0
0
1
2
1
1
2
0
0
0
0
1
2
0
1
0
1
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
6
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
1
2
1
2
0
0
0
1
0
2
0
2
0
0
0
0
2
0
0
0
0
3
1
0
0
1
0
1
0
0
0
0
1
2
0
0
0
2
2
0
0
0
0
1
1
0
0
1
0
2
1
0
0
0
1
0
0
0
0
0
1
0
3
0
1
1
1
0
0
0
0
0
0
1
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
2
2
2
1
2
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
2
1
1
1
0
0
0
2
2
0
2
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
2
2
0
0
2
1
0
0
2
0
0
0
3
2
1
0
0
0
1
0
1
1
0
3
3
0
1
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
2
1
1
0
0
2
1
0
0
2
0
0
1
1
4
0
0
1
2
1
1
0
0
0
0
2
2
3
0
2
0
0
0
0
2
0
2
2
0
1
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
2
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
2
2
4
0
2
2
0
0
0
0
0
3
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
2
0
0
2
0
1
1
0
0
0
0
0
1
1
0
2
0
0
2
0
0
2
0
0
2
0
0
1
2
2
0
0
2
2
2
0
0
0
0
1
1
0
1
0
3
0
1
0
0
0
0
0
2
1
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
3
0
0
1
1
2
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
1
1
1
2
2
2
0
0
0
1
0
2
0
1
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
2
0
2
3
3
0
0
0
0
0
5
2
2
0
1
2
0
3
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
1
0
1
0
0
1
2
0
0
1
0
2
0
2
1
2
0
0
2
0
0
3
0
0
1
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
3
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
1
0
2
2
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
2
0
2
1
2
0
0
0
0
0
0
1
1
2
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
1
0
0
0
1
1
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
4
0
1
0
0
1
0
0
2
2
0
0
2
0
2
2
0
0
2
1
0
0
0
1
0
0
0
1
0
0
2
0
0
0
2
0
1
2
0
0
0
0
2
1
0
2
3
0
1
0
0
0
0
0
4
2
1
0
1
0
6
1
0
0
0
0
0
2
0
0
2
0
0
1
1
0
1
4
1
1
0
0
1
0
0
1
1
1
0
2
0
0
0
0
0
0
0
2
1
0
0
4
3
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
1
1
3
1
0
0
0
0
0
2
0
1
0
0
2
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
1
2
0
0
0
0
1
0
0
2
0
0
0
0
2
1
2
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
1
0
2
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
3
0
0
2
0
2
0
0
0
0
0
0
2
0
1
0
0
2
2
1
0
2
0
3
3
0
0
2
1
1
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
3
0
0
0
0
3
0
0
0
0
1
2
0
0
1
0
0
0
1
0
2
0
1
2
0
0
0
0
2
1
0
0
1
0
0
1
0
0
0
1
1
0
0
0
1
2
0
0
0
1
0
1
0
0
0
0
2
2
0
0
2
0
1
0
2
0
0
0
0
0
2
0
2
0
0
1
0
0
2
1
0
0
2
1
2
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
1
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
1
0
0
2
0
0
0
0
1
0
0
2
2
0
0
0
0
0
1
0
0
0
1
1
0
0
0
2
2
0
1
1
0
0
0
1
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
2
0
1
1
0
0
2
0
0
0
2
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
2
1
0
0
0
1
0
0
0
2
2
0
0
2
0
1
1
0
0
1
1
0
0
0
1
1
2
0
0
2
1
0
0
0
0
1
0
1
0
2
0
0
0
1
0
0
2
0
1
1
1
3
0
0
0
2
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
2
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
2
0
0
0
2
1
0
2
0
0
2
1
2
0
0
1
1
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
5
1
0
0
0
0
2
0
1
0
0
0
0
1
2
0
0
0
0
1
0
0
5
1
0
0
0
2
0
2
2
0
1
2
1
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
2
0
0
0
3
0
0
0
2
0
2
1
2
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
2
1
0
1
0
0
0
1
2
1
0
3
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
1
2
0
0
0
0
0
3
0
2
0
0
2
0
0
0
0
3
0
2
3
1
1
0
0
0
0
0
2
0
0
1
0
2
2
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
1
2
1
0
0
0
1
2
0
0
0
1
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
1
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
1
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
2
1
0
2
3
0
1
1
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
2
2
0
0
0
1
0
0
1
1
0
2
2
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
5
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
3
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
2
0
0
0
0
1
2
0
1
0
4
0
0
0
2
1
0
0
0
2
0
0
1
1
0
0
1
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
1
0
2
0
0
0
0
1
2
1
0
1
2
0
1
3
2
0
2
0
2
0
0
0
0
1
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
3
0
0
1
1
2
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
1
0
0
1
1
1
0
1
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
2
2
0
0
0
0
2
1
1
4
0
0
0
0
0
2
0
1
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
2
1
0
1
0
0
0
2
1
2
2
1
0
0
2
2
1
2
0
3
3
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
3
0
1
0
1
0
1
0
0
1
1
0
0
0
2
2
2
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
2
0
0
0
0
0
1
0
1
0
2
0
0
0
2
3
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
1
1
2
0
0
1
1
0
0
1
3
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
3
0
1
1
2
2
2
1
1
0
2
0
0
0
0
2
0
0
1
1
2
0
0
0
0
0
1
2
0
2
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
4
0
0
1
0
3
0
0
1
2
0
0
0
0
2
0
0
3
0
2
1
0
2
0
0
0
1
0
2
1
0
2
0
0
1
2
0
0
0
2
0
0
0
1
1
0
2
0
0
0
0
5
0
0
0
0
2
0
1
0
0
0
0
0
4
2
0
0
1
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
2
0
0
1
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
2
2
1
0
2
0
1
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
3
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
1
0
0
0
0
0
3
1
0
0
0
0
1
0
1
2
0
0
0
0
1
2
1
3
1
0
0
0
2
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
1
0
4
1
3
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
2
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
2
0
2
2
1
0
0
0
0
3
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
1
2
1
0
3
0
0
0
2
0
0
2
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
2
1
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
2
0
0
1
0
1
0
1
2
0
0
0
0
0
1
0
0
0
1
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
3
0
0
0
2
0
0
2
2
0
1
0
0
2
1
0
0
0
0
0
3
0
1
0
0
0
2
0
1
0
2
2
2
0
0
1
1
2
2
2
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
2
0
0
2
0
0
0
2
0
1
3
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
2
2
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
1
1
0
1
1
1
0
0
0
2
1
1
2
0
1
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
2
2
2
0
0
0
2
1
1
1
3
1
1
0
0
0
0
0
0
3
0
0
1
0
2
0
0
0
1
2
3
0
0
0
0
0
4
0
0
1
0
0
1
0
2
1
1
0
0
0
0
1
2
0
0
0
0
0
0
5
3
3
0
0
1
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
2
0
0
1
0
0
0
2
1
1
0
0
0
2
0
0
0
0
2
0
0
0
0
1
2
2
1
0
2
0
0
0
0
1
0
3
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
2
0
1
0
2
0
0
0
0
0
1
2
2
1
0
2
2
2
0
0
0
1
0
0
0
2
0
0
0
0
1
1
0
0
1
0
0
2
0
0
0
0
0
1
1
0
0
1
0
0
2
0
2
0
0
0
0
0
0
1
2
2
2
0
0
0
1
1
1
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
2
0
0
0
0
1
0
0
0
2
0
2
2
0
0
0
1
0
2
0
0
0
0
0
2
2
0
0
1
0
0
2
1
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
2
0
1
1
2
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
2
2
2
1
1
2
1
0
1
0
0
0
2
0
0
0
3
0
1
0
0
0
2
2
1
0
0
2
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
4
1
4
1
2
0
0
1
0
0
0
0
0
0
1
0
0
0
5
0
0
0
2
0
0
1
0
0
0
1
0
0
0
1
2
0
2
0
0
2
1
0
2
0
1
0
0
1
1
1
0
0
0
0
2
0
2
0
0
0
0
1
2
2
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
2
2
0
0
0
0
0
1
3
1
2
1
0
1
2
0
2
2
0
2
0
0
0
2
2
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
2
0
0
0
0
0
1
0
0
0
2
0
0
0
1
2
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
2
1
0
0
1
0
0
0
0
0
1
0
1
2
0
1
2
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
2
0
2
0
1
0
0
0
1
0
2
2
0
1
0
2
1
0
2
0
0
0
0
3
0
0
0
0
1
1
1
1
0
1
2
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
2
1
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
4
0
0
0
0
3
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
1
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
1
1
1
2
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
3
0
0
0
2
0
0
0
0
1
2
1
2
2
0
2
2
1
0
0
3
2
0
0
2
1
1
2
0
0
1
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
1
0
0
0
0
1
2
0
1
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
1
0
2
0
2
0
2
3
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
5
1
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
2
0
1
0
1
1
0
2
2
0
0
0
1
0
0
0
1
0
0
2
0
2
0
0
1
0
0
0
2
1
0
0
2
0
0
0
1
0
0
0
2
1
0
1
2
2
1
0
0
0
0
1
0
2
0
0
0
2
0
0
2
2
0
4
0
2
0
0
0
1
0
0
1
0
1
1
0
2
2
0
0
0
2
1
2
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
2
0
0
0
0
0
0
0
2
2
0
4
2
0
0
1
1
0
1
0
0
0
0
0
0
0
2
2
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
1
0
1
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
3
1
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
2
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
2
0
2
1
0
0
0
0
0
0
1
0
0
1
2
0
0
1
0
0
2
1
0
1
0
0
0
2
0
0
1
1
0
0
0
2
0
0
1
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
1
2
0
0
0
0
0
2
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
3
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
4
2
0
1
1
0
0
0
0
0
1
0
1
0
0
1
0
0
2
0
0
0
1
1
1
0
0
2
1
0
0
0
0
2
0
2
0
2
1
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
3
1
1
0
0
2
1
1
0
0
1
0
0
0
0
2
1
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
2
1
0
1
1
0
3
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
1
1
0
0
0
2
0
1
2
1
0
0
0
1
1
2
0
0
0
1
0
0
0
0
0
0
7
1
0
1
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
1
1
2
0
1
0
1
1
0
0
0
1
0
0
5
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
1
2
0
1
0
0
3
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
1
0
5
0
2
0
0
2
0
0
5
0
0
0
0
2
2
0
0
1
0
0
1
0
0
0
0
0
0
2
2
0
0
2
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
4
3
0
1
2
1
0
1
2
2
0
1
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
2
2
1
0
0
0
0
2
0
0
1
0
0
0
2
0
0
2
0
0
1
1
2
0
1
0
0
0
1
1
0
0
1
0
2
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
2
6
1
0
2
1
0
0
0
5
0
0
2
1
0
0
0
0
0
0
0
0
0
1
1
1
0
2
1
2
1
0
0
0
0
0
2
1
1
0
0
2
2
0
0
1
0
2
2
1
0
0
0
2
0
2
0
0
0
0
1
0
1
2
0
0
0
2
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
3
0
0
1
0
2
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
2
0
0
1
3
2
0
0
0
0
0
0
1
0
2
2
1
0
0
0
0
1
0
0
0
0
0
2
0
1
2
0
0
2
0
0
0
2
1
0
2
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
1
1
0
2
0
0
2
0
0
0
1
0
0
0
2
1
0
0
2
0
2
1
0
0
0
1
0
2
1
1
2
0
8
0
0
0
1
2
0
2
0
2
0
0
0
0
1
0
1
3
2
0
0
0
2
0
0
2
0
0
0
0
0
2
2
2
0
0
0
0
2
0
1
2
1
0
1
0
0
1
0
2
2
0
0
1
0
1
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
2
2
0
2
3
0
0
0
1
0
0
2
0
2
0
2
0
2
0
1
0
1
0
2
2
1
2
0
2
0
0
0
0
2
0
5
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
1
1
2
0
1
0
0
1
0
0
0
1
3
1
0
1
0
1
1
0
0
0
2
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
1
2
0
0
0
2
1
2
0
2
0
3
2
2
1
0
0
0
0
0
1
0
1
1
0
0
0
0
2
1
1
0
0
0
0
2
0
0
1
1
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
2
0
2
2
1
0
1
1
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
2
3
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
2
1
0
0
0
0
0
2
2
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
2
1
1
0
0
2
2
0
3
1
0
0
0
0
3
2
1
1
0
1
2
1
0
1
0
0
0
0
1
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
1
0
0
0
0
2
0
0
0
1
2
0
0
2
0
0
2
0
0
0
0
1
1
2
0
0
1
0
2
0
0
0
0
2
2
0
0
1
0
0
0
1
0
2
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
10
0
0
1
1
0
0
0
0
1
2
0
2
1
0
3
0
2
0
0
1
0
1
0
0
2
2
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
1
2
0
0
2
2
0
0
1
0
0
2
0
0
0
0
0
1
1
0
0
2
0
0
0
0
1
0
4
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
2
1
0
0
0
1
1
2
1
0
0
0
2
0
3
0
2
0
2
0
1
0
0
0
3
2
0
1
0
0
0
1
0
0
2
0
0
2
0
0
0
2
0
0
0
1
1
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
1
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
10
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
2
0
0
1
0
1
0
1
2
0
0
0
0
0
0
1
1
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
2
0
0
1
0
3
0
1
0
0
0
1
0
0
0
2
2
0
1
0
0
2
0
2
0
0
0
1
2
0
0
0
0
2
0
0
1
0
2
0
0
0
2
2
0
0
1
0
0
1
1
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
1
0
1
0
0
0
0
0
1
1
0
1
0
1
2
0
0
0
1
0
4
0
0
0
0
2
0
0
2
0
0
2
2
0
2
1
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
3
0
2
0
1
0
0
0
0
0
1
4
3
0
0
1
0
0
2
1
0
1
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
7
1
0
1
0
2
2
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
1
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
1
2
0
0
0
0
0
2
0
1
0
0
2
0
0
0
1
0
0
0
1
1
1
0
0
0
2
3
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
2
0
0
0
0
0
0
3
0
2
2
2
1
3
0
0
0
1
0
2
0
2
0
0
1
0
1
0
0
0
0
0
2
1
0
1
0
0
0
0
1
0
0
3
0
1
0
0
2
0
0
1
0
2
0
0
0
2
0
1
0
0
2
1
2
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
1
0
2
2
0
0
2
0
0
0
1
2
3
2
0
0
1
0
0
0
0
0
0
3
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
2
0
0
2
0
0
2
1
0
1
0
0
0
0
3
0
0
1
2
1
0
0
2
0
0
0
0
0
0
2
0
1
0
0
2
0
1
0
2
0
1
0
2
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
2
0
1
2
2
3
0
0
4
0
0
0
0
0
1
2
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
2
0
1
3
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
1
0
1
0
2
0
2
0
1
0
0
0
2
2
2
1
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
2
2
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
2
0
0
6
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
3
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
2
2
0
1
2
0
0
2
2
0
0
0
0
0
2
0
0
0
1
0
1
0
0
2
0
0
2
2
0
0
0
2
0
0
0
0
1
1
2
0
0
0
0
1
0
2
0
0
0
0
2
2
0
0
0
2
1
0
0
1
1
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
1
0
1
0
3
0
0
2
0
2
0
0
2
0
0
0
1
2
1
0
0
0
2
2
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
3
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
2
1
1
0
2
1
0
1
2
1
0
0
0
1
1
0
0
1
0
0
0
2
2
0
4
0
0
0
0
1
0
2
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
4
1
0
2
0
0
2
1
0
0
0
0
0
2
3
2
0
0
2
2
0
0
0
0
0
1
0
0
1
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
1
0
2
2
1
0
0
1
0
1
2
0
0
3
0
1
0
0
2
0
0
1
2
2
0
1
0
0
0
0
0
1
2
0
2
0
0
2
0
0
0
2
1
0
0
5
1
0
0
0
0
0
0
0
0
0
0
2
1
1
0
2
0
0
2
1
1
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
3
2
0
0
0
1
0
0
0
2
0
0
0
1
0
1
1
3
1
0
0
0
0
0
1
0
0
0
0
2
0
1
0
1
0
1
1
0
0
1
1
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
10
1
0
0
0
3
0
0
0
0
0
5
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
1
0
0
0
0
0
0
1
2
1
0
0
0
0
0
1
1
2
1
0
0
0
3
0
0
0
0
0
1
0
0
2
0
0
2
0
2
0
0
0
0
0
0
2
2
2
0
0
0
2
0
0
0
2
0
0
2
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
2
2
0
2
0
2
0
1
0
2
0
0
0
0
0
0
1
0
2
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
1
2
0
0
0
1
0
0
0
2
2
0
2
1
1
0
2
0
0
0
1
0
1
1
0
0
0
1
0
0
0
2
2
0
6
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
1
0
2
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
1
2
1
2
0
2
0
0
1
0
2
2
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
1
1
1
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
2
1
1
2
0
2
1
2
0
0
1
1
1
1
2
1
0
1
11
1
2
2
0
1
0
1
2
0
1
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
5
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
2
0
2
0
2
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
1
4
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
3
2
3
0
4
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
2
0
0
1
0
2
0
0
0
0
0
0
3
1
0
2
2
4
0
0
0
0
0
0
2
0
0
1
1
2
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
2
2
2
1
0
0
0
1
1
2
2
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
5
0
2
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
1
0
1
2
2
2
2
2
0
1
0
5
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
2
0
1
1
1
2
0
0
2
0
1
0
0
13
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
1
0
0
0
0
4
2
3
0
0
0
2
1
0
0
3
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
1
1
2
0
1
0
1
2
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
1
2
1
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
3
1
3
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
2
0
3
0
1
0
0
6
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
2
1
0
2
1
2
0
2
0
0
0
0
1
0
0
0
2
2
0
2
0
0
0
0
1
0
2
1
2
0
0
0
0
0
0
0
2
2
0
0
0
2
2
2
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
2
0
0
0
1
0
2
1
0
0
0
1
0
0
0
0
1
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
1
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
2
2
2
0
0
2
0
1
3
0
0
1
1
2
1
2
2
0
0
0
0
2
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
1
0
1
0
0
1
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
2
2
0
1
0
1
0
0
0
2
0
0
0
3
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
2
1
0
1
0
0
1
0
0
0
0
0
2
0
2
0
1
0
0
0
0
3
0
2
0
0
0
0
1
1
0
1
3
0
0
0
1
2
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
1
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
2
0
0
1
0
2
0
1
2
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
1
1
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
1
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
1
0
0
0
0
2
2
1
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
1
8
0
0
1
0
0
0
2
1
0
0
0
2
2
0
0
0
1
0
0
0
1
1
0
1
0
0
4
1
2
0
0
0
0
2
2
0
0
0
1
0
1
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
2
0
0
2
0
2
0
1
2
1
0
0
1
0
2
0
0
0
1
0
2
0
2
0
0
0
2
3
2
1
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
2
2
0
2
1
0
2
2
0
0
0
0
1
1
2
2
1
2
3
0
1
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
6
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
2
1
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
1
1
1
0
1
2
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
1
2
0
0
2
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
1
1
0
0
0
0
2
3
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
3
2
0
2
1
0
1
0
0
2
0
0
0
2
0
0
6
0
1
2
0
2
0
0
0
0
1
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
1
0
0
1
0
1
2
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
2
0
1
1
0
0
0
2
2
1
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
1
2
1
0
0
0
0
1
2
0
0
0
0
2
0
0
2
2
0
0
0
2
2
0
0
0
0
0
2
0
0
0
2
2
0
2
0
3
2
0
0
2
0
0
0
1
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
3
1
0
0
0
0
1
0
0
0
3
1
1
1
0
1
0
0
1
0
0
0
0
0
2
0
1
0
1
2
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
1
0
1
0
0
2
0
0
0
1
0
0
1
0
0
2
1
0
1
1
0
0
1
0
3
0
0
0
1
0
0
0
1
2
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
2
0
1
0
1
1
0
0
1
0
0
4
0
0
2
1
0
1
2
0
0
0
1
2
0
0
1
1
0
2
0
0
1
0
2
2
0
0
0
0
0
1
0
0
1
2
1
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
4
0
0
1
2
2
0
1
2
0
2
0
2
0
0
1
0
0
0
2
2
0
0
2
1
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
1
1
0
0
0
0
2
0
0
0
2
0
0
4
1
0
0
0
2
0
0
2
0
1
2
0
0
0
0
0
1
0
0
1
0
0
2
0
3
1
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
2
1
2
0
2
1
0
0
1
2
0
0
0
0
1
0
2
0
0
0
1
0
2
1
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
3
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
2
0
0
0
0
0
1
0
0
0
1
3
0
0
1
0
2
1
0
1
2
1
0
0
1
0
0
0
0
0
1
1
0
0
4
1
1
0
1
0
0
0
1
2
1
1
0
1
2
0
4
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
2
0
0
0
0
1
2
0
1
0
0
0
0
0
1
1
0
0
1
5
1
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
2
1
2
0
0
0
0
0
1
0
1
0
1
0
0
2
2
0
2
0
0
0
4
2
0
0
0
0
2
0
0
1
0
0
2
0
4
0
1
2
0
0
0
2
3
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
2
0
0
2
1
0
0
0
0
2
0
1
2
0
0
1
0
0
0
1
2
1
1
0
2
1
3
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
2
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
1
2
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
2
1
0
1
0
0
0
0
2
2
0
0
1
0
1
0
0
0
0
2
4
0
0
0
0
3
0
2
0
1
0
0
0
3
1
0
0
0
0
0
0
1
0
0
3
0
1
0
0
2
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
1
1
1
2
0
0
0
0
0
3
1
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
2
0
0
1
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
2
3
0
1
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
1
0
3
2
0
1
4
2
0
1
0
0
0
0
0
2
2
0
0
0
2
1
2
0
0
0
0
0
0
0
2
0
0
3
1
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
1
0
2
1
0
1
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
2
0
0
0
0
2
0
0
2
2
0
2
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
1
2
2
0
0
0
1
0
0
1
0
0
0
0
0
2
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
2
2
0
0
0
2
1
0
0
0
0
0
1
0
1
0
1
0
0
1
0
2
1
0
0
1
0
0
0
2
1
0
0
0
0
1
1
1
0
0
0
1
3
0
2
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
2
2
3
2
0
0
1
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
2
3
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
2
0
0
2
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
2
0
2
1
0
2
2
1
2
0
2
0
2
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
1
2
1
0
0
0
4
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
2
0
2
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
2
4
0
0
0
0
0
0
1
0
1
0
2
0
0
2
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
2
2
3
2
2
1
2
1
2
1
0
0
0
0
2
0
0
1
2
0
0
0
0
0
2
0
2
0
2
0
0
1
2
0
0
1
1
0
2
0
0
0
0
0
0
0
2
6
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
5
0
1
0
1
1
2
1
3
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
2
2
0
0
0
2
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
2
0
1
0
0
0
0
2
2
0
1
0
1
0
0
2
1
0
0
1
0
0
0
0
3
2
0
0
0
0
0
0
1
2
1
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
3
2
1
0
0
3
0
2
0
0
1
2
0
0
1
0
0
2
2
1
1
0
1
0
0
1
1
0
0
0
0
1
0
0
0
2
1
2
0
1
0
0
2
1
1
0
1
0
0
0
1
0
0
0
1
0
2
2
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
1
4
2
0
1
0
2
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
1
4
3
2
0
2
6
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
1
0
2
1
2
1
1
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
2
0
0
1
0
0
0
1
0
2
0
0
0
2
0
0
1
0
0
2
1
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
2
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
1
1
1
0
0
0
2
3
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
1
0
0
1
0
0
0
0
2
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
6
0
2
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
2
0
0
2
2
1
3
0
0
0
0
1
0
0
0
0
0
0
0
3
0
2
0
0
0
2
2
2
0
1
0
0
0
2
2
1
2
0
2
0
0
0
0
0
0
1
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
2
0
0
0
0
1
1
1
0
0
0
0
1
3
0
0
0
2
4
1
0
0
0
1
0
2
3
1
0
1
2
0
0
0
1
0
0
0
0
2
2
0
0
2
2
2
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
2
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
2
4
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
3
1
2
0
2
1
2
0
8
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
4
0
0
2
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
2
0
0
0
0
2
0
0
5
0
0
3
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
4
1
0
0
0
0
0
0
0
0
0
0
0
1
1
3
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
2
0
0
0
2
0
0
3
1
5
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
1
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
2
1
0
4
0
1
0
0
0
1
0
1
1
0
0
1
0
0
2
1
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
2
1
2
2
1
0
2
2
1
1
0
1
0
0
0
0
0
1
1
0
2
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
2
2
0
0
0
0
0
1
2
0
0
2
0
2
0
0
0
2
2
0
0
0
1
0
0
2
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
2
0
0
2
1
1
0
2
1
0
0
2
1
2
2
0
1
0
0
0
2
0
0
0
0
1
0
0
1
1
3
2
0
0
0
0
0
2
0
0
1
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
1
0
2
0
0
0
0
0
2
1
0
0
0
1
0
1
2
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
1
0
2
2
0
0
1
0
1
0
2
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
1
1
0
0
2
1
0
1
2
0
0
0
0
0
0
0
1
0
0
0
1
0
1
2
2
0
1
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
1
0
0
0
2
0
2
2
0
0
1
2
0
0
2
0
0
2
0
0
1
2
2
2
0
2
0
0
1
2
1
1
0
0
3
2
0
0
1
0
2
0
0
1
1
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
5
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
2
0
1
0
0
2
1
2
0
0
0
0
0
0
3
1
1
0
0
0
2
3
0
0
0
1
4
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
2
0
1
2
0
0
0
0
1
0
0
0
2
0
0
2
1
1
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
1
0
1
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
2
1
1
0
1
2
1
0
1
4
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
2
0
2
0
0
0
0
1
2
0
1
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
2
1
0
1
2
0
0
0
0
2
2
0
0
0
0
1
1
0
0
1
0
0
3
1
0
1
0
0
0
2
0
0
0
0
0
0
4
0
0
1
0
0
1
2
0
4
0
0
0
2
3
2
2
3
0
0
0
2
1
2
0
2
0
1
0
0
0
2
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
3
2
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
5
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
3
1
1
0
1
0
1
2
1
0
1
0
0
0
1
0
2
0
0
0
0
0
1
0
1
2
0
0
0
0
0
2
0
0
3
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
2
1
0
2
0
2
0
2
0
0
2
0
2
2
0
0
4
1
1
0
0
0
0
1
0
0
0
0
2
1
0
0
0
1
1
0
0
0
0
0
2
2
0
0
3
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
2
5
0
0
2
2
0
0
0
0
0
2
0
1
0
0
2
0
0
1
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
2
1
0
0
0
0
0
0
5
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
9
0
1
0
0
0
0
2
1
0
1
0
0
1
0
1
0
1
1
0
2
1
1
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
3
0
1
0
0
0
0
2
1
0
0
0
0
0
4
0
0
0
0
0
0
0
1
2
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
2
1
0
0
2
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
1
1
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
4
2
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
3
1
2
0
1
0
0
2
0
6
0
1
1
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
2
1
0
0
0
0
0
0
2
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
2
6
0
0
0
1
0
2
0
0
2
0
2
2
1
0
0
1
0
1
0
0
0
0
1
1
0
1
0
0
1
0
2
1
1
2
0
0
3
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
2
0
1
0
0
1
2
2
0
0
0
0
2
0
0
0
1
0
2
2
0
0
12
0
2
0
1
0
0
0
0
1
1
4
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
1
0
2
0
0
2
0
2
0
0
0
1
0
0
2
2
0
0
1
0
2
0
0
0
3
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
2
0
1
0
2
1
2
0
1
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
1
0
2
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
1
1
0
0
0
0
2
0
2
0
0
0
1
2
1
2
2
0
1
0
0
0
0
0
1
1
0
0
0
0
1
2
2
1
0
0
0
2
2
1
1
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
1
0
1
1
0
2
0
2
0
4
1
0
0
0
0
0
0
1
0
1
2
0
0
0
0
1
0
0
0
1
1
0
0
0
0
2
2
2
0
0
1
0
0
2
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
2
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
2
3
2
3
0
1
2
3
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
1
0
0
2
2
0
0
2
2
0
1
1
0
0
2
0
0
0
1
0
0
3
3
0
0
1
1
0
1
2
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
3
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
1
0
0
1
0
0
0
0
1
0
0
0
1
1
0
2
1
0
0
2
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
4
0
0
0
0
2
0
1
0
0
0
0
1
5
0
0
0
0
0
0
0
2
0
0
2
0
1
0
1
0
0
0
0
2
1
0
0
0
0
0
1
0
2
2
2
0
0
0
2
1
0
2
0
2
3
0
0
1
0
0
0
1
0
0
0
2
2
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
2
2
0
1
1
0
0
0
0
7
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
3
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
1
2
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
1
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
1
1
0
3
0
0
0
0
1
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
1
1
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
2
0
0
0
0
1
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
2
1
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
3
1
0
1
0
1
2
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
1
2
0
1
1
0
2
0
0
0
2
0
0
2
2
1
0
0
0
2
0
0
0
2
2
0
2
0
0
0
0
0
0
1
1
2
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
2
0
0
0
0
1
0
2
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
2
0
0
0
1
0
0
2
1
3
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
2
5
0
2
3
0
0
0
1
0
0
2
0
0
2
2
0
7
0
0
0
0
1
0
1
1
0
0
0
0
0
1
2
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
2
1
2
0
0
0
0
1
2
1
1
0
0
0
3
1
2
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
1
1
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
4
2
0
0
0
1
0
1
0
1
1
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
2
0
2
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
2
0
2
0
0
0
0
1
0
0
1
1
0
0
0
3
2
0
1
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
2
2
0
2
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
2
1
0
0
0
0
1
0
1
0
3
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
5
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
1
2
0
2
1
0
1
0
0
2
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
3
2
1
0
1
2
2
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
2
2
1
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
1
2
1
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
2
0
2
0
0
1
1
0
1
2
0
0
0
1
2
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
2
0
3
0
0
0
0
0
0
0
2
4
0
0
0
0
1
0
0
0
0
0
1
0
0
1
2
0
0
0
1
0
0
0
0
2
0
2
1
0
0
1
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
1
2
0
0
2
0
0
3
0
0
0
2
0
2
0
2
0
5
0
0
1
2
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
2
1
2
0
0
0
0
0
1
0
1
0
2
0
0
0
2
0
0
0
0
1
1
0
1
1
1
1
0
1
3
0
0
0
0
2
1
0
0
0
0
1
1
2
0
0
0
0
0
3
0
2
1
2
0
0
0
0
0
2
2
0
0
0
2
0
0
2
0
0
1
0
1
0
1
0
0
0
2
0
1
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
2
0
0
2
0
0
1
0
0
3
2
0
0
1
2
1
2
1
0
3
0
2
0
2
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
2
1
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
2
2
1
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
1
3
2
1
1
0
2
0
0
0
1
0
0
1
1
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
1
2
0
2
0
2
0
0
0
0
0
2
2
2
0
4
0
0
2
0
1
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
1
2
0
1
1
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
2
0
2
0
1
1
0
0
0
2
0
2
2
0
3
2
1
0
2
0
0
0
0
0
2
1
0
2
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
1
1
1
0
0
3
0
0
0
0
2
0
0
0
2
0
0
0
0
1
2
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
2
0
2
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
1
0
1
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
1
4
1
0
0
0
2
2
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
1
0
0
1
2
0
0
0
0
1
2
0
0
0
0
0
0
1
1
1
0
1
2
0
2
1
0
0
1
3
2
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
4
0
0
0
0
3
0
0
2
0
0
0
1
0
2
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
2
2
0
0
0
1
1
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
1
0
2
1
0
3
0
1
2
0
0
1
0
0
1
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
2
1
2
1
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
1
2
0
0
1
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
2
0
0
0
1
0
1
0
0
2
0
0
0
1
0
0
0
2
1
0
1
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
3
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
1
2
0
0
0
1
2
0
0
1
2
0
2
0
1
0
0
2
6
0
0
0
0
0
2
2
0
4
0
0
0
2
0
2
0
0
0
0
0
1
0
1
1
0
0
0
1
2
0
0
2
1
1
0
3
0
0
0
0
0
0
2
0
0
0
0
1
2
2
1
1
0
0
0
0
0
2
1
1
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
6
0
1
2
0
1
2
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
2
0
1
2
0
1
0
0
0
0
6
0
0
1
0
1
0
0
0
0
7
0
1
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
1
0
1
0
2
0
0
2
0
0
0
0
1
0
1
1
0
0
0
4
2
1
2
0
0
2
0
2
0
2
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
2
0
2
1
0
0
0
0
1
1
0
1
0
2
0
2
0
0
0
0
0
1
0
2
0
0
1
2
0
0
3
0
2
1
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
4
0
0
1
1
1
1
2
1
0
0
3
0
2
2
0
0
1
0
0
2
1
0
0
0
0
0
1
1
0
1
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
3
0
0
2
0
2
1
1
0
0
0
0
0
1
0
0
2
1
1
3
0
0
2
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
3
0
3
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
2
1
2
0
0
1
0
1
0
1
0
2
2
0
0
0
0
2
1
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
2
1
1
0
0
0
0
1
0
0
1
0
0
0
0
1
3
1
1
0
0
0
0
0
1
0
0
3
1
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
2
0
0
2
1
0
0
0
1
0
0
0
0
0
1
0
0
3
1
0
1
1
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
2
0
0
0
0
0
0
0
1
0
1
2
1
0
0
2
0
0
1
0
2
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
2
1
0
0
0
0
0
1
0
1
2
1
1
2
0
0
0
0
2
0
1
0
1
1
0
1
0
2
0
0
0
1
2
0
0
1
0
0
1
0
1
2
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
2
0
2
0
1
0
2
0
1
0
2
0
1
0
0
2
0
2
0
0
0
3
0
2
0
1
1
0
0
0
0
2
1
0
0
0
1
0
1
2
2
0
2
0
2
0
0
0
2
0
1
0
0
0
1
0
0
2
2
0
0
1
0
2
1
2
2
1
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
2
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
2
0
2
0
3
0
0
0
0
0
1
0
1
0
3
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
3
0
1
0
0
1
1
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
1
0
0
2
0
1
0
1
0
0
1
1
1
2
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
2
2
0
2
2
0
2
0
0
0
0
0
0
1
0
2
1
0
0
0
1
1
0
0
2
5
0
0
0
2
0
2
0
0
1
0
0
1
0
1
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
1
1
0
0
2
0
1
0
1
0
0
0
0
0
1
0
7
0
0
1
0
0
0
3
0
0
2
0
0
3
0
0
0
0
2
1
0
1
0
0
0
0
0
2
2
0
1
0
0
1
2
2
2
0
2
0
0
0
2
0
2
0
0
0
0
2
0
1
0
2
1
4
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
5
0
0
0
0
0
0
1
1
0
2
0
0
0
0
2
0
2
0
2
2
0
2
0
0
0
0
0
0
2
0
1
1
1
0
0
0
1
7
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
1
0
2
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
2
2
0
1
0
0
0
1
2
0
0
0
0
0
1
0
0
2
0
0
2
0
0
2
0
0
0
1
0
0
1
0
1
0
1
3
0
0
0
2
0
0
2
0
0
0
4
1
0
1
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
3
0
2
0
0
3
0
0
1
0
1
0
0
2
0
0
0
0
0
1
2
0
4
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
1
0
2
2
2
0
1
0
1
0
0
1
0
0
1
0
1
0
0
2
0
0
2
2
1
3
0
0
0
1
1
0
1
0
0
1
1
0
2
1
0
0
0
1
0
0
0
0
1
2
0
2
0
0
0
0
0
2
0
0
1
0
2
0
3
2
0
0
0
0
1
0
0
2
0
2
0
0
3
0
0
2
1
2
0
0
0
0
0
0
0
1
1
1
0
0
0
2
0
2
3
2
0
0
0
1
1
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
1
2
0
0
1
0
3
1
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
1
0
2
1
1
0
0
0
1
0
0
1
0
2
2
2
0
0
1
1
0
0
0
0
0
0
1
1
0
0
1
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
3
0
0
0
1
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
1
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
2
0
2
0
1
0
0
0
2
2
2
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
4
0
2
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
2
2
3
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
2
1
0
1
2
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
1
1
1
0
1
0
0
0
0
2
2
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
2
0
0
1
1
0
0
0
0
1
1
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
1
0
1
1
0
1
1
0
1
0
0
1
0
2
0
0
0
0
1
1
1
0
0
0
0
1
1
0
0
0
2
3
0
0
0
0
2
0
1
3
1
2
1
2
0
0
2
0
0
0
0
2
0
0
0
2
1
1
2
2
0
1
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
2
0
1
1
2
2
1
0
0
0
0
2
1
0
0
0
0
0
1
2
0
1
0
2
0
2
0
3
2
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
2
2
4
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
1
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
2
0
0
0
0
0
1
0
0
0
2
0
0
1
1
0
2
0
1
2
0
0
0
0
2
3
0
0
0
2
0
0
4
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
1
2
0
1
0
2
1
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
3
0
0
1
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
2
2
1
1
2
2
0
1
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
3
0
0
0
1
0
1
0
0
2
1
0
2
2
0
1
2
2
0
0
0
0
0
0
0
2
0
3
0
1
0
0
0
1
0
0
2
0
2
1
0
2
2
0
0
1
0
0
0
2
2
0
0
0
3
1
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
3
0
0
0
0
0
3
0
2
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
2
0
0
0
0
0
2
1
0
0
1
0
1
0
0
2
0
1
0
2
0
0
2
2
0
2
0
1
0
2
0
2
1
0
3
3
0
0
0
2
0
2
0
0
1
0
0
0
2
1
1
0
1
0
0
0
0
0
0
0
0
0
2
2
1
0
0
1
0
1
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
1
0
0
3
2
0
0
2
0
1
0
1
0
0
0
0
0
0
0
1
1
0
1
5
0
0
0
0
0
0
0
0
0
1
2
0
2
0
2
0
1
0
0
0
0
1
2
0
0
0
0
2
2
0
0
1
0
0
0
4
0
0
0
2
1
0
2
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
2
1
0
2
0
2
0
0
0
0
1
0
0
2
0
1
0
0
0
3
0
0
0
1
1
1
1
2
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
1
0
0
0
1
2
2
0
1
2
0
0
0
0
0
3
0
0
0
0
0
0
0
1
2
0
0
4
0
2
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
1
2
0
0
0
2
0
2
4
1
1
1
0
0
0
1
2
0
1
0
0
0
0
0
0
1
0
0
0
1
2
0
1
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
1
0
1
1
3
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
3
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
2
0
2
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
2
0
0
0
0
0
4
2
2
0
0
0
0
4
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
2
2
0
0
0
2
2
2
1
0
1
0
2
0
0
0
0
1
1
1
0
1
2
0
0
2
0
0
0
0
1
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
5
0
0
0
2
0
1
1
0
0
0
1
1
0
0
2
1
1
0
0
0
1
1
0
0
0
1
0
0
1
2
0
3
0
2
2
0
0
0
2
2
0
0
1
1
0
0
2
0
0
0
0
0
0
0
5
0
0
0
1
1
0
0
1
0
1
0
0
2
2
0
0
2
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
1
2
1
0
0
0
1
1
1
0
2
0
2
0
0
0
0
1
0
0
0
0
1
2
3
0
0
1
0
1
2
0
2
0
1
0
0
0
0
0
0
0
2
0
2
2
0
0
1
0
1
0
0
0
1
0
1
0
1
1
1
1
0
0
0
2
1
2
2
0
0
0
2
0
0
1
0
0
1
0
1
0
0
0
2
0
2
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
2
0
0
3
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
2
2
0
2
0
6
1
1
0
1
0
2
2
0
0
2
0
2
0
0
2
0
1
2
0
2
1
3
2
0
0
0
0
0
3
0
0
0
2
0
0
0
1
2
2
2
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
1
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
1
0
0
3
0
0
0
2
0
3
2
0
0
1
0
0
0
1
0
0
0
1
1
1
2
1
0
0
0
0
0
2
0
0
0
2
2
2
0
0
0
0
1
0
0
0
0
0
0
2
0
2
1
0
1
0
1
1
0
0
3
0
0
0
0
0
2
0
0
0
0
3
0
0
1
0
1
0
3
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
2
3
2
2
0
0
3
0
1
1
0
1
2
2
0
0
0
0
1
1
3
1
2
1
0
0
0
1
0
0
0
3
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
4
0
2
2
0
1
0
0
2
0
2
0
0
1
0
2
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
3
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
2
0
1
0
0
1
0
2
0
2
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
2
2
0
1
2
0
2
0
2
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
2
0
2
2
0
0
1
0
2
1
0
0
1
1
0
0
1
0
1
0
0
2
0
0
1
2
0
0
2
0
0
0
0
0
1
0
0
2
2
2
0
0
0
0
2
0
1
0
1
0
0
2
0
1
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
3
0
2
0
5
1
0
1
0
0
0
0
0
0
0
1
0
3
2
2
4
0
0
0
0
0
1
2
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
4
0
0
1
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
1
0
0
0
2
0
3
0
0
0
3
0
0
0
0
0
2
0
0
1
0
0
2
0
1
1
0
0
4
3
0
1
0
0
0
0
1
0
2
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
1
2
0
0
2
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
2
2
0
0
0
2
0
2
2
2
3
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
4
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
10
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
2
2
0
2
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
1
0
0
2
0
0
2
0
2
0
1
0
0
0
0
1
0
2
0
1
0
1
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
3
1
2
0
0
2
0
0
0
0
0
0
0
0
3
0
0
1
0
2
0
0
0
0
0
0
2
1
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
5
0
0
0
0
7
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
3
1
0
2
0
0
0
0
2
0
1
3
0
2
0
1
0
0
4
0
0
0
1
0
1
0
0
1
0
0
7
0
0
0
2
0
0
1
0
0
1
0
0
0
2
0
0
1
0
0
2
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
1
0
0
0
3
2
1
1
0
1
1
0
0
1
1
0
1
2
0
1
2
1
1
0
2
0
0
2
0
2
0
0
0
2
1
0
2
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
2
1
2
0
0
1
0
0
7
1
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
2
2
2
0
0
1
0
1
2
1
0
2
0
2
1
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
2
0
1
0
1
0
0
2
0
0
1
0
0
2
0
0
2
0
0
1
0
2
0
2
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
1
2
0
1
0
0
2
0
0
0
0
0
1
0
0
0
3
0
2
0
1
2
1
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
2
0
1
0
0
1
1
0
0
0
2
0
0
1
1
0
1
1
1
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
1
1
0
2
0
0
0
0
2
0
3
0
1
0
0
0
2
0
2
0
3
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
2
1
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
1
2
2
3
3
0
0
0
0
0
0
2
2
0
0
1
0
1
0
0
0
2
2
2
0
1
2
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
12
2
0
1
2
1
0
2
2
0
0
0
2
0
0
1
0
0
2
1
0
0
2
0
2
0
0
1
1
0
0
4
0
0
0
0
1
1
0
0
2
1
0
0
0
2
2
0
0
2
0
0
0
4
0
0
2
1
0
0
0
0
0
1
0
0
0
4
0
0
1
0
1
0
0
0
0
2
0
0
2
0
0
0
1
1
0
1
2
2
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
2
0
1
1
0
0
0
0
0
0
0
0
0
0
3
0
1
2
2
1
0
1
0
1
0
0
0
0
1
1
0
0
0
1
1
0
0
0
1
3
1
0
0
0
2
1
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
1
1
0
0
0
1
0
2
1
0
2
0
2
2
0
0
2
0
0
1
2
0
0
3
0
0
1
0
0
2
3
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
2
0
0
1
3
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
2
1
0
0
0
1
0
3
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
1
0
2
0
2
0
0
0
0
0
1
0
0
1
0
2
0
0
1
2
0
0
0
0
2
0
4
2
1
0
0
0
0
0
2
0
3
2
1
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
1
2
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
1
2
0
0
1
0
2
0
2
0
0
0
0
2
2
0
0
2
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
2
0
0
0
0
0
1
0
1
2
0
1
0
2
0
0
1
2
3
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
2
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
5
1
1
2
0
1
0
1
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
1
0
0
0
0
1
2
2
1
2
4
1
0
2
2
0
0
1
0
2
0
0
1
0
0
0
0
0
1
2
1
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
2
0
2
1
0
0
0
0
1
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
2
0
0
1
0
2
0
0
1
0
1
1
2
0
0
0
1
0
2
2
0
1
0
0
1
0
0
0
0
2
1
0
0
0
2
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
2
4
1
0
0
2
0
0
2
0
0
0
0
0
2
0
2
2
2
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
2
2
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
2
0
0
1
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
3
0
2
0
1
0
0
2
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
1
0
0
3
2
0
0
2
1
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
1
0
2
1
0
0
0
1
1
0
2
2
0
1
0
0
0
1
0
0
2
0
2
0
0
0
2
0
0
1
0
1
0
0
2
0
0
3
1
1
0
0
0
0
2
0
0
2
1
0
2
0
2
2
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
1
0
0
0
1
1
0
0
2
0
0
0
1
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
3
0
0
1
1
0
0
3
2
0
2
1
0
0
2
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
1
3
0
0
0
0
0
0
0
1
0
1
3
2
2
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
2
0
0
2
0
1
2
2
2
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
1
1
0
0
1
0
1
0
1
0
0
3
2
0
1
0
0
2
2
0
0
1
0
0
0
0
1
0
1
0
0
1
1
1
0
0
0
0
0
1
0
0
0
3
0
1
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
3
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
2
1
0
3
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
2
0
1
0
1
0
0
0
0
0
0
1
2
0
0
0
2
1
2
2
0
1
0
2
0
1
0
0
2
0
0
1
0
1
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
2
1
2
0
1
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
3
0
0
2
0
0
1
0
2
0
0
1
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
1
2
0
1
0
1
0
2
0
0
0
2
1
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
2
0
1
0
0
2
2
1
1
2
0
2
2
1
2
5
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
1
2
0
2
2
0
0
0
0
0
0
0
0
0
2
1
0
0
2
1
0
1
0
2
0
0
1
1
2
0
1
0
1
1
1
0
0
2
2
1
0
0
0
0
0
0
2
2
0
0
0
0
1
0
1
0
0
1
2
0
0
0
0
1
1
3
0
0
0
0
3
0
0
1
2
0
1
0
0
1
0
2
0
1
0
1
0
0
0
0
2
0
2
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
2
0
0
3
0
0
3
0
2
0
0
4
2
0
2
0
0
0
2
0
0
4
1
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
1
2
0
1
0
0
1
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
2
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
2
1
0
0
2
0
1
0
0
0
2
2
1
0
1
6
0
0
1
0
0
2
0
0
2
2
0
0
2
0
0
0
3
0
1
0
0
0
0
0
0
1
2
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
4
2
0
0
1
0
0
1
0
2
2
2
0
0
0
0
1
0
2
3
0
0
0
1
0
0
0
0
2
2
2
3
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
3
0
0
0
0
0
0
2
1
0
0
0
1
1
0
0
0
0
0
0
0
2
0
2
1
0
0
0
2
1
0
0
1
1
0
2
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
1
0
0
1
1
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
1
2
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
2
0
0
0
0
2
1
1
0
0
0
1
1
0
0
2
0
1
1
0
0
2
2
1
4
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
1
3
1
0
2
0
1
0
0
1
0
1
0
2
0
0
2
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
1
0
2
0
0
2
0
2
1
1
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
1
0
0
1
0
1
0
1
0
4
0
0
1
0
2
2
0
0
0
1
2
0
0
0
2
0
0
0
1
2
0
2
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
2
0
0
0
0
0
1
0
0
0
2
1
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
2
0
2
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
2
0
0
2
0
2
6
1
1
0
0
2
2
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
1
2
0
1
0
2
1
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
1
1
0
0
2
0
0
3
1
0
1
0
1
0
2
0
0
0
1
1
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
2
2
2
0
0
0
1
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
1
0
0
0
0
2
2
2
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
2
2
0
0
2
0
2
0
4
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
3
0
1
2
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
1
2
1
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
1
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
6
1
0
0
1
0
2
2
2
1
0
0
0
2
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
2
2
0
0
2
0
0
2
3
1
2
0
0
0
0
0
2
0
3
0
0
0
0
1
0
0
2
2
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
2
1
0
0
1
0
0
0
0
2
2
0
2
0
1
2
2
1
1
0
1
1
1
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
3
0
2
0
0
1
0
0
2
1
0
0
2
0
0
0
0
1
0
1
0
0
0
3
0
0
1
0
0
1
0
0
0
3
2
0
2
1
1
0
0
0
3
0
2
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
1
0
2
1
3
1
2
0
0
0
0
2
2
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
1
0
2
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
1
1
0
2
0
0
0
0
0
1
0
0
7
0
0
0
0
0
2
0
0
3
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
2
2
0
0
0
1
1
1
0
2
0
0
2
0
0
1
2
0
0
0
0
0
0
3
0
1
0
1
0
1
1
2
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
2
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
2
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
1
1
1
1
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
1
0
0
0
1
0
2
1
1
0
0
0
0
0
1
1
0
2
2
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
2
0
0
1
0
0
1
0
0
0
2
1
1
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
2
1
2
0
1
0
0
0
1
0
2
1
3
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
1
2
0
0
2
1
0
1
2
0
0
0
0
1
0
0
0
1
2
2
0
2
1
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
2
4
0
2
0
1
1
0
2
0
0
0
0
4
0
2
2
0
0
0
0
0
0
0
2
0
0
1
0
2
1
0
0
1
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
1
3
0
5
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
1
1
2
1
0
2
2
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
1
0
1
3
0
0
2
0
1
0
0
0
0
0
1
1
3
2
0
0
2
0
0
0
1
0
0
1
1
0
3
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
1
0
2
1
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
2
2
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
2
0
0
0
3
0
0
3
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
4
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
1
0
2
1
0
2
0
0
0
0
0
0
1
2
0
1
0
2
0
0
0
0
0
1
1
0
2
0
1
2
0
0
2
0
0
1
0
0
0
1
1
0
1
1
1
2
0
0
0
0
0
0
1
0
0
2
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
2
0
2
2
0
2
0
0
2
2
1
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
1
0
2
2
0
1
0
0
0
10
0
3
1
0
0
0
0
0
0
0
1
0
0
2
0
0
2
2
0
1
0
1
0
2
1
0
0
1
0
0
1
0
1
0
2
3
0
0
1
0
0
0
1
0
2
1
0
0
0
0
0
3
1
0
1
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
3
2
0
0
1
0
0
0
2
0
0
1
2
0
0
2
0
0
1
0
0
1
0
1
0
1
0
0
0
2
0
0
0
2
1
2
0
0
1
1
0
0
0
1
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
1
0
0
7
0
0
0
0
0
0
3
0
0
1
0
0
1
0
3
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
2
2
0
0
0
2
0
0
0
0
0
2
0
0
3
0
0
3
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
4
2
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
2
2
0
0
0
1
0
1
0
1
0
0
0
0
2
0
0
0
2
0
0
2
0
2
0
0
0
0
0
1
0
0
0
1
0
2
2
2
0
0
0
0
1
2
0
0
0
0
2
0
0
1
1
1
0
1
0
0
0
0
0
1
0
0
2
0
2
0
1
0
1
1
2
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
2
0
0
0
1
0
1
0
2
0
0
1
0
0
1
2
0
1
0
0
3
1
0
0
0
2
2
1
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
1
2
0
1
0
0
0
0
0
2
0
1
0
2
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
1
0
1
0
0
3
0
1
2
0
2
0
0
2
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
1
0
0
0
1
3
0
0
0
2
1
0
0
0
0
0
0
0
2
1
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
2
0
2
1
0
0
2
0
0
0
0
2
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
1
1
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
1
1
0
1
0
0
0
1
0
0
2
0
0
0
0
3
1
0
0
0
0
0
0
0
1
0
3
0
2
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
1
0
1
2
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
5
1
0
2
2
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
3
2
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
1
3
0
0
0
2
1
1
0
1
1
0
0
1
1
1
0
0
2
2
0
1
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
1
3
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
2
0
1
2
2
2
2
0
0
0
0
0
1
0
2
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
4
2
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
2
0
1
1
0
0
0
0
0
0
1
0
0
0
3
0
0
2
1
0
2
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
3
1
0
0
0
0
2
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
2
0
0
2
0
1
0
2
1
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
2
1
0
0
0
2
0
1
0
0
0
0
1
0
0
3
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
2
1
0
1
0
0
1
1
0
0
0
0
0
0
0
2
0
2
1
0
0
2
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
4
0
1
2
0
0
0
2
0
0
1
0
0
0
3
0
0
0
2
0
1
1
0
0
0
2
1
0
0
1
0
0
0
0
2
0
0
1
0
0
1
0
1
0
2
0
2
0
2
0
0
2
2
1
1
2
1
2
0
0
0
4
0
1
0
0
0
2
0
0
2
3
0
0
0
0
1
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
2
0
1
2
0
0
0
0
0
0
0
0
0
2
0
1
0
3
0
1
0
0
0
2
2
1
1
2
2
0
2
0
1
1
0
0
1
0
0
0
0
0
0
0
2
0
1
1
2
0
0
0
1
0
0
1
0
0
2
0
0
1
0
3
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
2
1
0
2
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
2
0
0
0
0
0
2
0
0
2
0
2
0
2
2
0
1
0
2
2
0
2
0
0
1
1
0
1
2
0
2
1
0
0
3
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
1
0
1
2
0
0
0
0
0
2
2
0
0
5
1
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
3
1
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
2
1
0
0
0
0
3
3
0
0
0
0
1
0
0
0
0
0
3
0
1
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
1
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
3
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
1
0
2
0
1
0
0
1
1
0
0
1
0
0
1
2
0
2
2
0
1
0
0
0
0
0
0
1
1
3
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
1
0
0
2
1
1
0
4
1
0
1
3
0
2
0
0
2
1
0
0
2
2
0
0
3
1
0
0
0
0
0
0
0
2
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
1
0
0
0
3
0
0
0
0
0
3
1
2
2
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
1
2
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
1
0
0
1
1
1
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
2
2
0
0
2
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
1
0
3
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
1
0
0
0
0
2
0
0
2
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
2
0
0
2
0
0
2
2
0
0
3
3
1
0
0
0
1
0
2
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
1
2
0
0
1
0
0
0
2
0
0
0
4
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
2
1
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
3
0
2
0
0
0
2
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
2
0
0
0
0
2
1
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
2
1
1
0
2
1
3
0
1
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
2
0
0
0
0
0
0
1
1
0
0
4
0
0
0
0
0
0
0
0
1
0
2
0
2
0
1
0
0
0
0
1
0
1
0
0
0
1
0
1
2
1
0
0
2
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
2
0
0
8
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
2
0
2
0
0
2
0
2
0
2
0
2
0
2
2
1
2
0
2
0
2
0
0
0
0
0
0
1
3
0
4
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
2
1
0
0
0
2
0
21
1
1
0
0
2
0
0
2
3
0
1
0
1
0
0
0
2
1
0
0
0
2
0
2
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
1
2
0
0
2
1
1
0
0
1
0
3
0
2
0
0
0
0
3
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
3
1
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
2
0
0
2
0
0
0
0
0
0
1
0
4
0
0
2
0
1
0
0
0
0
0
0
0
0
1
1
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
1
0
0
2
0
0
1
0
2
0
0
1
0
0
2
2
0
1
0
1
0
0
2
0
1
1
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
1
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
1
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
2
2
0
1
0
2
0
2
1
0
0
1
0
1
3
2
0
0
0
3
1
2
2
0
1
0
0
1
2
0
3
0
2
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
2
1
0
0
0
0
3
0
0
2
0
1
2
1
0
6
1
0
0
0
0
0
0
0
0
2
0
1
2
1
2
0
0
0
0
0
0
2
0
0
0
1
2
0
2
1
1
0
1
0
0
0
0
2
0
1
0
2
1
0
2
0
0
0
1
0
0
0
0
1
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
2
0
2
0
2
0
0
0
0
0
0
2
0
1
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
1
1
2
1
0
2
2
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
1
1
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
2
0
1
1
0
1
0
2
2
0
0
0
0
2
0
0
0
1
1
0
0
1
0
1
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
1
0
2
2
0
0
1
0
1
0
0
2
0
0
0
0
0
2
0
0
2
0
0
1
7
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
2
1
1
3
0
2
1
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
6
3
0
0
0
1
2
2
2
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
2
0
2
0
0
0
1
0
2
1
0
0
1
0
2
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
2
1
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
1
0
1
2
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
1
0
1
0
1
0
2
0
0
2
0
0
1
2
0
0
1
2
0
0
0
5
0
0
0
0
0
0
2
1
0
0
0
1
0
0
2
0
1
1
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
1
2
0
0
1
1
1
0
0
0
1
0
0
0
2
2
0
0
2
2
0
2
0
0
4
2
0
0
0
3
0
0
1
0
0
1
0
0
0
0
0
2
2
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
6
0
1
0
1
0
0
2
0
0
2
0
1
2
0
0
1
0
1
1
2
0
0
0
1
0
0
0
0
0
0
5
1
0
1
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
2
1
2
0
2
0
0
0
0
0
0
0
1
2
0
2
1
0
2
1
1
0
1
0
1
0
1
0
2
0
0
0
2
0
0
1
1
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
4
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
2
4
0
0
2
2
0
1
1
1
0
0
0
0
0
2
0
2
3
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
2
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
5
0
0
2
1
0
1
0
0
0
0
0
0
1
1
0
2
0
0
0
7
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
3
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
3
0
0
0
0
0
0
0
1
0
0
0
3
1
0
0
0
0
0
0
2
0
1
0
0
2
2
0
2
0
2
2
0
0
2
0
2
1
1
1
0
0
0
2
0
1
0
0
0
2
0
0
0
0
2
2
3
0
0
0
2
0
0
3
0
1
0
0
1
0
0
2
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
3
1
1
2
0
2
2
0
0
0
0
2
0
2
0
0
0
1
0
2
2
0
0
1
0
1
1
0
0
0
0
4
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
2
2
2
1
0
0
0
2
1
0
0
0
2
2
0
0
1
0
1
2
2
1
0
0
2
0
0
0
2
0
0
0
2
3
0
0
3
0
0
1
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
5
1
0
0
2
2
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
2
2
0
1
0
0
0
0
0
2
0
1
0
2
0
1
1
2
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
2
2
2
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
3
0
4
0
0
0
1
0
0
0
0
0
0
0
2
1
2
0
2
0
0
0
4
0
0
0
5
0
0
1
1
1
0
2
2
1
0
2
0
1
2
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
3
0
0
0
1
0
0
0
0
0
3
2
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
5
2
0
0
1
0
0
1
1
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
2
2
0
2
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
2
1
3
2
2
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
2
3
0
0
0
0
1
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
2
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
1
0
2
0
0
1
1
1
0
1
0
0
1
0
0
2
0
3
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
2
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
1
1
2
0
1
3
0
0
0
0
2
0
1
2
0
1
2
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
3
2
1
2
2
1
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
2
0
2
0
0
1
2
0
0
0
0
1
0
0
0
0
0
1
2
0
3
2
2
4
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
1
1
1
2
0
2
2
0
1
0
0
0
2
0
0
0
2
0
0
1
0
0
1
0
0
2
2
0
2
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
3
1
0
1
0
0
0
2
0
0
0
0
2
0
2
1
1
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
4
1
0
2
0
0
0
0
1
2
2
0
1
0
0
0
0
0
2
0
0
0
2
2
0
0
1
0
2
0
0
0
3
0
0
0
0
0
1
2
2
0
0
0
0
0
2
0
2
1
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
1
0
0
2
3
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
1
2
0
0
3
1
3
2
1
0
2
2
0
1
0
2
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
1
0
0
0
0
3
0
1
0
0
0
0
1
0
1
1
0
0
0
2
0
0
0
1
0
1
0
0
3
0
0
0
0
0
0
1
0
1
1
2
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
1
0
2
0
0
2
0
0
0
2
1
2
0
0
0
2
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
2
0
1
3
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
3
2
2
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
1
0
1
0
1
2
0
0
3
2
2
0
0
0
0
1
0
2
1
0
0
4
2
0
0
0
0
1
2
0
0
0
0
2
0
1
1
3
1
2
0
0
0
0
0
1
2
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
2
0
0
1
1
1
2
0
0
1
3
0
0
0
0
1
0
0
2
0
0
2
1
1
0
1
0
0
1
1
2
0
1
2
0
1
2
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
2
0
1
0
0
0
0
1
0
1
0
0
1
0
0
2
0
0
1
0
0
2
1
2
0
2
0
3
1
0
0
0
0
2
2
0
1
1
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
1
0
0
2
0
0
1
0
0
1
2
1
0
0
2
1
0
2
0
1
2
1
0
0
0
1
0
0
2
1
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
2
2
2
1
2
0
2
0
0
3
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
2
0
1
0
0
0
1
3
0
0
0
1
2
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
2
2
0
1
1
0
0
1
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
1
3
0
0
0
0
0
2
0
0
0
1
0
0
0
2
1
0
0
0
0
0
2
0
0
0
3
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
3
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
2
1
1
1
0
2
0
3
1
3
0
0
3
2
0
0
0
1
2
0
1
1
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
1
1
1
1
0
3
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
1
0
0
2
2
2
2
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
1
1
2
2
2
2
0
1
0
0
1
1
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
1
0
2
1
1
2
1
0
1
1
0
0
2
1
0
0
0
1
0
1
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
1
3
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
3
1
0
0
1
0
0
2
0
0
0
0
1
0
0
4
1
1
0
0
1
0
0
1
0
0
0
2
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
1
1
0
0
1
0
2
3
4
0
0
0
2
1
0
0
0
1
2
2
0
0
0
2
0
2
0
0
0
0
0
1
0
1
1
0
2
0
0
0
0
2
0
0
2
0
1
0
0
2
2
0
2
0
0
1
0
2
2
0
2
0
0
0
0
0
0
0
1
1
1
0
0
2
0
0
2
0
0
2
0
2
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
2
1
1
0
0
0
0
0
1
0
0
1
0
0
2
0
2
2
0
0
2
0
1
0
2
2
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
1
1
0
0
0
0
0
1
2
0
2
1
1
0
0
0
0
1
0
0
1
0
2
0
0
2
0
1
0
0
0
0
0
0
1
1
0
2
2
0
1
2
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
1
0
2
1
0
1
0
0
2
0
0
1
0
1
0
0
0
0
0
0
2
0
0
1
0
0
1
0
1
3
2
0
2
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
1
0
0
0
2
1
0
1
1
0
0
0
0
2
0
0
0
1
1
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
2
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
4
0
0
1
0
2
0
0
0
0
0
1
0
2
2
0
0
1
0
0
0
0
0
3
2
0
1
2
3
0
0
0
0
0
0
0
2
1
0
2
0
1
0
2
0
0
1
0
0
0
0
0
1
2
0
0
0
1
1
0
2
3
0
2
0
0
2
2
0
0
0
2
0
0
1
0
0
0
1
2
1
1
0
2
1
0
0
2
0
0
2
2
1
0
1
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
3
0
0
0
1
0
0
0
2
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
2
0
0
0
0
0
1
3
2
1
1
0
0
3
1
0
0
1
0
1
3
0
0
2
0
1
0
1
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
4
0
2
1
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
1
0
0
0
4
2
1
0
2
2
1
0
0
0
2
0
0
0
1
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
3
2
0
0
1
2
0
0
0
0
1
0
2
0
0
0
1
1
0
0
2
2
2
0
0
7
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
1
0
5
0
0
0
0
1
2
0
0
0
0
0
0
1
0
1
0
0
2
2
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
2
1
2
0
0
1
0
1
0
0
1
1
2
5
2
0
0
2
0
0
1
0
2
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
1
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
1
2
0
0
5
2
0
1
0
1
0
1
0
0
0
0
3
1
0
2
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
2
2
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
2
0
0
0
0
3
0
2
1
0
0
0
0
1
0
0
0
0
2
2
0
2
0
0
1
1
1
0
1
1
0
0
2
1
0
0
0
0
2
0
0
0
0
1
0
1
1
0
2
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
3
0
0
2
1
0
0
0
0
0
0
0
6
0
2
0
0
0
0
0
0
2
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
2
0
2
0
0
0
0
0
4
0
2
0
1
2
0
0
1
0
0
2
2
0
1
0
1
0
3
3
1
1
0
1
2
0
1
0
3
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
2
1
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
8
0
2
3
0
2
0
0
0
0
8
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
1
0
0
0
0
0
1
0
0
0
0
2
2
0
2
0
1
0
0
1
0
2
2
2
1
0
0
1
0
1
2
1
0
0
2
0
0
2
0
0
2
0
0
0
0
2
0
2
3
1
0
0
1
0
2
0
0
1
0
1
0
0
0
0
0
2
0
1
2
0
0
0
0
2
0
1
0
0
2
0
0
0
0
1
1
0
0
0
1
0
2
0
2
0
0
2
0
1
0
1
0
2
0
3
0
0
0
2
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
2
0
0
2
1
0
2
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
1
2
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
2
0
0
1
2
2
0
0
2
0
0
2
0
1
3
0
1
1
0
0
0
2
1
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
2
0
1
1
0
0
0
0
0
2
2
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
9
2
0
1
1
2
0
0
0
0
2
1
2
0
0
0
2
0
1
0
0
0
0
0
2
1
0
0
2
0
3
0
0
0
0
0
0
1
2
0
0
2
1
1
0
2
0
5
1
1
2
1
0
0
1
1
3
2
0
0
0
1
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
1
0
2
1
1
0
2
0
0
2
1
2
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
1
2
8
1
2
2
0
0
0
2
2
0
2
0
2
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
3
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
4
0
0
0
2
0
1
2
0
1
1
1
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
1
2
0
1
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
2
0
0
0
2
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
2
1
0
2
2
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
2
1
1
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
1
0
4
0
1
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
3
0
0
0
2
0
1
0
0
2
1
0
0
0
0
0
2
0
6
0
0
1
0
0
1
0
2
0
1
2
2
2
1
0
0
0
0
0
0
0
0
2
1
0
4
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
1
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
2
0
4
0
1
0
3
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
2
2
0
0
0
0
0
1
0
0
1
2
1
2
1
1
2
0
0
2
0
0
0
2
0
0
0
1
0
1
2
0
0
1
2
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
2
0
0
0
0
0
1
0
0
2
0
2
1
0
1
2
1
0
1
0
1
2
0
0
0
2
0
0
0
1
2
2
1
0
0
0
0
0
1
0
1
2
0
0
3
0
2
1
1
2
0
1
0
2
1
0
0
0
2
1
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
2
1
0
1
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
2
0
0
0
2
0
0
0
0
0
1
3
0
2
0
0
1
0
0
2
2
0
2
0
1
0
0
0
2
2
1
0
1
0
1
0
0
0
0
0
0
0
0
0
3
1
0
4
0
1
2
0
1
2
0
2
1
0
0
0
0
0
0
0
0
0
4
0
2
1
0
0
0
0
2
1
0
0
1
0
0
0
1
0
0
0
2
1
0
0
1
0
1
0
0
4
4
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
1
0
2
0
0
0
3
0
0
0
0
0
1
2
1
0
3
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
1
1
0
2
0
0
2
0
0
0
0
2
1
0
0
0
0
0
2
0
1
0
1
0
2
0
0
0
0
2
5
0
2
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
1
1
0
1
0
0
0
0
1
2
2
0
1
2
2
2
2
0
0
0
2
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
2
1
1
2
0
0
0
0
2
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
2
1
0
0
1
2
0
0
0
1
0
0
0
0
1
0
4
1
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
3
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
4
0
0
0
0
3
2
1
0
0
0
0
4
2
0
0
0
0
0
2
0
1
2
0
0
3
0
0
1
1
0
0
1
1
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
1
0
2
0
0
2
0
0
0
2
2
1
1
0
0
0
0
0
0
2
2
0
2
0
0
0
1
0
0
2
1
1
2
1
1
1
0
0
2
0
0
0
1
0
0
0
0
1
1
0
0
0
5
1
0
0
0
0
3
0
1
0
3
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
1
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
2
1
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
3
1
0
2
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
2
2
0
0
2
2
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
2
2
0
1
2
0
0
0
0
2
0
0
0
1
1
2
2
2
0
0
1
2
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
4
0
0
1
2
0
2
1
3
0
0
0
0
1
0
0
2
0
0
2
0
0
0
1
0
0
2
1
1
0
0
0
0
1
0
0
2
2
0
0
0
0
1
0
1
0
3
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
2
0
0
0
0
2
2
0
0
0
0
0
2
0
0
1
4
0
0
0
0
1
1
2
1
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
2
2
1
2
1
0
0
0
0
0
0
0
3
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
2
1
1
0
0
0
0
1
2
1
0
1
0
0
0
0
1
0
0
1
2
4
1
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
2
0
2
0
0
0
0
0
1
2
0
2
1
0
1
2
0
0
2
0
0
0
2
0
0
2
0
2
2
0
1
0
0
0
0
1
0
0
1
0
1
0
1
2
3
0
1
0
0
1
0
1
0
1
0
1
2
0
2
1
4
0
0
0
4
0
1
6
2
0
2
0
0
1
0
2
0
0
1
2
0
0
1
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
3
1
0
0
0
0
0
2
0
2
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
3
2
2
1
2
0
0
0
1
0
0
0
0
0
0
2
1
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
3
2
2
0
0
1
0
2
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
2
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
6
1
0
1
2
3
0
0
2
1
0
3
2
0
2
0
1
0
1
3
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
1
0
0
6
2
0
0
1
2
0
0
1
0
0
0
0
1
2
0
0
0
0
0
2
0
2
3
0
2
0
1
0
0
0
0
1
2
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
2
1
0
1
1
0
3
0
0
0
2
0
1
0
0
1
0
0
0
0
0
2
0
1
0
0
0
1
2
2
0
0
2
0
0
0
0
8
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
1
0
1
1
0
2
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
1
2
0
0
1
0
0
0
0
0
1
0
2
1
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
3
0
0
0
1
0
2
3
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
1
0
2
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
2
2
0
0
1
1
0
0
0
0
2
0
1
0
0
2
0
0
0
1
0
2
0
0
2
0
0
0
0
1
2
0
0
0
0
2
0
2
0
0
0
2
1
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
1
1
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
1
2
0
2
3
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
5
1
1
0
0
2
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
4
2
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
2
1
2
0
2
4
0
0
0
0
0
0
0
0
0
0
2
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
1
0
0
1
3
0
0
0
0
2
1
3
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
4
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
1
1
1
2
0
0
0
2
1
0
0
2
2
0
0
0
0
1
1
0
3
0
0
0
1
0
1
2
1
0
0
0
2
0
0
1
0
0
0
0
1
0
2
1
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
2
2
0
1
0
1
0
2
2
0
1
0
0
1
0
0
1
0
1
0
0
0
2
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
1
1
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
1
0
1
0
0
0
1
0
0
0
0
2
0
0
2
0
1
3
3
0
0
0
2
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
2
0
1
0
0
0
2
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
2
0
1
1
0
0
0
2
3
0
2
0
2
0
0
1
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
2
0
0
0
2
1
0
1
0
0
0
1
1
1
3
0
2
0
0
0
2
2
0
0
0
0
0
0
1
0
1
0
5
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
1
0
0
0
0
2
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
1
2
2
1
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
2
0
1
0
1
1
2
1
2
1
0
0
0
1
0
0
1
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
1
1
0
0
0
1
2
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
2
0
0
0
2
1
2
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
1
1
0
2
0
1
0
0
0
0
2
0
1
1
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
2
0
1
1
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
1
1
1
2
0
1
0
0
0
0
0
1
0
1
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
1
0
0
0
0
0
3
1
0
0
2
1
2
2
0
0
0
0
0
0
0
3
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
1
0
0
2
0
2
1
0
2
0
0
1
0
0
2
1
0
1
0
0
0
2
0
3
0
0
2
0
0
1
0
0
0
0
0
2
3
1
3
1
1
0
0
2
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
1
2
0
1
2
2
2
0
0
0
0
2
0
1
1
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
1
1
1
0
1
3
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
1
2
1
1
0
2
0
0
0
0
0
0
0
0
1
0
1
1
2
0
1
0
0
0
1
0
0
1
2
2
2
0
2
1
2
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
1
0
1
1
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
2
0
0
1
0
2
2
0
0
0
2
2
0
0
2
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
1
1
0
0
0
2
0
1
3
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
3
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
1
1
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
3
1
0
0
0
0
0
0
1
0
0
0
1
0
2
1
2
2
1
1
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
2
0
1
2
2
1
2
1
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
4
0
0
0
0
0
0
0
3
0
2
2
0
0
1
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
1
1
2
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
1
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
2
2
2
0
0
1
2
0
0
0
2
2
0
0
2
0
2
0
2
1
0
0
1
0
0
0
1
2
6
1
0
2
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
1
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
1
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
1
2
0
0
0
0
1
2
2
0
0
0
2
0
1
0
1
0
0
0
1
1
2
1
0
0
7
5
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
2
0
0
1
0
0
0
2
1
0
0
6
0
0
0
2
1
0
0
0
2
0
0
0
0
1
1
0
1
1
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
2
2
0
0
0
1
1
0
0
1
0
0
2
0
0
0
2
0
0
0
0
2
1
0
0
1
0
1
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
3
0
0
0
2
0
0
0
0
1
0
2
0
0
0
3
0
3
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
2
0
2
0
3
1
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
2
0
0
2
0
2
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
2
0
0
0
2
0
0
0
2
1
0
1
0
1
0
0
0
1
0
0
0
2
0
2
2
0
1
0
0
0
0
0
0
0
2
0
3
0
0
0
0
2
4
0
0
1
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
1
0
0
3
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
2
3
0
0
0
0
0
1
0
2
2
1
2
2
1
0
0
2
0
0
2
1
0
1
0
0
0
0
0
0
0
0
1
0
1
2
1
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
5
1
0
0
0
0
1
2
0
2
0
0
0
0
1
0
1
1
0
0
1
0
2
0
0
0
1
0
2
0
0
1
0
2
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
2
1
0
2
0
2
0
1
1
0
1
0
0
1
2
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
4
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
2
1
0
2
0
0
0
0
2
3
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
3
2
0
0
0
0
1
1
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
5
1
0
2
0
1
0
0
2
0
0
3
0
0
0
0
2
2
0
1
1
2
0
0
3
2
5
0
0
0
3
0
0
0
1
0
0
2
0
1
0
4
2
0
0
1
0
2
2
0
0
2
0
1
0
1
2
0
0
0
2
1
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
2
0
0
0
6
0
1
1
1
0
0
0
0
2
1
0
0
2
2
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
3
0
2
0
0
0
0
0
0
1
1
0
0
2
1
1
0
0
0
1
2
0
0
2
2
1
0
0
1
0
0
1
0
0
0
2
0
1
1
0
0
0
1
0
0
0
1
0
0
1
2
0
1
0
1
0
0
0
1
0
1
0
0
0
2
1
2
0
0
1
0
0
0
0
0
1
0
2
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
1
0
0
1
0
0
0
0
2
0
2
0
1
2
0
1
2
0
1
1
2
2
1
0
0
0
1
0
0
2
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
2
0
1
0
0
1
0
2
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
2
0
0
1
0
0
0
2
0
0
2
0
1
4
0
1
2
0
2
0
0
0
0
1
1
0
1
0
0
0
0
0
2
0
2
0
0
2
2
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
1
0
2
0
1
1
0
2
0
1
1
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
1
0
2
1
0
2
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
3
0
1
0
2
0
2
0
1
0
1
0
0
0
0
0
2
0
0
0
0
2
3
1
0
0
2
1
2
2
2
0
0
0
0
0
1
0
1
0
0
2
2
2
0
0
0
0
0
0
0
1
1
2
2
0
2
0
2
0
1
0
0
0
1
1
0
0
2
0
0
1
0
0
0
0
0
0
1
0
2
1
0
2
1
0
2
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
1
1
0
0
0
1
0
0
0
0
0
0
0
0
3
2
2
0
2
0
0
0
0
0
1
2
0
0
0
1
3
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
2
0
2
0
2
2
1
0
0
2
0
0
0
0
0
0
0
2
2
2
0
0
1
0
1
0
0
0
0
0
1
2
1
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
1
1
1
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
2
0
0
0
0
0
0
1
1
1
0
0
2
5
2
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
1
2
1
2
0
0
2
0
1
1
2
0
4
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
2
1
2
0
0
0
2
0
0
0
2
2
0
0
0
0
2
0
1
1
0
0
0
0
0
1
0
0
2
0
2
0
5
0
1
0
0
0
0
0
0
0
2
2
0
3
0
0
1
0
1
2
2
0
2
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
2
2
0
1
0
0
2
0
0
0
0
0
1
1
2
4
1
0
0
3
1
0
2
0
2
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
2
1
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
2
0
0
0
0
0
0
3
1
2
1
0
0
0
2
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
2
2
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
1
2
2
0
3
0
0
2
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
2
0
0
0
0
1
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
2
0
1
2
0
0
0
0
2
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
2
0
0
0
3
1
0
1
0
0
0
0
2
2
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
2
1
0
0
0
0
0
1
1
2
0
0
0
0
1
0
0
0
0
1
2
1
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
2
2
0
0
0
2
0
2
0
0
0
0
2
0
1
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
1
0
3
0
0
0
2
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
2
2
2
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
1
1
0
1
0
0
0
0
0
0
0
3
1
1
1
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
7
0
2
0
2
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
2
0
0
1
1
0
2
2
3
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
2
0
0
2
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
2
3
0
0
0
0
2
2
0
0
0
4
0
4
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
3
0
1
1
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
2
0
2
0
2
1
0
0
2
1
0
2
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
3
0
1
0
0
0
0
0
0
0
0
2
0
1
0
3
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
2
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
2
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
1
3
0
0
1
0
0
0
0
0
0
1
0
1
0
1
2
0
0
0
1
0
2
0
0
0
1
0
2
0
1
1
0
0
0
0
0
2
1
0
0
0
0
1
0
0
1
1
2
0
0
0
0
1
1
2
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
2
0
0
1
1
0
1
2
1
0
0
1
0
2
0
0
2
0
0
2
2
0
1
0
2
2
0
0
0
2
1
0
1
3
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
3
1
0
0
4
0
0
0
2
0
1
1
3
0
2
0
0
1
2
0
0
0
0
0
2
1
0
1
0
1
3
1
0
0
2
2
0
0
0
2
0
1
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
2
0
2
0
0
0
0
1
1
0
0
0
1
1
2
0
2
1
0
1
0
0
0
0
0
0
2
0
2
1
0
2
0
1
0
0
0
2
0
1
0
1
0
0
0
0
0
0
2
0
2
0
0
3
0
2
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
3
0
2
2
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
2
0
0
2
1
0
2
0
0
0
1
0
0
0
0
0
1
2
3
0
2
0
0
1
2
0
1
0
0
1
1
0
0
2
0
0
2
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
1
0
0
2
0
0
0
0
0
1
0
0
0
4
1
2
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
1
3
0
0
2
0
0
0
0
2
0
0
2
0
0
0
2
0
0
2
0
0
0
5
1
2
0
0
4
1
1
1
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
2
2
0
0
2
0
1
0
0
0
0
1
0
2
0
0
2
0
2
0
0
2
1
1
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
1
0
1
0
1
2
0
0
0
0
0
0
0
2
0
1
3
0
0
0
0
3
2
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
2
1
0
2
0
1
0
0
2
0
0
1
0
0
1
0
2
0
0
0
2
0
0
0
6
2
0
0
2
0
0
1
1
2
2
0
1
0
1
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
3
0
2
0
0
2
0
2
0
0
0
0
0
0
2
0
0
3
0
0
0
1
1
0
2
0
0
1
2
1
0
0
2
0
2
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
2
1
0
0
2
1
0
0
1
2
0
0
2
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
1
1
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
1
0
1
0
1
0
0
0
3
0
1
0
1
0
0
2
0
1
0
0
0
0
0
0
0
2
2
2
0
0
2
1
0
0
0
1
0
0
0
0
0
0
1
1
0
3
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
5
1
0
0
2
0
0
2
2
0
1
0
8
0
2
0
0
0
0
2
0
0
0
2
0
0
0
2
1
0
0
0
2
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
1
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
4
1
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
2
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
2
0
0
0
0
1
1
0
0
0
0
1
0
0
2
0
0
2
0
1
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
1
1
0
2
2
0
0
1
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
2
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
2
2
2
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
2
0
1
2
0
2
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
3
1
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
1
2
0
0
0
0
0
1
0
1
0
2
0
1
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
2
2
0
0
0
0
1
0
0
0
5
4
0
2
0
0
0
2
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
1
2
1
0
0
0
0
0
0
2
0
0
1
2
0
1
0
0
2
0
0
0
0
1
2
0
0
0
2
2
0
0
0
1
0
1
0
2
0
0
2
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
2
0
0
0
0
1
0
0
4
1
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
1
0
0
2
0
2
0
0
0
0
0
2
1
0
1
0
0
0
2
0
1
2
1
1
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
5
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
2
2
0
0
2
2
0
1
4
0
0
0
0
1
2
0
0
2
2
0
1
1
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
2
1
0
0
0
1
0
0
2
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
1
1
0
0
1
1
0
0
0
2
0
0
0
2
2
2
1
0
2
1
0
0
0
1
2
0
0
0
2
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
2
0
1
0
1
0
2
0
1
0
0
0
0
0
0
4
0
0
0
0
2
0
1
0
3
0
1
0
0
2
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
2
0
1
0
0
1
0
1
0
0
3
0
0
0
1
1
0
1
0
0
7
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
1
0
1
2
2
0
0
0
2
0
2
0
0
2
1
0
2
0
0
0
1
0
1
0
2
0
0
0
0
2
2
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
1
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
1
1
0
0
0
0
2
0
2
0
0
2
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
1
2
0
1
0
0
1
0
2
0
0
0
1
0
0
2
0
2
1
0
2
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
3
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
2
1
0
0
0
0
2
0
1
0
2
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
2
0
0
0
0
0
0
0
2
0
0
1
1
1
0
3
0
0
0
1
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
2
2
0
0
0
0
0
2
0
2
2
1
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
2
0
1
0
3
0
1
1
0
1
2
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
1
0
0
1
2
5
0
0
0
0
0
1
0
2
1
0
2
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
1
0
1
0
0
0
0
0
0
2
0
3
2
0
0
0
0
1
2
0
0
0
0
2
1
0
2
0
3
2
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
2
2
0
2
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
3
0
1
2
2
1
2
0
0
1
0
1
0
0
0
2
5
0
0
2
0
0
0
2
1
0
0
0
0
3
0
1
1
2
0
0
0
0
2
0
0
1
0
1
3
0
0
0
0
0
1
1
0
1
0
0
0
1
2
0
1
0
0
0
0
2
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
1
1
2
0
0
2
0
7
0
0
1
1
0
0
0
2
0
2
1
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
2
0
1
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
2
1
0
0
2
2
0
2
0
1
0
1
0
0
2
1
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
1
0
0
0
1
2
1
0
0
0
2
2
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
2
2
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
1
1
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
4
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
1
1
0
2
0
0
1
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
1
1
0
2
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
1
0
0
0
1
3
0
2
1
0
2
1
0
3
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
1
0
1
0
1
0
0
1
2
1
0
0
0
1
0
1
0
2
0
0
0
1
0
1
0
1
2
0
0
2
0
0
1
2
0
0
2
0
0
2
2
0
0
1
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
2
0
3
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
2
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
3
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
1
0
0
0
2
0
1
0
2
0
2
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
2
2
0
0
0
0
0
2
0
1
0
2
1
0
0
2
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
2
1
0
0
1
5
2
0
0
0
6
2
0
2
0
0
0
0
0
2
1
0
1
0
0
2
0
2
1
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
1
2
2
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
1
1
0
0
1
0
1
0
1
0
0
2
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
4
0
2
0
2
2
1
0
1
2
1
1
2
1
0
0
1
1
1
2
1
0
0
0
0
0
0
0
0
2
0
0
1
1
0
2
0
0
0
2
0
0
0
0
0
1
1
0
6
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
2
0
0
0
0
1
0
0
0
0
0
2
5
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
1
0
2
0
1
2
2
0
0
1
0
2
0
0
0
1
1
0
0
3
0
0
0
0
0
1
0
0
1
2
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
1
2
1
1
0
0
0
0
0
0
2
0
0
0
0
2
1
2
2
1
0
1
0
0
0
0
0
2
0
0
1
0
1
0
2
0
2
0
0
1
2
2
0
1
0
1
0
1
1
1
0
0
0
0
0
0
0
2
2
0
0
0
1
0
2
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
1
0
0
0
2
0
0
0
0
0
1
2
0
1
2
0
1
0
0
0
2
0
1
0
2
0
2
0
0
0
2
0
2
0
0
0
1
0
0
0
1
0
1
1
0
0
0
1
2
0
0
2
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
2
1
0
2
1
1
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
2
2
0
1
0
0
0
0
1
2
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
1
1
1
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
2
0
1
0
3
2
0
0
0
0
0
2
0
1
1
2
3
0
0
0
0
0
1
1
0
0
0
0
0
2
0
1
0
0
0
2
2
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
2
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
1
0
2
0
0
0
0
1
0
0
0
1
1
0
0
2
0
0
0
2
0
0
0
0
2
2
0
2
0
1
0
1
2
2
0
0
1
0
0
0
2
0
0
3
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
2
2
2
1
1
1
1
0
0
0
0
0
0
0
0
0
2
2
0
2
1
0
4
0
0
2
0
0
0
0
0
3
0
1
0
1
0
1
0
0
0
0
1
0
1
1
2
0
1
0
0
0
0
0
1
2
1
2
0
2
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
2
0
2
2
2
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
2
0
0
1
2
2
0
1
2
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
4
2
1
0
0
0
0
0
1
1
2
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
2
0
0
1
0
0
2
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
2
0
0
0
0
1
0
2
3
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
1
0
0
0
2
0
2
2
2
1
0
0
2
1
1
0
0
0
1
0
0
2
0
0
2
1
1
0
1
0
0
0
1
1
0
1
0
0
0
0
0
1
2
0
0
2
2
0
0
0
2
0
0
0
0
0
1
1
0
0
0
2
0
0
5
0
1
2
0
0
0
0
0
1
1
0
1
0
1
0
2
0
2
0
1
2
0
1
0
0
0
0
0
0
2
1
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
2
1
1
0
1
0
0
1
0
2
2
2
0
0
0
2
0
1
2
0
2
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
2
0
0
3
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
2
2
0
1
0
0
3
2
1
0
0
1
0
1
3
0
0
0
1
1
1
0
1
0
0
0
0
0
2
0
1
2
0
0
1
0
0
3
2
0
1
0
3
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
1
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
1
0
0
0
2
1
0
2
1
0
0
0
4
0
0
0
1
1
0
0
0
0
2
0
2
0
0
0
0
0
1
8
0
0
0
1
2
0
1
0
0
2
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
1
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
1
2
2
2
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
2
0
0
0
0
3
2
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
2
2
1
0
0
0
1
0
0
1
3
0
0
2
0
2
1
0
0
2
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
12
0
1
1
3
0
0
1
0
2
2
0
1
0
0
0
0
0
0
0
0
1
4
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
2
0
2
0
2
0
1
0
0
1
0
1
0
0
0
0
2
1
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
1
0
1
0
1
0
0
2
0
0
0
0
0
3
0
3
1
0
0
0
0
1
0
0
0
1
0
0
0
2
0
2
0
0
0
2
0
2
0
1
1
0
1
0
0
0
1
2
1
1
0
0
2
1
0
2
0
0
0
2
1
0
1
4
1
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
2
1
0
0
1
0
0
0
0
1
0
0
0
0
0
2
1
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
2
2
2
0
2
2
2
0
0
1
0
1
0
2
0
0
0
0
0
2
1
0
1
2
0
0
0
1
0
1
0
0
2
0
0
0
2
1
0
2
0
2
0
2
2
0
0
1
0
2
0
0
0
0
2
2
0
2
0
2
0
0
0
0
0
0
2
0
1
1
0
0
1
2
0
1
0
1
2
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
2
0
0
3
0
2
0
3
0
0
0
1
1
2
3
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
1
1
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
1
0
2
0
2
0
0
2
0
1
1
0
0
1
1
3
3
2
2
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
2
0
2
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
2
0
2
0
0
0
2
0
0
1
0
2
0
2
0
2
0
0
0
2
0
3
0
2
7
0
0
0
0
0
3
2
0
0
0
0
0
2
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
2
1
2
0
0
0
0
1
0
0
0
0
0
0
3
0
1
0
0
0
0
2
0
2
1
0
0
1
0
0
0
0
0
5
0
0
2
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
3
1
0
0
0
0
0
3
0
0
0
1
2
0
1
3
0
0
0
1
0
0
0
1
1
0
0
0
2
0
0
2
2
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
2
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
2
1
0
2
1
0
0
1
2
0
0
0
2
2
0
0
1
0
0
0
0
3
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
2
1
0
1
2
0
0
0
1
1
2
0
1
1
0
0
1
0
0
0
0
0
2
0
2
0
2
1
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
2
1
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
1
0
2
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
2
2
0
2
0
0
0
2
2
1
1
0
0
0
0
2
0
2
2
0
0
1
1
0
2
2
2
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
2
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
1
0
0
0
0
0
0
0
3
0
1
0
1
2
0
0
0
0
3
2
0
2
2
0
1
0
0
0
0
2
1
0
0
0
0
1
0
2
1
0
0
1
0
0
3
0
0
0
1
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
5
0
0
2
2
0
2
0
0
0
1
0
0
4
0
1
0
2
0
0
1
1
0
0
0
0
1
0
2
0
2
0
1
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
1
1
3
0
0
0
0
2
0
0
1
0
2
0
0
0
2
2
2
2
0
1
0
2
0
0
1
0
5
0
0
0
0
0
1
1
0
2
0
0
2
2
2
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
1
0
0
2
0
0
0
0
0
0
0
2
1
0
0
2
0
0
2
0
0
0
2
0
1
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
1
0
1
0
2
1
0
1
0
1
0
0
1
2
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
1
2
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
1
0
0
2
1
1
0
0
1
3
0
0
2
3
0
1
0
0
0
2
0
0
0
0
1
0
2
0
2
2
3
2
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
2
0
0
0
0
0
1
1
1
0
0
0
2
0
0
0
0
2
0
0
0
1
0
2
1
0
2
3
2
0
0
2
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
2
3
2
0
1
0
0
1
0
0
0
0
0
2
0
2
2
1
1
0
0
0
2
0
0
0
0
2
0
0
0
0
1
2
0
0
0
6
0
1
0
2
1
3
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
1
0
0
2
3
2
0
0
0
1
0
1
0
0
1
1
0
1
2
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
1
0
0
1
0
1
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
2
1
0
0
0
2
0
0
2
0
0
0
2
1
0
2
1
0
2
0
0
0
0
0
0
0
3
1
0
1
2
0
0
0
2
0
2
1
0
1
0
0
2
0
2
0
1
0
4
0
0
1
0
0
0
0
0
2
2
2
0
2
0
1
0
0
2
1
0
4
1
0
0
0
2
1
0
0
0
1
0
2
0
0
0
1
0
0
0
1
0
2
0
3
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
1
2
0
0
0
3
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
2
0
1
3
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
1
1
0
0
0
1
0
0
0
0
2
1
6
0
0
0
1
0
0
0
2
0
0
0
1
2
0
1
0
0
2
0
0
0
2
0
1
2
0
1
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
2
0
2
0
2
0
0
0
1
0
0
0
0
1
0
1
0
0
0
2
0
2
2
4
0
0
0
0
0
0
1
2
0
0
0
2
0
1
2
0
0
0
0
0
0
1
2
0
0
0
0
1
0
1
2
2
0
2
0
1
0
1
0
0
0
0
2
1
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
2
0
0
0
2
1
0
0
0
0
1
0
0
2
2
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
2
1
0
1
0
0
2
0
0
2
1
0
2
0
0
2
1
1
0
0
3
0
0
0
0
0
0
0
0
0
0
2
1
1
2
0
1
0
2
0
2
0
1
0
0
2
0
6
0
2
2
2
0
3
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
2
1
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
1
0
2
2
0
2
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
1
0
0
2
1
1
1
1
0
0
0
1
2
1
0
2
1
0
0
1
0
0
0
2
0
1
2
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
1
0
5
1
1
0
1
1
0
0
1
0
0
0
0
2
0
0
0
0
0
2
2
0
1
0
0
0
0
0
2
2
1
0
0
1
0
1
0
1
0
0
0
0
2
1
1
0
2
0
2
0
0
0
0
2
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
1
0
2
0
3
1
0
2
0
0
1
2
1
2
0
0
0
0
2
2
0
0
0
0
2
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
1
2
1
0
0
1
2
0
0
2
0
1
0
1
0
0
1
3
0
1
5
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
2
1
0
1
3
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
3
1
1
0
0
0
0
0
0
2
1
0
0
3
0
0
0
0
0
0
2
2
0
0
0
0
3
0
0
6
0
1
0
0
0
0
0
0
1
0
2
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
1
0
2
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
1
1
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
2
0
1
0
2
1
0
2
2
1
0
0
0
0
1
0
0
2
0
1
2
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
1
0
1
0
0
2
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
2
2
1
0
2
2
0
0
0
0
1
0
2
0
1
1
2
1
1
0
2
0
0
2
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
1
0
2
1
0
0
0
0
0
2
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
1
0
0
2
5
0
0
1
1
0
0
2
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
4
0
0
0
0
1
0
1
0
1
1
0
0
0
2
0
2
1
0
0
1
0
0
2
1
0
2
0
0
0
0
2
0
0
3
1
2
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
1
0
1
2
2
1
0
4
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
1
0
2
0
0
2
0
1
0
2
0
0
0
1
0
1
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
1
0
0
5
0
0
0
1
0
1
0
0
0
1
0
0
2
1
2
0
0
0
0
1
0
0
0
2
1
3
1
2
0
2
3
2
0
0
0
2
1
0
0
0
0
2
0
1
2
1
0
0
1
1
0
1
0
0
0
1
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
6
0
0
0
0
2
1
2
1
2
1
3
1
0
0
2
0
2
0
0
0
1
1
2
0
0
0
0
2
0
1
0
3
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
1
0
2
1
0
0
0
0
0
0
2
0
1
0
2
1
1
0
2
0
2
0
2
2
0
0
1
0
2
0
1
0
0
0
0
2
0
0
0
0
0
1
1
2
0
1
0
1
0
0
0
0
3
1
0
0
0
0
0
0
0
1
2
0
0
2
0
0
4
0
0
0
2
1
0
0
0
0
0
2
0
0
1
3
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
0
1
1
0
0
2
0
0
1
0
0
0
0
0
1
0
2
4
0
1
0
1
0
0
1
0
0
2
1
0
0
1
0
0
0
2
1
0
2
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
2
1
1
1
2
0
0
1
0
1
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
1
2
0
0
2
0
0
2
0
0
2
2
0
0
0
1
0
0
0
1
2
1
0
0
2
0
1
0
2
1
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
2
0
3
0
0
0
1
0
2
1
0
2
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
1
0
0
0
0
2
1
2
2
2
1
0
0
0
3
3
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
2
0
0
0
0
0
0
0
2
2
1
0
0
0
0
2
2
2
0
0
0
1
0
2
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
1
1
2
0
0
0
0
0
2
1
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
2
2
0
0
0
2
2
2
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
2
0
0
1
0
1
0
0
0
0
0
2
1
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
1
2
1
0
0
0
0
0
1
1
0
2
2
2
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
2
3
2
1
0
0
1
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
2
0
0
0
2
1
0
0
1
2
0
0
0
1
1
0
1
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
1
2
0
0
0
0
0
1
3
0
0
0
1
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
2
0
0
2
0
2
0
2
0
0
0
0
1
2
0
1
1
0
0
0
0
0
1
1
0
0
0
1
1
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
4
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
2
0
1
0
1
0
0
0
0
2
1
1
0
0
0
0
1
1
2
1
0
0
1
1
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
2
0
2
0
2
1
0
0
0
1
0
0
0
0
2
2
0
0
0
1
2
0
0
0
0
2
0
0
0
1
1
0
0
0
0
2
0
1
0
2
2
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
1
2
1
0
0
3
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
2
1
0
0
5
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
2
0
0
0
0
0
1
0
2
1
0
0
1
0
1
0
2
0
2
0
0
2
1
0
0
0
0
2
0
2
1
2
1
0
2
0
0
2
0
0
1
0
2
0
0
0
2
2
0
1
0
0
1
1
1
0
0
2
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
1
2
2
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
1
2
0
0
0
0
1
0
0
0
0
0
3
1
0
0
1
1
0
1
0
2
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
2
1
0
1
0
0
0
0
1
0
0
0
2
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
2
2
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
2
1
0
0
2
0
0
0
1
0
2
1
0
0
0
1
1
0
0
0
1
0
0
0
0
1
1
1
2
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
2
2
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
1
0
2
0
2
3
0
0
0
0
1
1
1
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
2
2
0
1
0
0
1
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
2
0
4
0
0
0
0
0
1
2
1
1
0
0
0
0
1
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
2
0
1
0
0
0
2
0
0
1
0
2
0
0
0
2
1
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
1
0
2
0
0
0
2
0
0
1
0
2
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
2
0
1
0
1
0
1
0
0
1
2
0
1
0
0
2
0
2
2
1
1
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
2
0
2
1
0
0
0
1
0
2
0
8
2
0
2
0
1
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
2
0
1
0
1
0
2
0
1
0
0
0
0
2
0
0
0
0
3
2
0
1
1
0
0
0
1
0
0
0
1
1
0
0
0
2
0
0
2
0
0
0
2
0
0
0
2
1
1
0
2
1
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
1
2
0
0
0
0
0
0
0
1
2
2
0
0
1
0
0
0
0
7
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
4
2
2
3
0
1
0
0
0
1
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
2
0
2
1
0
2
0
0
1
1
1
0
0
1
0
0
0
1
1
2
0
1
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
1
0
1
0
0
0
0
0
3
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
2
2
0
0
0
0
2
1
0
0
2
0
5
1
1
2
0
2
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
1
1
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
2
0
0
0
2
1
2
2
0
1
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
2
0
0
0
0
0
0
0
2
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
1
0
0
2
1
0
1
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
1
0
1
0
1
1
0
0
0
0
0
0
3
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
2
2
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
2
1
1
0
2
1
0
0
0
0
2
2
0
2
2
2
1
0
0
1
2
2
2
0
0
0
0
0
2
0
0
1
0
0
2
2
0
1
0
1
2
0
0
0
0
0
0
2
0
0
2
3
0
2
0
0
1
0
0
0
0
0
2
2
1
3
0
1
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
7
2
0
0
0
0
2
1
0
0
0
0
2
0
3
2
0
2
0
0
1
1
2
0
2
0
0
0
3
3
0
1
0
0
0
0
0
1
0
0
2
3
2
1
0
2
0
0
5
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
2
0
0
2
0
0
0
1
0
0
0
0
1
0
1
0
2
3
0
0
0
2
0
0
0
0
0
0
0
0
1
2
3
0
1
0
0
0
0
1
1
2
2
0
0
0
0
1
0
5
1
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
2
0
2
0
0
0
1
1
2
1
0
0
0
0
0
1
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
1
2
0
2
1
0
0
2
0
0
0
0
2
0
1
1
0
2
0
0
2
0
0
1
0
0
0
1
0
1
0
0
2
0
1
0
0
1
2
2
1
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
1
2
0
2
1
0
2
0
0
0
0
0
0
1
0
0
0
0
2
1
2
2
0
0
2
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
1
1
0
0
0
1
0
0
0
0
0
2
0
3
0
0
0
0
2
1
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
4
0
0
0
0
0
0
1
0
1
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
2
0
0
0
0
7
0
1
0
0
1
0
1
0
0
0
0
1
0
2
2
2
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
1
2
0
2
0
0
1
0
3
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
3
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
3
1
0
0
4
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
1
1
2
0
0
2
0
0
1
0
0
0
0
2
0
2
0
1
0
0
1
0
0
0
0
1
0
1
0
0
2
0
0
2
1
0
2
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
2
0
0
2
1
0
0
1
0
0
0
2
0
0
2
1
0
2
0
1
2
0
2
0
0
1
1
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
2
0
0
0
0
0
2
0
0
2
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
3
1
0
1
0
0
3
0
0
0
1
1
2
0
0
0
0
2
0
0
2
0
1
0
0
2
0
1
0
1
1
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
1
0
0
2
0
1
0
0
0
1
0
2
1
0
0
0
3
0
0
0
1
2
1
2
1
1
0
1
2
0
0
0
1
0
8
2
0
2
1
1
0
0
0
0
2
0
0
0
0
1
0
0
0
3
2
0
0
0
0
0
0
2
0
0
4
0
0
0
2
1
0
2
2
0
1
2
1
1
0
0
0
0
0
0
1
0
0
0
1
2
0
2
1
0
1
0
0
0
2
1
0
0
0
1
0
2
0
2
0
0
3
0
1
0
0
2
0
0
0
0
0
2
1
0
0
0
2
1
0
0
0
0
0
0
2
1
0
0
3
0
2
0
0
0
2
0
1
0
0
0
2
2
2
1
0
0
1
0
1
2
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
2
1
0
2
0
0
0
0
0
2
0
1
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
2
2
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
1
2
0
2
0
0
2
0
0
2
0
0
3
3
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
2
0
0
2
1
2
0
0
1
1
0
0
0
0
0
2
2
0
2
1
2
0
0
1
1
0
0
0
6
0
2
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
1
1
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
2
0
1
0
0
0
3
0
1
0
1
0
0
2
1
2
2
2
2
0
0
0
2
0
0
1
0
0
4
2
1
2
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
2
0
0
0
2
0
0
0
0
1
0
2
1
0
0
0
3
1
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
2
1
0
0
0
0
0
2
1
0
1
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
2
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
1
1
2
0
2
0
0
0
0
0
0
0
2
0
0
1
0
1
0
3
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
2
4
2
1
1
0
0
0
2
0
3
0
0
1
0
1
2
3
0
0
1
2
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
1
1
0
2
0
0
0
1
0
0
1
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
3
0
2
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
5
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
3
0
0
0
1
0
0
2
0
0
2
2
0
2
0
0
0
0
1
0
0
0
0
2
1
0
1
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
2
0
2
1
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
1
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
3
0
0
2
2
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
2
0
3
0
0
0
0
0
2
0
0
1
0
0
1
2
2
0
0
1
0
0
0
1
1
2
0
0
0
1
1
2
0
0
0
2
2
0
0
0
0
0
1
0
0
0
1
1
3
1
0
1
1
0
0
0
0
0
2
0
1
0
0
0
0
0
3
0
0
0
0
1
0
1
0
2
1
1
0
1
1
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
2
2
0
0
1
0
1
0
0
1
2
0
0
0
0
1
0
0
0
0
2
0
2
0
1
1
0
0
3
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
2
1
1
0
0
1
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
1
0
0
2
0
2
0
4
0
2
0
1
1
0
0
1
1
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
1
1
4
2
1
0
2
0
0
3
0
0
4
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
1
0
0
0
0
2
2
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
2
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
5
2
0
2
0
0
0
0
2
0
0
2
2
2
0
0
0
0
0
1
0
0
1
0
0
1
0
2
0
2
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
2
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
1
0
0
0
2
2
0
0
0
0
1
0
0
0
2
0
3
2
2
0
0
1
2
0
0
1
1
0
2
0
2
1
0
0
0
0
2
0
0
0
0
0
2
0
2
1
0
1
0
1
2
1
0
0
0
1
0
0
0
3
0
1
0
0
0
0
0
0
0
2
2
1
0
2
0
0
0
0
1
0
0
2
0
1
0
2
2
2
2
0
2
0
2
0
2
3
2
0
0
0
0
0
1
0
0
0
1
2
0
2
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
1
2
2
0
2
2
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
2
0
2
0
1
0
2
0
1
1
1
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
3
0
0
1
0
0
2
1
0
0
1
2
0
1
1
0
1
0
0
0
1
3
1
1
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
1
0
2
2
1
0
0
1
0
0
0
0
2
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
1
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
2
0
0
0
2
3
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
2
0
1
0
2
1
0
0
1
0
0
2
0
1
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
3
2
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
1
0
1
0
0
2
2
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
2
1
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
2
1
1
2
0
0
0
3
0
2
2
0
0
0
0
0
0
2
0
0
2
5
2
1
2
0
0
2
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
1
0
0
3
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
2
0
1
0
0
1
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
2
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
2
0
2
0
0
2
2
0
0
0
1
0
0
0
0
2
2
2
0
1
0
0
1
0
0
0
1
2
1
2
0
0
0
2
0
0
3
0
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
1
0
0
2
4
0
0
0
1
1
2
1
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
1
0
0
1
2
0
0
0
0
1
1
0
2
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
2
2
2
0
0
0
0
1
0
0
1
0
2
0
4
0
0
1
0
0
1
0
0
0
1
0
2
0
2
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
4
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
2
0
0
2
0
1
5
2
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
2
0
2
0
2
2
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
2
5
0
1
0
0
0
4
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
1
2
1
2
0
0
0
1
2
1
0
0
0
0
0
1
1
3
1
0
0
0
0
0
0
2
0
0
0
2
2
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
1
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
3
2
1
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
2
0
2
0
1
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
2
1
0
0
0
0
0
0
1
0
2
0
0
2
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
9
0
1
1
1
0
0
1
3
0
0
0
2
0
0
0
0
1
0
0
2
1
0
0
2
1
0
0
0
0
0
1
1
2
0
0
0
0
0
0
2
2
0
0
1
0
2
0
1
2
2
0
0
1
0
0
1
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
4
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
1
0
0
1
0
2
0
2
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
1
0
1
2
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
1
0
2
0
2
0
0
1
0
0
2
0
2
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
1
4
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
1
1
0
2
0
0
2
0
0
0
2
0
1
0
0
1
0
1
0
3
0
0
0
0
1
0
2
0
2
0
0
3
0
0
0
0
2
2
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
1
0
0
0
0
2
2
0
0
7
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
3
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
3
0
2
1
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
2
2
0
0
0
1
2
0
0
0
2
7
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
2
0
3
1
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
1
0
0
1
2
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
3
1
0
0
1
2
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
2
2
0
0
0
0
1
1
0
1
0
1
1
0
1
0
0
2
1
0
1
2
0
1
2
0
1
0
0
0
1
1
0
2
0
1
1
1
0
1
0
1
0
0
2
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
1
0
0
0
0
3
0
2
1
0
0
0
0
3
2
0
0
1
1
0
0
2
0
1
0
1
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
1
1
1
1
0
0
0
2
0
0
0
1
2
0
2
2
2
0
0
0
0
0
0
0
5
1
0
0
4
2
0
0
1
0
0
2
0
0
0
0
0
0
0
2
4
0
2
0
0
0
2
1
1
0
1
0
2
1
1
0
0
0
2
0
0
4
0
0
1
0
3
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
3
1
1
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
2
2
0
2
0
2
0
0
1
0
0
2
2
0
1
3
0
0
0
0
2
0
1
2
0
0
2
0
0
0
2
2
0
1
0
1
2
0
0
0
0
2
0
2
1
0
0
0
0
0
0
2
1
0
2
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
3
0
3
0
0
1
2
1
0
0
2
0
0
0
0
1
2
0
0
1
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
2
0
2
1
0
0
2
0
2
0
1
1
0
2
0
1
0
0
0
1
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
2
0
2
0
1
0
1
1
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
1
0
0
0
0
2
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
2
1
1
0
1
1
1
1
0
2
0
2
0
0
1
0
0
2
2
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
2
2
0
2
0
1
0
0
1
0
0
0
0
0
2
0
1
0
0
1
0
0
0
2
0
1
0
0
2
0
0
0
0
2
3
0
0
0
4
0
1
0
0
0
0
2
0
2
0
0
0
0
2
1
1
1
0
3
2
0
2
0
1
0
0
0
2
2
2
0
1
0
0
0
0
1
2
0
1
3
0
3
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
3
0
0
0
2
0
2
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
2
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
2
0
1
2
0
0
0
2
2
0
0
1
0
2
0
1
0
0
2
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
2
2
0
0
0
1
2
0
0
0
0
0
0
0
0
3
0
0
2
2
2
1
1
0
0
1
1
1
0
0
0
0
0
0
0
2
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
1
0
4
0
0
2
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
4
1
0
1
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
1
1
0
2
3
0
0
0
2
1
0
1
1
0
0
1
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
2
0
0
2
0
1
2
1
2
0
2
0
0
1
1
2
0
0
0
0
0
0
0
0
0
2
0
0
2
1
1
2
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
6
2
2
0
3
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
1
0
2
1
0
0
2
1
1
1
0
0
0
0
4
1
0
0
0
0
0
0
0
2
0
1
0
0
0
1
2
0
2
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
2
0
0
0
1
0
0
1
0
1
0
0
1
2
0
2
0
0
0
1
2
0
0
1
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
2
0
2
0
0
1
0
0
0
0
2
2
0
0
1
0
0
1
0
0
2
0
2
1
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
4
0
0
0
0
2
2
0
3
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
2
1
2
0
1
0
1
0
1
0
0
1
2
0
0
1
1
0
0
0
0
0
0
1
2
0
0
1
1
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
1
0
0
0
3
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
1
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
3
0
0
0
1
1
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
3
0
1
0
2
3
3
0
0
1
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
1
0
2
0
0
1
0
1
2
1
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
1
1
1
2
1
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
2
0
0
1
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
1
0
2
0
0
0
2
1
0
0
0
1
0
0
1
0
0
1
0
1
0
2
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
1
0
2
1
2
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
3
2
0
2
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
1
0
1
0
3
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
2
1
0
1
24
0
0
0
0
0
0
2
0
2
1
1
2
0
1
0
0
0
1
0
2
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
1
2
0
0
0
0
0
0
2
0
0
2
0
1
0
1
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
1
1
0
0
2
0
0
0
0
1
0
2
2
0
0
1
0
0
2
1
1
2
0
0
1
0
2
0
0
0
0
0
0
1
0
2
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
4
1
1
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
2
0
2
0
0
2
1
2
0
0
1
0
1
0
0
0
1
1
0
2
0
0
0
1
0
0
0
1
2
0
0
0
0
1
2
2
0
4
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
1
0
0
1
2
0
0
0
0
1
0
1
2
0
1
1
0
2
2
0
0
1
2
1
0
0
0
1
1
1
1
0
0
0
1
0
0
0
0
0
3
1
2
2
1
0
0
0
2
0
1
1
0
0
1
0
0
2
0
0
1
0
2
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
2
0
1
1
0
0
1
0
0
2
0
0
3
1
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
1
2
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
2
4
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
1
7
2
0
1
0
0
0
0
0
0
3
2
0
0
0
0
2
5
0
0
0
0
0
0
2
2
0
0
2
0
1
0
0
0
0
0
2
0
1
1
0
0
0
2
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
2
0
2
0
2
2
0
1
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
1
0
2
2
2
0
0
0
0
0
4
2
0
1
1
0
4
0
0
2
2
2
0
0
0
0
0
0
1
0
0
0
0
1
1
0
2
0
0
1
0
2
1
1
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
1
4
0
0
1
1
0
0
0
0
0
0
0
0
1
0
2
1
0
1
0
0
0
2
3
0
0
0
2
0
3
0
0
1
0
0
0
0
0
1
0
0
2
0
2
0
3
0
0
2
1
3
1
1
1
1
0
3
2
0
0
0
0
1
0
1
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
2
2
0
2
0
2
0
0
0
0
0
7
0
1
2
0
1
0
0
0
0
0
0
1
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
2
1
0
2
0
0
0
0
2
2
1
3
0
2
3
0
0
0
0
1
0
0
0
0
0
2
0
1
0
1
1
0
0
1
0
1
0
0
0
2
1
0
0
0
0
2
1
0
0
0
0
2
0
1
0
1
2
0
1
2
2
4
0
0
0
1
2
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
3
1
2
2
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
2
2
0
0
0
0
1
0
0
0
1
0
1
0
1
0
2
0
0
0
0
0
0
0
0
6
0
0
0
1
0
0
1
0
2
1
0
1
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
1
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
1
0
2
0
0
2
1
0
0
0
1
2
1
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
3
1
1
0
2
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
5
0
0
2
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
2
0
2
0
2
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
2
0
0
1
0
4
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
2
3
0
1
0
0
0
1
0
1
0
2
0
2
2
0
0
0
1
0
0
0
0
0
2
0
1
0
1
2
0
0
0
0
2
2
1
0
0
3
1
0
0
1
0
0
0
0
1
1
0
0
1
1
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
3
0
0
0
2
1
2
1
1
2
0
0
1
0
0
1
3
2
2
0
1
0
3
0
2
0
0
1
0
0
0
0
1
0
0
0
2
2
0
1
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
2
0
0
1
0
0
0
0
0
0
1
1
0
0
2
2
0
2
0
2
0
0
1
0
1
0
0
2
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
2
0
2
0
0
0
0
1
1
2
0
0
0
2
0
2
1
0
1
0
1
0
0
0
0
0
1
0
2
1
0
0
0
1
1
2
1
0
2
0
0
1
1
1
2
0
0
0
3
0
0
0
1
1
0
0
3
0
2
1
0
0
0
0
0
1
0
2
0
1
5
0
1
1
1
0
0
2
0
1
1
0
0
0
0
0
1
0
2
2
1
0
1
0
0
2
0
2
0
1
0
0
0
1
3
0
0
0
1
0
0
0
0
0
1
1
2
0
1
1
0
0
2
0
0
0
0
2
1
0
0
1
1
2
0
2
2
8
1
0
0
0
1
0
1
0
2
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
2
0
0
2
2
4
0
0
0
2
0
0
0
0
3
0
1
0
1
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
4
0
4
0
0
1
0
0
1
1
1
0
0
0
1
0
0
1
0
0
0
1
2
0
1
0
0
0
4
0
0
0
0
6
0
0
1
0
0
1
3
0
0
0
0
0
0
2
2
0
1
1
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
2
1
1
0
0
0
0
0
0
2
1
2
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
3
2
0
0
0
1
0
0
1
1
2
1
0
1
2
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
3
2
0
1
0
0
0
2
0
3
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
3
0
0
1
0
0
1
0
0
0
2
3
2
0
2
1
1
0
0
2
0
0
0
1
0
2
1
0
1
0
1
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
4
2
0
1
0
0
0
1
0
0
2
0
1
2
0
1
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
2
1
0
0
2
2
0
0
1
0
0
1
0
0
2
0
0
0
0
2
0
0
0
2
0
3
1
0
2
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
1
3
0
1
0
0
0
1
0
2
2
1
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
2
0
2
0
1
0
0
2
1
0
2
0
0
1
1
3
0
2
1
1
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
3
0
0
0
2
1
2
0
0
0
0
0
0
2
0
1
2
0
1
1
0
0
0
4
0
0
0
1
0
2
0
0
3
0
0
1
0
1
0
2
0
3
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
2
1
0
0
0
0
0
0
0
0
1
0
1
2
0
1
1
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
3
0
1
2
0
6
0
2
1
0
1
0
1
0
0
0
2
2
0
0
0
1
1
0
0
2
0
1
1
2
0
1
0
0
0
0
7
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
2
3
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
2
1
0
1
0
0
0
1
0
0
2
5
0
2
0
0
3
0
0
0
1
0
0
2
1
0
2
0
0
0
0
0
0
0
0
1
1
2
0
0
0
1
0
1
0
0
1
1
0
0
1
0
1
1
0
0
2
0
0
0
0
0
0
1
0
0
1
2
1
0
0
4
0
1
3
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
2
0
1
0
2
0
0
0
0
0
2
2
0
2
0
0
0
0
1
0
2
2
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
2
0
1
0
0
2
0
0
2
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
1
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
2
1
0
0
0
0
0
2
2
0
2
0
1
0
0
0
3
1
0
1
0
0
0
0
3
0
1
0
0
2
1
2
3
2
0
0
0
1
0
0
0
1
0
0
0
3
2
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
2
2
3
0
2
0
0
0
0
3
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
3
1
0
0
0
2
1
1
2
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
1
1
0
0
0
0
4
1
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
4
0
0
1
0
0
0
0
0
2
0
0
1
2
0
1
0
2
2
0
0
1
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
3
0
1
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
1
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
3
0
0
0
2
1
0
2
0
0
2
0
1
2
2
2
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
2
0
2
0
1
2
1
0
0
0
1
0
1
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
1
2
0
0
0
0
2
0
0
2
0
0
0
0
1
2
4
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
3
2
1
0
1
0
0
2
1
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
2
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
3
0
1
1
0
0
0
7
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
2
0
1
1
1
0
4
0
1
2
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
2
2
2
0
2
1
0
1
1
0
0
2
1
2
0
0
2
2
1
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
3
0
2
2
0
0
0
0
0
1
3
0
1
1
0
0
0
3
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
2
0
0
2
0
0
0
0
1
0
3
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
1
0
1
0
1
0
1
0
0
0
1
0
3
2
0
0
2
0
2
0
0
1
0
0
0
1
0
3
0
2
2
0
3
1
2
0
2
0
0
2
0
0
0
0
0
1
2
0
0
2
0
0
0
0
1
2
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
2
1
1
3
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
1
0
1
0
0
1
0
0
0
2
2
0
2
2
2
1
0
0
2
0
0
0
1
0
0
0
8
1
0
2
0
3
0
0
0
0
1
1
0
0
0
0
3
0
0
1
2
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
3
0
0
2
2
1
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
3
0
0
0
0
2
0
2
1
3
3
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
2
1
2
0
0
0
2
1
2
0
2
0
0
0
0
0
2
1
0
1
2
0
1
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
1
1
2
2
0
0
0
1
0
2
1
0
0
0
0
0
0
0
1
0
2
2
0
2
2
2
1
2
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
2
1
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
2
1
0
0
0
4
0
1
0
0
0
2
0
2
2
2
1
0
3
1
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
3
1
0
2
2
0
0
0
1
0
0
4
0
0
0
0
0
0
1
0
1
2
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
2
4
0
0
3
0
0
0
0
1
0
0
0
2
0
0
0
0
2
1
1
1
2
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
1
2
0
0
0
2
0
2
0
0
0
1
0
0
3
0
0
0
3
0
0
0
2
3
0
1
2
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
1
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
1
0
1
0
0
0
2
0
2
2
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
2
2
0
0
4
0
0
3
2
0
0
0
0
2
0
0
0
0
1
0
0
2
1
0
2
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
1
0
1
2
1
0
0
0
0
0
1
2
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
4
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
2
0
1
0
2
2
0
0
0
0
0
2
1
0
1
0
1
0
0
0
0
1
0
2
1
0
1
1
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
7
0
0
1
0
0
0
0
3
0
0
0
0
1
0
2
1
1
0
0
0
0
1
0
1
0
2
1
1
0
0
0
0
0
0
0
0
3
0
1
2
2
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
3
2
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
2
1
1
0
1
0
3
0
0
0
0
2
1
0
0
0
1
0
0
0
0
1
1
0
1
2
0
1
0
0
0
0
0
0
0
0
2
2
1
1
0
1
0
2
0
0
0
1
1
4
0
0
1
0
2
0
0
2
2
2
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
4
0
0
0
2
1
2
1
0
0
1
1
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
1
0
2
1
1
1
0
0
0
0
0
0
1
0
2
0
0
0
0
1
1
0
2
1
1
0
0
0
2
0
0
0
0
0
2
1
0
0
0
5
0
0
2
0
1
3
1
1
0
0
0
0
5
1
0
0
0
0
0
2
2
1
1
0
2
1
2
0
2
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
5
2
0
0
0
0
1
0
1
0
0
0
0
3
2
1
1
1
1
0
0
0
0
2
0
0
0
2
0
0
1
2
0
0
0
0
0
1
1
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
5
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
1
1
3
0
1
0
0
0
2
1
0
0
2
0
2
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
2
0
0
0
3
2
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
3
0
0
2
2
3
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
1
1
0
2
0
0
0
0
0
1
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
1
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
2
0
0
0
0
0
2
0
0
0
1
2
0
2
0
0
0
0
0
1
0
0
0
2
2
1
0
0
0
1
1
0
0
0
2
0
3
2
0
0
2
0
0
0
0
2
0
0
2
2
2
0
0
0
1
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
2
0
2
1
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
1
3
0
2
0
0
0
0
0
2
0
1
1
2
0
2
1
2
0
2
0
0
0
0
0
0
1
2
3
0
0
0
0
0
0
3
2
0
0
2
0
0
0
3
0
0
0
0
1
0
0
0
1
0
1
1
1
0
0
2
1
0
2
0
0
0
0
0
0
2
1
0
0
0
0
1
0
1
0
0
1
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
3
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
1
1
0
0
0
1
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
1
0
2
2
0
2
0
1
0
0
3
0
2
0
0
0
2
0
2
1
0
1
0
1
0
2
2
2
0
0
1
1
1
2
0
3
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
2
0
2
2
1
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
2
2
0
0
0
1
0
0
0
2
2
0
0
1
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
1
0
0
0
1
0
2
0
3
0
0
0
0
2
2
2
0
0
2
2
0
0
1
0
0
0
1
2
2
0
0
0
0
0
0
0
2
0
1
0
0
1
0
5
0
0
1
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
2
1
0
0
2
0
0
2
0
1
0
0
0
0
2
0
0
0
2
1
0
3
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
9
0
0
1
0
2
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
1
0
0
1
0
2
1
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
2
1
1
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
1
0
0
0
0
1
0
1
2
4
1
0
2
0
0
0
0
1
0
1
0
0
1
1
0
0
0
2
0
0
0
0
0
1
1
2
0
1
0
2
0
0
0
2
0
0
2
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
1
3
0
0
1
1
2
0
3
0
0
0
1
0
2
0
0
0
0
2
0
3
3
1
0
1
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
4
0
0
0
0
0
4
0
0
1
1
0
0
0
0
0
2
0
4
0
1
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
3
0
1
1
2
2
1
0
0
0
0
0
0
1
0
1
2
0
0
2
0
1
0
0
2
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
1
0
1
0
0
0
1
2
0
1
0
1
0
1
1
0
2
0
0
0
2
0
0
1
1
0
2
0
0
1
2
0
3
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
1
1
2
0
0
1
0
0
1
0
2
2
2
2
0
0
0
1
2
0
2
2
0
0
0
0
1
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
1
0
1
1
0
1
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
3
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
2
1
1
0
0
0
0
1
0
0
0
2
0
2
0
0
1
0
2
0
0
1
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
1
0
0
0
0
0
2
2
0
0
0
3
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
1
0
0
2
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
2
0
0
2
0
0
1
1
1
1
0
1
0
0
2
3
2
0
0
0
0
0
0
0
2
0
0
1
0
1
1
0
3
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
1
2
0
2
0
0
0
0
1
0
0
0
0
1
0
0
2
2
0
0
0
2
0
0
2
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
2
0
0
0
0
0
0
1
0
0
4
0
0
0
2
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
2
0
0
1
2
1
0
1
0
0
1
0
0
0
0
2
1
3
0
2
3
1
0
0
0
2
0
2
0
1
0
3
0
0
2
0
0
2
2
1
0
2
0
0
2
0
0
0
2
0
2
0
0
4
2
0
1
0
1
0
0
1
0
0
0
2
2
0
0
2
0
1
0
0
1
2
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
1
2
0
1
0
0
2
0
2
0
0
2
0
0
1
2
0
2
0
3
0
1
2
1
2
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
2
0
0
0
2
0
1
0
1
0
2
1
0
2
0
1
0
0
0
1
0
2
0
0
2
0
0
0
1
0
0
2
0
1
0
0
0
0
0
1
0
1
2
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
1
1
1
1
1
0
2
0
2
4
0
1
0
1
2
1
0
0
0
0
0
0
0
0
0
1
0
2
0
1
2
0
0
0
0
0
1
0
0
1
2
0
2
1
3
1
1
0
0
0
1
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
1
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
1
0
2
1
0
1
1
2
0
0
0
0
1
0
0
0
2
0
0
0
0
2
1
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
2
0
1
2
0
0
0
1
1
0
4
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
1
1
0
0
0
0
0
1
3
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
3
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
2
2
0
0
0
0
2
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
2
0
3
1
0
1
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
2
0
2
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
1
2
0
1
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
5
0
2
0
0
0
0
1
0
7
2
6
0
0
0
0
2
0
0
0
1
0
0
0
2
2
0
2
0
0
2
0
1
2
0
1
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
3
0
0
0
0
0
3
0
0
1
1
0
0
1
0
0
2
1
0
0
0
0
2
0
1
0
0
0
0
0
1
1
0
1
0
0
1
0
1
0
0
1
0
2
0
0
0
3
2
0
0
0
0
0
0
4
0
0
0
0
1
0
1
1
0
0
1
0
3
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
2
1
0
0
1
2
0
0
0
1
0
0
0
0
1
0
0
1
1
0
1
0
2
0
0
0
0
0
0
3
1
0
0
2
0
0
2
0
3
1
0
1
0
3
1
0
0
0
2
0
0
2
0
0
3
1
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
1
1
1
1
1
0
0
0
0
1
0
2
1
0
1
2
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
1
0
2
0
0
1
2
0
0
0
0
1
0
0
0
2
0
2
1
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
3
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
1
0
2
0
0
1
0
2
1
0
0
0
0
0
3
0
2
2
0
0
2
0
0
1
0
0
2
0
3
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
2
2
0
0
1
0
0
0
1
2
0
0
0
1
1
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
1
0
1
0
2
2
2
1
0
1
1
0
0
0
0
0
3
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
2
2
0
0
0
2
0
0
0
0
2
2
2
0
1
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
1
0
0
0
3
2
1
0
0
2
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
2
2
1
2
1
0
0
0
0
0
2
0
1
2
0
1
2
2
2
0
0
2
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
1
1
1
1
2
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
1
0
5
0
0
1
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
2
0
0
1
1
0
2
0
0
1
0
0
1
2
0
0
2
0
0
0
0
2
0
1
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
1
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
2
1
0
0
2
0
1
0
0
3
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
5
0
0
0
0
0
1
0
5
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
1
0
0
6
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
1
2
0
0
0
0
0
3
0
0
0
0
0
0
1
0
3
0
2
0
0
0
0
3
2
0
0
0
2
0
0
1
1
0
1
0
0
0
0
0
2
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
1
0
0
0
0
0
2
2
0
0
0
0
0
1
2
0
0
0
1
0
0
1
0
2
0
2
0
2
0
0
2
0
2
1
0
0
2
0
1
0
0
0
1
1
1
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
1
0
0
1
1
0
0
0
3
1
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
2
1
0
0
3
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
1
1
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
2
0
0
2
1
0
0
0
0
2
0
1
0
2
0
0
0
2
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
1
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
2
1
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
2
1
2
0
0
0
0
0
0
0
1
2
1
0
0
0
2
1
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
1
2
0
0
0
0
1
2
0
2
0
0
0
1
0
2
2
0
0
1
0
0
0
1
0
0
2
0
0
0
1
0
3
1
0
1
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
3
0
0
2
1
0
2
0
0
0
0
0
0
1
1
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
1
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
1
0
0
1
1
0
1
0
0
2
4
0
1
0
1
0
0
0
2
0
2
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
1
0
2
2
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
1
0
1
1
0
0
2
0
1
2
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
1
2
2
2
0
0
0
2
0
1
0
0
0
2
0
2
0
2
0
0
0
0
0
1
0
0
2
2
1
1
0
0
0
0
0
0
1
0
0
3
2
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
2
0
1
2
2
0
0
0
0
3
0
0
0
2
0
2
2
0
0
0
2
0
1
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
7
0
1
0
0
0
0
0
3
0
0
0
0
0
0
2
1
2
1
2
2
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
1
1
0
2
0
0
0
0
0
2
0
0
0
0
0
3
2
2
0
1
0
2
1
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
2
1
0
0
2
1
1
2
1
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
2
1
0
0
0
0
0
0
0
0
2
0
5
0
0
2
0
0
0
0
0
0
1
1
3
0
0
2
2
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
1
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
1
1
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
8
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
2
2
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
3
0
0
0
0
0
2
0
2
0
1
0
0
0
1
1
1
0
0
0
1
2
1
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
2
0
1
0
0
0
2
0
0
0
0
0
1
0
1
0
2
0
0
0
0
1
1
2
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
3
0
2
1
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
1
1
2
2
0
0
0
0
2
0
2
0
0
1
1
2
0
0
0
0
1
1
0
2
0
0
0
2
0
0
1
0
1
1
0
0
0
0
0
0
2
0
1
0
1
0
0
2
0
1
0
0
0
2
1
0
1
0
1
0
1
0
1
0
3
0
0
0
2
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
2
1
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
3
2
1
2
0
0
0
1
0
3
0
1
0
0
0
2
0
2
0
0
1
0
1
0
1
1
0
0
0
0
2
0
1
1
0
0
0
1
0
2
1
0
0
2
1
3
2
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
2
0
0
2
0
0
0
2
0
1
0
0
0
0
3
1
0
1
0
0
0
5
0
0
1
0
1
0
0
0
0
1
0
1
0
2
0
1
1
0
1
0
0
1
2
2
0
0
1
0
0
0
5
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
1
0
2
1
0
0
1
0
0
1
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
2
0
2
1
0
2
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
1
0
2
1
2
0
0
2
0
0
1
0
0
0
0
1
1
0
2
1
0
2
0
0
2
1
0
2
1
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
1
3
0
0
2
0
0
0
1
2
2
0
0
2
0
2
0
0
1
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
2
0
2
0
2
0
0
1
0
1
0
0
1
1
1
1
0
0
3
0
2
0
0
0
2
2
1
3
0
1
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
1
2
0
0
0
0
0
2
0
0
2
0
2
0
1
3
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
1
0
1
0
0
0
1
0
3
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
2
2
2
0
2
0
1
0
0
2
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
2
2
1
1
0
0
0
3
0
0
0
0
0
1
0
0
1
0
0
0
1
2
2
3
0
1
0
0
2
1
2
0
0
2
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
1
0
2
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
2
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
2
0
1
2
2
2
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
1
0
2
1
0
1
2
0
0
0
0
1
5
0
0
1
0
2
1
0
0
0
1
1
0
1
1
2
0
9
0
2
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
3
0
3
2
4
0
4
0
1
2
0
0
0
1
0
0
0
0
2
0
0
2
2
0
0
0
2
2
0
0
1
0
0
0
0
2
0
0
2
1
0
0
1
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
3
0
0
2
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
1
2
0
1
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
4
0
0
0
2
0
1
2
0
0
1
0
0
2
0
0
2
0
0
1
0
0
2
0
0
0
0
0
3
0
2
2
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
2
0
2
3
0
0
0
0
1
1
0
2
0
1
0
2
0
2
1
1
0
0
0
0
1
1
0
0
1
2
0
0
0
0
2
2
0
0
4
0
0
2
0
1
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
4
2
0
2
2
1
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
1
0
0
0
0
0
2
2
0
0
2
0
2
0
2
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
3
0
1
0
1
2
0
0
2
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
4
0
0
1
2
0
2
2
0
2
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
2
2
0
0
0
0
0
1
2
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
1
2
0
0
0
3
2
1
0
1
2
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
2
0
1
0
0
0
1
0
0
1
0
0
2
0
1
0
0
0
0
0
1
0
0
0
4
2
0
3
1
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
2
3
1
1
0
0
1
0
1
0
0
1
0
1
2
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
1
6
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
2
0
0
1
0
0
0
1
0
0
1
2
1
0
1
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
2
2
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
2
1
0
0
0
1
0
0
4
0
0
0
0
2
1
0
0
0
5
1
0
0
0
0
1
0
1
0
2
0
0
0
1
0
1
1
0
0
0
0
0
1
0
2
0
2
0
1
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
2
0
1
0
0
2
1
0
1
0
0
0
0
0
0
0
1
0
1
5
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
2
0
0
2
0
2
0
2
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
2
0
0
0
1
2
0
0
0
2
0
0
0
0
4
0
0
1
1
2
0
1
0
2
0
0
0
2
0
0
0
2
0
1
0
0
0
2
0
0
0
0
1
2
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
2
0
0
0
0
0
4
2
1
0
0
0
0
0
2
1
2
1
0
0
2
0
1
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
3
0
0
2
0
1
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
2
0
1
0
1
2
3
0
2
0
1
0
2
1
1
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
1
2
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
4
1
0
0
2
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
2
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
2
2
0
0
0
2
0
2
1
0
0
1
0
0
0
1
0
1
0
3
0
1
0
0
1
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
3
3
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
1
0
0
2
0
0
0
2
1
0
0
0
2
0
3
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
2
0
0
1
3
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
2
2
0
0
2
0
0
1
9
2
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
2
0
0
2
0
0
1
0
0
2
0
0
0
2
1
0
3
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
1
0
1
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
1
0
0
1
0
2
2
0
1
0
1
0
2
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
2
0
1
3
0
1
0
0
0
0
0
1
2
0
1
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
2
2
3
0
0
2
0
0
0
0
1
0
2
0
0
0
1
2
0
0
0
0
0
0
2
0
1
0
0
1
1
0
2
0
0
0
0
0
0
0
2
2
0
1
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
2
0
1
0
0
1
0
1
0
0
0
0
0
2
0
1
0
3
1
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
1
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
2
1
1
1
0
2
0
1
0
2
2
0
0
2
0
0
0
0
0
0
2
0
2
0
2
2
2
0
0
0
0
0
1
1
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
5
1
0
1
0
0
0
0
0
0
1
1
0
0
0
2
0
3
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
2
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
3
0
1
0
0
0
0
0
0
0
0
0
2
2
1
0
1
2
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
2
2
0
0
1
2
3
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
2
0
1
0
1
3
0
7
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
2
4
0
0
1
1
0
1
1
0
0
2
0
0
0
1
2
0
0
2
1
0
1
0
0
0
0
0
0
3
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
1
0
1
1
1
0
0
0
2
1
0
0
0
1
1
0
0
0
0
0
1
0
2
0
0
1
0
0
0
3
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
2
1
0
1
3
0
2
0
0
0
0
2
3
2
0
0
0
0
0
0
2
0
1
0
1
0
2
0
2
2
1
0
2
1
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
1
1
0
2
0
0
2
0
0
0
0
0
1
0
0
0
1
1
0
0
4
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
1
0
0
3
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
3
0
0
2
1
2
0
0
0
2
0
0
2
0
0
0
1
0
0
2
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
1
2
0
0
0
0
0
3
1
2
0
0
0
0
1
0
2
0
2
1
0
2
0
0
2
0
0
0
0
0
0
0
1
0
2
0
1
0
2
0
0
0
0
0
3
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
1
0
0
1
0
0
2
0
0
0
2
0
2
1
0
0
1
0
2
0
2
0
0
2
0
0
0
1
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
2
0
0
0
1
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
2
2
0
0
0
0
0
0
2
0
1
0
1
0
0
0
1
2
0
0
0
0
1
0
0
1
0
0
2
3
1
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
1
1
0
0
2
0
2
1
0
0
0
0
0
2
3
0
0
1
0
0
0
0
1
2
1
0
1
1
0
3
0
0
0
4
0
1
0
2
0
0
0
0
0
1
6
0
0
1
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
1
2
3
0
0
1
0
0
0
5
0
0
0
0
2
0
1
2
2
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
1
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
7
1
0
0
0
1
0
0
1
1
0
2
1
4
1
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
1
2
0
0
1
2
0
1
0
2
0
0
0
0
0
2
0
1
1
0
0
0
2
2
0
0
1
1
0
0
0
2
0
0
2
2
0
3
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
1
0
1
0
1
0
0
0
0
3
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
2
0
0
0
0
3
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
2
2
0
0
3
0
0
1
0
0
0
0
0
0
0
0
2
0
0
3
2
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
1
0
1
0
1
2
0
1
0
2
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
3
0
2
0
2
0
3
2
0
1
2
0
0
1
3
2
2
0
0
0
3
0
1
0
1
0
8
0
2
0
2
2
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
1
1
1
0
2
0
0
1
1
1
1
0
2
1
1
0
0
0
0
0
0
1
1
0
0
1
2
0
0
0
1
0
0
0
1
1
0
1
1
0
0
0
0
0
0
2
0
3
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
4
0
0
0
0
0
2
1
5
0
0
0
0
0
0
0
2
2
0
0
3
0
0
0
1
2
1
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
2
2
0
0
3
2
1
0
0
2
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
1
0
0
2
0
0
2
0
0
0
0
2
0
2
0
1
0
1
1
1
1
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
2
2
0
1
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
12
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
1
0
0
0
2
1
1
1
1
0
0
2
0
1
0
0
2
0
0
1
2
0
0
0
0
0
2
0
0
1
2
0
1
0
2
2
1
0
1
0
0
2
0
1
2
0
2
0
2
0
0
4
2
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
2
0
9
2
0
0
0
0
5
0
1
0
0
0
0
2
0
2
0
0
0
3
1
0
0
1
1
0
0
2
0
0
0
0
1
3
0
0
0
1
1
2
0
1
0
0
0
0
0
0
1
4
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
3
2
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
2
0
1
0
1
2
1
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
1
2
0
0
0
4
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
1
0
3
0
0
0
2
2
0
1
0
2
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
2
0
0
0
1
0
0
0
0
0
1
2
0
1
0
0
3
0
0
0
0
0
0
2
0
0
0
1
1
2
2
0
0
1
0
6
2
0
0
2
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
1
0
2
0
0
0
2
0
0
0
4
0
0
0
0
0
0
2
2
0
3
0
0
0
0
0
1
1
0
0
0
2
0
2
0
2
0
1
0
0
0
0
0
2
0
0
1
1
0
2
2
1
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
2
0
0
2
2
0
1
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
4
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
2
2
0
1
0
1
1
0
1
0
0
0
2
2
2
0
1
0
2
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
2
2
1
0
0
0
2
1
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
1
0
0
2
1
0
0
1
0
0
1
0
2
0
0
0
1
3
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
2
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
2
1
1
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
5
0
0
0
0
0
0
0
0
1
2
1
0
0
2
0
0
1
3
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
3
3
0
0
2
0
2
0
0
3
0
0
0
1
1
0
2
2
0
0
0
1
0
0
1
2
0
1
0
2
0
0
0
1
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
1
5
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
2
0
0
1
0
0
2
0
1
0
0
3
1
0
2
0
2
0
2
0
0
0
2
0
0
0
4
0
2
1
0
0
1
2
1
2
0
0
0
1
1
0
0
0
8
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
3
0
0
2
0
1
1
2
0
1
0
0
2
0
0
0
4
2
0
1
1
2
0
0
2
0
0
1
1
0
0
0
0
1
2
0
2
2
0
2
2
0
0
0
1
1
0
0
0
0
0
0
0
2
0
1
0
1
2
0
1
0
0
0
1
1
0
0
0
0
1
2
0
0
0
0
2
0
1
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
3
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
2
0
0
2
0
1
1
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
2
1
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
2
0
1
0
0
0
0
2
0
0
1
2
0
2
0
0
0
3
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
4
0
3
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
2
2
1
0
1
2
0
2
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
1
1
0
2
0
0
2
2
0
0
0
0
0
0
0
2
0
2
0
0
0
1
2
2
0
0
0
1
1
0
1
0
1
0
0
0
2
1
0
0
0
0
0
0
1
2
0
2
0
0
1
0
0
2
0
0
0
1
0
1
0
2
0
2
2
0
1
0
0
0
0
1
0
0
0
0
1
0
2
0
1
0
0
0
8
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
1
0
0
0
1
2
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
3
1
0
0
0
1
0
1
1
0
0
2
0
2
2
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
1
0
2
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
1
0
2
2
0
2
0
0
2
0
2
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
2
0
2
0
4
0
0
0
0
0
1
0
0
0
1
0
0
2
1
0
0
0
1
2
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
2
0
1
0
0
1
3
1
0
2
1
1
0
0
0
2
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
1
3
2
0
0
0
0
1
2
0
0
3
0
2
0
0
0
0
0
0
1
0
1
0
0
0
2
2
0
0
0
0
0
1
0
2
0
1
0
0
3
0
1
2
0
0
0
0
0
0
0
0
2
0
4
2
0
1
0
1
2
3
1
0
0
0
3
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
2
2
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
1
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
3
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
1
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
2
0
0
2
0
0
0
3
2
0
2
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
2
0
0
2
0
0
2
0
1
2
1
0
0
0
1
0
2
0
0
0
1
0
1
1
2
1
2
0
2
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
2
0
0
0
2
1
0
0
0
0
1
2
0
0
1
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
2
2
1
0
0
0
0
0
0
1
2
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
2
2
0
0
0
0
0
1
0
0
0
1
1
0
3
1
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
2
0
1
2
1
0
0
1
1
0
0
0
0
0
0
0
4
2
0
0
0
1
0
0
0
2
0
2
0
2
0
0
0
0
0
1
0
0
1
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
1
1
2
0
0
1
0
2
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
3
2
2
0
1
0
2
1
2
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
7
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
1
2
0
1
0
0
0
2
1
2
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
1
0
0
0
1
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
2
0
1
2
1
0
2
2
0
1
1
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
2
0
1
1
0
2
0
1
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
1
1
0
0
3
0
1
0
2
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
4
0
0
1
0
0
0
0
0
1
2
0
1
3
1
1
3
2
0
0
0
1
0
0
2
2
0
1
2
0
0
0
0
0
0
0
0
1
2
1
0
1
1
0
0
2
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
2
0
9
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
2
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
4
0
0
2
2
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
1
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
1
0
0
0
0
0
0
2
0
0
1
0
0
2
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
1
2
0
0
1
0
0
2
0
0
4
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
3
0
1
0
0
0
0
0
2
0
2
0
0
0
2
1
2
0
0
2
1
0
2
0
0
2
0
0
1
0
0
1
0
1
0
2
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
2
0
0
0
0
2
0
0
0
0
1
1
0
2
0
0
0
7
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
2
2
0
0
0
0
0
4
0
0
0
0
0
2
2
1
0
0
0
0
0
2
1
0
2
0
0
0
0
0
2
0
0
3
2
0
0
0
1
2
2
1
0
0
0
2
1
1
0
1
0
0
0
0
2
0
0
1
1
1
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
1
0
0
2
0
0
0
2
0
0
1
1
0
2
3
0
1
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
2
0
2
1
0
0
0
3
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
2
0
1
0
0
0
0
0
1
0
0
1
5
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
2
1
0
0
1
2
3
0
2
2
2
1
1
0
0
2
1
0
0
0
2
0
0
0
0
4
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
2
2
0
0
0
0
2
1
0
0
2
1
0
0
0
3
0
1
0
0
2
0
2
0
3
0
1
1
0
1
0
0
0
0
0
2
0
0
2
0
2
0
0
2
0
2
0
0
0
0
1
0
0
2
0
1
2
3
0
0
2
2
0
2
0
1
0
0
0
5
1
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
2
2
0
0
0
0
0
1
1
0
0
0
2
1
0
1
0
1
0
0
1
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
3
0
0
0
0
1
2
0
2
0
3
2
0
0
0
2
1
0
0
1
0
2
0
0
0
0
3
0
1
2
2
2
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
2
0
2
0
0
2
0
2
0
0
1
0
0
2
2
0
0
0
1
0
3
2
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
2
0
4
2
0
0
0
0
0
0
1
0
0
3
2
0
3
0
0
0
0
2
1
0
0
0
0
2
0
1
1
0
0
0
0
0
1
0
0
1
1
0
0
0
2
0
0
2
0
0
0
0
2
0
1
1
0
0
1
1
1
2
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
2
0
0
2
2
0
0
1
0
0
1
0
0
0
0
1
0
1
2
2
0
0
2
2
1
1
0
2
0
0
1
0
2
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
2
0
2
0
0
0
2
0
0
0
1
0
0
0
1
0
1
1
2
0
0
0
2
0
0
0
0
0
1
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
1
1
1
0
0
0
0
1
2
0
0
2
0
2
0
0
0
0
0
4
0
2
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
3
0
0
0
0
1
0
1
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
3
1
2
0
0
3
0
1
0
2
0
0
2
0
0
0
0
1
3
0
0
1
0
1
0
3
0
0
0
0
0
0
3
1
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
2
0
1
0
0
0
2
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
2
1
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
1
1
0
0
0
1
0
0
1
0
0
2
0
0
0
0
2
1
1
1
0
0
0
0
0
0
0
1
0
2
0
0
0
2
6
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
2
0
0
1
0
1
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
2
0
0
2
0
3
1
0
0
0
0
0
0
2
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
1
1
2
0
0
1
2
1
0
0
2
2
0
0
4
0
0
0
0
2
5
0
0
0
0
0
2
0
2
0
0
1
2
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
3
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
1
0
0
1
0
0
0
1
1
1
1
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
3
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
1
1
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
3
0
0
0
0
1
0
2
0
2
1
0
0
0
0
1
0
2
2
0
1
0
2
1
0
0
0
0
0
0
2
1
4
0
0
0
0
0
0
0
0
2
2
1
1
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
2
1
0
0
0
0
2
1
2
0
0
0
3
0
0
0
0
2
2
0
0
1
0
0
0
0
0
1
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
1
0
1
2
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
1
0
1
0
4
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
2
1
0
0
0
0
1
2
0
1
0
1
0
1
1
0
0
2
2
0
1
0
2
0
2
0
0
1
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
2
0
0
2
1
0
0
0
3
0
0
2
2
1
3
1
1
1
1
1
0
0
1
0
0
0
0
2
1
0
0
0
3
1
0
0
0
2
0
0
1
0
0
0
0
0
1
1
2
2
0
0
0
1
0
0
1
0
0
0
2
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
2
0
1
2
0
0
0
0
0
0
2
4
2
0
0
2
2
0
1
0
2
0
0
0
1
0
1
0
2
0
0
0
0
1
3
0
0
2
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
3
0
2
2
1
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
1
0
2
1
1
0
0
0
0
0
0
0
1
0
1
0
2
0
1
2
0
1
1
0
1
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
1
1
0
0
2
0
2
0
2
0
0
0
2
1
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
1
1
0
0
1
1
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
1
1
2
1
1
0
1
2
0
0
0
0
0
0
0
1
1
1
0
1
1
2
0
5
1
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
2
1
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
1
2
0
0
2
0
0
1
0
0
0
1
1
0
4
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
1
0
2
3
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
1
0
2
2
2
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
2
0
2
0
0
1
0
1
0
0
0
1
1
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
2
2
1
0
1
0
0
0
0
0
0
2
0
1
1
0
2
0
1
0
0
0
0
0
1
2
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
1
0
1
0
0
2
2
2
0
1
0
0
2
0
0
0
2
0
1
0
1
1
3
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
2
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
3
0
0
0
0
1
0
1
0
2
2
0
0
0
0
1
0
0
1
2
0
0
0
1
1
0
0
0
0
0
1
1
0
1
0
0
2
0
1
0
0
0
2
2
1
0
0
3
0
0
0
1
0
0
1
2
0
0
1
0
1
0
1
2
0
0
0
0
1
0
0
0
0
1
2
2
2
0
2
2
0
0
2
2
0
0
1
2
1
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
2
1
0
0
1
0
4
0
2
0
0
0
1
0
2
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
1
0
2
0
2
1
0
1
0
2
0
2
0
0
2
1
0
0
0
0
0
0
4
0
1
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
1
2
0
0
1
1
0
0
0
0
0
2
1
0
1
0
0
0
0
0
1
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
2
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
2
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
2
1
4
2
0
0
0
0
0
0
1
1
2
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
3
0
2
2
2
0
1
0
0
0
0
0
2
0
1
0
2
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
2
1
0
2
2
2
0
2
2
2
1
0
1
0
1
0
0
0
0
3
0
0
1
0
0
0
3
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
1
2
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
4
0
2
2
0
2
0
2
0
0
0
0
0
0
0
1
0
0
2
0
2
1
3
1
0
2
1
0
0
0
0
0
0
0
2
0
0
0
3
0
2
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
2
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
2
2
2
0
1
0
2
0
0
2
0
0
2
0
2
1
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
2
0
0
0
0
2
2
1
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
2
0
0
0
1
1
0
1
2
0
1
2
0
1
0
2
1
3
0
0
0
4
2
0
0
1
0
2
0
0
0
2
4
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
2
3
1
2
0
0
0
0
1
0
0
1
0
0
2
0
2
2
0
0
2
0
0
0
2
0
1
0
0
0
1
0
1
0
0
0
1
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
2
1
2
2
0
0
1
0
0
2
0
1
1
0
0
0
0
2
0
0
0
0
0
0
2
0
3
0
0
0
2
1
0
0
0
0
3
0
1
0
2
1
3
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
2
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
3
0
1
0
0
0
2
0
1
1
0
1
0
0
2
0
0
0
1
1
0
0
0
2
2
0
0
0
1
1
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
3
0
1
0
1
0
2
1
2
0
2
2
0
0
0
0
0
0
1
3
0
0
0
0
0
2
0
1
0
2
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
2
2
0
0
2
0
0
2
0
2
0
2
2
0
2
0
0
1
0
0
3
2
0
1
2
0
0
0
1
1
0
0
2
0
0
3
0
0
2
2
2
2
0
1
1
1
3
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
1
1
0
2
2
0
1
0
1
0
1
1
2
0
1
0
1
0
0
3
0
0
0
0
0
1
0
1
2
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
1
1
0
0
0
0
0
2
0
0
0
1
2
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
2
2
0
0
0
2
0
0
0
2
0
4
0
0
0
2
0
2
1
0
0
1
1
2
2
0
2
0
0
0
0
1
2
2
0
0
1
0
0
1
2
0
0
0
1
0
1
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
2
0
1
1
0
2
0
1
1
0
1
0
1
0
0
0
0
1
0
0
1
0
0
1
2
2
0
0
0
0
0
1
1
2
0
2
0
1
2
0
1
0
0
2
0
0
1
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
2
1
2
2
0
0
0
2
0
2
0
0
1
0
0
0
2
0
0
1
2
0
0
0
0
1
0
2
2
0
0
0
3
2
0
0
0
2
0
0
2
0
0
1
1
2
0
0
0
1
0
2
0
1
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
3
1
0
0
0
2
0
1
0
0
2
0
1
0
0
0
0
0
0
0
2
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
5
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
1
1
0
3
1
0
2
0
0
2
0
0
0
4
0
0
0
0
2
1
1
0
0
0
0
2
0
2
0
0
0
2
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
1
0
0
0
0
0
0
0
2
2
0
0
1
0
1
2
0
0
0
2
0
2
0
0
1
0
0
0
0
0
2
0
2
2
1
0
0
3
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
2
0
0
5
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
2
0
0
0
1
0
1
0
2
2
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
1
2
1
0
0
0
0
0
0
0
0
1
0
2
1
2
1
1
0
2
0
0
1
2
1
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
1
0
1
2
0
0
0
2
0
0
1
0
0
0
0
2
2
1
0
3
3
0
1
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
2
2
0
0
0
2
0
0
2
2
1
0
0
0
2
1
0
0
2
0
0
1
2
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
3
1
0
2
0
2
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
1
2
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
1
2
0
0
1
0
0
2
0
0
2
0
1
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
1
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
1
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
2
1
0
1
0
0
2
2
2
0
2
3
2
3
2
0
0
0
0
1
0
0
0
0
1
1
0
3
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
1
0
2
0
2
0
0
2
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
2
0
2
0
0
2
0
0
2
0
2
0
1
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
1
0
0
3
2
3
1
0
0
1
2
0
2
0
1
5
1
1
0
2
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
1
0
1
1
0
0
0
0
1
2
0
2
1
2
0
0
0
0
0
0
0
0
0
2
1
0
0
2
2
0
3
0
0
0
0
0
0
0
2
2
1
0
1
2
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
4
1
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
2
0
2
0
0
2
0
0
2
0
0
2
0
0
0
2
1
0
0
0
2
0
0
2
0
1
1
2
0
1
0
0
0
0
1
0
3
0
0
0
0
0
1
0
0
0
0
0
1
2
0
1
0
0
0
1
2
0
1
0
0
0
0
0
0
2
3
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
2
0
2
1
0
2
0
1
0
1
3
0
2
0
0
1
0
2
0
0
1
0
0
2
2
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
1
0
0
2
2
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
2
0
3
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
4
1
2
0
1
0
0
0
0
1
0
0
2
1
2
0
0
1
0
0
0
0
0
0
1
2
1
0
2
0
2
0
1
0
0
1
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
1
0
2
0
2
0
0
2
0
2
1
0
0
0
0
1
0
1
2
0
0
2
0
1
1
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
2
2
0
0
2
0
1
0
0
2
2
1
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
1
2
0
0
1
0
0
2
0
0
0
1
0
0
0
2
0
7
0
0
0
2
0
2
0
0
0
2
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
3
0
0
2
1
1
0
2
1
0
0
1
0
0
0
1
1
0
1
0
2
0
1
0
0
0
0
0
0
0
0
1
2
0
2
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
1
2
0
0
0
2
0
1
1
0
1
1
1
1
0
0
2
0
0
0
0
2
0
2
0
1
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
1
0
1
1
0
0
0
1
0
1
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
3
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
2
4
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
2
1
1
1
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
1
1
0
0
0
1
1
2
0
0
0
0
6
0
0
0
1
0
0
3
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
1
1
0
2
0
1
0
0
0
0
3
0
0
0
0
0
1
0
0
2
3
0
0
0
1
2
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
1
1
2
0
2
0
0
0
2
1
1
0
0
0
3
1
0
0
0
0
0
2
0
0
2
1
2
0
0
1
0
2
0
1
1
0
0
0
0
1
5
3
0
4
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
4
0
0
2
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
2
1
0
3
0
0
0
1
2
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
1
5
0
1
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
3
0
1
0
1
1
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
2
0
0
0
0
0
2
0
0
0
2
1
0
0
1
1
0
0
1
1
2
0
0
0
1
0
0
0
0
1
2
0
0
3
0
0
1
0
0
0
1
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
6
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
1
1
0
0
2
0
0
0
0
2
0
0
2
3
1
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
2
0
0
0
3
2
0
1
2
0
0
0
4
2
3
0
0
1
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
1
2
0
0
1
0
0
0
2
0
2
0
1
0
0
0
0
2
0
2
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
2
1
0
2
0
0
1
2
1
2
3
0
0
2
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
2
1
0
0
0
2
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
1
0
0
2
1
0
1
0
0
1
1
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
3
0
1
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
2
2
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
2
0
1
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
1
2
0
2
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
1
1
0
0
3
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
4
0
2
0
0
0
2
0
1
1
0
1
2
3
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
1
0
1
0
2
2
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
2
0
0
0
2
0
2
2
0
2
0
0
0
2
0
0
0
0
2
0
2
1
2
0
0
0
1
0
1
0
0
0
0
2
2
0
1
0
0
0
2
0
2
1
1
0
3
0
2
1
0
0
0
1
0
0
0
0
2
0
0
2
0
1
0
0
0
1
0
0
2
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
3
1
0
0
0
1
0
2
2
0
0
0
0
0
2
0
0
2
1
2
0
2
0
1
0
0
0
1
0
0
1
2
0
1
1
0
1
2
1
2
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
3
2
2
2
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
2
1
0
0
0
0
0
0
0
3
1
0
2
0
0
2
1
0
0
0
3
0
0
0
1
0
0
0
0
3
1
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
2
1
1
2
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
2
0
2
1
0
0
1
1
0
0
1
0
0
0
3
0
1
0
0
2
0
0
0
1
0
1
0
0
0
0
0
4
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
1
0
0
0
2
0
2
0
0
0
0
1
2
2
0
2
0
0
0
0
2
0
0
0
0
0
1
0
1
2
0
2
0
1
2
0
1
1
2
0
1
1
0
0
5
0
0
1
0
0
1
0
0
0
0
0
0
0
2
1
0
3
0
0
0
0
0
2
2
2
0
0
0
0
0
1
7
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
1
3
1
0
0
0
1
0
2
1
0
0
0
0
0
2
0
2
1
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
2
0
0
1
0
2
0
0
0
2
2
0
0
0
0
0
1
1
0
0
1
2
0
0
0
0
0
1
2
1
3
0
1
0
0
0
0
0
1
1
1
0
2
1
0
0
4
0
1
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
1
2
0
0
0
0
3
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
1
0
2
0
0
2
0
2
2
0
0
1
0
1
2
0
0
0
0
0
1
0
1
0
0
0
5
0
0
1
1
0
0
0
2
2
0
0
1
0
2
0
0
0
0
0
3
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
3
2
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
2
2
1
0
0
2
0
0
2
1
1
0
0
0
0
0
0
2
0
0
1
0
0
1
0
2
0
0
2
0
0
0
3
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
1
1
0
1
0
0
0
0
2
1
0
0
0
0
0
0
1
1
0
0
1
0
0
1
2
1
0
0
1
2
1
0
0
0
1
0
0
1
0
1
0
0
0
3
0
3
0
1
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
1
1
2
1
0
0
1
0
2
0
0
0
1
0
0
0
2
1
2
3
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
1
3
0
1
0
0
0
0
1
2
2
1
5
2
2
1
0
5
1
0
2
1
5
0
2
2
1
1
0
0
0
2
2
1
0
0
0
2
0
0
0
0
0
2
1
2
0
0
2
2
2
2
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
3
0
2
0
0
0
2
0
0
1
0
0
0
3
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
2
0
2
0
2
2
0
0
0
0
1
0
0
2
0
3
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
2
4
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
2
1
0
3
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
2
1
0
0
1
0
0
0
0
0
1
2
2
1
0
0
0
1
1
0
0
1
1
0
0
1
0
0
2
0
0
1
2
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
2
0
0
2
1
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
5
1
1
2
0
2
2
0
0
0
0
1
0
0
3
0
0
2
1
0
0
0
2
0
2
0
0
0
0
0
1
1
2
0
0
1
2
0
5
0
4
1
4
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
2
1
0
0
0
1
1
0
2
0
2
1
0
1
2
0
1
0
0
1
2
2
0
0
0
0
0
0
2
0
2
0
1
0
0
1
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
2
1
2
0
0
0
0
1
1
1
0
0
2
1
1
0
0
2
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
1
0
1
0
0
2
0
1
0
0
2
1
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
1
0
2
0
0
0
2
1
0
0
1
0
2
0
0
1
2
0
0
2
0
1
1
0
1
2
0
0
0
0
0
1
0
0
1
1
2
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
2
0
1
2
1
0
0
0
0
0
0
1
0
0
0
1
0
2
1
1
0
0
1
2
1
2
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
3
0
0
2
0
0
0
0
0
0
1
0
0
1
2
0
0
1
4
2
2
0
4
2
1
0
0
2
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
2
2
1
1
2
0
0
0
0
0
2
0
2
1
0
0
0
1
3
1
1
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
1
0
4
0
0
0
0
0
0
3
0
0
1
0
1
0
0
2
0
2
0
1
0
0
0
2
0
1
0
0
0
1
0
1
2
2
0
1
0
0
0
0
0
2
0
0
2
2
0
0
2
0
0
0
1
0
0
0
2
0
0
1
1
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
1
2
0
0
2
2
1
3
0
0
2
1
1
1
0
2
0
2
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
1
3
2
0
0
0
0
0
0
2
0
3
0
2
1
0
0
2
0
2
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
2
0
0
1
0
1
0
1
0
0
0
2
2
1
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
2
0
0
0
3
0
1
0
0
1
0
0
0
0
0
2
0
0
4
0
0
0
0
0
0
1
0
1
0
0
1
0
2
2
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
1
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
2
2
0
0
0
0
0
2
1
0
0
1
1
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
1
0
2
0
2
0
0
1
4
1
2
2
0
0
0
0
2
0
0
0
1
0
0
3
0
0
1
0
0
0
2
1
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
1
2
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
1
2
2
0
0
1
0
0
0
3
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
3
0
0
0
2
0
1
0
0
0
0
1
2
1
0
0
2
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
1
1
0
2
0
0
0
0
0
0
2
2
0
2
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
2
0
0
1
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
1
0
0
1
0
0
0
2
0
1
0
0
1
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
2
1
2
0
0
2
0
1
0
0
0
0
0
2
0
0
2
0
3
0
0
2
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
2
2
2
2
0
0
0
0
1
0
0
0
1
1
0
1
0
2
0
0
0
0
0
0
0
2
2
2
2
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
1
1
2
4
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
5
1
0
1
0
0
0
1
2
1
0
0
2
0
0
0
0
1
2
0
1
0
3
2
4
0
0
0
0
0
0
0
0
3
0
1
0
0
0
2
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
1
2
0
1
0
2
0
0
1
0
2
1
0
0
1
4
2
3
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
1
0
2
0
1
1
0
0
0
0
0
0
1
1
0
2
0
2
0
0
0
2
2
2
1
0
0
4
0
0
0
2
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
1
0
2
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
1
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
1
1
2
0
0
0
0
2
0
0
0
1
0
1
0
2
0
1
0
0
0
1
1
3
1
0
0
1
0
0
0
0
0
0
0
1
4
1
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
1
0
1
0
0
0
2
1
0
0
0
0
0
0
1
2
0
0
0
0
2
2
0
0
2
1
0
0
0
0
0
2
2
0
0
0
0
2
1
1
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
3
0
0
0
2
0
1
2
2
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
2
0
2
2
0
0
0
2
0
0
0
2
0
1
0
2
0
2
0
0
1
2
0
0
1
0
1
1
0
0
1
1
0
0
1
1
0
0
3
1
0
0
0
0
2
2
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
2
0
2
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
2
1
1
3
0
0
0
1
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
3
1
0
2
0
0
0
2
2
2
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
2
0
1
0
0
0
4
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
1
2
8
2
2
0
0
0
0
0
3
2
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
3
0
2
1
2
0
0
0
0
0
2
1
0
0
1
2
0
0
0
0
1
3
0
2
2
0
2
1
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
1
2
0
0
0
2
0
0
2
0
0
0
2
0
3
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
2
1
0
2
0
2
0
0
0
0
0
1
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
3
2
0
0
0
2
0
0
1
0
0
0
1
0
0
1
2
0
1
2
1
0
0
2
0
1
1
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
3
2
2
1
0
0
0
1
0
1
0
1
1
0
2
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
2
0
0
2
0
0
3
0
2
0
0
3
0
0
0
0
0
0
1
2
0
2
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
1
2
1
0
2
0
2
0
1
2
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
1
0
1
1
0
0
2
0
1
0
0
1
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
1
0
0
0
0
0
2
0
1
0
0
0
0
0
4
1
0
0
0
0
0
0
1
2
0
0
2
0
1
2
0
0
0
0
0
2
0
0
0
0
0
2
0
2
1
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
3
0
0
0
1
0
0
2
0
0
2
0
0
0
1
0
0
2
2
2
2
2
0
0
0
1
0
0
0
0
1
0
0
1
2
2
0
0
1
2
0
0
2
2
0
1
1
0
0
0
0
0
0
0
2
2
0
1
0
0
1
0
0
2
2
2
0
2
0
1
0
0
0
0
2
0
0
0
1
1
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
1
1
0
2
2
0
2
0
1
0
0
0
2
0
0
0
2
3
2
1
0
2
0
0
2
0
0
0
0
2
2
0
2
0
0
1
0
2
0
0
0
1
1
0
0
0
1
2
0
1
0
1
0
1
2
0
0
0
0
0
1
0
0
2
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
1
2
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
1
0
0
2
0
1
0
1
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
2
0
2
2
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
2
1
2
0
2
1
0
0
0
0
1
0
0
0
0
0
2
1
0
2
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
2
1
0
0
0
2
2
1
2
0
0
2
0
0
0
0
2
2
2
0
0
2
1
0
0
0
0
2
0
0
0
0
1
2
0
1
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
2
1
0
0
0
2
0
0
4
0
0
0
0
0
0
2
0
2
2
0
0
1
2
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
1
0
0
1
1
2
0
2
1
0
2
0
0
1
1
0
0
4
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
3
1
0
0
0
1
1
0
1
1
0
1
0
0
2
0
0
0
1
1
2
1
2
1
0
0
0
2
0
1
1
2
2
2
2
0
0
0
0
2
0
0
0
1
2
0
1
1
0
0
2
0
1
0
0
2
2
0
0
2
6
1
0
1
0
0
0
0
2
0
2
0
0
0
0
1
0
3
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
2
2
0
0
0
1
0
0
0
0
0
2
0
2
2
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
3
0
2
0
0
1
0
1
2
1
0
2
0
0
0
0
0
0
0
1
2
1
0
2
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
1
1
0
0
2
0
0
0
1
0
1
6
0
1
0
1
1
1
0
3
0
0
0
0
2
2
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
4
0
2
0
1
2
2
0
0
1
0
1
2
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
1
1
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
3
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
2
0
0
2
0
1
0
1
0
3
0
0
0
1
0
0
2
2
0
1
0
0
4
0
0
2
0
2
2
0
0
2
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
2
0
2
0
0
1
0
2
0
1
1
1
0
2
0
2
1
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
1
0
2
2
1
0
0
0
2
0
2
2
0
0
0
1
0
1
2
0
1
0
0
0
0
5
0
2
2
2
0
0
0
0
0
0
1
0
0
2
2
0
0
1
1
0
1
0
0
1
0
0
0
0
1
1
2
0
0
0
0
0
2
0
1
1
0
0
0
0
0
1
2
0
0
0
0
0
1
0
1
0
0
0
1
2
0
0
0
2
0
1
0
0
1
0
0
2
1
0
0
0
0
1
0
2
1
0
0
1
0
0
2
0
2
0
0
0
1
1
0
0
1
0
1
0
0
2
1
0
1
0
0
0
0
0
0
0
1
1
1
0
0
1
1
1
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
1
0
0
0
2
0
2
0
0
1
1
0
2
0
0
1
0
2
0
0
0
0
1
1
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
2
0
0
4
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
1
1
0
2
0
1
2
1
0
0
0
0
1
0
1
0
1
0
0
2
2
0
0
0
0
1
1
0
0
0
0
2
1
2
0
0
2
1
1
1
0
0
0
1
0
2
1
0
0
0
0
2
0
0
0
1
1
0
0
2
7
0
0
0
1
2
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
2
1
1
1
1
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
1
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
2
1
0
0
0
0
1
0
0
0
0
3
2
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
2
0
0
0
1
0
1
0
1
0
0
11
0
0
1
0
1
2
0
2
0
2
0
0
0
0
0
0
0
1
1
0
1
0
0
0
2
1
0
0
3
1
0
0
0
2
1
0
0
0
5
0
1
2
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
2
0
1
0
0
0
2
2
0
2
1
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
4
1
0
2
1
1
0
0
0
2
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
2
0
3
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
5
0
0
0
0
1
2
0
0
1
1
0
2
0
0
1
0
2
0
2
0
2
0
2
1
1
0
0
0
1
2
2
0
0
0
0
0
1
2
2
0
0
0
1
0
0
0
1
2
1
0
0
0
3
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
3
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
2
1
2
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
2
0
0
2
0
1
0
0
2
1
1
1
2
0
0
2
0
1
1
0
6
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
4
2
1
0
0
1
1
2
0
1
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
1
0
3
0
0
0
0
0
0
2
1
2
2
0
0
0
2
1
0
1
0
0
0
0
2
0
5
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
2
1
2
0
1
2
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
2
2
3
0
0
0
1
0
1
0
3
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
1
2
1
2
0
0
1
2
0
2
0
0
0
0
0
1
0
0
1
1
0
2
2
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
1
0
0
0
2
0
1
2
0
1
1
0
0
1
0
2
0
0
0
1
0
1
0
0
0
0
2
2
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
2
0
0
1
2
0
0
0
0
3
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
1
1
2
0
0
0
2
0
2
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
1
0
0
0
0
0
2
2
2
1
1
1
0
0
2
0
0
0
0
1
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
4
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
2
0
0
0
1
1
1
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
2
0
0
0
1
0
1
2
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
3
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
1
2
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
2
0
2
2
0
0
0
3
1
0
0
0
0
0
1
1
0
3
0
0
1
0
1
0
0
0
0
2
2
0
0
2
0
2
0
2
3
0
2
0
0
0
3
0
4
1
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
4
0
0
1
0
0
3
0
0
2
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
1
3
0
0
2
1
0
0
0
2
0
2
0
2
0
0
0
2
0
1
1
0
1
0
2
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
1
0
2
2
1
0
1
1
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
1
0
0
3
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
2
0
1
2
0
0
0
0
1
0
4
1
0
0
1
0
4
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
3
0
0
0
0
0
0
1
2
0
0
0
1
0
2
0
2
0
1
1
0
0
0
0
2
0
2
1
0
0
0
2
1
0
0
1
0
1
0
0
0
0
1
0
2
1
0
0
0
1
1
0
1
4
0
0
0
1
0
0
2
0
0
1
0
2
0
1
0
2
0
0
1
2
0
0
0
0
0
0
0
0
3
2
2
0
0
1
1
0
1
2
0
2
0
0
0
0
0
2
0
2
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
2
2
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
4
1
0
0
1
0
0
0
0
2
2
0
1
1
0
0
0
1
0
0
1
0
0
2
1
0
0
0
0
1
0
0
0
0
3
2
1
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
1
0
0
1
0
0
6
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
1
5
2
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
2
0
0
0
1
1
2
0
2
0
0
0
0
0
2
2
1
1
0
1
0
0
0
1
0
0
3
0
1
1
0
0
1
0
0
0
0
0
2
0
0
4
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
3
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
3
0
0
0
2
0
0
1
0
0
0
1
0
2
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
4
0
0
0
0
2
1
2
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
1
0
0
2
2
0
0
0
0
2
1
0
1
0
2
0
0
0
1
0
0
0
2
2
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
3
0
0
0
0
2
0
1
1
3
0
0
0
2
0
1
0
2
2
0
2
1
2
0
0
1
2
0
0
1
0
0
0
0
1
0
0
0
1
0
4
0
0
1
0
0
2
0
0
3
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
2
0
0
1
0
0
2
1
0
0
0
0
0
0
2
2
2
0
0
5
0
0
2
2
0
0
0
0
0
0
0
0
0
1
1
2
0
2
0
0
0
2
0
0
2
0
0
0
0
0
2
1
3
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
2
0
1
0
0
6
0
0
0
0
0
0
0
2
0
1
0
1
0
1
1
0
0
1
0
1
0
1
0
1
2
0
2
0
1
1
0
0
2
2
1
0
1
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
1
2
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
2
2
0
1
1
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
3
0
0
0
1
0
0
1
2
1
0
0
2
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
1
1
0
0
0
2
1
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
4
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
1
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
2
0
0
0
0
4
0
1
0
1
3
0
2
0
0
0
1
0
0
1
1
0
0
1
0
2
0
0
1
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
1
1
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
2
2
1
2
0
2
1
0
0
0
0
0
0
2
1
0
0
1
1
0
0
1
0
0
0
0
1
2
0
0
2
3
0
0
2
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
2
2
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
1
1
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
4
0
0
0
0
0
0
0
0
2
1
0
2
0
0
3
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
3
0
2
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
3
0
0
0
0
1
0
0
0
1
1
0
2
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
1
0
2
0
0
0
0
0
1
0
0
0
0
2
1
0
2
2
0
0
0
1
2
2
2
0
5
2
0
2
2
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
2
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
1
1
2
0
0
0
0
0
0
0
1
2
0
2
1
0
0
0
0
0
2
2
1
0
0
0
0
0
2
0
0
1
0
0
1
3
1
0
0
0
0
1
0
2
0
2
0
2
2
0
0
1
1
1
3
2
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
2
2
0
0
1
0
0
2
0
0
0
0
0
2
2
0
0
0
2
2
0
0
0
0
0
2
3
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
1
1
2
1
0
0
1
0
4
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
1
2
0
0
2
4
0
2
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
1
1
2
0
1
0
0
2
0
0
2
0
0
2
0
0
0
2
0
0
2
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
2
0
2
1
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
1
0
1
2
2
0
1
1
0
0
2
1
0
2
0
0
2
0
2
3
0
0
1
2
1
0
2
0
0
0
0
2
0
2
0
0
2
0
1
1
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
3
2
2
0
2
0
1
0
0
2
1
0
2
0
0
2
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
3
0
0
1
0
0
2
2
2
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
2
2
0
0
2
0
0
0
1
2
0
0
0
0
0
1
0
0
1
0
2
2
0
0
1
0
1
1
0
1
1
0
0
0
1
0
1
0
2
7
2
2
1
0
1
0
1
0
0
2
1
0
0
0
0
0
0
0
2
0
2
1
3
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
1
1
0
1
2
6
0
0
0
0
0
2
0
8
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
1
0
0
2
1
0
2
0
0
0
2
0
1
0
0
1
2
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
1
0
0
2
2
0
2
2
0
0
0
0
1
2
0
1
0
1
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
2
1
1
0
2
0
1
0
0
0
2
0
0
2
0
0
0
1
0
0
1
0
1
0
4
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
2
1
0
0
0
0
1
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
1
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
3
0
2
0
0
0
2
0
1
0
0
1
0
2
2
0
0
0
0
2
2
0
0
2
0
0
0
0
2
1
1
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
2
0
3
0
0
2
0
0
1
0
1
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
1
2
2
1
0
0
0
0
0
2
0
2
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
3
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
3
1
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
1
0
2
4
1
1
2
0
1
2
1
0
3
0
1
1
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
2
1
1
2
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
3
0
0
0
1
1
0
0
0
2
2
1
1
2
0
1
0
1
1
3
0
1
2
0
0
0
0
0
0
2
1
2
2
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
2
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
2
0
0
1
0
1
0
0
1
0
2
3
0
0
2
0
2
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
1
0
0
1
0
2
0
0
0
0
0
2
2
2
1
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
2
0
0
2
0
1
1
0
0
2
0
0
0
1
1
1
1
0
0
0
0
0
0
2
0
4
0
6
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
3
0
1
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
1
3
0
0
2
3
1
0
0
5
2
1
0
2
0
0
0
0
0
1
0
0
1
1
2
2
0
0
0
0
2
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
1
2
0
0
0
0
0
1
0
1
0
1
0
6
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
2
11
0
0
1
2
1
0
0
0
0
0
3
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
1
0
0
3
2
0
2
0
0
0
2
0
0
0
0
2
1
0
2
3
1
2
0
0
0
0
0
2
0
0
1
0
1
0
0
0
2
0
0
2
0
0
0
1
0
0
2
2
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
1
1
0
0
0
1
1
2
0
2
2
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
2
3
0
3
0
0
2
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
1
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
1
0
1
0
0
1
1
0
2
2
0
0
0
0
1
1
0
0
2
0
2
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
1
0
1
1
1
0
0
0
2
0
1
0
1
0
0
1
0
2
0
1
2
2
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
1
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
4
2
2
0
0
0
0
3
0
2
0
0
2
2
2
0
0
0
0
3
0
1
0
1
2
0
0
1
0
0
1
0
2
0
5
2
0
1
1
0
2
1
0
0
0
0
1
2
0
1
0
0
0
0
0
1
2
0
1
0
2
0
0
1
1
0
0
1
1
0
0
1
0
0
0
0
4
0
0
3
2
0
2
1
0
0
3
1
0
0
1
0
1
1
0
0
2
0
0
1
1
0
0
0
0
0
1
2
0
2
1
2
0
0
0
1
3
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
1
1
0
0
0
1
2
0
0
0
0
2
1
0
0
0
1
0
1
0
1
0
0
0
2
0
0
0
1
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
1
0
0
0
1
0
0
0
3
2
2
2
0
0
0
2
2
1
2
0
1
0
0
0
0
1
1
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
1
1
0
0
0
1
0
0
3
0
0
0
0
4
2
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
2
0
0
0
2
3
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
2
1
0
0
2
0
1
1
0
0
1
0
0
1
0
0
1
0
2
1
1
1
0
0
0
0
0
0
0
0
1
0
2
0
6
0
0
2
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
1
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
2
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
2
1
0
2
2
0
1
3
0
0
1
0
0
0
2
0
0
3
1
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
3
1
1
0
0
0
1
0
1
0
1
0
0
0
1
0
0
2
0
2
3
0
1
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
2
0
0
1
2
2
1
1
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
1
1
1
1
3
2
4
0
1
2
0
0
0
0
0
1
0
1
0
0
2
2
0
2
2
0
1
1
0
1
2
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
2
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
6
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
1
0
0
2
0
0
1
1
2
0
0
2
0
0
0
0
1
2
0
0
0
0
0
2
1
0
0
1
2
0
0
1
0
2
1
1
0
2
0
0
0
0
0
2
0
0
0
1
1
2
0
0
2
0
0
0
0
0
3
1
0
2
0
0
2
6
0
0
0
2
0
0
0
0
0
0
0
2
2
1
2
1
0
0
0
1
1
0
0
0
2
0
2
0
0
1
2
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
2
1
0
0
0
1
0
0
2
0
0
0
1
0
3
0
1
2
2
2
0
1
0
0
2
2
0
0
0
3
0
2
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
2
0
0
0
2
0
1
0
1
1
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
1
2
0
0
0
1
0
1
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
2
1
0
0
2
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
1
1
0
0
2
0
3
2
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
2
0
0
0
0
0
0
0
0
1
1
2
0
1
0
0
2
0
1
0
0
2
0
0
4
1
0
2
1
0
2
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
3
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
1
0
0
2
0
0
3
2
0
0
0
2
2
0
1
0
0
0
0
2
1
1
0
1
1
1
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
2
1
2
0
0
0
1
2
1
0
0
3
0
1
0
0
1
2
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
1
0
0
0
0
2
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
3
0
0
0
1
2
2
2
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
1
0
0
0
1
0
0
0
0
0
2
0
1
7
1
0
2
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
1
1
1
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
2
0
2
2
2
0
0
1
1
0
0
3
0
1
2
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
3
0
0
1
1
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
2
1
0
0
0
2
0
1
0
0
0
4
2
1
2
0
0
0
1
1
2
4
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
1
1
2
3
0
0
0
0
0
0
0
2
1
0
1
0
0
3
2
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
1
0
2
0
2
0
0
0
1
0
0
3
0
0
0
1
0
0
0
0
0
0
0
2
3
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
2
2
0
0
0
0
0
0
1
0
2
0
2
3
0
1
2
0
0
0
0
3
1
2
0
0
0
0
2
0
0
1
0
2
0
0
0
1
0
2
0
0
0
2
0
0
4
2
0
0
2
0
0
1
0
0
0
0
0
1
0
0
1
0
0
4
0
2
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
3
2
0
2
0
2
0
0
0
0
0
0
0
3
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
2
2
0
0
0
0
0
0
1
0
0
2
3
0
2
0
2
2
2
0
1
0
0
2
0
0
2
0
1
0
0
0
0
2
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
3
0
0
2
0
0
0
0
0
0
0
2
0
1
0
2
0
0
2
0
0
1
2
1
0
2
0
0
0
0
1
0
1
0
2
2
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
2
0
2
1
1
1
1
0
0
0
0
0
0
1
2
1
2
0
0
0
0
1
0
2
0
0
2
0
0
0
0
1
1
0
0
0
0
1
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
2
0
2
2
0
0
0
3
1
0
2
0
0
0
0
0
0
1
1
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
3
1
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
2
2
0
0
0
3
0
0
4
2
0
0
2
0
0
2
2
0
0
0
0
2
2
1
0
0
0
0
1
0
2
1
0
0
1
2
0
0
0
1
2
1
0
0
0
1
0
0
3
2
3
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
1
0
2
1
2
0
0
0
1
0
0
3
0
1
0
0
1
0
0
0
0
1
2
1
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
3
0
1
3
0
1
2
0
1
2
3
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
3
0
0
0
0
0
2
0
1
1
0
0
0
0
1
0
0
2
0
0
0
1
2
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
3
0
0
0
0
2
0
2
0
1
0
0
1
2
2
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
2
2
0
0
0
0
0
1
0
0
2
0
2
0
2
0
0
0
0
2
0
2
0
0
1
0
0
0
2
0
1
3
0
0
0
1
0
2
1
0
0
0
0
0
0
0
1
2
1
0
1
2
0
0
4
2
0
0
0
2
0
0
0
2
1
0
2
0
0
0
2
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
2
3
0
1
0
2
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
2
0
1
0
0
2
2
0
1
1
0
0
0
1
0
0
2
0
0
3
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
2
0
0
0
2
2
0
0
1
0
0
2
1
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
1
0
0
1
1
0
2
1
0
1
0
0
2
0
1
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
2
2
0
2
0
1
0
0
0
0
2
0
0
0
2
2
1
0
0
0
1
0
1
0
2
0
2
0
0
2
2
0
2
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
2
1
0
0
0
2
0
0
0
0
0
0
1
1
2
0
1
0
0
0
2
1
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
1
0
1
1
0
1
1
0
0
0
0
5
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
2
0
0
0
0
2
1
0
0
3
2
0
1
1
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
1
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
3
0
0
1
2
2
0
1
1
1
0
0
0
2
1
1
0
0
2
1
0
2
2
2
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
1
0
2
0
1
3
1
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
2
4
0
0
0
0
0
1
2
0
0
1
1
0
1
0
0
2
0
0
2
1
1
0
0
0
0
0
2
0
0
0
1
5
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
2
1
1
1
1
0
0
2
0
1
0
1
2
0
0
0
1
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
3
0
0
0
0
2
1
3
0
1
0
2
0
0
0
0
0
0
3
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
8
0
0
0
0
2
2
0
0
0
0
0
3
0
1
1
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
2
2
0
1
0
0
1
3
0
0
0
1
0
0
3
2
2
0
1
0
0
2
2
0
0
0
1
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
1
1
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
1
0
1
0
0
1
1
1
0
0
1
0
1
0
0
1
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
2
0
0
2
0
1
1
0
0
0
0
1
1
2
0
0
0
0
0
0
3
0
0
0
0
0
0
1
3
0
1
2
0
1
1
0
0
0
0
0
2
0
0
0
1
3
0
2
0
0
2
0
0
0
0
2
0
1
0
1
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
3
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
1
0
2
1
1
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
2
1
0
0
2
0
0
0
2
0
5
0
0
2
2
0
2
0
0
2
2
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
1
2
2
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
3
0
0
0
0
0
0
0
1
0
2
1
0
1
2
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
1
2
1
0
2
1
1
1
0
2
0
0
0
2
0
0
0
2
0
0
0
0
2
0
2
0
0
1
0
0
2
1
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
2
0
2
0
0
0
0
0
0
0
1
1
4
1
0
0
1
0
2
0
2
0
0
3
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
1
0
1
1
1
1
1
1
0
1
2
0
2
1
0
0
0
0
1
0
0
2
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
3
2
0
0
0
1
0
0
2
0
0
0
2
0
0
0
1
2
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
1
1
1
0
0
0
0
2
0
0
2
0
3
0
0
1
1
2
0
0
2
0
1
0
0
6
2
0
0
1
0
0
0
0
1
2
0
0
0
0
2
2
3
0
0
1
0
0
2
0
0
2
0
2
0
1
0
2
0
0
0
2
0
1
0
0
0
0
0
1
1
0
0
1
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
2
0
1
2
1
0
1
1
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
2
0
0
0
1
2
4
0
0
0
2
2
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
2
3
0
0
0
2
1
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
3
0
2
0
0
0
0
0
0
2
0
1
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
9
3
0
0
0
0
0
0
4
0
0
1
0
0
0
0
1
0
0
2
1
0
4
1
0
1
2
0
0
1
0
0
0
1
0
2
2
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
2
0
2
0
0
0
0
0
1
1
0
0
0
0
2
2
0
0
0
2
0
0
0
1
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
1
0
0
0
2
0
1
0
2
0
0
0
0
2
1
0
0
2
2
2
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
2
0
1
1
1
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
1
1
0
1
2
0
2
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
3
0
2
1
2
0
0
0
0
0
0
0
3
2
1
0
0
0
0
2
0
2
0
0
0
0
1
0
1
0
0
0
1
1
1
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
2
0
0
0
2
0
2
0
0
2
0
0
0
0
2
0
0
0
0
2
2
0
1
0
3
0
0
0
0
1
2
0
6
1
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
1
0
0
0
2
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
2
1
1
0
0
0
1
1
0
0
0
1
0
0
0
2
2
0
0
0
0
3
0
0
2
0
0
1
1
0
0
2
2
0
0
1
1
1
0
0
0
1
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
1
1
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
2
0
0
3
0
0
0
0
1
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
2
0
1
0
0
2
0
1
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
2
1
0
0
1
0
0
1
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
2
2
1
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
2
3
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
1
0
0
0
0
1
2
0
0
1
0
1
0
0
3
3
1
1
0
0
3
1
1
0
1
0
0
0
1
0
2
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
3
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
4
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
1
1
2
0
0
2
0
2
1
0
0
2
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
1
0
0
1
2
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
3
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
2
0
0
1
0
0
2
0
0
2
0
0
0
0
0
10
1
0
0
0
0
0
0
2
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
2
0
0
0
3
2
0
0
1
0
0
0
2
0
1
0
2
2
2
0
0
0
2
2
1
0
2
1
0
0
0
0
1
0
1
2
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
4
2
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
1
0
0
0
0
1
1
0
0
1
2
2
0
2
2
0
2
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
6
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
2
0
0
0
4
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
2
0
0
0
2
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
1
0
0
3
0
0
0
4
2
0
0
0
0
0
0
0
0
1
0
0
1
2
0
2
0
0
2
1
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
2
0
0
0
3
3
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
4
2
2
3
0
2
1
3
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
3
0
1
0
3
0
0
0
0
1
2
0
2
2
0
0
3
5
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
2
0
0
0
3
0
0
2
0
2
2
1
0
0
4
2
3
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
2
0
2
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
2
1
0
2
0
1
1
0
0
0
1
0
2
1
2
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
1
1
1
0
0
2
0
0
0
0
2
0
0
2
1
0
0
0
0
1
0
1
2
0
1
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
1
1
2
1
3
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
1
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
2
1
0
0
0
0
0
2
0
1
2
2
0
2
2
0
0
2
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
1
0
0
0
1
1
0
2
1
1
2
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
1
0
0
0
1
0
0
1
0
3
0
1
0
0
0
0
0
3
0
1
0
1
0
0
0
0
5
2
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
2
2
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
1
0
2
0
1
1
0
0
0
1
0
0
1
0
1
2
2
0
1
0
0
1
0
0
0
0
2
0
2
1
2
0
0
0
3
1
0
1
0
0
1
4
0
0
2
2
0
0
0
0
2
0
1
2
0
0
0
0
0
0
1
0
2
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
2
1
5
0
0
1
0
0
1
0
1
0
2
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
1
2
0
1
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
1
1
0
0
1
2
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
1
0
0
0
1
0
0
0
1
0
0
0
2
4
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
1
2
0
1
0
1
0
0
2
3
0
1
0
0
0
0
0
0
2
0
0
2
0
4
0
2
0
1
0
0
0
2
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
3
1
2
0
0
0
2
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
3
0
0
0
0
2
0
0
2
0
1
0
1
0
1
3
0
0
0
2
2
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
1
0
0
0
0
0
0
0
0
0
1
12
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
1
1
0
0
0
1
1
1
1
0
2
0
0
0
0
3
0
1
0
0
1
0
0
0
0
0
3
1
1
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
1
0
1
0
2
0
1
0
1
2
0
1
0
0
0
0
0
2
1
0
1
0
1
1
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
3
1
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
1
0
0
1
0
2
0
0
0
3
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
1
0
2
0
0
0
0
1
0
0
0
1
0
2
1
1
0
2
0
0
0
3
0
0
1
2
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
2
1
0
2
1
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
2
0
1
1
0
0
2
0
0
0
0
1
1
0
1
1
0
0
0
0
0
2
0
1
0
5
0
0
2
1
0
0
0
0
2
0
0
3
0
0
2
0
0
0
1
1
0
1
0
1
2
1
0
3
0
0
0
3
0
0
0
2
0
0
1
0
2
2
0
1
2
1
0
0
1
1
0
1
0
2
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
1
3
2
2
0
1
0
0
2
2
1
0
0
0
1
1
0
0
0
2
0
2
0
0
3
0
0
0
1
0
0
0
0
0
0
0
1
2
2
0
0
0
1
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
1
2
0
1
0
1
0
2
0
0
0
0
2
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
2
0
2
0
0
0
0
1
0
2
0
2
1
0
0
0
0
2
2
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
1
0
0
2
0
0
2
2
2
0
0
0
1
0
2
1
0
0
0
0
2
2
0
0
1
0
0
0
2
1
2
1
0
1
2
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
2
1
3
0
4
0
0
0
0
2
0
0
0
1
0
0
1
0
2
0
2
0
0
1
0
0
3
2
0
0
0
0
0
0
0
0
2
3
0
0
0
2
1
0
1
0
0
0
1
0
0
2
0
2
1
0
0
0
0
0
1
0
2
0
0
0
2
2
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
1
0
0
2
2
0
0
0
0
1
0
0
0
2
1
0
1
0
0
0
2
0
1
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
2
0
2
0
0
2
0
0
1
0
2
1
2
0
0
0
0
1
2
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
1
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
2
2
1
0
0
1
0
0
2
0
1
2
0
0
0
0
1
2
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
1
2
0
2
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
1
0
0
1
0
0
0
0
0
0
2
1
0
2
0
1
2
0
0
0
0
3
2
0
0
3
0
0
0
2
1
4
0
1
0
2
0
0
1
1
1
1
0
0
0
1
2
0
0
1
0
1
1
0
0
0
0
0
2
0
1
1
2
2
0
1
2
0
0
0
0
2
0
2
2
0
1
2
0
0
0
2
0
0
0
2
1
2
0
0
0
0
1
0
2
0
0
1
0
0
1
0
2
0
0
0
1
0
2
0
2
2
0
0
0
0
0
0
0
0
2
0
1
1
0
1
2
0
2
0
0
0
1
0
1
0
1
1
0
2
2
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
1
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
1
1
1
1
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
1
2
1
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
3
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
1
1
0
0
0
0
10
1
2
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
1
0
0
0
0
0
3
1
0
1
2
1
0
0
0
0
2
0
0
2
2
0
0
2
0
2
0
0
0
1
0
1
0
0
0
2
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
2
1
0
0
0
0
0
0
2
1
2
1
0
0
0
2
0
0
0
1
0
0
0
0
3
5
0
1
1
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
1
0
6
1
0
0
0
0
2
0
1
0
2
0
1
0
0
1
0
1
0
1
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
2
0
2
0
0
1
1
0
2
0
1
1
0
0
0
0
4
0
0
0
0
0
2
0
2
2
1
0
0
3
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
2
0
2
0
1
1
0
2
0
1
0
0
0
2
0
1
2
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
2
1
0
0
1
0
0
0
2
1
2
2
1
1
2
2
2
0
0
1
0
0
0
2
2
2
1
2
2
0
2
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
3
0
0
0
2
0
0
0
1
1
0
0
0
0
1
0
0
0
0
2
0
3
0
0
0
0
0
0
2
2
0
2
0
0
3
0
0
0
3
1
2
0
0
0
0
1
2
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
2
2
2
3
2
0
0
0
0
0
0
2
0
1
0
0
0
0
1
1
1
0
0
0
0
0
1
0
1
0
3
1
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
2
0
0
0
0
1
1
3
1
0
0
2
2
0
1
1
0
0
0
0
0
2
0
0
0
0
2
1
0
0
3
0
0
0
0
3
0
0
0
0
0
0
0
1
1
0
2
0
2
2
0
2
1
0
1
0
0
0
1
0
0
0
2
0
0
3
0
0
1
0
1
3
3
0
0
0
1
3
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
3
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
2
2
0
2
1
0
0
0
2
0
2
0
0
2
1
0
0
0
0
1
1
0
0
2
0
0
1
0
0
4
0
0
1
0
0
0
1
0
1
1
0
0
1
0
0
0
1
0
0
2
1
0
0
0
0
0
2
1
2
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
12
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
1
2
0
2
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
1
2
0
0
0
0
0
0
2
0
0
2
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
2
0
0
2
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
2
0
0
2
0
0
2
0
0
0
1
0
0
0
0
3
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
2
4
1
0
0
0
0
2
0
0
0
1
2
0
1
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
3
1
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
10
2
0
0
0
0
0
0
0
15
2
2
0
3
2
0
2
0
0
0
0
0
0
2
0
2
0
0
1
2
0
0
0
0
0
0
2
1
0
0
0
6
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
2
1
1
2
2
1
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
1
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
3
0
1
2
0
1
1
1
0
0
0
0
0
2
0
2
0
1
2
1
4
0
0
0
0
0
2
0
0
2
2
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
2
1
0
2
0
0
0
1
0
2
1
0
0
0
0
0
0
1
0
2
0
0
2
2
2
1
0
2
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
1
1
0
3
2
0
0
0
0
2
0
1
0
0
0
0
1
1
0
1
0
2
3
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
1
1
0
2
0
1
0
1
2
0
0
0
2
0
0
0
2
1
0
0
1
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
1
0
3
0
0
1
2
3
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
1
1
0
1
0
2
0
1
0
0
0
0
1
0
2
1
2
0
0
1
0
0
0
3
2
0
0
0
1
0
4
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
1
0
2
2
0
1
0
0
2
0
0
3
0
0
0
2
0
0
2
4
0
2
0
0
0
0
0
0
2
0
0
2
0
1
2
1
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
5
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
1
1
0
2
0
0
0
1
1
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
3
0
0
0
0
0
0
2
1
2
0
0
0
1
0
0
1
1
0
0
0
1
0
7
0
7
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
1
1
2
1
0
2
0
2
0
2
0
1
0
1
0
0
0
2
0
0
0
0
0
1
2
0
0
1
1
0
0
2
0
0
0
0
2
1
1
1
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
4
0
0
0
2
0
0
0
0
5
0
0
0
0
1
0
1
0
0
2
0
0
0
0
1
0
1
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
2
0
0
2
0
2
0
2
0
0
0
0
0
2
1
0
0
1
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
1
2
0
0
0
1
0
0
2
2
0
0
0
0
0
1
0
0
0
0
1
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
2
0
0
1
1
2
1
0
1
1
0
1
1
0
1
0
0
0
0
0
1
0
0
0
2
1
2
1
0
2
3
0
0
0
2
0
1
0
2
0
0
0
1
4
0
0
0
2
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
1
0
2
1
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
3
0
0
2
0
2
1
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
1
0
2
0
0
0
0
2
0
0
0
2
2
2
2
0
1
0
1
0
0
0
2
0
2
0
0
1
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
2
0
1
0
0
1
0
2
4
1
0
0
1
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
2
1
0
2
0
0
0
1
0
0
0
0
0
1
2
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
2
1
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
2
2
2
0
0
0
0
0
0
2
1
1
2
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
2
2
1
0
0
0
0
0
0
2
0
0
0
0
3
2
0
1
2
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
1
1
3
0
0
1
2
0
0
0
0
1
0
1
1
2
0
0
0
0
0
0
0
0
2
0
2
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
1
7
0
0
2
1
0
2
2
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
2
2
1
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
1
2
0
2
0
0
0
0
7
0
0
1
0
1
0
2
0
1
1
1
0
0
1
1
0
0
2
0
2
2
0
0
2
1
0
1
2
0
1
0
0
0
1
0
2
2
1
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
1
0
0
3
0
2
2
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
1
0
0
2
2
0
1
0
0
0
0
2
1
1
1
0
0
0
2
0
1
2
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
2
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
1
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
2
1
2
1
0
2
0
3
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
1
0
0
2
1
1
1
0
1
0
1
2
0
2
2
1
0
0
0
0
0
2
1
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
2
5
1
0
0
1
0
2
2
3
1
0
0
0
2
0
0
0
0
0
0
0
0
3
2
2
0
0
0
0
0
2
0
0
0
0
2
0
1
1
0
2
0
2
2
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
4
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
1
1
0
2
0
3
0
0
0
2
0
1
0
0
0
0
3
1
0
0
1
0
0
0
0
0
0
0
4
0
1
0
0
2
1
0
0
1
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
3
3
2
0
0
0
0
0
0
0
1
0
0
0
0
6
1
0
0
0
0
1
0
0
0
0
0
0
2
0
1
4
0
1
1
0
0
0
2
0
0
2
0
2
0
0
2
1
0
0
4
0
1
2
0
0
0
1
2
1
0
1
0
2
2
0
0
2
0
1
0
0
0
1
0
0
1
0
3
2
0
0
0
2
0
0
0
1
0
2
0
2
1
1
2
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
2
2
2
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
1
0
2
0
0
2
2
0
1
2
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
2
0
0
1
0
2
0
1
0
0
0
2
1
2
2
0
1
2
0
0
0
0
2
0
0
1
0
0
0
0
1
3
1
0
2
0
2
0
1
0
1
1
0
0
2
0
2
0
0
1
0
2
0
0
1
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
1
1
0
0
0
0
3
2
0
0
1
0
0
0
0
0
2
0
0
0
0
1
2
1
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
1
0
3
0
0
2
2
0
0
1
0
0
0
0
0
0
0
1
0
0
3
0
0
3
0
0
0
3
0
0
1
0
0
0
0
0
0
3
0
1
0
1
0
0
0
0
1
2
0
0
0
0
1
2
2
0
1
0
0
0
2
1
2
2
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
2
0
0
0
0
1
0
3
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
1
0
0
0
2
0
1
2
1
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
2
0
2
0
0
2
0
0
1
1
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
1
2
1
2
0
0
0
0
0
1
0
0
0
0
2
0
1
2
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
2
1
0
0
1
0
0
0
0
1
0
1
0
1
2
2
0
0
1
0
0
0
0
2
0
1
0
1
0
0
2
0
0
2
1
0
0
0
0
2
2
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
2
0
1
2
2
0
0
0
0
0
1
0
2
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
1
1
2
0
0
0
2
0
0
0
1
0
5
0
1
0
0
0
0
0
0
0
0
0
1
4
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
1
0
2
1
0
2
1
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
2
0
0
0
1
1
0
0
2
1
1
0
0
1
0
1
0
0
0
0
0
0
2
1
0
2
0
1
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
1
4
0
2
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
4
1
0
0
0
1
0
0
0
1
0
0
2
2
0
0
0
0
0
1
1
0
2
4
0
0
0
2
0
0
1
3
0
0
0
0
0
0
0
0
1
0
0
3
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
2
1
1
1
0
0
0
0
0
0
0
2
3
1
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
1
0
0
1
2
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
2
0
2
0
0
2
0
1
0
0
0
0
0
1
0
1
0
1
0
1
1
0
0
1
0
0
0
2
0
1
0
2
1
2
0
0
0
2
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
1
0
0
0
2
1
1
0
0
2
0
0
0
0
3
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
2
0
2
1
1
4
0
0
0
2
2
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
3
0
0
0
0
0
0
3
0
2
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
2
0
1
0
1
3
0
0
1
0
0
4
2
0
0
1
0
1
0
0
0
1
2
1
0
0
0
2
0
2
0
1
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
1
0
2
0
2
0
1
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
2
0
1
2
0
0
0
2
0
0
3
0
0
1
3
0
2
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
2
0
0
0
0
2
2
0
2
0
0
0
0
1
1
0
0
2
0
0
1
0
0
0
2
0
0
0
0
5
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
1
0
0
2
2
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
3
2
0
0
0
2
0
2
2
0
0
0
0
0
2
0
0
0
1
2
3
0
0
0
2
2
0
3
1
0
0
0
0
1
0
0
1
0
0
0
1
0
2
0
1
2
0
2
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
2
1
0
2
1
0
0
2
0
0
0
2
2
0
0
0
0
2
2
0
2
0
0
0
1
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
2
0
2
2
0
0
0
0
0
0
0
4
1
2
2
1
0
2
0
0
1
0
0
0
2
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
2
0
1
0
0
2
2
0
0
1
0
0
1
2
0
0
0
0
0
1
0
1
0
2
0
0
1
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
1
2
0
1
1
2
1
0
1
0
0
0
2
2
0
1
0
2
2
0
0
1
0
0
0
1
1
4
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
2
2
0
0
3
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
2
0
0
0
0
1
2
0
2
1
2
0
0
1
0
0
2
2
0
2
0
2
3
0
1
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
1
1
0
1
1
0
2
0
1
1
0
2
0
0
0
1
1
0
0
2
1
1
2
1
0
0
2
2
0
1
0
1
0
0
0
0
1
0
0
0
2
0
1
2
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
3
0
3
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
3
0
0
1
0
0
0
0
0
2
0
0
2
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
1
0
0
0
0
2
3
0
0
0
2
0
0
0
2
0
0
2
0
0
0
2
1
2
2
0
0
0
1
0
0
0
2
0
0
2
0
1
0
1
6
0
0
0
1
0
0
0
0
2
2
0
2
0
2
2
0
0
1
0
1
0
0
1
0
0
0
0
0
2
1
1
0
0
0
0
0
3
2
0
0
1
1
0
0
2
2
0
3
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
2
1
2
3
0
0
1
3
0
1
0
0
0
1
0
2
0
0
0
1
0
0
2
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
1
1
2
1
1
2
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
2
0
1
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
2
1
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
2
3
1
2
0
0
0
1
0
2
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
2
0
1
0
2
0
4
0
0
3
0
0
0
0
2
0
0
0
2
2
2
2
2
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
5
1
0
0
2
1
0
0
0
2
0
0
0
3
0
0
0
0
0
2
1
2
2
0
0
0
0
0
1
0
0
1
3
0
1
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
12
0
1
0
0
0
0
0
1
2
0
2
0
1
0
1
2
0
0
0
2
0
0
0
1
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
4
2
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
2
0
2
2
0
0
0
0
0
0
0
3
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
3
2
0
0
0
1
6
2
0
1
0
0
1
0
0
0
0
0
2
2
1
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
2
0
0
1
0
2
0
0
0
1
0
1
2
0
0
3
1
2
2
0
1
0
0
2
0
3
1
2
0
0
0
0
1
0
0
0
1
2
2
0
0
2
0
1
0
0
1
1
1
2
0
0
0
1
2
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
4
2
0
0
2
3
0
0
2
0
0
0
0
1
1
0
1
0
1
0
0
0
1
0
2
0
2
0
1
2
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
3
1
0
0
0
1
0
1
0
0
0
3
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
2
2
0
1
0
1
3
0
2
0
0
0
0
0
2
1
2
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
2
1
1
0
0
0
1
0
0
2
5
0
4
0
0
2
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
1
0
0
0
1
2
0
2
1
0
2
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
2
1
1
5
0
0
0
1
0
2
0
0
1
0
0
2
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
3
1
2
0
0
0
2
3
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
1
2
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
1
0
1
0
0
1
2
0
0
1
1
0
0
1
1
2
1
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
3
2
0
2
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
1
1
2
1
0
2
0
0
0
0
3
1
0
1
19
1
0
0
0
3
0
0
0
0
3
1
0
1
0
2
0
0
0
0
0
2
0
0
1
0
1
2
0
0
3
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
1
1
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
1
0
0
0
0
1
3
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
2
0
2
0
0
1
0
0
0
2
4
0
0
0
2
2
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
2
0
0
0
0
0
0
0
1
1
1
0
5
0
0
0
1
0
1
0
2
0
0
0
3
0
0
0
0
0
1
0
0
1
0
0
0
1
2
0
1
2
0
2
0
0
1
0
1
2
1
3
2
0
0
1
0
0
1
0
0
1
0
0
2
0
2
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
3
0
2
0
2
0
2
0
1
1
0
0
0
2
1
0
0
0
2
0
2
0
2
2
0
2
1
0
2
2
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
3
1
1
0
0
0
0
2
0
0
2
0
0
2
0
2
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
4
2
1
0
0
0
2
0
0
0
1
0
0
1
0
2
0
1
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
2
0
0
0
0
1
0
1
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
1
0
0
0
1
0
0
1
2
0
0
0
2
0
2
2
0
0
1
0
0
1
2
0
0
0
2
2
0
0
0
0
2
0
0
1
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
1
0
0
1
2
0
0
0
0
0
0
0
1
2
0
0
3
0
0
0
0
0
2
0
1
1
0
0
2
0
0
0
2
0
0
2
0
1
0
0
2
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
1
0
2
0
1
1
1
0
0
2
2
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
2
0
2
0
0
1
0
1
3
0
0
0
1
1
0
1
0
1
2
0
0
2
0
2
0
0
3
1
0
0
0
0
0
0
0
0
0
1
1
2
0
0
1
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
1
1
0
1
0
2
0
0
0
1
2
0
0
0
0
0
1
1
2
1
0
0
0
0
2
2
0
5
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
2
0
5
0
2
2
2
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
1
0
0
2
0
0
3
0
1
0
0
0
3
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
1
0
0
0
1
1
0
2
0
2
1
2
0
1
0
0
2
0
0
0
3
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
2
0
0
0
2
2
0
0
0
0
0
2
0
2
0
1
0
2
0
6
0
0
1
0
0
0
2
3
0
0
0
2
1
0
0
0
0
0
2
1
2
0
0
2
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
2
1
0
1
0
0
1
0
3
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
3
2
0
1
0
2
0
0
0
0
0
2
4
0
0
0
2
0
0
4
2
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
3
0
2
3
2
0
0
1
1
0
0
0
1
0
0
0
0
0
3
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
4
1
0
0
0
0
0
0
0
1
2
0
2
0
0
0
2
0
2
0
0
1
0
3
0
0
0
0
0
0
0
2
2
0
0
2
1
0
1
2
0
2
2
2
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
1
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
2
2
1
0
0
1
0
2
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
3
0
0
1
2
0
1
0
2
0
0
2
3
0
2
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
2
2
0
0
2
0
0
1
0
0
2
0
1
0
0
1
0
2
0
2
0
1
0
0
0
0
0
2
0
2
1
1
0
0
0
0
0
0
0
0
1
2
3
0
0
2
1
0
0
1
0
2
0
2
0
0
1
0
0
2
3
0
2
0
0
2
1
0
1
0
0
0
0
0
0
0
0
1
2
0
2
2
0
0
1
0
1
0
0
1
1
0
0
0
0
2
0
0
0
0
0
1
2
0
0
1
0
1
0
2
0
0
0
2
3
5
0
0
0
0
0
2
0
0
2
1
0
0
0
2
0
0
4
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
2
0
2
0
2
1
0
0
1
0
0
1
0
2
0
0
0
0
0
2
0
2
0
0
0
1
1
4
1
2
0
0
0
0
1
0
1
0
2
0
0
0
1
0
0
0
1
0
0
1
0
1
0
2
0
0
1
3
0
0
0
0
0
1
2
0
0
0
3
0
0
2
0
0
7
0
0
2
1
0
0
1
2
0
0
2
2
1
0
0
0
0
0
2
3
0
0
1
2
0
0
2
1
2
1
0
2
3
2
2
0
0
3
1
0
0
1
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
4
0
0
0
2
0
0
0
1
0
1
1
2
2
0
0
0
1
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
2
1
0
3
0
2
2
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
1
2
0
0
1
1
0
1
0
1
0
0
2
2
1
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
4
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
1
2
1
2
2
1
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
1
0
0
0
0
2
0
0
2
0
0
2
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
3
0
0
1
0
1
0
0
0
0
0
0
2
0
2
1
2
0
0
2
0
0
2
0
0
1
1
0
2
1
1
0
2
2
0
2
0
0
0
1
0
0
0
1
1
0
0
0
0
2
0
1
1
1
1
1
0
2
0
0
1
0
0
1
0
0
0
2
2
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
1
0
0
2
2
3
0
0
2
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
3
0
1
0
1
3
1
1
0
0
0
1
0
1
2
0
0
0
2
0
0
3
0
1
0
0
2
2
0
0
2
0
0
2
0
0
0
1
1
1
2
0
2
0
0
0
0
0
1
0
0
0
2
2
2
1
0
2
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
6
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
1
2
1
0
0
0
1
2
0
0
0
0
0
1
0
0
1
2
0
0
0
2
0
0
0
2
1
0
2
0
1
1
0
1
0
1
3
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
2
1
0
0
2
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
1
0
0
1
1
2
0
3
2
0
1
0
0
3
2
2
1
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
4
0
0
0
2
1
0
0
1
0
0
0
0
1
2
0
2
0
0
0
1
0
1
0
2
1
0
0
2
0
0
0
2
2
0
1
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
1
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
2
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
2
0
1
0
0
0
2
1
0
0
0
0
0
2
1
0
0
0
0
0
1
2
0
0
0
0
2
1
2
3
0
0
1
0
0
3
1
0
0
0
0
4
1
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
1
0
0
1
2
2
0
0
0
0
0
0
0
0
1
2
0
0
0
6
2
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
5
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
1
0
0
0
2
2
4
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
1
0
0
1
0
0
0
0
0
2
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
2
0
0
0
1
2
0
0
0
4
0
2
0
0
0
1
1
0
1
0
0
2
0
0
0
1
2
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
1
0
0
1
3
0
2
0
1
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
2
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
1
0
2
0
3
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
3
1
2
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
1
3
0
0
0
2
0
0
1
0
0
0
0
0
2
1
0
0
1
0
0
1
1
0
1
0
3
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
2
2
1
1
2
1
1
0
0
0
1
2
0
2
0
2
0
0
0
1
2
0
0
2
5
0
0
0
0
0
0
0
0
0
2
2
2
0
2
0
2
0
0
0
0
0
1
0
3
0
0
2
0
0
2
1
0
2
2
1
1
0
3
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
2
0
1
0
0
1
2
0
4
2
0
0
3
0
0
1
0
3
0
2
0
0
0
2
1
0
0
0
0
0
1
2
0
0
0
2
2
0
2
0
0
0
0
1
2
0
0
0
0
1
0
2
4
0
0
0
0
2
3
0
1
2
1
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
2
0
2
0
1
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
1
0
1
2
2
0
1
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
2
1
1
3
0
0
0
0
0
0
0
1
1
0
1
1
0
1
0
0
3
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
1
1
1
1
0
1
0
0
0
0
0
2
0
0
2
2
0
0
2
0
2
2
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
2
1
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
5
0
0
0
0
0
1
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
1
0
3
1
0
0
3
2
0
2
4
0
0
1
0
0
0
2
1
0
0
0
0
0
0
1
2
0
0
3
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
2
0
1
0
1
0
0
0
0
0
1
0
0
2
0
1
6
2
2
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
2
1
0
0
1
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
2
2
1
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
2
1
1
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
2
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
2
1
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
5
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
1
2
0
2
2
0
1
0
0
1
2
0
0
0
0
2
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
2
1
0
2
2
1
0
0
0
0
1
0
1
2
0
0
0
3
0
0
0
2
2
0
0
8
0
1
0
0
0
0
0
2
1
0
1
0
0
0
0
1
0
0
0
0
2
0
2
0
2
0
0
2
2
0
0
2
0
0
1
1
1
2
0
0
0
0
2
1
2
0
0
0
0
0
2
0
4
0
1
0
0
1
0
0
2
1
0
0
2
0
0
2
0
0
2
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
1
2
1
0
2
0
2
0
0
0
2
0
0
1
0
0
2
2
0
0
0
0
1
0
0
0
0
2
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
2
2
2
0
2
1
0
0
0
1
1
0
0
0
0
0
2
2
1
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
2
0
2
0
1
0
0
0
1
0
4
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
3
0
0
2
1
0
3
0
0
0
0
3
0
1
0
0
0
1
0
0
0
1
0
0
0
2
0
1
0
0
0
2
0
1
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
3
0
1
0
2
0
1
2
0
1
0
0
0
0
0
1
0
0
1
0
0
0
3
1
0
1
2
2
2
1
0
0
1
0
0
0
0
0
1
2
0
1
0
2
0
1
2
2
0
1
0
0
1
0
2
0
2
0
0
1
2
0
0
0
0
1
1
0
0
0
0
0
0
2
4
0
0
0
0
0
2
3
0
0
0
0
0
0
2
0
1
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
1
0
0
0
0
1
0
1
3
0
1
2
0
2
0
0
1
1
0
1
1
2
3
0
2
2
2
1
1
0
0
2
0
2
0
1
1
0
0
1
0
0
0
1
0
0
3
1
0
2
0
0
0
2
0
0
0
1
0
2
1
0
1
1
0
0
0
0
0
0
0
0
0
2
0
5
1
0
0
0
0
0
0
0
0
0
1
0
1
2
1
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
5
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
3
0
0
1
1
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
3
0
3
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
2
0
2
0
0
0
1
0
1
1
0
0
2
1
0
0
0
0
1
0
0
2
1
0
1
1
2
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
2
0
2
0
1
0
2
0
0
0
2
0
0
1
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
2
2
0
0
1
2
0
1
0
2
0
0
0
1
0
1
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
1
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
2
0
2
1
0
1
0
2
0
0
1
2
1
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
1
1
2
0
0
0
0
1
4
0
0
0
0
0
0
0
0
2
2
0
1
1
0
0
0
0
1
0
2
1
1
0
0
0
2
0
2
0
2
0
0
1
0
0
0
0
1
0
0
2
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
2
1
0
1
0
0
0
0
0
0
1
1
0
0
0
2
0
0
2
0
0
0
3
0
2
2
0
2
0
1
0
0
0
0
0
0
2
0
0
1
2
0
0
0
4
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
1
0
0
3
1
2
0
0
0
0
1
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
2
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
3
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
2
2
0
0
0
2
3
0
0
0
0
0
0
1
0
0
2
2
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
2
0
2
0
2
1
0
1
3
0
1
0
0
0
0
0
0
2
0
0
2
1
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
3
2
1
1
3
0
0
0
0
0
0
1
0
0
0
3
1
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
3
4
1
0
0
0
0
0
0
2
0
0
0
2
2
0
1
3
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
2
0
2
0
1
2
0
1
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
2
1
0
0
2
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
2
2
0
0
0
1
1
0
0
0
0
0
0
2
0
2
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
2
1
0
0
0
1
2
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
1
1
3
2
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
1
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
1
0
3
0
0
1
2
2
0
1
0
0
0
0
0
0
0
1
0
1
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
2
0
0
0
1
0
2
0
2
0
0
1
0
0
1
0
1
1
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
2
0
1
2
0
0
0
0
0
1
0
0
1
4
0
1
3
4
1
1
1
0
2
0
2
0
0
0
0
2
2
4
2
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
1
1
2
1
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
1
2
1
0
3
0
0
0
0
2
0
0
1
0
0
0
1
0
0
1
1
0
0
2
0
0
1
1
2
2
0
0
0
3
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
4
0
2
2
1
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
2
0
0
1
0
2
1
0
0
1
0
0
1
2
2
0
0
0
0
0
2
0
0
3
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
2
3
1
0
0
0
0
0
0
8
1
2
3
1
0
0
0
0
0
0
0
0
2
2
1
0
0
1
0
0
0
0
0
1
0
1
0
0
1
2
1
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
2
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
2
0
1
1
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
3
1
0
0
2
2
0
0
0
1
0
0
1
2
0
0
1
2
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
1
1
2
0
1
2
1
0
1
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
1
0
2
0
2
0
0
0
0
1
1
1
2
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
1
0
0
0
1
2
0
0
0
0
0
0
3
1
1
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
2
0
1
0
0
0
3
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
2
0
1
0
2
0
2
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
2
2
0
1
0
0
0
0
0
1
1
2
1
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
3
0
0
2
0
1
0
0
1
0
0
0
2
0
0
0
2
0
3
0
0
2
1
0
1
0
1
0
0
1
0
1
0
0
1
0
2
0
0
2
1
0
2
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
2
0
1
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
1
0
3
0
0
1
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
1
1
0
4
0
2
0
1
0
0
0
0
0
0
1
1
0
1
0
0
2
0
4
1
1
0
2
0
1
0
2
2
0
1
1
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
4
0
0
0
0
1
3
0
0
2
0
1
1
0
0
2
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
3
0
0
0
0
1
0
0
0
4
1
2
2
3
0
0
0
0
1
0
0
0
0
2
0
2
1
0
3
1
2
0
0
0
0
0
0
0
0
3
1
1
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
1
1
0
1
0
0
0
0
2
0
0
0
2
1
0
0
0
2
0
2
0
2
0
1
0
0
2
0
0
1
0
0
2
0
0
0
0
2
0
1
1
0
0
0
2
0
0
0
0
2
0
2
0
2
1
1
0
0
0
0
0
1
0
0
0
0
1
3
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
2
0
0
1
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
1
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
2
2
0
0
2
0
0
0
0
2
0
1
0
0
1
0
3
1
0
1
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
2
1
2
0
0
0
2
0
0
0
1
0
0
0
0
1
0
2
0
2
2
1
0
0
0
0
0
0
0
0
2
1
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
2
1
1
0
0
1
0
0
2
0
2
1
0
1
0
1
0
0
2
1
1
0
1
1
0
0
0
0
3
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
2
0
5
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
1
1
0
3
2
2
5
2
1
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
1
1
0
3
2
0
0
0
0
2
1
0
0
1
0
1
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
2
3
0
2
1
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
2
3
1
0
0
2
0
0
2
1
2
1
0
0
0
2
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
2
0
1
0
2
0
0
2
1
0
3
1
2
0
0
2
2
2
0
0
4
0
3
0
1
1
0
0
0
2
0
1
1
0
1
0
1
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
2
0
0
2
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
1
1
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
1
2
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
3
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
1
0
0
2
0
2
2
0
1
0
2
0
0
1
1
0
0
1
1
4
0
0
0
0
1
0
2
2
0
0
0
1
0
0
2
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
1
0
0
0
0
7
0
0
0
0
1
0
1
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
2
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
1
2
1
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
2
0
0
2
0
0
0
0
0
0
0
2
0
0
2
1
1
1
0
2
2
0
1
1
2
0
0
0
0
1
0
2
0
0
0
0
0
0
1
1
1
0
0
1
0
2
0
0
0
0
1
2
0
0
2
0
0
0
0
1
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
2
0
2
0
0
0
0
0
1
0
0
0
0
3
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
1
0
0
0
1
0
1
0
0
3
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
2
0
2
0
0
0
1
3
0
1
3
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
1
0
0
1
2
2
0
0
3
1
1
0
2
0
2
0
0
0
0
0
0
0
0
2
1
0
1
1
0
0
0
0
0
2
0
3
0
0
0
1
1
0
0
0
0
2
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
6
0
2
3
1
0
1
0
0
0
3
0
0
0
0
0
0
0
0
2
2
2
0
2
0
2
2
0
0
0
0
2
0
0
1
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
1
0
3
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
2
0
0
2
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
2
1
0
1
0
2
0
0
0
0
0
2
0
2
0
0
3
0
1
2
0
2
1
0
0
0
1
2
0
2
2
0
0
0
0
0
0
1
3
0
0
1
1
0
0
2
1
1
1
1
0
0
0
0
0
0
0
2
0
1
2
0
1
0
0
0
2
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
3
2
0
2
0
0
0
0
2
2
2
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
2
2
0
2
0
0
0
0
2
1
0
0
0
0
2
0
0
1
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
1
0
2
0
0
0
0
2
1
2
0
0
0
0
1
0
1
0
0
1
0
0
0
2
0
2
0
2
0
0
2
0
0
0
1
0
0
1
0
1
2
2
1
0
0
1
0
1
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
1
0
2
0
0
0
0
2
2
1
0
0
1
0
6
0
3
2
0
0
0
1
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
2
1
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
2
0
1
0
0
1
0
0
0
1
0
0
0
0
2
0
1
2
2
0
0
0
0
0
0
1
0
3
0
2
0
0
1
0
2
0
0
0
0
2
2
0
0
1
1
0
1
0
0
1
0
0
0
2
0
0
2
0
2
0
0
0
3
0
0
0
0
1
0
1
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
2
1
0
0
0
1
0
6
0
0
0
0
0
2
2
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
2
0
1
2
1
0
1
0
1
0
3
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
2
0
0
0
2
0
0
2
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
2
0
1
2
0
0
0
0
0
1
3
0
1
0
0
11
0
0
0
1
0
0
1
0
2
1
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
1
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
2
1
1
2
1
1
0
0
0
0
0
0
1
0
0
1
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
1
2
1
0
1
4
0
0
2
0
0
0
1
0
0
2
1
0
0
1
0
0
0
0
2
1
2
0
0
0
0
0
2
0
3
0
2
0
1
0
0
1
2
2
1
0
0
1
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
1
0
1
0
0
1
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
1
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
2
0
1
0
0
0
1
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
2
0
4
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
2
2
0
0
2
1
0
0
1
0
0
2
1
0
0
1
1
0
0
0
2
2
0
0
0
0
1
0
0
2
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
4
1
0
0
2
0
1
0
2
0
0
0
0
1
2
2
0
0
0
1
2
1
2
0
1
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
1
0
1
0
0
0
1
0
2
0
0
1
0
2
0
0
0
0
0
0
0
1
2
0
2
1
0
1
0
0
1
0
1
1
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
1
0
0
2
2
0
0
0
2
0
0
0
2
0
3
2
0
2
0
0
0
0
0
0
0
2
1
0
1
0
0
2
0
0
0
0
4
0
0
0
0
0
1
1
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
2
0
0
1
0
2
1
0
0
2
0
0
0
0
2
1
0
0
0
1
0
0
0
1
0
0
0
1
0
1
1
1
0
0
0
0
0
0
1
0
1
2
0
0
2
0
0
1
0
0
2
2
0
0
0
0
2
1
0
2
0
0
2
0
0
0
0
0
7
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
8
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
1
0
2
0
1
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
2
0
1
2
1
3
0
0
0
2
0
0
0
2
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
5
2
0
0
2
0
0
4
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
2
1
0
0
2
0
1
0
1
0
2
0
1
2
2
3
0
0
0
1
2
0
0
0
2
0
1
0
0
0
2
1
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
1
0
4
0
2
0
1
3
0
0
2
0
1
0
1
0
0
0
1
2
2
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
1
3
1
0
2
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
2
1
0
1
2
2
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
1
1
0
0
0
0
2
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
2
4
0
0
0
2
1
0
1
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
1
0
1
2
0
0
0
0
0
2
0
1
3
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
1
0
0
0
1
0
2
0
0
0
0
4
2
1
0
0
0
2
1
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
2
2
1
0
0
0
2
0
0
3
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
4
0
0
0
0
0
4
0
2
0
0
1
1
2
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
1
0
2
0
0
0
2
0
0
0
0
1
2
0
1
0
6
0
0
0
0
0
0
0
2
0
1
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
3
0
0
0
1
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
2
2
0
2
0
0
0
1
0
2
0
0
0
0
0
0
8
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
2
0
1
0
2
2
2
3
2
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
1
0
2
2
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
2
2
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
3
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
2
1
0
0
0
0
2
0
2
0
0
0
0
0
3
0
0
0
2
2
1
1
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
3
1
0
2
0
2
0
0
0
2
1
0
0
0
0
0
0
0
2
1
0
0
2
2
0
0
0
0
0
0
0
3
0
1
0
0
2
0
0
0
0
0
0
0
2
2
0
1
1
0
0
1
0
0
0
0
0
2
1
2
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
1
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
2
0
3
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
1
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
2
0
3
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
1
0
0
2
0
0
2
4
2
0
2
2
0
0
1
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
2
2
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
2
0
0
1
1
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
1
0
4
2
0
2
0
0
0
2
0
0
0
3
0
0
0
2
0
0
0
2
0
0
2
0
0
2
2
0
0
0
0
2
1
2
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
1
0
0
1
2
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
1
0
2
0
1
0
0
0
2
2
1
0
1
2
3
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
2
1
0
0
1
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
3
0
0
0
0
0
2
1
1
1
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
5
0
1
0
2
0
3
2
0
0
2
2
0
1
0
0
1
0
0
0
0
1
0
0
1
0
3
0
0
0
2
2
0
0
0
1
0
1
0
2
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
1
0
0
2
1
0
2
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
1
0
1
0
0
1
0
1
1
0
0
0
0
2
0
0
0
1
1
3
0
0
0
2
0
0
0
0
0
0
1
2
1
1
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
3
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
1
1
1
0
0
0
0
0
1
2
2
2
0
0
2
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
1
0
0
0
0
2
2
0
0
2
0
0
0
2
0
2
1
0
0
1
0
2
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
11
0
0
0
0
3
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
2
0
0
0
3
0
0
0
0
0
0
1
0
0
2
3
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
2
2
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
1
0
1
1
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
3
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
1
0
0
2
1
1
1
0
0
2
0
0
0
0
0
0
0
2
0
0
2
1
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
1
2
1
0
0
0
0
1
1
2
0
0
0
2
0
2
0
2
1
0
0
0
2
0
0
0
1
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
2
0
2
0
1
1
0
0
0
0
0
1
0
0
0
7
2
0
4
0
0
0
0
2
0
2
0
1
0
0
0
1
0
3
0
0
2
1
1
1
3
0
0
1
1
0
1
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
2
0
5
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
2
1
1
3
0
0
1
2
0
0
3
1
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
2
0
2
0
0
0
0
2
2
2
0
0
0
2
3
0
0
0
0
0
1
0
0
1
0
0
0
0
3
3
0
0
0
0
0
0
0
3
2
0
0
2
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
2
0
0
1
0
1
0
0
0
0
0
3
0
0
2
5
1
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
3
2
0
3
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
1
0
2
0
0
2
0
1
1
0
2
0
0
0
0
0
0
0
0
0
2
2
2
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
1
0
2
2
0
0
0
0
2
2
0
0
2
0
0
0
0
1
1
0
0
0
0
1
0
2
1
0
0
0
0
2
2
0
0
0
3
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
2
2
0
2
0
0
0
0
0
4
0
3
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
2
2
0
0
0
0
1
1
0
1
0
0
2
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
1
2
0
2
0
1
0
0
0
0
0
1
1
1
2
2
0
0
1
0
2
0
0
0
0
4
0
0
2
2
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
3
2
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
2
0
1
1
0
1
0
0
1
0
2
0
0
0
0
1
0
0
0
2
1
0
2
0
0
3
0
0
0
0
1
0
0
1
2
0
3
2
0
0
0
1
0
0
0
3
1
1
0
1
2
0
1
1
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
3
0
1
0
0
1
0
1
0
0
0
1
1
0
0
2
0
0
0
0
0
2
0
1
0
0
0
2
0
1
0
0
3
0
2
0
0
0
0
0
0
1
1
3
0
1
2
0
0
0
0
0
1
2
0
1
0
2
0
1
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
2
0
1
0
0
0
0
3
0
0
3
1
0
2
2
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
1
0
1
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
1
1
0
0
1
0
2
0
2
2
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
3
2
2
2
0
0
1
1
0
2
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
2
0
0
2
0
2
0
0
0
2
2
0
1
0
2
0
2
2
2
0
0
0
0
0
2
0
0
0
2
2
4
1
0
0
2
0
0
0
0
0
0
3
0
1
0
1
1
2
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
1
2
0
0
2
1
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
2
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
1
2
0
2
0
0
0
0
4
0
0
0
0
0
1
0
0
2
0
0
0
0
1
2
1
0
0
0
2
3
1
0
0
2
0
0
0
0
2
1
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
2
2
2
0
2
1
2
2
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
2
0
2
0
0
4
4
0
2
0
0
1
2
1
0
0
0
0
0
1
0
0
1
0
0
2
2
1
0
0
1
0
2
2
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
2
0
0
0
2
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
1
0
2
0
0
0
0
0
0
0
0
1
0
1
0
2
1
0
0
0
2
0
0
0
1
0
2
0
0
0
0
1
0
2
2
1
1
1
2
1
1
2
0
1
0
2
0
0
0
0
0
0
1
0
1
1
3
1
0
0
1
0
0
0
1
1
1
0
0
0
0
1
0
2
0
0
3
0
0
0
1
0
0
1
0
0
0
1
0
0
0
4
0
0
0
0
1
0
0
2
0
0
1
0
2
0
0
0
0
2
0
0
0
0
2
1
0
1
0
4
2
0
1
0
0
1
0
2
1
0
0
2
0
0
3
1
0
2
1
0
0
1
0
1
1
0
0
1
0
0
1
0
1
1
0
0
2
0
0
2
1
0
2
0
1
0
1
2
0
0
0
0
0
0
2
0
0
2
2
0
2
1
0
1
0
0
1
0
0
0
0
2
0
0
2
0
0
0
1
2
0
0
0
3
1
0
0
2
2
0
1
0
1
0
0
2
5
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
1
0
0
1
0
1
1
0
0
0
0
0
2
1
3
1
0
0
2
0
1
1
0
2
0
0
1
0
0
1
2
0
2
2
0
0
0
1
2
0
0
0
0
2
0
1
2
1
0
0
1
1
0
1
0
0
1
1
2
0
2
0
0
0
0
2
0
1
0
0
1
0
0
0
3
0
1
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
1
3
0
1
0
0
2
1
0
2
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
1
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
2
0
0
1
2
0
1
1
3
1
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
2
5
0
0
1
0
3
0
0
0
0
0
5
0
8
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
2
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
1
1
1
1
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
1
1
0
0
0
1
0
1
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
1
0
0
0
0
1
2
1
0
1
2
0
0
1
0
0
0
0
0
2
1
1
0
2
0
0
1
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
2
1
0
0
0
1
2
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
2
0
0
2
1
0
0
1
1
0
0
3
0
1
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
1
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
1
0
2
0
0
2
0
0
2
0
0
0
0
0
1
0
2
2
0
0
0
0
1
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
2
0
0
1
1
0
2
0
0
0
0
0
2
0
0
1
2
0
0
2
2
0
1
0
1
2
1
1
0
0
1
0
0
0
1
0
1
0
0
11
0
0
2
1
0
2
2
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
2
0
1
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
4
0
1
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
3
0
0
0
0
0
2
0
2
2
0
0
1
2
0
2
2
0
0
0
0
0
0
1
2
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
1
1
0
1
1
0
0
2
0
1
0
0
2
4
0
0
0
0
0
0
4
1
0
0
0
0
0
2
0
2
0
1
0
1
3
0
2
0
0
0
0
1
1
0
0
2
0
2
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
1
0
2
0
0
0
1
0
1
0
1
0
0
3
0
0
0
3
1
0
0
0
1
0
0
0
0
2
1
3
0
0
1
0
2
2
0
0
2
0
2
3
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
1
0
2
0
0
1
0
1
0
1
0
2
0
2
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
1
0
0
0
2
1
2
0
0
2
2
0
0
0
0
0
0
2
2
0
0
1
2
0
0
0
0
1
0
1
1
0
1
0
0
1
0
0
2
0
2
1
0
0
1
0
0
0
0
2
2
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
3
1
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
2
2
1
0
0
0
0
0
1
0
2
0
2
0
0
1
0
0
2
0
0
0
0
2
0
2
2
0
0
1
2
1
0
0
0
0
0
1
1
0
1
0
3
0
0
2
0
2
0
1
0
0
1
0
2
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
1
2
1
0
1
0
0
0
0
2
0
0
0
0
0
2
1
2
1
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
1
2
1
1
1
0
2
0
0
0
2
0
1
0
2
2
1
1
2
0
0
1
1
0
0
0
3
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
4
2
0
0
1
0
1
0
0
2
0
1
0
2
1
0
0
1
2
2
0
0
2
0
0
0
0
2
0
0
2
0
1
1
0
0
0
2
0
0
2
0
1
4
1
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
5
0
0
1
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
1
2
0
2
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
2
0
0
0
3
1
0
0
1
2
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
2
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
3
0
0
0
1
2
1
1
0
0
2
0
0
1
4
0
0
0
0
2
1
0
1
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
1
0
0
0
0
0
1
2
0
2
0
0
2
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
3
1
1
0
1
0
0
0
0
0
1
0
1
0
1
2
0
1
0
0
0
2
0
1
0
2
0
2
1
0
2
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
3
1
2
0
0
0
0
0
1
1
0
2
2
3
0
0
2
2
0
0
2
2
0
0
0
4
3
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
1
0
1
0
0
0
2
0
0
3
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
1
0
2
0
0
0
0
2
0
1
2
1
1
2
0
0
3
0
2
0
0
1
0
0
0
0
3
1
0
0
1
0
0
2
1
0
0
0
0
3
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
2
1
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
2
1
2
1
2
0
0
0
1
0
0
2
0
2
1
1
0
0
0
0
2
2
0
2
0
0
0
1
2
2
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
1
2
0
1
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
3
3
0
0
0
0
0
1
0
0
0
2
0
0
0
1
2
0
1
0
2
1
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
3
2
0
0
0
0
0
0
0
2
0
0
1
2
2
2
0
0
3
0
0
1
0
1
0
0
1
2
1
0
0
1
4
2
0
0
2
0
2
0
0
0
1
0
0
0
1
3
1
2
0
0
0
0
0
2
0
0
1
1
0
0
2
2
1
0
0
2
0
1
0
0
0
1
0
2
0
2
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
2
0
0
0
1
2
0
0
0
2
0
1
2
0
0
0
1
2
2
0
0
0
2
2
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
2
0
4
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
1
1
0
0
1
0
0
1
0
5
0
0
0
0
2
0
1
0
0
0
0
3
0
0
0
0
1
1
0
4
0
0
3
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
1
2
2
0
1
0
2
0
0
0
0
2
0
0
0
2
0
2
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
1
0
0
0
0
0
0
0
2
2
1
2
2
0
1
0
1
2
0
2
0
2
0
2
0
2
0
0
1
0
1
1
1
2
1
1
0
0
0
0
1
0
1
0
2
0
1
0
3
0
0
0
2
1
0
0
1
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
6
1
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
1
2
0
1
0
0
0
2
0
3
1
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
1
2
1
0
0
1
0
1
2
1
4
0
0
2
1
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
1
0
0
3
0
0
0
1
2
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
2
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
1
2
1
2
0
0
2
0
0
0
1
1
0
0
0
0
0
0
2
0
2
0
1
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
1
1
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
3
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
3
2
0
0
1
1
0
1
0
0
0
1
0
1
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
4
1
1
0
1
2
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
2
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
6
0
0
0
0
0
0
2
0
0
0
0
1
2
1
1
0
2
0
2
2
0
0
0
1
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
1
0
1
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
2
1
2
1
0
1
0
0
2
3
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
3
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
1
2
1
0
2
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
1
0
0
0
2
2
0
0
0
0
0
0
2
3
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
2
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
3
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
3
0
1
0
0
0
0
0
2
0
1
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
4
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
4
0
0
0
0
0
0
0
2
0
0
2
0
0
6
2
0
3
1
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
1
0
2
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
1
0
0
3
0
0
0
1
0
0
0
0
0
0
1
0
2
2
2
2
0
1
0
0
0
2
0
0
0
3
0
0
1
1
0
0
0
1
3
0
0
2
0
0
0
0
1
0
0
0
0
2
1
0
1
0
0
0
0
0
1
0
0
0
0
1
2
2
0
0
0
0
0
1
0
2
0
1
3
1
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
1
0
2
3
2
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
2
0
0
0
2
0
0
2
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
1
0
1
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
2
0
0
0
1
0
2
0
0
2
1
0
0
3
0
0
0
1
0
0
2
1
0
1
1
0
0
0
1
0
0
0
2
1
1
2
0
0
1
0
1
0
1
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
2
0
1
1
0
1
0
0
0
2
0
3
2
0
0
0
1
1
0
0
0
0
1
1
0
0
1
1
0
0
0
0
2
1
4
0
0
0
0
1
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
1
3
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
2
0
1
2
1
2
0
2
1
0
0
0
0
3
0
0
0
0
1
2
1
0
1
2
2
0
0
1
2
1
2
1
0
0
2
2
2
0
2
1
0
2
0
0
0
0
1
0
0
2
0
0
1
0
1
2
0
0
1
1
0
0
0
0
1
0
0
2
0
0
2
0
2
0
0
0
2
0
0
0
2
0
0
2
1
1
1
0
0
0
0
0
1
0
2
0
1
0
1
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
1
2
1
0
0
0
0
1
0
1
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
2
0
2
1
0
0
0
0
0
0
0
0
2
3
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
1
2
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
2
2
1
1
2
1
0
0
1
0
2
1
1
0
0
0
1
0
0
0
0
0
1
0
1
0
2
0
0
0
2
5
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
1
0
0
2
2
1
0
2
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
2
3
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
2
0
0
2
2
2
0
0
0
2
2
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
1
0
2
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
2
0
0
0
0
0
0
1
2
2
0
0
0
1
0
0
2
0
0
0
0
1
1
0
1
0
1
3
0
0
0
0
0
2
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
1
1
0
2
1
0
0
0
0
0
0
2
1
0
0
0
0
0
2
2
0
1
0
2
0
0
0
1
1
2
2
0
0
0
0
0
0
1
2
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
2
3
0
0
0
2
0
0
0
0
0
2
1
2
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
4
2
2
0
0
0
0
2
0
1
0
1
0
0
3
1
0
2
2
0
0
0
0
0
1
1
0
0
0
1
0
0
0
4
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
3
0
0
0
0
1
1
0
0
2
2
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
2
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
2
7
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
1
0
2
0
0
2
1
0
0
1
0
0
0
0
0
0
1
0
1
0
4
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
1
0
1
1
0
0
0
0
0
0
3
0
0
2
0
0
1
1
3
0
0
0
2
0
2
0
1
2
3
0
0
0
0
0
1
1
2
1
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
1
2
2
2
0
0
0
0
0
2
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
2
0
0
1
4
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
4
0
1
2
0
0
0
0
0
0
2
0
2
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
2
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
2
0
2
1
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
2
1
0
0
1
1
0
2
0
0
0
0
0
3
1
0
0
1
2
0
0
3
2
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
1
0
0
3
0
0
1
0
0
2
0
0
0
0
2
0
0
0
2
1
0
0
2
1
2
0
0
0
0
0
0
1
0
0
0
0
3
1
0
0
1
2
0
0
2
0
0
1
0
2
0
0
0
2
2
0
0
0
0
0
1
0
0
1
2
0
1
2
1
3
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
3
0
0
2
0
0
0
2
2
0
0
1
1
1
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
1
2
0
2
0
3
0
0
0
0
0
0
0
0
3
1
0
0
0
1
0
2
0
0
0
0
0
1
2
1
0
0
0
0
2
0
1
1
0
0
0
0
0
2
0
1
2
0
0
1
0
0
0
1
1
2
1
2
0
1
0
4
0
1
1
1
0
0
2
0
1
0
0
0
0
2
0
0
0
0
2
0
1
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
1
0
2
1
1
1
0
1
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
1
0
0
2
0
0
2
1
0
0
0
0
1
0
0
0
2
0
2
0
2
2
1
2
1
0
0
0
0
0
2
1
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
3
2
1
0
0
0
0
0
2
0
1
0
1
0
0
0
2
2
0
0
0
0
1
0
2
1
0
0
0
2
0
1
1
0
0
2
0
2
0
0
2
0
1
0
0
0
2
2
1
1
0
1
0
0
2
1
0
1
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
2
0
1
0
0
0
0
1
1
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
2
0
1
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
3
1
0
1
0
1
0
0
0
0
0
0
2
0
1
0
1
3
1
0
1
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
2
0
0
0
0
2
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
2
1
0
0
2
0
1
0
1
0
1
0
0
0
2
0
1
2
0
0
2
0
2
0
0
0
1
0
0
4
2
2
0
0
0
0
1
0
0
1
0
0
0
8
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
1
0
0
0
2
0
0
1
0
0
0
1
1
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
1
2
1
0
1
0
0
1
0
3
0
0
0
0
0
2
0
1
0
0
1
2
0
2
0
0
1
0
2
0
1
0
0
0
0
0
0
2
1
0
0
2
1
0
0
2
0
0
0
2
1
2
0
2
0
3
0
1
0
0
0
0
1
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
2
1
2
0
1
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
1
1
0
2
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
1
1
2
0
0
2
0
1
0
0
2
0
0
2
0
0
0
0
0
0
2
0
1
0
1
1
0
3
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
1
2
0
0
2
0
2
0
2
2
1
1
0
0
0
2
1
1
1
1
0
1
0
1
0
2
0
2
1
0
2
1
0
2
2
1
0
4
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
1
0
0
0
2
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
3
1
2
1
1
0
2
1
0
0
0
0
1
0
0
0
0
4
0
1
1
0
0
0
3
0
0
0
0
0
0
0
2
0
0
2
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
1
2
0
1
0
0
2
0
1
0
2
1
0
2
0
0
1
1
0
0
0
0
3
0
0
0
0
1
0
1
0
1
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
2
1
2
0
0
0
0
1
0
1
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
1
1
0
4
2
0
1
0
0
3
0
0
1
1
2
1
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
2
2
0
2
0
0
2
0
0
0
0
2
0
2
0
0
2
0
0
0
2
0
2
0
0
2
1
0
0
0
0
0
1
0
0
2
0
2
0
0
0
1
0
0
0
0
0
6
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
3
0
2
0
2
2
0
0
0
0
0
0
0
1
2
1
2
0
0
1
0
0
0
2
0
2
0
2
0
1
1
0
2
2
0
2
1
0
2
1
0
3
2
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
1
1
2
1
0
0
0
2
1
1
0
0
0
2
2
1
0
0
1
0
0
0
0
0
0
4
3
0
0
0
0
0
0
1
0
1
0
1
0
0
2
2
0
0
1
0
2
2
0
2
0
0
1
1
3
0
0
1
0
0
0
0
4
0
0
2
0
1
2
1
2
0
1
0
0
0
0
0
3
2
0
0
0
1
1
2
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
1
1
0
2
1
1
0
0
0
0
1
0
1
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
7
1
0
2
0
0
0
0
0
0
0
1
2
0
1
0
0
4
0
0
0
0
0
0
1
2
0
1
2
0
0
0
1
2
3
0
2
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
2
2
2
0
0
0
0
2
1
0
0
1
0
0
1
0
0
1
2
0
0
0
0
2
1
2
0
0
2
2
0
0
0
1
0
1
0
2
0
0
0
0
2
0
0
0
2
0
2
0
0
0
1
0
0
0
1
0
1
0
0
5
0
1
0
4
1
0
0
2
0
0
0
0
2
3
0
0
0
0
0
0
2
0
0
0
4
0
1
0
0
2
0
3
1
0
0
0
1
0
0
0
4
2
0
0
1
0
0
0
0
1
1
0
0
0
1
0
2
1
1
1
1
2
1
0
2
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
3
3
0
1
0
0
0
0
0
2
0
1
0
0
2
0
0
0
1
0
0
0
1
0
2
2
1
0
2
2
0
0
2
1
3
0
0
1
3
2
2
1
0
0
1
0
1
0
0
0
0
0
2
0
3
1
1
0
0
1
0
2
0
1
1
0
2
0
0
2
0
1
0
0
2
1
0
0
0
1
0
0
0
1
1
0
0
1
0
2
0
1
2
1
2
0
1
1
0
0
0
0
1
0
0
0
0
1
1
0
0
1
1
0
0
0
0
2
2
3
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
2
2
1
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
2
0
0
2
0
1
0
0
1
2
0
0
0
0
1
0
2
1
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
3
0
1
1
0
2
1
1
0
0
0
2
1
0
2
0
0
4
3
2
0
0
2
0
1
0
2
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
1
2
0
0
0
0
2
3
0
0
0
0
0
3
0
1
0
0
0
0
2
0
0
1
0
3
0
0
1
1
2
2
2
1
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
1
0
5
0
1
0
0
0
0
1
2
2
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
2
0
0
1
1
1
7
1
0
1
0
0
1
2
2
0
3
0
2
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
1
2
1
0
0
3
1
2
2
2
0
0
0
1
1
0
2
1
0
0
2
2
1
2
1
1
0
0
0
1
0
0
0
0
0
0
2
0
0
1
2
0
1
1
0
0
2
2
2
3
1
0
1
0
2
1
0
2
0
1
0
0
1
0
0
1
1
0
2
2
0
1
0
0
0
3
0
2
0
3
2
0
0
3
0
0
0
4
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
1
0
1
1
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
2
0
3
2
0
1
1
2
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
1
0
0
0
0
2
2
0
0
1
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
2
0
0
1
0
0
2
0
2
0
0
1
0
0
0
0
0
2
1
3
0
0
1
2
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
2
0
2
0
2
0
1
0
0
0
0
0
0
0
2
1
0
0
1
0
0
2
0
0
0
4
1
0
0
0
2
0
0
0
0
0
2
0
0
0
1
1
1
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
3
0
0
0
1
1
1
0
0
2
2
0
2
0
0
1
0
0
0
1
1
0
0
0
2
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
2
2
2
1
0
0
0
0
9
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
1
2
1
0
0
0
0
0
0
0
0
1
2
2
1
2
0
0
0
1
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
3
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
4
2
0
0
0
1
1
0
0
0
1
2
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
1
3
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
4
0
1
2
2
0
1
0
0
2
0
0
2
0
0
2
2
0
1
1
0
1
2
1
0
1
0
2
1
0
0
0
2
2
1
0
0
3
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
2
0
0
0
0
1
0
0
0
1
0
0
1
2
0
0
2
1
1
0
0
0
0
0
1
0
0
0
2
2
0
2
0
0
0
0
0
0
2
1
1
1
0
2
1
1
2
0
3
1
0
1
0
1
1
0
0
0
0
0
5
1
0
1
0
0
0
0
2
0
0
0
1
2
0
0
0
0
2
1
0
1
0
0
0
0
0
0
2
0
1
0
0
3
0
2
0
3
0
0
0
1
1
0
0
1
0
0
0
1
0
2
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
2
2
0
1
2
0
0
0
0
3
0
2
2
5
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
1
2
0
2
0
0
2
0
2
2
3
0
0
2
0
0
0
2
1
0
0
2
0
0
0
1
1
0
1
1
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
1
0
0
2
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
2
2
1
0
0
0
1
0
0
2
0
0
3
0
0
2
0
0
1
0
0
2
0
4
2
0
0
0
0
3
2
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
2
0
0
0
0
2
0
0
0
0
1
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
1
0
1
1
0
3
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
2
0
0
1
2
0
2
0
0
0
0
0
1
2
0
0
1
0
0
0
0
1
2
0
0
2
2
0
0
0
1
0
2
0
0
1
0
0
1
0
4
1
0
0
0
3
1
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
2
1
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
1
3
0
0
0
0
0
0
1
0
0
0
2
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
2
2
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
1
0
3
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
3
2
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
2
0
0
0
2
0
0
0
3
0
0
2
0
3
0
0
2
0
0
1
3
0
4
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
1
2
2
1
3
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
2
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
1
3
0
0
0
2
0
0
0
0
0
2
0
0
1
1
2
1
0
1
0
0
0
0
2
2
1
0
0
2
0
2
2
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
1
0
0
0
1
2
0
0
2
1
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
1
0
2
0
3
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
2
0
0
0
7
0
0
0
0
0
1
2
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
1
1
0
0
1
0
0
2
0
0
2
3
0
0
1
0
0
3
0
8
2
0
0
0
1
3
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
1
2
0
1
1
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
1
2
2
0
0
0
0
2
0
0
1
2
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
3
0
0
0
1
0
1
2
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
3
3
2
0
1
0
1
0
0
0
2
0
0
0
2
0
1
0
2
1
2
0
0
0
0
0
2
0
2
2
0
0
0
1
0
0
0
0
0
0
4
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
3
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
1
1
0
0
0
0
0
1
0
7
0
0
0
0
0
0
0
1
1
0
1
0
1
1
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
2
0
0
0
0
0
1
0
0
2
2
2
0
0
0
0
0
0
0
0
6
0
0
0
1
0
0
0
0
2
3
0
0
0
0
2
1
2
0
1
0
0
0
0
2
0
0
0
0
0
2
2
1
1
0
2
0
0
1
0
1
0
1
0
0
0
1
1
0
2
0
1
0
0
1
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
2
0
1
0
2
3
0
0
0
0
2
3
0
0
0
1
1
0
0
0
0
0
0
0
2
2
0
2
2
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
2
0
0
2
0
0
2
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
1
4
3
0
0
0
0
1
1
1
2
0
0
0
0
1
2
0
1
0
1
0
0
0
3
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
2
3
1
1
0
0
0
2
3
1
3
0
0
0
0
0
1
0
0
0
2
0
0
2
0
1
2
2
2
0
1
0
0
0
1
0
0
3
0
2
0
0
0
0
0
2
0
0
2
0
2
0
0
0
1
4
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
1
1
0
0
0
2
1
0
1
1
0
0
1
0
0
0
0
1
0
0
2
0
0
0
2
2
0
0
0
0
2
2
0
0
0
2
3
0
2
1
0
1
1
0
2
0
0
0
0
2
0
0
0
0
1
0
0
1
2
0
1
0
0
1
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
2
0
2
1
2
2
0
2
2
0
0
0
0
0
0
0
1
0
2
1
0
0
1
2
2
3
1
7
0
0
0
0
0
2
3
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
2
0
2
0
0
1
2
0
0
0
0
1
0
1
0
2
2
0
0
2
0
0
0
0
0
0
0
0
2
0
1
1
1
0
2
0
0
0
0
2
0
0
1
1
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
2
2
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
1
1
1
2
1
1
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
4
2
0
0
0
0
2
2
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
3
1
1
0
0
0
2
2
3
3
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
1
2
0
0
1
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
1
3
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
4
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
1
4
0
0
1
0
0
0
2
1
2
0
0
1
0
0
2
0
0
1
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
2
0
3
1
1
0
3
2
0
0
1
0
3
1
2
2
0
0
0
0
1
0
0
1
0
2
0
0
1
0
0
0
0
0
2
1
1
0
0
1
1
0
0
0
0
3
2
2
0
0
2
2
1
0
2
1
0
3
0
0
2
1
0
2
1
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
2
0
1
2
1
0
0
2
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
2
1
0
0
1
0
0
0
2
0
0
0
1
0
0
0
2
1
2
0
0
0
2
0
2
0
0
1
0
1
0
0
1
1
2
0
1
0
1
0
1
0
2
2
2
0
0
0
1
0
0
1
0
2
0
1
0
0
1
2
0
1
1
0
0
0
1
0
0
1
2
0
0
0
2
0
0
0
0
0
1
0
2
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
1
0
0
0
2
0
1
1
1
0
0
0
0
0
0
1
0
0
2
0
1
0
2
0
0
1
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
1
0
0
0
0
0
2
1
2
0
0
0
0
0
1
2
1
1
2
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
2
2
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
3
4
0
0
0
2
0
0
4
0
2
0
0
0
0
1
2
1
0
1
0
0
0
0
0
0
0
0
2
0
0
1
1
2
0
0
0
2
0
0
1
0
0
0
0
0
0
2
2
1
0
1
0
1
0
1
0
1
2
0
0
1
0
2
1
9
1
0
0
0
1
0
3
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
2
1
0
1
1
1
2
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
1
2
0
1
2
1
0
1
0
2
1
0
2
1
3
0
0
0
0
2
0
0
0
0
2
0
2
0
0
2
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
2
1
2
0
0
0
0
0
0
2
0
1
0
2
0
0
2
0
0
1
1
0
0
1
1
0
0
3
5
0
0
0
0
0
1
0
0
0
0
0
1
0
2
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
5
2
1
2
0
0
0
1
0
1
0
2
0
2
2
2
2
2
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
1
2
2
0
0
0
0
0
0
0
2
1
1
0
0
2
0
0
0
0
1
0
1
2
4
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
2
0
2
1
0
0
2
4
0
0
0
0
1
1
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
7
2
0
1
3
1
0
0
0
0
2
1
1
0
1
0
1
0
0
0
0
0
2
0
1
2
0
0
0
1
0
1
0
2
1
0
1
0
1
2
0
2
0
0
1
2
2
0
1
0
2
0
0
0
0
2
1
1
0
0
1
0
0
0
0
0
0
0
0
2
0
2
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
4
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
2
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
1
0
1
5
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
1
2
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
2
0
2
0
0
0
1
0
0
0
0
0
0
1
0
1
1
2
2
0
1
0
1
0
2
0
1
0
0
0
3
0
0
3
0
0
0
0
1
0
0
2
0
0
1
0
0
1
1
1
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
1
0
1
4
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
2
0
0
2
0
3
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
1
2
0
0
0
0
1
0
0
6
0
0
0
2
1
0
2
2
0
0
1
1
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
1
0
1
0
1
2
0
2
0
0
3
0
0
0
0
0
0
1
3
0
0
0
1
0
1
1
1
0
2
1
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
3
0
0
0
1
2
1
0
0
2
2
0
1
1
0
0
2
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
18
0
2
0
0
2
0
2
0
0
0
0
1
2
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
1
0
1
0
0
2
0
1
1
0
0
0
0
1
0
1
0
2
1
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
1
2
2
2
0
1
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
2
0
0
0
0
1
0
1
2
2
1
1
2
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
1
2
3
0
0
1
0
0
0
2
1
2
0
1
0
0
0
0
0
0
2
0
0
0
2
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
1
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
1
0
1
0
1
0
0
2
0
2
0
0
1
0
3
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
2
1
0
2
0
0
0
0
0
0
0
5
0
0
1
1
1
0
1
0
1
0
1
0
0
0
0
1
0
1
0
2
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
2
2
0
1
1
1
1
0
2
2
0
0
0
0
0
2
0
0
0
0
0
2
1
1
0
2
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
2
2
0
2
2
2
0
0
0
2
0
0
0
0
0
1
3
0
2
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
1
0
0
1
0
2
1
1
5
1
0
0
0
0
1
0
1
4
0
0
0
0
2
0
4
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
1
0
0
0
0
1
0
0
0
2
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
2
2
4
3
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
3
2
2
0
2
1
2
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
1
2
0
0
0
0
2
0
1
0
3
1
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
3
1
0
0
0
0
1
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
2
2
0
1
0
1
1
1
1
0
0
0
0
0
0
3
0
2
1
0
2
1
0
2
2
2
0
0
0
0
0
0
0
0
0
1
0
1
2
0
2
0
0
2
0
1
0
0
0
0
0
1
0
1
0
2
0
0
1
2
3
2
2
0
1
0
0
1
0
0
1
0
2
0
0
1
6
0
0
0
3
2
0
0
0
0
0
0
1
2
0
0
0
0
2
0
1
0
0
2
0
1
0
2
0
2
1
0
0
0
0
0
0
0
1
1
1
2
0
0
0
2
0
2
0
0
0
0
2
0
0
1
0
0
1
2
2
1
0
0
2
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
2
0
0
2
0
0
1
0
0
0
0
0
0
4
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
2
2
1
0
0
0
0
2
0
2
0
0
0
2
2
0
0
2
2
0
0
3
0
0
1
3
2
0
0
0
0
2
2
0
0
0
2
0
1
3
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
2
0
0
2
0
3
0
0
2
1
0
0
0
0
0
1
0
0
3
0
2
1
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
2
1
1
0
1
0
0
1
1
0
0
0
1
0
2
0
0
0
1
0
0
1
0
0
2
0
1
0
2
1
1
1
1
0
2
1
0
0
1
0
0
0
0
0
2
0
0
0
0
2
2
1
1
0
1
1
0
0
2
0
1
0
0
1
0
1
0
0
0
0
1
0
0
3
0
0
0
2
0
0
2
1
0
0
0
1
2
0
0
0
2
0
2
1
2
0
0
0
0
2
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
1
0
0
1
0
2
0
3
0
2
1
2
0
0
1
2
0
0
0
0
0
0
2
0
2
2
2
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
5
0
0
0
0
0
2
1
1
0
0
0
1
0
2
0
0
0
0
1
2
0
0
0
2
0
2
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
5
0
0
0
1
0
0
0
0
0
1
0
0
0
3
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
2
0
1
0
0
1
0
0
0
0
0
4
0
1
1
0
0
0
1
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
2
0
1
2
0
2
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
1
2
0
0
1
0
0
0
1
0
2
1
0
0
1
1
0
0
1
0
2
0
0
2
0
1
0
0
6
2
0
1
1
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
3
0
0
0
1
2
0
1
2
0
0
0
3
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
3
1
1
2
2
0
2
2
0
1
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
1
0
0
3
1
1
0
0
0
0
0
0
0
0
0
2
2
3
0
0
1
0
0
0
0
1
1
0
0
1
0
0
2
0
0
2
2
0
0
0
0
1
0
0
2
0
2
0
0
0
0
1
2
0
0
3
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
2
0
0
0
1
0
1
0
3
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
3
0
0
5
1
0
2
0
0
0
0
1
0
2
0
0
1
0
0
2
0
0
0
2
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
2
2
2
2
1
0
0
0
0
1
0
0
1
0
0
2
1
0
0
0
1
0
0
1
0
0
3
2
3
0
2
1
1
0
0
0
2
2
1
0
1
0
0
0
0
2
1
0
2
1
0
0
0
0
4
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
2
1
3
0
2
0
2
3
2
2
0
0
0
0
1
0
0
1
0
2
2
0
0
0
2
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
2
0
2
0
0
1
0
0
0
1
1
0
0
0
3
1
0
0
0
2
0
0
0
0
0
0
0
0
2
1
2
2
0
0
0
2
0
0
2
0
0
0
0
2
0
1
1
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
2
0
2
0
1
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
2
0
0
2
0
0
2
1
1
0
1
0
0
2
2
0
1
0
0
0
0
0
0
2
0
2
0
0
3
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
2
0
0
0
2
0
2
2
0
0
0
2
2
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
3
0
0
1
2
0
1
1
0
1
0
0
0
1
2
0
1
1
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
2
2
0
3
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
1
2
0
0
0
0
1
0
2
0
1
0
2
0
1
0
0
0
0
0
0
0
1
1
0
2
2
2
2
0
2
0
0
1
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
1
0
0
1
0
0
0
0
2
0
0
0
1
0
2
2
1
0
0
2
0
0
2
0
2
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
2
2
0
0
1
0
0
1
0
1
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
1
0
0
2
0
1
0
0
2
0
2
0
0
0
0
0
0
1
1
0
0
1
0
3
1
0
1
1
0
0
0
2
0
0
3
1
0
1
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
3
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
3
1
0
0
0
3
0
2
0
1
1
0
1
0
0
0
0
0
3
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
4
0
1
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
3
0
2
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
1
0
0
1
1
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
2
0
0
4
0
1
0
0
0
0
0
0
0
2
0
1
0
0
1
2
0
2
1
2
0
1
0
2
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
1
0
2
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
1
2
2
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
1
1
0
2
2
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
2
1
0
2
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
2
0
0
2
1
2
0
0
0
0
2
1
1
3
0
0
1
2
0
0
2
0
0
2
0
2
0
0
0
0
0
1
0
0
1
0
2
2
0
2
0
3
0
0
2
0
1
0
0
0
0
2
0
0
0
2
0
4
2
0
2
0
0
0
2
0
0
0
2
2
0
2
0
0
0
2
0
1
2
1
0
0
0
0
1
1
0
0
0
0
0
2
0
1
1
0
0
0
0
0
1
0
0
1
0
0
3
0
0
2
0
0
1
0
2
0
0
0
0
0
1
3
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
2
2
0
0
0
0
0
1
2
2
0
0
2
2
0
0
2
0
0
0
2
1
0
1
1
0
0
0
1
0
1
0
0
1
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
1
1
1
0
2
0
2
2
0
1
0
0
0
2
0
1
0
0
0
0
2
0
1
2
2
0
0
0
0
4
0
0
2
0
0
0
0
1
0
2
0
0
0
1
0
0
1
0
0
0
1
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
2
0
2
2
0
1
0
2
0
2
1
2
2
1
1
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
4
0
0
2
3
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
2
2
1
0
2
0
0
0
0
0
1
1
2
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
1
1
2
0
0
1
0
2
0
0
0
3
0
0
0
5
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
1
0
0
0
0
2
0
1
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
2
0
0
2
0
4
2
0
2
0
0
0
0
3
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
1
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
2
0
0
0
2
2
2
0
2
0
0
1
1
1
0
1
2
0
0
2
0
0
0
2
2
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
2
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
1
2
2
2
0
0
0
1
0
3
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
1
2
1
0
1
1
0
0
2
2
1
0
0
0
0
2
0
1
0
0
1
0
0
0
2
0
0
0
1
0
0
2
0
2
0
0
0
2
0
0
0
0
0
2
0
1
0
1
1
1
1
0
0
1
0
0
0
0
1
1
2
0
2
0
2
1
0
2
0
0
2
0
1
0
0
0
1
0
1
0
0
0
1
1
1
1
0
0
0
0
1
2
1
0
0
0
3
2
0
0
0
1
2
0
1
1
0
0
0
0
0
2
0
0
0
0
0
2
1
1
2
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
2
1
0
1
0
0
1
0
1
0
0
0
1
1
2
0
2
2
0
2
1
0
2
2
2
0
0
0
0
0
0
0
2
0
0
0
2
1
3
1
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
1
0
0
0
0
2
0
0
0
0
1
1
0
1
0
1
0
0
0
2
0
0
0
3
0
0
0
1
0
1
1
0
2
0
0
1
2
0
0
0
1
2
2
0
2
0
1
1
1
0
2
2
0
0
0
0
0
0
0
0
3
0
0
0
0
1
2
0
1
0
0
0
3
1
1
2
0
1
2
1
2
0
0
0
0
0
2
0
1
0
1
0
0
0
0
1
0
4
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
1
1
0
0
0
1
0
0
2
0
3
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
2
1
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
4
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
2
0
1
2
0
2
0
3
0
0
0
0
0
0
0
1
0
3
0
0
0
2
0
0
2
0
1
0
0
0
0
2
2
0
0
0
0
1
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
2
1
2
0
0
0
0
1
4
2
1
0
1
0
0
1
0
1
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
2
1
0
1
1
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
1
1
0
1
0
2
0
0
0
1
0
1
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
1
0
1
2
0
0
2
0
0
0
1
0
0
0
0
0
1
0
1
0
2
1
0
0
0
2
0
2
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
2
1
0
5
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
1
1
1
2
0
0
0
0
0
0
0
1
0
0
1
2
1
0
3
1
0
2
0
3
0
0
2
0
0
0
4
0
0
0
0
2
1
0
1
1
0
1
1
2
0
0
0
1
0
2
0
0
0
0
0
1
0
0
2
1
0
1
0
2
1
2
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
1
2
1
1
2
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
3
0
1
0
0
1
0
0
0
6
0
0
0
1
2
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
7
0
0
0
0
0
0
2
0
0
0
2
2
0
1
0
0
0
0
3
1
2
0
0
0
0
0
0
2
2
2
0
1
0
0
1
0
1
1
0
1
0
0
0
3
2
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
1
2
2
1
2
1
1
2
0
1
0
0
0
2
0
0
1
0
0
0
6
0
0
1
0
1
1
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
2
2
2
1
1
1
4
0
0
0
0
0
0
0
0
0
1
1
0
1
0
2
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
4
2
2
0
0
0
0
0
1
1
1
2
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
8
0
2
0
0
0
0
0
0
2
0
6
0
0
0
0
1
1
0
0
0
0
0
0
1
1
1
0
1
1
0
2
0
1
2
0
2
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
4
1
0
0
2
0
1
0
1
0
0
5
1
2
0
0
0
0
0
1
0
2
0
2
0
0
1
0
0
3
2
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
3
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
1
0
1
0
13
1
0
1
0
2
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
4
0
2
0
0
3
0
1
1
1
0
0
0
0
2
2
0
1
3
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
2
0
0
1
0
0
2
0
0
1
0
0
1
0
7
1
0
1
0
0
0
2
0
1
1
0
2
0
1
1
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
2
0
1
0
0
0
2
0
2
0
0
0
0
2
0
2
0
0
0
0
1
0
2
2
1
0
2
0
1
0
1
0
0
1
0
0
0
0
2
0
0
1
5
1
0
0
2
1
0
2
0
0
0
0
1
2
0
1
0
2
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
1
1
2
2
0
3
0
0
2
0
1
0
3
0
0
0
0
0
0
0
0
2
1
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
1
0
0
0
2
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
2
0
0
0
3
0
0
2
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
1
1
0
0
0
0
0
0
0
3
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
4
0
0
0
2
2
0
0
0
2
0
0
2
2
0
0
1
0
0
0
0
0
0
0
1
1
2
0
2
0
1
0
0
2
0
0
2
0
0
0
0
2
1
0
0
7
0
0
0
2
0
0
2
0
0
0
0
0
2
1
2
0
0
1
0
0
0
0
0
1
1
0
2
2
0
1
0
0
0
0
2
2
0
1
0
0
1
2
0
2
0
2
2
0
2
2
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
3
1
0
0
0
0
2
0
3
0
0
2
0
0
0
0
1
0
2
1
0
0
2
0
2
0
0
0
3
0
1
0
0
0
0
0
0
1
2
1
0
0
0
0
0
2
2
1
2
1
0
0
0
2
2
0
0
2
2
0
0
0
2
0
0
0
2
0
0
1
1
2
0
0
0
0
1
0
1
1
0
1
0
1
0
0
0
2
0
0
0
4
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
1
0
0
0
0
1
0
2
0
1
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
2
0
1
2
0
2
1
0
0
0
0
2
0
0
0
1
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
1
1
0
0
0
0
0
3
0
0
0
0
2
2
0
2
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
2
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
1
0
0
1
2
2
1
0
0
0
0
0
1
1
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
1
0
0
2
0
1
0
0
0
0
2
0
0
0
2
0
2
1
2
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
1
0
3
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
15
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
2
2
1
2
0
2
0
3
0
0
0
0
2
1
0
2
2
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
3
2
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
1
1
2
0
0
1
0
0
0
0
0
3
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
1
3
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
6
0
0
0
0
0
3
0
2
2
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
2
1
2
1
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
1
0
1
1
2
2
0
0
2
0
0
1
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
1
2
1
0
0
0
0
2
0
0
0
2
1
0
0
0
0
1
0
0
0
2
0
0
1
4
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
1
0
0
1
2
0
0
0
1
0
0
0
1
1
2
0
2
3
1
0
0
0
0
4
0
0
1
0
0
0
1
2
0
0
0
1
0
0
1
0
2
0
0
2
0
0
0
0
0
2
1
1
1
0
0
3
1
0
2
0
0
0
0
0
0
0
3
2
1
0
2
0
0
0
0
0
4
0
2
0
1
0
2
0
0
3
2
0
0
2
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
2
2
0
0
1
2
0
1
2
0
2
2
1
0
0
2
0
1
0
0
0
1
0
1
1
0
1
0
0
2
0
0
0
0
0
2
0
3
2
1
4
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
2
2
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
3
3
0
0
0
0
0
0
0
0
0
0
3
1
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
2
0
0
0
0
0
0
2
2
0
0
0
0
2
0
2
0
0
2
0
0
0
3
0
0
1
0
2
0
2
0
3
0
2
0
2
0
0
0
0
2
0
2
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
2
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
1
3
0
0
2
2
1
0
2
0
1
0
0
3
0
2
2
0
0
0
1
0
0
0
2
0
0
2
2
0
1
0
0
4
0
0
1
1
0
1
0
0
0
0
0
2
0
0
1
1
2
0
0
0
0
3
0
2
4
0
0
0
0
0
1
0
0
0
2
2
1
1
0
0
0
0
0
0
2
2
0
1
2
0
0
0
0
0
0
1
0
0
1
0
2
0
2
0
1
2
0
0
0
0
0
1
0
2
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
2
2
0
0
1
2
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
3
0
0
2
0
0
4
2
0
0
0
2
0
1
0
0
0
2
3
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
2
0
2
0
1
0
1
3
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
1
1
1
2
1
0
2
0
2
1
0
0
0
1
1
0
0
0
0
1
2
0
0
0
0
0
2
0
1
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
2
1
0
0
1
0
0
2
0
2
3
0
4
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
2
2
0
1
0
0
2
0
0
2
0
0
2
0
4
0
1
0
1
0
0
0
0
2
0
0
0
2
1
1
0
0
1
0
2
1
2
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
1
1
0
0
0
3
1
3
1
0
2
0
2
2
2
2
2
1
0
1
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
3
0
0
0
0
0
0
0
2
2
0
0
0
0
0
4
0
0
0
1
0
0
0
1
2
0
0
1
0
2
0
0
0
0
1
0
0
0
1
0
0
0
1
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
2
2
0
2
1
1
2
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
1
0
2
0
4
0
0
0
5
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
1
0
1
2
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
3
3
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
1
0
0
3
1
0
0
0
0
0
0
3
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
1
0
0
0
0
1
0
1
0
2
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
2
0
2
0
1
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
1
0
0
0
2
1
0
0
0
4
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
1
3
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
3
0
3
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
6
0
2
0
0
2
0
0
0
0
0
2
0
0
0
2
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
1
2
1
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
1
1
0
0
2
2
0
2
0
0
2
3
1
0
2
1
0
3
1
0
0
0
0
0
0
2
2
0
0
0
2
0
0
1
0
2
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
2
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
2
4
0
0
0
0
0
0
1
1
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
1
0
2
2
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
1
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
1
1
0
0
2
1
0
0
1
0
0
0
0
2
1
0
0
0
0
1
0
0
0
1
2
2
0
1
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
3
2
0
0
2
0
0
1
0
1
0
0
1
0
0
1
1
1
1
0
0
2
2
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
1
2
2
3
0
0
1
1
1
2
0
0
0
1
0
1
2
1
0
0
0
2
2
0
0
2
0
0
1
0
0
0
0
1
0
1
2
1
2
1
1
1
0
0
2
2
1
0
0
0
0
1
0
4
2
0
0
0
2
0
1
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
2
0
2
0
0
0
3
0
0
1
2
1
1
0
1
0
0
2
0
1
0
1
0
0
1
5
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
1
2
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
2
0
0
0
1
2
0
1
0
3
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
4
1
1
0
0
0
0
0
0
0
1
1
0
0
0
3
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
2
0
2
0
0
1
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
1
0
0
2
0
0
2
1
2
2
2
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
2
0
0
0
3
0
2
2
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
2
0
0
2
3
0
2
0
0
0
0
1
0
3
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
2
0
0
0
0
0
1
2
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
1
1
0
2
0
0
0
0
0
0
0
2
0
0
2
2
1
0
2
0
0
2
4
1
2
0
2
0
0
2
0
0
0
0
0
0
0
2
0
1
1
2
1
0
2
0
0
0
2
0
2
0
1
1
0
0
0
1
2
2
0
0
1
2
0
0
0
0
1
2
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
3
0
0
2
1
0
0
0
1
0
0
2
0
0
0
2
1
1
0
2
2
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
2
2
0
0
0
0
0
0
1
2
1
0
1
2
1
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
1
6
0
0
2
0
2
0
1
1
0
0
0
0
0
0
2
1
0
2
2
0
0
2
0
0
1
0
0
0
2
0
0
0
0
1
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
1
0
1
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
1
0
0
0
0
2
0
0
0
0
1
2
0
0
0
1
0
2
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
2
0
3
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
1
0
0
2
0
0
0
2
3
2
3
0
0
0
2
0
1
0
0
2
0
0
0
0
1
0
0
0
0
2
1
2
0
0
0
0
0
2
0
2
1
0
2
0
2
0
0
0
0
2
0
0
0
1
0
2
2
0
1
1
2
0
2
0
3
0
0
0
3
0
0
1
0
2
2
0
1
2
0
1
3
0
0
0
0
0
0
1
2
2
0
0
1
0
2
0
0
0
0
0
2
0
0
0
2
2
2
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
4
0
0
0
0
0
0
0
1
0
0
0
1
0
1
3
0
2
0
2
2
0
0
2
0
0
0
0
0
0
3
2
1
1
0
0
0
0
0
2
0
1
0
3
0
0
0
0
0
0
2
0
0
0
1
2
0
0
1
2
0
0
1
2
0
2
0
2
0
2
0
2
1
0
0
0
0
0
0
2
2
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
1
0
0
0
1
0
0
1
0
0
0
0
2
0
0
2
2
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
1
0
5
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
1
1
2
0
0
1
0
2
0
1
3
2
2
0
0
2
0
0
1
0
1
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
2
1
0
1
2
0
2
0
1
0
2
1
0
0
2
0
0
1
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
1
0
0
2
0
0
0
1
2
2
2
0
0
0
1
0
0
0
0
1
2
1
2
0
0
1
0
0
0
0
2
0
1
2
0
0
2
2
0
0
0
1
0
0
2
1
0
0
2
1
2
0
0
0
0
0
1
1
2
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
1
5
0
1
1
1
0
1
2
1
2
0
0
0
2
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
2
2
0
0
1
0
2
0
0
0
0
1
1
1
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
1
0
1
1
0
0
0
0
2
0
0
0
0
1
2
0
0
2
1
1
2
2
1
0
0
1
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
2
0
0
0
0
0
1
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
1
1
1
0
0
0
2
0
0
2
1
0
0
1
0
1
4
2
0
0
0
0
0
0
6
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
3
7
0
1
1
0
1
0
0
0
2
0
0
0
0
0
1
0
2
0
1
0
0
1
0
2
1
0
0
0
0
0
0
0
2
0
2
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
5
1
0
1
0
0
0
3
0
0
2
0
0
0
0
2
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
2
0
1
0
2
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
3
0
1
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
2
3
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
3
0
2
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
2
2
0
0
2
0
0
9
0
0
0
0
7
0
0
0
3
0
1
2
0
2
1
0
0
0
0
2
0
0
0
0
0
0
2
1
1
0
0
0
0
2
1
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
4
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
7
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
2
1
0
0
1
1
1
0
2
0
1
2
2
1
2
0
0
1
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
2
0
2
0
2
2
1
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
5
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
1
1
1
0
0
0
0
0
0
0
0
0
3
1
0
1
0
1
1
0
0
5
1
0
1
0
0
3
0
0
0
0
0
0
0
0
1
0
1
0
1
2
0
1
2
0
0
1
1
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
2
0
0
3
0
0
0
1
1
0
0
0
1
0
0
0
3
0
2
0
0
0
4
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
2
0
0
1
0
2
1
0
0
0
0
0
0
1
0
0
2
2
2
0
0
0
0
1
0
0
2
0
0
0
13
0
3
1
0
1
2
0
0
0
0
0
0
0
1
0
2
3
0
1
0
0
0
2
0
0
0
0
0
3
0
0
1
0
0
0
0
1
0
0
0
0
0
4
1
2
0
0
0
0
2
4
0
0
0
0
0
4
0
0
0
0
1
1
0
1
0
0
1
2
0
0
0
2
1
0
0
3
1
0
0
0
0
4
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
2
2
0
0
0
0
0
0
0
0
0
3
0
2
1
2
0
0
0
0
0
0
0
2
2
0
0
1
0
1
0
0
1
0
1
0
0
3
0
2
3
0
0
0
0
2
4
0
0
0
1
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
2
1
0
0
1
2
0
2
1
0
2
1
0
2
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
2
0
2
1
0
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
2
1
1
0
1
0
0
2
2
3
0
2
2
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
1
1
2
1
0
0
2
2
0
1
0
0
0
1
0
2
1
1
0
1
3
0
0
0
0
0
3
0
0
1
0
4
0
2
1
2
0
3
0
2
0
3
2
1
0
0
0
0
0
1
1
0
2
0
0
1
1
0
0
0
0
0
2
0
0
1
0
0
0
0
1
1
2
1
0
0
0
0
0
0
0
2
0
0
0
2
1
1
3
0
2
0
0
0
1
0
0
0
0
1
2
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
1
1
0
0
2
3
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
1
0
1
1
0
0
2
1
0
0
1
0
2
0
1
1
2
0
0
0
1
0
2
0
0
0
2
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
2
0
0
0
0
0
0
0
2
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
2
1
0
2
2
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
2
2
0
2
1
2
0
2
0
0
0
0
2
0
2
0
1
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
2
2
0
0
1
2
0
0
1
0
1
0
0
0
2
0
2
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
2
0
3
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
1
1
2
1
2
0
1
0
5
1
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
2
0
1
0
0
1
0
0
0
2
1
2
0
1
2
0
0
1
0
0
0
0
2
0
1
0
0
4
0
0
0
1
3
0
2
2
3
0
1
2
0
0
2
0
0
0
2
1
0
0
0
0
0
1
0
2
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
1
0
0
1
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
3
2
0
2
0
0
0
0
2
0
2
1
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
1
0
0
0
2
0
0
1
0
1
0
0
0
2
0
0
0
0
1
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
2
0
1
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
1
2
0
0
2
2
0
2
1
0
0
0
0
1
0
0
2
0
0
0
5
0
0
0
2
0
3
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
1
0
2
0
0
0
1
1
0
1
0
3
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
3
0
0
4
1
0
0
0
0
2
0
0
0
1
0
0
0
0
4
0
2
2
1
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
1
2
2
0
0
1
0
2
0
0
0
5
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
2
1
2
2
1
0
0
0
1
0
2
0
1
2
0
2
3
1
2
0
0
0
1
0
0
0
0
1
0
2
0
0
0
2
0
1
2
0
1
0
0
6
0
1
1
1
0
0
0
0
0
2
0
0
0
0
0
1
1
2
0
1
0
1
0
0
0
0
0
2
0
0
2
2
0
2
0
0
2
0
0
0
0
1
1
0
2
2
0
1
0
2
0
0
0
2
0
0
0
0
0
0
2
1
0
0
2
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
2
0
0
3
0
0
0
0
0
1
0
0
0
0
2
0
0
2
2
1
0
0
0
1
6
0
0
0
1
0
2
2
0
0
0
0
0
1
0
0
1
0
0
1
0
2
0
2
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
1
1
2
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
2
2
0
1
0
0
0
4
1
0
1
0
2
1
1
1
0
0
0
0
1
0
0
0
2
0
1
0
2
1
0
0
0
0
2
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
2
0
2
0
1
0
0
2
0
0
0
0
2
0
0
3
2
0
0
2
1
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
1
0
2
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
2
0
0
0
2
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
2
1
1
1
1
1
0
0
0
1
0
1
0
0
0
2
1
0
2
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
1
0
0
1
1
0
0
2
0
0
0
1
1
3
0
0
2
0
0
1
0
0
0
3
2
0
0
0
2
0
0
0
0
0
0
2
1
1
2
2
0
2
0
0
0
0
1
2
1
0
0
0
0
0
0
4
0
0
0
1
0
1
0
2
1
0
2
0
0
1
0
0
2
0
1
0
1
1
0
0
0
2
0
0
0
0
2
0
0
0
0
2
1
0
0
0
2
1
0
0
1
2
1
0
2
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
2
0
1
0
0
0
0
2
1
1
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
4
0
0
1
0
3
4
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
3
0
0
0
2
1
1
0
0
0
0
0
3
1
2
1
0
1
1
1
0
0
0
0
1
2
0
1
0
0
1
1
1
2
0
0
2
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
4
0
0
0
2
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
3
0
1
0
0
0
1
0
0
1
0
0
0
0
0
2
0
2
2
0
2
0
0
2
1
0
2
1
0
4
0
0
0
1
0
0
1
1
2
0
2
0
1
2
0
0
0
0
0
0
0
0
2
2
2
2
2
0
0
0
0
1
0
0
1
0
3
1
2
0
0
1
0
0
0
2
3
2
0
2
1
1
0
0
0
1
1
0
0
0
0
0
1
0
3
0
2
0
0
0
0
1
0
1
0
2
0
2
1
0
0
0
1
1
4
0
2
2
0
0
1
0
2
0
2
0
1
1
1
0
0
0
2
2
0
0
0
0
0
0
2
0
2
1
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
1
7
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
1
2
0
0
1
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
3
0
1
1
0
0
0
2
0
0
0
3
2
0
0
0
0
2
0
1
0
0
0
2
0
0
3
0
0
0
0
0
0
0
1
0
1
1
0
2
1
2
0
0
0
0
1
2
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
1
0
0
0
2
1
0
0
2
2
0
0
0
0
1
0
2
0
6
0
0
0
1
0
0
0
1
1
1
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
2
2
0
2
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
2
2
0
2
0
0
0
0
0
0
0
1
2
0
1
0
0
1
0
2
0
0
0
0
2
0
0
1
2
1
0
0
1
1
0
0
0
0
2
0
1
0
1
2
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
1
2
0
4
2
2
0
0
0
0
0
0
0
0
1
1
1
2
0
1
1
0
2
0
2
0
2
0
0
0
0
2
0
2
1
1
0
0
0
0
0
0
2
2
0
2
0
0
0
2
0
0
0
0
2
0
3
0
0
1
0
1
0
0
2
0
0
2
3
0
1
0
0
0
0
1
0
2
0
2
0
0
0
0
2
0
0
0
1
2
0
1
1
0
0
1
0
1
1
0
1
2
0
7
0
2
1
0
0
2
0
0
0
0
0
0
0
1
1
0
1
2
0
0
0
0
1
1
0
2
0
0
0
0
2
2
0
2
1
1
0
1
0
0
3
1
0
0
0
2
0
2
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
2
0
0
0
0
1
2
0
0
0
1
0
0
0
0
2
0
2
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
1
1
0
0
0
0
1
1
0
0
0
0
0
1
2
2
1
2
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
2
1
0
0
2
0
2
0
2
1
0
1
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
1
3
0
0
0
2
0
0
1
1
2
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
2
0
2
0
0
0
0
1
0
0
0
1
1
0
0
0
0
2
0
1
0
1
1
0
2
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
2
0
1
2
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
3
0
1
2
0
1
2
0
0
2
2
0
2
0
0
2
1
0
2
0
0
0
0
0
2
0
0
2
1
0
0
1
0
5
1
0
2
0
1
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
2
2
1
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
2
0
2
1
1
2
2
0
0
0
0
0
0
0
0
0
1
2
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
2
2
2
0
0
2
0
1
0
1
2
0
0
0
0
1
0
0
1
1
0
0
2
0
0
0
0
3
1
1
1
0
1
0
0
1
0
4
1
0
0
2
1
1
0
0
0
0
1
0
0
0
0
2
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
1
1
0
0
0
2
0
2
2
0
2
1
1
0
0
0
0
1
3
0
0
0
0
2
0
2
2
0
1
1
2
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
3
0
0
0
0
1
0
1
0
0
0
0
2
0
0
3
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
1
0
3
0
0
2
2
0
2
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
1
0
1
0
2
2
0
0
0
0
1
2
0
0
0
0
0
0
1
2
1
0
2
0
1
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
1
0
2
0
2
0
2
0
0
1
0
0
2
1
0
0
0
0
0
1
0
0
2
2
0
2
0
2
0
0
2
0
0
1
0
2
1
0
0
0
1
2
0
0
0
0
2
0
0
2
0
1
0
2
2
0
0
0
0
0
2
0
0
0
0
0
1
1
0
1
0
2
0
0
2
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
1
1
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
3
0
0
0
0
2
0
2
0
2
1
0
0
2
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
2
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
2
0
1
0
2
0
0
2
0
0
0
2
0
0
3
0
0
2
0
0
0
0
2
0
0
0
2
1
2
0
0
2
0
0
0
0
2
3
0
2
2
1
0
2
0
0
0
0
0
0
2
0
1
3
0
0
0
2
0
2
7
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
5
1
0
0
1
2
0
1
1
0
3
2
1
3
2
0
0
0
0
2
1
0
2
1
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
1
0
0
0
0
2
0
0
0
1
2
1
1
0
0
2
0
1
1
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
2
0
1
0
1
0
2
0
1
1
0
2
0
0
0
2
0
0
1
0
1
0
2
0
2
2
1
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
2
0
0
2
0
0
1
0
0
0
4
0
2
1
0
0
0
0
0
2
0
0
0
0
2
1
1
2
0
2
2
0
1
0
0
0
0
2
1
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
2
1
1
0
0
0
0
2
0
1
1
0
0
0
1
2
0
2
2
2
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
2
0
2
0
2
0
0
0
0
0
0
2
0
0
0
1
1
0
0
1
0
1
2
0
1
0
2
3
0
0
0
0
1
0
2
1
0
1
3
1
5
0
2
0
2
0
0
0
0
2
1
2
2
2
0
0
2
0
2
0
2
0
0
0
0
0
0
1
0
2
0
1
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
1
0
0
0
2
1
1
2
0
0
0
0
2
1
0
1
3
2
2
0
0
0
1
0
0
1
1
0
2
0
2
0
2
0
0
3
0
0
1
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
1
0
1
1
0
0
0
0
3
0
0
1
0
0
0
2
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
2
1
1
1
0
0
0
1
0
0
0
0
5
2
0
1
2
2
0
2
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
2
0
1
2
0
0
0
0
0
3
2
1
0
4
2
2
1
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
2
0
1
1
0
0
1
2
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
2
2
2
2
0
0
0
2
1
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
1
1
0
0
0
0
1
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
1
0
0
0
4
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
2
0
0
0
1
0
0
0
2
2
3
2
0
1
1
0
0
0
2
0
0
0
0
1
0
2
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
2
0
3
1
0
0
0
0
0
1
1
3
0
0
0
1
0
2
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
3
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
2
2
0
2
0
0
0
0
0
0
1
2
0
2
0
0
2
0
2
2
0
1
0
0
2
2
0
0
0
2
0
0
0
0
1
0
1
0
1
0
0
1
0
0
2
2
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
2
2
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
1
2
0
0
2
4
0
1
0
2
1
0
0
0
0
0
0
1
0
2
1
0
0
2
0
0
2
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
1
1
1
0
2
2
0
0
0
2
0
2
0
0
0
0
0
1
0
1
0
0
0
1
1
0
1
3
1
0
0
2
0
0
1
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
1
3
2
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
1
2
1
0
0
0
0
0
0
2
0
0
2
0
1
0
1
0
0
0
0
2
0
1
0
0
2
0
0
2
0
1
2
2
1
0
2
0
0
0
0
2
1
0
0
1
1
0
0
2
0
0
5
1
0
0
0
0
0
3
0
2
0
0
0
0
0
1
1
2
2
0
0
0
0
2
0
0
0
0
0
3
0
0
1
0
0
0
0
1
1
1
2
0
0
0
3
2
0
0
1
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
2
0
1
0
3
0
0
0
0
4
2
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
1
1
0
0
0
0
1
1
0
0
0
2
0
0
2
3
0
1
2
0
0
0
0
0
1
0
0
0
0
1
0
0
2
1
0
1
2
0
0
2
0
2
0
0
0
0
1
0
0
1
0
1
2
2
1
0
0
1
0
0
2
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
2
0
0
3
0
0
1
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
2
2
0
0
0
0
0
0
0
1
2
2
0
0
0
1
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
2
2
0
0
1
2
0
0
0
0
0
2
1
0
0
2
0
0
1
0
0
0
0
3
0
0
0
2
0
0
0
0
2
0
1
4
0
0
0
0
0
0
1
0
2
0
2
0
0
0
2
1
2
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
1
4
0
1
0
2
2
0
0
7
0
2
0
0
1
1
1
0
2
0
1
0
0
0
2
1
0
0
1
1
0
0
0
2
0
0
5
0
2
2
2
1
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
3
0
2
1
0
2
0
1
0
1
0
0
0
2
0
0
0
0
1
1
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
1
0
1
0
1
0
0
0
1
0
0
0
1
1
0
1
0
2
0
0
2
0
2
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
1
2
2
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
3
0
0
1
0
0
0
0
1
2
0
0
0
3
0
1
0
2
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
1
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
1
0
2
0
0
2
1
2
0
2
2
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
2
1
2
0
2
0
1
0
0
1
1
0
1
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
2
1
0
0
0
2
0
0
1
3
0
0
2
1
0
0
0
0
2
0
0
2
1
0
0
0
0
2
0
0
1
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
2
0
0
1
0
0
0
2
0
0
0
0
1
2
2
0
2
0
0
0
2
0
1
0
2
0
0
1
2
2
0
2
0
0
0
0
0
0
1
1
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
1
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
2
0
0
1
2
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
5
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
1
0
5
2
0
0
0
3
0
0
0
0
0
0
1
1
0
1
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
2
2
0
0
0
0
1
2
0
1
0
0
0
0
0
2
1
0
2
0
0
0
1
1
2
0
0
0
0
0
0
1
1
0
1
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
1
0
0
0
0
0
0
3
1
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
1
1
0
1
2
0
2
1
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
2
1
0
2
0
1
0
0
1
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
2
1
0
2
0
0
0
2
0
1
0
2
2
0
0
0
0
1
0
0
2
0
0
2
0
0
1
0
9
1
0
0
0
1
0
0
0
0
2
2
0
0
0
0
2
1
0
2
0
0
0
1
3
1
0
0
0
2
0
0
0
1
0
0
0
2
1
0
0
0
0
2
1
2
0
1
1
0
0
0
0
1
2
1
0
1
0
0
2
0
2
0
0
3
0
1
7
0
2
0
6
2
2
0
0
0
1
1
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
2
0
2
2
0
0
0
0
1
0
0
0
0
0
2
0
0
2
1
3
1
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
2
2
1
0
0
1
0
0
0
1
2
0
0
0
1
1
1
0
0
0
0
2
2
0
0
0
0
0
0
1
0
1
2
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
1
1
0
0
2
2
2
0
2
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
1
1
2
0
1
2
0
0
0
0
0
0
1
0
0
1
2
2
0
0
0
0
0
8
0
0
1
0
0
0
2
3
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
1
1
2
0
2
0
0
0
3
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
2
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
1
1
1
0
2
0
0
1
1
0
0
2
1
2
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
3
0
0
7
2
0
0
1
0
0
0
0
0
1
0
0
0
2
1
0
0
5
0
6
1
0
2
1
0
0
0
1
0
0
2
2
1
1
0
0
0
0
0
2
1
0
0
0
1
2
0
1
0
1
1
0
0
2
2
2
0
0
0
0
1
2
0
0
1
0
0
3
2
2
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
2
0
0
2
0
0
2
0
0
0
1
1
0
0
2
0
0
2
1
0
0
1
0
0
2
2
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
4
0
0
0
2
0
1
0
5
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
1
2
0
0
2
0
2
0
0
0
1
0
2
0
0
1
0
1
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
2
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
1
0
2
1
1
1
0
0
0
0
0
2
2
4
0
0
0
1
1
0
0
0
0
0
0
1
2
0
1
0
0
2
0
0
0
0
0
1
0
0
0
2
2
2
0
0
0
0
0
0
2
2
0
1
0
1
0
1
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
1
0
2
1
0
2
0
2
1
1
0
0
0
0
0
3
4
0
0
0
0
0
0
0
1
2
0
1
0
0
2
0
0
0
0
1
1
1
0
3
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
1
1
2
2
0
0
0
0
0
1
2
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
1
0
1
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
2
0
0
1
1
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
1
0
0
2
1
2
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
1
1
1
0
1
0
0
1
0
0
0
0
0
1
0
0
1
1
0
1
0
1
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
2
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
1
0
2
0
0
1
0
2
0
2
0
0
0
0
0
0
2
0
4
3
0
0
0
0
2
0
2
0
2
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
4
2
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
3
1
13
1
0
0
1
1
2
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
3
2
0
0
0
0
0
1
1
0
0
0
0
1
0
2
0
2
0
2
1
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
9
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
1
0
0
0
0
2
2
2
0
2
2
0
0
0
0
0
0
0
0
3
1
1
0
0
2
2
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
1
1
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
2
2
2
2
0
0
0
0
0
0
0
0
6
0
0
2
0
4
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
4
0
3
1
0
1
0
2
0
1
1
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
1
2
0
1
0
2
0
2
0
0
2
2
0
0
0
0
0
2
0
2
0
1
0
1
0
0
0
0
2
0
0
2
0
0
1
0
1
0
0
2
0
0
2
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
1
0
0
1
0
0
0
2
0
0
0
0
2
1
0
2
1
1
0
0
0
1
2
0
2
1
0
1
0
1
0
0
0
0
0
0
2
2
0
1
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
4
0
13
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
1
1
0
3
0
0
0
1
1
0
0
0
0
0
0
1
0
0
2
1
0
2
2
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
2
2
0
0
0
0
1
0
4
1
3
1
0
0
1
0
1
2
2
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
2
2
2
0
0
2
2
0
0
0
1
0
1
0
1
2
0
0
0
2
2
0
0
0
2
0
1
2
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
1
0
3
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
1
0
6
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
1
1
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
1
2
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
2
0
2
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
4
1
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
2
1
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
1
0
0
1
2
0
0
0
0
0
0
1
0
1
1
0
0
1
2
1
0
2
0
0
2
1
0
0
2
0
1
0
4
0
1
0
1
2
1
0
0
1
1
1
2
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
6
2
0
0
0
0
0
0
0
2
0
1
1
0
2
0
0
0
1
2
2
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
1
0
1
2
0
1
0
0
2
0
0
0
1
0
1
0
2
0
2
2
1
2
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
1
0
2
2
0
3
1
0
0
0
0
2
0
0
2
1
0
1
1
0
0
3
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
2
0
3
0
2
2
0
0
0
2
0
1
2
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
2
4
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
1
2
0
0
0
1
4
2
0
0
0
1
0
0
0
1
0
2
1
1
1
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
1
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
2
1
0
1
1
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
1
0
0
2
2
2
0
1
0
0
0
1
0
0
1
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
2
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
1
2
0
0
0
1
1
0
0
0
0
0
3
0
1
0
0
2
2
0
0
0
0
2
0
0
0
1
1
0
0
0
0
3
0
0
0
0
0
0
0
2
0
1
3
0
0
1
0
2
2
0
0
0
0
4
1
2
0
5
0
1
0
0
2
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
4
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
1
0
0
3
1
1
0
0
0
0
1
0
0
0
0
5
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
1
2
0
0
0
0
0
2
0
1
0
0
0
1
2
0
1
1
2
2
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
1
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
3
0
1
0
2
0
0
2
0
0
1
2
1
0
0
0
0
0
0
4
0
3
1
0
0
0
0
0
0
2
0
2
0
2
0
2
0
0
0
0
0
2
0
0
2
0
2
0
0
0
2
0
0
0
0
1
1
1
0
2
0
1
2
2
1
0
0
0
1
3
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
1
0
0
2
0
1
0
0
0
2
2
0
2
1
2
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
3
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
3
2
0
0
0
0
1
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
2
0
3
0
0
0
2
1
2
0
0
1
2
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
1
0
1
0
0
0
0
1
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
2
3
0
1
0
0
1
0
0
1
0
2
0
1
0
1
0
1
0
0
0
0
2
0
0
2
0
1
0
0
1
1
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
4
0
0
2
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
1
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
2
2
0
0
2
2
0
0
0
2
0
0
1
1
0
0
0
0
0
1
0
2
0
0
2
0
0
0
2
0
2
2
3
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
1
0
0
0
1
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
3
1
0
0
0
0
0
1
1
1
0
0
2
0
0
0
2
3
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
2
1
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
1
0
0
0
0
2
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
2
0
0
4
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
3
1
1
0
0
2
0
0
2
1
0
0
0
2
1
5
0
2
0
2
0
1
1
0
1
1
2
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
1
1
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
2
0
2
0
2
0
2
1
0
2
2
1
0
0
0
0
0
0
6
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
3
1
0
0
0
1
2
0
2
0
1
0
0
1
0
4
0
0
0
0
0
0
2
0
1
0
1
2
2
0
2
0
2
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
5
2
0
0
2
0
1
0
1
1
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
1
0
0
2
0
1
0
1
0
1
0
0
0
0
2
0
0
1
0
0
0
4
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
2
2
1
0
3
0
0
2
0
0
0
1
0
0
0
1
0
3
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
1
0
0
1
0
1
0
2
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
2
3
0
0
0
0
0
2
0
1
0
1
0
0
0
0
1
3
2
0
2
4
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
1
0
1
1
0
0
0
0
1
2
1
0
3
0
1
0
0
0
0
0
5
0
0
2
0
0
2
0
0
1
0
2
0
3
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
2
1
0
0
1
0
0
1
0
3
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
1
0
1
0
4
0
1
0
0
0
1
0
1
0
1
0
0
0
3
0
1
3
0
0
0
2
0
0
1
2
2
2
4
2
2
0
1
0
0
2
2
0
0
1
0
0
0
0
0
2
2
10
1
2
1
0
2
1
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
1
0
0
1
0
0
2
0
0
0
0
2
1
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
2
2
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
1
0
2
1
0
2
0
1
1
1
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
1
1
1
0
2
0
0
0
2
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
2
0
0
0
1
0
0
1
0
2
0
0
0
0
0
2
1
1
0
1
0
6
0
0
1
0
0
0
2
0
0
0
0
1
0
0
2
7
0
1
0
2
0
0
0
2
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
1
0
0
1
2
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
1
1
0
1
0
1
0
0
2
0
0
1
0
0
0
0
2
0
0
1
2
0
2
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
1
2
0
0
1
0
1
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
2
1
1
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
2
2
0
0
2
0
0
1
2
0
0
0
2
0
11
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
1
0
0
1
0
3
2
0
0
0
1
0
0
0
2
2
0
0
0
0
1
2
0
1
2
2
1
0
1
0
0
1
2
1
0
0
2
0
0
0
0
1
0
0
1
0
4
0
0
0
2
0
0
0
6
0
0
2
0
2
0
0
2
0
0
2
0
0
0
1
3
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
3
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
2
1
1
0
0
3
0
0
0
0
1
1
0
0
0
0
1
0
0
2
1
2
2
1
0
2
0
0
1
0
2
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
2
1
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
2
1
0
0
0
0
0
1
1
0
2
2
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
1
0
1
0
0
3
1
2
3
0
1
0
0
0
0
0
0
0
1
2
0
3
0
0
1
0
4
2
0
0
0
1
0
0
2
0
0
6
0
0
2
0
0
0
2
0
0
0
0
0
0
1
1
2
0
2
1
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
2
1
0
0
2
3
2
0
2
0
0
0
0
3
0
2
0
0
0
0
0
1
0
0
0
1
0
4
0
0
1
0
2
0
1
5
0
0
1
0
2
0
0
0
0
1
2
2
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
1
4
3
0
0
0
0
0
0
0
1
2
2
0
0
1
0
2
0
0
1
0
0
0
2
0
2
0
2
0
0
4
0
0
0
2
0
0
1
0
1
0
0
0
0
0
2
0
0
1
0
0
3
0
2
3
2
0
0
2
1
0
0
0
0
1
2
2
2
0
0
1
0
0
1
0
1
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
1
1
0
0
0
0
0
0
2
2
2
0
0
0
0
0
1
0
0
0
3
0
1
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
2
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
3
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
2
1
1
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
2
0
0
1
0
0
0
1
0
0
0
0
2
0
2
0
1
2
1
0
0
0
0
0
0
0
0
1
3
1
1
0
2
1
1
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
2
1
1
0
0
0
0
2
0
0
0
0
0
0
0
4
0
2
1
2
0
0
2
1
0
0
1
0
0
0
0
0
2
1
0
2
2
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
2
0
1
2
0
0
2
0
2
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
1
0
0
0
1
2
3
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
10
0
0
0
2
0
0
0
0
1
2
0
2
0
0
1
0
0
3
0
0
0
0
1
1
0
0
2
1
0
0
2
0
1
0
1
2
0
0
0
2
0
2
0
0
0
2
0
0
0
0
2
1
0
2
0
0
1
0
2
1
0
0
0
0
2
0
0
0
2
0
0
0
0
2
2
0
1
0
0
0
0
1
2
1
0
0
0
0
0
4
0
0
0
2
0
1
0
0
2
0
2
0
0
0
0
1
1
1
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
3
0
0
1
0
0
2
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
1
0
1
0
0
3
0
2
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
3
0
0
0
1
2
0
2
0
0
0
1
0
0
2
2
0
0
1
1
2
1
2
1
0
0
0
0
0
0
0
0
3
0
7
2
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
1
2
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
2
0
0
0
1
1
2
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
2
1
0
1
0
0
1
2
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
1
2
3
0
0
2
0
0
0
0
0
0
0
0
1
2
0
1
1
0
2
0
0
0
2
0
0
2
1
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
2
2
1
0
2
0
0
1
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
1
0
0
0
2
1
2
1
0
0
0
2
0
0
0
0
2
0
2
0
0
0
1
0
0
2
3
0
0
5
0
0
1
0
2
0
0
2
2
0
2
0
0
0
1
1
2
1
2
0
3
0
0
0
1
4
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
1
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
1
2
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
1
1
0
1
2
0
0
2
0
1
2
2
0
2
2
1
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
1
0
0
0
2
2
1
2
0
1
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
2
0
1
0
0
2
0
5
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
3
0
0
0
0
0
1
0
0
2
1
0
0
1
0
0
0
0
0
0
1
1
2
0
0
0
1
0
2
0
0
0
1
1
1
1
0
0
1
1
0
0
0
0
0
1
2
0
0
1
0
1
1
0
3
0
0
0
0
0
2
2
0
2
0
0
2
0
1
0
2
0
0
0
0
0
0
2
0
2
0
0
0
1
2
2
0
0
0
2
0
0
2
1
0
0
0
0
1
1
0
0
1
0
0
0
2
2
0
0
0
0
2
0
2
0
0
2
0
0
1
0
2
1
0
1
2
1
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
2
0
2
0
0
0
2
0
0
2
0
2
2
0
3
0
0
0
0
0
2
0
0
0
0
0
1
2
1
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
2
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
2
0
0
2
2
0
0
4
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
2
2
1
0
0
2
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
3
2
1
1
2
0
1
0
0
0
1
2
4
2
1
0
0
1
2
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
2
1
0
1
2
0
5
0
0
1
0
0
7
0
0
0
0
0
2
2
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
8
0
3
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
1
2
3
0
3
0
0
2
0
2
0
0
0
0
2
1
0
0
2
0
2
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
2
0
1
0
1
0
1
2
0
0
0
2
1
2
0
1
0
0
0
0
0
0
3
0
1
0
2
0
0
1
2
1
2
2
0
0
2
0
0
2
2
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
5
2
0
1
1
1
1
0
0
0
0
1
1
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
2
0
0
1
1
0
2
0
0
0
0
1
0
0
0
2
0
0
0
3
0
1
0
0
1
0
2
2
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
1
0
2
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
2
0
1
0
2
2
0
0
0
1
2
0
0
1
0
0
0
1
2
1
0
2
0
0
0
0
0
1
1
4
0
0
1
0
0
2
0
0
0
0
0
0
2
2
11
0
2
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
1
1
0
0
0
3
2
2
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
1
0
2
0
0
1
0
2
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
3
0
0
1
1
0
1
0
0
0
2
0
2
1
1
0
0
1
0
0
0
0
0
1
2
0
2
0
0
1
0
0
2
0
2
0
2
0
0
0
0
1
0
0
1
1
0
0
1
2
0
0
2
2
2
0
2
1
0
1
0
0
2
1
1
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
1
1
0
0
0
0
3
2
0
2
1
0
1
1
0
0
0
0
2
0
0
0
2
0
3
0
2
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
1
3
0
0
0
2
0
0
4
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
1
0
2
0
0
2
0
0
2
0
0
5
2
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
1
3
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
1
0
1
2
0
0
2
0
1
0
0
0
0
0
1
1
0
0
0
0
0
2
0
1
1
0
0
0
0
2
0
0
1
2
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
2
1
0
0
0
0
0
0
0
2
1
0
0
2
1
0
0
0
2
0
1
0
0
1
0
0
1
0
0
1
0
0
2
2
0
0
0
0
0
0
2
1
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
4
0
1
0
0
0
0
0
1
1
0
1
2
0
0
4
1
0
0
0
0
1
1
1
1
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
3
0
0
2
0
0
1
0
0
0
0
0
0
1
1
1
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
1
3
1
0
2
0
0
0
1
0
0
0
0
1
1
3
1
0
0
0
0
1
0
0
1
0
1
0
0
2
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
1
0
1
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
2
0
0
0
1
0
2
1
2
0
0
1
0
1
2
0
0
0
2
0
2
0
2
1
1
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
2
1
2
1
0
0
0
0
0
2
0
1
0
0
0
1
2
0
0
0
0
2
0
2
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
1
0
2
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
2
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
2
0
1
0
0
0
0
0
0
2
1
1
1
0
0
0
0
0
2
3
0
0
0
2
0
0
0
2
0
0
0
2
0
0
1
1
0
0
2
1
0
0
0
1
0
4
0
0
3
0
0
2
0
2
0
0
2
0
1
0
2
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
1
0
2
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
3
2
0
0
4
0
1
2
0
0
0
5
0
0
1
1
0
0
0
0
2
0
1
0
0
1
0
0
0
3
0
0
0
0
0
0
0
1
0
2
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
3
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
1
0
2
0
0
2
1
1
0
2
0
0
0
0
0
0
1
1
0
1
2
1
0
2
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
2
0
2
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
1
0
0
0
3
0
1
2
0
1
0
0
0
0
1
0
2
0
0
1
0
1
0
1
2
1
0
0
0
0
1
0
0
0
0
0
0
1
3
0
0
0
2
0
0
0
0
1
2
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
3
0
4
6
1
0
0
0
0
0
0
0
0
0
2
0
2
0
2
2
0
2
2
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
2
0
1
0
0
0
1
0
0
1
0
1
0
1
0
0
2
2
0
1
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
1
1
0
0
0
0
0
1
2
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
2
1
0
0
0
0
0
3
1
2
0
0
2
0
0
2
1
0
0
2
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
2
1
0
1
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
1
3
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
2
1
1
0
1
0
1
0
0
1
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
1
2
2
2
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
2
0
2
0
0
0
0
0
2
0
2
2
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
1
2
0
0
0
2
0
0
3
0
0
0
0
2
0
2
0
1
0
1
0
0
0
0
0
2
0
1
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
1
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
2
0
2
1
0
2
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
1
1
0
0
2
0
0
0
3
0
0
0
2
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
6
1
0
2
0
1
0
0
1
0
0
0
0
0
0
0
3
0
0
0
2
0
0
1
0
1
0
0
0
2
1
0
0
0
2
2
0
0
0
0
0
3
0
1
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
3
0
0
0
0
2
2
0
1
0
0
0
1
1
2
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
1
0
0
1
0
0
0
0
2
0
0
0
3
0
0
0
2
2
1
1
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
3
0
1
1
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
2
2
0
1
0
0
5
0
0
0
1
0
0
0
0
2
0
0
0
3
2
0
0
1
0
0
2
0
1
0
2
0
0
0
0
0
0
2
0
2
0
3
0
0
2
0
0
0
1
0
0
4
0
0
1
0
2
1
0
0
1
0
0
0
0
0
2
0
0
1
0
0
1
0
1
2
0
0
1
7
1
0
1
0
0
0
0
0
0
0
2
3
0
2
1
1
0
0
0
1
0
1
1
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
2
0
2
1
0
0
0
0
2
0
0
1
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
1
0
1
2
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
2
0
0
0
1
1
1
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
1
2
0
2
2
2
0
2
2
2
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
2
2
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
1
0
1
3
2
0
0
2
0
0
0
0
1
0
2
0
0
0
1
2
0
3
0
0
0
2
0
0
0
1
3
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
3
0
0
2
2
0
0
0
1
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
2
0
0
0
2
0
0
1
0
0
0
1
0
0
2
0
0
0
0
1
0
0
1
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
2
2
1
0
0
2
0
0
0
2
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
1
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
4
0
0
0
1
0
1
0
2
0
0
0
0
1
0
0
0
2
2
1
0
3
0
1
2
1
1
1
0
2
0
2
0
0
2
0
0
1
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
2
1
0
0
0
0
1
0
0
1
0
0
3
2
0
0
0
2
0
0
1
0
1
2
0
0
0
0
0
2
1
0
0
0
1
2
0
2
0
2
2
2
0
0
0
2
0
0
0
1
0
0
1
2
1
0
0
0
0
0
2
0
0
1
0
2
0
0
0
1
0
1
2
0
1
0
0
0
0
1
1
0
0
0
1
2
0
2
1
0
0
3
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
3
1
0
0
0
1
1
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
3
1
0
2
0
2
0
0
0
1
0
2
0
0
0
0
0
1
0
0
1
1
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
1
1
0
0
3
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
7
0
1
0
0
2
0
0
0
0
1
0
0
2
2
0
0
0
1
0
1
3
0
2
0
0
3
2
2
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
3
0
0
0
1
0
0
2
0
0
0
3
0
0
0
0
0
2
2
1
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
1
2
0
0
0
0
0
2
2
0
0
0
0
0
3
0
0
0
2
0
0
2
1
0
0
2
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
3
2
0
2
0
0
0
4
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
2
1
0
1
0
2
0
2
0
0
1
0
0
0
0
0
1
0
2
0
0
4
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
1
0
1
0
0
2
0
2
0
0
1
0
0
4
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
3
0
0
0
2
0
0
0
0
0
0
2
2
0
1
1
1
0
1
1
0
0
0
4
2
0
3
1
0
1
2
0
1
0
0
0
0
0
0
0
1
1
0
1
1
0
0
1
0
0
0
0
1
0
2
2
3
2
0
0
2
1
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
1
1
0
0
0
1
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
4
0
0
0
1
0
0
2
0
0
1
0
1
0
1
1
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
2
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
1
2
0
1
0
2
0
0
2
0
0
1
0
0
0
3
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
2
1
2
0
0
2
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
1
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
2
0
3
0
0
2
1
0
0
2
0
1
0
0
0
0
0
0
1
2
0
0
0
0
1
2
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
1
0
0
0
0
2
2
1
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
2
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
1
0
2
2
0
1
0
2
0
1
0
2
2
0
2
1
0
0
0
2
0
1
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
2
0
0
2
1
0
2
0
1
0
0
1
1
1
0
2
0
0
2
1
0
0
1
3
1
0
0
0
1
0
0
0
2
1
0
2
0
0
0
0
3
1
0
1
2
1
0
0
3
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
1
0
2
2
0
0
1
0
3
0
0
2
0
0
2
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
1
1
2
0
0
0
0
0
2
2
0
2
0
2
2
1
0
0
1
0
0
1
2
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
4
0
0
0
1
1
0
0
1
0
1
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
2
0
0
2
3
0
0
0
0
0
0
0
0
2
0
0
0
3
2
0
0
2
0
0
1
0
0
1
0
0
0
2
0
0
0
2
0
0
0
1
1
2
0
0
1
0
0
0
1
0
2
0
2
0
1
0
0
0
0
0
3
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
2
0
2
1
0
2
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
2
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
2
2
0
0
0
1
1
1
0
0
0
0
1
4
0
1
0
0
2
0
1
0
0
0
1
0
0
1
1
2
0
2
0
0
2
0
0
0
2
0
0
0
1
0
1
2
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
2
1
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
2
1
0
0
2
1
0
2
0
0
0
1
2
2
1
0
2
0
2
2
2
2
0
2
1
0
0
2
0
2
2
1
1
3
0
2
0
0
2
0
0
0
2
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
2
2
1
0
2
0
0
0
0
0
0
0
0
0
2
1
0
1
1
0
2
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
2
3
2
0
0
0
0
0
1
1
0
0
1
1
3
1
1
0
1
0
0
1
0
2
3
2
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
1
0
1
2
0
1
0
2
0
1
0
0
0
1
0
1
0
2
0
0
0
0
0
2
2
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
1
0
2
0
2
2
0
0
2
3
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
1
2
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
3
2
0
0
2
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
2
0
3
1
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
5
0
0
1
0
0
2
1
0
0
0
1
1
1
0
0
0
2
0
0
3
1
1
1
0
1
1
1
0
2
1
2
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
2
0
0
2
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
2
0
2
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
3
0
0
1
0
0
0
0
0
0
3
0
0
0
1
0
0
1
0
1
2
0
0
0
0
0
0
0
1
2
0
1
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
2
0
0
2
0
0
1
0
0
0
1
0
0
0
0
2
0
1
0
0
2
0
1
1
0
0
2
0
2
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
2
0
0
0
1
3
1
0
0
0
2
0
0
1
1
0
0
3
1
0
0
0
0
2
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
2
0
0
1
1
0
0
2
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
2
1
0
2
1
0
5
0
0
0
0
0
2
0
2
0
0
0
8
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
2
3
0
0
1
0
0
0
2
0
0
0
0
2
0
2
0
0
1
0
0
0
0
1
1
0
0
0
2
0
0
2
4
0
1
2
1
0
0
1
0
2
2
0
0
0
0
3
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
3
0
1
0
0
1
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
1
0
0
0
0
1
2
0
0
2
0
2
1
0
0
2
0
0
0
1
0
2
0
0
0
3
0
0
1
0
0
0
0
0
0
2
1
1
0
0
2
1
0
0
2
1
1
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
2
1
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
2
2
2
0
0
0
2
0
0
0
2
2
2
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
1
2
0
1
1
0
0
1
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
1
0
1
0
0
1
3
0
2
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
2
1
0
0
1
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
5
0
3
0
2
4
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
3
0
1
0
0
0
0
0
0
0
1
0
3
2
2
2
0
2
2
1
0
0
2
0
0
0
1
0
0
0
1
2
1
0
1
0
0
0
0
0
0
1
0
2
0
0
0
2
2
0
0
0
1
2
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
3
1
0
1
0
0
0
0
2
0
2
0
0
3
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
2
0
0
2
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
1
0
3
0
0
0
1
0
1
0
0
0
0
1
2
3
0
2
0
2
0
1
1
0
0
4
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
3
0
1
0
0
0
0
0
0
0
0
0
2
5
0
0
0
0
0
2
0
1
1
0
0
1
2
1
0
0
0
0
0
2
0
0
0
1
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
2
2
0
0
0
2
0
0
1
0
0
2
2
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
3
0
0
0
2
1
0
0
0
0
1
1
0
0
1
1
0
0
1
0
0
2
4
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
2
1
0
0
0
0
2
0
4
0
0
2
0
2
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
1
3
0
1
0
1
1
0
4
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
2
3
3
0
1
0
2
0
0
2
0
0
0
5
0
0
0
0
0
2
2
0
0
0
0
1
0
1
0
0
0
1
0
0
2
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
2
3
2
0
0
0
2
3
0
2
0
0
0
0
0
1
0
0
1
0
1
3
0
0
0
0
0
0
1
4
1
0
2
0
2
0
0
0
0
1
0
0
0
0
3
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
1
0
1
0
0
1
1
0
0
2
0
2
2
0
3
0
1
0
0
6
2
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
2
2
0
0
0
0
1
1
0
0
0
1
1
1
0
0
0
1
0
0
3
0
1
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
4
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
1
2
1
2
2
0
0
2
1
0
0
0
0
0
2
1
0
0
0
2
3
0
1
0
0
0
0
0
1
1
2
0
0
2
1
0
0
0
0
0
0
0
0
1
0
2
3
1
0
2
2
0
1
0
0
2
0
0
0
0
2
0
0
0
1
2
0
2
0
0
2
0
0
0
1
2
0
0
0
1
0
1
0
2
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
1
0
2
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
7
2
0
1
0
0
0
0
0
0
0
2
1
0
0
2
2
0
0
1
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
2
2
0
0
2
0
1
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
1
2
1
0
0
0
0
1
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
1
0
2
0
0
0
3
0
0
0
2
1
0
0
0
0
2
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
1
0
0
0
2
3
3
0
0
0
0
2
2
0
0
0
1
2
1
2
0
0
0
0
0
1
0
2
4
2
0
0
0
0
1
0
0
0
0
1
0
1
1
2
0
0
0
2
1
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
3
0
1
2
0
1
0
3
2
0
1
0
0
0
2
0
0
1
1
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
2
0
0
0
0
2
0
0
0
1
0
0
1
2
0
0
1
0
0
2
0
2
0
2
0
0
0
0
0
0
1
2
0
0
0
2
2
0
0
2
0
1
0
1
1
0
0
1
0
0
0
2
2
1
0
0
3
0
0
0
1
1
0
4
0
0
0
0
0
3
0
1
0
0
0
0
1
0
2
1
2
3
2
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
1
2
1
1
1
0
0
0
0
1
0
0
0
0
0
2
0
1
0
1
0
0
0
1
1
0
0
0
0
1
2
0
0
4
2
0
1
0
0
2
0
0
2
0
1
0
0
0
0
3
0
0
2
0
2
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
2
0
0
1
1
0
0
1
0
0
2
1
1
0
0
1
0
2
0
0
2
0
0
2
0
0
0
0
0
1
0
1
0
2
0
1
2
1
1
0
1
3
0
0
0
0
1
0
2
0
1
1
0
1
0
0
0
0
2
0
1
2
0
0
0
1
2
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
2
2
4
0
0
0
0
0
0
1
0
1
2
0
0
3
0
2
0
0
1
0
0
1
0
2
0
0
0
2
0
1
0
0
0
6
1
0
0
0
0
1
0
0
0
1
1
1
0
0
0
1
0
0
1
1
0
0
0
0
2
0
0
0
2
0
0
0
2
0
2
0
0
0
2
0
1
0
0
0
1
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
2
0
4
1
1
0
3
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
1
0
0
0
1
0
2
5
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
2
0
0
1
0
0
2
1
0
0
1
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
3
0
0
2
0
0
0
0
2
1
2
1
2
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
1
1
0
0
1
0
0
0
1
0
0
0
0
1
2
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
2
0
2
1
0
0
1
1
0
0
0
0
2
1
1
0
1
0
0
0
0
3
2
0
0
0
0
0
1
0
1
0
2
0
4
0
2
2
0
1
2
0
0
0
0
2
0
1
0
2
2
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
2
1
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
2
1
6
1
0
0
2
0
0
2
0
2
0
1
0
0
0
0
0
0
0
1
5
0
0
0
0
0
0
1
1
1
0
2
0
0
3
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
2
0
0
2
2
0
0
0
0
0
4
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
2
2
2
0
0
0
2
0
0
0
0
0
1
2
1
0
1
0
1
2
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
1
1
0
0
2
0
1
1
0
2
0
0
0
1
2
1
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
1
4
0
1
2
0
1
1
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
1
1
2
0
2
0
2
1
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
1
1
0
0
0
0
1
0
0
0
2
0
2
1
0
0
2
1
0
0
0
0
0
1
2
0
2
0
1
0
0
0
0
0
0
1
0
2
1
1
0
0
2
2
0
2
0
3
0
0
0
0
2
2
3
0
0
1
2
0
0
1
0
1
0
1
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
1
2
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
4
0
0
2
0
0
2
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
2
2
0
0
2
0
0
2
2
2
0
0
0
0
2
1
2
0
0
0
0
0
2
2
0
0
0
0
0
2
0
1
1
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
2
2
2
2
0
1
1
0
0
0
1
0
0
1
2
0
3
0
0
0
0
2
0
1
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
2
0
1
4
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
2
1
0
0
1
1
0
0
0
0
1
0
0
1
2
0
0
1
2
0
0
0
0
2
3
8
0
0
0
0
1
2
0
0
0
0
0
2
2
0
0
0
0
2
1
1
1
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
2
0
0
2
0
2
0
1
2
0
0
2
0
1
0
0
0
2
0
0
0
0
1
0
1
0
2
0
2
0
1
0
3
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
1
2
2
0
2
0
7
1
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
1
1
2
0
0
0
2
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
2
0
1
0
1
0
0
2
0
0
0
0
1
0
0
0
1
0
0
2
0
1
0
0
0
1
2
0
1
0
0
2
0
0
0
0
2
2
2
0
2
0
0
0
0
2
2
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
1
1
0
0
1
2
0
0
0
0
0
0
0
1
0
0
1
2
0
0
2
0
0
2
2
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
3
0
0
0
0
2
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
2
2
0
0
1
0
0
1
0
0
0
1
0
2
1
0
0
0
2
0
0
0
2
0
2
1
0
0
0
1
0
0
0
0
0
2
2
0
0
0
1
0
0
2
0
1
0
1
1
0
0
0
0
0
0
1
0
2
1
0
0
0
1
0
0
0
0
4
0
0
1
2
1
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
2
1
0
0
0
0
2
0
2
4
0
0
0
2
0
0
0
0
0
3
0
0
4
0
0
2
0
0
1
0
0
0
0
0
1
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
2
2
2
0
1
0
2
1
0
1
0
0
1
1
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
1
1
0
0
0
1
2
0
1
2
0
0
0
0
0
0
1
0
1
3
1
0
2
0
0
5
2
0
0
2
0
0
1
2
0
0
2
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
1
2
0
2
0
2
0
0
1
1
1
0
0
0
0
0
3
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
1
0
0
1
0
1
2
0
0
0
0
0
1
2
0
2
0
3
0
0
2
1
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
1
0
0
1
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
1
0
0
2
1
0
0
1
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
4
0
0
0
0
1
0
1
2
0
2
0
1
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
6
5
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
2
0
0
1
1
0
2
0
1
1
0
0
0
0
0
2
2
0
2
0
0
0
2
0
1
0
1
1
0
1
2
0
1
0
0
1
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
3
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
2
2
0
2
0
0
2
2
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
2
1
0
2
0
0
0
4
1
1
0
0
0
0
1
0
0
1
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
3
0
0
1
0
0
2
0
1
2
1
2
0
2
2
0
0
0
0
1
1
2
0
0
0
0
0
0
1
2
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
2
0
0
0
3
0
0
0
0
0
0
2
2
0
0
1
0
1
0
2
0
0
1
0
0
0
0
2
1
0
2
0
0
2
1
0
0
0
0
1
0
0
1
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
2
0
0
0
0
2
1
0
0
2
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
3
0
0
0
1
0
2
0
0
0
0
2
4
2
0
0
1
0
0
0
1
0
1
0
0
0
2
0
2
0
1
0
0
1
0
0
2
0
0
0
2
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
1
2
0
2
0
0
2
0
0
1
2
0
1
0
0
1
0
0
0
1
0
0
1
2
1
0
0
0
0
0
0
1
0
3
0
10
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
1
0
2
1
1
0
0
0
0
0
0
0
0
1
0
2
2
2
0
0
0
2
1
0
2
0
0
0
0
0
0
2
0
0
2
0
2
0
2
0
0
0
0
0
2
1
0
0
0
2
0
0
0
1
2
1
1
1
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
2
1
1
0
0
2
0
0
0
0
1
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
1
0
0
0
2
2
0
0
2
0
2
0
0
0
1
0
2
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
1
2
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
2
1
0
0
1
1
0
0
2
0
2
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
2
2
0
2
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
1
0
1
2
0
1
0
2
0
4
2
0
0
1
0
0
0
0
0
0
1
1
0
2
0
3
1
1
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
1
0
1
2
0
2
2
1
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
3
1
1
0
0
2
0
0
1
0
0
0
1
0
0
0
0
2
0
2
0
0
0
1
0
0
1
0
0
0
0
2
0
1
0
0
0
1
0
0
2
0
0
0
0
0
1
2
0
0
0
1
2
0
0
0
2
1
1
1
0
0
2
0
0
1
0
0
0
2
0
0
1
2
0
0
1
0
0
2
1
0
0
0
0
2
0
0
5
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
2
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
2
0
0
2
0
2
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
1
1
1
0
0
0
1
2
0
2
0
0
1
1
0
0
0
0
2
2
0
0
0
0
0
0
1
1
2
0
1
1
1
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
4
0
0
0
4
0
1
0
1
0
0
2
0
2
1
0
0
0
0
2
1
0
2
2
0
0
1
4
2
0
0
1
0
0
0
1
1
0
0
2
2
0
0
1
0
0
0
2
1
2
2
1
0
0
0
2
0
0
0
0
0
0
1
3
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
2
1
0
0
0
0
3
0
0
2
0
0
1
0
0
1
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
3
0
0
1
2
2
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
5
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
1
2
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
2
2
0
0
3
0
0
1
2
0
4
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
4
0
0
2
0
0
3
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
5
1
0
2
0
0
1
0
2
0
0
0
0
0
0
1
0
2
0
1
0
0
3
0
1
0
1
2
1
1
1
0
0
0
1
1
2
0
0
1
0
0
1
1
0
1
0
2
0
0
0
0
0
1
0
2
1
1
2
0
2
2
2
0
2
0
0
2
0
2
1
0
0
0
0
1
2
2
1
0
0
0
2
0
2
0
0
1
1
2
0
0
1
0
0
0
0
0
1
2
1
0
0
0
0
0
1
0
2
2
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
1
5
0
0
1
0
2
1
0
0
0
0
1
0
1
1
0
0
2
1
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
1
0
0
1
0
0
0
0
2
0
0
0
1
0
2
1
1
0
0
1
0
0
0
2
0
1
2
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
3
0
0
2
0
0
2
0
1
0
2
1
1
0
0
0
2
0
0
1
2
1
0
0
0
2
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
1
2
1
0
0
1
0
2
1
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
1
1
0
1
2
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
2
1
0
0
0
0
1
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
4
1
0
0
0
1
0
2
2
1
0
0
2
2
0
0
2
2
0
0
0
0
1
2
1
0
2
0
1
2
2
0
0
0
0
2
1
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
3
0
2
1
0
0
1
0
1
0
0
0
2
0
1
3
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
2
0
0
1
1
0
0
0
0
0
0
1
0
0
2
1
0
0
0
1
0
0
4
0
2
0
0
0
0
1
1
1
0
0
0
0
2
2
0
0
0
3
1
0
1
0
1
0
0
1
2
1
0
0
0
0
0
2
0
0
3
2
2
1
1
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
1
0
0
2
0
0
0
1
0
0
0
1
2
0
0
0
0
0
2
0
0
1
0
0
1
0
1
0
0
2
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
1
0
1
3
0
0
0
0
0
0
2
0
2
4
2
0
0
1
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
1
1
0
0
0
1
2
0
0
0
2
0
1
0
2
0
2
2
3
2
0
1
1
0
1
0
0
0
0
1
1
2
0
0
1
0
0
0
1
0
0
0
0
2
1
0
0
0
1
0
2
0
0
0
0
0
3
0
0
2
0
2
0
0
1
0
1
0
1
0
0
3
0
0
1
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
2
2
0
0
4
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
3
0
1
0
0
0
0
2
0
2
0
2
0
0
0
2
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
1
2
0
1
0
1
2
0
0
0
0
2
0
0
0
0
0
3
0
2
1
0
2
0
2
2
1
0
0
0
1
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
3
5
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
2
0
2
1
2
2
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
1
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
2
1
0
1
2
2
0
0
0
0
0
0
3
0
0
1
1
0
0
1
0
1
2
1
0
0
0
0
1
1
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
1
0
0
0
0
0
0
2
1
0
0
0
0
0
2
2
0
0
0
0
1
1
0
0
2
0
0
1
0
2
0
2
1
0
1
0
0
3
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
3
0
0
0
1
0
0
1
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
5
0
0
0
1
1
0
1
0
1
0
0
2
2
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
4
1
1
0
0
1
0
0
2
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
2
0
2
0
0
0
0
0
0
0
1
1
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
1
0
1
1
0
0
2
0
0
2
0
1
0
1
0
0
0
0
0
2
1
2
0
1
1
0
1
2
2
1
0
0
0
0
2
0
1
0
0
0
1
2
3
0
2
0
1
0
1
0
1
1
2
1
2
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
1
2
1
0
0
0
0
1
13
0
0
0
2
2
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
2
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
3
0
0
0
1
1
0
0
0
0
0
0
0
1
1
1
2
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
2
2
1
2
0
2
0
2
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
2
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
1
0
0
2
0
1
0
0
0
2
0
0
0
0
1
1
2
0
1
0
0
4
0
0
0
1
0
1
2
0
0
1
1
0
0
0
2
0
0
0
0
0
2
0
4
0
0
2
2
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
1
0
9
0
0
0
0
0
0
1
1
0
1
3
1
2
0
0
0
0
0
1
0
2
1
0
3
0
0
1
0
2
0
1
0
0
4
0
0
0
2
0
2
0
0
0
0
0
2
0
0
1
0
2
2
0
1
0
1
0
0
0
0
2
2
0
0
1
0
2
0
1
0
0
1
0
0
0
0
1
0
0
1
0
1
0
1
1
0
2
0
1
0
2
0
0
1
0
0
1
0
0
2
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
1
1
0
0
2
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
1
0
1
1
1
2
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
2
1
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
3
1
0
1
0
2
0
0
0
0
2
1
0
0
0
0
0
0
2
0
2
0
0
0
2
2
2
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
2
1
2
0
0
2
1
0
0
0
0
2
0
0
2
2
2
0
1
3
2
0
0
0
0
2
1
1
0
0
0
2
0
0
1
0
1
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
1
0
2
0
1
2
0
0
0
0
0
0
0
0
0
1
2
2
0
0
2
0
0
3
0
0
0
0
0
0
1
0
0
0
3
4
3
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
2
1
1
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
2
0
2
2
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
2
1
0
0
0
1
1
0
0
0
0
0
0
2
1
0
1
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
1
0
0
2
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
1
1
2
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
2
4
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
1
1
2
2
0
0
0
0
1
0
0
0
2
2
0
0
0
1
0
1
0
2
0
1
0
1
0
0
0
0
0
1
0
3
0
0
0
0
1
0
1
0
0
0
1
2
0
2
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
3
1
0
0
0
0
0
2
1
0
2
0
1
1
0
0
1
0
0
1
0
0
1
2
0
0
1
0
3
0
0
0
2
1
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
2
0
2
7
1
2
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
2
1
1
0
0
0
2
0
0
0
0
0
2
2
2
0
0
1
0
0
1
0
0
2
1
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
1
0
0
0
0
0
2
0
1
0
0
1
1
0
0
2
0
3
0
1
0
0
0
0
0
0
0
0
3
0
1
0
0
0
1
1
0
2
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
1
2
0
3
1
0
2
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
2
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
1
0
0
0
2
0
0
0
0
2
1
0
1
1
0
0
3
0
0
0
0
0
2
0
2
0
0
0
2
1
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
2
1
0
2
0
0
2
0
0
0
0
0
2
2
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
2
1
2
0
2
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
2
0
1
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
2
0
2
2
0
1
0
0
0
0
0
1
2
0
0
1
0
1
0
2
0
0
0
0
0
0
0
1
1
2
1
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
3
1
2
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
6
0
1
0
1
0
2
1
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
2
0
1
0
2
0
0
2
0
5
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
2
2
0
1
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
1
3
0
0
0
0
0
2
1
2
0
2
0
2
0
2
2
0
0
0
1
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
3
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
1
2
0
2
0
1
0
1
1
0
1
1
3
1
2
0
2
0
0
1
0
2
0
2
0
0
1
1
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
2
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
3
0
2
0
0
0
1
0
0
0
0
2
0
0
0
1
2
2
2
3
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
2
1
2
2
0
0
0
1
2
0
2
0
0
0
2
0
0
0
0
0
2
0
1
1
2
1
2
0
0
0
0
1
0
0
0
0
2
0
0
1
1
0
1
0
0
0
0
1
1
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
2
1
1
0
2
1
0
0
0
0
0
1
0
2
0
1
0
1
0
0
1
1
0
0
0
1
0
0
1
2
0
0
2
0
0
0
0
1
0
1
0
0
2
0
0
2
0
1
3
0
0
2
0
0
1
0
2
1
0
0
1
0
0
2
1
2
1
0
0
2
0
0
0
0
0
0
1
1
2
0
0
2
1
0
0
0
0
0
1
0
2
0
1
0
1
1
0
0
2
3
2
0
0
0
2
0
0
0
0
2
1
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
1
0
2
0
0
0
0
0
3
0
0
1
3
0
0
0
2
0
0
0
1
1
0
1
1
0
2
1
1
0
0
0
2
2
2
0
0
0
2
0
0
0
0
0
0
0
5
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
1
0
0
1
0
2
2
0
0
0
1
0
0
0
1
0
0
2
0
0
0
1
0
1
0
0
0
1
0
4
0
0
0
0
0
1
0
0
0
0
0
2
0
1
3
0
2
0
0
0
2
2
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
1
0
0
2
0
2
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
2
0
0
2
0
0
1
1
2
2
0
0
0
1
0
0
2
3
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
2
0
1
0
0
2
0
1
1
0
0
1
0
0
2
0
0
2
4
4
0
1
2
0
0
1
1
0
2
0
0
0
2
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
3
0
1
0
1
0
0
1
0
0
2
5
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
2
0
1
1
2
0
0
0
1
0
0
2
0
1
1
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
1
0
0
1
0
2
0
0
2
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
3
1
0
0
0
0
0
1
0
0
0
2
2
2
0
1
0
0
0
1
0
0
2
0
2
0
0
0
0
2
3
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
3
0
1
0
2
0
0
0
0
0
0
0
2
0
1
0
1
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
2
1
0
0
1
0
1
0
0
2
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
3
0
0
0
1
0
0
1
0
1
1
0
1
0
0
1
2
0
0
1
0
0
0
2
0
0
0
1
0
2
2
0
0
0
1
0
0
1
0
0
0
0
3
0
3
0
2
0
0
0
1
4
0
0
0
0
1
1
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
4
2
0
2
2
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
1
1
2
2
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
2
0
1
1
0
0
2
0
1
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
3
0
2
0
3
2
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
1
1
0
0
1
0
2
1
0
0
0
1
0
0
3
0
0
1
1
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
3
0
0
2
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
2
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
2
0
0
0
0
2
0
2
1
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
2
1
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
1
0
1
1
0
0
0
2
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
2
1
0
0
0
2
1
0
1
0
2
0
2
0
0
2
0
0
0
0
0
1
1
2
1
2
0
0
0
1
2
0
0
1
2
1
0
0
2
0
2
0
0
0
3
0
0
0
2
1
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
4
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
1
1
2
2
1
0
0
0
1
0
1
0
2
0
0
0
0
2
0
1
0
0
0
0
2
0
2
1
0
1
1
3
1
2
0
0
0
0
2
2
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
1
0
0
2
0
0
0
2
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
2
0
1
2
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
2
2
0
1
0
0
0
0
2
0
3
1
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
2
0
2
0
0
0
2
1
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
1
1
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
3
0
2
0
0
1
2
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
2
2
0
1
0
0
0
2
0
2
0
1
2
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
1
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
2
1
0
1
0
2
0
0
0
2
1
1
1
1
0
0
8
1
0
0
0
2
0
0
2
0
1
0
0
0
3
1
0
0
0
1
2
1
1
0
3
0
1
0
0
1
0
1
3
0
3
1
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
1
0
0
0
0
0
0
4
2
2
1
0
0
1
1
0
1
1
0
0
0
0
0
0
0
1
0
0
2
1
0
1
0
0
2
0
0
1
1
0
0
0
2
2
0
0
0
0
2
2
1
0
0
0
2
1
0
2
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
3
0
1
0
0
1
2
0
0
0
0
2
2
1
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
1
0
0
2
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
2
2
0
0
1
2
0
0
0
0
2
0
0
2
2
0
2
0
2
0
0
0
0
1
0
0
2
1
0
1
0
0
0
0
3
0
2
0
2
0
0
1
2
0
0
0
4
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
2
0
0
0
1
1
0
0
0
0
0
0
2
0
1
0
0
0
1
1
0
0
0
2
8
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
1
1
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
1
2
0
1
1
0
1
1
0
0
2
0
1
2
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
2
0
1
1
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
1
2
0
0
2
0
1
2
0
0
0
0
2
3
2
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
1
3
0
1
1
0
0
0
0
0
0
0
2
0
2
0
1
0
2
1
0
1
0
0
1
1
0
2
0
0
0
0
1
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
2
1
2
0
0
2
0
0
1
2
0
1
0
0
0
0
0
1
0
2
2
0
0
2
0
0
0
0
0
2
1
0
2
1
0
0
1
0
0
1
2
0
0
0
1
1
6
0
0
0
1
2
1
5
3
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
2
1
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
2
2
0
2
1
2
0
0
2
2
1
0
0
0
1
0
0
0
0
3
0
1
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
2
2
2
0
1
0
0
2
0
0
0
0
0
4
1
0
0
0
0
0
0
2
1
0
0
2
0
0
2
0
0
1
0
0
0
2
0
0
1
0
1
3
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
2
1
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
1
0
1
2
1
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
2
0
2
0
1
0
0
2
0
0
0
3
0
0
0
0
2
1
1
0
0
0
2
0
0
1
0
0
1
2
0
1
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
2
0
2
2
0
0
1
0
0
0
0
2
0
0
0
3
2
2
2
0
0
1
1
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
2
1
1
0
0
0
0
0
0
1
0
1
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
1
0
1
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
2
0
1
1
0
0
1
2
0
0
1
0
0
1
1
2
0
0
0
3
1
0
0
0
0
2
0
1
1
0
0
1
2
0
0
0
1
0
2
0
0
0
0
0
2
3
2
3
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
1
0
3
0
1
0
0
0
0
1
1
1
0
0
0
0
1
0
2
1
0
2
2
1
0
0
2
1
0
1
1
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
2
0
0
0
0
0
2
1
0
0
2
2
0
0
0
0
0
2
0
0
1
0
0
2
0
0
2
0
0
2
0
0
0
0
1
0
0
0
1
2
0
0
0
1
1
1
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
2
0
0
1
0
2
0
0
3
9
0
0
0
0
2
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
1
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
1
0
0
2
0
0
2
1
0
0
2
2
0
1
0
2
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
3
0
0
0
0
2
0
2
0
0
2
0
1
2
1
0
0
0
1
0
0
1
0
0
0
0
1
0
1
1
0
0
2
0
0
1
0
2
2
0
2
0
0
0
0
0
0
2
0
0
0
2
1
1
0
0
0
0
1
0
0
0
0
0
0
2
0
4
1
4
0
0
0
3
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
2
1
0
0
3
3
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
3
2
0
0
1
0
0
0
0
0
1
2
2
2
0
2
0
0
0
0
0
2
0
0
0
0
1
3
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
3
2
0
3
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
1
0
0
3
0
0
0
2
0
2
0
2
0
0
1
1
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
1
0
0
2
2
0
4
0
0
0
0
2
2
0
0
1
0
0
0
0
0
1
2
0
0
1
0
3
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
2
1
0
1
2
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
1
1
0
0
0
2
0
8
1
0
0
0
0
2
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
1
0
2
0
1
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
1
0
2
1
1
1
0
1
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
1
1
0
0
2
1
0
0
1
0
2
0
0
1
2
0
0
0
0
0
2
0
2
0
1
0
2
1
0
0
1
0
0
0
1
0
0
2
0
2
2
0
0
2
0
2
2
0
0
2
0
1
2
1
0
2
1
1
0
0
0
0
0
0
2
0
1
0
1
0
0
0
1
0
2
0
0
1
0
0
0
0
1
0
0
0
0
2
1
0
0
3
1
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
1
2
0
0
0
1
0
0
1
4
0
2
0
0
0
0
0
0
0
0
1
0
2
1
1
0
1
1
0
0
2
0
2
2
0
2
0
0
1
0
1
0
2
0
0
0
0
0
0
0
2
0
2
1
0
0
2
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
3
2
0
0
0
0
1
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
1
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
1
0
2
0
1
1
1
1
2
2
0
0
0
0
0
0
1
0
0
1
4
1
0
0
0
0
0
0
0
0
0
3
0
2
0
0
1
0
0
1
0
0
0
0
2
0
2
0
0
2
3
0
0
0
1
0
2
0
2
1
3
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
2
0
2
1
0
1
2
0
1
0
0
1
0
0
3
0
0
1
0
2
0
0
0
0
2
0
2
1
0
0
0
1
2
0
0
0
0
1
2
0
0
0
0
0
1
0
0
3
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
2
2
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
2
0
0
1
2
0
0
2
0
0
0
1
0
0
1
0
0
1
0
2
2
0
0
0
0
0
0
0
1
1
0
1
2
0
2
1
1
0
0
0
1
0
0
1
0
2
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
2
0
0
0
0
0
0
1
0
3
0
0
0
0
0
1
0
2
2
0
0
0
0
0
2
0
2
2
0
2
0
0
1
0
0
1
0
0
0
0
2
0
0
0
4
1
2
0
0
2
1
2
0
2
1
0
0
0
0
0
2
0
2
0
0
0
0
1
2
1
2
0
0
0
0
0
0
0
2
0
1
0
1
0
1
0
2
0
1
1
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
2
0
0
2
1
0
4
0
2
1
0
0
0
0
0
1
0
0
0
7
0
2
4
1
13
0
0
0
0
0
2
2
0
0
0
1
0
0
0
2
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
2
2
2
2
1
0
0
0
2
1
0
1
0
1
0
1
0
0
2
2
1
0
0
0
2
0
0
1
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
5
0
0
0
6
0
1
0
1
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
2
1
0
0
3
0
1
1
2
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
2
2
1
0
0
0
0
1
1
0
0
2
1
0
0
0
2
2
1
1
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
2
3
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
2
1
0
0
0
1
0
4
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
1
0
1
1
0
2
0
0
0
0
0
0
0
1
3
0
3
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
3
1
0
1
2
0
0
1
1
0
2
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
1
0
1
1
0
1
0
0
2
0
0
0
0
2
2
1
0
0
1
1
0
0
0
0
2
0
2
2
0
0
4
0
0
0
0
0
1
0
2
0
0
0
2
0
2
0
0
0
0
2
0
2
0
8
0
0
0
0
0
0
6
0
0
1
0
0
1
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
1
0
1
0
0
0
2
2
2
3
0
0
1
1
0
0
0
1
3
0
2
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
2
1
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
2
1
2
0
0
2
0
0
3
0
2
0
0
0
1
0
1
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
1
0
1
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
2
0
0
0
3
0
1
0
2
0
2
0
3
1
3
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
1
2
2
0
0
2
0
0
0
0
0
0
0
2
2
0
1
0
1
0
0
1
0
0
2
0
2
1
1
0
0
0
1
0
0
0
2
0
0
1
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
3
2
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
3
1
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
2
2
1
0
0
0
0
3
2
0
0
2
0
3
1
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
1
0
0
1
0
1
0
1
0
0
0
0
2
0
2
1
2
0
0
0
0
1
1
0
0
0
2
0
0
3
0
0
1
0
0
0
0
0
9
0
1
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
2
1
2
0
0
0
0
0
0
1
0
0
0
2
0
0
3
0
0
0
1
0
0
0
0
0
0
1
3
2
0
0
2
0
0
0
0
0
0
0
1
0
1
0
2
0
1
0
1
0
0
0
0
0
2
0
2
0
0
1
0
1
0
2
0
2
0
2
0
0
0
0
2
0
2
1
1
1
1
0
3
1
2
2
0
4
2
0
2
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
2
0
2
3
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
1
1
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
2
0
2
1
1
0
1
0
0
0
0
0
2
0
0
1
0
0
1
0
2
0
2
0
0
0
0
2
0
0
0
1
1
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
2
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
2
0
0
0
0
3
2
0
0
2
0
0
1
1
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
3
0
0
2
0
1
1
1
0
0
2
1
0
1
0
1
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
4
1
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
1
0
0
0
1
2
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
1
3
0
0
0
0
2
0
0
0
5
1
2
0
0
0
0
0
2
1
0
0
2
0
1
1
0
0
1
0
0
0
0
2
0
0
2
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
2
1
1
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
2
0
1
0
0
2
3
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
1
0
0
2
0
7
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
4
1
0
0
1
1
0
0
0
0
1
2
0
0
0
3
0
0
0
0
0
0
0
0
1
4
0
0
0
2
2
0
2
0
1
0
0
0
2
0
0
3
2
0
0
0
5
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
2
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
1
2
0
0
2
0
1
1
2
0
0
0
0
0
0
1
1
0
2
0
0
1
0
2
1
0
0
0
0
1
2
0
1
1
1
0
0
0
0
0
2
0
0
0
0
1
0
0
2
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
1
2
1
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
1
2
0
1
0
2
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
1
0
0
0
0
0
0
0
0
2
1
0
4
1
1
1
1
0
0
2
1
2
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
1
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
2
1
0
2
1
0
2
0
0
2
0
0
0
0
1
2
0
0
0
2
1
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
1
0
0
0
0
0
1
0
0
0
2
0
2
5
1
0
0
0
0
1
0
0
0
0
5
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
1
2
1
2
0
1
3
1
1
1
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
5
2
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
1
0
0
2
0
0
0
1
2
2
0
0
0
2
0
0
0
1
2
2
0
0
2
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
2
0
0
2
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
1
2
1
2
0
0
1
0
1
1
0
0
0
0
2
2
0
2
2
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
2
0
2
2
0
0
0
2
0
0
2
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
3
0
0
2
0
1
0
0
0
0
0
1
0
2
0
0
0
3
0
0
1
0
1
1
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
2
1
0
0
2
0
0
0
0
0
2
0
0
3
1
2
0
1
1
0
0
1
1
3
2
0
0
0
0
2
0
0
0
0
2
0
0
1
0
1
0
0
1
0
0
1
1
0
0
0
2
0
0
2
0
0
1
2
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
2
2
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
1
1
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
3
0
2
0
0
0
1
1
0
0
2
1
0
0
0
0
2
0
0
0
0
4
1
0
0
2
0
0
0
1
3
2
0
1
0
0
0
0
0
0
0
0
0
0
1
5
1
0
0
1
2
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
2
0
0
3
0
0
4
0
0
0
0
2
0
0
0
2
1
0
2
0
0
1
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
2
2
0
0
2
0
0
1
2
0
0
0
1
2
2
0
1
1
1
0
2
0
2
0
1
0
0
2
1
0
2
2
1
0
0
0
2
0
2
1
0
1
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
2
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
2
1
0
2
0
2
0
0
2
2
2
0
0
2
0
1
0
0
0
0
0
0
0
1
2
2
2
0
1
1
0
0
0
2
1
0
0
0
0
2
0
0
0
0
2
0
0
2
3
0
0
0
0
3
0
0
0
1
0
0
0
0
1
0
0
0
1
2
0
0
4
1
0
2
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
2
1
3
0
0
0
0
0
0
2
0
2
0
2
2
2
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
2
2
0
0
1
0
1
0
0
0
0
1
0
2
2
3
0
1
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
1
0
1
0
2
0
1
0
0
1
0
0
0
1
0
2
3
0
2
2
2
0
0
0
0
1
0
1
2
0
0
2
1
1
1
0
0
1
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
2
3
0
0
0
0
2
0
0
1
0
0
1
0
0
0
2
2
0
0
0
0
0
0
1
3
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
4
0
2
0
3
2
0
0
2
0
2
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
1
2
0
0
0
3
0
0
2
10
2
0
1
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
1
0
0
1
1
0
0
2
2
1
0
0
0
0
0
0
2
2
2
0
0
1
0
0
0
2
0
0
0
1
1
2
0
1
0
0
1
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
1
2
0
2
2
0
0
0
0
2
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
2
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
3
2
0
0
2
0
2
0
0
0
0
0
2
1
0
1
1
1
0
1
1
0
0
3
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
2
1
0
2
0
1
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
1
0
1
0
3
0
0
0
2
0
2
0
1
0
1
0
0
0
2
1
1
0
1
0
0
2
0
0
0
8
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
2
0
1
0
1
2
0
0
0
0
0
0
0
2
3
1
0
0
0
3
0
2
0
0
0
1
1
2
0
0
1
0
0
0
1
0
1
1
2
0
2
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
1
0
0
4
0
0
2
0
0
0
1
2
0
1
1
2
0
0
1
0
1
0
0
0
1
0
1
0
1
0
0
0
1
2
2
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
1
0
4
2
0
0
0
0
0
2
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
1
0
2
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
2
0
1
0
1
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
2
2
2
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
2
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
1
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
5
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
2
0
0
2
1
0
1
1
2
1
0
2
0
0
0
1
0
0
1
0
1
2
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
1
2
0
0
0
1
1
0
0
2
0
1
0
0
0
1
0
0
2
2
0
2
2
0
0
0
1
0
0
0
2
0
1
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
1
0
0
1
0
0
2
0
0
0
1
2
2
2
1
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
2
0
0
0
0
2
2
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
3
0
2
1
0
0
0
0
0
2
0
0
0
2
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
1
0
1
0
6
0
0
2
0
0
2
0
1
0
0
1
2
0
0
0
0
1
0
1
0
2
0
1
0
0
1
1
0
1
1
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
1
0
1
0
0
0
0
1
0
2
0
2
0
0
0
0
1
3
0
1
1
0
2
2
1
0
0
3
0
2
0
0
1
0
2
0
0
0
2
0
0
0
1
1
3
0
0
2
2
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
2
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
1
2
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
2
0
2
2
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
2
2
0
0
0
0
0
1
2
0
1
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
2
0
1
0
0
2
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
2
0
5
0
0
0
2
2
1
2
0
2
0
0
0
0
2
1
0
2
0
2
2
0
0
0
2
0
1
2
0
1
1
0
0
2
1
6
0
1
0
0
2
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
1
0
0
2
0
0
2
0
2
1
0
1
0
1
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
1
1
2
2
0
0
0
2
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
3
0
1
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
2
0
1
0
0
0
2
0
2
1
0
5
1
0
0
0
1
1
1
2
0
0
0
0
0
2
2
0
0
1
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
3
1
2
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
2
4
3
0
1
0
0
0
1
1
0
4
2
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
1
1
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
2
1
2
2
1
0
0
0
0
0
1
0
0
0
0
2
3
0
0
0
0
0
1
0
0
1
0
0
1
2
0
0
0
1
3
0
2
0
2
0
0
0
0
2
2
0
0
0
2
0
1
1
0
0
0
0
2
0
2
2
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
1
0
1
1
2
0
0
0
2
0
1
2
0
0
0
0
0
0
1
1
0
0
0
0
1
0
2
1
0
0
0
0
2
0
0
0
0
1
0
0
1
2
0
0
0
0
1
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
1
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
2
0
0
0
0
2
1
0
2
1
0
0
0
1
0
1
0
0
1
0
1
0
2
1
1
0
0
1
0
2
1
0
2
0
0
0
0
1
1
1
0
2
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
2
2
2
0
0
0
1
1
0
0
0
0
0
2
0
0
2
0
0
2
0
2
0
2
0
1
0
2
1
1
0
1
0
0
1
0
0
0
0
0
2
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
6
2
0
1
0
2
0
0
0
0
0
1
5
0
0
0
0
2
2
0
0
0
2
0
2
0
0
2
0
2
0
0
0
2
0
0
0
0
2
0
2
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
1
0
1
2
1
0
1
2
1
2
0
2
2
0
1
2
1
2
0
0
0
2
2
0
2
0
0
0
3
0
0
2
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
1
0
0
2
2
0
1
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
2
1
2
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
1
0
0
2
0
1
0
0
0
1
0
0
0
2
2
0
0
1
0
0
0
0
0
1
0
1
2
0
2
1
0
0
0
0
0
1
0
0
0
1
1
0
2
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
2
0
8
0
1
0
0
1
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
1
0
1
1
2
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
1
0
2
0
2
0
0
0
2
0
0
0
0
0
1
2
1
0
0
0
2
2
2
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
2
2
0
0
2
0
0
0
0
0
2
5
0
0
0
2
0
0
1
0
0
1
1
1
0
0
2
0
0
2
0
0
0
0
0
0
1
1
0
0
3
0
0
0
3
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
2
0
2
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
2
1
0
1
0
2
2
0
0
3
0
0
0
0
1
0
0
4
2
0
0
0
2
0
0
1
2
0
0
2
0
0
0
0
0
1
0
0
2
2
1
1
0
0
0
1
2
0
0
1
2
0
0
0
0
0
2
0
2
2
2
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
1
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
1
1
0
1
0
1
0
0
2
0
0
0
0
2
0
1
0
0
0
0
1
0
2
0
1
0
2
0
0
0
1
0
0
2
0
0
0
2
2
1
0
0
2
3
0
0
0
0
0
1
0
2
2
0
1
0
0
0
0
0
1
1
2
0
1
0
0
0
2
0
1
2
0
0
0
0
0
2
0
0
0
2
1
2
2
0
2
1
0
2
0
0
2
2
0
0
0
0
0
0
0
2
0
1
2
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
2
2
0
2
0
0
0
0
2
1
0
0
0
1
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
2
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
2
0
0
0
2
1
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
2
0
0
0
1
1
2
0
0
0
1
1
0
0
0
1
0
0
4
0
3
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
2
2
0
0
0
1
0
0
0
0
1
0
0
0
2
1
2
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
2
2
0
8
0
1
0
1
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
1
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
1
0
2
1
0
0
2
0
1
0
1
0
2
2
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
1
0
2
0
0
1
0
0
2
0
1
2
2
2
0
0
2
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
2
0
0
0
1
0
2
0
1
0
0
0
0
2
2
1
1
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
1
0
2
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
2
0
0
1
0
2
2
0
2
0
0
1
0
0
0
0
1
0
2
0
0
2
0
0
2
0
2
0
0
2
1
0
1
0
1
1
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
3
0
0
0
0
2
0
0
0
0
0
1
2
2
1
0
1
0
3
2
0
0
0
0
0
2
0
1
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
2
1
1
0
2
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
1
0
2
1
1
0
0
0
0
1
0
1
0
2
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
2
0
1
0
1
0
0
0
0
1
0
3
2
0
0
0
0
0
0
0
0
0
2
1
0
0
3
0
0
1
0
0
0
0
0
2
0
0
0
1
1
0
0
1
1
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
2
2
0
1
2
1
0
0
0
2
1
1
0
2
0
1
0
0
0
2
1
2
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
2
0
2
2
0
1
0
0
0
0
0
0
1
2
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
7
0
1
2
0
0
0
1
1
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
5
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
3
1
1
0
0
0
1
2
0
0
0
1
2
3
0
2
0
0
3
0
1
0
2
0
0
0
0
0
2
0
1
0
1
0
0
0
1
0
2
0
1
1
1
0
0
1
2
1
2
1
1
0
0
0
1
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
1
0
2
0
0
2
2
0
2
0
0
0
0
0
2
2
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
2
1
2
0
0
2
0
0
2
1
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
2
0
0
1
0
0
2
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
2
2
2
0
2
1
1
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
1
0
0
1
0
2
2
2
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
1
0
0
0
2
2
0
0
1
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
2
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
6
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
2
0
0
2
0
0
2
0
1
0
0
2
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
2
0
0
2
0
1
1
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
2
0
0
2
1
2
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
2
0
0
2
2
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
2
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
2
2
1
0
0
0
2
0
0
2
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
2
0
2
2
1
0
2
5
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
2
0
1
0
1
2
0
0
0
0
1
0
2
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
5
0
0
0
0
0
0
2
0
2
1
1
0
1
0
1
1
0
2
1
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
1
0
0
1
1
0
2
0
0
3
0
0
2
2
0
0
1
0
0
0
2
0
0
2
0
0
1
1
6
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
1
2
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
3
0
2
0
0
2
1
0
0
0
2
0
0
1
0
0
0
1
0
0
0
2
1
0
3
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
1
1
0
0
0
0
1
0
2
1
0
1
0
0
2
0
0
0
0
0
2
0
0
4
0
0
0
0
0
0
1
0
3
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
6
1
0
1
3
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
2
0
0
0
0
2
4
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
2
0
0
3
0
0
0
0
0
1
0
5
0
0
0
0
0
0
2
2
0
0
0
2
3
0
0
0
2
0
0
0
4
1
1
0
2
1
0
0
1
2
0
0
0
2
2
3
0
0
0
0
0
0
1
0
2
0
0
1
0
0
2
2
0
0
0
0
0
0
2
0
0
0
3
1
3
0
0
2
2
0
0
0
0
0
0
2
2
0
0
0
1
2
2
0
0
0
0
3
1
0
1
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
1
0
0
2
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
1
1
0
0
1
0
0
1
0
1
0
0
2
0
0
1
0
2
0
0
0
2
0
0
1
1
0
2
1
0
0
1
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
2
0
0
0
0
0
0
1
0
0
2
2
0
0
1
0
0
0
0
2
0
0
4
0
2
0
0
1
0
0
0
3
2
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
4
0
0
0
0
2
0
0
2
0
1
0
0
2
0
2
2
0
0
1
4
1
0
0
2
2
0
0
2
1
0
1
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
1
1
0
0
2
0
0
0
0
2
3
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
3
0
0
2
0
0
0
6
0
0
2
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
3
0
0
1
0
1
0
0
0
0
0
0
0
1
2
0
0
1
1
0
2
2
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
2
0
1
0
2
0
0
0
0
0
2
2
0
0
3
0
0
0
0
2
0
0
1
1
2
0
0
0
0
1
0
5
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
1
0
0
0
0
1
0
0
1
0
0
4
0
0
0
0
0
2
1
0
2
2
0
0
1
0
1
0
3
0
1
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
2
2
0
0
0
0
0
0
0
1
1
1
0
2
0
0
1
0
1
0
0
0
1
0
0
3
0
0
0
0
0
3
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
1
0
0
2
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
1
2
1
2
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
2
2
1
1
1
2
1
0
3
0
1
1
0
0
1
0
2
1
0
0
0
2
0
2
0
0
0
3
0
3
0
2
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
1
1
1
0
0
1
0
0
1
0
0
2
0
0
1
1
0
2
0
2
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
2
0
2
0
1
0
1
3
0
0
0
2
0
0
0
1
2
2
0
0
2
0
0
0
0
2
3
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
2
0
2
0
0
0
0
0
1
0
1
0
1
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
1
0
0
1
1
0
1
0
2
0
1
0
0
0
0
0
0
2
1
2
3
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
1
1
0
1
0
0
2
0
2
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
1
2
0
1
0
1
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
2
0
1
0
0
0
0
0
2
0
0
6
0
4
0
0
0
0
0
0
2
1
0
2
0
0
2
0
1
0
2
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
1
0
0
0
1
2
2
0
2
0
0
1
2
0
2
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
3
0
0
0
3
1
1
0
2
0
0
0
0
0
0
0
0
1
1
0
1
0
2
1
1
1
0
2
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
2
1
2
2
0
1
0
0
0
2
1
0
0
0
0
0
0
1
0
0
2
0
0
0
1
1
0
2
2
2
0
3
3
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
2
1
0
0
3
0
1
0
0
2
0
3
1
0
2
0
0
2
0
1
1
1
0
0
0
1
0
0
0
0
0
2
1
2
0
0
0
0
1
1
0
0
1
0
3
0
0
2
2
3
0
0
1
0
1
0
0
0
2
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
2
0
1
0
0
0
1
0
0
1
2
1
1
0
0
0
0
0
0
0
2
0
0
1
2
0
2
0
0
0
0
0
2
2
0
0
2
0
0
0
0
1
2
0
0
2
0
0
2
0
0
0
0
3
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
1
0
0
1
0
1
0
3
0
1
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
3
0
0
0
2
0
0
0
1
1
0
1
0
0
0
0
0
0
1
2
0
2
0
1
0
0
1
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
2
1
1
1
0
2
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
1
1
0
0
0
1
0
0
1
2
2
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
3
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
1
3
2
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
2
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
2
1
1
0
0
0
0
0
1
3
0
2
0
0
0
1
1
1
0
1
1
0
0
1
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
2
0
0
0
0
2
3
2
0
2
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
5
0
0
0
0
2
2
0
0
0
0
0
1
0
2
0
2
2
1
0
0
2
0
0
1
0
0
0
0
1
0
3
0
1
0
1
1
0
2
2
0
1
2
2
1
1
0
0
0
2
0
2
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
1
2
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
2
1
2
0
0
0
0
0
2
1
3
2
0
0
1
2
0
0
0
0
1
0
0
0
0
1
2
2
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
3
0
2
2
0
1
0
0
0
2
0
0
0
1
0
0
3
0
1
0
6
0
0
2
0
2
4
0
0
0
2
2
0
0
0
0
2
0
2
2
0
0
1
0
1
2
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
1
0
0
0
1
0
1
0
2
0
2
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
2
1
2
1
0
0
0
1
2
0
2
0
3
0
2
0
2
2
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
3
2
1
2
0
0
2
0
2
0
1
0
0
0
1
0
3
2
1
1
2
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
2
1
1
0
2
0
0
0
1
0
0
2
2
0
1
0
1
0
0
0
0
1
1
3
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
6
1
0
4
0
0
1
0
0
1
0
0
2
0
2
2
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
2
1
0
0
0
2
0
1
0
0
0
0
0
0
1
1
1
0
0
1
1
1
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
1
0
0
2
0
0
2
0
0
1
0
2
0
0
0
0
1
2
0
0
1
0
2
0
0
1
0
0
2
0
0
0
0
1
0
0
0
2
2
3
2
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
3
0
0
0
0
1
0
1
0
2
0
1
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
1
0
0
1
0
0
0
0
0
1
2
0
2
1
0
2
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
6
2
0
0
0
2
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
4
2
0
0
1
0
0
1
0
0
0
2
0
0
1
2
0
0
0
0
3
0
0
2
0
0
0
0
0
2
2
1
0
1
1
0
1
0
0
0
0
1
0
0
2
0
3
0
0
0
0
0
2
2
0
2
0
0
0
0
0
2
0
2
0
2
0
0
0
2
0
0
1
0
0
2
2
0
0
0
0
2
0
2
0
0
0
2
0
0
2
0
0
2
0
0
0
2
0
2
1
0
0
0
2
0
0
0
0
3
2
0
0
0
1
0
1
2
0
0
1
2
2
1
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
8
0
0
0
0
0
0
1
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
2
1
0
0
2
0
1
0
2
0
2
2
0
0
6
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
1
0
1
0
0
0
0
0
0
1
0
0
0
1
3
2
2
0
0
0
0
1
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
3
0
0
0
1
0
2
0
0
0
3
0
0
1
0
1
4
0
0
0
0
0
1
2
1
0
0
2
2
2
0
1
1
0
2
0
0
0
0
0
0
0
0
2
2
1
2
0
0
0
0
2
0
0
2
0
1
0
3
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
2
0
0
0
2
0
0
2
0
1
6
0
0
2
0
1
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
7
0
0
0
3
0
2
0
2
1
0
0
0
0
0
1
0
0
2
1
0
2
1
0
0
0
0
0
0
0
2
0
0
1
2
0
2
0
2
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
3
0
2
1
0
0
0
0
0
1
2
0
3
0
0
1
0
0
0
2
1
0
2
0
0
0
1
0
0
1
1
0
0
0
0
1
2
0
0
1
0
0
1
0
0
0
1
0
0
0
2
0
1
2
0
0
2
2
0
1
0
0
4
0
2
2
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
3
1
0
1
2
0
0
1
1
0
0
0
0
0
2
3
2
3
1
0
1
0
2
0
0
0
2
0
0
1
0
0
2
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
2
2
2
1
0
0
3
1
0
0
1
2
2
3
3
0
0
0
0
0
0
2
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
1
2
0
0
0
2
0
1
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
3
0
0
0
0
1
0
2
0
2
1
0
0
0
2
2
2
0
2
0
0
0
0
2
0
1
0
0
0
1
0
2
4
3
2
0
0
0
0
3
1
5
0
2
1
0
1
0
0
0
3
0
0
1
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
1
2
0
0
0
3
1
0
2
0
0
0
2
0
2
0
0
0
2
0
0
2
1
1
0
0
1
0
1
0
3
0
2
0
0
2
0
0
0
0
2
0
0
2
0
1
0
0
2
1
1
1
0
0
1
0
0
3
0
0
0
3
0
0
0
0
0
0
0
2
0
0
2
0
2
3
0
1
0
0
1
3
2
0
0
1
0
1
2
1
0
0
1
0
2
0
0
0
2
0
0
0
0
2
0
2
1
0
0
1
0
0
0
0
1
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
1
0
0
2
0
1
0
0
0
2
0
3
1
0
0
0
2
2
0
0
1
0
0
0
0
0
1
0
0
0
2
1
0
0
2
0
0
1
0
0
2
0
0
1
0
0
0
2
0
0
2
0
2
0
0
1
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
1
2
0
2
1
0
3
1
0
0
0
0
0
0
2
1
1
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
1
1
0
1
1
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
2
3
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
1
1
2
0
1
0
0
0
0
3
0
1
1
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
2
0
1
2
0
0
0
0
4
0
1
0
2
0
0
2
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
2
2
0
1
2
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
2
0
0
1
0
0
2
1
2
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
3
0
2
0
1
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
3
2
2
1
0
0
2
0
2
1
0
1
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
1
0
2
0
0
0
1
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
1
0
2
0
2
2
2
2
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
3
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
1
0
1
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
2
2
0
2
1
1
0
0
1
0
0
1
2
0
0
0
0
0
1
0
1
0
0
1
0
2
0
2
0
0
0
1
2
2
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
2
0
2
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
1
0
0
0
2
0
0
0
1
0
0
2
1
1
1
0
0
2
0
1
3
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
1
1
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
2
0
2
0
0
2
3
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
2
0
0
0
1
1
5
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
1
0
3
0
0
0
0
0
1
1
2
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
1
0
0
0
0
1
0
2
2
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
2
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
5
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
1
0
2
0
1
1
0
0
2
0
0
0
1
0
1
0
0
4
0
2
0
0
0
0
1
1
0
2
2
2
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
1
0
1
2
0
1
0
0
1
0
2
2
1
0
0
0
3
2
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
2
0
1
2
0
0
2
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
2
0
0
0
0
1
2
0
0
1
2
0
0
1
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
1
0
0
0
2
0
2
2
0
0
1
2
0
0
0
2
1
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
3
0
0
0
1
0
2
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
1
2
3
0
0
0
2
0
2
0
0
0
0
0
0
2
2
0
0
1
0
2
0
2
0
0
2
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
2
4
1
0
0
0
0
1
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
2
1
2
1
2
0
0
2
1
0
0
0
0
1
2
0
0
0
0
0
0
1
2
0
1
3
1
2
0
2
1
2
0
0
0
0
2
0
2
0
1
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
1
0
1
2
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
2
0
0
0
0
0
0
1
0
0
0
1
1
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
1
1
0
0
0
0
2
2
2
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
3
0
0
0
0
1
1
0
0
0
0
0
0
1
0
2
3
0
0
2
1
1
2
0
2
0
0
0
0
0
1
2
0
3
3
0
2
0
1
0
0
0
0
1
0
0
0
2
2
0
1
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
1
1
1
0
1
2
1
0
0
0
0
1
0
0
1
0
0
2
0
0
0
1
1
0
0
2
2
2
1
1
0
0
0
3
2
0
0
1
0
1
2
0
0
0
1
0
0
1
0
0
0
0
1
0
0
2
0
2
0
3
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
3
2
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
2
0
0
0
0
1
2
0
0
1
0
0
0
0
0
3
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
1
0
3
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
2
0
0
0
0
0
0
1
0
0
1
0
0
2
2
0
0
0
0
0
2
0
1
0
0
0
2
0
1
0
0
0
1
0
0
0
2
0
0
1
0
0
2
1
1
0
0
0
1
0
2
0
0
3
0
0
2
0
0
1
0
0
0
0
0
0
0
2
1
0
1
0
1
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
2
0
0
1
0
0
0
0
0
2
3
0
0
0
0
1
0
1
0
1
1
0
0
0
0
2
1
0
0
1
0
0
2
0
1
0
0
2
0
0
1
0
1
2
1
1
2
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
1
0
2
0
0
4
0
0
0
0
1
0
0
0
1
0
0
0
0
2
1
2
0
1
0
0
0
1
0
5
1
2
0
1
0
2
1
2
0
0
0
0
0
2
1
1
0
0
0
3
2
0
0
0
0
1
0
0
0
0
2
1
0
0
0
1
0
0
3
1
0
1
0
0
0
0
0
0
0
0
1
3
1
0
2
0
1
0
1
0
1
0
1
2
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
1
0
0
4
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
3
0
0
2
0
2
0
1
0
0
0
1
0
2
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
2
1
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
1
2
0
0
1
0
0
0
0
2
0
0
0
2
0
2
2
0
0
0
0
0
0
1
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
1
0
2
2
0
0
0
1
2
0
2
0
2
0
0
0
1
0
1
0
1
2
0
0
0
3
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
4
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
1
2
0
0
1
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
2
0
0
2
1
0
1
1
1
0
1
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
1
1
0
0
0
0
1
0
2
1
0
1
0
0
0
1
2
1
1
0
1
0
0
0
2
2
2
2
0
0
0
1
0
2
0
1
0
4
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
1
0
0
1
0
0
1
0
0
1
0
1
0
2
0
1
2
0
1
2
0
0
0
3
0
2
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
1
0
0
0
1
0
0
1
5
0
2
2
2
0
0
0
1
0
2
0
1
0
0
0
0
1
0
0
1
0
1
0
0
2
0
0
0
0
1
0
0
1
0
0
0
1
2
0
0
1
0
0
0
1
2
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
1
1
2
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
2
2
0
0
0
0
0
0
2
0
2
0
1
1
0
0
1
0
1
0
0
0
3
0
2
2
0
2
2
0
0
0
0
3
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
2
0
0
0
2
0
0
0
2
1
0
0
0
0
1
0
0
2
0
2
0
0
2
3
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
2
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
7
0
0
2
0
2
2
0
0
0
3
0
0
1
0
0
0
0
0
0
2
3
0
0
6
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
1
2
0
2
0
1
0
0
0
0
0
0
3
2
0
1
0
0
1
0
2
0
0
2
1
1
2
0
0
0
0
1
1
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
1
0
1
0
2
0
0
1
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
4
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
2
0
0
0
1
1
0
0
7
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
1
2
1
0
0
0
1
0
0
1
0
0
1
0
1
2
0
3
0
2
0
2
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
3
1
1
2
1
0
0
0
0
0
0
0
1
1
3
0
0
0
1
0
1
0
2
1
0
0
1
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
1
0
2
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
2
2
0
0
0
3
0
0
0
0
0
0
0
0
0
5
0
1
1
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
2
2
1
2
0
3
0
2
2
0
0
0
2
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
2
0
0
0
0
0
2
2
1
0
0
2
2
0
2
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
1
2
0
0
0
0
0
1
0
0
2
1
2
0
0
0
0
3
3
1
1
0
0
0
2
0
1
0
1
0
0
2
0
0
0
1
1
0
0
0
0
2
0
0
2
0
2
0
0
2
0
0
0
0
0
0
1
1
0
0
5
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
1
0
1
0
0
0
0
1
0
0
0
2
1
0
1
1
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
1
0
0
0
0
0
0
1
1
0
0
1
0
1
0
2
0
0
1
2
1
1
0
0
0
0
0
3
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
2
0
1
1
0
0
2
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
2
0
0
1
1
0
0
0
0
0
0
1
0
3
1
0
0
1
0
0
0
1
0
2
1
0
0
0
0
0
1
0
0
0
1
0
0
0
7
4
1
2
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
2
0
0
0
1
0
1
2
2
0
1
0
0
2
0
1
0
0
0
2
1
0
0
2
2
0
2
1
1
1
0
1
0
1
0
2
0
0
0
0
0
1
0
0
0
1
2
1
0
0
0
1
1
0
0
1
2
2
0
2
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
7
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
2
0
0
1
0
0
0
1
1
2
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
2
0
0
2
0
0
0
2
0
2
2
0
0
0
0
0
1
0
0
1
1
0
0
2
0
0
0
0
0
0
1
0
0
2
3
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
3
1
0
3
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
3
0
2
0
1
0
0
0
0
1
0
2
0
0
2
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
9
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
2
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
1
2
0
0
2
3
2
2
0
0
0
0
0
0
0
2
0
0
0
1
3
0
0
0
2
0
0
0
0
1
4
0
0
0
0
1
2
0
2
0
0
2
0
0
2
1
0
0
2
1
0
0
0
0
0
2
0
0
0
0
1
2
0
0
2
0
0
0
0
3
0
0
2
1
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
1
2
0
0
1
0
1
1
0
0
0
2
0
0
0
0
1
4
0
2
2
0
1
0
2
0
0
1
0
0
1
1
0
0
2
0
0
2
1
0
1
2
0
2
1
1
2
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
1
0
0
2
0
1
2
1
1
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
1
3
0
1
0
0
2
0
0
0
1
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
1
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
2
2
0
2
0
2
2
0
0
0
2
0
0
0
0
1
0
1
0
2
0
2
0
0
0
0
0
2
1
0
0
2
0
0
0
0
1
0
2
0
0
3
0
0
1
0
0
0
2
0
0
2
1
0
0
2
1
2
0
0
0
0
0
2
2
0
0
1
2
2
0
0
0
1
0
1
1
2
1
0
0
0
0
0
0
2
0
0
0
0
2
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
2
0
0
0
1
0
0
0
0
0
0
2
5
5
0
0
1
0
3
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
3
2
0
2
0
0
0
1
0
2
0
0
0
2
0
0
3
2
0
0
0
0
1
0
0
3
2
2
1
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
2
2
3
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
1
2
0
0
0
3
2
4
2
0
0
1
0
0
0
0
1
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
3
0
0
0
0
1
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
2
0
0
0
0
1
0
0
5
0
0
0
2
0
0
0
0
1
2
0
1
0
2
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
1
2
0
2
0
0
1
2
1
1
0
2
0
0
0
2
0
1
0
2
2
2
0
0
2
1
2
0
0
0
0
0
1
2
2
1
0
0
0
0
2
0
1
0
0
2
0
0
1
0
0
1
1
0
1
1
1
0
0
0
0
0
0
0
5
1
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
3
2
0
0
2
1
0
0
1
0
0
2
0
0
0
0
0
3
0
0
0
2
0
0
2
2
3
0
0
0
0
2
0
0
2
0
1
1
0
1
0
1
0
0
3
2
2
1
0
0
0
1
1
0
0
0
2
0
1
0
1
0
0
1
2
1
0
0
0
0
0
0
0
1
0
1
0
0
0
3
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
3
0
2
0
0
0
2
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
3
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
4
1
2
1
0
2
0
0
1
0
0
1
0
1
0
1
0
5
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
1
1
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
1
2
2
0
1
0
0
0
1
2
1
0
0
0
2
2
1
0
0
0
2
0
0
0
0
0
0
2
2
1
1
0
0
1
0
0
0
3
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
1
1
2
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
1
0
0
1
0
2
0
1
0
2
0
2
0
2
2
2
0
1
2
0
1
0
0
0
0
2
2
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
1
4
2
0
2
2
2
0
0
0
0
0
1
1
0
0
0
4
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
1
0
0
0
0
1
0
0
0
0
2
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
2
1
1
0
4
0
2
0
1
0
0
1
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
2
0
0
0
0
2
3
0
3
0
0
0
0
0
0
1
2
0
2
2
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
1
0
0
1
0
0
1
0
3
0
0
2
0
2
0
0
1
0
2
1
2
1
0
0
1
1
2
1
0
0
0
0
1
1
1
2
0
0
0
0
2
1
0
0
1
0
0
0
1
2
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
1
1
1
0
0
0
2
0
4
0
0
1
0
0
1
2
0
0
0
0
0
2
2
0
0
1
2
0
0
0
1
0
2
2
0
0
0
1
0
0
1
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
2
0
5
0
1
1
0
0
0
0
0
2
1
0
1
2
0
0
0
0
1
0
1
0
0
1
0
2
0
0
0
0
0
0
2
1
1
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
3
1
1
3
0
0
0
2
2
0
0
1
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
1
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
4
1
0
0
0
0
0
0
1
0
3
0
1
0
1
2
1
3
0
1
0
0
0
0
0
2
0
1
0
2
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
2
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
2
0
0
3
0
0
2
2
3
0
0
2
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
2
0
1
1
1
0
0
0
2
0
0
1
0
1
0
0
0
1
1
0
0
1
0
0
1
0
0
0
2
0
1
0
0
1
0
1
2
5
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
2
0
1
0
0
0
1
2
0
3
0
0
0
0
0
1
0
0
2
0
2
1
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
2
0
2
2
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
7
0
0
0
0
2
0
0
0
2
0
0
0
0
1
1
0
1
2
2
0
1
3
0
2
2
3
1
2
2
0
2
1
0
0
0
1
0
2
0
1
2
1
0
2
0
0
0
1
0
0
0
0
2
0
2
0
2
0
2
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
2
0
1
3
2
0
0
0
2
2
0
2
4
3
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
3
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
1
1
1
3
0
0
0
0
0
0
1
4
0
1
0
0
0
0
0
2
0
0
0
0
0
2
1
1
2
2
2
1
0
0
0
1
4
0
1
0
2
1
0
2
0
0
2
1
0
0
2
1
0
0
0
1
0
1
1
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
2
2
2
0
2
0
0
2
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
2
0
0
2
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
1
0
2
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
1
2
0
0
0
0
0
3
2
2
0
0
2
0
1
2
0
0
1
0
0
1
0
0
2
0
1
1
0
0
2
0
0
0
0
2
1
0
0
0
0
1
2
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
2
1
0
0
3
1
2
0
1
0
0
6
1
0
1
0
0
2
0
3
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
2
3
0
0
0
0
0
2
0
0
0
0
0
0
2
1
2
0
0
0
0
2
0
0
0
2
2
0
0
0
2
0
0
0
2
2
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
3
3
0
0
0
0
0
1
1
0
0
0
1
0
2
0
0
0
3
1
0
0
0
1
1
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
7
2
0
0
2
0
0
2
1
0
0
0
0
0
0
2
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
1
0
0
2
2
0
0
2
1
0
0
1
0
0
2
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
2
1
0
0
0
2
0
2
0
0
0
1
0
0
0
0
1
0
1
0
2
0
0
0
1
0
1
2
0
0
1
0
0
0
0
0
1
4
0
0
0
0
0
0
0
1
0
0
2
1
1
0
0
1
0
0
0
2
1
0
0
2
0
0
0
0
0
2
0
1
2
0
1
0
0
2
0
2
0
2
0
0
0
0
0
0
2
0
0
0
1
2
0
1
2
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
2
1
0
3
0
1
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
2
2
0
0
1
0
2
3
0
0
0
0
1
0
2
0
0
1
2
0
0
0
2
0
0
0
1
1
2
1
0
3
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
6
1
0
2
0
1
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
1
2
1
1
0
0
0
0
0
2
1
1
0
0
0
2
0
0
0
2
2
0
1
0
2
0
0
0
2
0
0
0
1
0
2
0
3
0
1
0
0
0
0
0
1
0
0
1
0
2
0
0
2
0
0
0
1
5
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
1
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
2
2
2
0
0
0
0
0
0
2
0
0
1
1
2
0
0
0
3
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
1
0
4
0
1
0
0
0
2
0
0
3
3
1
0
0
0
1
2
3
0
1
1
0
0
0
1
0
1
0
1
0
0
1
1
0
0
1
1
1
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
2
0
0
2
2
0
0
0
0
0
2
2
0
0
0
0
0
1
2
1
0
2
0
0
0
1
0
0
0
2
0
2
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
2
1
0
0
1
1
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
2
0
1
0
2
0
0
0
2
1
3
1
0
0
0
0
2
3
0
0
0
0
0
0
0
1
0
1
2
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
1
2
0
2
2
0
2
0
2
6
1
0
0
1
0
2
1
3
0
0
0
0
0
0
0
2
1
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
2
2
0
2
0
2
0
2
0
0
0
0
0
1
2
0
0
2
2
0
0
0
2
1
0
0
0
3
1
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
1
1
0
0
1
0
2
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
2
0
1
0
2
2
0
0
0
2
0
0
0
0
0
1
1
2
1
0
0
1
1
3
0
0
0
1
0
0
1
0
0
2
0
1
0
0
1
0
0
0
0
8
0
0
0
2
0
0
0
0
1
0
0
0
0
1
1
1
0
3
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
2
1
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
2
0
0
0
2
0
0
0
2
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
2
0
0
2
1
0
1
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
3
0
2
0
0
0
1
0
0
1
1
0
1
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
2
0
2
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
2
1
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
2
0
0
2
0
0
0
0
0
6
0
2
0
0
0
1
1
1
0
2
1
0
1
0
0
0
0
2
1
0
1
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
2
0
1
0
0
0
2
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
3
1
0
2
0
0
0
4
0
2
0
0
2
0
2
0
0
0
0
0
4
0
0
0
1
0
2
2
0
0
0
1
2
11
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
1
0
0
0
2
0
0
2
1
1
2
0
0
0
0
0
2
0
2
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
3
1
2
0
2
0
1
0
0
0
2
2
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
1
1
0
0
1
0
1
1
1
2
0
1
0
1
1
0
2
1
0
2
2
0
0
0
0
1
0
3
2
1
0
0
0
0
1
0
2
0
5
2
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
1
1
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
4
1
0
0
0
0
0
0
1
0
2
0
0
3
0
0
0
6
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
3
2
2
2
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
2
0
2
0
1
0
0
3
0
2
0
0
4
0
0
1
0
0
0
0
0
2
0
2
2
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
3
1
2
0
0
1
0
2
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
1
3
1
2
0
0
0
0
0
2
5
0
0
0
0
0
0
2
0
2
0
0
0
1
0
4
0
0
0
2
0
0
0
0
0
2
1
0
3
2
0
0
1
0
1
0
0
4
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
1
2
0
0
1
0
0
0
2
1
2
0
0
0
0
1
0
0
1
0
0
0
0
2
2
0
1
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
2
0
1
0
0
0
3
1
0
2
0
0
2
0
0
0
1
0
0
0
0
0
2
0
2
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
1
0
1
0
2
0
0
0
0
1
0
0
2
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
2
1
2
2
0
0
0
0
1
0
1
2
0
0
2
0
0
2
0
0
0
0
2
1
0
0
0
0
0
2
0
1
1
1
0
0
1
1
1
1
1
0
2
1
0
0
0
0
0
0
0
1
2
0
0
1
0
2
0
0
0
0
0
2
0
2
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
2
2
0
0
1
1
0
0
2
2
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
3
0
3
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
2
2
2
0
0
0
3
0
0
0
2
0
3
0
0
2
2
0
3
2
2
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
1
2
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
4
2
1
0
0
0
1
0
0
0
0
0
1
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
2
0
1
5
0
1
1
0
0
0
1
0
0
1
0
0
0
0
3
0
2
1
0
0
0
0
1
1
0
0
2
1
0
0
0
4
0
1
0
0
0
1
1
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
2
2
0
1
2
0
1
3
0
0
0
0
0
2
0
0
0
0
0
0
2
2
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
2
3
0
2
0
2
0
1
2
0
0
0
2
1
0
0
0
0
0
0
0
1
1
2
0
2
0
0
0
2
1
2
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
3
0
0
2
1
1
0
0
0
2
1
2
1
0
1
0
2
0
0
0
0
1
1
0
0
0
2
1
0
1
0
0
0
2
0
2
0
2
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
3
1
2
2
2
1
2
1
0
1
0
1
0
0
0
1
0
0
2
1
2
0
2
2
6
0
0
0
0
0
0
0
3
1
1
0
0
0
2
0
1
0
0
0
0
0
0
2
0
2
1
1
0
2
0
1
0
0
0
2
0
0
1
2
0
0
2
0
0
2
0
1
0
1
0
0
0
2
0
0
2
0
2
0
0
0
0
1
0
0
0
0
3
0
0
2
0
0
2
0
1
0
2
0
0
0
0
2
0
0
0
2
2
0
1
0
2
0
1
0
0
0
0
0
0
0
0
3
2
0
0
0
2
0
0
1
0
0
0
2
0
0
2
0
2
0
0
2
2
2
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
2
0
2
1
1
0
1
1
0
0
0
0
0
0
2
0
1
2
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
2
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
1
0
0
2
0
1
1
0
0
2
0
1
1
2
0
0
0
2
0
0
1
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
2
0
8
0
1
0
0
2
0
0
1
3
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
2
0
0
2
1
0
0
0
2
0
0
0
0
0
0
1
2
0
2
0
0
0
3
2
0
1
2
0
2
1
0
0
1
0
0
0
1
1
0
1
0
2
1
0
0
0
0
0
0
1
2
5
2
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
1
0
1
0
2
2
0
1
2
0
0
1
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
2
0
0
0
0
0
0
2
1
1
2
3
0
0
0
0
2
0
0
0
0
1
2
0
1
0
0
0
1
2
0
1
1
0
1
0
0
1
0
0
0
3
0
2
0
2
0
1
0
1
2
0
0
4
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
6
0
0
0
0
0
0
0
1
0
1
0
0
8
2
0
0
0
0
0
1
0
0
2
0
0
2
1
1
0
0
0
1
1
0
0
0
0
1
1
1
0
0
0
0
0
1
0
2
0
0
0
1
0
0
1
2
3
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
1
0
0
0
2
1
0
0
8
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
1
2
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
1
0
1
1
0
1
0
2
1
0
0
1
0
0
1
0
1
0
2
0
0
0
2
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
1
0
0
0
0
1
3
0
0
2
0
0
0
2
0
0
2
2
2
1
1
0
0
0
1
0
0
0
2
1
0
0
2
0
2
0
2
2
1
1
0
2
0
0
2
0
0
0
1
1
0
0
0
1
0
2
0
0
1
0
0
0
0
1
0
0
1
0
1
2
2
0
1
2
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
1
0
0
1
0
0
0
2
2
2
0
2
3
0
0
0
2
1
0
0
0
0
1
0
1
2
0
0
2
0
0
0
0
0
2
0
1
1
0
0
0
0
0
2
0
0
0
2
1
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
1
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
2
0
2
2
1
0
7
0
1
1
0
1
1
1
1
0
0
0
1
0
0
0
2
2
0
1
0
0
0
0
0
0
1
1
1
0
1
0
0
0
2
2
2
2
0
0
2
1
0
5
0
1
0
0
1
0
0
0
0
2
1
0
0
2
2
1
0
2
0
2
1
2
1
1
0
0
2
2
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
3
0
0
0
1
1
2
0
0
0
0
2
0
0
1
1
0
1
0
2
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
2
1
0
1
0
5
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
2
1
0
0
0
1
1
2
0
0
1
0
3
0
0
0
0
1
0
0
2
0
0
2
0
0
1
0
0
0
2
0
0
0
2
0
0
2
2
0
2
0
0
0
2
0
3
0
0
0
0
1
2
2
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
1
1
0
2
3
2
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
3
1
0
2
3
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
1
0
1
2
2
0
0
0
0
1
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
1
1
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
2
1
0
2
1
2
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
2
0
2
1
0
2
0
0
1
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
4
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
1
1
0
0
0
0
1
0
0
0
2
0
2
2
1
0
0
0
0
2
2
0
0
1
0
2
1
0
0
2
0
0
0
0
0
0
0
1
1
0
2
0
2
2
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
3
0
0
2
0
1
1
0
0
0
3
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
3
0
0
0
2
0
3
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
1
0
2
0
0
0
4
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
2
0
0
1
0
0
2
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
1
0
0
0
1
0
0
0
0
2
0
1
0
2
2
0
0
0
0
0
0
2
0
0
1
0
1
1
0
0
0
1
0
3
0
0
0
0
1
1
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
1
0
1
2
0
0
3
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
2
0
2
0
0
0
0
0
0
1
0
2
2
0
0
1
2
1
0
0
0
0
0
0
0
1
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
2
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
2
1
0
5
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
3
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
2
1
2
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
3
0
1
1
0
2
0
3
0
2
0
2
0
2
0
1
0
0
0
0
0
0
1
5
2
0
1
2
0
0
2
0
2
0
0
0
3
1
0
0
0
0
1
0
0
0
0
2
0
0
1
0
2
0
2
1
0
0
0
2
2
0
0
0
0
0
1
0
0
2
2
0
0
0
0
1
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
3
0
1
0
1
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
2
2
0
0
0
2
3
0
0
2
0
2
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
2
1
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
2
0
0
0
2
1
0
0
0
0
1
0
0
1
0
0
2
0
0
2
0
0
2
0
0
0
0
2
0
0
0
2
0
3
1
0
2
0
1
0
0
2
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
2
0
0
0
0
1
2
2
0
2
4
0
2
1
1
0
2
0
0
0
1
0
0
0
0
0
2
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
1
1
2
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
2
1
0
0
0
2
1
3
0
0
0
0
0
0
2
0
0
1
1
0
1
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
1
0
1
0
0
0
2
1
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
3
0
1
0
0
2
0
1
4
0
1
3
0
0
0
1
0
0
0
0
2
0
0
2
1
1
0
0
0
0
0
1
5
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
1
1
2
1
0
2
2
0
0
0
0
0
2
2
2
0
1
3
0
0
1
0
3
2
1
0
2
0
0
0
0
0
1
4
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
2
1
0
0
0
0
0
2
1
2
0
1
0
0
0
1
0
0
0
0
0
1
2
2
1
0
2
0
1
0
0
1
2
0
1
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
1
1
0
0
2
1
0
1
0
0
0
2
0
1
0
2
2
0
0
2
0
0
0
0
2
1
0
0
0
2
1
1
0
0
0
1
2
0
0
0
1
0
0
1
3
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
2
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
2
0
0
2
0
2
0
0
0
1
0
0
0
1
0
2
1
0
0
0
1
0
0
1
0
0
0
1
2
0
0
0
0
1
2
0
0
1
1
0
0
0
0
1
1
0
1
2
2
1
0
0
0
1
1
0
0
0
0
0
1
2
0
0
1
3
2
0
0
0
2
0
0
0
0
2
0
0
0
0
2
2
0
2
2
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
1
2
0
0
0
0
2
1
0
0
2
0
2
0
0
0
0
0
1
0
0
0
1
2
1
0
0
0
0
0
1
2
0
0
2
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
9
1
2
1
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
3
1
1
1
0
0
0
0
2
2
0
0
0
0
0
1
1
1
1
0
1
0
2
0
1
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
2
3
0
0
0
0
1
2
0
2
1
0
1
1
0
2
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
1
1
0
0
0
1
3
1
0
0
0
2
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
1
0
0
1
0
0
0
1
0
1
0
1
0
0
0
2
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
3
1
2
2
0
0
3
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
1
1
0
1
0
3
0
0
2
0
0
2
0
0
0
0
0
8
0
2
0
2
2
0
0
0
0
0
0
0
1
0
0
0
2
2
0
1
2
0
0
0
0
1
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
2
0
1
2
0
2
0
0
0
2
2
0
1
0
0
2
0
1
0
0
0
0
2
1
0
2
0
0
0
0
1
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
2
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
1
2
2
1
0
0
0
1
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
1
2
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
2
2
0
0
0
0
2
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
2
0
0
0
1
0
0
0
1
1
0
0
1
2
0
0
0
2
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
1
0
2
2
0
1
0
3
1
0
2
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
3
0
2
0
2
0
1
0
0
1
0
1
1
0
0
2
0
2
1
0
0
0
1
0
0
0
2
0
1
0
0
0
1
1
0
2
1
0
1
0
0
0
1
0
0
2
0
0
0
0
0
1
0
2
0
1
0
2
0
1
1
0
0
0
2
0
0
0
0
0
0
2
3
1
2
2
0
2
0
2
0
4
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
2
0
2
0
1
1
1
1
1
1
1
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
1
0
2
0
3
1
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
3
0
0
0
0
1
0
2
0
0
0
1
0
0
2
0
0
1
0
0
0
0
1
5
0
1
1
2
2
4
0
0
0
1
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
2
0
1
2
1
0
0
0
1
0
1
1
0
0
0
0
0
0
1
1
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
1
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
2
1
1
0
0
3
0
2
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
1
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
3
0
0
1
1
2
1
0
2
1
0
0
1
2
2
0
0
1
1
0
3
0
0
0
0
3
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
2
0
0
1
0
0
0
0
4
0
1
0
0
0
0
1
0
1
1
0
0
0
1
2
1
0
1
0
3
1
0
0
0
1
0
0
1
0
0
2
0
2
0
0
1
0
2
0
0
4
2
0
2
1
0
2
0
0
1
0
0
2
0
6
1
2
0
3
0
1
0
0
0
0
0
0
0
0
1
1
0
1
2
1
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
1
1
1
0
1
1
0
0
0
0
2
1
0
2
0
0
1
0
0
2
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
2
1
0
1
2
2
2
0
0
0
1
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
2
0
3
0
0
0
0
0
4
0
0
0
0
0
1
1
0
0
2
2
1
0
2
0
1
0
1
0
1
0
0
0
0
0
0
0
0
3
0
0
0
1
0
1
0
2
1
4
0
0
0
0
1
0
0
0
0
0
0
2
0
3
0
2
0
0
0
0
0
1
2
2
3
1
2
0
3
0
2
0
2
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
2
0
1
1
0
1
1
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
1
1
0
2
2
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
2
1
2
0
0
0
0
0
2
0
0
0
4
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
1
0
2
0
0
2
0
2
0
0
0
0
1
0
0
1
0
0
0
0
2
1
0
0
0
3
0
0
2
0
1
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
1
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
3
0
0
0
4
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
2
1
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
2
2
0
0
1
0
2
2
1
2
2
2
2
0
1
2
0
0
0
0
0
0
1
2
0
0
4
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
2
0
0
2
1
0
0
5
2
0
1
2
0
1
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
2
3
0
2
2
0
0
0
0
1
2
0
0
1
0
1
0
2
0
0
0
1
0
0
2
1
0
0
0
1
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
1
1
2
1
0
1
1
0
1
2
1
1
0
0
0
0
2
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
1
1
1
2
1
0
3
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
2
1
0
2
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
2
1
1
0
0
1
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
1
0
0
0
1
1
0
0
2
0
0
0
0
1
2
0
0
0
1
1
0
2
0
0
2
1
0
0
0
0
2
0
0
0
0
2
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
10
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
2
3
2
0
0
0
0
0
0
0
1
0
2
1
0
1
0
1
0
0
0
0
0
0
2
0
0
2
1
1
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
4
0
0
2
2
0
0
1
0
2
0
0
0
0
0
2
2
2
0
1
1
0
0
0
3
0
0
1
2
2
0
1
2
0
0
0
1
0
1
2
0
0
1
1
0
0
0
0
0
2
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
5
1
2
0
0
0
0
0
3
0
0
0
1
0
0
3
0
0
4
2
0
2
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
2
0
0
1
0
1
0
1
1
1
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
1
2
0
2
0
1
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
1
1
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
2
0
0
0
1
2
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
2
0
1
2
0
0
1
0
2
0
0
0
2
0
1
1
0
0
2
0
0
0
0
2
0
0
2
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
11
0
2
0
0
0
0
1
0
0
1
1
0
3
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
2
0
0
1
1
2
0
1
0
0
0
1
0
1
0
0
0
0
0
2
0
2
0
0
2
0
2
0
1
1
2
0
0
0
5
2
1
0
1
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
4
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
2
1
0
1
0
1
2
1
0
0
1
0
2
0
2
0
0
0
0
0
0
1
1
2
4
0
0
0
0
1
2
0
2
0
2
0
0
0
0
0
2
0
2
0
1
0
0
2
2
1
0
0
0
0
0
1
2
0
2
0
2
0
0
0
0
0
0
5
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
1
0
0
2
0
0
3
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
3
0
2
0
0
1
0
0
0
1
0
0
0
0
1
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
2
1
0
2
0
1
0
1
0
0
2
0
1
0
0
0
0
0
0
2
2
2
0
0
2
1
2
1
2
1
0
0
0
0
2
0
0
0
4
0
0
0
0
2
2
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
2
1
4
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
1
0
1
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
2
0
2
0
1
0
2
0
2
0
0
2
2
1
2
0
2
0
1
2
1
0
0
3
0
2
2
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
2
0
2
2
2
2
0
1
2
0
0
0
2
0
1
0
2
0
0
2
2
0
0
0
1
0
0
0
0
0
1
1
0
0
2
2
2
0
1
0
0
0
0
0
0
0
0
2
1
0
2
0
1
0
0
0
0
1
2
0
2
0
0
2
1
0
0
0
0
2
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
4
0
2
2
0
0
2
2
2
2
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
3
0
0
2
0
0
0
2
2
0
0
1
0
0
2
0
0
0
0
0
0
2
0
2
0
3
2
0
1
0
0
2
0
0
1
0
0
2
0
0
0
2
2
0
1
0
0
1
0
0
0
0
1
0
0
0
1
2
0
0
0
1
0
0
0
0
0
4
0
1
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
2
2
1
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
1
1
0
2
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
1
0
2
1
0
2
0
0
0
2
0
0
2
0
0
0
2
1
0
0
2
0
0
0
2
0
2
0
0
0
2
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
1
0
0
0
2
0
0
0
1
0
1
3
0
1
2
1
0
0
2
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
1
0
0
4
0
0
0
0
0
0
1
1
0
0
0
6
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
1
0
0
0
1
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
2
0
0
0
0
1
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
6
1
2
0
1
0
0
0
0
0
2
0
2
0
0
0
0
1
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
1
1
1
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
4
0
2
0
0
0
0
3
0
0
1
2
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
2
0
0
1
0
2
0
0
0
1
1
0
0
0
0
0
4
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
1
0
2
3
0
2
0
2
0
0
0
0
2
2
1
2
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
1
4
0
0
0
0
0
0
2
2
3
0
0
0
0
1
0
0
0
2
1
1
0
0
0
1
3
0
0
0
1
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
1
0
0
1
0
0
0
0
2
0
2
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
7
0
0
0
2
2
0
0
0
0
3
0
0
2
0
0
4
0
2
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
3
1
2
0
0
0
1
0
0
0
1
1
2
0
0
0
0
0
2
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
2
2
0
0
0
0
0
2
0
0
0
0
0
1
1
2
0
0
2
1
1
2
0
0
0
0
0
0
1
1
0
0
2
4
0
0
1
0
3
0
0
0
0
0
1
0
0
0
0
0
1
0
2
1
0
0
0
0
0
1
0
0
2
0
0
1
2
0
0
1
0
0
2
1
0
0
0
0
1
0
0
2
0
2
0
2
0
0
0
0
0
1
3
1
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
2
1
0
1
1
0
2
0
2
0
0
0
1
0
2
1
0
1
0
0
0
0
0
0
2
0
2
1
0
0
0
1
2
0
0
2
1
1
0
0
0
3
1
0
2
0
0
0
0
0
0
0
2
0
0
1
2
1
0
0
0
0
2
0
1
1
2
2
2
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
1
2
2
0
0
4
0
0
0
0
1
0
0
1
2
0
0
0
1
0
0
0
0
3
0
0
0
0
2
2
2
0
1
0
1
0
0
0
1
0
2
1
3
7
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
2
0
0
1
2
0
2
0
0
0
0
2
0
0
1
0
0
2
0
0
0
1
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
1
0
1
0
0
0
2
0
0
1
0
0
3
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
1
1
0
1
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
1
1
2
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
2
0
0
6
0
0
0
0
2
0
0
0
0
0
0
1
0
2
2
0
0
2
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
2
0
0
0
1
1
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
3
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
2
0
1
0
1
3
0
0
0
0
2
1
1
1
0
3
0
0
0
1
0
3
1
0
0
0
0
0
1
2
0
0
2
0
0
2
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
1
2
2
0
2
1
0
1
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
1
0
2
0
0
1
1
3
0
0
1
0
2
0
2
0
0
0
2
0
0
2
2
0
0
2
0
0
3
0
2
1
0
2
2
0
0
0
1
0
0
0
3
2
0
1
0
0
0
1
0
0
0
2
2
2
0
0
0
0
1
0
0
1
3
0
2
0
0
0
2
0
2
0
0
0
0
0
2
4
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
3
0
2
0
0
0
0
2
0
1
0
2
0
0
0
2
4
2
1
0
0
2
0
1
2
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
2
0
3
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
4
0
1
2
0
1
0
0
0
0
0
0
0
0
2
1
0
2
0
0
1
1
0
0
1
0
1
0
1
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
1
0
0
0
2
2
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
1
2
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
3
0
0
0
1
0
0
0
1
0
0
2
0
1
0
1
1
0
2
0
0
0
0
2
1
0
0
1
2
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
2
1
0
0
2
0
0
0
0
1
0
1
0
1
0
0
0
0
0
2
0
2
0
0
2
0
1
1
0
1
0
0
0
0
1
0
0
0
2
0
2
1
0
1
3
0
0
0
1
0
0
0
3
0
0
0
2
0
2
0
0
0
1
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
2
0
2
1
1
0
1
1
0
2
0
2
0
1
2
0
1
0
2
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
2
2
1
0
0
0
0
1
2
2
1
0
0
0
1
2
0
2
0
0
0
1
0
0
0
0
0
0
0
1
2
0
1
2
0
0
0
0
2
0
0
0
3
0
3
0
1
0
0
0
0
0
1
0
0
1
2
1
0
2
0
2
0
0
0
0
2
0
2
1
0
0
0
0
2
0
0
0
0
0
2
1
1
2
2
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
2
2
1
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
2
1
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
2
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
2
7
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
1
0
1
1
2
0
0
1
1
0
0
0
0
2
0
0
1
0
0
1
0
1
0
2
2
1
0
1
2
0
0
0
0
2
2
0
0
0
0
1
0
2
0
0
1
1
0
0
0
1
2
1
1
0
0
0
0
1
0
0
0
0
0
1
0
2
2
2
0
0
0
0
2
2
0
0
0
0
3
0
0
0
0
0
0
3
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
2
0
0
0
0
0
2
2
3
0
0
0
1
0
0
0
3
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
1
1
0
2
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
1
1
0
1
0
0
2
2
1
1
0
0
0
0
0
0
0
0
2
2
0
1
0
0
1
0
0
0
0
2
0
0
2
1
2
0
2
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
1
0
0
0
0
2
0
1
0
2
0
0
0
2
0
0
0
2
0
2
0
1
1
3
0
0
0
2
2
0
2
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
2
0
0
3
0
0
0
1
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
2
0
0
0
0
1
0
0
0
0
0
0
2
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
1
1
0
0
0
0
0
2
1
0
2
1
0
1
0
0
0
0
2
2
0
0
1
2
3
2
0
0
0
0
2
0
0
0
0
1
1
0
2
0
0
0
1
2
1
0
0
0
0
0
4
2
1
0
2
1
0
0
0
3
0
0
0
0
0
1
0
2
0
1
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
2
1
1
0
1
0
0
0
0
0
0
0
2
0
1
0
3
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
4
0
0
0
1
2
2
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
1
0
0
2
1
0
1
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
1
3
1
0
2
0
3
0
2
0
1
0
0
0
0
0
1
2
2
1
0
0
0
2
2
0
0
1
1
0
0
0
4
0
0
1
1
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
3
1
0
0
1
1
2
0
0
0
0
1
0
2
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
1
0
2
0
0
1
2
0
3
0
2
0
0
0
1
1
0
0
1
2
0
1
0
0
1
2
0
1
0
0
1
2
2
2
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
2
0
2
2
0
0
0
0
1
1
2
0
0
0
0
0
2
0
2
1
0
0
2
2
0
0
0
0
0
0
1
1
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
1
0
0
1
0
2
0
1
0
0
1
2
0
2
0
0
0
1
2
0
0
0
0
0
1
0
1
0
0
2
0
0
0
2
2
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
3
2
0
1
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
1
5
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
1
1
0
0
1
0
2
0
2
1
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
2
1
0
1
1
2
0
2
0
0
0
0
2
0
0
1
1
3
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
1
2
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
3
1
1
0
0
0
0
0
2
0
1
0
1
0
0
0
2
0
1
1
0
0
0
0
0
1
2
1
0
0
0
0
0
0
1
0
2
0
0
1
0
1
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
2
0
0
0
0
1
1
2
0
0
1
1
0
0
0
0
4
0
0
1
2
0
0
0
2
0
0
1
2
0
0
0
2
1
1
0
0
0
1
2
0
0
1
1
0
3
0
0
0
1
0
2
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
3
1
0
0
1
0
2
0
2
2
0
0
0
0
1
0
2
0
2
0
1
1
1
0
5
1
1
0
0
2
0
0
0
0
2
0
2
0
1
1
0
2
0
1
1
0
1
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
3
1
0
6
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
2
1
1
0
0
1
0
2
0
0
0
0
0
0
1
1
0
1
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
1
0
0
0
1
2
0
3
0
0
0
0
0
2
0
1
2
1
1
3
2
0
0
0
1
0
0
0
1
0
2
0
2
0
0
0
0
1
0
0
2
1
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
3
2
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
1
0
0
0
1
1
1
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
1
1
1
0
1
2
2
0
1
0
0
2
1
0
1
0
2
2
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
2
2
0
2
0
0
0
0
0
3
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
1
0
1
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
1
0
0
2
0
1
2
0
0
0
2
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
4
1
0
1
0
0
1
0
2
0
0
0
1
0
1
0
2
0
1
0
0
3
0
3
0
2
0
0
2
0
0
2
0
0
0
2
1
1
0
0
1
2
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
2
1
0
2
0
0
2
1
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
3
0
1
0
2
0
1
0
0
0
1
1
1
0
0
0
0
0
0
2
0
2
0
0
1
0
0
1
0
1
0
0
3
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
1
2
0
1
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
2
0
1
0
0
0
0
0
1
1
4
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
2
0
0
0
0
1
2
0
0
0
0
0
1
1
0
0
1
2
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
1
1
2
0
0
0
1
0
0
1
0
2
0
2
0
0
0
0
1
0
0
0
0
0
1
1
2
0
0
1
0
0
1
1
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
3
1
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
3
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
3
0
0
2
0
2
0
1
2
0
0
0
0
0
0
0
3
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
1
0
0
0
0
1
2
2
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
2
0
0
0
1
2
1
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
2
2
3
0
0
0
2
0
0
0
0
1
0
2
0
2
1
0
0
0
0
0
0
0
0
0
2
1
1
0
2
0
0
1
0
0
2
0
0
1
0
2
1
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
2
0
0
1
0
2
1
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
2
2
2
0
1
0
0
0
2
0
0
0
0
0
4
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
2
2
0
0
0
2
0
0
2
1
1
0
0
0
0
0
0
1
0
1
0
1
2
0
2
0
1
0
0
3
2
1
0
0
0
0
0
0
0
1
1
1
0
2
0
0
0
0
3
2
3
0
0
2
0
0
0
0
2
0
0
2
0
1
0
0
1
0
1
0
2
0
0
0
4
2
0
0
0
0
0
0
0
1
0
0
0
3
0
2
0
0
2
1
0
0
0
0
2
0
0
0
3
2
0
0
0
1
0
0
2
0
0
1
0
0
0
2
0
1
0
0
2
0
1
1
0
0
2
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
1
2
0
2
4
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
2
0
0
0
4
0
2
0
0
0
2
0
0
0
0
0
0
0
2
1
0
2
0
0
0
1
1
0
0
0
0
1
3
7
1
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
3
0
1
0
0
0
0
2
2
2
0
0
1
0
0
2
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
5
0
0
0
0
0
3
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
3
0
0
0
1
0
0
0
2
0
0
2
2
0
0
3
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
1
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
7
0
0
0
0
0
0
3
0
0
0
0
3
0
1
1
2
2
1
0
2
1
2
0
1
2
0
0
2
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
1
2
0
1
0
1
1
2
0
0
2
0
0
0
2
2
1
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
1
2
0
0
2
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
1
2
3
0
0
1
0
0
2
0
0
0
0
0
1
0
0
3
0
0
0
2
3
2
0
0
1
0
0
0
0
4
0
0
0
3
0
3
2
0
0
0
1
0
0
0
0
2
0
0
0
1
0
1
1
0
0
2
0
0
4
1
0
0
0
0
0
0
0
1
2
0
1
2
0
0
0
0
0
3
0
4
0
0
0
1
1
0
0
0
2
0
2
0
0
0
1
0
1
0
0
0
1
1
0
2
0
1
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
2
0
1
1
0
1
0
0
1
0
0
0
1
1
0
3
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
2
0
0
2
0
2
0
0
0
0
0
0
3
0
0
1
3
2
1
1
1
1
0
0
2
0
0
2
2
1
1
1
1
2
1
2
0
1
0
0
0
0
0
2
2
1
0
0
0
0
0
1
0
0
0
9
0
0
0
0
2
0
0
0
2
0
3
0
0
0
3
0
1
2
0
2
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
1
0
0
2
2
0
0
0
0
1
0
0
2
0
0
2
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
1
2
2
0
3
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
1
0
1
0
2
1
1
2
0
0
1
1
2
0
2
0
1
0
3
0
0
1
0
0
0
2
0
0
1
0
0
0
1
2
0
0
3
0
0
0
0
0
1
0
2
0
0
0
2
0
0
1
0
0
1
2
0
0
0
1
2
0
0
0
1
0
0
2
0
0
0
0
2
1
2
2
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
1
2
1
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
2
0
4
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
2
2
0
1
2
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
1
0
0
2
0
1
1
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
3
1
1
0
0
0
2
0
0
1
0
0
1
0
0
0
2
0
0
0
3
3
0
2
0
0
0
1
0
2
2
0
1
0
0
0
0
2
0
0
0
0
0
1
1
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
2
0
1
1
0
2
0
0
2
0
0
0
0
1
0
0
1
2
0
0
2
0
0
0
0
3
3
0
0
2
0
0
1
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
2
2
1
0
1
0
1
1
0
0
0
0
0
0
0
2
1
0
1
0
2
2
0
0
0
2
0
1
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
1
0
0
1
0
3
0
0
0
1
1
1
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
2
2
1
2
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
2
0
1
0
0
0
3
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
1
2
1
0
0
0
2
0
0
2
0
0
0
1
0
0
1
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
1
2
0
3
0
1
0
2
1
2
0
0
0
0
0
0
1
0
2
2
0
2
0
1
2
0
1
0
1
0
0
0
1
0
0
0
1
0
0
2
0
1
0
0
0
2
2
0
1
0
2
0
2
2
2
0
0
0
4
0
0
1
0
0
2
0
0
0
2
0
0
0
1
0
1
2
0
0
0
0
0
2
1
0
0
0
1
0
2
1
1
1
0
0
2
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
3
0
0
0
1
0
0
0
2
2
0
0
2
0
0
0
0
0
2
0
2
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
1
0
0
0
0
2
0
0
0
1
0
0
0
2
1
0
0
2
1
0
0
2
0
0
1
1
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
3
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
2
0
2
1
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
1
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
2
0
0
0
3
0
1
1
0
11
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
8
2
0
0
1
2
0
0
0
0
0
2
0
2
2
1
2
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
2
0
2
0
3
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
1
0
0
1
0
1
0
1
1
1
2
2
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
1
0
0
0
0
2
0
2
0
1
2
0
0
0
0
0
2
0
0
0
0
0
3
0
0
2
2
1
0
0
0
2
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
1
1
0
1
1
3
0
0
1
1
0
0
2
0
0
0
0
0
2
0
1
1
0
2
0
0
2
0
0
0
0
1
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
1
2
0
0
2
0
0
2
0
2
1
0
2
0
3
2
0
1
2
0
0
0
0
0
0
2
2
0
0
0
1
1
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
2
4
3
0
0
0
1
0
0
1
0
1
0
0
0
1
0
1
0
1
0
1
0
2
1
3
0
1
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
2
2
0
2
1
0
0
0
0
2
3
0
0
0
0
0
0
1
0
2
0
2
0
1
2
0
2
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
1
2
1
0
0
2
2
0
0
0
2
0
0
2
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
1
0
2
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
2
2
1
0
2
0
1
0
2
0
1
0
3
0
0
0
0
0
2
0
0
2
0
1
1
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
1
2
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
4
0
0
4
0
2
0
2
2
2
1
0
0
0
1
2
0
2
0
2
0
1
1
3
0
0
1
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
2
2
0
0
1
0
2
1
0
0
0
0
0
2
0
1
0
1
0
0
3
1
0
0
0
0
0
0
0
3
0
0
0
0
0
2
3
2
0
0
1
2
0
0
1
1
0
2
1
2
1
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
2
0
2
0
2
0
0
0
0
0
0
1
0
0
0
3
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
1
1
0
2
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
3
0
0
0
1
0
0
0
3
3
2
0
0
0
0
3
2
1
1
0
0
0
0
2
0
0
2
1
0
0
2
0
1
0
0
0
0
0
0
0
2
1
0
0
1
0
0
2
5
2
0
1
0
0
1
0
2
0
0
1
0
0
0
0
2
0
0
1
0
0
2
0
0
2
2
2
1
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
3
1
0
1
2
2
0
2
1
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
2
0
1
0
2
0
2
0
0
1
1
0
1
0
0
0
2
0
0
0
0
0
2
2
2
0
0
0
1
2
0
0
0
0
1
0
2
0
0
0
0
2
0
1
1
0
2
0
0
0
1
0
0
1
0
0
3
1
0
0
0
0
1
0
3
1
1
0
0
1
0
0
1
0
2
0
0
0
0
1
1
0
0
0
0
0
2
0
0
1
0
0
2
2
2
0
0
0
0
3
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
3
4
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
1
0
0
2
2
0
0
2
1
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
2
2
1
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
4
2
1
3
0
0
0
1
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
6
0
0
1
2
0
0
0
1
4
0
1
0
1
0
2
1
2
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
3
0
2
2
0
0
0
1
2
0
0
0
0
0
2
0
0
2
1
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
6
0
1
2
0
0
0
3
0
0
2
0
0
0
0
0
0
4
1
2
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
1
0
2
0
3
1
0
0
2
2
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
2
0
0
2
0
0
0
1
0
0
0
2
0
1
0
0
0
0
2
1
4
0
2
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
1
2
0
1
0
1
0
1
0
0
1
0
1
0
0
1
3
0
0
0
0
1
0
2
2
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
2
2
0
0
3
0
0
0
0
2
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
2
1
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
2
4
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
2
1
2
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
2
0
0
0
2
0
3
1
0
0
0
7
1
0
1
1
0
1
1
0
0
4
0
0
0
1
0
0
2
0
1
0
0
0
1
1
1
0
0
2
2
0
0
0
0
0
0
1
1
2
1
0
2
0
1
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
2
0
0
0
4
2
0
0
0
0
2
0
0
0
2
0
0
0
0
4
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
2
0
2
2
0
0
2
2
0
1
0
0
0
0
0
2
2
0
0
0
0
1
2
0
0
1
0
0
0
0
1
0
0
0
2
0
2
0
1
0
3
2
1
0
0
2
1
0
2
0
0
0
2
2
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
2
0
1
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
2
2
3
0
0
2
0
0
0
0
0
0
3
2
3
1
2
0
0
0
0
0
0
1
1
1
0
0
0
1
1
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
1
1
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
1
2
2
0
2
0
0
0
0
0
1
0
3
1
1
2
1
1
0
0
1
0
0
2
4
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
1
3
0
0
0
2
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
9
0
2
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
2
1
0
0
0
1
2
0
0
0
0
0
1
2
1
0
0
3
0
0
0
2
2
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
1
0
2
0
2
0
1
1
1
2
2
2
1
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
2
3
0
1
0
1
0
1
0
0
0
2
3
1
2
0
0
0
1
0
0
2
0
2
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
1
1
1
1
0
1
2
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
4
2
0
0
0
0
2
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
1
0
1
0
2
1
0
1
0
1
2
2
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
2
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
1
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
2
3
1
2
0
0
1
0
0
0
2
0
1
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
2
0
2
0
0
0
0
1
1
0
0
2
2
0
0
2
0
0
0
1
0
0
0
0
2
1
1
0
0
2
0
2
0
0
0
1
2
1
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
2
0
1
0
0
3
2
2
0
2
1
0
2
0
0
0
0
0
2
2
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
2
0
1
1
2
0
0
0
2
0
2
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
2
1
0
3
0
0
3
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
3
0
0
0
0
0
1
0
1
0
0
1
1
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
1
1
0
0
0
0
1
0
0
0
1
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
1
0
2
0
2
0
0
1
2
2
2
0
0
0
0
0
2
0
3
0
0
0
0
0
0
2
1
0
0
0
0
0
0
3
2
0
2
0
0
0
0
0
0
0
1
0
2
0
0
1
2
0
2
0
0
0
0
1
0
0
2
0
0
0
0
2
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
3
0
0
1
3
2
0
0
1
1
0
0
1
0
1
0
1
0
2
1
0
0
1
2
1
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
2
0
1
0
3
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
2
0
0
0
0
2
0
0
14
1
0
1
2
0
0
0
1
0
2
0
0
1
1
0
2
1
0
1
2
1
0
2
0
2
0
0
2
0
0
1
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
1
0
0
1
0
2
0
0
0
0
0
1
0
1
0
2
1
0
1
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
3
1
0
0
1
1
0
2
0
0
0
1
1
0
0
2
0
2
0
1
0
0
0
1
1
0
1
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
2
0
2
0
0
1
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
1
1
2
2
1
0
0
0
2
0
0
0
2
1
1
0
1
0
0
0
1
2
2
0
0
1
0
2
0
0
0
0
0
0
5
0
1
0
0
0
0
3
0
1
0
0
1
1
2
0
1
1
0
0
0
0
2
2
0
0
1
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
2
0
3
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
2
2
2
0
3
0
0
2
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
1
0
2
0
0
0
0
0
3
1
1
0
1
1
2
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
4
0
1
0
1
0
0
0
2
1
0
0
0
0
0
1
0
0
0
2
0
0
2
0
2
2
0
0
1
0
0
1
1
1
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
3
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
1
2
0
0
0
1
2
2
0
2
0
0
0
1
0
2
2
0
2
2
0
0
0
0
0
0
0
2
0
2
0
0
0
4
0
1
0
1
0
2
0
1
0
0
0
1
0
0
0
2
1
0
0
2
0
3
0
0
0
7
0
1
0
0
0
0
0
0
1
0
2
0
0
0
2
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
1
2
0
2
2
0
0
1
2
0
1
0
0
0
0
0
2
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
1
0
0
0
2
0
0
1
0
0
0
2
0
1
0
0
2
0
0
0
1
0
2
1
0
0
0
0
0
1
0
2
0
1
2
1
2
2
0
0
2
1
0
0
1
0
1
0
2
1
0
0
1
0
0
0
0
2
0
2
0
2
0
0
0
0
1
0
2
0
2
1
1
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
2
0
2
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
2
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
1
0
0
6
1
3
2
1
0
0
2
0
2
2
0
0
0
1
0
0
0
0
0
1
1
0
0
2
0
0
1
2
0
1
0
0
0
1
0
0
0
1
0
0
0
0
2
0
1
2
0
1
1
0
2
0
0
0
1
2
0
0
3
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
7
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
4
2
0
0
1
1
0
1
2
0
0
2
1
0
0
2
0
3
0
2
0
0
0
0
1
0
0
0
0
0
3
3
0
0
0
0
0
2
0
0
0
0
2
1
0
1
0
1
1
1
0
2
0
1
2
1
3
2
0
0
0
1
0
0
0
2
2
1
0
5
0
0
0
0
3
0
2
2
0
0
0
0
0
2
2
0
0
1
0
2
0
0
1
0
1
0
0
2
0
0
0
0
0
2
2
0
0
0
2
0
2
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
2
0
0
0
0
2
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
4
0
1
0
0
0
0
0
1
1
2
0
1
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
2
1
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
2
1
2
1
0
0
0
0
0
3
1
0
0
0
2
0
0
2
0
1
0
0
0
2
0
1
0
2
1
0
0
2
0
0
1
1
0
0
0
2
0
2
0
0
0
2
0
0
2
0
0
0
0
1
0
1
0
2
0
1
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
3
0
0
0
0
0
1
5
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
1
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
1
2
2
0
0
0
0
0
1
0
2
2
2
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
2
1
0
2
0
1
2
4
0
0
1
2
0
0
0
0
0
0
1
0
2
0
0
2
2
0
0
2
2
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
1
2
0
0
0
0
0
2
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
2
0
1
1
0
0
0
2
0
3
0
0
1
0
1
2
0
0
0
0
1
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
1
2
0
0
0
1
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
2
0
2
0
0
0
1
2
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
1
0
1
0
1
2
2
0
2
1
0
2
0
2
0
0
1
0
1
0
1
0
0
0
3
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
3
0
0
1
0
2
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
2
2
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
2
3
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
1
2
0
1
0
0
0
2
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
2
0
2
0
0
0
0
0
2
0
2
0
0
0
0
1
0
1
1
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
1
0
2
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
1
2
0
1
1
0
1
0
1
1
0
3
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
3
0
0
0
0
5
0
0
1
2
1
0
2
1
0
1
0
0
2
4
2
2
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
2
0
1
0
4
1
0
2
0
0
0
2
0
2
0
1
0
1
0
1
1
0
0
0
0
2
0
1
0
0
1
0
0
2
0
0
0
0
0
1
1
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
5
0
0
2
0
0
0
1
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
1
2
1
0
0
0
0
2
0
0
0
2
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
3
0
1
1
2
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
1
1
1
2
0
0
0
0
0
0
1
2
0
0
0
0
1
2
0
0
3
1
2
0
0
0
0
2
0
0
2
5
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
2
0
1
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
2
0
0
0
2
2
0
1
0
0
0
0
1
0
0
0
1
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
1
1
2
0
2
0
0
0
1
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
2
0
1
0
0
0
0
0
3
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
1
4
1
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
2
1
0
2
0
2
0
2
0
0
2
0
0
0
1
0
0
0
3
1
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
2
1
0
0
2
0
0
2
0
0
0
0
3
2
0
2
0
0
0
0
1
0
0
7
0
6
0
0
0
0
1
2
0
0
0
0
2
1
0
0
1
0
0
2
0
0
2
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
2
0
2
0
2
0
0
0
2
0
0
2
0
0
0
5
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
2
0
1
2
0
0
0
2
0
2
0
0
0
0
1
1
0
0
0
1
2
0
0
0
0
0
1
0
0
1
1
1
2
0
2
0
0
1
1
0
0
0
0
0
0
0
3
0
0
1
0
1
0
2
0
0
0
1
0
0
1
0
0
1
0
0
1
2
2
0
1
0
0
0
0
0
2
1
0
2
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
2
0
2
0
0
5
0
1
0
0
0
0
1
0
3
0
2
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
1
2
0
0
0
1
2
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
1
1
0
0
2
0
0
0
0
0
2
0
0
0
2
2
1
1
0
0
2
1
0
0
3
1
0
0
1
0
1
1
0
0
0
0
2
0
2
0
0
1
0
2
2
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
2
0
0
1
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
1
0
0
0
0
1
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
2
1
0
0
2
0
2
0
2
0
0
0
2
0
0
1
2
2
0
0
1
1
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
1
0
0
6
1
0
0
0
1
2
1
2
0
0
0
1
0
1
1
2
0
2
2
1
1
0
0
0
0
1
0
3
0
1
1
1
0
0
0
0
1
0
0
0
0
0
1
2
1
0
1
0
0
0
0
4
0
0
1
2
0
0
2
1
0
0
0
0
0
2
2
1
2
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
2
0
1
0
0
0
0
0
1
0
0
0
0
2
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
2
0
2
2
1
0
1
0
0
1
2
0
2
0
0
1
0
0
0
2
0
0
0
2
1
1
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
3
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
2
0
0
0
1
2
0
0
0
0
0
7
0
1
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
2
3
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
1
1
0
0
0
0
0
0
2
1
0
0
2
0
0
0
6
0
0
1
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
2
0
2
0
0
1
2
0
0
0
1
0
0
0
3
0
0
0
2
0
1
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
2
2
1
2
0
0
2
0
0
0
0
0
0
2
2
1
1
0
0
0
1
0
5
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
2
0
0
0
4
0
0
3
0
2
1
0
0
2
0
1
0
3
0
0
2
1
0
2
2
0
2
0
1
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
2
0
2
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
2
0
0
0
2
0
0
0
0
2
0
2
1
1
0
0
0
2
3
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
2
0
0
1
1
0
2
1
2
2
0
0
3
0
0
1
0
0
2
1
0
0
2
3
2
1
0
0
1
0
0
0
1
1
0
2
1
0
1
0
0
0
0
0
2
1
0
4
0
0
0
2
0
10
0
0
1
1
0
0
0
0
2
0
1
1
0
2
0
0
0
0
1
0
0
2
2
2
0
0
2
0
0
0
0
0
2
0
1
0
0
2
0
0
0
1
0
2
1
0
0
0
0
2
3
2
0
0
2
1
1
0
0
0
5
2
0
2
0
2
0
0
0
0
0
10
0
2
0
2
1
3
0
0
0
0
1
0
0
0
2
0
2
0
0
1
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
2
2
0
0
1
0
0
0
1
0
0
1
1
0
0
2
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
1
0
4
0
2
0
0
0
0
0
0
3
0
1
2
0
0
0
0
0
1
0
1
1
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
2
1
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
2
0
0
1
1
0
0
2
0
2
0
2
0
2
2
0
1
1
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
2
1
0
0
0
2
1
0
0
0
0
0
2
2
0
2
1
0
1
0
0
2
0
0
0
0
0
1
0
0
0
1
0
2
0
1
0
0
0
2
1
2
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
1
3
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
4
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
1
0
2
2
0
1
2
1
1
0
2
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
1
0
3
1
2
2
1
3
2
0
0
0
0
0
3
1
0
0
2
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
3
0
2
0
0
0
2
0
0
1
0
0
0
0
1
0
2
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
2
2
0
0
0
1
0
0
1
0
1
0
0
1
0
0
2
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
2
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
3
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
1
0
2
0
0
0
2
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
2
2
0
2
1
2
0
2
0
1
1
0
0
0
0
0
0
3
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
2
1
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
2
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
2
0
2
2
0
1
0
0
0
0
0
3
0
2
1
2
0
0
0
2
0
0
0
2
1
0
0
0
0
0
1
0
3
0
1
3
0
2
0
0
1
2
0
0
1
0
5
0
1
0
0
0
0
0
1
0
0
3
1
1
0
0
0
0
0
0
1
0
2
1
0
1
0
0
0
3
2
0
0
0
1
0
0
0
0
0
0
0
2
0
2
2
0
0
1
0
2
0
0
0
0
0
1
1
0
3
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
5
0
2
0
0
0
2
0
0
2
1
2
2
1
0
0
0
1
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
3
2
0
0
0
0
1
0
0
0
0
0
0
2
4
2
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
1
0
0
2
1
0
1
2
0
0
0
3
0
0
0
0
3
0
2
0
0
7
2
0
2
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
2
0
0
2
0
2
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
2
1
2
0
1
0
1
0
1
0
0
0
1
0
0
3
1
0
1
1
0
0
1
0
0
0
2
0
0
0
1
2
1
2
0
0
2
0
0
2
0
1
0
0
0
0
2
0
0
0
0
2
2
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
2
0
1
1
2
5
0
0
0
0
0
0
1
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
1
2
2
0
0
2
0
2
1
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
3
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
1
1
0
0
0
0
0
1
2
0
0
0
0
2
2
0
2
0
2
0
0
0
0
0
1
0
0
0
0
1
2
3
1
1
0
0
0
0
0
3
0
0
0
0
2
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
1
0
5
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
1
0
1
2
0
0
0
2
0
0
0
1
7
0
0
2
0
0
0
3
0
0
0
2
2
0
2
0
0
2
0
0
0
1
2
0
0
1
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
1
2
1
0
2
1
0
0
0
0
0
1
0
1
1
1
0
1
3
0
0
0
0
0
0
2
1
2
0
1
0
0
0
0
0
0
0
1
0
0
0
2
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
3
1
1
0
0
0
1
1
0
1
0
0
2
1
1
0
1
0
1
2
0
2
0
0
1
0
2
1
0
2
2
0
2
0
0
0
0
0
1
0
2
0
3
0
1
1
0
2
0
1
0
1
0
10
0
0
0
0
4
1
0
2
0
0
0
1
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
1
3
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
2
0
0
1
0
0
0
0
0
1
2
2
0
0
0
0
0
3
0
0
2
1
0
0
0
0
0
0
0
0
1
0
3
0
0
1
0
0
2
0
2
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
3
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
6
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
2
0
0
0
1
2
2
0
0
0
0
0
2
1
0
0
0
1
2
2
1
0
0
0
0
0
2
0
0
0
2
0
1
2
0
0
2
0
1
0
0
2
0
2
0
1
0
0
2
5
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
2
1
2
2
1
0
0
0
1
1
2
3
2
1
0
0
0
1
1
2
0
0
0
0
0
0
0
1
0
0
2
1
0
1
0
0
0
0
2
2
0
0
0
0
0
2
0
1
0
0
1
0
1
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
2
0
0
1
1
0
2
0
0
2
0
0
2
2
1
0
0
0
0
0
1
0
1
1
2
2
2
0
1
3
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
6
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
1
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
2
1
0
1
2
2
0
2
1
2
2
1
2
2
2
0
1
0
0
1
1
1
0
2
3
1
0
0
2
2
0
0
0
0
1
0
0
0
2
0
2
0
1
0
1
1
0
0
0
1
0
0
0
2
1
0
0
1
1
1
0
4
0
0
0
1
0
3
0
0
0
1
2
2
1
2
1
0
2
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
3
2
0
0
1
0
0
0
0
2
1
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
1
1
0
0
0
2
0
0
2
0
1
1
1
0
1
0
2
0
0
0
1
0
0
0
1
5
1
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
4
0
0
0
3
0
0
1
0
2
0
2
1
0
0
2
0
0
2
0
1
0
0
1
0
1
2
0
1
0
0
1
0
2
1
0
2
1
0
2
0
0
5
1
2
2
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
2
0
0
0
0
1
1
0
0
2
0
0
0
0
1
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
3
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
1
1
0
2
3
1
1
0
1
2
0
0
0
1
1
0
0
1
2
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
1
1
0
0
0
1
0
0
2
0
0
0
0
2
1
0
0
0
2
2
0
0
2
0
1
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
1
1
0
0
2
0
1
0
0
0
0
1
0
1
0
0
1
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
3
0
0
0
0
2
2
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
2
0
2
0
2
0
1
0
1
1
2
3
0
1
0
0
2
0
1
0
0
0
0
0
3
0
0
2
0
0
1
1
2
0
0
2
1
0
0
0
2
2
0
0
0
1
2
0
0
2
2
1
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
3
0
0
0
0
0
1
0
0
0
1
2
0
0
2
0
0
0
0
0
0
2
0
0
1
1
0
0
0
1
0
2
0
0
1
1
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
5
0
0
0
2
0
0
0
2
1
1
0
2
0
0
1
0
0
0
0
1
2
0
0
0
1
0
0
0
0
2
0
2
0
2
0
0
1
0
2
0
0
0
1
0
2
1
0
0
0
0
1
1
0
0
0
2
1
0
2
1
0
1
2
1
1
0
0
0
1
2
1
0
0
2
0
1
0
1
3
0
0
0
0
0
2
2
0
0
0
1
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
1
2
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
1
0
0
1
1
1
2
0
0
0
0
0
0
0
2
1
0
3
1
1
1
2
0
0
1
1
0
2
1
0
0
2
0
0
0
1
0
0
2
2
0
0
0
0
0
1
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
2
0
0
0
0
0
0
1
0
2
1
2
2
0
0
3
0
0
0
0
0
3
0
0
2
0
0
0
0
7
0
2
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
2
0
1
0
0
0
2
0
0
0
0
4
0
0
1
2
0
0
0
0
0
1
0
0
3
1
0
0
0
0
0
0
0
0
1
2
0
1
1
2
0
0
2
0
1
0
0
0
0
0
1
0
1
1
3
0
0
0
0
1
0
0
1
1
2
0
2
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
1
0
0
2
2
0
2
0
3
0
0
2
0
2
0
0
3
0
0
2
2
0
0
2
0
0
1
0
0
2
0
0
0
1
1
0
1
0
0
1
2
0
1
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
3
0
2
2
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
1
1
0
1
1
0
0
2
2
1
0
1
2
1
1
0
0
2
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
2
0
0
2
4
0
0
2
2
0
2
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
1
0
0
0
0
0
5
0
0
0
0
0
1
0
0
0
1
2
0
0
0
1
0
0
1
0
0
1
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
2
0
1
1
0
1
0
0
2
1
0
0
2
6
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
4
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
4
2
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
3
2
1
0
0
0
0
1
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
1
0
2
0
2
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
1
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
1
2
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
2
0
1
0
0
0
2
0
0
0
1
0
0
0
2
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
1
1
0
0
3
0
0
1
0
0
0
1
1
2
0
0
1
2
2
0
0
0
1
1
0
0
0
0
2
2
0
1
0
0
2
0
1
1
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
3
0
1
1
0
1
0
1
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
2
0
0
2
0
0
0
1
2
2
0
1
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
2
0
0
1
1
0
2
1
1
0
0
0
0
2
0
0
0
1
2
0
1
2
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
2
0
0
0
0
0
2
1
0
1
0
1
0
0
1
0
0
0
0
1
2
0
2
0
2
0
1
0
0
0
2
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
5
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
7
0
0
0
0
1
0
0
1
0
3
1
1
0
2
0
0
0
2
0
0
1
2
0
1
2
0
0
0
0
1
0
0
0
0
0
0
3
0
2
0
0
1
0
0
0
0
0
1
0
0
5
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
2
0
3
1
2
1
0
0
0
1
2
0
0
0
2
0
2
1
0
0
0
0
0
2
0
0
1
1
3
0
0
0
0
0
0
0
0
2
1
1
1
2
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
3
0
0
0
1
6
0
0
1
0
0
1
0
0
0
2
0
2
2
2
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
3
0
1
0
0
0
0
2
2
1
0
0
0
1
2
0
3
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
2
2
3
0
0
0
2
0
2
1
0
2
2
2
0
1
0
1
0
1
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
1
0
3
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
2
1
0
0
0
1
1
0
1
0
1
0
0
3
0
1
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
1
1
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
2
0
1
0
0
0
0
1
1
0
1
0
1
2
2
0
0
1
0
2
0
0
0
0
0
2
0
0
0
2
2
0
1
0
0
0
0
0
0
1
0
0
0
2
2
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
2
2
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
2
0
1
0
2
2
0
0
1
1
0
0
0
1
2
0
0
1
2
1
0
0
0
2
0
2
2
2
0
1
0
1
0
0
2
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
3
2
0
0
0
1
1
2
0
1
2
0
1
0
1
2
0
2
0
2
1
2
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
1
1
0
0
2
1
0
2
0
0
1
0
0
0
0
0
0
0
2
2
0
0
2
2
1
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
1
1
2
1
0
0
1
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
2
1
0
0
0
2
0
2
0
0
1
2
0
1
0
0
1
2
2
0
2
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
1
0
0
1
0
2
1
0
0
0
2
2
0
2
1
0
0
1
0
2
0
0
0
0
2
0
0
3
0
0
0
0
0
0
1
0
1
2
0
1
2
0
1
2
0
3
1
0
1
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
1
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
1
2
2
2
1
2
0
2
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
2
0
1
0
2
1
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
2
0
2
0
0
0
0
5
2
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
2
0
0
3
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
2
3
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
4
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
2
0
2
1
2
0
2
2
0
0
0
0
0
0
1
1
0
0
2
3
0
3
0
0
0
1
0
0
2
0
0
0
1
0
0
0
3
0
2
0
0
0
2
0
0
0
0
2
0
1
0
2
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
1
0
2
0
0
0
0
0
1
1
1
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
1
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
3
0
0
0
0
1
0
0
2
0
0
2
0
1
0
0
0
2
0
0
0
2
2
1
2
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
2
2
0
0
0
1
3
1
1
0
0
1
2
2
3
1
1
1
1
1
0
1
0
0
0
0
1
3
0
0
1
1
0
0
0
0
0
0
0
1
2
1
0
2
0
2
0
0
1
0
1
0
0
1
0
3
0
0
2
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
1
0
0
1
1
0
1
1
0
0
0
0
1
0
3
0
1
0
2
1
0
2
0
0
0
0
1
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
2
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
2
0
2
0
0
0
0
2
1
0
1
0
0
0
2
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
2
0
1
1
0
1
1
0
0
0
0
2
0
0
2
0
0
2
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
1
0
0
2
2
0
0
3
2
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
1
0
0
0
2
1
0
0
0
1
2
0
0
1
0
1
1
0
1
1
0
1
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
4
0
2
3
1
2
0
0
0
0
0
1
0
1
0
2
0
1
2
1
0
1
0
0
0
1
2
1
0
2
0
0
0
0
1
1
2
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
1
1
2
0
0
0
0
2
0
0
0
0
1
0
0
0
1
2
0
1
1
0
0
2
1
0
1
0
2
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
2
2
0
0
1
0
0
2
0
2
0
0
0
1
0
0
1
2
0
0
0
1
0
2
0
1
0
0
2
0
0
0
2
0
2
0
0
3
0
1
0
2
0
2
2
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
2
0
0
1
1
0
1
0
0
0
0
3
1
0
0
0
2
2
1
0
0
0
0
0
1
2
0
0
2
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
2
2
2
0
2
0
0
0
2
2
0
0
3
0
1
0
0
0
2
0
0
2
0
0
0
0
1
1
0
0
0
0
0
4
0
0
0
2
1
2
0
2
0
1
0
2
2
0
3
0
0
0
0
2
0
0
1
2
0
0
1
0
0
2
0
0
1
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
1
0
0
1
0
4
0
0
1
0
4
0
0
0
0
0
1
0
2
2
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
4
1
0
1
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
1
5
0
0
0
1
3
0
0
1
0
2
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
2
0
0
0
1
2
0
0
0
0
1
1
0
0
0
0
1
2
2
4
1
0
1
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
1
0
0
2
2
2
0
0
1
2
2
2
0
0
0
1
0
0
0
0
1
0
0
1
0
2
1
0
0
0
1
1
0
0
3
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
2
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
1
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
4
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
1
1
2
1
0
0
3
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
1
1
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
3
0
2
2
1
3
0
0
0
0
3
1
0
1
1
2
2
0
0
2
0
0
0
1
0
0
1
1
2
0
0
1
0
0
0
0
0
4
0
0
2
0
0
0
0
1
0
2
0
0
2
2
1
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
2
1
0
3
1
2
0
0
0
0
1
0
1
0
2
2
0
1
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
4
0
3
0
0
3
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
5
0
3
0
0
0
0
0
0
0
2
0
2
1
1
0
1
0
1
0
0
0
0
0
0
1
0
1
2
0
2
0
0
2
2
0
0
0
0
3
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
3
1
0
0
2
0
3
0
0
2
1
2
1
0
0
0
0
1
2
0
2
1
0
1
1
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
2
0
1
2
0
0
0
0
0
0
0
2
0
0
2
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
1
0
0
0
2
0
0
0
0
0
0
0
1
0
1
2
1
2
0
0
0
0
0
2
0
10
0
1
1
0
0
0
0
0
0
0
2
3
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
3
0
1
0
0
0
1
1
0
2
0
0
0
0
1
0
0
2
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
4
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
1
2
0
0
1
2
0
1
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
3
0
0
0
0
1
0
2
1
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
1
0
1
0
0
2
0
0
2
0
1
2
0
0
2
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
3
0
1
0
0
0
0
0
2
0
0
2
0
0
2
0
3
0
2
0
0
0
1
2
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
2
1
0
1
2
1
1
2
2
1
0
3
2
0
1
0
0
0
0
0
0
2
0
2
0
0
0
2
1
2
0
1
1
0
2
0
0
0
0
1
4
1
0
2
7
2
1
0
0
0
1
3
0
0
0
0
0
1
1
0
1
3
1
0
0
0
0
0
2
1
1
0
0
3
0
1
0
0
0
2
0
0
0
2
0
1
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
1
1
2
1
0
0
2
0
0
1
2
0
1
0
0
0
2
2
2
0
0
0
3
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
3
2
0
0
0
0
2
0
0
0
0
0
0
2
0
11
1
0
2
2
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
1
1
1
1
0
0
3
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
2
2
0
0
0
0
0
1
0
0
0
1
0
0
2
1
2
0
2
0
2
0
2
0
0
0
0
0
0
0
1
2
4
2
0
0
2
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
4
1
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
3
0
0
0
0
0
2
0
0
1
0
0
0
2
2
2
0
0
0
0
1
1
1
0
0
1
2
0
0
1
0
0
0
0
2
1
0
0
0
0
2
0
1
0
3
3
0
0
0
1
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
1
0
0
2
3
0
2
3
0
0
2
1
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
3
0
0
1
1
0
1
0
0
0
1
0
0
2
0
0
2
0
0
0
3
0
1
1
0
2
1
0
0
0
0
0
1
2
0
2
0
0
0
0
0
2
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
2
0
1
2
0
0
1
0
0
0
2
0
0
0
1
0
1
0
1
2
2
0
0
0
0
0
0
0
2
0
1
0
0
0
1
1
0
0
0
1
2
0
1
1
0
2
0
2
0
0
2
1
2
2
2
2
2
0
0
1
1
2
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
2
2
1
2
0
0
0
1
0
2
0
0
0
2
1
0
0
2
0
2
0
0
0
0
1
0
0
1
0
2
2
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
2
0
2
0
0
0
1
0
3
0
0
0
0
4
0
0
0
0
0
4
0
1
0
0
0
0
0
1
2
0
0
1
1
1
0
2
1
1
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
4
2
0
1
2
0
0
0
0
0
1
2
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
2
1
0
2
0
0
0
2
1
0
0
2
0
1
0
0
0
4
0
0
2
0
2
0
0
0
2
2
0
0
0
0
0
1
1
0
0
0
0
1
0
0
2
0
0
2
2
1
0
0
0
0
2
2
0
2
1
0
0
1
0
0
2
0
0
0
0
0
0
1
2
2
0
0
0
1
0
0
2
0
0
0
0
0
1
1
0
0
1
0
3
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
1
2
0
0
0
0
0
0
2
0
3
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
3
2
2
0
0
0
0
1
0
2
2
0
0
0
0
1
3
0
0
0
0
0
0
0
0
3
0
1
0
0
1
0
0
0
0
3
2
0
0
0
1
0
2
0
2
0
0
1
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
2
1
1
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
1
0
1
0
2
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
2
0
0
0
0
0
0
0
2
0
3
2
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
1
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
2
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
3
2
0
1
1
0
0
0
0
1
1
0
0
2
0
0
0
0
1
0
2
3
0
0
3
2
2
0
0
2
0
1
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
2
1
0
1
2
1
1
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
1
1
0
2
1
0
0
3
0
2
0
0
0
2
2
0
2
2
0
2
2
0
0
0
0
0
0
0
0
0
3
0
0
0
3
1
0
0
0
0
3
0
0
0
1
6
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
1
2
1
0
2
0
0
1
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
1
2
0
2
0
0
2
2
0
0
0
1
1
0
0
0
0
0
0
2
1
1
1
0
0
0
1
0
2
0
0
0
0
2
2
0
0
0
0
2
2
1
0
0
0
0
3
4
1
0
0
0
1
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
3
0
2
0
1
2
0
1
0
0
0
2
0
1
0
2
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
2
0
2
0
1
1
0
0
1
0
2
0
0
0
0
0
1
0
2
0
2
0
0
1
0
0
0
2
0
0
0
2
1
1
0
0
0
2
0
0
2
2
0
0
2
0
2
0
0
1
0
1
2
0
2
0
0
0
1
2
0
0
0
0
1
2
0
0
2
0
2
0
1
2
2
0
1
0
0
0
0
2
1
0
0
0
0
0
1
0
0
2
0
2
0
1
0
1
0
0
0
2
2
0
0
0
0
1
0
1
1
0
2
0
0
0
0
0
0
1
1
0
3
0
0
2
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
1
0
0
1
2
0
2
0
0
0
0
2
1
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
1
0
0
1
0
2
0
0
3
1
0
0
2
0
1
0
0
0
0
0
0
0
1
0
2
2
1
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
2
1
0
0
1
0
0
1
0
0
2
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
2
0
3
1
1
1
0
2
0
2
4
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
1
0
2
0
0
1
0
0
0
0
2
1
1
0
0
0
0
0
3
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
1
0
1
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
2
0
0
0
2
2
2
0
0
1
1
0
0
2
1
1
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
11
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
1
0
3
0
0
0
0
2
0
0
1
0
2
0
0
0
1
0
0
0
0
2
3
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
1
0
1
0
2
0
1
0
2
0
0
0
1
0
0
1
2
0
0
2
1
0
0
2
0
0
3
2
0
1
0
2
0
0
0
0
0
2
3
2
1
0
1
0
1
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
1
3
2
0
1
0
1
0
0
0
0
1
0
7
0
0
0
0
0
0
0
0
0
0
4
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
2
4
0
1
1
0
0
1
1
0
2
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
2
0
0
2
0
0
2
1
0
0
0
0
1
0
0
2
0
0
0
1
1
0
0
0
1
2
0
1
0
0
1
0
2
0
0
2
0
0
1
1
0
0
0
0
1
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
2
1
0
1
0
0
0
0
2
0
0
1
3
0
0
0
2
1
0
0
0
1
0
0
0
0
0
1
0
0
2
1
0
0
2
0
0
0
0
0
0
0
1
0
1
0
1
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
1
1
0
1
0
0
0
1
2
0
0
3
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
1
0
2
2
0
1
2
0
0
0
0
0
2
0
0
0
0
2
1
2
0
0
1
2
1
0
1
0
3
0
1
0
0
3
2
0
2
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
1
0
1
0
1
0
0
0
1
0
2
0
3
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
2
0
0
0
1
0
0
2
1
1
3
4
1
2
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
2
0
0
0
2
2
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
2
0
0
0
1
4
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
3
2
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
1
0
1
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
4
0
0
0
0
0
0
0
0
0
2
0
2
3
0
0
0
2
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
1
2
0
2
1
0
2
0
1
0
0
0
1
0
0
0
0
0
1
2
0
0
1
2
0
0
0
0
0
0
1
0
1
0
0
0
2
2
0
1
2
0
0
0
1
1
0
0
0
2
0
0
2
2
0
2
0
0
0
1
0
1
2
1
0
2
2
2
1
0
1
0
0
0
0
3
0
0
1
0
0
1
0
1
0
2
0
0
0
0
2
0
0
0
0
0
2
1
3
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
2
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
2
1
1
0
1
0
0
2
0
0
1
1
0
0
1
1
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
1
2
0
1
1
0
2
1
0
0
0
0
0
3
0
0
1
0
0
0
0
1
1
2
0
1
2
0
0
2
2
2
0
0
0
0
0
0
1
1
1
2
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
2
0
2
0
0
0
1
0
0
0
2
0
1
0
0
0
1
0
0
0
0
2
1
0
0
0
2
0
1
0
1
0
2
3
0
0
0
0
0
0
1
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
2
2
0
1
5
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
3
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
2
2
1
0
2
0
0
0
0
1
1
0
1
0
0
1
0
1
0
0
0
0
4
0
1
0
0
0
0
0
1
2
0
0
0
1
2
2
0
2
1
0
1
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
5
2
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
1
1
0
2
0
2
0
0
0
2
0
0
0
0
2
2
0
0
0
1
0
1
0
0
0
0
2
1
2
0
0
2
2
0
1
0
0
0
1
0
1
2
0
0
2
2
2
0
0
0
0
0
0
0
0
0
1
2
0
0
1
2
1
0
0
1
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
1
1
2
0
0
1
1
0
0
2
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
3
0
0
2
0
0
0
0
0
1
1
0
0
0
0
2
1
1
0
0
1
2
2
0
0
0
0
0
0
2
1
0
0
0
1
1
2
0
0
2
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
1
0
2
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
2
0
0
0
0
0
0
1
1
0
1
3
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
1
2
0
2
0
2
1
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
1
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
1
0
2
1
1
1
0
1
0
1
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
3
0
0
1
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
2
1
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
2
0
0
2
0
2
1
0
2
2
0
0
0
1
0
0
1
0
0
0
0
2
0
1
0
0
0
2
1
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
1
1
1
0
0
0
0
0
1
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
1
2
0
1
2
0
0
1
2
2
0
0
4
0
0
3
0
1
1
0
0
0
0
2
0
0
2
0
1
0
0
0
2
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
2
1
0
0
1
2
0
0
0
0
1
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
1
0
0
0
1
2
1
2
0
0
1
0
0
0
0
0
0
2
1
0
1
0
0
0
2
1
1
0
0
1
0
1
1
2
2
2
0
0
0
0
5
0
0
0
1
0
0
0
0
0
0
0
0
2
1
2
0
1
1
1
2
0
0
0
2
2
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
1
1
1
1
0
0
0
4
0
1
0
2
1
0
1
0
0
1
0
0
0
2
1
0
0
0
3
1
0
1
0
0
0
2
2
2
2
0
3
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
1
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
3
0
2
0
1
1
0
0
0
0
1
1
2
3
1
0
2
4
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
2
1
2
0
0
1
0
0
1
0
0
0
1
2
0
0
1
1
0
0
0
0
1
1
0
1
0
1
0
0
0
2
0
0
0
0
0
1
1
1
0
2
1
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
3
1
0
0
2
0
0
0
1
1
3
0
0
0
0
0
0
6
0
0
0
0
0
0
0
3
2
0
0
0
0
0
2
1
1
0
0
2
0
1
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
1
1
0
0
1
1
2
0
0
1
0
2
0
0
2
0
0
0
2
1
0
0
2
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
4
2
2
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
2
0
0
0
2
0
0
0
1
2
0
0
0
0
2
1
2
0
0
0
0
0
2
0
2
0
2
0
2
2
2
0
0
1
0
0
0
0
1
3
0
0
2
0
1
2
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
2
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
1
1
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
2
2
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
2
0
0
0
1
1
1
0
0
0
2
0
0
0
0
0
1
0
0
3
0
1
0
0
1
0
2
1
0
0
0
0
0
2
0
2
0
0
0
6
0
0
0
0
0
1
0
2
2
0
0
2
2
0
2
0
0
0
0
0
2
1
0
2
1
0
0
0
2
0
0
0
0
1
1
0
1
1
0
1
1
0
0
0
0
0
1
0
0
0
2
0
2
2
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
2
3
0
2
0
2
0
0
2
0
0
0
0
0
1
1
0
2
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
2
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
2
2
0
0
0
0
0
3
0
1
0
0
0
1
0
2
0
1
2
1
0
0
0
2
0
0
1
0
0
2
0
0
0
1
2
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
2
1
0
2
0
0
0
0
0
0
0
1
1
0
3
1
1
0
0
0
2
0
0
2
0
0
0
0
0
2
1
0
0
2
1
2
1
0
2
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
2
2
0
1
2
1
0
1
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
1
2
2
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
2
2
0
0
0
0
1
0
0
0
0
0
0
0
1
2
1
0
0
1
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
1
0
0
0
2
1
1
2
2
0
2
0
0
1
0
0
2
1
0
1
2
0
0
0
0
2
0
0
2
0
0
2
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
1
0
2
0
1
0
1
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
4
0
0
0
0
0
4
0
1
2
0
0
0
0
0
2
1
0
0
0
0
0
1
1
0
0
0
0
1
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
2
1
1
0
0
0
1
0
2
0
0
0
0
1
1
2
2
0
0
0
0
0
0
2
1
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
3
2
1
2
2
0
0
1
2
0
0
2
0
0
0
0
0
0
1
0
0
0
2
1
0
1
0
0
0
1
1
2
0
0
0
0
1
2
0
0
2
0
0
0
2
1
0
2
1
0
2
0
1
0
1
2
0
1
0
0
2
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
2
0
2
2
0
2
2
2
0
0
0
2
0
0
0
0
0
0
1
1
0
0
4
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
3
0
2
0
2
2
0
0
1
0
0
0
0
0
0
1
1
2
0
0
0
2
0
2
2
0
0
1
0
0
1
0
2
0
10
5
0
0
0
0
5
0
2
1
0
1
0
0
0
0
0
2
0
2
0
1
5
0
1
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
2
1
0
0
3
0
1
0
0
0
1
0
1
0
0
2
0
1
0
1
0
2
1
0
0
0
1
0
0
0
1
0
1
0
0
0
1
2
0
0
0
0
0
1
0
0
0
1
0
0
1
0
2
0
1
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
2
0
2
0
0
2
1
0
0
3
0
0
2
1
0
0
1
0
2
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
2
0
14
0
2
0
9
0
0
0
0
2
0
0
2
2
0
0
0
1
0
0
0
0
2
0
0
0
2
0
1
0
1
2
2
0
0
0
1
0
0
2
0
0
4
0
0
0
0
2
0
0
2
2
0
1
0
0
0
0
0
0
0
3
1
1
0
0
0
0
0
2
0
0
0
0
0
1
0
4
0
0
0
2
1
0
0
0
0
2
0
0
1
1
0
0
1
0
0
0
1
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
7
1
0
0
1
0
0
1
0
0
1
0
1
0
2
3
2
2
0
2
2
2
1
0
0
0
0
2
0
0
0
1
0
0
2
2
0
0
0
0
1
1
2
0
4
0
1
0
0
0
2
2
2
0
0
0
0
0
0
1
0
0
0
0
3
1
0
2
0
0
2
1
0
1
0
0
0
1
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
1
0
1
0
2
0
0
2
1
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
3
0
0
2
1
0
0
2
0
0
0
0
2
0
0
1
1
2
0
1
1
0
2
0
2
0
0
0
0
0
0
0
1
0
0
2
2
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
1
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
1
0
0
0
0
1
1
0
0
0
0
2
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
2
1
2
0
0
0
0
0
0
0
0
0
3
0
0
1
3
2
3
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
1
0
2
1
1
0
0
2
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
2
0
0
2
1
0
2
0
0
0
0
0
0
4
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
1
1
0
0
0
1
1
1
0
0
0
0
2
2
1
0
0
0
0
2
0
0
0
1
2
0
0
2
1
0
0
0
0
1
0
1
0
0
0
4
0
1
0
0
0
0
1
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
1
0
2
0
0
0
0
0
0
2
0
0
0
0
2
3
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
2
0
0
0
0
2
0
1
2
0
1
0
0
2
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
1
2
0
0
1
0
0
2
2
0
0
0
0
2
0
1
0
0
1
0
3
0
0
2
8
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
2
0
1
0
3
0
0
0
0
1
0
2
0
0
0
0
6
0
0
1
1
0
0
0
4
1
3
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
3
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
1
1
0
0
2
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
3
2
0
0
1
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
3
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
1
0
1
0
0
2
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
1
4
2
0
0
0
0
0
0
0
0
2
1
0
1
1
1
1
2
0
0
2
0
0
1
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
3
1
0
1
1
1
0
0
2
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
1
2
2
1
1
2
0
0
0
2
1
0
0
0
0
0
0
2
1
2
0
0
0
0
0
1
0
0
2
2
1
0
1
0
0
0
1
1
0
0
2
0
0
0
3
0
0
1
0
0
1
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
1
0
0
0
2
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
1
2
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
3
1
1
0
0
0
2
1
0
2
0
2
0
0
0
0
0
1
0
0
0
1
1
0
2
1
0
0
2
2
0
0
2
2
0
0
2
2
3
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
3
0
0
0
1
0
0
1
0
0
1
0
1
0
1
2
0
2
0
1
0
0
0
2
1
0
0
0
1
0
1
2
1
1
0
2
1
0
0
2
0
2
0
0
2
1
0
0
0
0
0
2
0
0
1
0
1
0
0
1
0
0
0
0
0
0
2
0
1
1
0
0
1
0
0
2
0
0
0
0
0
1
2
1
2
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
2
0
0
1
0
2
0
0
1
1
1
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
1
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
2
0
0
1
0
0
0
0
0
0
2
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
2
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
2
0
0
3
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
3
2
1
0
0
1
0
0
0
1
1
2
0
0
0
0
0
0
2
2
0
0
0
2
0
1
2
1
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
1
0
1
0
0
3
0
0
1
0
1
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
3
2
0
2
0
0
1
0
1
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
1
2
0
2
0
0
0
0
0
0
2
2
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
2
1
2
0
0
0
0
0
0
3
0
0
0
1
0
0
2
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
1
1
0
1
0
0
0
2
0
0
0
2
2
0
0
0
1
1
0
0
2
0
0
3
1
0
0
0
2
2
0
0
0
0
3
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
2
0
3
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
1
0
3
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
3
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
2
1
2
0
0
0
0
1
0
1
0
0
2
1
1
0
0
1
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
1
0
0
1
1
3
0
0
4
2
0
1
2
0
0
0
0
2
0
0
0
2
0
0
0
0
2
2
1
0
0
0
0
0
0
2
1
2
2
0
0
1
1
0
1
1
2
3
1
0
0
0
1
1
0
0
0
0
2
1
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
2
0
0
0
0
0
0
1
1
1
0
1
1
0
0
1
0
1
0
1
0
0
2
0
0
0
1
0
0
1
0
2
0
1
0
0
1
1
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
1
0
0
0
1
3
2
0
0
4
0
1
1
0
1
1
0
0
0
1
0
0
0
0
0
1
2
1
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
2
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
2
0
1
0
0
0
2
0
0
0
1
0
0
2
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
2
2
2
3
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
4
1
1
0
2
0
0
0
0
2
0
0
2
0
2
1
0
0
0
2
0
0
0
2
0
1
1
0
0
0
1
2
1
0
1
2
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
1
0
0
0
2
2
2
0
0
1
1
0
2
2
0
0
0
2
1
1
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
2
0
0
0
3
2
0
1
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
2
0
1
0
2
0
0
0
2
4
0
2
0
1
2
0
0
2
1
0
0
0
1
1
0
0
2
2
5
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
2
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
1
1
0
3
1
1
0
0
1
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
1
0
3
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
2
4
1
3
2
0
0
3
0
0
0
0
2
2
2
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
2
0
0
0
2
0
2
0
2
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
2
0
0
1
0
0
1
2
0
2
1
0
0
2
0
0
0
0
2
0
0
4
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
3
0
0
1
1
0
0
2
1
2
0
0
0
0
0
0
1
0
2
0
2
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
2
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
1
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
1
1
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
1
0
0
0
2
2
1
1
0
0
2
0
0
3
0
2
2
0
0
3
0
0
0
0
0
1
1
0
1
0
0
2
1
0
3
2
5
2
0
1
0
0
0
0
1
1
2
0
0
0
1
0
0
0
0
0
2
0
1
2
0
0
1
1
0
0
0
0
1
0
0
1
0
2
2
1
0
0
1
0
3
2
2
1
0
0
1
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
1
0
0
0
0
0
2
0
2
1
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
2
0
0
2
0
2
0
1
0
0
0
0
0
1
3
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
1
3
1
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
2
0
1
0
1
2
0
0
0
0
0
1
1
2
0
0
2
2
2
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
3
0
0
2
1
0
0
0
0
3
3
0
2
1
0
1
0
0
0
0
0
0
2
0
1
3
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
2
0
0
3
0
0
0
1
2
0
0
2
7
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
3
1
0
0
1
0
2
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
2
3
0
1
0
1
0
0
0
1
2
2
0
1
1
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
3
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
1
0
0
1
0
1
1
0
1
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
1
1
0
0
3
0
0
0
0
0
0
0
1
1
1
1
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
2
0
1
3
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
3
1
3
0
2
0
2
0
0
1
0
1
0
1
0
1
0
0
2
0
0
0
2
0
2
0
1
0
0
0
1
1
2
0
0
1
0
2
0
0
0
0
0
0
1
1
0
0
1
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
1
0
3
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
2
2
1
2
1
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
2
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
1
0
0
3
0
2
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
1
2
2
2
0
0
0
1
2
0
1
1
1
0
0
0
2
0
1
0
0
1
2
0
3
2
0
0
1
2
0
2
2
0
0
1
0
0
1
0
0
0
0
4
0
3
0
2
0
0
0
2
0
0
0
3
0
0
1
1
0
1
1
0
1
0
0
1
2
0
1
1
0
0
0
6
0
0
0
0
0
2
1
0
0
2
2
0
1
2
0
0
0
0
0
2
0
0
0
0
0
1
2
1
0
0
0
0
2
0
1
2
0
0
0
0
2
1
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
1
2
0
0
2
0
0
1
0
0
2
1
0
1
0
0
1
0
2
0
0
2
2
0
1
0
3
0
2
0
0
0
2
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
1
2
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
1
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
3
2
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
5
0
8
1
2
0
0
1
1
1
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
2
0
1
0
0
0
0
5
1
0
1
0
0
0
2
0
1
0
0
0
0
0
2
0
0
1
0
0
2
2
0
2
1
0
2
0
1
0
0
1
0
0
1
2
0
1
0
0
2
2
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
2
2
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
1
0
0
0
1
2
0
1
0
0
0
2
0
0
0
1
2
3
0
2
0
1
0
1
0
4
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
1
5
1
0
0
2
1
0
0
0
2
1
0
2
0
0
0
0
0
2
0
1
2
0
2
0
3
0
0
0
0
0
2
2
3
2
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
2
0
2
0
1
0
0
0
2
1
1
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
1
0
0
0
0
2
1
0
0
2
1
2
2
1
0
0
1
0
0
0
2
3
0
0
0
0
0
0
0
2
2
0
1
0
2
0
2
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
2
2
0
0
2
0
0
2
0
0
0
2
0
3
0
0
2
1
0
2
0
0
0
2
0
2
0
2
0
2
0
0
1
1
0
0
0
2
0
2
0
0
1
0
0
0
0
0
2
0
2
0
2
0
0
0
1
0
0
0
1
0
0
5
0
0
1
2
0
0
0
2
0
0
0
0
1
0
2
1
0
4
0
2
1
0
0
0
2
0
0
0
1
0
0
0
1
2
0
3
0
1
2
0
0
4
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
2
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
5
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
2
4
1
1
0
0
0
1
0
0
0
0
0
0
0
0
5
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
2
0
1
0
0
0
2
0
2
2
0
0
0
2
1
0
0
0
0
1
0
0
2
0
1
1
0
0
0
2
2
0
3
0
0
0
0
0
8
1
2
0
0
0
2
0
1
2
0
0
0
0
0
1
2
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
1
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
1
3
1
2
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
3
2
2
0
0
0
1
1
1
0
0
0
0
2
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
2
2
0
1
0
0
0
0
0
2
1
0
0
2
1
2
2
0
0
2
0
1
3
0
0
2
1
0
0
0
0
1
2
1
2
1
2
0
0
1
0
5
0
1
0
0
0
2
0
0
2
0
0
3
3
0
0
0
0
0
1
2
0
0
0
0
0
0
4
0
3
0
0
0
1
1
0
0
0
2
1
2
2
0
0
0
0
0
2
0
0
1
0
0
0
2
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
2
0
2
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
1
0
0
3
0
1
0
4
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
2
0
2
0
0
2
0
0
0
0
4
2
2
0
0
1
0
0
2
2
0
0
1
1
2
1
0
0
0
2
0
0
0
0
0
1
2
0
0
1
1
2
1
1
0
0
0
0
2
0
0
0
0
0
1
2
3
0
2
0
0
0
0
0
0
1
1
0
2
0
1
0
0
1
0
0
0
0
0
2
3
1
0
0
1
0
0
0
0
1
0
2
0
0
2
2
0
2
0
0
1
4
0
0
0
0
0
2
1
0
0
0
2
1
2
2
0
1
0
2
0
0
1
1
2
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
2
2
0
0
0
2
2
0
1
0
0
0
2
2
0
0
0
0
0
0
2
1
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
1
0
1
2
1
0
0
0
0
0
0
0
1
1
0
4
2
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
2
0
2
0
2
1
0
0
0
0
0
0
0
0
2
4
1
2
2
1
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
1
9
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
1
1
0
1
2
0
2
0
2
0
1
1
1
2
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
2
2
0
0
1
0
1
0
1
0
0
0
4
0
0
0
0
1
2
2
0
0
0
0
0
0
0
1
1
0
2
0
1
0
1
0
1
0
0
0
1
1
1
0
0
0
0
2
0
1
0
0
1
0
0
1
0
4
0
0
0
2
1
0
0
0
2
0
0
0
0
1
0
0
2
1
0
1
0
2
2
0
2
0
1
0
0
0
2
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
1
2
2
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
1
0
1
0
1
2
0
2
2
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
2
0
1
0
1
0
0
2
0
2
0
0
0
2
0
0
1
0
0
0
0
2
2
0
1
0
0
0
0
3
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
2
0
0
4
0
0
0
1
0
0
0
0
0
2
1
0
2
0
1
0
0
1
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
1
3
0
0
0
0
0
0
0
2
2
0
1
1
0
0
2
0
0
0
1
0
0
0
0
0
2
1
1
0
0
0
1
1
0
0
0
2
0
0
0
0
1
0
1
0
0
1
1
0
0
2
0
2
0
0
0
0
0
1
0
0
0
2
3
0
0
1
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
2
2
0
1
0
0
2
0
0
1
0
1
0
0
0
1
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
3
2
0
0
0
0
0
2
1
0
0
0
0
0
2
1
1
2
0
1
0
1
0
0
0
2
5
0
2
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
1
0
7
0
0
0
0
1
3
2
1
2
0
0
6
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
3
0
0
2
0
2
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
1
1
0
1
2
2
0
0
0
1
1
0
0
0
0
2
1
2
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
1
0
0
2
0
0
1
1
2
0
1
2
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
1
2
0
2
0
1
2
2
0
0
0
0
0
1
1
2
0
0
2
1
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
2
0
1
2
0
0
1
2
2
0
0
0
0
0
0
1
2
0
1
0
2
0
1
0
0
0
0
0
2
1
2
0
0
1
0
0
1
0
0
2
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
2
2
0
0
1
0
0
0
0
1
2
0
2
0
1
2
0
3
0
1
0
1
1
0
1
0
0
3
0
0
0
0
2
0
0
4
0
0
1
1
0
1
0
0
0
0
0
2
0
0
0
0
3
0
2
0
2
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
3
0
0
0
0
0
6
0
0
2
0
0
0
2
0
2
0
4
0
0
1
1
0
0
3
0
0
1
2
1
0
0
0
0
0
0
1
2
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
1
0
0
1
0
0
2
0
1
0
0
1
0
2
0
0
0
0
1
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
1
0
0
0
2
0
0
0
0
0
0
4
0
1
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
1
0
1
0
2
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
3
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
2
0
2
0
0
2
2
0
0
1
0
0
2
0
0
3
2
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
1
2
0
1
0
0
2
2
0
0
0
0
2
0
0
1
0
0
0
2
1
0
0
0
1
1
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
2
3
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
1
0
0
0
0
2
1
0
0
0
2
0
0
1
0
0
1
0
2
0
0
2
0
1
1
1
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
8
0
0
0
0
3
5
0
0
0
0
0
1
0
0
2
2
0
1
0
0
1
0
2
2
0
0
0
0
0
0
0
0
2
2
1
0
0
0
2
2
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
3
0
0
0
0
0
1
1
1
0
2
3
3
0
0
0
0
0
0
1
0
1
1
2
0
1
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
2
1
2
0
1
0
0
2
2
0
0
0
0
0
1
0
0
2
0
1
0
1
0
0
0
2
0
0
1
0
0
2
1
1
0
2
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
1
0
0
1
10
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
7
0
0
1
0
1
0
0
2
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
2
0
2
0
0
1
2
0
0
0
0
0
1
0
2
2
0
3
0
0
0
0
3
1
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
1
0
2
3
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
2
1
0
0
0
2
0
1
1
0
0
1
0
0
0
0
0
2
0
0
0
0
1
1
3
2
0
2
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
3
2
2
0
1
0
0
0
1
2
1
1
3
1
0
1
2
0
0
0
1
2
1
0
0
2
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
5
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
2
2
0
1
2
2
2
2
0
3
0
1
1
0
1
1
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
1
2
0
1
2
2
0
0
2
0
0
0
0
2
0
0
2
1
1
0
0
0
0
0
1
2
0
0
1
0
0
0
0
2
2
0
0
0
1
0
0
1
2
0
2
0
1
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
2
0
0
0
0
1
0
0
0
0
0
1
1
2
0
0
0
0
0
1
2
1
0
2
0
0
2
2
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
2
0
0
0
1
0
0
0
1
0
0
0
1
1
2
1
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
2
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
2
0
0
2
0
2
0
1
0
1
0
0
0
1
0
0
0
0
0
0
2
1
2
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
2
0
2
0
2
0
2
0
2
0
1
0
2
0
0
0
0
1
0
0
4
1
0
0
0
0
3
0
1
0
0
0
0
2
3
0
0
0
0
1
1
0
0
0
0
1
0
1
1
2
2
3
0
2
1
0
0
0
0
0
0
1
2
2
0
0
1
0
0
1
0
0
2
2
0
0
0
0
3
0
0
1
2
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
1
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
2
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
3
2
0
0
0
2
0
0
1
4
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
3
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
1
1
0
1
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
1
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
3
0
1
0
2
2
0
1
7
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
4
2
0
0
2
0
0
0
2
1
0
0
2
1
0
0
0
0
1
1
0
0
0
0
0
1
0
2
1
0
1
0
0
0
0
0
0
2
0
1
1
0
0
1
1
2
2
2
1
0
2
1
2
0
2
0
0
0
0
1
0
0
0
2
2
0
0
1
0
0
2
0
0
0
2
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
2
0
0
0
2
0
0
1
1
2
0
0
1
0
1
1
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
2
1
0
2
1
0
0
0
1
1
0
3
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
1
2
0
0
5
0
0
2
2
0
0
1
2
2
1
0
2
0
2
2
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
2
1
0
1
0
2
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
1
2
0
2
0
2
0
0
0
3
0
0
1
0
0
0
0
0
0
1
2
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
1
0
2
2
1
0
2
0
2
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
3
0
0
0
0
0
0
0
1
0
2
1
1
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
1
0
0
2
1
0
0
1
0
0
1
2
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
2
0
0
0
2
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
1
0
1
2
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
1
0
2
1
0
0
2
3
2
2
0
0
0
1
1
1
0
1
0
0
1
0
0
2
0
2
0
2
3
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
2
3
2
0
0
1
1
2
0
2
0
0
0
0
0
2
0
0
0
1
1
0
2
0
0
0
2
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
1
1
0
1
1
0
2
2
0
2
0
0
0
0
0
0
0
0
1
3
0
0
0
0
1
1
2
0
1
1
0
0
2
2
0
0
2
2
2
0
0
0
0
1
0
0
0
2
0
0
1
2
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
2
0
0
1
0
2
2
0
0
0
1
1
0
2
0
0
0
0
1
0
0
0
2
1
0
0
2
1
0
1
0
0
0
0
0
3
0
0
0
3
0
1
1
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
3
1
0
0
0
0
0
2
0
2
0
1
0
1
2
0
0
0
2
0
2
2
2
0
0
4
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
1
0
0
0
0
0
2
0
1
0
0
0
1
4
0
2
2
1
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
2
1
2
0
0
0
0
0
0
3
4
0
1
3
0
2
0
0
0
1
1
0
2
0
0
0
0
0
1
0
1
1
0
0
0
0
0
2
2
0
0
0
0
0
0
3
0
0
0
0
0
0
2
1
0
1
4
0
1
3
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
2
3
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
2
1
3
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
2
0
0
0
0
0
0
0
0
3
0
0
0
3
0
0
5
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
2
0
1
2
0
0
4
0
2
0
0
0
0
0
0
0
0
2
2
0
0
2
0
2
2
0
5
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
2
0
2
0
2
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
1
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
1
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
3
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
1
2
1
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
2
0
0
2
1
0
2
0
0
0
0
1
0
1
0
0
1
0
3
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
1
0
6
0
0
2
0
2
2
0
0
0
0
0
0
2
0
0
2
0
2
1
0
2
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
1
0
0
2
1
1
0
0
2
1
1
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
1
2
1
1
2
1
0
0
0
0
0
2
1
0
4
0
2
2
0
1
0
0
0
2
0
2
3
1
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
3
1
0
0
1
0
3
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
2
0
1
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
1
2
2
1
1
0
1
1
1
0
0
2
0
0
0
0
0
0
1
1
1
1
2
0
0
0
0
0
1
0
0
0
0
2
0
2
0
2
0
1
1
0
0
2
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
1
0
1
0
1
0
1
1
0
1
1
1
0
0
0
0
0
0
0
0
0
1
1
2
1
0
0
0
1
0
1
0
1
0
1
1
0
0
0
0
0
0
2
2
0
0
0
0
2
1
2
0
0
0
1
1
0
1
1
0
0
1
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
2
0
0
0
0
2
0
0
0
1
0
0
0
1
0
2
0
2
4
1
0
0
2
0
2
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
1
1
1
1
0
2
0
1
0
1
0
0
2
0
0
0
2
0
2
0
0
0
1
0
0
0
0
3
2
0
0
0
3
2
0
1
1
0
1
0
1
0
0
0
1
0
1
0
2
0
0
3
0
0
0
1
2
0
0
2
1
0
0
1
0
2
2
0
2
0
0
3
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
3
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
1
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
2
0
0
0
2
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
4
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
1
0
0
1
1
0
0
0
2
0
0
0
1
0
2
0
0
1
1
0
1
2
0
1
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
1
2
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
3
1
2
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
2
1
0
0
2
0
0
1
0
0
0
2
0
1
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
1
2
1
0
0
2
1
1
0
0
2
0
1
0
0
0
0
1
0
0
0
3
2
0
0
0
0
1
0
0
1
1
0
2
0
2
0
1
0
0
0
2
1
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
2
1
0
0
0
0
3
0
0
0
1
0
0
0
2
0
0
0
0
2
1
0
0
2
0
0
2
1
2
0
1
0
3
1
0
0
0
0
0
1
0
0
0
0
2
0
0
2
2
1
0
0
0
2
2
0
2
0
0
1
0
0
0
1
0
1
2
2
0
0
2
2
0
0
2
0
0
0
0
3
0
2
0
2
0
2
0
1
0
0
1
0
0
0
2
1
0
1
0
1
0
0
0
1
0
2
2
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
4
0
0
0
0
0
1
1
0
1
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
6
0
0
0
2
0
0
2
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
2
0
1
2
1
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
1
0
0
0
2
0
3
0
0
0
0
0
0
0
2
0
1
0
0
0
2
2
0
0
0
3
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
3
2
0
0
0
0
2
0
0
5
0
0
0
1
2
0
0
2
1
1
0
0
0
0
1
0
1
0
2
2
0
0
2
3
0
0
2
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
2
0
1
0
3
0
0
0
0
1
1
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
1
2
0
0
2
0
2
0
1
0
2
1
0
0
0
0
0
0
4
3
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
2
1
2
0
0
2
0
0
2
0
0
1
0
0
0
0
0
2
3
0
1
0
0
0
1
0
1
0
1
1
0
1
0
0
0
1
0
0
0
0
9
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
2
0
1
0
2
0
0
0
0
0
0
2
2
0
2
0
2
1
2
0
0
2
0
0
1
0
0
0
0
0
1
1
0
2
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
2
0
0
2
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
1
0
1
0
1
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
4
0
1
2
0
0
0
1
0
0
1
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
3
1
0
0
0
0
2
0
0
2
0
0
0
2
0
0
2
0
2
2
0
0
2
0
2
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
4
0
0
1
0
3
0
0
0
0
2
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
2
0
2
0
2
0
3
0
2
1
0
0
0
0
2
0
0
0
0
0
2
1
1
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
1
1
0
4
0
0
2
0
0
0
0
0
1
2
0
0
0
2
0
2
5
0
0
0
0
0
0
1
2
0
0
0
0
1
1
0
2
0
0
0
0
0
1
0
0
0
2
1
1
2
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
3
0
2
0
1
0
0
3
1
2
0
0
1
0
3
0
0
2
0
0
0
0
1
0
0
0
2
1
0
1
1
0
0
2
0
2
1
0
0
0
0
0
2
3
0
1
2
0
2
0
0
0
0
0
2
0
0
0
0
1
2
2
2
2
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
2
0
2
0
0
0
0
2
0
2
0
0
0
1
0
0
0
2
0
0
0
0
1
1
1
2
0
1
0
0
2
0
0
0
0
2
2
0
0
0
1
0
0
1
3
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
1
2
0
2
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
2
1
0
0
2
0
1
1
0
0
0
0
2
1
1
0
0
2
0
1
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
1
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
2
0
0
0
0
1
1
1
0
0
2
2
3
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
1
2
0
0
1
0
1
2
0
0
0
2
1
0
0
0
0
1
1
1
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
1
2
0
2
0
2
0
0
2
0
1
2
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
2
2
0
1
0
2
2
1
0
0
2
2
0
0
0
1
0
0
0
2
0
2
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
1
1
1
0
0
1
1
0
0
2
1
0
0
0
2
0
0
0
0
0
0
2
2
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
4
0
0
0
0
0
2
0
1
1
1
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
1
0
0
2
0
1
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
2
0
1
0
2
1
2
1
0
0
0
0
0
0
0
0
1
1
4
2
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
1
0
2
0
3
1
1
1
1
0
2
0
0
0
2
1
1
0
0
2
0
0
2
0
0
1
0
1
0
1
0
2
0
0
1
0
0
0
2
1
1
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
2
0
2
2
2
1
1
2
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
2
0
0
1
0
2
0
0
2
2
0
0
0
0
2
0
1
2
0
3
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
2
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
1
0
0
0
2
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
3
1
1
0
0
0
1
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
2
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
1
0
0
1
2
0
1
2
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
2
2
0
2
2
0
0
2
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
5
0
0
1
1
0
0
0
0
2
0
1
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
2
0
1
1
2
0
0
0
0
0
1
1
0
0
0
0
0
3
0
2
3
0
1
0
1
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
2
0
0
2
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
3
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
1
2
0
2
2
1
2
1
0
2
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
2
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
2
0
0
0
0
0
2
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
1
0
2
1
2
0
8
0
4
0
0
2
2
0
0
2
2
0
0
0
0
2
2
0
0
2
0
0
0
2
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
4
1
0
0
0
0
1
4
0
1
1
0
2
0
2
0
0
0
1
2
0
0
1
0
0
1
0
0
2
0
0
0
1
0
0
0
1
0
1
2
1
1
0
0
0
0
0
0
0
0
0
1
2
3
0
0
0
0
2
0
1
1
3
0
1
0
0
2
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
1
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
2
0
1
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
3
0
1
0
0
0
2
0
1
0
1
0
1
0
0
0
0
3
1
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
2
0
1
2
1
1
1
2
1
1
0
3
1
0
1
0
0
0
1
2
1
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
2
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
1
1
0
0
0
0
2
0
1
1
0
0
2
1
0
2
0
0
1
1
0
1
0
0
2
4
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
3
0
0
0
2
0
0
0
1
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
1
2
0
1
0
0
2
0
1
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
4
0
2
0
0
0
0
0
1
0
2
1
0
0
0
2
0
1
2
1
0
0
1
0
0
1
0
2
0
0
0
2
0
1
0
0
2
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
1
1
0
0
0
2
0
0
2
2
0
0
2
1
0
0
0
0
0
0
4
0
0
1
0
0
1
0
0
0
0
4
2
0
1
0
0
0
1
0
7
2
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
2
0
0
1
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
2
0
1
0
0
0
1
0
0
2
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
2
0
1
0
3
2
0
0
0
0
0
0
2
1
1
0
0
1
0
0
0
3
3
0
0
1
2
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
4
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
2
0
1
1
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
2
2
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
2
0
2
0
0
0
2
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
1
1
1
2
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
5
0
0
0
1
0
0
1
0
1
0
0
0
0
1
2
0
2
2
1
1
1
0
0
0
1
1
0
0
0
2
0
1
0
0
2
0
0
1
0
1
0
0
0
1
0
1
0
2
0
0
2
0
0
2
0
0
2
0
0
0
1
2
0
0
1
2
0
1
0
1
3
2
0
0
0
0
0
1
0
0
4
0
1
2
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
2
0
0
1
0
3
0
3
0
1
2
0
1
0
2
0
0
1
0
1
0
0
1
1
2
2
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
1
0
1
1
0
1
8
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
1
0
0
2
0
1
0
2
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
2
2
2
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
1
2
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
2
0
2
0
2
0
1
0
0
1
0
0
2
0
0
0
0
1
0
0
0
1
0
1
2
1
0
0
0
1
2
0
2
1
0
0
2
2
2
0
0
0
3
2
1
0
0
3
1
0
1
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
2
1
0
0
0
2
0
0
0
2
0
2
0
1
0
1
1
0
0
0
2
2
2
0
0
1
0
0
0
2
0
0
0
0
0
1
1
0
0
1
1
1
1
0
0
0
0
1
1
1
0
0
2
0
0
2
0
0
0
1
0
1
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
2
3
1
2
0
0
0
2
0
0
0
0
0
1
2
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
1
1
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
2
0
0
0
0
2
0
0
0
0
0
2
2
0
0
1
0
0
1
0
0
2
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
1
1
0
0
1
0
1
0
0
0
1
2
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
4
0
0
2
1
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
2
2
0
1
1
1
1
0
0
0
0
0
2
1
0
0
0
0
2
1
1
0
0
0
0
3
0
0
1
1
0
0
0
0
2
0
0
2
2
0
3
2
1
0
0
0
0
1
0
1
0
0
0
0
0
1
3
1
0
2
1
1
0
2
3
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
2
1
1
0
2
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
1
0
0
0
2
0
1
2
0
2
1
2
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
2
0
1
2
2
2
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
1
1
0
2
0
0
1
2
2
0
1
2
1
0
0
2
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
2
0
3
0
0
0
0
0
2
0
0
0
2
2
1
2
0
0
0
2
3
0
0
0
0
1
1
0
0
0
0
2
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
1
0
1
0
2
0
0
0
1
0
1
1
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
2
1
1
0
0
0
2
0
1
0
0
0
1
0
0
3
0
0
1
0
2
0
0
0
0
0
0
0
0
3
0
0
2
0
0
1
0
2
0
1
0
0
1
0
1
1
0
2
0
1
1
0
0
2
0
1
0
0
2
0
0
1
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
2
0
0
1
0
0
0
0
1
0
0
0
2
0
1
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
1
1
0
2
0
0
1
0
0
0
2
0
0
0
0
2
1
0
0
2
0
1
0
1
2
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
2
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
1
0
0
2
0
0
4
0
0
2
1
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
2
0
1
0
1
1
0
0
0
0
2
0
0
0
2
0
5
0
0
0
0
2
0
2
0
1
1
0
0
0
0
2
2
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
1
0
0
0
2
0
1
0
2
0
0
0
2
2
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
2
0
2
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
2
0
0
0
0
1
0
2
0
1
0
0
1
0
1
0
0
0
0
2
0
0
7
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
2
0
1
2
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
1
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
2
0
0
0
0
1
0
2
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
1
0
0
3
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
3
1
0
0
0
0
2
1
1
0
0
2
0
0
2
1
2
0
0
0
0
3
0
1
0
3
0
2
0
6
0
0
2
2
1
0
0
0
0
0
1
1
0
0
1
0
0
0
2
1
2
0
0
0
0
0
2
2
3
0
0
0
0
2
1
0
2
0
5
0
0
1
0
2
0
2
0
0
0
0
1
1
0
0
0
1
0
1
0
0
4
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
2
0
1
0
0
0
1
0
2
0
0
0
1
0
0
1
0
0
0
0
0
2
1
0
0
3
0
0
1
0
0
0
0
6
0
0
0
0
0
1
0
0
0
0
2
1
3
0
2
2
0
5
1
0
2
2
0
0
2
0
1
0
0
1
1
1
2
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
2
0
2
0
0
0
0
1
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
2
2
0
1
0
0
1
1
2
3
2
3
0
0
0
0
0
2
0
0
0
1
2
0
0
2
0
2
1
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
2
0
0
1
0
3
2
0
0
0
3
0
2
2
0
0
0
0
0
0
0
0
0
5
2
0
0
0
0
2
2
2
0
0
1
0
1
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
1
0
1
1
0
2
0
0
2
0
2
0
0
3
0
0
0
0
1
1
0
1
0
3
0
2
0
0
0
0
0
2
1
1
1
0
1
1
2
1
2
2
1
2
1
2
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
2
0
1
0
2
0
1
0
0
0
0
1
0
4
1
0
0
0
0
0
1
0
0
2
2
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
2
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
3
4
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
2
2
0
0
0
0
0
0
1
0
0
0
2
0
1
2
0
2
0
2
1
0
0
0
1
2
0
0
2
2
0
0
2
2
0
5
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
2
2
0
0
0
1
0
1
0
0
0
0
1
2
0
0
2
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
1
0
0
1
2
0
0
0
0
2
0
0
2
0
1
1
0
0
2
1
1
2
0
0
2
0
0
0
0
2
0
2
0
0
1
0
2
0
0
2
1
0
0
1
0
1
0
0
0
0
1
0
0
1
0
2
0
0
2
2
0
0
0
0
0
2
0
0
2
0
2
0
2
0
0
0
0
0
1
0
0
0
1
1
2
1
0
0
0
2
0
0
0
0
0
0
0
4
0
1
0
2
0
2
0
0
0
0
0
1
2
1
0
0
1
0
0
0
2
0
1
0
0
0
0
0
1
0
2
1
2
0
0
0
1
0
0
1
0
0
0
2
0
2
0
0
1
0
2
0
0
1
2
0
0
1
0
1
0
1
2
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
2
2
0
2
0
0
0
0
0
2
3
1
1
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
1
1
0
0
2
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
2
0
0
0
0
1
0
2
1
0
0
2
0
0
0
0
0
0
0
2
2
2
0
0
0
2
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
3
1
1
0
0
2
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
1
1
2
0
0
2
0
0
0
1
1
0
0
0
1
1
0
0
2
0
0
1
1
0
3
0
0
7
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
1
1
2
0
3
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
4
0
0
1
0
0
0
1
0
0
0
0
0
2
0
1
0
2
1
0
0
0
0
2
0
1
0
1
0
0
2
0
0
0
0
0
1
1
0
1
0
0
0
4
2
0
3
1
0
2
0
0
0
0
2
1
0
0
0
0
0
2
1
1
0
0
0
0
1
3
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
2
2
2
0
1
0
0
2
0
1
1
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
3
2
0
0
1
0
1
1
1
2
2
0
0
1
0
1
0
2
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
4
2
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
1
2
0
1
2
0
0
0
0
0
1
0
0
1
1
0
1
0
0
3
1
0
2
0
0
0
2
0
0
2
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
2
0
0
2
0
2
1
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
1
2
2
0
3
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
3
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
5
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
6
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
2
2
1
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
1
2
0
0
0
0
0
0
0
2
1
1
2
0
0
2
0
0
3
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
5
0
0
1
1
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
3
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
2
0
0
1
1
1
0
1
0
1
0
0
0
1
0
2
0
1
0
0
2
0
2
1
2
2
0
1
1
0
0
1
0
0
0
1
0
0
0
1
1
0
1
2
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
1
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
1
0
2
0
0
3
0
1
1
0
0
0
1
0
1
5
0
0
0
1
0
0
2
1
0
2
2
1
0
3
0
2
0
1
2
1
2
2
2
0
0
0
2
1
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
2
1
0
1
2
0
2
0
0
0
2
1
2
0
0
2
2
0
2
2
0
1
2
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
2
2
1
2
0
1
0
0
0
1
1
0
1
0
0
0
0
2
2
0
0
0
2
0
0
0
1
0
0
0
0
0
1
2
0
1
3
0
1
0
0
2
0
0
0
0
0
0
1
1
0
0
0
1
2
0
1
2
0
0
0
2
2
1
0
0
0
0
0
0
0
1
0
0
0
2
0
2
1
0
0
1
0
0
0
1
2
0
1
1
0
0
0
1
0
2
0
0
1
1
2
3
1
0
0
1
0
0
0
0
0
0
0
0
3
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
3
2
0
1
0
0
2
0
2
0
1
2
2
0
0
2
2
1
0
0
0
0
0
6
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
2
0
1
1
2
0
0
0
1
0
1
0
2
0
2
1
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
1
2
0
0
0
0
3
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
2
0
0
0
2
1
0
0
0
1
0
0
2
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
1
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
1
2
3
0
0
3
0
0
1
2
2
1
0
2
2
0
0
0
10
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
2
1
1
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
2
2
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
1
2
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
1
6
1
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
1
0
2
0
1
1
0
1
0
1
0
1
0
0
0
1
0
2
1
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
3
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
1
0
2
0
0
0
2
0
2
1
0
0
2
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
2
0
0
0
2
2
0
5
0
0
0
0
2
5
1
0
0
1
2
0
0
0
0
0
1
2
2
2
1
1
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
1
1
0
1
2
6
2
0
1
2
1
0
0
2
2
0
0
0
0
0
0
1
0
0
1
2
1
1
0
2
0
2
0
2
0
0
0
2
1
0
2
1
1
1
2
1
0
1
1
1
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
3
0
0
2
0
2
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
3
0
2
3
2
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
2
2
0
0
1
1
0
1
0
1
1
0
0
4
0
0
1
0
0
0
0
0
2
0
0
0
0
4
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
4
0
0
2
0
1
0
0
0
0
0
0
1
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
2
1
1
0
2
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
2
0
1
1
0
0
0
2
0
2
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
3
0
3
0
2
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
2
0
1
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
2
0
1
0
1
0
0
2
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
1
0
0
0
1
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
2
2
0
1
0
2
0
0
0
1
1
1
2
0
0
0
1
0
0
0
1
1
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
3
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
2
0
0
1
0
2
0
0
0
1
0
0
0
1
1
0
0
0
0
1
1
0
2
0
0
1
0
2
0
0
0
0
0
0
1
0
0
1
0
2
0
2
0
0
2
0
1
0
2
1
3
2
0
0
0
0
1
0
0
0
2
1
0
1
1
1
0
0
2
0
0
0
1
1
0
2
0
2
1
0
0
0
0
0
0
3
2
1
0
0
0
0
0
1
1
0
1
2
1
0
2
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
4
0
2
1
0
2
0
3
1
1
0
0
0
1
1
0
0
0
0
5
1
0
2
1
0
2
0
0
0
1
0
0
2
0
2
0
2
0
0
0
0
3
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
2
2
0
1
0
2
0
0
1
1
0
0
0
1
0
0
0
0
0
2
2
2
1
1
0
0
1
0
0
0
1
0
0
0
2
0
2
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
3
4
0
0
0
0
0
0
0
0
3
1
2
0
3
2
0
1
2
0
0
0
0
0
0
2
0
0
1
1
0
0
0
1
0
0
0
2
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
4
2
0
2
2
2
0
0
0
1
0
0
1
1
0
2
0
0
0
0
0
0
2
0
2
0
1
0
3
2
1
0
0
1
0
0
1
2
0
2
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
1
1
2
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
2
0
0
0
0
0
1
0
2
1
0
0
0
0
2
0
0
0
0
2
1
1
0
1
0
0
0
1
0
1
0
0
0
2
0
0
0
0
2
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
2
3
0
2
0
1
3
0
0
0
0
0
2
1
0
0
1
2
0
0
0
2
0
1
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
2
0
1
0
3
0
0
0
0
0
0
0
2
2
1
0
0
1
0
0
0
3
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
2
2
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
1
2
1
0
1
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
5
3
3
0
0
2
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
2
2
0
0
0
0
1
4
0
0
0
0
2
0
1
0
0
2
1
2
0
0
0
1
0
3
0
1
0
0
0
3
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
1
0
2
2
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
1
2
0
1
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
1
2
0
1
0
0
1
2
2
3
0
0
0
0
0
0
0
0
0
2
2
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
1
0
0
2
2
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
2
0
0
0
1
1
2
1
1
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
2
0
0
0
0
1
0
0
0
2
0
2
0
3
0
1
0
0
0
1
0
1
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
2
2
2
2
2
1
0
2
0
0
0
0
2
0
1
0
0
0
0
2
0
0
1
2
2
0
2
0
2
3
1
1
0
1
0
2
2
1
0
0
0
0
1
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
1
1
0
0
0
0
0
0
4
0
1
0
0
0
1
0
0
0
0
0
1
2
0
0
1
0
0
0
1
0
1
0
1
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
3
0
0
0
0
0
0
1
0
0
1
1
0
2
0
0
2
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
2
2
0
2
0
0
0
2
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
1
0
2
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
2
0
1
0
1
0
0
2
0
0
0
0
1
2
1
15
0
0
0
1
0
0
0
0
0
0
2
2
1
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
2
0
2
0
0
2
0
1
0
6
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
2
0
1
0
0
2
0
0
1
0
0
1
2
0
0
0
0
0
0
4
0
0
2
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
2
2
0
0
0
0
0
2
0
2
0
2
2
0
2
3
0
2
0
0
3
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
1
0
3
1
0
0
0
0
0
0
0
2
0
0
3
0
2
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
1
1
1
1
2
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
3
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
2
2
0
0
0
0
0
0
0
0
1
3
0
1
1
1
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
2
1
1
0
0
1
3
1
0
2
1
0
0
2
0
1
0
0
0
0
1
1
1
0
0
1
0
0
1
0
2
1
0
2
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
2
0
2
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
1
0
0
0
1
0
0
0
1
0
2
2
2
0
1
1
1
2
1
3
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
7
0
0
0
0
2
0
0
14
2
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
2
1
2
0
0
3
0
3
0
0
0
0
0
0
1
1
0
0
2
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
2
0
0
2
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
1
2
1
0
2
0
3
0
2
1
0
1
2
0
0
0
0
0
2
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
3
0
0
1
1
0
2
0
0
0
1
0
0
0
2
2
2
0
0
1
0
0
0
0
1
1
0
0
2
0
1
2
0
0
1
0
0
1
0
0
0
2
0
3
0
0
0
1
0
2
0
0
2
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
2
1
2
0
0
0
0
2
0
0
0
1
0
0
0
1
1
1
0
0
2
2
0
0
2
0
0
1
0
0
0
2
0
0
0
1
0
3
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
3
0
1
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
1
0
0
0
1
0
0
1
0
2
0
0
0
0
1
2
0
0
2
2
0
0
0
0
1
0
0
1
0
1
2
1
0
2
0
1
0
0
2
0
0
0
0
0
0
2
1
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
1
0
0
1
1
0
0
1
1
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
1
0
0
2
0
0
2
1
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
6
2
2
2
0
0
0
0
1
0
1
2
2
1
0
0
0
0
0
1
0
1
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
2
2
0
1
0
0
0
2
2
0
2
0
0
0
0
0
0
2
1
0
0
1
0
2
0
0
0
0
2
1
0
2
1
0
0
2
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
3
2
3
0
0
0
2
2
0
0
0
0
2
0
4
0
0
1
1
0
0
1
2
2
0
2
1
0
0
1
0
2
4
0
0
0
0
0
0
1
0
0
2
2
0
0
1
0
0
1
0
0
3
2
0
1
0
0
2
0
1
0
1
1
1
0
0
0
0
2
0
0
1
2
0
0
0
0
1
5
2
0
1
1
1
0
2
0
0
0
0
2
0
0
0
2
0
2
0
0
0
2
0
2
1
0
1
0
0
1
2
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
1
2
1
2
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
2
0
1
0
1
1
0
2
2
0
0
0
0
2
1
0
0
0
0
0
2
0
0
1
2
0
4
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
2
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
1
0
7
0
1
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
3
1
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
2
2
1
0
0
0
0
0
1
1
0
0
1
0
0
2
0
0
0
0
1
2
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
5
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
1
2
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
2
0
0
0
1
0
0
0
2
1
2
1
0
2
0
0
0
3
2
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
4
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
1
0
0
0
1
0
1
1
1
0
2
2
0
0
1
0
0
0
0
0
2
2
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
1
2
0
3
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
1
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
1
2
0
0
0
0
1
1
2
0
0
2
0
1
0
0
0
0
2
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
2
2
0
1
2
0
1
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
2
0
1
0
1
2
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
1
3
0
2
2
0
0
0
2
2
2
0
1
0
2
2
0
0
2
0
0
0
0
0
0
2
2
2
0
0
0
0
2
0
0
1
0
0
0
0
0
2
1
1
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
1
0
1
2
4
2
1
0
0
0
0
0
0
1
0
0
1
2
1
0
0
2
0
2
0
0
2
3
2
2
0
1
1
0
0
0
2
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
3
2
0
0
2
0
1
2
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
1
0
1
0
0
1
1
1
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
2
0
0
3
2
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
2
2
0
0
2
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
1
2
1
0
0
1
0
0
0
1
2
2
0
1
0
2
0
3
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
2
0
2
2
0
0
1
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
1
2
0
0
0
0
0
1
0
1
1
2
2
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
1
0
1
3
0
1
1
0
0
2
0
2
0
1
0
0
1
2
0
0
6
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
4
0
0
0
2
0
0
0
0
0
2
0
2
0
2
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
3
0
1
0
0
4
2
2
1
0
0
0
0
2
1
0
2
0
0
0
0
0
0
2
2
1
0
2
0
0
0
0
1
0
1
0
2
2
0
0
4
2
1
2
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
2
2
0
0
0
0
0
0
2
0
0
2
0
2
1
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
2
1
0
2
0
2
1
0
0
0
3
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
1
1
3
0
0
0
2
0
0
0
1
2
1
0
0
0
0
1
0
1
0
2
1
2
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
2
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
1
1
0
0
1
0
0
0
1
1
0
0
0
0
1
0
1
2
0
1
0
1
0
0
0
0
0
0
1
0
0
2
0
0
2
0
1
0
0
0
1
0
2
0
0
0
1
2
1
0
1
0
12
4
0
0
3
2
0
1
0
0
0
3
0
0
1
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
2
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
2
1
0
1
0
2
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
2
0
0
2
1
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
2
1
0
0
2
0
1
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
2
0
1
2
0
0
0
0
2
0
2
0
2
1
0
1
2
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
1
1
2
0
0
0
4
0
2
1
0
0
0
0
0
1
0
2
0
2
0
0
1
0
0
2
0
1
3
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
3
2
1
0
0
0
0
1
0
0
1
0
1
0
2
4
0
1
1
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
1
0
2
1
0
0
0
1
0
2
1
0
0
0
0
0
2
0
0
0
2
1
0
0
2
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
1
0
0
0
2
0
1
1
2
2
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
2
0
0
0
0
2
0
2
0
0
0
1
2
0
1
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
2
2
1
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
2
0
1
2
0
0
2
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
3
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
4
0
2
0
2
0
2
0
0
1
0
0
2
2
3
0
0
0
1
0
0
1
1
0
0
0
2
0
0
0
0
2
2
2
0
2
0
1
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
2
1
1
0
1
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
9
0
0
0
0
1
0
1
0
1
2
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
1
0
2
2
0
4
1
2
1
0
0
1
0
2
0
0
0
0
2
0
0
0
1
2
0
0
0
2
0
2
0
0
1
0
0
1
0
2
0
0
0
0
2
0
0
0
0
4
1
2
2
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
3
2
0
0
0
3
0
1
2
0
0
2
1
0
0
0
0
0
0
0
2
1
0
1
2
1
0
2
2
3
0
0
1
4
1
0
0
2
0
0
0
0
0
0
0
0
4
0
1
10
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
2
0
2
2
0
0
2
2
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
1
2
0
3
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
1
0
2
0
2
0
0
0
0
0
1
0
3
0
0
0
0
0
0
2
0
1
2
0
0
1
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
2
0
0
1
0
2
0
2
0
0
2
1
0
0
0
1
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
1
5
0
0
0
0
0
0
1
0
1
0
1
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
2
0
0
0
2
0
1
0
1
2
0
1
0
1
0
3
1
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
2
0
0
2
0
0
0
1
1
0
0
0
0
2
1
2
0
0
0
3
0
0
1
1
0
0
1
1
1
0
1
0
0
0
0
1
0
1
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
2
1
0
0
0
0
0
2
0
2
0
0
0
1
2
2
0
0
0
0
0
2
1
0
0
0
0
2
0
2
2
1
1
2
0
2
3
0
1
1
0
0
1
0
0
4
0
0
1
2
2
0
0
4
0
1
3
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
1
2
0
0
0
2
1
0
0
0
0
0
1
1
2
0
0
2
1
0
1
0
4
0
0
0
1
0
0
0
2
0
1
0
1
2
0
1
1
2
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
2
0
0
0
0
0
5
2
0
0
0
0
2
0
0
1
0
1
0
0
2
1
0
2
0
0
2
0
0
0
0
0
0
3
2
0
1
0
0
0
0
0
0
0
2
2
2
0
1
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
3
0
3
0
0
1
0
0
0
0
0
0
0
1
2
2
1
0
0
0
0
0
2
1
0
0
0
0
1
1
0
2
0
0
2
1
1
2
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
7
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
3
0
1
2
1
1
0
0
1
0
0
0
0
2
0
0
1
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
6
0
0
0
0
0
0
5
3
0
0
0
0
1
0
0
2
0
0
2
2
1
0
0
0
1
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
1
0
0
1
0
1
1
0
0
2
0
0
0
1
0
0
0
0
2
2
0
0
1
0
3
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
2
2
2
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
2
4
0
0
0
0
2
0
1
0
0
1
0
0
0
0
1
3
0
1
0
0
0
0
0
5
0
1
0
2
0
0
0
1
0
0
0
0
0
2
0
1
2
1
0
0
2
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
3
0
2
0
0
0
0
0
0
2
1
2
0
0
1
1
2
2
0
2
0
0
0
0
1
0
0
2
0
0
1
0
0
0
2
2
0
2
0
1
0
1
0
2
0
0
0
1
1
1
0
0
0
1
3
0
0
0
2
0
2
0
1
2
1
0
1
0
2
0
0
0
0
0
1
0
2
1
1
0
0
0
0
0
1
0
2
2
0
0
1
1
0
0
0
1
0
1
1
0
0
1
0
2
0
0
0
1
0
1
0
0
0
2
0
1
2
0
0
0
0
0
0
1
0
2
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
1
0
2
2
2
0
0
2
0
1
0
0
1
0
1
0
3
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
3
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
3
0
1
0
1
0
0
0
1
0
0
0
0
2
0
1
0
0
1
2
2
0
0
0
1
1
0
0
0
0
0
0
0
0
2
2
2
1
0
7
0
0
2
0
0
1
0
2
0
1
1
0
3
0
0
0
0
0
1
0
2
0
0
2
0
0
0
3
0
0
0
0
0
0
1
0
0
2
2
0
0
1
2
0
0
1
1
0
0
2
3
0
1
1
2
1
0
0
1
0
0
2
0
1
0
0
0
1
1
0
2
0
0
0
0
0
0
0
1
0
0
0
3
0
0
1
0
1
1
1
3
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
2
0
2
0
0
0
2
0
3
0
0
0
0
0
2
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
2
0
2
0
0
2
1
0
0
0
0
2
0
1
0
2
0
0
2
0
0
2
0
2
2
0
0
0
0
0
2
0
1
0
1
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
3
1
2
2
1
2
2
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
1
0
1
0
0
0
0
0
2
3
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
1
0
0
2
0
2
1
0
0
0
0
1
0
2
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
5
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
1
3
2
0
1
2
2
2
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
2
1
1
0
0
0
0
0
1
3
0
1
0
0
0
0
0
1
0
0
4
1
1
2
0
0
0
0
0
0
1
0
2
0
1
0
1
0
0
0
1
0
3
0
0
1
0
1
1
0
0
2
0
0
1
2
0
0
2
0
2
0
2
2
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
2
3
2
0
0
0
0
0
0
0
1
0
0
0
3
1
0
0
0
0
0
0
1
2
3
0
0
0
0
0
2
1
1
0
1
0
0
0
0
0
4
2
0
1
1
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
1
0
0
1
0
0
0
2
2
0
0
1
0
2
1
0
0
1
2
0
1
0
1
0
2
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
1
0
0
2
0
0
0
0
1
0
1
2
0
0
1
2
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
2
1
0
1
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
2
1
0
0
2
1
0
1
2
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
2
2
0
0
0
0
0
0
0
2
0
4
2
0
0
0
0
1
1
0
0
1
0
0
0
0
2
1
0
1
0
2
0
0
0
2
0
0
0
0
2
1
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
1
0
2
0
0
0
0
2
0
0
3
0
0
0
0
3
0
0
2
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
2
3
0
0
0
0
2
0
0
2
2
0
0
0
0
1
0
0
0
0
2
0
2
0
1
0
0
0
0
0
1
1
2
2
2
1
0
0
1
0
2
1
0
0
0
0
0
0
0
1
0
3
1
1
0
0
0
1
0
0
3
0
1
0
0
0
0
0
0
0
0
1
1
2
1
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
4
2
0
2
0
0
3
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
2
0
0
1
1
2
0
1
0
0
2
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
2
1
0
0
2
0
0
0
2
0
2
0
1
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
2
1
0
1
0
0
0
0
8
1
1
0
0
1
1
0
1
2
0
0
0
0
0
1
0
0
1
0
0
0
3
2
0
0
1
1
2
0
2
2
2
0
1
0
2
0
0
1
2
2
0
2
0
1
0
0
1
0
0
2
0
1
0
0
1
1
2
0
1
0
2
0
2
0
0
0
0
0
0
0
2
0
1
0
0
3
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
3
0
2
2
0
2
2
0
0
0
0
0
0
0
1
0
2
1
0
0
2
1
0
0
1
0
1
0
0
0
0
2
0
0
0
2
2
0
0
0
2
2
0
1
0
0
0
2
0
0
0
1
2
2
1
0
0
2
0
0
0
0
2
0
1
0
0
0
3
0
0
0
1
0
0
2
1
2
0
0
0
2
1
0
1
0
0
0
3
3
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
1
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
1
0
1
1
0
0
1
0
0
2
1
0
1
0
1
0
0
0
0
1
2
0
2
0
0
0
0
0
0
3
2
0
0
0
0
2
0
1
2
0
2
0
0
0
0
2
2
2
1
0
0
0
1
0
0
2
0
1
0
2
1
0
0
1
0
2
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
1
1
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
1
0
0
0
1
0
0
1
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
1
1
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
1
1
0
0
1
0
0
0
3
1
0
0
1
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
1
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
1
0
0
1
1
2
0
1
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
2
1
1
0
0
2
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
2
1
0
2
2
0
2
0
0
0
0
0
3
0
0
0
1
0
1
0
0
0
3
0
1
2
1
0
0
0
0
1
0
1
1
1
0
0
1
0
2
0
0
1
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
1
2
0
1
0
1
0
0
1
1
2
0
2
1
0
0
1
0
2
1
0
0
0
0
1
0
0
2
1
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
4
2
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
1
0
0
2
0
1
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
9
0
0
1
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
2
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
2
0
3
0
0
0
0
6
0
0
0
0
0
0
1
2
0
0
2
2
0
2
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
3
0
2
0
0
0
0
2
2
2
0
0
2
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
2
0
0
0
0
2
2
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
3
5
1
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
2
1
2
1
0
0
2
0
0
0
0
0
0
0
0
2
0
1
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
4
0
0
1
0
2
0
0
0
0
0
0
1
0
3
0
2
0
1
1
1
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
2
2
0
0
3
2
0
0
0
0
2
0
3
0
0
0
2
2
0
0
0
1
1
0
0
2
2
0
0
1
2
1
0
0
0
1
1
0
0
0
0
2
0
0
1
0
0
0
0
3
1
0
2
0
2
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
1
2
0
1
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
2
0
1
0
0
0
0
1
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
2
1
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
2
0
1
1
0
0
2
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
2
0
1
2
0
0
0
2
2
0
0
2
0
3
0
0
0
0
0
0
1
0
1
1
0
3
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
1
2
2
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
3
0
0
2
0
0
1
0
1
0
0
0
0
2
0
0
1
0
4
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
2
0
2
0
0
0
0
2
0
1
0
0
0
0
1
0
0
1
2
0
0
7
0
0
0
2
0
0
0
2
2
0
0
0
0
0
2
1
3
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
1
1
1
1
0
0
2
0
0
1
0
0
1
0
2
0
2
0
1
2
4
0
1
0
1
0
1
1
0
1
1
0
1
0
0
1
0
0
0
0
0
2
0
0
3
0
0
2
0
0
0
1
0
0
0
1
0
1
0
0
4
0
0
0
0
0
2
2
0
2
1
0
0
0
0
0
0
0
0
0
1
1
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
4
0
2
0
0
0
0
0
4
0
0
0
2
0
0
0
0
1
2
1
0
0
0
0
0
3
2
0
1
0
1
3
0
0
1
1
0
0
0
1
0
0
0
2
0
0
0
1
0
0
2
0
0
2
0
4
0
2
0
0
2
2
1
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
1
5
0
1
2
3
1
0
2
0
0
0
0
0
1
1
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
2
1
1
2
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
2
0
0
2
3
0
0
0
1
0
0
0
2
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
3
1
0
0
1
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
5
2
2
0
0
0
1
0
1
0
0
0
1
0
2
2
0
2
2
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
1
2
0
0
0
1
0
0
0
0
1
0
0
2
2
0
2
0
0
1
1
1
0
0
0
0
0
0
1
0
3
2
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
2
2
2
1
0
0
2
0
3
0
0
0
0
0
0
0
2
0
5
1
0
0
0
2
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
1
1
1
0
2
0
5
2
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
2
1
1
0
0
0
0
0
0
0
3
2
2
0
0
0
0
0
2
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
2
0
0
0
2
0
0
2
2
0
0
0
2
0
0
0
0
0
0
2
4
0
0
2
0
0
0
1
1
2
0
1
0
0
2
2
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
1
0
0
2
0
0
0
0
2
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
4
0
0
0
1
0
0
0
1
0
2
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
2
2
0
1
1
0
0
0
0
1
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
2
3
0
0
2
0
2
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
2
3
0
0
0
0
2
0
1
0
1
0
1
0
1
2
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
2
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
2
0
2
0
0
2
1
0
0
0
0
0
1
1
2
0
0
2
2
0
0
1
3
2
0
1
0
0
3
2
0
1
0
0
1
2
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
2
0
2
0
0
3
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
3
1
0
0
0
0
4
2
0
0
0
1
1
2
2
0
2
1
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
1
0
2
0
0
0
1
0
0
2
0
3
0
0
0
3
0
2
0
0
0
0
0
0
0
0
2
0
0
2
2
0
1
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
1
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
2
0
1
1
0
0
1
0
0
0
1
1
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
2
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
3
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
3
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
2
0
0
3
0
0
0
1
0
0
1
0
0
0
9
2
1
2
0
2
0
0
0
0
8
0
1
1
2
0
1
0
0
1
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
1
0
0
0
1
0
1
2
1
2
2
2
2
0
0
0
0
0
2
0
2
3
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
1
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
1
0
0
0
0
0
1
2
0
2
0
2
2
0
2
0
0
1
1
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
2
1
0
1
0
1
1
0
0
0
0
0
0
1
0
0
1
0
2
0
0
2
1
3
0
0
1
0
0
1
2
0
0
0
2
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
1
0
0
1
1
2
0
2
0
0
0
0
0
1
0
0
0
0
2
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
1
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
1
1
2
2
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
1
0
2
2
0
0
0
2
0
0
2
0
0
2
0
0
2
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
1
1
1
0
0
0
2
0
2
0
5
0
2
0
0
0
2
1
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
2
0
0
0
2
0
0
0
2
0
0
2
1
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
6
1
0
3
0
3
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
2
2
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
3
0
0
0
0
2
1
0
0
3
2
0
0
0
0
0
0
0
1
0
2
0
2
0
0
6
0
0
0
0
0
0
0
1
0
2
0
1
1
0
0
1
0
0
1
0
0
1
4
0
0
2
0
1
0
2
0
0
0
3
0
2
2
1
0
0
2
1
2
2
0
0
0
1
0
0
0
1
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
3
1
4
0
0
1
0
6
0
0
0
0
0
3
0
0
0
0
2
1
0
0
0
3
0
2
0
0
0
0
3
2
0
0
1
0
1
0
0
2
0
2
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
3
0
0
0
0
3
0
0
3
0
0
0
0
0
0
0
0
0
1
1
0
2
1
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
3
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
1
2
2
0
2
0
0
6
1
1
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
3
1
0
2
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
2
0
0
0
2
3
2
2
0
2
0
0
1
0
2
0
0
2
3
0
0
0
2
0
0
0
2
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
2
1
0
0
2
0
1
0
0
1
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
3
2
0
2
1
0
0
0
0
2
0
2
0
2
0
3
0
2
0
0
0
0
0
0
1
1
2
0
0
1
1
1
0
2
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
6
0
0
2
2
2
1
0
0
1
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
1
2
0
0
1
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
5
0
0
0
0
0
2
2
0
0
2
1
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
1
1
1
0
0
1
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
1
0
0
0
9
0
0
0
0
0
2
2
0
0
2
0
0
0
4
0
0
3
2
0
0
0
0
0
0
0
0
4
0
1
0
3
0
0
0
3
4
3
0
0
0
1
0
0
0
1
2
0
0
0
0
1
0
1
2
0
0
2
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
2
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
2
2
0
2
0
0
0
1
0
0
0
1
0
0
1
2
0
0
1
0
0
0
0
0
0
1
0
1
2
2
0
0
0
1
0
3
0
0
0
0
0
0
0
3
3
0
0
2
0
0
0
0
0
3
2
0
0
0
2
0
0
0
0
0
3
0
0
0
0
2
0
1
0
0
0
1
0
1
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
5
0
0
0
0
0
0
2
0
1
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
3
0
4
0
1
0
0
1
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
2
0
2
0
0
0
0
2
0
0
1
0
1
3
2
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
2
2
2
1
0
0
0
0
0
0
2
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
2
0
0
2
0
2
1
0
0
0
0
0
0
2
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
2
0
3
2
0
0
2
0
0
0
0
2
0
2
2
3
2
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
1
0
0
1
0
0
2
0
1
1
0
1
0
1
0
0
1
0
0
2
2
0
1
2
0
2
0
1
0
0
0
0
1
0
0
0
1
2
1
2
1
1
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
6
0
1
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
1
1
2
0
0
2
1
0
0
2
0
0
1
0
1
0
2
0
0
0
0
0
0
0
2
0
1
2
0
2
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
2
2
0
2
1
2
0
2
0
0
0
0
5
0
0
0
2
1
0
0
0
0
0
0
3
1
2
2
1
0
3
2
1
3
0
1
0
0
2
0
1
2
6
0
0
2
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
2
0
0
0
1
3
0
2
1
0
0
0
1
7
0
1
0
0
0
0
0
0
0
2
0
0
2
0
1
4
0
0
2
2
0
0
1
0
0
0
0
2
1
2
0
1
0
2
0
2
0
1
0
0
1
1
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
3
2
3
7
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
3
0
2
2
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
2
0
0
0
2
0
2
0
0
0
1
0
2
0
0
0
1
4
2
0
0
2
1
0
1
2
0
0
0
0
4
0
1
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
6
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
4
1
0
0
2
0
0
1
0
2
1
0
1
0
1
0
0
1
1
1
1
1
1
0
2
2
2
1
0
0
0
0
1
0
0
1
0
2
0
0
0
0
1
0
0
0
1
0
2
0
2
0
3
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
2
2
0
0
0
1
0
2
1
0
1
2
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
5
0
0
0
0
0
0
0
0
1
0
2
1
2
0
1
0
2
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
4
0
0
0
1
2
0
2
2
0
0
0
0
0
1
0
1
1
0
0
2
2
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
1
0
2
0
0
1
0
0
1
1
0
4
0
1
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
5
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
2
1
0
0
0
1
0
2
1
0
0
0
2
0
0
1
0
0
0
0
2
0
2
0
1
0
0
1
2
0
0
0
1
1
0
0
2
0
0
0
2
1
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
2
1
0
0
0
1
1
0
0
0
0
0
2
0
1
0
2
0
0
0
0
2
1
1
1
4
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
2
1
0
0
0
1
1
0
0
0
1
0
0
0
0
2
0
1
0
1
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
1
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
2
0
0
3
2
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
3
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
1
0
0
0
2
0
1
0
0
0
1
0
0
1
1
2
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
2
0
0
1
0
1
0
2
0
0
0
0
1
0
2
0
0
0
2
1
0
0
0
1
0
0
0
1
1
0
0
0
1
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
2
0
0
0
0
0
0
2
1
0
0
1
0
2
0
0
1
1
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
3
1
1
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
2
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
2
0
1
0
4
2
1
1
0
1
2
1
0
0
2
0
0
0
0
0
0
0
0
2
0
1
2
1
2
0
1
0
0
0
0
1
0
1
0
0
0
4
0
0
1
0
0
2
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
1
0
0
1
1
0
0
1
1
0
1
0
0
1
0
0
0
1
1
0
0
0
0
2
1
0
0
0
0
0
4
0
0
2
0
0
0
2
1
2
2
0
0
0
0
0
0
0
2
0
0
2
4
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
5
2
0
2
0
0
0
2
3
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
4
2
0
0
2
0
0
2
0
2
0
1
0
1
0
1
1
1
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
2
0
0
1
0
1
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
2
0
0
0
0
1
0
0
2
5
0
2
0
0
0
3
0
2
0
0
0
0
1
2
0
1
0
0
1
0
0
2
0
0
2
0
1
0
0
0
0
0
2
1
0
1
0
0
1
0
0
1
0
0
2
0
3
0
1
0
0
0
0
2
0
0
0
1
1
0
2
1
0
0
0
0
3
2
0
0
1
2
2
1
0
0
0
0
0
1
0
1
0
1
0
0
0
3
2
0
2
3
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
2
1
0
2
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
5
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
0
2
1
0
0
0
0
2
2
0
2
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
1
1
2
1
0
4
0
0
2
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
1
1
0
1
1
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
1
0
2
0
0
0
1
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
1
1
0
2
0
0
2
0
2
0
0
1
2
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
2
0
1
0
0
1
1
1
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
2
0
1
2
0
0
0
1
2
0
2
0
2
2
0
1
0
2
0
0
0
0
0
2
2
0
0
1
1
0
1
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
2
0
2
1
0
2
0
0
5
2
1
0
0
0
0
0
0
3
1
0
0
0
0
1
1
1
0
0
0
0
2
0
0
0
3
2
1
1
2
1
1
0
0
0
2
0
1
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
1
2
2
1
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
5
0
0
2
0
0
0
0
2
2
0
0
3
0
0
0
0
2
1
2
1
0
0
1
2
2
0
4
0
0
1
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
2
0
1
1
0
0
2
0
0
1
2
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
2
1
0
1
0
1
0
1
1
0
0
0
2
1
3
0
0
0
0
1
0
2
0
0
0
0
1
1
0
1
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
3
2
1
1
0
0
0
0
0
0
1
0
0
0
4
0
1
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
3
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
1
2
0
0
1
3
0
0
0
0
0
0
0
0
2
2
0
1
0
1
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
2
0
0
1
0
1
0
0
3
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
1
3
2
1
0
0
2
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
1
0
3
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
2
1
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
1
2
2
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
1
0
0
1
0
1
0
0
0
2
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
2
1
0
1
1
0
1
0
0
0
1
0
0
0
0
4
0
0
1
0
1
1
0
2
0
3
0
2
0
0
2
2
1
0
0
0
1
0
0
0
0
0
1
3
2
0
1
0
3
0
2
1
2
0
2
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
1
2
0
1
0
0
0
0
0
0
0
1
0
1
1
3
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
1
1
3
0
0
0
1
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
1
0
0
1
0
4
2
0
0
0
0
0
0
0
2
1
1
1
0
0
0
2
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
2
2
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
2
1
0
0
0
2
2
1
2
0
0
0
0
1
0
1
1
0
0
0
2
2
0
0
1
0
3
0
0
2
2
0
0
2
0
2
2
0
0
0
0
0
0
1
1
2
0
0
0
2
0
0
2
0
0
0
0
1
4
0
0
1
0
2
0
2
0
1
4
2
0
2
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
3
0
3
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
2
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
1
0
1
0
0
0
0
3
1
0
0
0
0
0
1
0
0
0
2
2
0
0
3
2
0
2
0
0
2
1
1
0
0
2
1
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
1
0
0
0
2
0
2
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
3
0
1
0
0
2
0
3
0
0
2
0
1
1
2
0
0
0
0
1
0
0
1
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
1
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
4
2
0
0
1
1
0
0
0
0
4
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
15
0
0
2
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
3
0
0
0
1
0
0
0
0
0
2
0
2
0
3
0
5
2
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
14
0
3
0
1
0
2
1
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
2
0
2
2
0
1
0
1
2
0
0
1
0
0
0
3
3
1
0
0
0
2
0
1
1
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
4
0
1
0
0
2
2
0
2
0
0
2
0
2
0
2
0
0
1
3
1
0
0
0
0
0
1
0
0
0
0
0
3
0
1
3
1
0
0
0
0
2
2
1
0
0
3
2
0
0
0
0
1
0
0
0
0
2
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
2
1
0
0
0
0
4
2
1
0
0
0
1
1
0
0
2
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
1
0
0
0
1
0
0
0
0
0
1
0
2
1
2
0
0
1
0
1
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
1
0
6
0
0
2
2
0
1
2
0
2
0
0
1
0
2
0
1
2
0
0
2
1
1
2
0
1
2
0
1
4
0
2
0
1
2
0
0
0
1
0
2
0
0
2
3
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
1
1
0
4
3
0
0
0
2
1
1
0
4
3
0
0
0
0
1
1
1
1
0
0
0
0
0
0
2
0
0
1
0
2
6
0
0
2
0
0
1
2
0
0
2
2
0
0
0
2
0
0
1
1
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
2
1
2
0
2
2
0
0
0
0
0
2
1
0
0
0
0
0
1
0
1
2
0
2
2
0
2
1
0
0
0
0
2
0
0
0
1
0
1
0
1
1
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
2
0
1
0
0
2
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
2
0
2
0
0
1
0
0
1
2
0
0
0
0
0
0
1
0
0
1
2
1
0
0
0
2
0
0
0
5
1
0
0
0
0
0
0
2
0
0
3
0
0
0
2
0
3
1
0
1
0
2
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
1
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
2
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
1
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
1
2
2
0
2
0
1
2
0
0
0
0
0
0
4
1
0
0
0
1
0
0
0
0
0
0
1
1
0
2
2
0
2
2
0
1
1
0
0
0
1
0
0
3
2
0
3
2
1
7
0
2
0
0
0
0
3
0
1
2
0
1
0
0
0
1
0
0
1
0
2
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
1
0
3
0
0
2
0
0
2
0
0
0
0
2
1
1
1
1
1
0
0
0
2
2
1
2
0
0
1
1
0
0
1
0
0
0
0
0
0
1
2
0
0
2
2
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
1
0
1
4
0
1
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
4
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
3
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
2
3
0
2
0
0
0
1
0
0
0
0
0
2
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
2
0
0
0
0
2
0
1
0
0
1
0
0
1
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
3
1
0
1
0
2
0
1
0
2
0
0
0
1
0
2
0
0
8
0
0
0
0
3
0
1
0
0
2
1
1
2
0
0
0
0
0
0
6
0
0
0
0
2
1
0
0
2
2
0
3
0
0
1
0
0
3
0
1
2
2
0
0
1
1
2
0
2
2
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
6
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
2
1
0
0
0
1
1
0
0
0
0
0
0
2
2
0
0
0
1
0
1
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
4
0
0
0
0
2
0
2
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
8
1
0
2
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
2
0
4
2
0
0
0
0
0
0
0
1
1
1
1
2
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
1
0
2
2
0
2
0
3
1
5
1
2
1
0
2
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
1
0
2
2
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
1
2
1
0
0
2
0
0
1
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
1
0
0
0
3
0
2
1
0
0
1
0
0
0
0
1
0
0
0
0
2
1
0
0
0
2
1
0
2
2
1
1
0
0
0
1
0
3
0
0
0
0
0
2
2
2
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
1
0
2
0
2
0
1
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
4
2
2
0
2
2
0
0
2
1
0
0
1
0
0
0
0
0
0
0
1
2
1
0
3
0
0
0
0
0
3
0
0
2
2
0
1
0
0
0
1
0
0
0
0
0
0
0
3
0
2
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
2
0
0
0
0
0
1
0
1
0
0
2
2
0
0
0
1
0
0
0
0
1
0
0
0
3
0
1
1
3
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
9
0
0
1
1
0
0
0
1
2
1
0
0
0
0
0
0
1
2
0
2
0
0
0
0
2
1
0
0
0
1
0
2
0
0
2
0
0
1
2
1
2
0
0
0
0
0
1
2
0
0
1
1
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
2
1
0
0
0
1
0
0
0
1
0
1
0
1
0
1
0
0
0
0
2
0
0
2
0
0
2
1
2
0
0
0
0
1
0
0
0
0
2
0
0
2
2
1
0
1
0
1
3
0
0
2
0
0
2
2
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
1
0
2
2
0
1
0
1
0
0
1
0
2
2
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
1
0
2
2
3
0
2
0
1
0
1
0
0
1
0
0
0
1
0
2
1
0
0
0
0
2
6
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
1
0
1
0
0
0
0
1
0
0
1
1
0
1
0
0
0
1
1
0
0
0
0
0
2
0
1
0
1
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
1
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
0
0
2
2
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
4
2
3
3
0
2
2
0
0
0
0
1
0
2
0
0
0
2
2
0
3
0
1
0
0
8
1
0
1
0
2
0
8
0
0
1
2
0
0
0
3
0
0
2
1
0
0
0
1
0
0
2
1
2
0
0
0
0
0
0
0
2
0
0
2
2
1
2
0
2
0
0
0
1
0
3
0
0
3
0
0
0
1
0
0
0
0
0
1
0
0
2
1
0
2
2
2
0
0
0
1
2
0
0
0
0
0
2
1
0
0
1
0
1
0
2
0
0
0
2
0
0
0
2
0
2
2
0
0
0
1
1
3
2
1
0
1
2
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
1
0
0
1
1
1
0
2
0
1
2
0
2
0
2
0
0
0
0
1
0
1
1
1
1
0
0
1
1
0
0
0
2
0
2
0
0
0
0
0
2
2
1
1
0
0
0
0
1
0
2
0
2
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
5
1
0
2
0
1
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
3
1
2
1
2
0
1
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
2
0
2
0
2
1
0
0
2
1
3
0
1
0
2
0
0
2
0
0
0
0
1
0
0
2
2
0
1
2
2
0
2
0
4
0
1
2
1
2
0
0
0
1
0
1
0
0
2
3
0
1
2
2
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
2
0
2
0
2
0
1
0
0
0
0
0
0
3
2
0
0
0
0
2
2
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
2
1
0
2
1
0
0
1
2
1
2
2
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
2
2
2
1
1
2
0
1
0
0
2
0
0
0
0
1
0
2
2
1
2
2
0
0
1
1
0
0
0
0
0
1
2
0
0
0
0
2
0
1
0
1
2
0
0
1
0
2
0
0
0
0
0
0
2
1
0
1
3
2
0
0
0
0
0
2
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
1
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
2
1
0
0
0
0
0
0
1
0
2
0
0
1
2
0
1
0
0
1
0
0
2
0
1
0
2
0
0
0
0
0
0
0
2
1
0
0
1
1
0
1
4
2
3
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
2
3
0
1
0
0
0
2
2
2
2
0
0
4
1
0
7
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
2
2
1
0
0
0
2
2
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
2
0
2
1
1
0
2
0
0
0
2
0
0
2
1
3
2
0
1
0
0
0
1
0
1
0
0
0
1
1
0
2
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
1
0
2
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
1
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
2
0
0
2
2
0
1
0
0
0
0
0
0
0
0
3
2
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
2
0
2
2
2
0
1
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
1
0
0
0
2
0
0
3
2
0
3
2
0
0
0
1
1
0
1
0
2
2
0
0
1
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
2
2
0
0
2
1
1
0
1
0
2
1
1
0
0
0
1
0
3
0
0
1
0
0
0
1
0
0
1
1
0
2
0
0
0
0
0
0
0
0
5
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
2
2
1
0
0
0
1
0
2
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
1
3
0
2
4
0
1
0
0
0
2
2
2
0
0
0
0
2
0
0
0
1
1
0
0
1
0
0
2
2
0
3
1
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
1
2
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
3
0
0
1
2
1
0
0
1
0
2
0
2
1
0
0
0
0
0
1
0
1
0
2
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
4
1
0
1
0
0
0
0
0
1
0
1
1
2
1
2
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
1
2
0
0
0
0
1
0
2
1
0
1
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
5
0
1
1
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
1
0
3
0
0
0
0
1
0
0
0
0
3
0
1
0
0
0
0
0
0
1
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
2
0
0
1
0
0
0
1
1
0
1
1
0
0
2
0
1
1
0
0
1
0
0
1
0
0
0
0
2
0
0
0
1
2
0
1
2
4
2
1
0
0
1
0
0
0
0
0
0
0
2
2
0
0
1
0
0
2
1
0
0
2
3
0
0
0
0
0
0
1
0
0
6
0
0
2
0
1
2
0
0
2
0
0
1
0
5
1
0
1
0
1
0
0
0
3
0
2
0
1
0
2
0
0
1
0
3
1
0
2
0
2
0
0
0
0
2
0
0
0
1
0
1
2
0
1
0
0
0
0
0
0
2
0
1
1
1
0
2
0
0
0
0
2
0
0
1
0
2
1
0
3
1
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
3
0
0
0
1
0
2
0
1
0
1
0
0
1
2
0
1
0
0
0
0
0
4
0
0
2
0
0
0
2
0
0
1
3
0
0
2
2
0
0
0
2
1
0
0
1
0
0
0
0
0
0
2
1
0
0
2
0
0
2
0
0
0
2
2
0
0
1
0
0
0
1
0
0
0
2
1
3
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
2
0
1
0
2
0
1
1
2
0
0
3
2
0
2
0
1
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
4
2
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
2
1
0
0
0
0
1
0
1
0
1
0
1
0
0
1
1
0
2
0
1
1
0
0
3
0
0
0
1
2
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
1
0
2
0
0
0
0
0
0
0
1
2
0
2
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
3
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
2
2
1
0
0
2
1
0
0
2
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
1
0
4
0
0
1
0
0
0
0
0
1
0
0
0
0
1
3
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
5
0
2
0
0
3
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
3
3
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
3
0
1
0
0
2
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
1
2
0
2
0
1
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
1
1
0
0
1
0
0
2
0
0
2
2
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
2
0
0
1
0
0
2
0
2
0
1
0
0
0
4
0
2
0
0
0
0
1
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
2
3
0
0
0
1
0
1
2
0
0
0
0
2
0
0
0
0
0
2
2
0
2
2
2
3
2
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
2
1
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
2
0
1
2
0
0
0
0
2
0
0
0
2
0
0
0
0
1
2
2
0
0
1
2
0
0
0
1
0
2
2
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
1
0
0
0
3
0
2
0
2
0
0
2
0
0
0
1
0
0
4
0
1
0
0
0
0
1
1
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
5
0
1
0
1
2
2
0
0
0
0
0
2
1
0
0
2
0
0
2
0
1
0
0
2
2
0
2
1
0
0
1
0
2
1
1
0
1
1
0
1
0
2
0
0
2
2
2
2
2
0
1
1
2
1
2
0
0
0
0
1
1
1
0
0
5
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
1
1
0
0
2
2
0
0
0
0
0
0
2
2
0
2
0
0
0
0
3
0
3
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
2
1
0
0
1
1
0
0
0
1
0
0
0
3
0
2
1
0
2
2
1
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
1
0
2
1
2
2
0
0
1
0
0
0
0
2
0
1
0
0
2
2
0
0
0
1
0
3
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
2
0
0
1
0
1
2
0
0
0
0
2
0
0
2
0
0
1
2
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
3
1
0
0
0
2
0
0
0
0
0
0
3
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
2
1
0
2
0
0
0
1
2
1
0
0
0
0
1
0
0
0
0
0
0
2
1
4
0
0
0
0
0
1
0
2
0
0
0
2
2
0
1
1
0
1
1
1
0
0
1
0
0
1
0
0
0
2
0
0
1
0
0
1
1
0
0
1
1
2
1
0
0
0
0
0
1
0
1
0
0
0
0
1
2
2
2
2
3
0
0
0
1
0
0
0
0
1
1
0
0
2
0
2
1
1
0
2
2
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
3
1
2
0
2
0
0
2
0
1
0
0
0
0
0
0
2
0
2
0
0
1
0
1
0
0
0
2
0
0
2
3
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
2
1
0
0
0
2
1
0
1
0
1
0
2
2
0
0
0
0
0
2
0
2
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
1
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
1
0
0
0
1
1
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
3
0
2
0
0
0
2
0
1
0
0
2
0
0
2
2
0
0
2
2
0
0
0
1
2
0
0
1
2
1
0
1
0
1
1
1
0
0
2
0
1
0
0
1
1
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
1
1
0
2
0
1
0
0
1
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
3
1
1
1
0
2
2
0
0
1
0
0
0
2
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
3
0
2
0
0
0
0
0
1
2
0
0
0
0
3
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
3
0
0
0
0
0
0
0
1
0
0
0
0
2
2
2
0
2
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
1
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
2
1
0
0
0
1
0
0
0
0
2
2
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
3
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
1
2
0
0
2
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
2
0
0
0
2
0
0
2
0
0
1
0
0
0
0
1
0
0
0
2
0
0
3
1
0
1
2
2
2
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
1
0
2
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
1
2
0
2
0
0
1
1
0
0
0
1
0
0
0
0
0
0
2
1
1
0
0
0
0
0
2
1
0
0
1
2
0
0
0
0
1
0
1
2
2
0
0
0
2
0
0
0
0
0
0
3
1
0
0
1
2
0
2
0
0
3
0
2
2
0
2
0
0
2
2
0
0
0
1
2
0
0
1
0
0
0
0
1
0
0
0
0
1
2
2
1
0
2
2
1
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
1
1
1
0
0
3
0
0
0
0
0
1
1
0
2
1
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
2
2
4
0
0
2
0
0
1
0
1
0
0
0
0
0
2
0
1
0
0
0
1
0
0
2
0
0
1
0
0
3
1
2
2
0
2
2
0
0
1
0
1
0
2
0
0
1
0
0
0
0
0
0
1
2
0
0
2
0
1
0
0
0
0
0
0
2
0
0
1
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
1
0
1
0
2
2
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
6
2
1
2
0
1
2
2
0
0
2
0
0
2
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
2
0
0
0
2
0
0
1
0
2
0
1
0
0
0
2
0
0
0
0
0
2
2
0
0
0
3
2
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
3
1
0
0
1
1
0
0
0
3
0
0
2
0
2
0
0
0
0
0
0
0
0
2
1
0
1
0
1
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
2
1
2
0
1
0
1
0
0
0
0
4
0
0
0
0
0
0
1
0
2
1
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
1
2
0
1
2
0
0
0
0
0
0
1
2
1
3
0
0
2
0
0
1
2
2
0
1
1
2
0
0
1
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
2
0
1
0
1
0
0
0
2
0
0
0
1
0
2
0
0
0
0
1
0
0
1
0
2
0
0
0
0
2
0
2
2
0
0
2
1
1
0
0
0
1
0
0
0
3
0
0
0
0
0
2
2
1
1
0
1
0
2
0
0
0
2
0
2
2
0
0
2
1
0
2
1
0
0
0
0
0
0
0
6
1
1
1
0
0
1
0
0
1
0
2
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
3
2
3
0
0
1
0
0
0
0
2
0
0
2
0
0
0
2
2
1
0
0
2
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
2
0
0
2
0
0
1
0
0
1
0
0
1
2
1
1
0
1
0
0
0
0
2
0
2
2
0
0
0
1
1
0
1
1
0
0
2
4
0
1
1
0
2
0
1
0
0
0
0
3
0
0
0
0
0
0
1
0
0
1
0
0
0
1
2
0
1
0
0
1
0
0
0
0
0
0
0
1
3
0
4
0
2
0
3
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
1
1
0
0
0
1
0
2
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
1
2
1
0
0
0
0
1
0
0
1
0
0
2
0
1
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
1
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
1
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
2
1
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
2
0
0
1
1
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
2
0
0
1
2
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
1
2
2
2
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
1
2
0
1
2
0
0
1
1
0
0
0
0
2
1
0
0
2
0
2
1
0
0
1
0
0
0
1
1
4
0
2
0
2
0
2
0
0
0
0
1
0
0
0
0
1
2
1
2
0
1
1
0
1
0
4
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
2
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
3
0
1
0
0
0
1
0
0
0
2
0
2
1
2
0
0
0
2
1
0
0
1
1
0
0
0
1
1
0
0
0
2
0
4
1
0
0
0
2
0
0
0
1
0
0
0
1
2
3
0
0
0
0
0
0
2
0
0
0
1
0
1
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
4
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
1
1
1
1
0
0
0
2
2
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
2
5
1
1
1
0
4
0
0
1
2
2
1
0
0
0
1
2
0
0
0
1
0
0
0
1
1
0
2
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
1
0
0
1
0
2
0
2
2
0
0
0
3
2
0
0
0
0
0
0
3
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
2
1
0
0
1
0
0
2
2
0
0
0
0
0
1
0
1
0
1
14
1
2
0
0
0
0
3
0
0
0
0
0
0
2
1
0
0
0
0
1
1
0
2
2
0
1
0
0
2
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
3
0
2
0
0
0
0
0
2
1
2
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
6
0
0
1
0
1
0
0
0
0
1
0
2
0
0
2
0
1
0
0
0
0
0
0
0
2
2
0
1
1
2
0
4
0
0
0
0
0
2
1
2
0
0
0
0
1
2
0
0
0
0
2
0
0
1
0
0
0
0
1
2
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
2
0
0
0
0
0
3
0
1
0
0
0
1
2
1
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
2
0
0
0
2
0
0
2
2
0
0
0
1
0
0
0
3
0
2
2
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
1
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
2
0
0
0
0
4
2
2
0
3
0
1
0
0
0
2
1
0
0
1
0
1
2
1
0
0
0
1
2
0
0
0
1
0
0
1
0
2
0
0
0
0
1
0
0
2
2
0
0
1
0
0
2
0
0
0
0
0
0
0
2
2
1
0
2
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
2
3
2
0
1
0
1
1
0
3
1
1
0
0
0
0
0
2
1
0
0
0
0
2
2
0
0
2
2
0
1
1
2
0
0
1
0
2
1
0
0
1
2
0
1
3
0
0
0
0
0
2
1
0
1
2
0
1
0
4
0
1
0
0
1
0
1
0
1
2
0
0
0
1
0
0
2
0
1
0
1
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
5
0
0
0
0
0
4
0
1
0
0
2
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
3
0
1
0
0
1
1
3
0
0
0
1
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
1
0
0
0
3
1
0
2
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
10
0
0
2
0
0
0
0
1
0
1
0
0
1
1
0
1
0
0
0
0
3
0
0
1
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
1
2
0
2
0
0
0
1
1
3
0
1
1
0
1
0
0
2
0
0
0
0
0
1
3
2
1
0
0
0
0
0
0
0
0
0
3
1
0
1
2
2
0
2
0
0
0
0
0
0
0
0
3
0
2
0
0
3
1
1
0
0
2
1
1
0
1
2
0
2
0
0
1
0
0
0
0
1
2
0
2
0
1
0
1
1
0
1
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
9
0
0
0
0
0
1
0
0
0
2
0
1
0
0
1
0
0
2
1
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
2
0
0
0
0
2
2
0
0
0
2
0
2
0
1
0
0
0
2
1
0
2
0
0
0
1
0
1
1
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
1
0
2
0
2
1
0
1
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
2
0
0
0
2
0
0
2
0
2
0
0
0
2
2
2
0
0
0
0
1
0
0
1
0
0
0
1
0
1
5
1
2
0
8
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
1
1
0
2
1
0
1
1
2
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
3
0
0
0
0
0
0
5
0
0
2
0
0
1
2
0
0
1
1
0
1
2
0
2
0
0
2
2
0
0
0
0
3
5
0
0
0
0
0
1
2
1
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
1
1
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
2
0
0
2
2
0
0
3
0
0
2
0
1
0
1
1
0
0
0
0
2
0
0
0
3
2
0
0
2
2
0
0
2
1
0
2
0
3
1
0
0
0
2
2
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
2
1
0
0
0
2
0
0
2
0
0
0
1
0
2
1
0
0
0
0
1
2
2
1
0
0
0
0
0
0
0
0
0
2
0
2
0
1
2
2
0
0
0
1
0
0
0
0
1
0
2
0
2
0
1
0
0
2
2
0
0
0
2
0
0
0
0
1
1
0
1
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
2
0
0
2
2
0
0
1
0
2
0
1
1
0
2
2
0
0
0
2
1
0
0
0
0
0
0
1
0
2
0
0
2
0
2
4
4
3
0
0
1
0
0
0
0
0
1
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
1
0
2
0
2
2
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
2
0
0
0
0
0
1
1
1
0
0
0
1
0
1
0
1
0
0
0
0
2
0
2
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
1
3
0
2
0
0
0
1
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
2
0
2
0
0
0
0
1
0
0
0
2
1
0
1
0
1
1
0
0
2
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
2
0
1
1
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
1
0
2
0
1
1
1
2
0
0
0
1
0
0
2
0
0
2
3
0
2
1
0
0
0
0
1
0
0
0
0
4
1
0
0
3
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
5
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
1
0
0
0
0
0
3
0
0
1
2
2
0
0
0
0
0
0
1
0
2
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
2
0
1
1
0
0
0
0
3
0
2
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
2
2
2
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
3
2
2
1
0
0
1
0
2
0
4
2
2
2
3
2
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
2
3
0
0
0
2
0
0
0
1
0
2
2
0
0
0
0
0
3
0
2
1
0
0
0
0
0
2
1
1
0
2
1
1
0
0
0
0
3
2
0
0
2
0
0
2
0
0
2
0
1
1
1
0
0
0
3
1
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
2
0
0
2
0
0
2
0
0
0
1
0
1
2
0
0
0
1
1
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
2
0
0
0
0
5
0
0
0
1
0
1
0
0
0
1
2
1
0
0
0
0
1
0
0
2
2
0
0
1
0
3
0
0
2
0
1
0
3
0
0
0
2
0
0
1
0
0
0
0
0
0
1
1
5
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
4
1
0
0
0
0
0
2
1
1
0
2
0
0
0
1
0
0
1
3
2
0
1
2
0
0
2
0
0
0
0
0
2
1
1
0
0
0
0
0
2
0
1
0
2
0
0
0
1
0
0
0
2
0
0
2
0
2
0
2
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
2
1
0
0
0
0
0
0
0
0
4
0
2
0
1
0
2
0
2
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
1
0
0
0
2
0
0
3
1
0
1
0
0
1
2
0
0
2
2
1
0
0
1
1
0
2
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
2
1
1
2
2
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
1
1
1
0
0
0
0
2
0
0
0
0
0
1
1
0
0
1
2
0
1
2
3
2
0
1
1
0
0
0
0
2
0
0
1
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
2
0
0
1
1
5
0
0
2
0
0
0
0
1
0
2
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
1
0
0
0
1
6
0
0
0
0
0
0
0
4
0
2
0
0
2
0
0
0
2
0
1
0
1
0
0
0
0
2
2
0
2
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
2
3
0
2
0
0
0
0
0
0
1
1
1
0
2
0
0
0
0
2
2
1
0
0
0
0
4
2
0
0
0
0
0
0
0
2
2
0
2
0
0
1
0
0
0
0
0
2
0
0
0
2
0
1
0
1
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
1
0
0
0
2
0
0
0
0
2
0
3
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
3
2
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
1
1
0
4
2
0
1
1
0
1
0
0
2
0
0
0
0
0
0
0
0
1
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
3
2
1
0
0
0
0
6
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
4
1
0
0
0
1
1
0
0
2
0
0
1
2
2
0
0
0
2
1
0
0
0
1
2
0
0
0
1
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
1
1
0
1
0
0
1
0
2
1
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
2
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
1
2
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
1
0
1
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
2
0
0
0
1
0
1
0
0
0
1
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
1
1
4
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
1
0
4
1
0
2
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
1
0
1
0
0
3
1
0
0
2
0
1
1
0
0
0
0
0
0
1
2
0
0
2
0
1
0
0
1
1
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
1
0
0
3
0
0
1
1
0
0
0
3
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
2
1
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
2
1
0
0
0
0
0
0
5
2
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
3
1
2
2
0
0
1
0
0
0
1
1
1
0
1
1
0
0
0
0
2
2
1
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
2
2
0
0
2
0
0
0
1
0
0
2
0
2
0
0
0
1
2
1
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
2
2
2
2
0
0
0
0
0
2
0
1
1
0
0
2
1
2
0
2
0
2
0
1
1
0
3
0
0
3
0
0
0
2
1
0
0
1
2
0
1
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
1
0
3
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
1
1
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
1
0
1
0
0
0
3
2
2
0
0
1
1
0
2
1
0
0
0
0
1
0
2
1
0
0
0
0
1
0
0
2
0
1
2
0
0
1
0
1
0
0
0
0
1
1
1
2
0
1
0
2
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
6
0
0
0
0
0
0
1
1
2
0
0
2
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
2
0
0
0
2
0
0
0
1
0
1
0
1
0
0
1
0
1
3
1
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
4
1
0
0
0
1
1
0
0
0
0
0
0
3
0
1
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
3
0
1
0
0
0
0
0
0
0
1
2
1
0
0
1
0
0
0
0
1
1
0
2
0
0
0
0
2
0
1
1
0
0
0
0
2
2
0
0
0
2
0
6
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
3
4
2
0
1
0
0
0
0
3
0
0
0
1
2
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
1
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
3
2
1
0
1
0
0
0
0
2
0
0
0
0
5
3
0
0
0
0
0
1
0
0
2
0
10
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
2
0
0
1
0
2
1
2
2
1
0
0
0
1
0
2
0
0
0
2
0
0
0
3
0
0
0
0
2
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
1
0
0
1
1
2
2
1
0
2
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
2
0
0
2
1
1
0
1
0
1
1
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
2
0
0
0
2
0
3
0
0
0
0
1
2
1
0
0
0
0
2
0
0
2
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
1
3
2
2
4
2
0
2
1
1
0
3
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
2
2
0
2
0
0
0
1
0
0
0
0
2
2
0
1
0
0
0
3
0
0
0
0
0
0
0
2
2
0
0
4
0
2
2
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
2
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
2
2
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
1
1
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
2
2
0
0
2
0
0
1
0
0
2
2
0
0
1
2
1
0
0
0
0
0
1
0
0
0
1
0
0
0
2
1
0
0
1
0
0
2
0
0
1
0
1
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
1
3
0
2
2
0
0
1
3
0
2
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
1
0
2
1
3
0
0
0
0
0
0
2
0
0
0
1
0
2
3
0
0
6
2
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
1
0
1
0
0
1
2
3
2
0
2
2
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
1
0
2
2
0
0
0
1
1
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
2
0
4
0
2
0
2
1
0
0
0
2
1
1
0
0
1
0
0
0
2
0
2
2
2
1
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
1
0
0
0
1
0
2
1
0
0
0
0
1
0
0
0
0
1
2
0
0
2
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
2
0
2
0
0
0
0
0
1
0
0
3
0
0
0
2
1
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
2
0
0
2
2
0
0
0
1
0
0
1
2
0
1
0
0
0
1
0
1
0
2
0
2
0
0
0
0
2
2
0
0
0
2
2
0
2
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
2
0
1
1
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
1
0
0
1
2
2
3
2
0
2
0
1
1
1
2
1
2
0
2
1
1
2
0
2
0
2
1
0
2
0
2
0
1
0
0
0
2
2
0
0
0
1
0
2
3
2
0
0
2
1
0
0
0
0
0
1
0
2
0
2
1
0
2
0
2
0
2
0
2
0
0
0
0
7
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
4
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
1
0
0
2
1
0
0
1
1
2
2
0
1
0
0
1
1
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
1
0
0
4
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
2
0
0
0
1
0
4
2
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
2
1
0
0
0
0
1
2
0
1
0
0
0
0
0
0
1
0
1
0
1
0
2
0
0
0
3
1
0
0
3
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
2
1
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
1
0
1
0
0
0
2
0
1
0
1
1
0
1
2
0
4
0
0
0
0
2
0
0
0
0
2
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
8
0
2
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
3
0
1
2
0
0
2
0
0
2
0
0
2
0
0
0
2
2
0
0
0
1
0
0
1
2
0
0
0
0
0
2
2
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
2
0
2
1
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
1
0
1
0
2
1
2
1
1
2
0
0
0
1
0
0
0
0
1
2
0
1
1
1
2
0
2
2
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
2
2
0
0
3
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
2
0
2
0
0
2
0
0
0
0
0
0
1
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
3
1
0
1
0
2
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
2
1
2
0
0
1
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
1
0
1
0
0
0
3
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
2
1
3
0
0
0
2
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
3
0
0
0
1
0
0
1
1
1
2
0
0
0
3
0
0
1
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
3
0
1
0
0
2
0
1
0
0
0
2
0
0
0
0
3
0
0
2
2
1
3
0
0
0
0
0
0
1
0
1
2
0
0
0
1
0
2
2
1
2
0
0
1
2
0
0
0
2
0
0
0
1
1
1
1
0
2
3
0
0
0
1
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
2
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
2
0
3
2
0
0
0
2
4
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
2
0
0
0
0
1
1
0
3
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
2
0
2
2
0
1
1
0
0
0
2
2
2
0
0
1
0
0
0
1
0
0
1
0
2
1
0
2
0
1
1
0
0
0
0
0
1
0
2
0
2
0
0
0
2
0
0
1
1
2
0
1
0
1
0
0
0
1
2
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
5
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
1
0
0
0
1
0
0
0
0
2
0
0
2
2
1
0
0
0
0
0
2
0
1
0
1
2
0
2
0
0
2
1
0
0
0
0
0
0
2
2
0
0
0
2
2
0
0
2
1
1
2
3
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
1
0
2
0
0
0
2
0
0
2
0
0
0
2
1
1
1
2
2
0
0
0
1
1
0
0
2
0
0
1
4
0
0
0
0
1
1
0
0
2
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
1
0
0
1
0
2
0
0
1
1
0
2
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
1
2
0
2
1
0
0
0
0
1
0
0
0
2
2
0
0
2
0
0
0
1
0
1
0
1
1
1
0
1
0
0
1
1
0
2
0
0
0
0
0
0
0
2
0
0
2
0
2
8
0
0
2
1
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
1
0
1
0
0
0
3
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
1
0
0
0
0
2
0
1
1
1
0
3
2
0
0
0
2
0
0
2
0
0
0
1
0
2
2
9
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
6
0
0
2
2
2
2
4
1
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
2
0
0
1
0
1
0
0
0
0
0
0
1
0
2
0
0
2
0
0
2
0
1
0
1
0
0
0
0
3
0
0
3
1
1
0
1
0
2
1
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
2
0
0
0
1
2
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
1
4
2
0
0
0
2
0
0
0
2
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
1
1
1
1
0
0
2
1
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
1
1
0
0
0
0
4
0
0
0
0
2
0
1
0
0
0
3
0
0
0
2
0
0
1
2
0
2
1
2
1
0
0
2
2
1
0
0
0
2
0
2
0
0
1
2
0
0
0
2
1
0
1
2
1
1
0
0
0
2
0
0
0
2
1
0
0
0
0
0
4
0
0
0
0
0
2
1
1
0
1
2
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
1
0
0
0
1
0
0
1
0
0
3
0
0
1
0
2
0
0
1
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
2
2
0
0
1
0
0
0
0
2
0
2
0
2
0
2
0
0
1
0
0
2
0
0
1
0
2
0
0
0
2
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
1
1
1
0
0
0
0
0
2
0
1
1
0
0
0
0
1
0
1
1
0
2
2
1
0
0
1
1
1
0
0
2
1
0
0
0
2
0
0
1
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
1
1
0
0
0
0
1
0
2
0
0
0
1
0
3
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
2
0
1
0
0
0
2
2
0
1
0
0
1
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
2
1
2
0
0
0
0
0
1
1
0
0
2
0
2
0
0
2
1
0
0
0
0
0
1
0
1
0
0
0
2
0
1
0
3
0
0
0
0
1
0
2
0
1
2
0
0
1
0
0
2
1
0
0
0
2
0
0
0
0
0
1
2
0
0
2
0
1
2
1
0
0
2
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
1
1
3
0
0
0
0
0
1
2
1
0
1
0
1
0
0
0
0
1
0
0
0
2
0
0
2
0
2
0
0
1
0
1
0
0
0
2
0
2
2
0
0
0
0
2
4
0
0
0
4
0
2
0
0
0
1
3
0
2
1
0
0
0
0
0
2
0
2
0
0
0
0
0
2
1
1
1
0
0
2
0
0
0
0
0
4
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
1
0
1
1
1
3
0
0
0
1
0
2
1
0
0
1
0
0
0
1
0
2
0
0
2
0
1
2
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
3
1
2
2
1
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
2
3
1
2
2
0
1
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
3
0
1
1
3
1
0
0
0
0
0
0
1
0
0
1
1
2
0
0
0
0
1
0
0
0
2
2
0
2
0
0
0
2
2
0
0
0
1
0
0
1
1
0
0
0
4
0
0
0
2
0
2
0
2
1
1
3
0
0
2
1
0
0
0
0
0
0
1
0
1
0
0
1
2
2
0
1
1
0
0
0
3
0
0
0
0
0
0
1
2
2
0
1
0
0
2
0
0
0
0
0
2
0
2
1
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
1
0
0
0
0
1
0
0
1
1
0
1
2
1
0
0
0
0
0
1
0
0
0
1
0
0
0
4
0
2
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
2
2
0
1
1
2
0
3
0
0
0
0
0
1
0
0
2
0
0
2
2
1
0
0
2
0
0
0
0
1
0
3
3
0
0
0
0
3
0
0
0
1
2
0
2
0
0
0
0
0
0
1
0
0
2
0
2
0
2
0
0
0
2
0
0
3
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
4
0
0
0
0
0
0
1
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
3
0
0
1
0
0
0
2
0
0
0
3
2
2
0
2
2
3
0
0
1
0
1
1
0
0
0
0
0
1
0
1
1
0
2
0
0
0
3
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
1
0
2
0
0
2
0
0
2
0
1
2
0
0
0
1
0
1
1
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
3
1
0
0
2
0
0
0
0
2
2
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
2
0
0
0
0
2
0
1
1
3
0
2
0
2
0
2
0
2
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
1
3
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
1
0
1
0
2
2
0
0
1
0
0
0
0
0
0
0
1
0
2
2
2
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
2
1
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
1
0
2
1
0
0
0
1
0
0
2
2
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
1
0
0
0
2
5
2
0
0
0
3
0
0
0
0
3
0
2
0
0
0
0
1
2
3
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
2
0
2
0
0
0
0
1
0
1
0
0
2
2
0
0
0
1
0
2
0
2
0
0
0
1
1
0
3
1
2
0
0
0
2
0
2
0
2
0
0
0
0
0
2
0
0
1
2
0
0
1
0
0
0
0
2
0
0
1
1
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
2
1
2
0
0
0
0
0
0
1
0
0
1
0
1
0
0
2
1
0
0
0
1
1
2
0
0
0
0
0
0
2
2
0
0
8
1
0
2
1
1
0
0
0
0
0
0
0
0
2
1
0
2
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
2
0
1
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
4
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
2
0
0
6
0
3
0
0
2
0
0
1
0
0
0
0
1
1
0
0
1
3
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
1
0
0
2
2
2
1
3
0
0
0
2
0
0
0
0
3
1
0
0
0
2
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
2
0
2
2
0
1
0
1
0
0
0
2
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
1
2
0
0
2
0
2
0
2
0
2
0
2
1
0
1
2
0
0
0
1
1
0
0
0
0
2
0
0
0
1
2
2
1
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
2
2
0
0
1
0
0
2
0
2
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
1
1
2
0
0
2
2
0
0
2
0
0
0
2
2
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
2
2
2
0
0
3
0
0
0
3
0
0
0
0
1
0
0
3
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
1
1
0
0
1
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
1
0
0
0
1
1
2
0
1
1
1
0
0
1
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
3
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
1
5
1
0
0
2
0
0
0
2
0
0
0
0
0
1
0
1
0
2
0
0
0
2
0
0
2
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
1
0
3
1
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
3
2
0
0
0
2
1
0
1
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
1
2
1
0
0
0
2
1
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
3
2
2
2
0
0
0
0
2
0
1
0
0
1
0
0
1
2
0
0
0
0
0
2
1
0
0
0
0
2
1
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
2
3
0
0
1
2
0
0
0
0
0
1
0
2
0
1
2
0
1
2
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
3
2
0
2
1
0
2
0
1
0
2
0
0
0
0
2
2
2
1
1
0
2
0
0
2
0
2
0
1
0
0
0
0
1
1
0
0
0
0
0
3
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
3
0
0
1
0
2
1
0
1
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
1
2
0
1
0
0
2
0
0
0
0
0
0
2
1
0
0
0
2
2
0
1
0
2
1
0
1
0
2
0
1
1
2
0
0
1
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
1
0
1
0
1
1
0
0
0
0
1
0
0
2
2
0
0
0
1
0
0
1
0
0
2
0
2
0
0
2
0
0
0
0
2
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
1
2
0
1
0
1
3
1
2
4
0
2
1
0
0
2
0
0
2
0
2
0
2
0
2
0
0
0
2
1
0
2
0
0
2
0
0
2
0
1
0
1
0
0
1
1
2
0
0
0
1
0
0
0
0
2
1
0
1
0
1
0
0
0
0
0
0
1
0
0
2
1
0
0
0
2
0
3
1
1
1
2
0
0
0
0
0
0
1
0
1
0
2
0
0
2
0
1
2
0
1
0
0
0
1
0
0
1
0
0
0
0
2
0
1
0
2
2
0
0
2
0
0
0
0
0
1
0
1
1
0
1
0
2
1
0
2
0
0
1
1
2
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
1
2
0
2
0
0
0
2
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
2
0
0
3
0
0
0
0
0
0
1
1
1
2
0
0
1
0
1
0
1
0
0
2
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
2
0
4
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
2
1
2
1
0
0
0
0
0
1
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
2
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
4
0
0
0
0
1
2
1
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
1
0
2
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
2
2
0
1
2
0
0
1
0
0
2
0
0
1
0
2
3
0
1
1
0
0
3
0
2
1
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
2
0
2
0
1
0
0
0
0
2
2
3
2
0
2
0
0
1
1
0
0
2
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
1
4
0
0
1
0
2
0
0
0
0
0
0
3
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
5
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
1
0
1
0
1
0
0
1
0
0
2
0
0
2
0
2
0
2
2
1
0
2
0
0
1
0
1
0
0
0
2
0
0
1
1
0
0
0
0
2
0
1
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
2
1
2
0
0
2
2
0
0
0
1
0
1
0
2
0
2
1
0
0
0
0
0
0
0
1
0
2
2
0
0
2
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
2
0
0
3
0
0
0
0
0
0
2
3
0
2
1
0
0
2
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
1
0
2
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
2
0
0
2
2
0
0
0
0
0
0
0
0
2
1
2
0
1
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
1
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
3
0
0
0
1
1
0
0
0
2
0
0
0
0
2
2
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
1
2
0
2
1
2
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
2
1
0
0
1
1
1
1
0
1
2
0
1
1
0
2
0
0
2
0
2
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
4
0
0
0
1
0
2
0
1
0
0
2
0
2
0
0
2
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
2
0
0
0
0
0
1
0
0
1
0
0
2
1
3
0
1
0
1
0
0
0
1
1
3
0
0
0
1
0
0
3
0
0
0
0
0
2
2
0
0
3
0
1
0
2
0
0
1
0
0
1
0
2
0
1
0
0
2
0
0
3
0
0
0
0
1
0
1
1
0
0
2
0
0
1
0
2
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
1
2
1
1
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
1
0
0
2
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
1
1
0
0
0
0
1
1
0
2
0
0
0
0
0
2
4
3
2
0
0
3
0
0
4
0
0
0
0
0
0
0
0
0
1
3
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
2
0
0
1
1
1
0
2
1
0
0
0
0
0
1
2
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
2
0
0
0
1
0
0
0
0
2
0
0
0
2
0
1
0
0
0
4
0
1
0
0
0
1
0
1
2
1
0
0
0
1
0
0
0
0
4
2
2
0
1
0
0
0
0
0
0
2
1
0
1
0
0
0
2
2
0
1
0
2
0
0
0
2
2
0
1
1
2
0
0
0
2
0
1
0
0
0
1
0
0
2
0
2
1
0
2
3
1
0
1
0
0
0
0
0
0
5
0
0
0
2
0
1
0
0
3
0
0
0
2
0
1
0
0
0
0
0
4
1
0
1
2
0
2
0
0
2
0
0
0
0
0
1
0
1
2
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
2
1
0
2
2
1
0
2
1
0
1
3
2
0
0
2
0
0
0
0
2
0
1
0
0
0
1
1
0
0
0
0
2
0
2
2
0
3
0
0
1
1
0
1
1
0
0
0
2
0
0
2
0
0
0
3
0
1
0
1
1
0
0
0
0
2
0
0
0
0
1
1
0
0
1
4
1
0
0
0
2
0
0
0
1
2
1
0
0
0
1
0
0
2
1
0
1
0
1
0
0
0
2
0
2
1
0
2
1
0
0
1
1
2
0
0
1
0
1
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
1
2
3
1
0
0
0
1
0
0
2
0
0
1
3
0
1
0
1
0
1
2
2
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
3
3
0
0
1
0
0
0
0
0
0
0
2
0
0
2
2
2
2
1
0
2
0
0
1
0
0
2
2
0
0
0
1
0
2
0
1
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
2
1
2
0
2
0
0
2
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
14
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
1
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
1
0
0
2
1
1
0
2
4
0
0
0
1
2
2
0
0
0
0
2
0
1
1
0
2
0
0
0
2
1
0
2
0
0
0
0
0
2
1
0
2
0
2
1
0
0
0
2
0
0
0
1
2
0
2
4
1
0
0
0
1
0
0
0
0
0
3
0
0
0
2
0
2
1
0
2
0
1
1
0
0
0
2
2
0
0
0
1
1
1
0
0
0
0
1
1
2
0
0
0
0
1
2
0
0
1
0
0
0
1
0
0
0
2
1
0
0
0
7
2
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
2
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
2
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
1
1
0
0
3
0
0
0
0
2
0
0
1
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
1
0
1
1
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
3
0
0
4
0
2
0
1
0
2
0
1
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
2
2
0
2
0
0
0
2
0
0
2
0
3
1
0
0
1
3
0
0
0
0
0
0
0
2
1
0
0
0
2
0
2
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
4
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
2
1
0
3
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
1
0
2
0
1
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
3
0
1
1
0
0
1
0
0
0
0
0
0
0
2
4
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
2
0
0
1
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
2
0
2
0
0
2
0
1
1
2
0
0
0
0
2
0
0
2
2
0
0
0
5
0
2
0
0
1
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
1
2
1
2
1
0
0
0
3
0
0
0
1
3
3
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
1
0
0
0
0
1
0
2
0
5
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
2
1
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
2
0
0
0
3
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
1
2
4
0
2
0
0
0
0
2
0
0
0
0
0
1
0
2
1
0
0
2
0
0
0
0
0
0
0
1
0
2
1
0
2
2
0
0
0
0
0
2
0
0
0
0
0
2
1
1
0
1
0
0
2
0
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
2
1
0
1
0
2
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
2
4
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
2
1
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
1
1
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
3
2
0
2
0
1
0
0
0
0
0
0
1
0
1
1
1
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
2
0
2
1
0
0
2
0
0
0
1
0
2
0
1
0
0
0
0
2
2
3
0
0
0
0
0
2
1
1
5
2
1
0
0
0
0
0
0
2
2
0
1
1
0
0
1
0
1
0
0
0
2
2
0
0
0
0
0
2
0
0
1
1
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
2
1
0
0
2
2
0
0
0
0
2
0
0
2
2
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
1
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
1
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
2
0
0
1
1
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
1
0
0
2
0
1
0
2
1
0
0
0
2
0
0
0
2
0
0
0
0
2
0
2
0
0
0
1
2
0
0
0
0
0
1
1
0
1
1
1
2
1
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
4
1
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
1
1
0
0
0
0
2
2
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
1
1
1
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
2
0
0
6
0
1
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
2
0
2
1
1
2
0
0
0
2
0
0
0
0
2
3
0
0
0
0
2
2
0
2
0
0
1
0
0
0
2
0
0
1
1
0
0
2
0
0
0
0
2
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
2
0
1
0
0
0
0
0
1
0
3
1
0
0
2
1
2
1
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
1
0
0
2
0
0
0
2
0
0
1
2
2
1
1
0
0
0
0
0
0
0
0
0
3
0
0
4
2
0
1
3
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
1
1
1
0
0
0
0
0
2
0
2
0
1
0
0
0
2
2
0
0
0
2
0
0
0
1
0
2
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
2
0
0
0
2
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
4
0
1
0
0
0
2
0
0
0
0
1
2
0
0
2
2
2
0
1
2
0
0
2
0
0
0
0
2
0
0
2
0
0
2
0
0
4
0
2
0
0
0
0
2
0
0
1
0
0
1
1
2
1
3
0
2
0
0
0
0
1
2
0
0
0
2
0
0
2
0
0
3
0
2
0
0
1
2
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
2
2
0
2
0
0
0
2
0
1
2
1
1
0
0
0
0
3
0
0
0
0
2
1
0
0
2
2
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
2
0
0
0
0
1
2
0
1
0
0
0
0
0
2
1
2
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
1
0
1
1
0
0
0
2
0
2
0
1
2
0
0
0
0
0
2
0
1
3
0
0
1
2
0
0
0
0
4
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
1
0
1
0
0
1
2
0
0
0
2
0
0
1
0
0
1
0
0
2
0
2
0
0
0
0
0
1
0
1
0
1
0
0
0
1
2
0
1
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
1
1
0
0
0
2
0
0
0
1
0
0
1
0
0
1
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
4
0
0
1
3
0
1
0
0
0
3
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
2
0
1
1
0
0
2
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
6
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
1
0
2
3
3
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
1
2
0
0
0
0
2
0
0
0
0
1
3
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
1
1
1
1
1
0
2
0
0
1
0
1
1
0
0
0
0
1
0
0
2
0
0
1
2
1
0
1
0
1
2
0
0
2
1
0
0
0
0
0
0
1
1
0
0
0
2
0
0
1
0
0
1
0
0
0
2
1
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
3
1
0
3
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
1
0
2
0
1
0
0
0
2
0
0
0
2
0
1
1
0
0
0
0
0
1
0
3
0
0
0
0
1
0
3
0
0
0
2
0
0
0
2
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
1
0
0
2
0
1
0
1
0
0
0
0
1
0
0
0
0
2
0
3
3
0
0
0
0
6
1
0
0
1
0
0
0
2
0
0
0
0
1
2
2
0
1
0
3
0
0
1
1
3
0
2
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
4
0
2
0
1
2
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
2
1
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
4
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
3
0
1
2
0
1
0
2
5
2
0
0
2
1
0
0
0
0
1
0
0
1
2
0
0
1
0
0
3
4
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
2
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
4
0
3
1
2
2
0
3
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
10
0
2
0
2
1
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
1
0
0
0
0
1
0
2
1
2
0
0
0
0
2
4
2
2
2
2
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
2
1
1
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
3
0
0
0
0
0
1
3
0
0
1
0
0
0
0
0
1
2
0
0
1
0
0
0
3
0
0
1
1
0
0
0
1
2
1
0
5
0
0
5
2
0
2
2
0
1
1
0
1
0
0
0
3
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
1
1
2
0
2
0
0
0
0
0
0
2
2
0
0
2
0
0
2
0
0
1
1
0
0
0
0
0
1
2
0
0
0
3
0
1
1
0
0
3
0
0
0
0
0
1
0
0
2
2
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
2
2
2
2
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
2
0
0
1
0
0
0
0
2
0
8
0
2
0
0
2
0
0
0
2
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
2
0
0
0
1
0
1
7
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
1
0
2
2
1
1
0
0
1
0
0
0
1
0
0
0
0
0
2
0
1
0
0
1
0
0
0
1
0
2
0
0
0
1
0
0
0
1
0
3
0
0
0
2
1
3
0
2
2
0
0
0
1
0
2
2
2
0
0
1
0
0
16
0
0
0
0
0
1
0
0
0
3
0
1
0
0
0
3
0
2
0
0
2
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
1
0
3
0
2
0
0
1
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
2
0
2
1
0
0
2
1
2
0
1
2
2
3
0
0
0
2
1
0
2
0
2
0
0
0
0
0
0
1
1
0
1
0
2
0
1
0
1
0
2
2
0
1
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
3
0
2
0
0
1
2
0
3
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
1
2
0
2
1
0
0
0
1
0
0
0
1
0
1
2
3
2
1
0
0
0
1
0
2
2
2
0
1
0
1
0
0
0
0
0
0
13
2
0
0
1
2
2
0
0
3
0
0
1
0
1
0
0
0
0
0
2
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
4
0
2
0
1
0
0
0
1
0
1
0
0
1
0
0
2
0
2
0
2
0
2
0
1
1
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
2
1
0
4
0
0
1
0
3
1
0
0
1
0
0
1
0
0
0
2
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
1
1
0
2
0
0
0
1
2
1
0
0
1
0
1
0
0
0
2
1
0
0
0
2
0
0
1
0
0
2
0
1
2
0
0
0
0
0
3
2
1
1
0
0
1
0
3
0
2
0
0
0
1
0
0
2
1
0
1
1
2
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
1
6
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
2
0
2
0
1
0
0
0
1
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
1
0
2
0
0
0
2
0
1
1
0
0
0
0
0
3
1
0
1
0
2
0
0
0
2
6
2
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
1
0
0
0
0
0
1
2
0
1
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
2
0
1
0
3
0
1
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
1
2
2
2
0
0
2
2
0
0
1
1
3
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
4
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
2
0
2
0
1
1
1
0
0
0
0
0
0
0
0
2
3
2
0
1
2
1
2
0
0
1
0
3
0
0
1
0
0
1
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
1
0
2
0
1
2
0
1
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
2
1
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
3
0
0
2
0
0
0
1
0
0
2
3
0
0
0
0
0
0
0
1
0
0
1
0
0
2
2
0
1
0
1
1
0
0
0
1
2
0
1
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
4
1
0
1
1
0
0
0
0
0
1
0
3
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
4
0
0
0
1
1
0
0
0
0
0
0
2
0
1
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
3
0
3
0
1
0
1
0
0
1
1
1
0
3
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
1
0
0
0
0
0
1
0
1
0
1
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
2
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
2
2
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
2
0
0
2
1
0
0
2
0
2
0
0
0
2
2
2
0
0
0
1
1
2
0
0
3
0
2
0
2
1
1
0
0
2
2
1
0
2
1
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
1
1
0
0
2
2
1
0
1
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
2
0
3
0
0
0
0
1
0
0
0
1
2
0
0
2
2
0
0
0
0
1
0
0
1
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
2
2
1
0
2
0
1
0
0
0
2
1
3
0
5
0
0
0
1
2
2
0
0
0
3
1
0
0
0
0
0
0
0
2
0
1
0
1
0
1
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
1
4
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
1
1
1
1
0
0
3
0
2
2
0
2
0
0
1
0
2
1
0
0
0
0
0
1
1
0
1
2
2
0
0
1
2
0
2
0
0
0
1
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
3
1
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
1
1
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
1
0
2
0
0
0
0
1
2
1
0
2
0
3
0
0
0
2
0
0
0
0
0
0
0
0
7
1
0
0
0
2
0
2
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
2
2
0
2
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
1
0
2
0
2
0
0
1
0
2
1
0
1
1
0
0
2
1
1
2
2
0
1
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
3
0
0
1
1
1
0
1
0
0
2
1
0
3
1
0
0
2
2
0
1
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
2
0
1
1
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
3
2
1
0
0
0
1
0
1
2
0
0
1
0
0
0
0
3
0
3
0
2
1
2
0
0
1
0
0
2
0
1
1
0
0
5
0
0
0
0
1
0
0
0
2
0
0
2
1
0
1
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
4
0
0
2
0
0
2
2
1
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
3
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
1
1
2
1
0
0
0
3
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
1
0
2
0
0
1
0
0
0
0
0
2
2
0
2
2
2
0
2
0
0
0
1
0
2
0
0
0
0
2
0
0
1
0
1
0
3
1
0
1
2
0
0
1
0
0
3
1
1
0
1
0
1
0
1
0
0
1
2
0
0
2
0
0
0
0
0
0
1
0
6
1
0
0
0
0
0
0
0
0
1
0
3
1
0
1
1
0
2
1
0
0
1
2
0
2
0
0
0
2
0
2
0
1
1
0
0
0
1
0
0
0
0
1
2
1
0
1
0
0
0
2
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
7
0
2
0
0
0
2
0
1
2
2
1
1
0
0
2
0
2
0
0
2
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
1
2
0
2
0
0
1
0
1
0
2
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
2
0
0
0
2
0
2
2
2
2
0
0
1
0
2
1
2
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
2
0
3
0
0
1
2
0
0
0
1
2
2
2
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
3
0
0
0
0
0
0
1
0
0
0
3
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
1
2
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
2
1
0
5
0
2
0
2
0
1
2
1
0
1
0
0
1
0
0
1
0
2
0
0
1
0
3
0
0
0
0
2
1
1
1
0
2
0
2
1
0
0
1
2
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
2
0
2
1
1
2
1
0
1
1
1
0
1
0
0
1
0
0
1
0
0
0
0
0
1
2
0
0
0
0
1
0
2
0
0
1
0
1
0
0
0
2
1
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
2
0
0
0
0
0
1
0
2
1
1
0
0
0
0
0
2
0
0
0
1
1
2
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
2
0
2
1
0
0
1
0
0
2
0
0
0
0
0
1
2
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
1
2
1
0
0
2
0
0
0
2
0
2
0
0
3
1
0
0
0
0
0
0
2
0
0
0
0
2
1
0
2
0
4
0
1
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
2
1
0
0
0
1
0
0
0
0
1
0
0
1
0
1
2
1
2
2
0
0
1
0
0
2
0
2
0
0
1
0
1
3
0
0
0
2
2
1
0
0
0
0
2
0
0
0
0
1
0
0
0
3
0
0
0
0
0
1
0
1
0
0
3
0
0
2
0
0
0
0
0
0
0
0
10
0
0
0
2
0
1
0
2
1
1
2
0
2
2
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
2
1
0
2
3
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
2
1
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
1
0
1
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
3
0
2
2
0
0
2
0
0
0
0
1
0
0
2
1
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
4
0
0
2
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
2
2
0
0
2
0
0
0
2
0
0
0
0
0
0
2
2
2
0
1
0
1
2
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
1
2
0
0
0
1
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
2
1
0
0
0
1
0
2
0
1
0
2
0
1
1
2
0
5
1
0
0
0
0
0
2
0
0
1
0
1
0
0
0
2
2
4
0
0
2
0
0
0
0
0
0
1
1
0
0
4
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
2
0
1
0
0
2
1
1
0
2
2
0
2
0
0
0
2
0
2
0
0
0
0
0
0
1
1
2
1
0
3
0
2
1
2
0
1
0
0
0
0
1
1
0
0
2
0
0
2
0
2
0
0
1
0
0
0
1
0
1
0
0
2
0
0
0
3
0
3
2
2
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
1
0
0
0
0
2
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
2
2
2
0
0
0
1
0
1
0
2
0
0
1
0
0
0
4
0
0
1
0
1
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
1
0
0
2
0
1
0
1
0
0
2
2
2
1
0
2
0
0
0
1
0
0
0
0
0
2
2
1
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
1
1
0
2
1
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
3
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
4
0
1
0
1
1
2
0
0
1
0
0
1
1
0
0
2
0
0
0
0
2
0
0
2
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
2
0
0
0
0
2
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
2
0
0
0
0
0
0
1
2
2
0
1
1
0
2
2
0
0
3
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
2
2
1
0
0
0
2
0
2
1
0
0
0
1
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
2
0
0
1
0
0
0
0
1
0
0
1
0
3
0
1
1
0
0
1
0
1
1
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
2
2
0
1
0
0
1
0
3
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
1
0
0
1
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
2
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
46
0
2
3
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
1
0
1
2
0
1
0
1
0
0
3
0
0
0
1
0
3
0
2
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
2
0
1
0
2
0
0
0
0
0
0
1
0
1
0
1
1
2
0
0
1
1
0
0
1
1
0
0
2
0
1
0
0
1
0
2
1
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
3
0
0
1
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
2
0
0
1
2
0
0
2
0
0
1
0
0
0
1
0
2
0
0
2
0
0
0
0
0
2
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
1
0
3
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
1
1
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
1
1
3
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
2
2
1
1
0
0
0
2
0
0
0
1
2
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
2
0
1
0
0
0
2
0
0
1
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
2
0
1
2
0
0
0
0
1
1
1
0
1
0
0
0
3
0
0
2
0
0
0
2
1
0
2
0
0
0
1
0
2
2
0
0
0
0
0
2
0
2
0
2
2
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
2
2
0
0
0
2
0
0
2
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
2
0
2
1
0
0
2
0
0
2
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
1
0
0
2
2
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
2
0
1
0
0
0
2
0
1
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
1
0
0
1
3
1
0
0
0
1
0
0
0
0
1
1
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
1
0
0
2
0
1
0
0
1
0
3
3
0
0
0
3
0
0
3
0
1
1
0
2
2
0
0
2
1
1
0
2
0
0
0
0
0
0
1
0
2
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
3
0
0
0
1
2
0
1
3
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
1
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
3
0
0
1
0
0
0
1
0
0
3
0
1
1
0
0
2
1
0
1
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
2
0
3
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
3
1
0
0
1
1
0
0
3
0
0
0
0
0
1
0
2
0
1
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
6
3
0
2
1
0
0
2
0
3
0
0
0
1
0
1
0
0
1
1
0
0
0
1
1
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
1
0
2
1
0
0
1
6
0
0
0
0
2
1
2
0
4
1
0
1
3
1
0
0
2
2
2
0
0
0
0
0
0
0
3
3
0
0
0
0
0
0
0
1
0
0
0
0
0
2
4
0
1
0
1
0
0
2
0
0
1
0
0
0
0
1
0
1
2
1
0
0
0
2
1
0
0
2
0
1
0
0
0
0
0
0
1
0
3
0
1
0
1
0
2
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
3
1
2
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
3
0
2
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
2
1
1
1
2
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
4
0
0
1
2
0
1
2
2
0
1
2
2
0
2
0
1
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
1
0
2
1
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
1
1
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
3
1
0
0
0
0
0
0
2
0
0
3
0
0
2
0
0
0
2
2
2
0
1
0
0
1
0
3
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
3
2
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
1
0
0
2
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
1
0
0
0
2
0
0
0
0
0
2
2
2
0
0
0
0
3
0
2
0
2
0
1
0
1
0
2
1
2
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
2
0
2
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
2
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
2
0
0
0
0
2
1
0
1
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
2
0
0
6
0
2
0
0
1
2
0
0
2
0
4
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
2
2
1
0
3
1
0
1
0
0
0
0
0
0
1
0
0
1
2
0
0
2
1
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
1
0
0
2
0
0
0
0
3
0
2
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
1
1
0
2
0
0
0
0
2
0
0
0
1
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
2
0
0
2
0
0
1
0
2
2
0
0
2
2
0
1
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
2
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
2
1
1
2
0
0
0
1
2
2
0
0
0
1
1
0
2
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
2
1
2
2
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
1
2
0
1
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
1
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
2
0
0
0
0
1
2
0
0
0
0
2
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
1
2
0
3
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
1
0
0
0
1
0
1
2
2
0
2
0
0
0
0
0
2
0
0
0
1
0
0
2
2
2
0
1
0
2
0
0
1
2
1
0
0
1
0
0
0
0
0
1
0
1
2
1
0
0
0
0
1
0
1
0
1
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
5
0
0
2
0
1
1
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
1
0
0
0
2
0
2
0
0
0
2
1
0
0
0
0
1
0
2
1
4
2
0
1
0
1
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
2
4
2
2
2
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
3
1
0
1
2
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
1
3
2
0
0
2
1
1
0
1
0
0
0
0
0
1
0
0
3
0
0
4
2
1
0
0
0
0
0
1
1
2
2
2
2
0
1
0
2
2
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
2
0
0
2
0
2
2
0
0
0
1
2
0
0
0
2
0
1
0
0
0
2
0
0
2
2
0
0
2
1
0
1
0
1
0
0
0
0
2
0
1
1
0
0
0
0
2
0
0
0
0
0
0
1
0
1
1
0
0
2
0
0
2
0
2
2
0
0
1
1
0
2
0
0
0
1
0
1
0
1
1
0
0
0
2
0
0
0
1
0
1
0
0
0
2
0
0
2
1
0
1
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
2
0
1
2
1
0
0
2
0
0
0
0
1
0
1
1
1
0
2
1
1
1
1
0
0
0
1
0
3
2
1
0
0
0
0
0
2
0
0
1
0
0
3
0
0
1
0
0
2
2
0
0
0
0
2
0
0
0
0
0
3
2
0
2
2
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
2
0
0
0
2
0
1
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
2
1
1
0
0
0
0
0
0
0
0
0
1
2
0
0
1
2
0
2
0
1
0
2
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
2
2
0
0
2
0
2
0
0
0
0
2
0
0
0
0
1
0
1
0
1
2
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
1
2
0
2
0
0
1
0
2
2
0
1
0
2
1
0
0
1
2
2
0
2
1
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
2
0
0
0
0
1
1
1
2
0
0
0
0
0
1
1
1
0
0
1
1
2
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
1
3
0
0
0
0
0
0
0
0
4
0
1
0
1
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
2
0
2
2
1
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
3
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
1
0
0
0
3
0
0
1
1
0
3
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
2
2
1
0
0
0
0
1
0
2
2
2
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
2
1
0
2
3
0
0
0
0
0
0
1
0
0
0
1
0
3
0
0
2
0
0
0
0
0
1
0
1
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
1
0
2
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
2
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
1
0
0
1
0
0
0
0
0
0
0
0
0
2
1
1
2
1
0
0
0
0
1
0
2
0
2
0
2
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
1
0
2
0
2
0
2
1
3
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
5
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
1
2
1
2
0
0
1
0
0
0
0
2
2
0
0
2
0
0
2
1
0
2
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
2
0
0
1
0
1
1
0
2
1
2
0
2
1
0
0
0
1
0
1
2
4
1
1
1
2
0
0
4
0
0
1
0
0
0
1
0
0
1
3
2
2
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
1
0
0
1
0
0
3
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
2
0
1
0
1
0
0
0
1
1
1
0
2
0
0
0
0
0
2
0
0
0
2
2
1
0
0
2
0
0
0
3
0
0
0
1
0
0
0
0
1
0
1
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
1
2
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
1
0
0
0
2
0
0
3
0
0
2
0
0
0
1
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
1
0
0
0
0
0
2
0
1
2
2
0
0
2
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
1
0
0
2
0
2
0
2
2
0
2
0
0
0
0
1
0
3
0
0
0
2
0
1
0
2
1
0
0
2
0
2
0
3
1
0
0
0
0
0
2
0
0
2
1
2
0
1
1
0
2
2
0
1
1
0
0
1
0
0
0
1
0
1
0
2
2
2
1
0
1
0
2
3
1
0
1
0
2
2
0
1
1
0
0
3
0
0
0
2
0
0
1
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
2
0
2
0
0
0
0
0
2
0
1
0
1
0
2
0
0
2
2
0
0
2
0
0
0
0
5
0
0
2
0
0
0
1
0
0
1
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
3
0
0
0
4
1
2
0
0
0
2
0
3
0
0
0
0
0
0
0
0
1
2
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
2
3
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
1
1
0
0
0
0
0
0
1
2
0
0
0
1
2
0
1
0
2
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
1
2
0
0
0
0
1
0
2
1
0
1
0
0
0
1
1
2
2
1
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
2
0
3
1
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
1
2
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
1
0
0
0
0
0
0
2
0
2
1
2
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
1
0
3
0
2
0
0
2
0
2
0
0
0
0
1
3
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
1
0
2
0
2
0
2
0
0
0
1
1
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
6
1
0
2
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
1
0
0
1
0
0
0
0
0
2
0
1
0
0
1
0
1
0
0
6
0
0
0
0
0
1
0
1
2
1
2
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
3
2
0
2
0
0
0
0
0
0
2
2
2
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
2
0
0
2
0
0
0
3
1
3
2
0
2
0
0
0
1
0
0
0
0
2
0
4
2
3
0
2
0
0
2
0
1
1
0
1
2
2
0
0
0
2
0
0
2
1
0
0
0
0
3
1
2
1
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
1
1
0
0
0
0
0
2
1
2
1
0
6
0
0
0
2
0
0
1
0
2
3
1
1
0
0
0
0
0
0
1
1
0
2
0
0
2
0
2
0
1
1
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
1
3
0
0
1
0
1
0
0
2
0
0
3
2
0
1
0
2
0
0
0
0
0
0
2
2
0
2
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
4
1
2
0
0
2
0
0
0
0
1
1
2
0
0
0
0
1
2
0
0
0
1
0
0
1
0
1
0
0
2
0
0
1
0
0
0
2
0
0
0
0
1
0
0
2
3
1
2
0
1
0
2
0
0
4
2
2
0
0
1
2
0
2
2
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
1
1
0
2
1
0
2
0
1
0
1
0
1
1
0
0
1
2
0
2
0
3
0
2
0
1
2
1
0
1
1
1
1
1
0
1
2
0
0
0
0
0
2
1
0
1
0
1
3
1
0
1
0
0
2
0
0
1
1
0
0
0
3
0
0
1
0
0
1
0
0
0
1
1
2
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
2
0
1
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
2
2
0
0
2
2
0
2
0
0
0
0
0
2
0
1
0
1
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
1
2
0
0
1
0
0
1
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
1
0
0
0
1
1
1
0
1
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
1
0
1
0
0
0
1
1
0
0
4
0
0
0
2
1
0
0
0
0
0
0
0
0
1
1
2
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
3
0
0
0
0
0
0
0
1
0
4
0
2
0
0
0
0
2
0
1
0
0
0
1
2
0
0
0
0
0
0
0
1
2
0
2
2
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
2
0
2
0
2
3
0
1
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
1
2
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
2
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
2
2
0
2
0
2
10
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
3
0
2
0
0
0
0
2
2
0
2
0
0
0
0
1
1
0
0
0
2
0
0
0
0
1
0
1
0
0
2
2
1
2
1
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
3
0
2
0
0
0
0
0
1
0
0
1
1
1
0
0
0
1
0
0
0
0
2
0
0
2
2
0
0
0
0
2
1
0
0
0
0
0
1
2
2
0
1
0
0
0
0
0
0
0
2
0
0
1
0
3
0
0
0
0
2
0
0
0
0
0
0
0
3
2
0
0
0
0
1
0
0
0
0
3
0
0
2
0
0
0
2
1
0
0
0
0
0
1
0
0
1
0
1
2
2
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
3
0
3
0
1
0
0
0
0
0
0
2
1
0
0
2
0
2
0
0
0
0
0
1
0
0
0
1
0
2
2
0
1
0
0
0
2
0
1
0
2
0
0
0
1
1
0
1
1
0
0
2
2
0
0
1
0
4
2
1
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
1
3
11
2
0
0
0
2
0
1
0
0
2
0
0
0
0
0
2
0
1
0
1
0
1
0
1
2
0
0
0
1
0
0
0
0
3
0
2
0
0
0
0
0
1
2
0
0
1
1
0
2
0
0
3
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
2
0
0
1
1
0
0
0
0
0
1
0
1
2
0
2
0
0
2
1
0
0
0
0
0
0
2
0
0
0
1
0
1
2
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
3
0
1
0
0
0
0
0
2
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
2
1
0
1
2
2
0
2
0
2
0
2
0
1
0
0
0
0
2
0
0
0
1
0
1
0
1
0
2
2
0
1
0
1
0
1
1
0
0
2
0
0
0
0
0
2
0
0
0
1
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
2
0
0
2
0
2
2
0
0
0
1
1
1
0
2
1
1
2
0
0
0
0
0
2
0
0
1
0
0
1
0
1
0
0
0
1
0
2
0
2
1
2
0
0
0
0
1
0
0
1
0
1
0
1
0
0
2
0
1
0
1
6
0
1
0
1
0
0
0
2
0
2
0
1
0
0
0
0
0
2
2
2
2
0
0
0
0
1
0
0
1
2
0
0
2
0
0
2
0
1
0
2
0
2
2
5
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
1
0
3
0
0
0
1
0
2
0
0
0
2
0
1
0
1
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
2
0
0
0
0
2
0
2
0
1
0
0
0
0
0
1
1
0
0
0
2
2
0
0
0
1
0
0
0
2
1
0
0
1
0
2
0
2
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
1
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
2
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
1
2
1
1
1
2
3
0
7
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
2
2
0
0
0
0
1
0
0
0
0
0
1
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
1
0
0
2
0
1
2
0
0
0
0
0
1
0
1
0
2
0
1
0
0
1
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
3
0
0
2
0
3
0
0
0
0
1
2
2
0
2
2
2
1
0
1
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
2
3
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
1
2
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
2
2
0
1
0
0
1
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
2
3
0
1
0
1
2
0
0
0
3
0
0
0
1
0
2
1
0
1
1
0
0
0
0
0
0
1
0
1
0
0
8
0
1
0
1
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
2
0
0
1
0
2
2
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
2
1
0
0
3
2
0
0
2
0
2
0
0
0
0
0
0
0
0
1
4
0
0
2
0
2
2
0
0
0
2
0
0
1
0
0
0
2
0
0
1
1
0
0
1
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
2
0
0
2
0
2
0
0
0
1
0
2
0
1
0
0
1
0
0
0
2
0
1
2
0
2
0
0
0
2
0
0
0
2
0
0
0
0
1
2
2
0
0
0
0
1
0
1
1
1
2
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
1
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
2
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
2
1
0
0
1
0
0
3
0
2
0
2
0
2
0
2
0
0
0
0
1
0
0
2
0
0
2
0
0
0
2
1
0
0
0
1
0
0
0
2
2
1
3
0
2
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
2
0
0
1
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
1
0
0
0
0
0
0
1
0
0
2
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
1
0
0
0
1
0
0
1
0
3
1
1
0
2
0
0
0
0
1
0
1
0
1
0
0
2
1
0
0
1
0
0
2
1
1
0
0
1
1
1
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
3
0
0
0
0
2
2
2
1
0
2
0
0
2
0
0
2
1
0
0
1
0
0
1
0
2
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
3
0
0
0
2
0
2
0
0
1
0
1
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
2
0
0
0
0
2
0
2
0
0
3
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
3
2
1
0
0
0
1
2
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
1
1
0
2
0
3
2
0
2
2
1
0
2
0
0
0
0
1
1
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
3
2
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
1
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
2
2
0
0
0
2
0
0
0
0
0
0
1
0
2
0
2
2
2
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
1
0
2
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
2
2
0
0
1
2
0
2
0
1
0
0
2
2
1
0
0
0
0
0
0
2
2
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
2
0
0
1
1
0
0
2
1
0
0
0
0
0
3
0
1
0
1
3
2
0
0
0
1
1
0
0
0
0
2
1
0
1
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
2
0
0
1
0
0
2
2
0
0
0
2
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
2
0
0
1
2
0
1
2
0
0
0
0
1
2
0
2
2
0
1
0
1
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
2
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
2
0
1
0
0
0
0
0
1
0
0
3
0
0
0
1
0
2
0
0
1
0
2
1
0
0
0
3
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
2
0
1
0
0
2
2
0
0
0
0
1
2
0
2
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
3
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
1
0
0
1
2
3
0
1
3
0
0
1
0
0
0
0
0
0
0
0
1
2
0
1
0
2
1
1
0
1
0
1
4
3
0
0
0
0
0
0
1
0
0
1
0
3
0
1
1
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
1
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
3
0
0
2
1
0
0
0
1
1
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
1
0
0
0
0
0
1
0
1
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
3
0
1
0
2
0
0
0
0
2
0
0
2
1
0
0
0
0
1
0
2
0
0
2
0
2
1
0
0
0
2
1
0
2
0
0
0
1
3
0
2
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
1
1
0
0
4
1
0
1
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
2
1
3
0
0
0
8
1
0
0
0
1
0
0
2
0
0
1
0
0
2
0
0
0
0
1
3
0
0
0
0
0
0
3
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
1
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
2
1
0
2
1
0
2
0
0
2
0
0
2
2
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
2
2
1
0
0
2
0
1
0
1
1
0
0
0
0
1
0
0
2
2
0
0
0
0
1
1
2
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
2
2
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
2
1
2
0
2
0
1
0
0
0
0
2
0
3
0
0
0
1
2
0
2
1
2
0
2
0
1
0
0
0
0
2
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
1
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
2
2
0
1
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
2
2
2
0
1
6
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
1
0
0
2
0
0
0
0
0
1
0
0
2
2
0
0
1
0
0
1
1
2
0
1
0
2
2
0
0
0
0
1
0
2
2
0
0
0
0
0
2
1
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
2
0
2
0
1
0
0
2
0
3
0
0
2
0
0
0
0
0
1
0
0
0
2
2
0
1
0
2
2
0
1
0
0
2
0
2
0
0
0
1
2
1
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
3
0
1
0
0
0
2
0
0
0
0
0
2
0
1
1
2
0
0
7
1
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
1
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
3
1
0
2
0
0
1
0
0
1
2
0
0
1
0
0
2
1
0
1
0
0
4
2
0
2
0
3
0
0
0
3
0
1
0
0
0
0
0
0
0
0
4
1
0
0
2
0
1
0
0
0
1
2
2
1
2
0
0
0
0
0
1
0
3
0
1
0
0
0
1
1
0
2
0
0
0
0
1
0
0
1
0
0
0
1
0
0
2
1
0
1
0
0
0
2
0
0
0
0
2
0
0
2
1
2
0
2
0
0
0
0
0
0
0
1
2
1
2
3
1
6
0
1
0
0
0
1
0
0
0
3
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
1
2
0
1
0
0
0
1
1
1
0
2
1
2
0
0
0
0
2
0
0
0
2
1
2
0
0
1
0
0
0
0
2
1
0
0
0
0
0
1
0
2
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
5
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
3
0
0
0
2
0
0
2
0
0
1
0
0
0
0
2
2
4
0
0
0
2
0
0
0
0
0
0
2
1
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
5
2
0
0
2
2
0
1
0
0
0
1
1
2
0
0
0
2
2
0
2
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
1
0
0
2
1
0
2
0
2
0
0
2
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
2
0
0
1
0
0
0
3
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
2
1
0
0
0
0
1
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
1
0
0
0
2
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
1
2
0
0
2
0
1
0
0
0
0
0
2
0
0
0
3
0
0
1
0
1
0
0
2
0
3
1
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
1
0
1
0
0
1
2
0
0
2
1
1
0
0
0
0
1
1
1
1
0
0
0
0
1
4
2
4
0
1
2
0
2
2
0
0
3
1
0
0
0
2
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
2
0
0
0
0
3
0
0
0
2
1
0
0
1
2
0
0
2
0
0
1
0
0
1
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
1
3
0
0
2
1
7
0
0
0
0
0
0
0
2
1
0
1
0
2
0
2
0
1
0
0
0
0
2
0
3
0
0
0
0
0
0
2
0
0
1
2
2
0
0
0
0
2
1
1
1
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
2
1
0
2
0
0
1
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
1
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
2
0
2
1
2
0
0
0
0
6
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
1
0
0
1
0
0
2
5
0
0
0
0
1
2
0
2
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
2
2
0
1
0
0
0
0
1
0
0
0
1
0
0
2
0
1
2
0
0
0
0
0
1
1
1
1
1
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
1
0
0
2
0
0
2
1
0
2
0
1
2
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
1
1
0
2
1
0
0
2
0
0
0
0
1
1
0
2
1
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
3
0
1
0
2
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
1
0
2
0
0
0
0
2
0
1
0
2
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
2
1
2
0
0
2
0
1
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
2
0
0
2
0
0
0
0
0
0
0
3
0
2
0
1
0
0
0
2
2
1
1
0
3
0
5
0
1
0
0
2
0
0
1
2
0
0
1
0
1
0
0
0
0
1
0
0
3
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
3
2
0
0
1
1
2
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
2
1
0
1
0
1
1
2
0
0
0
0
0
0
0
3
0
0
0
0
1
1
4
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
2
1
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
2
0
0
2
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
2
0
0
0
2
1
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
2
1
0
1
3
0
2
2
0
2
0
2
2
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
1
2
5
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
1
2
0
0
2
0
0
0
1
0
1
0
0
2
2
0
0
1
0
0
0
1
0
1
3
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
2
0
0
1
2
1
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
2
0
1
0
1
2
0
0
2
1
0
2
1
2
0
1
0
1
1
1
0
0
0
0
0
1
0
0
0
2
0
2
2
1
0
1
1
0
0
0
0
2
0
2
1
0
4
3
0
0
1
0
0
1
0
0
0
0
1
2
0
2
2
0
0
1
0
1
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
1
0
0
0
1
0
1
2
0
0
0
0
0
0
0
1
0
1
2
1
0
2
0
3
0
0
0
1
0
2
2
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
2
2
0
3
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
3
2
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
3
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
3
1
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
2
1
0
2
0
0
1
0
0
0
0
1
0
0
0
0
4
0
0
1
0
2
3
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
1
1
0
0
0
2
0
0
0
2
0
7
0
0
0
1
0
2
0
0
0
1
0
0
0
0
2
0
0
0
2
0
2
0
0
0
2
0
0
2
2
2
1
2
0
2
0
0
0
0
2
2
0
0
0
0
0
1
2
0
0
1
1
1
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
2
0
2
2
2
0
0
0
0
0
2
0
2
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
1
2
0
0
0
0
0
1
2
0
1
0
0
0
1
0
2
2
0
2
0
0
3
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
1
1
0
0
3
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
1
2
0
0
0
0
0
1
0
0
3
0
0
0
1
0
0
2
0
0
0
0
2
0
2
0
0
0
1
2
2
2
2
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
1
0
1
0
0
0
1
0
0
2
0
0
0
4
0
0
2
0
0
0
0
1
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
2
1
0
0
2
1
0
0
3
2
0
0
0
1
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
1
3
1
0
0
0
2
0
0
0
2
1
0
0
0
2
0
1
0
2
0
0
0
2
0
1
0
0
0
0
2
1
0
0
0
1
1
0
0
0
1
0
3
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
1
1
3
0
0
2
1
0
0
0
2
2
0
1
4
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
2
1
1
1
0
1
0
2
1
1
6
2
2
1
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
1
0
0
2
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
2
0
0
0
2
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
1
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
2
2
0
0
2
0
0
1
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
2
3
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
2
3
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
2
0
0
2
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
3
0
0
0
2
0
0
0
0
3
0
1
0
1
0
0
1
0
2
1
0
0
2
0
0
0
0
0
0
0
2
2
1
0
0
3
0
3
4
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
3
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
2
0
1
0
0
3
0
0
0
1
0
0
3
2
0
1
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
3
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
1
0
2
0
0
0
0
0
3
1
0
1
0
31
0
0
0
0
1
2
0
0
0
0
2
2
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
3
0
0
0
2
1
0
0
0
0
0
2
0
2
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
2
0
0
2
1
0
0
0
0
1
2
0
0
2
0
0
2
0
0
0
0
3
2
0
8
0
1
0
0
0
1
2
0
0
2
0
2
0
1
1
0
0
0
1
2
3
0
0
0
0
0
1
2
2
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
1
0
0
1
0
1
0
1
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
3
0
0
0
0
0
1
1
1
0
0
0
1
1
1
1
2
0
5
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
1
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
1
1
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
2
0
0
1
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
2
2
0
2
0
0
1
0
0
0
0
0
0
2
2
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
2
3
0
2
0
0
0
0
2
0
1
1
2
2
2
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
2
1
1
0
1
1
0
0
0
1
0
0
2
0
0
0
0
0
1
1
0
2
0
2
0
2
0
0
1
2
0
0
0
0
0
1
0
1
1
1
0
1
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
2
0
0
0
1
1
0
0
1
1
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
1
0
2
2
0
0
0
2
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
1
0
0
0
0
2
2
0
0
2
2
0
0
0
0
3
0
0
0
0
0
0
4
0
0
8
2
0
0
1
1
2
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
1
0
0
0
0
0
0
0
1
1
0
3
0
1
0
0
2
0
2
0
0
1
0
1
2
1
0
0
2
0
2
0
2
0
1
2
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
2
1
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
2
2
1
0
0
0
4
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
1
0
0
2
0
0
0
0
1
2
0
0
1
0
0
0
0
0
1
1
2
1
0
0
3
0
0
0
0
0
0
0
4
0
0
3
0
0
1
0
0
0
0
2
2
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
2
1
0
0
2
1
1
0
1
3
0
2
1
3
0
0
0
0
0
1
0
0
0
2
0
0
1
0
2
0
2
0
0
0
2
0
0
1
2
0
1
2
0
0
0
3
0
0
0
0
0
0
2
2
3
0
2
2
0
0
0
0
0
3
2
0
0
0
0
0
0
0
1
0
1
0
0
0
3
1
0
0
0
0
1
0
0
1
1
2
0
2
2
0
2
0
1
1
0
1
2
1
5
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
4
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
4
0
0
2
1
2
1
2
0
2
0
2
0
0
0
0
0
2
0
2
0
0
1
1
2
0
1
1
0
0
0
5
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
2
0
0
1
0
0
1
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
2
3
1
1
2
0
1
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
4
2
1
0
0
0
0
1
0
0
0
1
0
1
1
0
1
0
0
0
0
2
0
0
1
0
2
0
0
4
2
0
0
1
0
0
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
1
0
0
1
0
3
2
2
2
0
0
2
2
0
2
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
1
0
1
0
1
0
0
2
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
3
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
2
2
0
0
0
1
1
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
2
2
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
3
0
0
0
0
0
0
2
2
0
1
0
1
2
0
1
0
1
0
0
0
0
2
0
0
0
1
0
2
3
0
0
0
0
4
0
0
0
0
0
0
2
0
1
2
0
0
0
2
0
0
1
1
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
2
0
0
1
1
0
3
2
2
1
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
1
2
0
0
1
0
0
0
1
2
0
0
0
0
0
3
0
0
0
0
0
2
0
0
2
0
0
1
0
0
1
0
0
1
0
0
1
2
3
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
1
0
0
0
0
1
0
0
1
2
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
5
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
2
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
2
1
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
1
0
0
2
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
2
0
1
1
0
3
7
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
2
0
0
1
0
3
2
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
6
0
0
0
0
1
1
0
0
2
4
0
3
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
2
2
0
1
0
0
0
0
0
1
0
0
0
2
1
2
2
3
0
0
0
0
0
2
0
2
0
0
1
0
0
1
0
0
1
2
0
0
0
0
0
0
0
1
1
0
2
2
1
0
0
0
0
1
0
0
2
0
0
1
0
1
2
2
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
1
1
0
0
0
0
0
0
0
2
2
0
0
0
1
1
0
0
2
0
0
0
1
1
2
0
0
0
0
0
1
1
0
2
0
0
2
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
1
2
4
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
2
2
0
0
0
0
0
1
0
0
1
0
0
0
0
2
2
2
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
2
3
3
0
0
0
2
4
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
1
1
0
0
0
0
1
0
3
0
0
0
1
0
1
0
2
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
2
1
1
2
0
1
2
0
0
0
0
0
1
0
0
2
0
2
0
1
0
0
0
2
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
2
4
0
0
0
1
2
0
2
0
1
0
0
0
0
0
0
0
1
0
2
2
0
1
1
0
0
1
0
2
1
0
1
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
1
1
0
0
1
0
0
2
2
0
1
0
0
2
1
0
0
0
0
1
0
0
0
0
4
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
1
1
2
1
1
0
0
1
1
0
0
0
1
1
2
0
0
1
0
3
0
0
0
0
2
0
2
0
2
0
0
0
1
0
1
1
0
0
0
0
2
0
0
0
0
0
1
1
0
1
2
2
1
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
2
0
1
3
1
0
0
2
1
0
0
0
0
2
0
0
3
2
0
1
0
0
1
1
0
0
0
2
1
3
0
0
0
0
0
0
0
1
2
0
0
0
1
1
0
0
1
0
1
0
0
1
1
0
1
1
1
2
0
0
1
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
2
2
0
2
0
1
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
2
1
0
0
2
2
2
0
0
0
0
2
0
0
0
2
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
2
0
1
0
2
2
2
2
0
0
0
0
0
0
0
0
1
0
0
0
2
2
1
3
3
0
1
0
1
2
1
0
0
2
0
0
0
2
0
0
1
1
1
0
0
0
0
0
2
0
1
1
0
0
1
0
2
0
2
0
1
0
0
2
0
0
0
1
0
1
1
1
0
2
0
0
0
3
3
2
3
2
0
1
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
3
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
1
1
0
2
1
3
2
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
2
2
0
2
0
0
2
2
0
2
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
2
2
1
0
0
0
0
2
0
0
2
1
0
0
1
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
4
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
2
2
1
2
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
2
0
0
0
1
0
0
1
0
0
1
0
0
1
4
0
0
0
0
1
1
0
2
2
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
2
0
0
0
2
3
0
1
0
0
0
0
0
0
0
1
1
1
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
6
2
1
0
0
1
0
0
0
0
1
0
0
1
2
2
0
0
0
1
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
5
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
1
0
5
0
1
2
0
0
0
2
2
1
2
0
2
1
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
2
1
0
1
2
1
0
0
0
5
0
2
0
3
1
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
1
0
1
0
0
1
0
2
0
1
2
0
0
0
2
0
3
0
0
0
0
0
0
0
2
1
1
0
2
3
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
2
0
0
1
1
1
1
4
0
0
1
0
0
0
0
2
0
1
2
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
2
2
2
2
1
0
0
1
0
0
0
3
0
2
0
0
0
0
1
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
2
2
2
0
1
1
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
2
2
1
0
1
2
1
2
0
0
0
0
1
1
2
2
1
0
0
0
1
2
0
0
0
1
0
0
1
1
0
1
1
1
1
1
0
0
1
1
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
1
0
0
2
0
0
0
3
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
1
1
2
1
0
0
2
0
0
1
1
2
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
3
0
0
1
1
1
0
0
0
1
0
2
0
2
0
0
0
1
2
0
0
2
0
0
0
2
0
1
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
1
0
2
0
0
2
0
2
0
1
3
0
0
0
2
0
0
0
0
0
0
1
1
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
2
0
2
1
0
0
0
2
1
0
0
0
4
0
2
0
1
0
0
0
0
0
0
0
0
2
1
1
2
0
0
0
0
1
0
0
0
0
0
0
1
1
2
2
3
3
0
1
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
9
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
1
0
2
1
0
1
0
1
1
1
2
0
0
0
0
1
2
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
2
0
1
0
3
0
2
0
2
1
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
2
0
1
1
0
1
2
0
0
0
0
0
1
2
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
2
3
0
2
0
1
0
0
0
0
0
0
2
0
2
0
1
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
1
0
1
2
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
5
1
0
0
2
1
0
2
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
2
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
2
1
1
1
0
2
1
1
0
0
0
0
0
1
0
0
2
1
1
2
1
0
2
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
2
2
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
2
0
0
0
0
1
0
0
1
1
0
0
0
0
3
0
0
0
0
0
1
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
1
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
2
0
0
2
0
2
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
1
1
2
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
2
0
0
0
0
0
0
0
1
2
0
0
1
0
0
1
1
0
0
1
0
0
0
1
0
2
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
2
1
0
0
0
1
0
1
0
0
0
2
0
3
4
0
0
0
0
0
1
0
0
0
0
1
0
2
2
0
0
0
2
0
1
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
1
0
1
0
1
0
0
2
2
0
0
0
1
0
1
0
0
0
0
0
2
0
2
0
1
0
3
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
3
2
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
3
0
0
1
1
1
0
0
1
2
0
2
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
1
1
0
0
2
0
2
0
1
0
1
4
1
0
0
0
0
0
0
1
2
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
1
2
3
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
1
2
0
0
1
2
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
2
2
0
2
0
0
0
0
0
1
0
2
1
0
0
0
0
0
1
0
0
0
3
0
0
1
0
0
0
0
0
1
0
0
0
0
0
3
0
1
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
2
0
1
0
2
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
3
0
2
0
0
4
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
1
1
2
0
0
0
1
0
0
2
0
2
0
0
0
0
0
1
0
0
2
1
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
2
0
2
1
2
1
0
0
2
0
0
0
2
1
0
1
2
2
2
0
1
0
0
0
0
0
0
0
2
0
0
0
2
1
2
0
2
0
1
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
1
2
2
0
0
0
2
2
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
1
2
0
1
0
3
0
0
2
0
0
0
0
2
3
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
1
2
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
2
1
0
0
2
0
0
0
4
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
1
0
0
0
1
2
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
1
0
0
0
0
0
0
1
0
0
0
1
0
3
0
0
0
0
2
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
2
0
0
3
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
2
0
0
0
0
0
2
0
2
1
0
1
0
0
0
2
3
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
6
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
1
1
7
0
0
0
3
0
2
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
2
1
0
1
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
2
1
0
0
1
1
0
0
0
0
2
1
0
0
0
1
0
2
0
0
2
2
0
2
2
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
2
2
0
0
1
0
0
0
0
2
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
3
2
2
1
0
0
0
2
0
1
1
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
2
2
0
0
0
1
0
0
0
0
1
1
0
0
1
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
1
1
0
0
0
0
1
2
1
1
1
0
2
0
0
0
0
2
1
0
0
1
1
1
1
0
0
0
0
0
0
0
0
3
0
0
1
0
1
0
1
0
0
0
0
1
2
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
1
1
0
0
2
0
3
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
2
1
0
2
1
0
0
0
2
0
0
0
1
0
1
0
2
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
2
0
0
0
0
1
3
1
1
0
2
0
0
1
0
0
0
0
1
0
0
0
0
2
0
1
0
2
0
0
2
0
0
2
0
0
1
1
0
1
0
1
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
3
0
0
0
0
2
2
0
1
3
1
0
0
0
1
0
0
2
2
1
0
0
1
2
0
0
0
0
0
0
1
1
0
1
0
2
0
0
1
0
0
0
1
0
0
1
0
0
0
2
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
3
0
2
0
0
1
2
2
0
0
0
2
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
3
1
1
0
2
0
0
0
0
0
0
0
0
0
0
1
2
2
2
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
1
2
0
2
1
0
0
0
1
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
2
2
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
2
0
0
1
0
0
2
2
0
0
1
0
1
0
0
0
0
1
1
1
0
0
0
2
0
0
2
0
0
1
0
0
0
0
1
0
0
1
0
2
0
2
0
0
1
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
1
0
2
2
0
1
0
0
0
2
2
1
2
0
1
2
1
0
3
2
0
2
2
0
0
0
0
0
1
3
0
1
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
2
1
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
7
0
0
0
0
6
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
1
2
0
0
1
0
0
1
1
1
1
2
1
0
4
0
0
0
1
0
0
0
2
0
0
3
1
1
0
2
1
2
0
0
0
0
0
1
0
0
2
1
1
0
0
0
2
0
2
1
1
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
2
0
0
0
0
1
1
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
4
0
0
0
0
0
0
2
2
1
0
0
1
0
1
1
0
1
0
0
3
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
2
1
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
2
2
0
2
0
3
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
3
2
1
0
1
3
0
2
0
1
0
0
2
0
1
0
2
0
0
0
0
2
0
0
1
1
1
0
1
3
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
2
2
0
0
1
2
0
0
0
0
1
0
3
0
0
1
0
1
0
0
0
0
2
0
1
2
0
2
0
0
0
1
1
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
2
2
1
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
2
2
2
1
2
1
0
0
0
0
2
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
2
0
1
0
2
0
0
1
0
1
0
0
0
0
0
2
0
0
0
1
1
1
3
0
0
0
1
0
0
2
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
3
0
0
0
0
0
1
0
1
1
2
0
1
2
0
0
0
0
0
0
0
0
0
0
2
2
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
2
0
1
0
0
0
0
0
1
1
2
1
0
0
0
0
1
1
2
0
0
2
0
2
2
0
0
0
0
1
0
1
0
0
0
2
1
0
0
0
0
0
0
1
1
1
2
0
1
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
4
3
0
0
2
1
1
0
0
1
2
0
0
0
2
0
1
1
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
1
0
0
1
1
0
0
1
0
0
2
0
0
3
0
1
1
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
2
0
1
2
0
0
0
0
0
4
2
0
0
0
1
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
1
0
1
2
0
0
0
1
2
1
0
0
2
0
2
1
0
0
3
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
1
1
1
0
0
2
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
2
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
2
0
1
2
0
2
2
0
1
0
1
2
0
0
2
0
0
0
2
0
1
0
0
0
0
1
0
2
0
0
0
3
1
0
0
0
0
0
0
2
0
0
2
0
0
1
2
1
0
0
2
0
0
2
2
2
0
0
0
0
0
4
1
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
2
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
2
0
1
0
0
1
0
2
2
0
0
2
0
2
0
0
0
0
2
1
0
1
1
0
0
0
0
0
0
0
0
0
1
2
4
0
0
0
0
0
0
2
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
6
0
0
1
0
0
0
2
0
2
0
2
1
1
2
1
0
0
0
1
0
0
2
0
1
0
0
2
1
0
2
0
0
0
0
0
0
0
1
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
1
3
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
1
2
0
0
2
1
1
0
0
2
0
2
1
2
0
0
1
2
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
1
0
0
0
1
1
0
0
0
2
1
0
0
0
0
0
0
0
2
3
0
1
0
0
3
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
2
1
1
0
0
0
0
0
0
0
0
1
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
1
0
0
0
2
5
0
2
0
0
0
8
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
1
0
1
2
0
2
2
0
0
0
0
1
0
0
0
1
1
0
0
0
0
2
0
1
0
0
0
0
2
0
0
2
0
0
1
1
2
0
0
0
0
0
0
1
2
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
1
3
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
3
0
2
2
0
2
2
1
0
0
0
0
0
1
0
0
2
0
2
0
1
0
0
2
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
1
0
0
0
0
4
2
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
2
0
0
0
0
2
1
1
1
0
0
0
0
0
1
0
0
0
0
0
2
0
4
2
2
1
1
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
2
2
2
0
1
1
0
0
0
0
2
2
2
0
2
0
3
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
5
0
0
1
0
0
0
0
0
2
0
1
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
1
2
0
0
0
2
2
0
0
1
2
1
0
0
0
1
0
2
0
1
0
0
2
2
1
2
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
1
0
0
1
2
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
2
0
0
1
0
1
1
1
2
0
0
0
0
0
2
0
0
0
0
0
0
1
1
2
0
0
1
0
0
2
2
0
0
0
0
1
0
0
2
0
1
2
2
2
2
0
0
0
0
0
1
2
1
0
0
0
1
0
0
2
0
1
0
0
0
0
0
2
2
0
0
0
0
0
1
2
0
0
2
2
2
3
1
0
0
1
1
1
3
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
1
0
0
0
3
1
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
2
2
0
0
2
0
1
0
1
0
0
0
0
0
1
0
1
2
0
1
2
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
1
1
0
0
0
2
1
2
0
0
1
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
2
2
0
2
2
2
1
2
0
0
2
1
0
0
1
0
0
0
2
0
0
0
2
3
0
0
0
2
2
0
1
0
0
0
2
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
3
2
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
1
2
0
2
0
1
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
2
0
0
1
1
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
1
1
0
0
0
2
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
9
0
0
4
3
0
0
0
0
1
1
2
0
1
1
0
2
0
2
0
1
0
0
1
2
0
2
0
0
0
0
2
0
0
0
2
0
2
0
3
2
0
1
1
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
1
2
2
0
0
0
0
0
0
3
0
2
0
0
0
1
2
1
1
2
0
0
0
0
1
0
1
0
0
0
0
1
0
2
1
0
2
2
0
2
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
3
1
0
0
2
0
0
0
1
0
0
3
0
0
1
0
0
0
0
0
0
0
2
0
0
1
5
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
2
0
2
1
0
0
0
0
0
3
4
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
4
1
1
0
0
0
0
2
0
2
1
1
0
0
1
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
1
0
1
0
0
1
1
1
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
1
2
0
0
2
0
1
3
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
1
0
2
0
0
2
0
1
0
0
1
1
0
1
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
1
2
0
0
0
0
0
0
2
3
0
1
0
0
1
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
1
0
0
2
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
2
0
1
1
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
4
0
1
0
2
2
0
2
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
9
2
0
0
2
1
1
1
1
1
2
1
0
0
0
0
0
0
0
1
3
2
2
0
3
0
1
2
0
1
0
1
0
0
0
0
0
0
2
1
0
1
0
2
0
0
2
0
0
2
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
1
0
0
0
0
1
1
0
0
0
0
0
2
1
0
2
0
0
0
1
0
0
5
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
2
2
0
0
0
0
2
2
0
0
1
0
0
1
1
0
0
0
0
0
0
2
1
2
0
0
0
1
0
0
2
0
0
2
2
1
0
0
2
0
2
1
0
0
0
1
0
2
2
0
0
0
2
0
0
0
1
0
0
0
1
0
0
2
0
0
1
0
0
0
1
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
2
0
1
0
0
0
2
0
0
0
1
0
2
0
0
2
0
0
0
0
1
0
1
1
1
0
0
0
0
1
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
3
0
2
0
0
0
2
2
0
0
0
0
0
2
1
3
2
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
1
2
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
3
1
0
0
1
2
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
3
0
0
1
0
0
0
0
2
0
0
2
2
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
1
0
0
2
0
2
2
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
1
0
3
1
0
0
0
2
1
1
2
2
0
0
2
2
0
1
1
2
1
1
1
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
2
1
2
0
2
0
2
0
0
0
0
1
0
0
0
1
0
1
2
0
0
1
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
3
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
2
2
0
0
2
1
1
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
2
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
2
2
0
0
1
2
0
2
1
0
0
2
0
0
0
0
1
2
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
3
0
2
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
3
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
2
0
2
1
2
0
0
0
0
3
2
0
1
1
2
2
2
0
0
0
0
0
0
1
2
0
2
0
0
2
0
1
0
0
0
2
0
0
1
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
2
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
2
2
0
0
0
1
2
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
3
2
2
0
0
0
0
0
1
1
0
2
0
2
0
1
0
0
2
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
4
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
2
0
0
2
1
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
1
1
0
0
1
0
0
0
7
0
1
0
0
0
0
0
0
1
2
0
0
0
0
3
1
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
1
0
1
2
0
1
0
2
0
1
0
0
0
0
0
0
1
0
1
3
0
0
1
0
1
2
0
2
2
0
2
0
0
0
0
0
1
0
0
0
5
0
0
0
0
0
0
1
0
0
1
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
2
1
0
0
2
0
0
0
0
0
3
0
1
0
0
2
0
0
4
0
1
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
1
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
1
2
1
1
0
2
2
0
0
2
7
4
2
0
0
2
8
0
0
0
0
2
2
0
1
2
2
2
0
0
0
0
0
0
1
0
1
1
0
0
0
2
1
0
1
0
0
0
2
0
1
2
0
0
0
0
2
0
2
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
2
1
0
1
0
2
1
1
2
0
3
1
0
0
1
1
1
0
0
0
2
1
0
0
0
1
0
0
2
1
0
0
0
2
0
0
0
0
1
0
1
0
3
0
0
0
0
2
0
2
4
1
1
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
3
1
1
0
1
0
2
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
3
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
1
0
1
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
2
0
1
0
0
0
1
0
0
5
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
3
2
3
0
1
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
5
0
2
0
0
0
0
0
2
0
0
2
5
1
0
0
0
2
2
0
0
1
1
2
0
0
1
0
0
1
2
0
0
0
0
0
2
1
0
0
1
0
0
2
0
0
4
0
1
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
1
1
1
2
2
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
1
0
0
0
0
0
1
0
2
1
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
1
0
1
2
0
0
0
1
0
0
2
1
1
0
0
2
0
3
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
3
0
0
0
0
0
1
2
1
1
1
0
2
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
2
2
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
1
0
3
3
0
1
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
5
1
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
3
1
0
0
0
0
0
2
2
0
0
0
0
1
0
1
0
0
2
0
0
0
1
1
1
1
1
2
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
1
0
0
2
0
0
3
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
2
0
1
2
0
0
0
4
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
1
0
1
0
4
0
2
0
0
0
1
3
1
0
0
1
1
1
0
2
1
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
1
1
0
0
0
0
2
0
0
3
0
2
0
2
2
0
0
2
0
0
0
0
0
0
3
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
1
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
2
2
0
4
1
0
0
0
1
0
0
1
1
0
0
1
2
0
1
0
0
0
4
2
0
0
0
9
0
0
0
2
2
2
3
0
2
0
2
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
3
1
0
0
1
1
2
2
0
1
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
2
2
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
2
2
0
1
0
0
0
0
0
0
1
0
2
1
0
1
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
4
0
0
0
3
0
0
0
2
0
0
0
3
0
0
2
0
0
0
2
0
0
0
2
0
0
2
0
1
1
0
0
0
0
0
0
3
0
2
0
0
2
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
1
0
0
0
0
1
2
0
1
0
4
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
2
0
0
0
0
0
1
0
1
0
0
5
1
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
2
2
0
1
0
1
0
4
0
0
2
2
0
2
0
0
2
0
0
0
2
0
1
1
0
2
2
0
0
0
0
0
0
1
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
3
2
0
1
0
1
0
0
2
0
2
2
1
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
2
3
2
0
2
0
0
1
0
0
1
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
4
0
2
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
5
1
0
0
0
5
1
1
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
2
0
2
0
1
0
1
0
2
0
2
1
0
0
0
0
0
0
0
2
1
0
0
1
2
2
0
0
0
2
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
1
0
0
0
1
2
1
1
3
1
1
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
1
0
0
0
1
0
1
0
0
2
0
0
2
0
1
0
0
0
2
0
0
0
9
0
2
2
0
2
2
0
1
0
0
0
1
1
2
0
0
0
1
1
3
0
1
0
0
1
1
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
3
1
1
4
2
0
0
0
1
2
0
1
1
2
5
0
2
1
0
0
0
0
1
2
0
0
1
2
0
0
1
0
1
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
1
0
3
0
1
0
1
0
0
0
1
2
0
0
1
0
0
0
9
0
2
1
0
0
1
0
1
0
0
0
0
1
0
2
0
2
0
2
0
0
2
0
2
1
0
2
1
0
3
0
0
2
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
2
0
0
0
0
1
1
0
0
2
1
0
0
0
0
1
2
3
0
2
0
0
2
0
0
1
2
8
2
1
0
2
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
2
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
1
0
0
2
0
0
1
2
0
0
0
1
0
0
0
1
1
0
1
0
0
0
1
0
0
2
2
0
2
0
0
0
2
0
2
0
1
0
0
2
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
2
0
0
2
1
0
1
0
0
0
0
2
0
0
2
0
0
3
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
2
3
0
0
0
0
1
0
2
1
0
2
0
2
0
3
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
1
0
0
0
2
2
0
0
1
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
1
0
2
0
0
2
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
2
2
1
0
0
1
0
0
0
1
2
0
0
0
0
2
0
2
2
1
0
0
0
1
0
1
0
0
2
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
1
2
0
0
0
2
0
0
0
0
1
2
1
0
0
0
2
0
0
0
0
2
0
0
0
0
4
0
0
0
1
0
0
2
0
2
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
1
1
0
0
0
1
0
0
1
2
0
2
0
2
1
1
0
0
0
3
2
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
1
1
1
0
0
2
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
1
2
2
0
2
2
0
0
2
0
0
0
2
0
0
0
0
0
2
2
0
1
1
0
0
2
0
2
0
2
0
0
0
2
0
2
0
0
0
2
0
0
2
1
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
1
4
1
0
0
1
0
1
0
0
0
0
0
0
2
2
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
1
0
0
2
0
2
2
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
2
0
0
1
1
1
0
0
0
0
0
2
1
0
2
2
0
2
0
1
0
4
0
0
0
0
0
2
0
0
0
0
1
1
1
0
0
0
0
2
2
0
2
2
0
0
1
0
2
0
1
1
2
0
1
3
0
0
0
2
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
2
0
2
0
1
0
2
1
3
0
2
0
0
0
1
1
0
1
0
0
2
0
1
0
0
0
0
2
3
2
0
1
0
2
0
0
2
0
0
0
0
0
2
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
2
0
0
2
1
0
0
0
2
1
1
0
2
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
2
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
1
2
2
0
0
0
0
0
0
0
2
2
0
0
0
1
1
1
0
2
3
0
2
0
0
0
2
0
0
0
0
2
2
0
1
0
0
0
0
0
0
1
1
4
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
3
0
1
0
0
0
0
2
1
0
0
0
0
1
1
0
0
0
0
1
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
1
2
0
0
0
0
0
2
1
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
2
0
0
4
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
2
2
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
2
0
0
0
0
1
2
0
1
1
0
1
2
0
0
0
0
0
1
2
0
0
4
0
2
1
2
0
0
2
1
1
0
0
0
0
0
0
2
2
0
4
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
2
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
1
0
2
3
0
2
0
0
0
0
0
2
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
1
0
0
0
1
0
0
0
0
1
1
1
0
2
0
0
0
2
1
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
1
0
0
3
0
2
0
2
0
0
1
2
2
0
0
0
0
2
2
0
0
0
0
2
2
2
0
0
0
0
0
0
2
1
1
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
2
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
1
0
1
0
2
0
1
1
0
2
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
1
1
0
2
1
2
0
0
2
0
2
0
0
0
0
2
0
1
0
1
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
2
0
1
1
0
0
2
0
1
0
1
2
2
0
0
1
1
0
0
1
3
0
0
0
1
1
2
2
3
0
0
2
2
1
0
0
0
0
0
2
1
0
0
0
0
4
2
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
2
0
0
2
0
0
0
4
0
2
0
1
1
1
0
0
0
1
3
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
2
1
1
0
0
0
2
0
1
0
0
3
0
2
2
0
2
0
0
3
0
0
0
4
0
0
1
1
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
2
0
3
0
1
1
0
0
0
2
0
2
0
2
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
2
0
2
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
4
0
0
0
0
0
2
1
0
0
0
3
0
0
0
0
2
1
0
2
1
0
1
4
2
0
3
0
1
0
0
2
0
0
2
2
2
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
2
2
1
0
1
0
3
0
2
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
2
3
0
0
0
2
0
0
2
0
0
0
1
2
0
0
0
1
0
2
0
1
0
2
2
0
0
0
3
0
0
0
2
0
3
0
0
2
0
0
1
0
2
1
1
0
2
0
1
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
1
2
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
1
2
0
0
0
0
0
0
1
2
0
2
0
0
1
0
0
0
0
4
0
0
1
0
0
0
2
0
1
1
2
0
2
0
2
0
1
0
0
0
1
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
2
2
0
0
0
2
1
1
0
0
1
0
0
2
0
4
0
0
0
1
0
0
1
1
0
0
0
0
1
2
0
1
0
1
2
2
0
2
0
1
0
0
0
1
0
1
0
0
1
2
2
0
0
0
0
1
2
2
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
1
2
0
2
2
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
3
0
2
1
0
0
0
0
0
0
2
0
2
1
2
0
0
2
0
2
0
0
1
1
0
0
0
0
0
5
1
0
1
0
0
0
1
0
0
2
2
4
0
1
0
2
0
1
1
1
0
0
0
0
0
0
0
1
0
0
2
2
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
1
1
1
1
0
0
3
0
1
2
0
0
2
0
0
1
0
2
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
3
0
1
2
0
3
0
0
1
1
1
0
1
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
1
1
1
1
0
0
0
1
2
6
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
6
0
1
0
1
1
2
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
2
2
0
0
1
0
1
0
0
0
0
0
2
0
0
0
1
0
1
0
0
1
0
0
0
2
0
2
0
0
0
2
1
0
0
2
2
2
0
0
0
0
0
0
2
0
0
0
1
1
0
0
2
3
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
1
1
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
2
3
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
1
0
2
0
2
0
0
0
0
0
3
0
0
2
0
1
3
0
0
0
1
0
0
0
0
2
0
2
2
0
1
1
0
2
1
0
2
0
0
2
2
0
2
0
0
0
1
2
1
0
0
0
4
1
0
2
0
1
0
0
0
0
1
0
1
1
2
0
0
0
1
0
1
0
0
0
2
0
0
1
0
2
1
0
2
1
2
2
0
0
0
1
3
2
2
0
0
2
0
1
0
2
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
1
0
4
0
0
0
0
0
1
1
0
1
0
2
0
0
2
0
1
3
0
1
2
1
0
1
0
1
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
2
3
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
3
0
0
0
4
0
2
0
2
0
0
0
0
2
0
3
1
0
0
2
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
2
0
0
0
2
1
0
0
0
1
1
1
2
1
2
1
0
0
0
1
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
5
1
0
0
0
0
1
1
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
2
0
0
0
1
0
2
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
1
0
0
1
0
0
5
2
0
3
0
0
2
0
1
2
2
0
0
0
0
2
1
2
0
0
0
2
2
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
2
2
1
1
2
0
0
0
0
0
0
0
0
2
1
0
2
2
0
0
0
0
0
1
0
1
2
3
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
2
0
2
0
0
1
0
0
1
2
0
0
2
0
0
0
0
0
0
1
3
0
0
0
0
0
2
0
0
0
0
0
2
2
2
1
0
1
1
1
0
0
1
0
0
1
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
1
2
0
1
1
0
0
2
0
2
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
2
0
1
1
0
0
2
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
1
2
0
2
0
1
0
1
0
0
0
1
0
0
0
0
2
0
0
4
0
0
0
1
0
7
0
2
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
3
0
0
0
2
0
0
1
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
2
2
0
2
1
2
0
0
1
0
1
3
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
1
0
1
0
0
2
0
2
1
0
0
0
2
2
0
0
1
0
0
0
1
0
0
1
1
0
1
1
0
2
2
0
0
0
0
0
5
2
0
0
2
0
0
2
0
2
1
1
2
0
0
1
1
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
2
5
0
0
0
0
2
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
3
0
0
2
2
1
0
0
0
0
0
1
0
0
2
2
0
0
2
0
0
2
0
0
0
0
0
0
2
0
1
2
2
1
0
1
2
0
0
0
0
1
0
1
1
2
0
1
2
2
2
2
0
0
0
2
2
0
2
0
0
0
2
0
0
2
2
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
2
0
2
0
0
0
2
2
2
0
0
2
0
0
1
0
0
0
0
7
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
2
0
0
2
0
0
0
0
2
1
2
0
0
0
0
0
0
0
2
1
2
2
0
1
0
2
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
2
0
0
0
0
0
1
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
2
0
3
0
0
2
0
0
0
0
1
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
2
1
2
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
2
0
2
0
0
0
2
0
0
1
0
0
0
1
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
2
1
0
3
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
2
0
0
0
2
2
0
0
0
0
0
1
0
0
0
2
0
3
0
0
0
2
2
0
0
0
0
1
0
0
1
1
0
1
1
0
0
0
0
0
0
0
1
4
0
1
1
0
2
2
0
0
0
2
1
0
0
0
0
0
0
0
2
3
2
0
2
0
0
1
0
0
0
2
2
0
0
0
2
1
3
0
0
2
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
2
1
0
0
0
2
0
0
0
0
1
4
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
1
0
0
2
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
1
0
0
0
1
6
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
2
1
1
1
0
0
2
0
1
2
1
0
0
0
0
2
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
1
0
0
1
0
0
0
0
1
3
0
2
0
0
2
0
0
0
0
1
0
3
0
1
0
0
0
1
2
0
0
0
0
0
1
0
2
0
2
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
2
1
0
2
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
2
0
1
0
0
2
0
0
0
0
2
0
2
0
0
2
2
0
0
2
0
0
2
0
2
0
2
0
0
0
0
0
2
0
2
0
0
0
1
2
2
1
1
0
2
0
0
2
0
0
2
0
0
0
2
2
2
3
2
1
2
2
1
2
0
2
4
2
0
2
0
0
0
2
2
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
1
1
1
0
2
0
0
0
2
2
0
0
0
2
0
2
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
2
1
2
2
0
0
0
2
0
0
3
1
0
2
4
0
0
0
0
0
0
2
2
0
2
3
2
2
2
1
1
0
0
1
2
1
0
0
0
1
0
0
0
0
0
0
1
0
5
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
1
2
2
0
1
0
0
0
0
1
0
0
0
0
3
0
0
0
1
0
2
0
0
2
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
2
2
0
0
2
2
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
3
2
0
0
0
0
2
2
1
0
2
2
0
0
0
0
2
0
0
2
1
0
1
0
2
0
0
0
1
0
0
3
0
0
1
1
0
0
0
7
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
1
0
1
2
0
2
3
2
0
0
0
0
0
2
0
0
0
2
0
0
2
0
2
0
3
2
0
0
1
0
0
1
1
0
0
0
0
3
2
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
1
0
0
2
1
2
0
0
0
1
0
0
1
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
1
3
0
0
0
0
0
0
1
0
2
2
0
2
0
2
1
1
0
0
3
1
0
0
0
55
0
1
1
0
0
0
0
0
2
1
2
0
0
0
2
0
2
0
0
0
0
0
3
0
3
0
3
1
0
0
1
0
0
1
0
0
1
1
1
0
2
0
2
0
0
0
1
1
0
0
0
1
3
0
0
0
0
2
2
0
0
0
2
0
0
0
2
0
1
2
0
3
0
0
1
1
0
0
0
0
0
1
0
0
2
0
1
0
0
2
0
0
1
1
0
0
1
0
1
1
1
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
1
2
2
0
0
0
2
0
2
0
0
0
1
1
0
0
3
0
0
1
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
2
0
0
2
0
1
0
0
0
0
0
2
2
0
0
0
0
0
3
0
1
0
0
0
0
0
1
1
2
2
1
3
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
1
2
0
0
0
0
1
3
0
0
0
3
0
3
2
0
0
0
7
0
0
3
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
4
0
0
0
0
0
0
0
0
0
1
0
0
1
2
2
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
3
2
1
0
1
0
0
1
0
1
1
2
0
1
1
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
2
1
0
0
0
1
2
2
1
2
0
0
2
2
0
2
0
0
1
0
0
0
0
3
0
4
0
1
1
0
0
0
1
2
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
2
0
2
0
1
0
0
1
0
0
0
1
0
0
0
0
1
2
0
0
1
0
0
0
0
0
2
0
2
1
0
2
1
2
0
0
2
0
0
0
0
2
0
0
0
3
0
0
2
0
2
0
1
0
0
0
0
0
4
0
0
0
0
0
0
1
0
1
1
2
2
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
1
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
1
2
0
0
0
1
1
0
2
2
2
0
0
2
0
0
1
0
0
1
0
2
0
0
0
0
0
1
0
1
0
0
2
0
0
1
0
0
2
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
2
2
2
1
2
0
2
1
0
1
3
1
2
2
1
0
0
1
0
0
1
0
0
6
1
0
0
1
0
1
1
1
0
0
0
0
0
4
1
0
1
0
1
0
0
2
0
2
0
1
1
0
1
1
1
1
0
0
0
2
1
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
2
0
1
0
0
2
0
0
3
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
2
2
0
2
0
2
0
2
0
0
1
1
0
0
0
1
0
0
0
1
0
0
3
1
0
0
1
0
0
0
0
0
1
0
0
0
5
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
1
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
2
0
0
3
3
0
0
0
1
0
0
0
0
1
2
0
0
1
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
2
0
0
0
5
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
2
0
2
0
0
2
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
1
0
2
0
2
2
2
1
1
0
0
0
0
3
5
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
1
0
7
0
0
1
1
0
0
0
2
0
0
0
2
0
0
2
0
1
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
2
2
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
2
1
0
0
1
0
0
0
0
2
0
0
0
0
1
1
0
0
0
3
0
0
2
0
2
0
2
0
0
0
1
1
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
2
0
1
0
0
1
2
0
0
0
3
0
0
3
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
2
0
3
2
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
3
0
4
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
1
1
1
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
1
1
0
0
5
2
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
1
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
1
4
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
1
0
2
0
2
1
2
2
2
0
0
0
0
0
0
2
1
0
0
1
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
2
0
4
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
13
2
0
0
2
0
2
1
0
0
2
0
2
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
2
1
2
0
0
1
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
3
0
2
0
1
0
0
0
0
2
0
0
3
1
3
0
0
0
0
2
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
2
1
2
1
1
3
0
3
0
0
0
2
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
2
1
0
2
0
0
0
0
0
0
0
1
1
2
0
0
1
0
0
0
0
0
0
0
0
1
0
2
1
0
2
0
0
0
0
0
0
0
1
1
1
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
1
1
1
0
0
0
2
0
2
1
0
5
0
2
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
1
4
0
0
1
0
0
0
1
2
1
2
2
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
1
0
2
2
0
0
0
1
0
0
0
0
0
1
0
2
0
1
1
0
0
1
2
0
0
2
0
1
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
3
0
1
1
0
0
2
2
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
2
0
1
0
0
1
1
1
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
1
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
2
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
2
1
0
2
0
0
0
0
2
0
0
4
2
2
0
3
2
0
2
2
0
0
0
1
2
0
1
0
0
0
0
0
0
0
1
0
0
2
2
0
2
0
0
0
0
0
2
0
2
2
1
0
0
2
0
0
0
2
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
2
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
2
3
0
0
0
0
2
0
0
1
1
0
0
2
2
0
0
0
0
0
0
0
0
2
0
2
0
0
2
2
0
0
0
0
0
2
1
2
0
2
0
0
2
0
0
2
1
0
2
0
0
0
2
0
1
0
2
0
1
0
0
1
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
3
2
2
0
0
0
0
2
0
0
3
0
1
1
0
2
0
2
0
2
0
2
0
0
2
2
1
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
1
0
0
0
0
0
1
1
1
0
0
2
2
0
0
2
0
2
0
0
0
1
0
2
0
0
2
0
0
0
0
2
2
0
1
0
1
0
1
3
0
0
0
2
0
2
2
0
0
0
0
0
0
2
0
0
1
0
1
2
0
1
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
1
0
1
0
1
0
1
0
0
2
0
1
0
2
2
0
0
1
2
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
2
0
0
1
2
0
0
2
0
0
1
2
1
1
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
2
1
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
1
0
0
1
2
0
0
0
1
0
2
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
2
2
0
2
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
3
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
3
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
2
2
0
1
0
0
0
0
0
0
1
2
2
6
0
0
0
0
2
1
0
2
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
3
0
1
1
0
2
0
2
0
2
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
1
0
0
0
1
2
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
5
0
1
0
2
0
0
0
2
0
2
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
1
1
1
0
1
1
0
0
0
0
0
0
0
3
2
0
0
0
0
1
0
0
0
1
0
0
2
2
0
1
2
0
0
2
0
0
0
2
0
2
1
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
2
0
2
2
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
2
0
0
2
1
0
1
0
0
0
2
1
0
1
1
0
0
1
2
0
0
2
0
0
0
2
2
0
0
2
3
2
2
1
0
1
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
4
2
2
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
2
0
2
0
0
0
1
0
0
2
0
0
2
0
0
1
2
0
1
2
0
0
0
2
1
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
1
0
2
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
6
3
1
1
0
2
0
2
2
0
4
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
1
0
1
0
0
4
0
0
0
2
0
0
0
1
1
3
0
0
1
0
2
3
0
0
2
0
1
0
2
2
0
0
0
0
0
2
1
1
0
0
0
0
1
2
0
0
0
0
0
1
1
0
3
1
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
1
1
0
0
2
1
2
0
0
2
1
0
1
2
0
0
0
2
2
0
0
0
1
1
1
0
0
0
2
0
2
0
0
1
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
2
0
2
1
0
0
0
0
0
2
0
0
2
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
1
0
0
0
2
2
0
1
0
0
2
1
0
0
0
0
0
0
0
1
2
0
1
0
0
0
2
0
0
0
0
2
2
0
0
2
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
1
0
1
1
1
0
0
2
0
0
0
0
2
0
2
0
1
1
0
0
0
2
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
4
0
0
0
2
1
1
1
0
0
7
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
2
0
0
0
0
2
1
0
0
0
2
0
1
1
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
1
0
0
0
1
0
0
0
3
0
0
2
1
0
3
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
2
1
0
0
0
0
0
0
3
2
2
1
2
0
0
0
1
0
0
2
2
0
0
0
0
2
0
0
0
3
0
1
1
1
0
0
0
0
2
0
0
2
0
0
1
0
0
2
0
1
2
0
0
4
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
2
0
0
0
0
0
1
2
0
0
2
0
1
0
2
0
0
1
0
0
1
2
0
0
1
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
1
0
0
0
0
0
0
1
2
0
1
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
2
0
2
2
3
0
0
0
0
0
0
2
0
2
0
1
0
2
3
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
3
1
0
1
0
2
0
0
0
0
0
1
4
0
2
0
0
2
0
0
0
2
0
1
1
1
1
0
0
1
0
2
0
1
0
0
3
1
0
0
2
0
1
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
2
0
0
0
0
0
2
0
1
0
1
0
0
0
0
2
0
1
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
2
2
2
0
0
2
0
0
0
1
0
1
0
2
0
0
2
0
0
0
2
1
1
0
0
1
0
0
0
1
2
0
0
0
0
1
1
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
5
0
0
1
0
0
0
2
1
0
0
0
1
2
0
2
0
0
0
2
2
2
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
2
2
0
0
0
2
0
0
1
1
1
0
2
0
0
1
0
0
0
2
1
0
2
2
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
1
0
0
0
0
0
2
1
5
3
0
0
2
1
0
0
0
0
2
0
0
0
1
1
2
2
1
0
0
0
0
1
0
0
1
0
2
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
1
0
2
0
0
0
1
0
1
0
0
0
0
0
3
0
0
0
0
1
2
0
3
0
0
2
1
0
0
0
0
0
0
0
0
1
0
1
1
0
1
2
0
1
0
1
2
0
0
0
0
0
1
0
0
1
2
1
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
2
0
2
0
3
1
1
0
2
1
0
0
0
2
0
0
0
0
0
2
2
1
1
0
2
3
0
0
0
0
0
2
1
0
0
0
0
0
2
2
0
2
0
0
0
3
0
2
1
0
2
0
1
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
2
0
0
0
2
0
3
0
2
0
0
2
1
0
1
1
0
0
0
3
0
1
1
0
0
0
0
1
0
2
0
1
0
1
2
0
2
2
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
3
1
0
3
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
1
2
0
0
0
1
0
0
2
0
0
0
0
0
1
1
0
1
0
0
0
1
0
1
0
1
0
1
0
0
0
2
0
0
1
0
1
1
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
3
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
1
0
1
1
2
0
0
2
1
1
0
0
0
0
1
0
1
2
2
1
0
0
0
2
0
2
0
1
1
0
3
1
0
0
0
0
2
0
2
1
1
4
2
0
0
0
0
0
2
1
0
0
0
0
0
0
1
2
1
3
1
0
0
0
0
1
2
0
0
2
1
0
0
0
1
0
3
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
1
0
3
1
0
3
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
2
3
0
0
0
0
0
0
0
0
4
2
0
2
2
3
2
0
0
2
0
0
2
2
0
2
2
0
0
2
2
0
0
0
0
1
1
2
4
0
1
0
0
0
0
2
2
1
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
2
0
2
0
0
1
2
0
0
1
1
1
1
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
1
1
1
0
1
2
0
0
3
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
3
0
0
0
0
1
2
2
0
0
0
0
2
0
0
0
0
0
2
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
1
0
2
3
2
0
1
0
3
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
2
1
1
2
0
1
0
1
0
0
1
0
4
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
2
2
2
0
0
0
0
0
0
0
1
0
1
0
0
2
0
1
0
0
1
0
0
0
0
0
0
2
1
2
0
0
0
0
0
2
0
0
0
2
0
0
0
1
1
0
0
0
2
1
2
0
0
0
0
0
0
0
0
1
0
0
2
1
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
2
2
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
1
0
0
1
2
0
2
0
0
2
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
2
0
1
0
1
0
1
0
0
1
0
0
0
0
0
1
2
3
3
0
2
0
0
0
1
2
0
0
2
0
0
0
2
1
0
0
2
2
0
1
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
4
0
2
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
1
2
0
1
0
0
1
0
2
2
1
1
2
2
0
1
0
1
0
2
2
0
2
0
1
0
0
0
2
0
1
1
2
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
1
2
1
0
2
0
1
2
0
0
0
0
0
1
1
2
1
0
0
2
1
1
0
0
1
1
1
0
0
0
0
1
1
0
0
0
0
0
0
2
0
2
0
0
0
1
1
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
1
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
1
1
2
0
0
0
0
1
2
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
2
0
0
4
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
1
2
6
0
0
0
0
0
0
5
0
0
2
0
0
0
2
1
0
0
0
0
0
2
0
0
4
1
0
0
0
0
1
0
0
0
0
0
0
0
1
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
2
1
1
0
0
0
2
2
3
2
0
0
0
0
0
2
1
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
2
2
1
2
0
0
0
4
1
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
1
1
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
3
0
0
2
0
3
0
0
0
0
1
0
2
3
1
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
1
0
1
0
0
1
0
3
0
0
1
3
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
1
2
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
1
2
0
2
1
2
1
0
0
0
0
0
0
1
2
1
6
0
0
1
1
0
0
0
2
0
1
0
1
1
0
3
0
0
0
0
2
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
2
3
0
0
0
1
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
4
2
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
2
2
1
0
0
4
0
0
0
2
0
0
0
0
3
0
0
1
0
3
0
0
0
0
2
1
1
1
0
3
0
0
0
0
2
0
2
0
1
1
0
0
0
0
1
2
1
0
0
0
0
0
2
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
2
1
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
1
0
0
1
2
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
2
0
2
4
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
6
2
3
0
0
2
0
0
0
0
0
0
2
0
2
2
3
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
2
2
0
1
0
1
0
0
0
2
1
1
0
1
0
0
0
0
0
2
2
0
0
0
0
4
1
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
3
1
1
0
1
2
0
0
0
0
2
2
1
2
1
1
0
0
0
1
0
0
1
1
0
1
0
1
0
0
2
0
0
0
1
0
2
0
1
1
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
1
1
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
4
1
1
0
2
1
0
0
0
1
0
2
0
1
2
0
1
2
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
2
2
0
0
1
1
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
1
0
1
0
2
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
3
0
0
1
0
0
0
0
1
0
1
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
2
2
0
0
0
0
0
0
2
0
0
1
1
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
6
0
2
2
2
0
0
1
2
0
0
2
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
1
1
0
1
0
0
0
0
0
1
0
0
0
3
0
1
0
0
1
0
0
0
0
0
2
0
1
0
4
0
1
1
0
2
1
1
0
0
0
2
2
0
0
0
0
2
1
0
0
0
0
1
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
2
0
2
1
0
0
0
2
2
2
1
2
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
1
0
0
0
1
2
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
2
0
1
0
0
0
2
0
2
1
0
2
1
2
1
1
2
0
0
2
1
0
2
0
0
0
0
2
0
2
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
2
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
3
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
1
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
2
1
0
0
0
0
1
1
1
2
1
0
0
0
0
0
2
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
2
0
0
1
0
0
0
1
0
0
0
3
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
2
2
0
0
0
1
0
0
2
2
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
1
0
0
0
0
1
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
1
0
0
1
0
0
1
0
0
0
2
2
0
2
1
3
0
0
0
0
1
0
1
0
0
2
2
0
0
0
2
1
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
3
0
0
0
0
0
0
2
0
4
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
2
2
0
1
0
0
0
0
0
0
0
0
1
2
2
0
0
0
2
0
0
0
2
0
3
0
1
0
0
1
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
1
0
0
0
1
0
1
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
2
1
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
2
2
0
0
0
0
2
0
0
0
2
3
0
0
0
5
2
0
0
0
0
0
0
0
0
2
1
1
0
0
2
0
0
0
2
0
1
0
0
1
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
2
1
1
0
0
0
0
2
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
2
2
1
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
2
0
0
1
0
1
0
0
2
1
2
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
2
1
1
0
0
1
2
2
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
3
0
2
0
0
0
1
0
0
1
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
3
2
0
0
1
0
0
2
0
2
0
1
0
0
0
0
0
1
0
1
0
0
0
0
2
1
1
0
0
2
4
2
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
5
0
0
0
0
1
1
0
0
0
0
0
2
0
0
2
1
0
0
2
4
0
2
0
0
0
0
1
0
1
2
3
0
0
0
1
0
1
2
0
0
1
1
0
0
1
0
0
0
2
2
1
0
0
0
0
0
0
0
0
1
0
2
2
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
3
0
0
1
0
0
2
1
1
2
0
0
4
0
0
0
2
3
0
2
0
2
0
2
2
0
2
0
0
0
0
0
1
2
0
0
1
0
0
0
0
2
0
2
0
2
2
0
0
0
0
1
0
1
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
2
0
0
0
1
2
0
0
2
1
3
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
1
2
0
0
0
2
1
0
0
1
3
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
1
1
2
0
0
1
0
1
0
3
0
1
0
3
0
0
0
2
0
0
2
3
1
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
1
0
0
0
0
0
1
1
0
1
0
0
1
0
0
2
0
0
0
2
0
0
2
0
0
0
0
2
1
0
1
1
2
0
0
2
2
0
1
1
1
1
0
1
0
0
0
1
0
0
2
2
0
0
3
1
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
3
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
1
1
2
0
0
0
1
0
0
1
0
1
2
0
0
0
0
0
0
2
3
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
2
1
2
0
0
0
0
2
1
0
0
0
0
1
1
2
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
4
1
1
1
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
2
2
0
0
0
2
0
0
0
2
0
1
0
2
3
0
1
0
0
5
0
1
0
1
0
0
0
0
0
2
2
0
0
0
0
2
0
1
0
2
2
0
2
0
0
0
0
0
0
4
1
0
0
0
0
2
1
3
0
0
0
0
5
0
2
0
0
0
1
0
2
0
0
2
0
0
2
0
0
0
0
2
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
2
1
0
1
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
2
0
2
2
2
0
0
0
0
0
1
0
1
0
0
0
2
2
0
2
0
0
1
0
0
0
0
1
0
0
0
0
2
2
0
2
0
1
1
1
1
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
2
1
0
2
0
2
1
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
1
6
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
2
1
0
0
0
0
2
2
0
0
2
0
0
2
2
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
1
2
0
2
0
0
0
0
2
1
0
1
2
2
0
2
0
0
0
0
2
2
1
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
2
0
1
0
0
2
0
3
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
2
1
0
0
2
0
2
1
2
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
1
1
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
1
0
0
1
2
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
2
0
1
0
0
1
0
2
0
2
0
1
1
0
0
1
2
0
1
0
0
0
0
3
1
0
0
0
1
1
2
2
0
0
1
0
1
2
0
2
0
0
0
0
0
0
1
0
0
2
1
0
0
2
0
0
0
2
2
2
2
1
0
1
0
1
0
0
0
0
0
1
1
0
0
0
1
0
1
2
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
1
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
3
1
1
2
1
0
1
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
2
0
1
0
0
1
2
0
0
1
1
0
0
0
2
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
1
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
1
0
2
1
0
0
0
2
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
1
2
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
3
0
1
0
0
0
0
4
1
0
0
0
2
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
2
1
0
1
0
0
0
0
2
0
1
0
0
0
0
1
0
2
0
1
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
1
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
2
0
1
0
2
0
0
2
0
0
0
0
0
0
2
0
1
0
0
1
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
3
0
1
0
0
0
2
2
0
2
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
2
0
2
0
0
0
1
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
3
0
0
2
1
0
0
0
1
0
1
0
0
2
0
0
2
0
0
1
2
1
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
2
0
1
1
1
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
7
4
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
6
0
2
2
0
0
2
0
3
0
0
0
1
0
0
0
0
1
0
0
2
0
2
0
1
0
1
1
3
0
2
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
1
1
0
0
0
0
0
2
0
1
1
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
2
1
3
1
1
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
3
0
0
0
0
2
0
2
0
2
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
1
2
0
2
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
5
1
1
0
0
2
1
1
0
2
2
2
0
2
0
2
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
3
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
4
0
0
1
1
0
1
3
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
2
0
2
0
1
1
1
0
0
0
0
0
0
2
2
0
3
2
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
3
2
1
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
1
0
0
0
2
0
0
0
1
1
0
0
1
0
2
0
1
1
2
5
0
2
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
3
6
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
2
1
0
0
0
1
1
3
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
1
0
0
2
1
0
0
0
0
3
0
0
1
1
0
0
0
0
0
0
0
3
0
1
0
1
2
0
0
0
0
0
2
0
0
2
2
0
2
2
1
0
1
0
0
0
0
0
1
0
2
0
0
0
1
3
0
2
5
0
0
0
0
0
0
2
0
0
0
0
2
4
0
0
2
2
0
0
2
3
0
0
0
0
0
0
2
1
3
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
2
2
0
1
2
0
0
1
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
4
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
1
0
2
1
0
1
2
0
2
0
2
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
1
1
0
0
2
0
5
1
0
1
0
4
1
0
8
0
0
2
0
2
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
1
0
0
0
0
0
0
3
0
2
0
1
2
0
1
1
0
2
1
0
2
0
21
0
0
2
0
1
0
1
0
0
1
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
2
2
0
0
1
0
0
1
0
0
1
0
0
0
2
4
1
1
0
0
0
0
0
1
1
1
2
0
0
0
0
1
0
0
1
0
0
1
1
1
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
2
1
0
1
0
0
0
1
1
0
2
0
2
0
0
0
0
0
1
0
0
1
0
2
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
1
0
2
0
2
1
0
0
0
1
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
1
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
3
0
0
1
0
0
0
0
0
1
3
0
0
1
1
0
2
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
3
0
5
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
1
1
2
0
1
0
0
0
4
0
1
2
2
0
0
0
0
3
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
5
3
2
2
2
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
3
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
2
0
2
1
0
1
2
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
1
2
1
0
0
0
0
1
0
0
0
0
1
4
0
2
0
0
0
2
1
2
0
1
2
0
2
2
1
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
2
2
0
0
0
0
0
1
2
0
2
0
2
4
1
0
2
0
0
0
0
0
9
0
2
0
0
0
0
0
4
2
1
2
0
0
0
0
2
0
1
1
0
0
0
4
2
0
0
3
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
1
2
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
3
2
2
0
0
1
0
0
0
0
0
1
0
2
2
2
0
0
0
1
0
0
2
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
1
0
0
2
0
0
0
1
2
0
1
0
0
0
0
0
1
1
0
0
1
1
0
0
2
0
2
1
0
0
1
1
0
2
2
1
2
0
0
0
0
0
0
0
1
0
0
0
1
16
1
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
1
0
0
1
0
0
0
1
2
3
1
11
0
2
0
0
0
2
0
0
2
1
0
2
0
0
0
0
1
0
2
0
0
1
0
2
0
3
0
5
2
2
2
1
0
0
0
0
1
2
2
0
2
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
2
0
2
0
1
0
0
1
0
0
0
2
0
0
2
0
1
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
1
0
0
0
3
1
3
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
2
0
0
0
0
1
3
1
0
1
0
0
0
0
0
2
1
0
1
2
0
0
0
1
0
1
0
2
0
0
1
0
1
0
0
2
0
2
0
0
2
0
0
0
0
1
2
2
0
1
1
1
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
2
1
0
3
0
0
2
0
2
0
1
1
0
0
2
0
0
0
0
0
2
0
0
2
1
0
4
0
0
1
0
0
1
0
2
3
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
1
0
2
1
1
0
1
1
0
1
0
2
0
0
0
0
0
1
2
0
0
0
0
0
1
2
0
0
2
0
0
0
0
2
0
0
2
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
1
2
1
3
0
3
0
1
0
2
0
2
0
0
2
1
0
0
1
2
0
1
0
0
2
0
0
0
3
0
2
0
2
0
0
1
0
0
0
2
0
1
2
1
1
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
1
0
0
0
0
0
0
3
1
2
0
0
2
0
2
0
0
1
0
0
2
0
0
2
2
0
1
1
0
0
0
0
1
0
0
0
2
0
1
0
0
1
0
2
0
1
2
0
0
0
0
2
2
1
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
1
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
1
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
2
0
0
0
1
2
0
0
3
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
3
0
1
3
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
2
0
1
2
1
0
2
1
6
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
1
0
0
2
0
0
2
0
0
0
1
0
1
0
2
0
0
2
0
0
0
1
4
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
2
0
0
1
0
0
0
0
0
0
0
2
2
0
0
2
1
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
1
2
0
0
0
0
0
1
1
0
0
0
1
0
0
3
1
0
2
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
1
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
5
1
2
0
0
0
0
0
1
2
0
0
1
0
2
0
0
2
0
1
0
2
0
2
0
0
0
0
2
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
6
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
2
0
0
2
1
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
2
0
0
2
0
0
0
3
0
0
0
1
1
2
0
1
0
3
2
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
2
1
0
0
1
0
1
0
0
0
2
0
0
0
3
0
0
0
0
1
1
2
0
0
0
2
0
0
1
2
0
0
1
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
3
0
2
0
0
0
0
1
0
0
0
2
0
2
0
1
0
0
1
1
1
0
2
0
0
0
1
1
0
0
2
0
0
2
0
0
0
2
2
0
0
2
0
0
0
0
0
0
2
0
0
1
2
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
1
0
2
2
0
0
1
0
0
0
0
1
0
0
0
0
0
3
0
0
0
2
0
1
0
0
0
5
0
2
0
0
1
0
0
0
0
2
0
0
4
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
1
0
2
0
1
0
0
0
3
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
2
2
2
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
6
0
0
2
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
2
0
2
0
0
1
2
0
0
0
1
0
0
0
2
1
0
0
1
1
0
2
2
0
0
0
0
4
0
0
2
0
0
1
2
0
2
0
1
0
0
0
0
2
0
0
0
0
2
3
0
1
0
0
0
0
0
0
1
0
1
1
1
1
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
2
2
0
0
1
1
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
1
0
0
1
3
0
0
0
0
0
0
0
2
4
0
2
0
0
1
0
0
0
2
0
1
1
0
2
0
1
0
0
2
0
0
0
0
0
3
0
1
1
1
0
0
0
0
0
2
0
0
1
0
0
1
0
0
2
0
0
1
0
0
0
1
1
0
0
2
0
0
0
0
2
0
2
2
1
0
2
0
0
0
0
0
2
0
1
1
0
1
0
0
1
1
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
2
0
1
1
0
1
2
1
3
2
0
0
0
0
0
0
0
3
0
3
0
0
0
0
2
0
0
1
0
0
0
0
0
2
1
1
0
1
0
0
1
1
0
0
0
1
0
0
0
0
1
2
0
3
2
1
0
0
0
0
4
0
1
0
0
1
1
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
2
0
1
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
4
0
0
0
0
2
1
0
0
0
0
1
0
0
2
0
0
0
2
0
2
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
2
0
2
0
2
0
0
0
2
0
0
0
1
1
0
0
2
1
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
2
2
1
2
0
0
0
2
2
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
1
2
0
0
0
0
0
0
0
0
3
0
0
1
0
3
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
2
1
0
0
1
0
0
0
2
0
0
0
2
0
1
0
0
0
0
2
0
3
0
0
1
0
0
0
0
0
0
2
3
4
1
0
1
0
0
0
0
0
2
0
0
0
1
1
1
0
1
2
0
1
1
0
1
0
0
0
0
2
0
2
0
0
0
2
2
0
2
1
0
1
0
0
2
0
0
0
0
2
0
0
0
1
1
0
1
2
2
0
1
2
0
0
0
0
3
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
1
0
1
2
0
2
0
0
0
4
0
0
0
0
2
0
2
0
2
1
0
2
0
0
0
3
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
2
2
1
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
2
0
0
1
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
1
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
1
1
0
0
0
0
2
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
2
1
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
2
2
0
0
1
0
0
2
2
1
0
2
0
1
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
2
1
0
1
0
2
0
0
4
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
2
2
0
0
0
1
0
0
1
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
2
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
1
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
2
0
0
1
2
0
0
2
0
0
0
2
1
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
2
1
2
1
3
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
1
0
0
0
0
0
0
3
0
1
1
0
2
0
0
0
0
0
0
1
0
2
2
0
0
0
2
0
0
2
0
0
0
0
1
0
1
0
0
0
1
1
2
0
1
0
0
0
0
0
0
0
2
1
1
2
0
2
2
0
0
0
0
0
1
0
0
3
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
1
2
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
2
1
2
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
1
2
0
0
0
0
2
0
1
2
3
0
0
0
0
1
0
0
1
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
6
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
1
0
2
0
0
2
0
1
0
0
0
0
0
0
1
1
0
0
0
0
2
2
0
0
1
0
0
0
0
2
0
2
2
0
0
0
0
1
1
2
2
0
1
2
2
0
0
2
0
0
1
0
2
1
3
0
0
1
2
2
0
1
2
8
0
0
2
2
2
0
0
1
0
0
0
1
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
2
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
2
2
3
0
2
0
0
0
0
4
0
2
1
0
2
2
0
2
0
0
0
2
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
1
2
2
1
0
0
0
2
2
1
1
2
1
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
2
0
2
0
0
0
0
0
5
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
2
2
0
1
0
0
0
1
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
1
0
0
2
0
1
0
2
0
0
2
1
2
0
1
2
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
2
1
4
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
1
2
2
0
0
4
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
2
4
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
2
0
0
2
0
0
0
0
2
0
0
2
2
0
0
0
2
0
0
0
0
2
0
2
0
0
0
1
0
0
3
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
2
1
1
1
0
0
0
0
0
0
0
0
0
3
2
0
0
2
0
0
2
2
0
1
0
0
0
0
0
0
1
1
2
1
0
0
0
0
0
2
2
1
0
0
0
0
0
1
0
0
0
2
1
0
1
0
1
0
0
0
1
0
3
2
0
0
0
0
2
0
0
1
0
3
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
2
0
0
0
0
1
0
2
2
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
3
0
1
0
0
0
2
2
0
0
0
0
0
1
8
2
1
0
2
0
0
1
0
0
0
0
0
0
1
2
0
0
1
0
0
0
1
1
0
1
1
0
0
2
0
0
0
0
2
0
0
1
2
0
0
2
0
0
0
2
0
0
0
0
0
0
2
1
0
2
1
2
2
0
1
2
0
0
3
0
2
0
0
0
2
1
0
0
0
1
2
0
1
2
0
2
1
0
0
0
0
0
0
0
2
0
0
1
0
0
1
1
2
1
1
0
1
1
1
0
0
0
2
0
0
2
2
0
0
0
1
1
3
0
0
1
0
0
2
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
2
0
0
0
0
0
1
3
1
0
2
0
0
3
1
2
0
2
0
1
0
2
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
3
0
0
0
1
0
0
0
0
0
0
0
1
0
2
5
0
0
2
0
0
0
1
0
1
0
1
0
0
0
2
2
0
0
0
0
1
0
3
0
11
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
1
1
2
0
0
0
1
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
1
0
1
0
1
0
0
1
1
0
2
2
3
2
0
2
1
0
0
0
0
2
0
1
2
0
0
3
0
2
0
1
0
2
1
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
2
0
2
2
2
0
0
1
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
4
0
3
2
2
0
0
0
0
4
1
0
0
0
0
1
0
0
0
0
0
1
0
4
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
2
2
0
1
0
0
0
0
1
0
2
1
0
0
0
0
0
2
0
4
2
0
3
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
4
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
3
1
0
0
0
2
2
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
2
0
1
0
2
2
0
2
0
0
0
2
1
3
0
0
2
0
2
1
0
0
1
2
0
0
0
0
0
0
0
0
1
1
2
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
2
1
0
0
0
3
0
0
0
2
0
0
0
2
1
0
1
2
0
3
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
1
2
1
0
0
0
0
2
2
2
0
1
0
0
0
1
2
0
0
1
1
2
0
1
0
0
0
0
1
3
0
1
0
2
1
2
0
0
1
0
2
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
3
0
2
2
1
0
0
0
0
1
0
0
0
1
0
2
0
0
0
1
0
0
0
3
0
0
0
0
0
2
0
0
0
0
1
1
2
1
1
0
0
4
1
0
1
0
1
0
0
1
0
2
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
2
2
4
0
1
0
2
2
0
0
2
2
0
2
0
2
0
4
0
0
0
1
0
1
2
0
0
1
0
0
1
0
1
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
2
2
2
2
1
1
0
0
0
0
0
1
2
0
0
1
0
0
1
0
10
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
2
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
1
2
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
1
0
0
1
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
2
1
1
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
1
0
0
0
0
0
2
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
1
0
1
0
0
1
2
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
2
0
1
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
2
2
0
1
0
0
1
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
1
7
0
1
0
0
2
0
1
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
3
0
1
2
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
3
0
0
0
0
1
0
0
0
0
1
1
0
1
0
1
2
0
2
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
1
0
1
0
2
0
0
0
2
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
2
1
0
2
0
0
2
1
0
0
0
0
1
0
0
1
0
1
0
0
1
0
2
1
0
0
1
0
0
2
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
2
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
4
0
1
0
0
2
0
0
0
2
0
0
0
1
0
0
0
2
0
1
0
0
0
1
0
0
0
0
5
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
1
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
1
2
0
2
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
2
0
1
4
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
2
0
1
0
0
4
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
3
2
0
3
0
2
0
0
0
0
0
2
0
1
0
2
0
0
2
0
0
0
0
3
0
0
0
1
1
3
3
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
2
1
0
0
1
0
0
0
1
0
0
2
1
1
0
0
0
2
0
1
1
0
0
3
1
6
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
4
3
1
0
0
1
0
0
0
2
0
0
1
1
0
2
0
0
0
0
1
0
0
0
0
2
2
1
2
0
3
0
0
0
1
2
0
0
0
0
4
0
0
0
0
0
1
0
0
0
1
0
0
2
0
1
0
2
0
0
0
0
0
1
0
1
1
0
1
0
0
0
1
2
1
0
0
1
0
0
0
1
0
1
0
0
0
0
2
2
1
0
0
2
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
4
0
2
1
0
1
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
1
1
1
0
0
2
1
3
0
1
0
0
0
0
0
1
0
0
2
1
0
1
1
1
0
0
0
2
0
0
0
1
0
0
1
0
0
0
1
4
0
0
2
0
0
0
1
2
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
1
0
0
3
2
0
0
1
1
1
2
0
2
0
0
0
2
0
2
2
0
2
0
0
0
2
0
0
0
1
1
3
0
0
0
0
0
1
0
0
2
0
0
0
0
2
2
0
2
0
1
1
2
1
2
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
1
0
0
2
1
0
0
2
0
2
0
1
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
2
2
2
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
2
1
0
0
0
0
2
1
3
0
1
0
0
1
0
0
0
0
1
1
2
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
2
0
0
2
2
0
0
0
1
1
0
0
2
0
0
0
0
0
0
1
2
1
2
2
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
2
3
0
0
3
0
2
0
0
2
0
1
0
1
0
2
0
0
0
0
1
2
2
2
0
0
0
0
0
5
3
0
3
2
0
0
2
1
2
2
0
0
1
3
0
1
2
0
0
2
0
0
0
2
0
1
0
1
0
0
0
3
1
0
0
0
0
1
2
1
0
0
1
2
0
0
1
0
0
1
0
0
1
0
2
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
1
2
0
0
0
0
2
0
0
0
0
2
0
0
1
2
0
2
0
0
1
2
0
2
0
0
2
0
0
0
1
0
1
0
1
0
0
1
0
0
0
1
0
0
1
0
2
0
0
3
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
2
0
0
0
2
0
1
1
1
0
0
0
0
0
1
0
2
2
2
0
0
0
2
0
0
0
1
0
1
1
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
2
2
1
0
1
2
0
0
0
0
0
0
2
1
0
2
0
2
3
5
0
0
0
0
0
3
0
0
0
0
0
2
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
2
1
2
2
0
0
0
0
3
0
0
1
1
0
0
0
1
0
2
1
2
2
0
1
0
0
0
0
0
0
1
0
0
0
0
1
4
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
2
0
2
1
0
1
0
0
0
0
0
0
0
2
0
0
1
0
1
2
0
0
0
1
0
1
0
0
2
0
0
0
0
2
0
0
2
2
0
0
0
1
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
1
0
2
0
1
0
0
1
0
0
1
0
0
1
0
1
1
0
0
0
2
0
1
2
0
0
0
1
0
0
0
0
2
0
0
0
3
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
1
2
0
0
1
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
2
0
2
2
0
0
0
1
1
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
2
0
0
0
1
2
1
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
1
0
0
0
0
2
0
0
2
3
4
0
0
2
0
0
0
0
2
2
0
2
0
3
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
3
2
0
0
0
2
0
0
0
1
0
0
2
1
2
0
0
0
2
0
0
0
2
0
0
2
0
0
2
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
2
0
0
0
2
0
2
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
2
1
2
0
2
0
3
2
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
2
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
1
2
3
0
2
0
0
1
1
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
1
1
0
2
0
1
2
2
0
0
0
0
2
0
0
0
2
1
0
1
0
0
1
0
0
0
0
1
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
1
2
0
0
0
0
2
1
0
0
0
1
0
1
1
0
2
0
0
0
2
2
0
0
0
2
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
1
1
3
0
0
0
0
0
0
0
2
0
0
1
1
1
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
1
0
1
0
1
1
0
0
0
0
2
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
1
0
0
0
0
2
0
0
2
0
0
2
0
2
0
0
0
2
1
1
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
2
2
2
0
2
1
0
1
1
2
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
1
1
0
0
2
0
0
0
0
0
2
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
2
1
0
0
2
0
0
1
0
0
0
0
1
0
2
2
0
1
1
0
3
2
2
0
1
1
2
0
1
1
0
2
0
1
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
2
1
0
0
0
1
0
0
0
0
2
0
0
0
1
1
0
0
3
1
0
0
2
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
2
0
1
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
2
0
0
2
0
0
1
0
1
0
0
0
0
0
1
0
1
4
0
0
0
0
2
0
1
2
0
0
0
0
0
0
1
2
0
3
0
0
1
0
0
0
2
0
0
0
3
1
1
2
0
0
2
0
2
0
2
0
0
0
0
0
2
2
2
0
0
1
0
0
0
0
0
1
0
2
0
0
1
0
0
2
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
4
0
0
1
4
0
0
2
0
2
0
0
0
2
1
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
1
2
2
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
2
0
2
2
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
2
3
3
0
0
0
1
0
0
2
0
2
0
4
2
0
1
0
1
0
0
0
1
0
2
2
0
0
0
0
0
0
0
1
2
2
1
0
0
0
2
2
2
0
0
0
0
0
1
1
0
0
0
0
0
3
0
0
1
0
2
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
3
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
2
1
2
1
0
0
0
0
0
1
0
0
0
0
0
2
1
1
0
0
0
1
0
0
0
1
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
1
0
0
2
1
2
2
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
2
0
0
1
2
0
0
0
0
0
0
0
0
1
0
2
0
2
1
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
3
0
2
0
0
0
0
0
1
1
0
0
1
2
2
2
0
0
0
0
0
0
1
1
0
0
0
5
0
2
0
2
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
4
2
0
2
0
0
0
2
0
0
0
2
0
0
4
1
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
1
0
0
0
0
0
4
3
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
1
0
2
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
2
2
1
0
5
0
0
1
0
0
1
0
0
0
0
2
1
1
0
0
2
2
2
4
1
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
2
2
0
2
1
0
1
0
1
1
0
0
1
2
0
0
1
0
0
1
0
0
0
1
0
1
0
0
2
0
0
2
1
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
2
1
0
2
2
0
2
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
1
0
1
0
0
2
2
1
0
2
0
0
0
2
0
0
2
1
0
2
0
0
0
0
2
2
2
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
2
0
2
0
0
1
0
1
2
1
2
2
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
2
0
0
0
0
2
1
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
2
2
1
1
0
0
0
0
2
0
0
2
1
2
2
2
0
0
0
0
2
0
2
0
0
0
2
0
0
0
1
0
2
0
0
0
2
0
2
0
0
2
0
1
2
2
0
2
2
0
0
0
0
2
0
0
0
0
0
0
1
2
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
2
0
0
0
0
0
0
0
3
1
1
0
0
1
0
0
0
1
0
0
3
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
2
1
0
1
1
0
0
1
0
0
1
0
2
0
0
3
2
1
2
1
0
0
0
2
0
0
2
0
0
0
2
0
2
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
1
3
0
0
0
0
0
0
0
0
0
1
1
2
2
0
0
2
0
3
1
0
0
2
0
0
0
0
0
1
1
1
0
2
3
0
0
0
2
0
2
2
0
0
2
0
0
2
2
1
0
1
0
2
2
0
1
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
2
2
0
0
1
0
0
0
2
0
0
0
0
3
0
0
0
0
2
1
1
0
0
1
1
0
2
0
1
2
0
0
2
1
0
0
2
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
2
1
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
1
1
1
0
0
0
1
1
0
1
0
0
0
0
0
2
1
1
0
0
2
0
0
2
0
0
2
2
0
2
1
0
1
0
2
4
0
0
1
1
1
0
1
0
0
2
0
0
2
1
1
1
0
1
0
0
2
0
2
0
0
2
1
2
0
0
0
2
0
0
1
0
1
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
4
0
0
0
0
0
1
2
0
0
0
1
0
1
0
0
1
0
0
0
3
0
1
1
0
0
0
0
0
1
0
1
0
2
0
2
0
0
1
0
0
2
0
0
0
3
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
8
1
2
0
2
1
0
2
1
1
2
3
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
3
0
3
2
1
0
0
1
0
1
0
2
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
2
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
1
1
0
2
2
0
1
0
1
0
0
0
0
0
1
2
0
2
0
0
2
0
0
0
0
2
1
0
0
2
2
1
0
1
0
2
0
1
1
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
1
0
0
0
1
0
1
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
1
4
1
0
0
0
0
2
0
1
2
2
0
1
0
1
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
1
0
0
0
1
0
0
0
0
1
0
0
0
2
1
0
1
0
2
0
0
3
0
0
1
0
5
0
2
0
0
0
0
0
0
1
1
0
1
0
0
0
0
2
0
1
1
0
0
1
0
2
1
0
0
0
0
0
1
0
0
0
3
1
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
2
2
0
1
4
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
1
1
0
2
0
0
0
0
0
0
1
1
1
0
2
0
0
2
1
0
3
0
1
3
0
0
0
0
1
1
2
0
0
0
0
0
0
3
2
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
2
2
0
0
0
0
0
1
3
0
0
0
1
2
0
0
0
1
1
0
2
2
1
0
0
0
2
2
2
3
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
3
0
0
0
0
2
1
0
0
0
2
0
0
0
2
0
4
0
0
10
0
2
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
1
1
1
0
0
0
1
0
1
0
0
1
1
0
0
0
2
1
0
1
1
0
0
1
2
0
0
1
2
1
0
0
0
1
2
4
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
1
0
2
2
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
1
1
0
0
5
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
1
0
0
0
2
0
2
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
6
0
0
0
5
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
1
1
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
2
0
0
1
0
2
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
5
0
0
0
1
0
0
0
0
1
2
0
1
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
2
1
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
7
2
1
0
2
0
0
1
2
0
0
0
0
2
0
2
3
0
0
0
0
1
1
2
0
0
1
0
0
2
0
0
2
0
0
0
0
0
2
2
0
0
2
0
0
0
2
0
0
3
0
0
0
2
0
1
1
0
2
2
0
0
0
0
0
1
2
0
0
1
4
0
1
0
1
0
0
0
1
0
1
0
0
0
1
1
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
1
1
0
2
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
1
2
2
0
2
0
0
0
0
0
0
1
0
1
1
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
2
0
0
0
1
0
2
0
0
2
0
0
0
1
0
0
0
0
3
0
0
0
2
3
0
0
0
0
0
0
0
1
0
2
0
2
2
0
0
0
0
0
0
0
1
0
0
1
1
0
0
3
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
1
0
3
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
3
2
0
3
2
1
0
1
0
0
2
0
0
1
0
2
0
1
0
2
0
2
0
1
0
3
0
0
2
0
1
0
1
1
0
0
2
0
0
0
0
0
6
0
0
0
0
1
0
0
2
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
3
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
2
2
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
3
3
0
0
0
0
0
4
1
0
2
0
0
2
0
2
0
1
1
0
0
2
2
0
0
1
0
0
2
0
2
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
2
2
0
0
0
4
0
1
0
1
1
0
2
0
1
0
0
2
0
0
1
2
0
0
2
0
0
1
0
0
0
1
0
2
0
2
1
2
0
0
0
0
2
3
1
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
2
0
0
0
2
2
0
1
0
0
0
0
2
2
0
2
0
0
0
0
0
2
0
0
2
0
1
0
0
1
1
0
0
0
0
0
2
0
0
0
5
0
0
0
1
0
0
1
0
0
2
0
0
0
0
2
2
0
0
0
0
1
2
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
2
0
1
2
0
2
0
2
1
0
2
0
0
3
2
1
0
0
1
2
0
2
0
3
0
1
0
0
2
0
0
0
0
0
0
0
0
0
3
0
1
0
1
2
2
0
0
0
0
0
2
0
0
0
2
1
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
1
0
0
0
1
0
0
1
2
0
0
0
5
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
1
3
0
1
0
0
0
1
0
3
0
0
0
1
2
0
0
2
1
0
0
2
2
2
1
0
3
0
0
0
2
2
0
2
0
2
1
0
0
1
0
3
2
0
1
0
2
0
0
0
1
1
0
0
0
0
2
0
0
2
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
1
0
1
2
0
0
2
1
1
0
1
0
0
0
1
0
1
3
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
3
0
1
0
2
0
2
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
2
0
0
1
0
2
0
0
0
2
0
0
0
2
1
0
0
0
1
0
3
0
0
1
0
0
0
0
0
5
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
2
2
0
1
2
0
0
2
0
0
0
2
0
0
1
0
2
0
0
0
0
0
2
0
1
0
0
1
2
0
0
0
0
0
1
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
3
0
0
0
0
2
1
6
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
2
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
1
0
2
0
0
0
1
0
0
1
4
0
1
2
0
1
0
0
2
0
0
0
2
0
0
0
0
1
2
0
2
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
1
0
0
1
0
2
0
0
0
1
3
0
0
0
0
0
0
1
0
1
0
0
2
1
0
1
0
0
0
0
0
0
0
2
2
0
1
0
2
3
1
2
2
2
2
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
3
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
1
0
2
0
0
1
1
0
0
0
0
0
2
0
1
1
0
4
0
0
0
1
0
0
0
1
3
0
2
1
0
0
0
0
0
0
0
0
0
0
3
7
0
0
0
0
0
0
2
0
1
0
0
0
1
1
1
2
0
0
0
0
0
0
2
1
2
0
0
1
2
2
0
1
1
1
1
0
0
0
2
2
1
0
2
2
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
2
2
1
0
2
1
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
2
1
0
1
0
1
0
2
1
1
0
1
0
0
0
1
9
2
0
2
0
0
1
0
0
1
0
0
1
0
1
0
1
0
1
2
0
0
0
2
0
0
0
0
0
0
0
3
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
10
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
2
0
2
2
2
0
0
0
0
2
2
0
0
0
0
1
0
0
4
0
0
0
1
0
0
1
0
0
1
1
1
0
0
1
0
2
0
0
1
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
2
0
2
0
1
2
2
1
0
0
1
0
1
0
0
2
0
1
0
0
2
0
0
0
0
0
0
1
0
0
2
0
1
0
0
2
2
2
2
2
1
0
1
2
0
0
0
0
1
0
2
0
0
0
0
3
0
2
2
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
2
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
2
1
0
1
1
0
0
0
1
0
0
0
0
0
1
0
1
4
1
0
0
0
0
0
0
1
0
2
2
0
2
1
2
0
0
0
1
2
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
2
0
1
1
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
2
1
1
0
3
2
2
4
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
4
0
1
0
0
0
1
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
2
0
0
0
0
0
3
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
1
0
0
2
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
2
0
2
0
3
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
2
0
0
0
0
0
1
0
0
0
0
0
3
1
0
0
0
1
0
1
2
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
2
1
0
2
0
0
0
0
0
8
2
0
0
0
0
6
2
0
3
2
4
0
2
1
0
0
0
0
1
0
2
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
3
1
0
0
3
3
0
0
0
0
2
0
0
1
0
3
0
2
2
0
0
2
0
0
0
1
0
0
1
2
0
1
0
0
1
0
0
1
2
0
0
2
0
0
0
2
1
0
1
0
0
0
2
0
0
3
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
2
0
0
0
2
0
0
0
1
0
1
1
0
2
0
1
3
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
2
0
2
2
0
0
0
0
0
0
1
0
2
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
1
0
0
2
2
1
0
0
0
0
0
1
0
0
1
0
1
2
0
0
0
2
2
2
0
0
0
2
0
0
2
0
0
1
0
0
0
0
2
0
1
0
0
1
0
1
0
0
2
2
0
0
0
2
1
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
3
0
3
0
0
0
0
1
4
2
1
0
0
0
0
0
3
0
0
0
0
0
1
0
2
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
2
2
2
3
0
0
0
0
0
1
0
0
1
0
0
2
0
3
0
0
0
0
2
0
0
0
0
0
2
1
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
2
1
0
0
0
0
0
1
2
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
2
0
2
2
0
2
0
0
0
2
2
1
0
2
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
1
2
0
0
0
0
0
1
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
3
1
2
0
0
0
1
0
2
1
0
0
1
2
0
3
2
0
0
0
0
0
2
0
1
0
0
0
1
0
2
1
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
1
2
0
0
0
0
3
0
0
0
1
0
0
0
1
2
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
1
1
1
1
2
2
1
2
1
0
0
2
0
0
0
1
0
0
1
1
1
0
0
1
0
0
2
2
1
0
5
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
1
0
0
1
0
0
2
0
0
0
0
0
0
2
2
1
0
2
0
0
3
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
8
1
0
0
0
2
0
1
0
3
0
0
0
3
0
0
1
2
0
2
0
0
1
1
2
0
0
1
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
1
2
4
2
2
1
0
0
1
0
2
2
2
2
0
2
0
0
1
0
0
0
0
0
0
4
0
0
2
0
3
1
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
2
2
2
0
0
0
1
0
4
0
0
1
3
0
0
1
0
2
2
0
0
0
0
0
1
2
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
2
0
0
0
0
1
1
0
0
3
0
2
0
2
0
2
1
0
0
1
0
2
0
1
0
2
0
0
0
0
1
1
0
0
6
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
2
2
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
1
0
1
2
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
1
0
0
0
2
2
1
0
2
0
1
1
0
0
2
0
0
0
2
0
0
0
0
2
1
2
0
1
1
2
0
1
0
0
1
1
1
0
0
2
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
1
2
1
0
0
1
0
2
0
0
2
0
0
2
0
3
0
0
2
1
1
1
0
2
0
0
2
0
2
0
2
0
0
2
0
3
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
1
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
1
0
2
0
0
2
3
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
1
0
3
1
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
2
0
0
1
2
2
0
2
1
0
0
1
0
1
3
0
1
2
4
0
4
2
0
0
2
0
0
0
0
2
1
0
0
0
0
2
1
0
0
2
1
0
1
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
2
0
0
0
2
0
1
0
0
0
1
1
3
0
0
0
0
0
0
0
0
0
1
10
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
2
0
2
2
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
1
1
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
2
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
3
0
2
0
0
0
2
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
2
1
1
2
0
0
0
0
2
2
0
1
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
2
0
2
0
0
0
2
0
0
1
0
0
2
0
2
2
2
2
0
0
2
0
1
0
2
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
1
2
1
0
0
1
0
0
1
0
0
2
1
0
0
0
1
1
0
0
0
0
0
2
0
2
0
0
2
1
0
0
0
0
0
1
0
0
0
0
1
0
2
0
1
0
0
1
0
1
0
0
0
2
0
0
1
2
1
3
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
3
1
0
0
2
0
1
1
1
2
1
0
0
0
4
0
0
0
0
1
3
1
0
0
0
0
0
0
0
1
0
0
1
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
2
4
0
0
1
0
0
1
0
1
0
0
0
2
0
3
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
1
1
0
0
2
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
2
0
0
0
2
2
1
0
0
0
1
0
0
3
1
0
0
0
2
0
0
2
0
2
0
1
0
0
2
0
0
0
2
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
3
2
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
2
1
0
1
1
2
0
2
0
0
1
0
0
0
0
0
0
3
1
0
0
1
1
0
0
2
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
2
1
0
0
2
0
2
2
0
0
0
0
0
0
0
0
1
2
1
2
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
2
1
0
2
1
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
7
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
2
0
0
0
2
0
2
0
0
0
2
0
2
0
3
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
2
2
1
1
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
3
0
0
0
0
0
0
1
2
0
0
0
2
2
1
0
0
0
2
1
0
0
0
1
0
0
2
0
0
2
0
2
0
0
0
2
1
1
0
2
2
0
2
1
0
3
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
2
0
0
0
0
1
0
0
0
1
1
0
0
1
1
2
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
1
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
6
0
0
1
0
0
0
1
5
0
0
0
0
0
2
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
2
2
0
0
5
2
2
1
0
0
1
3
0
2
0
2
0
1
0
0
0
0
2
0
0
1
1
1
0
1
0
0
1
0
1
0
2
1
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
1
0
0
2
1
0
1
0
0
2
0
1
1
1
0
0
3
0
0
1
0
2
0
0
0
0
0
0
1
1
0
0
0
1
0
0
4
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
1
2
0
0
1
2
0
0
1
3
0
0
0
2
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
2
2
0
2
0
1
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
4
1
2
2
1
0
0
0
0
2
0
2
1
0
0
0
0
1
2
0
0
0
6
0
2
0
0
0
0
0
0
1
1
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
1
2
2
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
2
0
0
2
2
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
3
0
0
0
3
0
0
1
2
0
1
1
1
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
4
0
0
0
2
0
0
1
1
2
0
0
0
0
3
2
0
0
0
1
0
2
0
0
1
1
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
2
1
0
1
0
0
4
2
1
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
1
0
0
2
0
1
0
0
0
0
2
0
0
1
3
0
1
0
0
0
0
2
0
1
0
3
0
0
2
0
1
2
2
0
0
0
0
0
4
0
2
0
0
0
2
0
1
0
1
0
0
0
1
2
0
0
0
2
0
0
3
0
1
1
3
0
0
0
0
2
0
2
2
0
0
3
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
4
0
0
0
2
0
0
0
0
1
4
0
0
2
0
1
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
1
0
0
1
2
0
0
0
0
2
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
1
1
0
2
0
0
0
2
1
0
1
0
2
0
0
2
2
0
0
0
0
0
2
2
1
0
2
2
0
0
0
1
0
2
0
2
0
0
1
0
0
0
0
1
1
0
0
0
2
1
0
1
0
0
2
0
0
0
3
0
2
2
1
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
2
0
2
1
1
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
1
2
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
2
0
1
0
0
0
4
0
0
1
2
0
0
0
1
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
3
2
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
1
0
2
1
2
0
2
3
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
1
2
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
2
0
1
0
0
2
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
2
1
0
0
0
0
0
1
0
2
0
0
0
1
1
2
0
0
2
0
2
0
1
0
0
2
3
0
0
0
0
2
0
2
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
3
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
4
0
0
0
1
5
0
0
2
2
0
0
0
1
0
0
0
0
1
0
2
0
0
2
0
1
0
0
2
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
1
0
0
0
2
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
1
0
1
2
0
0
1
1
0
0
0
0
1
0
0
1
1
0
0
2
0
2
0
0
2
0
0
2
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
1
1
0
0
0
0
1
5
0
0
1
0
1
1
1
2
2
0
0
0
0
0
0
2
0
1
0
1
1
2
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
2
0
3
0
0
2
0
0
0
1
1
0
0
2
0
0
1
0
2
2
1
0
0
0
2
0
2
0
4
2
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
2
2
1
0
1
0
0
1
0
3
2
2
0
1
0
2
2
0
2
0
3
0
2
1
0
0
0
1
0
1
0
1
0
0
1
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
2
0
0
1
0
2
2
0
0
1
0
0
1
0
0
2
2
0
2
3
0
0
0
0
2
0
1
1
1
0
1
2
0
2
0
0
2
0
0
0
2
2
1
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
2
5
0
1
2
5
0
0
0
0
0
1
1
0
2
0
1
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
1
0
0
1
0
2
1
0
2
0
0
0
3
0
0
1
1
0
1
0
0
2
0
0
1
0
0
0
1
0
2
0
0
1
1
0
2
0
0
2
0
2
0
0
0
2
0
0
0
0
3
0
2
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
1
2
0
1
2
0
2
0
0
5
0
1
2
0
0
0
2
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
2
2
0
2
2
0
0
0
0
0
1
0
0
1
1
3
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
1
0
0
0
2
0
0
0
0
1
2
1
0
0
0
2
2
2
0
0
1
0
0
0
0
2
0
0
1
0
0
0
1
0
3
0
2
0
0
0
0
0
0
2
0
1
2
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
4
0
0
1
0
0
0
1
2
0
0
0
0
2
1
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
2
0
1
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
1
1
2
2
4
1
1
0
0
0
1
0
0
2
0
1
0
0
2
0
1
2
0
2
0
0
0
0
4
0
0
0
2
0
0
2
0
2
0
0
1
2
1
0
1
0
2
2
2
1
0
2
0
0
0
1
0
0
2
0
0
0
0
1
0
2
2
0
1
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
2
0
0
1
0
2
1
0
0
0
1
1
0
0
0
1
2
0
0
0
0
0
1
0
0
2
0
1
1
0
0
0
1
0
3
0
1
2
0
0
0
0
0
0
0
0
2
2
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
4
0
1
0
2
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
2
12
1
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
2
1
0
0
0
1
2
0
0
0
2
0
0
0
0
2
0
0
8
0
1
0
2
0
0
2
0
0
0
0
1
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
3
0
0
0
0
1
0
0
0
1
1
0
2
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
1
0
0
1
2
0
0
1
0
0
0
0
0
3
0
1
0
1
1
0
1
2
1
0
2
0
0
0
0
2
0
2
2
0
1
0
0
2
2
0
0
0
2
3
0
0
0
2
2
2
0
0
0
0
0
0
2
0
2
0
0
1
1
1
0
2
0
1
1
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
2
1
3
2
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
3
1
2
0
0
0
0
0
1
2
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
2
0
1
3
0
0
3
0
0
2
1
0
3
0
0
0
0
0
1
2
0
0
1
0
0
11
0
2
2
0
0
0
0
0
0
0
0
0
0
3
1
2
0
2
0
0
1
0
2
0
0
0
1
2
1
0
0
3
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
1
2
0
0
0
2
1
0
0
0
0
0
1
1
1
1
0
0
1
1
3
3
0
0
0
0
2
0
1
0
0
1
1
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
1
0
2
0
0
2
2
0
0
2
0
0
0
0
0
1
1
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
3
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
1
1
0
1
0
0
5
1
0
2
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
2
0
0
1
0
0
0
0
0
0
2
2
0
0
0
5
0
0
0
2
1
1
0
0
0
0
0
0
0
0
5
0
2
0
1
0
0
2
0
0
0
1
0
0
0
1
0
2
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
3
0
0
0
0
0
1
0
0
2
2
0
2
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
1
2
0
2
0
0
0
1
0
0
3
0
0
0
1
0
0
1
3
0
2
0
0
1
0
1
2
4
0
2
0
0
0
0
1
2
0
0
2
1
0
1
0
0
2
1
2
0
0
0
2
2
0
0
0
0
2
0
0
0
1
0
1
0
1
1
2
1
0
0
0
0
3
1
2
0
0
1
2
2
1
1
0
2
0
0
0
1
1
1
0
0
2
0
0
0
0
0
1
0
0
0
0
1
2
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
3
2
1
0
0
2
0
0
0
0
0
0
1
2
0
3
0
0
0
2
0
1
0
0
0
2
1
0
0
1
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
2
2
0
0
0
1
0
0
0
3
0
2
1
0
3
0
0
0
2
0
0
2
0
2
3
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
2
0
0
1
0
0
2
0
0
1
0
0
1
0
1
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
1
0
2
0
2
0
1
0
0
1
2
0
0
0
3
2
1
0
0
0
0
0
0
0
0
0
1
2
0
1
2
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
2
1
1
0
2
0
0
0
1
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
1
0
1
0
0
1
0
0
0
0
0
2
0
2
1
0
0
1
0
2
3
0
0
0
0
1
0
2
0
1
1
0
2
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
1
1
1
1
0
2
2
0
1
0
0
0
0
0
2
0
0
0
1
0
6
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
2
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
2
0
0
1
0
0
1
1
0
0
0
2
0
2
0
0
0
2
0
2
0
0
3
0
0
0
0
0
1
0
2
0
2
0
1
0
0
0
0
1
0
1
1
0
0
0
2
0
0
0
0
0
1
0
1
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
1
0
3
0
0
0
0
0
2
0
0
0
1
0
1
2
1
2
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
3
0
0
0
0
1
0
1
1
0
0
0
0
0
2
3
2
0
1
1
6
0
0
0
1
2
0
0
1
0
0
0
7
0
0
0
2
0
0
0
1
2
0
0
0
1
2
0
1
0
1
0
2
2
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
2
1
0
2
3
1
0
4
0
1
0
1
0
0
0
0
0
0
1
0
3
2
0
0
1
0
2
2
0
1
0
0
0
0
0
1
0
2
0
0
3
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
2
1
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
2
2
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
3
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
2
2
1
0
0
2
0
4
0
0
0
0
2
0
0
0
3
0
2
0
2
1
0
4
0
0
0
0
0
0
0
1
1
0
0
0
0
0
4
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
3
2
0
0
2
0
0
2
0
0
3
0
0
0
0
0
2
3
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
1
1
0
0
1
0
3
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
1
0
0
4
2
1
0
0
0
2
0
0
0
2
0
0
1
0
0
2
0
0
1
1
0
0
0
0
0
1
0
0
2
0
0
2
0
1
2
0
2
0
0
0
0
1
0
1
2
0
2
0
0
0
0
2
3
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
2
2
1
0
1
0
1
0
2
0
5
0
0
0
2
0
1
0
0
0
1
0
1
2
0
0
0
0
1
0
2
3
2
0
1
2
0
0
0
4
0
1
0
0
0
2
1
0
0
1
0
0
0
2
0
1
0
1
1
0
4
2
0
0
0
0
0
1
0
0
7
0
0
0
1
0
0
0
1
2
0
0
0
2
0
0
0
0
2
1
0
0
1
0
0
2
0
0
1
0
0
2
1
0
0
0
2
0
0
2
0
0
0
0
0
1
2
1
0
2
0
1
0
0
0
2
2
0
1
0
0
0
0
2
0
2
2
2
0
0
0
0
2
0
0
0
0
0
1
0
0
2
2
0
0
0
1
0
0
0
0
2
0
1
0
1
1
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
3
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
3
0
2
0
0
0
0
2
0
0
0
0
1
0
0
2
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
1
0
6
2
0
0
0
1
2
0
0
0
0
2
0
0
2
1
0
2
0
2
1
0
0
0
0
0
2
0
0
1
2
1
0
0
0
1
0
0
1
1
0
2
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
1
1
2
0
0
0
2
0
0
0
0
0
2
1
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
1
1
0
1
0
0
0
0
2
0
0
1
1
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
1
0
1
0
0
0
1
0
0
1
2
0
0
0
1
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
2
2
1
0
1
0
0
2
0
2
0
0
0
3
2
0
0
1
1
0
0
0
1
2
2
0
0
0
1
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
2
2
2
2
2
0
0
0
0
0
0
1
0
2
0
0
3
2
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
2
0
2
0
0
1
1
0
0
1
0
0
0
1
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
1
1
0
2
0
0
0
0
0
0
1
2
0
2
0
2
0
0
0
0
0
0
2
2
2
0
2
1
1
0
0
0
0
0
0
0
2
0
0
0
1
1
0
2
0
0
0
2
0
0
0
1
0
2
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
2
0
0
0
0
0
3
0
1
0
0
2
0
1
0
0
0
0
0
0
2
0
0
3
0
4
0
2
1
0
2
0
2
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
2
0
1
0
0
2
2
0
0
0
0
0
1
0
0
2
0
0
2
1
1
0
0
2
1
0
2
2
2
1
0
0
0
0
0
0
0
0
0
2
1
2
1
0
1
2
0
2
2
1
2
2
0
0
0
1
1
2
0
1
0
0
1
1
0
1
2
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
1
0
4
0
0
0
0
2
0
0
1
1
2
1
0
0
1
0
1
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
1
0
0
2
0
0
0
1
1
0
0
3
0
0
0
0
2
0
0
2
0
0
2
1
0
0
2
0
1
1
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
2
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
2
1
2
0
0
0
1
0
0
0
2
2
1
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
3
0
0
0
1
2
1
0
1
0
0
0
0
0
2
0
1
1
0
1
0
2
0
4
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
2
1
0
2
0
1
0
0
0
0
0
0
1
1
2
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
1
0
3
0
0
1
2
0
0
0
0
1
0
0
2
0
0
0
1
0
1
0
1
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
1
2
1
2
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
2
0
1
0
0
0
1
0
2
0
2
2
1
2
3
2
2
0
0
0
0
1
1
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
1
0
2
0
2
0
1
1
0
1
2
2
6
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
1
0
0
0
0
2
1
0
0
5
0
2
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
3
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
3
0
0
0
2
0
0
0
1
2
0
1
0
0
1
0
0
0
0
2
0
0
3
2
0
0
1
0
0
1
0
0
1
0
0
0
0
3
0
0
0
3
0
0
2
0
0
0
0
0
0
1
1
1
2
0
1
0
1
0
0
2
0
2
0
1
4
0
0
0
0
0
2
0
2
0
0
0
2
0
1
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
2
1
3
2
2
2
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
1
3
2
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
2
0
3
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
1
2
2
0
1
0
0
0
0
1
0
0
2
3
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
3
1
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
2
1
1
0
2
0
2
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
2
0
2
0
0
2
0
1
0
2
1
0
2
1
2
4
2
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
1
0
0
2
0
0
1
2
0
0
1
2
0
0
1
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
1
0
0
1
3
0
1
0
2
0
0
0
2
3
0
0
0
0
0
2
0
2
1
0
0
2
0
0
0
1
1
2
0
4
0
1
0
1
2
3
1
0
2
0
0
2
1
0
0
2
0
0
2
1
0
1
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
2
1
2
0
0
1
0
0
1
0
0
0
2
0
0
0
1
0
0
0
1
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
1
0
3
0
0
2
0
0
0
0
1
0
2
2
0
1
0
1
0
1
0
1
0
1
0
0
0
0
2
0
2
1
0
2
0
0
0
2
2
2
0
2
3
0
1
0
0
0
1
1
1
0
0
1
2
1
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
1
2
0
0
3
2
0
3
0
2
0
0
0
0
2
0
1
0
0
2
5
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
1
0
1
0
0
0
2
0
0
0
2
0
0
2
0
0
2
1
2
0
0
0
1
0
0
0
1
5
0
0
0
0
0
0
0
2
0
1
1
0
0
0
3
0
0
1
0
0
0
2
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
2
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
4
0
2
2
0
0
1
2
0
0
0
0
0
0
0
2
0
3
0
0
0
0
1
0
0
1
0
2
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
2
3
0
1
0
3
0
1
0
0
0
0
0
2
0
0
0
1
3
2
1
0
1
1
0
2
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
1
2
2
1
0
1
0
2
1
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
1
0
1
2
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
1
0
1
0
0
2
0
0
0
0
4
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
2
0
2
1
2
1
0
0
0
0
1
2
0
0
4
0
0
0
0
1
0
3
2
0
0
1
0
0
2
0
1
1
0
0
0
0
1
0
0
0
0
1
0
2
6
0
3
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
2
1
2
2
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
1
2
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
2
0
0
2
0
0
2
0
0
2
2
0
0
2
1
1
2
0
0
0
0
0
0
1
1
0
1
0
1
0
2
3
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
2
0
1
2
1
0
0
0
2
0
1
3
0
0
2
3
0
0
0
0
1
2
0
0
0
0
0
0
0
3
0
0
0
0
4
0
0
3
1
3
2
0
0
0
2
0
0
1
0
0
2
0
2
0
1
0
0
0
0
0
2
2
2
0
0
1
0
0
2
2
0
0
0
0
1
0
2
0
1
1
0
0
1
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
2
2
0
2
0
0
2
2
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
2
2
0
0
0
0
0
3
0
1
0
0
2
2
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
2
1
1
0
1
2
0
0
0
0
0
0
4
2
0
0
1
0
2
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
2
0
2
2
2
0
2
2
2
0
2
0
0
0
0
2
1
1
1
0
0
0
0
1
0
2
0
0
0
1
0
0
0
1
0
1
1
0
2
0
2
0
2
1
0
0
0
0
2
0
0
0
0
0
2
2
0
1
0
0
3
0
1
2
0
1
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
1
0
0
2
0
0
0
2
1
0
1
1
1
1
0
0
2
2
0
1
0
0
0
1
0
0
0
1
0
0
1
2
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
1
2
0
0
0
0
1
0
2
0
1
2
0
0
0
1
0
0
0
0
1
0
0
0
0
2
2
2
1
0
2
0
1
0
0
0
0
0
0
2
0
3
0
0
0
0
0
1
1
0
0
0
0
1
2
0
0
0
0
2
1
0
2
0
0
0
2
0
1
0
0
2
0
2
0
0
0
0
2
2
2
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
1
2
2
2
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
2
2
0
0
0
2
0
0
2
0
0
0
0
2
2
0
0
2
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
6
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
7
0
2
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
1
0
1
1
1
1
0
3
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
2
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
2
2
0
2
0
1
0
0
0
2
1
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
5
0
0
1
0
1
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
2
1
0
1
0
1
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
2
2
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
1
0
2
0
0
0
0
0
2
3
1
2
1
2
0
0
1
0
0
0
0
1
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
1
0
0
2
0
0
1
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
11
0
0
0
2
0
0
2
0
0
2
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
2
1
2
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
12
0
2
0
0
2
2
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
2
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
4
2
0
0
0
0
0
0
0
1
4
1
2
0
0
3
0
0
0
0
0
0
2
2
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
1
1
2
2
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
1
2
1
1
0
0
0
0
0
0
0
0
0
1
2
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
1
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
3
0
0
2
0
2
0
2
2
0
0
2
2
0
2
0
0
2
0
0
1
0
1
2
0
0
0
2
1
0
1
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
3
1
0
1
0
1
0
2
0
1
0
1
1
2
2
0
1
2
0
0
0
2
2
0
0
0
0
0
1
1
1
0
0
1
2
0
2
0
1
0
0
0
0
0
0
0
0
2
7
0
0
0
2
2
1
3
1
0
0
0
0
3
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
2
2
0
0
2
1
1
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
1
0
2
0
1
0
2
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
1
0
1
0
0
1
1
0
0
1
2
2
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
1
0
0
1
0
1
0
0
0
0
2
1
0
1
2
0
0
1
1
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
5
0
2
0
0
1
1
0
0
0
1
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
1
2
0
0
3
0
0
1
2
0
0
0
2
0
2
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
1
0
0
0
2
0
0
0
0
0
2
0
0
1
2
2
1
0
2
0
0
0
0
0
0
0
3
2
1
0
0
0
2
0
3
0
0
0
2
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
2
0
3
2
0
0
0
1
2
2
1
2
3
0
2
0
2
1
2
0
1
0
0
0
2
0
0
0
0
2
1
2
2
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
3
0
1
1
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
2
0
1
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
1
1
0
0
0
2
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
2
0
0
2
2
0
1
0
0
0
0
1
0
0
0
0
0
2
2
2
0
1
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
2
0
0
1
1
0
0
0
1
0
2
2
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
1
0
0
2
0
0
0
0
2
0
2
0
0
4
0
0
0
2
0
0
0
0
2
0
0
6
0
0
0
1
0
2
0
0
0
1
0
2
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
1
0
1
2
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
1
0
0
0
0
0
3
0
0
1
1
0
2
2
1
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
1
0
0
0
2
1
1
0
0
1
0
0
1
0
0
1
0
1
2
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
2
0
0
0
1
0
0
1
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
3
0
0
3
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
1
0
9
0
0
0
2
2
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
4
0
0
1
0
0
1
0
2
0
0
1
0
2
2
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
1
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
3
0
2
0
0
1
0
3
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
2
0
2
0
0
2
0
0
0
0
0
1
2
0
1
1
0
0
2
2
0
0
0
0
2
1
0
2
1
0
0
0
0
1
0
2
0
0
4
0
0
1
1
0
1
1
0
0
2
1
1
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
2
0
2
0
0
0
0
3
0
0
0
2
2
0
0
1
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
1
2
0
3
0
2
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
2
0
0
2
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
4
2
1
1
0
0
0
0
2
2
0
1
0
1
1
0
0
2
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
1
2
0
2
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
2
0
2
1
2
2
0
0
0
0
0
3
1
0
0
0
1
0
1
2
0
2
0
0
0
0
0
0
0
2
0
2
2
1
0
2
2
2
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
2
0
2
1
0
2
3
0
0
1
0
0
2
0
2
0
1
1
0
0
0
1
0
0
0
2
2
0
0
0
0
2
0
0
0
0
2
1
0
3
1
2
2
1
0
0
0
0
0
0
0
3
2
0
2
0
0
1
0
0
0
0
1
1
3
0
1
3
1
0
0
0
0
2
2
2
3
0
2
0
0
0
0
0
1
1
0
0
1
2
0
0
0
0
0
0
0
1
0
0
2
0
1
1
4
1
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
2
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
2
1
2
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
1
2
1
0
2
1
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
7
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
1
2
2
2
0
0
0
2
3
0
0
0
1
0
0
1
0
1
0
2
0
0
0
2
0
0
0
2
0
2
2
0
0
0
0
1
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
2
2
0
3
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
3
2
1
0
1
0
0
1
0
0
0
0
0
2
0
0
1
0
0
2
0
0
2
1
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
1
2
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
2
1
0
2
2
2
0
3
0
2
1
0
3
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
2
2
1
2
1
1
2
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
1
1
0
1
2
0
0
0
0
2
0
0
0
0
2
2
1
0
0
1
0
0
1
0
2
0
0
2
0
0
0
0
1
0
0
0
3
0
0
2
3
1
0
0
0
1
0
0
0
1
0
0
2
0
2
2
0
0
1
0
0
0
0
0
0
1
0
0
1
0
2
0
2
1
3
5
0
0
3
0
0
0
0
0
2
0
0
2
0
0
0
0
1
1
0
0
3
0
0
1
1
0
0
1
0
1
0
2
0
0
0
0
0
0
1
0
0
2
0
1
0
1
0
0
2
0
0
0
0
2
0
1
0
0
0
2
0
0
1
1
0
0
1
0
2
0
2
0
1
0
1
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
2
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
2
0
0
0
2
0
0
0
2
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
2
2
1
0
0
0
2
0
0
0
0
0
1
0
2
2
3
1
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
2
2
0
3
0
1
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
1
1
0
2
0
0
2
2
0
0
0
0
0
0
0
1
1
1
2
0
1
0
2
0
0
2
0
0
0
0
0
2
2
0
0
1
1
0
0
1
1
1
0
0
2
1
0
1
0
0
0
3
0
2
0
0
1
0
0
1
1
0
3
0
0
1
0
0
2
0
0
2
2
2
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
1
0
0
0
2
0
2
2
0
1
1
0
0
0
0
0
0
0
2
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
2
1
2
0
0
2
0
0
1
0
2
1
2
0
0
0
2
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
2
0
1
0
0
0
1
1
0
2
0
0
0
2
0
2
2
2
2
0
4
1
0
0
2
1
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
2
0
2
2
0
0
0
0
0
2
2
1
0
3
0
0
1
0
0
0
1
2
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
3
0
0
2
0
0
0
2
0
0
0
0
1
2
2
2
0
1
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
3
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
3
2
2
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
1
0
0
0
1
0
1
0
0
0
2
0
1
2
2
1
1
0
0
0
0
0
0
2
0
5
0
2
2
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
1
2
0
2
0
2
2
0
0
0
0
1
2
2
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
2
1
0
1
0
0
0
0
3
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
1
2
0
0
0
1
0
0
0
1
1
2
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
1
2
0
2
1
1
0
1
1
1
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
1
1
0
1
0
0
0
3
0
0
1
0
1
2
0
1
0
0
0
0
1
0
2
0
2
1
0
1
0
1
0
0
0
0
0
0
0
0
0
2
1
2
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
2
2
2
2
2
2
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
2
0
0
0
1
2
0
0
0
0
0
3
0
0
0
0
2
0
2
0
0
0
0
0
2
1
0
0
2
2
2
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
2
0
0
2
0
2
0
0
2
2
1
0
0
0
2
0
1
0
0
0
1
2
0
1
0
1
0
2
0
1
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
1
0
0
0
1
0
0
1
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
2
0
2
2
0
0
0
0
2
0
0
0
0
0
1
1
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
3
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
1
2
0
0
0
0
2
2
0
5
4
0
0
0
0
0
0
0
2
1
1
1
0
3
0
0
2
1
0
1
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
1
0
0
2
0
0
0
0
2
1
0
1
2
0
0
0
3
0
2
0
2
0
0
2
1
2
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
1
1
2
0
1
0
0
0
0
0
0
1
0
0
2
0
2
0
0
2
0
0
1
0
0
0
2
0
0
0
0
1
1
0
2
0
0
1
0
1
2
1
0
2
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
2
1
0
0
1
0
0
0
2
1
0
0
0
0
0
0
2
7
0
1
3
0
0
0
2
1
0
0
0
2
2
2
0
0
0
0
1
0
1
2
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
2
1
0
2
0
1
0
3
0
0
0
0
3
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
1
0
1
2
2
1
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
2
0
1
1
0
0
0
1
0
0
0
2
0
0
2
0
2
1
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
2
0
1
3
2
2
0
0
1
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
7
0
2
0
1
0
2
0
0
1
0
1
0
0
0
0
0
2
0
4
0
0
0
0
5
0
1
2
0
0
2
1
0
0
1
2
2
2
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
1
0
1
2
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
2
0
0
2
0
0
0
2
0
0
0
1
2
0
2
0
0
0
0
0
1
2
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
2
0
0
0
4
0
0
0
1
0
0
0
2
1
1
0
1
0
0
0
0
0
0
2
0
0
0
1
2
0
0
1
2
0
1
2
1
0
0
0
0
0
2
0
0
1
0
0
2
1
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
5
2
0
0
2
2
0
0
2
2
0
0
1
1
1
0
0
0
0
0
1
0
2
0
0
4
0
0
0
0
1
2
0
0
1
0
0
2
2
0
1
0
0
3
0
2
0
0
1
0
0
0
2
1
0
0
0
3
0
0
0
2
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
3
0
2
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
2
0
0
1
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
1
2
0
0
0
0
0
3
1
0
0
1
0
0
2
2
2
1
0
2
0
1
1
1
1
2
0
0
0
0
4
1
0
0
0
1
0
0
2
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
1
0
2
2
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
2
2
0
0
2
1
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
3
0
0
0
0
1
0
0
2
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
2
0
1
0
0
1
0
3
0
0
0
0
0
0
3
3
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
1
0
0
1
2
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
2
1
2
0
0
0
0
1
2
0
0
0
2
0
0
2
1
1
1
1
0
1
1
2
0
0
2
1
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
1
1
0
1
0
2
0
1
0
0
2
1
2
3
0
1
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
2
0
0
0
1
0
1
2
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
1
0
0
0
2
0
1
0
0
0
2
0
0
0
0
3
0
2
1
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
2
1
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
1
1
0
0
0
0
2
5
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
1
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
3
2
0
2
1
0
1
0
0
0
0
2
2
0
3
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
1
2
0
0
0
0
0
0
1
0
0
0
1
0
2
2
0
1
0
1
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
1
0
1
0
3
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
1
0
2
0
1
0
1
0
0
0
0
0
0
3
1
0
1
0
0
0
0
3
0
0
1
1
0
0
0
2
1
0
0
0
0
2
2
0
0
4
0
5
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
2
1
2
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
4
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
2
1
0
0
0
1
2
0
0
0
0
2
1
1
0
1
0
0
0
1
4
0
0
0
1
0
2
0
0
0
0
0
0
2
2
0
0
1
3
0
1
0
2
0
0
1
1
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
4
2
1
1
0
0
0
0
0
0
0
1
0
0
1
2
2
0
2
0
1
0
0
0
3
2
0
0
0
0
2
0
0
2
0
0
0
2
1
0
0
0
1
1
0
0
0
1
1
2
0
0
1
1
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
1
2
0
0
0
0
0
0
0
3
1
2
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
2
0
1
2
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
3
0
2
0
0
0
0
0
2
2
0
0
1
0
0
1
0
0
0
0
0
0
2
2
0
2
2
2
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
2
0
2
0
0
2
0
2
1
0
1
0
2
2
0
0
0
2
0
0
1
0
0
1
1
0
0
2
0
2
0
1
1
0
0
0
0
2
0
0
0
1
0
2
0
0
2
2
2
0
0
0
0
0
2
1
2
1
0
0
1
0
0
0
2
0
0
2
2
0
3
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
2
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
3
1
0
0
0
0
2
0
2
1
2
0
0
0
0
0
0
1
1
0
0
2
1
0
0
0
3
0
1
0
0
0
0
2
0
0
2
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
2
0
1
0
0
2
1
0
0
2
0
0
1
2
0
0
2
0
2
1
0
0
0
0
2
1
1
5
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
1
2
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
3
0
0
0
0
1
0
4
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
1
0
2
0
0
1
0
0
0
2
0
0
0
0
1
2
0
1
0
0
1
0
1
0
0
0
3
0
1
0
0
0
0
0
1
2
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
2
0
1
0
0
1
4
0
0
0
1
0
2
0
1
0
0
0
0
2
2
0
0
0
0
1
0
1
0
0
0
2
2
9
0
2
0
0
1
0
0
0
0
0
2
2
0
1
1
0
1
0
1
0
0
0
0
0
0
0
2
1
0
3
0
0
1
0
0
1
0
2
0
0
2
0
0
0
2
2
1
0
2
1
2
2
1
0
0
2
0
1
0
2
0
1
0
0
0
0
0
0
0
0
1
1
0
0
2
4
1
0
2
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
3
0
0
0
0
0
0
0
2
1
4
0
0
0
2
0
0
0
1
0
3
0
0
0
0
0
0
0
5
1
0
2
0
2
0
0
0
0
0
0
1
0
1
0
5
0
0
0
0
0
1
0
1
0
0
1
0
2
1
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
1
0
0
0
4
1
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
1
2
0
2
1
0
2
0
0
0
0
1
1
3
0
0
0
0
0
0
0
6
0
0
0
0
3
1
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
3
0
2
0
2
0
0
2
0
0
0
1
4
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
2
1
2
2
0
1
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
2
0
2
0
0
7
0
0
3
2
0
0
0
2
0
0
2
0
2
2
0
0
1
0
0
0
0
0
0
2
2
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
2
1
0
0
0
3
0
2
0
1
1
1
2
0
4
0
2
1
0
3
0
0
0
0
1
2
0
1
0
0
4
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
2
0
0
1
1
0
2
2
0
0
0
0
0
0
1
0
3
1
0
0
2
0
0
3
0
0
0
0
1
2
0
2
0
2
0
0
0
0
2
2
1
0
4
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
2
2
0
1
0
0
1
0
0
0
1
0
0
0
2
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
1
1
0
0
2
0
0
0
2
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
1
0
0
0
1
1
1
0
2
0
1
0
0
0
0
2
0
0
0
1
1
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
4
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
1
0
2
0
2
2
0
0
1
2
2
0
0
0
1
0
1
0
0
0
2
0
0
1
1
0
1
2
0
0
0
3
1
2
0
0
0
0
0
0
0
0
0
3
2
3
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
2
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
3
2
2
0
5
1
0
0
1
2
0
0
0
0
1
2
0
1
0
1
0
2
0
1
2
0
0
0
2
0
0
0
0
1
2
1
1
0
0
0
0
2
0
0
4
5
1
1
1
2
2
4
2
0
2
2
0
1
0
0
2
1
0
1
0
2
0
1
1
0
2
0
2
1
0
0
0
0
0
2
0
0
0
0
2
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
3
2
0
0
0
2
0
1
0
0
0
1
0
1
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
1
0
3
1
0
2
0
0
0
0
0
1
0
0
0
2
1
2
0
0
0
2
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
2
1
0
0
2
0
0
0
1
1
0
0
2
1
0
0
2
0
0
0
0
1
0
0
0
1
2
1
0
0
2
1
0
0
1
0
2
0
1
1
1
0
2
0
5
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
1
3
0
0
2
0
2
0
1
0
2
0
0
0
0
1
1
0
3
0
1
0
0
1
0
0
0
0
2
0
0
0
1
1
0
2
0
0
2
0
0
0
0
0
2
0
0
0
1
2
1
0
0
1
1
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
1
0
1
0
2
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
4
0
1
1
0
0
0
1
0
0
0
2
2
0
2
0
2
0
0
0
1
0
0
0
0
1
0
0
1
1
2
0
2
1
1
0
2
0
1
0
0
0
0
0
5
0
0
0
0
0
0
0
1
0
0
1
2
2
1
0
2
0
0
0
0
0
1
0
0
0
0
2
1
1
0
2
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
1
1
0
0
0
0
0
0
2
1
0
0
3
0
0
0
1
2
0
0
1
2
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
1
2
1
1
0
5
0
2
2
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
2
2
1
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
2
2
1
8
0
0
1
2
1
3
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
2
0
0
0
1
1
2
0
0
0
0
0
0
2
0
0
0
1
0
0
2
2
0
0
0
0
0
0
1
2
0
1
0
3
0
0
2
1
0
0
0
0
0
2
0
3
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
2
0
0
2
0
3
1
2
0
0
0
0
2
0
0
1
0
0
2
0
0
2
0
0
2
0
0
1
0
1
0
0
1
1
2
2
0
1
3
0
2
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
2
0
0
2
1
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
1
3
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
2
1
0
0
2
0
0
1
0
0
1
0
0
0
1
0
0
1
2
0
0
2
0
0
0
0
0
1
1
2
2
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
2
3
2
2
0
0
3
0
1
2
0
0
0
0
2
1
0
2
1
1
0
0
0
1
0
0
2
0
0
2
1
0
0
0
0
0
0
3
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
1
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
2
0
0
0
2
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
1
0
1
2
2
0
2
0
0
2
3
0
1
1
0
0
0
0
0
2
0
0
0
1
0
0
2
0
4
0
0
0
0
0
2
0
1
0
1
1
0
0
2
0
2
2
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
2
1
0
1
0
0
0
1
0
0
2
1
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
1
0
0
0
1
0
0
1
0
1
0
0
0
3
2
0
0
2
2
0
0
0
2
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
2
1
0
0
0
1
0
0
2
0
0
0
2
0
2
2
0
1
2
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
1
1
2
0
0
0
1
0
0
2
2
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
4
0
0
2
0
0
0
0
1
0
2
0
0
0
0
2
0
0
2
0
0
0
0
1
1
2
0
3
2
0
2
1
12
1
0
1
0
0
1
3
1
1
2
0
0
1
0
0
0
0
2
0
1
0
0
1
0
0
1
1
1
4
0
0
0
1
0
0
2
1
0
1
1
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
1
2
1
0
2
0
0
0
0
2
2
1
0
2
0
0
0
1
0
1
0
2
0
0
2
0
0
0
1
0
0
0
2
1
1
1
1
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
1
0
1
2
0
0
0
0
0
2
0
1
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
3
0
0
0
1
0
0
0
1
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
1
2
0
0
1
0
1
0
2
3
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
2
1
0
2
1
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
4
0
0
0
0
0
2
2
2
0
3
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
3
0
0
0
1
2
0
1
0
2
2
0
2
0
1
1
0
2
1
0
1
1
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
2
0
1
2
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
2
0
2
0
0
0
2
0
1
0
0
1
0
0
0
2
2
0
0
0
0
0
2
0
0
2
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
1
1
0
1
1
0
0
0
0
1
0
1
0
0
2
0
0
2
0
0
2
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
5
0
0
0
0
1
1
2
3
2
2
0
2
0
4
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
2
0
0
2
3
0
1
0
0
0
2
0
0
0
3
0
0
1
0
2
0
0
0
0
0
1
0
2
2
0
0
0
2
1
0
0
3
0
0
1
1
0
1
0
0
0
0
6
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
1
0
0
1
0
1
2
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
1
0
1
0
0
0
2
2
0
1
0
0
3
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
6
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
1
0
2
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
2
0
2
0
2
0
1
0
2
1
0
1
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
1
2
1
0
0
1
0
0
0
1
2
1
0
0
0
1
2
0
0
0
0
0
0
1
2
0
1
0
1
0
0
1
0
0
2
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
1
0
0
7
1
5
0
2
0
0
1
0
0
0
2
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
2
0
2
1
0
0
0
1
2
1
0
0
2
1
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
2
0
1
0
2
0
0
0
0
0
2
0
1
0
0
0
1
1
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
2
2
2
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
3
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
3
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
1
0
3
0
0
0
0
2
0
3
0
0
1
1
2
0
0
0
0
2
0
0
1
2
0
2
0
1
0
0
0
0
0
0
0
1
1
0
2
2
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
2
1
1
0
2
0
2
0
0
0
0
1
1
2
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
1
2
1
0
0
0
0
0
0
0
2
0
0
2
2
0
1
0
0
0
1
0
0
0
1
0
1
3
0
0
0
0
0
0
2
1
1
0
0
2
1
1
0
0
1
1
0
0
2
1
0
0
0
0
0
0
8
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
3
0
0
0
1
0
0
2
1
0
0
0
0
2
0
0
2
0
0
0
0
5
0
1
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
3
0
0
2
0
2
0
0
0
2
1
2
0
0
0
0
6
0
2
0
0
0
0
0
1
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
2
1
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
1
2
2
0
0
0
1
2
2
2
0
1
1
0
0
0
0
0
1
1
1
0
2
0
0
0
1
2
2
2
0
0
1
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
1
2
1
1
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
4
0
0
2
1
1
0
0
0
0
1
1
0
0
2
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
2
2
0
0
1
0
0
1
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
2
2
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
1
0
2
0
0
0
1
2
0
0
4
0
2
0
0
1
0
0
0
2
0
1
0
0
2
0
2
0
0
0
0
0
0
0
1
0
1
0
0
1
0
4
0
1
0
2
2
0
0
0
1
0
0
2
2
0
1
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
1
1
0
0
2
0
1
0
0
0
1
0
0
2
0
2
2
0
0
0
2
0
2
1
0
0
0
0
0
0
1
0
0
2
0
2
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
2
0
1
2
0
0
0
0
0
0
1
1
2
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
2
0
1
2
0
0
0
2
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
2
0
0
0
0
2
0
1
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
2
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
4
0
2
0
0
2
0
0
0
0
3
0
1
0
0
0
0
0
1
0
0
2
0
0
1
0
0
1
0
2
0
2
0
0
0
0
2
0
1
0
0
2
0
0
0
1
1
0
0
1
0
2
0
2
0
1
0
0
0
1
0
0
3
0
2
0
0
0
1
3
0
0
0
0
2
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
2
1
0
2
0
0
1
0
1
2
2
0
0
1
0
2
0
0
2
2
0
1
1
0
1
0
0
0
0
1
0
0
2
0
0
0
1
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
2
1
0
2
2
0
0
3
0
0
0
1
0
0
3
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
2
0
0
0
0
1
1
2
0
1
0
0
0
1
2
0
1
0
0
2
2
0
0
0
2
0
2
0
1
0
0
0
0
0
0
2
2
3
0
1
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
2
0
0
0
2
0
0
0
1
0
1
0
1
2
0
0
0
2
1
0
0
0
1
2
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
2
0
0
0
0
2
2
2
1
0
0
0
1
0
3
0
0
0
0
1
0
0
0
1
1
1
1
2
0
0
2
0
2
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
2
0
2
0
2
1
0
1
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
2
0
1
1
1
2
2
2
1
0
0
0
0
0
1
0
0
0
0
0
0
3
0
2
0
0
1
0
0
0
2
1
0
0
0
0
1
4
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
2
0
0
0
0
1
2
0
0
0
2
0
2
2
0
1
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
2
1
0
0
1
0
0
0
0
0
2
1
0
2
0
0
2
0
3
0
0
0
1
2
0
2
2
2
0
0
2
0
0
0
0
3
0
1
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
1
0
2
0
1
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
2
0
1
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
1
2
1
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
1
0
1
0
0
0
2
0
1
0
0
0
2
0
0
1
2
2
1
1
0
2
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
2
0
1
0
2
2
0
0
0
2
0
0
0
3
0
1
0
0
0
1
3
0
1
2
2
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
4
0
0
1
0
2
1
2
0
0
0
0
2
1
2
1
0
0
0
0
2
0
0
0
1
0
3
0
0
0
0
0
0
2
2
0
0
0
0
0
1
2
2
0
1
2
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
1
2
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
1
0
2
0
1
0
0
0
2
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
3
0
0
0
0
0
2
0
1
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
3
1
0
0
2
0
0
0
0
0
2
2
3
1
0
2
0
1
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
2
1
2
0
0
0
0
0
2
0
0
3
0
2
2
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
1
1
0
1
0
1
0
0
0
3
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
1
1
1
1
0
2
2
0
2
1
0
1
0
0
0
2
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
1
0
0
2
0
0
1
0
0
2
2
0
0
0
4
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
2
0
0
1
1
3
0
0
0
0
0
0
0
2
2
0
0
0
1
0
2
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
2
1
1
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
2
0
0
0
2
0
2
2
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
1
2
2
0
0
0
0
1
0
1
1
1
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
2
0
3
2
0
0
0
0
0
0
2
0
9
0
0
0
0
2
0
0
2
1
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
2
0
1
0
2
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
6
0
0
0
2
1
1
0
2
0
2
2
0
0
2
0
0
2
1
0
0
2
0
0
0
0
0
2
1
0
1
0
0
0
0
2
2
0
0
0
0
2
2
0
1
2
1
0
0
2
2
1
1
1
0
1
0
0
0
0
2
0
3
2
2
2
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
1
0
2
0
1
0
3
1
0
0
3
0
0
4
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
1
2
0
0
0
0
2
0
1
0
0
0
0
2
2
0
0
0
1
0
1
0
1
0
1
2
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
2
0
0
3
0
2
3
2
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
2
0
2
0
0
0
0
1
0
7
0
1
3
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
2
2
0
1
0
0
0
0
0
1
0
1
0
2
2
2
0
0
0
2
0
0
1
0
0
0
0
0
1
1
1
1
0
2
0
0
2
2
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
1
2
0
3
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
1
5
0
0
2
0
2
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
2
0
2
5
0
3
2
0
0
0
1
0
0
1
0
1
0
2
0
2
0
1
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
1
0
0
2
1
2
0
1
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
2
0
2
0
2
0
0
2
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
6
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
3
0
0
1
2
0
0
0
0
0
0
1
0
1
1
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
2
0
0
1
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
1
1
0
2
0
0
1
1
0
0
0
0
0
0
2
1
1
0
0
2
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
5
0
0
2
1
2
1
1
2
0
0
0
0
4
0
0
1
0
0
1
0
0
1
0
0
0
0
0
2
0
0
1
0
0
1
0
2
0
2
0
0
0
0
0
0
2
1
0
1
0
0
1
0
0
1
0
0
2
0
0
0
1
0
0
2
0
0
0
0
2
0
0
1
0
0
0
1
0
1
1
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
3
0
1
0
0
1
0
2
0
0
1
0
0
0
1
0
0
0
0
1
3
0
0
1
0
1
2
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
1
2
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
2
0
0
0
3
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
3
0
1
0
0
0
1
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
2
0
2
0
1
0
0
0
1
0
1
0
0
1
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
3
1
1
2
0
0
0
0
0
0
0
0
2
2
2
0
2
0
0
0
1
0
2
0
1
1
7
0
0
0
0
0
0
0
1
0
0
1
0
0
2
2
0
0
0
0
0
0
2
0
2
1
2
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
2
1
0
0
0
2
0
2
0
0
0
0
2
0
2
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
2
0
0
1
2
0
1
0
0
2
0
1
0
0
1
0
2
1
2
0
1
0
2
1
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
1
0
1
1
0
1
2
1
3
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
2
0
1
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
2
1
0
0
1
1
0
2
0
0
0
0
0
0
0
3
1
0
0
0
2
0
2
0
2
0
1
0
0
2
0
0
0
1
0
0
0
1
0
0
1
2
0
0
0
0
0
1
0
0
3
1
0
0
2
3
0
0
0
1
0
0
0
2
2
0
0
0
2
2
0
2
0
0
1
0
0
2
0
0
2
0
0
1
0
1
1
0
1
0
2
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
3
2
0
2
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
1
2
2
0
2
0
0
2
2
1
1
0
2
0
0
2
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
3
2
2
0
0
1
1
0
0
1
0
0
1
1
0
4
0
0
1
0
2
0
0
2
0
2
0
0
0
1
1
2
0
2
1
0
0
0
0
0
0
0
0
1
1
0
1
1
0
2
1
0
0
0
0
0
2
0
3
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
2
0
0
2
0
0
1
1
1
0
2
0
0
0
2
0
1
1
0
0
2
0
0
0
1
0
0
0
1
0
0
0
2
0
0
2
0
0
2
0
0
0
1
0
0
0
1
2
2
0
0
0
0
0
2
0
2
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
2
0
0
1
0
0
1
0
0
0
0
0
3
0
0
2
0
0
1
2
0
0
0
0
0
2
4
0
1
0
1
0
0
0
0
1
1
1
0
0
0
1
6
1
1
1
0
0
1
0
0
0
0
0
0
0
1
2
2
0
1
0
1
0
2
0
0
0
1
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
3
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
2
0
0
1
0
0
2
2
1
0
0
0
0
0
1
0
0
2
2
0
0
2
3
0
0
2
2
0
0
1
2
0
0
2
2
0
0
2
1
2
0
0
1
0
2
1
0
0
0
0
0
1
0
1
0
2
0
0
0
2
0
4
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
1
0
1
1
1
1
0
0
0
0
0
0
0
1
1
0
2
0
0
1
0
1
1
1
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
1
0
2
1
1
0
0
0
0
0
0
0
2
1
0
1
2
2
2
0
1
0
1
0
1
0
1
2
0
1
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
1
2
0
1
0
4
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
1
0
1
0
2
2
2
0
3
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
1
2
0
0
0
0
1
0
0
0
0
0
1
0
2
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
7
0
0
0
2
1
0
1
0
0
1
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
1
0
0
1
2
0
0
0
0
0
0
0
1
1
0
0
1
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
1
0
4
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
3
2
0
2
0
1
2
0
0
1
0
0
0
0
0
0
1
2
1
0
0
0
1
3
0
0
3
0
0
1
2
0
0
1
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
1
0
3
0
3
0
1
1
1
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
2
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
1
1
0
1
0
0
0
1
0
0
0
2
0
0
0
1
2
0
0
1
2
0
0
0
0
2
0
0
0
1
0
0
0
5
0
0
0
0
0
0
2
0
2
2
0
0
2
0
0
0
0
2
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
1
0
0
1
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
8
0
3
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
2
0
2
0
0
0
0
0
1
0
0
0
2
1
2
0
1
0
0
1
1
1
1
0
0
1
1
0
0
1
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
1
1
0
0
0
2
2
0
1
1
0
2
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
3
0
0
0
0
1
0
2
0
1
2
0
0
0
0
1
0
0
1
2
0
2
1
0
2
2
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
2
2
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
1
0
1
2
1
0
0
0
0
1
1
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
2
0
2
1
0
3
0
0
0
0
1
0
2
1
1
0
0
0
2
0
1
0
1
1
2
0
1
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
1
0
2
0
1
2
0
0
0
1
3
0
1
0
0
1
0
1
0
1
0
0
0
0
2
1
0
0
1
0
0
4
0
0
0
1
2
0
0
0
0
2
1
3
0
0
0
0
0
0
0
0
0
0
2
1
0
2
2
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
3
1
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
3
0
2
4
2
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
2
0
1
1
1
0
0
0
0
0
1
0
0
1
2
0
1
7
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
2
2
0
1
2
2
0
0
1
1
1
0
0
1
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
2
0
1
0
2
3
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
2
0
0
1
1
0
0
2
2
0
0
0
2
0
0
0
0
0
1
0
2
0
1
0
0
1
0
1
0
1
0
0
1
0
1
0
3
0
0
2
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
1
0
0
2
0
0
1
1
2
0
2
0
2
1
0
0
0
0
1
1
0
0
1
2
0
0
2
0
1
0
1
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
2
0
0
2
0
0
0
0
0
1
0
0
0
2
0
1
0
2
0
0
1
0
2
1
1
1
0
2
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
1
0
0
7
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
1
0
1
2
0
0
1
1
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
1
2
0
0
0
1
0
2
1
0
0
0
2
0
0
0
1
0
0
0
0
0
1
2
3
0
0
0
0
0
0
0
2
1
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
4
1
2
0
0
0
0
0
0
3
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
2
1
1
2
1
0
3
0
0
2
0
0
1
1
0
0
0
0
0
1
1
0
1
1
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
2
0
1
0
1
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
1
1
1
1
7
0
3
0
0
0
1
2
1
0
3
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
1
4
0
0
2
0
2
0
1
2
0
2
0
0
0
0
0
0
0
1
2
0
3
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
2
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
3
2
1
0
0
2
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
2
1
1
0
0
2
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
3
0
2
0
1
0
0
2
2
0
0
2
0
0
1
0
2
1
2
2
1
1
0
0
0
0
0
1
0
0
1
0
0
1
2
2
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
3
0
3
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
1
0
1
0
0
0
2
0
0
0
0
2
1
0
1
0
1
0
2
0
1
0
0
0
2
0
2
2
0
2
2
1
1
1
0
0
1
1
0
2
1
0
1
1
0
2
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
2
0
0
1
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
6
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
2
0
0
2
3
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
2
1
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
3
0
4
0
1
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
1
2
0
2
0
2
2
0
1
0
0
0
2
0
4
1
0
0
2
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
2
1
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
1
0
2
0
0
0
1
0
0
3
0
1
0
0
0
2
2
2
1
0
0
0
0
0
2
1
0
1
0
0
1
0
2
0
1
0
1
2
1
1
3
0
0
1
1
0
0
3
0
0
0
0
2
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
1
0
0
0
1
2
0
0
0
0
0
0
3
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
2
1
1
0
0
0
0
1
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
2
1
1
0
2
0
0
1
0
2
1
1
0
0
0
0
0
1
0
1
2
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
3
1
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
1
0
0
0
0
3
1
1
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
1
0
0
1
1
0
3
2
0
0
0
0
0
2
0
2
0
0
0
1
1
1
0
1
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
2
0
0
1
0
0
1
0
0
0
2
0
0
1
0
3
3
0
0
1
0
2
1
1
0
0
0
0
1
1
1
0
0
0
1
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
2
0
1
0
0
0
0
0
1
0
1
0
0
0
2
0
0
2
1
1
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
2
2
0
0
0
0
2
0
2
0
0
0
0
0
1
0
4
0
0
0
2
0
0
0
0
0
1
2
5
0
0
0
0
1
1
0
0
0
0
2
1
0
0
0
0
1
2
2
0
0
0
0
1
3
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
3
0
1
0
0
1
2
1
1
0
2
2
2
0
0
3
1
1
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
2
0
0
0
0
1
0
0
0
2
1
0
1
0
3
0
0
0
0
0
0
0
0
0
2
1
2
0
1
0
0
0
2
0
1
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
2
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
2
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
3
0
6
1
1
1
0
0
0
3
0
0
0
0
1
2
1
0
0
0
0
3
0
0
0
0
0
0
1
0
3
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
1
2
0
2
0
0
0
0
1
2
2
0
0
0
0
0
1
0
1
1
0
4
2
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
1
0
1
0
2
0
0
0
5
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
1
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
1
1
2
0
2
0
0
2
0
0
2
5
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
2
2
1
0
3
2
0
1
0
2
0
1
2
2
0
0
0
5
0
0
0
1
0
0
0
2
1
1
2
0
0
0
0
0
0
2
0
1
0
1
1
0
0
1
0
0
0
2
0
2
3
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
2
1
0
2
2
0
0
1
0
2
1
0
0
2
0
0
0
0
2
2
0
0
0
1
0
0
0
0
2
1
0
0
2
0
2
0
0
1
2
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
3
0
2
1
0
0
1
0
0
0
0
1
2
1
2
0
1
0
0
0
2
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
1
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
1
0
0
2
0
1
2
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
2
1
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
1
0
1
0
2
1
0
0
0
2
0
2
2
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
4
0
0
2
0
0
1
0
1
1
0
0
0
2
0
1
0
0
1
0
0
0
2
0
0
2
0
1
2
0
1
0
1
2
0
0
0
0
0
0
1
0
1
0
0
0
2
6
2
0
0
3
1
2
0
1
0
2
0
0
2
2
0
0
1
0
2
0
1
0
3
2
2
0
0
2
0
1
1
0
0
1
2
0
0
2
2
2
0
2
0
0
0
0
0
0
2
0
1
2
2
0
0
1
1
2
4
0
0
1
2
0
0
0
2
0
0
2
0
0
0
2
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
1
4
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
2
2
0
1
1
0
3
0
1
2
0
3
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
8
0
1
1
2
1
1
0
0
0
0
2
3
0
0
2
2
2
1
2
0
1
0
2
0
0
0
1
0
1
4
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
1
0
2
0
2
0
0
0
0
0
3
0
0
2
0
2
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
1
1
2
0
0
0
1
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
5
1
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
1
2
0
0
0
2
2
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
3
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
1
0
0
0
3
2
2
2
0
0
0
0
2
0
0
0
2
5
0
0
2
0
2
2
0
2
0
0
0
0
2
0
0
2
0
0
0
2
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
3
1
1
2
0
1
0
0
2
0
0
0
1
0
0
0
1
1
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
2
2
0
2
2
0
0
1
0
0
0
1
0
1
3
1
1
0
2
0
1
2
1
2
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
1
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
2
1
1
2
0
0
0
2
0
0
2
2
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
1
2
0
1
0
2
0
0
1
2
1
0
0
2
1
0
0
0
0
3
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
1
0
2
0
0
0
1
0
1
0
2
0
0
2
0
1
0
1
0
1
0
1
0
2
0
0
1
1
2
1
0
2
3
0
0
0
0
2
0
1
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
1
0
1
2
0
0
1
0
0
0
4
0
2
2
2
0
0
0
0
0
0
0
1
3
2
0
1
0
0
0
0
2
0
0
2
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
1
2
0
2
2
0
0
2
0
2
1
1
1
1
1
0
0
2
0
0
0
0
1
2
0
0
0
0
0
2
0
0
1
1
3
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
5
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
3
0
0
0
1
1
0
0
0
0
0
1
2
1
0
0
0
2
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
1
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
1
0
2
0
0
0
2
0
2
1
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
1
3
0
1
1
0
2
0
0
0
1
1
0
0
0
0
0
0
1
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
1
0
0
0
3
0
2
0
1
0
0
0
0
0
1
2
0
0
0
0
3
1
0
0
2
2
0
0
0
0
1
2
1
0
2
2
0
0
0
0
1
0
0
4
1
0
0
1
0
1
0
2
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
3
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
2
0
0
2
2
2
1
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
5
1
0
0
0
0
0
0
0
0
1
1
0
1
2
1
0
0
1
0
0
0
2
2
0
1
0
2
2
0
1
3
2
1
1
2
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
1
1
2
2
0
0
0
0
0
0
1
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
3
0
0
1
0
0
0
0
7
0
2
0
0
2
0
0
2
0
1
0
2
2
0
1
0
0
1
0
0
2
1
2
2
0
1
0
0
0
0
0
1
1
1
1
1
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
2
0
2
2
1
0
1
1
1
0
0
0
0
0
0
0
2
0
0
0
0
2
3
2
2
0
0
2
0
0
0
0
0
0
1
0
0
1
0
2
2
2
2
0
0
0
0
0
0
1
1
1
2
0
0
0
0
1
1
0
0
2
0
2
0
0
0
0
1
0
0
2
1
0
0
0
0
0
18
1
0
0
2
0
2
3
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
1
3
1
0
0
1
0
0
2
0
0
2
0
0
0
1
0
3
0
1
0
0
0
0
0
0
2
2
0
0
1
0
0
1
2
0
0
0
0
2
2
2
2
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
1
2
0
2
1
0
0
0
0
2
1
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
2
0
0
0
1
0
0
2
2
0
3
0
0
0
0
0
1
0
0
0
0
2
1
1
0
0
0
0
2
1
0
0
1
0
0
3
0
0
0
1
1
0
0
0
0
2
2
2
0
0
0
0
0
3
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
3
0
3
0
0
0
1
0
0
0
0
2
0
0
2
0
1
0
2
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
2
2
1
0
1
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
8
0
1
0
2
1
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
2
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
2
5
1
2
0
3
2
3
1
1
0
2
0
0
0
0
1
0
1
0
0
0
0
1
2
2
0
0
0
0
1
0
0
0
0
2
2
0
2
0
0
0
0
0
2
2
1
1
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
1
0
1
1
0
0
0
2
2
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
1
1
2
0
0
0
1
0
0
0
0
0
2
1
3
0
2
0
1
0
0
2
0
0
0
2
0
0
2
1
0
2
2
4
0
0
0
1
0
0
1
0
1
0
0
1
0
0
1
0
0
2
0
0
0
0
2
0
2
4
0
1
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
2
1
0
1
0
0
1
2
0
0
2
0
0
0
0
0
0
1
0
1
1
1
2
2
2
0
0
4
0
0
0
0
2
0
0
2
0
0
2
0
0
0
2
0
1
1
2
2
0
0
0
0
0
0
3
0
1
0
2
2
0
2
0
1
2
3
0
0
2
1
1
0
1
0
0
2
0
1
0
0
0
1
0
0
2
0
0
0
1
1
0
2
0
1
0
0
0
0
0
0
0
1
0
1
1
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
2
1
0
4
0
2
0
0
2
0
2
1
0
0
2
0
1
0
1
0
2
2
0
0
1
2
1
0
0
0
0
0
3
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
2
2
0
0
0
0
0
2
0
1
0
1
0
2
0
0
0
0
0
2
2
1
0
0
2
2
4
0
0
2
1
0
3
1
1
0
0
2
0
0
0
0
1
3
0
1
1
0
0
2
0
2
2
0
0
0
0
0
2
0
0
0
0
2
0
0
2
1
1
0
4
0
0
0
0
0
2
0
0
2
0
1
2
0
1
0
4
2
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
2
2
0
1
0
0
0
1
0
0
0
0
2
0
0
3
2
0
0
2
1
0
0
0
1
1
1
3
2
2
0
0
1
0
2
1
0
2
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
2
3
2
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
2
0
2
0
3
0
1
0
1
1
1
4
2
0
0
1
2
0
2
2
1
0
1
0
0
2
0
0
0
1
2
0
0
0
3
0
0
1
1
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
3
4
0
0
2
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
3
0
0
0
3
0
0
0
0
3
0
0
2
0
0
0
0
2
0
0
1
0
0
1
0
1
0
1
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
2
0
1
0
0
0
2
1
0
0
2
0
1
0
3
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
1
0
0
1
2
0
0
2
0
2
2
0
3
1
2
1
0
0
0
0
1
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
3
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
2
0
1
0
0
2
2
1
0
2
1
0
0
3
0
0
0
2
0
0
0
0
1
0
2
0
0
5
0
1
0
0
0
1
2
1
0
2
0
0
0
0
0
2
3
0
0
0
1
0
0
0
0
2
0
1
1
0
0
0
0
2
0
2
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
2
1
0
1
1
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
2
2
2
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
1
0
2
0
1
2
0
0
2
0
0
0
1
0
2
0
0
2
0
0
1
0
0
0
0
0
0
1
2
1
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
2
2
0
0
2
1
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
2
6
1
0
3
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
1
0
0
0
1
3
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
1
1
1
0
0
0
4
0
1
2
2
0
0
0
1
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
1
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
8
0
2
2
2
0
2
0
0
0
0
2
3
0
0
2
0
0
0
0
1
0
0
2
2
0
1
0
1
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
2
1
0
0
1
0
0
2
1
0
0
0
0
0
2
0
1
2
0
1
1
1
0
0
1
0
0
0
11
0
0
0
0
0
0
1
1
0
0
0
0
3
0
0
0
0
2
1
0
0
0
0
1
2
0
0
0
0
3
1
0
0
0
2
0
1
1
0
0
0
0
1
1
0
0
0
2
2
0
0
0
2
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
1
0
0
1
1
0
2
2
0
0
0
1
0
0
0
1
0
0
0
1
1
0
2
0
0
0
0
2
2
1
0
0
0
0
0
1
0
0
1
0
0
2
0
1
0
3
0
0
0
1
0
3
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
2
2
0
0
2
1
0
0
0
1
0
0
2
0
0
2
1
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
1
9
2
1
1
0
0
0
1
1
2
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
2
2
1
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
3
0
1
0
1
1
0
0
1
2
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
3
0
1
2
1
2
0
0
0
0
1
0
0
0
1
0
0
1
0
2
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
2
0
0
0
1
1
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
2
2
2
0
0
1
0
2
0
0
1
0
0
0
0
0
0
2
1
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
2
4
1
1
2
0
0
2
1
0
0
2
0
0
2
0
0
0
1
0
0
0
1
2
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
6
0
0
0
1
0
0
0
2
0
2
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
3
2
0
2
0
0
0
2
1
0
0
0
2
0
0
0
1
2
0
2
0
0
2
0
0
0
3
0
2
0
0
0
0
3
0
0
0
1
0
0
0
0
2
0
2
0
1
1
0
0
0
0
0
0
1
1
2
1
0
0
0
0
0
0
1
1
0
1
0
0
2
0
0
2
0
0
0
0
1
0
0
0
2
1
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
3
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
2
1
2
0
0
0
0
0
0
0
0
2
2
0
1
0
2
0
0
0
0
0
1
2
0
0
1
0
2
0
0
1
1
0
1
4
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
1
1
3
0
2
1
0
0
0
1
2
0
0
0
0
0
0
0
2
0
1
0
0
0
3
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
1
0
2
0
1
2
0
0
0
0
1
2
0
2
0
0
0
0
1
1
1
2
2
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
1
0
0
1
0
1
2
2
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
1
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
2
0
0
2
0
0
0
0
0
1
2
2
1
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
2
1
0
3
0
0
0
0
0
0
0
2
0
1
1
0
1
0
0
0
0
1
0
1
0
1
2
0
3
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
2
0
0
0
0
1
0
1
0
2
0
2
0
5
0
1
1
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
1
1
0
0
0
1
0
0
2
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
4
1
2
1
2
0
3
1
0
0
2
0
0
0
0
2
9
2
2
1
0
2
1
0
0
0
0
0
2
0
0
0
1
0
0
0
2
2
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
3
0
2
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
4
3
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
9
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
4
1
0
0
0
2
2
0
0
0
0
0
1
1
0
0
0
0
2
2
0
1
0
0
2
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
3
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
2
1
2
0
1
0
0
0
0
1
3
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
1
0
1
0
0
2
1
0
1
0
0
1
0
0
0
0
1
0
2
0
3
0
0
0
0
0
1
1
0
0
2
2
0
1
0
0
0
0
2
0
2
1
2
0
0
0
0
1
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
4
0
0
2
1
0
0
0
3
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
5
0
0
1
0
0
0
3
0
0
3
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
1
0
2
0
3
0
0
0
1
0
0
2
0
0
1
0
0
0
2
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
2
0
3
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
1
2
0
1
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
2
2
2
0
0
2
2
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
2
0
2
3
1
1
0
1
0
1
1
0
0
0
2
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
1
0
0
0
4
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
2
0
1
0
0
0
0
2
1
0
0
1
0
0
0
1
3
0
2
0
0
0
0
0
0
2
0
0
4
0
1
0
0
1
1
0
0
0
0
4
0
0
1
0
0
2
3
0
2
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
1
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
1
2
0
0
2
2
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
3
0
2
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
1
0
2
1
0
4
0
0
2
2
0
0
1
0
1
0
0
1
1
0
0
1
0
1
1
2
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
2
0
1
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
1
1
0
2
0
0
0
2
2
0
2
2
1
2
0
0
3
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
1
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
2
0
2
2
2
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
2
0
0
0
1
4
0
2
0
1
0
3
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
4
1
0
1
0
3
0
2
0
2
0
0
2
1
2
0
0
1
3
1
0
0
0
0
0
0
0
2
4
0
2
0
0
2
0
2
2
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
1
1
2
2
0
0
0
0
1
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
1
1
2
2
2
0
0
0
0
1
0
0
1
0
0
1
1
2
2
0
1
0
3
2
0
2
0
0
3
2
4
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
1
0
2
0
0
2
0
0
0
0
0
0
1
0
0
2
1
0
1
0
2
0
0
0
1
0
0
0
0
2
1
0
1
0
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
3
1
0
0
0
0
0
1
1
0
3
0
1
0
0
1
2
0
0
0
0
0
0
1
0
0
1
3
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
2
0
1
0
0
0
2
0
2
0
2
2
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
2
0
1
0
1
1
0
0
1
0
0
1
1
0
2
0
2
0
0
0
0
1
0
0
0
0
1
3
0
0
1
0
1
1
0
0
0
0
0
2
0
0
3
1
0
0
0
1
0
0
0
1
0
2
2
0
0
0
0
1
0
1
0
0
1
2
0
0
1
0
0
0
2
0
0
1
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
2
0
0
0
2
2
0
1
1
0
2
0
0
2
0
0
0
0
0
0
1
0
1
1
0
2
1
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
1
0
0
0
3
0
0
0
2
0
0
2
2
2
0
2
0
0
0
0
0
0
3
0
2
1
0
0
1
0
1
0
0
0
2
2
0
1
1
0
0
0
2
0
0
0
0
2
0
2
2
0
2
1
0
0
0
1
1
0
0
0
2
1
0
0
2
0
1
1
0
0
0
0
0
0
0
2
0
2
0
0
2
0
2
0
0
2
4
0
0
0
2
0
1
2
0
0
2
1
2
1
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
2
1
0
0
0
2
0
0
2
0
0
1
0
0
1
2
0
0
2
0
2
0
0
1
0
0
0
2
2
0
0
1
0
0
1
2
1
0
0
1
0
2
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
1
0
2
1
0
0
0
1
2
2
0
0
0
0
0
0
0
0
2
0
0
2
1
2
3
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
2
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
3
0
1
0
5
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
2
2
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
1
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
2
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
2
2
0
0
0
0
0
0
2
2
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
1
0
0
0
2
2
2
0
1
0
0
2
0
1
1
0
0
0
0
0
0
0
1
0
2
3
0
1
0
3
0
2
1
1
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
2
2
2
0
2
0
1
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
1
1
0
0
0
2
0
0
0
0
0
2
0
1
2
0
0
0
2
0
1
2
0
1
2
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
2
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
4
0
0
1
0
0
0
0
0
0
0
0
10
0
2
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
8
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
1
0
2
0
3
1
1
0
1
0
0
0
2
0
0
0
3
0
0
0
0
2
0
0
0
1
0
2
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
2
2
2
6
0
2
1
0
0
3
2
2
0
0
1
2
0
0
0
0
0
1
0
1
1
0
1
0
0
0
4
0
0
0
1
0
0
2
0
0
3
2
0
0
0
1
0
2
2
0
2
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
1
1
0
0
0
0
0
1
1
1
3
0
2
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
2
2
2
0
3
0
0
0
2
0
4
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
3
1
0
0
0
1
0
0
1
0
2
0
0
2
2
0
0
1
0
0
0
2
0
0
2
2
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
1
1
0
0
0
0
1
3
0
0
0
0
0
0
1
2
0
0
1
1
0
0
1
0
0
0
0
0
0
0
10
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
1
2
0
2
0
0
0
0
0
0
0
0
0
2
2
1
0
1
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
4
1
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
2
0
1
0
0
0
0
2
1
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
1
0
2
0
1
0
1
0
0
2
1
0
0
0
0
0
2
0
0
0
0
5
2
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
1
0
1
0
0
2
0
0
3
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
3
0
1
2
0
1
0
2
0
0
2
0
0
1
2
0
2
0
0
0
0
1
0
1
0
1
2
2
2
0
0
0
0
0
1
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
1
0
0
2
2
0
1
0
0
2
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
2
2
0
1
0
0
0
0
0
0
2
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
3
1
0
0
0
0
0
1
0
0
0
0
0
2
1
1
2
0
0
0
1
0
2
0
0
0
2
1
0
0
2
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
1
0
0
2
0
1
1
1
2
2
2
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
2
0
2
1
0
0
2
0
0
1
1
0
0
1
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
1
2
0
1
0
0
0
1
0
0
1
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
1
1
0
1
0
0
0
2
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
2
0
0
1
0
0
2
2
1
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
2
2
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
1
0
2
1
0
0
1
0
0
0
0
0
1
1
0
0
2
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
2
1
1
0
0
2
0
0
2
0
0
1
0
0
0
1
0
0
0
1
1
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
2
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
2
2
0
0
2
0
0
2
2
1
0
1
0
0
0
1
1
0
0
0
2
0
0
0
2
0
1
0
2
0
1
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
1
0
1
0
0
1
0
1
1
1
0
0
0
0
2
1
2
1
0
0
2
0
0
1
0
0
0
0
1
1
0
1
2
2
3
0
1
0
2
0
0
0
2
2
2
0
0
0
0
1
0
1
0
0
0
0
1
2
2
0
0
1
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
2
0
2
0
2
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
1
1
0
1
0
1
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
1
0
0
2
0
0
1
0
2
0
0
0
2
0
1
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
1
0
1
0
4
2
1
0
0
1
0
1
2
0
2
1
0
0
0
0
0
1
0
0
1
2
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
2
0
2
1
0
0
0
0
1
2
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
2
0
1
1
0
0
1
0
1
1
1
0
1
2
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
1
2
2
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
2
0
0
0
1
0
0
0
2
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
2
1
0
0
0
2
1
0
2
0
2
0
0
2
0
1
0
0
0
2
0
2
0
0
1
3
0
0
3
0
0
0
1
0
0
2
0
0
4
1
0
0
0
0
2
0
0
0
0
3
3
0
0
0
2
0
1
0
0
0
0
2
1
2
0
0
2
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
3
2
2
1
0
0
0
0
0
0
0
1
0
0
0
2
2
0
1
1
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
3
0
0
2
0
0
2
0
0
0
0
0
0
4
0
2
0
2
0
0
2
0
0
2
1
0
1
0
0
0
2
0
0
1
3
0
1
0
4
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
2
0
1
0
3
0
0
0
0
0
0
2
0
2
0
0
2
1
0
0
4
0
1
0
1
0
1
0
5
0
0
0
1
1
1
0
0
0
2
0
1
0
0
0
0
1
2
1
0
2
7
0
0
0
0
2
1
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
3
0
0
2
2
2
0
0
2
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
1
0
0
0
0
1
1
0
0
0
0
1
0
2
0
1
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
2
2
0
1
0
0
2
2
2
2
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
1
1
0
0
1
1
0
0
1
2
0
2
0
0
1
0
0
0
0
0
2
1
1
0
0
0
1
1
0
3
1
0
0
1
0
0
0
2
0
2
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
2
0
2
2
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
3
2
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
1
1
0
0
0
2
0
2
0
0
0
0
2
2
1
0
0
1
0
0
0
2
0
1
2
0
0
1
0
0
1
2
5
0
0
0
0
0
0
0
2
1
1
0
2
0
0
2
2
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
2
0
1
3
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
2
1
0
0
0
1
0
0
0
2
0
0
2
1
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
1
1
0
0
5
0
2
0
1
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
7
1
1
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
4
0
0
0
0
2
0
0
0
2
1
0
0
1
0
0
1
0
0
0
2
0
1
2
0
0
0
0
2
0
0
0
0
3
0
1
0
0
0
0
3
0
0
0
2
0
0
2
0
2
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
2
0
0
0
2
1
0
1
2
1
0
1
0
0
0
1
2
1
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
1
3
0
0
0
1
2
0
0
0
1
1
0
0
0
0
2
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
1
0
4
0
0
2
0
0
0
2
0
0
0
1
1
0
0
0
0
4
0
2
0
1
0
0
0
2
0
0
1
0
0
0
0
0
2
0
1
1
0
1
0
2
1
0
0
0
0
0
0
2
1
1
1
0
0
2
1
3
0
0
0
2
2
4
0
2
0
0
2
2
0
2
0
1
0
1
2
0
0
0
0
0
0
0
2
2
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
1
0
0
2
2
0
4
0
2
2
3
0
0
0
1
0
0
0
0
1
2
1
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
2
0
2
2
0
0
3
0
0
0
0
0
0
2
0
0
0
1
0
2
1
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
1
0
2
0
2
0
0
0
1
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
1
2
0
0
0
1
1
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
2
1
2
0
2
1
0
0
0
0
2
0
0
1
1
0
2
1
2
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
2
1
0
0
0
1
2
1
3
0
0
2
0
0
0
0
0
0
2
7
1
2
0
0
0
0
0
1
0
0
0
0
2
1
1
1
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
3
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
2
0
2
0
1
0
0
0
2
0
0
0
2
0
0
2
1
0
2
0
0
0
2
2
2
0
1
0
2
0
0
0
0
2
2
0
1
1
2
2
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
1
0
0
4
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
2
1
0
0
3
1
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
1
3
0
0
0
0
0
1
2
1
2
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
1
1
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
2
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
1
0
0
1
1
0
0
0
2
0
0
0
1
1
1
2
0
1
0
1
0
2
0
1
0
0
0
0
0
0
0
2
1
0
1
0
0
0
1
0
0
0
0
2
0
0
1
1
0
2
0
0
2
1
0
2
1
1
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
1
1
3
0
0
2
0
0
0
0
0
2
0
2
2
0
2
0
0
1
0
0
0
0
0
0
1
0
3
0
0
4
2
0
0
1
2
0
0
2
0
0
1
0
0
0
0
0
0
2
1
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
1
1
0
0
1
0
0
2
0
0
0
0
1
0
0
2
0
2
0
1
2
1
0
0
0
0
0
1
0
0
2
0
0
0
0
2
1
0
0
1
2
2
0
0
2
0
0
0
2
1
3
0
0
0
0
0
0
2
0
1
0
2
1
0
0
2
1
2
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
2
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
2
1
1
2
2
0
1
0
1
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
1
2
1
0
0
1
0
2
0
1
0
0
0
0
1
0
2
1
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
1
2
0
0
0
0
0
2
0
1
0
0
0
0
3
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
2
0
1
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
2
0
0
0
5
1
0
0
0
0
2
3
2
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
1
0
0
1
0
1
0
2
1
0
0
2
0
0
1
1
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
3
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
1
0
1
2
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
1
2
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
2
0
0
0
0
1
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
2
0
0
0
2
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
1
0
0
2
2
1
0
0
1
2
1
1
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
6
0
0
0
0
2
0
0
2
0
0
0
1
1
0
2
0
0
0
1
2
0
0
0
2
0
0
2
2
0
0
0
0
0
2
0
1
2
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
2
3
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
2
2
0
0
0
0
1
0
1
1
0
1
0
3
0
1
2
0
0
0
2
2
0
0
1
0
1
0
2
1
0
1
1
0
0
0
0
2
0
1
0
0
1
0
0
1
0
0
0
1
0
0
2
0
0
2
0
0
1
0
2
0
0
2
0
0
2
0
0
0
2
1
0
0
0
2
0
1
1
0
1
0
1
1
0
1
2
0
0
0
1
2
0
0
0
0
1
0
0
0
4
0
0
1
0
0
1
0
2
0
1
0
1
0
2
0
0
2
0
0
2
0
0
0
0
0
0
2
0
2
0
2
0
0
0
5
0
0
1
0
1
1
3
0
2
0
0
2
1
2
2
0
2
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
2
1
2
0
0
1
0
0
1
3
0
0
0
0
2
0
0
1
1
0
0
0
0
0
1
2
0
0
0
2
4
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
2
0
1
0
0
0
0
0
0
0
2
1
0
4
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
2
2
0
0
0
0
0
2
1
0
0
0
1
0
2
1
0
0
2
0
3
0
2
0
1
0
1
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
1
4
1
0
0
0
2
0
0
2
0
0
0
1
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
2
2
2
0
0
2
0
0
0
0
0
1
0
4
2
0
0
2
2
0
1
1
0
0
0
0
0
2
0
2
1
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
3
2
0
2
0
0
2
0
2
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
3
0
0
0
0
0
0
0
3
0
2
0
0
0
1
0
0
0
0
1
0
0
2
2
2
0
1
0
0
0
2
2
1
0
0
3
2
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
2
0
2
2
0
0
0
2
1
2
0
0
0
0
3
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
2
1
0
1
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
2
0
1
1
2
0
1
2
1
0
0
0
0
0
0
2
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
3
0
0
0
0
1
0
0
0
2
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
2
1
0
1
0
3
0
2
0
0
1
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
2
1
0
2
2
1
0
3
1
1
0
1
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
1
0
0
0
0
2
0
1
0
3
2
1
1
1
0
0
3
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
2
0
1
0
1
0
2
0
0
0
0
0
1
2
1
0
1
1
0
0
2
0
2
0
0
0
0
0
0
0
1
2
0
1
0
2
2
2
0
0
1
1
0
0
0
0
2
2
0
0
0
0
0
2
0
1
1
0
2
0
1
0
3
2
0
0
0
1
0
0
0
2
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
3
0
1
0
2
6
0
0
0
2
0
0
2
2
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
2
2
2
2
0
0
0
0
1
0
0
1
0
0
0
9
1
0
0
0
0
1
2
0
0
0
2
0
5
2
0
0
0
2
0
2
0
2
0
1
1
2
0
1
0
1
1
4
0
1
0
0
2
0
0
2
3
0
0
0
0
1
0
0
0
2
0
0
2
2
0
0
0
1
2
0
1
0
0
0
1
1
0
0
2
0
0
0
2
2
0
0
1
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
1
0
2
0
0
0
2
0
2
0
0
0
1
0
1
0
2
0
0
1
0
0
0
0
1
0
2
1
2
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
2
2
0
0
1
0
0
0
0
1
0
0
1
0
0
2
0
0
0
2
0
2
0
1
0
1
0
9
0
0
0
0
0
1
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
2
2
0
0
0
0
2
0
0
0
1
0
0
2
0
0
1
0
1
1
0
2
0
0
2
0
1
2
1
1
2
1
0
0
2
0
0
1
0
2
0
0
0
0
1
0
1
0
1
0
0
3
0
2
0
2
0
0
0
2
0
2
0
0
0
0
0
2
0
1
0
1
0
1
2
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
3
0
2
2
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
2
2
0
2
3
0
0
0
0
0
0
0
0
2
2
2
0
1
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
3
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
1
2
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
1
0
1
2
1
0
0
0
0
1
0
0
0
1
0
2
2
2
0
0
2
0
0
2
2
0
2
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
2
0
0
0
4
2
0
0
2
0
1
3
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
2
0
0
0
1
2
1
2
0
0
1
0
2
2
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
2
1
1
0
2
0
0
1
2
2
2
0
0
0
0
0
0
0
1
0
3
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
2
0
1
0
0
4
0
0
0
1
0
2
0
0
0
1
0
10
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
2
0
0
1
0
0
0
0
1
1
0
0
0
1
0
2
1
2
2
0
1
0
0
1
0
0
0
0
2
0
0
0
1
1
2
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
2
1
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
2
1
3
0
1
0
0
1
2
0
1
1
1
0
2
1
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
1
1
0
1
1
0
1
1
0
0
0
0
0
1
0
2
0
0
0
0
1
2
1
1
2
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
2
1
1
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
1
3
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
2
1
0
0
0
0
0
0
2
2
0
0
1
1
2
2
0
0
0
0
0
2
0
0
0
0
2
1
0
1
0
0
0
0
1
0
0
0
1
0
2
0
0
0
2
1
2
0
0
1
0
0
0
0
0
2
2
2
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
2
2
1
0
0
2
0
0
0
0
2
2
2
0
1
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
3
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
4
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
2
0
0
0
0
2
0
1
0
1
0
3
0
2
0
0
0
0
0
5
2
0
1
0
0
1
2
0
2
3
1
0
0
2
1
0
1
0
1
0
0
0
2
0
0
0
0
0
0
1
2
0
2
0
0
0
1
0
2
3
2
0
0
1
0
0
0
0
2
2
1
2
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
2
0
0
0
1
0
2
0
2
1
2
0
0
0
2
0
2
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
1
0
2
1
0
2
0
2
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
2
2
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
6
0
0
0
2
0
2
1
0
0
0
3
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
3
2
2
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
2
2
0
1
1
2
0
1
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
2
2
0
0
2
0
1
0
1
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
2
3
1
1
0
1
0
2
1
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
3
1
0
1
3
0
2
0
0
0
0
0
0
1
0
1
0
0
1
0
2
0
2
0
0
0
3
1
2
0
2
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
1
1
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
1
1
0
0
0
3
0
0
2
1
1
0
0
0
0
0
2
0
0
1
0
2
2
0
3
0
2
0
2
0
0
2
1
1
0
2
2
2
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
1
2
1
0
2
0
0
3
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
3
0
2
0
0
0
0
0
0
2
3
2
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
1
0
2
0
0
0
1
2
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
1
2
2
0
0
1
0
0
0
2
0
0
0
0
3
0
1
2
0
0
0
4
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
2
0
0
0
3
0
0
0
0
0
0
1
1
1
3
0
0
4
0
0
0
0
0
0
0
0
1
1
0
2
0
2
0
0
0
1
0
0
1
2
1
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
4
0
2
0
0
1
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
2
2
0
0
0
0
3
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
2
4
0
2
2
0
0
0
1
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
8
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
1
2
1
1
0
0
1
0
1
0
2
0
0
1
0
0
0
0
0
1
3
0
0
0
0
2
0
2
0
2
1
0
0
1
0
0
0
0
2
1
0
0
0
3
0
0
1
0
1
0
1
0
0
0
0
2
0
0
0
2
0
0
1
0
2
0
0
0
0
3
0
2
0
2
1
0
0
0
2
0
1
0
4
2
0
2
0
0
2
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
2
2
0
0
0
2
1
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
1
0
0
2
0
0
0
0
2
0
1
0
0
1
0
0
0
1
0
0
2
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
2
0
1
2
2
0
0
0
1
2
0
2
2
0
0
0
2
0
0
0
5
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
1
0
0
1
0
0
0
0
0
0
0
2
3
1
0
1
0
0
0
0
2
2
0
0
0
1
2
0
0
2
0
0
0
0
2
1
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
1
0
1
0
4
0
0
2
0
0
1
2
2
0
1
0
0
1
0
0
0
2
0
2
0
1
0
0
1
2
0
0
1
2
0
0
0
3
0
0
1
2
2
2
0
0
0
0
0
1
0
0
0
2
2
0
1
1
2
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
2
0
3
0
0
0
0
0
0
0
0
0
2
0
1
0
0
3
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
2
0
0
0
0
2
0
0
0
0
1
2
1
0
3
0
2
0
0
0
0
0
2
2
0
0
1
2
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
1
0
0
0
1
0
2
0
1
1
0
0
0
0
1
1
0
2
1
0
1
0
0
0
2
0
0
0
0
2
3
2
1
2
0
1
2
1
0
1
0
0
1
0
2
1
2
0
0
0
0
0
2
0
1
2
0
0
0
2
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
1
0
3
2
0
2
0
0
0
2
2
0
0
2
0
0
3
0
0
0
0
3
0
0
0
0
0
0
3
0
1
0
0
0
2
0
0
1
1
0
5
0
0
2
0
0
0
0
0
0
2
4
0
0
2
0
2
2
1
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
2
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
1
0
0
1
2
0
0
0
1
1
0
0
0
0
1
0
0
0
2
0
2
1
2
0
2
0
0
1
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
7
0
0
1
1
0
0
0
0
2
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
2
0
0
2
2
1
0
0
2
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
2
0
0
2
1
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
1
2
2
0
0
1
0
2
0
0
0
0
0
0
1
0
0
1
2
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
2
0
2
2
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
1
0
0
0
1
2
2
0
0
2
1
2
1
0
0
0
1
0
2
0
0
2
3
0
1
1
0
2
0
0
0
0
0
0
1
2
2
0
0
0
0
3
0
0
2
0
1
1
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
1
2
0
2
0
0
0
0
0
2
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
3
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
2
1
2
1
0
0
0
0
2
1
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
3
0
2
0
0
2
0
0
0
2
1
1
1
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
3
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
1
0
0
1
0
1
0
0
0
1
0
2
0
1
1
0
1
0
0
1
0
2
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
1
0
2
2
2
0
0
0
2
0
1
0
1
0
0
1
1
2
0
0
0
2
2
0
0
0
1
2
2
0
1
0
0
0
4
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
1
1
0
0
1
1
0
0
0
2
0
0
0
1
0
2
3
0
1
0
1
2
1
0
0
2
0
0
0
9
0
0
4
0
0
0
1
2
0
0
1
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
1
2
2
0
0
0
1
0
1
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
2
2
1
0
0
2
0
0
4
0
2
0
0
0
2
0
3
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
1
2
0
1
4
2
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
2
0
2
0
1
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
2
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
3
0
1
2
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
2
0
0
0
2
0
2
0
1
1
0
0
0
0
2
2
0
1
1
0
0
0
0
2
0
0
2
0
0
0
2
1
0
0
0
1
5
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
4
2
0
0
0
0
0
1
1
0
0
2
1
0
0
0
0
0
2
0
1
1
0
1
0
0
0
0
0
0
0
2
0
1
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
2
2
0
0
0
0
0
0
2
0
1
1
2
0
0
0
0
3
0
2
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
2
1
0
0
0
1
2
2
1
0
0
0
0
0
2
2
1
7
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
3
0
1
1
3
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
1
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
2
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
1
0
1
3
2
2
0
0
1
1
0
0
0
2
0
0
0
2
0
1
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
1
1
2
3
0
0
1
1
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
1
0
0
5
2
0
0
2
2
0
5
0
0
2
0
0
0
2
1
0
1
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
2
0
0
2
2
0
0
2
0
7
0
0
2
1
0
0
0
1
0
0
1
0
2
4
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
1
0
2
0
0
0
5
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
2
2
0
0
0
0
2
0
1
0
2
0
0
0
0
1
1
1
0
1
1
0
2
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
1
1
1
10
0
0
0
0
0
0
0
0
1
1
2
0
0
0
3
0
0
1
2
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
2
0
2
0
0
4
1
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
2
1
0
0
0
3
1
0
2
0
0
0
0
0
1
0
2
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
1
0
1
3
0
0
0
0
0
0
0
1
0
0
2
2
0
2
0
0
0
1
0
2
1
0
2
0
0
0
0
0
0
0
2
0
0
2
0
2
0
1
0
1
0
0
0
3
2
1
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
1
0
2
0
1
0
0
0
2
1
0
0
0
1
0
1
0
0
2
0
0
2
0
0
2
1
1
1
0
0
1
0
0
2
0
1
3
1
0
0
1
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
2
2
2
0
0
0
0
2
2
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
2
0
3
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
1
0
0
0
2
1
0
0
1
0
2
0
0
1
0
2
2
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
1
0
1
0
0
0
0
0
0
0
6
1
1
0
1
1
1
1
0
2
1
0
2
2
0
0
2
0
0
0
0
0
2
2
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
1
0
3
2
0
0
0
0
2
1
1
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
2
0
1
1
0
0
1
1
0
0
0
0
1
0
0
0
2
1
2
1
0
0
0
0
1
0
0
2
0
1
0
0
3
1
0
1
1
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
2
1
0
4
1
2
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
4
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
2
1
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
3
0
1
0
1
0
0
0
1
0
0
2
1
0
0
1
2
0
0
1
0
1
2
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
1
0
2
2
0
0
0
2
1
0
0
0
1
0
0
1
0
0
0
2
2
0
0
0
0
2
0
0
2
0
0
0
1
1
3
2
0
1
0
0
1
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
2
5
0
0
1
1
1
0
0
0
0
0
2
0
3
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
5
0
0
0
0
2
1
2
2
0
0
0
0
0
0
2
2
0
1
1
0
0
2
0
0
0
0
0
1
0
0
0
0
1
2
0
1
2
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
1
1
2
0
1
1
1
0
1
0
2
1
1
1
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
1
0
0
1
0
2
2
0
2
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
3
1
0
0
0
0
0
0
1
1
0
0
0
2
2
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
1
0
0
3
2
0
0
0
0
0
2
0
3
0
0
0
0
2
0
0
2
0
2
1
0
0
0
0
1
0
0
2
0
0
0
0
0
3
2
0
0
4
2
1
2
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
1
0
0
0
0
1
2
1
1
0
0
0
2
0
0
1
0
0
0
1
1
0
0
1
0
0
1
1
0
0
3
0
1
0
2
2
0
1
1
2
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
2
1
0
0
0
2
3
0
0
0
0
1
2
0
0
0
7
0
0
2
0
2
0
0
0
0
3
0
0
0
0
2
3
0
0
0
2
0
0
0
0
2
0
1
0
0
1
1
0
0
1
0
3
1
1
0
1
0
1
0
1
1
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
2
0
1
0
1
1
2
0
0
0
1
3
1
1
0
0
0
0
2
0
0
2
1
0
0
0
0
0
2
2
2
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
2
0
0
1
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
2
2
1
0
0
0
0
2
0
0
0
0
0
2
2
0
2
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
1
0
0
2
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
2
3
0
1
2
2
0
2
0
1
1
0
0
0
0
1
0
1
0
2
0
0
2
1
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
1
0
0
2
0
2
0
0
3
0
1
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
3
1
3
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
2
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
2
0
0
0
2
0
0
1
3
5
8
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
1
2
0
5
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
3
0
0
0
2
1
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
1
0
0
2
0
0
0
0
0
1
1
0
1
0
1
0
0
2
1
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
1
0
0
2
2
1
0
0
0
0
0
0
0
0
1
2
0
2
1
0
0
2
0
1
0
0
0
0
0
0
1
2
1
1
0
0
0
0
2
1
1
0
0
2
0
0
0
1
0
0
0
0
1
1
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
1
0
0
1
1
0
0
0
2
0
0
0
0
0
1
0
1
3
0
1
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
2
2
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
2
0
1
0
1
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
2
2
0
0
2
0
0
1
2
0
2
2
0
0
0
2
0
0
1
0
0
0
4
0
1
2
1
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
2
0
2
2
0
0
0
0
0
2
0
0
4
0
0
2
0
0
3
0
0
1
0
0
0
1
0
0
0
0
0
1
1
3
1
2
1
0
2
0
1
0
0
0
2
0
0
1
0
0
0
3
1
1
2
0
1
2
0
0
0
1
2
0
1
1
0
2
2
2
0
0
2
0
2
0
0
0
0
0
1
0
0
0
3
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
1
2
0
1
0
0
0
1
2
0
0
0
0
2
2
0
1
0
3
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
1
2
0
0
0
0
1
1
2
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
1
1
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
3
0
0
0
1
2
0
2
1
0
0
0
2
2
0
3
2
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
3
0
2
0
0
2
1
0
2
0
2
0
0
0
0
0
0
0
2
0
0
1
2
1
0
0
0
0
2
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
2
0
0
0
0
2
1
0
0
1
0
2
0
0
0
2
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
2
0
1
0
1
0
1
0
0
2
0
0
1
2
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
5
0
0
0
0
1
0
0
0
0
4
0
0
0
0
2
0
0
2
0
1
0
0
0
1
0
2
0
7
0
2
0
1
0
0
2
0
0
2
0
2
0
0
1
2
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
1
1
3
0
2
2
0
0
0
0
0
0
0
0
2
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
2
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
2
2
1
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
1
1
0
0
1
1
0
1
0
2
1
0
0
2
0
2
0
1
1
0
1
0
0
0
0
0
2
0
0
5
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
6
0
2
0
2
0
0
0
2
1
3
0
0
3
2
0
0
0
0
0
1
2
0
0
1
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
2
0
1
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
2
4
0
0
2
0
1
0
1
0
0
0
2
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
2
1
2
2
0
0
2
0
3
0
0
2
0
2
2
2
1
0
0
0
2
0
0
2
0
2
0
0
1
0
0
2
0
1
0
0
0
0
0
3
0
0
0
0
0
0
1
1
0
2
3
1
0
0
2
0
2
0
0
0
0
2
0
0
0
3
0
0
2
0
0
0
0
0
3
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
2
2
1
0
2
0
1
0
0
0
0
3
1
0
0
1
2
0
2
0
0
2
0
0
2
0
0
0
0
1
2
2
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
2
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
2
2
0
4
0
0
0
0
2
0
1
0
2
4
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
2
2
1
3
2
0
0
0
0
0
2
3
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
2
1
1
0
3
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
4
0
0
1
0
2
0
2
0
0
0
1
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
2
1
4
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
1
0
0
2
2
0
0
0
2
0
0
1
1
2
0
2
1
1
0
0
2
1
0
0
0
0
2
1
2
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
2
0
1
0
0
0
0
1
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
1
0
0
0
2
1
0
2
0
4
2
0
0
2
0
1
0
0
2
0
0
0
0
0
2
2
0
0
2
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
2
2
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
1
0
0
1
3
0
1
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
1
2
2
2
0
2
0
0
1
2
1
0
0
0
2
2
0
0
0
2
1
0
0
0
0
0
0
2
2
1
2
0
0
0
1
0
0
0
2
0
1
3
0
0
0
0
0
2
0
2
1
2
0
0
0
2
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
1
1
1
1
0
0
2
0
0
2
0
0
0
1
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
1
1
0
0
1
0
3
0
1
2
1
0
0
2
2
0
0
0
1
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
2
0
2
0
1
2
0
0
1
2
1
4
0
0
3
3
3
2
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
2
2
0
0
0
1
2
2
0
1
2
0
0
0
1
0
0
2
0
0
0
0
1
0
0
2
0
1
0
2
0
1
0
0
0
1
0
2
0
0
0
0
2
0
2
0
0
2
0
0
1
0
0
0
0
0
0
2
1
0
1
0
0
0
2
0
2
0
1
0
0
0
0
2
0
0
2
2
1
0
0
0
2
1
0
2
0
0
0
1
0
0
1
2
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
2
2
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
2
0
1
0
2
1
0
0
2
1
0
3
0
1
0
1
0
0
1
0
0
0
1
2
0
0
0
0
1
0
0
2
1
2
0
0
2
0
0
1
0
2
0
0
2
2
1
0
1
2
0
0
1
2
0
2
2
2
0
2
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
1
2
2
0
0
2
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
2
0
2
0
0
0
0
0
0
0
1
2
0
2
0
2
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
1
1
0
1
0
1
1
0
0
2
1
0
4
0
1
0
2
0
2
2
1
0
0
0
0
0
0
0
6
0
0
2
0
0
1
0
2
1
0
0
2
3
0
0
0
0
2
0
1
1
1
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
2
0
3
0
3
0
0
1
0
2
0
0
2
0
0
0
0
3
0
1
0
0
0
2
0
4
0
0
1
2
0
0
1
0
0
0
0
0
0
1
3
0
2
0
0
0
2
0
0
0
0
0
1
1
0
2
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
1
1
2
2
0
3
1
0
2
0
0
2
0
1
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
1
2
2
0
0
0
0
1
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
1
0
0
0
1
1
2
0
0
2
0
2
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
2
2
0
2
0
2
0
1
2
0
2
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
3
0
2
1
0
3
0
0
0
1
1
2
0
1
0
0
0
0
2
2
0
2
0
3
1
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
2
2
0
0
1
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
3
1
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
1
0
2
0
0
0
1
2
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
1
0
1
2
0
0
2
2
0
0
1
1
0
0
0
2
2
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
2
0
3
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
1
1
0
0
0
1
0
1
5
0
0
0
2
0
1
2
0
0
0
0
0
0
0
1
2
0
0
2
0
2
0
1
1
0
1
1
0
0
0
0
1
0
0
2
0
0
2
0
1
0
1
0
3
2
1
1
2
0
0
1
0
0
0
0
2
2
0
0
1
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
3
3
0
3
1
1
0
2
2
0
0
0
1
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
2
1
2
0
0
0
2
0
1
1
0
2
0
0
4
0
0
2
0
2
0
0
1
1
2
0
0
0
0
0
0
2
0
0
2
1
0
4
0
0
0
2
0
0
1
0
0
2
1
0
0
2
2
2
0
0
0
0
0
0
0
2
1
2
0
0
0
0
1
0
0
0
0
2
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
2
0
2
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
1
0
1
0
2
1
0
0
2
1
0
2
3
0
2
0
0
0
0
1
5
0
0
0
1
0
0
0
0
1
1
0
0
0
1
2
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
3
0
2
0
0
0
2
2
3
0
0
0
0
1
2
2
3
0
2
2
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
3
3
1
0
0
0
1
0
3
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
1
0
2
0
0
0
0
2
1
0
0
2
0
0
0
1
0
1
1
0
0
0
0
1
0
0
1
3
2
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
3
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
2
0
2
0
1
0
0
2
0
0
0
0
0
1
2
3
1
0
0
0
0
1
0
0
2
0
0
0
1
2
1
0
2
0
0
0
3
0
0
2
0
0
0
2
0
2
0
0
0
2
2
0
3
0
1
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
2
0
0
2
0
3
0
2
0
0
0
1
1
2
0
0
0
0
0
1
0
1
1
0
0
0
0
0
2
1
0
0
0
3
2
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
2
0
7
2
2
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
2
0
0
3
0
0
1
1
0
0
0
0
0
0
0
1
5
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
1
2
0
1
0
2
0
0
0
1
2
2
2
0
0
2
0
0
2
2
3
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
3
2
0
0
1
0
1
0
0
0
2
0
1
0
0
1
0
2
0
0
0
1
0
2
0
1
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
2
0
0
0
0
0
0
2
0
1
0
1
2
0
0
0
0
0
0
2
0
1
2
0
0
0
1
1
0
0
2
0
0
0
1
0
0
0
2
0
0
1
1
1
0
0
0
0
0
0
0
2
2
2
1
1
0
2
0
0
0
1
0
2
2
0
0
0
0
0
2
0
0
1
1
0
0
1
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
1
1
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
2
1
2
0
0
0
0
0
0
0
2
0
1
2
0
0
5
0
0
0
1
1
2
2
0
0
2
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
1
8
0
0
0
0
0
0
1
1
1
2
2
3
0
2
0
0
1
0
0
0
0
1
2
0
2
0
2
0
1
0
0
2
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
1
0
0
0
2
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
2
2
0
0
0
1
2
2
2
0
0
1
0
2
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
2
0
2
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
2
0
0
2
0
2
1
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
1
0
1
0
0
0
2
1
0
2
0
0
1
2
0
1
1
0
0
1
0
0
0
0
0
1
0
2
0
0
0
1
0
0
2
0
2
2
0
1
1
0
2
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
1
0
0
2
2
3
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
1
4
0
2
0
0
1
2
2
2
0
2
0
0
2
6
0
0
2
0
0
2
0
2
2
0
0
0
1
2
0
3
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
3
0
0
1
0
3
1
0
2
1
0
1
2
0
0
2
2
1
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
2
0
2
0
2
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
3
1
0
1
0
2
0
0
1
1
1
2
1
2
1
1
0
0
0
0
1
0
0
0
0
2
1
0
0
0
2
0
0
2
0
0
0
2
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
1
0
0
1
0
2
1
0
0
0
0
0
0
0
0
2
0
3
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
2
0
1
1
3
0
0
0
0
2
0
0
2
2
1
0
0
0
0
2
0
0
0
0
0
0
0
1
1
1
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
2
0
0
0
2
0
1
0
0
1
0
2
2
0
2
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
1
0
0
0
1
1
0
0
0
5
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
2
0
0
2
3
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
3
0
0
1
2
0
0
0
0
0
0
3
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
2
2
0
0
0
0
0
0
1
0
0
2
4
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
1
3
0
0
2
0
0
1
2
1
0
0
2
0
0
0
0
1
0
0
0
0
0
1
2
0
1
0
0
0
2
1
0
2
0
0
0
3
0
0
0
1
0
3
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
2
0
0
0
2
0
0
0
0
0
2
1
0
1
0
0
0
0
2
1
2
0
0
0
1
1
0
0
0
1
0
0
2
0
2
1
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
1
0
1
1
1
1
0
1
0
1
0
2
0
1
0
0
1
1
2
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
4
1
0
1
0
2
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
2
2
2
1
0
2
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
3
2
0
0
0
2
2
0
0
0
0
0
0
2
0
0
2
0
2
0
2
3
0
0
0
3
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
1
0
0
0
0
3
0
0
0
2
0
0
2
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
1
0
1
4
0
0
0
0
3
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
2
4
1
0
0
2
3
0
0
1
0
1
1
0
0
0
0
0
1
7
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
2
0
2
0
1
0
0
1
1
0
2
0
0
0
0
0
0
2
1
0
2
0
0
0
2
0
2
0
0
0
0
1
0
3
2
0
2
0
1
0
2
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
1
0
0
1
3
2
0
1
0
1
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
1
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
1
1
0
0
2
0
1
0
0
1
0
3
0
2
0
0
0
0
0
1
0
1
1
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
1
1
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
1
0
0
0
0
0
3
0
1
0
2
0
0
0
0
0
0
1
0
5
0
0
0
2
3
0
1
0
0
2
2
2
0
0
0
1
0
0
3
0
0
1
1
1
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
1
0
0
3
0
0
1
1
0
2
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
3
0
0
0
0
0
2
1
0
1
2
2
0
0
0
2
0
2
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
2
0
1
0
1
0
0
1
0
1
0
0
0
1
2
0
0
2
1
0
1
0
2
0
0
3
2
1
1
2
0
2
0
0
2
0
6
2
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
1
0
0
1
1
2
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
2
1
0
2
0
2
0
0
0
0
0
2
1
2
0
0
2
0
0
3
1
0
0
1
0
2
0
0
0
0
1
2
3
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
1
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
1
1
1
0
2
0
0
0
0
0
2
2
0
0
2
2
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
2
0
2
0
0
0
0
0
1
1
2
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
9
0
0
2
3
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
1
1
0
0
0
0
3
0
0
1
1
2
0
0
0
0
0
1
0
0
1
1
1
0
0
1
0
0
0
0
0
1
1
0
1
0
3
0
0
0
1
0
1
2
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
3
0
0
1
0
0
1
1
0
0
0
1
2
0
2
0
0
2
0
1
0
2
0
0
0
2
2
2
0
0
1
1
0
0
2
0
0
0
2
1
1
1
1
2
6
1
0
0
1
1
0
2
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
1
2
0
2
2
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
1
1
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
1
2
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
3
1
3
2
1
1
1
2
0
1
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
2
1
3
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
1
3
0
0
0
1
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
2
0
0
0
1
0
1
0
2
0
0
4
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
2
1
0
2
0
1
1
0
0
1
2
0
0
0
0
0
1
0
0
0
3
0
0
0
0
1
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
8
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
2
0
0
0
1
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
3
0
0
0
0
2
2
2
0
0
1
1
0
0
2
0
0
0
1
1
1
0
0
0
0
0
0
0
2
0
1
0
1
0
0
2
1
2
1
0
2
1
0
0
0
0
0
0
2
0
0
2
0
2
0
4
0
0
0
0
1
0
0
0
1
1
0
1
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
2
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
1
0
0
2
2
0
0
3
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
3
2
0
0
2
1
1
1
1
0
0
0
0
1
0
0
1
0
2
0
2
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
2
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
2
0
0
0
2
2
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
2
1
2
0
2
2
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
1
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
2
0
2
0
0
0
1
0
0
1
0
1
0
2
0
0
0
0
0
2
1
1
2
0
0
0
1
1
0
1
0
0
1
0
0
0
0
4
0
3
2
0
2
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
2
0
3
0
0
1
0
0
0
0
0
2
1
0
0
1
0
1
0
1
1
0
0
2
1
0
0
0
0
0
0
2
2
0
1
0
1
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
1
0
2
0
0
1
1
1
2
2
2
0
0
0
1
0
2
0
0
0
0
1
0
2
0
1
1
4
0
0
0
0
0
1
0
0
0
2
2
0
1
0
0
0
1
0
0
1
0
1
0
1
0
1
1
2
0
0
0
0
2
0
2
0
0
2
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
2
0
2
0
0
2
0
2
1
1
0
0
0
0
0
3
0
1
0
0
1
1
0
0
0
2
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
3
2
0
0
0
1
2
0
1
0
0
0
0
0
3
0
1
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
1
1
0
1
0
2
0
1
2
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
2
0
3
0
1
0
3
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
2
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
2
2
0
0
1
2
0
0
0
1
3
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
1
1
0
0
0
0
2
0
0
0
0
2
0
1
3
0
0
0
0
0
0
0
0
0
3
0
1
0
2
0
1
2
0
0
0
0
2
1
2
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
1
0
0
2
0
0
1
1
2
1
0
0
1
1
1
2
2
1
0
2
0
0
0
0
0
0
3
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
3
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
3
2
0
0
0
0
0
2
0
2
0
1
0
1
2
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
1
0
1
0
0
0
2
0
2
2
0
0
3
0
0
2
0
1
1
0
0
0
0
0
0
0
0
2
2
1
0
1
0
0
0
2
0
0
0
1
0
0
0
0
2
1
1
1
1
0
2
0
1
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
1
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
1
2
0
0
0
2
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
7
0
0
1
2
0
0
0
0
0
1
1
0
0
3
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
3
1
1
5
0
0
0
3
0
2
1
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
2
2
0
1
0
0
0
1
0
2
0
0
1
0
0
2
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
2
3
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
4
0
1
1
0
0
0
2
1
1
0
0
1
0
0
0
0
1
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
2
2
0
1
1
0
1
0
0
0
2
1
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
4
1
0
1
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
1
0
2
1
0
0
0
0
0
0
1
1
2
1
0
0
0
0
1
0
0
2
0
0
0
0
0
2
2
2
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
1
0
1
1
0
0
0
0
3
0
2
0
0
2
0
0
1
1
0
1
2
0
0
1
2
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
2
0
0
2
0
0
4
0
2
0
0
0
1
4
2
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
1
1
0
2
0
1
0
2
0
0
1
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
2
2
1
0
0
0
0
0
3
0
0
0
0
5
0
0
0
0
2
1
2
0
1
2
0
0
4
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
1
0
0
0
2
2
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
4
1
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
3
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
2
1
0
0
1
1
0
2
0
1
0
0
0
0
0
2
0
0
0
1
0
0
1
0
2
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
1
1
0
2
0
1
0
1
0
1
0
0
0
0
0
2
0
1
0
0
0
1
0
0
2
0
0
0
1
0
2
2
0
2
0
0
1
2
2
0
0
1
1
2
0
0
0
0
2
1
0
0
0
1
0
0
1
2
1
1
2
0
1
0
2
4
1
1
1
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
3
2
3
0
2
1
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
3
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
3
1
0
1
0
1
3
0
2
0
0
2
1
0
0
0
0
1
0
0
0
0
2
0
1
0
2
0
0
6
0
0
0
0
0
1
0
2
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
2
2
1
0
0
0
0
1
0
2
0
1
2
1
0
2
0
2
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
3
1
0
1
0
0
2
0
0
2
2
0
0
0
1
1
1
1
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
1
0
0
0
1
0
3
0
0
1
0
0
0
0
1
0
0
0
0
1
2
2
0
0
0
0
1
1
3
2
0
2
0
0
1
0
0
0
2
2
0
2
0
0
0
0
2
2
0
0
1
1
0
0
2
0
0
0
2
0
0
0
0
1
4
0
1
0
2
2
0
0
0
2
0
5
0
0
1
0
0
0
0
0
1
2
0
2
0
0
1
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
1
1
0
0
2
0
0
2
0
2
2
0
0
0
0
2
0
0
1
0
0
1
0
0
0
2
0
1
0
0
1
0
2
2
0
0
2
2
2
0
0
0
0
0
2
0
1
0
2
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
3
0
2
0
1
0
0
0
2
0
0
0
0
2
1
0
0
1
2
0
0
0
2
0
0
3
1
0
1
1
0
2
8
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
1
2
0
1
0
0
1
0
2
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
2
2
0
1
3
2
1
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
2
2
1
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
1
3
0
6
0
0
3
2
0
0
1
2
0
0
0
0
0
1
2
2
0
1
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
1
0
1
2
0
0
0
0
2
1
1
0
0
2
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
3
0
0
0
2
0
2
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
2
0
2
0
0
0
0
0
1
0
1
2
1
0
1
0
1
0
0
2
0
0
0
0
0
1
0
0
0
1
1
0
0
0
2
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
1
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
2
0
5
0
3
0
0
2
0
0
0
0
1
0
2
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
8
2
0
1
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
3
0
0
2
0
0
1
0
0
0
1
0
2
0
0
2
0
0
0
2
2
2
0
0
0
2
1
0
1
1
0
0
0
0
0
0
0
2
0
0
1
0
4
0
0
0
0
0
0
0
0
0
4
2
0
1
2
0
1
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
2
1
0
0
0
1
0
1
5
0
0
0
4
2
2
0
0
1
0
0
2
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
3
2
0
0
0
2
1
0
0
0
2
0
1
0
0
0
0
3
0
1
0
0
0
0
0
2
0
0
2
0
0
3
2
0
2
0
1
5
0
0
0
1
0
1
2
0
0
0
1
1
0
0
0
2
0
1
2
0
0
0
0
2
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
2
3
0
0
0
2
0
0
2
0
1
0
0
0
0
1
0
2
0
0
2
0
0
0
1
2
0
1
2
0
0
0
0
2
1
0
1
0
0
1
2
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
2
0
2
1
0
2
0
1
0
0
0
0
2
1
5
1
0
2
1
0
0
0
1
1
0
1
0
1
0
1
0
0
0
0
1
1
0
1
0
0
0
1
0
0
2
1
3
0
1
1
1
0
0
1
0
0
0
0
0
0
0
1
2
0
2
0
0
1
0
2
1
0
1
0
0
0
0
2
0
2
0
0
4
0
1
1
0
0
2
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
2
0
0
0
0
2
1
0
2
0
2
0
0
0
0
0
2
3
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
2
1
2
0
1
0
0
2
2
1
2
1
0
0
0
0
2
0
3
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
1
2
0
0
0
1
0
0
2
1
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
2
0
2
2
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
1
1
0
2
0
2
0
0
0
1
0
2
0
0
0
1
0
3
0
0
5
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
1
0
4
1
1
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
2
0
0
0
1
0
3
2
0
1
1
0
1
3
2
0
0
1
0
0
0
3
2
0
0
2
3
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
2
1
2
1
0
2
0
0
0
1
0
0
2
0
0
0
2
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
3
0
0
2
0
0
2
0
0
1
1
2
2
2
0
0
0
0
1
2
0
1
2
0
1
0
0
0
0
0
0
0
2
1
4
0
2
0
1
0
0
0
0
1
2
1
2
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
1
0
2
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
2
1
1
0
1
0
0
2
0
3
1
0
3
1
0
0
0
0
0
0
0
0
3
0
0
1
0
1
1
1
2
0
0
0
2
2
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
2
0
2
1
0
2
1
0
0
0
0
2
2
0
0
1
0
0
0
0
0
3
1
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
2
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
1
0
0
3
0
2
0
2
0
1
0
2
0
0
0
1
2
0
0
0
2
0
0
0
0
0
1
0
1
2
0
0
3
2
0
3
1
0
0
1
0
1
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
5
0
0
0
0
0
0
0
1
2
1
0
1
2
0
2
0
0
0
1
1
0
0
0
0
0
2
0
2
0
0
0
2
1
0
0
1
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
1
0
0
0
2
0
1
0
2
1
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
1
0
2
3
1
0
1
3
2
0
1
2
0
0
0
0
0
0
2
0
0
1
0
1
0
0
2
0
1
0
0
0
1
0
1
2
0
1
0
1
0
0
2
1
1
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
1
2
0
4
1
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
1
0
1
2
0
0
1
0
1
0
0
0
1
0
2
0
0
1
0
0
2
0
0
1
0
0
0
2
1
2
0
2
2
2
0
0
0
0
2
2
0
0
1
0
2
2
0
7
0
0
0
0
0
1
3
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
2
1
2
0
1
0
0
0
0
2
0
1
0
2
0
0
0
0
2
0
0
0
0
2
1
0
0
0
1
1
0
0
0
0
1
3
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
3
0
1
0
0
0
1
2
0
1
2
0
2
0
0
0
2
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
5
0
0
0
0
0
1
2
2
0
0
2
2
0
2
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
2
0
1
0
0
0
0
0
2
2
0
0
2
0
2
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
2
0
0
0
0
4
3
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
1
1
3
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
3
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
1
3
0
0
0
0
1
0
1
0
0
0
1
2
0
0
2
0
2
0
0
0
3
0
0
0
5
2
1
0
0
2
0
0
1
0
1
0
1
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
2
2
1
0
1
0
0
0
2
0
1
0
1
0
0
2
1
0
0
2
2
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
1
3
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
3
1
1
0
0
0
0
0
0
0
0
1
0
0
2
0
1
2
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
1
2
0
0
0
1
0
2
0
0
0
0
5
0
1
0
2
1
1
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
2
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
2
2
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
2
1
3
2
0
3
0
2
0
2
1
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
1
0
1
0
1
0
0
0
1
1
0
0
0
2
2
2
0
1
0
1
1
1
2
0
0
2
0
0
2
0
0
0
1
1
0
1
0
1
2
0
1
0
2
0
0
2
1
0
0
0
0
2
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
2
1
0
0
0
0
0
2
0
1
0
0
2
0
0
2
1
0
0
2
0
0
2
3
0
0
0
0
1
0
2
2
2
0
0
0
0
1
0
0
1
0
2
0
0
0
1
0
2
0
0
2
1
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
1
0
0
2
0
0
1
0
2
1
3
1
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
5
1
1
0
0
0
0
3
0
2
1
0
0
1
0
1
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
1
2
0
2
0
0
0
1
0
2
2
0
0
2
3
0
2
0
0
0
2
0
0
0
0
1
0
1
2
1
0
0
0
1
2
0
0
0
2
0
0
0
0
2
2
0
0
1
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
3
0
0
1
0
1
0
0
2
0
0
2
1
0
0
0
0
0
0
1
0
0
1
0
0
0
2
1
0
0
1
0
0
0
1
0
4
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
1
0
0
1
2
0
0
0
0
1
0
0
0
0
0
1
0
0
2
1
0
1
0
0
1
1
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
2
0
2
1
2
0
2
1
0
0
0
1
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
1
0
0
0
1
0
1
1
0
1
0
1
1
0
0
0
0
0
1
2
4
1
0
0
0
0
0
2
0
0
0
0
1
0
1
2
0
1
0
0
2
1
0
0
2
0
2
0
0
0
1
4
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
2
0
0
3
0
0
0
0
0
3
0
0
0
1
0
0
0
0
1
1
0
1
2
0
0
0
2
2
0
0
0
2
0
0
0
3
0
1
0
2
0
2
2
0
0
1
1
0
2
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
2
0
0
2
0
0
2
0
0
0
0
0
3
0
1
2
0
0
1
0
0
2
0
0
0
0
1
0
0
2
0
0
1
0
2
0
0
0
0
3
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
1
1
2
0
0
0
2
2
1
0
2
0
0
0
0
0
2
0
2
0
3
1
0
0
0
0
0
2
1
0
0
1
1
0
0
0
0
0
0
3
1
0
1
2
0
3
2
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
1
0
0
2
3
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
2
2
1
2
1
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
1
0
2
0
0
0
0
3
0
1
2
0
2
1
1
0
0
1
0
0
3
0
0
0
3
1
0
0
1
2
0
0
0
0
0
0
1
0
0
2
2
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
3
0
1
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
2
0
0
4
0
0
0
1
0
3
2
2
0
0
0
2
0
0
2
1
0
3
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
1
0
1
0
2
3
0
0
1
3
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
5
2
1
1
0
0
5
0
1
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
3
2
0
0
0
0
1
0
0
0
3
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
2
2
1
0
0
1
2
2
1
3
1
0
0
0
0
2
1
2
0
1
0
1
0
0
0
0
2
0
2
0
3
0
1
1
0
0
0
0
0
0
1
0
0
3
1
1
1
3
0
0
0
0
1
0
2
0
0
0
2
0
3
0
0
3
2
2
0
0
1
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
3
0
0
2
0
0
2
0
1
4
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
1
0
2
2
0
0
2
2
1
0
0
0
1
0
0
1
2
0
0
0
0
2
0
0
3
3
1
2
0
0
0
0
2
0
0
1
0
0
2
2
1
1
0
0
0
0
2
0
2
6
1
0
0
3
0
2
2
3
2
0
0
2
1
0
1
0
0
1
0
0
0
0
2
0
1
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
1
0
5
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
1
0
0
3
0
2
0
0
0
2
0
2
0
0
0
0
0
1
2
0
0
2
1
2
0
2
1
2
1
0
2
0
0
0
1
0
0
0
1
1
1
1
0
2
2
0
0
1
0
1
2
0
0
0
0
0
0
1
0
1
0
0
0
1
2
1
0
0
0
0
0
0
2
0
0
1
3
0
1
0
0
1
1
0
0
1
2
2
1
2
0
1
2
2
0
0
0
0
0
2
0
1
0
1
0
0
0
2
0
0
3
0
0
0
0
0
1
0
2
0
2
1
0
2
6
1
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
3
0
0
1
2
0
0
0
0
0
2
3
0
2
0
0
0
0
2
0
1
0
0
0
0
0
2
2
0
2
0
0
0
3
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
3
7
0
0
0
0
1
2
0
2
0
0
1
0
2
0
0
0
2
0
1
1
0
0
0
0
0
0
0
3
0
0
0
1
0
1
0
0
2
0
0
1
0
1
0
1
0
1
0
0
1
0
0
0
0
2
0
2
0
0
2
4
1
0
1
2
0
0
0
0
2
0
1
2
2
2
0
0
0
0
2
0
0
0
2
0
2
1
0
0
1
0
0
2
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
1
2
0
0
0
0
2
2
0
2
3
0
1
0
0
4
0
2
0
0
0
2
0
0
0
0
0
1
2
0
1
0
2
1
0
0
0
0
2
0
1
0
2
0
1
1
0
1
0
0
1
0
0
2
0
0
2
0
0
0
0
2
0
0
1
0
0
1
1
1
0
0
1
0
0
2
2
1
0
0
5
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
2
1
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
1
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
2
2
1
2
0
0
0
2
1
0
2
0
1
0
0
2
0
0
0
0
2
0
0
0
1
2
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
1
0
2
2
0
0
1
0
1
1
0
0
2
0
0
0
0
2
1
0
0
0
0
0
1
0
0
1
1
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
2
2
1
1
0
2
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
1
0
1
1
0
0
4
2
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
1
0
0
1
2
0
1
0
0
0
1
3
0
0
2
1
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
1
0
0
3
2
0
0
0
0
0
2
0
0
0
0
0
1
4
0
1
0
0
0
0
0
1
1
1
1
2
1
0
0
0
0
1
0
0
0
0
0
2
0
1
2
0
0
0
1
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
4
0
0
0
2
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
11
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
3
2
1
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
1
0
0
0
3
2
1
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
2
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
2
0
0
0
0
2
0
0
0
0
1
1
2
0
0
1
2
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
2
3
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
1
1
4
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
3
2
2
1
2
1
0
0
0
1
1
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
3
0
0
0
1
0
0
2
0
0
0
0
1
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
3
0
0
0
1
0
2
0
0
0
0
1
2
1
0
0
0
0
1
1
0
0
0
0
3
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
6
0
1
0
0
0
0
3
0
3
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
3
1
0
0
0
0
1
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
1
0
0
2
0
2
0
1
2
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
6
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
1
2
2
1
0
0
0
2
0
0
2
0
0
1
3
0
2
0
0
2
0
0
0
0
0
2
1
0
1
0
2
0
0
2
2
2
0
0
0
1
1
0
2
0
0
0
0
1
0
0
2
0
0
0
0
3
0
2
0
0
0
2
0
1
0
0
0
0
0
1
1
1
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
7
0
0
0
2
1
0
0
1
0
0
2
0
0
2
0
0
0
0
0
2
2
0
2
0
0
0
2
0
1
2
2
1
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
1
0
0
2
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
5
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
2
0
3
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
1
0
1
2
0
0
0
0
1
0
0
0
1
1
0
1
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
1
0
1
1
1
1
0
2
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
2
2
0
0
3
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
2
4
0
0
0
0
3
1
0
0
0
2
0
2
0
2
0
2
2
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
3
2
1
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
1
0
0
0
1
0
1
0
0
0
2
0
0
1
0
0
0
2
1
0
0
1
1
1
1
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
1
3
0
0
1
0
0
0
0
0
2
0
3
0
0
1
0
1
2
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
1
0
1
2
0
0
0
0
0
1
1
1
1
2
0
1
2
0
0
0
0
1
0
3
0
0
0
0
1
2
0
2
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
3
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
2
2
0
3
0
0
0
0
3
0
0
0
2
0
2
2
2
0
0
0
1
3
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
7
0
0
0
0
2
0
0
2
2
1
0
2
0
1
1
0
0
1
1
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
3
1
0
2
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
5
0
0
1
0
0
0
2
1
0
1
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
5
2
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
1
0
2
0
0
0
2
2
0
0
0
2
2
0
0
3
2
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
2
0
0
0
0
0
1
1
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
1
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
1
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
7
0
0
1
0
1
4
0
0
2
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
2
1
0
2
0
3
0
3
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
4
0
2
0
0
5
0
1
1
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
1
3
0
0
0
1
2
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
2
1
0
2
2
0
0
0
0
0
0
0
0
1
2
0
0
4
0
1
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
1
1
2
2
2
0
2
0
0
0
1
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
2
0
0
0
1
0
1
0
1
0
0
0
2
1
0
0
0
0
0
1
2
1
3
0
1
1
3
0
0
0
0
2
0
0
0
0
3
0
0
0
2
2
2
1
0
0
0
0
2
0
0
2
2
0
0
0
1
0
0
0
2
0
0
1
0
0
1
0
1
2
2
0
2
0
0
1
1
1
0
0
2
1
0
2
1
0
2
0
0
0
1
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
1
1
1
1
1
0
0
2
0
0
1
2
0
2
1
0
2
1
0
1
0
0
2
0
2
1
2
0
2
3
0
0
2
0
0
0
0
2
0
0
0
0
2
0
3
2
0
0
0
0
0
0
0
1
2
0
0
3
0
1
0
2
0
0
2
0
0
0
0
2
0
0
0
0
1
2
0
1
0
0
0
0
2
2
0
2
0
1
1
2
0
0
0
0
2
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
1
0
0
1
1
0
0
2
1
0
0
2
1
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
3
2
2
0
1
1
0
0
2
2
0
0
0
0
2
0
0
0
2
1
0
2
3
1
0
0
0
0
0
0
0
0
0
0
1
0
0
3
1
0
1
0
1
0
2
1
1
0
0
2
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
2
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
2
0
0
2
0
1
0
2
2
0
1
0
0
1
0
0
0
2
1
0
0
2
0
0
2
0
0
0
0
0
2
2
0
2
2
1
0
1
1
0
0
2
0
5
0
2
0
1
0
2
1
1
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
2
2
0
2
0
2
2
1
2
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
3
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
2
0
1
0
0
1
0
1
0
1
0
1
0
0
0
0
0
2
0
0
0
3
0
1
0
0
1
2
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
2
0
1
2
0
0
2
0
0
1
0
2
0
0
0
2
0
2
0
2
0
3
1
0
0
2
0
0
0
2
0
0
0
2
0
0
2
1
0
2
0
2
0
1
0
0
2
0
1
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
2
0
0
0
0
0
0
0
0
1
1
3
0
2
0
0
0
2
0
0
2
1
0
0
2
0
1
2
0
0
0
0
0
0
1
0
0
0
0
1
2
3
0
0
0
0
0
1
1
1
1
0
2
0
1
1
2
2
0
0
0
3
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
1
2
2
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
2
0
1
2
0
2
0
0
0
0
2
3
3
0
1
2
0
2
2
0
0
0
0
1
0
1
0
2
2
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
2
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
2
0
2
0
0
3
0
0
2
0
0
4
0
0
0
1
0
0
0
1
1
4
1
0
0
2
0
0
0
0
0
0
1
0
0
1
0
1
2
0
0
0
0
0
0
0
1
0
0
2
1
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
3
0
0
0
1
0
1
1
2
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
2
0
0
1
0
0
2
0
0
4
0
1
2
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
9
2
0
0
0
1
0
1
1
0
3
2
1
0
1
0
0
0
0
1
1
2
1
1
0
2
0
0
1
0
1
0
0
0
2
0
0
0
1
0
3
0
4
0
0
0
2
0
1
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
2
0
1
0
2
0
0
0
1
2
0
0
2
0
0
2
2
4
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
2
1
2
0
0
1
0
2
1
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
1
0
2
0
0
0
2
1
0
2
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
4
1
0
0
2
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
2
1
0
6
2
4
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
2
2
0
2
1
2
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
1
0
0
0
0
1
0
1
0
2
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
2
0
1
0
0
0
2
0
1
0
1
0
0
0
0
1
1
0
1
0
0
1
2
3
1
0
0
2
2
0
0
1
2
2
0
0
0
0
0
2
0
2
2
2
0
0
0
0
0
1
1
1
0
0
0
0
1
0
2
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
1
0
1
0
0
2
1
1
0
0
0
1
2
0
2
0
1
2
0
1
1
0
0
0
0
0
0
3
0
0
0
0
4
0
0
2
2
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
2
1
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
1
1
2
0
0
0
0
0
2
0
3
2
0
1
0
3
2
0
2
2
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
7
0
0
0
0
0
0
0
1
4
0
0
0
1
0
0
1
0
1
0
2
0
0
0
0
2
1
0
0
0
0
1
0
1
0
0
1
0
2
0
0
0
2
0
0
1
0
0
0
0
0
1
0
1
2
0
0
0
1
0
0
0
0
0
0
1
0
2
0
2
0
1
0
2
0
0
1
0
1
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
2
1
0
0
1
1
0
0
1
0
2
0
0
0
0
0
0
0
2
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
1
0
2
0
0
0
0
1
1
0
2
0
2
0
0
0
0
2
0
0
0
0
1
1
2
0
0
0
2
2
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
1
0
2
0
0
7
0
0
0
1
0
0
0
0
0
0
1
0
0
2
2
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
1
0
1
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
2
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
3
1
0
0
0
0
2
0
0
2
0
0
2
0
1
0
2
3
0
0
0
2
0
0
0
0
0
1
0
1
1
2
0
2
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
1
0
2
0
2
1
1
1
1
0
0
0
1
0
2
0
1
2
0
2
0
2
1
0
0
2
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
2
2
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
2
1
2
1
2
0
0
2
2
2
0
0
2
0
0
0
3
0
2
2
0
0
1
0
0
1
2
1
0
1
0
0
2
0
0
0
0
2
2
0
1
3
1
2
2
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
1
1
0
0
2
1
4
2
0
0
0
2
0
0
1
0
1
3
0
0
0
0
0
0
2
0
1
0
1
0
2
0
0
0
0
0
0
0
1
2
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
2
3
1
0
0
2
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
1
0
1
1
1
1
2
0
0
0
0
0
2
0
4
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
2
0
0
0
2
0
0
0
2
0
0
0
0
1
2
0
0
0
0
2
2
0
2
0
2
0
0
0
0
0
0
0
0
3
6
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
2
0
0
1
2
3
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
1
0
0
0
0
5
1
2
0
1
0
0
0
0
0
0
0
0
0
2
2
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
2
0
0
1
1
3
0
1
1
4
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
4
0
1
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
2
3
2
0
2
1
0
0
0
2
0
0
0
0
0
2
1
2
0
0
0
0
1
4
0
0
2
3
1
0
1
2
1
0
2
0
0
0
1
0
1
0
0
0
0
0
2
0
0
3
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
2
1
2
0
0
1
2
0
2
0
0
2
0
1
0
2
2
0
2
0
0
0
0
0
2
0
0
0
1
2
3
1
1
0
0
0
0
1
1
1
1
1
0
0
0
0
2
4
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
3
0
1
2
0
2
2
0
0
1
2
0
2
1
1
4
0
0
2
0
1
2
0
0
0
0
0
1
0
2
0
2
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
1
0
0
3
0
0
0
0
2
1
0
0
10
0
1
0
1
1
0
0
0
2
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
2
0
0
0
1
0
2
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
2
0
1
0
0
1
0
0
2
1
0
1
2
0
0
0
1
0
0
0
1
0
0
0
1
0
1
5
0
0
1
0
0
0
2
0
1
0
2
2
2
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
2
3
0
1
0
0
1
2
2
0
0
2
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
1
0
1
2
0
0
2
2
1
0
0
1
0
2
0
0
0
0
2
0
0
2
0
0
4
0
0
1
0
1
0
2
2
0
0
0
0
0
2
2
0
0
2
1
2
2
0
2
2
0
0
2
1
0
2
0
0
0
0
1
0
2
0
0
0
0
1
0
1
0
0
0
0
2
1
1
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
1
1
5
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
3
2
3
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
1
0
2
2
0
2
0
0
0
1
0
0
0
3
1
0
0
0
2
0
0
2
1
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
2
1
0
1
0
2
0
2
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
1
0
1
3
0
1
0
0
0
0
0
3
1
0
0
1
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
1
0
2
5
2
0
2
0
0
0
0
0
2
2
1
1
2
0
1
2
2
0
0
0
1
0
1
1
0
0
1
0
2
0
0
0
2
0
0
2
0
0
3
0
2
0
1
0
2
2
0
0
1
0
1
0
0
2
2
0
2
2
2
0
0
1
0
1
0
1
1
0
1
0
0
0
0
0
0
1
0
1
1
0
4
0
0
2
0
0
0
0
0
2
1
0
0
0
0
2
0
0
1
1
0
0
0
0
0
2
0
2
0
2
0
1
0
0
0
1
2
0
0
0
1
0
2
2
0
0
3
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
1
0
2
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
2
0
4
0
1
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
2
1
3
0
0
1
0
0
0
0
0
0
0
1
2
2
0
0
1
0
0
0
0
0
3
0
1
1
1
0
2
0
0
2
0
0
0
0
2
0
2
0
1
2
1
0
2
0
0
1
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
3
1
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
7
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
2
0
0
0
2
0
0
1
1
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
2
0
0
2
2
2
1
0
0
0
0
0
0
0
2
1
2
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
2
1
0
2
0
1
0
0
0
2
0
0
0
0
0
2
1
1
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
1
0
1
2
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
2
0
2
3
1
0
0
0
0
0
0
0
0
5
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
8
0
0
1
0
0
1
1
0
0
0
1
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
2
0
1
0
0
0
0
1
0
2
0
1
3
0
0
0
1
0
1
1
1
0
2
1
0
0
0
2
0
2
4
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
1
2
2
0
0
0
0
2
0
0
1
0
1
2
0
0
0
0
1
0
1
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
1
3
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
2
2
5
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
1
0
2
1
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
1
0
0
1
0
0
0
5
0
0
0
0
2
0
1
2
0
2
0
0
0
0
1
2
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
1
2
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
2
0
2
1
2
0
2
0
1
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
1
2
0
1
0
0
0
2
1
0
2
0
1
0
0
1
0
0
0
0
1
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
3
0
1
0
0
3
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
1
2
0
3
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
5
0
2
2
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
2
2
0
0
2
0
0
0
0
2
0
0
0
2
0
2
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
2
0
2
1
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
3
2
0
2
0
2
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
1
0
0
0
0
1
2
0
1
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
2
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
1
0
1
0
0
1
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
2
2
0
0
1
0
0
1
0
0
1
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
2
0
3
0
0
0
1
1
1
2
0
0
2
0
2
0
0
4
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
2
0
1
0
0
0
1
1
1
0
2
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
2
2
0
0
0
0
2
0
0
2
1
1
0
0
0
0
0
0
2
0
1
0
0
0
3
0
0
0
0
0
1
1
1
1
0
0
1
0
1
0
1
2
0
0
3
2
0
0
0
0
1
0
0
0
0
0
1
4
0
0
0
0
0
1
1
0
2
0
1
2
0
0
0
0
0
2
2
1
2
0
0
0
3
0
1
0
2
0
0
1
0
1
1
1
0
0
0
0
0
0
0
4
0
0
1
2
0
0
0
0
0
3
0
2
1
1
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
1
1
4
2
1
0
0
0
0
2
0
0
1
0
3
1
0
0
0
0
0
1
1
2
0
0
0
0
0
1
0
0
2
0
1
0
0
3
0
1
1
0
0
0
0
0
1
1
0
1
0
0
0
0
4
3
0
0
2
1
3
2
1
1
2
1
0
0
0
2
0
2
0
0
0
0
0
1
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
2
1
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
2
2
0
0
1
0
1
0
0
0
2
0
0
2
2
0
0
0
2
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
1
0
0
1
0
0
0
3
1
2
0
0
1
2
0
0
0
0
0
0
2
1
1
1
0
0
2
0
2
1
0
0
0
2
0
0
2
0
1
0
0
0
0
2
0
0
0
1
2
0
1
0
0
0
0
1
1
0
1
0
0
2
0
1
0
1
0
0
2
0
1
2
0
1
0
1
2
0
2
2
0
0
0
0
0
2
2
0
0
0
2
0
1
1
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
1
1
0
2
0
0
0
2
0
0
0
0
1
0
0
2
0
0
5
5
2
0
1
2
0
0
2
0
2
0
0
1
0
0
2
0
3
0
0
0
1
0
2
0
0
0
0
2
0
1
2
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
2
0
0
0
0
1
2
0
2
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
2
1
2
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
2
1
2
0
2
0
0
0
0
0
2
0
2
0
0
0
0
3
0
2
0
0
0
1
1
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
2
1
1
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
3
1
2
1
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
1
4
0
1
0
0
0
0
0
3
1
0
1
0
0
0
0
0
0
4
2
2
1
4
2
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
3
0
2
1
0
2
2
2
2
0
1
0
2
3
0
0
2
2
0
0
2
0
0
0
0
0
0
2
0
1
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
3
1
0
2
3
0
0
1
0
0
0
0
1
0
1
1
0
0
2
3
0
0
2
0
0
1
0
0
0
0
0
0
6
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
1
1
2
0
2
0
3
2
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
1
0
2
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
4
2
0
0
0
0
0
1
1
0
2
0
0
1
0
4
2
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
2
1
0
0
1
0
0
2
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
1
0
0
1
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
3
2
0
1
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
1
1
2
0
3
0
0
0
1
0
1
0
1
2
0
0
0
0
0
0
0
2
0
0
2
0
2
2
0
0
0
1
1
1
0
1
2
2
0
0
2
2
0
0
2
0
0
0
0
0
0
3
1
2
0
0
1
2
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
2
0
2
2
0
0
0
1
0
0
2
2
0
2
1
0
2
0
1
0
0
1
0
4
0
0
0
3
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
1
3
0
0
0
0
1
0
0
0
2
0
0
0
2
3
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
1
0
1
0
1
1
0
2
1
2
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
1
0
0
0
1
0
2
0
1
0
0
1
0
0
0
0
2
0
2
1
0
1
0
2
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
2
0
4
0
2
1
0
0
2
0
0
0
0
2
1
0
1
0
0
0
0
1
1
0
4
0
0
1
1
0
9
1
0
0
0
1
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
3
0
0
1
2
5
0
2
0
2
0
1
0
0
2
2
0
0
0
0
0
0
0
0
2
0
3
0
1
0
1
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
2
2
0
0
2
0
0
0
0
0
2
0
1
2
0
1
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
2
2
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
1
0
1
2
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
3
0
0
1
1
0
0
1
2
0
2
1
1
0
2
0
2
0
2
0
0
0
0
0
0
0
0
1
0
1
0
2
0
2
2
0
0
0
0
2
0
0
0
0
1
0
1
0
2
0
3
2
0
1
0
0
0
2
0
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
2
2
0
1
0
2
0
0
0
2
0
1
1
1
2
1
0
0
0
0
0
0
2
1
0
0
1
1
1
0
0
0
0
0
6
0
3
1
0
0
0
3
2
0
1
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
2
0
2
0
2
3
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
2
0
0
0
0
2
2
2
0
0
0
0
2
1
1
0
0
2
3
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
2
0
1
0
2
2
1
0
0
1
0
0
2
1
2
0
0
0
0
1
2
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
2
2
2
0
0
2
2
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
2
0
6
0
1
0
0
0
0
0
2
1
0
1
0
1
1
1
2
0
0
0
1
2
0
0
1
0
0
2
0
0
1
0
4
0
0
2
0
2
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
1
0
1
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
5
0
0
0
0
0
0
0
0
2
2
2
1
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
1
0
0
0
2
0
0
1
0
2
0
0
0
0
1
0
2
0
0
0
0
1
1
1
0
0
0
1
1
0
0
0
1
1
0
0
0
0
2
0
3
0
0
2
2
2
2
0
0
2
0
0
1
0
0
0
1
0
2
0
0
1
0
2
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
2
2
1
0
0
0
0
0
0
0
0
1
2
0
0
2
2
0
1
0
2
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
1
0
0
2
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
2
0
2
0
0
0
0
2
1
0
0
0
0
1
0
1
0
2
2
0
1
0
0
1
0
0
0
2
0
0
0
0
0
2
2
0
0
0
2
0
2
0
1
0
2
2
0
0
0
0
2
1
1
0
1
0
0
0
0
1
1
0
0
0
0
3
0
0
0
2
1
0
2
0
0
2
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
2
2
0
2
0
0
0
1
0
2
0
0
2
0
0
0
3
0
2
0
0
0
2
0
0
2
1
2
0
0
0
2
0
0
0
2
0
2
0
1
0
1
2
1
0
0
0
0
0
0
0
0
0
0
1
2
0
3
0
0
2
1
0
0
0
2
0
0
2
1
1
1
0
0
0
0
0
2
0
0
0
1
0
1
2
1
1
2
2
0
2
2
0
1
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
1
0
1
1
0
0
0
2
2
0
0
2
0
0
0
1
0
0
0
2
2
0
0
0
0
0
1
0
0
0
2
0
0
2
1
0
3
0
0
0
1
2
0
0
0
2
1
0
2
0
1
1
2
0
0
0
0
1
0
0
0
0
2
0
2
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
5
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
2
1
0
0
0
1
4
0
0
0
0
0
3
1
0
0
2
0
1
0
2
2
1
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
2
0
1
1
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
1
0
2
0
1
0
0
4
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
5
2
1
1
3
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
2
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
2
0
1
1
2
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
4
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
2
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
1
1
0
0
1
0
2
0
0
2
2
0
0
0
0
0
0
2
0
0
2
3
0
3
0
0
1
0
1
0
0
1
3
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
2
2
1
0
0
0
4
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
3
1
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
2
0
0
6
0
0
1
0
0
0
2
0
2
2
1
0
1
1
0
0
0
0
1
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
2
0
0
1
0
1
0
0
0
0
1
1
0
2
0
1
0
0
0
1
0
0
1
0
0
1
0
0
2
0
0
2
0
2
0
0
2
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
2
0
0
0
0
2
2
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
2
0
2
0
0
0
1
2
1
0
0
2
1
0
0
3
3
0
0
1
2
1
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
1
2
0
0
0
0
2
2
0
2
2
0
0
0
2
0
0
0
1
0
1
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
4
0
0
0
1
2
0
0
0
0
0
2
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
2
0
0
0
2
2
0
0
2
0
2
0
2
1
0
2
0
1
1
2
2
1
1
0
0
1
2
2
1
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
1
2
0
1
2
0
0
0
0
0
0
0
2
0
1
2
0
3
0
0
0
2
1
1
0
2
0
1
0
0
0
0
1
1
0
1
0
0
1
1
1
0
2
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
3
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
1
0
2
0
2
0
0
0
0
1
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
2
2
2
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
2
0
0
0
1
0
0
1
1
0
1
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
2
1
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
2
1
0
0
0
0
1
0
0
1
1
0
0
1
2
0
2
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
1
2
0
1
0
1
0
0
1
1
0
3
1
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
1
1
1
0
0
2
0
0
2
1
0
0
2
0
2
0
3
2
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
2
0
0
0
1
2
0
2
5
0
2
0
4
1
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
3
2
0
0
0
0
0
2
2
5
1
0
2
4
0
2
0
0
2
0
0
0
0
0
0
2
2
0
2
0
0
2
0
1
2
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
1
0
4
2
0
1
1
0
0
1
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
2
2
0
0
0
0
2
2
0
0
0
0
0
1
0
1
2
1
0
0
0
0
0
0
0
1
1
0
2
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
1
3
2
2
0
0
0
0
0
2
0
0
1
0
0
1
2
0
0
0
2
0
2
0
2
1
0
0
0
0
0
0
2
2
0
0
0
0
1
0
2
0
2
2
2
0
0
0
2
0
1
0
0
1
0
0
1
0
0
0
0
2
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
2
0
1
1
0
0
0
1
0
0
0
0
0
3
0
0
0
0
3
1
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
3
0
0
4
1
0
2
0
0
2
0
0
1
1
2
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
2
0
1
0
0
1
0
0
1
1
0
1
0
0
0
1
0
0
0
1
2
0
0
0
0
0
1
0
1
0
0
0
2
0
0
1
0
2
2
1
0
0
0
1
2
0
0
0
1
0
2
1
0
0
0
1
0
2
0
1
2
0
1
1
2
0
1
1
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
5
2
0
0
2
0
0
2
0
1
0
0
0
2
1
1
0
0
1
0
0
3
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
2
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
2
1
6
0
0
1
1
0
0
0
0
0
1
0
2
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
1
1
1
2
0
0
4
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
2
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
1
0
2
0
0
0
0
6
0
0
0
2
0
0
1
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
2
0
1
1
1
0
0
1
0
2
0
1
0
1
2
0
2
0
0
2
0
0
0
0
1
0
0
2
1
3
1
0
2
2
0
1
0
0
0
0
2
0
2
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
5
0
0
0
1
0
0
0
2
1
0
0
0
2
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
2
2
2
10
1
0
0
0
0
1
1
2
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
4
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
2
2
0
0
1
0
1
0
0
0
0
2
0
1
2
0
1
2
1
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
1
2
1
0
0
0
0
0
0
0
0
0
0
5
0
2
4
1
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
3
0
0
0
0
1
2
0
2
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
4
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
2
0
0
0
1
2
0
0
0
1
2
2
0
0
1
0
2
0
0
0
1
1
0
1
1
0
0
0
0
0
0
2
2
0
3
1
0
0
0
2
0
4
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
2
2
0
0
3
1
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
2
0
1
0
1
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
1
0
0
0
2
0
0
1
0
0
2
0
0
1
2
0
2
0
0
1
0
2
1
0
0
0
1
1
2
0
0
0
1
2
0
0
0
2
0
1
1
0
0
0
1
0
0
0
0
0
4
1
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
2
0
0
1
1
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
1
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
1
0
0
2
0
2
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
2
0
2
1
0
0
1
0
0
0
2
1
1
0
0
2
1
1
0
0
1
0
6
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
1
1
2
0
2
1
0
1
0
1
0
1
2
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
1
0
2
0
0
1
1
0
0
1
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
2
0
0
0
0
2
2
0
1
2
0
2
0
2
0
2
0
0
0
2
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
3
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
6
1
2
0
0
0
1
1
0
0
0
4
0
1
0
0
0
1
0
0
2
0
0
0
0
1
2
1
0
0
2
0
0
2
0
0
0
0
3
0
0
0
0
0
1
0
0
0
2
2
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
2
2
2
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
2
3
0
0
0
0
0
1
2
0
1
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
1
0
2
0
1
0
2
2
0
0
2
2
2
3
2
2
0
3
0
1
0
1
3
0
0
0
0
2
0
0
0
1
0
2
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
2
0
2
0
0
0
0
2
2
0
0
0
1
0
2
0
0
1
1
0
1
0
1
0
0
0
0
0
0
2
0
2
0
2
2
1
0
2
0
0
0
0
0
0
0
1
2
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
2
1
2
1
0
0
0
1
1
0
1
3
0
0
2
0
0
0
0
1
1
2
0
1
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
1
0
0
0
0
1
0
1
2
0
0
0
1
1
0
0
1
0
0
1
1
1
2
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
2
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
1
2
0
0
1
0
1
0
2
2
0
0
0
0
0
1
0
0
2
0
0
0
1
0
2
0
0
2
0
2
1
0
0
0
0
0
0
3
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
2
0
2
0
1
0
0
0
1
2
0
1
0
8
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
1
0
0
1
2
0
1
0
1
0
0
0
0
0
0
2
0
3
0
3
0
2
0
0
2
0
0
0
0
0
1
0
1
1
0
1
0
1
0
1
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
8
1
0
0
2
0
2
2
0
0
0
0
1
0
1
0
2
1
0
2
0
0
0
1
0
0
0
3
0
0
0
0
1
1
0
0
0
0
2
0
0
0
1
1
0
1
0
0
1
1
2
0
0
0
2
0
2
0
0
0
1
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
1
0
2
1
0
2
0
3
0
0
0
0
0
1
1
2
1
0
0
2
0
0
0
1
0
1
0
0
0
2
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
2
2
0
0
0
0
2
2
1
0
1
0
0
1
0
2
0
1
0
0
0
3
2
0
2
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
1
0
0
1
1
4
0
0
1
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
2
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
2
0
1
0
1
0
2
1
0
0
2
0
6
0
0
0
0
0
1
0
2
1
0
2
1
2
0
2
0
0
0
0
2
2
0
0
2
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
2
2
0
2
0
0
0
0
1
0
2
0
2
2
0
1
1
0
4
0
1
3
2
0
1
6
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
1
2
0
2
1
1
2
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
3
1
2
1
1
0
2
0
0
0
2
0
0
1
0
6
0
1
0
3
3
1
2
0
0
0
1
2
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
3
2
2
0
0
0
0
0
0
2
2
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
1
1
1
0
0
1
0
1
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
2
0
0
1
0
2
0
0
0
1
0
2
0
0
0
0
2
2
0
0
1
0
0
0
1
0
0
0
1
0
2
0
0
2
2
0
2
0
1
2
0
1
0
0
0
7
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
5
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
1
3
3
1
1
0
0
0
0
1
0
1
1
0
1
0
1
0
0
1
0
0
0
0
1
0
1
0
1
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
5
0
0
0
2
0
0
1
0
0
2
2
0
0
2
0
2
2
1
0
0
0
2
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
3
0
1
2
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
4
0
1
0
2
2
1
1
2
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
1
2
0
1
0
0
3
2
0
2
0
1
2
0
2
3
2
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
5
0
1
3
0
1
2
0
2
3
0
0
0
0
0
1
2
1
0
0
0
0
2
1
0
2
0
0
5
0
1
0
0
0
1
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
1
0
0
0
2
2
0
0
2
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
2
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
2
2
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
1
1
2
0
2
2
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
1
1
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
2
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
1
2
0
3
1
0
0
0
0
1
0
0
2
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
2
0
0
2
0
0
0
2
0
0
2
2
2
0
0
0
0
1
2
0
0
0
0
3
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
2
0
1
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
1
2
2
0
0
0
0
0
0
0
0
1
0
1
1
2
0
2
2
0
2
0
0
0
1
0
1
2
0
0
4
1
0
0
1
0
2
2
1
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
2
1
0
1
1
1
1
0
0
1
0
2
2
0
0
0
2
0
0
0
2
1
0
0
0
2
1
2
0
0
0
1
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
1
1
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
2
2
2
2
0
1
2
0
0
1
0
0
0
0
1
0
0
0
0
1
2
0
3
0
0
0
0
2
0
2
0
0
0
1
0
0
3
1
0
0
0
0
1
0
0
5
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
1
0
1
0
0
0
2
0
0
0
1
2
0
2
2
0
0
1
0
0
0
0
1
4
0
1
0
1
0
1
2
0
1
2
1
0
0
0
2
4
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
3
1
0
2
0
2
0
2
0
0
2
0
0
0
1
1
0
1
0
0
0
0
0
0
2
0
3
0
2
0
0
2
3
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
1
0
0
0
0
3
1
0
0
1
0
0
0
0
0
1
0
2
0
0
1
3
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
4
0
0
0
0
2
0
2
2
0
0
0
2
2
0
2
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
1
0
0
0
4
0
0
0
1
0
1
2
0
0
0
0
0
0
1
0
0
1
2
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
3
0
1
0
0
0
0
0
1
0
2
0
1
1
0
1
0
0
1
0
1
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
5
0
1
0
3
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
1
1
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
4
0
3
0
0
1
0
2
0
1
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
3
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
2
0
1
2
2
1
0
0
0
2
1
0
0
0
0
2
0
0
0
1
3
1
0
0
2
0
4
3
0
0
0
0
0
0
2
2
0
0
0
0
1
0
2
2
0
0
1
0
1
0
0
1
1
1
0
0
0
0
3
2
0
0
0
1
0
0
0
0
1
2
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
1
1
3
2
0
0
0
0
0
0
1
0
2
0
0
2
0
2
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
3
1
0
0
2
0
0
0
1
2
1
0
2
0
0
0
2
2
4
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
1
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
1
0
0
0
1
0
0
0
0
0
2
0
2
2
0
1
0
0
0
0
1
0
2
0
2
1
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
2
1
0
0
3
2
0
0
3
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
2
1
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
2
1
1
0
0
0
1
0
0
2
0
1
0
0
2
0
1
0
0
0
0
1
0
2
0
0
2
1
0
5
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
1
2
2
0
0
0
0
2
2
1
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
1
0
3
0
0
1
1
1
0
0
0
1
0
0
2
0
1
0
1
1
0
0
0
0
3
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
2
6
0
0
0
0
0
2
0
0
0
2
0
1
2
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
2
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
1
1
0
0
0
0
1
2
2
3
2
2
2
0
0
2
0
2
1
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
1
0
0
3
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
2
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
1
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
3
1
2
2
0
0
0
2
0
3
0
1
2
0
0
1
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
2
0
1
2
1
0
2
0
0
2
0
0
0
2
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
2
1
1
2
0
0
1
0
1
0
0
0
0
0
0
4
0
0
2
0
1
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
2
0
1
1
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
1
2
1
0
2
0
0
2
0
1
0
0
0
0
1
0
2
0
0
0
1
0
0
0
1
1
0
1
1
0
2
0
0
2
1
1
0
1
4
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
3
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
2
2
2
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
2
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
2
2
0
0
7
1
0
2
0
0
0
2
0
0
1
0
1
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
1
0
0
0
0
3
2
0
1
0
0
0
0
0
2
2
1
0
0
2
0
0
0
0
2
0
0
1
0
0
0
1
1
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
2
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
2
0
2
0
0
2
0
0
6
0
0
0
0
1
0
2
1
0
2
0
0
1
1
1
2
0
0
0
0
1
0
2
2
1
0
0
2
0
2
0
5
1
0
0
0
0
0
0
0
0
0
0
2
1
3
0
0
0
0
0
0
0
0
2
1
0
2
0
0
1
0
0
0
0
0
0
1
0
2
1
0
0
0
3
0
0
0
0
0
2
0
2
1
3
0
1
2
0
1
1
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
2
2
2
0
0
2
0
0
1
0
0
0
0
3
0
0
0
1
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
2
0
1
0
0
0
0
0
1
0
1
0
0
1
2
0
0
0
0
0
0
0
1
0
0
3
1
0
0
0
2
0
1
0
0
2
0
0
2
4
0
2
1
0
2
0
2
0
0
2
0
0
0
0
4
0
1
2
2
0
0
0
2
0
0
0
0
1
0
0
6
0
2
1
1
0
0
0
0
3
0
1
2
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
4
0
0
2
0
1
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
2
0
2
2
1
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
2
2
0
0
1
0
1
1
0
0
1
0
2
1
4
0
2
2
1
0
1
0
0
0
1
0
2
1
0
2
3
0
0
0
0
1
0
0
1
3
0
0
2
1
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
2
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
1
0
1
0
0
2
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
1
3
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
3
0
1
0
0
0
2
0
0
0
3
1
0
0
0
1
0
3
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
2
1
0
2
1
0
0
0
0
0
0
0
0
0
1
0
2
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
2
0
2
0
0
0
0
0
0
0
0
2
0
0
1
1
1
0
1
1
0
2
0
0
0
0
0
0
0
0
0
3
1
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
3
1
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
2
0
1
0
2
0
0
1
1
0
1
0
0
2
0
0
0
1
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
2
1
0
0
0
0
0
2
0
1
0
3
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
2
0
2
0
0
0
0
0
1
0
1
0
2
0
0
0
0
1
0
1
2
0
0
0
1
2
0
1
0
0
0
2
0
7
3
1
0
0
2
0
2
3
0
1
0
0
0
0
0
0
0
1
0
0
2
0
1
0
2
2
2
0
1
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
1
2
0
1
0
1
0
0
2
0
1
2
0
3
2
0
0
0
0
2
2
2
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
2
1
0
1
0
0
1
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
2
0
0
0
0
2
1
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
5
0
0
1
2
0
0
0
1
0
0
3
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
2
2
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
1
0
1
0
0
2
0
0
0
2
1
0
1
0
0
1
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
2
0
0
0
0
0
2
0
0
2
0
0
0
2
2
0
0
0
0
1
2
0
0
0
2
0
0
2
1
2
2
0
0
2
0
2
3
2
0
0
0
1
0
0
0
1
0
7
2
2
0
2
1
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
1
0
2
1
0
1
0
0
0
0
1
3
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
1
2
0
1
1
1
0
2
2
0
3
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
5
1
0
2
2
0
1
2
0
2
2
0
0
0
2
0
0
0
2
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
2
2
4
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
2
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
1
1
1
2
1
0
0
0
0
0
4
0
0
0
2
0
0
0
2
2
2
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
1
0
2
0
0
0
0
3
2
0
1
0
0
0
1
0
0
1
1
0
2
0
2
0
0
2
0
0
0
0
2
0
0
2
1
2
0
0
0
0
0
0
1
1
3
1
0
0
1
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
1
0
2
0
0
0
1
2
0
0
0
0
0
2
0
0
1
0
0
0
1
1
2
1
2
0
0
0
0
1
0
0
1
0
2
2
0
1
0
0
0
0
0
0
0
1
0
1
0
0
8
2
2
0
0
0
1
1
1
0
2
1
0
1
0
0
0
0
0
0
0
0
2
1
0
0
2
0
1
2
0
0
0
0
0
0
1
0
2
1
0
0
0
1
0
3
4
0
0
2
0
0
0
0
1
0
0
2
2
0
1
0
0
1
1
0
0
0
0
1
2
0
0
0
0
2
1
0
1
2
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
2
1
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
2
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
1
0
0
0
2
1
1
0
0
0
0
2
0
2
1
0
1
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
2
0
0
0
0
1
0
2
0
0
0
0
2
0
0
2
0
0
0
2
3
0
0
0
0
0
1
0
4
0
2
0
0
0
0
0
1
0
2
2
0
0
0
2
0
0
0
0
0
1
0
0
0
1
2
0
2
0
2
1
0
0
1
2
1
0
2
0
1
1
0
0
1
2
1
0
0
2
0
0
0
3
2
0
0
1
0
1
0
0
0
0
0
0
2
3
1
1
0
0
0
1
0
0
1
1
2
0
0
1
0
1
2
0
0
0
0
1
2
1
1
0
5
1
0
0
0
2
2
0
0
0
0
0
1
0
1
0
1
0
0
2
1
0
0
0
0
0
2
0
2
1
1
1
0
0
0
0
0
0
2
0
0
0
4
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
4
0
0
0
1
0
1
0
0
2
0
0
1
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
1
0
0
0
0
4
0
1
0
0
0
3
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
2
0
2
1
0
2
0
1
1
0
2
0
1
0
0
0
0
2
0
0
2
0
2
1
1
2
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
2
0
0
3
0
0
2
0
0
1
9
0
0
0
0
0
0
0
2
0
1
0
2
1
0
0
0
2
3
1
0
0
0
0
0
1
2
1
0
0
0
0
2
1
1
0
1
0
0
2
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
1
2
0
1
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
2
0
2
0
1
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
1
0
2
0
0
0
2
1
0
3
0
0
0
1
0
0
2
1
2
3
0
0
0
2
0
2
0
0
0
2
2
0
0
0
0
1
0
0
0
0
2
0
1
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
8
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
2
0
3
0
0
2
0
2
0
2
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
1
0
1
2
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
3
0
0
0
0
0
1
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
5
0
1
2
0
0
2
0
0
0
1
1
0
1
0
0
0
2
0
2
0
0
0
2
0
0
3
5
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
2
0
0
2
2
0
0
0
0
2
0
0
0
2
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
2
1
0
0
0
1
0
0
2
0
0
1
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
2
2
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
2
1
0
2
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
1
1
2
0
0
2
0
0
2
0
0
2
0
0
0
1
0
0
1
0
0
1
0
2
0
3
0
0
0
2
0
1
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
3
0
0
0
2
1
1
0
0
1
2
0
2
0
2
1
0
0
0
1
0
0
0
0
1
2
1
1
1
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
1
1
2
0
0
0
2
0
2
1
0
0
0
2
1
0
0
1
0
1
0
0
1
0
0
7
0
0
0
0
0
2
0
1
0
0
0
1
2
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
2
0
2
2
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
3
0
0
0
1
0
2
0
0
1
0
0
0
0
2
0
2
0
1
0
1
0
0
2
0
0
0
0
0
0
1
2
2
2
1
2
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
2
2
0
0
3
0
2
1
0
0
1
0
0
1
0
2
0
3
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
2
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
2
5
0
0
0
2
0
0
0
0
0
0
0
2
0
1
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
2
0
2
0
0
1
0
2
0
0
0
0
0
2
0
3
2
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
3
1
1
0
0
0
1
2
0
0
2
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
2
1
1
0
1
0
1
1
0
0
1
1
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
1
0
1
2
2
0
0
2
2
1
0
0
1
0
0
2
0
0
1
1
1
0
0
0
2
0
0
3
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
2
2
0
0
1
0
1
0
0
0
0
0
2
0
0
2
0
0
1
0
0
1
0
2
0
0
0
0
2
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
2
1
0
0
0
0
1
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
4
1
0
2
0
1
0
0
1
3
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
2
1
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
1
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
2
3
0
0
0
0
0
0
1
1
5
0
2
0
6
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
1
1
2
0
0
0
1
2
1
0
0
2
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
2
0
2
0
1
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
5
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
2
2
0
0
0
0
0
0
1
0
1
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
1
0
2
0
2
1
0
0
2
0
0
1
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
1
0
0
2
2
0
1
3
2
1
2
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
1
0
1
2
0
1
1
0
0
2
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
2
2
1
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
2
0
0
0
1
2
0
0
0
0
1
0
2
0
2
0
0
0
1
1
0
0
2
1
0
1
0
2
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
2
1
2
0
0
1
0
0
2
0
0
0
0
2
1
0
0
0
1
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
2
0
1
0
1
0
0
0
2
0
0
1
0
0
2
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
2
0
1
0
0
1
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
2
0
0
0
0
1
1
0
0
3
2
0
0
0
0
0
1
0
0
0
0
0
0
3
0
2
0
0
0
0
1
2
2
0
0
0
0
2
0
1
1
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
1
2
0
0
0
2
2
1
0
0
1
2
0
0
2
0
0
0
1
0
1
0
0
0
2
0
0
2
2
0
0
0
0
2
0
1
0
2
1
2
0
0
0
2
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
2
2
1
1
0
0
0
1
0
0
0
0
0
1
0
2
1
0
0
2
0
1
2
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
1
0
0
1
0
3
0
3
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
7
0
0
0
0
1
0
0
1
0
0
0
0
0
2
2
0
2
0
2
0
0
1
2
2
0
3
0
0
0
0
0
0
2
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
2
0
2
1
0
0
2
2
0
0
0
0
2
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
3
0
0
1
0
0
1
0
0
0
0
1
0
2
0
2
0
0
2
1
4
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
3
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
2
2
0
0
0
1
0
0
0
1
0
2
2
0
4
2
1
0
1
0
0
0
1
2
0
2
0
0
0
2
0
2
0
3
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
2
0
2
2
0
2
0
0
0
0
2
2
0
0
2
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
3
0
0
0
1
0
2
0
1
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
2
1
2
0
0
0
1
2
0
1
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
1
0
0
1
2
0
0
1
0
2
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
2
0
1
2
1
1
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
2
2
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
3
0
0
0
2
0
1
1
0
0
0
0
2
2
0
1
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
1
0
2
0
1
0
0
0
1
0
1
0
1
1
1
0
0
0
2
2
0
1
0
2
0
0
3
2
0
0
0
1
1
0
0
0
1
0
0
0
2
0
0
0
1
0
0
1
2
0
1
0
0
2
0
1
0
0
0
0
0
0
2
2
0
1
0
3
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
2
0
0
3
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
1
1
2
0
2
0
0
0
0
0
0
2
0
1
0
0
3
0
1
0
2
0
0
0
0
0
0
1
2
1
3
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
1
0
1
1
0
0
1
0
1
1
0
1
0
0
1
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
2
1
3
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
1
1
2
2
0
0
0
0
2
0
1
0
0
1
0
0
0
2
1
1
1
0
0
1
1
0
1
0
0
1
0
0
2
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
2
1
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
1
2
2
0
1
0
0
0
1
0
0
0
2
5
0
3
0
0
2
0
2
0
1
0
0
2
0
0
0
0
0
1
0
0
2
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
11
0
2
0
1
0
0
0
1
0
1
2
0
1
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
3
0
1
0
2
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
1
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
1
0
1
2
0
1
0
0
0
0
0
0
1
2
1
1
0
0
1
2
0
2
0
0
0
1
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
2
0
0
0
2
0
0
0
0
1
0
0
2
0
1
3
0
2
0
0
4
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
1
2
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
2
5
1
0
3
0
0
0
1
2
2
0
0
0
0
1
1
0
0
1
0
2
0
0
0
0
0
0
1
0
2
0
2
1
0
0
0
2
5
0
0
2
0
2
0
3
0
0
2
2
0
2
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
1
0
1
2
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
2
0
0
1
2
0
0
0
0
1
2
2
0
0
0
0
0
0
0
1
0
3
1
0
0
0
0
0
0
0
0
0
4
1
2
0
2
2
2
0
1
0
0
0
2
0
1
0
1
0
0
2
0
0
1
1
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
2
1
0
1
1
2
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
3
1
2
0
2
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
1
1
0
0
0
1
0
1
2
0
0
0
0
0
0
2
0
1
0
2
4
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
2
2
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
2
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
2
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
3
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
2
2
0
0
0
1
0
0
1
0
1
0
1
0
0
1
2
0
2
1
1
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
3
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
3
0
1
3
0
2
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
2
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
2
2
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
3
2
0
6
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
2
0
2
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
1
0
2
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
1
0
0
0
1
0
1
0
0
1
1
0
1
3
0
0
1
0
2
0
0
0
1
0
2
0
0
2
1
0
0
0
0
0
2
0
0
0
3
2
0
0
2
1
0
2
0
0
2
3
0
0
1
0
0
0
1
0
0
0
0
2
11
0
0
1
0
1
0
0
0
0
0
0
2
2
0
3
0
0
0
0
0
0
0
0
0
2
3
1
0
0
0
0
2
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
1
0
2
0
1
2
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
2
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
2
2
2
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
2
0
3
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
2
0
0
1
0
2
0
0
0
0
0
1
1
0
1
0
0
0
2
0
0
0
0
0
0
0
4
0
0
3
1
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
1
1
1
2
1
0
2
0
0
0
2
0
0
0
0
1
2
0
0
0
1
1
2
2
1
0
0
0
2
0
1
1
2
1
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
1
6
2
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
2
0
0
1
0
2
0
0
1
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
2
1
3
0
0
2
0
0
1
0
0
0
2
0
0
0
2
2
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
1
1
2
0
1
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
1
0
1
0
0
0
1
2
0
2
0
0
0
2
0
3
1
0
0
0
0
0
1
0
2
0
0
0
1
0
2
4
0
0
0
0
4
0
0
0
0
0
0
2
2
0
0
1
1
0
0
0
0
0
0
0
1
0
0
2
0
2
2
3
3
0
0
4
0
2
3
2
1
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
2
0
2
0
0
2
2
1
0
3
0
1
1
5
0
0
1
0
0
0
0
0
1
0
1
0
0
2
0
0
1
0
0
0
2
0
0
2
0
1
0
0
0
2
1
4
2
0
0
1
0
0
0
0
0
2
0
2
1
0
1
0
0
0
0
0
0
1
1
0
2
1
0
3
3
0
0
1
0
1
2
0
0
0
0
2
2
2
0
2
2
0
3
0
0
0
0
0
2
2
0
0
1
1
1
0
0
0
0
0
3
2
1
0
0
1
2
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
2
1
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
1
0
2
1
1
0
2
0
0
0
0
1
0
0
2
0
2
1
0
0
2
0
0
0
2
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
1
0
1
0
1
1
0
2
2
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
2
2
0
0
2
1
0
0
1
0
1
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
2
1
2
2
0
0
0
1
1
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
5
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
1
0
1
0
0
0
0
4
0
0
2
0
0
1
0
0
0
0
3
1
2
0
0
0
0
0
0
2
0
2
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
2
2
4
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
1
2
1
0
2
0
0
0
0
2
0
1
0
0
0
4
2
2
0
1
0
0
2
0
2
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
1
2
0
0
0
2
1
0
0
1
0
3
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
2
0
3
0
0
4
0
0
1
1
2
2
2
1
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
1
0
1
2
0
0
0
0
1
0
1
0
2
0
0
1
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
3
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
3
2
0
0
0
2
2
0
2
0
0
0
0
2
2
0
0
0
0
3
0
2
0
0
2
0
0
1
1
2
0
0
0
2
0
2
1
0
0
0
2
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
3
1
2
0
1
0
1
1
2
0
0
0
0
2
0
2
0
2
2
0
0
0
0
0
0
3
0
1
0
0
3
0
0
0
1
0
0
0
4
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
2
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
1
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
2
0
2
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
5
0
2
1
0
2
1
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
2
1
0
0
0
0
0
1
0
1
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
2
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
2
1
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
2
2
0
0
0
2
2
0
2
0
0
0
1
1
0
0
0
2
2
1
1
1
1
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
3
2
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
2
0
2
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
1
2
0
0
0
2
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
2
0
0
2
2
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
1
0
0
2
1
0
0
1
0
2
0
0
0
0
0
2
1
1
0
2
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
2
2
0
1
0
0
0
1
0
0
0
4
3
0
0
0
2
0
2
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
2
2
2
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
2
1
0
2
0
0
1
0
5
0
2
2
2
1
0
0
2
2
1
1
2
1
0
0
0
2
1
1
1
0
0
0
3
1
0
0
0
1
2
0
3
2
0
1
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
3
1
0
1
0
1
2
2
0
0
2
0
4
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
2
1
0
5
0
0
0
0
0
0
1
0
1
0
0
2
0
1
0
3
0
0
2
0
1
1
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
2
2
0
1
0
0
0
0
0
1
2
1
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
2
2
2
0
0
1
5
0
1
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
3
2
2
0
1
0
0
0
0
2
1
0
1
2
0
0
2
2
0
0
1
1
0
2
1
0
0
0
0
0
0
4
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
3
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
3
1
0
0
2
1
1
2
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
2
0
0
2
2
2
0
1
2
0
1
2
0
3
0
1
2
0
0
2
0
2
0
0
1
0
0
1
2
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
3
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
10
0
2
1
0
0
2
2
0
0
2
3
0
0
1
2
1
0
0
0
0
0
0
0
1
0
0
0
3
0
1
0
0
1
0
1
0
2
0
0
0
0
1
0
1
1
2
0
0
0
2
2
0
0
1
0
1
0
0
0
1
0
2
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
2
2
0
0
0
0
0
0
1
0
2
1
1
0
1
2
1
3
0
0
0
0
2
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
2
2
0
2
2
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
4
0
0
0
1
3
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
2
1
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
2
0
1
0
2
0
0
0
1
0
0
0
0
1
3
1
0
2
0
0
2
1
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
4
2
0
0
0
0
0
0
2
2
0
0
5
0
0
2
0
2
0
0
1
0
0
1
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
2
0
2
0
0
2
0
0
0
0
3
0
0
0
0
0
2
2
0
0
0
0
0
1
2
0
1
2
1
0
0
0
1
0
0
0
0
0
6
0
0
0
2
0
0
0
1
0
1
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
2
0
6
3
1
1
0
1
0
0
1
0
0
1
0
0
2
1
0
0
1
0
1
1
2
0
0
2
2
2
1
0
0
0
0
0
0
1
2
2
1
0
0
0
1
0
0
1
1
3
0
0
0
0
2
0
0
0
1
0
1
0
2
0
0
1
0
2
2
0
1
0
0
0
0
2
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
2
0
1
0
1
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
2
1
0
1
0
0
0
1
3
1
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
2
2
2
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
5
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
1
2
0
0
0
0
2
0
2
0
2
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
2
3
3
1
1
0
0
1
0
2
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
2
0
2
0
2
0
2
0
0
0
3
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
2
0
5
0
2
0
0
0
1
1
0
0
2
0
0
2
0
0
0
0
0
0
1
1
0
0
4
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
2
0
0
1
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
2
1
2
4
2
0
0
0
2
0
1
1
0
0
0
0
1
0
0
2
2
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
2
0
0
0
1
2
0
0
2
0
0
0
1
1
1
1
0
0
0
4
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
2
1
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
3
2
1
0
0
0
0
1
1
2
0
2
1
0
0
1
1
1
0
2
0
2
1
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
2
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
5
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
4
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
2
0
1
0
0
0
0
2
1
0
0
0
1
2
0
0
0
1
0
0
2
1
0
0
2
1
2
0
0
0
2
0
1
2
0
1
0
0
0
2
0
2
0
0
2
0
2
0
0
0
0
0
0
2
2
4
3
0
0
0
0
0
2
0
2
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
2
1
0
0
0
0
0
1
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
3
0
0
0
0
1
2
1
0
0
0
2
0
1
2
0
0
2
2
1
0
0
2
3
0
1
1
0
0
1
1
2
2
0
0
0
0
2
0
0
3
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
1
2
0
0
3
0
0
2
0
2
1
0
0
1
0
0
2
0
0
0
1
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
2
0
1
0
0
5
1
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
1
0
0
0
0
1
0
0
0
2
0
0
2
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
1
2
0
0
1
0
3
0
0
2
0
0
0
0
0
2
0
1
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
1
2
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
2
2
0
0
0
0
0
2
0
0
3
0
0
1
2
0
0
1
0
2
0
0
0
0
1
0
0
0
2
0
2
1
1
4
0
0
0
1
0
1
2
1
2
0
0
0
0
2
1
2
0
0
2
2
0
1
2
0
1
0
0
2
0
0
0
0
0
0
0
1
1
1
1
3
1
4
2
0
0
0
0
0
0
0
1
2
0
0
2
2
0
2
3
2
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
1
0
0
0
2
1
0
0
2
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
3
2
0
0
2
1
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
1
0
0
2
0
1
2
0
0
3
0
0
0
0
0
0
7
0
2
0
3
0
0
2
0
0
2
2
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
3
0
1
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
2
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
2
1
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
2
0
2
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
2
1
2
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
1
0
2
2
0
0
3
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
4
2
6
0
0
2
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
2
2
0
0
2
0
1
0
0
0
0
2
0
0
1
2
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
1
1
0
0
2
1
0
0
2
3
2
0
0
2
0
0
0
1
0
0
2
0
3
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
1
3
1
0
0
2
1
0
0
2
2
1
2
0
0
1
0
0
0
1
0
0
0
0
0
1
1
3
0
1
1
0
0
2
1
0
0
0
1
1
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
1
2
1
0
0
0
0
1
0
1
2
0
2
0
0
1
1
1
0
0
0
0
2
0
5
0
0
0
0
1
0
0
0
0
0
0
0
2
0
4
0
2
0
0
1
1
0
0
2
0
0
3
2
0
0
2
0
0
0
0
2
2
0
2
2
2
0
1
2
3
2
0
1
2
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
2
2
0
2
0
0
1
0
0
2
0
1
0
0
1
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
3
0
0
0
0
0
0
1
4
0
3
1
0
0
1
2
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
1
1
1
0
0
0
0
0
1
0
0
0
2
2
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
1
0
0
1
0
0
1
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
2
0
0
0
2
1
3
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
1
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
2
1
0
0
1
0
2
0
3
0
2
0
0
0
2
0
0
2
0
0
2
2
1
2
0
0
3
0
0
0
0
1
2
0
1
0
2
0
0
1
0
2
0
2
0
1
0
1
0
2
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
1
0
1
0
1
0
0
2
0
2
1
0
2
0
0
0
2
0
1
0
0
2
0
0
0
0
1
0
0
0
2
0
2
0
0
1
0
0
0
1
2
2
1
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
8
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
1
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
1
1
0
0
2
0
1
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
1
0
0
1
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
1
2
2
0
0
0
2
0
2
0
0
0
2
0
0
0
2
2
0
0
1
2
1
0
0
0
0
0
0
0
1
2
0
1
0
1
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
2
0
0
0
0
2
0
0
0
2
0
1
1
0
2
0
0
0
2
0
0
5
0
1
0
0
0
2
0
0
0
0
3
0
2
0
0
0
0
1
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
1
2
0
2
2
0
0
0
0
2
0
0
0
2
3
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
5
0
0
0
0
2
0
0
0
1
0
2
0
3
0
1
3
0
0
1
0
0
2
2
0
2
2
0
2
0
0
1
0
0
2
2
0
2
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
1
0
2
0
1
0
0
1
1
1
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
1
0
3
0
0
0
0
0
0
0
0
0
0
4
1
2
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
1
0
0
2
0
1
0
0
2
1
1
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
2
0
0
0
1
2
0
0
0
2
0
1
2
2
0
0
0
0
0
1
1
0
2
0
0
0
2
0
1
0
0
2
2
0
0
2
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
2
0
1
0
3
0
2
0
0
0
0
1
2
0
1
2
3
2
1
0
1
0
0
0
0
0
2
0
1
1
1
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
1
2
0
2
0
1
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
2
0
0
2
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
5
0
0
0
0
0
0
0
2
1
0
2
1
0
0
0
1
1
0
0
0
2
1
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
1
2
0
1
0
0
0
3
2
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
2
1
0
0
0
0
0
0
0
1
0
3
0
0
4
2
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
2
1
0
1
0
0
0
1
2
1
0
0
0
0
0
5
0
0
0
1
0
0
2
2
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
2
0
2
0
1
0
0
0
1
0
0
1
0
0
0
0
3
2
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
2
1
0
2
0
0
0
0
2
0
0
3
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
3
1
2
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
1
5
0
2
0
2
1
2
0
0
0
0
0
1
2
0
0
5
1
4
0
0
0
0
1
0
0
0
1
2
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
1
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
1
0
0
0
2
1
0
3
0
0
0
0
0
0
0
2
0
2
2
1
0
1
0
0
3
1
1
0
0
0
0
2
1
0
0
0
0
0
0
0
1
2
3
2
1
0
2
1
2
0
1
1
0
0
0
1
0
1
0
1
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
1
0
0
2
1
0
1
1
0
0
2
0
1
0
0
0
2
0
0
2
0
0
0
0
0
1
2
0
1
2
2
0
0
1
0
0
0
0
0
0
0
3
0
2
0
2
0
1
2
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
1
0
0
2
1
0
1
2
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
1
0
0
0
0
0
1
1
0
1
3
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
8
0
2
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
1
1
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
1
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
2
2
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
2
0
1
0
8
0
0
0
0
3
0
0
2
0
4
0
1
0
0
0
2
0
0
0
2
1
3
2
0
0
1
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
3
1
1
2
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
2
2
0
2
2
0
0
1
0
1
1
2
0
2
2
2
1
1
0
2
0
0
0
1
0
1
0
0
0
0
0
4
2
3
0
0
0
0
2
0
2
0
2
2
0
1
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
1
1
2
2
0
0
0
2
0
2
1
1
0
2
2
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
2
3
0
0
0
1
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
3
0
0
0
2
1
4
0
0
1
0
0
0
0
1
3
0
2
0
0
1
3
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
3
0
2
1
0
2
0
0
1
1
3
0
0
0
2
0
1
0
1
2
0
0
1
1
1
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
1
1
0
0
2
0
0
0
0
0
0
2
2
2
0
2
2
0
0
2
0
2
1
1
0
0
0
0
0
2
0
2
0
0
2
0
2
0
0
0
0
0
1
2
1
0
3
0
1
0
1
0
1
0
1
0
2
1
0
0
0
0
1
0
1
0
0
0
0
0
2
0
2
0
3
0
0
0
0
0
1
0
0
1
2
2
0
0
0
2
1
2
0
1
0
0
0
2
2
2
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
2
1
2
1
0
0
2
2
0
1
0
2
0
0
1
2
0
1
1
0
0
1
2
0
0
1
1
0
2
1
1
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
2
3
0
1
0
0
0
1
0
0
2
0
2
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
1
1
1
0
1
1
0
3
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
1
0
2
0
0
2
1
0
0
0
2
2
2
0
1
0
1
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
1
0
0
2
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
1
0
5
0
0
2
2
1
0
0
0
0
0
0
0
0
3
0
0
0
0
1
2
3
2
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
1
0
1
2
0
2
2
0
0
3
0
2
0
2
0
0
0
1
2
1
0
0
0
2
0
0
2
2
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
2
1
0
0
0
0
0
1
2
0
0
0
1
2
0
0
1
0
1
0
0
2
0
0
2
0
2
2
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
1
1
0
0
0
2
2
2
1
1
0
3
0
1
1
2
0
0
1
1
0
1
3
0
0
0
0
1
2
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
5
0
1
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
2
0
0
2
2
2
2
0
0
2
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
1
0
3
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
2
0
1
2
0
1
0
1
0
2
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
1
0
2
0
0
0
0
0
2
0
2
0
0
1
1
3
0
2
0
0
0
0
0
0
6
0
2
1
0
0
2
0
0
0
0
0
2
0
0
2
1
0
0
0
1
0
2
1
1
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
1
0
0
2
1
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
2
0
3
0
0
0
2
0
0
0
0
0
1
2
4
0
2
0
0
0
2
0
2
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
3
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
1
0
0
1
0
1
0
1
0
2
3
0
0
0
1
2
0
0
3
1
3
3
0
1
1
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
2
2
0
0
2
2
0
0
0
0
1
2
2
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
1
0
2
2
0
0
0
1
0
0
1
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
1
0
0
1
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
1
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
1
2
0
2
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
2
0
0
2
2
1
1
0
2
2
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
2
0
2
0
2
1
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
2
1
0
1
0
0
0
0
1
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
6
1
0
0
0
0
1
2
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
2
2
0
0
0
0
0
7
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
4
2
1
0
0
0
3
0
1
0
0
0
0
0
2
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
1
2
1
2
2
0
0
0
0
1
2
0
0
0
0
2
0
2
0
0
0
2
0
0
2
0
1
0
1
2
0
0
2
0
0
0
0
2
2
0
2
0
1
0
0
0
1
1
2
0
1
0
0
0
0
0
2
3
0
0
1
0
0
2
0
0
0
0
2
2
0
0
1
0
0
2
2
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
1
1
0
0
3
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
3
1
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
1
0
0
2
0
1
0
0
2
2
0
0
0
0
0
2
1
0
0
1
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
2
2
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
2
0
0
2
1
0
0
3
0
1
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
1
0
2
0
1
0
0
0
1
4
2
3
0
0
0
0
1
0
1
2
0
2
1
0
0
2
1
2
2
0
0
0
2
0
0
1
1
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
2
1
0
1
2
2
1
0
0
0
0
2
1
1
0
0
0
1
0
2
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
2
0
0
0
0
3
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
2
4
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
4
0
2
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
1
1
2
1
0
0
0
0
1
0
0
1
1
2
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
3
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
2
1
1
0
0
2
1
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
2
0
1
0
1
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
1
0
1
0
0
2
4
2
0
0
0
1
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
2
0
0
0
3
0
0
0
2
2
0
2
0
0
1
0
1
1
0
0
0
2
1
0
0
0
0
1
0
0
1
1
0
0
0
1
2
0
0
3
0
0
0
1
0
0
0
0
1
0
1
0
2
2
0
0
0
0
0
0
2
1
1
0
0
1
0
0
1
0
1
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
2
1
2
0
0
0
3
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
1
0
1
0
1
2
0
0
0
0
2
2
0
0
0
0
0
1
2
2
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
2
3
0
2
0
0
0
0
6
0
0
0
1
0
2
0
2
0
1
2
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
1
1
1
0
0
0
2
1
3
1
0
1
0
1
0
2
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
2
0
0
0
1
0
2
0
1
0
1
0
2
0
0
0
0
3
0
0
1
2
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
1
2
1
1
2
1
1
1
1
0
1
2
0
0
4
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
2
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
1
1
2
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
2
1
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
2
0
2
1
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
1
0
0
2
0
0
2
2
0
1
1
0
1
0
0
0
1
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
2
0
0
0
1
2
0
0
2
0
0
1
0
3
2
0
1
0
0
0
1
0
0
0
0
0
1
0
0
4
0
3
0
0
0
1
0
1
0
0
0
1
0
0
0
4
0
0
2
0
0
0
1
0
0
0
0
2
2
0
0
0
1
3
3
0
0
0
0
2
0
0
2
0
3
0
2
0
2
2
0
0
0
2
0
0
0
1
1
0
0
2
2
2
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
2
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
1
0
0
0
0
2
1
2
2
1
0
0
2
0
0
0
1
0
0
0
0
1
0
2
0
2
0
0
0
2
0
3
0
0
0
0
1
0
0
1
0
1
0
2
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
1
0
0
2
1
0
7
0
0
0
0
3
0
0
0
0
2
3
0
0
2
0
1
0
1
0
0
0
0
0
1
2
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
3
2
1
1
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
2
1
1
0
1
0
2
1
0
0
0
2
0
1
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
1
0
0
1
1
0
0
2
1
0
0
0
0
0
0
0
2
0
0
2
1
0
1
0
1
0
0
0
1
2
0
0
1
0
0
0
0
0
2
0
2
1
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
1
2
2
0
2
1
0
0
0
1
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
7
5
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
2
1
0
0
2
0
2
1
0
2
0
0
0
3
0
0
0
0
2
0
2
2
0
1
2
2
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
1
0
0
0
0
1
2
0
0
0
1
0
1
0
2
1
1
0
0
0
0
1
0
0
0
0
0
1
2
0
0
1
0
1
0
0
1
0
0
1
0
0
2
0
0
0
4
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
1
0
1
0
0
2
0
0
1
0
1
0
2
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
1
0
0
1
0
0
2
0
0
0
0
1
1
0
0
0
3
0
0
0
1
0
0
1
0
0
0
0
2
0
0
2
0
0
0
2
1
0
0
0
3
0
0
1
0
3
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
2
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
1
0
0
2
2
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
5
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
2
0
1
0
1
3
2
2
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
1
1
1
0
0
2
2
2
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
2
2
2
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
2
0
0
0
0
2
0
0
1
0
2
0
1
1
0
0
0
2
0
2
3
0
0
0
2
0
1
1
0
0
0
4
0
0
2
1
2
0
0
1
1
3
4
1
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
2
5
0
2
0
2
0
1
0
0
0
2
0
1
1
1
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
3
0
0
0
2
2
0
0
0
0
0
0
0
2
0
2
3
2
2
1
0
1
0
0
1
0
1
0
0
1
2
1
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
3
5
0
1
0
2
0
2
0
2
0
0
0
0
0
0
0
0
2
1
0
0
1
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
4
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
2
2
1
0
0
0
0
1
0
0
2
0
2
0
0
0
0
1
3
0
0
1
0
0
0
2
0
0
2
0
0
1
0
0
0
1
0
0
0
1
0
2
2
0
2
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
2
0
0
1
0
0
1
4
0
4
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
2
0
1
1
1
0
0
0
0
0
1
0
2
0
1
0
1
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
2
1
1
2
0
2
0
0
0
5
0
1
0
2
0
3
0
0
1
0
0
0
1
0
0
1
0
0
1
1
0
1
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
1
0
0
1
0
1
2
0
0
0
0
0
2
0
0
0
5
0
3
0
0
0
2
0
0
0
0
1
2
0
0
0
2
0
2
0
1
1
0
2
0
0
1
0
1
1
2
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
1
2
1
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
2
1
0
0
2
1
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
3
1
1
2
0
0
0
2
2
0
2
0
0
3
2
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
2
0
1
1
0
0
0
0
1
2
0
0
0
1
0
1
3
2
0
0
1
2
1
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
3
0
0
1
2
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
2
2
0
2
3
0
2
0
2
0
0
0
0
2
2
0
2
0
2
0
1
0
0
0
3
0
4
1
2
0
0
0
0
2
0
0
0
0
0
1
0
2
1
0
0
2
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
1
0
0
1
0
0
2
0
1
0
2
1
0
0
0
0
1
1
2
3
2
0
0
0
0
2
0
0
2
0
2
0
0
0
1
0
0
2
0
2
2
0
0
0
0
2
0
0
0
2
0
1
1
0
0
2
1
0
0
0
1
2
0
1
0
0
1
2
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
1
0
0
0
1
2
0
0
3
2
0
2
1
0
0
0
0
3
0
1
2
0
1
1
0
1
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
2
3
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
1
1
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
1
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
3
0
2
1
0
0
1
2
0
1
2
1
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
2
0
0
0
0
0
0
0
2
1
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
1
0
0
0
0
0
1
0
1
4
0
0
1
2
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
3
2
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
2
1
1
0
0
0
0
1
0
2
1
0
1
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
5
2
0
1
1
0
2
0
1
0
1
0
0
0
2
1
0
0
0
0
3
0
0
2
0
2
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
1
0
0
0
2
0
0
0
0
0
1
0
0
1
2
0
0
0
0
1
1
0
0
0
0
0
0
0
3
0
1
0
0
0
1
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
1
0
3
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
2
2
2
0
0
1
0
0
1
0
0
0
0
0
0
3
0
5
2
0
2
1
0
2
0
0
2
1
2
2
0
0
0
0
0
2
2
0
0
0
0
1
0
0
2
1
0
2
2
0
0
0
0
0
2
0
3
0
2
0
3
0
0
0
0
0
0
1
2
0
0
0
0
0
2
1
0
2
1
0
0
0
1
1
1
4
0
0
0
0
0
0
2
0
2
1
1
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
2
0
2
2
0
1
0
0
1
2
0
0
0
1
1
2
0
0
0
2
0
0
1
1
0
0
0
1
0
2
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
2
0
0
0
2
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
1
1
0
2
0
0
0
1
0
2
1
0
0
0
0
0
0
1
0
0
1
3
1
1
0
2
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
2
0
1
2
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
3
2
0
5
1
0
0
1
0
0
2
0
2
1
1
0
2
0
0
1
0
1
0
0
2
2
0
0
2
2
0
0
2
0
1
2
0
5
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
2
1
0
0
1
0
1
0
0
3
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
2
0
1
1
1
0
2
0
3
1
1
0
0
2
4
0
0
0
1
0
0
0
0
2
0
0
1
2
0
1
1
0
3
0
4
0
0
0
0
1
1
2
0
0
1
0
2
1
0
1
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
1
0
2
0
1
1
0
0
1
0
2
0
0
3
0
1
0
2
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
1
0
2
0
0
1
0
1
0
0
0
2
0
0
0
0
3
2
0
2
0
0
0
0
0
0
1
0
1
1
0
0
1
0
2
2
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
2
0
2
2
0
0
1
0
3
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
1
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
5
2
0
2
0
0
0
0
0
0
1
4
2
1
0
0
0
2
0
1
0
2
0
1
0
3
0
0
0
0
0
0
2
3
0
2
0
0
0
2
1
2
0
0
0
1
1
0
0
1
0
0
0
2
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
7
0
1
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
1
1
0
1
0
0
1
0
0
0
0
0
1
0
0
1
2
0
1
0
0
0
1
1
0
0
1
0
0
0
0
2
2
0
1
0
1
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
1
0
2
0
0
0
0
0
2
1
0
0
0
1
1
0
0
1
2
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
1
0
1
0
3
0
0
0
2
1
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
3
0
0
0
2
2
3
0
0
0
0
0
0
0
0
0
3
0
1
2
0
2
0
0
0
0
1
1
0
2
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
1
1
2
0
0
2
1
2
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
2
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
4
0
0
1
1
1
0
2
2
1
0
0
0
0
0
0
2
0
0
1
0
1
0
0
2
0
0
2
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
2
2
0
2
0
0
0
0
0
0
0
0
0
2
1
1
1
2
0
0
0
0
0
0
0
0
1
3
0
2
2
0
0
0
0
1
0
0
0
0
0
2
0
0
2
1
2
2
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
2
0
0
2
0
0
0
2
3
0
0
0
0
0
0
1
2
0
0
0
6
0
0
0
0
0
2
2
0
0
0
2
1
0
2
0
2
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
1
2
3
0
0
2
0
1
0
0
1
1
0
4
0
0
0
0
1
1
0
0
2
0
0
0
0
2
1
0
1
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
1
2
2
0
0
0
0
2
1
3
1
0
2
0
2
0
2
0
2
0
0
1
0
1
0
2
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
3
0
1
1
2
0
0
0
0
1
0
0
1
2
2
1
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
2
1
0
0
0
1
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
1
2
0
0
0
3
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
1
1
0
0
2
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
1
1
1
0
0
0
0
2
0
0
2
0
0
0
2
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
2
0
0
0
0
1
0
0
0
0
1
0
0
3
1
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
1
0
0
0
2
0
0
1
0
2
0
1
0
0
0
1
4
0
2
0
0
2
0
2
0
0
0
2
1
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
1
1
0
0
0
2
0
1
0
2
0
1
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
1
1
0
2
0
2
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
2
0
1
3
0
0
0
2
0
0
1
0
0
2
0
0
0
1
0
0
0
0
2
0
2
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
4
1
0
0
0
2
0
0
1
0
2
0
1
0
0
0
3
1
0
0
2
1
0
0
0
0
0
0
1
2
0
0
0
0
2
0
2
0
2
0
0
0
0
1
0
0
0
0
1
2
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
2
0
3
0
0
2
0
1
0
0
2
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
2
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
2
1
2
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
1
0
0
0
2
0
0
0
0
1
0
0
0
2
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
2
1
0
0
0
1
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
2
4
1
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
4
1
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
1
2
0
1
0
0
2
0
1
1
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
1
1
0
1
0
0
1
0
1
0
2
0
2
0
0
0
1
0
0
2
2
0
0
0
2
1
2
1
1
0
2
3
0
0
2
0
1
0
2
0
3
0
0
0
1
0
0
2
2
0
1
2
0
0
2
0
2
0
0
2
0
2
0
1
0
1
0
2
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
1
2
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
5
0
0
0
1
1
2
3
0
0
2
1
0
0
0
0
2
1
3
4
0
1
2
0
2
0
0
0
1
0
1
0
0
2
0
0
0
0
0
2
1
2
3
0
6
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
2
1
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
2
0
2
1
0
0
0
1
3
0
0
0
0
1
0
0
0
2
0
1
0
0
0
2
0
0
2
1
0
2
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
1
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
1
0
0
0
1
0
0
2
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
1
1
1
0
0
2
1
3
0
0
0
0
0
0
0
0
0
1
0
0
2
0
11
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
2
0
1
0
1
1
0
0
3
3
1
2
0
0
0
0
1
0
0
1
1
0
0
2
2
0
2
0
0
0
0
0
2
0
2
0
0
1
0
1
1
0
0
0
0
0
1
1
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
1
0
2
0
5
0
0
0
0
0
0
0
1
1
2
3
3
0
2
0
0
1
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
2
0
0
1
0
1
0
0
2
0
2
0
0
1
2
0
0
2
0
0
0
0
0
7
0
2
0
1
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
2
0
0
2
0
0
4
0
0
0
0
1
0
0
0
2
0
2
2
0
0
2
0
2
0
0
0
1
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
3
0
0
2
1
0
0
1
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
1
0
0
3
0
2
0
0
0
0
0
0
0
0
1
0
1
2
3
2
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
1
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
2
0
2
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
2
0
0
2
1
0
2
0
1
0
0
0
0
0
0
0
0
0
5
0
0
1
0
1
0
3
0
0
0
0
0
0
0
0
1
3
0
0
0
1
0
2
0
3
0
0
0
0
0
2
0
0
1
0
0
2
2
0
0
2
2
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
1
0
0
0
2
0
0
0
0
0
1
0
0
2
2
0
0
2
2
0
0
0
2
1
0
2
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
1
1
0
0
0
0
2
2
0
0
2
0
0
1
2
0
0
0
1
1
1
1
0
0
0
1
1
0
0
0
0
3
0
2
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
6
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
2
0
0
0
2
0
0
0
1
0
0
1
0
1
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
2
2
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
2
0
1
2
0
0
0
0
0
3
0
0
0
0
1
1
2
1
0
1
0
1
0
1
3
0
0
1
0
1
0
0
1
0
0
1
3
0
0
0
0
0
0
1
0
0
1
3
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
2
1
0
0
0
2
0
0
0
0
0
0
0
0
1
4
2
0
1
0
0
1
0
2
4
1
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
2
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
2
0
1
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
3
0
0
2
0
2
0
1
2
3
3
0
3
2
0
1
0
0
0
0
0
0
1
0
0
0
2
2
0
1
5
0
0
0
0
0
2
0
1
0
0
2
1
2
5
0
1
1
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
8
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
1
1
1
2
0
1
0
0
1
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
1
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
2
0
2
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
2
0
0
0
0
0
2
1
0
0
0
0
3
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
3
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
1
0
0
2
0
0
0
0
0
1
1
1
2
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
4
0
1
2
0
1
2
0
3
0
0
0
0
0
0
0
0
0
2
3
0
1
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
4
1
0
0
0
2
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
3
3
1
2
2
1
0
0
1
2
2
1
2
0
2
0
2
0
0
0
2
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
2
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
2
0
0
0
0
0
2
0
0
0
3
0
1
0
2
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
1
1
0
0
1
0
1
0
2
2
2
0
0
3
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
1
1
1
0
0
0
2
1
0
0
4
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
3
2
1
0
2
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
2
0
3
2
2
0
0
0
0
0
0
1
1
2
0
1
1
0
0
0
0
1
0
0
0
3
2
1
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
1
0
0
0
3
2
2
2
0
0
0
1
1
2
1
0
0
2
0
2
0
0
0
0
0
1
0
2
0
2
2
0
0
0
4
6
0
1
1
2
0
0
2
2
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
1
0
0
0
0
1
0
0
0
1
3
0
0
0
0
1
0
0
0
1
2
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
2
0
0
0
0
1
1
2
2
1
0
0
0
0
0
1
0
2
0
0
2
1
0
0
0
0
5
0
2
0
1
1
2
1
0
0
1
2
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
3
2
0
0
0
0
0
2
1
0
1
1
0
0
0
1
2
0
0
2
1
0
2
0
0
0
0
0
1
2
0
0
0
1
1
0
0
0
0
0
0
1
2
0
0
1
1
0
0
0
1
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
1
0
0
0
1
2
0
0
0
0
1
0
2
1
0
0
0
0
0
1
1
1
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
1
2
2
0
0
0
0
0
1
0
2
0
0
2
0
2
2
2
0
0
1
1
1
0
0
2
0
0
0
1
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
1
1
0
2
0
1
0
0
1
2
0
0
0
0
0
0
0
0
1
0
2
2
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
1
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
2
2
0
2
0
2
0
0
0
1
0
0
0
2
0
0
2
0
0
1
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
2
1
0
1
0
5
0
2
0
1
2
0
0
4
0
3
0
1
2
0
0
2
0
0
0
1
0
1
1
2
1
0
0
0
2
0
0
0
1
1
0
1
0
2
0
1
1
0
3
1
0
0
0
0
1
0
0
0
0
0
0
0
1
2
2
0
0
2
1
0
0
0
0
2
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
3
2
0
0
0
2
1
0
0
0
0
2
0
2
0
0
2
0
2
0
0
0
0
2
3
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
2
0
0
0
0
0
2
2
1
0
2
0
0
0
0
0
2
2
0
0
2
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
3
0
0
0
1
2
0
2
1
1
1
0
0
0
0
2
3
0
1
2
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
2
0
0
0
4
0
0
0
2
1
2
0
0
0
0
0
1
0
0
0
1
1
1
2
1
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
1
2
0
2
0
1
1
0
0
2
0
1
0
0
0
2
0
0
1
1
0
0
0
3
0
0
0
7
0
2
2
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
1
2
1
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
1
0
3
2
0
0
1
1
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
1
1
0
2
0
0
1
2
1
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
1
1
1
0
1
0
0
0
7
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
2
0
0
0
0
0
3
0
2
0
0
1
0
0
1
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
2
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
2
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
2
1
0
1
2
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
1
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
1
0
0
0
0
1
2
0
0
0
0
2
0
0
2
0
2
0
2
0
1
0
1
0
2
3
1
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
1
0
2
1
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
2
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
1
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
5
1
0
2
0
0
0
1
1
1
0
2
0
0
7
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
2
1
2
1
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
2
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
2
0
0
0
1
0
0
0
1
2
0
1
2
3
0
0
0
0
0
0
1
2
0
0
0
4
0
0
0
0
0
1
1
3
0
0
0
0
2
0
0
0
0
1
1
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
1
0
0
0
0
2
2
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
3
2
1
2
1
1
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
2
0
0
0
0
4
1
0
0
0
1
0
2
0
0
0
0
1
2
0
0
0
0
0
2
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
2
4
2
1
0
2
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
1
0
0
2
0
2
0
0
0
0
2
0
2
5
1
0
1
0
1
2
1
0
1
1
2
2
2
0
1
2
0
1
0
0
0
2
2
0
0
2
0
0
2
2
3
1
1
0
0
0
0
1
0
1
1
1
0
2
0
1
1
2
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
4
0
0
0
0
1
0
0
5
2
0
0
0
3
1
0
0
1
0
1
3
0
0
1
1
1
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
3
0
0
0
3
0
0
0
0
2
1
0
0
0
0
0
4
2
2
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
2
1
0
0
1
0
0
0
1
0
0
2
0
0
2
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
7
0
2
2
0
0
0
0
0
1
0
0
0
0
1
1
0
0
2
0
0
0
1
1
2
0
0
3
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
2
0
0
0
2
1
0
0
2
0
0
0
2
1
2
1
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
2
2
0
2
2
0
0
0
0
0
0
0
1
1
0
0
0
0
2
1
2
2
0
0
0
1
0
0
0
0
2
2
1
2
2
0
0
0
0
2
0
0
0
0
2
0
1
0
2
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
10
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
3
2
0
2
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
1
0
0
2
2
0
0
1
0
2
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
1
2
0
2
2
0
1
0
0
1
0
0
1
0
0
1
2
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
1
0
2
0
0
0
0
0
1
2
0
1
0
2
0
2
0
2
1
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
2
1
0
1
3
1
0
0
1
0
0
0
0
0
0
3
0
0
1
0
2
0
0
2
0
0
0
2
2
0
2
2
2
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
2
2
0
3
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
3
1
0
2
1
0
2
3
0
0
0
0
0
0
0
1
2
1
2
1
0
0
0
2
1
1
0
1
1
1
2
1
2
0
4
2
0
0
0
1
0
0
2
0
0
0
2
0
0
2
0
1
2
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
2
0
1
1
0
4
0
0
0
1
0
0
0
0
0
0
2
0
1
1
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
2
1
1
0
0
0
2
0
1
1
0
0
1
0
2
0
0
0
0
0
0
3
0
1
0
0
0
0
0
1
0
0
0
0
0
3
0
2
0
0
2
1
0
0
0
1
0
0
0
2
0
0
0
0
1
1
0
1
0
0
0
2
1
1
0
0
0
0
0
0
0
2
2
1
0
0
0
0
2
0
1
0
0
1
0
0
0
2
0
0
0
2
0
1
0
1
0
0
0
1
0
0
0
2
2
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
2
1
0
2
0
1
1
2
0
0
3
0
0
0
0
1
2
0
0
3
2
0
0
1
0
1
0
0
0
0
0
0
0
1
2
2
0
1
2
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
1
0
0
6
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
2
0
0
2
0
0
0
2
2
0
2
1
5
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
17
5
0
0
0
1
0
1
2
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
2
1
1
1
2
0
0
0
0
1
0
0
0
1
0
0
1
1
1
0
1
2
0
0
2
1
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
2
0
0
2
2
0
1
0
1
0
0
0
1
0
0
0
2
0
0
4
1
1
0
0
1
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
1
0
0
0
0
1
0
3
0
1
8
0
0
2
3
0
0
2
0
0
2
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
2
0
0
1
0
0
2
0
0
0
4
1
0
0
0
0
0
0
3
0
0
2
4
0
1
2
0
1
0
1
1
0
0
0
0
0
2
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
4
0
1
0
1
0
1
0
0
2
0
0
0
0
2
0
0
1
0
2
0
0
0
0
1
2
1
2
0
1
0
0
0
2
0
1
0
0
0
0
0
0
2
2
0
1
0
3
1
0
2
0
0
0
0
0
0
2
0
2
0
0
0
1
1
0
0
3
0
0
1
0
0
2
0
0
0
0
0
2
1
0
1
1
0
0
1
1
0
0
0
1
0
2
0
0
0
1
1
0
0
2
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
3
0
1
0
0
1
0
0
0
0
1
0
0
0
0
3
1
0
0
0
0
0
1
0
2
0
0
1
2
0
1
0
0
0
0
0
0
0
1
3
1
1
0
2
2
0
0
0
0
2
0
0
0
1
0
0
2
2
2
0
2
0
2
1
0
0
1
0
0
2
0
2
0
0
0
0
0
0
2
0
1
1
1
2
0
0
0
0
2
0
1
2
2
0
0
0
0
0
0
2
2
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
2
0
0
2
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
3
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
1
2
0
0
2
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
2
1
0
0
2
2
2
1
1
0
0
0
0
0
0
0
0
2
2
3
1
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
3
1
2
2
1
0
0
0
2
0
0
0
1
0
3
0
0
2
0
1
0
0
1
0
0
2
0
1
1
0
1
0
0
0
0
0
1
2
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
1
0
0
0
3
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
1
0
0
0
2
1
1
0
0
0
2
1
0
1
0
1
0
0
0
1
2
1
0
0
1
0
0
0
0
0
2
1
1
0
0
10
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
1
2
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
1
2
0
0
0
0
0
0
2
2
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
2
2
0
2
0
1
1
0
1
0
1
0
2
0
0
1
3
0
0
0
0
0
0
0
2
2
0
0
0
1
3
0
0
2
0
2
0
2
2
0
2
2
0
0
0
0
1
0
0
1
0
3
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
4
2
0
1
0
2
0
2
1
0
0
0
5
0
0
0
1
0
0
3
0
0
0
0
2
1
0
0
3
2
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
2
0
0
0
1
0
3
1
0
2
1
0
1
2
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
2
1
0
0
0
0
2
0
0
0
0
1
0
1
0
3
0
1
0
0
0
1
0
6
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
2
0
1
0
2
1
0
2
2
0
1
0
0
0
0
0
0
3
0
0
0
0
2
0
2
0
2
2
1
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
1
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
1
4
0
0
2
0
0
2
0
1
1
0
2
0
0
0
3
0
1
2
2
2
1
1
0
0
0
0
0
2
0
1
0
1
1
1
0
2
1
0
2
0
0
2
4
0
0
3
0
1
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
1
0
0
0
2
0
2
1
0
2
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
1
1
0
4
0
0
0
0
0
0
2
1
0
0
2
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
1
0
0
4
1
1
0
1
0
0
1
0
0
4
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
2
1
2
0
0
0
0
0
2
0
0
0
0
0
6
0
0
0
1
0
0
2
1
1
0
1
0
0
0
2
0
0
0
0
0
0
2
0
1
1
0
1
1
0
0
0
0
1
0
0
1
2
0
0
2
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
2
0
0
2
0
0
0
0
0
1
1
1
0
0
0
2
1
0
0
0
0
0
0
1
2
0
0
0
8
0
0
2
0
0
0
0
0
1
0
4
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
2
0
2
0
1
0
0
1
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
1
2
0
0
0
2
0
0
1
1
1
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
3
0
1
0
1
2
0
0
0
0
1
0
0
0
0
0
2
1
1
0
1
0
0
0
0
0
0
0
1
0
0
2
0
2
0
1
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
5
0
3
0
0
0
0
3
2
0
2
1
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
1
0
1
0
2
0
0
0
0
0
0
1
0
0
1
0
0
2
1
1
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
1
2
1
0
2
0
0
1
1
0
0
0
0
3
0
0
0
0
0
2
0
1
0
0
2
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
1
0
1
5
0
0
0
0
2
0
0
0
0
0
0
2
1
0
2
1
0
1
0
2
0
0
0
0
2
1
2
0
0
0
1
0
0
0
0
2
0
1
0
1
0
2
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
1
1
0
0
2
0
0
2
4
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
3
1
1
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
2
1
0
3
0
0
2
0
0
0
0
1
1
0
2
0
0
1
1
2
0
1
0
0
0
1
0
0
0
1
0
0
0
0
5
2
0
0
0
2
4
0
0
0
4
2
2
1
1
0
2
1
2
2
0
1
2
0
0
1
2
0
0
1
0
1
0
2
0
0
2
0
0
2
0
0
0
0
2
0
1
0
1
0
0
0
2
0
0
0
1
2
0
0
3
0
0
2
2
0
0
0
0
0
1
0
0
1
3
0
0
1
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
1
0
0
8
0
0
2
0
1
0
1
2
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
2
1
0
0
0
0
1
0
0
1
0
1
2
0
1
1
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
2
0
0
0
0
0
0
5
2
0
0
0
0
1
2
0
0
1
1
0
1
0
0
0
1
0
2
1
0
0
1
0
0
1
0
0
0
0
1
2
0
0
1
0
0
0
0
0
2
1
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
2
2
1
1
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
2
0
1
2
0
0
0
4
0
0
0
2
0
2
0
2
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
2
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
2
1
0
1
0
0
2
2
0
0
0
0
2
1
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
2
0
0
2
2
1
1
2
0
0
2
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
2
3
0
0
1
0
0
1
0
0
0
0
0
2
0
1
0
2
2
0
1
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
1
0
0
2
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
2
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
2
0
0
0
2
0
1
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
3
0
1
0
3
2
1
2
0
1
0
2
0
0
0
0
1
0
2
2
0
0
0
0
0
2
0
0
0
2
0
1
1
0
1
2
0
0
0
0
0
0
2
0
1
2
1
0
0
1
0
0
1
0
0
1
0
0
1
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
2
0
2
2
0
0
0
1
1
0
0
2
0
0
2
0
0
1
0
0
0
0
0
1
1
0
0
0
2
0
1
2
0
0
1
0
1
1
0
1
0
0
0
7
0
1
0
0
1
1
0
0
2
1
2
0
0
0
1
0
0
1
0
0
2
0
0
4
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
2
2
0
0
0
2
2
0
0
0
1
0
1
0
1
2
0
0
0
0
2
0
1
0
0
1
1
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
2
2
2
1
0
0
0
0
0
0
0
1
4
0
0
1
0
2
0
3
1
1
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
2
2
0
0
0
0
0
0
0
1
1
1
2
0
0
0
0
0
2
1
0
0
0
0
0
0
1
3
0
0
1
3
0
2
0
1
1
1
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
3
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
1
1
0
0
2
0
0
2
0
0
1
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
1
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
1
0
0
2
1
0
0
3
0
0
0
0
0
1
1
0
2
2
0
2
1
0
0
0
0
1
0
0
0
0
3
0
1
0
0
0
2
1
0
0
2
0
5
0
0
2
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
4
0
0
0
0
2
1
0
0
5
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
2
2
2
1
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
2
0
2
2
0
0
0
1
0
1
1
0
3
0
2
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
1
4
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
1
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
3
0
0
0
4
1
0
0
0
0
0
2
0
1
0
0
0
0
2
0
1
1
0
0
1
0
1
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
2
0
4
2
0
0
1
0
1
0
0
0
0
0
0
0
1
2
3
1
0
2
0
1
0
2
0
2
0
0
2
0
0
2
1
0
1
2
0
1
3
0
0
0
0
0
0
1
2
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
1
0
2
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
1
0
1
2
0
0
0
14
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
2
0
0
0
2
1
2
0
2
2
0
0
2
2
2
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
2
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
1
1
1
0
1
0
0
0
1
0
0
0
0
0
0
3
0
0
0
1
1
1
1
0
0
2
0
0
1
2
2
0
0
0
0
0
0
0
0
1
2
2
0
0
0
2
0
0
1
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
3
1
2
2
0
2
0
0
0
2
0
1
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
1
2
0
2
0
0
1
2
0
0
0
0
2
0
2
2
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
4
2
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
1
0
2
0
0
0
0
2
2
1
1
1
1
0
0
0
1
1
2
1
2
0
1
0
2
0
0
0
1
1
3
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
2
0
0
0
0
3
2
0
0
0
0
0
2
1
0
2
1
0
0
1
2
0
2
1
0
1
0
2
0
0
2
1
0
0
0
0
0
1
1
2
0
0
0
2
1
0
0
0
2
0
0
0
3
0
2
0
0
0
0
0
2
7
0
0
0
1
0
2
0
0
1
0
0
0
1
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
1
0
3
3
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
2
0
0
1
2
0
0
0
0
3
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
2
2
2
0
0
1
3
0
0
0
0
0
1
0
0
1
0
2
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
2
2
2
1
1
1
0
0
2
0
0
2
0
2
0
0
0
0
2
1
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
1
2
0
2
0
0
0
0
0
2
3
0
0
0
2
1
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
1
0
0
1
4
0
0
0
12
2
2
0
0
2
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
2
2
2
1
0
0
0
0
0
2
0
0
0
1
0
0
1
2
0
1
0
0
0
1
4
2
0
0
2
0
2
0
0
0
1
0
0
0
1
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
4
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
1
0
1
0
0
1
1
0
1
1
0
0
0
3
0
1
0
2
2
2
0
0
0
0
0
0
0
0
0
6
2
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
2
2
0
0
0
1
2
1
0
2
2
1
2
0
0
0
1
0
0
1
1
0
0
2
2
0
2
0
0
0
0
1
0
3
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
3
2
0
0
2
0
0
0
0
0
2
0
0
0
0
1
2
0
0
1
2
0
1
1
2
0
0
0
0
0
0
0
0
1
2
3
1
0
3
1
3
1
0
0
0
0
1
0
0
5
0
0
0
0
0
0
0
0
1
1
0
0
0
0
3
0
0
0
1
3
0
0
1
2
2
0
2
0
1
4
2
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
1
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
2
5
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
1
1
0
0
0
0
0
2
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
3
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
2
1
0
0
1
0
0
0
1
0
1
1
0
2
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
2
7
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
1
3
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
2
0
2
0
0
1
0
0
0
0
2
0
0
2
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
2
0
2
1
1
0
0
0
0
0
1
2
2
1
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
1
0
2
1
2
0
0
1
2
2
0
2
0
0
1
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
1
0
0
0
1
0
2
0
1
0
1
0
0
0
0
2
0
0
0
0
1
1
1
1
0
0
0
0
2
2
0
0
0
2
0
2
2
0
1
1
2
1
0
0
0
2
0
2
1
0
0
1
2
1
0
0
0
2
3
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
2
1
0
0
0
0
0
0
0
1
1
2
0
1
0
2
0
0
0
0
1
0
0
1
0
0
3
2
2
2
0
0
0
2
2
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
1
0
0
0
0
0
0
0
2
0
1
1
0
6
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
2
0
0
1
0
0
0
2
0
0
0
0
2
5
0
0
0
1
0
0
5
2
2
0
1
2
0
0
2
0
2
0
2
4
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
3
2
0
0
2
0
1
0
0
2
1
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
3
0
2
2
0
8
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
2
1
1
0
1
1
2
0
0
2
0
1
0
0
3
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
7
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
2
0
2
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
2
0
1
0
0
2
0
1
0
0
0
0
1
0
0
0
1
2
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
4
0
0
1
0
0
0
2
0
2
0
2
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
2
1
0
1
1
0
2
0
1
1
1
0
0
0
6
0
1
1
0
1
2
0
0
0
0
0
0
0
2
0
0
2
0
0
4
0
1
0
0
0
0
3
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
2
0
2
0
0
3
0
0
0
0
0
1
0
0
1
2
2
0
5
0
0
0
0
0
0
1
1
1
0
0
0
2
0
2
0
2
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
1
0
0
0
3
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
1
0
2
0
0
0
2
0
1
3
0
0
0
2
1
1
0
0
0
0
0
2
0
0
0
1
1
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
3
1
0
1
0
1
0
0
2
0
2
0
2
3
0
0
2
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
2
0
1
0
0
3
0
0
0
0
0
0
0
1
0
2
2
0
1
0
4
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
1
1
1
0
0
0
0
2
0
0
1
0
2
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
2
0
0
0
0
1
0
0
2
2
1
1
0
0
0
0
2
0
0
0
0
1
3
0
0
1
0
1
0
0
0
1
0
0
2
0
3
0
0
0
2
2
0
3
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
2
0
0
1
0
0
0
1
0
0
0
1
3
1
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
2
1
2
0
2
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
6
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
2
1
0
0
2
1
1
0
2
0
2
0
0
1
2
0
3
0
0
0
0
0
1
2
0
0
0
0
0
0
1
2
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
1
0
0
0
1
2
0
0
2
2
1
0
0
0
2
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
1
0
1
0
0
0
0
0
0
2
2
0
0
2
0
0
2
1
0
1
0
5
0
0
1
2
0
0
0
0
1
0
1
0
1
0
0
0
2
2
0
0
0
1
0
2
0
5
0
2
0
1
0
0
0
0
2
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
3
1
0
0
1
2
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
1
1
0
2
2
2
0
2
3
1
2
1
0
2
2
1
0
2
1
0
0
1
0
0
2
0
2
2
2
2
0
0
0
0
0
0
0
1
5
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
1
0
2
0
1
0
0
0
0
0
0
0
1
0
3
0
0
1
0
0
0
2
3
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
2
0
1
0
0
0
0
0
2
2
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
2
2
0
1
0
0
0
0
0
0
0
3
1
0
2
2
0
0
1
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
2
0
2
0
0
0
1
0
0
0
2
2
0
0
1
0
1
2
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
1
2
1
0
0
0
1
0
0
0
0
0
0
0
3
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
3
2
1
0
2
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
2
1
0
2
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
1
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
2
0
2
2
0
2
2
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
3
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
2
0
1
0
2
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
2
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
3
0
2
0
0
0
0
1
0
0
1
0
0
0
1
1
2
0
0
2
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
2
0
2
1
0
1
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
1
1
3
0
1
0
2
0
0
0
0
0
0
0
1
0
2
0
1
2
0
0
0
1
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
2
1
0
0
3
2
0
3
0
0
2
0
0
1
0
0
0
0
0
1
2
2
2
0
0
0
0
0
0
0
1
2
1
1
1
0
0
0
1
2
2
1
2
0
0
0
0
2
0
0
2
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
1
2
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
3
1
0
2
2
0
0
1
0
2
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
3
2
0
2
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
3
0
0
1
0
1
0
0
0
0
1
1
2
2
1
2
2
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
1
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
1
0
1
0
0
0
1
1
0
0
2
0
0
0
1
0
2
1
2
0
1
0
0
0
0
0
2
2
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
1
0
2
0
0
0
0
0
1
0
0
0
1
1
0
2
0
0
1
0
2
0
0
1
0
0
0
0
2
0
0
1
0
0
0
1
2
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
2
0
1
1
1
0
3
2
2
0
1
0
0
1
0
0
1
0
0
1
0
2
2
1
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
2
0
5
1
0
0
0
0
0
1
2
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
1
2
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
2
0
1
2
0
1
0
0
1
1
0
0
0
2
0
3
2
1
0
0
0
0
0
0
0
2
0
0
2
2
0
2
0
0
0
2
0
0
0
1
1
0
1
0
0
0
0
2
0
0
0
2
0
1
0
3
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
2
0
0
1
3
2
0
1
0
1
0
0
0
0
0
0
0
0
3
1
0
2
0
0
1
0
3
1
2
0
3
0
1
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
1
0
1
0
0
0
2
0
0
2
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
1
3
1
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
2
0
0
0
2
0
3
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
2
1
3
2
0
1
2
0
1
0
0
1
1
1
0
0
1
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
3
0
0
0
2
0
0
0
0
0
2
2
1
0
0
0
3
0
0
2
1
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
2
0
0
0
2
0
1
2
0
0
2
1
0
2
0
2
0
2
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
1
0
0
0
0
0
2
2
0
0
0
1
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
2
2
0
2
0
2
0
1
0
0
0
0
1
0
1
0
0
0
0
1
2
0
2
0
0
0
0
0
0
2
2
0
3
2
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
2
2
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
3
0
2
0
0
2
0
2
0
0
0
0
2
0
1
0
0
1
0
0
1
1
0
1
2
0
0
1
1
2
2
0
2
0
0
0
2
1
1
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
5
0
0
0
1
0
0
1
0
0
0
2
0
0
1
0
1
0
0
0
0
0
1
2
0
0
1
2
1
0
0
1
2
2
1
1
0
3
2
0
0
2
0
2
0
0
2
0
0
0
0
0
1
2
0
0
2
2
1
0
0
1
1
0
0
2
0
2
2
2
0
0
0
0
2
1
0
2
0
1
0
0
0
0
1
1
0
1
2
1
2
1
1
1
0
1
0
0
4
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
1
0
0
2
0
0
0
1
1
1
0
2
0
0
0
0
0
2
0
5
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
2
0
0
1
0
0
1
2
2
1
0
0
0
0
0
0
0
1
0
2
2
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
2
0
0
3
0
0
2
0
0
1
0
0
3
0
0
0
0
0
1
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
2
1
0
1
1
0
0
0
0
0
2
0
0
0
0
2
1
0
0
1
2
0
0
0
0
0
4
0
0
0
1
1
0
2
0
0
0
0
2
1
2
0
0
0
0
1
0
0
2
0
0
0
0
1
1
0
2
1
0
2
2
0
0
0
1
1
0
0
0
1
0
2
2
0
0
0
0
0
0
0
4
0
0
1
0
0
0
1
0
0
2
0
3
0
2
0
1
2
0
0
0
0
0
0
0
0
2
2
0
2
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
3
0
0
0
0
1
0
3
0
1
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
1
0
0
0
7
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
2
1
0
2
2
0
1
1
0
0
1
2
0
1
2
0
0
0
5
0
0
0
2
0
0
2
1
2
2
2
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
1
3
1
0
1
0
2
0
1
1
0
3
2
1
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
2
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
1
1
0
0
0
2
2
0
0
0
0
0
0
1
0
1
2
0
0
1
1
0
0
0
0
0
0
2
0
3
0
0
2
0
0
2
0
0
0
2
2
0
0
0
0
0
2
2
0
0
0
0
1
1
0
2
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
2
2
1
0
0
0
1
0
0
0
0
0
0
2
1
0
0
2
0
2
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
3
0
1
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
1
2
2
0
0
0
2
0
0
0
0
2
0
0
1
4
0
0
0
0
0
0
0
2
0
1
1
2
1
2
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
2
3
0
0
0
1
0
0
2
0
1
0
2
0
0
0
2
0
0
3
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
1
1
0
2
0
0
0
0
2
0
0
0
0
0
0
2
1
1
0
0
0
0
1
0
3
0
0
2
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
2
1
2
1
0
0
0
0
0
0
0
0
1
2
0
0
0
1
3
0
0
3
0
0
0
0
1
0
2
0
0
0
0
0
3
3
0
0
0
1
0
0
1
0
3
1
0
0
0
2
0
1
1
0
0
1
0
1
1
0
1
3
0
0
0
1
0
0
0
2
2
1
0
0
0
0
0
1
0
2
0
0
0
0
2
3
0
2
1
0
1
0
0
1
2
0
2
0
2
0
0
0
1
0
1
1
0
0
0
2
0
1
2
2
1
0
0
0
0
0
0
0
2
0
0
1
0
1
3
2
0
2
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
1
0
1
0
1
0
0
0
2
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
1
4
0
1
0
1
0
0
2
0
2
0
0
0
2
1
0
0
0
0
2
2
0
0
0
1
0
1
2
2
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
2
0
0
2
0
2
0
1
0
1
0
0
1
2
0
1
0
0
0
1
2
0
0
0
2
1
0
0
1
0
1
0
0
0
0
2
0
3
0
0
2
0
3
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
6
1
0
0
0
0
2
0
0
0
0
3
0
1
0
0
1
0
1
0
1
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
1
0
1
0
1
1
0
1
3
2
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
4
1
0
2
0
0
0
0
0
2
0
2
0
2
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
2
0
0
0
2
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
7
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
2
3
1
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
1
0
2
0
1
0
0
0
1
0
2
0
0
1
0
2
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
2
0
2
0
0
2
0
0
4
0
0
0
0
1
0
0
1
0
0
0
2
1
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
2
0
4
1
0
2
0
0
0
2
1
0
1
0
0
0
0
2
1
0
2
0
0
0
2
0
0
2
0
2
0
0
0
2
1
0
3
0
0
1
1
1
2
0
0
2
0
1
0
0
0
0
2
0
0
0
1
0
1
0
0
1
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
2
2
0
1
3
1
2
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
1
0
0
2
0
0
1
2
0
0
2
3
0
0
2
0
0
0
0
2
0
0
0
0
1
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
1
1
0
0
1
4
0
0
2
0
0
0
2
1
2
1
1
0
0
0
0
1
0
0
1
2
1
0
1
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
2
0
1
0
0
1
0
2
0
0
0
1
0
0
1
0
2
1
0
0
0
1
0
0
1
2
2
1
0
0
0
2
0
0
2
1
0
0
0
0
1
0
0
0
0
0
2
1
0
1
0
1
1
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
2
1
0
0
0
0
2
2
0
0
1
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
3
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
1
0
3
0
1
0
0
1
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
2
0
1
0
1
1
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
1
2
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
1
1
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
2
2
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
2
2
0
0
0
3
3
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
1
0
2
0
0
0
0
2
0
0
2
2
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
3
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
3
0
0
0
1
0
2
0
0
1
1
0
0
0
1
1
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
1
1
2
1
0
1
0
0
0
0
2
0
0
0
0
2
2
0
0
3
0
1
1
2
1
0
2
0
0
0
2
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
2
0
3
2
1
1
2
2
0
0
0
0
0
0
1
0
2
1
2
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
3
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
1
0
0
3
2
1
0
0
0
0
0
0
0
0
0
1
3
2
0
0
0
0
0
0
0
0
1
0
2
1
0
1
2
1
0
1
0
0
2
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
1
1
1
0
0
0
1
0
0
0
1
0
0
1
0
0
2
1
1
0
0
3
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
1
1
0
1
0
2
4
0
1
0
4
0
1
0
0
2
0
2
0
1
0
2
0
2
0
0
2
0
0
0
1
0
1
2
0
0
0
0
0
0
0
2
0
0
1
0
0
1
1
0
0
0
0
0
1
0
2
0
2
0
1
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
1
1
0
0
0
0
0
0
0
2
0
3
0
0
0
2
1
0
1
0
0
0
0
2
2
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
2
2
2
0
0
0
0
0
0
0
0
0
0
3
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
1
1
0
0
0
0
0
0
3
3
0
0
0
0
0
1
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
4
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
1
2
0
0
0
0
0
0
0
1
0
0
2
1
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
1
5
0
1
3
0
0
0
0
0
0
2
0
0
2
2
1
0
3
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
1
1
0
1
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
1
2
0
2
0
0
2
1
1
0
0
0
0
0
2
0
0
2
2
0
0
0
0
2
2
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
2
2
2
0
1
0
0
1
0
0
0
3
0
2
0
0
1
0
0
0
0
2
1
0
0
1
0
1
0
0
1
0
2
2
1
0
2
0
0
1
2
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
2
0
2
0
2
0
2
0
0
0
1
0
1
0
0
2
0
0
0
1
0
0
0
0
2
0
0
1
0
0
1
1
1
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
2
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
2
2
0
0
0
0
0
2
0
1
0
0
0
2
2
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
1
2
0
0
1
0
1
0
0
3
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
2
2
1
0
0
0
3
0
2
0
0
6
0
2
0
0
0
2
0
0
0
0
2
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
2
1
2
0
0
0
0
1
2
0
0
3
2
1
0
1
0
0
0
1
0
0
1
1
4
3
2
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
5
2
0
0
0
0
1
3
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
2
0
0
1
3
1
0
0
4
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
1
1
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
2
2
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
3
0
2
2
1
0
0
0
0
0
0
1
0
0
1
2
0
0
0
1
0
0
2
0
1
2
0
0
0
0
1
0
0
0
2
1
0
1
0
3
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
1
0
2
2
0
2
0
0
0
2
0
0
0
0
1
2
0
0
1
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
3
1
2
2
0
3
1
0
0
0
0
2
0
1
0
2
0
0
0
3
1
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
1
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
1
1
2
0
0
0
0
1
0
0
0
0
0
1
0
1
2
2
0
0
0
1
1
0
0
0
1
0
0
1
0
2
0
2
1
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
3
3
0
3
2
0
0
0
1
0
2
0
1
0
0
0
2
0
2
2
0
2
1
0
0
0
2
0
0
2
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
3
1
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
2
2
0
0
0
0
0
2
2
2
0
0
2
1
0
0
0
0
0
0
0
0
0
2
1
0
2
1
0
2
0
0
1
0
2
2
0
0
0
0
3
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
4
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
2
0
1
0
0
0
0
1
3
0
1
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
1
0
0
2
2
1
0
0
0
2
0
0
0
0
3
0
0
0
0
1
4
1
2
0
0
0
0
0
2
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
2
0
1
0
2
2
0
0
3
0
0
0
0
0
2
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
1
0
0
0
0
3
0
0
2
0
0
1
2
1
2
1
2
0
0
0
0
0
2
0
2
2
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
2
1
2
0
0
0
0
3
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
2
2
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
2
0
1
1
2
2
0
0
0
0
0
0
1
2
0
2
1
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
2
1
0
0
2
0
0
1
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
3
1
0
0
1
0
0
2
0
0
0
0
1
0
0
3
1
2
0
1
0
0
0
0
0
0
0
0
1
1
0
2
1
0
0
0
0
2
2
0
0
2
3
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
2
2
1
0
1
0
0
0
0
0
0
0
3
1
2
0
1
1
2
0
0
0
0
0
2
0
0
0
2
0
1
0
2
0
2
0
0
0
0
1
2
0
0
3
2
0
1
0
2
2
2
0
1
1
0
1
0
0
0
2
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
4
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
4
0
0
0
2
2
0
1
0
2
0
0
1
0
1
0
1
0
0
0
0
2
0
2
0
0
0
1
0
1
0
0
0
2
1
3
0
0
1
1
1
2
1
0
0
2
1
2
0
2
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
2
0
2
2
2
2
0
1
0
0
0
0
0
0
1
2
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
2
0
4
0
2
0
0
0
0
1
1
1
2
0
0
4
2
3
0
2
1
0
2
0
0
0
2
0
0
1
0
0
0
0
1
0
0
2
0
2
0
2
0
1
2
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
1
1
0
1
0
0
0
1
1
1
0
0
2
2
0
0
0
0
3
0
1
2
0
2
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
1
0
0
2
0
1
0
0
0
0
0
2
0
0
0
1
1
2
0
2
0
0
0
1
0
1
1
0
0
0
0
0
2
2
0
0
0
1
1
0
0
0
0
0
0
3
1
0
0
0
0
0
2
2
0
0
0
2
0
1
2
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
1
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
1
0
1
2
0
1
0
0
0
0
0
0
1
1
0
2
0
2
1
0
0
0
0
0
0
1
0
0
1
3
2
0
0
0
9
0
1
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
4
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
2
1
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
2
0
0
2
1
0
0
0
0
1
0
0
7
0
0
0
0
2
2
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
1
0
3
0
2
0
0
0
0
0
0
2
7
1
1
1
0
1
0
0
1
1
1
1
2
0
1
0
0
1
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
1
0
4
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
1
2
0
0
0
2
2
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
3
0
2
2
5
2
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
2
1
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
2
2
0
0
0
0
0
0
0
2
1
0
0
2
1
0
0
2
0
0
2
0
0
0
4
0
4
0
0
0
2
3
1
0
0
2
0
1
1
1
1
0
0
0
0
1
0
0
0
2
1
0
0
2
0
0
1
2
0
0
2
0
3
2
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
2
0
7
0
0
0
2
1
0
0
0
1
1
0
0
0
2
1
1
0
0
0
0
0
0
1
1
2
0
0
0
1
0
2
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
1
0
0
1
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
1
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
1
2
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
2
0
2
2
0
1
2
0
0
0
0
0
2
0
0
4
2
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
3
0
0
2
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
2
0
2
0
0
0
1
0
1
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
3
0
0
0
1
0
0
1
0
2
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
1
1
0
2
0
2
0
1
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
5
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
2
0
0
1
0
2
0
2
0
0
1
4
3
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
2
0
2
0
1
2
1
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
1
2
0
0
0
0
0
0
0
0
1
1
0
2
0
0
1
1
0
2
0
2
1
0
0
2
0
2
1
0
0
1
2
0
0
0
3
0
2
0
0
1
1
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
1
1
1
0
1
1
0
0
1
0
2
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
2
0
0
0
1
1
2
0
1
0
0
2
0
0
1
0
0
0
0
1
0
2
0
0
1
0
1
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
2
2
0
1
0
0
3
1
2
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
4
2
1
0
2
0
0
2
0
0
1
0
0
0
0
0
0
2
2
0
1
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
1
0
2
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
2
0
2
0
0
3
0
0
0
0
0
0
0
0
0
3
0
1
1
0
0
1
2
0
1
0
0
0
1
2
2
0
0
0
0
4
0
0
0
0
0
0
0
1
2
0
0
0
2
1
2
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
2
1
0
0
1
1
2
0
2
2
3
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
3
0
1
0
2
0
2
0
0
3
0
0
0
2
1
0
1
2
1
0
0
1
0
0
2
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
2
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
1
2
1
0
0
1
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
1
0
2
1
1
0
2
0
2
1
0
0
0
0
0
2
0
2
1
0
2
0
2
2
0
2
0
0
1
0
0
2
0
3
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
2
0
1
0
0
0
0
2
1
1
0
0
1
1
0
0
2
0
0
0
2
1
0
0
0
0
0
1
0
0
0
4
3
0
1
0
0
0
0
0
2
2
1
2
0
0
2
0
0
0
0
0
2
0
1
0
0
4
0
0
0
0
0
0
1
0
0
2
2
0
1
0
1
2
2
2
0
1
0
0
1
2
0
1
1
2
1
2
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
2
1
2
0
2
0
2
0
2
0
1
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
2
1
0
0
0
1
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
2
1
0
1
0
0
2
0
4
0
0
0
0
1
0
1
0
1
0
0
1
0
0
1
2
0
2
0
0
0
1
2
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
1
1
0
0
2
0
0
1
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
2
0
2
3
0
1
0
0
1
0
0
3
0
0
2
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
3
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
1
0
2
0
1
0
0
2
2
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
1
2
2
0
1
0
0
0
0
0
1
0
0
0
1
2
0
0
0
1
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
1
0
2
0
1
2
0
0
1
0
1
2
0
1
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
2
1
2
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
1
0
0
2
0
0
1
1
2
0
0
1
0
1
0
0
0
0
0
0
3
1
1
2
1
0
1
0
3
0
0
1
0
1
0
0
0
0
3
0
0
0
1
1
0
0
0
2
0
0
3
0
0
1
0
0
1
2
1
0
0
1
0
2
0
0
1
0
0
4
0
1
0
0
0
0
0
0
1
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
7
0
0
2
2
4
0
0
1
1
0
0
0
2
2
1
0
0
1
0
1
0
0
0
1
0
0
0
2
2
0
3
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
1
0
0
2
0
3
0
2
0
0
0
0
2
0
0
1
2
0
1
0
1
0
0
0
0
2
0
1
0
0
0
2
0
1
0
0
0
0
1
0
1
2
0
1
1
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
2
1
0
1
0
1
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
2
0
0
2
0
0
0
0
0
0
0
2
2
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
1
0
2
1
0
1
2
4
0
0
2
0
0
0
0
2
1
0
1
0
2
2
0
0
0
2
0
0
0
0
0
0
2
0
1
0
1
0
0
0
1
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
1
0
2
2
0
0
0
0
2
0
1
1
2
0
0
0
2
0
1
0
0
2
1
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
3
2
0
0
0
0
0
2
2
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
1
0
0
1
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
1
1
0
0
0
0
0
0
1
2
0
0
1
0
2
2
0
1
0
2
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
2
1
0
0
2
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
2
0
1
0
1
0
0
1
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
2
2
2
3
0
1
1
0
0
0
0
0
3
1
2
0
2
2
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
3
1
1
0
0
2
0
2
0
0
0
2
1
1
0
0
0
0
0
0
1
0
0
2
2
0
0
0
2
0
1
2
2
2
1
0
0
0
0
3
0
0
0
3
0
0
1
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
1
2
1
0
1
0
0
0
1
1
2
0
1
0
2
2
1
0
0
2
0
0
0
1
2
0
2
2
1
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
3
1
1
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
2
0
0
1
1
0
2
0
2
0
1
0
0
0
0
0
2
1
2
0
0
0
0
0
1
2
2
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
2
3
0
0
4
2
2
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
1
2
3
0
2
0
3
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
1
1
1
1
0
0
2
2
0
1
0
3
1
0
1
0
0
2
0
0
2
0
2
1
0
0
0
0
0
0
4
2
2
0
1
0
0
1
1
1
0
0
2
2
0
0
0
1
1
2
0
0
0
1
0
2
3
0
0
0
0
0
0
1
0
0
0
0
0
0
1
5
0
0
0
0
0
1
0
0
0
1
2
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
8
1
2
0
0
0
0
0
2
0
0
2
0
2
1
2
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
1
1
2
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
3
0
1
3
2
0
0
0
1
0
0
0
2
1
2
0
0
0
0
0
2
1
0
0
1
2
0
0
0
0
0
4
0
0
0
0
0
2
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
1
0
1
0
2
2
0
0
1
0
2
2
2
0
1
0
0
1
2
0
1
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
3
0
0
0
2
3
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
7
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
1
0
1
2
0
0
0
1
0
0
0
2
2
0
0
2
0
3
1
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
1
0
1
1
2
0
0
1
0
1
2
0
0
2
1
0
2
0
0
0
0
0
0
0
2
0
0
2
1
0
1
0
0
0
1
1
2
0
0
0
0
1
1
0
0
0
1
0
1
4
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
3
0
0
0
2
2
0
1
0
1
0
0
2
0
0
0
0
2
0
1
0
2
1
0
0
0
1
0
0
1
0
1
1
0
2
0
1
0
0
0
0
0
2
0
0
0
2
1
0
2
0
0
1
2
2
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
6
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
1
0
2
0
2
2
1
3
1
0
0
0
2
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
1
1
0
1
0
0
2
0
2
0
0
2
0
1
0
1
0
2
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
1
0
0
2
0
3
0
0
1
0
0
0
2
1
1
0
0
0
0
2
1
0
0
0
0
2
1
0
1
1
1
1
0
0
0
3
0
0
0
0
1
2
0
0
2
2
0
0
0
0
1
0
0
4
0
0
1
0
2
0
0
0
0
1
0
0
0
0
3
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
1
1
1
0
0
1
2
0
2
0
0
2
0
2
3
1
0
0
0
2
4
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
2
2
2
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
4
1
0
2
0
2
0
1
0
0
2
1
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
2
4
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
1
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
1
1
0
0
2
2
0
2
5
1
2
0
1
1
0
0
0
1
1
1
0
2
2
2
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
3
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
1
0
3
0
1
0
2
2
0
0
1
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
2
2
2
0
0
3
0
0
1
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
1
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
1
0
0
2
2
0
0
2
1
0
0
1
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
2
1
1
0
2
0
0
1
1
0
1
2
0
2
0
2
0
2
0
0
1
0
0
2
2
0
2
2
0
0
2
1
2
0
2
0
0
0
0
0
0
0
0
1
0
0
7
0
0
0
0
1
0
0
0
2
2
2
0
1
0
0
0
2
0
0
2
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
1
1
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
2
0
0
0
3
0
1
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
2
1
0
0
0
0
1
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
1
2
0
1
0
0
2
2
0
0
0
0
0
2
2
0
0
0
1
2
0
2
0
0
3
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
2
2
2
0
0
1
0
0
2
2
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
1
1
0
0
2
0
0
2
0
0
0
1
0
0
0
1
0
0
2
0
0
2
0
0
1
0
0
0
2
0
0
2
0
0
1
0
1
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
2
2
2
1
0
2
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
1
1
2
3
0
0
2
0
2
0
1
0
0
2
0
1
0
0
1
0
0
0
0
0
3
0
0
1
0
1
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
1
0
0
0
3
0
2
0
1
2
0
2
0
2
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
4
0
0
0
0
0
0
2
0
0
3
0
0
2
2
1
2
1
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
2
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
3
0
2
0
0
2
1
0
0
2
0
3
0
0
2
1
0
1
1
0
0
0
0
0
2
2
0
1
0
2
1
0
0
2
1
3
1
0
0
0
1
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
1
0
1
0
0
1
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
1
1
0
0
0
2
1
0
4
2
2
0
0
0
0
1
0
1
0
2
0
0
3
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
1
2
2
0
0
0
2
0
0
1
2
0
4
0
0
2
0
1
0
2
0
0
1
0
0
2
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
1
2
0
0
0
0
0
0
2
1
2
1
0
4
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
2
2
0
0
0
0
2
0
3
1
1
0
2
0
0
0
0
0
0
2
0
0
1
0
0
2
2
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
1
0
1
0
0
0
1
0
2
1
1
0
0
0
1
1
0
0
1
0
0
0
2
1
0
0
0
0
0
3
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
2
0
1
1
2
0
0
1
0
0
2
0
1
2
2
0
1
2
0
0
2
0
1
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
2
0
1
0
0
0
0
0
10
2
0
1
0
1
2
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
2
0
0
0
1
2
0
1
0
2
2
0
0
0
0
1
0
1
3
0
0
2
0
0
0
1
0
2
0
3
2
0
0
2
2
0
0
0
2
0
0
1
0
0
0
0
0
0
1
2
2
1
0
0
0
0
0
2
1
0
0
2
0
0
0
2
0
2
0
0
1
0
2
0
0
0
1
0
0
0
0
5
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
2
2
0
0
0
0
0
0
0
0
0
2
1
0
1
0
2
2
0
0
0
0
1
0
2
2
0
0
1
2
0
1
0
0
0
0
0
2
0
0
0
1
0
1
0
0
2
0
3
1
1
2
0
1
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
1
0
0
2
1
1
0
0
0
1
0
0
0
1
0
2
1
0
0
0
0
0
0
0
1
1
0
1
0
2
2
1
2
0
0
0
1
2
2
0
0
0
0
0
1
0
1
1
1
0
7
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
2
0
2
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
2
1
1
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
3
0
0
2
1
2
2
0
1
0
0
2
0
0
0
1
0
2
0
0
2
0
2
2
2
0
1
0
0
0
0
2
0
0
0
1
0
0
2
1
0
0
2
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
2
0
2
0
2
1
0
0
0
0
1
0
0
0
0
2
0
2
1
2
0
0
0
0
0
0
0
1
0
1
0
1
3
0
0
0
2
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
3
2
0
0
0
1
1
0
0
0
2
0
0
0
1
0
2
0
0
0
1
1
2
2
0
0
2
2
0
0
1
0
2
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
1
2
0
0
1
1
0
0
0
2
1
0
0
0
0
2
0
0
0
1
0
0
3
2
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
2
0
0
1
0
0
1
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
2
0
0
0
0
0
1
0
3
0
0
0
0
0
1
3
0
2
2
0
0
0
0
2
3
0
0
2
0
0
1
0
0
0
1
1
1
0
0
3
0
0
2
0
0
2
2
0
1
0
0
0
0
2
0
0
2
0
2
0
0
0
0
1
0
1
0
0
0
0
0
1
0
2
2
3
0
1
0
0
2
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
1
0
0
2
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
1
0
0
2
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
1
2
0
0
4
0
1
0
2
2
0
0
2
0
0
0
2
0
1
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
2
1
1
0
2
0
0
0
0
0
1
0
1
2
0
0
0
0
2
1
0
1
1
0
0
0
1
0
0
0
0
2
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
3
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
1
0
0
0
1
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
1
2
2
1
0
2
0
0
2
0
3
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
1
0
0
2
0
1
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
3
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
1
0
0
1
0
2
0
2
2
1
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
1
2
1
0
0
0
0
0
1
0
0
0
0
1
0
2
0
2
1
3
0
2
0
0
1
2
2
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
2
2
1
0
1
0
2
0
0
2
1
0
0
0
0
2
0
0
0
0
1
0
0
2
2
0
1
1
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
2
1
0
0
1
0
0
1
0
2
1
0
0
1
0
0
2
0
1
0
1
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
2
3
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
2
0
1
0
0
2
0
0
0
0
0
0
1
1
0
1
0
0
0
0
4
0
0
2
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
1
2
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
1
0
1
0
0
1
0
0
1
0
3
0
0
0
2
0
0
2
1
0
0
0
0
0
2
0
1
0
0
0
0
0
1
1
1
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
2
2
0
0
0
2
4
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
1
0
0
1
2
1
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
1
0
0
0
0
2
0
0
1
1
0
2
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
1
0
5
2
3
0
2
0
0
0
0
0
0
0
0
0
1
0
1
2
0
2
0
0
2
0
0
0
0
0
2
0
0
0
2
1
0
0
2
0
0
0
3
0
0
2
1
0
0
0
0
0
0
3
0
2
2
0
2
1
0
2
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
1
0
1
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
1
0
0
1
0
0
2
4
0
0
0
0
0
0
0
5
0
0
1
2
0
2
0
2
0
0
0
2
0
0
1
0
1
0
0
0
2
2
2
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
3
0
0
0
0
1
2
0
1
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
1
0
1
2
0
6
0
0
3
0
2
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
2
0
0
0
0
1
1
0
0
1
0
1
0
2
1
0
0
1
3
0
0
0
0
0
2
2
2
0
0
0
0
1
0
0
1
0
2
0
0
1
0
0
0
0
0
0
1
2
2
1
3
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
1
1
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
1
0
0
0
2
0
0
0
2
2
0
0
0
0
0
2
1
0
0
0
2
0
0
1
0
0
0
0
1
0
2
2
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
5
1
0
0
3
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
1
0
0
1
0
0
0
2
0
2
3
2
2
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
3
2
0
0
0
0
0
1
1
0
4
0
1
0
2
1
0
0
0
0
0
0
0
1
0
0
2
0
0
1
1
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
3
0
0
3
1
0
1
0
0
0
2
0
0
1
1
1
2
0
2
0
0
1
0
0
1
0
2
0
0
1
0
3
0
0
0
0
0
2
1
0
1
0
2
0
1
1
2
2
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
1
0
0
0
1
0
1
0
0
0
1
2
3
2
0
0
0
0
0
0
2
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
5
1
2
0
1
1
0
1
0
1
0
0
0
0
4
0
0
0
0
0
0
1
1
0
2
0
0
0
2
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
1
0
2
0
0
0
0
0
0
2
0
0
2
1
0
1
0
0
0
0
2
0
2
0
0
3
2
0
0
0
2
0
0
1
0
0
0
2
0
0
0
2
0
0
2
1
0
1
2
0
2
0
0
0
0
0
0
2
2
2
0
2
0
0
0
0
1
0
2
1
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
2
0
0
1
0
0
1
1
2
0
0
0
2
1
5
0
0
2
0
0
0
0
2
1
0
1
0
1
1
1
0
1
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
2
1
0
0
1
0
0
0
2
2
1
0
0
0
0
0
0
0
2
0
0
2
0
4
3
0
1
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
2
0
0
0
0
2
0
2
0
0
1
2
0
0
0
2
3
0
0
0
0
1
0
3
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
1
0
1
0
0
1
0
1
5
0
1
0
0
2
1
3
0
0
0
0
0
0
2
0
0
1
1
0
2
2
2
0
0
0
0
0
1
0
2
0
2
0
0
1
1
0
0
0
0
1
0
2
1
0
0
0
1
1
1
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
1
2
1
1
2
0
2
0
0
2
0
0
1
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
1
2
0
1
1
0
0
0
0
0
1
0
2
1
0
0
0
0
1
1
0
1
1
1
0
2
0
0
0
2
0
3
0
1
4
1
0
0
1
2
0
2
0
1
1
3
0
2
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
3
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
2
2
0
0
0
2
0
0
1
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
3
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
2
1
0
0
0
0
2
2
0
0
0
1
1
0
2
0
0
0
2
1
1
1
0
0
0
0
0
2
0
0
0
1
0
0
0
1
1
0
0
2
2
1
0
2
3
0
0
0
1
0
0
0
2
0
5
0
0
0
0
1
2
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
2
2
2
0
2
1
2
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
1
1
2
0
0
2
0
0
1
0
0
0
0
0
0
2
0
2
2
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
1
3
0
1
0
0
0
0
1
0
0
0
2
1
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
2
0
0
0
3
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
2
2
0
0
0
2
2
0
0
0
0
1
1
0
1
0
0
2
0
2
2
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
2
0
0
0
0
1
0
1
1
0
0
1
0
0
1
1
0
0
0
2
1
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
1
2
0
2
2
0
0
0
0
0
1
0
1
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
2
0
1
1
2
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
2
0
0
0
1
2
0
0
0
1
0
0
2
0
2
1
2
2
0
0
1
0
0
0
2
1
0
1
0
1
1
0
3
0
2
2
0
0
1
0
2
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
2
0
0
0
0
1
0
0
2
0
2
0
0
0
0
1
1
2
0
1
0
2
0
0
1
0
0
0
0
1
0
2
2
2
0
0
0
0
2
2
0
2
2
2
1
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
1
1
0
2
0
0
0
2
2
0
0
2
0
0
1
1
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
1
0
0
0
0
1
0
1
0
3
1
1
0
1
0
0
0
1
0
0
0
0
2
2
0
2
0
1
0
0
1
0
0
0
0
0
2
1
0
0
0
0
1
2
2
1
0
0
1
1
0
2
3
0
2
0
0
0
0
0
1
0
2
2
0
0
2
0
9
0
0
0
0
0
0
2
0
0
1
0
2
0
0
1
0
2
0
0
0
0
0
0
0
2
1
3
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
2
1
0
0
0
0
2
1
0
0
0
0
2
0
0
2
0
2
0
0
1
0
0
0
2
2
0
0
0
0
1
0
0
0
0
1
0
0
0
1
2
0
2
0
0
0
0
1
0
1
0
2
1
0
1
1
0
1
0
2
0
0
1
1
2
0
0
0
2
0
2
0
0
1
2
2
1
0
1
0
0
1
1
0
2
1
0
1
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
2
1
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
1
1
1
2
2
0
0
1
2
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
3
0
2
0
0
1
0
0
2
0
0
0
0
2
0
3
0
0
2
0
0
0
0
0
1
0
0
4
0
0
0
1
0
1
0
3
0
0
0
0
3
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
2
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
4
3
0
1
1
2
1
0
0
1
1
0
0
0
0
3
1
0
0
0
0
2
0
0
0
0
0
1
0
1
2
0
1
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
3
0
1
0
0
0
0
0
0
0
1
0
0
1
2
1
2
0
0
2
0
0
0
0
0
3
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
7
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
3
0
2
1
0
0
0
0
1
1
3
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
2
0
1
2
0
1
0
3
0
2
0
0
0
0
0
0
2
0
1
0
0
0
3
0
0
0
0
0
0
1
0
0
2
0
1
0
0
3
0
0
0
1
0
2
0
0
0
1
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
3
0
2
2
0
2
1
0
1
2
1
0
0
3
0
1
0
1
0
0
1
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
3
0
1
1
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
2
1
1
1
1
3
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
1
0
2
0
0
0
0
4
0
0
0
0
0
0
3
1
0
0
0
0
0
1
3
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
2
0
0
2
2
0
2
0
0
1
2
7
0
0
0
1
0
2
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
1
0
0
2
0
1
0
0
1
0
0
0
0
2
0
2
1
0
1
0
0
0
0
0
0
1
1
2
0
2
0
0
0
0
2
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
2
3
0
0
0
0
0
0
0
0
1
0
1
0
2
1
2
0
2
0
0
0
2
3
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
1
0
2
0
1
0
2
0
0
0
2
0
1
1
0
0
0
1
0
2
0
0
2
0
0
0
1
0
1
2
1
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
1
0
2
1
0
1
1
0
0
0
0
0
0
3
2
0
1
2
0
0
0
0
0
0
0
2
2
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
1
0
2
0
1
0
1
0
0
1
0
0
0
1
1
0
0
0
1
2
0
0
1
2
0
2
1
0
0
0
0
0
0
0
1
0
2
2
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
8
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
2
0
0
0
0
1
0
0
1
0
0
0
2
0
0
2
0
0
1
0
2
1
2
0
0
1
0
0
0
0
0
0
0
2
2
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
2
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
1
3
1
0
0
1
0
0
2
2
0
2
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
1
1
0
2
0
1
0
0
2
2
1
0
0
0
0
2
4
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
1
2
0
2
2
2
0
0
2
3
0
0
2
2
0
0
0
0
0
0
0
0
1
0
1
1
2
2
0
0
2
2
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
3
0
0
0
2
0
0
0
2
0
1
0
0
2
0
6
2
0
0
2
0
0
0
0
0
0
5
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
2
1
0
0
1
0
2
0
1
1
0
1
1
0
0
0
0
1
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
1
0
0
0
2
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
1
2
3
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
2
1
2
0
0
4
1
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
3
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
3
2
0
1
2
0
0
1
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
2
2
0
0
0
3
1
1
1
2
1
0
0
0
2
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
8
0
0
0
0
2
0
0
2
0
0
0
1
1
0
0
2
2
0
0
3
0
0
0
0
1
2
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
1
1
2
0
2
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
2
0
0
2
0
0
0
2
0
1
4
0
0
0
0
1
0
2
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
1
0
0
1
0
2
2
2
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
2
0
2
0
1
0
0
0
2
0
2
2
0
0
0
0
0
2
0
1
0
0
1
0
0
1
0
2
1
0
0
1
0
1
0
0
1
0
0
1
0
4
0
0
1
2
1
2
1
2
0
0
0
0
1
0
2
0
0
0
2
0
6
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
2
1
0
1
0
3
0
0
0
2
1
2
0
2
2
2
0
0
0
2
0
0
0
0
1
1
0
0
1
0
2
0
0
1
0
0
0
1
2
1
0
0
0
2
1
0
1
1
0
0
2
0
1
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
2
0
0
1
2
0
0
1
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
2
0
2
0
2
0
0
1
0
0
0
2
1
2
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
2
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
2
0
1
0
0
0
0
1
0
0
0
3
1
0
1
0
2
0
0
0
0
2
0
0
0
0
1
0
1
0
1
0
0
1
0
1
0
1
0
1
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
3
0
0
0
0
0
0
1
0
3
1
0
0
0
0
2
0
0
2
1
0
0
3
0
2
0
0
0
0
2
2
0
0
0
0
1
2
0
0
0
1
0
2
0
2
0
0
2
0
1
0
0
0
0
0
2
1
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
1
0
1
0
2
3
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
2
2
0
1
2
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
1
2
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
2
0
0
1
0
0
1
0
3
0
0
0
0
0
1
1
0
0
0
2
0
3
2
1
0
2
0
2
1
3
1
2
0
1
0
0
3
0
0
0
0
2
0
0
2
0
0
3
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
2
2
0
1
0
1
2
0
0
3
0
0
0
2
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
2
0
1
0
1
2
0
0
2
0
2
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
1
1
0
0
0
1
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
1
0
0
2
0
0
0
1
0
0
1
0
0
3
2
0
0
0
0
0
1
0
2
0
2
0
0
0
1
0
0
1
0
0
0
2
2
0
0
0
2
2
0
0
0
0
0
0
1
0
0
1
2
0
0
1
0
0
2
2
2
0
0
0
0
1
0
2
0
1
2
0
1
0
1
1
1
2
2
2
0
0
0
1
1
0
0
0
0
0
0
0
3
1
2
0
2
2
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
2
0
0
2
1
2
3
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
1
1
1
0
2
0
0
2
2
0
0
0
0
1
0
0
0
0
0
1
0
1
2
0
0
0
0
0
1
3
2
1
0
2
1
3
1
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
1
0
2
0
2
0
0
0
1
2
0
2
0
1
1
0
2
0
0
0
1
1
0
1
0
0
2
4
0
0
0
1
0
0
1
0
0
0
0
0
1
2
0
1
0
2
0
0
0
2
0
1
0
0
2
0
0
0
3
0
1
0
0
2
2
7
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
1
1
0
1
2
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
3
0
0
0
0
0
0
0
1
0
1
2
0
0
0
2
1
0
0
0
0
0
2
2
0
1
0
1
0
2
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
1
1
0
0
0
2
1
0
2
0
0
0
1
0
0
1
0
0
2
0
3
1
2
0
1
0
0
0
1
0
1
2
0
1
0
0
0
0
1
1
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
2
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
1
2
0
0
0
0
0
0
0
0
0
1
2
1
0
1
0
0
1
0
2
0
0
0
1
0
2
1
2
0
0
0
0
0
0
1
2
0
1
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
2
2
3
2
0
1
0
1
0
0
2
0
0
0
0
2
1
0
0
0
1
0
1
0
2
0
0
3
2
0
0
2
2
2
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
2
1
0
1
0
1
0
0
0
1
3
0
1
0
0
0
0
2
1
1
1
0
0
0
0
0
0
1
2
1
0
0
0
1
1
0
2
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
2
2
0
0
0
0
0
2
2
2
0
0
3
1
0
0
0
0
0
0
1
0
0
1
2
0
0
0
1
0
0
0
2
1
0
0
0
1
0
0
0
0
0
3
0
2
0
0
0
0
2
2
0
1
0
2
0
1
1
0
0
0
0
0
0
1
0
2
0
0
2
1
1
0
1
0
1
0
2
1
2
1
0
0
0
0
0
0
2
0
0
0
0
1
0
4
0
2
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
2
3
0
0
1
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
2
1
0
0
1
0
0
3
2
1
0
1
2
0
2
0
0
0
0
1
1
0
0
2
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
2
0
1
2
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
2
0
3
0
0
0
0
0
0
1
4
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
2
0
2
1
0
0
2
1
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
2
0
0
0
1
0
0
0
0
2
1
0
0
1
0
1
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
2
0
2
0
2
0
0
0
0
2
1
0
0
0
1
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
2
1
6
1
0
2
0
0
0
0
0
0
0
0
0
1
0
2
3
0
0
0
1
0
2
0
0
2
0
1
0
7
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
2
2
1
0
0
2
0
0
0
0
0
2
0
2
0
2
0
0
0
1
1
0
0
0
1
0
1
2
0
0
1
0
0
0
0
1
1
0
0
0
2
0
0
1
0
2
0
0
1
0
2
0
0
0
0
0
0
3
0
1
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
1
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
2
0
0
1
2
0
0
1
2
0
0
0
2
0
0
0
2
0
0
0
1
0
1
0
0
3
2
0
2
0
0
0
0
0
0
0
0
0
0
1
5
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
2
0
0
1
0
0
0
2
2
0
0
4
0
2
0
0
1
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
2
2
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
2
0
1
0
1
1
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
3
1
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
2
0
0
0
0
1
1
0
0
0
2
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
5
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
2
0
0
0
0
2
0
0
0
0
0
1
2
0
0
4
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
3
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
2
2
0
2
0
0
0
2
0
0
0
0
3
3
1
0
0
0
0
3
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
1
0
0
0
0
1
0
0
1
1
1
0
0
1
1
1
0
0
0
0
0
1
0
0
1
1
1
0
0
1
2
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
3
1
0
0
1
0
0
0
1
0
0
1
2
0
3
0
2
1
8
0
0
0
2
0
0
0
3
1
0
1
2
1
3
2
1
0
0
0
1
0
0
2
1
3
0
0
0
0
3
0
4
0
1
1
0
2
0
2
1
0
0
0
0
2
2
3
0
0
0
0
0
0
5
0
0
0
2
0
0
0
5
0
0
0
0
1
0
2
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
4
0
0
0
0
2
1
1
2
2
0
1
1
0
2
2
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
2
0
2
0
0
2
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
1
0
0
2
0
0
1
0
3
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
3
0
0
3
0
2
0
0
2
0
2
0
0
2
2
0
0
0
0
2
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
2
1
2
0
0
0
0
0
0
0
0
0
1
1
0
0
2
1
0
0
1
2
0
0
2
1
0
0
1
1
2
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
2
0
2
1
0
2
0
0
0
2
0
2
0
0
0
3
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
3
1
2
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
1
2
0
0
0
4
2
1
0
1
0
0
0
2
0
0
0
4
0
0
3
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
1
1
1
0
0
0
0
0
0
3
0
0
1
1
0
0
1
2
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
1
0
0
2
0
2
1
0
0
0
0
0
1
1
0
0
0
0
0
2
2
2
2
0
3
1
0
0
0
0
1
2
0
1
0
6
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
10
1
1
1
0
0
0
1
0
2
0
1
0
2
0
0
0
0
0
1
2
1
0
0
1
0
0
2
0
0
0
1
2
0
1
1
0
2
2
0
2
0
0
0
1
2
0
0
2
3
0
0
0
0
1
0
0
0
0
1
2
0
0
1
2
0
0
0
0
1
0
2
2
0
0
1
0
0
3
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
2
0
2
0
2
0
0
0
1
2
0
0
0
2
0
0
0
2
2
0
0
0
1
0
0
0
0
2
0
1
1
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
1
0
0
2
1
0
0
3
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
2
1
2
0
0
1
0
0
0
0
3
0
0
0
0
0
3
2
2
0
2
0
0
0
0
0
0
1
1
1
0
0
2
0
1
0
1
1
1
0
0
0
0
2
0
0
2
0
0
1
1
0
0
2
0
0
0
0
0
0
0
1
0
0
2
1
0
2
1
0
0
0
0
0
0
0
1
2
1
0
1
1
2
0
0
0
0
0
0
0
0
2
2
0
0
1
2
0
0
1
0
1
2
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
2
1
2
0
1
0
1
2
0
0
0
2
0
0
0
0
5
0
0
0
0
0
0
0
1
0
1
0
0
0
3
0
1
1
0
1
0
1
0
0
0
0
2
0
0
1
0
1
0
0
0
2
0
0
2
1
0
0
1
0
0
0
0
1
1
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
2
2
2
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
3
0
2
1
0
0
0
1
0
0
2
1
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
3
0
1
0
0
2
2
4
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
2
2
0
0
0
1
0
2
0
0
1
2
0
0
2
0
0
0
0
0
0
1
2
1
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
2
0
1
3
0
0
2
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
1
0
0
0
2
0
0
0
2
1
1
1
0
2
1
2
0
0
0
0
0
0
0
0
1
3
2
0
0
0
2
1
0
2
2
0
2
0
0
0
0
11
2
0
0
1
0
0
1
0
3
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
3
2
0
0
0
0
1
3
0
0
2
1
2
1
0
1
0
1
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
3
0
0
0
1
0
1
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
2
1
0
3
1
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
1
1
0
0
0
0
2
2
1
0
2
2
0
0
5
0
1
0
0
2
1
0
0
0
0
1
1
0
0
2
0
0
0
0
2
1
0
1
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
2
0
2
0
2
2
0
0
2
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
2
1
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
3
0
0
0
2
2
5
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
5
2
1
0
0
1
0
0
0
2
1
1
0
0
0
0
0
1
0
2
0
2
0
0
0
3
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
2
1
0
0
0
0
3
2
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
1
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
3
0
0
0
2
1
0
0
2
0
0
1
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
2
1
0
2
0
1
0
1
1
2
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
2
2
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
1
1
2
0
2
0
0
2
0
0
0
0
2
1
0
0
1
0
1
1
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
2
0
2
0
0
1
2
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
2
0
0
2
1
0
0
0
0
0
0
2
0
0
0
1
0
2
2
0
0
0
2
0
0
1
0
2
1
0
1
2
0
2
2
0
1
0
1
0
0
0
0
1
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
1
2
0
1
0
1
0
0
0
1
0
0
0
0
1
2
2
1
5
0
2
0
0
0
1
0
4
1
0
0
0
0
0
3
0
0
1
0
2
0
2
0
0
0
1
1
0
0
3
1
0
1
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
1
0
0
0
0
2
1
0
0
1
2
2
5
0
0
0
1
0
0
0
0
1
0
0
1
0
0
3
0
0
1
2
0
1
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
1
1
0
0
1
0
3
0
0
0
0
2
0
2
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
2
2
0
0
0
2
0
2
0
1
0
3
1
1
1
2
1
1
0
0
0
3
0
0
0
0
0
1
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
2
0
2
0
0
0
2
0
0
0
0
2
0
0
0
2
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
2
0
2
2
0
0
0
0
0
1
2
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
2
2
0
3
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
2
0
2
2
0
0
0
0
0
0
0
2
1
2
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
1
1
0
0
0
0
0
0
0
2
0
1
3
0
0
0
1
0
2
0
0
0
3
2
0
0
0
0
0
2
0
2
2
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
2
1
0
0
0
0
1
0
0
3
1
0
0
0
2
1
0
1
0
0
3
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
2
2
0
0
2
1
0
0
2
2
0
0
0
0
1
0
1
0
0
2
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
2
1
1
0
0
3
2
2
0
1
0
0
0
0
0
0
0
2
0
1
1
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
3
1
0
0
0
2
1
2
0
0
1
0
0
0
1
0
0
0
3
0
1
2
0
1
2
0
0
0
4
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
1
1
2
0
2
0
2
1
1
0
0
0
0
0
0
0
0
0
2
0
2
1
0
2
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
2
1
0
1
2
0
1
2
2
0
2
1
2
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
1
0
2
0
2
0
0
3
0
0
0
0
2
0
0
0
1
0
2
0
0
1
0
1
2
2
1
0
2
0
0
1
0
0
0
1
0
0
1
0
1
1
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
2
1
0
0
2
0
0
1
0
0
2
0
2
0
0
1
1
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
5
0
0
1
1
0
0
0
1
0
2
0
0
3
1
3
0
0
0
0
0
1
0
0
1
0
0
0
2
3
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
2
1
3
3
2
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
4
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
2
2
1
0
0
3
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
2
0
1
0
2
1
0
0
1
2
0
0
2
1
0
2
1
0
0
2
0
0
0
0
0
2
1
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
2
2
0
0
0
1
2
4
0
1
0
1
0
2
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
2
2
5
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
2
0
1
1
1
0
0
1
2
0
2
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
2
1
2
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
2
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
3
0
0
0
0
2
0
0
2
0
0
2
0
2
0
2
2
0
0
2
0
2
0
0
0
0
2
2
0
1
0
0
0
0
1
0
0
0
0
0
2
0
1
1
0
2
0
0
1
1
1
1
2
1
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
5
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
2
2
0
2
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
2
2
2
1
1
0
1
0
0
0
1
1
0
0
0
0
2
1
0
1
0
1
0
1
1
0
2
0
0
0
0
0
1
0
1
0
1
2
0
0
2
0
3
1
0
0
0
0
0
0
0
0
2
0
0
1
0
4
1
0
0
0
0
1
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
3
0
0
0
0
0
3
0
0
0
0
2
0
0
1
2
1
0
0
0
0
0
0
0
0
1
0
1
1
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
1
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
1
2
0
2
0
0
0
0
2
0
0
0
0
1
2
0
2
2
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
3
2
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
1
0
0
2
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
6
2
0
0
0
3
0
0
2
0
2
0
1
3
1
2
0
1
0
0
1
2
3
0
1
0
2
1
1
0
0
1
0
0
0
0
0
0
0
1
2
0
2
1
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
3
0
0
0
2
2
0
0
2
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
2
0
2
1
3
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
2
0
0
1
1
0
1
0
0
0
0
0
2
0
1
1
2
0
0
2
0
2
0
0
2
6
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
2
0
0
0
2
0
0
2
2
2
2
2
1
2
0
0
0
0
0
2
2
2
1
0
0
0
0
3
0
0
1
0
0
1
0
0
0
4
1
0
0
0
1
0
2
0
2
2
1
0
3
2
1
1
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
2
0
2
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
4
0
0
0
0
0
0
1
2
0
1
0
0
2
1
2
0
2
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
2
1
4
1
0
1
0
0
0
0
2
0
0
1
0
0
1
0
0
2
3
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
3
0
0
0
0
0
1
0
7
0
0
1
0
0
0
0
0
0
0
1
1
0
2
0
0
2
2
0
4
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
3
0
0
1
0
0
0
2
4
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
3
1
1
0
2
2
0
0
0
1
0
0
2
1
0
2
0
0
1
1
0
1
1
1
1
0
2
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
1
0
0
0
0
0
2
0
0
2
1
2
1
2
1
0
0
0
0
0
0
0
0
0
0
2
2
1
1
0
0
1
0
2
1
1
1
2
1
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
2
2
1
1
1
0
0
1
1
0
0
0
0
0
0
0
0
3
1
0
3
0
0
0
0
0
2
0
0
1
0
0
0
0
0
5
0
2
4
0
1
0
0
0
0
1
1
0
0
0
0
3
1
2
1
0
0
0
0
0
2
0
0
0
0
6
1
0
0
1
0
0
0
0
0
0
0
1
2
2
0
2
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
1
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
1
4
0
0
0
0
2
0
1
0
0
0
2
0
0
1
4
1
0
1
0
2
0
1
0
2
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
2
1
0
0
0
0
1
4
0
0
0
0
0
0
0
1
0
0
1
3
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
1
0
0
3
0
1
2
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
3
0
2
1
0
0
0
2
1
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
2
1
1
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
2
2
0
2
0
2
2
2
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
2
1
0
0
0
0
0
2
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
6
2
0
0
0
5
0
0
1
0
0
0
2
0
0
0
0
2
0
2
0
2
0
1
1
0
0
0
4
0
3
0
1
1
0
2
0
1
1
2
0
0
0
1
0
0
0
0
2
0
0
2
2
2
0
0
0
0
0
1
0
0
0
2
7
0
1
0
1
1
1
0
2
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
5
2
8
0
0
0
0
0
0
0
3
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
2
0
1
0
0
2
0
2
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
3
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
1
0
1
4
0
2
0
2
0
1
0
2
0
0
2
0
0
1
0
1
0
0
0
0
0
1
2
2
2
1
0
0
0
2
0
1
0
2
0
0
1
0
0
0
2
0
4
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
1
1
0
5
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
2
0
0
1
0
2
1
2
0
2
0
1
0
0
0
1
0
0
2
0
1
2
0
0
2
0
0
2
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
2
0
0
0
0
0
1
0
0
0
0
0
2
0
2
2
1
0
0
1
1
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
2
1
2
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
1
0
0
2
1
0
1
0
0
0
0
0
2
2
2
0
1
1
0
1
1
2
2
1
0
0
0
1
1
0
0
0
0
0
0
1
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
3
0
1
1
0
2
0
0
2
0
2
0
0
0
0
0
0
1
0
5
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
2
1
0
0
2
0
0
0
0
0
0
1
1
2
0
1
0
2
1
0
0
2
0
0
2
1
1
2
4
0
0
0
1
2
1
0
2
2
0
0
3
1
0
2
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
3
0
0
0
2
2
2
0
2
0
2
0
0
1
0
0
1
0
1
2
0
2
1
0
0
1
1
1
0
0
1
0
0
0
0
2
1
0
2
0
0
0
1
0
0
0
0
0
0
4
3
0
1
0
0
2
1
0
0
0
1
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
2
1
1
0
0
0
0
0
1
2
0
0
0
0
1
0
2
0
0
0
0
0
0
2
1
1
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
1
0
0
1
0
2
0
2
1
0
0
0
3
0
0
0
2
0
0
0
0
0
1
0
0
0
2
2
2
2
0
0
0
0
0
1
1
2
1
0
0
0
0
1
0
1
1
1
0
0
0
0
3
2
0
0
4
1
1
0
0
0
1
0
0
0
0
0
1
1
0
0
2
0
0
0
1
0
2
3
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
1
2
0
2
1
0
2
0
0
2
0
0
0
0
0
0
2
0
0
1
0
2
0
0
3
0
2
0
0
0
1
1
0
0
0
0
0
1
2
2
0
2
0
1
0
0
0
0
0
1
0
1
0
2
0
2
0
0
0
0
1
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
1
2
1
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
3
0
1
2
0
0
2
0
0
0
0
0
1
0
0
2
3
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
1
0
0
0
0
0
1
2
1
0
1
2
3
3
3
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
6
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
2
0
0
0
1
0
0
2
0
0
2
1
1
1
1
0
2
0
2
0
2
0
0
0
0
0
1
0
0
1
0
0
0
2
0
1
0
0
0
0
0
2
0
1
2
0
1
0
0
0
0
0
0
1
2
1
0
0
2
7
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
2
0
0
0
0
2
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
2
0
0
0
0
0
1
2
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
1
4
0
1
0
0
0
3
2
1
1
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
2
2
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
1
0
0
0
2
2
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
1
1
0
2
2
2
0
0
2
1
0
0
2
2
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
3
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
1
0
2
2
3
3
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
2
2
0
1
0
1
2
1
0
1
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
2
0
0
2
0
0
0
0
0
1
0
2
0
1
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
1
0
0
2
0
0
0
2
2
5
0
1
0
2
1
0
0
0
1
1
0
2
0
2
0
0
2
0
0
2
0
1
0
0
1
1
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
1
1
0
3
1
0
0
1
1
0
0
2
0
0
3
0
0
0
0
0
1
0
1
1
1
0
0
1
0
0
0
1
2
0
1
0
1
0
2
1
0
1
0
0
2
0
0
1
0
0
2
0
0
2
0
0
0
0
0
1
1
2
0
0
0
0
0
3
0
0
4
0
2
0
0
0
1
0
0
2
0
0
0
2
2
0
2
0
1
0
0
1
2
2
0
0
2
1
0
0
0
0
1
0
0
2
2
0
2
0
0
0
0
0
0
1
1
0
1
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
1
0
0
1
0
1
1
0
2
0
0
2
0
0
1
0
0
2
0
0
0
0
0
1
0
2
2
2
5
0
0
0
1
0
0
0
0
2
0
0
0
1
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
1
1
0
0
1
0
0
1
0
3
0
0
0
0
2
0
2
0
1
0
0
2
0
0
1
0
1
3
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
2
1
0
3
0
0
2
1
0
0
2
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
3
2
0
6
0
2
3
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
3
1
0
0
0
1
0
0
0
0
1
1
2
0
0
0
2
0
2
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
2
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
2
0
0
2
1
2
0
0
0
0
2
0
1
0
0
0
0
2
0
1
0
0
0
1
0
0
3
3
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
3
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
4
1
0
0
0
0
2
1
2
0
0
2
0
0
2
0
1
0
0
1
0
0
0
2
0
0
1
0
0
0
0
3
0
3
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
5
1
2
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
1
0
0
1
0
0
2
2
0
0
2
1
0
2
0
2
1
0
2
0
0
0
0
0
0
0
2
1
2
1
0
0
0
0
0
2
1
0
2
0
1
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
3
0
0
4
0
1
1
0
2
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
3
2
0
0
0
1
0
0
0
0
0
2
0
0
3
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
2
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
1
0
2
1
0
0
1
6
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
1
0
0
0
0
0
1
1
0
0
1
1
2
0
0
0
0
0
0
2
0
0
1
0
1
0
0
1
2
0
2
0
0
1
0
0
0
1
0
0
0
2
3
0
0
3
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
2
2
2
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
1
1
0
1
2
0
0
0
2
1
0
0
0
0
0
0
0
0
2
1
0
0
1
1
0
2
0
0
0
2
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
1
0
4
1
0
1
0
0
0
0
0
0
0
0
1
1
0
2
0
1
2
0
2
1
0
2
0
0
0
2
3
0
0
5
0
0
2
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
9
3
2
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
2
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
3
2
0
1
0
2
1
0
2
1
2
3
0
0
0
3
2
0
0
0
0
1
0
0
0
0
1
5
0
0
0
0
0
0
0
0
3
0
2
1
0
1
0
3
0
1
0
0
0
0
0
1
0
2
0
1
1
0
0
2
0
0
1
2
1
0
1
1
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
2
2
0
0
0
0
0
0
0
0
1
2
0
4
0
0
2
2
2
1
0
0
0
0
2
0
2
0
2
1
0
0
0
1
2
0
0
0
0
0
1
0
0
1
1
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
1
1
0
0
2
0
0
1
2
0
0
2
1
0
0
0
2
0
0
0
0
0
1
1
1
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
2
1
0
0
1
0
0
0
1
0
1
0
0
0
0
1
1
0
2
1
0
2
0
0
0
0
0
0
0
0
2
2
7
1
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
1
0
0
1
0
2
1
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
3
0
0
0
0
2
0
0
0
1
0
2
0
0
0
2
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
1
0
0
0
0
0
0
0
0
2
2
0
2
1
0
0
0
0
1
0
0
0
2
0
2
0
0
0
1
0
0
0
3
2
0
0
1
2
0
0
1
0
0
2
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
2
0
0
2
0
0
3
0
0
0
0
0
0
2
0
0
2
0
5
0
0
0
1
3
0
1
2
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
1
0
0
1
1
0
0
0
0
2
0
0
0
2
3
0
2
0
0
0
0
0
2
0
0
1
1
0
0
1
2
2
2
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
5
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
2
1
2
0
0
2
0
0
2
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
2
0
0
3
0
0
1
0
2
2
3
0
0
0
0
1
0
2
0
0
2
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
2
0
0
0
0
2
1
0
0
1
1
0
0
0
1
0
2
0
0
0
0
0
2
2
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
2
0
2
0
2
2
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
2
0
4
0
0
0
2
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
1
0
0
0
0
0
1
2
0
0
2
0
0
1
0
0
2
1
0
1
0
0
0
0
1
0
2
1
0
2
0
0
0
2
1
0
0
0
3
1
0
0
0
0
0
1
0
2
1
0
0
1
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
2
0
2
0
0
0
1
0
1
1
0
0
0
2
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
2
0
0
4
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
1
2
0
0
0
0
2
0
0
0
0
1
2
1
0
0
0
0
0
2
2
1
0
1
0
0
0
0
1
0
2
0
1
1
0
2
1
1
0
1
0
1
1
0
1
0
2
1
2
0
1
0
2
2
0
0
0
0
0
0
0
2
0
0
1
0
0
3
0
0
7
0
1
0
2
0
1
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
4
0
0
2
0
0
0
1
0
0
0
1
0
1
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
2
2
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
1
0
0
0
2
1
0
0
0
1
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
3
0
0
2
0
2
1
0
0
2
0
0
0
1
0
2
2
1
3
2
2
0
0
0
0
2
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
1
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
3
0
1
2
0
0
0
1
0
3
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
4
0
1
0
0
0
3
0
0
0
2
0
0
0
2
0
0
0
2
0
1
1
0
1
0
0
0
0
0
1
1
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
2
0
0
0
2
0
1
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
1
0
0
1
2
2
0
0
0
0
2
0
0
0
0
0
1
2
0
0
2
0
0
1
1
0
1
0
0
0
0
1
0
1
0
0
2
1
1
0
0
1
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
2
2
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
1
0
1
0
0
0
0
2
2
1
0
0
2
0
1
0
0
0
0
0
0
1
3
1
2
0
2
0
0
0
0
0
1
0
0
0
0
2
0
3
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
2
3
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
1
1
0
1
0
0
0
0
0
0
4
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
2
2
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
3
0
2
0
0
1
0
0
0
2
1
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
1
0
3
1
0
0
0
0
0
2
0
0
0
2
2
0
0
0
2
1
0
0
0
0
0
0
1
0
2
0
0
2
1
0
0
0
0
2
0
0
1
0
3
0
1
1
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
1
0
1
1
0
0
2
1
0
2
0
2
0
0
1
1
2
1
2
0
0
0
0
1
1
3
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
2
0
0
2
0
1
1
0
0
2
0
1
2
0
2
0
0
1
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
2
1
1
1
0
0
2
2
0
2
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
2
0
0
0
1
2
1
1
0
0
1
1
1
0
2
0
0
2
0
0
0
0
0
1
0
2
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
1
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
2
0
2
3
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
1
0
0
2
0
1
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
1
1
1
2
1
0
3
1
0
3
0
0
2
1
2
0
0
2
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
3
1
2
0
2
0
2
0
0
0
0
0
0
1
1
0
0
1
2
2
2
1
0
2
0
0
0
0
0
3
0
0
1
0
0
0
1
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
2
0
0
0
0
0
1
0
1
2
1
1
0
0
1
0
0
2
2
0
0
0
2
2
1
0
2
0
0
0
1
2
0
0
1
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
4
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
4
0
0
1
0
0
0
0
0
0
0
2
3
1
0
0
0
0
1
0
2
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
2
0
0
2
1
0
1
0
0
3
0
0
0
0
0
2
0
0
10
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
2
1
0
0
2
0
1
0
0
1
0
0
0
3
0
2
0
0
1
0
0
0
0
0
1
1
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
2
0
1
2
0
0
0
0
1
0
0
0
1
0
1
1
0
1
0
2
0
0
2
0
0
0
0
0
2
1
0
0
2
1
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
1
0
0
0
2
0
0
2
2
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
5
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
5
2
0
0
1
2
0
0
0
0
1
1
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
2
0
0
2
0
2
1
0
0
1
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
1
4
1
0
0
0
0
0
2
2
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
2
0
2
0
0
1
1
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
4
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
7
0
0
1
0
2
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
1
3
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
2
0
1
0
0
0
0
1
1
0
0
1
0
0
0
3
1
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
3
1
2
0
1
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
1
0
0
0
2
0
3
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
4
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
1
1
0
2
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
1
2
0
0
2
0
1
0
0
1
3
0
0
0
2
1
1
0
0
1
0
0
0
1
0
0
0
0
0
1
3
0
0
0
0
0
2
1
2
0
0
3
0
2
0
1
0
0
0
2
0
0
0
0
0
0
2
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
2
0
1
0
2
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
4
1
1
1
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
2
1
0
0
0
0
0
0
0
0
2
0
3
2
2
0
0
0
0
0
0
2
2
1
0
0
0
1
0
0
0
2
2
0
1
2
0
0
0
0
2
2
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
2
0
1
0
0
1
0
2
2
0
0
1
2
1
0
0
1
0
0
0
0
0
1
1
2
0
0
0
1
0
0
0
1
2
0
0
0
1
1
1
2
2
0
0
2
0
0
1
2
0
3
0
0
1
0
0
0
0
0
0
2
2
2
1
0
0
2
1
2
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
6
0
0
0
2
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
2
0
0
0
2
0
2
1
0
2
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
1
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
2
0
0
1
0
0
2
0
1
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
2
0
1
0
0
4
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
2
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
1
2
2
1
0
0
0
1
2
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
3
0
0
0
0
0
0
1
1
0
0
0
2
0
3
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
2
0
0
1
0
0
0
2
0
0
0
0
3
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
2
3
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
2
1
0
0
2
0
0
0
0
0
2
1
0
0
0
0
2
0
2
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
2
2
1
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
1
0
1
0
2
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
2
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
1
2
0
0
0
1
0
0
0
2
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
1
0
1
0
1
0
0
0
0
2
0
0
1
2
0
0
1
0
1
0
0
1
0
0
0
3
1
0
0
0
0
8
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
1
0
2
0
0
2
1
0
1
0
1
0
0
0
2
2
1
0
2
0
1
0
0
0
2
0
3
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
2
2
2
0
1
0
0
0
0
0
2
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
1
0
0
1
0
0
0
2
2
3
2
0
2
0
1
0
0
0
2
3
0
1
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
1
0
2
0
0
1
0
0
1
0
1
0
4
0
0
2
2
0
0
0
0
2
4
1
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
1
0
0
2
2
2
0
1
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
2
1
2
2
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
1
1
0
0
0
0
0
0
2
0
2
2
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
2
0
3
0
0
2
1
0
0
0
0
1
0
3
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
2
0
3
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
1
0
0
0
2
0
0
1
0
0
1
3
0
0
0
0
0
0
2
1
0
1
4
0
1
5
0
0
1
2
0
0
1
1
0
2
0
1
0
0
1
0
1
0
2
0
2
0
0
0
1
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
3
2
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
1
2
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
5
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
2
0
0
1
0
1
1
2
2
0
3
0
0
1
0
0
2
1
0
0
2
0
0
0
1
1
0
0
0
6
0
0
0
0
2
0
0
0
1
2
2
2
0
0
1
0
0
0
1
0
3
0
0
0
0
0
1
0
0
0
0
1
2
0
0
1
0
0
0
1
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
1
0
2
2
0
0
0
0
1
0
1
1
1
1
4
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
8
0
1
2
1
1
0
0
1
0
0
0
1
2
0
0
1
0
0
1
0
0
2
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
2
0
2
0
0
2
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
1
2
0
2
2
0
3
0
1
0
0
1
0
1
0
2
1
0
0
2
2
0
0
0
0
4
0
1
2
3
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
2
1
0
0
1
1
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
2
0
1
0
0
0
1
1
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
1
2
0
0
0
1
0
1
2
0
0
0
0
0
1
1
0
1
0
2
0
1
2
0
0
0
0
0
2
2
2
2
1
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
1
0
0
0
0
0
0
2
0
1
0
3
0
2
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
1
0
1
0
1
0
1
0
0
0
2
1
0
0
2
0
0
0
0
3
2
0
1
1
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
2
0
0
0
0
1
2
0
1
0
0
2
0
1
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
2
2
0
0
2
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
3
2
0
2
0
0
0
0
2
0
0
2
0
0
2
0
1
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
1
2
1
0
1
0
1
2
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
2
0
1
1
0
0
0
2
0
0
0
0
1
2
1
0
0
2
0
0
2
0
0
0
0
2
0
0
2
0
1
1
2
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
2
0
0
2
0
1
0
2
1
0
1
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
5
2
0
0
2
1
0
2
1
1
0
0
0
0
0
0
0
1
0
0
0
0
2
3
0
2
0
1
0
0
0
0
3
2
0
1
0
0
0
1
2
2
0
0
0
0
2
0
0
0
0
0
2
0
1
1
3
2
0
2
1
0
0
1
2
1
0
0
0
0
0
2
0
2
0
2
0
0
0
2
2
0
0
2
0
1
2
1
0
0
3
0
0
2
0
0
0
0
1
0
0
0
1
0
2
2
0
0
0
2
0
1
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
2
0
2
1
0
0
1
0
1
2
0
3
0
0
0
1
0
0
0
0
2
2
0
2
0
0
0
1
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
6
0
1
2
0
0
1
0
2
0
1
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
2
0
3
1
1
0
0
0
0
0
0
2
0
2
0
1
1
0
0
2
0
0
0
0
0
2
0
0
3
0
1
0
1
0
1
2
0
2
0
0
0
0
0
0
2
1
0
0
1
2
1
0
1
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
2
2
0
0
1
1
2
0
1
0
2
0
1
0
0
0
1
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
2
2
0
0
0
0
0
0
2
0
2
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
1
0
1
2
2
0
0
0
2
0
0
1
0
0
0
0
2
0
0
3
0
1
0
1
3
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
8
1
1
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
2
0
0
2
1
2
0
0
0
0
0
0
1
3
0
1
1
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
4
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
1
0
2
0
2
2
0
0
1
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
1
1
0
0
0
0
0
1
2
2
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
2
3
0
0
0
0
1
0
0
0
1
1
1
0
0
0
2
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
5
3
0
0
0
0
2
0
1
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
2
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
2
0
0
0
2
1
0
2
0
0
1
0
0
0
1
1
0
2
3
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
2
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
1
1
0
0
0
3
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
2
2
0
0
1
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
2
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
2
0
0
2
0
2
0
0
1
0
0
2
1
0
1
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
3
0
1
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
1
2
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
2
0
0
2
3
0
0
0
1
2
0
2
1
1
0
2
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
3
0
1
2
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
1
0
2
0
2
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
2
2
0
0
1
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
2
2
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
1
0
1
0
2
0
0
2
0
2
4
1
0
0
1
2
0
0
1
2
0
1
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
2
1
1
0
2
0
0
0
2
1
0
0
0
0
0
1
0
1
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
2
1
0
2
2
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
1
2
0
0
1
0
1
0
1
0
2
0
0
1
0
2
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
2
0
1
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
2
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
3
0
0
1
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
1
0
2
2
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
2
0
0
0
3
2
0
0
0
1
0
0
0
4
0
1
1
1
2
2
1
0
1
0
0
0
0
0
1
0
0
0
3
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
2
1
1
0
0
0
1
3
2
0
0
0
2
0
1
1
0
0
0
0
0
2
0
2
1
2
0
2
0
0
0
0
2
2
0
1
1
1
3
0
0
0
1
2
0
0
0
0
0
1
2
5
0
0
1
1
2
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
1
2
0
2
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
1
1
2
0
1
0
0
0
1
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
2
2
0
4
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
6
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
2
0
0
0
1
2
2
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
4
2
1
0
1
0
3
0
0
0
1
0
2
0
0
1
0
0
2
0
1
0
0
0
1
0
1
0
1
2
0
0
0
2
1
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
1
2
1
1
0
2
2
0
2
0
2
0
0
0
0
0
0
1
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
4
0
1
0
0
1
0
1
0
0
0
0
1
1
0
2
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
1
1
1
0
0
0
0
0
0
0
4
3
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
4
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
1
0
0
1
1
0
0
0
3
0
0
0
0
0
0
0
0
1
1
2
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
3
1
0
0
1
0
3
0
0
2
0
2
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
4
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
1
0
1
1
0
1
0
2
0
2
1
0
0
0
0
1
0
1
0
2
0
1
2
0
0
0
1
2
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
1
1
2
0
2
0
2
0
0
1
2
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
1
0
0
0
0
3
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
3
0
0
0
1
2
0
0
0
2
0
0
0
0
2
2
0
0
0
2
0
0
1
1
2
0
0
0
5
0
0
0
0
1
1
2
0
4
0
1
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
2
0
4
0
0
1
0
0
2
2
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
2
0
2
1
0
1
0
2
0
0
2
0
0
0
6
1
0
0
0
0
0
0
1
1
2
3
0
1
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
1
1
1
2
0
2
1
2
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
4
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
1
2
1
0
0
0
0
0
1
1
1
0
0
1
0
0
1
1
2
0
0
0
0
1
0
2
0
0
0
1
0
0
2
2
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
2
1
0
0
0
0
0
2
0
0
1
0
1
0
1
0
0
0
0
0
0
0
2
0
0
1
2
1
1
0
0
0
1
0
2
1
0
0
0
0
2
0
0
0
0
3
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
1
0
1
1
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
3
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
2
0
3
0
2
0
1
0
0
0
0
1
0
0
1
2
2
0
0
0
3
0
1
0
2
1
1
0
0
0
2
0
2
0
0
0
0
0
0
2
0
1
0
1
0
0
0
2
0
0
0
0
3
2
0
2
1
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
2
0
1
0
8
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
2
0
0
0
1
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
2
0
0
1
0
0
0
0
1
0
2
0
1
0
1
0
0
0
2
0
2
0
2
0
0
1
0
0
2
0
0
2
0
1
0
0
0
1
0
0
2
3
1
0
1
1
0
0
0
2
0
2
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
3
2
0
0
2
0
0
0
2
0
2
1
0
0
0
0
2
2
0
1
0
0
0
1
1
0
0
1
0
0
2
0
0
0
0
2
0
0
1
2
0
0
1
0
0
0
1
0
1
0
2
0
0
1
2
0
2
0
2
0
0
1
0
0
1
0
0
1
1
0
0
1
0
0
0
1
0
1
2
0
2
0
1
2
0
0
0
1
1
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
1
1
0
0
0
0
1
2
0
0
1
0
1
0
0
0
1
1
0
0
1
0
1
0
0
0
1
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
2
1
0
1
2
1
0
0
0
0
2
0
0
1
3
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
2
2
0
0
0
1
2
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
2
2
0
0
0
2
0
0
1
0
1
0
0
0
0
0
3
2
0
1
2
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
2
1
2
0
2
0
0
0
0
0
0
3
1
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
2
3
0
1
0
3
2
2
0
0
1
0
1
0
2
2
0
2
0
0
1
0
0
0
0
0
1
2
3
0
0
1
1
0
1
2
0
0
4
0
0
1
1
1
0
0
3
0
0
3
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
1
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
2
0
1
0
0
0
2
2
1
0
0
0
0
0
2
1
1
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
2
0
1
0
0
2
0
0
2
0
0
2
0
2
0
1
0
0
1
0
0
0
1
0
2
1
0
4
1
0
0
0
0
0
0
0
0
0
2
0
2
1
0
1
0
2
0
1
0
1
0
1
1
4
2
0
0
1
1
1
0
0
0
2
3
0
0
0
0
0
2
0
0
0
0
0
0
3
0
1
0
0
1
0
1
0
0
0
2
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
2
2
1
2
0
1
0
0
0
0
0
1
1
1
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
2
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
2
0
0
2
0
1
2
0
0
2
1
0
0
0
0
0
1
0
2
0
1
0
0
1
1
1
0
0
0
0
0
0
0
2
0
1
0
0
2
0
2
1
1
0
0
2
0
1
0
2
0
4
2
0
0
1
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
1
2
1
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
2
0
0
0
0
2
1
0
2
0
1
0
2
0
0
1
0
0
0
0
1
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
1
0
2
4
0
1
2
1
0
0
0
0
0
0
0
2
0
0
1
2
0
0
2
0
0
7
1
0
1
0
2
0
1
0
2
0
1
0
2
2
1
2
0
0
0
0
0
2
2
0
2
0
1
2
0
0
0
2
0
2
0
0
2
0
0
0
2
1
1
2
2
0
0
0
3
1
0
0
0
0
0
1
0
2
1
0
2
2
2
0
2
0
0
0
3
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
1
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
2
0
0
0
2
0
0
2
0
2
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
1
3
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
2
3
1
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
1
3
1
1
1
0
0
0
0
0
1
0
0
0
2
0
2
0
0
1
0
0
0
1
0
2
1
2
0
0
0
0
2
1
0
1
0
0
2
1
2
2
0
0
2
0
0
3
1
2
0
2
2
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
1
0
3
0
1
0
0
2
2
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
2
0
0
2
1
1
1
0
0
0
2
0
0
0
1
0
1
0
0
2
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
1
0
0
0
1
2
0
0
0
0
0
2
0
2
4
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
2
1
1
0
0
3
2
1
0
2
0
0
4
1
0
0
2
2
0
0
0
0
2
2
0
2
0
0
0
0
0
2
0
0
0
2
1
0
2
0
0
1
0
0
2
1
0
1
2
1
0
0
0
0
0
2
0
1
0
0
2
1
2
0
2
2
0
0
2
5
1
0
0
2
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
1
0
0
1
2
1
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
2
0
1
0
1
0
1
0
0
2
0
2
0
0
0
0
1
0
0
1
2
0
1
4
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
2
1
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
2
0
1
0
6
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
2
0
2
0
0
0
0
3
3
0
0
0
0
0
0
2
0
0
0
3
0
0
0
1
1
7
1
4
0
2
0
0
0
0
0
1
0
0
0
1
0
1
2
0
1
2
1
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
2
2
1
0
0
1
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
2
0
2
2
1
0
2
0
0
2
2
0
2
0
1
0
0
1
0
2
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
1
2
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
1
0
3
1
0
2
0
0
0
0
0
1
1
0
0
1
2
0
3
0
0
0
2
0
0
1
0
2
0
0
3
0
0
0
3
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
1
1
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
1
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
1
2
0
0
1
2
2
2
2
0
0
2
0
1
0
0
0
2
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
1
0
0
0
2
0
2
1
0
2
1
3
1
0
0
2
0
1
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
3
1
0
0
0
2
0
2
0
2
0
0
1
0
0
0
1
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
2
0
0
3
0
0
0
0
0
0
2
0
6
0
0
0
0
0
2
1
0
1
2
0
0
0
0
2
0
0
2
2
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
2
2
1
0
0
2
2
0
0
1
0
0
0
0
2
0
0
0
1
2
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
4
1
0
0
1
0
0
0
1
0
0
2
0
0
2
2
0
1
0
3
0
0
1
2
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
2
2
0
2
0
1
0
0
0
1
0
1
0
2
4
0
2
0
2
0
0
0
0
2
0
0
0
0
2
0
2
1
0
0
2
0
0
0
0
1
2
2
1
0
0
0
1
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
2
0
0
1
1
0
0
2
0
0
0
2
1
0
0
0
1
2
0
4
0
0
0
2
2
0
2
1
2
1
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
1
0
0
0
3
0
0
4
0
2
0
2
0
1
0
0
0
1
0
3
0
0
0
0
0
1
2
0
2
0
0
0
1
0
2
0
0
0
2
2
0
0
2
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
1
0
2
4
0
2
2
0
2
1
0
2
0
0
0
0
0
0
2
0
0
1
1
0
2
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
1
3
2
0
0
0
0
2
0
0
1
0
0
2
0
4
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
2
2
0
0
0
1
2
0
0
0
2
3
0
0
0
0
2
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
3
2
0
3
2
0
1
0
0
0
0
2
0
2
0
3
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
1
0
0
0
1
0
2
3
1
0
0
0
0
1
0
0
0
0
0
0
0
3
0
1
0
0
0
0
2
2
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
1
1
0
2
2
2
0
0
0
0
0
1
1
0
2
0
0
0
1
0
0
1
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
2
0
0
0
8
0
0
0
1
0
1
0
0
0
0
0
0
1
1
1
0
2
2
0
0
0
2
0
0
2
3
0
0
0
0
0
0
0
0
0
0
3
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
1
1
1
2
0
0
0
0
0
1
2
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
2
0
2
2
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
1
0
0
1
0
2
0
0
1
0
0
0
1
0
0
0
1
0
0
2
0
1
1
0
0
0
1
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
3
2
1
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
1
0
4
0
0
0
0
0
6
2
0
1
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
3
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
3
0
0
0
2
0
0
2
1
0
0
0
3
0
0
0
0
0
1
0
0
0
0
1
0
0
3
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
2
0
1
0
3
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
2
0
2
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
2
0
1
1
1
0
0
2
0
4
0
0
0
2
2
0
0
0
0
0
2
0
2
2
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
1
0
1
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
1
2
1
0
0
0
0
2
0
0
0
0
1
2
1
1
0
0
0
1
0
0
1
0
0
0
1
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
2
0
2
0
0
1
2
0
0
0
1
0
0
0
0
2
0
1
1
1
0
0
0
0
0
5
0
0
2
0
0
1
0
0
0
1
0
1
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
2
7
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
2
1
0
0
0
0
1
0
6
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
2
1
0
0
2
0
0
0
1
1
1
0
1
0
0
0
2
2
0
1
0
0
0
2
1
0
2
0
0
0
0
0
0
1
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
1
2
2
2
1
2
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
2
1
2
0
0
0
4
2
0
0
1
2
0
1
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
1
0
1
0
0
1
0
2
0
1
0
0
3
0
0
0
0
2
0
0
0
1
2
0
0
0
0
1
0
0
2
1
1
2
0
2
0
0
0
0
2
0
0
5
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
1
0
0
3
3
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
2
0
0
4
0
0
1
0
0
0
0
0
0
3
0
0
2
0
1
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
1
2
1
0
0
0
0
2
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
1
2
0
1
0
2
0
2
0
2
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
3
1
2
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
2
2
0
1
3
0
0
0
2
1
0
0
0
0
0
1
0
2
0
0
0
1
2
0
0
1
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
7
2
0
0
0
0
0
0
0
3
0
1
2
0
2
0
0
0
0
0
1
0
1
0
0
2
2
0
0
0
1
0
1
1
3
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
2
0
0
2
1
2
0
0
0
0
0
1
2
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
2
1
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
1
4
2
1
1
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
2
2
2
0
0
0
0
6
0
0
2
0
0
0
2
0
1
2
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
1
1
0
0
3
0
1
0
2
1
6
0
0
0
0
0
0
0
2
3
0
0
0
2
0
1
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
2
2
2
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
1
1
0
1
0
0
1
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
1
2
0
0
0
0
0
0
0
0
2
2
0
1
0
0
1
0
1
0
1
2
1
0
0
0
0
0
2
1
0
0
0
0
0
1
0
1
0
0
2
0
1
0
2
0
0
1
0
0
2
2
0
2
1
0
0
0
0
0
0
0
0
0
1
1
3
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
1
0
0
0
0
1
0
1
1
2
0
2
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
1
0
0
0
0
1
0
0
0
0
1
1
0
2
0
0
0
0
0
7
1
0
2
0
0
0
0
0
0
0
2
0
0
1
2
1
0
2
0
0
1
0
0
0
0
3
1
0
0
2
0
0
0
0
0
1
0
2
1
0
0
2
0
0
0
0
2
0
2
0
2
3
0
0
0
0
2
1
0
0
0
1
0
0
1
2
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
1
0
1
0
0
2
2
4
0
2
2
0
0
2
0
2
0
2
0
0
0
0
0
0
1
0
2
2
1
0
1
0
0
0
0
1
0
2
0
2
0
2
0
1
2
0
0
0
0
2
0
2
0
1
1
0
0
2
0
0
2
3
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
1
0
1
0
3
1
0
0
3
0
0
0
0
1
0
2
0
0
0
0
1
1
0
0
0
3
1
0
0
0
0
0
0
6
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
1
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
3
0
0
3
2
2
0
0
1
0
0
0
2
2
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
2
1
0
2
1
0
0
1
2
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
2
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
3
1
0
0
2
0
1
0
0
0
0
0
0
2
0
0
2
1
0
0
1
0
1
0
0
1
0
0
6
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
2
0
1
0
0
0
0
1
0
0
2
0
0
2
0
1
2
2
0
0
1
2
1
0
3
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
6
0
2
0
1
0
0
1
0
0
0
0
0
0
2
1
0
2
0
0
2
1
2
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
4
0
0
0
0
2
0
0
1
0
1
0
0
2
3
0
0
0
0
1
0
0
0
3
0
0
2
0
2
1
4
0
0
0
2
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
1
0
2
2
2
0
2
0
0
0
1
1
12
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
2
2
0
0
0
0
0
1
1
2
0
2
2
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
1
1
0
0
2
0
0
2
0
1
0
1
0
0
0
1
1
2
0
0
2
4
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
3
1
0
1
0
0
0
0
0
2
1
0
2
3
1
2
1
0
2
1
0
1
0
0
0
1
2
2
0
0
0
0
2
1
0
0
0
0
0
3
0
0
1
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
2
3
0
0
0
0
2
0
0
0
2
0
1
0
0
0
2
0
0
2
2
4
6
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
2
1
0
0
0
0
0
2
0
0
4
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
2
0
0
0
1
2
1
2
0
0
0
0
1
0
0
0
0
0
1
0
0
6
0
0
0
0
0
1
1
0
1
0
0
2
0
0
0
0
0
2
0
3
0
0
0
0
0
1
0
0
1
0
0
2
1
3
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
2
0
0
2
0
0
0
0
2
2
0
0
0
1
1
0
0
0
0
0
2
1
1
0
0
0
2
2
2
3
1
0
0
2
0
0
0
2
0
2
1
0
0
0
0
0
0
0
1
0
0
0
2
0
1
1
0
0
2
0
0
3
1
0
1
0
0
0
0
2
1
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
2
2
0
0
0
1
0
0
0
3
1
0
0
0
4
0
0
2
1
1
2
2
2
0
0
1
2
0
0
0
2
0
0
0
0
0
2
0
1
0
1
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
1
0
2
0
1
0
0
2
0
0
1
0
0
0
2
0
1
2
0
0
0
0
2
2
0
1
2
2
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
4
1
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
1
1
1
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
1
0
2
0
0
1
0
0
1
0
0
0
0
2
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
2
1
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
2
0
2
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
1
0
0
0
1
2
0
1
2
0
0
0
0
2
0
2
2
0
2
0
1
0
0
0
2
2
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
1
1
0
2
0
0
0
0
2
0
2
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
2
1
0
2
0
0
0
0
2
2
3
1
0
2
2
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
1
3
0
0
0
0
0
2
0
1
5
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
3
0
0
1
0
0
0
0
1
2
0
1
2
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
1
3
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
2
0
0
0
2
1
0
0
1
0
1
3
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
4
4
0
2
1
0
2
0
1
1
0
0
0
2
0
1
0
1
0
0
0
0
1
0
1
0
0
0
2
0
0
2
0
7
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
1
3
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
2
0
0
2
1
0
1
1
2
0
0
0
1
0
0
2
0
1
1
2
1
1
0
0
0
1
1
0
0
1
2
0
2
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
2
2
0
0
0
2
2
0
0
1
1
0
1
0
0
2
0
0
0
1
0
1
0
2
0
0
0
0
0
1
0
0
2
0
1
2
0
1
0
0
0
2
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
2
0
1
0
0
0
1
0
1
0
2
0
0
0
4
0
0
0
1
2
1
1
0
0
0
7
2
0
0
0
0
0
0
0
0
1
0
0
2
4
0
0
0
2
0
0
0
2
2
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
2
0
0
2
0
1
2
0
0
0
0
0
0
0
0
1
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
1
2
2
1
0
0
1
2
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
1
2
0
0
2
0
0
1
0
0
1
0
0
0
0
2
2
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
2
0
0
0
1
0
0
1
0
0
0
0
2
0
0
1
2
0
2
2
0
1
0
0
2
2
1
0
1
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
2
1
2
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
2
0
1
0
2
1
2
0
0
1
0
2
0
0
1
0
2
1
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
2
0
0
2
0
5
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
3
0
1
0
0
0
2
1
1
1
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
1
1
0
0
0
2
0
0
1
2
1
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
1
3
1
0
1
0
0
0
0
1
0
0
1
2
0
2
0
0
0
1
1
0
2
0
0
0
0
0
0
1
0
0
0
2
0
1
2
2
0
0
1
0
0
1
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
4
1
0
0
0
0
0
1
0
1
1
1
0
0
0
1
4
0
0
1
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
2
1
2
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
3
0
3
1
0
0
0
0
0
2
0
2
0
2
0
0
1
2
1
2
0
0
2
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
2
0
1
0
1
0
0
0
0
0
0
1
1
0
0
1
2
0
1
0
2
2
0
2
0
2
2
0
0
0
2
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
1
1
0
0
0
0
0
2
0
0
7
0
0
0
1
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
1
0
0
0
1
0
1
2
2
0
0
0
0
0
0
2
2
0
0
0
0
1
2
2
0
0
0
0
1
1
0
2
0
1
1
0
1
0
1
0
2
0
0
0
1
2
0
0
0
1
2
0
1
1
0
2
0
0
0
0
3
0
0
0
0
0
1
0
0
1
2
1
0
0
0
0
2
0
2
0
0
1
0
0
1
1
2
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
1
0
1
2
0
2
0
1
0
0
0
0
0
0
0
0
3
0
2
0
3
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
4
0
0
2
0
0
1
2
0
2
0
0
0
1
2
0
0
2
2
0
0
0
0
0
0
0
0
0
5
1
1
0
0
0
1
1
0
0
0
3
1
0
0
0
0
0
0
0
2
0
0
0
0
0
3
1
0
1
2
0
0
0
0
0
1
1
1
0
0
0
0
1
0
1
2
0
0
0
0
1
3
0
0
1
0
2
6
0
1
0
0
0
0
0
0
1
0
1
0
0
0
2
0
2
0
0
1
0
0
0
2
2
2
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
1
0
0
2
1
2
2
0
0
0
1
0
1
0
0
0
2
0
0
2
0
0
1
0
0
0
0
2
0
0
0
1
0
2
1
1
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
3
3
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
2
2
0
2
0
8
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
1
0
1
0
2
0
0
0
0
0
0
2
2
0
0
0
1
0
0
1
0
0
0
0
2
0
1
2
1
0
0
3
0
0
0
0
0
0
0
0
2
0
0
1
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
2
0
2
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
1
0
2
2
1
2
2
1
1
0
1
0
1
1
1
0
0
2
2
0
0
2
0
1
0
1
1
0
0
3
0
0
0
3
0
2
0
3
1
0
1
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
1
2
0
0
0
0
1
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
2
1
0
0
0
0
0
0
0
0
0
2
0
1
1
1
0
0
0
0
0
0
0
0
1
2
0
2
0
2
1
0
2
0
0
0
3
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
1
2
0
1
0
1
0
0
0
0
0
1
5
0
0
1
0
2
1
0
3
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
1
3
0
1
2
0
0
1
0
0
0
0
4
0
1
2
0
0
0
1
0
2
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
3
0
1
2
0
0
0
0
0
0
2
0
2
0
0
0
1
0
2
2
0
0
2
2
1
1
0
0
0
0
0
0
0
2
7
0
2
0
1
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
1
0
2
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
2
1
0
2
0
0
1
1
1
2
1
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
4
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
1
0
2
0
0
2
1
0
2
1
0
1
0
0
0
2
4
0
0
1
0
0
0
0
0
1
0
1
2
1
2
0
1
0
0
0
2
0
0
0
3
0
0
1
1
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
3
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
2
1
0
1
2
0
0
0
2
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
2
1
0
1
0
2
0
0
0
0
0
1
0
2
0
0
2
0
0
1
0
2
0
0
0
0
2
1
0
1
0
2
0
1
0
0
2
0
0
1
1
0
0
2
0
0
0
2
0
1
0
0
1
0
0
0
1
0
2
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
2
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
2
1
2
2
0
2
0
1
0
0
0
0
2
1
0
1
0
0
0
1
1
1
3
0
0
0
0
3
2
0
0
0
1
1
0
0
1
0
1
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
3
0
1
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
1
2
0
2
2
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
4
1
2
0
0
0
0
0
0
3
0
2
2
1
2
0
0
0
0
0
0
2
1
2
1
0
0
0
2
2
0
1
4
0
0
0
0
1
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
1
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
1
1
2
0
0
0
1
1
1
0
0
2
0
2
0
0
2
0
3
0
1
0
0
0
0
0
2
2
1
0
0
0
1
0
3
0
0
0
1
0
0
2
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
1
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
2
2
0
0
1
2
2
1
1
0
0
2
0
2
0
0
0
0
0
0
2
1
1
0
1
0
0
0
0
0
2
1
0
0
0
0
0
1
1
1
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
1
1
0
0
0
0
2
0
6
0
2
1
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
2
0
0
2
0
0
0
1
2
0
0
0
0
1
0
0
0
2
2
3
0
0
2
1
0
1
0
2
1
0
0
1
1
0
0
0
0
0
2
0
0
3
0
1
0
1
1
0
0
0
0
0
1
5
4
0
0
0
0
0
1
1
2
0
0
0
1
1
2
0
2
1
0
0
0
1
0
0
0
0
2
0
0
3
0
0
2
0
0
2
2
1
1
2
0
1
0
0
0
0
0
1
0
1
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
5
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
2
0
0
0
0
0
3
1
0
0
0
0
2
0
0
0
0
1
0
1
2
0
0
5
0
0
1
2
0
0
2
0
1
2
1
0
0
1
0
0
0
1
2
1
0
0
0
2
0
0
1
1
0
1
0
0
0
2
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
2
0
1
0
0
0
2
0
2
1
0
0
0
2
1
0
2
0
2
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
2
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
2
1
4
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
1
0
2
0
1
1
1
0
0
2
0
0
0
1
1
1
0
2
0
0
0
0
0
0
0
0
0
2
0
12
0
0
0
0
0
0
0
2
0
1
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
1
1
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
1
0
0
1
0
0
2
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
3
0
0
3
0
0
0
0
0
0
0
2
3
1
0
0
0
1
2
1
0
1
2
1
0
3
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
10
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
1
0
0
0
1
0
0
1
2
0
3
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
2
0
0
0
1
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
3
0
1
0
0
2
0
0
2
0
0
0
0
0
3
0
1
0
0
1
2
3
1
0
0
0
0
2
1
2
1
2
0
0
0
1
0
0
1
2
0
1
2
2
0
0
0
3
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
7
1
1
0
2
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
2
2
0
0
0
2
2
0
2
1
0
0
1
2
0
0
0
1
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
1
0
2
1
1
0
0
0
2
0
0
2
0
0
2
1
0
0
0
0
0
1
1
0
1
0
0
1
0
1
0
2
0
1
2
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
3
0
1
0
2
0
1
2
0
0
0
0
0
0
2
0
0
0
1
2
0
2
2
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
2
0
2
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
1
1
2
2
0
1
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
3
1
0
0
2
0
0
0
2
0
0
0
3
2
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
1
4
0
0
0
2
0
2
2
0
0
2
0
1
0
0
3
0
1
0
0
3
0
0
0
1
0
0
0
0
0
0
5
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
2
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
1
0
2
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
12
0
0
0
3
0
1
0
0
1
1
0
0
2
0
0
2
0
3
1
0
1
1
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
7
0
0
1
0
0
0
4
0
0
0
4
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
2
1
0
1
0
0
0
0
3
0
0
0
1
0
0
2
2
2
0
0
1
0
1
0
2
1
0
0
2
1
1
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
2
2
1
1
0
0
0
0
2
0
3
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
3
0
0
2
0
0
2
3
0
0
0
0
3
0
1
0
0
1
0
0
0
3
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
2
0
0
0
2
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
2
0
0
0
0
2
0
2
0
2
0
2
1
1
0
0
3
0
0
4
1
0
0
0
2
0
0
0
0
0
0
0
8
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
2
0
0
0
0
1
0
0
2
0
1
1
4
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
1
2
2
0
1
3
0
0
1
0
0
0
1
0
0
1
2
2
1
1
1
1
2
0
1
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
2
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
1
0
1
0
0
0
1
0
1
0
2
0
0
0
0
0
1
0
1
1
0
0
0
2
0
0
0
1
1
2
1
1
0
1
0
0
1
0
0
0
1
0
2
0
1
0
0
1
0
0
0
1
0
2
1
1
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
2
2
0
0
1
1
0
1
1
0
0
0
2
0
0
0
0
1
0
0
2
0
2
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
2
0
1
0
0
1
2
0
0
4
3
0
0
1
0
0
0
0
1
0
2
0
0
0
3
0
1
0
1
0
2
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
2
0
0
2
2
0
0
0
2
2
0
0
0
0
0
0
1
0
1
2
0
2
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
2
1
0
3
0
2
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
2
0
2
0
0
1
0
1
0
0
2
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
2
2
0
1
0
0
1
1
1
0
0
0
0
0
1
0
1
3
0
1
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
2
2
0
0
2
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
2
2
2
0
0
0
0
0
0
2
0
0
2
2
1
1
0
0
0
0
0
0
0
2
2
0
3
0
2
0
0
1
0
0
0
0
0
1
0
1
2
2
0
0
0
0
1
2
2
3
0
0
0
0
0
0
0
2
2
0
0
0
2
0
1
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
4
3
0
0
1
0
0
2
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
2
1
0
2
2
0
2
0
0
0
1
0
0
2
0
1
1
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
2
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
1
1
0
0
3
0
0
0
1
0
0
1
0
0
0
0
0
2
1
2
0
0
0
0
0
1
1
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
2
2
3
2
1
2
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
2
0
0
0
2
0
0
0
1
1
2
0
0
0
0
0
1
0
0
0
1
0
3
0
0
0
0
3
0
0
0
1
0
0
0
0
0
2
0
4
0
1
0
1
0
2
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
2
0
3
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
2
0
0
2
0
0
0
2
1
0
0
0
0
0
0
1
1
0
1
1
1
0
1
1
0
0
0
2
0
0
1
0
0
0
2
1
0
2
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
2
1
1
1
0
0
0
0
0
2
0
0
0
0
1
1
2
1
1
0
0
0
0
1
5
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
1
0
2
0
0
1
1
1
0
0
0
2
2
0
1
0
1
0
2
0
0
0
0
0
1
0
1
2
1
5
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
2
1
0
0
2
2
0
1
1
2
1
0
0
1
0
0
0
0
2
2
0
0
1
2
1
2
0
0
0
0
1
0
0
0
0
1
0
0
0
3
0
1
0
2
0
1
4
0
0
2
3
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
1
2
0
2
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
1
2
2
0
0
0
2
0
0
2
0
0
0
2
0
0
2
1
0
0
0
0
0
4
1
0
2
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
2
0
2
0
0
0
1
0
0
0
0
3
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
3
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
1
0
0
0
0
0
1
0
2
0
0
0
2
0
2
1
0
0
0
0
0
0
0
2
0
3
0
0
0
1
0
0
0
0
1
0
1
0
2
2
0
0
0
2
0
2
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
1
0
2
2
0
0
1
1
2
2
0
0
0
1
0
0
1
0
0
0
1
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
3
2
2
2
1
0
0
1
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
2
0
2
0
0
0
0
1
1
0
0
1
0
2
0
0
0
2
2
0
0
0
1
1
0
0
2
0
2
0
2
2
0
0
0
0
0
0
0
1
0
1
0
1
0
2
0
0
1
0
2
0
0
0
0
1
1
2
0
1
0
2
0
2
1
1
4
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
2
1
0
1
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
1
0
2
0
0
2
0
0
2
2
1
0
0
1
0
0
0
0
1
1
2
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
1
0
1
2
0
0
1
1
0
0
4
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
2
1
0
0
0
2
0
0
2
2
0
2
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
3
0
0
2
0
0
2
0
0
0
0
0
2
1
1
0
0
0
3
1
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
2
2
0
0
0
0
0
2
0
1
2
0
0
1
2
0
0
2
1
0
4
0
0
0
1
0
0
2
0
1
1
0
1
0
0
2
0
0
0
0
0
0
0
2
1
0
2
0
0
0
2
2
0
1
0
0
0
2
0
0
1
1
1
0
1
2
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
2
1
0
0
1
2
0
2
0
0
1
0
0
0
0
2
0
1
0
0
1
2
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
2
0
0
1
1
1
0
0
0
0
0
0
2
0
4
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
2
1
0
7
0
2
1
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
5
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
2
0
0
0
1
2
2
2
0
2
1
0
0
0
0
2
1
0
1
0
2
0
2
2
0
1
0
0
0
1
0
2
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
2
1
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
1
0
0
0
2
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
2
1
0
0
1
1
0
0
0
2
0
0
0
1
2
0
1
2
0
0
0
2
0
0
0
1
1
0
3
1
0
0
0
0
0
3
0
2
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
2
0
1
1
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
1
0
2
0
0
2
0
0
7
0
2
2
0
2
0
0
2
1
1
1
2
2
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
3
2
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
2
0
2
0
0
0
2
1
0
5
0
0
0
1
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
1
1
2
2
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
2
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
3
0
0
1
1
0
0
0
0
0
0
1
2
1
0
1
0
2
0
0
0
2
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
3
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
1
0
2
0
2
0
0
0
0
1
0
0
1
0
1
0
0
0
2
0
0
0
0
1
0
2
0
0
0
1
0
0
0
1
0
2
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
1
0
2
0
0
0
0
1
2
1
0
1
1
3
0
0
0
0
1
0
0
0
2
0
2
1
0
0
0
2
2
0
0
0
0
2
0
0
0
1
0
2
2
0
0
0
1
0
0
0
2
2
2
0
0
0
1
0
0
1
2
2
2
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
2
0
2
0
0
0
2
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
2
0
1
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
3
0
1
0
0
0
0
2
0
2
2
2
0
0
2
0
0
2
0
3
2
2
0
0
0
2
1
0
3
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
3
2
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
2
0
3
0
0
2
0
2
2
0
2
2
2
0
0
1
2
1
0
1
2
0
2
0
0
2
0
0
0
1
2
2
2
0
1
0
0
0
0
2
3
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
2
0
0
1
0
0
0
2
0
0
0
0
0
0
1
1
2
0
0
0
2
1
0
0
0
3
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
2
0
0
2
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
1
2
3
2
1
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
3
2
0
0
0
1
0
3
0
0
2
0
0
0
0
3
1
0
0
2
0
0
5
0
0
3
0
0
1
0
0
0
0
0
2
0
0
0
0
1
1
2
0
0
0
3
0
1
0
0
2
1
1
1
0
3
1
0
0
1
0
0
2
0
1
1
0
0
0
0
1
0
1
2
0
0
0
0
4
1
0
0
0
0
0
2
1
0
0
0
2
2
0
0
0
1
1
0
0
1
0
2
2
0
0
1
0
3
2
0
0
0
1
2
0
0
0
0
2
0
0
2
3
1
2
0
0
2
0
2
0
2
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
3
0
2
0
0
0
0
3
0
0
0
0
0
1
0
0
1
0
2
0
1
2
1
0
1
2
0
0
0
0
0
2
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
4
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
1
0
2
0
0
0
3
1
0
2
1
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
3
0
2
0
0
1
0
1
0
2
0
0
0
0
2
0
2
0
1
1
0
0
0
0
0
1
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
3
0
0
0
5
0
2
0
0
0
0
3
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
2
5
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
1
2
0
0
2
2
0
0
1
0
2
0
0
0
0
0
0
0
2
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
2
0
2
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
2
1
0
0
4
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
1
0
0
0
0
0
3
1
1
1
1
5
0
2
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
2
0
0
1
0
2
0
0
1
0
0
0
0
1
0
1
1
0
2
1
0
0
0
0
0
1
0
0
1
1
0
0
0
2
0
0
2
0
2
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
1
0
1
0
1
0
1
0
1
0
0
0
0
0
0
1
2
1
0
0
0
0
2
0
0
0
0
9
2
0
1
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
2
1
0
0
0
0
0
1
2
0
1
0
1
0
0
0
1
0
2
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
1
0
0
2
2
1
0
0
0
0
0
0
0
3
3
0
0
0
0
0
0
0
0
0
0
2
0
0
3
1
1
0
0
1
1
0
1
0
0
1
1
0
0
1
0
1
0
2
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
2
0
0
2
0
0
3
0
0
2
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
1
0
3
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
1
4
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
3
3
0
1
4
0
0
0
0
1
0
0
0
1
2
0
2
2
2
0
0
0
2
0
2
1
7
0
1
0
2
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
3
2
1
0
0
0
1
0
1
0
4
0
2
0
0
5
0
1
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
4
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
1
0
1
0
1
0
0
0
0
0
0
2
0
0
1
0
0
1
0
1
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
2
2
0
2
1
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
1
0
2
0
0
0
0
0
2
0
0
1
0
2
0
0
2
0
0
0
2
0
0
0
3
0
1
4
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
2
1
0
0
1
0
2
1
0
1
0
0
0
0
0
0
0
0
1
2
0
2
2
0
0
0
4
0
1
2
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
3
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
2
0
1
0
0
2
1
3
0
1
2
3
0
0
1
0
0
0
0
2
0
0
0
1
1
2
0
0
0
1
0
0
0
1
0
0
1
2
0
1
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
1
0
2
1
0
0
2
0
2
1
0
2
1
0
1
0
1
0
1
0
0
0
2
2
1
0
1
0
0
0
0
0
2
0
2
1
2
0
1
0
0
0
3
1
1
1
0
0
2
0
0
0
0
0
2
1
0
0
4
0
1
0
0
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
6
0
1
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
2
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
1
0
2
2
2
0
0
1
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
3
0
0
0
1
1
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
2
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
2
1
0
0
0
0
1
3
0
0
1
0
0
0
4
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
1
0
2
2
0
1
0
2
0
0
2
0
2
1
2
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
2
0
0
2
3
0
0
0
0
2
0
0
0
0
0
0
1
0
3
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
2
2
0
2
0
0
0
0
0
1
0
2
0
0
2
0
0
2
0
0
0
2
0
0
1
0
0
0
2
0
1
1
3
0
0
0
0
0
0
0
0
2
2
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
1
0
1
10
1
0
1
2
2
1
0
1
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
2
0
0
0
0
0
0
1
1
0
2
1
0
2
0
0
1
0
1
1
0
0
1
0
1
1
0
1
0
0
0
0
2
0
1
0
0
0
3
0
1
0
1
0
0
0
1
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
1
1
0
0
0
1
0
1
0
0
2
0
0
0
0
1
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
2
3
3
0
2
2
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
1
0
0
1
0
1
0
0
0
0
4
1
0
0
0
0
2
0
2
0
2
0
2
2
0
2
0
0
2
2
0
0
0
0
0
5
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
2
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
3
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
3
2
2
0
3
3
0
0
0
0
0
0
0
1
0
2
0
0
2
0
1
0
2
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
2
1
0
0
1
0
0
1
2
0
0
0
0
0
2
0
0
2
0
2
5
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
1
0
1
0
1
2
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
5
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
2
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
3
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
1
0
0
2
0
0
4
0
1
1
0
1
0
0
0
0
2
0
2
2
0
2
0
0
1
2
0
1
0
1
1
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
1
0
2
0
2
0
3
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
3
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
2
1
2
0
0
0
0
2
0
0
2
1
0
0
0
0
0
1
1
0
0
0
0
0
0
2
2
0
0
1
0
1
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
3
3
0
0
0
0
2
0
0
0
0
3
0
1
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
3
0
3
0
0
1
0
0
0
0
0
0
2
3
0
0
4
0
0
1
1
2
2
0
2
2
2
0
1
2
0
0
0
0
1
1
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
2
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
1
0
0
1
2
0
1
0
0
0
1
3
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
2
1
0
0
2
2
0
0
0
1
2
0
0
2
0
0
0
0
2
3
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
2
2
2
0
0
0
0
2
2
1
0
2
2
0
1
0
1
0
0
0
0
3
1
0
0
3
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
2
0
2
0
1
0
2
0
0
0
0
0
0
0
2
1
0
2
0
0
0
1
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
1
1
2
0
0
1
2
0
0
1
0
3
0
0
0
0
0
1
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
6
0
2
0
0
0
3
1
5
0
0
3
2
0
0
1
1
0
3
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
1
0
0
1
0
0
0
0
2
0
0
1
0
0
0
2
1
0
2
0
2
0
0
0
4
0
0
2
0
1
0
0
3
0
0
0
2
0
0
1
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
2
2
0
0
1
0
2
0
1
0
1
2
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
1
1
2
0
0
0
0
2
0
0
0
0
0
0
1
2
2
0
2
0
0
0
0
0
2
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
3
2
0
0
0
0
2
0
2
0
2
0
2
0
0
1
1
0
0
0
0
0
0
0
0
2
1
2
2
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
2
0
0
1
0
0
2
0
0
0
0
1
0
0
0
1
0
2
2
0
1
0
0
0
0
2
1
0
2
0
0
0
2
0
0
1
0
2
0
1
3
2
2
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
3
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
2
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
3
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
1
1
1
0
0
1
2
0
2
0
0
2
0
2
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
1
2
0
0
3
0
0
0
0
1
1
1
2
0
0
1
2
1
2
0
1
2
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
1
0
1
0
0
4
0
0
2
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
1
0
0
0
0
1
0
1
0
1
1
0
0
2
0
2
0
1
1
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
2
4
3
1
1
2
0
0
1
0
0
0
0
0
0
0
1
0
2
2
0
0
0
2
0
0
1
0
2
0
0
0
1
0
1
0
0
0
0
2
0
0
1
1
1
0
0
3
0
0
0
0
1
0
3
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
1
0
0
2
1
6
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
3
0
0
0
0
0
1
0
1
1
0
0
1
2
1
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
2
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
2
0
0
0
1
0
1
0
2
0
2
0
1
1
1
2
0
0
0
0
0
1
2
3
2
1
0
0
1
0
0
0
0
0
1
0
1
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
1
0
0
0
1
0
0
0
1
0
1
2
2
2
0
1
2
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
2
2
2
0
0
0
2
0
0
0
0
0
1
3
0
3
2
3
0
0
1
0
0
0
0
0
0
2
1
2
2
0
1
0
3
2
2
6
0
0
2
0
0
0
2
1
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
3
3
1
0
0
0
0
0
0
2
1
0
2
2
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
1
1
1
1
0
3
0
1
0
0
0
0
0
0
0
2
0
0
2
0
1
2
0
2
2
1
2
0
2
0
0
0
0
0
1
1
0
0
1
1
0
0
0
1
0
2
0
2
0
1
0
1
1
0
0
2
0
0
0
0
0
0
1
2
0
2
1
0
0
10
0
2
0
2
0
0
0
0
0
2
0
0
1
0
0
0
2
0
2
2
2
0
1
0
1
0
0
0
2
2
2
1
2
1
0
0
2
2
1
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
3
1
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
2
0
0
0
1
1
0
1
2
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
2
0
1
0
0
0
0
2
0
0
2
1
1
0
0
0
0
0
0
0
0
0
2
1
0
2
2
0
1
0
1
2
2
2
0
1
0
0
0
2
2
0
0
0
0
0
0
2
1
0
2
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
3
0
0
0
0
2
2
0
0
0
1
0
1
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
2
0
1
0
0
1
0
3
2
0
1
1
2
0
1
0
0
0
2
2
0
0
0
0
1
2
0
0
3
0
0
0
1
0
3
0
0
0
0
0
0
1
1
0
5
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
1
3
1
0
0
0
2
2
0
0
0
0
1
0
2
1
0
0
2
0
0
0
2
0
2
0
0
0
3
0
0
2
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
2
0
2
3
2
0
3
1
1
0
0
2
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
1
2
2
0
1
0
1
0
0
1
1
0
0
0
0
2
1
0
0
2
0
0
3
0
2
1
0
0
2
0
1
2
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
1
0
0
0
3
1
0
2
2
0
0
0
0
0
0
2
2
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
2
0
2
0
0
2
0
1
0
0
0
0
1
0
2
0
0
3
0
1
0
0
0
2
1
0
0
1
0
0
0
1
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
2
0
3
0
0
0
0
2
5
2
0
0
0
0
0
0
2
2
0
1
0
0
1
0
2
0
0
0
2
0
1
1
0
2
0
2
2
0
0
0
2
0
0
0
1
0
2
0
0
0
2
0
1
2
2
1
0
0
2
5
0
1
0
0
0
0
0
7
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
2
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
2
2
2
1
1
2
1
1
0
0
0
0
0
0
2
0
0
1
0
0
2
0
2
0
0
2
0
0
1
0
2
3
0
0
0
0
0
0
0
0
0
2
2
1
2
1
1
0
0
0
2
0
2
0
1
2
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
2
0
0
2
0
0
0
0
1
3
0
0
0
1
1
0
1
0
2
1
3
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
2
2
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
1
0
1
0
1
2
0
0
0
2
1
0
0
0
0
3
0
0
0
5
0
0
0
1
2
2
3
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
1
3
0
2
0
2
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
1
0
0
4
2
0
0
3
0
0
0
0
0
0
0
0
4
2
0
1
1
1
2
0
0
0
2
2
1
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
1
0
2
0
2
2
0
1
3
0
0
0
0
3
0
0
1
1
0
1
0
0
0
0
1
0
1
0
0
0
0
3
2
2
0
1
0
0
0
0
0
4
0
0
0
1
2
1
0
2
0
0
1
0
0
1
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
2
1
0
0
0
2
0
0
1
0
1
1
1
0
0
1
0
0
0
2
0
1
0
0
0
0
0
1
1
0
0
1
0
1
0
2
3
0
2
2
0
1
2
0
2
0
0
0
0
1
1
1
0
0
0
5
0
0
1
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
1
0
2
2
1
0
0
1
2
0
0
0
0
1
2
0
0
1
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
1
0
0
1
1
0
0
0
0
1
1
0
0
2
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
1
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
2
0
0
2
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
1
1
0
0
0
1
1
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
2
2
2
0
0
0
0
8
2
0
0
1
1
0
0
0
0
0
2
1
0
0
4
1
1
0
0
0
4
0
0
3
0
1
2
0
0
0
0
1
1
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
2
2
0
0
0
2
1
0
2
1
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
1
0
2
0
2
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
9
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
1
1
0
0
1
0
2
0
0
0
2
0
0
1
2
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
2
2
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
1
2
2
0
2
0
0
2
0
2
0
0
0
0
1
0
1
2
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
1
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
2
2
0
1
0
0
2
0
1
0
2
0
0
2
0
0
3
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
2
2
2
2
0
0
1
0
2
0
2
0
2
0
0
0
4
1
0
0
0
2
1
0
0
2
0
0
0
1
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
3
0
1
0
1
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
4
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
1
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
1
1
0
3
0
0
0
2
0
0
0
1
0
0
1
0
1
0
1
2
0
0
0
0
1
0
1
0
2
2
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
4
0
2
0
2
3
1
2
2
0
0
0
1
0
0
0
4
0
0
0
1
0
0
0
2
0
1
0
0
0
2
0
0
0
1
2
1
0
0
0
0
0
0
0
0
2
0
1
0
1
1
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
1
0
1
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
2
3
0
1
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
1
1
0
1
0
1
2
0
0
0
0
0
1
0
0
2
0
2
0
1
0
0
0
0
2
1
0
0
0
0
1
0
0
0
1
0
3
0
0
0
0
0
0
0
3
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
2
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
2
0
2
2
0
0
1
0
1
0
2
0
0
0
1
0
1
2
2
0
0
2
0
1
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
1
2
2
1
2
0
1
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
1
2
0
0
2
0
3
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
1
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
2
0
0
0
2
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
2
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
2
0
1
0
0
2
3
0
0
0
1
0
2
0
2
1
0
0
0
2
2
0
0
0
2
2
0
0
0
0
0
0
0
0
1
2
0
1
2
0
2
1
0
0
0
1
0
0
1
2
0
1
0
1
7
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
3
1
0
1
2
0
2
0
1
0
1
0
0
0
0
0
2
0
0
1
2
0
1
0
2
1
2
0
0
0
1
0
0
2
1
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
2
0
0
0
0
0
0
3
3
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
3
0
2
1
1
0
1
0
2
0
0
0
1
2
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
1
2
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
2
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
2
0
1
2
0
0
2
1
0
0
2
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
2
2
0
0
1
1
2
0
0
1
1
2
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
1
0
1
0
0
2
1
0
0
0
0
0
1
0
0
4
0
0
0
1
2
0
2
2
1
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
2
0
0
2
0
0
0
1
1
2
0
0
2
0
3
1
2
2
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
1
0
2
1
2
0
0
3
1
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
5
0
0
0
4
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
4
2
0
3
1
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
4
0
0
1
2
0
0
0
2
2
1
1
2
0
0
0
0
0
3
2
0
2
0
1
2
0
1
0
0
0
0
0
0
0
1
0
0
1
0
2
0
1
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
2
0
2
2
0
2
0
2
0
2
2
0
2
0
0
0
0
0
1
1
0
0
0
3
0
0
2
0
0
1
0
1
0
0
0
0
0
0
1
2
0
2
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
2
0
0
0
2
3
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
2
0
2
0
1
3
0
0
0
0
3
1
0
0
1
0
2
5
0
0
1
0
0
0
0
1
1
0
0
2
0
0
0
1
1
2
2
2
0
0
2
0
0
0
2
1
0
0
0
0
0
0
2
16
1
0
0
0
0
2
0
0
0
1
0
0
0
0
5
0
1
1
0
0
1
0
1
0
2
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
1
0
1
1
1
0
1
2
1
0
0
0
0
0
1
2
2
0
0
1
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
1
2
0
1
2
0
0
2
0
1
0
0
1
0
0
1
0
0
2
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
1
3
0
0
0
0
0
3
0
2
3
2
0
0
0
4
2
2
1
0
2
0
0
0
2
1
3
3
0
2
0
0
0
0
0
0
0
0
0
1
2
1
2
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
1
0
0
1
2
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
1
0
0
0
2
2
1
2
0
0
0
0
0
2
3
0
0
0
1
0
0
1
1
3
1
0
0
0
0
1
1
0
0
0
2
0
1
1
1
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
1
1
0
0
1
0
2
0
0
0
1
1
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
2
1
0
2
1
0
1
0
0
2
0
0
0
0
3
0
0
0
0
0
1
0
1
0
0
2
0
0
0
1
2
0
0
0
0
0
2
0
0
0
2
0
0
0
2
2
1
0
2
2
0
2
0
0
0
0
2
2
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
3
0
2
0
1
1
0
0
2
0
0
1
0
0
0
0
2
0
1
0
0
0
0
2
1
2
0
0
0
0
0
2
0
1
0
1
0
0
1
0
0
0
0
0
0
2
0
0
3
2
0
0
1
1
0
0
0
0
0
0
2
1
0
2
2
0
0
0
2
0
5
1
2
0
2
2
0
2
1
0
1
0
0
0
0
0
0
2
0
0
0
1
2
1
0
1
0
0
1
2
0
2
2
0
0
0
1
0
0
0
2
0
0
1
1
1
1
2
0
0
0
3
2
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
2
0
1
0
0
0
0
2
1
0
0
1
3
0
0
0
0
0
0
0
1
0
0
0
3
0
0
2
0
0
0
0
0
1
2
2
0
1
0
2
2
0
0
0
2
0
0
0
0
1
2
2
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
2
0
1
0
1
3
0
0
1
0
1
1
0
1
0
0
0
0
2
0
0
0
1
0
0
0
2
0
1
0
1
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
2
0
1
4
0
0
1
1
0
2
0
0
1
0
1
2
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
1
0
0
0
0
1
0
0
1
2
0
1
0
0
2
0
2
0
2
1
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
4
1
1
0
1
1
0
0
0
1
1
2
0
0
0
0
0
0
0
0
1
2
1
0
0
1
2
2
1
0
0
0
1
2
0
0
1
2
0
0
0
0
0
0
0
2
2
3
0
2
0
2
1
0
0
1
0
1
0
0
0
0
0
1
2
0
2
0
0
0
0
0
2
0
0
0
0
1
2
0
3
0
0
0
1
0
2
0
2
2
2
2
0
1
0
2
0
1
1
2
2
4
0
0
0
2
0
1
0
0
0
0
1
1
0
0
0
0
0
0
3
0
0
0
0
1
1
2
2
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
3
1
2
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
2
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
2
0
0
2
0
1
0
0
0
0
1
0
0
2
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
2
2
2
1
1
3
0
3
0
0
3
2
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
2
2
2
0
0
0
0
0
2
0
0
2
0
2
0
0
2
0
0
0
1
0
0
2
0
0
0
3
2
1
0
0
2
0
0
1
0
1
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
1
0
2
0
0
0
2
0
0
1
3
0
0
0
1
2
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
1
0
0
0
0
9
0
0
0
0
0
1
2
2
0
1
0
0
1
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
2
1
0
0
0
0
1
2
0
0
1
1
0
2
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
2
2
1
1
0
2
0
0
0
0
0
5
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
3
0
0
2
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
2
0
1
0
1
0
1
2
0
0
0
0
0
0
0
2
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
2
1
2
0
1
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
2
0
1
0
0
2
1
2
0
2
0
2
0
1
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
2
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
7
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
2
0
0
0
2
0
0
2
0
0
0
2
2
0
0
2
0
0
1
0
0
0
0
0
1
1
0
2
2
2
2
0
0
0
0
0
1
0
0
0
0
0
2
1
2
0
0
1
1
0
1
0
3
0
0
1
1
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
3
0
2
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
1
5
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
2
0
2
0
2
3
0
0
0
0
0
3
0
1
1
0
0
2
0
0
7
0
1
1
3
0
3
0
2
0
0
0
0
0
2
0
0
1
0
1
1
0
1
3
0
1
1
2
0
2
1
0
0
0
0
2
0
0
2
1
0
1
2
0
2
0
0
0
2
0
2
0
2
1
0
1
0
0
0
2
0
0
0
2
1
0
1
0
2
0
2
0
0
2
0
0
0
0
0
1
0
0
1
0
2
2
0
1
0
0
0
1
0
0
0
0
2
1
0
0
0
1
0
1
0
0
1
0
0
2
0
0
0
2
2
4
0
1
0
1
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
1
0
1
0
1
2
0
0
0
0
2
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
2
0
0
2
0
0
0
0
0
3
0
0
0
0
0
1
2
0
0
2
0
0
0
2
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
1
0
3
1
0
2
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
1
1
3
0
0
2
0
0
1
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
4
2
0
0
0
1
3
0
0
0
2
1
0
0
0
0
2
1
0
2
0
1
0
0
1
0
2
2
1
0
2
0
2
2
0
0
0
1
0
0
0
2
2
0
0
0
0
0
1
2
0
0
0
1
3
0
0
1
0
2
2
2
0
1
2
0
0
0
0
1
0
3
2
0
1
3
2
0
2
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
2
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
1
0
2
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
7
0
0
1
0
0
1
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
2
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
1
0
2
0
2
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
3
1
0
0
0
0
2
0
2
0
2
1
0
0
0
2
2
0
0
0
0
1
2
1
1
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
4
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
2
0
3
2
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
2
2
0
2
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
1
0
0
0
2
0
1
1
0
0
0
2
0
2
0
2
1
2
0
0
0
0
2
0
1
2
0
1
0
2
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
1
2
3
0
0
0
0
0
0
3
2
0
0
2
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
2
0
1
0
0
0
0
0
2
0
1
0
2
0
2
6
0
0
2
1
1
0
1
0
0
0
2
5
0
0
0
0
2
0
1
0
0
0
2
1
1
0
2
0
3
1
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
1
1
2
1
0
0
0
0
2
0
1
0
2
0
0
2
0
0
2
1
0
0
0
0
2
2
0
0
0
0
2
0
1
0
10
1
1
2
0
0
1
0
2
2
1
0
1
0
1
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
8
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
2
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
2
1
0
0
0
0
2
1
2
0
2
0
0
2
1
0
0
0
0
2
0
1
0
1
0
1
1
2
1
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
2
0
2
1
0
0
2
0
0
1
3
0
1
0
0
1
0
0
1
2
0
0
2
2
0
0
0
2
0
1
0
0
1
1
1
2
0
2
0
0
0
0
0
1
2
0
0
0
1
1
0
0
0
0
0
1
2
0
0
2
1
1
4
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
2
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
2
2
0
12
2
0
2
0
0
0
2
2
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
2
2
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
1
0
2
2
2
0
1
1
0
0
2
0
1
2
0
0
0
1
0
0
1
0
0
0
2
6
3
1
0
0
0
0
0
1
0
0
1
0
1
1
1
0
0
1
0
0
0
2
1
0
2
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
2
1
2
0
1
0
0
1
0
2
2
0
1
0
0
0
2
0
0
2
2
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
1
2
0
4
1
1
0
0
0
2
2
1
0
1
1
1
0
0
1
0
0
0
1
0
1
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
1
0
1
0
0
0
2
0
2
1
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
2
0
0
1
2
0
2
0
1
1
0
0
0
0
0
2
2
0
0
0
2
0
0
0
3
1
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
1
0
1
2
0
2
0
0
2
0
0
0
0
0
2
2
1
0
2
0
1
0
2
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
2
1
2
0
1
0
0
3
0
0
0
0
0
0
0
0
0
1
2
0
2
1
1
0
0
1
0
0
2
2
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
2
1
1
0
0
3
0
0
0
0
2
0
0
2
1
0
1
1
0
0
2
1
2
0
1
0
1
3
0
0
0
1
1
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
1
0
2
0
0
2
0
0
0
0
2
1
1
0
0
0
0
0
2
0
0
0
0
2
0
2
1
0
1
2
1
0
0
1
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
1
2
0
0
3
1
0
2
0
0
0
0
1
1
0
1
0
0
0
0
0
2
0
2
0
0
2
0
2
2
2
0
2
0
0
1
0
0
1
2
2
0
2
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
2
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
2
2
0
0
0
2
0
0
2
0
2
0
0
1
1
0
0
0
1
0
2
0
1
1
3
0
0
0
1
1
0
0
1
0
0
0
0
0
0
2
0
0
0
2
3
0
0
0
0
0
0
0
2
0
0
1
6
2
0
0
0
2
0
0
0
1
1
0
1
2
0
2
0
3
0
0
0
0
0
1
1
0
2
0
0
2
2
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
3
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
2
1
0
0
0
0
1
0
0
1
0
0
0
0
1
2
2
2
0
0
0
0
0
1
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
1
0
1
1
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
1
2
0
2
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
1
2
3
0
0
0
0
0
2
2
1
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
2
1
0
0
2
11
0
1
0
0
0
1
0
2
1
0
3
0
0
0
0
0
0
0
0
2
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
1
0
0
2
2
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
2
3
0
2
0
0
1
0
0
2
0
1
0
0
0
0
0
1
1
1
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
2
2
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
3
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
2
4
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
2
0
1
2
0
0
1
1
0
0
0
0
0
2
0
1
0
0
2
2
2
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
2
0
2
0
0
0
2
0
2
0
0
0
1
1
0
1
0
0
1
0
0
2
1
0
2
0
0
0
0
1
0
0
2
0
6
0
0
0
0
0
0
2
0
4
2
0
0
0
2
0
2
0
2
0
0
1
0
1
0
1
0
0
0
0
1
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
2
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
2
1
1
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
2
2
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
2
2
4
0
0
0
0
0
2
0
0
0
3
0
0
4
0
0
0
0
0
1
0
0
0
1
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
3
0
0
2
0
0
0
2
2
0
0
0
0
0
1
0
3
1
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
1
2
1
2
0
1
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
2
0
1
0
0
0
2
0
4
0
0
2
2
0
3
0
0
0
0
1
2
0
1
1
0
0
0
0
0
0
2
0
2
0
2
0
0
1
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
2
2
0
1
1
0
1
0
2
0
4
2
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
1
1
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
2
0
0
2
1
2
0
0
1
0
0
2
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
1
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
1
0
0
2
0
0
0
0
4
1
0
0
0
3
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
3
0
2
0
2
3
0
3
1
4
0
1
1
0
0
0
1
1
2
0
0
0
0
0
0
0
0
1
7
1
0
2
0
0
0
1
0
0
1
0
2
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
2
2
1
0
1
3
1
2
3
2
0
0
0
0
1
0
1
0
0
1
0
1
0
0
2
2
2
0
1
1
1
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
1
0
2
2
2
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
2
1
2
0
2
0
0
0
0
0
1
1
0
0
1
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
2
2
0
0
2
1
0
1
0
0
2
0
5
0
0
0
0
0
1
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
2
0
2
0
2
0
0
0
2
0
1
0
2
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
2
2
2
1
0
0
1
0
0
3
1
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
2
1
1
5
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
3
1
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
2
1
0
0
0
1
0
1
0
0
0
2
1
0
0
0
0
0
2
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
1
2
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
1
0
1
0
0
1
0
4
2
1
0
0
0
0
0
0
0
0
2
3
0
0
0
0
1
0
3
0
1
2
0
0
1
1
0
0
0
0
0
2
0
2
2
0
0
2
0
0
0
0
1
0
0
0
1
0
2
0
0
1
0
0
0
0
2
0
0
1
2
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
2
0
1
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
2
0
2
0
0
0
0
0
1
0
1
0
2
0
0
1
0
3
2
0
1
0
0
0
0
0
1
3
0
0
0
2
0
1
2
0
1
0
0
0
0
2
0
0
0
0
1
0
2
0
2
1
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
1
1
2
0
2
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
2
0
0
0
1
0
0
2
0
0
0
1
0
2
0
0
2
1
0
0
0
0
1
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
1
0
2
0
0
1
0
2
2
0
0
0
0
0
0
0
0
1
0
3
0
1
0
0
0
0
0
3
0
0
1
0
0
2
0
0
1
0
2
0
2
0
4
0
0
0
0
2
0
3
3
0
0
0
0
0
0
2
2
2
0
2
0
0
1
2
0
0
0
0
0
0
1
0
2
0
1
1
0
0
0
0
0
0
0
1
0
0
1
1
2
0
0
0
0
1
0
0
0
0
1
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
1
2
1
1
1
0
0
1
0
0
2
0
0
1
0
0
0
0
2
0
1
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
1
0
2
0
1
1
1
0
0
2
0
0
8
2
0
1
0
1
0
0
0
1
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
2
1
0
0
0
0
2
0
1
0
0
0
0
1
2
1
1
0
1
0
0
0
1
1
0
0
2
0
0
0
2
0
4
0
0
1
0
0
0
0
2
1
1
1
2
0
0
6
0
0
1
0
2
0
0
0
1
0
0
0
4
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
1
0
0
2
0
0
2
2
0
0
1
3
1
1
0
0
3
2
0
0
3
2
0
0
1
1
1
0
0
0
2
0
1
0
3
0
0
1
0
0
0
0
2
0
0
0
0
0
1
2
0
0
1
2
0
0
0
0
0
0
0
1
0
2
0
2
0
2
0
0
1
2
0
1
0
0
0
2
0
0
1
0
0
0
0
1
2
0
0
0
1
3
0
0
0
0
0
0
2
0
2
2
0
0
0
0
2
0
0
0
0
0
1
2
2
0
2
0
1
2
1
2
0
3
2
2
0
0
0
0
0
2
2
0
1
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
1
1
2
0
1
0
1
3
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
1
2
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
1
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
3
0
1
0
0
0
0
0
0
0
1
2
2
0
0
0
2
1
0
0
2
0
2
1
2
2
0
0
0
0
0
1
1
2
0
2
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
4
0
1
1
0
1
1
0
1
0
2
0
0
1
0
1
2
2
0
0
0
2
2
0
0
1
0
0
0
3
1
2
0
2
0
0
0
2
0
0
0
2
3
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
1
0
1
1
2
0
0
0
0
2
1
0
4
1
0
3
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
2
0
1
0
2
0
1
1
2
0
0
0
1
0
0
0
3
0
2
0
0
0
1
0
0
0
2
0
0
3
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
6
1
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
2
2
0
0
0
0
1
4
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
2
2
2
1
0
0
2
0
0
0
0
2
0
0
2
1
0
1
0
0
0
1
2
2
0
0
0
0
2
2
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
1
2
2
0
1
2
0
0
0
0
0
0
1
2
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
2
1
0
0
1
0
4
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
1
1
0
2
0
0
0
0
2
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
1
1
2
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
1
0
0
0
0
0
2
2
0
2
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
2
0
0
0
0
0
0
2
0
2
1
1
0
0
2
0
0
0
1
0
1
2
0
4
2
0
3
4
0
0
0
0
1
0
2
0
0
3
0
2
2
2
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
3
0
0
0
1
0
2
0
0
3
0
2
0
0
1
0
0
0
0
1
0
2
2
0
0
0
0
2
0
0
0
0
0
1
0
0
2
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
8
2
2
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
8
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
2
0
0
1
0
2
0
2
0
0
0
0
0
3
0
0
1
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
2
1
0
2
1
1
0
2
1
0
0
0
0
0
1
2
0
0
1
2
0
1
6
4
0
0
0
2
2
0
0
1
1
0
0
0
0
0
0
0
0
0
1
2
0
0
3
1
0
0
1
0
1
2
0
0
0
0
0
2
1
1
0
0
1
0
0
0
0
0
1
0
1
2
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
1
2
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
3
0
0
0
0
0
1
0
2
1
2
1
0
0
1
3
3
1
0
1
0
2
1
0
0
2
2
0
2
2
1
0
0
0
1
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
1
2
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
3
1
0
0
0
2
0
0
0
1
0
0
1
0
0
0
2
0
0
1
0
2
0
3
2
0
0
1
0
0
3
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
2
2
0
0
3
2
0
0
0
0
2
0
1
0
0
0
0
3
1
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
3
0
0
0
1
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
4
1
0
2
1
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
3
1
0
0
0
0
2
0
1
0
2
1
0
1
2
0
1
2
2
0
1
0
0
0
0
1
0
2
1
0
1
0
0
0
2
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
1
0
3
0
0
0
0
2
1
0
0
3
0
0
2
0
0
0
1
0
2
1
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
1
0
1
0
0
1
1
1
0
2
0
2
0
1
0
0
0
0
0
0
0
3
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
2
0
2
0
1
1
0
0
0
0
0
2
0
2
0
0
2
0
0
0
2
0
0
0
1
0
1
2
0
1
1
0
2
1
2
0
0
0
0
0
0
2
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
2
2
2
0
2
1
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
2
0
0
2
0
2
0
1
2
0
0
2
0
0
2
0
0
0
1
1
0
0
0
4
2
0
0
0
0
1
1
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
2
1
1
0
2
0
2
0
0
0
1
2
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
2
1
0
0
1
0
0
0
0
1
0
0
1
2
0
2
0
0
0
2
0
0
0
0
0
0
1
2
2
1
0
0
0
3
2
0
0
0
1
1
0
1
2
2
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
2
3
3
2
1
1
0
0
1
0
0
2
0
0
0
0
3
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
4
1
1
1
1
0
0
0
0
1
0
0
2
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
2
2
0
2
0
2
0
2
0
0
2
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
1
2
0
1
1
0
1
0
0
1
2
0
2
1
0
2
0
0
0
0
0
0
2
0
2
0
1
0
2
0
2
0
2
0
1
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
2
2
0
2
0
0
0
0
0
0
2
0
1
0
1
2
0
0
1
2
2
0
0
0
1
0
0
0
1
0
0
0
0
1
3
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
4
3
1
1
0
0
1
0
2
0
0
0
1
0
0
2
2
2
1
0
0
0
2
0
0
0
0
0
0
1
0
2
2
1
0
2
1
0
0
2
0
0
0
0
2
1
3
0
0
0
2
0
0
0
1
1
0
0
1
0
1
0
0
2
1
0
0
0
2
0
2
0
1
0
1
1
0
1
2
0
0
0
0
2
0
0
0
0
1
0
1
2
0
0
0
0
2
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
2
0
0
1
1
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
2
0
2
0
0
0
0
0
1
2
0
1
1
1
1
2
0
2
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
4
3
0
2
2
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
1
2
4
0
2
1
0
2
0
0
0
0
2
0
0
3
1
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
2
1
0
3
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
2
5
1
3
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
2
2
0
1
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
2
0
2
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
2
0
1
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
2
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
2
13
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
2
0
2
0
0
2
1
0
0
0
4
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
2
2
0
1
0
2
1
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
1
0
0
2
2
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
2
0
0
1
0
1
1
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
2
0
0
1
0
0
2
0
0
3
0
0
2
0
3
0
0
4
1
0
1
0
1
2
0
0
0
0
0
2
0
0
2
0
1
2
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
2
1
0
2
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
2
0
0
2
0
2
0
3
0
1
0
1
0
0
2
1
2
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
3
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
2
0
1
1
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
11
0
0
2
2
1
0
2
1
1
1
0
0
0
0
0
1
2
0
2
2
0
2
0
1
0
1
2
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
2
0
0
0
2
7
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
2
2
0
0
0
0
2
0
2
2
0
7
3
0
1
0
0
0
0
0
0
0
3
0
2
1
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
1
0
2
0
0
1
1
1
0
0
0
0
1
0
0
1
0
0
0
2
2
0
0
0
0
0
0
2
0
3
0
0
1
2
2
0
2
0
0
2
0
2
0
0
0
0
1
0
2
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
2
1
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
2
1
1
0
2
1
0
0
0
0
1
0
2
0
1
0
0
1
2
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
1
2
2
0
0
0
6
0
2
0
1
0
0
0
0
0
1
0
2
2
0
0
0
0
1
0
0
1
0
2
0
3
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
3
1
0
0
0
2
1
0
0
0
0
2
0
1
0
0
0
0
1
0
1
0
0
1
1
2
1
0
0
3
0
0
2
0
0
0
0
1
0
1
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
2
2
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
1
2
2
1
0
0
0
0
0
0
1
1
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
4
0
0
0
0
0
0
0
2
1
1
1
1
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
1
0
0
1
0
2
0
1
4
2
0
0
0
5
0
1
2
0
2
0
1
2
0
0
0
1
0
0
1
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
1
0
0
0
2
0
0
0
1
2
0
2
1
0
0
0
0
0
0
1
0
2
2
1
2
0
0
2
2
2
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
1
4
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
1
0
1
0
0
3
1
0
1
0
0
2
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
1
2
2
0
0
0
0
2
1
0
0
2
1
1
0
0
0
1
0
1
0
0
0
0
2
0
2
0
1
1
2
0
0
0
0
0
0
1
0
6
0
1
1
0
1
0
0
2
0
0
0
0
0
1
2
0
1
1
0
0
3
0
0
2
1
0
0
0
0
2
0
0
0
1
2
0
0
0
1
2
1
0
0
0
0
2
0
0
0
1
1
0
2
0
0
2
0
0
2
1
2
1
0
0
1
0
0
0
2
1
1
0
1
0
2
2
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
1
2
0
0
2
2
0
0
0
0
0
0
2
0
4
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
1
0
0
1
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
3
1
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
1
1
0
0
0
2
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
1
2
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
1
1
1
2
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
2
1
0
0
1
0
0
1
0
0
0
0
1
2
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
4
0
0
2
0
1
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
2
2
0
0
0
0
0
0
0
3
2
1
0
2
0
0
1
2
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
6
2
1
2
1
2
1
1
1
1
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
2
0
1
2
2
0
0
0
1
0
0
2
2
0
1
1
0
0
0
1
0
0
1
0
0
2
2
0
0
0
0
0
1
0
0
3
0
0
0
0
0
1
0
1
1
0
1
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
3
2
1
2
0
0
2
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
2
2
1
0
0
2
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
1
0
2
0
0
1
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
3
0
3
0
0
0
2
0
0
1
0
0
3
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
2
1
0
2
0
0
1
0
0
1
0
0
2
0
0
0
0
3
0
2
2
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
2
0
2
0
1
0
0
0
1
3
0
0
0
1
0
3
0
0
3
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
5
0
0
2
0
0
0
1
0
2
0
0
0
0
2
0
0
0
1
1
0
0
0
5
0
0
0
0
1
2
1
2
0
2
2
0
2
1
2
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
3
2
1
0
0
1
0
0
0
1
0
2
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
2
0
0
2
0
0
0
0
0
2
2
2
0
0
2
4
0
0
1
0
0
2
0
2
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
1
1
0
0
2
0
1
1
0
0
0
2
0
0
1
1
0
1
0
0
0
0
0
1
0
2
0
0
0
2
1
2
0
0
0
0
1
0
0
1
0
0
0
1
1
1
0
5
0
2
0
0
1
1
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
1
2
1
4
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
2
1
2
1
1
0
0
2
0
0
0
0
0
0
6
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
12
1
0
1
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
2
0
0
3
0
2
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
1
0
2
0
0
2
2
2
0
1
1
0
2
0
0
0
0
3
0
0
3
2
0
0
1
1
0
0
0
0
1
0
1
0
1
0
1
0
1
3
0
0
0
0
1
0
0
0
1
1
0
0
0
2
1
0
0
2
0
0
8
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
1
0
0
0
0
0
0
1
1
2
2
2
0
2
1
0
0
2
2
0
2
0
3
0
0
0
0
0
0
0
5
0
0
2
0
2
2
1
0
0
3
0
0
1
0
1
1
0
1
0
0
0
2
0
1
0
2
0
0
0
0
0
0
2
0
0
2
2
0
2
0
0
0
0
0
1
2
0
2
0
0
2
1
0
1
0
3
3
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
3
0
0
2
0
0
2
1
0
0
0
0
0
0
1
0
3
0
1
0
0
0
1
0
0
0
2
0
0
0
0
2
2
0
0
2
0
2
0
0
0
2
0
0
0
1
0
2
2
0
2
0
0
1
2
0
2
0
0
0
0
2
1
0
0
1
1
1
3
2
0
0
0
0
2
0
0
0
0
3
2
0
0
3
1
2
1
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
2
1
0
4
0
1
1
1
1
0
2
0
3
1
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
4
0
0
0
1
1
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
1
2
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
2
0
0
2
0
1
0
0
0
0
0
0
3
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
2
2
2
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
1
0
0
0
0
1
1
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
2
0
2
0
2
0
0
2
0
1
0
0
0
2
0
0
0
0
1
3
0
0
0
0
1
1
0
0
1
0
2
0
1
0
0
0
1
2
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
1
2
0
1
0
2
0
0
0
0
0
2
1
0
1
1
0
0
0
2
0
0
2
0
1
0
0
1
1
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
2
0
0
2
1
1
0
0
1
1
0
0
3
2
0
0
0
1
0
0
0
3
0
0
0
1
2
0
2
0
2
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
5
0
1
2
0
0
0
0
0
2
1
1
0
0
0
0
0
0
1
2
2
0
1
0
0
1
2
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
2
1
0
1
2
2
0
1
0
0
0
2
1
0
0
0
1
0
1
0
0
1
0
1
0
0
0
3
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
3
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
2
0
1
3
0
0
1
0
0
0
0
2
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
2
2
0
1
1
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
1
0
2
1
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
5
0
0
1
1
2
0
0
0
0
0
0
0
1
0
2
2
1
0
1
0
0
1
0
0
0
1
2
1
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
2
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
2
3
0
2
0
0
1
0
0
0
1
1
0
0
2
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
4
0
0
0
0
0
0
1
1
1
2
0
0
0
0
0
0
0
1
0
1
0
2
0
0
2
2
0
1
0
0
0
2
0
0
1
0
2
0
2
0
0
0
0
3
0
0
1
0
0
2
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
2
1
1
0
0
0
0
0
0
0
1
0
0
1
2
1
0
2
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
1
0
0
0
2
1
0
0
0
1
0
1
1
1
0
1
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
2
1
0
0
2
1
0
0
0
0
0
0
2
0
2
0
0
0
0
1
4
2
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
1
5
0
0
2
0
0
0
1
1
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
2
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
2
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
2
1
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
1
0
3
2
0
2
0
0
0
0
2
0
0
3
0
0
0
0
0
0
2
0
1
0
0
2
0
4
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
2
0
1
1
0
0
2
2
2
0
0
0
0
2
0
0
0
2
1
2
0
0
2
4
2
1
0
0
2
0
1
0
2
0
1
0
0
0
0
0
0
0
1
1
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
1
0
2
0
0
0
2
0
0
0
1
1
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
6
0
1
2
0
0
0
0
0
2
0
0
0
1
0
0
1
0
1
1
1
1
2
3
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
1
0
2
1
0
1
2
0
0
1
0
2
0
0
0
0
0
2
2
0
2
0
1
0
0
0
1
0
1
0
2
1
0
0
0
0
0
0
2
2
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
4
0
2
0
0
0
2
0
4
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
2
0
0
1
0
0
0
0
0
1
1
0
0
0
3
0
0
1
1
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
2
1
0
0
1
0
0
0
0
0
0
1
2
1
0
0
0
0
1
1
2
0
0
0
0
0
0
2
0
1
0
2
2
0
0
0
1
0
3
0
1
0
0
1
2
1
0
1
0
0
0
0
1
0
0
0
1
2
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
2
0
2
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
2
0
3
0
0
2
2
0
2
1
0
0
3
0
2
0
0
0
0
3
0
0
0
0
0
0
2
1
1
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
2
2
0
1
0
0
1
0
0
0
2
0
1
0
1
0
0
0
1
0
0
1
1
1
0
0
2
0
0
0
2
1
0
2
0
0
2
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
2
0
2
0
1
2
2
0
0
0
0
0
0
2
0
0
2
0
2
0
0
1
0
0
1
0
2
1
2
2
0
1
0
0
1
2
0
0
0
1
2
1
3
0
0
0
0
0
1
1
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
2
2
2
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
3
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
2
1
0
1
0
0
1
0
0
0
2
0
2
0
0
1
1
1
0
1
1
0
0
1
0
2
0
0
0
1
0
0
0
1
1
0
0
2
5
2
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
2
1
1
0
2
0
0
0
0
0
4
0
2
0
0
3
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
3
7
0
1
1
0
0
0
0
0
0
2
2
0
0
1
0
0
1
0
0
2
1
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
2
0
1
0
0
0
0
0
1
2
2
0
0
2
1
0
2
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
4
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
2
1
0
0
2
0
0
1
2
0
3
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
2
0
1
0
0
0
1
2
0
2
0
1
1
0
0
0
0
0
0
0
2
1
0
0
0
1
2
1
0
0
3
0
0
0
2
0
0
0
0
0
2
1
0
0
1
0
0
0
2
0
0
0
8
1
2
0
1
0
0
0
3
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
1
1
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
2
0
0
0
2
0
2
1
0
1
1
1
0
2
0
0
0
2
0
0
0
2
2
0
0
0
1
0
0
1
1
0
0
0
2
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
2
2
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
1
1
0
0
1
0
0
2
0
0
0
2
0
2
0
0
2
0
0
0
0
0
1
2
0
0
1
0
1
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
3
1
0
0
0
1
0
2
0
0
1
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
1
0
2
0
2
2
3
0
0
0
0
0
1
0
2
0
0
0
1
0
0
1
1
0
2
0
2
0
0
3
0
0
0
0
0
0
1
0
3
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
1
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
2
0
2
2
2
0
2
0
0
0
0
1
2
0
2
1
0
0
0
0
2
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
1
2
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
2
3
0
2
2
0
0
2
0
0
0
1
0
0
2
0
1
0
0
0
3
0
2
0
0
0
2
0
1
0
1
2
0
0
1
2
0
4
0
0
0
0
0
0
1
0
0
2
2
0
2
0
1
0
1
1
0
1
1
0
0
1
0
2
0
1
2
0
0
2
0
0
0
0
0
2
3
0
0
0
1
1
1
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
2
2
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
1
0
1
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
3
0
0
1
0
0
0
0
1
3
0
3
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
2
2
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
1
1
4
1
0
0
0
0
1
0
1
1
1
0
0
0
1
2
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
5
0
0
0
0
0
0
2
2
2
0
0
0
0
1
0
1
0
0
2
0
0
0
0
3
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
2
0
1
0
2
0
0
1
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
2
1
2
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
1
2
2
0
2
0
0
0
2
2
0
0
2
0
0
0
2
2
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
2
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
5
1
0
2
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
6
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
2
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
2
1
2
0
0
0
0
0
0
0
0
2
1
0
1
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
2
0
2
0
2
2
0
0
0
0
0
0
0
2
1
0
0
1
2
0
0
0
1
2
0
0
0
0
0
0
1
0
0
1
0
2
2
0
0
0
2
0
0
2
0
0
1
0
1
0
0
0
0
2
0
0
0
2
0
1
0
0
2
0
2
1
1
1
0
0
2
1
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
2
0
0
4
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
1
0
2
0
0
0
2
0
0
0
2
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
2
2
0
0
1
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
1
0
1
0
0
0
2
2
1
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
2
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
2
1
1
2
1
0
0
0
0
0
0
1
0
2
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
2
1
2
0
0
1
0
0
0
1
0
0
0
2
0
1
1
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
1
0
0
0
0
0
0
3
2
1
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
2
0
1
1
0
0
0
2
0
1
0
2
2
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
2
0
0
1
1
0
0
1
0
0
0
1
0
0
1
0
1
2
0
0
0
0
5
1
0
0
0
0
0
0
1
2
1
2
2
0
1
0
2
0
0
0
0
0
2
0
1
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
1
1
0
0
0
0
0
0
4
2
0
0
0
3
0
0
2
0
0
0
0
2
2
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
1
2
2
1
2
0
0
2
1
0
0
0
1
0
1
0
0
0
0
0
1
2
0
0
0
0
0
2
0
2
1
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
2
0
0
0
2
0
2
0
0
0
1
1
4
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
2
5
0
1
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
2
2
0
1
2
0
1
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
2
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
2
0
0
1
0
2
1
2
0
0
0
0
0
1
1
0
0
0
0
3
2
2
2
0
0
1
2
0
0
2
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
2
0
0
0
1
0
2
0
0
1
1
0
1
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
4
1
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
1
1
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
3
0
0
0
0
1
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
2
2
1
1
0
0
0
0
0
2
0
1
0
10
2
0
0
0
0
0
0
0
1
1
0
0
0
3
0
1
0
2
0
1
0
2
2
0
0
2
0
4
0
1
0
2
0
1
0
3
2
2
0
0
1
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
1
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
3
1
0
0
0
2
0
1
0
0
0
0
2
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
3
0
0
2
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
1
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
1
2
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
2
1
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
2
0
0
1
0
1
1
1
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
1
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
1
0
2
0
0
0
0
0
0
0
1
3
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
2
0
0
0
0
2
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
1
0
0
1
2
1
2
3
0
1
0
0
0
0
0
0
0
1
0
2
0
0
3
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
1
0
2
2
1
1
0
0
0
1
2
0
1
0
0
0
0
0
0
0
1
0
1
0
0
2
0
3
0
0
1
1
0
1
0
0
1
1
1
2
0
0
2
0
2
1
0
0
0
0
2
0
0
0
1
1
0
1
0
0
0
0
2
0
0
0
1
2
0
1
0
0
1
1
1
1
1
0
3
1
0
1
0
0
0
0
2
0
0
3
0
1
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
3
0
1
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
1
0
1
0
0
1
1
0
2
4
0
1
0
0
2
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
1
0
1
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
2
2
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
1
2
0
0
0
2
0
2
1
0
2
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
4
2
1
1
2
0
2
0
0
0
0
0
0
0
5
0
2
0
3
0
0
0
0
0
0
2
1
2
1
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
2
2
0
0
0
1
1
0
1
0
2
1
0
1
0
0
2
5
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
2
2
2
0
1
1
1
1
0
3
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
2
0
0
2
0
0
0
1
0
2
0
0
0
0
4
0
4
0
0
0
3
2
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
2
3
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
2
1
2
2
1
1
2
0
1
0
0
0
1
3
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
1
0
0
2
0
0
2
1
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
1
5
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
2
0
1
0
1
0
2
2
0
0
0
2
0
2
0
0
1
0
0
0
3
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
3
0
1
0
0
0
0
0
0
0
2
2
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
2
0
1
0
1
1
0
0
2
1
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
2
0
1
0
0
1
0
2
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
2
0
0
0
0
2
0
2
0
0
2
2
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
5
0
0
0
0
0
0
0
1
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
1
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
3
2
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
2
0
2
4
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
1
0
1
2
3
0
0
2
1
0
3
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
2
1
0
0
0
2
2
0
0
2
1
0
1
2
0
0
1
0
0
0
0
2
0
2
2
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
2
0
0
1
0
1
0
0
0
1
1
1
2
1
1
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
2
2
0
2
0
2
0
1
0
0
1
0
0
0
0
2
0
2
1
0
0
0
4
2
1
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
2
1
0
0
2
2
2
0
0
5
1
2
1
0
0
0
2
0
0
2
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
2
0
0
0
2
0
0
1
0
0
2
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
2
0
0
1
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
2
0
0
2
2
0
0
1
1
0
0
0
0
2
0
2
0
1
2
2
0
0
1
1
1
0
0
0
1
2
0
0
0
0
0
0
0
2
2
1
0
0
2
0
0
0
0
0
1
0
0
1
0
0
2
2
0
0
2
0
0
0
0
2
0
1
0
0
2
0
0
0
0
1
0
1
0
0
1
0
2
1
0
1
0
0
0
4
0
0
0
1
0
0
2
0
0
1
2
0
0
0
0
1
1
2
0
1
0
1
0
0
0
0
0
0
2
0
1
2
0
0
2
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
1
1
0
0
0
0
2
0
2
1
0
0
3
2
0
0
0
2
0
2
0
1
1
0
3
2
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
1
2
3
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
2
0
10
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
2
0
0
0
1
2
0
1
0
0
0
2
0
0
2
0
0
2
0
2
0
0
1
0
0
0
0
1
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
2
0
0
0
0
3
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
3
0
0
2
0
1
0
0
1
0
0
0
0
3
0
0
0
1
0
1
0
0
0
0
1
0
2
0
1
0
2
0
0
2
0
2
0
1
0
1
0
0
1
0
0
0
2
0
0
3
2
0
0
0
0
2
0
0
1
3
0
0
1
0
3
0
0
2
2
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
3
3
0
2
2
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
4
0
0
0
0
0
0
1
2
0
1
0
1
0
0
0
0
4
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
1
1
0
1
0
0
1
0
0
0
0
0
1
2
0
2
2
0
15
1
0
0
0
0
0
0
0
0
0
2
2
2
2
0
2
2
2
0
0
2
0
0
2
3
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
1
1
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
1
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
3
3
2
0
1
1
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
7
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
2
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
1
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
2
1
1
2
2
0
0
2
0
0
0
0
1
2
0
1
1
0
0
0
0
3
0
0
1
0
3
0
0
0
0
0
2
0
1
0
1
0
0
2
0
1
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
3
2
0
1
0
0
1
0
1
0
0
0
0
2
0
0
1
0
2
0
0
0
2
1
0
1
0
0
3
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
3
0
2
1
1
1
2
0
1
1
1
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
1
0
2
0
2
3
0
2
0
0
0
2
0
0
2
2
0
0
0
0
1
0
0
2
0
2
1
2
1
0
2
0
2
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
1
0
2
0
2
0
0
2
1
2
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
2
0
0
1
0
0
1
1
0
0
0
2
0
0
0
1
0
0
1
0
0
2
0
1
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
2
1
0
0
2
0
1
0
0
2
0
0
3
0
2
0
0
1
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
1
1
1
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
3
2
0
0
0
2
1
0
0
0
1
0
1
0
0
0
1
2
0
0
0
0
0
0
0
1
1
2
2
0
1
0
0
2
4
4
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
2
1
1
0
0
0
0
0
1
0
0
1
2
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
1
0
0
2
1
1
1
1
0
0
9
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
2
1
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
2
0
0
0
0
0
0
1
0
1
1
0
0
2
2
0
1
2
0
0
0
0
0
1
1
0
2
0
0
1
0
1
0
2
0
0
1
0
0
1
0
1
2
1
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
1
0
0
2
0
0
0
0
0
0
1
0
1
0
0
3
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
1
2
2
0
1
1
2
0
0
0
0
2
0
0
0
0
1
2
0
0
0
2
1
0
0
0
2
0
0
0
0
1
0
1
0
2
2
1
2
0
0
0
0
0
1
0
2
2
0
0
0
0
1
0
1
0
0
0
0
2
0
1
1
0
2
0
2
1
0
0
2
2
0
1
1
0
0
0
0
0
0
0
3
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
1
0
0
1
1
0
3
0
2
0
0
1
0
0
2
0
2
0
0
1
0
3
2
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
3
2
0
1
0
0
0
0
1
0
0
0
2
0
1
0
0
0
1
2
0
0
0
2
0
0
2
2
0
1
1
0
0
0
0
0
2
0
3
0
0
0
2
0
0
0
0
0
2
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
1
1
0
0
0
2
0
0
0
1
2
0
3
0
0
0
0
0
0
0
0
0
3
1
1
1
2
1
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
1
1
0
0
0
0
2
0
1
0
0
2
0
1
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
1
0
0
0
2
2
0
1
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
1
2
0
0
1
1
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
1
0
1
0
0
2
0
0
0
0
0
1
0
0
2
1
0
0
0
0
1
0
0
0
0
0
1
3
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
2
1
0
0
1
1
1
0
1
3
2
0
0
0
0
0
0
0
1
0
0
0
0
0
4
1
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
2
0
0
2
0
1
2
2
0
0
0
5
0
0
2
0
0
1
4
1
2
2
0
2
0
0
0
1
2
0
0
2
4
0
1
0
3
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
2
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
3
1
0
0
0
0
1
2
0
0
2
1
0
1
2
2
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
1
0
2
0
0
1
0
0
0
2
0
0
0
0
0
3
1
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
3
0
2
1
2
0
1
0
0
0
0
0
1
1
0
0
0
0
0
2
0
11
0
1
2
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
1
2
0
8
0
0
1
4
1
0
0
1
2
1
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
2
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
5
0
2
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
1
0
1
0
2
0
0
0
0
1
1
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
2
2
2
0
0
1
0
0
0
0
2
0
0
6
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
1
0
0
2
0
2
0
0
1
0
2
0
1
0
0
0
0
2
0
1
0
1
0
0
0
0
1
0
0
0
0
2
1
2
1
2
2
0
0
0
2
1
2
0
2
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
1
0
1
0
0
0
0
0
0
3
0
0
0
1
2
0
0
0
1
0
0
1
0
2
0
0
0
1
0
2
0
0
2
1
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
1
1
0
0
2
0
0
1
0
0
0
0
1
2
0
2
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
1
0
0
8
2
0
0
0
1
0
0
0
2
0
0
1
0
0
0
1
0
0
0
3
0
1
0
0
0
0
1
2
2
0
2
1
0
0
0
0
0
0
0
3
1
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
1
0
2
1
1
0
0
1
0
2
0
1
0
0
0
1
2
1
0
0
2
2
0
0
0
0
0
2
0
0
1
2
0
0
0
0
1
0
0
0
2
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
1
11
0
0
0
0
0
0
1
2
0
0
0
0
1
1
1
0
0
0
2
0
1
1
0
0
1
1
0
1
0
0
2
2
0
1
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
1
0
2
1
0
0
0
0
0
2
0
0
1
2
0
0
1
1
0
0
1
1
2
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
2
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
1
2
1
1
0
1
0
2
0
2
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
3
0
0
0
1
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
2
0
0
0
2
2
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
1
2
2
1
0
1
0
0
0
0
0
3
0
0
0
0
2
3
0
0
0
0
0
0
0
1
1
2
0
0
1
0
0
2
0
0
0
2
0
0
3
0
0
0
0
2
0
0
1
1
1
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
2
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
2
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
1
1
1
0
1
0
0
0
1
0
4
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
2
0
2
1
0
0
0
0
0
0
2
2
1
0
2
1
1
0
0
0
1
5
0
0
3
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
3
0
0
0
0
0
1
0
0
2
2
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
2
2
2
0
0
6
0
2
0
0
2
1
3
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
2
0
2
0
2
0
0
0
2
0
2
0
0
0
1
0
0
0
0
2
1
0
0
1
2
0
1
0
2
1
0
3
0
0
0
0
2
0
2
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
3
0
0
0
0
0
2
0
1
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
3
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
1
2
0
4
1
0
0
0
0
0
0
1
2
2
0
0
0
2
0
0
0
0
3
0
0
0
1
0
0
0
2
0
2
0
2
5
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
1
0
1
1
3
0
1
0
0
0
1
0
1
1
0
0
3
0
0
1
0
2
0
2
0
0
2
0
0
0
0
0
0
2
0
1
1
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
3
0
1
1
0
0
2
0
0
1
0
0
2
2
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
2
0
0
0
0
0
1
0
3
0
0
0
2
2
0
0
0
2
2
0
0
0
2
1
0
3
1
0
0
0
0
0
0
1
0
5
0
0
2
2
1
0
1
0
0
2
0
0
0
0
2
2
0
0
0
0
0
2
3
1
0
0
0
0
0
0
2
0
3
2
0
0
1
0
1
0
0
0
1
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
2
2
1
2
1
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
2
1
1
2
0
2
2
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
2
1
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
3
0
0
0
2
0
2
2
0
1
1
0
3
0
0
0
2
2
2
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
1
1
0
0
2
0
3
2
0
0
0
0
0
0
2
0
0
0
0
2
1
2
0
3
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
2
1
2
0
2
0
0
2
0
0
0
0
2
0
1
0
0
1
1
0
2
1
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
5
0
0
0
0
0
2
0
0
2
0
2
0
0
1
0
0
1
0
0
0
0
0
0
3
1
0
0
1
0
1
1
0
0
2
0
1
0
1
0
0
0
0
0
0
0
1
1
0
3
4
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
1
0
2
0
2
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
1
0
3
2
0
0
1
4
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
11
1
0
0
0
0
1
0
1
0
0
4
0
0
0
3
0
0
2
0
1
0
0
0
0
0
0
0
0
2
2
0
0
1
2
0
0
1
0
2
0
0
2
0
0
1
0
0
1
2
1
0
0
0
1
0
2
0
1
0
0
1
1
0
0
1
2
0
0
0
0
2
0
2
1
0
0
0
2
1
0
1
0
0
0
0
0
0
0
4
2
1
0
1
0
0
2
0
2
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
1
0
0
0
1
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
2
0
0
1
0
0
1
2
0
1
0
3
0
0
0
0
0
0
2
0
0
3
1
0
0
0
1
2
0
0
0
1
0
0
2
0
0
0
3
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
3
1
2
2
2
0
0
0
0
1
0
1
0
0
2
1
0
0
0
0
2
0
0
0
1
2
1
1
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
3
1
1
0
3
0
0
2
0
0
0
0
1
0
0
0
4
1
2
0
0
5
1
2
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
2
0
1
0
0
2
0
1
0
1
0
1
0
2
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
4
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
2
2
0
0
5
0
0
0
2
2
0
2
1
2
0
0
1
3
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
2
4
0
2
0
2
0
0
0
0
0
1
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
2
2
3
0
0
2
0
0
2
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
1
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
2
0
1
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
1
2
1
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
2
1
0
2
0
0
3
0
0
1
0
5
2
0
2
0
1
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
2
0
0
2
1
1
0
0
2
0
1
0
0
1
2
0
0
0
0
0
0
0
1
0
2
0
1
0
0
3
0
1
0
0
0
0
0
0
0
2
2
0
0
0
4
0
0
0
2
0
2
0
1
2
1
0
0
1
2
0
4
0
0
0
0
0
0
2
0
0
1
1
0
1
2
0
2
0
2
0
2
0
2
0
0
0
1
0
1
6
0
0
0
0
2
0
0
2
2
0
0
0
0
1
0
0
2
0
0
1
2
0
2
0
1
1
0
0
0
1
0
0
0
0
2
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
1
4
0
0
0
0
1
0
2
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
1
0
0
0
0
2
4
1
0
2
0
0
0
0
0
2
0
1
0
1
0
0
0
2
0
2
0
0
2
1
3
0
0
2
0
0
0
0
0
2
0
0
0
0
1
1
0
2
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
1
0
0
2
2
0
2
2
0
0
3
0
0
1
1
0
0
0
3
0
0
0
2
1
1
2
0
0
0
2
0
0
0
1
1
0
0
1
0
2
1
1
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
4
0
0
0
0
1
1
3
1
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
2
0
2
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
1
0
1
0
0
0
1
0
0
2
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
2
0
0
0
0
0
0
3
0
0
0
0
2
3
1
2
0
0
1
0
0
0
1
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
1
2
0
0
0
2
2
0
0
0
0
0
0
0
1
1
0
0
1
0
1
1
0
1
0
0
1
2
1
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
2
0
0
0
0
2
0
0
1
1
2
0
0
0
0
0
0
0
1
0
3
0
0
0
0
2
0
3
0
0
0
1
1
2
1
0
0
0
0
0
0
1
1
0
0
0
0
1
1
2
1
2
0
1
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
3
1
0
1
1
1
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
2
0
2
0
0
1
0
0
0
1
2
0
1
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
2
1
0
0
5
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
3
0
0
0
0
0
2
0
2
0
0
1
0
0
1
0
2
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
1
4
0
1
1
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
1
2
2
0
0
0
2
0
1
0
0
2
1
3
0
2
2
0
0
0
0
0
1
0
0
0
3
0
1
0
0
0
1
0
0
2
0
0
0
2
0
0
0
2
2
0
0
2
0
0
1
0
0
0
1
2
0
0
0
1
0
0
1
0
2
1
0
0
0
0
0
0
2
2
1
2
0
1
0
0
2
2
2
0
0
1
5
0
1
0
0
2
1
0
1
1
0
0
0
3
4
2
0
1
0
3
2
0
1
0
2
0
1
2
2
0
0
0
1
0
0
0
0
0
0
0
2
1
2
0
0
1
0
0
0
0
4
1
0
1
2
0
0
0
2
0
0
0
0
0
0
2
2
0
0
1
0
2
0
1
0
0
0
3
0
0
0
0
0
1
0
0
1
1
0
1
0
1
1
0
2
0
2
0
0
0
1
0
1
0
0
0
2
0
2
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
1
3
0
0
0
2
2
0
0
2
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
6
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
5
0
0
0
3
0
0
2
0
0
0
0
2
0
2
2
1
0
0
2
0
1
0
2
0
0
1
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
2
0
2
2
0
0
0
2
0
3
1
0
0
0
2
0
2
5
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
3
1
0
0
0
0
0
2
0
0
0
0
3
1
0
3
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
2
0
0
1
0
3
1
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
1
1
0
0
0
0
0
0
1
5
0
1
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
2
0
2
1
0
0
2
0
0
1
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
1
0
0
0
0
3
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
3
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
1
2
0
0
2
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
3
2
0
2
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
2
1
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
1
1
0
0
3
0
0
0
0
0
2
2
3
1
0
2
0
1
2
2
1
0
2
2
0
0
0
0
2
0
2
0
1
0
0
2
2
0
1
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
2
0
0
3
0
0
0
3
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
1
0
1
1
0
2
0
0
0
0
0
1
0
3
3
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
3
0
2
0
0
0
2
0
5
0
0
0
0
0
0
0
2
0
0
0
1
3
2
0
0
0
0
0
1
0
0
0
0
0
0
2
1
1
2
0
1
0
0
0
0
1
0
0
1
2
0
0
0
2
3
0
0
1
0
0
2
0
0
1
0
1
2
0
0
0
3
2
1
0
0
0
2
0
0
0
0
0
1
2
0
1
1
0
2
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
5
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
1
0
1
0
0
0
0
4
0
0
0
1
0
0
1
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
2
0
0
0
1
3
0
0
0
0
1
0
0
2
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
2
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
1
1
2
0
0
1
1
0
1
0
0
0
2
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
2
2
0
1
0
0
1
0
0
1
0
0
0
0
1
0
2
1
0
0
2
3
2
1
2
0
1
0
0
2
2
2
0
2
0
1
1
0
0
1
2
0
0
2
2
1
0
0
0
0
0
0
0
0
0
2
2
2
0
1
2
0
0
0
1
0
2
1
0
2
2
0
0
0
1
1
2
0
0
1
0
1
4
0
0
2
0
0
0
1
2
0
1
2
0
0
0
2
1
0
0
0
0
2
0
0
0
1
0
0
1
2
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
1
0
1
0
0
0
0
0
0
0
2
0
0
3
2
0
0
0
1
0
1
0
2
0
2
0
1
0
2
0
0
2
1
0
0
1
2
0
0
0
1
0
1
0
0
2
0
2
2
2
0
1
0
0
0
0
0
1
2
2
0
2
2
1
0
0
1
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
1
2
0
2
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
5
0
2
0
0
0
2
0
0
0
1
0
0
2
1
2
0
0
0
1
1
0
2
1
0
0
2
2
0
2
2
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
2
0
1
0
0
0
0
0
1
0
4
0
0
0
2
0
2
3
0
0
2
0
1
0
3
1
0
1
1
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
1
0
1
0
1
2
0
0
0
0
1
0
2
3
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
2
1
0
0
2
2
0
0
2
0
0
0
1
0
0
2
2
0
0
0
0
0
2
0
0
0
0
2
2
0
2
0
0
0
1
2
0
0
1
2
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
2
0
1
0
0
0
6
0
3
10
0
0
0
1
1
0
0
2
0
1
0
0
0
0
2
0
0
0
0
1
1
1
0
0
0
0
0
1
1
0
1
0
2
0
2
3
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
2
0
2
0
1
0
0
0
1
0
1
1
0
0
0
2
0
0
0
1
0
0
2
1
0
0
0
0
1
1
2
0
0
2
0
2
1
0
2
2
3
2
0
0
2
0
0
1
0
1
0
0
0
1
2
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
1
1
1
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
2
1
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
2
2
0
0
0
0
2
2
2
2
0
1
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
2
0
0
1
0
0
0
0
0
2
1
1
2
0
2
0
0
1
0
0
0
0
1
0
0
1
0
2
1
0
0
0
0
0
1
0
0
1
1
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
5
0
0
0
1
1
1
0
0
0
1
1
1
0
2
0
0
3
2
0
0
0
0
0
2
0
1
0
0
2
2
1
0
0
0
2
0
1
0
0
2
2
0
0
0
0
0
0
0
1
1
0
1
2
1
2
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
2
1
0
0
2
0
0
0
0
1
1
2
0
0
0
1
2
2
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
2
0
0
2
2
0
0
1
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
2
1
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
1
0
0
1
0
0
1
1
1
1
0
2
0
1
0
0
0
1
0
0
2
1
0
15
0
1
1
2
0
0
0
1
1
0
0
1
0
2
0
0
3
2
2
0
0
0
0
0
0
0
0
2
1
1
2
0
0
2
0
0
2
0
2
1
1
0
2
2
0
0
1
1
0
1
2
0
0
0
3
0
0
0
0
0
2
0
0
0
1
1
0
0
2
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
1
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
3
0
0
0
2
2
0
0
7
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
5
1
1
2
0
0
2
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
1
0
1
2
0
0
2
1
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
2
2
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
2
2
2
1
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
12
0
1
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
3
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
2
0
2
0
5
2
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
1
0
1
0
2
0
0
1
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
3
0
2
2
0
0
2
2
2
1
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
1
0
0
1
2
1
2
0
0
2
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
4
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
2
0
2
0
0
0
4
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
1
1
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
1
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
1
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
3
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
4
0
0
0
2
1
0
0
0
0
3
0
0
0
1
0
0
0
0
2
0
1
0
0
0
1
0
2
0
0
0
0
0
0
1
0
1
1
2
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
1
0
0
2
0
1
0
0
0
0
2
2
1
0
0
2
0
7
0
0
0
0
0
2
1
3
0
0
0
1
2
2
0
0
0
1
0
0
0
2
0
2
0
0
0
0
2
0
1
0
1
3
3
0
2
0
1
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
2
1
0
2
0
2
1
0
0
0
0
1
0
0
1
0
1
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
1
1
2
1
0
1
2
1
1
0
2
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
1
2
1
1
0
0
2
1
0
2
2
0
1
0
2
0
1
0
0
2
2
0
1
0
2
2
0
1
0
2
0
0
0
0
1
1
0
0
2
0
2
0
1
0
1
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
2
0
2
0
0
0
3
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
1
2
4
0
0
0
0
2
1
2
0
0
0
0
0
0
1
1
0
2
0
2
0
1
0
0
0
0
0
1
0
2
0
2
0
0
2
0
0
2
0
0
0
0
2
0
1
2
0
0
1
0
1
1
0
0
1
0
2
2
2
1
0
0
3
0
2
2
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
2
0
2
2
0
3
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
3
0
4
1
0
1
2
0
0
0
2
1
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
1
4
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
1
0
0
0
1
0
3
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
2
1
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
4
0
2
0
0
0
0
0
0
2
1
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
2
0
2
0
1
1
0
0
0
2
1
0
0
0
2
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
2
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
1
2
3
0
1
0
1
2
0
0
0
1
0
0
0
1
0
2
1
1
0
0
1
0
0
0
1
0
0
2
2
0
2
0
0
1
2
0
1
0
0
2
1
0
1
0
0
0
0
0
0
0
0
2
0
1
1
0
2
0
0
0
0
0
0
0
0
2
1
0
0
1
2
1
2
0
0
0
0
0
0
0
0
1
1
0
1
0
1
2
2
2
0
2
2
1
0
0
0
0
0
0
0
0
2
0
2
1
0
0
2
0
0
0
0
2
1
0
1
2
1
0
2
0
0
2
0
0
2
0
0
0
0
0
5
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
2
0
2
2
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
2
0
0
3
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
2
0
0
0
0
2
2
1
1
0
0
2
0
2
0
2
0
0
0
1
0
0
0
0
0
2
2
2
0
1
2
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
2
2
2
1
0
0
0
0
0
0
0
3
0
1
1
1
0
0
2
0
0
0
1
0
0
1
0
1
0
1
2
1
0
3
0
0
1
0
2
0
3
1
1
2
0
0
0
2
2
0
2
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
4
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
1
0
1
0
0
0
0
2
1
2
0
0
0
1
0
0
2
1
1
1
3
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
2
0
1
2
1
0
0
0
0
0
1
0
0
1
0
3
0
0
0
2
2
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
2
4
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
2
1
0
0
1
2
1
0
4
0
2
0
1
0
0
2
0
1
1
0
0
1
2
0
0
1
0
0
2
1
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
1
0
1
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
2
2
1
0
2
0
0
2
0
2
0
1
0
0
1
0
0
1
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
1
2
0
0
1
0
2
0
1
2
1
0
0
0
0
0
2
1
0
0
2
3
0
0
5
2
1
0
0
2
0
2
0
2
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
2
0
0
0
0
2
0
0
0
1
0
1
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
2
2
1
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
1
0
2
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
3
0
0
2
2
0
0
0
0
0
2
0
1
0
0
0
0
2
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
1
0
0
0
1
0
2
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
1
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
1
0
1
0
0
1
2
0
0
0
2
0
2
0
1
0
3
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
1
3
0
0
1
1
1
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
4
0
0
1
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
2
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
4
2
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
2
0
0
0
1
3
0
0
2
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
2
0
0
2
2
2
0
2
0
0
2
0
2
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
1
4
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
6
0
0
1
0
3
0
0
0
0
0
0
1
1
0
0
3
0
1
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
1
1
0
0
1
0
0
0
1
0
0
1
2
0
3
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
2
2
0
0
0
2
1
2
0
1
0
1
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
2
4
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
2
0
0
2
2
0
0
1
0
0
0
0
1
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
2
0
0
1
2
2
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
2
1
2
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
6
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
1
0
1
0
0
0
2
0
0
0
0
1
2
2
0
2
0
0
0
1
0
0
0
0
0
1
0
0
3
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
2
0
3
0
0
2
0
0
0
0
0
1
1
2
0
0
2
1
0
1
0
2
0
2
1
0
0
1
0
0
1
0
0
1
0
0
0
0
2
0
2
0
0
2
0
0
0
2
0
0
0
0
2
2
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
2
0
0
0
0
1
2
2
0
0
2
1
0
2
0
0
0
0
1
0
0
0
1
0
0
2
2
0
0
1
0
1
0
0
0
0
0
1
0
2
4
0
2
0
0
0
0
0
2
0
0
2
1
1
0
0
0
0
0
2
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
1
0
1
2
0
0
0
0
0
0
1
0
6
2
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
1
0
1
0
0
0
0
1
1
0
1
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
2
0
1
0
2
0
0
0
1
2
0
3
0
0
0
0
2
0
0
0
0
1
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
2
3
0
1
0
0
0
2
1
0
1
1
0
2
0
2
1
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
1
2
0
1
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
2
1
0
1
0
0
0
0
0
0
0
0
2
2
2
1
0
0
0
0
1
1
0
1
2
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
1
1
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
1
0
1
0
0
0
1
0
0
0
0
2
0
0
0
1
0
2
2
0
1
1
0
2
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
2
1
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
1
2
0
0
0
1
2
0
0
1
0
1
0
1
0
0
1
0
0
0
3
0
0
0
0
0
0
2
0
1
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
1
0
2
0
2
0
2
0
0
0
1
0
0
1
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
1
0
0
2
2
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
4
0
2
0
0
0
1
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
6
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
1
0
1
0
2
0
0
0
2
0
0
0
1
0
0
0
2
0
0
2
0
2
0
0
1
0
2
0
0
0
1
1
0
6
2
0
0
0
2
0
1
0
0
3
2
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
3
4
0
2
1
1
2
3
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
1
0
0
2
2
1
0
0
0
2
0
1
0
0
0
1
0
0
1
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
1
0
0
0
0
0
3
0
0
0
0
2
1
0
2
1
0
0
1
2
1
0
0
1
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
2
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
3
2
0
2
0
1
3
1
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
2
2
0
0
2
0
0
0
1
1
3
0
0
0
0
0
1
0
0
0
0
0
2
2
0
1
0
1
0
3
0
2
0
0
0
0
0
2
1
0
0
2
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
1
0
0
1
0
1
0
2
0
0
0
0
0
0
0
1
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
1
0
3
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
2
3
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
1
0
2
0
0
1
0
0
0
0
2
0
1
0
1
0
1
1
1
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
1
1
4
0
0
1
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
2
2
0
1
0
1
2
0
2
2
2
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
2
0
0
0
0
2
2
1
2
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
2
2
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
1
1
0
0
1
2
2
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
2
0
0
0
1
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
1
0
0
0
1
1
0
0
3
1
1
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
1
0
0
2
2
2
0
0
0
0
0
0
0
3
2
0
0
2
0
2
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
2
0
0
0
0
0
1
3
2
0
0
0
2
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
2
0
0
0
1
0
0
1
0
1
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
2
1
0
0
0
1
2
2
0
0
3
0
0
1
1
0
0
2
1
0
0
0
0
0
1
1
1
0
0
1
0
0
0
1
0
0
2
0
2
0
0
0
1
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
2
0
0
0
3
0
1
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
1
2
1
0
0
0
2
0
0
2
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
2
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
1
0
2
0
1
0
0
0
0
3
2
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
2
5
2
0
0
0
1
0
3
0
0
2
0
0
0
0
0
1
3
0
1
2
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
2
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
1
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
3
3
0
0
0
0
1
0
0
0
4
0
1
0
1
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
2
0
3
0
0
0
0
0
1
0
0
0
0
4
3
0
0
3
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
1
4
0
0
0
1
1
2
2
1
0
1
2
0
3
0
0
2
0
0
0
0
0
2
0
2
0
0
0
1
2
2
0
0
0
2
2
0
0
0
0
0
0
0
1
1
0
1
0
0
3
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
1
2
0
0
0
0
1
2
0
2
0
0
0
0
2
0
0
0
0
2
3
1
0
0
0
2
0
0
0
2
0
0
0
1
0
0
1
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
1
0
1
0
0
0
1
2
0
0
0
1
0
0
0
1
1
0
3
0
2
1
0
0
0
1
0
0
2
0
0
0
2
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
3
0
0
0
0
2
1
1
1
0
0
1
0
1
0
0
3
0
0
2
0
1
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
3
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
3
0
1
2
1
1
0
0
2
0
0
0
1
0
0
0
1
0
2
0
6
2
2
0
0
3
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
2
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
1
0
1
2
2
0
0
0
0
0
0
1
4
0
0
0
2
0
0
0
0
0
0
3
1
2
0
1
2
1
0
0
0
1
1
0
0
1
2
0
0
2
0
1
0
2
0
1
0
0
0
1
0
0
0
0
0
0
3
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
3
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
4
2
0
0
2
1
1
0
0
2
3
2
0
0
2
0
0
0
2
1
0
2
2
0
3
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
2
1
0
0
0
1
2
0
0
0
0
2
1
3
0
0
2
2
1
0
0
2
0
1
0
0
0
5
0
0
0
0
0
1
2
1
0
0
0
2
2
0
0
1
0
0
0
2
0
0
1
1
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
3
0
0
1
0
0
0
1
0
0
1
0
0
0
2
2
0
1
0
0
2
0
0
2
0
5
2
1
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
3
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
2
1
0
0
0
1
3
0
0
0
0
4
0
2
0
2
0
0
0
0
1
0
0
1
1
0
0
0
0
2
0
0
0
0
2
0
2
1
1
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
3
0
2
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
1
0
3
0
0
2
0
1
0
0
0
0
0
1
2
0
0
0
0
1
1
2
1
0
1
1
4
1
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
2
1
0
2
0
2
0
2
0
2
1
0
2
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
1
2
1
0
0
4
0
2
2
0
1
0
0
1
0
0
0
2
1
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
2
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
2
1
1
0
1
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
6
0
0
0
0
0
2
0
0
0
0
2
1
1
1
1
0
0
2
1
0
0
2
0
0
0
2
0
0
0
0
2
2
1
2
0
0
0
0
0
0
0
2
0
2
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
1
0
0
2
2
0
2
0
0
2
0
0
0
0
0
1
2
0
0
0
2
0
1
0
1
1
0
0
0
1
0
0
0
0
0
1
0
3
1
1
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
2
2
2
2
0
0
1
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
6
0
0
0
2
0
0
2
0
0
2
2
2
0
0
0
2
0
1
0
2
0
0
1
0
0
1
1
0
0
0
0
0
0
2
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
2
0
0
0
2
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
1
0
1
0
1
0
1
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
1
1
0
1
0
0
2
0
0
2
1
2
0
2
0
1
2
0
0
3
3
1
0
0
0
1
2
0
4
1
0
1
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
2
1
2
2
0
1
0
0
0
2
0
0
0
2
0
1
2
0
0
0
0
2
0
0
0
0
0
0
2
0
2
2
2
0
0
0
1
3
0
0
0
3
2
0
2
0
0
0
1
1
0
2
0
0
0
2
0
2
2
0
0
1
1
0
1
0
0
0
0
0
1
1
1
0
1
2
1
2
0
0
0
2
1
0
0
0
0
0
0
0
0
2
1
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
1
0
2
0
2
0
0
0
0
1
1
2
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
2
0
0
1
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
2
0
1
1
0
0
0
1
1
0
2
0
1
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
1
0
1
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
1
2
0
5
0
0
1
1
0
0
2
0
0
1
0
0
0
0
0
0
2
2
1
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
2
1
0
0
3
0
0
0
0
1
2
0
2
0
2
0
1
2
0
1
2
0
1
2
0
0
0
3
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
1
0
2
0
0
0
2
1
0
0
0
0
0
2
0
1
1
0
2
0
0
1
0
0
0
0
0
1
1
1
0
1
0
0
2
0
1
0
1
0
0
0
0
0
2
0
0
0
2
0
1
1
1
0
0
0
0
1
0
0
2
2
2
0
1
2
0
0
0
2
0
0
0
0
3
1
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
1
0
0
2
0
2
0
0
0
0
2
0
0
2
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
1
2
0
2
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
2
0
0
0
1
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
3
0
0
0
0
0
1
0
2
1
1
0
1
0
0
4
0
0
0
0
0
0
0
1
0
3
0
0
0
2
2
0
0
0
0
0
3
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
3
0
0
2
0
1
0
0
0
2
0
2
0
0
0
0
0
0
3
0
0
0
0
1
0
1
1
0
1
3
2
0
0
5
1
0
0
1
0
2
0
0
0
1
0
0
1
0
1
0
0
2
2
2
0
0
0
0
0
0
0
0
1
1
2
1
0
1
0
1
1
0
0
0
0
0
1
2
0
0
0
2
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
2
4
1
0
0
2
1
0
0
0
0
0
0
3
2
0
0
0
2
0
0
2
0
0
0
2
1
0
0
0
0
0
0
2
0
0
1
2
1
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
2
0
2
1
2
2
1
0
0
0
0
0
2
4
0
0
0
3
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
2
1
1
0
0
0
0
1
2
0
1
0
1
0
1
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
2
0
0
2
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
2
1
0
1
0
0
0
1
0
0
1
0
0
0
2
0
0
1
2
0
1
0
0
0
2
0
0
2
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
1
2
1
0
0
0
1
0
0
2
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
3
0
0
0
1
0
1
0
2
0
1
2
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
2
1
0
0
2
0
0
0
2
2
0
1
2
0
0
0
0
1
2
1
2
0
0
0
2
1
2
1
0
0
0
1
0
2
0
2
0
0
2
3
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
1
2
0
2
0
0
3
2
0
0
0
0
0
2
0
0
1
2
2
0
0
0
5
1
0
0
2
0
1
0
1
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
3
2
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
1
0
2
0
0
1
0
1
1
0
0
0
2
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
1
0
2
0
0
2
0
0
0
0
0
0
2
2
1
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
1
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
3
0
0
0
0
0
2
0
1
2
0
1
0
2
0
3
0
0
0
2
0
0
2
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
6
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
2
3
0
0
1
0
0
0
2
0
0
0
0
0
1
2
0
2
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
2
1
0
2
5
2
4
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
2
6
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
2
0
0
1
0
2
0
0
0
2
0
0
1
0
0
1
0
0
2
0
0
2
4
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
1
0
3
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
2
0
0
5
0
0
0
0
0
0
0
1
1
0
1
0
2
0
1
0
2
2
0
0
0
0
0
1
0
0
2
0
3
1
1
0
2
0
0
0
1
0
0
4
0
5
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
10
0
0
1
1
0
2
0
0
0
0
0
0
0
1
2
2
0
1
0
1
1
1
0
0
2
0
1
0
0
0
4
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
1
1
2
1
0
0
0
0
2
2
0
0
2
1
0
0
3
0
1
0
2
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
1
1
0
0
1
0
0
0
1
2
3
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
3
0
0
0
2
0
1
2
2
0
0
2
0
2
0
2
0
0
2
0
0
2
0
2
0
0
1
1
0
3
0
0
0
1
0
0
0
1
1
1
0
1
0
0
0
0
0
0
2
3
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
1
1
0
2
0
0
2
0
0
1
0
1
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
2
0
0
1
0
2
1
2
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
2
0
2
2
0
0
0
0
0
0
2
0
0
0
1
1
2
0
0
0
2
0
0
2
0
0
1
0
2
2
0
2
1
0
4
1
0
0
0
0
0
1
2
0
1
0
0
0
2
0
1
0
0
0
2
0
0
0
0
1
2
1
1
0
0
1
2
0
0
0
2
3
3
0
0
1
0
0
0
0
4
2
0
0
0
0
0
0
0
1
1
0
0
0
2
0
2
0
0
1
2
0
0
1
0
0
0
2
2
0
0
1
0
1
3
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
2
0
2
2
0
0
1
0
2
1
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
2
0
0
2
2
0
0
0
0
0
0
0
1
0
1
0
1
0
2
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
2
0
0
1
0
0
0
0
3
1
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
1
0
2
0
0
0
0
0
0
2
1
1
2
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
2
2
0
1
2
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
1
3
0
5
1
0
0
3
0
1
2
0
2
0
1
0
0
0
2
1
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
1
2
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
2
0
1
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
3
0
0
0
1
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
6
0
1
0
1
0
1
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
3
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
1
1
0
2
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
1
4
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
2
2
0
1
0
1
0
0
0
2
1
1
0
1
0
1
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
1
0
1
0
1
1
0
0
2
0
0
1
0
2
2
0
3
0
0
1
1
0
2
0
2
0
0
1
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
1
2
0
1
0
0
0
0
0
0
0
0
3
2
2
1
0
2
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
1
2
0
2
2
0
0
0
2
0
0
0
0
0
1
2
0
2
0
0
0
0
2
0
0
1
0
1
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
1
2
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
2
2
2
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
2
1
0
1
1
1
3
0
0
0
0
0
0
1
0
1
0
1
0
0
0
2
0
0
0
0
1
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
2
0
3
0
0
2
1
0
2
4
2
0
0
0
0
2
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
2
0
0
0
0
2
0
0
0
2
0
2
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
1
0
1
1
1
0
0
2
0
2
0
0
0
0
0
2
0
2
0
1
0
2
0
0
0
0
0
3
0
0
0
0
0
0
1
0
3
0
2
0
0
1
0
0
2
0
0
1
0
0
0
1
0
2
0
0
0
2
0
2
0
0
0
2
0
1
0
0
0
0
0
2
2
0
0
0
0
0
1
0
2
0
0
2
0
0
2
1
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
2
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
1
1
0
0
0
0
2
0
1
0
0
0
2
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
2
0
0
0
0
1
0
3
0
4
0
2
0
0
0
0
0
0
2
0
0
0
0
2
2
1
0
0
0
2
1
0
0
0
1
2
0
0
1
0
0
0
0
0
0
1
1
0
0
5
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
2
0
0
1
1
0
0
3
0
0
0
0
0
0
0
2
1
0
1
1
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
4
0
1
2
2
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
9
0
0
1
0
0
0
0
0
0
2
0
0
4
1
0
2
0
0
0
0
0
3
1
1
0
0
0
2
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
3
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
1
2
3
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
3
0
0
2
2
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
3
0
1
0
0
2
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
1
3
0
5
0
0
2
1
2
0
0
1
0
0
0
1
0
0
1
0
1
0
2
2
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
2
0
0
1
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
2
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
2
1
2
0
0
0
2
0
2
0
0
4
2
0
2
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
2
0
0
1
3
0
0
0
2
1
0
2
1
1
0
2
0
2
1
3
0
0
2
1
2
0
2
0
0
0
1
1
0
2
0
0
0
0
2
0
0
3
0
0
2
2
0
2
2
0
1
0
2
1
0
2
0
0
0
0
0
1
0
1
5
2
0
0
0
1
0
0
2
1
0
0
0
2
0
0
6
0
0
0
2
0
0
0
7
2
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
1
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
2
1
0
1
0
0
1
1
0
1
1
0
2
0
0
0
0
4
0
1
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
1
0
0
2
0
0
0
1
5
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
1
1
2
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
4
1
3
0
0
2
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
1
2
0
0
2
0
2
1
0
0
2
2
0
0
0
0
1
2
0
1
0
0
0
0
2
3
0
3
2
0
2
0
2
2
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
1
1
2
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
2
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
1
2
0
1
0
1
0
0
2
2
1
0
0
2
0
0
0
0
0
0
0
2
0
1
1
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
1
0
0
0
0
1
0
0
2
0
0
0
4
1
1
0
2
0
0
0
2
0
0
0
2
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
3
0
0
0
1
2
0
1
0
0
0
2
0
0
1
0
0
0
0
2
0
1
1
0
2
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
2
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
1
1
0
0
2
1
1
2
0
0
0
1
0
0
2
0
0
0
1
2
2
2
0
0
0
0
0
0
0
3
0
2
0
1
0
0
1
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
1
0
0
2
0
1
1
0
0
0
0
0
0
0
2
0
0
1
0
0
3
0
0
1
1
0
1
0
2
0
1
0
2
0
0
2
1
2
1
0
2
0
0
1
0
1
0
0
1
4
2
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
3
0
1
0
0
0
0
2
0
2
0
0
2
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
1
0
0
7
2
2
0
0
0
0
0
2
1
0
1
0
2
1
0
0
0
1
1
1
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
2
2
0
1
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
1
0
1
0
2
1
0
0
0
2
0
0
1
2
1
1
1
2
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
1
0
0
0
1
0
0
1
1
0
0
0
1
0
2
0
3
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
2
0
1
0
2
2
0
0
2
0
0
0
0
0
1
0
0
0
4
0
0
1
2
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
2
2
0
0
1
1
0
0
4
0
0
1
0
0
1
0
0
2
0
1
2
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
2
0
2
0
1
0
2
1
0
0
0
2
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
3
0
0
0
1
0
0
1
0
2
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
2
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
1
0
1
0
2
0
2
0
0
0
2
0
0
2
0
0
0
0
2
0
0
2
0
1
0
0
0
2
2
0
0
0
2
0
1
1
0
0
0
3
1
0
0
0
0
2
1
0
0
0
0
0
0
0
1
1
0
0
1
2
0
2
0
0
0
0
0
0
0
3
2
0
1
0
0
2
1
0
0
0
0
0
0
0
2
0
1
0
1
0
0
1
1
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
1
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
2
1
0
0
2
0
0
1
2
0
0
0
0
4
0
0
0
1
2
0
0
2
0
0
0
1
1
0
0
0
0
0
9
0
0
0
2
1
2
1
0
0
0
0
2
2
0
1
0
1
3
0
0
2
0
2
5
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
2
2
0
0
0
3
0
1
2
0
0
0
1
1
0
1
2
0
0
0
1
0
0
2
0
2
0
2
2
1
1
2
0
0
2
0
0
2
0
0
0
0
1
2
2
1
2
0
0
0
0
0
2
1
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
2
2
0
0
2
0
0
0
3
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
2
1
2
0
0
0
2
3
1
0
1
0
1
1
0
0
0
0
0
0
2
0
3
2
1
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
2
0
0
1
2
0
0
1
0
0
0
0
2
0
0
0
3
0
0
1
2
0
0
0
1
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
3
0
0
0
0
1
0
0
2
0
1
0
2
0
0
2
0
1
0
1
2
0
0
1
2
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
2
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
2
1
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
2
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
2
0
0
0
2
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
1
1
0
2
0
0
2
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
3
0
0
0
0
0
2
2
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
2
0
0
1
2
0
0
3
0
0
2
2
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
3
1
0
0
2
1
0
2
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
1
0
0
0
0
2
0
0
1
0
0
0
2
2
1
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
1
5
0
0
1
0
0
0
0
0
1
2
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
2
1
0
1
0
0
0
0
0
1
1
2
0
2
0
1
0
10
0
6
0
1
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
1
0
1
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
7
1
0
1
0
1
0
0
0
0
2
0
0
2
2
0
0
2
0
0
1
1
0
0
0
0
2
1
2
0
0
2
0
0
2
0
0
0
2
1
1
0
0
0
0
0
0
2
0
0
1
2
0
1
0
1
0
2
0
2
0
2
2
0
2
0
0
2
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
1
2
0
2
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
1
0
1
0
0
0
0
0
1
0
1
0
0
2
2
0
1
0
3
2
1
0
0
0
0
0
1
0
0
0
0
2
5
0
0
0
0
1
0
0
0
0
1
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
2
1
0
0
0
1
2
2
2
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
3
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
2
1
1
0
1
2
1
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
3
0
0
1
2
0
0
0
2
0
2
0
0
4
0
0
0
1
0
0
0
2
1
1
0
0
0
0
0
2
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
2
1
1
4
0
0
0
3
0
0
1
1
0
0
1
0
0
0
0
3
0
1
0
0
0
0
1
0
2
0
1
0
1
1
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
2
0
0
2
0
0
0
3
0
0
0
2
0
0
2
2
0
0
0
0
0
5
3
0
0
0
0
0
3
2
0
0
2
0
0
2
0
1
0
0
2
1
2
0
0
0
0
1
0
1
0
2
0
0
0
0
2
0
0
0
1
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
2
0
0
1
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
1
0
4
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
1
1
0
0
2
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
1
1
1
0
2
2
0
2
0
0
2
0
0
1
0
0
0
1
1
1
1
0
2
0
2
1
0
0
3
2
0
1
0
2
0
0
1
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
3
0
0
0
1
0
0
0
0
2
0
0
0
0
1
3
0
2
0
2
2
0
0
0
2
1
0
0
0
1
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
1
1
0
0
0
0
1
0
0
0
2
0
1
1
2
0
2
0
0
0
0
0
2
0
2
0
0
2
0
0
0
1
0
0
0
2
2
1
0
0
0
0
2
0
1
0
1
1
0
2
0
1
0
2
1
1
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
1
2
0
0
0
0
2
3
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
1
2
2
0
0
2
3
0
2
1
2
0
2
0
0
0
4
1
0
0
1
0
0
0
0
2
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
2
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
2
1
1
0
2
2
2
0
0
1
0
0
0
2
0
0
0
2
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
2
0
1
1
0
0
0
0
2
0
2
0
1
0
2
0
0
0
0
2
1
0
0
2
0
0
0
2
0
2
1
0
0
1
0
0
0
0
0
0
2
0
2
3
0
0
1
1
0
0
0
1
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
3
0
1
0
1
0
0
0
0
0
0
0
0
1
1
1
0
1
0
2
0
1
0
1
1
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
2
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
2
0
2
0
0
3
0
0
0
2
1
0
0
2
0
0
2
0
0
1
1
1
0
0
0
0
0
0
1
2
1
0
0
0
1
0
0
2
0
0
0
2
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
1
2
2
1
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
1
0
0
0
0
3
4
2
1
2
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
5
0
1
0
0
0
1
0
0
0
0
0
2
0
1
0
0
2
0
3
0
0
0
0
0
0
0
2
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
2
2
0
1
0
0
1
2
0
0
0
0
2
0
0
2
2
0
2
0
0
0
2
0
0
0
0
0
2
2
0
0
2
0
0
1
4
0
0
0
2
0
2
1
0
1
0
0
0
1
2
0
0
0
1
0
2
0
0
0
0
1
2
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
1
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
5
0
1
0
2
0
0
0
2
0
1
0
0
0
2
5
0
0
2
1
0
0
0
0
0
3
0
0
0
0
0
2
1
1
2
0
0
0
0
0
0
2
1
2
0
0
0
2
0
1
0
2
0
2
1
0
0
0
0
0
0
0
1
2
0
0
2
0
0
1
0
1
0
1
1
2
2
0
1
2
2
0
0
0
0
0
1
0
2
0
0
3
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
2
0
4
0
4
0
0
0
0
2
0
0
2
1
2
0
5
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
1
1
0
2
2
0
2
0
2
0
1
0
2
2
1
1
0
1
1
2
1
0
0
0
0
2
0
1
0
0
0
4
0
0
2
2
2
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
2
1
0
0
2
1
0
0
0
0
0
0
2
2
0
1
1
1
0
1
0
1
2
0
1
0
3
1
1
0
1
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
3
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
2
0
6
0
1
1
0
0
0
0
1
1
1
0
0
3
2
0
6
0
3
2
2
0
0
0
0
1
0
0
2
0
0
1
0
2
2
0
0
0
0
0
2
0
0
0
0
0
1
0
4
0
0
0
0
0
0
7
1
0
0
0
0
0
0
0
0
2
1
0
2
1
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
3
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
2
2
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
1
1
2
1
1
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
2
0
0
2
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
2
2
2
3
0
0
2
1
0
1
0
0
2
0
0
0
0
0
4
0
1
0
0
1
1
0
0
0
0
0
0
2
0
2
0
0
2
0
1
2
3
0
0
1
0
0
1
0
0
2
0
0
2
0
0
0
0
0
1
1
2
0
1
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
1
0
0
0
3
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
1
0
0
1
0
0
2
0
1
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
3
2
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
1
0
1
0
0
0
0
0
0
0
2
1
0
0
0
2
1
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
1
0
2
1
0
0
0
0
0
0
2
0
1
0
1
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
1
0
1
2
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
3
0
3
0
2
0
0
2
0
0
0
0
2
0
2
3
0
0
0
2
0
3
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
3
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
1
0
1
0
0
0
0
0
1
0
1
1
0
0
0
2
0
2
1
4
0
0
0
0
0
2
1
0
0
2
0
0
0
1
2
0
0
0
2
0
0
0
0
2
0
0
3
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
1
2
0
0
0
2
0
0
1
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
3
1
1
2
2
0
0
1
0
1
2
4
0
0
0
0
0
0
0
0
0
0
0
1
2
1
1
0
0
2
0
1
0
0
2
1
1
1
1
0
2
0
0
0
0
2
1
0
0
1
0
0
2
1
2
0
0
4
0
0
0
2
0
0
0
0
0
0
1
0
1
0
1
2
0
0
0
0
3
2
0
0
2
4
0
0
0
4
0
0
1
0
0
0
1
0
0
1
1
1
0
0
1
0
2
1
0
0
0
1
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
2
1
0
1
2
0
0
2
0
2
2
0
0
0
0
0
0
2
1
3
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
5
0
1
0
2
0
2
0
2
0
0
1
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
2
2
1
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
1
1
0
0
0
0
0
1
0
3
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
1
0
0
0
0
1
0
1
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
1
0
0
2
0
0
0
0
0
0
1
0
0
3
1
0
0
1
0
2
1
1
0
3
2
0
1
0
3
0
0
0
0
0
2
0
0
1
1
1
0
2
2
0
0
2
0
1
0
1
0
3
0
0
0
0
0
0
1
0
2
1
0
0
0
1
0
0
0
2
1
2
2
0
0
1
0
5
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
4
0
1
0
0
0
0
0
2
0
2
1
2
2
1
0
0
0
0
0
1
0
0
0
2
3
1
2
0
0
1
1
0
0
1
2
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
2
2
1
0
0
2
0
1
0
1
2
0
1
0
0
2
0
0
0
2
1
0
0
0
0
0
1
2
0
0
2
2
1
1
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
4
2
2
0
2
2
0
0
1
0
2
0
2
0
2
0
2
0
0
0
2
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
1
0
1
1
0
0
0
2
0
0
0
0
0
1
1
2
2
2
0
0
0
2
3
0
2
2
0
0
0
0
2
1
0
0
0
2
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
2
0
0
1
0
2
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
1
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
2
0
2
0
1
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
2
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
2
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
1
1
1
3
1
0
1
0
2
0
0
0
0
0
2
0
2
0
2
1
0
0
0
0
0
2
0
0
2
2
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
1
2
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
3
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
3
0
1
0
0
0
1
2
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
1
2
1
0
1
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
1
1
0
0
1
2
0
0
2
1
0
0
0
1
0
0
0
0
0
1
2
0
0
0
2
0
1
0
0
0
1
0
1
1
0
0
0
2
0
0
0
1
1
2
0
0
0
1
0
0
1
0
1
2
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
2
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
1
2
0
0
1
0
0
0
0
2
0
0
1
0
1
4
0
0
0
1
0
0
0
0
2
4
2
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
1
0
0
0
5
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
2
0
0
0
0
0
0
0
2
0
4
0
0
1
0
3
2
0
0
0
1
1
0
0
0
0
0
1
1
2
6
0
2
0
2
4
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
1
2
0
0
2
0
0
0
0
0
2
2
2
0
0
2
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
3
2
0
0
0
0
2
0
0
2
0
1
0
0
1
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
1
0
0
1
2
0
0
0
0
1
0
2
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
3
2
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
1
0
2
1
1
1
1
0
0
0
5
0
0
0
0
0
0
1
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
1
1
0
0
0
0
0
1
0
1
0
5
0
0
3
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
3
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
2
2
7
1
1
0
1
2
0
0
0
1
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
3
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
3
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
2
0
2
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
2
0
1
2
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
2
0
1
0
3
1
1
0
0
0
1
0
1
1
0
1
0
0
2
1
2
1
1
0
0
0
0
0
0
1
0
1
4
2
1
2
0
0
2
1
0
0
2
0
0
2
0
0
0
0
0
0
0
4
2
1
2
0
0
0
0
0
2
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
3
0
1
0
0
0
0
0
0
0
3
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
1
1
1
0
0
1
0
0
0
0
1
0
0
2
0
1
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
1
3
0
1
2
2
0
2
0
0
0
3
1
0
0
0
0
1
0
0
2
0
0
3
0
0
3
0
0
0
1
2
0
0
0
0
2
1
0
0
0
0
0
0
2
2
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
3
0
0
2
0
1
2
2
0
0
2
0
0
0
2
0
0
1
1
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
2
1
2
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
2
0
2
0
0
0
1
0
0
1
0
3
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
2
0
0
2
0
0
0
0
0
0
0
1
2
0
0
1
1
0
2
0
0
0
0
2
0
0
2
2
2
0
1
0
0
0
2
0
1
0
2
0
2
0
0
0
1
2
2
0
0
0
1
0
0
0
0
1
0
2
0
0
0
2
0
0
1
0
0
0
2
0
1
0
0
0
3
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
1
0
0
2
0
0
3
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
2
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
2
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
2
2
0
0
0
1
2
0
0
0
2
2
0
1
2
2
0
0
2
1
0
1
0
2
0
0
0
0
1
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
1
0
2
1
0
2
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
2
0
3
0
3
0
0
0
2
0
1
2
2
2
0
2
0
0
0
1
0
0
0
0
1
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
1
1
3
0
0
0
2
0
2
0
0
1
0
0
0
0
2
0
0
1
0
2
1
0
2
0
0
0
1
0
2
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
2
1
1
2
0
0
1
0
0
1
0
0
0
1
0
0
0
1
1
2
0
1
3
2
0
0
1
0
7
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
2
2
7
0
0
0
0
1
0
0
1
0
2
1
0
0
1
0
2
0
1
0
0
0
2
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
2
2
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
1
1
0
1
0
0
0
0
0
2
0
1
0
1
1
2
0
3
1
0
2
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
1
0
1
0
1
0
0
0
0
0
0
2
0
2
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
2
0
0
0
0
0
4
0
1
0
0
0
0
1
0
0
3
0
1
0
0
1
2
0
0
1
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
1
1
0
0
2
0
0
0
0
2
0
2
1
6
1
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
2
1
0
0
0
0
3
0
2
1
0
2
0
0
0
0
1
3
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
2
1
0
0
0
3
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
1
1
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
1
2
1
1
0
0
3
0
0
0
1
0
0
0
4
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
2
0
1
2
0
1
1
0
0
0
0
0
0
1
1
2
2
1
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
3
0
1
0
1
1
1
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
1
2
0
1
2
1
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
2
0
1
0
0
0
2
0
2
0
2
0
0
0
2
0
1
0
3
0
2
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
2
0
1
1
3
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
2
2
0
2
0
1
2
0
0
0
2
0
0
2
1
1
3
0
2
0
2
0
0
1
0
0
0
0
0
0
3
0
0
1
0
0
1
0
0
0
0
2
1
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
3
2
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
1
0
0
0
0
1
1
0
0
0
0
0
0
5
0
0
2
0
0
0
1
2
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
2
0
3
2
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
1
0
0
3
2
1
0
0
0
0
0
0
0
4
0
0
0
0
1
2
3
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
2
1
0
1
0
0
0
1
0
0
0
0
1
0
1
1
0
2
2
0
0
1
0
3
0
0
0
0
1
0
0
2
0
0
1
0
2
0
2
1
2
2
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
2
1
0
1
0
0
0
2
2
0
2
2
0
0
0
0
2
2
0
0
0
1
0
4
0
0
0
0
0
0
2
2
0
1
0
0
0
2
0
0
2
1
0
2
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
3
0
2
1
0
0
0
0
1
0
2
0
0
0
0
0
3
0
0
0
0
0
2
0
0
2
0
0
1
2
2
0
0
0
0
2
0
1
3
1
0
0
2
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
2
2
0
0
0
0
2
2
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
1
0
0
2
0
1
0
0
4
0
0
2
0
0
0
3
0
0
0
0
1
0
1
2
0
0
1
2
0
0
0
0
0
0
0
0
4
0
0
2
1
2
0
0
0
2
0
2
0
3
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
2
2
0
1
1
0
0
0
1
0
0
0
1
1
0
0
2
2
0
0
0
1
0
2
0
0
0
1
0
0
2
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
2
0
0
1
0
1
0
0
0
2
2
0
1
0
0
0
0
1
0
0
0
0
0
3
2
2
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
2
1
1
1
2
0
2
0
2
0
1
1
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
1
0
1
0
0
2
1
2
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
4
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
2
1
0
0
0
2
0
2
0
0
3
1
2
1
0
0
0
0
2
1
2
1
8
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
1
2
2
1
0
0
0
0
1
2
0
0
0
0
1
0
2
0
0
0
0
0
0
3
0
1
0
0
0
0
0
2
0
0
0
0
2
0
2
1
0
0
0
0
1
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
2
2
2
2
2
1
0
0
0
0
0
2
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
1
0
2
0
1
0
2
0
0
1
0
0
0
2
0
0
0
1
1
1
0
2
0
2
4
0
2
0
1
1
2
0
1
0
0
1
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
1
0
0
0
2
2
1
0
0
0
2
0
0
0
1
2
0
0
2
0
0
2
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
2
3
1
0
0
0
0
0
1
1
0
0
2
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
2
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
3
2
2
1
1
1
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
1
1
1
1
0
0
0
2
3
1
3
0
0
0
3
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
1
0
1
2
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
2
0
0
0
1
2
4
0
0
0
0
0
2
0
0
0
0
4
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
3
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
2
1
0
0
0
0
0
2
0
1
2
1
0
0
2
0
0
1
0
0
3
1
1
0
1
0
1
2
0
0
0
1
0
0
0
1
0
1
0
2
3
0
0
0
2
0
0
0
1
0
0
0
1
1
2
0
0
0
0
1
0
2
0
0
0
4
0
0
1
2
0
0
1
0
0
0
1
0
2
0
2
0
0
0
0
1
2
0
0
1
0
1
2
0
0
0
0
1
0
2
0
1
4
0
1
2
0
0
0
2
0
1
0
1
0
0
0
0
0
1
1
0
0
2
0
1
0
0
0
0
0
5
0
2
0
0
2
0
0
1
4
0
1
1
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
2
0
0
3
1
0
2
0
0
0
2
1
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
2
1
0
2
0
0
0
0
1
0
2
2
0
0
1
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
1
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
1
2
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
3
0
2
2
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
2
0
0
1
0
0
1
0
0
3
0
0
0
0
1
3
0
0
1
1
0
0
0
0
0
4
5
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
1
2
0
0
1
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
2
2
2
0
0
1
1
0
0
0
1
1
0
0
1
0
0
0
2
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
5
2
0
0
1
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
2
1
0
0
0
0
0
1
0
2
0
2
0
0
0
0
1
0
0
0
0
2
1
0
0
0
1
0
0
0
1
2
0
0
0
2
1
1
3
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
1
0
0
1
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
1
1
3
0
0
0
2
1
2
0
0
0
1
2
0
1
3
0
0
2
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
1
0
2
0
0
0
1
2
0
0
0
1
1
0
2
0
0
0
0
0
3
1
2
0
0
1
0
1
0
0
1
0
0
0
0
1
2
1
2
2
2
2
1
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
1
1
0
0
0
1
0
1
1
0
0
0
0
2
0
1
1
0
1
0
0
0
0
2
1
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
2
2
0
0
0
0
0
0
2
0
2
2
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
2
0
1
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
1
0
0
0
0
0
2
0
0
1
2
2
0
1
0
0
0
1
0
0
0
2
1
0
1
0
0
0
2
1
0
0
0
0
2
0
4
0
1
0
0
0
1
2
2
1
0
2
0
1
0
2
1
1
0
0
1
0
2
0
1
0
1
0
0
0
2
2
1
0
0
1
0
0
0
0
1
2
0
0
0
2
1
1
2
1
2
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
2
1
1
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
1
0
0
1
0
0
0
0
1
0
2
0
1
0
0
0
2
0
0
0
2
0
1
0
0
0
1
0
0
2
0
1
2
0
0
0
0
1
1
0
2
2
1
0
2
0
0
0
0
6
0
2
0
0
3
2
0
2
0
0
0
2
2
0
0
2
0
0
0
0
0
2
2
2
0
0
1
0
0
3
1
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
5
0
0
2
0
2
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
1
2
0
2
0
2
1
0
2
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
4
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
1
0
0
0
2
0
0
0
3
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
3
1
0
0
0
1
1
0
0
0
3
0
0
1
1
0
2
2
2
0
2
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
2
0
2
2
0
1
0
0
2
0
4
0
3
0
0
0
1
0
0
0
5
0
0
0
0
0
1
0
1
0
0
2
0
0
1
0
2
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
2
1
4
2
2
0
1
0
1
0
0
0
0
0
2
2
2
1
0
0
2
2
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
3
0
1
0
0
0
0
2
0
0
2
1
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
3
3
0
0
0
1
1
0
0
0
2
1
0
1
0
2
0
2
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
1
0
0
0
4
0
0
1
0
0
1
1
0
0
2
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
2
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
2
1
1
0
0
2
0
0
2
2
0
2
0
0
0
1
0
2
0
1
0
0
2
3
0
0
1
0
2
0
2
2
0
0
0
0
0
0
0
2
0
2
1
1
0
0
2
0
0
1
5
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
2
0
2
0
0
0
0
2
1
2
1
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
2
0
3
0
1
0
0
0
0
0
3
5
0
1
0
0
0
0
0
1
0
0
0
2
1
0
0
1
0
2
1
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
1
1
1
0
2
0
0
0
1
0
0
0
0
2
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
2
1
2
0
2
2
0
1
0
0
1
0
2
0
3
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
2
0
10
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
1
2
1
2
0
0
0
0
0
0
0
0
2
2
1
1
0
1
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
2
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
2
0
0
0
0
1
0
0
2
0
3
0
0
0
0
0
1
0
2
0
1
1
0
0
3
2
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
2
1
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
1
0
0
2
0
0
2
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
1
2
0
1
1
1
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
1
1
0
2
0
0
2
0
0
0
0
2
2
0
0
0
0
2
0
0
1
0
1
0
0
0
1
1
2
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
2
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
1
0
1
2
1
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
3
2
0
0
0
0
3
0
2
1
0
1
0
0
2
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
2
0
1
0
0
1
1
0
0
2
2
0
2
0
0
0
0
1
0
1
0
2
0
2
1
0
0
1
1
0
0
0
1
0
2
1
2
0
0
2
0
2
1
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
2
1
0
2
2
0
0
0
1
2
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
2
0
1
0
0
1
1
0
0
1
2
0
0
0
2
2
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
1
0
1
0
1
2
9
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
1
0
2
0
0
2
0
1
0
1
0
2
0
0
2
0
1
2
0
0
0
0
2
1
0
0
0
0
2
0
2
1
0
0
0
0
2
0
1
0
0
0
0
3
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
2
2
1
0
0
0
0
0
0
0
1
2
2
0
1
0
0
3
0
0
0
1
0
0
0
0
1
0
0
0
2
1
0
0
2
0
3
2
0
0
2
1
0
2
0
0
0
0
0
1
2
0
0
2
2
0
0
1
2
1
0
1
0
0
0
3
2
1
0
0
0
0
0
0
0
0
3
2
0
0
3
0
0
0
0
3
1
2
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
2
1
0
1
0
0
2
1
0
2
0
0
0
0
0
0
2
0
0
0
2
1
0
2
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
2
2
0
2
2
2
6
0
1
0
1
0
2
1
1
1
1
2
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
5
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
1
0
0
0
0
0
0
2
2
1
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
1
0
0
2
0
0
0
2
0
0
3
2
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
1
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
1
1
0
0
0
0
0
2
1
0
0
0
0
2
0
0
1
2
1
0
0
0
1
0
1
0
0
0
0
0
0
0
2
1
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
2
2
0
0
0
0
0
0
9
1
0
0
2
0
0
0
2
2
2
0
1
0
0
0
5
0
0
0
0
2
1
1
0
0
1
3
0
1
0
0
0
2
0
0
0
0
0
0
0
0
5
0
2
0
1
0
1
2
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
3
1
0
0
0
0
0
0
0
1
0
1
1
0
2
0
0
4
0
0
0
1
0
0
0
0
0
2
0
0
2
3
0
1
0
0
2
0
1
1
1
2
0
2
0
1
0
3
1
0
0
0
0
0
0
2
0
1
0
1
1
0
0
0
7
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
1
0
0
0
0
0
2
1
5
1
0
0
0
1
0
1
1
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
3
1
0
1
2
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
4
0
0
1
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
1
0
2
0
2
0
0
0
0
0
1
0
0
2
2
0
1
0
0
0
0
2
0
0
0
2
2
0
0
0
0
2
2
0
1
1
0
0
0
1
1
2
1
0
0
0
1
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
1
0
0
0
2
0
1
0
0
0
0
1
0
2
2
0
0
0
1
1
0
0
0
0
0
0
1
0
3
2
0
0
2
2
0
2
1
2
0
2
0
0
0
0
1
0
0
0
1
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
3
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
7
0
0
0
2
0
1
0
1
0
2
0
0
2
0
1
0
0
0
0
2
0
0
0
0
2
0
2
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
2
1
2
0
1
1
1
0
0
0
3
0
0
0
0
1
0
1
2
0
0
0
3
1
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
1
2
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
2
0
0
0
0
1
0
2
0
1
0
0
0
1
0
0
0
0
0
2
1
1
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
3
0
1
1
1
1
0
0
1
0
2
0
1
0
0
2
0
0
2
1
0
0
0
0
2
1
0
0
0
0
5
1
2
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
2
2
1
0
0
2
0
1
2
2
3
0
0
1
0
0
3
0
0
0
1
0
0
0
1
2
0
1
1
0
0
0
0
2
1
0
0
1
0
2
1
1
0
0
0
4
0
0
1
0
0
0
0
0
0
1
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
1
0
0
0
2
0
0
0
2
2
0
3
1
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
6
2
0
0
0
2
0
0
2
0
0
1
0
0
0
5
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
2
3
0
0
0
1
0
0
2
0
0
0
1
0
0
2
0
1
1
0
2
2
3
0
0
0
0
2
1
0
1
0
0
1
0
0
2
0
2
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
1
3
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
2
0
0
1
3
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
1
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
3
0
0
2
1
2
0
0
0
2
0
0
1
0
1
2
2
2
3
0
2
0
0
1
0
0
0
2
0
1
0
0
0
2
0
0
0
1
0
1
2
0
0
1
1
0
2
1
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
1
2
0
0
0
1
0
0
0
1
1
0
4
1
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
2
1
0
0
1
0
0
0
0
1
0
1
1
2
0
0
1
0
0
1
2
0
1
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
2
0
0
0
0
0
0
1
0
0
2
3
0
1
0
0
0
1
0
1
0
0
0
4
0
0
0
0
2
0
0
0
1
1
0
2
0
0
0
1
0
1
2
0
2
2
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
1
0
2
0
0
0
1
0
0
0
0
1
0
0
0
2
1
0
0
2
0
0
0
0
1
0
2
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
3
0
0
0
1
2
0
1
0
1
2
2
0
1
2
1
0
2
0
1
0
0
1
1
0
1
1
2
0
1
0
0
2
0
0
0
0
3
2
0
0
1
1
1
0
0
0
0
0
2
0
1
2
1
0
0
1
0
2
1
0
2
1
2
1
0
0
2
1
1
4
1
0
0
2
0
0
4
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
4
0
0
0
0
0
0
0
0
0
2
0
3
0
0
2
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
2
1
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
1
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
2
1
2
0
2
0
0
0
0
3
2
0
1
0
0
0
0
1
1
0
0
0
0
2
0
0
0
2
1
0
0
1
0
0
0
2
1
0
0
1
2
0
0
0
0
0
0
0
2
0
2
0
0
0
3
0
2
0
2
0
0
1
0
0
2
0
0
1
0
2
1
1
2
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
1
0
2
0
0
2
2
0
1
0
1
2
0
0
0
2
0
1
1
0
0
0
0
0
0
1
1
2
1
0
0
0
1
0
0
1
2
0
0
1
1
4
0
1
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
1
0
1
0
0
0
0
1
2
2
0
0
0
0
0
0
1
2
2
1
0
0
2
0
3
2
0
2
0
0
0
7
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
1
0
1
2
2
0
0
1
2
0
0
1
1
1
0
0
2
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
3
0
0
2
0
0
0
2
1
2
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
2
0
3
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
3
2
0
0
0
0
3
1
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
1
2
2
1
0
0
0
1
1
0
0
0
0
0
2
0
0
1
3
0
0
0
0
1
2
0
2
2
2
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
2
2
0
1
1
0
1
0
2
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
3
1
0
2
1
0
0
2
2
0
1
0
2
0
0
0
1
0
2
4
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
1
1
0
0
2
0
0
1
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
1
2
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
4
0
0
0
5
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
1
1
2
0
0
1
0
1
2
0
0
1
0
0
2
1
2
0
0
0
0
1
0
2
0
1
0
2
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
1
2
2
1
3
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
2
0
0
2
1
0
1
0
0
0
2
0
2
2
2
0
0
1
0
1
0
2
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
3
0
0
2
0
0
0
0
0
2
0
0
3
0
0
0
0
0
2
0
1
0
0
2
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
1
3
1
1
2
0
3
0
0
1
1
2
0
2
0
1
0
0
0
3
0
1
0
0
0
0
2
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
2
2
2
3
0
0
1
0
0
0
0
0
0
0
1
0
2
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
4
0
0
0
0
0
0
0
0
0
0
2
2
0
1
2
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
3
0
0
0
0
0
0
0
1
0
1
0
0
1
3
1
0
1
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
1
2
0
2
0
0
2
0
0
0
0
1
0
0
0
0
1
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
2
1
1
4
0
0
0
0
1
0
1
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
2
2
2
0
3
0
0
0
2
0
0
0
2
1
0
0
0
0
3
0
0
0
0
0
0
3
0
0
0
2
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
2
0
1
0
0
1
2
0
1
0
0
0
1
1
1
1
0
0
0
0
0
1
0
0
0
1
0
0
2
0
1
1
0
0
0
2
0
0
0
0
1
1
0
2
0
0
0
0
2
0
0
3
0
2
2
0
1
0
1
1
1
0
0
0
1
0
0
2
0
0
2
0
2
0
2
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
1
0
2
0
1
0
2
2
0
0
0
0
0
0
1
0
2
4
0
1
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
1
0
0
8
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
3
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
2
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
1
1
0
0
2
0
1
0
0
1
0
0
4
0
2
0
0
0
0
0
2
0
0
0
0
0
1
1
1
2
0
0
0
0
0
0
15
0
1
1
2
1
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
2
0
0
0
1
2
1
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
3
0
0
0
0
2
1
0
0
0
1
0
2
0
1
0
0
1
0
0
1
1
0
1
0
0
3
0
1
0
0
1
0
0
1
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
1
0
1
2
2
1
0
0
0
2
0
0
0
0
2
0
2
2
0
1
1
0
0
1
2
0
2
2
0
0
0
0
0
2
0
0
0
0
2
3
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
1
0
1
1
0
1
1
0
0
0
2
1
0
0
0
0
0
0
1
2
1
0
2
0
2
0
0
1
1
2
1
0
1
0
0
1
0
1
1
1
0
1
0
0
0
3
0
2
2
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
2
1
0
2
1
0
1
0
0
0
0
0
2
0
0
0
0
1
1
0
2
1
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
2
2
0
2
1
0
0
0
0
1
0
2
0
0
0
0
0
0
3
0
0
1
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
3
1
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
2
0
0
2
1
2
0
0
0
0
1
0
0
0
2
0
0
1
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
1
0
1
0
0
0
0
2
2
0
0
0
0
0
0
1
2
0
0
1
0
1
0
0
2
0
0
3
0
0
4
0
2
2
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
2
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
3
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
2
0
2
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
2
2
0
1
0
0
2
0
0
0
0
0
0
3
2
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
2
0
0
0
0
8
0
3
1
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
1
0
2
0
0
2
0
0
0
0
1
0
0
2
0
2
0
0
0
1
0
1
0
0
0
0
2
3
0
2
0
1
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
2
0
0
2
0
1
2
0
1
0
0
0
1
1
0
3
0
1
0
0
0
1
1
2
0
0
0
0
0
2
0
0
0
2
0
0
1
2
1
0
2
2
0
0
0
0
0
0
2
1
0
0
0
3
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
1
2
2
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
2
2
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
3
0
0
2
0
0
0
3
0
0
0
0
0
0
0
1
0
2
4
0
0
0
0
5
0
0
0
0
0
0
1
0
0
2
1
0
0
0
2
0
1
2
0
0
1
0
2
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
3
1
2
0
2
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
1
0
2
1
1
0
0
0
0
0
0
2
2
1
2
1
0
0
2
2
0
0
2
0
0
2
2
2
0
0
1
3
0
0
2
1
0
0
3
0
0
0
5
2
0
0
0
0
0
0
1
0
2
0
0
0
0
4
0
4
0
0
2
0
0
0
0
2
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
4
2
1
0
0
1
1
2
0
0
1
0
0
1
0
1
0
0
3
1
0
0
0
0
0
0
2
0
3
2
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
2
0
0
0
1
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
1
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
3
0
0
1
0
2
1
1
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
3
0
2
1
0
0
1
0
0
0
2
1
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
4
0
0
0
1
1
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
2
1
0
1
0
0
3
2
1
1
0
0
0
0
0
1
1
2
0
1
0
0
0
1
0
0
1
0
1
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
3
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
1
2
0
0
0
0
2
0
0
0
1
2
0
1
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
1
0
0
1
1
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
2
2
0
0
2
0
0
0
0
1
2
0
0
1
0
0
0
3
1
1
0
2
1
1
0
0
2
0
1
0
0
2
2
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
3
3
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
3
0
0
0
0
0
3
5
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
1
0
1
3
1
0
0
2
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
1
0
1
0
0
0
0
1
1
0
0
3
0
0
1
0
0
3
0
0
2
0
0
1
0
0
0
2
0
2
0
0
2
0
0
0
0
2
0
1
0
2
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
3
2
0
2
0
0
1
1
0
0
1
2
3
0
0
0
0
0
0
0
0
0
0
1
0
1
1
6
0
0
2
13
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
2
3
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
2
0
7
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
1
0
2
0
0
1
2
1
0
0
0
0
1
0
0
0
2
1
0
0
2
0
0
0
0
0
2
2
1
0
2
1
1
0
0
0
2
0
2
2
1
0
1
0
0
1
0
0
0
0
1
1
0
2
2
1
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
5
1
0
0
1
2
0
0
0
0
0
2
0
2
0
1
1
0
0
0
2
0
0
0
0
2
0
0
1
0
2
0
0
0
0
1
0
3
2
0
0
0
0
1
0
1
0
2
0
1
2
0
0
0
1
0
2
0
0
2
0
2
1
2
1
0
0
0
2
0
1
1
0
1
0
2
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
2
2
0
0
0
0
3
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
2
0
2
0
0
1
1
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
1
3
1
0
0
0
0
0
0
0
0
0
3
0
0
2
1
0
1
2
0
2
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
2
1
0
1
0
0
0
0
2
3
0
1
0
1
0
0
0
0
0
0
2
0
0
3
1
1
1
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
2
2
0
1
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
1
0
0
0
0
0
0
0
1
6
0
0
0
0
0
0
0
2
2
1
2
0
1
2
0
2
0
1
2
1
0
2
0
0
0
0
0
0
0
0
0
0
1
2
1
1
1
0
3
1
2
0
0
1
0
2
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
2
0
1
0
1
0
1
0
0
1
0
0
2
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
9
4
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
2
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
5
0
2
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
3
2
0
0
11
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
2
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
2
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
1
2
0
0
0
0
0
0
2
1
0
0
0
2
11
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
2
0
2
0
0
1
3
0
0
0
0
0
1
1
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
1
2
0
2
0
0
0
0
0
0
2
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
1
1
1
0
0
0
0
1
0
1
0
3
0
0
1
0
0
0
0
3
2
2
2
2
3
0
0
0
0
1
0
1
0
2
0
0
2
0
0
0
0
2
2
2
0
3
0
0
2
2
0
2
2
1
0
2
0
0
1
2
1
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
2
1
0
0
2
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
1
2
0
0
4
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
3
0
1
1
1
0
2
0
0
0
4
1
1
2
2
0
0
0
1
2
2
2
2
1
2
0
2
0
2
0
1
3
2
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
2
0
0
0
0
2
0
2
0
0
0
1
0
1
0
0
1
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
1
2
0
0
0
0
2
0
0
0
0
0
1
1
0
2
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
4
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
5
1
3
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
2
0
0
6
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
1
2
1
0
2
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
2
0
0
0
2
0
2
0
0
0
2
0
0
0
1
1
0
2
0
0
1
3
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
1
0
4
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
3
0
0
0
0
0
0
2
1
0
2
0
0
1
3
0
2
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
2
2
0
2
0
2
2
0
0
0
1
0
0
3
2
0
1
1
2
0
0
2
0
0
2
1
0
0
0
0
1
1
1
1
0
2
2
0
2
1
2
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
3
0
0
0
0
0
1
0
1
0
4
1
0
0
0
0
1
0
0
1
0
0
0
1
2
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
4
1
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
2
1
0
0
0
2
0
0
0
0
0
2
1
0
0
2
2
0
0
2
0
0
0
0
0
3
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
3
0
0
0
2
0
2
0
3
0
0
2
2
0
0
0
0
0
0
1
0
0
0
2
1
0
0
2
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
2
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
2
0
2
0
1
0
0
0
2
1
2
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
1
2
0
4
0
1
0
0
1
0
1
1
2
0
0
0
0
1
1
0
0
0
3
0
0
0
2
0
0
0
2
3
0
0
0
1
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
1
1
2
0
0
0
1
0
0
0
2
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
1
2
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
2
2
0
0
2
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
2
2
0
1
1
3
0
0
0
0
0
0
0
0
0
1
0
3
1
4
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
2
0
3
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
2
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
1
0
0
1
1
0
0
0
2
0
1
2
1
0
0
1
1
0
1
1
2
0
1
0
0
0
2
0
1
0
0
0
2
1
0
0
0
0
1
1
0
0
1
0
0
0
3
2
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
2
2
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
2
1
1
0
0
0
0
2
0
2
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
3
0
1
0
1
0
0
1
0
0
0
0
0
2
2
0
0
2
0
1
0
0
0
2
0
0
0
1
0
0
0
0
3
1
0
0
0
2
0
2
0
0
2
0
3
0
0
1
2
0
1
0
6
0
0
0
0
0
3
0
2
0
0
2
0
2
1
1
0
1
1
0
0
0
0
3
0
0
0
2
0
0
1
2
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
3
0
1
2
0
2
0
3
0
0
0
0
0
2
0
0
0
2
2
0
8
1
1
2
0
0
0
0
0
2
0
1
4
2
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
2
0
1
0
2
0
0
2
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
1
3
0
2
1
0
0
0
0
1
0
0
0
1
0
0
1
2
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
3
0
1
0
0
0
0
1
0
2
2
2
0
0
0
0
0
0
2
0
0
0
2
1
0
2
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
2
2
0
2
0
0
2
0
0
0
2
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
1
2
1
2
0
1
0
0
2
2
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
1
2
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
1
0
0
2
3
0
0
0
2
0
1
0
0
0
2
0
0
0
1
0
0
2
2
1
0
0
1
0
0
0
3
0
0
0
1
0
0
0
2
0
0
0
4
2
1
0
1
0
0
2
1
2
2
0
0
2
0
1
0
0
0
1
0
1
0
2
0
0
0
1
4
0
0
3
2
0
2
0
2
2
2
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
2
0
2
0
1
0
0
0
0
0
0
0
2
2
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
3
0
2
2
0
2
0
1
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
1
2
0
0
0
0
3
1
0
8
0
0
0
0
1
2
0
1
0
2
0
1
0
0
0
0
0
1
0
2
1
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
3
1
2
0
0
0
0
1
0
0
0
0
0
0
0
3
0
1
2
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
1
3
2
2
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
2
0
2
1
1
0
0
2
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
2
0
2
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
3
1
0
0
0
0
2
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
1
2
0
0
2
0
0
0
0
1
0
0
2
0
2
1
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
4
0
1
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
2
1
0
3
0
0
0
0
2
0
0
2
1
0
1
2
1
0
3
2
0
2
0
1
0
0
0
0
0
0
1
0
0
0
2
0
1
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
2
2
0
0
0
0
0
2
2
0
2
0
4
1
0
2
0
0
0
0
0
1
0
1
2
0
2
0
0
0
2
0
2
0
0
0
3
0
0
2
1
0
1
0
0
0
0
0
0
0
1
2
0
0
2
1
0
0
1
0
0
0
0
0
0
1
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
1
3
0
1
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
2
1
1
2
0
0
1
1
0
0
0
0
1
0
1
0
2
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
2
4
0
0
0
0
0
1
1
2
0
0
0
3
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
3
0
2
1
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
2
2
2
0
0
2
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
1
0
4
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
3
0
0
2
0
0
2
0
0
0
0
1
0
0
0
2
1
0
0
0
0
2
0
2
0
0
4
0
0
0
0
0
0
0
0
2
1
1
1
0
0
0
1
2
1
1
0
1
0
1
0
0
3
1
0
0
0
0
0
0
0
1
0
0
2
0
0
2
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
1
2
2
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
1
0
0
0
0
0
3
1
0
0
1
2
0
0
0
0
1
0
1
0
1
1
0
0
0
1
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
2
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
6
1
1
0
0
1
0
1
2
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
5
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
1
0
0
0
1
0
0
1
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
2
2
0
1
0
0
0
0
2
2
0
0
0
0
1
0
1
0
2
0
0
0
0
1
0
2
1
0
0
1
0
0
1
0
0
0
0
1
0
2
0
2
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
4
1
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
2
0
2
1
0
0
0
1
0
1
1
2
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
2
0
0
2
2
1
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
1
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
2
2
0
0
1
0
0
0
0
0
2
0
1
1
0
1
0
0
0
1
0
0
2
0
0
0
0
1
0
1
1
2
0
0
2
1
2
3
0
0
0
0
1
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
2
4
0
1
1
1
0
1
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
1
0
1
0
0
1
1
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
4
1
0
0
0
2
1
1
0
0
0
0
1
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
1
2
4
1
1
2
2
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
2
0
2
0
0
0
0
0
0
0
2
0
1
2
1
0
1
0
0
0
0
1
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
2
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
1
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
2
0
0
1
0
2
0
4
2
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
1
0
1
0
3
0
0
1
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
2
0
1
0
1
0
2
0
0
2
0
2
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
1
0
2
1
0
1
0
2
0
0
0
0
0
3
0
0
0
0
0
0
1
2
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
3
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
1
0
2
0
0
1
1
0
0
0
0
1
0
0
2
0
2
0
0
2
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
2
1
0
0
4
1
0
0
0
2
2
2
0
0
0
0
1
0
1
0
1
2
2
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
1
0
0
0
1
0
2
0
0
0
0
2
0
0
0
3
2
0
1
1
2
0
0
0
0
1
1
2
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
2
4
0
0
2
0
1
0
0
0
0
1
0
0
0
0
1
1
2
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
2
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
1
0
3
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
2
1
0
0
0
0
2
2
0
0
1
0
0
1
1
2
0
0
0
0
3
0
0
0
2
0
0
1
0
0
0
1
0
0
0
2
2
0
0
0
2
0
0
2
1
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
1
1
2
0
1
0
1
0
0
0
0
0
0
0
1
1
4
0
2
0
2
2
0
0
2
0
1
0
0
0
0
0
2
2
0
0
2
2
1
0
0
0
1
0
1
0
1
2
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
1
2
1
0
0
1
1
0
1
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
2
1
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
3
2
2
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
1
2
2
2
0
3
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
2
0
0
0
1
1
1
0
0
2
0
2
0
1
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
2
1
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
1
0
0
2
2
0
3
0
0
2
0
0
1
2
3
0
0
0
1
3
2
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
2
2
2
0
1
0
0
0
2
0
0
0
0
0
0
4
0
2
1
0
0
2
1
0
2
0
0
2
0
0
0
2
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
1
0
1
0
1
0
2
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
1
1
1
0
0
0
1
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
1
2
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
2
0
0
1
0
0
0
1
0
0
0
1
0
1
0
1
1
0
0
1
0
1
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
2
0
0
0
3
0
0
1
0
0
2
0
1
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
2
1
0
0
0
1
0
1
1
2
2
2
2
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
1
0
0
0
0
0
0
1
1
0
2
0
0
0
1
0
2
1
0
1
0
0
0
1
0
2
0
1
0
0
0
0
0
0
1
0
0
2
0
1
2
0
0
0
3
0
4
2
0
2
0
0
0
2
0
0
0
0
1
0
2
3
0
2
0
1
4
0
0
2
1
0
2
1
0
0
1
1
0
0
1
1
0
0
0
0
2
0
0
0
1
0
0
1
2
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
1
0
2
1
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
1
1
0
2
0
2
3
0
0
0
0
0
2
3
1
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
2
1
0
0
2
0
0
1
0
0
0
1
0
2
0
0
0
1
0
2
1
0
2
1
0
0
0
0
0
2
2
0
1
2
1
0
1
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
2
0
0
2
0
2
0
0
2
0
1
0
2
2
0
2
0
0
1
1
0
2
0
0
0
0
0
0
0
1
0
3
0
0
1
0
0
1
2
0
0
0
1
1
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
1
0
0
0
1
0
0
1
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
3
2
2
2
2
0
0
1
0
1
0
2
0
2
2
0
2
0
0
1
0
0
2
0
1
2
0
0
1
2
0
0
2
2
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
1
2
0
0
1
0
0
0
0
0
1
0
0
2
0
1
0
2
2
0
0
0
0
0
0
2
0
0
2
0
1
4
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
2
2
0
0
1
0
0
2
0
2
0
0
2
0
0
2
0
1
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
1
3
2
0
2
1
0
1
1
0
0
0
0
2
2
1
1
0
2
2
0
0
0
2
0
0
0
0
3
0
0
0
2
0
1
0
3
0
0
0
1
0
0
0
1
0
1
1
0
0
1
0
6
0
2
0
0
0
0
1
1
1
1
0
0
1
2
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
6
0
1
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
2
0
0
0
0
6
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
1
0
3
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
1
0
1
1
0
0
1
0
1
2
0
0
0
2
1
0
0
0
2
0
0
0
4
1
0
0
0
0
0
0
0
0
2
2
0
1
0
0
1
0
0
0
1
0
2
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
2
0
0
0
2
0
0
2
0
0
0
0
0
2
0
1
1
0
1
2
0
0
2
0
0
0
0
0
1
0
1
1
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
1
0
1
0
0
1
0
1
0
2
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
2
3
0
0
1
0
0
0
0
0
1
0
0
0
2
2
0
0
4
0
0
2
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
2
0
8
0
1
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
2
1
2
0
1
0
1
0
2
0
0
0
1
0
0
0
0
0
1
3
0
0
0
0
2
0
2
2
0
1
0
0
0
0
0
0
0
0
0
1
3
1
0
0
0
2
1
2
0
2
2
0
0
1
0
2
0
2
0
0
0
0
0
0
0
2
3
2
1
0
1
6
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
3
0
2
1
1
0
1
0
0
0
0
4
2
0
2
1
1
1
1
1
0
0
0
2
0
1
0
0
0
3
0
2
1
1
2
0
0
0
1
0
0
0
2
0
0
0
1
0
1
0
2
2
2
0
0
0
1
0
0
0
2
0
1
2
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
6
0
0
0
0
0
0
2
1
3
0
0
1
2
1
1
0
1
1
0
0
0
1
1
0
2
0
1
0
0
1
1
0
0
0
0
0
0
0
3
1
1
2
0
0
2
0
0
0
0
1
0
2
0
0
0
0
4
1
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
2
1
2
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
2
0
0
1
0
2
0
0
2
0
2
1
0
0
0
0
0
0
2
1
3
0
3
0
0
0
1
0
0
2
0
2
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
4
0
0
2
1
1
0
2
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
2
0
0
2
0
0
1
0
1
0
1
0
0
0
1
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
1
0
2
0
2
0
1
1
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
2
0
0
1
3
0
0
7
1
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
2
2
1
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
1
0
0
0
1
1
0
0
2
1
0
0
0
0
2
1
0
0
0
1
0
1
2
0
0
0
0
0
2
0
1
0
0
0
2
0
2
0
0
2
1
1
2
0
2
3
2
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
6
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
2
3
0
0
3
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
2
1
2
2
1
0
0
1
0
2
0
2
0
2
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
1
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
3
0
0
0
1
0
2
0
0
0
4
0
0
0
2
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
2
0
1
0
0
1
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
2
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
2
0
2
0
2
1
1
1
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
2
1
0
2
0
0
0
2
0
0
4
0
2
1
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
2
0
0
1
0
0
0
2
0
0
0
1
2
2
3
0
0
0
0
1
0
2
3
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
2
0
2
1
1
1
0
0
0
0
3
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
1
0
2
0
0
2
0
0
0
2
0
0
2
1
3
0
0
0
1
0
0
0
0
0
0
2
1
0
1
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
2
0
1
0
1
0
1
0
0
1
0
0
0
1
2
2
0
2
0
1
0
2
0
3
1
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
2
0
0
2
0
0
2
2
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
1
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
2
1
4
1
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
1
0
2
0
0
0
4
0
0
2
2
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
1
0
3
0
0
1
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
1
2
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
3
0
1
0
3
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
1
0
1
0
0
2
1
0
0
1
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
7
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
5
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
0
0
2
2
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
2
0
2
3
0
2
0
0
0
0
0
1
0
1
0
0
1
2
0
1
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
1
0
2
1
1
0
2
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
3
0
3
2
0
0
0
0
0
0
0
0
2
0
3
2
0
0
0
2
0
0
0
0
0
2
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
2
0
2
0
1
0
0
0
0
1
2
1
2
2
1
0
0
0
2
2
0
1
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
1
0
0
2
2
1
0
1
0
0
1
0
4
0
0
0
1
2
0
0
2
1
1
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
2
0
1
1
2
5
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
1
2
0
0
0
0
1
1
0
0
0
2
0
3
0
3
2
0
0
2
2
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
3
1
0
1
0
2
2
0
0
0
0
0
0
0
2
0
2
1
4
0
0
2
0
1
2
2
0
0
0
0
0
1
0
1
0
2
0
0
1
0
0
0
0
0
0
0
1
3
1
0
0
0
0
2
0
1
0
1
0
0
1
0
2
0
1
2
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
3
0
0
1
0
0
0
1
0
2
0
0
1
1
2
0
0
0
0
0
0
1
0
0
0
0
1
2
0
1
2
4
0
0
3
0
0
0
0
2
1
1
2
2
2
0
0
1
0
2
0
1
2
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
4
0
2
1
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
1
0
2
0
0
1
0
2
0
1
0
3
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
3
2
0
2
1
2
0
1
0
0
1
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
3
0
0
2
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
2
1
0
0
0
0
0
2
0
0
0
1
0
2
1
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
1
0
0
2
0
2
3
0
0
2
1
1
0
0
0
0
0
0
0
0
2
1
3
0
0
0
0
0
2
0
0
0
1
1
4
2
0
0
0
0
2
0
0
0
2
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
2
1
1
2
0
0
0
0
2
0
2
2
0
0
0
0
0
1
1
0
0
0
0
4
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
2
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
1
0
3
0
0
0
2
2
0
0
1
0
0
4
0
0
0
1
0
0
2
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
4
0
1
2
0
0
0
0
0
0
1
0
0
0
1
6
2
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
1
3
0
1
0
0
1
0
2
0
2
0
0
1
2
0
0
0
0
0
2
1
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
3
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
2
0
0
1
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
2
0
0
0
2
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
1
0
2
0
2
0
0
0
0
1
0
2
2
0
0
1
2
2
0
0
0
0
1
2
0
2
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
4
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
2
0
1
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
3
0
0
0
1
0
1
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
1
1
1
0
1
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
1
1
0
1
1
0
0
0
1
2
1
2
1
1
1
0
3
0
1
6
1
0
2
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
1
0
1
0
2
0
2
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
1
0
0
1
0
2
0
1
1
0
0
2
0
0
0
0
1
0
11
2
0
2
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
2
0
0
1
2
2
2
0
0
0
1
0
0
0
2
1
2
6
0
2
0
1
0
0
0
0
0
1
0
1
2
0
0
0
2
0
1
0
0
1
1
0
2
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
2
2
0
1
1
2
0
0
0
0
3
0
2
0
0
2
0
0
1
0
1
0
0
0
0
0
0
1
3
2
0
2
1
0
0
0
0
0
0
0
3
0
1
2
1
0
0
0
2
0
0
0
0
0
0
2
0
1
0
2
0
5
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
1
0
2
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
2
0
2
0
0
0
0
0
1
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
2
1
0
1
0
0
0
3
0
0
0
0
0
1
0
1
1
2
2
0
0
1
0
2
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
2
1
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
2
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
2
2
0
0
3
0
0
0
0
0
0
0
1
2
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
3
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
2
2
1
2
0
0
1
2
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
2
2
0
1
0
1
0
0
2
0
3
0
0
0
0
0
1
2
0
2
0
0
2
1
2
0
1
0
1
2
0
1
0
0
1
0
0
4
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
1
0
1
1
2
0
1
0
0
0
1
0
0
0
0
0
2
2
0
0
2
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
2
1
0
0
2
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
2
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
1
0
0
6
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
4
0
0
2
0
1
0
0
0
2
1
0
1
0
0
2
0
0
0
2
1
1
0
2
0
0
1
0
0
0
0
2
0
2
0
3
0
0
0
0
2
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
2
5
2
0
0
0
0
0
0
2
3
2
1
0
1
1
0
0
0
2
0
0
0
3
2
0
0
2
1
0
0
0
0
0
0
1
1
0
3
4
0
2
3
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
3
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
1
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
2
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
2
2
0
0
0
1
1
0
0
0
2
2
0
0
0
0
2
4
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
2
0
0
0
1
2
1
0
2
2
0
0
2
0
0
0
0
0
1
1
0
0
0
0
2
0
1
0
1
2
2
0
0
0
0
0
0
0
1
0
1
0
1
0
2
0
0
0
1
0
1
1
0
0
0
2
0
0
0
2
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
2
2
0
2
2
0
0
0
0
2
1
1
0
3
0
0
0
2
0
0
0
1
0
0
0
2
0
0
1
0
2
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
6
2
0
0
0
9
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
3
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
2
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
2
3
3
0
0
1
2
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
2
2
1
0
1
0
0
0
2
0
2
0
0
0
2
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
1
1
1
3
0
1
2
2
0
0
0
2
3
0
0
0
4
1
0
2
0
0
0
0
0
0
2
0
1
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
3
2
1
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
2
1
2
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
1
0
0
0
2
0
2
4
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
1
0
3
1
1
0
0
1
1
0
0
1
0
0
2
0
0
0
0
1
3
0
0
3
0
0
2
0
2
0
0
0
2
0
0
0
0
1
0
1
0
0
2
0
4
0
0
0
2
2
0
0
0
0
0
1
2
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
2
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
3
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
3
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
3
2
0
0
0
0
2
2
0
0
0
0
1
0
0
2
0
2
0
0
2
0
2
0
2
0
0
0
0
5
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
5
0
0
0
0
0
1
2
0
2
0
0
1
0
0
0
2
0
0
0
0
0
8
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
1
5
1
0
0
1
2
2
0
0
0
0
0
1
0
0
0
1
0
0
2
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
2
1
0
0
0
0
0
2
0
1
0
2
0
1
0
0
0
0
0
1
2
0
0
2
0
2
0
1
0
2
0
0
1
2
0
0
0
0
1
0
0
0
0
2
2
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
2
2
0
1
0
0
2
0
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
2
2
2
0
1
1
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
2
2
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
2
1
1
0
0
2
0
2
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
1
2
2
0
2
1
0
2
1
0
0
1
0
3
0
0
2
0
0
2
1
1
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
2
0
1
0
0
0
2
0
0
2
0
0
0
0
4
0
2
0
0
0
1
0
1
0
0
3
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
2
0
0
3
0
0
3
0
0
0
1
0
1
0
0
0
0
0
0
1
2
2
3
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
5
0
0
0
1
2
0
0
0
0
2
1
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
2
0
0
2
1
0
1
0
0
1
0
1
0
2
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
1
1
2
0
2
1
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
7
0
0
2
1
0
0
0
1
1
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
2
1
1
0
2
3
0
0
0
0
3
2
0
2
1
0
1
1
0
1
0
0
0
0
0
1
0
2
1
1
0
1
0
0
0
0
1
0
0
0
1
0
0
2
1
0
0
1
1
0
0
1
0
1
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
2
0
2
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
2
0
1
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
2
0
2
0
0
0
0
0
1
0
2
0
1
0
0
1
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
2
0
1
0
2
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
2
1
1
1
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
2
0
1
0
0
0
0
0
0
1
0
0
0
7
0
2
0
2
2
2
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
2
0
2
1
2
0
0
2
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
2
1
0
2
2
0
1
0
2
2
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
2
2
1
0
2
7
0
0
0
1
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
2
0
0
0
2
2
0
0
0
0
0
1
1
0
0
0
2
2
0
0
2
2
0
0
0
0
2
0
0
0
0
0
1
2
4
2
0
0
1
1
0
1
0
1
1
0
0
0
0
0
0
2
0
2
0
1
2
0
0
0
0
1
0
0
0
2
2
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
3
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
1
2
0
0
0
1
1
0
0
0
0
3
2
0
2
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
1
0
1
0
2
1
2
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
1
2
2
0
2
0
0
2
0
0
1
0
1
0
0
0
3
1
0
0
0
0
2
0
0
2
0
2
2
2
1
0
1
4
0
0
0
3
0
0
1
0
0
0
8
1
0
0
0
2
1
1
1
0
2
2
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
2
2
0
10
3
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
1
1
0
0
2
0
0
0
0
0
0
3
0
0
0
2
1
0
0
0
0
0
3
0
2
1
2
0
2
0
0
0
1
2
0
4
1
0
1
0
0
1
0
0
0
0
1
0
0
2
1
0
2
0
0
1
0
0
2
0
1
0
2
1
0
0
0
1
0
2
0
0
2
0
3
2
2
0
0
0
1
0
0
3
0
0
0
2
1
1
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
2
3
0
0
1
0
0
1
1
0
1
0
0
1
2
0
1
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
2
0
0
0
0
2
0
2
0
1
0
2
0
2
0
0
0
0
0
0
1
1
0
0
0
1
2
0
0
0
0
2
0
1
0
1
1
1
0
1
1
0
2
1
0
0
0
0
0
1
1
0
2
0
3
0
0
0
2
0
0
0
0
3
0
0
1
0
0
1
1
0
3
0
0
0
0
0
1
2
0
0
0
1
0
0
0
1
2
0
0
14
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
3
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
2
0
0
1
0
3
0
0
1
0
0
1
1
0
0
2
0
1
2
8
0
0
0
0
0
0
1
2
0
2
0
0
3
0
0
0
2
2
1
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
2
0
0
2
0
4
0
2
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
1
0
1
2
2
0
2
0
0
0
1
1
0
0
2
1
0
1
0
0
0
2
1
0
0
2
0
0
1
2
0
2
0
1
0
0
2
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
1
1
2
0
0
1
0
0
2
2
1
0
1
0
0
2
0
0
0
3
1
2
0
2
2
0
0
0
2
2
1
2
0
1
0
0
0
0
4
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
1
2
0
2
0
3
0
0
1
0
2
2
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
2
2
0
0
2
1
1
0
1
0
1
0
2
0
0
1
0
0
0
0
0
0
1
0
3
1
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
2
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
4
0
2
0
1
0
0
0
0
0
1
0
0
0
0
1
2
0
0
1
0
0
0
2
0
0
0
1
0
2
0
0
0
1
1
0
2
3
0
6
2
0
1
0
2
0
0
1
2
0
1
0
0
2
2
1
0
0
0
0
2
0
1
1
2
0
0
0
0
1
0
0
2
2
2
0
0
3
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
8
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
2
0
2
2
2
2
0
1
0
2
1
1
1
0
0
0
0
2
0
2
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
5
0
0
2
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
2
2
0
2
0
0
0
0
1
0
0
0
1
0
1
0
2
0
0
1
0
0
1
2
0
0
0
0
2
3
0
2
0
0
0
0
0
2
0
0
2
2
2
0
0
2
0
0
1
0
1
1
0
0
1
0
0
0
2
2
0
1
2
0
0
0
0
0
2
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
1
0
0
0
2
0
3
0
1
0
0
0
2
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
3
0
0
0
2
0
0
0
1
1
0
1
1
0
0
0
0
0
2
1
0
0
0
2
2
2
2
1
2
0
0
0
0
0
1
0
0
1
0
0
0
0
1
2
1
0
0
0
1
0
1
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
3
2
1
0
1
0
0
1
0
1
0
1
0
0
0
0
0
2
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
2
0
0
0
0
2
2
1
1
0
0
0
0
1
2
0
0
0
0
0
0
1
0
2
0
1
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
3
2
0
2
0
2
1
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
2
2
0
0
1
1
0
2
0
2
0
2
1
1
0
0
2
0
1
0
0
1
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
1
2
1
0
0
0
0
0
1
2
3
2
0
2
2
1
2
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
1
1
0
1
0
2
0
2
2
0
2
0
5
0
0
0
0
0
1
0
1
0
2
0
2
1
2
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
2
0
0
0
2
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
1
1
0
1
2
1
1
1
0
0
0
0
1
4
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
1
0
2
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
1
0
2
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
4
0
2
2
0
0
0
0
0
1
1
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
2
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
1
1
0
0
0
2
0
1
2
1
2
0
0
1
2
0
0
2
1
0
1
2
1
0
0
1
1
0
0
0
0
2
0
0
2
2
1
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
4
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
2
1
2
0
0
2
2
0
0
2
0
0
1
0
0
2
0
0
1
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
2
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
2
1
0
2
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
1
0
0
1
6
0
0
0
3
0
1
0
1
2
0
1
2
0
1
0
0
0
3
0
0
0
0
1
2
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
2
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
5
0
1
0
0
0
0
0
0
0
1
2
0
0
5
1
0
2
1
2
0
0
1
0
0
0
2
0
2
0
2
0
0
0
0
0
0
2
0
2
0
1
0
0
2
0
1
0
0
0
2
0
1
2
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
4
0
0
0
1
0
0
0
2
2
0
0
0
0
9
2
0
0
1
1
0
0
0
2
0
1
2
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
1
0
0
0
0
0
2
0
0
0
1
0
0
0
1
2
2
1
3
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
2
1
2
0
0
0
1
2
0
0
0
1
0
1
2
0
0
1
1
0
0
2
0
0
0
0
3
1
0
1
2
2
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
4
1
0
0
0
0
0
0
0
1
0
0
2
1
2
0
1
0
0
0
0
1
0
1
3
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
2
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
1
2
0
4
0
2
0
1
0
0
0
0
1
0
0
0
0
2
0
1
2
0
0
0
0
0
0
1
0
1
0
0
2
0
1
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
2
1
0
0
1
1
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
2
0
2
1
2
0
0
0
1
0
1
1
0
2
0
0
3
2
3
0
2
2
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
5
0
0
2
0
0
0
0
2
2
0
0
0
1
1
0
0
0
0
0
0
0
0
2
1
2
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
1
0
4
0
0
0
2
0
2
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
3
0
1
0
2
1
0
2
0
0
0
0
1
3
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
3
2
0
3
0
0
2
1
0
0
0
3
2
0
1
2
0
1
2
2
0
1
1
0
3
1
0
0
0
0
0
0
0
0
2
1
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
2
0
0
1
1
2
1
0
0
0
0
2
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
3
0
0
2
0
1
0
0
1
2
2
0
0
0
1
2
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
3
0
1
0
0
0
1
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
1
6
0
2
0
0
2
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
1
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
1
2
0
0
0
0
0
0
2
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
6
0
0
0
1
0
0
0
0
2
0
0
1
0
0
1
2
2
2
1
0
0
1
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
2
0
1
0
2
0
2
0
0
0
0
0
0
1
1
1
1
0
2
0
0
0
2
1
2
0
2
0
2
0
0
0
0
0
0
1
0
1
0
4
0
0
0
0
2
0
0
1
0
0
1
0
2
0
0
0
0
1
0
0
0
0
2
0
0
1
1
0
2
0
0
0
2
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
1
0
2
0
1
0
0
0
0
3
0
2
0
0
0
1
0
2
1
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
2
0
0
0
2
0
0
1
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
2
0
1
1
3
1
0
1
2
1
1
2
0
0
1
2
0
2
0
1
0
0
3
1
0
1
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
2
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
2
1
0
1
0
0
2
2
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
8
0
2
0
0
0
0
0
0
0
2
4
1
0
0
2
0
0
0
0
2
1
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
7
2
0
1
0
0
2
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
1
0
0
1
0
1
0
0
2
0
0
2
0
0
0
0
1
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
2
0
0
1
0
0
0
1
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
2
0
0
2
0
0
2
1
0
1
2
0
1
0
0
0
1
2
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
2
1
2
1
0
2
1
0
0
0
2
0
2
2
0
0
1
0
0
0
1
0
0
0
2
0
0
2
2
0
0
0
0
0
2
0
2
2
0
0
1
0
0
0
0
0
0
1
0
2
0
2
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
1
2
0
0
0
0
0
2
1
0
4
0
0
1
0
2
0
0
0
0
0
0
0
2
2
0
0
2
0
0
1
0
1
1
1
0
0
0
0
0
0
2
1
1
1
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
1
2
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
2
2
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
1
1
0
2
1
0
0
2
0
2
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
2
2
1
2
2
3
1
0
2
0
2
1
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
1
0
2
0
0
2
0
0
1
3
1
0
0
1
0
0
0
0
0
0
0
0
2
2
0
2
0
1
2
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
2
0
2
0
1
0
1
0
0
0
0
0
3
0
0
5
0
0
0
0
0
2
0
0
1
1
0
0
2
0
0
3
0
0
1
2
0
0
0
0
0
3
0
3
0
0
0
2
2
2
1
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
1
1
2
2
0
0
0
0
0
0
3
1
1
1
0
0
1
0
0
0
2
1
0
0
0
2
0
2
2
0
1
0
1
0
0
0
0
0
2
1
1
0
0
0
2
0
1
1
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
3
0
0
1
0
0
2
1
0
2
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
1
2
0
0
2
0
2
1
2
0
0
0
2
0
2
0
1
1
0
0
2
0
0
0
1
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
1
1
0
0
0
1
1
0
1
1
0
0
0
0
0
1
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
4
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
3
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
1
2
2
0
0
1
0
2
0
3
0
0
0
0
0
0
3
0
2
1
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
2
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
1
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
3
1
1
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
2
1
0
0
1
0
2
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
2
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
4
0
0
0
0
2
2
2
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
5
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
1
0
0
0
1
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
2
0
0
0
0
1
0
2
2
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
3
0
2
0
2
2
0
0
0
0
1
0
0
1
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
1
1
2
2
1
0
0
1
0
1
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
2
0
0
1
0
0
3
0
1
0
2
0
0
1
0
1
3
1
2
0
2
0
0
0
0
1
0
2
1
0
0
1
0
1
1
2
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
1
0
0
1
1
2
0
0
0
0
4
1
0
0
0
0
0
1
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
1
2
0
2
0
1
0
0
2
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
1
0
4
1
0
0
1
0
0
1
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
1
1
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
4
1
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
1
3
0
0
0
0
2
1
2
1
1
0
1
1
1
0
0
0
1
0
3
0
0
0
0
1
2
3
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
2
3
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
2
2
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
1
1
0
2
1
2
0
2
0
0
1
2
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
4
0
0
2
0
0
0
0
0
1
0
2
2
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
3
1
0
4
0
0
0
1
0
0
0
1
0
0
3
0
0
0
0
2
0
0
0
0
2
2
0
0
2
1
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
2
0
0
0
2
1
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
1
2
0
0
2
2
1
3
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
1
0
0
2
1
0
0
0
1
1
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
1
0
2
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
3
2
3
0
0
0
3
0
0
2
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
1
0
2
2
2
2
0
0
0
0
0
1
1
0
1
3
4
0
1
0
2
2
0
0
2
0
0
0
0
2
0
1
1
0
0
0
2
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
1
2
0
0
0
0
0
0
1
0
3
0
1
1
0
0
0
0
1
2
0
1
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
1
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
1
2
2
2
3
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
2
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
2
0
1
0
0
2
6
0
0
0
1
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
4
0
0
2
0
1
0
2
2
0
0
0
0
0
3
0
2
0
0
0
0
2
6
0
0
0
0
0
0
0
0
0
1
1
0
1
2
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
1
0
2
0
0
1
0
0
0
0
1
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
2
1
0
0
1
0
2
0
0
5
0
0
0
3
1
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
2
3
2
0
3
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
3
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
1
1
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
2
1
0
1
1
0
0
1
0
1
2
0
4
2
0
0
0
2
0
0
0
1
1
2
0
0
3
0
0
2
0
3
0
0
0
0
0
0
1
0
0
1
1
2
0
0
0
1
0
1
0
1
0
0
2
2
0
0
0
1
0
0
0
2
0
1
0
0
0
1
0
1
0
0
0
0
0
2
2
0
0
1
0
0
1
0
0
0
2
1
0
0
0
0
3
1
0
0
2
1
0
1
0
2
1
0
0
2
0
0
3
0
0
2
0
0
0
1
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
1
3
0
0
0
1
0
0
0
0
1
0
0
2
3
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
1
0
5
1
0
0
0
1
2
2
0
3
0
0
0
0
1
2
0
0
0
0
0
0
2
0
1
0
1
0
1
0
0
1
0
1
0
3
1
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
2
2
1
0
0
4
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
2
0
0
1
0
0
1
4
0
0
2
0
0
0
1
1
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
1
0
0
0
1
2
0
0
0
2
0
2
2
0
0
0
0
0
1
0
0
1
1
1
0
5
0
0
1
2
2
0
0
3
0
0
2
0
0
0
1
0
0
2
1
0
1
0
1
0
0
2
0
0
2
1
0
0
2
0
1
0
2
0
0
0
0
0
2
0
2
1
1
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
1
0
0
1
0
1
0
0
1
1
1
0
2
2
0
2
1
0
0
0
0
0
1
1
2
0
0
0
2
0
0
1
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
1
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
1
2
1
1
2
0
0
0
1
3
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
3
2
0
0
0
0
0
0
0
0
2
0
0
2
1
0
1
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
1
1
8
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
1
1
0
3
1
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
3
1
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
1
2
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
5
0
0
0
1
0
1
0
1
0
0
0
0
0
1
2
0
0
0
2
1
0
0
1
0
2
0
0
1
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
1
0
0
0
1
1
0
2
1
0
0
1
0
1
0
0
0
0
1
2
1
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
1
0
1
0
2
2
0
0
0
0
1
0
2
0
0
1
1
0
0
1
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
2
1
2
0
3
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
2
0
0
0
0
0
1
0
2
2
3
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
3
2
0
2
0
0
1
0
0
0
0
0
0
1
2
2
2
2
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
3
0
0
2
0
0
0
0
0
0
0
0
3
1
0
0
1
0
0
1
0
0
0
0
1
2
0
0
0
1
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
2
1
0
0
1
0
0
0
1
0
0
0
0
1
2
0
1
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
2
1
0
2
0
0
2
0
0
2
0
2
2
1
0
0
0
0
0
0
0
2
0
2
0
1
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
2
3
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
2
0
5
0
0
0
1
0
1
3
0
0
1
0
0
1
0
1
2
0
0
0
0
0
1
0
0
1
1
0
0
2
1
0
0
0
0
0
5
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
1
0
0
1
0
0
2
0
0
0
0
2
0
2
0
1
0
2
1
0
1
0
0
0
1
2
0
0
2
0
0
2
0
0
1
5
2
0
0
0
0
0
2
2
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
2
2
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
3
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
1
3
1
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
6
0
2
0
2
1
2
0
1
0
0
1
2
0
0
0
2
0
0
3
0
0
0
0
2
2
0
0
0
2
2
0
1
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
1
0
1
0
0
1
0
0
1
2
0
2
1
0
0
0
0
0
0
2
0
0
1
0
2
2
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
1
1
0
2
0
0
0
0
1
2
1
0
0
0
0
2
0
1
0
2
2
0
0
4
0
1
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
2
0
0
2
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
1
1
1
0
1
0
0
0
2
1
1
2
0
1
0
2
0
2
2
0
1
0
0
0
1
2
1
0
1
0
0
0
1
0
0
2
2
0
0
1
1
1
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
2
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
2
0
0
0
1
2
0
0
0
1
0
2
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
2
0
0
2
0
0
1
0
0
0
0
0
0
2
2
0
0
0
1
2
0
0
1
0
0
0
2
1
0
0
0
2
0
0
1
2
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
3
1
0
2
1
0
1
2
0
0
0
0
0
1
1
0
0
2
0
1
0
1
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
3
0
1
0
1
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
5
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
2
0
1
1
0
1
2
0
0
2
1
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
3
2
0
1
1
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
3
0
0
1
0
0
0
0
0
0
0
1
2
1
0
0
0
0
2
1
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
2
0
1
0
0
0
2
2
0
0
1
1
2
0
1
1
0
0
2
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
2
1
0
0
0
1
2
0
0
2
0
0
0
0
0
0
2
0
1
0
0
1
2
2
0
2
1
1
2
0
0
0
0
0
0
1
0
2
2
2
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
2
0
2
0
2
0
1
2
0
0
0
0
2
10
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
2
2
0
3
2
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
1
2
0
0
0
0
0
2
0
1
1
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
1
1
2
0
2
0
0
0
0
2
2
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
3
2
0
0
2
2
0
0
2
0
2
0
1
1
5
1
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
2
2
2
2
0
2
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
2
0
10
1
2
0
0
0
3
2
1
0
0
1
0
1
0
1
0
0
2
2
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
2
0
0
4
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
6
0
2
0
0
0
1
2
2
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
3
1
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
1
2
2
0
0
0
2
3
2
0
0
2
2
2
0
0
1
0
0
2
0
0
0
1
2
0
2
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
2
0
0
0
0
1
1
0
0
1
0
2
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
2
0
0
1
0
0
2
0
0
1
9
0
2
0
2
0
1
0
0
0
1
0
0
0
0
2
0
0
2
3
0
0
0
0
0
0
2
0
0
2
0
0
1
2
2
0
0
0
1
0
0
0
0
2
0
2
0
1
0
0
0
0
2
1
3
0
3
0
1
0
1
0
2
0
0
0
2
2
2
2
2
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
2
0
0
0
1
0
0
0
0
2
1
0
3
0
1
2
0
0
0
0
0
4
3
0
0
0
0
4
1
0
0
0
0
0
0
1
1
0
0
1
0
2
2
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
2
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
2
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
1
0
1
0
0
0
2
1
2
1
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
2
2
1
3
0
0
0
0
1
0
2
2
2
0
1
0
5
0
0
0
2
0
1
2
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
1
1
2
0
0
0
0
0
2
0
0
2
0
2
4
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
2
1
2
0
0
1
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
2
0
0
7
0
0
0
0
0
0
0
1
0
0
0
0
0
5
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
2
0
0
0
2
2
0
1
0
0
0
0
2
0
0
1
1
0
0
0
0
0
1
0
0
2
2
1
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
2
0
0
0
1
1
0
0
1
4
0
1
0
0
0
2
0
0
0
0
0
0
0
2
1
2
2
2
2
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
2
0
0
1
0
0
2
0
1
0
0
0
0
0
0
1
2
0
1
2
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
1
1
0
0
1
0
2
0
0
0
0
0
0
2
5
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
1
0
2
0
0
0
0
2
2
0
1
1
0
1
0
0
0
4
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
2
0
0
0
1
0
0
2
0
2
2
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
2
0
0
1
0
2
0
0
2
2
1
0
0
0
0
0
2
0
0
1
1
0
0
0
0
1
0
1
3
1
2
0
0
0
0
0
1
0
0
1
1
1
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
2
0
2
3
0
0
0
1
1
1
2
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
4
2
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
4
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
2
0
1
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
3
0
2
0
0
0
0
1
2
2
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
1
0
3
0
0
1
0
0
1
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
2
0
0
1
0
2
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
2
0
1
2
0
0
0
2
1
1
0
0
0
0
0
0
1
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
2
2
1
0
0
2
0
0
0
1
0
0
0
0
0
2
0
3
1
0
1
1
1
2
0
2
0
1
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
2
0
0
1
1
0
2
0
0
2
0
0
3
1
0
0
2
2
2
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
5
0
0
0
0
0
0
1
0
2
1
1
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
1
2
1
0
1
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
3
0
3
1
2
0
0
3
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
1
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
1
0
2
1
2
0
0
0
0
3
1
2
2
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
1
0
0
0
2
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
2
0
2
0
0
0
2
0
1
0
1
1
3
0
2
0
0
3
0
0
0
0
2
0
2
1
0
1
0
0
0
4
0
0
0
1
2
0
1
2
1
0
0
2
0
0
0
0
2
6
0
0
0
2
0
0
2
1
1
2
0
0
0
1
1
0
0
0
0
0
0
2
2
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
2
0
0
0
2
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
3
2
2
0
2
1
0
1
0
2
0
0
0
2
1
0
0
0
0
1
1
2
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
2
0
2
3
1
0
0
0
0
3
0
2
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
1
0
2
0
2
2
0
2
0
1
0
0
3
0
0
0
1
1
0
2
0
1
0
0
1
0
2
2
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
1
1
1
0
0
2
0
0
2
0
0
0
3
2
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
4
1
1
2
0
0
0
1
0
0
0
2
2
0
0
3
1
0
0
0
1
3
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
1
0
1
0
0
0
7
0
6
2
1
0
2
0
0
0
2
0
0
1
1
0
4
0
1
1
0
0
1
2
1
0
0
0
1
0
0
1
1
1
0
1
2
0
0
1
0
6
2
0
1
0
0
1
1
0
0
0
2
2
1
0
0
0
0
2
0
0
0
2
0
0
2
1
0
0
2
0
1
0
1
0
2
0
1
0
1
2
2
0
0
1
0
0
0
0
0
1
1
8
0
0
3
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
1
0
0
1
2
2
1
2
0
0
2
1
0
0
0
0
0
1
2
2
3
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
1
1
0
2
0
0
0
1
2
2
0
0
2
0
0
0
0
1
1
0
0
0
2
0
0
0
2
2
1
0
1
1
0
0
0
2
0
2
1
0
0
1
0
2
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
4
0
0
2
2
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
1
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
2
2
0
0
0
0
0
0
2
0
0
0
1
0
1
1
2
0
0
1
0
1
0
0
0
0
2
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
2
2
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
1
0
0
0
0
2
0
0
4
0
0
0
0
1
0
0
2
2
2
2
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
3
1
1
0
1
2
0
0
0
0
0
3
2
0
2
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
2
0
0
0
0
1
0
0
1
0
2
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
1
0
0
0
1
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
2
0
1
1
2
0
0
0
2
0
0
2
0
0
2
0
0
2
2
0
0
2
2
0
0
0
0
3
0
0
1
0
0
0
2
2
0
2
1
1
1
1
0
0
1
0
2
4
0
1
0
0
0
1
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
1
0
2
0
2
1
1
0
0
0
0
1
0
1
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
2
0
0
2
3
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
2
0
0
1
0
2
0
0
0
1
2
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
4
0
0
0
0
0
5
2
0
0
0
2
0
1
1
6
0
2
1
0
0
1
0
0
2
0
0
0
1
3
0
0
0
0
0
1
2
0
0
0
0
0
2
2
0
1
0
2
0
0
1
0
0
0
0
0
0
1
2
2
1
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
1
1
0
2
0
0
0
1
0
0
0
2
0
0
0
1
0
2
2
0
0
2
0
2
0
5
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
2
1
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
6
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
1
0
1
0
3
0
0
0
0
0
1
0
0
0
1
3
1
0
0
0
1
0
2
0
0
1
0
2
1
0
0
0
0
0
0
2
0
1
2
0
0
1
1
2
0
0
0
0
1
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
1
0
0
0
2
2
0
0
2
0
0
0
0
0
6
0
2
0
1
0
0
0
0
1
2
0
1
0
0
1
2
0
2
0
1
0
2
0
2
0
0
3
0
0
1
0
7
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
2
0
2
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
1
0
2
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
1
0
2
0
1
0
0
0
2
0
0
2
4
1
0
0
0
0
1
0
0
0
3
0
0
2
1
1
0
0
0
0
0
1
0
2
2
0
0
0
0
0
1
0
2
0
0
1
0
0
2
0
0
0
0
1
0
1
2
0
0
0
1
0
0
0
0
0
0
1
0
1
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
5
2
1
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
1
1
2
0
1
1
0
2
2
0
0
0
1
0
0
0
0
2
0
0
1
1
0
0
2
1
0
0
2
1
0
0
0
2
0
0
2
1
1
2
0
0
0
2
1
1
0
0
0
2
2
1
1
2
2
0
2
0
1
0
0
1
0
2
1
2
1
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
6
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
3
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
1
1
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
2
2
0
1
2
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
1
0
0
1
0
0
1
1
2
0
0
0
2
0
0
1
2
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
2
2
2
1
0
0
0
3
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
1
2
0
0
0
1
0
1
2
1
0
0
0
2
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
5
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
4
0
0
1
0
2
0
0
2
1
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
2
0
0
2
0
1
0
2
0
1
0
0
0
1
0
2
0
0
2
0
1
0
4
0
0
0
0
0
0
1
0
2
3
1
0
1
3
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
3
1
0
0
0
4
0
1
0
2
0
0
0
1
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
2
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
3
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
1
0
1
0
0
0
0
0
0
0
0
0
1
3
1
2
0
1
0
0
0
0
1
0
2
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
2
2
0
0
0
2
0
0
2
0
0
2
1
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
2
0
1
1
0
0
0
0
1
0
0
0
2
0
0
2
2
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
3
0
0
2
3
0
0
1
0
0
1
1
0
0
0
0
0
2
0
2
0
1
0
0
2
0
0
2
0
0
3
2
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
4
0
0
1
2
0
0
0
0
0
0
0
2
1
0
2
0
0
2
0
0
0
0
0
0
3
0
1
0
1
0
0
0
2
0
2
0
2
1
2
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
1
3
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
1
1
0
2
0
0
0
0
0
2
1
1
0
0
0
2
0
1
0
3
0
1
2
0
0
2
2
0
0
0
0
0
1
0
1
0
1
1
1
0
1
2
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
2
0
3
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
1
0
0
1
1
0
2
0
0
1
1
0
0
0
0
0
0
4
2
0
0
2
2
0
2
0
0
1
2
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
6
0
1
2
0
2
2
0
0
0
0
0
1
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
3
2
1
0
1
5
2
1
1
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
4
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
1
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
3
0
0
0
1
0
1
3
1
1
0
3
2
1
2
1
0
0
0
0
0
1
3
1
1
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
2
0
0
0
0
1
0
1
0
0
2
3
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
3
0
0
0
0
0
0
0
0
2
0
1
0
1
0
2
3
0
0
0
0
1
1
0
2
0
0
0
0
1
1
1
2
2
0
0
0
0
0
3
2
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
2
0
1
1
0
1
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
5
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
3
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
1
0
1
0
0
0
0
0
0
2
2
0
2
1
0
1
0
0
0
2
0
0
0
0
1
1
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
2
0
1
4
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
3
0
0
0
1
0
0
0
2
1
1
0
0
1
2
0
2
0
1
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
2
0
2
1
2
0
2
0
1
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
1
0
0
1
0
2
1
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
2
0
1
0
0
0
1
2
0
0
0
0
1
0
3
0
2
2
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
1
2
0
0
0
0
0
0
2
2
2
1
0
0
1
0
0
2
2
3
0
1
0
0
3
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
3
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
3
1
0
0
1
0
0
0
1
0
0
1
3
0
0
1
0
0
0
2
0
0
0
0
1
1
4
0
0
0
1
0
2
1
2
0
1
0
0
0
0
1
2
0
0
0
1
2
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
2
0
0
1
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
1
1
0
0
0
0
2
0
0
1
2
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
1
1
1
0
0
0
1
1
0
0
4
0
0
3
2
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
1
1
0
1
0
0
1
3
2
2
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
1
2
1
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
1
2
0
2
0
1
0
11
1
0
0
0
0
1
1
0
0
0
0
0
2
1
0
0
0
0
0
1
1
2
0
0
1
0
0
1
2
0
0
2
0
2
1
2
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
4
0
2
1
0
0
0
2
0
4
2
0
1
0
0
2
0
0
0
0
2
1
0
1
0
1
2
1
0
0
0
0
1
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
3
1
0
0
0
0
1
1
2
1
3
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
2
1
3
0
1
0
2
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
2
0
0
1
1
0
0
0
0
2
2
0
0
2
0
1
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
2
0
0
0
0
2
2
0
2
0
0
0
1
1
2
3
0
0
0
0
2
1
2
0
0
0
2
0
0
3
1
0
0
0
0
0
0
0
0
1
3
2
2
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
1
0
1
2
3
1
0
2
2
0
1
0
0
0
2
0
0
0
1
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
2
1
0
0
1
0
0
0
0
0
2
1
2
0
0
1
1
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
4
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
1
3
2
0
0
0
1
3
0
0
0
0
0
0
1
0
0
1
1
3
0
3
0
0
0
0
2
0
1
1
1
0
0
0
0
2
0
2
2
1
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
2
1
0
2
0
0
0
1
0
0
0
0
0
2
1
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
2
0
0
2
0
0
0
0
2
0
0
0
3
2
0
2
0
0
0
0
2
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
1
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
3
2
1
0
0
0
1
0
1
0
0
2
0
0
1
2
1
1
0
0
2
2
0
0
0
0
0
0
2
0
0
0
1
0
0
1
2
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
1
1
2
0
0
2
0
0
0
4
0
0
0
0
0
2
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
3
0
2
4
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
2
0
0
0
2
1
0
0
0
2
1
0
0
0
0
2
0
0
0
2
3
1
5
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
2
0
2
0
0
4
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
4
0
0
1
0
0
0
0
2
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
1
4
1
0
0
0
1
2
0
0
1
0
2
2
0
0
0
2
0
0
0
0
0
0
0
3
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
2
0
0
0
2
0
2
2
0
0
0
0
1
1
0
0
2
0
0
0
2
2
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
2
2
0
1
0
2
0
0
2
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
2
0
2
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
3
2
0
0
1
1
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
1
2
0
0
0
0
0
0
2
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
2
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
1
3
1
0
0
0
2
2
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
2
2
0
1
2
1
0
2
0
1
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
2
3
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
1
0
1
0
0
1
0
2
0
1
0
0
1
0
0
0
0
1
0
1
0
0
6
0
0
1
0
2
0
2
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
1
0
2
0
1
1
1
0
1
0
0
1
0
0
1
2
2
0
0
0
0
0
0
0
1
3
0
5
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
3
0
0
0
0
2
1
2
1
0
1
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
1
0
0
1
0
0
0
0
0
0
1
0
4
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
3
2
0
0
0
0
1
0
0
0
1
0
2
2
0
0
0
0
0
2
0
0
3
0
0
0
0
1
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
2
0
0
0
0
0
0
1
0
0
0
0
1
2
0
2
2
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
6
0
2
0
0
0
2
0
0
0
0
1
0
0
1
0
0
1
0
2
0
0
0
0
0
4
0
0
0
0
1
0
0
2
7
1
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
5
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
1
0
0
0
0
2
0
1
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
2
0
0
0
0
0
2
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
1
1
1
0
0
0
2
4
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
2
1
0
0
0
2
0
0
0
0
2
0
0
0
0
3
2
0
0
2
0
0
0
1
2
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
1
3
0
1
2
2
0
0
2
0
1
2
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
1
0
5
1
2
1
1
0
2
0
0
0
1
0
0
2
0
0
0
1
0
0
0
2
2
1
0
3
0
0
2
0
2
1
0
0
2
2
0
2
3
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
1
1
0
0
0
0
2
0
2
1
0
0
0
2
0
1
0
0
0
0
2
0
0
1
0
0
1
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
2
0
0
0
1
2
0
0
1
2
0
2
0
0
0
0
0
2
0
0
0
1
0
1
0
0
2
2
1
3
0
1
0
0
2
0
2
0
2
0
0
0
0
0
1
2
1
0
0
1
0
0
0
1
0
1
1
0
0
0
0
3
2
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
2
1
0
0
0
2
0
0
0
1
2
2
0
1
0
0
2
2
0
2
2
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
1
0
0
0
1
1
2
0
1
0
2
0
2
1
0
1
1
0
0
0
0
0
2
0
2
0
2
1
0
0
0
2
1
0
0
0
0
2
0
0
0
0
1
0
0
3
1
0
0
0
1
0
2
0
0
2
2
1
0
0
0
0
0
0
0
0
2
2
1
0
1
0
0
2
0
2
0
0
1
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
1
1
2
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
2
0
3
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
1
2
2
2
5
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
1
0
0
2
0
4
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
3
0
2
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
1
0
0
0
0
2
0
1
0
0
1
0
0
2
0
0
0
0
0
1
0
0
2
2
1
1
0
0
0
0
0
0
0
0
2
2
0
0
0
1
2
0
0
0
0
0
0
0
2
2
0
0
2
1
0
0
0
0
0
0
1
0
0
3
2
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
2
0
2
0
2
0
0
0
1
0
1
0
0
0
1
0
4
1
1
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
2
0
1
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
2
1
0
1
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
1
0
2
0
1
0
0
0
0
2
0
0
1
1
0
0
1
0
2
1
1
1
0
0
0
0
1
3
2
0
0
0
0
1
0
0
2
0
0
2
2
0
1
0
0
1
0
0
2
1
0
1
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
1
1
0
1
0
0
2
0
0
0
1
0
0
1
2
0
0
1
0
2
0
2
0
0
0
1
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
2
0
0
2
0
1
0
1
0
0
0
0
0
3
1
0
0
0
0
3
0
0
0
0
0
0
0
1
1
3
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
2
2
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
1
1
2
0
1
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
1
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
2
2
0
1
0
0
0
0
2
0
0
0
0
2
2
1
1
0
0
2
2
0
0
0
1
0
2
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
1
0
3
0
1
0
0
0
0
1
7
0
0
0
0
1
0
2
0
0
0
1
0
1
0
1
0
1
0
2
0
0
1
0
1
2
0
0
0
1
0
1
2
0
2
0
0
0
0
0
0
2
1
1
0
0
0
0
2
0
0
1
3
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
1
1
0
3
1
0
0
1
0
2
1
1
0
0
0
2
1
1
1
1
0
0
0
0
0
0
1
0
0
0
1
2
0
0
1
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
3
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
1
0
2
0
2
0
0
0
1
0
0
2
0
0
0
0
3
0
0
0
1
1
0
0
0
0
0
2
1
0
1
2
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
4
0
5
2
0
0
2
1
0
0
0
0
0
0
0
2
2
0
3
1
0
0
0
1
0
0
0
0
0
0
0
3
1
0
0
0
0
1
0
2
0
0
1
0
0
0
0
1
0
2
0
2
8
3
2
0
0
3
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
7
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
1
0
2
0
0
0
0
0
1
0
0
1
0
2
0
2
0
1
0
1
1
1
0
0
1
0
0
2
0
0
0
0
2
1
0
0
0
2
2
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
2
0
1
2
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
2
0
0
0
2
0
0
2
0
0
0
0
0
1
0
2
2
0
0
2
0
0
0
2
1
1
0
1
0
0
0
0
1
2
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
3
0
2
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
1
3
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
5
2
0
2
0
1
2
0
0
2
0
0
0
0
2
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
2
0
2
0
2
0
1
2
0
2
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
3
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
1
2
1
0
2
0
0
0
0
0
2
1
0
2
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
2
0
0
0
1
0
3
0
2
0
1
2
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
2
1
0
0
0
0
2
0
2
0
0
1
2
0
0
1
2
1
1
1
0
3
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
1
0
0
3
2
0
2
0
0
2
0
1
1
0
2
0
0
2
1
1
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
1
1
0
1
0
1
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
1
0
0
5
3
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
2
0
1
0
1
0
1
2
1
1
2
0
0
0
0
0
0
0
2
0
0
0
0
1
3
0
0
0
1
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
2
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
1
2
0
0
0
2
0
3
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
2
1
0
0
2
3
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
1
0
2
2
0
0
0
0
0
3
0
0
0
0
1
0
1
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
1
0
0
0
3
0
0
0
0
1
1
0
0
0
0
0
1
2
0
2
0
0
0
0
1
1
1
0
0
5
2
0
0
1
0
0
2
0
0
0
1
0
2
0
2
2
0
0
0
2
0
0
2
0
1
0
2
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
1
1
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
3
0
1
0
0
0
0
0
0
0
3
0
0
3
2
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
1
0
0
0
3
0
1
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
2
0
1
0
0
0
0
1
0
0
0
2
0
0
0
2
0
1
0
1
2
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
1
1
0
1
0
0
0
1
0
1
0
1
0
0
0
2
0
2
2
0
0
0
0
2
2
0
0
2
0
2
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
1
1
0
0
0
1
2
2
0
0
2
0
0
0
0
0
0
3
0
0
2
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
2
0
0
0
0
1
0
1
1
4
2
0
1
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
3
2
0
0
2
1
0
8
0
2
0
2
1
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
2
2
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
3
1
0
1
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
4
0
0
2
0
2
1
0
1
0
0
1
0
0
2
2
0
0
2
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
1
1
2
0
0
1
2
2
1
0
2
0
0
2
0
2
2
0
0
2
1
0
0
0
0
1
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
2
0
2
0
1
0
0
2
0
0
1
0
1
2
0
0
2
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
2
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
2
3
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
2
2
0
1
0
3
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
2
1
1
0
0
2
0
0
0
1
2
0
2
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
2
0
1
1
0
1
0
0
3
0
0
0
0
1
1
1
1
0
0
1
2
2
0
0
0
1
0
2
0
0
2
1
0
2
2
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
1
2
0
1
0
2
0
0
0
4
2
0
0
0
1
2
2
0
0
2
0
0
0
2
2
0
0
0
2
1
1
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
2
2
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
1
0
0
0
0
7
1
1
2
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
2
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
2
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
2
0
2
0
1
2
3
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
2
0
1
0
0
0
0
1
0
0
0
0
0
3
1
0
1
0
0
2
1
0
0
1
0
0
0
0
2
0
3
0
0
0
0
1
2
0
0
0
0
0
3
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
2
0
3
2
0
0
1
0
0
1
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
1
2
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
2
1
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
1
0
3
1
0
0
0
0
0
0
0
0
1
2
0
0
2
1
0
2
1
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
1
1
0
0
1
0
0
0
0
0
2
0
0
1
1
0
0
2
0
1
0
1
0
0
2
0
1
0
0
1
0
2
0
2
0
0
1
0
1
0
2
2
1
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
1
2
6
0
2
0
2
0
1
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
1
0
0
2
2
2
1
0
1
0
0
1
0
0
0
0
0
2
0
0
0
1
2
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
2
1
0
0
1
0
1
0
2
2
1
2
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
3
1
0
0
0
0
2
2
2
1
0
0
1
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
2
0
0
0
1
0
4
0
1
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
1
2
0
0
0
1
1
0
0
0
1
0
0
2
2
2
0
0
0
0
2
0
2
0
0
1
0
1
0
3
2
0
0
0
0
2
0
2
1
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
1
0
0
2
2
0
1
0
0
2
0
1
1
0
0
2
1
2
1
0
0
2
1
0
0
0
0
0
0
1
3
2
0
0
0
0
0
1
2
2
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
1
0
2
0
0
2
0
0
0
0
1
2
0
0
0
0
0
2
0
0
1
0
1
0
3
1
0
0
0
0
2
3
2
0
0
0
2
1
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
1
0
1
4
0
0
0
0
0
0
0
1
0
0
0
3
2
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
1
1
0
0
1
1
1
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
3
0
0
1
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
3
0
0
0
0
0
0
1
2
2
0
1
1
2
0
0
0
0
1
0
2
2
1
0
0
0
0
0
0
4
0
0
2
2
0
0
1
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
2
0
0
1
0
2
1
2
1
2
0
0
1
0
0
0
0
0
1
0
1
0
2
0
0
1
1
0
0
1
2
0
0
2
0
1
0
0
0
0
2
0
0
3
0
1
0
2
0
0
0
4
0
0
0
0
0
2
0
2
0
0
0
1
0
3
1
1
1
0
0
1
2
0
0
2
0
1
2
1
0
0
0
0
4
2
1
2
1
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
1
1
0
4
1
1
0
2
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
1
2
1
0
1
0
0
0
0
0
1
2
3
0
0
0
2
1
0
0
1
0
0
0
0
0
2
1
0
0
0
1
0
0
0
2
1
0
0
0
2
0
0
0
2
0
1
1
0
0
1
0
0
1
2
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
3
0
0
1
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
2
0
2
0
0
1
1
0
1
2
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
2
0
0
0
1
0
0
0
2
0
2
1
1
0
0
0
1
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
2
1
0
1
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
3
1
0
0
1
0
0
0
2
1
0
0
2
1
0
2
0
2
0
0
2
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
1
0
0
0
0
1
2
0
3
1
0
0
4
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
1
0
0
0
0
2
2
0
2
2
1
0
2
0
0
0
2
0
1
0
0
3
0
0
0
0
0
0
0
4
2
0
2
0
1
0
0
0
0
0
1
0
1
0
0
0
2
2
0
0
0
1
0
3
0
0
1
2
1
2
2
0
3
0
0
0
0
0
2
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
2
2
0
2
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
3
0
0
2
1
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
3
0
0
0
0
0
0
0
0
0
2
0
1
0
1
2
1
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
3
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
1
0
2
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
1
0
0
2
0
0
2
1
2
0
0
0
0
0
0
4
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
1
0
0
0
1
0
0
0
2
0
0
0
2
0
0
1
2
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
2
2
0
2
0
3
2
0
0
0
1
2
0
0
0
0
0
1
0
2
1
1
0
2
0
2
0
1
0
0
0
0
0
2
0
0
3
0
1
1
1
0
0
2
1
0
2
0
0
1
0
0
1
0
0
0
2
0
0
0
0
1
1
2
0
0
0
3
0
0
2
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
2
1
3
2
0
1
0
0
0
2
2
1
0
2
0
1
0
1
2
0
0
0
0
2
2
0
0
0
0
1
0
2
1
0
0
1
2
1
0
2
2
0
0
0
2
0
0
2
1
0
0
1
0
2
0
0
0
1
0
0
0
2
0
2
0
0
2
3
0
0
1
0
0
2
0
2
1
0
1
0
0
0
0
0
0
0
1
0
1
0
4
1
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
2
0
2
0
3
1
0
5
0
0
0
0
0
0
0
2
0
0
2
0
1
0
1
0
0
2
0
0
1
0
0
2
0
1
0
0
1
2
6
0
0
0
4
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
1
0
3
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
2
2
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
3
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
2
1
1
0
0
0
1
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
1
1
0
0
0
1
2
1
2
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
4
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
3
1
0
1
0
2
0
0
1
0
3
2
0
1
1
0
0
3
0
0
2
0
0
0
2
0
3
1
0
3
0
0
0
1
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
1
2
0
1
0
0
0
0
1
2
0
1
2
2
0
0
0
2
0
0
2
0
0
1
0
0
0
3
0
0
0
2
0
0
0
2
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
1
2
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
2
1
0
2
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
2
0
2
0
0
0
0
1
0
1
0
0
1
1
0
0
3
0
3
0
0
1
0
0
0
0
0
0
2
0
1
2
0
0
0
1
0
0
0
0
0
0
0
2
3
0
1
0
0
0
0
0
2
0
0
0
0
1
1
1
1
0
0
1
1
2
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
2
0
3
2
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
1
3
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
2
1
2
0
1
4
1
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
1
1
0
2
0
0
1
1
1
0
0
0
5
0
0
0
0
0
3
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
1
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
2
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
1
0
2
1
1
0
3
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
2
0
1
0
1
1
3
2
1
0
0
0
0
1
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
2
2
0
0
1
0
0
0
0
0
1
3
0
0
2
1
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
2
2
0
0
1
0
0
2
0
0
1
0
2
3
0
1
0
0
0
1
2
0
0
0
0
0
2
0
0
0
2
0
2
0
2
0
0
0
2
3
0
0
1
2
1
0
0
1
0
1
0
0
0
0
0
2
1
0
0
3
0
0
0
3
2
0
2
0
0
0
0
0
1
1
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
1
3
0
0
1
1
0
0
0
2
0
0
0
0
2
2
0
0
1
0
0
2
2
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
4
0
0
3
0
0
0
0
2
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
2
0
2
0
0
0
1
2
2
0
0
2
0
1
0
0
2
2
0
0
1
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
1
0
2
0
2
2
1
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
2
2
2
0
0
0
2
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
1
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
9
2
0
0
0
1
0
0
0
2
2
2
2
2
0
2
0
0
0
0
0
2
0
0
4
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
2
0
2
2
3
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
1
0
1
0
0
2
1
1
0
0
0
2
0
0
2
1
2
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
2
1
0
0
1
0
3
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
1
0
2
1
0
0
0
0
3
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
2
3
1
1
1
0
2
1
0
0
0
0
0
0
9
2
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
2
0
1
0
2
0
0
0
0
1
2
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
1
0
2
0
0
0
3
1
0
1
1
0
1
0
0
2
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
1
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
1
0
0
1
0
0
1
1
0
2
0
1
1
1
1
2
0
2
1
1
0
0
0
2
0
0
0
0
3
2
0
0
0
2
0
2
1
2
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
3
3
0
0
2
0
0
2
0
0
2
0
1
0
2
0
0
2
0
1
0
1
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
1
5
1
1
0
1
0
0
0
0
0
2
1
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
1
2
0
1
4
0
0
2
0
0
2
0
1
0
0
2
0
1
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
3
0
0
2
0
0
1
3
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
2
0
2
0
0
0
0
1
0
1
1
1
0
2
1
0
0
1
0
0
0
2
1
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
1
2
0
0
0
0
1
0
0
0
0
2
1
1
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
2
0
1
2
2
3
0
1
0
1
2
0
0
1
0
2
0
0
1
2
0
1
0
1
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
1
1
0
3
0
0
0
0
0
0
2
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
2
1
0
1
2
0
0
3
0
2
0
0
0
0
0
0
0
0
1
1
0
0
1
3
0
0
0
1
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
2
0
0
0
2
0
0
0
1
0
2
1
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
2
2
3
1
1
0
0
0
0
0
0
0
1
1
1
2
0
1
0
0
0
0
0
0
0
0
1
2
2
1
0
1
0
1
0
0
0
0
2
0
0
0
0
1
0
0
1
0
1
0
1
2
0
0
2
0
2
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
2
0
1
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
1
0
0
0
0
0
3
0
1
0
0
2
0
2
0
0
0
0
2
0
2
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
1
2
0
1
2
2
0
0
1
0
0
0
3
8
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
3
0
0
0
2
0
0
1
5
0
2
1
1
0
1
0
0
0
2
2
0
0
0
2
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
1
0
0
0
0
0
1
1
0
1
0
0
1
0
0
2
0
1
0
9
0
0
0
0
0
2
0
0
2
2
2
0
1
1
2
0
0
2
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
1
0
0
0
1
2
0
1
0
0
0
1
1
0
2
0
1
1
0
2
3
0
0
0
1
2
1
0
0
0
0
0
0
0
12
0
3
0
1
0
0
0
5
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
3
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
2
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
3
0
0
0
2
0
0
0
2
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
1
0
1
2
2
0
0
1
0
1
0
0
2
0
0
1
0
0
0
0
2
0
0
0
1
0
3
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
1
2
1
2
0
3
0
0
0
0
1
0
2
0
0
0
0
1
0
2
0
2
1
0
0
1
1
0
0
0
0
0
0
0
0
2
1
2
0
1
0
2
1
1
0
1
0
3
3
1
0
2
0
0
0
0
2
0
0
0
3
1
0
2
2
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
2
0
2
1
0
2
0
6
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
2
1
0
1
0
1
0
1
0
2
0
0
2
0
1
0
0
0
0
2
1
0
1
0
2
0
0
0
2
0
1
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
2
2
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
1
2
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
2
0
0
1
2
0
0
0
1
2
0
1
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
2
0
0
0
1
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
1
0
1
0
2
0
1
0
2
0
0
3
0
2
0
2
0
1
0
0
0
0
2
0
1
1
0
1
2
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
1
0
1
1
2
2
0
0
2
2
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
1
2
0
1
2
0
0
2
2
2
0
1
2
0
0
1
0
0
1
1
2
0
0
2
1
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
1
2
0
2
2
2
0
2
2
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
1
0
0
3
1
1
0
0
0
2
0
0
6
2
0
1
0
0
2
0
0
2
0
0
2
0
1
0
0
0
1
0
2
1
2
1
2
0
1
0
0
0
0
2
0
2
3
0
0
0
0
0
0
0
0
2
1
1
0
2
0
0
0
2
0
0
1
0
0
1
2
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
1
4
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
2
0
1
1
0
3
1
0
2
0
0
0
2
0
2
2
1
0
0
0
1
3
0
0
0
1
0
1
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
4
0
0
0
1
2
1
1
0
1
0
0
0
2
1
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
2
2
2
0
0
1
1
2
1
0
0
0
0
1
2
0
0
0
0
1
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
2
1
0
0
1
0
0
0
0
2
2
0
0
0
0
2
0
0
1
0
0
1
0
0
1
2
0
0
2
0
0
2
0
1
2
2
2
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
3
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
1
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
11
0
0
1
0
0
0
0
0
0
0
0
1
1
2
0
1
0
0
0
0
0
1
0
1
1
0
0
4
1
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
2
0
1
0
0
0
0
0
1
2
1
1
6
1
0
0
0
1
0
2
0
0
0
1
0
1
0
0
0
0
0
1
4
0
0
1
0
0
0
2
2
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
2
0
1
0
1
0
2
2
2
0
0
2
1
0
2
1
0
1
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
1
0
0
2
0
0
2
0
1
2
0
0
0
1
0
0
0
3
5
0
0
0
1
0
1
2
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
1
0
1
0
0
0
0
6
2
0
0
1
0
0
1
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
1
1
0
0
1
0
0
0
2
0
0
0
2
0
1
1
0
0
0
1
0
2
0
1
0
0
0
0
2
0
0
0
1
0
0
1
0
0
2
1
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
1
1
0
0
2
1
0
0
0
2
0
2
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
3
0
0
2
2
1
0
0
0
0
1
0
1
2
0
0
0
0
1
0
2
0
0
2
2
0
1
0
0
0
0
0
0
1
0
2
1
1
1
2
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
1
0
2
0
0
0
2
2
0
0
0
3
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
1
2
0
0
0
2
1
0
0
0
2
1
2
0
0
0
1
0
0
0
1
2
2
1
2
0
0
1
2
2
0
0
0
2
2
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
2
0
0
0
0
4
1
0
0
0
0
2
2
1
0
1
0
2
0
2
0
0
2
1
2
0
0
0
0
2
1
0
0
3
0
1
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
1
2
1
0
0
0
1
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
2
1
4
0
2
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
1
2
0
0
0
0
2
2
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
1
0
0
2
0
1
0
2
0
3
2
0
1
1
0
0
1
1
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
1
0
2
2
0
0
2
1
0
0
0
2
1
0
0
0
2
0
1
2
3
0
0
2
0
0
0
0
0
0
2
2
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
2
1
0
1
2
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
3
2
2
1
0
0
1
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
4
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
3
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
1
0
0
3
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
2
0
0
1
0
0
0
1
0
0
0
0
0
0
2
2
1
0
0
2
0
0
0
0
3
0
2
2
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
2
2
1
0
0
0
0
2
0
0
2
0
3
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
2
2
1
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
1
2
0
0
1
0
0
2
0
1
1
0
0
2
1
2
1
0
0
0
0
0
2
0
0
0
2
0
0
2
1
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
2
2
2
0
0
1
0
1
0
1
2
1
0
2
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
4
2
0
0
0
2
2
2
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
2
0
1
0
2
0
0
1
0
2
2
0
0
0
1
0
0
0
0
2
1
2
0
1
2
1
0
0
0
0
1
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
1
0
2
1
2
3
0
0
0
0
0
0
0
0
2
2
0
1
1
0
0
0
1
1
0
3
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
2
0
0
2
3
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
1
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
1
2
0
2
0
3
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
2
0
1
0
2
1
0
0
1
0
0
2
1
0
0
8
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
2
0
2
1
0
1
0
0
1
0
1
2
0
0
0
0
0
1
1
0
0
2
2
3
0
0
1
1
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
3
2
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
1
1
1
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
6
0
0
0
2
1
0
3
0
1
0
0
0
2
0
0
0
1
0
0
1
0
2
0
1
1
3
2
1
2
0
0
0
0
0
2
0
0
0
0
2
1
1
0
2
2
0
0
2
0
0
0
0
0
1
0
0
2
1
0
0
1
1
2
1
0
1
0
2
0
2
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
1
0
0
0
1
1
1
0
0
2
0
0
1
1
2
1
0
0
0
2
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
3
2
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
2
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
1
0
0
2
2
0
1
0
0
0
0
0
1
0
0
1
4
0
2
0
1
0
0
3
0
3
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
1
0
0
1
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
1
0
0
0
0
2
0
1
0
1
0
2
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
3
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
2
2
0
3
0
0
0
0
0
0
2
0
0
3
0
2
0
4
2
2
2
0
0
2
0
0
11
0
2
0
2
0
1
0
0
0
1
0
0
0
0
0
10
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
2
1
0
0
0
0
1
0
1
2
0
0
0
0
3
0
0
0
4
2
0
0
0
0
0
0
1
0
0
2
2
0
1
2
0
0
0
0
2
0
0
0
0
0
1
1
0
0
2
0
0
0
0
1
0
2
3
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
2
0
2
2
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
1
0
3
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
1
2
0
0
0
0
2
2
0
0
0
2
2
2
0
1
0
2
2
0
2
0
0
0
0
0
0
1
2
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
1
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
2
0
0
0
0
0
0
2
0
0
2
1
0
0
0
2
1
0
0
0
0
2
0
0
2
0
1
2
1
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
1
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
1
0
0
0
2
0
2
0
1
2
0
2
0
0
0
1
0
0
0
1
0
1
1
1
0
2
1
0
0
0
2
0
1
0
0
1
0
0
0
1
0
0
0
0
2
1
1
2
2
3
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
2
0
0
0
3
0
0
1
0
0
0
2
1
1
2
1
1
0
0
0
0
1
2
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
2
4
0
1
1
1
1
1
0
0
1
0
0
0
1
0
2
0
0
1
2
1
2
2
0
1
0
1
2
0
0
0
0
0
0
0
1
0
0
1
1
0
1
1
2
0
0
0
0
0
1
0
0
0
0
1
0
2
1
0
0
1
0
0
0
1
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
3
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
3
0
0
0
1
0
0
1
0
0
1
0
0
2
0
0
1
1
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
2
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
1
0
0
1
2
0
1
0
2
2
0
0
0
0
4
2
0
0
0
0
0
1
0
1
0
0
0
2
2
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
1
4
1
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
1
3
0
0
2
0
1
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
1
1
0
0
2
3
0
0
0
0
0
0
1
1
2
0
2
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
2
0
0
0
2
1
0
2
1
0
0
2
1
0
0
0
0
0
0
0
2
2
0
1
1
2
0
0
1
1
0
2
0
0
1
0
0
0
0
0
0
0
2
0
1
1
0
0
1
2
0
0
0
1
0
0
0
0
2
0
0
0
2
0
1
1
2
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
3
0
2
0
0
0
0
0
0
2
0
0
0
2
0
2
1
0
2
1
1
2
2
0
0
2
0
1
0
0
2
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
1
1
0
1
0
0
0
0
1
2
0
0
0
1
1
0
0
2
2
0
0
0
1
2
2
2
1
2
0
0
0
0
0
0
1
0
6
0
0
0
1
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
1
1
0
0
0
3
0
2
0
1
0
0
0
0
1
0
1
0
1
2
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
3
0
0
2
1
0
1
1
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
3
1
1
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
2
2
1
3
0
0
0
0
2
0
0
0
0
0
2
2
2
1
0
0
0
2
0
0
0
0
0
1
1
2
0
2
0
0
0
4
0
0
0
0
1
0
0
0
1
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
1
0
0
1
0
0
0
1
0
0
0
2
2
0
2
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
1
1
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
2
0
0
2
1
0
0
0
0
0
7
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
4
0
0
0
7
0
0
0
0
3
0
0
2
0
1
2
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
2
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
2
0
1
1
0
0
1
2
0
1
0
0
0
3
1
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
1
0
1
2
2
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
2
0
2
1
1
0
2
0
0
0
0
2
1
0
2
0
3
2
2
0
1
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
2
1
2
0
1
0
0
1
0
0
0
0
1
0
0
0
0
2
2
1
2
0
1
1
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
3
0
0
0
5
0
0
0
0
0
0
1
1
1
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
1
2
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
3
1
0
2
0
0
0
0
2
0
2
2
1
2
0
0
1
0
0
0
2
0
0
2
0
0
2
0
3
0
0
1
1
1
2
0
0
0
0
0
0
0
2
0
0
3
0
0
3
0
0
0
0
2
0
0
4
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
3
0
2
0
1
0
2
5
0
0
0
0
2
0
0
0
1
0
2
0
0
0
2
3
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
2
2
1
2
0
0
0
0
0
0
1
0
2
1
0
0
0
2
0
0
0
0
0
2
0
1
0
0
2
1
0
0
2
2
0
0
2
0
0
1
2
0
0
0
0
0
1
1
1
0
0
1
0
2
2
0
0
1
1
0
0
0
2
0
1
0
1
0
1
0
3
0
0
0
0
2
1
0
2
1
1
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
2
0
1
0
0
0
0
1
2
0
0
0
0
0
0
2
2
0
2
1
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
2
2
2
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
4
0
1
2
0
0
0
1
0
2
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
1
2
0
0
0
0
2
0
0
0
0
1
0
0
2
2
0
0
2
0
3
0
0
1
0
0
2
0
0
0
2
3
0
2
2
0
0
0
0
0
2
2
2
0
2
0
1
2
0
0
0
0
0
1
0
0
1
4
0
1
12
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
7
0
0
0
0
1
0
3
0
0
0
0
3
0
1
0
0
2
0
0
0
0
0
0
0
3
2
0
2
1
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
2
1
1
0
0
1
5
0
0
0
0
0
1
0
0
1
0
1
1
0
0
1
0
0
1
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
2
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
2
2
1
0
0
1
1
2
1
0
0
0
1
0
0
0
1
0
0
2
0
0
1
0
0
1
0
2
2
0
0
0
1
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
1
0
2
0
0
0
0
0
0
0
0
1
3
1
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
1
0
0
1
0
0
0
1
0
0
0
2
0
1
0
0
1
2
0
0
0
1
3
0
2
1
0
0
0
2
0
0
0
0
1
0
0
1
6
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
2
0
0
1
0
3
0
1
1
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
1
2
0
0
0
9
0
0
0
1
0
0
0
0
0
2
0
0
2
1
1
0
0
2
1
1
0
2
0
0
0
2
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
2
0
0
1
0
0
1
0
0
2
1
0
4
0
1
0
0
0
0
0
1
0
1
0
1
2
0
0
0
0
0
1
0
2
0
2
0
0
0
3
0
0
0
0
2
2
0
0
2
0
6
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
2
0
1
0
2
0
0
0
2
0
1
1
0
0
0
0
0
2
0
0
0
0
2
2
1
0
0
0
0
0
2
0
2
1
1
0
0
0
0
1
0
2
1
0
0
0
2
1
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
4
0
1
0
0
0
0
1
2
0
0
0
0
5
0
2
0
0
0
0
0
1
0
3
0
0
0
4
0
1
0
0
0
0
0
0
1
2
2
0
0
0
1
2
0
0
2
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
1
3
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
2
1
2
1
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
2
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
3
2
0
2
1
0
0
0
0
2
0
0
1
0
2
2
1
0
0
3
0
2
1
0
0
1
0
5
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
2
1
0
1
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
2
2
0
2
0
2
0
0
0
2
1
0
2
0
2
0
1
0
2
0
0
0
1
3
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
2
2
0
0
0
1
1
0
0
0
2
0
0
0
2
0
0
0
1
0
0
2
0
0
1
0
0
2
0
0
0
0
4
1
0
0
0
0
2
0
1
1
0
2
0
0
0
2
0
0
0
0
0
2
0
1
2
1
0
0
0
0
1
3
2
1
2
0
1
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
3
2
2
2
2
0
0
0
0
0
5
0
2
0
2
0
0
0
0
0
0
2
1
6
1
2
0
0
0
3
0
0
0
1
2
0
0
2
2
0
1
1
0
0
3
0
0
0
0
2
0
3
1
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
1
2
0
2
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
1
0
0
0
2
2
0
0
1
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
1
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
2
1
0
0
0
3
0
2
1
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
2
0
2
0
0
0
3
0
0
0
1
0
1
0
2
0
0
0
2
0
0
0
4
0
0
0
0
0
1
2
0
0
1
0
0
1
1
0
0
0
0
0
0
2
0
0
0
1
0
2
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
3
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
2
0
1
0
0
2
2
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
2
0
0
1
0
1
0
0
0
0
0
0
2
0
2
0
0
0
2
0
2
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
5
2
0
0
0
8
0
0
0
0
0
0
0
1
0
3
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
1
0
2
0
0
4
1
1
3
0
0
1
2
2
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
1
0
0
3
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
1
1
1
2
1
0
0
0
0
1
0
0
1
1
0
2
0
0
2
0
0
0
2
1
1
0
0
0
3
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
2
2
2
0
2
2
0
0
0
0
0
3
0
1
2
0
1
0
0
2
0
0
1
2
1
0
0
0
0
0
0
1
0
0
1
2
2
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
1
0
0
1
0
1
0
3
0
0
2
0
1
0
0
1
1
0
0
2
0
0
3
2
0
1
0
0
0
0
2
3
0
0
1
0
0
1
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
2
0
0
2
1
0
1
0
0
3
1
0
0
1
0
0
1
0
0
0
0
0
3
0
1
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
1
2
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
2
2
0
1
2
0
0
0
0
0
0
0
0
2
2
2
0
3
0
2
2
0
0
2
2
0
0
0
1
1
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
1
0
1
0
0
1
1
0
0
0
0
0
0
1
4
0
2
0
2
0
0
0
0
0
0
1
0
1
0
2
0
2
0
0
2
2
0
0
3
1
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
2
1
1
0
0
0
0
0
3
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
2
1
2
1
1
0
1
0
1
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
1
0
0
2
0
2
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
2
1
1
0
0
0
1
0
1
0
2
0
2
2
0
0
0
0
2
2
0
0
0
0
1
0
2
0
2
0
1
0
2
1
5
0
0
0
0
0
1
0
0
0
0
1
5
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
3
0
0
0
1
1
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
3
0
0
3
2
0
1
0
2
2
0
1
1
1
2
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
2
2
2
0
0
2
2
0
0
0
2
0
2
0
0
0
3
0
0
1
0
0
0
0
0
0
3
2
0
0
1
6
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
1
0
0
0
1
1
0
1
2
1
2
0
0
0
0
0
0
0
2
0
1
0
2
0
2
0
2
0
1
1
0
0
0
0
2
1
0
3
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
2
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
2
1
0
0
2
2
0
0
1
2
3
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
2
0
0
1
0
2
0
0
0
2
0
0
0
3
1
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
1
0
0
0
0
1
2
3
0
0
0
0
0
0
0
0
0
1
2
0
0
2
2
0
1
0
0
2
1
0
2
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
1
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
1
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
3
1
0
0
0
0
0
0
1
1
1
0
0
5
0
2
0
0
0
1
1
1
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
1
1
3
0
0
0
1
1
0
0
0
1
0
0
0
2
1
0
1
2
0
0
0
0
0
3
1
0
1
0
0
0
0
0
2
2
0
0
0
0
3
0
0
3
2
0
2
2
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
2
1
0
0
0
0
0
1
0
0
3
1
0
0
2
0
0
0
1
0
0
0
3
0
2
0
0
0
5
0
2
0
0
0
2
0
4
0
0
0
3
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
2
0
8
1
0
0
0
5
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
1
0
0
0
2
1
0
0
3
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
2
1
0
2
0
0
0
0
1
2
2
0
1
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
1
0
0
3
0
0
4
0
2
0
1
1
2
0
2
0
0
2
0
0
0
1
0
2
0
0
1
0
0
0
0
1
0
0
0
2
0
0
1
0
1
0
2
0
2
0
2
0
1
1
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
1
0
3
1
2
2
0
0
1
0
0
0
1
0
0
0
0
1
2
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
2
2
0
0
1
1
0
2
1
2
0
2
0
0
0
3
2
0
0
1
1
0
2
0
0
2
4
0
0
0
0
2
0
0
0
0
2
0
0
1
0
2
2
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
3
1
1
0
0
0
0
0
2
0
2
2
0
0
0
0
1
0
1
0
0
0
0
2
0
0
1
0
0
2
2
0
0
0
2
0
0
2
0
0
0
1
0
0
2
2
2
2
0
2
2
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
1
0
1
1
0
1
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
2
0
2
1
2
0
2
0
0
2
0
1
0
0
0
0
1
1
0
1
0
0
0
4
0
2
0
0
0
1
0
1
1
0
0
1
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
3
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
1
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
2
1
2
1
1
1
0
1
0
0
0
0
0
0
0
2
3
0
0
0
0
4
0
2
1
0
1
2
3
1
2
0
1
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
1
0
2
0
0
0
2
0
1
0
1
0
3
0
0
1
0
0
4
2
3
0
0
0
0
1
2
2
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
3
0
0
0
2
0
0
2
0
0
4
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
2
1
0
0
3
1
1
1
0
0
1
0
1
5
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
1
0
0
2
0
0
1
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
3
0
2
1
2
2
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
2
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
1
0
0
2
2
0
2
0
1
1
1
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
2
2
0
0
0
1
0
0
2
0
2
3
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
2
1
3
2
0
2
0
1
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
2
2
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
2
2
0
2
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
2
0
0
0
2
0
0
1
2
0
0
3
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
1
0
0
0
0
1
1
0
1
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
1
0
1
0
0
0
0
3
0
1
0
2
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
2
0
1
0
0
0
1
0
0
0
0
0
0
2
1
0
3
0
0
0
0
0
2
0
0
2
0
0
3
0
2
0
1
0
2
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
3
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
1
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
2
0
0
0
2
0
0
0
0
2
1
0
0
0
2
1
3
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
1
0
0
2
0
0
0
2
1
2
0
1
0
2
2
0
0
2
2
0
2
1
0
2
0
2
0
0
1
0
0
1
0
0
2
0
0
0
1
0
0
2
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
2
0
0
0
0
1
0
1
2
0
0
3
0
0
2
0
0
1
1
0
0
0
0
2
0
0
0
0
2
1
2
0
0
0
0
0
0
0
5
2
2
1
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
1
0
0
2
2
0
0
0
0
2
0
2
0
2
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
2
0
1
2
0
0
0
1
0
2
1
1
2
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
1
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
1
2
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
2
0
0
1
1
1
1
0
1
0
0
0
0
0
1
2
1
0
2
0
1
0
0
0
1
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
1
2
0
0
1
0
1
0
4
1
2
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
4
0
0
2
0
0
0
1
2
0
2
2
2
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
2
1
0
0
1
0
2
1
1
0
0
0
0
2
2
1
1
1
1
0
1
2
0
0
0
2
0
0
0
0
0
0
1
2
0
2
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
3
2
0
0
2
0
1
0
2
0
2
3
0
2
0
1
0
2
0
2
2
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
2
1
1
0
0
0
0
0
0
0
2
1
1
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
2
0
0
0
1
0
2
0
1
1
0
0
0
3
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
2
1
0
9
1
1
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
1
2
1
0
0
0
2
0
2
0
0
0
1
0
0
2
2
0
1
0
2
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
2
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
3
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
1
0
1
0
2
0
1
0
0
0
2
0
0
0
1
0
1
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
1
0
2
0
0
1
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
1
0
0
0
0
2
0
2
0
0
0
0
1
0
2
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
2
2
0
0
2
0
0
2
0
1
2
0
0
0
2
0
0
2
1
0
1
0
2
0
0
0
1
0
2
1
2
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
2
2
0
0
0
2
1
1
0
0
0
3
1
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
1
0
1
0
0
2
0
0
0
0
0
2
0
3
0
0
0
0
1
3
2
0
0
0
1
0
0
2
0
0
0
2
2
1
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
1
0
2
4
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
1
2
0
0
0
1
0
0
2
0
0
0
1
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
3
2
0
0
0
0
1
0
1
0
0
0
2
0
1
0
2
2
0
0
0
0
3
0
0
1
0
0
0
2
1
0
0
0
0
2
0
0
0
0
2
2
1
1
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
1
1
1
0
0
2
0
0
2
0
0
1
0
0
2
0
3
0
0
0
0
0
0
1
0
1
2
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
2
1
0
0
2
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
1
1
2
0
0
1
0
0
0
0
0
1
0
0
2
2
2
0
0
0
2
0
4
0
0
0
3
0
2
2
2
0
0
0
2
0
0
0
0
2
0
0
2
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
3
0
1
1
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
1
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
4
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
2
0
0
2
0
0
0
1
0
0
1
0
0
2
1
0
2
0
1
0
0
0
1
1
2
2
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
2
2
3
1
0
0
2
0
1
0
0
0
2
0
0
0
1
0
0
1
1
0
0
2
2
1
0
0
1
2
0
0
0
0
0
1
5
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
2
1
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
3
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
3
0
2
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
2
2
2
0
0
0
2
0
1
0
0
0
1
0
2
0
1
1
0
0
0
1
1
0
0
1
0
0
1
0
0
1
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
2
0
1
1
2
0
0
1
0
0
0
2
0
2
0
0
3
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
2
1
0
0
0
0
1
0
3
0
0
2
2
0
0
0
0
0
3
0
1
0
0
0
0
1
0
0
1
0
2
5
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
2
0
0
1
0
0
0
2
0
1
0
0
0
1
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
2
0
0
2
0
0
2
2
2
0
0
0
0
0
0
2
1
2
5
0
0
0
2
1
0
0
1
2
1
0
1
1
0
2
2
1
1
2
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
1
1
0
0
2
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
2
0
0
0
2
2
2
0
0
2
0
0
0
0
0
0
1
0
5
1
0
1
2
0
1
2
2
0
2
0
0
3
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
2
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
2
2
2
0
0
0
0
0
0
1
0
1
3
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
2
0
1
2
0
1
2
2
0
2
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
1
1
2
3
1
2
0
0
0
2
0
2
0
0
0
0
2
4
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
3
0
3
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
2
0
2
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
1
0
0
0
4
2
0
2
0
1
0
0
0
0
0
4
0
0
0
0
2
1
1
0
0
1
2
2
2
0
0
0
1
0
0
0
0
2
0
0
0
1
0
1
0
2
2
0
0
1
0
4
4
0
1
0
2
0
2
0
0
2
0
0
0
0
2
0
0
2
0
1
1
0
2
0
1
0
0
0
5
0
0
0
1
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
3
0
0
2
0
0
0
1
1
0
0
0
3
0
2
0
0
0
1
2
0
0
1
0
2
2
0
0
0
1
2
1
2
0
0
2
0
0
2
0
0
0
0
0
0
4
0
0
0
1
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
1
0
0
1
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
1
0
0
1
0
0
0
3
0
2
0
0
0
0
1
2
0
2
2
0
2
0
0
0
0
0
0
0
0
0
3
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
1
0
2
2
0
1
0
0
1
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
11
0
0
3
0
0
0
1
0
2
0
1
0
1
0
1
0
0
0
2
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
2
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
2
0
1
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
1
1
0
2
0
0
0
2
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
1
0
0
2
0
0
0
1
0
0
0
2
1
2
0
0
0
0
0
0
1
7
1
0
0
0
0
0
0
0
0
2
2
3
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
2
0
0
1
3
0
0
0
0
0
0
2
0
1
2
0
0
0
1
2
5
2
2
0
1
0
2
1
0
2
1
0
0
0
1
0
0
1
1
0
1
2
2
0
0
0
0
0
0
0
0
1
1
0
0
2
0
2
0
0
0
1
1
3
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
1
2
0
2
1
0
1
3
0
1
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
2
0
2
0
0
1
1
2
1
1
0
0
0
0
0
0
0
1
0
1
0
1
0
1
1
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
0
1
1
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
1
0
2
0
0
0
0
2
4
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
6
1
2
0
0
0
0
0
1
2
0
0
0
0
0
2
1
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
2
0
0
0
3
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
2
1
0
0
0
1
1
2
2
2
0
0
1
0
1
0
0
0
0
0
0
0
1
2
0
0
3
2
0
0
1
3
0
0
1
0
0
2
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
3
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
2
0
0
1
0
0
1
0
2
1
1
1
0
0
0
0
0
0
0
1
4
1
1
0
1
0
0
0
2
2
2
0
0
0
0
1
0
0
0
0
0
1
0
0
2
2
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
1
1
1
1
3
0
0
2
1
0
0
0
0
0
0
1
0
2
2
0
1
0
0
2
0
2
0
1
0
0
0
0
2
4
0
0
0
0
2
0
0
0
0
0
0
1
1
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
2
2
0
0
0
0
0
1
0
0
0
1
1
0
0
1
3
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
3
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
3
0
2
2
0
0
1
0
0
0
1
0
0
1
1
0
2
2
0
2
0
2
0
0
0
0
0
5
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
1
1
0
2
2
0
2
0
0
0
2
0
7
0
0
0
0
0
2
0
0
0
2
1
2
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
2
1
0
0
0
1
0
2
0
0
2
0
0
0
2
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
2
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
1
0
2
0
0
1
2
0
1
0
0
0
0
1
0
1
2
0
0
0
3
0
1
1
3
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
2
3
0
2
0
1
0
0
0
2
0
0
1
0
0
0
0
2
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
2
0
2
0
1
2
0
0
0
0
0
0
0
1
2
2
0
0
0
0
1
0
0
2
0
0
0
0
1
0
2
2
0
0
2
2
0
0
1
0
2
0
1
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
2
0
1
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
1
1
1
0
0
1
0
0
0
0
2
0
1
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
6
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
2
2
2
1
0
0
0
0
0
0
1
2
0
0
0
1
0
2
0
0
0
0
0
1
0
7
0
2
0
0
1
0
1
0
0
2
0
2
4
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
3
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
3
0
0
2
0
0
0
1
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
2
0
0
3
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
1
0
2
0
1
2
0
1
2
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
4
0
0
0
2
1
0
2
0
0
0
0
0
0
5
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
2
0
1
2
2
1
1
2
0
0
1
0
0
2
0
0
0
0
4
0
3
2
0
0
0
2
0
0
5
1
0
1
0
0
0
0
0
0
0
1
0
2
0
1
1
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
1
0
1
1
1
0
0
0
0
2
0
0
2
2
2
0
0
5
2
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
3
0
2
0
0
0
0
0
0
2
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
3
6
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
3
0
2
0
3
0
0
0
1
0
0
0
0
0
1
0
0
2
1
0
0
4
0
0
1
1
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
3
2
0
0
0
0
2
2
1
0
0
0
0
0
2
0
4
0
1
0
2
0
0
0
2
1
0
0
2
0
0
0
0
0
1
0
1
2
0
0
0
1
1
0
0
0
1
2
0
0
3
0
1
1
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
3
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
2
1
0
0
0
2
0
0
0
0
0
2
1
2
0
0
0
2
0
0
0
0
0
0
2
0
2
0
2
0
0
1
0
0
0
2
0
0
2
1
0
1
2
0
0
0
5
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
2
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
2
2
1
0
0
2
1
1
0
0
0
0
0
1
0
2
1
2
0
1
0
1
2
0
1
0
0
1
1
0
0
0
1
0
0
0
3
2
0
3
1
2
0
2
0
0
2
0
0
0
2
2
0
0
0
0
0
0
2
0
0
1
1
2
1
0
1
0
0
1
0
1
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
1
2
1
2
0
0
2
2
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
2
0
0
0
1
0
0
0
0
4
0
0
0
1
0
1
0
0
1
1
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
1
0
0
0
1
1
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
3
6
0
0
0
0
0
2
0
2
0
0
0
0
5
2
0
0
1
0
1
0
2
2
0
0
1
3
1
0
1
0
0
0
0
0
2
2
1
0
3
0
2
2
0
0
0
0
1
0
3
1
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
1
1
1
0
0
2
0
0
2
0
0
2
0
2
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
2
0
0
1
0
0
0
3
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
4
0
0
0
1
0
0
2
0
0
0
0
0
0
3
1
0
0
1
0
0
2
0
1
2
0
0
0
0
4
0
0
0
1
0
0
0
2
3
1
0
1
1
1
0
1
1
0
2
1
0
0
2
0
0
0
1
1
0
0
1
2
1
0
0
2
0
1
0
2
0
0
0
0
0
0
0
1
2
2
1
0
0
0
0
0
2
0
2
3
2
0
0
2
0
0
2
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
2
0
1
0
0
2
0
0
0
1
2
1
0
0
0
0
0
0
1
0
2
2
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
2
0
3
0
2
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
3
3
1
2
2
2
0
0
1
0
0
2
0
0
0
0
0
2
1
1
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
3
0
1
0
1
1
0
0
2
2
0
0
1
5
0
1
0
0
0
1
2
1
0
0
0
0
0
2
0
0
0
1
0
2
0
0
1
2
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
3
2
0
0
2
0
1
0
0
2
1
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
1
1
1
3
1
0
0
0
0
0
0
0
0
0
3
0
0
0
2
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
3
0
3
0
0
4
0
2
3
0
2
0
2
0
1
0
0
0
0
0
0
3
0
0
0
1
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
3
0
0
0
0
1
1
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
2
0
0
1
0
0
0
2
2
1
1
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
1
1
0
3
0
0
0
0
0
0
2
1
1
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
4
0
0
0
2
0
2
0
0
1
1
1
0
0
2
0
0
0
0
0
2
2
0
0
0
1
2
1
1
0
2
2
0
0
0
0
1
0
1
0
0
2
3
0
2
1
0
1
0
1
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
1
1
3
0
0
0
2
1
0
0
1
2
0
0
0
3
0
2
0
0
0
1
0
0
0
1
2
0
2
0
0
0
1
2
0
0
1
0
0
3
1
0
0
0
2
2
0
0
1
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
1
0
1
0
0
0
2
2
0
2
0
1
0
0
0
0
0
0
0
1
0
2
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
3
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
1
0
0
0
0
2
1
0
0
1
1
1
0
5
0
0
0
0
0
0
2
0
2
1
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
2
0
0
2
2
2
0
0
0
0
1
0
0
0
0
0
1
0
4
0
1
0
0
0
0
0
0
2
0
0
1
1
1
0
1
0
2
2
1
0
0
0
2
0
1
0
2
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
3
0
1
3
2
0
0
0
3
2
0
2
2
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
1
0
0
1
0
0
3
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
3
0
1
1
0
1
0
2
0
0
0
2
0
1
0
1
0
0
2
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
6
0
2
1
3
0
0
0
0
0
1
0
0
0
2
0
0
0
0
3
2
1
0
1
0
1
0
0
0
1
0
0
2
0
2
1
0
2
0
2
0
2
0
5
0
0
0
0
0
0
0
2
1
0
2
2
0
1
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
2
3
0
0
0
0
1
0
0
1
0
1
2
0
0
0
0
0
0
2
0
6
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
1
2
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
3
0
0
1
2
0
2
0
0
0
0
0
0
0
2
1
2
3
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
3
1
0
0
1
0
0
0
0
1
1
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
2
0
5
0
0
2
0
1
0
0
1
1
0
0
1
0
0
1
0
1
0
2
0
2
0
0
0
0
0
2
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
1
0
1
1
0
1
0
2
0
2
1
1
2
0
0
1
1
1
0
1
3
0
0
0
0
2
2
0
2
0
0
0
0
0
1
1
0
0
0
2
0
0
0
1
2
0
0
1
1
1
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
1
0
1
0
0
0
0
2
0
2
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
2
0
1
0
1
2
0
0
2
0
0
0
1
0
1
2
0
0
2
0
0
5
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
1
0
2
2
2
0
0
1
0
0
1
0
2
2
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
1
2
3
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
2
2
0
0
1
1
1
0
1
0
0
1
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
2
1
0
0
0
2
0
1
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
2
3
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
2
1
0
0
0
2
0
5
1
1
0
0
2
0
0
0
2
1
0
1
0
0
0
2
1
0
0
0
0
2
2
2
2
1
0
0
2
0
2
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
3
2
0
1
2
1
0
0
0
0
2
0
1
0
0
0
0
0
1
2
2
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
5
0
0
0
0
1
0
0
0
2
3
3
0
0
1
0
0
0
0
0
1
0
0
2
0
1
1
2
0
1
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
3
2
0
0
3
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
1
1
1
0
0
1
2
1
0
0
0
0
2
0
2
1
2
2
1
0
0
1
0
2
0
2
0
0
0
0
0
0
1
0
1
2
1
0
0
0
2
0
0
0
5
1
0
0
0
0
0
0
0
0
2
2
0
1
0
2
1
0
0
0
0
0
1
1
2
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
1
0
1
0
0
2
0
1
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
1
0
1
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
1
0
0
3
0
2
0
0
0
0
0
1
1
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
1
0
0
0
1
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
1
2
0
2
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
2
1
0
1
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
2
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
1
2
2
0
3
0
1
0
0
0
0
0
2
1
0
0
0
2
1
0
2
2
1
1
0
0
0
2
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
1
3
1
0
0
0
0
0
0
0
0
8
0
2
2
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
1
0
2
1
0
0
7
0
2
0
1
2
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
2
0
2
2
1
1
0
0
2
0
1
0
2
2
1
0
0
0
0
0
2
2
0
0
0
0
3
0
0
0
0
2
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
4
0
0
1
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
2
2
0
0
0
0
0
0
0
2
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
1
0
0
0
0
0
0
1
3
0
0
0
1
1
2
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
4
0
0
2
0
2
2
0
0
0
0
0
1
1
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
1
2
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
2
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
2
0
2
0
2
1
0
0
0
0
2
0
0
0
0
0
2
2
1
0
0
0
0
0
2
0
0
1
0
0
3
0
0
0
3
0
1
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
2
0
0
0
2
2
0
0
2
2
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
1
0
0
0
3
0
2
0
0
0
3
0
1
0
1
2
0
1
0
0
0
0
0
2
1
2
2
0
0
0
1
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
3
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
5
0
0
1
0
2
0
2
2
4
1
2
0
0
0
0
0
0
1
2
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
2
0
2
0
0
1
1
0
0
0
0
0
1
0
0
2
0
0
0
0
1
2
0
0
1
1
0
1
2
0
0
0
0
0
0
0
0
2
2
0
2
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
2
2
0
0
0
1
0
1
2
2
1
0
0
0
0
0
2
0
0
0
1
0
1
0
1
0
0
3
1
1
1
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
2
0
1
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
3
0
1
0
2
0
2
0
0
1
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
2
2
2
0
3
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
1
0
0
2
0
1
1
0
0
1
0
0
3
0
4
2
0
1
0
0
0
0
0
0
2
2
3
0
0
0
0
1
1
0
0
0
2
0
0
2
3
0
2
0
0
2
0
3
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
2
0
1
1
0
0
0
1
0
0
1
2
1
0
0
0
1
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
1
2
2
2
0
0
1
0
0
0
1
0
1
3
5
0
0
0
0
0
2
0
2
0
2
0
0
2
1
2
1
0
1
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
4
0
0
2
0
0
2
0
0
0
0
1
0
2
1
0
0
0
4
0
3
0
2
0
0
3
0
2
0
0
0
4
0
0
2
0
0
1
0
0
0
0
3
1
0
1
0
2
0
0
0
2
0
1
1
0
2
1
1
0
0
3
0
1
0
0
1
0
2
0
0
0
0
2
1
0
0
2
1
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
1
0
0
2
2
0
0
0
0
0
1
2
0
0
1
2
0
0
0
2
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
4
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
1
0
0
1
2
0
0
0
0
0
2
1
1
1
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
2
2
2
0
1
0
1
0
0
0
2
0
0
2
0
1
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
2
0
0
0
3
0
0
0
1
1
0
0
0
0
3
2
0
0
0
0
0
2
0
0
0
4
0
0
2
0
0
2
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
1
0
1
0
0
2
0
0
1
0
0
2
3
2
0
2
1
0
2
0
0
0
6
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
1
2
0
2
0
4
0
0
0
0
0
0
0
2
2
0
0
0
1
0
1
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
1
0
2
0
1
1
0
0
0
0
2
2
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
2
0
2
1
0
0
2
0
2
1
0
2
1
0
0
0
0
0
0
2
0
0
3
0
3
0
1
1
0
2
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
4
0
3
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
1
0
0
2
1
0
0
0
2
0
0
0
0
2
0
2
0
1
1
1
0
0
0
0
0
0
1
1
0
0
0
1
2
0
0
0
4
0
1
0
0
2
2
0
3
0
2
2
1
0
0
0
0
0
0
0
0
7
1
2
0
0
0
0
0
2
2
2
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
2
2
0
0
0
2
0
3
0
0
5
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
1
3
0
0
0
0
0
2
0
1
0
1
0
2
0
0
2
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
2
0
0
2
1
0
2
2
6
0
1
0
1
0
0
0
0
2
2
0
2
0
0
0
0
3
1
3
0
0
0
0
0
2
0
0
0
2
0
2
0
1
0
0
1
0
1
2
0
0
0
0
1
0
2
0
0
0
2
0
2
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
2
0
4
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
2
0
0
1
3
0
2
0
0
0
0
0
2
0
0
0
3
1
2
0
0
0
2
0
1
1
0
3
1
0
0
0
2
0
0
0
1
0
1
0
0
2
0
0
3
0
0
0
0
2
2
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
1
2
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
3
0
0
5
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
1
2
0
0
1
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
2
0
1
0
1
2
0
0
0
1
0
0
2
0
2
1
0
1
0
0
0
0
1
0
0
0
0
0
0
2
2
1
0
2
0
0
0
1
0
0
0
2
0
0
0
3
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
1
1
0
0
2
0
0
0
2
0
0
0
0
0
1
0
1
0
1
0
2
5
0
0
0
1
1
0
0
1
2
0
0
0
0
0
0
0
0
0
2
1
2
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
2
0
0
1
0
0
2
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
2
0
2
0
1
0
0
2
0
0
0
1
0
0
0
1
1
0
2
0
3
0
2
2
0
0
0
1
0
0
0
0
0
0
0
3
1
0
0
0
1
2
0
0
1
2
0
0
0
2
0
0
2
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
1
1
0
1
2
0
0
1
0
2
0
0
0
0
0
0
2
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
2
2
0
0
2
0
0
1
0
0
0
0
1
2
0
0
2
0
0
0
0
1
0
0
0
0
1
2
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
2
2
1
0
2
2
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
1
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
1
1
0
1
0
0
2
0
0
1
0
0
4
0
0
2
1
1
0
1
0
1
0
2
0
0
0
1
0
0
1
1
2
0
3
0
2
2
5
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
2
0
2
0
1
0
2
1
0
1
1
0
2
0
2
1
1
0
0
2
0
2
0
0
0
0
0
0
2
1
2
0
2
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
2
0
1
0
0
1
0
0
0
1
0
1
0
2
2
0
1
0
1
0
2
0
0
1
0
0
0
1
0
0
1
0
2
0
1
1
0
0
2
0
1
0
1
0
3
0
0
0
3
1
2
1
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
1
0
0
1
0
0
0
0
1
1
0
1
1
0
0
0
0
2
1
3
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
2
3
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
3
0
4
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
2
1
0
0
2
2
0
0
0
1
0
0
0
3
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
5
0
1
0
1
0
0
0
1
2
3
0
0
2
0
0
0
1
0
2
2
0
2
0
2
0
0
0
2
0
1
0
0
2
0
0
2
0
0
0
1
0
0
2
0
0
2
2
1
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
4
2
0
0
0
0
0
0
1
0
0
2
2
2
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
1
0
0
0
2
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
1
2
0
1
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
1
0
2
0
0
1
0
1
0
0
0
5
0
0
0
0
1
0
2
0
2
0
0
2
0
1
0
0
0
0
0
0
0
2
1
0
0
0
1
3
0
0
1
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
2
0
1
2
0
0
0
0
1
0
2
0
0
1
1
0
0
0
0
0
0
0
1
2
0
0
2
0
0
2
0
0
1
0
0
1
2
2
0
0
0
0
0
0
1
0
0
2
0
2
0
0
1
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
1
1
1
2
2
0
0
2
0
0
0
0
0
2
0
2
1
0
3
1
0
0
0
0
2
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
2
0
2
0
0
2
2
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
2
0
2
0
0
1
0
0
2
0
2
0
0
0
1
0
2
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
4
0
0
0
1
0
0
0
0
1
0
0
0
2
2
0
0
1
2
0
0
0
0
0
2
2
1
0
0
1
1
0
2
1
0
1
0
0
1
3
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
2
1
0
2
0
0
0
0
2
0
0
0
0
1
1
0
2
0
1
0
1
0
2
1
0
0
2
2
1
0
0
0
0
0
0
2
0
0
0
2
2
2
0
1
0
0
0
0
0
0
1
2
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
2
2
0
2
0
0
0
0
0
1
3
0
1
1
0
0
0
0
3
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
3
0
0
0
0
2
0
2
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
1
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
1
0
0
0
2
0
0
0
0
1
2
0
0
5
2
0
2
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
2
0
3
1
0
0
0
0
2
1
1
1
1
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
1
1
0
0
1
0
0
0
2
0
1
0
2
2
0
0
0
2
0
0
0
1
0
3
1
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
2
0
0
0
2
0
0
1
0
1
0
0
0
1
0
1
0
0
2
0
0
0
0
0
2
2
2
0
0
0
0
0
2
0
0
0
0
0
6
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
2
2
0
1
1
0
0
0
0
0
2
0
0
0
1
0
2
0
1
0
0
0
1
1
2
0
1
0
1
0
2
0
2
0
2
1
0
2
0
2
2
0
2
0
3
1
1
2
0
2
2
0
0
0
0
2
0
0
0
1
2
0
0
1
0
0
2
1
0
2
0
0
0
1
2
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
2
2
0
0
0
2
2
0
0
1
0
2
0
0
0
0
0
1
0
2
0
0
0
0
3
0
4
0
2
1
2
1
1
1
0
0
4
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
2
1
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
3
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
3
0
0
0
0
1
0
0
1
0
0
2
2
1
0
2
2
0
0
0
1
0
0
1
2
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
1
2
1
2
0
1
0
2
0
0
0
0
0
0
0
0
2
1
0
1
0
0
2
1
0
0
0
1
0
0
0
0
2
0
4
0
0
2
0
0
0
1
0
1
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
1
1
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
9
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
1
2
0
0
1
0
0
3
0
0
0
0
0
0
2
0
1
2
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
2
0
3
0
0
0
0
0
1
1
1
0
0
3
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
3
0
0
0
2
0
0
0
3
0
1
0
0
0
0
0
0
0
0
1
0
2
1
0
2
2
2
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
3
0
0
2
1
0
0
0
0
0
2
0
0
0
2
0
0
3
0
0
0
3
0
1
0
0
0
0
2
0
0
0
2
0
0
0
1
0
3
0
0
1
2
0
1
2
1
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
1
0
0
0
1
0
0
0
0
1
2
0
0
0
0
2
1
0
0
1
2
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
2
0
0
0
0
2
0
1
2
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
2
2
0
0
0
0
3
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
2
0
0
3
2
0
2
1
0
0
0
0
1
0
2
0
1
0
1
0
2
1
2
0
0
0
0
2
0
0
0
0
2
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
2
1
1
1
0
2
2
2
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
1
3
0
1
0
2
0
0
3
0
2
2
0
0
0
0
1
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
2
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
2
1
1
0
0
0
0
3
0
0
1
0
0
0
1
2
0
1
0
1
0
0
2
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
3
0
1
0
0
1
0
0
2
0
0
1
0
3
0
2
0
0
0
2
0
1
0
0
0
0
0
1
1
1
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
3
3
0
0
0
0
0
3
0
0
1
0
0
0
0
0
2
0
1
0
0
2
1
0
1
0
0
0
0
0
2
0
0
2
0
0
0
2
1
0
0
0
0
0
1
0
1
3
0
0
0
2
1
2
0
2
1
0
0
0
2
2
2
1
0
0
0
0
0
0
0
0
0
1
2
1
0
2
0
0
0
2
3
0
0
0
0
0
1
2
0
0
0
2
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
1
1
1
0
0
0
1
2
0
2
0
0
2
0
0
0
1
2
0
0
0
2
0
0
0
1
1
1
2
0
0
2
0
0
0
1
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
2
1
1
2
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
1
0
3
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
1
2
0
0
0
0
0
2
1
0
0
0
1
2
0
1
0
0
2
0
0
3
1
1
0
0
3
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
1
0
0
0
1
2
0
0
0
2
2
0
0
0
0
0
0
2
2
0
2
0
1
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
3
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
3
1
12
0
0
0
0
1
0
2
1
0
0
1
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
3
1
2
0
0
0
0
1
0
2
3
0
1
0
0
0
0
0
2
0
0
0
2
0
1
1
1
0
2
0
2
0
1
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
3
1
0
0
1
0
0
0
1
0
0
0
1
0
3
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
1
0
2
0
2
2
1
0
0
0
4
0
2
0
0
0
2
0
1
0
2
2
0
2
0
2
2
0
0
0
0
1
1
1
0
2
0
0
0
0
1
0
0
0
0
2
2
0
0
2
0
0
0
0
2
0
0
2
2
0
3
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
3
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
1
2
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
4
0
2
0
1
2
2
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
2
2
0
0
0
2
0
1
0
0
2
0
0
2
2
2
0
0
0
0
0
2
0
1
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
1
1
2
0
0
0
0
0
1
2
0
2
3
0
0
1
0
0
2
0
0
0
0
2
0
0
0
2
0
2
1
0
2
1
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
4
2
0
0
1
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
1
2
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
2
2
2
0
1
0
2
0
2
0
0
1
0
0
1
0
2
0
0
0
0
0
0
1
0
2
0
1
1
2
0
1
0
1
0
0
1
0
2
0
0
2
0
0
2
0
3
0
0
0
0
2
0
0
0
1
7
1
0
0
1
1
1
0
2
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
2
1
0
0
1
0
0
0
0
0
1
0
0
2
0
0
1
1
0
2
0
2
0
1
0
0
0
0
2
0
0
2
2
0
0
0
4
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
1
0
0
0
1
0
0
1
2
0
0
2
2
0
2
0
0
0
0
1
0
3
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
2
2
2
2
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
2
2
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
2
1
0
1
1
0
0
0
0
2
0
2
0
0
2
0
2
2
1
2
0
0
1
0
0
1
0
2
0
2
0
1
0
0
2
1
0
0
3
0
0
0
0
0
2
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
2
0
2
0
1
0
0
1
0
3
2
0
0
2
0
1
4
2
0
2
0
0
0
0
3
1
0
0
0
1
1
0
0
2
0
0
0
0
0
0
1
1
0
0
2
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
1
0
0
2
0
0
0
1
1
1
1
2
1
0
0
0
0
0
2
0
0
0
2
0
4
2
2
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
3
1
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
3
1
0
2
0
0
2
2
0
1
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
1
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
2
1
1
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
2
0
2
3
2
0
0
1
0
0
0
1
0
0
0
0
4
0
0
0
1
2
1
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
1
1
0
0
0
1
2
0
0
1
1
0
2
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
2
1
0
0
2
0
0
0
0
2
0
1
4
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
2
2
0
2
2
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
1
3
2
1
1
0
0
0
0
3
1
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
2
2
0
0
0
2
0
2
2
0
0
0
0
1
0
0
0
9
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
3
1
0
0
0
0
0
2
2
0
0
0
0
4
0
0
2
0
0
0
1
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
2
0
0
1
0
2
0
2
0
0
0
0
1
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
2
0
0
1
0
2
0
1
0
0
2
0
2
0
0
0
0
3
0
3
2
0
0
0
0
0
0
2
0
2
1
1
1
0
0
0
2
0
1
0
1
2
0
2
0
2
1
3
0
9
0
0
0
2
2
2
0
0
0
1
0
0
0
0
2
3
1
0
2
1
1
0
0
0
0
1
0
0
0
0
2
0
2
0
2
0
0
1
0
0
0
2
2
0
2
1
0
0
2
0
0
0
0
2
0
3
0
2
2
0
2
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
3
1
2
0
0
0
2
0
1
1
0
0
0
3
0
0
2
0
0
1
2
0
3
1
0
0
0
0
3
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
1
0
2
2
1
0
2
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
2
1
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
2
0
2
0
0
0
2
1
0
1
0
0
0
0
1
4
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
2
1
0
0
2
1
2
0
2
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
2
0
0
0
0
1
0
1
2
1
2
0
0
0
0
0
0
0
0
2
1
0
3
0
0
0
0
2
0
0
3
0
1
2
1
1
0
0
1
0
0
0
1
5
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
3
2
0
0
0
0
0
1
2
0
0
0
0
0
2
0
1
0
0
0
0
1
2
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
1
0
0
0
0
1
1
0
2
0
0
1
0
0
0
2
2
0
2
1
0
0
0
3
2
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
2
2
0
2
0
2
1
0
0
0
0
4
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
2
2
1
2
0
0
0
0
0
2
2
0
2
3
3
1
0
0
0
0
2
0
0
0
3
0
1
0
0
0
2
0
0
0
0
1
0
1
0
1
0
1
1
1
0
0
1
0
0
2
0
0
0
0
0
4
0
4
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
2
1
0
2
3
0
0
0
0
0
0
0
0
1
1
0
2
0
0
2
1
0
0
0
2
0
0
0
1
2
1
0
3
0
0
0
0
0
0
2
0
0
1
2
2
1
0
0
1
2
2
0
1
0
0
1
0
0
1
0
0
2
0
1
0
0
0
0
0
3
0
3
0
0
1
0
0
4
1
0
1
2
0
1
2
2
0
2
0
0
0
6
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
1
0
2
2
1
2
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
2
2
2
0
0
0
2
2
0
0
3
0
1
0
0
0
0
0
0
0
0
1
0
1
0
4
1
0
0
1
2
0
1
3
2
2
2
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
1
2
1
0
0
0
0
1
0
6
1
0
0
0
1
0
0
1
0
0
1
3
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
2
0
0
0
0
2
0
1
0
1
2
1
2
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
1
0
2
0
1
2
0
0
0
1
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
5
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
1
2
2
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
6
1
0
0
0
0
0
0
0
1
1
0
0
0
0
2
1
0
2
0
0
2
3
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
2
1
0
0
0
1
0
1
0
1
2
0
0
2
0
0
3
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
3
2
1
0
2
3
0
0
0
0
0
0
0
1
0
0
2
3
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
3
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
2
0
2
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
2
0
0
0
2
2
3
0
0
3
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
2
1
0
0
2
2
1
1
0
1
0
0
3
0
2
2
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
2
1
0
0
0
0
0
1
2
0
2
0
0
0
0
1
0
2
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
2
2
2
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
5
0
1
0
0
0
2
0
0
3
0
2
0
1
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
4
0
0
0
1
1
2
2
1
0
0
1
0
0
0
0
1
0
0
1
0
0
1
2
0
0
0
0
2
0
0
0
0
1
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
3
0
1
1
0
0
0
2
0
0
0
1
0
0
1
0
0
0
2
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
3
0
0
0
0
0
0
0
0
1
0
0
1
2
1
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
3
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
3
0
0
1
0
2
0
0
0
0
0
2
1
2
0
0
2
0
0
0
2
1
0
2
0
0
1
0
0
1
2
0
0
0
0
0
1
0
0
2
0
0
0
2
1
0
1
2
0
3
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
1
0
3
0
2
2
1
0
0
0
0
1
0
0
0
2
0
1
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
2
0
0
1
1
2
3
1
0
0
0
0
0
0
0
2
0
2
2
0
0
1
0
1
2
0
0
0
0
5
0
0
2
0
0
0
0
2
3
1
0
2
0
0
0
0
0
2
1
0
0
1
0
3
0
0
1
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
1
2
0
0
1
0
1
2
0
0
0
0
0
1
2
2
0
0
0
1
2
2
1
3
2
1
1
0
0
2
1
0
1
0
0
0
2
0
0
0
0
2
1
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
4
0
2
0
0
2
0
2
0
0
0
0
0
2
0
0
0
1
1
0
0
2
0
0
0
2
0
0
0
2
0
0
0
2
2
1
0
1
2
0
0
2
0
1
0
1
0
1
3
0
0
0
0
0
2
2
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
1
1
0
2
0
0
1
1
0
0
0
1
1
1
0
0
1
0
0
0
2
0
2
2
1
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
2
1
2
0
0
0
0
1
0
0
0
0
0
2
2
0
1
0
0
0
0
1
0
2
2
0
0
1
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
1
1
0
2
0
0
0
0
1
2
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
1
0
0
1
0
2
0
2
0
0
2
0
0
0
1
0
1
1
0
2
1
1
0
2
0
0
0
0
2
1
0
0
1
0
1
0
2
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
2
1
0
0
1
1
0
1
0
0
0
2
0
2
0
2
0
0
0
2
0
2
1
1
2
0
2
0
0
1
0
0
0
1
0
1
1
0
0
0
1
3
0
0
0
2
0
1
2
0
0
0
1
1
0
3
0
0
0
0
0
0
2
0
0
0
2
1
0
2
0
1
0
1
1
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
2
1
0
1
1
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
1
1
0
0
0
0
1
2
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
5
0
2
1
0
0
1
1
1
0
2
2
0
0
0
0
0
1
1
0
1
0
0
0
0
0
2
3
0
2
0
0
0
0
0
1
2
2
0
0
0
1
0
0
1
0
0
1
0
1
1
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
3
0
0
0
1
0
1
0
0
0
2
0
0
0
1
0
1
2
0
0
2
0
2
0
0
1
0
0
4
0
0
0
0
1
0
2
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
3
1
0
1
0
0
0
1
1
0
0
0
2
0
0
0
1
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
5
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
3
0
0
1
2
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
3
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
2
0
0
2
2
2
0
0
0
0
6
0
0
2
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
1
1
2
0
0
1
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
2
2
1
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
2
2
0
0
2
2
1
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
3
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
2
2
0
0
1
0
0
1
1
0
1
1
0
1
2
0
0
2
0
0
0
0
0
0
2
0
1
4
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
2
0
0
1
2
2
2
0
4
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
2
0
3
2
0
0
0
2
0
0
0
0
1
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
1
0
1
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
3
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
2
1
0
2
0
0
0
2
0
0
0
0
0
0
2
2
0
1
0
2
0
3
0
0
0
1
0
0
0
0
1
0
0
0
3
1
1
0
0
1
0
0
0
3
2
0
0
2
2
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
1
0
1
0
0
0
3
0
0
2
1
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
2
0
2
0
0
1
0
0
0
0
1
0
0
0
0
3
0
2
1
0
0
1
2
1
0
0
0
0
0
0
2
0
2
0
2
1
0
1
1
2
0
2
0
1
0
0
2
0
0
1
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
2
1
0
1
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
2
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
4
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
4
0
1
1
0
0
1
4
0
0
2
0
2
0
0
0
0
1
1
1
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
2
2
0
0
1
0
0
1
3
2
0
1
1
4
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
2
1
1
0
0
1
2
0
0
0
2
0
0
0
1
0
0
0
1
0
0
1
1
0
0
2
1
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
1
0
0
1
1
1
1
0
0
0
5
2
0
2
2
2
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
1
0
1
0
4
0
0
0
0
0
0
1
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
2
0
1
1
0
0
2
0
0
0
0
1
0
0
0
0
0
1
2
0
0
2
0
0
1
2
2
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
3
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
4
5
0
2
0
3
0
0
0
0
0
0
0
0
0
2
1
0
2
0
1
3
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
1
0
3
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
1
2
2
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
1
1
2
1
0
2
2
2
0
0
0
1
0
0
0
0
2
0
0
0
1
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
1
2
3
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
2
0
1
0
0
0
1
0
0
2
2
0
0
0
1
3
0
2
2
2
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
2
3
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
1
3
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
3
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
1
1
2
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
2
0
0
3
2
0
1
0
0
2
0
0
1
0
3
1
0
1
0
2
0
3
0
5
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
1
0
1
0
0
1
0
2
0
1
0
2
0
2
0
1
2
0
0
0
0
0
3
2
1
1
0
0
3
2
2
0
1
0
2
0
0
0
0
0
2
0
0
1
0
1
1
0
0
1
0
0
0
0
0
2
0
1
0
2
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
2
0
1
0
0
0
2
0
0
0
0
0
3
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
2
0
2
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
3
0
0
0
0
2
2
0
1
0
0
0
2
0
1
0
0
0
1
0
1
0
0
0
0
2
0
1
2
4
0
2
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
1
0
0
2
2
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
6
0
0
1
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
2
0
0
3
1
0
0
0
1
0
2
0
0
2
0
1
0
2
0
2
0
0
0
0
0
0
0
0
2
0
2
1
1
0
0
0
0
2
0
1
0
0
0
1
2
0
1
2
0
0
0
0
3
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
2
0
0
1
0
2
0
0
2
0
0
1
1
0
0
0
1
0
1
0
0
0
2
0
0
2
6
0
0
0
2
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
3
0
2
0
0
2
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
1
0
0
0
5
1
1
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
2
1
0
2
0
2
2
0
0
0
0
1
2
0
0
0
1
0
1
0
1
2
2
1
1
0
0
0
2
1
1
2
0
2
0
2
0
0
0
0
1
0
2
1
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
2
0
1
0
0
3
0
0
1
0
0
0
0
2
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
1
0
2
0
0
1
0
0
6
0
2
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
1
0
0
0
0
0
3
0
0
0
2
0
1
1
1
2
0
1
2
0
0
0
0
0
0
2
0
2
2
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
2
1
0
0
0
5
0
5
0
0
3
0
0
1
1
0
2
2
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
2
0
0
1
0
1
2
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
2
0
0
1
0
2
2
0
1
0
1
1
1
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
2
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
3
0
0
0
0
1
0
7
2
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
2
0
1
2
0
0
1
0
0
1
0
0
0
0
2
0
2
0
1
2
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
3
2
0
0
1
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
2
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
3
0
0
0
0
0
0
0
0
2
1
1
0
0
2
1
0
1
0
0
0
0
0
0
2
3
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
3
0
0
2
0
2
0
1
0
2
0
2
0
0
0
1
0
0
1
0
0
2
0
2
0
2
0
0
2
2
1
0
0
0
0
2
0
1
2
0
1
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
1
1
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
3
2
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
1
0
0
0
0
1
2
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
2
0
0
1
2
0
0
0
3
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
1
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
2
2
1
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
2
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
3
0
1
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
2
2
0
2
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
3
1
0
0
0
1
0
2
1
1
0
0
0
0
0
1
1
2
1
2
0
0
2
0
1
0
2
0
0
0
1
2
0
0
0
2
1
1
0
0
0
1
1
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
1
0
1
1
0
2
0
0
0
2
0
0
0
0
0
0
0
2
1
0
1
0
0
0
2
1
2
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
3
0
1
0
0
0
2
0
2
0
0
3
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
1
2
0
0
0
0
1
0
0
0
1
0
1
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
1
2
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
2
1
0
1
0
3
2
0
0
0
2
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
7
2
1
1
2
0
0
0
2
0
0
0
0
0
6
1
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
1
0
0
1
2
1
0
2
0
0
3
0
1
0
0
0
0
0
0
0
0
3
2
1
2
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
2
0
0
0
0
0
0
1
0
5
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
1
0
0
0
1
0
2
0
1
0
0
2
0
1
0
2
0
1
1
0
1
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
2
0
0
1
0
2
2
0
1
0
0
2
2
0
0
0
0
0
0
0
0
1
0
1
0
1
0
2
2
0
1
0
0
0
0
0
1
0
1
2
1
0
2
1
4
0
0
1
0
1
0
0
1
0
1
0
0
0
0
2
0
0
0
2
1
2
2
0
0
1
0
0
0
0
0
0
3
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
6
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
2
0
2
0
1
0
1
1
0
2
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
1
0
1
2
0
3
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
2
0
1
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
2
0
1
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
2
1
0
1
0
2
1
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
2
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
3
2
1
0
1
0
2
0
0
2
0
2
0
0
2
0
3
2
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
1
1
2
0
0
0
0
0
2
0
1
0
1
0
0
1
0
0
0
3
2
0
0
0
2
2
1
2
1
0
1
0
1
2
0
2
0
4
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
2
0
0
2
0
1
0
2
0
2
1
0
0
0
0
2
1
2
1
1
1
0
0
0
0
1
0
0
0
1
2
0
2
0
0
2
0
0
0
0
0
0
1
1
0
0
1
0
0
0
2
1
2
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
6
0
2
2
0
0
0
0
2
0
0
1
0
0
0
0
0
2
1
0
0
0
2
0
2
0
1
1
0
0
1
0
0
2
0
0
0
1
0
1
0
0
2
1
3
0
0
0
1
0
0
0
1
0
2
0
3
1
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
2
1
0
2
0
0
0
0
1
1
0
2
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
1
0
0
0
1
1
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
2
1
0
2
0
0
1
1
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
1
0
0
2
1
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
1
1
0
0
0
1
2
0
0
2
1
2
1
2
0
0
0
13
0
2
0
0
1
2
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
2
1
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
2
0
2
0
0
1
0
1
0
1
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
2
0
0
0
2
2
0
1
0
1
0
0
1
0
5
0
0
0
1
1
0
2
3
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
2
0
0
2
0
0
0
0
1
0
1
0
0
0
2
3
0
0
2
0
0
2
1
2
0
0
1
0
0
2
1
1
0
0
2
0
0
0
0
0
0
1
2
0
0
0
2
0
1
0
0
1
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
2
0
2
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
3
0
2
0
1
0
1
0
0
0
1
0
0
0
0
0
3
0
0
0
0
1
0
0
2
0
0
2
1
1
0
1
3
0
0
2
0
0
0
1
0
2
1
0
0
0
3
2
0
0
2
2
2
0
2
0
0
0
2
0
2
0
0
2
0
0
0
1
0
2
0
2
0
1
0
0
0
1
2
0
0
1
0
0
3
0
1
0
0
1
2
2
2
0
0
0
0
2
1
0
0
2
0
2
0
1
0
0
0
0
1
2
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
3
0
1
0
0
1
0
0
0
2
0
0
0
1
3
2
0
0
1
0
0
0
0
2
0
0
0
1
0
0
2
0
2
1
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
2
1
2
0
2
1
0
0
0
0
1
0
1
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
3
0
0
2
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
3
0
0
0
0
1
0
1
1
0
1
2
0
2
0
0
0
0
1
0
0
0
1
2
0
0
0
0
3
1
0
0
0
0
0
0
1
2
1
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
1
0
3
1
4
1
0
0
0
2
2
0
0
0
0
0
1
0
0
1
3
1
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
1
0
0
1
2
0
3
0
2
0
1
2
0
0
2
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
2
3
1
2
0
0
0
2
0
1
0
2
0
0
2
0
0
2
2
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
1
0
1
0
0
0
2
3
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
5
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
2
3
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
3
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
1
0
0
0
2
1
0
0
0
1
3
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
1
1
0
0
0
0
2
4
1
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
1
1
1
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
4
2
0
0
1
0
2
0
0
1
1
0
0
0
0
0
0
2
0
0
0
2
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
1
2
0
0
0
0
0
1
1
0
0
0
2
0
0
0
2
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
2
0
0
0
0
1
1
1
0
5
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
1
0
0
2
0
0
0
0
1
0
1
2
1
2
1
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
2
2
0
4
3
0
1
1
0
3
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
2
2
2
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
2
1
0
0
2
0
2
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
1
2
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
3
0
2
0
0
0
0
1
1
0
0
0
0
1
2
0
0
0
1
2
0
2
0
0
0
0
0
1
0
0
0
2
2
0
0
1
0
1
0
0
1
0
2
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
1
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
3
0
0
0
0
0
1
1
1
2
0
0
0
0
1
0
0
1
0
1
0
2
0
2
1
1
2
2
0
1
0
0
0
0
0
1
0
0
0
2
0
7
2
0
0
0
0
1
0
0
0
1
1
0
1
1
0
0
0
0
2
1
1
0
2
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
2
0
0
0
0
0
0
1
1
1
2
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
1
2
0
0
0
1
0
0
0
2
1
2
0
0
0
0
1
2
1
0
0
0
2
0
0
0
0
2
0
1
0
1
1
0
0
0
0
3
0
2
1
0
0
2
0
1
0
2
0
2
0
0
1
2
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
1
1
0
0
0
0
2
0
0
0
0
2
0
1
0
1
0
0
0
0
2
2
2
0
2
0
0
0
0
0
0
0
3
2
9
0
0
0
0
0
2
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
2
0
0
3
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
2
1
0
0
0
2
0
2
1
0
0
0
0
0
1
3
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
3
2
0
0
0
1
0
0
0
0
0
6
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
2
0
0
2
0
0
2
1
1
1
0
0
1
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
4
0
1
2
2
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
3
0
2
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
1
0
0
2
0
1
0
0
0
0
1
0
0
1
2
1
0
2
2
0
2
0
0
0
1
0
0
2
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
1
0
2
2
2
0
1
2
2
2
0
1
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
2
0
0
3
2
0
1
0
0
2
2
0
3
0
0
1
1
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
2
2
0
2
1
1
0
0
1
0
0
0
0
1
0
0
0
1
0
5
0
0
0
1
0
2
0
0
0
0
0
2
0
0
2
2
0
1
1
0
0
2
2
1
0
1
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
2
0
1
0
1
0
1
0
0
0
1
1
1
1
1
0
2
0
0
0
1
0
0
2
0
2
0
0
0
1
0
0
1
0
0
0
2
0
0
0
3
0
2
0
0
0
1
2
0
0
0
0
0
0
2
0
0
1
1
0
2
0
0
0
6
0
2
2
0
0
0
1
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
3
1
0
0
0
0
3
1
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
2
1
2
1
1
0
2
3
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
2
1
0
1
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
3
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
2
0
1
0
0
1
0
3
2
0
0
1
3
0
0
0
0
0
0
2
2
0
1
1
2
0
2
3
1
0
0
0
0
2
0
0
0
2
3
0
1
0
1
1
1
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
2
2
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
1
2
0
2
0
0
0
1
2
0
0
2
0
1
0
0
0
0
1
2
0
0
0
4
1
0
0
0
0
0
0
0
0
1
1
3
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
2
0
0
0
1
0
0
1
0
2
0
0
0
0
0
1
2
0
0
2
0
0
0
1
2
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
1
0
2
1
0
0
0
2
2
0
0
0
0
2
0
0
2
1
0
1
0
2
0
2
0
0
0
0
0
2
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
2
0
2
3
2
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
2
1
0
2
2
0
0
0
0
0
3
0
0
0
3
0
0
0
0
0
0
2
0
0
2
0
0
2
0
1
2
0
0
0
0
1
0
0
2
1
0
0
0
2
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
4
0
0
0
0
0
0
6
0
0
2
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
2
0
8
2
0
0
0
0
0
0
2
2
0
0
1
1
0
2
2
2
0
0
0
0
2
2
0
2
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
1
0
2
0
0
0
0
2
0
0
0
0
1
0
3
2
0
1
3
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
3
1
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
2
2
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
3
1
0
0
0
0
0
0
0
1
1
0
1
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
2
0
1
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
2
2
0
0
0
1
2
0
0
0
2
0
2
0
0
0
0
0
0
2
1
1
1
1
0
1
0
0
0
0
0
0
1
0
2
0
2
1
0
1
1
2
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
1
2
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
3
0
0
0
0
2
2
0
2
0
1
0
0
0
0
1
2
2
1
0
0
2
0
0
1
2
0
0
0
0
1
0
0
2
0
1
0
0
0
1
0
2
1
3
0
0
0
2
1
2
0
2
1
0
4
0
0
0
0
1
0
0
2
0
0
2
0
0
1
0
1
0
1
2
0
1
1
1
1
0
2
0
0
0
0
1
0
5
0
2
0
0
0
0
0
0
2
1
1
0
0
0
1
0
2
0
2
0
1
0
2
2
2
0
0
0
0
0
1
0
0
2
0
1
0
0
3
0
0
1
1
1
0
0
2
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
1
0
3
0
0
1
1
2
2
0
0
0
2
0
2
0
0
1
0
0
1
0
3
0
0
2
0
0
1
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
1
1
0
1
2
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
3
0
2
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
2
1
0
0
0
0
0
0
1
0
1
0
2
0
2
0
0
1
0
2
0
0
0
1
7
0
0
0
0
0
0
0
1
0
1
2
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
2
2
0
2
0
1
0
0
2
0
0
0
0
3
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
1
0
2
0
1
1
1
0
0
0
0
1
0
0
1
2
0
0
0
4
0
0
0
0
0
0
1
0
1
0
0
1
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
2
0
0
2
0
0
2
0
0
0
0
0
0
2
0
1
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
2
0
2
2
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
1
2
1
2
0
2
0
1
0
2
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
1
0
2
0
1
0
0
0
0
2
0
0
2
0
1
0
0
2
0
1
0
2
0
1
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
2
1
1
0
0
1
0
0
0
0
0
0
3
1
3
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
3
0
1
0
2
1
0
0
2
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
2
2
1
2
1
2
0
0
0
1
0
0
1
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
2
0
0
0
0
2
0
2
0
2
0
0
1
2
0
0
0
0
6
1
0
2
0
0
0
0
4
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
5
1
1
4
0
0
0
2
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
1
0
0
0
3
0
0
0
0
0
1
3
1
0
1
1
0
2
2
0
0
2
1
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
3
0
1
0
0
2
0
1
0
1
1
4
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
2
0
2
0
0
0
0
1
1
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
1
1
0
1
0
0
0
0
2
1
0
0
0
2
2
0
0
1
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
1
1
0
0
1
3
0
1
1
2
1
0
0
0
1
0
0
0
1
1
0
1
0
2
0
1
2
0
1
2
4
0
1
1
0
0
0
0
0
3
1
1
1
2
0
0
1
0
2
1
0
0
0
0
0
0
0
2
1
3
0
0
1
0
0
2
1
0
0
1
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
1
0
2
1
1
0
0
0
0
0
0
0
2
1
0
0
1
1
0
0
0
0
1
0
2
0
0
2
1
0
0
0
0
2
0
2
0
0
1
2
1
3
0
0
1
0
1
0
0
0
0
0
3
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
3
1
0
0
0
1
1
0
2
3
1
0
2
0
0
0
0
0
1
0
2
0
0
1
0
2
0
0
0
2
0
1
1
2
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
1
2
0
0
0
2
0
0
2
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
2
2
1
2
2
0
1
2
1
0
0
0
0
0
1
1
0
0
0
0
3
0
0
1
0
0
2
0
0
5
2
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
1
0
2
1
2
1
0
0
2
0
0
0
0
0
0
1
2
1
6
2
0
2
0
0
0
0
0
0
2
0
5
7
2
2
0
2
0
2
1
0
0
1
3
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
3
0
0
0
2
3
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
1
1
0
1
0
1
0
1
2
0
0
0
0
2
2
0
1
0
2
1
3
0
2
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
2
0
1
0
0
0
0
0
0
0
1
2
2
2
0
2
0
2
0
2
0
0
2
0
0
0
1
0
0
1
2
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
1
0
9
2
2
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
3
0
0
3
2
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
1
0
2
0
0
0
0
0
1
2
2
0
0
0
0
2
0
1
3
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
2
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
1
0
0
0
2
0
1
0
0
0
0
0
1
1
0
0
2
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
8
0
0
2
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
3
0
2
2
0
0
5
0
0
0
0
2
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
1
2
0
0
0
3
0
0
0
1
0
1
0
0
0
0
3
1
1
2
0
2
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
2
0
0
1
2
0
0
2
0
2
0
0
1
0
0
1
1
0
0
0
2
0
0
1
1
0
0
0
0
1
0
2
2
2
0
2
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
3
0
1
1
0
1
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
2
2
0
0
2
0
0
2
0
0
1
1
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
2
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
3
1
0
0
1
0
0
1
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
2
1
0
0
1
3
0
1
2
0
2
0
0
0
0
0
2
2
1
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
2
2
0
0
0
2
0
2
2
0
2
0
0
0
1
0
0
2
0
0
0
1
0
2
0
0
0
2
0
1
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
2
0
2
1
0
1
1
2
0
1
0
0
0
0
0
0
0
1
1
2
2
0
2
2
0
0
0
3
0
0
0
2
0
0
1
0
0
0
0
0
1
2
1
0
1
0
1
2
0
0
0
0
1
0
0
2
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
1
0
0
0
4
6
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
1
1
0
0
0
0
2
0
0
0
2
1
0
1
1
1
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
2
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
2
1
3
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
2
1
2
2
0
0
0
1
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
1
0
0
2
0
1
0
0
1
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
1
0
0
2
0
2
2
0
0
1
2
0
0
1
0
2
0
0
0
0
0
0
0
0
2
2
2
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
1
1
0
0
0
1
0
0
1
2
4
1
0
1
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
1
0
2
0
0
0
0
0
1
1
0
0
2
0
0
0
2
2
0
1
0
1
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
1
0
0
2
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
2
4
0
0
0
2
1
0
0
0
0
0
0
0
0
1
1
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
2
0
0
1
0
1
0
2
0
2
0
1
2
0
0
2
1
0
0
1
1
0
0
2
0
1
0
0
2
0
2
0
2
1
0
3
0
5
0
1
0
0
0
0
0
0
0
0
0
1
0
2
2
2
0
2
1
1
0
0
0
0
2
0
0
2
0
1
0
2
2
0
0
0
1
0
0
0
0
2
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
2
2
2
0
1
0
0
2
0
2
0
0
2
0
2
2
0
0
0
2
1
0
0
1
0
0
0
0
1
0
2
0
0
2
2
0
0
0
1
0
0
0
1
0
0
0
1
0
2
0
1
0
1
0
0
2
0
0
2
2
2
0
1
0
2
1
0
0
0
3
0
2
1
2
0
1
2
3
0
3
2
2
1
0
2
1
0
0
2
0
3
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
2
0
2
0
3
0
1
2
0
0
0
0
0
2
4
0
0
0
2
1
0
0
2
1
2
0
1
0
0
2
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
1
2
0
1
5
0
2
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
11
2
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
2
1
0
0
6
2
0
1
2
0
2
2
0
0
0
0
0
2
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
1
0
0
2
1
0
1
0
0
2
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
2
0
1
0
2
1
0
2
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
3
0
0
0
0
0
4
0
0
0
0
0
3
2
0
0
0
0
1
2
2
1
0
2
1
0
1
1
5
2
0
1
0
0
0
1
0
0
0
0
2
0
1
0
0
2
0
4
0
0
0
0
0
0
2
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
4
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
4
1
2
0
0
2
3
2
0
0
0
0
0
0
0
0
0
52
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
2
3
2
0
2
0
0
2
0
1
2
5
0
1
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
4
0
0
1
0
0
3
0
0
2
0
0
1
0
2
0
0
0
0
0
0
1
0
1
0
7
0
0
1
2
0
0
0
0
0
2
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
1
2
1
0
0
0
0
2
0
1
0
1
0
0
0
2
0
2
2
2
1
0
0
3
0
0
0
1
0
0
2
1
0
0
2
0
1
2
0
1
0
1
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
1
0
2
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
10
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
2
1
0
2
0
0
0
0
0
0
0
0
0
0
1
1
1
4
0
0
0
0
0
1
7
2
0
0
1
0
2
0
0
0
3
2
2
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
2
3
0
0
0
3
1
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
1
0
0
2
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
1
1
0
0
2
1
0
0
0
0
0
0
0
1
0
2
0
1
2
0
1
0
0
0
0
1
0
2
1
0
1
0
0
0
1
3
0
0
0
2
3
0
0
1
0
0
0
1
3
0
1
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
4
1
0
0
0
0
1
0
3
0
2
0
0
0
0
0
2
0
6
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
1
0
3
0
0
0
0
0
0
2
1
0
0
0
0
2
2
0
0
0
2
1
0
0
1
0
0
0
0
1
0
1
0
0
2
2
2
1
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
2
0
0
0
1
0
0
0
0
2
0
0
2
0
0
2
1
2
2
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
1
0
1
1
0
2
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
2
0
0
2
1
0
2
0
2
0
1
0
0
2
0
1
0
0
1
0
0
0
1
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
2
2
0
4
0
0
2
0
0
1
1
0
2
0
1
2
1
0
0
1
0
3
0
2
1
0
0
2
0
4
0
0
0
2
0
0
0
0
0
0
3
1
0
0
1
1
0
1
1
0
0
0
2
0
0
3
0
2
2
0
0
1
1
0
1
2
0
2
0
2
0
0
1
0
1
0
0
0
0
2
1
0
1
1
0
0
2
2
0
0
0
1
1
0
1
2
0
2
1
0
0
0
0
1
2
0
0
2
0
2
1
0
2
0
1
0
0
0
0
2
1
0
0
0
1
0
2
1
0
0
3
0
0
0
1
1
0
0
0
0
2
0
1
2
0
0
0
2
0
1
0
1
0
1
2
0
2
1
0
0
2
0
0
0
3
0
3
0
2
2
3
0
0
0
0
0
0
2
0
0
0
0
5
0
0
0
0
2
0
0
1
2
0
0
0
0
1
0
1
2
0
0
1
0
0
2
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
2
2
0
0
2
0
0
0
0
1
1
0
0
0
1
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
2
0
3
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
2
1
3
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
1
2
0
0
1
1
1
6
0
0
0
1
0
0
2
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
1
0
0
2
0
0
2
2
0
0
0
1
0
1
0
0
1
0
0
1
2
1
1
0
0
0
0
6
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
1
0
0
2
1
0
0
0
2
1
0
0
0
1
0
1
1
0
0
0
0
0
0
1
2
0
4
2
0
0
0
2
0
0
0
1
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
1
0
2
0
1
1
1
0
1
2
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
2
1
0
0
0
1
0
0
2
0
0
0
0
3
0
0
0
1
2
0
0
0
0
2
0
0
0
2
0
0
2
1
0
1
0
1
1
1
0
1
0
2
1
0
0
0
0
1
2
0
0
1
0
0
0
0
0
1
0
0
1
0
0
3
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
2
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
1
1
0
1
2
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
2
0
1
0
1
0
0
2
0
0
1
0
2
1
2
0
2
0
3
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
1
6
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
1
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
1
1
1
0
0
0
1
2
1
0
0
0
3
0
1
2
0
1
0
0
2
1
0
3
0
0
1
0
1
0
2
1
0
0
0
0
0
0
2
2
0
0
1
1
0
0
2
2
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
2
1
0
0
0
0
0
0
2
2
0
1
0
2
0
0
0
0
2
0
0
1
2
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
2
4
2
0
1
3
0
0
0
0
2
2
0
3
0
2
0
1
0
0
0
2
0
0
0
2
1
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
2
0
1
0
0
0
0
0
1
0
2
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
1
1
0
0
2
1
0
0
0
0
1
2
1
0
1
0
0
0
1
5
1
0
1
2
1
0
1
1
1
0
0
0
1
2
2
2
0
0
4
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
1
2
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
1
1
1
0
0
2
0
0
0
1
0
0
0
0
3
0
1
0
0
0
2
0
0
0
1
0
2
1
0
0
2
1
0
0
2
0
0
0
0
4
0
0
0
0
0
0
0
2
0
0
1
1
3
2
0
0
0
1
0
2
0
2
1
0
1
2
2
0
0
1
0
2
1
2
0
0
0
2
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
7
2
0
0
0
0
0
2
0
0
0
2
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
1
1
0
1
0
0
2
0
1
0
1
0
1
0
3
2
0
0
1
0
0
2
0
0
0
1
0
0
2
1
0
2
0
1
0
0
2
0
0
0
0
1
1
0
2
2
0
0
0
2
0
2
1
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
2
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
2
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
1
0
3
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
3
1
0
0
1
0
2
3
0
1
0
0
0
0
2
2
0
2
2
0
0
1
0
0
0
2
0
0
0
0
1
0
0
2
2
0
0
0
2
1
0
0
0
1
0
0
2
0
0
0
6
2
0
0
0
0
2
0
2
2
0
2
0
0
2
1
0
0
0
2
0
1
0
1
0
2
1
1
0
2
0
0
1
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
8
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
2
0
1
2
0
2
0
0
0
0
0
1
3
0
0
1
1
1
0
0
0
0
0
2
0
3
0
0
2
2
0
1
0
2
0
0
1
2
1
1
0
0
2
0
0
0
2
4
0
0
0
0
0
0
1
0
0
1
0
2
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
1
0
3
1
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
2
2
0
1
0
2
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
2
2
0
0
0
0
1
2
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
2
2
1
0
2
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
5
1
0
0
2
0
0
1
1
0
0
0
2
0
0
0
0
2
1
0
1
1
1
0
1
1
1
0
1
2
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
1
4
1
0
1
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
2
0
3
0
0
2
1
1
2
0
2
0
2
1
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
1
0
1
2
0
1
0
0
0
0
0
0
2
0
2
0
0
2
1
0
0
0
0
4
0
0
0
1
2
0
1
2
0
2
2
2
0
5
0
0
2
0
0
2
2
0
0
0
2
2
1
0
1
2
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
1
0
2
2
1
0
0
0
0
0
1
0
2
0
0
0
0
2
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
1
3
0
2
2
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
4
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
3
0
0
0
0
1
0
0
0
0
1
0
1
0
0
3
0
0
0
0
2
1
0
0
2
0
2
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
1
1
1
0
1
0
0
1
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
4
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
1
0
0
0
0
2
1
1
0
0
0
2
0
1
0
0
1
1
0
3
0
2
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
2
0
0
2
1
2
0
0
2
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
2
2
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
3
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
2
0
0
0
2
1
2
2
0
0
0
2
1
0
0
0
2
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
1
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
3
2
0
0
0
2
0
0
2
0
0
0
1
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
2
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
2
2
2
1
0
1
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
1
0
2
0
0
0
1
2
0
0
1
0
0
2
2
0
0
0
0
2
0
0
6
0
1
0
2
0
0
0
0
0
1
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
2
0
0
0
4
0
0
1
0
0
0
0
2
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
1
0
0
1
0
6
0
0
0
2
3
1
1
0
2
0
0
1
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
2
1
1
0
0
0
2
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
2
2
0
1
0
1
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
6
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
1
2
1
0
2
0
0
0
0
0
9
0
0
2
0
0
0
1
2
0
1
2
0
0
0
1
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
2
0
2
2
0
0
1
0
0
3
2
0
0
2
0
2
0
0
0
0
1
1
0
0
0
2
0
2
0
2
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
2
2
0
2
0
0
0
1
0
1
0
0
0
0
1
0
0
2
1
1
0
0
8
0
2
0
1
0
2
0
2
1
0
1
2
0
1
0
0
0
3
1
1
0
0
1
0
0
1
1
0
2
0
1
0
0
2
0
0
0
0
0
4
0
0
2
1
0
0
5
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
2
2
1
0
0
0
2
0
0
2
2
0
0
1
2
2
0
0
0
1
0
0
1
2
0
7
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
5
0
1
2
0
0
0
0
1
0
0
0
1
0
0
2
2
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
2
0
0
0
0
0
2
2
0
0
1
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
1
1
0
0
2
0
0
0
0
0
3
0
0
0
0
2
0
2
1
0
0
0
0
2
2
2
1
0
0
0
2
0
1
0
1
0
1
1
0
0
1
2
2
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
3
1
0
0
0
0
0
0
1
1
0
0
0
3
2
0
0
2
0
0
2
2
1
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
1
0
1
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
2
2
0
1
0
1
0
1
2
0
0
0
0
0
0
2
4
0
2
0
0
1
0
0
1
0
0
2
0
1
0
0
1
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
2
2
1
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
2
1
0
2
0
0
1
1
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
4
0
1
0
0
0
1
0
0
0
0
2
0
0
1
2
0
0
0
0
2
1
2
0
0
0
0
1
3
0
0
0
0
0
1
0
0
2
1
2
0
0
0
0
1
0
1
0
0
0
1
2
0
0
0
1
0
3
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
2
0
1
0
1
0
1
0
0
0
0
1
0
1
2
0
0
2
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
2
0
2
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
6
0
0
0
4
8
0
0
2
0
0
0
0
3
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
7
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
1
0
1
0
0
0
2
0
3
0
1
0
0
0
0
0
2
0
0
0
0
0
2
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
2
0
0
2
2
0
2
0
2
0
2
0
2
2
0
0
2
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
1
0
2
0
0
0
2
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
4
0
2
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
3
1
2
2
0
1
4
0
3
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
5
0
0
0
0
2
1
1
0
0
0
1
0
0
0
0
2
0
0
2
0
3
0
3
2
1
0
0
0
0
0
0
1
0
1
0
2
0
2
0
2
0
3
3
1
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
1
2
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
2
0
0
0
1
1
3
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
1
1
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
3
2
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
2
0
0
1
2
0
0
0
2
0
0
0
0
0
0
3
0
0
0
4
0
0
1
0
0
0
0
0
2
1
0
2
0
2
0
0
1
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
1
1
0
0
0
0
0
3
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
2
0
0
0
0
0
2
0
0
1
0
2
2
1
0
1
0
1
0
0
0
0
2
0
2
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
1
0
0
2
0
0
2
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
2
1
0
1
0
2
2
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
1
2
1
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
3
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
6
2
2
0
2
1
2
0
0
2
2
0
3
0
0
1
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
1
0
0
1
2
2
0
1
0
0
0
0
1
0
0
9
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
2
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
3
2
0
2
0
0
1
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
2
0
0
2
0
2
0
0
0
1
0
2
0
0
0
0
0
4
0
0
3
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
2
2
1
0
1
1
0
0
0
0
0
2
4
0
0
0
0
2
2
1
0
0
0
0
0
1
1
0
1
2
1
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
2
0
0
5
2
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
1
2
0
1
0
1
1
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
1
1
0
2
0
0
3
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
4
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
2
2
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
1
1
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
1
0
0
0
2
0
0
0
4
0
2
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
1
0
0
1
0
0
1
0
2
0
1
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
1
0
3
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
2
2
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
2
2
0
2
0
2
0
0
0
0
2
1
2
1
0
0
2
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
2
0
0
2
1
2
0
0
0
0
0
0
1
0
0
1
0
0
3
1
0
0
0
0
0
0
0
2
2
2
0
2
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
1
3
0
0
3
0
0
1
1
2
2
0
0
0
0
2
0
0
4
2
0
0
0
0
2
1
1
0
0
1
2
0
0
0
2
1
0
2
0
0
2
0
0
1
0
0
0
1
0
0
0
2
1
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
5
0
2
0
0
2
0
0
0
0
0
2
0
3
0
0
1
0
0
2
2
0
0
0
0
0
0
3
0
0
1
0
2
1
0
2
1
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
2
2
0
1
1
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
5
0
0
0
0
0
2
1
0
0
0
3
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
2
1
2
0
2
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
4
2
0
0
0
0
0
1
2
0
0
1
0
0
0
1
0
2
0
3
0
0
1
0
0
0
0
0
1
0
2
0
3
0
1
0
1
0
2
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
4
2
0
0
0
1
2
1
0
0
1
0
2
0
0
0
0
0
1
0
0
2
0
3
1
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
1
0
1
0
0
1
0
0
1
0
3
0
0
3
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
1
0
0
2
0
0
1
0
0
2
0
0
1
0
0
2
0
2
0
0
1
2
0
0
0
0
2
0
0
0
0
2
1
0
0
1
0
0
0
0
2
0
1
0
0
0
0
1
0
1
1
1
0
0
0
0
0
2
2
0
0
0
0
0
3
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
2
1
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
1
0
2
0
0
1
0
0
2
0
1
0
0
1
0
2
0
0
1
0
2
0
2
2
2
0
0
2
0
0
2
1
0
1
0
0
0
1
0
0
0
0
0
2
2
0
3
0
1
0
0
0
0
3
0
0
2
0
2
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
2
0
0
0
2
3
0
0
2
0
1
2
0
1
0
2
0
0
2
0
1
2
2
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
2
2
0
0
2
0
0
0
0
1
0
0
2
1
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
1
0
2
2
0
0
2
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
2
2
1
0
2
0
0
1
0
0
0
1
2
2
2
1
1
0
0
2
2
0
0
0
2
3
0
2
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
2
0
0
2
0
0
0
1
0
1
0
2
5
1
0
0
0
0
1
0
1
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
1
1
0
0
0
2
0
0
0
2
1
0
0
0
0
1
2
1
0
3
1
0
0
0
2
0
2
0
0
0
2
1
0
0
2
0
4
0
2
4
2
0
1
0
2
1
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
2
1
2
0
5
1
0
0
0
0
1
2
3
0
0
1
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
2
1
1
1
0
0
0
1
0
0
2
0
0
1
0
2
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
2
0
2
1
1
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
1
0
0
0
0
4
0
0
1
0
2
2
0
0
0
1
2
0
0
0
2
0
2
2
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
2
0
2
2
3
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
2
1
0
2
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
1
0
2
5
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
2
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
2
1
0
1
1
2
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
2
1
0
0
0
2
1
1
0
1
0
2
0
1
0
0
0
2
2
0
0
1
2
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
2
0
3
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
1
2
1
1
2
2
0
2
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
1
0
2
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
1
2
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
1
0
2
0
1
2
1
0
2
0
1
4
2
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
2
1
0
0
4
0
2
1
0
2
0
0
0
0
4
2
2
0
0
0
0
1
0
0
0
0
2
0
0
2
0
3
1
1
1
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
2
2
0
0
1
0
0
1
0
2
0
0
0
0
0
2
2
1
2
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
5
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
1
1
0
0
4
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
2
2
2
0
0
0
0
0
2
0
0
2
1
0
0
1
0
0
1
0
6
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
7
0
0
0
0
1
2
0
2
0
1
2
0
2
0
0
0
2
1
1
0
0
1
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
2
1
0
0
0
0
0
0
0
1
2
1
0
0
0
2
3
0
1
0
1
0
2
2
0
1
0
1
0
0
0
0
0
0
0
0
3
3
2
0
4
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
2
0
1
0
2
0
0
1
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
1
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
1
2
1
0
0
2
0
0
0
2
0
0
2
0
0
1
0
2
1
0
0
2
0
0
0
0
2
0
0
0
2
2
0
0
1
0
0
0
1
0
0
2
0
0
1
0
1
2
0
0
0
6
2
1
2
0
2
0
1
0
2
0
3
0
0
1
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
2
2
2
0
6
2
0
0
0
0
0
0
2
1
3
0
2
1
0
0
0
1
0
6
0
0
0
2
1
0
0
0
0
1
0
1
1
3
1
2
1
2
0
0
3
0
0
0
0
0
0
2
2
1
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
3
0
0
2
2
1
0
0
3
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
1
2
0
2
0
0
0
2
0
0
0
0
2
1
3
0
1
0
1
0
0
1
0
0
0
2
2
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
3
0
2
0
0
1
0
1
0
2
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
1
1
1
0
2
2
0
0
2
0
0
1
1
1
0
0
3
2
0
0
0
1
1
0
2
0
0
2
0
2
1
0
0
0
0
0
0
0
0
1
0
1
0
2
0
1
1
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
3
0
0
2
0
2
2
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
3
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
1
0
2
4
0
0
0
0
0
0
1
0
0
0
0
1
0
3
0
2
0
0
0
2
2
0
2
3
0
0
0
0
1
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
2
1
0
0
1
1
0
0
0
0
2
0
0
0
1
0
0
0
2
1
0
0
0
2
1
0
1
1
0
0
0
3
0
0
0
1
0
0
0
1
2
0
0
0
0
2
1
0
0
2
0
2
0
0
2
0
0
0
2
1
0
0
0
2
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
2
2
1
1
0
0
1
0
0
0
6
0
0
1
0
0
0
1
2
0
2
0
0
0
0
0
0
1
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
1
2
1
0
0
2
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
2
3
1
2
0
2
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
2
1
2
0
0
0
0
3
0
0
0
0
0
1
0
0
2
2
1
2
0
3
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
3
1
0
0
0
0
0
0
0
2
0
2
1
4
2
0
0
2
2
0
0
2
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
1
1
0
0
0
2
2
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
2
2
1
0
1
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
1
0
2
0
5
1
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
1
0
0
0
1
0
2
1
2
0
0
2
0
0
0
0
0
3
1
0
1
2
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
2
0
1
2
0
0
0
1
0
2
2
0
0
2
0
2
0
0
0
1
2
0
2
0
1
0
2
0
0
0
0
0
0
8
1
0
0
0
1
0
0
1
2
0
0
0
2
0
0
0
0
0
2
1
0
1
1
0
1
2
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
1
0
3
0
14
0
0
2
1
0
0
4
0
2
0
0
0
1
1
0
0
0
0
2
3
2
2
1
0
1
1
0
2
0
0
0
0
5
0
0
1
0
1
0
0
3
0
3
0
0
1
0
2
0
3
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
1
0
0
0
0
1
2
1
0
0
2
2
0
2
1
2
0
2
0
1
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
1
0
0
1
0
0
2
0
1
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
2
1
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
1
0
0
1
0
0
2
2
0
1
1
0
0
0
2
0
0
0
0
1
2
1
0
0
2
0
0
0
0
2
0
0
1
0
0
0
1
1
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
1
2
0
1
2
1
0
0
2
0
0
0
0
3
0
0
2
0
2
0
0
0
2
0
0
0
2
2
1
0
0
0
0
0
1
0
3
0
14
2
0
0
2
1
3
2
0
0
0
0
0
0
1
0
2
0
0
2
0
0
1
0
0
0
1
0
2
0
0
0
1
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
4
0
2
0
2
1
0
3
0
0
0
0
0
2
3
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
1
0
0
0
0
0
0
1
2
1
0
0
2
1
0
0
2
2
0
0
0
0
0
1
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
1
2
0
0
1
1
0
2
0
0
0
0
1
0
0
2
1
0
1
0
0
0
0
1
2
2
0
0
0
2
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
2
0
2
0
0
0
2
0
0
0
2
0
0
2
1
0
1
2
0
2
0
0
0
1
0
0
0
0
1
1
0
0
0
0
2
0
0
1
0
0
2
1
0
0
0
0
0
2
1
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
1
1
2
0
0
0
3
0
0
3
0
2
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
4
0
0
1
0
2
0
0
0
0
1
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
2
0
0
2
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
1
0
3
2
0
1
0
0
0
1
1
2
2
2
0
2
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
2
0
0
0
2
0
1
2
0
2
5
0
0
4
0
1
1
0
0
0
0
2
2
0
0
0
1
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
3
3
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
3
2
0
0
1
0
0
0
1
0
0
0
0
1
0
2
1
3
0
0
0
1
2
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
1
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
1
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
2
2
2
1
0
2
0
1
0
0
0
1
1
1
2
0
0
0
1
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
1
0
2
0
2
0
0
0
0
0
2
0
0
2
0
1
0
0
0
1
0
0
2
1
1
0
0
0
0
2
2
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
1
2
1
0
0
0
0
1
1
4
1
0
0
3
0
0
2
0
3
2
2
0
0
0
1
0
0
1
0
0
0
0
0
3
0
1
1
1
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
1
1
0
0
0
0
2
0
2
2
0
0
0
0
3
0
0
0
1
0
0
0
3
2
0
0
0
3
3
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
1
1
0
0
9
1
0
1
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
3
1
0
0
1
0
1
0
0
0
0
1
0
0
0
1
2
1
0
0
0
0
0
1
0
1
0
2
0
0
0
2
0
0
0
1
0
0
2
1
2
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
2
1
1
0
0
0
0
1
0
0
2
1
0
0
0
3
2
0
1
1
0
0
0
0
2
3
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
2
0
1
2
0
3
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
2
2
2
3
0
0
0
0
2
4
2
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
1
0
0
0
2
0
1
0
0
0
1
0
1
0
0
0
1
1
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
1
0
0
3
1
0
1
0
0
0
0
0
0
2
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
3
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
2
0
0
0
0
1
0
0
2
1
0
0
0
2
0
3
2
0
2
0
1
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
2
0
0
0
0
2
1
0
0
0
0
2
0
1
0
0
2
0
2
4
0
0
0
0
0
0
1
0
0
0
3
3
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
5
0
0
1
1
0
1
2
0
0
0
2
0
0
2
1
1
0
0
0
2
0
0
0
0
0
0
3
0
0
0
2
1
2
0
2
0
0
0
0
1
0
0
0
2
0
0
0
2
0
1
0
0
0
0
2
1
1
0
0
2
2
0
1
0
0
0
0
0
2
1
1
0
1
3
2
2
0
1
0
2
0
0
0
0
3
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
2
0
0
1
0
2
1
0
0
2
0
0
0
2
2
0
5
0
0
1
2
0
0
2
0
2
0
0
1
1
0
0
0
0
1
0
2
1
1
0
0
1
1
0
1
0
1
0
0
0
2
0
0
0
0
1
0
0
1
0
0
1
2
1
1
0
0
0
0
0
0
0
1
1
1
0
2
0
0
0
0
0
0
0
2
2
1
1
1
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
2
0
0
2
0
0
0
1
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
2
0
0
1
0
0
0
1
5
2
0
0
0
2
1
0
0
0
0
0
2
0
0
1
1
0
0
0
1
0
0
0
0
1
1
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
3
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
1
0
1
2
0
0
0
2
0
2
1
2
0
0
2
0
0
0
2
0
0
2
0
0
0
3
0
0
0
2
0
1
0
2
3
0
1
0
2
0
0
2
0
0
0
2
0
0
1
0
1
1
0
0
4
0
0
0
1
0
0
0
0
2
0
13
0
0
1
0
0
0
0
2
1
0
1
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
1
0
1
0
0
2
3
0
2
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
4
2
0
0
2
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
2
0
0
2
0
3
1
2
0
1
0
0
0
0
0
0
1
0
0
0
1
2
1
1
1
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
1
0
0
2
0
0
0
0
1
0
0
2
2
0
1
0
0
1
0
0
1
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
2
1
0
0
1
2
1
1
2
0
0
0
0
2
1
2
1
1
0
0
0
0
0
1
2
0
2
0
0
1
2
2
3
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
2
0
2
0
1
0
0
0
1
0
1
0
0
2
0
0
2
0
4
0
0
0
1
0
0
0
1
2
0
0
0
0
1
0
1
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
1
0
0
0
0
0
4
0
3
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
2
1
0
0
3
0
5
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
1
2
0
0
3
3
0
0
0
3
0
0
0
1
2
0
1
0
0
1
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
1
2
1
2
2
0
1
1
0
1
2
0
1
0
0
0
0
1
0
2
0
0
0
2
0
1
1
2
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
2
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
1
3
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
2
1
2
6
0
1
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
1
1
0
0
2
0
0
0
0
0
0
0
7
0
0
0
0
0
2
2
0
0
0
0
1
0
0
1
0
2
0
1
2
0
0
1
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
2
0
2
1
2
0
0
2
0
0
1
0
2
2
0
0
0
1
0
0
0
0
2
1
0
0
2
2
0
0
1
0
0
2
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
1
0
1
0
0
1
1
1
2
0
0
0
0
0
0
0
2
1
0
0
0
1
2
0
0
1
0
0
0
1
0
3
0
0
1
0
0
0
0
1
0
1
1
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
2
0
0
1
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
1
1
2
0
2
1
1
0
0
0
1
3
0
0
2
0
1
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
2
0
0
0
0
3
1
0
5
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
1
1
0
0
2
2
0
2
0
0
0
0
0
0
2
3
0
0
1
0
0
1
1
2
0
0
0
2
1
0
0
0
2
2
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
1
2
0
1
1
0
1
0
3
0
0
1
2
0
1
0
2
0
0
0
2
0
1
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
2
0
0
1
2
1
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
2
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
2
0
0
0
0
0
2
0
0
2
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
2
1
0
0
0
0
2
0
1
0
0
1
0
0
0
4
0
0
0
0
2
0
0
1
0
0
1
1
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
2
2
1
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
1
1
0
6
1
0
0
0
0
1
2
0
0
1
0
1
1
0
0
1
1
0
0
0
0
2
0
0
1
2
0
2
0
0
0
1
2
0
0
0
2
0
5
0
0
0
0
0
0
1
0
0
0
0
2
0
0
3
0
0
1
3
1
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
2
0
2
2
0
0
0
0
0
0
2
1
2
0
0
1
1
0
0
2
0
2
0
1
2
0
0
0
2
1
2
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
1
3
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
1
2
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
2
0
0
0
2
1
1
0
0
1
2
0
0
0
0
0
2
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
1
0
0
0
2
0
1
0
0
0
2
1
0
0
0
2
0
3
0
1
0
0
0
3
0
0
0
0
0
0
0
2
1
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
3
0
0
2
1
0
0
0
0
0
2
3
1
1
1
0
1
0
0
0
0
1
0
0
1
0
0
2
0
0
0
2
1
1
0
0
0
1
0
0
0
0
3
2
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
1
0
1
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
2
0
0
0
0
2
0
2
1
1
0
0
3
0
0
1
2
0
1
0
0
0
0
0
0
0
1
0
3
0
2
1
0
0
2
0
0
0
1
1
1
1
2
0
1
2
3
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
3
1
0
1
0
0
0
0
0
2
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
2
1
0
0
0
0
1
2
0
0
0
0
2
0
3
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
3
0
1
0
0
2
0
0
0
0
1
2
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
1
1
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
1
0
1
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
1
0
1
0
0
2
2
0
2
1
0
0
2
0
0
0
2
2
1
0
0
1
3
0
2
2
0
0
0
3
0
0
2
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
2
0
1
3
1
1
0
0
0
1
0
2
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
2
0
2
0
2
5
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
3
2
0
0
0
0
0
1
2
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
1
0
0
2
1
0
1
0
0
1
0
1
0
0
0
2
0
0
2
0
0
0
0
1
0
0
2
2
2
1
0
2
0
1
2
0
2
0
0
1
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
1
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
2
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
2
0
0
0
2
0
1
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
1
0
0
0
3
1
0
1
2
0
1
0
1
1
0
0
0
0
0
2
0
1
0
0
1
2
0
0
0
2
2
0
1
0
0
0
0
1
0
2
0
0
2
0
0
0
1
2
1
0
1
0
1
2
1
0
0
0
0
0
0
2
0
1
0
0
0
4
5
0
2
0
0
0
0
0
0
0
3
2
3
0
0
3
0
0
0
1
0
0
0
0
2
2
0
0
0
2
0
0
2
0
2
4
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
2
2
1
0
0
0
0
0
1
0
1
2
0
2
0
0
0
0
2
0
0
2
0
0
0
1
0
1
0
1
1
0
0
2
0
0
0
0
0
0
3
0
0
3
0
0
0
0
1
0
0
0
0
0
0
1
2
1
0
0
0
0
0
1
1
1
0
0
0
2
3
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
1
0
0
1
1
2
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
3
0
0
0
1
0
0
2
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
1
2
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
2
1
0
1
2
0
0
0
1
2
1
0
0
1
0
3
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
2
0
2
2
0
2
3
0
1
0
0
0
3
2
0
0
1
0
0
0
2
0
0
0
0
1
0
1
3
0
0
2
1
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
0
1
2
0
2
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
2
0
2
2
2
0
1
2
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
2
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
2
0
0
0
2
2
1
1
2
2
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
1
2
1
1
0
1
2
0
0
0
0
1
2
2
0
0
2
0
0
0
0
14
0
2
2
0
0
0
0
0
0
0
1
1
1
1
0
0
0
1
0
0
1
1
2
0
0
1
1
0
1
0
2
1
1
0
2
0
0
1
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
1
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
2
0
0
0
0
1
0
2
2
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
4
0
0
2
0
0
0
0
1
3
0
2
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
4
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
1
0
0
0
0
0
0
0
0
7
0
1
0
0
1
2
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
1
0
0
1
0
0
0
0
1
0
0
2
0
0
0
1
0
1
1
2
2
0
0
1
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
1
1
0
0
2
0
0
2
0
0
1
0
0
0
2
0
0
0
3
0
0
0
0
2
1
0
0
0
2
0
0
0
0
1
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
2
1
2
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
3
0
1
0
0
0
2
2
2
0
0
0
0
2
2
1
0
0
0
0
2
0
0
1
1
2
1
0
0
0
1
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
3
0
2
2
1
0
1
0
0
0
0
2
1
2
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
3
1
0
0
1
0
0
4
0
0
2
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
1
1
0
2
0
0
1
0
0
0
0
0
2
0
2
2
0
0
2
1
0
0
1
0
0
0
0
1
2
1
0
0
0
0
0
1
0
0
0
2
0
1
1
1
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
1
2
0
0
3
1
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
1
1
0
2
0
4
3
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
1
0
2
1
2
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
1
2
0
0
0
0
2
1
0
2
0
0
2
1
1
2
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
5
0
1
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
2
0
0
2
2
0
0
5
0
0
0
0
2
0
2
3
1
0
0
0
0
2
2
0
0
0
0
0
0
2
0
2
0
0
1
0
0
1
1
4
1
0
1
0
1
0
1
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
2
0
1
0
2
2
0
0
0
0
2
1
0
1
1
1
1
0
0
0
0
1
0
2
0
0
2
2
0
0
0
2
0
0
1
1
2
2
1
0
0
0
1
0
0
0
1
2
1
1
0
0
0
0
0
0
0
0
0
1
0
0
3
0
2
0
2
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
2
0
2
0
0
0
0
1
0
0
2
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
1
0
2
2
0
0
0
0
0
0
2
0
0
1
1
0
1
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
4
2
1
0
1
0
2
0
1
1
0
0
0
0
1
0
0
1
2
0
2
0
0
1
0
0
1
2
1
0
0
0
0
0
1
1
2
0
1
0
0
1
0
1
1
0
1
1
0
0
0
0
0
5
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
2
1
0
2
0
0
0
1
0
2
0
1
0
0
0
0
2
1
2
0
2
0
0
2
0
0
0
0
1
0
0
0
0
1
1
2
0
0
3
0
0
0
0
0
0
0
0
2
2
0
1
3
0
0
0
0
2
1
0
2
0
0
0
0
1
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
3
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
1
2
0
0
0
2
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
1
0
0
0
0
4
0
2
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
2
2
0
1
1
0
0
0
0
3
1
2
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
2
0
2
0
0
2
1
3
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
2
0
3
0
2
2
0
0
0
0
2
0
0
1
0
0
2
0
1
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
3
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
3
0
1
0
2
1
2
0
0
1
0
0
2
0
0
0
2
2
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
1
0
0
0
0
1
0
0
0
0
0
0
1
2
2
0
0
1
0
0
0
0
0
1
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
3
2
0
4
0
2
0
0
0
3
0
0
1
0
0
0
0
0
2
1
0
0
1
0
3
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
2
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
1
0
0
1
0
0
2
0
2
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
3
0
2
0
0
0
1
1
1
0
0
0
0
0
0
0
0
2
1
2
0
2
0
1
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
3
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
1
4
0
3
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
3
0
0
0
2
1
0
1
0
0
2
0
1
0
0
0
1
0
0
0
2
0
2
0
0
0
1
0
1
0
0
1
0
0
3
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
2
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
3
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
1
0
2
0
2
0
1
0
2
1
1
0
2
0
0
0
2
0
0
0
0
10
0
0
0
0
1
0
0
0
0
0
1
1
0
1
1
0
1
3
0
0
0
0
0
0
3
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
2
0
0
1
2
1
0
0
0
2
0
0
2
0
0
0
1
0
0
1
1
0
1
0
0
2
2
1
0
0
0
0
0
1
2
2
1
1
1
0
0
0
0
0
2
2
0
0
1
2
2
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
2
0
0
2
0
0
2
0
0
1
0
0
3
0
0
2
0
0
0
0
2
3
0
1
0
2
0
0
0
0
1
0
4
0
2
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
3
0
0
3
0
2
0
0
0
1
0
0
1
0
2
0
0
1
0
1
1
0
1
2
1
1
0
1
0
1
1
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
3
0
1
0
1
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
1
3
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
1
0
2
0
0
0
2
1
0
0
1
0
0
0
0
1
2
0
1
0
2
1
0
2
1
2
2
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
3
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
4
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
1
2
2
0
0
1
0
0
0
1
1
0
0
0
0
2
0
0
1
0
1
2
0
0
0
2
2
2
0
0
0
0
0
2
0
3
2
1
2
0
0
1
1
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
2
1
1
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
1
0
1
2
0
0
0
0
0
2
2
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
1
1
2
0
1
0
0
2
0
1
2
0
0
0
1
2
0
0
0
0
0
0
5
0
3
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
1
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
3
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
2
0
0
2
2
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
2
0
1
1
2
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
2
0
2
1
0
2
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
6
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
3
0
0
1
0
0
0
1
0
1
1
0
0
0
0
1
2
0
0
0
2
0
0
0
0
1
0
0
0
1
2
0
0
2
0
1
0
1
0
0
0
2
0
0
0
0
1
0
1
0
0
2
1
0
0
1
2
0
0
0
2
0
2
2
0
2
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
2
3
1
0
0
0
0
0
0
5
0
2
0
1
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
2
0
0
2
0
1
0
2
0
0
0
0
1
2
0
1
1
0
1
0
0
0
0
1
1
1
2
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
2
0
0
0
2
0
0
0
1
2
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
1
1
1
1
2
0
0
2
0
0
0
0
0
1
0
0
0
1
2
0
0
1
0
1
0
0
2
0
0
0
1
2
1
0
0
0
3
0
0
0
0
6
1
0
0
0
0
0
0
0
1
1
1
2
1
0
0
0
1
2
0
0
0
2
0
0
2
0
0
2
0
0
0
2
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
3
2
2
0
0
0
0
0
2
0
0
1
0
1
0
2
1
0
2
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
3
0
2
0
2
0
0
0
0
1
0
0
0
2
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
2
1
1
5
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
3
0
2
0
1
0
0
0
0
0
0
1
0
2
2
0
0
1
0
0
0
0
1
1
0
0
0
0
0
2
1
0
1
3
0
0
2
0
1
2
0
0
0
0
2
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
2
0
0
2
0
1
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
1
2
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
4
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
1
1
2
0
0
0
0
0
2
0
1
0
0
2
0
1
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
1
2
2
1
2
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
2
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
1
0
2
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
2
6
0
0
0
0
0
1
0
0
1
1
1
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
2
2
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
1
0
0
0
2
1
1
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
2
0
0
2
2
0
1
1
0
0
0
2
0
0
0
0
0
3
0
0
0
2
0
2
2
2
0
1
1
0
0
0
0
0
0
0
0
1
1
0
1
1
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
1
1
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
3
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
3
0
0
0
1
0
1
1
0
0
0
2
0
0
0
2
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
2
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
2
2
0
0
0
3
1
2
1
0
1
1
1
0
0
0
1
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
3
0
1
0
0
0
0
4
1
0
0
0
3
1
2
1
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
3
0
0
0
0
2
3
0
1
0
0
0
0
0
0
1
2
0
1
0
1
0
0
2
0
0
0
1
2
3
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
2
0
1
0
0
1
1
0
0
1
0
0
2
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
2
1
0
1
4
2
1
0
2
1
2
1
0
0
0
1
0
0
1
1
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
1
0
1
2
0
2
2
0
0
0
2
1
0
1
2
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
2
3
0
0
0
2
0
0
0
1
0
2
0
0
2
0
2
1
0
0
1
1
0
2
1
1
0
0
0
1
2
0
1
0
0
0
0
1
0
0
0
1
4
0
1
2
0
0
3
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
5
1
2
3
0
2
0
3
0
1
2
0
0
1
0
0
0
0
0
2
0
0
1
0
2
0
1
0
0
2
0
0
0
0
0
2
0
0
0
1
0
1
0
4
0
0
0
0
0
1
1
1
2
0
1
0
2
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
2
2
6
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
3
0
1
0
3
0
0
2
0
2
0
0
1
1
0
0
2
0
0
1
0
0
0
0
1
0
2
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
2
0
1
1
0
0
0
2
1
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
2
0
0
3
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
2
0
0
0
2
1
0
0
2
0
0
0
0
0
0
2
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
4
0
0
2
1
2
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
2
1
0
1
0
0
0
0
0
2
0
2
0
0
0
1
1
1
0
1
0
1
1
0
2
0
0
2
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
1
1
2
2
0
0
0
2
1
0
0
0
0
0
2
2
0
1
1
0
0
2
0
0
1
0
0
0
1
0
0
0
0
1
0
2
1
0
0
2
0
0
2
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
2
2
0
1
0
0
1
0
0
2
0
0
0
0
0
0
1
1
0
0
0
4
0
2
0
0
2
0
0
1
0
0
0
1
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
1
2
0
0
1
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
2
0
0
2
0
2
0
1
0
0
0
1
2
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
2
0
1
0
1
0
0
0
2
0
0
0
0
0
2
0
1
1
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
1
2
0
0
0
0
0
0
0
0
3
1
0
1
0
0
1
2
0
0
0
0
0
0
1
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
1
2
0
0
0
0
1
0
0
0
0
0
1
0
1
0
2
2
0
2
0
0
2
0
0
0
0
0
0
0
2
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
1
1
0
1
1
0
2
0
0
2
1
0
2
0
0
0
0
2
1
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
4
2
0
3
1
0
1
0
0
0
0
4
0
0
0
0
2
1
0
0
0
0
1
3
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
2
0
1
1
1
1
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
1
1
0
1
0
0
2
1
0
0
0
1
0
0
0
1
0
0
2
1
2
2
0
0
2
0
3
1
2
0
1
0
0
0
0
1
0
1
0
0
2
0
1
0
0
0
3
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
2
0
1
0
0
0
0
2
0
1
1
0
0
0
2
1
1
0
0
1
0
2
0
0
1
0
0
2
0
0
1
2
1
2
0
2
0
0
0
0
1
0
1
0
0
1
0
1
0
2
1
2
0
0
2
0
0
0
1
2
3
0
2
1
2
0
0
0
1
0
0
0
1
0
0
1
1
0
0
2
0
0
0
0
1
2
0
1
0
0
0
0
0
1
1
2
6
0
0
2
0
0
0
0
0
3
1
0
0
0
0
0
1
0
0
1
0
1
0
0
2
0
0
0
0
0
0
1
2
0
2
0
0
2
0
1
0
0
1
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
2
0
1
1
0
1
0
3
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
2
2
0
0
0
0
0
0
1
1
2
2
0
0
0
0
2
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
1
0
2
0
0
0
0
0
2
0
2
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
2
1
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
1
0
2
2
0
1
0
0
2
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
2
0
0
1
0
0
1
1
0
0
2
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
3
0
1
0
0
1
1
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
2
1
0
0
1
1
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
2
0
0
1
1
0
0
2
0
0
0
1
2
0
2
1
0
2
0
3
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
1
0
0
1
0
1
0
0
2
0
1
0
1
0
0
0
0
0
1
2
0
0
1
1
2
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
1
0
1
0
0
2
0
1
2
0
0
0
0
0
1
0
2
0
1
2
2
2
1
0
0
0
0
0
1
6
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
1
0
1
2
0
0
1
2
2
0
5
0
2
1
0
1
0
0
0
0
0
1
3
1
2
0
3
0
0
1
0
1
0
0
0
0
2
2
0
1
1
0
0
0
0
0
3
0
1
0
0
1
1
0
0
2
1
0
0
1
0
0
0
0
1
2
2
0
0
1
2
0
0
1
0
2
2
0
0
0
0
2
0
1
1
2
0
2
0
0
0
3
3
0
0
2
1
0
0
0
0
1
1
0
2
1
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
1
0
0
1
1
0
2
4
0
0
0
0
0
0
0
0
2
0
0
1
2
0
1
1
1
3
1
1
0
0
0
0
0
0
2
1
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
1
0
0
1
0
0
1
0
0
2
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
4
0
1
0
2
0
0
0
0
0
2
2
2
2
0
1
4
0
0
1
0
0
1
1
6
1
1
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
2
0
0
0
1
1
0
2
0
0
1
2
0
0
1
2
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
2
1
0
0
2
0
2
1
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
2
0
0
0
1
2
0
1
0
0
1
0
0
0
0
0
0
1
0
1
1
0
3
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
1
0
3
1
0
0
1
0
0
0
1
1
2
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
1
2
0
0
0
1
1
0
0
0
2
2
0
0
0
1
0
0
0
1
1
1
1
2
3
1
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
1
0
0
0
1
0
3
0
2
0
0
0
2
0
0
1
2
0
0
1
2
0
0
1
2
2
0
0
2
0
0
2
0
0
1
0
0
0
3
0
0
0
0
1
1
2
0
2
1
0
0
1
0
0
0
2
0
2
0
0
0
0
1
0
0
0
2
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
5
0
2
0
0
1
0
0
0
1
0
0
2
0
0
2
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
2
0
0
0
0
1
0
2
0
1
2
0
0
0
0
1
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
1
1
0
4
0
1
0
0
2
0
0
0
0
5
1
2
0
1
0
1
1
0
0
0
2
0
4
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
1
2
0
2
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
1
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
2
0
2
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
1
0
0
0
3
0
4
0
0
0
0
1
1
0
2
2
0
0
0
1
1
0
0
1
0
0
3
0
0
1
0
2
0
0
1
1
1
0
0
2
2
2
2
1
2
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
1
2
1
1
2
1
0
0
0
0
0
2
0
1
0
0
1
0
1
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
2
1
0
0
2
0
0
1
0
0
2
3
2
1
2
0
0
0
0
0
2
0
0
1
1
0
0
1
2
1
0
3
0
2
2
3
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
1
0
0
1
1
0
1
0
1
1
1
0
1
2
0
0
1
0
5
1
0
0
1
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
2
0
2
2
1
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
1
1
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
2
2
1
0
1
0
2
0
0
1
2
0
2
0
2
1
0
1
0
1
0
0
0
1
4
0
0
0
0
1
0
0
2
2
0
0
0
1
0
2
0
0
0
0
1
0
1
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
1
2
8
0
0
2
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
1
0
2
0
2
0
0
0
2
0
0
0
1
1
2
0
0
0
0
0
0
4
1
0
1
0
0
1
1
1
0
0
0
2
2
3
0
0
0
0
3
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
3
0
4
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
2
0
0
0
1
0
0
1
0
1
0
0
0
0
0
2
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
1
0
0
0
1
1
0
0
0
2
1
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
2
0
0
2
0
1
2
0
0
0
0
0
1
2
0
0
0
1
0
2
2
0
1
0
0
1
2
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
2
0
2
0
0
0
1
0
0
0
1
0
2
0
0
0
0
2
0
2
0
2
0
9
2
1
1
0
2
1
2
0
2
0
0
0
0
0
1
0
0
0
2
4
0
0
0
0
0
0
2
0
0
2
1
0
2
0
0
1
0
1
2
0
0
0
0
0
1
0
1
0
2
0
3
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
1
1
0
3
0
1
0
0
5
3
2
0
0
0
0
0
0
2
2
0
0
1
1
1
0
1
0
0
0
0
1
0
0
1
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
3
0
0
2
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
1
0
1
0
0
1
0
1
0
0
1
0
0
0
2
0
0
5
0
2
0
4
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
2
1
0
1
2
0
2
0
1
0
0
0
2
1
0
2
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
3
0
2
0
0
0
1
2
0
2
0
1
0
0
0
0
0
1
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
1
0
0
1
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
1
0
0
0
2
1
0
0
1
0
0
0
1
1
0
0
0
2
2
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
2
0
0
2
2
0
1
2
0
0
2
0
0
2
0
0
1
0
0
3
0
2
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
1
0
0
0
2
2
0
0
0
0
0
2
0
0
0
1
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
2
0
2
0
2
2
0
0
0
2
2
1
0
0
2
0
0
0
1
2
0
2
0
0
3
2
0
0
0
2
2
1
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
2
0
0
4
1
1
0
2
0
0
1
0
0
0
2
0
0
0
2
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
2
1
2
0
2
0
0
0
0
0
1
0
3
0
0
2
0
0
0
0
1
0
1
0
1
0
0
0
0
1
1
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
2
3
0
1
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
1
0
2
0
2
0
0
1
1
0
0
0
0
0
0
0
0
1
0
2
3
1
0
0
2
0
0
2
0
1
0
2
0
0
1
2
0
1
0
1
0
0
1
1
1
1
1
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
1
0
0
1
2
0
0
1
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
3
0
0
0
0
1
0
0
0
1
1
1
0
2
0
0
0
0
1
0
2
0
0
0
0
1
0
1
0
0
0
2
0
0
0
1
0
0
1
1
1
0
2
0
1
0
0
0
2
0
1
0
0
1
0
0
0
0
0
2
0
0
2
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
2
0
0
2
2
0
1
1
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
1
0
0
3
0
0
2
0
0
0
0
0
1
0
1
1
0
0
0
0
0
3
0
0
0
0
2
0
3
0
0
1
0
2
0
0
2
1
2
0
0
5
0
0
0
0
0
0
2
2
0
0
3
0
2
1
0
0
0
0
0
0
1
1
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
2
1
0
0
0
0
0
2
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
3
2
0
0
2
0
2
1
0
0
0
2
0
2
0
0
0
0
1
0
0
4
0
0
1
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
1
2
0
2
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
1
1
0
0
2
1
0
0
1
1
2
0
0
2
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
2
0
1
4
0
0
0
0
0
0
2
0
2
1
2
0
2
1
1
0
0
0
1
0
0
0
0
0
1
0
2
0
2
0
2
0
1
0
0
0
0
0
0
0
2
0
2
0
2
0
0
2
1
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
2
0
0
1
1
2
0
0
2
0
1
1
0
3
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
3
0
0
0
2
0
0
4
0
2
2
0
0
0
0
0
0
1
0
0
2
1
1
0
1
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
1
0
2
0
0
1
0
0
0
0
1
0
0
0
0
3
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
1
1
0
2
0
1
1
0
3
0
0
0
0
2
0
0
1
0
2
0
2
0
0
0
0
0
2
1
2
0
0
0
0
0
2
1
1
0
0
0
4
0
2
0
1
0
1
0
0
4
4
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
4
0
0
0
1
0
0
1
0
1
0
1
2
0
1
0
0
0
0
0
0
1
0
0
2
1
0
3
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
1
2
1
2
3
2
0
0
0
0
2
1
1
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
2
1
2
0
0
0
1
0
1
2
2
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
1
0
1
0
1
1
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
2
0
0
2
0
1
0
1
0
0
0
0
2
0
0
0
0
2
2
0
0
1
0
0
0
0
2
2
2
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
2
2
0
1
3
0
0
0
0
0
2
0
0
1
0
0
2
1
0
0
0
0
0
2
0
0
3
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
1
0
0
0
0
1
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
2
0
1
0
0
1
0
0
0
0
0
0
2
0
3
1
2
0
0
0
4
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
2
0
0
0
2
0
0
3
0
2
0
0
0
0
0
0
0
0
0
3
0
2
0
1
0
0
1
0
0
0
1
1
1
2
1
1
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
2
1
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
4
2
0
0
0
0
0
1
0
1
0
0
0
0
0
2
1
0
0
3
0
0
0
0
1
0
0
0
3
1
0
1
0
0
2
0
2
0
1
0
2
0
0
4
0
0
0
0
0
2
0
1
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
2
0
1
0
1
1
0
0
1
0
0
1
0
0
0
1
3
1
3
0
0
1
0
3
0
0
0
0
2
0
0
0
2
1
0
2
0
1
0
0
0
0
0
0
1
3
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
1
0
0
1
0
0
0
2
0
0
1
0
0
1
0
1
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
2
0
0
0
2
1
0
1
1
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
2
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
2
3
0
2
0
0
2
0
4
0
0
0
0
1
1
0
0
0
1
0
3
0
0
0
1
0
0
0
0
0
0
2
1
0
1
0
0
0
1
0
2
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
1
0
0
0
1
0
0
0
2
0
2
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
4
0
2
2
0
2
1
2
1
1
1
2
0
1
0
0
2
2
0
0
1
2
0
0
2
0
0
0
1
3
2
0
2
0
0
1
1
1
0
0
2
0
0
0
0
2
2
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
2
2
1
0
2
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
2
2
2
0
0
0
2
2
0
1
0
0
0
0
3
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
2
0
4
4
0
0
2
1
0
3
1
0
0
2
0
0
0
1
0
0
2
0
2
0
0
2
0
1
2
0
0
0
0
3
3
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
1
0
0
1
1
0
0
0
1
2
0
1
0
0
2
2
0
0
0
0
0
0
0
0
1
2
1
2
0
0
2
2
0
3
0
0
1
1
0
1
0
0
2
0
0
2
2
0
1
0
0
0
2
0
0
2
0
2
0
0
0
0
9
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
2
2
0
0
0
0
0
0
2
0
1
0
0
2
1
1
2
0
0
0
0
2
2
0
1
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
2
2
0
0
0
2
0
0
3
0
2
0
0
1
0
1
1
1
0
0
0
1
1
0
0
2
1
0
1
0
0
0
3
1
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
2
0
0
0
1
2
0
2
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
2
0
0
0
1
1
0
0
0
0
0
2
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
2
0
1
0
0
1
2
2
2
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
5
0
0
0
0
0
1
0
0
1
3
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
2
0
1
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
6
0
1
2
0
0
2
0
0
0
3
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
1
0
2
0
0
0
2
0
0
0
0
0
2
0
0
2
2
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
1
1
2
5
1
0
0
0
5
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
1
0
2
1
3
0
2
0
0
1
0
0
0
1
2
1
6
3
1
0
2
0
3
1
1
0
0
0
0
2
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
3
0
2
1
0
4
0
0
0
1
0
2
0
0
0
1
0
2
3
0
0
3
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
3
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
2
2
0
0
0
0
0
2
0
1
0
1
1
7
0
0
0
0
0
0
1
1
2
0
0
1
0
0
0
0
2
0
0
4
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
3
0
2
2
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
2
1
0
2
0
0
2
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
2
0
0
0
1
1
0
0
0
0
2
0
1
2
2
1
0
0
0
0
0
1
1
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
2
0
0
0
0
0
1
0
2
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
1
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
2
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
1
0
1
0
0
0
2
0
2
0
2
0
2
0
0
0
0
0
0
2
2
0
1
1
0
1
0
1
0
2
0
0
2
1
0
2
2
0
1
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
0
0
3
0
0
0
0
0
1
2
1
1
1
2
1
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
4
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
1
0
1
1
0
0
1
2
2
0
0
0
2
0
1
2
3
0
0
2
0
0
0
1
0
0
2
0
0
1
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
3
1
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
2
0
1
0
0
2
0
0
2
0
4
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
1
1
0
1
2
1
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
2
0
0
0
0
0
0
0
1
1
0
1
2
0
0
0
1
0
0
0
1
1
1
4
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
2
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
2
1
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
2
0
2
0
2
2
0
1
0
2
0
1
0
3
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
2
2
0
0
1
3
2
0
1
0
1
1
0
1
0
0
0
0
1
1
1
0
2
2
0
0
0
2
1
0
0
1
0
1
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
3
2
2
0
2
0
0
0
0
1
1
0
0
2
0
1
2
2
0
0
1
1
0
0
0
1
2
1
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
2
0
2
0
0
0
0
2
0
0
0
0
0
2
2
1
4
0
1
0
0
2
0
0
1
1
1
0
1
0
0
0
0
2
2
5
0
2
0
0
0
0
0
0
0
2
0
1
0
2
0
1
0
1
3
2
1
1
0
0
1
0
2
2
0
0
0
0
0
1
2
1
0
0
1
12
1
0
0
0
0
0
2
3
1
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
4
1
0
2
0
0
1
0
0
0
0
0
0
0
2
0
2
0
1
0
0
4
0
1
0
1
0
0
0
2
0
2
0
0
0
0
0
1
1
0
3
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
3
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
2
1
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
1
1
1
0
0
0
0
3
1
0
0
0
0
0
1
0
0
0
0
1
0
2
1
0
0
2
1
3
0
0
2
0
0
2
2
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
1
1
0
0
0
0
1
0
1
0
2
1
0
0
0
0
0
0
3
0
0
1
0
0
0
2
0
2
2
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
1
0
4
0
0
0
2
0
1
0
0
1
0
0
0
4
2
0
0
0
0
0
0
0
0
0
0
0
0
2
3
1
2
2
1
0
0
2
0
0
1
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
2
2
0
0
0
0
1
0
0
3
0
0
1
0
0
0
0
0
1
0
2
0
0
2
0
0
7
0
0
2
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
2
0
0
0
0
3
3
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
3
0
0
0
2
0
0
0
0
0
1
3
0
0
0
0
0
2
1
0
0
0
0
0
2
0
3
0
1
1
0
2
2
0
0
1
2
0
0
0
1
0
0
1
0
2
0
0
0
1
1
4
0
0
0
0
0
1
0
0
1
1
3
0
0
0
1
0
1
0
2
1
2
0
0
0
2
0
0
0
1
0
2
1
2
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
4
0
1
0
4
2
0
0
0
0
0
1
0
0
0
1
0
1
0
2
1
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
3
0
0
2
2
0
2
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
1
0
1
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
2
1
2
1
0
2
0
0
1
0
0
0
0
2
1
3
1
0
1
0
0
0
0
3
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
1
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
2
0
0
0
2
0
1
2
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
4
0
0
0
1
0
3
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
3
1
0
0
0
2
1
0
0
0
2
0
0
0
0
2
1
0
0
0
2
2
1
0
0
0
0
0
0
0
1
0
0
0
0
3
0
1
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
1
0
0
0
0
3
2
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
2
0
2
2
3
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
3
0
1
0
1
0
0
2
2
1
1
0
0
0
1
0
0
0
2
0
2
1
1
2
0
0
1
0
0
0
2
0
2
1
1
1
0
0
0
0
0
2
1
0
0
1
1
0
0
1
0
1
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
1
0
0
0
1
2
0
0
0
0
0
2
0
0
0
3
1
2
0
0
1
0
0
2
0
0
1
0
0
0
0
1
2
2
2
2
0
0
1
2
0
0
0
2
0
0
1
1
2
0
1
1
0
0
1
0
2
1
3
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
2
2
0
0
0
0
1
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
4
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
2
1
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
1
0
0
1
0
1
0
8
1
0
1
0
0
0
0
0
1
1
2
0
0
1
2
0
0
0
0
0
1
0
1
0
2
2
0
0
0
0
0
1
2
0
2
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
3
1
0
1
0
1
0
1
0
0
2
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
1
0
0
0
4
0
2
0
0
0
2
0
2
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
2
0
2
0
0
0
0
1
0
0
1
0
0
2
0
1
0
1
4
1
0
0
0
0
3
0
1
2
0
0
0
2
1
1
0
1
0
1
1
0
0
0
0
2
1
0
0
0
1
1
0
1
1
3
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
2
0
2
1
1
0
0
1
0
3
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
3
0
2
0
1
2
0
2
0
0
1
0
0
1
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
2
2
0
0
3
0
0
0
0
0
4
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
1
0
0
0
2
0
0
2
0
0
2
0
0
1
0
0
0
0
1
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
2
0
0
0
1
0
2
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
1
2
0
0
1
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
2
0
0
2
2
0
0
0
0
0
0
1
2
0
0
0
1
0
6
0
0
0
2
0
2
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
1
1
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
1
2
0
0
0
0
1
0
0
0
2
0
1
0
0
2
0
3
1
0
0
0
2
0
1
2
0
0
0
3
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
1
0
0
1
0
0
2
0
0
1
0
0
3
0
0
0
0
0
2
0
0
0
0
0
2
2
2
1
1
1
0
0
0
2
0
0
2
1
1
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
2
0
0
0
1
0
0
1
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
2
1
0
2
2
0
0
0
0
0
0
2
0
2
0
0
1
9
0
0
0
2
1
0
1
0
0
0
0
1
0
0
0
3
0
0
0
0
0
1
1
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
3
0
0
1
1
0
1
0
0
0
0
0
2
1
0
0
0
2
2
0
0
0
2
0
0
0
0
1
2
1
0
0
1
1
2
0
0
2
0
1
2
0
0
0
0
1
2
0
3
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
2
3
0
0
0
0
0
0
0
0
0
0
2
1
1
1
2
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
1
1
2
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
3
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
2
0
1
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
1
0
3
1
1
0
0
0
0
0
0
0
0
0
0
2
1
2
2
0
2
0
0
0
3
1
0
0
1
0
0
0
0
0
2
0
0
1
2
0
1
1
0
0
0
0
0
0
3
0
0
0
0
1
2
3
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
3
0
4
0
2
1
0
0
0
2
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
2
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
1
2
0
2
0
2
0
0
2
0
0
0
1
1
2
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
2
0
0
1
2
0
0
2
0
0
0
2
0
0
0
0
0
3
0
2
0
0
0
0
0
2
0
3
0
0
0
2
0
0
0
1
0
3
0
0
0
0
0
2
0
1
0
0
0
2
0
1
1
4
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
2
0
0
1
2
3
1
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
3
0
2
1
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
1
0
0
0
0
2
0
1
0
2
0
1
2
0
0
0
0
0
0
3
1
0
0
2
0
0
0
0
1
0
0
0
0
2
0
1
2
2
0
0
0
0
0
0
0
1
4
0
2
0
1
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
1
2
3
0
2
2
1
0
2
0
0
0
0
2
0
0
0
0
2
0
1
0
0
1
0
0
0
0
2
0
2
4
0
1
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
1
0
0
3
1
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
1
0
3
0
0
0
2
0
0
0
0
0
2
0
1
3
0
0
0
0
2
0
0
1
3
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
1
1
0
0
0
1
0
0
0
0
1
1
2
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
1
2
0
2
1
0
0
0
0
0
0
0
0
4
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
2
0
0
0
2
1
1
3
0
0
2
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
3
0
2
0
2
0
2
0
0
2
0
0
0
1
0
0
0
0
1
2
2
3
2
0
2
1
0
0
0
0
0
0
0
2
0
6
0
1
0
1
0
2
0
0
0
1
4
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
2
3
1
2
0
0
0
0
0
2
3
0
2
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
4
0
0
1
2
0
0
0
0
2
0
1
0
2
0
1
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
2
0
0
2
1
0
0
0
2
0
0
1
0
2
2
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
2
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
3
0
0
2
2
0
0
0
0
0
1
1
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
2
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
1
0
0
0
2
0
1
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
1
1
1
0
0
1
1
1
1
3
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
1
2
0
2
0
0
0
2
0
1
0
0
0
0
2
2
0
2
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
1
1
1
0
0
1
0
2
0
0
0
2
0
2
0
0
0
0
0
0
1
1
0
0
0
2
1
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
3
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
3
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
2
0
0
1
2
2
2
0
0
1
0
0
1
2
0
0
2
0
0
0
0
1
3
0
0
1
0
0
2
0
0
1
0
2
0
0
0
2
2
2
0
1
0
0
1
0
2
0
1
0
0
0
0
1
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
3
3
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
2
1
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
2
2
0
3
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
2
0
1
0
0
2
1
0
0
2
1
0
1
2
0
2
2
1
0
1
0
0
0
0
0
2
0
0
1
0
1
0
0
2
1
0
2
0
0
0
0
0
1
0
0
1
2
1
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
1
0
2
0
2
0
1
2
0
0
0
1
0
2
0
0
0
0
0
0
2
1
1
1
0
1
1
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
2
0
1
0
1
0
1
0
0
2
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
1
0
2
0
0
2
1
0
0
0
0
0
0
0
0
1
2
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
6
0
1
2
3
0
0
2
1
2
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
2
0
0
1
0
0
1
1
0
0
0
0
0
0
1
1
2
1
0
2
2
0
0
0
0
0
1
0
1
2
0
0
0
0
2
0
0
0
2
2
1
0
0
0
2
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
11
0
2
0
0
2
0
0
0
0
2
0
0
0
0
1
2
0
1
1
0
0
0
0
0
0
2
0
0
1
1
0
3
2
2
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
1
0
2
0
0
2
0
1
0
0
0
1
2
1
0
0
0
0
0
0
1
0
0
1
2
0
1
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
1
0
0
3
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
3
2
0
0
0
0
0
2
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
2
0
1
0
3
0
2
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
3
0
0
2
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
2
0
3
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
2
0
2
0
0
2
0
0
0
0
0
0
2
0
3
0
2
0
0
0
2
2
0
0
3
0
1
0
1
1
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
1
2
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
2
0
0
0
0
0
0
2
2
1
0
0
1
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
7
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
3
0
0
0
1
0
0
0
0
0
0
2
3
0
1
0
0
0
0
0
0
0
5
1
0
1
0
0
1
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
2
1
2
0
0
2
1
0
2
2
2
1
2
1
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
1
1
0
2
5
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
3
0
0
1
0
2
0
0
0
0
2
0
1
6
1
2
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
4
0
0
2
0
0
0
2
0
3
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
2
0
1
0
0
0
0
1
2
0
2
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
1
2
0
3
0
0
0
2
0
0
0
1
3
2
2
0
0
2
0
1
2
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
2
1
0
0
0
0
0
1
2
0
1
0
0
0
2
1
2
2
0
0
0
0
0
0
1
1
1
2
0
0
2
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
6
0
3
0
0
0
3
0
5
0
0
2
0
0
0
2
0
0
0
0
0
1
6
1
2
1
0
0
0
2
2
2
0
0
0
0
0
1
2
1
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
1
2
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
2
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
3
0
1
1
2
0
0
0
0
0
2
3
0
0
0
1
0
0
0
0
1
0
0
0
0
7
0
0
0
2
0
0
0
0
0
2
3
0
0
0
2
2
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
2
2
0
0
0
0
3
0
0
0
0
3
2
1
0
0
0
0
1
2
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
2
0
0
1
0
2
0
0
0
2
4
1
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
1
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
1
2
0
2
1
0
0
0
0
2
2
2
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
1
2
4
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
2
2
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
2
1
2
1
0
0
0
2
0
0
0
0
0
1
2
0
0
0
3
0
1
2
0
0
0
0
0
0
1
1
2
2
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
2
0
0
2
1
0
0
2
0
1
2
0
0
0
2
0
1
1
0
0
0
2
2
0
1
0
0
2
0
1
1
1
2
0
0
1
0
0
2
2
0
0
0
0
0
2
3
0
0
1
0
1
0
1
0
1
1
2
0
1
0
0
2
1
0
0
2
2
1
2
1
0
2
2
2
0
0
0
2
0
0
1
0
2
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
4
2
0
2
0
2
0
0
0
1
1
2
0
0
0
1
0
0
5
0
2
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
2
1
0
0
0
0
0
0
0
2
0
0
2
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
3
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
4
0
2
0
0
2
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
1
2
0
2
0
0
0
0
0
4
0
0
0
1
2
2
0
0
2
0
0
0
0
0
1
2
0
1
1
0
0
1
1
0
1
0
2
0
0
0
0
0
0
2
0
0
0
2
0
1
1
0
3
0
0
1
1
1
0
0
1
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
2
0
0
1
0
0
0
0
1
0
0
1
2
0
0
0
0
2
3
0
0
0
3
0
2
0
0
0
1
2
1
1
0
0
1
2
2
1
0
0
0
1
0
0
2
1
0
1
1
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
7
0
0
0
0
0
0
0
8
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
2
2
1
0
2
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
3
0
1
0
0
0
0
1
0
0
0
0
0
0
1
2
1
1
0
0
1
0
0
0
0
1
0
1
3
2
3
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
2
1
0
0
1
0
0
2
4
0
0
0
2
0
5
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
1
0
0
0
0
4
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
2
0
2
0
0
1
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
3
0
0
1
0
2
0
1
2
0
0
2
0
1
2
1
0
1
0
0
1
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
1
0
1
0
0
0
2
0
0
0
2
2
0
1
0
1
1
1
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
3
1
0
0
0
0
2
0
0
0
2
1
0
0
1
0
2
0
2
0
0
0
0
0
2
0
1
0
2
1
0
0
0
0
4
0
0
0
0
0
3
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
3
2
0
0
0
2
0
0
2
0
4
2
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
2
1
0
0
0
0
1
2
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
1
0
2
2
0
0
0
0
2
0
2
2
0
2
0
2
0
0
0
0
0
0
2
0
0
0
1
2
0
1
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
1
2
0
1
0
2
0
1
0
0
0
0
2
0
0
0
0
2
0
1
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
1
0
1
1
1
0
0
1
0
1
1
2
0
2
2
0
1
2
0
0
1
0
0
0
3
2
3
0
0
3
2
0
0
2
0
1
1
0
0
1
0
1
0
1
2
1
0
2
0
0
0
0
1
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
2
1
0
0
2
0
0
0
2
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
1
2
0
0
0
0
0
2
1
2
1
0
3
0
2
0
0
0
2
0
0
0
0
4
2
0
1
0
0
0
2
2
1
0
1
0
0
0
3
0
0
0
0
2
0
0
3
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
1
1
0
2
2
0
0
0
2
1
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
2
2
1
0
0
0
1
0
0
0
1
0
0
0
2
2
0
0
2
1
0
0
0
0
0
1
0
2
2
0
0
2
0
0
1
2
3
0
0
2
0
0
2
0
1
0
0
0
0
1
0
2
1
1
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
1
1
0
2
0
0
0
0
2
1
1
0
0
0
1
1
1
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
5
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
2
2
0
0
0
0
2
1
0
0
0
1
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
2
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
2
0
1
0
0
0
1
2
0
0
0
1
1
2
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
3
1
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
2
2
0
0
0
0
2
2
0
2
0
0
0
2
0
0
1
1
3
1
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
2
0
3
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
1
0
2
0
0
2
0
1
1
0
0
1
0
2
2
0
0
1
0
0
0
0
2
0
0
3
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
7
2
0
0
0
0
0
2
0
0
0
1
0
1
0
0
1
0
0
0
0
2
0
1
0
0
2
0
1
0
1
0
2
2
0
0
0
0
0
0
1
1
1
1
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
1
2
0
0
0
0
1
1
1
0
0
0
0
0
5
2
2
0
0
0
0
0
0
0
0
4
0
1
0
1
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
2
2
1
0
2
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
3
0
1
2
0
0
0
0
0
0
0
0
0
2
0
2
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
1
1
0
0
2
1
0
3
3
2
0
1
0
0
0
0
4
0
0
0
3
1
3
0
0
1
0
2
0
0
2
2
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
2
0
2
2
1
0
2
0
0
1
0
0
1
1
0
0
0
1
2
3
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
2
1
0
0
0
1
0
0
1
1
0
2
2
0
0
0
0
0
1
0
0
0
0
2
0
0
2
1
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
2
0
2
0
0
1
2
1
2
1
0
0
1
0
0
0
1
0
1
0
0
0
2
0
2
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
2
1
0
2
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
1
0
0
0
0
0
1
0
0
3
0
0
0
0
2
0
2
0
0
0
0
0
0
0
3
1
3
0
0
1
0
1
0
2
0
1
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
1
0
0
1
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
2
0
0
2
1
1
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
2
0
3
3
0
0
0
0
1
0
0
2
0
3
0
2
0
2
0
0
0
2
0
0
1
0
2
0
1
1
0
1
0
1
1
0
0
0
2
2
1
1
0
0
0
0
1
1
0
1
3
2
0
0
0
0
2
1
0
2
0
0
0
2
0
1
0
0
0
0
0
0
1
2
1
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
2
0
0
0
0
2
1
3
0
0
0
0
0
1
0
1
2
0
0
1
0
0
2
0
1
0
0
0
2
0
0
0
1
0
0
7
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
4
0
0
0
0
1
0
0
0
2
0
1
1
0
2
0
0
1
0
1
0
2
4
0
0
0
2
0
0
0
1
1
0
0
2
3
0
2
0
0
0
0
0
0
1
2
3
1
2
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
1
0
0
1
2
0
0
0
1
1
1
0
0
0
0
1
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
2
0
0
2
1
1
0
0
1
0
1
0
2
0
1
4
2
0
0
2
0
0
0
0
1
1
0
1
2
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
1
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
2
1
1
1
1
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
2
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
2
0
0
1
2
0
2
0
0
0
0
2
2
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
3
1
0
0
0
2
0
0
0
3
0
0
0
2
0
0
3
0
0
2
0
0
1
0
0
0
0
0
0
6
0
0
2
0
0
0
2
0
2
0
1
4
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
1
0
3
1
1
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
1
7
0
2
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
2
0
0
0
2
1
0
2
0
0
0
1
0
0
2
0
1
2
0
3
2
1
0
0
0
0
1
0
0
2
0
3
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
2
1
0
2
0
0
0
2
1
0
2
1
2
2
0
0
0
0
0
0
0
0
2
3
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
2
1
0
0
0
2
2
0
2
0
0
2
0
3
0
2
0
0
3
1
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
2
0
1
0
0
0
0
0
0
0
2
5
0
2
0
0
0
2
0
0
0
2
2
0
2
0
0
0
1
0
0
1
1
0
1
2
0
1
1
0
0
0
1
2
1
1
0
0
0
0
0
0
0
2
2
1
0
0
2
0
0
0
0
1
0
1
3
0
1
0
0
1
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
2
0
0
2
0
0
2
0
0
1
0
2
1
0
0
0
0
1
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
3
0
1
0
0
0
2
0
1
1
0
0
0
0
0
1
4
0
0
1
3
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
3
0
2
2
1
0
0
2
1
2
2
3
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
2
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
2
0
0
1
2
0
0
1
0
0
0
1
0
0
0
2
3
0
0
0
2
2
1
1
1
0
0
0
1
0
0
2
0
0
1
0
0
2
0
1
0
1
0
0
2
0
0
0
0
0
0
0
4
0
0
0
0
0
0
2
4
2
0
1
0
2
2
0
0
2
0
2
2
0
0
0
0
0
2
0
2
0
1
2
0
1
12
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
2
0
2
0
2
2
2
0
0
1
0
1
0
2
2
0
0
0
0
0
4
0
0
1
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
2
1
0
0
2
1
1
0
0
3
1
2
0
0
0
0
0
0
0
1
0
1
3
0
0
0
0
2
0
0
0
2
1
0
1
0
0
0
0
0
0
0
1
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
1
1
2
2
0
2
1
0
0
0
0
0
1
0
0
2
0
0
1
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
3
1
2
0
1
1
2
2
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
3
0
2
1
0
0
1
2
3
0
1
2
1
0
2
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
6
2
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
4
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
2
0
1
0
0
2
3
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
2
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
1
0
3
2
1
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
1
1
0
1
0
0
3
0
0
0
2
3
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
3
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
2
1
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
2
0
0
0
0
0
2
0
2
0
2
0
0
1
0
2
1
2
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
2
1
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
2
0
2
1
0
0
1
0
1
1
0
2
0
2
2
0
2
0
1
0
0
0
0
1
1
0
0
0
0
2
0
1
2
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
1
1
0
1
0
0
0
0
0
2
0
3
1
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
1
2
1
2
1
0
1
0
2
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
2
1
0
1
0
2
2
1
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
1
0
0
0
3
0
1
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
1
0
1
0
2
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
2
0
0
1
1
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
3
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
2
0
3
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
2
0
2
0
0
0
0
0
0
0
0
4
0
2
2
0
0
2
2
0
6
0
2
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
1
0
0
2
0
2
0
2
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
3
0
2
0
2
0
1
1
0
0
0
0
0
1
0
0
0
2
1
0
0
0
1
2
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
2
0
0
1
0
0
1
0
0
1
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
2
0
1
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
3
0
1
0
2
0
0
2
0
1
0
0
2
2
1
0
1
0
0
0
4
0
2
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
2
1
2
1
0
3
0
0
1
0
2
0
1
0
0
2
0
0
2
1
1
0
3
0
1
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
1
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
2
1
2
0
0
0
2
0
3
0
0
1
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
4
2
0
0
0
0
0
0
1
0
0
0
0
2
1
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
3
0
0
0
0
1
2
0
2
2
0
3
0
2
0
0
0
0
1
0
0
1
2
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
2
0
0
0
1
0
0
2
2
1
0
1
2
0
2
1
0
2
2
0
0
2
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
2
1
2
3
2
0
0
3
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
2
1
0
2
1
2
0
1
2
2
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
1
0
0
0
2
4
2
1
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
1
0
0
1
1
2
3
0
0
2
14
0
0
0
0
2
0
1
0
0
0
2
1
0
4
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
1
1
1
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
2
0
0
1
2
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
1
1
1
1
0
2
1
0
0
2
0
0
2
0
0
1
1
0
2
0
0
0
2
3
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
1
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
3
0
0
0
0
0
1
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
1
0
0
2
0
1
0
0
0
1
2
2
0
0
0
0
0
0
0
0
2
5
0
3
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
1
2
2
0
0
1
2
1
0
0
2
0
0
11
0
0
0
1
0
1
0
2
0
0
1
0
0
1
2
0
0
0
0
1
1
2
0
2
1
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
2
2
0
1
0
1
0
3
1
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
2
0
0
0
1
0
2
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
1
2
0
0
0
0
0
4
2
0
0
2
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
4
1
1
0
0
1
1
0
1
1
1
0
2
0
1
0
0
0
0
2
0
0
1
2
1
0
0
2
0
0
0
0
2
1
0
1
1
1
0
5
0
0
0
0
0
0
1
2
3
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
1
1
1
0
1
0
0
1
0
0
0
0
0
2
0
1
0
1
0
2
0
0
0
0
1
0
2
0
0
0
1
1
1
0
0
3
0
1
0
0
2
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
3
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
1
1
0
2
0
0
2
0
0
0
0
1
0
1
1
1
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
2
2
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
2
2
0
0
0
0
2
1
0
0
1
0
0
0
0
3
0
0
0
1
0
0
2
2
2
0
1
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
2
0
0
1
0
0
3
0
1
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
2
1
2
0
0
0
0
0
3
0
2
1
2
1
0
2
1
1
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
4
0
0
0
0
0
0
0
0
0
1
0
2
1
1
0
0
0
0
0
0
1
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
1
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
2
0
0
1
6
0
0
0
0
1
0
1
2
0
0
0
0
2
0
0
0
1
0
0
3
6
0
2
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
1
0
0
0
3
0
0
0
3
1
0
1
0
0
1
0
1
0
1
1
1
0
2
0
1
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
2
1
1
0
2
2
0
2
2
0
0
0
0
1
1
1
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
2
0
2
1
0
0
0
0
0
0
0
2
0
1
1
2
2
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
1
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
2
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
4
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
2
1
0
0
0
0
0
2
0
0
0
1
0
0
0
2
1
0
1
2
1
0
2
2
0
3
1
0
0
0
1
0
2
1
3
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
1
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
2
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
2
1
1
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
6
0
1
0
0
1
0
1
0
0
0
2
0
1
1
1
0
2
0
0
0
1
0
0
0
0
0
2
4
0
2
0
3
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
2
3
1
4
0
3
0
0
0
2
0
0
0
0
0
0
2
3
0
0
0
0
0
1
0
0
1
1
2
3
0
1
1
0
0
0
2
2
0
0
0
2
2
0
1
0
1
2
3
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
3
1
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
2
2
2
0
0
0
0
1
1
1
0
0
0
0
2
1
0
2
1
0
2
1
0
0
0
0
0
2
0
2
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
1
2
2
2
1
2
1
0
6
2
0
1
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
1
0
0
0
1
1
2
3
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
1
1
3
0
0
0
0
0
0
0
2
0
1
0
1
0
0
2
0
0
0
0
0
1
3
0
1
1
2
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
3
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
1
1
0
0
2
2
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
6
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
2
0
1
2
1
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
2
2
1
0
0
0
0
2
0
0
0
0
5
0
1
0
0
1
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
2
3
0
1
0
0
0
1
2
0
0
0
0
1
0
1
0
1
2
1
0
4
2
0
1
2
0
0
0
2
1
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
2
0
2
1
0
0
2
0
1
0
1
2
2
0
1
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
5
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
1
0
1
2
0
0
0
0
0
1
2
0
0
1
0
2
1
0
0
0
0
0
2
2
2
0
0
0
0
1
2
1
0
0
0
0
1
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
1
0
0
0
0
0
0
2
0
2
2
0
0
2
0
2
0
1
2
0
0
1
0
3
0
0
0
0
0
1
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
2
0
2
1
1
1
0
1
0
1
0
0
0
1
2
0
2
0
2
0
0
0
2
0
0
2
1
1
0
1
0
0
1
0
0
0
0
2
2
0
0
0
2
0
0
2
0
0
2
0
1
1
0
1
2
1
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
1
0
0
1
0
0
0
0
3
0
0
0
1
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
1
0
0
2
0
0
0
1
0
0
1
2
0
0
0
1
2
0
0
1
0
0
0
2
0
2
0
0
0
1
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
1
1
2
1
0
0
0
1
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
1
0
0
2
2
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
1
5
0
0
1
1
0
0
0
1
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
2
0
0
0
3
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
1
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
3
0
0
2
0
0
0
0
5
1
2
0
0
2
0
1
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
1
2
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
2
0
0
0
0
0
1
0
1
2
0
1
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
2
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
4
0
0
0
0
0
6
0
1
2
2
0
0
2
0
0
2
0
2
1
0
0
2
1
2
0
1
0
0
0
1
1
0
1
1
0
0
0
1
0
0
1
0
0
5
0
0
4
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
2
1
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
2
0
1
0
0
1
0
0
1
0
2
2
0
0
0
0
2
0
0
1
2
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
2
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
1
0
0
1
2
0
0
1
0
0
1
1
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
2
0
0
1
0
0
0
1
0
1
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
2
0
1
0
0
0
0
1
0
0
2
0
0
1
0
4
2
0
0
2
0
0
2
0
0
0
1
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
1
0
1
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
1
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
2
0
0
1
2
1
0
5
0
0
2
0
0
1
2
1
1
0
0
0
0
0
0
2
2
0
0
0
0
0
1
6
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
1
0
0
0
0
0
0
0
2
0
0
1
0
1
0
1
2
0
2
0
0
0
0
0
0
0
1
2
0
0
3
5
2
0
2
0
0
1
0
1
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
3
0
0
1
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
2
1
0
0
0
0
0
0
0
1
2
1
1
2
2
2
0
1
0
0
0
0
2
1
0
2
0
4
0
1
0
0
0
2
0
2
0
0
1
0
0
2
0
0
0
0
1
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
3
0
0
0
0
1
0
2
0
0
0
1
0
4
0
0
2
1
0
0
0
0
0
0
1
0
0
2
2
1
2
2
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
2
0
0
0
1
1
0
0
1
1
0
0
0
1
1
0
0
0
0
1
1
1
0
0
1
0
1
0
1
1
0
2
0
1
1
0
0
0
0
0
2
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
2
0
1
0
1
0
0
0
0
0
7
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
1
0
0
0
2
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
1
2
0
0
1
1
1
2
2
0
1
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
1
0
0
0
0
2
0
1
0
2
1
0
0
0
2
1
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
1
2
0
1
2
0
0
2
1
1
2
0
0
0
1
0
0
1
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
1
0
2
0
0
2
1
0
0
0
0
0
1
1
3
0
0
1
2
0
0
0
1
0
0
0
0
0
2
0
0
0
2
1
2
0
0
0
0
2
0
1
0
0
1
0
1
1
0
0
1
0
1
0
1
0
0
0
0
0
0
2
1
0
2
2
1
0
2
0
2
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
2
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
4
1
0
2
1
1
0
0
3
0
0
2
1
0
0
2
0
0
1
0
0
0
0
1
0
0
0
2
0
0
1
1
0
2
1
0
2
1
1
0
2
2
1
1
2
0
0
0
1
0
2
0
1
0
1
0
0
0
0
1
2
0
1
0
0
0
2
0
2
0
0
3
0
0
0
0
1
0
0
0
2
0
2
1
1
0
4
0
0
0
0
0
0
0
0
1
0
4
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
2
2
0
0
2
0
2
0
0
0
0
2
0
1
0
0
2
0
2
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
2
1
0
0
0
0
1
0
0
0
0
0
2
2
0
2
0
0
2
1
2
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
2
1
0
0
2
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
4
2
0
0
0
0
0
0
2
1
0
0
0
0
3
1
0
5
0
0
2
0
0
2
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
2
0
1
0
1
0
0
0
1
1
2
0
0
0
2
1
1
0
0
0
0
0
1
1
1
0
0
0
0
1
0
1
0
1
2
1
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
2
0
0
0
0
0
2
1
2
0
0
2
0
2
2
0
0
0
2
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
1
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
2
0
0
0
1
0
2
0
2
0
0
0
1
0
0
1
0
2
2
0
2
0
0
0
0
2
1
0
0
0
0
0
0
3
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
2
0
0
2
1
0
0
0
0
0
1
0
0
1
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
1
0
0
2
0
0
0
2
0
1
0
1
0
2
1
1
2
2
2
0
2
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
4
0
0
0
0
0
3
0
0
0
0
0
0
0
1
4
0
2
0
1
2
0
3
0
1
0
0
0
0
0
0
2
2
2
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
2
0
0
0
4
1
4
2
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
3
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
2
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
1
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
2
0
0
0
3
0
0
0
0
0
2
1
0
0
0
1
0
1
0
1
0
0
3
0
1
0
0
0
0
2
1
1
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
2
1
0
0
2
0
2
0
0
0
2
2
0
2
1
3
0
0
0
0
0
2
0
1
2
4
1
1
0
0
0
2
0
0
0
0
0
0
1
0
1
2
1
3
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
1
2
0
0
0
0
1
0
0
0
2
0
0
0
1
1
0
2
0
0
2
1
2
2
0
1
0
0
0
0
0
2
0
0
1
0
2
0
0
2
0
2
1
2
0
0
0
0
0
3
0
0
0
1
1
0
2
0
1
1
0
0
1
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
1
2
0
2
0
0
0
1
1
0
2
0
2
0
0
0
0
0
2
1
0
0
0
0
1
0
1
0
4
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
1
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
1
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
1
2
0
0
2
2
0
0
0
2
1
0
2
1
0
0
0
0
0
2
0
0
0
1
0
6
0
0
2
0
1
0
0
0
0
0
2
0
1
0
1
2
1
2
0
2
1
1
2
1
0
2
0
0
0
2
1
1
0
0
1
1
0
1
0
1
0
0
0
1
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
1
0
0
2
0
1
1
0
0
0
0
1
0
0
1
0
0
2
0
0
0
1
0
0
0
1
0
0
0
1
1
1
0
2
1
0
1
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
2
1
0
1
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
2
0
0
0
1
1
0
3
0
2
1
2
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
2
5
0
0
2
0
0
0
1
0
0
0
0
0
2
0
1
6
0
0
0
1
2
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
2
1
2
1
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
1
2
0
3
1
0
2
0
0
0
0
0
0
1
0
0
0
5
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
1
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
3
0
1
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
2
0
0
2
2
0
0
0
2
0
1
0
0
1
0
0
2
0
0
0
1
0
0
0
2
3
0
0
0
0
0
0
0
1
1
0
2
6
1
0
2
0
1
0
1
0
0
4
0
1
0
0
0
0
3
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
2
0
2
0
0
0
0
0
1
3
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
1
1
1
0
0
2
0
2
0
0
1
0
0
1
0
0
0
1
0
2
1
0
1
1
0
0
1
0
0
2
1
0
0
0
1
0
0
0
0
0
0
1
2
0
2
0
1
0
0
0
2
1
0
0
1
0
0
0
1
0
3
0
0
2
0
0
0
2
0
1
0
0
0
0
0
1
0
1
3
0
0
0
0
0
1
0
1
0
0
0
1
0
1
1
0
1
0
1
0
0
0
0
2
3
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
2
0
0
1
0
0
2
1
0
0
1
1
0
2
0
0
0
0
1
1
1
0
2
0
0
0
0
1
2
0
2
1
0
0
0
0
1
1
0
0
0
0
2
2
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
2
2
0
0
0
2
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
1
1
4
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
1
1
3
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
2
1
2
1
1
1
0
0
0
0
0
1
1
0
2
1
0
2
3
0
0
0
0
0
1
0
0
2
3
1
2
2
0
2
0
1
0
3
0
4
0
0
1
1
2
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
1
1
2
0
1
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
2
0
1
1
0
0
2
2
0
2
0
0
2
0
0
0
0
1
0
0
0
1
0
2
0
0
2
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
1
1
1
0
0
1
0
2
0
0
2
1
0
2
2
3
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
1
0
0
0
1
0
1
0
1
0
0
0
2
3
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
1
3
2
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
2
0
2
1
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
1
0
0
0
2
2
0
0
0
2
1
0
1
4
0
0
0
0
0
1
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
2
0
1
1
2
0
1
0
0
0
0
0
0
2
0
1
0
1
0
3
1
0
0
0
0
0
3
0
1
0
0
0
0
2
0
1
5
0
0
2
0
0
1
0
0
3
0
2
0
0
1
0
0
0
1
1
0
2
2
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
1
2
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
2
1
2
0
0
0
0
3
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
2
0
1
0
1
2
0
0
0
0
0
1
0
0
0
0
1
3
0
1
1
0
0
3
2
0
0
0
0
1
2
0
1
0
1
1
1
0
0
0
0
0
0
0
2
0
0
1
2
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
4
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
1
2
0
2
0
2
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
1
0
1
0
1
0
2
2
0
0
0
1
0
0
0
0
0
2
1
2
0
0
0
0
1
1
0
4
0
0
1
2
0
2
2
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
1
2
0
0
1
0
0
0
0
0
0
0
0
2
1
1
0
0
3
0
0
0
3
2
0
2
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
2
0
0
2
2
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
2
0
0
0
2
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
3
0
1
0
1
1
0
0
3
0
0
0
2
0
1
2
0
2
0
0
2
0
0
0
2
0
1
0
1
0
1
0
1
0
1
0
0
3
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
3
2
1
0
0
0
0
0
1
0
2
2
0
0
0
0
0
2
0
3
0
2
0
0
1
0
0
0
1
2
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
2
0
0
2
0
0
0
0
1
1
0
2
0
0
0
0
0
0
2
1
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
4
0
0
0
0
0
1
1
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
2
1
2
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
1
0
1
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
2
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
2
2
1
1
0
0
0
0
0
0
2
1
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
2
0
0
1
3
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
1
1
2
0
2
1
0
1
0
0
1
3
1
3
0
3
2
1
2
0
0
0
2
0
0
1
2
0
0
0
1
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
2
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
4
0
2
0
0
1
1
2
2
0
0
2
0
0
2
0
1
0
2
1
2
0
1
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
1
2
1
1
0
0
3
0
1
2
0
2
0
0
0
0
0
2
0
0
2
1
1
2
0
2
0
0
0
0
0
0
2
0
1
0
1
2
10
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
1
2
0
2
0
2
0
0
0
2
2
0
2
2
0
0
2
0
0
2
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
2
2
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
2
0
0
2
0
0
0
1
0
2
1
2
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
2
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
2
1
0
2
0
1
0
1
0
0
0
0
3
0
0
2
1
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
2
0
2
0
0
0
0
1
2
0
2
1
0
2
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
2
2
0
1
1
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
2
0
0
1
1
1
0
0
0
0
0
0
0
0
3
0
0
1
0
3
0
0
0
1
0
0
1
1
0
0
3
0
2
0
0
0
2
0
2
0
1
0
1
3
1
1
0
4
3
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
1
1
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
2
0
2
1
0
2
0
0
0
0
0
0
0
0
0
2
0
1
1
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
2
1
0
1
0
2
1
0
1
0
2
1
0
2
1
0
2
1
2
0
0
1
1
0
1
0
1
1
1
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
2
1
3
2
0
1
2
1
4
0
1
0
0
0
0
0
0
0
1
0
2
2
0
0
2
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
1
0
0
2
1
0
0
0
1
2
1
1
6
0
1
1
1
0
2
2
0
2
2
0
2
0
0
0
0
0
1
0
0
0
0
7
2
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
1
0
0
0
0
1
0
1
0
1
2
1
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
2
1
1
0
0
0
1
0
4
0
0
0
0
1
0
0
2
0
2
0
0
0
1
2
0
2
0
0
0
0
0
2
0
0
0
0
0
1
3
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
2
0
2
0
0
2
0
2
0
0
2
0
0
0
0
0
2
0
2
0
2
1
0
0
0
2
0
3
0
0
0
0
2
0
0
2
1
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
1
2
0
0
0
1
0
0
1
0
0
0
2
0
0
2
0
2
1
0
2
2
1
0
0
0
0
0
1
1
0
1
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
1
0
0
0
0
0
7
1
0
0
2
0
0
0
1
0
0
0
0
1
0
2
2
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
4
1
2
0
2
0
0
1
0
1
0
0
2
0
1
5
0
3
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
1
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
3
0
0
0
0
0
0
0
2
3
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
3
2
0
3
0
2
0
1
0
0
0
0
0
0
0
2
1
0
0
4
1
2
0
1
1
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
1
0
2
0
3
1
0
1
0
1
0
0
1
0
0
2
0
2
0
0
1
0
2
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
2
0
0
2
0
0
0
2
0
0
2
1
2
3
1
0
0
0
0
2
2
2
2
0
0
0
0
0
0
0
0
1
0
0
2
4
0
0
0
2
0
0
2
1
0
0
0
0
0
2
0
1
0
0
0
0
1
3
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
2
0
2
0
0
1
1
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
1
0
0
1
1
0
0
0
1
3
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
1
1
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
1
2
0
1
0
0
0
0
2
0
1
0
0
0
0
0
2
2
2
0
1
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
2
2
0
0
0
1
0
2
0
0
0
0
1
0
1
2
1
0
2
0
0
0
1
0
0
0
2
2
1
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
9
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
2
3
1
2
2
1
0
0
0
2
0
0
0
0
2
0
0
1
0
1
0
2
1
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
2
2
0
1
2
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
1
0
0
0
3
0
0
0
0
0
2
0
0
1
0
1
0
0
3
0
0
0
0
0
1
2
2
2
0
1
2
0
2
0
0
0
1
2
0
0
0
2
0
2
0
0
0
1
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
2
0
0
1
1
0
0
2
0
0
0
2
0
1
1
0
2
0
0
2
4
0
0
2
0
0
0
0
2
1
0
1
0
0
2
0
2
0
0
2
1
0
5
1
3
4
1
0
1
0
0
0
2
2
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
1
0
2
2
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
1
2
0
1
2
0
0
0
1
0
0
2
2
0
1
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
5
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
3
0
0
1
1
6
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
3
0
0
0
0
0
1
0
1
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
4
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
3
0
0
0
0
0
0
0
1
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
1
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
1
2
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
1
4
5
1
1
1
0
0
0
0
0
1
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
2
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
1
0
0
0
0
0
1
2
0
0
0
1
2
0
0
0
0
1
2
0
0
0
0
1
0
2
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
2
1
2
0
0
0
1
0
2
1
2
0
0
2
1
0
0
0
2
0
0
0
1
0
2
1
0
0
0
0
2
1
0
0
0
0
0
0
0
1
1
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
3
1
0
0
0
0
1
2
0
2
1
1
0
2
0
3
0
0
2
0
2
1
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
3
0
0
0
0
0
0
1
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
1
1
2
1
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
1
1
0
2
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
2
1
1
0
0
0
0
0
0
1
2
0
0
1
0
0
1
0
2
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
2
0
2
0
5
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
1
0
2
1
0
2
1
0
0
0
0
0
0
3
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
1
2
1
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
1
1
0
1
0
2
3
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
2
2
0
0
0
2
1
2
1
0
0
0
0
1
0
2
0
0
0
0
0
2
0
1
2
0
3
0
0
0
2
0
0
0
0
0
0
1
1
1
2
1
0
2
2
1
0
0
0
0
0
0
3
2
0
0
0
2
1
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
1
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
2
2
0
0
0
1
2
0
0
1
0
1
0
0
0
1
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
3
1
1
0
0
0
0
0
0
12
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
3
0
0
0
0
0
0
0
4
0
0
2
3
0
3
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
2
0
1
0
0
3
0
0
0
0
0
2
0
2
0
1
2
2
1
2
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
3
9
2
1
0
1
0
0
2
0
0
1
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
2
0
2
2
1
0
0
0
0
1
0
0
2
1
2
0
2
0
0
1
0
0
1
0
0
0
2
0
1
0
4
1
0
1
1
4
0
1
2
1
1
0
2
0
0
0
2
0
0
2
0
0
0
2
0
0
1
0
2
0
0
0
0
2
2
2
0
2
0
0
0
1
1
0
0
0
0
3
0
5
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
2
0
0
1
0
0
2
0
1
0
2
1
0
1
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
3
0
0
0
0
2
0
0
0
0
1
0
0
2
1
2
3
0
0
0
1
1
3
2
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
3
2
0
0
4
0
0
0
7
0
1
0
0
0
3
1
2
0
2
2
1
0
2
2
1
1
0
0
0
1
0
0
2
2
0
0
0
0
3
0
2
0
2
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
2
1
0
0
0
0
0
0
1
0
0
1
1
1
0
1
2
0
2
0
0
0
0
1
0
0
1
0
0
2
0
0
0
3
2
0
0
0
0
0
0
0
0
1
0
1
1
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
1
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
1
0
0
0
2
0
0
0
1
0
2
1
2
0
0
2
0
1
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
2
0
4
0
2
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
1
0
2
2
0
0
0
4
0
1
1
2
2
0
0
0
0
2
1
0
0
1
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
2
0
2
1
0
0
0
0
0
1
1
0
3
3
2
0
1
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
1
0
2
0
0
2
0
1
2
2
0
0
2
0
0
0
0
2
0
0
6
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
2
0
0
1
2
2
2
0
0
2
2
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
2
0
1
0
0
1
0
0
0
0
0
1
1
2
0
0
2
0
1
2
0
0
0
0
0
0
0
2
1
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
2
2
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
1
1
0
0
2
0
0
0
0
0
1
2
3
2
0
0
0
0
4
0
0
2
0
3
2
0
0
0
0
1
0
0
0
1
0
7
1
0
1
0
0
2
0
0
1
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
1
2
0
0
2
0
0
0
0
1
0
0
0
2
2
0
1
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
1
1
1
0
3
0
1
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
3
2
0
1
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
1
2
0
0
0
1
0
0
2
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
1
0
0
0
1
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
2
2
0
2
2
2
2
0
0
0
0
0
2
0
2
0
1
2
1
0
0
0
1
2
3
0
0
0
2
2
2
1
0
0
0
0
18
2
1
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
2
2
0
0
0
2
0
0
0
0
2
0
2
1
0
2
0
0
0
0
0
0
0
3
0
2
0
0
0
2
0
1
0
1
0
0
0
2
0
0
3
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
2
0
0
0
1
0
1
0
1
2
2
2
0
0
0
0
2
2
3
0
0
0
0
0
0
0
0
2
0
0
1
2
1
0
1
0
1
2
0
0
0
0
0
0
0
0
3
0
0
2
1
2
1
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
7
0
1
0
0
1
0
2
1
1
0
3
1
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
2
0
5
0
0
0
2
2
0
0
0
2
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
2
0
2
0
0
2
1
0
1
0
2
0
1
1
2
0
1
2
0
0
3
1
1
0
1
0
0
0
0
2
0
2
6
0
0
0
0
1
1
0
0
0
2
0
0
0
0
1
1
1
1
0
1
0
0
0
2
0
0
0
2
0
1
2
0
0
0
0
0
1
0
2
0
1
2
0
0
0
0
1
0
0
2
2
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
2
0
3
0
2
0
0
0
1
1
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
4
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
1
0
1
0
0
0
1
2
2
2
0
2
0
0
2
0
0
1
0
0
2
0
0
1
0
2
1
2
0
2
0
0
2
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
2
0
0
0
3
2
0
0
0
1
0
2
0
0
0
0
2
0
0
1
0
3
0
0
0
0
2
0
0
1
2
2
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
1
0
2
0
4
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
1
0
1
0
1
0
1
1
0
2
0
0
1
1
2
0
0
0
2
0
0
0
2
0
1
2
1
0
0
2
1
2
1
0
0
3
0
0
1
1
2
0
0
1
0
0
0
2
0
0
0
0
2
2
1
0
0
0
1
2
0
1
0
0
1
3
1
0
0
2
0
2
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
1
0
1
0
1
0
1
1
2
4
0
0
2
0
2
0
1
1
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
2
0
0
0
1
0
9
1
0
0
2
1
1
0
0
2
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
2
0
1
0
0
0
3
0
0
0
3
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
1
0
2
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
3
2
1
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
2
0
2
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
4
2
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
1
0
0
1
9
0
0
2
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
1
2
2
0
1
0
0
0
0
0
1
0
0
0
0
1
2
0
0
2
1
0
2
0
0
0
2
0
0
0
6
0
1
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
2
3
1
0
0
2
0
1
0
0
0
2
1
0
0
0
0
2
0
0
0
1
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
1
0
0
0
0
0
2
0
0
0
1
2
0
1
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
1
3
1
0
0
0
3
0
0
0
1
2
2
0
0
1
0
0
1
2
0
0
0
0
2
0
1
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
2
4
2
0
1
0
0
0
0
3
0
0
1
2
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
1
0
2
0
2
0
0
0
0
0
3
0
2
0
0
1
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
2
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
2
1
3
0
0
2
1
0
0
0
0
1
0
0
0
0
3
3
0
0
1
1
0
0
2
2
0
0
0
0
0
1
2
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
3
0
0
0
0
0
2
0
0
1
0
2
0
0
0
1
0
0
1
2
0
0
0
0
1
2
1
2
0
0
0
0
1
2
0
3
2
0
0
0
0
5
0
0
1
0
0
0
0
0
2
0
1
2
0
1
0
0
1
0
0
3
0
0
1
0
2
0
1
0
0
1
0
5
0
2
0
0
0
0
0
0
1
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
2
3
0
0
0
0
0
2
1
1
2
0
0
0
0
1
1
0
0
0
0
1
2
0
2
0
1
0
0
0
1
0
1
2
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
2
2
1
0
0
0
0
0
2
1
1
0
1
0
0
1
0
0
0
0
3
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
2
2
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
4
0
1
0
2
0
0
0
0
0
0
3
0
0
1
0
0
0
0
2
0
0
4
0
2
2
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
3
1
2
0
0
0
0
2
2
0
1
0
0
0
1
2
1
1
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
1
1
0
2
0
2
0
1
1
3
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
1
1
0
0
0
2
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
3
0
3
1
2
0
1
2
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
2
0
1
0
1
0
0
1
0
0
2
1
0
0
0
0
2
1
0
0
2
1
0
0
0
2
0
0
0
0
0
1
0
0
1
0
2
0
0
0
2
0
2
0
0
0
0
2
0
2
0
0
0
0
0
1
3
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
2
0
2
0
0
0
2
1
0
0
2
2
1
3
0
0
1
0
2
0
1
0
0
1
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
1
2
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
1
2
0
0
0
1
1
0
2
0
0
1
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
2
2
1
2
0
0
2
2
0
0
0
1
0
1
0
0
1
0
0
1
0
2
0
0
0
2
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
2
0
0
2
0
0
1
0
0
2
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
1
0
1
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
2
0
1
1
0
0
0
2
0
0
0
0
0
0
0
2
1
0
2
0
0
4
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
1
1
0
0
2
1
0
0
2
1
0
0
0
1
0
1
3
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
1
0
0
0
2
0
0
0
2
2
2
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
2
0
0
2
2
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
1
0
0
2
0
0
0
2
0
2
0
0
0
0
1
2
2
0
2
0
1
0
0
0
0
0
0
0
1
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
2
2
0
1
0
0
1
0
0
0
0
0
0
0
2
1
0
0
1
0
0
1
3
0
2
0
0
0
0
0
4
0
2
1
0
2
0
0
1
1
2
2
0
3
0
2
0
1
0
0
0
1
0
2
0
1
0
0
0
0
2
4
1
0
2
0
0
1
1
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
2
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
1
2
0
1
2
2
0
4
0
1
1
2
0
0
0
0
0
0
1
2
2
2
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
1
1
1
2
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
3
1
0
1
0
0
0
0
2
1
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
1
2
0
3
0
1
0
0
2
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
4
1
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
1
1
2
0
1
1
0
0
0
0
0
1
0
0
2
1
2
1
0
3
0
1
2
3
0
0
0
1
0
0
1
2
1
1
0
2
0
0
0
0
1
0
0
0
3
0
0
0
0
1
1
0
0
0
0
0
0
3
2
0
0
0
1
0
0
1
2
0
0
2
2
0
1
0
0
0
1
1
0
3
1
0
1
2
0
1
0
0
7
0
0
0
0
0
1
0
2
4
2
0
2
1
0
1
0
2
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
2
0
0
1
0
2
2
3
0
0
0
1
0
1
0
0
2
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
4
1
1
0
4
1
2
1
2
1
1
0
0
1
0
0
2
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
2
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
1
0
0
1
0
2
2
0
1
0
0
0
0
0
0
0
1
2
0
0
1
1
0
0
1
2
0
2
0
0
0
2
0
0
2
1
0
0
0
0
2
2
0
3
0
1
1
0
0
0
0
0
0
0
2
3
1
0
0
0
0
0
2
0
2
1
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
1
2
0
0
2
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
1
1
1
0
1
0
2
0
0
0
0
2
1
0
2
0
0
3
0
2
0
0
0
0
2
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
2
0
1
0
2
0
0
1
2
1
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
1
0
2
0
2
0
0
0
9
0
0
2
0
0
1
0
2
2
0
0
0
0
0
2
2
0
1
0
0
0
2
1
2
0
0
2
2
2
0
0
0
0
0
0
2
0
1
0
0
0
0
2
2
1
0
1
0
0
2
0
3
1
2
0
0
0
0
0
1
6
0
2
1
0
0
2
0
0
2
0
2
0
2
1
2
0
0
0
0
2
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
2
0
2
0
0
0
1
0
0
2
0
0
0
0
1
1
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
9
0
1
0
0
0
0
1
1
2
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
3
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
1
0
0
0
0
0
1
2
1
1
0
0
0
0
0
2
0
1
0
0
0
1
0
0
1
0
1
0
0
0
3
0
0
0
0
1
1
2
0
0
0
2
0
0
3
0
1
4
2
2
0
0
0
0
0
2
0
1
2
0
0
0
0
0
2
0
3
0
1
1
1
0
0
0
1
2
0
0
0
0
1
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
2
0
1
0
2
1
0
0
2
0
0
1
1
0
0
1
0
1
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
2
0
0
1
1
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
1
2
0
0
0
0
1
1
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
2
0
1
0
0
0
1
0
0
0
0
0
0
0
3
1
0
1
0
0
0
0
1
0
4
0
2
2
0
2
0
0
0
1
2
0
0
2
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
1
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
3
1
2
0
3
0
0
1
0
0
3
1
3
0
0
0
0
0
2
0
0
2
0
0
0
0
1
1
0
0
0
0
1
1
0
0
1
1
2
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
2
0
0
0
0
0
0
4
1
0
1
0
0
0
2
1
0
0
0
0
2
0
1
0
3
7
0
0
1
0
1
0
0
0
0
1
0
0
1
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
1
1
3
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
1
0
0
1
0
0
2
1
0
2
0
1
0
0
1
0
0
0
2
2
0
0
2
1
0
0
0
3
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
2
0
2
1
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
2
2
1
0
2
2
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
1
0
1
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
2
1
0
0
2
0
0
0
0
0
1
3
0
2
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
2
2
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
1
1
0
1
3
2
2
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
2
0
1
1
0
1
0
2
0
3
0
0
0
0
2
2
0
0
0
0
0
0
2
1
0
0
2
2
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
1
1
0
1
0
1
0
0
0
0
2
2
1
0
2
0
1
2
0
0
0
1
0
0
0
2
1
0
1
0
0
1
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
3
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
3
0
0
0
2
0
4
0
0
0
0
0
0
0
0
1
0
2
0
1
3
0
1
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
1
2
0
0
0
1
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
4
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
5
0
0
0
1
0
0
2
0
2
0
2
0
0
0
0
3
0
0
2
2
0
1
0
0
0
0
0
0
2
0
1
2
1
1
2
0
2
0
1
0
1
1
0
0
0
0
0
2
0
3
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
3
3
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
3
2
0
2
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
2
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
3
2
0
2
0
1
1
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
3
2
5
0
1
0
2
0
0
2
2
0
1
1
0
0
2
0
0
0
0
0
0
1
3
1
0
1
2
0
0
0
1
1
0
0
0
0
0
0
2
1
0
2
0
0
0
3
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
2
0
1
2
5
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
2
0
1
3
0
0
1
0
1
0
0
0
0
0
1
2
1
0
0
0
0
0
0
1
0
0
1
0
0
0
3
1
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
2
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
2
2
0
4
0
0
1
1
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
5
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
3
1
0
0
0
0
0
0
2
0
0
2
0
0
1
2
2
0
1
1
1
1
0
1
0
0
4
0
2
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
2
3
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
1
0
2
0
2
1
0
0
1
1
0
2
0
0
0
0
0
2
0
0
2
0
0
0
1
2
0
0
0
2
2
2
0
0
0
0
3
0
0
1
0
0
3
1
0
0
0
0
0
2
0
0
0
3
1
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
1
0
1
1
0
2
1
0
0
0
0
2
0
0
0
3
1
0
0
1
0
0
0
0
0
2
3
2
0
0
0
1
0
2
0
0
0
1
1
1
0
1
1
0
1
1
0
3
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
1
1
0
2
0
0
0
0
1
1
0
0
0
0
3
1
0
1
0
0
2
2
2
0
0
0
0
0
2
1
0
1
0
0
2
0
1
0
2
0
0
0
0
0
1
1
2
0
0
2
0
0
1
0
2
1
0
1
0
3
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
2
0
3
0
0
2
0
0
2
2
0
0
1
1
0
0
0
0
0
2
0
0
1
0
1
1
2
0
0
0
0
0
0
0
0
2
2
0
1
1
0
0
0
2
0
2
0
2
2
0
0
1
2
0
0
3
0
1
2
0
0
1
1
0
0
0
3
0
2
0
0
1
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
2
2
1
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
2
0
2
0
0
0
0
0
2
1
0
2
0
0
0
0
2
0
1
3
1
0
0
2
0
1
0
0
0
1
0
0
0
1
1
0
0
0
2
0
2
2
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
3
1
1
2
0
0
0
1
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
1
0
2
1
2
0
1
0
0
0
2
0
1
0
3
0
0
0
2
0
1
0
0
0
1
0
0
0
0
1
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
2
0
1
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
1
0
5
2
1
0
0
1
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
2
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
3
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
2
0
0
0
1
0
0
0
0
0
0
8
0
0
0
0
3
0
0
0
0
2
2
0
0
2
0
2
0
2
3
1
0
2
0
3
2
0
0
0
1
0
0
1
0
2
4
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
2
2
1
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
1
2
0
0
0
0
1
0
0
0
3
0
2
0
0
1
1
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
2
0
3
1
7
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
1
0
0
1
0
1
0
2
0
0
0
0
1
1
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
2
2
1
0
0
0
0
0
0
2
2
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
2
2
0
0
2
0
0
2
0
0
1
0
0
1
0
0
0
0
0
2
1
0
0
0
1
0
1
0
0
0
3
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
1
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
1
0
0
0
0
1
0
1
0
0
1
0
0
4
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
3
2
2
2
0
1
0
0
0
1
2
0
0
5
2
0
0
0
1
1
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
1
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
1
0
2
1
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
1
1
1
0
0
0
0
0
0
0
0
2
0
0
2
1
2
0
1
0
2
0
1
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
5
1
0
0
0
0
0
1
0
1
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
1
1
1
0
0
0
0
0
0
1
2
0
0
1
0
1
0
0
0
2
0
2
2
0
0
1
1
0
0
2
0
0
0
0
2
0
1
2
0
2
1
1
0
2
0
0
0
1
0
0
0
2
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
1
0
0
0
0
0
2
1
1
0
1
1
0
0
0
1
0
0
0
0
0
1
0
3
0
0
1
0
0
0
0
3
4
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
1
0
2
0
0
0
1
1
1
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
1
0
1
1
2
0
0
0
0
3
0
0
0
0
0
2
1
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
2
1
0
1
1
0
2
0
2
1
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
1
3
1
0
0
0
0
1
1
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
1
1
0
0
0
2
0
0
2
1
2
1
0
0
0
0
0
2
0
1
1
0
2
0
0
0
0
0
1
1
0
2
2
0
0
0
0
1
0
1
0
0
2
0
0
0
2
0
0
1
1
0
2
2
0
1
0
0
1
1
0
0
0
0
0
1
0
0
2
2
0
2
0
0
1
1
1
0
0
2
1
0
0
2
0
2
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
1
0
0
0
0
0
2
0
1
0
0
2
1
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
2
1
0
2
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
2
0
0
1
0
0
2
1
1
0
5
0
2
0
2
0
0
1
2
3
1
0
0
1
0
0
0
0
0
0
1
2
0
2
0
0
2
2
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
2
2
0
0
1
2
2
0
1
0
1
2
1
1
1
0
0
0
0
0
1
2
1
0
0
2
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
3
0
0
0
2
0
0
0
0
0
2
4
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
2
0
0
1
0
1
0
0
0
2
1
0
0
1
2
1
1
0
0
1
2
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
1
0
1
2
2
1
2
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
1
2
0
0
0
0
0
0
0
1
0
2
0
1
2
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
3
2
0
0
0
0
1
0
1
1
1
2
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
1
0
0
2
0
11
0
0
0
2
2
0
0
1
2
0
0
0
0
1
0
2
0
0
0
0
1
2
1
0
0
2
0
0
0
1
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
3
3
0
2
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
2
2
2
0
0
0
1
0
2
0
0
0
2
0
0
0
0
2
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
3
0
0
2
0
0
0
1
0
1
0
2
0
1
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
3
0
0
1
2
0
0
1
0
1
0
0
1
0
0
2
2
0
0
0
0
2
2
0
2
0
0
1
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
3
2
0
2
0
0
1
1
0
0
0
0
2
2
0
0
1
0
0
0
0
0
3
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
1
3
0
0
0
2
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
2
0
0
0
2
1
2
1
0
0
0
1
0
1
0
4
0
0
2
0
0
0
2
0
0
0
0
0
2
0
2
0
0
2
1
0
2
0
0
1
0
0
1
0
0
2
0
1
1
0
2
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
1
1
1
0
1
0
0
0
0
2
3
0
0
0
1
0
1
1
0
0
0
0
2
0
0
0
1
0
0
0
0
1
1
0
0
1
0
2
0
0
0
0
0
0
2
2
0
0
1
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
1
0
2
0
2
1
1
1
0
0
0
0
2
0
1
2
0
2
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
1
2
0
0
2
0
0
0
1
0
0
2
1
3
0
0
1
0
0
0
1
2
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
2
0
1
4
2
0
0
1
0
0
3
0
0
0
2
0
1
0
4
0
0
1
0
0
0
0
2
1
0
2
2
0
0
1
0
1
3
2
0
0
0
0
2
2
0
0
0
0
0
0
1
2
0
1
2
1
0
0
2
0
0
0
1
0
0
2
2
2
2
0
0
0
2
0
2
0
0
2
0
0
2
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
2
0
0
2
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
2
0
0
0
1
0
0
2
0
0
6
0
0
0
0
0
0
1
1
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
1
2
1
0
2
0
0
1
1
2
1
3
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
2
0
0
2
3
1
1
0
0
0
0
0
1
0
2
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
3
1
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
1
3
0
0
0
0
0
2
0
2
2
0
1
0
0
2
0
0
0
0
0
1
1
0
0
0
1
0
1
0
2
1
0
2
0
0
0
3
0
0
2
0
0
0
2
0
4
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
1
0
0
0
0
1
0
2
0
2
1
2
2
2
0
0
0
0
3
3
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
1
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
2
2
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
1
0
2
1
1
0
0
0
2
0
0
0
1
1
1
0
1
1
0
1
0
0
0
5
1
0
0
1
0
3
0
2
0
2
0
0
1
0
0
2
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
1
0
1
1
0
0
0
0
1
0
1
2
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
1
2
0
0
0
0
0
1
0
0
2
0
0
3
1
2
0
2
0
1
1
0
0
2
0
2
0
1
2
0
0
0
2
0
0
0
0
0
0
0
2
4
0
0
3
0
0
0
0
1
1
0
0
0
1
1
0
2
0
0
0
0
0
0
1
1
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
1
0
1
2
2
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
1
2
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
1
1
0
0
1
2
0
0
1
2
0
0
1
1
1
2
0
2
0
0
2
0
0
1
2
2
2
0
0
0
0
1
0
0
0
1
0
2
1
0
0
1
0
0
0
0
0
2
0
0
1
2
0
1
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
3
3
0
2
2
2
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
4
4
1
1
0
0
0
0
0
0
0
0
1
0
6
0
0
0
0
0
0
2
2
0
0
0
1
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
1
0
0
2
0
1
1
0
0
1
0
0
1
0
0
2
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
1
0
2
0
2
0
0
0
5
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
2
0
1
1
1
0
1
1
0
1
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
2
1
0
1
0
0
0
0
0
1
2
0
0
0
0
1
0
2
0
0
2
0
0
2
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
1
2
0
0
0
0
0
0
0
3
0
2
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
4
0
1
1
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
1
2
0
0
0
0
0
3
0
0
0
0
0
0
1
1
0
1
0
0
0
2
0
1
0
2
0
0
2
2
0
0
1
2
0
0
0
1
0
0
0
1
1
1
0
2
0
0
2
0
1
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
3
2
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
2
0
2
1
1
1
0
0
1
0
0
0
0
0
2
0
0
2
0
2
0
1
0
1
0
0
2
0
0
0
0
3
2
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
3
0
0
0
0
0
2
1
1
0
3
0
0
2
0
0
2
3
1
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
1
2
2
2
0
2
0
0
2
0
1
1
0
0
0
2
0
0
1
0
0
1
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
2
1
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
1
2
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
1
0
0
0
2
0
0
1
2
2
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
1
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
2
1
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
4
0
2
0
0
0
0
1
0
0
1
0
0
2
0
2
0
0
0
0
2
0
8
0
2
1
0
0
1
0
2
0
0
2
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
1
0
0
0
0
0
2
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
1
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
2
2
1
0
0
0
3
1
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
3
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
2
0
0
0
1
0
0
2
0
0
3
0
0
0
1
2
0
0
1
0
0
0
0
1
0
0
0
0
3
2
0
2
1
0
0
1
1
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
3
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
3
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
2
0
2
2
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
1
0
2
0
1
1
0
3
0
1
2
2
0
2
1
0
0
0
0
1
1
0
0
0
2
2
0
0
1
2
0
2
0
1
1
0
2
0
0
0
0
1
2
1
3
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
1
0
0
2
2
0
0
0
1
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
1
0
0
0
2
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
1
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
2
0
0
0
0
0
2
0
0
2
2
0
0
1
0
0
2
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
3
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
1
0
0
0
0
1
0
1
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
2
2
0
0
2
1
0
0
4
2
0
1
0
0
0
1
0
0
0
0
0
1
0
2
1
0
2
0
0
0
0
0
1
1
1
0
0
1
0
0
0
1
0
2
0
2
0
2
0
0
0
0
0
2
1
0
0
0
2
0
1
0
1
0
0
0
2
0
0
0
0
2
0
3
2
0
0
0
1
0
0
1
1
0
0
0
0
0
1
2
0
2
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
2
0
1
0
2
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
2
5
0
0
0
3
0
0
0
0
0
1
0
2
1
0
0
0
2
0
0
0
0
0
0
0
1
2
1
0
0
2
0
0
2
3
1
0
2
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
5
0
1
0
0
0
0
1
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
2
2
2
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
3
0
0
0
0
0
1
4
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
4
0
0
0
1
0
1
0
1
0
0
0
1
0
1
1
0
0
0
0
2
3
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
2
2
0
2
0
4
0
0
0
0
0
2
0
0
0
2
0
0
2
1
2
0
0
2
0
2
0
0
1
0
0
8
0
0
1
0
2
2
0
1
0
1
0
3
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
1
0
0
0
0
0
1
0
2
1
0
0
0
0
0
2
0
0
0
2
1
0
0
2
0
1
0
1
0
1
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
2
0
2
0
0
0
0
0
0
2
0
0
2
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
2
2
0
1
0
1
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
2
0
2
2
0
0
0
0
0
1
2
1
0
0
0
0
0
0
3
0
0
0
2
0
0
1
2
1
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
2
0
1
0
0
0
0
0
1
0
0
2
1
2
0
1
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
4
2
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
3
2
1
0
0
0
0
0
0
4
2
0
1
0
0
2
0
0
5
0
2
0
0
0
0
0
2
0
0
0
2
0
2
0
1
0
0
1
3
0
0
1
0
0
0
2
0
2
0
1
0
2
0
3
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
1
3
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
1
0
2
0
1
1
0
2
1
0
2
0
0
0
0
1
0
0
0
0
2
1
2
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
2
1
1
2
0
0
3
1
2
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
2
2
0
0
0
0
1
0
1
0
3
0
0
0
1
1
1
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
2
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
3
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
1
0
0
1
1
0
1
3
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
2
3
0
0
2
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
3
0
0
0
1
1
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
2
0
0
0
1
0
0
1
0
0
2
0
0
2
1
0
1
0
0
1
0
0
0
0
2
1
0
3
0
0
2
0
0
0
0
1
1
2
1
0
0
0
2
0
0
0
0
1
0
0
1
1
2
0
3
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
1
0
2
0
2
1
0
0
0
2
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
5
0
1
0
0
0
0
1
0
2
0
0
1
2
0
0
2
0
1
0
0
0
0
2
0
0
1
2
1
0
1
0
1
0
0
0
1
0
1
0
5
0
1
0
0
2
1
0
0
0
0
2
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
1
0
2
0
0
2
1
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
6
0
0
1
0
0
3
2
0
0
2
1
4
0
0
0
2
0
2
0
0
2
0
0
2
0
2
0
0
0
0
1
0
5
0
2
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
2
1
0
2
0
2
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
1
1
2
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
2
1
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
1
1
1
0
0
0
2
0
1
0
0
1
0
0
0
0
2
0
0
0
2
4
0
0
1
0
0
1
0
0
0
1
0
1
0
0
1
0
0
2
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
2
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
1
0
0
1
0
2
0
1
1
0
0
0
0
1
0
0
0
2
0
2
2
0
0
0
2
1
0
2
0
0
0
2
0
2
0
0
0
1
1
0
0
2
0
1
2
0
0
0
0
4
0
2
0
0
2
0
0
1
0
2
1
2
0
0
0
0
0
0
0
0
1
2
0
0
3
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
1
1
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
2
1
0
2
0
0
0
0
1
0
0
0
1
1
2
1
2
0
0
1
2
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
1
1
0
0
0
2
0
0
0
0
0
0
1
1
1
1
0
3
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
1
0
2
2
0
0
2
0
1
0
0
2
0
2
0
0
0
0
2
0
0
1
1
0
1
1
2
2
1
0
0
0
1
0
2
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
11
0
0
2
0
2
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
2
4
0
0
0
1
0
2
2
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
1
1
2
0
3
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
1
0
0
0
0
4
0
1
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
2
1
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
1
2
0
2
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
2
0
2
1
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
2
1
0
3
0
0
1
0
2
2
0
0
0
0
0
1
1
1
0
2
0
0
2
0
0
0
0
0
1
3
0
0
0
2
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
1
0
0
0
0
2
0
0
0
1
0
1
0
2
0
3
0
1
0
0
3
1
0
2
0
2
0
2
0
0
1
1
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
3
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
2
2
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
2
1
0
2
0
0
0
5
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
1
0
0
2
1
0
1
0
0
0
1
0
0
0
0
1
3
0
0
1
1
0
0
0
2
0
1
0
1
2
0
8
1
0
3
0
0
0
0
0
0
1
3
2
0
0
2
0
0
0
2
0
0
0
1
1
2
1
0
0
0
1
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
1
2
0
0
0
0
2
0
1
2
0
0
0
0
2
0
0
1
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
3
0
2
0
0
0
2
2
0
1
0
0
0
2
1
2
0
0
0
2
0
0
0
1
0
0
0
0
0
2
1
0
0
1
0
4
0
2
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
1
2
0
2
0
0
0
0
2
0
0
2
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
2
0
0
1
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
1
0
0
0
5
0
2
0
0
0
2
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
5
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
5
1
0
1
2
0
0
1
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
1
2
0
0
0
0
0
2
1
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
1
0
2
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
1
0
0
1
1
0
0
0
0
1
2
0
1
2
0
2
0
0
1
1
0
0
0
1
0
0
0
3
0
2
3
0
1
2
1
0
0
2
2
1
0
0
3
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
5
2
0
0
1
2
0
0
2
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
1
0
0
2
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
2
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
1
1
0
0
3
0
0
1
0
0
0
0
0
0
0
1
3
0
0
1
0
0
0
1
0
1
1
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
3
0
0
0
1
1
1
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
4
2
0
1
0
1
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
2
1
0
0
0
1
0
1
0
0
2
0
1
1
0
1
0
1
0
0
0
0
0
0
1
0
0
2
0
1
0
0
2
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
1
0
0
2
0
0
2
0
0
0
2
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
2
0
2
2
2
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
2
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
1
2
0
0
0
2
1
1
0
2
1
1
2
1
0
0
0
0
0
0
2
1
2
0
0
0
0
2
0
1
1
1
0
3
0
1
0
1
2
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
2
0
2
3
1
1
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
1
0
0
3
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
3
0
0
0
4
1
4
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
1
1
2
0
0
1
0
1
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
2
0
2
0
0
0
2
1
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
1
3
0
0
0
0
0
0
2
0
1
1
0
0
2
0
1
0
0
0
3
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
1
0
0
0
1
0
1
2
0
1
3
0
1
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
3
0
0
1
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
2
1
0
2
0
2
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
2
1
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
2
4
1
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
2
2
1
0
0
1
0
0
0
0
0
2
0
1
1
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
1
2
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
3
2
1
0
0
0
0
0
1
0
0
0
0
0
2
0
2
2
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
2
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
1
0
2
1
0
0
0
0
0
0
0
0
2
1
0
1
1
2
1
1
0
2
0
0
1
0
0
2
0
0
0
1
0
0
0
0
2
1
2
1
0
0
7
0
2
1
0
0
1
1
0
0
0
0
0
0
1
0
2
2
0
2
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
1
1
0
0
0
1
0
0
1
2
1
0
0
3
1
0
1
0
0
0
1
2
0
0
1
2
2
1
0
1
0
1
1
0
1
2
2
0
2
0
1
0
3
2
2
0
0
0
0
2
0
0
1
0
0
0
0
3
4
2
2
1
1
1
0
2
0
0
1
0
0
0
0
1
0
2
0
1
0
0
0
0
2
1
8
0
0
0
0
2
0
0
0
2
1
1
0
0
0
0
2
0
0
2
0
2
0
0
2
0
2
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
2
3
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
1
2
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
1
0
1
0
1
2
0
0
0
1
0
1
2
0
0
1
0
1
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
3
0
2
0
0
3
2
0
0
0
0
5
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
1
0
0
0
2
0
0
2
3
0
3
6
0
1
0
0
0
2
0
0
0
0
2
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
1
1
0
1
0
0
0
3
2
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
1
2
0
0
0
0
1
0
0
0
0
2
0
0
2
2
0
2
0
0
3
0
0
2
4
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
1
0
0
0
1
3
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
3
0
0
0
1
0
0
0
2
1
1
1
0
1
0
1
0
0
0
0
0
0
1
0
0
5
0
2
1
3
0
2
0
1
0
1
0
2
0
0
1
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
2
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
2
0
2
0
0
1
0
2
0
1
0
0
0
2
0
0
2
2
0
1
2
0
0
0
0
0
1
0
5
0
0
0
0
2
0
0
0
1
0
0
0
0
1
2
0
0
0
2
2
0
0
2
0
0
0
0
2
0
0
0
0
4
2
0
1
0
0
0
1
2
1
2
0
3
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
2
4
0
3
0
0
2
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
3
0
1
0
2
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
2
1
2
0
2
0
0
2
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
1
2
0
0
2
0
0
0
0
1
2
2
0
0
0
1
0
0
0
2
0
0
3
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
3
2
0
0
0
1
2
0
0
0
1
0
0
3
1
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
3
0
0
0
0
3
2
0
1
0
0
0
0
2
0
2
2
0
1
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
1
2
0
0
0
3
0
0
0
0
1
2
1
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
1
0
0
0
7
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
1
0
1
0
1
1
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
1
2
0
1
0
0
0
0
1
1
0
1
0
0
1
0
0
0
2
0
0
2
0
0
2
0
0
5
0
1
1
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
2
2
0
0
3
0
0
0
0
0
0
2
2
1
0
2
0
0
0
0
2
0
1
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
1
0
1
0
1
0
0
0
2
2
1
0
2
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
2
0
1
0
1
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
2
0
0
0
0
2
5
2
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
5
1
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
10
0
1
0
0
0
2
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
4
2
1
1
0
0
0
0
4
1
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
9
0
0
0
0
2
0
0
0
1
0
0
2
4
0
2
0
0
0
0
3
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
1
0
2
0
0
0
2
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
2
0
3
1
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
1
2
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
1
0
1
2
0
1
2
1
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
6
2
2
4
0
0
0
2
0
2
0
0
2
0
0
1
0
2
0
0
1
2
1
1
0
0
0
0
2
3
1
1
0
0
0
2
0
0
0
2
1
0
0
2
0
0
0
0
0
1
0
0
0
0
2
2
1
2
0
0
1
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
1
0
2
0
1
0
0
0
0
1
2
0
0
1
1
1
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
1
0
0
0
3
0
0
0
0
1
2
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
1
2
0
1
0
1
0
0
0
0
1
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
1
0
0
2
1
0
0
0
2
2
0
1
1
0
2
2
0
0
0
1
0
0
0
0
2
2
0
0
2
2
0
0
2
1
2
0
3
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
1
0
3
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
3
0
1
0
1
1
0
0
0
1
0
0
1
4
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
2
0
1
0
2
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
2
0
0
0
0
1
0
1
3
0
0
0
1
2
1
0
0
0
0
2
2
0
0
0
2
0
0
0
0
1
0
2
1
0
0
0
0
0
0
1
1
0
0
0
1
1
1
4
1
0
1
2
0
0
0
0
1
1
1
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
2
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
1
1
2
0
1
3
3
0
0
0
0
0
0
2
0
0
0
4
0
0
1
0
2
0
1
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
1
1
1
0
0
2
2
0
4
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
2
2
3
0
0
1
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
3
1
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
2
1
0
0
1
1
1
2
0
0
0
0
0
0
1
0
1
0
0
1
0
2
2
0
0
0
0
1
0
2
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
2
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
1
2
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
1
0
2
0
0
0
0
1
0
0
1
0
0
0
2
0
2
2
2
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
2
1
0
2
0
0
0
4
0
1
0
0
0
1
2
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
1
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
6
0
0
0
0
2
2
0
2
0
0
0
2
2
0
0
0
0
0
0
0
2
0
1
0
1
2
0
0
0
7
0
0
0
1
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
5
0
0
0
0
0
0
1
2
2
2
0
1
0
0
0
0
0
2
2
2
0
2
0
0
2
1
0
0
0
3
0
1
0
1
2
0
0
2
0
0
0
0
2
1
0
1
2
1
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
1
1
2
0
1
1
1
0
2
0
1
0
3
0
2
0
2
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
4
0
0
1
0
0
0
2
0
2
0
0
0
4
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
3
1
0
0
1
1
0
0
0
0
3
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
2
0
1
0
0
3
0
0
2
0
0
1
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
2
0
0
0
2
0
1
0
0
0
2
0
2
2
0
0
0
1
0
0
2
0
0
0
0
3
2
0
0
0
0
0
0
1
0
2
0
2
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
3
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
4
2
1
0
1
0
1
0
0
0
0
1
1
1
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
2
2
2
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
2
0
2
2
0
1
0
0
0
1
1
0
0
0
0
2
2
0
0
0
1
1
0
0
0
1
0
0
0
3
0
0
1
1
3
2
0
0
0
0
0
0
0
0
1
1
3
0
0
0
2
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
2
1
0
0
0
0
1
1
0
0
3
0
4
2
0
0
0
0
0
0
0
1
2
0
2
0
2
0
0
1
0
2
0
0
0
9
0
1
0
3
1
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
1
0
2
0
0
0
3
0
1
0
0
1
0
0
0
1
1
0
1
1
0
2
0
1
0
0
0
0
0
0
0
0
5
0
0
0
1
2
0
1
2
0
0
1
1
1
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
1
0
1
0
0
2
0
0
2
0
0
2
4
1
0
1
0
2
0
2
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
2
0
0
2
0
0
0
0
2
2
1
2
1
1
0
0
1
0
2
3
0
1
1
0
0
0
0
0
3
2
1
0
0
0
1
0
0
0
2
0
0
2
2
0
0
0
0
0
1
1
0
0
1
1
0
0
0
1
0
0
0
2
0
0
0
0
7
0
2
0
0
0
0
0
0
2
0
0
2
0
0
3
0
1
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
4
1
0
0
0
0
1
2
1
1
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
1
0
0
0
0
2
0
0
0
2
1
0
2
2
0
0
0
0
0
0
1
0
0
1
0
2
1
0
0
0
1
0
2
0
0
0
0
1
0
0
2
2
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
3
1
0
1
2
0
1
0
1
0
0
3
0
0
0
0
0
0
2
2
0
2
0
0
1
0
0
0
0
4
1
0
0
1
1
0
1
0
2
0
1
0
1
4
0
2
0
0
0
0
0
0
0
0
0
0
2
1
2
0
1
4
2
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
2
0
1
0
0
1
0
0
1
0
0
2
0
0
0
0
0
3
0
0
0
0
2
0
1
0
0
2
0
0
0
1
0
0
0
2
2
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
2
2
2
0
0
1
0
1
0
1
1
2
1
1
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
4
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
3
0
0
0
0
1
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
2
0
0
0
1
0
1
0
0
0
0
3
0
0
0
0
0
1
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
4
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
2
0
0
0
0
0
0
3
2
2
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
3
1
0
0
1
2
1
1
0
0
2
0
0
1
0
0
1
0
2
0
0
0
1
0
0
1
0
0
0
0
2
0
1
1
0
0
0
0
1
2
0
0
0
0
6
1
0
1
1
1
2
0
2
0
2
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
4
4
0
1
1
1
0
0
0
0
2
3
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
1
3
2
0
0
2
2
0
1
0
1
0
0
0
0
0
0
2
0
0
1
0
2
0
2
3
1
0
2
2
0
0
0
0
2
0
0
0
1
0
1
2
0
0
0
0
2
0
0
2
0
0
0
1
1
3
3
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
3
0
2
0
1
0
2
0
1
2
1
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
2
0
0
0
1
0
0
0
0
1
0
0
3
0
0
0
1
0
2
0
0
1
0
2
0
1
0
0
0
0
0
1
0
0
3
0
0
0
0
0
2
0
0
1
1
0
0
0
2
1
0
0
0
2
3
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
2
0
0
0
1
1
0
0
1
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
2
2
0
0
0
1
0
0
0
1
2
0
1
0
0
0
0
0
0
2
0
0
2
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
4
3
0
2
1
2
0
0
0
1
0
0
0
1
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
2
1
0
2
0
0
0
3
1
0
0
0
1
0
2
3
1
0
0
0
0
0
1
0
1
2
0
3
0
0
1
0
0
2
1
0
0
2
0
1
0
0
0
2
1
0
0
0
0
0
0
1
0
1
5
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
1
2
2
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
3
3
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
2
1
1
1
0
1
0
0
0
0
0
0
2
2
1
0
2
2
0
2
1
2
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
2
1
3
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
4
0
1
0
1
2
1
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
2
0
1
0
2
2
3
0
0
0
1
1
0
0
0
2
0
1
0
0
0
0
0
4
0
2
0
0
1
2
0
0
0
0
0
0
2
0
4
1
1
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
1
1
1
2
0
0
1
0
0
2
0
0
0
1
1
0
0
0
2
0
0
0
0
2
0
1
0
0
0
1
2
1
0
0
1
0
0
3
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
1
0
0
0
3
2
5
1
2
0
2
0
0
0
0
0
2
0
0
2
0
0
1
1
0
0
2
0
0
0
0
0
0
0
1
6
0
0
0
1
1
0
1
1
2
0
0
0
0
0
0
0
0
0
2
2
0
0
3
0
1
0
0
2
0
0
0
0
0
0
0
2
4
0
2
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
1
1
0
2
0
2
0
1
1
0
2
0
0
0
0
1
2
0
3
0
2
0
1
2
0
2
0
2
2
1
2
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
2
0
0
0
0
0
1
0
2
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
1
0
0
1
0
0
0
0
1
2
1
0
1
0
2
0
0
0
2
0
0
3
0
0
0
0
0
1
0
3
0
1
0
0
0
0
2
0
1
0
0
0
1
1
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
2
2
0
0
1
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
1
0
0
0
2
0
3
1
1
0
0
0
0
0
0
0
1
0
2
0
0
0
1
2
0
0
1
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
2
0
0
2
0
1
0
0
2
1
0
1
0
0
1
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
2
0
0
2
1
0
0
0
2
0
5
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
1
0
1
1
2
1
2
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
2
0
1
1
0
2
0
0
0
0
0
1
2
0
1
0
0
0
2
1
0
0
0
0
0
2
2
3
1
0
0
0
0
3
0
0
0
0
1
0
2
0
1
2
1
0
0
2
2
0
0
0
2
0
0
0
3
0
3
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
3
0
0
0
1
2
0
2
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
1
0
10
1
0
0
0
1
0
0
0
0
0
0
4
1
0
1
0
0
0
0
0
0
2
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
2
3
0
1
1
0
2
1
0
0
0
2
0
1
1
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
2
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
2
0
6
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
3
3
0
1
2
0
0
0
3
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
4
0
0
1
0
1
0
0
2
0
0
0
0
2
0
2
2
1
3
1
0
0
2
2
1
0
0
1
0
0
0
0
0
2
1
2
1
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
5
2
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
2
2
0
5
2
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
2
2
1
0
1
2
0
0
0
1
0
0
1
0
0
0
0
3
0
0
0
0
1
2
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
3
1
2
1
1
0
0
0
0
0
0
0
0
0
0
0
1
3
1
0
1
0
0
1
0
0
0
1
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
3
0
0
0
1
1
1
0
0
0
0
0
2
0
0
1
1
0
2
0
2
2
1
3
2
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
2
0
0
0
0
2
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
2
0
1
0
2
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
2
0
2
0
1
0
1
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
4
0
3
2
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
3
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
3
1
0
0
1
0
2
2
0
1
1
0
0
1
0
2
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
1
2
0
2
1
0
0
0
2
0
0
2
0
0
0
0
0
1
0
1
1
2
0
0
1
0
0
0
0
0
0
0
1
0
1
2
1
0
0
0
0
3
2
8
1
0
0
0
0
2
0
2
0
1
2
0
2
0
1
2
0
0
0
1
1
0
1
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
2
0
0
0
2
2
0
2
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
2
0
0
2
0
1
0
0
2
0
0
2
3
2
1
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
1
1
2
0
0
0
1
0
2
2
0
0
0
0
0
1
3
0
0
1
0
2
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
1
0
0
2
0
0
0
0
2
0
2
1
2
0
0
0
0
0
1
0
0
0
0
0
2
0
2
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
1
0
1
0
0
5
1
0
0
1
2
2
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
1
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
2
0
1
0
2
0
2
0
0
0
2
0
0
1
0
0
2
1
0
1
3
0
1
1
2
1
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
1
0
2
0
1
0
0
0
0
2
1
0
0
0
1
0
3
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
2
1
0
0
2
0
2
0
0
2
0
0
0
0
2
2
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
1
2
0
0
1
2
0
2
0
0
0
0
0
0
0
0
1
1
2
0
0
0
1
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
2
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
1
2
3
0
1
0
0
3
0
0
1
2
0
1
0
2
0
0
0
1
0
1
2
1
0
2
1
2
2
3
0
0
0
1
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
2
0
1
2
0
0
1
0
0
0
1
0
0
0
0
1
0
1
2
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
3
1
0
1
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
4
2
0
2
1
2
0
0
1
2
0
0
0
0
2
0
2
0
0
1
0
2
1
2
0
2
1
0
0
2
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
2
0
1
0
1
2
2
0
0
0
0
2
3
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
2
0
2
0
2
0
2
0
0
0
0
1
0
0
0
2
0
0
1
1
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
2
1
0
0
2
0
0
0
0
0
0
2
2
1
0
0
0
3
1
0
0
0
0
0
0
1
1
2
0
0
2
0
2
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
4
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
2
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
1
0
2
2
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
5
0
1
0
0
0
1
2
0
0
2
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
2
2
1
2
0
1
0
0
2
0
3
0
0
2
0
2
0
0
0
2
0
1
0
0
0
0
2
1
0
2
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
3
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
5
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
1
0
2
0
0
0
0
2
0
1
1
2
2
0
0
0
1
1
0
1
0
0
0
2
2
3
0
0
0
0
2
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
2
0
0
2
0
0
0
0
1
1
0
0
2
0
0
0
0
2
1
0
1
0
0
0
1
2
0
3
0
0
0
1
0
0
2
0
3
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
1
0
2
2
0
1
0
2
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
4
0
0
0
0
2
0
0
0
2
0
2
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
1
1
2
0
2
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
2
0
0
0
0
0
0
3
0
0
1
0
0
1
1
1
0
0
0
0
2
0
0
0
1
2
1
0
0
2
2
0
0
1
0
1
0
2
0
0
2
1
0
0
0
2
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
2
0
0
1
0
0
1
8
0
3
0
1
0
1
1
0
0
2
0
0
2
0
0
0
0
2
2
2
0
2
1
2
1
0
0
0
0
0
0
0
0
0
2
2
0
0
3
2
2
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
2
0
2
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
5
1
0
0
0
0
1
2
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
1
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
2
2
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
1
1
1
0
0
2
0
0
2
0
0
0
1
2
2
2
4
1
0
0
0
2
0
0
0
0
0
0
0
2
1
1
0
2
1
0
2
0
1
2
0
0
0
0
0
0
0
1
0
0
0
2
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
5
0
1
0
0
0
1
2
0
2
1
0
0
1
0
0
2
0
2
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
2
2
0
1
0
0
0
0
3
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
1
2
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
2
2
0
0
0
2
0
0
1
2
0
0
0
0
0
0
2
2
1
0
0
2
0
1
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
2
0
0
1
0
0
1
0
1
2
0
0
2
2
0
0
4
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
3
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
3
1
0
3
0
0
0
1
0
0
1
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
1
0
0
3
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
1
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
1
1
1
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
1
2
0
1
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
1
8
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
7
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
3
2
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
2
1
0
3
0
3
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
1
1
0
0
0
0
2
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
2
0
0
0
0
0
1
0
0
1
0
1
2
0
0
1
0
1
0
0
0
2
1
0
0
0
1
2
1
0
0
0
2
0
2
2
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
2
1
0
0
0
0
0
2
0
2
1
2
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
1
1
1
0
0
0
0
1
3
2
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
1
0
0
2
0
1
1
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
2
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
3
0
0
0
0
0
0
0
1
2
0
2
0
1
0
0
0
2
0
0
1
1
0
0
0
2
3
2
0
0
0
1
2
0
0
1
0
1
0
1
1
0
1
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
1
1
0
1
1
1
1
0
0
0
2
0
1
0
0
0
1
1
0
0
0
0
0
1
1
0
1
0
2
0
1
0
2
0
0
0
0
0
0
0
2
5
0
2
0
1
0
0
0
1
0
6
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
1
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
2
2
2
0
0
0
0
2
2
0
0
0
0
1
1
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
3
2
0
1
1
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
2
2
0
1
0
0
2
0
4
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
5
2
0
0
0
2
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
1
0
2
0
0
0
2
2
1
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
1
2
0
2
0
0
0
2
0
0
0
0
0
1
2
0
2
1
1
1
0
0
0
3
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
7
0
1
2
0
1
1
1
0
0
2
2
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
1
0
0
2
0
1
1
1
1
0
0
1
0
3
2
0
0
1
0
0
3
2
0
1
0
0
0
2
1
2
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
1
5
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
4
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
2
0
0
0
1
0
0
4
0
1
0
0
2
1
1
0
0
0
2
1
1
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
2
0
2
2
3
0
1
0
0
1
0
1
1
0
0
1
0
2
0
3
0
0
0
0
0
1
1
0
0
0
0
0
1
2
2
0
0
1
0
0
1
0
0
0
1
0
0
1
0
3
0
0
0
0
1
0
0
0
2
2
0
1
0
0
0
0
0
1
2
3
0
3
1
1
1
0
0
1
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
1
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
1
3
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
4
2
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
2
2
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
3
0
2
3
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
2
0
0
0
0
0
2
1
2
0
0
0
0
0
0
1
0
0
1
0
1
0
3
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
2
0
1
0
0
0
1
0
2
0
1
0
0
0
0
1
2
1
1
0
0
0
0
0
1
0
1
0
2
1
0
0
1
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
2
3
0
2
0
0
0
2
0
2
1
1
1
1
0
0
0
0
0
2
1
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
3
1
2
1
0
1
0
0
1
0
2
0
0
0
0
2
0
1
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
1
0
0
2
2
1
0
2
0
2
0
2
0
0
1
0
0
0
0
3
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
2
1
2
0
1
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
2
3
0
0
1
1
0
0
0
0
0
2
0
1
1
2
1
0
0
0
0
2
0
0
0
1
0
0
2
2
0
2
0
0
0
0
0
0
0
1
3
0
1
0
0
0
0
0
2
0
1
3
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
2
1
0
0
0
0
2
0
1
2
0
2
0
0
0
1
0
3
0
0
0
3
2
2
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
3
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
1
1
2
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
3
0
2
2
2
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
3
2
0
0
0
0
2
0
2
0
0
0
0
0
2
2
1
2
0
1
0
1
0
0
2
0
0
0
1
0
2
0
0
0
2
0
2
0
2
1
2
0
1
2
2
0
0
1
1
0
0
0
3
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
3
3
1
0
0
0
0
0
0
0
10
0
0
0
0
0
0
0
0
0
4
0
1
1
0
1
1
1
0
0
0
0
0
0
0
7
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
3
2
0
2
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
3
0
0
1
0
0
0
0
0
0
1
2
0
0
1
1
2
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
2
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
1
0
5
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
1
1
0
0
1
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
3
0
0
0
4
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
3
0
1
2
0
0
1
0
2
0
0
0
0
0
0
1
1
0
0
0
0
2
1
2
0
1
1
0
0
1
0
2
1
0
0
1
0
0
0
2
0
0
0
0
0
1
1
2
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
4
0
0
0
1
0
0
0
0
2
0
1
0
0
0
1
2
0
0
0
0
4
0
0
0
2
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
2
0
0
2
2
1
0
0
0
0
0
0
5
2
0
0
0
4
2
2
2
0
0
0
1
0
0
0
0
1
0
0
1
1
1
0
1
0
0
0
0
0
0
2
0
2
1
1
0
2
0
0
2
0
3
0
1
2
0
4
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
3
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
2
2
0
1
1
0
1
2
2
2
0
1
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
1
1
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
3
0
0
0
0
0
0
2
2
1
0
2
0
1
0
1
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
2
0
2
2
0
0
0
1
0
0
2
0
2
2
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
3
4
0
1
0
3
2
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
1
1
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
1
1
2
0
0
0
2
0
2
2
0
2
3
1
0
0
2
2
0
0
0
0
3
0
0
0
1
0
0
2
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
2
2
2
0
0
2
2
2
4
1
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
2
2
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
3
2
0
2
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
2
1
0
1
0
0
2
1
1
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
2
3
0
0
1
0
0
0
1
0
2
2
0
1
0
0
1
0
1
1
1
1
1
2
0
3
0
0
0
1
2
2
3
1
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
1
1
0
1
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
2
0
2
0
1
2
0
0
0
0
2
0
0
0
0
1
2
2
0
0
1
0
0
1
2
0
0
0
0
0
0
0
1
0
3
0
2
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
2
1
0
0
2
0
0
0
0
1
3
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
1
1
1
0
0
1
0
1
0
0
0
3
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
2
0
0
2
0
0
0
2
0
2
0
0
0
2
0
1
0
0
3
0
0
1
0
0
0
1
0
0
0
0
2
1
0
0
0
3
0
0
0
0
1
0
4
1
0
0
1
1
2
0
0
1
2
0
0
1
0
1
2
0
1
0
2
0
0
0
1
1
1
0
0
1
0
0
1
0
1
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
2
0
0
3
1
2
1
1
0
0
0
0
0
0
0
1
0
0
1
2
2
0
0
0
2
1
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
1
2
0
0
1
2
3
0
0
0
0
0
0
1
0
0
0
3
2
0
0
0
1
0
0
0
0
0
0
1
2
1
0
2
4
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
2
1
1
0
0
1
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
3
1
0
0
0
0
4
0
0
0
0
1
2
2
0
2
0
0
0
0
2
0
0
0
1
2
0
0
0
3
2
0
1
0
0
0
0
0
2
2
0
0
0
2
0
0
0
1
2
0
2
0
1
0
0
0
2
1
0
0
0
0
2
0
1
0
0
0
0
0
2
2
0
0
6
0
2
0
0
0
2
0
0
0
0
1
1
0
0
0
2
0
0
1
1
2
0
0
3
0
0
1
2
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
1
0
0
0
0
3
0
0
0
2
0
0
1
0
1
0
0
0
1
2
0
2
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
2
2
0
0
1
0
2
0
0
1
0
0
0
1
1
2
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
4
2
1
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
1
0
1
0
0
2
2
0
1
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
1
1
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
3
0
2
2
0
0
1
2
2
0
0
2
0
0
0
2
0
0
1
0
0
0
2
0
2
1
0
0
1
0
0
2
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
1
0
1
0
0
1
1
0
2
0
0
2
2
0
2
3
5
0
0
0
0
0
1
2
0
1
1
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
2
2
0
0
1
0
0
0
2
2
0
0
0
1
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
2
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
2
0
0
2
1
0
3
0
1
1
0
0
1
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
2
2
0
0
0
2
1
0
2
0
0
1
1
0
0
2
0
0
0
0
0
0
2
1
0
2
1
2
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
2
2
16
0
0
2
2
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
3
0
0
1
0
0
5
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
1
1
0
0
0
0
2
0
2
0
0
0
1
0
0
1
6
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
2
1
2
0
3
0
0
0
1
1
1
0
0
0
0
1
4
0
0
1
0
0
0
0
2
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
3
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
2
1
1
0
2
1
0
0
1
0
1
1
0
0
0
1
0
0
2
1
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
2
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
2
0
1
2
1
0
0
0
1
0
0
0
2
0
0
0
1
0
2
0
0
1
2
0
0
0
0
0
1
2
0
1
1
0
0
0
2
0
0
0
3
0
1
2
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
2
2
0
1
0
3
0
0
0
0
1
2
1
0
0
0
0
2
2
0
0
0
1
2
1
1
0
1
2
3
0
2
0
0
2
0
0
0
0
0
4
0
0
2
2
0
2
0
5
0
1
1
3
0
1
0
0
0
1
0
2
2
0
0
0
2
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
2
1
1
0
0
0
2
1
0
0
0
0
0
0
1
0
2
0
0
1
0
2
0
0
0
1
0
1
0
0
0
2
0
1
0
0
4
2
0
2
3
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
2
2
0
0
0
0
0
0
0
0
0
1
3
0
0
2
1
0
1
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
2
0
1
0
0
0
0
0
2
0
4
0
1
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
1
2
0
0
1
0
0
0
0
0
3
0
2
0
0
0
0
2
0
0
0
0
1
0
0
1
1
0
2
0
0
0
2
0
1
0
2
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
2
2
0
0
0
1
1
0
0
0
2
0
1
0
2
1
1
0
2
2
0
1
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
1
0
1
1
0
4
1
2
0
1
0
0
2
1
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
2
0
0
4
0
0
0
1
2
0
1
0
0
0
1
0
0
2
0
0
1
1
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
1
0
2
0
0
2
0
0
0
0
0
0
2
0
1
4
0
2
1
0
2
0
0
0
0
0
1
0
0
1
0
0
0
2
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
4
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
1
1
0
0
0
0
2
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
1
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
2
2
1
0
0
0
1
1
2
0
1
0
0
2
0
0
0
0
0
2
0
2
0
0
1
1
0
1
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
3
3
1
1
0
2
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
2
2
0
5
1
2
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
1
2
2
0
0
1
0
0
0
0
1
0
0
2
0
2
0
0
0
2
0
0
1
1
0
0
0
0
0
2
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
1
0
0
0
0
1
1
0
0
2
1
0
1
0
1
2
0
0
0
0
0
4
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
1
2
1
0
2
1
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
2
0
0
2
0
1
1
0
1
1
0
0
0
2
0
0
0
1
1
1
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
2
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
3
0
2
0
0
1
0
2
1
0
2
0
8
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
2
0
4
0
0
0
0
1
0
0
2
0
1
0
0
2
1
3
0
1
0
0
3
0
2
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
1
0
0
2
0
0
1
0
0
2
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
1
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
3
0
2
1
2
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
1
1
1
3
0
0
0
0
1
0
0
2
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
1
0
0
0
0
3
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
2
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
1
0
1
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
1
0
1
1
3
2
0
0
0
3
0
2
0
0
0
0
2
0
0
1
2
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
1
0
0
0
0
2
2
1
0
1
0
0
2
2
0
0
0
0
0
0
0
1
1
2
0
0
1
0
0
1
2
0
0
0
2
3
0
0
1
0
0
0
1
0
0
0
4
2
0
0
3
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
1
0
2
1
0
2
0
0
4
0
0
1
0
0
0
1
0
1
0
2
0
0
1
5
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
1
0
0
2
1
0
0
0
1
0
9
0
0
0
2
2
1
0
1
0
0
0
0
1
1
0
0
1
1
0
5
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
2
3
0
0
0
2
2
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
2
0
2
0
2
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
2
0
1
0
0
2
0
0
2
1
0
0
0
2
1
0
1
0
0
1
0
0
0
2
0
0
2
2
2
0
0
1
1
1
0
3
0
0
0
0
0
1
0
0
0
2
0
1
1
0
1
0
0
2
0
0
0
0
0
0
1
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
1
1
0
3
1
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
2
0
0
0
0
3
1
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
1
0
0
2
2
1
0
2
0
3
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
2
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
3
0
2
0
0
1
0
1
2
1
0
0
0
0
0
1
0
2
1
0
1
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
2
2
0
1
0
1
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
1
0
1
0
0
0
0
0
0
1
2
0
2
0
0
2
0
0
0
0
4
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
2
1
0
0
0
0
1
0
0
0
2
0
2
0
0
2
0
1
1
0
2
1
0
0
0
2
0
1
0
0
0
1
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
1
0
0
1
1
2
0
0
2
1
2
0
1
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
3
2
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
3
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
2
0
1
0
0
2
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
2
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
3
1
0
0
0
1
0
1
2
0
1
0
0
0
0
1
2
2
0
0
1
2
0
1
0
1
0
0
0
0
0
0
0
1
0
2
0
0
1
3
1
0
0
2
0
2
0
1
0
2
0
0
1
1
1
1
0
0
0
0
0
1
0
0
1
0
3
1
0
0
0
0
2
0
0
2
2
2
0
2
0
0
0
0
0
0
0
0
1
2
0
1
6
0
0
1
0
2
0
2
0
0
0
1
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
2
1
0
0
2
2
2
2
0
2
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
4
1
0
0
0
0
1
1
1
0
0
0
1
0
0
2
0
0
0
0
0
0
1
2
3
0
0
0
0
2
0
1
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
2
0
0
1
0
2
1
0
0
0
1
0
0
0
0
0
2
0
1
0
2
1
0
0
0
0
0
6
0
2
0
3
0
2
0
1
0
2
0
2
0
1
0
0
2
1
0
2
1
0
0
0
1
0
0
8
2
0
0
1
2
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
3
0
0
1
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
4
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
4
0
3
0
1
2
1
2
2
0
0
1
1
0
0
1
1
2
0
0
0
1
2
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
1
2
0
2
1
0
2
1
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
2
0
1
1
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
3
1
1
0
0
1
1
0
0
2
0
0
0
3
0
0
0
0
2
0
2
0
0
0
0
0
2
2
0
2
0
4
0
2
0
0
2
0
0
0
0
3
0
0
2
0
0
2
0
0
0
0
2
2
0
0
2
0
0
1
0
0
0
0
2
2
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
2
0
2
2
0
0
2
2
0
0
0
0
0
0
0
2
2
1
2
0
0
1
0
0
2
0
0
1
0
0
0
0
2
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
1
0
3
2
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
2
0
2
2
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
7
1
1
2
0
0
0
2
0
0
0
0
2
0
0
1
1
4
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
1
2
0
0
2
0
0
2
2
2
0
0
0
0
0
0
0
1
1
0
1
0
0
3
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
1
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
3
0
0
2
1
1
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
2
0
2
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
2
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
1
1
2
2
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
3
2
0
0
0
2
1
0
0
0
0
1
0
1
0
1
2
0
0
1
1
0
0
0
0
2
0
0
2
0
0
1
0
0
0
2
0
2
0
2
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
1
1
0
3
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
2
1
2
0
1
1
0
1
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
1
1
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
2
0
0
1
1
2
2
0
0
0
1
0
1
2
0
2
2
2
0
0
0
3
2
0
1
1
2
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
1
1
2
1
0
0
0
0
0
1
2
2
2
0
0
1
1
0
0
1
3
3
1
1
2
0
2
0
2
0
0
0
0
1
2
0
1
0
1
2
0
0
0
2
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
2
1
0
1
2
0
1
0
0
0
0
1
2
1
0
0
0
2
0
2
0
2
1
0
0
2
0
0
0
0
0
0
0
1
0
2
3
0
0
0
1
0
0
4
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
2
0
1
0
0
0
2
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
2
0
0
2
0
0
0
0
0
0
0
0
0
2
2
1
2
0
2
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
1
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
1
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
1
2
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
2
0
0
0
0
2
1
0
0
1
0
0
0
1
2
0
1
2
0
0
2
1
1
0
0
0
0
1
0
3
0
3
0
0
1
0
0
2
0
0
0
1
2
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
2
1
1
0
0
1
0
0
0
2
1
2
0
0
1
0
1
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
3
0
0
0
1
2
0
0
0
0
0
0
2
1
0
0
2
1
0
0
0
2
1
1
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
3
0
0
0
0
2
1
0
0
0
0
2
0
1
0
2
1
0
0
6
1
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
1
2
0
2
0
1
0
2
0
0
0
2
0
0
2
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
2
4
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
3
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
2
0
1
1
0
0
1
1
0
0
0
2
0
0
0
0
1
0
0
2
1
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
2
1
0
0
0
0
2
0
0
2
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
2
2
0
2
0
1
1
2
0
1
0
1
0
0
0
0
3
3
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
2
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
2
2
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
2
0
1
3
1
0
3
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
1
2
0
1
0
0
0
0
2
2
0
0
2
0
0
0
0
0
1
1
2
0
1
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
2
2
3
1
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
2
0
0
2
1
0
2
0
2
1
1
1
1
0
0
0
2
2
3
0
0
1
0
0
1
3
0
0
0
1
0
0
0
0
1
0
0
2
0
0
2
1
0
0
0
0
2
0
5
1
0
0
3
2
0
0
0
0
1
2
0
2
1
0
0
2
2
0
0
2
0
1
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
1
3
0
0
0
0
0
0
0
1
0
1
1
0
1
0
1
2
0
1
2
0
0
0
0
1
1
2
1
0
0
0
0
0
0
2
0
0
1
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
1
0
0
2
0
0
0
0
2
0
1
0
2
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
1
2
0
0
0
3
0
0
0
1
0
0
1
0
0
0
1
0
0
6
1
1
0
0
0
0
0
0
0
2
2
2
0
0
1
2
0
1
0
2
0
1
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
2
3
0
0
0
2
2
2
2
2
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
3
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
3
1
2
1
0
1
1
0
0
0
0
0
1
1
2
0
12
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
2
0
1
1
0
0
0
2
2
0
0
0
0
0
0
0
2
2
2
0
1
0
0
3
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
1
0
1
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
2
1
0
0
0
0
0
0
1
0
4
0
0
0
1
3
0
0
0
0
0
0
0
2
0
0
3
0
0
0
1
1
0
1
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
2
0
0
2
0
0
0
1
0
0
0
1
2
0
0
1
0
1
0
2
0
0
1
0
0
1
0
0
2
0
0
0
0
2
0
0
0
1
3
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
4
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
1
1
2
0
0
0
1
0
2
1
4
2
0
0
0
0
0
0
1
0
1
2
0
1
0
0
1
0
0
0
0
0
4
1
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
3
0
0
0
5
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
1
1
0
0
0
0
2
2
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
3
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
2
0
0
1
1
0
0
2
0
0
0
2
0
0
0
0
3
0
2
0
2
2
0
0
2
1
0
2
3
0
0
0
2
0
0
0
0
0
0
1
2
2
0
2
2
0
0
0
1
0
2
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
2
0
0
0
0
3
0
0
0
1
0
2
0
0
2
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
2
0
0
4
0
6
1
0
2
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
1
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
2
1
0
1
1
1
7
2
2
2
0
0
0
1
0
0
0
0
0
2
0
1
1
0
1
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
2
5
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
1
1
0
3
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
3
0
1
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
1
2
0
1
0
0
1
2
0
0
0
1
0
0
1
1
5
0
0
0
0
6
0
0
1
3
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
1
1
4
0
0
0
2
1
2
0
1
1
0
2
0
0
0
2
0
0
1
0
1
1
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
2
0
2
2
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
1
0
1
1
1
2
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
2
2
2
0
0
0
0
0
1
1
2
0
2
2
0
1
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
1
0
0
0
6
0
0
0
0
0
2
1
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
2
0
0
7
2
1
0
0
0
0
2
0
0
0
0
0
1
1
1
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
1
2
0
0
1
0
0
2
0
2
0
0
0
0
0
1
5
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
1
0
1
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
1
3
1
0
0
0
1
1
0
0
0
0
0
3
0
1
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
1
0
2
0
2
0
0
0
0
2
0
2
0
1
0
2
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
3
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
2
0
0
0
0
1
2
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
1
0
0
0
2
2
0
0
2
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
2
0
2
1
2
0
0
1
0
0
0
0
0
0
0
3
0
0
1
1
0
0
2
0
2
0
0
2
0
0
0
2
1
0
0
2
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
1
2
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
3
0
1
0
0
0
2
1
2
0
0
1
2
2
0
0
0
0
0
0
0
0
0
2
0
2
0
3
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
1
1
0
0
2
0
1
0
0
0
1
0
3
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
2
0
2
2
2
0
0
0
1
0
1
0
0
2
2
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
2
0
0
1
1
2
0
1
0
0
0
0
1
0
0
0
0
1
1
2
0
0
0
0
1
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
1
0
0
0
0
3
3
2
2
1
0
0
3
1
1
0
1
2
1
8
0
0
0
0
1
0
2
0
0
0
4
1
2
2
1
0
0
0
0
4
0
2
0
0
0
0
0
0
0
1
0
3
0
0
0
2
0
1
0
0
0
3
0
0
0
2
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
8
0
0
0
0
0
1
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
1
0
2
1
0
1
1
0
0
0
0
0
1
0
0
0
2
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
1
0
0
2
0
0
2
2
1
0
3
3
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
3
3
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
2
0
0
0
1
2
0
0
0
0
0
7
0
1
1
0
0
0
0
0
0
2
0
1
0
0
1
0
0
5
0
0
0
0
0
0
0
0
0
2
1
0
3
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
2
1
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
1
2
0
1
0
0
1
0
2
2
0
0
1
0
2
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
1
0
2
1
2
0
0
0
0
0
0
2
0
0
0
1
2
2
0
0
0
2
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
2
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
2
0
2
0
1
1
0
1
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
2
1
0
0
0
0
0
1
1
0
0
2
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
1
0
2
2
0
0
0
1
0
1
1
1
1
2
0
0
0
0
2
0
1
1
1
0
1
0
0
1
0
0
0
0
0
0
2
1
2
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
1
2
1
0
0
2
0
0
0
2
0
1
3
0
2
0
0
0
0
0
1
0
0
0
2
3
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
1
0
0
1
2
0
0
1
0
2
0
0
2
0
2
0
0
2
0
0
0
0
0
2
0
0
2
0
3
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
2
0
2
1
1
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
3
0
0
0
0
0
2
3
3
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
1
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
2
1
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
2
0
1
0
1
3
0
0
1
0
0
0
0
0
0
0
2
0
1
2
0
0
0
2
0
0
0
1
0
1
0
2
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
1
0
0
0
1
0
0
0
0
2
2
0
1
2
0
1
0
2
4
0
0
0
0
3
0
0
0
0
4
0
0
0
0
1
0
0
0
0
1
2
2
0
0
5
0
1
0
1
3
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
2
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
2
1
0
1
3
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
2
0
0
0
2
0
0
0
3
0
0
1
0
0
0
0
1
0
0
2
0
0
2
1
1
0
1
0
0
0
0
2
0
0
0
0
1
0
1
1
0
1
2
0
1
0
0
4
0
2
0
0
0
1
1
1
0
1
0
0
2
0
1
0
1
0
0
0
0
0
1
0
2
2
2
0
0
0
0
0
1
0
1
3
0
0
0
0
0
0
2
2
0
1
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
5
0
0
0
0
2
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
7
1
1
2
0
1
0
1
0
3
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
2
2
0
0
0
2
0
1
2
2
0
1
0
0
0
1
0
0
0
0
0
0
2
0
1
2
0
2
0
0
0
0
0
0
0
1
0
2
2
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
3
2
0
0
0
0
2
0
0
1
0
6
0
0
0
0
0
0
1
1
1
2
0
0
0
0
2
0
2
0
1
0
0
2
0
0
2
0
0
3
0
0
0
2
0
0
0
2
2
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
2
0
1
0
0
0
0
1
0
2
0
1
1
0
0
0
0
0
2
1
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
5
0
0
1
0
3
0
0
1
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
5
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
1
0
2
0
0
2
0
0
2
2
2
0
0
1
0
0
0
0
0
2
2
1
1
0
1
0
0
0
1
0
0
3
0
0
1
1
0
0
0
2
0
0
0
0
2
2
0
0
0
0
2
0
0
3
0
1
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
3
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
2
0
0
0
1
0
0
3
0
0
2
0
2
0
0
0
0
0
0
5
2
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
2
0
0
2
0
2
0
0
1
0
2
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
2
0
0
2
2
0
1
1
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
1
2
0
2
0
0
0
1
0
0
1
0
0
0
3
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
1
2
0
0
5
0
0
0
1
0
0
0
0
1
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
1
0
0
2
0
0
0
0
0
0
1
2
1
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
2
2
0
2
0
0
0
0
0
0
2
0
2
2
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
2
0
0
0
0
2
1
1
0
0
0
0
0
1
2
2
0
0
0
1
1
1
0
0
2
0
0
3
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
2
1
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
2
6
0
0
0
0
0
0
2
0
0
0
0
1
2
0
4
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
2
0
1
1
0
0
1
2
0
1
0
0
0
0
0
0
0
0
2
0
2
2
0
1
0
0
0
0
1
0
0
0
0
3
1
2
3
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
1
2
2
2
1
0
1
2
0
2
0
0
2
0
2
2
0
2
0
0
2
0
0
2
1
0
0
2
2
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
9
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
2
2
2
0
0
0
0
0
2
1
1
0
0
0
1
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
2
0
1
0
5
2
4
0
0
0
0
1
0
0
0
0
0
0
1
1
0
2
0
0
0
0
2
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
2
1
0
1
2
0
1
1
0
0
0
2
0
0
5
0
0
0
1
0
0
0
0
2
0
2
0
2
0
0
0
0
2
2
2
0
0
0
0
0
0
1
0
0
1
0
2
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
1
1
0
1
0
2
0
0
2
0
0
0
0
0
0
1
1
0
0
0
2
1
0
0
0
1
0
0
1
0
0
0
3
2
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
2
2
1
0
0
0
0
2
1
0
2
0
0
2
2
0
0
0
0
1
1
2
0
1
1
0
0
0
0
1
2
0
0
2
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
5
0
0
4
2
0
0
0
1
1
0
0
1
3
0
1
0
0
3
0
0
0
0
1
0
0
2
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
1
0
0
0
3
0
0
0
1
0
2
2
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
3
0
1
0
1
2
0
1
2
0
1
0
0
2
2
2
0
0
0
2
0
0
1
0
0
1
1
1
2
1
0
0
0
0
0
0
0
2
2
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
1
2
4
1
0
0
0
1
0
0
0
2
0
0
2
1
0
0
0
1
0
0
0
0
0
2
0
0
1
1
0
0
4
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
2
0
0
1
0
1
0
0
0
0
1
0
2
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
3
0
1
0
0
0
2
0
0
0
2
0
0
2
0
0
2
1
2
1
2
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
2
0
0
1
1
0
3
2
0
0
0
2
0
0
1
0
0
0
0
0
0
1
2
2
0
1
0
0
0
0
0
0
0
0
1
1
1
2
0
1
0
0
2
0
0
0
2
0
1
0
0
0
1
0
0
2
0
2
1
2
0
3
1
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
1
0
1
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
1
0
0
2
1
0
9
0
1
0
0
2
1
0
0
0
1
0
0
3
2
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
2
0
0
1
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
2
2
0
0
2
2
1
0
0
0
1
2
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
2
0
1
0
0
2
2
0
0
1
1
0
0
0
0
1
0
0
0
1
1
2
0
0
2
0
1
1
0
0
1
1
0
0
0
0
0
2
0
2
3
1
1
0
0
0
2
0
1
0
0
2
0
0
0
2
2
0
0
1
1
0
2
0
0
0
1
2
0
0
0
1
0
1
0
1
0
1
0
1
3
0
0
0
2
1
0
3
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
2
1
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
2
0
0
1
0
0
0
1
0
0
2
0
0
3
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
1
2
1
0
0
2
0
0
0
0
0
1
0
2
0
0
0
4
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
2
1
1
1
2
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
1
3
1
1
2
2
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
2
3
0
0
2
0
0
1
2
0
0
2
0
0
0
1
0
0
0
0
2
1
1
0
0
0
1
2
0
1
1
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
2
2
1
0
0
3
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
1
1
1
0
2
0
1
1
0
0
0
0
2
0
0
0
0
0
1
1
1
0
0
0
0
2
1
0
0
0
0
0
0
1
0
1
0
2
0
2
0
0
1
2
0
0
2
0
1
0
0
0
1
0
0
0
2
0
0
0
0
2
2
1
1
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
2
0
1
0
0
1
0
0
0
0
1
0
2
0
1
0
2
0
0
0
0
0
1
0
2
0
0
0
0
1
1
0
0
0
2
2
0
0
2
0
0
2
0
0
1
0
1
1
1
0
2
1
1
0
0
1
1
0
0
0
1
1
1
1
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
2
2
2
1
0
0
0
1
0
1
2
0
0
1
4
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
1
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
4
0
0
2
5
2
1
0
0
0
2
0
0
0
0
1
0
0
2
3
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
1
2
0
1
0
0
0
0
0
0
1
0
1
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
1
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
1
0
2
0
0
2
3
0
1
0
2
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
1
0
2
0
2
2
1
4
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
2
2
1
0
2
1
0
1
1
2
0
0
1
0
0
0
1
0
2
0
0
2
0
0
0
1
0
0
0
0
0
2
2
0
2
0
0
0
0
1
2
0
0
0
3
0
0
0
0
0
1
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
2
0
0
1
1
0
1
0
0
0
0
0
0
0
3
5
0
2
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
2
0
5
0
0
0
0
0
0
0
3
2
0
1
0
1
0
3
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
4
2
0
0
2
0
2
3
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
2
0
0
2
0
0
0
1
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
3
2
0
2
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
2
0
1
1
0
1
0
0
0
2
2
0
1
0
0
0
2
2
5
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
3
1
0
0
0
0
1
2
0
0
0
0
1
0
1
0
2
0
1
0
2
2
0
0
0
0
2
2
0
0
2
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
1
2
0
0
3
0
2
0
0
0
1
0
1
1
0
0
0
0
1
2
0
0
0
0
0
2
2
0
1
0
0
0
2
0
1
0
0
0
0
2
0
0
0
3
0
1
0
0
0
0
2
0
0
0
0
3
2
0
1
0
0
0
0
0
0
1
0
0
2
0
1
0
2
0
2
1
1
3
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
1
2
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
2
0
2
0
1
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
2
0
2
0
0
0
1
0
6
0
0
0
1
2
0
0
1
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
1
1
2
0
2
0
1
0
2
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
2
1
0
0
3
2
0
2
0
0
0
1
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
1
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
1
2
1
1
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
1
0
1
0
0
0
2
2
0
1
0
0
1
1
0
2
0
0
1
0
1
0
2
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
2
2
1
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
10
1
0
2
0
0
1
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
2
0
2
0
0
0
2
0
0
2
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
3
2
1
1
1
0
0
2
0
2
0
2
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
3
5
1
1
2
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
2
2
0
0
0
2
1
0
0
0
1
0
0
1
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
1
0
1
1
0
2
0
0
0
2
0
3
0
0
0
0
0
0
0
0
1
2
1
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
2
0
0
1
0
0
0
0
6
1
2
0
0
1
0
2
0
0
1
0
0
1
2
1
0
1
0
1
0
0
0
2
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
1
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
1
1
0
0
0
0
0
0
2
0
0
3
3
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
2
0
1
0
0
3
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
2
5
1
1
0
0
0
0
2
0
0
1
2
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
2
0
0
1
0
0
0
0
1
2
1
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
4
0
2
0
1
1
2
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
3
0
2
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
1
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
4
0
0
0
2
0
0
2
1
0
0
0
1
0
0
0
0
3
0
1
0
0
0
0
1
0
2
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
2
0
0
0
0
1
0
0
0
2
2
0
0
1
0
1
0
0
0
1
1
0
0
0
0
2
0
0
2
0
2
2
0
3
2
0
5
2
0
4
0
2
0
2
0
5
0
0
0
1
0
0
0
2
1
0
0
2
0
0
2
1
0
0
0
0
2
0
1
0
0
3
0
0
0
0
1
2
0
2
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
2
0
0
2
1
0
2
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
1
2
3
0
0
1
0
1
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
1
1
0
3
0
0
0
0
0
0
1
2
0
1
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
1
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
3
2
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
3
0
0
0
2
0
0
0
0
4
0
0
0
5
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
3
0
0
1
1
0
1
1
0
2
0
0
1
0
2
0
0
0
0
3
0
0
1
1
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
1
0
0
1
0
1
1
0
0
2
2
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
1
2
0
0
0
0
0
2
2
2
0
0
3
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
1
2
0
0
0
2
0
1
0
0
1
2
0
0
2
3
0
0
0
0
1
1
0
0
0
0
0
1
2
0
1
0
0
0
1
0
0
0
0
0
1
1
2
0
0
0
0
0
2
1
0
0
0
1
0
0
2
0
0
0
2
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
3
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
1
2
1
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
1
2
1
2
0
0
0
0
0
0
1
0
2
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
4
0
0
0
0
2
0
0
0
2
0
0
0
0
2
1
1
0
0
3
0
3
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
2
1
0
0
2
0
0
0
0
0
1
0
0
0
0
4
0
1
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
1
1
1
0
0
0
1
0
2
0
0
0
1
0
0
0
0
3
0
0
0
0
0
3
0
0
0
1
2
1
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
2
0
2
0
1
2
0
2
2
0
1
2
0
0
2
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
1
0
0
2
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
3
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
1
0
0
1
2
0
0
0
0
0
0
0
1
2
0
2
0
1
0
0
2
2
0
0
0
0
2
2
0
0
0
3
0
0
1
0
1
0
1
1
2
2
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
2
1
2
2
2
2
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
4
1
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
1
0
0
0
1
0
2
0
0
0
2
0
0
0
3
0
2
0
0
0
0
0
1
0
0
0
1
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
1
0
2
2
2
1
0
1
0
0
0
0
0
6
0
0
0
0
0
1
0
1
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
2
5
0
2
2
0
0
0
0
2
0
0
2
0
0
0
0
1
0
2
0
2
1
0
0
0
0
0
2
0
0
0
2
1
0
0
1
0
0
2
0
0
1
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
1
2
1
0
2
2
0
0
0
1
0
2
0
0
0
0
0
0
1
0
1
2
1
0
0
0
0
0
2
0
0
1
2
2
1
0
0
0
0
3
1
0
0
0
2
0
0
1
0
0
2
2
1
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
3
3
0
0
1
0
2
0
0
1
0
1
0
1
0
2
3
2
0
2
0
0
0
1
0
1
0
3
2
1
2
0
1
0
0
2
0
0
0
0
1
0
0
1
0
0
0
2
6
2
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
3
1
0
1
1
0
0
2
0
0
0
2
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
2
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
1
2
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
1
0
0
0
0
2
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
1
0
1
0
0
0
2
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
1
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
2
1
0
0
1
0
0
0
0
8
0
0
0
0
0
0
0
0
1
2
0
0
0
1
1
0
0
2
2
0
2
0
2
0
0
1
0
0
0
1
0
2
1
0
0
0
1
1
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
2
0
2
1
0
2
0
2
0
2
1
4
2
0
4
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
1
1
0
0
2
1
1
0
0
0
0
0
0
1
0
2
1
0
0
2
1
0
1
0
0
0
2
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
2
0
0
0
0
0
2
2
2
0
0
0
0
0
0
1
3
0
0
0
1
0
1
0
1
2
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
5
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
1
0
4
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
1
0
1
0
0
0
2
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
1
3
0
0
0
0
0
0
2
0
0
0
0
2
0
1
2
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
2
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
3
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
1
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
1
0
0
0
2
0
0
0
0
1
0
0
1
0
2
0
0
0
0
1
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
5
0
0
0
2
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
1
2
2
2
1
0
0
0
0
0
0
0
1
1
2
1
1
1
0
0
0
1
2
0
0
0
0
2
0
0
2
1
0
0
0
1
0
0
2
0
4
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
1
2
0
2
1
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
1
0
0
0
0
1
1
0
1
1
0
0
2
2
1
0
2
0
0
1
0
0
0
0
0
0
1
3
0
2
0
0
0
2
0
0
0
3
0
0
0
1
1
0
3
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
2
0
2
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
2
0
1
0
0
2
2
0
1
0
0
2
2
2
0
0
0
0
1
1
0
1
0
0
2
0
0
0
1
1
1
0
0
1
0
0
0
0
2
0
2
0
1
0
0
1
0
0
2
0
2
0
0
3
0
0
0
1
0
1
0
0
1
1
0
0
2
0
0
0
0
0
2
0
0
2
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
1
2
0
4
0
0
0
0
1
0
0
0
3
0
0
0
0
0
1
2
0
0
0
0
0
1
0
1
0
0
0
2
0
0
1
1
2
0
0
0
0
0
0
1
0
2
0
2
0
0
1
0
0
0
1
1
0
1
0
0
1
0
4
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
2
4
0
0
1
2
3
1
0
0
2
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
2
2
1
0
1
0
2
0
2
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
4
3
1
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
1
1
1
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
1
1
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
2
0
1
0
0
2
0
0
0
0
3
0
0
0
0
2
0
1
0
0
3
1
0
0
0
1
1
0
0
0
3
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
2
0
1
0
0
0
0
0
1
0
0
0
0
1
3
2
1
0
2
0
3
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
3
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
1
0
1
0
0
2
0
0
0
0
0
0
0
2
2
0
1
2
2
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
2
0
1
0
1
0
0
0
0
0
0
0
2
2
2
0
2
2
2
0
2
1
1
0
0
0
2
1
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
2
0
2
0
4
0
1
0
4
0
1
2
1
2
2
4
0
1
0
0
2
0
0
0
0
0
0
4
0
2
0
2
0
0
0
0
2
2
0
0
1
2
0
3
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
1
1
0
1
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
1
2
2
0
2
0
0
0
2
0
0
2
0
1
0
0
2
1
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
2
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
2
2
0
2
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
3
1
0
1
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
1
1
0
0
1
0
0
1
0
3
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
1
0
0
3
0
1
1
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
2
1
0
1
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
6
0
0
0
0
0
0
0
0
0
0
2
2
2
0
1
0
1
0
0
1
2
2
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
2
0
9
2
0
1
0
0
0
1
0
4
0
0
1
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
4
0
0
1
2
1
1
0
0
0
0
0
1
0
1
0
2
0
0
0
0
1
0
0
1
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
2
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
1
0
0
0
0
2
0
0
2
1
0
1
2
0
0
1
1
1
1
0
0
0
0
3
1
0
0
0
0
0
0
2
2
0
0
0
2
2
1
1
2
1
0
0
0
0
1
0
0
0
0
2
0
2
0
1
0
0
0
2
0
0
0
0
2
0
2
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
1
0
1
0
2
0
1
1
0
0
0
0
0
1
2
0
1
0
0
0
2
0
0
0
2
0
1
0
1
0
2
1
2
0
0
0
0
0
0
2
0
2
1
0
1
0
0
0
1
0
1
2
2
0
0
2
0
0
0
0
0
1
2
4
0
0
0
0
0
0
2
0
1
1
0
2
0
1
0
1
0
0
0
0
2
0
0
0
3
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
1
2
2
0
2
2
2
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
3
1
0
0
1
0
0
0
1
1
0
0
0
0
2
2
0
1
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
2
1
3
0
0
2
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
2
1
0
0
0
2
0
2
0
0
0
0
0
1
0
0
4
0
0
1
1
1
1
0
0
0
0
0
0
2
1
0
0
0
1
1
0
2
4
0
0
0
0
1
2
2
0
1
0
0
1
0
0
0
2
0
1
0
0
0
1
2
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
2
2
1
0
2
0
4
0
0
0
2
0
2
0
0
0
2
1
0
0
2
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
1
2
0
2
0
2
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
5
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
1
1
1
3
2
0
0
0
1
2
0
1
0
0
0
0
0
2
0
1
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
3
2
1
1
1
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
11
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
1
0
0
0
0
2
0
2
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
3
1
2
3
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
2
2
0
3
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
1
3
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
3
1
0
0
0
0
0
4
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
1
1
0
2
0
0
1
0
0
2
2
1
1
2
0
2
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
2
0
0
0
0
2
2
1
0
1
1
2
2
0
0
7
2
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
1
0
0
0
1
1
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
2
2
1
2
1
0
0
0
1
2
0
1
0
0
1
0
0
2
1
1
0
0
0
0
0
1
1
1
0
1
2
0
0
0
2
0
2
0
3
0
0
2
0
0
1
0
0
2
0
0
1
2
0
2
0
0
2
1
2
0
0
2
0
2
0
2
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
1
2
0
0
0
0
1
0
3
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
2
1
1
0
1
2
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
2
1
0
0
1
0
0
1
0
0
1
1
1
0
0
0
2
2
0
1
0
3
1
0
0
0
0
3
0
1
0
0
3
1
1
0
1
0
3
2
0
2
2
0
0
0
0
0
0
0
0
1
0
0
1
0
2
1
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
1
0
0
0
1
0
2
0
0
1
3
0
1
0
2
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
5
0
0
0
2
2
0
0
1
1
0
0
2
0
2
0
0
0
0
0
0
2
0
1
1
1
0
0
0
0
0
0
0
1
2
1
0
0
2
1
3
1
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
4
2
0
0
0
0
1
0
4
0
0
0
1
0
0
0
2
0
0
2
0
2
0
2
2
0
2
0
0
1
0
2
0
1
0
1
2
1
0
0
1
2
0
1
0
0
1
0
0
0
0
1
0
0
0
2
0
1
1
2
0
2
0
0
0
2
0
1
0
0
0
0
2
0
0
1
0
0
2
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
1
2
0
0
0
2
0
2
0
0
2
1
0
0
0
0
2
3
2
0
0
0
0
0
0
2
0
2
0
2
0
0
3
1
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
2
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
2
1
0
0
0
2
0
0
0
1
0
2
0
2
0
1
0
3
0
1
1
0
0
2
2
2
1
2
0
1
0
1
0
2
1
0
0
0
6
0
1
1
2
0
2
0
0
0
1
2
0
0
0
1
0
0
0
0
1
2
0
0
0
1
3
0
0
4
0
0
0
0
0
2
0
2
0
2
0
2
0
0
0
3
0
1
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
4
5
1
1
2
0
1
1
0
0
2
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
1
2
1
0
1
0
0
0
0
2
2
0
0
0
0
0
0
2
0
1
1
2
1
0
0
0
0
2
2
2
1
0
2
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
1
0
1
1
0
0
0
1
0
1
0
1
1
0
0
0
2
1
1
0
0
2
1
0
0
0
2
1
0
1
2
0
2
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
2
0
0
0
0
3
2
0
0
0
0
0
0
1
0
0
0
0
0
0
3
1
2
1
0
0
0
0
0
1
1
0
2
0
0
0
0
1
1
0
1
1
0
2
0
0
0
0
4
2
0
1
1
0
0
1
0
1
0
0
2
0
1
0
1
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
1
1
0
0
5
0
0
0
1
1
2
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
2
2
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
1
1
2
1
0
0
0
0
0
2
0
0
3
2
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
3
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
2
2
2
9
0
0
0
0
0
2
0
0
0
0
2
0
1
1
0
4
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
2
1
1
0
0
3
0
0
0
0
1
2
0
2
1
0
0
1
2
0
1
1
3
0
1
1
0
0
0
0
0
2
2
1
0
0
2
1
1
0
0
1
0
0
0
0
0
0
2
1
0
0
0
2
2
0
0
0
2
1
0
0
1
0
1
0
0
0
0
1
0
1
1
2
2
3
2
0
0
0
0
0
2
2
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
3
0
1
0
0
1
0
0
0
0
0
0
1
2
0
0
1
1
0
0
2
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
2
0
0
1
1
0
2
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
8
0
0
0
1
0
0
1
1
0
0
2
3
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
4
2
0
0
2
0
0
0
1
1
0
0
0
0
1
0
2
0
3
0
0
1
0
0
1
2
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
2
0
2
0
0
4
0
0
2
0
2
2
0
1
2
0
0
0
0
0
0
0
1
0
3
1
0
2
0
2
1
0
1
0
0
0
9
1
0
0
0
0
2
0
0
0
0
0
2
2
2
0
0
0
0
2
2
0
2
0
0
1
3
0
3
0
0
0
0
0
0
0
0
2
2
0
0
0
2
2
0
0
0
3
2
0
0
1
2
5
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
3
1
0
0
1
0
0
0
0
0
2
2
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
1
2
0
2
2
0
0
0
2
0
0
2
0
0
2
1
1
0
0
0
0
0
2
0
0
0
1
1
0
0
0
2
0
2
0
0
0
1
3
0
1
0
2
0
1
1
0
0
0
0
1
1
0
0
3
0
0
0
0
0
2
1
0
0
1
0
1
0
1
0
0
1
0
0
1
0
1
0
0
0
2
0
0
2
0
0
0
1
0
0
0
1
0
1
1
0
0
1
2
0
0
1
0
0
0
0
1
0
3
0
0
4
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
1
7
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
2
0
0
0
0
2
0
0
0
1
0
1
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
2
4
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
1
0
0
1
0
0
1
0
3
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
2
2
0
1
0
0
0
2
0
0
0
1
0
1
0
0
4
1
1
0
1
2
0
0
0
1
0
3
0
0
0
3
4
0
0
1
2
1
0
0
2
0
0
0
0
1
0
1
0
2
0
1
0
0
2
2
2
0
1
0
0
0
0
3
1
0
0
1
0
0
3
0
0
0
1
0
0
0
0
1
2
1
2
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
1
2
7
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
3
0
0
0
1
0
0
0
0
0
0
2
1
0
0
2
1
2
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
4
0
0
0
2
1
0
2
1
0
0
0
0
1
2
0
1
0
0
0
0
2
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
2
0
1
0
2
0
0
0
0
1
1
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
1
0
0
0
2
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
3
0
0
0
2
2
0
0
2
1
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
2
0
0
0
0
0
1
2
0
1
0
2
2
1
1
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
1
1
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
1
2
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
3
1
1
0
2
0
0
0
1
1
0
0
0
0
0
2
1
0
1
0
2
0
2
1
0
0
2
0
0
2
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
1
0
0
0
0
0
0
0
2
0
0
0
0
3
0
1
2
0
0
0
0
0
2
0
2
3
0
2
0
0
0
0
0
0
0
1
0
2
0
1
0
2
0
2
1
1
0
0
0
1
0
0
1
0
2
0
0
2
1
1
0
1
0
0
1
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
3
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
1
1
2
0
0
0
0
0
4
2
0
0
0
1
2
0
0
0
0
0
2
0
0
2
0
1
2
1
0
0
0
0
0
2
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
1
1
4
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
1
2
0
0
0
0
2
0
0
0
0
2
1
0
0
3
0
0
0
0
1
0
0
1
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
2
0
0
0
2
0
0
6
0
0
0
0
2
0
0
0
0
0
0
0
0
5
2
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
2
2
0
0
1
1
0
0
0
2
0
1
0
4
1
2
0
1
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
2
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
2
0
1
1
0
0
1
2
0
1
0
0
0
1
0
0
0
2
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
4
2
0
1
3
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
1
0
0
1
0
0
0
2
0
2
2
0
1
0
0
3
1
0
0
2
0
0
0
0
0
0
1
2
0
1
1
1
0
0
0
2
0
0
0
2
0
1
2
0
0
4
0
0
0
0
0
0
1
2
0
2
2
0
0
2
0
1
0
0
2
2
0
0
2
0
0
0
2
0
0
0
0
1
0
1
0
2
2
1
0
1
0
0
3
0
0
0
0
0
2
0
0
0
2
0
3
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
7
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
2
2
0
0
0
2
0
1
0
2
0
2
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
1
0
2
0
0
0
0
0
0
0
2
1
2
0
0
0
1
1
4
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
2
0
4
0
0
0
0
6
1
0
0
2
2
0
0
0
0
0
2
2
0
0
0
0
0
3
0
0
2
1
0
0
0
2
2
0
1
0
1
0
1
0
2
0
2
1
0
0
0
0
0
1
0
3
1
0
1
2
0
0
1
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
8
1
0
1
2
0
0
2
0
0
0
1
0
2
1
1
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
1
0
0
2
1
1
0
2
2
0
0
6
1
1
0
0
0
0
0
2
0
1
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
1
0
0
1
2
1
0
1
1
2
0
2
0
0
1
0
1
0
0
0
1
0
0
0
0
0
6
0
0
1
0
0
1
0
1
0
0
2
0
0
2
0
0
2
2
0
2
0
0
9
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
2
0
2
0
1
0
2
2
2
2
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
7
3
2
0
2
0
2
0
0
0
2
0
0
0
0
0
3
0
2
0
0
0
0
0
1
0
0
4
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
2
0
1
0
1
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
2
0
0
0
2
2
1
0
1
0
1
0
1
3
0
0
0
0
1
0
0
0
0
2
2
0
2
2
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
1
0
0
2
0
1
0
2
0
0
0
0
2
0
1
0
0
2
2
0
2
0
0
0
1
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
2
2
0
0
0
2
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
1
1
0
0
2
0
1
0
0
2
0
0
1
2
3
1
0
0
0
0
2
0
2
0
0
0
0
0
1
2
0
0
0
0
0
2
2
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
2
2
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
1
1
0
0
0
0
0
0
0
0
3
1
2
0
0
2
0
1
0
1
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
1
0
2
3
2
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
3
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
1
0
1
0
0
1
0
1
0
0
1
1
0
1
0
1
0
0
1
0
0
0
0
1
1
0
2
0
0
0
1
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
4
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
1
2
2
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
2
0
0
2
2
0
3
0
0
0
0
0
2
0
2
0
0
2
2
0
0
0
0
1
1
2
1
2
0
1
2
0
0
0
0
0
2
0
0
1
0
2
1
1
0
0
0
0
0
0
0
1
8
0
0
0
0
2
0
1
0
2
2
0
0
0
0
0
1
0
0
1
1
2
0
0
1
0
0
2
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
1
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
2
0
1
2
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
3
0
2
1
0
2
0
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
3
0
1
0
0
0
0
0
2
0
0
2
0
0
2
0
0
2
0
0
0
9
5
1
0
0
0
0
0
2
0
0
0
0
0
2
0
3
2
0
0
2
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
2
0
0
2
2
0
2
2
0
1
0
0
0
0
0
2
0
0
0
2
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
1
0
0
2
0
0
0
1
2
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
2
2
0
0
0
0
0
1
0
0
4
1
0
0
2
1
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
1
2
0
1
0
0
0
0
3
0
2
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
3
2
1
0
3
0
0
0
0
2
0
0
0
1
3
0
3
0
0
0
2
0
0
0
2
0
3
1
2
0
0
1
0
0
0
2
0
0
0
0
2
1
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
4
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
2
0
0
0
2
0
0
0
0
0
0
2
1
2
0
0
2
0
0
2
0
0
2
0
1
1
0
0
1
0
1
0
0
0
0
0
2
0
2
0
2
0
1
2
2
1
0
0
0
0
2
0
2
2
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
1
0
1
0
2
0
0
2
2
0
2
0
3
0
1
0
0
0
0
1
2
0
0
0
0
0
2
1
0
0
0
4
1
0
1
0
0
0
0
1
2
0
4
0
1
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
2
0
0
0
2
1
1
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
1
0
0
2
1
2
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
2
3
0
0
0
0
1
0
1
2
0
1
0
0
0
2
1
0
1
0
0
0
0
3
0
0
2
0
2
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
1
0
2
2
0
0
0
1
0
0
5
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
1
2
1
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
1
0
1
0
1
0
6
1
0
1
0
1
2
0
0
0
0
0
1
2
2
0
1
0
2
2
1
1
0
1
0
0
0
0
4
0
4
0
2
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
1
2
0
3
0
1
0
0
0
0
0
1
2
1
0
5
2
1
1
0
0
1
0
1
0
0
0
2
0
1
0
1
1
0
1
0
0
0
0
0
1
1
3
0
0
0
0
1
3
0
0
0
2
0
0
0
1
0
0
2
2
2
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
1
2
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
1
0
2
0
0
3
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
1
0
0
0
0
0
2
0
2
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
2
1
0
2
0
0
1
0
0
0
0
2
0
0
0
0
2
0
2
1
4
3
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
2
0
2
0
1
0
0
0
2
2
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
1
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
2
1
0
1
0
0
0
0
0
0
0
0
2
2
1
0
0
4
0
0
0
0
0
0
0
0
0
0
2
2
1
1
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
1
2
0
0
0
2
2
0
0
0
0
0
0
0
2
1
0
2
1
0
0
0
0
0
1
0
1
1
0
0
0
2
0
2
0
0
0
0
0
0
2
2
3
0
0
1
1
2
0
0
0
2
1
2
1
2
2
0
2
2
0
0
0
0
0
0
2
0
0
0
1
1
0
2
0
0
0
2
0
2
0
8
0
2
0
0
1
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
1
0
0
2
0
0
2
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
2
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
1
0
2
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
1
2
0
2
0
2
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
2
1
2
0
0
0
2
0
0
0
2
0
0
3
4
2
1
0
2
1
3
1
0
2
0
1
0
9
0
0
0
0
0
4
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
2
1
1
0
1
1
1
0
2
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
3
0
0
2
0
0
0
0
0
1
2
0
0
2
0
0
0
2
0
1
0
0
0
0
2
1
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
1
0
0
1
0
1
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
2
0
2
0
0
1
2
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
1
0
2
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
2
1
0
1
0
2
0
0
0
0
0
0
2
1
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
2
2
0
0
0
0
0
2
2
0
2
0
0
0
2
0
2
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
3
2
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
1
2
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
7
0
0
0
0
0
0
0
0
1
3
0
0
1
0
0
0
4
2
2
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
1
0
0
0
0
0
2
1
2
0
0
0
1
1
0
0
0
0
0
1
0
2
1
2
0
3
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
2
2
2
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
1
1
3
0
2
1
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
1
0
3
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
3
0
0
0
2
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
1
0
0
2
1
2
2
2
0
2
1
0
1
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
3
0
0
1
0
2
0
0
1
2
0
1
0
2
0
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
3
0
0
3
2
3
0
2
0
0
0
0
0
1
0
0
1
3
0
1
0
0
0
0
0
2
0
1
0
0
0
1
0
1
0
0
2
0
0
1
2
0
0
0
1
1
4
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
2
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
2
2
0
0
2
0
1
1
0
1
2
0
0
0
2
0
2
1
0
0
2
0
0
0
0
0
4
0
0
0
0
0
0
1
2
0
0
1
2
0
0
0
0
0
1
0
0
1
0
3
1
0
1
0
0
0
0
2
0
0
0
0
0
0
2
2
2
0
2
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
2
1
2
0
0
0
0
1
2
2
0
0
3
0
0
1
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
2
0
0
1
2
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
2
0
2
0
0
0
3
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
2
0
0
1
2
0
0
0
2
0
3
0
0
1
1
0
0
0
0
0
0
0
2
0
1
1
1
0
0
0
0
2
0
0
3
0
0
2
0
2
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
1
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
2
1
0
0
2
0
0
0
0
1
2
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
2
0
2
0
0
1
2
2
0
0
0
0
1
0
2
2
1
0
1
1
2
1
0
0
0
3
0
1
0
0
1
1
0
2
0
0
0
0
0
1
1
2
0
3
0
0
2
1
0
0
0
0
0
2
1
0
3
0
0
2
0
0
0
2
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
1
1
0
1
0
1
1
1
1
0
0
2
0
3
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
1
0
0
1
8
0
0
1
2
0
1
0
1
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
2
2
0
2
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
1
2
1
0
2
0
0
0
0
1
2
2
0
2
0
0
0
2
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
2
1
0
2
0
2
0
0
0
0
2
0
1
0
1
0
0
2
1
0
1
0
1
0
2
0
1
4
0
0
1
1
1
2
0
0
0
2
0
0
2
0
0
1
1
0
0
2
0
0
0
0
2
1
0
2
2
0
2
0
0
2
1
0
0
0
0
0
0
0
2
0
0
2
1
0
1
2
0
1
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
1
1
0
0
0
2
0
0
0
1
0
0
1
0
0
2
0
0
1
0
2
1
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
2
0
1
0
1
0
2
0
3
0
0
0
0
3
1
3
2
0
0
0
0
2
2
0
0
0
0
2
1
2
0
0
0
2
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
2
0
3
1
0
0
0
0
0
2
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
2
1
0
0
0
1
0
0
3
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
1
1
0
0
1
2
1
0
0
0
0
0
0
0
2
0
0
2
0
1
4
3
0
2
2
0
1
0
0
1
0
0
2
3
0
0
2
0
1
2
0
1
0
2
0
1
0
2
0
0
5
2
0
1
0
2
0
0
5
2
0
1
0
0
0
1
0
0
0
0
0
0
1
0
2
1
4
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
2
2
0
2
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
2
0
0
1
2
0
0
0
0
2
1
1
0
2
4
0
0
0
2
0
0
2
0
0
0
4
0
1
2
0
0
2
2
1
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
1
0
0
0
0
0
0
6
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
1
2
0
0
1
0
1
1
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
3
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
1
0
0
0
2
0
2
0
0
7
0
0
0
2
0
2
0
0
1
2
1
2
0
0
0
2
0
0
4
2
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
2
0
2
0
0
0
0
0
0
1
2
0
1
2
0
1
2
0
0
2
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
1
1
0
0
0
0
3
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
2
0
0
1
1
0
0
0
0
1
2
0
0
0
0
0
2
0
2
0
0
1
0
0
0
4
1
0
1
0
2
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
2
2
1
0
1
0
0
0
0
0
2
0
0
0
2
1
0
0
2
0
0
1
0
1
0
0
2
0
0
1
0
2
1
0
1
2
0
2
1
0
0
1
2
0
0
1
0
0
1
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
2
0
3
0
0
0
0
0
1
2
0
0
1
0
0
0
0
1
0
0
0
1
0
0
3
0
2
0
0
0
2
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
2
3
0
0
0
1
1
2
0
1
0
0
0
1
0
0
1
2
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
2
0
1
0
0
0
0
1
0
1
0
2
1
1
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
3
1
0
1
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
5
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
1
0
1
0
2
0
0
2
0
2
0
0
0
2
0
0
1
1
0
2
1
1
3
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
2
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
1
0
3
0
0
1
0
0
1
0
3
1
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
1
2
0
1
0
1
3
0
2
0
0
0
0
2
0
2
0
1
0
0
1
0
1
0
0
0
2
0
0
0
1
0
2
0
1
1
0
0
5
0
3
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
3
0
1
0
1
0
0
0
2
4
0
2
0
1
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
1
0
2
0
2
2
0
0
2
1
8
0
1
0
0
1
0
0
2
0
0
0
0
0
1
0
2
0
0
2
2
0
1
1
0
0
0
0
2
4
3
2
1
2
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
2
0
2
2
0
0
0
0
1
0
0
2
1
0
1
0
0
0
0
0
0
1
0
0
1
0
2
0
0
1
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
2
0
0
1
4
1
3
0
0
0
2
2
0
0
0
2
2
0
2
0
1
1
0
2
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
3
0
0
0
5
0
0
2
2
3
0
0
1
0
1
0
1
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
1
2
0
0
1
0
0
0
1
2
0
0
1
1
1
0
0
1
0
0
2
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
2
1
0
3
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
1
0
2
3
2
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
1
1
2
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
1
0
0
0
2
3
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
1
0
0
2
2
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
2
0
2
0
1
0
0
0
0
1
0
0
2
1
2
1
0
0
0
0
0
0
0
0
0
0
0
2
3
2
0
0
1
2
1
0
1
0
0
0
1
0
1
1
2
0
2
0
0
0
0
1
1
2
0
0
0
0
1
1
1
0
0
2
0
2
0
0
2
1
0
0
0
2
2
2
1
0
0
0
0
0
2
0
2
0
0
0
1
2
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
1
0
8
2
2
1
0
1
0
2
0
1
0
0
2
0
1
0
0
1
0
0
2
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
1
0
2
1
0
0
0
0
1
0
0
2
1
0
0
0
1
0
1
0
2
2
0
2
0
0
0
0
2
1
0
0
0
0
2
0
0
0
1
0
2
0
0
1
0
0
1
0
0
1
0
0
1
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
3
0
0
0
0
0
3
2
1
0
1
0
1
2
0
2
0
2
0
0
0
0
0
0
0
0
0
2
2
2
0
2
0
0
1
2
0
0
0
2
0
0
1
0
1
0
0
0
0
2
0
0
0
2
0
1
0
0
2
0
1
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
1
0
1
0
0
0
2
0
0
3
0
2
1
0
0
0
0
0
2
3
0
1
0
0
1
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
1
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
2
0
0
0
0
0
0
0
1
0
1
0
1
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
1
0
0
0
1
0
2
3
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
1
0
0
0
0
6
6
0
0
0
0
0
0
2
0
0
2
1
0
0
0
1
0
1
0
1
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
1
0
2
0
1
1
0
3
2
0
1
2
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
1
0
0
0
0
0
2
2
0
0
0
2
1
0
2
2
0
1
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
2
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
2
1
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
3
1
0
0
0
2
0
0
0
0
1
0
0
2
1
2
0
5
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
4
1
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
1
3
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
1
0
0
0
1
0
1
0
0
0
0
1
2
0
0
1
0
0
0
0
0
2
0
2
0
0
2
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
1
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
3
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
1
2
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
2
0
2
0
1
0
0
0
0
2
0
0
1
0
0
2
0
0
2
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
2
1
2
0
1
1
0
0
1
0
0
0
0
3
0
1
0
2
0
0
2
0
0
1
0
0
0
0
1
2
2
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
1
1
2
0
0
0
0
0
0
2
2
0
0
1
1
2
0
0
0
0
1
0
0
0
3
0
0
0
3
0
0
1
1
0
2
2
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
1
1
0
4
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
3
0
1
0
2
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
2
3
1
0
0
2
1
0
1
0
0
1
0
2
1
1
1
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
1
0
2
2
0
0
0
0
2
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
1
0
0
1
0
0
0
1
1
0
6
0
1
0
0
1
0
0
0
0
0
1
2
0
0
2
0
0
0
0
1
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
4
0
0
0
0
2
0
0
0
0
2
0
3
0
1
0
1
0
1
1
1
0
1
0
0
0
0
0
2
0
0
0
1
0
1
2
0
1
0
1
2
0
0
0
1
1
0
0
3
0
0
1
3
0
2
1
0
0
0
0
1
1
1
0
1
2
2
0
0
0
0
0
2
0
1
0
2
2
0
0
2
1
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
2
0
1
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
2
0
0
1
2
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
2
0
0
2
0
0
1
1
0
1
0
0
0
0
2
2
0
2
0
0
2
0
0
0
1
0
0
0
0
3
0
1
1
0
2
0
0
3
0
0
3
2
0
2
0
0
2
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
3
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
2
0
1
0
0
0
0
2
0
0
2
1
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
1
0
2
0
2
0
1
0
0
0
0
1
0
2
2
3
0
2
0
0
0
0
0
0
0
0
1
0
2
3
2
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
1
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
1
1
1
1
0
1
0
2
1
0
0
1
0
0
1
0
4
2
3
0
2
0
0
0
1
1
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
2
0
0
0
2
0
1
2
2
2
0
0
2
1
2
0
0
0
1
0
2
0
0
1
0
0
0
2
0
0
1
2
0
0
0
0
0
0
2
2
2
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
1
1
1
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
2
1
1
2
2
0
2
0
0
4
0
0
2
0
2
0
0
2
2
0
0
1
2
1
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
2
0
0
2
0
0
0
0
1
0
0
0
1
1
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
2
0
1
2
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
2
0
1
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
2
0
2
1
1
0
2
0
1
0
2
0
0
0
0
0
0
0
0
3
1
1
0
1
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
3
1
0
1
0
2
2
0
2
0
1
2
0
2
2
1
1
2
0
0
1
0
0
1
1
2
0
0
2
2
2
0
0
2
2
0
0
3
0
0
2
0
0
0
0
0
0
0
2
0
1
1
1
0
0
0
1
0
0
0
0
0
0
2
1
1
0
0
0
3
0
0
0
0
2
1
0
1
1
1
0
0
0
0
1
0
0
1
2
0
0
0
0
0
2
2
0
0
2
0
2
1
2
1
0
0
0
3
0
1
0
1
0
0
0
0
0
1
2
0
0
2
1
1
0
0
0
0
0
0
2
0
0
0
1
0
1
0
2
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
2
2
1
0
0
1
0
0
1
0
0
2
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
1
1
0
0
1
0
0
2
0
2
2
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
1
1
0
0
0
2
0
0
5
1
0
0
0
1
0
0
0
1
1
0
2
1
1
0
1
0
0
0
0
1
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
2
1
2
0
0
0
0
0
0
0
0
1
2
0
0
1
2
2
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
4
1
0
0
0
1
2
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
2
2
0
2
1
0
0
5
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
1
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
1
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
3
1
0
0
0
0
0
0
0
2
1
2
0
0
0
2
1
1
3
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
3
0
0
0
1
1
2
0
0
0
0
0
0
2
0
0
2
2
1
0
1
0
1
0
2
0
2
0
2
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
2
0
2
2
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
3
0
0
1
0
1
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
2
0
0
0
1
0
2
2
3
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
2
1
1
0
0
2
3
2
0
0
0
0
0
1
0
0
0
1
2
1
1
2
0
1
2
0
0
0
0
0
2
1
0
0
0
0
3
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
2
2
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
1
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
4
1
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
2
2
0
0
3
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
1
0
0
0
1
2
0
0
2
0
0
5
0
2
0
2
0
6
2
0
3
0
0
0
0
1
0
0
0
0
2
0
2
3
0
0
0
0
1
1
0
0
0
0
1
1
0
4
1
0
2
1
0
0
0
2
2
0
1
1
1
0
0
1
2
0
0
1
0
1
3
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
1
1
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
2
0
1
0
0
0
0
1
0
2
0
0
0
2
0
0
0
2
0
2
0
0
1
0
2
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
4
0
2
2
0
0
0
2
0
0
0
0
1
1
0
0
0
0
2
3
0
0
0
0
0
1
0
0
0
0
2
0
0
3
0
3
0
1
0
1
0
0
3
0
1
1
0
0
0
2
1
0
0
0
2
0
2
0
0
2
1
0
0
2
0
0
2
2
0
0
1
0
2
0
0
2
0
0
0
2
1
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
2
0
0
0
0
3
0
0
0
1
2
0
0
0
1
0
0
1
0
1
2
0
1
0
0
0
0
0
0
2
0
0
2
0
0
2
1
0
0
0
0
1
0
0
1
0
2
1
0
0
1
2
0
0
0
3
1
1
0
1
0
0
2
1
0
0
0
3
2
0
0
2
0
1
2
2
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
3
0
0
1
0
0
1
0
5
2
0
1
1
2
0
2
1
0
0
0
0
0
0
0
0
0
2
2
1
5
0
0
2
0
2
0
0
1
0
0
1
2
2
1
0
0
0
1
0
0
2
1
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
1
0
1
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
3
1
0
0
0
3
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
2
0
0
0
0
2
2
2
0
0
0
0
1
0
0
0
0
0
0
1
2
2
1
0
1
0
0
2
3
1
1
0
0
0
2
1
0
0
1
0
0
1
3
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
2
0
1
0
0
0
2
0
0
2
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
1
1
0
2
0
2
0
1
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
2
0
0
0
0
3
0
2
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
3
1
1
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
1
2
0
0
0
0
2
2
1
0
1
1
0
0
0
0
2
0
0
1
0
0
3
1
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
2
0
0
2
0
0
0
2
2
0
0
0
2
2
0
0
0
0
2
0
2
1
0
1
2
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
2
4
0
2
1
0
0
1
2
0
0
2
0
1
0
0
0
0
0
0
1
1
1
0
2
0
1
0
0
0
1
1
2
0
0
0
0
3
0
0
0
0
2
1
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
2
2
0
2
0
0
0
0
1
0
1
1
1
0
0
0
2
0
0
0
1
0
1
2
0
2
0
0
0
1
2
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
2
1
0
1
3
0
3
0
0
2
0
0
0
2
0
1
2
2
2
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
2
2
0
0
0
1
0
1
0
0
1
0
2
0
0
1
2
0
1
2
0
0
0
0
0
2
0
2
1
0
0
0
1
5
0
1
2
0
0
0
0
0
0
0
1
0
0
2
2
2
0
0
0
0
2
0
1
0
2
0
1
0
2
1
0
0
2
0
0
1
0
0
2
0
1
0
0
0
0
2
0
1
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
1
0
0
0
0
5
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
3
0
1
0
2
0
2
2
0
0
1
0
2
0
0
0
1
0
1
1
0
0
2
0
0
2
0
2
1
3
1
2
0
2
0
4
0
0
2
3
0
0
0
0
2
0
0
1
3
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
2
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
2
1
0
0
0
0
1
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
2
1
1
2
2
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
2
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
6
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
3
1
1
0
0
0
0
0
0
1
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
1
2
0
0
0
0
0
0
0
0
2
0
1
2
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
2
0
1
0
2
0
0
0
1
0
0
1
0
0
2
2
0
0
1
0
0
4
0
0
0
1
0
0
2
2
0
0
0
3
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
1
3
1
2
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
2
0
2
0
1
0
0
0
0
1
2
0
0
0
3
1
2
0
0
1
2
1
0
0
1
1
1
1
0
0
0
0
0
2
0
1
0
0
0
1
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
5
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
1
0
0
0
2
0
0
0
0
0
2
1
2
2
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
1
0
0
0
2
0
2
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
1
2
0
0
2
4
0
0
0
0
2
0
1
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
2
0
0
0
0
0
0
1
1
1
2
3
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
2
0
0
2
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
1
5
1
1
0
0
0
1
1
0
1
2
0
2
0
0
2
0
0
1
0
0
2
0
0
2
0
0
2
0
1
1
0
1
1
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
2
0
2
0
0
2
1
0
0
1
0
1
0
0
0
2
0
0
0
0
2
0
0
3
0
2
3
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
2
0
1
0
1
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
1
0
2
0
2
1
0
0
1
1
2
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
3
1
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
2
0
2
0
1
0
0
0
0
0
0
1
3
0
2
0
0
2
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
1
2
0
2
0
1
0
0
0
0
3
1
1
2
0
0
0
0
2
0
0
0
2
0
2
0
0
2
0
0
2
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
2
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
1
0
0
0
0
1
0
2
1
2
0
0
1
0
0
1
0
0
1
1
0
0
2
1
0
0
0
0
0
0
2
0
3
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
2
0
2
1
0
2
1
1
0
0
0
0
2
2
0
1
0
1
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
1
0
0
2
1
0
0
0
1
0
1
0
2
0
1
0
0
0
2
0
0
0
0
0
0
1
2
2
1
0
0
0
0
0
1
0
0
0
0
1
1
0
2
0
0
1
1
2
0
0
0
2
0
0
0
0
0
2
0
1
0
2
0
2
0
1
0
0
2
0
0
0
0
0
1
1
2
0
2
1
0
6
0
1
0
0
1
1
0
2
0
0
1
0
1
2
2
0
2
0
0
0
0
0
0
0
3
0
2
0
0
0
0
1
1
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
3
0
0
2
0
0
0
0
1
0
1
0
0
0
2
2
1
2
1
0
1
0
0
0
0
0
1
0
0
2
0
2
2
0
0
2
0
1
1
0
0
0
2
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
5
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
1
1
0
2
2
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
2
0
2
0
2
0
0
0
2
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
1
0
1
1
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
3
1
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
2
0
0
3
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
2
0
0
2
2
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
2
0
1
0
1
0
0
1
1
0
0
0
0
0
1
2
2
1
1
0
1
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
1
0
0
2
0
0
0
2
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
6
2
2
0
2
0
0
0
2
0
0
2
1
1
0
0
0
0
0
0
0
3
0
1
0
0
2
0
0
0
0
0
0
1
0
0
3
0
0
1
0
0
2
2
1
1
0
0
2
1
1
0
0
0
0
0
1
2
0
0
2
1
0
0
1
2
0
0
1
0
0
0
0
0
2
1
0
1
0
0
0
1
0
0
0
0
1
0
1
2
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
2
2
1
1
0
0
1
0
2
1
1
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
2
0
0
0
0
3
2
0
0
1
0
4
0
0
1
2
0
1
0
0
0
1
2
1
0
0
0
0
2
0
0
0
0
1
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
2
0
0
2
0
3
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
2
0
2
2
1
0
0
0
0
1
0
0
5
1
0
0
2
0
0
0
0
0
0
0
1
0
1
2
0
0
2
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
1
2
0
1
1
1
0
2
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
1
1
0
2
2
0
0
4
1
0
0
2
0
0
0
2
2
3
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
1
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
2
2
0
2
1
0
1
0
0
1
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
2
0
0
1
0
1
0
3
0
0
0
0
0
1
0
0
2
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
2
2
1
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
1
0
0
0
0
3
0
3
0
1
0
0
2
2
0
1
0
0
0
2
0
2
3
0
0
2
0
1
1
0
0
0
0
0
0
1
0
0
1
2
0
0
2
0
2
0
0
0
0
2
2
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
2
0
2
1
1
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
2
1
1
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
2
2
2
0
0
0
0
0
2
0
2
1
3
0
2
0
0
0
0
0
0
1
0
0
1
2
0
0
0
1
2
0
0
1
0
0
0
2
0
0
0
0
2
0
5
0
0
0
0
1
1
0
0
0
1
0
0
0
1
2
4
2
1
0
2
0
0
0
2
0
0
0
3
2
0
0
0
3
0
3
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
4
0
2
0
2
1
0
0
0
2
0
2
2
2
0
0
0
2
2
1
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
1
3
0
0
2
0
2
5
0
2
0
0
0
0
1
0
0
0
1
0
1
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
3
0
0
0
0
1
1
0
1
1
0
0
1
0
0
0
0
0
0
0
2
4
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
1
0
1
0
0
0
2
0
0
0
1
2
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
2
0
2
0
1
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
2
0
1
0
0
1
0
1
2
0
2
2
0
1
0
1
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
2
2
1
0
0
0
1
0
0
0
0
2
2
0
2
0
0
0
2
0
0
2
0
0
2
1
0
2
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
3
1
2
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
2
0
1
1
0
1
0
0
0
0
0
0
0
0
3
3
0
0
0
1
0
2
2
0
0
0
1
0
1
2
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
2
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
2
1
2
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
5
2
0
0
0
0
2
2
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
3
0
0
0
1
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
1
0
0
1
0
0
2
0
0
0
2
0
1
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
4
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
2
2
0
4
2
0
0
0
0
0
0
2
0
3
0
0
0
1
5
0
3
2
3
2
2
0
0
4
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
1
0
2
0
0
0
0
2
8
0
1
0
1
0
0
0
0
0
1
2
1
0
5
1
1
2
0
0
0
0
0
0
1
2
3
0
3
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
2
0
0
1
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
1
1
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
1
0
0
0
2
1
0
0
2
1
0
0
2
2
0
0
0
4
4
0
1
0
0
0
0
3
0
1
1
1
0
2
0
1
1
1
1
1
0
0
0
0
0
0
0
4
0
1
0
0
0
2
0
0
0
1
1
0
0
0
1
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
1
0
1
0
0
0
1
0
0
0
0
1
0
1
0
1
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
1
2
0
0
5
1
1
2
0
1
1
1
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
2
1
0
0
2
0
1
0
0
0
0
0
5
0
5
0
1
1
0
0
1
2
2
2
1
0
0
0
0
1
0
2
0
0
0
0
0
0
2
1
1
0
2
0
0
0
1
0
0
2
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
4
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
3
1
1
1
0
1
0
0
0
0
2
0
2
1
0
0
0
1
0
4
2
0
0
2
0
0
2
0
0
2
2
0
0
0
2
0
0
1
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
1
1
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
1
2
0
3
0
1
0
0
1
1
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
3
0
0
0
1
0
1
0
0
0
0
1
0
2
1
1
0
0
0
3
0
3
1
1
0
0
0
0
2
0
1
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
1
5
0
0
1
0
0
2
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
3
2
0
1
2
0
2
0
0
0
0
0
2
2
2
1
0
1
0
0
2
2
2
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
2
2
1
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
1
0
1
0
1
1
0
0
0
0
1
2
0
0
0
1
0
0
0
0
2
2
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
2
2
0
0
1
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
2
2
2
1
0
1
0
2
1
2
1
0
2
0
1
1
0
2
1
0
0
0
0
0
0
0
0
0
1
1
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
2
0
0
0
1
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
1
1
2
2
1
0
1
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
2
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
3
0
1
1
2
0
0
0
1
2
0
0
2
2
1
1
0
0
1
4
2
0
2
2
0
1
0
2
0
1
1
0
1
0
3
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
2
1
0
1
0
2
0
0
2
1
1
0
0
0
3
2
0
1
0
0
1
0
2
0
2
0
0
0
2
0
2
0
1
0
1
0
0
0
0
2
0
0
2
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
3
0
2
2
2
0
0
0
0
1
2
2
0
0
0
0
1
0
1
0
0
1
0
2
0
0
0
0
1
3
0
0
0
2
1
3
1
0
0
0
0
2
0
0
1
2
0
0
0
0
2
0
0
0
0
7
3
1
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
1
1
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
3
0
1
0
2
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
3
0
1
0
0
0
2
0
2
1
3
0
3
0
2
0
0
1
0
2
0
0
0
0
0
0
1
0
2
3
2
0
0
0
2
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
1
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
2
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
1
0
1
0
1
0
0
0
1
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
2
0
2
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
1
1
0
0
1
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
3
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
2
0
0
1
1
0
2
1
0
1
2
2
0
0
0
3
0
1
0
0
0
3
0
1
0
2
0
0
1
4
0
2
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
1
3
1
0
0
0
0
0
0
1
0
2
1
4
0
0
1
2
0
1
2
0
0
1
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
4
2
0
0
0
1
2
0
2
0
0
1
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
2
2
0
0
0
2
1
0
0
7
0
0
1
0
0
1
2
2
0
1
3
0
2
0
0
1
2
0
0
0
0
2
2
0
0
0
0
0
0
0
1
1
0
0
0
0
1
2
0
1
0
0
2
2
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
2
1
1
0
0
2
0
2
1
0
0
0
1
0
0
1
1
1
1
0
0
1
0
0
0
2
0
0
0
1
1
0
0
2
1
2
0
0
0
1
2
1
0
0
0
0
1
3
0
0
0
0
3
0
0
2
1
0
0
2
0
0
1
1
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
1
2
0
0
0
2
1
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
2
1
2
0
1
0
2
2
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
2
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
1
0
0
0
1
4
0
0
1
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
3
2
0
0
2
0
0
0
2
0
1
0
0
0
0
0
13
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
3
0
0
0
1
0
0
0
0
0
2
1
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
2
0
0
1
1
2
3
1
0
2
1
0
1
0
0
0
0
0
0
0
1
1
0
2
1
1
0
0
0
0
0
0
1
1
2
1
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
2
1
0
2
0
0
0
2
3
3
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
2
0
1
0
0
1
0
4
0
1
1
0
2
0
0
0
0
0
2
3
0
0
0
1
0
0
1
0
0
0
1
1
0
1
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
4
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
1
0
0
0
0
2
1
0
0
2
1
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
2
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
2
0
0
1
1
0
0
1
0
1
0
1
2
0
2
2
0
0
2
1
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
3
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
1
0
0
1
0
1
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
1
1
0
0
0
0
2
0
0
2
0
1
0
2
0
2
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
1
0
0
0
0
0
3
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
5
0
1
0
0
1
0
2
0
0
0
0
1
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
1
2
0
1
0
1
0
0
0
0
1
2
1
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
3
0
0
1
1
0
0
2
1
0
0
0
0
0
0
0
2
0
2
1
0
1
0
0
0
1
3
0
1
2
2
3
0
2
0
2
0
0
0
2
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
2
1
0
0
0
1
0
0
0
1
1
0
2
0
0
0
2
3
0
0
0
5
2
1
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
1
0
1
0
0
2
0
0
0
0
0
3
0
0
0
2
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
4
0
2
1
1
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
2
0
0
0
2
1
0
0
0
0
1
1
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
2
1
0
0
1
0
1
1
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
2
0
1
2
0
0
1
0
0
0
0
0
0
0
2
0
2
0
1
0
0
2
2
1
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
1
0
2
1
0
1
0
2
0
2
0
2
1
0
0
0
0
0
2
0
0
1
0
0
2
1
2
0
0
0
0
1
0
1
1
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
2
0
0
0
1
2
1
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
2
2
1
2
0
2
0
0
1
0
0
0
1
0
0
0
0
4
3
2
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
6
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
3
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
1
2
0
2
0
1
0
0
0
0
5
1
0
0
0
0
0
0
0
0
2
0
1
0
2
0
2
1
1
0
0
0
0
2
0
0
0
0
2
0
2
1
0
2
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
2
4
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
1
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
2
1
0
1
0
0
8
0
0
0
0
0
1
2
0
1
0
0
2
0
0
0
1
0
0
0
2
7
0
2
0
2
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
7
0
0
0
2
0
0
2
0
0
0
1
0
2
2
2
2
1
4
2
0
0
0
0
0
3
0
1
2
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
1
0
0
1
0
0
0
0
0
0
3
0
0
0
0
2
2
0
0
0
1
0
0
1
0
0
2
2
2
2
0
0
2
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
6
0
1
0
0
0
2
2
2
0
0
0
0
0
1
1
0
0
0
0
2
0
2
0
1
0
0
2
0
1
0
2
0
0
2
0
4
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
9
0
0
0
0
3
1
0
0
0
0
2
0
0
1
0
0
0
0
1
1
0
0
0
2
1
2
1
2
1
1
0
0
0
1
0
0
0
2
5
0
0
0
0
1
0
0
2
1
0
0
2
0
0
0
0
2
1
0
1
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
4
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
2
0
2
2
0
0
2
0
0
0
1
0
0
5
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
1
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
2
1
2
0
3
0
0
0
0
0
0
0
1
0
2
0
0
1
2
3
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
1
1
2
0
0
0
1
0
0
0
1
2
0
0
0
1
0
3
0
0
0
0
1
1
4
0
0
0
0
2
4
2
0
2
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
2
1
1
3
2
0
0
0
1
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
1
0
0
1
2
0
0
1
2
0
3
0
0
0
0
1
2
1
0
2
1
2
2
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
2
0
0
0
1
2
2
0
2
0
2
0
0
0
1
1
0
0
0
2
0
0
0
0
0
2
0
2
5
0
2
1
1
0
0
0
0
0
0
1
2
2
0
0
1
0
1
0
0
0
0
5
2
0
0
3
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
2
0
0
0
3
0
0
2
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
1
2
0
0
0
0
3
0
2
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
1
1
0
0
0
2
0
1
0
0
1
2
0
2
2
0
2
2
1
1
0
0
0
0
0
1
1
1
0
0
2
0
2
0
1
0
0
0
2
0
0
3
2
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
2
5
1
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
2
1
0
2
2
2
2
0
1
0
2
0
0
2
0
2
0
1
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
1
0
2
0
0
1
0
0
1
1
2
0
2
1
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
2
0
2
0
0
0
1
1
0
0
0
0
1
7
0
0
1
0
0
4
0
1
2
1
0
0
0
2
0
0
0
1
0
0
0
2
2
0
0
0
2
0
2
0
0
0
0
0
0
1
1
2
0
0
1
2
2
0
2
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
3
0
0
1
0
2
0
3
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
3
1
0
0
0
1
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
2
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
5
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
1
0
1
0
0
0
2
0
1
0
0
0
0
1
1
0
1
0
0
0
0
1
2
0
0
3
2
2
0
1
0
0
1
0
0
0
0
0
0
0
2
1
1
1
0
0
1
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
2
0
1
1
4
2
0
0
2
0
2
0
0
2
0
0
0
0
1
0
0
0
0
2
1
0
1
2
0
1
1
1
0
0
0
2
0
0
1
1
0
0
2
0
0
0
0
1
2
0
0
0
0
2
0
0
2
1
0
0
1
0
0
2
0
0
0
2
1
0
0
1
1
2
2
0
1
0
0
2
1
0
2
0
0
4
1
3
0
0
0
0
0
0
0
2
1
0
2
0
1
0
0
0
1
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
2
2
0
0
0
1
0
1
0
0
0
0
0
0
3
0
0
0
0
0
1
1
2
0
1
0
0
0
0
1
0
1
0
0
0
0
2
5
2
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
2
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
1
1
2
0
1
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
2
1
1
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
3
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
2
0
2
0
2
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
2
1
0
0
0
0
0
1
0
0
0
1
0
0
1
1
1
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
2
0
2
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
2
1
0
0
0
0
0
1
0
0
1
0
2
0
0
2
0
0
2
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
2
1
0
2
0
0
2
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
1
2
0
0
0
0
0
1
1
2
0
0
0
0
2
0
2
1
0
0
0
1
1
0
2
0
0
0
0
1
0
0
0
1
0
2
2
0
0
2
2
0
0
2
0
0
0
0
0
1
0
2
0
0
0
1
2
0
0
2
2
0
1
0
0
0
1
2
0
0
0
2
0
0
0
1
3
0
0
0
0
0
3
0
0
2
0
0
2
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
1
0
2
1
1
2
1
0
0
2
0
3
1
0
0
0
0
3
1
0
1
0
0
0
2
0
0
1
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
2
0
0
5
2
1
0
1
0
2
3
2
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
1
2
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
3
1
1
0
0
0
0
0
0
2
0
0
3
1
0
1
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
2
1
0
1
0
2
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
2
2
0
2
0
0
0
1
0
2
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
1
0
0
2
2
1
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
5
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
1
0
2
1
0
2
0
0
0
0
0
3
0
0
2
2
0
0
0
2
0
0
1
2
1
2
2
2
0
0
2
2
2
0
0
1
2
1
0
0
1
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
2
0
0
3
0
2
0
0
0
2
0
2
0
1
0
0
2
0
0
2
0
0
0
0
2
0
2
0
0
1
0
0
0
1
1
0
0
1
2
2
3
0
0
0
0
0
2
0
0
1
0
1
1
1
1
0
0
0
0
2
3
0
0
0
1
1
0
1
0
0
0
2
0
2
0
0
0
0
3
0
0
0
1
1
1
0
0
0
0
2
0
0
0
1
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
3
1
1
0
1
0
0
0
0
2
0
2
0
0
2
1
2
0
0
2
1
0
2
1
0
0
2
1
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
1
1
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
1
1
0
2
2
0
2
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
1
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
3
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
3
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
1
0
2
0
0
1
2
0
0
0
0
0
0
2
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
2
1
0
2
3
0
2
0
0
1
1
0
0
0
0
2
0
0
2
0
1
2
2
0
0
6
1
0
0
0
0
0
2
0
0
0
1
0
0
2
1
0
1
1
0
0
1
2
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
1
0
0
0
2
2
3
0
0
0
0
1
0
0
0
1
2
0
0
0
0
2
0
0
0
1
2
0
0
3
0
1
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
2
0
0
1
0
0
0
0
1
2
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
3
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
3
1
0
3
1
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
2
2
0
0
1
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
1
1
0
0
0
0
2
2
0
0
0
1
2
2
0
0
0
2
0
0
0
0
0
1
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
2
0
0
0
0
0
2
0
0
0
0
6
1
1
0
0
0
0
0
0
0
1
0
1
1
0
2
0
0
0
1
0
0
1
0
0
2
0
0
0
5
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
2
3
1
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
6
2
0
0
1
0
2
0
1
1
0
2
3
0
0
0
0
2
2
0
0
0
1
1
1
0
2
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
8
0
0
1
2
2
1
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
2
0
1
1
0
1
0
4
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
2
1
0
0
1
0
0
0
0
1
2
0
0
0
1
2
0
1
1
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
1
3
0
0
0
0
0
0
0
0
1
1
1
0
0
1
2
0
0
0
1
0
0
0
0
2
0
2
0
0
2
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
1
2
0
1
0
2
0
1
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
1
0
1
0
3
2
2
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
1
0
0
0
3
0
0
2
0
1
1
0
0
2
0
0
0
0
2
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
2
0
0
2
0
0
0
0
0
2
1
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
2
3
0
0
2
1
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
1
0
0
5
0
0
2
0
0
0
2
0
2
0
0
0
0
2
1
0
0
0
0
0
0
1
0
1
1
2
0
3
0
0
0
0
0
0
0
2
2
1
0
0
0
0
2
0
0
0
0
2
2
0
1
2
0
2
0
0
2
0
1
0
0
0
0
0
1
0
1
2
0
0
1
0
2
2
0
0
0
0
0
2
0
2
0
0
1
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
1
3
0
1
0
0
1
0
2
0
0
0
0
3
0
0
6
2
0
0
0
0
0
0
2
2
0
1
0
3
1
0
1
0
0
2
0
2
0
0
0
0
0
0
1
1
1
0
0
2
0
1
0
0
0
2
2
1
2
1
2
1
0
1
0
0
2
0
0
2
0
1
0
2
1
0
2
1
2
0
0
1
0
0
1
0
0
0
2
2
0
1
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
5
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
1
0
0
2
1
0
1
0
2
0
0
0
1
2
0
0
0
0
0
0
1
2
0
0
1
0
0
2
2
2
5
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
3
2
0
0
2
3
2
4
2
2
0
4
2
0
0
1
0
0
1
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
2
4
0
0
0
2
0
0
0
3
0
0
2
1
0
0
3
0
1
1
0
0
2
4
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
2
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
2
2
0
0
2
16
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
2
0
2
0
0
0
0
3
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
2
0
3
0
0
0
2
0
0
3
0
2
0
0
0
1
0
0
0
0
0
1
0
4
0
2
0
0
0
4
2
0
0
4
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
1
0
0
2
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
2
1
0
0
2
0
0
0
0
0
2
0
0
1
7
0
0
2
1
0
2
0
2
0
1
0
3
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
1
0
0
2
0
1
1
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
2
0
1
1
2
0
1
1
1
0
1
0
2
0
0
0
0
0
0
1
1
0
0
0
0
1
2
2
0
0
0
3
0
2
1
0
0
0
0
0
0
0
0
3
2
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
1
0
1
0
0
0
0
0
2
0
1
1
0
0
1
1
4
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
2
0
0
0
1
0
1
0
1
1
0
0
1
0
0
0
0
0
0
1
0
1
0
1
3
0
0
0
0
2
0
0
0
0
1
0
0
2
1
1
2
1
0
6
1
0
1
3
0
0
0
0
1
1
0
1
3
0
0
0
1
0
2
0
0
0
0
0
0
0
2
2
0
0
1
0
2
0
0
0
1
0
0
1
2
0
0
0
2
0
1
0
1
1
1
0
0
2
0
0
0
2
0
2
1
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
10
2
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
3
2
2
0
0
1
0
1
0
0
1
0
3
1
1
0
0
0
0
1
0
1
1
7
0
0
0
0
0
1
2
0
1
2
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
2
2
2
0
0
0
0
0
0
1
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
1
0
2
2
0
0
3
0
0
0
0
1
0
0
2
0
1
1
2
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
1
2
0
0
0
2
0
0
0
0
1
0
0
0
2
3
0
1
0
1
0
0
5
2
0
0
0
1
0
2
0
1
2
0
0
0
0
0
0
1
2
0
0
2
0
0
0
1
0
2
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
2
1
0
0
1
0
0
0
0
0
0
2
0
0
2
1
0
0
0
2
0
2
0
0
0
0
1
1
0
1
2
1
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
3
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
1
0
0
0
0
0
1
2
0
2
0
0
0
0
1
2
0
3
0
2
2
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
2
1
0
0
2
1
2
0
1
1
0
1
0
0
0
0
0
0
0
0
2
1
2
0
1
1
2
2
2
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
2
2
0
1
0
0
2
0
2
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
2
1
2
0
2
1
0
0
0
0
0
1
0
0
2
0
0
0
0
1
1
1
2
2
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
1
1
0
0
2
1
0
0
0
1
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
5
2
1
0
0
0
2
0
0
0
0
0
0
2
1
0
2
0
0
0
2
0
0
0
0
0
2
8
0
0
1
0
0
0
1
0
3
0
0
0
0
2
1
0
0
0
1
0
1
2
0
1
0
0
1
0
0
0
1
0
0
1
1
0
1
1
0
1
0
0
0
0
2
0
0
1
1
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
2
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
3
2
0
0
0
0
0
0
3
1
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
1
2
0
1
0
0
2
0
0
1
0
0
0
2
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
1
1
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
1
1
1
0
0
0
1
0
2
0
0
2
3
0
0
0
0
2
13
0
0
0
0
0
1
1
0
1
0
1
0
0
0
1
2
0
0
0
1
1
0
2
0
2
0
0
2
1
2
2
0
0
0
2
0
2
0
2
0
0
0
0
3
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
1
0
0
0
5
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
1
0
2
0
0
0
0
0
1
0
2
0
0
0
2
0
2
0
2
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
2
0
1
0
1
0
0
2
0
0
0
0
1
0
1
0
0
5
0
0
0
1
1
0
0
1
0
2
0
0
0
0
0
2
0
1
0
0
0
0
2
1
2
2
0
2
1
2
0
0
0
1
0
0
0
1
0
0
0
2
2
0
1
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
2
3
0
0
2
0
2
2
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
2
2
3
1
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
1
0
0
0
0
2
0
1
0
1
0
0
2
0
1
3
0
6
1
0
0
0
1
0
1
1
0
0
0
0
0
0
1
2
0
0
0
2
2
0
0
0
0
0
0
2
2
2
0
0
2
2
0
1
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
2
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
2
2
0
0
2
1
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
2
1
0
0
0
0
2
0
0
0
1
3
0
0
2
0
2
0
0
1
0
0
0
2
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
3
2
0
0
0
0
0
0
2
1
0
0
2
2
0
0
1
4
2
0
0
1
0
2
0
0
1
0
0
0
0
2
0
0
2
4
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
2
2
0
0
0
0
1
2
0
1
0
1
0
0
0
1
1
0
2
1
2
0
0
0
0
2
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
3
2
0
0
1
0
0
0
2
2
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
1
2
0
0
6
1
1
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
1
0
0
0
1
0
0
1
0
0
0
0
3
0
1
1
0
0
3
1
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
2
0
1
0
1
0
0
0
0
1
2
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
1
0
0
0
2
2
0
2
0
0
2
1
0
0
1
0
0
0
2
0
2
0
0
1
2
0
1
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
2
2
0
0
0
0
3
2
1
0
0
0
1
0
0
2
0
1
0
0
1
2
1
0
2
1
2
0
0
0
0
2
1
1
1
1
5
0
0
0
2
0
0
0
1
1
0
0
0
1
0
1
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
1
0
2
1
2
1
2
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
3
0
0
0
0
0
0
2
0
1
2
1
2
0
1
2
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
1
1
0
0
0
0
1
1
0
2
0
0
0
0
2
0
0
0
2
0
0
2
0
1
0
1
1
1
2
2
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
2
1
1
0
0
0
0
0
0
0
2
2
0
0
0
2
0
2
1
0
0
0
0
0
1
1
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
1
0
1
17
0
2
0
0
4
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
3
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
2
2
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
1
3
0
0
1
1
0
0
1
2
0
2
0
0
1
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
2
0
1
1
0
4
0
0
2
0
0
1
2
1
2
2
1
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
2
2
0
0
0
0
1
1
0
0
0
14
0
2
1
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
1
0
2
2
3
0
0
0
1
0
0
0
2
0
0
0
0
1
0
2
0
0
1
2
0
0
0
4
0
0
0
1
0
1
0
0
1
0
1
0
3
0
0
1
1
1
0
0
0
0
0
0
0
5
0
0
2
2
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
1
2
1
0
0
0
0
1
0
0
0
0
0
0
2
1
3
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
6
1
0
0
0
1
2
1
1
0
2
0
1
0
0
2
0
0
2
2
0
0
0
0
2
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
2
0
0
0
0
2
1
3
0
1
0
0
0
1
2
0
0
0
0
1
0
0
0
0
2
0
2
2
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
2
2
0
0
0
2
2
0
2
0
0
0
2
0
1
0
0
1
0
0
0
2
1
0
2
0
0
2
0
0
0
0
2
0
2
2
0
1
0
0
0
1
1
0
0
0
0
3
2
0
1
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
1
0
0
0
2
0
0
2
1
0
0
0
1
0
1
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
3
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
2
0
0
2
1
1
0
0
0
2
0
0
2
0
0
3
1
1
1
0
0
2
0
0
0
0
2
1
0
1
1
0
0
2
0
0
0
2
0
1
1
0
1
0
0
0
2
0
1
0
2
0
2
1
0
0
2
1
0
2
2
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
2
0
3
0
0
0
0
2
0
0
2
1
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
2
0
2
1
0
0
0
0
0
1
2
1
0
1
0
2
0
0
2
2
2
0
2
0
0
1
2
0
2
0
2
0
2
1
0
0
0
0
0
1
0
0
0
0
0
2
2
0
1
0
0
2
0
0
0
0
2
1
0
0
0
0
0
1
2
0
2
0
0
0
2
0
0
0
2
1
2
0
0
0
2
0
0
0
1
0
1
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
3
0
0
2
2
0
0
0
0
1
0
0
0
0
2
0
1
0
2
0
0
1
0
2
2
0
2
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
2
1
1
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
1
0
2
1
2
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
1
3
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
1
0
1
2
1
0
2
0
0
2
0
0
0
0
1
0
0
1
0
1
0
3
0
1
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
2
0
1
1
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
2
1
0
1
0
0
0
2
3
0
0
0
1
0
2
0
0
0
0
3
2
0
2
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
2
1
0
2
0
1
0
2
1
0
0
0
0
0
0
0
0
2
2
0
2
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
2
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
2
0
0
0
2
0
2
0
0
0
1
0
2
0
0
0
0
0
6
0
0
0
5
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
2
2
1
0
0
0
1
0
0
0
2
0
1
0
0
0
0
3
0
0
0
0
0
5
0
0
1
0
1
3
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
2
0
2
1
2
1
0
0
0
0
2
0
0
0
0
1
1
0
0
3
0
2
0
1
0
0
1
2
0
0
0
0
2
0
2
0
0
1
2
0
0
2
0
0
0
0
0
0
2
2
0
3
2
2
1
0
0
2
0
0
0
2
0
0
0
0
0
1
0
2
2
0
0
0
0
1
0
0
1
0
4
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
2
0
0
1
4
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
2
0
2
3
5
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
2
3
0
3
2
0
0
0
0
2
1
0
0
1
2
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
3
0
0
0
0
0
1
0
1
0
0
0
0
2
0
2
1
1
0
3
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
1
1
0
0
2
0
0
0
0
1
1
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
2
0
0
2
0
0
0
4
0
2
0
0
0
0
2
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
2
2
0
0
0
0
0
0
1
1
1
0
0
0
0
0
2
0
3
2
1
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
8
1
0
1
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
2
0
0
0
3
0
0
0
1
0
1
0
0
3
0
1
1
2
0
1
1
2
0
0
1
0
2
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
3
0
0
0
2
2
0
3
1
1
0
0
1
0
0
0
1
0
2
0
0
1
0
0
0
3
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
1
0
0
0
2
4
1
3
1
0
1
1
2
1
1
0
0
0
0
0
0
1
2
2
0
0
0
1
0
2
0
2
0
0
0
0
1
2
0
0
0
0
0
0
2
1
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
2
2
2
0
4
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
2
0
0
2
2
0
2
3
2
2
0
1
1
0
2
1
0
2
1
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
1
1
0
0
0
0
1
2
1
0
2
0
2
0
2
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
2
0
0
2
0
3
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
2
1
1
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
1
2
0
1
0
0
1
0
1
1
1
0
1
0
0
0
0
0
1
0
3
1
0
0
1
1
0
0
2
0
0
1
0
1
0
2
0
0
0
0
0
0
1
0
1
1
0
5
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
2
0
2
1
1
0
1
0
0
2
1
0
5
0
1
0
0
2
0
2
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
2
0
0
1
0
0
2
0
5
2
0
0
0
0
0
0
0
0
1
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
3
0
0
0
4
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
1
0
0
0
0
0
0
0
1
1
0
1
1
1
0
0
1
0
2
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
2
0
1
1
1
0
1
0
0
2
2
1
2
0
1
0
0
0
1
0
3
0
0
1
0
1
0
1
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
1
0
0
1
2
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
3
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
2
1
0
0
0
1
1
2
0
0
0
0
0
0
0
1
0
0
3
0
3
2
1
0
2
0
2
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
3
1
2
0
1
1
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
2
0
0
2
0
0
1
4
0
0
0
2
1
2
0
0
0
0
0
0
0
3
2
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
1
0
0
0
1
2
0
2
0
0
0
2
0
0
2
0
0
0
1
0
0
0
1
0
2
0
0
0
0
1
0
2
2
0
0
0
2
0
1
0
0
0
2
0
2
0
0
0
1
2
0
0
1
2
1
0
0
0
1
2
0
0
0
2
0
0
0
0
0
1
0
0
0
2
1
1
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
5
5
2
2
0
1
2
2
0
0
0
0
0
2
0
0
1
0
0
0
1
1
0
2
0
1
0
0
0
2
4
0
1
1
0
0
0
2
1
2
0
5
2
0
0
0
2
0
0
0
0
1
3
0
0
0
0
0
2
2
2
1
0
2
0
0
1
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
5
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
3
0
0
0
0
1
0
1
0
1
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
1
0
0
0
0
2
0
1
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
2
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
2
0
0
0
0
1
0
2
2
2
2
0
0
0
0
2
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
3
0
0
2
0
0
0
0
0
2
1
0
2
2
1
0
3
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
3
0
0
0
2
0
2
2
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
1
0
1
0
1
0
1
0
0
0
2
2
0
0
0
1
1
0
0
1
1
0
2
0
0
1
0
0
0
0
1
0
0
2
2
0
0
0
1
0
0
0
0
0
1
0
0
2
1
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
2
2
5
2
0
0
1
1
0
0
3
0
2
0
0
0
0
0
2
2
1
0
1
1
4
0
0
0
0
2
0
0
1
1
0
0
1
0
0
1
1
0
0
0
0
1
2
1
1
0
1
2
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
3
0
1
0
2
0
1
0
1
1
2
0
1
2
0
2
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
2
0
0
2
1
0
0
0
0
0
1
0
1
0
1
0
2
2
1
1
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
2
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
2
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
1
1
0
0
0
0
1
2
1
2
0
1
0
1
2
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
2
0
0
1
1
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
1
2
0
0
2
0
0
0
2
0
0
1
2
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
2
0
4
0
0
0
2
1
0
0
0
2
1
0
0
0
1
0
0
0
0
2
1
0
2
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
3
0
0
0
0
0
0
1
2
2
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
7
2
2
3
0
1
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
1
2
0
0
0
3
0
0
0
0
1
2
0
0
2
1
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
1
0
0
1
1
0
1
2
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
2
2
1
0
0
1
3
0
0
0
0
2
1
0
1
0
0
2
0
1
0
0
1
1
1
1
0
0
0
0
2
0
1
0
3
0
0
1
0
2
0
0
1
0
1
0
0
0
0
0
2
0
0
0
2
2
0
2
2
0
0
1
0
0
0
0
0
2
2
0
0
0
2
1
0
0
2
0
0
0
0
2
0
0
0
0
2
0
2
1
2
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
1
1
0
2
0
1
0
0
2
0
2
0
0
0
1
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
1
0
1
0
2
0
2
2
0
0
1
0
0
1
0
1
0
0
0
2
0
0
0
2
2
0
0
1
0
1
2
0
1
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
1
1
0
0
0
2
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
1
1
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
3
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
2
0
0
2
2
0
2
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
3
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
2
0
0
2
2
0
1
0
0
0
0
0
2
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
3
0
0
0
2
0
1
2
0
0
0
0
0
0
1
0
0
0
4
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
3
0
0
1
0
1
0
0
2
0
0
2
0
2
0
2
0
1
1
0
0
0
0
2
0
2
0
0
0
0
0
2
1
0
2
2
2
2
0
2
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
2
0
0
2
0
0
0
1
2
0
2
0
1
0
1
0
0
0
1
2
0
0
0
0
1
0
2
0
0
2
2
1
0
0
0
0
0
0
2
1
2
2
1
0
0
1
0
1
0
1
0
0
0
0
2
3
0
1
0
3
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
3
2
0
2
0
2
1
4
0
0
0
0
1
1
1
0
0
0
0
3
0
0
0
0
1
4
0
1
0
0
0
0
0
2
0
4
0
1
1
0
0
0
0
0
0
1
0
0
0
2
2
0
3
0
1
0
0
0
1
0
1
0
0
0
0
0
2
0
1
0
1
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
1
0
3
0
3
0
2
1
0
0
1
0
2
1
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
1
1
0
2
3
0
0
0
3
0
0
1
2
0
0
0
0
0
2
4
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
1
1
0
1
1
0
1
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
3
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
1
0
0
0
0
1
0
2
0
1
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
3
0
0
0
1
0
0
0
2
1
3
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
2
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
1
0
0
0
0
0
3
0
0
0
0
1
2
0
0
0
0
0
2
1
0
0
2
0
0
1
0
0
1
0
0
0
0
1
0
1
1
0
1
0
1
0
0
0
2
1
0
0
0
0
1
0
1
0
0
1
1
1
0
1
0
3
1
0
0
0
0
0
0
0
0
0
0
0
2
0
3
1
0
0
0
2
0
0
0
1
0
0
0
2
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
8
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
1
1
0
0
0
0
1
0
0
2
0
0
0
2
0
2
1
0
0
0
0
0
0
3
0
4
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
2
0
0
1
0
1
0
0
0
0
0
0
1
0
0
2
0
1
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
1
2
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
3
2
0
0
1
0
2
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
1
1
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
3
0
2
0
0
0
0
0
0
0
1
0
0
0
2
1
4
2
0
0
2
2
0
0
0
2
0
0
0
0
1
0
2
2
1
0
0
0
0
1
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
4
2
1
2
0
2
0
0
2
0
0
1
0
1
1
0
1
0
1
0
7
0
1
0
0
0
2
2
2
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
2
0
0
2
1
0
2
0
0
0
0
1
2
2
0
0
0
1
0
1
0
1
0
2
0
0
0
0
0
0
1
0
1
0
1
2
0
2
0
2
2
2
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
2
1
0
1
1
0
0
2
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
4
0
0
0
2
0
0
0
2
0
2
0
1
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
1
2
0
0
2
0
1
0
5
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
3
0
0
0
0
0
0
2
0
1
0
1
0
0
1
0
2
0
1
0
2
0
0
2
0
2
2
0
1
0
0
0
0
1
0
0
1
0
0
0
2
0
2
1
0
0
0
2
0
1
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
4
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
2
1
0
0
2
0
0
0
0
2
4
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
3
0
0
0
0
2
0
1
0
0
1
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
2
0
0
0
2
2
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
5
2
2
2
4
1
1
0
0
0
0
2
0
0
0
0
0
0
1
1
0
2
0
2
1
2
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
2
2
1
0
2
0
0
0
9
2
1
2
0
1
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
2
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
2
2
0
2
0
0
0
0
0
4
2
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
2
2
0
0
0
2
2
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
2
4
0
2
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
1
2
1
0
0
0
2
0
1
2
1
0
0
0
0
2
1
1
0
0
0
2
0
0
0
0
0
0
1
0
1
1
0
0
1
1
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
2
2
1
0
0
0
2
0
0
0
2
0
0
0
1
2
0
0
0
0
2
2
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
2
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
1
0
0
0
0
1
1
0
3
0
0
0
0
0
0
2
0
0
0
2
0
0
3
1
0
0
0
0
2
0
2
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
2
1
2
0
1
2
1
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
3
0
2
1
2
0
1
0
0
0
2
0
1
2
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
2
0
2
1
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
1
0
1
0
2
0
0
0
0
0
0
0
0
2
0
3
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
3
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
3
1
0
2
0
3
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
1
0
3
0
0
0
1
0
0
0
0
0
1
2
1
2
1
0
0
1
0
0
0
0
1
1
0
4
1
1
1
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
1
0
2
0
2
1
0
0
0
1
0
0
0
0
2
0
1
0
2
2
0
0
1
0
2
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
2
0
0
0
1
1
2
2
0
0
0
0
0
3
0
2
0
0
0
2
3
0
2
2
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
1
0
4
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
1
2
0
0
0
1
2
1
0
0
2
1
0
0
0
1
1
3
1
2
0
2
1
0
0
0
2
1
1
0
0
1
1
0
0
0
1
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
3
1
0
2
2
0
0
0
2
0
1
0
0
0
3
1
1
1
0
1
2
0
0
0
0
0
3
0
0
0
0
1
2
2
1
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
2
0
2
1
0
1
0
0
1
0
0
0
0
2
2
1
0
0
1
0
0
0
0
0
1
0
0
1
1
1
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
2
1
0
0
0
1
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
1
1
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
2
0
1
0
2
1
2
0
1
1
0
0
1
0
0
0
1
0
0
0
2
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
3
0
0
0
1
1
1
0
0
1
2
0
2
0
0
0
0
0
2
0
0
0
0
2
1
2
0
0
2
0
0
2
0
2
2
0
0
0
0
2
0
0
0
2
0
0
1
0
2
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
2
1
0
0
2
0
0
1
1
1
2
0
0
1
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
3
2
0
1
1
2
0
0
0
1
0
0
1
0
0
0
2
0
0
0
2
1
1
1
1
3
0
0
1
0
1
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
3
0
0
0
1
0
0
0
2
0
1
0
1
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
2
0
1
0
1
0
0
2
0
2
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
1
0
1
1
0
2
2
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
1
1
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
1
0
0
1
1
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
1
0
1
0
2
0
1
0
2
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
2
1
0
2
0
0
0
2
0
0
0
0
0
2
0
0
1
2
1
2
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
1
1
0
0
0
0
2
1
0
0
0
0
2
2
4
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
2
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
11
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
1
2
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
3
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
2
0
3
0
2
2
0
0
0
0
0
1
0
0
2
2
1
0
0
0
0
0
0
1
4
2
0
0
0
0
0
0
0
1
0
0
2
1
1
0
0
1
0
0
1
3
0
0
0
0
0
1
2
0
1
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
1
0
2
2
2
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
1
0
2
2
0
0
1
0
2
2
0
0
0
0
2
2
1
1
0
2
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
1
2
0
2
1
1
0
2
3
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
1
1
1
2
0
1
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
1
2
0
2
0
1
0
0
2
0
0
0
1
1
0
0
0
0
0
1
2
0
0
0
2
0
2
0
2
2
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
1
0
0
0
0
2
1
0
0
0
2
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
1
1
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
1
0
0
1
0
0
0
1
0
3
0
2
2
3
0
0
1
1
0
0
4
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
3
0
0
3
0
0
1
0
0
0
0
0
0
0
0
7
0
0
2
1
1
0
0
0
0
1
0
0
0
2
2
1
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
2
0
0
1
0
1
1
2
0
0
0
0
3
0
0
2
2
0
0
0
0
0
1
2
0
4
2
0
1
0
2
2
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
1
1
1
4
1
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
6
2
2
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
1
1
2
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
1
0
4
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
1
2
0
0
2
0
1
0
1
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
2
1
0
0
0
2
0
0
0
2
0
0
1
1
0
0
0
0
3
0
5
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
1
1
0
1
1
2
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
2
1
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
1
0
0
2
0
1
0
0
0
0
2
0
2
0
0
1
0
1
1
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
2
1
0
1
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
2
1
0
0
2
1
0
0
2
0
0
1
0
0
0
0
0
0
1
2
0
0
1
0
0
0
2
2
2
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
2
0
0
0
1
2
0
1
0
0
0
0
3
0
0
2
2
1
0
0
0
0
0
3
2
0
0
0
0
0
2
0
2
0
0
0
0
1
2
3
0
0
0
0
0
0
2
0
1
0
1
1
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
10
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
2
0
0
1
1
0
0
1
1
0
0
0
0
0
1
0
0
0
1
2
2
0
0
0
0
0
1
0
1
1
3
3
2
0
0
0
0
0
0
0
2
0
0
0
5
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
1
0
1
1
0
0
2
1
2
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
2
0
0
1
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
1
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
1
2
10
1
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
2
0
0
0
1
0
0
1
0
0
3
0
0
1
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
2
3
0
0
2
0
0
1
0
0
0
0
0
2
2
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
1
0
0
3
0
1
0
0
0
0
0
0
0
0
1
1
2
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
6
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
2
0
0
1
0
0
1
0
0
1
0
2
0
1
3
2
0
0
0
0
2
2
0
0
1
0
0
2
0
1
1
0
0
1
2
0
0
0
3
2
1
1
0
1
2
0
2
0
0
0
2
0
1
2
1
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
1
2
2
0
2
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
3
1
2
0
0
1
0
0
0
1
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
2
0
2
0
1
0
0
0
0
3
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
1
1
0
0
1
2
0
12
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
2
2
0
0
3
1
0
3
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
1
0
2
1
2
0
0
1
2
1
2
0
0
2
0
0
3
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
7
0
0
0
0
2
3
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
2
0
1
1
0
2
4
0
0
2
2
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
4
0
0
2
0
0
2
3
1
0
0
0
0
0
3
0
0
0
2
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
2
0
1
1
0
0
0
0
0
2
0
1
0
0
0
0
1
2
0
0
0
3
0
0
0
1
1
1
0
1
0
4
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
2
0
2
2
0
0
0
0
2
0
0
0
0
2
1
1
1
0
0
0
0
0
0
0
2
2
0
2
0
0
1
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
2
0
1
0
1
0
0
1
1
0
0
1
0
0
0
2
0
0
0
1
2
1
0
1
0
2
2
0
0
0
0
0
0
0
2
0
2
2
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
1
0
0
0
3
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
3
0
1
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
1
1
0
2
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
3
1
2
0
0
0
0
0
2
2
0
1
0
1
1
1
0
1
0
0
0
1
2
2
0
0
3
0
0
0
0
2
1
0
0
0
0
0
2
1
0
1
0
0
0
0
1
2
0
0
0
0
1
0
1
1
1
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
3
1
1
1
2
2
0
1
0
1
0
0
2
1
0
0
0
0
0
0
0
0
2
2
2
0
0
0
3
0
0
0
1
0
1
0
2
0
0
2
1
1
0
2
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
2
2
0
0
2
0
2
2
0
0
0
1
2
0
0
2
0
1
2
0
0
0
0
2
1
2
0
0
2
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
1
0
2
0
4
0
0
2
1
0
2
4
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
2
0
0
0
0
1
1
0
0
0
1
1
1
0
0
0
0
0
2
2
1
2
2
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
2
0
2
4
1
3
0
2
0
0
0
2
1
2
0
0
0
0
0
1
0
1
0
0
1
0
1
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
1
0
2
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
2
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
1
0
3
0
2
0
2
0
0
1
1
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
1
0
1
2
1
2
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
2
0
0
0
0
0
1
0
0
1
0
1
0
0
4
0
2
0
0
0
0
2
0
0
0
0
1
0
0
1
2
4
0
0
1
2
2
1
1
0
0
0
2
0
0
0
2
0
1
0
0
2
0
0
1
0
0
0
0
0
0
3
0
1
1
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
1
0
0
5
1
2
0
0
1
0
0
0
0
0
3
0
1
0
0
0
1
0
0
0
0
2
0
1
0
0
0
2
1
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
7
1
0
0
0
0
0
0
0
0
1
0
0
1
0
2
2
0
1
0
1
2
2
1
1
2
1
0
2
2
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
1
1
1
0
1
0
0
0
0
1
1
1
1
0
2
0
0
2
0
0
1
0
0
0
1
0
0
0
1
2
1
1
2
1
3
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
2
1
0
0
0
1
0
0
1
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
2
0
1
2
0
0
0
0
0
1
0
0
0
0
1
0
2
1
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
2
1
0
0
3
0
5
0
0
2
3
2
0
0
0
0
0
0
0
1
0
1
0
0
1
2
1
0
0
0
0
0
0
3
0
0
0
0
0
4
0
0
1
0
1
3
1
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
2
2
0
0
2
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
2
0
1
2
0
0
0
0
0
0
2
2
0
1
0
0
0
0
3
2
1
1
1
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
3
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
3
0
0
0
0
1
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
2
1
0
0
1
3
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
1
0
0
1
0
0
2
0
1
1
0
1
0
0
3
0
2
0
0
0
0
1
2
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
1
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
1
1
0
0
0
0
2
2
0
1
0
0
0
1
0
2
0
0
0
0
2
1
0
0
1
0
0
1
1
2
1
3
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
4
0
2
0
1
0
0
0
0
1
0
7
0
0
0
0
0
0
1
2
0
2
0
0
0
2
2
2
0
2
0
2
1
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
6
0
2
0
0
1
0
0
0
2
0
2
1
0
0
0
0
2
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
1
1
0
2
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
3
0
0
0
2
0
0
1
0
2
1
0
0
0
3
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
2
0
0
0
1
0
1
0
1
0
0
0
1
0
1
0
2
0
0
0
1
1
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
2
0
1
1
1
3
1
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
3
0
0
1
1
1
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
2
1
1
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
2
0
0
1
0
1
1
0
0
0
1
1
0
1
2
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
2
0
0
0
1
0
1
2
0
1
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
2
1
0
0
0
1
0
0
1
0
0
0
1
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
2
0
1
0
0
0
2
0
1
1
0
0
2
0
0
0
0
0
2
0
2
0
0
0
1
1
0
0
0
1
0
0
2
0
2
1
1
2
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
2
1
1
0
0
2
3
0
0
0
0
0
1
1
0
0
1
2
0
2
1
0
0
0
0
1
0
0
0
2
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
1
2
0
0
2
0
0
0
0
2
0
0
3
0
0
0
0
4
0
1
2
0
2
0
0
0
1
0
0
0
0
0
4
1
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
1
1
0
3
0
0
0
1
0
0
0
0
0
1
0
0
2
2
3
0
0
0
1
1
3
2
0
2
0
0
0
0
1
2
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
2
1
0
0
1
0
0
1
0
1
0
2
0
2
0
0
0
2
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
2
1
1
0
1
0
0
0
2
2
0
0
3
2
0
0
0
1
1
0
0
0
1
1
2
1
0
1
0
0
0
0
1
0
2
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
1
0
0
1
0
0
0
1
0
1
1
1
1
1
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
4
1
1
0
2
0
0
0
3
0
1
1
2
0
1
1
2
0
0
0
0
1
0
0
2
2
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
2
2
2
0
1
2
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
2
0
3
0
2
0
1
2
0
0
0
1
2
2
0
0
2
0
0
0
0
0
2
2
0
1
0
0
2
3
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
1
1
0
0
1
1
0
1
0
1
0
0
2
0
2
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
1
2
1
2
1
0
0
0
0
2
0
0
1
0
0
0
1
0
1
2
0
0
0
0
2
2
2
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
1
0
1
0
0
2
0
1
0
0
0
0
0
2
0
2
1
0
0
0
0
1
0
0
0
0
1
3
0
0
0
0
2
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
1
0
1
1
0
0
1
2
0
0
2
0
2
0
0
0
0
1
2
0
0
0
2
0
2
0
0
0
1
1
1
0
1
1
1
1
0
1
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
2
0
2
0
0
0
2
1
0
0
0
0
3
0
1
2
0
1
1
0
0
0
0
1
2
1
1
5
1
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
2
3
2
0
1
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
2
0
3
0
0
0
0
2
0
2
2
0
0
0
0
2
0
1
0
0
1
1
0
0
0
0
0
1
2
0
1
0
0
0
0
0
2
1
0
1
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
10
2
0
0
3
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
1
2
0
0
1
0
2
0
2
0
1
2
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
2
0
1
0
1
0
0
0
0
0
0
0
3
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
2
0
1
0
1
0
0
1
2
0
3
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
2
0
2
2
0
0
0
1
1
1
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
2
2
2
0
1
0
0
1
0
1
1
3
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
1
0
0
2
0
0
2
1
0
0
0
1
0
0
0
0
0
0
2
0
0
1
2
0
0
0
2
2
2
0
0
0
4
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
1
0
0
3
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
2
0
4
4
1
2
0
2
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
2
0
1
0
1
0
1
2
0
0
0
0
0
1
1
0
0
1
2
0
4
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
6
1
0
0
0
0
0
0
1
0
2
2
0
2
0
2
2
0
0
2
2
0
0
0
1
2
1
0
1
0
0
2
1
2
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
1
1
7
0
0
0
2
1
0
5
1
0
2
0
0
0
0
0
0
0
1
0
0
2
1
1
2
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
2
0
0
3
1
0
1
0
0
0
2
0
0
0
0
0
0
0
2
1
0
3
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
1
2
1
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
2
0
1
1
0
1
2
0
1
0
0
0
2
0
0
3
0
0
1
0
0
0
0
2
2
0
1
0
2
1
2
0
0
0
0
0
0
2
3
0
0
0
2
0
0
1
0
0
2
0
2
0
2
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
2
2
0
0
0
0
0
1
0
1
0
0
1
0
3
0
0
0
1
0
0
2
1
0
1
1
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
2
2
1
0
1
0
0
0
0
2
2
2
1
2
0
0
2
0
2
0
1
0
0
0
1
2
0
1
4
1
1
2
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
2
0
2
0
1
1
2
2
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
1
0
0
2
2
0
0
0
2
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
3
4
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
1
0
0
0
0
2
0
0
2
0
1
0
0
0
2
0
1
4
2
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
5
0
0
0
1
0
0
2
2
0
0
0
1
0
0
0
0
1
0
1
1
1
1
0
0
0
0
0
1
0
0
0
1
1
1
0
0
1
2
2
2
0
5
0
0
0
3
2
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
2
2
1
2
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
2
0
1
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
3
1
0
0
0
0
1
2
0
2
0
0
0
1
0
0
0
0
0
3
0
2
2
1
1
1
0
2
0
0
0
1
0
0
2
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
9
2
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
3
0
0
1
0
0
0
3
0
0
0
2
0
0
1
0
0
0
0
2
1
0
0
2
1
0
0
0
2
0
0
0
1
3
0
2
2
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
2
1
0
0
2
2
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
2
0
0
0
0
0
0
2
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
6
1
0
0
1
0
2
0
0
2
2
1
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
2
0
1
0
2
0
1
1
2
0
2
2
2
2
0
0
2
0
0
0
0
1
2
2
0
0
2
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
2
2
1
5
1
0
0
2
0
0
1
3
2
0
1
1
0
2
0
1
1
0
0
0
2
5
2
0
1
2
0
0
3
0
1
2
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
1
1
0
1
0
2
0
0
1
0
0
0
0
0
0
0
2
2
2
0
0
0
0
1
0
2
0
0
1
5
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
2
0
0
0
0
1
0
1
0
0
2
1
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
5
2
0
0
0
0
5
0
0
0
0
0
0
1
2
0
0
2
0
2
0
0
1
2
1
0
0
0
1
1
0
1
0
0
0
0
1
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
1
1
2
0
0
0
0
4
2
2
0
0
3
1
2
0
0
1
0
1
0
0
0
0
0
4
1
0
0
0
1
2
0
2
1
0
1
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
1
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
1
0
0
1
2
1
0
0
0
2
1
2
0
1
0
2
2
0
0
2
3
2
0
0
0
2
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
1
12
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
1
0
1
2
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
3
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
3
0
0
3
2
3
2
0
1
0
0
0
0
0
0
1
0
1
0
0
2
0
0
5
0
1
0
2
0
0
0
2
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
2
0
0
0
0
3
2
0
1
0
0
1
2
0
0
1
0
2
0
0
0
2
1
2
0
0
2
1
0
0
1
2
0
0
0
0
2
0
2
2
2
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
2
2
0
2
0
0
0
2
0
0
0
6
0
3
0
0
4
2
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
1
0
1
0
0
0
0
2
0
1
0
0
0
1
0
1
1
2
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
4
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
3
1
2
0
0
2
0
2
0
1
1
0
0
0
0
2
0
0
1
1
0
1
1
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
8
0
1
0
0
1
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
1
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
1
1
0
2
0
0
0
0
0
0
2
1
0
1
1
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
1
1
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
1
0
1
0
1
0
0
0
1
2
0
0
1
1
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
1
0
0
3
2
1
1
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
3
0
0
0
1
0
2
0
0
2
0
0
0
0
1
0
4
1
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
2
0
0
0
2
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
2
0
0
3
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
2
6
2
0
0
0
0
2
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
4
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
2
0
0
2
0
2
0
2
0
1
0
0
0
0
0
2
2
0
0
0
0
2
0
2
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
3
1
0
0
0
2
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
2
1
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
2
1
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
2
2
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
3
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
2
1
0
2
0
2
1
0
0
0
0
1
0
11
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
3
2
2
2
0
0
2
0
0
0
13
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
1
2
2
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
2
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
1
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
2
0
5
2
1
0
2
2
0
1
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
1
4
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
2
2
0
0
3
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
3
3
1
1
1
0
0
0
1
1
2
0
1
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
2
2
0
0
1
0
0
1
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
0
2
0
1
0
0
2
0
0
0
4
0
1
0
0
0
0
1
2
1
0
0
1
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
1
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
1
0
2
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
2
0
1
0
0
2
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
1
0
0
1
0
1
0
0
2
0
0
0
0
3
0
2
1
0
2
0
1
0
1
0
0
1
0
1
0
0
0
0
0
2
2
1
0
0
0
1
0
0
0
0
1
0
2
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
1
0
1
1
2
0
0
0
0
0
0
1
2
0
0
0
1
2
0
0
1
1
11
1
2
0
0
0
0
0
0
1
2
0
0
2
0
0
0
2
2
2
0
0
3
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
2
0
2
0
1
1
2
0
0
1
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
1
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
2
2
1
0
2
0
1
2
0
0
2
1
0
2
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
2
2
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
5
1
0
0
2
2
2
0
0
0
0
0
0
1
2
1
0
0
2
0
0
1
2
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
2
1
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
1
0
2
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
1
0
0
0
0
1
0
1
0
2
1
0
2
0
1
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
1
1
0
0
2
1
0
2
0
0
0
2
0
0
1
0
0
0
0
0
2
0
3
0
2
0
0
0
0
1
1
2
1
1
2
0
1
1
1
0
0
0
0
0
1
0
0
0
2
1
3
2
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
2
3
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
1
1
2
0
0
1
1
2
2
2
0
1
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
1
0
0
0
0
2
0
1
0
0
1
0
2
0
2
1
1
0
0
0
0
2
0
1
0
0
0
0
1
1
0
0
0
0
0
0
2
0
2
0
0
2
1
0
2
0
0
0
2
1
0
1
0
0
0
0
2
3
2
0
0
0
0
0
2
3
0
0
0
2
1
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
1
0
0
0
2
2
0
0
0
0
2
0
0
0
0
1
0
1
1
0
2
2
0
3
0
0
0
3
0
0
0
0
0
0
0
4
2
2
1
0
0
0
0
2
0
0
0
0
0
0
1
2
2
0
2
0
0
0
2
0
0
0
1
2
0
0
0
0
0
1
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
1
0
2
0
1
0
0
0
0
1
0
1
0
2
0
1
0
0
0
1
0
1
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
2
1
0
1
0
0
0
2
0
0
0
0
0
0
0
1
2
0
2
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
3
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
2
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
2
0
0
0
1
0
0
0
1
0
0
2
2
1
2
1
0
0
1
2
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
2
1
0
0
2
0
0
2
0
2
0
2
0
0
0
0
0
0
1
0
1
0
0
2
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
2
2
1
0
0
0
0
2
0
1
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
2
3
1
0
2
0
1
0
2
0
0
0
0
1
0
1
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
2
0
2
0
0
0
0
1
0
2
0
0
0
0
3
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
1
0
0
2
0
0
0
1
0
1
0
0
2
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
2
0
1
1
0
0
1
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
1
0
1
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
5
1
0
0
0
0
1
0
0
0
0
0
2
0
1
0
2
2
1
0
1
1
0
2
0
0
0
0
0
0
1
1
1
1
0
0
3
2
0
1
1
0
0
2
1
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
1
0
0
0
1
1
1
0
1
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
10
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
2
0
0
1
1
0
0
2
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
1
1
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
6
0
0
2
1
0
0
0
0
0
1
0
0
2
2
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
2
0
1
0
2
0
1
0
1
0
0
2
2
0
0
1
0
2
3
0
0
1
0
2
0
0
2
2
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
2
1
1
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
2
0
0
0
0
0
0
0
3
1
0
1
0
1
0
1
0
0
0
0
1
0
2
2
3
0
2
0
0
0
1
1
1
0
2
0
0
0
0
0
0
1
1
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
1
0
0
0
2
0
1
2
0
1
0
0
0
3
0
1
1
0
0
2
1
2
2
0
2
1
1
0
0
0
0
0
0
4
0
2
0
1
0
0
0
2
1
2
0
0
0
2
0
1
0
2
1
0
0
0
1
1
0
0
0
2
2
1
1
0
1
0
2
0
4
2
0
1
0
2
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
1
0
0
0
4
0
0
0
0
0
0
0
2
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
2
1
0
2
0
0
2
0
1
0
2
0
1
1
1
0
0
0
0
0
0
0
0
0
10
1
2
0
0
0
0
2
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
3
0
0
2
0
0
0
0
1
6
0
0
0
2
3
0
0
0
0
0
2
1
0
0
0
2
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
3
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
2
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
1
1
2
1
0
1
0
1
2
2
1
2
0
2
1
1
0
0
0
0
0
3
1
0
0
1
0
0
0
1
0
2
3
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
2
0
0
0
0
0
0
0
0
2
2
3
0
0
1
0
0
1
0
1
0
0
0
6
0
1
1
0
1
0
0
0
0
0
1
1
0
2
2
0
1
2
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
2
3
0
2
0
0
0
0
1
2
1
0
0
2
0
0
0
0
0
1
0
0
2
2
1
0
1
0
2
0
0
0
0
2
0
0
2
0
1
1
0
0
0
6
1
0
0
0
2
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
1
0
0
0
1
0
2
1
1
0
0
3
1
1
1
0
2
0
0
0
2
0
0
0
1
3
0
0
1
0
0
0
2
0
0
0
1
1
0
0
0
0
0
2
2
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
3
0
1
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
2
2
1
0
0
11
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
2
0
2
2
0
0
0
2
2
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
2
1
0
3
2
0
0
2
0
0
0
3
2
0
0
1
1
0
0
0
2
1
0
0
1
0
0
2
0
0
0
2
1
0
1
0
0
2
0
1
0
0
1
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
2
0
2
0
0
0
2
0
0
0
1
1
0
0
0
0
0
2
0
2
0
0
2
2
0
0
1
0
0
2
2
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
2
1
0
1
0
2
3
0
0
0
0
2
1
0
1
1
0
0
0
0
0
0
2
2
0
0
1
0
1
0
2
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
2
0
1
0
0
0
2
0
0
0
0
0
1
0
2
0
2
0
2
0
0
0
1
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
3
2
1
3
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
1
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
1
2
2
1
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
1
2
2
0
0
0
2
3
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
1
2
0
0
1
2
0
0
0
0
1
0
2
0
0
1
2
1
2
0
2
0
6
1
2
0
0
1
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
1
1
0
0
0
2
0
1
0
2
2
1
0
0
0
0
0
2
0
4
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
3
0
0
2
0
0
2
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
3
0
1
1
1
0
0
0
0
0
1
0
0
2
0
2
2
1
0
2
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
2
0
1
2
2
2
0
0
0
0
2
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
3
0
1
1
0
0
1
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
2
2
0
0
0
2
0
2
2
1
2
0
2
0
0
0
0
2
1
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
1
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
2
0
0
0
1
0
0
0
1
1
1
0
0
2
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
1
2
0
2
0
2
0
0
0
1
0
1
3
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
2
1
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
1
0
0
1
3
0
0
1
0
2
0
2
0
3
0
0
0
1
0
1
2
0
2
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
1
0
7
1
0
0
0
2
0
2
0
2
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
1
0
0
1
0
0
0
0
0
1
0
1
0
0
2
0
0
0
1
0
0
0
0
0
3
0
0
3
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
1
0
1
0
0
2
0
0
1
1
0
0
0
1
0
2
0
0
1
0
0
2
0
2
0
0
1
0
1
0
1
1
0
0
0
1
0
1
1
0
0
0
3
0
2
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
1
0
3
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
2
1
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
3
0
1
0
0
0
0
1
0
0
1
0
0
5
0
0
3
0
0
2
2
0
0
1
0
0
2
0
0
0
0
0
2
0
0
3
0
1
2
0
0
0
0
0
2
2
0
0
2
2
1
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
1
0
1
2
0
0
2
0
2
0
0
1
2
2
1
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
7
0
0
0
1
0
1
0
0
2
2
1
0
1
0
2
0
1
0
2
1
0
0
1
0
2
0
0
0
0
0
0
1
0
0
1
1
2
1
0
0
1
2
0
0
0
0
2
1
1
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
1
1
0
1
0
0
1
0
0
0
0
1
0
2
0
0
0
0
2
1
0
1
0
1
0
0
2
2
0
0
0
0
0
0
3
0
0
0
1
0
0
2
1
2
0
0
0
0
1
0
0
0
0
2
0
2
0
4
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
1
0
2
0
2
0
0
0
0
0
0
2
3
2
0
0
0
0
1
2
0
0
0
2
0
0
0
2
0
3
1
2
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
1
3
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
3
1
2
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
2
0
0
0
2
0
0
3
0
0
2
0
1
3
0
1
2
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
8
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
4
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
1
2
0
0
1
0
0
1
0
0
0
0
5
0
0
1
0
2
0
0
1
2
0
0
0
2
0
0
0
0
0
3
0
2
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
2
0
0
1
0
1
0
0
0
1
4
0
0
0
1
0
0
1
2
0
0
2
2
0
0
0
2
0
1
0
0
1
0
1
1
0
2
0
0
2
0
0
0
4
0
0
0
0
0
2
1
0
2
0
2
1
1
0
1
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
4
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
5
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
2
1
0
1
0
0
3
0
2
0
0
0
2
1
0
1
1
2
2
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
3
0
0
0
2
1
0
2
1
2
1
0
0
0
0
3
0
2
2
0
0
0
0
2
1
0
0
0
2
0
2
1
0
0
1
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
4
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
2
0
1
1
1
0
1
0
0
0
0
0
2
0
1
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
1
1
1
3
0
0
0
1
0
0
0
2
1
1
0
1
0
0
0
0
1
0
0
0
0
1
2
0
1
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
9
0
0
0
2
0
0
0
2
1
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
2
0
0
0
0
2
0
1
1
0
1
3
0
1
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
4
0
0
0
0
1
0
2
0
4
0
0
0
0
0
0
0
1
0
1
0
2
0
0
2
0
0
1
1
0
1
0
2
0
0
0
1
0
2
1
0
1
2
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
2
0
0
0
0
2
0
1
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
1
0
2
1
1
0
0
0
0
0
6
3
0
0
0
0
2
1
0
0
0
0
2
0
0
0
1
2
2
0
0
0
0
0
1
0
2
0
0
1
2
0
2
0
2
4
0
0
2
2
0
0
0
1
2
0
0
0
1
0
0
0
2
2
2
0
0
0
0
3
0
0
1
2
0
0
2
0
0
1
0
0
0
0
0
1
0
1
5
1
1
0
0
1
0
0
1
0
1
2
0
1
0
0
0
1
2
2
0
0
2
2
0
0
2
0
2
1
0
0
0
0
2
0
0
1
0
1
0
0
0
2
2
1
1
0
0
1
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
2
0
3
1
0
0
0
0
2
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
1
4
1
0
0
0
3
0
0
0
0
0
0
1
0
0
1
0
0
0
1
2
0
0
1
0
0
1
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
1
2
1
0
1
0
2
0
0
2
1
0
0
0
0
0
0
1
0
1
0
2
0
0
0
1
0
2
0
2
0
0
1
0
0
0
2
2
1
3
1
0
0
0
0
0
1
1
0
0
0
1
0
1
2
0
2
0
3
0
0
0
0
0
4
0
0
0
1
2
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
7
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
5
2
0
0
0
0
1
0
0
0
0
0
1
1
0
4
2
1
2
3
0
0
1
0
0
1
0
0
0
1
0
5
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
1
0
2
0
0
3
0
0
0
0
1
2
0
1
0
0
1
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
2
2
0
0
0
2
0
0
0
0
0
2
0
1
0
0
1
2
2
1
0
2
0
2
2
0
1
0
1
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
2
0
2
0
0
1
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
3
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
1
1
0
2
0
2
0
0
0
0
2
0
2
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
1
0
1
2
1
2
2
0
0
0
1
4
0
0
0
1
0
0
0
0
0
0
0
1
1
0
2
0
0
0
1
1
0
1
0
0
0
1
1
0
2
2
0
3
0
0
0
0
1
0
0
0
0
0
0
0
2
4
0
2
1
0
1
1
1
0
1
0
2
0
0
0
0
3
0
0
1
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
1
0
0
2
0
0
0
1
0
0
3
1
1
0
1
2
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
2
4
0
2
2
0
0
0
2
0
0
1
0
0
2
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
1
0
0
2
2
2
0
0
1
2
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
2
2
0
0
2
2
1
0
0
1
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
6
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
2
0
0
1
1
0
0
0
1
1
0
0
6
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
2
0
0
1
0
0
0
2
0
2
2
2
2
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
2
1
0
2
1
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
2
0
0
1
0
1
0
0
0
0
2
3
0
0
0
2
1
0
0
0
0
0
0
2
0
0
1
0
1
2
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
2
1
2
0
5
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
1
0
0
0
2
0
2
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
2
0
2
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
2
0
0
0
2
0
0
0
5
0
0
0
2
2
1
2
0
2
0
0
0
0
0
2
1
0
2
0
2
0
2
0
0
0
0
1
0
0
0
0
1
2
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
1
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
1
0
1
0
0
0
1
1
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
2
0
0
1
1
0
0
2
0
0
2
2
2
2
0
1
0
0
2
2
2
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
3
7
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
1
1
3
0
0
0
0
2
0
0
0
0
1
2
1
0
1
0
2
0
1
0
0
2
0
0
1
2
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
7
0
0
0
0
0
0
2
1
0
0
2
0
2
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
1
2
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
1
0
2
1
1
1
0
0
4
0
0
0
2
0
0
1
2
1
0
0
1
2
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
2
0
0
2
0
2
0
2
1
0
0
2
0
0
0
0
2
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
1
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
1
0
0
0
1
2
0
2
1
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
2
1
0
0
1
0
0
0
0
0
1
0
0
1
0
2
1
0
0
0
0
0
1
1
0
2
0
0
0
2
0
2
2
2
1
0
0
0
1
0
1
2
0
0
1
1
1
1
2
1
3
0
0
0
0
0
4
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
1
0
1
0
0
0
2
1
0
4
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
2
2
0
2
2
0
0
2
0
0
0
0
1
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
2
1
0
0
2
0
1
2
1
1
0
0
2
0
0
0
2
0
2
1
0
0
1
1
0
5
2
0
2
0
0
0
2
2
0
0
1
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
2
0
1
1
2
0
2
0
1
0
0
0
2
2
0
0
1
0
2
0
0
0
0
2
0
1
3
0
0
2
1
1
0
0
1
1
2
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
2
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
1
0
0
2
1
0
0
3
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
2
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
2
2
0
0
0
1
0
1
2
1
0
4
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
1
4
2
2
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
2
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
3
2
0
0
2
0
0
1
0
0
0
0
0
0
0
3
0
1
0
0
0
1
1
2
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
1
1
1
0
0
0
0
0
0
2
2
0
2
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
2
0
2
1
1
2
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
2
2
0
0
0
0
2
3
2
0
1
1
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
1
1
0
0
1
1
1
2
0
0
0
0
0
0
0
1
0
0
1
2
1
2
1
0
1
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
2
1
0
2
3
0
0
1
2
0
2
0
0
0
2
1
2
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
1
2
1
0
0
2
0
0
1
1
2
0
0
0
0
0
1
0
0
1
0
0
3
0
0
5
0
2
0
2
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
1
2
0
1
6
0
0
0
0
2
0
0
0
4
0
0
1
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
2
0
1
0
1
0
1
0
0
0
0
0
1
0
1
2
1
0
0
0
2
0
0
0
0
0
1
0
0
5
0
1
0
2
2
2
0
1
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
2
0
2
1
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
1
0
3
0
0
0
0
0
0
1
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
2
2
2
2
0
2
0
0
0
0
1
0
0
0
2
0
7
0
0
3
0
0
0
0
3
0
0
0
1
0
0
0
2
0
2
0
1
0
0
0
1
2
2
0
0
0
0
0
0
3
0
1
0
0
0
1
0
0
2
2
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
2
2
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
1
0
2
2
0
2
0
2
2
0
1
0
0
2
1
0
0
0
1
2
1
0
0
1
1
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
2
0
0
0
0
2
0
2
2
2
0
1
0
0
3
0
5
0
0
0
3
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
2
0
2
1
0
3
0
2
0
2
1
0
0
0
0
2
0
0
0
0
2
3
0
2
0
3
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
1
0
2
1
0
1
2
2
3
0
0
0
0
0
0
2
0
0
1
0
8
1
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
1
0
1
0
2
0
0
0
2
0
0
0
0
0
0
2
0
3
0
0
0
2
0
3
2
0
0
0
1
2
1
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
3
0
0
0
0
1
0
2
0
2
2
0
0
2
1
0
1
0
1
0
1
1
0
1
0
2
2
0
0
0
0
0
0
0
2
2
0
0
3
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
2
0
0
3
0
1
1
0
0
1
0
0
0
0
7
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
1
0
1
0
0
4
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
1
2
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
2
0
0
1
3
0
0
0
0
2
0
0
0
1
0
2
2
0
1
0
1
0
0
0
3
0
3
0
0
0
0
0
0
3
2
2
1
3
2
0
0
0
3
0
0
0
3
0
0
0
1
1
2
1
2
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
2
2
2
0
0
2
0
0
1
0
1
2
2
0
1
0
0
0
2
0
0
1
0
0
0
2
0
2
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
1
0
0
0
0
1
0
2
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
1
1
2
0
0
0
0
0
1
1
0
0
0
0
1
0
1
2
2
0
0
5
1
2
0
0
1
0
0
0
1
0
1
1
1
1
1
2
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
2
1
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
2
1
0
1
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
1
0
3
0
2
0
0
0
1
0
0
0
2
0
0
1
0
0
2
0
0
0
1
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
5
0
0
0
0
2
2
1
1
1
0
3
0
0
0
1
0
0
0
0
2
1
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
5
0
0
0
2
2
0
2
3
0
1
2
2
0
0
0
0
0
2
0
2
0
1
1
6
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
3
0
3
1
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
6
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
2
0
0
2
0
0
3
0
0
1
0
1
0
0
0
1
1
2
0
0
0
1
0
0
0
1
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
2
0
1
0
0
0
1
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
4
2
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
2
1
1
0
1
0
0
1
0
0
0
0
0
0
0
2
0
2
1
0
11
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
2
1
1
0
0
0
0
0
0
0
2
0
2
0
1
1
0
1
2
0
0
0
0
2
0
0
2
0
0
0
1
0
0
1
0
2
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
3
1
0
0
0
1
0
0
1
0
2
0
0
1
1
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
1
1
0
4
2
0
0
0
0
0
0
2
1
1
0
1
0
0
1
0
0
0
2
0
0
8
0
0
0
0
0
0
2
0
0
1
1
0
0
2
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
3
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
2
0
0
0
0
2
1
0
0
0
2
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
1
0
0
0
2
2
2
0
0
0
0
0
0
0
0
1
3
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
2
2
0
2
0
0
0
1
2
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
2
1
1
0
0
2
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
2
0
2
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
1
3
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
2
0
1
1
0
2
0
0
1
2
2
0
1
0
0
0
0
2
1
1
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
1
0
0
1
2
0
4
2
0
0
0
2
0
0
0
0
2
0
0
0
1
4
2
2
0
0
0
1
0
1
1
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
1
1
2
0
2
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
2
0
1
1
0
1
0
0
3
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
2
1
0
0
1
2
0
0
0
0
0
0
2
1
2
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
2
0
2
0
0
0
2
0
0
1
1
0
2
0
0
2
2
0
0
0
1
0
4
2
0
2
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
2
2
1
0
1
0
0
1
1
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
1
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
1
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
1
1
0
0
2
0
0
3
1
1
0
0
1
3
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
3
0
2
0
1
0
0
0
1
1
0
2
0
1
1
2
0
0
0
0
0
1
0
0
1
2
2
0
2
1
1
0
0
0
0
1
1
3
0
2
1
0
0
0
0
1
0
2
1
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
1
1
1
0
0
1
0
0
3
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
3
0
0
2
0
0
0
0
0
1
0
0
0
0
1
2
0
1
0
0
1
0
0
1
0
0
0
0
0
2
2
1
0
0
1
0
2
0
0
1
0
0
0
0
1
1
1
1
2
0
0
0
0
3
2
0
1
0
0
3
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
3
0
2
0
1
0
0
1
2
0
0
0
0
2
0
0
0
0
0
2
1
1
2
0
0
0
0
0
2
0
0
0
2
0
0
2
0
2
0
0
1
0
0
0
0
2
2
0
2
0
0
0
1
0
0
0
0
2
2
0
1
1
0
1
0
0
1
1
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
2
0
1
0
0
0
2
0
0
2
1
2
1
1
1
0
2
2
1
1
1
2
0
0
2
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
2
3
0
0
2
0
0
2
0
0
0
1
0
0
0
2
0
0
1
0
0
1
0
2
0
1
0
1
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
1
1
0
2
0
0
2
2
0
2
0
0
0
0
0
4
0
0
2
1
0
0
0
0
2
0
4
1
3
0
0
0
0
2
0
0
1
0
2
0
4
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
2
0
2
0
1
2
0
3
0
0
0
2
0
0
1
0
0
1
0
1
0
0
1
0
2
0
0
0
0
0
1
0
0
1
1
0
0
0
3
0
2
0
0
1
0
0
0
1
2
0
0
1
0
1
0
0
2
0
1
2
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
1
2
1
2
0
2
0
0
0
2
0
0
2
0
0
3
2
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
1
1
0
2
0
2
0
2
0
0
0
2
0
1
1
1
0
1
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
1
1
1
0
0
2
2
0
0
0
0
1
0
0
2
0
0
1
1
0
0
0
0
2
2
2
0
0
0
3
0
0
0
0
0
2
2
0
1
0
2
1
1
0
0
0
0
1
0
2
1
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
1
0
1
0
1
0
2
0
1
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
2
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
2
2
0
0
2
0
0
0
0
0
0
1
2
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
2
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
3
1
1
2
0
2
0
1
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
1
1
2
0
0
0
0
1
2
1
0
0
2
2
0
1
0
3
2
1
0
0
0
0
0
0
0
0
0
0
0
4
3
0
1
0
0
2
0
2
0
0
1
0
0
0
1
2
2
0
0
2
0
0
0
0
3
1
2
0
0
2
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
3
2
2
0
0
1
3
0
0
0
0
1
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
2
1
0
0
1
0
0
0
2
0
2
0
0
4
0
2
0
0
0
0
0
1
0
0
0
0
1
0
1
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
1
1
0
0
1
0
0
0
1
0
4
0
0
0
0
0
2
1
1
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
6
4
0
0
0
2
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
2
0
0
0
0
1
0
1
2
0
0
0
0
0
1
2
0
2
0
0
2
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
9
0
1
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
3
0
0
1
2
2
0
0
0
1
0
1
0
2
0
0
0
1
0
0
0
2
0
2
1
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
1
2
1
2
0
0
2
0
0
0
1
0
1
0
0
0
2
0
1
0
1
0
0
1
2
0
2
0
2
0
1
0
0
0
1
2
0
2
2
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
2
1
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
1
0
0
0
3
1
1
0
0
4
0
0
0
2
2
2
0
0
0
0
6
0
0
0
0
0
0
0
2
2
0
2
1
0
1
1
0
0
2
0
0
0
0
0
0
1
0
0
2
2
0
2
0
0
0
1
0
0
0
1
1
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
3
0
2
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
4
1
1
0
0
0
0
0
1
1
0
0
2
3
0
2
0
1
0
2
2
0
0
0
0
1
0
0
0
1
1
2
1
2
2
2
3
1
0
2
0
0
0
0
0
1
2
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
3
1
0
1
1
1
0
1
0
1
0
0
2
1
2
0
0
0
0
2
0
0
0
4
2
1
0
1
1
0
2
0
0
3
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
3
1
0
0
2
2
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
4
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
1
1
1
1
1
0
0
0
1
2
1
1
1
0
0
3
0
0
0
1
1
3
0
4
0
2
2
0
0
1
0
1
0
0
1
2
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
2
0
2
0
0
2
0
0
0
0
2
1
0
0
3
1
0
0
0
0
2
2
1
1
3
2
0
2
0
2
0
0
2
0
0
0
2
0
0
2
1
2
1
2
0
0
0
2
2
0
3
2
0
0
1
0
0
0
0
5
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
2
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
2
1
1
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
1
2
0
1
0
4
0
3
0
2
0
1
0
0
0
2
0
1
0
0
1
0
3
1
0
0
0
1
4
0
0
0
1
0
2
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
2
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
1
1
1
1
1
2
0
2
2
1
0
0
2
2
1
0
0
0
0
0
0
0
2
0
0
3
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
2
0
0
0
0
0
0
0
2
0
0
2
1
2
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
1
0
0
0
1
1
1
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
3
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
2
1
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
1
0
2
0
2
1
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
3
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
2
0
0
0
2
0
2
0
2
0
1
0
1
2
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
3
5
0
0
2
1
0
0
1
0
2
1
0
0
2
2
1
0
0
1
1
2
0
2
0
0
2
0
1
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
2
0
2
1
0
1
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
3
0
0
0
1
0
0
1
0
2
3
0
0
0
1
2
0
0
2
0
1
0
0
2
0
1
5
0
1
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
1
3
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
4
0
2
0
0
0
0
2
0
1
0
2
6
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
2
0
0
0
0
3
0
0
2
0
1
1
0
1
0
0
0
1
0
0
0
0
2
1
2
1
0
0
1
2
0
0
0
0
0
0
0
1
0
2
1
1
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
2
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
2
0
0
4
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
1
0
2
2
0
0
1
0
0
0
4
0
0
2
0
0
0
0
0
1
0
2
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
3
0
0
1
2
0
0
1
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
2
0
1
0
0
0
0
1
0
0
0
1
0
3
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
3
0
0
0
1
0
0
2
0
0
0
0
1
0
0
2
0
0
1
0
1
3
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
1
0
1
0
0
1
0
0
0
2
0
0
2
2
2
1
0
1
0
0
2
1
0
2
1
1
1
0
1
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
2
2
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
2
0
1
2
0
1
0
0
1
2
0
1
1
0
0
0
0
0
0
0
2
3
2
0
0
0
0
0
1
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
2
0
2
0
0
0
0
2
2
2
2
2
0
0
1
2
1
2
0
0
0
0
1
2
0
0
1
0
0
0
2
1
1
0
1
0
0
1
0
0
1
0
1
2
2
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
3
0
2
0
0
0
0
0
4
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
3
0
0
0
0
0
6
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
2
1
2
0
2
3
1
0
0
1
0
0
3
0
0
0
0
0
2
0
2
0
3
1
0
2
0
3
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
2
1
1
1
0
0
0
0
0
0
2
0
0
0
0
0
4
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
3
0
0
0
0
1
1
0
0
0
0
2
1
0
2
2
0
0
1
0
0
0
1
3
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
1
1
1
0
0
1
0
2
1
0
0
0
1
1
2
0
0
1
0
2
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
2
0
0
0
0
0
3
0
0
0
1
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
1
1
2
1
0
0
0
0
0
7
0
0
0
2
2
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
1
3
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
1
0
0
0
0
2
1
0
0
2
0
3
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
1
2
2
0
1
0
0
1
0
1
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
3
0
3
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
1
0
0
1
0
0
0
0
1
1
0
0
0
0
2
0
1
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
1
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
4
1
0
0
0
1
0
2
0
0
1
0
1
0
0
0
1
0
2
2
0
4
0
2
0
0
0
1
2
0
1
0
0
2
1
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
2
0
0
2
1
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
3
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
1
0
2
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
1
1
2
0
2
2
0
0
0
1
0
0
0
1
2
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
1
0
2
0
0
0
1
1
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
2
1
2
0
2
0
2
0
0
3
0
0
2
0
0
0
1
0
0
0
0
1
2
1
0
2
1
0
0
0
0
0
0
0
1
0
0
5
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
1
1
2
1
0
2
0
0
2
2
0
0
0
0
2
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
1
0
1
3
2
2
0
1
0
0
0
0
0
1
1
0
0
2
0
1
0
0
2
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
1
2
0
0
3
0
2
1
1
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
1
2
0
2
0
0
0
0
0
0
2
1
0
1
0
1
1
0
0
0
0
7
0
1
0
2
3
0
0
4
1
1
1
0
0
0
3
1
0
2
0
0
1
1
1
1
0
2
1
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
3
2
2
0
1
0
1
1
0
2
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
2
1
1
1
0
0
2
0
0
2
0
0
1
1
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
2
1
0
0
2
2
0
2
0
2
0
0
0
2
2
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
2
0
1
0
0
0
0
0
0
6
0
0
0
0
0
0
1
0
1
1
0
3
0
0
2
0
0
0
0
0
1
0
0
1
2
1
0
0
2
0
0
0
0
0
1
2
0
1
0
0
0
2
0
0
0
0
2
1
0
1
0
0
0
0
1
0
0
1
2
0
0
1
2
0
0
0
0
1
0
0
1
1
0
0
0
0
3
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
5
0
0
0
0
0
4
0
0
0
0
0
2
1
0
2
2
2
0
2
0
0
0
7
0
0
0
0
0
0
1
0
0
0
1
0
0
4
0
0
0
1
0
1
0
0
0
0
0
1
0
0
2
1
0
0
1
1
1
2
2
2
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
4
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
3
2
0
0
2
0
2
2
0
0
0
2
2
2
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
1
1
1
0
0
0
2
0
0
2
0
0
1
0
0
3
0
2
0
0
2
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
1
1
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
1
0
0
1
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
3
0
0
0
0
0
0
4
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
1
0
0
1
2
0
2
1
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
2
2
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
3
0
0
0
2
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
2
1
0
0
0
2
0
1
0
3
0
0
2
2
2
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
3
1
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
2
2
1
0
1
0
0
0
0
2
0
2
2
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
2
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
1
0
1
0
1
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
2
1
1
0
0
0
2
3
1
2
0
0
1
9
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
4
0
0
4
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
2
2
1
0
0
1
0
0
0
3
0
2
0
2
2
2
2
0
0
0
2
1
0
0
0
0
0
2
2
0
0
1
2
0
0
0
0
0
0
0
1
2
0
0
0
0
2
1
2
0
2
1
0
0
0
0
0
2
0
0
3
2
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
3
1
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
2
0
0
0
0
1
1
0
0
1
1
0
0
0
1
2
1
0
1
2
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
2
1
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
1
2
0
0
0
0
0
0
2
0
0
2
0
0
1
1
0
0
2
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
2
2
1
0
0
2
1
3
0
0
1
0
0
0
1
0
2
0
0
0
0
0
2
0
0
2
0
2
2
0
1
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
1
0
1
0
0
2
1
0
0
0
0
0
0
1
0
4
2
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
2
0
0
0
4
0
2
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
6
0
3
1
0
0
1
0
0
1
0
2
0
3
2
0
0
0
2
1
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
1
2
1
2
2
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
2
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
1
0
0
0
5
2
1
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
2
0
1
0
0
2
2
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
2
2
0
0
0
1
0
0
1
0
0
0
1
0
0
1
2
0
0
0
1
1
1
2
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
1
0
2
3
2
0
2
0
0
2
0
1
1
2
0
0
1
0
0
1
0
2
2
2
0
0
2
0
2
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
1
2
3
0
2
0
0
0
1
0
0
0
0
0
0
3
0
0
1
1
1
2
0
0
0
0
0
1
0
3
0
0
0
0
0
0
2
0
0
0
2
7
1
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
2
2
0
3
0
1
2
0
0
0
3
1
0
1
2
0
0
0
1
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
2
1
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
2
2
0
0
0
0
0
0
2
0
2
0
0
0
1
2
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
2
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
2
0
2
0
0
1
0
0
0
2
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
1
0
2
2
0
0
2
2
0
0
0
1
1
2
1
1
0
0
0
0
2
2
1
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
3
0
0
0
2
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
3
0
0
0
0
0
0
2
2
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
2
2
0
0
2
2
0
0
0
0
0
2
0
0
2
1
2
1
0
1
0
2
0
0
0
1
0
0
0
2
0
0
0
2
0
1
0
0
0
0
3
1
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
1
2
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
2
1
0
2
0
0
2
2
0
0
0
0
0
1
0
2
0
1
0
0
0
1
0
3
0
0
0
2
2
0
3
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
2
1
1
1
0
1
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
3
2
2
0
2
0
2
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
1
1
2
1
1
0
0
2
0
0
0
0
1
1
0
0
3
0
0
2
1
2
0
0
1
0
0
0
1
0
0
0
0
0
0
2
2
0
0
1
0
0
0
1
0
0
1
2
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
8
0
0
0
1
1
0
1
2
0
0
2
0
0
0
0
0
2
0
2
1
0
1
0
0
0
0
1
1
0
2
0
0
3
3
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
1
1
0
0
0
1
2
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
3
0
1
0
0
2
0
0
0
1
0
0
0
1
0
0
1
0
2
0
2
1
2
1
0
0
0
0
0
5
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
3
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
1
1
3
0
0
0
1
0
0
1
0
3
0
1
1
0
1
1
0
2
2
1
0
0
1
1
2
0
0
0
1
0
0
1
0
0
0
1
0
2
1
0
2
3
0
1
2
0
0
2
0
0
0
0
0
0
2
0
1
2
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
2
1
0
2
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
1
1
3
0
0
0
0
0
0
0
1
0
1
0
1
0
0
2
0
1
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
4
0
4
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
1
0
1
1
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
1
0
2
0
0
1
0
1
0
1
2
0
2
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
1
2
2
0
0
0
0
0
3
0
2
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
5
0
1
0
3
2
0
0
0
0
0
0
0
0
3
0
1
0
0
2
0
0
1
0
2
2
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
1
2
1
0
0
0
0
0
0
1
0
0
1
2
2
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
4
0
0
1
0
0
0
2
0
1
0
0
0
1
0
3
1
0
0
1
0
0
0
2
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
2
0
0
1
0
4
0
2
0
0
0
0
0
0
1
0
2
0
2
2
0
0
0
0
0
0
0
9
0
2
0
0
0
2
0
0
0
1
1
1
0
2
1
1
1
0
0
0
2
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
1
0
0
0
2
0
0
2
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
2
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
1
0
1
2
0
2
1
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
3
0
0
0
1
0
2
3
0
2
0
0
3
0
0
1
0
1
0
0
0
1
0
0
0
0
0
2
2
0
0
2
3
0
0
0
0
0
0
0
1
1
2
0
0
0
0
2
2
0
0
2
0
0
0
0
2
0
0
0
0
3
0
0
1
0
0
1
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
2
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
2
0
0
0
0
2
1
0
1
3
0
0
0
1
0
0
0
4
3
1
0
2
0
1
0
0
0
1
5
1
0
0
0
0
1
0
1
0
0
0
2
0
1
2
0
0
1
1
0
1
0
0
0
0
0
0
3
1
0
0
1
2
0
2
0
0
1
0
0
3
0
0
2
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
1
0
5
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
3
0
2
3
0
1
0
0
0
0
0
2
0
0
0
0
2
1
3
1
0
2
0
0
2
2
0
0
2
0
0
1
1
0
0
0
0
1
2
1
1
1
0
1
0
0
0
3
0
2
3
0
0
0
0
2
0
0
0
0
2
1
3
0
0
0
0
1
2
0
0
2
0
1
2
1
1
2
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
2
1
2
1
0
2
0
4
3
1
0
2
0
2
0
1
0
2
2
0
0
0
1
0
0
1
0
0
0
1
3
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
1
3
1
0
2
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
1
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
2
0
3
2
0
0
1
0
1
0
1
0
0
3
0
6
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
2
0
2
0
2
0
1
0
2
0
0
0
0
0
0
1
1
0
0
1
0
0
2
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
10
2
1
0
0
2
2
0
0
0
2
3
0
0
0
0
0
3
1
0
0
0
1
0
0
0
0
0
2
0
2
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
1
1
3
1
2
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
2
2
0
0
0
0
0
0
1
2
0
2
2
0
3
0
0
1
0
2
0
1
2
0
1
5
1
1
2
1
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
1
2
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
3
1
0
2
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
2
0
0
1
1
0
0
0
0
0
1
0
0
4
0
0
0
0
0
2
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
1
0
2
1
0
2
1
0
0
0
0
0
0
3
0
0
1
0
2
2
0
0
2
0
0
0
0
3
0
0
0
0
2
1
1
0
2
2
0
0
0
0
0
0
0
0
0
2
5
0
2
3
0
0
0
2
1
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
1
2
0
0
0
1
0
0
0
1
0
2
1
0
1
1
0
0
1
3
0
0
0
1
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
3
0
1
1
0
0
0
0
0
0
0
3
0
0
0
2
3
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
2
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
2
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
2
1
0
0
1
0
1
0
0
0
0
0
0
0
3
0
0
0
0
4
1
0
0
0
1
2
0
0
2
0
0
1
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
7
0
1
2
2
2
0
0
0
3
0
2
2
0
2
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
1
0
0
1
0
0
0
0
0
1
3
0
2
0
0
1
0
1
1
2
0
1
2
0
0
0
1
0
4
0
0
0
3
0
2
0
2
0
1
2
0
0
0
0
0
0
2
2
2
1
0
1
0
2
1
0
0
1
1
0
1
2
1
0
0
2
0
0
0
1
0
0
0
0
2
0
0
2
0
0
1
0
1
2
2
0
2
0
0
0
0
0
0
0
2
3
2
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
3
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
7
0
0
0
0
2
0
0
0
2
2
1
1
0
0
1
0
0
2
0
0
2
2
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
1
1
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
1
0
0
2
1
0
0
2
0
0
0
0
1
0
0
1
1
0
0
1
0
2
0
2
0
0
0
3
1
0
0
1
0
0
1
0
0
2
3
4
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
4
0
2
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
2
0
0
1
2
2
0
1
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
1
0
0
0
0
3
2
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
1
0
2
0
1
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
1
0
2
0
0
5
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
1
2
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
1
1
0
0
0
1
0
0
2
0
0
1
1
0
0
1
0
2
0
2
0
0
2
2
0
2
0
0
0
0
2
0
0
2
3
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
1
1
1
2
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
2
2
1
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
3
0
0
1
0
0
0
0
2
0
0
0
1
0
1
0
2
1
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
1
0
0
1
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
4
0
5
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
1
2
2
0
1
0
0
0
3
2
2
2
2
4
0
0
0
1
0
0
2
0
0
0
7
0
0
0
2
0
1
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
2
1
0
0
0
1
2
0
1
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
2
2
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
2
0
1
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
1
0
2
1
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
2
0
1
0
1
1
0
0
1
0
0
10
0
1
0
1
0
0
1
0
1
0
1
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
2
1
2
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
1
0
0
0
4
0
0
0
3
0
0
0
1
2
0
0
0
2
0
0
0
2
1
0
2
0
0
2
0
2
0
0
0
1
0
0
0
2
1
0
0
0
2
2
4
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
2
0
0
2
0
1
1
1
0
0
1
0
2
0
2
0
1
1
2
0
1
2
0
0
0
0
0
0
1
0
1
0
1
2
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
3
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
1
2
0
1
0
1
1
0
1
0
0
1
0
2
0
3
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
2
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
6
0
1
0
2
2
0
0
0
0
2
0
0
0
2
0
0
1
2
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
2
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
2
0
0
0
0
2
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
5
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
3
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
1
0
0
1
1
0
2
0
0
2
0
0
1
0
1
2
0
1
0
0
0
0
0
1
1
0
2
0
0
0
1
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
1
0
0
6
0
0
2
0
0
1
0
0
0
1
0
2
0
1
1
3
0
0
1
0
0
0
1
1
0
2
0
0
1
1
0
0
0
2
0
0
0
0
0
1
0
1
0
1
2
0
0
0
1
0
1
0
1
1
1
0
0
0
2
2
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
1
0
2
2
0
0
0
0
0
0
0
0
0
1
0
2
2
3
2
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
1
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
1
0
1
0
0
2
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
2
1
0
0
1
8
2
3
2
2
0
0
0
0
2
0
0
0
6
0
2
2
0
0
0
1
0
0
2
0
2
0
0
0
1
4
2
0
1
0
0
1
1
1
1
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
2
3
0
1
0
0
1
0
0
0
1
0
1
0
2
0
0
0
0
2
0
0
2
0
0
1
0
0
1
0
1
0
2
0
0
1
0
0
2
3
0
1
1
0
0
9
2
0
0
0
1
0
0
3
2
0
0
0
1
0
0
0
2
3
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
2
2
0
0
0
5
1
0
1
0
0
1
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
1
1
1
0
1
0
1
1
0
0
2
0
1
0
0
1
2
1
2
2
0
0
0
0
1
0
0
1
1
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
2
2
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
3
0
1
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
1
2
3
3
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
1
0
1
0
1
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
2
0
2
0
2
2
0
1
0
0
0
0
0
2
0
0
0
1
0
1
0
0
2
2
0
0
0
0
0
0
2
2
0
0
0
3
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
3
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
1
1
0
0
0
1
0
0
2
0
0
0
0
0
2
0
2
2
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
1
1
0
2
0
0
2
2
0
0
0
0
0
2
2
0
1
1
1
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
2
0
0
1
0
2
2
0
0
2
0
0
1
0
0
3
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
1
1
0
1
1
2
1
1
2
2
0
0
2
2
0
0
1
0
2
2
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
1
0
0
1
1
0
0
1
2
2
0
2
1
0
0
0
0
0
2
0
2
0
1
0
0
1
0
0
1
1
0
0
1
0
1
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
3
2
2
0
1
3
2
0
0
0
0
1
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
1
2
0
0
2
0
0
0
0
0
0
0
2
2
1
2
0
1
1
0
0
1
1
0
2
0
0
0
0
1
0
0
0
0
1
1
2
1
0
0
1
2
0
1
1
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
1
0
2
0
2
0
2
0
0
0
0
2
0
0
2
0
0
1
0
0
2
2
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
1
1
0
0
0
0
2
0
2
1
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
3
2
1
2
0
1
0
0
0
2
1
6
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
2
0
1
0
0
1
0
0
0
0
2
0
1
0
0
3
1
1
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
2
0
1
0
1
3
2
2
2
4
0
0
0
2
0
0
1
1
2
0
0
3
0
3
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
3
1
1
0
1
2
1
2
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
2
2
0
1
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
2
0
2
0
2
2
1
0
0
3
0
2
0
0
0
0
0
1
2
0
1
0
0
2
0
2
2
0
0
0
1
2
0
0
0
0
0
0
2
0
0
1
2
0
0
1
1
2
0
0
0
0
0
0
2
0
0
0
0
0
1
1
1
0
0
2
0
0
0
0
1
2
0
0
0
2
0
1
2
0
0
2
0
1
0
0
1
5
2
1
0
1
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
3
1
0
0
0
0
0
0
2
1
1
2
0
1
0
2
0
1
0
1
0
0
0
1
0
2
1
0
0
1
0
0
1
1
1
0
0
0
1
2
0
0
2
0
2
0
0
0
2
2
1
4
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
2
2
0
0
0
2
1
0
0
0
0
1
0
0
0
1
2
0
0
2
0
0
1
0
0
0
1
0
0
1
0
2
2
2
0
0
0
2
2
1
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
1
2
0
1
0
2
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
1
1
0
0
1
0
2
2
0
0
0
2
1
1
0
2
1
2
0
0
0
0
0
1
1
0
2
1
1
0
3
0
1
0
2
0
2
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
2
0
0
0
5
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
1
1
0
2
0
0
0
0
0
0
1
0
0
2
2
3
0
0
1
0
1
0
1
0
1
0
0
0
0
3
0
0
2
0
3
2
0
0
2
1
0
1
1
1
0
0
0
1
0
1
0
0
0
0
0
2
2
0
1
0
0
0
0
0
1
1
0
1
1
1
0
0
0
2
2
0
0
0
0
2
0
1
2
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
2
4
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
1
2
2
0
0
2
0
0
1
0
0
0
0
0
4
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
2
0
2
3
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
1
0
0
0
1
4
0
0
1
0
0
0
1
2
2
1
0
0
2
0
0
0
0
0
3
0
1
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
2
2
2
0
1
0
0
0
0
3
1
0
0
0
2
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
1
0
0
4
0
0
3
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
2
0
0
2
2
1
2
0
0
0
1
0
0
0
0
0
1
0
0
2
3
0
0
0
0
0
1
2
1
0
0
2
0
2
0
0
2
0
0
0
2
0
2
1
1
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
1
0
0
4
0
0
0
0
0
0
1
2
0
0
0
1
0
0
1
3
0
1
0
2
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
1
0
0
0
5
2
0
0
1
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
2
0
2
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
1
2
0
0
1
0
1
2
0
1
1
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
2
0
1
2
0
3
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
3
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
3
0
0
0
0
2
0
2
0
2
0
1
0
0
0
0
1
2
1
0
0
2
0
2
0
2
2
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
2
0
3
1
0
0
0
1
3
0
1
0
2
0
0
0
0
0
2
2
0
1
3
1
0
2
0
0
2
0
2
0
1
0
1
2
0
0
1
2
2
0
0
0
2
1
0
2
0
1
0
0
1
1
1
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
1
0
0
3
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
2
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
3
0
1
0
0
1
0
0
0
0
0
0
0
1
0
2
1
1
2
3
2
3
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
1
2
0
0
2
2
0
0
0
0
1
0
0
0
1
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
1
1
2
2
0
2
2
0
2
0
1
2
0
0
0
0
2
0
0
2
0
2
0
1
2
0
0
1
0
1
2
0
0
0
2
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
2
0
0
0
5
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
2
2
0
2
2
0
0
2
2
0
0
1
0
0
1
1
0
1
1
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
1
0
1
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
1
2
0
0
1
1
0
3
0
2
0
2
0
0
0
0
2
2
0
0
0
0
7
0
0
0
1
0
0
0
0
2
0
3
0
0
1
0
0
0
1
3
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
1
0
3
2
0
0
0
0
2
2
2
0
0
0
1
0
2
1
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
2
1
2
1
2
0
1
0
1
0
0
0
0
0
3
2
2
0
0
3
0
0
0
1
1
0
1
0
0
0
0
2
0
0
2
0
1
0
1
2
0
0
2
0
0
3
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
2
2
0
0
0
0
0
2
1
2
0
1
2
1
1
0
1
0
1
0
0
0
0
0
1
0
2
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
2
2
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
5
0
1
0
0
1
2
0
0
0
2
0
2
0
0
2
1
1
1
0
4
0
2
0
2
0
0
0
0
1
0
0
1
2
0
0
0
1
0
0
0
0
2
0
2
1
0
1
1
0
0
0
1
0
0
0
0
2
1
0
1
2
0
2
0
1
0
1
0
0
2
1
1
0
2
0
0
0
1
0
0
1
0
0
0
1
2
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
2
2
0
0
0
0
0
0
0
1
1
2
0
0
0
1
1
0
0
3
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
2
0
2
0
0
2
2
0
0
0
0
0
0
0
0
3
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
1
6
0
0
0
1
4
0
0
0
0
0
0
2
0
0
0
0
2
0
2
1
0
0
0
0
0
0
2
0
1
0
0
4
2
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
4
0
1
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
3
4
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
1
2
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
5
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
4
0
0
1
0
1
2
0
0
0
0
0
0
0
9
0
2
0
0
5
0
0
0
0
0
0
2
0
0
0
0
1
3
0
0
0
0
0
0
1
0
1
1
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
1
0
0
0
2
0
3
0
0
0
3
0
0
4
0
0
2
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
2
0
1
1
1
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
1
0
1
2
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
3
2
2
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
3
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
3
1
1
1
2
0
1
0
0
2
1
1
0
0
1
0
0
0
2
0
0
0
0
2
0
1
0
0
0
3
0
2
0
2
1
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
3
0
2
2
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
1
2
0
1
0
2
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
2
1
2
0
1
0
0
2
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
4
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
2
1
1
0
0
2
0
5
1
0
0
0
0
1
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
2
0
0
0
2
1
0
2
0
1
1
0
0
2
0
0
0
0
0
0
0
3
0
0
2
1
0
0
2
0
2
1
4
0
0
0
2
0
1
0
2
0
1
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
3
0
2
0
0
0
3
0
2
0
2
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
2
0
2
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
1
1
0
1
0
0
0
2
1
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
2
2
2
0
1
0
1
2
0
0
0
0
2
1
0
2
1
0
1
1
0
0
0
1
1
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
2
3
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
6
0
1
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
1
1
0
0
2
0
0
1
0
0
2
1
1
0
1
1
2
1
1
0
0
2
1
1
0
0
2
0
1
0
2
1
1
0
2
0
2
0
0
0
0
0
0
0
1
2
1
2
2
2
0
1
0
0
0
2
1
1
1
0
1
1
0
1
2
2
1
2
1
0
0
2
2
0
0
2
0
0
0
2
1
2
2
0
0
5
0
0
2
0
3
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
3
0
1
0
2
0
0
0
0
0
0
0
1
1
0
2
0
0
1
0
0
1
2
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
4
5
0
0
0
3
1
1
1
1
0
1
1
1
0
2
0
0
0
1
0
0
1
0
1
0
1
0
6
0
0
0
0
0
0
1
0
0
1
1
2
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
3
0
0
0
0
0
0
2
2
0
0
0
0
1
1
0
0
0
2
0
1
0
2
1
0
2
1
0
0
0
0
0
2
1
0
2
2
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
2
1
0
0
2
0
0
1
0
1
0
3
1
2
0
2
2
2
0
0
0
0
1
0
0
0
1
2
0
0
1
0
1
2
1
0
2
0
2
0
2
0
0
1
0
1
3
0
0
0
0
2
0
2
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
2
0
0
1
0
0
2
2
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
1
2
0
0
0
0
2
0
0
3
3
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
2
0
1
0
0
0
2
2
0
0
2
0
0
1
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
1
1
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
3
1
0
0
0
0
2
0
0
0
0
1
0
0
0
1
2
0
0
0
0
2
1
1
0
0
0
2
0
0
2
0
0
0
0
0
1
0
1
2
2
0
0
2
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
2
1
0
0
2
1
2
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
2
1
0
2
0
0
0
1
0
0
2
0
0
1
0
0
0
2
1
1
1
0
0
4
1
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
2
0
0
2
0
0
2
0
0
0
0
1
0
0
0
1
0
1
0
0
2
0
2
0
0
0
0
2
0
2
0
2
0
0
1
2
0
0
1
0
2
0
1
0
0
0
2
2
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
2
0
1
1
0
0
2
6
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
2
0
1
0
0
0
2
0
0
0
2
0
0
0
2
1
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
3
1
2
0
0
0
0
0
0
0
0
0
1
0
0
2
1
3
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
2
2
2
0
0
0
0
1
1
1
0
0
2
1
0
3
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
2
0
0
2
2
1
0
0
1
0
0
0
1
0
0
0
0
3
0
0
0
0
1
3
0
0
0
0
2
0
0
1
0
2
0
1
0
1
0
1
0
2
0
2
0
0
2
0
2
0
2
0
1
0
1
2
3
0
0
1
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
1
0
0
0
0
0
0
0
2
2
0
0
1
2
0
2
0
2
2
0
0
2
2
0
2
0
0
0
0
2
0
0
0
0
2
1
2
2
3
0
0
2
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
3
0
1
1
1
0
0
1
1
0
0
1
0
0
0
0
2
0
0
0
1
0
0
1
0
0
1
0
0
3
1
0
2
0
0
1
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
3
0
0
4
0
0
1
0
0
2
0
0
1
0
0
1
0
0
2
2
0
2
0
1
0
0
0
0
0
0
2
0
0
0
3
0
0
0
2
0
0
1
0
1
0
0
0
0
0
3
0
0
1
1
0
0
0
2
0
0
0
2
0
0
2
3
0
2
0
0
0
0
3
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
2
1
0
0
0
0
2
0
0
0
1
0
1
0
0
1
5
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
2
0
0
0
0
1
2
0
2
0
1
2
2
1
0
1
0
0
5
2
0
0
0
1
0
0
0
2
2
0
2
0
1
0
0
0
0
0
3
2
2
0
0
0
0
0
0
0
0
0
1
2
0
1
0
1
3
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
3
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
5
0
0
1
0
2
0
0
0
2
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
2
1
1
0
2
0
1
0
2
0
0
2
0
0
2
1
0
0
2
0
2
0
0
0
2
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
2
0
0
0
2
0
2
0
0
0
1
0
0
0
2
2
2
2
0
1
0
0
0
1
2
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
1
0
2
1
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
3
0
0
1
2
3
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
3
0
0
2
0
0
1
0
1
0
0
0
1
0
1
0
0
2
0
0
0
0
1
2
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
2
0
0
1
2
0
1
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
4
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
2
1
0
1
1
1
0
1
0
0
1
0
1
0
0
0
2
1
0
1
0
1
0
0
0
1
0
0
0
0
0
4
0
0
1
0
0
0
0
2
1
0
0
5
0
1
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
3
0
2
0
0
1
0
0
0
0
0
2
2
0
3
0
0
0
3
0
0
0
2
0
2
2
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
3
0
0
0
0
4
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
3
2
1
0
0
1
0
0
0
0
0
1
4
0
0
0
0
0
0
0
1
3
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
2
0
0
1
0
0
0
0
4
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
3
0
2
2
0
0
2
0
0
1
0
0
0
0
0
1
0
2
1
1
0
0
1
2
1
2
0
1
0
2
1
0
0
0
0
2
0
0
0
1
0
2
0
1
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
2
0
1
0
2
0
0
3
0
0
2
0
3
0
0
0
0
2
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
6
0
1
2
1
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
1
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
6
1
0
0
0
0
0
0
0
0
0
3
0
0
2
0
1
0
0
0
1
1
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
1
0
0
0
2
2
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
2
1
1
0
2
0
6
0
0
2
2
2
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
4
0
0
0
0
0
1
0
2
1
0
0
2
0
0
2
0
2
1
0
0
0
2
0
0
0
1
0
0
2
0
0
2
0
2
0
0
2
0
0
2
1
0
0
1
0
0
0
0
1
1
1
0
0
0
0
1
0
0
1
0
1
0
0
2
0
0
2
1
0
0
2
2
1
0
0
0
1
0
1
1
1
2
2
2
2
0
0
0
1
4
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
1
3
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
2
1
0
1
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
1
0
2
0
0
2
2
1
1
1
1
1
2
0
0
1
0
0
0
0
0
0
0
0
1
0
3
0
2
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
3
2
0
0
0
1
0
1
1
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
1
1
0
1
2
1
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
2
0
2
0
0
2
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
2
0
0
0
1
0
0
2
0
0
1
0
2
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
1
3
0
0
2
0
2
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
2
0
2
0
1
0
1
0
0
2
0
2
0
0
3
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
2
1
0
0
2
0
2
0
1
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
3
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
2
2
0
2
0
0
0
1
0
0
0
0
0
0
2
0
2
2
1
2
0
0
1
0
0
2
0
0
0
2
0
2
1
0
1
0
0
1
0
2
2
3
1
1
0
0
2
0
1
1
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
1
1
2
0
0
0
0
0
2
1
1
10
2
0
0
0
0
2
0
4
1
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
1
2
2
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
2
0
2
0
0
0
1
1
1
2
0
2
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
1
0
0
2
0
0
0
2
0
1
1
3
0
0
2
0
1
11
0
0
0
0
0
0
0
0
4
0
3
0
0
0
2
0
1
0
0
0
1
0
2
1
1
0
0
2
1
3
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
1
0
0
1
0
0
1
2
0
1
0
0
0
4
1
2
0
0
1
2
0
1
0
0
1
1
1
0
0
0
1
1
0
3
2
0
0
0
2
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
2
1
0
0
5
0
0
0
1
0
2
0
1
1
0
0
0
0
3
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
1
1
0
0
1
0
1
2
0
2
0
0
0
0
0
2
0
0
2
0
0
0
2
2
0
1
1
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
3
1
3
0
2
0
0
0
0
0
0
2
0
2
0
0
0
2
2
2
0
2
2
0
0
0
1
0
0
0
0
1
0
2
0
0
0
2
1
0
1
0
0
2
2
0
4
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
3
0
0
2
0
0
0
1
0
0
0
0
2
1
0
0
0
0
1
1
0
2
2
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
2
0
2
4
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
2
0
0
2
0
1
1
2
0
0
6
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
2
1
2
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
5
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
1
0
5
1
3
0
0
2
2
2
0
2
3
1
3
0
0
0
0
0
1
0
1
1
0
0
0
1
1
2
0
0
1
0
0
0
2
0
2
1
0
0
1
0
1
2
2
0
0
0
0
0
2
0
0
2
1
0
1
0
0
2
2
0
2
0
0
2
1
0
0
0
0
0
0
2
1
0
0
0
2
0
2
0
1
0
0
0
0
1
2
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
2
4
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
3
1
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
2
0
0
0
0
0
0
2
1
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
2
0
1
0
0
1
0
0
0
0
1
2
1
1
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
3
2
1
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
1
1
0
2
0
0
0
2
0
2
0
0
0
0
0
2
0
1
1
0
0
0
0
0
1
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
1
0
1
0
0
1
0
0
2
0
0
0
0
2
2
0
0
11
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
1
0
0
0
0
0
0
3
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
2
5
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
2
2
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
3
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
1
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
2
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
3
0
0
2
1
0
0
0
0
0
0
0
2
0
1
2
2
0
0
1
3
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
1
0
0
2
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
1
0
2
0
0
0
0
2
2
2
0
0
1
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
1
1
0
0
0
1
0
0
1
1
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
2
2
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
1
1
0
1
0
0
2
0
0
3
0
1
1
0
2
0
0
2
0
1
0
1
2
0
1
0
0
2
0
0
2
0
1
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
1
3
0
0
0
0
0
2
0
0
1
2
0
0
2
0
1
0
0
2
1
2
0
2
1
0
1
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
1
1
0
0
2
1
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
2
0
0
2
0
0
0
2
2
0
0
0
0
0
0
1
2
0
0
0
0
2
1
0
1
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
2
3
2
1
2
0
0
0
0
1
0
2
1
0
0
0
0
0
1
0
2
0
2
1
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
1
0
2
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
2
0
0
3
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
5
0
0
1
0
0
0
0
2
0
2
2
0
0
0
1
0
0
0
0
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
2
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
1
0
2
0
2
0
0
0
0
2
0
0
0
0
1
1
0
0
2
0
1
0
1
0
0
2
2
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
1
2
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
2
1
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
1
0
2
0
1
1
0
1
0
0
1
0
0
2
0
1
3
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
3
1
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
1
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
1
5
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
2
0
2
1
1
0
0
0
4
2
2
0
0
0
0
8
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
2
1
0
2
0
0
0
0
1
0
2
1
0
0
0
0
0
2
0
2
0
0
1
0
0
0
4
0
2
0
0
0
0
2
1
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
3
2
2
1
5
0
0
0
0
0
0
4
0
0
2
0
0
0
0
1
0
0
0
2
0
1
1
1
2
1
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
2
2
1
0
0
0
0
0
2
0
0
0
0
0
0
3
1
5
0
1
0
0
1
2
1
1
1
0
0
2
0
0
0
1
0
0
0
2
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
4
0
0
0
4
0
0
0
0
1
2
2
1
0
1
0
1
2
0
0
0
0
2
0
0
1
2
0
0
2
0
0
0
1
0
0
0
1
1
0
2
3
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
2
0
0
0
2
0
2
2
0
0
2
1
2
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
3
1
0
0
0
2
2
1
0
1
1
0
0
1
0
0
1
0
0
0
0
0
1
2
0
1
0
0
2
0
0
0
2
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
9
0
0
0
0
0
0
1
2
2
0
0
1
1
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
3
0
1
2
0
0
0
2
0
0
0
2
0
0
3
0
0
0
0
0
2
0
2
1
2
2
0
0
1
0
1
1
1
0
2
0
2
0
0
11
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
2
2
1
1
0
3
0
0
0
1
4
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
1
0
0
3
2
1
0
0
0
0
0
0
0
2
0
2
1
0
2
1
0
0
0
1
2
0
1
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
1
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
1
2
1
0
0
2
2
0
3
0
2
2
1
1
1
2
2
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
3
1
2
1
0
0
0
0
0
0
1
0
1
0
1
1
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
4
0
3
0
0
1
2
0
0
0
0
1
1
0
2
0
1
0
2
0
0
2
0
0
0
0
0
3
0
0
2
0
0
2
0
0
2
1
1
0
0
1
0
0
0
0
0
1
1
1
15
1
0
2
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
2
0
0
1
0
0
0
1
1
0
0
0
0
0
0
2
2
0
0
0
0
2
2
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
2
2
0
0
0
0
2
0
0
0
2
0
0
0
0
1
4
0
0
0
1
0
0
0
2
0
1
0
1
0
0
2
1
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
3
2
0
0
1
0
0
0
0
2
0
1
2
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
7
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
2
0
0
2
0
0
1
0
0
0
0
1
0
0
2
0
2
0
2
0
0
2
1
0
0
0
0
1
1
0
0
1
0
2
0
6
0
0
0
1
2
2
0
0
11
0
0
0
0
0
1
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
2
3
0
1
1
2
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
2
1
1
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
2
1
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
4
1
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
2
0
0
3
0
1
0
0
1
0
0
0
1
0
0
0
2
0
2
1
0
0
0
1
1
1
0
1
0
1
0
3
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
3
0
1
0
0
3
1
1
0
2
0
0
1
0
0
2
0
1
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
9
0
1
2
2
0
0
0
0
0
1
0
0
0
0
0
1
2
0
3
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
1
9
0
0
0
0
0
0
3
0
4
0
0
0
0
0
1
1
1
0
0
0
0
0
0
8
0
2
0
0
0
1
0
0
1
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
3
0
0
1
1
2
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
1
2
0
0
0
1
1
0
2
0
0
0
4
0
0
0
0
0
2
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
2
0
1
0
0
0
2
1
0
1
1
0
0
0
0
0
0
2
0
1
0
0
0
0
2
2
0
0
0
0
0
2
2
1
1
0
0
1
0
0
0
0
0
2
0
0
1
1
0
2
0
0
0
0
0
2
0
1
1
0
0
2
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
2
0
2
2
0
0
0
0
0
2
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
3
1
0
0
0
0
0
0
3
2
0
0
0
0
3
0
0
7
0
0
0
0
2
2
0
0
0
2
0
0
0
2
0
0
0
1
2
1
0
0
0
0
1
1
0
0
0
2
0
0
0
1
0
1
0
3
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
2
0
1
1
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
2
1
0
0
1
0
0
0
1
7
0
0
0
1
0
0
0
2
1
0
0
0
0
1
0
1
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
4
0
1
0
2
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
2
3
1
0
1
1
0
0
0
0
2
0
0
0
2
0
0
1
0
1
3
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
2
0
3
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
3
0
0
0
0
1
0
2
0
1
2
0
2
0
0
1
0
2
1
0
0
0
0
4
0
0
0
0
0
0
0
3
0
1
1
2
0
2
0
0
0
2
0
0
2
0
0
0
2
1
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
2
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
3
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
5
2
0
0
0
2
0
0
0
0
0
2
1
0
1
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
2
1
0
0
1
0
2
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
1
0
1
0
2
0
0
0
0
1
0
3
0
0
0
0
1
0
1
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
2
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
2
0
0
1
0
2
3
0
1
0
0
0
2
1
1
0
0
1
0
1
0
0
4
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
2
1
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
0
0
1
0
0
1
0
0
0
2
2
0
0
1
0
0
0
0
0
1
0
0
0
0
1
2
0
1
0
0
0
0
0
1
0
0
0
1
0
3
2
0
0
1
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
1
0
1
0
0
0
2
0
2
2
0
1
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
2
1
1
0
0
0
2
0
1
2
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
2
1
0
0
0
0
0
0
1
0
1
0
3
0
0
0
0
1
0
2
1
0
0
0
3
0
0
2
0
1
1
0
0
1
0
0
0
2
0
2
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
2
0
2
0
1
1
0
0
1
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
2
0
0
1
1
2
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
2
0
0
2
0
2
0
0
2
1
0
0
4
1
0
0
0
0
1
0
3
1
0
0
0
0
0
0
0
0
2
2
1
0
1
0
0
0
0
0
0
0
0
2
1
0
0
2
0
1
0
0
0
1
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
3
1
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
1
0
1
2
0
0
0
0
1
1
0
2
3
0
0
0
0
1
0
2
0
2
0
2
1
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
2
1
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
1
2
0
4
0
0
2
2
0
2
0
0
1
0
0
0
2
0
0
0
0
2
0
0
1
0
0
2
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
3
0
2
0
2
0
2
2
1
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
1
0
1
1
0
0
1
0
1
0
0
0
1
1
0
0
2
0
2
1
0
0
3
2
0
0
0
3
0
1
2
0
2
0
0
1
0
2
1
0
1
1
3
0
0
0
1
2
0
0
2
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
1
2
0
0
0
4
0
0
0
0
2
1
0
2
1
0
0
1
0
1
0
0
2
1
1
2
0
1
2
0
0
0
3
0
1
0
1
0
0
0
0
0
0
0
4
2
0
0
0
0
0
1
1
2
1
0
1
2
0
0
0
1
0
0
0
0
0
0
1
2
0
2
0
0
1
0
0
1
0
0
4
0
0
0
0
0
0
1
2
0
1
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
1
0
1
0
0
2
0
0
0
2
2
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
2
0
1
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
2
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
1
2
1
1
0
2
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
2
2
0
0
3
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
2
0
2
0
0
0
0
0
1
0
0
0
0
3
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
2
0
11
2
1
2
0
0
0
2
0
2
0
0
0
0
0
0
1
0
1
0
0
2
2
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
2
1
0
2
0
0
2
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
2
0
0
1
2
3
0
3
0
0
3
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
2
2
0
1
0
0
0
0
1
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
1
0
0
0
0
0
2
0
1
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
1
0
2
0
0
0
0
0
2
1
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
1
0
2
2
0
1
0
2
0
0
0
0
2
0
0
0
2
2
2
0
0
0
2
0
0
2
0
2
0
0
0
1
0
1
0
0
0
0
1
3
0
2
0
3
2
5
0
0
0
1
0
1
0
0
2
0
2
0
0
0
0
0
2
1
2
2
0
2
2
2
0
1
0
2
2
0
1
0
2
0
0
0
0
1
0
0
0
0
0
2
0
2
0
3
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
5
0
2
0
0
3
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
1
0
0
2
2
2
1
0
0
0
0
1
1
0
1
1
3
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
1
0
0
2
1
0
0
1
0
3
2
0
0
2
0
0
0
0
1
2
2
2
0
2
0
2
0
1
0
0
0
2
0
0
0
2
0
0
4
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
1
0
2
1
1
2
2
1
1
0
0
5
0
2
2
0
0
0
1
0
2
0
2
2
0
0
1
0
0
0
0
0
1
0
2
0
2
0
0
2
0
0
0
1
4
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
1
0
2
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
1
1
0
1
1
0
1
1
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
3
0
1
0
1
0
4
1
2
0
2
1
0
0
0
0
0
1
0
2
0
0
4
1
0
1
0
0
0
2
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
2
4
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
2
1
0
0
0
1
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
15
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
1
2
0
1
2
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
1
0
2
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
3
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
2
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
1
0
0
0
2
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
2
2
0
1
2
0
0
0
0
0
2
1
0
0
0
2
0
0
0
2
0
1
0
1
1
0
0
0
0
0
3
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
2
1
0
0
0
1
1
0
0
0
0
0
2
2
0
0
0
0
0
0
2
1
2
0
0
0
2
2
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
2
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
2
1
2
0
0
0
1
1
1
1
0
2
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
2
0
1
0
0
2
0
0
0
2
0
0
2
0
2
0
0
0
2
0
0
2
0
1
1
0
2
0
1
0
0
0
2
0
0
1
0
1
0
2
1
0
0
1
0
0
0
0
1
3
0
0
1
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
2
0
2
0
0
2
0
0
1
1
0
0
0
0
0
2
0
2
0
1
3
0
1
0
2
0
0
1
1
0
2
2
0
0
0
0
1
1
0
0
0
0
0
0
2
2
1
0
1
2
1
0
2
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
2
1
0
0
1
0
0
0
0
2
0
1
0
1
0
2
2
1
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
4
2
0
0
2
0
0
0
2
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
2
1
3
1
0
2
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
1
0
9
2
0
0
2
2
0
0
2
0
0
0
0
2
2
0
0
0
0
3
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
2
0
1
0
2
2
0
0
0
0
0
0
0
2
1
2
1
0
0
0
0
1
1
0
2
0
0
2
0
0
0
1
3
1
0
0
0
0
0
0
1
0
0
1
0
0
2
2
0
0
1
1
0
0
0
0
1
1
0
0
2
0
2
1
0
2
0
0
0
0
0
0
3
0
2
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
2
0
0
1
0
0
0
2
0
0
6
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
7
0
1
0
2
0
1
1
1
0
0
1
1
0
0
0
1
0
1
0
2
2
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
3
0
1
0
0
0
0
0
2
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
2
0
1
0
0
0
0
2
2
0
1
3
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
2
2
0
1
0
1
0
0
0
2
0
0
0
0
0
1
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
1
1
0
0
0
1
3
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
2
0
0
2
2
1
0
0
0
0
0
1
0
3
2
1
0
0
6
4
0
0
0
0
1
0
0
0
2
2
1
0
2
0
0
0
1
0
0
1
2
0
0
0
1
0
0
0
0
1
3
1
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
3
0
0
1
0
0
0
0
3
1
0
2
2
0
1
0
0
0
0
2
2
0
0
0
2
1
0
0
2
0
0
1
1
0
0
2
0
0
0
3
0
1
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
1
0
2
0
2
0
0
0
0
0
1
3
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
1
0
0
1
0
1
1
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
4
0
0
0
0
0
1
0
0
0
0
1
1
0
0
2
2
2
0
0
1
1
0
0
0
2
0
2
0
0
2
3
1
0
0
0
0
1
0
2
0
0
0
2
2
0
0
0
1
0
1
0
0
0
0
0
2
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
3
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
2
0
2
0
2
1
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
5
1
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
6
0
2
2
0
0
0
2
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
1
2
0
5
2
0
0
0
0
1
2
0
1
1
1
0
0
0
2
0
1
0
2
1
0
1
2
0
0
0
2
1
2
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
2
2
1
0
1
0
2
4
2
0
0
2
0
0
0
0
0
0
0
0
2
0
2
1
0
0
1
1
0
2
0
0
0
2
0
2
0
0
0
2
1
1
2
1
1
0
0
0
3
0
0
0
6
0
1
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
2
2
0
2
0
0
1
0
0
2
0
3
0
1
0
1
2
2
0
0
0
0
0
2
2
2
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
6
2
0
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
2
1
0
1
1
1
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
2
1
0
0
2
2
0
0
0
0
2
0
2
1
0
0
1
0
1
1
2
0
0
0
0
0
1
1
0
0
0
0
1
4
0
0
1
0
0
0
1
0
2
0
0
0
0
2
2
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
1
2
0
0
2
1
0
0
0
2
0
2
2
0
0
0
1
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
1
0
0
2
1
0
0
0
2
1
0
2
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
2
2
0
1
0
2
5
2
2
2
0
0
0
0
0
1
10
0
0
1
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
1
2
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
2
1
2
0
0
0
0
1
1
0
3
0
0
1
0
0
1
0
2
0
0
0
0
2
1
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
1
0
0
0
2
0
0
2
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
8
0
0
0
0
0
1
2
0
1
1
0
0
0
2
0
1
0
2
0
1
2
1
1
0
1
0
0
0
0
0
1
0
0
0
3
2
2
2
2
0
0
1
0
0
0
0
2
0
0
2
0
0
1
0
2
2
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
2
1
0
2
1
1
0
0
2
0
0
0
0
2
0
0
0
0
0
2
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
1
2
0
2
1
1
1
1
0
0
0
0
0
0
1
0
0
1
0
1
0
2
0
3
0
0
0
2
1
1
1
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
2
3
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
1
0
0
2
0
1
0
0
0
2
0
2
0
0
2
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
1
2
0
1
2
0
0
1
0
1
0
0
0
3
0
2
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
4
0
0
1
0
0
1
0
0
0
1
0
2
0
0
0
0
0
2
0
0
1
2
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
5
1
0
2
2
2
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
2
0
0
0
0
1
0
2
2
1
1
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
2
0
1
1
0
2
0
0
0
1
1
0
0
0
0
0
0
4
0
0
0
1
0
0
2
0
0
2
0
0
1
0
0
2
0
1
1
0
1
0
1
0
0
3
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
2
1
2
1
0
1
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
1
0
3
0
0
1
0
0
0
0
0
0
3
1
0
0
1
0
2
0
0
0
1
5
2
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
2
1
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
1
3
0
3
1
1
0
0
0
2
0
0
0
0
0
2
0
0
2
0
1
1
0
0
2
2
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
3
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
2
0
0
1
0
2
1
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
2
0
1
0
0
2
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
2
2
0
1
2
0
0
0
1
0
0
0
0
1
2
1
2
0
0
0
1
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
8
7
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
1
1
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
2
0
2
2
0
0
4
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
2
2
1
1
0
0
0
1
0
1
0
0
0
2
0
3
0
2
0
0
0
0
3
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
2
0
1
0
0
0
0
0
1
0
2
2
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
2
2
2
0
0
0
1
0
0
0
1
0
0
0
0
1
4
3
1
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
1
0
1
0
2
0
0
1
0
0
0
0
0
0
1
0
2
2
1
1
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
4
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
4
1
0
0
0
1
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
2
1
0
3
0
1
0
0
1
1
0
0
1
1
1
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
1
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
1
0
0
1
0
0
0
0
1
0
0
0
1
2
0
0
0
0
3
2
1
0
0
0
0
0
2
0
0
2
2
1
5
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
2
0
0
0
2
2
0
0
0
0
0
2
2
0
0
4
0
0
0
0
1
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
1
1
2
2
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
2
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
2
0
2
0
0
2
1
0
0
0
1
1
0
2
0
0
0
0
1
1
0
0
1
2
0
0
0
0
0
1
7
0
1
0
2
0
0
1
2
0
0
0
0
2
2
2
1
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
2
0
2
0
1
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
2
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
2
0
0
1
0
0
2
0
0
2
0
0
0
0
4
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
1
3
0
0
0
0
0
0
6
0
0
0
0
2
2
0
0
1
2
1
0
0
2
0
1
2
3
0
0
0
0
0
0
0
1
2
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
1
4
0
0
0
0
0
0
0
0
0
1
0
4
1
1
2
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
5
0
0
0
0
0
2
2
2
0
1
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
2
2
1
0
0
2
3
1
0
1
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
2
2
2
1
0
0
2
1
0
0
0
0
1
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
1
1
1
0
0
2
0
1
0
0
2
0
0
1
0
1
0
0
0
0
2
0
0
1
0
0
2
2
0
1
0
0
0
0
0
1
0
1
2
3
0
0
2
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
1
0
2
1
0
0
1
0
0
2
0
0
2
0
0
1
0
0
0
2
0
2
1
0
0
2
1
2
1
1
0
0
0
0
1
0
2
0
0
1
2
0
0
2
0
1
0
0
2
0
1
0
0
0
0
2
0
0
1
2
0
0
5
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
1
1
0
0
2
0
0
1
0
1
0
0
2
0
0
1
0
1
2
0
1
0
2
0
0
0
0
4
1
0
0
1
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
2
1
0
0
1
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
2
0
0
1
1
1
0
0
0
1
0
2
0
0
0
2
1
0
0
0
2
0
0
1
0
0
2
1
2
0
2
0
1
1
0
0
0
1
2
0
0
2
0
2
2
2
2
0
0
2
1
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
11
0
0
1
0
0
0
0
0
1
0
1
0
2
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
4
0
3
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
1
2
2
0
0
0
0
1
1
2
0
0
1
0
0
0
1
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
1
0
1
2
0
4
0
0
0
1
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
2
0
0
0
0
0
0
1
0
1
0
2
1
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
3
1
0
1
0
2
2
1
0
1
0
0
3
0
0
0
0
1
1
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
2
0
2
3
0
1
0
0
0
0
0
2
1
1
0
0
5
0
1
0
0
0
0
3
0
0
1
0
0
1
0
1
0
0
0
1
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
5
0
0
2
1
0
0
1
0
2
2
1
0
0
1
2
2
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
3
2
0
2
0
0
2
0
2
0
1
0
0
5
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
2
1
0
2
0
1
1
0
0
0
1
1
0
2
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
3
3
3
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
4
0
1
2
5
0
1
1
1
0
2
0
0
2
0
0
0
0
0
2
1
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
2
1
0
0
0
2
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
4
2
2
0
3
0
0
2
1
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
1
0
1
0
0
0
0
2
0
0
0
0
2
0
1
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
2
0
1
2
2
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
2
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
3
0
2
0
0
1
1
0
1
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
2
0
1
0
0
2
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
6
2
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
2
2
2
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
2
0
2
2
0
2
0
0
0
0
1
2
0
0
0
0
0
2
0
2
2
1
0
1
0
0
0
0
0
2
0
0
0
0
0
3
1
1
0
2
0
0
0
0
0
2
4
0
0
1
0
3
0
0
0
0
0
4
0
1
2
0
2
2
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
1
2
0
0
0
2
2
0
0
2
2
0
2
1
0
0
0
0
0
0
0
4
2
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
1
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
2
0
2
0
2
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
6
0
1
2
2
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
4
0
2
0
0
0
1
0
0
0
0
2
2
0
0
2
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
1
0
2
2
0
0
0
2
0
0
2
0
0
1
1
2
0
0
0
0
1
0
0
2
2
0
0
0
0
1
0
1
3
0
1
1
0
2
0
0
0
0
0
0
1
1
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
2
0
1
2
0
0
3
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
1
2
1
0
1
0
0
2
0
0
0
2
0
2
2
0
0
0
3
2
0
1
0
0
0
1
0
0
0
5
2
0
0
0
0
0
1
2
0
0
2
0
0
2
0
1
1
0
0
0
0
0
1
8
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
1
0
4
0
0
0
0
2
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
1
1
1
0
0
0
0
1
0
3
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
2
0
2
0
2
0
1
0
0
0
0
0
0
1
0
0
2
2
2
0
0
0
1
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
1
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
2
0
0
0
0
0
0
0
0
1
2
1
0
1
0
2
0
2
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
2
0
3
0
2
2
1
2
0
0
0
1
0
0
0
0
0
0
2
2
0
3
1
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
1
0
2
0
0
0
1
0
0
1
1
0
3
0
0
1
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
8
0
0
0
0
0
0
1
0
0
0
1
2
0
1
0
0
0
2
0
0
2
2
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
3
1
1
2
0
1
2
0
0
2
0
0
0
0
0
2
0
2
1
2
1
0
0
0
0
0
0
0
2
0
0
2
0
2
2
2
3
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
1
0
0
2
0
0
0
1
2
0
1
3
3
0
0
0
3
0
0
3
0
1
0
1
2
2
1
0
1
1
0
0
0
0
2
0
2
0
1
0
0
0
2
1
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
2
1
0
1
0
2
0
2
1
3
1
0
0
0
1
1
2
0
0
0
3
1
0
1
0
1
1
1
0
6
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
1
1
1
1
2
1
0
0
0
1
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
2
2
1
0
0
1
1
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
2
0
0
1
0
0
0
2
0
0
1
1
0
2
0
0
0
0
0
1
1
2
2
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
3
0
2
1
0
0
1
0
0
2
0
2
0
1
1
2
0
0
1
0
0
1
0
0
0
0
0
2
0
1
0
3
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
2
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
2
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
1
2
2
0
0
0
0
0
0
1
0
0
2
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
2
0
2
0
1
0
2
0
0
2
2
0
1
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
1
1
0
0
1
0
0
2
0
1
2
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
2
0
2
0
0
0
0
0
2
1
0
0
0
0
0
2
1
0
2
0
0
1
5
0
0
1
0
2
0
1
0
2
0
2
0
0
3
0
0
0
1
0
2
1
2
2
0
0
1
0
0
2
2
0
0
0
1
0
0
0
1
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
3
1
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
1
0
0
0
2
0
2
2
2
1
0
2
0
0
0
0
0
0
0
3
1
0
2
0
1
2
1
1
0
0
3
0
0
0
0
2
0
0
0
3
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
4
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
2
0
2
0
0
0
3
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
1
0
0
2
0
0
0
2
0
1
0
1
2
0
1
0
0
2
0
0
0
0
3
0
1
0
0
0
1
0
2
2
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
1
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7
1
1
0
0
1
0
0
1
0
2
2
1
0
1
1
0
0
0
0
2
0
0
0
0
0
0
2
2
2
2
0
0
0
2
2
2
0
0
1
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
1
0
1
3
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
1
1
0
0
0
0
1
2
2
0
0
1
1
1
0
0
0
0
0
2
1
2
0
0
0
0
2
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
2
0
2
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
2
2
2
0
0
0
0
1
0
0
0
2
1
0
1
0
4
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
1
1
2
0
0
0
0
0
0
2
2
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
2
0
1
0
5
2
2
0
0
0
0
1
0
0
1
2
0
0
1
0
0
1
2
0
2
0
1
2
1
0
0
0
0
0
0
0
2
0
2
0
3
0
0
2
0
1
1
2
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
3
0
3
0
1
2
0
0
1
0
0
0
0
0
4
0
0
1
0
2
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
2
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
3
2
0
2
1
0
2
0
0
1
0
0
1
0
0
0
0
0
3
0
0
2
0
0
0
0
0
2
1
0
1
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
3
0
0
0
0
0
1
0
0
2
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
2
0
0
2
0
0
1
0
0
0
2
0
2
0
2
0
0
0
2
1
1
0
0
0
2
0
0
1
1
1
0
1
1
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
2
2
0
1
0
0
1
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
3
0
2
1
1
2
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
3
1
1
2
0
0
2
0
0
0
2
3
0
0
0
0
1
0
0
0
0
0
1
0
0
2
2
0
0
1
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
2
0
3
0
1
1
2
0
0
3
0
1
1
0
1
0
0
0
0
0
0
0
2
1
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
1
1
0
0
1
0
1
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
2
1
0
0
1
0
0
0
0
0
0
0
3
0
0
2
0
0
2
0
0
0
3
0
1
0
0
1
0
1
0
2
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
1
0
1
1
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
1
0
7
0
0
0
0
0
0
0
0
0
0
0
0
0
6
2
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
1
1
2
1
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
4
0
0
0
2
0
1
2
0
2
0
0
0
0
2
0
1
0
0
0
5
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
1
3
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
2
3
0
0
2
0
0
2
0
2
0
0
0
3
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
1
0
0
0
0
0
2
1
1
0
0
2
2
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
1
0
5
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
2
1
0
2
0
0
0
2
0
1
2
3
0
2
2
2
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
1
2
1
1
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
1
1
2
1
2
0
0
1
0
0
2
1
0
0
0
2
2
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
2
0
2
0
1
2
1
0
0
4
1
0
0
7
0
2
0
0
2
0
0
0
1
0
0
1
0
2
1
0
0
0
0
2
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
1
1
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
2
2
0
0
0
0
2
0
0
0
4
0
0
0
1
2
2
0
0
0
1
0
0
0
2
0
0
0
0
1
0
1
2
2
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
4
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
1
0
1
0
0
2
0
2
0
1
0
5
3
0
0
0
0
0
0
0
0
1
2
1
0
0
2
0
1
0
0
1
0
0
1
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
2
2
0
1
1
0
2
0
0
2
0
1
0
0
0
0
3
0
2
0
0
0
2
2
1
0
0
2
1
0
0
1
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
1
0
0
2
0
0
1
0
1
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
1
0
0
0
0
0
6
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
3
0
1
1
0
0
2
1
0
0
0
2
0
0
0
0
5
1
2
2
0
1
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
2
5
0
0
0
2
1
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
1
2
0
1
2
0
2
3
0
1
1
0
1
0
0
0
1
0
0
2
0
0
2
6
0
0
2
0
0
1
0
0
0
0
1
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
3
0
0
1
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
2
1
0
0
0
0
1
2
0
0
2
1
0
2
2
0
0
3
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
1
1
1
0
0
1
1
1
2
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
2
0
2
0
5
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
3
2
2
0
0
0
0
0
0
0
1
0
1
0
4
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
2
2
3
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
2
5
0
0
1
0
0
0
0
1
2
0
0
0
2
0
2
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
1
0
2
0
0
0
1
0
1
0
1
2
0
1
2
2
2
0
1
0
0
0
0
0
0
0
1
2
2
0
1
0
0
0
2
1
1
2
0
1
0
0
2
0
0
1
0
1
2
2
0
0
1
1
0
0
0
1
0
0
2
0
0
2
0
0
2
0
0
0
0
0
2
3
0
0
0
1
0
2
0
0
2
2
0
0
0
1
0
2
1
0
0
0
0
0
1
2
1
1
2
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
1
0
0
2
0
2
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
1
6
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
1
1
0
4
1
0
2
0
0
2
3
0
1
0
1
0
1
0
0
0
1
0
0
0
3
0
2
1
1
0
2
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
2
0
5
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
2
0
1
0
0
2
0
1
0
1
0
1
0
3
0
0
1
2
0
2
3
0
0
1
0
0
0
0
0
1
2
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
2
1
0
0
4
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
2
0
0
1
0
4
0
1
1
0
2
0
4
0
0
0
2
0
0
1
0
2
0
2
0
0
0
2
0
2
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
2
0
2
0
0
3
0
1
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
2
0
0
0
2
0
0
0
1
0
2
2
0
0
0
0
0
2
0
0
0
3
0
1
2
1
2
0
0
0
0
0
0
1
0
2
1
1
0
2
1
0
2
0
0
0
2
2
1
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
1
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
3
0
4
1
2
0
0
1
0
2
0
0
0
0
1
1
1
0
0
2
0
0
2
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
2
0
0
1
2
0
1
0
2
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
3
0
1
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
2
1
2
0
0
0
0
1
2
2
1
0
1
0
2
2
0
0
0
0
0
0
0
0
1
2
2
0
0
2
0
0
0
2
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
4
0
1
0
0
0
0
0
1
0
0
1
2
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
1
0
0
0
3
0
0
0
0
0
0
2
2
1
1
1
2
2
0
3
2
3
0
2
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
1
0
1
0
2
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
1
0
0
2
2
0
0
0
1
5
0
1
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
3
0
2
0
0
0
0
2
0
2
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
1
0
0
0
1
1
0
1
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
4
2
0
0
2
0
0
2
1
0
0
2
0
1
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
3
0
0
0
0
0
0
0
0
1
0
2
1
0
2
0
2
0
2
0
0
1
3
0
0
0
2
1
3
0
0
1
0
1
0
2
0
2
1
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
1
0
0
0
2
0
1
0
0
0
2
2
0
1
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
1
0
2
0
0
0
3
2
0
0
0
0
1
0
0
0
0
1
0
0
2
2
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
1
0
0
0
1
2
0
0
0
0
0
0
0
1
1
2
0
1
0
3
4
0
2
0
1
0
0
1
0
0
0
0
2
0
1
0
0
0
0
2
2
1
0
0
0
2
0
0
0
2
0
3
0
0
0
0
0
1
1
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
1
0
0
1
0
0
1
0
0
1
0
1
0
2
0
0
0
1
0
0
1
0
0
0
1
2
0
0
2
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
3
0
2
0
1
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
2
1
3
1
1
1
2
0
0
0
0
2
0
1
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
2
2
0
0
2
0
2
2
0
0
0
2
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
2
0
2
0
3
1
0
0
0
0
0
0
1
0
0
0
0
3
1
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
2
0
0
2
0
1
0
0
0
2
1
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
3
0
0
1
0
2
1
0
0
2
0
0
0
0
1
1
1
0
2
0
0
2
1
1
0
0
1
2
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
8
2
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
2
0
0
0
0
0
2
0
1
1
0
0
0
1
1
0
0
0
3
0
1
0
0
0
0
0
1
0
1
0
0
2
0
2
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
4
0
0
2
1
0
1
1
0
0
0
0
0
0
1
1
0
0
1
0
1
2
0
0
0
1
1
0
0
0
3
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
2
2
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
5
0
0
0
0
1
1
0
0
2
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
2
0
0
0
2
1
2
1
5
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
2
1
2
1
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
1
1
0
3
2
0
0
0
0
1
2
1
1
0
0
2
0
0
0
18
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
3
2
0
0
0
0
0
1
0
2
0
0
2
2
2
0
2
0
0
0
0
0
0
2
1
0
0
1
0
0
0
2
2
0
0
2
0
0
0
0
2
0
0
2
1
1
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
3
0
0
0
0
0
0
0
3
1
0
0
1
0
0
2
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
2
1
0
3
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
3
0
1
1
0
0
0
1
1
2
2
0
0
0
0
0
3
0
0
0
0
2
0
1
1
0
0
0
0
0
2
0
0
0
1
1
1
2
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
1
0
2
0
2
0
0
0
0
0
1
2
0
0
1
0
0
2
0
2
0
1
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
2
0
2
0
0
1
0
1
0
0
1
2
4
0
1
1
0
1
1
0
2
0
2
2
0
0
1
1
2
0
0
12
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
1
1
0
1
0
1
2
0
0
0
1
0
0
0
2
1
0
2
3
0
1
1
0
0
3
0
0
2
0
0
1
1
2
1
0
0
1
1
2
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
1
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
2
0
0
2
1
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
1
1
0
0
2
0
0
0
0
0
0
0
1
0
0
2
4
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
2
1
0
0
0
0
2
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
2
2
0
0
2
0
0
0
1
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
1
11
0
0
3
0
1
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
1
2
0
0
2
0
1
2
1
0
0
0
2
1
0
2
0
1
2
0
0
0
0
0
0
0
1
2
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
1
1
0
1
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
2
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
2
1
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
2
0
1
1
0
0
0
0
2
2
0
1
0
0
2
0
0
0
0
0
2
0
0
0
3
2
0
0
0
0
1
0
0
1
1
0
0
0
1
1
0
0
1
0
1
0
2
0
1
0
2
0
0
2
0
0
0
1
1
2
0
0
2
2
0
2
0
2
0
0
0
2
0
2
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
2
2
0
0
2
0
0
2
2
0
0
0
2
0
1
2
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
2
1
2
0
0
0
0
2
2
0
0
0
2
0
0
1
0
2
0
0
0
3
0
1
0
1
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
3
2
0
0
2
2
0
1
1
0
2
2
1
0
1
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
1
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
1
1
1
2
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
1
0
0
1
0
2
0
0
0
0
0
0
0
1
1
1
0
3
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
1
1
0
1
2
0
0
1
0
0
0
0
0
0
0
0
5
0
0
0
0
2
0
2
4
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
2
2
0
1
2
0
10
1
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
1
2
0
0
0
0
1
0
0
0
0
2
0
1
2
0
2
0
1
0
0
3
1
0
1
0
0
1
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
3
2
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
4
1
1
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
6
0
2
1
2
0
0
0
0
2
0
0
2
0
1
0
2
1
0
0
2
2
0
0
0
0
0
0
2
0
1
0
3
6
0
0
2
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
1
2
0
0
1
2
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
4
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
2
0
2
0
0
1
1
0
2
0
0
2
0
1
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
1
2
2
0
2
0
2
0
2
2
0
0
2
0
2
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
2
0
2
0
0
0
2
0
0
3
0
2
0
0
0
1
0
0
0
1
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
3
1
0
2
0
0
0
0
1
0
1
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
2
0
0
2
0
0
2
1
0
1
0
0
0
0
0
2
2
0
0
4
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
3
2
2
1
0
0
0
0
0
3
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
2
3
0
0
0
2
0
1
0
2
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
2
1
0
0
1
0
0
0
1
0
2
0
0
0
0
2
0
0
1
0
0
2
0
2
0
2
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
2
0
0
3
2
1
1
0
0
0
0
0
0
2
1
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
3
0
1
1
0
0
0
0
2
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
3
0
2
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
2
0
0
0
0
0
0
0
2
4
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
2
1
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
2
0
0
1
0
2
0
0
0
1
2
0
0
0
0
0
0
0
2
0
1
0
0
1
2
0
0
0
0
0
2
0
0
0
0
2
0
1
2
1
3
0
0
2
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
3
3
0
0
0
0
2
2
0
0
0
2
0
0
1
2
1
2
2
0
1
2
2
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
1
1
0
0
0
2
0
0
0
2
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
1
0
0
0
2
0
0
2
1
0
0
1
0
0
0
2
0
1
0
0
0
2
2
0
1
0
0
1
0
0
2
0
0
2
0
1
0
0
0
1
1
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
1
0
2
0
0
0
1
3
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
2
1
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
1
0
2
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
2
1
2
2
2
0
0
0
0
0
2
1
2
0
0
0
0
1
0
3
0
0
0
2
1
2
0
0
2
0
2
2
2
2
0
0
2
1
3
0
2
0
2
0
2
0
1
0
2
0
0
0
0
0
2
2
2
0
0
0
1
0
0
0
3
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
2
5
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
3
2
0
0
0
0
0
2
1
0
1
0
0
0
2
2
0
0
0
0
0
4
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
1
0
9
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
1
2
0
2
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
2
1
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
2
2
1
0
0
0
0
0
0
0
0
3
2
0
0
1
1
0
0
2
1
2
0
0
1
2
1
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
2
1
1
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
1
0
0
0
2
0
2
0
1
0
2
0
0
0
0
1
0
0
0
0
1
0
3
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
2
0
0
2
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
1
1
0
3
0
5
0
0
0
0
0
0
2
0
0
1
0
0
1
0
1
0
2
1
1
0
2
1
1
0
1
2
0
0
0
0
2
0
0
1
0
2
0
2
2
1
0
0
2
0
0
0
2
1
0
0
0
0
1
0
1
0
0
0
2
4
0
4
0
0
1
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
1
2
0
0
0
0
0
1
2
0
0
0
1
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
2
1
0
0
2
0
2
0
5
0
2
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
1
2
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
6
0
0
1
0
2
0
1
0
0
1
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
1
0
1
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
2
2
0
0
1
0
0
0
1
0
0
1
0
2
2
0
1
1
0
1
0
0
0
3
0
1
1
0
0
0
1
0
0
2
0
0
2
0
0
2
0
1
0
1
0
0
0
3
0
0
3
0
0
0
0
2
2
0
0
2
0
2
0
1
1
1
0
2
0
2
2
0
1
0
0
1
0
2
0
1
0
0
2
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
6
0
0
0
0
1
0
0
2
0
0
0
0
2
2
0
1
0
1
2
0
5
1
0
2
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
2
0
0
0
5
1
0
2
1
1
0
0
0
1
0
0
2
0
1
2
0
0
0
0
0
0
1
2
0
0
1
2
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
2
1
1
0
2
0
0
2
0
0
2
2
0
0
0
0
1
0
2
0
0
0
7
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
1
0
0
0
0
3
0
1
1
2
2
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
3
2
2
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
2
0
3
0
1
0
0
0
1
2
0
0
1
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
2
1
2
0
0
0
1
0
1
0
1
0
0
1
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
3
1
0
0
0
2
0
0
2
0
0
1
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
1
1
2
0
2
0
1
0
0
0
0
0
0
0
3
0
0
0
3
0
0
0
0
1
1
0
0
0
0
2
2
0
2
0
0
5
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
2
1
0
2
2
0
4
0
0
0
1
0
0
0
0
0
0
1
1
1
1
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
1
3
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
2
0
1
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
18
1
2
0
0
0
2
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
2
0
1
2
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
1
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
2
0
0
2
0
2
2
1
0
0
1
2
0
0
0
0
0
0
0
0
0
2
3
2
1
1
0
4
0
3
2
3
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
2
0
2
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
3
0
0
0
0
1
2
0
0
0
0
0
0
0
1
2
0
0
2
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
1
0
0
2
0
1
0
1
0
1
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
2
0
2
0
2
0
1
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
1
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
4
0
0
1
0
0
0
3
1
1
0
0
0
0
1
1
0
0
1
0
1
2
2
0
1
0
1
1
0
0
0
0
0
0
0
0
2
0
1
2
0
1
0
0
0
0
1
1
1
0
0
1
0
2
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
3
0
0
2
2
0
0
0
0
0
0
1
2
1
0
0
1
0
0
0
2
1
0
0
2
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
2
2
0
0
1
0
2
0
0
0
0
3
0
0
2
0
0
0
0
1
0
2
0
0
1
2
0
1
0
1
1
2
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
1
1
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
2
0
0
1
0
0
1
3
0
2
0
0
0
0
0
0
2
2
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
3
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
1
0
2
1
0
0
0
0
0
1
0
1
1
2
2
0
0
1
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
1
0
0
1
0
1
2
2
0
1
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
2
2
0
0
0
0
0
2
1
2
0
0
2
0
0
0
1
4
0
0
0
0
1
0
0
1
0
0
2
1
0
0
2
0
0
0
2
0
0
1
3
2
0
0
1
2
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
1
2
0
2
0
0
2
1
0
2
0
0
0
0
2
0
1
0
1
0
0
0
4
1
1
0
0
2
0
0
2
1
0
2
0
0
1
1
3
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
2
2
2
0
0
0
1
0
0
2
1
1
1
1
0
3
0
0
0
1
0
0
2
1
1
1
0
2
0
0
1
0
0
2
0
1
0
0
0
0
2
0
0
0
2
2
0
2
0
1
0
0
0
0
2
0
3
0
0
0
0
2
2
0
2
0
1
0
0
1
0
0
0
0
1
0
0
2
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
1
0
2
0
4
2
1
3
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
2
0
2
0
0
2
0
0
1
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
1
0
0
0
2
2
1
0
1
0
2
0
0
1
1
0
0
1
0
1
0
0
0
0
2
2
1
0
0
0
1
2
0
0
1
1
2
0
0
0
2
0
0
0
0
0
3
1
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
2
0
1
2
1
0
0
2
1
2
0
1
0
0
0
2
0
2
0
0
0
2
0
0
0
0
1
2
0
0
1
0
1
2
0
2
0
2
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
1
0
1
1
1
0
0
0
0
0
0
0
0
1
0
7
0
1
2
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
3
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
2
0
0
1
0
2
0
0
0
1
2
2
1
0
2
1
0
0
1
0
1
1
2
0
0
0
0
0
0
2
0
0
0
0
3
3
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
1
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
2
3
0
1
1
2
0
0
1
0
0
2
2
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
1
1
0
0
1
1
2
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
6
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
2
2
1
0
0
0
0
1
0
2
1
1
0
0
0
0
2
3
0
0
0
0
0
0
0
0
1
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
2
0
0
2
1
2
0
0
1
0
1
0
2
0
0
0
2
0
0
1
2
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
1
2
0
0
0
2
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
1
0
1
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
6
0
0
0
1
1
0
1
0
0
0
0
0
0
1
2
1
1
0
0
2
1
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
2
0
0
1
2
1
2
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
1
0
3
0
0
0
0
0
1
0
2
0
0
0
0
1
2
1
0
0
2
3
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
5
2
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
1
0
2
0
1
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
1
2
0
1
0
0
0
0
0
10
3
0
2
2
2
6
0
0
0
1
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
1
2
1
0
6
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
2
1
1
0
0
2
0
0
0
2
1
2
0
0
0
1
0
0
0
0
0
0
0
1
1
0
2
1
0
0
0
0
1
3
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
2
1
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
5
1
0
0
0
0
0
0
1
2
0
1
0
0
0
0
1
0
0
2
0
0
0
0
2
3
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
2
0
0
2
1
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
4
0
0
0
0
0
5
0
1
0
0
0
0
1
0
0
4
0
0
0
1
0
0
0
0
2
0
0
2
1
3
4
0
0
0
0
0
1
2
5
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
1
2
0
2
1
0
1
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
2
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
2
0
2
0
2
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
2
0
2
0
0
2
0
1
0
0
2
0
2
1
0
0
0
0
2
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
2
0
1
1
0
1
0
0
0
1
0
0
1
2
2
2
0
2
0
0
0
0
2
0
0
0
0
0
1
2
1
0
0
1
0
0
2
0
0
2
2
2
1
2
0
1
0
0
0
0
1
2
0
0
0
0
0
1
2
0
0
2
0
0
2
0
1
0
2
0
2
0
0
0
3
0
2
0
0
0
0
0
2
1
2
0
2
0
0
0
2
0
0
2
2
1
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
2
1
0
2
0
1
0
3
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
2
0
1
2
1
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
2
0
0
1
0
1
2
1
0
0
0
2
2
2
0
1
0
2
3
1
2
0
1
0
0
1
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
3
0
0
0
1
0
1
2
0
2
0
0
0
1
0
0
1
0
2
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
2
1
2
1
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
2
0
2
2
0
1
0
0
1
0
0
0
1
0
3
0
2
1
0
1
1
1
0
2
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
1
0
0
0
0
1
2
0
0
0
0
1
2
0
2
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
2
1
0
1
0
2
1
1
0
0
0
0
24
0
0
0
2
0
2
1
0
0
0
0
1
2
1
0
2
1
2
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
2
0
1
0
0
2
3
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
2
0
0
1
0
2
2
0
0
2
0
2
0
0
2
2
0
1
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
1
0
1
2
1
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
3
1
0
0
0
0
0
1
0
0
2
1
0
0
0
1
0
0
0
0
0
0
3
0
0
1
0
1
0
0
2
2
0
0
0
0
0
1
4
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
5
1
0
0
0
2
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
3
0
2
0
0
0
0
0
0
0
1
2
0
1
1
0
0
3
0
0
1
3
0
2
2
0
0
0
0
0
1
0
0
0
3
1
1
1
0
0
0
0
0
0
1
0
0
2
2
0
0
1
0
0
1
0
2
0
2
0
0
1
0
0
0
7
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
2
0
2
2
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
2
2
0
0
0
0
0
1
1
1
3
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
3
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
2
0
2
0
2
1
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
2
2
0
0
2
0
0
0
0
0
0
2
2
2
0
0
1
0
0
1
0
1
1
0
0
0
3
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
3
0
0
0
2
0
0
0
2
0
0
3
0
2
0
0
0
0
2
0
1
0
0
2
0
0
0
0
2
1
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
2
0
0
2
1
0
0
3
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
1
0
0
1
0
0
3
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
2
0
0
3
0
0
1
0
0
0
2
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
2
0
3
0
0
2
0
0
0
0
2
0
1
0
2
0
0
0
2
0
0
0
0
0
1
0
2
0
0
1
0
2
1
0
2
2
0
0
1
0
0
2
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
1
1
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
3
0
0
1
0
0
3
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
3
1
2
0
1
0
2
1
0
1
0
1
1
0
0
2
0
0
0
0
1
0
0
0
2
2
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
3
1
1
2
2
3
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
2
0
0
1
2
7
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
1
3
0
0
0
1
0
1
2
0
1
0
1
0
0
0
0
2
1
2
0
2
0
0
0
0
0
3
2
0
0
0
0
0
2
2
0
0
0
0
0
1
0
1
3
0
9
0
0
0
1
2
1
0
0
0
0
2
0
0
0
2
0
0
2
1
1
0
0
2
0
0
1
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
1
0
1
1
0
0
1
2
2
0
0
1
0
2
1
0
0
2
1
1
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
3
1
0
0
2
0
2
1
0
1
0
0
0
1
2
2
0
1
4
2
1
0
0
0
0
2
0
0
0
0
0
2
3
0
0
0
0
2
2
0
0
0
0
0
2
2
0
1
0
0
0
0
1
1
0
0
0
2
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
1
0
0
1
2
0
2
2
1
1
1
3
0
2
0
0
1
0
1
0
2
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
2
0
0
2
0
0
2
0
0
0
1
2
0
1
0
0
0
1
0
0
0
2
0
0
0
1
0
2
0
1
2
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
1
0
0
0
1
2
1
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
1
1
0
2
3
2
0
0
0
0
0
0
1
1
0
1
0
0
0
2
0
0
1
1
0
0
1
0
2
0
0
2
0
0
0
1
0
0
1
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
1
0
1
0
0
1
0
0
3
0
2
1
0
0
0
0
1
0
0
0
0
2
0
1
2
2
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
1
0
2
0
0
2
0
0
0
0
2
0
0
1
2
0
0
0
2
0
0
1
0
1
0
2
0
0
2
1
2
1
2
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
2
0
0
0
0
0
3
0
0
1
0
0
0
1
1
0
0
0
1
1
0
1
1
0
2
0
2
1
2
0
0
2
0
0
0
0
1
3
0
2
0
0
2
0
0
0
0
1
0
2
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
2
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
6
2
1
3
0
0
2
0
0
0
0
1
2
0
0
7
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
1
0
0
2
0
1
2
0
1
1
0
0
0
1
2
0
0
2
1
2
0
3
1
3
1
2
0
0
0
0
1
2
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
2
2
0
0
0
0
0
0
0
0
0
3
0
0
1
2
1
0
0
2
0
0
1
0
0
0
0
0
0
3
2
0
0
0
1
2
2
1
0
0
3
0
0
0
0
1
0
0
0
1
0
0
1
4
0
2
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
2
0
2
0
2
0
0
0
0
2
1
0
1
1
0
1
3
0
0
2
0
1
0
1
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
5
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
2
0
3
0
0
0
0
1
0
2
2
0
1
2
0
0
0
1
2
0
0
1
0
0
0
0
5
0
2
2
0
1
0
0
0
0
1
0
2
0
0
1
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
3
1
2
0
2
1
2
2
0
1
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
2
3
0
2
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
1
1
0
0
1
0
0
4
1
0
0
1
0
0
1
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
2
2
0
0
2
0
1
0
3
2
0
2
0
0
1
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
1
0
0
2
3
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
3
1
0
0
0
1
0
2
1
0
0
0
1
0
0
0
0
2
3
0
0
0
0
2
0
0
1
0
0
0
0
0
2
2
2
0
1
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
1
1
0
0
0
0
1
1
2
2
0
0
2
0
1
0
1
0
0
2
0
0
0
0
0
0
0
4
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
2
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
1
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
2
0
1
0
2
0
0
0
3
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
4
0
0
0
2
0
0
0
2
0
0
0
0
2
1
0
2
2
0
0
1
3
1
0
0
0
0
2
0
0
2
3
1
0
0
0
0
0
0
0
0
1
0
1
0
0
2
2
0
0
1
0
0
0
0
2
0
0
0
0
2
2
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
1
2
2
0
1
0
0
0
0
0
0
0
1
1
0
2
0
0
0
1
2
0
0
0
0
2
2
2
2
0
1
1
0
0
0
0
0
0
0
3
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
5
0
6
0
0
3
0
1
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
5
0
0
0
1
2
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
2
1
0
0
0
2
2
0
2
0
3
0
0
6
0
0
2
2
1
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
2
0
1
0
3
2
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
1
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
3
0
2
2
1
0
0
0
2
0
0
0
2
0
2
0
0
0
0
2
0
0
0
2
0
0
1
0
1
0
0
1
0
0
2
2
0
2
0
0
1
1
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
4
0
0
0
0
0
1
0
1
0
0
2
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
2
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
2
0
0
0
0
1
2
0
0
1
0
0
0
0
0
1
1
0
2
0
0
0
1
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
2
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
2
0
1
0
3
2
0
0
0
0
0
0
0
0
0
3
0
0
1
2
1
0
0
2
0
0
0
0
0
0
1
3
0
0
0
0
0
1
2
0
1
2
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
1
0
0
3
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
1
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
2
5
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
4
1
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
3
0
0
0
0
1
0
2
0
0
0
3
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
1
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
3
0
2
0
0
0
0
1
0
0
2
0
1
0
0
0
0
1
0
0
0
0
2
0
1
1
0
1
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
1
0
1
0
0
1
0
0
0
1
0
0
0
1
2
0
0
2
0
1
1
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
5
0
0
0
0
1
0
0
2
1
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
2
2
0
0
0
2
0
2
0
2
0
0
0
1
0
0
0
2
0
1
0
2
0
0
0
1
1
0
0
1
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
2
0
0
0
6
0
0
0
1
0
0
0
2
0
0
0
2
3
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
1
1
0
1
2
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
4
2
0
2
0
1
0
0
1
0
2
0
0
0
1
0
0
0
2
2
1
2
0
2
0
0
3
0
0
0
0
0
0
2
2
0
1
0
1
0
0
3
2
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
2
1
1
0
0
0
1
0
0
2
0
3
0
0
0
0
0
2
2
2
0
0
0
4
0
0
14
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
2
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
2
2
0
0
0
2
1
0
0
0
2
0
1
0
1
0
1
1
0
0
3
0
1
0
3
0
0
0
0
1
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
3
0
0
4
2
0
0
0
1
0
0
0
2
0
0
1
0
2
2
0
1
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
1
0
0
2
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
5
0
1
0
0
1
0
0
0
1
2
0
1
0
0
2
0
2
0
0
0
0
0
0
2
0
3
0
4
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
1
2
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
2
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
1
0
2
0
0
1
0
2
3
2
0
0
0
0
2
0
2
1
3
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
2
0
5
2
0
1
0
3
1
0
2
0
0
0
2
0
0
0
0
0
3
0
0
0
2
6
0
2
0
0
2
0
0
0
2
0
2
0
2
0
1
0
0
0
1
0
0
1
0
2
0
0
0
0
2
2
1
2
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
4
0
0
0
0
2
0
4
0
0
0
0
0
1
0
0
0
0
2
0
1
2
0
1
0
0
0
0
2
0
0
0
0
3
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
1
3
0
0
0
0
2
0
0
0
0
1
0
0
2
4
0
0
0
1
0
1
0
0
4
0
0
2
0
0
0
0
3
1
0
0
0
0
0
1
0
2
2
2
0
0
0
0
0
1
0
0
2
1
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
2
0
2
0
2
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
1
0
0
0
2
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
1
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
2
2
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
3
2
0
0
0
2
0
0
0
0
3
0
0
1
1
0
2
0
1
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
3
0
0
0
2
0
0
0
2
1
0
0
1
0
0
0
0
0
0
3
1
2
0
0
0
1
0
1
2
0
0
1
0
0
0
0
0
2
1
0
0
0
1
0
1
0
0
0
0
0
0
2
0
1
1
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
2
0
0
0
2
2
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
1
0
0
0
3
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
1
0
2
1
0
0
1
0
0
0
2
0
2
1
1
0
0
2
1
0
0
1
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
2
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
1
2
2
0
2
2
0
2
0
3
0
2
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
4
0
0
2
0
0
0
0
2
1
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
2
0
0
3
0
2
0
0
0
0
1
3
0
0
3
2
0
2
1
2
0
0
0
1
0
0
1
0
1
2
0
0
0
0
0
2
1
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
5
0
1
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
1
0
0
1
0
0
1
1
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
2
2
0
0
0
0
0
2
2
0
0
0
1
0
0
0
1
0
2
0
2
0
2
0
0
0
0
0
1
2
1
2
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
1
2
0
1
1
0
2
0
2
0
2
0
2
1
0
0
0
0
1
2
3
4
2
2
0
0
1
2
0
1
0
0
0
1
0
0
0
1
1
2
1
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
2
1
0
0
1
0
1
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
3
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
4
2
0
1
0
0
1
0
0
0
3
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
2
1
0
2
0
0
0
0
2
2
0
0
0
0
0
0
2
0
1
3
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
6
0
0
0
1
3
0
0
0
0
2
0
0
1
0
0
2
0
0
0
1
0
0
0
0
2
0
2
0
0
1
1
2
0
0
3
1
0
0
0
1
0
2
0
0
1
0
1
2
0
0
0
1
1
0
0
1
0
1
0
2
0
0
2
0
0
0
2
1
0
0
0
0
0
2
0
0
1
0
2
2
0
0
0
0
1
1
0
0
0
1
0
2
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
2
0
0
2
2
0
0
0
2
0
1
0
0
0
0
1
0
4
0
0
2
0
0
0
1
0
0
3
2
0
0
1
0
0
2
1
0
0
0
0
0
0
2
0
2
0
0
0
0
2
2
0
0
1
0
2
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
1
0
0
0
2
1
1
0
0
0
0
0
0
2
0
1
2
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
3
0
0
2
1
1
0
0
1
0
0
0
0
0
0
1
1
1
1
1
0
2
1
0
0
0
0
0
0
1
3
2
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
2
0
1
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
1
1
2
0
0
0
0
2
1
0
0
0
0
2
2
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
2
1
0
2
0
1
0
0
0
0
0
1
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
1
0
0
6
1
0
0
0
0
2
3
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
2
0
0
1
0
0
1
0
2
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
2
1
0
1
3
0
0
0
1
0
0
2
2
0
1
0
0
0
0
0
0
0
1
0
1
0
3
0
0
0
2
2
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
2
0
1
1
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
2
2
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
2
2
0
1
1
1
1
0
0
2
0
0
1
0
0
0
0
3
0
2
0
2
0
1
2
0
0
1
0
2
0
0
0
0
2
0
1
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
2
0
0
0
3
0
2
0
0
4
0
0
0
0
1
0
2
0
1
0
0
1
0
0
0
0
0
1
1
6
0
0
1
0
0
0
0
0
1
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
2
1
0
0
0
2
1
1
1
0
1
0
0
0
0
2
0
0
2
2
0
2
0
2
2
1
0
1
0
0
1
0
1
2
0
0
2
2
0
0
1
1
0
0
0
0
0
1
1
1
0
1
0
1
1
0
1
1
2
0
0
2
0
0
1
0
0
0
2
0
1
1
2
0
2
0
1
2
0
1
2
0
1
0
0
0
0
2
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
3
0
0
0
1
0
2
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
2
1
0
0
0
2
2
0
0
2
0
0
1
0
0
1
0
2
0
0
0
2
0
0
4
1
0
0
0
2
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
9
0
0
0
0
0
1
1
2
2
0
0
0
0
1
2
0
0
1
0
1
0
0
4
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
5
0
0
0
0
2
1
2
1
0
2
0
0
2
0
0
0
0
0
2
2
1
2
0
0
0
0
2
0
0
0
0
0
1
1
0
0
3
1
1
1
1
0
0
0
1
2
0
2
0
0
0
2
1
2
0
2
0
1
0
0
0
0
2
0
0
1
1
2
0
0
2
0
1
0
1
0
2
0
0
0
0
0
5
3
2
1
0
2
0
0
2
1
0
0
0
0
1
0
3
0
0
0
2
0
0
1
1
0
0
0
1
1
0
0
0
0
1
1
2
0
0
2
0
0
0
2
0
0
0
0
2
0
1
0
0
1
0
0
0
1
1
1
1
0
0
2
0
1
1
0
1
2
0
0
2
3
2
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
2
3
1
0
0
3
6
0
2
0
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
2
2
1
0
0
2
0
0
0
1
1
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
3
2
0
0
2
0
0
1
2
0
2
1
0
0
0
0
0
1
0
4
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
3
1
0
0
0
3
0
0
0
2
1
0
0
2
1
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
2
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
2
2
0
0
1
2
1
0
0
2
1
2
1
0
0
0
1
2
2
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
3
1
0
0
1
2
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
2
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
1
2
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
4
0
0
0
0
0
0
2
0
0
1
2
0
2
0
0
0
2
0
0
0
2
0
1
0
0
0
1
2
0
0
0
2
2
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
1
0
2
0
0
2
1
1
1
0
2
0
0
1
0
0
0
2
2
2
0
2
2
0
0
2
0
2
2
0
0
0
0
0
3
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
1
1
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
1
2
0
0
0
0
1
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
5
0
0
0
0
0
2
0
0
0
2
0
1
0
3
1
0
1
2
1
0
0
1
3
0
0
0
0
1
0
2
0
2
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
6
2
0
0
0
2
2
0
2
0
1
0
1
0
0
0
0
0
0
0
2
0
2
1
2
0
0
0
0
1
2
0
0
0
0
0
1
0
2
0
2
0
2
0
2
1
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
3
0
0
0
1
5
0
0
0
0
0
0
0
4
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
3
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
2
0
0
2
0
2
1
0
0
1
2
0
0
4
0
0
0
2
0
0
1
0
1
0
0
2
0
0
1
0
2
0
0
1
1
0
1
0
1
0
0
0
0
4
0
0
3
1
0
1
0
2
0
0
0
0
0
2
0
1
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
1
0
0
1
1
0
0
0
0
0
0
3
0
0
2
0
0
1
0
0
1
0
2
0
0
0
1
0
2
0
0
1
0
0
0
0
1
0
0
1
2
1
0
0
0
2
0
0
0
0
0
1
4
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
1
0
0
0
1
1
0
0
0
0
2
2
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
2
2
0
0
0
1
0
0
1
0
0
3
0
0
1
2
0
0
2
0
0
0
2
0
0
0
0
1
0
3
1
2
1
1
1
3
0
0
0
0
3
0
0
2
2
0
4
0
2
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
1
0
2
0
0
5
4
0
2
0
0
2
0
0
1
1
0
1
2
0
0
1
0
0
1
1
3
0
0
1
0
0
0
0
3
1
2
0
1
0
0
1
0
1
0
0
0
0
0
0
1
2
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
1
0
0
0
2
0
0
1
1
0
0
2
0
0
1
1
1
0
0
0
0
0
0
2
1
2
0
0
2
2
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
3
2
0
0
1
0
1
0
1
2
0
0
0
2
1
0
7
2
2
0
0
0
2
0
0
0
2
0
0
3
0
2
0
0
0
0
0
2
2
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
1
2
2
1
0
0
2
0
2
0
0
2
2
0
0
0
0
2
0
2
1
0
1
0
0
3
0
0
0
0
1
3
0
1
0
0
0
1
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
1
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
2
0
0
1
1
0
0
0
1
0
2
1
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
1
1
0
0
0
1
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
2
0
0
1
1
1
0
1
2
0
4
2
1
1
0
0
2
0
2
0
2
1
0
1
0
0
0
0
0
1
2
0
1
1
1
1
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
8
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
2
2
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
1
1
1
0
0
1
1
1
0
0
1
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
1
1
0
0
1
1
0
0
1
0
0
3
0
0
0
0
2
0
0
2
0
1
0
0
2
0
0
2
0
1
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
2
1
0
2
0
0
0
0
1
0
1
2
0
2
1
0
1
0
0
0
2
0
0
0
0
1
1
0
0
1
0
1
1
1
0
0
2
1
0
0
3
0
2
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
3
0
0
0
1
0
3
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
1
0
1
0
0
1
2
6
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
3
0
0
2
0
0
0
1
0
0
2
2
1
0
0
1
0
0
0
0
0
1
0
4
0
0
0
2
0
0
0
0
1
0
1
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
1
1
2
0
2
0
0
0
0
0
0
1
2
0
0
3
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
1
0
0
2
3
1
0
1
1
0
2
0
0
0
2
0
0
0
2
0
1
0
0
1
2
0
1
0
0
1
0
0
2
1
1
1
0
2
1
0
0
1
1
2
0
0
2
0
2
0
2
0
1
1
0
0
3
1
2
0
2
0
0
0
0
0
0
0
2
2
1
0
0
1
1
1
1
1
2
0
0
0
0
0
0
1
1
3
0
0
0
0
0
0
0
0
0
2
1
2
0
4
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
4
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
2
1
0
1
0
0
0
0
0
2
0
2
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
1
0
0
13
0
0
1
2
1
1
0
2
0
0
0
0
0
0
0
2
0
0
0
2
2
0
1
2
2
0
2
0
0
0
0
0
0
0
0
0
0
1
1
2
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
2
0
1
0
1
2
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
3
0
0
0
0
1
1
2
0
0
0
0
1
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
1
0
1
2
1
0
0
1
0
2
0
0
2
0
2
2
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
1
0
0
1
0
0
3
0
0
0
0
0
2
0
2
1
0
0
0
0
1
0
0
0
3
0
0
1
0
0
2
0
0
0
1
2
0
0
0
2
0
1
0
2
1
0
0
2
2
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
4
0
0
0
1
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
2
0
0
0
2
3
0
2
3
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
2
0
2
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
5
0
0
0
0
0
1
1
0
1
0
0
2
0
2
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
1
0
1
0
3
2
0
0
0
0
2
3
0
0
1
0
1
0
1
0
0
3
0
0
0
0
0
2
0
0
1
1
0
2
0
0
3
2
0
0
0
1
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
2
2
0
0
0
2
4
0
0
0
3
2
0
2
0
2
0
1
2
0
0
0
1
0
0
1
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
1
0
2
2
0
1
0
2
0
0
0
1
2
0
0
0
1
0
2
1
4
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
2
3
0
2
1
0
0
0
0
3
0
2
0
0
0
0
2
2
0
0
0
1
0
0
0
1
0
0
0
2
2
5
1
1
0
0
0
0
1
1
1
1
0
0
0
0
1
0
0
2
0
2
0
0
0
0
2
0
0
0
0
1
2
2
0
0
0
1
0
0
1
0
0
0
0
1
2
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
1
1
1
2
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
3
0
0
1
0
0
3
0
2
0
0
0
2
3
2
2
0
2
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
2
0
5
0
0
0
0
1
0
0
0
0
1
0
1
2
0
0
2
0
0
0
2
1
0
2
0
2
0
1
0
1
0
2
2
1
1
1
0
1
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
3
0
2
0
0
0
1
0
2
0
1
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
2
2
0
3
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
1
1
0
2
0
1
2
1
0
0
0
0
0
0
0
4
2
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
2
0
0
2
0
1
0
1
0
0
2
0
0
0
1
2
3
0
0
1
0
0
3
1
0
0
0
0
0
2
1
0
0
0
1
0
2
1
1
0
2
0
0
2
0
2
0
0
0
0
0
1
0
2
2
1
0
0
0
0
0
0
2
0
0
2
0
2
1
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
2
1
1
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
0
2
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
4
0
1
1
0
0
1
1
1
0
1
0
0
0
2
0
0
0
0
1
2
2
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
1
2
1
0
0
0
1
2
0
2
2
1
2
2
0
1
1
1
1
2
2
0
2
0
1
0
1
0
3
0
1
2
0
1
1
0
0
2
0
0
0
0
2
1
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
2
0
4
2
1
0
0
0
0
0
1
2
2
2
2
1
1
0
0
0
2
1
0
0
0
1
0
0
1
2
0
0
0
1
1
0
0
1
1
1
0
0
3
2
0
0
1
2
0
2
0
0
1
1
3
0
1
3
0
0
0
0
0
1
0
1
0
1
1
0
1
0
2
0
2
2
0
0
0
2
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
2
0
1
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
2
0
1
0
0
3
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
7
0
3
0
0
0
1
2
0
3
0
2
1
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
1
0
1
0
2
4
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
3
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
3
0
0
0
1
0
0
2
0
0
0
0
1
2
0
0
0
1
0
1
0
0
0
3
0
0
1
0
1
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
2
0
2
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
1
2
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
2
1
0
0
0
1
0
0
1
1
1
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
3
0
0
0
0
1
0
2
1
0
0
2
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
1
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
4
1
0
0
0
0
2
0
1
2
0
1
0
1
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
1
0
1
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
8
1
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
2
2
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
1
0
2
1
0
2
0
2
0
1
2
0
1
0
0
1
2
0
1
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
2
0
4
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
3
0
0
0
2
1
0
1
0
1
2
0
5
0
2
0
0
1
1
0
1
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
2
1
0
1
0
1
0
1
3
0
1
0
0
2
2
0
0
0
4
0
0
2
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
3
0
0
5
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
1
0
0
3
0
1
0
0
2
1
0
0
0
0
2
0
2
2
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
2
0
0
0
2
0
1
1
0
2
2
0
0
0
0
1
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
5
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
2
0
0
1
0
0
0
0
1
0
0
1
0
2
0
4
2
0
0
0
1
3
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
1
2
0
1
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
2
1
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
1
0
0
0
0
0
0
3
0
0
0
0
0
2
0
1
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
1
0
2
1
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
1
1
0
0
0
0
0
2
0
0
1
1
0
0
2
1
2
0
0
2
2
2
2
0
2
1
2
1
0
2
0
0
4
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
1
0
0
0
0
1
2
1
0
0
0
2
3
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
1
2
2
0
4
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
1
2
2
0
2
0
0
0
1
0
0
2
0
3
0
1
0
1
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
3
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
3
1
1
0
0
0
0
0
0
1
0
0
1
8
1
0
0
2
0
2
2
1
2
0
0
0
0
1
2
0
0
0
0
2
1
1
0
0
0
0
2
0
0
0
0
0
0
2
1
0
2
0
0
0
2
2
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
2
0
0
2
2
0
0
0
0
0
2
0
2
2
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
1
0
1
0
0
1
0
1
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
2
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
2
0
1
0
2
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
4
2
2
0
0
2
0
1
2
1
0
1
0
3
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
4
0
2
1
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
2
0
0
0
2
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
3
1
0
0
0
0
0
0
0
0
4
0
2
0
0
3
1
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
2
3
0
0
0
0
0
2
3
0
1
0
0
1
3
1
0
0
0
1
2
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
1
1
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
3
11
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
2
0
0
1
0
0
0
0
1
1
0
1
2
2
0
0
0
1
0
0
0
2
0
0
0
1
2
0
1
0
0
0
0
0
0
0
1
1
0
1
0
2
0
1
2
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
4
2
0
1
0
0
0
1
1
0
2
0
0
0
0
0
0
1
0
0
0
4
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
2
2
0
0
0
2
0
0
0
1
0
0
3
0
2
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
3
0
2
0
0
0
0
2
1
0
0
0
3
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
1
0
1
1
0
1
0
1
0
0
0
0
0
1
0
0
1
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
2
0
2
0
0
0
1
0
0
2
2
0
0
0
0
1
3
2
1
1
1
0
0
0
2
0
2
0
0
0
0
0
1
2
1
0
0
0
0
0
1
0
1
0
0
4
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
1
0
0
0
1
0
0
1
1
3
2
0
0
0
0
0
0
1
2
0
0
0
0
2
1
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
1
2
0
0
3
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
1
0
0
2
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
2
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
1
0
2
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
3
1
0
1
0
0
0
0
0
2
2
2
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
6
0
2
0
2
0
0
2
0
2
2
0
0
5
0
0
0
0
0
0
2
0
2
1
0
0
0
0
2
0
2
0
0
2
0
0
3
0
1
0
2
0
1
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
2
1
0
2
0
1
0
0
2
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
1
0
2
0
0
1
1
0
1
2
0
0
0
0
2
0
0
1
0
0
2
0
2
1
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
2
1
2
0
0
0
1
0
2
1
0
0
0
0
0
0
2
0
0
0
0
2
0
2
2
0
0
0
1
0
0
0
0
0
2
1
1
0
1
0
0
0
0
0
0
2
1
0
0
2
0
0
0
1
0
0
0
0
0
2
0
1
0
1
2
0
0
0
2
0
1
2
2
0
0
1
0
0
2
2
0
0
1
0
0
0
1
0
0
2
1
2
0
0
2
2
0
0
2
1
0
0
1
1
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
2
1
1
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
2
1
0
0
0
0
0
0
1
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
3
1
2
1
0
2
0
0
0
2
0
0
0
0
0
2
1
1
0
1
0
0
0
1
1
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
2
1
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
2
1
0
0
0
0
0
0
0
0
0
1
1
1
1
1
0
0
0
0
0
0
0
0
3
0
5
1
1
2
0
0
0
0
1
0
0
2
2
0
1
6
0
1
0
0
0
0
0
2
0
0
1
2
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
2
0
1
0
0
0
3
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
1
0
0
1
0
0
0
2
0
1
0
0
0
0
0
1
0
1
0
0
0
1
1
2
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
1
1
0
0
1
0
2
0
0
1
1
1
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
2
0
0
0
0
1
0
1
2
0
1
1
0
0
0
2
0
0
0
0
1
0
0
3
0
0
2
0
0
1
1
2
1
0
0
0
0
2
0
0
1
0
0
1
0
2
0
2
0
0
0
1
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
3
0
0
2
0
0
0
0
0
2
0
0
3
0
0
0
0
1
2
0
0
1
0
8
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
2
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
1
0
1
2
0
0
0
3
0
1
0
0
0
0
0
0
1
2
2
0
0
0
1
2
0
0
0
0
2
1
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
2
0
1
0
0
1
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
2
3
0
2
1
0
0
0
2
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
1
1
2
0
0
0
2
2
0
0
0
0
0
0
0
3
0
3
2
0
1
1
1
0
1
0
0
1
2
0
1
0
0
4
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
2
0
0
0
0
0
1
2
2
0
1
0
0
2
0
0
0
0
0
1
0
2
1
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
1
0
0
0
2
0
0
0
0
0
0
2
2
0
2
0
0
0
2
0
0
0
0
1
0
0
2
2
0
0
0
0
0
1
0
1
0
0
0
1
1
2
0
0
2
0
0
0
2
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
2
2
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
3
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
1
0
0
0
0
3
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
5
2
0
0
0
0
0
0
7
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
2
0
0
0
1
0
0
2
1
2
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
1
0
0
1
0
3
0
2
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
1
1
2
0
0
3
0
0
0
0
2
1
2
0
0
2
0
0
0
0
2
0
0
0
2
1
2
0
0
0
0
1
1
0
0
1
1
0
0
1
0
1
2
1
0
0
1
0
2
1
1
0
0
2
0
2
0
0
0
0
0
1
0
2
0
0
0
0
2
1
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
2
0
2
1
1
1
0
1
0
0
0
2
1
0
1
0
1
2
0
0
1
0
0
1
0
0
2
0
0
0
0
0
2
0
0
1
2
1
1
1
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
2
12
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
2
2
0
0
0
2
3
0
2
0
1
1
0
0
0
0
0
0
0
2
2
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
3
0
0
0
0
0
2
1
0
0
0
1
0
1
2
0
0
0
6
0
0
2
0
0
0
1
0
1
0
0
0
1
0
2
1
3
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
2
0
0
1
0
0
0
0
0
0
2
1
2
0
1
1
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
1
0
2
2
1
0
0
0
0
0
0
2
0
0
0
0
2
0
3
0
0
1
0
1
0
0
0
2
0
0
0
1
1
0
0
0
0
2
0
2
0
1
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
2
2
0
0
0
1
0
0
0
0
1
0
3
2
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
2
0
1
1
0
0
0
1
1
0
0
0
2
0
1
0
1
0
2
1
0
2
2
1
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
3
0
2
1
3
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
2
0
0
0
1
0
0
0
5
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
2
0
0
1
0
0
2
0
0
0
1
0
0
0
2
0
1
0
0
1
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
1
2
1
0
2
3
0
0
0
1
2
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
2
1
0
1
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
3
0
0
0
0
1
0
0
2
2
1
0
4
0
2
0
0
1
2
0
0
1
0
0
0
0
2
2
0
2
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
1
4
2
0
2
0
0
1
2
0
2
0
0
0
0
1
2
1
0
0
0
2
0
0
0
0
2
0
2
0
1
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
1
0
0
0
2
1
0
0
0
4
0
0
2
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
6
0
0
0
1
0
1
0
0
1
0
4
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
1
0
2
0
0
2
1
1
0
0
0
0
1
1
3
0
0
0
0
0
1
0
5
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
2
1
0
1
0
0
2
0
0
0
2
0
0
0
0
1
2
1
0
1
0
0
0
0
0
1
0
2
0
0
0
1
0
0
10
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
2
0
1
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
3
1
0
2
0
0
0
0
0
2
2
1
2
0
2
0
1
0
1
1
0
0
1
0
0
0
1
0
2
1
2
4
1
1
0
1
0
0
1
0
0
0
0
0
1
2
0
0
2
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
1
0
0
1
0
2
2
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
2
0
2
0
0
1
0
2
0
0
0
1
0
1
0
0
0
0
0
0
1
0
2
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
3
0
0
0
0
0
1
2
0
2
0
1
0
3
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
10
0
0
0
0
0
1
0
0
2
0
0
0
3
0
0
0
1
0
0
2
0
1
0
0
1
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
6
0
2
0
0
0
2
2
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
1
2
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
3
0
0
2
0
1
0
0
0
0
0
1
2
0
0
0
2
0
0
0
1
2
1
0
2
1
0
2
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
5
0
0
1
4
0
1
0
4
2
0
1
2
3
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
2
1
3
0
3
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
1
0
0
1
1
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
3
0
0
1
1
0
0
0
0
2
2
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
2
0
5
2
0
2
0
0
0
1
0
0
0
0
0
2
0
1
2
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
2
2
0
1
0
0
0
3
0
1
0
0
0
0
1
0
1
0
0
1
0
2
1
0
0
0
2
0
0
1
0
0
0
0
4
0
1
1
2
0
1
1
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
1
0
1
0
0
0
0
1
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
1
0
0
0
2
0
0
0
4
2
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
1
0
1
1
1
2
2
0
0
0
1
0
0
0
0
1
1
0
3
0
0
0
2
4
0
0
1
2
1
0
0
0
2
0
1
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
2
1
0
0
0
2
1
0
0
2
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
2
0
0
1
1
0
0
2
0
0
0
0
2
0
3
0
0
0
0
1
0
0
0
4
1
0
0
0
2
2
0
0
3
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
2
0
2
2
1
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
2
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
4
0
0
0
2
0
0
8
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
2
0
1
0
0
2
0
0
1
2
0
0
1
0
0
2
0
0
0
1
0
1
0
0
4
0
0
0
2
1
0
0
0
1
0
1
0
0
1
2
0
0
0
1
0
2
0
2
0
0
0
0
0
2
1
2
1
0
1
2
1
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
1
1
0
0
0
2
0
0
0
0
1
0
2
2
0
0
2
1
0
0
0
0
2
2
0
0
2
1
0
2
2
2
0
4
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
4
0
0
0
0
0
4
0
0
7
0
0
0
0
2
1
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
3
0
1
0
0
0
2
2
0
1
2
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
2
0
1
2
0
0
1
0
2
1
2
0
0
0
0
1
0
2
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
3
1
0
2
0
2
0
0
1
0
0
3
1
0
0
0
0
0
0
1
0
1
0
0
1
2
0
0
4
0
0
1
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
3
0
2
1
0
0
1
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
2
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
2
0
0
2
0
1
1
0
0
0
0
1
0
0
0
0
2
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
2
0
2
0
0
0
0
0
0
0
0
1
3
2
0
1
0
0
0
1
0
0
1
0
3
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
2
3
0
0
1
1
2
0
2
0
0
0
1
1
1
0
0
0
0
5
0
1
0
4
0
0
1
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
2
0
1
0
0
0
1
0
0
0
3
1
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
1
0
0
0
0
1
0
3
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
2
1
0
0
0
0
2
0
1
0
0
0
1
0
0
0
2
0
0
1
0
1
0
0
1
0
2
0
1
0
2
0
0
1
1
1
2
2
0
0
0
0
2
0
0
1
2
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
2
0
1
0
1
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
4
1
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
3
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
2
2
0
1
0
0
0
0
0
0
3
0
1
0
2
1
0
0
0
2
0
3
0
0
0
0
3
0
1
0
0
0
0
2
2
3
0
1
0
0
2
1
0
2
1
1
2
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
2
0
0
1
2
2
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
1
2
1
0
0
0
0
0
0
3
1
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
2
1
0
0
0
2
0
1
0
2
0
2
1
1
0
0
0
3
0
0
0
1
3
0
0
0
1
0
1
1
0
3
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
1
0
1
1
1
0
0
2
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
2
0
1
2
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
8
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
1
0
0
1
2
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
1
0
3
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
1
0
5
0
0
1
2
0
0
0
0
0
0
2
0
1
0
1
1
0
0
0
0
0
0
0
2
0
0
2
3
0
3
0
0
0
0
0
0
2
2
1
1
2
0
2
0
0
0
0
0
3
2
2
0
0
2
0
1
0
0
0
0
0
0
0
1
2
0
0
1
0
2
0
1
0
0
0
0
2
1
1
2
1
0
1
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
1
3
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
3
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
1
1
2
0
2
2
0
1
1
0
0
0
2
1
0
0
0
0
0
0
0
1
0
2
2
0
2
0
0
0
1
1
0
1
0
0
0
2
0
1
0
0
2
2
0
0
0
0
0
1
0
2
1
0
0
0
0
1
2
0
0
0
0
7
0
1
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
2
0
0
1
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
2
0
2
1
0
0
0
0
0
1
0
0
0
0
1
1
0
1
2
1
0
0
0
0
1
3
1
0
0
2
0
1
7
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
2
1
1
0
1
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
2
0
0
4
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
2
1
0
1
0
0
0
0
2
0
0
0
0
0
0
4
1
0
1
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
1
0
0
1
2
2
1
0
0
0
0
0
4
0
0
0
1
2
0
3
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
2
0
0
0
0
2
0
0
2
2
2
0
4
1
0
0
0
0
3
2
0
0
0
0
0
1
1
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
1
0
0
0
3
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
7
0
0
1
1
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
1
1
0
0
3
1
0
0
1
1
0
1
0
0
1
0
0
2
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
2
1
1
0
1
0
0
2
0
0
0
2
0
1
0
1
2
2
1
0
0
1
0
2
0
1
0
0
1
2
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
2
2
0
0
2
0
0
0
0
0
1
0
3
2
0
0
1
0
1
0
0
0
0
0
1
0
0
2
1
0
0
0
2
1
1
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
1
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
3
1
0
1
0
0
0
0
0
2
0
1
0
2
1
2
0
0
2
1
0
0
0
0
0
0
2
2
2
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
1
0
0
2
0
2
0
0
1
0
2
0
0
1
0
0
2
0
2
1
2
0
0
2
0
0
0
1
0
0
0
0
2
0
0
1
1
0
0
1
0
0
1
0
0
0
0
1
1
0
0
2
0
0
1
0
0
1
2
2
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
2
2
0
0
0
2
2
0
1
0
2
0
0
0
0
0
1
0
0
1
1
0
1
0
1
0
0
1
0
1
0
1
1
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
1
0
0
0
1
1
0
0
1
1
5
2
2
0
2
0
0
2
0
0
2
0
0
0
0
0
0
2
0
1
0
0
1
0
1
0
0
0
0
0
1
2
0
2
0
2
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
3
1
2
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
2
0
0
3
0
0
0
0
2
0
0
1
1
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
2
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
2
1
1
2
0
1
0
1
1
0
0
0
0
0
0
0
2
0
2
0
1
0
0
1
0
1
0
0
2
3
0
2
0
1
0
2
0
0
0
2
2
2
0
1
0
0
0
0
0
0
0
1
0
2
1
2
0
2
1
1
2
0
0
2
0
0
0
0
1
0
0
2
0
1
1
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
3
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
2
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
2
0
2
4
0
2
0
2
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
1
1
2
0
1
0
0
2
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
2
0
1
0
0
0
0
1
0
0
0
0
2
2
0
1
0
0
0
0
1
2
0
2
0
0
0
1
0
2
0
1
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
2
4
1
0
0
2
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
2
0
1
0
1
0
0
0
1
3
0
0
0
0
0
2
0
2
0
0
2
0
1
0
2
0
0
0
0
1
0
0
0
0
0
2
3
0
0
0
0
1
1
0
2
1
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
3
0
0
2
0
0
0
2
1
0
2
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
2
0
0
2
0
2
0
2
0
0
2
3
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
1
2
0
0
1
0
0
3
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
2
0
2
1
2
0
0
0
2
0
2
1
2
0
0
0
1
2
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
2
3
2
1
0
2
3
1
0
0
1
2
0
0
0
0
0
0
0
2
0
2
0
0
0
1
2
0
0
1
0
1
0
0
0
0
2
1
0
0
2
1
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
1
1
0
1
0
0
2
0
2
0
0
2
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
1
0
0
2
0
1
0
0
2
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
1
0
1
0
0
1
0
0
0
2
1
0
0
1
2
0
0
0
0
2
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
3
0
5
0
0
0
0
0
0
2
0
1
0
0
3
1
0
0
0
2
0
0
0
2
0
0
2
2
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
1
0
1
0
0
0
6
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
2
0
2
0
2
2
0
4
1
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
2
0
0
0
2
1
0
1
0
0
0
0
0
0
0
2
1
1
0
0
1
0
0
1
0
0
2
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
2
2
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
2
4
0
0
0
1
0
0
0
0
1
2
2
0
0
0
0
0
0
0
2
1
0
3
1
2
0
0
0
0
2
2
1
0
2
0
0
0
0
1
0
0
0
3
0
0
0
1
0
0
0
4
1
0
0
0
0
1
2
0
1
3
0
2
1
1
0
1
0
0
2
0
0
0
2
2
4
1
0
0
1
0
2
0
0
2
0
1
0
1
0
0
2
0
0
0
0
1
0
0
2
1
0
1
0
0
1
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
1
0
1
0
0
0
4
0
0
0
1
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
1
0
0
0
0
4
0
1
0
0
1
2
2
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
2
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
3
0
2
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
2
1
0
0
0
1
1
0
0
0
6
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
2
0
0
2
0
0
2
2
0
1
1
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
1
2
2
1
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
3
2
0
1
0
0
2
0
0
0
0
2
2
0
0
0
2
0
2
0
0
2
0
0
0
0
1
0
1
2
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
2
1
0
1
0
0
0
0
0
0
5
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
2
1
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
2
0
1
0
0
1
0
0
2
0
0
0
2
2
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
3
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
1
0
2
0
0
2
0
0
0
0
0
1
1
0
1
1
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
2
2
0
0
0
0
0
0
1
1
0
1
0
0
0
1
3
0
0
0
1
3
0
0
2
1
0
0
0
1
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
2
3
0
0
0
0
0
6
2
2
2
0
5
0
0
2
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
2
2
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
1
1
2
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
2
1
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
2
2
0
0
0
2
2
0
0
1
0
0
0
1
0
0
0
2
0
1
1
0
0
1
7
3
0
0
0
2
2
1
0
0
1
0
2
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
1
0
1
0
6
0
2
1
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
6
0
0
2
0
0
0
2
0
0
0
0
4
1
0
0
2
0
2
2
2
0
1
2
1
0
0
0
0
0
4
0
0
3
0
0
0
0
0
0
0
0
2
2
2
0
1
0
1
0
1
0
1
0
2
0
2
0
0
3
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
4
2
0
0
0
2
1
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
2
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
5
0
2
0
0
3
2
0
0
1
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
1
0
1
0
0
3
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
2
0
0
2
0
0
0
1
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
2
0
0
0
0
1
0
1
0
1
2
2
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
4
1
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
1
0
0
0
2
0
1
0
0
1
3
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
3
1
1
0
1
1
0
0
1
2
2
2
0
0
0
0
2
1
2
0
0
0
0
3
2
0
0
0
0
3
0
0
0
0
1
0
1
3
1
0
0
0
0
2
0
0
2
2
0
0
0
1
2
0
0
0
0
0
0
2
0
1
2
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
2
0
0
0
0
0
6
0
0
0
0
1
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
2
0
6
1
0
0
3
0
0
0
0
2
0
1
2
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
1
2
2
0
2
0
1
0
0
0
2
1
0
1
0
2
0
0
2
1
0
0
0
0
0
2
0
0
0
3
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
2
2
1
0
0
2
0
0
0
4
0
0
0
2
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
1
2
0
1
0
2
0
1
1
0
3
0
0
1
0
0
0
2
2
0
1
0
2
1
1
0
0
0
1
0
2
1
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
2
2
0
0
0
1
0
0
1
1
0
0
0
0
0
2
0
1
0
1
1
0
2
0
1
1
0
0
1
2
0
2
2
0
0
0
0
0
0
0
0
0
2
2
0
2
2
2
0
0
0
0
0
1
0
2
2
1
0
0
2
0
3
0
0
0
0
0
0
0
0
1
0
1
2
2
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
2
6
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
1
0
2
0
1
0
2
1
0
0
0
2
2
0
0
0
0
0
0
3
0
1
0
0
0
1
0
0
0
2
0
2
0
1
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
2
0
1
2
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
1
1
0
0
0
0
2
2
0
0
2
2
0
0
0
4
0
0
1
2
0
0
0
0
2
1
1
1
0
0
1
2
0
0
0
0
2
0
2
0
0
1
2
1
1
0
0
2
0
0
3
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
2
0
1
0
1
0
0
0
0
0
0
0
1
2
0
0
0
2
2
0
1
0
0
0
2
0
2
0
3
0
0
2
1
1
0
0
0
0
4
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
2
0
1
0
0
1
1
0
0
0
0
0
0
1
1
0
0
1
2
3
0
0
1
1
0
1
0
2
0
2
0
0
0
1
2
0
2
0
0
1
0
0
0
0
0
3
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
7
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
2
2
1
0
1
0
0
0
0
1
0
2
0
2
1
2
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
1
0
2
0
2
1
0
0
0
0
2
0
0
2
0
0
2
0
0
0
5
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
2
2
2
0
0
1
0
4
0
1
4
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
2
2
0
0
0
2
2
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
4
0
0
0
1
0
0
1
0
0
0
0
0
0
1
2
0
0
1
0
0
0
2
3
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
4
1
1
0
0
2
0
1
2
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
2
0
1
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
3
0
2
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
1
2
0
2
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
2
0
2
1
0
0
0
0
1
0
0
0
0
2
0
2
1
0
0
0
0
0
0
1
1
0
2
0
1
0
0
0
0
0
0
0
0
0
1
1
2
2
0
2
1
0
1
0
4
0
0
0
0
2
1
0
1
0
1
1
0
1
0
0
0
0
0
0
1
2
1
0
0
2
1
0
2
0
2
0
0
2
0
2
0
0
0
1
0
1
2
0
0
0
0
0
2
0
1
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
1
0
2
1
2
2
0
0
0
0
1
0
0
0
0
3
2
1
0
0
2
0
0
0
1
0
1
0
1
1
3
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
3
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
1
0
0
1
0
0
0
1
0
0
1
0
0
1
2
0
0
0
0
1
0
0
0
0
1
1
0
0
2
0
0
1
1
2
1
0
0
0
0
1
2
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
3
0
1
2
0
4
1
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
1
1
0
0
0
2
0
0
1
2
2
0
0
0
0
0
0
3
0
2
0
1
0
0
0
0
0
0
2
0
0
0
1
2
1
2
0
0
2
0
0
2
0
0
0
0
1
0
2
2
0
0
1
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
3
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
3
1
0
0
0
1
0
0
2
0
1
0
0
3
2
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
2
1
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
19
0
0
0
0
0
0
0
1
0
1
1
3
0
2
0
0
1
0
0
0
0
1
3
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
2
0
0
2
0
1
0
0
0
2
2
0
1
0
0
1
0
0
0
0
0
0
1
0
0
2
0
1
0
2
0
2
0
1
0
0
0
0
2
1
0
0
1
0
0
0
0
2
0
2
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
2
1
0
2
0
1
1
2
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
2
0
0
3
1
0
0
2
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
1
0
0
1
0
0
1
2
0
0
0
2
1
0
1
2
0
0
2
1
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
2
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
1
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
2
0
0
7
0
0
0
0
0
0
1
1
0
0
0
0
3
0
2
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
2
0
0
0
0
0
2
5
2
1
1
0
1
0
2
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
1
1
1
2
0
0
0
0
1
2
0
0
0
1
0
1
0
2
0
0
0
2
1
0
0
1
0
0
0
0
2
0
2
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
2
0
1
1
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
1
1
0
0
0
2
0
1
1
2
1
0
2
0
0
0
1
0
0
0
0
2
1
0
2
2
0
2
0
0
0
0
1
2
1
1
1
0
0
2
0
0
0
0
0
0
0
2
0
1
2
0
2
1
0
0
2
1
0
0
2
0
0
0
1
2
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
1
2
0
3
1
1
0
1
0
0
0
0
0
0
1
1
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
2
0
1
1
2
0
0
0
2
1
2
0
7
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
2
0
0
1
0
0
0
0
0
2
0
1
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
1
4
0
0
2
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
3
0
0
1
3
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
2
1
0
0
0
3
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
3
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
2
0
0
0
1
0
2
0
1
2
0
0
2
0
0
0
0
1
0
1
0
2
0
4
0
0
0
0
0
2
2
0
3
0
0
0
0
0
1
0
2
0
0
2
0
1
0
0
1
0
0
1
0
0
0
0
0
2
0
1
1
0
1
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
1
1
0
0
0
0
2
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
1
4
0
0
0
0
1
0
0
1
1
0
0
0
1
1
1
0
0
2
0
1
0
1
0
7
2
1
2
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
2
0
1
1
0
0
1
1
2
1
0
0
0
0
0
0
0
0
0
0
0
1
2
2
2
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
5
0
0
2
0
2
0
0
0
2
2
2
0
2
0
0
0
0
0
3
0
4
0
0
1
0
0
0
1
1
1
0
0
1
0
2
0
2
2
0
0
0
0
0
5
0
0
0
1
0
0
1
2
2
0
2
3
0
0
0
0
0
1
0
1
2
3
1
0
1
2
0
0
1
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
2
0
2
2
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
2
1
0
0
0
2
2
1
2
0
0
2
0
3
1
1
0
0
0
0
2
0
0
2
0
0
0
0
2
1
0
2
1
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
2
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
2
1
0
2
2
0
2
0
1
0
0
0
3
1
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
3
0
1
1
2
0
2
1
1
2
0
1
0
0
0
1
1
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
1
2
0
0
3
0
0
0
1
2
0
2
2
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
1
2
0
1
2
0
0
0
0
3
1
0
1
2
1
0
0
3
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
1
3
0
0
0
4
0
0
0
2
2
0
0
2
2
2
1
0
0
0
0
1
1
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
4
2
0
0
2
1
0
0
0
2
0
2
0
0
1
0
0
0
0
2
4
0
0
2
1
2
3
1
0
0
0
0
0
0
0
2
0
0
0
2
1
2
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
3
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
1
1
0
0
1
2
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
2
0
2
0
2
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
1
3
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
8
0
0
2
1
2
2
0
0
1
0
0
0
2
1
2
1
1
0
2
3
0
0
0
0
0
0
0
0
0
0
2
3
2
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
1
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
2
0
2
1
2
0
1
1
2
2
2
0
0
0
0
1
0
2
1
0
0
0
1
1
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
3
0
0
0
0
0
1
0
2
0
0
0
2
1
0
0
2
0
4
0
0
2
0
2
0
0
1
0
2
0
0
0
1
5
2
0
0
1
2
1
0
2
0
1
0
0
2
0
0
0
2
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
2
0
3
0
0
2
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
2
2
2
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
2
0
1
0
1
0
0
1
2
0
0
2
1
0
0
0
0
0
0
2
1
2
0
0
0
1
2
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
2
0
1
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
1
3
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
1
1
1
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
7
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
6
0
0
2
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
2
0
0
6
1
0
0
0
1
2
0
0
0
1
2
0
0
0
1
1
0
0
1
0
1
0
2
0
0
1
0
2
1
0
0
2
0
0
0
5
0
0
0
1
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
3
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
3
0
0
0
0
2
0
2
0
0
0
3
2
0
1
0
0
0
2
2
0
0
0
1
0
1
1
1
0
1
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
1
0
0
0
0
2
0
1
4
1
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
2
0
0
2
0
0
2
3
0
3
1
1
2
1
1
0
4
1
0
0
2
0
1
2
1
0
0
0
0
0
3
2
0
0
0
0
2
2
0
1
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
3
0
3
0
0
0
0
0
0
0
1
0
0
0
3
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
2
1
2
2
1
0
2
0
0
0
1
2
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
1
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
1
0
0
1
1
5
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
1
0
1
0
2
2
0
2
1
1
0
0
1
0
0
0
0
0
1
1
3
0
0
0
2
0
1
0
1
0
0
0
0
2
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
1
2
0
0
0
0
0
0
0
2
0
2
1
0
0
0
1
1
0
1
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
3
0
2
0
1
2
2
1
0
0
2
0
0
1
0
3
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
1
1
0
0
0
1
0
0
1
2
0
0
1
1
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
1
2
0
1
2
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
2
1
0
0
0
0
2
0
1
1
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
1
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
2
0
0
0
2
1
1
1
1
0
0
0
1
1
0
0
0
0
2
0
0
1
0
0
0
2
1
2
0
0
0
0
4
0
0
0
1
0
0
1
1
0
0
0
0
0
1
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
1
1
2
2
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
2
2
0
0
0
0
0
1
2
0
2
0
2
0
1
1
2
1
1
2
0
0
2
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
2
1
1
0
0
0
1
2
0
0
2
1
1
2
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
1
0
1
0
0
0
0
1
1
2
0
0
0
2
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
2
1
0
1
0
0
2
0
4
0
1
2
1
0
0
1
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
1
0
0
2
1
0
2
0
0
0
0
0
0
0
2
0
1
2
0
1
0
0
0
0
0
0
0
2
2
1
2
2
0
0
2
2
0
2
0
1
2
0
0
1
1
0
2
0
2
2
0
2
0
0
2
0
0
1
0
2
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
2
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
1
0
2
2
0
1
0
4
2
2
2
2
2
0
0
2
0
0
0
0
2
3
2
2
1
0
0
0
0
0
0
0
0
0
2
0
0
2
1
2
0
1
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
1
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
2
0
2
0
2
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
1
0
0
2
2
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
2
1
1
1
0
0
0
0
3
0
0
0
0
2
0
0
0
1
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
2
0
1
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
2
0
1
0
1
2
0
0
4
1
1
2
0
0
1
3
0
1
0
0
1
0
2
2
0
2
3
0
4
0
2
0
0
0
0
0
0
0
1
0
3
3
0
0
0
0
0
0
1
0
0
0
3
0
1
0
1
0
2
2
1
2
1
0
1
0
1
1
0
0
0
1
0
0
2
0
1
1
2
2
0
0
1
0
0
0
0
1
1
0
0
1
1
0
1
0
0
2
0
0
0
0
0
0
2
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
5
2
0
2
0
1
1
0
0
0
0
0
1
1
0
0
2
0
0
0
0
1
0
0
2
1
2
1
1
0
0
1
0
0
0
2
0
0
2
1
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
1
1
0
0
1
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
2
0
2
0
1
2
0
1
1
3
0
0
0
1
0
2
2
2
2
1
0
1
1
3
0
1
0
2
1
1
0
0
0
2
2
0
0
2
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
2
2
2
0
6
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
2
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
3
0
1
1
0
0
0
1
0
0
0
0
0
0
0
2
2
2
1
0
0
4
0
0
0
0
0
0
0
3
0
2
0
2
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
2
0
1
0
0
0
0
0
2
0
0
3
0
0
0
4
0
0
0
1
2
0
1
4
0
0
0
0
0
0
0
0
0
5
0
0
0
1
0
0
2
0
0
0
1
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
2
0
2
0
0
0
0
1
0
0
0
2
2
0
0
0
0
1
0
1
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
2
2
0
1
1
0
0
0
0
2
1
0
0
0
0
0
1
0
0
1
0
0
2
0
0
1
2
0
1
0
0
0
0
0
0
0
0
2
0
1
0
3
0
0
0
0
0
1
1
0
0
0
1
2
0
0
0
1
0
0
1
0
0
1
0
0
2
1
0
0
0
2
0
1
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
1
3
0
0
0
2
0
1
0
2
0
0
2
0
0
3
0
0
2
0
1
0
0
0
2
0
0
0
0
3
0
0
0
0
2
0
0
0
2
1
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
2
2
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
2
1
0
1
0
2
2
2
0
1
0
0
0
0
0
0
2
2
0
2
0
0
2
0
1
0
2
0
1
2
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
2
2
0
0
0
2
0
0
0
0
2
0
0
0
2
1
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
2
0
0
2
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
2
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
4
0
0
1
0
0
1
0
0
0
1
1
1
0
3
0
0
0
0
0
0
2
1
0
4
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
3
1
0
0
0
0
1
0
0
0
1
0
0
2
1
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
2
2
2
0
0
2
2
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
2
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
1
2
0
0
2
0
1
1
0
2
0
1
1
0
1
2
3
0
0
0
0
0
0
1
0
2
1
1
0
2
0
2
0
0
0
0
2
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
1
1
2
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
2
0
1
1
3
1
0
0
0
0
2
0
3
0
0
1
1
1
1
0
0
2
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
1
2
4
3
2
1
0
1
2
0
0
2
0
2
1
0
0
0
0
0
0
2
0
0
0
2
0
0
2
2
0
2
3
4
3
0
0
0
1
1
0
2
0
2
0
0
0
0
0
2
0
0
0
1
1
2
1
2
0
0
0
1
0
0
2
0
0
0
0
2
1
2
0
0
1
0
0
0
2
1
0
6
0
0
0
1
2
0
1
2
1
0
0
0
1
2
0
2
0
0
1
0
3
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
1
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
10
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
1
0
4
1
2
0
0
0
0
2
1
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
2
0
1
1
2
0
0
2
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
1
4
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
2
0
0
0
2
0
2
2
2
2
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
1
2
1
0
0
0
0
0
1
2
0
0
0
0
1
0
1
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
1
1
1
0
0
0
1
1
0
0
0
5
0
0
1
1
1
0
0
0
0
0
1
1
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
2
1
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
4
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
9
0
0
2
2
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
3
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
2
2
2
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
2
0
0
2
2
0
0
2
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
2
2
0
2
3
0
1
1
0
1
2
0
1
0
0
1
0
3
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
3
0
1
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
3
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
2
0
1
0
2
0
0
7
0
0
0
0
1
0
0
0
0
0
2
0
0
0
3
1
0
0
0
2
0
0
1
0
2
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
3
0
0
2
0
0
1
0
0
1
0
0
0
0
0
1
2
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
1
2
0
1
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
3
2
0
0
0
0
1
1
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
1
1
1
0
2
1
3
0
1
0
0
2
0
1
2
2
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
2
1
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
1
0
1
0
0
1
0
2
0
0
0
0
3
1
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
2
2
1
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
1
0
2
5
0
0
0
0
2
0
0
0
2
2
1
0
0
0
0
2
0
0
0
0
1
0
3
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
2
0
1
0
1
0
0
0
0
2
0
1
0
0
0
0
3
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
1
0
3
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
1
1
2
0
0
0
0
2
0
0
0
0
1
1
1
0
0
0
2
2
2
0
4
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
1
1
1
0
0
1
2
2
1
1
0
0
0
0
1
0
0
1
0
0
0
3
0
1
2
1
0
0
2
0
0
2
0
1
0
0
1
2
0
0
1
3
0
0
0
0
0
0
0
2
1
1
2
2
0
0
3
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
1
0
0
0
0
2
0
0
0
0
1
2
0
1
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
2
1
0
1
1
2
0
1
1
0
0
2
0
0
1
0
1
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
2
1
0
0
1
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
1
0
1
0
2
0
1
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
2
1
0
1
0
0
0
2
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
3
0
0
3
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
1
0
0
1
0
2
0
0
0
0
2
0
0
1
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
1
0
2
3
2
0
0
0
0
2
0
0
0
1
0
1
0
0
0
2
0
0
0
1
0
0
0
1
0
0
1
2
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
2
1
1
1
0
0
0
2
0
0
0
1
1
0
0
0
0
0
1
0
2
0
1
1
2
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
2
0
0
0
1
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
5
0
0
0
0
0
2
1
2
0
0
2
0
0
2
0
0
1
0
2
2
2
0
0
0
0
1
0
1
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
3
0
2
2
0
0
0
0
0
2
0
0
1
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
2
0
1
0
0
0
2
2
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
1
0
4
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
2
2
0
2
0
0
0
1
0
0
0
0
0
0
2
2
0
0
3
0
0
1
0
0
1
0
0
1
0
0
0
0
2
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
1
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
4
0
1
0
2
1
0
0
0
0
0
0
0
0
2
0
2
0
1
2
0
0
0
2
1
3
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
3
0
2
0
0
0
0
0
7
1
2
0
0
0
1
1
0
2
1
0
0
1
0
0
1
0
0
2
0
2
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
1
0
2
1
0
0
0
0
2
0
1
2
0
1
0
0
1
0
0
1
0
2
0
1
4
0
0
0
2
0
1
1
0
2
0
0
2
0
1
2
1
2
0
0
0
1
0
2
2
0
1
0
2
0
2
1
0
0
1
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
1
0
1
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
2
0
1
2
0
1
1
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
4
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
7
0
0
4
1
0
3
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
2
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
2
1
2
0
0
1
2
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
3
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
2
2
0
2
1
0
0
0
1
0
1
0
1
0
0
1
0
0
1
0
0
0
2
0
0
2
0
0
2
0
2
0
0
1
0
0
0
0
0
0
2
1
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
1
0
0
0
1
0
0
0
1
0
0
2
0
1
2
0
0
0
0
1
2
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
1
0
1
0
1
0
1
2
1
0
0
0
1
1
1
0
1
0
0
1
2
1
1
0
0
3
1
0
0
0
0
0
0
5
2
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
2
0
2
0
0
0
0
0
1
0
0
1
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
2
1
0
0
0
0
2
0
0
0
1
1
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
2
0
1
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
3
1
0
2
0
0
1
0
3
0
0
0
1
0
0
0
0
2
0
2
0
0
2
2
0
1
2
3
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
1
0
1
0
0
0
0
2
0
1
0
0
1
0
0
2
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
2
0
0
0
1
2
0
0
6
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
1
0
0
2
0
1
3
3
0
0
0
0
0
2
1
1
1
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
1
2
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
1
0
0
2
1
0
1
0
0
0
0
1
0
0
0
0
1
2
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
2
0
0
0
0
5
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
3
2
0
0
0
1
0
0
2
1
0
0
0
2
0
0
1
0
0
0
1
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
1
0
0
1
0
2
1
1
0
0
0
0
1
0
0
0
0
3
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
1
4
0
1
1
0
1
0
0
0
1
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
2
0
0
1
0
1
0
1
0
1
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
2
0
0
0
1
0
0
2
1
0
1
0
1
0
0
0
1
0
0
0
1
0
3
0
0
0
0
3
0
1
0
2
0
3
0
0
2
0
0
0
1
2
0
2
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
3
0
0
2
0
0
1
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
3
0
2
1
0
0
0
0
1
1
2
1
0
0
1
1
0
0
0
2
1
0
0
0
0
0
1
1
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
1
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
1
0
2
0
0
1
0
0
0
0
0
0
3
0
3
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
2
1
1
2
0
2
0
1
0
0
0
0
0
0
4
0
1
1
3
0
0
1
0
0
0
0
0
0
0
2
0
2
2
1
0
2
1
0
0
0
0
1
1
2
0
0
0
0
0
0
1
1
0
0
0
1
0
2
2
0
0
0
0
0
0
2
2
0
0
2
0
2
1
1
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
3
0
2
2
1
0
0
0
0
1
0
1
2
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
2
2
1
0
2
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
1
1
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
1
2
3
0
0
0
0
0
0
2
1
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
2
0
1
0
0
3
0
0
0
2
0
0
0
0
1
0
0
2
0
2
0
1
0
0
2
0
0
2
1
0
0
0
0
1
0
2
2
0
0
0
0
0
0
2
0
0
0
1
0
1
1
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
2
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
2
1
0
2
0
0
0
3
2
0
0
0
0
0
1
0
0
0
5
0
0
2
1
2
0
2
0
0
0
0
0
0
0
3
1
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
2
2
0
0
0
1
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
2
1
0
0
0
0
0
1
0
2
1
2
0
0
1
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
2
0
2
0
0
1
0
0
0
0
1
6
1
1
2
0
0
0
0
2
1
1
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
2
0
1
1
1
0
0
0
1
0
1
2
2
0
2
0
2
0
0
0
0
0
0
1
0
2
0
0
2
0
0
2
0
0
2
1
0
2
0
1
1
0
1
0
0
2
0
0
0
0
2
0
0
0
4
0
0
0
1
0
0
0
0
0
0
1
2
0
0
1
1
0
0
0
2
0
0
0
0
0
1
0
0
2
2
0
0
1
3
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
1
2
1
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
2
0
0
1
1
0
1
0
2
0
0
0
0
1
1
0
4
2
1
0
0
0
1
1
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
1
1
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
2
1
0
0
0
4
0
0
1
2
0
1
0
1
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
1
2
0
0
0
0
0
0
1
3
3
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
3
2
5
0
0
0
1
1
0
2
0
5
4
0
0
0
0
1
0
2
0
0
2
1
0
1
2
0
2
0
3
1
1
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
4
0
0
1
0
1
0
0
0
0
0
0
0
1
1
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
1
0
2
0
0
0
1
2
2
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
7
0
2
0
1
0
1
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
3
3
2
2
0
0
0
4
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
2
1
0
1
0
2
1
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
3
0
2
0
0
0
0
2
0
0
0
3
0
0
4
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
2
2
2
0
0
2
0
2
0
3
0
0
1
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
1
1
0
0
0
0
3
1
0
2
0
2
1
1
3
0
0
2
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
2
1
0
0
2
1
3
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
2
0
2
2
0
2
1
0
0
3
0
1
1
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
2
2
2
1
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
2
0
0
0
0
1
0
1
0
0
2
0
0
0
1
2
0
0
0
0
2
0
0
0
3
2
0
0
0
2
0
0
1
0
3
1
2
0
1
0
0
0
1
1
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
1
2
3
0
0
3
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
3
0
0
2
0
0
1
0
1
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
1
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
1
0
2
0
2
2
2
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
1
0
0
0
0
1
3
3
0
2
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
1
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
2
1
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
1
2
0
0
2
1
1
2
2
2
0
0
0
0
0
3
1
2
2
0
2
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
1
2
1
0
1
2
0
0
0
0
0
0
0
0
2
1
0
1
0
0
3
0
0
0
1
0
0
0
1
0
2
2
0
0
1
2
0
1
2
0
0
2
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
2
0
1
2
0
2
0
0
0
1
0
0
0
0
0
4
0
2
0
0
0
0
0
2
0
2
0
0
0
0
1
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
1
0
2
2
1
0
1
0
1
0
1
0
0
0
2
0
0
0
2
0
2
1
1
0
0
3
1
0
0
0
0
0
2
0
3
0
3
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
3
1
2
1
2
0
0
0
2
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
3
1
0
0
0
0
0
0
0
1
0
0
0
2
2
2
0
2
0
0
3
0
0
0
0
0
2
0
2
1
0
0
0
2
0
0
0
0
2
2
2
2
0
1
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
1
3
0
1
1
1
0
0
0
0
0
2
2
0
1
0
0
0
0
1
0
0
0
2
0
0
4
0
0
0
0
0
1
1
0
2
0
3
0
0
0
0
0
1
0
0
0
1
0
0
1
2
0
1
3
2
0
2
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
3
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
2
1
0
0
0
2
0
0
0
1
2
0
0
2
0
2
0
0
0
0
1
2
0
0
0
0
0
4
0
0
0
0
0
2
1
0
0
2
2
0
0
0
1
0
2
0
1
1
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
3
0
1
0
1
0
0
2
0
0
1
0
0
0
2
2
1
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
1
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
2
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
2
2
0
0
0
1
0
0
1
0
0
0
2
2
1
0
0
2
1
0
1
0
2
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
1
0
0
3
0
1
1
0
2
1
0
2
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
2
0
0
0
0
0
0
3
0
2
1
0
2
1
2
0
1
0
2
0
0
2
0
0
0
0
0
0
0
2
1
4
1
1
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
1
1
0
4
0
1
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
2
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
1
2
0
0
2
2
0
0
9
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
2
0
2
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
2
1
0
2
0
1
3
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
2
0
0
0
3
1
0
0
0
0
0
2
0
2
3
0
0
0
0
0
3
0
0
0
0
0
0
5
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
2
0
0
2
0
0
3
0
0
0
2
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
2
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
6
0
0
2
0
1
0
0
0
0
0
4
2
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
3
3
0
0
0
2
1
0
0
0
2
1
0
0
2
1
1
0
1
1
0
3
1
1
2
2
0
1
4
0
0
0
1
0
1
1
0
2
0
0
2
0
3
0
0
0
1
0
0
0
2
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
2
0
1
2
0
1
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
1
2
0
0
0
2
1
0
2
0
2
0
0
0
2
0
0
0
1
0
2
2
0
0
2
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
2
0
2
0
0
0
2
1
0
0
1
1
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
1
0
1
1
0
0
2
1
0
0
0
0
0
2
0
1
6
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
3
1
0
2
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
7
0
0
0
0
1
2
0
1
2
0
1
1
2
0
2
2
0
0
0
0
1
1
2
2
0
0
0
0
2
0
2
2
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
3
0
0
2
2
0
0
1
2
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
1
0
1
1
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
1
2
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
6
0
0
0
2
0
0
1
0
0
2
1
1
0
0
0
0
3
0
0
0
1
0
1
2
0
2
0
2
1
0
2
0
0
0
0
0
0
0
0
0
2
1
2
1
0
2
0
1
0
0
1
0
0
2
0
2
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
2
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
3
2
2
0
1
0
1
0
0
2
2
0
0
0
2
0
0
0
2
0
0
2
1
0
1
2
0
2
0
0
0
0
0
2
0
0
0
2
0
1
1
0
0
1
2
0
0
0
1
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
2
0
1
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
2
0
2
2
1
1
0
0
0
0
0
0
2
4
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
2
2
1
0
0
8
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
1
0
2
0
0
0
2
0
0
3
0
0
0
1
0
0
0
1
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
4
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
3
1
6
0
1
0
0
1
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
2
0
0
0
1
0
0
0
2
0
0
0
0
2
0
2
2
0
0
1
0
2
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
2
2
2
0
0
0
0
0
0
0
2
0
0
0
0
2
2
2
0
0
1
2
0
0
1
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
4
0
0
0
0
1
0
0
3
0
0
0
0
0
1
0
0
2
0
1
0
1
3
0
0
0
1
2
0
0
0
2
0
0
0
1
0
0
1
0
0
0
2
2
0
0
0
0
0
1
2
2
1
0
1
0
0
0
0
3
0
0
0
0
1
1
0
0
0
1
6
2
1
0
0
1
0
2
2
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
1
1
0
0
0
1
0
0
0
3
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
1
1
1
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
2
0
1
0
2
0
0
2
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
2
0
2
0
1
0
0
0
2
1
2
0
0
1
0
0
0
0
3
0
0
0
0
0
1
2
0
0
2
0
0
0
0
3
0
0
2
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
1
0
2
0
0
2
0
0
2
1
1
1
0
0
1
0
1
0
0
1
0
0
0
1
1
0
3
0
1
0
0
0
1
2
0
0
0
0
0
0
2
3
0
1
0
0
0
0
0
0
0
2
1
1
0
0
0
2
0
1
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
5
0
0
0
3
1
0
0
0
0
3
0
2
0
0
0
0
1
1
1
2
3
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
1
1
0
0
0
4
0
2
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
2
2
1
0
1
0
1
0
0
0
2
6
0
2
2
1
0
0
0
3
0
0
0
0
0
0
0
0
0
2
1
0
0
2
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
1
2
1
0
0
0
0
0
0
0
0
2
2
2
1
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
2
0
1
0
1
2
0
0
0
0
2
0
0
0
2
0
1
5
2
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
1
0
1
0
1
0
2
0
0
0
0
0
0
0
3
0
1
0
0
1
0
3
0
0
2
0
1
2
0
2
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
1
0
0
2
2
1
2
1
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
1
1
0
0
0
0
2
1
1
0
0
0
0
0
0
2
0
0
0
0
2
0
2
2
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
2
0
0
2
1
1
2
0
0
1
1
0
1
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
3
2
3
2
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
2
0
0
2
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
2
1
0
0
2
0
0
2
0
0
0
0
0
0
0
2
1
0
3
0
1
0
0
0
1
0
0
0
0
1
2
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
1
0
2
0
0
0
1
1
0
1
0
0
1
0
2
1
0
1
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
2
0
0
1
0
0
1
0
0
0
1
0
1
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
3
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
1
0
0
0
2
0
0
2
0
0
2
0
1
1
0
0
0
0
1
0
2
1
1
1
0
0
0
0
2
2
0
0
0
0
0
2
0
0
2
2
1
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
5
0
1
0
1
0
0
1
3
1
0
2
0
5
1
0
0
0
2
0
0
2
2
1
0
0
0
2
0
1
0
0
1
0
0
2
1
0
2
1
0
1
0
1
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
2
0
0
0
0
0
0
1
2
0
0
1
0
2
0
1
0
0
0
0
1
2
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
1
0
2
0
0
0
1
2
1
0
1
1
0
0
2
0
0
0
1
0
1
2
0
0
0
0
2
0
2
0
0
0
0
0
2
0
2
1
0
0
0
2
0
0
0
0
0
1
2
0
1
0
0
1
0
1
0
0
0
0
2
2
0
0
0
1
1
3
0
0
1
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
1
0
1
2
2
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
2
1
1
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
1
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
1
0
2
0
1
0
0
0
0
1
0
0
1
2
0
0
0
2
3
0
1
2
0
1
0
0
0
0
0
0
2
2
0
11
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
2
0
1
0
0
0
2
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
1
2
0
0
0
0
0
0
0
0
2
2
0
0
3
1
0
0
0
4
0
0
2
0
0
0
2
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
2
2
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
3
2
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
2
0
1
1
2
0
1
1
0
0
0
1
0
0
1
0
2
1
0
0
2
2
1
1
2
1
2
0
0
0
0
0
2
2
0
3
0
3
0
1
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
1
3
2
0
0
0
2
2
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
1
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
1
1
0
0
1
3
0
2
2
1
1
2
0
2
0
1
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
2
1
0
2
0
0
2
0
0
1
1
2
1
2
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
1
2
3
2
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
5
0
0
0
2
0
0
0
0
0
0
0
1
0
0
3
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
2
0
2
1
2
0
2
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
1
0
0
0
1
1
1
0
0
2
0
1
0
2
0
0
2
0
1
2
1
0
0
2
2
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
1
0
3
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
3
1
0
0
3
0
2
2
0
1
0
0
1
0
1
3
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
1
1
0
1
0
4
0
1
1
0
2
0
2
0
0
1
0
1
2
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
2
1
0
4
0
0
2
0
0
0
1
2
0
0
0
1
0
1
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
2
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
1
2
3
0
0
0
0
5
0
0
0
2
0
0
0
2
0
1
0
0
0
1
1
0
1
2
1
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
2
0
2
0
1
2
2
2
1
2
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
2
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
3
0
0
0
1
0
2
0
0
0
0
2
0
1
2
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
1
2
0
0
0
1
0
0
0
2
0
0
1
0
2
0
0
1
0
0
0
2
1
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
2
1
0
0
1
0
2
0
0
0
0
2
1
1
0
1
2
1
0
1
0
0
0
2
0
0
0
0
2
1
0
0
4
0
0
2
0
0
0
0
0
1
0
3
0
0
0
0
0
0
1
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
8
0
2
0
0
0
0
0
0
4
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
1
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
3
2
1
0
2
0
0
2
0
0
0
1
0
0
0
1
2
0
2
0
2
2
0
0
0
0
0
0
1
0
0
0
1
2
3
1
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
2
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
9
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
2
0
0
0
0
1
0
2
0
0
3
0
2
0
0
0
0
0
2
0
0
1
0
1
2
0
2
1
0
0
0
0
2
2
2
0
2
0
3
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
6
2
0
0
0
1
0
0
0
1
1
0
2
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
2
1
1
0
0
0
0
0
1
0
5
2
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
1
1
0
0
4
0
0
0
2
2
0
2
1
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
1
0
2
0
2
0
2
0
0
1
0
0
1
1
0
1
0
0
0
0
0
1
0
1
0
0
0
2
1
0
0
3
1
2
0
0
0
0
1
0
0
0
0
0
2
0
2
0
1
0
1
1
0
0
0
2
3
0
0
0
1
0
2
0
0
0
1
0
1
0
0
1
0
0
1
1
2
1
0
0
0
1
0
0
0
0
0
0
0
1
1
2
2
1
2
1
0
0
0
0
2
0
0
4
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
3
0
0
0
2
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
2
1
1
4
0
0
0
0
2
0
0
0
1
1
0
0
0
0
3
1
2
0
0
0
3
0
0
0
0
0
1
2
1
0
0
0
1
1
1
2
0
0
1
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
2
0
1
1
0
0
0
0
0
1
1
0
0
0
1
0
0
2
0
0
0
0
0
1
0
1
0
3
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
1
0
2
0
0
6
2
2
3
1
0
1
1
0
0
0
1
0
0
0
2
0
1
1
0
2
0
0
2
0
1
1
1
0
0
0
0
0
2
0
2
0
0
0
2
1
0
0
0
1
2
0
0
4
0
1
0
0
0
1
0
2
0
0
0
1
0
0
0
1
0
1
1
0
0
1
0
2
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
2
2
0
0
0
0
0
2
0
3
2
1
2
0
0
0
0
1
1
0
0
0
1
0
1
2
0
0
1
1
0
1
0
2
0
2
0
0
1
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
2
0
0
2
0
0
3
1
0
0
0
1
0
0
2
0
1
0
0
0
0
0
2
0
2
0
1
0
2
0
0
1
0
0
0
1
2
0
2
0
1
1
1
0
0
2
2
2
0
0
0
0
0
0
0
2
2
0
7
1
0
2
0
0
0
0
1
0
0
0
1
1
0
0
0
1
2
2
0
2
2
0
0
1
0
2
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
3
0
0
1
0
2
0
0
0
0
0
0
0
0
2
1
2
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
2
0
0
0
3
0
0
0
0
2
0
0
0
1
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
1
1
0
1
0
3
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
2
2
0
0
0
0
0
1
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
2
2
1
2
0
0
0
0
0
0
1
2
0
1
2
2
1
2
0
2
2
2
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
2
0
0
0
2
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
3
2
0
0
2
0
0
0
1
0
2
0
0
2
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
2
0
2
0
6
2
0
0
1
0
2
2
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
3
0
0
2
0
2
0
1
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
3
0
0
0
2
0
0
2
0
1
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
2
0
3
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
4
0
0
1
4
0
2
1
0
1
1
0
1
0
0
0
0
0
1
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
1
0
1
1
2
0
0
2
0
0
0
2
2
0
0
2
0
0
0
0
1
0
0
2
0
0
0
2
0
1
1
1
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
2
0
2
1
2
0
0
0
0
0
0
2
0
0
0
2
1
0
1
1
0
0
0
1
1
0
2
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
2
1
0
2
0
0
0
0
1
2
0
1
0
2
0
0
1
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
1
0
1
0
1
2
0
2
0
0
0
0
2
0
2
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
1
0
2
0
0
0
3
3
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
1
4
0
0
0
1
2
0
0
0
1
2
0
0
1
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
2
0
1
1
0
0
0
1
2
0
2
0
0
0
1
0
0
1
2
2
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
1
0
0
2
0
2
4
0
2
0
1
0
0
0
2
0
0
0
1
0
0
1
2
0
0
2
2
0
0
1
0
0
2
3
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
2
0
2
0
0
0
1
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
1
2
0
0
1
2
0
0
0
0
0
0
0
4
0
0
0
2
2
2
2
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
2
0
0
1
0
0
0
0
2
2
0
0
1
1
1
0
0
0
2
2
0
2
0
2
0
2
2
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
4
0
0
0
0
2
1
0
0
0
0
0
2
0
1
0
1
2
0
0
1
0
2
1
0
1
2
0
2
0
2
0
0
0
0
2
0
0
0
1
0
0
0
1
0
2
3
0
2
0
1
0
1
0
0
2
0
0
0
1
1
1
0
0
0
0
1
2
0
0
7
0
3
0
0
0
1
0
0
1
1
0
0
1
2
0
0
0
0
0
0
0
1
0
1
2
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
1
1
0
2
3
0
0
1
0
2
2
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
2
0
0
0
1
0
0
4
0
0
1
0
0
1
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
5
0
0
0
0
2
0
0
0
2
1
0
2
0
1
3
0
0
0
0
0
2
0
0
2
0
0
0
2
1
2
0
0
1
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
2
0
0
2
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
3
0
0
1
0
0
2
0
0
0
0
0
1
2
0
2
1
0
0
0
2
0
1
4
2
1
1
1
2
2
0
1
0
2
0
5
0
2
0
0
4
0
0
1
0
1
0
1
1
1
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
2
0
0
0
1
0
1
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
4
1
2
1
0
1
0
0
1
0
1
0
3
0
1
0
3
0
0
0
2
1
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
2
0
0
1
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
10
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
1
0
0
0
0
1
1
0
1
2
1
0
1
0
1
0
3
0
2
1
0
0
0
1
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
4
0
0
1
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
3
0
2
2
1
0
0
2
3
0
1
0
1
1
0
1
1
0
2
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
1
1
0
0
1
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
1
0
2
0
0
0
2
0
2
1
0
2
2
0
0
2
0
0
3
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
2
0
0
0
0
1
2
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
2
4
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
1
2
2
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
4
0
2
2
2
2
0
2
0
8
0
0
2
0
0
0
0
3
1
0
0
0
0
1
2
0
0
0
0
2
2
2
0
3
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
4
0
2
0
0
2
0
0
2
3
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
1
0
0
1
0
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
3
0
0
1
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
2
0
0
2
4
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
1
0
1
0
0
1
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
2
1
0
0
0
4
0
0
3
0
2
1
0
1
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
2
1
0
0
0
2
0
1
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
5
2
1
2
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
2
0
0
1
0
1
0
2
3
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
1
0
2
0
1
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
5
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
1
0
1
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
3
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
3
1
0
0
0
0
2
0
0
0
3
0
2
1
0
3
1
0
2
2
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
1
0
1
0
0
1
0
0
1
0
0
1
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
3
1
0
1
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
1
0
2
2
0
2
0
0
0
0
0
0
0
0
2
0
2
1
1
2
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
1
0
1
1
0
0
0
0
2
0
0
0
1
2
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
3
0
2
1
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
1
1
1
0
0
0
0
0
0
0
3
1
1
0
0
0
1
0
0
0
2
1
0
0
1
0
0
0
1
0
0
0
0
1
0
2
0
0
1
3
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
2
0
0
2
2
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
2
4
2
0
2
0
0
1
1
0
2
1
4
7
0
0
1
1
0
0
0
0
0
1
0
0
1
1
1
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
3
1
0
0
1
0
1
0
0
2
0
0
0
2
0
2
0
0
1
2
0
0
0
0
0
0
0
0
3
0
1
1
2
0
0
0
0
1
0
2
2
2
0
0
0
0
2
0
0
0
0
0
4
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
1
2
1
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
1
3
0
0
0
1
0
1
1
0
0
0
0
1
0
0
2
0
1
0
1
1
1
0
0
0
1
2
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
1
0
1
1
0
1
1
0
1
0
0
0
2
0
1
0
0
0
0
1
0
2
2
0
2
0
0
1
0
2
0
2
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
2
1
0
0
0
2
4
0
0
0
2
1
0
0
0
0
1
0
0
1
0
0
0
2
0
2
0
1
0
0
0
1
0
0
1
0
0
0
0
1
2
0
0
2
0
0
0
0
1
0
0
0
2
2
0
0
3
0
1
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
1
1
1
0
1
0
1
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
3
2
1
0
0
0
0
0
0
3
0
1
2
0
0
1
0
2
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
2
3
2
3
0
0
0
0
0
0
0
0
1
0
2
1
0
2
0
1
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
1
0
3
0
0
0
0
0
3
0
0
0
0
0
1
1
0
1
1
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
2
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
3
2
0
0
0
0
1
0
0
1
0
1
0
2
0
2
0
0
0
1
0
2
0
5
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
3
0
0
0
0
0
2
0
2
1
1
2
0
0
0
0
0
2
1
1
0
6
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
2
1
3
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
2
0
0
0
2
0
0
0
1
1
0
0
0
0
0
1
0
3
0
0
0
5
0
0
0
0
0
0
3
0
0
0
0
1
7
0
0
0
2
2
2
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
1
2
1
0
0
0
0
2
0
1
0
0
0
1
2
0
2
0
0
0
0
6
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
1
1
1
1
0
1
2
0
0
2
0
2
0
0
1
0
0
1
0
0
0
1
1
0
0
2
1
1
0
1
0
3
0
2
2
1
3
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
2
0
1
0
2
0
2
0
0
0
2
0
0
0
1
3
0
2
0
1
0
0
1
0
0
0
0
0
3
1
1
1
0
2
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
1
0
0
1
0
0
1
6
0
0
0
0
0
0
0
2
2
2
1
2
0
1
0
0
0
1
0
2
2
0
2
0
0
0
2
1
0
0
0
0
0
0
1
2
0
0
0
1
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
2
2
2
0
0
1
0
0
0
0
0
2
2
0
0
2
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
1
2
0
0
0
0
2
0
0
0
2
0
0
1
0
0
3
0
2
1
0
2
2
0
0
1
0
0
1
0
0
0
0
0
2
0
0
1
0
2
2
0
0
1
0
1
0
0
1
0
0
0
0
2
2
0
1
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
3
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
2
0
1
0
5
0
2
2
1
0
0
0
0
0
2
0
0
0
2
2
2
2
3
0
3
1
0
0
0
0
0
0
0
1
0
2
0
1
0
2
0
2
0
0
1
0
1
0
0
0
0
2
2
1
3
1
0
2
1
0
0
0
1
1
0
2
0
2
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
3
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
3
0
1
1
0
0
0
0
0
0
1
1
0
1
0
0
0
1
2
2
0
0
0
0
1
0
0
1
2
2
0
4
0
0
0
2
2
1
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
1
0
0
2
0
0
1
2
0
1
0
0
0
1
0
2
0
0
0
0
2
1
2
0
2
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
2
1
0
1
1
0
0
1
0
0
2
3
0
0
2
0
0
1
1
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
4
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
5
0
0
0
2
0
0
0
3
2
1
0
2
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
1
0
1
1
0
1
1
1
0
0
1
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
1
2
0
2
2
2
0
0
1
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
1
3
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
3
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
8
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
2
1
1
0
4
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
4
0
1
0
2
0
0
0
2
0
0
0
1
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
1
1
0
0
0
3
0
0
2
0
0
1
0
0
0
1
2
0
2
0
0
0
0
0
0
0
1
0
2
1
2
0
0
3
1
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
2
1
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
2
1
2
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
1
1
0
0
2
0
3
0
0
0
0
0
0
1
2
0
1
2
3
0
2
0
0
2
0
1
0
1
0
0
2
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
2
1
2
1
0
0
1
2
0
1
0
1
1
2
0
7
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
2
2
1
1
0
0
0
0
0
0
2
1
1
0
0
0
1
0
0
1
0
0
2
1
0
0
2
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
2
1
3
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
1
0
0
0
2
0
0
0
0
0
1
0
2
2
1
0
1
0
0
1
0
0
0
0
0
0
1
0
2
0
0
1
0
1
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
2
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
4
0
0
0
0
1
2
0
0
0
1
0
1
5
1
0
0
0
0
1
2
0
0
0
1
0
1
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
1
2
0
0
1
1
0
1
0
2
0
1
0
2
1
0
0
0
0
0
0
2
0
0
0
0
7
2
3
2
2
2
0
0
0
2
1
0
0
0
0
2
1
0
0
0
1
0
0
0
2
1
2
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
2
0
0
1
1
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
3
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
2
0
1
2
0
0
0
0
0
0
1
0
1
2
2
0
0
2
0
0
0
0
1
1
0
2
1
0
0
0
2
2
0
0
3
0
7
0
0
0
1
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
1
0
1
0
2
0
0
0
0
0
1
1
0
0
2
1
0
1
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
3
0
0
0
2
0
0
2
0
1
0
3
1
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
1
0
2
2
0
0
0
0
2
0
1
2
0
0
1
1
0
1
3
0
0
0
3
0
1
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
1
0
0
0
2
2
0
0
0
1
0
0
0
2
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
1
1
0
1
0
0
0
0
0
0
0
2
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
2
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
2
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
2
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
3
0
0
0
2
1
1
0
0
0
0
0
2
2
0
1
0
0
2
0
0
0
0
0
0
1
0
1
0
2
0
0
0
2
0
0
1
1
5
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
1
1
0
0
0
0
2
2
0
0
1
2
2
0
0
0
1
0
0
0
0
2
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
1
1
0
0
0
2
2
0
2
1
2
1
2
0
2
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
4
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
2
0
0
0
1
2
0
1
0
0
0
0
0
1
0
2
0
0
0
0
1
1
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
2
2
1
0
0
2
0
0
0
1
0
0
0
0
2
1
0
3
0
2
2
0
1
0
1
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
2
2
0
0
2
0
0
4
1
0
2
0
2
3
0
1
0
0
0
0
6
0
0
0
0
0
0
0
1
2
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
3
0
0
1
1
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
2
1
0
3
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
2
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
1
1
0
2
2
0
0
0
2
0
0
0
0
1
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
1
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
2
0
0
2
2
0
0
0
1
0
2
1
1
0
1
0
0
1
3
0
2
1
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
2
3
0
0
4
0
0
2
0
0
0
1
0
3
1
1
4
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
5
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
3
0
1
1
0
0
0
2
0
1
0
0
1
1
0
0
0
0
2
0
1
0
1
0
0
1
1
0
2
2
0
3
0
0
0
0
0
0
1
1
0
2
1
2
0
1
0
0
1
0
1
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
1
2
0
2
0
0
1
0
0
0
1
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
2
2
2
1
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
1
1
1
1
0
0
0
2
0
0
0
1
1
1
0
0
0
3
0
1
0
2
2
0
2
0
0
0
2
0
0
3
0
0
2
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
2
1
1
1
1
2
0
0
2
0
2
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
2
2
2
0
1
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
1
0
0
0
3
0
2
3
0
2
0
1
1
0
0
2
2
4
1
0
0
2
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
2
0
0
2
0
2
2
2
0
0
3
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
1
0
2
0
1
0
5
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
1
1
0
1
1
0
0
0
2
3
1
0
0
0
3
1
0
0
0
1
0
1
0
0
0
1
0
0
0
1
2
0
0
1
0
0
0
0
2
0
1
0
0
3
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
2
2
2
0
0
1
2
0
1
0
0
1
1
1
1
1
0
2
0
0
0
2
0
2
2
0
0
0
2
0
0
0
0
0
2
0
0
2
1
1
1
1
2
0
1
2
1
0
1
0
0
2
0
0
0
0
2
0
0
2
0
0
0
1
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
1
1
0
0
6
0
0
0
0
2
0
0
0
1
0
0
1
2
0
0
0
0
0
2
1
0
1
0
2
2
2
0
0
0
0
0
1
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
1
2
0
0
4
0
0
0
0
1
2
0
0
2
0
0
2
0
0
2
1
1
0
2
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
1
2
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
3
0
3
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
3
0
0
0
2
2
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
2
1
1
2
1
0
0
0
0
0
0
2
0
2
2
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
6
2
0
3
2
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
1
0
0
1
1
0
0
1
2
0
0
0
0
0
0
3
0
0
0
2
1
0
0
1
1
0
2
2
1
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
2
0
2
3
0
0
0
0
1
2
1
0
1
0
0
0
0
2
0
2
0
1
1
2
2
0
0
1
0
2
0
0
2
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
1
0
2
5
0
2
1
1
0
1
0
0
2
0
0
0
1
1
0
4
0
0
0
0
3
2
0
1
0
0
2
0
0
0
0
0
0
1
1
0
0
0
2
1
2
0
0
0
1
0
3
1
2
0
3
0
0
0
1
0
0
0
0
2
3
0
0
0
3
0
0
0
1
0
2
0
0
0
0
1
1
0
0
0
0
0
2
0
1
0
0
2
0
0
0
2
2
1
0
3
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
3
2
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
3
2
0
1
0
0
0
2
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
1
0
0
0
1
0
0
3
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
2
1
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
6
0
0
0
0
0
0
0
5
0
1
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
2
0
2
0
0
0
1
0
0
2
2
0
0
0
0
2
0
0
0
0
1
2
0
0
1
0
1
2
3
0
0
2
0
0
1
1
2
0
1
0
1
1
0
0
2
0
0
2
0
0
0
2
0
0
1
1
0
1
0
1
2
0
0
0
0
1
0
1
0
1
0
1
0
0
0
2
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
1
2
0
0
2
0
1
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
2
0
2
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
2
1
0
0
2
1
0
1
0
1
0
0
2
0
0
2
1
0
0
1
0
1
0
0
1
2
1
0
0
0
0
2
0
0
1
0
0
2
4
0
1
0
0
0
0
2
0
0
0
3
0
0
0
0
0
1
1
0
0
0
0
2
0
1
0
0
0
2
2
0
2
0
0
0
0
1
1
0
0
1
0
3
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
1
0
1
0
0
4
0
0
0
0
1
0
1
0
0
0
0
1
2
5
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
3
0
0
0
2
2
0
0
0
0
0
1
0
0
0
1
0
2
2
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
1
0
1
0
0
1
0
0
2
1
1
0
0
0
0
0
1
0
0
0
1
0
2
2
0
1
1
2
0
0
0
0
0
1
0
2
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
1
2
2
1
0
1
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
2
0
0
1
2
0
0
1
0
1
0
0
0
0
2
2
0
0
1
0
1
0
0
0
0
2
2
1
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
2
2
0
0
2
0
0
1
0
0
0
3
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
1
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
3
0
0
1
0
2
0
1
2
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
2
2
0
2
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
1
2
0
0
0
1
0
0
1
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
2
0
1
0
0
1
1
0
2
2
0
0
2
2
2
0
2
0
0
2
0
1
2
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
1
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
2
3
0
0
1
2
0
2
0
1
1
0
1
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
5
0
2
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
2
1
1
0
8
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
2
0
2
0
0
2
0
2
0
0
0
2
0
0
1
0
1
0
0
0
0
1
0
3
1
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
4
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
2
2
2
0
0
1
0
1
0
0
0
0
0
0
1
1
2
0
0
0
0
2
0
0
0
0
0
1
1
0
0
2
0
0
1
0
0
0
5
0
5
2
0
0
0
0
0
1
2
1
0
0
0
1
0
0
0
0
0
5
0
0
0
0
0
0
2
0
2
1
0
1
1
0
2
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
3
0
2
2
1
2
0
0
3
0
1
0
0
0
1
2
2
0
1
0
2
2
0
0
0
0
2
2
0
2
0
0
0
1
2
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
5
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
2
0
0
1
0
0
0
0
2
0
0
4
0
0
0
4
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
1
0
1
3
0
1
0
0
0
0
2
1
0
0
2
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
1
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
3
0
0
0
0
2
0
0
1
0
0
2
0
0
4
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
4
0
2
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
2
1
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
1
3
1
1
0
1
0
0
1
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
1
1
2
2
1
1
0
0
1
0
0
0
0
3
0
0
0
2
0
1
0
0
1
0
0
2
1
0
0
0
0
0
0
0
1
2
2
0
0
0
0
1
0
2
2
0
0
0
0
2
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
2
1
0
2
1
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
3
2
0
1
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
2
0
1
1
0
0
2
0
0
0
0
0
0
0
0
1
2
0
2
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
1
0
1
0
0
0
0
0
1
1
0
0
2
0
0
1
0
0
2
2
2
4
0
0
2
0
0
0
1
0
1
1
1
0
2
0
0
1
2
2
0
0
0
2
0
0
0
0
0
0
1
1
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
2
3
0
0
1
1
0
0
0
3
0
0
0
1
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
1
2
0
1
1
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
1
0
2
0
3
1
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
1
0
0
1
0
1
0
0
0
0
0
0
0
2
0
3
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
1
1
0
0
1
0
1
0
2
0
0
0
0
0
1
0
0
2
1
0
1
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
1
1
0
1
2
0
0
0
0
0
0
2
0
0
0
1
1
1
1
0
1
2
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
3
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
2
2
0
0
1
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
2
1
2
0
0
0
1
1
0
0
0
0
2
2
0
0
5
0
2
2
2
0
0
2
2
1
0
0
0
0
2
0
1
2
0
0
1
1
2
0
2
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
4
2
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
2
2
0
0
0
0
1
0
1
0
2
0
1
0
0
2
0
2
2
0
0
0
0
1
2
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
1
0
0
0
2
2
1
0
0
3
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
2
1
0
0
1
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
7
0
0
2
1
1
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
2
0
0
1
10
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
1
0
0
1
0
0
0
6
0
0
0
1
0
2
0
2
0
0
0
0
2
0
0
4
0
1
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
1
3
2
3
1
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
2
0
1
1
1
0
0
0
0
0
3
0
0
2
0
1
0
0
1
0
1
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
1
0
0
0
0
0
0
1
2
2
1
2
0
0
0
0
1
0
3
0
0
0
0
0
0
0
2
0
2
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
1
1
1
0
1
0
0
0
0
0
0
1
0
1
1
2
2
0
0
1
0
0
0
1
0
0
2
2
0
0
0
0
1
1
0
0
0
0
2
0
0
0
1
0
0
1
0
0
2
1
1
0
0
1
2
0
1
0
0
0
0
1
0
0
2
0
0
1
2
0
1
2
2
2
0
0
0
0
0
1
2
0
4
0
0
0
0
0
1
1
1
1
1
0
1
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
3
0
0
3
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
3
0
0
0
0
2
0
0
0
0
3
0
0
1
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
1
1
0
0
2
0
1
2
0
0
0
0
0
1
0
1
1
0
0
3
1
3
1
0
0
0
0
2
0
0
1
0
3
1
0
0
1
0
1
0
0
2
0
1
2
0
1
0
0
2
1
0
0
2
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
2
0
3
0
1
1
0
0
0
0
0
2
0
0
1
0
0
0
3
2
0
2
0
0
0
1
0
2
0
0
0
0
2
1
0
0
1
0
1
0
1
0
1
0
0
0
0
0
2
2
2
3
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
2
2
1
0
0
1
0
2
0
2
1
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
1
2
0
0
1
2
0
0
0
0
0
0
0
0
2
1
2
2
0
0
0
0
0
2
1
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
5
0
0
1
0
0
3
0
1
0
0
0
2
1
0
2
2
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
1
3
0
1
0
0
2
2
0
0
0
0
0
4
0
2
1
0
2
0
0
1
0
2
0
0
0
1
0
2
0
1
0
5
2
0
0
0
1
0
0
0
2
0
1
2
0
1
0
1
0
2
3
0
2
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
2
0
2
0
0
2
0
0
0
0
1
0
0
0
1
1
0
0
0
0
2
1
0
2
0
0
0
0
0
5
0
0
2
0
0
1
2
1
0
0
2
0
1
0
1
0
0
1
2
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
2
0
1
0
0
3
0
2
0
0
1
2
2
0
2
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
1
0
1
0
0
2
1
0
2
0
1
2
0
0
0
1
0
0
0
1
0
0
2
0
0
2
0
0
1
0
2
0
0
1
1
2
1
2
0
1
1
2
0
0
0
0
0
1
2
0
2
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
2
2
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
1
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
2
0
0
1
2
1
0
0
0
1
0
2
0
0
2
1
0
0
2
0
1
0
0
0
2
0
1
0
2
0
3
0
2
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
3
2
0
1
0
0
0
2
0
0
1
1
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
2
0
0
1
0
1
1
0
1
0
0
0
1
0
0
2
0
0
0
1
0
0
1
0
0
1
1
0
4
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
3
0
0
1
1
0
0
0
2
0
2
0
1
0
0
1
0
0
4
0
2
0
0
2
0
0
0
0
0
3
1
0
0
1
5
2
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
3
1
0
1
2
0
2
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
1
2
0
2
0
1
0
0
1
0
0
0
0
2
0
3
0
0
0
2
0
0
1
0
1
0
0
2
0
0
0
2
0
1
0
0
1
0
1
0
0
0
2
2
0
1
0
0
0
0
0
3
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
1
0
0
1
0
0
3
0
0
1
0
0
1
0
1
2
2
0
0
2
0
0
0
0
1
0
3
0
0
0
0
0
0
2
2
2
1
0
2
0
0
0
1
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
2
1
0
2
2
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
1
0
0
1
0
2
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
2
0
0
2
2
0
0
0
0
0
0
0
1
0
0
1
1
0
2
2
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
2
3
0
0
1
0
0
0
0
0
0
2
0
0
6
2
0
0
0
2
2
2
0
4
0
0
0
0
1
1
0
0
0
2
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
1
0
1
0
0
0
2
1
0
2
0
0
0
0
2
0
3
0
1
0
0
0
1
0
0
1
2
0
0
0
2
0
1
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
1
3
0
1
0
0
0
1
2
0
0
0
0
1
0
0
2
0
2
0
1
2
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
2
1
1
0
0
2
1
0
0
1
2
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
2
0
1
1
1
0
2
2
1
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
3
1
2
0
2
1
0
0
2
2
0
0
0
1
0
1
0
0
3
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
1
1
0
0
0
3
0
1
0
0
0
0
2
0
0
2
0
1
0
2
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
3
1
0
1
0
0
0
0
0
2
0
0
0
1
0
0
1
1
1
0
0
0
2
0
0
0
0
0
0
0
1
0
1
1
2
0
1
0
0
0
0
0
0
0
2
1
1
0
2
1
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
1
0
2
1
0
0
0
0
1
2
0
0
1
0
6
0
0
0
0
0
0
2
1
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
2
2
0
2
0
0
2
0
0
0
2
0
0
0
0
0
1
2
0
1
1
2
0
0
1
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
5
1
0
2
0
0
2
1
0
0
0
2
1
0
0
0
2
0
0
0
0
2
0
0
2
0
2
1
2
2
0
0
2
0
0
1
0
2
1
0
0
1
0
0
0
0
1
0
0
3
1
0
1
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
1
1
0
0
0
2
0
6
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
2
3
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
2
2
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
2
0
1
5
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
1
1
0
2
1
2
2
0
0
0
1
0
0
0
1
0
1
1
0
0
1
0
0
2
1
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
1
0
1
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
2
0
8
0
0
0
1
2
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
2
0
0
1
2
1
1
0
0
3
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
2
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
1
0
1
0
0
0
2
0
1
1
1
2
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
1
0
2
0
1
1
0
0
0
0
2
0
3
2
2
1
0
2
2
0
0
0
0
0
0
0
0
0
1
1
1
0
0
2
0
2
0
2
0
0
0
0
1
0
0
0
0
0
1
0
1
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
1
0
0
2
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
1
0
1
0
2
0
3
0
0
1
1
2
0
1
0
0
0
0
0
2
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
2
0
2
1
0
0
0
2
7
0
2
2
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
2
2
2
1
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
3
0
0
2
1
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
1
0
5
2
0
0
0
0
0
0
0
2
0
2
2
0
0
1
0
0
0
0
1
0
2
0
1
1
2
0
0
1
0
0
2
1
2
0
0
0
2
1
2
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
3
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
2
0
0
1
0
0
0
0
0
1
1
0
0
3
2
0
0
0
0
0
2
0
0
1
0
0
0
2
0
2
2
0
0
1
2
1
0
0
2
1
1
1
0
1
1
0
0
0
1
1
2
1
0
2
0
7
0
0
0
1
0
0
0
0
0
0
0
0
0
3
2
2
0
0
0
2
0
0
0
0
1
2
1
0
0
0
0
1
0
0
0
2
0
0
2
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
1
0
1
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
2
1
1
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
3
2
0
2
0
0
2
0
0
0
0
0
2
0
0
1
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
1
0
0
2
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
2
2
0
0
0
0
0
2
1
2
1
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
1
0
1
0
2
0
1
0
1
3
0
2
2
2
0
2
3
0
0
0
0
1
0
0
0
0
0
2
0
1
0
2
3
3
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
1
2
0
1
0
0
0
0
0
2
2
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
2
4
0
1
0
0
1
0
0
0
2
0
2
0
0
0
0
2
0
1
0
1
0
1
1
0
1
1
3
0
0
7
0
0
0
0
1
0
0
0
0
0
1
3
0
0
0
1
0
1
0
0
1
0
0
1
0
2
1
2
0
0
0
0
0
0
2
1
1
0
0
0
2
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
2
0
1
0
0
0
0
0
1
0
1
3
0
2
1
1
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
1
0
1
2
0
2
6
1
1
0
0
1
0
1
3
0
0
0
1
0
0
0
0
0
0
2
2
2
0
0
0
1
0
1
0
1
0
1
0
0
0
0
1
1
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
1
0
0
2
1
0
0
0
1
3
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
2
0
2
2
0
0
3
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
2
2
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
2
0
0
1
1
2
0
3
0
2
0
0
0
2
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
1
1
1
0
1
2
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
4
1
0
0
0
0
2
0
0
0
0
1
0
0
1
3
0
0
0
3
2
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
2
0
1
1
1
0
0
0
1
1
3
1
1
0
0
0
0
1
0
2
3
1
1
1
3
0
1
4
0
0
0
1
1
0
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
2
0
2
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
3
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
3
0
1
0
0
0
1
0
2
0
0
0
1
1
0
1
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
2
0
2
2
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
2
0
2
2
0
2
0
0
0
2
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
1
1
3
1
0
0
2
2
0
1
2
0
0
2
2
1
0
0
2
1
0
1
0
1
0
1
0
2
0
2
0
1
0
2
1
0
0
0
0
0
0
0
0
5
0
1
0
2
3
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
1
0
0
2
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
2
0
1
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
2
0
2
1
0
1
0
0
0
0
1
0
0
0
2
0
1
0
3
0
0
1
0
0
1
0
2
0
1
1
0
0
2
0
0
2
0
0
0
2
2
0
6
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
1
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
1
0
1
0
1
0
1
0
0
2
1
0
0
0
1
1
2
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
2
0
2
1
2
0
4
4
1
0
0
2
0
0
2
0
0
2
0
0
1
1
2
0
1
1
0
0
1
0
2
0
0
0
1
2
0
0
4
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
3
0
0
2
2
2
0
2
2
0
0
0
1
0
0
1
2
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
1
2
1
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
7
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
3
2
0
1
0
0
0
0
0
0
3
0
0
2
1
2
0
1
1
0
0
0
1
1
1
2
0
3
0
1
0
3
1
0
3
0
0
2
0
1
1
2
1
1
0
0
0
0
2
0
0
0
2
0
2
0
0
0
1
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
1
3
0
2
0
2
1
0
0
0
1
1
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
2
1
0
0
0
0
0
1
0
2
0
1
0
0
1
1
0
0
0
2
0
0
1
2
0
2
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
2
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
1
1
2
0
2
0
0
0
0
0
0
2
1
0
0
0
0
2
3
1
0
1
1
1
1
0
1
0
0
0
0
1
2
0
0
0
1
0
3
1
0
0
0
3
1
1
0
0
0
1
2
0
0
0
1
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
2
0
0
0
1
0
2
1
0
2
2
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
2
0
2
0
2
2
1
0
0
1
0
2
1
0
0
2
2
5
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
1
0
2
0
1
0
0
0
0
0
0
0
1
1
2
0
0
2
0
0
0
1
2
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
2
0
0
0
2
0
0
2
1
2
1
0
0
0
0
0
1
0
0
0
1
3
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
3
1
1
0
0
2
1
0
0
0
0
1
0
0
0
0
1
0
0
5
0
0
1
0
0
1
0
2
0
2
0
0
0
3
0
0
7
0
0
0
1
0
0
0
0
0
0
0
0
0
6
3
2
0
1
0
0
0
1
0
0
0
2
5
0
2
0
1
0
0
0
2
2
0
0
2
0
0
0
0
4
0
1
0
1
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
3
1
1
0
0
1
0
0
2
0
0
0
0
1
0
2
0
1
0
0
0
0
0
2
2
2
0
0
0
0
2
2
0
0
0
1
2
2
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
2
0
0
0
2
0
1
0
0
0
0
0
2
1
0
0
0
0
2
2
1
2
0
1
0
0
0
1
1
0
0
0
0
2
2
3
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
2
0
0
2
0
0
2
0
0
2
1
1
0
1
0
0
2
1
2
0
0
0
0
0
1
0
2
0
1
0
1
0
0
0
0
0
1
2
0
0
2
0
0
0
1
0
0
1
0
1
4
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
1
2
0
0
0
1
1
0
0
1
2
1
0
0
0
1
0
0
0
2
0
0
1
0
0
2
0
0
0
1
0
0
1
0
0
1
0
1
2
0
1
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
2
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
3
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
2
0
2
0
0
0
2
0
2
0
2
0
1
0
0
1
2
2
2
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
1
1
0
0
2
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
2
0
1
0
2
0
1
1
2
2
0
0
2
1
0
0
0
0
3
1
0
0
0
4
1
0
0
0
3
0
0
0
2
1
0
0
0
0
0
1
0
3
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
2
2
0
0
0
0
0
0
0
1
0
1
2
0
2
2
0
2
0
0
0
2
0
0
1
0
4
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
2
0
2
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
3
0
2
0
0
0
0
2
3
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
3
0
0
0
1
15
0
2
0
0
4
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
1
0
0
0
2
0
0
1
2
0
2
0
0
0
0
1
2
0
0
0
1
0
0
0
1
2
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
2
0
1
0
1
0
0
7
0
0
0
0
1
1
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
2
0
1
2
0
0
0
0
2
2
4
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
2
0
0
1
0
0
0
3
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
1
2
1
0
1
0
1
0
2
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
3
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
2
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
1
0
0
2
1
0
0
1
2
0
0
0
2
0
2
0
0
0
1
0
0
1
1
2
3
0
0
0
2
2
2
0
1
0
1
0
2
0
1
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
2
3
0
0
0
5
2
0
1
0
0
0
0
1
0
1
1
2
0
0
0
0
0
0
0
0
0
2
2
0
0
2
3
0
0
1
1
4
0
0
0
0
0
0
2
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
1
2
2
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
3
0
0
2
2
0
2
1
0
1
2
0
2
0
1
0
3
2
0
2
1
0
0
0
1
0
1
0
2
0
2
0
0
2
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
1
2
1
2
0
2
1
3
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
2
0
0
0
2
0
4
2
1
0
0
0
2
3
0
0
0
0
0
2
0
0
0
0
2
0
0
0
3
2
0
0
0
0
1
0
0
0
2
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
3
0
0
0
2
1
0
1
0
0
0
0
2
0
0
2
2
0
1
0
2
2
0
1
0
0
0
0
1
2
4
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
1
0
0
0
0
1
2
0
0
0
0
2
0
1
1
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
3
0
0
2
1
0
0
0
0
0
1
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
3
0
0
0
1
0
0
0
0
0
0
3
0
3
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
1
0
0
0
2
0
1
0
0
0
0
0
0
3
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
3
2
1
0
0
0
0
0
1
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
2
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
4
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
1
0
2
0
1
0
0
1
0
0
0
1
2
0
2
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
2
0
1
0
0
1
2
2
2
2
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
3
1
0
0
0
8
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
1
0
2
0
0
0
5
1
0
0
0
2
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
2
0
2
3
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
2
0
1
0
0
0
0
0
3
0
0
0
0
2
1
0
2
2
1
1
1
0
0
0
0
0
0
2
0
0
0
2
2
0
2
0
1
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
1
1
0
0
0
0
2
1
1
0
2
1
0
1
0
0
0
0
0
0
0
1
3
1
0
0
1
2
0
0
0
2
3
2
0
1
0
0
1
0
1
0
2
0
2
2
2
2
0
0
0
1
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
2
0
1
0
0
0
2
1
1
0
0
2
0
1
0
0
0
1
1
1
0
2
0
0
2
0
0
0
1
0
0
2
0
0
0
0
1
1
0
2
1
0
2
1
0
0
0
0
0
1
1
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
1
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
1
0
0
2
0
0
0
0
0
3
2
1
0
0
0
1
2
2
0
1
0
0
0
1
0
0
0
0
0
0
1
0
3
1
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
3
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
1
0
1
0
1
0
0
1
2
0
0
0
0
1
0
0
0
3
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
2
0
0
0
0
0
0
0
1
2
0
2
1
0
0
2
1
0
1
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
1
2
0
1
1
1
2
2
0
0
2
1
1
2
0
0
0
0
0
0
2
0
0
2
1
0
0
0
2
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
1
1
0
0
1
0
1
2
0
2
2
7
0
0
0
0
2
0
0
2
0
0
2
0
0
0
4
0
0
0
1
0
1
2
1
0
0
0
0
2
2
0
0
2
0
0
0
0
2
0
0
0
1
1
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
1
0
0
1
3
0
2
0
0
0
0
0
2
0
0
0
0
0
2
1
1
2
1
0
0
0
0
0
3
0
1
1
1
0
0
0
0
0
4
1
0
0
3
1
1
0
1
0
0
0
2
2
0
1
0
2
0
0
0
2
4
0
0
0
1
0
0
0
0
2
1
2
0
0
0
0
0
0
2
0
0
3
0
0
2
0
0
1
0
2
0
2
0
0
1
0
0
2
0
5
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
2
0
1
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
4
1
0
0
0
0
0
0
1
2
2
2
0
1
0
0
0
0
0
0
0
0
0
1
2
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
3
1
3
0
0
0
0
0
0
1
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
1
0
0
0
3
2
0
2
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
3
2
3
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
2
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
2
2
0
2
0
1
1
0
0
0
0
2
2
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
2
0
0
0
2
0
0
0
2
0
0
0
1
0
2
0
0
0
1
2
0
2
0
2
0
2
0
0
0
0
0
3
0
0
0
3
1
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
2
0
0
1
0
0
0
1
0
0
0
0
0
0
9
2
0
0
0
0
0
1
2
0
1
0
0
0
1
1
0
0
2
4
3
2
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
2
0
1
0
0
2
0
1
2
0
2
0
1
1
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
1
1
0
0
0
3
1
0
0
0
2
0
1
0
0
2
0
2
2
0
0
0
2
1
0
0
1
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
2
2
0
0
2
0
0
1
0
0
0
1
0
0
0
1
2
2
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
1
3
0
0
0
2
0
0
0
0
2
0
0
1
0
2
1
2
0
0
1
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
2
3
0
0
2
0
1
2
6
0
0
1
0
0
1
0
2
0
2
1
0
0
0
0
1
0
0
2
2
2
0
0
2
0
0
2
0
1
2
1
0
2
2
2
0
0
0
0
0
1
0
0
2
1
0
0
0
0
2
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
1
0
3
0
1
0
1
0
0
0
2
0
0
1
0
1
2
1
1
2
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
2
2
0
2
0
2
3
1
2
0
1
0
1
2
0
5
1
0
0
2
2
0
0
3
1
0
1
0
0
2
0
0
0
2
0
2
2
2
4
0
0
0
0
0
2
2
1
0
0
0
1
0
0
0
0
0
2
0
1
0
1
0
0
0
3
0
0
2
1
0
1
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
1
0
2
2
2
2
0
0
2
0
0
0
0
0
0
2
0
1
1
0
2
0
0
0
0
0
2
0
0
1
4
0
0
0
0
0
0
1
1
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
2
0
1
0
1
2
0
0
1
0
1
0
0
0
0
2
0
2
0
0
0
2
0
1
0
1
1
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
1
0
2
2
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
2
0
0
0
2
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
2
1
0
6
0
0
2
0
1
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
5
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
2
0
0
0
0
0
2
0
0
0
0
2
2
0
0
2
0
0
0
0
0
4
1
0
0
0
1
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
3
1
0
2
1
0
0
0
0
0
1
2
0
0
0
0
1
0
1
0
0
0
2
2
0
0
0
0
0
0
3
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
1
0
0
2
1
0
0
2
2
0
0
0
1
0
0
0
0
0
0
2
2
0
0
1
0
0
4
0
0
0
0
0
2
1
1
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
6
0
1
0
0
2
0
0
0
0
2
1
2
1
1
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
2
0
1
0
1
0
2
0
0
2
2
1
0
0
2
0
2
2
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
2
2
0
0
0
1
0
0
1
1
1
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
2
0
2
0
2
0
0
2
0
0
0
1
1
2
0
0
0
0
0
0
0
1
0
0
2
0
2
3
0
0
0
0
0
2
0
0
0
0
2
1
0
1
2
1
1
2
0
2
0
0
1
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
2
0
0
1
1
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
2
0
0
0
2
1
0
0
0
2
1
0
0
0
2
0
1
1
0
1
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
1
0
4
0
0
1
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
2
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
1
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
1
0
1
0
0
2
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
1
1
2
0
0
0
0
0
0
1
0
1
1
0
0
0
1
2
0
0
0
0
1
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
2
2
2
1
1
2
0
1
0
0
0
0
1
2
0
2
2
1
2
0
0
0
0
2
0
0
0
1
0
0
0
0
1
1
1
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
1
2
1
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
6
0
1
0
0
0
2
1
0
1
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
1
0
2
0
0
3
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
1
1
0
0
0
0
0
1
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
2
1
1
1
0
0
0
0
0
2
1
2
0
0
0
0
0
2
1
0
0
0
1
4
2
1
0
0
0
0
0
2
0
0
0
2
0
2
1
0
0
0
2
2
0
1
1
0
0
0
0
1
1
2
2
0
0
0
0
0
0
2
0
0
0
1
0
2
0
2
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
1
0
2
0
0
0
0
0
1
0
1
0
0
0
4
0
1
0
0
0
0
1
0
0
1
0
0
0
1
4
1
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
1
1
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
2
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
1
1
0
0
1
1
0
1
0
0
0
0
0
0
2
0
1
2
0
0
0
1
0
2
2
3
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
2
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
9
0
0
1
1
0
0
2
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
1
0
0
2
0
2
0
1
0
2
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
1
2
2
2
0
3
0
0
2
2
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
1
1
0
0
1
0
1
0
0
0
1
0
0
0
2
0
0
2
1
0
0
1
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
2
0
0
0
1
0
1
0
0
0
0
1
0
0
2
0
2
0
1
1
1
0
1
0
0
0
0
0
4
0
3
2
0
1
0
0
0
0
0
2
2
0
2
0
1
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
3
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
2
1
0
1
0
0
0
1
0
0
2
1
1
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
3
0
1
0
0
2
3
0
1
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
4
0
0
1
4
0
1
0
1
0
0
0
0
3
0
2
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
1
0
0
0
0
1
2
0
2
0
0
0
1
0
3
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
2
1
0
0
0
0
0
2
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
1
0
0
2
0
0
0
0
1
3
2
0
1
2
0
0
0
2
1
1
0
0
2
1
4
0
0
1
4
0
2
0
0
0
1
0
0
2
1
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
1
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
2
1
0
0
2
0
0
0
0
1
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
2
0
1
0
1
0
0
0
0
0
1
0
0
1
0
2
0
0
1
0
0
0
2
2
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
1
0
0
2
0
0
0
0
0
0
1
2
1
0
0
2
0
1
0
0
0
1
0
0
0
1
1
2
2
1
0
1
0
0
0
1
0
0
0
0
0
1
2
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
1
0
1
0
2
0
0
1
0
0
2
0
2
0
2
0
0
0
3
1
0
0
2
0
7
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
3
1
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
1
1
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
4
0
1
0
0
0
2
2
0
1
1
0
0
0
2
0
3
0
0
0
0
2
0
0
1
1
0
0
1
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
1
1
0
1
2
0
1
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
2
0
1
0
2
0
0
1
2
2
0
0
2
0
0
0
0
0
0
2
0
3
1
0
0
2
0
1
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
10
1
1
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
3
1
2
0
1
0
2
0
2
1
0
1
0
0
1
0
0
0
1
0
0
0
0
2
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
2
0
0
0
2
0
0
2
2
0
0
0
2
1
0
1
1
1
2
0
1
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
1
2
5
2
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
11
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
1
0
2
0
2
2
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
2
1
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
2
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
1
0
3
0
0
1
0
1
4
0
0
0
1
0
0
2
0
1
0
0
1
0
3
0
0
0
1
0
2
0
0
0
0
1
0
0
0
2
1
1
0
2
1
0
0
0
2
0
0
0
0
0
0
2
3
2
0
0
0
0
1
0
0
0
5
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
1
2
0
0
3
0
0
1
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
3
1
0
0
0
1
0
1
0
1
2
2
1
0
0
2
0
0
0
0
0
2
1
2
0
0
0
1
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
2
0
1
1
0
0
0
0
0
2
0
0
1
0
2
1
0
0
0
0
2
0
1
1
0
0
0
0
1
1
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
2
1
0
0
0
0
2
3
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
2
2
0
1
0
2
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
3
0
0
1
0
2
8
0
0
1
0
2
0
0
2
0
1
0
1
0
0
0
2
0
0
0
0
0
1
0
2
2
0
0
2
0
0
2
0
2
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
1
2
1
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
2
2
2
1
0
0
0
2
3
0
0
1
0
0
0
2
0
1
2
1
0
0
2
0
0
0
0
0
0
1
2
1
0
0
0
0
2
1
0
0
1
0
0
7
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
2
1
1
1
0
0
1
0
0
0
0
1
0
2
2
0
1
0
2
0
0
0
0
0
0
1
1
2
0
1
0
0
2
0
0
0
0
2
0
2
0
0
0
2
0
2
3
2
2
0
1
1
0
0
0
1
0
0
0
0
4
2
2
0
0
1
0
1
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
2
1
0
0
1
0
0
0
0
1
0
1
2
0
2
1
0
0
1
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
1
2
1
0
0
0
1
1
1
0
0
1
0
1
0
0
0
2
2
0
0
0
0
0
0
0
2
1
2
0
2
0
2
0
0
1
2
0
2
2
0
2
0
1
1
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
2
2
0
0
5
0
0
0
2
0
0
0
0
1
1
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
2
0
2
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
3
0
0
2
2
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
1
0
2
2
0
0
0
2
2
0
2
2
3
0
0
0
3
2
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
3
1
0
2
0
0
0
2
0
2
1
0
0
0
1
0
1
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
2
1
2
1
0
2
0
1
2
0
0
2
2
2
1
1
0
0
0
0
0
4
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
1
1
2
1
0
0
1
1
0
1
0
0
0
0
0
1
0
2
0
2
2
0
0
0
0
0
0
0
2
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
4
2
0
0
2
1
0
0
2
0
3
2
0
0
0
0
0
1
2
0
1
0
1
0
2
0
0
0
0
0
2
2
0
0
1
0
1
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
1
0
0
2
0
0
0
2
2
1
0
1
1
0
0
0
0
2
0
2
1
0
0
0
2
0
0
1
0
1
1
0
2
2
1
0
1
0
0
0
2
1
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
5
0
1
0
0
0
2
0
2
2
1
2
0
0
0
1
1
1
0
1
0
1
0
1
0
2
1
0
0
2
1
0
0
2
0
0
0
0
2
1
0
1
1
0
1
1
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
2
0
0
0
1
0
0
0
0
0
3
1
1
1
0
3
0
0
0
0
4
4
0
1
0
0
4
0
0
0
0
2
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
1
1
2
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
1
1
1
2
2
1
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
1
0
3
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
1
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
2
0
0
0
0
2
5
2
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
1
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
2
0
1
2
0
0
1
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
4
1
2
0
0
0
0
0
1
0
2
0
0
0
0
2
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
2
3
1
0
0
0
0
0
0
1
1
0
1
0
3
2
0
3
2
0
1
0
2
0
0
0
0
3
1
0
2
2
0
0
1
1
2
0
0
1
0
1
1
0
0
0
0
2
3
1
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
2
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
1
0
1
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
2
0
2
2
0
2
0
2
0
0
0
2
0
0
1
0
0
0
2
0
1
0
0
0
0
1
0
0
2
0
2
0
1
0
1
1
0
0
1
2
0
0
0
0
2
2
0
0
2
0
1
0
0
0
0
0
4
0
0
0
1
2
0
1
0
2
0
0
0
0
2
0
0
2
2
2
0
0
0
2
0
0
0
1
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
3
1
0
0
0
0
0
0
0
0
2
1
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
2
0
2
0
0
0
0
1
0
1
1
0
1
0
2
0
0
1
3
0
0
2
0
0
0
0
0
0
0
0
3
0
1
0
0
2
1
1
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
5
0
0
1
1
0
0
2
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
5
1
0
0
0
0
1
0
0
0
0
1
0
0
3
0
0
1
1
0
0
1
3
0
2
1
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
4
0
0
0
0
5
2
0
0
1
2
2
0
1
0
1
1
0
0
0
0
2
0
0
3
0
0
0
0
0
1
0
2
0
0
0
2
0
1
0
0
0
0
1
0
1
1
0
0
1
0
1
2
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
1
0
2
0
0
1
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
1
1
0
2
0
2
1
0
0
1
1
0
0
2
1
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
2
0
0
1
0
0
0
1
0
0
2
1
0
0
0
0
0
2
0
2
0
0
1
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
2
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
2
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
7
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
1
3
0
0
0
0
0
2
2
0
2
0
2
0
0
0
0
0
1
2
0
0
0
0
2
1
3
0
2
1
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
2
1
1
0
1
0
0
1
0
0
1
0
0
0
1
1
1
0
2
0
5
0
2
2
0
1
0
0
2
0
0
2
0
1
0
0
0
2
1
1
0
2
0
0
1
0
2
12
1
0
1
0
0
2
0
2
0
2
1
0
1
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
2
2
0
2
2
0
0
2
4
0
0
1
1
0
2
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
2
2
0
0
0
1
3
2
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
1
0
0
1
3
2
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
1
3
0
0
0
0
0
1
0
2
2
0
0
1
2
0
3
0
1
0
0
1
0
0
2
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
2
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
1
3
5
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
1
0
0
3
0
0
0
0
2
0
1
0
0
0
0
2
0
1
1
0
0
2
0
0
1
0
2
0
2
0
0
1
0
0
2
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
1
0
0
2
1
1
0
1
2
0
1
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
1
2
0
0
0
0
3
0
2
0
1
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
1
2
0
2
0
0
0
1
5
1
0
2
1
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
2
0
1
0
1
1
2
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
2
1
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
2
0
0
0
1
2
0
0
0
0
7
0
0
0
0
0
0
3
0
0
0
0
1
0
1
2
2
6
0
2
0
1
0
0
0
0
1
2
0
2
0
2
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
1
1
0
0
0
0
0
0
1
0
1
1
0
2
1
0
0
0
0
0
2
0
2
2
0
0
0
1
0
0
0
0
0
1
0
0
3
1
0
0
0
1
0
3
0
0
0
2
0
0
1
7
2
0
2
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
2
0
0
0
0
1
0
0
0
0
0
1
0
1
0
4
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
2
2
0
2
0
0
2
0
0
0
0
0
0
0
1
2
1
0
0
0
2
0
0
1
0
1
2
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
2
0
0
0
2
1
0
1
0
0
0
0
2
1
2
0
1
0
1
0
0
2
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
3
0
0
0
0
0
2
1
2
0
0
1
0
1
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
1
1
1
0
0
0
0
0
0
2
0
0
0
2
0
1
0
1
0
0
0
0
0
0
4
2
1
0
0
0
0
2
0
2
1
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
2
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
1
1
1
0
0
1
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
6
0
2
1
0
0
0
0
0
0
2
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
1
1
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
1
0
2
2
0
0
0
0
0
0
2
0
3
1
0
1
2
0
1
2
0
1
0
0
0
1
0
0
1
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
1
0
1
0
20
0
1
2
2
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
3
0
2
4
2
0
1
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
2
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
2
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
2
0
0
2
1
0
0
0
0
0
0
0
1
2
0
0
2
0
0
1
1
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
2
2
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
2
0
2
0
0
1
1
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
1
0
0
0
0
0
2
1
0
0
0
1
0
2
0
0
0
0
0
0
3
0
0
1
0
0
0
0
2
2
0
0
0
0
2
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
3
9
0
0
0
0
2
2
0
0
0
0
1
0
2
0
0
2
0
0
0
0
2
0
2
0
1
0
0
0
1
0
0
1
1
1
0
0
0
0
3
2
0
2
0
2
0
0
0
0
0
0
0
0
1
0
3
2
0
2
0
0
0
1
0
0
0
0
0
1
2
1
0
0
0
1
0
0
0
0
0
0
2
0
2
1
0
1
1
0
0
2
0
2
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
2
0
1
0
1
0
0
0
1
2
2
1
0
0
5
0
1
1
0
0
0
0
0
0
0
0
2
0
4
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
1
1
0
0
0
0
0
0
1
0
0
1
0
0
2
2
1
0
0
1
1
1
0
0
0
0
0
0
0
1
0
2
1
0
2
1
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
3
2
2
0
0
1
0
2
0
2
1
1
1
0
0
2
0
2
0
4
0
0
0
0
2
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
2
3
0
0
1
0
1
2
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
2
0
0
0
0
2
1
2
2
1
0
0
0
2
1
0
0
0
0
0
2
0
2
1
0
0
0
0
1
2
1
2
6
0
2
0
0
0
0
1
1
1
0
0
0
0
0
2
0
0
3
0
0
0
3
0
0
0
0
0
0
0
2
0
1
0
0
1
1
0
0
0
0
1
2
2
0
0
3
0
2
0
0
0
1
0
0
2
1
1
1
1
0
1
0
0
2
0
1
2
0
0
4
0
0
0
1
0
0
0
0
2
0
1
0
1
2
2
0
1
0
0
0
1
2
1
0
2
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
1
0
0
0
0
2
2
2
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
2
0
0
1
2
0
0
0
2
0
0
0
2
2
0
0
0
0
0
1
0
1
0
0
0
2
1
0
2
1
0
3
1
0
1
2
0
0
1
0
0
1
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
1
1
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
2
1
1
0
2
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
3
0
0
0
1
1
3
0
2
0
0
1
0
0
0
0
1
0
4
1
0
0
0
0
2
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
2
0
0
1
0
0
2
0
0
2
0
2
0
0
0
0
4
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
3
0
2
0
0
0
2
2
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
1
0
0
1
1
2
0
0
0
0
0
0
3
0
0
0
0
6
0
0
2
0
0
0
0
1
0
2
1
3
0
0
2
1
0
2
0
0
1
1
3
0
0
0
2
0
0
0
0
2
0
3
0
2
0
0
0
0
3
0
0
1
0
2
0
0
0
0
0
0
0
1
0
1
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
3
0
1
0
0
0
0
0
0
0
3
1
0
0
1
0
1
2
2
0
0
1
0
0
0
1
0
3
0
0
2
2
1
0
0
0
0
0
0
0
2
0
1
0
0
0
2
2
0
0
0
1
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
2
2
1
1
1
0
0
0
0
1
0
0
0
0
1
0
2
0
2
0
0
2
0
2
0
0
2
0
0
0
0
2
0
0
0
1
2
1
1
0
0
0
0
0
0
0
2
0
0
0
0
1
4
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
1
1
0
0
2
0
1
1
0
0
0
0
2
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
1
2
0
0
2
0
1
0
0
0
0
0
3
0
1
0
0
0
0
0
2
0
0
1
2
0
2
1
1
0
0
0
0
1
1
0
0
0
0
0
1
2
1
1
0
0
0
2
0
0
0
0
1
0
0
0
2
0
1
0
0
4
0
1
0
0
2
1
0
0
0
0
2
0
1
0
0
0
0
2
3
1
0
0
1
1
1
2
0
0
0
0
1
2
0
0
3
1
0
0
1
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
1
1
0
0
0
0
2
2
1
0
0
2
1
0
0
0
2
0
1
0
0
0
1
1
2
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
1
1
3
1
0
1
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
2
0
1
0
0
0
5
0
0
0
0
0
0
0
0
3
0
1
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
7
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
2
5
0
0
2
1
0
1
0
2
0
0
0
0
2
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
2
1
0
0
0
0
2
0
2
0
1
0
0
2
3
0
0
1
2
0
2
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
2
1
0
3
2
1
0
0
2
2
0
3
2
1
0
2
0
0
0
0
0
0
2
0
0
3
2
2
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
3
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
2
2
2
0
0
0
0
2
0
0
1
0
0
0
1
0
0
2
0
2
2
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
1
0
0
2
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
1
1
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
2
2
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
4
0
0
2
0
1
1
0
1
2
0
1
0
2
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
1
0
2
0
0
0
1
0
0
2
2
0
0
2
1
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
1
0
4
0
0
2
0
0
0
1
0
2
1
0
0
2
0
0
0
0
0
1
0
0
1
0
0
2
0
0
1
1
0
1
0
0
0
3
0
0
0
0
0
1
1
0
0
0
0
3
0
0
0
0
1
1
2
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
1
2
0
1
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
2
1
0
1
0
2
0
0
0
0
0
1
2
0
2
2
0
0
0
0
0
4
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
1
1
0
0
1
1
0
2
0
2
0
2
1
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
1
0
1
2
1
0
0
1
3
0
1
0
0
1
2
0
0
5
2
1
0
0
0
0
1
1
0
0
0
0
2
2
0
0
2
4
0
0
0
0
0
0
0
1
0
2
2
0
4
2
0
0
2
0
2
0
0
0
2
0
0
0
3
0
0
0
0
0
7
1
2
0
0
1
0
0
2
1
0
1
0
0
2
0
2
1
2
0
0
0
0
0
0
0
2
1
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
2
3
0
0
0
0
1
2
0
1
10
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
2
1
0
0
0
0
1
0
1
0
2
5
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
4
0
0
1
0
1
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
5
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
2
2
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
1
2
0
0
0
0
3
2
0
0
1
0
0
0
0
0
1
0
2
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
2
1
0
0
1
2
0
2
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
2
0
0
0
0
2
0
0
0
0
3
0
1
0
0
2
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
2
2
0
1
0
0
0
3
0
0
0
0
0
2
0
3
0
0
0
0
0
0
1
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
1
0
1
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
3
2
1
4
0
1
2
1
0
0
0
0
1
0
0
0
2
0
0
0
0
2
2
0
0
0
1
1
0
1
0
0
0
2
0
0
1
0
2
0
1
0
1
0
2
0
0
0
1
0
0
0
0
2
0
0
0
2
1
2
0
0
1
0
0
0
0
0
0
0
1
3
0
0
1
0
2
0
0
1
0
0
3
0
0
0
2
2
1
0
1
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
2
0
0
0
3
0
0
1
0
1
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
2
0
2
0
1
0
0
0
1
0
2
0
2
0
0
0
0
0
1
2
0
1
0
0
0
0
2
2
0
0
1
0
1
2
0
0
0
0
1
1
0
0
0
0
0
5
1
2
2
2
0
2
0
1
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
2
0
2
0
2
0
0
2
0
1
3
0
2
0
0
2
0
0
0
1
0
1
0
1
0
0
0
1
1
1
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
1
0
0
1
0
0
0
1
0
0
0
1
1
0
0
1
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
3
1
0
2
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
1
3
0
0
3
0
0
0
0
0
2
0
0
2
0
1
2
0
0
0
2
0
1
0
0
1
1
1
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
2
0
0
2
1
0
2
4
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
2
2
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
2
1
0
0
2
1
1
0
1
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
1
0
2
0
1
0
0
0
2
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
5
0
0
4
0
0
0
0
1
0
2
3
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
1
2
0
1
0
0
2
0
2
0
0
1
0
2
2
0
0
2
0
2
0
0
1
0
1
0
0
0
2
6
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
2
1
0
1
0
0
0
0
0
0
1
0
1
2
0
0
1
0
1
2
0
0
0
0
2
0
0
2
0
0
0
0
2
4
2
0
0
0
1
1
0
2
0
3
0
1
0
0
0
0
2
0
2
0
2
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
3
0
0
2
0
2
0
2
0
0
0
0
0
1
0
0
0
0
1
0
3
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
1
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
2
1
2
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
3
0
0
0
0
0
1
1
0
0
0
0
2
2
2
0
2
2
0
0
0
2
0
0
0
1
1
0
0
2
0
0
2
2
0
0
2
0
1
0
0
3
1
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
2
2
0
2
0
0
2
1
0
0
0
0
1
2
0
0
0
0
2
0
0
2
1
0
1
0
0
1
0
2
0
2
0
2
0
0
1
3
0
0
0
1
2
0
0
2
2
1
0
0
0
0
2
0
0
2
2
1
0
2
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
1
0
2
0
0
0
1
2
1
0
0
0
1
2
2
1
0
2
0
0
0
2
1
0
0
1
0
0
1
0
0
0
1
0
2
2
0
0
0
1
2
0
0
0
0
0
0
0
1
1
0
0
2
2
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
5
2
0
0
0
2
1
1
0
0
0
0
0
1
0
0
2
1
0
0
2
0
0
0
0
0
1
1
2
1
2
0
0
0
0
0
0
2
1
2
2
0
0
0
0
0
0
2
1
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
1
0
2
0
0
3
0
0
0
0
2
0
0
1
0
3
0
0
2
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
2
0
0
0
0
1
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
3
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
1
0
0
0
1
2
1
0
0
0
1
0
1
0
1
0
0
0
3
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
2
2
1
1
2
1
0
2
0
0
0
1
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
2
1
1
0
0
2
0
1
2
1
0
2
0
0
0
2
0
0
0
2
1
0
0
0
0
3
0
0
2
0
1
0
0
3
1
2
0
0
0
0
2
0
2
2
1
0
0
1
0
0
0
0
0
0
1
1
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
2
0
1
1
0
1
0
0
0
0
0
0
0
4
0
1
0
0
1
2
0
3
2
0
0
0
0
2
1
0
0
1
0
0
2
0
0
0
2
1
0
0
1
2
0
0
0
0
0
2
0
2
0
0
4
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
4
1
0
0
0
0
0
0
1
0
0
1
0
0
0
2
2
1
0
0
0
0
0
3
0
0
1
0
0
1
0
0
0
1
1
0
2
2
1
1
0
0
0
2
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
1
0
0
0
2
0
0
2
2
0
1
1
1
2
2
1
1
0
2
2
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
2
0
1
0
0
0
2
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
3
2
2
0
2
0
0
0
0
1
1
0
0
1
0
0
0
2
2
1
0
0
2
0
1
2
2
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
2
2
1
0
0
2
0
0
0
0
2
4
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
2
3
1
0
0
0
0
0
1
1
0
1
0
0
2
0
0
1
2
0
1
0
0
2
1
0
0
2
3
0
1
0
0
0
0
0
2
0
0
0
0
0
9
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
2
0
1
0
0
0
0
0
2
1
0
0
0
0
2
0
0
2
2
1
1
0
2
1
1
0
0
2
0
1
2
0
1
2
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
1
2
0
2
0
0
0
1
0
0
3
0
0
0
0
1
0
0
3
0
1
3
2
2
2
1
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
2
1
2
0
0
1
0
0
3
0
2
0
0
1
0
0
2
0
2
1
0
0
0
0
2
0
2
2
0
0
1
1
0
0
2
0
0
0
0
2
0
0
0
2
0
0
1
2
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
1
2
1
2
0
0
1
1
0
0
0
1
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
2
0
0
1
1
2
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
3
0
0
2
0
0
0
2
0
0
1
2
1
2
0
0
2
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
2
1
2
0
1
0
0
0
2
0
1
0
0
2
0
0
2
0
0
1
0
0
2
0
0
0
0
1
0
0
2
2
0
1
0
0
1
0
2
1
1
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
3
0
0
1
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
2
1
2
0
0
1
0
2
2
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
1
1
0
0
0
0
0
2
0
0
0
1
1
0
0
0
2
0
2
0
0
3
0
0
0
2
0
2
0
0
1
0
0
1
0
0
0
1
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
2
3
0
2
2
2
1
2
0
1
0
3
0
2
0
2
0
0
0
0
1
0
1
0
0
0
0
0
2
0
3
0
0
1
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
1
1
1
0
0
0
0
2
1
0
0
2
2
0
0
0
2
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
3
0
0
14
0
0
0
1
1
0
0
1
1
1
1
2
0
2
1
0
3
0
5
0
0
2
0
0
1
2
0
2
1
0
0
0
0
0
0
2
1
0
2
0
0
0
0
1
0
0
0
1
2
0
0
0
1
0
0
0
1
0
6
0
0
2
0
0
2
0
0
2
0
1
1
1
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
3
0
0
0
0
0
0
0
1
4
0
0
0
0
0
1
0
1
0
0
0
0
0
4
0
3
0
1
0
0
2
1
0
0
0
2
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
5
1
1
0
0
0
0
1
1
0
0
1
0
2
0
0
0
2
1
0
1
3
0
0
1
2
0
0
0
0
0
0
3
1
2
0
2
2
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
2
0
0
2
0
0
0
0
0
0
4
1
1
0
1
0
0
1
0
0
0
2
1
0
0
1
1
0
0
0
0
0
0
1
0
0
2
0
0
2
2
0
2
0
1
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
2
1
1
0
0
1
0
0
1
1
0
2
0
2
0
0
2
0
0
2
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
1
1
1
0
2
0
0
0
2
2
2
0
0
0
2
0
0
0
0
0
0
1
0
0
1
2
0
1
0
1
0
0
0
0
2
0
0
2
0
0
2
1
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
3
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
3
0
2
0
0
0
0
2
0
2
0
0
3
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
2
2
0
0
1
0
2
1
0
2
0
0
2
0
0
2
0
2
0
1
0
0
0
2
0
1
1
0
0
1
0
2
0
2
1
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
2
1
2
0
0
0
0
0
1
0
0
2
2
0
0
1
0
2
1
0
0
1
0
0
2
0
0
0
1
0
1
0
0
2
0
0
4
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
5
2
1
2
0
2
0
0
1
0
1
0
0
1
0
1
0
0
0
0
1
0
2
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
1
2
0
0
1
0
2
0
0
2
1
2
0
0
0
1
0
0
1
1
0
0
1
0
0
0
2
0
0
0
0
0
1
0
2
1
0
1
1
1
0
1
1
0
0
2
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
3
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
3
0
2
0
0
0
2
0
0
1
2
2
0
1
3
0
0
1
2
1
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
2
0
1
2
0
0
2
0
2
0
0
0
0
1
0
3
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
1
1
0
0
2
0
0
0
1
2
0
0
0
0
0
2
1
2
0
0
0
0
2
0
1
0
1
0
0
2
0
0
0
0
2
0
0
0
1
2
2
0
0
0
0
0
2
0
0
1
0
2
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
1
0
3
0
2
0
0
1
2
0
0
1
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
2
0
1
0
2
2
2
0
3
0
0
0
0
1
2
2
0
2
1
0
2
3
0
0
2
0
0
2
0
0
3
0
0
0
0
0
1
0
1
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
2
0
2
2
2
0
1
0
0
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
2
2
3
0
2
0
0
0
0
2
0
0
1
0
1
0
2
0
0
1
0
0
0
2
1
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
1
1
0
0
2
2
0
1
1
1
0
0
0
2
0
2
0
1
0
2
0
0
3
0
0
1
0
0
0
1
0
4
1
0
0
0
2
0
0
2
2
0
0
2
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
2
0
0
1
2
0
0
1
0
2
1
0
0
2
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
2
0
0
2
2
0
0
2
0
1
0
0
0
0
0
0
0
0
3
1
1
2
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
1
2
0
0
0
0
1
1
1
0
0
1
1
0
0
1
0
0
0
0
2
0
1
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
7
0
0
0
2
0
2
0
0
0
1
1
2
0
0
0
1
0
0
0
0
1
1
0
2
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
2
2
1
2
1
0
2
1
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
2
0
0
2
1
0
0
0
1
3
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
9
0
1
0
2
1
0
0
2
0
0
0
0
1
0
0
0
1
2
2
1
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
2
0
0
0
2
0
1
0
1
0
0
1
0
2
0
1
0
0
0
3
0
1
0
0
0
0
0
1
0
0
2
0
3
1
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
2
5
0
0
0
2
0
0
1
1
0
0
3
1
1
0
2
1
0
1
0
3
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
1
0
0
2
2
2
0
0
0
2
1
2
0
2
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
1
1
2
0
0
3
0
5
0
0
0
1
0
0
0
2
0
1
1
0
0
2
3
0
0
0
1
0
0
0
0
2
1
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
1
2
0
0
2
2
1
2
2
0
2
0
2
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
2
0
1
1
0
0
1
1
9
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
1
0
2
0
0
2
0
0
0
1
0
4
0
2
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
7
0
1
0
0
0
0
1
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
6
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
3
2
0
2
0
0
0
0
0
0
0
0
1
2
0
3
0
1
2
0
2
1
0
0
0
0
1
2
1
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
2
0
1
1
1
0
0
2
0
2
4
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
3
0
0
1
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
2
2
0
1
0
2
0
1
0
1
0
0
0
2
0
1
0
0
0
0
1
1
0
2
0
0
0
1
1
0
0
0
0
0
1
0
2
1
1
2
0
0
0
0
3
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
2
0
0
0
2
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
2
1
2
0
0
1
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
1
2
0
0
2
0
2
1
4
0
1
0
2
0
0
1
0
0
2
0
1
0
0
2
0
2
0
0
0
0
0
1
2
0
1
0
1
0
2
2
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
2
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
1
1
1
0
0
0
1
0
2
0
0
1
0
1
1
0
0
3
0
0
2
0
0
0
1
2
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
2
0
0
2
7
1
0
0
0
0
0
2
0
0
1
1
1
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
5
0
0
0
0
0
0
0
0
2
1
0
0
2
0
1
2
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
3
0
1
0
1
0
0
0
0
1
0
0
2
2
2
1
0
0
0
0
0
0
0
4
1
0
0
2
0
2
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
2
3
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
2
1
0
0
0
2
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
2
0
2
1
0
0
0
0
0
0
2
1
0
0
0
2
0
0
3
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
7
1
0
0
0
1
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
6
1
0
0
2
0
0
6
0
2
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
1
2
0
0
3
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
1
1
0
2
1
2
2
1
0
0
0
0
0
0
5
1
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
1
0
0
2
0
0
2
0
0
1
0
0
1
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
1
0
0
0
2
2
0
1
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
5
1
0
0
2
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
1
0
0
0
1
0
1
0
0
1
0
1
2
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
7
1
0
2
0
0
0
0
0
0
0
0
4
0
0
2
0
0
2
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
4
1
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
2
2
0
0
0
1
1
0
2
0
3
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
2
1
0
2
1
1
0
0
0
2
2
2
0
0
2
0
1
0
2
1
0
0
0
1
0
3
1
0
0
0
0
0
0
0
1
0
2
0
0
0
1
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
2
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
3
0
0
1
0
0
4
0
2
2
0
3
1
0
0
2
0
0
0
0
0
1
2
2
0
0
0
0
0
0
2
0
0
0
2
1
0
1
2
2
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
1
0
1
1
0
0
1
1
0
0
1
0
2
0
0
0
2
0
2
0
0
1
0
0
0
0
0
1
2
0
2
2
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
3
1
1
0
0
0
2
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
4
2
0
0
0
0
0
0
0
2
0
0
0
5
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
1
0
0
1
0
0
0
3
0
0
0
1
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
10
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
3
0
0
0
0
0
0
1
0
0
0
0
1
2
0
1
3
0
1
2
0
0
0
2
0
0
0
0
0
2
2
1
0
2
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
2
0
2
2
0
0
0
2
0
0
1
0
0
2
0
0
0
0
1
0
2
0
0
1
0
1
2
0
2
0
0
0
0
2
0
0
0
2
2
0
0
0
2
0
0
0
0
0
2
2
0
0
0
2
0
1
0
0
0
0
2
0
0
0
1
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
2
0
2
0
0
0
1
0
2
0
0
2
0
0
2
0
3
0
0
1
0
0
0
2
1
3
0
0
1
0
0
1
0
0
1
0
0
0
2
2
0
1
0
0
0
1
0
0
0
3
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
2
3
2
1
1
2
0
0
1
0
1
0
1
2
1
0
0
0
1
0
0
2
0
1
0
4
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
1
0
2
0
2
0
0
3
0
2
0
0
2
0
0
1
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
3
0
0
2
2
1
1
0
3
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
1
1
0
2
1
0
1
2
0
0
2
0
0
2
2
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
3
0
0
0
0
0
0
1
2
0
0
0
0
0
0
3
0
0
0
0
0
2
1
0
2
0
0
0
0
0
2
0
2
0
2
0
0
0
0
1
0
0
3
0
0
2
1
1
1
0
0
0
0
0
2
1
0
0
1
1
1
2
0
2
1
0
0
0
1
1
0
2
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
1
2
0
0
1
0
2
2
1
0
0
0
0
0
3
0
0
1
0
0
2
0
0
2
2
0
2
3
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
1
0
0
2
2
0
1
0
0
0
1
0
1
0
1
1
0
2
0
0
2
1
0
0
0
1
2
1
0
0
0
0
5
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
2
2
1
0
0
0
0
0
1
2
2
0
0
1
2
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
2
0
0
2
2
0
0
0
1
0
0
1
0
2
2
0
1
0
1
0
1
2
2
0
0
0
0
4
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
2
0
2
2
1
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
1
2
0
2
1
0
2
2
0
0
0
0
2
0
1
0
1
0
1
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
3
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
2
0
0
2
1
0
0
0
1
0
2
0
1
0
0
2
0
2
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
1
2
0
2
2
0
0
0
0
1
1
0
0
2
0
1
0
0
0
1
0
3
2
0
2
0
0
0
0
2
0
0
1
1
1
0
1
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
2
2
3
1
0
0
0
0
0
0
0
0
0
2
1
2
1
0
3
2
0
1
1
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
1
2
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
2
7
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
2
0
0
0
0
0
2
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
3
1
0
0
1
1
0
0
0
0
2
0
2
1
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
1
2
1
0
0
2
0
2
0
0
0
0
1
0
0
0
4
2
0
0
1
0
0
0
2
0
0
0
0
0
1
2
0
0
0
1
0
0
2
0
0
1
0
1
0
0
0
0
0
2
0
0
1
1
0
0
0
2
0
0
2
1
1
0
2
0
0
0
1
0
1
0
0
0
1
0
2
1
0
2
0
0
3
0
0
0
0
1
2
0
0
0
0
0
2
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
2
2
1
1
1
3
1
1
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
1
1
0
0
0
2
2
2
0
0
0
0
3
2
1
0
0
1
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
1
2
0
2
0
5
0
2
0
2
0
0
2
0
0
0
2
1
0
2
0
3
2
1
0
1
0
0
2
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
2
0
0
0
2
0
0
0
0
1
0
1
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
2
1
2
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
1
1
0
0
2
0
0
3
0
0
0
2
2
0
0
0
0
2
0
0
2
0
0
1
2
3
1
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
4
0
1
0
2
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
2
0
1
2
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
1
2
2
0
0
0
1
0
0
3
0
2
0
1
0
0
0
2
0
2
2
0
0
0
1
2
0
0
0
0
2
3
2
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
1
2
1
0
0
0
1
2
1
0
0
0
0
0
0
1
0
0
0
0
0
3
1
0
0
0
0
0
0
2
3
1
2
0
0
2
0
1
0
0
0
0
0
1
2
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
3
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
3
0
0
0
1
0
3
0
0
0
0
1
0
1
2
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
2
1
0
2
0
0
0
2
0
0
0
1
0
1
0
0
0
0
1
1
1
1
3
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
2
1
0
1
0
2
0
2
0
2
0
0
2
1
0
0
2
2
0
0
1
0
0
1
0
0
1
2
1
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
2
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
3
1
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
5
0
1
2
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
2
2
1
0
2
0
1
0
0
0
0
2
2
0
0
2
0
0
0
0
2
1
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
2
2
0
0
2
2
0
0
0
0
0
1
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
2
0
2
2
0
2
0
0
0
1
0
0
0
5
0
0
1
2
0
0
0
0
0
0
0
0
0
2
1
0
2
2
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
1
0
0
0
0
0
1
2
2
3
2
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
1
0
0
0
2
0
0
1
0
0
1
1
0
0
0
1
1
2
1
4
1
1
0
0
2
0
0
0
8
0
1
0
0
0
2
1
0
2
2
0
3
0
1
1
0
0
0
2
0
1
0
0
4
1
0
0
0
0
0
0
0
0
2
2
0
1
2
0
0
0
0
0
2
2
0
2
1
0
2
0
2
0
0
0
1
0
2
0
2
0
0
0
1
0
0
0
0
2
0
0
0
5
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
4
1
0
0
1
1
0
0
0
0
0
2
0
1
0
0
0
0
0
1
2
0
1
2
3
0
0
0
0
1
0
0
0
0
0
1
2
1
0
1
0
0
0
0
0
1
0
0
2
0
0
3
0
0
0
0
2
0
0
0
0
0
0
2
2
1
0
0
1
0
0
1
0
1
0
2
0
0
0
0
0
0
3
0
0
0
2
1
2
0
0
0
0
1
2
0
0
0
0
0
0
3
0
0
3
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
2
1
0
1
0
0
2
0
0
0
4
0
4
0
0
0
0
2
1
0
0
0
1
0
0
0
2
0
0
1
2
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
1
0
0
1
2
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
2
0
0
2
1
0
2
0
2
0
0
0
0
0
0
2
2
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
2
1
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
1
1
2
3
2
1
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
1
1
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
2
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
2
0
1
0
2
0
0
0
0
1
2
2
2
0
0
0
0
0
1
1
0
0
1
0
0
0
1
1
0
0
1
0
1
0
0
0
0
3
0
2
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
2
3
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
1
0
2
1
0
0
0
1
2
2
0
2
0
0
0
2
1
2
0
0
0
4
2
0
0
1
1
2
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
1
0
0
1
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
2
0
1
0
0
1
2
0
2
0
0
0
1
0
0
3
1
0
0
1
0
1
0
0
1
5
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
6
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
6
0
1
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
3
0
3
0
3
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
1
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
1
0
2
0
1
0
0
2
0
0
2
0
2
1
1
5
0
0
2
0
0
0
0
0
5
0
0
1
0
0
0
0
3
0
0
1
1
1
0
0
0
1
0
0
2
2
2
0
0
0
1
0
0
2
0
1
0
0
0
2
0
1
0
0
2
0
0
0
0
1
0
0
0
2
0
0
2
0
2
0
0
0
2
1
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
2
0
0
0
1
0
0
0
1
4
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
3
2
0
1
3
0
1
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
1
1
0
3
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
2
0
1
0
4
1
0
0
0
0
1
0
0
1
0
2
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
1
0
0
0
0
0
1
0
1
0
0
0
1
1
1
2
2
6
0
0
0
0
0
0
0
2
1
0
1
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
2
1
0
1
2
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
3
0
0
0
0
0
0
0
0
3
2
0
2
0
0
0
2
0
0
1
0
2
1
0
0
1
0
3
0
0
0
0
0
2
0
2
0
0
1
0
2
0
0
0
1
0
0
4
1
2
1
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
2
1
0
0
2
0
0
0
2
0
1
0
0
2
0
1
1
0
2
0
1
0
0
2
1
0
0
0
2
0
0
3
0
0
0
1
0
0
0
2
2
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
2
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
2
0
0
1
0
0
0
0
1
0
0
1
2
4
2
1
1
0
0
2
2
0
0
1
0
0
1
0
0
1
2
0
0
2
1
1
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
1
2
3
0
0
0
0
2
0
2
0
2
2
1
0
0
1
0
0
1
0
1
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
2
2
1
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
1
0
0
3
0
4
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
1
2
0
1
0
1
1
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
4
2
0
0
0
0
0
0
2
1
1
3
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
1
0
1
0
0
0
2
0
1
1
1
0
0
0
2
0
0
1
0
0
0
0
0
5
2
0
0
2
2
0
0
0
0
1
0
2
0
0
1
0
0
0
2
1
0
0
2
1
2
3
0
0
0
2
2
0
1
0
1
0
0
2
0
1
1
0
0
0
1
1
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
2
0
2
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
3
1
2
3
0
0
0
0
0
0
0
0
0
2
2
1
0
2
0
1
0
0
2
0
2
0
0
2
0
0
0
2
1
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
1
2
0
0
1
1
1
1
0
3
0
0
0
1
1
0
0
2
1
0
0
2
0
0
1
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
1
0
1
2
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
2
3
2
1
0
0
0
0
0
1
0
2
2
0
0
1
1
2
0
1
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
1
2
1
1
0
0
0
0
1
2
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
3
0
0
0
2
0
2
1
0
0
0
0
0
0
0
2
2
0
0
0
0
3
0
0
1
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
1
0
2
0
1
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
1
0
0
0
0
0
2
1
0
0
0
3
0
0
1
1
0
0
0
2
2
3
1
0
0
0
0
0
0
2
1
2
0
2
0
0
1
0
0
1
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
4
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
2
2
0
2
1
0
1
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
2
0
0
1
0
0
0
0
0
0
2
0
3
2
3
0
0
0
0
2
0
2
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
2
3
0
0
0
0
2
0
0
1
0
0
0
0
0
1
1
1
1
2
3
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
2
0
1
0
2
0
0
0
1
1
0
0
1
0
2
0
1
0
2
3
0
0
0
0
0
0
0
1
2
2
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
2
0
2
2
1
0
0
0
2
0
0
2
0
1
0
1
0
0
2
0
0
0
1
0
1
0
0
0
0
0
3
0
0
0
4
1
1
0
0
0
0
2
1
0
0
1
1
0
0
1
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
2
5
0
1
0
1
2
0
1
0
0
2
1
0
2
2
1
3
1
0
0
1
0
0
0
0
0
0
1
0
1
2
0
5
0
0
2
0
2
0
0
0
0
1
0
2
0
0
1
1
0
0
0
0
2
2
0
2
0
0
0
0
1
1
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
1
0
0
0
1
3
0
0
0
1
1
0
1
0
0
0
0
2
0
0
0
1
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
1
0
0
0
2
0
2
0
0
2
0
2
1
0
0
0
0
0
0
0
0
2
3
0
0
0
2
0
0
1
2
0
0
0
0
0
1
1
0
2
0
2
0
0
0
0
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
1
1
1
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
1
2
0
0
0
0
0
0
0
0
2
0
0
1
0
2
2
0
0
0
0
0
0
0
2
2
0
0
2
1
2
0
0
0
0
0
0
0
2
0
0
0
0
1
4
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
1
0
2
1
0
0
1
0
0
0
1
0
0
0
0
2
0
1
0
0
0
2
2
0
0
1
0
0
2
0
0
0
1
0
1
1
1
2
0
0
2
0
0
0
4
7
2
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
2
0
2
0
2
0
0
0
2
0
1
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
2
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
1
1
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
1
0
2
0
0
0
0
0
0
0
0
1
0
2
2
1
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
2
0
2
0
2
0
0
0
1
0
2
2
0
0
2
0
2
2
1
1
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
2
1
0
0
2
0
0
0
0
0
2
1
1
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
2
0
0
0
2
1
0
0
0
1
1
0
0
0
1
0
4
2
0
0
0
0
3
0
0
0
0
0
0
1
2
0
2
2
0
0
1
2
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
2
0
2
0
0
2
0
2
0
1
0
0
0
0
0
0
3
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
2
0
0
0
1
0
1
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
2
2
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
2
0
2
0
2
2
1
1
0
1
1
0
2
0
2
2
0
0
0
0
1
0
0
1
1
0
0
0
0
0
4
2
1
0
0
0
0
0
0
1
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
2
1
0
0
0
0
0
2
0
1
1
0
2
1
0
0
0
0
0
0
0
0
2
0
0
1
0
1
1
1
0
1
0
1
1
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
2
1
1
0
0
0
0
0
0
1
2
1
0
0
0
0
0
3
1
0
0
0
0
4
0
0
2
0
0
2
0
0
0
3
1
0
2
0
0
2
0
0
2
1
0
0
0
0
3
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
1
2
0
1
2
0
3
1
0
0
0
0
0
0
0
0
1
0
3
0
2
2
0
2
0
0
0
0
0
0
0
1
0
3
1
0
0
2
0
1
0
3
2
0
0
0
1
0
1
0
0
3
0
2
0
0
2
1
0
1
1
0
2
1
0
0
2
0
0
0
3
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
1
1
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
1
0
2
0
0
1
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
3
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
2
0
1
0
1
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
3
3
2
2
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
3
0
2
0
0
0
0
1
3
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
1
1
0
2
5
2
0
0
0
0
2
1
2
0
0
0
2
2
3
0
0
0
2
0
0
0
0
0
0
1
0
2
1
0
0
0
1
0
2
0
1
0
0
0
0
2
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
1
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
2
0
1
0
0
0
2
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
1
1
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
3
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
3
0
2
0
0
1
2
0
0
0
0
0
0
0
0
1
1
0
0
0
1
3
0
3
1
2
0
10
0
1
0
0
0
0
2
2
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7
2
1
0
0
1
0
0
0
2
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
1
2
1
1
0
2
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
1
0
0
0
1
1
2
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
2
1
0
2
1
0
1
0
2
0
0
0
0
0
1
1
0
0
0
2
2
0
4
0
2
0
0
1
0
0
2
1
1
0
0
0
0
1
0
0
2
0
0
2
1
0
0
0
2
0
1
1
0
0
2
2
2
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
2
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
4
2
3
0
1
0
0
5
0
0
0
0
0
1
0
1
0
0
3
2
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
1
4
1
0
0
0
0
0
1
2
0
0
0
2
3
1
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
3
0
0
0
2
0
1
0
1
2
2
0
0
0
0
1
1
0
2
0
0
0
0
0
2
0
0
0
1
0
0
1
2
1
0
0
1
0
0
2
0
1
1
2
0
4
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
2
0
2
0
1
0
0
0
3
0
0
0
0
0
0
0
1
2
0
1
0
0
3
0
0
0
0
2
2
1
0
0
1
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
2
2
0
0
0
0
1
0
1
0
1
0
0
2
2
0
1
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
3
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
8
0
0
0
0
1
0
1
1
1
2
0
0
0
0
3
1
2
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
3
0
2
2
1
0
0
0
1
2
0
2
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
2
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
2
0
1
1
0
0
0
2
2
0
2
0
0
0
0
2
0
0
0
1
0
4
0
0
2
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
2
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
3
2
0
1
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
2
2
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
1
0
1
2
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
2
2
0
1
0
0
0
3
0
2
0
1
0
0
0
0
0
0
0
2
1
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
1
0
1
0
0
0
0
0
2
1
0
0
0
1
0
0
0
2
1
0
0
0
2
2
0
0
0
0
0
3
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
2
2
0
0
2
1
0
0
0
3
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
1
0
2
0
2
0
0
0
2
2
2
1
0
0
0
0
0
2
0
0
1
2
0
2
0
0
0
0
0
0
1
0
2
1
0
0
1
0
0
0
0
0
1
1
0
1
0
2
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
2
1
1
0
1
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
2
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
2
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
1
2
0
1
1
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
2
1
0
1
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
2
2
2
1
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
3
0
1
1
2
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
3
1
1
1
2
0
2
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
2
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
1
1
0
0
0
1
0
2
1
0
1
0
1
3
2
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
1
0
0
0
2
2
1
0
0
0
0
1
1
1
0
1
0
2
0
0
0
2
2
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
3
0
0
2
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
4
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
1
0
0
2
2
1
0
0
0
2
0
0
1
0
3
1
0
0
0
0
0
3
2
2
0
0
0
0
0
0
0
1
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
1
0
2
0
4
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
1
0
1
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
1
0
0
0
0
0
0
0
1
0
2
1
0
0
0
3
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
2
0
0
2
0
1
0
2
4
1
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
3
0
0
0
2
0
2
0
2
0
0
0
2
0
3
1
1
1
0
0
0
0
0
0
2
2
2
0
0
0
2
0
1
0
1
0
0
0
0
1
0
1
0
0
3
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
2
0
1
1
2
0
0
0
0
0
2
0
2
3
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
3
0
0
2
0
0
1
2
2
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
3
0
2
0
0
0
0
3
0
0
3
1
0
0
2
0
0
0
2
0
0
0
1
1
1
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
2
0
1
0
0
0
1
1
0
0
0
2
2
1
0
0
0
1
0
1
0
5
0
2
7
2
0
0
0
1
0
0
1
0
0
0
2
2
1
0
0
2
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
2
1
2
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
1
0
0
0
0
1
0
1
2
0
0
2
0
2
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
2
0
0
1
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
3
0
2
1
2
0
2
0
1
0
1
2
2
0
0
0
0
2
0
1
0
0
0
0
1
1
0
0
0
0
2
0
0
1
0
0
1
0
1
0
0
0
0
2
0
3
1
0
0
1
1
0
2
2
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
7
0
2
0
0
1
0
0
0
1
0
0
0
3
0
0
0
2
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
2
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
1
0
0
0
2
0
0
0
0
0
1
2
0
2
0
1
0
0
0
0
1
0
0
1
0
0
2
1
0
0
0
0
2
0
0
2
1
0
0
2
0
0
2
0
2
1
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
2
1
0
1
0
3
1
1
1
2
0
0
0
1
0
0
0
3
2
0
1
0
0
1
1
0
0
0
0
0
2
0
3
0
0
2
0
0
1
0
0
3
0
0
0
2
0
1
0
1
0
1
0
0
0
0
0
0
2
2
0
0
0
2
3
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
1
0
0
1
0
2
1
0
0
0
2
0
2
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
12
0
0
0
0
2
1
1
0
0
0
0
0
2
0
0
1
0
0
0
2
0
2
0
0
0
0
1
0
0
0
2
0
2
0
0
1
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
2
1
1
2
1
2
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
1
3
1
2
0
0
2
0
0
0
3
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
2
2
0
1
0
1
2
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
3
0
1
2
0
2
2
0
2
0
1
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
2
0
0
1
2
0
1
0
0
0
0
0
1
0
0
0
0
1
2
1
0
0
2
0
0
3
2
0
1
2
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
1
0
1
0
0
1
2
1
2
1
2
1
1
0
2
1
0
2
0
0
2
1
0
3
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
3
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
1
2
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
2
2
1
0
2
0
2
0
2
0
0
0
0
0
0
0
0
1
1
0
2
2
0
0
0
0
0
1
0
0
5
0
2
0
1
2
1
0
0
1
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
2
4
0
0
0
1
0
0
0
0
0
3
0
2
0
1
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
3
1
0
1
0
0
0
0
0
0
0
0
1
0
3
0
2
0
0
0
2
0
1
0
1
0
0
2
0
2
2
0
0
0
0
0
2
0
2
2
2
0
4
2
0
0
1
0
0
1
0
1
0
2
2
1
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
1
2
0
0
1
0
3
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
1
2
0
0
0
1
0
0
2
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
2
0
1
2
2
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
1
3
2
0
0
0
0
2
2
0
0
1
0
1
1
1
1
0
1
0
1
2
0
0
0
0
0
1
0
0
1
0
0
0
1
1
1
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
2
0
2
1
0
0
2
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
2
1
1
0
2
1
1
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
6
0
0
2
0
1
0
0
0
1
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
1
0
0
2
0
0
2
0
2
0
0
1
0
0
0
2
1
0
0
0
1
0
0
2
0
0
2
2
3
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
3
0
2
0
3
1
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
3
1
1
0
0
0
0
0
0
2
0
2
2
0
0
0
2
1
0
0
0
0
3
0
0
0
0
0
0
2
0
0
2
0
1
0
1
1
0
0
2
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
1
0
0
0
0
2
1
1
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
3
0
0
0
2
1
0
0
0
2
1
1
3
0
0
0
0
2
1
0
0
0
0
1
1
0
1
1
1
1
5
2
1
1
0
2
2
1
1
1
2
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
2
1
0
1
2
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
1
0
2
0
2
0
0
0
0
1
2
0
1
1
0
0
0
2
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
4
1
1
0
0
4
1
0
0
0
2
0
0
0
1
0
4
0
4
0
1
2
0
1
0
0
3
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
2
1
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
1
0
1
0
2
0
2
0
0
0
1
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
1
0
0
1
0
2
0
1
0
1
2
0
1
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
2
1
2
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
3
0
0
0
0
1
0
2
1
0
0
0
0
0
2
0
2
0
0
2
0
2
0
0
0
0
2
3
0
1
0
0
0
0
0
1
0
1
2
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
7
0
0
0
1
0
2
0
0
2
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
1
0
1
0
1
0
1
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
2
0
0
0
2
0
2
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
5
0
0
2
0
0
0
1
0
0
1
0
0
1
0
0
0
1
1
1
0
0
0
1
1
0
1
0
1
0
2
0
0
2
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
1
0
0
0
0
2
0
1
2
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
1
0
0
2
0
0
0
2
0
1
3
0
0
1
1
2
0
1
2
0
0
0
2
1
1
1
2
0
0
0
0
0
0
2
1
0
0
2
0
4
0
0
1
0
0
1
0
2
2
0
0
0
2
0
2
0
0
0
0
0
0
1
3
2
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
2
2
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
1
0
0
0
0
2
1
2
0
0
1
0
0
0
1
0
0
1
2
1
0
0
0
0
0
0
0
0
1
2
2
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
1
0
0
0
0
2
0
0
1
0
0
1
2
2
0
0
0
0
2
0
2
0
1
0
0
3
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
2
1
1
0
1
4
0
2
2
0
0
0
0
2
2
1
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
2
4
0
1
0
2
0
1
0
0
1
0
0
0
0
0
1
1
0
0
2
2
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
1
0
1
4
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
3
1
0
2
0
0
0
0
0
0
4
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
1
0
1
0
0
0
0
0
1
2
0
1
0
0
0
2
0
0
2
0
0
0
1
0
0
1
0
2
0
0
0
0
1
0
1
0
0
0
2
0
3
0
0
2
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
1
2
0
0
1
0
0
0
1
2
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
2
0
1
0
4
0
2
2
0
1
0
2
1
0
1
1
1
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
2
1
0
2
1
2
0
0
2
0
0
2
0
2
1
0
1
2
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
2
0
0
2
0
0
0
0
1
0
0
2
0
2
0
0
0
0
2
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
2
1
0
1
2
0
2
0
0
1
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
4
2
0
0
0
0
1
4
2
2
2
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
1
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
2
1
0
0
2
0
0
0
1
0
1
0
0
1
2
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
2
2
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
3
2
0
1
0
2
0
0
0
0
0
0
0
0
1
0
1
0
7
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
2
0
0
3
0
1
0
0
1
0
0
0
3
0
0
1
0
0
2
0
0
0
0
0
2
1
0
0
0
0
2
0
1
1
0
1
3
2
1
0
1
1
0
1
2
0
0
0
1
0
1
2
0
1
0
1
0
2
1
0
1
2
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
10
0
0
1
1
0
0
1
0
0
0
2
0
0
1
2
1
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
1
1
0
2
0
0
0
0
0
1
0
2
2
0
1
0
1
0
0
0
2
0
0
2
0
0
0
0
1
2
0
2
2
2
0
2
0
2
1
0
0
1
0
0
0
0
1
0
0
2
0
1
2
1
2
1
0
0
2
1
0
0
1
0
0
0
0
3
3
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
1
1
0
1
0
0
0
2
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
1
0
0
0
0
4
0
1
0
0
1
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
0
0
1
2
4
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
2
0
6
1
0
0
0
0
0
3
1
0
0
1
0
1
0
0
0
2
2
0
0
0
0
0
2
1
1
0
0
2
0
0
1
0
2
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
2
1
0
0
0
0
0
1
2
0
0
0
1
0
5
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
1
0
2
0
2
4
0
0
0
0
2
0
1
2
2
0
1
2
0
2
0
0
2
0
0
0
9
0
2
0
0
1
2
1
0
0
4
0
2
0
0
2
0
0
0
0
0
0
0
5
2
1
1
2
0
0
0
0
0
0
0
1
2
2
0
2
0
0
1
2
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
2
3
0
0
0
1
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
2
0
0
0
1
0
2
0
0
1
0
2
0
0
0
0
1
0
2
0
1
2
0
0
2
0
0
2
0
0
0
0
0
1
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
2
2
0
0
1
0
0
0
0
0
1
0
0
0
2
0
1
1
0
1
0
0
0
0
0
0
2
0
1
2
0
0
0
1
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
4
2
0
1
2
1
0
0
0
1
1
0
1
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
3
0
1
1
0
0
0
0
0
0
0
0
0
1
2
2
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
7
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
1
0
2
2
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
1
2
2
0
0
2
0
3
0
0
0
0
0
2
2
1
1
0
1
3
0
1
0
0
0
0
0
4
0
0
2
0
0
0
3
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
5
0
0
2
2
0
1
2
2
0
2
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
1
2
0
2
0
2
0
2
2
2
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
1
0
0
0
0
1
1
1
1
0
0
0
0
1
3
0
3
2
0
0
3
0
0
1
0
0
0
0
0
0
2
0
1
2
2
0
0
1
0
0
0
2
0
2
2
0
0
1
2
2
2
2
0
3
0
1
0
0
0
0
0
1
0
1
2
2
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
3
0
0
2
0
0
0
0
1
2
0
0
0
0
0
2
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
2
1
4
0
1
1
0
0
0
7
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
2
0
0
0
0
2
0
0
2
2
2
0
0
1
1
0
0
0
0
2
1
2
2
0
0
0
0
1
0
1
1
1
0
2
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
1
0
0
0
1
1
0
0
0
1
0
1
2
0
0
0
0
2
2
0
0
0
2
0
0
0
1
0
1
0
0
0
0
1
1
2
0
0
4
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
1
0
2
1
0
0
0
2
0
1
0
0
0
0
2
0
0
1
0
0
2
0
0
2
0
0
0
2
2
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
5
0
0
0
0
0
2
0
1
0
0
0
0
1
4
0
0
0
1
0
0
0
0
0
2
0
4
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
1
2
1
3
0
0
0
1
0
0
0
0
2
1
0
2
0
0
1
3
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
1
0
2
2
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
4
0
2
2
1
0
2
0
0
0
0
2
0
0
1
2
3
0
0
1
2
0
0
0
0
2
0
0
0
0
0
3
2
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
2
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
2
2
3
1
0
2
4
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
2
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
2
2
0
3
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
5
1
0
0
2
1
0
1
1
0
0
0
1
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
1
2
0
0
1
1
0
2
0
1
0
1
0
0
2
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
2
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
2
0
1
0
0
0
1
2
0
1
2
0
1
0
2
1
0
0
0
0
0
0
1
0
1
1
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
3
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
1
1
0
0
0
2
1
2
0
0
1
0
2
0
0
2
0
2
0
0
0
1
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
1
0
1
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
1
0
1
2
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
2
1
0
0
2
0
2
0
0
0
2
0
0
0
1
5
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
2
0
3
0
0
0
0
1
0
2
0
0
3
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
1
0
0
1
0
0
0
1
2
0
0
0
0
1
0
2
0
0
1
1
0
0
0
1
2
0
0
4
0
1
0
2
0
1
0
5
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
2
0
1
3
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
1
0
2
0
0
3
0
0
1
0
0
0
1
0
2
2
2
0
0
2
3
0
0
0
1
2
0
2
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
2
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
1
0
0
1
2
0
1
1
0
0
3
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
2
2
0
0
1
0
0
2
0
0
0
6
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
1
0
0
0
1
1
0
2
0
0
0
1
0
2
0
2
0
0
0
0
0
0
1
0
0
0
3
0
2
0
2
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
2
1
1
0
2
0
0
0
0
2
2
0
2
0
0
2
0
0
1
0
0
0
2
0
1
0
8
1
0
0
0
0
0
0
2
0
1
0
0
1
0
2
1
0
1
0
2
0
0
2
0
1
0
2
0
0
0
0
0
0
0
2
2
0
2
0
0
1
1
0
0
0
0
2
0
1
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
3
0
0
0
0
0
3
0
0
0
0
0
2
1
1
0
2
0
0
0
2
1
0
0
0
0
0
0
0
3
2
0
0
0
0
0
2
0
2
0
0
1
0
1
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
2
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
1
0
0
1
0
0
4
0
0
0
0
0
0
1
0
0
1
0
0
1
1
1
2
0
0
2
0
0
1
1
1
1
0
0
2
0
1
0
0
0
0
2
0
1
0
0
2
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
2
0
0
0
2
0
0
0
2
1
0
1
0
0
1
2
1
1
2
0
0
1
0
0
0
2
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
1
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
1
2
1
0
1
2
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
2
0
2
1
0
2
1
2
0
0
0
0
0
1
0
0
3
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
3
0
1
2
2
0
2
0
1
0
0
0
2
0
0
0
0
0
2
0
2
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
1
1
2
0
0
1
0
0
2
0
2
1
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
2
2
0
2
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
1
2
0
2
0
0
0
1
0
2
2
0
0
0
0
1
0
0
1
0
0
1
2
0
3
0
2
0
2
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
2
0
1
3
0
0
0
0
1
13
0
0
2
0
0
1
0
0
0
2
0
2
0
2
0
1
0
0
0
2
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
2
0
0
2
0
2
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
4
0
12
0
0
0
1
0
2
0
2
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
4
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
1
1
1
4
0
0
0
0
0
2
2
1
0
0
1
0
0
0
0
0
0
0
2
0
4
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
1
2
0
0
2
0
0
2
0
1
2
0
0
0
1
1
0
0
0
0
1
0
0
0
1
2
2
0
4
0
0
0
0
4
0
0
2
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
2
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
3
0
0
2
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
1
4
1
0
0
2
0
0
2
0
0
0
1
3
8
0
0
1
0
0
0
0
0
3
1
0
0
0
2
1
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
1
1
0
2
0
0
0
0
0
0
1
0
2
0
0
1
1
0
0
0
0
0
1
0
0
0
2
0
9
0
0
0
0
0
0
0
1
3
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
3
2
0
1
0
0
2
0
0
0
1
0
2
0
0
2
1
1
0
0
0
2
1
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
3
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
1
1
2
2
0
2
0
0
0
0
0
0
0
0
2
1
2
2
1
0
0
0
2
1
0
0
3
0
0
0
0
0
0
0
0
2
0
2
2
2
0
1
2
0
1
1
0
0
0
1
0
0
0
0
0
3
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
2
0
0
1
2
0
0
1
0
2
0
0
0
0
0
0
0
3
1
0
0
0
3
1
2
4
0
2
0
0
0
0
0
0
0
2
1
0
2
0
2
0
2
0
0
0
1
0
0
0
0
0
0
3
4
2
0
0
0
0
0
0
0
0
0
0
2
3
0
1
0
0
0
2
0
1
1
0
0
0
0
2
2
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
1
2
2
0
1
1
1
0
0
2
0
0
8
1
0
1
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
1
1
0
1
0
3
0
0
1
0
0
0
2
0
7
2
2
0
0
2
1
1
1
0
0
0
1
0
3
0
0
1
2
0
1
0
1
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
1
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
2
2
1
1
0
0
0
0
0
0
0
0
2
0
1
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
2
1
0
0
1
0
2
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
2
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
1
2
2
0
0
0
2
0
0
0
4
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
3
3
2
1
0
0
2
0
0
0
0
1
0
0
1
2
0
0
1
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
2
2
0
0
1
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
1
0
2
0
2
2
0
1
0
0
0
0
1
0
0
0
2
1
3
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
4
0
0
0
0
2
1
2
0
2
0
1
0
0
0
1
0
0
0
0
1
3
0
1
0
0
0
0
2
0
0
0
0
0
1
2
0
1
0
0
1
0
1
2
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
1
0
0
1
0
1
0
0
2
1
0
0
0
0
1
0
0
2
1
0
3
2
2
0
2
0
0
0
0
0
2
0
0
0
2
0
1
1
0
1
0
1
0
0
0
0
1
0
0
0
2
1
0
1
4
0
2
0
0
0
0
2
0
2
0
0
2
0
0
4
0
0
0
0
0
1
0
0
2
3
0
2
0
1
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
1
4
0
0
4
1
0
3
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
2
1
0
0
1
0
0
0
0
0
0
1
2
1
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
3
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
1
2
3
0
0
0
2
2
0
0
0
1
2
1
1
1
2
2
2
0
0
0
2
0
0
0
0
0
0
2
0
1
0
1
4
2
1
0
0
0
2
1
0
0
0
0
1
0
2
0
1
1
2
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
2
0
0
1
3
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
1
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
2
1
0
0
1
1
0
0
0
2
1
0
0
0
0
0
0
5
2
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
1
0
0
1
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
4
3
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
1
0
0
0
2
0
2
0
2
0
0
1
0
0
0
0
0
0
0
2
2
2
3
1
1
0
0
0
0
1
0
2
1
0
0
0
2
0
0
0
0
2
0
3
0
0
0
0
2
2
1
0
0
2
0
0
1
0
0
2
0
3
0
0
2
0
0
0
0
3
0
0
1
0
0
1
0
2
0
0
0
0
0
2
0
1
1
0
0
1
0
2
2
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
1
0
3
0
2
2
1
0
4
3
0
0
0
0
2
0
1
0
1
0
0
2
0
1
0
0
0
0
2
0
0
0
2
2
1
1
1
0
1
0
0
0
0
0
1
0
1
0
2
0
2
0
0
2
0
0
1
0
1
2
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
1
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
1
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
1
2
1
1
0
0
0
1
0
1
0
0
1
2
0
1
2
2
1
1
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
1
0
0
1
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
3
2
0
1
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
5
1
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
4
0
0
2
0
0
0
0
1
1
0
0
0
0
2
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
5
0
0
2
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
1
2
1
0
0
0
0
1
1
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
2
0
1
1
0
2
0
0
0
1
0
0
1
0
0
0
1
2
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
1
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
2
2
0
0
2
0
1
0
1
0
0
2
0
0
2
1
0
0
0
0
2
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
1
0
0
1
0
1
2
0
0
2
0
1
2
0
0
0
0
0
2
0
0
0
0
1
1
1
0
0
0
0
0
2
1
1
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
1
0
0
2
2
1
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
1
2
0
1
2
0
0
0
1
0
0
0
1
0
0
0
1
3
0
4
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
2
0
0
0
2
0
0
2
0
0
0
0
2
0
1
2
0
0
0
0
1
1
3
0
1
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
1
2
2
0
0
1
1
0
0
0
0
2
2
1
2
0
0
0
0
0
2
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
1
2
0
0
2
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
2
2
0
0
2
0
1
5
0
0
2
0
0
1
0
1
0
0
0
4
0
0
0
1
0
2
1
2
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
1
2
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
2
0
2
0
1
1
0
0
0
1
0
0
1
0
0
0
0
1
2
0
2
0
0
1
0
0
2
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
2
0
2
1
1
0
0
0
0
0
3
0
1
0
0
0
0
2
0
0
2
2
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
2
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
3
0
0
1
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
2
0
0
2
0
0
3
0
0
0
0
0
0
0
3
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
6
1
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
1
2
0
1
1
1
1
0
0
0
0
0
0
2
0
3
0
1
1
1
1
3
2
2
0
0
1
0
0
0
2
2
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
1
2
2
0
0
0
1
0
0
1
0
1
0
3
0
0
0
1
0
0
0
0
1
2
2
1
0
0
0
0
0
1
2
1
0
0
0
0
0
2
0
0
2
3
1
0
0
0
0
0
0
2
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
2
0
2
2
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
2
0
1
0
0
0
0
0
0
0
0
2
0
0
1
2
2
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
3
2
2
2
0
0
2
0
0
2
2
0
0
0
0
2
0
0
0
0
2
0
0
0
2
1
0
0
1
0
0
0
0
0
1
0
1
1
2
0
0
0
0
0
2
2
0
3
1
2
0
1
0
0
0
2
0
0
0
0
0
1
0
2
0
3
1
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
3
0
1
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
5
0
2
2
1
1
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
3
0
0
0
0
0
1
0
0
1
2
0
0
2
0
1
0
0
0
0
0
1
2
0
0
0
1
2
0
0
0
0
0
1
2
0
1
4
2
3
2
0
0
0
0
0
0
1
2
0
0
0
1
2
1
1
0
2
1
0
2
1
1
0
0
0
0
0
0
0
0
0
2
0
2
1
2
0
2
0
1
0
0
1
0
0
2
0
1
0
0
0
0
4
0
0
2
0
2
1
0
0
0
1
0
0
0
0
0
1
0
0
0
4
0
0
2
0
1
0
0
1
0
0
0
0
2
0
2
0
0
2
2
0
0
2
0
2
0
1
1
0
0
1
2
0
1
0
0
4
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
1
1
1
2
1
0
2
1
0
2
0
0
1
0
0
0
2
1
0
2
0
0
0
0
0
0
0
1
1
1
2
0
0
0
0
0
0
2
2
2
0
0
0
2
0
0
0
0
0
0
2
1
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
1
0
0
0
0
3
0
0
0
2
1
0
2
0
0
0
0
1
0
0
0
2
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
1
0
0
0
0
2
2
1
2
2
0
0
2
0
2
2
0
0
1
1
0
0
0
2
1
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
2
1
0
2
0
0
0
2
0
0
0
0
0
2
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
7
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
2
0
0
0
0
0
0
2
0
3
0
2
0
1
0
0
1
0
0
2
0
0
0
1
0
2
2
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
1
0
2
0
0
0
2
4
0
0
2
0
2
0
0
0
0
2
2
1
0
2
1
0
1
0
0
1
0
0
0
1
1
2
0
0
0
0
0
0
2
2
1
0
2
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
1
1
2
0
0
1
0
1
0
2
0
0
3
3
0
2
0
0
0
0
0
2
2
0
0
0
1
0
0
1
2
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
1
1
2
0
0
1
0
0
1
0
0
0
0
1
0
2
2
0
0
0
0
0
0
1
0
1
7
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
1
0
0
0
0
0
2
0
2
0
0
0
0
1
2
2
0
0
0
0
1
0
1
2
1
0
2
0
0
2
2
0
0
0
0
1
0
0
0
0
3
0
0
1
1
4
0
0
0
0
2
0
0
2
0
0
0
0
2
0
2
0
2
0
2
0
0
0
0
0
2
0
1
2
0
2
1
2
2
0
0
1
2
2
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
1
2
1
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
1
3
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
1
2
0
0
0
0
0
2
1
0
2
0
0
0
0
3
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
2
3
1
1
0
1
0
0
0
0
0
0
7
0
0
2
2
0
3
1
0
0
0
2
1
0
0
0
0
2
0
1
1
0
0
2
0
1
0
0
0
0
3
0
2
1
2
0
0
0
2
0
3
0
0
0
2
0
2
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
1
2
0
1
0
0
0
1
0
0
0
0
0
2
3
0
1
4
0
0
0
2
2
1
0
1
0
0
0
0
0
0
2
0
4
1
0
5
0
0
0
2
2
1
2
3
1
0
4
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
2
0
1
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
1
2
0
0
0
0
2
1
1
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
2
0
2
1
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
5
2
0
0
2
0
0
1
1
0
2
0
1
0
0
0
0
2
0
0
2
0
2
0
1
1
0
1
3
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
2
0
0
2
0
0
0
0
0
0
2
0
0
1
2
1
1
0
1
0
0
0
0
0
0
0
0
4
2
1
0
0
2
1
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
2
2
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
1
0
2
2
1
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
2
1
0
0
2
1
1
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
2
2
0
0
0
0
0
0
0
3
1
1
3
0
0
0
2
0
0
0
0
0
1
1
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
1
0
0
2
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
4
0
1
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
2
0
1
2
1
0
1
0
0
0
0
0
1
0
2
0
0
1
2
2
0
0
2
0
0
0
0
0
1
2
1
1
0
0
0
0
0
0
0
2
0
0
1
2
2
2
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
1
2
0
1
0
0
0
1
1
0
0
2
1
0
3
0
0
0
0
0
0
2
1
0
1
3
0
0
0
0
0
0
1
0
0
0
2
1
0
1
0
0
0
3
0
0
0
2
1
1
0
0
0
2
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
2
1
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
1
1
0
0
0
2
0
0
0
1
2
1
0
0
0
2
0
0
0
2
0
0
0
0
0
1
1
0
3
1
1
2
0
1
0
0
3
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
3
0
0
0
0
1
0
2
2
2
0
0
1
2
0
0
0
1
2
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
1
2
6
0
0
2
0
0
0
2
0
0
2
0
1
0
2
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
4
1
0
0
0
0
0
0
0
0
2
2
2
0
0
0
2
0
1
0
0
2
0
2
0
0
0
0
0
2
0
2
0
1
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
2
0
0
0
2
0
1
1
0
1
2
0
2
2
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
2
1
2
0
0
0
0
1
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
3
1
1
2
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
2
1
3
0
0
0
0
0
2
2
0
0
0
0
0
5
0
2
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
2
0
0
1
2
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
1
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
2
0
0
0
0
1
1
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
3
2
1
1
0
1
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
2
1
3
0
1
1
0
0
0
0
0
0
2
0
2
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
1
0
0
0
1
0
0
2
0
1
0
2
1
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
2
0
0
2
0
2
0
2
0
0
0
1
0
1
0
0
2
1
0
0
2
0
0
0
0
0
0
0
2
2
0
2
0
2
1
0
0
1
0
0
2
1
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
3
1
2
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
1
0
2
1
0
0
2
0
1
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
4
2
0
0
0
2
3
0
0
0
0
0
0
1
0
0
0
0
0
0
1
3
1
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
1
1
0
1
0
0
1
1
0
0
0
2
0
1
0
0
2
1
0
0
0
2
2
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
1
0
0
0
3
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
2
0
1
2
1
0
0
0
0
0
0
2
0
2
2
0
0
0
1
2
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
5
2
0
0
2
0
2
1
2
2
2
1
0
0
0
0
2
0
1
2
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
3
0
0
2
1
0
0
2
2
0
0
0
1
0
2
0
0
2
1
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
5
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
1
0
1
0
0
2
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
1
0
0
0
0
0
0
1
0
2
2
0
2
2
1
0
1
0
0
1
0
0
0
0
1
0
0
3
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
2
1
0
1
0
0
0
0
1
1
0
0
2
2
0
1
3
0
0
5
3
0
0
1
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
2
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
3
0
1
0
0
0
3
0
2
0
2
1
0
0
2
0
0
1
0
1
0
0
3
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
2
2
2
0
0
0
1
0
0
0
0
0
1
1
1
3
2
0
2
1
0
0
0
0
0
1
3
0
0
0
0
5
0
2
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
2
0
1
2
2
0
0
2
0
0
0
1
0
0
0
0
2
0
0
2
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
1
0
2
0
2
2
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
2
0
0
1
0
2
0
0
2
0
0
3
0
0
0
0
0
6
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
3
0
2
0
0
0
0
2
1
0
0
0
0
0
0
2
2
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
2
0
1
1
0
1
0
2
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
2
0
2
0
0
1
0
0
0
0
0
0
2
0
2
0
2
2
1
2
0
0
0
0
2
0
1
0
1
1
0
2
0
0
0
1
0
0
2
0
2
1
0
0
0
0
0
0
1
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
2
0
0
2
2
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
1
1
0
0
1
0
1
0
0
1
0
0
1
2
0
2
1
0
4
2
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
1
0
0
1
0
0
3
0
2
0
0
2
0
0
0
0
0
0
0
5
3
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
2
0
0
2
0
1
0
3
0
1
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
2
3
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
1
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
5
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
2
0
0
1
1
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
1
3
0
0
0
1
1
0
0
3
2
1
0
2
0
0
3
0
0
1
2
2
0
1
1
2
0
0
0
0
0
1
2
0
1
0
0
2
0
0
0
0
0
2
0
2
2
1
1
0
0
0
0
2
1
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
3
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
1
1
0
0
1
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
1
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
1
1
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
5
1
1
2
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
1
1
0
0
0
1
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
1
1
0
1
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
1
1
2
0
2
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
2
4
0
0
3
1
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
3
1
0
1
1
0
0
0
4
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
1
0
0
3
0
1
2
0
0
1
0
1
1
1
0
1
0
1
2
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
2
1
0
0
0
0
2
0
1
0
1
0
0
0
0
2
2
0
0
0
0
0
3
1
0
1
2
1
2
2
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
3
2
0
0
0
0
0
1
1
1
0
2
0
0
0
0
0
2
1
0
1
0
0
0
0
2
1
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
1
1
0
0
0
0
2
0
2
0
2
2
0
2
1
2
0
1
0
0
1
0
2
3
0
0
0
0
0
0
0
0
1
5
2
0
0
0
3
0
0
0
1
0
1
2
0
0
0
0
0
0
2
1
0
0
0
2
0
2
2
2
0
0
0
1
0
0
1
0
0
0
0
2
1
2
0
1
0
0
2
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
2
0
0
2
1
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
2
0
1
0
0
1
0
1
0
0
2
0
2
2
0
0
0
0
2
1
0
2
0
2
0
0
3
0
0
0
1
1
2
1
0
2
0
0
0
2
4
0
1
0
0
0
0
0
1
1
0
5
1
1
0
0
0
0
0
0
0
1
1
0
1
0
2
0
0
0
0
1
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
1
0
0
1
0
1
0
0
2
2
2
2
1
3
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
1
1
0
2
0
0
0
2
2
2
0
0
0
1
0
2
2
0
2
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
3
1
0
2
1
0
1
2
2
2
0
0
0
0
1
1
0
0
2
0
0
0
1
1
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
3
0
0
2
0
2
0
0
0
0
1
2
2
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
1
2
3
0
0
0
0
0
1
1
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
1
1
2
0
0
0
0
1
0
0
1
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
4
2
0
1
0
2
0
0
2
0
0
0
0
2
0
0
1
0
1
2
0
0
2
0
0
0
0
1
0
0
0
1
2
1
0
0
0
2
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
2
1
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
3
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
2
2
0
2
1
2
0
1
0
1
2
1
1
1
0
1
0
2
3
2
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
1
2
2
2
2
0
0
0
2
2
1
0
1
0
2
0
1
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
1
0
0
0
0
0
1
2
0
0
0
2
0
0
3
0
0
0
0
0
3
0
0
0
1
0
0
0
0
1
0
3
0
0
1
2
0
0
0
2
0
0
0
0
1
2
0
0
0
1
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
2
2
1
0
1
0
0
0
0
0
1
4
0
0
0
0
1
0
0
0
2
1
0
0
1
2
0
0
2
0
0
2
0
0
1
1
2
0
1
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
1
0
1
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
2
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
1
1
2
0
0
2
2
0
2
0
0
1
2
0
0
0
1
0
1
0
0
0
0
0
2
0
0
2
2
0
2
0
0
1
2
0
0
0
1
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
2
0
1
3
0
0
0
0
1
0
2
1
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
0
2
0
2
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
3
0
1
0
1
0
2
0
0
0
0
0
2
2
1
0
0
0
0
0
0
2
2
0
1
4
0
0
0
1
0
2
1
0
0
0
0
0
0
4
2
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
1
0
0
0
0
1
0
2
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
2
2
2
0
0
1
0
0
2
0
2
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
1
0
0
1
0
2
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
1
0
0
0
1
0
0
1
1
0
0
1
0
0
2
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
1
0
0
2
0
1
1
2
0
0
0
0
0
2
0
0
0
0
1
0
2
2
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
3
0
3
1
0
1
0
3
0
3
0
0
0
1
0
2
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
3
0
1
0
0
0
0
0
0
2
2
0
0
2
2
0
0
0
0
0
0
0
2
0
1
1
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
2
0
0
0
0
0
1
2
0
2
0
0
1
0
0
0
2
0
1
0
2
0
0
1
3
0
0
0
0
0
1
1
0
0
0
0
0
2
3
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
3
0
1
3
5
0
2
0
0
2
1
0
0
1
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
2
0
1
0
0
0
0
0
0
0
1
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
3
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
1
0
0
0
2
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
2
0
2
2
0
0
1
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
1
1
0
2
0
0
1
0
2
1
3
0
1
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
1
0
1
2
0
0
2
1
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
1
0
2
0
0
0
0
0
0
4
0
0
2
0
2
0
0
0
1
0
0
0
1
0
0
0
2
2
0
0
1
0
2
0
2
4
0
0
0
2
0
0
0
2
3
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
2
0
2
1
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
1
0
1
1
0
0
0
2
1
0
0
1
2
2
0
2
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
2
0
0
1
0
1
0
0
0
2
1
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
2
2
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
4
0
0
0
4
1
0
3
0
2
0
1
0
1
0
1
0
0
0
1
0
0
2
2
0
0
1
0
0
1
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
2
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
3
1
2
3
0
0
2
1
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
6
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
2
0
0
2
0
0
1
0
0
2
0
2
0
2
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
3
1
0
0
0
0
0
0
1
0
2
0
1
0
3
1
0
1
2
0
5
0
0
2
0
1
2
1
3
4
0
0
0
1
2
0
0
0
0
0
0
2
0
2
1
0
0
2
0
4
0
2
2
2
2
0
1
0
1
0
0
0
1
0
0
3
1
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
1
3
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
2
0
1
2
0
0
0
0
0
0
0
2
1
0
2
0
1
0
2
0
0
1
0
0
1
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
1
0
1
2
0
2
3
0
1
0
0
0
1
0
0
1
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
4
2
0
1
0
0
3
1
1
0
0
0
2
0
1
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
3
2
0
0
0
2
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
5
0
0
1
0
0
2
1
0
1
0
1
0
1
0
0
1
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
5
0
0
4
0
0
2
2
2
0
1
0
0
0
0
0
0
2
0
0
3
1
0
1
0
0
1
1
0
0
0
1
1
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
1
0
0
0
0
0
1
0
2
1
0
0
0
2
0
0
0
2
0
2
0
0
2
2
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
3
2
0
1
2
1
1
0
0
0
1
0
1
0
0
1
0
1
0
2
0
0
0
1
0
0
1
0
0
0
1
0
1
0
2
2
2
0
0
0
2
1
3
0
0
1
0
0
0
1
0
0
0
1
1
0
0
2
0
1
0
2
0
1
2
1
0
0
0
0
0
1
0
3
0
2
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
1
2
2
0
0
0
0
2
0
2
1
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
1
0
4
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
1
0
2
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
2
1
0
0
0
1
2
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
1
3
0
2
0
3
2
2
2
1
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
4
2
0
2
1
0
1
0
0
0
0
0
0
0
1
2
5
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
2
1
0
1
2
0
1
0
0
0
2
1
1
0
0
0
0
0
0
3
2
0
0
1
1
0
2
0
0
1
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
1
2
0
0
0
1
2
1
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
1
0
1
0
0
0
0
0
3
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
2
0
1
1
0
0
1
0
0
2
5
0
2
2
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
2
0
2
0
0
0
2
0
0
3
0
2
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
4
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
1
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
4
0
2
1
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
1
0
4
0
0
0
0
1
1
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
1
1
1
0
0
0
0
0
0
0
1
0
2
0
0
1
2
0
2
0
0
0
2
1
3
2
2
2
2
1
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
2
3
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
1
0
0
0
2
0
2
0
2
0
1
2
0
0
0
0
0
1
2
1
2
0
0
0
0
0
0
1
0
1
0
2
3
0
0
0
1
0
1
2
0
0
0
2
2
2
0
0
2
0
0
0
1
0
2
0
2
0
0
0
2
2
0
0
0
1
0
0
1
0
0
0
0
2
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
2
2
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
1
3
0
0
3
1
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
2
0
0
1
0
0
2
0
0
2
0
0
0
0
1
0
1
2
1
1
0
0
1
0
1
0
1
0
2
0
0
0
0
0
0
2
0
2
2
0
1
0
2
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
3
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
1
0
0
0
1
0
2
0
0
0
0
0
2
1
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
2
0
0
3
2
2
0
0
0
0
5
0
0
0
1
0
3
2
1
1
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
2
0
0
0
2
0
1
3
0
0
0
2
0
0
0
0
5
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
2
0
2
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
1
0
0
0
1
0
2
0
0
0
1
0
1
0
2
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
1
1
2
0
0
3
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
1
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
5
0
0
0
0
0
0
0
1
1
0
1
0
2
2
2
2
0
2
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
1
1
0
0
0
0
0
1
0
0
1
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
1
1
2
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
1
1
3
0
0
2
1
0
0
1
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
2
0
4
0
0
0
2
0
2
0
0
0
0
2
2
0
0
1
2
1
2
0
0
0
0
0
1
0
2
1
0
0
1
0
1
2
0
0
0
1
2
1
0
2
0
0
0
0
0
1
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
2
0
0
3
1
2
0
1
0
0
2
2
0
0
2
0
0
1
1
0
0
1
4
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
3
2
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
6
1
0
2
0
0
2
0
0
1
0
0
0
0
1
2
0
0
0
1
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
2
1
1
0
1
0
0
2
0
0
0
1
0
2
0
2
2
0
1
2
0
2
0
0
0
2
0
2
0
0
0
0
1
1
0
2
0
0
1
0
0
2
3
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
5
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
3
0
1
2
0
0
1
1
0
0
1
2
0
0
0
0
0
1
2
0
2
1
0
1
0
2
0
2
0
0
0
0
1
1
0
0
0
0
0
2
0
1
0
0
0
2
2
0
0
2
0
0
0
1
0
0
0
0
2
0
2
0
0
2
0
0
2
0
0
1
1
0
2
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
3
0
0
3
0
2
2
2
0
0
0
0
0
0
0
0
1
2
0
2
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
1
3
0
2
0
0
2
2
0
1
2
0
1
3
0
2
2
0
0
1
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
1
0
2
0
0
1
2
2
0
0
0
2
0
0
1
0
0
0
2
0
0
2
2
0
2
0
2
0
0
2
1
2
1
0
1
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
2
0
0
1
0
2
0
0
0
2
0
0
0
0
2
1
1
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
1
0
0
1
0
0
0
0
1
3
0
0
0
0
0
0
0
3
1
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
2
1
1
0
2
0
0
0
0
0
0
2
0
0
0
1
0
1
0
7
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
2
0
2
2
0
0
1
2
0
0
0
0
2
0
0
0
0
0
1
0
3
0
3
0
0
1
0
0
0
0
2
0
0
0
1
2
0
0
0
2
0
2
0
1
1
2
4
1
0
2
1
2
0
0
0
0
1
0
2
0
0
1
1
2
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
2
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
5
0
0
1
1
0
0
0
0
1
0
3
1
0
1
0
0
2
0
1
0
1
1
2
0
0
0
0
0
0
0
2
0
0
1
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
3
0
1
0
0
1
4
0
0
0
2
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
1
0
0
2
0
2
0
0
2
1
0
1
2
1
0
0
0
0
0
0
0
1
1
0
2
0
0
2
2
0
1
0
3
0
0
0
1
0
0
2
0
2
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
3
0
0
0
0
0
0
0
2
0
2
2
2
0
2
0
1
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
3
2
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
4
1
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
1
2
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
1
1
0
0
1
0
0
0
2
0
0
2
0
1
5
0
0
0
0
1
0
0
2
1
2
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
2
1
0
0
1
0
0
0
0
2
0
0
1
1
0
0
2
1
2
0
0
2
0
1
0
2
2
0
0
0
1
0
2
0
0
0
2
0
3
0
0
0
2
0
0
0
1
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
2
2
0
0
3
0
0
1
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
4
0
0
0
0
0
0
3
2
0
0
0
1
0
3
0
0
0
0
1
0
1
1
0
1
0
0
1
1
0
1
0
0
0
0
0
0
3
0
1
1
2
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
1
0
0
0
0
1
1
2
1
1
2
0
4
0
0
0
1
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
2
2
0
0
1
0
2
0
1
0
0
2
0
0
1
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
1
0
0
0
0
1
0
1
2
0
0
1
0
0
2
1
0
1
0
0
0
0
1
0
0
0
0
0
2
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
3
0
0
0
2
0
1
2
4
0
0
1
2
10
2
0
0
0
1
0
1
0
1
2
0
0
1
0
0
0
0
0
3
2
0
0
2
0
0
0
1
0
1
0
0
0
2
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
2
0
0
0
0
0
2
2
2
1
0
0
0
0
0
1
0
0
6
0
0
0
1
2
0
0
3
1
1
0
1
0
0
0
0
0
0
0
0
1
2
0
2
0
1
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
2
0
4
0
2
0
0
0
2
1
1
0
0
0
0
1
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
4
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
1
0
0
1
0
0
1
2
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
2
2
0
3
1
1
0
2
1
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
4
0
0
0
0
1
0
0
0
1
0
0
0
1
3
0
0
0
0
0
0
0
1
0
0
2
1
1
0
0
0
1
0
2
0
2
0
2
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
2
0
3
0
0
0
0
0
0
6
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
3
1
0
0
0
0
2
0
1
0
0
2
0
0
0
2
0
0
1
1
0
2
2
1
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
1
1
1
2
0
1
0
1
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
3
3
0
0
0
0
0
2
1
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
2
0
0
3
0
3
0
0
0
2
0
0
0
0
1
1
0
0
0
2
1
1
0
0
0
1
0
0
0
1
0
0
0
1
2
0
0
2
0
2
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
1
5
0
0
2
0
0
0
0
1
0
1
2
1
1
0
0
2
1
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
2
2
0
1
0
1
0
0
3
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
2
2
1
1
0
2
1
0
0
0
2
0
0
2
0
0
0
1
5
1
2
1
1
0
2
0
2
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
1
1
0
1
2
0
0
2
2
0
0
1
0
0
0
0
2
0
0
2
0
0
1
1
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
2
0
1
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
2
1
1
0
0
1
0
1
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
3
3
0
2
0
0
1
0
0
1
1
1
0
0
0
1
0
0
0
0
2
0
0
1
0
2
2
0
2
0
0
1
1
0
0
2
0
0
0
0
0
2
0
2
0
0
0
1
1
0
1
0
0
2
0
0
0
2
2
0
0
2
1
0
0
0
0
2
0
0
2
0
1
0
3
0
0
0
0
1
2
0
0
0
0
1
0
0
0
2
1
0
0
1
5
0
0
0
2
0
0
1
2
0
0
0
1
0
0
0
0
7
0
2
0
0
8
0
1
0
0
0
0
0
0
0
0
2
4
2
0
0
0
0
0
0
0
0
1
1
2
0
0
0
1
0
0
1
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
2
0
2
0
0
1
2
0
1
0
0
1
0
0
0
0
0
0
0
2
0
2
0
2
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
2
0
2
0
0
2
1
0
0
0
0
0
2
1
0
0
0
0
0
1
2
2
0
0
0
0
1
2
0
2
0
0
1
0
0
1
0
1
0
0
0
2
1
0
1
0
0
0
2
1
2
0
0
0
2
0
0
0
1
0
0
0
3
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
2
2
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
0
3
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
1
2
0
0
1
1
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
1
1
0
0
0
0
1
0
0
2
2
0
0
2
5
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
1
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
2
0
3
0
1
0
1
4
0
1
2
0
0
0
1
1
2
0
0
0
0
0
0
0
2
2
1
1
3
0
0
0
0
0
0
2
0
0
0
0
2
0
0
3
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
2
2
0
0
2
2
0
0
2
1
0
1
0
1
0
0
2
0
2
0
0
0
0
0
0
0
2
0
3
0
0
1
2
0
2
0
0
0
0
0
1
0
2
2
1
0
0
2
0
2
1
0
0
0
0
2
2
0
0
0
0
0
0
1
2
0
0
2
2
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
1
0
0
2
1
0
0
2
0
2
1
0
0
0
0
0
1
0
0
1
1
0
0
1
0
2
0
0
0
0
1
4
2
0
1
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
1
1
0
2
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
1
2
2
1
0
0
0
0
1
0
0
0
2
2
0
2
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
1
1
0
0
0
0
2
0
0
0
0
4
0
2
0
0
0
0
2
0
0
1
0
2
2
0
0
0
0
0
2
0
0
3
0
1
1
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
2
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
2
3
0
0
0
2
0
0
0
0
0
0
2
0
1
0
1
0
0
0
2
0
3
0
0
1
0
2
1
0
1
1
0
2
0
1
0
1
2
2
1
2
0
0
0
1
2
0
0
0
0
1
0
0
0
2
1
0
0
0
1
0
0
1
2
1
0
0
2
3
0
0
0
3
2
0
1
0
3
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
3
2
0
0
2
0
0
2
0
2
2
1
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
3
0
0
0
2
0
0
0
0
1
0
1
0
0
0
3
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
1
0
0
2
0
0
0
0
0
1
1
0
1
0
0
1
2
2
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
1
0
0
1
2
0
0
0
0
1
0
0
0
0
0
1
0
0
2
1
0
1
2
0
2
0
0
1
0
0
0
0
2
1
0
1
0
1
1
0
0
0
0
1
1
0
0
2
0
0
0
0
0
2
2
0
0
2
0
0
4
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
1
2
0
2
0
1
0
0
0
0
0
0
0
0
1
0
1
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
1
0
0
3
0
0
0
1
0
0
0
0
0
12
0
0
0
0
3
1
0
0
0
2
1
0
0
0
0
0
0
1
1
0
2
1
0
2
0
0
0
0
2
2
0
1
0
0
0
0
0
2
0
2
2
1
0
0
1
0
0
0
0
0
2
0
1
0
0
3
2
0
0
0
0
0
0
0
0
1
1
0
0
1
2
0
1
0
0
0
0
0
2
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
3
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
3
1
2
0
0
0
0
0
0
3
0
1
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
2
1
0
1
0
0
0
1
0
0
0
1
0
2
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
2
0
0
0
1
2
0
0
0
1
0
2
2
1
1
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
2
3
0
2
4
2
0
0
3
1
0
1
0
0
2
0
0
0
1
0
0
0
0
3
2
2
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
1
1
0
4
0
1
1
2
0
0
0
0
0
2
0
1
1
2
2
0
0
2
4
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
2
1
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
1
1
0
0
2
2
0
0
0
0
1
1
2
1
0
1
1
2
2
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
2
2
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
2
1
0
0
4
0
0
1
0
0
0
2
2
0
0
0
1
0
0
0
0
1
2
0
0
0
0
1
1
2
0
1
2
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
1
2
1
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
2
0
0
1
0
0
2
0
0
2
1
2
0
0
0
1
0
0
0
1
0
0
0
2
2
2
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
2
2
2
0
1
0
0
2
0
0
0
0
2
1
0
0
0
0
2
0
0
2
1
0
0
0
0
2
2
0
0
0
2
1
2
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
1
0
0
1
0
1
0
2
0
2
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
1
0
0
4
0
2
2
0
0
0
1
0
1
0
0
0
0
3
0
0
2
0
0
0
0
0
0
4
0
0
4
0
2
0
0
0
0
1
0
0
0
3
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
1
3
0
0
1
1
0
2
0
2
2
0
1
1
0
0
2
0
3
1
0
0
2
0
0
0
0
0
2
2
1
0
0
1
0
1
1
1
2
0
0
3
0
2
0
0
0
0
0
1
0
0
2
1
0
0
2
2
2
0
2
0
2
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
4
0
1
2
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
2
0
0
2
0
2
1
0
0
2
0
2
0
0
2
0
0
1
0
2
0
2
0
0
0
0
0
2
0
0
2
0
0
2
1
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
2
0
0
0
0
1
0
0
0
2
0
1
0
0
1
0
0
0
2
0
0
0
0
2
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
2
2
0
0
0
2
0
0
2
1
0
0
2
2
1
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
1
0
0
0
0
1
2
0
0
1
2
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
1
0
0
4
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
5
0
0
0
2
0
0
0
0
0
0
3
1
0
0
0
1
0
0
1
0
0
1
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
2
2
0
1
0
1
1
1
0
0
1
2
0
0
2
0
0
2
2
0
0
3
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
1
2
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
1
0
0
0
1
2
0
1
0
2
1
0
0
0
0
0
0
4
1
0
2
0
0
0
0
0
0
0
0
2
0
1
0
2
2
0
1
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
2
0
0
2
1
0
2
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
1
1
2
0
0
1
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
5
0
1
2
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
2
0
0
0
0
0
1
2
0
1
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
3
0
0
2
0
6
0
0
0
2
0
1
1
0
2
0
2
2
1
2
0
0
3
0
1
2
0
0
0
0
0
0
0
0
1
0
0
1
2
1
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
1
1
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
1
0
0
0
1
0
2
1
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
1
0
0
0
1
0
2
2
2
0
2
2
0
0
1
2
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
1
0
2
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
2
2
0
0
0
2
0
0
1
0
2
2
1
0
0
0
1
0
2
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
1
0
1
2
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
3
0
2
0
0
1
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
1
2
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
1
0
2
2
0
0
1
0
0
0
0
1
0
0
2
1
2
2
0
0
0
0
1
0
1
2
0
1
0
0
2
2
2
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
1
1
2
0
0
0
0
2
0
0
0
2
0
1
2
0
0
0
0
1
1
0
1
0
2
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
2
1
0
0
0
0
0
2
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
4
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
1
0
2
0
1
1
0
1
0
2
1
1
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
2
0
0
2
2
1
1
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
3
1
0
1
0
0
2
2
1
0
1
0
1
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
2
2
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
4
2
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
2
1
0
2
0
2
0
1
1
2
0
0
1
0
2
0
0
0
2
0
1
0
2
2
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
2
1
0
2
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
3
0
0
0
4
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
4
0
0
0
3
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
3
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
2
1
0
0
2
3
0
0
0
0
0
0
2
0
0
2
1
0
0
1
0
0
0
2
1
0
1
1
2
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
4
0
2
0
0
0
1
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
1
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
1
2
1
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
3
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
2
0
2
0
1
0
0
0
1
0
1
0
0
2
0
2
0
1
0
0
0
1
0
0
0
0
2
0
2
0
6
0
0
0
0
1
0
0
0
1
0
1
4
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
2
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
3
2
0
3
1
0
0
0
2
1
0
0
2
1
0
0
2
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
3
1
1
0
0
0
1
0
0
0
1
0
0
0
2
0
0
2
0
0
1
2
0
2
1
2
0
1
2
2
0
2
1
1
1
0
0
2
0
2
0
0
1
1
1
0
0
0
2
0
0
1
0
0
1
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
1
1
2
0
0
0
3
1
0
0
1
0
1
0
0
1
1
0
0
0
1
1
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
1
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
2
0
0
0
0
2
0
1
2
0
0
0
3
2
2
0
0
3
0
0
2
2
1
0
1
0
0
0
0
0
2
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
1
2
0
0
0
1
1
2
1
0
0
0
0
2
3
0
0
0
0
0
0
1
0
1
0
3
0
2
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
1
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
2
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
4
1
0
0
0
0
0
1
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
1
0
2
1
0
0
0
0
1
0
0
1
0
1
0
2
3
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
2
0
0
1
1
0
0
0
0
0
0
0
0
2
3
0
1
0
1
0
1
0
0
0
0
0
0
1
0
4
1
2
1
1
0
2
3
4
0
0
2
0
1
0
0
0
0
2
0
2
1
0
0
1
10
0
2
0
0
0
2
2
0
0
0
1
2
2
1
0
0
0
1
0
0
0
0
0
1
0
0
2
3
0
3
0
0
0
0
0
4
1
2
0
1
0
2
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
1
2
1
1
2
1
2
2
0
0
2
4
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
2
1
2
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
2
0
2
0
0
1
0
2
0
0
3
2
0
0
0
0
0
0
1
0
0
0
1
0
1
2
0
0
0
0
0
0
0
1
2
12
0
2
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
4
1
0
0
2
1
1
2
1
0
2
2
0
2
1
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
2
0
1
0
2
0
2
0
1
0
0
0
0
0
0
1
0
0
2
2
0
2
2
1
0
0
0
0
0
0
1
0
3
2
0
0
2
0
0
1
0
0
0
2
0
0
1
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
3
1
0
0
1
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
3
0
0
0
0
2
0
0
0
2
0
0
0
3
0
0
0
0
2
1
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
2
1
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
1
0
0
0
0
0
1
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
3
1
2
0
0
0
0
0
0
0
1
1
3
0
0
0
2
1
2
2
0
0
2
3
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
2
0
2
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
1
1
2
0
1
0
0
0
0
0
2
0
1
1
0
0
1
0
2
0
2
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
2
0
0
0
1
0
0
0
1
0
2
0
2
0
1
0
2
1
2
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
2
1
0
0
2
0
0
2
0
0
0
1
0
0
0
0
1
1
0
1
0
0
1
3
2
1
0
0
0
0
0
0
0
1
2
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
1
2
1
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
4
0
2
0
0
1
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
2
2
0
0
0
1
0
0
1
0
0
2
2
0
0
2
2
0
0
0
0
3
0
0
1
1
0
0
0
0
0
0
0
1
0
1
2
2
0
0
1
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
1
1
0
0
3
0
0
0
2
1
0
0
0
2
1
1
0
1
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
53
0
0
0
0
0
3
0
0
2
0
2
0
1
0
0
0
1
1
2
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
2
1
0
1
1
0
0
1
0
0
2
0
0
1
0
1
0
0
0
0
0
0
3
0
0
0
0
1
0
0
1
0
0
0
1
0
2
0
0
2
2
0
0
1
0
3
0
1
2
2
2
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
2
1
0
0
1
0
0
0
0
0
1
2
0
1
1
2
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
3
3
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
1
0
0
0
2
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
1
1
0
0
0
0
0
1
0
2
0
0
0
1
0
1
0
2
0
2
0
0
0
2
0
0
1
1
0
0
0
0
1
2
0
2
0
2
0
0
0
3
1
0
0
0
3
0
2
0
0
1
0
0
0
1
2
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
2
0
2
1
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
2
2
0
1
0
2
0
0
0
1
0
2
0
0
3
0
0
2
0
1
2
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
2
0
0
2
0
0
0
0
2
2
0
4
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
2
1
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
1
0
0
0
0
0
0
1
1
0
0
1
2
1
1
1
2
0
0
1
1
0
3
0
0
1
1
0
2
3
0
3
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
1
1
1
1
0
2
0
0
0
1
2
0
2
1
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
2
1
0
3
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
2
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
3
0
0
2
0
2
2
0
2
2
0
0
0
1
1
1
1
0
4
0
1
2
0
0
0
1
0
0
0
0
1
8
0
0
2
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
1
2
0
0
0
3
0
2
0
0
0
2
0
0
1
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
2
2
0
0
0
2
0
2
2
0
0
1
0
0
0
0
2
0
0
0
1
0
0
2
0
1
6
0
0
1
0
2
0
0
0
0
1
1
2
0
0
0
1
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
1
2
1
1
0
0
0
0
0
1
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
1
0
2
1
0
0
1
0
2
0
1
0
0
2
0
2
0
0
0
1
0
0
0
0
3
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
2
1
0
0
0
0
0
0
2
1
0
0
0
2
0
0
2
0
0
2
2
0
2
2
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
1
1
0
0
0
1
2
0
0
2
1
1
0
1
2
1
0
0
1
0
1
0
0
2
0
2
1
0
1
2
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
1
0
2
0
1
1
0
0
2
2
0
0
0
3
0
0
2
1
1
0
0
1
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
2
4
0
0
4
0
0
1
2
0
2
0
0
0
2
5
1
1
0
0
0
0
0
2
4
0
0
0
2
0
0
1
2
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
2
2
0
0
0
0
0
2
0
2
0
3
0
1
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
2
0
1
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
6
0
0
2
2
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
1
0
0
0
1
0
0
2
0
2
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
2
3
0
0
0
0
1
0
0
1
0
0
0
0
1
1
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
3
1
0
0
1
0
2
1
0
0
0
0
0
2
0
0
0
2
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
2
0
0
0
2
0
1
0
0
2
0
1
2
0
0
0
0
1
1
0
2
0
0
2
2
0
0
0
0
0
2
1
0
0
0
0
0
1
4
0
0
0
2
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
5
0
0
0
0
0
2
0
2
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
3
2
2
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
16
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
3
0
0
0
0
2
0
0
2
2
0
0
1
1
0
0
0
1
0
0
2
2
2
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
2
2
0
0
2
0
2
0
0
0
2
0
1
0
0
0
0
2
0
2
0
2
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
3
1
2
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
1
0
0
2
0
2
2
0
0
0
0
1
0
2
2
2
2
0
0
0
0
0
0
2
0
2
0
0
0
0
2
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
1
1
0
1
0
0
0
0
0
4
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
2
0
0
2
1
0
3
0
2
0
0
0
1
0
2
0
0
2
0
0
1
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
2
3
0
0
1
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
2
2
1
0
1
0
2
1
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
2
0
0
3
0
0
4
0
0
0
1
0
0
2
0
0
0
0
0
1
0
2
0
3
0
0
0
1
0
0
0
0
2
0
1
1
0
0
0
0
0
0
1
2
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
4
0
3
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
4
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
2
1
0
0
0
1
3
0
2
0
1
0
1
0
2
0
0
0
0
1
2
0
0
0
0
0
0
1
0
3
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
2
0
0
0
0
2
1
0
0
1
0
2
0
0
2
1
2
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
3
0
1
0
0
0
0
0
0
2
2
3
4
0
0
0
0
2
1
0
0
1
2
0
0
0
1
0
0
0
0
2
1
1
0
0
0
0
0
0
1
0
0
0
0
2
5
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
6
1
2
0
0
3
2
0
0
1
0
0
2
2
0
0
0
0
0
1
0
2
2
2
0
0
0
0
0
0
0
1
3
0
0
0
2
1
2
0
0
0
0
2
3
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
2
0
2
0
0
0
2
1
0
0
1
0
2
0
0
2
0
0
2
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
1
2
2
0
1
1
0
1
0
2
0
0
0
0
2
0
1
0
0
0
0
1
0
2
0
2
1
0
0
0
2
0
3
1
0
2
1
2
0
0
0
0
2
3
0
0
0
1
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
3
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
5
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
1
1
0
2
0
0
0
2
0
0
1
2
0
1
2
2
2
2
3
0
2
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
1
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
1
0
0
3
0
0
2
2
4
0
0
2
1
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
15
0
0
0
0
0
1
0
2
0
2
2
2
0
0
2
0
0
1
0
2
1
0
0
0
2
0
0
0
0
2
1
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
4
1
0
1
4
1
0
0
2
2
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
2
0
0
2
2
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
2
0
2
0
0
0
0
2
0
2
0
1
1
2
0
2
0
0
1
0
0
0
2
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
2
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
7
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
2
2
1
2
1
2
0
0
0
1
2
2
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
1
1
0
0
1
0
0
0
0
0
0
3
0
2
1
3
0
1
0
0
3
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
2
1
2
0
2
2
0
0
4
0
0
0
0
2
1
0
0
0
0
0
2
2
0
0
2
0
0
0
1
0
0
2
2
1
2
0
7
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
3
0
0
2
0
0
0
0
0
0
2
1
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
1
1
0
2
0
1
0
3
0
0
0
1
1
0
0
1
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
2
9
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
3
1
2
0
0
0
0
0
1
2
0
0
0
1
1
0
1
0
1
0
0
0
3
0
0
0
0
0
0
0
2
4
2
2
1
0
1
0
2
0
0
0
2
0
0
1
0
0
0
2
2
0
1
3
1
1
1
1
0
1
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
2
0
2
0
0
0
0
2
5
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
1
2
0
0
0
1
0
0
0
0
2
2
2
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
3
0
0
5
0
0
0
1
3
0
2
0
2
0
0
1
0
1
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
1
1
0
0
1
2
0
1
2
0
1
0
1
0
2
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
1
0
0
0
3
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
2
1
2
1
1
0
0
0
0
0
0
0
0
3
2
2
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
3
1
1
2
2
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
1
3
1
2
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
2
0
0
2
1
0
1
2
1
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
1
1
1
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
1
0
2
2
0
0
1
0
0
0
1
0
2
0
2
2
0
0
1
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
1
2
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
1
2
0
2
0
1
0
1
2
1
2
1
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
1
0
3
0
0
0
0
0
0
0
2
1
2
3
0
0
1
0
1
0
0
0
0
2
0
4
0
0
0
2
1
0
2
0
0
0
2
0
0
0
1
0
2
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
1
0
1
3
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
2
2
0
0
0
2
0
0
0
0
1
0
1
0
0
0
4
0
0
2
0
0
3
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
2
0
2
0
0
0
1
0
0
1
0
0
2
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
1
1
2
0
0
1
0
0
0
0
0
0
4
0
1
0
0
1
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
4
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
2
0
0
2
0
3
3
0
1
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
1
2
0
0
1
0
0
0
0
0
2
0
0
0
1
2
0
0
1
1
0
2
5
2
0
0
0
2
2
0
2
0
0
0
0
2
1
0
3
0
2
0
0
1
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
2
1
0
1
0
0
1
1
2
0
0
0
1
3
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
2
0
3
0
2
0
0
0
2
4
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
2
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
2
0
0
0
0
1
0
1
0
1
2
0
0
2
0
1
0
0
0
3
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
2
0
0
1
3
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
2
0
2
1
3
0
1
1
0
0
0
0
2
0
0
0
2
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
3
0
2
0
2
0
2
1
3
0
2
2
0
0
2
0
1
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
1
0
1
0
0
0
0
1
2
0
0
0
1
0
2
0
1
0
2
0
2
0
2
0
0
0
1
0
0
0
0
2
0
1
0
0
2
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
1
1
2
2
0
0
0
0
3
0
3
0
0
2
0
1
2
1
0
0
1
0
0
1
4
0
0
0
0
2
0
0
0
2
2
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
1
0
2
0
2
0
0
0
0
2
1
1
0
0
4
1
0
0
0
1
1
0
2
0
0
0
0
0
1
0
0
2
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
1
0
2
4
0
0
0
0
1
1
0
1
1
1
1
0
0
0
0
0
0
0
1
1
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
2
0
0
1
0
0
1
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
2
0
1
2
0
2
0
0
0
0
0
0
5
0
0
0
1
1
0
3
2
0
0
1
0
0
0
0
0
0
0
0
5
2
1
0
2
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
1
1
0
2
1
0
0
0
0
2
2
1
0
0
0
0
2
3
1
0
0
0
2
0
1
2
0
0
0
0
0
0
2
1
0
3
1
3
0
0
5
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
2
0
0
2
3
0
0
0
0
0
1
0
0
0
0
0
2
2
2
0
0
0
0
2
0
0
1
0
0
0
2
0
1
3
1
2
0
0
0
0
0
4
0
0
0
0
0
0
0
2
0
0
1
3
2
2
0
0
2
0
2
0
0
0
2
3
1
2
0
1
0
0
1
2
0
0
0
2
0
0
3
0
0
0
0
1
0
0
0
0
0
1
0
1
0
2
1
0
1
0
0
1
0
2
0
0
0
2
0
0
0
0
2
1
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
2
0
0
2
1
2
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
7
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
2
2
2
0
2
0
0
0
0
2
1
0
0
0
0
0
2
0
0
4
4
0
1
0
0
0
2
1
1
0
0
0
0
0
0
0
2
1
2
0
0
0
0
1
0
0
1
0
1
2
0
7
0
0
0
1
0
1
0
0
0
0
0
2
0
1
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
2
0
0
0
1
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
1
0
0
0
2
0
1
1
0
0
0
0
0
0
0
2
0
1
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
2
4
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
2
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
1
2
0
0
1
3
0
2
0
0
0
0
4
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
1
0
1
2
0
0
1
0
0
0
0
2
2
0
0
0
1
0
0
1
2
0
2
2
0
0
1
2
0
2
0
1
1
2
1
0
0
0
0
2
2
0
1
0
0
0
1
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
1
0
0
1
2
0
0
2
0
2
1
0
1
0
0
0
2
0
0
0
0
0
5
2
0
0
0
1
1
0
0
0
0
0
2
0
0
1
0
2
0
0
2
2
0
2
0
2
0
0
0
0
0
0
0
1
1
0
0
0
1
2
0
0
0
0
0
1
0
1
0
1
1
0
0
2
0
0
1
0
0
2
0
2
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
1
3
0
0
0
2
0
2
0
0
0
0
0
2
8
0
0
0
2
2
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
1
3
0
0
1
0
1
0
0
0
3
0
2
0
0
2
1
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
2
0
0
0
0
0
1
0
2
1
0
0
0
0
2
0
4
2
0
0
1
0
1
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
3
0
8
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
2
0
1
2
0
0
0
1
1
1
2
0
0
0
0
0
2
0
1
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
2
0
2
5
0
1
0
0
2
0
0
0
0
1
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
3
0
0
1
0
0
0
0
1
0
1
1
1
1
0
0
1
0
2
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
2
1
0
3
0
0
0
2
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
2
0
0
0
1
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
3
0
2
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
1
0
2
0
0
0
0
0
0
2
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
2
2
1
0
0
0
2
0
1
2
1
0
0
2
0
0
0
2
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
3
0
0
0
0
1
0
0
0
0
1
2
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
3
0
0
2
3
0
0
0
0
0
0
0
0
1
2
0
1
0
2
1
2
0
1
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
2
2
2
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
16
0
1
1
0
1
0
0
1
1
0
0
8
2
0
2
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
2
2
0
0
0
2
0
1
1
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
13
0
0
0
0
0
0
0
0
0
0
0
0
7
2
0
0
0
0
0
0
0
1
2
1
1
0
0
1
3
0
0
0
0
0
0
4
0
1
1
0
1
0
1
0
0
1
1
0
0
0
1
1
0
2
0
0
0
4
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
1
2
2
0
0
2
2
0
0
0
0
8
0
0
1
0
2
0
0
0
1
0
0
0
1
0
2
2
0
2
0
1
1
0
2
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
1
1
0
0
0
0
0
0
0
2
1
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
1
1
0
0
0
0
2
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
1
0
1
0
0
0
0
0
2
2
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
2
0
2
2
0
2
1
0
0
2
0
0
0
0
0
2
1
2
0
0
0
0
0
1
1
0
1
0
1
0
0
0
2
0
0
2
0
1
2
0
2
0
0
0
0
0
1
1
0
2
0
2
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
3
0
0
2
0
0
0
0
0
2
0
2
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
3
0
0
1
0
0
2
1
2
1
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
2
0
1
0
0
0
0
0
1
5
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
2
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
2
0
0
2
1
0
0
0
3
0
0
0
0
0
2
2
0
0
0
0
0
2
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
2
2
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
1
0
0
0
0
2
0
3
0
0
0
0
0
0
3
0
0
2
0
2
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
2
1
2
0
0
0
0
0
0
3
0
1
1
2
0
0
0
0
0
2
1
2
0
0
0
0
0
2
1
0
4
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
2
0
0
0
0
2
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
1
0
1
0
0
1
1
2
2
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
2
0
0
2
1
0
1
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
2
1
0
0
2
2
0
0
0
1
0
2
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
4
0
0
1
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
2
0
0
0
0
0
4
0
2
0
1
2
3
0
0
0
1
1
0
0
1
2
1
0
0
0
0
0
2
2
0
2
2
0
0
1
0
3
2
1
0
1
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
1
0
0
1
0
1
7
0
0
0
0
1
1
2
0
1
0
2
0
1
2
0
2
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
2
3
1
0
0
0
2
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
1
1
2
0
12
2
2
2
2
0
0
1
0
0
2
0
0
0
0
0
2
0
1
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
1
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
2
2
2
2
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
2
1
0
0
1
0
1
0
2
1
0
0
0
1
0
0
0
0
1
0
1
2
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
1
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
1
1
0
0
1
2
1
2
3
0
1
0
0
0
2
1
0
0
0
0
2
0
0
0
2
2
0
0
2
1
0
0
0
0
0
0
0
1
3
0
0
2
0
1
0
2
0
0
0
0
0
0
0
2
1
0
0
2
0
0
3
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
2
1
0
0
0
0
2
0
2
2
0
0
0
0
2
0
1
2
1
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
1
2
3
0
1
0
0
2
1
0
0
2
0
0
0
0
1
0
1
0
2
0
0
2
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
1
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
1
2
0
0
0
0
1
0
2
1
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
1
0
2
0
3
0
2
0
1
0
0
0
2
0
0
0
0
0
1
0
3
0
0
1
0
4
0
1
0
0
0
1
1
1
0
0
2
0
0
0
0
2
2
1
0
1
0
1
0
2
0
0
0
2
1
0
2
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
2
0
1
0
0
2
0
0
0
2
0
0
3
0
1
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
2
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
2
0
0
2
4
1
0
1
0
0
0
0
0
8
1
1
0
0
2
0
0
1
0
0
0
0
3
0
0
0
0
0
0
2
0
0
1
2
0
0
1
0
0
0
0
2
0
5
0
0
0
0
1
0
1
0
0
2
0
0
3
0
0
0
1
1
0
1
0
0
0
3
0
0
0
3
1
0
0
0
0
2
2
0
0
2
0
2
0
0
0
2
1
0
0
0
0
1
0
0
0
1
0
0
1
2
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
1
1
0
0
0
0
0
0
1
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
1
0
1
7
0
1
0
0
0
0
0
1
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
2
2
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
1
2
0
0
0
1
0
0
0
0
1
0
0
0
4
0
0
0
0
1
0
2
2
1
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
1
0
3
0
0
0
2
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
1
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
2
2
0
1
0
0
2
0
0
0
1
1
0
2
2
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
2
1
0
0
0
0
1
1
0
0
1
1
0
2
0
1
0
1
0
0
2
0
1
0
0
1
2
0
0
0
0
1
0
1
3
0
2
1
1
0
1
0
0
0
1
0
1
1
0
0
1
1
0
3
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
2
0
0
2
0
1
1
1
2
0
0
0
1
1
0
2
0
0
0
0
0
0
0
5
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
2
0
0
1
0
0
2
2
0
2
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
3
0
2
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
2
0
1
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
2
0
0
1
2
0
0
1
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
1
2
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
1
0
1
0
1
2
0
0
1
1
0
0
0
0
3
0
0
2
0
0
0
0
0
2
1
0
0
0
0
2
0
0
1
0
0
0
0
0
2
1
2
0
0
0
0
2
1
0
0
0
0
0
0
0
3
0
5
0
0
0
0
4
0
0
0
0
8
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
2
0
0
4
1
1
0
1
2
0
1
0
0
0
1
0
1
0
2
0
0
1
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
2
0
1
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
3
0
1
3
0
0
0
0
0
0
0
0
0
0
2
2
0
2
1
0
1
1
0
0
1
0
1
0
2
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
2
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
3
0
0
0
2
0
0
3
2
0
0
1
0
1
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
2
0
2
2
1
2
0
0
0
1
0
0
0
1
2
0
0
0
0
0
2
1
0
0
0
0
0
1
0
3
0
2
0
1
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
3
0
0
0
0
0
2
2
0
0
0
1
0
0
3
2
1
0
1
0
0
2
0
0
0
0
0
1
1
2
0
1
0
0
0
2
1
2
0
0
1
0
1
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
1
1
0
3
0
0
0
0
1
0
0
0
0
1
0
2
1
1
0
0
0
2
1
0
0
1
0
0
1
0
0
0
2
0
0
0
1
0
4
2
0
0
0
0
3
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
1
3
0
0
1
1
0
0
0
0
0
0
0
1
0
2
1
0
2
0
0
0
0
0
0
1
2
3
0
0
2
0
0
0
0
1
2
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
4
0
0
0
0
0
0
3
1
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
1
0
0
1
0
2
0
1
0
0
0
0
1
3
0
0
0
2
0
0
0
1
1
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
2
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
1
1
2
0
0
2
0
0
0
0
1
0
1
0
0
0
1
0
3
1
0
2
1
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
5
0
0
2
0
2
0
0
0
1
0
3
2
2
0
0
2
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
2
0
0
0
1
2
0
0
0
0
2
2
1
0
0
1
0
0
2
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
1
0
1
1
0
1
2
2
0
0
1
2
0
2
1
0
2
0
1
0
0
2
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
2
2
0
1
1
0
0
0
0
0
0
1
0
1
0
5
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
2
2
1
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
2
1
0
0
1
0
1
0
2
1
0
0
0
0
0
0
0
0
2
0
1
1
0
1
2
1
0
1
0
2
2
0
0
1
1
0
3
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
1
1
0
1
1
0
1
2
0
0
0
1
0
0
0
2
2
2
0
2
0
0
0
2
1
0
0
0
1
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
5
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
1
0
0
3
0
0
0
0
2
2
1
0
0
1
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
4
5
2
1
0
2
0
1
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
5
2
0
2
2
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
2
0
0
2
2
0
0
2
1
0
0
1
1
0
2
0
0
2
2
0
2
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
1
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
2
0
1
0
0
0
2
0
3
0
0
0
0
1
1
0
0
2
0
0
2
0
0
0
1
0
0
1
1
0
0
2
2
0
0
4
0
2
0
0
0
0
0
2
0
0
2
2
2
1
0
0
3
0
0
0
0
1
0
2
0
0
3
2
0
0
0
0
0
1
2
2
1
0
0
0
0
3
2
0
2
0
2
3
1
2
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
3
0
0
2
0
0
0
0
0
1
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
1
2
0
1
2
1
3
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
1
0
3
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
1
1
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
1
1
2
1
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
2
0
1
2
2
0
0
0
0
3
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
2
1
0
0
0
1
0
1
0
4
1
0
0
0
1
0
0
0
0
2
1
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
1
0
3
0
2
0
1
1
18
0
0
2
0
1
1
0
1
0
0
0
0
0
2
2
2
2
0
3
2
3
1
2
0
0
0
1
0
0
1
3
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
1
0
2
0
0
0
0
0
0
0
0
2
2
0
1
2
0
1
1
0
1
0
0
0
2
0
0
0
3
2
0
1
1
1
2
1
0
2
0
1
2
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
1
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
1
1
0
0
0
2
1
1
1
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
1
0
1
2
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
1
1
0
0
3
2
0
0
1
1
0
2
0
2
0
0
2
0
0
0
0
0
2
0
2
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
1
0
1
0
0
1
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
2
1
0
0
1
1
2
1
0
0
0
0
0
0
0
2
2
0
0
2
0
2
0
3
1
0
0
0
2
2
1
1
2
0
1
1
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
1
0
0
2
1
0
3
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
1
1
0
0
0
0
2
0
3
0
1
0
0
0
0
1
0
0
0
0
2
6
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
1
0
2
2
0
1
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
2
0
0
1
2
0
1
2
0
0
2
0
1
0
0
0
2
0
0
0
2
1
0
2
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
1
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
3
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
2
0
3
2
0
0
0
1
2
0
0
1
1
0
2
0
0
2
6
2
1
2
0
0
0
0
0
0
2
2
2
0
0
1
0
0
2
1
0
0
1
0
0
1
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
3
0
0
0
2
0
0
2
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
1
1
0
0
0
0
0
1
0
0
0
2
0
0
1
0
2
1
0
0
0
0
0
1
1
0
0
1
1
0
2
0
3
2
1
0
0
0
0
0
0
0
1
0
1
2
0
2
0
0
0
0
0
0
1
0
0
0
2
3
0
0
2
4
0
2
0
1
1
0
0
0
0
2
1
0
2
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
2
1
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
4
0
0
0
1
4
0
0
0
1
0
0
0
0
0
0
0
2
1
2
0
0
0
1
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
1
0
2
0
1
1
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
2
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
1
0
1
0
0
1
0
3
0
0
0
2
1
1
1
1
0
2
2
1
0
0
0
0
0
1
0
1
1
1
2
2
2
1
0
0
0
2
0
0
0
2
0
2
0
2
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
2
0
1
0
2
0
0
0
0
2
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
2
1
2
1
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
2
1
0
0
0
1
0
1
1
0
2
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
2
0
2
1
2
1
2
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
2
0
3
0
0
0
0
1
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
2
1
0
0
0
0
0
1
3
1
0
1
1
0
0
0
2
1
2
1
1
0
1
0
0
0
0
0
2
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
2
7
4
0
2
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
1
2
1
0
0
0
0
0
0
0
0
0
5
2
0
0
0
0
0
0
1
0
0
0
0
0
5
0
0
0
0
0
1
2
0
0
0
2
1
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
2
2
0
1
0
0
1
2
0
4
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
1
0
2
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
2
0
2
1
0
0
0
1
0
0
2
0
0
1
2
0
2
0
0
0
0
0
0
0
1
0
4
0
0
0
2
0
0
0
0
0
2
0
1
1
0
1
0
3
0
0
0
0
0
0
2
0
1
0
1
0
0
0
2
2
1
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
1
1
2
1
1
2
0
0
0
0
0
2
0
0
0
2
3
0
0
0
1
0
0
0
1
0
1
0
2
2
0
1
2
0
1
0
2
0
0
1
2
0
0
1
0
2
0
0
0
1
1
1
1
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
3
2
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
1
1
2
0
0
1
0
0
3
0
1
0
0
0
2
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
1
0
2
0
1
0
0
0
2
1
0
0
2
0
0
1
2
0
1
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
1
1
0
0
0
0
1
1
2
2
1
2
0
0
0
0
1
1
1
0
2
0
0
0
0
2
0
1
0
1
2
2
1
0
1
0
0
0
0
0
1
0
0
0
1
2
0
0
1
0
1
2
0
3
0
2
1
0
1
0
0
2
0
1
1
2
0
1
0
0
2
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
1
2
2
0
5
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
2
0
0
0
0
1
2
4
0
0
0
0
0
0
0
2
0
0
0
0
0
5
0
1
0
0
0
1
2
1
0
0
0
0
2
0
2
1
0
0
1
1
0
0
2
0
0
2
0
0
2
0
0
0
2
0
0
1
2
0
0
2
0
0
2
2
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
2
2
2
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
2
0
0
1
2
0
0
0
2
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
2
0
3
1
0
0
0
0
0
1
0
0
0
2
1
2
0
0
0
0
0
0
0
0
4
2
0
2
2
0
0
0
0
2
0
0
0
0
2
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
3
1
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
2
1
0
0
0
0
0
1
2
0
0
0
0
2
0
0
1
2
0
0
1
0
0
0
2
0
2
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
3
0
0
0
2
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
1
1
0
2
0
2
0
0
0
1
1
2
2
1
1
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
7
0
0
0
0
3
0
0
0
1
0
3
0
0
0
0
2
0
0
0
0
2
2
0
0
0
2
0
3
0
1
0
3
0
0
0
0
0
3
0
1
0
0
2
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
1
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
1
3
0
0
0
0
0
0
2
0
2
0
1
0
0
0
2
0
0
0
1
0
1
2
0
0
0
0
1
0
0
4
0
3
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
2
2
0
0
1
0
0
1
0
0
2
0
0
0
0
2
2
0
0
0
1
2
0
2
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
3
0
1
3
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
3
0
2
0
0
0
2
2
0
0
1
0
0
1
0
0
0
0
0
3
2
1
1
0
1
0
2
0
0
0
5
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
1
2
0
0
2
0
0
0
0
1
0
0
0
0
1
0
1
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
2
1
0
2
2
5
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
2
1
0
0
2
1
3
0
0
0
0
1
0
0
0
0
0
2
3
0
2
0
0
0
1
1
0
0
0
1
0
0
0
0
0
2
0
1
0
1
0
0
0
2
0
0
2
0
0
0
2
0
1
0
0
2
0
2
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
2
0
0
3
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
2
0
0
0
2
0
0
1
1
2
0
0
0
2
0
0
0
0
0
2
2
0
2
0
2
0
0
0
1
2
1
0
0
0
0
0
1
0
2
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
2
1
2
0
0
0
2
1
0
5
1
0
0
0
1
0
3
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
3
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
2
0
2
2
1
0
0
0
0
1
1
0
2
0
2
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
1
1
1
1
0
0
0
0
0
2
0
1
0
0
0
0
1
0
4
0
0
0
1
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
2
0
0
0
1
0
0
0
0
1
1
2
1
0
0
0
0
0
1
0
1
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
2
2
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
2
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
3
1
1
0
2
1
1
0
0
2
0
0
0
0
1
1
0
0
1
2
0
1
0
1
0
0
1
0
1
0
2
0
2
0
0
0
0
2
1
0
0
0
1
0
4
0
1
0
1
0
0
0
0
2
0
1
0
1
0
0
0
2
0
0
0
0
1
0
3
0
0
0
0
0
0
6
0
0
1
0
0
2
0
0
1
0
0
1
0
0
3
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
1
0
2
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
2
0
0
2
0
3
2
2
0
0
2
0
2
0
0
0
0
0
0
2
0
2
1
1
0
2
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
1
2
2
0
0
2
2
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
1
0
0
2
0
0
2
2
0
1
1
0
0
0
1
0
2
1
2
0
1
0
1
0
0
1
0
0
3
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
1
1
0
3
2
1
0
0
0
2
0
5
0
0
0
0
0
1
1
2
1
1
1
2
1
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
3
0
0
2
0
2
0
0
0
2
0
1
0
1
2
0
2
1
0
0
2
0
0
1
2
2
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
2
2
1
0
1
0
0
0
0
2
4
0
0
0
1
0
0
2
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
2
0
0
1
2
3
1
0
1
0
0
2
0
0
2
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
2
1
0
0
3
2
0
1
0
2
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
1
2
0
1
0
1
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
3
0
0
1
1
0
0
1
3
0
0
0
2
0
2
0
1
0
0
0
0
0
0
1
2
2
0
0
0
0
0
1
0
0
0
0
1
3
0
0
0
0
1
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
1
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
2
0
1
0
0
0
1
0
0
2
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
3
2
0
1
0
0
0
0
0
2
0
2
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
4
5
0
0
0
0
2
0
2
2
0
2
0
1
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
2
0
0
0
0
0
2
1
0
2
0
1
0
0
3
0
0
0
2
2
2
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
2
0
0
0
1
0
1
0
1
0
0
1
2
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
1
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
1
2
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
1
0
1
0
0
0
2
0
0
2
0
0
0
1
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
3
0
0
2
1
0
0
0
0
0
1
0
0
2
2
0
0
2
0
0
0
0
2
2
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
2
2
3
0
0
0
2
4
0
0
0
0
0
1
2
3
0
0
0
2
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
4
0
1
0
2
1
1
0
0
0
2
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
1
0
2
0
0
0
1
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
3
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
3
5
1
2
0
2
0
2
0
0
2
1
0
0
0
1
1
0
0
1
0
4
0
2
0
0
0
0
2
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
2
0
1
0
0
0
1
2
0
1
0
0
2
0
0
0
1
0
0
1
1
0
0
0
1
1
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
1
0
2
1
2
0
0
0
2
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
2
1
0
2
1
0
0
0
2
0
1
0
0
0
0
1
0
0
1
0
1
1
1
2
0
1
0
1
2
0
0
1
0
0
1
2
0
0
0
1
1
0
1
0
0
1
0
0
0
0
1
0
2
0
1
0
0
1
0
1
1
0
2
0
0
1
0
0
0
0
0
2
1
2
0
0
0
0
0
2
0
0
1
0
0
0
4
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
2
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
1
1
0
0
0
0
3
2
2
1
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
2
0
0
0
1
0
1
0
0
0
0
2
0
2
0
0
0
0
0
1
2
1
0
0
0
2
1
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
2
2
2
0
3
0
2
1
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
1
1
0
2
0
0
1
0
1
0
0
0
0
0
0
6
0
0
0
0
2
0
0
6
0
1
0
0
0
0
0
0
1
0
0
0
2
0
2
0
1
0
2
1
0
0
8
2
0
0
2
2
0
2
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
2
0
0
1
0
0
1
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
3
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
2
0
1
2
2
2
0
2
0
2
0
1
0
0
0
1
0
0
0
0
3
0
0
1
0
2
2
0
0
2
0
0
1
2
0
2
0
0
0
0
0
0
0
2
2
0
0
0
1
0
2
1
0
1
0
0
0
1
0
0
0
1
2
0
0
0
0
2
1
0
0
0
2
2
0
0
0
0
1
1
0
0
0
1
0
6
1
0
0
0
2
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
1
0
1
1
0
0
1
2
0
2
0
0
0
1
2
1
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
3
0
0
0
2
0
0
0
0
0
2
1
0
0
2
0
0
0
0
1
3
0
0
2
1
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
1
0
1
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
2
1
0
0
1
0
0
1
0
1
0
0
1
1
0
2
0
0
1
0
0
0
2
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
2
0
2
1
0
0
8
0
3
2
0
0
0
1
2
0
0
2
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
2
0
2
0
0
0
2
2
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
2
2
0
0
2
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
1
0
2
0
0
1
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
2
0
1
0
3
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
1
0
2
0
0
0
1
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
1
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
1
0
2
0
1
1
2
3
1
1
0
1
0
0
2
1
1
0
2
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
4
1
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
2
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
2
0
0
1
0
0
1
2
0
0
0
0
2
0
0
0
2
0
1
0
2
2
1
0
0
0
2
0
0
3
0
0
0
0
2
3
0
0
0
2
0
2
0
0
2
0
0
0
2
0
0
0
2
0
1
2
0
0
0
0
0
0
4
2
0
0
0
0
0
1
0
3
0
0
0
3
0
0
0
1
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
4
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
2
0
0
3
1
0
2
1
0
0
0
0
0
2
0
0
1
0
0
0
0
1
1
2
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
1
0
0
0
0
2
1
0
1
1
0
0
0
0
0
2
2
0
0
1
1
0
0
0
0
0
0
0
0
1
0
2
1
0
0
1
2
0
2
0
0
0
0
2
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
2
0
0
0
0
0
1
0
2
2
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
1
0
1
0
0
0
2
0
1
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
3
0
0
2
3
0
0
0
1
0
1
1
0
1
2
0
0
1
2
1
0
2
0
0
0
0
0
0
4
2
0
0
0
0
0
0
0
2
1
0
1
1
0
3
0
2
2
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
2
2
0
0
0
1
0
1
2
0
2
2
0
0
1
0
0
0
1
0
0
0
0
2
1
0
0
0
0
3
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
1
0
1
1
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
1
2
0
0
0
2
0
2
0
2
1
1
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
2
0
1
0
0
1
1
0
1
0
0
0
3
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
2
1
0
0
2
0
2
1
0
0
0
0
2
0
0
0
1
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
1
0
6
0
0
0
0
2
1
4
0
0
2
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
3
0
0
2
0
1
0
0
0
0
0
0
0
3
1
0
0
2
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
4
2
0
1
0
0
0
1
1
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
1
0
0
0
2
0
3
0
1
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
1
0
0
0
2
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
3
0
1
2
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
2
5
0
3
0
0
0
0
0
1
2
0
1
2
1
0
0
0
1
0
0
2
0
2
2
2
1
1
0
0
0
2
2
0
0
1
0
0
0
2
0
1
2
1
1
1
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
7
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
4
1
0
0
0
2
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
1
0
1
0
0
2
1
2
0
2
0
0
3
0
0
0
0
1
0
1
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
1
2
2
0
2
0
1
2
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
1
1
0
0
0
0
1
0
0
0
1
0
0
0
2
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
3
0
1
0
0
0
0
0
2
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
2
0
2
0
2
1
0
0
0
2
1
0
0
2
0
0
0
1
1
0
2
0
0
1
2
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
1
2
0
0
0
1
1
2
0
0
0
0
1
1
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
2
2
0
4
1
0
1
0
0
1
0
0
0
0
0
2
1
0
0
0
0
1
0
2
0
0
2
1
1
0
0
0
1
0
0
2
0
1
0
2
0
0
1
3
0
5
0
2
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
10
1
2
0
3
2
1
2
0
4
0
0
0
1
1
0
0
2
0
3
2
1
2
2
0
0
0
1
0
1
2
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
3
0
2
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
2
0
0
2
0
0
2
0
0
0
2
2
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
4
2
2
0
0
0
0
0
2
1
2
2
0
0
2
2
0
0
0
2
0
0
2
2
0
1
0
0
0
1
2
2
0
0
0
0
0
0
0
1
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
1
0
1
0
4
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
3
1
0
0
0
0
0
1
2
0
0
4
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
2
1
2
2
0
0
1
0
3
1
2
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
2
2
0
2
2
0
2
0
1
1
0
0
0
0
0
0
0
1
2
3
0
0
0
0
3
1
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
2
1
1
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
1
0
1
0
1
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
1
0
0
2
0
1
0
2
2
0
1
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
2
0
1
1
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
6
0
0
0
1
0
2
0
2
1
0
0
0
0
3
0
0
1
0
0
0
1
0
0
0
0
2
1
0
1
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
1
1
1
0
0
0
0
2
0
0
2
0
3
3
0
0
0
0
0
2
0
0
2
0
0
1
0
0
2
2
0
0
0
0
1
2
2
0
1
0
0
0
0
0
1
0
0
0
1
3
1
0
0
1
1
0
0
0
1
0
0
0
0
2
1
0
0
0
1
0
0
2
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
1
1
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
2
0
0
2
0
1
2
0
0
0
3
0
0
0
0
2
0
0
0
1
0
3
0
2
2
2
0
0
1
1
1
0
0
0
0
0
0
0
2
2
0
3
0
2
2
2
0
0
0
1
0
0
0
1
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
2
1
0
0
2
0
2
0
0
2
2
0
0
0
0
0
1
0
1
0
0
1
0
0
0
2
0
0
0
0
0
2
0
2
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
3
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
1
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
2
2
0
0
5
2
1
1
0
1
4
0
0
0
0
0
0
2
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
1
0
0
0
1
0
0
3
2
2
0
0
1
2
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
4
0
0
1
0
0
0
0
0
2
0
0
0
1
0
2
0
0
1
0
1
0
2
0
1
2
0
0
0
1
0
0
2
1
0
1
0
1
1
2
0
2
2
2
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
2
1
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
1
2
7
2
1
0
1
1
0
2
0
0
2
0
0
0
0
0
1
0
0
3
2
2
0
2
1
0
1
0
2
0
0
0
0
1
0
2
2
0
0
0
0
0
2
2
2
1
0
0
0
2
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
1
2
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
2
0
0
0
1
0
0
0
1
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
1
0
2
0
2
0
2
1
7
0
0
0
0
0
1
0
0
2
0
0
0
2
0
1
0
0
0
1
2
0
1
0
0
0
0
2
0
0
0
0
0
2
1
0
1
2
1
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
1
2
2
0
2
0
0
0
2
0
1
0
0
2
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
1
2
0
2
2
1
1
0
0
0
0
0
0
0
0
0
3
1
0
1
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
1
2
5
0
0
0
0
0
3
0
0
0
1
2
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
2
2
0
0
2
1
0
0
0
0
2
3
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
1
0
1
0
0
2
0
1
0
0
1
0
0
0
1
0
0
2
1
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
1
0
2
0
0
0
0
2
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
3
0
0
0
0
0
1
0
0
1
0
2
2
2
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
2
2
2
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
1
1
3
0
0
1
0
7
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
5
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
2
1
2
3
0
2
0
2
2
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
2
1
0
0
0
0
0
2
1
1
0
1
0
0
0
0
1
0
0
1
2
0
0
1
5
0
0
2
0
0
2
1
1
0
1
1
1
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
1
0
0
0
0
1
2
0
2
0
0
1
0
0
0
0
2
0
2
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
1
1
0
0
0
0
0
2
0
1
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
1
0
0
2
0
0
1
0
0
0
4
2
0
0
0
0
0
0
2
0
0
2
0
1
0
0
2
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
1
0
2
2
1
0
1
0
0
1
2
0
0
1
2
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
1
0
2
1
2
0
0
2
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
2
0
2
0
1
0
0
1
0
3
0
2
1
0
1
2
0
1
0
0
0
0
0
0
2
1
0
1
2
2
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
2
0
0
0
2
0
1
1
0
0
0
1
0
1
0
0
0
1
1
2
1
0
3
2
0
2
0
2
0
0
0
2
0
2
0
0
4
0
0
0
0
0
0
0
1
0
1
3
0
0
2
0
0
0
0
0
2
0
0
0
3
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
6
0
0
0
0
2
0
1
0
0
0
0
1
0
2
0
2
0
1
2
0
0
0
0
0
2
0
1
1
0
0
0
0
1
2
2
1
0
2
2
2
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
3
2
0
1
1
0
1
6
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
2
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
2
0
0
2
0
1
0
4
0
1
0
1
1
0
1
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
1
3
0
0
3
0
0
1
0
0
0
0
0
1
0
1
0
0
0
4
0
0
0
2
0
0
0
0
2
0
3
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
2
0
2
1
0
0
0
0
2
0
0
0
0
1
2
2
2
0
0
0
0
0
0
0
0
2
2
2
2
2
0
0
0
2
1
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
2
0
1
0
0
1
0
0
3
0
2
0
1
0
0
1
0
3
0
0
0
2
0
0
2
1
0
2
0
0
1
2
0
0
0
0
1
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
1
2
0
0
1
2
1
0
0
2
0
2
0
0
0
0
0
0
0
1
0
4
1
0
1
2
0
0
0
0
1
1
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
1
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
2
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
2
2
0
0
1
0
0
2
0
0
2
0
0
1
1
0
1
2
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
2
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
1
5
0
0
0
0
1
1
0
0
0
0
0
2
1
2
1
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
2
2
2
0
0
0
1
2
0
0
0
0
1
0
2
2
0
0
0
2
2
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
1
2
0
1
0
4
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
1
0
1
0
1
0
1
0
0
0
2
0
0
0
0
1
0
2
1
0
0
0
0
1
0
0
1
0
0
0
2
1
0
2
0
1
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
1
0
9
0
3
2
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
2
2
0
2
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
1
1
2
0
0
0
0
0
0
0
2
1
0
0
3
0
0
1
0
1
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
5
0
0
1
0
2
0
1
0
2
0
0
0
0
0
0
0
2
2
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
2
1
0
0
0
2
1
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
3
0
2
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
1
1
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
4
0
1
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
3
0
0
1
1
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
1
2
0
2
0
0
4
0
1
7
0
0
1
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
3
0
0
0
0
1
0
1
0
2
2
0
0
0
0
1
0
1
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
1
1
7
0
2
0
2
0
0
2
0
2
0
2
0
2
2
3
0
2
2
1
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
2
0
2
0
2
0
1
0
1
0
0
1
0
0
2
2
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
2
2
0
0
1
2
0
0
0
0
0
0
0
0
3
1
1
0
0
2
0
0
0
0
1
0
2
1
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
1
1
0
0
0
0
0
0
5
2
0
0
1
0
0
0
0
0
0
0
1
0
2
1
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
3
0
2
0
6
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
3
2
0
0
0
0
1
0
0
0
0
2
0
0
2
2
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
2
0
1
1
1
0
2
1
0
0
0
0
0
2
0
1
0
1
2
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
3
1
0
0
0
0
0
2
0
3
0
1
0
0
0
0
0
3
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
2
0
1
3
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
3
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
1
0
1
0
1
0
0
0
1
0
2
4
0
0
0
0
0
0
0
2
2
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
1
0
0
1
0
0
3
0
2
0
0
0
0
0
5
2
0
0
0
1
1
0
0
0
0
2
1
8
0
0
1
1
1
1
1
0
1
0
0
0
2
0
0
0
2
0
0
3
2
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
1
2
1
0
2
1
0
0
0
1
0
0
0
0
0
1
2
0
2
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
1
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
2
0
2
0
0
1
0
0
0
1
0
0
0
0
1
2
0
0
0
0
1
0
0
0
2
0
1
2
0
0
1
3
0
0
1
0
0
0
1
0
0
1
0
0
2
0
0
1
0
0
1
0
2
0
0
0
0
0
2
2
2
1
0
1
0
2
0
0
2
0
0
1
0
0
2
0
0
0
1
1
0
0
1
1
2
0
0
0
0
0
2
0
0
2
0
0
1
1
0
2
1
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
1
0
0
0
1
0
0
3
0
0
0
0
0
0
1
0
2
2
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
2
1
0
0
0
3
1
2
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
2
4
2
1
2
0
0
0
2
1
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
2
1
1
0
0
1
2
0
0
0
0
2
0
1
0
2
0
1
0
0
2
1
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
1
0
1
0
0
1
0
0
0
2
0
0
0
1
1
0
1
1
2
0
0
0
0
1
0
3
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
5
3
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
2
1
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
2
0
0
0
2
2
0
0
0
3
0
0
0
0
0
1
0
0
1
0
0
0
2
2
3
0
2
0
0
0
0
2
0
2
1
0
0
1
2
0
0
0
0
0
3
0
0
0
1
1
0
1
0
0
2
2
1
2
1
0
1
0
1
0
0
2
1
0
2
0
2
0
0
2
0
2
0
0
0
1
0
0
1
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
2
0
4
0
0
1
2
0
0
1
0
0
1
2
0
2
0
0
0
2
4
0
1
0
0
0
0
2
2
2
0
0
0
1
0
2
0
0
0
0
0
2
0
0
2
0
2
0
0
0
3
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
2
0
0
0
1
0
2
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
3
0
0
0
0
0
0
0
2
0
2
0
2
0
0
1
2
1
0
2
0
0
0
0
1
0
0
0
1
3
0
0
0
0
3
2
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
1
0
0
0
0
2
2
0
1
0
0
0
0
0
0
1
0
0
1
0
3
0
0
3
0
0
2
0
0
0
0
2
1
2
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
1
3
0
1
3
0
0
0
2
0
0
0
2
1
0
0
0
2
0
2
3
1
1
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
2
0
0
1
2
1
2
0
1
0
2
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
2
1
1
0
0
0
0
0
1
0
0
2
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
3
0
0
0
0
0
1
1
1
2
4
0
0
0
0
0
2
1
0
0
0
2
0
3
0
2
0
0
0
0
2
2
0
0
0
1
0
1
0
0
0
0
3
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
2
0
0
2
0
1
0
0
2
0
0
0
0
0
0
2
1
0
0
0
1
0
5
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
3
0
0
0
1
2
2
0
2
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
2
0
0
3
2
0
0
0
0
3
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
2
1
0
0
0
2
0
0
0
0
0
3
2
0
0
1
2
1
0
0
0
0
0
3
1
0
2
2
0
1
4
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
2
1
2
0
2
1
0
0
0
2
1
2
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
4
0
1
0
1
0
0
1
0
2
1
0
2
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
2
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
2
3
0
0
0
0
0
1
0
1
1
0
0
0
0
1
2
0
1
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
1
0
0
0
5
2
0
0
0
1
2
0
0
0
0
0
0
0
1
0
2
0
2
2
1
1
0
1
2
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
2
1
0
0
2
0
0
0
0
0
2
0
2
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
4
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
1
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
1
2
0
0
0
0
2
2
0
0
0
1
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
2
0
0
0
0
0
4
0
0
0
2
1
0
2
0
3
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
3
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
2
2
0
0
0
0
0
0
0
1
0
6
0
2
0
0
0
0
1
0
1
0
0
0
0
0
3
2
1
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
2
0
0
1
2
2
0
2
0
2
0
0
1
1
0
0
1
0
0
2
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
5
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
3
1
5
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
5
0
0
3
1
0
0
0
2
0
1
0
0
2
1
1
5
0
2
0
0
0
0
0
0
0
0
2
1
2
0
3
0
0
0
0
2
0
0
1
0
0
0
1
0
1
1
2
0
0
0
1
2
0
0
5
0
0
1
0
0
1
0
2
0
0
0
1
0
0
2
0
0
1
1
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
2
0
0
2
0
2
1
1
2
0
0
0
0
0
0
1
0
2
0
1
1
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
1
1
2
2
0
0
2
0
0
0
2
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
1
3
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
1
0
2
1
0
0
0
0
0
0
0
1
2
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
2
2
1
0
0
0
0
0
3
1
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
1
1
0
2
0
0
0
0
0
1
2
0
0
1
0
2
1
0
0
0
0
0
0
0
0
1
0
2
1
2
0
0
2
2
0
0
0
0
0
1
0
2
3
1
0
0
1
2
1
0
0
1
1
0
0
0
0
0
2
0
0
2
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
1
0
1
0
2
0
0
2
0
2
0
2
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
2
2
0
8
0
2
0
1
0
1
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
1
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
2
0
0
0
0
0
0
1
0
0
0
1
2
0
2
0
0
2
2
0
0
0
1
0
0
0
0
2
2
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
1
0
0
3
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
3
2
1
0
0
0
0
0
0
3
0
0
2
0
0
2
0
1
2
0
1
0
0
0
0
1
0
0
0
1
0
3
2
0
2
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
1
2
0
0
2
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
1
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
1
3
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
2
0
0
14
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
2
1
1
1
0
2
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
1
2
1
1
0
0
1
5
0
1
0
2
0
0
0
2
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
2
2
0
2
1
0
0
2
2
2
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
1
0
2
1
2
1
0
0
0
2
1
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
2
0
0
3
0
1
0
0
1
0
0
2
1
0
1
0
0
0
0
3
0
0
0
0
2
0
1
0
3
0
1
0
0
0
0
0
0
1
0
2
0
0
3
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
1
3
0
0
1
2
0
0
0
0
0
0
0
0
0
2
7
0
2
0
0
1
1
0
2
2
0
0
0
1
2
0
1
0
0
1
0
3
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
1
2
2
0
0
0
3
1
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
3
1
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
1
2
0
2
1
0
3
0
0
0
0
2
2
0
0
1
0
1
3
0
0
0
0
0
0
0
4
0
0
3
1
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
2
2
0
2
0
1
1
0
0
0
0
2
0
0
0
1
2
1
0
0
0
0
0
1
1
2
0
0
0
0
2
0
0
1
0
0
0
0
1
0
2
0
2
1
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
2
0
0
2
1
0
0
0
0
2
0
1
1
2
0
0
0
0
0
0
0
1
0
0
2
1
0
2
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
1
0
3
4
0
0
2
3
0
0
2
2
0
0
0
0
0
0
2
0
4
0
0
0
1
0
0
0
0
2
0
0
0
0
0
3
0
4
0
0
0
0
0
1
1
0
0
2
0
2
0
2
0
1
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
1
0
0
1
1
0
0
5
1
2
0
1
0
2
1
1
0
1
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
2
2
0
0
1
1
0
0
1
0
0
0
0
2
0
1
2
0
1
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
2
1
1
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
2
2
0
2
0
0
0
0
2
2
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
2
2
2
1
2
0
0
0
1
0
0
0
0
0
0
3
0
2
1
0
0
0
3
1
0
0
1
0
0
0
2
1
0
2
0
0
2
0
0
0
0
0
0
2
3
0
2
1
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
1
5
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
2
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
1
0
4
0
2
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
1
0
2
0
0
1
0
0
0
0
2
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
4
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
1
1
0
0
0
1
0
0
0
0
0
2
0
0
1
2
4
0
0
1
1
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
3
0
0
0
1
0
0
2
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
2
0
1
0
0
1
0
1
1
1
2
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
2
2
1
0
1
0
0
0
0
1
0
0
1
0
0
2
0
0
1
2
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
5
2
0
0
1
0
0
0
0
0
0
0
0
2
0
2
2
0
2
0
0
0
1
2
0
0
0
0
2
2
0
2
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
2
0
0
2
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
2
0
0
0
0
1
0
0
1
2
2
0
0
2
0
4
0
1
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
3
0
1
0
2
0
0
2
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
6
0
1
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
4
0
0
2
0
0
1
0
0
0
0
2
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
2
0
2
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
1
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
2
0
0
0
0
2
2
1
0
0
1
0
0
0
0
1
1
0
6
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
1
0
2
0
0
0
1
2
3
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
1
0
0
2
1
1
0
0
0
0
2
1
1
2
0
0
0
0
0
2
0
2
1
0
0
2
0
0
1
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
1
0
0
1
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
5
1
0
0
0
2
0
0
0
0
1
0
1
0
2
3
2
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
2
1
0
2
0
0
0
0
0
0
0
0
2
2
2
0
0
0
1
0
2
0
0
0
1
1
0
1
0
1
0
2
0
0
0
0
0
4
0
0
0
2
0
0
0
0
2
0
2
2
0
2
0
0
0
0
0
0
0
0
3
3
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
2
0
0
2
0
0
0
2
3
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
2
2
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
3
1
0
0
0
2
1
0
1
2
0
0
1
0
0
1
2
1
1
1
0
0
0
0
0
0
0
1
1
0
1
2
2
1
1
0
0
2
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
1
0
2
1
0
0
0
0
1
1
0
0
0
1
2
0
0
3
0
1
0
1
1
0
0
0
2
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
2
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
4
0
1
0
5
1
1
0
0
0
1
0
0
0
1
1
1
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
1
0
2
1
0
2
1
0
2
0
0
0
0
0
0
2
0
3
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
2
0
0
1
0
2
0
2
2
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
2
2
1
0
0
0
2
0
0
0
0
0
1
1
0
2
0
2
1
3
0
1
0
0
0
0
1
5
0
2
0
1
2
0
2
0
0
2
2
0
0
0
2
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
1
0
0
0
0
2
0
0
2
0
0
1
0
0
2
1
1
2
2
0
1
1
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
2
3
3
0
0
0
0
0
0
0
0
0
1
1
2
1
0
0
0
0
0
2
1
0
0
0
2
0
0
1
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
1
1
0
0
0
0
1
1
1
0
3
0
0
0
0
3
2
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
11
1
0
2
0
0
2
0
2
3
1
2
0
0
0
0
0
1
0
0
1
3
2
1
0
0
1
0
0
0
2
2
1
2
0
2
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
1
2
0
0
0
0
0
1
0
1
0
1
0
0
0
2
0
2
0
0
2
0
1
0
0
3
1
4
0
0
0
0
2
0
2
1
2
0
0
0
0
2
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
2
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
16
0
1
0
2
0
0
1
0
2
0
0
0
2
1
0
0
0
0
2
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
1
3
0
2
2
0
0
0
0
0
0
1
0
2
0
0
2
1
0
1
0
1
0
0
0
0
1
0
1
0
2
1
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
2
2
0
0
2
2
2
0
2
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
1
2
1
2
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
2
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
2
0
2
2
0
0
0
0
2
0
0
0
2
0
0
2
1
1
2
0
0
0
2
0
0
0
0
0
2
1
0
2
0
0
0
0
1
0
0
2
0
0
2
0
1
2
1
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
2
2
0
2
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
1
1
2
0
0
2
0
0
0
0
3
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
2
2
1
0
2
0
0
1
0
4
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
1
0
0
0
3
0
0
2
0
3
2
1
2
0
0
0
0
0
1
2
0
0
0
1
0
0
0
2
2
0
0
1
0
1
1
1
0
1
0
0
2
1
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
5
0
1
1
0
0
0
2
0
2
1
2
0
0
3
2
0
0
1
0
2
0
0
0
1
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
1
1
0
0
0
0
0
3
2
2
0
1
1
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
1
2
1
0
1
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
1
0
0
1
2
1
0
2
0
1
0
0
0
0
0
2
0
0
1
1
2
0
2
3
2
1
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
2
0
3
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
2
0
0
1
0
2
5
1
0
0
0
2
0
0
0
1
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
1
1
2
0
0
2
0
0
1
0
2
0
0
1
2
0
0
0
0
1
0
0
0
1
0
1
4
2
1
0
0
1
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
2
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
2
0
0
1
0
2
1
0
1
2
0
0
0
2
2
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
1
0
3
0
2
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
3
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
2
0
0
1
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
3
0
0
2
0
2
1
0
2
4
0
2
0
2
3
1
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
2
0
0
1
0
2
2
0
0
2
3
0
0
2
0
2
2
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
1
0
1
0
0
1
3
0
0
0
0
1
3
0
0
0
0
0
0
1
0
0
0
2
1
1
0
0
0
3
0
0
1
2
0
0
1
1
1
2
2
1
0
0
0
0
1
1
0
1
0
1
0
2
0
0
2
0
0
0
0
0
2
0
1
5
0
1
0
1
0
1
0
0
0
2
0
0
0
0
1
4
0
2
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
1
0
2
1
0
0
2
0
0
0
1
3
0
0
2
1
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
1
1
0
0
0
1
0
1
0
1
2
0
1
0
0
0
1
1
0
1
0
0
1
0
1
0
1
0
0
0
0
4
0
1
0
0
1
1
3
0
0
0
2
0
0
0
1
0
0
0
0
2
0
2
0
0
3
0
1
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
2
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
1
3
0
0
2
1
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
0
2
2
0
2
0
1
0
0
1
0
0
0
1
0
0
0
1
2
0
1
1
1
1
0
1
0
0
0
0
0
0
1
0
2
0
0
4
0
1
0
1
2
1
0
0
3
4
1
0
0
0
1
0
0
0
6
0
0
0
3
0
0
2
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
1
2
0
0
1
0
0
0
3
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
2
2
0
2
0
0
0
0
0
4
0
0
0
0
0
0
2
0
2
1
3
0
2
0
3
0
2
0
2
0
0
2
0
0
0
0
0
3
0
0
0
0
0
2
1
1
0
0
0
0
2
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
2
1
1
4
0
0
0
1
1
0
0
0
0
0
2
1
0
1
2
0
0
0
0
0
0
0
2
1
0
0
0
1
2
0
0
0
2
0
0
1
0
1
0
0
0
1
0
1
3
0
0
1
0
0
2
0
1
0
0
2
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
1
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
2
0
0
3
0
0
1
0
2
3
0
0
2
0
0
0
0
2
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
2
1
0
1
0
2
0
1
0
0
1
1
0
0
0
0
0
0
0
3
0
2
1
2
2
2
0
0
0
0
0
2
1
0
1
0
3
0
0
2
1
1
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
2
1
1
0
2
0
0
0
0
0
1
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
1
0
0
2
0
1
0
0
0
2
0
0
1
1
0
0
0
3
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
2
2
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
5
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
3
0
0
1
1
0
2
1
1
0
2
0
0
0
0
1
0
1
2
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
2
2
0
1
1
0
0
0
0
0
0
1
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
2
0
4
2
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
3
0
0
0
0
0
0
0
0
2
0
2
1
2
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
3
0
0
1
1
0
0
1
0
2
3
2
0
0
0
0
0
1
1
1
0
0
2
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
1
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
3
2
2
0
0
0
0
0
1
0
0
0
1
0
0
1
2
0
0
1
0
0
2
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
2
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
2
2
2
0
0
0
0
0
1
0
1
0
0
2
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
1
3
1
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
1
2
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
1
0
1
0
0
2
0
2
0
0
0
4
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
1
0
3
1
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
2
1
0
7
0
0
0
0
0
2
0
0
3
0
1
1
0
2
0
0
1
0
0
0
2
2
0
0
1
1
0
0
0
1
0
3
0
2
0
2
0
0
0
0
1
0
2
2
1
1
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
2
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
1
0
0
0
0
2
0
1
0
2
1
2
0
0
1
0
0
1
0
0
2
1
0
1
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
2
0
0
1
0
2
0
0
0
0
0
1
2
0
3
0
1
3
0
0
0
5
0
2
0
0
0
0
0
2
2
3
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
1
2
1
0
1
1
0
0
1
1
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
1
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
1
1
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
2
0
0
2
0
0
2
1
1
0
0
2
2
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
2
1
1
0
0
0
0
2
0
0
0
2
0
2
3
0
0
2
0
1
0
0
0
2
0
1
0
2
2
1
0
4
0
0
1
1
0
2
0
0
1
0
2
2
0
0
0
0
0
2
0
1
0
0
1
2
0
2
0
1
2
2
2
2
0
5
0
0
1
0
0
0
1
0
2
2
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
3
0
2
0
0
0
0
0
0
2
2
1
0
0
0
0
2
0
1
2
0
3
0
0
0
1
0
0
0
0
12
1
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
1
1
0
1
1
2
0
2
0
0
0
0
0
2
0
0
0
6
0
1
0
1
0
0
0
0
1
0
0
0
1
2
0
0
0
2
1
0
2
0
0
0
0
5
0
0
1
0
3
2
1
0
0
0
0
0
0
0
0
0
2
1
0
3
0
0
0
0
1
1
0
0
0
0
2
0
1
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
2
1
0
1
0
0
1
0
0
0
0
2
2
0
0
0
1
2
0
0
0
0
0
1
0
2
0
0
0
0
1
0
1
0
0
1
2
0
0
0
0
1
0
2
0
0
2
0
1
2
2
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
2
0
1
0
1
1
0
0
1
3
0
0
0
0
2
1
0
2
0
0
0
0
1
0
1
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
2
0
0
0
1
0
2
0
0
0
0
0
2
4
2
0
0
1
1
0
2
0
1
0
2
0
0
2
0
2
0
1
1
0
0
2
0
0
0
0
0
1
2
4
0
5
0
0
1
0
0
0
0
2
0
4
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
3
0
0
2
0
2
0
0
1
0
0
0
0
0
2
0
2
0
3
0
0
0
0
2
1
0
0
1
1
0
0
2
0
0
2
2
0
0
2
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
2
3
0
0
0
0
0
2
0
0
1
5
0
1
0
1
2
0
2
0
0
0
1
2
0
0
0
1
0
1
1
0
1
0
2
0
0
1
0
2
0
2
1
1
0
0
2
0
0
0
1
1
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
1
0
1
2
2
2
1
1
0
0
3
0
0
1
0
0
0
0
1
2
2
1
2
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
2
0
0
0
0
3
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
2
2
0
0
0
0
0
0
1
3
2
0
0
0
2
0
2
0
0
0
1
1
2
2
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
3
0
1
0
0
1
1
0
0
0
0
1
0
0
0
1
2
0
0
2
0
1
3
0
2
0
0
0
0
0
2
1
0
3
0
0
1
0
0
0
2
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
1
2
0
3
0
0
0
2
0
0
0
0
0
0
0
0
2
2
3
0
1
3
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
3
2
1
1
0
0
1
0
1
0
2
2
0
1
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
4
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
3
1
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
2
0
2
0
0
0
2
0
0
0
2
2
1
2
0
0
0
2
0
0
2
1
0
0
3
0
0
1
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
3
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
2
1
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
2
0
3
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
5
0
0
0
0
0
0
1
0
0
1
2
0
0
2
0
0
1
0
1
0
0
1
2
0
1
0
0
0
0
0
2
3
0
0
0
2
2
0
0
0
1
0
2
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
4
0
1
0
1
1
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
2
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
1
3
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
2
2
3
1
0
0
1
0
0
3
2
0
2
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
1
0
2
0
2
0
1
0
2
0
1
0
0
0
0
3
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
1
0
0
0
2
2
0
0
2
0
0
0
0
1
2
2
0
1
0
0
0
0
0
1
2
0
0
3
0
2
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
1
1
0
0
0
1
0
0
0
0
0
1
2
0
3
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
2
2
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
1
2
0
0
0
2
1
0
1
0
1
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
1
0
0
1
0
0
0
2
0
0
0
0
1
2
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
1
0
0
2
0
2
1
0
0
0
0
0
1
2
1
0
0
1
0
0
1
0
2
0
2
4
1
0
2
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
3
2
2
0
0
0
0
0
1
0
0
1
2
1
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
1
0
0
1
0
1
1
2
0
0
0
1
0
0
2
0
0
1
0
1
1
0
1
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
2
0
0
1
0
1
2
0
0
1
0
0
2
4
0
0
0
0
0
3
0
2
2
0
0
0
0
0
1
0
0
0
2
2
0
0
1
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
2
3
1
0
0
6
0
2
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
3
0
0
3
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
2
0
1
0
0
0
0
3
0
0
0
0
1
0
3
5
0
2
1
0
0
1
0
1
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
1
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
2
0
2
0
1
0
1
0
2
0
2
0
0
3
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
2
0
1
0
1
2
1
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
3
0
1
0
1
0
2
0
0
0
0
0
1
0
0
0
0
2
2
0
2
2
0
0
0
2
1
0
0
0
0
2
1
0
0
0
1
0
0
1
0
0
2
2
0
0
0
2
0
0
0
0
1
0
2
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
1
0
0
0
1
2
2
0
1
0
0
1
2
1
0
1
0
1
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
2
0
2
0
2
0
0
3
0
0
2
2
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
1
0
0
0
2
2
0
2
0
0
1
2
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
2
0
1
0
0
0
1
0
1
0
0
0
2
1
1
0
0
2
0
2
0
0
2
1
1
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
2
0
7
2
0
0
2
0
0
0
1
2
0
1
0
0
1
0
0
0
1
2
0
1
0
0
0
1
0
1
1
0
1
0
0
0
0
2
2
0
1
0
0
0
1
0
0
2
0
2
0
0
0
0
2
2
0
0
0
0
1
2
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
4
0
0
0
1
0
2
0
0
0
2
0
3
1
0
0
0
3
0
0
0
0
3
0
0
2
1
1
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
1
1
0
2
2
0
1
0
0
1
0
0
0
0
0
2
1
1
1
2
1
0
0
1
0
0
1
0
0
0
2
0
0
0
0
3
0
0
2
1
0
0
2
1
1
0
0
0
0
4
0
0
0
2
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
1
0
0
0
0
3
0
0
1
2
0
0
0
0
2
1
2
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
1
3
2
1
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
3
0
1
0
0
5
2
0
3
1
0
0
1
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
3
0
2
1
0
1
0
2
0
0
0
0
0
0
0
8
0
0
0
0
0
0
2
0
1
1
0
1
0
2
0
0
0
0
2
0
0
0
0
1
0
0
1
2
2
0
1
0
0
2
0
3
1
1
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
2
0
0
2
0
0
0
1
0
0
4
0
0
0
0
2
2
0
0
1
0
0
2
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
1
2
0
0
0
0
1
2
0
0
0
2
0
2
0
2
1
0
1
0
2
0
0
0
0
2
0
1
1
1
0
0
0
0
1
0
2
1
0
0
0
0
1
0
1
2
0
0
2
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
2
0
0
2
0
0
3
2
1
0
0
0
2
1
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
3
1
0
0
1
0
0
0
2
0
1
2
0
0
4
0
0
3
0
0
0
0
0
0
0
1
2
0
0
0
2
2
1
1
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
1
0
0
1
2
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
3
0
0
1
0
0
1
0
2
0
0
0
2
0
0
0
1
0
0
1
0
0
2
0
1
0
2
0
1
0
2
0
0
2
0
1
0
0
0
1
0
1
0
0
0
0
0
3
2
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
2
2
3
0
0
2
1
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
2
0
0
0
1
0
0
1
1
0
0
0
1
0
1
1
0
2
0
5
0
0
0
0
1
2
0
0
0
2
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
1
0
0
4
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
2
0
1
2
0
0
0
2
0
0
3
0
2
0
2
3
2
0
0
0
1
3
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
3
0
0
0
0
0
1
0
0
0
2
0
1
2
2
3
0
1
0
0
2
1
0
0
0
0
0
3
0
1
0
1
0
0
0
1
0
0
1
1
0
3
0
2
0
0
0
0
1
0
0
2
1
0
0
2
0
0
0
3
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
2
0
1
0
0
2
1
0
0
2
2
2
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
2
0
0
1
2
2
1
0
0
0
0
0
1
0
1
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
2
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
1
0
1
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
1
0
1
2
0
0
0
0
0
1
0
3
0
2
0
2
2
2
0
0
0
1
2
0
0
0
0
1
0
0
2
1
1
0
1
2
0
2
0
1
0
0
0
0
0
0
2
1
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
1
0
0
2
0
1
2
0
2
0
2
0
0
0
2
0
0
3
2
1
0
0
0
0
1
0
1
0
1
0
2
0
0
1
1
1
0
2
2
0
0
1
0
0
0
1
0
1
0
2
0
1
1
1
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
1
2
0
1
2
0
0
1
1
0
0
0
0
0
1
1
0
0
1
0
2
0
0
0
0
0
0
0
2
0
3
2
1
0
1
0
0
0
0
0
1
0
2
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
2
2
2
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
1
1
1
0
1
0
0
2
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
2
0
0
1
0
2
2
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
4
0
0
1
0
0
0
2
0
1
0
2
1
0
2
2
1
2
0
0
0
2
0
0
0
2
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
1
3
1
0
1
0
0
0
0
0
2
2
3
0
1
0
0
0
0
2
1
0
1
1
0
0
1
2
0
1
0
0
0
0
0
1
0
2
0
0
1
2
5
0
1
0
2
0
2
0
2
0
0
0
2
2
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
2
0
1
0
2
0
0
0
0
1
2
3
0
0
0
0
2
1
1
2
0
1
0
0
0
2
2
0
0
0
0
1
0
2
0
0
0
0
1
2
0
1
0
2
0
0
0
0
2
4
0
0
1
0
3
2
2
0
0
0
0
0
0
0
0
1
0
0
4
0
1
0
0
2
0
2
0
0
0
1
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
1
0
1
0
0
2
1
0
2
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
2
2
3
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
1
0
0
1
1
0
0
3
0
0
0
0
0
0
2
0
1
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
1
1
0
2
0
0
0
0
0
1
0
0
0
0
2
0
2
0
2
2
2
0
0
0
1
2
0
2
0
0
2
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
3
2
0
1
1
2
1
0
0
0
0
0
9
0
0
0
4
1
0
2
0
0
0
0
1
0
0
0
0
1
0
2
2
2
2
1
0
0
0
0
0
0
3
0
0
0
1
1
1
0
0
0
0
5
1
2
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
2
1
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
2
3
0
2
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
1
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
1
2
0
1
0
2
0
1
0
0
0
0
2
0
0
2
0
0
0
5
0
0
0
3
2
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
1
2
0
1
1
0
1
2
2
0
0
1
1
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
2
1
0
0
0
0
1
0
0
1
1
0
0
1
4
1
0
2
1
2
0
0
0
1
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
2
0
0
1
1
0
0
0
0
1
1
2
0
0
3
0
0
0
0
0
0
3
0
0
0
1
3
0
0
2
0
0
0
0
0
2
3
0
1
0
0
0
0
0
0
2
0
0
2
1
0
1
0
0
2
0
1
0
0
0
0
1
1
0
0
1
2
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
3
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
1
2
0
0
0
0
2
1
0
0
2
2
1
0
0
2
1
4
0
1
3
0
0
0
0
2
2
0
0
0
0
2
2
0
0
0
0
0
1
1
0
0
2
0
1
2
0
0
0
0
2
0
2
0
0
0
3
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
2
1
0
0
0
1
0
0
1
1
0
2
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
1
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
4
0
1
0
0
0
1
0
1
0
0
1
0
0
0
2
1
0
0
3
0
2
1
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
1
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
2
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
1
0
0
0
1
0
1
0
0
1
2
0
0
0
0
0
1
0
1
0
0
2
0
1
1
1
1
0
0
0
0
0
1
0
2
0
0
2
0
2
0
0
0
3
1
0
1
2
2
0
0
2
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
2
2
0
1
1
0
1
1
1
0
0
0
1
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
1
0
1
0
1
0
2
2
0
2
0
0
0
2
0
0
1
0
0
0
0
2
0
1
0
0
0
2
0
1
0
0
2
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
4
0
0
1
1
0
0
0
0
0
0
3
0
0
0
0
1
0
2
0
0
2
0
3
0
0
0
0
0
1
1
0
0
2
0
0
0
1
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
1
2
0
1
0
1
0
0
0
2
1
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
4
0
0
0
0
0
1
1
0
0
3
1
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
2
0
0
1
0
2
1
0
0
0
2
0
0
0
0
0
0
2
0
1
2
1
2
0
2
1
0
1
1
0
1
3
0
0
0
0
1
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
3
2
2
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
3
0
1
1
3
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
2
0
2
0
0
0
0
0
0
0
1
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
1
2
0
2
0
1
0
0
2
0
0
1
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
1
0
0
0
2
0
0
1
0
0
1
0
2
2
0
0
0
0
0
1
0
2
1
0
0
0
0
1
0
1
2
0
0
2
0
2
0
1
0
1
0
0
0
0
0
0
2
0
0
1
1
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
2
2
0
2
4
0
0
3
0
0
0
6
0
0
1
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
1
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
1
2
0
1
2
0
0
1
1
1
0
2
0
0
0
0
1
0
0
0
0
2
0
0
1
2
2
0
0
1
0
1
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
2
2
1
1
2
0
0
0
1
0
2
1
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
2
2
0
0
2
0
0
0
2
2
0
2
2
0
2
0
2
0
0
0
0
0
8
0
2
2
0
0
0
0
0
0
3
0
0
0
3
0
2
3
0
0
2
2
0
0
0
0
0
0
0
0
2
1
1
1
1
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
2
1
1
0
0
0
0
0
2
1
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
1
0
1
0
0
2
0
1
0
1
2
1
2
1
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
3
0
0
2
2
2
2
2
0
2
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
2
0
0
2
1
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
3
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
2
0
2
0
2
0
3
0
0
0
0
1
1
2
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
1
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
2
0
1
0
1
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
3
1
0
0
2
0
0
0
0
0
0
0
2
0
2
1
0
0
1
1
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
1
1
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
1
0
2
0
2
0
1
2
0
2
1
2
2
0
0
1
0
0
1
0
1
0
1
0
0
0
1
1
0
1
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
2
0
0
2
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
1
0
2
0
0
1
1
0
0
0
1
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
2
3
0
0
1
2
0
1
2
1
1
1
0
1
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
1
0
2
3
1
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
1
2
2
1
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
5
1
0
0
0
0
2
2
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
6
2
1
0
0
1
0
0
0
0
0
0
0
3
2
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
2
2
1
0
1
1
3
0
2
0
2
0
1
0
0
0
3
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
5
0
1
1
2
0
0
2
0
0
0
2
2
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
2
2
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
4
0
2
2
1
4
0
0
0
0
2
2
0
2
0
0
0
0
0
1
0
3
0
2
1
0
0
0
3
1
0
0
0
0
0
3
2
0
1
0
2
2
0
0
1
1
0
0
0
4
0
3
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
2
0
0
2
1
2
0
2
1
0
0
0
3
2
0
1
0
0
1
1
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
6
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
1
1
0
0
0
0
1
2
1
1
0
0
2
0
0
1
2
2
1
1
0
0
3
0
0
0
0
1
2
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
1
0
1
0
1
0
0
2
0
0
0
0
0
0
2
0
1
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
1
0
0
2
0
0
1
0
1
3
1
0
0
4
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
1
2
0
0
2
0
0
0
0
0
0
0
1
0
1
1
2
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
3
0
1
1
0
0
0
0
1
1
0
0
0
0
2
2
0
0
1
2
0
0
0
2
0
1
0
0
0
0
1
1
2
0
1
1
0
0
0
0
1
1
0
0
1
0
0
2
0
1
2
0
2
0
0
0
1
0
0
0
0
0
0
3
0
0
4
1
1
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
1
0
0
1
0
0
1
2
0
0
0
0
2
0
0
0
1
0
0
0
2
3
0
4
0
0
0
0
0
0
0
1
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
1
0
2
2
1
0
0
0
0
2
2
1
0
0
2
3
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
2
0
0
0
0
0
0
0
0
1
3
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
1
3
0
1
0
0
0
0
0
0
2
0
1
0
0
2
0
0
2
0
0
1
0
1
1
2
0
0
1
0
0
0
0
0
0
2
2
0
1
0
1
1
1
0
0
0
0
0
1
0
1
0
2
0
0
2
0
3
2
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
2
0
0
0
0
1
1
0
0
1
0
0
2
0
0
0
0
3
0
0
0
1
0
2
0
0
3
1
2
0
1
1
0
0
0
0
1
0
0
2
2
2
1
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
1
2
0
0
0
2
2
0
0
0
0
1
1
2
0
0
0
0
0
8
0
1
0
0
0
0
3
0
1
0
0
0
0
0
0
1
0
0
0
1
2
0
1
0
0
1
0
0
0
0
3
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
1
0
2
2
2
0
1
0
0
2
2
1
0
0
0
2
1
4
1
0
0
2
2
0
0
1
0
0
3
0
0
1
0
1
0
0
2
0
0
0
2
2
2
0
2
0
0
2
0
0
0
3
0
0
0
0
2
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
1
1
0
0
3
0
0
0
1
0
0
1
0
1
2
0
0
2
0
2
1
2
5
0
0
0
1
2
0
2
0
0
0
1
0
1
2
0
0
0
0
0
0
0
2
2
0
0
4
0
0
1
0
1
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
2
0
1
2
0
0
0
2
2
0
0
0
0
0
1
0
0
2
0
0
1
0
0
1
1
1
0
2
1
2
0
1
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
2
0
2
0
1
1
1
1
2
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
2
0
2
0
0
0
0
2
0
1
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
7
0
1
0
0
2
2
0
2
1
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
2
0
2
2
2
0
0
0
1
0
0
0
2
1
0
2
1
0
0
0
1
2
0
0
1
0
2
0
0
0
2
0
3
0
1
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
1
1
1
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
1
1
1
0
0
2
0
6
0
0
0
2
0
0
2
2
0
2
0
2
0
0
1
0
2
1
1
2
1
0
0
0
0
1
4
0
2
0
0
1
1
0
2
1
0
0
0
0
0
0
3
0
1
0
1
0
1
3
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
1
1
0
0
1
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
2
0
0
2
0
0
1
2
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
1
2
0
0
0
0
0
2
1
2
0
0
0
0
0
0
2
1
0
0
0
1
0
0
2
0
1
0
0
0
0
0
1
1
1
2
0
0
2
2
1
2
1
0
0
0
0
1
0
0
0
0
1
1
1
2
0
0
2
1
0
2
0
0
0
0
2
0
2
2
0
0
0
2
0
0
0
1
0
1
0
0
16
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
5
0
2
1
0
0
0
0
2
0
9
0
0
0
2
0
0
0
0
2
1
0
0
1
0
1
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
2
0
2
0
0
2
1
0
1
0
0
2
0
0
0
0
0
6
1
0
0
1
0
1
0
0
0
2
2
0
1
0
0
2
1
1
0
0
0
2
0
2
0
0
1
0
0
2
0
0
0
0
1
2
0
0
2
0
3
0
0
0
0
0
4
0
0
2
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
2
0
2
2
0
0
3
0
3
2
0
0
1
0
0
0
0
2
0
0
0
3
2
0
2
1
0
0
0
2
0
0
2
0
1
0
0
0
0
1
0
3
0
0
2
0
0
0
1
1
0
0
1
0
0
1
0
0
3
0
1
0
1
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
3
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
2
0
0
2
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
1
2
2
0
1
0
1
1
0
2
2
0
1
2
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
2
0
1
2
0
1
0
0
2
0
0
2
1
1
0
1
0
0
0
1
0
0
1
0
3
0
0
0
0
0
0
0
0
2
1
2
2
0
3
0
3
1
0
3
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
3
0
0
0
0
0
1
2
0
0
1
0
0
0
0
3
0
0
1
0
2
0
0
1
1
0
1
0
1
0
0
2
0
0
2
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
1
1
0
3
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
1
2
0
2
0
0
2
0
0
0
2
0
0
0
1
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
1
0
2
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
2
0
0
2
0
0
2
2
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
2
0
0
0
0
2
0
0
0
3
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
1
2
1
0
0
0
0
0
0
0
2
0
0
1
0
0
1
1
1
0
1
0
1
1
0
1
0
0
2
0
2
0
1
0
1
2
0
2
0
0
0
0
0
0
1
2
1
0
0
0
0
1
1
0
0
0
0
1
2
0
0
2
1
0
0
1
2
0
2
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
1
0
0
0
0
0
2
0
0
2
1
0
1
0
0
0
0
0
2
0
0
1
2
1
2
0
0
1
2
3
0
1
0
0
2
0
0
0
0
2
2
2
0
1
0
1
0
2
2
0
0
0
0
0
2
1
0
1
3
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
1
0
10
2
0
1
0
1
0
0
1
0
2
1
0
0
2
0
2
2
2
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
1
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
2
1
1
0
2
0
0
2
0
0
2
0
0
0
0
1
8
0
0
0
0
0
0
3
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
3
2
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
1
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
1
1
0
0
0
0
0
0
3
2
2
2
0
1
0
0
0
1
0
2
0
0
0
2
0
2
0
0
0
0
1
0
0
2
0
0
0
3
0
2
2
2
1
0
0
1
1
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
1
3
0
0
0
1
0
1
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
1
0
2
2
1
0
1
0
0
0
3
1
3
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
1
2
0
0
1
1
0
0
0
0
1
2
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
3
2
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
1
0
0
0
0
2
2
0
1
0
0
1
0
0
1
0
0
0
0
3
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
1
0
2
0
0
1
0
0
2
0
2
0
1
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
2
0
0
0
3
0
0
0
1
0
1
0
0
1
2
2
1
0
2
1
0
0
1
0
6
0
1
0
4
0
0
0
1
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
6
0
0
0
2
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
1
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
2
0
0
2
1
0
0
2
0
0
0
0
0
1
1
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
1
0
0
1
0
2
0
0
2
0
1
0
2
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
2
0
4
0
3
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
3
0
0
0
0
0
0
0
0
0
0
0
4
1
0
2
0
0
0
0
0
0
1
0
1
0
2
0
2
0
0
0
0
0
2
1
0
0
1
0
0
0
0
1
3
1
0
0
1
2
0
0
0
0
0
0
1
0
0
2
2
0
0
1
0
1
2
1
0
0
0
0
0
1
1
0
0
0
0
0
2
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
1
0
0
4
0
0
2
1
0
0
1
0
2
0
0
2
0
0
1
0
1
2
2
1
0
0
3
0
0
1
0
0
0
0
0
0
2
1
0
1
0
0
2
0
0
0
0
0
2
0
2
1
0
2
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
2
0
0
1
0
0
0
0
0
0
2
1
0
2
1
2
0
1
2
0
2
2
1
0
0
1
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
4
0
1
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
2
0
1
2
1
0
2
1
0
0
0
2
0
0
0
0
0
0
0
1
4
2
1
2
0
0
2
0
2
2
0
2
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
1
2
0
2
0
0
0
2
3
0
0
0
0
0
0
1
2
2
0
2
0
2
0
0
1
0
0
1
0
0
1
0
0
0
2
0
1
0
0
0
2
0
2
0
0
1
0
0
0
2
1
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
3
3
0
0
0
1
0
0
3
1
0
0
2
1
0
1
1
0
0
1
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
2
0
1
0
0
3
2
0
0
0
0
0
0
1
0
2
0
0
0
2
1
3
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
2
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
1
2
0
0
0
0
0
0
0
1
2
0
0
0
1
1
1
0
0
2
1
3
0
0
0
0
0
2
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
1
2
0
2
0
1
0
1
1
0
0
0
0
2
1
0
0
2
0
0
2
0
0
0
0
4
0
4
0
2
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
1
1
0
1
2
0
2
0
0
0
0
0
0
1
0
2
1
1
0
2
8
0
0
0
0
3
0
0
0
1
0
0
0
0
3
0
0
0
0
0
1
1
0
2
1
0
0
1
0
0
1
4
0
2
0
1
0
2
1
0
0
0
2
0
2
3
0
2
3
1
0
0
0
0
1
0
2
3
0
2
0
1
0
2
2
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
2
2
0
0
0
0
1
2
1
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
2
0
1
1
0
0
1
0
2
0
0
2
0
1
0
0
1
0
0
2
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
2
0
1
0
0
1
2
0
0
0
0
0
2
1
0
2
0
0
2
1
2
0
1
0
0
0
2
0
0
0
2
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
3
2
0
1
0
0
0
0
0
1
0
0
0
2
0
3
0
0
2
2
1
0
0
2
0
1
2
0
0
0
0
0
1
2
2
2
0
0
0
2
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
2
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
2
1
0
1
0
0
0
0
0
0
2
1
0
1
0
0
5
0
2
0
0
0
0
1
1
3
0
0
1
0
0
0
0
3
0
0
0
1
0
1
2
0
0
2
0
0
0
0
2
0
0
1
0
0
0
1
0
2
0
0
7
2
0
0
0
3
1
1
1
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
2
3
0
0
0
0
1
0
1
0
0
5
0
2
0
1
0
0
2
2
1
0
0
0
0
2
2
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
2
1
0
2
0
0
0
1
2
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
2
0
0
2
0
0
0
1
0
2
0
0
0
0
2
1
0
0
1
2
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
2
0
0
2
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
2
0
2
1
0
0
0
0
2
0
2
0
1
0
3
0
3
0
2
0
0
0
1
2
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
3
0
0
0
1
0
0
0
1
0
0
0
0
2
1
0
0
0
0
1
3
2
1
0
0
0
0
0
0
0
1
1
2
1
2
0
1
1
0
2
0
0
0
0
0
0
2
0
0
0
1
3
0
0
0
1
1
0
1
0
3
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
2
2
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
1
1
1
0
0
0
0
0
0
2
1
0
0
0
0
1
2
0
0
1
2
1
0
0
0
0
0
0
0
0
3
0
2
0
1
0
0
0
0
0
0
0
0
1
2
0
2
0
0
2
0
0
1
2
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
2
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
2
1
1
0
0
0
0
0
0
0
2
1
1
2
0
1
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
2
1
1
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
3
0
0
0
2
0
0
0
1
1
1
1
0
2
2
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
1
0
2
0
0
2
0
0
0
0
2
0
0
1
0
1
1
1
2
2
0
1
0
0
0
0
0
3
0
1
0
2
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
1
0
1
1
0
0
0
1
0
0
2
0
4
0
0
1
2
0
0
1
2
1
2
1
0
0
0
2
0
0
1
0
0
0
0
2
0
2
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
1
1
2
0
0
0
2
0
2
0
0
0
2
0
3
0
2
0
1
0
0
0
0
0
0
0
1
0
2
0
0
2
1
0
0
2
0
0
0
0
0
1
0
0
2
3
0
0
0
2
2
0
0
2
1
2
0
0
0
0
2
0
2
0
0
0
1
0
1
1
0
0
2
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
1
3
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
2
0
2
2
0
1
0
1
0
2
0
2
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
1
0
0
1
1
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
1
0
1
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
2
1
2
1
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
2
0
1
0
0
3
2
0
0
1
1
0
0
1
0
1
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
2
1
0
0
0
3
0
0
0
1
2
0
0
1
0
0
0
0
1
0
0
0
2
0
1
0
0
0
2
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
1
2
0
1
2
3
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
2
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
1
2
0
0
2
0
0
0
0
1
0
0
2
2
2
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
2
1
2
0
0
2
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
1
0
2
0
0
0
1
0
0
2
0
0
1
1
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
1
0
0
2
0
0
0
7
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
1
0
1
3
0
0
0
2
2
0
2
0
0
0
1
0
2
1
0
1
2
0
0
2
0
0
0
0
2
0
0
0
0
1
1
0
0
3
0
2
1
1
0
0
0
0
1
0
0
0
0
2
0
0
3
0
0
0
0
1
0
0
0
2
0
0
0
1
2
0
2
0
4
0
0
0
0
0
1
1
0
0
0
0
2
2
0
0
0
2
0
1
0
2
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
2
1
0
1
0
0
0
0
1
0
0
0
0
2
2
0
0
3
0
0
1
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
2
1
1
0
2
2
4
0
2
2
2
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
2
2
0
0
0
2
0
0
0
0
1
0
2
0
0
7
0
1
0
0
0
1
1
0
1
6
0
2
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
2
3
0
0
1
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
2
0
2
3
0
2
0
1
0
1
0
2
0
0
0
0
1
0
0
2
1
0
0
0
1
0
1
2
2
0
1
2
0
0
0
2
0
1
0
0
2
0
2
0
0
0
0
4
0
0
0
0
0
2
0
0
1
0
1
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
1
2
0
0
0
1
0
1
0
0
0
1
1
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
1
0
0
0
0
0
0
1
1
1
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
2
0
0
4
1
0
1
0
2
0
0
2
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
2
2
2
0
0
0
0
0
0
0
0
0
1
1
0
0
2
2
0
0
2
2
0
2
0
0
2
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
2
2
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
1
0
0
0
2
0
0
2
0
1
1
1
1
0
0
2
0
3
0
0
0
2
1
0
0
0
1
0
0
7
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
2
0
1
1
0
0
0
2
0
0
1
0
0
0
0
1
1
0
0
2
0
2
1
0
0
1
0
0
0
0
2
0
0
2
1
0
1
0
0
0
0
1
0
0
0
1
2
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
2
0
0
0
2
2
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
1
2
1
0
0
0
1
0
1
2
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
2
2
2
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
7
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
2
1
2
2
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
2
0
1
2
0
0
1
0
1
0
0
0
0
1
0
1
0
1
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
2
0
0
1
1
0
0
0
0
1
1
0
1
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
9
0
2
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
1
1
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
1
0
2
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
1
1
2
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
3
0
1
1
0
2
1
2
1
0
2
3
0
0
2
2
2
0
0
0
0
0
0
0
0
0
1
0
1
2
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
2
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
3
0
0
2
0
0
2
0
0
0
0
0
0
0
1
3
0
0
0
2
1
0
1
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
2
1
0
0
0
0
0
0
0
0
1
2
0
0
0
1
1
0
1
0
0
0
2
2
1
0
2
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
1
0
1
0
0
1
0
1
0
2
1
0
0
0
1
2
0
0
1
1
2
0
0
0
0
1
0
0
0
0
1
4
1
0
0
0
2
3
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
3
5
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
1
1
1
0
0
0
0
0
0
2
0
0
2
2
0
0
0
1
0
2
0
0
1
0
2
0
0
1
0
2
0
0
0
2
1
0
0
0
1
1
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
3
0
0
0
0
0
2
1
0
0
2
0
0
1
1
0
0
1
2
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
2
3
2
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
1
2
1
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
2
2
0
2
0
3
1
0
0
4
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
1
0
0
2
2
0
0
0
2
1
0
0
0
0
0
1
1
0
4
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
2
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
1
0
2
0
0
1
0
1
1
2
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
1
0
2
0
0
0
0
2
0
0
1
0
1
0
2
0
0
1
1
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
2
0
1
2
0
0
0
0
0
0
0
2
2
1
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
2
0
2
0
1
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
2
0
0
2
0
4
2
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
2
0
3
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
2
3
0
0
0
1
0
0
0
0
0
0
0
5
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
4
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
3
0
2
2
2
0
0
0
0
2
2
1
0
0
2
0
0
0
0
1
0
0
2
3
2
0
0
0
0
0
0
1
0
0
2
1
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
2
1
0
1
1
0
0
0
0
1
0
0
0
0
2
2
0
1
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
3
0
0
0
0
1
0
0
1
2
0
0
0
0
1
0
3
1
0
0
2
1
0
1
0
0
0
0
4
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
2
1
2
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
4
1
2
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
2
0
1
0
4
0
0
1
0
0
2
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
3
2
1
0
0
0
0
2
1
1
1
0
0
1
0
0
2
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
1
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
2
0
3
2
0
2
1
0
1
0
0
0
1
0
1
0
0
2
0
0
0
0
2
0
2
0
1
1
1
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
2
1
0
0
0
0
1
1
0
1
1
2
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
2
1
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
5
1
0
1
2
9
0
0
0
1
0
0
2
0
0
2
0
0
0
0
1
0
1
0
0
0
0
1
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
1
0
0
5
0
2
0
0
0
0
1
0
0
0
3
0
0
2
0
0
0
0
0
0
0
1
0
2
2
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
2
3
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
1
0
0
0
0
3
2
2
0
0
1
0
2
0
0
1
0
0
0
1
0
0
0
0
2
2
2
0
1
0
0
1
1
0
0
1
0
0
1
1
1
0
1
2
3
1
0
0
0
1
2
0
0
0
2
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
11
0
0
0
0
0
0
2
1
2
1
1
0
0
0
1
0
0
2
0
2
2
0
1
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
1
0
0
1
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
1
1
2
0
0
1
1
0
2
0
1
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
2
0
0
0
3
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
2
2
0
0
1
0
0
0
0
1
1
0
0
0
0
2
1
0
0
1
1
1
0
0
0
0
0
0
2
0
0
0
1
1
1
0
0
0
0
3
0
2
2
0
1
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
3
0
3
0
0
1
0
0
1
0
2
0
1
0
2
0
2
2
3
0
1
0
0
0
0
0
1
0
1
1
1
0
1
1
0
0
4
0
0
0
0
0
0
0
2
2
1
0
2
0
0
0
2
0
0
0
0
0
1
0
0
2
2
1
0
0
1
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
2
2
0
0
0
0
4
1
0
2
0
0
0
1
0
0
0
2
0
1
2
2
0
0
1
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
3
1
0
0
2
0
0
0
1
1
0
1
0
0
2
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
2
2
0
0
1
2
0
3
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
2
2
0
0
2
0
2
0
4
2
0
0
0
2
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
1
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
2
0
1
0
2
0
0
0
2
1
0
2
0
0
2
1
0
0
0
0
0
0
2
3
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
4
0
0
2
2
0
2
1
0
2
0
0
0
1
0
2
2
0
0
2
6
0
2
0
0
0
2
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
5
2
1
2
0
0
0
0
0
2
0
1
1
0
0
0
1
0
1
0
0
0
3
0
0
2
0
0
1
0
0
0
0
2
1
0
0
1
0
0
4
0
2
0
0
0
0
1
0
0
1
0
0
0
1
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
3
2
1
0
0
3
3
0
0
1
0
2
0
0
0
1
0
4
0
1
0
0
0
0
0
1
0
4
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
1
4
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
1
0
0
2
0
1
1
1
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
3
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
3
0
1
1
0
1
1
0
0
0
0
3
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
3
0
0
1
1
2
0
1
2
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
8
0
0
2
2
0
0
0
0
1
2
0
0
0
0
0
2
0
2
0
0
0
2
0
0
3
1
1
0
0
0
0
3
0
0
0
2
0
0
0
2
1
0
0
0
2
0
0
0
0
2
1
0
2
0
0
0
0
0
2
0
1
0
0
1
0
0
0
1
1
2
0
1
0
0
1
0
0
0
0
1
0
1
0
0
2
0
2
0
1
1
3
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
1
0
0
0
1
3
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
2
0
0
2
1
0
0
1
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
1
1
2
1
1
2
0
0
1
2
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
2
0
1
0
2
3
1
0
0
0
0
2
0
2
1
1
0
0
0
0
0
0
0
1
0
0
1
2
1
2
0
1
0
0
1
0
0
2
0
0
2
0
0
2
0
0
0
0
1
3
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
2
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
1
0
2
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
2
1
0
0
0
0
1
0
2
0
0
0
0
0
1
1
1
0
0
0
0
0
2
0
2
0
0
0
0
0
2
2
0
1
1
0
1
0
2
0
4
0
0
2
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
1
2
1
1
2
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
2
2
0
0
0
1
2
3
0
0
1
0
1
0
0
0
0
1
0
1
0
2
0
0
0
3
0
1
1
1
2
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
2
0
2
1
1
0
0
0
0
0
0
0
1
0
0
4
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
2
0
0
0
1
5
0
0
0
1
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
3
1
0
0
0
0
0
1
2
0
1
0
0
0
0
2
2
0
0
3
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
2
2
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
2
1
2
2
0
0
0
0
0
1
2
1
0
0
2
0
2
0
0
0
1
0
0
6
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
2
0
2
2
1
1
2
0
1
1
0
0
0
0
0
0
0
1
5
0
0
0
0
0
0
0
0
3
1
2
0
1
0
2
1
0
0
1
2
1
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
1
1
2
1
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
1
0
0
1
2
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
1
2
0
2
0
0
2
0
2
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
2
2
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
2
2
1
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
3
0
2
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
2
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
1
0
3
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
2
0
0
1
1
2
0
0
0
2
0
0
1
6
0
0
0
0
0
0
1
1
2
0
0
1
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
1
2
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
2
2
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
1
2
1
1
0
0
1
0
0
2
1
0
1
0
0
0
0
2
0
3
0
0
0
4
0
1
0
0
0
0
1
1
0
0
0
3
2
0
0
2
2
0
3
0
1
0
3
0
0
2
1
0
1
1
0
0
0
0
0
0
2
0
0
2
1
0
2
0
0
0
0
1
0
0
0
0
2
0
2
3
0
2
1
0
2
1
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
1
0
1
1
0
0
2
0
2
0
0
0
0
0
1
2
0
2
2
0
0
1
0
0
1
1
0
0
1
0
0
0
2
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
1
1
0
0
2
1
0
0
0
1
0
0
0
0
2
1
2
2
0
0
0
1
0
0
1
1
0
0
2
0
1
2
0
0
0
0
2
0
0
0
0
0
2
0
0
3
0
1
0
0
0
1
1
1
0
0
1
0
0
1
1
1
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
2
0
2
0
1
0
0
1
0
0
0
0
0
0
0
1
0
3
0
2
0
0
2
0
1
1
2
3
0
0
0
2
2
0
1
1
0
0
0
0
0
2
1
0
0
0
0
2
2
0
0
2
0
1
0
0
0
0
1
0
2
1
2
0
0
1
0
0
2
0
0
0
0
1
1
0
0
0
0
0
3
0
0
0
0
1
1
0
0
0
1
0
1
0
0
2
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
2
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
3
0
0
1
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
1
2
0
1
0
1
0
0
0
2
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
2
2
1
0
0
0
0
0
0
0
1
0
1
0
0
0
2
1
0
0
1
0
0
0
0
0
2
0
0
1
0
2
1
0
1
0
1
0
0
0
0
2
0
0
3
0
0
0
0
0
2
1
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
1
3
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
6
0
0
1
1
1
0
0
1
0
0
0
0
0
2
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
2
2
0
0
0
0
2
0
0
2
0
0
0
2
0
0
2
0
0
1
2
1
1
0
0
0
0
1
0
2
0
7
0
2
3
0
0
1
0
0
1
0
0
0
0
0
3
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
2
0
1
1
1
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
1
0
1
0
0
2
1
3
0
0
1
0
0
0
1
0
0
2
0
0
1
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
2
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
2
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
1
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
1
1
0
0
0
2
0
1
0
0
0
0
0
1
1
2
0
1
0
0
0
0
0
2
2
2
0
0
1
2
0
1
0
0
0
0
0
0
0
1
2
1
8
0
1
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
2
2
0
0
0
0
0
2
2
0
0
2
0
1
2
0
1
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
1
0
2
0
1
0
1
0
2
0
2
1
2
2
2
1
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
1
0
0
1
0
2
2
2
0
0
1
2
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
1
1
0
0
0
1
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
1
0
0
1
1
0
0
1
1
2
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
1
5
0
1
0
0
0
1
0
0
0
0
2
1
1
2
0
0
0
2
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
3
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
2
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
4
1
2
0
1
0
0
3
0
0
0
0
0
2
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
2
1
2
3
1
0
1
2
0
0
0
1
1
0
1
0
0
2
0
2
0
0
2
0
0
0
2
0
0
0
0
2
0
0
1
0
1
0
1
1
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
2
2
0
1
0
1
1
0
2
0
1
0
0
1
0
0
1
0
0
0
1
2
0
0
2
1
0
0
0
2
1
0
0
0
0
1
0
0
0
1
0
2
0
1
0
0
0
0
0
2
0
3
0
0
1
0
1
0
1
1
0
2
0
2
2
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
1
0
0
2
1
0
0
2
0
0
0
0
0
1
5
0
0
0
3
1
0
2
2
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
2
2
0
0
0
0
0
0
0
0
2
0
1
2
0
2
0
1
0
1
0
1
1
0
1
2
1
0
0
0
2
2
0
2
0
0
0
0
1
0
0
1
0
0
0
0
3
0
0
1
0
0
2
0
0
2
1
0
0
0
1
0
0
3
2
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
2
2
0
0
0
1
1
0
2
0
0
2
0
1
0
3
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
2
2
0
0
0
0
2
2
1
0
2
1
0
1
3
4
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
6
0
1
0
3
1
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
1
0
3
1
0
1
0
2
0
0
0
0
0
2
0
0
2
1
2
1
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
2
0
1
0
0
2
2
2
0
0
0
0
0
1
0
2
1
0
2
2
0
0
0
2
0
1
0
3
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
3
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
2
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
1
1
0
0
2
3
1
0
0
0
0
1
0
1
1
0
2
1
1
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
2
0
1
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
1
1
0
0
2
2
1
1
2
0
0
1
1
0
1
0
0
2
2
0
0
2
3
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
1
2
0
1
0
2
0
2
2
0
0
0
2
0
1
0
0
0
1
2
0
5
2
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
2
4
0
1
0
1
0
0
0
0
0
0
2
0
2
0
2
2
0
1
2
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
2
0
0
1
0
2
1
2
0
0
0
0
2
0
0
0
1
1
0
1
1
3
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
4
1
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
1
0
0
2
0
0
4
2
2
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
1
2
0
0
0
0
0
0
0
2
0
0
1
0
2
1
0
0
0
2
0
0
2
0
0
1
0
1
0
2
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
2
3
1
0
2
0
0
1
0
0
0
0
0
0
5
0
2
1
2
0
0
0
0
0
0
1
1
2
2
0
0
2
0
1
0
0
0
0
0
3
1
2
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
2
3
2
0
0
0
1
0
3
4
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
1
1
0
1
0
0
3
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
2
1
0
0
1
1
2
0
0
0
1
0
3
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
2
1
3
2
0
0
0
2
0
2
0
0
1
0
1
0
0
0
3
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
3
0
0
1
0
1
0
1
0
0
1
1
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
2
0
0
1
0
0
0
0
1
0
0
1
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
2
0
0
0
1
0
0
1
2
0
0
4
0
0
1
0
0
0
1
0
1
0
0
1
0
0
2
0
0
0
0
0
1
1
1
0
1
2
2
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
2
0
2
0
0
0
0
0
0
0
0
1
2
0
1
1
0
2
1
0
0
0
0
2
0
0
1
0
1
1
1
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
1
2
2
0
0
0
0
1
0
3
1
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
2
0
2
2
0
0
0
0
0
0
3
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
2
0
0
2
0
0
2
0
2
1
0
1
2
0
2
1
0
0
0
0
2
2
0
2
0
1
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
2
0
0
0
0
0
0
1
2
0
2
0
0
0
1
0
1
1
0
0
0
1
1
0
0
1
0
0
0
2
0
2
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
1
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
2
0
0
0
0
2
0
0
0
1
1
0
2
2
0
2
0
2
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
9
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
2
0
2
3
0
0
1
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
2
2
2
0
0
2
0
0
1
1
2
0
0
0
1
0
0
0
0
0
0
1
2
1
2
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
2
0
2
0
1
0
0
0
1
0
1
1
0
0
1
2
1
0
0
0
0
0
2
0
1
0
1
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
1
0
2
0
2
0
2
0
0
0
0
0
0
3
3
0
0
1
0
1
0
0
0
0
0
4
1
0
1
0
0
0
2
0
0
0
2
0
0
1
1
0
2
0
0
0
0
1
0
4
0
2
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
3
0
5
2
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
1
1
0
0
0
0
0
0
3
1
2
0
2
1
0
0
1
1
0
0
0
0
0
2
2
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
4
1
0
0
0
0
0
1
0
0
0
2
0
2
0
0
1
2
1
1
0
1
2
0
1
0
0
1
2
0
1
0
0
0
0
2
5
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
7
2
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
3
0
2
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
1
0
3
0
0
2
0
0
2
0
0
0
0
1
0
0
2
1
0
2
0
0
0
0
2
0
2
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
2
0
2
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
1
1
2
0
0
0
2
1
1
0
0
0
0
2
0
0
0
0
2
0
0
1
0
3
0
0
2
0
0
2
0
0
0
0
0
2
1
1
0
1
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
2
0
2
2
0
0
0
0
1
0
1
0
0
0
1
0
1
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
4
1
1
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
2
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
3
1
0
0
0
0
0
2
2
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
2
1
0
0
4
0
0
1
1
3
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
1
0
0
0
0
2
3
0
0
0
0
0
2
0
1
0
0
0
0
3
1
0
0
0
0
0
2
0
0
2
0
2
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
2
2
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
1
1
1
0
1
0
2
0
0
0
0
1
1
2
0
1
0
0
1
0
0
3
0
0
0
0
2
0
2
0
2
0
1
1
0
0
0
0
0
0
0
0
1
1
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
2
0
0
1
0
1
0
0
2
1
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
1
0
3
0
0
7
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
2
0
0
0
0
0
0
0
0
2
0
1
2
1
0
0
0
0
1
1
0
2
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
2
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
3
0
2
0
0
0
0
0
2
2
0
0
1
0
0
0
2
0
0
1
3
0
3
1
0
0
4
2
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
2
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
1
0
3
0
1
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
2
1
0
0
0
2
0
2
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
1
2
1
1
0
2
0
0
2
0
0
3
0
0
2
0
0
0
1
0
0
0
2
0
0
0
1
2
0
3
0
1
0
0
0
1
0
0
1
1
0
2
0
2
0
0
0
0
0
2
0
0
2
0
0
0
1
2
0
1
2
2
0
1
0
0
0
0
1
0
0
2
2
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
1
0
3
0
0
0
0
0
2
0
0
0
2
0
0
0
2
3
0
0
2
0
0
0
0
0
0
2
1
0
1
0
1
0
0
0
0
2
0
0
0
2
0
2
0
0
0
1
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
3
0
2
1
2
0
1
0
0
0
0
0
2
2
0
2
0
0
0
0
2
0
0
0
0
2
1
0
0
2
0
0
1
0
0
0
0
2
0
2
1
0
0
0
0
2
0
0
2
0
0
0
2
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
2
2
0
1
0
1
1
0
2
1
0
0
2
0
0
0
0
1
0
0
0
2
0
0
2
1
0
2
2
1
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
1
1
0
0
2
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
2
1
0
1
1
2
0
0
0
0
0
2
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
3
0
1
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
3
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
1
2
0
0
1
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
2
3
0
2
0
0
0
1
0
0
2
2
5
3
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
2
2
1
2
0
0
2
0
1
1
0
0
0
1
1
1
0
0
0
0
9
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
1
2
0
0
0
0
0
1
1
1
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
2
3
1
0
0
0
0
3
0
2
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
3
0
0
2
2
0
0
2
0
0
0
2
1
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
2
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
1
0
2
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
1
0
3
0
0
2
0
0
0
2
0
2
2
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
3
0
1
0
0
0
0
2
0
0
2
1
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
2
0
2
0
1
0
3
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
2
0
2
1
0
0
0
3
0
3
0
0
1
1
1
1
0
0
2
1
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
1
0
0
0
0
2
0
0
0
1
0
0
2
4
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
2
0
2
0
2
0
1
2
0
1
0
0
0
1
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
3
0
0
0
1
1
0
2
0
0
0
0
1
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
2
0
7
1
0
0
0
0
0
2
1
2
0
2
0
0
0
0
0
0
0
2
1
0
0
2
1
0
0
0
2
0
1
1
2
0
0
1
0
1
0
0
0
0
4
0
2
0
0
1
0
0
1
2
0
2
1
0
1
1
2
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
1
1
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
2
3
2
0
2
0
2
0
0
0
2
0
2
0
0
2
1
0
0
0
1
2
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
3
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
2
3
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
5
2
2
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
4
1
1
2
0
0
0
0
3
0
0
1
0
0
0
0
0
1
0
2
1
0
2
1
0
0
0
2
2
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
1
1
0
0
2
2
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
2
1
0
0
0
1
0
0
0
1
0
0
0
0
0
2
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
1
1
0
0
1
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
2
0
2
0
0
0
0
3
0
1
0
0
0
0
2
0
2
0
0
0
2
0
0
3
0
0
1
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
1
1
0
0
2
0
0
0
0
0
0
2
2
0
1
0
0
0
1
3
2
0
1
0
0
0
0
0
1
0
2
2
0
1
0
0
0
0
0
0
2
2
0
0
0
4
2
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
9
1
0
2
0
1
1
1
4
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
1
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
1
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
6
0
0
1
0
0
2
2
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
2
2
0
1
1
0
0
0
0
0
0
2
0
4
2
0
0
0
1
0
0
0
0
0
0
2
1
1
2
1
1
1
0
0
0
0
2
1
0
0
0
2
1
1
0
2
0
0
0
0
2
1
0
2
0
0
0
1
2
0
0
0
1
0
3
1
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
2
1
1
0
0
1
0
0
0
2
2
0
0
0
0
2
0
0
2
0
0
2
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
1
2
0
1
1
0
0
0
0
4
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
2
2
0
0
0
0
3
0
0
0
2
2
2
0
0
0
0
0
1
0
0
4
0
0
2
0
0
0
2
0
1
1
0
0
0
0
0
0
0
1
0
0
0
2
1
2
4
0
0
1
1
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
1
1
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
1
0
0
1
2
0
1
0
1
2
0
0
0
0
0
0
0
0
3
0
0
2
1
0
0
0
2
1
0
2
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
1
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
1
2
0
0
1
0
2
2
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
1
1
1
0
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
1
0
0
1
0
4
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
1
7
2
1
0
0
0
2
2
2
0
1
0
1
0
0
1
2
1
0
0
2
0
0
1
0
0
2
0
0
2
0
0
0
2
0
0
0
1
0
1
0
0
0
2
0
0
1
0
1
0
0
1
0
1
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
1
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
2
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
2
2
1
0
0
0
0
0
1
2
2
0
2
0
2
0
2
0
0
1
0
0
0
1
0
1
0
0
0
0
2
0
0
0
1
0
0
1
2
1
0
0
0
0
0
2
1
0
0
2
1
2
0
0
0
1
0
0
1
0
0
0
0
0
0
1
2
1
3
2
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
2
2
1
0
0
0
0
5
0
1
0
0
0
1
0
1
0
1
0
0
0
0
2
2
0
0
0
0
1
0
0
0
1
0
0
3
0
0
2
0
1
1
0
0
2
0
0
0
1
1
1
0
0
0
2
0
1
1
0
0
1
0
2
3
2
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
1
0
0
2
0
1
0
0
1
0
3
0
0
0
0
3
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
1
2
0
1
2
0
0
2
0
2
0
0
0
2
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
1
0
0
0
2
0
1
0
0
0
0
0
0
1
1
2
1
1
0
0
1
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
2
1
2
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
1
0
0
1
2
2
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
2
0
0
0
2
0
2
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
10
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
1
1
2
0
2
2
0
0
0
0
0
2
0
1
0
2
1
0
1
0
0
2
0
0
0
5
0
0
0
2
0
0
0
0
1
0
0
0
0
1
2
1
0
0
1
2
1
2
0
0
1
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
3
2
0
0
1
0
2
0
2
1
3
0
2
0
0
0
0
0
0
2
0
2
1
0
0
3
1
0
1
1
0
0
0
1
0
2
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
3
1
0
0
0
0
0
1
2
1
0
0
0
1
0
1
1
0
0
2
0
1
2
1
1
0
0
1
0
0
1
0
0
0
0
2
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
2
2
0
0
0
0
0
1
1
0
0
0
0
5
1
0
0
1
0
0
1
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
1
5
1
0
0
1
0
0
0
2
2
1
1
0
0
3
0
1
3
0
1
2
0
0
2
0
2
0
0
0
1
2
0
0
1
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
2
2
0
2
2
1
0
1
0
0
0
2
0
0
2
0
3
0
0
0
1
0
2
0
0
2
0
1
1
0
2
0
0
0
1
1
0
0
2
0
1
0
0
0
0
0
2
0
0
2
1
0
0
0
0
2
3
2
0
2
1
0
2
2
0
0
1
0
0
0
0
0
5
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
2
0
0
0
2
0
0
0
0
1
0
1
0
2
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
2
0
2
3
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
2
0
0
0
0
2
1
3
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
2
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
1
0
0
2
0
1
0
0
0
0
1
2
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
3
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
2
0
1
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
2
0
1
1
1
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
1
0
1
1
2
3
2
0
0
2
0
1
1
0
1
0
0
2
1
0
1
0
0
0
1
0
1
0
0
0
2
0
1
1
2
2
1
1
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
2
0
1
0
1
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
2
0
2
0
2
2
0
0
0
0
0
0
3
0
0
0
2
0
0
0
1
0
0
0
2
0
2
3
0
0
0
0
1
0
2
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
5
0
2
2
0
2
0
0
0
0
2
0
1
0
0
3
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
1
0
1
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
2
0
0
1
0
2
3
0
2
0
0
1
0
1
0
2
0
0
0
1
1
0
0
0
0
2
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
2
1
0
1
1
0
0
0
0
1
3
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
3
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
2
0
0
1
0
1
0
0
0
1
1
0
0
0
4
0
0
0
0
0
1
0
2
0
0
1
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
3
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
7
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
1
1
1
0
0
0
1
0
5
0
0
0
0
2
1
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
2
1
0
0
2
0
1
2
2
2
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
3
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
1
0
0
0
2
1
0
1
0
0
1
0
1
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
4
2
0
1
0
2
0
0
0
0
2
0
0
2
2
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
1
2
0
0
0
0
1
0
2
1
2
0
2
2
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
3
0
0
1
0
1
0
0
0
0
2
2
1
0
1
0
1
0
0
1
1
1
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
6
0
0
2
0
1
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
1
0
2
1
0
0
1
1
0
2
1
0
2
2
0
1
0
0
0
2
1
0
0
0
0
1
0
1
3
0
0
1
0
0
0
0
0
1
0
0
0
2
3
0
0
1
0
0
1
0
0
0
2
0
0
0
2
0
2
1
0
1
0
0
0
0
3
3
0
0
0
1
0
2
0
0
0
2
2
0
1
0
2
0
0
0
2
4
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
2
1
0
0
2
0
0
1
0
0
0
0
0
0
2
1
2
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
1
0
0
2
1
2
0
0
0
0
2
0
0
1
0
3
2
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
2
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
1
2
1
2
0
2
0
2
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
4
1
0
0
1
0
0
0
0
0
0
0
1
2
1
0
1
1
1
0
0
0
3
0
0
0
2
0
0
0
2
3
0
0
2
0
2
0
2
0
0
0
1
3
0
0
1
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
2
1
0
2
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
1
1
0
1
0
0
1
0
1
0
0
0
0
4
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
3
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
1
0
2
0
0
1
0
2
2
1
0
1
0
0
0
0
0
0
0
0
0
1
2
0
2
1
0
1
0
1
0
2
1
0
2
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
1
1
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
1
1
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
5
0
2
2
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
3
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
3
1
2
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
5
0
1
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
1
2
0
2
0
0
0
2
2
2
1
2
2
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
2
0
0
3
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
1
2
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
2
0
2
0
0
1
1
2
1
0
1
0
0
2
0
1
1
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
1
0
0
1
0
0
2
2
0
0
2
0
0
1
0
0
2
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
5
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
1
3
0
0
0
0
2
0
0
2
0
2
0
1
0
0
1
0
0
1
2
1
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
2
2
1
1
4
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
2
2
0
2
2
1
1
0
2
2
0
0
2
0
0
2
0
0
0
0
3
1
0
1
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
3
0
0
2
0
0
0
2
2
4
1
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
1
5
1
0
0
2
2
4
0
2
0
0
0
0
0
3
1
1
1
0
0
0
0
1
0
0
0
0
0
5
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
2
1
2
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
1
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
3
1
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
2
0
0
0
1
1
0
1
2
2
2
1
0
1
0
0
0
0
0
0
0
0
2
3
0
0
0
1
0
1
0
0
0
0
2
0
0
4
0
0
0
1
0
0
0
2
0
2
1
1
0
2
1
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
1
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
1
0
0
0
0
1
0
3
0
0
0
0
2
2
1
0
0
0
0
0
2
0
0
2
0
0
2
2
0
0
0
0
0
1
1
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
1
2
0
1
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
2
1
0
0
0
2
0
0
0
2
0
1
0
0
2
1
0
0
1
1
1
0
0
0
1
0
0
1
1
0
1
2
2
3
2
0
0
0
1
3
0
2
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
1
2
1
0
0
0
4
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
1
1
0
0
1
0
2
0
2
1
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
1
0
1
1
0
1
0
1
0
0
1
1
0
1
0
0
1
1
1
0
0
1
1
2
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
2
2
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
4
0
2
0
0
0
0
2
2
1
0
0
0
0
0
1
0
2
0
2
1
1
0
0
2
0
3
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
1
0
2
0
0
1
0
0
0
2
1
1
0
0
1
2
0
0
0
1
2
0
1
0
0
0
2
0
1
3
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
2
0
0
1
0
0
2
5
0
2
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
4
0
1
0
2
0
3
0
0
1
2
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
1
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
2
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
2
0
1
2
0
0
0
2
0
0
0
2
1
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
3
3
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
1
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
2
0
2
0
0
0
0
0
2
1
0
2
0
0
0
0
0
1
1
0
2
0
0
0
2
0
0
0
0
1
0
2
2
0
0
0
0
0
2
2
0
3
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
3
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
2
1
1
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
2
0
0
1
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
1
2
0
0
2
0
2
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
1
1
0
2
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
1
1
0
0
0
0
0
3
0
1
0
0
0
0
0
1
0
9
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
4
0
0
0
1
3
0
0
1
1
3
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
2
0
2
3
0
0
0
1
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
1
1
0
0
0
0
1
4
0
2
0
0
0
0
1
0
1
0
1
0
1
0
0
2
2
0
0
0
0
0
0
0
5
0
2
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
1
0
3
0
0
0
0
2
0
1
0
2
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
5
0
0
0
0
0
0
0
2
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
1
0
3
0
0
0
2
1
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
1
1
0
0
0
0
1
3
0
0
0
2
0
0
0
0
2
0
2
0
0
2
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
2
0
0
0
0
1
0
2
0
1
0
0
2
0
0
0
2
1
2
0
2
0
1
0
0
0
1
0
0
1
1
1
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
2
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
2
2
0
1
0
0
0
0
0
2
0
0
0
0
0
1
2
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
3
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
1
3
4
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
3
0
0
1
0
0
2
0
0
5
1
0
2
0
0
0
1
0
1
0
0
0
0
2
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
2
0
0
0
1
0
2
0
0
0
1
0
2
1
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
2
2
0
0
2
0
1
0
0
0
0
2
1
0
0
2
0
0
1
0
0
2
1
0
0
2
3
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
2
1
0
0
1
0
4
0
1
5
0
1
2
0
0
0
1
0
0
0
2
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
3
1
0
0
0
0
0
0
0
2
1
0
2
0
0
2
0
1
2
0
0
0
2
0
0
0
1
2
0
1
2
2
0
0
0
0
1
1
2
0
0
0
3
0
0
2
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
2
1
0
1
0
0
0
1
1
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
3
1
0
0
2
2
0
0
0
0
0
2
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
2
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
2
1
0
0
1
0
3
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
2
0
0
0
2
0
0
2
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
2
0
1
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
1
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
2
1
2
0
3
0
2
0
2
1
0
0
0
0
0
0
1
0
0
0
2
3
2
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
4
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
1
0
2
0
0
0
0
0
0
0
0
2
2
1
0
1
2
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
2
2
0
0
2
1
2
0
1
0
0
2
1
1
0
2
0
0
2
0
2
0
0
1
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
1
2
0
1
4
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
3
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
1
0
1
0
2
1
1
0
0
0
0
0
0
0
2
0
2
0
0
2
2
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
1
2
0
0
2
0
2
0
2
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
2
0
3
0
2
2
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
4
2
0
0
1
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
2
0
1
2
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
2
0
0
2
2
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
2
0
1
2
0
0
0
0
2
0
0
0
0
0
4
2
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
1
1
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
7
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
2
1
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
1
0
5
4
0
0
0
2
1
3
2
2
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
3
0
1
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
2
0
0
1
0
1
0
0
3
0
0
0
0
0
0
0
0
1
1
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
2
2
0
0
0
0
0
1
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
2
0
0
1
2
0
0
0
0
1
2
2
2
0
0
0
1
0
0
0
2
3
0
4
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
4
0
0
0
0
0
0
0
0
0
2
1
2
0
1
2
0
0
1
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
2
0
0
0
1
2
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
2
1
3
2
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
4
0
0
0
0
3
0
0
0
3
0
6
0
0
1
0
0
0
0
2
0
0
1
2
2
0
2
0
0
1
1
0
0
0
0
1
1
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
2
3
2
0
0
1
0
2
0
0
0
0
0
1
0
2
0
2
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
2
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
2
0
2
2
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
2
1
0
0
1
3
1
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
3
0
0
1
0
0
0
0
0
1
0
3
0
3
0
3
0
0
2
0
0
0
1
0
0
0
2
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
1
0
0
0
2
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
1
1
1
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
0
1
2
0
0
0
0
0
0
2
2
0
1
0
0
0
0
2
0
0
1
1
0
2
0
0
0
1
2
0
2
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
2
0
2
0
1
0
0
0
2
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
2
0
1
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
8
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
3
0
0
0
0
0
0
0
2
0
2
0
0
2
0
1
0
0
1
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
2
0
0
0
0
2
1
0
0
0
1
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
2
0
1
0
0
0
2
0
0
2
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
4
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
1
2
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
2
0
0
3
0
0
2
2
0
0
0
1
0
1
0
1
0
0
0
0
2
0
0
0
1
2
0
1
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
1
0
1
0
2
0
6
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
2
0
1
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
1
1
2
3
2
0
1
0
2
0
2
0
0
0
0
0
0
0
0
1
1
0
1
2
0
0
0
0
1
0
0
0
0
1
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
2
1
3
0
1
1
0
0
0
0
0
0
0
1
2
0
0
2
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
2
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
3
1
0
3
0
0
1
0
1
1
1
1
0
1
2
1
1
1
0
1
2
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
2
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
1
2
0
0
0
0
0
1
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
1
1
0
0
0
2
0
0
1
2
2
0
0
0
3
2
0
1
0
1
0
1
0
3
0
1
0
2
0
0
0
0
2
0
2
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
1
0
0
1
1
2
0
0
0
0
1
0
1
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
2
1
2
1
0
2
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
2
0
2
2
0
1
0
0
0
0
0
0
1
1
0
2
0
1
0
0
0
0
1
2
0
1
0
0
2
0
0
0
1
0
0
2
0
0
1
0
0
0
2
0
0
2
0
2
0
2
1
0
0
0
0
2
1
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
1
0
2
0
0
2
0
1
0
0
1
0
0
0
0
1
2
1
2
0
0
0
0
0
0
0
2
0
1
1
0
0
0
2
0
0
0
0
1
2
0
0
0
0
1
2
0
0
2
0
2
0
0
0
1
0
0
2
0
0
2
0
1
0
0
5
0
0
0
0
0
1
0
0
0
2
2
0
0
3
2
0
1
2
0
1
0
0
0
0
0
0
0
2
1
1
0
0
1
0
0
0
0
1
0
0
0
2
2
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
1
0
3
0
0
0
0
2
2
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
1
2
1
0
0
0
0
0
1
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
2
0
2
2
1
0
1
2
2
0
3
0
0
0
1
0
0
0
4
1
0
1
0
0
5
2
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
2
10
0
0
0
2
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
3
0
0
1
2
0
0
1
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
1
0
0
0
3
0
0
0
1
0
3
2
0
0
1
0
1
0
0
0
0
0
1
1
0
3
0
0
0
1
0
0
0
1
0
1
0
2
0
1
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
3
2
0
1
2
0
0
0
3
0
1
0
1
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
2
1
0
0
0
0
0
2
0
0
0
2
0
1
1
1
0
0
1
0
1
0
0
0
2
3
0
0
0
0
0
2
2
0
0
2
0
1
1
1
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
2
0
0
1
0
1
0
0
0
1
2
0
1
0
1
0
1
0
0
1
0
0
0
0
2
2
0
0
0
1
0
0
2
0
1
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
5
0
1
0
0
2
0
0
0
0
0
0
0
1
1
0
2
2
1
1
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
2
1
0
0
0
0
2
0
1
2
0
0
0
0
2
1
0
0
1
0
1
0
0
2
0
0
0
1
0
1
0
0
0
0
2
0
0
3
1
0
0
0
0
0
0
1
1
1
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
2
0
0
0
2
1
2
1
1
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
1
2
0
0
1
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
1
0
1
0
3
1
0
0
0
1
0
0
1
1
2
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
2
0
3
0
0
0
1
0
0
0
0
0
5
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
3
0
2
1
1
0
0
1
1
6
0
0
0
0
1
2
0
0
0
1
1
0
0
1
0
2
2
0
2
1
0
0
0
0
0
0
1
0
0
1
2
0
0
0
2
0
0
0
0
1
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
1
0
1
1
1
0
0
1
1
0
0
1
0
0
0
0
0
2
0
0
1
0
3
0
0
1
2
2
0
0
2
0
1
2
2
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
2
4
0
0
1
0
2
2
2
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
2
0
0
2
0
0
2
2
2
2
0
0
0
0
0
0
0
0
1
1
2
0
2
2
0
0
2
0
0
1
0
0
2
1
0
0
2
2
0
2
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
2
2
0
0
0
0
2
1
0
1
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
3
2
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
1
0
2
0
0
13
0
0
2
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
1
0
3
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
2
0
0
0
0
2
0
0
1
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
1
0
2
0
0
0
1
2
0
0
1
2
0
0
0
0
2
1
0
2
1
0
1
0
1
2
2
0
0
2
0
2
2
0
0
2
0
0
0
0
0
0
0
0
1
2
1
0
0
1
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
2
0
0
0
2
0
2
0
0
0
1
0
0
2
0
0
2
2
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
2
1
0
1
3
0
0
1
2
0
2
0
0
0
0
2
2
0
0
0
0
2
0
1
0
3
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
2
2
0
1
0
0
0
0
1
0
1
0
0
1
0
1
0
0
1
0
0
0
0
1
2
0
0
0
4
0
2
0
1
0
0
0
0
0
0
1
1
0
0
1
0
2
0
0
0
2
1
0
0
0
0
1
0
1
0
1
0
1
2
0
0
0
0
0
1
2
2
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
1
0
1
0
0
0
0
0
0
2
1
0
1
0
2
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
4
0
0
1
0
1
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
1
0
2
0
0
0
0
2
1
3
1
0
2
0
0
1
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
1
2
0
0
2
0
0
1
0
1
0
0
0
2
0
0
0
0
0
1
2
1
0
0
1
0
2
2
0
0
0
0
2
2
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
1
0
0
1
0
1
1
0
0
0
0
3
1
0
0
0
2
0
0
2
0
0
0
1
0
2
0
2
1
0
0
2
0
0
1
0
1
0
0
0
0
4
0
0
0
2
0
0
0
0
0
3
0
2
4
0
0
0
1
0
0
1
1
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
1
1
4
2
0
0
0
1
3
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
2
0
2
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
1
0
0
0
1
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
2
0
0
0
1
2
2
0
1
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
6
0
0
0
3
2
0
0
1
0
0
1
2
2
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
2
2
0
1
2
0
2
0
0
3
0
0
1
1
1
0
1
1
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
2
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
1
2
1
1
0
0
1
0
0
0
1
0
0
0
0
1
0
3
0
0
0
1
0
0
0
0
0
0
0
0
1
2
1
0
3
0
0
0
0
2
2
2
0
0
2
0
1
2
0
0
0
0
0
2
0
2
0
3
1
0
2
0
1
0
0
2
1
1
2
0
0
0
2
0
0
1
1
1
0
0
0
1
1
0
0
0
0
2
2
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
3
0
0
1
4
0
0
4
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
1
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
2
0
0
2
0
0
1
2
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
1
0
2
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
2
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
2
1
0
0
0
1
0
0
1
0
0
2
0
0
1
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
3
2
0
0
1
0
4
0
0
1
4
0
0
1
0
0
0
0
2
2
2
1
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
1
2
3
4
0
1
0
0
1
0
0
3
0
0
0
2
0
4
0
0
0
0
0
0
0
2
1
1
0
1
0
1
0
0
2
0
1
0
1
0
0
0
1
1
1
0
0
0
0
1
0
1
0
2
0
0
0
2
0
0
0
0
2
2
2
0
2
0
1
0
0
0
0
0
2
1
0
0
1
0
0
2
0
0
1
2
1
0
2
0
0
1
0
0
0
1
1
2
1
0
0
1
1
0
0
1
0
1
0
0
0
0
0
1
2
0
0
1
1
1
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
5
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
3
0
2
0
0
1
2
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
1
0
0
0
0
2
2
2
2
2
0
2
0
0
2
1
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
1
0
2
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
4
0
0
1
2
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
1
0
1
1
0
0
1
0
1
0
0
0
0
2
1
0
3
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
1
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
3
0
1
0
0
0
2
0
0
0
0
2
0
1
0
0
0
1
0
2
0
2
3
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
3
1
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
3
2
0
0
2
0
1
0
0
0
0
0
1
1
1
1
0
2
0
0
0
1
0
0
2
0
1
0
0
0
0
1
1
0
0
1
1
2
0
0
0
1
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
2
0
1
0
1
0
0
0
2
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
2
2
0
0
0
0
2
0
1
0
0
0
0
0
1
0
2
0
1
2
0
0
1
0
2
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
3
0
2
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
2
0
0
2
2
2
0
0
0
1
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
2
1
1
0
0
0
2
0
0
0
1
0
1
0
2
0
0
1
0
0
1
0
1
0
0
0
2
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
1
0
2
0
0
2
1
1
0
0
0
0
2
0
0
0
0
0
0
2
1
3
0
2
0
1
2
2
0
0
0
1
0
0
0
0
0
2
0
2
1
0
1
0
0
0
0
0
0
0
0
2
4
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
2
1
1
0
0
0
0
2
0
0
2
2
0
2
0
1
0
0
1
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
2
0
2
1
1
2
4
0
0
0
4
0
3
1
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
2
0
2
1
0
0
0
0
0
1
3
0
2
1
0
0
4
0
0
0
0
0
1
2
0
0
0
0
2
0
0
1
1
0
0
0
0
3
1
0
0
4
2
0
0
2
1
1
1
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
2
1
0
5
0
0
0
2
2
0
0
2
0
0
2
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
4
1
0
2
0
1
2
0
0
2
0
0
2
2
1
0
1
0
0
0
2
0
0
1
2
1
2
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
2
2
0
0
1
0
1
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
1
0
0
0
1
1
4
0
0
1
0
2
0
0
0
0
1
2
0
0
2
0
2
0
0
0
0
0
0
0
0
2
1
2
1
1
0
1
2
1
0
0
0
1
2
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
3
0
0
2
0
1
0
0
2
0
0
1
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
2
1
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
1
0
0
1
0
1
0
1
2
0
0
2
0
2
2
2
3
0
0
2
1
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
2
2
3
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
2
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
3
0
0
2
0
0
1
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
1
0
0
0
0
0
1
0
0
2
1
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
2
3
0
1
1
4
0
1
0
1
1
0
1
1
0
0
0
0
0
0
0
4
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
2
1
1
0
0
2
0
0
0
2
0
0
0
0
1
1
2
0
0
0
0
2
0
0
0
0
3
0
1
0
1
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
3
0
0
0
3
0
1
0
2
0
4
0
0
2
0
0
1
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
1
2
0
0
1
0
2
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
4
2
2
2
0
0
2
0
0
0
1
0
3
0
0
0
0
0
0
0
0
1
7
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
6
3
0
0
0
0
0
1
0
0
0
2
2
0
0
2
2
2
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
2
0
0
1
1
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
2
2
1
2
0
0
0
0
1
2
1
2
0
1
0
2
1
0
1
1
0
0
2
0
2
0
1
0
0
0
0
2
1
2
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
10
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
2
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
3
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
1
1
0
2
0
1
2
1
0
2
2
0
1
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
1
0
2
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
2
0
0
1
0
0
0
2
0
0
0
2
2
1
0
0
0
0
0
1
1
0
1
0
0
0
1
0
1
0
2
1
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
2
0
2
0
0
0
1
0
0
2
1
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
1
1
0
0
0
0
2
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
3
0
0
0
0
0
2
2
0
1
0
0
0
1
2
1
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
2
2
1
0
0
0
0
0
0
0
4
0
0
0
0
0
4
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
1
0
3
2
2
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
1
2
1
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
2
1
0
0
0
2
0
2
1
0
1
0
0
1
0
0
0
0
0
0
2
0
0
2
0
1
1
0
0
0
2
0
0
0
2
0
0
0
0
1
2
4
0
0
3
1
0
0
2
2
0
2
0
1
0
0
1
0
2
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
2
0
2
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
3
0
0
2
1
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
1
1
1
0
0
0
0
0
2
0
0
0
1
3
0
1
2
2
0
5
0
0
0
0
0
2
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
4
0
0
0
0
0
2
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
1
2
1
0
0
0
0
1
0
0
2
0
1
0
1
2
0
0
0
0
0
1
2
2
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
2
2
0
0
1
1
0
1
0
2
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
2
2
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
6
1
2
0
0
0
0
0
1
0
1
0
0
1
1
0
2
2
0
0
0
2
0
1
1
2
0
2
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
2
2
0
2
0
6
2
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
2
2
2
0
0
0
2
2
2
0
0
2
0
1
1
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
2
0
1
0
0
1
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
1
1
1
0
0
0
1
2
0
0
2
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
1
2
0
0
0
0
2
0
2
0
2
0
1
1
1
0
0
0
2
0
0
0
0
0
0
1
0
2
0
2
0
1
5
1
0
0
0
0
0
1
0
0
0
2
0
0
2
0
1
0
2
0
1
0
0
0
0
2
0
0
0
1
1
0
2
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
1
0
1
0
2
0
2
0
1
1
0
0
0
0
1
2
0
4
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
3
0
0
1
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
3
3
0
0
0
2
1
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
2
0
0
0
0
1
2
2
0
1
0
0
2
0
3
0
0
2
0
0
0
0
0
1
0
0
2
1
2
2
2
0
0
1
0
1
1
0
0
2
0
0
0
1
2
2
0
0
1
0
1
2
2
0
1
0
0
0
1
1
0
1
1
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
4
1
0
3
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
1
0
1
0
1
2
0
1
0
0
0
0
1
1
3
4
0
0
2
0
0
1
0
0
0
0
0
2
1
2
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
2
0
0
0
2
0
0
4
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
2
2
0
1
0
2
0
0
0
0
0
0
0
2
0
0
2
2
1
0
0
2
2
0
2
2
0
0
2
0
1
0
0
3
0
0
1
0
2
0
1
0
0
0
0
0
1
0
0
2
3
0
4
2
2
0
2
1
0
1
0
0
0
0
0
0
0
2
2
0
1
2
2
0
2
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
2
0
1
0
0
0
0
2
0
0
0
2
2
1
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
2
0
0
0
2
0
1
0
3
2
0
0
0
0
1
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
3
0
0
0
2
0
0
0
0
1
0
3
0
0
1
2
1
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
4
0
0
1
0
0
2
2
0
1
0
0
0
2
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
2
0
1
2
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
17
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
1
2
0
0
0
0
0
0
0
0
0
2
1
0
2
2
0
1
1
0
0
2
0
2
0
0
1
1
0
0
0
0
0
3
1
0
0
0
0
0
1
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
1
2
1
0
0
0
0
2
1
0
0
3
0
0
2
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
1
2
0
0
2
3
0
0
0
0
2
2
0
0
0
0
1
0
1
0
3
0
0
1
1
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
2
0
2
2
0
0
2
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
1
0
1
0
0
0
1
0
1
2
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
2
1
1
2
2
0
0
1
0
0
1
0
0
0
1
2
2
0
0
0
2
0
0
0
0
0
1
0
2
0
1
1
0
0
0
1
2
2
0
0
0
2
0
1
1
2
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
2
0
1
2
1
4
1
0
0
0
0
0
0
0
5
0
0
2
0
1
1
2
2
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
3
0
2
0
0
2
0
1
0
3
2
0
2
0
0
0
0
2
2
1
2
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
1
0
0
1
0
0
0
1
1
0
0
1
2
0
0
2
1
2
1
1
2
0
1
0
0
1
5
0
2
0
0
0
0
0
1
2
0
1
3
0
0
0
0
2
0
2
0
2
0
0
2
0
0
0
0
1
1
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
2
0
2
2
0
3
0
0
2
0
0
0
2
2
1
0
0
1
0
0
0
0
0
1
0
0
0
3
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
1
1
2
1
0
1
2
0
1
0
0
0
1
0
0
2
2
0
1
2
0
1
2
0
2
0
0
0
1
0
0
2
0
2
0
1
0
0
0
1
1
0
0
2
0
0
0
1
0
1
0
0
1
1
1
0
2
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
1
0
2
1
0
0
1
1
2
0
0
0
1
0
0
0
1
0
0
1
2
2
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
2
0
1
0
1
0
0
2
0
1
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
2
1
0
2
2
0
0
0
1
0
0
1
2
1
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
1
0
0
0
5
0
0
1
2
2
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
3
2
1
0
0
0
2
0
0
0
2
0
0
0
0
1
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
3
0
0
0
0
0
0
2
2
0
0
0
0
2
3
1
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
1
0
0
1
0
2
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
2
0
0
2
0
1
0
2
0
0
0
0
0
2
0
0
1
1
1
0
0
0
1
0
0
2
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
3
0
2
0
0
1
0
0
1
0
1
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
2
0
0
0
1
0
0
0
0
0
2
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
3
0
1
1
3
0
2
2
3
0
0
0
1
0
0
1
0
0
0
0
0
0
3
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
1
0
0
0
1
0
0
2
0
0
2
0
2
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
2
2
2
0
0
1
1
0
0
0
0
1
0
2
2
2
4
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
1
1
1
3
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
1
0
0
0
3
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
3
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
2
2
0
1
1
0
0
0
0
1
0
2
0
2
0
0
0
1
0
0
0
1
1
1
2
1
2
1
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
5
1
0
2
2
2
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
2
0
0
0
0
1
2
0
2
0
2
0
0
0
1
3
3
2
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
3
0
0
0
2
1
0
2
1
0
0
2
1
0
1
0
0
2
1
0
1
2
1
0
1
2
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
2
2
1
0
0
0
1
0
0
0
0
1
0
0
2
1
0
0
0
1
2
0
0
0
0
0
0
2
2
0
2
1
2
0
0
0
0
5
2
1
2
0
0
2
1
0
3
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
2
0
2
2
0
0
0
2
1
0
0
1
0
0
0
1
0
2
1
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
2
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
1
0
1
0
0
2
0
0
0
0
2
0
2
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
2
0
0
3
2
1
0
0
0
2
0
2
1
1
0
0
2
0
0
2
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
3
0
2
0
0
0
0
0
0
2
0
0
1
0
0
2
0
2
0
1
0
0
0
0
4
2
0
3
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
1
1
0
1
2
0
3
0
0
0
0
0
1
1
2
0
0
0
0
0
1
4
0
0
0
1
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
3
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
2
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
5
0
1
1
0
0
7
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
1
0
0
1
1
0
0
0
0
1
0
0
1
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
1
2
0
0
1
0
0
0
0
2
1
2
0
1
0
2
0
0
1
0
0
0
0
0
2
0
2
0
1
1
0
1
0
1
0
0
0
0
2
0
1
0
0
0
1
1
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
2
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
3
0
0
2
1
2
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
1
2
0
0
0
0
2
0
2
1
1
1
0
2
0
0
1
4
1
0
0
1
0
3
1
0
0
1
2
0
0
0
2
1
0
0
1
2
0
0
2
0
0
0
2
0
0
0
0
0
1
0
2
2
15
0
0
0
0
0
0
2
1
1
0
2
0
0
0
0
1
2
5
0
0
0
2
0
2
0
1
0
3
0
1
0
0
1
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
1
0
2
1
0
1
1
0
2
0
0
0
2
1
0
0
0
0
2
0
3
1
1
3
0
0
0
0
0
2
0
1
0
0
1
4
0
0
0
0
2
2
0
1
0
2
1
2
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
1
0
0
4
1
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
1
0
0
1
0
1
0
0
2
1
0
0
0
0
0
0
0
1
2
1
0
0
1
0
3
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
3
0
0
1
0
2
2
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
1
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
2
1
2
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
1
0
1
0
0
2
0
1
2
0
0
0
3
0
0
0
0
0
0
0
2
2
2
0
1
0
1
2
0
1
0
0
4
0
1
1
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
1
0
1
0
4
0
0
2
0
0
0
2
1
3
2
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
1
2
1
3
0
1
0
0
0
2
0
1
0
1
2
0
1
0
1
0
2
0
3
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
6
1
1
0
0
0
0
0
0
1
0
2
0
2
0
1
0
0
1
0
0
0
0
0
0
0
3
1
0
0
0
1
3
1
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
5
0
2
2
0
1
0
2
0
0
0
1
0
1
1
2
0
0
2
0
1
0
2
0
1
2
2
0
0
0
0
0
1
0
2
0
1
0
0
0
2
1
0
2
0
3
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
1
0
0
0
0
0
5
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
2
1
0
0
0
0
0
2
0
0
0
4
0
0
2
0
0
1
0
0
0
0
0
0
0
2
2
2
0
1
0
2
3
0
0
0
1
0
1
0
0
0
0
0
0
0
2
1
0
0
0
2
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
1
0
0
0
0
0
1
1
2
0
2
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
2
1
0
0
0
1
0
2
0
0
2
0
1
0
2
1
1
1
2
0
0
0
1
0
0
0
0
1
3
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
1
0
1
2
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
1
0
2
0
1
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
1
1
2
0
0
1
0
1
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
2
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
2
2
0
0
1
3
0
1
0
0
0
2
0
0
0
1
1
0
0
0
2
1
0
1
0
2
0
0
0
1
0
1
3
0
0
3
0
2
0
0
0
0
0
1
2
3
0
0
0
3
0
0
2
3
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
1
0
0
1
0
0
0
0
0
3
0
1
0
2
1
0
0
0
1
0
0
0
0
2
2
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
1
0
0
1
4
1
0
0
2
0
1
0
0
0
0
0
2
0
0
1
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
2
1
0
3
0
0
2
0
0
0
0
0
0
6
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
6
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
1
0
0
2
0
0
1
0
4
0
2
0
0
1
2
1
0
0
2
2
2
1
0
0
1
1
3
2
0
0
0
0
1
1
1
0
0
0
0
1
2
0
0
0
0
0
1
0
2
2
0
1
0
1
1
2
0
0
0
0
2
0
0
1
0
0
0
0
1
3
3
0
2
0
0
2
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
2
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
3
0
0
0
0
1
0
0
0
2
0
1
0
2
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
4
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
2
0
0
2
0
0
0
0
0
0
0
0
1
1
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
4
1
0
0
1
0
0
2
0
2
2
0
0
1
0
0
1
0
2
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
2
0
0
1
1
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
3
2
0
0
1
0
0
2
0
1
0
0
1
0
0
1
2
0
0
0
2
0
5
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
1
1
2
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
2
0
0
2
2
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
2
0
0
1
0
1
0
0
1
0
0
0
2
0
0
1
0
0
2
3
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
1
2
0
0
0
2
0
0
1
0
1
0
0
0
0
0
1
1
0
0
2
1
0
2
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
1
2
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
3
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
2
0
0
1
0
1
2
0
1
0
0
0
2
0
1
3
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
2
2
2
2
0
0
1
0
0
0
1
2
0
0
0
2
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
2
0
0
0
1
0
0
0
2
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
2
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
2
0
0
1
0
1
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
2
0
1
1
1
6
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
4
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
1
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
1
0
0
2
2
0
0
0
2
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
1
1
0
1
0
1
0
1
2
2
0
0
1
1
0
1
0
0
1
1
2
0
0
2
0
1
0
0
2
0
0
2
2
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
3
0
0
0
1
0
1
1
2
0
0
0
0
2
0
1
0
0
0
0
0
1
0
2
0
1
0
0
2
0
0
0
0
1
0
2
2
1
1
0
1
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
1
2
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
2
0
1
0
2
2
0
2
0
0
1
0
2
0
2
0
0
0
0
1
2
2
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
2
1
1
2
1
0
2
2
0
0
0
0
2
1
0
0
0
2
2
0
1
0
0
0
1
0
0
0
3
0
0
0
1
4
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
3
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
2
1
0
1
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
2
0
1
0
0
2
2
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
1
2
1
0
0
7
0
0
0
1
1
0
2
1
0
2
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
6
0
1
0
0
1
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
1
0
0
2
1
1
0
0
0
0
0
0
1
0
3
0
0
2
2
0
0
1
0
3
0
0
2
0
3
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
1
0
1
0
0
1
0
2
0
0
0
1
0
0
0
0
1
2
0
0
0
1
1
0
0
1
0
0
1
1
0
0
0
2
0
1
0
0
2
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
1
2
0
0
2
0
0
0
0
0
2
2
1
1
0
4
0
0
0
0
1
0
2
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
1
0
0
0
0
0
1
0
7
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
1
2
0
0
0
0
0
0
2
1
0
0
0
1
2
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
3
0
2
0
0
1
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
4
0
0
0
0
0
1
1
1
2
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
5
1
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
2
0
0
2
0
1
2
2
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
1
0
2
0
0
0
2
2
0
1
2
2
0
0
0
0
0
2
0
0
2
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
8
2
1
0
0
2
0
0
0
0
2
0
0
0
0
2
0
1
3
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
3
0
0
1
2
0
2
0
3
1
0
0
0
0
0
2
1
2
0
1
1
0
0
3
0
0
0
1
0
0
0
0
0
0
2
0
1
2
0
2
1
0
2
2
0
1
2
0
0
2
0
0
0
1
3
0
2
0
2
0
0
1
0
0
0
2
0
0
0
2
0
2
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
3
1
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
1
1
1
2
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
2
0
3
0
2
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
2
0
0
2
0
0
1
0
0
2
0
0
0
1
0
1
0
0
2
1
1
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
2
0
0
0
0
2
0
1
0
2
1
0
0
0
0
2
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
4
0
0
1
0
2
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
2
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
2
2
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
2
0
2
0
0
0
2
0
0
3
0
0
3
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
1
1
0
0
2
0
0
2
2
0
0
0
1
0
0
0
1
2
0
0
0
0
2
0
0
0
1
1
1
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
3
0
2
1
0
0
0
0
1
2
0
0
0
0
2
0
0
1
1
0
0
2
0
0
0
0
2
0
0
0
0
0
3
0
0
0
2
0
3
1
1
0
0
0
1
2
0
0
0
1
2
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
2
2
1
0
0
0
2
0
0
0
2
0
0
0
3
0
0
0
2
0
3
0
0
1
1
1
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
3
0
2
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
3
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
2
0
0
0
2
0
1
0
2
1
0
0
0
0
2
0
0
1
0
0
0
1
1
0
0
0
0
0
1
1
0
2
0
0
0
1
1
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
1
0
0
2
2
0
0
0
2
0
1
0
0
1
0
0
3
0
0
2
0
1
0
3
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
2
0
0
0
1
1
0
0
5
2
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
2
0
2
0
1
0
1
0
1
0
0
1
0
0
2
0
1
0
0
0
2
0
0
0
2
1
0
0
0
1
0
0
1
0
0
2
2
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
2
2
0
1
3
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
1
0
0
0
0
1
0
0
0
0
0
2
0
2
3
2
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
2
2
0
2
0
1
1
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
1
1
0
0
0
2
0
0
0
0
3
0
1
1
0
0
0
0
0
0
2
0
0
0
1
0
2
0
3
0
2
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
3
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
2
0
2
0
0
2
0
1
0
1
0
0
2
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
2
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
1
0
0
2
7
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
1
0
0
0
2
3
1
0
0
2
1
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
2
0
2
0
0
0
1
0
2
0
0
0
2
1
0
1
0
1
0
0
0
1
0
0
0
0
1
0
1
1
0
2
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
2
0
0
12
0
0
0
1
0
0
0
0
1
0
1
1
0
1
1
0
0
0
0
0
0
2
1
0
0
0
3
0
0
0
0
2
0
0
4
0
2
0
0
1
0
0
0
1
0
0
0
1
2
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
2
0
0
0
1
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
6
0
2
0
1
0
1
1
0
0
0
0
0
0
0
1
3
2
2
0
0
1
0
0
2
1
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
1
2
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
3
0
2
1
0
1
3
0
1
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
1
0
0
0
1
0
2
0
0
0
0
2
0
1
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
1
2
0
0
0
1
2
1
1
0
0
0
0
0
0
1
2
1
0
0
1
2
1
0
0
1
0
0
0
0
2
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
1
1
3
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
1
1
0
0
1
0
2
0
2
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
3
0
1
0
0
1
1
3
1
0
0
0
0
1
0
0
0
0
0
2
1
0
1
0
2
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
3
1
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
2
1
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
1
5
0
1
3
0
0
0
1
0
0
0
0
3
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
1
0
0
0
0
0
2
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
3
0
0
2
2
0
0
0
0
2
2
0
0
0
0
1
0
1
0
0
3
1
1
0
0
0
0
0
0
2
0
0
2
1
0
0
0
1
0
1
0
2
1
0
0
0
1
0
0
2
0
0
2
0
2
0
3
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
3
0
0
0
0
0
0
0
4
1
0
0
0
0
0
1
0
2
2
1
2
0
0
2
1
0
0
1
2
0
0
2
2
0
0
0
0
0
1
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
1
4
0
2
0
1
0
0
0
3
0
0
2
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
3
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
4
0
0
3
2
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
1
2
0
0
1
1
0
2
0
1
3
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
2
0
1
2
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
4
0
0
1
1
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
2
0
2
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
2
2
0
0
0
0
1
1
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
2
0
0
0
0
2
0
1
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
1
2
1
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
1
0
1
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
2
0
0
2
0
2
2
0
0
2
0
0
0
0
0
0
0
2
0
1
0
1
0
0
1
0
1
0
0
1
1
0
2
1
0
1
1
0
1
0
0
2
0
0
1
4
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
1
0
1
1
0
0
0
0
2
0
0
0
2
0
0
0
1
2
0
0
2
2
0
0
0
0
3
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
1
2
0
0
1
1
0
0
1
1
0
0
0
0
0
0
2
2
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
2
2
0
1
1
0
2
2
0
0
2
0
0
2
3
2
0
1
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
1
0
3
1
3
0
1
0
2
1
0
2
2
0
0
0
2
0
0
0
1
0
1
1
0
0
0
0
0
0
2
0
0
1
1
0
0
0
2
0
1
0
0
0
0
2
0
0
1
1
0
0
0
0
1
0
0
2
2
0
0
0
0
3
0
0
1
0
1
0
1
0
0
4
0
1
0
0
3
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
1
0
2
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
2
0
0
0
0
0
0
2
1
0
1
2
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
2
0
0
2
0
0
0
4
2
2
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
2
1
0
1
2
0
0
2
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
2
1
1
1
2
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
2
1
0
1
0
0
0
0
0
0
1
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
1
2
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
2
0
3
0
1
0
1
1
0
2
4
0
0
4
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
1
0
0
0
2
2
0
0
1
0
0
2
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
1
2
1
0
0
0
2
3
0
2
1
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
1
0
0
2
0
0
0
4
0
0
1
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
2
0
1
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
3
0
1
0
0
1
1
0
0
0
1
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
2
0
4
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
1
0
2
0
0
0
0
2
2
1
1
0
0
0
2
0
0
0
0
1
3
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
2
0
2
1
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
2
2
0
1
2
0
1
0
1
2
0
0
1
0
0
2
0
0
0
2
2
0
1
2
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
1
2
0
0
0
0
2
0
1
0
0
0
0
0
1
2
0
0
0
2
1
1
2
0
1
1
2
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
2
0
0
2
0
1
0
2
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
2
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
2
0
0
0
0
0
0
0
1
0
1
0
2
0
1
0
1
1
2
2
1
2
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
2
1
0
1
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
5
0
0
0
0
1
1
0
0
0
0
0
0
3
2
0
0
2
1
0
0
2
0
1
0
0
0
0
0
2
0
0
2
0
2
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
1
1
0
2
2
1
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
10
0
2
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
1
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
2
0
0
2
0
0
1
1
0
0
0
0
2
0
0
1
0
1
2
3
1
0
2
1
1
0
0
1
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
1
0
1
4
0
0
1
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
3
0
1
0
2
0
2
1
0
0
0
2
0
1
0
1
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
4
1
0
0
0
0
0
0
0
1
2
0
1
0
0
2
0
0
0
0
2
0
0
0
1
0
0
2
3
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
4
2
2
0
0
2
0
0
0
0
1
0
0
0
0
0
2
1
0
3
0
0
2
2
2
0
0
0
1
1
0
0
2
0
1
0
1
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
1
2
0
0
1
0
2
0
1
0
3
0
0
0
0
0
0
0
1
0
1
0
0
0
2
1
0
0
2
0
1
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
1
0
0
3
2
2
0
2
0
0
0
0
2
0
0
1
1
0
0
2
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
2
0
2
0
2
0
6
0
0
3
3
1
0
1
0
4
0
0
2
0
2
0
1
0
0
1
2
1
0
1
0
1
0
1
0
0
3
2
0
0
3
0
0
2
0
0
0
0
0
0
0
0
1
1
1
0
2
0
1
1
0
0
0
1
2
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
3
1
0
1
2
0
0
0
1
0
0
1
1
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
1
1
2
0
0
0
1
0
1
2
0
0
0
0
1
0
2
1
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
2
0
5
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
2
0
2
2
0
0
0
1
0
0
0
1
0
0
0
0
2
1
0
0
1
0
1
1
1
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
1
0
2
2
0
2
1
0
0
1
0
2
0
0
2
2
0
0
0
1
1
3
0
0
2
1
1
0
1
0
0
0
0
0
1
0
0
2
0
1
0
0
2
0
0
0
0
2
0
0
2
1
2
0
0
0
0
0
0
0
1
1
0
0
3
0
0
0
0
2
0
0
0
0
0
3
3
0
1
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
2
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
2
0
1
0
2
0
0
0
1
0
1
0
2
0
1
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
2
2
0
0
0
1
0
1
2
0
0
0
2
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
2
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
3
0
3
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
2
2
1
0
1
0
1
0
1
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
1
0
1
0
3
0
2
2
1
0
1
0
0
0
0
1
2
0
1
0
1
0
0
1
0
0
0
0
0
1
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
2
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
1
2
0
0
2
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
1
1
1
0
0
0
1
3
2
1
0
2
0
0
0
2
1
0
3
2
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
1
1
0
0
1
1
1
1
0
0
0
2
3
0
0
0
0
0
3
2
1
0
2
2
0
0
0
0
1
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
1
2
0
2
1
0
0
2
0
0
1
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
1
1
0
0
1
1
0
0
1
2
0
0
0
0
0
0
0
0
0
2
2
1
0
2
0
0
2
0
0
0
0
2
1
3
0
0
2
1
0
0
0
1
2
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
2
0
0
1
2
0
0
2
0
1
0
0
0
2
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
2
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
1
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
1
0
0
0
1
2
0
0
3
0
2
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
2
0
0
2
1
0
2
1
1
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
1
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
3
1
2
2
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
10
0
0
0
0
0
0
1
3
1
0
1
0
0
0
0
0
0
2
1
0
2
0
1
1
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
2
1
3
0
3
1
0
0
3
0
0
0
0
0
2
0
1
0
0
0
0
2
4
0
1
0
2
1
2
2
0
1
1
0
1
2
0
0
1
0
2
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
2
0
2
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
2
0
2
1
5
0
2
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
1
0
2
0
0
2
0
1
0
0
1
2
1
1
0
0
0
0
1
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
1
0
0
2
2
0
2
2
2
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
3
2
0
0
0
1
0
2
3
0
0
0
1
1
1
2
0
0
0
0
0
0
0
0
0
3
3
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
2
0
0
0
0
1
0
0
3
1
0
0
0
0
0
1
1
2
0
1
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
2
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
5
2
0
0
0
0
0
0
2
0
1
0
3
3
0
0
3
1
0
0
0
3
2
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
1
1
1
0
0
0
2
3
0
0
0
0
0
0
0
1
0
1
2
2
1
0
0
0
0
0
0
0
4
2
0
0
0
0
0
0
1
2
2
0
0
1
0
0
0
1
0
2
0
0
0
2
0
2
1
1
0
0
0
0
0
3
1
0
1
0
2
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
1
2
0
2
0
0
0
0
2
0
0
1
0
1
1
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
6
2
0
0
2
1
0
0
2
0
0
0
0
0
0
1
3
0
0
2
1
0
0
0
1
2
0
0
0
0
2
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
2
0
2
0
3
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
2
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
1
0
2
0
1
0
0
0
0
1
0
2
0
1
2
0
0
0
0
0
0
1
0
2
0
0
0
4
1
1
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
1
0
2
3
0
0
1
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
2
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
3
0
2
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
2
1
4
0
1
1
0
1
0
3
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
1
0
2
0
0
0
0
1
4
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
1
2
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
1
0
1
0
1
0
0
2
1
1
0
0
4
0
0
0
0
0
2
0
0
4
1
2
0
1
1
1
1
2
0
0
3
0
0
1
0
0
4
1
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
2
2
0
2
0
0
0
0
0
1
0
0
0
1
0
0
2
1
2
0
0
0
0
0
0
2
1
0
0
1
0
2
2
0
0
0
1
1
1
0
1
0
0
1
2
1
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
1
0
0
3
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
2
2
0
0
0
1
0
0
2
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
3
2
0
1
0
1
0
0
0
0
1
1
2
0
0
1
0
0
1
1
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
0
1
0
3
2
0
0
1
0
2
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
2
0
1
0
4
3
1
1
1
0
2
0
0
0
0
0
2
0
0
1
0
2
3
0
0
0
0
1
0
0
4
0
0
0
0
0
1
0
3
1
0
0
1
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
1
0
0
1
3
0
0
0
0
0
0
0
0
0
2
2
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
2
3
2
0
1
1
0
0
0
0
2
1
1
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
1
0
0
0
0
2
0
0
2
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
2
0
0
0
2
1
1
0
2
0
1
0
0
1
0
0
1
0
2
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
1
2
0
1
2
0
1
0
0
0
2
2
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
2
0
0
0
0
1
0
0
2
0
1
5
0
1
1
0
2
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
1
2
0
0
0
0
0
0
0
0
0
1
0
2
0
2
2
2
0
0
3
0
2
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
1
1
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
3
0
0
0
2
2
0
0
1
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
1
1
1
0
1
1
1
0
1
0
0
0
1
0
0
3
0
0
2
0
0
0
0
1
2
1
1
1
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
2
1
0
0
0
2
0
1
0
2
0
1
2
0
1
3
0
0
1
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
1
1
0
0
0
0
0
2
1
0
1
0
0
2
0
1
0
1
0
0
0
1
2
2
1
0
1
2
0
0
0
2
0
0
1
1
0
0
2
1
0
3
0
2
0
2
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
2
1
0
0
2
0
0
0
0
0
1
3
1
0
2
0
0
1
0
1
0
0
0
0
4
9
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
1
2
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
2
1
1
1
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
1
0
2
1
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
2
0
0
1
1
0
0
0
0
2
0
1
0
0
1
0
2
2
1
0
1
1
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
2
1
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
2
0
2
0
1
1
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
1
0
2
0
0
2
0
2
0
0
0
2
0
0
0
0
0
2
0
0
1
2
2
0
0
0
0
0
0
1
0
2
0
0
1
0
0
2
1
0
0
0
0
2
0
1
0
0
0
2
0
1
0
0
2
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
2
0
0
2
0
0
1
2
0
0
1
1
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
1
2
0
0
2
0
2
0
0
0
1
1
2
0
0
2
3
0
0
0
0
4
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
2
0
0
0
2
2
0
0
2
2
0
0
1
0
0
0
1
1
2
0
0
0
0
0
0
1
0
2
1
0
0
2
2
0
0
3
1
1
0
0
2
2
1
1
0
1
0
0
0
3
3
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
2
1
0
0
0
0
1
2
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
2
0
2
0
0
0
2
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
1
0
0
0
0
0
1
2
2
0
0
0
0
7
0
0
0
2
0
0
1
0
1
1
1
2
0
1
0
1
0
0
0
0
0
0
0
0
2
1
0
0
1
2
0
1
0
2
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
3
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
3
0
2
0
2
0
0
0
0
2
0
1
1
0
2
0
2
0
0
2
0
1
1
1
0
0
2
1
2
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
2
1
1
2
0
0
0
0
0
2
0
2
0
1
0
0
1
0
2
6
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
1
2
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
2
0
0
0
1
0
2
1
0
1
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
1
1
2
0
0
0
0
2
0
0
0
2
1
0
2
0
2
0
2
0
0
2
0
0
0
2
0
1
1
1
0
0
2
0
0
0
0
0
2
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
2
1
0
0
1
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
2
5
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
4
0
2
1
2
2
2
1
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
4
1
0
1
2
0
0
1
3
0
0
0
0
0
1
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
1
0
0
0
0
3
1
0
0
1
2
1
0
1
0
0
0
0
0
0
1
0
2
2
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
1
2
2
2
0
0
0
0
0
0
1
1
0
0
0
0
1
0
2
0
0
0
2
0
0
0
2
2
2
0
1
0
0
4
0
0
0
2
0
0
2
1
3
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
2
2
2
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
2
0
1
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
3
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
2
0
0
1
2
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
1
0
1
1
0
0
0
0
2
0
2
0
2
1
1
0
1
0
2
0
0
0
0
0
1
0
1
1
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
1
0
0
2
2
0
1
0
0
0
0
0
0
0
2
0
0
0
4
3
0
1
0
0
0
2
12
0
1
2
1
0
1
1
0
0
0
1
0
0
0
2
0
0
0
1
0
2
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
2
2
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
2
0
2
0
7
1
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
3
0
0
0
0
0
2
0
1
0
1
1
0
0
0
0
0
1
0
1
1
0
1
0
1
1
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
3
0
2
1
0
0
0
1
1
2
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
8
0
0
0
1
0
0
1
2
0
2
0
0
0
2
0
1
0
2
3
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
2
2
0
0
3
0
2
0
1
0
2
1
1
0
2
0
3
0
0
0
1
1
1
1
0
0
0
0
0
0
1
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
2
0
1
2
0
1
0
2
2
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
1
0
0
2
0
0
0
1
0
0
2
3
0
0
2
0
0
0
0
2
0
0
0
2
0
1
1
2
0
2
0
1
0
0
0
1
2
2
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
1
0
0
0
2
1
2
0
1
0
2
2
1
0
1
5
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
1
1
1
2
0
1
0
1
0
2
0
3
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
1
2
1
2
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
2
2
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
2
0
1
2
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
2
3
1
2
0
0
0
0
0
0
0
1
0
0
0
2
0
2
2
1
0
0
2
1
2
1
2
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
2
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
1
1
0
0
1
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
2
4
0
0
0
0
1
0
0
2
2
0
2
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
3
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
1
1
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
1
1
0
2
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
3
0
0
2
2
0
0
0
1
2
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
2
1
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
1
0
0
0
2
0
2
0
0
0
1
2
2
0
0
0
0
0
4
0
0
3
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
8
0
0
0
0
1
0
0
1
0
0
0
0
1
0
2
0
0
4
0
1
0
1
0
1
2
0
0
0
1
0
1
1
0
2
0
0
1
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
2
0
0
1
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
1
1
0
0
0
2
0
0
1
1
0
0
0
0
2
0
0
0
0
0
2
0
2
0
2
0
1
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
1
0
0
1
1
0
1
0
1
0
0
2
0
2
0
2
2
1
1
0
0
0
2
2
0
0
0
0
0
1
0
1
0
0
1
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
2
0
0
0
1
0
0
0
0
0
0
0
6
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
2
0
0
1
0
0
2
0
1
0
0
1
0
1
0
0
1
0
0
2
0
0
1
2
0
0
0
0
1
0
0
2
0
0
1
0
1
0
0
4
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
4
2
0
1
2
0
2
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
2
0
1
1
0
0
0
0
0
0
2
0
6
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
3
0
1
1
1
0
0
0
0
0
1
2
1
0
0
0
0
2
1
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
1
1
2
1
0
0
2
0
0
2
1
0
0
0
0
0
1
0
1
0
0
1
0
1
1
0
3
0
0
1
0
1
0
2
1
0
0
0
1
0
0
0
0
1
1
1
0
2
0
2
0
2
1
0
1
0
0
0
0
3
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
2
0
0
2
1
0
0
2
0
1
2
0
0
1
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
1
0
2
0
0
0
0
0
3
0
1
0
0
2
1
1
0
2
0
0
0
0
2
0
0
0
0
0
3
2
2
0
0
0
2
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
1
2
0
0
0
1
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
1
2
0
2
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
3
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
2
1
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
1
2
3
0
0
0
1
0
2
1
0
0
0
0
2
2
1
0
1
0
0
0
1
1
1
0
0
6
0
4
2
0
0
1
0
0
3
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
1
0
1
1
2
0
0
0
1
1
0
1
2
2
2
3
0
2
0
0
0
2
0
0
1
0
0
0
3
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
2
0
0
0
0
1
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
2
0
1
0
2
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
3
0
0
2
0
0
0
0
0
0
2
1
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
4
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
1
1
1
0
0
0
0
2
0
2
2
1
4
0
0
0
0
1
1
0
0
0
0
5
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
1
1
0
0
2
0
2
0
0
0
1
0
0
2
3
0
0
0
0
0
1
4
0
2
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
2
0
2
0
0
1
7
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
3
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
3
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
1
0
0
0
1
1
0
1
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
4
2
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
3
4
1
0
0
0
0
2
1
0
0
0
2
0
0
1
0
1
3
0
2
1
0
0
1
0
0
2
0
0
3
1
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
1
1
0
0
1
0
1
0
1
3
0
0
0
1
2
1
0
0
2
0
0
1
0
0
2
0
2
0
0
2
0
0
1
0
2
0
0
1
0
0
3
0
0
1
0
0
1
1
0
1
2
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
2
0
1
0
0
3
0
3
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
2
0
2
2
0
0
0
0
0
0
2
0
0
2
1
0
0
0
1
0
0
2
0
2
0
0
0
1
1
0
2
0
0
0
1
1
2
0
1
0
0
0
1
0
0
2
1
2
0
0
1
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
2
1
2
0
1
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
2
0
2
0
0
3
2
2
0
0
2
0
2
0
2
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
3
2
0
2
0
1
0
2
0
0
0
0
0
0
0
0
2
2
2
2
1
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
2
0
3
0
0
0
0
0
0
0
2
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
2
0
0
2
2
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
3
0
0
2
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
1
2
1
0
0
0
1
0
0
0
0
0
2
0
0
1
1
2
0
0
1
2
0
1
0
0
1
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
1
0
1
1
0
2
0
0
0
1
0
1
3
1
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
5
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
7
0
0
0
2
0
1
0
0
3
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
5
0
0
0
0
0
1
1
1
0
2
0
2
0
0
0
0
0
4
1
0
0
1
1
1
0
0
0
3
2
0
1
2
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
1
0
1
0
0
0
2
1
0
0
0
3
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
2
0
0
0
0
0
2
0
0
0
2
1
2
2
1
0
0
2
2
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
1
2
0
0
2
2
0
0
0
0
2
0
0
1
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
2
2
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
2
1
1
0
0
0
0
0
0
2
0
0
2
1
0
0
2
1
0
0
0
0
0
3
0
2
0
0
0
1
0
2
0
0
3
0
0
2
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
6
0
0
2
0
1
0
0
0
0
0
0
1
0
0
1
1
0
2
0
0
0
1
2
0
0
2
3
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
2
3
0
2
0
0
1
2
0
1
2
0
2
0
0
0
0
2
0
1
0
0
1
0
0
2
0
0
1
0
0
0
1
2
0
0
2
0
0
2
2
0
0
0
0
0
2
0
0
0
1
1
1
0
0
0
1
1
0
0
0
0
0
2
0
1
2
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
3
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
2
0
0
1
0
0
0
0
1
2
1
0
2
0
0
0
1
0
1
1
2
2
2
0
7
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
2
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
2
0
0
1
0
0
1
0
0
0
3
0
0
1
0
2
0
2
0
0
0
0
0
1
0
0
1
4
0
2
0
0
2
2
0
0
1
0
0
0
0
0
2
0
1
0
2
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
2
2
6
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
2
2
0
0
2
0
0
0
0
0
2
2
0
0
2
0
1
0
2
0
0
0
0
1
0
1
2
2
0
0
0
0
0
0
1
0
0
1
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
2
2
0
0
1
2
2
0
0
1
0
0
0
2
0
0
0
1
0
1
0
0
0
2
0
0
2
2
0
1
0
2
1
0
3
0
1
0
0
0
0
0
2
1
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
2
1
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
3
3
1
0
1
0
2
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
4
0
3
0
0
2
2
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
3
0
0
0
2
2
1
0
2
0
1
0
2
0
0
1
1
1
0
0
2
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
1
0
1
2
8
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
2
0
1
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
2
1
0
0
4
2
1
1
1
2
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
3
0
0
0
0
1
0
0
0
2
2
0
0
0
1
2
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
5
0
0
2
1
1
0
0
0
0
2
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
4
2
0
2
0
0
0
0
1
0
1
0
1
1
0
1
2
1
0
0
0
0
0
1
0
0
0
3
1
2
1
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
1
2
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
2
0
0
1
2
0
2
0
0
0
0
1
1
0
0
1
0
0
2
0
1
0
2
0
0
0
0
2
0
0
1
1
0
0
1
1
0
2
0
0
1
0
0
0
1
0
1
0
0
0
0
2
0
0
1
0
0
0
1
1
0
1
0
1
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
2
0
0
0
0
0
0
1
0
3
0
1
2
0
0
0
1
0
0
2
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
1
0
0
2
0
0
2
1
0
0
0
0
1
1
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
3
1
0
2
0
0
0
0
0
1
1
2
0
0
0
2
0
0
0
0
0
0
1
1
0
1
0
10
1
0
0
2
1
1
0
0
3
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
2
0
0
0
1
0
0
0
0
2
1
3
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
4
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
1
2
0
0
1
0
0
0
0
0
2
0
0
0
5
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
1
0
0
3
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
1
1
0
0
1
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
1
0
2
0
2
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
1
0
0
1
2
0
0
0
0
1
2
1
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
1
6
0
0
1
0
1
1
0
0
0
3
2
0
0
0
0
1
0
1
0
2
2
2
0
0
0
0
0
0
1
1
2
2
0
0
0
0
0
0
2
0
0
7
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
2
2
5
2
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
1
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
1
1
2
3
0
0
1
0
5
0
0
0
0
5
0
2
0
0
2
0
2
0
0
2
2
1
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
1
2
0
0
0
1
3
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
1
0
1
0
0
1
0
0
0
2
1
0
0
0
2
0
0
0
1
3
3
0
2
2
2
0
5
0
0
1
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
3
0
0
0
0
1
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
2
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
2
2
0
0
1
0
2
2
1
0
0
1
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
6
2
0
0
0
1
0
0
1
0
0
1
3
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
4
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
3
0
0
1
0
0
0
0
0
2
0
1
0
0
0
2
0
0
1
1
0
0
0
0
1
0
0
0
2
0
0
3
0
0
1
2
2
0
0
0
0
1
0
0
2
0
2
0
0
0
1
0
0
1
0
0
2
2
1
1
3
0
2
2
0
0
0
0
0
0
0
0
2
0
1
2
0
2
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
1
2
0
0
1
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
4
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
2
1
0
2
0
0
5
0
0
0
2
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
1
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
1
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
1
0
0
4
0
2
0
1
0
1
1
0
0
1
1
0
0
2
0
1
0
1
0
2
0
0
0
0
0
1
0
2
0
0
2
0
0
1
0
1
2
0
1
0
3
0
0
0
2
0
0
1
2
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
1
1
1
2
1
0
0
0
1
1
0
0
1
0
3
0
0
1
2
0
3
0
0
1
0
1
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
1
0
0
0
0
0
0
0
0
2
0
2
0
1
1
0
0
1
2
0
1
0
1
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
6
0
2
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
6
2
0
0
0
0
0
0
0
0
1
0
1
3
0
1
0
0
1
0
1
0
6
2
0
1
0
0
0
2
0
0
0
1
0
1
2
2
0
0
1
2
0
0
2
0
2
0
1
6
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
2
2
0
0
1
0
0
2
0
0
2
1
2
0
0
0
2
0
1
2
0
0
26
0
0
0
1
2
1
0
0
1
2
2
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
2
2
0
0
7
2
0
0
0
2
1
3
0
1
0
2
1
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
2
0
2
0
1
1
0
0
1
2
0
2
0
0
0
0
0
0
2
0
0
0
1
1
1
0
0
1
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
3
2
1
3
1
2
0
0
0
2
0
0
0
0
0
2
1
0
1
2
0
1
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
1
0
0
2
1
0
0
0
0
0
0
0
2
1
0
0
0
1
1
1
0
0
1
0
2
0
1
0
0
0
2
0
0
1
0
0
0
0
1
0
2
0
0
2
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
2
1
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
4
0
2
0
0
1
0
2
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
2
0
0
2
2
0
1
0
0
2
0
0
2
0
0
0
3
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
1
0
0
1
0
1
0
0
2
0
2
1
1
1
1
0
2
0
0
0
0
0
0
0
1
0
1
4
0
1
0
1
0
0
0
2
0
0
0
0
0
0
3
1
1
0
3
0
2
0
0
0
0
0
2
1
0
4
2
0
0
0
1
1
0
2
0
0
0
0
7
0
0
0
0
0
2
0
3
0
0
1
0
2
0
4
2
1
1
2
0
0
0
0
1
1
0
0
0
0
0
1
2
0
2
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
3
0
0
0
2
1
0
2
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
3
0
2
2
0
0
0
1
0
0
2
2
0
0
1
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
2
0
0
0
2
2
3
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
3
0
2
1
0
1
0
2
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
3
0
0
1
0
0
0
0
1
1
0
1
2
0
0
4
0
1
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
2
0
0
1
1
2
0
0
1
0
0
0
0
0
2
0
0
0
3
0
1
0
1
0
1
0
1
2
0
2
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
4
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
2
2
0
0
0
0
1
0
0
2
0
2
1
0
0
1
0
2
0
1
0
2
0
0
1
0
2
0
0
0
2
0
0
2
0
0
1
2
0
1
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
3
0
0
0
0
2
0
0
0
2
0
0
2
1
0
0
1
0
0
0
0
2
1
0
0
3
1
2
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
1
2
0
1
0
0
0
1
0
1
0
0
0
2
0
0
0
0
2
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
2
2
0
1
0
0
2
2
0
0
0
1
0
0
0
2
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
3
2
0
0
2
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
2
2
0
0
1
1
0
0
2
0
0
1
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
2
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
3
0
0
0
1
0
0
0
2
0
0
2
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
1
1
2
3
0
3
0
2
1
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
2
0
0
1
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
1
1
1
1
0
0
0
0
2
0
0
0
2
0
2
0
0
0
2
2
0
0
0
0
1
0
1
0
0
1
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
2
0
1
0
2
0
0
1
1
0
0
0
0
0
0
0
2
0
1
0
1
1
2
0
0
1
0
0
0
0
0
0
0
0
2
2
1
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
2
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
2
0
1
0
0
2
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
2
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
4
0
0
1
2
1
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
2
0
2
1
0
1
0
0
0
0
2
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
1
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
2
1
0
2
2
0
1
1
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
2
0
2
0
1
0
0
3
2
1
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
1
0
1
0
0
0
0
1
1
2
1
0
0
0
0
1
0
0
0
2
1
1
1
0
0
0
0
0
0
2
0
0
0
0
1
2
2
2
0
0
0
0
0
1
0
0
2
0
4
2
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
1
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
5
0
0
0
4
0
0
2
0
1
3
0
0
0
0
1
2
0
1
2
5
0
0
0
0
1
0
1
0
2
0
4
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
2
2
0
0
0
4
3
1
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
3
2
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
2
0
0
2
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
6
0
0
1
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
2
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
1
0
0
2
0
2
0
0
6
0
0
0
2
1
0
2
0
1
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
1
1
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
3
0
0
1
1
2
0
2
0
0
6
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
1
1
1
0
1
0
0
0
2
0
1
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
2
2
1
2
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
2
1
0
0
0
0
1
1
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
3
0
2
0
1
0
0
0
0
0
2
0
0
0
0
1
1
0
0
2
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
3
0
1
0
0
1
0
0
1
0
2
0
0
0
0
1
0
0
0
1
0
0
0
3
0
6
0
2
2
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
2
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
2
2
0
0
0
0
0
0
3
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
1
0
0
2
0
2
0
0
1
0
1
1
0
2
0
0
0
2
1
1
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
2
0
0
0
0
0
0
2
2
0
0
2
0
0
2
0
1
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
3
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
1
2
0
0
0
0
1
2
1
0
0
0
4
2
2
0
0
0
0
0
0
1
0
2
1
0
0
0
1
0
1
1
0
0
1
0
0
7
0
0
0
0
1
0
0
0
0
0
2
0
1
1
1
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
2
2
0
0
2
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
2
0
1
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
2
0
1
0
2
0
2
0
0
0
1
0
3
2
0
0
2
1
1
2
0
0
0
0
0
1
0
1
2
2
0
0
0
0
0
2
0
2
1
2
0
1
2
0
1
0
0
1
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
2
0
2
0
1
0
0
1
0
2
0
0
0
0
2
2
0
0
0
2
1
0
0
1
8
2
1
0
2
1
2
2
0
0
0
0
0
0
0
2
1
0
0
0
3
0
2
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
2
3
0
0
0
0
3
0
0
1
0
0
0
1
1
0
0
2
0
0
3
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
4
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
2
0
2
0
0
0
1
1
0
0
0
3
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
5
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
1
0
2
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
1
2
1
1
1
0
0
0
0
3
1
0
0
2
0
0
2
0
0
0
2
0
0
2
0
2
3
2
0
0
0
0
2
2
0
0
1
0
1
0
0
0
0
0
2
0
0
1
0
1
0
6
1
1
0
0
1
0
0
0
0
2
2
0
1
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
2
1
0
1
0
0
2
2
2
1
1
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
3
0
0
0
1
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
1
0
0
0
0
1
1
0
0
0
5
0
0
0
0
0
0
0
0
2
1
1
0
0
1
2
2
3
0
0
0
0
0
0
0
0
0
0
1
5
0
0
2
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
1
2
0
0
0
1
0
0
0
2
0
3
0
1
2
0
1
2
1
0
2
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
1
0
0
1
1
0
0
1
0
0
0
0
3
2
2
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
2
0
1
0
2
0
0
0
1
0
0
1
2
1
2
0
0
2
0
2
0
2
1
0
0
1
1
0
0
0
0
0
0
0
1
2
1
4
1
1
1
0
1
0
2
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
2
3
0
0
0
0
1
0
0
0
2
0
2
2
0
0
0
2
0
1
2
1
0
0
0
0
0
0
3
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
2
0
1
0
2
0
0
2
0
0
0
0
0
1
1
1
1
2
1
1
0
0
5
0
1
1
2
0
2
0
1
0
2
0
0
0
0
1
0
1
0
0
0
3
0
0
0
1
0
4
2
2
0
1
1
0
0
1
0
0
3
0
0
0
2
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
1
0
2
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
4
2
0
0
0
0
0
1
0
0
0
0
0
0
1
2
2
1
0
2
0
0
0
1
2
1
3
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
1
1
0
0
1
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
6
1
0
0
0
2
0
0
2
0
0
0
1
0
0
0
3
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
3
1
0
1
0
0
0
2
0
0
1
0
1
0
0
0
1
0
1
2
0
0
1
1
0
2
2
2
1
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
2
0
2
0
2
1
2
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
2
0
2
0
0
0
1
0
1
0
1
0
5
2
0
0
0
0
0
1
1
1
0
0
1
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
2
0
0
1
1
0
0
0
9
0
6
0
1
0
0
0
0
2
2
0
0
0
4
0
0
0
0
0
0
0
1
2
0
0
0
1
2
2
0
0
1
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
2
5
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
1
1
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
3
0
0
0
0
0
2
2
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
1
1
0
1
0
0
0
1
1
0
0
1
2
0
0
0
0
3
0
0
0
0
0
2
1
0
1
7
0
0
0
2
0
0
2
1
0
0
0
0
0
2
0
2
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
1
2
0
0
0
0
0
0
0
1
0
0
2
2
3
0
0
1
0
0
1
0
2
0
0
1
2
1
0
2
0
2
0
0
0
2
0
0
0
0
0
3
2
2
0
0
0
0
1
2
0
0
0
0
0
2
0
0
3
0
16
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
2
2
0
1
0
2
3
1
1
2
0
1
0
1
0
0
0
0
0
1
0
0
0
2
0
0
2
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
2
0
0
0
0
2
0
1
0
2
1
1
1
2
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
2
1
2
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
1
2
0
0
0
1
0
1
0
0
2
2
1
3
0
0
0
2
1
0
0
1
0
0
1
1
1
0
0
2
0
0
0
0
2
0
0
0
2
3
1
2
0
0
2
0
2
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
1
2
1
1
1
0
0
0
4
0
0
1
0
0
1
0
3
0
1
0
0
0
0
0
1
2
0
0
2
0
0
0
4
0
0
0
0
2
0
0
2
0
0
0
0
7
0
2
0
0
0
1
1
0
0
1
0
0
0
2
0
0
0
2
1
0
0
0
0
2
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
1
0
0
0
0
0
0
0
1
4
0
0
0
1
0
0
0
0
2
0
1
1
0
0
0
0
0
1
0
0
0
0
2
0
2
1
2
1
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
2
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
1
1
0
0
0
0
0
2
0
0
4
0
0
1
0
0
2
0
0
0
4
0
0
2
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
1
3
1
1
0
2
0
0
0
2
0
0
1
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
2
0
0
2
0
1
3
0
0
0
0
1
0
1
1
0
1
0
2
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
1
0
0
0
0
2
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
1
0
2
1
2
0
3
0
0
0
0
1
0
0
2
2
0
0
0
1
0
0
2
0
0
0
0
0
1
1
0
0
1
2
0
0
1
0
0
0
0
2
0
2
0
0
1
0
3
0
0
1
1
2
1
2
2
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
2
0
1
0
0
0
2
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
3
0
0
1
2
2
0
0
1
0
2
0
2
2
0
0
2
0
0
1
0
2
2
0
0
0
1
2
0
0
0
2
0
0
0
0
3
0
0
1
1
0
0
2
0
0
0
0
0
0
2
2
0
0
2
0
0
1
0
1
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
3
1
0
0
0
0
0
0
1
2
2
0
1
0
0
0
0
0
0
2
0
1
0
0
0
2
1
0
0
0
0
0
4
1
1
0
5
1
0
1
0
2
1
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
4
0
1
0
0
0
0
0
1
0
0
0
0
2
2
2
0
0
0
1
2
0
1
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
2
2
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
4
0
0
0
2
2
0
0
1
0
2
2
2
1
0
0
0
4
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
1
1
1
3
1
0
2
0
2
0
1
0
2
0
2
0
0
1
0
0
2
1
0
2
2
2
2
3
0
0
2
0
0
2
0
2
0
0
0
0
0
0
2
2
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
3
0
1
0
2
0
0
2
2
0
0
0
2
0
0
1
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
3
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
2
0
0
4
0
0
0
0
0
0
1
0
2
0
0
0
0
2
2
0
3
1
1
0
3
0
0
0
2
0
0
0
3
2
0
2
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
2
0
0
2
0
0
0
0
0
0
1
5
0
0
1
5
1
0
0
0
0
0
0
0
0
2
2
2
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
2
0
0
1
0
0
0
1
1
1
0
0
0
0
1
1
1
0
0
0
0
0
2
1
0
0
0
0
0
2
2
0
0
0
0
2
0
0
2
0
2
1
0
0
0
0
0
3
0
0
4
0
0
1
0
0
0
0
1
2
0
2
0
0
0
0
1
2
1
1
0
1
0
1
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
2
0
2
0
0
0
3
1
0
5
0
0
0
0
2
0
1
2
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
1
1
0
0
2
0
0
0
0
0
2
0
0
1
0
1
0
2
1
0
1
1
0
5
1
0
0
0
2
1
0
0
1
0
0
2
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
2
1
3
0
0
1
0
2
0
0
2
2
0
0
0
2
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
2
0
2
0
0
0
0
0
0
2
1
3
0
1
1
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
1
2
2
2
0
1
2
1
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
1
2
0
0
1
0
0
2
0
1
0
0
0
3
0
1
0
2
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
2
1
1
2
2
0
1
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
2
1
0
0
0
0
0
0
3
0
0
0
0
3
0
0
0
0
0
0
0
2
2
0
0
2
1
1
2
1
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
2
1
3
0
1
1
0
0
0
2
0
2
0
3
1
0
0
0
0
0
0
0
2
0
0
1
1
2
0
0
0
0
0
2
2
0
0
2
0
0
0
2
1
1
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
1
0
2
0
0
0
2
1
2
1
0
1
1
0
0
0
0
0
0
1
2
0
0
2
0
3
1
0
0
0
1
0
2
9
0
2
0
2
2
6
2
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
1
2
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
1
0
3
2
1
0
0
0
0
0
0
0
3
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
1
0
4
0
3
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
2
2
1
0
0
0
0
5
0
1
0
0
0
0
0
1
0
3
2
0
0
0
0
0
0
0
0
0
0
3
0
0
2
2
0
0
2
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
1
2
2
2
0
0
2
0
0
0
0
1
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
2
5
0
1
0
0
0
0
2
0
0
0
1
0
1
1
0
0
0
2
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
2
0
0
0
2
1
0
0
1
0
2
0
1
0
0
0
0
2
0
0
0
1
1
0
1
0
0
2
0
0
1
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
1
1
1
2
0
0
2
0
0
0
0
0
0
0
0
2
1
1
0
2
0
1
1
0
0
0
1
0
0
0
2
0
0
1
0
0
0
3
6
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
3
0
1
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
1
0
1
0
2
0
0
0
0
0
2
0
0
1
0
2
1
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
2
0
1
2
5
0
2
0
0
0
0
0
0
1
0
0
3
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
2
0
0
1
0
0
1
0
0
1
0
1
1
0
3
0
0
1
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
1
3
0
0
0
0
1
1
0
0
0
2
0
2
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
1
1
0
2
1
1
0
1
1
0
0
0
1
2
0
2
0
0
0
0
1
0
1
1
2
0
0
0
0
1
2
0
0
1
3
0
0
0
0
0
0
0
1
0
1
0
2
1
0
0
0
0
1
0
0
1
0
0
2
0
2
0
0
0
1
2
0
0
1
0
0
2
1
2
0
0
1
0
0
0
2
0
2
1
0
2
3
0
0
0
0
0
1
2
0
0
2
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
2
1
1
2
2
0
0
0
1
0
2
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
2
0
0
0
2
2
2
0
0
0
0
1
0
0
1
0
3
1
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
1
2
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
1
0
0
1
0
0
0
1
0
0
0
2
0
0
1
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
2
0
0
1
0
0
1
0
1
3
0
2
2
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
2
3
0
2
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
1
0
1
0
0
0
2
2
2
0
0
0
0
1
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
2
0
0
1
0
0
0
3
0
1
2
0
0
0
1
0
0
0
0
2
0
1
0
0
3
1
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
1
2
1
0
1
1
1
2
0
0
2
0
0
1
0
0
0
0
0
2
0
1
1
0
0
1
0
0
0
0
1
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
1
0
0
2
0
4
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
2
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
6
0
0
2
0
0
0
1
2
0
0
1
0
1
0
0
0
0
2
0
0
0
2
1
2
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
1
0
1
3
0
3
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
1
0
0
2
0
0
2
0
0
0
2
0
2
0
0
0
0
1
0
2
0
0
0
0
0
1
1
2
1
0
1
0
0
0
0
0
0
3
0
1
0
0
2
0
2
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
3
1
0
0
0
2
0
0
0
2
0
0
0
2
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
2
0
0
1
1
0
15
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
3
1
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
2
0
0
1
0
2
0
0
2
2
0
0
0
0
1
0
0
0
2
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
1
0
1
1
2
1
2
0
2
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
3
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
2
2
1
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
2
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
4
0
0
0
0
0
0
1
0
0
0
0
1
2
0
2
3
1
2
3
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
2
1
2
0
0
0
1
0
0
0
0
0
0
2
2
1
1
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
5
0
0
0
1
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
2
2
1
0
0
0
0
2
0
0
2
1
0
0
1
0
0
0
0
0
0
2
1
0
1
0
0
0
2
0
2
0
2
1
2
1
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
3
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
2
0
1
0
0
1
0
3
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
3
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
1
0
0
2
1
0
1
1
0
0
1
3
0
0
0
0
1
0
0
2
1
0
2
2
1
0
0
2
1
0
0
0
1
0
2
2
0
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
4
0
0
0
0
0
1
0
3
0
0
1
2
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
2
2
2
0
1
1
0
0
2
0
0
0
0
0
0
3
1
1
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
1
0
0
1
1
0
1
3
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
2
2
0
2
0
0
2
1
1
2
0
2
0
0
0
0
1
0
1
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
3
0
0
0
0
2
0
0
1
0
0
1
2
0
0
0
0
0
3
0
1
0
1
8
2
0
0
0
0
1
0
0
1
1
0
1
2
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
1
0
1
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
2
0
0
0
1
0
0
0
0
0
1
2
0
7
0
0
0
0
5
2
2
0
0
0
0
0
2
0
0
1
0
0
1
0
1
2
0
2
0
0
1
1
0
1
1
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
2
0
3
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
2
3
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
1
2
0
1
0
0
0
2
1
0
0
2
2
0
0
0
2
1
2
0
0
3
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
1
2
2
0
0
2
0
0
2
1
1
0
2
0
1
0
0
0
2
0
0
0
1
0
0
2
0
2
2
0
2
0
0
0
0
0
0
0
1
0
0
1
1
0
7
0
0
0
1
4
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
2
0
0
1
0
1
0
0
0
1
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
2
0
0
1
0
0
0
1
1
0
1
1
0
0
0
1
0
0
0
0
1
0
1
5
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
1
0
1
1
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
2
1
0
0
1
4
1
1
0
0
1
0
0
0
0
2
1
0
2
1
2
0
0
0
2
2
1
0
0
0
2
0
2
1
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
1
0
0
3
0
0
0
0
0
0
2
2
0
2
0
2
1
2
0
0
1
0
0
1
0
3
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
1
1
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
20
0
1
1
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
2
12
4
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
2
6
0
0
2
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
1
1
1
0
0
0
0
2
0
7
0
1
0
0
0
1
0
0
1
1
1
1
4
0
0
0
0
0
1
0
2
1
0
0
0
0
2
0
2
0
0
2
0
6
2
0
0
2
0
1
2
0
0
0
3
3
0
0
0
0
0
1
0
1
1
0
6
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
3
2
0
1
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
3
0
2
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
1
3
0
0
2
0
0
0
0
0
2
2
1
1
0
0
1
0
0
0
0
1
1
1
0
0
0
1
0
2
0
1
0
0
1
1
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
2
0
1
0
2
0
2
0
0
0
0
1
1
1
0
3
0
0
0
4
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
2
0
0
2
0
0
0
0
2
1
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
13
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
1
2
0
0
0
0
0
0
0
0
2
0
0
2
2
1
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
1
1
1
0
0
0
1
0
2
0
6
2
0
0
2
1
1
1
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
1
0
0
0
2
0
2
1
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
4
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
4
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
2
3
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
2
2
0
0
2
0
0
0
2
0
0
1
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
1
0
0
0
1
0
0
0
0
0
1
2
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
2
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
6
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
1
2
0
1
2
0
0
0
0
2
2
2
2
1
0
3
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
1
0
0
0
0
0
1
0
2
1
0
2
0
0
0
0
1
0
1
3
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
1
0
2
0
0
0
0
2
0
0
1
0
2
0
0
2
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
2
0
3
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
2
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
2
3
1
0
0
0
3
0
0
0
0
0
2
0
1
0
0
0
1
2
0
2
2
0
0
0
0
2
0
2
0
1
0
2
0
0
0
0
1
0
0
0
0
1
0
2
0
1
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
2
1
0
0
2
0
2
0
0
0
0
0
0
1
2
2
0
3
1
0
0
0
2
3
0
0
0
2
0
0
1
3
3
0
0
0
1
0
2
0
0
4
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
3
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
2
0
0
2
1
1
0
0
2
0
5
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
1
0
1
0
0
0
2
0
0
0
2
0
0
0
0
1
2
0
0
0
0
1
1
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
2
3
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
1
3
0
1
0
0
0
1
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
1
1
0
2
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
4
2
1
2
0
0
0
1
0
0
3
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
2
0
1
3
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
2
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
2
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
2
0
1
0
2
0
1
2
0
0
2
0
1
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
5
1
3
0
0
1
0
6
0
1
2
2
0
0
0
1
1
2
0
0
1
0
3
1
3
0
1
0
1
1
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
2
0
1
2
0
0
0
0
0
7
1
0
1
0
0
0
0
0
0
1
1
3
2
2
0
2
2
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
1
0
0
0
1
2
6
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
4
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
2
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
1
2
0
1
0
3
4
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
2
2
1
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
2
0
2
0
0
0
0
1
0
0
0
2
0
2
0
8
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
1
3
2
5
1
1
0
0
2
0
0
2
0
0
0
0
0
0
0
5
1
0
1
0
2
1
0
1
0
1
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
1
0
2
1
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
2
1
3
1
3
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
2
0
0
2
0
0
0
2
2
1
1
2
0
0
0
2
0
0
0
0
1
1
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
2
1
0
4
1
0
0
0
0
2
0
0
0
0
0
2
1
2
0
1
1
2
0
0
2
0
2
0
0
0
3
0
0
3
0
1
0
2
0
1
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
5
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
5
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
2
0
0
3
1
3
7
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
2
2
3
2
0
1
0
0
0
0
0
0
0
2
0
2
0
1
0
0
2
0
0
0
0
0
0
2
2
0
0
2
2
0
0
0
0
2
0
2
1
0
0
0
0
0
1
0
2
0
0
2
2
0
2
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
2
0
0
1
0
0
0
0
2
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
1
0
1
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
2
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
1
3
2
0
2
0
0
0
0
0
0
0
2
0
2
1
0
0
0
1
0
0
0
0
0
2
1
1
0
0
0
0
0
0
2
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
2
0
2
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
2
0
0
1
0
1
4
0
1
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
2
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
2
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
2
0
2
2
0
0
1
0
1
2
1
0
1
2
0
1
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
1
6
0
0
0
0
0
2
1
0
1
0
1
0
2
0
0
1
0
0
0
0
1
0
3
0
2
0
0
0
1
0
1
1
1
0
0
2
1
0
0
2
0
0
0
0
1
2
0
2
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
1
2
0
2
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
1
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
1
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
2
1
0
2
0
0
0
2
1
2
0
0
0
0
0
0
2
0
0
1
2
0
0
1
2
0
2
0
1
0
0
0
2
0
0
0
0
0
1
2
0
0
1
1
0
0
2
0
0
1
0
0
0
2
0
2
2
0
2
1
2
0
0
1
0
6
0
0
1
0
2
0
0
2
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
1
0
2
0
0
0
1
1
1
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
1
1
0
0
0
0
2
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
2
0
0
0
0
0
0
1
0
9
0
3
2
0
0
1
0
0
1
0
0
0
2
0
1
1
0
1
2
0
2
0
0
0
1
0
0
2
0
0
0
1
4
1
0
0
1
0
0
0
0
2
0
0
1
2
1
1
0
0
0
0
0
0
0
0
0
2
1
1
0
1
2
2
0
2
0
0
0
0
0
0
6
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
2
2
0
1
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
1
0
0
1
1
0
2
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
5
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
2
0
1
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
2
1
3
0
1
0
0
2
2
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
4
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
1
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
2
0
2
0
1
0
2
0
0
0
0
2
0
0
3
0
0
2
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
2
2
0
2
0
0
0
0
3
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
4
2
0
0
1
0
0
0
0
0
0
1
1
0
0
5
0
0
2
0
2
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
2
1
0
1
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
1
0
0
0
2
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
3
0
2
1
1
3
0
0
1
2
0
1
1
0
0
1
0
0
0
2
0
1
3
0
0
0
0
0
0
1
1
0
0
0
0
5
2
0
1
0
0
0
0
0
2
3
0
1
0
0
1
0
1
0
0
0
0
2
2
0
0
0
0
2
0
2
0
0
0
2
0
2
4
0
0
0
0
0
0
0
0
0
0
0
2
2
2
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
2
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
2
1
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
1
2
1
4
0
2
0
1
0
0
0
0
0
2
0
1
1
2
0
0
1
0
0
1
1
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
2
0
1
3
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
3
1
0
0
0
0
1
0
0
3
2
0
0
0
1
0
0
1
1
0
0
1
0
0
0
1
0
3
0
0
0
0
0
0
0
2
0
5
0
2
0
0
1
1
0
3
2
0
0
2
0
0
0
0
2
2
0
2
0
0
0
0
3
0
0
1
0
0
0
0
2
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
1
1
1
0
1
2
0
1
0
2
2
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
2
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
5
1
0
2
2
0
2
0
0
2
0
0
1
0
0
4
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
3
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
1
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
1
1
1
0
2
0
0
0
0
0
0
1
2
0
0
0
9
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
2
2
0
0
2
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
1
2
1
0
1
0
0
0
1
0
3
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
1
0
0
1
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
1
0
0
0
0
0
1
0
0
1
1
2
0
1
0
2
2
0
0
1
1
0
2
0
0
0
0
1
0
0
0
0
0
0
2
1
0
2
1
0
1
0
1
1
0
0
2
0
2
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
2
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
1
0
0
0
0
0
0
0
0
1
2
1
0
0
0
2
0
0
2
0
3
0
0
0
1
0
0
3
0
0
0
0
1
1
0
0
2
0
1
0
1
2
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
2
0
0
0
0
1
2
0
0
3
0
0
5
0
0
0
0
0
0
1
1
1
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
2
2
0
0
0
1
0
0
2
1
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
2
3
0
0
1
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
1
0
0
0
0
0
1
2
2
0
0
1
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
4
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
2
0
1
3
2
0
0
0
1
1
2
0
1
2
0
0
0
0
0
0
2
0
0
1
2
1
0
1
0
0
2
0
0
0
2
0
0
2
0
2
1
0
0
0
1
0
1
0
2
0
0
2
0
1
0
2
1
0
0
2
2
2
0
1
0
1
0
0
0
0
0
0
2
0
2
0
0
0
4
0
0
1
2
2
0
1
2
2
2
0
0
2
1
0
2
0
0
2
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
3
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
2
2
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
5
0
0
0
1
2
1
0
0
0
0
0
0
0
4
2
1
0
0
0
0
0
1
0
0
0
0
2
2
2
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
1
0
2
0
2
0
1
0
0
0
0
0
1
0
0
1
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
3
0
1
0
3
1
0
2
0
2
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
1
0
2
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
2
0
4
0
0
0
0
0
0
1
1
0
2
0
0
0
0
2
0
0
0
0
1
0
2
2
2
0
1
0
1
0
0
2
0
2
0
2
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
2
0
3
0
1
0
0
0
0
1
0
1
0
0
0
0
2
2
0
0
0
0
0
1
1
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
2
0
2
0
2
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
4
0
0
3
2
3
1
0
0
1
0
0
1
0
4
0
2
0
0
0
0
0
2
2
0
5
2
0
0
0
2
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
1
2
0
1
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
1
1
2
0
2
0
0
0
0
0
3
0
1
0
2
0
2
1
0
0
0
1
0
2
0
2
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
3
1
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
1
6
2
3
0
0
1
1
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
1
0
0
0
0
1
0
0
0
0
1
2
0
2
1
0
0
0
0
2
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
1
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
4
0
0
0
0
2
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
2
2
1
1
0
2
1
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
2
0
1
0
0
0
1
2
0
0
0
1
0
0
1
2
0
0
2
0
0
0
2
2
0
0
0
2
1
0
0
0
1
0
0
0
1
0
2
1
0
2
1
0
0
0
0
0
4
1
0
1
1
0
0
0
1
3
0
0
1
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
1
0
0
0
1
1
0
0
2
0
0
0
0
0
1
2
0
0
0
1
2
2
0
2
0
0
0
0
2
1
0
0
0
0
1
0
0
0
5
2
1
0
0
2
2
0
0
0
2
0
0
0
2
2
0
1
0
0
0
0
0
0
0
1
0
0
1
0
2
0
2
1
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
2
0
1
0
3
2
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
2
2
0
0
0
1
0
0
1
0
0
0
1
2
2
1
0
0
0
0
0
0
0
2
1
2
0
0
2
0
0
0
1
0
0
0
1
2
0
0
0
0
0
2
1
0
1
0
0
5
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
3
1
0
2
2
1
1
0
1
0
1
3
2
1
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
3
4
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
1
0
1
0
0
0
0
0
0
1
0
0
1
2
0
1
0
0
0
0
0
1
0
0
1
2
0
2
3
0
0
0
2
2
2
0
1
1
0
0
0
0
0
3
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
1
2
2
2
2
0
0
0
0
0
0
0
1
2
3
0
2
0
1
0
0
1
0
1
0
2
0
3
0
0
1
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
2
0
0
5
0
1
1
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
1
0
0
0
0
1
1
0
0
2
0
1
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
1
2
2
0
0
0
0
2
0
2
0
0
0
0
2
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
6
0
2
0
2
0
0
0
0
0
0
0
0
0
2
2
1
2
4
1
1
0
2
0
0
0
0
1
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
3
0
1
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
1
2
1
1
0
0
0
0
0
0
0
0
0
2
1
0
5
1
2
3
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
2
2
0
0
0
1
0
0
0
2
0
1
0
0
0
2
2
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
2
0
2
0
0
0
1
2
0
2
0
0
0
0
0
2
0
0
3
2
1
0
0
1
0
2
0
0
1
0
0
1
0
0
1
0
2
1
0
2
1
0
0
0
0
2
2
4
2
0
0
0
0
0
1
0
0
1
0
1
0
2
1
1
0
0
1
2
1
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
2
2
0
0
0
0
2
0
1
1
2
0
0
0
0
1
1
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
3
2
2
1
0
0
0
0
2
0
0
0
0
1
2
0
0
0
1
0
1
2
1
2
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
2
2
0
0
0
1
1
1
2
0
0
2
0
0
0
0
2
0
1
0
5
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
3
0
0
2
0
0
2
0
0
3
0
1
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
4
0
0
0
2
2
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
5
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
1
1
0
0
1
0
0
0
0
0
0
2
1
0
0
1
6
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
3
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
2
0
2
0
1
0
0
0
1
2
0
2
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
3
0
0
2
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
2
2
0
0
1
0
0
2
2
1
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
2
0
0
1
0
0
0
0
0
1
5
0
0
0
2
2
2
0
1
0
1
0
2
0
0
2
1
0
0
1
0
0
2
2
0
0
0
2
1
2
2
0
2
0
0
1
0
0
0
0
2
1
2
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
1
2
0
0
1
0
0
2
0
0
1
0
3
0
0
0
2
1
0
0
1
0
0
1
2
1
0
0
0
0
0
3
0
2
0
1
0
0
1
0
1
2
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
2
0
0
2
0
2
1
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
2
0
2
0
0
1
0
0
2
0
0
0
1
0
0
0
2
0
0
0
2
0
2
0
0
2
0
0
0
2
0
1
1
2
3
0
0
1
0
0
1
4
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
2
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
1
2
0
0
0
0
1
0
0
0
2
0
2
1
0
0
1
3
0
0
0
2
0
0
0
0
2
1
2
0
0
2
0
0
4
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
1
2
1
2
0
0
0
1
1
2
0
0
0
0
0
3
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
2
1
0
1
0
0
0
1
1
2
0
0
2
0
0
1
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
2
0
4
0
0
0
0
0
1
2
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
3
2
0
0
2
1
0
2
2
0
2
0
2
0
0
0
0
0
1
0
0
0
2
0
0
2
0
2
0
1
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
2
1
2
3
0
0
0
0
0
1
3
0
0
1
0
2
1
0
0
1
1
0
0
1
1
0
1
2
0
2
0
0
0
0
1
0
2
0
0
0
1
0
0
2
2
1
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
1
0
0
1
0
1
0
0
3
0
1
0
1
2
0
0
2
0
2
0
0
2
0
1
2
0
0
1
2
0
0
0
0
2
0
0
2
3
0
0
0
0
0
1
2
0
0
0
2
0
0
1
0
0
0
0
0
1
1
0
4
2
1
0
0
0
1
0
0
1
1
0
0
0
1
2
0
2
1
0
2
0
0
0
0
1
2
2
0
0
2
0
0
0
2
1
1
0
0
3
0
0
0
1
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
2
0
0
1
0
0
0
2
0
3
1
5
0
0
0
0
0
2
0
0
1
0
2
3
2
1
1
2
0
1
0
2
0
2
1
0
0
2
0
0
0
0
0
2
0
1
0
0
1
0
1
0
2
0
0
1
2
0
1
1
1
1
1
0
0
2
2
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
2
0
0
0
0
1
0
0
2
3
0
0
1
0
0
0
0
1
2
0
0
0
2
0
1
4
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
1
0
2
0
0
0
2
0
1
0
1
0
2
0
0
0
0
0
0
0
1
0
1
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
1
1
3
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
1
0
0
1
0
0
1
2
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
3
0
1
2
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
1
2
1
0
0
2
2
0
1
0
0
0
0
2
0
0
0
1
2
0
0
2
0
0
0
0
2
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
1
0
1
0
0
1
2
1
0
0
0
0
0
1
2
0
0
4
0
2
0
0
0
0
2
2
0
0
0
1
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
3
0
2
2
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
1
0
3
0
0
0
1
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
1
0
0
0
2
0
0
0
1
0
1
2
0
0
0
0
0
2
0
2
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
2
2
0
2
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
5
0
0
3
0
2
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
1
4
0
2
0
2
0
1
0
1
0
0
2
2
0
0
1
2
0
0
0
0
0
0
1
1
1
0
0
0
0
1
1
2
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
1
2
1
0
1
0
0
1
2
2
1
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
3
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
1
0
1
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
1
1
2
1
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
1
1
1
0
0
1
2
0
2
0
2
1
0
0
2
1
0
0
1
0
1
0
0
3
0
2
0
1
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
2
2
0
0
1
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
1
0
0
1
1
0
1
1
0
3
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
1
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
1
2
1
0
2
2
1
0
0
0
2
2
5
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
2
0
0
0
3
0
1
0
2
0
2
0
3
1
0
6
0
0
1
2
0
4
1
2
0
0
0
1
0
2
0
0
0
0
1
0
0
0
2
2
2
2
0
1
0
0
1
0
2
1
0
0
0
1
2
1
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
1
2
2
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
2
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
5
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
1
0
1
0
2
0
2
0
0
2
0
0
0
1
0
2
3
2
1
0
0
0
0
2
0
4
0
0
1
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
2
2
0
1
0
0
1
0
0
1
0
0
0
0
1
1
0
0
1
0
1
1
0
0
0
2
2
0
0
0
2
0
0
0
0
2
1
0
0
0
3
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
7
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
3
2
0
0
0
0
0
0
4
0
0
1
2
0
0
1
0
0
0
1
0
0
0
2
0
0
1
0
0
0
3
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
2
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
5
0
0
3
0
0
0
0
1
0
0
0
0
0
0
1
2
0
2
0
0
4
2
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
1
1
0
0
0
2
2
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
2
1
0
0
0
1
0
0
0
1
0
1
0
1
2
0
0
0
1
2
0
0
0
0
0
0
1
1
0
4
0
0
0
0
0
2
2
2
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
2
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
2
0
0
0
1
0
0
0
2
0
0
0
2
2
0
0
0
0
2
2
1
4
0
1
0
2
0
0
2
0
0
0
0
1
0
1
0
2
0
0
0
0
2
0
1
0
0
0
0
1
0
3
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
2
3
0
0
2
0
0
0
1
0
0
0
0
1
1
1
0
0
0
2
2
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
2
0
0
0
0
1
1
2
2
0
1
0
0
2
0
2
0
0
0
1
0
0
0
0
1
2
3
0
0
0
0
0
2
2
0
0
0
0
0
0
2
2
3
0
1
0
2
1
0
0
0
0
0
2
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
1
1
0
2
0
0
1
0
2
2
0
1
0
2
0
1
0
0
0
1
0
0
0
0
0
2
0
2
0
2
2
0
0
2
1
2
0
0
0
0
0
0
0
1
1
0
0
1
8
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
2
0
0
0
1
0
0
0
0
2
0
1
0
2
0
0
0
2
0
0
0
0
0
0
1
0
2
1
0
0
1
3
1
1
0
2
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
2
3
0
1
1
0
1
1
0
2
0
0
0
0
2
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
3
2
0
0
3
0
3
0
0
0
0
0
0
1
0
0
9
0
0
0
1
0
0
2
0
0
0
0
1
0
2
2
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
2
0
0
0
2
0
0
2
0
0
0
2
0
2
0
0
1
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
1
1
0
1
0
1
0
0
0
1
0
0
0
0
1
2
3
0
1
2
1
1
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
2
2
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
1
0
2
0
0
0
0
2
0
0
2
2
0
0
1
0
0
0
0
0
0
3
0
1
0
0
0
0
1
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
1
2
0
1
2
1
0
2
1
0
0
0
1
0
2
0
2
0
0
0
2
2
2
0
0
0
2
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
2
1
0
2
0
0
0
2
0
0
0
1
0
0
2
0
2
1
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
3
0
1
2
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
4
0
0
2
1
0
0
0
0
0
1
1
0
0
2
1
2
0
0
0
2
0
1
1
0
0
0
0
1
0
1
0
0
2
2
0
0
1
2
0
0
0
1
2
0
0
2
0
2
0
0
0
0
1
0
2
0
0
0
2
2
0
0
0
2
1
0
0
0
2
0
0
0
0
3
0
2
2
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
1
0
2
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
2
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
2
1
2
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
5
0
0
0
0
0
1
0
1
0
2
0
0
2
0
2
0
0
0
2
0
0
1
0
1
0
0
0
0
0
2
0
2
0
1
0
0
1
0
2
0
2
1
2
0
3
0
0
4
0
0
0
1
0
0
0
3
0
2
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
2
1
0
0
2
0
0
0
1
2
0
1
0
0
0
1
0
0
2
0
0
1
0
0
2
1
0
0
0
0
2
0
0
0
0
1
2
0
0
0
1
2
0
0
0
1
1
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
1
0
0
0
2
0
1
0
1
0
2
2
1
0
0
0
0
0
0
0
0
3
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
3
3
2
2
2
0
2
0
1
0
0
0
2
1
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
1
2
0
2
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
1
2
2
1
0
0
0
3
0
0
0
2
0
0
1
2
0
0
1
0
0
0
1
0
1
1
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
2
1
0
2
0
2
0
0
0
0
2
0
0
3
1
0
0
0
1
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
1
0
0
1
0
0
1
0
0
0
0
0
2
1
0
0
0
0
3
2
1
0
0
2
0
1
0
1
0
0
2
0
0
1
0
1
0
1
2
1
0
0
0
0
2
2
0
0
1
0
0
1
0
0
0
2
1
2
1
2
0
0
0
0
0
0
1
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
1
0
2
0
1
0
2
0
0
0
0
0
2
0
0
0
0
2
0
2
0
2
2
2
0
1
0
0
1
1
6
0
3
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
1
0
2
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
2
1
0
2
0
1
0
2
2
3
0
0
2
1
0
0
0
0
0
2
0
2
0
2
2
0
0
0
0
0
0
0
0
10
1
0
0
0
0
0
0
0
0
0
0
2
2
4
2
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
2
0
0
0
1
2
2
2
0
0
0
2
2
0
1
0
0
0
0
0
0
1
0
0
0
1
2
1
0
0
0
1
1
1
0
2
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
1
0
0
0
0
0
2
5
0
2
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
2
0
0
0
2
2
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
1
2
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
2
0
0
1
2
0
0
1
0
0
0
2
0
0
0
0
1
0
0
1
4
0
0
2
2
0
0
0
0
2
2
1
0
0
0
0
0
3
3
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
2
2
0
1
3
1
0
0
1
0
2
1
0
3
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
1
0
1
1
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
1
1
0
2
1
0
0
0
0
0
0
0
3
0
0
1
0
0
1
0
0
0
1
0
0
0
4
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
2
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
1
1
0
6
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
3
0
2
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
1
0
1
1
0
3
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
2
0
1
1
1
1
0
0
0
2
0
1
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
1
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
3
1
2
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
3
0
0
2
1
0
1
2
1
0
0
0
0
0
0
0
0
0
1
0
1
0
3
0
0
1
0
1
1
2
0
0
0
1
0
2
0
2
0
0
2
2
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
4
0
4
0
2
0
0
0
1
1
0
0
0
1
0
0
0
0
3
0
2
2
0
0
0
0
0
1
0
0
0
0
4
0
1
0
1
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
2
0
2
2
2
0
0
0
1
0
0
0
0
0
1
3
0
0
0
2
2
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
1
0
1
0
2
1
0
2
0
0
0
0
0
0
0
1
0
0
0
2
3
0
0
2
0
0
2
1
0
0
0
1
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
2
0
3
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
1
0
0
0
1
2
0
0
0
0
3
0
0
1
1
2
0
0
0
0
2
2
0
0
0
1
0
0
0
0
2
0
2
0
1
2
0
0
0
0
0
0
2
2
1
2
0
0
0
1
4
0
0
0
2
2
1
2
2
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
1
2
0
0
1
0
0
0
0
0
0
2
2
0
2
0
1
0
1
0
2
2
0
2
0
0
0
0
0
2
2
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
2
0
0
1
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
3
1
0
4
2
0
1
0
1
1
1
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
1
0
3
0
0
0
0
0
2
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
2
0
0
2
0
6
0
2
0
2
1
0
0
0
2
2
1
0
0
3
0
0
0
1
2
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
1
2
0
1
0
1
0
3
4
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
1
1
0
1
0
0
2
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
2
0
0
0
0
1
1
0
0
2
0
0
0
1
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
2
2
4
0
0
1
0
2
0
0
0
0
0
2
0
3
0
0
0
1
1
0
2
0
0
0
0
0
2
3
2
2
3
0
0
0
2
0
0
2
0
0
1
0
2
0
0
0
0
0
2
0
1
1
1
0
0
0
6
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
2
2
1
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
3
2
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
1
0
3
0
1
1
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
2
2
2
0
1
0
0
0
2
0
0
0
0
0
1
4
0
0
2
0
0
2
0
2
0
0
0
0
0
4
0
0
1
1
0
1
0
3
0
2
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
1
0
3
1
0
0
0
0
0
0
2
0
0
5
1
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
2
2
0
0
0
4
2
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
1
1
0
0
2
0
0
0
0
0
2
0
0
2
1
0
0
2
0
0
1
8
2
0
0
0
1
2
1
0
1
0
0
3
0
0
0
1
0
0
1
0
0
2
0
0
0
0
2
2
2
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
1
0
1
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
2
1
0
0
2
0
0
0
2
0
0
0
0
0
1
0
1
2
0
2
2
0
0
0
0
0
0
0
0
2
0
4
0
2
1
2
1
0
1
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
5
0
0
2
0
0
0
0
2
0
0
2
0
0
2
0
1
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
1
0
0
0
1
2
0
0
2
0
0
0
1
0
0
0
0
0
0
1
2
1
1
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
4
1
0
0
0
2
0
1
0
1
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
4
0
0
3
0
1
0
3
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
2
1
0
0
2
0
0
0
0
0
0
0
1
0
0
1
2
0
0
1
0
1
0
2
0
0
0
0
0
0
1
2
0
0
0
2
1
0
0
0
2
1
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
2
2
0
0
0
1
2
7
0
2
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
1
1
0
0
1
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
6
2
3
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
1
0
0
0
0
1
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
2
4
1
0
1
0
2
0
0
2
0
0
2
0
1
0
0
0
0
0
1
0
2
0
0
0
1
0
0
1
0
1
0
2
1
4
0
0
0
0
0
0
0
1
0
1
2
2
0
1
1
0
2
0
0
0
0
0
0
0
3
0
0
0
1
1
1
1
1
0
0
0
0
0
1
0
0
0
0
1
2
2
0
0
3
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
1
1
0
2
0
2
0
0
0
0
1
0
0
0
0
2
2
0
0
2
0
2
2
1
0
0
0
0
2
0
0
0
0
1
3
0
1
0
0
0
0
0
1
2
0
0
0
2
0
0
2
0
0
1
0
0
0
3
0
0
2
0
1
0
0
3
2
0
2
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
4
0
0
2
0
2
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
1
1
2
0
1
1
2
2
2
1
2
0
0
0
0
0
3
0
0
0
1
3
1
2
1
0
1
0
2
1
0
0
1
0
0
0
0
1
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
2
2
0
2
0
2
2
0
1
0
1
0
0
0
0
0
0
0
3
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
7
2
0
2
2
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
2
0
1
1
0
0
0
2
0
0
1
0
0
0
0
0
0
2
1
0
0
0
2
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
3
0
0
0
0
2
2
0
0
0
1
0
0
1
0
2
1
0
0
1
0
1
3
1
1
0
0
2
0
0
2
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
2
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
2
2
2
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
2
0
1
0
0
2
2
0
2
0
2
2
0
0
0
0
0
2
2
1
0
1
0
0
2
0
0
2
1
0
0
0
0
0
0
0
4
0
1
0
2
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
2
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
1
2
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
4
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
1
0
0
0
2
1
0
0
2
0
1
0
0
1
0
0
2
0
1
0
0
0
1
1
2
0
1
1
0
0
0
0
0
3
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
1
0
0
0
1
0
0
1
1
0
1
0
2
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
8
0
0
3
0
0
2
1
0
2
0
2
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
1
0
1
2
0
1
0
1
1
6
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
2
2
0
0
0
2
0
0
0
2
1
0
0
0
0
0
3
0
0
1
2
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
1
0
1
2
0
0
0
0
2
0
0
1
0
2
1
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
3
0
0
0
0
2
0
0
2
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
1
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
3
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
1
2
0
0
3
0
1
0
2
0
2
0
2
0
0
0
0
0
0
1
0
1
0
0
0
2
0
1
0
0
1
0
0
0
0
1
0
1
2
0
0
1
0
1
1
0
0
0
3
0
0
4
0
0
0
1
2
0
2
0
1
2
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
1
0
2
0
0
0
2
0
0
0
0
2
0
1
1
0
1
0
2
4
0
0
2
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
2
0
4
0
0
2
1
2
0
0
0
0
0
0
0
0
1
2
1
1
0
1
0
2
0
0
1
0
0
2
0
0
2
1
0
0
0
1
1
2
0
1
0
0
2
0
0
0
1
0
0
2
0
0
1
0
2
0
0
0
0
2
0
0
2
0
0
1
2
0
1
1
1
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
1
0
5
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
2
0
0
0
0
2
1
0
0
5
0
2
0
0
0
0
2
0
0
2
0
2
1
2
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
2
0
0
0
0
2
0
0
3
2
0
0
0
0
0
0
0
1
0
0
0
2
0
1
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
6
0
0
0
0
0
0
1
2
0
0
2
4
0
0
0
1
0
0
0
0
0
1
0
0
2
0
1
4
1
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
7
2
0
1
0
3
3
0
0
1
0
0
1
0
0
0
0
1
3
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
1
0
1
0
0
0
0
1
1
0
0
0
0
1
0
2
0
1
1
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
2
0
0
2
0
0
0
1
2
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
3
0
1
0
2
0
0
0
2
1
0
2
0
0
0
1
1
2
0
0
0
2
2
1
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
1
0
3
0
0
2
0
0
1
1
3
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
5
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
2
0
0
2
1
0
0
1
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
1
1
2
0
0
2
0
2
0
0
0
2
0
0
2
3
1
2
0
1
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
1
0
1
0
0
2
1
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
2
2
0
2
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
1
1
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
1
0
1
0
0
1
2
0
2
0
0
0
2
2
0
3
0
0
0
0
0
0
0
1
2
0
2
3
0
0
0
0
2
0
0
0
2
2
0
0
0
2
0
0
0
0
1
0
0
0
1
1
0
2
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
2
2
0
0
0
0
0
0
0
0
0
1
2
0
1
1
2
0
0
2
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
1
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
2
0
0
2
0
0
0
0
3
0
0
0
0
2
2
0
0
1
2
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
2
0
2
2
0
0
1
0
2
1
0
1
0
1
0
0
2
0
2
3
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
3
2
0
0
1
0
0
1
2
0
2
0
1
0
2
1
3
3
2
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
2
0
2
0
2
0
0
1
0
1
2
1
0
3
0
0
0
0
0
0
1
0
0
2
2
1
2
0
1
2
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
3
4
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
2
0
2
0
2
1
1
0
0
0
2
0
2
0
0
0
0
2
0
0
1
0
0
2
1
0
0
0
2
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
2
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
1
2
0
0
0
1
0
2
0
0
0
2
1
2
0
1
0
0
0
1
1
2
2
0
0
1
0
1
0
1
2
0
2
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
1
0
0
0
0
0
2
0
2
0
1
0
0
0
2
0
0
0
1
0
0
2
1
0
2
0
0
1
0
0
4
0
0
0
0
1
1
0
1
0
2
0
0
0
0
0
2
1
0
0
0
0
2
0
1
0
1
0
2
1
1
0
0
0
1
0
2
0
0
2
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
1
2
0
1
3
2
0
0
3
0
0
2
0
0
1
0
0
0
0
0
1
2
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
4
2
0
1
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
1
2
4
0
0
0
0
0
1
1
0
0
0
0
0
3
0
0
2
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
4
1
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
2
2
0
0
0
0
1
1
0
0
5
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
2
1
2
2
0
0
0
0
1
0
0
1
2
0
0
0
5
0
2
0
1
0
0
2
0
0
0
1
1
0
0
2
2
1
0
2
0
0
0
2
1
0
0
1
2
0
0
0
0
0
0
2
0
1
1
0
0
3
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
2
2
0
0
1
2
0
0
2
0
0
0
1
1
0
0
2
2
0
1
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
2
0
0
0
0
0
4
0
0
0
1
0
3
1
1
0
0
4
0
0
0
0
0
0
0
0
3
0
0
7
0
0
1
0
0
0
0
4
0
0
0
1
2
0
1
0
0
1
0
0
3
0
0
0
1
0
0
1
1
0
0
2
2
0
0
0
0
2
1
0
0
2
2
0
1
0
0
0
0
1
0
2
0
4
1
0
0
1
0
2
0
0
3
0
0
2
0
0
3
1
0
0
0
0
2
0
2
2
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
1
1
0
2
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
1
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
2
0
1
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
2
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
2
0
2
0
3
0
2
0
0
1
0
0
3
1
0
0
1
0
0
0
0
2
0
0
2
0
0
3
0
1
0
0
0
0
1
3
0
0
0
0
0
0
0
0
2
0
1
0
1
1
1
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
1
0
0
0
2
1
0
2
0
0
0
0
0
1
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
1
2
0
3
0
2
0
2
0
0
2
0
0
2
0
0
2
2
0
2
0
0
7
0
0
1
2
0
0
0
1
0
2
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
2
2
1
0
0
1
2
0
0
0
0
1
0
0
0
1
0
0
1
1
2
2
0
0
0
0
0
0
0
0
1
0
2
3
1
1
1
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
3
2
0
2
0
0
0
0
0
3
2
2
0
3
0
2
1
0
0
1
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
1
1
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
2
0
0
0
1
0
1
1
0
0
2
1
0
0
1
0
0
0
2
0
1
0
3
0
0
3
2
0
0
0
0
1
0
2
0
0
0
0
2
1
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
2
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
3
1
2
0
1
0
0
2
0
3
1
0
1
1
0
0
0
0
2
0
0
2
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
2
0
0
0
0
0
0
2
0
0
0
1
0
1
0
1
0
0
0
0
0
3
2
0
0
1
0
1
0
2
2
0
2
1
2
0
0
0
0
0
1
1
1
0
3
0
0
1
0
2
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
1
1
1
0
2
1
2
0
0
2
2
0
0
1
1
3
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
2
0
0
2
0
2
0
0
2
0
0
0
0
0
0
1
0
2
2
1
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
2
0
0
0
1
1
0
4
3
2
2
0
2
0
2
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
1
0
0
0
2
0
0
0
0
0
1
0
0
1
2
2
1
0
1
0
0
0
0
0
1
0
2
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
1
0
1
0
0
2
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
2
0
0
1
2
2
1
2
1
1
0
0
1
0
0
0
0
0
1
2
0
1
11
0
2
1
0
0
0
2
0
0
0
1
2
0
2
0
0
8
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
2
2
0
0
0
0
0
1
0
2
1
0
1
0
0
0
3
0
1
1
3
0
0
0
2
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
1
1
1
2
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
2
0
0
1
0
1
4
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
1
0
0
0
4
0
0
0
0
0
0
0
1
0
0
1
1
2
0
1
0
0
1
2
0
0
0
1
0
1
0
0
2
0
1
0
0
2
0
0
1
1
2
1
1
0
0
0
0
0
2
0
1
0
1
3
0
1
0
1
0
1
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
2
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
4
0
1
0
2
0
0
0
3
1
2
0
0
2
0
2
1
0
0
2
0
2
0
1
0
0
0
0
1
4
0
1
0
0
0
2
1
0
2
1
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
2
0
1
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
2
0
2
0
2
0
0
1
0
0
2
2
0
2
1
0
0
0
0
0
2
2
2
2
2
0
1
0
0
2
2
0
1
0
2
0
3
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
1
7
8
2
0
0
0
0
0
0
3
1
0
1
1
0
0
0
0
0
0
2
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
1
0
0
0
0
0
2
0
3
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
2
0
1
0
0
0
0
1
1
0
0
1
0
0
0
2
8
0
0
0
0
0
0
4
0
0
1
4
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
1
0
1
0
1
0
3
0
0
0
2
2
0
0
3
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
1
0
0
1
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
1
1
0
3
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
6
0
0
0
0
0
0
0
1
0
6
0
2
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
1
2
2
0
1
0
2
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
3
0
0
1
0
1
0
0
0
0
0
0
2
0
1
0
0
3
2
0
2
2
0
2
0
2
1
0
0
0
0
2
0
0
1
0
0
0
0
1
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
2
1
0
1
0
0
0
0
1
1
0
0
0
0
2
1
2
0
0
0
2
0
0
0
0
0
1
2
0
0
0
2
0
0
1
0
1
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
1
0
0
1
3
0
2
0
5
0
0
1
0
1
0
2
6
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
1
2
3
1
0
0
0
2
3
1
4
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
2
1
1
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
3
0
2
2
0
0
1
4
0
0
0
0
0
2
0
1
1
0
0
0
0
0
2
2
1
1
1
0
0
1
0
0
0
2
0
2
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
1
0
0
2
0
0
0
1
0
0
0
1
0
2
0
1
1
2
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
2
0
0
0
0
0
0
2
0
3
1
0
0
0
0
2
0
2
3
0
0
0
1
0
2
1
2
0
0
1
1
0
1
1
2
0
0
0
0
0
0
1
2
2
2
0
0
0
1
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
1
0
0
2
0
0
0
2
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
2
0
1
0
0
0
1
2
0
0
0
1
1
0
0
1
2
1
0
2
0
0
3
0
2
0
0
0
0
0
1
0
0
1
1
1
0
1
1
0
0
2
0
2
0
0
3
0
0
0
1
0
1
0
2
1
0
0
0
0
0
0
2
1
0
1
3
0
0
0
2
0
0
2
0
0
0
2
1
0
2
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
1
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
2
0
0
2
5
2
2
2
5
0
0
0
0
2
2
0
0
0
0
1
2
2
4
0
0
2
0
1
1
2
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
2
2
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
1
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
2
1
1
1
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
2
1
0
1
2
0
1
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
2
2
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
2
1
0
0
0
0
0
0
1
2
6
0
1
1
0
1
2
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
2
0
1
0
0
1
1
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
1
2
1
0
0
0
2
0
0
1
0
0
0
0
1
0
0
4
0
0
0
0
0
2
2
2
0
3
0
0
1
0
1
1
0
5
3
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
1
0
1
1
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
1
0
0
1
0
0
0
0
2
4
0
2
0
0
0
1
1
0
2
0
0
0
0
2
2
0
1
2
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
5
0
5
2
0
1
2
0
1
1
0
0
0
0
0
0
2
0
2
1
2
1
0
2
1
0
2
0
0
2
0
0
1
2
0
1
0
1
0
0
2
0
2
0
0
0
0
0
0
1
1
1
0
0
2
0
0
0
0
0
0
2
0
0
2
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
1
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
1
1
2
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
3
0
0
2
1
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
1
1
0
1
0
0
2
0
0
0
0
2
2
1
0
0
0
0
0
0
1
1
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
2
2
0
0
0
0
0
0
1
0
0
0
7
1
0
0
0
0
0
0
0
0
2
0
0
2
2
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
2
0
0
0
3
1
1
0
0
2
0
0
2
0
2
0
2
2
0
0
3
0
0
2
0
0
0
2
0
0
1
0
1
2
0
2
0
1
0
0
0
0
2
1
0
0
0
0
3
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
1
0
1
0
0
0
2
0
2
0
2
0
0
1
1
0
0
0
0
0
0
0
1
0
0
2
1
1
1
1
0
0
0
0
0
0
0
2
0
1
1
1
0
1
0
0
0
0
0
1
2
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
2
0
2
2
0
0
1
0
1
0
1
0
0
1
2
1
0
0
0
2
0
0
0
2
0
0
1
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
1
0
0
0
0
3
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
2
2
1
2
0
0
0
1
2
0
2
0
0
3
0
0
2
2
0
0
0
1
0
0
0
2
0
0
2
0
2
0
2
2
0
0
5
2
0
1
0
0
3
0
0
0
0
0
0
1
1
0
2
0
0
0
1
2
0
0
0
1
0
0
0
2
0
0
0
0
2
1
2
1
1
0
0
0
0
1
0
2
2
0
3
0
1
0
0
0
1
0
0
0
0
2
2
1
2
0
0
0
0
0
2
1
2
0
1
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
1
0
1
0
0
2
0
0
1
0
0
1
1
0
1
0
0
0
1
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
5
0
2
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
3
2
2
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
2
1
1
0
1
1
1
0
1
1
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
2
1
2
0
0
2
0
0
0
0
4
0
1
0
2
1
0
0
6
2
0
1
0
0
0
2
3
1
1
0
0
0
1
1
0
0
2
1
2
0
4
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
1
1
2
0
2
1
0
1
1
0
0
0
2
0
0
1
0
2
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
1
0
2
1
0
0
2
0
0
2
0
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
2
0
1
1
0
1
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
2
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
3
1
0
0
2
1
0
2
1
0
0
0
0
1
0
0
2
1
0
0
0
0
0
1
2
0
1
0
0
0
0
0
2
1
0
0
0
0
2
1
2
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
1
0
0
1
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
2
0
0
3
1
0
0
0
0
2
1
0
0
2
0
0
1
0
1
0
2
0
0
1
1
0
0
3
0
1
0
2
0
1
0
1
5
0
3
2
0
0
0
1
0
2
2
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
2
2
0
1
0
3
0
2
2
2
0
0
0
1
0
0
2
2
0
0
0
4
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
3
0
0
1
0
0
0
2
0
0
0
3
0
0
2
2
1
0
1
0
1
3
2
0
0
2
0
0
2
0
0
0
0
0
1
2
0
0
0
2
0
1
2
2
1
0
1
2
2
2
0
2
0
0
0
0
0
1
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
2
1
0
0
2
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
5
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
1
0
3
0
0
2
0
0
0
0
0
0
1
1
2
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
2
0
1
0
0
0
0
0
0
0
0
0
0
2
2
1
1
1
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
2
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
1
0
2
1
0
0
0
2
0
0
2
2
0
2
1
0
0
2
2
0
0
0
0
0
0
0
0
0
2
1
0
2
0
2
1
0
2
2
0
1
0
0
0
0
0
0
0
1
0
0
2
1
0
1
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
2
0
2
0
0
0
2
2
0
0
0
1
1
0
0
2
2
0
2
0
0
0
0
0
0
6
0
0
1
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
1
0
2
0
0
1
0
2
0
2
2
0
0
0
0
1
2
0
2
1
1
0
1
2
0
2
1
0
0
0
0
0
1
2
0
3
2
0
0
0
0
0
6
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
1
1
0
0
4
2
2
2
0
0
3
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
2
0
0
0
0
1
0
1
0
0
0
1
0
0
4
0
0
1
0
0
2
0
0
1
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
1
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
2
0
0
1
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
1
2
0
0
1
0
2
2
0
0
2
1
0
1
0
0
0
0
1
1
1
0
0
0
2
2
2
0
0
1
0
0
0
1
0
2
0
0
1
2
0
2
2
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
2
0
0
2
1
2
0
0
0
0
1
0
0
1
0
0
2
2
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
3
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
1
0
0
1
0
1
0
0
0
0
0
1
2
0
1
0
0
0
0
0
1
0
2
0
1
0
0
3
0
0
0
0
1
0
1
1
0
0
2
2
0
0
2
0
0
0
0
1
2
1
2
2
0
0
0
0
0
5
0
0
2
0
0
2
0
0
1
2
2
0
0
0
0
0
0
0
1
0
2
0
2
0
3
5
2
1
0
0
2
2
0
0
0
1
2
1
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
5
0
1
0
2
0
2
1
0
0
1
0
1
0
0
0
0
0
0
2
0
2
1
2
0
3
1
0
1
0
1
3
0
0
0
9
0
0
0
0
0
2
1
0
0
2
2
0
0
0
1
0
0
0
0
0
2
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
2
1
0
1
0
1
1
0
2
2
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
3
0
0
0
0
0
2
2
1
2
0
0
2
0
0
2
0
0
2
0
0
0
0
2
1
0
1
0
0
1
1
3
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
2
1
2
0
0
0
0
10
0
2
3
0
0
0
2
0
0
0
0
0
0
0
3
0
0
2
0
1
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
4
0
2
2
0
0
1
0
0
0
0
0
0
2
2
0
2
0
1
0
0
0
0
0
0
0
3
0
0
1
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
3
0
0
0
0
0
0
1
0
2
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
2
2
0
3
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
2
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
3
0
1
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
2
0
0
0
0
2
0
2
1
0
2
1
3
1
2
1
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
2
0
1
2
0
1
0
0
2
2
2
0
0
2
1
0
0
0
0
1
0
0
6
0
0
0
0
0
0
0
0
0
1
0
2
1
2
0
0
0
2
0
0
4
0
1
0
0
0
0
1
0
1
0
0
2
0
0
0
2
1
0
1
1
0
0
2
1
0
1
1
0
2
0
0
0
0
0
3
2
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
2
0
1
0
0
0
0
0
1
0
0
2
0
2
1
1
1
0
0
0
0
0
0
0
2
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
1
1
1
0
0
0
0
0
3
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
2
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
1
0
0
2
0
1
2
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
3
2
2
0
0
2
2
0
0
2
2
2
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
1
0
0
2
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
6
2
0
2
0
0
1
2
0
3
0
0
1
0
0
0
0
0
1
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
3
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
2
1
1
0
2
2
0
0
1
2
7
0
0
0
0
1
0
0
2
0
0
0
4
0
0
0
0
0
0
0
0
2
0
2
0
1
1
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
4
1
0
5
0
0
1
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
2
1
0
0
1
1
2
1
2
4
2
1
0
1
0
1
0
0
0
2
0
1
0
0
2
0
2
0
0
3
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
1
3
1
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
1
0
1
0
2
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
0
2
0
4
0
0
0
0
2
0
0
0
2
1
1
1
0
1
0
2
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
2
0
1
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
2
2
0
1
0
0
2
0
0
1
1
0
0
0
3
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
5
0
0
2
0
0
0
0
0
2
0
0
0
4
0
1
0
1
1
3
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
1
3
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
2
5
0
1
0
0
0
2
0
0
0
0
0
0
3
4
0
0
1
0
0
0
1
0
0
2
0
3
0
0
1
2
0
0
1
0
0
3
0
1
0
0
0
0
0
0
0
0
2
2
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
1
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
1
0
2
1
0
0
0
1
0
0
0
0
0
0
2
1
1
2
0
0
0
0
0
0
1
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
2
0
2
2
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
2
0
1
0
0
0
1
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
1
1
0
3
0
2
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
5
3
1
0
0
1
0
2
0
0
1
0
0
0
0
1
2
0
1
0
0
2
1
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
4
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
2
0
1
2
0
0
1
0
0
0
1
0
3
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
4
1
1
0
0
2
2
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
1
0
2
2
2
0
2
0
0
0
0
1
0
2
0
2
0
0
0
2
2
0
0
0
0
0
2
0
1
0
1
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
1
0
1
0
0
0
0
0
2
1
0
0
2
1
2
1
2
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
1
0
0
0
0
0
0
3
0
2
0
2
2
0
0
0
0
0
3
0
0
1
2
0
0
0
1
0
2
0
1
0
1
1
0
0
1
0
2
0
0
2
0
0
1
0
1
1
0
2
2
0
0
0
2
2
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
2
0
0
0
2
2
0
0
0
2
0
0
0
0
3
2
0
0
0
2
0
0
1
2
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
3
0
0
1
0
5
0
0
0
0
0
0
1
2
0
1
0
0
1
0
0
3
0
0
0
0
0
0
0
0
2
1
2
0
0
2
0
0
1
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
3
0
0
0
2
0
0
1
1
1
0
0
0
4
0
0
1
0
0
0
0
0
1
2
0
0
1
2
0
0
2
0
0
1
0
1
0
0
1
1
1
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
2
0
2
0
0
3
1
0
1
0
0
0
0
7
1
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
1
2
3
0
0
0
0
2
0
0
1
0
1
0
0
0
1
2
0
0
1
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
2
0
0
2
1
0
0
2
0
1
0
0
2
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
1
3
2
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
1
0
0
0
1
0
0
0
0
2
0
0
0
0
2
1
0
0
3
2
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
1
0
0
0
2
0
1
0
0
0
0
0
2
0
4
2
0
0
0
4
0
0
1
0
0
0
0
0
3
0
0
0
0
0
1
2
1
0
0
1
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
2
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
1
2
2
0
0
1
7
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
1
0
0
1
0
2
3
0
2
1
0
0
1
1
1
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
1
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
2
0
1
0
0
1
0
0
0
0
0
3
0
0
0
1
2
0
0
2
0
2
0
0
0
4
0
0
0
0
1
1
0
0
0
2
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
1
1
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
5
0
0
1
0
0
0
0
1
2
2
1
0
0
0
0
0
0
0
0
0
0
2
2
1
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
4
0
2
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
2
1
0
0
2
0
0
0
0
2
1
4
1
0
0
0
0
0
1
0
0
0
1
1
1
2
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
1
0
0
2
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
2
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
1
0
0
0
3
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
2
2
5
0
1
0
0
0
1
0
0
2
0
2
2
0
0
1
0
0
1
0
0
3
1
1
0
0
0
4
0
0
0
2
0
0
1
0
2
0
0
1
8
0
1
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
1
0
0
0
2
0
0
1
0
7
4
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
1
2
0
1
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
1
0
0
0
0
2
2
0
1
0
0
0
0
1
0
3
0
0
2
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
2
2
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
2
0
0
2
0
1
0
0
0
0
0
0
1
1
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
2
3
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
3
0
2
0
0
1
0
1
1
0
0
0
2
0
2
0
0
0
0
1
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
2
2
0
1
0
0
2
0
2
2
2
1
2
0
1
0
0
0
0
0
0
0
2
0
2
0
1
0
2
2
0
0
1
0
2
0
0
0
0
0
1
0
0
2
1
0
0
2
0
0
0
0
0
0
1
1
0
0
2
0
0
0
3
1
0
0
0
0
0
0
1
0
1
0
0
1
0
2
0
2
1
0
0
1
0
0
0
4
0
0
0
0
1
0
2
0
1
0
2
0
0
2
1
0
2
0
0
0
2
1
0
0
0
1
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
2
1
0
0
0
0
1
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
1
0
2
0
0
2
0
2
2
2
0
2
2
0
0
1
2
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
3
1
0
0
2
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
1
1
0
2
0
0
2
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
2
0
0
1
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
2
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
1
3
0
0
1
4
0
0
0
1
0
0
0
2
0
0
2
1
0
0
2
3
0
0
0
0
0
0
2
0
0
1
0
1
1
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
2
1
3
0
0
0
0
1
0
0
0
0
3
0
1
0
2
0
0
0
0
2
0
1
0
0
0
0
1
2
0
1
0
0
1
0
2
0
0
0
0
0
1
0
1
0
0
0
0
3
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
3
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
2
0
0
0
1
1
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
1
0
0
2
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
3
0
0
0
0
0
0
1
1
0
2
0
2
0
0
1
0
2
0
1
0
0
1
0
0
1
3
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
1
0
2
2
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
1
0
2
0
2
2
1
0
0
0
0
0
0
1
2
0
0
2
0
0
0
1
2
0
0
2
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
2
0
1
4
0
1
0
1
1
2
0
2
3
0
2
0
0
0
1
0
1
1
0
1
0
0
0
1
0
2
0
2
0
2
0
0
1
0
0
1
0
0
2
1
0
0
0
0
0
2
0
0
1
0
3
0
2
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
1
0
0
4
3
0
3
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
1
1
0
2
0
1
1
0
3
0
0
2
0
0
0
0
2
0
2
0
2
0
1
2
0
0
0
0
1
0
3
2
0
3
0
0
0
0
1
0
0
2
2
2
0
2
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
3
0
2
0
0
0
0
0
2
1
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
2
2
0
0
2
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
3
0
0
0
0
0
2
2
1
0
2
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
1
0
4
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
1
1
0
2
0
0
0
1
2
2
2
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
2
0
1
0
0
1
0
0
0
1
2
4
0
2
1
0
2
0
0
0
0
1
2
0
0
2
4
1
1
0
0
1
1
0
0
1
0
0
0
0
2
0
0
1
1
0
0
3
0
0
0
0
0
2
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
14
0
0
0
0
2
1
2
0
1
0
1
0
0
2
0
0
0
0
0
2
0
2
0
4
0
0
2
0
0
1
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
2
1
0
2
0
0
0
3
0
0
2
0
0
0
0
3
0
0
1
0
0
2
0
1
0
1
0
0
2
1
0
2
1
0
0
1
0
1
2
0
1
1
1
0
0
2
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
1
0
0
2
0
2
1
3
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
3
2
0
0
2
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
3
0
0
0
2
0
2
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
2
0
1
1
0
0
2
1
0
0
0
1
0
0
2
1
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
4
1
0
3
0
0
2
1
0
1
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
1
0
0
0
1
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
1
2
0
0
1
0
1
1
1
0
1
0
0
0
0
3
2
0
2
1
2
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
2
2
0
2
0
1
0
2
0
0
1
1
0
0
0
2
0
0
0
1
1
2
0
1
0
3
1
0
1
0
0
0
0
0
2
1
1
0
0
0
0
1
1
0
3
2
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
8
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
2
0
0
1
1
0
1
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
2
0
0
0
2
0
1
0
0
1
0
0
3
0
0
0
0
0
2
0
1
1
0
0
1
0
0
1
2
1
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
1
0
2
1
0
2
1
1
2
0
1
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
4
0
0
0
2
2
0
0
2
0
0
0
1
0
2
1
3
0
0
1
0
1
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
1
3
9
0
2
0
2
0
0
0
0
1
0
0
1
0
0
2
2
0
0
0
2
4
0
0
0
1
0
0
1
0
0
0
1
3
0
2
0
1
0
0
2
1
2
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
2
0
2
1
0
0
0
9
0
0
0
0
2
0
2
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
1
1
0
1
1
2
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
1
0
3
2
0
0
2
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
1
0
3
0
0
1
2
0
0
0
1
2
0
0
0
1
2
1
0
0
0
0
0
0
0
3
0
2
0
0
1
1
0
0
0
0
0
0
1
0
1
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
2
1
2
2
0
2
2
0
0
2
0
0
0
0
0
0
2
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
2
0
0
1
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
2
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
2
1
2
1
0
0
1
2
0
0
2
0
2
0
0
0
0
0
0
1
2
0
0
0
0
1
2
0
0
0
0
0
1
1
0
0
0
0
2
0
0
2
0
2
1
1
0
0
0
0
2
3
0
0
2
2
0
0
0
0
0
0
0
0
0
0
4
2
0
4
0
2
0
1
0
2
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
3
0
0
0
2
0
2
2
0
0
0
0
0
0
2
0
1
1
1
2
0
0
0
2
1
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
2
0
0
0
2
2
2
1
2
0
0
1
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
1
4
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
2
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
1
2
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
3
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
4
3
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
2
2
1
1
0
0
0
0
0
0
2
0
3
0
0
0
2
0
0
2
0
2
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
2
2
0
0
1
3
2
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
2
0
0
3
1
0
0
3
1
0
2
3
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
2
1
0
0
1
0
1
0
2
1
2
1
0
1
0
0
1
2
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
3
0
0
0
2
0
3
0
0
0
0
2
0
1
2
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
3
1
0
1
2
2
2
2
0
0
2
2
0
0
0
2
3
0
0
0
0
0
0
1
0
2
1
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
3
0
0
3
2
1
2
0
0
0
0
2
0
0
0
1
1
0
0
1
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
3
0
2
0
4
1
0
0
3
0
2
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
1
0
0
0
2
2
0
0
0
1
0
0
1
0
2
0
1
2
0
0
1
0
0
0
0
2
0
0
1
0
0
1
2
0
0
0
2
0
0
1
0
1
0
1
0
1
0
0
0
2
0
0
2
2
1
1
0
0
1
2
0
0
0
2
2
1
0
0
2
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
1
1
2
2
0
1
2
0
2
1
2
0
2
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
2
0
0
3
0
0
0
0
2
0
0
1
0
1
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
2
0
0
6
0
1
2
0
1
0
0
0
1
0
1
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
3
1
0
0
0
2
0
0
3
0
2
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
2
1
2
0
0
2
1
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
1
0
0
0
1
0
1
0
0
0
1
0
0
1
2
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
2
1
1
0
0
3
2
1
0
0
0
0
7
0
0
0
0
0
0
0
0
0
2
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
3
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
1
1
2
0
1
0
0
0
1
1
0
0
2
0
0
0
0
0
2
0
1
2
0
0
0
0
0
1
0
2
0
0
1
0
0
2
2
0
0
0
0
0
2
0
1
0
1
0
0
1
5
0
0
0
2
1
1
0
2
0
2
1
1
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
1
0
2
0
0
1
0
0
0
0
1
1
0
0
2
2
2
3
1
0
0
0
0
0
0
0
0
1
1
0
2
0
2
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
3
0
0
0
0
1
1
1
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
3
0
0
0
0
1
2
0
0
1
0
0
1
0
1
0
2
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
3
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
1
2
2
2
0
0
1
1
0
0
0
1
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
1
0
0
1
2
0
0
0
0
0
2
2
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
3
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
2
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
2
1
0
1
1
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
3
0
0
2
2
0
2
0
2
0
0
0
0
0
2
0
0
1
0
0
0
5
0
2
1
2
0
0
1
0
0
0
0
1
0
0
2
0
2
0
0
0
2
0
0
1
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
3
0
0
0
0
2
0
0
1
0
1
2
0
1
0
2
0
0
2
0
0
0
0
1
1
0
1
1
1
0
0
1
0
2
0
0
0
0
2
0
0
2
3
1
0
0
0
0
0
1
3
0
0
0
1
0
1
0
2
2
0
1
0
2
0
0
0
3
1
0
0
2
0
1
0
0
1
2
0
2
4
0
2
0
4
0
0
0
0
0
0
2
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
3
0
3
2
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
2
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
1
0
0
3
0
0
5
0
1
0
0
2
0
2
1
1
0
1
1
0
1
1
2
8
0
0
0
0
0
0
2
0
0
0
0
0
0
5
0
0
0
0
0
1
0
0
1
0
0
0
0
3
3
1
0
0
3
0
0
0
0
0
0
1
0
2
0
0
0
1
2
0
0
0
0
0
0
0
1
0
2
0
2
0
1
2
0
0
1
0
0
2
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
2
1
0
2
1
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
1
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
2
0
3
0
0
0
2
0
0
0
1
0
0
0
0
1
2
1
1
0
0
0
0
0
0
0
0
1
0
0
2
2
11
0
1
0
0
2
0
0
2
1
0
1
2
0
2
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
5
1
0
0
0
2
2
1
0
0
1
2
0
1
2
2
0
0
0
0
0
0
2
1
1
0
2
0
0
0
0
0
0
0
3
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
2
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
2
0
2
2
2
1
0
0
1
0
3
3
2
0
1
0
0
0
0
0
0
0
0
0
3
2
0
2
2
0
0
0
0
3
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
2
0
0
0
1
0
0
5
0
0
0
0
0
1
0
0
0
2
0
0
1
1
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
2
0
1
1
0
2
2
0
0
1
0
0
0
0
0
0
3
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
2
0
0
0
0
0
0
1
0
0
3
0
0
0
0
1
1
0
0
0
1
0
1
0
0
1
0
0
0
2
0
2
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
2
0
0
1
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
2
2
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
1
1
4
0
0
4
0
0
1
0
0
1
0
0
0
1
2
0
0
0
0
4
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
2
0
1
0
0
1
0
0
0
0
0
0
1
0
2
1
1
1
2
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
1
0
0
0
2
0
0
1
0
0
0
2
0
1
0
0
0
0
2
1
2
1
0
2
0
2
2
1
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
1
0
3
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
1
0
0
0
0
0
0
3
3
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
2
3
0
0
2
0
0
0
0
0
0
0
0
4
1
0
0
1
0
0
0
0
0
0
1
2
0
1
2
0
0
1
5
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
2
0
0
4
0
0
0
0
1
0
0
0
0
0
2
0
1
1
2
0
2
2
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
1
0
0
0
0
0
2
2
1
0
0
1
2
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
1
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
2
0
2
0
0
1
0
1
0
2
0
1
0
1
0
0
1
0
0
1
0
0
2
0
2
0
2
0
0
1
0
2
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
2
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
3
2
1
0
0
1
0
1
0
0
0
4
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
4
2
0
0
0
0
0
0
0
0
3
0
0
1
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
1
0
2
2
0
1
0
1
0
0
0
0
0
0
0
0
2
1
0
1
1
0
1
0
0
0
1
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
3
2
0
1
0
0
0
1
2
0
2
0
0
0
2
0
1
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
2
0
2
0
2
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
1
0
0
0
0
2
0
1
2
0
0
0
0
0
2
2
1
2
0
0
1
0
0
0
1
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
2
2
0
1
0
3
0
2
0
4
0
1
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
2
0
1
2
1
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
4
0
0
0
0
2
0
2
0
2
0
0
0
0
1
0
2
1
0
0
0
0
1
0
2
0
0
0
2
1
0
2
0
0
1
1
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
1
0
0
0
1
0
2
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
3
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
2
1
0
0
0
2
2
1
0
1
0
1
0
0
0
0
2
0
0
3
0
0
0
0
1
0
1
2
1
2
0
2
0
2
0
1
0
2
0
1
0
2
1
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
2
1
0
1
0
2
0
0
0
1
3
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
2
1
2
0
0
0
0
0
3
0
0
0
0
0
1
0
2
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
3
4
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
2
0
0
0
0
1
1
0
3
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
1
0
0
2
1
0
3
0
0
1
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
4
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
1
0
2
0
0
0
1
0
0
0
3
0
0
0
0
0
0
1
2
0
2
1
1
1
0
1
0
0
0
1
0
0
1
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
1
0
0
1
0
0
2
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
4
0
0
0
0
2
0
1
0
0
2
3
0
0
0
0
0
0
2
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
2
2
1
1
0
1
0
0
2
0
0
2
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
2
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
2
1
3
0
0
1
1
4
0
0
0
0
2
0
2
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
2
1
1
0
0
0
0
0
0
0
2
1
0
0
0
0
1
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
1
3
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
2
1
0
0
2
0
0
0
0
2
1
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
1
0
0
0
2
2
1
0
0
0
0
0
0
0
1
3
0
1
0
0
0
2
2
0
0
0
1
0
0
0
0
1
1
3
0
0
0
1
1
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
10
0
1
1
2
1
2
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
1
0
2
0
0
0
2
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
4
0
0
2
0
0
0
3
0
2
0
0
0
0
2
2
0
0
2
2
0
0
0
1
0
2
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
1
0
0
2
0
2
0
0
0
0
2
0
3
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
1
1
1
0
0
1
0
2
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
4
0
0
0
0
0
0
2
0
0
0
4
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
2
0
2
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
2
2
0
0
1
0
0
2
0
2
0
2
2
0
2
0
1
2
0
0
0
0
0
0
0
1
2
0
0
5
0
1
0
0
0
0
1
2
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
5
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
2
0
1
0
0
0
0
0
0
2
0
0
2
1
0
0
0
1
1
0
2
0
0
0
0
2
0
0
1
0
2
0
2
3
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
1
0
0
0
1
1
0
2
0
0
0
1
0
1
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
3
0
3
0
0
0
2
1
1
0
2
0
0
0
2
2
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
2
3
0
1
1
1
0
2
1
0
0
0
0
2
2
4
0
0
0
2
0
0
0
0
0
0
2
0
0
0
8
0
0
0
0
2
0
0
0
2
2
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
3
1
3
0
1
2
0
0
0
0
1
1
0
0
0
1
0
1
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
2
0
0
0
0
0
0
1
0
0
3
1
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
1
0
0
3
0
0
0
0
1
1
0
0
0
0
1
0
0
2
0
1
0
0
1
0
0
2
1
0
0
1
2
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
1
0
2
1
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
4
0
1
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
1
0
2
0
0
0
0
0
1
2
0
0
0
1
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
3
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
2
1
0
0
2
0
0
0
0
0
1
1
0
2
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
5
0
2
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
2
0
3
2
0
0
0
2
1
0
0
1
1
0
0
2
0
0
1
0
1
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
1
0
0
1
0
0
1
0
1
0
0
2
0
0
0
2
1
0
2
0
1
0
0
0
0
0
1
0
1
0
2
0
0
1
1
2
1
0
1
0
0
1
0
0
0
1
0
0
0
0
1
3
1
0
1
0
0
2
4
2
0
0
2
1
1
1
0
1
1
1
0
0
0
2
0
0
0
1
0
0
0
0
0
1
3
0
2
0
0
2
1
2
3
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
2
0
1
4
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
3
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
1
2
1
2
0
1
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
2
0
1
0
4
0
2
3
2
0
0
0
0
0
0
0
1
1
0
0
2
2
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
2
0
2
1
0
0
1
2
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
1
1
0
2
1
0
0
0
0
0
0
0
2
0
2
2
0
0
0
4
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
3
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
1
0
1
0
0
2
1
2
2
0
0
3
0
0
0
0
0
0
0
0
2
0
1
0
1
0
2
2
0
1
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
2
1
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
9
0
2
0
0
0
0
0
2
0
0
1
1
2
0
0
0
0
2
0
1
0
3
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
3
0
1
0
0
0
0
2
0
2
2
1
0
1
0
1
0
1
0
0
0
0
2
2
0
2
0
3
0
0
0
1
0
0
0
0
0
1
0
0
2
0
1
0
1
0
0
0
0
0
1
0
1
0
2
0
1
0
0
1
3
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
1
0
0
0
0
2
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
1
0
2
2
0
0
0
0
2
0
1
0
2
0
0
0
0
1
0
0
0
0
3
0
0
1
1
1
2
0
0
2
0
0
1
0
0
2
0
0
2
1
0
2
0
0
0
0
2
0
0
0
0
2
2
2
0
0
0
1
0
0
2
0
0
1
2
0
0
2
2
1
2
0
0
0
2
0
1
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
3
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
1
3
1
0
0
0
2
0
0
0
0
0
0
0
3
1
0
0
1
0
0
2
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
1
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
2
0
0
2
5
0
2
0
1
4
0
0
0
0
2
0
0
0
1
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
2
0
2
0
0
0
2
1
0
0
1
0
2
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
3
0
0
0
2
0
1
0
0
0
1
1
1
0
2
0
0
0
1
0
2
0
0
0
1
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
2
1
0
0
1
0
0
2
0
1
0
4
0
2
4
0
1
0
0
2
0
3
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
3
0
2
0
0
2
0
0
0
0
2
2
2
0
0
2
0
0
1
0
0
0
2
0
0
0
0
2
1
0
0
0
1
0
0
0
1
0
0
0
2
0
1
0
2
0
0
0
0
0
0
2
0
1
1
0
1
0
2
2
1
1
0
2
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
1
2
0
0
1
0
1
0
0
0
1
0
0
0
1
0
4
1
0
0
5
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
1
2
1
1
0
5
0
0
2
2
1
2
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
1
0
0
1
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
2
0
0
1
0
2
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
2
0
2
2
2
0
0
0
0
5
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
3
0
0
0
2
1
0
0
0
0
0
0
5
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
1
0
2
0
0
3
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
2
0
0
3
1
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
2
3
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
3
2
0
1
0
0
0
0
4
0
2
0
0
4
0
0
1
0
0
0
0
0
1
0
0
2
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
3
2
2
0
0
0
2
1
0
0
1
0
0
0
2
1
0
2
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
1
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
3
0
0
1
1
2
0
0
0
1
1
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
1
0
1
0
0
1
0
0
0
1
2
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
2
0
2
0
2
0
0
2
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
3
0
2
0
0
3
0
0
0
1
0
1
0
2
0
0
0
0
2
0
1
0
0
1
0
0
1
0
0
0
0
0
0
3
1
0
0
0
0
1
3
0
0
0
2
0
0
0
0
0
2
2
0
2
1
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
1
2
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
3
0
2
1
0
0
1
0
0
0
0
1
2
1
0
0
2
1
2
0
1
0
0
0
0
1
0
2
0
1
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
1
3
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
5
0
4
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
1
2
0
2
0
0
0
0
2
0
0
0
0
0
0
2
1
0
1
3
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
2
0
0
1
2
0
0
0
1
1
1
1
1
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
3
3
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
2
0
0
0
1
0
0
1
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
1
1
0
1
0
0
0
0
0
2
2
2
0
0
0
0
2
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
2
0
0
3
1
1
0
1
1
0
1
0
0
2
0
2
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
1
1
0
0
0
0
0
0
1
1
0
0
0
2
0
1
0
2
2
0
0
0
0
0
0
0
0
1
0
1
2
0
1
1
0
0
1
1
1
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
1
0
0
0
1
0
0
0
2
0
1
2
0
0
0
2
0
2
1
1
8
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
2
2
0
1
0
0
2
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
1
3
0
0
2
1
0
0
0
1
1
1
0
0
0
2
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
1
2
0
0
0
0
2
1
0
0
1
0
0
1
0
2
0
0
3
0
0
0
2
0
0
0
3
0
0
1
0
1
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
1
2
3
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
1
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
1
0
0
2
1
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
2
0
0
1
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
2
0
1
0
0
1
0
0
0
2
0
1
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
2
3
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
1
1
1
0
0
1
0
0
1
2
0
0
0
0
0
1
0
1
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
3
1
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
2
1
2
0
2
0
2
2
0
0
0
0
0
1
0
0
0
0
0
1
0
2
1
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
3
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
1
3
0
0
0
2
0
0
0
0
0
1
2
0
0
3
0
0
0
0
4
2
0
0
1
0
0
0
2
0
0
2
0
0
2
0
0
0
2
0
0
1
3
0
2
0
2
2
0
0
1
1
1
0
0
0
0
2
1
1
2
0
2
0
0
0
0
2
0
0
0
0
1
2
0
1
3
2
0
0
0
1
0
0
0
2
0
1
0
0
2
0
4
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
1
1
0
2
0
1
2
0
2
2
0
0
0
0
0
0
0
2
0
0
0
1
1
2
0
0
2
0
0
0
2
0
0
7
0
0
1
3
0
0
0
1
0
0
0
2
0
1
0
1
0
0
1
0
0
0
3
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
1
0
3
2
0
0
0
3
1
0
0
0
0
0
2
0
0
0
1
0
0
1
2
0
0
0
2
0
0
1
0
0
0
0
1
2
0
0
2
0
0
0
1
0
0
1
1
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
1
2
1
0
0
0
0
0
2
1
0
1
0
1
7
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
1
3
2
0
0
0
0
0
1
0
1
0
0
1
0
1
0
1
0
0
0
0
0
4
3
0
2
2
0
0
0
5
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
2
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
2
2
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
3
0
1
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
2
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
1
0
0
0
2
0
0
2
0
0
4
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
2
0
0
1
0
1
0
0
0
0
0
0
2
0
0
2
0
1
1
0
0
0
0
1
0
1
2
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
4
2
1
0
0
1
2
0
0
0
2
1
0
1
0
0
2
1
2
0
0
0
0
0
0
0
3
0
0
1
1
2
0
0
1
0
0
0
0
0
0
2
0
0
0
1
2
0
3
0
1
2
2
2
0
0
0
0
0
2
0
0
3
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
4
0
1
0
1
2
2
0
1
0
1
0
0
0
2
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
1
0
0
0
2
2
0
0
0
0
0
2
1
1
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
2
0
2
2
0
0
0
2
0
3
0
2
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
5
0
0
0
1
2
0
1
1
0
0
0
2
0
1
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
2
0
0
2
0
1
0
0
2
1
0
0
0
0
1
2
0
0
0
1
0
0
2
0
0
2
0
2
2
0
0
0
0
2
1
0
0
2
0
1
0
0
2
2
0
3
0
0
0
0
0
0
3
0
1
0
0
0
0
2
1
0
0
0
0
0
0
2
1
0
0
0
2
4
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
2
1
1
0
1
3
0
0
0
2
2
0
2
1
1
0
0
0
1
1
0
2
0
0
0
1
0
5
0
1
0
0
1
1
0
0
0
1
0
1
0
0
0
0
1
1
0
1
0
0
0
2
0
0
1
1
1
0
0
0
0
1
0
0
0
1
0
0
2
0
1
0
0
0
1
0
0
2
1
0
2
0
0
0
0
2
0
1
2
2
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
2
0
0
0
0
0
0
1
0
2
5
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
5
1
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
3
0
0
0
0
0
0
1
1
0
0
0
3
0
0
0
0
0
0
1
0
1
0
1
0
0
2
0
2
0
0
1
0
1
0
0
2
0
0
1
0
0
0
0
0
1
0
2
1
2
2
0
1
2
1
1
0
0
0
0
0
1
0
0
2
0
0
1
0
1
0
2
0
0
2
0
0
1
0
0
0
2
0
2
2
0
0
0
2
0
0
0
2
0
0
1
1
1
1
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
2
0
0
0
3
1
0
0
0
0
0
2
0
0
2
0
1
0
2
2
0
0
0
0
1
1
0
0
0
1
0
0
2
2
0
3
4
3
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
2
2
0
1
0
0
2
2
0
2
2
0
0
0
1
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
2
0
0
0
0
1
1
0
1
0
0
1
0
0
2
0
0
0
0
0
2
0
0
2
1
0
2
3
2
1
0
1
2
0
0
0
0
2
1
0
0
0
2
2
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
2
0
0
1
1
0
0
0
10
1
2
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
3
2
0
0
1
0
2
0
0
1
0
0
1
0
0
0
1
2
0
0
0
0
3
0
0
1
1
0
0
0
0
0
1
0
0
0
2
0
1
2
0
1
0
0
1
2
0
0
0
1
1
0
0
0
0
2
1
1
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
3
2
3
0
0
1
0
0
0
0
2
0
0
0
1
2
1
0
0
0
1
2
1
0
0
0
0
0
0
2
2
0
0
2
0
1
0
0
0
0
0
0
1
1
2
1
0
0
0
0
0
2
1
1
1
0
0
0
0
0
0
0
3
1
0
0
1
0
0
0
0
2
1
0
2
0
0
2
3
3
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
2
0
1
0
2
0
0
0
0
2
1
2
0
1
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
4
0
2
0
1
0
3
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
1
0
2
2
0
0
0
0
0
0
2
0
0
3
0
0
2
2
0
0
0
0
1
0
0
0
0
0
1
0
0
2
1
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
1
1
1
1
2
0
0
0
0
0
0
0
2
0
0
2
0
2
0
1
0
2
0
0
0
2
2
1
0
1
2
0
0
0
4
3
2
0
0
0
0
0
0
0
0
0
3
1
0
2
0
0
2
0
1
0
1
0
0
0
1
2
0
0
0
0
1
0
2
0
2
0
0
0
2
0
2
0
0
0
0
0
2
0
2
1
2
0
2
0
0
0
0
0
0
1
1
3
0
0
0
2
0
0
0
3
0
0
0
0
2
0
0
2
0
0
0
2
2
2
0
0
0
5
0
0
2
0
0
0
1
0
0
0
0
0
0
7
2
0
0
0
1
0
0
0
0
1
0
0
1
0
2
0
1
1
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
1
1
0
0
0
0
2
0
0
2
0
0
0
1
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
3
0
1
0
1
0
1
1
0
16
3
2
6
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
4
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
2
1
1
1
1
1
1
0
1
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
1
0
1
2
0
0
0
0
0
0
1
0
1
2
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
1
0
0
2
0
3
0
0
0
2
0
0
0
2
0
1
0
0
0
0
2
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
2
0
0
2
1
1
0
2
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
3
0
2
2
1
0
0
0
0
0
2
0
0
2
1
0
0
2
0
0
1
0
0
0
0
0
1
2
0
0
2
0
0
0
1
0
2
0
0
2
0
0
1
3
0
0
0
0
0
2
0
0
0
0
1
1
1
0
0
2
1
0
0
0
2
2
1
0
0
0
0
1
1
0
0
0
1
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
1
0
0
2
1
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
2
1
2
0
0
0
0
0
1
2
0
1
0
0
0
3
0
0
2
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
4
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
1
0
2
0
0
1
1
0
0
0
0
2
1
1
0
1
0
2
0
0
1
0
0
1
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
1
0
0
0
1
1
0
0
2
0
0
1
1
0
0
3
0
2
0
0
0
2
1
0
0
0
1
0
0
0
0
0
1
2
1
0
1
0
3
0
0
0
0
2
1
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
1
0
1
0
2
2
0
0
0
0
0
0
0
0
1
2
0
0
1
0
1
0
0
0
0
0
2
2
0
0
0
0
0
1
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
2
0
1
2
0
0
0
0
0
0
0
0
2
2
2
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
1
0
2
0
2
1
2
0
0
0
1
2
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
1
7
2
2
0
1
0
0
1
0
0
0
1
0
2
1
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
2
2
0
1
2
4
1
0
1
0
0
2
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
1
1
3
0
1
0
0
0
0
2
0
1
2
0
1
0
2
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
4
0
0
3
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
2
1
2
1
2
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
4
2
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
9
0
2
0
1
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
2
0
1
0
0
2
1
0
0
2
0
0
1
0
1
2
0
1
0
0
0
0
0
2
0
1
0
0
1
3
1
0
0
2
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
2
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
1
0
0
2
1
0
0
6
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
1
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
1
1
1
0
1
1
1
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
1
1
0
0
1
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
2
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
2
0
0
2
1
2
2
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
3
2
0
0
0
3
0
0
0
0
1
2
1
1
0
0
4
0
3
0
2
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
2
2
0
0
2
0
0
0
0
0
2
0
0
0
1
0
2
0
2
0
1
1
2
2
1
0
1
0
0
0
0
0
0
0
0
1
0
1
1
2
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
10
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
2
1
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
1
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
2
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
1
1
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
2
4
0
0
0
0
0
1
0
2
1
10
0
0
0
0
0
0
1
1
2
4
0
0
0
0
4
1
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
2
3
1
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
7
0
2
0
0
0
0
0
0
3
0
1
0
0
2
2
0
0
2
0
1
1
0
0
0
0
1
2
0
1
2
1
1
0
0
2
0
2
0
0
0
2
2
0
0
2
1
5
0
2
2
0
0
0
0
0
0
0
2
1
1
0
2
0
1
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
2
0
0
2
2
0
0
1
3
0
0
0
0
0
1
0
1
0
0
0
0
0
0
3
0
2
0
0
0
2
0
1
0
2
1
2
0
1
0
0
1
0
0
1
1
0
0
0
2
0
2
0
0
0
0
4
0
0
0
3
0
0
0
0
0
0
0
3
1
0
0
0
0
1
7
0
0
0
0
0
0
0
0
0
0
2
0
0
0
4
0
1
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
6
0
0
0
0
2
1
0
1
1
0
1
1
1
0
0
0
0
0
2
0
1
0
0
2
0
0
2
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
4
1
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
5
0
0
0
2
0
1
0
0
2
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
1
0
3
1
1
0
2
1
2
1
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
2
2
4
2
0
0
0
0
2
0
0
0
0
3
0
2
0
0
0
0
1
2
0
0
0
0
2
0
0
0
1
1
0
2
1
0
2
2
0
2
0
0
0
2
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
2
0
1
0
0
0
1
2
0
2
0
0
0
0
1
0
0
1
0
0
1
0
3
0
2
0
1
2
0
2
0
0
0
0
0
2
1
0
0
2
0
1
0
0
0
0
1
0
1
0
0
2
1
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
1
1
2
0
0
0
0
1
3
0
0
0
0
6
1
0
1
1
0
0
0
0
0
2
1
0
0
1
0
0
3
2
2
0
0
0
0
0
0
1
1
2
1
0
2
1
1
0
2
0
2
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
1
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
1
0
1
0
3
0
0
0
0
0
0
1
0
2
0
0
0
0
0
4
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
5
1
0
1
0
0
0
0
0
1
0
1
2
0
0
0
1
0
0
0
0
0
1
2
0
0
0
1
0
0
0
1
2
1
0
0
0
1
0
2
0
1
0
0
0
0
2
0
0
0
2
1
2
1
0
2
0
2
0
0
2
2
0
0
2
0
1
1
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
2
0
2
1
0
0
0
0
0
1
3
2
0
1
0
2
1
2
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
1
4
0
0
0
0
0
3
0
0
2
0
0
1
0
0
1
0
0
0
2
0
0
0
2
0
0
2
7
0
0
0
0
2
6
1
0
0
1
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
2
3
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
1
0
3
0
0
2
2
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
3
2
1
2
2
0
0
0
0
1
2
1
0
0
0
0
0
0
0
2
0
2
2
4
0
1
0
0
1
1
0
0
0
0
0
2
0
3
1
3
0
1
0
0
0
0
3
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
1
0
3
0
0
0
0
0
1
2
0
0
1
2
0
0
6
2
0
0
0
0
1
3
0
0
2
0
0
0
1
1
0
2
0
0
0
2
0
0
0
1
0
2
1
1
0
0
0
0
0
2
0
2
0
0
0
5
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
1
0
0
2
1
0
0
2
0
0
0
0
0
0
5
7
3
0
0
0
2
0
2
1
2
0
1
0
0
0
0
0
0
0
3
2
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
1
0
0
1
0
2
0
1
0
2
1
0
2
0
0
1
0
0
0
1
1
1
3
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
2
1
0
0
2
0
1
0
0
0
1
1
0
0
8
2
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
2
1
0
2
2
0
0
0
1
0
0
0
3
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
2
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
1
0
0
1
2
0
0
0
2
3
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
1
1
2
3
0
0
0
1
1
0
0
0
0
0
2
1
1
2
0
0
1
2
0
0
0
0
0
0
2
1
2
0
1
0
0
0
2
5
0
2
0
0
0
1
1
1
0
0
0
0
0
2
2
0
0
1
2
0
2
1
0
0
0
0
2
2
2
0
0
1
0
0
0
1
3
1
0
0
0
0
1
0
0
0
0
3
2
0
0
0
2
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
2
0
5
3
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
2
2
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
1
0
3
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
2
0
0
0
0
1
0
0
2
0
2
0
0
0
0
1
0
0
0
0
2
2
2
2
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
2
0
0
0
1
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
2
1
2
0
0
0
0
0
0
1
2
5
1
0
2
0
0
0
0
2
2
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
1
2
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
1
0
0
0
0
0
0
2
1
0
2
2
2
0
0
0
1
7
0
2
2
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
1
4
0
0
2
1
0
0
0
0
0
0
1
2
0
0
1
2
0
0
0
0
0
0
0
3
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
2
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
1
0
0
0
4
0
5
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
2
2
0
1
2
2
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
2
1
1
0
0
0
0
0
0
1
0
0
1
0
2
1
0
0
1
0
0
0
0
2
1
3
3
0
0
1
0
0
0
0
1
2
1
1
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
1
2
0
0
1
2
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
2
0
0
2
0
0
2
0
0
0
2
1
0
2
1
0
0
2
0
1
2
1
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
2
1
0
0
2
2
5
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
2
1
3
0
0
0
2
0
1
1
0
3
0
0
0
0
0
0
0
0
0
1
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
2
2
2
2
0
1
0
0
1
0
0
0
0
0
0
0
0
2
2
2
0
2
1
1
1
0
0
0
2
0
0
0
1
3
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
2
1
0
1
1
2
0
0
0
0
2
0
3
1
0
0
3
0
0
2
1
0
0
3
0
0
0
0
1
1
0
0
0
3
0
0
0
2
0
0
0
1
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
2
1
0
0
0
0
1
1
0
0
0
2
2
2
1
0
1
0
2
0
0
2
1
0
2
0
0
2
0
0
2
0
0
1
0
0
0
0
4
2
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
1
0
1
2
0
0
2
2
0
2
1
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
2
2
0
1
0
0
2
0
1
0
1
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
1
0
1
0
0
3
2
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
2
1
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
2
4
0
0
1
0
1
0
0
0
2
0
2
2
0
1
0
0
2
2
0
0
0
0
0
2
0
0
0
0
1
0
3
1
2
0
2
0
0
1
0
0
2
2
0
1
1
1
0
0
0
0
0
1
1
2
1
2
0
0
0
0
0
0
5
0
2
0
0
0
1
2
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
4
0
0
0
0
0
0
3
0
0
0
1
2
0
0
1
3
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
1
0
4
2
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
1
1
0
1
0
0
0
0
2
1
0
2
2
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
4
0
0
0
0
0
0
0
0
1
0
4
1
2
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
1
2
2
0
1
0
3
0
0
0
2
6
0
1
0
0
0
0
0
1
2
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
2
0
1
0
0
0
1
0
2
1
1
0
2
2
0
2
2
0
0
0
0
0
1
0
0
2
0
1
1
0
1
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
2
2
1
0
9
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
3
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
2
0
2
2
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
2
2
0
0
1
0
1
1
2
2
0
0
1
0
2
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
3
0
2
3
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
3
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
10
2
0
0
0
0
0
1
0
2
0
1
0
0
1
0
0
0
1
0
1
2
0
1
0
0
2
2
0
0
0
1
0
0
0
0
0
0
1
0
1
2
0
2
0
0
0
0
3
2
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
4
0
1
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
2
0
1
0
0
0
1
0
0
0
10
1
0
0
1
0
0
1
0
0
0
0
0
3
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
1
1
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
3
2
0
0
0
0
0
2
1
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
3
1
2
0
0
0
0
1
0
0
0
0
2
1
0
0
1
1
2
0
0
0
0
0
1
0
0
0
0
1
0
0
1
3
2
0
0
0
1
2
1
1
0
2
0
1
0
0
2
0
2
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
2
0
2
2
2
0
0
0
3
0
0
0
0
2
0
1
0
0
0
0
0
1
0
1
0
1
1
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
2
0
1
1
0
0
2
0
0
2
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
2
0
3
2
0
0
0
0
0
2
0
0
1
1
0
2
2
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
1
0
0
0
1
0
1
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
2
1
0
0
2
0
0
3
1
2
0
0
0
0
0
0
2
0
0
0
0
2
2
2
1
0
2
0
0
0
0
0
0
2
0
1
1
0
0
0
0
16
0
0
0
0
0
0
0
1
0
0
1
1
0
2
0
0
0
0
1
1
2
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
2
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
2
0
2
0
0
0
2
0
4
0
0
3
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
2
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
3
1
2
1
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
1
1
0
2
1
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
2
2
0
0
0
2
2
1
0
0
0
1
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
2
0
2
2
0
0
0
0
1
0
2
1
0
0
2
0
0
0
1
0
0
2
0
0
0
0
3
0
0
2
2
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
4
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
1
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
1
1
2
0
0
0
0
0
2
1
0
1
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
1
0
2
1
0
0
1
3
0
2
2
0
0
0
0
1
0
0
2
0
2
1
0
1
0
0
0
0
3
0
0
1
0
3
0
0
0
0
1
4
0
0
2
2
0
0
1
0
0
0
6
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
2
0
1
0
0
0
0
2
0
1
2
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
1
0
0
1
0
2
0
0
0
0
0
0
0
1
2
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
2
0
1
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
2
4
0
0
0
0
0
1
0
0
0
0
0
0
1
3
2
0
0
0
2
2
0
1
0
0
0
0
1
0
0
1
2
0
0
2
1
2
4
0
1
0
1
1
0
0
0
0
0
0
2
0
0
1
0
1
1
2
1
0
0
2
0
1
2
0
0
0
0
0
0
1
1
2
2
0
0
2
1
0
0
0
3
0
0
0
0
0
0
2
0
1
0
0
2
2
0
0
0
0
5
0
0
0
2
0
0
0
2
1
0
0
1
0
1
0
1
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
2
0
2
2
0
0
0
2
0
0
0
2
0
1
1
0
0
1
0
1
0
1
0
2
2
0
2
0
0
0
0
2
1
0
0
2
1
2
2
0
1
0
0
2
0
2
0
3
0
0
0
0
2
0
0
0
0
3
0
2
2
0
0
1
0
0
0
1
1
0
0
0
2
1
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
2
2
0
1
3
0
0
3
0
0
2
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
2
1
0
2
0
0
1
0
0
0
0
0
1
0
2
0
3
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
1
1
1
2
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
1
2
2
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
2
2
0
2
0
2
0
0
0
1
0
0
0
1
0
2
0
1
0
0
1
0
0
2
0
0
0
1
0
3
0
1
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
2
0
0
0
1
0
1
0
0
0
2
2
0
1
0
1
0
3
0
2
0
0
1
2
1
1
3
0
0
0
2
0
1
0
2
0
2
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
1
0
0
2
2
0
0
2
1
1
0
0
0
3
2
0
0
1
1
1
0
0
5
2
0
1
2
0
1
0
1
3
0
0
0
0
0
2
0
0
1
0
2
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
2
2
1
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
1
1
2
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
2
0
1
0
2
0
0
1
0
2
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
2
0
2
5
1
0
2
0
0
2
0
0
0
0
2
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
3
1
0
0
0
0
2
0
0
0
1
1
0
1
2
0
0
0
0
0
0
0
1
1
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
2
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
1
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
1
0
2
0
0
0
0
0
1
0
1
0
0
0
1
0
2
0
0
1
1
0
0
1
0
2
1
0
0
2
0
2
0
1
0
1
0
0
0
0
1
2
0
0
2
0
1
2
0
2
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
2
1
0
2
0
0
0
1
1
0
2
0
3
1
2
2
0
0
3
0
0
0
1
0
0
2
0
0
0
1
1
3
0
0
1
0
0
1
0
0
0
0
0
2
0
1
0
1
0
1
0
0
1
2
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
1
0
1
1
0
0
1
0
1
0
1
0
1
3
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
2
2
2
0
0
0
0
0
2
2
0
0
3
0
2
0
2
0
1
0
0
0
1
1
2
0
1
0
2
0
2
0
0
1
0
0
0
2
2
0
0
1
0
1
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
1
2
0
0
0
0
0
0
0
1
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
1
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
1
2
2
2
0
0
2
0
0
0
0
1
0
0
0
2
2
0
0
0
1
2
0
0
0
1
0
0
0
2
0
1
1
0
0
0
1
0
0
1
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
1
0
0
4
2
0
0
0
0
0
1
0
0
3
0
0
1
0
0
0
2
0
0
2
0
0
1
3
0
0
0
0
0
0
0
0
0
2
2
0
1
1
0
0
1
0
0
0
0
1
0
2
0
0
0
3
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
7
5
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
2
0
1
2
0
2
1
0
0
1
1
1
0
0
2
1
0
0
2
0
0
3
1
0
0
1
0
0
2
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
2
2
2
0
2
1
0
1
2
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
2
0
8
0
0
0
0
4
1
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
1
0
2
2
0
1
0
2
0
1
1
0
1
2
0
0
0
0
0
2
0
2
0
1
1
0
1
1
0
2
0
0
0
0
0
1
1
0
0
0
2
0
1
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
3
0
1
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
2
3
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
5
0
2
0
0
0
0
2
2
0
0
2
0
0
0
0
2
0
0
0
4
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
2
0
0
1
0
2
2
0
0
1
2
0
2
0
1
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
1
0
2
2
0
0
1
2
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
2
2
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7
0
0
2
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
2
1
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
1
1
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
1
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
3
1
1
2
0
0
0
2
1
0
0
1
0
0
0
0
0
1
1
1
0
0
2
1
1
0
0
0
2
0
0
0
1
2
2
1
2
0
0
2
2
0
3
0
2
0
0
2
0
2
2
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
1
0
0
1
1
1
0
1
0
0
0
0
0
2
0
0
2
2
0
0
0
1
0
0
1
1
1
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
2
2
0
0
2
0
1
0
1
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
1
2
0
0
1
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
1
0
0
0
0
2
2
2
2
0
0
0
0
2
0
3
1
3
1
0
2
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
5
0
1
1
0
2
0
0
0
1
0
0
0
2
0
2
0
0
0
0
2
0
0
1
0
0
0
3
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
1
0
1
0
0
2
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
2
0
0
0
1
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
2
0
1
0
2
0
1
0
0
0
2
3
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
2
0
1
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
3
0
1
0
0
0
0
0
1
0
1
1
0
2
0
2
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
3
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
2
0
0
1
0
1
2
0
1
2
0
0
2
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
1
2
0
0
1
0
2
2
0
0
0
11
0
0
0
0
1
0
0
0
0
2
0
0
1
0
2
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
2
2
0
0
0
0
2
0
0
1
5
0
0
0
0
0
0
1
0
2
0
4
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
1
0
0
0
1
0
2
1
0
0
1
0
7
0
0
1
4
0
0
0
0
0
2
0
2
1
0
0
1
0
1
0
0
0
0
0
1
1
0
0
2
0
0
0
2
1
0
0
0
0
0
2
0
0
1
0
1
0
2
0
2
0
0
2
1
0
0
2
1
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
1
2
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
2
0
2
1
0
1
0
5
0
2
2
0
0
0
2
2
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
1
0
0
2
0
0
2
2
0
0
0
0
0
0
0
1
3
2
2
0
0
1
0
0
0
0
3
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
6
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
3
0
2
0
0
1
0
0
2
0
0
1
0
0
2
2
0
0
0
1
0
0
1
0
0
0
0
1
2
0
1
2
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
2
1
1
2
0
0
1
3
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
2
2
0
0
0
0
0
4
2
0
2
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
4
1
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
2
1
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
2
2
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
2
0
1
1
0
1
1
0
0
0
0
0
0
0
2
0
0
1
0
2
3
0
0
2
0
0
0
2
0
1
0
2
0
3
0
0
0
0
0
0
2
1
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
3
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
1
0
1
0
1
0
2
0
0
0
2
0
0
3
0
1
2
1
0
0
1
0
0
2
0
0
2
2
0
0
0
1
0
0
0
3
2
0
0
1
0
0
1
2
0
0
0
0
1
0
0
2
2
0
0
0
2
2
0
1
2
1
0
0
0
1
0
0
0
0
0
0
2
1
0
0
2
2
0
0
0
0
0
1
2
1
0
3
0
2
0
0
0
0
0
0
1
1
0
1
0
1
0
0
1
2
0
4
0
0
2
2
0
1
1
2
2
2
1
0
0
0
0
0
5
1
0
0
2
2
2
0
2
0
0
1
2
1
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
2
2
0
1
1
0
1
2
0
3
0
0
1
2
2
0
1
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
1
1
0
0
1
0
0
0
4
0
0
2
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
2
1
0
0
0
0
0
2
0
3
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
3
0
2
2
1
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
2
1
0
0
0
0
0
0
1
0
3
2
0
0
1
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
2
0
2
0
0
0
0
1
0
0
0
0
0
1
0
2
0
2
2
2
0
2
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
1
2
0
0
2
0
1
1
2
1
0
0
0
0
0
1
0
2
0
0
0
0
1
1
0
0
0
0
0
0
4
0
0
0
0
0
2
1
2
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
1
0
0
2
1
0
2
0
0
1
2
2
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
1
0
0
2
2
2
0
2
1
0
0
0
1
0
0
0
2
0
0
1
2
0
2
0
2
0
1
0
1
1
0
0
1
0
0
0
2
0
0
0
0
1
1
0
2
2
2
2
0
0
0
0
0
0
0
0
2
0
0
1
1
0
1
0
0
0
0
2
2
0
2
0
0
2
4
1
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
2
0
0
1
0
0
1
1
0
0
0
0
2
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
1
4
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
4
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
1
0
0
0
0
0
0
1
2
0
0
0
1
0
3
0
0
0
1
1
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
2
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
2
0
0
2
0
2
2
1
0
0
1
0
1
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
1
0
0
2
1
0
0
0
2
0
0
1
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
2
0
1
1
0
2
2
0
0
1
0
0
0
0
0
4
0
0
1
3
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
2
2
0
1
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
2
0
1
1
0
2
1
2
0
0
0
0
1
0
0
2
1
0
0
0
2
2
0
1
3
0
1
0
0
1
3
0
1
1
0
3
0
0
0
0
0
0
0
0
1
1
0
2
1
1
2
2
0
0
0
0
0
0
0
1
0
0
2
1
0
2
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
1
1
1
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
3
2
0
2
0
0
0
0
1
0
0
1
2
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
4
0
0
0
2
0
2
0
0
0
0
0
0
1
2
0
0
2
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
3
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
1
2
0
2
0
1
0
1
1
2
0
0
0
0
0
0
0
1
1
3
0
1
3
1
0
2
1
0
0
0
1
0
0
0
0
2
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
2
0
1
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
2
0
0
1
2
0
0
0
2
0
0
3
0
1
1
0
3
0
0
1
2
1
1
0
0
0
0
1
0
0
1
0
1
1
1
0
0
1
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
2
2
0
2
2
0
0
0
0
0
0
2
1
0
0
0
2
0
1
0
0
0
0
0
0
3
1
0
0
3
0
0
0
0
2
2
0
0
0
0
2
0
2
2
0
0
0
0
1
0
2
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
3
0
0
1
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
2
2
1
0
0
2
0
0
1
1
2
2
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
2
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
2
1
1
0
1
1
0
0
0
2
0
2
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
1
0
3
1
7
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
3
0
0
0
1
2
0
2
0
0
0
0
1
0
2
0
0
0
0
1
0
0
2
0
0
0
1
1
2
0
0
1
1
1
0
0
0
1
0
2
1
2
0
0
0
0
0
0
2
0
0
0
2
0
2
0
2
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
2
0
0
1
0
2
2
0
0
0
1
1
0
0
0
0
0
0
1
1
0
2
0
1
2
1
0
2
0
0
0
0
0
2
2
0
5
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
2
0
0
2
0
2
2
0
2
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
1
0
0
1
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
1
0
2
0
1
1
0
0
1
1
1
0
1
2
0
1
1
0
0
3
0
0
0
1
2
0
0
0
0
2
2
0
1
0
0
0
0
0
1
0
1
0
0
0
2
2
0
1
0
3
1
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
1
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
1
0
0
0
0
0
1
1
1
1
0
0
2
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
1
0
2
0
0
1
1
0
0
2
3
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
3
0
1
0
0
0
2
0
2
0
2
0
0
0
1
0
0
2
6
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
2
1
1
0
0
2
2
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
3
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
2
0
0
0
1
3
0
0
0
3
0
1
0
0
1
2
2
1
0
0
1
0
2
0
0
1
1
2
1
0
1
2
0
0
2
0
1
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
2
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
1
0
0
3
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
3
0
2
0
0
2
0
0
0
0
0
2
0
1
0
0
0
2
0
2
2
2
1
0
1
0
0
0
0
0
0
6
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
3
0
0
0
0
0
0
0
2
1
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
2
0
0
2
0
0
0
0
1
2
2
2
1
0
0
0
2
2
2
4
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
2
2
0
0
4
0
0
1
2
2
1
0
0
0
1
0
0
0
0
3
0
0
0
9
0
0
0
0
0
2
0
0
0
0
0
0
11
2
0
0
0
0
0
1
0
0
2
2
1
0
0
0
0
0
1
0
0
0
1
1
0
1
1
2
0
0
1
1
0
1
0
0
0
0
0
0
2
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
1
2
0
0
0
0
0
1
2
0
0
0
1
2
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
2
2
2
0
0
1
0
0
0
2
0
1
0
0
0
7
0
0
0
3
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
3
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
1
1
0
3
0
0
2
0
0
2
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
3
0
0
0
2
2
0
0
1
2
1
0
0
0
0
0
0
0
0
0
1
2
2
3
1
2
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
1
0
6
2
0
1
0
1
1
2
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
2
4
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
2
0
1
0
0
0
0
3
0
0
0
2
0
0
2
0
0
1
2
0
0
0
2
0
1
2
0
0
0
0
1
0
0
0
7
0
2
2
0
0
0
0
3
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
4
0
0
0
3
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
2
2
0
2
0
1
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
2
2
0
2
0
1
0
0
0
0
0
1
1
0
1
0
1
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
3
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
1
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
3
0
0
0
0
1
0
0
0
0
3
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
1
0
0
1
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
2
0
2
5
2
2
0
1
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
1
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
2
2
0
4
2
0
0
0
0
2
0
2
0
2
3
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
2
1
0
2
0
0
2
0
2
0
0
0
0
0
1
0
4
1
0
2
0
0
0
0
1
0
2
2
2
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
1
2
0
1
0
0
0
0
2
0
0
0
1
0
2
2
0
0
2
0
0
0
0
0
0
0
1
0
1
1
0
0
2
0
1
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
1
2
1
0
0
0
0
0
0
1
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
2
0
0
0
0
0
3
0
0
0
0
2
1
2
3
0
0
0
0
0
0
0
0
2
0
2
0
1
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
3
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
1
0
2
2
0
2
1
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
6
0
1
0
2
2
0
0
0
0
0
1
1
2
0
0
0
1
0
1
2
1
0
0
0
0
2
1
0
0
0
0
0
1
2
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
1
1
1
1
0
3
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
2
0
0
0
0
0
0
1
1
1
0
0
1
2
1
2
0
0
1
0
1
2
2
0
0
2
3
0
0
0
0
0
1
0
0
1
1
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
2
1
0
0
0
0
1
2
4
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
1
0
2
0
5
1
0
2
1
0
1
0
2
0
0
2
0
2
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
3
1
2
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
2
0
0
2
0
0
0
0
0
3
0
0
0
1
1
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
2
0
1
0
0
1
2
0
2
0
0
0
0
0
0
0
2
0
1
2
0
0
1
0
2
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
2
0
0
0
1
1
0
0
0
0
2
0
0
0
0
2
1
1
2
2
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
2
1
1
1
0
0
0
0
2
0
0
2
4
0
1
1
2
1
5
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
2
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
4
0
0
2
2
0
0
0
0
2
1
0
1
0
0
0
1
2
1
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
4
0
1
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
1
0
0
2
1
0
3
0
1
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
1
0
2
0
1
1
0
2
1
0
0
1
0
0
0
0
0
0
0
0
2
1
1
0
1
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
2
1
0
0
2
2
2
2
0
1
0
2
0
0
0
2
0
0
1
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
2
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
1
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
2
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
2
0
2
0
1
0
0
1
5
0
0
0
0
2
1
0
0
2
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
2
0
2
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
4
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
2
1
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
2
2
0
0
0
1
0
0
1
0
0
1
0
0
0
0
2
2
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
2
1
1
0
2
1
0
0
2
0
0
0
0
0
0
1
2
0
0
0
1
0
0
3
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
2
4
0
0
8
2
0
0
0
1
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
3
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
1
0
0
0
0
0
1
0
0
4
0
0
2
0
1
0
0
1
2
1
0
2
0
3
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
1
1
0
2
0
0
0
0
1
0
1
0
0
1
0
0
2
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
1
0
1
0
2
0
0
2
0
0
1
0
2
2
1
0
0
0
2
2
2
0
0
0
0
0
1
0
2
0
0
0
0
2
0
2
2
1
0
0
0
0
1
0
1
0
2
0
0
0
2
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
2
0
0
0
2
0
3
0
0
0
1
1
3
0
0
0
0
1
2
2
0
0
1
0
0
0
0
0
2
1
0
0
0
0
2
0
1
0
0
0
0
2
1
2
0
0
0
0
0
2
0
1
2
0
0
0
0
0
1
0
0
0
3
0
0
1
0
0
0
0
0
0
5
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
1
0
2
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
1
0
1
0
0
0
0
0
1
0
2
0
0
0
0
1
0
1
0
1
0
0
3
0
0
2
1
0
0
0
0
1
0
0
0
0
0
2
0
2
2
0
0
0
0
0
2
0
0
0
0
1
0
1
0
1
0
1
2
4
0
0
1
0
0
0
0
0
3
0
2
0
1
2
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
2
2
0
0
1
1
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
3
1
0
0
1
2
0
0
0
3
0
0
2
0
0
0
1
1
0
0
0
0
1
0
1
2
0
1
2
1
0
0
0
0
0
1
1
1
0
0
0
1
0
1
1
2
0
0
0
0
0
0
2
0
0
0
0
0
2
1
1
0
0
1
1
0
0
0
1
2
0
0
0
0
2
0
0
2
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
1
0
1
1
0
0
0
1
2
0
0
3
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
4
2
0
0
0
0
2
1
2
1
0
0
0
2
0
2
2
3
0
0
0
0
0
3
2
1
0
0
2
2
0
0
0
0
2
0
0
1
0
3
1
0
0
0
0
0
0
0
2
2
1
0
1
0
2
0
0
1
2
1
0
0
0
1
1
0
0
0
1
0
2
0
0
2
1
0
0
0
1
1
0
1
0
1
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
3
0
2
0
1
2
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
1
0
0
0
0
0
2
0
1
1
1
0
2
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
5
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
3
1
0
0
0
0
0
0
0
1
0
1
0
0
2
3
0
1
1
2
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
1
0
2
2
0
2
2
0
0
2
0
0
0
0
0
1
0
0
0
0
5
0
0
0
2
4
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
2
0
2
1
0
2
2
0
0
0
1
2
0
1
0
0
0
0
0
2
0
2
1
1
0
1
2
1
0
1
0
2
0
1
0
0
0
2
0
1
1
0
3
0
0
2
0
2
4
2
0
0
0
0
0
2
0
0
1
0
0
0
0
1
1
1
0
0
0
1
3
0
4
0
1
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
2
0
1
0
1
1
0
2
0
0
0
0
0
1
1
0
0
2
1
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
2
0
0
2
0
1
0
0
1
2
0
2
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
1
2
2
0
0
0
0
1
1
0
2
0
2
0
0
1
1
2
1
0
0
2
3
1
0
0
2
0
1
2
1
0
0
0
1
3
2
0
0
0
0
0
0
2
1
1
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
1
1
0
0
1
0
0
2
0
2
0
0
0
0
0
2
0
0
0
1
1
0
0
2
2
0
0
0
2
0
1
0
2
2
2
0
2
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
2
2
2
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
1
0
1
2
0
1
1
2
0
0
0
2
2
0
0
0
0
0
2
1
0
2
2
0
0
2
1
0
0
0
0
0
0
0
0
1
0
1
2
0
2
0
0
0
2
0
0
0
0
2
0
0
0
2
1
2
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
1
0
2
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
2
0
0
1
2
0
0
0
0
1
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
1
2
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
4
0
0
0
0
0
2
0
1
0
1
0
0
0
1
0
2
1
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
2
0
0
2
1
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
2
0
0
0
1
0
2
0
2
2
0
2
0
1
0
0
2
0
0
0
0
3
0
2
2
1
1
2
1
0
0
1
2
2
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
2
0
2
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
3
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
1
0
2
0
1
0
0
0
1
1
0
1
0
0
0
0
0
2
1
1
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
2
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
2
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
2
0
0
3
0
2
2
2
1
0
0
0
3
1
0
2
0
0
0
0
1
0
2
0
2
0
2
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
2
1
0
1
0
0
2
3
0
0
0
0
0
1
1
1
0
0
1
0
2
1
3
0
0
0
0
0
2
0
0
2
0
0
0
2
2
2
0
0
0
0
0
0
4
0
0
1
0
0
7
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
2
2
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
2
0
0
1
0
0
0
0
3
0
1
2
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
2
0
1
1
0
0
0
2
0
0
1
0
0
0
2
0
1
0
2
0
0
1
5
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
4
0
0
2
0
0
2
1
0
2
0
0
0
0
1
0
0
1
2
2
0
0
0
0
1
0
2
1
0
0
0
2
2
1
1
0
0
2
0
0
0
2
0
0
0
0
0
2
1
1
0
0
0
0
0
1
0
2
1
0
0
1
0
0
2
3
0
0
2
1
2
2
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
3
2
0
0
0
0
0
2
0
2
0
1
1
0
0
2
0
3
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
3
1
2
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
2
1
1
1
0
1
0
0
0
0
1
1
0
0
1
0
0
2
0
0
6
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
2
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
1
2
0
0
2
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
2
2
2
0
1
0
0
1
0
3
2
2
0
0
0
0
2
0
0
0
0
0
0
0
2
1
2
0
0
1
6
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
3
1
0
0
0
0
2
0
0
2
1
0
2
0
0
1
0
1
3
1
1
1
1
1
1
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
2
0
2
0
0
0
2
1
0
1
0
0
0
0
0
2
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
1
0
2
0
2
2
0
0
0
0
7
2
0
3
2
0
2
0
0
0
0
0
2
0
2
0
0
1
0
0
4
0
0
0
0
0
2
0
3
1
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
5
3
1
0
0
0
0
1
0
2
0
0
1
0
1
0
0
0
0
1
1
2
0
0
0
0
2
0
0
0
2
0
0
2
2
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
3
0
2
0
0
0
2
0
0
0
0
0
0
3
4
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
1
6
0
1
2
2
0
0
0
0
0
1
0
0
0
1
1
0
0
0
2
1
2
0
0
3
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
2
0
0
0
1
2
3
4
0
0
0
2
1
1
0
2
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
2
0
0
0
3
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
1
0
1
0
1
0
0
0
0
2
1
0
1
1
0
1
0
3
2
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
2
0
0
1
0
0
0
1
0
0
2
2
0
0
4
1
1
0
0
2
0
0
0
0
0
0
0
0
3
0
0
2
0
1
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
4
0
2
0
0
0
0
0
2
0
2
0
0
0
0
1
0
2
2
0
0
1
1
0
0
0
1
0
1
2
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
3
0
1
1
1
1
0
2
0
0
0
0
0
0
2
2
1
0
0
1
1
0
0
0
0
0
2
2
2
0
0
2
0
0
0
0
0
2
0
0
1
0
1
2
1
1
0
0
0
2
1
1
2
3
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
3
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
3
0
0
2
0
0
1
0
2
0
2
0
0
1
0
0
2
0
0
0
4
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
2
3
1
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
2
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
2
1
0
0
0
0
0
0
5
2
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
2
1
1
2
1
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
2
0
2
0
1
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
1
1
0
0
0
2
0
2
0
0
0
2
0
0
0
2
0
2
1
0
0
0
2
1
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
4
2
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
2
0
1
1
2
0
0
4
0
0
0
1
2
0
1
0
1
0
0
0
0
0
2
0
1
0
1
0
0
0
0
2
0
2
1
2
0
2
1
1
2
0
2
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
2
2
0
2
0
2
0
0
0
0
0
0
2
2
0
0
1
2
1
0
0
0
0
2
0
0
1
0
4
0
2
2
0
0
0
1
0
2
2
3
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
1
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
4
0
2
0
0
0
0
2
0
1
2
0
0
1
0
0
0
2
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
2
0
1
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
1
2
0
0
0
2
0
0
1
0
0
0
0
0
0
1
2
4
2
1
0
0
1
0
0
0
0
0
1
0
2
0
0
0
1
1
0
0
0
3
2
0
0
1
0
2
0
0
0
0
2
0
1
2
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
4
1
0
2
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
2
0
1
2
0
0
0
0
0
0
0
0
2
1
1
1
0
0
0
0
15
0
0
3
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
1
0
0
2
1
0
0
0
1
0
0
0
0
2
1
0
1
0
0
2
0
0
0
0
0
1
0
2
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
2
0
1
0
2
0
2
0
0
0
0
0
1
1
1
0
0
0
2
0
0
2
0
1
0
2
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
1
2
6
1
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
4
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
2
1
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
2
2
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
2
1
0
0
1
1
2
0
2
1
0
1
2
1
0
1
0
1
2
0
0
0
0
0
2
2
0
0
2
0
2
0
1
0
2
0
0
2
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
5
1
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
4
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
1
1
0
0
0
0
0
1
3
0
0
1
0
4
1
0
0
0
0
0
1
0
2
0
2
0
0
0
0
2
0
2
0
2
2
0
3
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
2
0
0
1
0
0
0
0
2
7
2
0
0
1
0
0
0
2
1
0
0
1
0
3
1
0
0
0
2
0
0
1
0
0
3
0
0
0
0
0
0
1
0
0
1
0
1
2
0
0
0
1
0
0
0
0
0
2
0
0
0
1
2
0
0
0
1
1
0
0
0
0
1
2
2
0
2
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
3
1
2
0
1
2
0
0
1
3
0
0
0
2
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
2
0
0
0
1
0
0
0
1
0
1
2
4
0
2
0
1
0
2
2
0
1
2
0
0
1
0
1
0
1
1
0
3
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
2
0
0
0
0
0
1
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
1
1
2
0
0
3
0
2
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
1
0
0
0
2
0
0
1
1
0
1
1
1
2
1
2
5
0
0
0
1
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
1
0
0
2
2
0
1
0
0
1
3
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
2
0
1
0
0
0
2
1
0
0
0
0
0
0
0
2
2
0
1
1
0
0
2
0
0
0
0
0
0
0
0
1
0
2
2
0
0
2
0
3
2
2
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
1
1
0
0
0
2
0
0
2
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
2
0
0
0
0
1
0
1
2
2
0
0
0
0
0
3
0
0
2
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
2
2
2
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
2
0
1
0
0
1
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
1
0
0
0
1
2
0
0
0
3
0
0
1
0
1
0
0
3
0
0
1
0
0
1
1
1
2
0
1
0
0
0
0
0
1
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
1
2
0
0
0
2
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
1
2
3
0
2
2
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
3
0
1
3
0
2
2
0
0
1
2
1
2
1
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
2
3
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
5
0
0
1
0
0
1
0
9
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
3
0
0
1
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
2
0
0
2
0
0
1
1
1
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
1
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
3
0
0
1
0
1
1
3
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
2
2
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
1
0
0
0
2
0
1
1
2
1
1
0
1
1
0
1
0
0
0
1
0
0
0
0
0
1
0
2
6
0
0
0
0
0
0
2
0
0
0
1
2
2
1
1
0
1
0
0
0
0
0
1
2
0
0
0
0
1
2
2
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
3
0
0
0
0
2
0
0
0
2
0
1
0
0
2
0
0
0
1
0
0
8
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
1
3
1
1
1
0
0
0
2
5
0
0
0
3
0
0
0
0
0
0
1
2
2
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
1
0
0
0
0
0
0
2
0
0
2
0
1
1
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
1
1
2
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
4
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
2
0
2
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
1
0
2
1
0
3
2
1
1
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
1
0
0
1
0
1
0
1
0
0
0
0
0
2
0
1
1
2
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
3
0
1
0
1
0
0
1
1
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
2
0
2
0
0
0
3
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
1
1
2
0
0
0
0
0
1
1
0
0
0
0
0
2
0
1
1
0
0
0
0
0
3
1
0
1
0
0
0
1
1
0
0
2
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
1
0
2
1
0
1
2
1
2
0
0
3
0
2
0
1
3
0
2
0
0
1
0
0
0
1
1
1
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
3
0
1
0
0
2
0
2
0
0
0
0
2
1
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
2
1
0
2
1
2
0
6
0
0
4
4
0
3
0
0
0
0
0
1
1
0
0
0
0
2
0
2
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
2
4
1
0
2
0
0
0
3
0
2
2
0
2
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
1
1
1
3
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
1
2
0
2
2
0
0
0
0
2
0
0
1
2
1
1
0
0
0
0
0
2
0
1
0
0
3
0
2
0
0
1
0
0
8
0
0
2
0
0
0
0
2
0
0
0
3
0
0
0
1
0
2
0
0
2
0
2
0
1
0
2
0
0
0
2
1
2
0
0
2
0
0
0
0
0
0
0
1
1
0
0
3
0
3
0
0
0
0
0
1
0
2
0
0
1
2
2
2
0
0
0
0
0
0
1
2
0
2
1
0
0
0
0
1
2
1
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
1
0
2
1
1
0
0
0
0
0
0
4
0
0
1
1
0
0
0
1
0
0
1
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
3
1
0
0
2
2
0
2
0
1
0
0
1
0
0
1
1
0
0
1
2
1
0
3
0
0
2
0
0
0
0
0
0
2
0
1
0
1
1
2
0
0
3
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
1
0
2
0
0
0
2
1
0
1
0
0
1
1
1
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
2
0
0
2
0
2
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
2
2
0
0
0
0
0
1
1
2
0
0
1
1
0
0
0
2
2
2
0
0
0
0
2
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
2
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
2
2
3
2
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
3
1
1
3
1
0
0
0
2
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
3
0
0
0
2
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
1
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
1
0
1
2
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
5
2
0
1
0
0
0
1
1
0
0
1
0
2
1
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
2
1
1
2
0
0
0
0
2
0
1
0
0
0
5
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
2
0
0
1
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
1
3
1
0
1
0
0
0
0
1
1
2
0
0
0
0
2
0
0
2
7
0
0
0
0
0
0
1
2
2
1
0
0
2
0
0
0
0
0
0
4
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
2
0
0
2
0
0
0
1
0
1
0
0
1
0
1
0
1
1
0
0
0
2
0
1
2
0
1
0
0
0
2
0
1
0
0
1
1
0
0
2
0
0
0
0
0
0
1
1
0
0
0
1
0
2
0
1
0
0
0
1
2
0
0
0
0
1
0
2
0
0
0
0
0
2
2
1
0
0
1
0
2
1
1
0
0
0
0
0
0
0
2
0
1
0
0
2
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
1
2
2
0
0
0
0
0
1
0
1
2
2
1
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
2
2
0
2
0
0
2
0
1
1
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
2
0
2
3
1
2
1
0
0
0
2
1
1
0
0
2
0
0
2
0
3
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
1
0
0
1
2
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
2
2
0
0
0
2
2
0
0
0
0
0
2
1
0
0
0
0
0
1
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
1
2
2
0
1
0
0
0
0
2
0
0
8
0
0
0
0
0
0
0
0
1
2
0
1
0
0
1
2
1
1
0
2
2
1
0
0
0
0
0
2
0
0
1
2
0
1
0
0
0
0
2
0
0
1
0
1
0
1
0
0
0
0
3
0
1
0
0
0
0
0
0
2
8
0
0
0
0
0
2
0
2
0
2
0
0
0
1
2
2
0
0
1
1
0
0
2
0
1
2
0
1
1
1
0
1
2
0
1
2
0
2
0
0
0
0
0
0
1
0
1
0
2
2
0
0
0
0
0
0
1
1
0
1
2
0
0
0
0
0
1
0
0
0
0
0
2
1
2
0
0
0
1
0
2
0
0
0
0
1
2
1
0
1
0
1
0
0
0
0
0
1
0
0
0
2
1
0
0
2
0
0
2
1
0
1
5
0
1
1
0
0
1
0
0
0
0
0
2
1
1
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
2
2
6
0
2
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
4
1
2
1
0
1
0
2
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
2
1
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
2
0
0
1
2
0
0
0
0
0
0
0
1
0
2
1
0
1
0
1
0
0
1
0
0
2
2
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
1
1
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
5
0
0
0
2
1
2
0
1
2
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
4
2
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
2
0
1
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
2
2
2
0
2
0
0
1
2
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
1
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
3
2
0
0
0
0
0
0
0
0
3
2
0
2
2
0
0
0
0
0
2
0
0
0
1
1
2
0
1
2
0
0
0
1
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
1
0
2
2
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
2
0
0
2
4
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
2
2
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
2
0
2
0
0
2
1
6
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
2
2
2
0
1
2
2
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
2
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
1
3
2
0
0
1
0
0
2
0
1
1
0
0
1
0
2
1
0
1
0
0
2
0
0
0
3
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
2
2
1
0
0
2
0
0
0
2
0
0
0
1
1
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
2
0
2
0
1
0
0
0
1
0
0
0
0
0
1
2
1
0
0
0
0
1
0
0
0
0
0
0
1
2
0
2
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
1
0
0
0
1
2
0
0
0
1
2
0
1
1
0
0
1
2
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
1
3
0
0
0
2
0
0
0
0
1
0
0
1
0
0
1
2
2
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
2
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
1
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
1
2
0
0
0
1
2
0
2
0
1
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
2
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
1
1
1
0
1
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
0
2
0
0
0
1
0
2
0
2
2
0
0
1
0
0
1
0
0
2
0
0
2
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
2
0
0
0
0
0
3
1
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
5
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
3
1
3
0
0
3
1
0
1
0
1
4
0
2
0
0
0
0
0
0
2
1
2
0
0
0
0
2
0
2
0
0
3
0
0
0
0
0
2
1
5
1
0
2
1
0
3
0
0
0
0
3
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
3
0
3
2
0
1
2
0
0
0
0
0
0
0
1
1
2
2
0
2
0
1
1
0
5
0
1
0
0
0
1
2
0
0
0
2
0
0
1
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
2
0
5
0
1
0
0
0
1
4
2
0
1
0
2
0
0
0
0
3
0
0
0
0
0
2
0
3
0
1
2
0
1
1
0
0
0
0
0
0
0
3
1
0
2
0
0
0
0
0
3
0
0
0
0
0
2
1
0
2
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
0
1
2
0
1
0
0
2
0
0
2
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
2
1
2
1
4
1
2
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
2
1
2
0
2
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
2
0
0
0
0
0
1
0
0
1
2
0
0
0
2
0
0
0
0
0
0
2
1
0
1
1
0
1
0
0
0
0
2
0
2
0
0
0
0
2
0
1
1
0
0
0
0
0
0
1
0
1
0
0
2
0
2
0
0
0
1
0
2
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
2
0
0
2
0
2
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
3
0
0
0
1
0
1
2
0
0
0
2
0
2
0
0
3
1
1
0
0
0
0
0
2
0
1
0
1
0
1
0
0
2
0
2
0
3
0
4
0
2
0
0
0
0
2
2
0
0
0
1
2
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
1
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
2
0
0
2
0
0
4
0
3
2
1
0
1
2
0
0
0
2
2
0
0
1
1
0
3
1
2
2
0
0
0
0
0
3
0
0
0
0
0
2
0
2
0
2
0
3
2
2
1
0
1
0
1
0
0
2
0
0
2
0
2
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
1
0
2
0
2
0
2
0
0
0
0
0
1
4
1
0
2
1
0
1
0
0
2
0
0
0
0
2
0
2
0
1
0
2
2
0
0
2
1
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
2
0
0
1
1
0
2
1
1
1
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
1
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
2
0
1
5
0
0
2
3
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
1
1
0
2
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
1
1
0
1
0
0
1
0
3
0
0
2
2
2
0
0
0
1
0
0
0
0
2
0
2
1
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
1
0
0
1
0
2
1
0
0
2
0
0
2
1
0
3
0
1
0
0
3
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
1
1
0
1
1
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
5
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
1
3
0
1
0
2
1
2
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
1
2
0
1
1
0
0
1
0
0
1
1
0
1
2
1
0
2
2
0
0
0
0
0
2
0
2
0
0
0
4
0
0
0
0
0
0
2
0
1
0
0
0
3
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
1
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
1
1
0
0
4
2
0
0
0
0
1
2
1
1
0
0
1
0
0
0
0
2
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
2
0
0
2
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
2
1
0
2
0
0
1
0
2
0
0
2
2
3
2
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
1
1
1
0
0
1
0
1
0
0
0
0
0
0
0
1
2
0
0
1
0
2
0
0
2
2
1
0
0
0
0
0
0
0
4
0
5
0
0
0
0
2
2
2
0
1
0
0
0
0
0
0
2
0
2
0
2
0
0
0
2
0
1
0
0
0
0
0
2
2
2
0
0
0
6
0
0
3
0
1
1
0
0
2
1
0
0
0
2
0
2
0
0
0
2
0
0
0
0
4
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
1
1
1
4
0
0
0
2
0
1
0
0
1
0
0
1
0
0
0
1
1
0
0
2
2
0
0
0
1
0
0
0
0
5
0
0
2
1
0
2
0
0
1
0
2
1
0
1
0
2
0
0
0
0
0
0
3
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
2
0
1
0
1
0
0
0
0
2
2
2
1
2
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
2
0
2
0
1
1
0
1
0
0
1
0
0
0
0
0
0
2
0
1
2
2
0
0
0
0
2
2
0
0
1
0
3
2
0
0
0
1
3
1
3
0
0
2
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
2
0
1
0
0
0
2
0
0
2
1
2
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
3
4
0
0
0
2
0
1
0
0
0
0
2
2
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
2
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
2
3
0
1
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
1
0
0
0
2
1
2
1
1
0
0
1
0
0
0
0
0
0
0
0
4
0
0
1
0
0
3
0
1
1
1
1
0
0
0
0
2
0
0
0
1
0
0
0
1
1
1
0
0
3
0
0
2
0
0
0
2
0
0
0
1
1
0
1
1
1
0
1
0
0
0
0
4
0
0
1
0
3
2
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
2
0
0
2
2
3
0
1
0
0
0
0
2
0
0
0
2
0
0
1
0
0
2
2
2
1
0
0
0
0
1
0
0
2
0
0
0
2
1
0
0
1
2
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
1
0
3
1
0
0
0
0
0
3
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
2
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
1
0
0
0
2
1
0
1
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
1
3
2
3
2
2
0
2
0
2
3
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
3
0
0
0
0
2
0
0
1
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
2
1
0
0
1
0
0
0
1
0
0
1
0
4
0
0
1
0
0
0
0
1
0
0
0
0
0
3
0
3
0
3
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
2
0
0
1
2
0
0
2
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
3
0
0
1
0
2
2
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
3
0
0
2
0
2
0
0
0
1
0
0
3
0
0
0
0
2
0
0
0
0
0
1
3
0
0
1
0
0
0
0
0
0
3
2
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
3
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
9
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
1
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
1
0
2
0
2
0
1
0
0
0
0
1
0
0
0
2
1
0
2
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
2
0
2
0
3
0
2
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
1
2
2
0
2
0
0
1
3
1
1
0
0
0
2
1
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
1
0
2
2
8
0
2
0
0
0
0
0
0
1
0
1
0
0
0
2
0
1
2
0
0
0
0
2
1
0
1
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
2
0
2
0
0
0
1
2
0
0
2
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
1
1
7
0
0
0
1
0
0
0
1
0
1
2
0
0
1
1
1
2
0
0
0
0
0
0
2
1
3
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
2
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
2
0
0
0
0
0
1
0
0
2
0
2
0
3
0
1
1
0
1
0
0
0
0
2
2
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
4
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
1
0
2
0
0
1
2
0
1
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
1
0
0
2
1
0
2
0
0
1
6
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
1
0
3
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
3
0
2
0
2
0
0
1
3
2
0
1
0
2
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
1
1
0
0
0
0
2
2
0
2
0
0
0
2
1
2
3
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
1
1
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
1
1
0
1
0
1
0
2
0
0
0
0
1
1
0
0
0
0
2
2
0
0
2
0
0
0
2
1
0
0
1
0
0
0
0
2
0
0
0
0
3
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
3
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
1
2
1
0
0
0
1
3
0
2
1
1
2
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
1
0
2
1
0
2
0
0
0
3
0
0
2
0
2
2
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
2
0
1
0
1
0
0
0
0
2
1
0
3
0
0
2
1
0
0
0
1
0
2
0
0
1
0
0
0
0
0
1
0
0
0
1
1
1
1
0
0
0
1
0
0
1
0
0
1
0
0
1
2
0
2
0
0
0
2
0
1
0
0
0
3
2
2
0
0
1
0
1
1
0
5
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
1
1
0
0
0
0
0
2
0
0
5
1
0
1
0
0
0
0
2
1
1
1
0
0
2
0
0
0
0
0
1
2
0
0
5
1
2
1
2
0
2
0
1
0
0
0
0
0
0
2
0
2
1
1
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
1
2
0
0
2
0
2
0
0
0
0
1
1
2
2
0
0
0
2
3
1
0
0
1
1
0
0
4
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
1
1
0
0
2
0
0
2
0
0
0
1
0
0
0
2
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
2
0
0
0
0
2
2
0
0
3
0
2
0
0
0
0
1
0
0
0
0
0
2
1
1
0
0
1
1
0
2
1
1
2
2
2
2
0
2
0
0
2
1
2
0
0
1
1
0
1
0
0
1
0
0
0
0
1
0
4
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
1
2
0
0
0
0
0
0
2
0
0
1
0
1
0
0
2
0
0
0
0
0
2
0
1
2
2
2
0
0
1
3
0
0
0
0
2
0
0
1
0
1
0
0
2
0
0
0
0
0
0
2
2
0
2
0
0
2
0
1
0
0
0
0
2
0
2
0
2
0
0
0
0
10
1
1
0
0
0
2
1
1
1
0
0
0
3
0
2
0
0
0
0
0
1
2
0
0
0
2
2
0
0
1
0
0
3
0
0
2
0
0
2
1
1
0
0
0
0
0
2
0
0
2
0
0
2
0
1
2
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
1
2
0
0
0
0
0
0
0
0
1
1
0
2
0
0
2
0
0
0
2
1
1
0
0
0
2
0
0
2
0
0
0
0
1
0
0
2
0
0
0
2
1
1
0
0
2
0
2
0
0
1
0
0
0
2
3
2
0
0
1
1
0
0
0
2
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
3
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
4
0
0
0
0
0
2
0
4
0
0
0
0
0
1
0
0
0
0
0
3
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
3
0
2
0
1
0
0
1
2
2
2
1
1
0
0
1
0
0
2
2
0
0
0
0
2
0
0
2
0
0
0
0
0
1
1
0
2
0
0
1
1
1
0
2
0
1
1
0
0
0
2
0
0
0
1
0
0
0
0
3
0
0
0
1
2
0
0
0
0
1
1
2
2
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
4
0
1
1
0
0
0
1
2
0
0
0
1
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
3
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
1
0
0
2
2
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
2
0
2
2
0
2
0
1
0
0
2
2
0
0
2
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
2
1
2
0
0
0
1
0
0
0
0
1
0
0
0
0
2
1
0
2
0
2
0
2
0
0
0
0
1
0
1
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
2
0
2
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
1
1
0
0
0
0
2
2
2
0
3
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
2
1
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
2
0
0
2
0
0
2
1
1
0
2
2
2
1
0
0
0
0
0
2
0
0
1
0
0
0
2
1
2
0
3
0
0
0
0
2
4
0
0
1
0
0
1
2
0
0
0
0
2
2
1
1
0
0
1
2
1
0
2
0
1
0
0
0
0
2
0
0
2
2
0
2
0
1
4
2
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
2
1
1
0
0
1
0
0
2
0
1
0
2
1
2
0
0
4
0
2
0
1
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
2
3
0
0
2
3
0
3
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
1
0
0
2
1
0
0
0
1
2
2
0
1
0
2
1
1
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
1
0
0
2
0
0
0
2
0
2
0
2
0
2
0
0
0
0
0
1
1
0
0
1
1
0
0
2
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
2
0
0
0
2
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
2
0
0
0
1
0
1
0
0
0
2
2
1
0
0
1
0
0
1
0
4
0
2
0
0
0
0
0
0
2
0
0
1
1
0
1
0
2
0
1
0
0
1
2
0
0
0
1
1
0
0
2
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
2
0
0
8
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
2
0
0
0
2
2
2
0
0
2
1
2
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
1
1
0
0
1
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
3
2
0
0
0
2
1
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
4
0
5
1
0
0
0
0
0
0
1
1
1
0
2
0
1
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
1
0
2
0
2
1
1
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
2
1
0
0
0
1
1
0
1
2
2
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
1
0
0
1
0
0
0
2
0
0
0
1
1
0
0
1
1
0
0
2
0
0
0
1
0
0
0
3
0
0
0
1
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
1
0
3
1
2
0
1
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
3
0
0
0
0
0
0
2
0
2
1
0
0
2
0
0
0
0
0
0
4
1
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
2
0
0
1
0
2
1
2
0
0
0
2
0
0
0
2
0
0
1
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
2
0
0
2
2
0
0
0
0
0
2
2
0
1
0
6
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
4
2
3
0
2
0
0
1
0
0
0
0
0
1
2
1
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
1
2
2
0
0
2
0
0
0
0
0
0
0
1
0
1
0
2
0
2
2
1
1
0
0
3
0
0
0
0
2
1
2
2
0
0
0
1
4
0
0
0
0
1
1
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
2
2
0
1
0
0
0
1
1
0
2
0
0
0
1
0
0
0
1
2
0
0
0
1
0
1
0
0
1
0
0
0
5
2
0
0
0
4
2
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
13
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
1
5
0
1
0
0
2
0
2
0
0
0
0
0
1
0
0
3
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
1
0
0
2
0
0
2
0
1
0
0
2
0
2
2
2
1
0
0
1
0
0
0
0
0
2
0
1
0
0
1
0
2
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
3
0
0
0
0
1
0
0
0
0
1
2
0
0
0
2
2
1
0
0
0
2
2
2
2
0
2
2
0
0
0
1
1
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
1
0
1
3
0
0
0
0
2
0
1
2
0
0
0
1
2
2
0
0
0
0
1
1
1
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
3
2
0
2
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
2
1
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
1
3
0
2
2
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
3
4
0
0
2
3
0
0
1
0
2
0
2
0
1
2
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
1
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
2
2
2
0
2
0
2
3
2
1
1
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
1
3
1
0
0
0
0
0
0
1
0
0
1
0
1
0
1
2
0
1
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
1
3
1
2
0
0
0
0
0
1
2
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
3
0
0
2
0
4
0
0
0
0
2
0
2
2
0
2
4
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
2
0
2
0
0
2
1
2
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
3
2
0
0
0
2
1
0
0
2
2
0
0
0
0
0
1
5
1
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
1
1
0
0
0
1
0
0
0
1
1
0
2
0
2
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
2
1
1
3
0
0
0
2
0
2
0
0
1
0
0
2
0
0
0
0
0
2
0
1
0
0
3
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
1
0
0
1
0
0
0
1
2
0
2
0
0
0
0
1
1
0
2
0
3
0
2
0
0
0
0
1
0
0
0
2
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
3
1
0
0
0
0
1
0
1
2
1
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
2
1
1
0
1
0
0
0
2
0
2
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
1
0
2
0
1
0
0
0
0
0
2
0
0
0
0
3
2
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
1
0
0
2
0
0
1
2
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
6
2
0
0
0
0
0
0
0
0
0
0
0
2
1
4
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
1
0
0
1
0
4
0
1
0
0
0
3
0
2
0
0
3
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
2
2
0
0
1
1
0
0
0
2
0
3
0
2
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
2
1
1
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
1
2
0
1
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
2
1
0
0
0
1
0
1
0
1
1
0
0
0
0
2
0
0
0
0
1
0
2
0
0
2
0
0
1
0
0
2
0
0
3
0
2
2
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
3
0
0
0
1
2
0
2
0
0
0
2
2
0
0
4
1
0
0
2
1
1
0
0
1
0
0
0
1
0
0
0
0
0
3
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
1
0
1
0
1
0
0
2
3
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
2
5
0
0
0
0
0
0
0
2
0
3
0
2
0
2
0
2
0
0
1
0
0
0
0
1
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
2
1
0
0
0
2
2
0
1
0
0
0
1
0
2
0
1
0
2
0
0
0
2
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
2
0
1
1
0
0
1
2
2
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
2
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
2
1
0
0
0
0
0
0
1
2
0
0
0
1
1
0
0
0
0
1
1
2
0
1
2
0
0
0
3
0
0
2
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
1
0
0
0
3
0
1
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
1
1
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
2
1
0
0
2
1
1
0
0
3
0
2
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
3
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
1
2
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
1
2
4
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
1
1
0
0
0
2
0
0
0
1
2
0
0
0
0
2
1
0
2
0
0
0
0
0
2
0
0
0
0
1
2
2
0
0
0
1
2
0
1
2
1
1
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
1
0
0
1
0
2
0
0
0
0
2
0
2
0
0
1
1
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
2
2
0
0
3
0
1
1
2
0
2
1
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
3
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
1
2
1
2
0
0
0
2
2
0
1
2
1
0
0
0
1
1
0
2
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
4
0
2
2
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
2
1
1
0
0
0
2
2
0
0
0
0
2
1
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
1
0
0
0
0
0
1
0
1
0
1
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
1
1
2
1
2
0
0
0
1
1
1
1
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
2
0
0
0
1
0
1
2
0
1
0
0
1
1
0
1
2
2
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
2
0
2
0
2
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
3
0
0
0
2
1
0
2
1
2
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
2
4
0
0
0
1
0
0
0
0
0
0
4
7
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
1
1
0
0
0
2
0
1
0
0
0
0
1
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
1
0
0
2
0
0
0
0
0
0
2
2
1
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
2
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
2
1
0
0
2
1
0
0
0
1
2
0
0
0
2
0
0
0
1
0
5
0
0
4
0
0
0
0
0
0
0
1
0
0
2
1
0
1
0
0
0
2
0
2
0
1
0
1
0
0
1
2
1
0
2
0
0
2
1
0
1
0
0
0
0
1
0
3
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
1
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
1
0
0
0
0
1
6
0
0
2
0
2
0
0
1
1
2
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
3
0
2
0
0
0
2
0
0
0
2
1
0
1
3
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
2
0
0
0
1
2
1
3
1
0
0
0
0
0
0
0
0
0
1
0
0
1
3
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
2
0
0
2
0
0
1
1
2
0
0
2
1
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
2
1
2
2
0
0
1
0
2
0
2
0
1
2
0
1
0
0
0
0
0
2
1
0
0
0
0
1
0
0
2
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
1
0
1
1
0
1
2
1
3
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
3
2
2
0
0
0
0
0
0
2
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
1
0
1
0
0
0
0
1
0
0
2
2
0
1
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
1
0
1
2
1
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
1
1
0
0
2
0
1
2
0
1
0
0
0
0
0
2
1
0
0
0
0
0
1
2
0
0
0
0
0
1
1
0
0
0
0
2
0
1
0
0
1
4
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
3
0
0
0
1
1
3
0
0
1
0
2
2
0
0
0
0
3
1
0
2
0
0
0
0
0
0
1
0
1
1
1
1
2
0
2
0
0
0
1
1
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
1
1
2
0
0
1
2
0
0
0
0
0
0
1
0
2
4
1
0
1
2
3
0
0
0
0
0
0
0
1
1
0
0
0
1
0
2
0
0
0
0
1
1
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
2
1
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
1
0
2
1
0
0
0
2
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
1
0
0
0
0
0
1
0
1
0
0
2
0
2
0
0
0
0
0
0
0
1
0
2
1
0
4
0
2
1
1
0
0
0
2
0
0
1
2
0
0
2
1
0
1
0
0
0
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
2
1
0
0
0
0
0
0
2
0
1
0
0
2
2
0
0
1
0
1
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
3
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
1
2
0
2
2
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
2
0
0
1
1
0
1
0
0
1
0
0
1
0
0
0
0
0
2
0
1
2
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
2
0
2
0
0
0
0
1
1
0
2
1
0
0
0
2
0
0
0
1
0
0
0
6
0
0
2
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
1
2
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
2
2
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
2
2
0
1
0
0
2
3
2
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
2
2
0
0
0
2
2
0
0
0
0
1
0
2
0
0
0
2
0
2
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
2
0
1
0
0
2
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
1
2
1
0
1
0
1
0
0
0
0
0
0
0
2
2
0
0
0
1
2
0
1
0
0
1
0
1
0
0
1
0
1
1
1
0
1
0
0
2
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
2
2
0
0
1
0
1
1
2
0
0
0
2
1
2
0
0
1
0
0
0
1
0
0
1
0
2
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
2
1
0
2
2
0
0
0
0
0
0
2
2
0
0
1
2
0
0
2
3
0
0
1
0
1
0
1
0
0
0
2
2
0
0
2
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
2
1
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
1
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
2
0
2
0
2
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
3
0
0
0
3
0
0
0
0
0
10
2
1
2
0
0
2
1
0
0
1
0
0
1
0
0
0
0
2
0
0
2
0
2
0
0
1
0
1
6
0
1
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
2
0
0
0
2
5
1
0
0
0
0
2
0
0
0
2
2
1
2
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
2
2
2
0
0
2
1
2
0
1
0
0
0
0
2
0
0
0
0
1
0
0
2
2
0
0
1
2
0
0
1
0
0
0
2
2
2
0
2
0
2
0
0
2
0
1
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
1
0
1
0
2
0
0
0
1
0
0
2
0
0
0
1
0
2
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
2
1
2
0
3
1
0
1
0
0
0
1
0
0
2
3
1
0
4
0
0
0
1
2
0
1
2
0
0
3
0
1
2
1
2
0
0
0
0
1
1
0
0
1
2
0
0
0
0
0
0
0
0
2
1
1
1
2
0
0
1
0
2
1
1
0
0
1
1
2
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
1
2
3
2
0
0
2
2
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
1
2
1
1
2
2
2
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
2
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
2
0
2
0
0
0
0
0
0
4
1
0
0
1
1
0
0
0
1
0
0
0
2
0
0
0
2
1
1
0
0
2
0
1
0
0
2
2
0
0
0
2
2
0
0
2
1
2
1
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
2
1
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
7
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
2
1
0
0
3
0
0
0
0
0
2
2
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
2
1
1
1
1
0
0
0
5
3
0
0
1
2
0
0
0
0
3
0
0
0
4
0
1
0
0
2
2
0
0
0
2
3
1
1
2
0
0
0
2
0
0
1
0
0
2
1
0
0
0
2
0
0
0
1
2
0
0
2
0
0
2
0
0
2
1
1
2
0
4
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
2
0
0
0
0
2
0
0
2
0
0
2
2
0
1
0
2
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
2
0
1
0
0
1
3
0
2
0
0
1
2
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
2
1
0
2
2
0
0
0
0
0
0
1
0
0
0
1
2
0
1
1
0
2
0
0
2
0
0
2
2
0
0
0
0
0
0
0
1
2
2
2
0
0
0
0
7
2
0
0
0
0
2
0
0
0
0
0
0
2
2
3
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
1
1
2
2
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
1
2
0
0
0
2
2
2
2
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
1
0
0
0
1
0
0
2
3
1
2
2
2
2
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
4
2
1
0
0
0
0
0
0
2
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
2
2
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
3
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
1
2
0
0
2
0
2
0
0
3
0
0
0
0
1
2
1
0
1
0
1
0
0
0
1
1
0
0
0
2
2
0
0
0
0
1
0
0
2
0
0
0
1
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
3
0
0
0
1
0
0
1
0
1
0
0
0
0
4
0
1
1
2
1
0
0
2
0
0
0
0
0
1
2
0
1
0
1
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
1
0
1
0
0
0
5
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
2
2
0
1
0
0
0
1
0
1
0
0
0
1
0
2
1
0
1
1
2
0
0
0
0
3
2
0
0
0
0
1
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
2
2
0
0
0
2
1
2
0
0
0
0
0
3
0
0
0
1
7
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
2
0
2
0
0
2
0
0
0
3
0
0
5
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
1
1
0
2
0
0
0
0
1
0
0
1
0
1
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
1
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
1
0
1
3
0
0
0
1
0
0
0
2
0
0
1
0
0
1
2
0
1
2
0
1
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
1
2
0
1
0
1
0
0
0
0
0
1
0
0
0
1
3
2
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
1
2
2
2
0
0
1
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
2
1
1
0
3
4
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
6
1
0
0
0
0
0
0
0
2
0
0
1
1
0
1
0
3
0
4
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
5
2
0
0
1
1
2
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
4
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
2
2
0
0
2
0
0
0
0
1
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
2
1
0
0
0
0
1
1
2
0
0
1
1
0
2
0
0
1
0
0
0
0
0
1
0
1
3
0
0
2
0
0
0
0
2
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
2
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
1
0
0
2
0
0
0
1
0
0
0
1
0
0
0
2
0
0
2
1
2
1
3
2
1
0
0
0
0
0
2
0
1
0
0
0
2
1
0
2
1
0
0
0
0
0
0
0
0
0
1
0
2
0
2
2
0
0
0
0
0
0
5
1
2
0
0
1
0
0
1
1
2
0
0
2
0
0
0
0
0
2
0
2
1
0
0
0
0
1
1
0
1
2
0
2
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
2
2
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
1
0
2
2
0
0
0
0
0
1
0
0
2
0
0
0
2
1
2
0
2
0
1
0
0
2
0
1
1
0
0
0
0
0
2
0
1
0
0
0
0
1
0
4
1
0
1
0
0
1
1
1
0
0
2
0
1
0
0
1
0
0
0
0
0
2
0
0
0
1
1
0
2
2
1
0
0
2
2
0
2
0
1
1
1
1
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
2
0
2
2
0
2
0
0
0
3
0
0
0
0
1
2
1
0
0
0
0
0
2
2
2
0
0
2
2
1
0
0
0
2
1
2
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
1
2
0
0
0
0
1
2
0
0
0
0
1
0
1
2
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
2
0
2
0
0
0
3
0
0
0
0
2
0
1
0
4
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
5
0
0
0
1
2
0
0
0
0
1
2
0
3
0
0
1
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
2
1
0
0
0
2
3
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
1
1
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
2
0
2
0
1
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
1
0
0
0
2
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
1
1
2
0
1
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
1
0
1
0
0
0
3
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
5
1
0
0
1
1
0
1
1
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
2
0
0
3
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
2
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
2
0
0
2
2
2
0
0
2
0
1
3
2
0
2
0
2
0
0
2
0
3
0
0
0
1
2
2
2
1
2
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
2
1
0
0
0
3
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
2
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
5
1
0
0
2
0
3
1
1
0
1
0
0
0
0
0
1
2
1
0
0
0
3
0
2
0
0
2
0
0
1
0
0
2
0
1
1
1
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
5
2
0
1
0
1
0
0
0
1
1
0
0
2
0
2
0
2
0
2
2
0
0
0
0
1
1
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
3
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
1
0
0
0
0
2
2
0
1
0
0
0
3
0
0
0
1
2
1
0
2
1
1
0
0
1
1
2
4
0
1
0
1
0
0
0
2
2
1
0
1
0
0
2
0
2
0
0
0
0
1
1
1
0
0
1
1
2
0
0
2
0
0
1
0
0
0
2
2
0
2
1
3
1
2
0
0
0
0
0
0
0
0
0
0
4
1
2
0
0
0
1
1
0
0
2
0
0
3
0
0
0
0
2
0
0
0
1
1
1
0
0
2
0
1
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
3
0
1
1
1
0
0
0
0
1
0
0
3
1
1
1
0
0
0
1
0
2
0
0
0
0
0
1
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
2
0
0
3
0
0
0
0
0
0
0
1
2
0
0
0
1
2
0
0
0
1
0
2
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
2
1
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
1
0
0
2
0
2
0
0
2
0
0
1
1
0
0
2
2
0
0
0
0
1
0
0
1
1
0
0
2
2
0
0
0
2
0
3
0
1
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
3
0
0
0
0
0
1
0
3
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
2
0
0
0
0
1
0
1
2
0
0
2
0
0
0
0
0
1
0
0
2
0
1
0
2
0
0
0
0
1
1
0
0
0
0
0
1
3
0
0
2
0
0
1
0
1
0
1
0
2
0
6
0
0
0
2
2
0
3
0
0
0
2
2
2
0
2
0
0
0
0
0
1
1
1
1
0
0
0
0
2
0
0
0
3
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
3
1
0
0
0
0
0
1
0
0
2
0
2
0
0
0
2
0
1
0
0
1
0
2
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
3
0
1
4
0
0
0
0
1
2
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
2
0
0
2
0
0
0
2
1
1
0
1
0
1
0
0
0
0
0
1
0
1
0
0
1
2
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
2
0
1
0
1
0
1
0
0
0
0
0
1
2
1
2
1
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
2
0
0
0
0
4
2
3
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
1
2
1
0
0
0
2
0
0
0
2
0
1
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
6
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
1
3
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
1
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
2
0
3
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
2
2
0
0
0
2
0
0
1
0
0
0
4
2
0
0
0
1
0
0
0
0
0
0
0
3
0
3
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
2
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
1
1
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
2
0
0
2
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
1
2
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
4
0
2
0
0
0
0
2
0
1
0
2
0
2
0
2
2
0
0
0
2
0
0
2
1
0
0
0
0
0
1
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
1
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
1
0
0
0
2
0
1
2
3
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
2
0
2
2
0
0
1
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
3
2
0
0
1
0
1
3
0
2
0
2
0
0
1
2
0
0
2
0
1
0
2
2
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
3
2
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
2
0
1
0
4
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
3
2
2
0
2
2
0
0
2
2
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
3
0
1
1
0
0
0
0
0
2
0
1
0
1
0
1
0
1
0
2
0
0
0
0
0
0
0
1
2
0
1
0
0
0
2
0
1
0
0
0
2
3
0
0
0
0
0
1
0
2
0
0
1
0
2
2
0
0
0
1
2
0
2
0
0
3
1
0
0
0
0
0
0
0
1
0
1
0
0
0
3
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
2
1
0
1
0
0
0
2
0
0
0
0
0
0
2
0
2
2
2
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
3
2
2
3
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
1
2
1
0
0
0
2
1
0
1
0
0
2
0
2
0
1
1
0
2
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
2
0
3
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
4
2
1
0
0
1
1
0
1
0
0
0
2
0
1
0
2
2
0
2
2
0
2
3
1
0
0
0
0
0
0
2
0
0
2
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
2
0
0
0
1
1
2
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
1
0
0
2
2
0
1
0
0
0
1
0
0
1
1
0
0
0
2
0
1
0
1
0
0
0
2
0
1
2
0
1
0
0
0
1
2
0
0
0
4
0
0
2
0
0
2
0
0
2
0
0
2
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
1
2
1
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
3
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
1
3
0
1
0
0
0
0
1
0
0
1
0
0
0
1
2
0
1
0
0
1
2
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
1
0
1
2
0
0
2
0
1
0
0
2
0
0
0
0
2
2
0
0
2
0
0
1
0
5
1
0
0
0
0
0
2
0
0
0
0
0
1
0
1
2
0
0
1
0
2
3
0
0
0
0
0
2
1
0
1
0
2
0
0
1
0
14
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
1
0
1
1
1
1
0
0
1
0
0
0
1
2
0
0
0
0
0
0
1
0
1
1
0
1
0
0
2
0
1
0
3
1
3
1
0
0
0
0
0
1
0
1
0
0
1
1
0
1
0
0
0
0
0
0
2
1
0
0
2
0
2
0
1
2
0
0
0
2
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
3
2
0
2
0
0
0
6
0
0
0
0
2
0
2
0
1
2
0
2
0
0
0
0
0
0
0
0
0
2
2
0
1
0
2
0
0
1
0
0
1
1
0
0
0
0
2
0
1
1
2
0
0
1
0
0
1
0
2
1
1
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
3
0
0
0
0
3
1
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
2
0
1
0
0
0
0
1
2
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
3
1
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
1
0
0
1
0
0
0
2
0
0
0
1
1
0
1
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
1
0
2
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
4
0
0
0
2
2
0
0
2
0
0
1
0
1
0
0
0
2
0
0
0
1
1
0
0
2
0
0
2
0
0
0
2
0
0
0
2
1
1
0
1
0
3
2
0
0
0
0
1
2
0
2
0
0
0
0
1
2
0
0
2
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
2
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
3
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
2
0
2
0
1
0
0
0
0
0
1
0
1
3
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
1
0
2
1
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
1
0
2
0
3
0
0
2
0
1
0
0
2
0
0
2
0
0
2
1
0
0
0
1
0
0
1
0
0
0
3
1
0
0
1
1
1
0
0
0
1
1
2
0
0
2
0
2
2
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
2
1
0
0
1
1
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
2
0
1
0
0
0
1
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
1
2
0
0
0
1
1
0
0
0
0
1
2
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
3
2
2
0
1
2
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
2
0
3
0
1
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
2
2
1
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
2
0
0
2
2
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
5
0
0
0
3
0
1
0
0
2
0
0
1
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
13
0
1
2
0
1
0
2
2
2
3
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
2
0
1
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
2
2
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
3
1
0
1
0
0
2
1
2
0
1
0
0
0
2
0
2
0
2
0
0
0
0
1
0
1
0
0
0
1
2
0
0
0
0
0
0
2
1
0
0
0
2
0
0
1
1
2
0
0
2
1
0
3
0
0
0
0
0
0
3
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
2
0
0
1
0
0
2
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
1
0
0
2
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
3
0
1
0
0
0
1
1
1
0
1
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
2
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
1
1
0
0
0
1
0
0
2
3
0
0
0
2
2
1
1
0
2
0
2
0
1
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
1
0
2
0
0
2
3
0
1
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
1
0
0
0
0
1
0
0
0
2
0
2
1
0
0
3
1
0
0
0
4
0
0
1
2
0
1
2
2
2
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
3
0
0
0
2
0
0
0
1
0
0
1
1
2
1
0
1
0
4
0
0
2
0
1
1
2
2
1
1
2
0
0
0
0
0
0
0
0
1
0
0
1
2
3
0
0
1
3
1
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
4
0
2
2
0
0
0
0
0
0
0
1
1
2
2
0
0
0
0
1
1
0
0
0
0
2
3
0
0
0
0
2
0
0
0
1
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
1
1
2
0
1
0
1
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
1
2
0
0
0
0
0
2
0
0
1
2
0
2
2
2
0
0
3
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
5
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
2
2
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
6
1
0
0
0
1
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
4
0
0
0
0
1
2
0
0
0
2
2
0
0
0
0
0
3
0
0
0
0
0
1
0
1
0
3
2
0
1
0
0
1
0
0
0
2
0
1
1
0
2
3
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
4
0
0
0
1
2
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
2
1
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
1
1
2
1
2
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
2
0
1
0
1
0
0
0
0
1
0
0
0
0
2
3
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
2
0
0
9
1
0
1
0
0
0
0
1
0
0
2
2
0
1
1
0
0
0
0
0
1
2
0
1
3
2
0
0
0
3
0
0
0
0
2
0
0
0
0
1
0
2
0
0
2
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
1
0
2
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
2
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
1
0
1
0
0
0
0
2
0
2
1
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
1
0
0
3
0
0
0
0
1
0
0
3
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
1
1
2
1
1
3
0
0
0
0
2
0
0
2
0
0
0
2
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
3
0
0
0
0
0
1
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
4
1
2
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
3
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
2
3
0
0
0
0
2
0
3
2
2
1
2
2
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
1
0
2
0
2
1
0
0
0
0
0
1
0
1
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
3
0
0
2
0
0
2
1
0
2
1
0
0
0
2
0
0
0
0
1
0
6
2
0
2
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
1
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
3
2
0
0
2
0
0
0
0
0
2
2
0
0
1
0
0
2
1
1
0
2
0
1
0
0
0
2
1
0
2
2
0
0
2
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
2
1
0
0
0
1
0
1
0
0
2
0
0
0
0
1
0
0
2
3
0
2
1
2
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
2
0
0
2
0
2
0
0
0
0
1
1
1
0
0
1
0
0
0
0
1
0
2
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
3
2
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
3
0
0
2
1
2
0
0
0
0
0
2
0
0
0
1
0
0
6
1
0
0
0
0
2
0
0
0
0
2
2
0
2
0
2
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
5
4
0
0
0
1
3
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
4
2
0
0
1
1
0
0
1
0
0
1
0
0
2
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
1
0
3
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
1
1
2
0
2
2
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
5
2
0
2
0
2
1
1
0
2
0
0
0
0
1
2
0
0
0
0
2
1
0
2
0
0
2
0
1
0
0
0
2
0
1
1
0
0
0
1
0
0
3
1
2
0
1
0
1
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
1
1
0
1
0
1
0
0
0
0
1
0
2
0
0
1
3
0
0
2
2
0
0
0
1
0
2
0
1
1
2
0
0
0
1
0
1
0
2
0
1
0
0
0
1
0
0
0
0
3
1
0
0
0
2
0
0
3
0
0
1
0
0
1
0
2
0
2
1
0
0
1
0
1
10
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
1
0
0
0
0
2
0
1
0
1
1
0
0
0
2
0
0
0
2
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
2
0
4
1
2
0
0
0
0
1
0
0
1
0
0
0
2
0
1
0
2
0
0
0
2
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
4
0
2
1
1
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
3
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
2
0
0
1
1
1
0
1
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
1
3
0
1
0
0
2
1
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
2
2
2
0
0
1
2
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
1
2
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
1
0
2
3
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
3
2
1
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
1
4
0
1
2
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
2
2
0
1
0
2
0
0
0
3
0
0
0
0
0
0
0
0
2
2
2
1
0
0
1
0
0
0
0
0
2
2
0
1
0
2
0
1
1
0
0
0
0
0
2
0
0
0
0
1
2
1
2
0
0
0
0
2
0
0
0
0
0
2
0
1
0
2
1
0
6
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
2
2
1
0
0
0
0
2
0
0
1
0
1
0
0
2
1
0
1
3
0
0
1
0
0
2
0
0
1
0
0
0
0
0
5
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
1
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
2
1
1
0
0
0
1
1
1
0
0
0
0
2
0
3
0
0
0
1
0
0
0
1
0
0
2
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
3
0
0
2
0
2
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
4
2
0
0
2
2
1
0
0
0
0
2
0
2
0
0
1
2
0
0
2
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
2
2
0
1
0
0
2
2
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
2
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
5
2
1
1
0
0
0
0
2
4
0
0
0
2
0
1
0
2
0
0
0
0
1
0
0
0
0
2
2
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
1
1
0
0
0
0
2
0
0
0
2
0
1
0
0
2
2
0
0
1
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
2
0
0
3
0
1
0
0
0
0
2
1
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
2
1
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
1
0
1
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
1
2
0
0
2
0
1
0
0
0
0
0
1
0
1
0
1
0
2
0
0
0
5
1
1
0
0
0
2
0
2
0
11
0
0
1
0
0
0
2
0
0
0
0
4
1
0
1
0
2
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
1
0
1
0
0
0
0
0
3
0
0
0
0
0
2
3
0
2
1
0
0
0
1
0
0
0
1
1
0
2
0
1
0
0
1
1
0
0
0
0
0
0
0
0
4
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
2
0
0
2
0
4
0
0
0
0
0
1
2
0
0
0
3
0
1
1
0
2
2
1
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
2
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
2
1
0
0
0
0
0
1
2
2
0
0
1
0
0
0
2
0
0
0
0
1
1
0
1
1
0
2
0
1
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
1
1
0
0
0
2
0
0
2
0
0
1
0
2
0
1
2
1
0
2
2
0
0
0
0
1
2
0
1
0
0
1
1
0
1
1
0
0
1
0
2
0
1
1
0
0
3
0
0
0
2
0
0
2
2
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
1
0
0
0
2
0
0
0
0
0
0
5
0
2
1
0
2
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
3
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
6
0
0
1
2
0
2
4
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
7
4
1
0
0
0
2
0
1
3
0
0
2
1
0
0
0
0
2
0
0
1
0
0
2
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
2
2
1
0
0
0
2
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
1
1
0
4
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
1
2
0
0
1
0
0
0
1
0
2
1
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
1
2
0
0
2
0
1
0
0
1
0
0
0
0
0
1
2
1
0
0
0
1
0
0
0
0
3
0
0
3
0
0
3
0
0
0
5
2
0
0
0
0
2
1
2
0
2
0
0
2
0
0
2
1
0
2
1
0
3
0
0
2
1
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
2
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
2
0
0
2
1
0
0
0
1
0
0
2
0
0
1
0
1
0
0
0
1
0
5
2
2
2
0
0
1
0
0
2
0
0
0
0
0
0
0
2
3
0
10
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
2
2
0
0
2
4
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
3
0
0
2
0
0
1
0
2
1
0
2
0
0
1
1
2
1
0
0
2
0
0
2
0
0
0
0
0
2
0
0
1
0
0
1
0
2
0
2
0
0
0
0
1
1
0
0
2
0
1
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
2
1
1
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
4
2
1
2
0
0
0
0
3
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
1
1
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
1
0
0
2
0
2
0
2
0
0
0
0
0
0
0
2
0
1
0
4
3
0
0
2
3
0
1
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
1
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
2
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
1
2
0
1
0
1
1
2
0
0
0
2
0
1
0
0
0
2
2
0
0
1
0
0
0
1
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
5
0
0
0
1
2
2
0
2
0
0
0
0
0
2
0
0
0
2
1
0
2
0
0
0
1
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
1
0
0
2
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
1
2
0
1
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
2
7
0
0
0
1
0
0
0
2
0
0
3
0
3
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
2
0
0
2
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
6
0
0
1
0
0
0
1
0
0
2
1
0
0
0
1
0
1
0
2
2
1
0
0
0
0
0
0
0
2
2
0
0
1
1
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
2
0
3
0
0
0
2
0
1
0
3
0
0
0
2
0
3
1
1
0
2
1
0
0
0
1
2
0
0
0
0
3
0
1
0
0
0
3
0
1
0
0
0
0
1
2
0
0
0
0
0
0
2
2
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
3
1
2
0
2
2
0
0
2
0
0
0
3
0
0
4
0
0
2
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
2
0
0
0
1
1
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
6
0
0
0
2
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
2
0
0
0
0
1
0
0
2
0
0
11
0
0
0
1
0
0
2
1
0
2
1
0
0
0
1
2
0
0
0
2
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
1
0
2
1
0
2
0
0
0
0
2
3
0
0
1
0
0
0
5
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
2
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
2
0
0
0
3
0
1
0
1
1
0
1
1
0
0
1
0
1
0
1
1
0
0
1
1
0
0
2
0
0
1
0
0
0
1
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
1
1
0
0
2
0
2
0
0
0
1
3
0
0
0
2
1
1
1
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
2
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
4
0
0
2
2
0
0
1
0
0
0
0
0
0
0
1
1
2
0
2
0
0
0
0
2
0
2
0
0
1
0
0
0
0
1
0
3
0
0
0
2
0
0
0
0
0
0
0
3
0
1
1
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
2
2
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
2
3
0
7
0
0
0
0
0
1
0
0
0
0
2
1
1
0
0
0
0
2
0
0
1
0
0
1
0
0
1
1
0
0
0
2
0
2
2
0
1
0
0
0
0
0
3
0
1
0
0
1
2
0
0
0
0
0
0
2
2
0
1
0
2
2
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
2
1
2
2
0
0
2
2
0
2
0
0
0
2
0
0
1
0
0
0
0
1
2
0
0
0
0
0
3
1
0
0
2
1
2
2
1
0
2
0
0
2
0
0
0
0
0
0
0
0
1
2
0
1
1
0
0
0
0
1
0
0
0
0
2
0
0
2
0
1
0
0
1
1
1
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
2
1
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
1
2
2
0
2
0
0
0
2
0
1
2
1
0
2
1
0
0
2
0
1
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
1
0
0
0
0
2
1
0
0
0
0
0
1
7
0
2
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
2
0
1
2
0
2
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
1
1
0
1
0
2
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
1
0
0
0
2
0
2
1
0
0
0
0
0
1
0
0
0
4
0
0
1
1
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
3
2
0
0
1
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
2
0
0
1
2
2
0
0
2
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
1
0
0
2
3
0
0
0
1
0
0
0
2
0
0
1
1
0
0
0
3
3
0
0
0
2
0
0
2
0
0
0
0
2
0
1
0
0
2
0
0
2
7
2
0
0
0
0
0
0
1
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
2
3
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
1
0
0
2
0
0
0
1
1
0
2
2
3
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
1
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
4
0
0
2
1
2
0
0
0
2
0
1
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
2
0
0
0
1
2
1
0
0
0
0
0
0
0
1
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
2
0
0
0
0
2
0
0
0
2
0
0
1
2
2
2
0
3
2
0
0
0
1
0
0
0
0
0
1
1
0
0
0
2
1
1
0
0
0
0
1
0
0
0
0
0
1
2
0
0
1
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
2
1
0
2
1
2
0
0
2
0
0
0
0
0
0
2
2
0
1
0
0
2
0
0
2
0
2
0
2
0
0
0
1
0
0
0
2
3
1
0
0
0
0
0
0
0
0
0
0
0
1
1
2
1
0
0
2
0
0
2
0
0
2
2
0
0
2
0
0
2
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
2
2
2
0
0
0
2
2
2
0
0
1
0
0
2
0
0
0
0
1
2
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
4
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
2
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
2
0
0
1
1
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
3
2
2
1
0
0
0
0
0
0
2
0
2
3
2
0
0
2
2
1
2
0
1
3
2
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
3
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
2
1
0
2
1
0
0
1
1
0
0
1
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
2
1
2
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
2
0
0
0
1
1
5
1
0
0
0
1
2
0
2
2
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
1
1
2
0
0
2
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
2
2
0
0
0
2
2
1
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
7
0
0
1
0
1
1
1
1
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
1
0
1
0
0
0
2
2
0
0
2
0
0
0
0
2
2
1
0
1
0
0
0
1
0
3
0
0
0
1
0
0
0
0
3
1
1
0
1
1
0
3
0
0
1
0
0
0
1
0
0
0
0
1
0
2
2
5
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
2
0
2
2
3
0
1
0
0
1
0
1
0
0
1
0
2
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
3
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
2
2
2
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
1
1
0
0
0
1
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
1
0
3
0
0
0
1
0
0
0
0
2
0
0
0
0
0
3
0
0
2
0
0
0
0
0
2
0
1
0
0
0
1
2
0
2
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
5
0
1
2
0
0
0
0
0
2
1
0
1
0
0
2
0
2
0
2
0
4
2
0
1
0
0
0
0
0
0
2
1
0
1
0
0
0
0
1
0
0
0
0
2
0
0
2
0
1
1
0
3
1
0
0
1
0
1
2
1
1
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
1
1
0
0
0
0
1
1
0
0
0
2
0
0
0
2
1
0
0
5
2
0
0
0
0
3
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
4
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
3
0
0
1
0
0
1
0
1
2
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
2
0
0
1
1
0
0
0
0
3
0
3
0
1
0
1
3
0
0
0
0
0
1
2
0
3
0
2
0
0
0
0
0
0
0
1
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
2
0
0
1
0
1
2
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
2
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
2
0
1
0
0
0
0
2
0
2
2
0
1
3
0
1
1
0
0
3
0
0
0
0
0
0
1
0
0
2
0
1
0
0
3
1
0
0
0
0
0
0
0
0
3
0
2
0
1
2
5
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
4
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
2
1
0
0
1
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
1
0
0
0
2
0
2
0
0
0
3
0
0
0
1
0
0
0
0
0
0
2
0
0
3
1
2
2
0
0
0
0
0
1
2
1
0
0
3
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
2
0
0
3
0
0
0
0
2
0
2
0
0
0
0
2
2
0
1
0
0
0
0
0
0
2
0
0
1
2
1
2
1
0
0
0
2
2
0
2
0
0
0
0
1
0
0
1
0
1
0
0
0
2
0
1
0
0
14
0
1
0
2
2
0
0
0
0
0
0
2
0
1
0
1
0
2
0
0
2
0
1
4
1
0
0
0
2
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
2
1
0
0
0
0
2
0
0
2
0
2
2
3
0
0
0
0
0
0
0
1
1
2
2
0
0
0
0
0
1
1
0
0
1
0
1
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
3
0
2
0
0
0
0
2
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
3
0
0
0
1
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
1
0
2
0
1
0
1
0
0
0
0
2
0
0
3
0
0
1
0
0
2
0
2
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
1
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
1
0
1
2
2
0
0
0
1
0
1
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
1
0
2
1
0
0
2
0
0
0
2
0
0
0
0
0
2
2
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
2
0
0
0
3
3
1
1
0
1
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
5
0
1
0
0
0
2
0
3
0
0
0
1
1
2
0
1
1
1
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
1
0
0
2
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
1
0
2
5
0
0
1
0
0
0
0
0
1
0
0
2
0
0
1
0
2
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
1
1
1
0
0
0
3
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
1
0
0
0
0
1
0
0
0
0
4
1
0
2
0
0
3
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
2
0
1
0
0
0
0
0
2
0
1
1
0
2
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
2
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
2
0
0
0
2
0
0
2
0
2
1
0
0
2
0
2
0
0
0
1
0
0
1
1
2
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
2
2
0
0
2
0
1
0
1
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
2
0
1
0
0
0
2
2
2
0
0
0
1
0
0
0
0
0
1
1
0
2
0
0
1
0
0
2
2
0
0
0
0
0
1
0
0
0
0
1
1
2
0
0
1
0
2
1
0
0
0
0
1
2
0
0
2
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
1
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
4
0
1
1
2
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
2
0
2
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
5
0
0
0
0
0
1
3
0
0
0
2
2
0
0
2
0
0
0
0
0
2
1
0
0
1
1
0
0
2
0
0
0
4
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
3
1
0
0
1
2
1
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
4
0
1
0
0
1
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
1
1
1
0
2
0
1
0
0
4
0
0
0
0
0
1
0
0
0
2
0
2
2
0
0
2
0
0
0
1
3
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
1
2
0
0
1
3
2
0
0
0
0
0
0
0
0
0
2
0
0
1
1
2
1
1
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
1
0
2
1
11
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
1
0
0
0
2
0
3
2
0
2
0
0
0
0
0
0
0
1
1
0
1
2
0
2
3
1
0
0
2
0
0
0
0
0
1
0
0
1
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
2
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
4
2
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
2
0
0
0
2
2
2
1
0
0
0
0
0
0
2
0
0
0
3
0
0
1
0
1
0
2
0
2
1
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
3
1
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
1
0
1
1
2
0
1
1
0
2
4
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
4
0
2
0
1
2
0
0
0
0
0
0
0
1
1
0
0
4
0
0
0
1
1
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
3
0
0
2
0
0
9
0
1
0
0
0
2
0
1
1
1
1
0
0
0
0
0
0
2
0
0
2
4
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
2
0
5
0
2
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
2
0
0
0
0
2
0
0
0
1
1
0
0
1
0
3
2
0
2
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
3
0
2
0
0
0
1
2
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
2
0
2
0
0
4
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
2
0
0
2
0
0
0
1
0
0
1
0
0
0
0
2
2
1
2
0
0
0
0
0
0
0
2
2
0
0
1
0
1
0
0
0
0
0
0
2
1
0
2
1
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
1
0
1
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
3
0
0
0
1
1
0
0
0
0
4
0
0
1
2
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
2
1
0
0
2
1
0
0
0
0
2
0
1
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
2
2
1
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
5
7
0
2
2
0
0
0
0
0
0
3
0
0
3
0
2
2
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
1
0
0
1
0
1
0
0
0
2
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
1
0
1
1
2
0
2
0
1
0
0
2
0
0
0
0
0
0
2
1
0
2
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
2
1
0
1
3
0
0
1
0
0
0
0
0
2
0
0
2
2
2
0
0
0
0
1
0
0
2
0
1
0
1
0
2
0
0
2
0
1
2
0
1
4
0
0
1
0
0
1
0
0
0
2
0
0
0
1
2
0
1
0
0
1
0
0
2
2
1
0
0
2
2
1
1
2
0
0
2
2
0
0
0
0
0
0
0
2
0
1
4
1
0
0
0
0
0
0
2
0
0
2
0
0
0
1
3
0
0
0
0
0
2
0
0
1
0
1
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
4
0
2
2
0
0
0
0
0
0
1
0
0
0
2
1
0
0
2
2
0
0
0
0
0
2
2
2
0
0
2
1
0
1
1
2
0
1
1
0
1
0
0
1
0
0
0
0
0
0
2
0
0
2
2
0
0
0
2
3
2
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
1
2
0
2
1
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
3
0
0
0
4
0
0
0
0
0
1
0
1
0
0
0
0
4
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
1
2
0
1
1
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
5
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
1
0
0
1
0
0
2
0
0
1
0
0
0
3
0
2
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
6
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
2
2
1
0
3
2
0
1
3
0
2
0
0
1
2
0
2
0
0
0
0
0
0
0
0
3
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
1
1
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
1
1
2
0
0
2
2
2
0
2
1
0
0
2
0
0
0
6
2
0
0
1
0
1
0
1
2
2
1
0
0
0
0
1
0
2
0
1
2
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
1
2
0
1
2
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
1
0
2
0
0
0
2
2
0
0
0
0
0
0
0
5
0
0
0
0
0
0
2
0
0
2
0
1
1
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
1
1
1
0
2
0
2
0
0
1
0
0
1
0
0
2
0
0
2
0
1
2
0
0
2
0
0
0
1
0
0
0
0
0
0
2
1
0
0
2
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
4
0
1
2
0
0
2
2
2
0
0
2
2
3
0
2
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
2
0
2
0
0
0
2
2
2
1
0
0
0
1
0
1
0
2
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
2
0
0
0
1
0
1
1
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
1
0
0
0
2
0
1
0
3
0
0
0
0
0
3
1
0
0
0
0
0
1
0
0
1
0
0
3
0
0
0
2
0
1
2
0
0
0
0
0
0
2
0
0
1
2
0
0
1
0
4
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
2
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
2
0
4
0
0
0
1
0
1
2
0
0
0
0
1
0
0
1
0
2
0
1
0
2
0
0
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
0
2
2
1
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
1
0
0
2
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
1
1
0
0
2
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
3
0
0
2
1
0
0
0
2
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
1
0
0
0
2
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
1
0
0
2
0
0
2
0
0
0
1
2
0
0
0
0
0
0
1
0
2
0
0
0
1
3
4
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
2
2
0
0
0
0
1
0
0
0
0
1
0
2
1
1
0
0
1
2
0
0
0
0
1
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
1
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
1
3
0
4
0
0
0
0
1
0
0
1
0
1
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
5
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
2
1
2
0
0
2
1
0
0
0
2
1
0
2
0
0
0
1
1
0
1
0
0
2
1
0
0
9
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
2
2
2
0
2
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
2
0
3
0
0
2
1
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
3
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
1
2
0
0
0
0
0
0
1
0
2
0
1
0
0
3
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
11
0
0
0
1
0
0
2
2
2
0
0
0
0
2
0
0
0
0
0
2
3
0
0
2
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
2
2
2
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
2
0
2
2
0
0
0
1
2
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
2
0
0
0
2
1
0
0
0
0
2
1
0
0
2
0
1
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
2
0
0
1
0
0
0
0
6
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
3
0
0
0
0
0
0
0
1
2
0
1
1
0
0
1
0
0
0
3
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
1
0
0
0
1
3
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
2
2
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
2
1
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
9
2
0
0
0
2
1
0
1
0
1
0
0
2
0
1
2
0
0
1
0
0
1
0
1
1
0
0
1
2
0
1
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
2
2
1
2
0
0
2
2
1
1
1
2
1
0
0
0
0
0
0
1
0
0
2
0
1
2
2
0
0
0
2
1
2
0
0
0
0
0
2
0
0
0
2
0
2
2
1
0
2
0
0
0
0
3
1
0
0
0
0
0
0
0
2
0
1
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
2
0
0
2
0
0
0
0
0
0
2
0
0
6
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
7
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
1
0
3
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
2
2
0
2
1
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
2
1
1
0
0
0
2
0
0
0
0
2
2
2
2
0
0
1
0
0
0
0
0
1
1
1
0
0
0
2
0
0
0
3
1
0
2
0
0
1
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
6
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
2
1
0
1
0
0
0
2
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
2
0
1
0
1
0
0
1
0
0
0
0
1
1
0
0
0
2
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
1
0
0
2
1
2
0
0
3
0
0
0
0
1
0
0
2
2
2
0
2
2
0
0
0
0
2
2
0
0
1
0
0
2
0
0
0
0
0
0
0
11
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
2
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
3
1
2
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
1
0
1
2
0
0
0
4
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
3
0
2
2
2
0
1
1
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
1
2
0
0
2
0
1
1
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
2
1
0
1
0
2
2
0
0
1
1
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
3
1
2
0
3
0
0
0
1
0
0
0
0
0
2
0
0
1
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
1
2
0
0
0
0
2
0
0
2
0
3
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
1
2
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
2
1
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
2
1
2
0
0
3
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
1
1
1
0
0
0
0
3
1
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
4
1
0
2
0
0
0
0
1
3
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
1
2
0
1
0
1
0
0
0
0
0
0
3
2
0
0
2
0
2
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
2
2
0
4
0
0
0
0
1
1
0
2
0
0
1
0
0
1
0
2
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
4
0
1
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
2
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
1
3
0
0
0
0
2
1
1
0
0
3
0
0
0
0
2
0
0
0
0
1
2
2
0
2
2
1
0
1
0
0
0
0
0
0
0
1
0
0
4
0
1
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
2
2
0
2
0
0
0
2
0
1
0
0
1
0
3
1
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
3
0
0
1
0
0
0
0
1
1
0
1
0
0
1
3
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
1
2
0
0
1
1
2
0
2
1
4
0
2
0
2
0
0
0
2
5
0
2
2
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
1
0
1
1
1
0
0
0
1
2
2
0
1
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
2
0
1
0
1
0
0
0
0
0
2
2
0
2
0
1
2
1
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
2
0
0
0
0
2
0
0
0
2
0
2
0
2
0
0
1
2
2
0
0
1
0
0
0
2
1
0
2
0
0
2
0
1
0
0
0
2
0
0
1
0
0
2
0
0
0
1
2
0
0
0
1
0
0
0
1
0
0
0
5
0
1
0
2
1
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
2
0
0
0
2
0
0
0
3
0
0
0
1
2
1
2
1
0
0
2
0
0
1
1
0
0
0
0
4
1
0
2
0
0
0
2
1
0
2
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
2
0
0
0
1
0
0
2
0
0
0
2
0
0
0
1
0
1
2
2
0
0
8
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
1
0
0
0
3
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
1
0
1
0
0
0
1
0
2
0
0
2
0
2
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
1
2
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
2
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
2
0
2
0
6
0
0
2
0
0
2
1
2
0
0
2
1
0
0
0
1
0
0
0
1
0
1
0
0
2
0
2
0
0
0
1
0
0
0
0
3
1
3
0
0
0
2
0
1
0
0
2
0
0
0
1
5
0
1
3
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
1
1
2
2
0
3
1
1
0
0
1
0
0
1
1
0
0
0
1
0
2
0
1
0
0
0
2
0
0
2
0
2
0
1
2
0
3
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
2
1
0
0
2
0
0
0
2
3
1
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
1
0
0
0
1
0
10
2
0
0
0
0
3
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
1
1
2
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
3
2
0
1
0
0
2
2
1
0
1
1
2
1
1
0
1
0
0
0
1
1
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
2
0
0
2
2
0
2
2
0
0
0
0
0
3
0
1
1
0
0
2
0
0
1
0
0
0
4
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
2
0
2
0
0
2
0
2
1
0
0
2
1
2
0
2
0
1
0
2
0
3
0
0
0
0
1
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
3
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
1
0
3
0
0
3
1
0
1
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
2
0
1
0
0
0
0
0
1
0
2
2
0
0
0
0
3
2
0
1
2
0
1
0
0
0
1
0
0
2
1
0
0
0
2
0
2
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
2
0
0
0
0
0
0
2
1
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
1
1
0
0
1
0
1
0
0
0
1
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
2
0
1
0
0
1
0
2
1
0
0
2
2
0
0
1
1
0
0
0
2
2
1
0
0
1
0
0
3
0
0
0
0
0
2
0
2
0
0
0
0
0
2
4
0
0
0
1
1
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
4
0
0
0
2
0
0
1
0
0
2
3
0
1
0
0
1
0
2
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
2
4
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
7
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
1
0
0
0
2
0
2
2
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
2
2
0
0
0
2
0
0
0
2
2
0
0
0
0
1
0
1
0
1
0
0
0
0
0
2
0
2
0
2
0
0
0
1
0
0
1
0
0
0
1
2
0
2
0
0
0
1
2
0
0
0
2
1
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
1
2
0
2
1
0
0
0
0
0
0
0
0
1
1
2
1
0
0
0
4
0
0
0
2
1
1
1
2
0
0
0
0
0
2
0
3
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
2
4
0
0
0
0
0
7
1
0
0
2
1
0
0
2
0
0
1
0
0
0
0
0
0
2
0
2
2
0
0
3
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
1
0
0
3
0
0
2
2
1
0
1
0
0
0
1
1
1
1
2
0
0
2
1
0
0
2
0
0
0
2
0
0
1
2
0
0
0
0
2
2
0
0
0
2
0
0
2
0
0
1
1
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
3
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
1
1
0
0
1
3
0
0
3
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
3
2
0
0
0
1
0
2
0
4
0
0
0
0
0
0
2
0
1
0
0
0
0
1
2
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
1
1
0
0
1
1
0
2
2
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
2
1
1
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
2
1
0
1
0
0
1
0
1
0
2
0
1
1
1
0
0
0
2
0
2
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
2
0
0
1
0
0
2
0
1
0
0
2
0
1
0
0
1
0
0
0
2
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
1
1
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
1
2
1
0
0
0
0
0
0
2
0
0
1
3
0
3
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
1
1
1
0
0
3
1
2
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
2
2
2
0
2
2
1
0
1
0
1
0
0
0
1
0
2
1
1
0
0
2
1
0
1
2
2
2
0
0
0
1
2
0
0
0
0
0
3
2
0
0
0
0
2
0
0
0
1
0
0
2
0
1
1
2
2
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
2
0
3
1
0
0
2
2
0
0
0
0
0
0
0
2
1
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
8
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
2
0
1
0
6
0
0
0
2
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
1
1
0
1
0
0
0
0
1
0
0
0
3
0
0
1
0
0
0
0
2
0
0
0
2
1
0
0
2
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
3
0
2
0
0
0
0
0
0
0
0
0
2
0
2
1
1
2
0
2
0
0
2
0
2
0
2
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
2
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
1
0
2
2
2
3
0
0
0
0
0
2
0
1
0
0
0
2
0
2
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
1
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
6
2
5
0
0
0
0
0
0
1
0
0
2
1
0
1
0
2
0
1
0
0
2
0
0
0
0
2
0
2
1
0
0
0
3
0
0
2
0
0
2
0
5
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
1
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
2
0
1
0
1
0
0
0
1
2
0
2
1
0
1
1
2
2
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
2
1
0
1
3
2
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
2
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
1
0
0
0
0
1
0
2
0
0
0
3
0
1
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
3
0
2
2
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
1
1
2
0
0
0
0
0
1
0
0
1
0
0
2
0
2
0
0
0
2
1
1
1
0
1
0
1
0
0
0
1
0
0
0
2
2
2
2
1
0
0
0
1
2
0
0
0
0
2
1
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
2
1
2
1
0
0
0
1
2
0
0
0
1
0
0
0
0
2
0
0
1
0
0
2
0
1
0
1
3
0
0
0
2
0
2
0
0
0
1
2
0
2
0
0
2
1
0
3
0
2
0
0
0
0
0
2
0
0
1
0
1
2
0
0
0
2
0
0
0
2
0
0
2
0
0
1
2
0
0
2
0
2
0
0
0
1
2
0
0
1
0
0
2
0
0
0
0
0
0
0
2
2
2
0
0
0
0
2
0
2
0
2
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
1
0
0
2
0
0
2
0
0
2
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
4
0
1
0
0
0
2
0
1
0
0
0
0
0
0
1
1
0
0
1
0
2
1
0
1
2
0
0
0
0
0
0
2
2
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
1
0
2
0
2
1
0
0
1
0
2
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
1
0
0
4
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
2
1
0
2
1
0
0
0
0
2
0
2
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
2
0
2
2
0
1
0
2
0
0
0
0
2
0
1
2
0
0
0
2
0
0
0
0
3
0
2
0
0
0
0
1
2
0
0
2
0
2
2
0
0
0
0
1
0
0
1
0
2
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
1
0
2
0
1
0
2
0
0
0
1
0
2
0
0
0
0
0
0
5
2
0
0
1
0
1
1
0
0
1
0
0
2
0
0
1
0
0
0
0
0
2
2
2
1
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
3
0
3
3
0
0
0
2
0
1
0
0
0
0
0
0
2
1
0
2
0
1
1
2
2
1
0
1
0
0
0
0
0
2
0
0
1
0
0
2
3
0
0
1
0
0
2
0
2
1
0
0
1
0
0
0
0
1
2
2
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
1
1
0
0
0
0
2
1
1
0
0
0
0
2
1
0
2
2
0
1
0
0
0
1
1
0
0
2
0
0
0
0
0
1
2
1
0
2
2
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
3
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
2
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
1
0
2
2
0
1
0
2
0
0
0
0
1
0
0
2
0
2
0
1
0
1
0
1
0
0
2
2
0
0
0
0
2
0
0
2
0
2
0
1
0
2
0
0
0
2
0
0
0
1
0
2
0
0
0
0
2
1
0
0
0
1
1
2
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
1
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
1
1
0
0
0
0
2
0
0
0
1
2
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
2
1
0
0
0
0
2
0
4
0
0
0
1
0
0
0
0
0
2
0
0
2
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
3
0
0
1
0
2
3
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
1
2
0
1
2
1
0
2
0
3
0
0
0
0
0
1
3
1
0
1
2
0
0
1
0
0
0
1
0
0
1
0
2
0
0
2
0
0
0
0
0
0
2
0
0
1
2
3
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
2
0
0
0
0
4
0
2
2
1
0
1
0
0
1
0
1
1
2
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
2
0
3
1
0
0
0
0
0
2
0
2
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
2
0
2
0
0
0
2
2
0
2
0
2
0
5
0
1
0
0
0
0
0
0
1
2
1
2
0
0
2
0
0
0
1
0
0
1
0
0
0
0
1
1
3
0
0
3
0
0
1
0
0
0
0
0
0
2
0
1
0
1
0
2
1
1
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
2
0
0
0
0
0
0
2
1
1
0
3
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
3
0
0
0
2
2
0
0
0
2
0
0
0
1
0
2
2
0
0
0
1
0
2
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
13
2
9
0
0
5
0
1
0
3
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
1
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
3
1
0
1
0
0
2
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
1
1
0
1
3
2
0
2
2
0
1
0
0
1
1
2
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
2
2
0
1
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
4
0
0
1
1
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
3
0
1
0
3
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
1
1
2
0
0
0
0
0
2
2
0
0
1
0
0
0
1
1
1
0
2
1
1
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
1
0
0
0
1
0
0
0
2
0
0
0
1
0
0
1
2
0
0
1
0
0
1
0
1
0
0
2
0
0
1
1
0
0
0
1
1
0
1
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
1
2
1
0
1
2
2
0
0
0
1
2
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
2
0
2
0
0
0
0
1
0
0
0
2
2
1
0
2
0
1
0
0
2
0
1
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
2
1
2
2
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
2
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
2
0
0
2
0
2
0
0
0
1
2
0
0
0
2
0
0
0
1
1
0
0
1
0
2
0
0
0
0
1
0
0
2
0
0
0
2
1
0
0
2
0
0
0
2
0
2
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
1
1
0
0
2
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
1
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
1
0
0
0
0
0
0
1
1
2
0
0
0
2
5
0
0
0
0
0
0
0
0
0
0
0
0
0
8
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
1
1
0
0
2
1
2
0
0
2
2
0
0
0
0
3
0
0
0
0
0
1
0
1
0
0
0
0
1
3
0
0
0
0
0
0
1
1
0
0
2
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
1
0
0
0
1
0
2
0
1
0
0
0
0
0
2
1
1
1
0
2
0
0
2
0
0
1
0
2
0
0
1
0
0
1
1
4
2
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
1
0
5
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
1
1
0
0
0
0
1
1
0
0
1
2
0
2
0
1
3
0
0
1
0
2
0
6
0
0
2
1
0
0
0
2
1
0
0
0
2
0
1
0
0
1
1
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
2
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
2
0
1
0
0
4
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
1
0
0
2
0
0
0
0
0
0
2
2
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
1
0
0
0
0
2
1
0
0
2
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
2
2
1
0
0
0
2
0
0
0
2
1
1
0
1
2
0
0
0
0
0
1
0
2
0
2
0
1
2
0
0
0
2
0
1
2
0
2
1
0
0
0
1
4
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
2
0
1
0
2
0
0
0
0
0
2
0
1
2
0
4
0
2
0
0
3
1
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
1
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
3
0
2
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
2
0
2
0
2
2
0
0
2
0
1
0
0
3
2
0
0
0
0
0
0
2
1
0
2
2
0
0
0
0
2
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
1
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
1
2
0
0
1
0
2
0
2
1
0
0
0
2
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
2
0
1
0
1
0
0
2
0
3
0
0
0
0
0
2
0
3
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
1
0
0
2
0
2
0
0
3
0
0
0
0
0
0
0
0
0
2
1
0
2
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
1
1
2
0
0
3
1
0
0
0
1
2
2
1
1
0
1
2
1
0
0
0
0
0
0
0
0
1
0
2
0
2
2
1
1
0
0
0
2
0
0
0
2
2
0
2
0
2
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
1
1
1
2
2
3
0
0
0
0
0
0
1
0
0
2
0
1
0
0
1
1
0
2
0
0
0
1
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
2
1
2
1
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
2
0
1
1
3
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
3
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
2
0
1
1
0
1
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
3
0
0
0
0
0
2
1
2
0
0
1
0
0
0
2
0
1
0
0
1
0
0
2
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
3
1
0
0
1
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
1
0
0
0
0
0
0
1
0
4
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
1
0
3
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
3
0
0
2
0
0
2
0
2
1
0
1
2
0
0
0
2
0
1
1
0
0
1
2
0
0
1
0
0
0
1
0
2
0
0
1
0
1
2
0
0
0
1
1
0
2
3
0
0
0
0
0
2
0
0
0
5
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
2
0
0
2
0
2
0
3
0
0
1
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
2
5
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
2
0
0
2
0
1
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
11
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
2
0
0
0
0
1
0
0
0
6
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
2
0
2
0
1
1
0
0
1
0
0
0
0
0
0
5
3
2
0
0
0
0
2
0
2
1
1
0
0
2
2
0
2
0
2
1
0
1
0
0
1
2
3
1
0
2
2
0
0
0
0
3
2
0
1
0
0
0
2
0
2
0
1
3
1
0
3
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
6
2
0
0
0
0
1
0
1
2
2
0
0
0
0
0
0
2
1
0
1
2
0
0
1
1
0
0
0
0
0
0
0
0
2
2
0
1
0
1
0
0
2
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
2
0
0
0
0
0
0
1
2
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
2
2
0
0
0
2
0
2
0
0
1
1
3
2
2
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
1
0
2
1
0
0
0
0
0
0
0
2
0
3
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
1
0
1
3
2
0
3
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
1
1
0
2
1
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
3
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
2
0
0
0
2
2
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
2
0
0
2
0
1
2
0
2
0
1
0
0
0
0
0
2
0
1
0
1
1
0
2
4
2
0
0
1
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
2
3
1
0
2
1
0
0
0
0
1
0
1
0
0
1
1
1
0
0
1
0
1
0
0
1
0
0
0
2
0
0
0
1
0
1
1
0
2
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
2
1
2
0
2
0
0
0
0
0
1
1
0
0
1
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
2
0
0
0
2
0
0
0
2
1
2
0
0
1
1
0
0
0
2
0
0
2
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
2
0
0
0
0
0
1
0
0
1
1
5
0
0
0
0
3
2
0
1
2
2
0
1
0
0
0
2
0
2
0
4
0
0
0
0
0
0
1
0
0
3
2
0
0
0
0
2
0
0
1
0
1
0
2
0
0
1
0
2
0
0
0
0
1
0
0
0
0
1
0
2
0
0
1
2
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
2
0
0
2
2
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
4
6
0
0
0
0
0
2
4
4
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
1
0
2
1
2
0
0
3
1
1
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
2
0
1
0
5
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
1
0
0
2
2
0
0
2
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
2
2
0
2
1
2
0
0
0
0
0
1
0
0
1
0
0
2
0
2
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
2
2
0
1
2
2
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
1
0
0
2
1
0
1
0
0
0
0
0
1
0
0
0
2
2
1
1
0
0
0
0
0
1
0
1
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
1
0
0
0
0
1
1
0
2
0
2
0
2
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
3
1
0
0
0
2
0
0
1
2
2
0
2
0
0
3
1
0
0
2
0
0
0
0
0
1
1
0
2
0
0
0
0
0
2
2
0
1
2
0
2
0
0
2
0
1
0
0
2
2
0
0
0
2
0
0
1
0
0
0
0
1
0
0
3
0
0
1
2
1
0
2
3
1
0
2
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
2
1
0
0
0
0
2
0
2
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
9
0
2
0
1
1
0
0
1
0
0
0
0
0
0
0
1
2
0
1
1
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
3
0
2
0
1
0
2
3
1
0
0
0
0
1
0
1
0
0
0
1
0
1
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
2
1
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
1
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
2
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
3
0
1
0
1
0
0
1
0
1
1
0
1
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
2
0
0
1
2
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
2
0
0
0
1
1
1
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
1
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
2
0
1
2
3
0
2
0
0
2
0
0
0
1
1
0
2
0
1
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
1
0
0
2
0
2
0
0
0
2
0
0
2
3
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
5
0
1
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
1
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
2
0
1
0
3
0
1
0
0
1
3
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
1
0
0
0
0
0
1
0
0
1
1
0
0
1
2
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
2
1
2
0
2
0
0
1
0
0
0
2
1
0
0
3
1
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
2
0
0
0
0
0
2
0
0
1
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
2
2
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
2
0
1
0
0
2
1
2
0
3
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
1
1
2
1
0
2
0
0
0
2
2
2
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
2
0
0
2
2
0
0
0
0
2
0
0
0
0
1
1
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
1
2
0
0
2
0
0
0
0
1
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
2
1
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
1
4
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
4
0
1
0
14
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
1
0
0
2
0
1
2
0
0
2
0
0
0
0
2
1
0
0
2
0
0
0
0
2
0
0
2
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
3
2
2
0
0
2
0
0
2
0
0
0
2
0
2
2
0
0
0
0
0
0
0
8
0
2
1
0
0
1
0
0
1
0
0
0
1
2
0
0
3
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
2
0
1
5
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
1
0
0
1
0
0
1
0
1
1
0
1
0
1
0
0
0
0
2
0
0
1
1
6
0
0
1
0
0
2
0
1
0
0
1
0
1
0
2
2
0
2
0
0
0
0
0
1
0
0
2
0
2
0
1
1
0
3
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
3
1
2
0
0
0
0
0
0
2
2
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
2
0
0
1
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
4
2
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
1
2
0
1
0
0
2
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
3
0
1
0
2
0
0
1
0
0
0
2
1
0
1
0
2
0
3
0
0
0
0
0
0
1
0
0
4
0
2
0
2
0
0
1
0
2
0
0
2
0
2
0
0
1
0
0
0
0
1
0
0
1
2
1
0
0
0
1
0
0
0
0
1
1
0
0
0
2
0
0
0
1
0
2
3
0
0
0
1
0
0
0
0
2
2
1
0
1
0
2
0
0
2
0
0
0
3
0
0
1
1
0
0
0
0
0
0
0
2
0
1
0
3
2
2
1
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
2
0
1
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
2
1
1
1
0
0
0
0
0
1
0
0
0
1
0
0
2
0
3
0
0
0
0
0
0
0
4
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
2
1
1
2
0
0
1
1
0
2
1
2
1
2
1
0
0
0
1
0
1
2
0
0
1
0
0
1
0
0
0
0
2
2
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
2
0
1
0
4
0
0
0
0
0
0
0
4
0
1
0
1
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
1
0
2
0
0
0
1
0
4
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
2
0
1
0
0
0
0
2
0
2
0
0
2
1
0
0
0
0
2
2
0
0
0
0
0
0
1
3
1
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
2
0
0
0
2
1
0
0
0
2
0
1
1
0
0
0
0
3
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
1
0
0
2
0
2
2
0
0
0
3
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
1
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
1
2
0
1
0
1
0
2
0
0
0
0
0
3
0
1
0
1
1
0
0
2
0
1
0
0
0
0
0
0
0
2
1
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
2
2
0
0
0
0
2
2
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
1
2
0
0
2
0
0
1
0
0
0
1
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
2
2
0
1
0
0
0
3
0
2
4
0
0
0
2
2
0
1
0
0
0
1
3
2
0
0
2
2
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
3
0
0
0
1
0
0
0
2
1
0
0
0
0
1
0
1
0
0
0
0
0
3
0
2
0
2
1
2
0
3
2
0
0
0
0
1
0
2
0
0
3
1
0
0
1
0
0
0
0
0
1
4
2
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
7
0
2
2
0
0
0
0
2
0
0
0
0
1
1
1
0
0
0
0
0
1
1
0
0
0
1
1
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
1
0
1
0
1
0
1
2
0
0
0
0
0
0
2
2
2
0
3
0
0
0
0
0
0
5
0
0
0
0
1
0
0
0
0
1
2
0
4
0
0
0
1
0
0
0
1
0
1
0
0
2
3
0
1
0
0
0
0
0
0
0
2
2
4
0
0
1
0
2
1
0
0
0
0
0
0
0
1
1
0
1
2
0
2
0
5
1
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
2
2
2
1
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
3
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
2
0
8
0
0
0
2
0
0
0
0
0
0
2
3
1
1
0
1
0
2
0
1
1
0
2
0
1
2
0
0
0
0
0
1
0
2
0
0
0
2
1
2
0
0
2
0
0
0
2
1
0
0
0
1
0
0
1
0
2
0
0
1
0
0
0
0
2
2
0
0
1
0
1
0
0
2
2
1
4
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
2
0
4
0
0
1
0
3
0
0
0
0
0
2
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
1
0
0
1
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
3
0
1
0
0
2
0
0
0
2
1
0
0
0
0
1
1
1
1
1
0
0
0
2
0
0
0
2
0
0
0
0
1
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
2
0
0
2
0
1
1
1
1
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
5
2
1
1
2
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
2
0
1
3
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
2
1
0
1
0
0
0
0
7
0
0
1
0
0
0
2
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
4
0
0
2
1
0
0
0
2
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
2
2
1
0
0
0
0
0
0
0
3
0
1
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
1
0
2
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
1
0
1
0
0
1
0
0
0
1
0
1
0
1
2
0
0
0
0
0
0
0
0
1
0
3
2
0
0
0
0
0
0
5
1
0
0
0
0
2
0
0
0
2
0
1
0
0
0
2
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
2
2
0
0
1
1
0
0
0
0
1
0
2
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
2
0
0
2
1
1
2
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
1
0
2
0
2
0
1
2
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
1
0
0
2
0
0
2
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
14
0
0
2
0
0
1
0
0
0
0
1
0
0
2
0
0
0
1
0
0
1
2
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
1
1
0
0
2
1
1
2
0
4
0
0
1
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
4
0
1
1
1
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
1
2
0
0
1
1
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
6
0
2
0
0
1
0
0
0
0
2
0
1
2
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
3
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
6
3
0
0
1
2
0
1
0
0
0
0
2
0
0
2
0
0
0
0
3
0
0
0
0
1
0
0
0
2
4
2
0
0
0
0
0
0
2
0
0
2
0
3
0
0
0
0
0
0
0
1
2
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
3
0
2
0
0
2
0
1
1
0
2
0
1
0
1
0
1
0
0
2
0
0
0
0
0
1
1
1
0
1
1
0
0
1
0
0
1
2
0
1
0
2
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
1
0
0
2
0
1
2
0
0
1
0
2
4
0
0
0
2
1
2
0
0
1
0
0
0
1
2
2
0
0
0
2
0
1
1
0
0
0
0
0
1
0
4
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
2
1
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
5
0
2
0
2
0
2
0
0
0
3
0
2
1
0
3
0
1
2
0
2
0
0
1
0
2
2
0
0
1
1
2
0
0
0
0
0
2
0
1
2
1
2
2
0
0
0
0
1
0
0
0
1
0
0
1
1
2
2
0
1
1
0
2
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
1
2
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
2
1
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
3
0
1
2
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
2
2
0
2
1
0
0
0
0
0
0
0
2
0
1
0
0
0
4
0
0
2
0
2
0
0
0
0
2
0
3
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
2
0
2
0
1
0
0
1
2
0
1
2
0
0
0
0
0
1
0
2
0
1
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
1
0
0
2
0
0
2
0
0
0
0
1
2
0
0
1
0
1
2
3
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
1
2
0
1
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
1
2
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
2
6
0
1
0
1
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
1
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
2
3
2
0
2
0
0
0
2
1
0
0
0
0
0
2
0
0
2
10
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
3
0
0
0
0
2
0
2
0
2
0
0
1
2
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
1
0
0
0
2
2
2
2
0
0
1
0
0
0
0
0
1
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
1
2
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
2
1
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
3
0
0
1
0
1
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
2
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
2
0
2
1
0
0
0
1
4
2
2
0
0
0
1
0
0
0
4
0
2
0
0
0
1
0
0
1
1
0
2
1
0
2
0
2
0
2
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
2
2
2
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
2
2
0
2
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
1
0
0
2
1
0
0
0
1
0
0
2
1
0
0
0
0
1
0
1
0
2
0
1
2
2
0
0
0
2
0
0
0
0
2
0
0
1
1
2
2
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
1
2
0
0
0
2
0
0
1
1
1
0
0
1
4
0
0
0
2
0
0
1
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
1
0
2
3
0
0
0
0
0
0
0
6
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
1
2
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
3
0
0
0
2
1
2
0
0
0
0
2
2
0
0
3
0
0
1
2
0
0
0
4
1
0
0
0
0
1
1
2
0
0
0
0
2
1
4
0
1
0
0
1
0
0
2
0
0
2
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
2
3
0
0
0
0
1
0
0
2
0
2
0
1
0
1
0
0
0
0
0
2
2
0
1
0
0
0
2
0
0
2
0
0
3
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
2
2
0
0
0
1
1
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
2
0
1
0
1
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
1
1
2
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
2
0
1
1
0
0
0
0
0
1
1
0
0
1
0
2
1
0
2
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
1
0
0
0
0
1
0
2
0
0
1
0
0
2
2
2
0
0
2
0
0
0
0
2
1
0
0
0
3
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
1
3
0
1
0
0
2
0
1
1
0
2
0
2
0
2
0
0
2
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
2
0
1
3
0
3
2
0
1
1
0
1
1
0
0
0
0
1
0
1
2
0
2
0
0
1
2
0
0
0
1
2
1
0
2
0
1
0
1
0
0
2
0
0
0
0
1
1
2
2
0
2
2
1
0
0
0
0
0
3
1
0
0
0
4
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
5
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
2
0
1
2
1
0
1
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
1
0
2
1
0
2
0
0
0
0
0
2
0
0
0
0
1
1
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
2
0
0
1
0
0
1
0
0
1
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
1
0
0
2
0
0
0
2
0
0
0
2
0
0
1
0
0
2
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
3
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
2
1
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
1
2
2
1
0
2
0
2
1
2
2
0
2
0
1
0
0
0
2
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
2
0
2
2
1
1
1
2
2
0
0
0
0
0
0
6
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
1
0
0
1
0
0
1
4
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
1
1
0
0
2
0
0
1
0
3
2
0
0
1
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
2
2
0
1
2
0
2
2
0
2
1
0
0
0
0
1
0
0
0
0
0
4
0
2
0
1
2
1
1
0
0
0
0
1
0
2
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
1
1
1
2
0
1
1
1
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
2
0
0
0
0
2
2
0
0
2
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
2
2
1
0
2
0
0
0
0
2
2
0
0
1
0
0
2
0
1
1
0
0
2
1
0
1
0
2
0
6
0
1
1
2
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
1
2
0
0
0
0
2
0
0
0
0
0
1
0
2
2
1
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
1
0
2
2
0
1
0
0
2
0
0
0
0
0
2
0
0
0
2
1
1
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
3
2
0
0
0
0
0
1
2
0
0
0
2
0
0
3
0
3
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
1
1
2
0
0
0
0
0
0
1
1
0
0
0
2
0
0
3
0
0
0
0
0
1
0
0
3
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
1
1
0
2
0
0
1
0
1
3
0
0
0
0
2
2
0
4
0
0
2
0
0
2
2
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
1
0
0
1
2
0
0
2
2
1
0
0
0
0
0
1
2
0
0
0
0
0
0
3
0
0
0
2
0
2
0
0
2
0
0
1
2
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
1
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
2
0
1
0
0
0
0
1
0
1
0
0
2
0
2
0
2
0
1
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
4
2
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
1
1
3
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
1
1
2
1
0
0
2
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
4
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
2
3
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
2
1
0
0
0
3
0
2
0
0
1
0
0
0
0
1
0
0
2
1
2
2
1
0
2
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
1
1
0
2
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
3
2
0
0
0
0
0
6
1
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
2
2
0
2
0
0
0
0
0
1
2
0
0
3
2
1
0
2
0
1
0
0
1
0
0
1
5
2
0
1
3
3
0
0
0
2
0
0
2
0
3
2
0
4
0
3
0
1
0
0
0
1
2
2
0
0
1
2
0
0
0
2
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
2
1
0
0
2
0
0
0
2
2
0
0
1
0
0
0
0
0
2
0
0
2
0
0
2
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
1
3
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
2
1
0
1
0
0
0
0
1
0
0
2
0
0
1
0
0
0
1
4
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
2
0
3
0
0
0
0
0
0
2
0
1
0
2
0
0
0
2
0
0
0
0
1
2
2
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
2
1
0
1
0
0
0
2
0
1
0
0
1
0
1
0
1
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
2
0
0
0
0
1
2
0
1
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
3
1
0
2
1
0
0
0
2
1
0
0
1
2
2
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
2
0
1
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
2
1
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
1
2
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
4
0
0
1
0
0
0
1
0
0
0
0
0
1
0
2
2
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
2
0
0
2
0
1
0
0
2
0
0
0
0
0
9
0
2
0
0
0
2
0
0
0
0
0
1
2
1
2
0
2
0
0
0
0
2
3
0
0
0
2
0
0
0
1
2
1
1
0
0
0
0
1
0
0
0
0
0
2
0
0
2
4
1
0
0
0
0
0
1
0
0
0
0
1
0
2
2
9
0
0
0
0
1
0
2
0
2
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
1
0
2
3
0
1
0
1
0
0
0
1
2
1
1
0
0
2
1
0
0
0
2
0
0
0
2
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
3
3
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
5
2
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
1
2
1
0
1
0
4
0
0
0
0
0
0
1
0
0
0
2
0
2
0
1
0
0
3
0
1
0
1
0
0
2
1
0
2
0
0
0
1
1
2
0
3
2
0
1
0
0
1
0
0
2
0
0
0
1
1
2
2
0
0
0
0
2
0
1
2
1
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
2
0
1
3
3
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
1
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
5
0
1
0
0
0
0
0
1
0
0
2
1
0
2
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
4
0
0
0
1
2
0
0
0
0
0
0
2
0
0
2
1
0
2
1
0
0
1
2
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
4
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
2
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
1
2
3
0
0
0
0
0
0
0
2
0
0
1
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
1
0
0
0
2
0
1
2
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
4
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
2
0
0
1
0
1
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
2
0
0
0
0
1
2
0
0
0
1
2
0
0
0
1
2
0
0
1
0
0
1
0
0
1
0
0
2
0
1
0
0
2
1
0
2
1
0
0
2
2
0
0
1
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
2
0
1
2
1
0
0
0
3
0
1
0
0
0
2
0
1
1
0
0
2
2
0
0
0
2
0
0
1
0
0
2
0
0
1
0
1
2
0
0
0
0
0
0
0
2
1
0
2
2
1
1
2
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
1
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
3
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
1
0
3
0
0
1
0
1
0
0
0
0
2
0
0
0
1
0
1
0
0
2
0
0
0
0
0
2
0
0
2
0
1
3
0
1
0
1
1
0
0
2
2
0
0
0
2
0
1
1
0
0
0
1
0
0
0
0
1
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
2
2
0
0
0
0
1
0
1
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
1
0
3
0
2
0
2
1
0
0
4
3
1
0
2
0
1
1
1
0
0
2
0
0
0
0
0
1
1
0
0
2
0
0
1
0
0
1
0
0
1
1
2
0
0
0
0
1
2
0
2
2
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
4
2
1
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
2
2
0
0
1
0
3
2
0
0
0
0
1
0
1
1
1
0
0
0
0
0
1
2
0
0
0
1
0
2
0
1
1
2
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
2
1
0
1
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
1
1
0
0
0
0
1
0
2
0
2
0
0
2
0
2
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
1
1
0
0
0
2
0
0
0
0
2
0
0
0
1
0
5
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
1
0
0
2
0
1
0
0
0
0
2
0
2
0
0
0
1
0
1
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
3
0
0
0
1
0
0
0
2
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
2
0
1
2
2
0
0
2
0
0
0
2
0
0
0
0
2
0
2
1
2
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
2
3
1
0
0
0
0
0
2
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
2
2
1
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
2
2
0
0
0
1
1
0
0
1
0
2
1
2
0
0
1
0
0
0
1
0
2
1
3
0
0
2
1
1
0
1
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
6
2
0
0
0
2
2
2
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
2
0
0
0
0
2
0
0
0
2
2
2
0
0
2
2
0
0
0
0
1
0
1
2
0
1
1
2
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
1
1
0
0
2
1
0
0
2
0
1
0
0
0
0
1
2
1
0
0
0
2
0
1
1
1
0
1
0
2
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
9
1
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
5
0
2
0
2
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
2
1
1
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
2
0
0
0
2
0
2
0
0
1
0
1
0
0
0
2
0
1
1
0
1
0
0
0
2
2
2
0
1
1
0
3
0
0
1
0
0
2
0
0
0
2
0
0
2
0
0
0
2
0
1
0
0
2
1
0
0
0
1
2
0
2
0
1
3
0
0
0
1
0
0
0
2
0
2
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
2
0
1
0
0
0
0
0
0
1
0
1
2
2
0
0
1
0
2
2
0
2
0
0
0
0
2
0
0
0
1
0
0
1
0
0
1
0
1
0
0
1
2
0
11
0
0
0
0
2
0
0
0
0
4
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
2
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
1
1
0
0
0
0
1
1
0
2
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
2
2
0
0
0
3
0
0
1
0
0
2
0
0
2
2
0
0
1
0
0
8
1
2
0
0
1
1
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
2
2
2
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
5
1
1
0
0
0
0
0
1
0
0
1
0
0
0
2
0
2
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
1
2
2
2
0
0
5
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
2
0
2
1
0
0
0
0
0
1
0
0
2
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
3
0
0
0
2
1
1
1
6
0
1
0
0
0
0
2
0
0
1
0
0
0
0
6
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
2
0
3
0
0
0
0
0
1
0
1
0
1
0
0
0
0
3
0
1
1
4
1
0
0
0
1
0
2
0
0
2
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
1
0
1
2
0
0
0
0
2
2
0
0
1
2
0
0
0
0
0
0
0
0
0
2
2
0
2
0
2
0
2
0
0
0
0
0
0
1
1
0
0
2
1
2
2
0
1
2
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
3
0
0
1
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
1
0
0
0
2
0
0
2
1
0
0
0
1
1
0
0
1
1
0
0
0
0
1
0
2
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
1
1
1
1
0
0
2
0
0
0
0
0
1
1
0
0
2
0
0
0
1
0
2
0
0
0
0
1
0
1
0
0
2
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
1
2
1
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
2
0
1
2
1
0
0
0
2
3
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
3
0
2
0
2
1
2
2
1
0
0
1
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
2
0
1
0
1
0
0
0
1
2
1
0
0
1
2
0
2
2
0
0
1
1
0
0
0
1
1
0
0
0
0
1
0
1
2
0
2
2
2
0
0
0
0
2
1
0
2
3
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
1
2
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
2
2
0
1
1
0
1
0
0
1
0
2
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
1
2
0
2
0
1
1
0
4
0
2
0
2
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
4
0
0
4
0
0
0
4
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
1
0
1
0
1
1
0
0
2
0
0
2
1
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
2
0
0
0
0
2
0
1
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
2
1
0
1
0
0
2
2
0
0
0
1
1
0
0
0
0
2
0
0
1
0
0
2
1
0
0
1
1
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
1
0
2
1
0
1
0
0
1
1
0
0
0
0
0
2
1
0
0
1
1
0
0
1
1
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
5
1
0
0
1
0
2
0
0
2
0
0
0
2
1
2
1
1
0
0
2
0
0
1
0
1
0
0
1
0
2
0
0
0
0
0
3
2
0
0
0
0
1
0
0
0
2
1
2
0
0
2
0
1
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
2
0
2
0
0
1
0
0
2
0
2
0
0
1
3
0
1
0
0
0
0
0
0
0
1
0
3
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
3
2
0
0
0
0
0
3
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
2
2
0
2
0
1
1
0
1
0
0
2
0
0
2
1
0
0
0
0
1
2
0
0
0
1
0
2
0
0
2
0
0
2
0
0
0
0
0
0
2
6
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
2
1
3
0
1
1
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
1
0
1
1
0
2
3
2
0
1
1
2
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
3
0
2
2
2
0
2
0
0
2
0
1
0
0
1
0
2
0
2
0
1
1
0
1
2
0
0
1
1
2
2
0
0
0
3
2
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
2
0
4
1
2
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
2
1
0
0
1
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
2
0
1
1
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
1
0
3
0
0
2
0
0
0
1
0
0
1
0
1
0
0
2
0
0
0
2
1
0
1
0
0
0
1
0
0
0
0
2
0
1
0
0
3
0
0
3
0
0
0
0
1
0
6
0
0
0
0
0
0
0
2
0
0
0
1
2
1
4
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
3
1
0
0
1
2
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
1
2
0
3
0
0
0
0
0
0
0
1
1
1
0
2
0
0
0
0
1
0
0
0
1
0
0
7
2
0
1
2
0
0
0
0
0
0
0
0
1
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
1
0
0
0
0
1
5
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
2
1
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
4
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
2
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
6
0
2
0
0
0
1
0
0
0
0
0
0
0
0
3
3
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
1
1
4
0
0
0
0
1
0
1
0
2
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
4
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
1
0
1
0
1
0
2
0
0
1
0
0
0
1
0
0
1
0
0
1
0
2
1
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
2
1
0
0
1
0
0
0
2
1
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
3
0
0
2
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
4
2
0
0
0
2
0
2
0
0
0
0
2
0
0
2
0
0
2
0
0
0
2
0
0
2
0
0
0
2
2
0
1
0
0
1
2
0
0
1
0
0
0
0
0
0
0
4
0
0
1
3
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
2
0
0
0
1
0
1
0
0
2
0
2
0
0
0
0
1
1
0
0
1
1
0
1
0
0
0
0
0
0
0
2
1
0
0
1
1
0
0
1
3
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
1
2
5
1
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
1
1
0
1
0
0
1
2
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
1
1
2
0
0
1
0
1
1
2
0
1
2
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
5
0
1
0
1
0
0
1
0
1
0
0
0
1
0
3
0
1
2
0
0
0
2
2
1
0
0
2
0
0
0
0
0
0
1
3
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
3
0
2
0
0
0
0
0
0
0
0
1
3
1
0
0
0
0
0
1
2
1
0
0
1
0
0
3
1
0
0
0
0
0
2
2
2
1
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
2
1
2
0
0
0
2
1
0
0
2
0
0
1
0
2
0
2
0
0
2
0
0
1
1
0
0
2
0
0
0
3
2
1
0
0
0
0
1
0
5
0
0
0
0
0
0
1
7
0
2
0
0
3
0
0
0
0
0
0
1
0
4
0
2
0
0
0
0
0
0
0
4
1
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
3
2
2
0
0
0
0
0
0
2
0
1
2
0
2
0
0
1
2
1
0
1
0
1
1
2
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
2
2
0
3
0
2
0
1
1
0
0
0
0
0
0
2
0
0
0
1
2
0
2
0
1
0
0
1
1
0
2
0
0
0
1
0
0
0
1
3
1
0
0
0
0
2
0
0
0
0
1
0
3
0
0
0
1
0
0
0
2
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
1
1
2
2
0
0
0
0
0
0
2
2
0
0
1
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
2
0
0
2
3
0
2
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
2
0
0
2
2
0
2
0
0
0
0
0
1
2
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
1
0
2
0
0
2
0
2
0
0
0
0
0
2
0
1
0
2
0
2
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
1
0
3
2
1
0
1
0
0
0
0
0
0
0
0
1
0
2
2
1
2
0
0
0
0
2
1
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
1
1
0
2
0
0
2
1
0
0
0
1
2
2
0
0
2
0
2
0
1
2
2
1
1
2
0
2
0
1
0
2
3
2
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
1
0
0
5
2
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
2
1
0
3
2
0
0
0
0
0
0
1
3
0
0
2
0
2
0
6
0
0
0
0
3
3
0
3
2
0
2
0
0
2
0
1
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
3
3
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
2
0
0
0
0
0
3
1
0
3
0
1
1
1
2
1
0
0
1
0
1
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
1
1
0
1
2
0
0
0
0
0
0
0
0
0
1
1
0
0
2
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
1
0
0
0
0
0
2
0
0
1
0
1
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
1
0
0
0
0
0
2
0
1
1
0
0
0
0
0
1
1
1
0
0
1
0
0
1
0
0
0
2
0
2
0
0
2
0
0
0
1
0
1
1
2
0
0
0
0
0
2
0
2
0
1
0
0
0
1
2
1
0
0
1
0
0
2
0
0
1
0
0
0
0
2
0
0
3
1
0
1
0
0
3
1
0
0
2
3
0
1
0
0
0
0
0
0
0
1
0
0
0
3
0
1
1
2
0
1
0
0
0
1
0
0
0
2
0
0
4
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
4
0
2
8
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
2
0
0
0
3
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
2
0
0
0
0
1
2
0
0
3
0
2
2
0
0
0
0
1
0
1
0
2
4
0
1
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
1
0
1
3
0
1
0
0
0
0
1
3
1
2
0
0
0
2
0
0
0
0
1
0
0
0
2
2
0
0
0
3
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
3
3
0
1
2
0
1
0
2
0
1
0
0
0
0
0
0
0
0
2
1
2
0
0
2
0
0
0
2
2
1
1
0
2
0
1
0
0
0
0
0
0
2
2
0
2
2
0
0
0
0
0
2
0
1
2
3
0
0
1
2
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
3
0
1
0
0
0
2
0
0
0
0
2
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
1
2
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
2
2
2
0
0
2
0
2
5
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
2
2
1
4
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
2
2
0
2
1
1
0
0
0
0
1
0
0
1
0
0
0
0
2
2
2
0
3
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
2
0
1
0
0
0
0
0
2
0
0
2
0
2
0
0
0
2
0
2
0
0
2
0
0
7
0
1
2
0
0
0
1
0
2
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
3
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
1
2
0
2
1
0
1
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
1
2
0
0
2
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
3
0
0
0
2
0
0
0
3
0
0
0
1
2
2
0
1
1
2
0
0
0
0
0
0
1
1
0
0
0
1
2
0
1
1
0
0
3
2
0
0
0
2
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
2
0
0
0
1
0
1
0
2
0
1
0
0
0
0
2
0
0
5
0
2
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
5
0
1
0
0
3
0
0
0
2
3
0
0
1
2
0
0
0
0
1
0
1
1
2
1
2
2
2
0
0
1
0
0
0
4
0
0
0
0
1
0
3
1
1
1
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
5
1
0
2
1
0
2
1
0
0
2
0
2
0
1
1
0
1
1
0
2
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
1
0
0
0
2
0
1
1
1
0
0
0
3
1
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
2
0
0
0
1
1
1
1
2
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
2
0
0
2
0
2
1
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
2
0
1
0
0
2
0
1
2
0
0
0
2
0
0
0
1
0
0
0
3
0
0
0
0
2
4
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
5
0
0
2
0
0
1
0
0
0
0
1
0
0
0
1
0
2
1
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
1
0
2
0
2
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
2
0
0
1
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
1
0
0
0
2
0
2
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
1
1
1
0
0
0
0
0
0
1
2
4
0
1
2
0
2
0
2
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
1
0
2
2
0
0
0
0
0
1
0
0
2
0
1
0
0
0
1
2
0
1
0
0
0
2
0
0
0
0
0
1
2
1
0
0
0
2
0
1
1
0
0
2
0
0
2
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
4
1
0
0
1
1
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
1
0
2
0
0
2
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
2
1
0
0
0
2
0
4
0
1
0
1
0
0
0
0
4
1
1
0
0
0
0
0
4
0
0
0
0
1
0
2
0
1
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
3
1
0
0
0
2
2
0
1
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
6
2
0
1
0
0
0
0
0
2
0
0
0
0
4
0
1
1
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
2
0
1
0
2
0
0
2
2
0
0
2
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
1
0
2
2
0
0
0
0
1
0
1
0
0
0
0
2
0
3
0
0
0
0
0
0
1
0
2
2
1
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
1
0
1
0
3
1
2
2
0
0
0
2
0
0
0
0
0
2
1
0
2
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
1
0
0
0
0
0
0
0
0
2
3
0
0
0
2
0
0
3
1
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
3
0
1
0
0
0
0
2
0
0
0
3
0
0
2
0
0
3
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
7
0
0
1
0
2
0
0
0
1
1
0
0
0
0
4
0
2
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
2
0
0
0
0
0
2
0
0
2
0
0
1
0
1
0
0
0
1
2
0
0
1
0
1
0
0
2
0
1
0
1
0
2
0
0
1
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
1
1
1
0
3
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
7
1
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
1
0
1
6
0
0
0
0
0
0
0
0
5
1
0
2
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
2
0
1
4
1
0
0
0
0
0
0
0
0
1
2
1
3
0
2
0
2
2
0
0
2
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
4
2
0
1
1
0
2
0
3
1
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
1
0
0
2
0
3
2
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
1
0
2
2
0
0
2
2
0
0
2
0
2
0
3
0
1
0
2
0
1
0
0
2
0
0
1
4
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
2
0
0
1
2
0
1
9
2
0
2
0
0
0
1
0
0
0
1
0
0
1
0
0
4
2
1
0
0
0
1
0
0
2
0
0
1
1
2
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
1
2
1
1
0
0
0
1
2
0
0
0
0
0
2
0
0
1
0
2
2
0
1
0
1
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
2
0
2
0
0
2
2
2
2
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
2
0
0
2
0
0
2
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
1
2
0
0
0
0
2
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
1
0
0
2
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
1
2
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
1
0
2
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
1
0
4
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
2
2
0
0
0
1
0
2
0
0
0
0
0
0
1
2
2
0
0
2
0
0
1
2
0
0
0
2
0
0
0
0
0
2
0
0
0
3
2
0
0
0
0
1
0
1
1
0
0
0
1
2
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
1
2
0
2
0
0
0
1
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
1
0
1
0
0
1
0
0
2
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
1
0
2
2
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
2
0
6
0
0
2
0
0
0
3
0
1
1
0
2
0
1
0
0
0
0
1
0
1
0
3
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
7
2
0
0
2
0
3
0
0
0
0
1
0
3
1
4
2
0
1
0
1
0
0
0
0
2
1
1
0
0
0
0
0
3
1
0
1
0
0
2
2
0
0
0
0
0
0
1
0
2
11
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
3
0
1
0
1
0
0
2
0
0
0
1
0
0
0
2
1
1
0
1
0
1
2
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
4
2
0
0
0
2
0
0
2
0
0
0
0
2
2
1
1
0
0
1
0
1
0
0
1
1
0
2
0
0
0
0
1
2
0
0
2
0
3
0
0
0
1
0
2
0
0
1
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
2
2
1
0
0
0
1
1
2
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
1
0
2
3
0
0
0
0
2
3
1
2
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
1
0
0
1
0
0
0
0
2
1
0
3
0
0
0
0
0
1
0
0
2
0
2
2
0
1
2
2
0
1
0
0
0
0
2
0
0
0
2
1
1
0
1
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
2
0
1
2
0
2
0
7
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
3
1
2
1
0
0
1
0
0
2
0
2
0
1
2
4
0
1
0
0
0
1
0
0
1
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
2
0
2
2
0
2
1
1
1
3
0
0
0
0
0
0
0
2
0
0
0
0
1
2
1
2
0
0
0
1
0
0
0
2
0
0
4
1
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
1
0
0
2
4
0
2
0
1
1
0
1
0
0
0
0
0
0
2
3
0
0
0
0
0
0
1
2
1
0
0
2
2
1
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
3
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
1
2
0
4
0
2
0
0
2
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
2
0
0
2
0
0
1
1
1
0
3
0
1
0
0
1
0
0
0
2
0
0
2
0
3
1
2
0
1
0
0
2
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
3
0
0
0
0
1
0
0
2
0
1
1
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
1
0
0
1
0
0
1
0
2
1
0
0
1
0
1
0
0
0
0
1
1
1
0
1
0
0
0
2
0
0
0
1
0
0
1
0
1
0
0
2
0
0
2
0
0
1
2
0
2
0
0
0
1
0
0
0
0
2
1
0
1
0
0
1
0
2
0
0
1
2
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
4
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
7
0
2
0
0
1
0
0
1
0
0
0
2
1
1
4
2
1
0
2
0
0
2
2
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
2
1
0
0
1
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
2
0
1
0
2
0
0
2
0
0
2
1
2
0
0
1
1
1
0
0
0
0
0
2
0
0
0
0
9
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
2
0
0
2
2
1
0
0
0
0
0
2
0
2
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
7
0
1
0
0
2
2
0
0
0
0
0
1
2
1
0
2
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
1
0
1
1
0
1
0
2
0
0
1
0
0
2
2
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
3
0
1
0
2
0
1
1
1
0
3
0
2
2
0
2
0
0
0
0
0
0
5
1
1
0
0
0
0
1
1
2
0
0
0
1
1
0
2
1
0
0
6
2
0
0
2
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
2
2
0
0
0
1
0
2
0
3
0
0
0
0
0
0
2
0
0
0
2
0
0
2
4
2
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
1
1
1
0
0
2
0
0
2
0
2
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
2
0
1
0
0
0
1
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
2
1
1
0
0
2
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
2
0
0
0
2
0
0
1
0
0
0
4
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
2
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
1
0
0
0
0
2
0
2
0
2
0
0
0
0
1
0
0
0
2
0
3
1
0
0
0
0
0
0
1
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
3
0
1
2
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
2
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
2
0
1
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
2
1
2
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
2
1
0
2
0
1
0
0
0
0
0
0
0
1
0
3
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
2
0
0
2
2
0
3
0
2
0
0
0
3
1
0
0
0
0
0
1
0
2
1
0
0
0
2
0
3
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
1
0
0
0
0
3
0
1
0
2
0
2
0
2
0
1
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
3
0
0
3
0
0
2
0
0
2
1
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
2
0
1
1
0
0
1
0
0
0
0
0
2
0
0
1
0
0
1
0
1
0
0
0
0
2
1
0
1
0
0
1
0
0
0
0
1
1
1
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
2
1
0
0
0
0
0
2
3
0
2
0
2
2
0
0
2
0
0
2
4
2
0
2
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
2
3
1
2
0
0
0
0
1
0
0
0
0
3
7
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
2
2
0
1
0
0
2
0
0
0
0
2
0
0
0
1
2
0
0
0
0
1
1
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
1
4
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
1
2
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
3
0
0
0
1
0
0
0
2
0
2
0
0
1
0
2
0
0
2
1
0
0
0
0
0
0
0
0
2
5
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
2
0
3
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
1
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
1
0
1
1
0
1
0
2
0
1
0
2
0
0
0
0
2
0
1
6
0
0
0
1
0
0
2
2
2
2
0
1
3
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
1
1
0
0
0
0
0
0
1
1
0
0
0
2
1
0
2
1
0
1
0
0
2
0
2
0
0
0
0
0
0
0
2
0
1
1
0
0
1
0
0
0
3
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
2
2
1
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
1
1
0
0
0
0
0
0
0
1
0
1
1
2
0
1
0
0
0
1
0
0
2
3
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
1
0
0
2
2
0
0
3
0
1
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
1
5
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
3
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
2
2
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
2
1
0
0
1
0
0
0
2
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
2
0
1
0
1
0
0
0
0
3
2
1
0
1
0
0
0
3
0
0
2
0
0
0
0
0
0
0
2
2
0
1
0
0
0
2
1
0
1
2
0
2
0
0
2
2
0
0
0
0
0
2
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
2
0
0
0
0
5
0
2
1
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
2
0
0
5
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
2
1
1
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
1
1
2
1
0
1
0
2
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
5
0
0
2
0
2
0
0
0
1
0
0
1
2
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
2
2
1
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
2
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
3
0
1
0
0
0
0
2
0
0
0
0
0
1
1
0
1
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
2
0
1
1
2
1
0
1
0
0
0
0
0
1
0
0
2
0
2
2
0
0
0
0
0
0
0
2
0
1
2
1
3
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
2
0
2
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
3
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
4
2
2
0
7
2
0
3
4
0
2
0
2
0
0
0
0
1
1
0
0
0
3
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
1
0
1
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
1
0
2
0
1
0
1
0
0
0
0
0
0
0
0
2
1
0
2
0
2
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
3
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
2
0
3
3
0
2
0
0
1
0
0
0
2
0
0
0
1
2
0
0
1
0
0
0
2
2
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
2
0
0
1
0
1
1
2
0
2
0
0
4
0
0
1
1
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
2
0
0
4
2
0
0
0
0
1
0
3
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
2
2
0
1
1
0
0
1
0
0
0
2
0
0
0
2
0
1
0
0
1
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
1
0
1
3
0
0
0
0
0
1
0
0
0
0
1
2
2
0
1
1
2
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
2
2
1
0
0
0
0
0
2
0
0
1
0
4
0
0
2
2
1
0
1
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
1
1
1
0
0
7
0
0
0
2
0
4
0
0
2
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
2
0
1
0
0
0
0
1
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
9
0
0
1
1
0
0
0
1
0
0
0
0
0
0
3
0
2
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
2
2
2
1
0
0
0
1
2
0
0
0
1
0
0
0
0
1
3
1
0
1
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
2
0
1
2
0
1
1
2
0
0
2
0
1
0
0
2
0
0
1
0
0
0
0
2
0
2
0
0
2
1
1
2
1
2
0
0
0
2
0
0
0
0
0
2
2
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
1
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
2
1
1
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
2
1
2
2
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
2
0
2
2
0
0
0
1
0
2
0
0
0
0
5
0
0
2
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
2
0
0
1
2
0
1
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
3
0
0
2
4
0
1
1
1
2
0
0
0
0
0
0
2
0
0
1
0
0
3
1
0
0
0
0
0
4
1
0
0
1
0
3
1
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
2
0
0
0
2
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
3
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
1
1
0
2
1
0
0
0
1
0
0
2
0
0
1
0
0
3
0
0
0
2
0
0
3
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
3
2
0
0
1
1
0
2
0
1
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
2
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
2
0
2
0
2
2
0
0
0
0
1
1
0
0
2
0
1
4
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
3
0
2
1
0
0
2
1
1
0
1
2
0
6
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
3
4
0
0
1
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
2
1
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
2
1
2
3
0
1
0
2
0
0
0
0
0
0
2
2
0
0
0
1
0
0
2
3
3
0
2
2
0
0
0
0
0
0
1
1
0
0
0
0
2
0
3
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
1
1
0
1
0
0
0
0
0
1
0
0
2
0
1
1
0
3
0
0
2
0
0
0
0
3
0
0
1
0
0
0
1
0
2
0
0
0
1
1
0
0
0
0
1
0
2
2
0
0
1
0
0
2
3
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
1
1
0
1
1
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
3
2
0
0
0
2
0
0
1
0
0
1
0
0
0
2
0
0
0
0
4
0
0
0
0
2
0
0
2
0
2
0
1
2
0
4
1
0
0
0
2
2
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
3
0
1
0
0
0
2
3
0
0
0
0
0
2
0
2
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
2
1
1
2
0
0
0
0
1
0
2
0
0
5
1
0
0
0
0
2
0
2
1
0
2
0
0
1
4
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
2
2
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
4
0
0
0
1
0
0
2
0
2
0
0
2
2
1
0
0
1
2
0
0
0
0
2
2
0
0
0
2
0
0
1
1
0
0
0
1
0
0
2
0
0
3
0
0
1
0
1
0
3
3
0
2
1
2
0
1
2
2
0
0
2
0
2
0
0
2
1
0
0
2
0
0
2
1
0
1
0
0
0
0
0
0
0
1
3
1
0
0
0
0
0
0
1
2
3
0
0
1
2
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
1
1
0
0
0
0
0
2
1
2
0
3
0
2
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
1
3
2
1
1
0
0
0
0
0
1
0
4
0
0
0
0
1
0
0
0
1
0
0
0
2
0
4
2
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
2
2
1
1
0
5
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
3
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
2
0
1
0
2
2
0
0
7
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
2
0
0
0
2
1
2
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
1
0
0
2
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
1
0
1
0
0
2
1
0
1
2
1
0
0
1
0
0
0
0
1
1
2
1
0
2
0
2
0
2
1
0
0
1
2
0
0
0
0
0
0
2
1
0
0
0
0
2
0
1
3
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
2
1
0
0
1
1
0
0
0
0
0
2
0
3
0
0
0
0
0
1
0
2
0
1
0
0
1
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
2
0
1
0
2
0
0
0
1
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
3
0
0
0
1
2
2
0
2
0
0
1
2
1
1
1
0
0
1
1
0
1
0
0
0
2
0
0
2
0
1
0
0
0
0
0
3
0
2
0
0
0
0
0
2
0
1
0
0
0
0
2
2
0
0
1
1
0
0
2
0
1
0
0
0
0
0
0
1
0
2
0
0
2
0
1
0
3
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
2
1
1
0
0
1
0
0
1
0
0
1
0
0
3
0
1
0
2
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
2
0
0
0
0
1
2
1
0
2
0
0
0
4
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
3
0
0
0
1
0
1
0
2
0
0
0
2
1
0
0
0
0
0
2
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
1
0
0
1
0
1
0
3
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
4
2
0
0
3
0
1
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
2
2
1
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
2
0
0
2
1
0
0
2
0
2
0
1
0
1
2
0
1
0
1
0
0
0
2
0
0
2
0
1
1
1
1
0
0
1
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
6
0
0
0
0
0
2
2
2
0
0
11
1
3
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
2
0
0
1
2
0
0
0
5
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
1
2
0
1
0
1
0
6
0
0
0
0
0
0
0
0
2
0
0
1
0
1
1
0
0
2
0
2
0
0
1
0
0
3
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
1
0
0
1
0
2
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
2
2
1
1
0
1
0
0
0
0
2
0
0
0
0
0
2
2
2
0
0
0
0
0
1
3
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
3
1
1
2
0
0
0
1
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
1
0
0
6
1
0
0
0
0
1
1
0
0
0
0
2
2
0
0
0
1
0
2
0
1
0
2
0
2
0
2
0
1
0
0
0
0
0
0
4
0
1
0
0
0
2
2
0
0
0
0
2
0
0
2
0
0
0
1
0
0
1
1
1
0
0
0
0
2
0
0
1
0
1
0
1
2
2
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
2
0
0
1
1
0
0
0
2
2
1
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
1
2
0
0
2
0
0
0
2
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
3
0
0
0
1
1
1
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
1
2
0
0
1
2
0
0
1
0
0
0
2
0
0
1
0
0
2
1
1
0
0
1
0
0
0
0
0
2
0
2
1
0
0
0
0
2
0
0
0
2
0
0
1
1
0
0
1
2
0
0
0
0
0
0
0
6
0
11
0
2
0
0
3
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
1
1
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
2
1
0
3
2
0
0
0
0
0
1
0
0
0
1
0
1
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
1
0
0
0
0
0
2
1
0
2
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
3
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
3
2
2
1
0
0
0
2
0
2
4
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
2
0
1
0
0
0
0
0
0
0
1
2
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
2
2
2
0
1
1
1
0
0
2
0
0
0
0
0
0
1
0
2
0
2
2
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
2
1
0
2
0
0
1
0
1
0
2
6
0
2
0
0
1
0
1
0
0
0
0
1
0
0
0
2
2
2
0
0
0
0
2
0
0
0
0
1
2
0
0
0
1
2
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
1
1
0
0
0
1
0
0
0
2
2
0
0
0
2
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
11
0
0
0
0
0
2
1
2
0
1
1
0
0
0
0
0
1
0
0
1
1
0
3
0
2
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
1
1
1
1
2
0
0
1
0
1
0
0
2
2
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
1
3
0
0
1
1
2
2
0
0
0
0
0
0
2
2
0
0
0
0
0
1
4
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
1
0
2
0
1
3
0
3
0
0
1
1
2
0
2
0
0
0
1
0
3
2
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
4
2
1
0
0
0
1
2
0
0
0
4
2
0
0
0
0
0
2
0
0
1
0
0
1
0
0
2
0
0
0
0
2
0
2
1
1
0
0
2
0
1
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
1
0
0
0
2
0
8
0
2
3
0
1
0
0
2
0
0
2
1
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
3
0
0
0
0
2
2
0
1
1
0
0
0
0
3
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
3
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
2
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
7
0
0
2
0
0
0
0
3
0
0
2
1
0
0
0
0
0
2
0
2
0
1
3
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
1
0
0
2
0
0
2
1
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
4
0
4
1
3
0
1
0
0
0
0
0
0
0
0
0
0
0
2
3
0
2
0
2
0
0
0
0
0
2
3
1
1
1
0
2
0
0
1
0
0
0
0
1
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
2
0
0
2
2
0
0
0
2
0
0
1
2
0
0
2
0
1
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
1
2
1
2
2
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
3
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
1
1
1
2
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
6
0
0
0
3
0
0
0
0
3
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
2
0
0
0
0
0
1
1
0
2
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
3
1
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
2
0
1
0
1
0
2
3
2
0
0
2
0
0
2
0
0
2
0
1
0
0
2
0
0
2
0
1
4
0
1
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
2
1
2
0
1
1
0
1
0
0
0
0
0
0
0
0
5
0
2
0
0
0
0
4
1
0
1
0
0
0
0
3
0
2
0
0
1
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
2
2
0
2
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
3
2
1
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
1
0
1
2
0
1
0
0
1
0
1
0
1
2
0
0
0
0
0
0
1
0
2
0
0
0
1
2
0
0
2
0
0
0
0
0
2
0
0
0
3
1
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
2
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
1
0
0
0
3
1
0
0
0
0
2
1
0
2
1
2
0
2
0
3
0
1
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
4
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
2
0
2
0
2
0
1
0
0
0
0
0
1
1
2
0
0
1
1
0
0
0
0
2
0
2
3
2
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
1
2
2
0
1
0
0
0
0
0
1
0
2
0
0
2
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
1
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
1
0
0
0
1
1
0
0
0
1
2
4
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
2
1
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
1
0
0
1
2
0
1
1
2
2
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
2
4
2
1
2
2
0
0
1
0
0
0
0
2
2
0
0
0
0
2
0
1
0
0
0
0
1
0
0
2
0
0
1
2
2
0
0
2
0
0
0
0
0
2
0
0
0
2
1
2
1
0
1
0
0
0
2
0
4
1
0
2
1
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
4
3
0
0
0
1
1
0
0
0
2
2
1
0
0
0
0
1
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
2
0
0
0
3
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
7
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
1
0
0
0
4
0
0
0
2
2
1
0
1
0
0
0
0
0
1
0
0
0
0
14
0
0
0
0
2
0
0
0
2
0
0
3
0
1
2
1
0
0
0
0
2
0
0
0
0
2
1
2
1
1
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
2
0
6
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
1
1
0
1
1
0
0
1
0
2
0
1
0
2
0
0
0
1
0
2
0
2
0
0
0
1
0
1
1
1
2
0
0
0
0
0
2
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
1
2
0
0
1
0
1
2
1
1
0
0
0
2
0
0
2
0
1
0
0
0
0
0
2
2
2
2
0
0
1
0
0
0
0
2
0
0
0
2
3
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
4
0
0
2
0
0
0
2
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
1
0
0
0
1
0
0
0
0
4
0
0
3
2
0
7
0
0
0
2
0
0
0
2
0
1
2
2
0
1
2
0
0
0
2
2
0
3
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
1
0
2
0
0
2
2
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
1
1
1
0
0
0
0
0
0
0
1
0
2
0
2
2
0
0
0
0
0
0
0
1
2
0
1
0
0
1
2
0
0
0
0
2
0
2
0
2
3
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
2
0
0
1
0
1
1
0
0
1
0
0
0
1
1
0
2
0
0
0
0
2
0
0
0
0
0
1
1
2
0
0
1
0
2
0
1
0
1
0
2
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
1
0
2
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
1
0
0
0
0
3
1
0
0
0
0
1
0
0
0
0
0
0
2
1
1
0
1
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
5
0
2
2
1
0
0
0
0
0
3
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
3
1
0
0
2
0
0
1
0
1
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
1
0
1
1
0
0
0
0
3
0
2
1
1
2
2
0
3
0
0
1
0
1
0
2
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
2
0
2
0
2
2
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
1
0
2
1
1
0
0
1
0
0
0
2
0
0
4
0
0
1
0
0
0
1
2
0
0
0
0
0
2
2
0
1
0
0
1
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
2
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
1
0
1
0
0
1
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
2
1
2
0
1
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
1
0
0
3
0
0
1
2
0
1
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
3
1
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
1
0
2
0
1
0
0
0
0
0
3
0
1
1
0
0
3
1
2
0
0
0
0
0
2
0
0
2
1
2
2
0
2
0
0
0
1
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
2
1
0
0
0
0
1
2
1
0
1
0
0
0
0
0
1
3
1
2
0
0
0
0
2
0
0
0
1
0
0
4
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
2
0
2
1
1
0
0
1
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
2
0
2
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
1
1
1
0
0
0
0
2
0
0
0
0
2
2
0
1
0
0
1
6
0
2
4
2
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
3
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
4
0
0
0
0
7
1
0
0
2
0
2
0
2
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
2
0
0
0
0
2
0
2
2
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
2
0
0
0
3
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
1
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
1
0
1
2
1
2
0
0
0
0
3
2
0
0
1
0
1
0
3
1
0
2
1
0
1
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
1
0
1
2
0
0
0
1
0
1
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
1
0
0
0
0
0
3
3
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
2
2
0
0
0
2
0
1
0
0
2
0
0
0
0
2
0
0
1
0
1
1
2
0
3
0
0
0
0
2
0
0
0
0
0
2
0
2
2
0
1
1
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
3
0
0
0
2
1
0
0
0
1
2
0
1
0
0
0
0
0
1
1
0
0
0
2
2
0
0
2
0
1
0
1
2
0
1
2
0
1
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
1
2
0
2
2
1
0
0
1
1
0
0
0
2
1
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
3
1
2
2
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
2
0
0
1
0
1
0
0
0
0
2
0
0
2
0
0
1
0
2
0
1
0
0
3
2
1
0
2
0
0
0
0
0
0
0
3
0
0
0
1
1
0
0
0
0
2
2
0
1
0
2
2
0
0
1
0
0
2
0
2
0
1
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
1
2
0
0
2
0
0
0
1
0
0
2
0
0
2
0
2
0
0
0
0
6
0
0
0
0
0
3
0
0
1
0
2
0
1
1
0
1
0
2
2
0
2
0
0
0
0
1
0
2
1
2
3
2
1
0
0
0
0
0
2
0
2
3
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
1
0
0
2
1
2
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
5
0
0
0
0
0
2
2
0
1
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
1
0
2
0
0
2
0
0
0
2
0
0
1
0
0
0
2
0
0
0
2
0
0
1
0
2
0
1
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
5
1
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
2
0
0
1
0
0
1
2
0
1
2
0
0
1
0
0
0
0
0
2
1
1
1
0
0
0
0
2
3
2
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
2
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
1
0
2
0
0
1
0
0
2
0
0
0
0
0
2
0
0
1
2
0
1
2
0
0
0
0
0
0
0
0
2
0
2
0
2
1
2
4
1
2
0
2
0
1
0
0
0
2
2
0
0
0
0
0
3
0
1
0
0
0
2
1
0
0
1
0
0
0
2
1
0
2
0
0
1
0
1
0
1
0
0
2
0
0
1
2
0
0
0
2
0
2
0
0
0
1
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
1
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
2
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
3
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
2
2
1
0
0
0
0
2
1
0
1
0
3
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
2
0
0
1
0
0
0
1
0
1
0
1
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
2
0
1
0
0
0
0
0
3
0
0
0
0
0
0
1
3
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
2
1
0
0
0
0
2
0
0
0
2
0
0
0
2
0
2
0
2
0
0
0
3
2
0
0
1
0
0
0
1
0
1
2
2
0
1
0
0
0
0
2
1
0
0
0
0
2
2
0
4
0
0
0
0
0
0
0
5
0
1
2
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
1
0
2
0
0
1
0
1
0
0
0
0
0
1
0
1
1
0
0
0
1
1
2
1
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
2
0
0
2
0
0
1
4
0
0
1
0
2
0
1
0
0
0
1
0
3
0
1
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
2
1
1
0
2
0
2
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
5
2
3
0
1
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
2
4
2
0
0
0
2
0
0
0
0
1
3
0
0
0
0
1
2
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
1
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
1
0
0
2
1
2
2
2
0
0
0
0
0
0
5
1
0
2
0
0
0
0
1
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
1
2
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
2
0
0
0
0
2
0
4
3
1
0
0
0
1
0
2
0
0
0
1
0
0
0
1
0
0
1
5
0
0
0
0
2
1
0
0
0
1
2
1
2
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
2
0
2
0
1
0
0
0
1
0
1
0
0
0
1
0
0
2
0
2
2
0
1
0
0
0
2
1
1
0
0
2
0
0
0
1
2
0
0
0
0
2
0
0
0
2
0
0
0
1
2
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
4
1
1
0
1
0
1
0
0
0
1
1
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
1
0
1
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
1
0
0
0
1
0
4
2
3
0
2
0
0
0
0
0
2
0
2
1
0
2
0
0
0
2
0
0
0
0
0
5
2
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
1
1
1
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
2
0
2
0
0
2
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
2
2
0
1
0
0
2
0
0
0
1
0
0
0
0
1
1
2
0
0
2
1
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
2
0
0
1
0
1
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
4
1
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
2
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
2
0
3
0
0
12
0
0
2
0
2
1
0
0
1
2
0
0
0
0
0
5
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
3
2
0
2
0
1
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
1
0
2
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
2
0
5
0
0
2
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
2
0
1
0
1
1
3
0
0
0
3
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
2
0
0
0
0
2
2
2
2
1
0
0
2
0
0
2
0
1
0
0
1
0
0
0
2
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
2
0
1
1
0
3
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
3
0
0
1
1
0
1
0
2
1
0
0
1
2
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
2
0
0
1
0
2
0
0
0
0
2
0
1
0
2
2
0
2
0
0
0
0
0
0
2
2
2
1
0
0
0
2
0
1
0
1
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
1
0
2
2
2
3
2
1
1
1
0
0
2
0
0
1
0
4
0
0
5
2
2
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
3
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
2
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
1
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
2
0
0
2
1
0
0
0
0
2
4
0
1
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
2
0
0
2
0
2
0
1
0
0
3
1
0
0
0
1
0
0
0
0
0
5
2
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
3
0
2
0
0
0
0
2
0
0
1
0
2
0
2
2
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
2
0
0
1
0
1
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
3
2
2
1
0
0
3
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
2
2
0
0
2
2
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
2
2
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
2
2
0
7
0
0
0
1
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
1
0
0
0
2
0
2
0
0
0
1
0
1
2
0
1
2
0
1
0
0
2
0
0
0
0
0
0
0
3
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
1
1
0
1
0
0
0
0
0
4
1
0
0
0
0
0
2
1
0
0
0
0
2
2
0
1
2
2
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
1
1
0
2
0
2
0
0
0
0
0
1
1
1
2
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
2
0
2
2
0
1
0
0
0
0
1
0
0
0
0
0
2
0
2
1
0
0
2
0
0
0
0
1
0
0
0
2
2
0
2
0
2
3
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
2
2
0
0
0
2
2
2
0
2
0
0
3
0
1
0
0
0
1
1
0
0
0
0
1
0
2
0
2
0
0
0
1
0
0
2
0
0
3
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
3
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
1
2
0
0
0
0
2
0
1
0
1
2
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
2
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
2
2
1
1
0
2
0
2
3
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
1
0
1
1
0
2
0
1
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
5
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
1
0
0
1
1
0
1
1
0
1
2
0
0
1
0
0
0
0
0
0
2
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
1
0
1
0
2
2
0
1
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
4
0
1
0
0
0
0
0
0
0
6
0
0
0
2
0
2
0
0
2
0
2
1
1
0
2
1
0
0
0
1
0
0
0
0
2
0
0
1
1
0
2
2
0
2
0
0
0
0
2
0
0
3
0
0
0
2
1
17
0
0
0
0
0
0
0
0
5
0
0
0
1
1
0
0
0
0
2
2
2
0
0
0
1
0
0
1
3
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
2
0
4
1
0
0
0
0
1
1
1
1
0
0
0
0
0
0
2
0
0
1
0
3
0
1
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
1
0
0
0
1
0
5
0
2
0
0
0
0
1
0
0
2
0
0
0
1
0
1
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
2
0
0
1
0
0
1
0
0
0
0
0
2
0
1
0
1
5
5
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
2
1
1
0
2
0
0
0
0
0
1
0
0
0
1
0
0
12
0
1
0
0
0
1
0
0
0
0
2
0
0
1
0
2
0
0
2
2
2
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
2
0
2
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
1
0
0
0
1
2
0
1
0
0
2
3
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
6
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
3
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
2
0
1
0
0
3
0
0
0
0
2
0
0
0
0
0
1
0
1
1
1
0
2
2
0
0
2
0
0
0
0
2
0
0
1
0
0
2
0
1
3
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
2
0
0
2
2
0
0
1
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
2
1
0
2
0
2
1
3
0
1
2
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
5
0
1
4
0
0
1
0
0
0
2
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
2
1
2
0
2
0
2
2
2
0
3
2
0
0
0
2
0
2
0
0
0
2
0
0
2
0
0
0
0
0
6
0
2
0
0
0
0
3
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
2
0
0
0
0
0
2
2
1
0
2
1
0
1
1
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
2
2
0
0
2
4
0
0
2
0
2
0
0
0
0
1
0
0
1
2
0
0
1
1
1
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
1
1
1
0
2
4
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
3
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
3
0
0
1
1
1
0
0
0
0
2
0
0
2
0
0
0
1
2
0
1
0
1
0
0
0
3
0
1
0
0
0
0
0
0
0
1
2
0
0
2
0
0
2
0
1
1
1
0
0
0
0
0
2
0
0
0
2
0
2
2
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
1
0
3
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
2
0
0
1
0
0
0
0
0
2
1
0
0
1
0
2
3
0
3
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
1
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
2
0
0
0
2
1
1
2
0
0
0
0
1
0
1
0
0
0
1
2
0
0
2
1
1
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
2
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
1
1
1
2
0
2
0
0
0
0
0
3
1
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
1
1
1
0
1
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
1
1
3
0
0
2
0
0
2
0
0
0
2
0
0
0
2
0
1
1
0
0
0
0
0
0
0
2
0
1
0
0
1
1
0
1
0
0
0
0
2
0
0
0
2
0
0
2
1
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
4
0
0
1
0
3
2
0
0
2
0
0
3
2
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
2
2
0
1
0
2
1
0
2
0
0
0
1
0
1
1
0
0
0
0
1
0
1
0
0
0
0
2
1
0
3
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
1
1
0
0
6
0
0
2
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
3
1
1
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
2
0
4
0
0
2
0
0
1
0
2
0
0
1
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
2
2
0
0
0
0
1
1
1
0
0
0
0
1
4
0
0
0
2
0
0
4
0
0
0
1
0
2
0
1
0
2
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
1
0
0
1
2
0
2
0
0
1
0
1
2
0
0
0
1
0
0
1
0
0
2
0
0
2
2
0
0
0
2
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
11
0
0
0
0
1
0
0
0
0
3
0
2
0
0
0
2
0
0
1
0
0
2
1
1
2
0
1
0
0
0
2
0
0
0
2
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
2
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
2
2
2
0
1
0
2
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
2
1
2
2
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
1
0
1
0
0
0
0
0
0
1
2
2
2
2
0
0
1
0
0
2
0
0
2
2
0
0
0
0
0
6
1
0
0
0
2
1
0
0
1
0
1
2
0
0
0
2
0
0
0
0
0
1
3
1
0
0
2
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
1
2
2
1
1
3
0
0
0
0
0
2
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
1
0
1
0
2
0
1
0
1
0
0
0
0
2
0
2
0
1
0
0
1
0
0
4
0
1
0
0
0
0
0
2
0
0
0
2
0
3
2
0
0
0
0
0
2
0
2
0
0
2
0
2
0
1
0
2
0
2
2
0
0
0
0
2
0
0
1
0
2
0
0
0
0
1
2
0
0
1
0
2
1
0
0
0
0
1
2
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
7
0
1
1
0
1
1
0
0
1
0
1
0
1
1
2
0
0
2
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
1
3
0
1
0
2
1
0
1
0
0
1
2
2
0
0
1
0
0
2
2
0
0
0
0
0
3
0
0
2
0
0
0
0
2
0
0
0
3
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
2
1
1
0
0
2
0
0
6
0
0
1
0
1
0
0
0
2
1
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
2
0
2
0
0
1
0
1
0
0
1
1
0
1
0
1
0
0
1
0
0
0
1
0
2
0
0
2
0
0
0
0
1
0
0
0
2
2
1
0
5
0
0
0
2
0
0
2
2
1
0
0
2
0
0
0
1
0
0
0
0
0
2
4
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
14
1
0
1
1
2
3
1
0
0
1
0
1
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
2
3
0
0
1
1
0
0
1
2
0
1
0
0
0
0
3
1
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
2
0
0
2
0
0
1
0
1
0
0
0
1
0
0
0
1
0
3
2
4
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
1
0
0
3
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
2
0
0
1
0
0
1
0
3
0
0
1
0
0
1
0
0
0
0
0
3
0
3
0
2
1
0
0
0
0
2
2
0
0
1
0
2
0
2
0
1
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
7
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
2
3
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
2
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
2
1
1
2
2
3
0
0
0
1
3
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
1
0
3
0
1
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
1
0
2
0
2
1
0
0
0
0
0
0
2
2
0
1
0
0
0
2
0
0
0
0
1
0
0
2
1
0
0
0
2
2
0
1
0
2
0
0
2
0
2
0
0
0
2
0
2
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
2
2
0
1
0
0
0
0
1
0
1
2
2
0
0
0
0
2
0
2
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
2
1
0
0
4
0
0
0
0
0
1
0
0
0
1
2
0
3
0
0
0
2
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
2
2
0
0
0
0
0
0
0
0
1
4
0
2
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
5
0
0
0
0
2
0
2
0
0
0
0
1
2
1
1
0
0
0
2
0
2
1
0
0
1
0
0
0
0
1
0
0
0
2
0
0
2
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
1
0
0
2
5
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
1
0
0
2
0
0
0
2
0
0
2
2
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
1
0
0
0
1
1
2
1
0
1
0
2
0
2
1
0
0
0
2
0
0
1
0
0
1
1
0
2
0
1
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
2
0
5
0
0
1
0
0
0
1
1
1
0
2
0
0
1
0
0
0
2
0
2
0
3
0
0
4
0
0
0
1
2
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
3
0
0
4
2
0
0
0
0
0
0
1
2
0
0
1
0
0
1
0
0
1
2
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
2
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
2
0
0
0
2
0
0
0
1
0
0
0
1
1
2
1
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
2
0
2
0
1
0
0
2
0
2
0
0
0
0
0
0
1
1
0
0
0
2
2
1
2
9
0
0
1
2
0
0
0
2
3
0
0
0
0
0
0
0
1
1
0
0
0
1
2
1
1
2
1
2
0
0
1
0
0
1
0
2
0
0
0
1
0
0
0
0
0
3
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
2
2
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
1
1
1
0
0
0
1
3
1
0
1
3
0
0
1
0
0
1
1
0
0
0
1
0
1
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
3
1
1
0
0
0
0
3
0
1
1
0
1
0
0
0
0
1
2
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
2
1
1
0
0
1
0
0
2
2
0
0
0
2
3
0
1
1
2
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
2
0
2
3
4
0
0
2
0
0
2
0
0
1
2
1
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
2
0
0
0
0
2
0
0
2
0
1
0
0
1
0
2
0
2
0
0
0
0
0
0
2
0
0
6
0
0
0
0
2
0
0
0
1
0
0
2
1
0
0
1
1
0
0
0
2
0
0
1
0
2
0
0
2
0
0
0
2
2
0
0
1
0
0
0
1
0
0
1
1
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
32
2
0
2
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
3
2
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
2
2
0
0
1
0
0
0
0
0
0
0
4
2
0
1
0
0
2
0
0
0
0
1
1
1
0
1
2
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
1
0
0
0
2
0
2
1
1
1
0
2
1
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
1
1
2
0
0
0
0
1
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
2
0
1
2
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
3
0
0
2
2
1
0
0
3
1
2
0
0
2
0
0
0
1
0
1
0
0
0
1
2
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
2
0
2
2
2
0
0
0
0
0
0
2
0
0
0
3
1
2
2
0
2
0
0
0
0
0
0
0
0
2
0
2
2
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
4
0
0
1
1
0
0
0
1
1
1
0
0
0
0
1
0
1
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
3
2
1
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
3
0
0
0
2
0
0
2
0
0
0
0
0
3
0
0
0
1
0
1
0
1
0
2
0
2
0
0
2
0
1
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
3
0
1
0
0
2
0
0
1
0
0
0
2
0
0
1
0
2
0
0
1
0
0
0
0
0
0
4
2
0
0
1
0
2
0
2
0
0
2
0
0
0
1
0
0
1
2
0
0
1
0
2
0
0
0
1
1
0
1
1
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
2
4
2
2
0
0
0
0
0
4
0
0
0
0
0
0
2
1
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
2
0
2
0
2
0
0
2
1
0
0
0
0
0
1
1
0
0
0
0
0
0
2
1
0
0
0
0
0
1
3
0
1
0
0
0
2
2
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
2
0
2
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
2
2
0
1
0
1
0
0
1
1
1
1
0
2
1
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
2
1
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
1
0
0
9
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
3
5
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
2
1
2
1
0
0
2
0
3
0
0
2
3
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
2
1
0
2
0
2
0
2
0
0
0
0
0
0
3
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
1
2
0
0
1
0
0
1
0
2
1
0
3
0
0
0
2
2
2
0
0
2
1
0
0
0
0
0
2
2
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
2
2
1
0
0
0
2
2
1
0
1
0
0
2
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
2
2
0
0
0
2
1
0
0
0
0
1
0
2
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
2
2
0
0
0
0
1
0
1
2
0
1
0
0
0
3
0
0
0
0
2
2
2
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
2
0
0
2
0
1
0
2
0
0
2
3
0
0
0
0
1
0
3
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
1
0
0
0
2
2
0
2
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
2
0
1
0
0
0
2
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
1
1
1
0
0
1
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
2
2
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
1
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
1
3
0
2
0
1
0
0
0
0
0
0
0
2
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
4
0
0
0
1
0
0
1
0
1
4
0
2
0
2
0
0
0
0
2
2
0
0
0
1
1
0
2
0
2
0
0
0
1
1
2
1
2
2
0
1
0
2
0
0
2
0
5
0
0
0
0
2
0
0
0
2
0
1
1
0
0
0
0
0
2
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
3
0
0
1
0
0
0
0
0
0
2
0
2
0
3
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
1
4
0
1
0
0
0
0
2
0
2
1
0
1
1
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
2
2
0
1
1
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
2
0
0
1
0
0
0
1
0
0
1
0
1
0
2
0
1
0
1
1
2
0
2
0
0
0
0
2
0
2
2
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
5
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
2
1
0
0
2
0
0
0
0
0
1
0
2
2
2
1
0
2
0
0
2
0
0
1
0
0
3
1
0
0
1
1
0
1
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
1
0
1
0
3
0
0
1
0
1
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
2
2
1
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
5
0
2
1
0
0
2
2
2
0
0
0
0
0
1
2
0
1
0
2
1
0
1
0
1
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
1
1
0
2
0
0
0
1
0
2
1
0
0
0
0
1
0
2
0
0
0
0
1
0
0
2
0
1
2
1
0
2
2
1
0
2
0
1
0
2
1
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
5
0
1
0
0
4
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
4
0
0
0
0
0
0
1
0
2
2
1
1
0
0
1
0
0
2
1
0
1
0
3
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
2
0
0
1
0
2
0
0
2
0
0
2
7
0
0
0
0
2
0
0
0
2
1
0
1
2
0
0
0
1
0
0
0
2
1
0
2
0
2
0
0
0
0
0
1
1
1
0
0
3
3
0
2
2
0
0
0
2
0
0
2
1
1
0
0
0
0
1
0
1
0
1
0
0
2
0
2
0
0
1
1
4
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
1
0
2
2
0
1
0
1
0
1
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
2
0
1
0
0
2
0
1
0
0
0
0
0
0
1
0
2
0
2
0
0
2
2
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
2
0
0
2
0
0
1
2
0
0
3
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
1
0
1
0
1
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
2
6
0
0
1
2
0
0
0
0
0
0
0
0
0
2
2
0
2
0
2
2
0
0
2
2
0
0
2
0
0
2
0
0
0
1
1
0
0
0
2
2
0
1
0
2
0
0
0
0
0
0
2
1
0
0
0
1
0
0
2
1
1
2
0
0
2
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
1
0
1
0
1
0
0
1
2
2
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
2
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
1
2
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
1
0
1
0
1
0
0
3
0
0
0
0
1
0
2
0
1
0
2
2
0
0
0
1
2
0
0
0
2
0
1
0
0
0
1
1
0
0
0
0
0
1
0
2
0
0
0
2
2
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
1
0
0
2
0
2
4
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
1
2
1
0
0
0
0
0
1
2
0
0
0
1
1
0
0
0
2
1
0
0
1
0
0
1
1
1
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
2
1
0
0
2
0
0
1
2
0
0
0
0
0
0
0
2
0
0
1
3
0
0
0
3
0
1
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
2
4
0
0
0
3
0
1
0
0
0
0
0
3
0
0
0
1
1
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
2
0
0
6
0
2
0
0
0
0
2
1
0
2
0
2
0
0
0
0
0
1
0
0
1
0
2
0
0
3
0
0
2
0
0
0
0
0
1
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
2
1
0
1
0
0
0
1
0
2
0
3
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
2
0
0
2
2
1
0
0
0
1
2
0
0
0
1
0
0
2
1
0
0
1
0
1
0
0
0
0
2
0
3
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
1
0
1
1
1
0
3
1
0
0
0
2
0
3
0
0
0
0
2
0
2
2
0
0
0
0
2
1
0
0
2
0
0
1
2
0
0
1
2
1
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
1
2
0
0
1
0
1
0
0
0
0
0
2
0
3
3
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
2
0
0
1
2
1
0
0
0
3
0
0
0
1
0
0
0
0
1
1
0
0
2
0
0
0
0
2
0
0
0
0
2
1
1
2
0
2
0
0
0
2
0
0
0
2
2
1
0
2
0
0
2
0
0
1
2
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
1
2
2
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
1
0
1
3
0
0
1
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
2
2
0
1
0
0
2
0
0
1
0
0
4
0
0
0
0
0
0
0
1
0
2
0
1
0
1
0
0
4
0
0
1
0
0
1
0
0
2
2
2
2
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
1
0
2
0
1
0
0
0
1
1
2
0
2
0
0
0
0
1
2
0
0
1
5
2
0
0
0
0
0
0
3
0
0
0
2
0
0
0
3
0
3
0
0
0
1
2
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
5
0
3
0
1
0
1
0
3
0
1
0
0
1
0
1
0
0
3
0
1
0
0
1
2
0
1
3
0
0
0
0
0
0
2
0
0
2
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
1
2
1
1
0
0
0
0
0
0
0
1
0
0
2
0
1
0
1
0
0
2
0
0
0
2
0
0
1
2
0
1
2
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
3
0
1
1
0
1
2
1
0
0
0
0
2
0
0
0
0
0
0
3
0
5
0
0
2
0
1
0
0
0
3
0
0
1
1
0
0
0
0
0
1
1
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
2
2
0
0
2
1
0
0
0
0
3
0
0
0
0
1
0
2
2
0
2
1
1
0
0
1
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
1
2
0
0
1
0
2
1
0
2
0
1
2
0
1
0
0
0
2
0
2
0
0
2
0
0
0
0
2
0
4
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
1
2
0
0
0
0
0
0
2
2
0
0
1
0
1
0
0
1
2
0
0
0
2
0
0
0
0
0
0
2
0
1
0
1
5
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
3
0
0
0
1
0
1
0
0
0
0
0
1
2
0
1
0
0
5
0
4
0
0
2
0
0
0
0
0
0
3
1
0
0
1
0
2
0
2
2
1
1
0
0
0
0
0
1
1
0
2
1
1
0
0
0
2
0
0
1
3
0
0
0
0
2
2
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
1
0
1
1
0
0
1
2
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
1
0
1
1
0
0
0
0
0
3
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
1
0
0
1
2
1
0
0
0
1
0
0
0
2
3
0
0
2
2
0
0
1
0
2
0
0
0
0
0
3
0
1
0
0
0
0
2
1
0
0
2
0
0
0
2
0
0
0
2
0
0
0
2
3
0
2
2
2
0
0
0
0
0
2
0
4
2
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
2
0
2
0
1
1
0
4
0
0
0
0
1
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
2
0
0
0
0
0
0
0
1
0
3
0
2
0
0
0
0
1
0
2
0
0
2
1
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
2
2
4
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
2
0
0
1
0
3
0
0
1
3
0
0
0
0
0
0
0
0
3
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
2
0
2
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
1
0
0
0
0
0
0
1
2
0
1
0
4
0
0
0
0
0
3
0
1
3
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
2
0
1
0
1
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
2
1
0
0
1
2
0
1
1
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
1
2
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
1
1
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
2
0
2
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
1
2
2
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
2
0
2
0
0
1
0
2
1
0
1
0
0
0
0
2
1
0
0
0
2
3
0
0
0
5
2
0
0
0
0
1
0
0
2
0
0
2
0
0
0
2
0
2
3
1
3
0
0
0
0
5
0
0
0
0
0
6
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
2
1
1
0
2
0
2
2
0
4
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
1
0
1
1
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
2
0
2
0
0
1
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
3
2
1
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
1
1
2
0
0
1
0
1
1
0
3
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
1
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
3
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
2
4
0
0
0
0
1
0
0
0
0
1
2
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
2
0
0
1
2
0
0
1
0
0
0
1
2
0
1
0
2
0
2
2
0
0
1
0
0
7
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
1
0
1
1
3
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
2
2
2
0
0
1
0
0
2
1
0
0
1
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
2
0
0
0
1
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
2
0
3
0
0
0
0
0
2
0
0
3
1
2
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
1
0
0
0
2
0
2
1
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
1
1
0
2
0
0
0
0
0
0
1
2
0
0
0
2
0
1
0
0
0
2
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
4
2
0
0
0
3
1
3
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
1
2
0
0
0
0
2
0
0
2
0
0
0
3
0
2
2
2
1
0
0
0
0
0
0
0
2
2
0
2
1
1
2
2
1
1
0
2
2
1
0
2
0
0
2
0
0
2
2
0
2
0
0
2
1
0
0
0
0
0
1
0
0
0
2
0
0
1
0
2
0
0
0
0
0
1
1
0
0
0
0
1
1
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
1
0
1
0
0
2
0
0
2
5
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
3
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
1
1
0
0
3
0
0
2
1
1
0
1
0
0
0
0
0
1
2
0
0
0
1
0
1
0
0
0
0
0
0
2
2
0
2
2
2
2
0
0
0
0
0
0
4
1
0
0
3
0
0
0
0
0
0
1
0
1
0
0
0
0
3
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
1
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
2
1
0
0
2
0
0
0
0
0
0
2
2
0
2
0
2
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
1
0
1
2
0
1
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
2
2
0
0
0
2
0
2
0
2
0
0
1
0
1
0
0
2
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
1
0
2
0
2
0
4
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
1
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
3
0
0
2
0
0
2
0
0
0
1
2
0
1
0
1
0
1
0
2
1
0
0
1
0
0
2
0
2
1
0
0
0
2
1
0
0
2
1
0
0
2
0
0
2
0
0
0
1
0
0
0
0
2
2
0
0
1
0
0
0
0
1
1
0
0
3
0
0
0
3
0
0
1
0
0
2
0
0
1
0
0
1
0
1
0
0
0
0
0
2
2
0
2
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
2
1
0
0
2
0
0
1
0
0
0
2
4
2
0
0
0
1
2
0
0
1
0
2
0
0
2
0
0
0
0
2
0
2
0
0
1
0
0
1
0
0
0
0
0
2
2
1
0
0
0
2
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
2
0
0
0
0
2
0
1
1
2
0
0
0
5
0
0
0
2
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
3
1
1
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
1
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
2
1
0
0
0
0
1
4
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
1
1
2
0
0
0
0
1
0
2
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
2
0
0
1
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
1
0
3
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
1
2
0
0
0
0
0
2
1
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
2
0
3
0
0
0
0
0
3
0
0
0
1
0
1
2
0
0
0
2
0
1
1
0
2
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
1
2
0
0
1
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
2
0
2
2
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
1
1
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
2
2
0
0
0
0
1
0
1
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
1
1
0
0
0
0
1
1
0
2
2
1
3
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
4
1
5
0
2
2
0
0
1
1
1
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
2
2
2
2
1
1
0
0
0
0
0
2
1
0
0
1
0
1
0
0
0
0
1
0
1
2
1
0
0
1
0
2
0
1
0
2
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
1
0
1
2
0
0
1
0
0
1
1
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
2
3
0
1
0
0
0
2
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
3
0
0
0
0
0
0
0
1
1
0
0
0
0
2
1
1
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
1
0
1
1
1
0
2
2
1
0
1
0
1
0
0
0
1
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
2
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
1
2
0
2
1
0
0
0
0
2
0
3
0
1
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
2
3
2
0
2
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
2
1
0
6
0
0
2
0
0
2
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
3
0
0
1
2
0
2
2
0
0
1
2
0
2
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
1
0
0
0
0
0
2
1
2
0
1
2
2
0
2
0
5
1
0
1
2
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
2
0
2
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
1
2
0
2
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
2
1
0
1
0
0
2
0
1
2
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
3
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
2
2
0
1
4
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
4
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
2
1
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
3
0
2
0
3
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
3
1
0
2
0
0
0
1
1
1
1
0
1
1
0
1
0
1
2
0
0
0
2
0
2
2
0
0
0
1
0
0
0
0
2
1
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
1
2
0
1
0
2
0
0
0
0
1
0
2
0
2
0
0
1
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
1
1
2
0
0
0
0
0
0
3
0
2
1
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
3
1
0
2
2
0
0
0
0
2
0
0
0
0
0
0
1
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
1
0
0
1
0
0
0
1
0
2
2
1
0
0
0
0
0
2
2
0
0
1
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
1
2
0
2
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
2
2
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
1
2
2
2
2
0
0
0
1
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
2
2
2
0
2
0
0
1
3
0
2
0
1
0
0
0
1
0
1
0
1
3
0
0
0
1
0
0
0
2
2
0
0
0
2
0
0
2
1
0
0
0
1
2
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
2
0
0
2
0
0
0
2
0
0
0
0
0
1
0
2
0
0
2
0
0
0
1
1
2
0
2
0
0
0
1
4
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
2
0
0
0
2
2
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
2
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
7
0
0
1
0
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
1
5
0
0
1
0
1
0
0
1
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
1
0
0
0
0
0
0
0
1
4
0
0
2
0
0
0
0
2
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
1
1
2
3
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
4
2
0
1
0
2
0
2
0
1
0
2
0
0
0
3
0
0
0
0
2
0
1
0
0
0
0
2
2
1
0
2
0
0
0
0
2
0
0
2
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
2
1
0
2
0
0
0
0
0
0
0
0
2
3
0
2
0
2
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
2
1
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
1
2
2
1
2
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
2
0
2
1
0
1
1
0
0
0
0
0
0
0
2
1
2
0
0
2
0
0
2
1
0
2
1
0
0
2
0
1
0
0
0
0
2
1
1
0
0
0
1
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
1
1
0
0
0
2
1
0
2
1
0
0
0
2
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
2
1
0
0
0
0
3
2
0
0
1
0
0
0
1
0
1
0
0
4
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
1
1
0
2
0
0
0
1
0
6
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
2
0
2
1
2
1
2
1
0
0
0
3
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
1
1
2
0
0
0
0
2
0
0
0
2
0
2
0
0
2
0
0
2
3
0
2
1
0
2
0
0
0
4
0
0
0
0
2
0
0
0
0
1
0
0
0
1
1
1
0
0
2
0
0
0
0
2
0
0
0
0
6
0
2
1
0
1
0
3
0
0
0
1
1
0
0
0
0
0
4
0
0
1
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
2
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
2
0
2
0
1
0
2
1
0
0
0
0
0
2
0
0
0
2
0
2
0
0
1
0
0
0
2
0
2
1
0
0
0
3
2
0
1
0
1
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
1
0
0
0
2
0
0
2
0
6
0
2
1
1
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
5
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
2
0
0
0
0
3
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
2
3
0
0
0
0
1
2
0
0
0
0
2
0
0
1
0
2
0
1
0
1
0
0
0
0
1
0
1
0
0
3
3
0
0
3
0
2
0
0
0
1
0
2
0
0
1
1
0
1
3
0
1
0
0
1
1
0
1
3
0
0
1
0
0
0
0
0
0
0
0
1
1
0
2
1
0
4
0
0
2
2
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
2
0
1
2
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
2
0
0
0
1
0
0
0
3
0
0
0
0
1
0
0
0
1
0
0
0
1
0
2
0
0
0
0
2
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
2
1
0
0
0
4
1
0
0
0
1
0
2
0
0
0
1
2
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
6
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
2
0
0
1
0
0
0
0
0
1
0
3
0
0
0
3
0
1
2
0
1
2
1
2
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
1
1
0
2
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
3
0
0
2
0
3
0
0
1
3
0
2
1
0
0
0
0
0
0
3
1
2
2
2
0
1
1
1
0
0
0
1
0
2
1
2
0
0
0
2
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
3
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
1
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
3
0
1
2
0
0
0
1
2
2
0
0
0
1
1
2
0
4
0
1
0
0
1
2
2
0
2
2
3
0
0
2
0
2
0
0
2
0
0
0
0
0
1
0
5
2
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
2
0
1
0
1
0
1
0
0
1
0
0
0
0
0
2
4
5
0
0
0
0
0
0
0
3
1
0
2
0
0
1
1
2
0
0
0
2
1
1
2
0
0
0
0
2
0
3
0
0
2
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
3
2
0
2
1
1
0
0
4
1
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
1
0
0
0
2
0
1
2
2
2
2
0
2
0
0
2
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
2
1
0
0
1
0
0
1
0
0
2
1
0
1
0
0
0
0
2
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
1
2
1
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
1
4
0
0
2
0
2
3
0
0
0
6
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
1
0
0
0
1
0
1
0
0
1
0
2
0
0
0
0
2
0
1
0
0
0
0
0
2
1
0
0
0
2
2
0
0
0
1
1
1
0
1
1
0
2
3
1
1
0
2
0
1
0
0
2
1
3
0
1
0
1
1
0
0
1
1
0
0
0
1
2
0
1
0
8
0
0
1
0
0
2
1
0
0
1
1
2
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
2
1
0
1
1
0
1
2
0
0
0
0
2
0
1
0
2
0
0
2
2
0
0
0
0
1
2
2
0
0
1
0
2
0
0
0
0
1
2
0
0
1
1
0
1
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
2
0
0
2
2
0
0
2
1
0
2
0
0
1
0
0
0
0
0
0
0
2
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
2
2
2
0
0
1
0
1
0
0
0
0
0
0
5
1
0
0
0
0
0
0
0
0
0
2
1
0
1
1
0
2
2
0
0
2
1
0
2
1
0
0
0
0
2
1
0
2
2
0
0
2
0
2
0
0
0
2
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
3
2
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
2
2
1
0
1
2
0
0
2
0
0
0
2
1
0
1
0
6
1
2
0
0
0
0
0
0
2
1
1
1
1
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
2
0
0
2
0
0
2
0
0
0
2
1
0
2
0
0
0
0
0
0
2
1
0
2
1
0
0
1
0
0
2
0
0
0
1
0
1
1
2
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
2
1
1
1
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
4
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
2
1
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
3
0
2
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
1
2
0
0
0
3
0
0
0
2
0
0
0
3
1
0
2
0
0
0
0
1
0
2
1
0
0
0
0
0
0
3
1
0
0
0
0
0
2
0
2
2
0
0
0
1
3
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
3
0
0
0
0
1
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
2
0
0
0
1
1
0
4
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
1
2
0
0
2
3
0
0
0
0
0
0
2
1
0
0
2
3
0
2
0
0
0
1
0
1
0
2
0
0
0
0
0
3
0
0
0
0
1
1
1
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
3
0
0
0
0
1
2
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
1
1
0
0
0
0
2
0
0
1
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
1
2
0
0
4
1
0
0
0
1
0
0
0
0
2
0
1
0
0
1
0
0
5
0
0
1
0
0
0
0
0
0
1
0
3
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
1
2
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
1
0
2
2
0
0
0
0
2
0
0
0
2
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
1
1
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
1
0
1
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
3
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
2
0
2
0
0
2
0
0
3
2
0
1
1
3
0
0
2
0
0
1
2
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
5
0
1
0
2
0
0
0
2
1
0
2
0
2
1
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
3
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
3
0
0
0
0
2
3
0
0
0
0
2
0
0
2
0
0
5
0
0
0
0
2
2
1
0
0
0
3
0
0
0
2
0
0
0
0
2
0
2
0
2
0
0
0
0
0
1
2
0
1
0
0
0
2
0
2
0
2
0
0
0
1
2
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
4
2
2
0
0
0
2
0
2
0
0
3
0
2
0
0
0
0
6
0
0
2
0
0
0
1
0
0
3
0
1
1
1
0
1
1
1
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
2
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
1
0
0
0
1
3
0
0
0
0
0
0
2
0
3
0
0
1
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
3
4
0
0
0
0
0
0
0
0
1
1
2
0
0
0
2
0
2
0
0
1
0
3
0
0
0
1
2
1
0
0
0
2
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
3
0
2
0
0
0
0
2
1
0
2
0
3
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
1
1
0
1
0
2
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
1
0
0
3
0
0
0
0
2
2
0
0
2
1
0
1
0
0
0
2
0
0
2
0
0
0
2
0
0
0
2
0
0
1
2
1
0
1
1
0
0
0
2
2
0
0
2
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
1
2
0
0
0
2
0
1
0
0
1
0
0
0
0
0
2
0
0
2
0
0
2
0
0
2
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
3
0
0
6
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
3
1
0
0
0
0
1
0
0
2
0
0
0
0
2
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
1
1
0
0
2
0
0
0
2
0
0
1
0
1
0
0
1
0
0
1
0
0
0
1
2
0
0
2
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
3
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
2
2
2
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
2
1
2
7
0
0
1
0
2
0
0
0
0
2
0
0
0
1
1
1
0
2
0
0
0
0
1
0
2
0
1
2
0
0
0
0
1
0
2
0
0
0
0
0
1
0
1
0
0
2
0
2
0
0
2
1
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
1
0
1
0
0
0
0
3
0
2
0
2
2
1
1
0
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
1
2
0
0
0
1
1
0
0
0
0
0
2
2
0
0
1
0
1
0
0
0
2
0
0
1
0
0
2
1
1
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
2
0
1
1
0
0
0
0
0
0
2
2
0
0
0
0
1
0
2
1
0
0
0
1
0
0
0
0
1
1
1
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
3
1
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
1
0
0
0
2
0
0
0
0
3
0
2
0
3
0
0
0
2
0
0
0
0
2
1
2
1
0
0
0
0
5
0
0
1
1
1
0
0
0
0
1
2
0
0
0
0
0
0
0
2
1
1
0
2
0
0
0
2
1
0
1
0
1
1
0
0
1
0
2
2
1
0
0
0
0
2
1
2
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
1
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
3
1
0
1
1
0
1
2
0
0
1
0
0
2
2
2
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
1
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
1
0
0
2
2
0
2
2
0
0
1
0
2
0
0
1
2
0
0
0
0
0
1
2
1
0
1
0
0
0
2
2
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
1
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
3
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
1
2
0
0
0
3
0
0
1
0
2
2
0
0
0
0
2
2
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
2
2
0
0
1
1
1
6
1
0
2
0
0
0
0
2
2
1
0
0
0
0
0
0
1
2
0
0
0
1
0
2
0
3
1
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
2
0
2
0
2
1
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
2
0
2
0
0
1
0
0
0
0
1
1
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
2
0
0
2
1
2
2
0
2
0
1
0
0
2
2
0
0
0
0
3
0
1
0
2
0
2
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
2
0
0
2
0
2
1
0
0
0
2
2
0
0
1
0
0
0
0
2
5
0
0
0
2
0
1
0
0
3
3
1
0
1
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
3
1
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
1
0
2
1
0
1
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
2
1
2
0
2
0
0
2
2
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
2
0
2
2
2
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
1
1
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
3
0
1
2
0
0
1
0
2
2
0
0
0
2
2
0
0
3
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
2
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
1
1
0
0
3
0
2
0
0
0
0
1
0
2
0
1
0
0
0
0
2
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
1
0
0
0
2
3
1
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
1
0
0
1
0
0
1
3
0
1
0
2
0
2
0
2
0
1
2
0
1
0
0
0
0
1
2
1
2
0
0
0
0
0
1
0
1
0
0
2
0
0
1
1
0
0
0
2
1
0
0
0
1
0
0
1
0
2
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
1
0
2
1
3
0
2
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
2
2
0
0
1
2
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
2
0
3
1
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
2
2
0
0
0
0
2
1
1
0
0
1
2
2
0
1
0
1
0
0
1
0
1
0
0
1
0
0
1
0
0
0
2
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
2
1
0
0
0
0
2
0
1
0
0
0
3
0
0
0
0
0
0
2
1
2
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
2
0
0
1
0
2
0
0
0
0
0
1
1
0
0
2
5
0
2
1
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
1
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
4
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
2
1
1
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
2
0
0
0
2
1
0
0
1
2
0
1
0
0
2
0
0
2
1
1
0
0
0
0
1
0
1
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
2
2
0
1
1
2
0
0
0
1
0
1
0
0
3
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
1
2
0
0
0
1
0
1
0
0
3
0
2
2
0
2
0
3
0
0
2
0
0
0
0
1
0
0
0
2
0
2
1
0
0
3
0
0
0
0
0
1
1
0
2
1
0
0
0
2
0
1
0
0
0
1
2
0
0
0
0
2
1
0
2
1
1
1
0
0
1
3
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
1
0
2
1
1
1
0
0
3
0
0
0
1
2
0
0
2
1
1
2
2
1
0
2
1
2
0
0
0
0
1
2
1
2
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
1
2
3
0
2
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
2
1
0
0
0
1
0
0
1
0
1
0
0
2
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
2
1
0
0
6
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
3
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
2
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
3
1
0
0
0
0
0
0
2
0
0
0
1
0
2
0
3
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
2
5
0
1
2
1
0
2
2
0
0
1
1
0
0
1
1
2
0
1
0
2
2
2
0
1
0
0
1
0
0
0
0
0
2
2
0
0
0
1
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
2
2
0
0
1
0
0
0
0
0
0
0
2
2
2
0
0
0
2
0
0
0
3
0
0
0
2
0
0
0
0
0
2
2
0
0
0
2
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
4
0
1
0
0
1
0
0
0
0
0
0
0
3
1
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
2
0
0
2
0
0
1
0
0
0
1
0
1
1
0
2
0
0
2
1
1
1
0
2
0
0
0
2
2
2
2
1
0
0
2
1
0
0
0
0
0
0
0
1
0
1
0
1
2
0
0
1
0
0
0
0
3
0
1
0
0
0
0
2
4
0
0
0
1
0
0
2
0
1
2
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
1
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
7
0
1
0
0
1
0
1
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
2
4
0
0
2
0
0
0
2
2
0
2
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
6
0
0
0
0
0
0
2
0
2
0
0
0
2
0
2
0
0
0
2
0
0
0
2
0
2
0
0
0
2
0
1
0
3
0
0
1
1
0
0
0
0
1
2
0
1
2
0
0
1
0
2
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
1
0
0
0
0
1
2
1
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
5
0
0
0
1
0
1
0
0
0
0
0
1
0
0
2
2
0
0
2
2
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
1
0
0
0
1
2
1
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
2
0
2
0
2
0
0
0
3
0
0
0
2
7
0
0
1
0
0
0
2
2
1
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
1
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
4
0
1
2
0
2
0
3
2
3
0
2
0
2
0
1
1
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
2
0
2
0
0
0
0
2
0
2
0
1
0
1
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
2
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
2
0
2
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
3
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
1
0
0
3
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
1
0
0
1
0
0
0
0
0
1
1
1
1
2
0
0
2
0
0
0
0
0
0
0
0
3
2
1
0
0
0
0
0
2
2
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
1
0
1
0
0
6
0
0
0
0
0
0
3
0
1
1
3
0
0
0
2
1
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
2
0
1
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
1
1
1
1
0
1
0
0
0
0
1
2
1
2
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
2
1
0
1
5
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
1
1
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
3
0
2
0
0
1
1
0
0
0
2
1
2
1
5
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
2
1
0
0
2
2
0
2
2
0
1
3
0
0
2
2
0
0
0
2
2
0
0
0
0
0
4
0
2
0
2
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
2
5
1
0
2
0
1
0
1
0
0
2
0
1
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
2
0
0
0
2
0
1
0
0
0
1
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
2
0
0
2
0
0
0
2
1
0
2
0
2
0
0
1
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
2
2
1
1
0
2
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
3
2
0
0
1
0
0
3
1
0
0
0
1
0
0
0
0
0
0
0
3
0
1
0
1
1
0
0
0
2
0
1
0
0
0
2
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
1
1
0
1
0
0
0
0
0
4
0
0
0
0
1
0
2
0
0
2
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
2
0
2
1
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
1
0
0
3
0
1
0
0
0
1
1
1
0
0
0
1
0
1
0
2
0
2
0
0
1
0
0
0
0
0
2
1
0
3
0
0
0
2
3
1
2
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
2
2
0
2
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
3
0
2
1
1
0
0
0
0
1
0
0
2
0
2
0
2
0
1
0
0
2
0
0
0
0
0
0
2
1
2
0
0
1
2
2
0
2
2
4
0
1
1
0
0
0
0
2
2
1
1
0
2
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
2
1
0
2
0
0
3
0
0
0
0
0
0
0
2
3
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
2
0
1
0
1
0
0
0
0
1
2
4
0
2
0
1
0
0
1
0
2
1
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
2
1
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
2
1
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
1
1
0
1
0
0
4
0
0
0
0
0
0
0
2
2
0
0
1
1
0
0
0
1
0
0
0
0
0
1
2
0
2
0
2
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
3
0
0
0
0
1
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
1
2
0
2
1
0
1
2
2
2
0
1
0
0
1
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
6
0
0
3
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
2
1
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
1
3
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
11
0
2
0
0
0
4
0
0
0
0
0
0
2
0
0
0
0
5
0
1
2
1
0
0
0
1
1
0
0
0
1
0
0
2
1
0
12
1
0
1
0
0
1
0
2
2
1
0
0
0
8
1
0
3
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
3
0
0
1
0
1
0
0
0
0
0
0
2
1
2
0
0
1
0
0
0
0
0
0
1
2
2
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
1
0
2
1
3
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
1
0
2
0
1
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
1
1
0
2
0
1
0
0
2
2
0
0
3
0
0
0
0
0
2
1
0
0
0
2
2
0
0
0
0
0
0
0
0
1
1
0
2
1
0
1
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
1
2
2
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
4
1
0
0
0
2
0
0
0
1
1
0
0
0
2
0
1
0
0
0
0
2
0
2
0
2
2
2
0
0
0
0
1
0
1
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
1
0
0
0
2
0
2
2
0
0
2
1
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
2
0
1
2
0
0
0
0
1
0
2
0
3
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
1
2
0
3
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
2
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
2
1
1
0
0
0
0
0
2
0
0
0
1
1
2
0
0
0
0
0
0
0
2
0
1
1
0
1
0
0
1
0
0
1
1
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
4
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
2
1
2
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
2
2
4
0
0
0
1
3
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
3
1
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
2
0
0
2
0
0
1
1
0
1
2
0
0
0
0
0
0
0
0
0
3
4
0
1
1
0
0
0
0
2
3
0
0
0
0
1
0
0
0
2
2
0
2
0
0
0
1
0
2
1
0
0
0
0
1
1
2
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
1
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
1
0
1
2
1
0
2
0
0
2
0
0
2
0
2
0
0
0
0
0
0
2
4
0
0
1
1
2
0
0
1
3
0
0
2
0
1
1
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
2
1
0
1
2
1
0
2
2
2
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
5
1
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
5
1
0
0
0
2
0
1
0
0
0
0
2
0
0
0
2
0
3
0
0
4
0
2
2
0
0
0
0
2
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
1
0
0
0
0
0
3
0
1
0
0
0
0
0
1
1
2
0
0
0
0
0
0
1
3
0
0
0
1
2
2
0
3
2
0
0
2
2
1
1
0
0
0
0
0
2
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
2
0
3
0
1
0
0
1
0
0
0
0
3
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
2
2
0
0
1
2
3
2
1
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
2
2
0
2
0
3
2
0
2
1
0
0
0
0
0
2
0
0
1
2
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
1
0
1
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
4
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
2
0
0
0
2
2
1
1
0
0
0
1
2
0
0
0
1
2
0
4
2
2
0
0
0
2
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
2
0
0
1
0
0
0
0
2
3
1
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
3
1
2
2
0
0
1
2
2
0
0
2
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
3
0
0
2
2
2
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
1
2
1
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
3
0
1
0
0
2
1
0
0
0
0
0
1
2
0
0
0
0
2
0
3
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
3
2
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
2
0
0
0
0
0
1
1
0
0
0
1
1
0
3
0
0
2
0
1
2
0
0
0
0
0
0
1
1
2
1
0
3
2
0
0
0
0
2
2
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
1
0
0
0
2
3
1
1
0
1
1
0
1
0
0
0
0
0
0
0
2
1
0
0
0
6
1
0
0
0
0
0
1
2
0
2
0
0
0
0
4
0
0
2
1
0
2
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
3
0
3
0
0
0
1
0
0
1
0
0
0
0
2
0
3
0
3
1
0
0
0
0
0
0
2
2
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
1
0
1
1
0
0
1
0
1
2
0
1
0
2
3
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
4
1
1
0
0
2
0
3
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
4
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
1
0
2
0
2
1
3
1
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
1
2
0
0
2
1
0
1
2
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
4
1
1
0
3
0
1
2
1
1
1
0
0
0
0
0
1
0
0
0
1
2
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
3
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
1
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
2
3
1
2
2
2
0
0
0
0
0
1
1
0
2
0
0
0
1
0
0
0
2
0
0
1
0
0
1
0
1
0
0
0
1
0
1
1
0
1
0
1
1
0
0
1
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
3
2
0
0
0
0
0
0
2
0
1
2
0
0
1
1
2
0
0
0
0
0
0
0
2
1
0
2
1
2
1
0
1
2
0
2
0
2
0
0
0
0
0
1
0
0
2
0
2
0
1
0
1
2
0
1
2
0
0
1
0
0
2
1
2
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
3
0
1
0
0
2
0
0
0
1
1
0
0
3
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
3
0
0
1
0
0
0
0
1
2
0
0
0
2
2
2
0
0
0
0
1
0
0
6
2
1
0
2
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
3
2
1
0
1
0
0
1
2
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
3
0
0
0
2
0
2
0
2
2
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
2
2
0
0
1
1
0
0
2
0
2
1
0
0
0
2
1
1
0
1
4
0
0
1
0
0
0
0
0
0
2
1
0
2
1
1
0
0
1
0
0
0
0
0
2
2
0
0
0
1
0
0
1
2
0
4
0
1
0
1
0
0
0
1
0
0
1
0
0
0
2
2
0
6
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
2
0
0
6
0
0
2
0
0
2
0
1
0
2
0
2
0
0
0
2
0
2
0
0
3
2
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
7
1
1
0
1
0
0
1
2
7
1
0
0
0
0
0
1
1
1
0
0
0
2
0
3
1
0
0
0
2
0
1
0
2
2
2
2
0
0
0
1
2
0
0
2
0
0
1
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
3
0
0
1
0
0
0
1
0
1
0
1
0
0
0
1
0
1
0
0
0
2
2
0
1
2
0
1
0
1
0
0
0
0
2
0
0
2
0
3
0
0
1
0
1
3
0
1
2
0
0
0
1
0
0
2
0
1
0
2
2
0
0
0
0
1
0
2
0
1
1
0
0
0
0
0
0
6
0
0
0
0
0
0
1
0
1
0
0
2
0
0
2
0
2
0
0
0
0
1
0
0
0
1
0
1
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
2
0
1
0
1
0
2
1
2
0
5
3
0
1
2
0
0
1
0
0
0
0
2
2
2
0
0
1
0
0
0
1
2
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
1
2
0
2
2
1
0
0
1
2
0
0
0
2
0
1
2
2
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
1
0
0
3
2
0
1
0
0
0
0
0
0
1
0
0
0
5
0
1
0
1
1
0
1
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
2
0
0
0
0
1
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
1
0
1
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
3
0
0
3
0
0
0
0
0
0
1
0
2
0
3
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
1
1
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
5
0
0
1
2
0
1
1
2
2
0
2
0
0
2
2
0
1
2
0
1
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
1
1
0
1
0
1
0
0
1
0
0
2
0
1
0
2
0
1
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
5
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
2
0
2
0
0
0
0
1
0
2
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
2
0
0
2
0
0
0
1
0
0
0
0
1
0
2
2
0
0
1
1
2
0
2
0
2
0
0
0
0
0
0
0
1
1
0
0
2
0
1
2
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
1
1
0
0
0
1
0
0
0
2
1
0
0
0
1
0
0
2
0
0
0
0
1
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
2
1
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
2
0
0
0
1
3
0
0
0
0
0
1
1
2
0
1
0
0
0
0
0
1
0
1
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
3
0
2
0
0
0
3
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
1
0
2
1
0
0
0
0
1
1
0
2
0
0
0
4
1
0
0
2
0
2
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
2
2
2
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
2
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
1
0
0
0
1
2
1
1
0
0
0
0
0
1
0
2
0
0
2
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
1
2
2
1
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
2
0
0
0
0
2
3
0
1
2
1
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
2
0
2
0
2
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
2
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
2
2
0
0
0
1
0
0
0
0
1
1
2
0
0
1
0
0
0
0
2
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
2
0
1
0
0
2
0
2
4
2
2
0
0
0
3
0
0
2
0
0
0
0
1
3
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
1
2
2
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
1
2
4
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
2
0
2
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
2
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
7
0
0
2
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
1
0
1
0
0
2
0
3
0
0
0
1
0
0
0
0
1
1
1
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
1
0
2
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
1
0
1
2
0
0
0
2
0
0
1
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
4
0
0
0
2
1
2
2
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
2
0
0
0
0
1
0
2
1
0
0
0
0
2
0
0
2
0
1
0
2
0
3
0
1
0
0
1
2
0
0
2
1
0
0
0
0
0
0
1
0
1
2
2
0
0
3
0
0
0
0
0
4
0
1
0
0
3
2
1
0
0
0
1
0
0
2
2
0
0
2
0
0
0
2
0
0
2
0
0
1
0
0
2
2
0
0
1
1
0
2
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
1
2
0
0
0
0
0
1
1
0
2
0
1
2
0
0
5
2
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
2
0
2
0
2
2
2
0
0
0
0
0
9
2
1
0
0
1
0
0
0
0
0
2
0
0
2
1
0
1
0
1
1
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
2
0
0
0
0
2
0
0
0
1
0
1
0
2
1
0
0
0
0
1
0
0
0
0
2
0
1
0
0
1
1
0
0
0
2
0
0
0
3
2
0
0
0
0
0
0
1
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
1
2
0
3
0
0
0
2
2
0
0
0
0
0
0
0
1
1
2
0
0
0
1
0
0
0
2
0
0
1
0
0
2
0
0
3
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
3
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
3
0
1
1
0
0
0
0
0
0
0
2
0
3
2
0
0
0
0
0
1
1
0
0
2
0
2
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
3
2
0
1
0
0
2
0
0
2
0
1
0
0
2
0
0
3
0
1
1
2
0
2
0
0
0
0
0
2
0
0
2
0
0
6
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
2
3
0
0
0
0
1
0
0
0
0
0
0
2
1
0
4
0
1
1
0
2
0
2
0
1
0
1
0
0
0
1
0
0
1
0
2
3
0
0
0
0
3
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
2
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
7
2
2
2
2
0
1
0
0
1
1
1
0
0
0
1
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
2
1
1
0
1
0
0
0
0
1
0
2
2
0
2
0
2
0
1
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
3
0
1
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
1
0
1
0
2
0
0
0
1
2
0
1
2
0
2
0
0
0
0
0
0
2
1
0
0
2
0
1
3
0
0
2
1
0
0
0
0
2
0
0
2
0
1
2
0
0
0
0
3
0
2
0
0
1
0
1
0
1
0
1
1
0
0
0
3
2
0
0
0
2
0
2
0
0
2
0
3
0
1
0
0
0
1
0
0
0
0
0
0
3
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
3
0
0
0
1
1
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
3
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
2
0
2
2
0
0
0
0
0
2
2
2
0
0
1
0
0
1
0
0
0
3
1
1
2
0
0
0
0
2
0
0
0
0
1
0
0
2
3
0
1
0
0
0
2
0
2
1
0
0
1
2
1
0
2
0
0
1
0
2
1
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
1
1
0
0
0
2
2
0
2
2
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
1
0
0
1
0
0
0
1
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
2
1
2
0
0
0
0
0
0
1
2
0
0
2
1
1
0
0
0
0
0
0
2
0
1
2
2
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
1
0
0
1
0
0
3
0
0
0
0
0
1
2
0
0
0
0
0
3
1
0
1
0
0
1
0
0
0
0
5
2
3
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
1
0
1
2
0
1
0
0
2
1
0
2
0
0
4
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
2
0
0
0
6
3
0
1
1
1
0
0
0
0
0
0
0
1
2
0
0
2
2
0
1
1
0
1
0
0
0
1
7
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
1
0
1
2
1
0
1
0
0
0
1
0
1
0
0
0
1
0
0
2
0
2
0
0
0
0
2
1
0
0
0
0
0
0
1
1
0
0
0
0
2
2
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
2
0
1
2
2
0
1
0
1
0
0
0
0
0
2
0
0
1
1
0
1
1
0
0
0
0
1
1
0
0
0
1
2
0
0
1
0
0
1
2
0
0
2
0
0
1
0
0
0
1
1
0
0
0
2
0
1
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
1
1
0
2
0
0
1
0
1
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
1
0
2
2
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
5
0
0
0
1
3
0
0
0
0
2
1
1
1
0
0
2
0
0
1
2
0
1
0
0
2
1
0
0
1
0
0
2
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
2
1
2
0
1
1
3
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
2
0
0
0
2
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
2
2
0
0
0
2
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
1
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
3
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
1
0
0
0
1
2
0
0
2
1
0
3
0
0
1
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
1
1
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
5
0
2
0
1
0
0
2
0
0
0
0
1
0
3
2
0
2
0
0
0
1
0
0
0
0
2
0
0
0
1
1
2
0
1
2
5
0
1
0
0
0
0
0
2
2
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
1
0
2
0
0
2
2
3
0
0
0
0
1
0
1
0
1
0
0
0
0
2
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
2
2
0
0
0
1
0
0
0
1
2
0
2
0
0
1
1
1
1
1
0
0
0
2
0
0
0
0
3
1
0
2
0
4
2
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
2
2
0
0
1
2
0
0
2
0
1
0
2
0
3
0
2
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
2
0
0
2
1
1
0
0
0
1
2
0
0
0
0
1
2
2
0
2
0
0
0
0
0
0
3
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
2
1
0
0
0
1
2
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
1
1
0
2
0
0
0
0
1
0
0
2
1
0
0
0
0
3
2
0
0
1
0
1
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
1
2
0
0
1
0
3
0
1
0
1
1
0
0
0
0
0
0
0
3
0
0
4
0
1
0
2
0
2
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
1
2
0
2
1
0
0
0
0
1
0
0
0
1
2
1
2
1
0
0
1
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
1
1
0
0
0
0
2
0
0
2
1
1
2
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
2
0
1
0
2
0
0
0
0
0
0
1
0
2
0
0
2
0
2
2
0
1
0
0
0
0
2
0
0
0
0
1
1
2
0
0
0
0
0
0
0
1
2
1
0
0
1
0
0
0
1
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
4
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
2
2
0
1
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
6
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
1
2
0
0
0
1
0
1
0
1
0
0
0
0
2
0
0
0
0
1
2
1
0
2
0
0
0
0
0
2
0
0
3
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
1
0
0
0
0
0
2
2
0
1
1
0
0
1
2
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
1
0
2
1
2
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
1
0
0
3
2
0
1
0
0
0
0
3
1
1
0
2
3
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
3
0
0
2
1
3
0
1
2
0
0
2
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
2
1
0
0
1
2
0
2
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
7
0
0
1
0
0
0
0
0
2
0
0
1
1
0
0
0
1
0
2
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
2
0
1
1
1
0
0
0
0
0
1
0
0
0
2
0
2
0
0
2
0
1
0
0
2
0
0
0
1
0
2
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
2
0
2
0
2
0
0
1
1
0
0
0
1
3
0
0
0
0
0
0
1
0
0
0
0
2
1
1
0
0
0
1
0
2
0
1
2
0
0
0
1
0
2
0
0
0
1
2
4
1
0
1
0
0
1
1
0
0
0
1
3
1
0
1
8
0
0
2
2
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
1
0
2
0
2
0
0
0
0
0
1
0
0
2
0
0
1
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
3
0
0
1
0
0
0
0
0
2
1
0
2
0
1
0
0
1
2
1
2
0
0
0
2
0
3
0
0
1
0
2
1
0
0
1
2
1
2
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
2
0
2
0
1
1
0
0
0
2
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
2
2
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
7
2
2
0
0
1
0
0
0
0
2
0
0
0
1
0
0
1
3
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
1
1
1
0
0
0
2
0
0
0
1
0
5
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
1
2
0
0
0
0
0
0
3
0
2
2
0
0
0
2
0
0
0
0
0
2
0
0
0
2
3
0
2
1
0
0
0
0
0
1
0
0
0
0
3
0
2
0
0
0
0
0
0
4
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
4
1
2
0
0
1
0
0
3
1
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
3
0
0
0
0
0
2
0
2
5
0
0
0
3
2
0
0
2
0
2
0
0
1
2
2
0
5
0
0
0
0
2
0
2
0
0
0
2
1
1
0
0
1
1
0
2
0
1
0
0
0
2
1
0
0
0
0
0
2
1
2
0
0
0
1
1
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
1
2
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
3
0
1
3
1
2
0
0
0
0
2
0
0
2
1
0
1
2
0
0
0
0
0
5
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
4
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
3
2
2
0
2
0
0
0
2
1
0
1
1
0
1
2
1
1
0
1
0
2
0
1
2
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
1
1
0
1
0
0
0
2
0
0
1
0
0
0
0
0
1
2
0
2
1
0
1
0
0
0
0
2
1
0
2
0
2
0
1
0
1
0
1
1
0
1
0
0
0
0
2
0
2
0
2
1
0
0
1
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
3
0
2
0
0
0
1
3
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
1
0
0
0
0
3
0
0
1
0
1
0
0
0
1
0
2
0
0
2
0
0
1
1
0
1
0
0
0
2
0
0
0
0
0
0
2
3
2
0
0
0
0
0
0
2
0
2
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
2
0
0
0
2
0
0
0
2
2
2
2
0
2
2
2
0
0
0
0
0
0
0
1
1
0
2
2
0
0
0
0
2
0
0
0
0
1
1
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
1
2
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
1
0
0
0
1
0
0
0
1
0
0
0
2
2
0
0
0
1
1
2
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
6
0
0
1
1
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
2
1
0
0
0
0
3
0
0
1
0
1
4
0
0
0
0
0
0
0
0
2
2
0
3
0
0
1
0
0
0
4
0
0
0
1
2
0
0
0
1
2
0
1
0
0
0
0
2
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
3
1
0
0
0
1
0
1
0
0
0
0
0
2
2
0
0
1
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
2
1
0
0
0
0
2
0
2
1
1
0
1
0
2
0
0
0
0
0
0
14
0
0
2
3
0
0
2
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
1
0
0
0
0
1
3
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
2
1
2
0
3
0
0
0
1
0
2
1
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
1
1
0
0
0
1
0
0
1
0
0
2
0
1
2
0
0
2
0
1
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
2
1
0
0
0
1
2
0
2
0
2
0
1
2
0
1
0
0
0
1
1
0
0
0
0
0
9
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
1
2
0
2
0
0
0
2
0
0
1
2
0
0
1
1
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
3
0
2
0
1
1
1
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
1
0
1
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
3
1
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
2
0
0
0
0
0
2
0
2
2
0
2
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
3
2
0
2
0
0
1
1
0
0
1
0
2
0
0
1
1
3
0
0
2
0
1
2
1
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
3
0
1
0
1
0
0
2
0
1
0
2
1
0
0
0
1
0
0
0
2
0
0
1
0
2
0
0
0
2
0
0
0
1
0
2
0
1
0
0
1
2
2
0
1
0
0
1
0
0
0
0
0
0
1
2
0
0
0
3
1
0
0
0
1
0
0
0
1
1
0
2
0
0
2
0
1
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
1
2
2
2
0
2
1
0
0
0
2
0
0
0
2
1
0
1
0
0
1
0
3
0
0
0
1
0
2
0
0
2
2
1
2
0
0
1
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
3
1
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
3
2
0
1
1
0
3
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
1
0
1
2
0
0
0
1
0
0
0
0
2
2
0
2
0
3
0
0
0
0
0
0
0
1
1
0
0
0
1
4
0
0
3
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
2
1
0
0
2
0
0
0
2
0
0
0
2
0
0
2
0
0
0
2
0
0
2
3
0
0
0
0
2
0
0
0
1
0
1
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
8
0
2
0
2
1
0
1
1
1
1
0
1
0
0
0
0
0
0
2
0
0
1
2
0
0
0
1
2
0
0
0
2
0
2
2
0
1
0
0
0
3
0
0
0
2
0
2
0
0
1
0
0
0
2
0
0
0
1
0
0
1
0
1
3
2
1
1
2
0
0
2
0
2
0
2
0
2
0
3
0
0
0
0
1
2
0
2
2
1
1
0
1
0
0
0
2
0
0
0
0
2
2
0
0
0
5
0
1
2
0
0
3
2
0
1
0
0
0
2
0
0
1
0
0
0
0
3
2
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
4
0
0
0
3
1
0
0
2
0
2
0
1
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
2
0
0
0
2
2
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
1
2
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
2
2
1
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
2
1
2
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
1
0
1
0
0
3
1
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
1
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
2
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
3
2
0
0
0
0
0
0
0
1
1
0
0
0
3
2
2
0
0
0
0
0
1
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
2
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
3
0
1
5
0
0
0
2
0
0
4
2
0
0
0
2
0
0
1
1
0
0
0
2
3
0
0
2
0
2
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
2
1
2
0
2
0
2
1
0
0
0
1
0
5
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
2
1
0
0
0
0
0
0
0
1
0
2
0
0
3
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
3
0
0
1
0
2
0
2
2
0
0
0
1
0
0
2
0
0
0
2
2
0
3
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
5
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
1
0
0
0
1
0
0
0
0
2
2
0
0
2
0
0
0
1
2
0
0
0
0
0
1
0
1
0
2
1
0
0
1
2
1
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
7
0
0
0
0
0
0
0
2
1
2
2
2
0
0
1
0
1
1
1
2
0
0
0
0
2
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
2
1
0
2
0
3
0
0
0
2
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
1
0
0
2
0
1
0
0
2
0
0
3
0
0
2
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
2
0
0
0
1
1
0
0
0
0
0
2
1
0
2
0
0
2
2
0
2
0
2
1
0
0
4
0
0
1
0
2
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
1
1
2
2
0
0
0
0
1
0
0
2
0
1
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
1
1
0
0
1
0
0
0
2
0
2
0
1
0
0
0
0
0
0
1
0
2
0
0
1
2
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
2
2
1
0
3
0
2
0
0
0
2
0
0
0
0
2
0
0
0
3
0
1
0
0
0
0
1
0
2
0
1
0
0
2
0
0
0
3
2
0
2
0
1
1
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
2
2
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
1
0
0
0
1
0
2
1
1
1
1
1
2
0
1
0
0
0
2
0
0
2
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
3
1
0
0
0
0
1
2
0
2
0
2
0
0
2
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
5
3
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
3
0
0
2
1
0
2
3
3
0
0
0
2
1
1
3
0
2
2
1
5
0
0
0
0
0
1
2
2
0
0
0
1
0
0
0
0
2
3
4
0
0
0
1
0
0
2
0
0
2
0
0
1
0
0
1
0
2
0
0
0
0
2
2
0
0
0
0
1
1
2
0
0
0
2
0
0
0
0
2
2
1
0
0
1
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
2
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
1
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
1
0
0
1
1
0
0
0
0
1
0
0
0
1
2
1
0
2
1
1
0
2
0
0
2
0
0
0
0
1
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
1
2
2
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
3
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
3
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
2
2
0
0
2
0
1
1
0
0
0
0
4
2
0
1
0
0
0
1
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
1
3
1
0
0
1
1
1
0
0
0
1
1
2
0
0
0
5
0
0
1
0
2
2
1
2
2
0
1
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
3
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
2
0
1
0
3
0
2
2
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
3
0
0
0
3
1
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
3
0
0
2
2
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
1
3
1
0
0
1
0
1
0
1
0
0
1
0
2
0
1
0
0
0
0
0
0
0
1
2
0
1
0
0
2
3
2
0
2
1
0
2
0
0
0
0
0
2
2
0
0
3
0
4
1
0
0
0
0
0
3
0
2
0
0
2
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
2
0
4
2
1
0
0
0
0
2
0
0
1
1
0
0
0
1
0
1
0
0
1
1
0
2
0
0
0
1
0
0
0
0
1
0
1
1
1
0
2
2
0
0
2
1
0
1
0
0
2
3
1
1
0
2
0
0
1
8
0
0
0
0
1
0
2
0
0
0
1
0
1
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
10
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
2
0
1
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
2
0
2
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
4
1
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
1
3
0
0
2
0
0
1
2
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
1
2
0
1
0
0
0
0
2
0
0
0
2
2
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
2
2
0
0
0
2
0
1
0
0
0
0
1
3
1
1
2
0
2
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
1
0
0
3
0
0
0
1
0
0
1
0
0
0
2
1
0
0
1
0
2
0
0
1
1
0
2
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
1
2
0
0
1
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
1
1
1
0
2
3
1
0
0
0
0
0
1
0
2
1
0
1
1
0
2
1
0
0
1
0
0
0
0
1
0
2
0
0
0
1
0
0
0
1
1
1
0
0
4
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
2
0
0
0
2
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
2
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
2
1
0
1
1
0
2
0
0
0
0
0
0
0
0
1
1
0
2
1
1
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
1
1
0
1
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
2
2
0
2
0
0
0
0
1
2
0
0
0
2
3
0
0
0
0
1
2
2
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
2
0
1
1
0
0
2
2
0
0
0
1
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
2
2
0
1
0
0
2
2
0
0
0
0
1
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
2
1
0
1
0
1
0
1
2
0
7
0
0
0
0
0
0
0
2
3
3
2
0
0
2
2
1
0
0
0
0
0
1
0
0
2
0
0
1
2
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
1
0
0
1
2
0
0
2
0
0
0
0
1
1
1
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
2
0
0
0
2
1
0
1
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
1
1
0
0
0
0
1
0
2
10
2
3
0
0
2
1
0
0
1
1
0
0
0
0
0
0
1
0
1
1
2
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
2
0
0
2
0
0
3
3
1
2
1
0
0
0
0
0
2
0
2
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
2
0
0
0
0
0
1
0
0
0
2
0
0
1
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
2
0
0
2
0
1
2
0
1
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
2
1
0
0
1
0
2
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
3
0
0
2
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
1
2
1
0
0
2
0
0
2
2
2
0
0
0
0
0
0
1
0
1
2
0
1
1
2
2
3
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
1
1
0
2
0
1
2
0
0
0
0
0
0
0
1
2
1
2
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
3
3
0
1
0
2
2
2
0
2
0
1
0
0
0
0
0
0
2
1
1
0
1
0
2
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
3
0
1
0
1
0
0
2
0
2
1
0
1
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
3
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
1
0
1
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
2
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
1
0
0
0
1
0
0
1
0
1
4
2
0
0
0
0
1
1
3
0
0
2
0
0
1
1
2
0
0
0
3
1
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
1
1
2
2
0
2
0
0
0
0
0
0
2
0
2
2
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
2
0
0
2
0
0
2
2
0
0
0
0
0
0
0
3
0
1
2
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
2
3
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
2
2
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
2
0
0
1
0
1
2
1
0
0
0
2
0
0
0
2
0
0
0
2
2
1
2
0
2
0
0
0
0
0
3
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
2
0
2
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
1
0
2
0
1
0
2
0
0
0
2
0
0
0
0
0
2
0
3
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
1
0
1
0
0
0
0
0
0
2
0
4
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
2
1
0
0
0
1
0
1
1
0
0
1
1
2
0
0
0
2
0
1
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
2
1
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
1
0
2
0
0
0
2
0
1
0
1
0
1
1
0
0
0
0
2
0
2
2
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
1
1
0
0
2
0
2
0
0
0
3
0
0
1
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
2
0
2
0
2
2
0
0
0
0
0
0
0
3
0
0
0
0
2
2
0
2
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
3
0
0
1
0
0
2
0
1
1
0
0
0
0
2
0
1
2
0
2
0
1
2
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
1
2
2
0
0
0
2
0
2
0
1
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
1
0
4
2
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
1
0
0
1
2
0
0
0
0
3
1
0
0
0
0
3
0
2
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
1
3
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
1
2
0
0
0
1
0
0
0
0
0
1
0
0
0
2
2
2
1
0
1
2
0
0
0
1
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
2
1
0
2
2
0
0
0
0
3
0
0
2
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
3
1
1
0
0
0
0
0
1
0
1
0
0
1
2
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
1
2
0
2
1
0
2
0
0
2
2
0
2
0
2
1
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
4
2
0
0
0
0
1
0
2
0
0
4
0
0
0
0
0
0
2
2
1
1
0
1
0
2
1
1
0
0
2
0
0
0
0
2
1
0
1
0
0
0
0
0
2
1
0
0
0
0
3
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
1
1
0
2
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
1
2
3
0
0
0
1
0
2
0
0
0
4
1
3
0
0
0
0
2
2
1
2
0
2
0
0
0
0
1
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
3
0
0
0
0
0
1
0
1
2
0
0
0
0
2
0
0
0
1
1
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
1
2
2
0
0
1
0
0
0
0
2
2
0
1
0
2
0
1
0
0
2
0
0
0
3
2
0
0
1
0
0
1
0
0
0
0
2
1
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
3
0
1
0
0
0
1
1
0
0
0
2
0
0
1
0
0
2
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
1
1
3
1
6
0
0
1
0
0
1
0
2
0
0
2
3
2
0
0
0
2
0
2
0
1
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
2
2
2
0
0
0
0
2
2
0
0
0
2
0
0
0
1
2
0
2
2
0
2
0
0
5
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
2
1
0
2
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
1
0
1
1
0
0
2
1
0
0
0
0
2
0
2
0
2
0
1
0
1
0
0
0
0
0
0
0
2
2
2
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
1
0
0
1
2
3
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
2
0
1
0
0
0
0
0
2
1
1
1
0
0
0
0
1
0
1
2
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
1
0
1
0
0
1
1
1
0
0
0
2
1
0
0
0
0
0
0
2
2
0
2
0
0
0
0
3
1
2
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
1
2
1
1
0
3
2
0
2
2
1
2
1
0
0
2
2
0
2
0
0
0
2
2
0
2
2
1
2
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
1
0
2
0
2
0
0
0
2
0
0
0
0
1
0
1
0
0
1
2
2
0
0
0
0
1
0
2
0
2
0
0
1
1
1
1
0
0
2
5
0
0
1
2
2
0
0
0
0
1
0
1
2
0
0
0
0
0
1
0
0
1
2
0
0
0
0
2
0
1
0
2
3
0
2
0
0
3
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
1
0
2
2
0
1
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
2
2
0
0
0
4
0
0
1
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
2
2
0
2
2
1
2
1
0
0
0
1
0
0
0
0
1
0
0
0
2
2
1
0
0
2
0
1
1
2
2
1
0
0
0
0
0
1
2
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
2
0
0
0
0
0
2
0
3
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
2
2
0
1
1
0
0
0
0
0
1
0
4
0
1
0
0
1
0
0
0
0
1
2
0
2
2
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
1
0
1
1
2
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
1
1
0
0
1
0
2
0
1
0
3
0
0
0
0
0
0
0
1
1
2
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
2
2
1
0
0
2
4
0
2
2
1
2
0
1
0
2
2
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
1
0
0
2
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
3
0
0
2
1
0
0
0
1
2
1
2
0
0
0
0
0
0
0
1
0
0
1
2
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
5
0
0
0
0
2
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
1
0
0
0
0
2
2
2
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
3
0
0
1
2
1
0
1
1
2
0
0
0
0
0
0
0
3
0
0
1
0
1
0
2
0
1
0
0
0
3
0
0
0
0
0
1
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
3
0
0
0
2
1
0
0
2
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
2
2
0
0
0
0
1
0
0
2
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
1
0
2
2
0
0
0
0
0
3
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
2
1
0
0
2
0
1
0
1
0
0
0
0
0
2
0
0
0
2
1
0
0
1
0
1
0
0
1
2
0
0
0
1
0
2
0
0
0
0
0
2
2
2
1
2
0
0
0
0
0
0
1
0
1
2
0
0
0
2
0
2
0
0
0
2
2
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
2
3
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
2
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
1
0
5
0
2
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
6
1
0
0
1
2
0
4
0
0
0
0
2
0
0
1
1
2
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
2
0
0
0
1
0
0
0
0
1
2
0
0
0
1
0
2
3
0
0
0
2
0
0
0
2
0
2
2
0
1
2
1
0
0
0
2
0
0
0
0
2
0
2
2
0
0
0
1
0
1
0
2
0
0
2
0
0
1
0
0
1
0
0
0
0
3
0
2
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
1
0
0
0
0
2
2
1
0
0
0
2
0
0
0
0
0
2
2
2
0
0
0
2
0
1
1
0
0
1
3
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
1
2
1
1
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
2
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
3
3
2
0
2
0
0
0
1
2
0
0
1
1
0
0
1
1
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
3
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
1
0
0
2
0
1
0
0
2
0
0
2
1
0
0
2
1
0
0
0
2
0
0
2
0
2
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
1
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
2
1
3
0
1
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
1
0
0
0
1
2
0
0
0
0
0
0
2
0
1
0
0
0
1
1
1
0
0
2
2
0
0
0
1
0
0
0
1
0
0
1
1
1
0
2
0
0
1
0
0
1
0
2
0
0
0
2
0
0
1
0
1
2
1
0
1
2
0
0
0
0
1
5
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
2
2
2
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
1
0
2
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
2
1
2
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
2
0
0
2
2
1
3
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
2
0
0
0
0
1
0
2
2
2
0
0
1
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
2
0
2
0
0
0
0
2
0
1
0
0
2
4
0
0
0
2
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
2
0
0
2
1
0
1
0
0
0
2
0
0
1
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
2
0
1
0
0
0
2
2
2
0
0
0
1
2
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
3
2
2
0
3
0
1
0
2
2
3
0
0
0
0
0
2
0
2
0
0
0
1
2
2
0
0
0
3
1
1
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
3
0
0
0
0
0
1
1
1
3
2
0
0
0
0
3
0
0
2
2
0
0
1
1
0
1
2
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
2
2
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
2
0
2
0
2
1
0
0
2
0
0
1
0
1
0
1
0
2
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
3
3
2
2
0
0
0
0
0
0
0
2
3
1
0
0
0
0
1
0
2
0
0
1
0
1
1
0
0
1
0
0
0
0
0
1
2
2
0
0
0
0
2
3
2
0
0
0
2
0
0
1
2
0
0
0
0
1
0
0
1
1
0
1
1
2
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
2
2
0
2
0
1
1
0
0
1
0
0
4
0
0
0
1
0
0
2
0
0
0
3
0
0
0
0
2
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
2
0
0
1
0
0
4
0
1
0
0
2
0
0
0
0
0
2
0
2
0
0
2
0
2
2
0
2
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
2
2
2
0
0
0
0
1
1
0
2
0
2
0
0
0
0
1
0
2
0
0
2
1
2
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
1
0
0
0
1
2
0
1
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
1
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
2
0
0
0
2
2
0
0
0
0
1
0
1
0
2
0
0
1
0
0
0
0
0
2
0
0
1
0
2
0
1
0
1
0
1
0
0
1
2
2
0
1
2
1
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
1
1
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
2
0
0
1
2
1
0
0
0
0
0
0
1
0
1
0
1
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
1
1
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
2
1
2
0
0
2
0
2
0
0
0
0
0
0
0
3
0
0
0
2
0
0
2
1
0
2
0
0
0
0
0
0
2
0
1
0
0
0
2
2
1
0
1
0
0
0
0
0
2
1
0
4
0
0
0
0
2
1
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
2
0
0
1
2
0
2
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
2
3
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
2
2
0
0
1
0
0
0
0
2
0
1
1
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
3
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
2
0
1
0
0
0
1
1
2
0
2
0
1
0
2
0
0
0
0
2
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
1
3
0
2
0
0
0
1
2
0
0
0
2
0
0
2
2
1
1
0
0
0
2
5
0
0
0
3
3
0
2
0
0
0
2
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
2
0
1
0
1
2
0
0
0
0
0
2
1
0
2
0
0
1
0
2
0
0
0
2
2
0
2
0
0
0
2
0
2
1
2
0
1
0
0
1
0
0
0
0
0
0
2
5
0
0
0
0
0
0
0
0
0
0
2
1
0
2
2
0
2
0
2
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
1
0
3
0
0
0
0
2
0
0
0
1
0
2
2
0
2
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
1
0
2
0
0
0
0
0
2
0
1
0
0
0
0
2
0
1
2
0
0
0
0
0
1
0
4
2
0
0
0
0
2
0
0
5
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
3
2
2
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
1
0
2
1
0
0
0
2
0
1
0
1
1
1
2
0
0
0
0
0
1
0
2
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
3
2
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
4
0
2
0
0
1
2
0
0
0
0
0
0
2
1
2
0
0
0
0
3
1
2
0
1
2
0
1
0
0
0
2
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
3
2
2
0
0
1
0
0
0
0
0
2
2
0
0
0
0
1
0
1
4
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
1
1
0
0
0
0
1
0
2
1
1
1
6
1
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
3
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
2
0
1
0
0
0
1
0
0
1
0
1
0
0
2
0
0
0
2
0
0
0
0
2
0
2
0
1
2
0
1
0
0
1
1
1
0
0
0
0
0
0
1
2
0
1
2
0
1
0
0
2
0
0
1
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
5
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
1
0
0
1
0
0
3
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
1
1
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
2
0
0
1
0
1
0
0
0
1
1
0
0
1
2
1
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
1
1
1
0
0
0
2
2
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
1
0
0
0
2
2
0
1
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
2
0
1
0
2
0
0
1
3
3
2
0
0
0
2
0
2
3
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
2
0
2
0
0
0
2
2
1
1
0
0
0
0
0
1
0
0
2
3
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
2
0
1
1
0
0
4
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
2
0
0
3
0
1
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
6
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
6
2
0
0
2
0
2
0
0
2
0
0
0
1
2
0
0
0
0
0
2
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
1
0
2
0
0
0
1
0
0
3
0
2
0
0
0
2
0
1
0
1
2
0
2
0
0
0
2
0
0
0
1
2
2
0
0
2
0
0
0
0
0
1
0
1
1
2
0
0
0
1
0
0
2
1
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
1
0
1
0
2
0
0
3
1
0
2
0
0
0
0
0
2
0
0
2
0
2
0
0
1
0
0
1
0
1
1
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
1
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
2
0
1
0
6
0
1
0
0
0
0
1
0
0
1
0
6
1
3
0
0
1
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
6
1
0
2
0
0
1
2
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
1
1
0
2
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
1
1
2
0
0
0
0
0
0
1
2
0
0
0
0
1
0
1
0
0
0
1
0
0
0
4
1
0
0
0
0
2
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
1
0
3
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
1
3
0
3
2
3
1
2
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
2
0
0
2
0
4
1
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
2
1
7
0
12
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
3
0
0
1
2
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
6
1
2
0
2
0
2
0
1
0
1
0
0
0
0
0
2
1
0
1
0
0
1
0
0
0
2
0
0
2
0
0
1
0
0
1
0
2
0
0
2
0
0
0
0
2
1
0
0
3
0
0
0
1
0
2
0
0
0
1
1
0
0
2
1
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
3
1
0
2
1
0
0
0
0
0
0
0
1
2
0
0
2
2
0
2
0
0
1
0
0
0
0
2
0
2
1
2
2
3
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
2
4
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
2
2
0
2
0
1
0
0
0
0
1
0
3
0
0
0
0
0
0
0
3
1
2
0
0
0
0
0
2
2
1
0
0
3
2
0
0
0
0
0
0
0
2
1
0
0
1
2
1
0
0
0
0
0
1
0
2
0
1
0
0
0
0
2
3
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
4
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
2
2
1
2
0
2
0
0
0
0
0
0
1
2
0
1
0
0
1
0
0
0
2
4
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
1
2
0
0
1
0
0
1
2
0
1
2
0
0
0
0
2
0
0
1
2
0
0
3
1
0
1
0
0
2
1
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
1
0
2
1
1
0
2
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
3
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
1
0
0
2
0
0
0
1
2
1
0
0
0
0
1
2
0
2
0
0
0
1
0
0
3
1
0
1
0
1
0
2
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
1
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
1
1
0
0
2
0
1
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
1
0
3
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
1
2
0
0
0
1
1
0
0
1
0
0
2
1
0
0
2
0
0
1
0
0
0
1
1
2
0
1
0
1
0
2
2
1
2
0
0
0
0
0
0
1
0
2
0
0
0
3
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
3
0
2
1
0
1
1
2
1
0
2
0
0
0
0
0
1
0
2
0
0
0
0
2
1
1
5
0
2
0
1
0
0
1
1
0
0
0
1
0
0
3
1
0
2
0
0
0
1
0
0
3
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
1
1
2
0
0
1
2
1
0
0
2
0
1
0
0
0
0
0
2
0
0
1
3
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
2
1
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
2
0
2
2
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
2
0
1
0
0
8
0
2
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
3
0
0
0
2
2
1
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
7
0
0
0
0
0
0
0
1
3
0
0
0
1
1
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
1
1
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
1
1
0
1
0
0
2
2
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
1
1
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
2
0
0
2
1
2
2
0
0
0
4
0
0
0
0
1
0
0
0
0
1
0
0
3
0
0
0
0
0
2
0
1
2
0
1
2
0
0
1
3
0
0
2
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
1
0
1
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
1
0
0
2
0
2
0
0
1
0
0
1
1
0
0
1
2
1
2
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
2
2
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
2
1
0
2
1
1
0
0
1
1
0
0
0
0
2
3
0
0
1
0
1
0
2
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
3
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
4
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
1
1
0
0
2
0
0
0
1
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
1
2
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
1
1
0
0
2
0
0
0
0
3
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
2
0
0
3
0
2
0
0
1
2
1
0
0
0
1
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
1
2
0
0
0
0
0
0
2
0
3
0
0
0
1
3
1
0
0
0
0
0
0
1
1
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
1
0
0
0
1
2
2
0
0
0
0
1
0
0
0
0
0
2
0
1
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
2
0
0
2
0
1
0
0
2
2
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
1
5
0
0
0
0
1
0
0
0
2
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
2
0
2
0
0
0
0
0
0
2
1
0
1
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
2
1
0
0
0
2
0
1
1
0
0
1
0
0
2
2
0
0
0
0
2
0
2
0
0
0
0
1
0
0
2
0
0
1
0
2
0
6
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
19
0
0
1
2
2
0
1
2
0
0
0
0
0
2
0
0
0
8
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
3
0
0
0
0
0
1
1
0
0
3
1
2
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
2
1
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
1
2
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
2
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
2
0
1
0
0
3
0
0
2
1
0
0
0
0
0
4
0
2
0
0
0
0
3
0
1
2
0
0
0
1
0
0
0
0
1
0
0
0
3
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
2
0
0
2
0
0
1
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
3
1
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
1
0
3
0
0
1
1
3
0
0
0
0
0
4
0
0
2
0
0
2
1
0
0
2
1
0
0
1
0
0
1
0
0
0
0
0
0
6
0
0
1
0
0
0
0
0
2
2
0
1
2
0
1
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
2
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
1
1
2
2
2
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
1
2
0
0
0
1
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
2
1
2
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
2
0
0
1
0
1
0
0
1
0
0
3
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
1
0
0
0
0
3
1
3
0
1
0
4
0
3
0
0
0
2
9
0
0
1
0
0
0
0
4
2
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
1
0
1
2
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
2
0
0
0
2
0
0
0
3
0
0
2
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
2
0
0
0
2
1
1
1
0
3
0
0
0
2
0
0
2
0
2
2
0
0
0
0
0
0
2
0
0
0
0
1
2
0
1
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
2
0
0
2
0
2
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
2
0
0
2
0
0
2
0
0
0
0
2
0
2
0
0
0
1
2
2
0
0
2
0
0
0
1
0
0
0
0
0
1
2
0
0
1
0
1
1
2
1
0
0
2
1
0
1
0
0
0
3
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
2
0
0
0
0
0
1
1
0
0
1
2
0
0
0
0
2
0
0
1
0
0
1
0
1
0
1
2
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
1
2
0
4
0
2
0
2
0
0
2
2
0
0
2
0
2
1
0
0
0
5
0
1
0
1
1
0
0
2
0
0
0
0
0
2
0
0
2
2
1
0
0
2
0
1
0
0
3
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
1
2
2
0
0
0
0
3
0
2
1
0
0
1
1
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
2
0
1
0
0
0
2
1
0
0
0
1
0
2
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
2
0
2
0
0
0
1
1
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
3
0
1
1
0
0
0
2
0
1
0
0
1
4
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
3
2
0
0
0
0
1
0
0
2
2
0
0
0
1
2
1
0
0
0
0
2
0
0
2
0
0
0
0
1
0
2
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
1
1
0
0
0
3
0
0
1
1
0
0
2
2
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
6
0
3
1
0
0
1
0
0
0
0
2
0
0
1
1
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
9
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
2
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
2
0
0
1
1
0
0
0
0
0
4
1
0
3
0
0
0
0
2
1
0
1
0
0
0
1
2
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
2
0
1
0
0
2
0
2
0
2
0
1
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
1
1
0
0
4
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
1
2
0
0
2
0
1
0
0
0
0
0
0
2
0
1
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
2
0
1
0
2
0
0
0
0
1
0
0
2
0
2
2
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
2
0
2
0
0
0
0
0
2
2
0
0
0
0
3
1
2
0
1
0
0
1
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
1
0
2
3
2
0
0
1
2
2
0
2
1
0
2
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
1
0
0
1
0
0
0
3
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
2
2
0
1
1
1
0
0
1
0
0
2
2
4
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
2
1
0
0
0
1
0
0
0
1
0
0
3
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
2
0
2
2
0
2
1
0
0
0
1
3
0
1
2
3
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
4
0
0
1
0
0
0
0
0
0
2
2
0
2
0
0
0
1
1
1
0
0
2
0
0
0
0
1
2
0
0
2
0
3
0
2
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
2
1
2
1
0
2
0
2
2
2
0
1
0
1
2
0
0
0
2
3
2
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
2
0
0
0
2
0
1
0
1
0
1
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
1
2
0
2
0
0
0
0
3
0
0
2
0
1
0
5
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
1
3
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
1
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
2
0
2
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
7
1
0
0
0
0
0
0
2
0
0
0
2
0
3
0
1
0
0
1
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
2
1
0
2
2
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
3
0
0
0
2
2
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
1
1
3
0
0
2
0
0
0
3
0
0
0
2
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
1
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
1
0
2
1
0
1
0
0
0
1
0
1
0
0
0
3
0
1
0
0
0
2
0
1
0
0
0
2
1
0
0
0
0
1
0
2
0
0
0
0
0
0
3
0
0
2
0
0
1
0
1
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
6
1
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
4
0
0
0
0
0
0
2
0
0
0
2
0
0
3
0
2
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
3
1
2
0
2
1
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
1
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
1
2
1
0
0
0
0
0
0
0
2
1
0
0
0
2
0
1
0
0
0
0
0
1
0
1
0
0
0
2
0
1
0
0
0
0
0
0
1
0
2
1
0
0
3
0
0
2
0
0
0
0
2
0
1
1
0
0
2
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
3
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
2
1
3
0
0
1
0
0
0
0
1
0
3
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
2
1
1
0
2
0
0
0
2
0
0
3
0
1
0
0
2
0
2
2
2
0
0
0
1
0
2
0
0
0
0
0
2
0
1
4
0
0
0
1
0
0
4
1
2
0
0
0
0
0
0
0
2
2
0
2
0
2
2
1
0
0
0
0
1
1
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
2
1
0
1
1
0
0
2
0
0
0
0
0
0
0
5
2
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
2
1
1
0
0
0
1
0
0
0
2
0
0
0
5
0
1
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
3
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
1
0
2
0
0
0
1
1
0
0
2
1
0
0
1
0
0
0
0
0
2
0
2
2
0
0
0
0
1
2
1
2
0
0
0
4
0
0
0
0
0
1
0
0
2
1
1
0
0
2
0
0
0
0
1
0
2
0
3
0
0
1
1
2
2
1
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
2
2
0
0
0
0
2
0
0
0
0
2
2
2
1
0
0
0
3
1
0
0
2
0
0
0
2
0
1
0
1
0
1
2
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
2
0
0
2
1
0
0
0
0
0
2
0
0
2
1
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
2
0
2
0
5
0
0
0
0
1
1
0
2
0
1
1
0
1
0
0
1
2
1
0
0
0
0
3
0
0
2
2
1
1
2
1
0
0
2
0
0
0
1
0
0
0
1
0
0
2
6
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
2
0
0
0
1
0
0
2
2
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
2
3
2
2
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
2
0
1
1
0
1
0
0
0
1
2
0
1
1
0
0
0
1
0
1
0
0
0
0
2
0
1
0
0
1
2
0
2
0
0
1
0
0
0
0
2
0
1
0
1
0
0
0
0
0
2
0
0
2
0
1
2
0
0
1
2
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
2
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
1
4
0
0
0
0
2
0
0
0
3
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
2
0
2
0
2
0
0
2
1
0
0
0
0
1
2
0
0
0
0
0
1
2
0
1
0
2
1
0
0
0
0
1
0
0
0
0
2
0
0
3
2
3
0
0
0
0
2
1
0
1
0
2
0
1
2
0
0
0
2
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
4
0
0
1
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
2
0
1
2
2
0
0
2
0
2
1
0
2
2
0
0
2
2
3
1
1
0
0
0
0
0
0
1
0
0
2
0
0
0
1
1
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
3
0
0
0
1
0
0
2
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
1
3
0
2
2
1
0
2
1
1
0
0
0
0
0
2
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
1
1
1
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
1
0
0
2
2
2
0
1
0
1
2
0
0
0
0
0
5
3
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
2
0
0
2
1
2
2
0
0
0
2
0
0
0
2
0
0
1
2
0
0
2
0
0
1
0
0
3
0
2
0
0
0
0
0
2
1
0
0
1
0
1
0
0
1
0
0
0
0
0
2
2
0
0
1
2
3
0
0
0
0
0
1
2
1
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
1
1
0
0
0
4
2
0
1
0
0
0
1
0
0
0
0
0
3
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
3
0
0
0
2
1
1
0
0
0
0
0
2
3
0
0
0
2
0
0
0
0
1
0
0
3
0
0
0
0
0
1
2
0
0
1
1
1
0
2
0
1
0
0
0
0
1
4
2
0
0
0
2
0
1
0
0
0
0
2
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
1
1
2
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
3
0
2
2
0
0
0
0
1
1
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
2
0
3
2
1
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
2
0
1
0
0
5
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
2
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
1
3
0
1
0
0
2
0
0
0
0
1
0
2
0
0
7
0
0
2
0
0
0
1
0
1
2
0
0
0
1
0
0
0
0
0
1
1
0
2
1
2
1
0
0
2
3
0
0
0
0
0
0
0
2
2
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
1
0
1
0
0
0
0
2
3
0
0
0
2
0
1
0
0
3
0
0
0
0
0
0
2
0
1
3
3
7
2
0
0
3
1
0
0
0
0
0
2
3
2
0
0
0
1
0
3
0
0
0
2
0
0
0
2
0
0
1
0
0
2
2
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
1
0
0
0
3
0
0
0
0
0
1
0
2
0
0
0
1
1
0
1
2
0
2
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
4
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
4
0
0
0
0
1
0
1
0
0
0
2
0
0
1
0
0
0
1
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
2
2
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
2
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
2
2
1
1
0
1
0
2
0
4
2
0
0
1
0
0
0
0
0
0
0
0
0
3
1
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
3
0
1
0
0
0
2
1
0
0
2
0
0
2
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
3
2
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
3
0
0
1
3
0
1
0
0
0
0
0
1
0
0
2
0
0
0
1
3
0
0
0
0
0
1
0
0
2
1
0
0
1
0
0
1
3
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
3
0
2
2
0
0
0
2
0
1
1
1
5
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
4
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
1
1
1
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
1
0
3
1
2
0
0
2
1
0
0
0
0
0
0
1
0
1
0
0
0
2
2
2
0
1
0
0
0
0
0
0
0
2
2
0
2
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
2
0
0
1
0
0
2
0
5
2
0
2
0
0
0
2
3
0
0
0
2
0
1
0
2
0
0
0
0
1
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
1
0
0
0
1
0
2
2
0
0
0
2
0
2
0
1
0
0
0
0
1
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
2
0
1
0
0
0
3
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
2
0
1
0
9
1
2
0
0
0
0
1
0
0
3
0
0
0
0
0
2
0
2
0
0
1
1
0
1
0
0
1
1
0
2
0
0
0
2
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
2
0
4
0
1
0
2
2
0
0
0
0
0
0
0
1
0
2
1
0
1
0
1
1
0
1
0
1
1
0
2
1
1
0
0
0
0
0
0
0
2
1
2
0
0
1
1
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
2
1
1
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
1
0
1
0
0
1
0
2
0
1
1
0
0
0
0
1
2
0
0
0
2
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
1
4
0
0
0
0
0
3
0
0
0
2
1
2
1
0
0
2
1
0
0
0
0
0
2
1
0
1
2
0
1
0
0
0
0
0
1
1
0
2
1
1
0
0
0
1
2
0
5
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
1
0
0
0
3
0
0
1
1
0
2
0
0
1
0
0
0
2
0
0
0
2
0
0
0
1
0
0
2
0
1
2
0
2
0
0
1
0
0
0
0
0
1
3
0
6
1
0
0
0
0
2
0
0
0
1
0
1
1
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
3
0
1
0
0
0
2
0
0
0
2
0
1
0
0
1
0
2
0
0
2
0
0
0
0
0
2
2
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
2
1
2
0
0
1
0
0
0
0
1
2
0
0
0
1
0
0
2
0
0
0
1
1
0
2
1
1
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
4
2
0
0
0
4
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
2
0
0
0
0
5
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
1
0
0
3
0
0
0
1
2
2
0
0
0
0
0
2
0
0
0
1
1
1
0
2
0
0
1
0
2
0
0
1
0
2
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
3
2
0
0
0
0
0
2
2
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
2
1
0
0
0
0
0
2
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
2
2
0
0
0
0
0
0
2
1
0
1
2
1
0
2
0
0
0
0
0
2
2
0
0
0
4
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
2
2
1
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
1
0
2
3
0
1
0
0
0
0
2
2
0
0
1
3
0
0
0
0
0
2
2
1
0
0
0
0
0
2
2
0
0
2
0
3
0
0
2
0
0
2
1
1
1
1
0
0
0
0
3
0
0
0
2
2
0
0
1
2
0
0
0
0
2
0
2
1
0
1
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
2
0
0
2
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
2
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
2
0
3
2
2
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
1
0
1
1
0
0
0
2
0
2
0
0
1
0
0
2
2
2
0
0
2
1
0
1
1
0
0
0
0
0
0
2
2
0
3
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
1
6
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
2
0
2
1
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
2
0
2
2
2
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
4
2
0
1
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
1
2
0
1
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
1
1
0
0
1
0
0
2
2
0
0
0
1
0
0
1
0
0
0
0
9
2
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
9
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
1
2
0
5
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
1
0
0
0
1
0
2
0
0
0
1
1
3
0
2
0
0
0
1
1
0
0
1
1
2
0
0
0
1
1
2
0
1
0
2
0
1
2
0
1
0
2
0
1
2
1
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
1
1
2
0
2
0
0
0
0
1
0
2
2
1
1
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
2
1
2
2
2
0
0
0
0
0
2
0
0
2
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
2
1
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
3
0
0
0
1
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
4
1
2
2
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
2
0
1
0
0
0
2
0
0
0
3
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
1
0
2
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
1
0
1
1
0
0
0
2
0
0
0
0
0
0
2
1
0
0
1
1
0
2
0
3
0
1
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
1
0
2
0
0
0
1
2
0
0
0
0
1
1
0
1
2
0
0
2
0
1
2
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
2
2
0
0
1
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
1
0
0
2
0
1
0
0
0
0
0
0
2
5
0
0
0
0
0
1
0
3
0
0
0
0
0
0
1
0
0
2
1
2
0
0
0
0
2
2
0
0
0
0
2
0
2
0
1
2
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
1
4
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
2
0
1
1
0
1
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
2
0
2
0
1
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
2
1
0
1
0
0
0
2
0
0
1
0
0
0
1
3
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
3
2
2
0
0
0
1
0
0
0
0
0
0
2
1
0
0
2
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
4
0
2
0
0
2
0
2
2
0
1
0
2
0
2
0
0
0
0
0
0
1
2
0
1
0
2
1
0
1
0
2
1
2
0
0
0
2
0
0
0
2
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
2
0
2
0
1
0
1
0
0
0
2
1
2
2
2
1
0
0
0
0
0
2
1
0
1
0
0
0
1
0
1
0
0
0
0
2
5
0
0
0
1
2
2
0
1
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
1
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
1
3
1
0
1
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
2
2
0
0
0
0
2
0
0
1
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
2
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
1
2
0
0
1
1
1
0
2
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
2
0
2
1
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
1
0
0
0
0
2
2
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
2
0
0
0
0
1
2
0
1
0
0
2
2
1
2
2
2
1
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
1
3
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
2
0
0
2
0
0
0
2
2
2
0
2
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
2
5
0
0
0
0
0
2
0
0
1
0
0
2
0
1
0
0
0
1
0
0
1
0
0
0
1
1
2
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
3
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
4
0
1
4
0
0
2
0
1
0
2
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
5
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
1
0
0
0
1
1
0
0
0
0
2
0
1
0
0
2
0
0
2
1
0
0
2
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
2
0
0
0
0
2
0
0
3
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
2
2
0
2
0
0
0
0
0
1
0
0
0
0
1
0
2
3
0
2
2
0
0
0
0
0
0
1
2
0
1
2
2
1
0
0
1
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
5
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
1
0
0
3
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
2
0
0
2
2
0
1
0
1
0
1
2
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
4
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
2
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
2
0
0
1
3
0
0
0
2
1
2
0
0
0
0
2
0
2
0
0
0
1
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
2
1
0
2
0
0
0
0
1
0
0
1
0
1
0
0
0
2
0
0
2
1
0
0
0
2
0
1
0
0
1
0
0
1
2
0
0
2
0
2
0
0
1
0
0
0
1
2
0
0
0
0
0
0
2
0
0
2
1
0
2
0
2
0
0
1
0
0
1
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
5
2
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
1
0
0
2
0
0
2
0
0
0
0
2
1
0
2
0
0
3
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
2
0
0
1
0
2
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
6
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
1
0
0
1
1
0
0
2
0
0
1
0
0
0
0
0
2
0
8
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
1
1
0
2
0
0
2
2
0
0
0
1
0
2
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
1
0
0
0
2
0
0
0
1
0
0
0
0
0
2
2
0
2
1
0
2
0
0
2
0
0
0
2
0
2
2
0
1
0
1
1
0
1
0
1
0
0
0
2
0
0
2
0
1
0
0
0
2
0
2
0
0
0
1
2
2
0
2
0
0
0
2
0
0
0
1
3
2
0
0
1
0
2
0
1
1
0
0
0
0
0
2
0
0
0
1
2
2
0
1
0
1
2
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
1
0
0
3
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
4
1
1
8
0
0
0
0
2
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
3
2
0
0
0
1
1
3
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
3
1
0
0
1
0
1
1
0
0
0
0
2
2
0
0
0
0
3
0
5
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
8
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
5
0
2
2
2
0
2
0
0
0
0
3
0
1
0
0
4
0
0
0
1
0
0
0
2
2
0
1
2
1
0
1
0
0
0
1
0
0
1
1
0
1
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
2
0
2
0
0
0
2
0
1
0
2
0
0
2
0
2
0
1
0
0
2
1
2
0
0
0
1
0
1
0
0
3
0
0
1
0
2
1
0
0
0
2
0
1
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
2
0
0
3
0
0
0
1
1
0
1
0
0
2
3
0
0
0
0
0
0
2
0
0
2
2
0
1
0
0
2
0
1
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
2
0
0
2
1
1
2
0
0
0
1
2
0
0
0
0
0
1
2
0
0
0
0
0
0
3
0
0
0
2
1
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
1
0
1
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
1
2
0
0
3
0
0
0
0
0
1
0
0
2
0
0
1
5
4
0
2
0
0
1
0
1
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
1
1
0
0
0
2
1
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
2
0
2
1
1
2
0
0
0
0
2
1
1
1
0
0
0
3
3
2
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
1
1
0
2
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
1
0
0
1
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
2
0
2
2
2
1
0
2
0
0
2
0
0
0
0
2
0
2
2
2
0
1
2
1
0
0
0
1
0
1
1
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
4
2
0
0
1
0
1
1
0
0
2
0
0
0
0
1
0
0
3
0
1
0
0
2
0
2
0
0
0
1
0
0
0
0
1
0
0
2
0
0
2
1
0
5
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
2
1
0
0
0
0
0
0
1
0
1
2
0
0
0
3
1
0
0
0
0
2
0
2
0
2
2
0
2
1
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
3
0
0
0
1
0
0
1
1
1
0
0
0
0
2
2
1
2
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
1
2
0
0
0
0
1
1
0
2
1
1
0
0
0
0
2
1
0
0
0
1
0
2
0
0
0
2
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
1
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
3
0
0
2
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
2
2
1
0
2
2
0
1
0
0
0
1
1
0
2
0
0
2
2
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
2
2
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
2
2
2
0
0
0
0
2
1
0
2
0
2
0
0
0
0
2
0
0
0
0
1
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
2
0
2
0
0
1
1
0
2
1
0
0
1
0
0
1
0
3
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
1
0
2
0
0
0
0
0
0
2
0
0
1
1
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
1
1
0
0
0
0
0
0
1
1
0
2
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
2
0
2
0
0
1
0
0
0
0
0
0
2
1
2
0
0
0
1
1
0
0
2
0
0
0
1
0
1
2
0
1
0
0
0
0
0
1
1
2
3
1
2
0
1
2
0
2
0
2
3
2
0
0
2
0
0
0
0
0
2
0
0
0
2
1
0
0
2
3
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
2
0
0
0
2
1
0
0
0
0
2
0
0
0
3
0
1
2
2
0
0
0
0
1
0
3
0
1
1
0
0
0
2
0
1
0
2
0
0
0
2
0
0
0
0
4
0
0
0
1
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
4
2
2
1
1
0
0
0
0
1
0
1
1
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
1
0
0
0
1
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
1
2
0
0
0
0
0
2
0
0
2
2
0
1
1
1
0
1
2
0
1
0
2
1
1
0
0
0
1
0
1
0
0
0
0
0
2
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
2
2
1
1
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
2
2
2
0
0
0
3
2
1
0
0
0
0
0
0
0
1
2
1
0
0
1
4
0
0
2
0
0
0
2
2
2
1
0
2
2
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
1
0
2
0
1
0
0
0
0
0
2
0
0
0
0
2
0
1
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
2
2
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
2
0
0
0
1
0
1
0
1
0
2
2
0
0
0
0
0
0
0
0
1
1
0
2
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
2
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
1
0
0
0
0
2
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
4
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
1
0
0
0
1
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
3
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
2
0
1
0
3
0
0
0
0
0
0
0
2
0
0
1
1
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
1
2
2
0
1
0
0
0
0
1
0
1
0
1
3
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
2
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
1
1
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
2
2
0
2
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
1
0
0
0
3
0
0
1
0
0
0
0
1
0
1
0
2
0
2
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
2
0
1
0
0
1
0
2
0
0
0
0
2
1
0
1
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
1
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
2
2
1
0
0
2
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
2
0
0
0
2
1
0
0
2
1
0
0
0
0
0
0
0
5
0
0
0
0
0
1
0
1
0
3
0
0
0
0
0
0
1
0
2
2
0
0
2
0
2
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
3
0
4
1
0
0
1
2
2
0
0
1
3
2
2
1
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
3
2
1
2
1
0
2
0
0
1
2
4
0
0
0
0
0
1
0
0
2
0
0
1
0
0
2
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
3
0
0
0
1
1
0
0
1
0
1
3
0
4
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
2
1
2
2
0
0
0
0
0
0
2
0
1
0
3
0
0
0
0
1
2
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
3
0
2
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
2
2
1
2
0
0
0
0
0
0
1
0
2
1
1
0
0
0
1
1
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
2
2
1
0
0
0
1
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
2
2
0
0
1
1
1
0
0
0
3
1
0
0
2
0
0
1
0
1
1
0
0
0
2
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
3
1
0
1
0
2
2
0
0
0
0
0
0
2
2
2
3
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
1
1
0
0
2
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
4
1
0
0
0
0
2
1
0
2
0
1
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
2
0
0
4
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
2
2
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
2
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
2
2
0
0
2
1
2
0
2
0
0
0
0
1
0
1
0
0
0
2
0
2
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
3
0
2
0
0
1
0
2
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
5
2
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
1
3
1
0
2
0
2
0
3
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
1
0
2
2
0
0
0
0
2
0
2
0
0
1
1
0
0
1
2
1
0
1
1
1
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
2
2
0
0
2
2
0
3
1
0
2
0
0
0
0
0
0
0
0
0
0
3
2
2
2
3
0
0
0
0
0
0
0
0
0
10
0
0
1
1
0
0
2
0
0
0
5
0
3
0
4
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
2
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
4
2
13
0
1
0
0
1
3
0
1
2
0
0
1
1
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
1
1
0
0
0
0
2
0
0
0
0
1
2
1
0
0
2
0
0
2
1
2
0
0
0
0
0
0
1
4
0
0
0
0
0
2
1
0
1
2
0
0
0
0
0
1
0
0
0
1
2
0
2
1
0
0
0
0
2
0
2
0
0
1
2
0
0
0
1
2
0
0
0
2
2
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
3
0
0
0
0
2
2
0
0
0
3
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
4
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
3
2
0
1
0
0
1
4
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
1
1
1
0
0
0
2
1
0
0
2
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
5
1
0
2
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
5
4
0
0
1
0
0
2
1
0
0
0
0
0
2
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
2
3
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
1
0
0
0
0
0
2
0
3
0
0
0
0
0
1
0
0
0
1
0
1
1
0
2
0
0
2
0
0
0
2
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
4
0
0
0
0
1
1
0
3
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
2
0
2
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
3
1
0
0
0
0
0
2
1
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
2
2
0
1
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
4
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
1
0
0
3
0
0
0
0
1
0
0
0
0
1
3
0
0
0
1
0
0
1
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
4
2
0
0
4
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
1
2
0
0
0
0
3
0
2
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
1
0
0
1
0
0
0
1
4
0
0
0
0
0
0
0
0
0
3
0
0
2
0
2
0
0
0
1
1
0
0
0
0
2
0
0
1
0
1
2
0
1
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
1
2
2
1
0
1
0
0
0
0
0
0
0
0
1
2
0
3
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
1
1
0
1
0
0
0
0
0
0
2
1
0
0
0
3
0
1
0
0
0
0
0
2
2
0
0
0
2
0
0
2
0
0
2
2
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
1
0
0
2
2
2
0
0
2
0
0
0
5
0
0
1
0
0
0
2
0
2
0
0
2
2
0
3
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
1
2
0
0
0
2
1
0
2
0
0
0
0
0
0
0
1
2
0
0
1
0
1
0
1
1
0
0
0
0
0
2
0
1
0
2
0
0
1
0
0
0
1
2
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
1
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
2
3
2
0
2
0
2
1
1
2
0
0
2
0
1
0
1
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
1
1
2
0
0
0
2
0
1
0
0
1
2
2
0
1
2
0
0
4
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
1
1
0
0
0
2
0
1
2
0
0
2
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
2
0
2
0
1
1
0
1
1
1
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
1
0
3
2
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
1
0
2
3
1
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
1
0
0
1
1
3
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
1
3
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
1
2
0
0
0
4
0
2
0
0
0
0
1
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
1
1
1
0
0
3
3
0
0
0
0
1
1
1
0
1
0
1
3
0
0
2
1
2
1
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
1
0
0
10
1
1
0
0
0
2
0
0
0
0
0
2
1
2
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
3
0
1
0
2
0
2
2
0
0
0
0
0
0
0
2
1
0
0
1
1
0
2
0
0
1
0
0
0
0
1
1
0
0
3
0
0
2
1
1
0
0
0
2
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
2
0
0
0
1
0
0
2
0
1
2
0
0
0
0
0
0
1
0
1
2
0
0
0
1
2
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
3
0
0
0
2
0
2
0
0
0
3
0
0
0
0
0
1
0
0
0
1
2
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
5
1
2
0
0
0
2
0
0
0
0
1
0
2
0
0
0
1
2
0
3
0
0
0
0
0
0
0
0
0
1
3
0
0
0
2
0
0
0
0
1
0
0
3
0
0
0
1
0
2
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
1
0
2
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
2
0
1
0
0
2
0
0
2
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
2
0
1
1
2
0
0
0
0
0
2
1
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
2
0
2
0
2
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
1
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
3
0
1
3
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
1
5
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
2
1
2
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
3
0
0
2
3
0
0
0
0
1
2
0
0
1
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
3
2
2
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
2
1
2
2
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
1
0
1
0
2
2
0
5
2
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
1
0
0
5
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
1
0
2
0
0
2
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
2
2
0
0
2
0
0
2
2
0
2
0
1
1
0
1
0
2
0
2
1
1
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
3
3
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
2
2
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
1
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
1
0
0
0
0
0
0
0
2
0
0
0
0
3
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
1
3
1
1
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
1
0
0
1
2
2
0
1
2
0
2
0
1
0
0
2
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
2
0
0
0
5
0
0
1
0
0
0
2
0
0
0
1
0
2
0
0
1
2
1
0
0
0
4
3
2
0
0
0
0
0
0
1
1
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
1
2
1
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
2
0
0
0
1
0
2
2
0
0
0
0
0
1
2
0
0
0
0
0
4
0
0
0
0
0
1
0
0
1
0
2
1
0
0
0
0
0
2
0
0
0
1
0
0
1
1
0
0
2
1
0
2
0
2
0
0
0
0
0
0
2
0
1
1
2
0
0
0
0
0
0
0
0
0
0
2
2
1
3
3
0
0
0
0
0
3
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
1
1
0
0
1
2
0
0
1
0
0
1
0
1
7
1
2
0
0
1
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
2
2
0
0
1
0
0
1
2
0
0
2
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
1
1
0
1
0
1
0
0
0
2
0
0
1
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
1
1
2
1
0
0
0
0
0
0
0
2
0
1
0
0
2
0
2
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
7
0
0
0
0
0
1
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
3
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
1
2
0
0
0
0
2
0
1
3
0
0
0
0
1
3
2
0
0
2
0
0
0
0
0
0
0
9
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
1
2
1
1
0
0
0
2
2
1
5
2
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
2
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
1
0
1
0
2
0
0
2
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
1
0
0
2
1
0
0
1
0
0
0
3
0
0
1
2
0
1
1
2
0
0
3
0
2
2
2
0
0
1
3
2
0
1
0
0
0
0
0
2
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
2
2
0
0
0
0
0
1
2
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
1
0
1
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
2
6
1
1
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
2
1
0
1
0
0
0
0
4
0
2
2
0
1
0
0
0
1
1
0
0
1
0
0
0
2
0
1
0
1
0
0
0
0
1
0
0
1
0
0
1
2
0
2
3
0
0
0
0
2
0
0
0
3
0
2
0
0
2
0
0
0
1
0
2
0
3
0
2
2
0
2
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
1
0
1
2
0
1
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
4
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
2
0
1
0
0
0
0
0
0
0
1
1
1
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
8
0
1
1
0
1
0
1
0
2
2
0
2
1
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
1
0
0
1
0
0
0
0
2
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
2
2
2
0
0
1
0
1
2
0
1
0
0
0
0
0
0
0
1
0
2
0
2
1
0
0
0
2
0
0
0
2
0
1
0
0
1
2
1
0
0
0
0
0
0
0
2
0
0
2
1
0
0
1
2
0
2
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
2
0
2
0
0
1
0
0
0
1
0
0
0
2
0
0
2
2
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
1
1
0
0
2
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
1
0
0
2
0
1
1
0
2
1
0
0
0
1
0
2
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
3
1
0
0
0
0
2
0
2
4
1
0
1
0
1
0
3
3
0
1
2
1
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
1
2
1
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
3
1
2
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
1
1
1
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
3
0
1
0
0
0
0
2
2
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
4
0
0
0
6
0
0
1
0
1
1
0
1
0
1
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
1
0
0
2
0
2
0
2
1
0
1
0
0
1
0
1
0
1
0
2
0
0
4
2
0
1
2
0
1
0
2
2
2
2
0
1
2
3
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
2
6
0
0
3
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
1
3
0
0
7
0
0
0
0
3
3
1
2
0
1
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
2
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
8
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
4
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
2
0
2
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
3
0
1
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
1
1
1
2
0
0
0
0
0
1
1
0
0
5
1
0
0
0
0
0
0
0
0
2
0
0
6
1
1
0
2
0
1
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
2
2
0
0
1
0
0
0
0
0
2
0
0
2
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
2
0
0
3
2
0
2
0
3
0
0
2
1
0
1
0
1
1
0
0
0
0
2
0
0
0
0
0
0
1
2
2
0
1
0
0
1
0
0
0
0
0
0
0
2
2
0
1
2
0
0
0
0
1
0
2
1
0
0
0
2
0
0
3
0
0
0
3
0
3
0
0
2
1
0
0
0
2
0
2
1
0
0
0
0
1
1
0
0
2
0
1
0
1
0
2
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
3
3
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
3
0
0
2
0
0
0
0
0
0
3
1
0
0
2
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
2
2
0
0
3
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
2
0
2
1
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
3
2
0
0
2
0
1
0
1
1
0
0
0
1
1
2
2
0
1
1
0
0
0
0
0
0
1
0
0
0
2
1
4
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
2
4
2
0
0
0
0
2
0
0
3
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
2
0
0
2
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
1
0
1
2
2
2
1
0
0
0
0
0
0
0
0
1
0
2
6
0
2
1
1
1
0
0
0
3
0
0
0
0
0
0
1
0
2
2
0
0
2
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
2
3
0
0
0
2
0
1
1
1
0
1
0
0
0
0
0
2
2
0
0
0
2
2
1
0
1
2
3
1
2
0
0
0
0
0
0
0
0
0
2
4
2
0
0
0
0
3
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
3
0
0
2
0
1
3
1
0
0
0
0
0
0
1
1
0
0
2
0
0
2
1
2
1
2
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
2
0
0
2
1
1
1
0
0
0
1
1
1
0
1
0
0
0
0
0
2
0
0
0
0
1
1
2
0
0
2
0
0
0
0
2
0
0
0
14
1
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
3
0
0
2
0
0
0
2
0
0
0
0
0
2
0
1
0
1
1
0
2
2
1
1
0
0
0
2
7
1
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
4
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
3
0
1
2
1
0
0
1
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
4
0
0
1
0
0
0
0
2
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
1
2
0
0
0
2
1
0
0
0
0
1
1
2
1
0
2
0
0
2
1
1
0
0
1
1
1
0
1
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
1
2
2
0
0
2
0
1
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
1
1
1
2
0
0
0
0
1
0
0
0
1
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
2
2
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
1
1
1
0
1
0
0
2
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
2
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
2
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
6
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
1
0
2
2
1
0
0
0
2
2
0
0
1
2
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
2
0
2
0
0
3
0
0
0
0
2
0
0
2
0
0
0
0
2
0
4
0
1
0
0
0
0
0
2
0
0
0
0
3
2
0
2
1
0
3
0
1
0
0
0
0
2
0
3
0
0
0
2
0
0
2
0
0
0
0
0
1
1
0
0
1
0
1
0
3
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
2
0
1
0
0
0
0
0
1
1
0
3
0
0
0
0
0
0
2
0
0
0
5
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
1
0
0
3
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
3
0
0
2
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
2
1
0
2
1
0
0
0
1
0
1
2
2
2
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
3
0
1
0
0
0
2
2
0
0
0
6
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
2
0
0
1
2
1
0
0
0
2
1
0
2
0
0
0
1
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
2
2
0
0
3
0
1
1
1
3
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
2
0
0
1
0
0
1
1
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
2
1
0
0
1
0
2
0
0
0
0
1
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
1
2
0
0
2
1
0
0
1
0
2
0
0
0
1
0
0
1
0
1
0
0
0
0
2
0
0
0
2
0
0
1
0
1
0
0
0
0
0
2
0
0
2
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
1
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
4
1
1
0
0
0
0
1
2
0
0
0
1
1
0
2
0
2
0
0
0
0
0
0
0
0
1
3
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
1
1
3
0
0
3
1
0
0
0
1
0
2
0
0
0
2
0
2
1
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
1
2
0
2
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
1
0
0
2
0
3
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
1
0
0
0
2
0
2
2
2
0
0
0
1
1
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
3
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
8
0
0
0
1
0
1
0
0
1
1
0
1
2
0
0
0
0
3
0
0
1
0
0
1
0
0
1
1
0
2
0
3
0
1
1
0
1
1
2
0
0
2
1
0
0
0
3
2
0
0
3
0
3
0
0
0
0
0
3
0
0
0
0
2
1
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
2
0
4
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
2
2
0
0
1
0
6
1
0
0
1
0
0
0
1
0
0
2
0
0
1
2
0
0
0
0
0
1
0
0
0
2
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
4
2
0
1
0
1
0
0
2
0
0
1
0
2
0
0
0
1
0
0
3
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
1
1
2
0
0
0
2
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
1
2
0
1
0
1
0
2
0
2
2
0
0
1
0
0
1
0
0
0
2
0
0
0
1
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
1
0
0
0
2
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
1
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
1
3
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
1
2
0
2
0
2
0
1
0
0
0
0
1
0
0
0
1
0
7
0
0
0
0
0
1
0
3
2
0
0
0
2
0
0
0
0
2
1
1
0
0
0
2
0
0
4
0
0
2
0
0
4
3
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
3
3
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
4
0
2
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
1
0
0
0
0
2
0
2
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
3
0
0
0
0
0
0
0
0
2
1
0
2
1
0
3
0
3
1
2
0
1
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
1
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
2
0
2
0
4
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
4
0
0
2
1
0
1
2
1
2
2
0
1
0
0
0
1
0
0
0
1
0
0
0
0
3
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
1
1
1
0
0
1
0
1
1
0
1
0
0
0
0
0
1
0
2
0
2
3
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
2
2
0
1
0
0
0
0
0
0
2
0
0
1
2
2
2
2
0
0
0
0
0
0
0
0
1
0
2
3
0
0
0
1
0
0
1
2
0
1
0
0
0
0
1
0
0
0
4
0
0
0
1
0
0
0
0
0
0
1
3
5
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
3
1
2
0
0
0
0
0
1
0
0
1
2
0
0
0
0
2
1
0
0
0
0
0
1
1
1
0
0
1
2
0
3
0
2
0
0
0
1
0
0
2
1
0
2
0
1
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
2
0
0
5
0
0
0
1
0
1
1
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
1
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
2
2
0
0
0
1
0
0
2
0
1
0
0
0
0
1
2
0
0
0
0
0
2
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
5
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
2
1
1
1
2
0
2
0
2
0
0
2
0
0
0
0
0
0
1
3
0
0
2
0
2
0
0
1
0
2
0
1
0
1
0
0
1
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
1
0
2
0
2
2
0
1
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
1
0
0
0
1
0
0
1
2
0
0
2
2
0
0
1
0
0
0
0
0
0
1
1
0
2
0
0
2
0
0
0
0
1
2
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
2
0
0
0
1
0
0
0
1
2
2
1
0
0
0
0
1
1
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
1
1
0
0
2
0
0
1
0
2
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
5
0
0
1
2
1
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
2
2
1
4
0
0
0
6
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
1
1
0
0
0
0
0
0
0
0
2
0
2
1
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
2
1
1
3
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
6
0
0
0
0
1
1
0
0
0
0
2
0
1
0
1
1
0
1
1
0
2
0
0
2
0
2
2
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
2
3
1
2
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
2
0
0
3
0
0
0
0
0
0
0
2
0
0
2
0
0
4
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
1
0
2
0
4
0
0
0
0
0
0
0
0
7
0
0
2
0
0
2
0
1
0
2
0
0
0
1
9
2
0
1
0
2
0
0
0
0
0
0
1
0
1
2
0
0
0
0
1
1
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
3
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
2
0
0
2
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
2
0
2
2
0
2
0
0
1
2
0
2
1
3
0
0
0
1
2
0
0
0
0
0
0
1
2
1
2
0
2
0
0
0
0
0
0
1
3
2
0
0
2
0
0
0
0
0
1
0
2
2
1
0
4
1
0
0
0
0
1
0
0
2
0
0
0
4
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
2
1
1
0
0
0
0
0
0
0
0
1
0
0
2
1
1
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
1
2
0
2
0
0
2
0
1
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
3
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
1
0
1
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
3
1
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
2
0
1
0
1
0
0
2
1
0
0
0
0
0
4
0
0
2
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
2
2
0
0
1
1
1
0
0
0
0
0
0
2
0
0
2
0
1
1
2
1
1
0
0
2
2
0
0
1
1
4
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
1
1
0
2
0
2
0
0
2
0
0
2
2
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
7
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
2
2
1
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
1
2
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
2
2
1
0
2
0
0
0
2
0
0
2
1
2
1
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
2
0
2
0
0
0
0
0
2
0
1
0
0
0
2
2
0
2
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
3
0
0
2
0
0
0
0
0
2
1
0
0
0
0
2
0
2
0
0
1
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
3
2
2
0
0
1
0
0
0
2
0
0
0
1
1
0
1
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
2
1
0
2
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
1
2
2
0
1
3
2
2
0
0
0
0
2
1
0
0
0
1
1
2
3
0
2
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
2
0
1
2
2
0
1
0
2
0
0
2
0
1
2
2
0
1
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
1
1
1
0
0
0
0
0
2
2
1
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
1
2
0
2
0
0
0
0
3
1
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
1
0
3
0
0
0
1
2
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
2
0
0
0
2
1
1
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
1
0
1
2
0
2
2
0
0
0
2
0
0
0
0
0
0
2
2
1
0
0
0
2
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
3
0
0
0
0
1
0
2
1
0
1
0
0
0
0
0
0
3
1
2
0
0
1
2
1
0
2
0
0
0
0
0
0
1
2
3
1
0
0
0
0
2
0
0
1
1
0
0
0
1
0
1
0
1
0
0
0
0
0
1
2
0
0
0
2
2
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
2
0
0
0
2
0
0
1
2
0
0
0
1
1
0
0
0
2
2
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
2
0
0
1
2
3
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
2
0
0
2
2
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
2
0
0
2
0
0
0
2
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
8
1
1
1
0
0
0
0
0
2
0
2
0
1
0
0
0
1
0
2
0
0
2
0
0
0
0
0
1
5
1
1
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
1
1
0
0
0
0
4
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
3
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
2
0
3
2
0
0
0
1
1
0
2
0
1
0
2
0
0
2
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
1
2
1
0
0
0
0
0
0
2
1
3
0
0
0
0
0
0
2
0
2
0
0
0
0
1
2
0
0
2
0
1
0
0
0
1
1
0
2
0
0
0
0
1
0
0
1
0
0
0
0
2
0
2
1
0
0
0
1
0
1
0
2
0
1
0
1
2
1
1
1
0
3
0
0
0
0
0
2
0
0
1
0
2
0
1
1
0
0
0
0
0
0
4
2
0
0
4
1
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
2
3
0
3
1
0
0
0
0
3
2
1
2
2
2
0
0
1
0
0
0
1
0
0
3
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
1
2
0
1
1
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
1
1
0
5
1
1
0
0
1
0
2
2
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
1
2
2
0
6
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
1
0
0
0
2
0
0
0
0
1
1
0
0
1
0
1
2
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
3
2
0
0
2
1
0
0
0
0
0
2
1
1
0
1
1
0
0
0
0
0
0
1
0
2
0
1
2
0
0
0
0
0
1
2
0
1
2
1
0
0
0
0
3
0
0
0
0
5
0
0
0
0
0
1
1
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
2
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
2
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
2
0
0
0
0
1
0
0
0
0
2
0
1
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
1
0
2
0
0
0
0
0
1
0
0
2
0
0
0
4
2
0
0
0
0
0
0
0
3
0
0
2
1
0
0
0
0
1
0
0
0
0
1
1
0
2
0
0
0
3
0
0
0
1
0
0
1
0
2
0
2
1
0
2
0
2
0
0
0
0
2
1
1
0
2
2
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
2
3
1
0
0
0
0
0
0
0
0
1
1
5
0
0
0
0
2
0
1
0
0
1
1
2
0
0
0
1
0
0
0
0
0
0
0
0
1
3
2
0
0
0
1
1
0
0
1
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
2
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
2
0
2
5
0
0
0
0
1
1
0
0
0
1
0
1
7
0
0
0
1
2
1
0
0
0
2
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
5
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
1
1
1
1
1
0
0
0
0
1
1
0
0
0
2
0
2
2
0
1
0
0
0
1
0
0
2
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
1
0
2
1
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
1
0
0
0
0
0
0
0
2
1
0
2
2
2
0
0
0
0
0
1
0
2
1
0
2
0
2
2
0
0
0
0
0
1
0
0
0
2
1
2
1
0
0
1
2
0
0
0
0
0
0
0
0
1
2
0
1
1
2
0
0
2
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
2
0
0
0
1
1
0
0
2
0
1
0
0
0
2
2
0
0
0
0
0
1
0
2
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
5
0
2
1
0
0
2
2
0
2
0
0
0
0
5
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
2
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
2
1
0
1
4
0
0
0
3
0
0
3
3
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
3
2
1
1
0
2
0
1
0
0
2
2
0
0
0
0
1
0
0
0
0
1
1
0
1
2
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
2
0
3
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
2
1
1
2
0
0
0
1
0
0
1
0
1
2
0
0
1
1
0
0
3
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
2
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
1
3
0
0
0
2
0
0
4
1
0
1
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
1
1
2
3
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
3
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
4
2
0
5
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
2
2
2
0
0
2
0
2
0
0
2
0
0
0
1
0
0
0
0
1
0
0
2
1
0
0
0
0
0
1
0
0
2
0
2
0
1
2
2
2
0
4
0
1
0
3
1
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
2
0
2
2
0
0
1
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
2
3
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
3
1
2
1
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
2
2
2
0
0
0
0
0
3
1
1
2
1
0
2
0
0
0
2
1
2
0
0
0
0
0
1
0
0
2
1
0
0
0
1
0
2
2
2
0
0
3
0
0
0
0
0
1
1
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
2
1
1
0
0
0
0
0
2
0
0
0
2
0
1
0
0
2
0
0
2
2
2
0
2
0
2
1
0
0
1
0
0
0
1
1
0
0
3
0
0
0
0
2
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
4
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
2
2
0
1
0
1
5
0
0
2
2
3
1
1
0
0
0
1
0
0
1
0
0
1
0
1
1
2
0
3
0
0
2
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
2
0
0
1
0
2
1
0
0
0
0
0
0
2
2
0
0
2
2
0
1
1
2
1
2
0
1
0
2
1
2
0
1
0
0
1
0
0
0
2
0
2
0
0
1
0
0
0
0
0
1
0
2
0
0
0
1
1
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
4
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
4
0
1
1
1
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
1
3
0
0
2
1
0
0
0
1
0
1
0
0
0
0
3
0
0
0
5
0
3
0
2
0
1
0
1
1
0
0
1
1
1
2
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
4
0
2
0
0
0
2
2
2
0
2
0
2
0
0
2
0
0
0
1
0
2
1
0
0
0
0
0
0
1
2
0
0
2
2
1
2
1
0
0
1
0
3
0
0
3
1
0
0
0
1
0
0
1
0
2
0
1
0
0
0
0
0
1
0
2
1
0
0
0
0
2
0
2
0
2
0
1
0
0
0
0
0
2
1
0
1
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
1
2
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
3
0
2
2
0
0
0
0
1
0
0
1
2
0
1
0
2
0
0
0
1
0
0
2
0
1
1
0
2
1
0
0
1
0
1
0
1
0
0
11
0
0
0
0
2
1
0
1
0
0
0
2
0
0
0
0
1
1
0
1
6
0
0
2
0
0
1
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
2
0
0
2
0
0
0
0
2
0
0
3
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
1
0
2
2
0
0
0
2
1
1
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
1
1
0
4
2
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
1
0
1
1
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
2
0
0
0
0
1
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
2
0
0
1
0
0
0
0
1
0
3
0
0
0
0
5
0
1
1
1
0
0
1
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
2
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
1
0
1
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
1
2
0
0
1
0
0
2
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
1
1
2
3
3
2
2
0
0
0
0
0
0
1
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
1
0
6
0
0
0
1
0
0
1
1
0
1
0
0
0
2
0
2
0
1
0
0
0
0
0
1
0
1
0
0
2
2
0
0
0
0
1
0
0
2
0
0
0
0
2
2
3
0
0
2
0
0
0
0
2
0
2
0
3
2
1
2
4
2
2
2
3
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
2
1
2
2
2
0
1
0
0
0
0
1
0
1
1
2
0
1
0
1
0
0
0
0
2
2
0
0
0
0
0
1
2
2
2
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
1
0
0
2
0
1
0
0
1
1
0
0
2
0
1
0
2
5
1
0
1
0
0
4
3
0
0
3
2
1
0
0
0
1
0
0
0
2
0
2
1
0
0
0
0
1
2
0
1
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
2
0
0
2
0
0
1
0
0
0
0
2
0
2
0
2
2
1
2
0
0
0
2
1
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
1
2
2
0
2
0
0
1
0
3
2
0
2
1
3
0
0
0
0
0
0
2
0
1
0
0
0
2
0
1
2
0
0
1
2
0
0
1
0
0
0
0
1
0
1
0
0
2
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
4
0
2
1
0
1
1
0
2
0
0
0
0
0
2
1
0
1
0
2
0
0
0
0
0
1
0
0
2
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
1
1
2
0
0
1
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
1
0
0
4
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
2
0
1
3
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
2
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
2
0
2
1
1
1
0
1
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
1
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
5
0
6
1
0
0
0
2
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
1
1
0
0
1
2
1
0
0
2
0
1
0
2
1
0
2
0
0
1
0
0
0
2
0
0
1
0
0
2
1
1
0
0
0
0
1
2
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
1
0
2
0
0
1
0
0
2
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
1
2
0
0
2
1
0
0
0
0
2
0
1
0
0
2
0
2
1
0
1
0
0
0
1
5
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
1
0
0
2
3
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
2
2
0
2
0
0
0
0
0
0
1
2
0
1
0
6
0
2
3
0
2
0
1
0
1
0
1
0
2
0
2
0
0
4
0
2
2
0
0
0
3
2
0
0
0
1
0
0
3
1
0
1
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
1
1
0
2
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
3
0
2
1
2
0
2
1
0
0
0
3
0
0
0
0
2
0
0
1
1
0
2
0
1
0
0
0
0
0
0
0
1
0
0
1
0
2
2
7
0
0
0
0
1
0
0
2
0
0
2
1
0
0
0
0
0
0
0
1
1
0
0
2
0
0
2
0
0
0
2
0
0
2
3
1
2
0
1
0
0
0
0
1
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
1
0
2
0
0
1
0
0
1
1
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
2
2
4
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
2
2
0
2
0
0
0
0
1
2
0
0
0
1
0
2
2
0
0
2
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
3
2
2
2
0
0
0
0
1
0
6
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
3
0
0
4
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
3
0
2
0
2
0
0
0
1
1
0
0
0
2
1
0
0
5
0
0
0
0
0
0
1
0
0
0
4
1
0
0
0
1
0
0
1
0
0
0
0
2
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
2
0
2
0
0
0
1
0
0
0
1
1
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
2
0
0
1
0
0
3
1
0
1
1
2
0
0
1
2
0
0
3
0
0
0
0
2
0
8
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
2
0
1
0
2
0
4
0
2
0
0
1
0
0
0
0
0
0
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
2
2
2
3
0
1
0
0
0
0
0
0
1
3
1
1
2
0
0
1
0
2
0
1
0
0
0
0
3
0
1
0
0
0
1
2
0
0
0
0
0
0
1
0
0
3
0
0
1
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
11
2
0
0
0
1
0
0
0
0
1
1
0
0
0
2
0
1
0
0
0
1
0
2
0
2
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
2
0
0
0
0
1
0
0
1
0
2
0
0
0
2
0
4
0
2
0
2
0
2
0
0
1
3
0
0
1
0
1
0
0
0
0
0
2
1
0
0
1
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
2
0
0
0
2
1
0
1
1
0
0
0
0
0
2
0
2
1
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
1
2
1
2
2
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
2
2
0
2
0
1
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
1
0
1
0
0
0
0
2
0
0
0
0
3
1
2
0
0
0
2
0
0
0
0
0
2
0
1
0
1
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
3
0
2
0
1
0
0
0
2
0
0
0
2
0
2
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
1
2
0
2
1
2
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
1
1
0
0
2
0
0
1
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
2
0
2
2
1
0
2
0
0
0
10
0
1
0
3
1
2
0
0
1
0
0
2
0
2
0
0
0
2
1
3
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
6
1
0
1
0
0
0
0
1
0
0
0
3
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
2
0
2
0
1
0
0
0
2
2
0
0
0
1
0
0
1
0
2
0
2
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
1
2
1
1
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
1
0
1
2
2
2
0
2
0
0
2
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
1
0
3
0
0
2
1
0
0
3
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
1
0
0
2
0
2
1
0
0
0
0
0
0
1
2
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
1
1
0
0
0
0
2
0
0
0
0
0
0
4
1
0
0
0
0
1
1
0
0
0
0
0
5
2
2
0
0
0
0
0
0
2
2
0
0
2
0
0
3
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
2
1
0
2
0
3
0
0
0
0
1
3
0
0
1
0
0
1
0
1
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
2
2
0
0
0
1
0
0
2
0
0
1
2
0
0
0
1
2
0
1
0
0
0
0
1
0
0
0
1
0
0
2
1
0
0
0
0
2
0
1
0
0
1
0
0
0
2
0
1
0
1
0
0
0
1
0
0
2
1
2
2
0
1
0
0
2
13
0
0
2
3
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
3
0
1
0
2
1
0
0
0
1
0
0
2
0
0
0
0
0
3
0
0
1
0
0
0
0
2
0
0
3
1
0
0
2
0
0
0
3
0
1
2
0
0
2
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
4
1
1
0
0
0
2
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
2
2
2
0
0
2
1
0
0
1
0
0
1
0
0
2
0
0
2
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
2
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
2
0
0
3
3
0
0
0
0
0
0
2
3
3
0
0
2
2
0
0
0
0
0
1
0
0
0
2
3
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
2
1
0
0
0
0
0
0
2
0
0
1
2
1
0
0
2
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
3
1
0
0
0
0
1
1
0
1
0
0
0
3
2
0
0
0
0
0
2
0
0
0
1
2
0
0
2
1
0
2
0
2
0
0
0
0
0
2
2
0
0
1
2
3
1
0
0
1
0
2
2
0
2
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
3
1
0
2
2
0
0
0
9
2
0
0
0
0
2
0
4
0
2
2
0
0
0
0
0
2
0
0
0
0
0
3
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
4
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
1
2
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
1
0
0
2
2
0
2
0
0
0
1
0
2
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
2
0
2
0
0
0
1
0
0
2
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
1
0
1
0
0
0
2
2
1
0
4
0
0
2
0
0
0
0
0
0
0
1
0
4
0
2
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
4
2
1
0
0
0
3
0
0
0
1
5
0
0
2
1
0
0
1
0
0
0
2
2
0
0
0
0
1
0
1
1
0
0
1
0
0
1
1
0
2
0
0
0
0
1
0
1
0
1
0
0
1
0
0
1
6
1
1
1
0
2
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
2
2
1
0
0
2
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
1
1
0
1
0
1
0
0
3
1
2
0
1
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
2
0
2
2
0
0
1
0
0
0
0
1
0
1
2
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
3
0
0
0
2
0
0
1
0
1
0
0
0
1
0
2
1
1
0
1
2
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
1
0
0
1
0
0
1
2
0
0
1
1
0
0
0
0
2
0
1
1
0
0
0
0
2
1
0
4
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
1
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
1
0
0
0
2
0
1
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
1
1
2
1
0
1
0
0
2
1
0
0
1
2
0
0
0
0
2
0
1
0
2
0
1
0
0
0
0
1
0
1
4
1
0
0
1
0
0
0
0
1
0
1
1
0
2
0
0
0
0
0
0
0
2
0
2
1
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
2
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
3
0
1
1
2
2
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
1
0
0
1
0
1
2
0
0
0
1
0
0
0
2
0
1
1
0
0
1
0
0
0
0
0
3
1
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
1
2
2
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
1
0
0
2
0
0
1
0
0
1
1
2
0
0
1
2
0
2
1
0
0
1
0
0
2
0
0
0
0
0
1
0
0
5
0
0
0
0
0
1
2
1
0
0
2
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
3
0
2
0
0
0
1
0
3
0
2
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
1
1
0
0
2
1
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
2
1
2
1
1
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
5
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
1
0
0
1
0
2
1
1
0
0
0
0
0
2
0
0
0
1
0
2
1
0
0
0
0
0
0
0
6
0
0
0
0
1
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
1
1
2
1
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
1
1
0
0
0
1
0
0
0
3
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
4
0
0
0
2
0
2
0
1
1
0
1
0
0
0
0
0
3
2
0
1
0
0
0
2
0
2
0
0
0
0
2
0
0
2
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
3
2
2
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
4
0
2
0
1
0
1
0
0
0
0
0
2
0
0
0
0
1
2
0
2
2
0
0
2
1
0
0
2
4
0
0
0
0
0
0
5
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
7
0
0
1
0
1
0
1
4
0
0
1
0
2
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
3
2
0
0
2
4
2
0
1
2
0
0
0
0
0
2
0
1
0
0
0
2
0
1
2
0
0
0
0
0
1
1
2
3
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
2
2
0
2
2
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
2
0
3
0
0
2
1
1
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
2
2
0
0
0
0
4
0
0
1
1
0
0
0
0
2
0
1
1
2
0
0
0
2
1
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
1
0
1
2
0
2
2
0
0
1
1
1
2
0
0
3
0
1
1
0
0
0
0
0
2
1
1
0
0
0
3
0
0
1
1
0
0
1
0
1
1
3
1
1
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
2
0
0
1
1
0
0
0
0
1
2
0
0
0
2
0
1
1
3
0
0
0
0
3
0
2
0
0
0
1
2
0
0
0
2
0
0
0
1
1
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
1
0
0
0
3
0
0
2
0
1
0
1
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
1
0
2
0
0
3
2
1
0
0
0
0
0
0
0
0
0
2
2
0
1
2
0
3
0
2
1
0
0
1
0
0
0
0
0
2
1
1
2
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
2
0
0
0
0
1
2
0
0
2
0
0
1
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
1
0
0
0
1
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
4
0
0
1
0
0
1
2
2
2
0
1
1
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
1
1
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
2
2
0
0
1
2
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
1
0
0
0
3
3
0
0
2
2
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7
0
0
0
2
0
0
1
2
0
1
0
1
0
0
0
0
2
1
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
1
2
2
0
2
0
0
0
2
1
0
0
0
0
0
0
1
1
2
2
1
1
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
1
2
2
1
0
0
0
3
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
1
1
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
2
1
0
0
0
1
2
0
0
2
0
0
1
2
1
0
0
0
0
1
2
0
0
0
0
2
2
1
1
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
1
0
4
0
1
3
0
0
0
1
0
0
1
0
0
1
0
0
0
2
0
1
2
0
0
3
0
2
1
0
1
2
2
0
0
0
1
0
0
0
5
0
0
2
2
4
0
0
1
0
0
0
2
0
2
1
0
2
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
2
0
0
0
0
0
0
0
1
1
1
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
1
0
0
1
0
1
1
1
2
2
1
0
1
0
1
0
0
0
1
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
4
2
0
1
2
2
3
0
2
0
0
0
0
2
1
0
0
0
1
0
0
1
0
0
2
0
0
0
5
0
0
0
1
0
3
2
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
3
0
1
1
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
4
1
0
0
2
0
0
1
2
0
1
0
2
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
1
2
1
4
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
4
1
0
0
2
0
0
2
0
0
0
0
3
0
0
0
1
2
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
2
0
0
2
0
3
0
0
0
1
0
0
1
2
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
2
0
1
0
2
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
2
0
2
0
0
0
1
0
0
0
0
0
1
0
1
0
0
2
0
0
1
0
0
2
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
2
2
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
3
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
1
1
1
0
1
0
0
0
0
0
0
0
0
2
1
0
0
3
0
0
0
1
0
6
1
1
0
0
1
1
0
3
1
0
3
0
0
2
0
3
0
0
2
0
3
0
0
1
2
0
0
0
0
0
0
1
1
0
0
2
2
0
0
0
0
0
2
2
0
1
0
2
0
1
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
1
0
1
0
0
0
0
1
0
2
0
0
0
0
4
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
2
0
0
0
0
0
0
2
0
2
0
0
5
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
3
1
0
0
1
0
2
1
0
4
2
2
0
0
0
3
0
0
0
0
1
1
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
6
0
0
0
1
0
0
0
2
0
0
2
1
0
2
0
0
0
0
1
0
0
0
0
2
0
0
2
1
2
0
0
0
2
0
2
0
0
0
0
0
3
0
2
0
1
0
1
0
0
0
1
1
0
0
2
0
7
0
0
0
2
0
4
0
0
0
0
0
3
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
3
0
0
3
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
2
0
1
1
0
0
0
0
0
0
1
0
0
2
0
1
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
1
1
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
4
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
2
0
3
0
1
0
4
0
0
2
0
1
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
4
2
0
0
0
0
0
0
0
2
2
4
0
0
2
0
1
3
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
1
0
0
1
0
2
2
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
2
2
1
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
1
0
2
0
0
0
0
0
3
1
0
1
0
0
0
0
0
0
0
2
0
0
2
1
3
0
0
0
0
3
1
0
0
2
0
0
1
0
0
1
4
0
1
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
2
2
0
1
1
0
0
3
0
2
1
1
0
0
0
0
0
0
1
0
1
0
2
0
0
2
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
2
2
0
0
1
0
0
2
0
0
0
0
0
3
2
0
2
0
0
0
0
2
2
0
0
1
1
1
2
0
0
0
0
2
1
2
0
0
0
0
0
0
1
2
0
2
1
1
0
2
0
0
0
2
0
2
2
1
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
2
0
0
2
0
1
2
0
1
0
2
2
1
0
0
0
1
0
0
0
0
2
0
1
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
3
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
2
0
2
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
2
0
3
2
0
1
0
3
0
0
2
0
3
3
1
0
1
0
0
0
0
0
1
2
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
2
0
1
0
0
4
0
0
0
1
0
0
0
1
0
0
0
0
2
2
2
0
0
0
0
0
0
1
2
1
0
0
0
1
0
2
1
0
0
0
0
0
2
0
0
0
1
1
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
1
0
0
0
2
1
1
0
0
0
2
1
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
1
0
2
0
0
1
0
2
0
0
0
1
0
1
1
1
0
0
0
0
1
0
1
0
0
0
1
1
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
3
0
1
1
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
1
1
0
2
3
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
7
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
1
1
0
0
1
0
0
1
0
0
0
0
4
2
0
0
2
0
0
0
0
0
1
0
0
0
1
1
0
0
1
1
0
1
1
2
0
0
1
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
3
3
0
2
0
0
1
0
0
0
0
1
1
2
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
1
2
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
1
1
0
0
0
3
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
1
2
0
1
2
0
0
0
0
1
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
1
1
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
2
2
0
0
1
1
0
4
0
0
0
0
0
0
1
0
1
0
0
4
1
0
0
0
4
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
2
0
2
2
1
1
0
0
0
0
0
2
2
0
0
1
0
2
0
0
0
0
0
0
0
0
3
6
1
0
1
0
0
7
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
8
1
0
0
0
1
2
1
0
0
4
0
2
0
0
0
2
0
0
0
0
1
2
1
3
0
1
0
0
0
0
3
0
1
0
1
0
0
0
1
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
1
0
1
1
0
0
0
0
2
2
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
2
2
0
2
1
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
2
0
0
2
1
4
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
1
0
2
1
0
0
0
2
2
0
0
0
2
0
0
0
1
3
0
0
0
0
2
0
2
0
1
0
0
1
0
0
0
2
0
2
1
0
1
0
0
0
0
0
0
0
1
1
1
0
2
0
0
0
1
1
0
1
2
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
1
0
2
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
7
0
0
1
0
0
0
0
0
0
0
5
1
0
0
0
1
0
0
0
0
1
1
1
1
0
2
0
2
0
1
2
0
2
0
0
0
0
0
0
3
0
0
0
0
2
0
0
3
0
0
0
2
2
1
0
1
0
3
1
2
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
1
3
0
0
0
0
2
0
1
0
2
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
1
0
0
0
2
0
3
0
0
0
2
2
0
0
0
1
0
0
2
0
0
2
0
1
0
2
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
1
0
1
2
1
0
2
0
2
0
0
0
0
2
0
0
0
1
2
3
0
0
0
0
0
0
0
0
2
0
0
0
0
4
0
1
0
1
0
0
1
2
2
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
1
2
1
0
0
0
2
1
0
1
1
0
0
0
0
1
1
0
1
2
1
1
0
0
0
2
0
0
1
0
0
0
3
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
1
1
2
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
3
2
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
3
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
1
2
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
1
0
1
2
0
0
0
0
2
0
11
0
0
0
1
0
2
0
0
0
2
2
0
2
0
0
0
0
0
1
0
2
0
0
0
0
5
0
0
0
3
3
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
6
0
0
0
0
0
3
0
2
0
0
0
0
1
0
2
0
0
2
2
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
1
2
0
3
0
1
0
0
3
2
0
1
1
1
0
0
0
0
1
0
2
0
0
1
0
1
1
1
1
0
1
0
0
0
0
0
1
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
2
0
1
0
0
0
2
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
2
1
0
0
0
0
0
0
2
0
0
1
0
1
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
3
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
1
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
4
1
3
0
1
0
0
0
2
0
4
0
0
0
0
2
1
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
5
0
1
1
0
0
0
0
2
0
0
0
1
0
2
2
0
0
0
0
1
1
0
0
1
0
0
0
2
1
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
1
0
0
1
2
0
3
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
1
2
2
0
0
1
0
0
0
0
0
2
2
1
0
0
0
0
2
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
2
1
0
0
2
2
0
3
0
0
1
1
0
2
1
0
1
0
0
0
2
3
2
0
1
1
2
0
0
3
1
2
0
1
0
0
0
0
0
1
0
0
2
1
0
0
0
1
1
0
0
1
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
3
2
0
0
0
0
3
0
2
0
1
0
0
0
0
1
0
0
0
0
0
3
0
0
1
2
0
0
0
0
0
0
2
0
1
0
0
2
0
0
2
0
1
0
1
0
0
0
0
1
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
1
2
1
0
0
0
2
0
0
1
1
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
2
0
0
1
1
0
0
0
0
2
1
0
0
0
0
1
1
0
0
0
0
1
0
2
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
2
0
2
0
0
0
0
2
0
0
1
0
1
1
2
0
0
1
2
0
0
0
2
0
2
0
1
0
0
3
3
2
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
2
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
4
1
0
0
3
4
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
1
0
0
2
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
1
1
0
2
0
0
1
0
0
1
2
2
0
0
2
0
0
0
0
0
0
0
1
0
0
1
2
0
1
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
2
2
0
0
0
1
1
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
8
0
0
2
0
0
1
5
0
0
0
0
0
1
0
0
0
0
0
0
1
2
1
2
3
0
0
0
0
2
0
0
1
1
2
1
0
0
0
2
2
2
2
2
2
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
2
2
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
2
0
4
0
2
0
1
3
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
3
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
1
0
1
1
1
2
0
0
2
2
0
0
2
0
0
0
2
0
0
0
2
1
0
2
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
1
0
1
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
3
1
0
0
0
2
2
0
4
3
2
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
1
0
0
2
0
0
2
0
0
0
1
0
0
2
3
0
0
1
0
0
0
1
0
1
2
0
0
2
1
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
1
0
0
0
2
1
0
0
0
2
0
0
1
0
0
2
1
0
0
2
1
1
0
0
1
0
0
0
3
0
1
0
1
0
1
0
0
1
0
3
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
1
0
0
1
0
0
0
2
0
1
3
1
0
1
0
1
0
0
1
0
1
0
0
1
2
0
0
1
2
0
0
2
0
1
0
1
2
0
0
1
0
0
0
0
2
0
0
0
2
1
0
0
1
0
0
0
0
1
1
1
0
1
0
0
0
1
0
2
3
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
1
0
2
0
0
0
0
2
0
0
2
0
1
2
0
0
0
0
0
3
0
0
0
2
0
0
2
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
2
0
1
2
1
0
0
1
0
1
0
1
3
1
0
0
0
1
0
0
0
0
0
0
0
1
2
0
1
0
0
2
0
1
1
0
0
0
0
0
0
1
1
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
3
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
1
0
0
3
0
2
2
1
0
0
0
0
0
2
0
0
0
0
4
0
0
0
0
1
1
2
0
0
0
0
0
1
0
0
2
1
3
1
1
0
0
2
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
1
2
3
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
2
0
2
1
1
2
1
0
0
0
0
1
0
3
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
2
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
1
1
0
1
0
0
0
1
0
1
1
0
2
2
0
0
1
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
4
0
0
0
0
0
0
2
2
2
2
0
0
0
2
0
2
0
0
3
0
1
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
2
0
0
3
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
2
0
2
0
0
0
2
1
2
1
0
1
1
3
0
0
0
0
0
0
1
0
0
2
0
1
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
2
2
0
0
0
2
2
0
0
0
2
0
1
0
0
2
3
0
0
0
1
0
0
0
0
0
0
1
0
2
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
1
1
0
2
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
2
0
2
0
2
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
5
0
0
0
0
0
1
0
0
1
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
3
0
0
1
0
0
1
0
0
1
0
0
1
0
1
0
0
1
0
1
0
0
0
2
1
0
2
2
0
2
0
0
0
0
0
1
0
0
1
0
0
1
0
0
2
0
0
0
0
0
1
0
0
2
2
0
0
1
2
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
8
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
1
0
1
0
2
0
0
0
2
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
2
0
0
0
2
0
0
2
3
1
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
2
1
1
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
1
0
2
0
0
0
0
0
0
0
8
0
0
0
2
1
0
2
2
0
2
0
1
0
2
0
1
1
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
2
2
1
1
1
0
1
0
0
2
0
2
0
0
2
0
0
1
1
0
2
0
4
1
0
1
2
0
0
0
0
1
1
0
0
1
0
0
0
2
1
0
6
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
3
2
2
0
0
0
0
2
0
0
0
2
0
2
0
3
0
0
0
1
0
0
0
1
0
0
2
0
0
1
0
3
3
0
0
2
2
0
0
0
1
4
1
0
2
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
5
0
0
0
2
2
1
0
1
1
1
2
1
0
0
0
0
0
0
1
2
0
0
0
1
0
1
4
0
0
0
0
0
0
2
0
0
0
0
2
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
1
0
1
0
2
0
0
0
2
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
2
7
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
2
0
0
0
1
0
1
1
0
3
0
0
3
1
0
0
1
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
1
0
2
0
0
2
1
0
0
0
1
0
1
0
2
0
1
0
0
0
0
1
2
0
0
0
0
0
1
1
0
1
0
0
0
0
0
3
1
1
2
0
2
2
0
1
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
2
0
1
0
0
1
2
0
0
0
0
0
0
1
0
7
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
3
1
2
0
0
0
2
0
0
0
1
0
2
1
0
2
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
3
1
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
4
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
2
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
1
2
0
2
0
0
0
2
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
2
2
2
0
1
0
2
0
1
0
2
1
0
0
0
1
1
2
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
3
6
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
1
0
3
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
1
3
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
2
0
0
2
0
0
0
1
0
0
0
0
2
0
1
2
0
2
0
0
0
0
0
0
1
0
2
2
0
0
0
1
0
0
0
0
2
0
0
2
0
0
2
0
0
2
0
1
2
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
2
0
0
4
0
2
0
4
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
2
3
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
2
1
2
0
2
0
0
0
0
1
0
0
0
2
0
1
0
2
5
2
0
1
0
0
0
0
2
0
2
0
0
3
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
1
1
0
0
3
0
0
0
1
0
0
1
0
0
3
0
2
0
0
0
2
0
2
0
0
2
0
0
0
1
1
2
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
3
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
2
0
1
0
3
0
0
0
0
3
0
2
1
2
0
1
0
3
0
2
4
0
1
0
2
2
0
1
0
0
0
1
0
0
0
0
1
0
2
0
1
1
0
0
0
0
0
0
4
0
2
0
0
0
1
0
0
0
0
1
1
1
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
1
0
0
0
1
4
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
2
2
2
0
2
1
0
2
2
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
2
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
2
2
0
2
1
0
2
2
0
2
2
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
2
2
0
0
0
0
1
0
2
0
2
2
1
0
0
0
0
2
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
1
0
1
0
2
0
0
0
0
0
0
2
0
0
2
2
1
2
2
0
0
0
0
0
1
0
0
2
0
0
0
1
1
2
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
0
2
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
3
1
0
0
3
6
1
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
1
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
2
0
2
0
0
2
0
2
2
1
2
0
0
1
2
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
1
2
0
2
0
2
0
0
3
0
2
0
0
0
0
1
1
2
0
0
1
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
1
2
0
2
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
2
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
10
0
2
2
1
8
0
0
0
2
0
0
1
3
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
1
0
0
0
3
1
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
1
2
0
0
0
2
0
0
1
0
2
0
0
1
0
2
0
0
1
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
1
0
2
2
0
1
0
0
0
0
1
0
0
0
2
0
1
2
0
0
0
1
1
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
2
0
1
0
0
1
1
2
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
2
2
2
1
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
1
1
1
0
0
1
0
2
3
1
3
0
0
4
0
0
0
1
1
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
1
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
2
0
1
0
0
0
2
0
2
0
0
0
0
6
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
3
0
1
0
1
2
0
0
0
0
0
1
2
0
2
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
8
0
0
0
1
1
0
0
2
1
0
0
0
1
0
0
2
1
0
0
2
0
0
0
0
0
1
0
0
0
1
0
2
2
2
0
0
0
0
2
0
1
0
3
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
3
0
0
1
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
2
2
0
0
0
2
3
0
1
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
2
2
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
3
0
1
0
0
1
0
1
0
0
1
1
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
1
1
0
0
0
0
1
0
1
1
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
5
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
2
3
0
0
0
1
2
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
1
2
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
2
0
0
0
2
0
0
0
1
0
1
0
2
5
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
4
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
2
2
1
0
0
0
0
2
5
0
0
0
2
1
0
0
0
2
0
0
0
1
0
0
4
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
3
2
0
2
1
3
1
2
1
0
0
0
0
0
0
0
2
1
1
2
0
2
0
2
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
2
0
0
1
0
0
1
0
1
1
0
0
1
1
0
2
0
0
0
0
0
0
0
2
1
2
0
0
0
0
2
0
0
0
0
0
0
4
1
0
2
0
2
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
2
0
0
1
0
0
2
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
1
0
0
2
0
0
0
0
0
1
1
2
1
0
0
0
2
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
4
2
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
2
0
0
1
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
2
2
0
1
0
0
0
0
7
1
2
0
0
1
1
0
0
0
0
2
1
2
0
3
0
2
0
0
1
2
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
1
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
4
0
0
1
0
1
0
0
2
1
0
2
0
1
1
0
1
0
2
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
2
2
1
0
1
0
2
0
1
1
1
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
1
2
2
0
0
0
1
0
0
0
0
2
0
1
1
0
0
0
2
2
2
1
0
0
0
0
1
0
2
0
2
2
0
1
0
1
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
3
3
1
1
0
0
0
0
0
0
1
2
2
0
0
2
0
0
0
0
1
0
0
0
0
1
1
0
0
2
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
2
1
3
0
1
0
3
0
0
0
0
1
0
0
0
4
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
2
3
0
0
0
0
1
2
2
0
0
0
3
0
0
0
0
2
3
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
1
1
1
1
0
0
0
1
0
0
0
2
2
0
0
0
0
0
1
0
1
2
0
0
2
0
0
2
0
0
2
3
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
2
0
0
0
0
0
0
1
0
5
2
0
2
1
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
1
0
0
0
1
0
2
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
3
1
1
1
1
2
2
0
0
0
2
1
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
1
0
1
0
1
0
1
0
2
0
0
1
0
0
0
2
0
0
2
0
0
0
1
1
0
0
2
1
0
0
0
0
2
1
2
1
0
0
0
0
0
0
1
0
2
0
0
1
3
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
2
0
4
0
0
0
2
0
0
0
0
0
2
3
0
2
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
1
0
0
1
1
0
6
0
2
1
0
2
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
1
2
0
0
0
0
0
0
2
0
0
4
0
2
0
0
0
0
0
0
2
1
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
3
0
2
0
0
0
3
0
0
3
0
4
0
2
0
0
2
0
1
0
0
0
0
2
1
0
0
0
0
0
2
0
0
1
1
1
0
0
1
0
1
0
2
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
3
1
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
3
0
1
0
0
1
0
0
0
0
0
0
2
2
1
0
0
1
1
2
1
0
0
0
0
0
0
0
0
0
3
0
2
2
0
0
0
2
0
0
1
0
0
2
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
2
1
6
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
1
0
0
1
1
2
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
1
2
0
0
0
1
2
0
0
0
0
0
1
3
2
0
3
0
0
2
0
0
2
0
0
0
0
2
1
0
0
0
2
1
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
1
1
2
2
0
2
1
0
0
0
0
2
1
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
2
0
2
2
0
0
0
2
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
1
1
0
0
2
2
0
0
0
0
0
0
2
2
4
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
1
0
1
1
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
4
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
1
0
3
2
1
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
2
1
1
0
0
1
0
0
0
4
0
1
0
0
1
0
0
0
2
0
2
0
0
2
4
0
1
0
1
0
0
0
0
1
0
0
0
0
2
2
0
1
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
2
2
2
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
2
0
2
0
1
0
1
0
0
0
5
1
0
0
1
0
0
2
1
2
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
2
0
1
0
0
1
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
3
0
0
2
5
0
2
1
0
0
1
0
0
1
2
0
0
1
0
0
2
0
2
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
2
2
1
4
1
2
1
1
2
0
0
1
0
0
0
1
0
2
0
2
0
1
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
1
0
1
0
0
0
2
0
0
0
3
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
2
0
2
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
1
2
0
0
1
1
0
0
1
2
0
0
0
0
0
0
1
2
2
1
2
0
0
0
0
0
3
0
0
0
0
2
0
1
0
2
0
1
0
2
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
2
3
2
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
5
0
0
0
0
0
2
0
1
2
2
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
1
1
2
1
0
0
0
3
0
0
0
0
0
0
0
0
1
1
2
5
2
0
0
2
0
1
0
1
0
0
0
1
0
0
0
1
2
2
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
2
0
1
2
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
1
3
0
1
3
1
0
1
0
0
1
2
0
1
1
0
1
1
0
0
0
0
0
0
0
4
1
0
0
0
2
0
1
0
0
0
0
0
2
2
0
1
0
2
0
1
0
0
0
0
0
0
0
0
2
0
8
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
2
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
5
1
2
1
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
2
0
1
0
1
0
0
2
0
2
0
0
0
1
2
0
0
1
1
0
0
0
0
0
0
2
0
0
1
2
2
0
1
0
0
2
0
0
0
0
0
2
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
1
0
2
2
2
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
1
0
1
0
0
2
0
0
2
0
0
0
0
2
1
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
1
2
0
0
2
1
0
1
0
0
0
2
1
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
2
2
0
2
0
0
0
2
0
0
2
2
0
1
0
0
0
0
0
2
0
0
2
0
2
1
1
2
0
0
0
0
0
0
0
1
1
1
1
0
0
0
1
2
0
0
2
0
0
2
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
3
0
0
0
0
0
1
1
0
0
5
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
2
0
0
0
0
1
1
0
2
0
2
3
0
0
0
0
0
0
0
0
0
2
0
0
1
2
1
0
0
0
2
0
0
0
0
2
1
0
0
2
0
2
0
1
1
0
0
0
0
3
0
0
1
0
0
7
0
0
0
0
1
1
0
2
2
0
0
0
0
2
0
2
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
3
0
3
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
4
0
1
0
0
0
2
0
0
1
0
2
0
0
0
0
1
2
6
0
1
0
1
0
0
1
0
0
3
0
2
0
0
2
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
6
0
5
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
3
0
2
0
0
0
0
2
2
1
0
0
0
2
0
0
0
0
2
0
0
2
1
0
0
0
0
2
1
2
0
1
3
0
2
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
1
1
0
2
0
2
0
0
2
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
1
0
1
0
1
2
0
0
0
2
1
0
0
2
0
0
1
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
1
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
1
0
2
2
0
0
0
0
0
0
1
0
0
0
2
0
1
0
1
0
0
0
1
1
1
0
0
0
0
2
2
0
0
4
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
2
1
0
0
0
0
0
1
0
0
2
0
0
0
0
1
1
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
1
0
1
0
0
0
0
0
3
0
3
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
4
2
0
2
3
0
1
0
0
0
0
0
1
0
1
2
0
1
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
6
0
0
0
2
2
3
0
0
0
1
0
0
0
0
0
0
0
2
1
2
0
0
0
1
0
0
0
0
1
2
0
1
1
0
3
0
0
3
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
1
4
1
4
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
1
2
0
2
5
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
2
0
0
1
0
2
0
2
0
0
0
1
1
0
0
0
0
0
0
0
1
2
0
1
3
1
0
0
0
0
0
0
7
2
1
1
1
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
9
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
2
0
0
3
0
0
0
0
0
1
1
0
0
0
1
0
0
0
3
0
1
2
0
0
3
0
2
0
0
0
4
2
2
1
0
0
2
0
0
1
1
2
0
3
0
0
0
1
2
2
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
2
2
2
2
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
1
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
1
1
0
1
2
0
0
2
2
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
5
0
1
0
0
0
1
2
1
0
0
0
0
0
0
1
1
0
0
1
2
1
2
0
2
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
1
0
0
2
0
0
1
1
2
0
0
0
1
0
1
0
0
2
0
0
0
0
0
5
0
0
1
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
2
1
0
2
1
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
1
0
0
0
0
0
2
1
0
2
1
2
2
0
0
0
0
0
0
1
1
2
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
2
0
1
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
2
1
0
0
2
0
0
1
0
0
0
1
0
0
0
2
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
3
1
2
1
0
2
3
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
1
6
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
1
0
0
0
0
1
0
2
0
0
0
2
0
2
0
0
0
0
0
0
2
0
3
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
1
0
0
0
3
0
2
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
3
1
0
0
6
0
0
2
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
1
3
1
0
2
0
1
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
1
1
0
0
0
2
0
2
1
2
2
1
0
0
1
0
0
0
1
1
0
0
0
0
2
0
2
0
0
1
0
0
0
0
2
1
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
1
1
0
1
0
2
1
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
1
2
3
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
1
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
3
1
4
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
3
0
0
3
0
0
0
0
1
0
2
1
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
1
0
0
2
2
0
2
1
0
0
0
1
0
0
0
1
0
0
0
0
0
3
0
1
1
0
0
0
2
2
0
0
2
0
0
0
2
2
2
1
0
0
2
0
0
0
0
1
1
2
3
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
2
0
0
0
2
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
1
0
3
0
2
1
1
0
0
1
1
0
2
1
0
1
0
3
0
2
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
3
0
2
0
1
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
2
0
2
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
5
1
0
3
0
0
1
3
1
1
1
2
0
0
2
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
2
1
0
0
4
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
2
3
0
1
0
0
1
0
0
0
2
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
2
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
1
0
3
3
0
3
2
0
2
0
0
1
0
0
1
1
1
2
0
0
0
0
0
1
0
0
0
1
1
1
2
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
1
0
2
0
0
0
1
0
0
1
0
0
0
0
1
2
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
1
0
0
0
3
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
1
1
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
1
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
2
2
2
0
0
0
2
0
0
2
2
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
1
0
0
2
1
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
2
1
2
1
1
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
1
0
0
0
0
0
3
1
0
1
0
2
0
2
0
0
2
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
1
4
1
0
0
0
1
2
0
1
0
0
0
3
1
1
0
1
1
0
0
1
0
2
2
2
0
2
0
0
0
0
0
0
0
3
0
2
0
2
0
2
0
2
0
0
0
0
2
0
0
1
0
0
0
0
2
1
2
0
0
1
1
0
0
1
0
2
0
1
0
1
0
2
1
0
1
2
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
2
0
0
0
0
0
1
0
2
3
2
0
0
0
1
2
0
0
0
0
0
0
0
0
3
1
0
2
0
0
0
0
0
0
0
0
0
2
1
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
2
3
0
0
0
0
1
1
0
0
0
2
0
0
3
0
0
0
1
0
0
0
2
3
1
0
5
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
2
0
1
0
0
0
0
0
0
1
2
2
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
1
0
0
1
0
4
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
1
0
1
0
2
0
0
1
0
0
2
3
0
1
0
1
0
2
1
0
1
0
0
1
0
1
0
1
2
0
0
0
1
0
2
0
0
0
0
1
0
0
4
0
0
0
3
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
1
1
4
0
0
1
0
0
1
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
2
0
1
2
0
2
0
0
0
0
0
0
2
0
0
2
2
0
0
1
0
1
0
0
0
0
0
0
0
2
0
1
1
0
3
0
0
0
0
2
0
3
0
0
0
0
2
1
0
2
2
1
1
0
2
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
2
0
0
2
0
0
0
5
0
0
0
1
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
3
1
0
2
1
0
0
0
1
0
1
0
0
0
2
0
0
1
0
0
0
2
1
0
2
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
1
0
2
1
0
0
0
0
3
0
2
2
0
0
1
1
2
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
1
0
1
0
0
4
0
0
2
0
0
0
2
0
0
0
0
0
1
2
0
2
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
1
2
0
2
2
0
0
0
0
0
1
0
2
0
0
2
1
0
0
0
0
0
0
0
0
2
2
0
1
1
0
2
7
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
4
0
0
0
3
0
1
0
0
0
0
0
0
3
0
0
2
0
0
0
2
2
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
3
2
0
0
0
1
2
0
0
0
0
0
0
1
1
0
0
2
1
0
0
0
1
0
0
0
1
2
1
0
0
0
0
2
1
0
2
0
0
1
2
0
1
0
0
0
0
0
2
0
0
0
1
1
0
2
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
5
0
0
2
0
0
0
2
1
2
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
2
0
2
0
0
1
0
0
2
1
0
0
2
0
2
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
2
0
3
0
0
0
2
1
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
3
0
1
0
0
1
0
0
1
2
0
0
1
1
1
0
0
1
1
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
8
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
1
1
0
1
0
0
0
4
0
3
1
0
0
0
0
2
0
0
0
2
1
1
0
1
0
0
1
0
1
0
0
0
3
0
0
0
0
0
0
2
1
0
0
1
1
0
0
0
0
1
1
2
2
0
3
0
3
0
1
0
0
2
2
0
0
2
0
0
1
2
0
0
2
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
2
0
0
2
0
0
0
3
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
3
0
0
1
1
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
3
1
1
0
0
0
0
1
1
0
0
5
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
2
2
0
0
0
1
0
1
0
1
0
2
0
0
0
0
0
2
2
0
0
1
0
1
0
1
0
0
1
1
0
1
2
1
0
0
0
0
0
0
4
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
2
2
1
0
1
2
2
2
0
1
0
0
0
1
1
1
0
0
2
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
1
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
1
0
2
0
0
1
0
0
0
3
1
0
0
0
0
0
2
0
2
4
0
1
0
0
1
0
1
0
0
0
0
0
1
2
0
0
2
0
0
0
0
1
0
0
2
0
2
0
0
0
0
2
1
0
0
2
0
0
0
0
1
2
2
2
0
2
0
2
2
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
2
1
0
0
0
3
2
0
1
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
2
1
1
0
0
6
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
2
2
2
0
1
2
0
0
4
1
1
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
1
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
1
2
1
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
1
2
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
1
0
1
0
0
1
0
2
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
2
2
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
2
1
0
0
0
0
1
0
1
0
0
0
0
2
0
3
2
3
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
1
0
1
0
2
0
1
0
0
1
1
0
0
0
2
2
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
2
0
2
2
0
1
1
2
0
0
0
0
0
3
1
0
0
0
2
2
0
2
0
2
1
1
0
0
1
0
0
0
2
2
2
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
2
0
0
1
2
0
0
5
1
1
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
3
1
2
0
0
1
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
2
2
0
1
1
2
0
0
0
0
1
0
0
0
2
0
0
0
2
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
2
2
0
2
0
0
2
0
0
0
0
4
1
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
3
0
2
0
0
0
0
0
2
0
0
2
0
1
1
3
0
0
0
0
0
2
1
0
1
0
2
0
2
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
4
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
1
1
0
0
0
3
3
0
2
1
0
0
0
0
0
2
2
0
0
0
0
0
0
1
2
0
2
2
2
2
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
1
0
2
0
1
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
1
0
2
1
0
0
0
1
0
1
0
0
0
1
2
0
0
0
0
2
0
0
0
1
2
0
2
3
0
0
2
0
0
1
0
1
0
0
0
2
0
0
2
0
0
2
1
1
1
0
0
2
0
0
0
0
0
1
0
0
1
0
0
2
0
1
0
0
0
0
0
2
0
2
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
2
1
0
1
2
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
4
0
0
0
1
3
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
1
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
1
0
2
2
0
0
1
0
0
1
1
0
2
0
1
0
1
1
0
0
0
3
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
1
0
0
2
0
0
0
1
2
2
0
0
0
1
0
0
0
0
1
2
0
2
0
0
2
2
0
0
1
2
0
0
0
0
1
0
0
3
0
0
0
0
0
0
2
0
1
2
0
0
0
1
0
0
0
0
2
1
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
3
2
0
0
0
2
0
0
0
0
2
1
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
2
0
4
1
0
0
0
0
0
2
0
0
0
0
3
0
0
2
0
3
0
2
0
1
0
0
0
1
1
0
0
0
0
2
2
0
1
0
2
3
0
0
0
1
5
0
0
2
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
2
0
0
0
5
0
0
0
1
1
0
1
0
0
3
0
1
0
0
3
0
0
0
0
1
0
0
0
2
2
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
1
0
0
2
1
2
2
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
2
1
0
1
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
1
0
1
2
0
0
0
0
0
2
0
0
0
0
2
1
0
0
1
0
2
0
0
2
1
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
8
0
0
1
2
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
3
2
2
0
0
0
2
0
0
2
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
2
1
2
0
0
2
1
2
1
0
0
0
1
0
0
1
0
2
0
0
0
0
1
0
0
0
1
0
0
0
3
0
1
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
1
2
2
0
0
2
1
1
0
1
0
4
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
2
1
0
0
2
0
2
0
2
0
3
1
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
2
0
0
1
0
0
0
2
2
1
1
0
0
0
2
0
2
1
2
0
2
2
1
0
0
0
2
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
3
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
1
0
0
1
0
1
0
3
0
1
0
1
2
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
4
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
4
0
4
0
1
0
0
0
2
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
2
5
0
0
0
1
0
0
0
0
0
0
0
0
3
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
2
2
0
0
0
0
1
0
0
0
0
1
0
0
0
2
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
3
0
0
1
0
2
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
1
1
1
1
0
0
0
1
0
1
1
0
1
0
0
0
0
2
2
3
0
2
2
0
0
0
0
2
2
1
0
0
0
0
1
0
0
0
0
0
0
3
2
0
0
5
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
2
0
0
1
0
0
2
0
0
2
0
2
0
1
0
2
0
0
0
0
1
1
0
2
0
0
1
0
0
2
0
3
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
2
0
1
0
1
2
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
1
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
3
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
2
0
1
0
0
2
0
1
0
0
0
0
2
0
0
0
0
2
1
2
0
0
0
0
0
0
3
2
2
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
2
0
2
0
0
0
0
1
0
0
0
9
0
0
0
2
2
1
1
0
0
0
0
0
2
3
0
2
0
2
0
2
0
0
0
0
2
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
3
0
0
3
2
1
0
1
2
1
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
1
1
0
0
0
0
0
2
0
0
2
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
1
0
2
0
0
1
0
0
2
1
0
0
3
2
2
0
0
0
4
2
2
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
3
2
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
1
1
0
2
0
0
0
0
0
1
0
0
2
0
1
0
0
0
2
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
2
1
0
0
1
1
1
0
0
1
0
0
0
0
2
2
0
1
3
1
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
1
0
0
0
2
0
0
2
0
0
2
0
2
0
0
4
0
0
1
0
0
0
1
0
3
0
2
2
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
1
0
2
0
0
0
2
2
0
0
0
0
0
3
1
0
3
0
0
2
5
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
2
0
2
1
4
0
0
1
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
2
0
0
0
0
0
0
2
0
1
0
2
0
2
1
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
1
1
0
3
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
3
0
0
2
2
0
0
0
0
0
2
1
1
0
0
0
0
2
0
1
0
1
4
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
1
2
0
0
0
2
1
0
5
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
2
0
0
6
0
2
0
0
0
1
1
4
2
0
2
3
0
0
0
0
1
0
0
0
0
0
0
0
3
0
2
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
1
1
2
0
0
2
0
0
0
1
1
0
0
0
0
2
2
2
0
2
0
2
1
0
0
0
2
0
1
0
0
0
1
2
1
0
1
0
0
0
0
0
0
0
1
0
0
0
2
2
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
1
0
0
2
0
1
0
1
0
1
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
3
1
0
0
1
0
0
0
0
3
2
0
0
2
0
0
0
0
0
2
2
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
3
3
2
1
0
3
0
0
0
0
0
2
0
1
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
3
0
1
0
3
0
0
0
0
1
0
0
0
0
2
1
2
1
0
0
0
0
1
0
2
0
0
0
0
0
0
1
1
2
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
2
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
7
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
2
0
0
2
1
2
0
0
2
0
2
0
0
0
0
5
0
0
0
3
0
1
0
1
2
0
0
2
2
1
2
0
0
0
1
0
0
0
0
0
0
0
2
2
1
0
0
2
1
0
0
0
1
0
2
0
0
1
0
0
1
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
2
0
2
1
5
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
1
2
1
0
0
0
2
0
1
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
2
0
2
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
6
0
0
1
0
0
1
1
0
0
0
0
3
0
1
1
0
0
1
0
1
0
1
0
0
2
0
1
0
0
0
0
0
0
2
1
0
0
0
0
1
2
2
0
0
1
0
0
0
0
2
0
1
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
2
0
0
2
1
0
0
1
0
0
0
3
0
1
1
2
0
0
0
0
1
0
2
0
0
2
0
0
1
1
0
0
0
0
0
2
0
6
0
0
0
0
0
2
1
0
0
1
1
1
1
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
1
3
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
4
0
0
0
0
2
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
1
0
0
1
0
2
2
0
0
0
2
0
2
0
0
0
2
0
0
0
0
1
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
4
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
1
0
0
0
2
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
1
2
0
0
1
2
0
0
0
0
2
1
0
0
0
0
2
2
0
2
0
3
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
3
0
0
2
0
2
0
2
0
0
0
1
0
0
2
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
4
2
3
0
0
2
2
0
0
0
1
2
0
0
0
2
2
0
2
2
0
0
0
0
0
2
4
1
0
1
1
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
2
0
2
0
1
2
0
0
0
2
0
2
1
0
0
1
2
0
0
1
1
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
4
0
0
0
1
2
2
0
0
0
0
0
0
0
1
0
0
11
0
0
0
0
0
1
0
0
2
2
2
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
1
0
0
2
0
0
1
1
2
0
0
0
0
2
1
0
1
0
0
2
0
0
2
0
2
0
0
0
0
0
2
0
1
0
0
0
1
5
3
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
3
1
0
0
1
2
1
0
2
2
0
3
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
2
1
0
1
2
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
1
0
1
0
0
2
1
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
2
2
2
0
0
0
0
1
1
0
1
1
0
2
0
0
2
1
1
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
1
3
0
0
3
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
1
0
2
2
0
0
0
2
0
2
2
2
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
8
0
0
2
0
1
0
0
0
0
1
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
1
1
0
1
0
0
2
0
0
1
0
0
1
0
0
0
0
2
0
0
1
2
0
1
2
0
0
0
1
0
0
0
0
2
2
0
1
0
2
0
0
1
0
2
0
0
0
2
0
2
0
0
0
2
0
0
2
1
0
3
0
1
0
0
0
0
1
0
0
2
1
0
0
2
1
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
2
1
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
2
1
1
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
1
0
0
0
0
0
2
0
1
1
0
1
0
0
0
0
2
1
1
0
0
0
2
2
2
0
0
0
0
0
2
2
0
0
1
0
3
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
4
4
0
0
0
0
1
0
0
1
2
0
0
0
3
3
0
1
0
0
1
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
1
2
2
0
1
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
2
1
0
0
0
0
2
1
0
2
2
0
0
0
2
0
0
0
0
0
2
1
1
0
0
0
2
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
1
0
0
0
2
1
0
3
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
1
1
1
1
8
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
2
1
0
0
0
0
0
1
3
0
0
0
0
0
3
1
0
0
0
2
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
3
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
2
0
3
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
4
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
1
0
1
0
0
1
0
1
6
1
2
1
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
2
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
2
2
0
0
1
0
0
2
0
2
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
2
0
2
0
0
1
1
1
3
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
2
0
0
3
0
0
0
2
2
0
0
2
0
0
2
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
1
1
2
2
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
1
1
0
3
0
0
2
0
0
0
0
0
0
1
0
0
2
2
1
0
0
1
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
2
1
0
6
2
0
0
2
0
0
0
0
0
0
0
0
0
2
2
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
2
0
0
3
0
0
0
0
0
0
1
2
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
5
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
2
2
2
0
0
0
0
0
1
0
0
1
0
0
1
2
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
1
2
0
0
0
0
2
1
0
0
0
0
0
2
2
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
1
0
2
0
0
0
2
0
0
0
1
1
1
1
1
3
2
2
0
1
0
1
0
2
0
0
3
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
1
2
0
0
0
2
1
0
0
2
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
1
2
0
0
2
0
0
0
1
1
0
2
1
2
2
0
0
0
0
2
0
2
1
0
0
0
1
0
2
2
0
2
0
2
0
2
0
0
0
1
0
0
0
1
2
0
2
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
1
2
0
0
0
0
0
0
0
0
0
2
0
5
0
2
1
1
2
0
0
0
0
0
0
0
0
1
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
1
0
0
0
0
0
1
0
0
0
2
0
2
2
0
0
0
1
0
0
0
2
0
1
0
2
1
0
0
0
0
2
0
2
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
3
0
0
2
0
1
3
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
2
3
0
0
2
0
0
0
0
1
0
0
0
2
0
1
1
0
1
0
0
0
0
2
0
0
1
0
2
3
2
2
0
0
0
3
0
0
2
0
0
0
0
2
3
0
1
0
0
1
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
2
2
0
1
0
0
0
0
0
0
1
0
2
0
0
1
0
1
0
0
1
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
2
0
2
0
0
2
0
0
0
3
2
1
0
0
1
0
0
0
1
0
0
2
0
0
0
0
2
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
1
2
1
2
0
0
0
3
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
1
2
0
0
0
2
0
0
1
1
2
4
0
4
0
0
2
1
0
0
2
0
0
2
2
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
2
1
2
2
0
0
0
0
0
0
0
0
3
1
1
1
0
0
1
0
0
0
2
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
4
0
1
0
0
1
1
0
0
1
0
0
0
0
2
1
0
0
0
0
0
6
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
9
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
2
2
1
0
0
0
1
0
0
0
0
1
0
0
0
2
2
0
0
1
0
0
0
0
2
1
1
1
0
2
1
0
0
2
0
1
0
0
0
2
0
0
1
2
1
0
0
0
0
0
0
1
0
0
2
1
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
2
0
2
0
2
0
1
13
2
2
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
2
0
2
0
0
1
0
0
0
2
0
2
0
0
0
2
0
0
0
2
0
2
0
0
0
2
2
3
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
2
2
1
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
3
2
0
0
1
0
0
1
0
0
0
2
1
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
1
1
0
0
2
1
1
0
0
0
0
0
0
0
0
1
2
1
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
1
0
1
0
0
0
0
2
0
0
2
2
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
3
1
2
0
0
1
0
3
2
0
1
0
0
0
0
4
1
0
0
0
0
0
0
0
7
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
1
1
0
2
1
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
1
0
2
0
0
0
2
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
1
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
2
0
0
0
1
0
2
0
0
0
1
0
2
0
1
0
0
0
1
0
3
0
1
0
1
0
1
2
0
2
0
0
0
1
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
2
0
1
0
0
0
0
0
1
2
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
3
3
0
0
1
0
1
0
2
2
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
2
0
2
2
2
2
2
0
1
1
2
2
2
0
0
0
0
0
0
2
0
2
0
0
2
0
1
0
0
2
0
0
0
0
0
1
0
1
0
0
2
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
1
2
0
1
0
1
2
0
0
0
0
3
0
0
2
1
0
0
0
0
0
0
0
0
0
0
3
0
0
2
1
2
0
1
1
1
2
0
0
0
0
0
0
0
2
0
0
0
0
4
0
1
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
3
0
0
1
1
2
0
0
1
2
0
1
0
0
0
9
0
0
2
2
0
0
0
1
1
0
2
2
2
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
2
2
0
3
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
2
0
0
1
0
0
0
0
2
0
0
0
2
0
1
1
0
0
4
1
1
0
0
0
0
3
0
1
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
1
2
0
0
0
2
0
3
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
1
0
2
0
0
0
0
1
3
2
0
0
1
0
2
0
0
2
0
0
0
0
1
5
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
1
0
1
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
1
2
0
1
0
0
0
1
0
0
3
0
1
1
3
0
0
1
0
1
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
2
1
0
0
0
2
0
0
2
2
0
0
2
0
0
0
0
0
0
0
2
0
2
1
0
1
0
0
0
0
3
0
0
0
0
2
0
3
1
3
3
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
1
0
0
0
2
0
1
0
1
0
0
1
0
0
0
0
1
0
0
2
0
0
1
0
0
2
0
0
0
2
0
1
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
2
2
0
0
1
3
1
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
4
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
1
0
0
0
1
1
0
0
2
0
0
2
1
0
2
0
0
2
0
0
0
0
0
1
0
0
2
1
0
0
2
0
1
0
0
0
0
0
5
1
0
2
0
0
0
2
2
2
0
2
1
0
3
1
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
2
0
0
1
2
0
1
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
1
1
0
0
1
3
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
3
1
0
0
2
0
0
0
0
0
1
0
2
1
3
2
0
0
0
0
1
1
0
2
0
0
0
2
0
0
0
1
0
0
0
3
0
0
0
0
1
0
0
0
0
1
0
3
1
2
2
0
1
2
0
0
2
0
0
0
2
0
0
0
0
2
1
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
5
2
0
2
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
3
1
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
2
1
2
1
0
1
0
0
0
2
0
2
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
1
2
0
1
0
0
0
2
0
0
0
2
0
2
1
0
0
0
0
0
1
0
2
2
2
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
3
0
0
2
2
0
0
3
0
0
0
0
0
4
0
0
0
0
1
1
0
0
0
1
0
0
2
0
2
0
0
2
2
0
3
0
0
0
2
0
2
0
2
1
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
3
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
2
0
0
4
0
2
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
3
0
0
3
2
0
0
0
3
0
0
0
0
2
0
2
0
0
2
2
0
0
0
0
0
0
1
0
2
0
0
1
1
0
0
0
2
0
2
0
0
0
1
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
2
2
0
0
0
2
0
0
0
0
1
0
1
0
2
2
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
1
3
0
2
0
0
0
4
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
2
0
0
0
0
2
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
1
0
0
2
0
1
2
0
2
0
0
2
3
0
2
1
0
2
0
0
2
0
2
2
0
0
0
0
0
0
0
2
0
1
1
0
0
1
0
3
0
0
0
0
2
3
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
3
1
0
1
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
1
0
0
1
0
0
0
0
1
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
2
1
2
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
2
0
3
2
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
2
0
0
2
1
0
0
1
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
1
2
0
0
2
0
0
2
5
0
0
6
0
2
3
0
0
2
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
1
2
2
0
0
0
0
0
1
2
0
0
2
1
2
1
1
1
0
11
2
2
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
3
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
2
1
0
0
0
2
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
2
2
0
0
1
0
1
0
1
0
1
0
0
2
1
0
0
0
0
0
2
0
0
0
1
1
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
3
2
2
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
1
0
2
0
0
0
2
0
0
1
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
3
1
0
1
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
1
0
0
2
1
0
0
0
2
1
0
0
0
0
0
2
0
0
0
2
2
2
0
1
0
0
0
1
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
2
1
1
0
0
0
0
0
2
0
1
2
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
1
1
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
2
2
0
0
1
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
1
1
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
2
2
0
2
0
3
2
0
0
0
0
5
2
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
2
2
0
1
0
2
0
0
2
0
1
0
0
1
1
1
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
1
0
0
2
0
0
0
0
1
0
0
2
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
3
0
0
2
1
0
1
2
1
0
2
0
1
0
0
0
2
2
0
0
0
0
2
0
2
0
0
0
0
0
2
1
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
2
0
0
0
2
0
0
0
0
2
0
0
0
2
0
1
0
0
0
1
1
0
0
0
3
0
2
0
2
0
0
0
0
2
0
2
3
1
0
2
0
0
0
2
1
0
0
0
1
0
2
2
1
0
0
3
0
0
0
0
2
2
0
0
1
1
0
0
0
2
0
0
1
2
0
0
1
1
0
0
2
0
2
0
0
0
0
1
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
1
0
4
0
2
0
0
0
0
2
1
0
0
0
2
0
2
0
3
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
2
2
0
0
2
0
0
2
1
0
0
0
0
0
2
3
0
0
1
0
0
3
0
0
2
2
0
0
0
1
1
0
1
0
0
1
0
2
0
2
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
2
0
1
1
0
0
0
3
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
3
2
0
0
0
0
1
1
1
0
2
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
1
0
1
0
2
2
1
0
0
0
0
0
1
2
0
2
1
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
1
2
3
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
1
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
2
1
0
0
0
1
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
1
0
0
2
0
2
0
0
1
0
1
2
0
0
0
0
1
0
0
0
0
0
2
0
2
1
0
1
0
0
0
0
0
0
0
2
0
0
0
1
2
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
1
0
2
1
1
1
1
0
0
0
0
0
0
2
0
1
0
0
2
0
0
3
0
0
0
0
0
2
0
0
2
0
0
0
1
1
1
0
1
2
0
0
0
2
0
0
0
1
2
0
2
1
0
0
1
0
0
1
0
0
0
1
0
2
0
0
0
0
0
1
0
0
1
1
1
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
2
1
1
3
2
0
1
0
0
2
0
0
1
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
1
2
0
1
2
0
0
0
1
0
1
0
2
0
0
0
0
2
0
1
0
0
2
0
1
0
0
0
2
2
0
0
0
1
1
1
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
3
2
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
7
0
2
0
0
1
0
2
0
0
1
0
0
0
1
3
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
1
2
1
0
0
0
0
2
1
0
3
1
0
0
0
0
3
0
0
2
1
0
0
0
0
0
0
1
0
0
2
1
0
2
1
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
1
0
1
1
7
0
0
1
1
0
1
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
3
0
0
0
2
0
0
0
0
0
2
1
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
2
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
1
2
3
0
0
0
1
0
1
0
0
2
0
0
1
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
3
1
1
0
0
1
0
0
0
2
0
0
0
2
0
2
0
0
1
0
0
0
0
2
4
0
0
2
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
2
0
0
0
0
2
0
1
0
1
2
1
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
1
0
0
2
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
2
0
2
0
0
0
0
2
0
0
1
0
0
0
1
0
1
1
0
2
0
0
0
1
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
2
2
0
0
0
0
0
0
1
0
0
0
1
0
0
3
1
0
0
1
0
2
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
1
1
0
1
0
0
0
0
3
0
0
2
2
2
1
1
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
1
0
1
0
0
0
1
2
2
0
0
0
0
0
1
0
0
0
0
3
2
0
0
0
0
0
0
2
3
0
0
1
2
0
2
2
0
0
0
0
0
0
0
0
0
1
1
2
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
2
2
3
0
2
2
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
1
1
0
2
0
0
0
0
2
0
2
1
2
0
0
0
3
1
0
0
0
0
2
0
2
0
0
1
1
2
0
0
0
0
0
0
0
0
0
2
0
1
0
4
1
0
0
0
0
1
1
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
1
2
1
0
2
0
0
0
0
0
2
0
0
0
19
0
2
1
0
1
0
0
2
0
0
0
1
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
2
0
0
0
0
1
0
0
0
1
0
1
0
0
1
1
0
0
1
0
0
0
0
2
0
0
0
0
3
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
1
0
0
2
1
0
0
1
0
0
2
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
5
0
2
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
1
0
0
1
0
0
0
2
6
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
4
0
0
0
2
0
0
2
0
1
1
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
2
0
0
2
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
2
0
0
1
0
0
0
1
3
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
2
0
1
0
1
0
0
0
1
0
2
0
0
0
0
3
3
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
1
0
2
0
0
0
0
2
1
8
0
1
0
1
0
2
1
0
1
0
0
0
0
2
0
1
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
2
1
2
1
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
2
1
2
0
1
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
1
1
2
2
0
2
0
0
0
0
0
0
0
9
1
0
0
0
2
0
0
0
0
0
4
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
2
1
0
0
0
2
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
1
2
0
0
0
1
1
0
2
0
2
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
1
0
2
0
0
2
0
2
2
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
1
0
0
2
2
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
2
0
0
0
0
1
2
0
1
0
0
1
0
0
0
2
4
0
0
0
1
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
4
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
1
3
0
0
0
0
0
1
0
0
1
0
0
0
1
0
2
1
0
0
1
2
2
1
0
0
2
0
0
0
2
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
1
0
2
1
0
1
0
0
1
0
2
0
0
1
2
0
1
0
0
0
0
0
0
1
0
0
2
0
0
1
0
2
1
2
0
1
2
0
0
1
2
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
1
2
0
2
0
0
0
2
1
1
0
0
0
0
1
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
1
0
0
1
0
0
0
2
1
1
0
2
0
2
1
0
0
1
0
0
0
0
0
0
2
0
2
0
1
0
0
0
2
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
2
0
0
1
2
2
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
3
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
2
0
0
0
0
0
0
2
1
0
0
0
2
1
1
2
0
0
0
0
0
0
0
0
1
1
1
0
1
1
0
0
2
0
0
0
1
0
1
0
2
0
1
2
0
0
1
0
2
1
0
1
0
0
0
2
1
0
0
0
1
0
0
2
0
0
0
0
2
1
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
1
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
1
2
0
0
4
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
2
0
1
0
1
0
1
0
0
0
0
4
0
0
0
1
2
0
1
2
0
2
0
0
0
0
1
0
1
0
0
2
0
1
1
2
0
1
0
1
0
0
0
0
1
1
0
2
0
0
0
0
0
0
1
0
1
0
0
0
3
2
0
0
0
0
0
0
0
1
1
0
0
2
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
1
1
0
0
0
2
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
1
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
3
1
0
3
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
1
1
0
0
3
0
0
2
0
0
0
2
0
0
0
0
0
0
2
2
2
0
2
0
0
0
0
0
1
0
2
1
1
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
1
1
1
2
0
0
1
0
0
3
0
0
2
2
2
2
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
4
0
0
0
0
1
0
0
1
0
1
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
2
1
0
2
1
0
1
0
1
1
0
1
0
0
0
0
2
0
1
0
0
2
1
0
1
0
1
0
0
0
0
0
1
2
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
4
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
1
0
0
0
1
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
1
0
2
0
1
1
0
2
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
2
0
2
0
0
0
0
2
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
2
0
0
1
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
1
1
2
0
0
1
1
0
0
2
0
0
0
0
2
0
0
3
2
0
0
1
2
1
2
2
0
0
0
0
0
0
1
0
3
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
2
0
1
0
1
2
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
1
1
0
0
1
0
2
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
1
1
0
0
2
1
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
2
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
1
0
0
0
2
0
0
2
0
1
0
0
0
6
0
2
0
3
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
1
2
1
2
0
2
1
0
0
2
0
0
2
0
1
2
2
0
0
0
1
2
0
1
0
0
0
5
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
3
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
3
0
0
2
2
0
0
0
0
0
0
0
1
0
2
0
1
3
1
0
0
2
1
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
1
0
2
0
0
0
0
0
0
0
0
3
0
0
1
0
1
0
1
0
0
0
1
0
3
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
2
2
0
1
0
0
1
0
1
0
1
0
1
0
0
0
3
0
2
0
0
0
1
1
2
0
3
0
0
0
2
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
1
0
2
2
1
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
1
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
3
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
1
0
1
0
1
3
0
2
1
1
1
1
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
1
0
0
1
3
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
2
0
0
1
0
1
0
0
1
2
2
0
0
1
0
0
0
2
2
2
2
2
0
0
0
0
0
2
2
0
2
1
1
1
0
0
2
1
2
0
2
2
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
3
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
1
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
4
2
0
2
0
0
1
0
2
0
0
3
0
0
0
1
2
0
0
0
0
2
0
2
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
1
0
1
0
0
0
1
0
0
0
0
3
0
0
0
0
2
0
2
0
0
1
0
0
0
2
1
0
0
0
2
2
2
0
4
2
0
0
1
0
2
1
0
0
1
0
0
0
0
0
2
1
3
0
1
0
0
4
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
2
1
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
3
1
0
0
0
0
0
2
0
0
0
2
0
0
3
0
0
1
0
1
0
5
0
0
0
0
0
0
1
0
2
1
1
2
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
1
2
0
0
0
1
0
0
0
2
0
4
0
0
0
0
1
0
0
0
1
1
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
6
1
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
1
1
0
2
1
0
0
2
0
2
2
4
0
2
0
0
4
2
0
0
1
4
0
0
0
0
1
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
2
0
0
0
1
2
0
2
0
2
0
0
2
0
1
2
1
0
0
0
0
0
1
0
0
2
1
0
2
0
2
3
0
1
0
0
0
3
0
0
0
0
0
0
0
2
0
1
2
0
0
0
1
1
2
1
1
2
4
0
0
0
0
2
5
0
0
1
0
0
0
0
0
1
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
1
0
1
1
2
2
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
1
0
2
0
0
1
2
0
0
0
0
4
0
3
0
3
0
1
0
0
1
0
7
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
2
1
1
2
0
2
1
1
0
1
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
2
1
0
0
0
0
0
0
1
0
2
1
0
0
0
1
0
1
1
0
2
0
0
1
0
2
0
2
2
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
2
2
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
2
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
2
2
1
1
2
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
1
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
1
0
3
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
3
2
0
1
0
3
0
0
1
0
2
0
0
0
0
2
0
2
2
0
1
0
0
1
0
0
2
0
0
0
0
2
0
0
0
1
0
1
0
2
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
3
1
2
0
0
0
0
0
0
1
0
1
0
1
0
0
2
0
2
0
0
2
1
0
0
3
0
0
0
0
0
0
1
0
2
6
0
0
0
1
2
0
1
0
0
0
1
0
1
0
0
3
0
2
0
0
0
0
0
2
1
0
0
2
0
1
2
0
2
1
1
1
0
1
0
1
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
4
0
1
1
0
0
0
2
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
2
0
1
0
0
0
1
0
0
0
0
2
0
3
1
0
0
7
0
1
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
1
2
1
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
1
2
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
2
0
2
0
0
2
1
1
0
1
0
0
0
3
1
0
0
0
1
0
2
0
2
2
0
2
1
0
0
0
2
0
2
0
0
1
0
0
0
0
0
2
0
0
2
0
4
0
0
0
0
0
2
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
2
0
1
1
0
2
0
0
0
0
2
2
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
2
2
2
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
1
2
2
1
3
0
0
2
0
0
2
1
0
0
0
0
2
1
0
2
0
0
0
0
1
2
0
1
0
1
0
0
2
0
0
0
0
1
1
0
3
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
3
0
0
0
2
0
1
2
2
0
1
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
2
0
0
2
0
0
1
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
3
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
1
0
0
0
0
0
0
2
1
0
1
1
0
0
0
1
0
2
0
0
0
0
1
2
8
0
0
1
0
0
2
0
2
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
2
2
0
0
2
0
1
0
0
1
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
2
2
0
4
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
2
0
0
0
2
2
1
0
1
1
2
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
2
2
2
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
1
0
1
1
2
2
2
1
1
0
0
0
2
0
0
0
0
0
0
0
2
1
0
2
1
1
0
2
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
2
1
0
1
0
2
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
2
0
1
2
0
2
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
2
0
0
1
1
0
3
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
1
0
0
1
0
1
0
1
0
0
0
2
0
2
1
2
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
1
2
1
0
1
0
2
0
2
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
1
1
1
3
1
0
0
0
1
2
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
2
2
2
2
2
2
0
1
0
0
1
2
2
0
1
0
0
0
1
0
0
0
3
0
1
0
0
0
0
0
0
2
1
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
1
2
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
2
0
0
0
0
0
1
3
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
1
1
3
0
1
0
0
0
0
0
2
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
2
1
2
0
0
0
0
0
0
1
2
1
0
0
2
1
0
0
0
0
1
0
0
1
0
4
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
1
1
1
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
1
1
0
0
0
1
2
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
1
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
2
0
1
0
0
1
0
0
1
0
1
2
2
0
2
0
0
3
0
1
0
0
0
0
0
0
3
0
0
0
1
0
2
0
1
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
1
4
2
1
0
0
0
1
0
0
2
2
0
0
0
2
0
0
3
1
2
0
0
0
0
0
1
0
2
0
1
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
4
0
3
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
2
2
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
2
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
2
1
0
2
0
2
0
0
1
5
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
2
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
1
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
1
1
1
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
1
0
3
0
0
0
2
0
0
0
0
0
2
0
7
0
0
0
3
0
0
0
0
0
1
2
2
0
0
2
0
0
0
0
0
0
3
0
0
2
0
1
0
2
2
0
0
0
2
0
0
0
0
2
0
1
0
2
2
0
0
2
0
0
0
2
1
0
1
0
0
0
1
0
0
2
0
1
0
1
0
1
2
0
0
0
0
2
0
0
4
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
2
0
2
2
0
0
1
0
0
0
2
0
4
0
2
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
2
0
1
0
0
1
0
1
0
1
0
2
0
2
0
2
0
0
0
0
0
0
0
2
0
2
0
2
1
0
0
1
0
2
0
0
4
0
0
0
0
0
2
1
0
0
2
1
0
0
0
0
2
0
0
2
1
0
0
1
0
0
0
2
0
0
0
2
0
1
3
1
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
3
3
0
0
1
2
2
1
0
1
0
0
1
0
1
0
2
0
0
0
0
0
0
2
0
0
0
1
1
0
0
1
0
0
0
0
2
0
1
2
0
0
0
0
2
2
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
1
0
1
2
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
1
1
1
0
0
2
0
2
0
3
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
2
1
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
2
0
0
0
0
2
1
0
0
2
0
0
1
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
1
2
0
0
0
2
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
4
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
1
0
1
1
0
1
0
0
0
0
0
2
1
0
0
1
0
0
0
2
2
0
0
0
0
0
3
1
1
0
0
0
0
0
0
0
0
0
2
0
0
1
5
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
1
2
0
0
0
0
0
2
0
0
2
0
0
2
2
0
0
0
1
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
1
0
0
2
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
1
6
2
0
0
2
2
0
0
0
2
0
0
1
2
0
0
0
0
2
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
3
0
1
2
0
1
3
0
0
0
2
0
0
0
0
1
0
0
2
0
1
2
0
0
0
0
2
0
2
0
0
1
0
1
0
1
2
4
2
0
0
2
1
0
0
2
0
2
2
0
0
2
0
0
0
0
0
2
2
2
1
0
4
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
3
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
1
0
0
0
2
0
0
0
1
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
2
0
1
0
1
2
0
0
0
0
0
4
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
3
0
1
0
0
0
3
0
0
0
0
1
1
0
0
0
2
0
0
0
1
1
0
0
0
1
4
1
0
0
2
0
0
0
0
0
0
2
0
0
2
1
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
1
0
0
0
1
0
1
0
0
0
0
2
0
0
0
1
0
2
0
0
2
0
2
1
0
2
0
1
1
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
1
4
0
1
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
1
2
0
0
0
2
0
1
2
0
0
0
1
2
2
0
0
0
0
2
2
0
1
0
0
0
1
0
0
6
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
1
1
0
0
0
2
2
1
2
0
0
1
0
1
0
0
0
0
0
1
3
0
0
0
1
0
0
0
0
1
2
2
0
0
0
1
2
0
0
0
1
1
1
1
0
0
0
0
0
0
0
2
0
1
2
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
2
0
0
0
0
2
0
0
2
0
2
1
0
2
0
2
0
0
0
0
0
0
0
0
1
0
3
2
0
0
0
2
1
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
2
0
0
0
2
1
0
0
3
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
1
1
1
1
3
0
0
0
0
0
0
0
0
2
0
2
2
0
2
0
0
1
0
1
1
0
1
1
0
0
0
0
0
0
2
1
2
0
1
0
1
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
2
0
0
1
0
0
1
1
0
2
0
0
2
1
0
0
0
3
0
0
0
2
1
1
2
0
0
2
0
0
0
0
2
2
2
0
0
2
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
2
0
0
0
0
1
2
0
4
0
1
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
1
0
0
3
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
4
0
0
0
1
2
0
1
0
0
0
4
0
0
1
1
0
2
0
0
0
2
2
1
0
0
1
0
1
0
0
0
0
0
0
2
2
0
0
0
1
0
0
1
0
0
0
1
0
5
0
2
0
2
0
2
2
1
1
0
0
1
0
1
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
2
1
0
1
0
1
0
2
0
2
0
1
1
1
0
0
4
0
2
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
2
1
1
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
3
0
1
1
0
0
3
1
0
1
1
0
0
0
0
2
0
1
0
2
1
0
1
2
0
0
0
0
1
0
0
3
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
3
0
1
0
0
0
1
2
0
0
0
2
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
2
1
1
0
0
3
0
1
3
0
3
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
1
0
0
0
3
6
1
0
0
0
0
1
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
2
0
0
1
0
0
0
0
2
0
1
0
0
0
0
1
0
0
1
1
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
1
5
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
2
1
0
1
0
0
0
1
0
0
1
0
1
2
2
0
1
0
0
2
0
0
3
0
0
0
2
0
0
2
0
0
0
1
0
0
1
2
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
2
2
4
2
0
0
0
0
0
0
0
0
2
3
0
1
1
1
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
1
2
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
3
0
0
2
0
0
2
1
0
0
1
0
0
2
0
1
0
0
0
2
1
0
0
0
0
2
2
0
2
1
0
0
0
0
0
0
0
0
0
0
2
2
4
0
0
1
0
0
1
0
2
0
0
2
1
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
1
2
0
0
2
0
0
1
1
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
1
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
1
2
2
0
2
0
0
0
1
0
1
0
0
0
1
2
1
0
0
0
2
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
1
2
1
1
0
0
4
1
0
1
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
1
1
0
0
2
1
1
1
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
5
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
2
0
1
2
0
1
0
0
2
3
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
2
0
0
0
0
1
1
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
4
1
0
0
0
0
0
0
1
1
1
1
0
1
1
0
1
0
0
0
1
2
2
2
0
0
0
1
1
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
1
0
0
0
0
0
1
0
0
0
1
1
3
0
2
0
0
2
2
0
1
0
2
0
0
0
3
1
1
0
3
1
0
0
0
0
0
2
0
0
0
0
1
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
1
1
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
1
1
0
0
2
2
0
0
0
0
0
1
1
2
0
0
0
2
2
0
2
2
0
0
0
0
0
0
0
0
2
1
1
2
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
2
0
0
0
0
1
0
1
3
0
0
0
0
0
0
0
0
3
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
2
2
0
0
1
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
2
0
0
0
0
1
0
1
0
0
0
0
2
0
0
4
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
2
3
0
0
0
0
0
3
0
0
0
0
1
1
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
2
4
0
0
2
0
0
0
0
2
2
0
2
1
2
0
0
0
0
0
0
0
1
0
0
1
1
0
0
2
4
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
1
2
0
1
0
0
0
0
0
1
0
3
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
2
2
0
3
2
1
0
0
0
3
0
0
2
2
0
2
0
0
0
2
0
0
0
0
1
0
2
0
1
0
0
0
2
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
2
2
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
1
0
0
1
0
1
0
1
0
2
1
1
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
2
0
0
0
0
0
2
2
0
0
0
2
0
0
0
1
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
4
0
0
2
1
0
1
1
0
0
0
1
0
0
1
1
2
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
3
0
1
0
0
1
0
0
2
0
0
3
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
2
2
0
0
0
0
1
0
1
1
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
1
1
0
0
0
2
1
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
1
0
0
2
1
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
2
3
0
0
2
0
0
0
0
2
1
0
0
1
0
0
0
3
0
0
0
2
0
1
0
0
0
0
0
0
3
0
0
1
0
2
0
2
1
1
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
1
1
2
3
0
0
0
0
0
2
2
0
0
0
2
0
1
2
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
2
1
1
1
0
0
2
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
5
0
0
0
0
0
0
2
0
1
0
2
0
0
1
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
1
2
0
1
0
0
0
2
0
0
4
4
0
0
0
1
0
0
0
0
1
0
0
1
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
3
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
2
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
2
0
1
0
0
0
0
0
0
0
2
1
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
2
0
2
0
0
0
0
0
0
0
0
2
1
0
0
1
1
0
0
0
3
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
2
2
1
0
2
2
0
0
1
0
0
5
0
0
0
0
0
3
0
0
0
1
2
0
0
2
0
0
0
0
1
0
2
4
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
2
2
0
0
0
1
2
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
4
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
2
1
2
0
0
2
1
0
0
0
0
0
3
2
1
3
1
2
2
0
0
0
0
1
0
0
0
3
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
3
0
0
0
2
1
2
1
0
0
0
0
2
0
1
2
0
0
2
0
0
0
3
0
0
2
2
0
0
2
2
0
0
0
1
1
1
0
2
0
0
1
0
1
5
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
2
1
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
1
0
0
0
1
2
2
3
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
1
2
1
2
0
0
1
0
1
0
1
0
0
0
1
0
0
0
1
0
0
2
2
0
0
0
1
0
1
0
0
2
0
0
0
2
0
0
1
1
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
2
0
2
0
0
2
0
2
1
0
0
2
0
1
0
0
1
1
1
0
0
0
1
0
0
0
0
2
0
0
2
0
1
1
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
2
0
2
0
1
0
2
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
2
2
0
0
0
0
1
0
2
0
0
0
0
2
5
0
1
0
1
2
0
0
0
2
0
0
1
2
3
0
0
2
0
0
4
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
2
0
0
0
1
0
2
2
0
0
0
0
2
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
5
0
0
0
2
1
1
2
0
0
0
0
0
0
0
2
0
1
2
0
1
1
0
0
0
0
0
2
0
3
0
2
1
0
2
3
2
0
0
0
2
2
0
0
0
1
0
0
2
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
2
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
2
2
1
0
2
0
0
0
0
2
1
0
1
0
0
0
1
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
1
2
0
1
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
5
0
2
2
1
2
0
0
2
2
0
1
2
1
0
1
0
0
0
0
0
0
2
1
3
1
2
0
2
0
0
1
1
0
0
0
0
1
0
0
0
0
2
0
3
0
0
1
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
5
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
2
0
2
0
0
0
0
1
1
2
2
2
1
0
2
1
3
0
0
1
2
0
0
1
1
0
0
0
2
0
3
2
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
1
0
1
1
0
1
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
1
1
0
0
2
0
0
2
0
0
0
1
2
1
1
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
1
4
1
0
1
0
0
2
0
0
1
1
1
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
2
2
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
2
0
0
1
3
3
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
1
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
1
0
0
0
0
1
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
1
0
1
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
2
0
0
0
2
0
0
0
2
0
0
0
1
0
1
1
1
2
0
2
1
2
1
0
0
0
1
0
2
2
0
0
1
0
0
0
0
2
0
0
0
2
0
2
0
0
1
0
0
2
1
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
1
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
1
1
1
0
2
1
0
0
1
1
0
3
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
1
1
2
0
0
0
1
0
0
1
1
1
2
1
0
0
2
2
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
1
3
0
0
0
2
1
0
1
0
0
2
0
0
1
0
2
0
0
2
2
2
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
1
0
0
1
2
1
0
2
0
0
0
0
0
1
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
1
0
0
0
0
1
0
1
2
2
0
0
0
0
1
1
0
0
0
0
1
2
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
1
2
1
2
0
1
0
0
1
1
0
3
1
0
0
2
0
0
0
0
0
6
0
0
1
0
2
0
0
1
0
2
1
0
0
1
2
0
0
0
0
3
1
2
0
1
0
0
0
0
5
2
2
1
0
0
0
2
0
0
1
0
2
2
0
0
0
0
1
0
0
0
3
0
0
0
0
2
0
1
2
2
0
0
5
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
1
2
0
0
2
0
3
0
0
1
0
3
0
0
2
0
0
1
1
2
0
0
1
1
0
0
0
0
1
1
0
1
0
1
1
0
0
0
0
0
0
2
1
4
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
1
0
0
2
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
1
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
1
4
0
0
0
1
1
1
0
0
0
0
0
0
2
0
2
0
0
0
0
2
1
2
2
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
1
0
0
2
1
1
0
3
0
1
0
0
0
0
2
0
0
3
2
0
0
1
0
0
0
2
0
5
0
0
2
1
0
0
1
0
0
0
0
0
2
2
0
3
0
4
0
0
0
0
0
0
2
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
2
0
0
0
0
2
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
3
1
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
1
0
1
2
1
0
0
0
0
0
2
0
2
2
1
0
2
0
1
0
0
0
0
1
0
0
0
0
5
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
4
0
1
1
0
0
0
2
1
0
0
0
0
2
0
0
1
0
0
1
0
2
0
2
0
2
1
1
0
0
0
2
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
4
0
0
1
1
0
2
2
2
0
2
0
0
2
3
1
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
3
2
0
0
1
0
1
1
1
0
1
2
0
0
0
1
2
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
1
0
1
1
2
0
0
0
0
0
1
3
2
0
1
0
0
0
0
2
0
0
0
0
3
0
2
0
0
1
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
1
2
2
1
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
3
0
1
0
0
2
0
0
2
0
0
0
0
1
0
0
0
1
1
0
1
0
1
2
0
0
1
0
0
0
0
0
1
0
1
0
0
3
0
0
0
0
2
1
0
0
0
1
0
0
1
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
3
1
1
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
2
2
0
0
0
0
1
0
0
1
2
0
2
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
3
0
4
0
0
0
0
0
0
2
1
2
2
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
1
2
0
0
1
0
6
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
2
0
0
0
4
0
0
0
2
0
3
0
1
0
0
0
2
0
0
1
1
1
4
0
0
0
0
0
1
3
0
0
0
1
0
1
1
0
0
0
2
0
1
1
2
0
0
0
1
0
2
0
1
0
2
1
0
3
0
0
0
1
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
2
0
0
0
1
1
0
2
1
1
2
0
0
0
0
4
3
2
2
0
0
4
0
0
0
0
0
2
0
0
0
0
2
1
3
0
0
0
0
0
1
0
1
1
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
1
0
2
0
2
2
1
1
0
0
1
0
2
2
0
1
0
2
2
1
0
0
0
0
0
1
0
0
0
1
2
0
2
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
2
1
2
2
2
0
0
0
1
0
4
0
0
0
0
2
0
0
1
1
0
0
2
0
0
0
0
2
2
0
0
0
1
2
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
2
1
1
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
2
0
2
2
0
1
0
0
0
2
0
0
0
1
0
0
2
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
1
2
0
0
0
0
0
0
0
2
3
0
1
0
0
0
1
0
2
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
2
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
2
1
0
0
1
0
0
1
0
3
0
0
1
3
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
1
1
0
0
0
1
1
0
0
0
2
0
1
0
0
2
0
0
0
0
3
0
0
0
0
2
0
0
1
0
1
2
0
1
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
1
2
0
0
0
0
1
0
0
0
0
0
2
0
0
1
1
1
1
2
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
4
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
1
0
0
2
0
0
2
1
0
1
0
1
2
0
2
0
3
0
0
3
2
0
1
0
0
7
0
0
0
0
0
2
0
1
1
2
0
0
0
1
0
0
0
0
0
0
2
0
0
2
2
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
5
2
2
0
0
2
2
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
3
0
0
0
0
0
1
2
0
2
0
2
0
1
0
0
0
0
0
0
0
0
4
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
2
0
1
0
0
2
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
2
0
1
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
1
3
0
1
0
1
0
0
0
2
0
0
2
0
4
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
1
2
0
0
1
2
0
0
0
2
1
0
1
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
3
2
1
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
1
2
0
1
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
1
2
2
0
0
0
0
0
0
2
1
0
0
3
0
0
1
0
2
3
0
2
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
4
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
1
0
0
0
0
0
0
1
0
2
2
0
0
0
0
2
0
1
0
2
0
1
1
0
0
0
0
2
0
1
1
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
1
0
0
0
0
2
0
0
4
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
2
1
1
0
1
0
0
2
1
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
1
0
2
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
3
3
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
2
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
1
2
2
0
0
2
0
0
2
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
1
2
0
2
0
0
0
1
0
0
1
2
0
0
0
2
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
2
0
3
0
0
0
0
0
0
2
0
1
3
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
2
0
0
0
0
1
0
1
5
2
0
1
0
0
0
0
2
0
0
2
0
0
1
0
0
1
0
0
0
0
2
1
2
2
1
0
0
0
1
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
6
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
2
0
2
2
0
1
3
1
0
0
1
0
0
0
0
0
0
1
0
0
2
0
1
0
1
0
0
1
0
0
1
0
0
0
3
1
0
0
0
0
0
0
0
2
0
2
1
2
0
0
0
0
0
0
6
0
1
0
2
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
3
0
0
0
2
1
0
0
4
0
2
0
1
0
0
0
2
0
0
1
1
0
0
0
0
1
0
3
0
4
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
1
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
1
0
0
0
0
0
0
0
2
1
0
1
0
0
2
0
0
0
0
2
1
0
2
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
1
2
0
0
2
0
0
3
0
0
0
1
0
5
2
0
1
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
2
2
0
0
0
1
1
0
0
1
0
3
0
0
1
1
2
0
0
0
1
2
0
1
1
0
0
1
0
2
0
0
1
0
1
0
0
0
0
0
1
0
0
0
3
1
1
0
0
0
0
0
1
0
2
0
0
0
2
2
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
6
0
0
2
0
0
0
2
0
2
1
0
0
0
1
0
1
2
0
0
0
1
0
0
0
0
1
0
0
0
2
0
2
0
0
2
0
3
0
0
0
0
0
1
0
2
0
0
0
0
2
4
2
0
5
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
2
0
1
0
2
0
0
0
0
0
0
0
0
2
2
1
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
1
0
2
2
0
1
0
1
0
0
0
0
0
0
0
1
1
2
0
0
0
2
0
2
0
1
2
1
0
0
1
0
0
0
0
0
3
0
0
2
0
0
0
1
2
0
0
2
1
0
0
0
2
0
0
0
0
0
2
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
2
2
2
0
0
0
0
0
0
0
1
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
4
0
0
2
1
2
2
2
0
1
0
0
1
0
1
1
0
2
1
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
3
0
0
0
2
0
0
0
2
0
0
0
0
1
0
1
0
2
0
0
0
1
1
0
0
0
7
0
0
1
2
0
2
2
2
3
0
1
0
0
0
2
0
1
2
1
1
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
1
0
3
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
1
2
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
2
0
1
1
1
0
1
0
0
1
0
0
0
0
0
1
0
2
1
0
0
1
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
2
2
2
0
0
1
1
0
1
0
3
2
1
0
0
0
0
0
4
2
0
0
1
1
0
0
1
0
0
0
0
3
0
0
2
0
0
0
0
1
0
0
0
0
0
3
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
1
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
2
0
0
2
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
2
2
0
0
0
0
5
0
1
0
0
0
0
1
2
0
2
1
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
1
2
0
2
0
0
2
2
2
3
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
3
2
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
1
0
1
2
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
4
0
0
0
0
0
0
0
2
1
0
0
2
4
0
1
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
2
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
2
2
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
2
0
0
1
1
0
1
0
0
0
0
1
0
0
2
0
2
0
0
1
0
1
0
0
2
0
3
1
0
0
0
0
0
2
2
0
0
2
4
0
2
0
1
0
0
0
0
0
1
0
0
0
2
0
2
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
3
2
0
2
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
1
0
2
1
0
1
0
0
5
0
0
0
0
2
2
0
0
0
2
1
0
0
0
1
0
2
0
2
1
0
1
1
0
2
1
0
0
3
0
3
0
0
0
1
0
0
0
0
0
1
2
0
0
2
1
2
0
0
2
0
2
0
1
2
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
2
5
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
1
2
2
0
1
1
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
3
0
0
0
0
0
1
0
2
1
0
0
1
0
2
0
3
2
0
3
2
0
0
0
2
2
0
2
1
2
1
0
1
1
2
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
3
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
2
1
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
2
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
2
0
0
0
2
5
0
1
2
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
2
0
2
0
1
0
0
0
0
0
1
0
0
1
1
1
0
0
1
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
2
0
0
3
0
1
0
3
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
2
0
0
0
2
0
0
1
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
3
0
1
1
2
0
0
1
0
1
0
2
0
1
0
1
0
1
0
1
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
2
0
0
2
0
0
1
0
2
0
0
1
2
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
5
1
0
4
2
1
0
0
0
0
0
0
0
0
0
4
1
2
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
1
0
0
1
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
2
2
0
0
0
2
1
0
0
1
2
0
1
0
0
2
1
0
0
0
0
1
0
0
0
1
0
3
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
3
0
0
0
0
1
0
0
1
0
2
2
0
2
5
1
0
1
0
2
0
0
1
1
2
0
0
0
1
0
0
0
1
0
0
1
2
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
2
1
0
3
0
0
2
0
0
1
1
0
2
0
2
1
0
0
0
0
0
2
0
2
0
1
0
0
0
0
3
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
1
2
1
1
0
0
1
0
0
0
0
0
2
1
2
0
2
0
1
0
0
0
0
2
0
0
2
3
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
1
1
0
1
0
1
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
2
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
2
2
0
1
0
0
0
0
2
0
0
1
1
0
0
0
0
1
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
1
0
2
0
1
0
0
0
0
0
0
2
2
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
1
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
2
2
0
1
1
2
0
0
0
0
2
2
1
0
0
0
0
0
0
4
0
0
2
0
0
0
3
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
2
1
0
0
0
1
0
0
1
0
0
1
0
2
2
1
0
0
0
1
0
0
3
0
0
2
2
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
1
3
0
0
0
0
0
0
0
0
2
0
1
0
0
17
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
1
0
2
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
2
2
0
0
0
3
0
2
1
0
0
0
0
0
0
0
1
1
0
0
2
1
0
2
2
0
0
0
2
0
0
0
0
2
1
0
0
0
1
0
0
2
0
0
1
0
0
0
1
0
1
0
1
0
3
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
2
1
0
0
0
2
0
1
0
0
0
0
0
1
1
1
2
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
1
0
0
0
1
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
4
0
2
0
0
0
0
2
1
0
0
0
0
1
1
3
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
1
0
1
3
0
2
2
0
1
0
0
1
2
2
0
0
1
1
0
0
3
0
0
0
0
0
0
0
0
1
2
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
2
0
0
0
2
1
0
0
0
0
0
1
0
1
0
2
0
1
0
1
0
0
2
0
0
3
0
2
0
1
0
1
0
2
0
0
1
2
0
1
2
0
1
0
0
1
0
0
4
0
0
0
0
0
2
2
0
0
0
0
2
1
1
0
2
0
0
2
0
0
0
1
2
0
0
1
0
1
0
0
0
0
1
2
0
2
1
0
0
0
0
1
1
0
0
1
2
0
0
1
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
2
1
0
0
1
1
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
2
0
1
4
2
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
4
0
9
0
0
0
2
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
1
0
0
2
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
1
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
2
0
2
0
2
0
0
0
1
1
0
0
0
1
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
3
0
0
0
1
2
0
1
0
0
2
0
0
1
2
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
1
1
2
0
0
1
0
0
3
0
1
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
1
2
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
7
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
2
3
0
0
0
2
0
2
1
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
3
1
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
1
0
2
5
0
0
0
0
0
0
0
0
2
1
0
0
2
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
3
4
7
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
2
2
0
1
2
1
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
3
0
0
0
0
2
0
0
1
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
1
0
2
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
3
2
2
0
0
1
0
0
1
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
2
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
1
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
2
0
2
2
0
0
2
3
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
1
0
0
0
0
0
1
1
0
2
0
0
1
0
0
1
1
0
0
0
1
2
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
3
1
0
0
0
0
2
0
0
4
0
2
1
0
1
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
1
0
2
0
0
0
0
1
0
0
0
1
0
2
1
0
0
0
0
0
1
0
0
0
0
1
2
0
0
2
0
0
2
0
0
0
0
0
1
1
2
0
0
1
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
1
0
3
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
2
2
0
0
1
2
0
2
1
0
0
0
2
0
0
2
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
3
0
2
2
1
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
2
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
3
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
1
2
0
0
0
1
0
0
1
0
1
2
0
0
0
2
0
0
1
1
0
0
1
0
0
0
2
0
2
2
0
0
2
1
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
2
2
2
0
1
1
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
3
1
0
2
0
0
0
2
0
3
0
2
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
2
0
0
1
0
4
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
2
0
3
0
4
0
0
0
0
2
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
1
0
0
0
0
2
1
2
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
3
4
0
0
0
0
0
0
2
2
2
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
2
0
0
0
3
1
0
0
0
0
2
0
0
0
0
0
2
0
2
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
1
0
2
0
0
0
2
0
0
0
0
0
0
0
2
1
0
2
0
0
0
1
0
1
1
0
0
1
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
1
0
1
2
0
0
1
0
0
0
2
1
0
0
1
0
0
1
3
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
1
0
2
0
0
0
2
0
0
3
0
0
0
2
0
0
1
0
0
1
0
0
0
1
0
1
1
5
0
0
2
0
1
0
2
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
1
1
0
1
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
3
0
2
0
1
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
3
0
3
0
1
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
2
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
3
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
2
0
1
2
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
3
0
0
1
1
0
2
2
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
2
2
2
1
1
1
1
0
1
2
0
1
2
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
2
0
0
1
0
2
1
0
0
2
0
0
0
0
0
2
0
3
2
1
0
0
0
0
2
0
0
0
2
0
1
0
0
0
2
2
3
0
0
0
0
2
1
0
1
1
0
0
0
0
2
0
2
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
1
1
0
0
2
0
0
1
2
0
0
0
0
2
0
0
0
3
1
0
0
0
0
0
0
0
0
2
0
0
1
0
6
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
2
0
0
0
2
1
1
0
0
0
2
0
0
1
2
5
0
0
2
0
0
0
2
2
0
2
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
2
0
2
0
2
0
0
0
2
0
0
1
0
1
0
1
0
0
0
2
0
2
0
0
0
1
0
1
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
1
3
2
2
0
0
1
1
0
5
0
4
0
0
0
0
0
1
0
0
2
2
0
0
0
1
0
2
0
0
4
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
2
1
0
0
0
1
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
2
1
0
0
0
2
1
2
1
1
0
0
0
1
0
0
1
1
0
0
0
2
0
0
0
6
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
2
4
2
2
0
0
1
0
0
0
0
0
0
1
0
2
0
1
2
0
0
0
0
0
0
2
2
2
0
1
0
0
2
0
0
0
0
2
1
0
0
0
0
1
1
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
2
0
0
0
0
2
0
0
1
1
1
1
0
0
0
0
0
0
0
0
2
2
0
2
2
0
2
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
10
1
2
0
1
0
0
1
0
0
0
1
1
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
3
0
0
1
0
0
1
1
1
0
0
0
0
1
0
1
0
0
2
0
0
2
0
2
0
0
2
1
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
2
3
2
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
1
2
0
0
0
0
1
0
2
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
2
1
1
0
0
0
1
0
0
0
2
0
3
0
0
1
2
0
0
0
0
0
4
0
0
0
0
0
2
0
2
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
1
2
0
2
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
2
1
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
3
0
0
0
1
0
0
0
2
1
0
1
0
0
2
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
4
0
2
0
0
2
0
0
0
2
1
0
0
0
0
0
1
1
2
0
1
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
1
4
0
0
1
0
2
0
0
0
0
0
0
0
0
2
1
2
0
0
3
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
2
1
3
0
0
0
1
0
0
1
0
2
0
1
2
0
1
0
2
2
1
0
1
0
0
3
0
2
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
2
2
0
0
2
2
0
0
0
1
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
2
1
0
0
1
0
1
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
1
2
2
0
0
0
2
0
0
2
0
3
0
0
0
0
0
0
0
2
2
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
2
0
0
1
0
2
4
1
0
0
0
0
0
0
1
0
0
1
2
0
0
0
2
2
1
2
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
5
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
2
2
0
0
2
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
1
2
3
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
1
0
1
0
0
2
0
0
0
5
0
1
1
0
2
0
0
2
0
1
2
0
0
0
0
0
2
3
2
0
0
0
0
4
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
1
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
2
1
3
0
0
0
0
1
0
3
0
3
1
2
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
1
0
3
0
0
2
0
0
2
1
0
1
0
0
0
0
0
0
0
1
0
2
0
1
1
1
2
1
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
2
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
2
1
1
0
2
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
2
1
0
0
0
0
0
1
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
3
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
1
3
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
1
2
1
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
3
1
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
5
0
0
2
1
0
0
0
0
2
0
0
2
0
2
0
1
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
1
0
3
0
0
1
0
1
0
1
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
1
2
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
2
2
1
0
0
0
1
2
0
0
0
0
1
2
2
2
0
0
1
0
1
0
0
0
1
1
0
0
2
2
0
0
0
0
0
1
0
0
0
0
1
0
0
3
0
1
0
0
0
0
0
0
0
3
3
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
3
2
0
0
0
3
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
9
0
0
0
2
0
0
0
0
1
0
0
3
4
2
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
3
0
1
0
1
1
2
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
4
0
2
0
0
0
0
2
0
3
0
0
2
0
2
0
1
0
0
0
0
0
2
1
0
1
2
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
1
1
0
1
2
0
0
0
0
0
2
0
0
0
0
2
1
0
2
1
1
0
2
1
2
1
1
0
0
3
0
0
1
0
0
2
1
0
0
0
0
2
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
1
0
0
1
2
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
1
0
2
0
1
1
0
0
0
0
0
0
1
2
0
0
0
0
1
1
2
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
3
0
0
0
0
0
2
1
0
0
2
1
0
0
0
0
2
0
0
0
0
3
1
0
0
0
3
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
4
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
1
0
1
2
0
0
0
2
0
0
0
0
0
2
0
0
1
1
1
0
0
0
3
0
2
0
0
0
0
0
0
2
0
1
0
0
1
0
2
0
2
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
3
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
2
1
0
2
2
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
3
0
0
0
0
0
1
1
4
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
1
2
2
0
1
1
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
3
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
1
0
1
1
0
2
0
1
0
3
1
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
2
2
1
0
5
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
2
1
1
1
1
0
2
0
0
0
0
2
0
2
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
2
2
1
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
1
2
2
0
0
2
0
0
2
1
0
0
0
2
0
0
0
0
1
2
2
0
1
0
1
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
2
1
0
0
0
0
1
1
0
0
0
2
0
3
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
3
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
2
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
4
0
0
1
0
2
0
2
3
0
2
0
0
0
1
0
0
2
0
2
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
1
0
1
1
0
0
1
0
0
0
0
3
0
0
0
0
0
3
0
2
0
0
0
2
0
0
0
0
0
2
1
0
0
1
2
1
0
0
0
0
0
0
2
0
0
0
0
4
0
1
0
3
0
1
0
1
0
0
0
0
1
0
1
0
0
0
2
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
1
2
0
0
2
0
2
2
0
4
1
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
1
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
4
0
0
0
2
0
0
0
1
0
0
1
0
1
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
5
0
1
0
0
0
0
0
0
3
1
2
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
1
0
0
1
0
1
2
3
0
1
1
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
2
0
0
0
0
2
2
1
0
0
0
0
0
0
1
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
2
3
0
3
0
0
2
0
2
1
2
1
2
0
2
0
0
0
0
1
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
1
0
0
0
0
0
1
0
0
2
1
0
0
3
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
1
1
1
1
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
4
0
0
0
0
2
1
1
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
1
0
0
2
0
1
0
0
0
6
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
2
0
2
1
0
2
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
1
0
2
0
0
2
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
2
0
0
1
0
2
0
0
0
1
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
2
1
2
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
2
1
2
0
2
0
0
1
0
0
1
0
0
1
2
0
2
0
0
0
1
0
2
0
0
0
0
2
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
2
2
0
1
0
0
0
2
2
0
0
2
0
2
0
0
0
0
2
0
0
0
2
0
3
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
2
0
2
2
1
0
2
0
0
2
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
2
0
0
2
0
0
0
0
2
2
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
1
0
0
0
1
0
1
0
3
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
2
0
0
0
2
2
0
0
1
0
0
0
0
1
1
0
2
2
0
0
0
0
0
2
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
2
0
2
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
2
0
0
2
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
2
0
0
1
0
0
1
0
0
2
0
0
0
0
6
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
2
0
1
3
1
2
1
1
0
1
0
0
0
0
4
0
0
1
0
0
2
0
0
0
0
1
3
0
1
0
0
0
0
0
3
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
4
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
1
0
7
0
0
0
2
0
0
1
0
2
2
0
0
0
0
2
0
0
0
1
0
0
1
1
2
0
1
2
0
2
0
0
0
0
3
0
0
2
1
1
2
0
2
2
2
1
0
0
0
2
0
0
2
3
0
0
2
0
0
1
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
3
0
0
0
0
0
1
2
2
1
0
0
0
2
2
0
0
0
1
1
1
0
0
0
3
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
2
4
0
0
0
3
0
2
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
3
1
0
0
0
1
2
1
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
5
0
2
0
6
0
0
0
0
0
1
2
0
0
0
1
0
1
0
0
1
1
0
0
0
1
0
0
1
0
1
0
0
0
2
0
1
1
0
0
0
0
1
0
0
2
0
2
0
0
1
4
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
2
1
1
0
0
6
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
2
0
2
2
2
2
1
0
2
0
2
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
1
0
2
0
2
0
2
0
0
0
3
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
2
0
2
1
0
0
1
1
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
2
0
1
0
1
0
1
0
0
3
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
1
0
3
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
2
2
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
1
0
1
1
0
0
3
0
0
1
2
0
6
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
1
0
3
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
1
1
0
4
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
1
0
2
0
0
0
1
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
1
2
0
3
2
0
0
2
2
0
0
0
0
2
0
2
0
0
1
2
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
2
0
0
0
1
0
0
2
2
1
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
1
2
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
2
2
0
1
2
1
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
1
3
1
0
0
1
0
1
0
0
0
0
2
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
2
0
2
0
2
7
0
2
0
2
0
0
0
0
1
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
1
0
0
0
0
0
1
1
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
2
0
2
1
0
0
2
0
0
0
5
1
1
0
2
1
2
0
0
1
0
1
0
1
0
0
0
2
1
1
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
1
3
2
0
0
0
0
1
0
0
0
0
0
3
0
0
0
1
0
1
0
0
1
2
0
2
0
0
0
0
0
1
2
1
0
0
2
2
0
1
2
0
2
0
0
1
1
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
3
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
2
1
0
1
2
0
0
0
2
0
0
2
0
0
0
1
0
0
1
1
1
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
2
1
0
0
0
2
0
0
6
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
3
3
2
0
0
0
2
2
0
0
1
0
0
0
1
0
1
0
0
0
0
1
2
1
0
0
2
0
0
2
0
0
0
0
0
0
1
0
5
0
0
2
2
1
0
0
1
0
3
1
0
0
1
1
0
0
0
0
0
2
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
2
0
0
0
1
1
1
0
0
2
0
0
0
0
0
0
0
1
2
1
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
1
0
0
1
2
0
0
1
0
0
0
1
0
0
0
1
2
1
0
1
0
0
0
0
0
2
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
2
0
2
1
1
0
0
0
0
0
3
0
0
1
0
0
2
0
1
0
0
1
7
0
0
0
1
3
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
3
0
3
0
0
0
1
0
0
1
0
0
0
6
1
0
3
0
0
1
2
1
0
1
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
1
1
1
1
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
2
1
0
0
0
2
0
0
0
2
0
0
1
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
2
0
2
2
2
3
0
1
0
0
3
0
0
0
2
0
0
0
2
2
1
0
0
0
0
1
0
0
0
2
0
2
0
1
0
0
1
0
0
2
1
0
0
0
0
1
1
2
2
2
0
0
0
0
2
1
1
0
1
0
0
1
1
0
0
0
2
1
0
2
0
1
0
2
0
0
0
0
0
0
0
2
0
1
1
3
1
0
2
0
0
4
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
2
0
1
0
2
0
0
2
1
2
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
2
0
2
3
0
0
3
1
0
2
1
0
2
0
0
0
2
1
0
0
0
0
0
0
0
2
1
0
2
0
2
0
0
0
0
2
2
1
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
4
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
2
2
0
1
0
0
2
2
0
0
1
2
0
0
0
0
0
5
0
0
0
0
0
0
0
0
1
0
1
0
1
0
2
0
0
3
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
1
1
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
1
1
2
0
2
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
2
0
1
2
0
0
2
1
0
0
0
2
0
1
2
0
0
0
0
0
2
0
0
0
0
4
1
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
1
2
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
2
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
1
0
0
1
0
0
0
2
1
0
0
0
0
0
2
0
1
0
0
1
0
2
2
2
2
0
0
2
0
0
0
0
1
0
1
0
0
0
2
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
2
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
2
0
0
2
1
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
2
0
0
1
0
1
0
2
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
2
0
1
0
0
2
0
0
0
2
0
0
0
1
0
0
1
4
2
0
1
0
0
2
1
0
0
1
2
3
0
0
1
0
2
0
0
0
0
0
0
0
0
0
3
2
1
2
0
0
2
1
0
0
0
0
1
0
0
2
0
0
1
0
0
1
1
0
1
1
1
1
3
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
3
0
2
0
0
1
0
2
1
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
2
0
0
1
0
0
0
1
0
0
1
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
2
0
4
0
1
0
0
3
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
1
0
2
0
0
1
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
2
0
0
1
0
0
0
0
3
0
0
0
2
5
0
1
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
2
2
0
2
3
0
1
0
0
0
0
0
0
1
0
0
1
3
0
0
0
0
2
2
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
2
1
2
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
3
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
2
0
2
0
0
0
0
0
0
2
2
2
0
0
1
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
2
2
0
0
0
5
1
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
2
2
0
0
2
2
0
4
1
0
0
0
2
0
0
0
1
0
0
0
2
2
2
2
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
3
0
0
0
2
1
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
2
7
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
5
0
0
0
1
0
1
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
1
1
0
2
0
2
2
0
0
2
0
0
0
0
0
0
0
2
2
1
2
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
1
2
2
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
2
1
0
1
1
0
0
2
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
3
2
0
3
2
0
0
0
2
3
0
0
2
1
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
2
1
0
2
0
1
0
0
0
0
1
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
2
2
0
0
2
0
0
0
0
2
1
0
2
2
0
0
0
0
1
0
0
1
2
1
0
0
0
0
2
1
2
2
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
1
2
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
1
0
1
0
1
2
0
0
0
0
0
1
0
2
0
0
3
0
0
1
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
2
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
2
1
0
0
3
0
0
0
1
1
2
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
3
0
0
2
0
0
2
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
1
0
0
1
0
2
2
5
1
0
0
2
0
0
0
4
0
1
0
0
2
1
0
0
2
0
2
0
1
0
0
1
0
1
1
2
0
3
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
3
2
2
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
2
2
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
1
2
0
0
0
0
1
1
0
0
0
3
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
1
1
2
0
0
1
0
0
4
0
0
0
1
1
1
0
1
0
3
0
0
0
0
1
3
1
3
0
0
0
2
0
0
1
0
0
1
0
1
1
3
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
2
1
0
0
0
1
0
0
0
0
1
1
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
1
1
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
2
0
1
0
0
0
1
1
1
1
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
1
2
0
0
0
0
3
2
0
0
2
2
0
0
2
0
0
0
2
0
0
0
0
0
1
2
0
2
0
2
0
2
0
0
0
2
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
2
2
0
0
0
0
1
0
1
0
0
0
2
0
2
2
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
2
0
0
1
1
0
1
0
0
0
2
2
2
0
2
0
0
1
0
0
0
0
1
0
2
0
1
0
0
1
2
0
0
1
0
6
0
0
0
0
0
0
0
2
1
0
0
0
0
1
2
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
1
2
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
2
0
0
0
8
2
2
1
0
2
1
0
0
0
2
0
0
2
0
0
1
0
1
1
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
1
0
2
0
0
4
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
2
1
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
6
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
1
0
2
2
0
2
2
1
2
1
2
1
0
0
0
0
0
2
3
0
1
0
2
0
1
0
3
2
0
0
1
1
0
0
0
1
0
1
1
0
0
0
0
0
0
2
1
1
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
3
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
1
2
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
1
2
1
0
0
1
1
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
2
0
0
2
0
2
0
0
0
0
2
9
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
1
0
0
1
0
1
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
3
0
0
2
0
1
1
0
0
0
0
0
1
1
6
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
2
2
0
0
0
1
1
0
0
0
2
0
1
0
2
0
0
0
0
1
0
0
2
0
1
3
2
5
1
2
1
1
2
2
0
0
1
1
2
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
1
0
2
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
2
0
0
1
2
0
0
2
0
0
0
0
1
0
2
0
3
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
4
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
1
1
0
0
1
0
0
0
1
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
1
0
2
0
0
0
0
0
0
0
0
2
2
2
1
0
2
2
0
2
5
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
2
0
2
0
0
0
1
0
2
0
0
0
0
0
2
0
0
2
0
2
2
0
1
1
0
1
0
4
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
1
2
0
0
2
0
1
1
0
0
0
1
2
0
0
1
0
0
0
1
0
1
1
1
1
2
0
0
0
3
1
0
1
0
2
2
0
0
0
0
2
0
0
1
0
0
1
0
2
2
0
0
0
3
1
1
0
0
0
0
0
2
1
0
0
2
0
1
1
0
0
0
1
0
1
0
1
2
0
1
0
0
1
6
0
1
0
0
0
0
2
1
0
0
0
0
0
0
2
1
0
2
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
1
2
1
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
2
0
0
1
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
1
0
1
0
0
1
0
1
2
1
0
1
2
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
5
0
1
0
1
0
2
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
2
1
0
0
1
2
0
0
0
1
1
0
1
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
1
0
1
3
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
2
1
0
0
0
3
0
0
1
1
1
1
2
1
0
3
1
0
0
1
4
1
0
3
0
0
0
1
0
0
0
2
0
0
0
2
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
5
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
2
5
1
2
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
1
0
0
0
2
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
1
0
0
2
1
0
0
0
2
0
2
0
2
0
0
0
2
0
2
0
0
0
2
2
2
2
1
1
0
3
3
1
0
2
0
0
0
2
1
0
0
0
1
0
2
0
2
2
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
2
0
1
0
1
1
0
0
0
1
1
0
0
1
3
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
14
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
1
1
0
2
0
0
0
0
2
1
0
0
0
2
0
1
1
0
0
0
2
1
0
2
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
1
0
2
0
2
0
2
2
0
0
1
0
0
0
0
0
0
0
1
0
1
2
0
0
0
1
2
0
0
0
2
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
2
0
1
1
1
0
0
0
0
0
0
2
0
0
0
2
0
5
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
2
0
0
0
0
0
0
8
2
0
0
0
0
0
0
0
0
0
0
2
0
3
0
1
0
0
1
0
0
3
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
1
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
2
0
2
1
0
0
0
0
2
0
0
1
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
1
1
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
2
0
1
0
2
2
3
0
0
0
0
0
0
0
0
1
3
0
0
0
0
1
1
1
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
1
0
0
1
2
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
3
1
0
0
1
1
2
0
0
2
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
1
2
2
0
0
8
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
1
2
0
1
2
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
3
1
0
1
0
0
0
1
1
0
0
1
0
1
0
2
0
0
0
1
0
1
2
0
0
0
1
0
1
0
2
0
2
2
2
0
1
0
0
2
1
0
0
0
0
0
0
2
0
1
0
0
2
0
1
0
2
2
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
1
2
0
0
3
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
2
2
0
2
2
2
0
1
0
1
0
0
0
0
2
0
2
1
0
1
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
2
0
0
0
2
0
1
0
2
0
0
1
1
2
0
0
0
3
1
0
0
1
0
2
1
2
0
0
0
0
0
2
2
0
1
1
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
1
0
0
0
0
2
2
0
2
0
1
2
0
1
1
0
0
0
0
0
8
2
2
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
4
0
0
2
2
0
1
0
0
1
0
1
0
1
2
0
0
0
1
0
0
0
0
2
2
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
1
0
0
1
0
0
0
0
1
0
0
0
0
1
2
0
0
1
0
1
0
2
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
2
0
2
0
0
0
2
2
1
0
0
0
0
3
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
3
0
0
0
0
0
3
0
4
0
0
0
6
0
0
0
0
3
0
2
2
0
0
0
0
2
1
0
0
1
0
1
1
2
0
1
0
0
2
0
0
2
0
0
0
0
0
1
0
2
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
1
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
1
0
0
0
3
1
2
0
0
0
0
0
2
0
1
0
0
2
0
0
3
0
1
0
0
0
0
0
1
1
0
1
0
1
1
0
0
3
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
3
2
2
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
1
0
2
2
0
0
0
1
0
0
3
0
0
0
0
1
0
1
0
0
0
1
0
0
2
0
0
0
0
2
2
0
0
2
0
1
2
0
0
2
0
0
0
1
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
2
0
0
1
0
0
2
2
0
0
2
1
0
0
1
0
0
0
0
1
2
0
0
0
0
2
0
0
0
1
2
0
0
0
2
0
0
0
0
2
0
0
1
0
0
1
0
1
1
0
2
0
0
1
2
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
2
5
0
0
1
0
1
0
3
1
2
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
1
0
0
0
2
0
1
1
1
1
0
1
2
1
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
2
2
0
0
0
1
0
0
0
0
0
2
0
0
1
0
2
0
0
2
2
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
3
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
2
0
0
0
1
1
1
0
1
2
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
2
0
4
1
0
0
0
0
0
0
0
0
3
0
1
2
0
2
0
0
0
0
0
2
0
0
8
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
2
0
0
2
2
0
0
0
1
0
0
0
2
0
0
0
0
1
1
0
4
4
2
0
0
2
0
0
0
0
0
0
2
2
0
2
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
2
0
2
0
2
2
0
2
0
0
0
2
0
1
0
1
0
0
0
1
2
0
2
2
2
1
0
0
1
2
0
0
2
3
2
3
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
2
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
3
0
0
0
2
0
2
0
0
0
0
1
1
0
2
2
2
0
0
1
1
1
3
1
1
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
2
0
0
2
1
2
0
0
0
0
2
1
2
0
0
0
0
0
0
0
1
0
1
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
3
0
2
1
0
0
1
1
1
0
0
0
0
0
0
0
4
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
2
1
0
2
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
1
2
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
2
5
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
3
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
12
1
1
0
2
0
0
1
0
0
2
0
0
0
2
1
1
1
2
0
0
0
2
2
1
0
0
1
1
3
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
3
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
3
0
1
2
0
0
0
2
2
0
2
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
1
0
1
0
0
2
2
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
1
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
2
3
2
0
2
0
0
0
0
0
0
0
0
1
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
2
2
2
1
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
1
0
1
2
0
0
0
1
2
0
0
0
1
0
2
2
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
4
0
0
0
0
1
0
1
0
0
2
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
2
0
3
0
1
0
0
2
0
0
0
0
2
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
2
1
1
0
0
0
1
0
0
1
0
0
2
3
0
1
0
2
0
0
1
1
0
3
1
0
2
2
0
0
1
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
2
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
1
2
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
4
0
0
2
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
1
0
0
0
3
4
0
1
1
0
0
0
0
3
0
1
1
0
0
0
0
0
0
0
0
0
2
0
1
2
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
2
0
1
0
2
1
0
3
0
0
0
0
0
1
0
0
0
0
0
0
5
2
1
0
0
0
0
0
2
0
0
2
1
0
0
0
1
2
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
1
0
0
0
1
1
0
0
0
0
0
0
1
2
0
2
2
1
0
1
0
0
1
0
2
0
0
1
0
0
0
4
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
3
1
0
0
2
0
0
0
2
0
1
1
1
0
0
0
0
2
0
0
0
0
0
0
3
0
1
1
0
0
0
0
0
0
1
2
0
0
0
2
2
2
2
0
0
0
1
0
0
0
0
0
0
2
1
0
1
1
0
0
0
0
1
0
0
0
1
4
0
0
0
1
1
0
0
2
0
0
0
1
0
0
2
0
0
0
0
2
1
0
0
0
4
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
1
0
0
1
10
0
0
1
2
0
0
0
1
1
0
0
1
0
0
0
0
0
0
2
0
0
0
1
3
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
2
0
0
1
0
0
0
2
0
0
1
0
2
2
0
0
0
3
2
0
0
0
3
0
4
0
0
3
0
2
0
0
0
0
0
3
0
0
0
1
2
1
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
5
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
4
2
2
0
0
3
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
2
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
1
1
0
2
0
0
0
1
1
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
2
0
0
1
3
0
0
1
0
0
0
0
0
0
3
0
0
2
0
2
0
0
0
1
1
1
2
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
7
0
0
1
0
1
1
0
0
2
0
0
0
0
0
7
0
2
2
1
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
2
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
3
1
0
0
1
0
0
0
1
0
0
0
3
0
0
2
1
0
1
1
0
0
0
0
1
1
1
2
0
0
0
0
2
1
0
0
0
1
2
0
1
0
0
2
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
2
1
3
0
1
0
0
2
1
0
0
4
0
0
1
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
1
2
2
0
0
0
0
0
0
0
0
0
0
5
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
3
2
0
0
0
0
0
0
0
2
1
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
1
0
0
0
2
2
2
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
1
0
1
2
1
0
0
0
0
0
0
0
1
0
0
0
1
1
2
0
1
0
2
0
0
0
1
2
0
0
1
0
0
0
0
1
2
0
2
1
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
1
0
1
2
1
0
0
1
1
0
0
3
2
0
0
0
3
0
0
0
0
0
2
1
4
0
0
2
0
0
0
0
2
0
1
0
0
2
0
0
0
0
2
2
0
1
1
0
1
0
0
0
1
0
0
2
1
2
0
0
1
0
0
2
0
1
1
1
1
1
0
0
1
0
0
1
0
0
0
1
0
3
0
0
2
0
2
0
0
0
0
0
3
0
0
0
1
2
0
2
1
1
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
2
1
0
2
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
4
1
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
3
0
0
0
0
1
0
2
2
0
0
0
0
0
0
2
1
0
0
1
2
0
2
0
0
0
3
0
0
0
0
0
2
0
1
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
1
0
1
0
0
0
1
2
1
0
0
2
0
0
2
0
1
0
1
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
3
1
0
2
0
0
0
0
0
0
0
2
1
1
0
2
0
0
0
0
0
0
1
2
0
0
1
0
2
0
0
1
2
0
2
0
0
0
0
0
2
0
0
0
3
0
1
3
0
0
2
1
2
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
1
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
2
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
7
2
2
0
0
2
2
1
2
0
0
2
0
0
0
0
0
1
0
3
0
0
0
0
3
2
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
1
2
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
1
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
3
0
0
0
0
0
1
1
1
2
0
0
0
0
0
0
2
2
0
0
1
2
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
3
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
2
2
0
0
0
0
0
0
1
1
2
0
0
0
0
0
2
0
2
0
0
0
0
1
0
1
0
2
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
1
0
3
0
0
0
2
2
0
0
0
1
0
0
0
0
1
1
0
2
0
2
1
2
0
0
0
1
0
0
2
0
1
2
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
1
0
2
3
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
1
0
1
2
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
1
0
0
0
0
0
0
1
2
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
1
1
2
0
1
1
0
0
0
1
1
0
0
2
1
0
0
4
0
0
1
0
0
1
1
1
0
0
0
0
1
0
1
0
1
3
0
1
0
0
0
0
0
0
6
0
0
0
0
0
0
2
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
2
0
0
0
1
0
2
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
2
0
2
8
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
1
0
1
4
0
1
1
0
2
1
0
0
0
1
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
2
2
1
2
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
2
0
0
0
0
2
1
1
0
0
0
2
0
1
2
2
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
1
1
1
0
1
0
0
0
1
0
0
2
0
0
1
0
1
0
2
1
0
0
0
0
0
0
2
2
0
0
0
0
4
1
0
1
1
0
0
0
2
1
0
0
0
2
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
1
2
1
0
1
1
0
0
1
1
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
2
0
1
0
2
1
4
2
2
3
0
0
0
0
0
0
0
2
0
0
3
2
1
1
0
0
0
0
2
0
0
0
2
0
0
2
0
0
1
0
2
2
0
0
0
1
4
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
3
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
1
2
2
0
0
2
0
2
1
0
0
1
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
1
1
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
1
2
1
1
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
4
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
2
2
1
2
2
1
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
1
2
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
1
0
2
0
0
0
0
2
0
3
0
0
0
2
1
0
0
1
1
2
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
1
2
0
0
0
3
1
2
1
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
4
0
0
2
2
0
0
2
0
0
0
2
0
1
0
0
0
0
1
2
0
0
5
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
2
0
3
3
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
1
0
1
2
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
1
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
1
4
2
2
1
0
1
0
0
0
2
0
0
0
3
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
2
0
1
2
2
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
2
2
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
6
0
0
2
0
0
0
4
1
0
0
1
0
2
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
2
3
2
0
0
0
0
0
0
1
0
2
0
1
4
1
0
1
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
1
0
4
0
2
0
1
4
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
2
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
3
0
0
0
1
1
0
0
0
0
0
0
1
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
3
0
0
3
0
0
0
0
2
2
2
1
0
0
1
0
0
1
2
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
1
1
0
0
0
2
1
0
0
4
0
0
2
1
3
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
3
0
0
0
1
1
0
1
0
0
0
0
2
0
0
2
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
1
0
0
0
2
0
3
0
1
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
1
0
0
1
1
2
2
0
0
0
0
0
1
0
0
0
0
0
6
0
0
1
2
0
0
0
1
0
2
0
2
0
0
2
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
1
0
2
0
0
0
0
0
2
0
1
0
2
0
0
1
1
1
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
2
0
0
0
2
0
2
2
1
0
1
0
0
0
0
0
1
0
1
0
2
0
0
0
2
1
0
0
2
0
0
0
0
0
1
1
0
0
2
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
4
2
0
0
0
1
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
2
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
4
0
0
0
0
2
2
0
0
1
1
0
0
0
1
6
0
0
2
1
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
1
0
0
0
1
0
2
0
0
0
0
0
1
4
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
2
1
0
1
0
3
0
0
2
0
0
0
1
0
1
0
0
1
1
0
0
0
2
0
0
0
0
1
0
1
0
0
1
2
0
0
1
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
1
2
0
1
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
2
0
0
0
0
0
0
0
0
0
1
0
5
1
0
0
1
0
2
2
1
0
0
2
0
0
0
0
0
2
0
4
0
1
0
2
0
2
0
2
0
0
0
3
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
2
2
0
3
1
0
0
2
0
0
0
1
0
0
2
0
0
0
2
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
3
1
0
0
1
1
0
0
1
2
0
1
0
0
0
2
1
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
2
2
2
2
1
1
0
2
0
0
0
2
2
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
1
0
1
1
0
1
0
0
3
0
0
0
7
0
0
0
0
0
0
0
1
0
1
1
0
2
0
0
1
2
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
1
0
0
1
0
3
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
2
0
1
0
1
0
0
0
0
3
0
0
2
2
1
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
1
0
0
1
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
1
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
2
0
0
2
3
0
2
0
0
0
2
1
0
0
0
1
2
0
2
1
0
0
0
1
0
0
0
4
1
0
0
0
0
1
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
2
0
1
2
2
0
0
0
0
2
0
1
0
1
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
3
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
2
0
0
0
2
4
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
1
2
0
1
1
0
1
0
0
0
0
0
1
1
2
5
0
0
0
0
0
2
0
1
0
1
0
0
0
0
2
0
0
0
0
1
0
0
2
0
1
2
0
0
0
1
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
2
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
2
2
0
0
0
1
0
2
0
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
3
0
0
0
1
2
2
1
0
2
0
0
0
0
1
0
2
0
1
0
1
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
1
2
0
0
2
0
2
0
2
0
0
0
0
0
2
0
0
2
1
1
0
0
2
1
1
0
0
0
1
2
0
1
0
2
0
3
5
0
0
0
0
0
0
1
0
0
0
3
0
2
3
1
1
0
0
0
2
0
2
1
2
0
1
0
1
0
0
0
0
0
0
1
2
0
2
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
2
1
0
0
1
0
4
0
1
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
1
0
0
1
0
0
0
0
1
0
0
2
0
2
1
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
5
0
0
0
0
0
0
0
0
6
2
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
3
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
2
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
2
0
4
1
0
0
0
0
0
1
0
0
3
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
1
0
1
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
1
0
0
3
0
0
0
2
2
0
1
0
0
0
0
2
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
1
0
2
0
4
0
0
1
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
7
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
2
0
0
0
0
1
0
0
0
0
2
2
1
0
0
1
2
1
1
0
0
0
1
0
1
0
2
0
1
2
1
1
0
1
0
0
2
1
2
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
4
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
1
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
2
0
1
0
0
1
2
0
0
1
0
0
0
2
0
1
2
1
0
0
1
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
2
0
2
0
0
1
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
2
2
1
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
1
1
0
1
2
0
2
1
0
0
0
1
0
0
3
2
0
1
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
4
0
2
1
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
2
0
0
2
0
0
0
0
1
0
1
1
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
2
0
2
0
1
0
0
0
0
0
2
5
0
1
0
0
0
0
2
0
0
0
4
1
0
0
1
2
0
0
1
3
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
2
1
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
3
0
0
0
0
2
0
0
0
0
0
0
3
0
2
0
0
1
0
2
0
0
3
2
0
0
0
0
1
1
1
1
2
2
0
0
1
0
0
2
1
0
0
0
1
0
0
0
7
0
0
0
2
0
2
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
1
2
3
0
0
0
0
0
0
0
1
4
0
0
1
2
3
0
2
1
0
1
0
0
2
0
0
3
0
2
0
2
0
0
0
0
0
1
0
0
2
3
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
7
0
0
0
0
2
1
0
0
1
0
3
2
2
1
0
0
0
2
1
0
1
0
0
1
2
0
2
0
0
0
0
1
0
1
0
2
0
0
0
0
2
0
0
1
0
0
0
5
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
2
0
0
1
0
1
0
0
0
2
2
0
0
0
0
0
0
1
0
0
2
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
6
0
0
0
2
0
3
0
0
1
0
0
1
0
2
2
0
1
2
1
0
0
0
0
1
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
2
0
0
1
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
2
0
0
0
0
1
0
0
1
1
2
0
1
1
3
0
0
2
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
1
5
0
0
0
1
0
0
0
0
0
0
2
2
0
2
0
0
0
0
2
0
0
0
2
1
0
0
3
0
0
0
2
1
0
0
0
3
0
0
2
2
0
0
2
0
0
0
0
2
1
0
2
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
4
2
0
0
0
0
0
0
0
2
0
0
0
1
2
1
2
0
2
2
0
1
0
1
0
0
1
0
0
0
0
2
0
0
4
0
1
2
0
2
0
5
0
0
0
0
3
0
0
0
0
0
0
0
3
0
0
0
2
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
2
1
0
2
0
0
2
1
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
1
0
0
3
1
1
0
2
0
0
5
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
8
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
2
1
0
0
0
1
0
0
0
1
3
1
0
0
1
0
1
0
1
0
2
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
1
0
2
0
1
1
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
2
0
1
0
3
0
0
0
0
3
4
0
2
1
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
1
1
1
0
0
1
0
2
1
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
2
0
2
0
0
0
2
1
0
0
1
0
0
0
0
1
2
0
1
0
2
0
1
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
1
3
0
0
0
1
1
0
4
0
0
0
0
0
1
0
0
0
0
0
2
2
0
4
1
0
2
0
2
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
3
1
0
0
1
2
0
1
1
2
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
2
0
0
1
0
1
0
0
0
0
0
2
0
0
1
0
0
1
0
2
0
2
0
0
0
0
0
0
4
0
0
0
2
0
2
0
0
0
0
2
2
0
0
0
0
2
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
2
0
0
2
0
0
0
0
2
0
1
2
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
2
0
2
1
0
1
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
2
0
0
0
0
0
1
2
0
0
1
0
1
0
3
0
2
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
2
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
2
2
0
2
5
1
0
1
2
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
3
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
1
1
0
1
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
1
0
1
0
2
0
3
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
2
2
0
1
1
1
0
0
1
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
1
5
2
0
0
0
0
0
0
0
0
0
0
2
1
3
1
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
2
0
1
0
0
0
2
0
3
0
0
0
1
0
3
0
0
0
3
0
0
0
3
2
0
0
1
0
1
1
1
0
2
0
0
0
1
0
0
0
1
0
2
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
2
2
1
6
3
1
0
0
0
0
0
2
0
0
2
2
1
0
2
1
0
2
0
2
2
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
2
0
1
2
1
0
0
0
0
2
1
2
0
0
0
0
1
2
1
0
0
0
1
3
1
0
0
0
1
2
0
0
0
0
0
1
0
0
0
2
2
2
0
1
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
1
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
1
0
1
0
1
0
1
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
4
0
2
2
0
2
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
1
1
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
1
1
0
1
2
0
0
0
0
2
2
0
0
1
0
2
1
0
1
0
0
0
0
0
3
0
2
0
0
0
2
0
0
1
2
2
0
0
0
1
1
0
0
0
2
0
1
0
2
0
0
0
3
0
0
2
2
2
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
3
0
0
2
0
0
0
0
0
1
2
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
2
1
0
0
1
0
1
0
3
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
1
0
2
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
5
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
4
2
0
0
0
0
0
2
0
0
5
0
0
0
2
0
0
0
0
1
0
0
2
1
0
0
2
0
2
0
0
3
0
0
0
0
2
2
1
0
0
0
0
0
2
0
0
0
1
2
0
1
0
0
2
0
2
0
0
0
1
2
0
0
1
0
0
0
0
0
0
2
0
0
1
1
0
0
2
0
0
1
0
0
1
0
0
2
0
0
2
2
0
0
1
2
1
0
0
0
2
0
1
0
2
2
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
2
2
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
1
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
1
2
0
0
1
0
1
0
0
0
1
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
2
0
2
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
2
0
5
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
2
0
1
0
0
0
2
0
2
3
1
0
1
0
0
0
0
0
0
1
1
1
0
0
1
2
0
0
3
0
0
2
0
0
0
0
0
0
0
0
2
2
0
1
0
0
3
2
0
0
1
1
0
0
0
0
1
0
0
1
0
1
0
0
2
2
1
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
2
0
0
0
1
3
0
0
0
0
0
0
2
1
0
0
0
2
0
2
0
2
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
4
0
3
3
0
0
0
1
2
0
1
0
0
0
0
0
2
0
1
0
2
1
1
2
0
0
0
2
1
2
0
0
1
0
3
1
0
2
0
0
0
0
2
0
0
0
3
0
0
0
1
0
0
0
1
8
1
2
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
2
1
0
0
3
0
0
0
0
0
2
1
0
0
0
0
0
0
0
3
2
2
0
0
0
1
1
0
0
4
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
3
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
1
2
1
1
0
0
2
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
2
0
1
0
0
0
0
1
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
1
1
1
0
0
1
0
0
0
3
0
1
1
0
0
0
0
0
0
0
1
4
2
0
2
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
1
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
2
0
1
2
3
0
1
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
3
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
3
2
0
2
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
1
2
0
1
2
0
0
4
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
4
0
0
0
0
0
0
0
2
0
3
0
2
0
1
3
0
2
0
0
0
1
0
2
2
0
0
0
0
0
0
2
0
1
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
2
2
4
2
0
0
1
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
2
2
0
1
0
2
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
2
0
1
0
1
0
0
1
0
0
3
0
0
0
0
0
0
1
0
1
2
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
1
1
0
0
1
2
0
0
1
2
1
2
0
1
0
0
0
2
0
0
0
1
0
1
0
0
0
3
1
0
2
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
3
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
2
2
0
8
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
4
0
2
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
2
0
0
0
3
1
3
0
0
2
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
2
0
0
0
2
0
0
0
2
3
0
0
0
0
0
0
1
2
0
1
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
1
0
0
2
0
0
2
0
0
2
0
0
2
1
1
1
2
1
0
1
1
2
0
0
0
1
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
2
0
0
1
0
2
0
0
1
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
1
1
2
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
2
0
1
0
2
1
2
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
2
0
0
1
0
0
0
7
3
0
1
0
0
0
0
0
3
2
2
0
0
0
1
0
0
1
0
0
3
0
0
2
0
2
0
0
1
0
1
0
0
1
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
2
0
0
2
0
2
1
0
0
0
0
1
0
2
0
0
2
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
1
2
0
0
1
3
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
4
0
0
0
0
1
1
2
0
2
1
2
0
2
0
0
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
3
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
2
2
2
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
2
0
2
0
1
2
3
0
0
2
0
2
1
2
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
2
2
0
0
1
0
2
1
0
0
0
0
3
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
2
0
0
3
0
1
0
1
0
0
0
0
0
0
3
0
0
1
0
0
1
0
0
0
0
0
2
1
0
0
0
5
0
0
1
0
0
0
0
0
0
0
0
0
1
0
3
2
4
0
2
2
0
2
1
3
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
1
0
1
2
0
0
0
0
1
0
2
0
2
1
1
0
1
2
1
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
1
1
0
1
2
0
0
0
1
0
2
0
1
2
1
0
0
3
1
0
0
0
2
0
0
0
2
0
0
0
1
0
2
1
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
2
1
0
0
2
2
0
0
0
0
0
0
0
0
1
2
3
1
0
0
0
0
1
0
2
1
0
0
3
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
2
3
0
0
1
2
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
1
2
2
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
2
0
0
3
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
2
4
2
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
2
1
0
0
2
1
2
0
0
0
0
1
2
1
0
0
1
2
0
0
0
1
1
1
5
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
5
0
1
0
0
0
0
1
0
0
0
1
3
0
0
1
0
1
0
0
2
1
0
1
0
2
2
0
2
2
0
0
2
1
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
2
2
0
1
1
1
0
0
0
2
0
1
0
1
0
0
0
2
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
1
2
1
0
0
0
0
1
1
0
1
0
0
1
0
0
0
2
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
2
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
1
2
3
2
0
0
0
0
0
2
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
1
5
0
0
0
0
0
0
0
0
2
3
0
0
2
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
2
2
0
0
4
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
1
2
0
1
0
0
2
2
0
1
0
0
0
1
0
0
1
2
2
2
0
0
2
0
0
0
0
0
1
0
0
0
0
2
2
0
1
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
1
2
2
0
1
0
0
0
0
0
2
0
0
0
0
2
2
0
0
9
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
3
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
1
2
0
0
2
0
1
0
2
2
0
2
2
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
2
0
1
2
0
0
2
0
0
1
0
2
0
0
0
1
2
0
0
0
1
0
1
0
0
0
0
0
0
1
2
0
0
2
0
0
0
1
0
0
0
1
0
3
0
0
2
0
0
1
1
1
0
1
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
1
1
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
1
0
1
0
0
0
0
0
0
0
2
0
2
0
2
0
1
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
2
0
0
0
0
2
0
0
1
0
0
4
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
2
3
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
1
0
0
0
0
2
0
1
0
1
0
1
3
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
1
1
2
1
0
2
0
1
1
0
0
0
1
0
0
1
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
1
0
1
0
1
0
6
0
0
1
0
0
0
0
0
2
0
2
0
0
1
0
3
1
1
1
0
0
0
0
8
0
0
0
1
0
0
1
2
0
0
1
2
0
1
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
3
1
0
0
0
0
0
0
2
0
0
2
0
2
1
1
0
2
0
4
0
1
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
2
2
1
0
2
2
0
0
2
0
0
2
1
2
0
0
0
0
0
0
2
4
0
0
2
0
2
0
0
0
0
1
1
0
2
0
0
1
4
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
3
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
2
0
1
3
0
0
1
0
0
0
0
0
2
1
2
0
0
0
0
2
2
0
0
0
0
2
0
4
3
1
2
0
1
0
0
0
2
0
1
0
0
0
2
0
3
0
1
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
2
0
2
1
1
0
0
2
0
2
0
0
0
2
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
2
0
0
0
0
2
3
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
3
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
2
0
1
0
0
1
0
0
2
0
1
0
0
2
1
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
2
0
2
0
2
0
2
0
0
0
0
1
0
0
0
0
1
0
2
2
2
0
2
0
2
1
0
0
1
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
1
2
0
1
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
1
2
2
0
2
0
2
0
0
0
2
0
0
0
0
0
2
1
0
0
2
0
0
0
0
1
0
2
3
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
1
2
1
0
0
0
0
0
2
1
0
0
1
0
2
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
5
2
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
3
2
1
0
1
1
0
0
1
0
0
0
2
0
0
1
0
0
0
2
0
0
0
1
2
0
0
0
0
2
0
0
0
0
3
0
2
0
0
0
0
2
5
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
1
1
3
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
2
0
0
1
3
3
0
2
0
0
2
0
0
0
0
2
2
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
2
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
2
1
1
0
0
2
0
0
0
0
1
0
3
0
0
0
0
0
0
2
0
2
1
0
1
1
0
2
2
1
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
1
1
2
2
0
0
0
2
0
0
0
4
0
0
0
0
3
1
1
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
3
0
0
1
0
0
0
1
0
2
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
6
0
0
1
2
0
0
0
0
0
1
2
0
0
1
0
0
1
1
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
2
0
2
0
0
0
0
0
2
1
0
0
2
0
1
1
2
2
3
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
5
0
0
1
0
2
1
0
0
0
1
2
0
0
0
1
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
2
0
1
0
0
0
2
1
0
0
0
3
0
1
1
0
0
0
0
0
2
0
2
2
0
1
2
1
0
0
0
2
0
2
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
2
0
1
2
0
0
2
1
2
2
2
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
1
2
0
0
0
0
1
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
1
1
0
0
0
0
0
2
1
2
2
2
2
0
0
1
1
2
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
2
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
1
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
1
0
0
2
0
2
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
2
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
2
1
2
1
0
0
0
0
1
0
0
2
0
0
0
1
2
0
1
2
0
3
0
0
0
2
0
0
1
2
0
0
0
0
0
2
2
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
3
2
1
2
2
0
1
0
0
1
0
0
0
2
0
0
2
1
0
2
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
4
0
1
0
0
0
1
1
1
1
0
0
1
0
2
0
0
0
0
1
2
1
2
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
1
3
0
0
0
2
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
2
1
0
0
0
1
0
0
3
0
0
0
0
0
0
1
0
1
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
1
1
0
0
2
2
0
0
0
0
2
0
0
0
0
0
1
1
2
2
0
0
2
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
2
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
1
2
0
0
0
2
2
0
0
0
1
0
0
1
0
0
0
3
0
0
1
0
0
1
1
2
2
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
1
0
0
0
0
2
1
0
0
0
0
1
0
0
0
1
2
0
2
0
0
1
1
0
2
2
1
2
0
0
0
0
1
0
0
1
2
0
1
0
0
0
0
2
0
3
0
0
0
1
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
1
0
2
0
0
0
0
2
2
0
0
1
0
1
0
0
0
0
2
0
1
0
3
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
1
0
0
1
0
0
4
0
0
0
0
0
0
2
1
0
0
0
0
1
0
1
0
0
3
0
2
4
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
1
2
4
0
0
0
0
0
2
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
3
1
0
2
0
1
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
2
0
0
1
2
0
3
2
0
1
0
0
0
0
1
2
2
1
2
0
0
0
0
0
0
2
0
2
2
0
1
0
0
2
0
0
2
0
2
2
2
1
0
0
0
2
0
0
2
2
2
1
2
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
1
0
0
1
0
1
1
0
1
0
0
0
3
0
2
0
0
0
2
0
0
2
1
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
1
2
0
0
0
2
1
1
0
1
0
0
3
0
0
0
0
0
2
1
0
0
3
0
2
2
2
0
0
0
0
0
0
0
0
0
3
2
1
0
1
0
0
0
0
0
0
2
0
0
3
1
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
1
2
2
0
0
0
2
0
0
1
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
3
1
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
2
0
3
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
3
0
0
1
1
2
0
0
1
0
0
4
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
2
0
2
0
0
0
0
0
0
0
0
0
5
2
0
0
2
0
0
1
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
3
1
0
0
0
2
0
0
1
0
0
0
0
0
2
1
0
3
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
3
1
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
2
4
1
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
1
2
0
1
0
0
0
0
2
1
0
0
2
0
0
0
0
1
0
0
0
3
1
2
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
2
0
2
0
0
0
1
1
0
1
0
0
2
2
0
0
1
0
0
0
1
0
0
0
1
0
2
0
1
0
2
0
0
0
0
0
2
0
0
2
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
5
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
2
2
0
0
0
5
0
1
0
1
0
0
3
3
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
1
2
1
0
2
2
2
2
0
0
0
0
2
1
0
1
1
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
3
2
0
0
0
2
1
0
2
0
0
0
2
0
0
0
0
0
0
1
0
2
0
2
0
0
1
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
3
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
2
2
0
0
0
0
1
0
2
0
0
0
1
1
0
0
1
0
2
0
0
0
0
0
0
2
0
2
0
0
0
2
1
3
0
0
0
1
0
4
0
1
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
1
0
7
0
0
4
0
1
0
0
0
0
1
0
2
0
1
0
0
1
1
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
3
2
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
3
2
0
4
1
0
0
1
2
0
1
0
1
2
0
0
1
1
0
0
2
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
3
1
2
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
3
1
0
0
1
0
0
2
0
0
0
0
2
0
7
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
1
0
0
0
2
0
0
0
2
0
2
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
2
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
1
1
0
0
1
0
0
0
0
1
0
1
3
0
0
1
0
0
0
2
2
0
0
1
2
1
0
0
2
2
0
0
1
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
2
0
3
3
1
0
1
2
0
0
0
0
0
0
0
2
2
2
0
0
0
0
4
0
2
0
0
2
0
0
0
0
3
0
2
4
0
0
2
0
2
0
1
1
0
1
0
0
1
2
0
2
0
2
2
0
0
0
0
0
0
0
4
1
0
0
2
0
0
0
0
4
3
0
0
0
0
0
0
0
2
0
1
0
5
0
0
1
0
4
0
0
1
0
0
0
0
2
1
0
0
2
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
2
0
0
2
0
0
0
0
2
0
2
0
0
0
0
2
0
2
1
0
3
0
2
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
1
0
0
3
1
0
1
0
0
1
0
1
3
0
0
0
0
0
2
0
3
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
3
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
2
0
3
2
0
0
0
0
0
4
3
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
2
0
2
0
3
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
1
1
0
2
2
0
0
0
6
0
0
0
1
1
0
3
0
0
3
0
0
0
0
5
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
1
2
0
0
1
0
0
1
1
0
0
0
0
0
3
0
0
0
0
1
1
0
2
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
2
1
0
0
2
2
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
3
0
0
0
0
2
1
1
0
1
0
4
2
0
0
1
0
0
0
0
0
1
0
1
1
0
2
1
2
1
0
0
0
0
0
0
0
0
2
0
0
0
4
1
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
1
2
1
0
1
0
0
1
0
1
1
1
0
1
0
2
2
0
0
1
2
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
2
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
2
0
1
0
0
1
1
0
0
0
0
1
0
0
2
0
1
0
1
2
3
1
3
1
0
1
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
2
0
4
0
0
2
2
2
0
1
0
2
4
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
3
1
0
0
2
2
0
1
0
0
0
2
1
0
0
0
0
0
0
0
3
0
1
3
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
1
0
4
0
2
0
2
2
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
2
0
2
0
3
0
0
0
0
0
2
1
1
1
1
0
0
0
1
2
1
0
0
0
2
2
0
1
0
1
0
0
0
0
2
2
0
2
2
0
1
1
0
2
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
1
2
2
0
2
0
0
4
0
0
1
1
2
0
2
0
0
0
0
0
0
2
2
2
0
3
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
4
0
0
0
0
0
1
1
0
0
0
0
0
1
2
1
1
2
0
2
0
2
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
1
2
0
1
0
1
2
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
2
0
2
0
1
1
0
4
0
0
1
0
0
3
1
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
2
0
0
2
0
0
0
1
0
0
1
0
2
2
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
2
1
2
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
5
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
1
0
2
2
0
2
0
0
0
2
2
0
4
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
3
0
0
0
0
2
0
0
1
0
0
0
0
2
1
0
0
4
2
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
2
2
0
1
0
3
0
1
0
3
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
1
0
1
0
0
2
0
3
0
0
2
0
0
0
0
2
0
1
2
0
0
3
1
0
0
0
2
2
0
0
1
0
0
2
0
0
2
1
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
1
1
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
2
0
0
2
0
2
2
0
0
2
2
1
0
1
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
3
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
2
2
2
0
2
0
0
0
0
1
0
0
1
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
1
0
0
1
1
0
1
2
0
0
2
2
0
0
1
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
1
2
2
2
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
2
2
4
1
2
0
0
0
1
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
3
0
0
0
0
2
1
2
2
0
0
0
0
0
0
0
0
2
0
5
0
0
1
1
0
1
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
1
1
0
3
2
0
1
0
0
1
0
2
2
0
0
0
1
0
0
0
1
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
3
1
0
1
0
0
0
2
0
1
0
2
1
1
0
0
1
0
0
0
0
2
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
2
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
1
3
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
1
0
0
1
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
6
0
0
0
0
0
0
2
0
0
0
1
1
0
1
1
0
3
0
1
3
1
0
3
1
0
0
0
0
0
1
0
1
3
0
2
0
1
0
0
0
0
0
0
1
0
0
1
2
0
0
1
0
2
0
0
0
0
1
0
0
1
0
0
1
5
4
0
3
0
0
1
2
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
1
0
0
1
0
0
0
1
2
0
1
2
2
0
0
0
0
0
0
0
1
0
0
0
2
0
1
1
2
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
2
0
2
0
0
2
1
0
2
0
0
0
0
0
0
1
0
0
2
0
3
0
0
1
0
0
2
2
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
1
1
0
0
0
0
2
0
0
1
0
0
0
0
2
1
0
0
0
0
3
2
1
1
1
0
0
0
0
0
2
0
2
2
1
3
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
1
0
0
0
0
1
2
0
0
2
0
0
1
0
0
0
0
1
1
0
2
2
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
2
1
1
0
0
2
0
0
3
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
2
0
0
0
2
1
0
3
0
0
1
0
2
2
0
0
0
0
0
2
0
1
0
0
0
2
1
1
2
0
3
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
2
0
2
2
2
1
0
2
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
2
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
2
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
2
1
0
2
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
1
0
1
2
1
0
1
1
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
1
0
1
0
3
1
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
2
2
0
0
1
1
0
2
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
1
0
0
4
0
0
0
0
2
2
0
1
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
2
0
1
1
0
0
3
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
1
2
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
3
1
2
0
1
0
1
2
0
1
0
0
1
0
2
0
0
2
2
0
0
0
0
0
0
0
0
2
0
1
0
1
1
1
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
2
0
1
1
0
0
1
0
0
1
0
0
1
0
0
0
2
0
0
1
1
0
0
1
5
1
0
1
0
0
0
0
0
0
0
1
0
2
1
0
0
1
0
0
0
0
0
0
0
3
2
0
0
0
0
0
2
0
2
0
0
2
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
2
0
1
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
1
0
2
0
0
0
0
0
0
0
2
0
3
0
0
0
0
2
1
0
0
1
2
1
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
1
0
2
2
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
1
3
0
1
1
0
0
0
2
0
0
0
0
0
0
1
0
1
1
0
2
0
1
1
0
1
0
0
1
0
0
0
0
2
0
1
0
0
0
1
1
0
1
2
2
0
2
0
2
0
0
0
0
0
0
1
2
0
0
0
0
3
2
1
0
0
2
0
2
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
1
1
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
3
1
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
1
0
1
1
0
0
0
1
2
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
1
0
0
0
3
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
2
0
1
1
0
2
1
0
2
2
0
0
0
0
0
1
0
4
0
1
0
0
0
0
2
0
0
1
0
0
1
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
1
0
1
0
0
2
2
2
2
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
1
2
0
0
0
1
0
2
2
2
0
2
2
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
3
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
1
0
0
0
3
1
2
0
0
2
0
1
0
0
2
2
0
0
2
0
0
0
0
0
0
1
0
1
2
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
2
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
4
1
3
1
2
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
4
4
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
2
0
0
0
2
0
1
0
1
0
1
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
5
0
2
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
2
1
1
1
0
0
3
6
2
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
1
1
0
0
0
0
2
2
2
1
0
0
0
0
0
1
1
0
1
0
2
2
1
2
2
0
2
1
0
1
1
0
0
2
0
2
2
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
3
0
0
0
0
0
2
0
0
3
0
0
0
2
1
0
0
0
0
1
1
3
2
0
0
0
1
0
2
0
0
4
0
1
2
1
0
0
0
0
0
0
0
3
2
0
0
2
0
0
0
0
1
0
0
0
2
0
2
2
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
2
3
0
2
0
0
0
4
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
1
0
3
1
0
0
0
0
0
1
0
0
0
0
2
1
0
2
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
1
0
0
0
0
0
2
1
0
0
0
1
2
0
0
0
0
0
0
0
3
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
1
2
0
1
0
0
1
0
0
0
2
0
0
1
0
2
0
1
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
3
0
0
1
1
0
1
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
1
0
2
0
0
2
0
1
1
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
2
0
1
0
1
0
0
0
1
1
0
0
0
1
2
0
0
0
0
1
0
0
0
1
0
0
0
2
4
0
1
1
2
0
1
0
0
0
0
0
2
0
0
0
0
0
2
2
0
2
0
0
0
2
2
2
0
2
0
1
0
0
1
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
3
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
2
0
2
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
2
0
1
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
2
2
3
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
2
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
1
0
0
0
2
3
0
0
1
0
0
0
1
1
0
0
3
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
2
0
1
0
0
0
5
0
0
1
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
2
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
3
2
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
1
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
1
0
9
2
0
2
0
0
2
3
0
0
0
0
3
0
1
0
0
0
1
2
0
0
1
0
0
0
1
0
0
2
1
3
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
1
1
0
0
1
0
1
0
0
4
0
0
0
4
0
1
0
0
1
1
2
2
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
3
0
2
4
0
0
0
1
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
1
0
1
3
0
0
1
0
0
0
0
2
0
0
1
2
2
2
0
1
0
1
0
2
2
1
1
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
3
0
0
1
0
0
1
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
1
0
1
2
0
1
2
0
0
0
0
0
0
2
1
1
0
0
0
0
1
2
0
0
1
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
1
0
0
1
1
0
2
0
0
2
0
0
2
2
2
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
2
1
0
2
0
0
0
0
0
0
0
2
0
0
0
6
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
1
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
1
1
2
0
2
1
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
2
1
0
1
0
1
2
4
0
1
0
0
0
0
0
4
0
0
0
0
0
2
6
0
0
0
0
0
0
1
0
0
1
4
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
2
1
2
2
0
0
0
0
1
5
3
0
0
2
2
0
2
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
1
0
1
0
0
2
0
1
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
2
2
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
4
0
1
0
1
1
2
0
1
0
0
1
1
1
0
0
0
0
1
0
0
2
2
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
1
1
0
0
0
0
0
2
1
0
2
0
1
0
0
0
0
1
2
0
2
0
0
0
1
0
0
0
1
0
0
0
3
0
1
0
0
0
2
0
0
2
2
0
3
0
0
0
4
0
0
0
0
2
1
0
0
0
2
0
0
0
2
1
0
0
2
0
2
1
2
0
0
0
1
2
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
2
0
0
0
1
0
1
0
0
0
3
0
0
0
0
0
0
0
1
1
3
1
0
2
0
0
0
0
0
0
1
2
1
2
0
4
2
0
0
0
0
1
2
2
0
0
0
0
0
0
1
3
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
2
0
2
1
0
0
1
0
0
0
0
0
0
1
2
0
2
1
1
0
1
0
2
3
0
0
0
0
0
0
4
3
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
2
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
2
0
1
0
0
0
0
6
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
2
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
1
2
0
0
2
0
1
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
2
1
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
1
0
1
0
0
0
2
0
2
0
1
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
2
0
0
1
1
2
0
0
0
2
0
2
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
2
0
0
1
0
0
0
0
0
2
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
1
0
4
0
0
1
0
0
0
0
0
2
0
0
0
1
0
1
1
0
0
3
0
2
0
1
0
2
1
2
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
1
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
3
0
0
0
0
0
0
0
0
0
2
2
1
0
2
1
1
1
0
0
0
2
2
0
0
0
2
2
0
0
0
1
1
0
2
1
2
2
0
0
1
1
0
1
0
4
0
0
0
0
2
0
1
2
0
2
2
0
0
1
2
0
0
0
2
0
0
0
0
2
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
1
0
0
0
0
1
1
0
0
0
0
1
0
2
0
0
1
0
3
0
0
0
0
0
1
0
2
0
0
0
0
0
3
0
0
0
4
0
2
0
1
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
1
1
0
1
0
2
0
2
2
0
0
0
0
2
0
2
2
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
3
2
0
2
2
0
2
0
0
2
2
0
0
0
2
1
0
0
0
2
0
2
0
0
0
0
0
1
0
0
1
1
0
0
1
0
1
0
0
0
0
2
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
3
0
0
2
2
0
1
0
0
0
3
0
1
2
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
2
4
0
1
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
1
0
0
2
1
0
2
0
0
0
0
2
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
1
1
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
2
1
0
0
1
2
0
0
0
1
0
0
0
0
3
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
3
0
0
1
0
0
1
0
0
0
6
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
3
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
1
0
0
2
0
0
2
0
0
1
0
2
0
0
2
1
2
0
0
0
0
1
0
1
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
2
0
1
0
0
0
1
0
0
0
0
0
3
2
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
2
2
0
2
2
2
0
0
1
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
4
3
0
0
1
1
2
0
0
1
1
0
2
2
0
0
2
0
1
0
1
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
2
2
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
1
2
2
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
8
1
2
0
0
0
0
1
0
0
0
1
2
0
1
0
3
0
2
0
1
0
2
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
2
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
3
0
0
0
3
0
0
0
5
0
0
1
0
0
0
0
1
1
0
2
1
0
2
0
0
0
0
0
0
1
0
1
0
1
0
0
2
0
1
0
0
2
2
0
0
5
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
1
0
1
4
0
0
0
1
4
0
0
0
1
0
2
0
0
2
0
1
2
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
2
3
0
2
0
1
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
3
1
0
0
0
0
0
0
0
1
2
2
0
0
0
1
1
0
0
0
1
0
0
1
0
0
1
2
0
2
0
1
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
2
0
8
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
1
0
1
0
0
2
0
1
1
3
0
1
0
0
1
0
0
1
0
2
0
2
0
0
1
0
0
2
0
0
0
0
1
0
0
0
2
1
0
1
2
0
2
0
2
0
0
0
0
0
1
0
0
2
1
0
5
0
0
4
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
2
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
1
1
0
0
2
0
1
0
0
0
1
1
0
1
0
3
1
2
3
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
2
0
1
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
3
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
2
0
2
0
2
1
1
2
1
2
0
0
1
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
3
1
0
0
0
1
2
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
2
2
0
0
0
0
0
0
0
0
0
1
3
0
0
0
1
1
0
0
2
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
2
0
0
1
0
2
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
1
0
3
0
0
0
2
0
0
2
0
0
2
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
1
1
0
0
1
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
1
1
0
0
0
2
0
1
0
0
0
0
0
0
2
0
2
2
1
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
7
0
1
0
0
2
0
0
0
2
0
0
0
0
0
1
0
1
1
0
2
2
2
0
1
0
0
0
3
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
3
0
0
1
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
1
2
0
0
2
1
0
2
1
1
0
0
0
1
1
1
0
0
0
2
0
0
0
1
0
1
0
0
1
0
1
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
3
2
2
1
0
1
1
2
1
0
0
0
2
0
2
1
0
0
1
0
1
2
0
4
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
3
1
0
0
1
1
0
0
3
0
1
0
5
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
2
3
0
0
0
0
0
2
1
2
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
3
1
0
0
0
0
0
0
2
0
1
0
0
2
2
0
0
0
1
0
0
2
0
2
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
3
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
1
2
0
1
2
1
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
2
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
2
0
0
2
0
0
4
1
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
1
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
1
0
0
1
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
4
0
1
0
1
3
0
0
2
0
0
0
1
0
0
0
0
2
0
0
2
1
1
0
0
0
0
0
1
1
0
1
1
1
0
0
0
2
0
1
1
0
0
0
2
0
0
2
0
0
1
2
0
2
0
2
2
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
1
0
0
1
0
0
0
0
0
2
1
1
0
0
2
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
1
0
2
0
0
2
0
0
0
2
1
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
4
0
2
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
5
0
0
0
1
0
1
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
2
2
0
1
0
0
0
0
2
0
0
0
0
1
2
0
0
2
1
0
0
0
0
0
0
1
2
0
1
0
0
1
1
0
0
0
1
0
0
0
1
0
0
1
0
2
0
0
0
1
1
1
0
0
2
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
2
0
0
0
1
0
0
1
0
0
1
0
0
0
2
0
0
2
0
2
2
0
0
0
1
0
1
2
0
0
2
0
0
0
0
2
2
2
1
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
6
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
2
2
0
0
0
2
0
0
1
0
0
1
0
2
2
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
3
2
0
2
0
0
2
1
1
1
0
2
0
0
5
0
0
1
0
0
1
3
1
1
0
0
1
0
1
0
3
0
0
1
0
0
0
0
0
1
2
0
1
0
1
0
2
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
2
0
0
0
0
5
0
2
1
2
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
2
0
0
2
0
0
1
0
1
0
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
2
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
2
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
2
1
2
0
0
0
0
2
0
0
1
0
0
0
2
2
0
0
1
2
1
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
3
0
2
2
2
2
0
0
1
0
3
2
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
10
0
0
1
0
0
0
0
2
0
3
0
0
0
1
0
2
0
2
0
0
2
0
1
0
0
2
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
2
0
0
2
0
7
0
0
2
2
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
2
0
0
2
2
0
1
0
0
0
0
0
0
1
2
0
0
0
1
1
1
0
0
2
2
0
1
0
0
2
1
0
0
0
0
0
0
0
1
0
0
2
2
0
1
3
0
1
0
0
1
0
0
0
2
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
3
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
3
0
0
0
0
2
2
0
2
0
0
1
2
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
3
0
0
0
0
2
0
1
0
1
2
0
3
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
2
0
0
0
0
2
1
2
0
1
0
0
3
0
0
0
1
1
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
2
2
1
1
0
1
0
0
2
0
0
0
1
0
0
0
0
0
2
1
2
2
0
2
0
0
0
1
0
0
0
0
0
1
0
0
3
0
0
1
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
4
0
0
0
0
1
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
1
1
1
1
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
2
2
1
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
4
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
1
1
0
0
0
0
1
0
0
0
3
0
0
0
0
0
2
0
3
0
1
0
0
0
2
0
0
5
0
0
0
0
0
0
0
0
1
1
1
1
0
0
2
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
3
0
0
0
0
1
0
1
0
0
2
1
0
0
0
0
2
1
0
1
6
2
1
0
2
2
0
0
0
1
2
0
0
0
0
0
1
0
0
2
0
0
0
2
1
2
2
1
0
2
0
0
0
0
2
0
0
2
0
0
0
3
1
0
0
2
0
0
1
2
3
0
0
2
0
2
0
0
1
0
0
0
0
1
0
0
0
0
3
0
2
1
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
12
0
0
0
2
0
0
0
0
0
0
2
2
1
0
2
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
3
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
1
2
2
1
0
0
0
0
0
2
2
0
1
1
0
0
0
0
0
0
3
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
2
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
1
0
0
0
2
1
0
0
0
0
0
0
1
2
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
2
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
2
2
2
0
2
4
0
2
0
0
1
0
1
0
0
4
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
1
0
0
1
1
0
2
0
0
0
0
2
0
0
0
1
1
2
0
0
2
0
1
1
0
0
0
0
6
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
2
0
0
0
1
2
1
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
2
2
2
0
0
0
1
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
1
2
0
1
0
1
0
3
0
0
2
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
2
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
2
0
0
0
2
0
0
0
0
1
2
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
1
0
2
0
0
2
0
0
2
2
0
0
1
0
2
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
1
0
0
0
2
0
0
1
0
0
0
2
2
4
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
4
2
1
0
0
0
0
0
0
0
2
0
1
0
2
2
0
0
0
0
0
0
1
0
0
0
1
0
0
1
2
3
0
2
0
1
1
0
0
0
0
3
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
2
0
3
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
2
1
0
0
0
0
0
2
0
1
0
0
0
1
0
4
2
0
1
2
2
2
5
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
5
2
0
0
0
0
2
5
0
0
1
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
2
1
0
0
1
0
0
0
0
2
0
0
1
0
0
1
0
2
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
2
1
0
2
0
0
2
0
0
0
3
0
0
0
1
0
2
0
0
0
2
0
1
0
0
1
0
1
2
0
1
1
0
0
0
0
0
2
0
0
0
1
0
1
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
2
2
2
1
0
0
2
0
2
1
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
10
2
2
0
0
0
1
0
0
0
1
0
0
0
0
2
1
0
0
1
2
0
1
2
0
0
2
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
1
1
1
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
2
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
1
0
0
0
0
2
1
1
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
1
0
1
4
1
0
0
2
1
0
0
1
0
0
0
1
1
0
0
0
0
0
2
0
0
0
4
1
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
1
2
0
0
2
0
2
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
2
0
2
2
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
2
0
1
0
0
2
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
1
1
0
1
0
1
2
2
0
1
0
1
3
0
2
0
0
3
1
0
2
0
0
0
2
2
0
0
0
0
0
2
0
2
0
1
2
0
0
0
2
0
0
0
1
0
1
0
0
2
0
2
0
4
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
2
0
0
4
4
0
0
1
0
0
0
2
0
2
0
2
2
2
3
0
0
0
0
2
1
0
2
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
4
0
0
2
0
2
1
0
0
3
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
2
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
2
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
2
1
1
0
1
0
0
0
0
0
1
0
0
10
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
5
1
1
0
0
0
0
0
0
0
0
0
0
1
3
0
1
0
0
1
0
1
0
3
0
1
0
0
0
0
0
2
0
2
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
1
0
0
2
0
0
0
0
4
1
2
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
3
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
2
0
2
0
1
0
2
0
1
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
1
0
0
2
0
0
0
2
0
0
1
2
0
0
2
2
0
0
0
1
0
5
2
1
1
0
1
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
3
0
5
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
1
1
3
0
0
2
0
0
0
0
0
0
2
2
3
0
0
0
3
1
2
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
3
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
2
0
2
2
0
0
1
0
1
0
1
0
0
2
0
0
2
1
0
2
0
0
0
2
0
0
1
0
0
1
0
0
0
1
2
0
2
0
0
0
0
0
0
3
0
0
1
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
3
2
2
0
0
0
1
9
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
4
3
1
0
0
0
1
1
1
0
1
1
0
0
0
0
2
0
0
0
0
2
0
3
0
0
0
0
1
2
0
1
0
0
0
0
0
0
2
2
0
0
0
1
2
0
1
0
0
0
3
3
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
2
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
1
2
2
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
1
1
0
0
1
0
0
0
1
1
0
3
0
0
0
1
0
0
2
1
3
2
0
1
0
1
0
0
1
0
1
2
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
1
0
3
0
0
2
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
2
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
1
0
2
0
1
0
0
0
0
0
0
0
1
1
2
0
0
2
0
0
4
0
2
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
3
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
1
2
0
0
2
0
0
0
2
0
0
2
1
0
1
0
2
1
0
0
0
1
1
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
1
1
0
1
2
0
0
3
0
2
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
2
1
0
1
0
2
1
1
0
0
0
0
0
0
0
1
4
2
2
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
2
1
0
0
0
2
0
4
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
1
8
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
2
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
3
0
0
0
0
0
2
0
1
0
0
1
3
1
0
0
0
1
0
2
0
1
1
1
0
0
2
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
2
0
0
1
2
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
2
2
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
2
0
2
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
1
1
1
1
1
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
2
0
3
1
0
0
0
1
0
0
0
2
1
0
0
0
2
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
1
2
0
0
0
0
0
2
2
2
0
1
2
0
0
0
1
0
0
2
1
1
2
1
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
2
0
0
2
1
0
1
0
2
0
0
0
2
0
0
1
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
1
1
0
0
1
0
1
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
1
0
1
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
1
2
0
1
0
0
0
1
1
0
0
0
1
0
0
1
0
0
1
1
2
0
0
1
0
0
0
0
1
0
0
0
1
0
2
0
0
1
0
0
2
0
0
0
3
0
0
3
0
0
0
1
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
2
0
3
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
1
2
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
2
0
2
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
2
1
1
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
2
0
0
2
0
0
1
3
0
0
2
0
1
1
0
0
0
0
0
1
0
0
0
1
2
0
2
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
2
2
0
1
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
2
0
1
0
2
1
5
0
0
2
1
0
0
0
1
0
0
2
1
0
2
0
1
1
0
1
1
2
2
0
1
0
2
2
2
2
0
0
0
0
0
0
1
1
1
0
0
0
2
0
1
0
1
0
0
1
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
1
0
2
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
2
0
2
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
2
0
2
1
0
0
2
1
0
0
0
0
0
0
0
0
0
1
1
2
0
2
0
0
1
1
4
2
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
2
2
0
0
0
1
0
0
0
0
1
0
0
3
1
2
1
2
0
0
2
0
0
0
0
3
0
0
0
2
0
1
0
0
0
2
1
0
1
1
0
1
0
0
0
2
2
0
0
3
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
2
0
2
0
0
0
0
0
0
2
0
0
0
2
0
1
0
1
0
2
4
2
0
0
0
0
0
0
2
0
2
0
2
0
2
0
0
0
2
0
1
0
0
0
0
0
1
6
1
0
2
0
0
0
2
1
3
0
0
0
0
2
3
0
0
0
0
1
0
1
2
0
2
0
0
2
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
2
0
0
0
1
1
1
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
4
0
0
1
0
0
1
2
0
0
1
0
1
1
1
2
0
0
0
1
0
0
0
0
0
3
2
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
1
0
1
0
2
0
0
1
0
0
0
0
0
2
0
1
0
0
1
0
0
1
2
2
2
1
0
1
0
0
1
0
0
0
0
0
2
8
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
2
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
2
0
0
0
1
1
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
3
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
2
0
0
1
0
0
0
2
1
1
2
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
2
0
0
0
0
0
1
0
2
0
2
1
0
0
0
1
0
1
2
0
1
2
0
0
0
1
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
2
0
0
0
0
1
0
1
0
0
3
2
0
2
2
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
2
1
7
0
0
0
0
2
0
0
0
14
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
1
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
2
1
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
2
0
2
0
0
4
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
1
1
0
0
4
0
0
1
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
2
0
0
1
0
1
0
0
2
0
2
0
1
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
1
1
1
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
5
1
3
0
2
0
0
0
1
0
2
4
2
0
0
0
2
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
2
2
0
2
1
0
0
0
0
2
0
0
2
0
0
0
1
0
1
0
1
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
1
0
1
0
0
0
2
0
1
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
2
2
0
0
2
0
0
0
2
4
0
1
0
0
0
2
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
1
0
2
0
0
2
0
0
0
0
2
1
0
0
0
2
2
0
1
0
0
0
2
0
1
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
1
0
1
1
1
1
0
0
2
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
1
1
0
0
1
1
0
0
0
0
2
1
0
2
2
1
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
1
0
0
1
3
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
1
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
5
0
0
1
1
0
0
0
0
2
0
0
2
2
0
2
2
2
0
0
0
0
0
0
1
0
2
0
0
0
1
0
1
0
0
2
0
0
0
1
0
0
0
4
0
0
0
2
0
0
0
0
2
1
0
0
1
1
1
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
1
0
1
2
1
1
0
1
0
0
2
0
0
0
2
1
0
0
2
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
2
0
0
3
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
2
1
2
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
1
0
1
3
0
3
0
0
1
0
0
0
4
0
0
0
0
1
1
1
1
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
1
0
0
0
0
2
0
2
2
1
1
1
2
0
2
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
2
0
1
0
0
0
0
2
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
1
0
1
0
0
0
2
1
2
0
0
0
0
1
2
4
0
0
0
0
0
0
1
0
0
0
0
1
0
2
2
0
0
2
0
0
0
0
0
0
2
0
2
0
2
0
0
1
0
2
2
0
0
0
1
1
0
0
0
0
1
0
2
0
0
1
2
2
2
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
1
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
3
0
1
0
2
0
0
0
2
0
2
0
0
1
1
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
1
1
0
0
0
2
5
2
1
0
2
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
2
1
0
0
0
1
0
0
0
1
0
0
0
1
0
1
3
0
2
0
0
2
1
0
0
1
0
1
2
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
2
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
2
1
2
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
2
2
0
0
2
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
1
0
0
0
0
1
1
0
0
0
0
2
1
0
2
2
0
0
0
1
1
0
0
0
0
0
2
0
2
1
1
1
0
0
0
0
2
1
1
0
0
3
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
2
0
0
3
0
2
0
0
0
0
0
0
3
0
0
2
0
1
0
0
0
1
0
0
2
0
0
1
1
0
2
0
2
0
0
0
0
1
0
1
0
0
0
3
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
1
2
2
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
1
2
1
1
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
3
1
0
0
1
0
0
0
1
0
0
0
0
0
2
1
0
0
2
1
0
0
1
0
2
1
0
0
0
2
0
1
1
0
0
0
0
2
2
0
0
0
0
2
0
2
0
0
1
0
1
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
1
0
1
0
0
2
1
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
1
2
1
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
4
0
2
0
0
0
0
0
0
0
2
2
0
1
0
0
7
1
0
1
0
2
0
2
3
1
0
2
2
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
1
0
1
0
0
0
0
1
0
2
2
0
0
0
0
0
0
2
0
0
0
0
1
1
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
1
0
0
0
1
0
1
1
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
1
6
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
1
0
0
3
0
0
0
1
0
0
0
3
0
0
0
1
0
1
0
0
0
0
2
3
0
0
0
0
1
0
1
0
1
0
0
0
0
1
1
4
2
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
3
1
0
0
0
0
0
0
1
1
0
1
2
1
0
0
0
1
1
0
1
0
0
0
0
0
2
2
1
0
0
1
1
2
1
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
1
4
0
1
0
0
2
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
1
0
1
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
1
0
0
2
3
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
2
0
1
1
0
0
2
0
0
1
2
0
0
1
2
0
0
0
0
0
0
2
1
0
0
2
2
0
0
0
0
0
1
0
0
1
2
0
0
2
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
2
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
1
0
0
0
2
0
2
2
0
0
0
0
1
0
0
0
1
2
0
0
2
1
0
1
2
0
1
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
2
2
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
3
1
1
3
2
0
0
2
0
0
0
0
2
0
2
0
1
0
3
2
0
0
1
0
2
2
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
2
2
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
2
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
1
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
1
0
0
0
2
0
2
0
2
0
1
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
1
1
3
2
0
1
0
2
2
0
0
2
1
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
1
0
2
0
0
2
0
2
2
0
0
0
0
0
2
0
2
0
4
0
0
0
0
0
1
0
0
0
1
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
2
0
0
0
0
0
2
1
1
0
0
1
0
1
2
0
0
0
0
0
1
0
0
0
0
2
1
0
0
1
0
0
0
0
1
0
1
1
2
0
3
0
0
0
0
1
0
2
2
0
0
2
1
0
2
2
1
0
1
0
0
0
0
2
0
0
1
0
0
2
0
0
1
3
0
0
0
0
1
0
2
0
0
2
0
0
0
2
0
0
0
0
2
0
2
2
0
8
0
6
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
2
0
4
0
0
0
0
2
1
0
0
0
0
1
0
1
0
0
0
2
1
4
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
2
0
2
0
1
0
1
0
2
1
2
0
0
1
2
3
0
0
0
1
1
0
0
0
1
0
1
1
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
2
0
0
1
2
0
2
0
3
2
1
0
0
0
0
1
0
0
0
2
1
3
0
0
0
0
0
1
0
1
0
0
0
2
0
1
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
1
2
0
2
0
0
1
0
1
0
0
1
0
0
0
2
2
2
0
0
1
0
2
0
2
0
0
1
0
0
3
0
2
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
2
0
0
0
1
0
0
2
0
2
0
1
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
2
0
0
1
0
1
0
0
2
0
2
2
1
0
0
0
1
2
1
0
0
2
1
0
0
0
0
4
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
1
0
0
1
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
2
0
1
1
0
1
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
2
1
2
0
0
2
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
1
0
1
2
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
2
0
1
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
1
0
0
1
2
1
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
2
1
0
0
0
0
2
0
0
0
0
3
0
0
2
0
0
0
0
1
2
0
4
3
0
2
0
0
0
0
2
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
2
0
0
3
2
1
0
0
0
1
0
0
0
0
0
3
0
4
0
0
0
0
1
0
0
0
0
0
3
0
1
0
3
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
1
2
0
2
1
2
0
0
2
2
2
1
0
0
0
0
1
2
0
1
1
0
0
2
1
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
1
2
1
0
0
2
0
2
0
0
0
0
0
1
2
0
1
0
0
1
1
1
1
0
0
2
0
0
0
2
0
0
2
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
2
2
0
0
1
0
2
0
0
1
0
1
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
1
2
0
0
0
2
0
1
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
4
2
2
0
1
2
0
0
0
1
7
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
3
0
2
0
0
2
0
1
1
0
0
0
2
0
0
1
1
0
0
1
1
2
0
1
0
0
2
0
1
0
0
0
0
1
1
0
1
0
0
0
0
2
2
0
0
0
1
0
0
1
3
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
1
0
0
0
2
1
0
0
0
1
0
0
0
0
3
0
1
0
1
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
1
0
1
3
2
0
0
0
2
0
0
0
0
0
0
2
2
2
2
0
0
2
0
0
0
0
0
1
0
2
2
0
0
2
0
1
1
0
1
2
0
0
0
0
0
1
0
0
1
3
0
0
2
0
0
2
0
1
0
0
0
1
1
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
1
2
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
2
0
2
0
0
0
0
1
0
0
2
0
0
1
2
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
2
1
3
0
0
0
0
1
0
1
2
0
0
0
1
0
0
0
0
0
1
1
2
0
0
0
1
1
0
1
2
0
0
0
1
0
0
0
1
2
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
3
0
0
0
0
2
1
1
0
2
0
0
0
0
0
0
2
0
1
0
1
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
1
2
1
0
4
0
0
0
0
0
0
3
2
0
2
0
1
0
1
0
0
0
0
2
1
0
0
2
0
0
0
1
3
1
0
0
0
1
1
1
0
0
0
0
2
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
1
0
2
0
2
0
0
0
2
0
2
0
2
3
2
0
0
0
0
0
0
0
0
0
0
0
3
1
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
1
1
2
1
2
2
0
1
0
0
0
0
0
0
0
7
0
0
0
2
0
0
2
0
0
1
0
2
2
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
3
0
0
2
1
0
0
0
0
0
1
0
0
3
0
4
0
1
1
0
1
0
1
2
1
0
0
0
1
0
2
1
0
0
0
0
0
0
1
1
2
0
0
1
0
2
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
2
0
2
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
1
3
2
2
0
0
2
0
2
0
0
0
3
1
0
0
0
1
2
0
0
3
0
2
1
1
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
1
1
0
0
3
2
0
0
1
0
1
0
2
0
2
2
0
0
0
0
0
0
0
1
1
0
0
0
1
2
0
0
0
0
2
2
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
4
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
2
1
0
2
1
0
2
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
3
2
0
0
3
3
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
1
2
2
0
2
0
0
0
0
1
0
2
1
0
1
0
0
2
0
0
2
3
0
0
0
2
0
0
0
0
0
2
3
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
1
0
0
1
1
0
0
1
0
2
0
2
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
2
0
2
0
0
0
0
0
2
0
2
0
0
0
1
1
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
2
1
1
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
3
2
3
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
1
0
0
0
0
3
0
2
0
3
0
0
0
0
0
0
2
1
0
0
0
0
3
1
0
2
0
1
0
0
0
0
0
0
0
2
1
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
2
0
3
2
2
1
0
0
0
1
0
0
0
1
0
2
0
3
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
2
1
0
2
0
0
0
0
0
0
3
0
0
1
0
0
0
1
0
1
2
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
1
0
0
1
0
2
1
2
0
0
0
2
0
0
0
0
0
0
4
1
1
0
0
2
2
0
1
1
0
1
0
0
0
0
0
0
2
8
2
0
0
1
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
1
1
0
0
0
0
3
0
0
0
3
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
1
0
0
0
2
0
2
0
0
0
0
0
2
0
5
0
2
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
2
0
0
0
0
1
0
0
1
0
0
1
1
2
0
1
0
0
0
1
2
0
0
0
2
0
0
0
1
2
1
1
0
1
0
1
0
0
0
0
1
1
0
0
1
0
0
1
1
1
0
0
0
0
0
5
1
0
2
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
1
0
2
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
1
2
3
1
0
0
0
0
1
0
2
0
0
1
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
1
0
0
0
2
0
1
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
1
2
0
0
0
1
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
1
1
0
3
0
1
0
0
1
0
2
2
0
0
0
0
1
0
2
0
2
1
0
1
0
0
0
2
0
0
1
4
0
0
0
1
3
1
0
1
2
1
0
7
0
0
0
0
0
0
0
1
1
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
1
2
1
0
0
0
0
0
0
0
0
0
3
2
0
0
1
0
2
0
3
1
0
0
2
1
0
0
0
0
0
0
6
0
2
0
1
4
2
0
0
1
1
2
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
2
1
0
0
0
1
0
0
5
0
0
2
0
1
1
0
0
1
1
0
0
0
0
0
0
4
1
0
0
0
1
0
0
1
0
2
0
0
1
0
2
0
1
0
0
0
0
0
2
1
0
0
0
1
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
1
0
2
1
2
0
0
0
0
2
0
1
1
1
1
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
2
1
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
4
0
4
1
0
1
2
0
0
0
1
0
0
0
0
1
4
0
0
0
0
0
1
1
1
0
2
0
2
0
0
0
1
0
2
0
0
1
0
0
1
0
0
0
1
0
2
2
2
0
2
0
0
2
3
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
5
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
1
1
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
3
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
3
1
0
2
1
1
1
0
1
0
0
0
2
0
1
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
2
0
7
0
0
0
1
0
2
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
1
0
1
1
2
1
2
2
1
0
0
0
0
0
2
2
0
2
0
0
0
3
0
1
0
0
0
0
0
0
0
2
0
1
0
0
2
0
1
0
1
3
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
3
0
1
0
2
0
0
1
0
0
0
1
1
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
10
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
2
0
1
1
0
0
0
0
0
0
0
2
0
2
0
0
2
2
0
0
1
1
1
1
2
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
4
1
0
0
0
0
1
0
0
1
0
2
0
4
1
0
0
0
2
0
2
0
1
0
0
2
0
4
1
0
0
0
0
0
0
3
4
0
0
0
1
0
0
0
0
2
0
0
2
1
2
0
2
2
0
0
1
0
0
1
1
0
4
0
1
0
0
0
0
0
0
1
10
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
2
0
0
2
0
3
0
1
1
0
0
3
0
0
0
0
1
0
0
1
0
2
1
2
0
1
0
2
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
1
0
0
2
2
0
0
1
0
0
0
1
0
0
2
0
1
0
0
0
2
0
0
0
0
0
1
0
0
1
0
1
1
2
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
1
2
0
0
1
0
0
1
1
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
1
0
0
0
0
1
2
2
0
0
1
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
1
1
0
0
0
0
1
2
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
4
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
2
1
0
0
0
1
0
1
0
0
0
0
0
1
1
0
1
1
2
0
0
0
0
0
1
0
0
2
1
2
0
2
4
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
1
0
0
2
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
1
1
1
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
1
1
2
1
1
0
1
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
3
0
0
4
2
0
0
0
0
0
0
0
0
1
2
2
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
2
1
0
1
1
0
0
0
1
0
0
0
0
0
3
0
0
1
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
3
0
2
2
0
0
0
0
0
0
0
0
0
3
3
0
0
0
0
0
2
2
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
1
0
0
1
3
0
2
0
0
1
0
0
0
2
0
1
1
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
2
2
3
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
2
1
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
3
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
1
0
0
0
6
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
2
1
0
0
0
0
2
2
0
0
0
2
1
2
0
0
3
0
2
0
0
1
1
0
2
0
2
0
1
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
1
2
0
0
1
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
2
3
0
2
3
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
2
0
2
2
2
0
0
0
1
0
0
0
0
0
0
1
0
1
0
2
2
0
2
0
0
0
2
0
1
1
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
2
1
0
1
1
0
0
0
0
2
0
0
0
1
0
1
3
0
0
0
0
0
1
0
0
2
0
2
0
0
1
1
0
1
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
8
3
0
0
2
0
0
0
0
0
3
1
1
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
3
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
3
4
2
0
0
0
2
0
0
1
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
3
0
2
0
1
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
1
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
1
0
0
1
0
4
2
0
0
0
0
1
2
0
0
0
0
0
0
0
1
2
0
2
2
0
0
2
0
2
0
0
1
3
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
1
1
1
7
0
1
0
0
0
0
0
3
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
3
2
1
0
2
2
1
0
0
1
0
0
1
4
2
0
0
0
0
0
0
2
3
0
2
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
2
0
2
0
0
0
2
0
2
0
2
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
2
1
0
0
0
0
5
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
1
1
2
0
0
1
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
3
2
0
0
0
3
1
0
0
0
0
1
1
1
0
0
0
0
0
0
2
0
0
3
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
1
0
2
2
3
0
1
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
1
1
1
0
0
0
0
2
1
2
2
1
0
0
0
0
0
0
1
0
1
0
0
0
3
0
0
2
0
0
1
0
2
0
0
2
2
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
1
0
0
0
1
0
1
0
1
0
2
0
0
0
0
0
0
1
0
0
1
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
1
0
2
2
1
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
2
1
0
0
0
2
0
0
2
0
0
0
0
0
0
3
2
1
0
2
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
8
0
0
0
2
0
0
0
2
0
1
0
0
0
2
2
0
2
0
1
0
0
1
0
0
0
0
1
0
4
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
1
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
2
0
1
0
1
0
3
5
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
2
1
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
1
2
0
3
0
0
0
0
0
0
2
1
1
0
0
2
0
2
0
0
1
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
1
1
2
1
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
3
0
0
0
0
2
0
2
2
0
0
0
4
1
0
2
0
0
0
0
0
0
0
0
6
0
1
2
0
0
0
0
0
3
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
1
2
2
1
0
0
0
0
0
0
8
0
1
0
2
0
0
2
0
2
0
0
0
1
1
0
1
0
0
2
2
0
1
1
0
0
0
0
0
0
2
0
0
1
0
1
3
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
1
0
0
0
1
2
0
1
0
0
0
0
2
0
0
0
0
1
1
0
0
3
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
2
1
1
1
0
0
1
2
0
2
0
0
1
0
0
3
0
0
0
0
0
0
0
2
1
0
0
1
2
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
2
0
0
2
4
0
0
2
0
0
0
0
1
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
1
2
0
0
1
0
3
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
3
2
0
0
0
0
2
0
0
0
1
0
0
0
3
0
0
0
1
0
0
1
1
1
0
1
2
0
1
1
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
2
1
0
2
0
2
0
0
0
0
0
2
0
2
0
2
0
3
0
0
0
3
0
0
2
0
1
0
0
0
0
0
0
2
0
0
1
2
0
0
1
0
0
0
2
0
2
0
0
3
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
3
0
0
0
1
0
1
0
0
0
0
0
2
0
2
0
1
2
0
0
0
0
0
2
0
0
0
2
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
1
0
0
0
2
0
0
7
0
0
0
0
1
1
1
2
0
0
2
0
2
1
1
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
1
0
0
1
0
0
0
0
1
0
2
0
0
0
1
0
0
1
0
0
0
4
1
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
1
1
0
2
0
0
0
1
1
3
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
3
0
0
0
0
0
3
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
2
0
0
0
2
0
2
2
0
1
0
0
2
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
5
0
0
1
0
0
0
0
1
0
2
2
1
0
1
2
0
0
0
2
2
0
0
1
0
0
0
8
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
2
0
0
0
1
0
0
5
0
1
1
2
0
0
0
9
2
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
2
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
8
1
2
0
1
0
0
1
1
0
0
0
0
0
2
0
2
0
0
0
0
1
1
2
0
0
0
2
6
0
0
0
2
0
0
1
0
2
1
2
3
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
5
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
1
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
2
1
2
0
1
2
3
0
1
1
0
2
3
2
0
0
1
0
0
0
0
0
0
2
2
0
0
2
0
0
0
1
1
0
0
0
1
1
0
0
0
1
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
1
0
0
0
1
0
0
0
3
0
0
2
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
2
0
0
1
0
0
0
1
0
2
2
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
3
1
0
0
0
2
0
0
0
0
0
0
0
0
1
2
2
0
0
0
1
0
2
0
0
0
1
0
2
2
0
2
0
1
1
0
0
2
2
0
2
0
0
0
0
0
0
0
2
3
2
1
0
0
0
0
2
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
4
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
2
1
1
0
2
2
0
2
0
1
0
0
0
0
0
0
0
2
0
0
2
1
0
0
1
0
2
0
0
0
1
0
0
1
1
0
0
2
0
2
2
2
0
0
0
0
1
1
2
4
3
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
1
0
0
0
0
1
3
2
0
2
0
0
1
2
0
0
0
1
0
0
0
0
7
0
0
0
1
0
0
0
0
1
0
0
0
4
0
2
0
0
2
0
1
0
0
0
2
0
1
0
0
0
0
1
3
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
5
0
2
0
0
1
0
0
2
0
0
0
0
3
1
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
1
0
0
1
2
0
2
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
3
0
0
3
0
0
2
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
3
2
2
2
2
1
0
2
2
0
0
0
0
0
0
2
0
0
1
0
0
1
2
0
1
0
0
0
0
0
0
2
0
0
0
2
0
2
1
0
0
0
0
1
3
0
0
0
1
0
0
1
0
2
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
2
1
0
1
0
0
0
2
2
0
0
1
0
0
0
0
0
1
2
0
0
2
1
0
4
0
0
1
0
0
0
1
0
0
1
0
2
0
0
3
0
0
0
2
0
0
0
0
1
3
0
4
1
2
0
0
0
1
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
1
2
0
0
1
0
0
1
1
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
2
1
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
1
2
0
0
1
0
4
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
2
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
3
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
1
0
1
0
0
1
0
2
0
2
0
0
3
0
0
0
0
0
0
1
0
0
0
6
0
0
1
0
2
0
1
2
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
4
1
0
3
2
0
2
0
4
2
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
1
0
2
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
2
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
2
0
1
0
0
0
0
0
3
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
3
2
0
1
2
0
0
0
2
0
2
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
2
0
0
0
2
0
0
1
0
2
2
2
1
1
2
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
3
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
1
1
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
4
0
2
2
2
1
0
0
0
2
0
0
3
0
1
3
2
0
1
0
0
0
0
0
2
0
0
0
0
0
1
2
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
2
1
0
2
1
0
0
0
0
1
0
2
0
1
0
2
0
0
0
0
0
2
1
2
0
0
0
0
0
1
0
0
0
5
0
0
2
0
6
0
2
2
1
0
0
2
0
0
0
0
1
1
2
0
3
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
3
0
1
1
0
0
0
0
1
0
1
1
0
0
1
1
3
0
0
0
0
1
0
4
1
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
1
2
0
1
2
0
0
0
0
2
0
0
0
2
0
0
0
0
5
0
0
1
0
0
0
0
1
0
2
2
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
2
2
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
2
2
0
1
0
0
1
0
2
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
3
0
0
2
4
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
2
1
2
0
0
1
0
1
2
1
1
1
1
0
1
0
0
2
1
0
1
4
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
2
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
2
1
0
1
0
1
0
0
0
0
2
0
3
1
0
0
1
0
1
2
0
1
0
0
0
1
0
0
2
0
0
0
0
0
2
1
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
2
1
2
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
2
2
0
0
0
2
2
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
6
0
2
0
0
1
1
0
0
1
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
2
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
3
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
1
1
2
1
1
0
0
0
0
0
1
1
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
3
0
0
2
2
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
3
2
0
2
0
0
0
0
2
0
3
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
1
2
0
0
0
1
0
1
0
0
1
2
0
0
0
1
1
0
2
1
2
0
2
1
2
0
0
1
2
1
0
0
2
0
1
0
0
0
0
2
1
1
0
2
0
0
0
0
2
2
0
1
3
0
0
0
0
2
0
0
0
2
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
4
3
0
3
0
0
2
0
0
0
0
2
1
0
0
1
0
0
4
2
0
0
1
1
0
2
2
0
1
2
5
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
1
0
2
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
1
0
2
1
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
3
2
1
0
2
2
0
2
0
0
0
0
0
0
1
1
0
1
0
4
2
0
0
0
3
0
0
2
0
0
0
0
1
0
0
0
1
5
0
2
0
0
0
0
0
0
1
0
1
2
1
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
2
1
4
0
0
2
0
0
0
0
3
2
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
2
0
0
1
2
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
4
0
0
0
2
2
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
1
1
2
0
1
0
0
0
2
1
1
0
0
2
0
0
0
0
0
0
0
2
3
0
1
0
0
1
2
0
0
1
0
0
0
0
2
0
1
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
1
1
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
4
1
2
0
0
1
3
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
1
3
0
0
0
0
1
0
0
1
0
3
1
0
0
2
0
1
0
0
0
1
0
2
0
0
2
2
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
3
1
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
1
2
0
1
0
1
0
0
1
2
1
2
0
0
0
0
0
1
0
0
1
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
2
0
0
2
0
0
2
0
0
0
2
2
1
0
5
0
0
0
0
0
0
0
0
2
0
0
0
0
1
3
0
2
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
3
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
1
0
0
1
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
2
0
1
1
1
0
0
2
0
0
0
0
0
0
2
0
0
0
2
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
0
4
1
0
0
0
2
0
1
1
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
3
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
1
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
3
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
2
1
3
0
0
0
0
0
1
0
0
2
0
3
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
2
1
0
2
2
0
0
0
0
1
1
4
3
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
2
1
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
3
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
3
1
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
2
2
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
3
0
2
2
0
0
1
0
2
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
1
0
1
2
1
0
2
0
0
1
0
0
0
0
2
1
1
0
3
2
0
0
2
1
0
0
0
0
0
0
0
0
1
2
0
2
0
1
0
1
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
2
3
0
2
0
0
1
0
2
0
0
0
0
0
0
2
0
1
0
2
1
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
1
0
0
1
2
0
2
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
3
1
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
1
0
0
0
0
2
0
1
1
0
0
2
3
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
4
0
0
2
0
0
1
0
0
1
1
0
1
1
0
2
2
2
5
0
0
0
0
2
1
0
0
0
2
1
0
3
0
1
1
0
0
0
0
0
1
0
0
3
0
0
3
1
0
0
2
0
2
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
2
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
1
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
2
1
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
5
0
0
0
0
0
0
0
1
0
1
0
0
0
1
2
0
0
0
1
0
1
0
1
1
1
3
0
0
0
0
1
0
2
0
0
0
1
1
0
0
1
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
2
1
2
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
2
1
0
0
1
0
0
0
3
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
3
0
2
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
4
0
0
2
0
1
0
0
0
0
1
0
2
0
0
2
1
0
2
1
1
1
0
1
0
0
0
1
2
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
1
1
0
0
2
2
2
0
0
2
0
0
2
2
2
0
0
3
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
2
1
0
0
1
2
0
2
0
7
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
2
0
2
0
0
1
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
1
0
1
0
0
0
0
1
0
5
0
0
0
0
0
0
0
2
0
0
0
2
0
0
3
0
1
1
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
2
0
0
2
2
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
1
2
1
1
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
1
0
1
0
1
2
0
2
0
0
0
1
2
0
0
0
0
0
1
0
0
0
6
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
1
1
1
0
0
1
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
1
1
0
1
1
1
0
2
0
0
1
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
3
0
4
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
2
1
0
0
1
1
0
0
0
0
0
0
1
0
2
0
3
0
0
0
0
0
2
0
0
0
4
0
0
0
0
2
0
0
0
0
0
1
0
1
1
0
0
2
0
0
2
0
0
0
2
1
0
2
0
0
2
0
4
2
0
0
2
0
1
2
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
1
0
0
3
0
0
2
3
2
2
0
0
1
0
0
0
0
0
1
0
1
2
0
1
3
0
1
2
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
4
2
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
1
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
1
1
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
2
1
1
0
1
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
1
5
0
0
0
2
0
0
2
0
0
3
0
0
0
1
0
2
0
1
0
0
2
2
0
2
0
3
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
2
1
0
0
2
0
1
0
2
0
1
2
0
0
0
0
1
0
1
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
5
0
0
0
0
0
0
0
7
2
0
2
0
2
1
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
1
2
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
2
0
0
0
2
0
1
2
0
0
1
0
0
0
1
0
0
0
1
0
3
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
2
1
0
0
3
1
0
1
1
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
2
0
2
0
2
0
0
0
0
1
0
0
0
0
1
0
2
1
0
0
0
1
1
0
1
0
0
0
1
2
0
1
2
0
2
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
1
0
2
1
0
2
0
0
0
1
0
0
0
0
0
0
0
1
2
0
1
0
1
1
2
0
2
0
3
2
0
0
0
2
4
0
0
0
2
0
0
1
0
0
0
1
0
0
2
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
1
0
2
0
0
0
0
3
1
0
0
2
0
1
0
0
2
0
0
3
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
3
1
0
0
0
0
0
1
0
2
2
1
0
0
0
0
0
2
0
1
0
0
0
1
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
3
1
0
0
2
2
1
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
1
1
0
0
0
0
0
1
0
0
3
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
1
2
0
1
0
0
0
1
0
0
2
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
2
2
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
2
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
1
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
2
0
0
2
2
0
0
0
0
0
1
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
1
0
1
2
0
0
0
0
0
0
0
0
0
0
1
1
0
2
1
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
2
0
1
1
0
2
0
0
0
0
2
0
2
0
0
0
0
2
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
1
0
3
0
0
5
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
6
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
1
0
1
0
0
3
0
0
0
0
0
0
2
0
0
1
0
0
1
2
0
2
1
0
1
1
1
0
0
1
0
2
0
2
0
1
0
0
1
2
0
1
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
1
2
0
2
0
2
0
1
2
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
2
2
1
0
0
1
0
5
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
3
0
1
0
1
0
0
0
0
0
1
1
3
0
0
0
2
0
0
0
3
0
1
2
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
1
2
0
1
1
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
2
2
2
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
3
2
0
0
0
0
0
0
2
2
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
1
1
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
2
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
1
0
0
2
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
3
0
2
0
0
0
2
0
2
0
0
2
0
0
0
0
2
0
0
1
2
0
0
0
0
10
0
3
0
0
0
0
0
1
1
2
0
0
2
2
1
0
2
0
1
0
0
2
0
4
2
1
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
1
0
1
0
1
1
0
1
2
0
2
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
1
0
0
0
1
2
0
0
0
0
0
0
0
2
0
1
1
0
0
0
1
2
2
0
3
0
0
0
0
0
0
6
0
0
0
2
1
2
1
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
1
3
0
0
0
0
1
0
0
2
1
0
2
0
0
0
0
0
2
0
0
2
2
0
0
0
0
1
3
0
0
0
0
0
1
1
0
0
0
0
2
0
1
0
0
0
0
2
1
2
1
0
0
2
0
1
0
0
0
0
0
1
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
2
0
0
0
1
0
0
1
1
0
0
1
2
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
3
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
2
2
2
0
0
0
1
0
2
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
3
0
0
1
0
0
0
0
1
0
0
0
1
1
2
1
0
3
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
2
0
0
2
1
0
0
1
0
0
0
1
0
0
2
2
2
0
0
0
1
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
2
2
0
0
0
3
1
2
0
0
0
2
1
1
1
0
1
0
1
2
0
0
0
0
1
1
1
0
0
0
1
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
1
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
3
2
0
0
2
2
2
0
0
2
0
0
1
0
0
0
0
0
2
2
2
0
1
2
0
2
0
1
0
0
0
0
5
1
0
0
1
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
2
1
1
0
0
0
0
1
0
0
0
0
1
2
0
2
1
0
0
0
0
2
2
2
0
0
0
0
1
0
0
1
0
0
2
2
0
0
1
0
0
3
0
0
0
1
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
3
2
0
0
1
0
0
1
0
0
0
0
0
2
0
2
0
1
0
0
0
7
2
0
0
1
1
0
0
0
0
1
0
0
0
0
0
2
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
4
2
1
2
0
3
0
0
0
0
0
0
2
0
2
0
0
0
2
0
2
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
3
0
0
2
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
2
0
0
0
1
0
1
0
2
2
0
0
2
0
0
0
0
0
1
2
2
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
2
2
2
0
0
0
0
0
1
0
0
0
0
3
3
1
2
0
2
1
0
0
0
0
0
0
0
0
0
0
2
2
3
0
2
0
0
0
0
2
1
1
1
0
0
3
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
3
2
5
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
2
0
0
2
0
0
0
0
0
0
1
0
0
1
1
0
0
2
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
1
2
2
0
0
1
1
2
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
2
2
0
1
0
0
0
0
2
2
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
2
1
0
1
0
0
0
3
1
1
0
0
0
2
0
1
0
2
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
1
2
0
0
1
0
0
0
2
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
2
0
1
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
6
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
1
0
2
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
1
0
1
2
0
2
1
0
0
0
0
0
0
1
0
0
2
1
2
0
0
3
0
0
0
0
0
1
1
0
0
2
0
0
0
1
0
0
2
0
2
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
3
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
2
0
0
1
0
0
0
0
2
0
2
1
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
2
0
0
2
1
0
1
0
1
0
0
2
0
0
0
1
1
0
0
0
3
0
1
0
0
0
1
0
1
0
0
0
0
2
0
0
0
1
1
0
2
0
0
0
0
0
0
1
1
0
0
0
0
3
0
3
0
0
2
0
0
0
0
1
1
2
0
0
1
0
0
0
0
0
1
1
3
0
2
0
2
1
2
0
1
2
0
0
0
1
2
2
0
1
2
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
1
0
0
1
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
2
0
1
1
1
0
0
1
0
0
0
0
0
3
0
2
0
0
0
1
0
0
0
0
1
2
2
0
0
0
1
0
0
0
2
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
3
0
1
0
0
0
0
1
0
1
0
0
1
0
2
1
0
2
1
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
1
1
0
0
0
0
0
0
2
0
0
1
0
1
1
2
0
1
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
2
3
0
2
0
0
1
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
1
0
0
1
2
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
2
0
0
1
2
0
0
0
0
2
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
1
0
0
2
0
0
2
0
0
1
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
3
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
1
0
0
1
2
1
0
1
0
0
0
0
1
0
2
1
1
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
1
2
2
0
2
0
0
2
3
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
3
0
2
2
0
4
1
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
1
2
0
1
0
0
2
1
0
2
0
0
0
0
0
0
6
0
0
3
0
2
1
0
0
0
0
0
2
0
0
0
0
2
1
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
4
1
0
0
0
0
2
1
0
0
2
0
1
0
0
0
1
0
1
2
1
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
2
2
2
1
2
1
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
2
2
0
0
0
0
0
1
1
2
0
2
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
2
2
1
3
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
2
1
0
2
0
0
0
1
0
0
0
1
1
0
0
0
1
2
1
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
2
0
2
1
0
0
2
1
0
1
0
0
1
2
0
0
0
2
0
0
0
1
0
0
3
2
0
0
2
0
0
0
0
0
1
1
1
0
2
2
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
3
1
0
1
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
1
0
1
0
4
0
2
0
0
0
0
0
2
0
0
0
1
1
0
1
0
1
1
0
0
0
0
0
0
2
3
0
0
2
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
2
1
1
1
0
0
0
0
0
0
0
2
2
0
0
0
0
3
1
0
0
0
2
0
0
0
2
1
0
1
1
3
0
0
7
1
0
0
2
0
0
2
2
3
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
2
1
0
0
0
1
2
0
2
0
0
0
0
2
1
1
0
0
0
0
1
1
0
2
0
0
0
6
2
0
0
1
2
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
1
2
0
0
4
0
2
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
3
2
2
2
0
0
0
0
0
0
2
2
0
1
0
2
0
0
0
2
0
0
3
0
0
1
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
2
0
2
0
0
0
0
1
0
1
1
0
0
0
0
1
1
0
2
0
1
0
0
0
2
0
0
0
1
1
0
1
0
0
3
0
1
1
1
11
1
0
0
5
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
2
2
0
0
0
2
0
0
0
2
0
2
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
1
1
0
1
2
6
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
2
0
0
0
1
0
1
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
2
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
7
0
1
1
0
0
0
1
0
5
0
0
0
0
0
0
1
0
1
0
0
0
0
0
3
2
2
0
0
1
1
0
0
1
2
0
0
0
0
0
0
0
0
0
2
1
0
1
3
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
1
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
2
0
0
0
2
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
2
0
2
1
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
2
0
0
0
0
0
0
0
1
2
1
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
1
0
0
2
1
1
0
0
0
2
1
5
1
0
0
2
2
0
0
1
0
0
1
0
0
0
1
2
0
2
0
0
2
0
0
0
0
0
0
0
2
0
2
0
1
2
1
0
0
0
0
1
0
0
1
1
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
2
0
0
0
0
2
3
0
0
0
3
2
2
3
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
1
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
1
0
0
2
2
1
2
1
1
1
0
0
0
0
0
1
2
0
0
0
1
2
0
0
0
0
0
0
6
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
5
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
1
1
0
0
2
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
1
2
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
1
0
3
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
1
1
1
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
5
1
1
0
0
2
0
0
0
0
0
0
0
1
2
0
3
2
1
0
0
0
2
1
0
0
0
2
0
0
2
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
2
0
0
0
0
2
0
0
0
0
0
3
0
0
1
1
0
0
2
0
1
2
0
0
3
0
2
0
1
0
0
0
1
0
0
0
0
2
2
2
0
0
0
0
0
2
0
2
0
0
0
0
1
1
1
0
0
0
1
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
1
0
2
1
1
0
1
1
0
0
0
0
0
0
2
1
0
0
0
0
1
0
2
0
0
2
0
0
0
0
7
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
3
0
0
0
1
1
2
0
0
2
1
2
1
5
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
2
0
0
2
2
0
0
2
1
2
0
0
0
1
1
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
2
2
1
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
1
0
0
0
1
2
0
2
1
2
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
2
3
0
0
4
2
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
3
1
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
3
0
2
2
0
2
1
2
0
0
0
0
0
0
2
1
2
2
0
1
0
2
0
0
0
2
1
2
1
1
1
0
2
1
2
0
2
3
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
2
0
2
0
0
0
0
1
2
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
1
1
1
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
2
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
3
0
1
2
0
0
0
2
5
0
2
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
1
2
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
3
2
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
1
0
2
1
3
0
0
0
0
0
2
0
0
0
2
1
2
2
0
0
0
2
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
1
0
1
0
2
0
2
0
0
3
0
5
0
0
1
0
0
0
0
1
1
2
2
1
0
1
1
1
0
0
0
2
0
0
0
2
0
0
2
0
0
0
2
2
0
3
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
2
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
1
1
0
0
4
1
0
0
0
4
0
0
1
0
1
0
0
0
0
0
2
0
2
0
0
0
1
1
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
5
0
2
2
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
4
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
1
0
0
2
1
2
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
2
3
0
0
0
0
3
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
1
0
0
2
0
2
0
0
2
0
2
0
1
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
2
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
1
1
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
2
0
2
0
0
0
0
0
0
1
0
1
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
2
2
0
0
2
2
3
0
0
0
1
0
0
0
0
0
2
0
0
0
1
2
4
0
3
0
3
0
1
1
0
2
0
1
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
1
1
0
0
1
2
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
2
2
0
1
0
0
0
0
0
0
0
1
0
0
1
2
0
2
0
0
0
0
0
2
0
0
0
0
3
0
0
1
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
1
1
0
2
0
0
0
0
2
0
0
2
2
0
0
0
1
0
0
0
1
0
2
2
2
2
0
0
0
0
0
2
2
2
0
1
0
0
0
0
0
0
3
1
0
0
0
0
2
2
0
0
1
0
2
0
0
0
0
0
0
0
2
1
2
0
0
2
0
2
0
1
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
1
0
0
0
0
1
2
0
2
0
2
2
0
0
0
0
3
2
0
0
0
1
2
0
0
4
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
2
0
1
0
1
0
0
1
2
0
0
0
0
2
1
0
2
0
2
0
2
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
2
1
0
0
1
0
0
3
2
0
3
0
0
0
0
0
2
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
3
0
0
1
0
0
0
0
0
0
0
2
3
0
0
0
2
0
2
1
2
0
2
1
0
0
0
0
2
0
0
1
2
0
0
0
0
0
2
0
0
2
0
0
1
0
2
0
2
0
0
0
0
1
2
0
3
0
0
0
0
1
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
1
0
0
0
2
0
0
1
0
1
1
0
0
0
2
2
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
2
0
1
0
1
0
0
1
1
0
0
1
1
0
0
0
1
1
0
0
1
2
1
0
0
0
0
2
0
0
0
0
3
0
0
0
0
2
0
2
2
0
2
0
0
0
0
0
2
0
0
1
0
2
0
0
0
2
0
2
0
0
1
0
3
0
0
2
0
1
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
1
1
1
0
0
0
0
2
0
1
1
2
0
0
0
0
1
0
0
0
0
2
0
2
2
1
3
0
1
0
0
0
1
2
0
1
0
0
2
0
1
0
2
0
0
0
0
2
1
0
1
0
1
0
1
0
0
0
0
0
0
0
1
2
5
0
0
1
0
2
0
2
0
0
0
1
0
2
0
1
2
0
0
0
3
2
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
1
0
0
0
0
1
2
0
1
0
0
0
0
0
2
0
1
0
2
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
1
2
1
0
1
0
0
0
0
0
1
0
0
0
0
2
0
1
0
1
0
0
1
0
0
0
2
0
0
0
0
0
2
1
0
0
2
0
0
1
2
0
1
0
1
0
0
2
0
0
0
2
0
0
0
3
0
0
0
0
2
1
0
0
1
0
0
1
1
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
2
0
2
0
4
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
1
0
1
2
0
0
1
1
0
1
0
0
1
0
0
0
1
2
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
2
1
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
1
0
0
2
0
0
2
0
0
2
0
0
0
0
1
2
0
0
1
2
0
0
0
1
0
0
0
2
2
2
1
0
4
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
10
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
3
1
0
0
1
0
2
0
1
2
0
1
8
2
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
2
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
5
1
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
1
0
2
0
2
0
0
1
0
0
0
2
5
0
0
0
1
0
2
1
0
0
0
1
0
0
1
0
0
0
0
2
1
4
0
0
0
0
0
0
2
0
1
1
2
2
0
0
0
0
0
1
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
1
6
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
7
0
0
0
0
0
0
1
0
0
0
2
0
1
0
2
0
2
0
2
0
2
0
0
0
0
1
0
0
1
0
0
0
0
1
2
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
2
2
0
0
0
1
1
0
0
0
0
1
0
1
0
0
1
0
0
3
0
3
2
2
0
0
0
2
0
0
1
0
0
0
0
1
0
0
3
0
0
0
2
2
0
2
0
0
0
1
2
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
4
0
0
1
1
0
0
0
0
0
6
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
1
1
1
0
1
2
3
2
0
0
0
0
0
0
1
0
2
0
0
3
1
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
2
1
0
1
0
1
2
0
0
0
0
0
0
0
2
0
2
2
0
0
4
0
0
0
0
0
0
1
2
0
0
2
2
0
1
3
1
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
2
0
0
0
1
2
0
0
0
0
2
0
2
0
2
0
2
0
1
0
0
2
1
1
0
0
0
0
1
0
1
1
1
0
2
1
0
0
0
0
2
2
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
1
1
2
0
0
0
1
0
0
2
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
2
1
2
1
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
1
1
0
0
1
0
1
0
0
0
0
2
0
0
1
0
2
0
0
0
0
11
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
1
2
0
1
0
0
0
2
0
0
0
1
0
0
1
2
2
0
0
1
2
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
1
1
2
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
3
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
2
1
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
1
1
0
0
0
2
1
0
2
4
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
1
0
5
1
0
0
1
0
0
3
0
0
0
0
0
0
1
0
0
0
2
2
0
1
1
2
1
0
0
0
0
0
0
0
2
0
2
2
6
0
0
1
1
0
2
0
0
2
0
1
1
0
0
3
2
0
1
0
1
2
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
7
0
0
2
0
0
0
2
0
1
0
0
2
0
1
0
2
2
1
1
0
1
1
2
0
1
0
0
0
0
0
0
4
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
1
1
2
2
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
1
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
2
0
1
2
0
0
1
1
0
0
0
1
0
1
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
2
2
0
0
0
2
0
0
2
0
2
0
0
2
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
2
1
0
2
1
2
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
2
0
2
2
0
2
0
2
1
0
0
1
2
0
0
0
0
1
1
0
3
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
3
0
0
0
2
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
1
0
0
2
2
0
1
0
0
0
1
0
2
0
2
1
1
0
0
0
1
0
1
2
0
2
0
1
0
4
2
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
2
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
5
2
0
0
2
0
1
0
0
0
0
2
1
0
0
1
2
0
1
0
0
0
0
2
0
0
1
0
0
0
2
1
0
0
1
0
2
0
0
0
2
0
1
1
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
3
3
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
3
0
1
0
0
0
0
1
0
0
0
1
2
0
3
2
0
0
0
0
1
1
2
0
0
4
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
2
1
1
0
0
0
0
2
0
0
0
0
0
1
0
2
0
2
0
0
2
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
1
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
2
0
2
1
1
2
1
0
0
0
1
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
2
0
2
2
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
1
2
1
2
0
0
0
0
0
0
3
0
2
0
1
1
0
2
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
1
0
0
0
0
1
1
0
0
0
0
0
2
0
1
0
0
1
0
0
0
2
0
0
0
0
0
3
2
0
0
0
0
1
1
0
0
0
0
0
0
0
1
2
0
3
0
0
0
0
1
0
2
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
1
1
1
1
0
0
2
0
1
2
1
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
1
0
0
1
2
2
0
0
2
1
0
0
0
2
0
2
1
0
3
0
0
0
0
1
0
0
0
1
1
0
2
0
1
2
0
2
2
1
1
2
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
9
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
2
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
3
2
3
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
1
0
1
0
2
3
0
0
0
0
0
4
4
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
1
1
0
0
2
1
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
2
2
0
0
0
0
0
0
0
2
0
3
0
0
0
0
1
0
2
0
2
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
3
0
0
0
1
0
0
3
0
0
0
1
0
0
2
0
2
0
2
0
1
0
0
0
0
0
1
0
0
0
0
2
2
1
0
2
3
0
1
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
5
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
3
2
0
1
0
2
0
1
0
2
1
2
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
1
1
3
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
3
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
2
0
2
0
0
0
0
0
3
0
0
2
0
0
2
0
0
0
2
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
3
0
0
0
1
1
1
5
0
2
0
2
2
0
4
0
1
0
2
2
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
3
0
0
2
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
2
0
1
0
0
1
1
0
0
0
3
0
0
0
0
0
0
4
2
0
1
1
0
1
0
0
4
2
0
0
0
2
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
2
0
2
0
1
0
1
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
2
0
3
4
0
0
2
0
2
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
1
0
0
0
2
0
0
0
2
2
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
2
2
0
1
0
0
0
0
2
2
0
0
0
2
0
0
2
0
0
0
1
0
2
0
2
0
0
0
1
2
1
0
0
0
1
2
3
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
1
4
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
2
0
2
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
2
1
2
2
2
0
0
0
0
0
1
0
1
1
0
0
0
0
2
0
7
0
0
2
1
0
0
0
0
0
0
0
1
0
0
5
0
1
0
0
0
1
1
0
0
0
2
0
0
1
1
0
0
2
0
0
0
2
0
0
2
0
2
0
0
0
0
0
4
1
0
0
0
0
1
1
1
0
2
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
2
1
0
2
0
0
0
1
0
0
2
0
0
0
0
0
2
0
5
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
2
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
1
1
0
0
0
1
0
2
0
2
1
2
0
0
0
0
1
0
0
0
1
1
0
1
0
1
2
0
2
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
1
0
2
0
2
0
0
0
0
4
2
0
2
0
0
0
0
0
2
1
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
3
2
1
0
0
0
0
0
0
0
1
0
1
2
0
0
2
2
0
0
4
0
0
0
0
2
0
0
0
2
2
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
2
0
2
0
1
2
0
0
0
0
2
1
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
2
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
2
1
0
0
2
0
2
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
2
2
0
0
1
0
0
0
3
0
0
0
2
0
2
1
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
3
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
2
2
0
0
2
1
0
1
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
11
0
0
1
0
2
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
2
2
1
0
0
0
1
0
0
0
0
0
0
0
0
2
3
0
0
1
0
2
1
2
1
3
0
0
0
0
0
1
0
1
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
2
0
0
0
2
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
1
0
2
0
0
1
0
0
0
0
2
0
0
3
0
2
0
0
0
0
0
0
4
0
0
0
1
0
1
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
1
2
0
2
1
1
0
0
0
1
0
0
0
0
2
0
0
4
2
1
0
2
0
0
0
0
0
0
1
1
2
0
2
2
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
2
0
1
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
2
2
0
1
2
2
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
1
0
3
2
0
2
0
0
0
3
0
0
2
2
0
0
3
1
1
0
0
0
1
0
0
0
2
1
0
0
2
0
0
0
2
0
1
0
0
2
1
6
2
0
0
0
2
0
1
0
0
1
0
1
3
0
1
0
0
2
0
0
0
1
0
0
0
3
0
0
0
0
1
3
0
0
0
2
0
0
1
2
0
1
1
3
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
1
2
1
0
0
0
0
1
2
2
2
0
1
0
0
0
2
0
0
1
2
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
3
0
1
2
0
0
0
0
0
0
0
0
1
0
0
1
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
2
3
0
0
2
0
0
0
1
0
0
2
1
0
0
1
0
2
0
0
2
1
0
0
0
0
1
0
2
0
4
0
2
0
1
0
0
0
0
0
1
0
0
1
0
0
2
0
0
2
0
0
0
0
1
0
0
1
0
3
0
0
0
2
1
0
0
1
0
0
0
0
1
0
0
0
4
1
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
3
0
2
0
2
1
0
0
2
0
1
0
2
0
0
2
2
3
0
2
0
0
0
0
2
2
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
3
0
0
0
1
0
0
0
2
0
0
0
0
1
1
2
0
0
0
2
3
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
2
0
1
1
0
2
2
0
0
1
0
0
0
2
0
0
0
2
4
1
1
3
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
1
0
1
1
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
2
1
0
1
3
1
0
0
2
0
0
0
1
0
0
2
2
2
0
1
0
1
0
0
0
2
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
1
0
0
0
1
2
0
2
2
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
1
0
2
0
1
1
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
2
0
0
1
2
0
2
2
0
0
1
0
0
0
0
0
0
3
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
2
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
2
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
1
1
0
2
2
1
2
0
0
2
0
1
0
1
4
0
2
2
0
1
0
2
0
1
0
0
1
0
0
2
0
1
2
0
2
0
0
1
0
2
1
4
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
2
0
0
2
1
0
14
0
0
0
0
0
2
0
2
0
0
0
0
1
1
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
2
0
4
0
0
0
3
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
1
0
0
1
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
2
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
1
2
0
0
0
11
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
1
2
0
0
0
2
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
2
0
8
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
2
2
0
0
0
2
2
2
0
0
1
0
0
0
2
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
2
0
0
1
0
1
0
0
0
0
2
0
0
0
1
1
0
1
0
0
0
0
0
0
1
1
0
2
1
0
0
0
1
2
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
2
0
0
0
0
3
0
2
2
0
0
4
0
0
1
0
1
0
0
0
2
1
0
2
0
2
1
0
2
1
0
0
0
0
1
2
0
1
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
1
0
0
0
0
0
0
2
0
0
2
0
2
2
2
5
2
1
0
1
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
4
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
1
0
0
0
0
1
1
0
0
0
2
2
0
0
0
2
0
1
0
0
0
0
1
0
0
2
1
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
1
1
0
0
0
2
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
2
1
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
1
0
0
0
2
0
0
2
0
0
2
0
0
2
2
0
0
3
1
0
0
0
1
2
0
2
1
2
0
1
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
2
1
0
1
0
0
1
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
4
1
1
0
0
1
0
0
1
2
0
1
0
2
0
0
0
1
0
0
1
0
4
2
0
0
2
0
0
0
0
0
2
0
0
1
0
2
0
1
0
0
2
0
1
0
0
0
2
0
0
2
2
1
0
2
0
0
0
0
1
2
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
3
0
1
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
1
1
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
2
0
1
0
1
1
0
0
2
0
0
0
0
1
2
1
0
1
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
3
2
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
1
1
0
0
3
0
0
0
0
2
1
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
4
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
1
1
1
0
0
0
0
1
0
2
0
2
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
1
0
0
2
0
1
0
2
0
0
0
0
0
0
2
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
1
0
3
0
0
0
2
2
0
0
2
0
0
0
0
0
0
2
0
2
0
1
2
0
0
0
0
0
2
0
2
0
0
0
0
1
0
1
0
0
0
0
0
2
1
0
0
0
0
1
0
0
2
0
0
2
0
1
0
1
0
0
1
2
0
0
0
0
0
2
0
1
0
0
1
0
1
0
1
0
0
0
0
2
2
0
0
0
0
1
2
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
2
0
0
1
0
2
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
2
0
2
0
2
0
0
1
0
2
0
2
0
0
9
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
3
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
3
0
2
1
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
2
1
2
0
2
0
0
1
0
1
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
5
1
3
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
2
2
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
2
1
0
3
2
0
2
0
2
0
3
0
0
0
0
0
0
0
3
4
0
0
0
3
0
1
0
0
0
0
0
0
2
1
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
8
0
0
0
0
0
2
0
0
0
3
0
2
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
1
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
2
0
0
0
0
0
2
2
0
0
0
0
2
0
0
2
0
3
0
0
1
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
1
2
0
0
0
1
0
0
1
0
0
0
1
2
0
0
0
0
0
0
2
0
5
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
18
1
0
0
0
0
0
1
0
0
0
0
1
0
2
1
0
0
2
2
1
0
0
0
1
1
2
2
0
2
0
0
2
2
0
0
0
0
1
2
2
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
5
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
1
0
0
0
0
0
2
0
4
0
0
0
0
1
0
0
0
0
1
0
0
3
0
0
1
0
0
0
3
0
0
0
1
2
0
2
0
0
0
0
1
2
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
1
1
0
0
2
2
0
2
0
0
1
0
1
0
0
0
1
0
0
1
0
0
1
2
1
0
0
0
0
0
0
0
0
2
0
1
1
0
2
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
1
0
1
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
1
2
0
2
0
2
1
0
0
1
0
0
1
2
3
2
0
1
0
2
0
0
0
3
0
3
0
1
0
1
0
2
0
4
0
1
3
0
0
0
0
1
0
0
0
2
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
3
2
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
2
2
1
1
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
2
0
0
1
2
0
1
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
2
1
0
0
2
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
2
0
2
0
0
1
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
2
0
1
0
2
2
0
1
2
0
0
0
0
2
1
2
0
0
1
0
0
0
0
0
1
0
4
1
0
2
0
0
0
1
0
1
0
0
1
2
0
0
1
1
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
3
0
0
0
1
1
0
0
0
0
2
1
2
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
1
0
2
0
0
1
0
0
0
0
2
0
0
0
2
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
3
1
2
0
0
0
0
0
0
2
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
2
2
0
2
2
1
2
1
0
2
0
0
1
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
2
0
1
2
0
0
0
0
0
1
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
1
2
0
0
0
0
0
0
1
0
0
2
0
0
0
2
2
1
0
0
3
0
0
0
1
2
0
5
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
1
0
0
3
0
0
0
0
0
0
0
2
0
1
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
3
1
0
1
1
1
1
2
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
1
0
0
0
2
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
1
2
0
0
0
1
0
2
0
0
0
0
0
0
3
0
2
0
3
0
1
0
0
0
0
0
3
0
0
0
0
1
3
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
2
0
2
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
3
2
1
0
0
0
0
0
3
1
2
0
1
0
0
0
0
2
0
0
4
0
0
2
0
0
0
0
3
0
0
1
0
0
0
2
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
2
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
2
0
0
1
0
0
1
0
0
8
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
2
2
2
1
0
0
0
1
0
2
2
1
0
0
1
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
5
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
2
0
0
0
2
1
1
0
0
1
2
0
0
0
0
0
4
1
0
2
2
0
0
0
3
0
3
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
2
1
1
0
0
0
0
1
0
1
0
0
2
10
2
0
0
0
0
1
0
0
0
0
2
0
4
0
1
0
0
0
2
0
0
2
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
2
0
1
0
3
0
0
4
2
2
0
0
0
0
2
1
1
1
1
0
0
0
0
0
1
1
0
1
0
1
0
0
0
1
1
2
1
0
0
0
0
1
0
2
0
1
0
0
3
2
3
0
1
0
0
0
1
0
2
0
0
0
0
2
2
1
2
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
1
0
0
2
2
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
1
2
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
2
2
0
2
2
0
0
0
2
0
1
0
0
0
1
0
2
2
0
1
1
0
0
0
0
2
0
0
0
0
0
3
0
0
0
2
0
0
1
2
1
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
4
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
2
0
2
0
0
0
0
0
0
0
2
1
0
0
2
0
1
0
1
2
2
0
0
0
0
0
1
0
0
1
0
0
0
2
2
1
2
1
0
0
0
0
1
0
1
0
2
1
0
0
0
2
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
2
0
1
0
0
2
0
1
3
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
2
0
0
0
1
3
0
0
0
2
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
3
2
2
1
0
0
1
0
0
0
0
1
0
0
0
2
0
0
2
0
0
1
1
0
0
2
0
2
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
1
0
1
0
0
0
2
0
0
0
0
2
3
0
0
3
0
0
2
2
0
2
0
0
0
2
1
2
0
1
0
0
2
0
0
2
0
1
1
0
0
0
2
0
1
0
1
0
0
0
2
1
2
0
0
0
2
1
1
2
1
1
0
1
0
0
1
0
0
0
0
0
0
1
5
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
6
2
4
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
1
1
0
0
0
0
0
0
1
0
1
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
1
0
0
2
0
0
0
0
2
2
1
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
3
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
2
0
1
2
0
2
0
0
1
0
0
2
0
0
1
0
0
1
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
5
0
0
0
0
1
3
0
2
0
0
0
0
3
0
1
1
0
0
0
1
2
0
1
1
0
0
0
4
2
2
0
0
0
0
1
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
1
2
2
1
0
2
0
0
0
0
0
0
0
0
1
0
0
5
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
1
2
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
2
0
2
0
0
1
2
0
0
0
0
0
2
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
5
2
0
3
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
2
0
0
2
2
0
1
0
0
0
0
0
1
2
0
0
0
0
1
0
1
0
0
2
0
0
0
0
1
1
0
2
0
0
1
2
2
0
0
0
0
1
1
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
2
1
2
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
1
0
2
0
0
1
0
2
0
0
0
0
2
0
0
1
0
2
3
2
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
2
0
2
0
0
2
0
0
2
0
0
1
0
0
5
0
2
0
1
4
2
3
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
1
0
1
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
1
2
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
1
1
0
0
0
3
0
0
0
1
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
1
0
0
2
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
5
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
4
1
0
0
0
0
2
0
0
2
0
0
2
2
1
0
0
2
0
0
1
0
0
2
0
0
1
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
2
0
2
1
1
2
0
1
0
0
0
3
0
0
1
0
1
1
2
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
3
1
0
2
2
0
0
2
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
3
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
1
1
0
1
0
0
0
1
0
1
0
0
0
0
0
2
2
1
0
0
0
0
2
0
2
0
0
0
0
0
3
0
0
1
0
2
0
0
0
1
0
2
0
0
0
2
0
2
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
1
0
2
1
0
1
1
0
0
1
1
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
1
0
2
2
0
0
0
1
1
2
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
1
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
2
0
0
2
0
0
0
0
1
0
1
4
0
0
0
0
0
0
0
0
0
0
2
3
0
1
2
0
0
4
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
3
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
2
0
5
0
2
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
2
2
0
0
0
0
0
1
2
2
0
0
2
2
0
0
1
1
0
0
2
0
0
0
2
0
2
0
0
2
2
0
0
0
0
0
0
1
1
2
2
0
0
0
0
0
0
2
0
0
0
1
1
2
0
0
0
0
2
0
2
0
2
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
1
0
0
1
1
0
0
0
0
0
0
2
0
0
0
2
1
0
0
2
1
0
0
2
0
1
1
0
0
0
2
0
0
0
0
1
0
0
2
1
0
0
2
0
0
2
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
1
0
0
2
0
0
2
0
0
1
0
0
2
0
1
0
1
0
3
0
1
0
0
1
1
0
3
1
2
0
0
0
0
0
0
2
2
0
1
0
2
0
0
1
2
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
2
1
0
2
0
0
0
1
0
3
0
2
0
0
2
0
1
1
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
1
0
5
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
1
0
1
2
1
0
1
0
0
0
0
1
2
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
2
0
2
2
0
2
2
0
2
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
1
0
2
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
2
0
0
1
1
2
0
0
2
0
0
0
0
1
0
1
0
1
0
2
0
2
0
0
0
0
0
0
2
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
2
3
0
0
0
0
0
1
2
0
2
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
3
1
3
0
1
1
1
2
1
1
0
0
0
0
0
1
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
1
0
0
0
2
1
0
1
3
0
1
2
0
0
0
0
0
2
1
0
1
0
1
2
1
2
0
0
0
0
0
0
0
0
0
0
1
5
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
2
0
1
1
0
0
0
0
0
0
1
0
2
0
0
1
2
1
1
0
2
2
0
1
0
0
0
2
0
1
0
0
0
0
1
1
2
2
0
1
0
0
4
1
1
0
0
2
1
0
0
0
0
1
0
0
2
2
2
0
0
0
0
0
0
1
1
0
0
2
0
0
0
1
1
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
3
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
1
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
4
0
1
6
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
1
0
3
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
2
2
0
0
0
0
1
0
1
0
0
0
0
0
7
0
0
0
0
2
1
0
1
2
0
2
2
3
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
2
0
3
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
1
0
2
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
2
0
1
1
0
2
0
2
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
1
0
0
1
0
2
0
1
0
0
0
0
1
0
1
2
0
0
0
2
0
0
1
0
0
0
2
0
3
0
0
2
0
0
2
0
0
0
0
1
2
0
1
0
2
0
1
0
0
0
0
1
0
1
0
0
2
0
2
0
1
3
2
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
1
2
0
2
1
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
1
0
0
2
2
0
1
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
1
1
0
0
0
0
3
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
5
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
1
1
1
2
1
0
2
0
1
0
0
0
0
2
1
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
3
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
1
2
0
0
0
0
2
0
1
2
0
0
0
0
0
0
1
2
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
1
1
2
1
1
1
0
0
0
1
0
0
0
2
2
0
0
0
0
0
1
1
0
4
0
0
1
1
0
0
2
0
0
1
2
0
0
1
0
0
2
0
1
1
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
3
0
1
0
0
0
0
0
0
0
3
2
0
1
0
2
0
2
0
2
0
0
1
2
0
0
0
0
0
0
1
3
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
1
1
0
0
1
2
0
2
0
0
0
0
3
1
0
1
0
0
2
0
2
2
2
0
1
1
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
1
0
0
1
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
1
1
0
1
0
2
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
3
0
0
0
2
0
0
3
0
2
0
1
0
0
0
0
0
1
0
1
0
2
2
0
0
1
0
1
0
0
0
0
0
0
0
2
1
1
1
0
0
7
0
0
2
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
1
0
2
0
0
0
1
0
0
1
0
1
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
1
0
0
3
1
0
2
2
2
1
2
2
2
0
0
1
2
0
0
2
0
0
2
0
0
1
0
1
0
0
1
0
0
0
0
0
1
3
0
0
1
0
0
0
1
1
1
3
0
0
3
0
0
0
0
0
2
3
0
2
0
0
0
1
0
2
1
0
2
2
2
0
0
0
0
0
0
0
2
3
0
2
0
1
3
2
2
0
0
1
0
0
1
2
0
0
0
0
1
0
2
0
1
0
0
1
0
0
0
0
1
2
2
0
0
0
0
1
1
0
0
2
0
0
0
0
0
1
1
0
1
0
0
2
0
0
0
0
0
0
3
2
0
0
0
0
0
2
0
3
0
2
0
0
1
6
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
1
0
2
0
1
1
0
0
1
0
0
0
0
2
0
0
0
2
0
2
0
0
1
2
0
2
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
1
0
2
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
1
0
2
0
1
1
0
0
0
0
0
4
0
0
0
2
1
0
0
0
0
1
0
1
3
1
3
2
0
0
0
0
0
0
0
2
2
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
3
0
1
0
0
0
2
2
0
1
0
2
1
0
2
0
1
0
0
0
0
0
3
1
0
0
0
0
0
6
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
3
2
0
1
0
0
0
1
0
0
1
1
2
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
2
1
2
1
0
1
2
0
2
0
0
0
0
0
1
1
0
1
2
0
0
0
0
2
2
0
1
0
1
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
2
1
1
0
2
6
1
0
0
0
0
1
0
1
0
0
0
1
0
0
2
0
2
2
0
0
3
0
0
2
2
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
2
5
0
0
0
0
0
0
5
2
0
0
0
0
0
2
2
1
0
0
0
6
2
0
0
0
0
0
0
0
6
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
2
1
0
0
2
1
0
2
1
2
4
0
0
0
0
0
0
5
0
1
2
0
2
0
1
0
1
1
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
2
2
2
1
0
0
1
1
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
2
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
2
0
2
1
1
0
0
0
1
0
0
1
0
0
2
2
0
2
0
3
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
1
2
0
0
0
0
2
2
0
0
2
0
1
0
0
0
0
0
1
0
2
1
0
0
0
0
0
2
1
0
0
2
0
0
0
1
0
2
2
2
0
0
1
0
0
1
0
0
2
0
0
1
0
0
2
0
2
0
1
0
0
0
1
0
1
0
0
0
2
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
1
2
0
0
0
1
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
1
0
1
2
1
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
2
0
1
0
1
0
0
2
1
1
1
0
4
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
3
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
3
1
0
0
0
1
0
2
0
0
0
0
2
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
2
3
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
3
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
2
0
0
0
2
2
0
0
2
0
0
0
2
0
0
0
0
3
0
2
0
1
0
2
1
1
0
0
0
0
0
0
2
2
0
1
0
2
0
1
0
0
0
1
2
0
0
0
0
0
0
0
5
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
2
0
1
0
1
0
0
2
1
0
0
0
1
0
0
0
0
1
0
2
0
2
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
2
2
0
1
0
0
0
0
0
0
0
0
3
0
0
0
2
1
0
0
0
1
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
1
0
0
2
0
2
1
3
1
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
3
2
1
2
0
3
0
0
0
0
0
1
0
0
2
0
0
0
0
2
2
0
0
1
0
1
0
0
2
0
2
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
2
0
0
0
1
2
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
2
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
1
8
0
2
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
3
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
1
1
1
0
2
0
0
0
1
0
0
0
0
1
0
0
3
0
0
0
2
2
1
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
1
0
0
1
0
0
1
0
0
0
1
1
0
2
2
0
2
0
0
2
0
2
1
0
2
0
0
0
2
2
0
0
0
0
0
0
0
3
0
0
0
0
2
1
0
0
0
0
3
0
4
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
3
2
0
0
0
0
0
0
3
0
1
1
0
0
0
2
2
0
0
0
0
1
0
0
3
0
0
0
1
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
2
2
0
0
1
1
2
0
1
0
0
0
1
0
0
0
2
2
0
0
0
0
1
0
0
1
0
0
0
0
1
0
3
0
0
1
2
2
0
0
2
0
2
1
3
0
2
0
1
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
1
0
2
5
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
1
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
2
1
0
0
0
2
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
2
0
0
0
3
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
4
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
2
1
0
1
0
0
0
0
0
0
2
2
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
1
0
1
0
0
0
2
0
0
0
1
0
3
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
1
0
2
1
2
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
2
0
0
1
0
3
0
0
0
14
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
3
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
3
0
0
2
0
1
0
1
2
1
2
0
0
3
1
1
2
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
1
1
2
1
0
0
2
0
1
0
0
2
0
0
0
0
1
0
1
0
1
1
0
0
0
0
2
0
0
0
2
0
0
1
1
0
0
0
0
0
0
1
2
0
0
0
2
2
2
0
0
0
4
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
1
0
0
1
2
0
0
0
0
0
2
0
0
0
2
0
1
1
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
3
3
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
1
2
0
3
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
5
0
2
0
2
2
0
0
0
1
0
0
1
0
2
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
3
2
0
0
0
0
0
0
0
0
1
1
0
2
2
0
0
2
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
2
1
2
0
2
1
0
0
0
13
0
1
2
0
3
0
0
2
2
0
0
0
0
1
0
0
2
0
1
0
1
2
1
1
1
0
2
0
0
0
0
1
0
2
0
0
0
1
1
2
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
1
3
3
0
0
0
0
0
1
0
0
0
0
1
3
1
0
0
0
0
0
0
0
2
0
0
0
0
0
8
0
0
1
0
0
0
0
2
2
2
1
0
1
2
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
2
0
0
3
0
1
0
0
2
1
0
0
2
0
1
0
0
0
2
0
0
0
2
0
0
1
0
1
0
2
2
1
0
2
0
0
0
0
0
0
1
0
3
0
0
0
1
0
0
1
0
1
0
0
0
0
0
5
1
0
0
2
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
3
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
2
1
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
2
0
0
1
2
0
1
2
0
0
0
6
2
2
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
1
2
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
2
0
0
2
0
2
2
1
2
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
3
1
0
0
0
0
0
0
3
0
0
0
0
1
1
2
0
1
0
0
0
0
2
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
3
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
1
0
0
0
0
5
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
2
0
1
2
0
2
0
0
0
0
1
1
2
2
0
0
0
1
0
0
0
0
0
0
1
2
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
2
0
0
1
0
1
0
2
0
0
2
0
3
0
0
0
0
2
0
2
0
1
0
0
0
1
0
2
0
2
0
0
1
0
2
0
0
0
0
0
1
2
0
2
2
0
2
2
0
0
1
0
1
0
1
0
0
2
0
0
2
2
1
0
2
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
3
0
0
2
2
0
0
2
1
0
0
1
0
0
2
0
2
13
0
1
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
1
1
0
1
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
2
1
3
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
2
2
0
0
0
0
1
0
0
0
1
0
2
1
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
1
0
0
0
3
2
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
1
0
2
2
3
1
0
0
0
0
4
1
0
2
0
0
0
2
2
1
0
1
2
2
0
0
2
0
1
3
2
2
0
0
2
0
1
0
0
1
1
0
0
0
0
1
0
0
1
0
0
1
2
1
0
1
1
0
0
0
2
0
2
0
0
0
0
0
1
0
2
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
4
1
0
1
0
0
0
0
0
1
0
0
1
0
1
2
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
2
4
2
2
3
2
2
0
1
0
1
0
2
0
0
0
3
0
0
0
0
5
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
2
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
2
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
2
0
0
0
2
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
3
1
2
2
0
0
1
1
0
1
0
2
1
0
0
2
0
2
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
1
2
2
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
3
1
0
0
1
0
1
0
0
0
0
0
2
2
0
1
0
0
2
0
0
0
0
0
2
0
1
4
0
0
1
0
1
0
1
1
2
0
0
0
2
2
1
0
0
0
0
1
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
3
0
3
0
0
2
0
0
0
1
2
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
5
0
2
0
0
1
0
0
2
2
0
0
0
2
2
2
2
0
0
0
2
0
0
0
0
1
0
0
0
1
0
1
1
1
0
0
0
0
1
0
0
2
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
2
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
2
4
1
0
0
1
0
1
0
0
2
0
1
2
0
0
0
0
3
2
0
0
0
1
0
0
0
0
0
2
0
2
0
1
0
0
0
1
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
1
1
2
0
0
0
0
0
2
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
2
1
0
0
0
0
0
2
1
0
0
2
2
0
2
1
0
0
0
0
0
0
1
2
0
0
0
0
1
2
0
0
0
2
0
2
2
0
2
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
2
0
0
4
0
2
0
0
0
2
2
0
0
0
0
3
0
0
2
0
0
0
2
0
2
0
2
0
1
1
1
3
2
0
0
4
1
2
2
2
1
0
0
0
0
0
1
1
0
2
0
0
0
1
0
0
0
3
4
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
1
2
0
0
0
2
1
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
2
0
2
7
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
2
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
1
0
0
1
0
2
2
0
0
2
1
0
0
0
1
0
2
0
0
0
2
1
2
0
0
0
0
0
0
1
0
1
0
1
0
0
0
2
3
0
0
0
4
0
0
2
0
0
2
0
1
2
1
2
0
1
0
1
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
1
6
0
0
1
0
1
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
2
1
0
1
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
3
0
0
2
1
0
2
2
0
3
2
0
0
1
0
0
1
0
1
1
2
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
4
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
4
1
0
0
2
0
0
2
1
0
0
0
3
0
0
1
0
2
0
1
1
1
0
0
0
0
0
2
2
2
1
0
0
0
1
0
2
0
2
1
1
0
1
0
0
2
0
0
0
0
1
0
0
0
0
1
1
0
0
2
2
1
0
0
2
0
0
1
1
0
0
0
2
0
1
0
0
0
1
0
0
1
0
3
2
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
2
0
0
0
0
1
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
1
0
0
0
1
1
0
1
1
0
2
0
4
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
1
1
2
0
2
0
0
0
0
3
0
0
0
0
0
1
2
1
0
1
0
0
0
1
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
1
3
1
0
1
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
2
0
3
0
0
0
0
2
0
0
0
0
0
2
0
2
0
2
0
0
0
1
1
1
0
0
0
0
2
0
2
0
4
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
3
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
2
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
2
1
3
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
3
0
27
0
2
1
0
0
0
0
1
1
2
0
0
2
0
2
0
0
2
3
2
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
2
0
0
1
2
2
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
5
2
0
0
0
0
2
1
0
0
0
0
1
1
1
0
0
0
0
2
0
0
0
1
0
1
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
2
0
0
1
2
2
0
0
2
0
0
1
2
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
2
1
0
0
0
0
1
1
0
0
3
0
1
3
0
2
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
1
1
2
2
0
0
0
1
0
1
1
0
1
0
1
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
2
2
0
1
1
0
0
1
1
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
2
1
0
0
0
6
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
2
0
2
1
0
1
0
0
0
0
0
1
1
3
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
4
0
0
1
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
2
1
0
1
0
1
0
2
1
0
0
2
0
1
2
0
0
2
2
0
0
0
0
0
1
2
1
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
3
0
0
0
0
0
0
2
2
0
0
0
1
0
0
2
0
0
2
0
0
2
0
0
0
2
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
2
1
0
0
2
0
9
0
0
0
1
0
2
0
1
0
1
0
0
1
0
2
0
0
1
1
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
3
0
0
0
2
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
3
0
1
0
1
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
2
0
5
0
5
0
1
0
14
0
0
0
0
0
0
0
0
1
1
2
0
2
1
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
1
0
0
0
0
3
1
0
0
0
2
0
1
2
0
0
1
0
0
2
0
0
3
1
0
0
0
0
0
0
3
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
2
0
0
0
2
0
1
1
0
0
0
2
0
2
3
0
2
1
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
1
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
1
0
0
2
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
2
0
0
3
0
0
0
0
2
0
1
4
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
2
1
0
0
0
0
0
0
0
3
0
0
0
2
1
0
0
0
1
0
0
0
0
1
0
0
4
0
0
0
0
1
1
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
1
1
0
0
3
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
4
1
0
1
2
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
1
2
0
0
0
1
2
0
0
0
1
2
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
2
0
0
0
2
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
9
2
1
1
0
0
2
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
9
0
0
2
1
0
2
0
0
1
0
0
0
0
0
0
0
3
1
0
2
0
2
2
0
2
1
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
1
0
0
0
0
3
0
0
1
0
0
0
0
0
0
1
1
4
0
0
0
0
0
0
0
1
2
0
1
0
1
0
2
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
5
0
2
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
1
5
1
0
0
0
2
1
0
1
0
3
0
0
0
0
0
3
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
1
3
1
0
0
0
1
2
6
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
2
0
0
2
0
0
0
1
0
0
0
2
0
0
0
1
2
3
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
2
0
0
1
2
0
0
0
2
0
0
0
0
3
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
6
2
1
0
0
0
0
0
0
3
0
0
0
0
1
0
2
0
2
2
0
0
1
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
2
0
1
0
2
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
2
0
0
1
0
0
0
5
0
1
0
1
0
0
0
0
0
0
0
2
2
1
0
0
5
0
0
0
0
0
0
0
1
0
0
0
1
2
2
0
0
0
1
0
1
1
2
0
1
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
5
0
2
2
0
1
1
0
2
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
2
0
1
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
2
1
0
1
2
0
0
0
1
2
0
0
0
0
1
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
2
0
0
1
1
0
0
0
0
1
0
1
2
0
0
0
2
0
0
0
1
1
0
0
0
0
2
0
0
1
2
0
0
1
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
3
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
1
0
1
0
0
0
0
2
0
1
1
0
1
0
2
0
0
0
1
0
0
2
2
0
0
1
1
0
1
0
1
0
0
1
1
2
2
1
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
1
5
1
0
0
0
0
1
0
0
0
1
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
1
0
0
0
0
1
0
1
2
0
0
0
0
1
1
1
0
2
1
0
2
2
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
2
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
4
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
1
0
1
1
0
0
2
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
4
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
2
0
0
1
0
0
2
2
0
0
1
2
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
3
1
0
1
0
2
2
0
1
1
0
0
1
1
0
0
0
0
0
0
1
0
2
0
0
3
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
2
2
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
2
0
0
1
2
0
0
0
0
2
2
0
1
2
2
2
2
0
0
1
0
0
0
0
0
2
1
0
3
2
3
3
0
1
0
1
0
0
3
0
0
0
0
0
2
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
1
0
0
0
2
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
1
0
1
1
2
0
0
2
0
2
2
0
0
0
0
0
1
1
0
0
1
2
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
2
2
2
0
0
1
0
2
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
1
0
1
1
0
1
0
2
0
0
0
0
0
0
0
0
6
2
2
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
1
2
1
3
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
3
1
1
0
0
2
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
3
0
0
2
0
2
1
0
0
3
0
0
0
2
0
0
2
2
2
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
1
0
0
0
0
0
1
1
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
17
1
2
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
1
0
1
0
1
0
1
2
0
0
1
2
0
0
0
2
0
0
0
0
6
2
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
3
0
1
2
0
2
1
3
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
1
0
0
1
0
2
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
1
0
3
1
1
0
1
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
3
2
3
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
3
0
0
0
0
2
0
0
0
0
0
2
0
2
1
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
2
0
0
7
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
1
0
0
2
1
2
2
0
0
0
2
0
0
0
0
0
0
2
0
1
2
0
0
1
0
0
0
2
0
0
1
0
0
1
1
2
1
2
0
0
0
2
3
0
6
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
2
0
4
0
1
1
3
0
1
0
0
0
0
5
1
0
0
0
0
0
2
0
0
3
0
0
1
1
0
1
1
2
0
0
0
0
0
0
0
2
2
3
0
0
0
2
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
2
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
1
2
1
1
0
2
2
0
0
2
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
1
1
0
0
3
2
0
1
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
3
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
2
0
0
0
1
0
0
0
0
3
0
0
1
0
0
0
0
0
0
2
0
1
0
2
1
0
1
1
0
1
1
0
0
0
0
0
0
0
0
3
1
0
0
0
0
3
0
0
0
0
0
3
2
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
2
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
3
2
0
0
2
0
1
0
0
0
0
0
0
0
2
0
4
1
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
3
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
1
2
0
0
0
0
0
2
0
0
1
3
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
2
0
2
1
2
0
0
0
0
0
0
0
0
1
2
2
2
1
2
1
0
0
1
2
0
0
0
2
2
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
3
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
2
2
0
1
0
0
2
2
0
1
0
1
0
2
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
1
1
0
2
0
1
1
1
2
0
0
0
0
0
2
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
2
0
2
0
0
0
1
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
1
0
1
2
0
0
0
0
1
2
0
2
0
1
0
0
0
2
2
3
0
0
0
1
1
3
0
0
0
0
0
0
0
2
0
0
2
2
1
0
0
1
2
0
0
1
0
1
1
2
0
0
0
0
2
0
0
2
1
1
0
0
0
1
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
2
2
0
1
1
0
0
0
0
0
0
0
2
2
1
0
2
0
0
0
0
2
0
2
0
1
0
0
0
3
0
3
0
2
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
1
1
0
2
2
0
0
1
1
0
0
0
0
2
0
1
0
0
0
0
1
1
0
0
3
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
4
2
2
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
4
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
1
0
0
0
2
2
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
1
0
1
0
2
0
2
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
2
0
0
1
0
0
1
0
0
2
1
1
0
1
0
2
0
1
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
2
1
1
0
1
0
0
0
1
1
2
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
2
2
0
0
0
3
1
2
0
0
0
0
0
0
0
0
1
3
0
2
2
0
0
0
0
0
1
0
0
0
1
0
1
1
2
1
1
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
1
0
2
0
0
2
0
0
10
0
0
0
0
0
1
4
0
0
0
1
1
1
2
1
2
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
2
0
0
2
1
1
1
0
0
0
0
0
2
1
1
2
1
0
2
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
3
0
1
3
0
1
0
0
0
0
3
1
3
1
0
3
0
3
0
0
2
0
0
0
1
2
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
2
1
1
0
0
0
2
0
0
0
1
0
1
0
2
2
0
0
0
0
0
0
2
9
0
0
2
1
0
2
0
0
2
2
0
0
0
2
0
0
0
0
2
0
1
0
0
0
2
0
0
0
1
2
0
0
2
0
1
0
1
1
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
2
2
1
0
0
1
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
2
1
0
0
2
0
0
0
0
1
1
0
0
2
0
0
0
0
2
3
0
0
2
0
0
0
0
1
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
4
2
0
0
0
0
1
7
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
2
4
1
0
1
1
0
0
0
0
0
3
0
0
0
0
1
0
0
2
0
0
0
1
1
0
3
1
0
0
0
0
2
1
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
2
4
0
0
2
0
0
0
0
1
0
1
2
0
0
1
0
0
2
0
0
0
0
2
0
0
0
1
2
1
3
1
0
0
1
1
0
0
5
0
1
4
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
3
0
1
0
0
5
6
0
0
0
1
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
3
2
2
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
1
3
2
0
0
0
0
0
0
0
0
2
0
2
0
1
2
1
0
3
2
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
2
0
0
0
1
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
4
0
0
0
0
1
0
0
0
2
2
0
0
1
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
3
2
0
0
1
0
0
1
0
0
0
8
0
0
0
1
1
0
0
0
0
0
4
1
0
0
1
2
0
0
2
1
0
0
2
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
3
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
1
1
0
0
0
2
0
0
0
0
2
0
1
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
2
0
1
3
0
0
0
0
2
1
1
1
1
0
0
0
0
1
0
0
0
0
2
2
2
0
1
1
1
0
0
0
2
0
0
1
0
0
0
0
0
3
0
0
0
2
1
0
2
0
0
0
0
0
0
0
2
2
5
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
2
2
0
2
2
0
1
0
2
0
1
0
1
1
0
0
0
0
0
0
3
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
2
1
0
2
1
1
1
0
0
0
2
0
0
2
0
1
2
0
0
0
0
0
1
4
0
2
0
2
0
0
0
0
0
0
1
1
0
2
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
2
0
1
1
0
1
0
0
0
0
0
0
5
0
1
0
0
2
2
0
0
0
2
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
2
1
0
0
0
0
0
1
0
0
0
0
0
1
1
2
0
0
0
0
2
2
0
1
0
0
0
0
1
2
0
0
0
1
0
0
0
0
1
1
0
2
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
2
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
1
2
0
0
0
1
1
0
0
2
0
0
1
0
0
0
0
0
1
0
1
0
2
1
1
0
2
0
2
0
2
0
2
0
1
1
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
8
0
1
0
0
1
0
1
0
0
0
0
1
0
0
1
0
2
0
0
0
2
1
1
0
1
0
0
0
0
2
1
0
0
0
1
1
0
0
0
0
1
0
0
2
2
0
0
2
1
2
0
0
0
3
0
2
0
0
0
0
0
1
2
0
0
0
3
0
1
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
2
1
2
0
0
0
0
0
0
1
2
2
0
0
2
0
1
0
2
0
1
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
1
0
2
2
1
2
2
1
0
0
2
4
0
0
2
0
1
0
2
0
2
1
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
1
0
0
2
2
0
2
2
0
0
2
3
1
0
0
5
0
0
0
0
0
1
1
0
1
0
0
0
2
1
0
0
2
1
0
4
1
2
4
1
1
0
0
0
4
0
1
0
0
2
1
0
1
1
1
0
1
0
0
0
0
1
2
2
0
2
0
2
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
1
0
1
3
0
0
2
0
0
0
2
1
1
2
0
0
0
2
1
0
0
0
0
1
0
2
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
1
2
0
0
2
0
0
0
0
0
1
0
0
0
6
1
0
0
0
0
0
3
0
0
0
0
2
2
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
2
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
2
2
1
1
2
0
0
1
2
0
0
3
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
1
0
0
1
0
0
0
0
1
2
0
0
2
1
0
2
0
0
2
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
2
0
0
2
0
1
0
1
1
1
0
2
1
2
0
2
0
0
0
2
0
0
0
1
0
3
0
2
2
1
3
0
0
2
0
1
2
0
2
0
3
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
1
1
0
0
1
2
1
1
1
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
2
0
0
2
0
0
1
1
2
0
0
0
0
4
0
2
0
0
1
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
5
2
2
0
0
2
0
0
0
1
0
0
1
0
1
1
0
0
1
0
2
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
1
0
0
0
1
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
1
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
2
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
4
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
4
2
0
0
1
0
0
0
2
0
1
0
0
2
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
2
2
2
1
0
1
0
0
0
2
0
0
0
1
0
0
0
0
1
1
1
0
0
2
0
0
0
0
0
0
1
2
2
0
0
0
0
0
2
0
0
0
1
1
0
2
0
0
2
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
1
0
0
0
0
0
2
3
0
2
0
2
2
0
2
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
3
0
0
1
0
0
1
0
2
1
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
2
0
3
0
3
0
0
0
0
0
0
3
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
2
0
1
2
0
0
2
0
1
1
0
0
1
0
0
0
0
0
0
2
0
0
2
1
0
0
1
0
0
0
0
1
1
2
0
2
1
0
2
0
2
0
0
2
1
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
3
1
0
0
0
0
1
1
0
1
0
0
0
5
0
0
2
0
2
0
1
0
2
2
0
1
0
0
0
7
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
1
1
0
2
2
0
1
0
0
0
0
1
0
0
1
0
2
0
0
0
0
4
0
0
0
0
0
1
1
0
0
1
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
3
2
1
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
3
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
1
1
1
1
0
0
1
0
0
1
1
0
0
0
1
2
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
2
0
0
2
0
1
1
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
1
0
0
1
0
2
0
0
0
0
2
0
0
1
0
1
2
0
1
1
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
3
0
3
0
0
1
2
2
0
2
0
0
0
2
2
0
2
0
0
0
0
0
1
1
2
0
2
0
0
0
0
0
1
1
1
1
0
2
0
0
0
1
0
0
0
3
6
0
0
0
0
0
0
1
5
1
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
6
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
5
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
1
1
0
2
0
0
0
0
1
0
0
0
0
0
3
0
0
0
4
0
0
1
0
0
1
1
0
0
2
0
1
3
0
0
1
0
0
0
0
1
0
2
0
0
2
0
0
1
1
0
3
1
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
7
2
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
1
1
0
2
0
0
0
0
0
0
0
0
1
2
0
0
3
0
0
0
0
0
1
0
0
0
0
1
1
0
2
0
0
1
0
2
0
0
2
0
2
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
1
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
1
0
0
0
0
1
3
0
0
1
0
2
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
10
1
1
0
0
0
3
2
0
0
0
0
2
0
0
1
0
2
2
0
0
1
0
0
0
0
1
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
2
1
0
2
1
0
1
0
1
0
2
0
0
0
0
1
1
2
0
0
0
0
3
0
0
2
0
0
0
1
0
0
0
2
1
1
0
0
0
0
3
0
1
0
1
0
0
1
1
1
0
0
0
0
0
1
0
0
0
2
0
0
1
0
1
0
0
2
0
0
0
0
4
0
0
0
2
0
2
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
3
0
0
0
2
0
0
1
0
1
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
1
0
0
0
4
0
2
2
0
2
1
2
0
0
0
2
0
2
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
2
0
1
0
0
0
0
0
2
3
1
0
1
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
3
0
0
0
0
0
0
6
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
1
0
0
0
1
0
0
0
1
2
0
0
0
1
4
2
0
2
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
8
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
4
0
0
0
0
0
0
2
2
1
2
0
1
0
1
0
0
0
2
0
0
2
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
1
2
0
1
0
0
0
0
0
0
0
0
1
3
1
0
1
1
0
0
1
3
0
0
0
0
1
0
1
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
2
1
0
0
0
0
0
2
0
0
1
0
0
2
2
0
0
1
1
1
0
0
0
0
0
1
0
4
0
0
0
0
0
1
1
2
1
1
3
2
2
2
0
0
1
0
0
0
0
0
0
0
1
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
2
0
0
0
1
1
0
2
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
1
1
1
1
0
2
0
1
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
1
2
0
0
0
0
2
0
0
0
1
1
0
2
0
0
0
3
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
2
8
1
1
0
4
2
0
0
0
0
0
0
2
1
2
0
0
2
0
1
2
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
2
0
1
0
2
0
3
0
0
0
1
0
0
0
2
1
1
0
0
1
2
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
4
2
0
2
0
2
0
0
0
0
0
1
1
0
0
0
1
0
0
0
2
1
0
1
2
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
3
1
2
0
0
0
1
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
3
0
0
2
0
1
3
1
0
0
2
0
1
1
0
2
0
0
1
0
0
0
0
0
0
0
0
3
2
0
0
1
0
0
0
2
0
1
1
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
3
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
3
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
1
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
3
0
0
1
0
1
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
1
0
0
0
2
0
2
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
4
2
0
0
0
2
0
0
0
1
2
1
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
2
0
0
1
0
2
0
0
0
0
2
1
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
2
0
0
0
2
1
0
0
0
0
2
4
0
1
0
1
0
1
0
0
0
0
0
0
1
0
1
2
1
0
0
3
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
1
2
0
0
2
0
2
0
0
2
0
0
1
0
0
0
0
1
1
0
2
1
0
0
0
0
1
2
1
0
0
0
3
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
3
2
0
0
1
0
2
0
2
2
0
0
0
1
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
1
1
2
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
2
2
4
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
2
0
0
0
2
0
0
2
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
3
0
1
0
2
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
1
0
0
0
2
0
1
1
0
0
0
0
2
0
4
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
2
3
2
2
0
1
0
0
0
0
3
2
0
0
0
0
0
2
2
0
0
0
0
0
2
2
1
0
0
1
1
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
3
0
0
1
0
0
0
1
0
1
0
0
0
0
2
2
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
2
1
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
3
2
0
1
0
8
1
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
1
2
1
1
0
2
0
0
0
2
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
2
0
1
2
0
0
2
1
0
0
0
2
1
0
0
0
2
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
3
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
3
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
2
0
0
2
0
0
0
2
0
1
0
0
0
2
0
0
0
2
1
2
0
2
1
1
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
3
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
1
0
1
1
0
0
0
0
0
0
7
0
1
0
0
1
2
2
0
0
0
0
0
2
0
3
0
0
2
0
0
1
0
3
2
0
0
2
2
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
2
0
0
2
1
0
0
0
0
0
1
0
2
1
0
2
0
0
0
0
0
0
1
0
1
1
0
2
2
0
0
1
0
0
0
0
0
0
2
6
0
0
0
0
1
0
0
0
2
0
1
0
2
0
0
0
2
2
0
2
0
0
0
0
0
2
0
2
0
2
0
1
0
0
0
0
2
2
0
0
1
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
2
1
3
2
1
0
0
1
0
4
0
2
2
0
1
0
2
2
0
0
0
2
0
0
2
0
2
0
1
0
1
0
2
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
14
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
1
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
1
2
0
0
0
1
0
0
5
0
0
0
1
0
0
1
0
0
0
0
3
0
0
0
2
0
2
1
0
1
0
0
0
3
4
0
0
0
0
0
0
0
0
0
2
1
1
0
4
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
2
2
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
1
0
1
1
0
0
3
0
2
0
0
1
0
2
0
0
0
0
0
0
0
2
0
1
0
2
0
1
0
0
0
0
1
0
0
2
0
1
0
0
2
2
0
0
0
2
0
1
1
1
1
1
0
0
1
0
0
0
0
2
1
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
4
2
0
1
1
1
0
4
0
0
0
0
2
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
1
0
0
1
0
2
0
1
0
0
0
2
1
0
0
0
0
2
0
2
0
0
1
0
0
0
1
0
0
0
0
0
2
0
1
1
0
2
2
0
0
6
0
0
0
1
0
0
0
1
0
0
0
0
5
0
0
2
0
2
0
0
0
0
4
1
0
0
0
0
0
0
2
1
0
0
2
1
2
2
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
2
1
0
0
0
0
0
0
1
0
0
0
0
1
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
9
0
2
0
3
1
2
0
4
1
0
1
0
1
2
0
0
1
0
0
0
1
0
0
0
0
0
2
0
2
2
1
0
0
0
0
0
0
2
0
1
0
2
0
0
0
2
0
2
0
0
0
0
2
2
0
1
0
0
2
1
1
0
0
0
2
1
1
0
0
0
7
0
1
1
1
0
0
2
0
2
0
1
1
0
0
2
0
2
1
0
0
0
0
0
0
0
2
2
1
0
0
1
1
0
0
0
0
2
1
2
0
0
1
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
2
0
4
0
1
2
0
0
2
0
0
0
2
2
0
0
0
0
0
2
0
0
0
1
1
1
0
2
0
2
0
0
0
1
0
0
2
0
0
0
3
2
1
0
0
0
0
0
0
2
2
0
2
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
5
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
2
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
2
0
2
2
3
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
3
0
1
1
3
0
0
0
0
3
1
3
0
0
0
2
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
2
0
1
1
0
3
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
1
1
0
0
2
0
3
0
1
0
0
0
0
0
1
0
0
1
0
0
2
0
4
1
0
0
1
3
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
2
2
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
2
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
2
1
1
2
0
0
1
1
2
0
2
0
2
1
0
2
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
2
1
1
0
0
1
1
0
3
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
2
2
0
0
2
0
0
1
1
1
0
1
3
0
0
1
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
3
0
1
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
2
0
0
3
0
0
0
0
2
1
0
0
4
2
0
0
0
1
0
1
0
0
0
2
0
2
2
0
0
0
0
1
4
0
0
0
0
2
0
0
0
0
1
0
1
0
2
5
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
1
2
0
0
0
2
2
0
0
1
0
1
0
0
0
1
2
0
0
1
0
0
0
1
0
0
0
2
0
2
0
3
1
2
0
1
0
0
0
0
1
2
1
1
0
1
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
6
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
1
0
0
0
0
6
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
1
2
0
0
0
2
0
1
2
0
1
0
3
1
0
0
1
0
0
1
1
0
0
0
2
0
2
0
2
0
0
0
0
3
0
1
0
1
0
0
0
2
2
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
2
2
0
0
2
1
0
0
0
1
0
0
0
0
5
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
2
2
2
1
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
2
0
1
0
1
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
1
0
0
0
2
1
1
0
2
0
0
0
0
0
1
0
0
7
1
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
3
1
0
2
0
0
0
3
0
3
0
0
1
0
0
1
2
0
0
1
1
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
1
0
2
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
2
1
0
2
0
1
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
1
1
0
0
0
1
1
0
2
2
0
0
0
2
0
0
0
0
1
0
1
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
2
0
1
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
1
3
0
2
0
0
0
2
1
0
0
1
1
2
1
0
2
0
3
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
1
0
2
0
2
0
0
0
0
1
1
2
0
0
0
1
1
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
1
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
2
1
1
0
1
1
0
1
1
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
2
5
0
0
0
0
0
0
0
2
1
0
0
3
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
8
0
0
0
2
0
1
0
0
3
1
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
1
0
1
1
1
0
1
0
1
0
1
0
0
0
2
0
0
1
0
0
2
0
1
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
2
1
1
0
1
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
2
2
0
1
2
0
0
2
2
2
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
1
0
0
0
2
0
2
0
2
2
0
2
0
1
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
3
1
0
2
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
1
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
3
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
3
2
2
0
0
0
0
1
0
0
0
1
0
0
0
1
1
2
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
2
1
0
0
0
0
0
0
3
0
1
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
2
0
0
4
0
0
0
1
0
0
2
2
0
0
0
1
0
0
2
0
2
0
1
0
0
2
0
0
0
1
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
1
3
0
1
0
1
1
0
0
0
0
0
2
1
0
0
2
0
0
0
1
0
1
2
0
0
0
2
0
0
4
0
0
2
0
2
0
0
1
2
0
2
0
0
0
0
0
0
0
2
0
2
0
1
0
2
2
1
0
0
0
0
1
0
0
0
1
2
1
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
2
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
2
1
1
0
2
1
0
2
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
3
1
0
1
0
3
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
1
0
0
1
0
1
0
0
0
0
3
0
0
1
0
0
0
0
2
0
0
0
1
0
2
2
1
0
0
0
2
0
2
1
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
2
2
0
0
1
1
0
0
2
1
0
2
0
2
0
0
0
4
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
1
0
0
2
0
2
0
3
2
0
0
3
0
1
0
0
0
0
1
0
1
2
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
3
0
0
1
1
1
0
1
0
0
0
0
1
0
0
0
4
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
1
0
6
0
0
0
0
0
2
0
1
2
0
0
4
0
1
0
0
3
1
0
0
0
0
2
0
0
0
0
0
1
0
2
2
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
2
2
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
3
0
0
2
1
0
4
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
2
1
0
1
0
0
0
1
0
3
0
1
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
1
0
0
0
0
0
1
1
2
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
1
1
2
0
0
1
0
0
0
4
0
0
2
0
0
0
0
0
0
0
2
3
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
4
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
2
1
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
3
0
0
0
2
0
0
2
1
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
1
0
1
0
0
0
0
0
1
0
0
1
2
1
0
0
0
0
2
0
0
2
0
0
2
0
0
2
0
0
0
0
0
2
2
2
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
3
2
0
0
0
1
0
1
0
1
2
0
1
0
1
0
2
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
1
1
0
0
2
2
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
3
0
1
1
0
0
0
0
0
0
0
1
0
2
0
0
1
2
0
0
0
1
2
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
1
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
3
0
0
0
2
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
1
0
1
0
1
0
0
0
2
0
2
0
1
1
0
2
2
0
7
2
2
0
0
0
0
0
1
0
0
0
2
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
3
1
0
0
1
0
0
1
2
0
1
2
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
1
0
1
9
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
1
0
0
1
0
0
2
2
0
0
1
0
0
0
3
0
3
0
0
0
0
0
0
4
1
0
0
0
2
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
1
0
1
2
2
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
3
2
0
0
3
0
2
0
0
0
0
0
2
0
0
2
2
0
2
0
1
2
2
0
0
2
0
2
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
2
0
0
0
0
1
1
2
1
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
1
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
2
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
2
1
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
1
1
0
0
0
3
0
0
1
0
0
1
0
0
2
1
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
5
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
2
1
1
1
0
2
0
0
2
0
0
2
0
0
0
0
0
1
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
3
0
0
2
0
0
0
2
0
0
1
0
0
1
0
1
0
2
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
1
1
0
1
0
0
0
0
0
1
0
2
0
1
0
1
0
0
1
0
0
1
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
4
0
0
0
0
2
0
0
0
0
1
0
1
0
1
1
0
0
0
0
4
1
0
0
0
0
0
3
2
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
1
1
1
1
0
0
0
0
1
0
0
0
0
2
2
0
0
2
0
2
2
0
0
1
0
0
0
0
4
2
0
0
2
1
0
2
0
0
0
0
0
1
0
0
0
0
0
2
1
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
2
0
0
0
1
0
0
0
2
2
0
0
2
0
0
0
0
0
1
2
0
0
0
2
0
2
1
0
0
0
0
2
0
2
0
0
0
0
0
0
1
1
2
0
0
2
0
0
2
0
0
2
0
0
0
2
0
2
0
0
2
2
1
0
1
0
2
0
1
0
0
2
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
2
2
1
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
1
1
0
0
0
0
2
1
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
2
1
0
0
0
0
1
0
1
0
2
0
1
1
0
2
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
1
0
1
1
0
0
0
0
2
2
2
0
0
0
0
0
1
0
1
0
0
0
0
1
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
3
0
0
1
0
2
0
1
0
0
0
0
2
0
0
0
0
0
3
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
2
2
0
0
0
1
0
0
0
1
4
0
0
0
0
0
0
0
0
0
1
2
0
1
2
1
1
1
0
0
2
0
1
2
5
0
0
0
0
2
0
0
0
0
0
1
3
2
0
0
0
2
0
1
0
0
3
1
0
3
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
2
0
0
0
3
0
1
0
0
4
0
0
1
0
0
2
0
2
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
1
2
2
0
0
0
1
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
2
1
4
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
2
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
6
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
3
0
0
0
1
1
2
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
1
0
1
2
2
2
0
1
2
1
2
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
1
2
0
0
0
1
1
0
1
3
0
0
2
2
0
0
2
0
0
1
1
2
0
0
0
0
0
0
2
0
3
0
2
0
1
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
2
1
0
2
2
3
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
2
0
1
4
1
2
0
0
5
1
0
0
2
2
0
1
0
0
1
2
0
1
0
1
0
0
2
0
0
0
12
0
0
0
0
0
0
0
0
0
2
2
0
0
4
0
2
2
2
1
0
2
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
8
0
0
0
0
0
2
1
0
0
1
2
0
0
0
0
0
0
0
0
1
0
5
0
0
0
2
0
2
3
0
0
0
1
0
1
0
2
0
0
2
2
1
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
2
0
0
2
2
0
1
0
1
0
0
2
0
1
0
0
2
0
2
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
2
1
0
1
0
0
0
2
0
1
0
0
1
2
2
0
0
1
0
2
0
0
0
2
0
2
0
0
1
1
1
2
0
0
0
1
0
3
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
3
1
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
4
2
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
1
1
0
0
0
1
0
0
1
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
1
1
0
0
0
0
2
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
2
2
0
2
0
0
0
0
0
0
2
3
1
1
0
0
1
0
0
3
2
0
0
0
0
2
2
0
0
2
0
2
0
1
1
0
3
0
2
0
0
4
2
0
2
0
1
0
0
0
1
0
2
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
2
2
2
0
0
2
0
0
0
2
1
0
0
1
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
5
2
2
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
2
0
2
1
1
0
0
0
1
2
2
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
1
0
1
0
2
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
3
2
0
0
0
0
1
0
1
0
0
2
0
2
0
0
0
0
0
1
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
2
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
3
2
0
1
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
2
1
1
2
2
0
0
0
0
0
2
2
0
1
1
1
0
0
0
0
0
0
1
0
1
3
0
1
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
1
4
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
2
2
0
0
2
0
2
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
3
0
1
1
1
2
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
2
0
0
3
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
1
3
2
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
2
0
0
0
2
0
0
1
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
2
0
0
4
0
2
2
0
0
1
2
0
0
2
2
0
0
1
2
1
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
1
2
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
1
1
2
0
0
2
0
0
0
1
0
10
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
1
2
0
0
1
0
1
0
0
0
1
0
2
0
0
0
0
0
0
3
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
2
0
2
2
1
0
0
0
0
0
0
1
0
0
0
3
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
1
1
0
0
1
4
0
0
0
1
0
1
1
0
1
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
1
1
0
1
0
1
0
0
0
0
0
3
2
1
2
0
0
1
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
1
0
0
1
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
1
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
1
1
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
3
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
3
3
0
1
0
0
1
0
0
0
0
0
0
0
1
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
1
0
0
1
0
0
1
1
0
0
0
0
0
2
0
0
0
1
2
0
1
0
0
0
0
0
0
0
1
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
1
0
0
1
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
1
0
2
0
0
1
2
0
0
0
2
1
1
2
0
0
0
0
0
0
1
0
0
0
0
2
0
2
1
0
0
0
0
1
2
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
2
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
5
1
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
1
0
0
0
1
0
0
3
0
3
2
1
2
1
0
0
2
0
0
1
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
3
0
0
0
0
2
1
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
2
0
0
1
0
0
0
2
0
0
0
2
0
0
2
2
0
2
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
2
3
0
0
0
1
0
2
1
0
0
0
2
0
0
2
0
2
0
0
2
2
0
0
0
2
0
0
2
0
2
0
0
0
2
0
0
1
0
2
1
0
0
0
0
0
0
2
0
1
0
0
1
0
1
0
3
0
0
0
0
2
0
2
0
0
0
2
2
0
0
2
1
3
0
0
0
0
0
0
2
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
3
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
1
1
2
0
2
0
2
2
1
2
0
0
5
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
2
0
0
2
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
2
2
0
1
0
0
0
0
4
0
0
1
0
0
2
1
2
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
1
2
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
2
2
0
3
0
1
0
0
0
0
0
2
0
0
0
2
2
2
2
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
2
0
1
0
0
0
0
2
0
2
1
1
0
0
1
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
2
1
2
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
2
5
0
0
0
0
0
2
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
3
1
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
3
0
0
0
0
1
1
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
1
1
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
2
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
2
1
0
1
2
2
0
0
1
0
0
1
0
0
2
0
2
1
0
2
2
0
1
0
0
0
0
2
0
0
1
0
2
0
1
0
0
0
0
0
1
0
0
2
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
1
1
0
1
0
2
0
0
0
0
1
2
1
0
0
10
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
2
0
1
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
4
2
2
0
0
0
0
0
0
0
0
2
1
2
0
1
2
1
0
1
0
2
2
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
2
2
1
0
1
2
0
0
0
0
0
0
0
2
2
0
2
0
0
1
0
1
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
2
2
0
0
0
1
0
1
0
0
2
4
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
3
2
3
0
0
0
2
0
0
0
1
0
1
0
0
0
2
2
2
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
5
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
2
0
0
1
0
2
0
0
0
2
0
2
0
1
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
2
0
0
0
2
2
1
3
0
0
0
2
0
2
1
0
0
1
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
1
1
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
2
2
2
0
0
0
0
1
0
0
0
0
3
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
1
0
1
0
0
1
0
0
0
0
1
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
2
0
0
0
1
1
0
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
1
5
0
0
0
1
1
1
2
0
1
1
0
1
3
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
2
1
0
1
0
0
0
2
0
0
0
0
2
1
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
2
2
0
0
0
1
0
2
2
0
0
0
1
2
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
1
0
2
1
0
3
1
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
2
0
2
1
0
0
0
0
1
2
0
0
0
0
1
0
0
1
1
2
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
2
2
1
0
0
0
0
0
1
0
0
0
2
0
0
1
0
2
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
2
2
0
1
1
0
0
1
1
1
0
1
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
2
0
1
2
0
0
2
0
0
0
0
0
0
0
2
0
1
2
2
0
1
0
2
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
2
0
0
0
2
0
0
2
1
2
0
0
0
1
0
0
0
0
0
0
1
1
0
2
0
0
0
1
0
2
2
2
0
1
0
0
1
2
1
0
0
0
3
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
1
1
0
0
1
0
0
0
0
2
2
1
0
0
2
1
0
1
0
0
2
0
0
0
0
1
0
3
0
0
0
0
0
1
1
7
2
0
0
0
0
2
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
3
0
0
0
0
3
0
0
0
1
0
0
1
0
2
0
0
0
1
0
2
0
1
1
0
0
0
2
0
0
0
0
2
0
2
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
6
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
5
0
0
0
0
0
0
0
0
0
2
0
1
0
0
3
0
0
0
0
0
0
3
0
0
0
0
0
0
0
5
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
3
0
0
0
1
0
2
0
0
1
0
2
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
5
4
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
2
0
2
0
0
2
0
0
3
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
2
1
1
1
0
1
0
1
2
0
0
2
0
2
0
0
2
1
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
8
0
0
3
2
0
1
0
0
0
0
1
0
0
1
2
2
0
0
0
0
2
1
1
2
4
0
1
2
1
0
2
0
1
0
2
0
0
2
1
0
1
1
2
1
0
2
0
0
1
1
2
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
2
0
1
0
1
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
4
4
0
0
0
1
0
0
0
0
0
0
0
1
2
4
0
0
0
0
0
1
0
2
0
0
1
0
1
0
2
0
0
1
0
0
1
2
0
0
0
3
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
4
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
2
0
0
0
3
0
1
0
2
2
0
0
0
0
0
1
0
0
3
0
1
2
0
2
3
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
1
2
0
0
0
0
1
0
0
2
1
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
1
0
0
3
0
0
0
2
0
2
0
0
0
2
0
0
1
1
2
2
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
2
0
1
0
0
0
0
1
0
0
1
0
0
2
0
0
2
1
3
2
0
0
2
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
3
0
0
2
0
2
0
0
1
0
0
1
0
1
0
0
0
0
1
3
0
0
0
0
1
0
0
0
0
1
1
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
1
0
0
0
0
0
2
2
2
0
2
0
0
2
1
2
0
0
1
0
0
0
2
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
5
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
3
0
1
2
0
1
0
0
2
1
0
0
0
1
2
0
0
0
1
3
0
1
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
1
1
0
8
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
1
0
1
0
2
1
0
0
2
1
0
1
0
0
1
0
0
2
3
0
0
1
0
0
2
0
0
0
0
0
0
1
3
1
1
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
2
0
0
2
0
3
1
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
2
0
1
0
2
0
2
0
0
0
1
3
1
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
2
2
1
1
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
1
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
2
1
2
0
0
0
0
0
2
1
0
1
0
0
0
0
1
2
7
2
0
1
0
0
0
2
0
0
0
1
3
1
0
0
0
0
1
0
1
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
1
1
0
2
0
0
0
2
0
2
1
0
1
2
0
0
1
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
1
0
2
0
2
1
0
4
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
2
0
1
0
2
0
0
0
1
0
0
2
0
1
2
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
3
0
0
2
0
0
2
2
0
0
0
1
0
0
0
0
2
2
1
0
0
0
2
2
0
1
0
0
2
0
1
2
1
1
0
0
2
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
2
0
1
0
0
0
0
0
2
0
1
0
2
3
2
0
2
2
0
0
1
2
1
1
1
0
1
2
0
0
2
0
0
2
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
2
0
1
2
0
0
0
0
0
2
0
1
0
2
0
10
1
2
0
1
1
0
0
0
0
0
1
0
0
2
2
0
0
0
1
2
2
2
1
0
1
0
0
0
0
0
2
2
0
0
1
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
2
0
0
0
1
1
0
0
0
1
0
0
1
0
0
2
2
0
0
0
5
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
2
0
0
2
1
3
1
2
0
3
0
0
0
0
1
0
0
0
2
0
2
2
0
1
0
2
1
0
0
2
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
4
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
2
0
1
0
0
0
0
2
1
0
0
0
2
1
0
0
0
2
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
2
0
0
0
0
2
0
1
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
5
0
0
0
0
2
1
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
1
0
0
1
0
0
2
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
1
0
0
1
0
0
0
1
0
0
2
0
0
0
2
2
1
1
0
0
2
0
0
2
0
3
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
1
1
0
0
1
0
0
0
0
0
0
0
1
2
0
2
1
0
2
0
2
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
3
0
3
0
1
2
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
1
2
0
1
1
2
0
0
0
1
0
2
0
0
2
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
1
0
0
0
1
0
2
1
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
2
0
0
0
3
0
0
2
2
0
0
0
1
2
0
0
0
0
0
2
1
2
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
2
0
2
1
2
2
2
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
2
1
2
2
3
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
2
0
0
0
0
0
2
2
0
2
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
1
2
0
0
0
0
0
1
1
0
0
0
2
0
0
1
0
0
0
1
0
1
0
2
0
1
2
0
0
0
2
0
0
0
0
0
0
2
1
0
4
2
0
0
0
2
0
1
0
2
2
0
0
1
0
2
0
0
1
0
0
0
0
1
0
0
0
2
1
0
0
0
1
1
0
0
0
0
1
1
2
1
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
2
1
0
2
1
0
2
0
2
1
1
4
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
8
0
1
1
0
0
0
0
0
0
0
2
0
0
2
0
1
0
2
1
0
0
0
0
0
2
0
0
0
4
0
0
0
1
0
1
1
3
0
0
1
0
0
0
0
0
0
1
2
2
1
3
0
0
1
0
0
2
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
7
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
3
0
1
0
2
0
0
1
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
1
4
1
0
0
1
1
2
0
0
0
0
0
0
0
1
0
0
3
0
1
0
0
0
0
0
1
0
1
0
0
0
0
2
1
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
1
0
1
2
0
0
1
2
0
1
0
0
0
1
0
0
0
0
0
0
8
0
0
1
3
1
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
3
1
0
0
1
0
0
0
2
1
0
0
0
0
2
2
2
2
1
2
0
0
1
0
0
0
2
0
1
0
0
1
4
2
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
3
0
0
0
0
0
1
0
0
6
2
2
0
0
0
0
1
2
0
0
0
1
0
1
3
0
0
0
0
2
0
0
2
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
5
0
0
0
1
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
3
1
0
1
0
0
0
0
0
0
1
2
0
0
1
0
0
0
2
1
0
0
0
2
0
0
2
4
0
0
0
1
0
1
2
0
0
1
0
0
0
0
0
0
2
3
0
0
0
0
0
2
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
3
1
2
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
3
1
0
0
0
0
0
0
1
0
1
2
2
0
0
0
0
0
2
0
10
0
0
1
1
0
2
0
0
1
0
2
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
2
0
2
2
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
1
0
1
0
0
0
2
1
0
0
0
1
0
3
2
2
2
0
0
0
0
0
1
0
0
1
0
1
0
0
5
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
2
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
2
0
0
2
1
0
0
0
0
0
0
0
2
0
1
2
0
0
0
2
0
2
0
0
2
0
2
3
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
4
1
0
0
0
0
0
0
1
1
1
2
0
0
1
2
2
0
0
0
0
2
0
2
0
0
0
2
0
0
1
0
7
1
2
0
1
0
0
2
3
1
0
0
2
2
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
2
2
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
1
0
0
2
0
0
0
1
0
0
3
0
0
0
2
1
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
5
0
1
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
3
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
2
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
1
2
0
0
0
1
0
0
0
2
0
2
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
2
2
0
2
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
4
0
0
1
2
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
3
1
1
1
0
1
1
1
2
0
1
0
2
0
0
0
0
1
0
0
2
0
2
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
1
0
0
0
0
1
1
1
0
0
0
2
0
0
0
2
0
0
0
0
1
3
0
3
0
1
2
0
0
0
0
0
0
0
0
0
3
0
0
1
3
1
0
0
0
2
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
1
2
0
0
3
3
0
0
0
0
1
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
1
2
0
2
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
2
1
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
2
0
1
0
0
1
1
2
2
0
0
0
0
0
1
0
0
1
0
1
1
1
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
2
2
0
0
0
0
1
0
0
2
1
0
0
2
0
1
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
1
0
1
1
0
1
0
2
0
0
0
0
0
0
2
1
4
0
0
0
3
0
3
0
0
2
2
0
0
0
0
2
2
0
2
0
0
0
2
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
2
0
0
0
0
0
0
0
1
0
5
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
1
2
0
0
0
2
0
1
0
2
2
0
0
0
0
2
0
2
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
6
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
2
0
1
2
0
0
1
0
0
0
0
0
1
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
2
0
0
0
0
1
0
0
1
0
0
0
0
2
0
1
2
2
0
2
0
0
3
0
1
2
1
2
0
0
0
1
1
0
0
0
0
0
2
2
0
0
0
1
0
0
1
2
0
0
0
0
2
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
1
0
2
1
0
1
0
0
2
1
2
0
0
0
0
0
1
3
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
1
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
1
0
0
0
1
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
2
0
2
5
5
1
2
1
2
0
0
2
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
3
2
1
0
0
1
0
0
2
1
0
0
2
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
1
2
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
5
1
0
0
0
0
0
0
0
2
0
2
2
0
2
0
3
0
3
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
5
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
3
0
1
2
2
0
0
0
2
0
0
0
0
0
1
1
0
1
2
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
2
0
0
1
0
2
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
1
9
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
1
2
0
0
0
1
0
0
0
1
5
2
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
1
2
0
0
1
0
1
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
2
1
0
0
0
0
0
0
0
1
4
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
3
0
0
0
0
2
0
2
1
4
2
0
1
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
2
0
0
0
2
2
0
1
0
2
0
0
0
0
0
0
3
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
4
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
2
0
0
0
0
3
0
0
1
0
2
1
0
1
0
2
2
0
0
0
0
2
0
0
0
0
1
0
0
0
1
3
0
0
0
0
3
0
1
1
1
0
1
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
1
0
0
0
2
0
1
0
0
0
0
2
1
0
2
0
2
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
1
0
0
2
0
2
2
1
2
1
0
0
0
0
0
0
0
1
0
0
6
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
3
0
0
0
0
1
1
0
0
2
0
0
1
1
0
3
1
1
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
2
1
2
0
1
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
4
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
3
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
2
0
0
0
0
2
0
2
0
0
0
0
4
0
0
0
0
0
1
0
1
0
0
3
0
1
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
2
0
0
2
0
0
0
0
1
1
0
2
0
0
0
2
1
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
1
0
3
1
0
0
2
0
1
0
0
0
0
1
3
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
2
2
0
0
0
2
0
0
1
0
1
1
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
1
0
1
0
2
0
1
0
2
0
2
1
0
0
0
2
0
0
1
0
0
0
0
3
0
0
0
1
0
0
0
0
0
2
0
1
1
0
1
0
0
2
2
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
3
2
2
0
0
0
1
0
0
0
0
0
1
0
0
2
1
2
0
0
2
0
0
1
0
2
0
0
0
2
0
0
0
2
1
0
0
2
1
0
0
0
0
1
1
0
1
1
1
2
1
0
1
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
2
0
0
0
2
0
1
0
4
0
2
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
1
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
2
0
2
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
3
0
0
1
0
3
0
1
0
1
1
0
0
0
2
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
2
0
0
1
2
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
1
2
1
0
0
2
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
2
0
1
1
0
0
1
0
0
0
0
1
0
0
2
2
2
0
0
0
0
0
0
0
0
3
0
2
0
2
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
2
0
0
2
0
4
0
0
0
0
0
0
2
0
0
0
0
1
2
0
1
1
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
3
0
0
2
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
2
0
0
0
0
1
0
0
1
0
0
3
1
0
0
0
0
0
2
2
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
1
0
2
1
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
1
2
0
1
0
0
1
0
1
2
2
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
3
0
2
2
0
0
1
1
0
1
2
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
2
0
2
0
0
2
1
0
0
2
0
0
0
2
2
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
1
0
2
1
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
1
0
2
0
0
0
1
0
1
0
1
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
3
0
4
0
0
1
1
0
1
0
0
2
2
0
0
1
1
1
0
1
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
5
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
3
2
2
0
0
1
1
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
2
0
1
0
0
11
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
6
1
0
0
0
0
0
2
0
2
3
0
0
1
0
1
0
0
1
3
0
2
0
0
5
2
2
0
0
0
0
1
1
0
0
0
0
2
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
2
0
0
1
2
0
0
2
0
0
1
0
1
2
0
2
0
0
0
0
0
0
0
1
1
0
0
2
2
2
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
2
1
0
0
1
0
0
0
0
0
1
2
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
2
2
0
0
1
0
0
0
1
0
1
0
0
1
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
2
0
0
1
0
2
0
0
0
1
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
3
0
0
1
0
0
0
2
2
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
3
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
1
1
1
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
1
0
2
1
1
0
2
1
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
1
4
0
0
0
2
0
0
0
2
0
0
0
0
0
3
0
1
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
1
0
0
2
0
0
2
2
0
1
1
0
1
0
0
1
0
0
3
0
0
0
2
0
0
0
2
0
1
0
1
0
2
0
0
0
2
2
0
0
1
0
1
0
0
1
1
0
0
0
2
1
0
0
0
1
1
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
2
0
2
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
1
4
0
0
0
0
0
0
0
1
2
0
1
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
2
0
1
0
0
0
0
0
0
2
2
0
1
1
0
0
1
0
2
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
2
0
2
0
0
0
1
0
0
0
0
0
2
0
1
0
0
1
0
2
0
0
2
0
2
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
2
1
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
4
2
0
2
0
0
0
0
2
0
0
0
0
3
2
0
1
0
0
0
1
2
2
0
0
0
0
1
0
0
2
1
0
0
1
0
1
0
0
3
0
2
2
1
2
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
3
0
0
0
1
2
1
0
0
3
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
2
0
0
0
0
2
0
1
2
0
1
0
1
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
1
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
2
3
0
2
0
0
0
0
2
0
1
0
0
1
0
1
0
0
0
1
0
2
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
1
3
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
2
0
1
0
0
0
2
1
0
0
1
0
0
1
0
2
3
0
3
0
2
0
0
0
0
0
0
2
1
0
0
7
2
0
0
1
2
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
4
0
2
0
0
0
0
0
0
2
1
0
0
2
1
0
0
2
1
1
0
0
1
2
0
0
0
2
1
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
1
0
2
2
0
2
0
1
1
0
1
0
1
2
1
0
0
0
4
0
0
0
0
2
2
4
0
0
0
1
0
0
0
1
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
8
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
2
0
1
2
1
0
0
0
0
2
0
2
0
0
0
2
0
1
0
0
0
2
0
0
2
0
2
1
1
0
0
0
0
2
0
3
0
0
1
2
0
0
0
2
3
0
1
2
0
1
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
2
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
2
0
1
0
1
1
2
0
2
0
0
1
2
0
0
0
1
3
0
2
2
1
0
2
0
0
3
0
0
0
3
0
0
0
0
1
0
3
0
0
3
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
2
0
1
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
1
0
0
0
0
0
0
2
0
0
2
1
0
0
4
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
2
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
2
0
2
1
0
0
2
0
0
0
2
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
2
0
0
2
1
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
2
0
1
1
0
0
1
0
0
5
2
2
2
2
2
2
1
0
0
1
1
0
0
0
2
2
0
0
0
0
0
2
0
1
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
4
1
0
0
0
0
0
0
1
0
0
1
1
2
0
0
0
0
0
0
0
1
1
0
2
0
0
0
2
1
0
0
0
2
1
0
1
0
0
1
1
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
2
2
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
2
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
1
0
0
3
0
1
0
0
0
0
0
0
1
2
2
1
0
4
0
0
0
0
1
2
2
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
1
0
0
2
0
0
0
1
3
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
1
6
0
1
0
0
0
0
0
0
2
2
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
5
0
1
1
1
3
0
0
2
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
1
0
0
1
1
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
2
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
2
0
0
0
0
1
0
1
0
0
2
2
3
0
0
4
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
1
1
0
1
3
1
0
2
1
0
0
0
0
0
1
0
0
0
1
0
0
1
3
2
0
0
1
0
0
0
0
0
0
0
3
0
2
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
1
1
0
1
0
2
0
1
0
2
0
1
0
0
1
2
1
0
0
0
2
2
0
0
0
0
0
1
0
0
2
2
1
1
0
0
0
0
3
0
0
1
0
1
2
0
0
2
1
1
1
2
1
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
3
1
2
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
2
0
2
0
2
0
0
2
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
2
1
0
1
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
3
0
0
0
0
0
0
0
0
1
2
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
3
1
1
1
0
2
0
0
2
0
1
0
0
0
0
0
0
0
2
0
2
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
2
1
1
0
2
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
2
0
0
2
0
0
0
2
0
0
2
0
1
2
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
4
0
2
1
0
0
2
0
0
3
0
0
0
0
0
0
2
0
0
0
0
2
0
1
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
1
4
0
1
0
0
0
0
0
0
1
0
0
0
0
0
3
1
0
2
0
0
0
0
2
0
0
0
1
0
0
3
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
3
0
0
5
1
0
0
1
0
0
0
1
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
1
2
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
2
2
2
0
0
2
0
0
0
0
0
0
0
3
1
4
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
2
2
0
0
0
2
2
0
0
2
0
0
0
0
1
0
1
0
2
0
1
2
0
0
2
0
1
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
1
2
0
0
0
0
0
0
0
1
2
4
1
1
0
2
0
0
0
0
0
0
2
0
1
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
1
2
1
0
0
4
0
0
1
0
1
1
0
4
1
0
0
0
0
0
0
1
2
0
0
2
0
0
1
0
1
0
1
0
0
0
0
2
2
0
0
0
0
1
0
1
0
0
0
0
1
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
3
0
0
0
2
0
0
0
0
1
0
2
0
0
0
2
0
0
0
2
0
3
2
0
0
1
0
0
2
0
2
0
2
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
2
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
2
0
2
0
2
0
0
0
2
2
0
2
2
0
0
0
0
0
0
0
1
1
2
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
4
2
0
0
0
0
1
1
1
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
2
0
0
1
0
1
0
1
0
0
3
0
0
0
1
1
0
1
0
1
0
0
1
1
2
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
4
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
3
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
3
1
0
0
0
0
0
0
2
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
1
2
0
2
0
0
0
1
0
0
1
0
1
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
2
4
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
2
0
0
2
1
2
0
0
3
0
0
0
0
0
1
0
0
2
2
0
0
1
0
0
0
2
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
1
0
2
1
0
0
0
2
0
2
0
0
1
0
1
2
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
1
1
0
2
0
1
4
0
1
0
0
0
2
1
1
0
0
1
1
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
2
3
0
1
1
0
2
0
0
2
0
0
2
2
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
1
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
2
2
0
0
0
2
0
1
0
0
0
0
2
1
0
11
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
1
0
1
3
1
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
2
6
0
0
0
1
0
0
2
0
0
1
0
0
1
0
0
2
0
2
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
1
0
0
2
0
1
0
0
0
3
0
0
0
0
1
2
0
0
1
0
0
0
1
0
0
1
0
2
0
1
1
2
0
1
2
0
0
0
0
2
0
0
2
0
0
0
0
1
1
0
0
0
0
0
2
2
2
0
0
0
3
2
0
0
2
0
2
0
2
0
0
0
0
0
0
2
0
0
1
0
1
3
0
0
0
0
0
2
2
0
2
0
0
2
2
2
0
1
0
0
0
2
0
0
0
1
0
0
2
1
0
0
0
0
0
1
1
1
0
0
2
0
1
3
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
1
1
0
2
0
1
0
0
1
4
0
0
0
0
2
2
2
1
0
2
1
2
0
3
0
0
3
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
1
1
0
1
2
0
0
0
0
0
0
1
2
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
2
1
2
0
0
0
0
0
0
0
1
2
1
1
0
0
0
0
2
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
1
2
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
1
0
0
0
2
1
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
2
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
3
0
0
0
2
1
0
0
3
0
1
2
0
0
0
0
0
0
1
0
0
0
2
0
1
0
1
0
1
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
3
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7
0
0
0
0
0
1
3
0
2
0
1
0
0
1
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
2
2
7
1
2
1
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
1
0
2
0
1
0
4
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
1
0
2
1
0
1
1
1
1
0
1
1
1
0
1
0
0
0
0
0
0
0
2
0
0
0
2
1
0
1
0
0
0
0
1
0
0
2
0
2
0
0
1
0
2
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
2
2
2
0
1
1
2
0
0
0
0
0
0
1
5
0
0
0
1
0
2
1
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
2
1
0
0
1
0
1
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
2
0
2
0
0
0
0
1
0
4
0
0
0
2
0
2
0
0
3
2
1
0
0
2
0
0
0
0
0
0
0
0
0
3
2
1
2
2
0
0
0
0
1
2
0
0
1
0
3
0
0
0
0
0
0
1
0
2
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
1
0
2
2
0
0
0
0
0
0
0
0
2
0
0
1
2
0
2
1
0
0
0
0
2
1
2
0
0
0
1
0
0
0
0
0
0
2
0
0
1
1
0
0
0
1
0
3
2
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
2
1
0
0
0
0
2
0
1
2
0
2
0
0
0
0
0
0
0
1
2
0
0
1
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
1
0
0
1
0
0
2
0
0
2
0
0
0
1
1
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
2
0
0
1
2
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
2
2
0
0
7
0
0
1
0
0
0
0
2
0
0
0
0
1
3
0
1
2
0
0
1
2
0
0
0
2
0
2
0
0
3
0
0
2
0
0
0
0
2
0
1
1
0
0
0
1
1
1
0
2
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
5
0
1
0
0
2
0
1
0
0
1
0
0
0
0
1
1
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
1
5
0
1
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
2
1
0
0
1
2
0
4
2
0
0
0
0
0
0
0
2
0
0
0
0
0
3
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
1
1
0
0
5
2
1
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
2
2
2
0
0
5
0
0
1
0
3
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
2
0
1
0
0
3
0
0
0
2
0
0
0
2
0
0
1
1
1
0
0
1
0
0
1
0
0
3
2
0
1
2
1
0
0
1
0
0
2
0
1
1
1
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
3
2
0
0
0
0
0
1
1
0
1
1
1
0
0
1
2
2
0
0
2
0
2
4
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
2
0
2
1
0
0
0
0
0
0
0
0
1
1
0
3
2
0
0
2
0
1
0
1
0
2
0
0
0
1
1
0
0
0
0
3
0
1
0
0
0
0
4
0
2
0
0
0
0
0
0
1
1
2
0
0
1
2
0
0
0
0
2
0
0
0
1
0
0
0
0
2
2
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
2
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
1
1
0
3
0
1
0
0
0
2
2
2
1
0
0
2
1
1
0
1
0
1
1
0
0
0
2
0
2
2
0
1
0
0
0
0
1
3
0
2
1
1
1
1
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
2
0
0
1
0
0
0
0
0
0
5
0
0
1
0
0
0
0
0
0
1
0
0
2
2
1
1
1
0
2
1
0
2
0
0
2
0
0
0
0
0
0
1
2
1
0
1
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
2
0
0
1
0
0
6
1
0
0
0
2
0
0
0
0
2
1
0
1
0
1
0
0
0
0
0
2
0
2
0
1
0
0
0
1
0
3
0
2
0
0
0
1
0
0
0
0
1
0
1
1
0
2
2
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
2
1
0
0
2
2
0
0
1
0
0
0
1
2
1
0
0
0
0
0
1
0
2
0
0
3
0
0
0
2
1
1
0
0
0
2
0
0
2
1
1
0
0
0
2
1
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
3
1
2
0
0
0
1
0
2
0
0
2
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
2
0
0
1
0
0
3
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
1
0
0
1
2
0
0
0
2
0
2
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
2
5
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
1
2
0
3
2
0
0
0
2
1
2
0
0
0
1
0
0
2
0
1
0
0
2
0
0
1
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
1
0
0
0
0
0
0
1
2
1
0
0
0
0
1
2
1
2
2
3
0
1
2
0
0
1
0
0
2
1
0
0
0
0
1
2
1
0
0
1
2
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
2
0
2
0
0
0
0
2
0
0
1
1
0
3
0
0
0
2
0
0
2
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
1
1
1
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
3
3
0
2
0
0
0
2
0
2
2
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
3
1
0
0
0
1
1
0
0
2
0
0
0
3
0
1
0
1
2
2
0
0
1
0
0
2
0
2
9
0
0
0
1
2
0
2
0
0
0
2
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
1
0
3
0
2
0
0
0
0
1
1
2
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
2
2
0
0
0
2
0
0
2
2
2
1
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
2
0
2
0
0
2
4
0
2
0
0
0
0
0
0
0
0
3
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
4
0
3
1
0
0
0
0
3
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
1
2
0
0
0
3
1
2
3
0
1
0
1
1
0
1
0
0
0
0
0
0
1
1
0
0
1
1
1
0
0
0
2
7
2
0
0
1
0
2
0
0
1
1
0
0
2
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
2
0
2
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
1
1
1
2
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
2
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
2
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
1
0
7
1
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
3
0
0
2
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
4
2
0
0
1
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
2
0
2
1
0
0
0
2
2
2
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
4
0
0
0
0
0
0
2
0
0
0
1
0
1
2
0
0
0
1
0
4
0
0
0
0
2
0
2
0
0
0
0
0
0
2
1
0
0
1
0
2
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
5
0
3
0
0
0
2
0
2
0
1
0
0
2
0
2
0
0
1
1
0
2
0
0
2
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
2
0
0
0
0
0
2
0
1
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
1
2
1
0
1
2
0
1
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
1
4
1
0
0
0
0
1
2
0
0
0
0
0
0
0
1
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
1
2
0
0
2
0
0
2
1
0
0
1
0
3
0
0
1
2
0
0
0
0
0
0
0
2
0
0
2
0
2
1
1
2
1
0
0
0
0
2
2
1
2
0
2
0
2
1
0
0
0
1
0
0
0
1
0
0
2
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
3
0
2
0
2
0
1
0
0
2
0
0
0
2
0
2
1
0
0
0
1
0
0
0
1
0
2
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
2
3
0
0
2
0
1
1
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
2
2
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
2
1
0
0
1
1
1
0
1
0
0
0
0
2
0
1
0
1
0
0
1
1
0
0
0
2
2
0
1
0
0
0
1
0
0
1
0
0
1
0
0
1
1
0
0
1
0
1
0
2
0
0
0
0
1
2
0
1
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
2
0
0
0
2
1
1
1
0
5
0
0
1
0
0
1
0
0
0
0
0
0
2
1
0
0
1
0
3
2
0
2
0
0
0
0
0
1
0
1
0
2
0
1
2
0
0
0
1
3
1
0
0
0
1
0
0
1
0
1
2
0
0
2
1
0
0
0
1
0
2
0
0
2
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
2
1
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
4
0
2
1
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
1
3
1
2
0
0
0
0
2
0
1
2
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
1
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
2
0
0
2
0
0
0
0
5
0
1
1
0
0
0
2
2
0
2
0
1
0
0
0
2
0
2
0
2
0
2
1
0
3
1
0
2
2
1
0
0
0
0
0
0
0
2
3
1
0
1
0
4
0
1
0
2
2
0
2
0
0
1
0
0
0
1
0
2
0
2
0
3
0
0
0
0
0
2
0
0
1
0
4
0
0
1
0
0
0
0
2
0
2
1
0
0
4
0
0
0
1
0
0
0
0
0
3
0
2
1
1
0
0
0
0
1
0
1
0
0
0
0
3
2
0
0
0
1
1
0
1
1
0
0
0
0
2
0
1
0
3
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
3
0
2
5
5
0
0
0
2
0
2
1
0
0
1
0
0
0
1
1
0
0
1
2
0
0
0
1
0
2
3
0
0
2
0
0
0
1
1
1
2
0
0
0
0
0
0
0
0
0
0
1
0
1
2
1
0
2
1
0
2
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
2
0
0
0
3
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
2
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
4
1
0
0
0
0
0
0
0
0
2
0
2
0
1
0
2
0
0
0
0
0
0
1
1
0
2
0
0
0
2
3
1
2
4
1
1
0
1
2
0
0
0
0
0
2
0
0
0
0
1
1
0
2
1
0
0
0
0
0
0
1
2
1
0
0
2
2
2
0
3
0
2
0
1
0
2
0
0
0
0
1
0
0
2
2
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
2
0
0
2
0
0
0
2
1
0
2
0
0
0
0
1
0
0
0
0
0
1
2
2
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
1
0
1
0
1
1
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
1
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
3
1
0
0
0
0
0
1
1
1
0
0
3
0
0
1
1
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
1
0
3
1
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
2
2
1
2
0
0
0
0
1
0
1
0
0
1
1
0
0
1
1
0
0
1
1
0
0
0
2
2
2
0
0
0
0
0
0
2
1
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
2
3
0
0
1
0
0
0
1
0
0
0
2
0
1
0
1
0
0
0
1
1
1
0
0
1
0
0
0
0
0
3
2
3
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
1
0
0
0
1
2
0
2
0
2
0
0
0
0
0
0
3
0
2
0
0
0
1
0
0
0
2
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
2
1
0
0
1
2
1
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
2
2
0
0
1
0
0
0
0
2
2
1
1
0
0
0
0
0
0
0
0
1
2
0
1
2
0
2
0
2
1
0
0
0
0
0
2
1
0
2
3
1
0
0
0
0
2
0
0
0
2
0
2
0
0
0
1
0
0
0
2
1
0
0
1
0
2
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
6
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
2
0
4
0
0
1
0
1
0
0
2
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
1
0
2
1
2
5
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
4
0
2
0
1
0
0
0
5
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
1
0
1
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
2
0
0
1
2
0
0
0
0
1
0
3
0
2
0
2
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
2
2
0
0
0
2
1
0
1
0
0
2
1
0
0
0
0
0
0
0
6
2
0
0
2
0
1
2
0
0
1
0
0
0
0
0
3
1
0
3
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
5
0
1
0
0
0
2
1
0
0
0
1
1
0
0
0
6
0
0
0
2
1
0
1
0
0
0
0
1
0
2
0
2
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
1
1
2
2
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
3
1
1
0
0
2
2
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
1
1
0
0
0
3
1
1
0
0
1
0
0
0
3
0
0
1
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
2
0
3
2
0
0
0
0
0
0
0
0
2
2
1
0
0
0
2
1
0
0
1
2
1
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
1
2
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
2
1
3
0
0
0
1
2
0
0
0
2
1
1
1
1
0
0
0
0
2
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
2
0
2
0
0
2
1
1
0
0
0
2
2
2
2
0
0
4
0
2
2
2
2
0
1
0
0
2
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
1
2
0
2
1
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
1
1
0
0
0
0
1
2
0
1
0
4
0
0
0
0
0
0
1
1
0
7
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
1
0
0
1
2
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
4
2
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
2
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
1
0
2
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
2
1
2
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
2
0
0
1
1
2
0
0
0
0
1
1
0
2
1
0
0
1
2
1
0
2
0
2
0
0
2
0
1
0
2
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
2
0
0
1
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
1
2
1
2
1
2
0
0
0
5
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
2
0
0
4
0
0
0
0
0
1
3
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
2
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
3
1
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
2
1
0
0
2
0
2
2
2
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
6
0
0
2
2
0
0
0
2
0
1
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
3
0
0
0
2
1
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
3
0
2
1
1
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
1
0
0
1
2
2
0
0
0
1
0
2
0
0
0
0
0
2
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
1
0
0
2
2
1
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
1
0
0
0
5
0
0
0
0
2
0
0
0
0
0
0
0
2
2
4
0
1
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
1
0
2
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
2
0
0
1
0
0
1
0
7
0
0
1
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
6
1
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
2
3
0
1
2
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
2
2
0
1
1
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
3
0
1
0
0
1
0
0
1
1
1
0
1
2
0
6
0
1
2
0
2
0
0
0
2
4
1
0
0
0
2
3
0
0
0
0
1
2
0
0
0
0
4
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
3
0
0
0
1
0
0
1
0
2
0
1
2
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
2
0
1
0
4
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
2
0
1
2
4
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
1
0
0
3
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
1
2
0
0
0
0
1
3
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
1
2
2
0
0
0
0
0
2
0
1
0
0
0
2
1
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
2
0
0
2
0
1
0
2
0
0
1
0
0
1
1
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
4
1
0
1
0
1
0
0
0
0
0
0
1
1
0
0
1
1
2
0
0
0
0
0
2
0
0
2
1
0
0
0
2
0
0
0
0
0
0
3
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
2
0
0
1
0
0
0
1
0
1
1
1
0
0
3
3
0
2
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
1
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
1
0
0
0
1
1
0
2
0
0
1
0
1
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
1
3
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
1
2
0
2
0
0
0
2
0
2
0
0
2
0
2
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
1
0
2
0
1
0
0
0
0
0
0
0
0
1
0
2
0
2
2
1
2
0
0
0
0
0
0
0
0
3
0
0
0
2
2
0
0
0
0
2
0
0
0
0
2
0
0
1
1
0
0
0
2
2
2
0
0
1
2
0
0
0
0
0
3
0
0
2
1
1
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
2
0
2
0
1
2
0
0
1
0
0
0
0
0
3
1
0
0
2
0
2
0
3
2
0
0
0
0
0
0
0
2
0
0
1
1
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
1
2
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
2
1
0
1
2
1
0
0
0
0
2
0
0
1
0
0
0
1
2
0
1
0
0
2
0
0
0
0
2
0
0
1
2
2
1
2
1
1
0
2
0
0
0
2
2
1
0
0
0
0
2
0
0
0
2
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
1
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
2
2
0
0
2
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
2
0
0
0
0
1
0
0
2
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
2
1
0
0
2
0
2
1
0
0
0
1
0
2
0
0
2
0
0
0
0
0
1
2
2
0
0
0
0
0
1
2
0
2
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
2
2
0
1
2
0
0
0
0
0
2
0
0
2
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
2
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
2
2
1
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
1
1
2
0
0
0
0
0
0
1
0
0
1
0
0
2
3
0
3
0
0
0
0
7
0
0
0
0
0
1
0
0
0
4
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
6
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
3
2
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
1
1
2
0
0
1
2
1
0
0
0
2
0
1
0
2
4
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
2
0
0
1
4
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
1
3
1
0
0
0
0
0
0
0
2
0
0
3
0
2
0
2
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
1
1
1
0
2
0
1
0
0
0
1
0
0
2
0
2
0
2
0
1
0
3
0
0
0
0
0
1
0
2
2
0
0
0
0
2
0
0
0
0
0
1
0
2
1
0
0
0
0
3
0
1
2
0
1
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
2
0
1
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
2
0
0
1
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
1
0
1
1
0
0
0
0
0
4
2
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
1
2
1
0
0
0
0
0
0
0
1
1
0
1
0
1
1
0
1
0
0
0
0
0
1
2
0
0
2
0
0
1
0
0
0
2
0
0
0
0
1
0
1
1
0
0
2
0
0
2
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
2
0
0
3
1
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
3
2
0
2
1
0
1
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
5
0
0
0
0
1
0
0
1
0
2
0
0
1
0
1
2
0
1
0
0
0
0
2
0
0
0
0
0
2
1
2
0
0
1
1
1
0
3
3
0
2
0
0
0
0
0
0
0
3
2
2
0
0
0
2
0
2
0
0
0
0
3
0
0
0
0
2
0
1
2
2
0
0
0
2
1
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
1
0
0
1
0
0
0
3
2
0
0
2
0
2
0
0
0
0
0
2
1
0
1
0
0
0
6
3
0
0
0
0
0
0
1
0
1
0
0
3
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
1
0
1
0
2
0
2
2
0
0
2
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
2
2
0
3
0
0
0
0
1
0
0
1
1
0
2
0
0
0
2
1
1
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
4
0
0
2
0
1
0
0
1
0
0
0
1
1
0
0
2
0
1
4
0
0
1
2
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
2
2
0
0
0
0
0
0
3
0
0
0
0
0
0
2
1
0
0
0
0
2
0
2
0
1
0
0
0
0
1
0
0
2
1
1
0
2
1
0
0
0
2
1
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
2
0
1
0
0
2
1
0
0
3
3
1
0
0
0
0
1
1
2
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
3
1
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
1
0
2
2
2
2
1
0
0
1
0
1
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
1
0
0
2
0
1
1
0
2
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
1
1
1
2
0
1
0
0
1
1
0
2
0
0
1
0
0
0
1
2
0
2
1
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
2
0
1
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
3
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
2
2
0
1
0
0
1
0
0
0
2
1
0
0
0
0
0
3
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
2
0
1
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
2
1
1
1
0
1
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
2
0
4
3
0
1
0
2
0
0
0
1
2
0
2
0
0
0
0
3
0
3
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
1
0
3
0
1
1
0
2
2
1
0
0
0
0
0
0
0
0
2
1
0
0
0
2
2
0
0
2
0
1
0
6
0
1
2
1
0
0
0
0
0
0
0
0
2
0
1
1
0
0
2
0
2
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
1
0
0
0
3
1
0
0
1
2
0
1
0
0
0
0
0
2
1
1
0
0
0
2
0
0
0
1
0
0
1
0
2
0
0
0
0
1
0
0
0
0
1
2
0
0
2
0
0
0
7
2
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
2
2
0
2
0
0
1
1
1
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
6
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
2
0
0
1
2
1
4
1
1
0
2
0
0
0
2
0
0
0
1
0
2
0
1
0
0
1
0
1
0
0
1
0
2
1
0
2
0
0
2
1
2
0
2
1
0
1
0
0
0
0
2
0
0
0
1
0
1
1
1
1
2
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
2
2
2
0
0
1
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
1
3
1
2
0
0
0
0
2
0
0
1
0
0
0
1
0
0
2
0
0
1
0
2
0
1
3
2
0
1
0
0
0
2
0
0
0
3
1
0
0
0
0
2
0
0
2
1
0
1
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
2
0
0
0
0
2
0
2
0
0
1
1
0
7
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
3
2
0
3
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
5
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
1
0
3
0
2
1
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
3
1
1
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
2
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
5
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
1
2
0
0
0
0
0
3
0
2
0
0
1
4
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
1
1
2
2
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
3
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
3
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
2
1
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
2
2
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
3
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
1
1
2
0
0
0
1
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
3
2
0
4
0
1
0
0
0
0
0
0
0
0
0
6
0
0
1
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
5
2
0
2
1
0
0
0
0
2
1
0
0
0
2
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
2
0
1
1
0
1
0
0
1
0
1
0
0
0
2
0
0
0
0
2
0
3
1
0
3
2
2
0
2
2
3
2
2
0
0
1
0
3
0
1
0
2
1
0
2
0
1
2
0
0
0
0
0
0
1
0
1
2
0
0
0
1
0
1
0
0
1
0
0
2
0
0
1
2
1
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
4
2
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
3
0
1
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
6
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
4
1
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
2
2
0
0
0
0
1
0
0
1
0
0
2
0
0
2
1
0
1
2
0
0
0
2
2
1
0
0
0
0
0
2
6
0
0
0
2
0
5
0
1
0
0
0
1
0
0
1
0
0
2
0
0
0
1
0
0
2
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
2
0
2
0
0
1
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
1
0
2
0
0
2
2
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
2
1
0
1
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
1
1
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
3
0
2
0
1
0
0
0
1
0
0
1
1
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
1
0
0
1
0
0
2
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
2
6
1
1
2
1
0
1
2
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
3
0
2
0
1
0
1
0
0
0
2
0
0
0
2
0
0
1
0
1
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
2
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
3
2
0
0
0
1
7
0
0
1
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
2
0
1
1
0
0
0
2
1
1
0
0
0
0
0
0
1
0
4
2
2
0
0
0
2
2
0
0
1
2
0
0
0
0
0
0
0
0
2
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
3
0
2
1
1
2
1
0
0
0
1
1
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
2
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
6
0
0
2
2
0
2
0
0
1
1
0
0
1
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
2
1
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
2
1
0
0
0
0
0
2
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
7
0
1
0
0
1
1
0
0
2
0
0
2
1
1
0
1
0
2
0
1
2
0
3
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
2
0
1
3
0
0
0
0
0
0
1
0
1
2
2
0
0
0
0
0
2
2
0
0
1
0
2
1
0
2
0
0
0
1
3
0
2
1
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
1
0
2
0
2
2
2
0
2
0
2
1
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
1
0
1
0
0
1
0
0
0
0
1
0
1
0
1
2
0
1
0
3
2
1
0
0
0
0
1
2
2
0
2
4
0
1
1
0
2
0
2
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
2
0
0
0
1
0
0
0
1
1
0
1
1
0
0
0
0
1
0
0
0
1
0
2
1
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
2
0
2
0
0
1
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
2
0
0
1
1
0
0
0
0
3
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
1
2
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
1
1
2
1
0
0
0
0
0
1
0
3
0
0
2
0
0
0
3
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
2
2
0
1
0
1
0
0
1
0
4
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
2
2
0
0
0
0
0
1
2
2
2
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
2
0
0
2
2
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
4
0
7
0
0
2
0
3
1
2
3
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
1
2
0
1
0
2
2
2
0
0
0
2
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
3
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
1
0
0
0
0
0
0
0
3
2
1
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
3
0
0
2
0
3
0
0
1
0
1
1
0
1
5
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
1
0
0
2
2
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
1
2
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
1
0
2
2
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
3
0
0
0
0
0
0
2
0
4
0
1
0
2
2
1
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
3
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
1
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
2
0
1
2
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
2
1
0
1
0
1
0
0
0
0
1
0
3
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
1
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
5
0
0
0
0
0
2
3
1
0
1
0
0
1
0
1
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
1
0
0
0
2
2
2
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
3
2
0
4
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
3
2
2
0
0
0
0
0
3
1
3
0
3
1
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
5
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
1
0
0
2
4
0
1
0
0
0
0
0
0
1
2
0
0
1
0
0
0
2
0
0
2
0
0
0
2
0
1
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
2
0
1
2
0
0
0
1
1
0
0
1
1
0
2
1
2
2
0
0
0
0
1
0
2
0
2
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
2
2
3
7
0
1
0
0
0
0
0
0
0
0
2
3
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
3
1
0
2
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
3
2
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
7
0
2
0
0
1
3
0
0
0
0
2
0
0
1
1
1
0
2
2
0
0
0
0
2
0
0
2
0
0
0
1
1
0
1
1
0
0
0
0
3
0
0
1
0
2
0
4
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
1
1
1
0
2
0
1
2
0
3
0
0
1
0
1
0
0
0
1
0
0
2
3
0
4
0
1
0
1
0
2
0
0
0
1
2
0
0
2
0
5
0
0
0
1
0
0
0
1
0
3
0
2
1
0
0
0
2
2
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
2
1
0
1
0
0
0
0
1
5
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
1
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
3
0
1
0
0
0
1
1
0
0
0
7
0
0
1
0
0
0
2
0
0
1
0
2
0
2
0
2
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
1
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
2
1
0
0
1
0
0
0
2
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
1
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
2
0
0
0
2
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
3
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
1
0
1
0
0
1
4
2
0
0
0
0
2
0
0
2
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
1
0
0
1
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
2
0
0
2
1
0
0
0
0
3
0
0
0
0
1
1
3
0
0
0
1
0
0
1
0
0
2
0
0
2
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
1
1
0
0
0
2
0
0
1
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
1
0
0
0
2
4
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
1
2
0
1
0
0
0
1
1
1
0
0
2
2
0
0
0
0
0
2
0
0
0
1
1
0
0
0
1
1
0
0
0
1
1
0
0
0
2
1
0
0
1
0
0
0
0
2
1
0
0
0
0
0
2
0
2
2
0
0
0
1
0
0
0
0
2
0
0
2
0
0
2
1
0
0
1
0
1
0
2
2
0
0
0
0
1
2
0
2
0
0
0
1
1
0
3
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
1
1
2
1
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
3
1
1
2
0
2
0
0
0
0
0
0
0
0
0
0
3
1
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
2
0
0
4
1
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
2
2
1
2
1
1
0
1
0
0
0
0
0
0
2
2
0
0
2
2
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
4
1
3
0
2
2
0
0
0
2
0
0
0
0
2
0
0
0
1
0
2
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
4
0
1
0
1
0
1
0
0
2
1
0
0
2
0
0
0
0
1
2
0
4
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
2
0
0
1
0
0
2
2
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
2
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
2
2
0
0
0
3
0
2
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
2
1
0
0
0
0
0
0
1
0
1
0
0
1
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
2
1
2
0
2
3
0
0
1
1
0
0
1
1
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
3
1
0
0
0
4
1
1
0
0
0
1
2
0
1
0
0
0
0
1
1
0
1
0
1
1
0
0
0
0
2
2
0
0
0
0
4
0
0
2
2
2
0
2
0
0
0
2
1
0
2
1
1
0
3
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
3
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
1
2
0
0
0
1
1
1
2
0
0
1
1
1
1
1
0
0
0
0
0
2
0
1
0
0
0
1
2
0
2
0
0
0
0
0
0
2
0
0
1
3
0
2
0
1
0
2
0
0
0
1
0
0
2
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
2
0
0
2
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
6
0
0
1
0
1
0
1
1
2
0
2
0
0
0
0
0
2
0
0
2
0
0
0
1
3
0
1
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
1
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
2
0
0
0
0
0
2
0
1
1
0
1
0
0
2
0
3
2
0
0
0
0
0
0
2
0
3
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
2
0
2
2
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
1
2
0
0
1
0
3
2
1
0
0
0
1
0
2
0
1
0
0
0
0
0
0
2
1
1
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
1
0
0
0
1
1
0
2
0
0
1
0
5
1
3
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
3
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
2
0
0
0
1
0
0
2
0
0
1
0
0
0
0
1
1
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
8
0
0
1
0
0
2
1
1
0
2
0
0
3
1
0
0
0
1
0
0
2
0
0
2
2
0
0
0
0
2
0
0
0
2
2
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
2
2
0
2
1
0
0
0
1
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
4
0
1
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
2
0
3
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
1
1
0
2
0
0
0
2
2
0
0
1
2
2
2
0
2
0
2
0
0
0
0
0
0
1
3
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
2
0
0
0
0
1
0
0
0
0
2
0
0
2
1
0
0
1
2
1
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
1
1
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
2
2
0
0
0
1
2
0
0
0
0
1
0
2
0
1
1
0
0
0
2
0
2
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
2
4
0
0
2
0
0
0
1
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
2
0
0
1
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
2
3
1
0
0
0
1
0
2
0
0
2
0
2
0
0
0
0
0
2
2
0
1
1
1
2
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
2
0
2
0
1
2
0
4
1
0
0
0
0
2
2
0
3
0
0
0
1
2
2
2
1
0
0
0
0
2
0
3
0
2
0
0
1
0
0
1
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
1
0
2
0
1
2
0
0
0
2
2
1
2
0
3
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
4
0
1
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
1
0
2
0
1
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
2
2
2
2
0
0
0
1
2
0
0
0
0
0
0
1
0
1
0
0
0
0
2
1
0
0
1
0
0
2
2
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
1
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
1
0
0
0
0
2
0
0
2
1
0
1
2
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
2
0
0
1
0
0
3
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
2
0
0
2
0
2
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
1
0
1
0
2
0
2
0
0
0
2
0
0
0
2
0
2
3
2
0
1
0
0
0
0
1
1
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
1
2
1
2
1
0
2
0
3
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
2
1
0
1
1
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
8
1
0
0
5
0
0
0
1
0
1
0
1
0
0
0
2
0
0
1
1
0
2
0
0
0
2
0
0
0
0
2
1
2
2
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
3
2
0
4
0
0
2
1
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
1
1
0
0
0
0
0
1
0
0
1
2
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
3
1
0
0
2
0
2
2
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
2
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
1
0
1
0
0
1
0
2
0
0
1
0
2
0
1
1
0
2
0
2
2
1
1
2
1
0
0
1
0
1
0
0
0
0
1
0
0
2
0
2
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
2
0
2
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
2
0
0
0
0
1
3
0
0
0
2
0
2
0
0
0
1
0
2
0
0
0
0
0
1
1
0
1
0
4
0
0
0
0
0
0
0
0
1
0
1
1
2
0
0
4
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
2
0
0
1
0
0
0
2
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
1
2
1
0
1
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
2
1
0
2
0
1
0
0
0
0
0
2
0
0
2
2
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
1
0
0
4
0
1
0
2
0
1
1
2
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
2
0
0
0
1
2
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
2
2
0
0
0
1
1
0
0
3
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
4
0
0
0
0
0
1
0
0
2
0
0
2
1
0
0
1
0
0
1
0
0
0
4
0
0
0
1
0
0
0
0
1
0
0
0
2
1
1
0
1
0
0
0
0
2
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
5
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
1
0
0
1
1
0
0
0
1
1
0
0
0
1
2
0
0
1
1
0
0
1
2
2
0
2
0
3
1
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
1
0
1
0
1
1
0
0
1
2
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
1
1
0
0
2
0
1
1
1
0
0
1
0
0
0
0
0
2
0
1
0
0
0
1
2
0
0
0
0
1
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
2
0
0
2
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
2
3
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
1
0
0
0
2
0
2
2
0
1
1
1
1
3
2
0
1
0
1
2
1
2
1
0
0
2
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
2
0
0
2
0
0
1
0
0
1
0
0
0
2
0
0
0
0
1
1
0
0
0
0
4
0
1
0
2
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
2
0
1
0
0
6
0
0
1
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
3
4
0
0
0
0
1
0
0
1
0
1
1
0
1
0
0
1
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
6
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
1
4
1
2
0
0
0
3
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
1
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
3
0
0
0
1
0
0
1
0
0
1
0
1
0
0
3
1
0
0
1
0
0
1
2
0
0
0
0
0
1
1
3
0
0
1
0
1
0
0
0
2
1
0
0
0
0
1
2
1
0
0
1
0
0
0
0
0
0
2
4
0
0
0
0
0
2
1
1
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
2
2
0
0
0
0
0
0
0
0
1
4
0
2
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
2
2
0
0
0
3
2
0
0
2
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
1
0
3
0
0
3
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
3
0
0
0
1
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
2
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
1
0
0
0
0
1
3
0
2
2
2
2
0
1
0
0
0
0
0
2
0
1
3
1
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
1
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
2
0
1
0
0
0
0
2
1
0
2
0
0
2
0
0
0
0
0
2
0
4
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
3
0
0
1
2
2
0
1
0
0
1
0
2
0
0
1
0
0
0
2
2
0
1
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
2
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
1
2
0
1
2
0
0
6
0
0
0
1
0
0
0
0
0
2
0
3
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
1
0
0
2
0
1
0
0
0
3
0
0
0
0
0
0
0
2
0
0
3
0
0
2
0
0
0
2
0
0
0
2
1
0
0
1
0
0
0
0
0
1
0
2
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
1
2
0
0
0
0
0
1
0
0
1
0
2
2
1
0
0
0
3
0
0
0
0
0
0
0
1
0
2
1
0
0
1
1
0
0
1
2
0
0
0
2
0
0
3
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
3
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
1
2
0
0
1
1
0
0
1
2
0
0
0
2
0
0
2
0
0
1
0
0
0
0
1
1
0
3
2
0
0
0
0
2
0
0
1
0
0
2
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
3
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
2
0
1
0
0
2
0
0
0
0
0
1
0
0
2
1
0
0
4
0
0
0
1
0
2
1
3
2
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
1
0
2
1
0
1
0
2
0
0
1
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
2
0
0
1
1
0
0
0
2
0
0
0
1
0
0
0
2
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
4
0
0
1
1
0
2
0
0
0
0
0
4
0
2
0
1
1
0
0
1
0
2
0
0
0
0
0
0
0
0
2
2
2
0
1
0
0
2
0
1
0
1
0
1
1
1
2
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
2
1
0
0
2
0
0
3
0
0
0
3
0
0
2
2
1
0
2
2
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
1
0
0
1
2
0
0
2
0
0
1
3
3
0
0
0
0
1
2
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
2
2
1
3
1
0
0
0
1
1
0
0
0
3
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
2
0
0
0
0
2
2
1
0
0
0
0
0
2
0
2
0
0
0
0
0
2
2
0
1
0
0
3
1
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
11
3
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
2
2
0
2
0
1
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
1
1
0
0
2
0
0
2
0
0
1
3
2
0
0
0
1
0
0
0
0
1
3
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
1
0
0
0
0
3
2
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
1
0
1
0
0
0
2
0
0
0
0
0
1
0
0
1
2
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
2
0
0
0
0
0
2
0
0
0
3
0
2
0
2
0
2
0
0
0
0
0
2
0
0
0
0
1
2
0
2
0
2
2
0
0
0
1
1
4
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
3
0
0
0
3
0
1
0
0
0
0
1
3
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
2
0
1
0
0
0
1
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
2
4
0
1
0
0
2
2
2
0
0
0
0
2
2
1
0
0
1
0
1
0
1
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
4
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
2
2
0
1
0
2
0
0
0
1
4
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
1
1
1
0
0
2
0
1
0
0
0
2
0
1
2
0
2
2
2
2
0
2
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
2
0
2
1
0
2
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
2
1
0
0
0
1
2
0
2
0
0
2
1
2
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
1
2
0
1
2
0
0
0
0
0
2
4
1
0
1
2
1
0
0
0
1
0
0
0
0
0
0
3
0
0
0
1
0
1
0
0
0
0
0
2
1
0
2
1
0
0
2
0
0
1
0
2
3
0
0
0
1
0
2
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
2
0
2
0
0
0
0
1
0
0
2
2
1
1
2
1
2
0
0
0
1
1
0
0
2
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
2
1
0
4
0
0
1
0
0
0
1
0
0
1
0
1
0
2
0
0
0
0
0
2
0
1
0
0
0
0
2
0
1
1
0
0
0
0
3
1
2
2
0
0
0
0
0
0
8
2
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
3
1
0
1
1
1
0
1
0
2
2
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
2
2
13
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
1
1
0
1
2
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
4
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
2
1
2
0
0
1
2
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
1
1
0
3
0
0
0
2
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
1
0
0
1
0
2
2
2
1
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
2
0
0
1
1
0
0
0
3
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
1
0
0
0
0
0
0
2
0
1
1
4
1
0
0
1
1
0
0
0
0
2
0
3
0
0
0
1
1
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
2
2
0
2
2
0
0
0
0
2
0
0
0
1
0
0
2
2
0
2
2
1
0
2
0
2
1
0
0
0
0
0
0
0
2
0
2
0
0
0
3
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
2
1
0
0
0
2
2
0
0
0
0
2
2
2
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
2
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
2
0
1
0
0
1
0
0
0
0
1
0
1
1
1
0
0
0
1
0
1
1
0
0
0
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
1
2
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
17
2
0
0
1
0
0
0
0
2
2
0
0
0
1
0
2
1
0
0
0
0
2
0
0
2
3
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
4
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
2
0
2
0
1
0
0
0
2
1
0
0
1
0
0
0
0
2
0
1
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
1
0
0
2
0
0
1
1
0
0
0
4
0
0
0
0
0
0
0
4
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
4
0
2
0
0
2
0
1
0
0
1
0
0
3
0
2
0
0
1
0
0
1
0
0
0
1
0
2
0
0
1
3
0
0
2
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
1
0
0
1
2
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
1
0
1
3
0
1
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
1
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
1
1
1
0
0
2
0
0
0
2
2
2
0
3
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
1
2
0
2
0
0
2
0
0
0
0
1
0
1
0
3
0
0
0
0
0
0
1
0
1
0
1
0
2
0
2
4
0
2
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
2
0
2
0
0
0
2
0
1
1
0
0
0
0
1
1
0
0
2
0
2
0
0
0
0
0
2
1
0
0
0
0
4
0
2
0
2
1
0
0
0
0
3
0
0
2
0
0
4
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
3
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
3
1
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
5
1
0
0
1
0
1
2
0
2
0
0
1
0
0
2
2
0
2
0
0
0
0
2
0
0
0
6
0
0
2
0
2
1
2
0
0
0
1
0
2
0
2
2
0
0
0
0
1
2
1
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
1
3
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
1
2
0
1
3
0
0
0
0
0
2
2
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
3
2
0
2
0
2
5
0
1
0
2
0
1
1
0
2
0
0
2
0
1
0
0
0
2
1
0
1
0
0
0
0
1
0
0
0
1
0
1
1
0
1
2
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
3
0
0
0
0
2
1
0
2
0
0
0
0
2
0
0
0
2
2
0
0
3
0
1
0
0
0
1
0
0
0
2
0
0
2
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
1
1
1
0
0
0
2
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
1
1
0
0
1
2
0
0
5
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
7
0
0
0
1
0
0
3
0
0
2
0
2
2
0
0
0
4
0
2
1
0
0
0
1
2
0
0
0
1
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
1
0
1
0
0
1
0
0
4
0
0
0
0
0
0
1
0
0
2
1
0
1
1
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
1
1
2
2
0
0
2
0
0
1
0
1
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
1
2
0
2
0
0
0
0
2
0
0
1
1
0
2
0
2
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
2
0
2
2
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
2
0
1
0
2
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
1
0
0
0
6
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
1
4
2
0
0
2
3
0
0
0
1
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
3
2
1
0
1
2
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
1
1
0
2
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
1
0
0
2
1
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
3
2
0
0
1
0
0
2
2
0
0
0
0
2
1
0
1
3
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
1
0
2
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
2
1
0
0
2
2
0
0
1
0
0
0
0
2
1
0
0
0
1
0
0
0
1
0
1
2
2
0
0
2
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
2
0
1
2
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
3
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
3
0
0
0
0
2
0
0
2
1
0
0
2
0
0
0
1
0
1
1
0
1
0
0
0
2
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
2
2
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
1
2
0
1
0
1
0
0
2
1
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
1
0
1
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
1
1
0
0
0
2
0
0
1
0
0
0
2
2
2
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
3
0
0
0
1
2
0
0
1
0
0
0
2
0
0
0
0
2
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
3
3
0
0
0
2
0
0
2
0
0
1
0
0
0
0
1
2
0
0
2
0
2
0
0
0
0
2
0
2
1
0
2
0
0
0
0
0
3
0
1
0
2
0
0
0
1
0
0
2
0
0
0
2
5
2
2
0
0
1
2
0
0
0
0
0
2
2
0
0
0
1
2
1
2
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
1
1
1
0
0
1
0
1
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
3
1
0
0
1
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
2
1
0
2
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
2
1
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
8
0
0
0
2
0
0
0
0
2
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
2
0
0
1
0
0
1
1
0
0
2
2
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
1
0
2
0
1
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
1
2
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
1
2
4
2
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
5
0
2
2
0
1
0
2
0
0
0
2
0
2
0
1
0
0
1
0
0
0
1
0
0
0
2
1
0
5
1
0
0
0
0
1
0
0
2
2
0
4
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
3
0
0
3
2
0
0
0
2
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
1
0
0
0
0
1
0
3
2
0
0
0
1
0
0
0
0
0
2
0
0
2
2
0
1
0
0
0
0
2
0
0
2
1
0
1
0
0
0
0
0
3
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
2
0
1
1
1
0
0
1
0
0
3
0
0
0
2
0
2
0
0
1
0
0
0
2
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
3
0
1
0
0
0
0
0
0
1
1
0
0
2
1
1
0
0
0
0
0
0
1
3
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
1
1
0
0
1
0
0
1
0
2
1
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
2
0
0
0
1
1
1
0
0
0
1
0
1
0
2
0
1
0
0
0
2
0
1
2
0
0
0
0
0
1
2
2
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
2
1
0
2
0
2
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
2
2
2
0
0
2
1
0
0
2
0
1
0
0
0
1
2
2
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
18
0
0
2
0
0
0
2
0
0
0
0
0
0
1
1
1
1
0
2
0
0
0
1
0
0
1
0
1
2
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
2
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
2
2
0
0
0
2
0
2
0
0
0
0
0
2
4
0
0
0
0
5
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
2
1
2
0
0
0
2
0
0
0
2
0
2
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
1
0
1
0
1
0
1
0
1
0
0
0
0
0
1
0
2
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
1
0
2
2
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
4
0
0
1
0
0
2
0
2
4
1
1
3
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
1
1
0
0
1
0
0
0
2
0
0
0
2
2
0
1
0
0
0
0
2
2
0
0
2
0
0
0
0
1
0
3
0
0
0
1
1
0
0
1
2
1
0
0
1
0
0
0
1
2
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
3
0
0
2
0
0
0
2
0
1
1
1
0
0
1
2
0
0
0
0
2
0
2
2
0
2
2
1
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
2
1
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
1
0
1
0
2
1
0
2
2
0
0
2
0
0
0
0
0
0
0
2
2
1
1
2
0
0
0
1
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
2
0
2
0
0
0
2
1
0
0
3
0
0
2
1
0
0
0
0
0
0
1
0
1
1
1
1
1
2
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
1
1
0
2
0
1
0
2
0
0
1
0
0
1
0
0
2
0
1
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
4
0
2
0
0
1
1
0
2
1
0
0
3
0
0
0
0
1
0
0
0
0
0
1
1
2
0
0
0
1
1
2
2
0
0
1
0
0
0
0
0
1
0
0
1
1
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
2
0
2
0
0
2
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
3
0
0
0
0
0
1
1
1
0
2
0
0
0
1
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
1
2
0
0
3
2
0
1
0
0
4
0
0
0
0
0
0
1
0
0
1
0
1
1
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
1
0
0
2
2
6
2
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
6
0
0
2
1
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
3
2
3
0
0
0
0
0
0
0
0
1
2
0
0
1
0
1
0
1
0
0
1
0
0
1
0
0
1
0
0
0
1
0
1
0
2
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
1
1
0
5
1
0
2
0
0
2
0
0
0
0
2
4
2
0
0
2
0
0
0
0
0
0
1
0
0
0
2
1
1
0
0
2
0
0
2
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
2
3
2
2
1
0
3
0
0
1
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
4
2
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
1
0
2
0
1
5
0
0
0
1
0
4
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
1
0
0
1
2
1
2
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
2
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
2
0
3
0
0
0
4
1
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
3
0
0
1
0
1
0
0
0
0
0
0
0
0
1
3
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
2
0
0
0
1
1
0
0
0
1
0
0
2
0
0
1
0
1
0
0
0
1
5
0
1
2
0
1
1
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
3
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
2
2
0
3
0
0
0
0
0
0
0
2
2
1
0
1
0
0
2
0
2
1
0
0
2
0
2
0
0
2
0
0
0
0
0
0
2
1
1
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
2
0
3
0
0
0
0
2
0
1
0
0
0
1
0
0
1
0
0
2
1
2
1
1
1
0
1
1
0
0
0
0
1
1
1
5
3
1
0
0
0
0
2
0
2
0
1
0
0
0
0
1
0
2
0
0
2
0
0
0
1
2
0
2
2
0
1
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
2
0
2
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
2
1
0
0
0
1
0
1
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
2
0
1
0
1
0
2
0
0
0
0
0
0
1
3
0
0
4
2
0
0
0
1
1
1
0
0
0
2
0
0
1
0
0
0
0
4
2
3
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
4
0
0
0
0
2
0
0
2
2
0
2
1
1
0
0
0
0
0
1
0
1
0
0
1
0
2
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
5
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
1
3
0
0
0
0
1
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
1
2
2
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
1
1
2
0
0
0
6
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
4
1
0
0
0
2
1
0
0
0
0
1
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
2
0
0
2
0
0
0
1
0
0
2
1
2
1
0
2
0
0
0
0
0
0
0
0
0
0
2
1
2
0
2
0
0
2
0
0
0
1
1
0
0
0
0
2
1
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
2
0
1
0
0
0
2
0
0
0
4
0
1
2
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
2
2
3
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
2
2
1
0
0
0
2
0
0
0
3
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
2
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
2
0
0
0
0
0
1
2
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
3
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
3
0
1
0
0
1
0
1
0
0
0
0
0
2
0
1
0
8
0
0
0
0
0
2
0
0
1
0
0
2
0
0
2
0
2
0
1
0
0
2
0
2
0
0
0
0
0
2
0
5
0
2
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
2
2
0
0
0
1
1
0
0
0
0
0
0
0
4
1
1
0
0
0
0
0
1
0
2
0
0
1
1
1
0
1
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
1
0
1
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
2
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
1
0
1
0
0
0
2
0
2
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
1
0
1
0
2
0
0
1
2
2
0
0
0
1
0
0
0
0
1
1
0
0
0
2
2
2
1
1
0
5
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
2
0
0
0
0
1
0
2
2
7
0
0
0
2
2
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
2
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
2
1
1
2
0
0
1
0
0
2
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
3
2
0
0
0
3
0
2
3
2
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
2
2
0
2
0
1
0
0
0
1
0
0
2
0
0
2
1
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
1
0
0
0
0
0
1
0
2
0
0
2
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
2
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
1
1
0
0
0
0
0
2
0
1
1
1
0
0
0
1
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
3
0
0
0
1
0
0
2
1
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
2
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
3
1
0
2
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
3
0
0
0
0
1
3
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
1
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
1
0
2
0
0
0
1
2
1
0
2
0
0
0
2
2
0
0
0
1
0
0
0
0
2
1
0
0
0
0
1
0
0
1
0
0
0
0
0
4
0
0
0
2
2
1
2
0
0
0
0
0
1
2
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
1
2
0
4
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
1
3
0
0
0
0
3
0
0
0
2
0
1
1
0
0
0
0
0
1
0
2
3
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
2
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
2
1
0
1
2
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
2
2
0
1
0
0
0
1
0
0
3
0
1
0
0
0
0
0
0
0
2
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
2
1
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
1
8
0
0
0
2
0
0
0
0
2
0
0
0
0
1
1
0
0
0
1
6
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
1
2
2
0
2
2
2
1
1
0
0
0
0
0
1
0
7
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
1
1
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
1
1
2
0
0
0
0
1
2
0
2
0
1
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
5
1
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
2
0
0
0
0
0
1
0
0
0
0
4
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
3
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
3
1
0
2
1
0
2
0
5
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
3
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
2
0
0
0
2
0
0
1
0
0
2
2
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
5
0
0
2
0
0
2
0
0
3
0
0
0
2
2
2
0
2
0
0
0
0
1
2
2
0
0
2
0
0
0
2
0
2
1
0
0
1
0
1
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
1
0
0
0
0
1
3
0
0
0
0
1
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
1
1
0
2
0
2
0
0
0
0
2
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
2
1
0
0
0
2
0
1
2
0
0
0
0
0
2
0
0
0
5
1
0
0
2
0
0
0
9
0
1
1
4
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
3
0
1
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
3
0
1
1
0
1
0
0
1
0
0
0
1
0
0
0
2
0
0
0
1
0
2
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
2
2
9
0
1
0
3
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
2
0
0
1
0
3
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
2
1
0
2
4
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
1
2
0
0
0
1
0
2
0
0
2
0
1
0
0
0
2
0
2
0
0
0
2
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
1
2
0
2
0
0
0
2
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
3
2
0
0
0
0
3
1
2
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
1
0
1
2
0
1
0
0
2
0
0
2
2
0
0
1
0
2
0
1
0
0
2
2
0
0
0
2
4
2
0
0
0
0
0
0
3
0
0
0
1
0
1
0
0
1
2
0
2
0
1
0
3
1
1
0
1
0
0
2
0
0
0
1
0
0
2
0
1
0
0
3
2
0
0
0
1
2
0
2
1
2
0
0
1
0
2
0
0
0
0
2
0
0
0
0
1
0
1
1
0
0
0
1
3
0
0
0
1
2
0
0
1
1
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
2
0
1
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
7
0
2
0
1
0
0
2
0
1
0
0
0
0
0
0
0
2
0
2
1
2
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
4
0
0
3
0
2
0
0
0
0
0
0
0
2
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
2
2
1
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
2
0
0
2
0
0
0
0
2
2
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
1
1
2
0
0
1
2
0
2
0
0
1
1
0
0
0
2
2
0
3
0
0
1
0
0
0
1
1
2
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
1
2
0
0
0
2
1
1
0
0
1
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
3
1
1
0
0
1
2
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
1
0
0
0
1
1
0
0
0
0
2
1
3
0
1
1
0
0
0
1
0
0
2
0
2
1
0
2
0
1
2
0
0
0
0
0
0
2
1
0
0
0
0
2
1
0
1
1
2
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
2
0
1
0
0
0
0
0
0
0
6
0
0
0
0
0
0
2
0
2
0
0
0
2
0
1
0
0
1
1
0
2
0
1
0
0
0
2
0
0
1
2
0
0
0
2
0
0
0
1
1
0
1
0
0
0
0
1
2
0
0
1
1
3
0
0
2
3
0
0
0
0
4
0
0
2
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
13
0
2
0
0
1
0
2
0
0
1
0
1
0
1
1
2
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
1
0
0
1
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
2
2
2
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
1
2
0
2
1
0
0
0
0
0
0
0
1
1
1
4
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
1
1
0
2
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
1
2
0
0
0
1
0
2
2
1
1
0
0
0
2
2
0
0
0
0
2
1
0
0
0
2
0
0
0
1
0
0
0
2
1
0
1
4
2
2
3
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
1
2
0
0
2
0
1
0
0
1
0
0
0
2
0
0
0
2
0
0
0
2
1
0
0
0
0
0
1
1
2
2
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
1
0
0
2
0
0
0
0
1
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
2
0
2
1
1
2
0
0
0
0
0
0
0
0
0
1
2
2
2
0
1
0
0
0
1
0
2
3
0
0
0
3
0
1
0
0
2
2
0
0
0
0
1
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
2
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
2
0
0
1
1
1
0
0
1
0
0
2
0
0
0
0
2
1
0
1
0
1
0
0
0
2
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
2
0
0
2
0
1
0
1
0
2
2
0
0
0
0
0
1
0
0
4
0
0
2
1
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
4
0
2
0
2
0
0
0
0
0
2
2
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
3
2
0
0
0
1
1
0
2
1
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
2
1
2
0
0
1
1
2
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
1
0
2
0
1
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
1
0
0
1
0
2
0
0
2
2
1
1
0
0
0
0
0
0
1
0
2
2
0
0
1
0
3
0
2
0
0
2
0
1
0
0
0
0
0
1
2
2
0
0
2
0
0
0
2
3
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
1
2
0
0
0
1
2
0
0
0
2
0
3
1
2
0
1
2
2
1
0
1
0
0
2
0
2
0
0
1
0
0
0
0
0
0
1
2
0
2
2
0
0
1
5
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
2
1
3
0
0
3
0
0
0
1
0
0
0
1
2
1
0
0
0
0
0
0
0
4
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
2
0
0
0
3
1
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
3
1
0
0
0
0
3
0
5
0
0
0
0
3
0
0
1
0
0
0
1
2
0
0
0
0
1
6
0
7
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
1
0
0
3
1
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
3
0
0
3
0
1
0
1
2
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
3
1
0
2
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
3
1
1
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
2
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
2
2
1
2
1
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
3
0
0
6
2
0
2
1
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
1
0
0
0
4
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
2
0
0
0
1
2
0
2
0
0
1
0
0
0
0
2
0
0
0
0
2
2
0
0
2
0
0
0
0
1
0
0
0
2
0
0
3
0
0
0
1
0
1
0
0
2
1
1
0
0
0
0
0
0
2
0
0
1
2
1
0
0
0
1
0
0
0
0
2
1
0
2
0
0
2
0
2
2
0
0
2
0
0
0
1
1
1
0
2
2
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
5
1
0
1
0
0
0
0
0
1
1
0
2
0
2
0
0
0
1
0
0
0
1
0
2
2
0
0
0
0
2
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
1
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
3
0
0
1
0
2
0
0
2
1
0
0
0
1
0
1
1
1
0
2
4
3
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
1
0
0
0
2
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
1
0
0
1
0
2
0
0
1
0
0
0
1
0
0
2
0
0
1
0
0
3
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
2
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
1
0
2
0
0
0
0
2
0
2
0
0
0
2
1
0
0
0
1
1
2
0
1
0
0
0
0
2
0
0
0
0
0
2
2
1
1
1
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
1
1
0
0
1
0
0
1
2
3
0
0
0
1
2
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
1
0
0
4
0
2
1
2
2
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
1
0
0
1
2
2
0
0
0
1
0
0
0
0
3
0
1
0
1
0
0
0
0
0
3
0
1
1
2
2
0
0
0
0
0
0
0
0
0
0
1
0
10
0
2
2
0
0
0
1
1
0
2
0
0
1
1
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
1
0
1
1
0
0
1
0
0
2
1
2
0
0
0
2
0
2
0
0
1
2
0
0
1
0
2
0
1
0
0
0
1
2
0
2
1
0
0
0
1
1
1
2
1
2
0
0
0
0
4
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
1
1
0
1
0
0
0
1
0
0
0
0
2
1
0
1
0
0
0
1
0
2
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
4
1
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
1
2
2
0
0
0
1
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
2
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
2
0
0
0
1
0
1
2
2
0
0
0
0
0
1
0
0
2
2
1
0
2
0
0
0
0
0
2
0
1
0
1
1
0
0
0
0
0
0
0
0
2
0
0
1
1
2
1
1
0
0
0
2
2
0
0
0
0
0
2
3
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
3
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
1
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
4
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
1
2
1
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
2
0
0
1
1
0
0
0
1
0
1
2
0
2
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
3
2
0
0
0
2
2
0
2
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
3
1
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
2
1
0
0
1
2
0
0
4
0
1
1
0
0
0
1
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
3
0
0
0
0
0
3
0
0
2
2
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
1
0
2
0
0
0
2
0
0
2
2
3
1
2
2
0
1
0
2
1
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
2
0
2
0
2
1
0
0
2
0
1
0
0
0
0
2
2
1
0
1
4
0
0
0
0
2
0
0
0
0
0
0
1
1
0
3
1
0
0
0
1
0
0
0
0
0
2
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
2
1
0
0
0
0
0
0
0
0
0
2
2
2
3
0
0
0
0
1
2
0
0
0
1
0
0
2
0
0
0
0
2
0
0
1
2
0
0
1
3
2
0
2
2
0
2
3
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
1
1
0
0
1
0
0
0
0
2
1
4
2
2
0
0
2
1
0
2
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
2
1
0
3
0
0
0
2
2
0
0
0
0
0
1
0
1
2
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
2
0
2
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
4
1
0
1
0
0
0
2
2
0
2
0
1
0
0
0
2
0
0
0
3
1
0
0
2
0
0
0
0
1
0
0
0
1
0
1
0
1
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
2
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
2
2
0
1
2
0
1
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
1
0
1
1
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
1
0
0
0
1
0
2
2
0
2
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
3
2
0
1
2
0
1
0
1
0
0
2
0
0
0
0
0
0
0
1
3
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
1
0
0
0
1
0
0
3
1
1
2
0
2
0
0
0
0
2
1
0
0
0
0
1
1
0
0
0
2
1
0
0
0
0
2
2
0
3
2
0
0
0
1
1
0
0
2
2
0
0
2
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
3
0
2
0
2
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
2
1
1
0
1
0
3
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
6
0
0
2
0
1
0
0
0
0
0
0
4
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
3
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
3
0
0
0
1
1
0
0
0
0
0
1
2
2
2
0
0
2
0
0
0
1
3
0
3
0
2
0
0
0
0
2
1
0
1
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
2
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
2
2
0
0
2
0
2
0
0
0
0
0
0
2
0
0
1
0
0
2
2
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
1
1
0
0
2
1
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
3
0
0
0
0
0
0
4
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
5
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
1
0
0
1
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
2
1
0
0
0
0
0
0
2
4
0
0
0
0
0
1
0
0
0
2
0
1
0
2
1
2
0
0
1
0
0
0
0
0
0
1
2
0
0
1
0
0
0
2
1
2
0
0
0
0
0
0
0
2
0
1
0
2
1
2
1
2
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
1
2
2
0
3
2
2
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
1
0
0
2
0
1
0
0
6
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
2
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
2
0
2
2
0
0
1
1
0
0
2
2
0
1
0
0
0
2
1
2
0
1
0
0
1
0
0
0
2
2
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
2
0
0
0
0
0
1
0
2
0
0
0
3
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
4
0
0
0
0
2
0
0
0
1
1
4
0
1
2
0
0
0
2
2
4
0
0
0
2
0
0
0
0
2
0
0
0
2
2
1
0
1
2
0
0
3
0
0
3
1
1
0
0
1
1
0
2
2
0
0
1
0
0
0
0
0
0
0
0
3
0
0
1
1
1
0
0
0
2
0
0
0
0
2
2
2
2
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
2
0
2
2
2
1
0
1
0
2
0
1
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
1
2
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
4
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
1
0
3
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
1
0
1
1
0
1
0
1
2
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
1
2
0
0
0
2
1
0
0
0
0
0
0
2
0
1
0
0
3
1
0
0
2
1
0
0
0
0
1
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
2
4
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
1
2
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
8
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
1
0
0
1
0
0
0
3
0
1
0
4
1
0
1
2
2
0
0
0
1
0
1
0
0
1
0
1
2
0
0
0
2
2
1
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
2
1
0
0
0
1
1
0
0
0
1
3
0
3
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
2
0
0
1
0
0
0
1
0
0
0
0
1
2
0
1
0
0
0
0
0
0
1
0
0
5
1
0
0
2
1
1
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
2
0
2
1
1
0
0
0
2
2
0
0
0
2
1
1
0
0
0
1
2
0
0
2
0
0
0
1
0
2
0
1
0
0
0
2
2
1
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
2
0
1
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
1
1
1
2
0
0
0
0
0
2
0
0
1
0
1
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
1
0
0
0
2
0
2
0
1
0
0
0
1
0
2
2
1
0
2
0
2
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
2
0
1
0
1
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
6
0
2
0
0
0
1
1
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
2
0
0
0
0
3
1
0
0
0
0
4
1
0
0
3
0
0
0
0
1
2
3
0
0
0
0
1
2
2
3
0
0
0
0
0
1
0
2
0
0
1
4
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
2
2
0
0
0
0
0
0
0
0
2
0
1
2
0
2
0
0
0
0
0
1
1
2
0
0
0
1
0
0
1
0
3
0
0
0
0
0
0
2
1
0
0
1
1
0
1
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
4
0
0
1
0
0
0
1
1
1
1
1
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
2
1
0
1
0
0
0
1
0
0
0
0
0
0
2
2
2
0
0
0
1
3
0
0
2
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
2
0
1
0
0
0
0
0
0
2
0
2
0
1
0
0
4
2
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
2
1
0
0
2
0
0
0
0
0
0
2
0
2
0
0
1
0
3
1
0
0
1
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
2
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
1
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
1
0
4
0
1
0
0
0
0
0
1
0
0
2
0
0
0
3
0
1
0
0
1
0
0
2
2
0
0
0
0
0
1
0
3
1
0
0
2
0
0
2
0
0
0
1
1
0
0
2
2
1
0
0
0
1
0
0
2
0
0
3
0
0
0
0
1
2
0
0
2
0
2
0
2
0
1
0
0
0
2
0
1
2
0
0
0
1
0
1
0
0
1
1
2
2
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
1
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
2
0
1
0
0
0
0
1
0
2
0
0
3
2
0
0
0
0
3
2
0
0
1
0
2
2
0
0
1
0
0
0
3
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
2
1
0
0
0
0
0
3
0
0
0
2
0
0
0
0
2
4
4
2
2
0
0
1
0
0
0
1
1
2
0
1
0
1
0
0
1
0
0
6
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
1
0
0
1
2
0
0
1
0
0
0
2
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
1
2
1
1
2
2
0
3
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
2
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
1
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
3
2
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
2
2
0
0
2
0
1
2
0
0
0
0
0
0
1
0
0
0
0
2
1
0
2
0
0
0
0
0
0
1
2
0
0
2
0
0
1
0
2
2
1
0
2
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
2
0
1
2
0
2
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
1
0
5
0
0
2
0
1
0
0
2
1
0
0
0
0
0
0
2
0
2
1
0
0
0
0
1
2
0
1
0
1
0
0
0
0
1
0
3
0
0
0
1
2
0
0
2
0
2
1
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
1
0
2
0
0
0
1
0
0
0
0
1
0
2
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
2
1
0
1
0
0
0
0
1
1
0
1
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
2
1
1
2
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
1
1
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
2
1
1
0
0
1
0
1
1
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
1
0
1
0
0
2
2
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
1
0
3
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
4
2
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
1
1
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
2
1
0
2
2
1
0
0
0
0
1
0
1
0
0
1
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
2
1
1
0
2
1
0
0
2
1
2
0
0
0
2
1
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
1
2
0
0
0
0
0
2
0
0
1
1
0
0
0
2
0
0
0
1
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
2
0
0
2
7
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
1
0
0
1
3
0
1
0
0
1
1
0
0
0
2
2
0
1
0
0
0
0
0
0
3
2
0
1
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
1
0
2
0
2
1
0
1
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
1
1
0
0
0
0
3
0
2
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
2
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
1
2
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
3
1
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
1
2
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
3
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
1
2
0
0
0
1
1
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
1
2
2
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
1
1
2
1
1
1
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
4
0
2
2
0
1
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
1
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
2
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
3
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
1
0
0
1
0
0
1
2
1
0
2
0
2
3
0
2
1
6
4
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
4
1
0
1
0
1
0
2
2
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
2
0
1
0
2
0
2
1
2
0
0
1
0
0
0
2
3
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
2
2
0
0
0
0
0
2
0
0
2
1
1
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
1
1
3
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
2
1
2
2
0
1
0
2
0
0
1
0
0
0
0
1
1
0
0
1
0
0
1
1
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
3
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
2
2
0
1
0
0
0
2
1
1
1
0
0
0
1
1
0
1
0
1
0
1
0
0
0
0
0
0
1
2
1
1
2
0
1
0
0
0
0
1
0
0
0
0
0
0
2
1
0
1
0
2
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
2
0
0
1
2
0
0
1
1
0
0
0
1
0
1
1
1
0
2
0
0
0
1
2
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
3
0
0
0
0
2
0
0
2
0
2
1
1
0
0
0
1
0
0
0
0
0
4
0
2
0
2
0
1
1
0
0
2
0
1
0
0
3
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
2
0
0
2
0
1
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
1
0
0
0
1
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
3
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
1
0
2
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
2
2
0
0
2
0
1
0
0
0
0
1
0
1
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
4
0
0
1
0
2
2
2
0
0
0
0
0
2
1
0
0
2
0
0
2
0
0
0
0
0
2
0
0
2
1
0
0
2
0
1
0
0
3
0
1
0
2
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
1
0
0
1
0
2
0
0
0
0
2
2
1
0
0
0
1
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
2
2
0
0
2
0
1
0
2
0
2
0
0
1
0
2
2
0
3
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
1
2
1
0
0
5
0
1
2
0
0
0
1
2
2
0
0
0
0
0
2
0
0
0
0
2
0
2
2
0
2
0
0
2
1
2
3
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
2
0
1
1
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
2
2
2
0
0
0
1
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
3
1
2
2
0
0
0
0
2
2
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
2
0
0
1
0
0
0
0
2
0
0
0
0
0
1
2
1
0
0
2
2
0
0
0
1
0
3
0
2
2
1
0
0
0
2
2
0
2
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
1
2
3
2
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
2
0
0
1
0
1
0
1
1
0
0
2
0
0
0
0
0
0
0
1
1
0
2
0
0
1
2
0
2
3
0
2
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
4
0
2
0
0
0
1
0
0
0
0
0
4
1
2
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
2
1
3
1
2
1
0
2
1
0
1
1
0
0
0
2
0
0
0
0
2
0
0
0
1
2
0
0
0
1
2
0
0
0
0
0
1
0
0
3
0
2
2
0
0
0
0
1
1
0
0
1
0
2
0
2
0
0
0
0
0
2
0
0
0
1
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
2
0
0
3
2
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
1
2
0
2
0
0
0
2
0
0
0
0
0
0
1
1
0
0
1
1
0
0
2
1
0
1
0
1
0
1
0
0
1
2
0
0
0
0
1
0
0
5
0
0
0
0
0
0
5
2
1
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
2
0
0
0
1
1
3
0
0
0
0
0
0
2
2
2
0
1
2
0
2
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
2
0
1
2
1
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
1
1
0
0
0
0
2
2
0
2
1
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
1
1
1
1
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
2
2
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
1
2
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
2
0
1
2
0
0
0
1
0
2
1
0
0
1
0
1
2
0
1
0
0
1
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
1
1
0
0
2
0
0
1
0
0
0
0
2
0
3
0
0
1
0
0
0
2
0
0
2
0
0
2
6
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
2
0
3
1
0
2
2
0
0
0
3
0
2
2
2
0
0
1
0
1
2
2
0
1
0
0
0
0
2
0
2
0
0
1
0
0
0
1
2
0
0
1
0
2
0
0
2
0
0
0
1
2
1
0
0
0
0
2
0
0
0
0
0
0
0
3
1
0
0
0
2
0
0
0
2
0
1
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
2
0
0
2
0
2
0
0
0
0
1
0
0
0
1
0
0
0
1
0
9
0
0
0
0
3
0
0
0
2
0
0
2
2
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
5
1
0
0
0
2
0
0
0
0
0
0
0
3
0
1
0
0
1
2
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
1
0
0
0
0
2
0
2
0
2
0
1
0
0
0
0
2
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
3
0
7
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
6
1
0
5
0
1
0
0
1
0
1
0
0
0
2
0
0
1
0
0
0
2
0
0
3
1
0
0
0
0
0
0
0
2
0
0
0
1
0
1
2
0
0
1
0
2
0
0
0
1
0
0
0
1
0
0
0
3
0
0
1
0
2
0
2
2
1
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
2
1
1
0
2
0
0
0
1
0
1
1
0
0
0
4
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
2
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
2
1
0
0
1
0
3
3
2
2
2
0
0
0
0
0
2
0
0
0
2
0
1
0
2
0
0
2
0
2
2
1
1
0
0
2
0
1
0
0
1
1
0
2
0
1
1
0
0
1
0
0
4
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
3
1
0
2
1
0
1
1
0
1
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
3
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
1
0
0
2
0
0
0
0
1
2
0
0
0
0
2
1
0
2
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
1
2
0
0
3
1
0
0
0
1
1
0
0
0
0
0
0
1
2
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
4
1
2
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
2
3
1
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
2
0
0
1
0
2
0
0
0
1
0
0
1
0
1
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
2
0
0
0
0
1
1
0
0
0
0
0
2
0
0
2
0
0
0
0
3
1
1
1
0
0
0
0
0
1
2
2
0
1
1
0
0
0
0
0
0
0
1
2
0
1
0
0
0
2
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
1
2
1
2
1
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
2
3
0
2
0
0
0
0
0
0
0
3
2
2
0
1
1
0
2
1
0
0
2
0
2
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
1
0
2
0
0
0
0
1
1
0
0
0
3
0
0
1
2
1
0
2
1
0
0
0
1
1
2
1
0
0
1
0
0
0
4
0
0
0
0
21
0
0
0
0
2
1
0
2
0
0
0
0
2
1
1
0
0
1
0
2
0
1
0
0
0
1
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
1
1
0
0
1
0
4
0
0
0
2
2
0
0
2
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
1
0
0
0
1
1
2
2
0
0
2
0
0
0
0
0
2
0
2
1
0
0
1
2
0
2
2
0
2
1
1
1
2
2
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
1
1
1
1
0
2
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
7
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
2
2
2
0
0
1
0
2
3
0
0
0
0
0
2
0
0
1
1
2
0
1
2
0
0
0
1
0
0
2
0
0
2
2
0
0
0
0
0
1
1
0
0
0
1
0
1
0
2
0
0
0
1
0
0
0
0
0
1
1
1
0
0
1
0
1
0
2
1
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
2
0
0
2
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
2
2
0
3
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
2
0
0
0
0
0
0
0
0
3
0
1
0
0
0
1
2
0
0
0
0
0
2
1
0
0
2
0
1
0
8
0
1
2
1
1
0
2
2
1
1
0
0
0
0
0
0
0
1
0
0
2
0
0
3
1
5
1
1
1
0
0
0
4
0
2
1
0
0
0
2
0
0
0
0
1
0
1
2
2
3
0
0
0
0
0
4
0
0
0
0
0
1
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
1
1
2
2
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
2
0
1
2
1
2
0
1
0
1
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
3
0
2
0
3
0
1
0
0
2
2
2
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
3
0
0
2
2
0
0
2
0
0
0
0
1
3
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
2
2
1
0
0
0
0
0
1
1
0
0
2
0
0
0
2
1
0
0
0
1
9
0
1
2
1
1
0
2
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
1
2
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
2
0
0
2
0
3
0
0
0
0
1
0
0
0
1
6
0
0
0
0
0
0
0
2
3
0
0
0
2
1
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
1
1
0
0
0
0
0
1
2
1
0
1
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
3
0
1
1
2
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
2
2
0
0
1
0
0
0
1
0
0
1
1
3
0
2
1
1
0
2
0
0
0
0
0
0
0
0
0
2
1
0
2
0
1
2
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
1
0
1
2
0
2
1
0
0
0
1
0
2
0
5
0
0
2
0
0
0
1
0
0
1
2
0
1
1
0
0
0
0
0
2
0
0
6
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
2
0
0
1
1
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
2
0
1
0
2
0
0
0
2
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
5
0
0
0
2
0
0
0
0
0
0
0
0
1
0
3
2
0
0
2
0
0
0
0
1
0
0
0
2
2
2
1
0
0
0
1
0
1
0
2
0
1
0
0
3
0
2
2
0
0
0
1
0
0
1
2
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
1
2
0
0
2
0
1
0
0
0
1
0
0
0
2
2
0
0
0
0
1
4
0
1
2
1
2
0
0
0
0
0
2
0
0
0
0
10
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
2
1
0
0
1
0
0
0
1
0
0
2
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
3
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
1
0
0
0
0
2
1
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
8
0
0
2
0
2
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
2
0
1
2
0
0
1
0
1
0
0
0
0
0
2
0
0
1
0
1
0
0
2
0
2
2
3
1
0
0
0
0
1
0
0
2
0
1
0
0
2
0
3
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
2
3
1
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
1
0
0
3
1
0
0
1
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
3
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
2
2
1
1
2
2
0
0
2
0
2
0
2
0
0
0
0
2
1
0
2
1
2
3
0
0
0
2
0
0
0
5
2
0
2
0
0
0
0
0
1
2
1
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
2
1
0
0
0
0
0
0
1
0
3
0
0
1
2
1
0
0
1
1
0
1
2
0
1
0
0
2
0
0
0
0
0
1
0
0
1
0
2
0
0
2
0
0
0
0
0
1
0
0
0
4
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
2
0
0
0
0
1
1
0
3
0
0
0
2
3
0
0
1
0
0
1
1
0
1
0
0
1
1
2
0
0
2
2
0
0
1
2
0
0
2
0
0
1
2
1
0
0
2
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
1
0
1
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
3
0
0
2
0
0
0
2
0
1
0
0
0
0
1
3
3
0
1
0
0
4
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
1
1
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
2
1
1
0
0
0
0
0
0
1
0
2
1
0
2
1
0
3
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
1
2
0
1
0
2
0
2
0
0
1
0
2
0
0
0
0
0
2
2
0
2
2
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
3
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
1
0
2
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
2
0
3
0
0
1
0
0
0
0
0
2
1
0
0
0
0
2
0
2
0
0
0
2
1
0
1
0
2
0
1
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
1
0
2
0
0
1
0
0
0
0
2
0
0
1
1
0
0
1
2
1
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
2
0
2
0
0
2
0
0
2
0
0
0
2
0
2
1
0
0
0
0
1
1
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
2
1
0
0
0
0
1
0
3
1
0
0
3
2
0
0
0
2
0
0
3
0
0
2
1
0
0
0
0
3
0
0
0
1
0
0
2
0
2
2
2
2
0
0
0
0
0
1
0
2
0
1
0
0
0
0
1
2
1
0
0
0
2
0
1
0
0
4
1
0
0
0
1
0
0
1
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
2
1
2
2
1
0
0
1
0
0
2
0
0
2
0
0
3
1
0
0
1
0
0
3
0
1
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
2
1
0
0
0
0
2
0
0
0
3
0
0
1
0
0
0
5
0
0
0
0
0
0
0
0
1
0
2
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
3
2
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
2
0
0
0
2
0
2
2
1
1
0
2
2
0
0
1
2
0
1
0
1
2
0
0
1
2
4
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
1
0
2
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
1
0
1
0
0
0
2
0
0
1
0
0
1
0
0
0
0
1
2
2
0
0
1
2
0
2
0
0
2
0
0
0
1
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
2
1
0
0
2
1
0
1
0
2
0
0
0
0
1
0
0
0
2
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
1
2
2
0
9
0
1
2
0
0
0
0
0
1
2
0
2
0
1
0
2
0
0
1
0
0
2
2
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
3
0
0
0
10
1
0
0
0
1
0
0
0
0
0
0
0
2
4
2
2
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
2
2
0
1
0
0
2
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
2
0
0
0
1
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
2
0
0
0
0
1
0
2
2
0
0
2
0
1
0
1
0
2
1
1
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
2
1
2
2
0
0
0
0
1
2
3
0
0
0
0
0
0
2
0
0
1
1
0
0
1
0
0
1
0
0
1
0
0
1
0
0
2
0
2
0
2
0
2
0
2
0
0
2
1
2
0
2
0
1
2
7
2
0
0
0
1
1
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
2
1
0
0
0
0
2
2
2
0
2
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
2
0
1
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
2
0
0
3
1
0
0
0
5
0
2
0
0
0
0
0
0
1
0
0
2
0
3
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
2
0
2
0
1
1
2
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
3
0
0
0
0
1
1
0
0
0
1
0
0
1
2
0
2
0
2
2
2
2
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
3
0
1
0
0
0
0
1
0
0
0
0
1
1
2
2
0
0
2
0
0
0
3
0
0
0
0
0
2
2
2
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
2
0
0
2
1
0
2
0
0
0
0
0
0
2
0
1
2
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
1
2
3
1
1
0
1
2
0
0
3
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
2
1
1
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
1
1
1
2
0
0
1
0
0
1
0
0
2
0
2
0
1
2
1
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
1
0
1
1
0
0
0
0
3
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
2
2
1
0
1
0
2
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
5
1
2
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
2
0
0
1
0
0
1
0
0
0
0
1
2
2
0
0
0
0
1
2
0
2
0
0
0
0
2
1
0
2
2
1
1
0
0
0
0
2
1
2
0
2
0
0
1
0
0
2
0
1
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
1
1
0
0
1
2
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
5
0
0
2
0
0
0
0
2
0
0
0
0
3
0
1
0
0
0
1
0
0
0
0
1
0
0
2
0
0
3
0
0
0
0
6
0
0
2
0
1
0
1
1
0
0
3
0
1
0
0
0
0
1
0
4
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
2
1
0
0
0
0
2
3
0
4
1
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
2
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
7
0
2
2
1
1
2
1
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
1
1
0
0
0
3
1
0
0
0
0
0
0
0
0
0
2
2
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
2
0
0
0
1
0
0
2
0
1
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
3
2
0
2
0
3
2
0
0
0
0
0
3
0
2
1
1
0
0
0
0
0
0
0
0
1
3
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
1
2
1
1
0
2
2
3
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
1
0
2
0
2
2
0
0
0
2
1
0
2
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
2
2
2
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
1
2
2
2
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
3
2
2
0
0
3
0
0
0
0
0
2
0
0
0
2
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
3
0
0
0
0
1
0
0
2
0
0
0
0
2
2
0
0
1
0
2
1
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
2
2
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
1
0
0
0
2
2
0
0
1
2
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
1
0
0
0
0
1
2
1
0
0
0
1
0
0
0
1
1
1
0
2
0
0
2
0
0
0
3
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
1
2
0
2
0
0
0
0
0
0
1
3
0
0
0
2
0
0
1
0
0
2
1
0
0
2
0
1
0
0
1
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
1
0
0
0
0
0
0
1
1
1
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
1
2
0
1
2
0
1
3
0
2
1
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
2
1
0
0
0
0
0
0
2
4
2
1
1
1
0
0
2
0
0
0
1
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
2
0
1
0
0
2
0
0
1
0
2
0
2
0
0
1
0
0
1
0
3
0
0
0
1
0
0
0
1
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
4
2
0
2
0
0
1
0
2
0
0
0
1
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
1
0
0
0
0
0
1
3
1
0
0
1
2
0
0
0
0
2
0
2
0
2
0
0
3
0
2
2
0
0
0
0
0
0
0
1
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
2
2
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
1
0
0
2
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
3
2
0
0
0
3
0
0
0
1
0
2
1
0
0
0
1
0
0
0
0
1
0
3
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
2
0
1
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
3
2
0
1
2
0
0
0
0
2
1
2
0
0
0
2
0
0
0
0
3
2
0
0
0
2
0
0
0
0
3
0
1
0
0
1
0
0
1
0
0
0
8
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
2
5
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
1
1
0
1
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
3
0
2
0
1
0
1
0
0
0
0
2
0
0
2
2
0
0
0
0
1
0
0
0
0
0
3
0
1
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
1
0
2
2
0
2
2
0
1
0
2
2
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
1
0
0
1
0
2
0
0
0
2
0
1
0
2
0
0
1
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
2
3
0
0
2
4
1
1
0
0
3
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
3
0
0
1
0
2
0
2
2
1
0
0
0
0
3
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
2
2
0
1
0
0
1
0
0
0
1
0
0
0
0
1
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
2
2
0
0
0
2
0
0
0
1
0
0
1
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
1
0
0
0
1
0
7
0
0
0
1
1
0
0
0
0
0
2
2
0
0
1
6
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
1
0
2
1
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
2
3
1
1
1
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
2
1
2
0
0
0
0
0
1
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
2
0
0
2
0
2
0
2
1
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
1
0
0
1
2
0
1
2
2
0
1
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
4
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
1
2
1
1
0
0
2
0
0
0
0
0
2
0
2
0
2
0
0
2
1
0
0
0
2
0
0
3
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
1
0
0
0
1
2
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
3
1
2
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
1
2
1
0
1
0
0
4
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
1
0
2
0
0
0
2
2
2
2
0
0
0
0
1
1
0
0
2
2
0
0
1
3
0
0
2
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
6
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
2
0
1
0
2
0
0
1
0
0
0
2
0
2
1
0
0
0
0
0
0
0
1
0
0
6
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
1
0
0
1
2
2
2
2
0
1
1
0
0
0
0
0
1
1
0
0
0
5
1
0
0
0
1
0
3
0
1
0
0
0
3
1
0
0
1
0
0
0
0
1
2
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
2
1
0
1
1
0
2
0
2
1
0
0
0
0
1
0
0
0
2
1
2
0
2
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
1
4
0
0
1
0
0
0
0
0
0
0
1
2
0
0
2
2
0
0
0
0
1
1
0
0
1
1
0
0
0
3
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
1
2
1
0
1
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
3
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
1
1
1
1
0
1
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
3
0
0
0
0
2
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
8
0
0
0
0
0
0
2
0
2
1
2
0
1
2
2
0
1
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
3
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
3
1
0
0
1
0
3
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
2
2
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
1
0
1
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
1
0
0
2
2
2
0
0
2
0
0
0
0
0
3
0
0
2
0
0
0
0
2
0
1
2
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
1
0
1
0
2
0
2
2
3
1
2
0
0
0
0
0
1
0
0
1
0
1
0
0
0
2
1
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
2
0
0
5
0
0
0
0
0
0
0
1
2
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
3
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
4
2
0
2
0
3
0
2
0
0
0
0
1
0
2
0
2
0
0
0
2
1
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
1
0
1
0
0
0
0
1
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
1
0
3
4
0
0
1
0
2
1
0
0
1
0
1
0
1
1
0
1
0
0
0
0
0
2
2
2
0
1
1
0
0
0
4
3
9
0
2
0
0
1
0
0
0
0
0
3
0
2
2
0
0
0
0
0
0
1
2
0
0
0
2
0
1
0
0
2
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
2
2
0
2
0
1
0
0
4
1
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
1
2
0
3
2
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
2
1
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
9
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
2
1
1
0
0
0
0
2
0
0
2
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
1
0
1
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
3
0
0
0
1
1
0
0
0
0
3
0
2
1
0
0
0
1
1
0
0
1
3
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
1
1
2
0
0
2
0
2
2
2
0
0
2
0
0
1
0
2
2
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
2
0
0
0
0
2
3
1
0
0
0
1
1
0
0
1
1
2
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
1
1
2
1
1
0
0
0
0
2
0
1
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
2
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
1
0
0
2
0
0
0
1
0
3
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
2
0
0
3
1
0
0
0
0
0
0
2
1
0
1
2
0
0
2
0
1
1
2
0
0
0
0
1
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
2
0
0
0
0
1
0
2
2
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
1
0
0
2
0
0
1
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
1
2
1
0
0
0
1
0
0
2
0
0
1
0
0
0
2
1
0
1
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
1
2
0
2
0
0
0
5
0
0
2
0
1
0
0
0
0
2
0
1
0
1
3
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
3
2
0
0
1
1
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
2
2
0
3
2
0
0
1
0
0
0
2
0
0
0
1
2
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
3
0
0
0
0
0
1
0
0
3
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
2
0
4
0
1
0
3
1
0
0
0
0
0
1
0
1
1
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
1
3
0
0
1
0
2
0
0
0
0
0
0
0
2
1
0
0
0
2
0
1
0
2
1
2
0
0
2
0
2
0
1
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
2
0
0
0
1
2
0
0
2
3
1
1
0
1
0
0
0
4
2
0
0
0
0
0
2
0
0
1
2
1
0
1
0
0
0
2
2
2
0
4
1
0
0
0
0
1
0
1
0
3
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
2
0
0
0
1
2
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
2
1
0
2
1
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
3
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
2
0
1
0
0
0
2
2
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
4
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
2
0
0
0
0
0
0
0
1
0
0
2
0
1
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
2
0
0
2
0
0
0
3
0
0
1
3
0
2
0
0
0
1
0
0
0
0
2
1
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
2
0
1
2
0
0
1
1
0
0
1
0
0
0
2
1
4
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
2
0
2
1
1
0
0
2
0
0
2
1
2
0
0
0
2
0
0
0
0
0
0
0
0
1
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
2
0
2
0
0
1
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
3
5
0
0
0
1
0
0
0
2
0
0
1
0
3
0
0
0
3
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
4
1
0
2
1
1
2
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
2
2
0
0
0
1
2
2
0
0
1
1
0
1
2
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
1
1
0
0
2
2
0
1
1
0
0
0
0
0
0
2
0
0
1
0
2
0
1
0
0
0
2
2
0
0
2
2
2
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
2
0
2
0
1
0
0
0
2
0
0
2
2
0
0
0
2
1
0
0
2
1
0
0
0
1
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
2
1
0
0
0
0
0
0
2
1
1
0
0
0
0
0
1
0
0
0
0
0
0
2
2
3
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
3
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
1
0
0
0
1
0
0
0
5
3
1
0
0
0
2
0
0
1
2
1
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
1
0
0
2
0
1
2
0
0
0
2
0
0
0
0
7
0
2
1
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
3
2
0
1
2
0
0
0
0
0
0
2
0
2
0
1
0
1
0
1
1
0
1
2
0
0
0
0
1
0
0
0
0
0
0
1
0
2
2
0
2
0
0
2
0
0
0
0
0
0
2
1
2
0
0
0
1
0
0
0
0
0
0
4
0
0
1
2
0
2
2
0
0
0
2
2
1
1
0
3
0
0
0
0
0
0
0
0
2
0
1
1
1
0
0
0
0
0
1
2
0
0
1
2
0
1
1
1
0
0
0
0
2
1
1
1
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
2
1
0
0
0
1
1
0
0
0
0
0
0
2
1
0
1
2
0
0
2
0
0
0
0
0
0
2
0
1
0
2
3
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
1
0
0
0
6
1
0
0
0
0
0
2
2
1
0
2
0
1
1
0
0
1
2
0
1
0
0
1
0
0
0
2
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
1
0
0
0
4
3
0
2
2
0
0
0
2
0
0
0
0
0
0
0
1
2
1
2
3
0
1
0
1
0
2
1
0
2
6
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
2
0
2
0
3
1
1
0
0
1
0
1
1
0
0
0
2
0
1
0
2
0
0
1
0
0
2
2
0
0
0
2
2
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
4
0
1
1
0
1
0
0
2
0
0
0
1
2
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
1
3
0
0
0
2
0
0
0
0
0
0
3
2
0
2
0
0
0
1
0
0
0
1
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
4
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
2
1
0
0
1
0
0
1
0
0
0
0
0
1
2
0
0
1
0
0
2
0
0
0
0
0
2
0
0
2
2
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
2
0
3
0
0
0
2
0
0
0
0
0
0
0
0
6
0
2
2
2
0
2
1
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
2
0
1
0
0
0
1
0
0
2
1
0
0
0
0
1
0
0
0
3
1
0
0
0
1
0
0
2
0
0
0
2
0
1
0
0
1
2
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
1
0
0
1
4
0
1
0
0
0
3
1
0
0
1
0
0
2
0
2
0
0
2
0
0
0
0
0
0
1
2
0
2
0
0
0
3
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
4
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
2
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
2
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
1
0
2
2
1
0
0
0
1
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
2
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
2
0
2
0
0
0
2
0
0
3
0
1
0
1
0
1
1
1
1
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
2
0
0
0
0
3
1
0
2
0
0
0
0
0
2
2
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
2
2
0
0
0
1
2
0
1
0
0
0
0
0
0
0
2
0
0
0
2
1
0
3
0
0
0
2
1
0
0
0
0
0
0
0
1
7
2
0
2
0
1
0
0
0
0
0
0
1
1
0
1
2
0
0
0
0
0
0
5
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
1
0
0
0
1
1
0
0
2
2
0
0
0
0
0
0
1
1
0
0
2
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
2
0
0
0
0
2
0
0
1
0
0
1
1
2
0
1
0
1
0
5
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
4
0
0
0
0
1
0
2
0
0
2
0
0
2
0
1
2
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
1
0
4
0
1
0
1
1
0
2
0
0
1
0
2
2
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
1
0
0
1
0
1
1
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
2
2
2
0
0
0
0
0
6
0
0
0
0
0
2
0
0
2
2
2
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
2
0
1
0
0
12
1
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
1
2
0
2
2
1
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
2
3
0
0
0
0
0
2
1
0
2
2
1
2
0
2
0
2
0
0
0
0
0
0
0
2
0
0
1
0
2
1
0
0
0
1
2
0
0
1
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
2
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
3
0
1
1
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
1
2
0
0
0
0
1
0
0
1
0
2
0
0
0
1
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
7
1
0
2
0
0
2
1
0
0
2
0
1
0
0
0
2
0
0
0
0
0
1
1
0
0
0
1
0
0
4
1
2
0
3
0
0
0
0
2
0
0
0
2
0
2
0
0
0
1
0
0
0
0
1
1
0
2
0
0
0
2
0
0
0
1
0
0
2
0
2
0
0
0
0
1
0
0
0
0
1
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
1
1
4
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
1
2
0
1
0
0
0
1
0
0
2
0
1
2
1
2
0
2
0
0
1
0
0
1
0
0
1
2
0
2
0
8
2
0
0
0
0
0
1
0
0
4
0
2
2
0
0
0
0
0
0
2
0
2
0
0
0
1
1
1
2
0
0
2
0
0
0
0
2
1
0
2
1
0
0
0
2
0
0
0
2
1
0
2
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
2
2
1
2
2
0
2
2
0
1
0
0
2
2
0
1
0
3
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
2
2
0
0
0
2
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
2
2
0
0
1
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
2
2
0
0
1
0
0
3
1
0
0
0
0
0
3
0
0
2
0
0
0
0
0
2
0
2
0
2
0
1
0
0
0
0
0
1
2
0
1
0
1
0
2
0
0
0
0
0
1
2
0
0
1
0
0
1
0
0
0
2
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
2
2
0
0
1
0
2
0
0
0
0
1
2
0
0
3
0
2
0
0
0
0
0
0
0
1
1
0
2
0
2
1
0
2
0
0
2
1
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
1
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
1
0
1
1
0
0
0
0
0
0
6
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
3
2
2
0
1
1
0
0
0
2
2
1
0
0
0
0
0
2
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
2
2
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
1
0
1
0
0
0
1
0
0
0
2
1
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
1
0
2
0
0
0
1
0
0
0
0
0
7
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
1
0
4
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
2
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
1
0
0
0
1
0
0
0
0
0
0
2
1
2
0
2
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
1
0
2
0
0
2
1
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
3
1
2
0
0
1
0
0
2
0
2
0
2
0
0
0
0
0
2
0
2
2
1
0
0
0
1
2
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
2
1
0
0
2
1
0
1
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
3
0
0
0
0
0
2
0
1
0
2
3
2
0
0
1
0
0
0
0
0
0
0
0
2
2
2
0
0
0
1
0
0
2
0
0
0
0
0
0
2
1
2
1
0
1
0
0
0
3
0
0
0
2
0
0
2
0
0
1
0
1
0
2
0
2
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
1
1
1
0
0
0
0
1
0
2
1
0
2
0
0
2
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
1
1
0
0
1
0
0
0
1
0
0
2
0
0
1
0
2
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
1
0
0
0
2
1
0
0
0
0
1
2
0
0
0
0
0
2
0
2
0
1
1
0
0
0
2
1
0
0
1
1
0
0
0
0
0
0
1
2
0
1
4
0
0
0
2
1
0
2
0
0
0
0
0
0
2
0
0
2
0
2
2
0
0
0
2
0
3
1
0
0
1
0
4
2
0
0
0
2
0
2
2
1
0
0
0
0
0
2
0
2
0
2
0
0
0
0
2
0
0
2
1
1
0
0
0
0
0
2
2
0
1
0
0
0
2
0
0
2
0
0
1
2
2
2
0
1
2
0
0
1
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
2
0
2
12
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
3
0
2
2
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
2
0
1
0
0
1
0
0
3
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
2
0
2
0
1
0
1
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
2
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
2
2
0
0
1
1
0
0
1
2
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
2
0
0
2
0
2
0
0
0
1
0
0
1
0
3
2
0
0
0
0
0
1
0
0
0
1
0
0
2
2
0
0
0
1
2
0
2
2
2
1
2
0
2
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
1
1
0
0
2
0
0
1
1
0
2
1
0
1
2
1
0
0
0
2
1
1
1
1
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
2
0
2
0
2
0
0
2
0
4
1
1
0
4
2
2
3
0
0
1
1
0
1
0
3
0
0
0
0
0
0
0
2
0
1
0
0
2
0
2
2
0
0
0
0
0
2
0
3
0
0
0
0
1
0
2
2
0
0
0
1
2
0
0
1
0
2
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
1
2
2
0
0
3
0
0
0
0
0
0
1
0
2
0
0
2
0
1
1
0
0
2
0
0
0
0
2
2
0
0
0
7
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
2
4
0
0
0
0
0
1
0
0
1
0
0
2
0
0
2
2
1
0
0
0
0
0
1
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
2
1
1
1
0
0
0
0
0
2
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
2
0
0
2
1
0
0
0
0
0
0
2
2
0
2
1
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
2
0
0
1
2
0
0
1
2
0
2
2
0
0
2
0
0
0
0
0
0
0
5
0
0
0
0
0
0
2
0
0
0
2
1
0
0
1
0
0
0
0
0
0
1
3
0
0
0
0
1
0
0
1
0
0
2
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
1
0
10
2
0
0
0
1
1
0
0
2
0
2
1
0
0
1
2
0
0
0
0
2
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
1
1
0
0
0
3
0
0
0
1
0
0
0
0
0
0
2
0
0
0
4
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
1
0
0
1
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
2
1
1
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
1
0
2
0
1
2
2
0
1
2
1
0
1
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
2
2
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
1
0
1
1
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
2
0
0
2
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
3
0
6
0
0
0
2
0
0
1
2
0
2
0
0
0
0
0
1
0
0
0
0
5
1
0
0
0
1
2
1
0
0
0
0
1
2
0
0
1
0
0
2
0
0
0
1
2
0
0
1
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
1
0
0
5
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
6
0
1
0
0
0
2
0
0
1
1
2
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
1
0
1
0
2
1
0
0
0
0
0
0
0
1
2
0
1
2
0
0
1
1
0
1
0
0
0
0
0
3
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
1
1
1
0
1
1
0
0
0
1
1
0
2
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
1
1
1
0
0
0
1
2
0
0
0
2
2
0
0
2
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
2
1
0
0
0
0
2
2
0
0
1
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
1
0
2
1
0
0
0
0
5
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
2
0
0
1
11
2
0
2
0
2
0
0
0
0
1
0
0
2
2
2
0
0
0
0
0
0
0
2
3
2
0
0
0
2
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
2
2
1
0
0
0
0
0
2
0
2
0
3
0
2
0
3
0
0
1
0
0
0
0
0
10
2
2
1
0
0
0
1
0
0
1
0
2
2
0
1
0
0
0
0
0
2
0
0
1
0
0
1
1
0
0
1
0
0
0
2
1
0
2
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
4
0
1
3
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
2
0
0
2
2
1
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
1
3
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
2
0
0
0
0
3
2
0
0
2
0
0
0
0
0
1
0
2
0
1
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
2
1
1
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
2
0
0
1
0
0
0
0
0
3
2
0
2
0
2
0
0
0
0
0
0
1
0
0
2
1
0
0
0
1
0
0
0
6
0
2
0
0
0
2
0
0
2
0
0
2
0
0
2
1
2
0
0
0
1
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
1
0
3
0
0
0
1
0
0
2
0
0
1
0
0
4
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
3
0
0
3
2
3
2
1
0
1
0
0
0
0
0
2
0
0
2
0
0
3
2
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
1
0
0
2
2
2
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
5
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
7
2
2
0
0
0
2
0
2
0
0
0
1
0
0
0
1
0
0
2
0
1
0
0
0
2
0
0
2
0
0
0
0
0
1
1
2
0
1
0
1
2
0
0
1
1
0
3
0
2
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
2
1
0
3
0
0
0
0
0
1
0
2
0
0
0
2
0
2
0
2
0
0
0
0
0
1
2
0
0
0
1
0
0
2
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
4
1
0
0
2
2
0
0
2
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
2
2
0
2
0
0
1
0
0
0
2
2
1
0
0
0
1
0
0
0
2
0
1
1
0
0
0
5
0
2
0
2
0
0
2
0
0
0
0
0
0
0
3
0
1
0
1
0
0
0
0
0
0
0
4
0
0
0
0
2
0
2
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
5
0
0
0
0
1
0
1
0
2
1
0
1
0
2
1
0
0
0
1
1
0
0
0
0
1
0
1
2
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
1
0
0
0
0
1
2
0
0
0
1
0
0
2
0
0
1
1
0
1
0
2
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
2
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
1
0
1
0
0
0
2
0
1
2
0
0
2
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
1
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
2
0
2
0
0
0
2
0
2
1
0
0
1
1
2
1
0
0
0
2
2
0
0
2
1
2
0
0
0
1
0
2
0
2
5
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
1
0
2
0
2
2
2
2
0
0
0
1
1
0
0
1
2
0
0
0
0
0
1
0
0
0
1
1
0
1
2
2
2
0
2
0
1
0
0
0
0
2
0
0
1
0
0
2
2
3
0
1
1
1
0
0
1
0
0
2
1
1
0
0
0
0
0
0
2
1
3
0
0
2
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
3
0
0
2
0
0
0
0
0
0
0
2
2
2
0
0
1
0
2
0
0
0
3
0
5
2
0
0
0
0
4
0
0
0
0
1
0
0
2
0
2
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
1
2
0
1
0
1
0
0
0
2
2
0
0
0
0
2
1
2
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
3
0
1
0
3
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
3
0
1
0
0
1
0
0
1
0
3
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
2
0
0
8
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
3
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
1
0
0
0
2
0
1
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
3
0
2
0
1
0
2
0
1
1
0
7
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
2
3
0
0
0
0
1
0
0
0
0
2
2
0
0
0
3
0
1
1
0
1
2
0
1
0
0
0
0
2
2
2
0
1
0
1
3
2
1
0
0
0
0
2
0
0
2
2
0
0
0
1
1
0
1
0
0
0
0
0
0
1
2
2
0
3
0
2
0
0
1
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
1
0
1
0
0
1
0
2
3
3
0
0
0
0
0
0
1
0
1
0
4
0
3
1
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
1
0
0
2
0
2
2
0
0
0
0
0
1
2
0
0
2
0
0
3
0
3
2
0
1
0
0
0
2
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
2
2
1
0
1
0
1
1
0
0
0
1
0
2
2
5
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
4
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
2
0
1
0
1
0
0
0
1
3
2
0
0
1
0
2
2
0
0
0
0
0
2
1
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
1
1
0
0
3
0
0
1
0
1
0
0
0
0
2
0
0
1
0
1
0
0
2
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
2
0
0
2
2
0
1
0
0
0
3
0
1
0
0
2
0
2
0
0
1
2
0
1
2
0
0
2
2
0
2
0
1
0
2
0
2
0
1
1
0
0
1
0
0
0
0
6
0
1
0
0
0
2
0
0
0
0
0
1
1
0
0
1
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
5
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
1
1
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
9
0
0
0
0
0
1
0
1
0
0
2
0
1
0
1
0
2
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
3
0
0
1
0
0
0
1
0
0
2
0
2
0
0
0
0
2
1
1
2
0
2
0
0
2
0
0
0
1
0
2
0
0
0
0
1
2
0
0
3
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
1
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
2
0
2
2
0
0
1
1
2
0
0
0
0
1
0
0
1
0
0
0
2
2
0
2
0
0
0
0
0
2
0
0
5
2
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
2
0
3
0
2
16
0
0
0
0
1
3
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
3
0
0
2
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
2
0
1
0
0
0
1
2
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
2
0
1
2
1
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
3
1
0
0
0
3
0
1
0
1
0
0
2
0
1
1
0
1
2
0
1
0
0
2
1
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
2
1
0
0
1
0
0
0
0
1
0
1
0
0
3
0
1
0
2
0
0
2
2
0
1
0
0
1
2
0
0
2
0
0
0
0
0
1
0
2
0
2
2
0
0
0
2
0
1
0
0
0
0
2
0
3
0
1
0
0
0
0
0
0
1
3
0
0
2
0
0
0
0
0
0
1
1
1
2
0
0
0
3
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
1
0
0
0
1
0
1
0
2
0
2
0
0
1
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
3
0
0
0
0
0
0
2
2
0
1
0
0
0
1
1
0
0
0
2
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
3
6
8
0
0
0
1
0
0
0
2
2
0
2
1
0
2
3
0
0
1
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
2
2
2
0
0
2
0
2
0
0
1
0
1
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
1
0
1
0
0
1
2
0
3
1
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
1
2
1
0
2
2
1
2
0
2
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
1
2
0
0
0
0
2
0
0
0
2
0
2
1
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
11
0
0
1
1
2
0
0
0
5
0
0
0
0
0
0
3
0
0
2
0
2
0
0
0
0
0
0
0
0
1
2
0
0
3
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
1
0
0
3
0
0
1
0
0
1
1
0
0
0
0
0
2
0
0
2
2
1
0
0
2
0
0
2
0
2
0
0
0
0
2
0
1
0
0
2
0
0
0
1
2
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
1
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
4
0
0
0
1
0
0
0
0
0
0
1
1
1
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
3
0
1
0
2
0
0
2
2
2
0
0
0
1
0
0
0
0
0
1
2
1
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
4
2
0
0
0
2
1
0
0
0
0
1
2
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
2
0
1
1
3
0
1
2
2
0
1
0
0
0
0
0
1
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
2
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
2
0
0
0
1
0
0
0
1
1
1
0
0
0
0
1
2
4
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
1
0
1
1
2
0
2
0
0
0
1
0
2
0
0
2
0
0
0
2
0
0
2
1
0
1
0
0
2
0
0
2
0
0
0
0
0
3
0
0
0
0
2
0
1
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
2
1
1
0
0
0
0
0
3
0
2
0
2
1
0
1
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
2
1
1
0
0
0
0
2
1
0
0
0
0
2
4
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
2
2
0
0
3
0
0
0
0
1
1
2
1
0
2
0
0
0
1
0
3
0
0
0
0
0
1
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
6
2
0
0
0
3
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
2
0
0
0
0
1
0
0
2
0
3
0
0
0
0
0
0
0
0
3
1
0
0
2
0
1
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
1
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
1
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
2
1
0
0
0
1
2
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
3
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
2
0
0
0
2
0
1
0
0
0
2
0
0
2
0
2
0
0
2
0
0
1
2
2
0
0
0
0
2
0
2
3
1
0
0
2
0
0
1
0
2
1
0
0
2
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
2
0
0
0
2
0
1
1
0
0
0
0
0
0
1
2
0
1
2
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
1
0
0
2
0
0
1
0
0
0
1
2
0
0
2
0
0
1
0
2
0
0
0
0
2
0
0
3
0
1
2
1
0
2
0
0
0
0
0
0
0
0
0
0
4
2
0
0
1
0
0
0
1
1
1
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
3
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
2
0
2
2
3
0
0
2
0
0
1
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
1
1
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
2
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
2
1
0
1
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
1
1
0
0
1
0
0
0
0
0
0
2
0
1
0
2
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
2
1
0
0
1
0
0
0
0
2
1
0
0
0
0
2
0
6
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
1
2
0
0
0
1
2
0
0
0
0
0
1
1
1
0
1
1
0
1
0
1
1
0
2
2
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
2
0
0
0
0
1
3
0
3
0
0
1
2
0
0
0
2
1
1
0
3
0
1
0
0
1
0
1
1
0
1
0
0
0
3
1
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
1
0
1
0
0
3
0
1
1
0
0
0
1
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
3
1
0
1
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
2
0
0
0
3
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
3
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
2
0
2
0
0
0
0
4
1
1
2
1
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
2
0
1
1
1
0
0
5
0
0
0
0
1
0
0
0
2
2
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
3
0
0
0
0
1
0
0
2
2
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
2
1
1
0
2
0
0
1
0
0
0
0
0
1
0
1
1
1
0
2
2
0
1
0
1
0
0
0
0
1
0
0
1
0
1
0
2
0
0
0
0
1
0
0
2
1
0
0
0
1
0
0
2
2
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
4
2
1
0
2
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
4
2
0
3
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
1
0
0
1
3
0
1
0
3
2
2
0
2
0
0
2
1
0
2
3
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
1
2
0
2
0
0
1
0
0
0
0
1
2
2
0
1
0
0
0
0
0
1
2
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
1
2
0
0
3
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
3
0
2
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
2
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
2
0
0
0
4
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
4
0
0
0
2
0
0
0
4
2
0
4
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
5
0
0
2
2
1
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
1
2
0
0
0
0
2
0
0
2
2
0
0
0
1
1
1
0
0
2
0
1
0
2
2
0
2
0
0
0
0
1
2
0
0
0
1
0
1
0
0
2
0
1
2
0
0
4
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
2
0
1
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
1
0
2
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
1
0
1
0
1
1
1
1
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
1
0
0
2
2
0
0
0
0
0
1
0
2
0
2
0
1
1
0
1
2
1
0
0
2
1
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
2
2
0
2
1
2
0
0
0
1
0
0
2
0
0
1
1
1
0
0
1
0
1
1
0
0
0
0
0
0
0
2
0
0
0
1
1
1
0
1
0
0
0
1
1
0
1
0
0
0
0
2
0
1
0
0
1
0
2
0
0
0
0
1
0
0
1
0
0
1
2
0
0
1
1
0
1
0
0
0
0
3
0
0
0
0
2
1
0
0
0
3
0
0
0
0
0
2
2
2
0
2
0
0
1
1
0
0
2
1
0
1
0
0
2
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
1
0
1
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
1
3
0
2
0
2
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
3
0
0
0
3
1
0
2
2
1
0
1
2
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
7
0
1
1
1
2
3
2
0
0
0
0
0
0
2
1
0
0
0
1
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
1
0
0
2
0
0
2
1
2
0
0
0
0
0
0
2
0
0
3
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
2
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
3
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
1
2
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
3
0
2
0
0
0
1
4
2
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
1
2
0
0
1
0
0
0
0
2
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
3
2
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
4
3
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
2
0
2
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
1
0
0
1
4
2
0
1
1
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
3
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
1
3
0
0
0
0
0
0
0
2
3
0
0
2
1
0
0
2
0
0
0
0
2
0
0
1
2
1
0
0
1
0
1
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
1
1
0
4
0
1
0
0
0
0
0
0
0
1
0
2
1
2
2
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
2
2
0
0
0
2
0
2
2
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
2
2
0
0
0
3
2
2
1
1
1
0
0
0
0
2
0
0
0
3
0
0
0
0
0
1
1
2
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
2
0
2
0
1
3
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
1
1
0
0
0
0
0
1
2
0
2
2
1
0
2
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
2
1
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
1
1
0
2
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
2
2
0
0
0
1
0
0
1
0
1
0
2
1
2
1
0
0
1
0
0
1
0
0
0
2
1
0
0
0
0
0
0
1
0
1
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
4
2
0
2
1
0
0
0
0
2
1
2
1
1
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
2
0
2
2
0
0
2
2
1
2
2
1
1
2
0
0
0
6
2
2
0
0
0
0
1
0
0
0
1
0
0
2
0
0
1
0
0
0
0
2
1
0
2
2
0
0
0
2
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
1
2
2
1
0
3
0
0
0
1
0
2
2
0
0
0
0
1
0
0
0
0
1
0
2
0
0
1
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
2
0
2
0
0
0
0
3
2
0
1
0
1
1
0
2
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
1
0
2
0
0
1
1
2
0
2
0
2
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
1
0
1
2
0
0
2
0
0
1
0
1
0
2
0
0
0
3
0
0
0
0
0
1
0
1
0
3
0
2
2
0
1
1
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
1
0
5
1
2
0
2
1
0
0
2
0
0
0
1
1
0
0
1
0
1
3
1
1
4
2
1
2
2
1
1
0
6
0
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
1
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
1
0
0
1
0
4
0
2
0
1
1
0
0
1
0
0
1
0
0
0
1
1
2
1
0
0
0
0
0
1
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
6
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
4
0
0
3
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
1
0
0
2
2
0
2
1
2
3
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
2
2
0
0
0
0
2
2
0
0
0
1
0
2
0
0
1
1
1
0
0
2
1
1
0
2
0
0
0
1
0
0
1
1
4
0
2
0
2
4
0
2
0
0
2
0
1
0
0
0
0
2
0
2
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
3
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
2
0
0
0
0
0
2
0
3
0
0
0
0
0
1
0
0
0
0
0
6
0
1
0
1
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
4
0
0
0
2
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
1
0
2
0
0
0
0
0
2
0
0
0
2
0
2
2
0
0
0
0
0
1
2
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
1
0
0
1
0
0
0
0
2
0
3
1
0
1
3
1
0
0
2
1
0
0
2
0
3
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
5
0
0
4
0
1
0
1
1
0
0
1
1
0
0
0
2
1
2
1
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
2
0
0
0
0
2
1
1
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
1
1
0
3
0
0
0
0
0
0
1
1
1
0
0
0
0
0
2
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
1
2
1
2
0
0
0
0
1
0
1
0
1
2
0
1
0
0
0
0
0
2
0
0
0
2
2
0
0
0
1
0
2
2
0
2
0
0
2
0
0
0
0
0
0
0
0
3
1
0
3
0
1
1
0
0
0
1
0
0
0
1
0
0
0
4
1
0
0
2
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
1
8
0
0
1
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
1
2
1
0
1
0
3
0
0
1
0
2
2
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
3
0
0
0
2
0
0
0
1
3
0
1
2
0
1
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
2
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
1
0
3
0
1
0
0
0
0
2
0
0
0
1
1
0
0
2
0
3
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
2
0
0
0
1
0
0
0
0
0
0
3
0
0
0
2
1
0
0
0
1
2
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
1
2
0
1
2
0
0
0
2
0
1
0
5
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
3
1
2
0
0
2
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
2
2
2
1
0
2
1
2
0
0
0
0
0
3
1
0
2
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
2
3
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
1
1
1
0
2
2
0
2
1
0
2
0
0
0
2
0
0
0
0
0
1
0
1
0
1
1
0
0
2
0
0
0
1
1
0
0
0
1
1
0
0
0
1
1
0
1
2
2
0
0
0
2
0
0
1
0
1
0
0
0
1
0
1
1
0
1
0
2
0
0
0
0
2
2
4
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
2
2
1
0
0
0
0
0
0
1
1
0
1
2
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
2
2
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
3
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
3
1
0
0
0
2
1
2
1
0
0
1
1
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
1
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
1
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
1
0
1
0
2
1
0
1
1
0
0
0
1
0
3
0
1
0
0
0
0
0
0
3
0
0
0
0
2
0
1
0
0
1
0
0
0
1
1
0
0
2
0
1
1
0
2
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
1
2
2
1
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
2
0
0
2
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
11
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
1
3
0
1
0
0
0
2
0
2
0
0
0
1
0
1
4
0
0
0
2
0
1
0
0
1
0
0
0
0
0
1
1
2
0
0
2
1
1
0
2
2
0
0
1
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
6
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
3
2
0
4
1
1
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
1
2
2
0
2
1
0
2
0
1
1
1
0
0
2
0
1
0
0
0
2
2
0
0
2
0
1
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
2
2
0
2
0
0
0
0
2
0
0
3
1
0
2
0
1
0
0
2
0
1
2
0
0
2
0
0
0
2
0
1
0
0
0
0
0
2
2
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
1
1
0
0
0
2
0
0
0
2
2
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
2
3
2
0
2
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
2
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
2
0
2
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
2
0
1
2
0
0
4
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
2
0
2
1
0
1
2
0
2
0
0
0
0
0
1
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
1
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
1
4
0
2
0
0
0
2
2
0
1
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
2
0
1
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
2
3
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
1
0
2
1
0
0
0
0
1
0
0
0
0
1
0
2
1
0
0
0
0
1
0
0
2
0
2
0
0
0
0
2
1
0
0
0
0
1
0
0
1
0
2
3
2
2
1
0
0
0
0
0
2
0
1
0
0
2
0
0
2
1
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
2
0
2
0
0
0
1
0
1
0
0
2
0
1
0
2
0
2
0
0
0
2
0
2
0
0
0
1
0
0
1
0
0
0
0
1
0
3
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
1
1
2
0
1
1
0
2
0
0
0
0
1
0
1
0
0
0
0
3
0
1
0
0
2
0
0
0
2
0
3
0
0
0
2
0
0
0
0
1
1
0
0
0
0
1
2
0
0
0
0
2
2
2
0
2
0
0
1
0
1
1
2
7
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
3
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
2
0
0
1
0
1
2
0
0
1
2
0
0
1
2
0
0
2
0
3
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
3
2
0
0
0
0
0
2
2
2
2
0
0
0
0
0
2
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
3
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
2
1
0
0
0
3
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
1
1
2
0
0
0
3
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
1
0
0
0
0
1
1
1
0
0
4
0
0
0
2
0
0
2
0
0
0
0
0
1
1
0
0
0
2
1
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
1
2
0
2
0
1
2
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
3
1
0
0
4
3
0
0
2
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
5
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
1
1
0
3
0
0
0
0
0
0
0
1
0
0
2
0
1
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
1
0
1
2
1
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
2
2
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
3
0
1
2
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
2
0
1
0
0
1
2
0
0
1
0
0
0
1
0
0
0
0
2
0
1
3
0
1
0
0
2
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
2
1
2
0
0
0
0
1
3
0
2
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
1
1
0
1
0
0
0
1
0
0
2
1
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
3
0
0
0
2
2
2
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
1
0
0
2
0
0
1
0
0
1
1
0
0
3
0
2
0
2
2
2
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
1
0
0
2
1
0
0
0
0
0
0
2
2
2
1
0
0
0
0
1
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
2
0
0
0
0
0
0
2
1
1
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
2
2
3
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
2
0
2
2
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
2
0
4
1
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
4
0
1
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
3
0
2
0
0
0
0
2
1
0
1
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
2
0
2
1
0
0
0
0
1
2
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
3
2
2
0
2
0
0
1
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
2
0
3
0
1
0
0
0
0
1
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
1
1
1
2
1
1
2
2
1
1
0
1
3
0
1
0
0
0
2
2
0
0
0
0
2
0
0
1
0
2
1
0
0
0
2
1
2
0
2
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
4
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
2
0
4
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
4
0
2
0
0
1
1
0
0
0
4
1
3
0
1
2
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
3
1
0
1
0
2
0
0
2
0
2
0
2
2
1
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
1
0
1
0
2
1
0
0
2
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
2
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
7
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
2
1
3
0
0
0
0
1
0
0
1
0
0
0
2
0
0
2
0
0
0
0
1
2
0
0
0
1
0
0
0
2
2
2
0
2
3
0
0
0
0
0
1
0
0
0
1
1
0
2
0
2
0
1
3
0
3
1
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
1
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
2
2
0
0
2
0
2
0
0
1
0
2
0
0
0
2
1
0
0
1
2
0
3
2
0
0
0
1
2
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
1
0
2
0
0
0
0
0
0
0
4
0
2
0
3
0
0
0
1
1
2
0
0
0
0
0
0
0
0
2
2
0
0
0
2
2
0
0
0
2
0
1
0
0
0
2
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
3
2
2
0
0
1
0
0
0
0
0
0
1
0
0
1
0
2
0
1
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
2
0
1
0
1
1
2
0
0
0
1
0
1
0
0
1
0
2
0
3
0
3
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
3
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
2
2
0
0
0
2
0
0
2
3
1
0
2
1
1
0
0
0
0
0
1
2
0
0
1
2
0
1
1
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
2
0
1
0
1
2
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
2
1
0
3
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
2
0
2
0
0
1
1
0
1
2
0
0
0
3
0
0
0
2
0
0
0
2
0
2
0
1
2
0
1
0
2
0
2
0
1
0
0
0
0
2
0
2
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
2
2
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
2
0
2
0
0
1
0
0
0
2
2
0
2
0
2
2
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
3
3
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
1
0
0
0
0
1
0
2
0
2
0
0
0
0
0
1
0
1
1
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
3
3
0
4
1
1
0
0
0
1
1
0
1
0
0
0
0
2
0
0
0
2
1
0
0
0
2
0
0
0
0
0
2
2
2
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
1
0
1
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
3
2
0
0
2
0
1
0
2
0
0
3
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
1
2
0
1
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
1
1
1
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
2
0
2
0
2
0
2
0
0
0
0
0
0
2
2
0
2
2
2
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
1
0
1
2
0
2
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
1
0
0
0
3
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
1
0
0
2
0
0
0
1
0
0
0
0
1
2
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
3
0
0
0
2
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
2
0
0
1
2
0
0
1
1
1
0
0
1
0
0
0
0
0
0
1
0
2
0
4
0
0
0
0
0
1
0
0
0
1
0
1
0
2
0
1
0
0
0
0
2
0
3
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
2
0
0
2
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
2
1
0
0
2
2
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
2
1
0
0
1
2
0
1
0
0
0
0
5
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
3
0
1
2
0
0
0
0
2
2
1
2
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
2
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
2
1
0
2
0
0
0
0
1
2
1
2
0
0
0
0
1
0
0
2
3
0
0
0
0
0
1
2
0
0
0
2
2
1
0
0
1
0
0
0
0
5
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
2
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
3
0
1
0
0
2
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
2
1
0
0
0
0
2
0
0
2
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
1
0
1
2
2
1
0
0
0
0
0
1
4
0
0
1
0
0
0
0
2
0
0
1
0
0
0
2
1
4
0
0
0
0
2
0
0
0
0
0
0
2
1
1
0
0
1
0
0
1
3
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
2
0
0
1
0
0
4
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
1
0
1
2
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
1
2
0
2
0
1
0
2
0
2
0
0
1
1
0
2
0
0
0
0
0
2
0
2
1
2
1
0
0
2
0
0
1
2
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
1
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
4
0
0
4
0
2
0
0
2
0
0
2
0
0
0
2
0
1
3
0
0
0
0
0
1
0
0
3
1
0
0
0
2
2
0
1
0
0
0
2
2
0
2
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
2
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
3
2
1
0
0
0
1
0
1
0
2
2
0
2
1
0
1
2
0
0
1
2
0
0
2
0
0
1
0
0
2
0
0
0
1
0
2
0
0
0
0
0
1
2
0
1
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
2
0
1
0
2
0
0
1
0
0
2
1
2
0
0
0
1
0
0
3
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
3
0
0
1
0
0
1
0
3
0
0
0
0
2
3
0
0
1
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
1
0
0
0
0
0
1
0
2
0
3
0
0
0
0
0
2
0
0
1
1
0
0
0
0
2
2
2
0
0
1
0
0
1
0
0
1
0
0
0
2
0
1
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
1
3
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
2
0
0
1
1
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
2
0
0
0
1
2
1
1
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
2
3
0
1
0
2
2
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
1
0
1
2
0
0
0
0
2
0
0
1
0
2
1
0
0
0
1
1
0
2
2
1
0
0
3
0
1
7
2
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
1
0
0
1
0
0
0
1
0
2
2
0
0
2
0
0
0
3
0
1
1
1
0
0
0
0
0
0
2
1
2
0
0
2
0
2
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
2
0
2
2
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
1
0
3
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
1
1
1
0
0
0
0
0
1
0
0
1
0
2
0
1
0
0
2
3
2
0
0
0
0
0
0
2
1
0
0
0
0
0
2
1
2
2
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
1
1
0
0
0
3
0
2
1
0
0
0
1
2
0
1
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
1
0
2
2
0
2
1
1
1
0
0
1
0
0
0
0
0
2
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
4
0
2
1
0
0
2
0
0
0
2
0
0
1
0
0
2
2
0
0
0
0
1
0
0
0
0
2
1
0
0
0
2
0
2
1
0
1
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
1
2
1
2
2
0
0
0
2
0
1
0
1
2
1
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
1
0
2
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
1
1
0
0
1
0
0
1
0
0
0
2
0
1
0
0
1
0
0
0
1
0
2
1
0
0
2
2
0
0
0
0
1
0
2
0
0
1
1
1
2
0
0
1
2
1
0
0
0
0
0
0
2
0
1
2
0
1
2
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
1
0
0
0
1
0
1
0
0
0
2
5
0
0
0
2
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
2
0
0
0
0
0
2
0
3
0
0
0
0
0
0
2
0
1
0
0
0
1
2
0
0
0
0
0
0
3
0
0
0
0
0
2
2
0
2
13
0
1
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
1
2
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
4
3
1
2
0
0
0
0
0
1
0
0
2
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
1
1
0
0
0
1
2
0
0
0
0
0
4
8
0
0
2
0
0
4
2
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
1
2
0
1
1
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
1
4
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
3
0
0
1
1
2
0
0
0
0
0
0
0
0
0
1
0
2
2
0
1
0
0
2
0
1
0
1
1
0
0
0
0
0
0
0
1
1
3
4
0
1
2
0
1
1
1
2
1
1
0
0
2
1
2
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
2
0
2
9
0
2
0
0
0
0
1
0
2
0
1
0
0
1
0
2
0
1
3
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
1
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
1
1
0
0
2
0
2
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
1
0
0
0
2
1
0
0
2
0
2
0
2
0
1
0
0
2
2
1
0
2
0
0
2
0
0
2
0
2
0
2
0
0
0
0
1
0
1
2
0
0
1
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
1
0
0
3
1
0
0
0
0
0
2
2
0
3
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
2
2
0
0
0
0
0
2
1
0
1
1
0
2
0
1
0
0
0
1
2
0
0
0
0
1
0
0
0
0
1
3
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
1
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
1
0
0
2
1
2
0
1
0
3
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
2
1
0
0
0
0
0
2
1
1
0
2
0
0
0
2
0
0
0
0
1
1
0
2
0
2
2
2
2
0
1
0
0
1
2
0
0
0
0
2
1
0
2
2
0
0
0
2
0
0
0
4
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
1
2
0
0
0
0
0
4
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
1
0
0
4
1
2
0
0
2
0
1
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
1
2
1
0
3
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
4
0
1
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
2
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
2
1
2
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
5
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
3
0
0
0
2
0
0
0
0
0
5
1
0
0
0
0
1
0
0
1
0
3
2
0
0
2
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
6
2
2
0
0
0
8
0
0
0
0
0
0
0
2
1
3
0
0
0
0
2
0
0
0
1
1
2
3
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
1
2
0
1
0
0
0
0
0
0
2
0
1
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
2
2
2
2
0
1
1
0
1
0
1
0
0
0
0
2
0
0
2
0
0
0
0
1
0
2
2
1
0
2
0
1
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
1
2
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
2
1
0
2
0
0
0
2
0
2
1
0
0
1
1
0
0
0
2
1
0
0
0
0
1
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
6
1
1
0
1
1
1
0
1
0
2
1
0
0
0
2
0
0
0
2
1
0
0
2
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
2
0
0
2
0
2
0
0
2
0
0
0
0
1
2
0
0
1
2
0
0
0
0
5
2
0
2
0
2
0
0
2
2
2
3
0
3
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
2
0
2
0
0
3
1
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
1
1
0
0
0
1
0
0
2
2
0
0
1
1
0
2
0
2
2
1
0
2
0
1
0
5
0
2
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
2
1
0
2
2
0
2
0
1
0
1
0
0
0
2
0
0
1
1
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
2
0
0
0
2
0
1
4
2
0
0
0
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
1
2
0
2
2
0
1
2
2
0
0
0
0
3
1
1
0
2
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
1
3
0
0
0
0
0
0
0
1
1
1
0
0
0
0
2
0
2
0
0
0
0
2
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
1
2
1
1
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
1
2
1
0
0
0
0
1
1
1
3
0
0
0
1
0
0
0
0
2
0
0
2
2
0
0
2
0
0
4
0
0
1
0
2
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
2
1
0
0
1
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
5
0
0
0
1
2
0
0
2
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
2
2
0
2
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
2
1
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
3
0
0
0
0
0
0
1
0
2
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
1
0
2
0
0
1
0
1
0
0
1
1
1
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
2
0
0
1
0
1
0
1
1
2
1
1
1
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
3
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
2
0
0
0
0
1
1
0
0
0
0
1
0
0
2
1
0
0
0
1
1
0
0
1
6
0
0
1
0
0
3
2
0
1
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
2
0
3
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
2
0
1
0
2
0
0
0
2
1
2
0
0
1
2
2
2
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
2
1
0
1
2
0
0
0
0
0
0
1
0
1
1
0
2
0
0
0
2
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
1
0
0
0
0
0
2
3
0
2
0
0
1
0
0
2
0
0
0
0
0
1
0
2
2
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
2
0
0
1
0
0
0
2
1
0
2
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
2
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
2
0
0
2
0
0
0
0
0
0
3
0
2
1
0
0
0
0
0
0
0
2
2
0
1
0
2
2
0
0
0
1
0
2
0
2
0
0
0
5
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
2
0
0
1
0
0
1
0
0
0
3
0
2
0
0
0
0
0
0
1
0
0
1
2
1
0
2
2
0
0
0
0
1
1
0
0
0
0
0
3
0
0
0
4
2
0
2
0
0
0
0
2
0
1
2
5
0
0
1
0
2
0
7
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
2
0
2
2
2
1
2
1
0
0
3
1
0
0
0
0
0
0
2
0
2
2
1
0
1
0
0
0
2
0
0
0
0
0
2
1
0
2
0
1
2
2
0
0
2
0
0
2
1
0
0
0
2
3
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
1
0
2
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
2
2
1
0
0
1
2
0
0
1
0
0
0
0
2
0
2
0
0
0
2
1
3
0
0
0
2
1
0
0
1
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
1
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
1
0
2
1
1
2
0
0
0
0
0
1
1
1
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
1
0
0
2
0
1
1
0
0
0
0
0
0
0
2
1
1
0
2
0
2
0
2
1
0
0
0
2
0
2
1
1
0
0
0
0
0
0
0
3
1
0
0
0
0
2
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
2
2
0
4
2
0
2
0
0
2
0
2
0
0
0
0
1
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
1
3
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
2
2
1
1
0
0
1
0
0
2
0
1
2
3
0
0
0
2
0
1
0
0
2
2
1
0
0
2
0
1
0
0
0
0
0
1
2
0
2
2
0
0
0
0
0
3
0
0
1
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
2
0
2
0
1
0
1
0
0
0
2
0
0
1
2
2
5
0
2
2
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
1
0
1
0
0
1
2
1
1
0
0
0
1
0
0
0
0
0
4
0
2
0
0
0
0
1
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
2
2
6
0
0
0
0
2
3
0
0
0
0
0
0
0
1
0
0
1
0
2
3
0
1
0
0
1
0
0
0
0
1
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
2
2
2
0
0
1
0
0
0
2
0
1
2
0
0
0
0
0
1
0
0
2
2
0
1
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
5
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
2
2
0
1
0
2
0
0
0
6
2
2
0
0
1
1
0
0
2
0
2
1
2
0
0
0
0
1
0
0
0
0
0
0
4
0
0
2
0
1
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
1
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
1
0
0
2
0
2
0
1
0
2
0
1
0
0
2
0
0
0
1
0
1
2
0
0
0
0
1
1
0
0
0
0
2
0
0
2
0
1
0
1
1
0
0
0
0
0
0
2
2
0
0
0
0
1
0
1
0
0
0
2
2
1
1
2
0
0
0
0
0
0
0
4
0
1
1
0
0
0
0
1
2
0
1
0
0
2
3
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
1
0
2
1
0
0
0
0
1
2
2
1
0
0
0
1
1
2
0
0
1
0
0
0
1
2
1
3
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
1
1
0
0
1
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
3
0
0
11
0
0
0
0
1
2
3
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
3
0
0
0
2
2
0
0
0
2
0
0
1
0
0
2
1
0
2
0
2
0
0
0
0
1
0
0
0
1
1
0
0
0
2
1
0
0
0
2
1
0
2
1
0
0
0
1
1
0
0
2
0
1
2
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
1
2
3
0
0
0
2
2
0
0
0
2
0
0
0
1
3
0
2
2
0
2
0
2
0
0
0
0
2
0
0
0
0
1
2
0
1
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
1
2
0
2
2
0
0
0
0
1
2
0
0
0
0
1
0
0
0
2
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
1
2
0
0
0
0
1
0
0
2
0
0
0
0
1
2
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
1
0
1
2
0
0
0
1
0
2
2
0
0
1
1
0
3
2
0
0
0
0
1
0
0
0
1
0
1
0
1
0
2
0
2
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
1
0
2
2
0
0
1
0
0
2
0
0
0
0
5
1
0
1
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
1
0
0
4
0
1
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
2
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
2
0
2
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
2
0
2
2
0
0
0
0
2
0
0
1
0
0
1
0
1
2
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
3
0
1
1
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
3
2
0
0
0
0
0
0
1
0
0
0
0
1
0
2
1
1
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
3
1
0
0
1
0
1
2
0
0
3
0
0
0
0
3
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
2
1
0
2
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
2
0
3
0
0
2
2
0
0
0
0
1
0
1
2
0
1
0
0
3
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
1
1
0
1
0
0
0
2
2
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
2
0
0
0
0
0
0
0
0
2
2
2
0
0
0
1
1
0
2
0
0
1
0
0
0
0
1
0
0
2
0
0
3
0
0
0
2
1
0
0
0
0
0
0
0
1
2
1
0
0
2
0
2
0
0
0
1
0
0
1
0
0
1
2
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
1
3
1
0
0
0
0
0
2
0
0
0
0
2
4
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
1
2
0
2
3
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
2
2
0
2
0
0
0
0
0
0
0
1
0
1
0
2
0
0
1
2
0
0
0
1
1
0
0
0
3
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
2
0
0
0
2
0
0
0
0
1
2
0
0
2
3
1
0
1
2
0
0
1
0
2
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
2
0
2
0
1
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
5
0
0
0
1
0
2
1
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
3
0
2
0
0
0
1
0
3
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
4
4
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
1
0
0
1
0
0
1
1
0
1
0
1
0
0
2
0
2
2
2
0
1
0
0
0
2
2
1
0
2
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
1
1
0
2
1
0
2
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
3
1
0
0
0
0
0
2
2
2
0
0
0
2
0
2
0
1
0
2
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
2
0
0
0
0
1
0
1
2
1
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
2
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
2
0
2
1
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
1
2
0
1
0
0
0
9
2
2
0
0
0
0
0
0
0
0
2
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
1
0
2
0
0
1
1
2
2
2
0
0
1
2
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
1
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
3
1
2
0
1
4
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
2
0
0
1
0
0
0
0
0
0
4
2
1
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
1
0
1
0
0
0
1
2
0
0
2
1
1
0
0
0
1
1
2
0
0
0
0
0
2
0
0
0
2
1
0
0
0
2
0
0
0
0
1
3
0
3
1
1
0
1
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
1
1
0
2
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
2
0
2
2
0
0
0
0
1
0
0
1
0
0
0
3
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
1
0
3
0
2
0
0
0
0
2
0
4
1
0
0
0
0
0
0
2
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
2
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
4
0
2
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
2
0
0
2
2
0
0
0
1
0
0
0
0
0
2
2
5
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
3
0
0
2
0
1
0
0
0
0
1
0
2
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
2
0
1
3
1
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
1
1
1
1
0
0
1
2
0
0
0
3
0
0
0
2
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
2
1
1
0
0
2
2
1
0
2
0
0
0
0
1
0
2
0
0
1
0
0
2
0
0
2
1
0
0
2
0
0
2
1
3
1
0
2
2
0
1
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
1
0
0
3
0
0
0
1
0
0
2
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
1
0
0
0
2
1
0
2
2
0
0
0
0
0
0
1
3
0
0
3
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
2
1
0
1
1
0
0
1
0
2
2
0
2
0
0
0
1
0
0
2
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
2
1
2
0
0
0
0
0
0
2
0
1
2
0
0
0
1
0
1
1
0
2
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
16
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
1
0
0
1
0
3
0
1
0
0
0
0
0
2
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
3
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
2
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
4
2
1
1
0
2
0
1
0
0
0
1
0
0
0
2
2
2
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
2
2
0
4
0
2
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
2
1
0
2
0
0
0
0
1
0
0
0
0
2
2
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
1
1
2
0
2
0
0
0
2
0
0
0
1
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
3
0
0
0
1
0
0
7
1
0
0
0
0
0
0
1
3
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
1
1
0
0
13
0
2
0
1
0
1
2
0
2
0
0
0
0
0
0
1
1
0
2
1
2
0
2
0
4
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
2
0
3
0
0
1
1
0
0
0
1
0
0
2
2
0
0
0
0
2
0
1
0
0
2
0
0
1
0
2
0
0
0
2
2
2
1
0
0
3
0
2
1
0
0
0
0
1
2
2
0
1
0
0
0
0
0
0
0
1
1
0
1
0
1
2
0
2
0
0
0
0
2
2
0
0
3
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
2
0
2
2
0
0
0
0
1
1
0
1
0
0
0
1
0
0
2
0
0
0
3
2
1
0
0
0
1
0
0
1
1
0
0
1
2
0
0
1
0
0
2
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
2
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
1
2
1
1
1
0
0
2
0
0
0
0
0
0
0
0
1
3
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
2
0
0
0
1
0
2
0
2
0
0
1
2
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
3
0
1
0
1
2
14
0
0
0
1
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
1
2
0
0
0
0
2
0
1
2
1
0
1
3
0
0
1
0
0
0
0
0
0
2
0
1
0
1
0
1
0
0
2
1
0
2
0
0
2
0
1
1
2
1
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
1
0
0
0
0
0
2
0
2
0
0
1
1
0
0
2
0
2
0
0
1
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
2
1
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
2
1
2
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
2
2
0
2
1
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
1
0
0
2
0
1
0
0
1
1
0
1
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
2
1
1
1
2
4
1
0
0
1
4
0
1
1
0
0
0
2
2
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
2
0
0
0
0
2
0
0
0
1
0
1
0
2
0
0
0
0
1
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
2
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
1
2
0
0
3
2
0
0
0
0
0
1
3
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
1
2
0
0
0
2
0
0
0
2
0
0
1
0
2
1
0
2
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
2
0
2
2
0
1
1
2
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
1
0
1
2
1
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
2
0
1
1
0
0
0
0
2
0
0
0
0
3
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
1
1
0
0
1
0
0
1
1
0
1
0
0
0
1
0
0
1
2
1
0
0
2
0
4
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
1
1
1
2
1
0
0
0
0
0
0
2
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
3
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
3
1
0
1
0
2
0
0
0
0
0
0
0
2
2
0
1
0
0
0
2
0
1
0
0
0
0
1
1
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
1
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
2
0
0
1
0
0
1
0
0
2
2
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
2
0
0
2
1
1
1
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
2
0
0
0
2
1
1
0
0
1
0
1
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
4
0
0
0
0
0
2
3
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
4
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
1
1
2
0
0
0
0
0
0
1
2
2
2
0
2
0
1
2
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
7
0
0
0
0
0
2
0
2
1
0
0
0
2
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
1
0
2
0
2
0
0
1
2
0
0
2
2
0
0
1
0
0
0
0
0
0
8
0
2
0
0
1
0
0
0
0
2
0
2
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
2
2
3
0
0
0
0
2
0
1
0
0
0
0
0
0
2
1
2
2
0
0
2
0
0
0
2
1
2
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
1
2
0
1
0
1
0
0
0
2
0
0
0
0
0
0
2
1
0
0
1
0
0
2
0
0
1
2
0
0
0
0
0
0
0
2
0
4
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
5
0
0
1
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
1
1
1
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
2
0
2
0
0
2
3
1
0
2
0
0
0
2
2
0
0
0
1
0
0
0
1
2
1
2
0
0
0
1
2
1
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
2
1
0
1
0
0
1
0
0
2
3
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
3
0
0
2
0
0
0
0
0
2
0
1
1
0
0
1
0
2
3
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
2
0
0
0
2
0
2
2
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
2
2
0
3
2
0
0
0
2
0
0
0
0
0
2
0
0
4
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
1
0
0
1
2
2
2
0
0
0
0
0
1
0
2
2
2
0
0
0
1
0
0
0
0
1
2
1
0
0
0
2
1
0
2
0
0
1
0
0
0
0
0
1
0
1
1
0
3
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
1
0
2
0
1
0
1
0
2
2
0
2
1
2
0
0
0
0
0
0
0
1
0
4
0
0
0
2
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
3
0
0
0
1
0
0
0
0
1
2
1
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
1
0
1
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
3
2
0
0
0
1
2
1
0
0
1
0
1
0
2
0
0
0
0
0
0
0
2
1
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
1
0
1
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
1
1
0
1
0
2
0
2
1
0
0
0
0
0
0
0
0
2
3
1
0
0
0
0
0
0
1
0
0
0
1
0
0
3
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
2
1
1
1
0
0
0
0
0
1
2
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
1
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
4
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
2
0
0
0
2
0
0
2
3
0
0
1
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
2
0
0
0
0
0
0
0
1
0
1
0
0
2
0
2
2
0
0
1
2
0
1
1
0
1
1
3
0
0
2
0
0
0
0
0
3
0
0
2
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
2
2
1
0
2
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
1
2
0
0
0
0
1
0
0
0
0
0
1
0
0
1
3
0
3
0
0
2
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
2
1
2
2
0
0
0
1
2
0
2
0
1
0
0
0
0
9
2
0
2
1
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
3
1
2
2
0
1
0
0
0
2
2
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
1
1
1
2
2
0
0
0
0
0
0
0
0
0
1
2
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
2
2
0
0
0
0
0
0
2
0
2
2
1
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
3
0
1
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
2
1
0
2
2
0
0
0
1
1
0
0
0
2
2
0
0
0
0
1
0
0
1
2
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
1
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
1
0
0
1
2
0
2
1
0
1
0
0
1
0
0
0
2
0
0
2
0
0
0
1
2
0
0
0
0
2
0
1
0
0
1
0
1
1
2
0
0
0
1
0
0
2
0
1
0
0
0
0
2
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
1
2
0
0
1
1
2
0
0
0
0
0
1
0
0
0
0
0
1
1
2
0
0
1
0
0
0
0
0
3
0
0
0
0
2
0
0
0
2
3
1
1
0
3
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
1
0
0
1
0
0
3
1
4
2
0
1
2
1
0
1
0
0
2
1
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
2
1
2
0
0
2
0
1
0
2
0
0
0
0
1
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
2
1
0
0
0
1
1
2
0
0
2
2
1
0
2
0
3
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
2
1
1
0
0
0
1
0
2
0
0
4
0
0
0
2
0
0
0
3
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
1
0
0
0
0
0
1
0
0
1
2
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
2
1
3
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
3
0
0
0
0
0
1
0
0
0
1
0
2
0
1
1
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
1
0
2
0
2
0
2
0
2
1
0
0
0
3
0
1
0
2
0
0
0
0
0
1
0
4
0
0
2
0
1
0
0
0
0
1
0
0
2
2
0
1
0
0
0
0
0
2
2
0
1
1
0
0
3
0
1
0
0
0
2
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
1
0
0
3
0
0
0
0
1
0
1
1
0
0
2
0
0
1
1
0
0
0
0
2
0
0
1
0
1
0
1
1
0
2
0
2
2
0
0
0
1
2
0
0
0
4
0
0
0
0
0
0
0
2
1
1
1
0
0
1
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
4
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
3
0
0
0
0
1
2
0
2
0
2
1
1
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
6
1
2
0
0
1
0
0
0
0
0
2
0
0
0
1
0
2
1
2
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
2
2
0
2
0
6
0
0
0
1
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
2
0
0
0
0
2
1
5
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
2
2
1
3
2
0
0
0
0
1
2
1
2
0
2
0
0
1
0
0
0
0
0
0
1
2
0
1
0
0
0
2
1
0
1
0
4
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
2
0
0
0
0
1
0
0
1
3
2
0
2
0
0
0
0
1
3
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
2
2
0
0
2
0
0
0
2
0
1
0
0
2
2
0
0
0
0
0
0
1
0
0
2
1
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
2
1
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
2
0
0
0
1
0
0
0
1
1
0
1
1
0
2
0
0
0
2
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
1
2
0
2
1
0
0
1
1
1
0
0
0
3
0
0
0
0
0
1
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
1
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
2
0
0
1
0
1
0
0
3
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
2
3
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
3
0
0
0
2
0
2
0
0
2
1
0
1
0
0
0
0
0
3
2
0
1
0
2
1
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
1
0
0
0
0
1
1
0
2
2
2
0
0
0
1
0
0
0
0
1
0
0
1
2
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
2
0
2
0
0
1
2
0
2
0
0
0
0
0
0
0
0
2
0
2
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
1
2
1
0
0
0
0
2
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
1
0
0
0
0
0
2
0
2
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
1
0
1
0
2
2
2
0
1
1
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
3
2
0
0
0
1
1
0
4
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
2
0
1
0
1
0
3
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
2
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
1
0
0
0
0
0
0
3
2
2
0
0
0
0
0
3
0
0
1
0
0
0
2
0
0
0
3
1
0
2
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
2
0
1
2
0
0
1
2
2
0
0
0
0
0
0
0
0
0
2
2
0
2
1
0
1
0
0
3
2
0
0
0
0
2
0
0
0
0
0
0
5
1
0
0
2
2
0
0
1
0
0
0
1
0
2
0
2
1
0
0
2
0
2
2
0
0
0
0
2
0
0
0
2
0
0
1
0
0
2
2
0
0
0
0
0
1
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
4
0
0
0
0
2
0
1
0
2
0
2
0
0
0
1
0
0
2
3
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
2
0
1
2
0
0
1
0
0
0
0
0
2
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
7
0
0
1
1
0
2
0
0
0
2
2
0
0
2
0
0
1
1
0
0
0
2
0
0
0
2
0
2
2
2
0
1
2
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
3
0
1
0
0
0
0
0
2
0
0
2
11
0
0
1
2
0
2
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
3
1
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
2
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
5
2
0
1
0
1
0
2
0
2
1
0
1
3
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
1
1
2
0
0
2
2
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
3
0
0
1
0
1
1
0
1
0
0
1
0
0
0
0
1
2
0
2
0
3
2
2
2
0
2
2
0
0
0
0
0
2
2
0
2
1
0
0
1
0
0
0
1
0
0
0
0
0
0
2
1
2
1
0
0
2
1
0
1
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
3
0
0
1
0
2
0
0
0
1
1
0
0
0
0
1
1
0
0
1
0
0
0
2
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
2
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
2
2
0
9
0
0
0
2
1
1
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
4
0
1
2
0
0
0
1
0
1
0
2
0
0
0
0
2
0
0
2
1
0
2
0
2
4
0
0
0
0
0
2
1
0
0
0
0
1
2
0
0
0
0
1
1
1
0
2
0
0
1
2
0
0
0
1
0
0
2
0
0
0
0
1
0
0
2
0
2
0
0
0
1
1
1
0
1
0
0
0
1
2
0
0
1
0
0
0
0
0
2
0
0
0
3
1
0
0
0
0
0
0
4
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
2
2
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
4
0
0
0
0
1
1
0
2
0
1
2
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
2
0
1
2
0
0
0
0
2
2
0
0
0
0
2
2
0
2
0
1
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
1
0
0
0
0
1
1
0
1
1
2
1
1
0
10
1
1
0
2
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
2
1
1
0
0
0
0
0
1
0
0
0
0
2
0
3
1
0
2
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
3
0
0
0
1
1
2
0
2
1
0
0
2
0
0
2
0
2
0
2
0
1
2
0
0
0
0
2
0
0
0
0
0
0
2
1
0
2
2
1
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
1
1
0
2
2
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
2
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
1
0
3
2
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
1
1
0
0
2
0
1
0
0
0
2
0
2
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
3
0
2
2
1
0
0
0
2
0
0
0
0
4
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
3
1
1
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
2
0
0
2
2
0
1
0
0
0
1
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
1
0
2
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
2
0
0
0
1
0
2
0
0
1
0
0
2
2
0
0
0
0
0
0
2
3
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
2
1
0
0
0
2
0
0
1
0
0
0
2
2
0
0
0
0
0
0
2
1
0
0
1
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
1
1
0
2
0
2
0
3
0
0
0
0
0
3
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
1
2
0
2
0
0
4
1
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
3
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
2
2
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
2
0
0
0
0
1
0
0
1
0
1
0
3
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
2
1
0
2
1
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
1
3
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
1
2
0
0
4
0
0
0
0
2
0
1
0
0
1
1
1
0
0
0
0
0
1
0
0
0
2
0
1
1
1
0
0
0
1
1
1
0
0
0
2
0
0
0
0
0
1
5
2
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
2
1
0
1
0
0
3
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
1
0
2
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
5
2
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
2
2
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
2
0
0
1
0
0
1
0
0
0
2
1
1
2
1
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
1
2
0
0
0
0
2
0
0
1
0
2
0
0
0
0
1
0
1
0
2
0
0
3
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
1
2
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
1
2
0
1
2
2
0
1
2
0
0
0
0
0
0
2
0
0
0
2
1
0
2
0
0
0
2
0
0
0
0
0
2
0
0
3
2
0
2
2
0
0
2
0
0
1
1
0
0
0
2
0
0
1
1
2
0
2
1
2
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
3
1
0
1
0
2
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
1
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
4
3
0
0
2
2
2
1
0
0
0
0
0
0
0
2
0
0
2
2
1
4
0
1
0
1
0
0
0
5
0
0
0
0
1
1
1
3
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
2
0
0
0
1
0
0
2
1
0
0
0
2
0
1
0
0
1
2
0
0
0
0
0
2
1
1
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
3
0
0
0
3
0
1
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
2
1
0
1
1
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
4
0
0
0
0
1
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
3
0
2
0
1
1
1
0
0
1
2
2
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
1
0
0
3
0
0
0
0
0
2
2
0
0
1
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
2
1
2
0
0
1
0
2
0
13
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
2
3
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
2
0
0
0
2
1
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
2
0
0
0
1
2
0
0
2
0
2
0
0
2
0
1
1
0
0
0
0
0
0
0
1
2
0
0
0
3
1
1
0
0
0
0
2
0
0
2
2
1
0
2
0
2
0
2
1
0
0
2
1
0
0
1
0
2
0
0
2
2
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
5
3
0
0
0
1
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
2
4
0
0
0
1
2
0
0
0
0
1
0
2
0
0
0
0
0
2
0
1
0
0
1
2
0
0
0
0
1
0
0
0
0
0
2
1
2
1
1
0
4
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
2
0
0
0
2
0
0
5
0
1
0
0
0
2
1
3
2
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
1
0
0
1
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
5
0
1
0
0
2
0
0
2
0
3
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
2
0
0
0
1
0
0
1
1
0
0
0
0
0
1
1
0
2
0
0
0
1
0
0
0
1
0
1
0
0
0
0
2
0
2
1
2
2
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
3
0
0
0
0
0
2
2
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
2
0
0
2
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
6
2
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
1
0
3
0
0
0
0
0
0
2
0
0
1
1
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
6
0
4
0
0
0
0
1
0
2
2
1
2
2
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
1
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
4
0
0
0
0
0
2
0
0
0
1
2
0
0
1
2
0
0
2
0
0
4
0
0
1
0
2
0
2
0
0
2
1
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
1
2
0
0
0
0
2
0
1
1
1
0
0
2
0
0
0
0
2
0
2
1
2
1
0
1
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
2
2
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
1
0
0
1
0
3
0
1
0
0
1
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
1
1
0
2
1
3
0
1
2
1
0
0
0
0
0
0
1
0
0
0
0
4
2
0
2
0
2
0
0
0
0
0
2
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
5
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
2
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
1
1
1
2
0
3
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
1
1
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
1
1
0
0
2
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
1
0
1
2
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
2
0
0
2
0
2
0
0
0
1
0
2
0
1
0
0
0
0
0
0
4
2
0
0
0
0
0
0
2
0
1
0
0
1
1
0
0
0
1
3
0
0
0
2
0
1
2
1
1
0
1
1
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
9
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
2
1
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
2
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
2
0
0
0
0
2
0
0
0
1
0
0
1
0
0
1
1
0
0
2
0
1
0
0
0
1
0
0
1
2
1
0
0
0
1
0
4
0
0
0
1
1
1
0
1
0
1
0
0
0
0
1
0
0
2
0
0
2
0
2
1
0
1
0
0
0
2
0
0
0
0
2
0
2
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
3
1
2
1
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
1
0
0
5
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
2
0
0
1
0
0
2
0
0
0
0
1
0
1
3
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
2
0
0
2
1
1
0
0
0
0
1
0
0
0
0
2
2
0
2
0
2
1
2
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
3
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
2
4
0
0
0
0
0
1
1
1
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
2
0
2
0
0
2
0
2
0
2
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
1
0
0
0
2
2
0
0
0
2
0
0
1
0
0
0
0
2
0
1
0
0
1
4
2
0
0
2
0
0
0
0
2
2
2
1
1
0
0
0
0
2
0
0
0
1
2
0
0
0
0
1
0
2
0
0
2
0
0
0
0
2
2
0
1
1
2
0
2
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
3
0
0
2
0
1
0
3
0
3
0
2
1
1
0
0
0
0
2
2
0
1
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
3
0
2
0
1
0
0
0
0
0
1
1
0
0
0
0
3
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
4
2
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
3
0
0
2
0
0
0
0
2
0
0
0
0
0
1
1
0
0
5
1
0
0
1
0
3
0
0
2
0
0
0
0
3
1
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
1
0
0
5
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
1
2
0
1
2
0
0
0
2
0
0
0
0
2
0
3
0
0
0
0
0
0
0
2
8
2
0
0
0
2
0
1
0
3
0
0
0
0
0
0
0
3
1
1
0
2
0
0
2
0
0
2
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
2
0
1
0
2
1
0
3
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
3
0
0
0
0
0
0
0
3
2
0
2
0
1
0
2
0
1
0
2
1
0
2
2
0
2
1
0
0
0
0
0
0
0
3
0
0
2
1
2
2
0
0
0
0
0
2
0
0
2
0
0
3
1
0
0
0
2
0
0
0
1
0
0
2
0
1
0
1
2
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
2
2
0
2
1
0
1
0
2
0
0
0
0
3
0
2
0
0
0
0
2
0
0
4
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
2
1
0
0
0
0
0
2
2
0
0
0
0
2
2
0
0
2
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
1
2
4
1
3
0
0
0
0
1
1
0
2
0
0
2
0
0
1
3
0
2
2
0
0
0
1
2
0
2
0
1
0
0
0
2
0
0
0
2
1
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
2
2
0
0
1
0
0
0
0
0
2
1
0
0
1
0
0
1
0
3
1
1
1
0
0
2
0
1
0
0
1
2
0
0
0
0
2
0
2
0
0
0
0
1
1
2
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
2
2
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
2
0
0
1
0
1
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
2
0
0
0
0
0
0
0
2
2
0
0
0
0
2
1
2
1
0
1
0
0
0
2
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
1
9
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
1
1
2
0
2
0
0
0
1
1
1
0
1
0
0
1
2
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
2
0
0
1
0
0
1
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
2
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
6
0
0
3
1
0
0
0
3
0
0
2
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
1
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
1
2
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
1
0
0
0
2
1
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
2
0
0
0
2
0
0
0
2
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
3
0
2
0
2
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
1
0
0
2
0
1
3
0
0
0
0
0
2
4
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
2
2
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
2
2
0
0
0
1
0
2
0
0
2
0
0
0
0
3
1
0
0
1
0
0
0
1
0
2
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
2
2
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
1
1
0
1
0
1
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
2
0
2
0
2
0
0
0
0
2
1
2
0
0
3
0
0
2
2
0
0
2
0
0
0
3
0
0
1
1
0
1
0
1
1
2
1
1
0
0
0
0
0
1
1
2
0
0
2
0
1
1
0
2
0
5
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
2
6
0
0
0
0
0
3
0
0
0
0
1
0
0
2
3
0
1
2
1
1
0
1
0
0
0
0
0
1
2
2
0
0
3
0
0
0
2
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
1
0
0
0
1
0
2
0
2
2
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
2
1
0
0
0
2
0
0
0
0
0
0
1
2
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
1
0
3
0
0
0
0
0
0
0
0
0
2
0
0
3
0
1
0
0
0
0
0
1
2
0
0
1
0
0
1
0
0
0
2
0
0
0
2
2
0
0
1
0
3
0
0
0
0
0
0
2
0
0
0
1
0
0
2
1
0
0
0
2
1
1
1
2
1
2
0
2
2
2
0
0
0
0
1
2
1
2
3
1
0
0
2
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
4
0
0
0
2
0
0
2
2
0
0
0
0
0
2
0
0
1
3
0
0
1
1
0
0
0
2
1
0
0
0
0
0
3
0
5
0
0
0
0
1
1
0
0
1
0
3
0
0
1
0
0
0
0
1
0
1
4
0
0
0
0
0
0
0
3
0
0
2
0
0
0
2
0
0
2
0
1
2
0
0
0
2
1
1
1
2
0
1
1
1
0
0
2
4
2
2
0
0
0
0
0
0
2
2
1
0
0
3
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
1
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
3
0
0
0
0
0
0
0
0
1
2
0
0
4
0
0
3
0
2
0
2
2
1
0
1
0
1
3
0
0
0
0
0
0
3
0
1
2
1
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
1
0
2
1
1
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
10
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
3
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
2
0
0
3
2
0
0
0
0
1
0
2
1
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
2
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
2
0
1
2
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
2
0
0
0
2
0
2
0
0
0
0
1
0
1
0
4
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
1
2
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
6
0
0
0
2
0
2
2
0
2
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
8
0
0
2
2
0
1
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
1
0
0
0
1
0
7
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
4
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
2
0
1
0
1
2
1
0
4
0
0
0
0
2
0
0
1
1
0
0
1
0
0
2
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
1
3
0
1
0
0
1
0
1
2
0
2
0
1
2
0
0
0
0
0
2
1
2
0
3
0
1
1
0
0
2
2
1
2
2
2
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
2
1
0
1
2
2
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
2
0
0
0
1
0
0
0
1
2
0
0
0
0
1
0
2
1
1
0
0
1
2
1
0
2
0
0
0
2
1
0
0
0
2
0
2
0
0
0
0
1
0
0
1
0
2
1
1
1
2
0
0
2
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
4
0
0
0
0
1
0
0
2
0
2
0
1
1
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
1
2
1
0
1
0
2
0
1
0
0
0
2
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
1
0
2
0
2
0
1
0
3
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
1
0
0
0
1
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
2
0
2
2
0
0
0
0
2
0
0
0
1
1
0
1
1
0
0
0
0
0
2
0
0
1
0
1
1
0
0
0
0
0
0
0
0
2
3
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
2
3
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
2
0
2
0
2
2
0
4
2
0
5
0
0
0
0
0
0
2
0
1
2
1
0
1
1
1
2
0
0
2
0
0
1
0
0
2
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
1
1
0
0
0
2
0
2
0
0
0
0
1
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
1
0
1
0
0
0
0
1
2
1
0
1
0
0
2
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
2
1
0
0
1
2
1
0
1
1
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
4
0
0
0
0
0
0
0
0
3
1
1
0
0
0
0
0
1
2
0
0
5
0
4
0
1
0
0
2
0
0
0
0
0
2
0
1
0
0
1
2
0
0
1
1
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
3
0
1
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
1
1
0
0
2
0
0
0
1
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
4
0
0
1
0
0
0
0
0
1
0
0
2
0
0
1
2
0
1
0
2
0
0
1
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
2
0
0
0
6
0
2
2
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
2
0
0
1
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
2
0
1
0
0
0
1
0
0
0
2
0
2
3
2
0
1
0
0
1
2
0
1
0
2
0
0
0
0
2
1
0
0
0
2
0
1
0
0
0
0
1
3
0
3
0
1
0
0
2
2
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
2
0
0
0
0
3
0
0
0
0
2
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
2
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
3
1
0
0
1
0
3
0
0
0
2
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
2
1
0
0
1
2
1
0
0
0
6
0
2
2
0
0
0
4
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
2
0
1
2
0
1
0
0
0
0
0
0
0
1
0
3
0
0
1
0
0
0
0
0
0
2
1
0
3
1
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
3
0
0
0
1
1
0
3
0
0
0
2
2
1
2
2
0
1
1
0
0
0
0
2
1
3
3
4
2
0
0
0
0
0
5
1
0
0
1
2
1
2
0
0
0
0
2
0
0
4
0
0
1
0
0
7
0
1
0
1
0
0
0
0
0
0
0
0
4
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
2
1
1
0
0
0
0
0
0
2
0
1
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
1
2
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
2
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
2
0
0
0
1
2
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
1
3
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
2
0
0
1
0
0
0
0
0
1
2
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
1
4
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
1
0
0
0
4
3
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
2
0
0
0
1
2
0
1
0
0
0
2
2
0
2
0
0
1
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
2
0
0
1
0
3
0
0
1
1
0
2
1
2
0
0
0
1
0
0
0
0
0
0
0
2
0
2
1
2
3
4
2
0
0
0
0
1
0
0
1
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
2
1
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
4
1
2
0
0
0
1
2
1
0
0
2
0
2
0
3
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
1
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
2
1
0
0
0
0
0
0
2
1
0
1
0
0
1
0
0
0
0
0
0
3
2
0
0
2
0
0
2
0
0
2
0
2
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
2
0
2
1
2
0
0
0
2
1
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
1
0
0
2
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
2
0
0
3
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
1
4
0
2
0
0
0
0
0
0
0
2
2
0
2
1
0
1
2
0
0
1
0
0
2
0
1
0
1
2
1
0
0
2
0
1
1
0
0
0
0
1
1
0
0
0
0
0
2
1
1
2
2
1
0
0
0
0
1
0
0
3
2
1
0
0
0
0
0
1
0
0
2
0
1
1
0
0
0
2
2
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
8
2
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
3
0
2
2
0
0
0
0
2
0
1
0
0
1
2
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
2
0
1
0
0
0
1
1
0
0
1
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
1
0
0
1
0
1
0
2
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
2
2
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
3
0
1
0
0
0
3
1
0
0
2
0
2
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
1
2
0
0
1
0
0
0
0
2
0
0
3
0
0
2
0
2
2
2
0
0
0
0
0
2
2
0
0
2
2
1
0
0
0
0
1
0
0
0
1
2
0
0
0
0
1
1
0
1
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
1
2
0
3
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
2
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
2
1
2
1
0
0
1
1
1
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
1
0
2
2
0
0
5
2
2
0
0
0
1
0
0
0
0
1
2
0
0
1
0
3
0
0
0
1
0
0
0
1
0
1
0
0
0
2
2
2
1
0
0
0
0
1
0
0
2
2
0
0
0
0
1
0
1
0
2
0
2
0
1
0
0
0
0
0
0
1
0
7
2
2
0
2
0
0
0
4
0
0
0
2
3
1
2
2
0
1
1
0
0
0
1
0
0
0
0
0
0
9
0
0
0
0
0
0
1
0
0
2
0
0
2
1
0
3
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
1
1
0
4
0
2
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
2
1
1
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
1
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
2
2
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
1
4
0
0
0
1
1
0
0
0
1
0
0
0
1
0
2
0
0
2
0
1
0
0
0
2
0
2
0
0
0
0
0
1
0
0
3
1
0
1
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
1
1
0
2
0
0
0
0
1
0
2
0
0
0
2
2
2
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
3
1
2
1
0
0
0
0
2
1
2
1
0
1
0
0
0
1
0
2
1
0
0
2
0
1
1
3
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
2
0
0
0
0
1
2
0
0
2
0
1
0
4
1
1
1
1
0
0
0
2
0
2
2
3
1
0
1
0
0
1
2
1
0
0
0
0
0
1
2
0
0
3
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
3
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
1
3
0
2
0
0
2
1
4
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
2
0
0
0
0
2
0
1
0
0
1
0
0
1
0
0
2
0
0
0
4
0
0
2
2
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
3
1
0
0
0
0
0
3
0
2
0
0
1
1
0
0
0
0
1
1
2
1
0
1
0
0
0
0
0
0
0
0
1
0
0
4
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
2
1
1
0
0
0
3
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
3
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
3
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
2
0
1
0
0
0
0
2
0
0
1
0
0
0
0
3
0
0
0
1
0
0
0
1
2
0
2
0
0
0
2
1
1
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
2
0
2
0
0
2
0
1
0
0
2
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
1
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
2
0
1
1
2
0
0
1
0
1
0
1
0
0
0
0
1
2
0
0
0
0
0
0
2
2
0
0
2
0
1
0
2
1
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
1
1
0
0
0
0
2
0
0
0
0
1
2
0
0
2
0
2
0
3
1
0
0
0
2
0
1
0
2
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
2
0
1
0
2
0
0
0
0
1
2
0
0
3
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
2
3
0
0
0
1
0
0
1
0
0
2
0
2
2
2
0
0
2
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
2
2
0
1
2
2
0
0
0
0
2
0
1
1
1
1
0
0
0
0
0
0
1
0
0
1
3
0
0
0
0
0
0
3
3
1
2
0
0
0
0
2
0
1
0
0
2
0
2
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
3
0
0
0
0
1
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
4
0
2
0
0
0
0
0
1
1
0
2
2
0
0
0
2
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
2
1
1
0
2
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
1
1
0
7
0
0
0
0
3
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
3
0
0
0
1
1
1
0
1
0
0
0
2
0
0
2
0
1
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
2
1
0
0
0
1
1
0
0
0
2
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
2
0
2
0
0
1
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
3
0
2
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
1
0
2
0
0
0
1
2
0
0
0
2
1
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
2
0
2
2
0
5
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
3
0
0
0
0
1
0
0
0
3
1
2
1
0
5
2
0
0
1
2
0
2
1
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
2
0
3
0
1
2
0
2
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
1
2
2
1
0
0
0
0
0
0
0
3
1
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
5
0
0
0
1
1
1
0
0
0
0
0
0
1
0
2
0
2
1
0
0
1
2
0
0
1
0
0
0
0
0
0
0
3
2
0
2
2
0
1
1
0
0
2
1
0
0
0
0
0
0
0
3
1
0
0
3
1
0
2
1
1
1
0
2
0
0
0
0
0
1
1
3
0
0
1
1
1
0
1
0
1
0
0
0
2
0
2
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
1
2
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
1
0
2
0
1
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
2
1
1
0
2
0
0
0
0
1
1
0
2
0
3
2
0
0
0
0
0
0
0
0
3
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
2
0
0
0
2
2
1
0
0
0
0
4
0
2
1
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
3
1
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
2
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
3
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
3
0
0
0
0
0
0
2
2
0
1
1
0
0
2
2
0
2
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
2
0
0
2
2
0
0
16
2
0
0
0
0
0
2
2
1
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
3
0
1
1
0
2
1
0
0
1
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
2
2
0
0
1
1
1
0
0
0
3
0
0
2
0
0
2
1
0
1
0
1
0
0
0
3
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
1
1
1
1
1
1
0
0
0
0
0
3
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
3
0
0
1
0
2
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
2
0
2
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
1
2
0
0
3
1
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
2
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
2
1
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
1
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
2
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
1
0
0
2
0
0
2
0
1
2
1
0
1
2
1
0
1
1
1
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
3
0
2
1
0
0
0
0
1
1
2
1
0
1
2
0
0
1
2
2
0
0
4
0
1
2
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
1
0
0
0
2
2
0
0
1
1
2
1
2
1
1
0
0
0
0
0
0
10
0
0
0
2
5
0
0
0
1
0
0
1
2
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
1
2
0
0
1
0
0
0
2
0
0
0
0
0
0
2
2
0
0
2
1
1
2
0
0
0
0
0
1
1
3
0
0
0
0
2
0
0
0
1
2
1
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
2
0
0
0
0
2
0
3
1
0
0
0
1
2
0
0
0
0
0
0
0
0
1
2
1
0
0
2
0
1
0
0
0
0
0
0
2
2
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
1
0
1
0
0
1
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
1
2
0
1
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
1
2
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
1
0
3
0
2
0
0
0
0
0
1
0
0
0
1
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
1
2
0
0
0
2
0
0
2
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
3
0
0
0
2
0
2
12
0
4
0
0
1
0
1
1
1
0
0
0
0
1
1
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
2
0
1
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
2
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
1
0
2
0
2
0
0
0
0
0
0
1
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
2
0
1
2
0
0
0
0
0
2
2
2
0
1
2
0
0
0
0
1
0
2
0
1
0
2
0
0
0
2
0
0
2
2
0
0
2
0
2
0
0
0
2
1
0
0
0
0
0
1
0
1
0
0
2
1
0
0
0
2
3
0
1
0
1
1
0
1
0
1
0
0
0
0
0
2
0
0
1
0
1
0
0
1
0
0
1
2
1
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
3
0
0
1
1
0
0
0
2
2
0
1
0
2
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
1
0
2
2
2
0
0
0
0
0
0
0
0
0
0
2
0
2
1
2
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
2
0
1
2
2
0
0
2
2
0
2
0
2
2
0
1
0
0
0
1
2
1
0
0
0
2
0
0
0
1
1
0
2
1
0
1
0
0
0
0
2
0
0
1
0
0
0
1
0
2
1
0
0
2
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
1
1
1
1
0
2
0
1
0
0
0
2
0
1
0
2
0
1
2
0
1
0
0
0
2
0
0
2
0
0
0
2
1
0
0
0
2
1
0
0
1
2
0
0
2
0
0
0
0
2
0
0
2
2
0
1
2
0
0
0
0
0
2
5
2
0
1
0
1
0
0
0
1
0
2
0
0
0
1
0
1
1
2
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
1
0
2
0
0
1
0
2
0
1
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
3
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
2
0
0
2
0
1
1
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
1
1
0
1
0
0
0
0
0
0
1
1
0
2
2
0
0
0
0
3
2
0
0
0
0
1
1
0
0
0
2
0
3
4
0
0
1
0
0
1
0
2
0
0
0
1
0
2
2
2
0
4
0
0
4
0
0
1
2
2
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
1
0
0
0
1
1
3
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
2
0
0
2
0
0
2
2
0
0
0
1
0
1
0
0
1
0
0
0
0
0
4
2
0
0
2
0
0
2
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
2
3
0
0
0
0
0
1
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
2
0
0
1
2
2
1
0
0
2
0
0
0
3
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
2
4
0
0
0
2
0
0
1
1
0
2
1
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
1
0
0
2
0
2
0
0
0
1
0
1
1
2
1
1
0
0
0
0
6
0
2
2
0
0
0
2
0
0
0
2
1
1
2
0
1
0
0
0
3
0
0
1
0
2
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
2
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
2
0
1
0
1
0
0
0
0
0
0
1
2
0
0
0
4
2
0
1
0
0
0
0
2
1
0
2
0
0
2
3
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
1
0
0
2
0
1
0
2
2
0
0
2
0
0
1
0
2
2
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
2
1
0
0
1
1
0
2
2
2
0
2
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
1
0
1
2
1
0
0
0
0
0
0
0
2
3
0
1
0
0
0
2
2
0
0
0
0
0
1
1
2
0
0
0
1
0
0
3
0
2
0
0
1
4
0
1
0
0
0
0
0
0
1
0
2
1
0
3
1
1
0
0
2
0
0
0
0
0
1
1
1
0
0
0
1
0
0
3
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
2
2
3
0
3
0
0
0
0
0
2
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
2
2
2
0
2
1
2
2
0
4
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
2
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
2
0
0
0
1
0
0
0
3
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
2
1
1
2
1
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
2
0
0
0
0
2
0
1
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
1
2
2
0
2
3
2
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
2
0
0
3
1
0
0
0
0
0
0
0
0
0
1
0
1
0
2
2
0
0
0
0
0
0
1
1
0
0
2
0
0
0
1
0
1
1
1
0
2
2
0
0
1
1
2
0
1
0
2
3
0
1
0
0
1
2
0
0
0
0
3
0
0
2
0
0
2
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
1
0
1
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
1
0
1
3
0
0
1
1
0
1
3
0
0
0
2
0
0
1
0
1
3
2
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
1
1
0
0
0
0
2
0
0
0
2
0
0
2
1
0
1
0
0
3
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
5
0
2
0
0
0
1
1
0
0
0
0
0
1
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
2
0
0
6
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
3
0
0
2
0
0
2
0
1
1
0
0
0
1
0
1
2
1
0
1
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
2
0
0
0
2
0
0
1
1
1
0
0
0
0
0
1
0
2
1
0
0
0
4
2
0
0
0
1
0
2
0
0
0
5
5
0
3
2
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
3
2
0
2
0
0
0
0
1
0
0
0
1
2
0
0
1
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
1
4
0
2
2
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
5
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
3
0
0
0
0
1
2
0
0
0
0
0
1
2
0
0
0
0
3
0
2
0
1
0
0
2
0
1
0
2
2
0
0
0
0
1
0
1
2
0
2
0
0
1
2
0
2
0
0
0
1
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
1
1
0
0
2
0
0
4
0
0
0
1
0
0
1
0
1
2
0
0
1
0
2
0
0
0
0
1
0
2
0
1
0
1
2
0
0
1
0
2
1
0
0
1
0
0
0
2
2
0
0
2
0
0
0
0
2
1
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
3
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
3
1
0
2
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
1
0
2
0
0
0
1
0
0
1
1
1
0
0
0
0
1
1
0
3
0
0
0
0
1
0
0
1
0
0
0
0
0
3
0
2
0
0
1
0
1
0
0
2
1
0
0
3
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
1
0
1
1
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
2
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
3
1
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
3
0
1
0
0
1
0
1
0
0
0
0
2
1
0
0
2
2
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
1
0
1
0
3
1
2
1
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
3
2
1
0
0
0
3
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
2
0
2
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
3
0
0
0
2
1
0
2
1
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
1
2
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
1
2
0
0
0
0
1
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
1
0
0
0
1
1
2
0
0
0
2
0
0
0
0
0
0
2
0
0
2
1
0
0
2
0
2
0
5
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
2
0
0
2
0
2
2
2
1
0
2
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
6
0
0
0
0
2
0
1
2
0
1
0
0
1
1
0
0
2
0
0
0
1
1
0
2
0
1
3
1
1
0
0
0
0
0
3
1
1
0
2
0
0
1
0
1
0
1
2
0
1
1
0
1
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
1
1
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
1
3
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
2
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
2
1
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
2
0
2
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
1
0
2
0
0
3
0
2
1
2
0
1
0
0
1
3
1
1
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
2
0
0
0
1
2
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
2
0
3
0
1
0
0
0
0
0
2
0
0
0
1
1
0
1
0
0
0
2
2
0
0
0
0
0
0
0
1
1
0
2
2
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
2
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
2
0
2
0
0
2
0
0
0
1
0
0
2
1
0
0
0
2
6
0
2
1
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
2
0
2
0
0
0
0
1
2
0
0
0
0
1
2
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
2
0
0
4
0
0
3
0
0
0
0
4
0
0
0
2
0
0
0
1
2
3
0
0
2
0
2
0
0
0
0
1
0
0
0
0
1
1
2
1
0
0
0
0
0
0
0
0
1
0
0
3
1
0
0
0
0
2
2
0
0
0
0
0
2
0
1
2
0
0
0
0
1
1
2
0
1
0
1
0
0
0
0
2
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
1
0
2
0
0
0
0
0
1
1
0
0
2
0
0
2
1
2
1
0
1
1
0
0
1
0
1
0
0
0
0
2
0
1
0
0
0
2
0
0
1
3
0
0
0
0
2
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
1
0
2
1
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
6
0
0
0
1
1
1
0
1
1
0
0
0
2
0
0
0
2
0
3
0
2
0
2
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
2
2
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
2
3
0
0
0
0
0
0
4
0
0
0
2
2
1
0
1
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
1
1
1
0
0
1
0
0
0
1
1
0
0
2
2
0
0
0
0
5
1
0
1
0
0
1
0
0
2
0
1
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
8
1
2
0
0
2
1
0
1
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
2
0
1
0
0
0
2
0
0
3
0
0
0
1
0
0
0
1
2
0
0
0
0
2
2
1
2
0
0
1
1
0
0
0
2
0
0
0
2
1
0
0
0
0
2
0
1
1
0
0
0
0
1
0
2
0
1
0
1
2
0
0
0
0
0
0
0
2
0
2
0
0
0
1
1
0
1
0
0
0
2
0
0
1
0
0
3
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
1
0
3
0
0
0
0
0
0
0
2
0
0
0
0
1
1
1
0
0
0
2
0
1
0
0
0
0
1
0
2
1
0
0
0
0
0
0
1
0
0
1
0
1
1
1
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
2
0
0
2
0
0
0
3
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
1
0
0
1
0
0
2
1
0
0
1
0
0
0
2
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
2
0
2
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
1
2
0
2
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
1
0
0
2
0
0
1
0
2
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
2
0
2
2
1
0
0
0
2
1
0
0
1
0
0
2
2
0
2
0
0
1
0
2
2
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
2
2
0
2
1
1
0
0
0
0
0
0
0
3
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
1
0
0
1
0
0
0
1
2
0
0
0
4
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
2
0
2
0
2
3
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
2
4
0
0
0
2
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
2
3
0
0
0
1
0
0
0
0
0
1
0
0
2
0
2
0
0
0
2
0
0
0
0
1
0
1
0
0
2
0
1
0
0
0
1
1
1
1
3
0
0
3
0
0
0
0
3
0
0
0
2
0
0
1
0
1
0
2
0
0
0
0
0
0
2
0
0
1
2
1
0
2
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
2
0
0
1
2
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
2
2
0
2
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
1
1
2
2
0
0
2
2
0
0
2
0
4
0
0
0
0
1
0
0
3
0
1
0
0
0
0
0
2
0
0
0
7
0
0
4
0
1
4
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
1
1
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
1
0
2
2
0
0
1
0
0
0
0
0
0
0
6
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
1
2
0
0
0
0
4
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
1
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
2
0
0
2
0
0
0
0
0
0
0
0
1
1
0
3
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
3
0
1
0
2
0
2
0
0
2
0
0
1
2
2
0
0
2
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
2
2
0
1
2
0
0
3
1
0
0
0
2
0
2
0
0
0
2
0
1
0
0
0
2
2
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
2
1
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
2
0
1
1
0
1
1
1
0
2
2
0
1
0
2
0
1
0
1
0
0
2
1
0
0
1
0
0
2
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
3
0
1
0
0
0
0
0
2
0
3
0
2
5
0
1
1
0
0
0
0
0
0
1
3
0
0
0
0
1
2
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
1
0
0
0
0
3
1
0
0
0
0
0
2
3
0
2
0
0
2
0
4
0
1
0
0
3
0
2
0
0
1
0
1
1
1
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
1
0
3
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
3
2
0
5
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
2
2
0
0
2
0
0
1
2
0
0
0
2
0
2
0
2
0
0
0
0
5
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
1
2
0
2
2
0
0
0
0
3
0
2
0
0
2
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
2
0
0
1
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
2
2
0
2
0
0
6
0
0
2
0
0
0
0
4
0
3
0
0
2
0
0
1
0
0
0
0
2
2
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
2
1
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
2
2
0
0
0
2
2
0
1
2
2
0
2
0
4
0
2
0
1
2
0
0
1
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
3
0
1
2
0
1
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
2
0
0
2
0
0
2
0
1
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
4
0
2
1
0
0
1
0
0
2
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
3
0
0
0
2
1
0
1
0
0
0
0
1
2
2
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
2
2
6
0
0
2
0
0
0
0
0
4
0
0
0
1
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
2
0
0
0
0
2
0
0
1
0
2
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
4
0
2
2
0
0
0
0
0
0
1
0
2
0
0
0
2
0
2
3
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
2
0
0
1
0
0
0
1
1
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
2
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
1
0
0
5
2
1
0
2
0
0
0
6
1
1
2
1
2
0
2
0
1
0
1
0
2
0
1
1
0
0
0
0
0
0
0
0
2
1
1
0
0
1
0
0
4
0
1
2
0
0
0
1
0
2
1
0
0
0
0
1
0
1
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
1
0
0
0
0
0
2
0
2
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
2
0
2
1
1
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
2
2
2
0
0
1
1
0
0
0
2
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
1
2
0
2
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
1
1
1
3
0
1
0
0
1
2
0
2
1
0
0
0
1
2
1
0
0
2
0
0
1
0
0
1
0
0
2
0
2
0
0
0
0
1
0
0
1
0
0
4
0
0
2
0
0
2
2
0
0
0
0
2
0
2
0
1
0
1
0
1
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
3
0
0
0
4
0
0
0
0
0
1
0
0
0
2
0
1
2
0
1
0
4
0
0
0
0
0
0
1
0
0
0
3
0
1
1
0
0
0
0
0
3
2
1
0
2
1
0
0
0
1
0
0
1
2
0
0
0
3
0
1
2
2
0
1
0
0
2
0
2
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
1
0
0
0
0
3
1
0
0
1
0
2
0
0
1
0
0
0
0
0
2
0
1
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
5
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
2
0
2
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
2
1
0
1
0
0
2
1
2
0
0
2
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
1
1
0
1
1
0
0
0
0
0
0
0
2
1
0
3
0
0
0
2
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
2
0
0
1
1
0
0
2
1
0
0
0
0
2
0
2
0
1
1
0
1
0
4
1
2
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
1
0
2
5
2
0
4
2
2
0
0
0
2
2
1
0
0
0
0
1
0
0
1
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
2
0
2
0
0
1
2
1
2
0
2
1
0
0
0
0
2
0
2
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
2
0
0
2
0
2
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
2
2
0
2
0
0
2
0
2
2
0
0
0
0
1
0
1
0
1
2
1
0
2
0
1
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
10
2
0
3
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
3
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
4
0
0
0
0
1
0
0
1
0
2
0
0
1
1
2
0
0
1
0
1
0
0
2
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
2
0
2
0
1
2
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
1
1
2
0
0
0
1
2
0
2
0
0
2
0
2
0
0
3
0
1
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
1
0
1
0
0
2
0
0
0
0
0
1
3
1
3
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
3
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
2
0
0
0
0
2
0
0
0
1
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
4
1
1
0
0
0
1
0
2
0
0
3
0
2
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
2
0
2
2
1
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
1
1
0
0
3
0
2
0
0
0
2
0
0
4
0
2
0
0
3
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
2
2
0
1
0
0
1
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
2
1
0
0
0
2
0
1
3
0
0
1
0
0
0
1
0
0
1
0
0
1
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
3
0
0
0
0
1
0
0
0
0
2
0
0
1
0
2
0
1
0
0
0
2
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
3
1
0
0
0
1
0
3
0
2
0
3
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
2
3
0
0
2
0
0
1
0
0
0
2
0
0
0
9
0
0
1
0
0
1
0
0
0
0
2
2
2
2
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
2
0
2
0
4
0
2
2
0
2
0
0
0
0
0
0
2
0
0
1
0
0
2
1
0
0
0
1
0
0
0
0
0
2
2
0
2
0
0
0
0
2
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
1
2
0
0
4
0
0
2
1
0
0
2
0
1
1
0
0
1
0
0
0
0
0
0
0
0
2
0
1
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
2
2
0
0
0
0
1
0
1
2
2
0
1
0
0
0
0
0
0
1
2
0
1
1
0
1
2
1
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
1
0
0
0
2
0
2
0
0
1
0
0
3
0
5
1
1
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
2
2
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
2
2
2
0
2
0
1
2
0
2
0
1
0
0
2
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
2
2
0
1
0
0
0
0
0
1
0
0
1
3
2
0
0
0
0
0
2
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
2
0
2
0
0
0
1
0
2
0
1
0
0
0
0
1
3
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
1
0
0
2
2
0
0
2
0
1
0
4
0
0
0
2
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
2
0
1
0
0
0
2
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
1
1
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
2
0
2
0
1
1
0
0
0
2
0
1
0
0
2
0
1
2
2
0
1
0
0
0
0
0
1
0
0
2
2
1
0
0
0
2
1
2
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
1
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
3
2
0
0
1
0
4
0
0
0
0
0
0
2
0
2
0
2
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
1
0
0
2
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
2
0
1
2
3
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
3
0
1
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
1
0
2
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
2
0
1
0
0
0
0
0
0
0
0
2
0
2
2
2
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
4
0
2
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
5
0
0
2
1
2
2
1
4
0
0
0
0
1
2
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
1
1
1
0
2
2
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
3
0
0
0
0
2
2
0
0
0
0
2
1
0
0
2
0
0
2
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
3
0
1
0
2
0
0
0
0
2
0
0
0
2
0
2
0
0
2
0
0
11
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
1
1
0
0
2
0
0
2
1
0
0
0
0
0
0
3
0
0
1
1
2
0
0
0
1
0
1
0
1
2
0
0
0
1
0
1
0
1
0
2
2
1
0
2
1
0
0
0
0
0
3
0
0
0
0
0
2
2
0
0
1
1
2
0
0
0
0
2
0
2
0
0
1
0
1
0
0
2
0
2
0
1
0
0
0
2
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
3
0
1
0
1
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
1
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
1
2
0
0
0
0
0
2
3
0
1
1
2
0
0
7
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
3
2
2
0
2
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
2
1
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
2
0
2
3
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
2
0
0
0
1
0
1
0
0
2
0
0
1
1
0
0
0
0
2
0
2
0
1
0
0
0
0
5
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
2
0
0
2
1
0
0
0
0
0
1
2
0
0
0
0
1
2
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
2
0
2
0
0
1
2
0
1
0
0
2
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
3
1
0
3
0
1
0
0
0
2
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
3
1
0
1
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
1
1
0
0
3
0
0
2
0
0
2
0
0
1
0
1
1
3
1
1
0
1
0
2
0
0
1
1
0
2
4
0
2
1
1
2
1
0
1
0
2
3
0
0
0
0
0
0
1
0
1
2
0
1
2
3
0
0
0
0
0
0
0
1
0
3
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
2
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
2
0
0
0
2
1
0
1
0
1
1
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
2
2
0
0
0
0
0
0
2
4
0
2
0
2
0
0
0
2
1
0
1
0
0
0
0
0
0
1
2
1
0
0
0
0
2
2
0
0
0
0
2
0
0
1
2
2
0
0
2
0
1
2
0
1
0
3
0
0
0
0
0
0
0
0
1
0
2
2
0
0
1
0
0
0
1
0
1
0
1
1
0
2
0
0
0
0
0
0
0
5
0
0
0
0
1
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
2
0
0
2
0
0
2
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
2
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
3
0
0
2
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
2
1
0
1
2
0
0
0
0
1
0
0
0
1
1
0
0
0
0
2
0
2
2
0
2
2
0
1
0
2
2
0
2
0
0
0
2
1
0
0
0
1
0
2
0
2
2
0
0
0
0
0
1
0
0
2
0
1
0
1
2
1
0
0
0
0
2
0
2
0
0
4
2
1
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
2
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
5
1
2
0
2
0
0
5
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
1
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
2
1
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
2
0
0
2
0
0
0
0
2
1
0
0
6
0
0
0
2
2
0
2
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
2
0
2
3
0
0
0
0
1
0
2
0
0
2
0
2
0
0
0
1
1
0
2
0
0
4
0
0
0
0
1
0
2
1
0
0
1
0
0
0
0
0
2
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
2
0
0
2
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
3
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
2
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
2
2
0
2
0
2
1
3
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
1
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
1
0
0
0
0
2
0
1
2
0
0
0
2
0
0
0
2
0
2
1
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
4
0
0
0
0
0
0
2
0
2
0
0
1
1
2
0
2
0
0
2
1
0
0
2
0
2
0
1
1
0
0
0
0
2
1
1
1
2
0
0
2
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
2
1
2
0
0
0
1
1
1
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
3
1
1
0
2
1
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
3
0
1
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
5
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
4
2
0
0
1
0
0
2
0
0
0
0
0
0
1
0
2
0
1
3
0
0
0
1
0
2
0
0
0
3
2
0
0
0
0
1
3
0
1
0
0
0
2
1
1
0
1
2
1
0
0
0
13
0
1
0
0
0
0
1
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
2
3
0
2
0
0
1
0
0
2
5
0
0
2
0
0
2
0
1
0
0
1
0
0
0
0
0
4
0
0
1
0
1
0
0
0
0
2
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
5
2
1
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
1
0
0
1
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
2
0
2
2
0
0
0
0
2
0
0
1
0
0
1
0
2
2
2
1
0
0
0
0
0
2
3
0
0
1
0
0
0
0
2
1
1
0
0
1
0
1
0
0
0
1
2
0
0
0
0
3
0
1
2
1
0
1
0
1
0
0
0
0
0
0
2
0
0
0
1
1
0
0
2
0
0
0
2
0
0
0
1
0
1
1
0
2
2
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
1
0
0
2
0
1
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
2
1
0
0
1
0
0
0
0
0
0
0
1
5
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
3
0
1
2
0
2
0
2
0
0
0
0
0
0
0
1
0
3
1
0
2
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
2
1
0
0
1
1
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
3
2
0
1
1
0
0
2
2
1
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
1
0
2
1
0
0
0
0
2
2
0
0
0
0
0
0
0
1
2
0
0
2
0
2
1
0
2
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
2
0
0
0
2
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
3
0
0
1
2
2
0
2
1
2
2
1
2
0
2
2
1
0
0
1
2
2
0
0
0
0
0
0
1
2
0
1
0
0
1
0
1
0
0
0
1
0
0
3
0
0
0
0
4
1
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
2
1
0
0
0
2
0
1
1
0
1
0
2
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
3
0
0
1
1
0
0
0
0
1
1
1
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
2
2
0
2
2
0
0
0
1
0
4
0
3
0
0
0
0
0
0
3
0
2
0
2
2
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
2
0
0
0
0
2
1
1
0
2
1
0
2
0
0
0
2
0
0
1
0
0
0
0
1
1
0
3
0
1
0
0
0
0
0
3
0
0
2
0
0
0
0
1
2
0
2
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
1
4
1
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
3
0
0
2
0
2
2
1
0
0
0
0
0
2
2
0
1
0
0
0
0
2
0
3
0
0
1
1
2
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
2
0
2
0
2
3
0
0
2
0
1
3
0
0
2
0
0
0
1
0
0
0
0
1
1
0
0
0
7
0
3
1
0
2
0
0
1
0
0
0
2
0
0
0
1
0
0
1
2
0
0
2
0
0
0
0
0
0
1
6
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
2
0
0
0
1
0
2
0
2
0
2
0
2
0
1
0
0
2
0
1
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
2
0
2
0
0
2
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
2
2
0
1
0
0
2
0
0
0
2
0
1
0
0
0
0
3
1
0
0
1
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
3
0
0
0
0
0
1
0
0
0
2
1
0
0
2
0
0
1
1
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
1
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
16
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
2
1
0
1
1
2
1
1
0
0
2
0
0
2
1
0
2
0
0
1
0
0
0
0
2
0
0
0
2
1
0
2
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
1
0
1
0
3
0
0
0
0
0
0
0
0
1
1
2
0
0
1
0
2
1
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
1
4
2
2
0
0
0
0
1
1
0
0
0
2
0
2
1
1
0
0
0
0
0
0
0
2
0
1
1
0
0
2
0
0
1
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
1
0
1
0
2
0
0
2
0
3
0
0
2
1
2
1
1
0
0
1
2
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
2
0
1
0
1
0
2
0
3
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
1
2
0
2
0
3
0
0
1
0
2
0
1
1
4
0
0
0
1
0
0
2
1
0
0
2
1
0
2
1
0
0
0
0
0
0
5
1
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
7
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
2
4
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
2
1
0
5
0
1
0
0
0
0
0
0
3
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
2
1
2
0
1
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
1
2
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
1
0
1
0
0
0
1
0
2
2
0
0
0
0
0
0
1
0
0
1
0
2
1
2
0
0
0
0
1
0
0
2
0
1
2
0
0
0
0
4
0
0
0
0
2
2
0
0
2
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
2
1
0
1
1
0
0
1
2
0
2
0
1
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
1
0
1
0
2
2
2
1
0
1
1
0
0
0
0
0
4
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
1
0
0
0
0
3
0
2
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
3
2
1
1
0
1
0
2
1
1
0
0
0
0
1
1
0
0
3
0
0
0
0
2
0
2
0
0
0
0
0
0
3
0
0
0
1
0
0
1
0
0
2
0
1
3
0
2
0
0
0
0
4
0
0
0
0
1
3
0
0
2
0
0
0
0
0
0
0
1
2
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
1
0
2
0
0
0
0
0
1
0
0
2
2
0
0
0
8
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
2
0
2
0
0
1
0
0
0
2
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
1
2
2
0
0
0
0
1
0
2
0
0
0
0
0
2
0
2
0
0
2
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
2
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
3
1
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
2
2
2
0
1
0
2
1
1
0
0
1
1
2
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
2
2
0
0
0
2
1
0
0
1
0
0
0
1
2
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
2
2
0
2
0
0
0
1
0
2
0
0
0
1
0
1
0
2
0
0
0
0
1
0
1
1
1
0
0
3
1
0
4
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
1
2
2
1
2
0
1
2
1
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
1
1
0
3
11
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
1
3
0
3
2
0
2
0
0
0
0
0
0
0
0
1
0
2
4
0
0
0
0
0
0
0
0
0
2
2
2
1
1
3
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
2
2
1
0
0
0
0
0
0
0
3
0
1
1
0
0
1
0
2
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
1
2
2
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
2
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
2
2
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
2
1
1
1
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
3
1
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
1
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
2
0
1
0
0
1
0
1
0
0
2
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
2
0
0
2
3
0
0
1
2
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
5
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
2
0
0
0
2
2
0
0
0
1
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
5
0
0
0
1
2
0
0
1
0
0
3
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
2
0
0
0
0
3
2
0
2
0
2
1
0
1
0
0
0
2
3
0
1
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
1
0
2
2
2
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
2
1
0
0
3
0
0
2
1
3
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
1
0
0
0
3
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
3
0
2
1
0
2
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
5
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
4
0
0
1
0
0
0
10
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
3
1
0
0
0
1
2
1
1
0
4
0
0
0
0
0
3
0
0
0
0
2
2
2
0
0
0
2
0
0
0
0
0
2
1
2
0
2
3
0
0
2
0
0
1
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
1
1
2
2
0
1
1
2
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
1
0
2
1
0
1
2
0
1
0
0
0
0
1
1
0
0
1
4
0
1
2
0
0
0
0
1
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
2
2
0
0
0
1
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
3
0
1
1
2
0
1
0
1
0
2
0
2
0
0
0
1
1
0
0
0
3
0
2
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
3
0
0
1
1
0
0
0
3
3
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
2
0
2
2
0
0
1
2
1
0
1
0
2
0
0
1
0
0
0
0
2
1
1
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
1
0
0
2
1
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
4
1
0
1
0
1
0
1
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
3
0
1
0
0
0
1
2
2
1
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
6
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
2
0
0
1
0
0
0
2
0
0
0
0
0
1
1
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
2
0
0
2
0
0
0
0
1
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
2
1
2
0
0
2
0
0
1
0
1
0
0
0
0
0
0
2
0
0
1
1
1
0
0
0
1
1
0
1
0
2
0
1
1
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
2
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
2
2
1
1
0
0
0
0
1
2
0
1
1
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
6
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
2
0
0
0
0
2
0
0
0
2
0
1
0
2
2
0
1
0
0
1
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
1
0
0
1
2
0
0
0
0
0
0
1
1
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
3
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
3
0
0
0
4
2
1
0
0
1
0
1
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
2
2
0
0
1
1
1
1
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
2
0
1
0
0
2
0
2
0
2
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
1
0
2
2
0
0
1
3
1
2
1
0
0
0
2
0
1
0
0
0
0
0
0
2
0
3
0
0
0
1
3
0
0
0
1
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
2
1
1
0
0
1
0
0
2
2
0
0
4
2
0
2
1
0
2
7
0
0
0
0
0
2
2
0
0
0
0
0
0
1
1
4
0
0
0
1
1
0
0
1
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
2
1
0
2
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
2
1
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
1
1
0
0
0
1
2
0
0
0
1
0
0
0
1
2
2
2
0
1
2
0
0
0
0
1
0
3
0
0
1
0
1
0
0
0
0
0
2
0
0
1
3
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
1
0
1
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
1
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
3
2
0
0
0
0
0
2
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
4
0
0
3
0
2
0
0
0
0
0
0
4
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
1
0
1
1
0
0
1
0
0
0
0
1
2
3
0
1
1
2
1
0
0
0
0
2
0
0
0
0
0
0
2
0
1
1
0
0
2
0
0
0
0
2
0
1
1
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
2
2
0
1
0
0
0
0
0
1
0
0
1
2
2
0
0
0
2
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
2
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
1
0
2
0
0
0
1
0
1
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
1
2
1
0
2
0
0
0
0
0
0
0
0
6
0
0
0
0
0
1
0
0
0
0
1
0
1
1
2
0
0
0
0
2
0
0
2
1
1
0
1
0
0
0
2
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
2
1
0
0
0
1
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
5
0
0
2
0
1
2
0
0
0
1
0
0
0
1
3
0
0
5
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
2
0
0
2
2
0
0
0
0
0
1
0
2
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
2
2
0
1
0
1
2
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
2
0
2
1
0
2
0
0
0
0
2
0
0
2
0
1
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
2
1
0
0
0
0
1
2
0
4
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
1
1
1
0
0
2
0
2
0
3
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
3
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
2
1
0
0
0
0
0
2
0
0
0
1
2
0
2
2
0
0
0
0
5
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
2
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
1
0
1
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
1
0
0
6
0
0
1
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
1
0
2
2
2
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
2
2
0
2
2
1
1
0
0
1
0
3
0
0
1
0
0
1
2
0
0
0
0
0
0
1
1
0
0
0
2
0
1
0
1
1
0
0
5
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
2
0
5
2
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
4
1
0
0
1
2
0
0
1
1
1
1
0
0
0
0
1
0
0
1
1
0
1
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
3
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
3
0
0
3
0
0
0
0
1
0
0
1
0
2
0
0
1
0
0
0
0
1
1
2
1
0
2
0
1
1
0
0
1
0
2
1
0
0
0
0
0
2
0
0
0
2
0
0
1
6
0
0
0
0
2
1
2
3
0
1
0
0
1
0
1
3
0
0
0
0
0
0
1
0
2
0
0
0
3
1
0
0
0
1
0
0
1
0
4
0
0
0
0
2
0
0
0
0
0
0
1
0
0
4
0
3
0
1
2
1
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
2
0
0
0
1
0
1
0
0
0
3
0
0
0
1
0
2
2
2
3
0
0
1
0
1
0
0
1
2
0
0
0
1
0
0
4
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
2
0
0
2
0
1
0
0
2
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
2
0
0
1
8
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
2
1
0
0
0
2
0
0
1
0
0
0
0
0
1
3
0
2
0
0
1
0
1
3
1
0
1
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
1
0
2
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
3
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
2
0
0
1
3
0
0
0
0
1
0
0
0
5
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
2
0
2
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
2
0
0
0
0
0
2
2
0
0
0
0
0
2
0
2
0
0
0
2
0
3
2
0
0
1
0
0
4
0
1
0
2
0
0
0
3
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
1
0
0
3
1
0
3
1
0
2
0
0
0
0
0
0
1
8
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
2
0
2
0
0
0
1
0
0
2
2
3
0
1
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
3
0
0
0
0
2
0
1
0
0
0
1
0
0
3
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
3
0
0
0
0
0
1
4
0
2
1
0
2
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
2
0
1
0
3
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
3
0
1
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
1
0
0
2
0
0
3
0
3
2
0
1
1
0
0
0
0
2
0
0
1
0
3
0
0
0
0
2
0
0
0
1
1
0
1
1
0
0
1
0
0
0
0
2
0
0
0
3
1
0
0
1
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
1
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
1
2
0
0
0
0
1
1
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
2
2
0
2
1
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
2
2
1
1
0
0
1
0
0
1
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
2
1
1
1
0
1
2
1
0
0
1
0
1
0
0
2
0
0
1
0
0
0
2
0
0
0
0
2
0
0
1
0
0
1
0
0
2
0
0
0
1
1
0
2
0
0
0
0
0
0
2
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
3
1
6
5
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
2
0
0
0
0
3
0
0
0
0
0
0
2
0
1
0
1
1
0
0
0
0
0
0
1
0
2
2
0
0
0
1
0
1
0
2
0
2
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
3
0
0
2
0
1
0
0
1
0
0
0
1
0
2
0
0
0
3
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
3
0
2
0
2
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
2
0
4
0
0
0
1
0
2
0
0
0
2
0
2
0
0
0
0
0
1
1
0
2
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
3
2
0
4
0
0
0
0
0
0
2
4
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
1
1
1
1
0
1
0
3
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
2
2
0
2
0
0
0
0
2
0
0
0
0
0
0
2
3
0
2
0
0
1
2
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
1
5
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
2
0
0
0
0
1
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
2
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
4
0
0
2
0
0
0
0
0
2
0
0
2
1
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
1
2
3
0
0
2
1
0
2
1
1
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
2
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
1
0
2
0
0
0
1
0
0
2
0
0
0
0
0
1
3
0
0
1
2
2
0
0
0
0
0
1
0
1
2
0
0
0
0
0
1
2
2
1
0
0
1
0
0
0
0
1
1
2
0
0
0
1
1
2
0
2
0
0
3
0
0
0
1
0
0
0
0
2
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
1
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
1
0
0
0
0
2
0
2
0
2
0
2
0
2
0
0
1
0
0
1
1
0
0
0
0
2
2
1
0
0
7
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
1
0
1
0
0
0
0
0
0
3
0
0
0
2
0
0
2
0
0
1
0
0
1
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
2
1
0
0
0
0
0
0
2
1
0
1
2
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
2
1
1
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
1
0
0
1
0
0
2
0
1
1
2
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
2
2
0
2
0
0
2
0
0
0
0
2
0
0
2
0
0
0
1
0
0
2
2
2
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
4
0
1
2
0
2
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
2
1
0
0
0
4
0
2
0
0
1
0
0
2
0
1
2
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
2
2
1
1
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
2
1
2
0
0
0
3
0
2
2
2
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
1
0
0
2
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
2
1
0
0
0
0
0
2
1
1
0
0
0
0
1
2
1
0
0
0
17
0
0
1
6
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
6
0
0
1
2
0
0
0
2
0
0
0
0
1
0
1
1
1
0
0
1
0
0
0
0
2
2
0
0
2
2
0
0
0
0
1
0
2
1
0
1
0
0
2
3
2
1
0
0
7
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
7
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
1
1
0
0
2
2
0
0
2
2
0
2
2
0
0
2
2
1
0
2
2
0
0
0
0
1
1
0
1
0
1
0
1
0
3
1
0
2
0
0
0
0
1
3
0
2
2
0
2
0
0
0
1
0
0
2
0
2
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
4
1
0
0
0
1
0
0
1
1
0
2
0
0
2
0
0
2
2
0
2
0
0
0
7
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
3
0
0
0
0
1
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
2
0
8
0
0
3
1
0
0
0
0
0
0
1
1
0
0
0
2
2
0
0
0
1
0
2
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
4
1
0
0
1
1
0
0
0
2
0
2
0
0
0
1
0
0
1
2
1
0
0
0
0
1
1
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
5
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
1
0
1
1
0
1
0
1
0
1
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
4
0
0
0
3
2
0
0
0
1
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
2
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
1
2
0
0
1
3
0
1
0
0
4
0
0
0
2
0
1
0
0
0
0
0
0
0
1
2
0
0
0
1
0
2
0
0
0
2
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
3
0
0
2
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
1
1
1
0
1
0
1
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
2
0
2
3
2
2
0
0
1
3
0
0
1
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
1
1
1
0
1
0
2
2
0
1
2
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
2
0
1
0
0
1
0
1
0
1
0
0
4
2
0
2
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
2
0
2
7
0
0
6
0
0
0
2
1
0
0
0
0
2
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
8
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
1
0
0
0
1
2
0
0
2
0
0
1
0
1
0
0
0
0
0
1
2
0
0
2
0
0
2
2
0
1
0
2
1
2
0
1
0
0
1
0
3
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
3
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
1
2
3
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
1
0
2
0
1
1
0
0
0
2
2
0
0
0
0
0
0
2
1
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
3
0
0
0
1
2
2
0
0
0
0
0
1
0
0
2
0
0
2
0
1
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
2
1
0
3
2
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
4
0
1
0
0
2
0
1
0
0
2
2
0
0
2
0
0
0
2
0
3
0
0
2
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
3
13
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
1
0
0
1
0
0
2
0
1
1
3
0
0
2
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
1
1
0
0
0
0
0
3
1
0
3
2
0
0
1
1
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
1
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
2
0
0
0
2
0
1
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
3
0
0
0
1
0
0
1
1
1
0
0
1
0
0
2
0
0
0
0
2
1
0
0
0
1
0
0
2
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
1
0
1
0
2
0
4
0
1
1
0
0
0
0
2
1
2
0
0
2
2
1
0
0
0
2
0
2
2
2
1
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
2
2
0
0
0
0
0
2
0
0
1
2
0
0
2
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
1
0
0
0
0
3
1
2
1
1
0
1
0
4
2
0
0
0
0
0
0
2
0
1
0
0
2
0
0
2
2
2
0
0
1
2
0
2
0
1
0
4
0
0
0
1
0
0
2
1
0
0
3
0
0
1
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
2
0
2
2
1
0
0
0
0
0
1
2
2
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
3
1
0
0
2
0
1
0
1
0
3
2
0
0
0
0
0
2
0
0
0
1
2
0
0
2
2
0
2
0
2
0
1
2
0
0
2
0
0
2
2
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
3
0
0
0
0
0
2
0
0
7
0
0
0
0
2
1
0
0
0
1
2
0
1
0
2
0
1
0
1
0
0
1
0
0
2
1
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
1
1
0
2
0
0
0
0
2
1
0
2
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
2
0
0
0
0
1
2
0
3
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
2
2
0
1
0
0
0
2
0
0
0
0
2
0
0
3
1
2
0
0
0
0
0
0
2
2
0
2
2
0
0
0
4
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
1
0
0
0
1
2
0
0
1
0
0
0
1
1
0
0
2
0
0
0
0
0
0
2
1
0
2
0
0
0
0
1
0
0
0
0
0
0
2
1
0
1
0
1
0
0
0
0
1
0
0
2
2
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
3
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
2
0
0
2
4
2
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
3
2
0
1
0
0
2
0
1
0
2
1
0
0
0
3
0
0
0
0
0
0
2
0
3
1
0
0
1
2
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
1
0
0
1
0
2
1
0
0
1
0
0
1
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
2
2
1
0
0
2
0
0
1
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
2
0
0
0
0
1
0
3
1
1
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
2
0
0
0
0
2
0
2
0
0
2
1
0
0
1
1
2
0
0
0
0
6
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
5
1
0
0
2
0
1
0
2
2
2
0
0
0
0
2
0
0
1
0
0
1
0
1
1
2
1
3
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
2
0
0
0
0
0
0
2
1
0
3
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
1
1
1
2
0
0
0
0
2
0
0
1
2
0
5
0
0
2
0
1
0
0
0
1
0
0
2
0
0
2
0
0
0
0
2
1
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
1
3
2
2
0
0
0
0
3
0
1
0
1
0
0
0
0
2
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
3
0
2
1
0
2
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
2
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
2
0
1
0
0
1
2
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
2
0
1
0
2
0
0
2
0
1
0
0
2
0
0
0
2
0
4
0
1
0
2
0
1
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
1
3
0
0
0
0
0
2
2
1
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
2
1
0
0
1
0
0
2
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
2
0
1
2
1
0
0
1
0
0
2
0
2
0
2
0
3
0
0
1
0
0
0
0
2
0
0
1
3
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
2
0
1
0
1
3
0
1
0
0
0
0
0
0
0
1
0
0
2
2
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
2
0
3
2
0
0
0
0
3
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
4
2
0
1
0
0
0
1
2
1
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
2
2
3
0
1
2
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
1
2
1
0
0
2
0
0
1
0
0
0
0
2
0
1
0
1
2
5
0
0
2
2
2
0
0
0
1
0
0
1
0
1
0
0
2
2
0
2
0
0
0
2
0
1
0
0
0
2
0
0
0
0
2
0
0
0
2
1
0
1
0
0
0
0
2
0
0
1
0
0
2
0
0
1
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
2
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
8
0
3
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
1
0
0
0
0
0
0
0
0
2
2
1
1
0
0
2
2
0
0
0
0
0
2
0
0
0
1
2
0
2
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
2
1
0
2
1
0
0
0
0
0
1
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
2
1
1
0
2
0
0
0
0
0
0
2
0
1
0
0
0
1
0
2
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
1
2
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
3
0
0
0
0
1
0
1
0
0
0
0
0
0
2
2
2
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
3
2
0
0
0
0
2
1
0
0
1
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
7
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
3
1
0
1
1
1
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
2
0
0
0
0
1
2
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
3
0
2
0
0
1
0
1
0
0
0
0
1
1
0
1
2
2
0
2
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
3
2
0
0
5
0
0
1
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
4
1
0
1
0
0
2
1
2
0
0
3
0
2
0
0
0
0
0
3
0
1
0
0
0
2
0
1
2
0
2
1
0
3
0
0
0
2
2
0
0
0
1
0
0
0
2
2
0
2
0
0
1
1
1
0
0
0
1
0
0
2
3
0
0
0
0
0
1
0
0
2
0
2
0
0
2
0
0
1
2
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
2
1
0
0
0
2
0
0
0
2
0
0
1
0
1
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
2
0
2
4
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
3
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
1
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
2
0
3
0
0
0
0
0
0
1
0
6
0
0
0
1
2
0
1
0
0
0
0
0
2
2
0
0
0
2
1
0
2
0
2
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
2
1
0
2
0
0
1
0
1
0
0
0
1
2
2
0
0
2
0
0
2
0
2
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
2
0
1
0
0
0
0
0
1
1
3
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
2
1
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
2
0
1
0
0
0
0
1
2
2
0
0
1
0
0
0
0
1
0
0
0
0
1
2
0
1
0
0
3
0
2
4
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
7
0
2
0
0
0
2
0
0
0
0
0
0
1
0
1
1
0
0
0
2
0
0
0
2
0
3
0
1
0
0
1
0
0
0
0
2
0
2
0
0
0
0
2
1
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
1
4
0
2
1
0
0
0
0
0
0
0
0
3
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
2
0
1
1
0
0
0
0
0
0
0
2
0
0
0
2
2
1
3
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
4
0
1
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
3
1
0
1
0
1
0
2
1
0
0
0
1
0
0
0
0
7
0
0
2
0
0
3
0
0
1
0
0
0
0
0
0
2
0
1
0
1
0
1
0
0
1
0
0
0
1
0
2
6
0
2
0
2
2
0
0
0
0
0
0
1
1
2
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
2
0
0
0
0
0
1
0
1
0
1
2
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
2
2
1
0
0
0
0
3
2
0
0
2
2
2
1
0
1
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
1
0
2
1
0
2
0
2
0
0
0
0
2
0
0
0
1
1
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
1
2
0
2
0
2
0
2
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
1
2
0
1
2
0
1
1
0
1
2
0
0
0
0
1
0
0
0
0
0
11
0
0
0
0
1
0
0
0
0
0
0
0
0
11
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
2
0
0
3
2
0
2
0
0
2
8
0
3
4
2
4
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
4
1
0
1
0
0
0
0
3
0
0
2
1
1
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
5
4
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
11
0
3
0
0
0
0
0
0
3
0
0
1
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
1
0
0
2
0
0
0
2
0
0
0
1
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
1
0
1
0
2
3
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
1
0
4
0
0
0
1
0
1
0
0
1
1
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
3
0
0
2
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
1
1
1
2
0
1
0
0
0
0
0
0
2
0
0
1
2
0
0
2
1
1
0
2
0
2
0
1
0
2
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
2
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
2
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
2
0
1
0
1
1
2
4
0
2
0
0
0
0
0
1
0
1
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
2
1
0
0
0
0
0
0
2
1
0
2
0
0
0
3
0
0
0
0
0
0
0
3
0
2
2
2
0
2
0
0
0
1
0
0
2
0
0
2
0
0
2
3
0
0
2
0
0
1
1
0
0
0
0
1
0
0
0
0
4
0
0
0
0
1
0
2
0
2
0
0
0
1
1
0
0
3
1
0
1
2
2
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
1
1
0
1
0
0
0
0
7
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
1
2
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
1
0
1
0
3
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
2
0
0
0
1
0
6
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
2
0
0
2
0
0
1
0
0
0
2
0
0
0
2
1
0
0
2
1
0
0
0
3
1
0
2
0
2
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
4
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
2
0
0
3
0
2
0
0
0
2
2
1
0
0
0
0
0
0
2
2
1
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
2
0
1
2
2
0
0
0
0
0
2
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
3
2
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
2
0
1
1
0
0
1
0
0
0
1
0
0
2
2
0
0
0
2
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
1
0
2
1
0
0
0
1
0
1
0
0
0
1
0
2
1
0
1
1
2
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
1
0
0
1
2
0
0
0
0
0
1
0
1
2
0
0
0
1
2
0
1
1
0
0
0
0
0
0
1
0
1
0
4
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
1
2
1
1
2
0
2
0
2
0
0
1
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
2
1
0
0
1
0
0
0
0
2
0
0
3
0
2
0
0
0
1
0
0
2
0
0
0
0
2
0
1
1
0
0
0
0
2
0
0
0
0
0
1
0
2
1
0
2
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
1
0
0
2
2
0
1
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
3
0
0
0
2
0
0
0
0
2
0
4
0
0
2
0
0
1
0
2
0
0
0
0
0
1
0
2
3
0
1
1
1
2
0
1
0
0
0
3
1
1
0
0
2
0
0
2
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
3
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
2
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
8
4
0
0
0
0
0
2
0
1
0
0
2
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
2
2
2
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
2
0
2
0
1
0
1
0
0
0
0
0
0
3
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
1
1
0
0
2
0
0
0
1
1
0
0
1
0
3
1
0
2
2
2
0
2
0
0
1
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
1
0
0
0
0
0
0
1
1
0
2
0
0
2
1
1
0
0
0
0
0
2
0
2
0
2
2
0
1
0
1
0
0
1
0
1
0
0
1
0
0
1
0
0
0
1
0
0
1
1
0
3
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
1
3
2
3
2
0
0
0
0
1
2
0
0
1
0
0
1
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
1
2
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
3
2
0
2
2
1
0
1
1
0
2
2
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
1
1
3
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
2
2
0
0
0
1
0
0
0
0
1
1
0
1
1
0
1
0
0
0
0
0
1
0
0
0
1
2
0
1
4
0
0
2
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
1
1
2
3
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
2
2
0
0
0
1
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
1
0
2
2
0
0
0
1
3
3
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
1
2
0
0
2
0
2
0
0
1
4
0
0
0
0
0
0
2
0
0
1
0
0
1
2
0
0
2
0
2
2
0
2
0
0
0
0
2
0
3
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
5
0
0
0
0
0
0
1
1
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
2
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
1
2
0
0
1
0
0
0
0
2
0
4
0
0
0
0
0
3
1
0
0
0
1
0
0
0
1
2
1
0
0
0
1
0
0
0
1
3
0
0
0
0
2
2
1
0
2
1
0
0
2
0
3
0
0
0
2
1
0
0
0
1
0
0
0
0
0
2
2
1
1
0
2
0
0
0
2
0
0
0
0
3
1
0
1
0
3
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
3
2
0
1
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
1
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
2
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
1
0
0
2
2
0
0
0
0
0
0
4
1
0
2
0
0
0
0
3
0
0
2
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
1
1
0
0
2
0
0
2
0
0
1
0
0
0
2
0
0
0
1
0
1
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
1
1
0
1
2
0
0
0
0
0
1
2
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
2
1
0
4
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
1
0
0
2
2
0
1
0
0
1
0
0
1
1
0
1
0
2
0
2
1
0
0
2
1
0
1
0
0
0
1
1
1
0
3
0
0
1
0
0
0
1
0
2
0
1
1
0
0
1
0
0
2
0
0
0
0
1
1
0
0
0
3
1
0
0
0
0
0
3
1
0
0
0
1
1
2
0
1
1
0
0
1
0
1
0
1
0
0
0
0
2
2
0
0
0
2
0
1
0
2
0
0
0
1
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
1
2
0
0
0
3
2
1
0
1
0
0
0
0
1
1
2
1
0
0
2
0
3
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
5
2
0
0
2
4
2
0
1
0
0
1
0
1
0
0
1
2
0
0
1
0
0
1
0
0
2
0
0
0
0
1
1
0
0
0
3
0
2
0
0
0
0
3
2
0
1
0
1
2
1
0
0
0
0
2
3
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
3
0
0
0
0
2
1
0
0
2
0
1
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
1
0
4
0
0
0
0
0
2
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
3
0
0
0
0
0
0
1
1
0
0
0
2
0
0
2
3
0
0
1
1
0
0
0
0
2
0
0
0
0
3
0
2
0
0
0
0
0
0
0
1
0
2
0
2
1
2
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
1
1
0
2
2
0
0
2
0
0
0
1
0
0
4
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
4
2
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
3
1
2
2
0
0
0
0
2
0
2
0
0
0
0
1
1
1
0
1
1
0
0
0
0
1
0
0
1
0
0
0
4
0
1
0
2
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
2
2
0
0
2
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
2
1
0
2
0
0
0
2
2
0
2
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
3
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
2
0
0
4
0
0
2
1
0
4
0
0
1
0
0
1
2
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
1
0
1
0
0
0
0
1
1
1
0
0
0
1
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
2
0
1
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
1
2
0
1
2
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
2
0
2
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
1
3
0
1
0
0
2
2
0
0
2
1
0
0
2
0
0
0
2
2
0
1
1
3
0
1
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
1
0
2
0
0
1
0
0
2
1
0
0
0
2
0
2
0
0
0
2
0
1
2
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
3
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
5
3
2
0
0
2
0
0
0
1
0
0
0
2
0
3
1
0
1
0
0
0
0
2
0
2
0
0
1
0
0
0
2
0
0
0
0
1
1
0
0
0
1
0
1
1
0
2
0
0
0
1
2
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
1
2
1
0
0
0
0
2
2
0
1
3
2
2
0
0
0
0
1
0
1
1
1
0
6
0
1
0
0
3
0
1
1
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
3
0
2
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
3
1
0
2
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
5
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
1
0
0
0
2
0
0
2
0
4
0
4
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
1
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
2
0
3
0
0
0
0
2
0
1
2
2
0
3
0
2
0
0
1
0
0
0
0
0
2
0
2
0
1
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
2
0
0
1
1
0
2
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
2
1
0
1
0
0
0
0
2
0
0
2
0
4
0
0
0
2
0
1
3
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
2
1
0
3
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
2
0
0
0
0
3
0
0
0
2
0
0
2
0
0
2
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
2
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
1
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
2
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
1
1
0
0
1
0
2
2
1
0
0
0
0
0
2
0
1
0
0
2
0
2
2
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
3
2
2
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
2
1
0
1
0
1
0
0
0
1
2
2
0
2
0
0
0
2
0
0
0
1
2
1
0
2
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
5
2
3
0
0
0
0
0
0
0
0
0
0
2
2
0
2
1
0
0
0
0
1
0
0
0
1
0
0
0
1
1
1
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
1
0
0
2
0
0
0
0
0
2
2
0
2
0
2
0
0
1
0
1
2
0
2
0
1
2
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
2
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
4
0
1
0
0
3
0
0
0
1
2
0
0
0
2
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
1
0
1
1
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
1
9
2
2
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
2
0
0
0
0
1
0
0
1
0
0
4
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
4
0
1
2
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
2
0
1
2
0
2
2
1
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
2
2
0
0
0
0
2
0
0
0
1
1
0
0
0
8
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
5
0
0
0
1
0
0
1
0
2
0
2
0
0
0
1
1
1
0
0
0
2
1
1
0
0
0
2
0
0
0
0
0
0
0
0
11
0
1
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
1
2
1
0
0
1
0
0
1
0
2
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
1
3
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
1
2
0
0
0
3
1
2
1
0
0
1
0
1
1
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
2
2
2
0
1
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
1
1
0
2
0
1
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
1
0
3
0
1
0
0
1
1
0
0
2
0
1
1
3
0
1
1
2
0
2
0
0
0
1
0
0
0
0
1
2
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
2
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
1
2
1
1
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
2
0
0
2
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
2
1
1
0
0
2
2
0
0
0
2
0
3
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
2
0
2
0
1
2
0
0
4
0
0
1
0
1
0
0
0
6
1
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
1
9
0
2
2
0
0
2
0
0
0
0
1
1
0
0
0
0
1
2
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
2
0
1
2
0
0
0
0
0
2
2
0
0
8
1
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
1
0
2
0
0
0
0
1
0
2
3
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
2
1
0
2
0
1
2
0
0
0
2
1
0
0
0
0
1
1
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
2
0
0
6
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
1
2
0
1
0
0
0
2
0
0
0
1
0
1
2
1
0
2
1
2
0
0
0
3
2
1
0
0
0
0
2
0
0
0
2
0
1
0
2
1
1
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
2
0
3
3
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
1
1
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
2
1
2
1
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
4
0
1
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
1
2
2
0
0
0
2
0
0
1
2
1
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
2
0
0
0
1
0
0
1
1
0
0
0
2
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
1
4
0
0
2
2
0
0
0
2
2
0
2
0
0
2
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
2
0
0
0
0
0
0
1
0
2
2
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
1
1
0
1
0
0
0
0
0
2
0
1
0
2
0
0
0
0
2
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
2
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
1
2
1
0
0
0
0
2
0
2
2
0
0
0
0
2
0
0
0
1
0
0
2
0
1
0
0
0
0
1
2
0
0
0
1
2
0
0
1
0
1
0
0
2
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
2
1
2
0
1
0
0
3
2
2
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
2
0
0
2
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
4
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
1
0
2
0
0
2
2
1
0
0
0
0
1
0
0
0
2
2
0
0
0
1
2
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
2
1
1
2
1
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
3
0
0
0
0
0
2
0
0
2
2
0
2
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
3
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
4
0
0
0
0
0
2
0
1
3
0
1
0
0
0
1
0
2
0
1
0
0
2
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
4
0
3
2
1
2
0
0
0
0
1
2
0
2
1
1
1
0
0
0
0
3
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
4
0
0
0
1
3
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
3
2
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
2
1
0
2
3
0
1
0
0
2
0
3
0
3
0
0
2
0
1
1
0
2
0
0
0
0
1
1
2
0
2
1
0
0
0
0
0
0
1
1
1
0
0
2
2
0
0
0
0
0
0
2
0
0
1
0
1
0
1
0
0
0
0
1
0
6
0
0
0
2
1
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
5
2
2
0
0
0
0
0
0
3
2
0
0
0
0
0
0
1
1
0
2
0
2
0
2
0
0
0
0
0
0
0
0
1
10
0
0
0
2
0
0
0
0
0
0
1
0
2
2
0
0
1
3
0
2
0
0
0
1
0
2
0
0
3
0
1
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
2
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
3
1
2
0
1
0
0
1
0
2
0
0
0
0
0
2
0
0
3
0
1
1
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
3
2
0
1
0
1
0
1
0
0
3
2
1
0
0
0
0
1
1
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
2
0
2
1
0
1
0
0
1
2
0
0
0
6
2
2
0
2
1
0
1
0
0
3
0
0
0
0
1
0
0
2
0
0
0
2
0
1
2
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
2
2
0
0
2
2
1
0
0
2
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
2
1
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
2
0
0
1
0
2
2
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
1
0
0
3
1
2
0
0
0
2
0
2
0
0
1
0
0
0
0
1
0
0
2
0
0
0
2
0
2
0
0
2
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
2
1
1
0
0
2
2
1
1
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
3
0
0
3
1
0
0
4
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
1
0
0
1
0
0
2
0
0
0
1
0
0
3
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
2
1
0
1
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
4
1
3
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
2
0
0
1
0
0
1
3
0
2
0
0
1
0
1
0
1
1
0
0
0
1
0
2
0
0
0
0
1
2
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
3
1
0
2
0
1
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
2
0
0
0
2
0
1
0
2
0
0
0
0
3
1
0
0
0
2
1
1
1
0
2
0
2
0
0
2
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
1
0
2
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
3
0
0
2
0
1
1
2
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
1
2
0
0
1
0
2
1
0
1
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
2
0
0
0
0
1
4
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
1
0
0
0
0
0
2
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
5
0
0
0
3
2
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
3
0
2
0
0
1
0
0
2
0
1
0
2
0
0
0
0
3
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
1
0
0
0
1
0
0
3
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
2
0
0
0
0
0
2
2
0
1
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
2
0
0
2
0
2
0
0
0
0
2
1
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
3
0
0
0
2
0
1
0
1
0
0
2
2
0
0
0
0
1
0
0
1
0
0
1
3
0
0
0
0
0
0
0
1
0
0
8
0
0
0
2
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
2
0
4
1
0
1
0
0
0
0
3
0
0
0
0
0
1
0
1
0
0
0
0
2
0
2
0
3
2
0
0
2
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
2
0
0
1
0
0
2
2
1
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
2
0
1
0
0
0
1
0
1
2
0
2
0
0
1
0
1
1
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
2
1
0
0
1
0
0
1
0
1
2
0
2
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
2
0
2
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
2
1
0
2
0
0
0
0
0
0
0
1
1
1
2
0
1
0
2
0
1
2
2
0
0
2
0
0
0
2
0
3
1
1
2
1
1
0
2
0
1
0
2
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
1
2
0
6
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
2
1
1
0
0
2
0
0
0
0
0
0
0
2
0
0
2
1
2
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
2
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
1
1
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
1
0
1
0
0
0
2
0
0
0
1
1
2
0
1
0
0
0
0
2
0
4
2
0
0
0
0
2
1
0
1
1
0
0
3
2
0
1
0
2
2
2
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
1
0
0
0
0
0
0
1
4
1
1
0
0
0
2
1
1
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
2
0
1
0
1
0
2
0
2
0
1
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
2
0
1
2
2
3
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
2
3
0
0
2
2
0
1
0
2
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
2
0
0
1
2
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
3
0
0
3
1
0
0
3
2
2
2
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
2
0
1
0
0
1
1
0
0
1
2
2
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
3
1
0
0
0
1
0
0
4
1
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
6
2
0
0
2
0
0
0
1
0
0
1
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
2
0
0
1
2
0
0
0
0
0
0
1
1
1
2
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
2
0
1
0
0
0
0
0
2
0
1
1
0
2
0
2
0
2
0
3
5
0
0
2
0
1
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
1
2
1
0
0
0
4
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
1
0
2
0
0
3
0
0
2
2
0
2
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
2
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
2
2
0
0
0
0
2
1
0
2
0
0
1
0
0
2
0
3
0
0
0
0
3
0
0
0
0
0
1
1
0
3
2
0
2
0
0
2
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
2
0
0
0
3
0
0
0
0
0
0
1
2
0
1
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
1
0
3
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
2
0
1
0
0
0
0
0
1
0
1
0
1
0
2
0
1
0
0
0
3
0
0
0
0
0
0
1
0
0
0
2
0
2
2
0
2
0
2
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
2
0
2
0
0
0
1
0
1
1
1
0
0
0
0
2
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
2
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
1
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
1
1
0
0
2
0
1
0
1
0
3
2
1
0
0
0
2
2
2
0
0
0
0
0
2
0
1
1
0
0
0
2
0
1
3
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
2
0
2
0
0
2
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
2
0
0
1
0
0
0
1
9
0
0
0
1
2
0
0
2
2
2
0
0
0
2
0
1
0
0
0
2
0
0
0
2
0
1
2
0
0
0
2
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
4
2
0
0
1
0
0
0
0
2
0
0
1
1
0
0
1
0
2
0
0
1
1
2
0
0
1
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
1
2
0
0
2
0
0
0
2
0
0
2
0
2
0
2
0
2
2
1
0
0
1
0
0
0
0
0
0
0
1
0
3
0
0
0
2
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
2
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
4
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
1
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
3
1
0
0
0
0
0
2
2
0
0
2
0
2
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
1
1
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
1
0
4
0
2
0
0
0
0
1
0
0
0
0
2
1
0
5
0
6
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
1
3
2
1
0
0
3
2
1
0
0
0
0
1
0
0
0
1
0
0
0
2
0
2
0
2
0
0
1
0
0
2
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
4
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
2
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
3
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
1
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
1
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
2
0
0
0
2
3
0
2
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
2
1
0
0
2
0
1
0
0
2
0
2
0
0
1
0
2
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
0
0
2
2
2
0
0
0
2
0
0
0
0
0
1
2
0
2
0
1
0
0
0
0
0
7
0
1
0
3
0
0
0
0
0
0
1
0
0
1
0
1
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
2
2
2
0
0
0
0
0
0
2
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
2
0
2
2
2
0
2
4
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
2
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
1
2
1
0
0
1
0
0
0
0
1
0
1
0
1
4
0
3
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
3
0
2
0
1
1
0
1
0
2
0
0
0
0
0
0
0
2
0
1
0
0
3
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
4
0
2
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
2
2
3
0
0
2
0
0
0
2
0
3
0
0
1
1
0
5
1
0
0
1
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
2
0
0
2
2
0
2
1
0
0
0
1
3
2
0
0
0
1
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
1
2
0
2
1
0
0
2
0
0
0
0
0
0
1
1
0
2
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
1
2
0
1
0
0
0
1
0
4
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
1
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
1
2
1
1
2
2
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
2
0
0
1
1
1
2
2
0
0
0
2
0
0
0
0
0
2
0
2
0
1
2
1
2
2
0
0
0
0
0
1
0
0
2
2
0
1
0
0
0
0
0
0
0
1
0
2
0
0
2
3
0
0
0
0
0
1
0
2
0
0
0
1
0
0
3
0
0
0
2
3
0
0
0
0
0
0
0
0
2
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
1
0
0
0
0
0
0
2
1
1
1
1
2
0
1
0
0
0
0
0
0
0
0
2
3
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
2
4
0
0
0
0
0
0
3
1
0
0
0
0
0
2
2
0
0
0
0
0
1
0
2
0
0
2
2
0
2
1
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
1
3
0
1
0
1
0
0
0
0
0
0
0
2
2
1
0
0
2
0
0
0
0
0
2
0
2
1
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
3
1
0
2
0
2
0
0
0
0
1
2
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
1
2
0
3
0
1
0
0
1
0
1
2
0
1
2
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
1
0
1
0
0
3
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
1
0
0
2
2
1
0
0
2
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
2
3
0
0
0
0
0
1
0
0
2
0
0
1
1
0
0
0
2
1
0
0
1
0
0
1
0
0
0
0
2
1
0
0
1
0
1
0
0
0
0
1
0
0
1
0
2
0
0
0
1
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
1
1
0
0
0
1
0
0
2
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
1
0
1
0
1
0
2
0
0
1
1
0
2
2
5
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
9
0
0
0
0
1
0
0
1
2
0
1
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
2
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
2
0
2
0
1
2
1
0
0
0
0
2
2
0
0
2
0
0
0
1
0
0
2
2
6
2
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
2
0
1
0
0
1
0
3
2
0
0
1
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
2
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
4
0
0
0
0
1
2
0
2
2
0
0
2
1
0
0
0
0
0
0
1
2
0
0
2
2
3
0
2
1
0
0
8
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
1
2
4
2
1
0
2
0
0
0
0
0
0
0
1
0
2
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
1
0
1
0
4
2
2
0
0
2
0
1
3
1
2
2
1
2
2
0
1
0
1
1
0
0
2
0
0
3
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
3
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
1
2
0
1
0
0
1
0
0
1
0
2
2
0
0
0
2
2
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
1
0
0
0
2
0
1
0
1
0
0
0
0
0
0
1
2
1
0
0
0
0
3
0
2
0
2
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
2
0
0
0
0
2
0
0
0
3
0
0
0
1
0
1
2
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
2
1
0
1
0
1
0
0
1
0
0
0
0
0
1
0
1
0
2
2
0
0
0
0
1
6
0
1
0
0
1
2
1
0
0
0
1
0
1
0
0
1
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
2
0
2
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
2
0
0
2
0
0
0
0
1
2
2
1
2
0
0
0
1
0
2
0
0
0
0
0
2
2
2
1
0
0
1
2
0
0
0
0
2
3
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
1
0
0
1
1
0
0
0
0
2
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
1
1
2
2
0
0
0
2
1
0
0
1
0
2
0
1
0
0
2
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
3
0
2
0
0
0
0
0
0
0
1
0
2
0
1
0
2
2
0
1
2
0
2
2
0
0
0
0
3
1
0
1
0
0
0
1
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
2
1
5
0
1
0
0
0
0
2
0
0
0
1
1
0
2
0
1
2
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
2
1
2
2
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
1
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
3
1
0
2
0
0
0
5
0
0
0
3
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
1
1
2
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
13
0
0
0
3
0
7
0
2
0
0
0
0
0
0
3
0
0
2
0
1
0
0
0
2
1
0
0
0
0
2
2
1
2
0
0
0
0
0
0
1
2
0
0
2
1
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
4
1
0
0
0
0
0
0
0
1
0
0
2
0
0
1
1
0
1
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
2
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
5
2
0
1
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
3
0
0
1
0
0
1
0
0
0
2
0
3
0
2
0
0
0
0
1
2
0
3
0
0
0
2
0
3
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
1
2
0
2
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
1
0
2
2
0
0
0
0
0
2
0
0
2
2
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
3
0
5
2
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
2
0
0
2
1
0
0
1
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
1
1
0
2
0
0
0
0
2
2
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
1
2
0
0
2
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
1
0
4
1
0
0
0
0
0
0
1
0
1
2
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
3
4
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
2
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
2
0
1
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
2
1
0
1
0
0
1
0
2
2
0
0
2
0
0
0
0
0
0
2
0
2
0
0
1
1
1
2
0
1
0
0
2
1
0
0
1
0
1
1
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
1
1
2
0
3
0
0
2
0
0
0
0
0
1
2
0
0
1
0
0
1
0
1
0
0
2
1
0
2
2
0
0
0
2
0
1
0
0
0
1
1
0
0
0
2
0
1
1
1
2
0
0
0
1
2
0
2
0
0
0
3
0
0
1
3
1
1
0
0
5
3
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
4
1
0
0
0
0
0
1
0
0
2
0
2
1
3
1
6
4
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
2
0
0
0
2
0
0
1
0
0
3
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
2
0
0
0
0
1
0
0
2
1
2
1
0
2
0
0
0
0
0
0
2
2
0
2
1
0
0
2
0
2
0
1
2
0
0
0
0
0
0
2
0
1
0
1
2
0
0
0
0
0
2
0
0
2
2
1
0
0
1
0
2
0
1
0
0
1
0
0
0
0
1
0
1
1
0
0
0
1
3
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
2
1
1
2
0
1
1
1
4
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
6
0
1
0
2
1
0
0
0
0
3
0
0
1
0
1
0
1
1
0
0
0
2
0
0
0
0
0
4
0
2
0
0
2
4
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
1
0
0
0
0
0
4
0
0
0
0
0
2
1
0
2
2
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
2
1
1
0
0
2
1
1
0
3
0
0
0
0
2
2
0
1
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
1
1
2
0
0
4
0
3
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
2
0
0
0
2
0
2
0
0
2
0
0
1
3
0
1
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
1
2
2
2
2
0
1
2
0
2
0
1
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
1
0
0
1
2
3
1
2
0
2
0
0
0
0
0
0
0
0
1
1
2
0
0
0
1
0
1
0
0
1
1
0
0
0
2
0
1
2
0
0
2
0
0
2
0
0
0
0
2
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
2
0
0
1
1
1
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
1
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
1
0
2
0
0
2
0
1
2
0
1
3
1
1
0
0
2
0
1
2
0
1
2
0
0
0
0
0
0
1
2
2
2
0
0
0
0
0
1
0
2
1
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
1
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
2
2
0
0
1
3
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
2
1
1
0
1
1
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
1
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
1
0
1
2
0
0
0
0
0
0
0
2
3
0
1
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
1
0
0
3
0
2
0
0
0
0
3
0
0
0
0
2
3
0
2
2
1
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
1
0
2
0
1
0
0
0
1
0
0
0
0
2
0
3
0
0
0
0
0
1
0
0
1
1
0
1
2
0
0
0
0
0
2
0
0
2
0
1
0
0
0
2
2
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
3
0
2
0
0
0
3
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
1
0
3
0
3
0
2
0
2
0
1
0
0
0
1
0
0
0
0
0
2
0
1
0
1
2
0
0
1
0
0
0
0
2
1
0
1
0
0
3
0
1
0
0
0
0
0
0
2
3
0
2
0
0
1
0
0
0
1
0
0
1
0
0
0
2
0
0
0
2
2
0
0
0
0
0
2
1
0
0
1
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
9
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
1
2
0
0
0
1
3
0
0
0
0
0
0
2
0
0
0
0
2
1
1
2
0
2
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
3
1
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
1
1
0
2
0
0
0
0
0
1
0
1
1
1
1
2
0
0
1
0
2
2
2
4
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
3
0
1
0
0
0
2
0
0
0
0
2
2
0
0
2
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
1
0
0
2
0
1
1
0
0
2
0
0
2
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
2
2
0
1
2
2
1
0
0
0
0
0
0
0
0
0
1
0
6
0
0
0
0
0
2
0
0
1
0
2
2
0
0
0
0
0
0
0
1
0
0
2
1
3
0
2
0
0
0
0
2
0
1
1
0
2
1
1
0
0
0
1
0
0
0
1
0
1
0
0
2
0
5
0
0
5
0
0
0
2
0
0
0
1
0
1
0
0
0
1
2
0
1
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
2
0
0
1
0
0
1
0
0
1
0
2
0
1
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
2
0
2
0
0
0
0
0
1
0
1
0
2
0
2
2
1
0
0
0
0
1
0
0
0
0
1
1
0
0
2
0
2
0
0
0
1
0
0
2
1
0
0
0
0
2
0
2
0
0
1
0
0
2
0
0
0
0
0
2
0
1
0
3
1
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
4
0
0
0
0
0
1
0
2
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
2
1
0
0
2
0
2
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
3
0
0
0
0
0
0
0
0
0
1
1
2
0
0
1
1
2
0
0
0
1
0
2
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
2
0
0
1
1
0
2
1
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
2
2
0
0
0
2
2
0
0
0
0
0
1
0
2
2
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
4
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
1
0
1
1
0
0
0
1
0
2
0
2
2
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
2
0
0
0
2
0
2
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
1
0
0
3
0
2
0
2
0
0
2
0
0
0
1
0
0
0
0
2
0
1
0
0
0
2
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
1
8
10
0
0
0
2
2
1
1
0
0
0
2
1
0
1
0
1
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
1
3
0
1
0
1
1
0
3
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
2
0
0
2
0
1
2
0
2
0
0
0
2
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
2
2
0
2
0
0
0
0
2
0
0
7
1
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
3
0
0
0
1
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
1
1
1
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
2
0
1
0
0
0
0
2
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
1
2
1
0
1
2
0
2
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
2
0
0
0
1
1
2
1
1
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
2
3
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
2
0
0
2
0
7
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
2
0
0
1
0
0
2
1
0
1
3
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
6
0
0
0
1
0
0
0
0
0
0
5
0
0
0
2
0
0
0
2
0
2
1
0
0
1
2
0
0
1
0
0
0
1
0
0
0
2
1
0
2
0
1
0
2
2
0
2
0
0
0
3
0
1
1
1
0
0
0
0
1
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
2
0
0
1
0
0
2
1
0
2
0
0
0
0
0
0
1
0
0
1
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
2
0
0
0
3
0
0
0
0
0
2
0
2
0
0
0
2
1
0
0
2
1
1
0
0
1
1
0
1
0
1
0
2
0
2
0
0
2
2
0
0
0
0
1
1
0
2
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
3
1
1
2
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
4
0
0
0
0
2
6
2
0
0
0
0
0
2
0
0
0
2
0
2
0
0
1
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
2
1
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
1
1
2
2
0
0
0
0
2
0
0
2
2
0
0
0
0
4
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
1
2
0
0
0
0
1
0
0
2
1
2
0
1
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
2
0
0
1
1
0
1
2
1
0
2
0
0
1
0
1
2
0
2
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
4
0
2
0
0
2
0
0
0
1
1
0
0
0
2
2
0
0
4
0
0
0
0
0
2
1
2
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
1
0
1
1
0
0
0
0
0
0
0
2
1
1
0
1
0
1
0
0
0
0
0
1
1
0
2
0
0
0
0
0
2
0
0
0
1
1
1
3
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
3
0
1
0
1
2
1
1
1
0
0
1
2
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
1
0
2
0
0
2
0
0
2
1
0
2
2
2
0
0
0
0
0
0
0
0
6
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
1
0
1
2
0
2
0
2
1
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
2
0
0
0
0
1
0
1
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
1
0
1
2
0
2
2
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
6
0
1
0
1
3
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
2
0
1
2
1
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
2
2
1
2
1
0
0
0
3
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
3
0
0
0
0
0
1
0
0
0
2
0
0
0
2
2
0
2
2
1
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
1
0
1
3
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
1
2
0
0
0
0
2
0
2
2
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
1
3
1
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
2
2
0
2
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
1
0
0
1
2
1
2
0
0
2
2
0
0
2
2
2
2
2
0
0
0
2
1
0
0
0
2
0
3
1
0
1
1
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
3
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
1
2
0
2
1
0
0
0
0
0
2
2
1
1
0
0
0
3
1
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
2
0
1
0
0
1
0
0
0
0
0
1
0
0
0
2
1
0
2
6
0
0
0
0
0
1
0
0
1
0
0
1
3
2
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
1
0
2
2
2
1
1
0
1
2
1
0
2
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
3
2
0
0
2
4
0
0
1
2
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
1
2
2
2
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
1
2
0
2
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
2
1
1
0
0
1
0
0
3
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
2
0
0
0
0
0
0
1
1
4
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
2
1
0
0
0
0
0
0
2
2
3
0
2
3
4
0
0
0
0
1
0
2
0
0
0
0
0
1
2
0
0
0
0
0
1
1
0
1
0
3
0
2
0
0
0
0
0
0
0
0
0
1
0
1
2
2
1
0
0
0
2
0
0
0
0
0
0
0
2
1
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
2
2
0
0
2
0
0
0
0
0
0
1
3
0
0
0
0
0
2
0
1
2
5
2
0
0
0
3
0
0
0
0
2
1
1
0
0
2
0
0
0
0
2
2
1
0
0
2
0
2
1
0
0
0
1
0
0
1
0
0
0
1
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
2
0
0
2
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
2
2
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
4
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
2
1
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
3
2
0
2
0
2
0
1
2
0
1
0
0
1
0
0
0
0
0
3
1
1
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
1
1
1
1
0
0
0
0
2
2
0
0
3
0
0
1
0
0
0
0
0
1
0
0
0
2
1
0
0
0
1
1
0
0
0
2
0
0
0
0
0
1
0
2
2
0
0
1
0
1
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
2
0
4
0
2
0
0
0
2
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
2
2
0
1
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
2
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
1
2
2
0
0
0
2
0
1
2
4
0
0
0
1
2
0
0
1
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
1
0
0
0
2
0
0
0
2
0
2
0
1
2
0
0
0
0
0
0
3
0
0
0
0
0
1
2
0
2
0
0
0
2
0
2
4
0
0
2
0
0
0
0
0
1
1
0
0
1
3
1
1
2
0
0
2
0
0
0
2
0
0
0
0
3
1
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
1
0
4
1
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
1
0
0
1
0
1
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
3
0
2
0
0
0
0
1
2
0
0
2
0
1
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
1
1
0
2
1
1
0
0
2
4
0
3
0
0
0
0
0
0
0
0
2
3
3
0
2
2
1
0
0
2
4
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
9
1
1
1
0
0
0
0
0
2
2
0
0
0
0
1
0
0
2
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
1
0
3
3
0
1
0
1
1
1
0
0
2
0
2
0
0
2
0
2
0
0
0
3
0
1
0
0
0
0
2
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
2
0
2
0
4
0
0
0
0
4
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
2
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
2
2
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
2
0
0
0
2
0
0
1
0
0
1
1
0
0
2
0
2
0
0
1
0
0
0
0
1
0
0
2
2
0
2
0
0
1
0
0
2
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
7
0
0
0
0
2
0
2
0
0
2
2
0
0
2
0
2
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
2
0
2
0
1
0
1
1
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
1
1
2
0
2
1
0
0
1
2
1
0
1
0
0
2
1
1
0
0
0
1
0
0
2
0
0
2
2
0
0
0
0
0
0
1
2
0
1
1
0
0
0
0
2
1
1
0
0
1
0
0
2
0
2
1
0
2
0
0
0
1
1
0
0
0
0
3
0
1
3
0
1
1
0
2
0
0
1
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
3
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
3
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
2
0
0
1
0
0
0
1
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
2
1
2
1
2
2
0
0
2
10
0
0
0
0
0
0
0
0
4
2
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
5
0
3
0
1
0
2
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
3
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
1
3
2
2
0
1
2
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
1
2
1
1
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
3
0
1
2
2
0
1
0
3
0
0
3
0
0
0
2
0
0
1
2
2
1
1
0
1
0
0
0
0
2
0
0
2
0
0
1
0
0
0
1
2
0
0
0
1
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
3
1
0
2
2
0
0
0
2
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
1
1
0
0
0
2
0
2
1
0
2
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
2
2
2
0
2
0
0
0
1
0
1
1
1
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
1
1
2
0
0
0
1
0
0
0
0
0
2
2
2
1
0
0
0
0
3
0
2
0
0
2
0
1
1
1
0
0
0
0
0
0
0
1
1
0
1
0
3
0
0
3
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
2
1
1
0
2
0
0
0
1
0
2
0
0
2
0
0
0
0
2
3
0
1
2
0
3
0
0
0
0
2
0
0
0
0
0
2
0
0
7
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
3
0
1
0
0
1
1
1
2
1
0
0
0
0
0
2
0
1
3
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
3
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
1
1
1
0
0
0
2
0
2
1
0
0
0
1
1
2
0
0
0
2
2
1
0
0
1
0
0
0
0
2
0
0
0
0
1
2
2
0
0
0
0
1
2
1
0
0
0
2
0
0
0
0
2
1
1
1
0
2
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
2
0
0
0
2
0
1
0
2
0
1
0
0
1
0
0
0
0
3
0
0
1
0
0
0
1
2
0
1
0
0
1
3
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
2
0
5
0
2
2
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
2
0
2
0
0
2
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
1
0
0
1
2
0
0
0
0
0
0
2
0
1
0
2
1
2
2
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
5
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
3
0
1
0
0
0
1
0
2
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
1
2
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
2
0
0
2
1
0
0
0
2
1
0
5
0
1
0
2
0
2
0
1
0
1
2
1
0
1
0
0
0
0
0
2
0
0
4
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
2
0
0
2
0
2
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
1
2
0
0
5
2
3
0
0
2
0
0
1
0
0
0
2
0
0
0
2
2
0
2
2
0
0
1
1
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
3
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
1
0
1
2
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
2
3
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
1
2
0
0
0
1
0
0
1
2
2
0
0
0
0
1
0
0
1
2
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
1
3
0
1
1
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
2
3
0
0
0
1
2
0
2
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
2
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
4
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
2
0
0
0
2
0
0
2
2
0
0
0
0
1
1
0
0
0
0
0
0
1
2
0
0
1
4
2
0
1
0
0
0
3
2
1
1
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
1
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
2
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
1
0
0
0
0
3
0
0
1
0
0
0
2
0
0
2
1
0
0
0
0
0
1
0
0
2
0
0
1
0
0
2
0
0
0
0
3
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
3
0
0
0
2
1
0
0
0
2
0
0
1
1
0
0
0
0
0
1
0
0
2
0
2
0
0
2
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
1
0
0
0
0
0
2
0
2
2
0
0
0
1
0
0
0
2
3
2
0
0
0
0
0
2
0
0
0
0
1
1
1
0
0
0
0
0
0
2
2
0
2
0
0
0
0
2
0
2
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
3
0
2
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
3
1
2
0
0
0
0
0
0
0
2
0
0
2
0
3
2
0
1
0
0
0
1
0
1
0
0
0
1
0
1
2
0
0
2
0
0
2
0
3
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
2
0
3
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
2
0
1
0
0
0
0
2
0
0
0
2
1
0
0
0
2
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
3
0
2
0
0
1
0
2
1
2
0
0
0
0
0
0
0
0
0
1
2
0
1
2
2
1
0
0
0
0
0
0
2
0
1
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
2
1
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
3
0
5
0
0
0
0
0
2
3
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
1
2
0
2
1
0
0
0
0
0
0
0
5
0
1
0
0
0
2
0
0
0
0
0
0
0
0
3
1
2
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
2
0
0
0
1
0
0
0
6
1
0
1
3
0
1
0
2
0
0
0
0
1
0
2
1
0
1
0
4
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
1
0
0
2
0
1
0
5
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
1
0
2
4
0
2
0
0
0
0
0
0
0
3
2
2
0
0
0
2
4
0
0
0
0
0
1
2
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
2
0
0
0
2
1
0
1
0
0
0
0
0
0
1
3
0
0
0
3
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
1
0
1
2
1
0
0
0
0
2
0
0
2
1
0
2
0
1
0
0
0
0
2
0
0
0
2
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
1
0
1
2
0
0
0
1
0
0
2
0
0
0
0
2
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
2
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
2
1
0
0
0
0
2
0
1
1
0
0
3
0
1
1
0
0
0
0
2
0
0
1
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
1
2
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
2
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
1
0
0
2
0
2
0
1
0
0
1
0
0
0
0
3
2
0
0
2
0
1
0
1
2
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
3
1
0
1
0
0
0
0
2
1
1
0
0
0
0
1
0
0
0
0
6
0
0
0
3
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
3
0
1
0
0
0
0
0
2
0
2
0
0
1
0
0
2
0
1
2
0
0
0
0
0
3
0
0
0
0
0
2
1
0
0
2
2
0
0
0
2
3
0
2
2
0
0
0
0
2
0
0
1
0
0
0
0
2
0
2
0
0
0
2
0
2
2
2
1
0
0
0
0
1
0
1
0
2
0
0
0
1
0
4
2
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
2
0
3
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
3
0
2
0
0
2
0
1
2
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
1
0
0
0
2
0
1
0
1
2
0
0
0
2
0
1
0
0
2
2
1
0
0
2
0
1
1
3
0
0
0
1
0
2
0
0
0
0
0
0
1
2
0
0
0
2
0
1
1
1
0
0
0
0
1
0
0
0
1
0
2
0
0
0
3
0
7
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
4
0
2
2
0
1
2
0
1
2
2
0
0
0
0
2
1
1
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
2
0
4
0
0
0
1
1
0
0
2
0
0
1
0
1
1
0
0
1
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
2
0
1
0
0
2
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
2
2
0
0
0
3
1
2
0
2
1
0
0
0
0
0
0
0
2
0
0
1
0
3
1
0
2
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
1
2
0
3
1
0
0
0
1
0
0
0
0
0
1
1
0
1
0
2
0
2
0
0
0
3
2
2
0
4
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
2
0
0
0
1
0
0
0
3
1
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
2
4
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
2
0
0
0
1
2
0
0
0
1
0
0
0
2
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
2
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
1
2
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
2
0
1
0
1
0
2
0
0
0
2
0
1
0
0
0
1
2
0
0
0
0
0
0
1
1
0
0
0
1
0
3
0
0
0
0
1
0
0
0
3
0
0
1
0
0
2
0
0
3
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
1
0
0
1
0
0
0
1
2
1
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
1
2
2
0
0
2
0
0
2
0
0
0
1
0
2
1
0
2
2
0
0
0
2
0
0
1
0
1
0
2
1
1
1
0
2
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
1
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
3
1
0
0
0
2
0
0
0
1
1
0
2
0
3
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
1
0
2
5
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
1
0
0
0
1
2
0
0
0
0
0
0
1
2
0
0
2
0
2
0
2
2
0
0
0
0
1
1
0
6
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
2
2
0
0
0
1
2
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
2
0
1
0
1
0
0
5
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
4
1
1
0
0
0
0
2
0
0
1
0
0
3
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
3
3
2
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
2
0
0
1
5
1
2
2
0
0
0
2
0
0
1
2
0
0
3
0
0
0
0
0
0
0
2
1
4
0
2
0
0
1
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
1
2
2
2
2
2
1
0
0
2
0
3
0
0
1
0
0
0
0
0
0
1
2
1
0
0
0
0
1
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
3
0
1
0
0
0
0
1
0
1
0
0
1
0
0
2
0
2
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
3
0
2
0
1
4
0
0
2
0
0
2
1
0
1
1
0
3
0
0
0
0
0
0
2
0
0
1
0
0
1
0
1
1
2
0
0
0
0
1
1
0
1
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
2
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
2
0
0
1
2
2
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
4
0
0
1
0
0
0
0
0
2
0
0
0
0
2
2
0
2
2
2
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
1
0
0
0
2
0
1
0
1
1
0
0
2
0
0
0
0
0
1
1
1
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
3
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
1
1
1
0
0
0
0
2
0
1
0
2
0
2
1
0
1
0
2
2
0
3
0
2
0
1
1
0
0
0
1
0
0
0
2
0
0
0
1
0
1
0
0
2
0
0
1
2
0
0
2
1
1
1
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
1
0
0
0
2
0
0
0
2
1
2
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
1
2
0
0
0
0
0
2
0
2
2
0
0
1
0
2
0
0
2
2
1
0
0
0
0
0
1
0
1
0
0
0
0
2
1
2
0
0
0
0
2
0
0
0
0
3
0
1
0
1
0
0
1
1
1
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
1
0
2
0
1
0
0
0
1
1
2
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
4
0
1
0
0
1
2
0
0
4
1
2
0
0
0
0
1
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
2
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
2
2
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
5
0
0
0
0
3
0
3
0
2
0
0
1
0
2
0
0
1
4
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
2
6
0
1
0
0
1
1
0
0
0
0
2
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
2
0
2
0
0
0
0
1
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
2
0
3
1
0
2
0
1
0
1
2
0
0
0
1
2
3
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
1
0
1
1
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
1
4
2
0
0
1
0
0
1
0
2
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
4
0
0
0
0
1
0
1
0
2
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
1
2
0
1
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
5
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
2
1
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
3
0
0
0
0
0
2
0
0
0
0
0
1
1
1
1
0
0
1
0
2
1
0
0
2
2
0
0
0
1
0
0
0
3
0
0
2
1
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
3
1
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
2
0
2
3
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
2
2
0
0
2
0
0
0
1
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
3
0
2
0
0
1
2
0
0
0
0
1
2
0
0
0
0
0
1
0
1
0
0
0
2
0
0
2
0
2
0
2
1
0
0
0
1
2
0
1
1
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
1
3
1
0
0
1
0
3
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
2
3
0
0
0
0
2
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
4
2
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
2
0
0
2
0
0
1
0
1
0
0
1
0
2
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
1
1
0
3
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
2
1
0
0
0
0
1
0
0
1
0
0
1
1
0
0
2
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
3
0
0
0
2
1
0
2
1
4
0
0
0
1
0
1
0
0
2
0
2
0
0
1
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
4
0
1
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
3
0
0
0
0
2
0
0
1
0
0
0
1
2
0
0
0
0
0
1
0
1
2
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
2
1
0
0
1
1
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
2
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
1
2
0
2
0
1
2
0
1
3
0
1
0
2
0
1
0
0
2
2
2
2
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
1
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
4
2
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
2
0
1
2
3
0
0
2
3
1
2
0
1
0
0
0
0
0
1
0
0
3
2
0
0
0
0
2
0
0
0
0
0
0
1
1
0
3
0
2
0
0
0
0
3
1
3
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
2
0
1
0
0
0
0
2
0
1
0
0
0
0
1
2
0
0
3
0
0
0
0
0
1
1
1
0
1
0
2
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
1
1
0
2
1
2
0
0
3
0
0
0
1
2
1
1
2
1
0
0
2
0
1
0
1
0
0
0
0
2
0
2
0
0
0
0
1
0
0
2
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
4
0
0
2
0
2
3
0
1
2
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
2
3
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
2
0
2
0
0
0
1
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
2
0
3
0
0
0
0
2
0
1
0
0
2
0
0
0
4
0
0
2
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
1
0
0
2
1
0
1
0
1
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
1
2
3
0
0
0
2
0
2
0
0
0
0
0
1
0
6
2
0
0
0
0
1
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
1
2
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
3
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
5
0
0
2
0
1
0
0
0
0
1
0
1
0
2
0
2
2
2
2
0
0
2
2
3
0
2
1
1
0
2
1
0
1
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
1
0
3
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
2
0
0
1
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
4
1
2
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
4
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
2
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
1
1
0
2
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
1
0
2
1
0
0
0
0
0
1
1
0
0
1
0
2
0
2
0
0
0
1
1
1
0
1
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
2
0
0
1
5
0
2
0
2
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
2
2
1
2
0
0
2
0
0
1
0
0
0
0
0
3
0
2
0
2
0
0
1
0
2
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
2
2
0
0
0
0
0
0
1
0
1
3
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
4
0
2
0
1
0
0
0
1
2
2
0
1
1
0
2
2
0
0
0
0
1
0
0
0
0
1
3
2
0
2
0
0
2
0
0
1
1
0
0
0
0
0
0
0
1
0
0
4
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
1
0
0
4
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
2
2
0
0
0
2
2
0
0
0
0
2
0
1
0
0
1
2
2
0
0
0
0
0
0
0
0
1
0
2
0
0
2
2
1
0
0
2
0
1
0
1
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
1
0
1
2
1
0
0
0
1
0
2
1
0
0
2
1
0
1
0
2
0
0
2
0
0
0
0
1
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
2
0
0
1
1
0
0
2
1
1
0
1
0
1
2
0
0
0
2
0
0
2
0
0
1
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
3
0
1
0
2
0
0
0
0
1
0
1
0
0
0
3
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
2
0
1
2
0
1
0
0
0
0
1
1
0
2
0
2
0
1
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
1
0
0
2
0
1
2
0
2
0
3
2
1
0
0
0
0
0
1
1
0
2
0
0
1
0
0
1
2
0
0
0
3
1
0
0
1
0
0
0
0
0
2
2
0
1
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
2
0
1
0
0
0
0
2
0
2
3
1
1
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
1
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
2
0
1
0
0
2
0
0
3
0
4
0
2
2
0
0
0
1
0
0
0
0
0
0
1
0
3
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
2
1
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
1
1
0
1
0
2
2
0
0
2
1
1
0
0
1
0
0
1
7
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
2
1
0
0
0
0
0
0
0
1
0
0
0
1
2
0
1
0
2
1
0
0
3
0
1
2
0
2
2
0
1
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
3
2
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
1
1
0
0
1
2
1
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
1
0
0
0
1
2
0
0
2
0
0
0
1
0
3
1
0
0
0
1
0
2
4
0
0
1
2
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
8
0
0
0
0
2
0
0
0
1
0
1
0
1
0
0
0
0
2
0
0
2
0
0
0
0
4
0
3
0
0
0
0
1
0
2
0
0
0
0
1
0
2
0
0
2
2
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
1
0
4
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
3
0
0
2
0
0
0
1
1
0
1
0
0
0
1
2
0
2
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
3
0
0
1
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
2
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
1
0
0
0
2
0
2
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
2
0
5
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
2
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
2
2
0
2
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
2
0
0
0
0
2
2
0
2
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
2
0
1
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
2
0
0
0
2
0
0
1
0
2
0
0
1
1
0
0
0
0
2
1
0
1
0
1
1
0
1
0
0
0
1
0
2
2
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
7
0
0
0
0
0
2
2
0
0
0
5
2
1
0
2
0
0
1
1
0
0
1
0
0
1
0
1
3
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
1
2
2
0
0
0
0
1
0
0
0
2
0
0
1
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
4
0
1
0
0
0
0
2
0
1
0
2
0
1
1
0
2
0
0
2
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
3
0
1
0
0
0
2
0
0
1
2
1
0
0
0
1
0
0
2
0
2
0
1
0
3
2
0
0
0
0
2
2
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
1
0
0
0
2
0
1
2
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
1
0
0
2
0
2
0
1
0
0
0
0
2
1
0
1
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
1
0
0
2
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
2
1
1
0
1
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
2
2
0
0
2
0
0
0
0
1
2
0
0
0
1
0
0
0
1
1
2
0
0
2
3
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
2
2
0
3
1
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
2
0
2
1
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
3
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
2
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
4
0
2
1
0
0
2
0
0
0
0
0
2
0
1
0
1
0
2
1
1
0
1
1
0
0
1
2
0
2
0
1
0
3
0
0
0
2
0
0
0
1
1
0
0
0
0
2
0
1
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
3
0
0
0
0
0
0
0
1
0
1
1
1
2
0
0
0
0
0
1
2
1
0
1
0
0
0
0
2
1
0
0
0
0
1
2
0
0
0
0
0
3
0
2
2
0
3
0
3
0
0
0
0
0
0
0
3
0
0
1
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
7
2
2
1
0
1
2
0
2
1
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
3
0
0
1
1
1
2
0
0
2
0
0
0
0
2
0
1
2
0
0
0
2
1
0
0
1
0
0
2
0
2
2
2
1
0
0
3
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
1
3
0
0
1
0
0
1
0
0
0
2
4
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
1
0
0
0
1
1
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
3
0
1
1
0
0
1
0
0
1
0
0
0
0
2
2
0
0
2
2
1
0
1
2
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
1
1
2
0
1
5
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
3
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
3
0
0
0
1
0
2
2
0
0
1
0
0
3
0
0
0
1
0
1
0
1
2
0
0
0
2
0
0
1
1
0
0
2
1
0
1
2
0
0
0
0
0
0
1
2
1
2
0
0
1
2
0
1
0
1
3
0
0
0
1
1
0
1
0
0
0
0
5
0
0
0
0
2
2
1
2
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
2
1
1
0
2
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
5
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
2
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
5
0
2
1
0
2
0
0
1
1
3
0
0
0
0
0
0
2
0
0
0
1
1
2
2
2
3
0
2
1
0
0
0
2
1
1
0
0
1
0
2
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
1
0
0
0
2
0
0
0
0
0
2
1
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
2
0
0
0
0
1
1
2
1
0
4
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
2
0
0
0
0
0
0
2
2
1
0
2
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
2
1
1
2
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
3
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
2
1
0
0
1
0
1
0
0
2
0
0
0
2
1
0
0
1
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
2
1
0
1
0
2
1
2
0
0
0
0
0
2
0
4
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
2
2
1
0
2
2
0
0
0
2
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
1
0
1
0
2
0
0
0
0
0
0
2
0
3
0
0
0
0
1
0
0
0
1
0
2
2
0
2
0
0
0
0
2
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
2
3
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
3
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
3
1
2
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
2
0
0
0
0
2
3
0
1
1
1
2
1
0
0
0
0
0
0
0
1
1
1
0
0
0
1
2
0
0
0
0
0
3
1
0
2
0
0
2
0
0
0
0
1
2
0
2
0
0
0
2
4
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
4
0
0
0
1
0
1
0
0
0
4
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
2
1
3
0
0
0
0
1
0
1
0
0
0
0
1
6
0
0
2
2
2
0
0
0
0
2
0
0
2
2
0
1
0
1
0
0
2
0
1
0
0
0
0
0
0
0
1
2
5
2
0
2
0
2
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
2
0
2
0
0
1
2
0
0
1
2
2
0
0
0
0
0
2
0
1
1
1
0
0
0
0
0
0
0
0
0
2
6
1
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
2
0
0
2
0
0
1
0
1
0
0
0
2
0
0
0
0
0
2
1
0
2
0
0
1
0
0
0
1
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
2
0
14
1
0
2
1
0
2
2
0
0
1
0
0
0
2
0
2
0
11
0
0
0
0
0
0
2
0
5
1
0
0
1
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
2
0
4
0
0
0
1
0
2
2
2
0
2
0
0
0
0
2
0
1
1
0
1
0
1
1
0
1
0
1
1
1
2
0
0
0
0
0
0
0
0
2
0
1
0
4
0
0
2
0
0
2
3
0
0
0
0
0
2
0
0
0
2
0
1
2
0
0
0
3
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
1
1
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
2
1
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
3
0
2
2
0
1
2
0
0
2
5
0
0
0
1
0
0
2
1
0
0
1
4
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
3
0
2
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
5
0
0
0
2
1
2
2
0
0
0
0
0
0
4
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
2
1
4
1
0
2
0
0
0
0
0
2
0
0
0
2
1
1
2
0
0
1
0
1
0
2
2
1
1
2
0
0
0
0
5
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
3
0
0
2
0
1
0
1
2
2
0
0
0
0
2
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
1
0
0
2
0
1
1
0
0
0
0
1
2
0
2
0
0
0
0
0
2
0
1
2
1
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
1
0
2
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
3
4
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
7
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
2
0
0
0
0
1
0
3
0
0
0
0
2
0
0
1
0
0
0
0
1
3
0
0
0
1
0
0
1
2
0
0
0
0
0
2
0
0
2
1
2
0
0
2
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
1
1
0
0
2
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
2
0
1
0
1
2
0
0
0
2
0
0
0
2
2
0
0
4
0
1
3
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
3
0
0
1
0
0
0
1
0
1
1
0
0
2
2
0
0
0
0
3
0
0
0
0
1
0
0
1
0
0
2
0
0
1
2
0
0
0
0
0
1
0
3
2
0
1
0
1
0
0
0
0
0
0
1
0
0
2
0
1
0
0
2
1
0
1
0
1
0
0
0
0
3
1
3
1
0
2
0
0
4
0
0
0
0
1
3
0
0
0
0
0
0
0
4
2
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
2
0
1
3
0
2
0
0
1
0
0
0
0
0
1
0
0
1
2
0
0
0
0
3
2
0
2
0
2
0
0
3
0
1
0
2
2
0
0
2
0
0
2
0
0
2
2
0
1
0
0
0
0
1
1
0
0
2
3
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
2
0
0
0
0
2
0
2
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
2
0
2
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
2
1
0
2
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
2
1
0
0
0
0
1
0
0
2
1
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
2
0
2
0
0
2
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
2
9
0
0
1
0
0
1
0
1
0
0
2
2
0
1
0
1
3
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
1
0
0
0
1
0
0
1
0
1
0
1
1
0
1
0
0
0
0
0
0
0
1
1
2
1
0
0
1
0
1
0
0
2
0
0
3
0
2
0
2
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
1
0
2
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
2
2
0
2
2
0
0
0
2
0
0
0
2
0
1
2
0
2
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
2
0
3
2
0
0
0
2
0
0
3
0
2
0
0
1
0
0
1
0
0
0
0
0
0
4
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
2
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
2
1
0
0
0
0
0
1
2
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
2
0
2
2
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
1
0
2
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
1
1
2
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
1
2
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
1
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
1
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
1
2
1
1
1
0
0
0
1
0
1
1
0
0
0
0
0
1
0
2
0
0
4
0
0
3
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
3
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
2
0
0
0
0
2
0
1
0
0
0
1
2
0
0
2
0
0
0
2
0
0
0
0
0
2
0
2
0
3
0
2
0
0
0
1
0
0
0
2
2
0
1
0
0
0
1
0
0
0
2
1
0
0
2
0
0
0
2
0
1
1
1
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
2
0
0
1
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
1
0
3
1
2
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
1
0
3
0
0
0
0
0
0
2
1
2
0
0
3
1
0
0
0
0
0
0
0
1
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
2
0
1
0
0
0
0
0
2
0
0
0
2
2
2
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
3
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
5
0
0
2
0
0
0
1
0
0
2
2
2
0
0
1
1
0
2
0
1
1
0
5
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
1
1
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
2
3
0
0
0
0
2
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
1
2
0
0
2
0
1
1
0
0
1
1
0
3
2
0
1
0
0
0
1
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
3
0
0
0
0
0
1
0
0
2
0
1
0
0
0
1
1
0
1
0
0
0
0
0
1
1
2
0
0
0
0
2
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
2
0
0
0
1
2
0
0
3
0
0
2
2
0
0
2
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
2
0
0
3
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
3
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
7
0
0
2
2
0
0
1
0
0
1
0
2
1
2
0
0
0
0
1
0
2
0
0
0
1
2
1
1
1
0
0
1
0
2
0
0
0
4
0
2
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
2
2
1
0
0
2
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
3
2
0
0
0
3
0
0
0
2
0
1
0
0
0
0
0
4
0
1
0
1
1
0
1
0
0
0
2
0
2
0
2
2
0
0
0
7
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
2
2
0
1
0
0
1
2
1
1
1
1
0
1
1
0
2
1
1
0
2
0
1
0
1
0
0
2
2
0
0
2
0
0
0
1
2
1
2
0
2
3
1
0
0
0
2
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
1
1
1
1
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
2
0
1
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
2
0
0
1
1
1
0
0
0
0
1
0
2
0
0
0
0
1
1
0
1
0
2
0
0
0
1
1
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
2
0
0
0
0
2
0
2
2
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
4
0
1
1
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
2
0
1
1
0
0
0
0
0
0
2
0
0
5
0
2
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
2
1
0
0
0
0
0
2
0
0
1
0
4
2
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
1
0
1
2
4
0
0
1
0
0
0
2
0
2
1
0
0
1
0
3
2
0
0
0
0
1
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
1
0
0
0
2
1
0
0
0
0
0
0
2
0
1
1
2
2
0
0
0
1
0
2
0
0
0
1
1
1
2
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
1
0
2
1
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
2
0
0
0
2
1
0
3
0
2
0
3
0
2
0
0
0
2
0
0
0
1
2
2
0
0
4
2
0
0
0
0
2
0
1
0
3
1
2
0
0
3
0
0
0
0
1
2
1
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
1
3
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
2
2
0
2
1
1
0
0
0
0
0
0
2
0
2
1
0
0
0
1
0
2
0
0
0
0
0
0
3
2
0
0
2
0
2
1
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
1
0
0
2
0
2
0
0
0
0
2
0
0
0
0
1
0
3
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
1
0
0
3
0
1
0
0
3
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
2
0
1
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
2
1
0
0
1
0
1
1
2
0
2
0
0
0
0
0
0
0
1
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
1
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
3
2
0
0
0
0
7
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
15
0
1
0
0
0
0
2
2
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
3
0
2
1
2
0
1
1
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
2
0
0
0
0
0
0
2
0
1
0
0
8
0
0
2
0
0
3
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
1
2
0
0
0
2
0
0
2
2
0
1
0
0
0
8
0
1
0
0
0
1
0
0
2
4
0
2
2
0
1
2
0
2
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
8
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
1
1
1
0
1
0
1
0
2
0
2
0
1
0
0
0
2
0
0
0
2
0
2
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
2
0
2
0
0
0
0
0
2
0
1
1
2
0
2
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
1
1
1
0
0
0
2
0
0
2
2
0
0
1
0
2
0
0
0
0
1
0
1
0
0
3
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
3
1
0
0
1
0
1
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
3
0
0
2
0
0
0
0
1
0
1
0
0
0
0
1
2
0
0
0
0
0
0
3
0
0
0
0
0
3
0
1
2
1
0
0
2
0
0
0
0
2
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
3
2
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
3
0
2
0
0
1
0
1
1
1
0
1
0
1
0
0
0
0
0
2
0
0
2
0
3
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
2
0
0
2
2
0
0
3
2
1
0
0
0
0
0
1
0
1
0
0
0
0
7
2
0
0
0
1
0
0
1
0
2
0
1
1
2
0
0
1
1
1
1
2
2
0
1
0
1
0
2
0
0
0
2
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
2
1
0
2
0
0
0
1
0
0
1
1
2
0
0
0
2
0
2
0
0
0
1
0
2
1
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
4
0
0
0
0
1
0
1
1
0
0
1
1
4
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
2
2
0
6
2
0
2
0
1
0
0
0
0
2
0
0
1
0
0
1
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
1
0
2
0
1
1
0
0
0
0
0
0
0
2
0
2
1
1
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
4
0
2
2
0
0
1
0
0
0
1
0
0
0
0
0
2
2
0
2
0
0
0
2
0
0
0
1
3
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
3
2
1
2
2
0
0
1
0
0
2
0
3
0
1
0
1
2
1
0
0
1
1
0
3
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
1
0
0
0
1
0
0
2
1
0
1
2
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
4
0
2
1
0
0
0
0
2
0
0
0
2
0
1
0
0
0
2
0
0
0
1
1
0
1
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
2
1
0
2
0
0
0
0
0
0
2
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
1
2
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
2
0
0
2
0
0
1
0
0
1
2
2
1
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
2
2
5
2
0
0
0
0
1
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
2
1
0
0
0
0
0
0
1
2
2
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
2
2
0
1
0
0
0
0
0
0
2
2
0
0
2
0
2
0
0
1
0
2
1
0
0
0
0
1
2
0
2
0
0
1
0
0
0
0
0
1
0
2
0
1
0
0
0
2
0
0
0
0
2
0
2
0
1
0
0
0
2
2
0
7
0
0
0
2
0
0
1
2
0
0
3
0
1
1
0
2
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
3
0
0
0
0
0
0
0
1
3
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
1
0
1
1
0
0
1
2
0
0
1
3
0
2
0
0
0
1
2
0
0
0
0
0
1
1
0
2
1
2
0
1
2
0
0
0
0
0
0
0
0
0
1
1
3
0
0
0
2
0
0
0
3
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
1
2
0
2
2
0
2
1
0
0
0
0
3
0
1
0
1
1
0
0
0
0
2
1
3
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
3
0
2
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
2
1
0
2
0
0
0
0
2
2
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
1
1
1
1
1
1
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
3
0
2
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
1
0
1
1
0
0
3
1
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
1
1
0
2
1
0
0
0
0
2
2
0
1
2
0
0
0
0
1
0
0
0
2
2
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
1
1
0
0
1
1
0
0
0
1
2
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
1
1
0
1
0
2
0
0
0
0
0
2
0
3
2
0
1
2
1
2
0
1
0
0
0
0
5
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
1
0
0
1
4
2
0
2
0
0
0
0
0
0
2
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
2
0
0
0
2
0
1
1
0
0
1
0
0
0
0
0
1
2
0
0
0
0
2
1
1
1
1
0
2
0
0
2
0
0
1
2
0
0
0
0
1
1
0
1
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
2
0
2
0
0
1
0
1
0
0
0
0
0
0
1
0
2
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
2
0
0
0
0
2
0
0
4
2
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
3
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
3
2
2
0
0
0
2
0
0
2
3
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
2
2
0
1
0
1
1
0
0
1
0
0
0
0
2
2
4
2
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
9
0
0
0
0
0
0
3
0
0
2
2
0
0
0
0
0
1
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
3
1
0
0
0
2
2
1
1
0
0
2
1
0
0
0
0
2
2
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
2
1
0
0
0
0
2
0
0
2
1
0
0
4
0
0
0
1
0
0
0
1
2
3
1
1
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
2
0
2
0
0
0
0
1
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
3
0
0
0
0
1
0
0
2
0
1
3
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
1
0
0
0
2
2
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
1
2
0
0
0
0
0
0
1
10
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
3
0
0
1
1
0
0
0
0
0
0
2
0
4
1
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
2
0
0
2
1
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
1
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
2
0
0
2
2
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
2
2
2
1
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
1
2
0
0
0
1
0
0
1
1
0
0
1
0
0
1
1
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
3
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
1
1
0
0
0
0
1
2
1
0
0
0
0
2
2
2
1
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
7
1
0
1
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
3
0
0
0
0
3
1
1
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
7
3
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
1
0
0
0
0
0
0
0
2
0
0
1
0
0
1
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
1
2
1
0
0
1
2
2
0
2
0
0
0
0
0
1
0
0
2
0
2
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
2
0
0
0
0
2
0
0
2
0
0
0
0
0
1
2
3
1
0
0
1
0
0
1
2
0
1
0
2
5
1
0
2
1
1
1
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
1
0
0
1
2
1
0
0
0
0
1
0
0
0
0
0
1
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
1
2
0
1
0
2
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
1
2
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
6
0
2
0
0
0
2
0
2
0
2
0
2
0
2
0
0
2
1
0
0
1
4
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
2
0
0
0
0
1
0
2
1
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
1
0
2
1
0
0
0
2
0
0
1
0
1
0
0
0
2
0
0
1
0
0
0
2
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
2
0
0
2
0
0
0
2
1
0
0
0
0
2
0
0
2
2
4
0
1
0
0
1
0
0
0
1
0
0
2
0
0
0
0
2
0
1
2
0
1
0
2
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
2
0
1
1
1
2
0
0
0
2
0
0
2
1
0
0
0
0
7
1
2
0
2
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
1
3
0
1
0
0
0
0
0
0
2
0
0
1
1
0
0
2
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
2
2
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
3
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
2
1
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
2
0
1
0
2
2
0
1
3
3
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
2
0
1
1
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
1
1
0
0
2
0
2
1
0
2
0
2
0
0
2
0
0
5
2
0
0
0
0
2
0
2
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
4
0
0
2
0
0
1
0
3
2
1
1
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
1
0
0
0
3
0
1
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
3
0
3
0
0
0
0
2
2
0
1
2
1
0
0
0
0
2
0
1
0
0
1
0
0
1
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
2
2
0
0
0
0
2
1
0
2
0
0
2
1
2
2
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
2
1
0
1
1
0
1
2
0
0
2
0
0
0
1
0
1
0
1
0
0
0
0
2
0
0
1
0
0
0
0
2
2
1
0
0
0
0
2
0
0
2
2
1
0
1
0
0
0
0
0
0
1
0
0
4
2
0
0
0
0
0
1
0
1
0
0
0
2
0
2
1
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
1
0
1
2
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
1
0
0
1
0
0
2
2
0
0
0
0
0
0
0
2
4
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
2
1
0
0
0
0
0
0
2
0
1
1
0
0
0
1
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
1
0
1
0
2
0
0
0
2
2
0
3
0
0
0
2
1
0
0
0
1
1
2
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
3
0
0
2
7
0
1
2
1
0
2
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
3
0
0
0
1
0
2
1
0
0
2
2
0
2
0
1
0
1
1
1
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
1
1
0
0
1
1
3
2
0
0
0
0
2
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
6
4
0
1
0
0
0
1
1
0
0
1
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
1
0
0
0
2
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
1
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
2
2
1
0
0
0
0
0
0
0
1
1
0
0
0
2
2
3
0
0
1
0
3
0
0
0
3
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
2
1
2
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
2
1
0
0
2
0
1
0
0
2
0
1
0
0
1
0
0
2
1
0
2
1
1
0
2
0
1
2
0
1
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
1
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
4
3
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
4
0
0
0
0
0
0
2
1
0
1
0
0
0
0
2
0
0
0
1
2
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
1
0
0
0
0
0
1
0
1
2
0
2
0
2
1
0
1
2
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
1
0
0
3
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
1
0
0
1
0
0
0
2
2
0
1
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
1
0
1
0
0
0
3
0
0
2
0
0
0
0
2
0
2
0
0
1
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
2
1
2
2
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
2
2
1
0
2
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
3
0
0
0
0
0
1
1
2
0
0
2
1
2
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
2
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
2
2
2
2
0
2
0
1
0
0
0
0
2
1
2
0
2
2
0
2
1
1
2
0
2
0
0
0
0
0
0
1
2
1
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
2
2
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
2
0
0
0
0
0
1
1
2
0
1
1
3
1
1
0
0
2
0
0
2
3
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
1
1
1
0
0
1
2
0
1
0
0
2
2
0
0
1
0
0
0
0
1
0
0
0
0
0
2
2
0
0
1
0
1
0
0
0
1
2
0
0
0
0
0
0
2
0
2
3
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
3
2
0
1
1
0
0
0
0
0
0
0
2
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
2
0
0
0
1
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
2
2
0
0
1
0
2
1
3
1
0
5
2
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
2
0
2
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
2
0
0
1
0
1
0
1
1
0
0
0
2
1
0
0
2
0
1
0
1
1
2
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
2
0
0
3
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
2
0
0
1
0
0
0
2
0
0
0
2
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
1
0
0
0
0
1
2
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
2
2
0
0
0
0
1
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
1
1
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
2
0
2
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
2
2
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
1
3
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
1
0
1
0
0
1
0
0
0
2
0
1
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
2
1
0
2
0
2
0
3
5
0
1
1
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
2
1
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
1
0
0
0
0
2
0
2
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
2
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
3
2
0
0
2
0
2
0
0
0
2
0
1
2
0
0
1
0
1
0
0
0
1
0
0
2
1
1
1
0
0
0
0
0
1
2
0
0
1
0
0
1
0
1
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
1
4
0
2
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
1
0
2
3
1
0
0
0
0
0
0
2
4
1
0
2
0
1
0
0
0
0
1
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
2
0
0
1
0
2
1
0
0
0
0
1
0
0
0
0
2
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
2
1
0
0
0
1
2
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
2
1
0
0
0
2
0
0
0
5
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
1
1
0
0
0
2
1
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
2
0
4
2
0
0
0
0
2
0
0
1
0
0
0
2
0
0
2
0
0
0
0
1
2
0
0
2
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
1
0
1
0
0
2
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
2
2
0
0
1
0
4
0
0
2
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
1
1
0
1
0
4
1
0
2
0
1
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
1
0
1
0
1
2
0
0
0
3
0
0
0
0
0
0
0
1
1
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
4
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
2
0
3
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
1
0
2
1
0
0
0
2
0
0
0
0
1
2
1
2
0
0
0
2
2
3
0
2
2
0
1
0
1
2
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
1
0
0
0
2
1
0
1
2
0
2
0
0
1
0
1
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
3
0
0
2
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
2
2
0
0
0
0
2
0
2
2
0
1
2
0
0
0
0
0
0
0
1
0
1
0
1
1
1
0
0
0
3
0
0
2
2
0
0
0
2
0
0
1
0
0
0
2
2
0
2
0
0
0
0
3
2
0
0
0
1
0
0
1
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
2
0
2
0
0
0
2
0
0
0
0
1
3
0
2
0
1
0
0
0
5
0
0
1
0
1
0
0
1
0
0
0
0
2
0
1
0
1
0
2
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
3
0
0
1
0
0
1
1
0
1
0
0
0
0
1
0
2
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
2
1
2
1
2
4
0
2
0
0
0
1
0
0
0
0
2
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
3
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
3
1
1
0
0
1
0
2
1
0
3
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
2
2
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
3
0
0
1
2
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
1
0
1
1
0
0
2
0
1
2
0
0
3
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
7
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
1
0
0
0
1
0
1
0
1
0
1
2
2
0
0
0
0
0
1
0
2
0
2
0
2
0
0
0
1
0
0
0
0
1
2
0
1
0
0
2
0
0
0
0
0
0
0
1
2
0
2
0
2
2
0
1
2
0
3
0
0
1
0
1
0
0
0
1
0
0
0
1
2
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
1
2
0
0
1
2
0
1
1
0
0
0
0
2
0
0
2
0
0
0
1
4
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
1
0
0
2
1
1
0
0
0
0
3
0
0
9
2
2
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
1
0
0
1
0
1
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
3
0
1
2
0
2
0
0
0
0
2
0
1
1
1
1
0
0
0
0
1
2
0
2
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
3
0
1
2
1
0
1
2
0
0
0
0
0
2
0
0
2
0
0
1
1
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
1
1
0
0
0
2
0
1
0
2
0
1
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
2
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
3
0
0
0
0
0
0
2
2
0
2
0
0
1
0
1
1
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
2
0
1
0
1
0
1
0
2
1
0
1
0
0
3
0
0
0
1
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
2
9
1
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
3
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
1
2
2
1
0
1
0
0
0
2
0
0
1
2
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
1
2
0
1
0
2
0
1
0
0
0
0
0
0
1
2
1
0
3
1
2
2
0
0
0
0
0
0
1
2
0
2
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
3
0
0
2
0
1
1
1
0
0
1
2
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
3
4
3
0
0
0
3
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
6
0
0
0
2
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
1
0
2
1
0
0
2
2
1
0
1
3
0
3
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
1
1
0
0
0
0
0
2
1
0
1
0
0
1
0
0
2
0
0
2
0
1
2
0
1
1
0
0
2
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
1
2
1
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
2
1
2
0
1
0
0
0
0
1
0
0
2
0
0
1
0
1
1
0
0
1
0
0
1
0
1
0
0
3
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
3
2
0
0
0
2
0
0
0
0
0
0
0
1
1
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
1
0
1
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
1
0
1
2
0
1
3
2
0
1
1
0
0
2
0
1
3
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
3
0
0
2
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
3
1
0
0
1
1
0
0
0
0
0
2
0
1
4
0
0
1
2
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
2
1
2
1
0
0
4
0
0
0
0
0
2
0
0
0
0
1
0
1
2
0
0
1
0
0
0
3
4
2
0
0
0
1
0
0
0
1
0
0
0
1
2
1
3
0
0
1
0
0
0
1
0
1
2
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
4
0
0
4
2
1
1
0
2
0
0
0
2
1
2
1
0
0
0
0
0
0
1
3
0
3
0
2
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
1
0
0
1
0
3
1
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
2
0
0
0
0
0
1
0
0
2
0
2
1
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
3
0
0
2
0
0
0
2
0
0
0
0
5
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
1
0
0
1
0
2
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
2
0
0
0
0
2
0
0
0
2
0
2
1
2
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
3
0
1
0
2
0
0
3
0
0
0
0
0
0
5
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
2
0
2
0
0
0
0
1
0
0
1
0
2
0
1
5
0
0
0
2
0
0
0
0
2
2
0
2
0
2
2
0
0
0
2
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
2
0
0
1
1
1
0
0
0
2
1
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
7
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
1
3
0
0
0
0
0
2
1
0
1
1
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
3
1
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
1
0
1
0
1
0
0
0
0
0
0
1
3
1
1
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
1
0
0
2
2
0
1
5
0
0
0
3
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
3
0
0
2
0
0
0
0
0
0
0
1
2
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
2
0
0
0
0
2
1
0
0
0
0
0
1
0
3
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
8
1
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
2
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
4
1
0
0
2
0
0
1
2
2
0
0
3
0
0
0
3
0
2
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
2
0
0
0
1
0
1
0
0
4
0
0
0
0
0
1
2
0
1
2
2
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
1
2
0
0
0
2
2
0
0
0
1
0
0
0
2
2
0
0
2
0
0
0
2
0
2
2
0
0
1
1
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
1
0
0
11
0
4
0
0
0
0
0
0
0
2
0
0
0
5
0
0
0
2
0
3
0
0
2
0
0
0
1
0
0
2
1
2
0
2
1
0
0
0
4
0
0
0
0
0
3
0
0
0
0
0
0
3
2
0
0
1
0
2
0
0
0
2
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
3
1
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
1
2
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
2
0
0
2
1
0
1
0
0
2
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
2
0
0
0
2
0
2
0
0
0
0
0
1
2
0
0
0
1
2
2
0
0
0
0
2
2
2
0
0
0
2
2
0
1
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
2
0
1
0
0
0
1
0
0
0
0
0
0
3
2
0
1
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
2
0
0
2
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
2
2
0
2
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
1
2
2
2
0
0
0
1
2
0
0
1
0
2
1
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
3
0
2
0
1
0
0
0
2
2
2
0
0
2
0
0
0
0
0
0
0
0
3
1
0
2
0
0
0
0
0
0
0
0
2
0
2
1
0
1
2
0
0
0
0
0
1
0
1
0
3
0
1
0
0
1
0
0
1
8
1
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
1
1
0
0
1
0
0
2
1
0
0
0
1
5
4
0
2
0
1
0
3
2
2
2
0
0
2
0
3
1
2
0
0
0
2
1
0
0
1
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
2
0
1
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
1
0
2
1
0
1
0
0
0
0
2
0
0
0
0
0
1
3
0
0
0
0
0
2
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
2
2
2
0
0
0
1
1
0
2
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
3
0
0
2
2
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
3
1
0
2
0
2
1
0
0
1
0
0
1
2
2
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
2
1
2
1
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
2
1
0
0
0
0
2
1
2
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
1
1
0
0
0
2
2
0
1
0
2
0
1
0
0
0
1
0
2
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
2
0
0
2
0
0
0
0
0
0
0
0
0
1
2
4
0
1
0
1
1
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
2
0
0
0
0
1
0
1
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
2
2
0
0
4
0
1
0
2
2
0
0
0
0
1
2
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
1
0
0
1
2
0
0
0
0
0
1
0
1
0
0
0
2
0
0
1
0
0
0
2
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
4
3
0
0
0
0
0
0
0
1
0
0
1
0
0
0
3
0
0
2
0
0
0
0
1
2
3
0
0
1
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
1
0
2
0
2
0
2
0
0
0
1
0
1
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
2
0
0
0
2
2
0
0
0
2
2
0
2
0
0
0
0
0
1
3
0
0
1
2
0
0
0
0
2
2
2
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
5
0
0
0
0
0
1
3
2
0
0
0
1
0
0
1
0
0
0
1
2
2
2
1
0
0
0
0
0
0
0
0
0
0
3
1
2
1
0
2
0
2
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
2
2
0
0
1
0
0
2
0
0
0
0
1
4
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
2
1
0
2
2
2
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
1
0
0
2
0
0
3
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
1
2
0
0
4
2
0
2
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
4
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
7
2
0
1
0
1
1
0
0
0
1
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
2
0
0
1
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
1
0
1
0
0
1
1
0
1
0
6
2
0
0
0
0
0
0
2
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
1
0
1
0
1
0
0
0
0
2
0
0
1
2
1
0
0
0
0
2
2
0
0
0
0
3
2
1
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
1
0
0
0
2
0
0
0
2
0
1
2
1
0
2
0
8
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
2
1
0
0
1
3
2
0
2
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
3
0
1
2
0
0
0
2
0
2
1
0
0
0
5
3
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
1
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
5
0
0
1
0
0
0
0
0
0
0
3
2
2
4
0
0
0
0
1
0
0
0
3
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
2
2
0
1
1
0
3
0
0
1
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
1
0
0
0
2
3
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
2
1
0
2
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
1
0
0
3
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
1
0
0
0
2
2
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
3
1
2
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
2
0
2
2
0
0
1
1
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
2
0
1
0
0
1
0
2
0
3
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
1
0
1
2
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
1
6
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
1
0
0
3
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
1
2
0
1
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
3
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
1
0
2
0
1
0
0
2
0
0
0
0
0
0
0
2
1
0
1
0
0
1
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
1
1
2
0
3
1
1
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
4
0
0
1
0
0
0
0
0
1
0
0
2
0
3
0
1
1
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
5
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
2
5
0
0
0
1
2
2
0
0
0
0
0
0
2
0
3
2
0
0
0
1
0
1
2
0
2
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
2
2
3
2
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
2
0
0
1
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
2
1
2
0
0
1
2
2
0
2
0
0
1
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
1
1
2
1
0
0
0
0
0
1
0
0
0
1
1
1
0
3
0
0
4
0
0
1
0
0
0
0
0
0
2
0
2
0
1
0
0
1
0
0
4
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
5
0
2
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
2
2
0
0
2
0
1
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
2
0
1
0
0
0
0
3
0
0
0
0
1
0
2
1
0
0
2
0
1
3
0
0
0
0
0
0
0
0
0
0
0
2
0
4
2
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
1
0
0
0
3
0
0
2
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
2
0
0
1
2
0
0
0
0
1
0
0
0
0
0
2
0
1
0
2
1
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
1
3
0
1
2
0
1
0
1
0
1
0
0
0
4
2
1
0
0
1
0
1
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
1
0
0
0
2
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
1
2
1
0
6
5
0
0
0
0
1
2
2
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
2
0
1
0
0
2
0
1
0
0
1
0
0
0
1
2
2
0
0
0
0
0
0
1
0
0
2
0
2
2
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
1
3
0
0
0
0
2
3
1
2
2
0
0
0
1
0
0
0
0
0
3
1
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
2
0
0
1
0
0
2
1
0
0
0
0
0
0
2
8
0
0
0
2
2
1
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
2
1
0
1
0
0
2
0
0
1
0
0
0
2
0
2
2
1
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
1
0
0
1
0
0
1
1
2
0
0
0
5
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
1
0
2
0
0
0
3
0
0
0
0
0
0
0
0
2
1
0
0
1
2
0
1
0
0
0
1
0
0
1
1
1
1
0
0
2
1
0
0
0
0
0
2
0
1
0
4
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
2
1
1
0
1
3
0
0
2
1
0
1
0
0
0
1
2
1
2
0
1
0
2
0
2
0
0
0
1
0
3
0
0
0
2
1
0
0
0
0
0
0
0
0
3
3
0
1
0
0
3
2
0
0
0
2
0
2
0
0
2
0
0
0
2
0
0
1
0
4
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
1
2
3
0
0
0
1
0
1
0
0
0
1
0
1
0
0
2
1
2
1
0
0
2
0
1
0
2
0
0
0
0
2
2
0
1
1
0
0
1
0
0
0
2
2
0
0
1
2
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
1
2
1
1
0
0
0
0
0
0
1
0
1
0
0
2
0
0
2
0
2
0
4
1
2
1
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
2
0
2
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
3
0
0
2
0
0
0
1
1
0
0
0
0
0
0
1
2
0
3
0
0
1
0
0
0
2
0
2
2
3
1
0
0
0
0
1
0
2
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
1
0
0
2
1
0
2
2
2
0
0
0
4
0
0
0
0
0
2
1
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
2
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
3
0
0
2
1
1
0
2
3
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
1
2
0
0
0
0
0
2
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
2
0
0
1
0
1
0
0
0
0
0
1
0
1
0
1
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
2
1
0
1
1
1
0
2
0
0
2
0
1
0
0
0
2
1
1
0
0
2
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
1
0
0
1
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
3
2
0
1
0
0
2
1
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
2
0
0
1
0
0
1
0
0
4
0
0
0
0
1
0
0
1
0
2
0
0
1
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
4
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
2
0
0
2
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
4
0
0
0
0
1
1
2
0
2
0
0
0
1
0
2
0
2
0
0
2
0
3
0
0
0
0
1
0
0
0
2
0
0
3
0
1
1
0
4
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
3
2
2
2
0
2
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
2
1
0
1
3
0
0
0
0
0
1
0
1
0
0
1
0
0
2
0
0
2
2
0
2
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
2
0
1
0
0
0
3
0
2
2
0
0
3
2
0
0
1
0
0
0
0
1
3
0
0
0
0
0
0
1
2
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
1
2
0
1
0
1
2
1
1
1
0
0
0
0
0
0
2
0
2
2
0
2
0
0
0
0
1
1
2
0
0
2
0
1
0
1
0
0
2
0
0
0
0
0
2
0
0
2
0
1
2
2
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
7
0
1
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
1
3
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
3
2
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
3
1
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
1
2
2
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
2
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
1
1
0
1
0
2
1
0
0
1
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
2
1
0
2
2
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
2
1
1
0
3
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
2
2
2
1
0
0
1
0
0
2
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
3
0
1
0
0
4
0
0
0
0
0
1
2
0
0
0
0
0
1
2
0
0
1
0
1
0
0
0
1
0
0
1
0
0
1
0
2
0
1
2
2
0
1
0
0
0
0
2
0
0
2
0
0
2
1
0
0
0
2
0
2
1
0
0
0
1
0
0
0
1
2
0
0
0
4
0
0
0
0
2
0
0
0
6
0
0
1
1
0
0
1
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
15
2
1
2
2
0
3
0
0
0
0
0
1
0
0
0
2
2
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
1
1
2
0
0
0
0
2
0
0
0
0
2
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
1
1
2
0
0
0
1
0
0
2
0
0
2
1
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
1
1
0
1
0
2
0
2
0
0
0
2
0
0
0
2
0
3
1
0
0
2
0
1
3
0
2
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
2
1
0
0
0
1
0
0
2
2
0
0
2
0
0
2
0
2
0
0
0
0
0
2
2
0
0
1
4
2
0
0
1
0
1
0
0
0
2
0
0
1
0
0
1
0
2
0
0
0
0
0
0
2
0
1
0
0
1
2
1
0
1
0
0
2
0
0
1
0
0
1
1
0
2
2
0
0
0
0
2
1
0
0
2
0
0
1
0
0
0
1
2
0
0
0
2
0
0
2
0
1
0
1
0
0
1
0
0
0
1
0
0
0
1
0
3
1
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
2
0
0
2
0
1
2
0
1
0
0
0
0
1
1
0
0
2
2
0
0
0
0
0
2
2
2
0
0
1
0
2
0
0
0
0
2
2
2
1
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
1
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
3
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
3
1
0
0
1
1
0
1
0
0
0
0
0
2
0
0
1
1
0
0
4
0
0
2
1
2
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
2
3
0
0
0
6
0
0
0
2
0
0
0
1
0
0
0
2
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
1
1
0
2
1
0
1
0
0
0
0
0
0
2
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
1
3
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
2
0
2
0
0
0
1
2
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
2
0
0
0
3
0
0
0
0
0
0
0
0
3
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
5
1
1
2
2
0
2
0
0
0
2
1
0
2
1
3
2
0
1
4
0
0
0
0
1
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
1
1
0
1
1
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
2
2
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
1
0
4
0
0
2
0
3
0
0
0
0
0
0
0
0
1
3
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
2
2
0
0
0
0
0
0
0
2
0
1
0
0
1
0
1
0
0
2
0
2
0
0
2
1
2
2
2
0
0
0
0
0
0
2
2
2
0
0
0
0
2
1
0
2
0
0
0
1
1
0
0
0
1
0
1
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
2
0
1
0
1
2
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
2
0
1
0
2
1
2
1
0
0
0
0
0
0
0
0
3
2
0
0
1
0
0
2
0
0
0
3
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
1
0
2
0
1
0
2
1
0
1
1
0
0
0
1
0
0
0
0
0
2
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
2
0
0
1
0
1
2
1
0
0
2
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
2
1
0
2
0
1
2
1
0
1
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
1
2
0
1
1
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
5
0
0
2
0
0
0
1
0
1
0
2
0
1
0
0
1
0
0
0
0
0
2
1
2
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
1
0
1
1
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
2
0
2
1
1
1
0
2
0
1
2
0
0
0
1
0
1
0
0
0
0
0
0
0
2
2
0
0
1
2
1
0
0
0
0
1
0
0
0
0
0
0
2
0
3
0
0
0
1
1
0
0
0
2
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
1
0
1
0
2
1
5
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
1
0
0
0
1
1
0
6
0
0
0
0
2
0
0
1
0
0
2
0
1
0
0
0
0
0
2
0
0
1
0
0
0
1
0
1
0
1
1
1
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
3
0
0
0
0
0
0
0
0
4
0
0
0
3
2
0
0
2
2
0
3
1
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
6
0
0
0
3
2
0
2
0
0
2
0
0
0
0
0
0
2
4
0
0
0
2
0
2
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
3
2
0
2
0
0
1
1
0
2
0
0
1
0
1
0
0
0
0
0
0
4
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
3
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
2
0
1
0
0
3
0
0
0
0
3
0
0
0
0
0
0
3
2
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
1
0
2
0
1
0
1
2
0
1
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
2
1
2
0
0
1
0
0
0
2
0
2
2
0
0
2
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
1
0
0
0
1
1
2
0
0
0
0
0
2
0
1
2
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
4
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
1
0
2
1
1
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
3
0
0
0
2
0
0
0
0
0
0
1
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
1
2
0
0
1
1
0
3
0
0
0
0
1
0
0
0
1
0
1
0
2
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
1
4
0
0
1
0
2
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
2
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
1
1
1
0
1
2
0
0
0
0
3
0
0
1
0
3
0
0
0
2
1
0
1
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
2
0
1
1
1
0
0
0
2
1
2
0
0
0
2
1
1
1
0
0
0
0
0
0
1
2
2
0
0
0
0
1
0
0
0
0
2
0
0
2
2
0
0
0
2
0
1
1
0
0
0
0
1
1
0
0
1
1
0
1
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
1
0
3
1
2
0
2
0
0
0
0
0
1
0
0
2
0
0
3
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
1
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
2
0
3
0
0
6
1
0
0
0
0
0
0
0
3
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
1
7
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
3
0
1
0
0
1
0
0
0
3
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
2
0
1
0
2
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
1
0
1
2
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
2
0
2
0
1
2
0
0
1
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
2
0
0
1
0
0
1
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
1
0
0
1
0
0
0
2
0
0
2
0
0
0
0
1
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
2
0
0
1
0
0
0
2
0
0
0
3
3
0
0
1
0
0
1
0
0
0
2
0
4
0
0
0
0
0
3
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
2
0
0
3
0
0
0
0
0
4
0
0
2
2
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
4
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
2
1
1
2
0
0
0
0
1
0
0
0
2
0
2
0
2
1
0
1
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
3
2
0
0
0
2
1
2
0
0
0
0
0
0
0
2
2
2
0
0
2
0
0
0
0
1
0
1
0
1
0
2
0
0
0
2
2
0
0
0
0
0
0
1
2
0
0
2
2
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
2
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
3
0
0
2
1
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
1
0
2
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
1
1
1
1
0
0
0
2
0
0
0
1
0
1
0
0
0
2
1
1
2
1
2
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
2
0
0
2
0
1
0
1
0
2
0
2
1
1
0
0
5
0
0
0
0
3
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
1
1
0
0
1
2
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
2
0
0
0
0
0
0
0
2
3
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
3
1
0
1
1
0
0
2
0
0
0
2
2
0
0
0
0
1
0
1
2
0
2
0
2
0
0
0
1
0
1
1
3
0
0
2
0
1
0
1
0
0
0
0
0
2
0
2
0
0
1
2
1
3
0
2
2
0
1
0
0
0
0
1
0
2
0
2
0
2
0
2
0
0
0
2
0
0
0
4
2
3
0
2
2
2
0
0
0
0
3
0
2
1
0
0
0
2
0
1
0
2
0
2
2
1
0
0
2
0
1
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
1
2
0
0
0
0
1
0
1
2
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
2
0
2
2
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
1
0
1
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
2
0
3
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
1
2
0
2
0
1
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
9
0
0
1
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
1
1
4
0
3
2
0
2
1
0
0
0
0
0
0
0
0
3
0
1
1
0
0
2
0
2
2
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
6
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
3
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
6
0
0
0
0
2
2
1
0
0
0
0
1
0
1
0
1
0
3
0
2
0
0
2
0
1
0
1
1
0
0
0
0
2
0
2
0
0
2
0
0
0
0
3
0
2
2
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
2
0
1
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
3
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
2
0
1
2
0
0
0
0
0
0
1
0
1
0
0
0
2
0
2
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
1
4
0
0
0
1
0
0
0
3
1
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
1
0
0
0
1
2
0
0
0
0
0
2
0
0
2
0
0
0
2
2
0
0
0
0
1
0
1
0
0
1
0
0
1
2
0
0
0
0
0
0
0
2
1
0
0
0
3
2
0
0
3
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
2
2
0
0
0
2
1
1
0
1
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
2
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
4
0
0
0
2
0
0
0
2
0
1
0
0
0
2
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
1
3
1
0
2
0
0
0
1
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
2
0
0
2
1
1
1
0
0
0
0
2
1
0
2
1
1
1
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
1
0
2
0
0
1
0
2
0
0
0
1
1
0
0
0
0
0
1
0
0
2
2
0
2
2
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
2
2
0
1
0
2
0
0
0
0
1
0
0
2
2
0
2
0
0
0
1
0
0
2
1
0
0
0
2
0
0
0
0
1
0
0
0
0
2
2
0
0
2
2
0
4
0
1
2
0
0
0
0
1
0
0
0
2
0
1
0
2
0
0
0
0
0
1
0
2
2
0
0
0
1
1
0
0
0
0
1
1
0
2
1
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
1
0
0
2
0
1
0
0
0
0
3
0
1
2
0
0
0
2
1
0
2
2
0
0
0
0
0
0
0
1
1
0
0
0
1
0
2
0
0
0
0
1
0
0
2
0
1
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
1
2
0
0
0
0
0
0
2
2
0
0
2
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
3
2
1
0
0
0
1
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
2
1
3
0
0
0
0
0
0
0
2
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
2
2
0
2
2
2
2
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
3
0
3
2
0
0
0
0
3
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
1
0
0
0
2
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
3
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
1
0
2
0
1
1
1
1
0
1
0
0
0
0
0
0
0
1
0
2
0
1
2
0
0
0
0
0
0
3
0
0
0
2
0
0
1
0
0
2
0
0
0
0
2
2
4
0
3
2
4
0
0
0
2
0
0
0
0
0
0
0
2
1
0
1
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
1
0
0
2
2
0
0
0
0
0
1
0
1
0
2
1
0
0
1
0
0
2
0
1
0
0
2
0
0
0
0
1
1
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
1
2
0
0
0
0
0
0
5
0
0
0
0
0
0
0
2
2
0
1
0
0
0
1
0
1
2
0
2
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
1
0
2
1
0
0
1
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
2
1
1
0
1
0
0
2
1
2
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
2
0
0
1
0
0
1
0
2
2
0
0
0
0
0
1
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
1
0
0
0
0
3
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
2
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
5
0
1
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
2
0
3
2
1
0
0
0
0
0
0
2
2
0
0
2
0
1
0
0
0
0
0
5
1
0
2
0
0
1
0
1
2
1
1
1
0
0
0
3
1
0
0
1
0
0
0
2
0
0
4
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
1
0
0
1
0
0
2
2
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
5
0
0
1
2
5
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
2
0
0
2
0
0
0
0
0
3
0
0
2
0
1
0
1
0
0
0
2
2
3
1
3
0
0
0
0
2
2
0
0
0
1
2
1
5
0
2
0
2
0
0
0
2
0
2
0
2
1
2
0
0
2
0
2
0
0
0
1
0
0
1
1
0
0
0
3
0
0
0
0
0
0
0
2
0
0
1
1
0
2
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
1
0
1
0
2
0
0
1
0
0
3
1
0
2
0
0
0
0
0
0
0
1
0
2
2
0
0
1
0
0
0
2
0
0
1
0
0
0
2
1
1
0
0
2
0
1
1
0
0
2
1
0
0
0
5
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
1
1
1
0
0
0
0
0
0
2
0
0
0
0
1
1
0
1
1
0
0
0
0
1
0
1
0
13
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
1
0
0
0
3
1
1
0
2
0
0
2
1
0
2
0
2
0
0
1
0
0
1
1
2
2
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
3
0
2
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
6
2
0
2
1
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
1
0
0
1
0
0
0
3
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
2
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
4
0
2
1
0
0
5
0
0
0
0
2
2
0
0
0
0
1
0
0
6
0
1
0
2
0
0
0
0
1
0
0
2
0
0
0
1
0
2
0
2
2
0
1
0
0
0
0
0
2
0
0
0
3
0
2
0
0
0
0
0
2
0
2
0
1
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
1
2
0
1
3
0
0
2
0
0
1
2
0
0
0
0
0
0
1
0
0
2
2
0
2
0
2
0
1
0
0
0
0
0
0
0
1
2
1
0
0
0
2
0
0
0
0
1
2
0
0
1
0
0
2
0
2
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
2
0
0
1
0
0
2
0
0
0
0
2
0
0
0
2
0
0
2
0
3
0
0
1
0
0
2
0
0
2
0
1
2
1
0
0
1
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
1
1
0
0
0
2
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
1
0
1
3
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
2
1
0
1
2
2
0
0
0
0
0
0
1
0
0
1
2
2
1
2
0
0
2
0
0
0
9
0
0
0
0
0
0
0
1
2
2
2
2
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
2
1
0
1
0
0
0
0
0
0
0
1
0
0
1
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
3
0
1
2
2
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
1
0
2
1
0
0
3
2
0
0
0
0
3
0
2
0
0
0
1
0
0
0
2
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
1
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
2
2
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
3
0
1
0
1
0
0
0
1
1
0
0
0
2
2
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
1
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
1
0
0
0
0
0
2
0
1
0
0
0
2
2
0
3
2
0
0
0
0
0
0
0
5
1
0
0
0
1
0
0
0
1
0
1
0
2
2
0
0
0
0
0
0
0
0
2
3
0
1
0
0
0
2
2
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
1
0
0
2
2
0
1
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
1
2
0
0
0
1
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
2
0
0
2
2
0
0
2
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
2
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
7
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
1
0
1
2
0
0
0
2
0
1
1
1
0
0
3
0
0
0
0
3
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
2
2
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
2
1
0
1
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
1
0
0
1
0
0
2
0
0
1
0
0
2
2
0
1
0
0
0
0
0
1
0
1
0
0
0
0
2
3
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
3
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
2
1
2
0
0
0
0
0
3
3
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
2
1
1
0
0
0
1
0
0
1
1
1
0
1
2
0
0
0
0
0
0
2
1
0
0
2
0
0
2
2
2
0
0
0
0
2
1
0
0
0
0
1
0
1
2
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
1
0
0
0
0
0
0
2
0
2
2
0
0
0
0
1
0
0
0
0
1
0
0
1
0
2
0
0
0
2
0
0
1
0
0
0
2
2
0
0
2
0
1
8
0
2
0
1
1
2
1
1
0
0
0
2
0
0
2
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
2
1
0
2
1
1
0
0
0
1
0
0
0
0
0
2
0
1
0
1
0
0
2
0
4
0
2
0
0
0
1
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
1
1
0
0
2
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
2
0
2
0
0
0
2
1
1
0
0
2
1
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
2
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
2
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
2
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
5
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
1
2
1
1
0
0
0
0
2
0
0
0
0
0
0
1
0
1
1
0
1
3
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
3
0
0
0
1
0
0
2
2
1
0
0
1
1
2
0
0
0
1
0
2
1
2
0
0
2
0
2
0
1
0
1
0
2
0
1
0
0
0
0
2
2
0
0
1
0
1
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
4
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
1
1
1
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
6
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
2
0
0
0
2
0
2
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
1
0
0
0
0
2
0
3
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
3
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
1
0
0
1
1
0
0
1
0
1
0
7
0
0
0
0
1
0
0
2
0
0
0
3
0
1
0
0
1
3
0
2
0
0
0
0
2
0
0
0
5
0
0
0
0
2
1
2
0
0
0
0
0
0
4
2
1
0
1
0
1
0
0
0
0
0
0
0
3
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
2
4
0
0
0
0
2
2
3
0
0
3
0
0
1
0
2
0
0
2
2
0
0
0
0
0
0
1
5
2
0
3
0
0
0
0
0
1
2
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
1
1
0
0
0
2
0
0
0
0
3
2
0
0
2
0
0
2
0
1
3
4
1
0
2
2
0
0
1
0
0
0
1
0
0
0
0
0
2
2
1
0
2
0
2
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
3
0
1
0
0
0
1
0
2
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
1
2
1
0
2
2
0
0
1
1
0
0
0
1
0
1
0
3
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
7
0
0
0
1
0
1
0
0
3
2
0
2
0
0
0
1
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
3
0
1
0
1
0
0
2
1
2
0
0
0
0
2
1
1
2
2
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
1
0
0
0
0
0
1
0
0
3
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
3
0
0
3
0
2
0
0
1
0
0
0
2
0
0
1
2
0
1
0
0
0
2
2
2
0
0
1
0
0
3
0
2
0
1
0
0
1
2
0
0
1
0
0
0
2
2
0
0
1
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
2
0
0
1
0
0
2
1
2
0
1
0
0
2
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
1
0
2
0
0
2
1
0
0
0
1
0
0
1
0
0
0
2
0
1
2
0
3
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
1
0
1
1
0
0
0
2
0
0
0
2
0
0
1
1
0
1
0
0
0
0
0
0
2
0
1
0
1
2
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
3
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
1
2
0
1
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
1
2
1
1
1
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
1
1
1
1
0
1
2
0
1
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
3
2
0
2
0
2
0
2
0
1
0
0
0
0
2
0
1
2
1
0
1
0
2
0
2
0
0
1
0
2
1
0
2
2
0
0
2
0
0
4
0
4
0
1
0
0
2
0
1
1
0
0
0
1
0
2
0
1
0
1
0
0
0
1
0
0
0
0
6
0
0
2
0
1
0
0
0
3
0
0
1
2
0
0
2
2
0
0
0
3
0
0
3
1
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
2
2
1
2
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
2
0
0
0
0
2
0
3
0
0
0
0
2
2
0
2
2
0
0
0
0
0
0
0
0
0
0
2
3
0
0
2
1
1
0
1
1
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
1
3
0
2
0
0
0
0
0
0
0
1
1
1
0
0
0
0
2
0
0
2
0
0
1
5
0
0
0
1
2
2
0
0
3
0
1
1
0
2
0
0
0
2
0
0
0
0
3
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
2
2
3
3
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
2
0
2
0
2
1
0
0
2
1
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
2
0
2
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
2
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
2
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
1
3
2
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
4
0
0
1
0
0
3
0
0
2
2
1
1
0
0
0
0
0
0
1
1
2
2
1
0
0
2
0
0
1
0
1
1
0
0
0
0
0
0
3
2
0
0
1
0
0
0
1
0
0
2
4
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
2
2
2
0
0
0
0
0
2
1
1
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
2
1
0
2
0
0
1
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
1
0
1
2
0
0
0
0
0
1
0
0
0
0
0
2
1
2
0
0
0
0
0
1
0
2
1
0
1
0
1
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
3
0
2
0
1
0
1
1
0
0
0
0
0
1
1
1
1
3
0
0
0
5
0
1
0
1
0
1
0
1
1
0
0
1
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
5
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
2
0
0
0
2
0
0
2
0
3
0
1
0
0
1
0
0
2
0
1
2
5
0
0
0
0
0
1
2
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
2
1
1
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
2
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
2
1
2
0
3
0
0
0
3
0
1
0
0
2
0
0
3
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
3
0
1
0
1
0
0
1
1
1
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
1
0
2
0
0
1
1
0
0
0
0
2
0
1
0
0
0
1
3
0
0
0
1
1
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
2
2
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
1
1
3
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
1
0
0
0
0
3
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
2
1
0
2
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
3
0
2
0
0
0
2
1
0
1
1
0
0
1
0
0
1
0
0
2
0
0
3
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
1
1
2
2
0
0
0
2
0
2
0
2
0
1
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
1
1
1
0
0
0
0
4
0
0
0
2
1
0
1
1
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
2
0
0
2
1
0
0
3
0
0
0
0
2
0
0
0
0
0
2
2
2
0
2
0
0
2
0
0
0
0
0
0
2
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
2
1
0
0
2
2
1
0
0
5
0
0
0
0
2
0
0
0
0
1
1
1
0
1
0
0
1
0
0
0
0
0
2
0
0
0
4
0
0
1
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
5
2
0
0
2
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
2
0
5
2
1
2
0
1
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
1
1
0
0
0
0
2
0
2
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
1
1
0
0
0
0
5
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
3
2
2
0
0
0
0
1
0
1
0
1
0
2
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
2
5
0
1
0
0
0
0
3
0
0
0
0
1
1
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
1
0
0
1
1
0
0
0
2
1
1
0
0
0
0
1
0
0
0
0
2
3
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
2
2
1
1
0
1
0
3
0
2
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
2
0
0
0
0
0
1
0
3
0
0
1
1
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
5
0
1
0
2
0
1
0
0
0
0
2
2
3
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
1
0
0
0
0
3
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
3
2
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
2
2
0
0
0
0
3
0
1
2
0
2
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
2
2
2
0
0
0
3
0
0
2
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
2
0
3
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
2
0
1
3
0
0
0
0
0
0
0
0
0
1
0
1
0
2
2
0
2
0
0
0
0
2
0
2
0
0
3
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
2
0
0
0
2
0
1
0
0
0
0
0
2
3
4
0
0
1
0
0
2
0
0
0
2
1
1
2
5
0
1
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
2
0
0
0
2
0
0
0
2
3
0
1
0
0
2
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
2
0
0
0
1
0
2
0
0
0
2
0
0
0
0
2
1
1
0
0
2
0
2
0
1
0
0
1
0
0
0
0
0
0
1
0
2
0
0
2
0
0
2
1
2
0
1
0
0
0
0
0
1
0
0
3
2
0
1
5
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
3
0
1
1
0
0
3
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
2
0
0
1
0
2
2
0
0
0
2
0
0
0
0
1
0
1
1
0
4
0
1
0
1
1
0
0
0
1
0
0
0
0
0
2
1
0
2
2
1
0
3
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
3
0
3
0
0
0
0
1
0
0
0
1
0
0
0
2
1
2
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
1
0
0
3
0
2
2
0
0
1
2
2
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
2
0
1
0
1
0
0
1
0
0
0
2
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
2
0
2
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
4
0
0
1
0
0
0
1
0
0
0
1
0
1
2
0
0
2
1
0
0
0
0
0
1
0
0
6
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
3
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
1
1
0
1
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
5
0
2
0
0
1
1
0
1
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
1
0
0
2
2
0
1
2
2
0
1
0
1
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
2
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
1
2
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
2
0
0
1
2
0
0
2
0
0
1
1
0
0
2
0
2
1
1
0
0
0
0
0
0
0
3
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
1
0
1
0
0
1
2
0
0
0
0
1
0
0
3
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
1
0
0
2
1
0
0
0
0
0
1
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
1
0
1
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
2
0
0
2
0
1
0
1
0
2
0
0
0
0
2
2
2
2
0
0
2
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
2
0
1
0
0
1
2
0
0
1
3
0
0
1
1
2
0
1
0
1
4
1
2
1
2
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
5
1
3
2
0
0
0
0
0
3
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
1
2
0
2
0
1
0
2
0
1
0
0
0
0
1
1
2
0
1
0
2
1
0
0
4
0
1
0
0
2
0
0
0
1
1
0
0
0
1
0
0
0
2
2
0
0
1
0
1
0
0
0
2
2
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
1
0
2
2
0
1
0
0
0
0
2
0
0
2
1
0
1
2
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
5
0
0
1
0
0
0
0
2
1
2
0
0
0
0
1
2
0
0
0
0
2
0
2
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
3
2
0
0
0
2
0
2
0
0
0
0
2
1
2
1
2
0
0
0
0
0
2
1
0
1
1
0
1
0
1
4
0
1
2
0
0
1
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
1
0
2
1
1
0
0
0
0
2
1
1
0
3
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
1
1
3
0
0
0
0
2
0
0
0
2
1
0
0
2
0
0
1
0
2
2
0
0
2
2
0
0
1
1
0
0
0
2
0
0
0
0
1
0
0
0
0
2
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
5
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
2
1
0
0
0
1
0
0
1
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
1
2
0
0
0
0
0
3
0
1
2
2
0
2
2
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
2
0
1
1
0
0
1
0
2
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
2
0
0
1
0
0
1
2
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
4
0
0
0
1
2
0
0
1
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
2
1
0
0
0
2
2
0
0
0
1
0
1
0
0
1
0
2
0
0
0
1
0
0
2
0
0
1
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
2
0
0
0
0
2
0
1
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
3
0
0
3
1
0
1
2
0
2
2
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
2
0
0
0
0
0
2
0
0
1
0
0
1
1
0
0
0
0
0
0
2
0
0
2
0
0
1
0
1
2
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
1
1
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
2
0
1
1
0
2
2
1
0
0
0
0
0
2
0
0
1
0
1
0
2
0
0
0
1
0
2
0
1
0
1
2
0
0
2
0
0
0
0
0
0
2
2
0
3
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
3
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
1
0
2
2
0
0
0
0
0
1
0
0
0
1
0
0
2
0
1
1
0
0
0
0
2
0
0
0
0
1
0
0
2
0
2
0
2
2
3
2
1
0
0
1
0
0
0
0
0
0
0
1
2
2
2
0
0
0
0
0
0
0
1
0
0
1
0
0
2
1
0
6
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
2
2
0
0
2
2
1
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
1
2
2
0
0
1
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
1
2
0
1
0
0
1
0
0
0
2
2
3
0
0
1
1
0
2
0
0
1
0
0
0
0
2
2
0
1
0
1
3
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
1
0
2
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
2
1
0
0
2
2
0
0
1
2
0
2
2
0
0
0
2
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
2
2
2
0
2
0
2
1
3
0
0
4
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
2
1
0
0
2
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
2
4
2
0
1
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
1
1
0
0
0
0
0
0
2
0
2
0
6
0
0
0
0
0
0
2
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
3
0
2
2
0
0
3
1
2
3
0
2
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
3
2
0
0
0
0
2
0
2
1
1
2
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
2
2
2
0
0
0
0
0
1
0
0
0
2
1
0
0
0
4
0
0
0
0
1
2
1
0
3
0
2
0
0
1
0
0
0
1
0
0
0
2
2
0
0
2
1
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
2
2
0
1
0
1
2
0
2
0
0
1
0
0
2
2
0
0
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
2
1
0
2
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
1
0
1
0
0
0
0
2
0
0
2
0
0
0
0
2
1
1
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
1
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
1
0
0
0
2
0
2
0
0
0
2
0
0
0
2
2
0
5
0
2
0
0
2
0
2
0
0
0
0
0
1
1
1
0
0
0
0
0
0
3
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
1
2
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
2
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
3
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
2
0
1
2
0
2
0
1
1
0
0
0
1
3
0
0
2
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
1
0
1
0
0
1
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
2
1
1
0
0
0
2
0
0
0
0
2
0
1
0
0
1
2
2
0
1
0
0
1
1
3
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
1
1
2
0
0
0
0
0
0
0
3
1
1
0
0
2
0
0
0
0
3
1
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
2
1
3
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
1
0
3
0
0
2
1
3
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
2
1
0
1
1
0
0
1
0
0
0
0
0
0
3
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
1
0
2
0
1
1
0
2
2
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
5
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
5
0
0
0
0
2
0
1
0
0
2
1
0
0
0
2
2
2
0
4
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
3
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
1
1
0
0
0
2
0
0
0
3
0
3
0
0
0
0
0
2
5
0
0
0
0
0
2
1
1
0
0
0
1
0
1
0
0
0
0
1
1
1
4
0
0
0
0
2
2
0
0
1
0
0
0
0
2
0
3
0
0
0
1
0
0
0
0
2
0
1
0
0
1
1
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
1
0
2
0
2
1
4
2
0
0
0
0
1
1
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
2
0
0
0
0
2
0
0
3
0
2
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
3
0
2
0
0
1
2
0
0
3
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
3
0
0
0
0
0
0
4
1
1
0
0
0
1
2
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
1
2
0
0
0
0
0
1
1
0
2
0
1
5
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
1
1
0
1
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
2
1
0
0
2
0
1
0
2
2
0
0
0
1
2
0
0
0
1
0
0
0
0
0
2
0
0
2
2
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
1
0
6
0
0
0
1
0
0
0
0
1
2
0
1
0
0
1
0
1
0
0
0
1
0
1
0
1
0
0
0
0
1
2
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
2
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
1
2
1
1
0
0
2
0
0
1
1
3
1
0
0
0
0
0
0
2
0
0
0
5
2
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
1
0
1
0
2
2
0
2
0
1
0
0
2
0
0
1
0
0
1
0
0
0
0
0
1
2
0
4
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
2
1
0
1
0
2
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
2
3
1
4
0
0
0
2
2
0
0
0
0
1
0
1
0
0
2
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
2
2
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
3
1
1
0
0
1
2
2
0
0
0
0
0
0
0
8
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
1
2
0
2
0
0
3
0
0
0
0
3
0
0
0
0
1
2
2
0
0
1
0
0
1
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
2
1
0
2
0
1
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
2
0
0
1
0
4
0
0
1
0
1
2
0
0
0
0
0
2
0
1
2
0
3
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
2
0
2
0
1
0
0
0
0
0
2
0
1
2
1
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
2
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
1
2
0
0
0
0
1
1
1
0
2
2
0
0
1
0
2
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
3
0
0
1
0
0
1
0
0
2
1
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
2
2
1
1
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
2
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
1
0
0
2
0
1
0
0
3
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
2
0
0
2
2
0
1
0
0
0
0
2
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
3
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
1
1
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
2
3
0
0
2
0
0
1
1
1
0
0
0
2
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
1
0
0
0
0
1
1
1
0
0
1
0
2
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
2
2
0
0
1
0
0
0
0
0
1
0
0
0
3
0
0
1
2
2
0
1
1
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
2
0
2
1
0
1
0
0
0
0
1
0
1
0
0
1
1
0
0
1
0
0
0
1
0
1
0
0
0
2
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
3
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
3
1
0
3
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
2
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
1
0
0
0
0
0
0
0
0
2
3
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
1
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
1
0
0
2
0
1
0
0
0
0
2
1
0
1
0
0
0
0
0
3
0
0
0
0
0
0
1
0
2
0
0
2
0
0
2
0
2
2
0
2
0
0
2
0
0
3
0
1
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
2
0
0
2
0
0
1
0
0
0
0
0
2
0
0
2
0
1
0
2
2
0
0
0
0
0
2
2
0
1
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
4
0
0
2
0
0
0
1
1
0
0
0
0
2
2
0
1
0
6
0
0
0
0
0
2
0
0
0
2
0
2
0
0
2
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
4
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
1
0
1
1
0
2
1
0
0
1
0
0
0
1
0
2
0
0
2
0
2
1
2
0
1
1
0
1
0
1
4
0
0
0
0
1
2
0
0
2
0
0
2
0
0
0
2
1
0
0
2
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
1
0
2
0
0
0
0
2
1
0
2
0
1
0
0
3
1
1
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
7
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
2
0
1
0
0
0
0
0
0
1
4
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
2
0
0
0
0
2
0
0
0
0
6
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
5
1
0
0
0
0
2
0
3
2
0
1
1
2
2
0
1
0
0
0
0
2
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
2
1
1
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
2
0
0
1
2
2
0
0
0
1
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
3
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
1
0
1
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
2
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
2
1
0
0
0
0
0
1
1
1
1
0
0
0
1
0
0
1
0
0
0
2
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
2
1
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
2
2
0
0
1
0
2
0
1
0
0
0
0
0
0
2
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
4
0
0
2
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
6
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
1
2
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
2
1
1
0
0
2
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
2
0
0
0
0
2
0
3
0
0
1
0
0
0
0
0
0
0
0
0
1
2
1
2
0
0
0
0
0
1
0
0
0
0
0
1
2
0
2
0
0
0
0
0
2
0
0
0
2
2
2
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
2
1
2
2
0
0
0
0
0
0
2
0
0
0
1
0
4
0
0
0
0
1
0
0
0
0
2
2
0
0
0
1
2
2
0
1
0
0
0
1
0
0
0
2
2
0
0
2
1
0
0
0
0
1
1
1
0
0
1
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
3
1
0
0
1
0
1
1
0
0
0
0
0
1
0
1
0
3
1
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
1
1
0
0
0
0
0
2
0
2
0
2
0
0
0
1
0
0
2
0
0
2
0
0
0
2
0
1
2
2
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
2
0
1
1
0
0
0
0
0
0
1
0
0
0
2
3
0
0
1
1
0
0
0
0
0
2
0
0
2
0
4
0
0
0
0
0
0
0
3
0
2
1
0
0
0
0
2
2
0
0
0
0
1
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
4
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
2
0
0
0
2
2
0
0
0
0
1
1
0
0
0
0
0
1
0
0
2
1
1
2
0
1
2
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
2
0
0
0
0
2
2
0
2
2
1
0
0
0
0
1
0
0
0
2
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
2
0
2
0
0
0
0
0
0
0
3
0
1
0
0
0
0
2
0
1
2
0
1
0
0
0
1
0
0
2
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
3
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
2
0
1
1
0
1
0
0
1
0
0
0
2
0
0
0
2
2
0
3
0
0
0
0
1
1
0
1
0
0
2
4
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
1
0
2
1
0
0
0
0
0
1
0
2
0
1
2
0
0
2
3
0
3
0
0
0
0
3
0
2
0
0
0
2
1
0
1
0
0
0
2
1
1
0
0
0
0
2
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
1
2
0
2
0
0
2
0
0
0
2
0
0
0
0
0
1
2
0
0
0
2
0
1
0
0
0
0
0
0
0
1
1
1
1
1
2
0
0
0
0
0
0
0
0
0
4
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
2
2
1
0
2
0
1
1
2
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
2
0
0
2
2
0
0
2
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
2
1
1
1
0
2
0
1
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
2
0
0
2
0
5
2
0
1
0
0
0
1
0
0
0
2
0
2
0
0
5
0
1
2
0
2
0
0
1
0
0
0
3
0
0
0
0
1
0
2
2
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
1
0
1
0
0
0
2
2
0
1
3
0
0
0
1
0
2
0
0
1
0
0
2
2
2
0
2
1
0
0
0
1
0
2
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
2
1
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
2
0
2
2
0
0
0
0
3
2
0
0
0
0
0
2
0
2
0
0
3
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
3
0
0
0
1
0
0
0
2
0
0
2
2
1
0
2
2
0
0
0
2
2
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
12
0
1
2
2
0
0
0
0
1
0
0
1
0
3
1
0
0
0
1
2
0
0
0
0
3
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
1
0
2
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
1
2
0
0
0
6
1
0
0
1
2
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
2
0
0
0
1
1
1
1
2
0
0
5
0
0
2
0
2
0
1
3
0
0
0
0
0
1
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
1
0
0
0
2
0
0
0
1
1
0
0
2
0
0
1
0
2
0
0
0
0
0
4
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
3
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
2
2
0
0
0
0
1
0
2
1
5
0
3
0
1
3
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
2
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
1
0
2
0
2
0
0
0
0
0
2
0
0
4
0
2
0
0
0
1
2
0
0
0
0
0
0
2
0
0
2
0
0
0
3
0
0
0
0
0
2
2
0
0
1
0
0
1
3
1
0
0
2
0
0
2
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
4
0
2
2
0
0
0
0
0
0
0
3
0
0
0
1
1
1
0
0
0
0
0
0
2
0
0
0
0
0
3
2
0
0
0
2
3
0
1
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
2
1
0
0
0
0
0
0
0
1
2
0
0
2
0
0
1
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
1
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
2
3
0
0
0
2
6
0
1
0
0
1
1
1
0
2
0
2
0
1
2
0
0
2
0
0
0
5
2
0
1
0
0
1
0
0
2
0
2
0
0
0
0
3
2
0
2
2
0
0
2
0
3
1
0
2
2
2
2
0
0
0
0
0
0
1
1
4
0
2
1
0
0
2
1
0
4
0
0
0
5
2
0
1
0
2
0
0
0
2
2
0
2
0
1
0
0
1
2
0
0
0
2
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
2
0
2
0
1
0
0
0
0
1
2
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
3
0
1
0
2
0
2
2
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
2
0
0
0
2
2
0
1
0
0
0
0
2
0
2
0
0
1
0
0
0
3
1
0
0
1
0
0
0
3
0
1
0
1
0
0
2
2
0
1
0
0
0
0
1
0
0
0
3
2
0
0
0
0
1
0
0
2
0
0
0
0
1
0
2
3
0
0
0
2
0
0
3
0
0
2
1
3
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
1
1
1
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
0
3
0
1
1
2
1
1
0
0
2
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
5
2
0
0
0
2
0
0
0
1
0
0
1
0
2
0
0
2
0
0
2
0
0
0
0
7
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
1
0
0
1
0
0
1
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
1
1
0
0
1
2
0
0
1
2
0
0
2
0
2
3
0
1
2
1
0
2
0
0
0
0
1
0
0
1
2
0
0
0
0
1
0
0
1
1
2
0
0
1
0
0
0
0
0
1
0
1
0
2
2
1
0
0
0
0
1
1
0
0
0
2
2
2
0
0
2
0
0
0
0
2
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
2
1
1
0
0
3
0
0
2
0
2
1
0
0
0
1
0
2
0
1
0
0
2
2
0
2
1
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
4
1
0
0
0
0
0
0
2
1
0
2
2
1
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
2
1
1
0
0
2
0
3
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
1
2
0
0
0
1
2
0
0
0
0
3
0
0
0
0
2
0
2
0
1
0
2
0
0
0
0
1
3
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
1
2
0
0
2
1
0
0
1
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
2
0
0
0
1
0
0
0
1
0
0
1
1
0
2
0
0
1
3
0
0
0
0
0
1
2
0
0
2
0
0
4
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
1
1
2
0
1
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
2
2
0
0
2
0
2
3
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
1
0
0
0
0
0
0
0
0
3
2
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
1
0
0
1
1
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
1
0
1
0
0
1
0
0
0
0
0
0
0
2
0
1
0
2
0
2
0
0
0
0
2
0
0
0
1
1
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
2
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
2
0
0
1
1
0
1
2
0
0
2
0
2
0
2
0
1
0
0
0
0
0
0
0
2
0
2
1
1
0
0
0
0
0
2
0
1
0
0
10
0
0
0
0
0
0
0
2
0
0
0
0
6
0
1
0
1
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
2
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
4
1
0
0
2
0
2
0
0
2
1
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
2
0
1
2
2
0
1
0
2
0
1
0
1
0
1
1
0
1
0
1
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
1
0
1
0
0
2
0
2
0
2
2
2
2
0
0
2
1
2
0
2
0
0
0
0
0
4
0
2
0
2
0
0
0
0
2
1
0
0
2
0
0
0
1
1
0
2
2
0
0
0
0
1
0
0
0
1
1
2
0
0
0
0
0
1
2
0
0
2
2
0
1
0
0
1
0
0
0
1
0
0
2
0
0
0
3
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
4
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
1
4
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
2
1
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
1
0
0
0
1
0
0
0
0
2
3
2
0
1
2
0
0
2
3
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
2
0
0
1
1
0
0
1
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
2
2
0
1
0
0
0
0
0
1
1
4
0
0
1
0
1
0
0
2
0
0
0
1
0
1
0
1
1
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
1
0
0
0
2
0
0
0
0
2
1
1
0
1
0
2
0
0
0
0
1
0
0
2
0
0
0
1
0
1
0
0
0
4
0
0
1
0
0
0
0
1
2
1
0
0
3
0
1
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
2
0
3
0
1
0
0
1
0
0
0
2
2
0
0
0
0
0
0
4
0
1
0
0
2
0
0
1
2
0
0
0
3
1
4
0
0
0
0
0
1
1
2
0
0
0
0
2
2
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
6
0
2
0
2
2
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
2
1
0
1
2
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
1
0
0
1
7
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
3
0
2
1
0
1
0
0
2
0
2
0
1
0
1
0
2
0
0
2
0
1
0
0
3
0
2
0
0
2
2
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
2
1
2
2
1
0
0
0
1
3
0
2
2
0
0
0
0
0
0
2
0
2
2
0
1
0
1
0
1
0
0
0
0
2
0
1
0
3
0
3
0
1
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
4
1
1
0
0
1
0
2
2
0
0
0
2
0
2
0
2
1
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
1
1
2
1
0
2
0
1
1
0
0
1
1
1
2
0
0
0
2
0
0
0
0
0
2
0
2
0
0
1
2
2
0
0
0
1
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
1
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
2
0
1
0
0
3
0
0
0
2
0
0
2
1
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
2
0
2
0
0
1
0
1
1
0
0
0
2
0
2
0
0
0
2
0
0
0
1
1
1
0
1
2
0
2
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
1
2
0
0
2
1
0
2
0
0
0
0
0
2
3
2
1
1
0
0
2
0
0
1
1
0
1
1
0
2
0
2
1
0
0
0
0
1
0
1
0
2
0
2
2
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
2
1
0
0
2
0
0
0
0
2
1
0
1
0
2
0
3
0
1
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
2
0
2
2
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
1
0
0
1
3
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
4
0
0
0
2
0
0
0
0
1
2
2
2
1
0
1
0
2
2
1
0
4
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
1
0
0
2
0
7
2
2
0
2
0
0
0
2
0
0
2
0
2
0
8
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
2
0
0
0
0
0
0
0
1
1
2
1
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
4
0
0
0
1
1
3
0
3
1
0
0
2
1
2
0
0
0
0
2
2
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
1
0
2
0
2
1
0
2
1
0
0
0
2
0
4
2
0
0
1
0
2
0
0
0
1
2
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
2
3
0
0
0
1
2
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
4
1
0
0
0
2
0
0
0
0
0
2
0
0
1
0
1
0
1
2
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
2
1
0
2
0
1
1
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
2
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
2
0
0
1
0
0
2
0
0
2
1
4
1
0
0
0
0
0
1
0
0
0
0
1
0
3
0
0
0
4
0
1
3
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
1
0
2
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
1
1
0
0
1
0
3
1
2
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
2
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
2
2
2
0
1
0
0
0
0
0
2
2
1
2
0
0
2
0
2
3
0
0
1
0
0
0
1
0
0
0
0
1
0
2
0
0
0
2
0
0
2
0
0
0
0
0
1
0
1
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
5
0
0
0
0
0
0
0
0
2
2
4
0
1
0
0
0
3
0
2
1
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
2
0
0
1
0
0
0
2
2
0
0
1
3
0
0
0
0
2
0
0
1
0
0
1
0
2
0
2
1
0
0
2
1
0
0
0
1
1
0
0
0
0
0
0
3
2
2
0
0
0
0
0
2
0
0
1
0
1
0
0
2
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
4
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
2
0
0
0
2
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
3
0
0
0
0
1
0
0
2
1
0
2
1
0
1
1
0
0
1
0
0
0
0
0
0
4
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
2
0
1
2
1
2
0
1
0
1
0
0
0
0
0
0
4
0
0
2
1
1
0
2
1
0
0
0
0
1
0
0
2
0
2
0
0
0
2
0
2
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
3
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
10
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
1
0
4
0
0
2
0
0
0
0
0
0
1
0
2
2
0
0
2
0
0
0
0
0
1
0
2
1
0
3
0
0
1
1
0
0
1
2
0
2
0
5
0
0
0
2
0
1
0
1
0
0
0
1
0
1
2
2
0
3
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
3
1
2
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
8
2
0
2
0
1
0
0
1
2
0
0
0
2
0
0
0
1
0
2
0
0
0
2
0
3
0
0
0
1
1
0
2
0
0
0
1
0
2
1
2
0
2
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
1
1
0
0
2
0
1
0
0
0
2
2
0
0
1
2
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
2
0
0
5
0
0
1
1
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
2
1
0
0
0
2
0
0
2
0
0
1
1
1
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
2
2
0
0
2
0
0
0
2
0
0
0
0
3
2
1
0
0
0
0
1
4
0
0
0
4
0
0
0
0
1
1
0
2
0
2
0
1
0
0
0
0
2
2
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
2
1
0
2
2
2
0
2
0
0
0
0
3
0
0
0
2
0
0
1
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
1
0
2
0
0
0
0
1
0
2
3
0
2
0
1
0
1
3
0
0
1
0
3
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
3
2
0
1
0
0
2
0
0
2
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
3
1
0
0
2
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
1
1
0
0
2
0
0
0
2
0
0
2
0
0
2
0
0
1
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
2
0
0
2
0
0
0
2
1
0
1
1
0
0
2
0
3
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
2
0
0
2
0
0
1
1
1
2
0
0
2
0
0
0
0
2
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
2
0
2
0
3
1
0
0
1
0
4
4
0
0
1
0
0
1
0
0
1
1
2
0
1
0
0
0
0
0
2
0
0
0
0
0
1
4
2
0
2
0
0
2
2
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
2
0
0
0
0
1
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
2
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
2
0
0
0
2
0
0
2
1
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
1
1
0
0
0
1
1
0
1
2
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
3
2
0
0
0
3
2
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
3
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
1
2
0
2
0
0
0
0
1
2
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
2
2
0
0
2
0
1
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
3
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
1
2
2
0
0
3
0
0
0
4
0
2
0
4
2
2
0
4
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
2
0
1
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
2
0
1
0
2
1
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
3
2
0
0
1
0
2
4
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
2
0
2
0
0
0
2
0
0
0
2
2
3
0
1
0
2
0
1
1
0
1
0
1
1
0
0
0
0
5
2
2
2
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
2
1
1
0
1
2
0
2
0
2
2
1
0
3
0
0
1
0
0
1
0
2
0
0
1
0
0
2
0
0
8
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
2
2
1
0
0
2
2
1
0
2
0
1
0
0
0
0
0
2
1
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
2
2
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
3
1
0
0
1
0
2
4
0
0
1
0
0
1
0
0
0
1
1
0
0
2
0
0
1
0
0
0
2
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
2
0
0
2
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
3
2
1
2
0
0
0
0
0
0
0
0
1
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
1
3
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
1
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
1
2
0
0
2
4
1
2
0
2
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
2
0
1
2
0
3
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
2
2
2
1
2
0
0
0
0
0
1
0
0
2
4
0
0
0
0
0
0
2
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
2
0
0
0
0
0
1
0
0
1
2
1
2
1
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
1
0
3
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
1
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
3
2
0
0
0
2
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
2
2
0
0
2
0
0
0
2
0
1
1
3
0
2
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
1
1
0
2
0
0
0
0
1
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
1
0
0
0
0
0
1
1
0
1
0
0
1
1
0
2
2
0
0
0
1
0
0
1
2
0
0
0
1
0
4
1
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
1
1
0
0
3
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
2
0
0
0
0
0
0
2
4
0
0
0
0
0
1
2
1
0
0
0
4
0
0
0
2
0
1
0
0
0
1
0
0
0
1
0
2
1
0
0
0
0
0
0
2
0
0
2
3
0
0
0
1
2
2
0
2
2
1
0
0
0
0
2
0
0
0
0
0
2
2
0
1
0
0
0
2
0
1
0
0
0
2
0
0
1
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
1
0
0
1
2
0
1
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
2
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
2
0
0
0
2
0
1
0
1
0
0
0
0
0
1
1
0
2
0
0
0
2
0
0
0
0
2
0
0
0
2
1
0
2
1
1
0
6
0
2
0
0
0
0
2
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
2
1
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
7
0
0
2
0
0
0
2
2
2
0
0
0
0
0
0
2
2
2
0
0
2
0
1
0
0
0
0
2
0
2
1
0
0
0
0
3
1
0
0
1
1
0
0
1
0
0
0
0
1
1
0
2
0
0
0
0
2
0
0
2
0
0
0
1
1
2
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
1
1
0
0
5
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
2
3
2
0
0
0
0
0
0
0
1
0
2
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
2
2
0
0
2
0
0
0
0
0
0
3
0
2
0
0
0
0
0
1
1
0
3
0
0
2
2
0
1
0
3
2
0
0
0
0
0
2
0
2
0
0
1
0
0
2
0
0
2
0
0
0
2
0
0
3
0
0
3
0
0
0
1
1
0
1
0
0
0
1
0
2
2
0
2
1
0
0
0
0
3
0
1
0
2
0
1
2
0
0
0
0
2
4
0
0
0
0
0
1
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
3
2
2
0
0
0
0
0
0
1
0
0
0
1
3
2
1
0
0
0
0
1
2
0
1
3
0
0
0
0
0
2
1
1
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
2
2
2
0
0
0
0
0
0
0
0
0
0
2
3
0
2
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
1
0
0
0
0
0
2
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
2
0
2
1
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
1
1
0
2
0
0
0
0
0
0
1
1
0
0
2
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
2
4
0
0
2
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
2
1
0
2
0
1
0
0
0
1
1
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
4
0
0
0
0
1
2
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
1
2
2
0
0
5
0
0
2
1
0
0
3
0
2
0
2
0
1
3
1
0
0
0
1
4
0
0
3
1
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
2
2
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
1
1
2
1
0
0
0
0
0
2
2
0
0
0
0
0
1
0
2
0
0
2
0
2
0
1
0
2
0
0
0
2
0
0
0
1
1
0
0
1
0
0
0
0
0
0
2
0
2
2
0
1
0
0
0
0
0
1
0
2
2
1
0
2
1
2
1
0
0
0
2
1
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
1
2
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
4
0
0
2
0
0
3
0
0
0
1
0
0
0
0
0
1
0
1
1
4
0
0
1
0
0
2
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
1
0
2
0
0
1
0
0
0
0
0
2
1
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
1
6
0
0
0
0
2
0
0
0
0
2
0
0
1
2
0
0
1
1
0
0
0
0
0
2
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
2
2
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
3
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
1
0
1
1
2
0
0
0
0
0
1
0
2
1
0
0
0
1
0
1
2
1
0
0
2
1
0
0
1
1
0
0
0
0
2
0
0
0
0
1
0
2
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
1
0
1
0
0
2
0
0
1
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
5
1
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
4
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
2
0
3
0
0
0
1
0
0
0
0
0
0
0
2
1
0
2
2
2
2
0
0
0
1
2
0
2
0
1
0
0
2
1
1
0
2
3
0
0
0
0
2
0
0
0
2
3
0
0
0
0
0
0
0
3
1
0
0
2
0
2
0
2
0
2
0
0
2
0
0
0
0
0
2
2
0
0
0
0
1
1
2
0
0
0
1
0
2
0
0
0
2
2
2
0
0
3
0
2
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
2
0
1
4
2
0
0
0
0
1
0
0
0
1
0
0
0
0
3
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
1
0
0
0
0
2
1
1
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
1
0
0
0
0
0
1
0
0
0
0
0
1
0
2
2
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
2
5
0
0
1
0
0
0
2
2
0
2
0
0
0
0
1
1
0
0
1
0
2
2
0
1
0
2
1
2
0
1
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
3
0
0
0
3
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
1
0
1
2
1
0
0
0
0
0
0
3
2
1
0
0
0
1
0
0
1
0
0
4
0
2
0
3
2
0
0
0
0
1
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
2
3
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
1
0
3
0
1
2
0
2
0
0
0
1
0
0
2
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
1
1
0
0
0
0
1
0
0
1
2
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
2
0
0
0
2
0
0
0
1
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
2
2
0
0
2
2
2
0
1
0
2
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
2
0
0
0
0
3
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
2
0
1
2
1
0
3
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
4
2
1
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
1
0
0
0
0
1
1
0
2
2
0
0
0
1
0
1
1
0
0
2
0
0
0
0
0
0
0
3
2
0
0
2
0
0
0
0
2
0
0
0
1
0
1
0
1
0
0
1
3
1
0
0
0
2
0
1
0
1
0
0
0
0
0
2
1
0
0
1
1
0
0
1
0
1
2
2
2
1
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
2
1
2
0
2
0
2
0
1
0
0
0
0
0
1
0
1
0
0
2
2
0
0
0
0
1
0
0
1
0
0
2
2
0
0
2
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
3
2
1
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
1
0
0
1
2
0
1
0
0
2
0
0
0
1
1
0
0
0
0
0
2
1
0
0
2
0
1
2
1
0
0
0
2
0
0
0
0
3
0
0
2
1
0
0
2
0
2
0
2
0
1
0
0
0
0
2
0
0
0
2
0
0
0
2
3
1
0
0
0
0
0
2
1
0
0
0
2
1
0
2
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
1
0
2
0
0
1
0
2
1
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
3
0
0
3
0
0
1
0
1
1
0
1
0
0
1
1
1
0
0
1
0
0
2
0
2
0
0
3
0
0
1
1
0
1
0
2
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
2
2
1
1
0
0
0
1
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
2
0
1
1
2
0
0
0
0
0
0
0
1
2
0
3
1
0
0
0
1
0
0
0
1
4
1
0
0
3
0
0
1
0
7
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
2
0
2
0
3
0
0
1
0
2
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
1
2
1
0
0
2
2
1
2
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
1
8
0
2
0
0
2
0
0
0
1
0
2
0
0
0
3
0
0
2
0
2
2
0
0
0
0
1
0
1
0
1
0
1
0
1
0
1
2
1
0
0
2
1
0
0
0
0
0
1
1
0
1
2
0
1
0
3
1
0
2
2
1
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
1
0
1
0
0
0
0
2
2
1
0
2
2
0
0
1
2
0
0
0
2
1
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
1
2
3
0
1
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
1
0
0
1
0
0
1
0
1
0
0
1
0
0
0
1
0
1
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
2
2
1
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
1
1
2
0
0
2
0
0
1
0
1
0
0
0
2
0
0
0
1
0
1
0
2
0
2
0
0
0
2
0
0
0
1
2
2
0
0
0
0
1
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
2
2
0
6
2
2
2
0
4
0
0
0
0
0
1
0
1
2
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
2
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
1
4
1
0
0
0
0
0
3
1
0
0
2
0
3
0
4
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
2
0
0
1
0
0
0
1
2
4
0
1
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
2
2
2
0
1
0
1
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
2
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
2
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
3
2
0
0
0
1
0
0
1
0
0
0
2
0
0
1
1
1
1
0
0
0
2
0
1
0
2
2
1
0
1
0
0
0
2
0
1
0
1
0
0
2
1
1
0
2
1
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
1
3
2
2
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
2
0
0
1
0
0
0
2
1
0
0
0
0
0
2
0
0
2
0
3
0
0
0
0
0
0
0
0
1
1
2
0
0
0
2
0
0
0
0
0
0
0
0
2
2
1
0
0
0
1
0
0
0
0
0
1
0
2
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
4
1
0
2
0
2
0
3
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
2
3
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
1
0
0
2
0
3
1
1
0
1
0
0
2
0
0
0
0
0
0
2
0
1
3
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
1
2
1
2
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
2
0
1
0
1
1
0
0
2
0
0
2
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
1
0
1
1
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
2
0
2
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
1
0
1
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
1
0
2
0
0
1
0
0
1
0
1
3
0
0
0
1
2
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
2
0
0
2
0
1
0
3
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
1
0
0
3
0
0
1
1
0
4
0
0
0
0
0
0
0
0
0
0
0
2
1
2
1
4
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
2
0
2
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
1
0
0
1
3
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
4
0
0
0
0
0
2
2
0
2
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
1
0
1
0
0
0
0
0
2
0
2
0
2
2
0
1
2
3
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
1
2
0
2
0
0
0
1
0
0
0
1
0
2
0
0
4
0
1
0
0
0
0
0
0
0
2
0
1
2
0
0
2
1
0
0
0
0
0
1
0
0
0
0
3
0
1
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
1
0
0
2
1
1
0
2
0
1
0
0
0
2
0
0
0
0
3
0
0
0
0
1
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
6
0
0
0
0
1
0
0
2
0
1
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
1
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
1
2
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
5
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
1
2
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
2
0
1
0
0
0
1
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
1
3
0
0
1
0
0
3
2
0
2
1
0
2
2
1
2
0
1
1
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
2
2
2
0
1
0
0
1
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
1
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
1
0
3
1
2
0
0
1
0
0
2
0
0
2
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
4
0
1
0
0
0
0
0
1
2
0
0
1
5
0
3
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
4
1
0
0
2
0
0
6
0
0
1
6
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
1
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
1
0
0
0
0
0
2
2
1
0
2
0
3
1
0
1
3
0
0
0
0
0
2
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
2
0
0
0
0
0
1
1
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
2
0
0
0
0
2
0
1
1
0
0
0
0
1
1
0
2
1
0
0
0
0
2
0
1
0
0
1
2
2
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
2
0
0
2
2
1
0
2
2
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
3
2
0
0
2
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
1
0
1
0
2
0
2
0
0
0
0
0
1
2
0
0
1
0
2
0
0
0
2
2
0
0
0
0
0
2
0
0
2
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
1
0
0
2
1
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
2
1
0
0
0
0
1
0
1
0
0
0
5
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
2
0
0
0
1
3
0
1
0
1
0
0
0
0
3
0
0
1
0
0
0
0
0
1
0
0
1
0
2
2
1
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
1
1
0
0
0
1
6
0
0
0
1
0
2
1
1
0
0
0
3
2
1
3
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
7
0
2
1
0
1
0
0
2
2
2
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
3
0
0
1
0
2
2
0
2
3
0
0
2
0
0
0
1
2
0
0
0
1
0
1
1
2
0
0
0
0
0
0
0
1
0
2
0
1
0
2
0
1
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
3
2
0
0
0
2
3
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
2
1
1
5
0
0
0
0
0
0
0
1
0
0
2
1
0
0
1
0
0
0
0
0
1
1
1
0
2
0
0
0
1
1
0
0
0
0
2
0
2
0
0
1
0
0
0
1
2
0
1
0
0
0
0
0
0
0
1
5
0
2
0
3
0
0
0
11
0
1
0
0
0
0
0
1
2
2
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
2
1
0
0
0
1
0
0
1
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
4
3
0
0
1
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
1
2
0
0
2
1
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
4
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
1
0
0
0
0
0
2
1
2
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
3
1
0
0
2
0
0
0
0
0
1
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
5
0
0
0
4
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
2
3
0
1
0
1
0
0
2
0
0
0
0
2
1
0
2
0
1
0
0
0
0
0
2
2
1
1
1
2
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
1
1
2
0
0
0
0
0
0
0
2
0
2
1
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
1
3
0
0
2
0
2
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
5
1
0
0
0
0
0
0
4
4
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
8
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
1
0
1
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
2
0
0
0
1
0
0
0
0
0
0
2
3
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
2
0
1
0
0
0
2
1
2
0
0
0
0
0
0
5
0
0
2
0
0
2
0
2
0
0
1
0
0
0
0
0
2
0
1
0
1
1
0
0
2
0
0
1
0
0
2
0
1
0
0
2
0
0
0
2
0
0
3
0
1
0
2
0
0
0
0
1
2
0
0
0
0
0
1
0
0
1
3
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
1
2
0
2
2
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
2
0
0
0
1
0
1
0
2
2
0
0
2
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
1
1
1
0
0
1
1
2
2
0
0
0
2
0
1
0
1
0
2
0
0
1
2
0
0
0
1
0
2
0
1
0
3
0
0
1
0
1
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
3
0
2
2
0
0
0
0
1
0
0
0
2
0
0
0
0
3
0
0
0
1
2
5
2
0
1
0
0
1
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
2
0
0
1
0
1
2
0
1
0
0
1
0
0
2
0
0
2
0
2
2
0
2
0
1
0
0
0
1
0
0
0
0
1
0
2
0
1
2
0
0
0
0
0
0
1
0
1
0
2
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
2
1
0
0
2
0
1
0
0
3
1
0
0
0
0
0
0
0
0
2
1
2
0
0
1
0
0
1
1
2
2
0
1
1
0
1
0
1
0
0
0
2
0
2
2
1
2
0
0
0
2
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
1
0
0
0
2
0
2
1
1
0
0
0
0
2
1
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
5
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
2
1
0
1
0
0
0
1
2
0
0
4
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
2
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
4
2
0
1
2
0
2
0
0
0
1
0
2
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
2
1
1
2
0
1
0
0
2
0
0
0
0
1
0
1
0
0
0
0
2
1
0
1
0
0
1
2
1
0
0
0
0
1
0
0
2
1
1
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
2
0
1
0
0
2
0
0
1
0
0
0
0
1
0
0
0
1
2
0
2
4
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
1
3
0
0
0
2
1
0
0
0
1
0
1
0
0
1
0
0
0
0
1
1
0
2
2
0
0
0
0
0
0
1
1
0
2
0
2
0
1
0
1
0
1
0
1
0
0
1
0
1
0
2
3
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
2
2
2
0
2
2
0
0
2
0
0
2
0
3
4
2
0
0
0
2
2
0
0
1
0
1
0
0
2
1
0
2
0
0
2
0
2
2
0
0
0
2
0
0
0
0
0
0
1
2
1
0
0
0
0
0
3
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
3
1
2
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
2
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
2
2
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
2
1
0
2
0
1
2
0
0
2
0
0
1
1
0
0
0
0
0
7
1
0
0
0
0
0
0
0
2
1
0
3
0
0
0
3
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
2
0
2
0
0
1
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
1
1
0
2
0
1
0
0
1
0
2
0
0
0
0
6
0
0
0
0
0
1
2
0
0
0
0
1
0
0
1
0
1
0
0
2
2
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
3
0
0
0
0
0
1
1
2
0
3
0
0
0
0
0
2
0
2
1
0
2
0
1
0
1
0
1
0
1
0
0
0
0
1
2
2
0
0
0
0
0
2
1
0
2
2
0
2
0
0
0
0
0
1
2
2
1
0
3
0
2
0
0
0
2
1
0
3
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
3
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
7
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
1
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
1
0
0
1
1
1
0
0
0
1
0
0
0
1
0
0
2
1
2
0
0
0
2
0
2
2
0
0
2
0
1
0
2
1
0
1
0
0
2
0
0
2
1
1
0
0
0
1
0
2
2
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
7
4
0
0
0
0
0
3
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
2
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
1
0
0
1
0
0
0
0
0
2
0
0
1
0
0
2
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
2
0
1
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
2
0
1
0
1
1
0
0
0
0
0
2
1
0
0
0
1
2
2
0
1
0
0
0
0
1
0
0
2
2
0
0
1
0
2
0
0
2
3
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
1
1
0
0
0
0
0
0
1
1
3
2
0
0
0
0
2
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
2
1
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
5
1
0
0
0
0
2
0
0
2
0
0
0
2
1
1
0
0
0
0
0
0
2
1
0
0
1
0
0
1
5
1
0
0
2
0
0
1
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
2
0
1
0
3
0
0
0
2
0
1
0
0
2
0
0
0
2
0
0
1
0
1
2
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
1
0
0
1
4
0
0
0
1
0
0
2
3
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
2
2
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
2
1
0
0
0
0
2
0
0
1
0
2
0
0
1
2
1
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
2
2
0
2
1
0
1
0
0
0
2
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
2
0
1
0
0
0
0
0
1
1
0
2
0
0
1
2
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
5
0
2
0
0
0
2
7
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
2
0
0
1
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
2
0
0
1
1
0
0
1
2
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
2
0
2
2
0
0
2
0
1
0
0
2
0
1
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
4
3
0
2
0
1
0
2
0
0
2
1
0
0
1
0
4
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
2
0
2
1
0
0
0
0
0
0
0
1
2
0
0
0
2
0
1
0
2
0
2
0
0
0
0
2
0
1
0
3
2
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
1
0
1
2
0
2
2
0
0
1
0
2
0
0
0
0
4
0
0
2
2
0
0
3
0
0
0
2
0
0
0
0
0
2
0
0
1
0
3
0
2
0
0
1
0
0
0
3
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
5
0
1
1
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
3
0
0
2
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
2
0
2
0
0
0
1
0
0
2
0
0
0
2
1
1
3
0
0
0
0
1
0
0
1
3
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
2
2
3
2
2
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
2
0
2
0
1
1
0
3
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
2
0
0
1
0
0
2
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
2
0
0
1
0
1
0
1
0
0
0
0
2
2
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
1
0
0
0
0
0
0
2
1
2
0
3
0
2
0
0
0
0
0
1
0
1
2
1
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
2
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
1
0
0
2
0
0
2
0
1
0
0
0
0
0
0
1
2
0
0
1
0
2
0
0
0
2
2
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
1
2
1
0
0
0
0
0
0
0
1
1
1
2
0
0
0
0
3
0
0
0
0
3
1
0
0
0
0
1
1
2
0
2
0
0
2
1
3
0
0
0
1
0
6
0
1
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
2
0
1
0
0
0
2
0
0
0
3
2
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
2
1
0
1
1
0
1
1
1
0
0
0
0
3
1
0
1
2
0
0
0
2
0
0
1
0
2
3
0
0
1
0
0
2
0
0
1
1
2
0
1
0
2
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
1
1
1
1
0
4
2
2
0
0
0
2
0
0
2
0
2
0
2
0
2
1
0
0
2
1
0
0
0
0
0
1
0
1
2
0
0
0
0
2
0
0
0
2
0
1
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
1
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
1
0
0
1
1
2
1
2
0
0
0
2
0
2
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
2
0
0
1
2
0
0
0
0
0
0
0
0
1
5
0
0
0
0
1
2
2
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
1
1
2
1
0
2
2
0
0
0
0
0
1
0
2
1
0
0
2
0
0
0
0
0
0
3
1
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
2
2
0
0
0
1
1
1
2
0
1
0
0
0
0
0
1
0
0
4
0
0
2
2
0
0
0
0
1
0
2
0
0
2
0
0
0
2
0
0
1
2
0
0
2
0
4
0
2
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
1
1
1
3
0
0
1
0
2
0
0
0
1
1
2
2
0
0
2
0
0
0
0
0
0
1
0
3
0
0
0
0
3
2
0
1
0
0
0
0
2
0
1
0
2
1
1
0
0
2
1
2
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
3
4
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
3
0
0
0
2
0
0
1
1
0
0
0
0
0
1
2
1
0
2
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
1
2
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
2
0
0
0
4
0
0
0
0
2
2
0
0
0
0
0
0
1
1
0
1
3
1
0
2
0
0
1
2
1
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
1
2
2
0
0
0
0
2
0
1
0
0
1
0
1
2
0
0
1
0
2
2
0
0
1
0
3
1
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
2
0
0
1
2
0
0
2
1
0
0
2
1
0
1
0
0
1
2
2
2
0
1
2
1
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
1
0
1
1
0
0
2
2
0
0
0
1
1
3
0
0
0
0
0
0
1
1
0
0
0
1
0
1
1
2
0
0
1
0
0
0
0
0
0
2
1
0
0
0
2
1
2
0
0
0
0
0
1
0
2
0
0
0
1
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
1
3
0
0
0
2
0
1
0
0
0
2
1
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
1
2
0
1
2
2
0
0
0
0
0
0
1
1
0
0
2
0
0
0
3
1
1
2
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
2
1
2
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
2
1
0
2
0
0
0
2
2
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
2
6
0
0
2
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
1
0
0
2
1
0
0
1
0
0
0
0
0
2
1
3
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
3
1
0
1
0
2
0
0
0
0
0
0
1
0
0
0
1
0
2
2
1
0
0
0
0
2
0
0
1
0
1
0
0
3
0
0
0
1
2
2
0
0
0
1
1
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
4
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
1
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
1
2
0
0
2
0
0
1
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
2
0
2
1
1
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
3
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
5
0
0
0
1
2
0
2
0
0
0
1
2
0
0
2
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
1
0
0
0
4
1
0
2
2
0
1
0
0
0
0
0
2
1
0
0
2
0
1
1
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
3
0
1
0
0
0
0
2
0
0
0
0
1
1
3
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
1
2
0
0
0
0
0
1
1
1
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
4
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
2
2
0
0
0
1
1
2
0
1
1
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
3
1
0
1
1
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
2
2
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
2
0
1
1
0
2
0
0
1
0
0
0
0
2
0
0
2
0
2
2
0
0
2
0
0
1
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
1
6
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
1
0
2
2
0
2
0
0
0
0
0
2
1
0
1
0
1
0
0
0
0
0
8
0
0
0
1
0
3
0
0
1
0
0
1
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
3
0
0
1
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
2
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
3
0
0
0
0
0
0
1
0
3
1
0
0
3
0
2
0
0
0
0
0
1
1
0
0
2
0
0
3
0
2
3
0
0
0
0
1
0
0
0
2
0
0
1
0
0
3
0
0
0
2
1
0
0
1
0
0
0
2
0
0
0
1
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
3
0
0
2
2
1
1
0
0
1
2
0
1
1
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
1
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
2
0
2
0
0
2
0
2
0
0
0
1
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
1
0
1
1
2
0
0
0
0
0
0
0
2
0
0
0
0
1
1
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
2
0
0
0
2
0
0
1
1
0
2
1
2
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
1
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
2
0
0
1
3
0
0
1
0
0
1
0
0
0
2
1
0
2
0
2
0
0
0
2
0
0
2
1
2
0
0
3
0
0
4
2
0
0
1
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
2
2
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
2
0
0
0
2
1
1
0
0
0
1
0
2
1
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
1
1
2
1
0
0
0
2
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
2
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
7
2
0
0
0
1
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
2
0
2
0
0
0
1
0
0
2
0
0
0
0
3
0
0
0
0
1
0
0
3
0
3
0
1
1
0
0
0
0
2
2
0
1
2
1
0
0
0
1
0
0
0
0
1
0
3
0
1
0
0
0
0
0
2
0
0
0
2
1
1
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
1
1
1
1
0
0
0
0
0
2
0
0
1
2
0
0
3
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
5
0
0
0
2
0
1
2
0
0
0
0
0
2
2
0
0
1
0
0
0
0
1
1
0
0
0
0
1
2
0
1
1
0
0
0
0
0
0
0
7
0
0
0
0
0
0
2
0
0
0
0
2
0
3
0
1
0
1
0
1
1
0
2
0
0
0
4
2
1
0
0
1
0
0
0
0
0
2
1
1
0
1
0
0
0
0
0
0
4
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
2
0
1
0
0
5
3
0
0
1
2
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
3
0
0
0
0
0
0
0
2
3
1
0
0
0
1
0
1
0
0
0
0
0
1
2
0
2
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
1
0
1
1
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
1
2
2
2
0
2
2
0
0
0
0
0
0
0
3
0
2
0
0
0
3
0
1
2
1
0
0
0
0
2
0
0
2
0
1
2
0
2
2
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
3
0
2
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
2
1
0
0
0
0
0
2
0
2
0
0
0
0
2
2
0
0
2
0
0
1
0
2
0
1
0
0
0
2
2
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
2
2
3
0
0
1
1
0
0
0
1
1
0
0
0
0
0
2
0
0
4
0
0
0
0
0
0
2
0
0
0
1
1
0
0
1
0
0
2
1
0
0
0
0
0
0
2
0
0
1
2
0
2
7
1
0
0
0
1
0
2
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
2
3
0
0
0
0
4
0
0
3
0
0
0
0
0
0
4
0
2
2
2
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
2
2
0
1
0
0
0
1
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
1
0
3
2
1
1
2
2
2
0
0
0
1
1
0
2
1
1
2
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
4
0
3
0
0
0
0
0
0
0
0
3
2
2
0
0
2
2
4
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
1
1
1
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
2
2
1
2
2
0
0
2
3
0
2
0
0
2
0
1
0
0
0
0
2
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
1
0
0
2
2
6
2
0
0
0
0
0
3
0
0
2
0
0
0
1
0
0
1
0
2
2
0
0
0
2
1
1
3
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
1
0
0
1
1
0
3
1
0
2
1
1
0
1
1
1
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
2
0
0
3
0
0
1
2
0
0
0
0
0
0
0
0
0
3
0
1
2
0
1
0
2
0
1
0
0
3
0
0
0
1
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
4
1
0
0
5
0
0
1
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
2
0
0
2
0
0
1
0
0
1
0
0
0
0
0
2
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
1
0
0
0
0
2
0
2
1
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
2
0
2
2
0
0
2
0
0
0
1
0
2
4
1
0
0
0
2
0
1
0
0
0
1
1
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
2
1
2
0
0
1
0
0
0
2
0
3
0
0
0
2
1
0
1
2
0
0
0
0
1
0
0
0
0
0
2
1
0
1
0
0
0
2
0
0
2
0
0
0
1
0
2
0
0
0
2
0
2
0
0
0
4
0
0
0
1
0
1
2
1
2
0
0
0
0
0
1
0
2
1
0
2
2
0
0
0
0
0
0
0
0
0
0
4
1
5
0
0
0
0
2
0
0
7
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
2
2
0
0
1
0
2
0
0
0
0
2
0
1
2
0
0
0
2
0
1
0
3
0
0
0
0
0
2
2
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
1
0
0
0
2
0
2
3
1
1
1
0
5
0
0
2
0
0
0
0
0
1
1
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
1
2
0
1
0
0
0
0
4
1
0
0
0
0
2
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
1
3
0
0
1
1
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
1
2
4
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
2
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
6
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
1
1
0
1
0
4
1
0
0
0
0
0
0
0
2
0
0
0
1
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
1
0
2
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
2
2
0
0
3
1
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
1
2
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
3
0
0
0
2
2
1
0
1
3
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
2
0
1
0
0
0
0
2
0
2
2
0
1
2
0
0
0
0
1
0
0
0
1
1
0
0
3
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
4
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
3
2
0
0
0
0
0
2
0
0
2
0
0
2
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
2
0
2
1
0
1
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
5
0
1
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
1
0
0
0
1
0
0
3
0
2
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
2
2
0
3
2
0
0
0
0
0
0
0
0
1
2
1
0
2
1
2
3
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
1
0
2
0
0
0
0
0
1
2
1
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
2
1
1
0
1
0
1
1
0
0
0
0
0
0
1
1
0
0
2
0
0
0
1
2
0
0
0
0
0
2
1
0
2
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
1
0
1
0
1
1
0
0
0
2
0
0
2
2
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
2
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
1
0
2
0
5
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
1
2
0
2
1
2
0
0
0
1
3
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
1
0
2
0
1
0
0
2
0
0
2
0
0
1
0
0
1
0
1
0
0
4
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
3
0
1
0
1
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
1
0
1
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
2
2
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
3
1
0
0
0
2
0
6
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
1
0
3
1
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
1
1
2
0
0
2
0
2
1
0
2
1
1
0
0
0
0
2
1
3
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
2
2
0
0
2
1
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
2
0
0
1
1
2
3
0
1
2
0
1
0
0
0
2
0
0
0
0
0
1
2
0
1
0
1
0
0
2
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
1
0
2
1
0
0
0
1
0
0
2
2
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
3
0
1
0
1
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
2
1
0
2
2
1
0
0
1
0
0
3
2
0
0
0
2
0
0
1
4
0
0
0
3
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
1
0
9
1
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
2
0
1
0
1
0
0
1
0
0
1
0
1
0
0
2
1
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
3
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
1
2
0
0
0
0
0
2
0
0
1
1
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
3
1
1
0
0
2
1
0
4
2
0
0
0
2
5
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
2
0
1
0
1
3
0
0
2
0
1
0
0
0
2
2
0
1
0
2
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
7
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
1
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
2
0
0
13
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
2
0
0
2
2
0
1
1
1
2
0
0
0
0
3
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
1
2
0
2
0
0
0
0
0
0
0
0
0
0
2
1
3
0
0
0
2
2
1
0
0
0
2
0
0
0
2
2
0
0
1
0
2
0
0
3
0
1
1
1
3
1
0
0
2
0
0
0
0
2
0
0
2
3
0
2
0
0
0
0
0
0
0
1
3
0
0
0
0
2
1
1
0
0
0
1
0
0
2
0
0
0
1
1
0
0
0
0
0
2
0
0
0
1
2
0
0
1
0
0
1
0
1
0
0
0
9
1
0
0
2
0
0
1
0
1
0
0
0
1
0
0
2
0
0
0
0
1
0
2
0
2
0
0
0
1
0
1
0
1
0
0
0
1
0
0
1
0
0
2
0
1
0
0
0
2
0
0
2
0
0
2
2
1
1
0
0
0
0
2
0
0
2
0
0
0
0
2
1
0
2
2
1
0
2
2
0
0
0
0
0
0
0
1
0
0
0
5
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
1
0
2
0
0
1
0
0
0
2
0
0
2
0
0
0
1
0
0
0
2
0
0
0
2
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
2
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
5
2
4
0
0
0
2
0
0
2
0
0
2
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
2
0
0
2
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
1
0
2
0
0
0
1
3
1
0
3
0
2
0
0
0
0
1
0
0
2
0
0
1
0
2
0
0
0
0
2
0
0
1
0
0
0
0
2
1
0
0
2
0
0
1
1
7
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
2
0
0
0
0
1
0
2
2
1
0
2
0
0
2
2
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
2
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
2
1
0
0
0
0
0
2
1
0
4
0
2
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
2
1
0
3
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
1
0
0
2
0
1
0
0
0
0
0
0
1
2
2
0
1
0
0
0
0
0
2
1
2
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
2
0
1
0
0
2
0
0
3
0
0
0
1
0
2
0
2
0
0
0
0
0
1
3
2
0
1
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
2
1
0
1
0
0
0
0
2
0
0
0
0
3
0
2
0
1
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
1
3
0
0
2
1
0
1
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
1
2
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
2
0
2
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
3
0
2
0
0
0
2
1
0
2
0
0
0
0
0
2
1
0
0
2
0
0
0
0
3
0
1
0
0
2
2
1
0
1
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
4
1
1
0
0
2
1
0
1
0
0
2
0
0
0
0
1
2
0
2
0
2
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
2
0
2
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
1
0
2
0
2
0
0
0
2
2
0
0
0
1
0
0
2
0
0
0
0
1
1
0
0
2
0
0
1
0
0
0
1
2
0
0
0
0
0
2
0
1
0
0
0
0
2
1
0
0
0
0
0
4
1
1
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
2
0
0
0
0
1
2
0
0
1
0
1
2
0
0
0
0
0
0
0
2
0
1
2
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
2
2
2
7
0
1
0
0
0
0
0
0
0
3
1
0
2
0
2
2
0
0
2
0
1
0
2
0
2
1
0
0
2
0
0
0
0
0
1
0
0
2
2
1
0
1
2
0
1
2
0
1
0
0
1
0
0
0
0
1
1
0
0
0
2
2
0
1
1
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
1
0
0
0
1
2
0
0
1
0
0
0
0
1
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
6
0
2
0
0
0
0
0
1
1
0
0
0
0
3
1
0
1
0
1
0
0
0
0
1
0
0
2
0
0
0
1
15
0
0
0
2
1
1
0
0
0
1
2
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
3
0
0
0
1
1
4
4
1
0
0
0
1
0
0
0
0
1
2
1
0
1
2
0
2
1
0
0
0
0
1
1
2
0
0
1
0
10
0
2
0
1
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
1
0
2
2
1
0
1
0
0
0
2
0
2
0
0
0
1
0
2
0
0
1
1
2
0
2
0
0
0
0
0
1
1
1
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
1
1
0
0
0
2
1
0
0
0
0
0
2
1
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
1
0
2
1
0
2
0
0
1
0
0
0
0
2
0
0
0
0
2
1
0
0
1
0
1
0
0
0
1
1
0
0
0
2
0
2
2
1
0
1
0
1
0
0
0
0
1
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
3
0
0
0
0
1
0
0
2
0
2
0
0
0
2
0
0
0
2
2
2
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
2
2
0
0
1
2
0
0
4
0
0
6
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
1
2
0
3
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
9
0
0
0
0
0
0
0
0
0
2
1
0
2
2
0
0
1
0
2
0
2
1
0
2
0
0
0
0
0
2
0
0
1
0
0
4
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
1
0
0
0
0
0
0
0
0
2
2
1
2
2
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
1
1
2
1
1
0
0
0
0
0
3
0
0
0
0
0
2
0
1
2
2
0
0
0
0
0
2
0
0
2
2
2
0
0
0
1
0
1
0
0
1
0
0
2
0
2
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
5
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
2
1
2
0
0
0
1
0
0
2
0
1
0
0
0
0
3
0
1
0
0
0
0
2
2
0
0
4
0
1
0
3
0
0
0
0
0
2
2
2
1
0
0
1
0
0
0
0
1
0
2
0
2
1
0
0
0
0
0
1
0
2
1
0
0
2
1
0
1
0
0
1
2
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
1
2
0
0
0
0
0
4
0
0
0
1
0
0
0
0
1
0
0
2
2
0
3
1
0
0
2
1
1
0
0
0
0
1
2
2
0
0
2
0
1
0
0
1
0
0
0
0
4
0
1
0
1
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
2
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
1
3
1
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
1
0
1
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
1
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
4
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
2
0
0
0
0
0
1
0
0
3
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
1
2
0
7
1
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
1
2
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
4
0
0
0
1
0
0
1
0
0
2
0
0
3
2
2
0
0
0
2
0
0
0
1
2
2
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
2
0
1
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
2
0
0
1
0
1
0
0
0
0
0
2
0
1
2
0
0
3
0
2
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
1
1
2
0
1
1
0
2
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
2
1
0
0
2
0
2
1
0
1
2
2
0
1
0
1
0
1
2
0
0
1
1
1
0
2
0
0
0
0
1
0
1
0
0
1
1
2
0
2
1
0
1
0
0
1
0
2
0
0
0
0
2
1
2
0
0
2
0
2
0
3
0
0
0
0
3
0
0
0
0
0
0
2
0
2
0
0
0
0
3
0
2
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
1
3
2
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
2
0
2
0
0
0
2
0
2
0
0
2
0
0
0
0
2
2
0
0
0
1
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
2
9
0
0
0
0
0
0
0
1
4
2
1
0
0
0
0
0
0
0
0
0
0
0
2
2
1
2
1
0
2
0
2
0
0
0
0
3
0
0
2
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
1
2
0
1
1
0
0
0
0
1
0
0
0
0
5
0
0
2
0
0
0
1
0
1
0
2
0
2
2
0
0
2
0
1
1
0
1
0
0
0
2
0
0
2
0
0
0
5
0
0
0
0
0
0
1
0
0
0
1
0
0
2
1
0
0
1
0
1
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
2
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
6
1
0
0
0
0
0
0
0
3
0
0
1
2
0
1
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
3
0
0
1
0
4
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
1
0
0
0
0
0
1
1
0
3
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
3
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
2
0
0
0
2
0
1
0
0
2
0
0
0
2
0
0
0
1
1
1
0
0
4
0
1
0
1
0
0
0
0
2
1
0
0
0
3
0
0
1
0
0
2
2
0
2
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
3
0
0
0
2
1
0
0
0
1
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
2
0
0
3
2
0
0
0
0
0
0
1
3
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
2
2
0
0
0
0
0
0
0
0
0
2
2
1
0
0
2
1
0
0
2
0
0
0
0
0
0
1
4
0
2
0
0
0
1
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
2
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
1
1
0
0
0
2
0
1
0
5
0
0
0
2
0
0
1
0
1
0
1
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
1
2
0
0
1
0
2
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
2
0
0
1
1
0
0
0
0
2
0
1
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
1
3
0
0
0
2
3
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
3
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
1
0
0
0
1
0
2
0
3
0
0
1
0
0
0
2
0
1
0
2
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
1
2
0
0
0
1
0
0
0
0
2
0
0
0
0
2
1
1
0
1
0
0
2
0
1
0
0
0
0
0
4
1
1
0
2
1
1
3
0
0
2
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
2
0
0
2
0
0
0
2
2
0
0
2
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
2
1
0
2
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
2
1
1
1
2
0
2
0
0
0
1
0
1
1
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
1
2
2
2
0
0
0
1
1
0
1
0
0
0
0
0
0
3
2
0
1
0
1
0
0
0
0
2
0
0
2
0
2
5
0
0
0
2
2
0
2
0
0
2
0
0
2
2
0
0
2
0
0
0
0
0
0
1
2
2
1
0
0
2
0
0
0
0
0
0
0
2
1
0
0
2
0
2
0
0
0
1
1
0
2
2
2
0
0
1
2
2
1
0
0
0
3
1
2
2
0
0
0
0
0
2
0
0
1
0
0
0
1
0
1
1
0
0
0
2
0
0
2
1
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
1
0
0
2
1
1
2
0
0
1
1
0
1
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
3
0
0
2
0
0
0
2
0
1
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
7
0
1
0
0
1
0
0
0
0
0
2
0
4
0
0
0
0
0
1
0
1
0
0
1
2
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
3
0
2
0
2
3
0
0
2
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
4
0
0
0
0
18
2
0
0
0
0
1
0
0
0
0
0
3
0
1
0
0
0
1
0
0
0
0
3
2
1
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
2
1
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
2
0
4
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
2
0
0
0
0
0
5
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
2
0
1
0
0
0
1
1
1
2
4
0
2
0
0
0
0
0
0
0
2
0
0
3
1
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
1
2
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
2
0
0
2
0
0
0
0
0
0
0
0
2
3
0
1
1
0
0
0
2
1
0
5
0
3
2
0
0
0
1
0
0
0
0
0
1
1
0
2
0
0
0
2
0
1
1
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
1
0
21
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
2
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
2
0
1
0
1
1
0
0
0
0
3
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
1
0
0
0
0
0
0
3
1
0
1
0
0
0
1
0
0
1
2
1
0
0
0
2
0
0
0
0
0
0
0
2
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
4
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
2
2
2
1
0
3
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
1
2
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
2
3
1
1
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
1
6
0
0
0
0
2
0
2
1
0
0
0
1
0
2
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
1
0
0
0
0
0
2
1
2
3
2
0
0
0
0
1
0
0
1
0
0
0
1
2
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
1
2
0
0
0
1
0
2
0
0
2
0
0
0
2
0
0
0
0
0
1
0
3
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
3
0
0
3
1
2
0
0
2
0
0
0
0
0
1
2
0
0
0
2
0
2
0
1
0
0
0
0
0
4
1
0
1
0
1
2
0
1
0
0
2
0
2
2
0
0
2
2
5
0
0
2
4
2
2
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
1
3
0
0
0
1
0
0
0
0
1
0
0
0
0
2
2
0
0
0
1
0
2
0
0
3
0
1
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
3
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
1
1
1
0
1
2
0
2
2
0
1
1
0
1
1
0
0
1
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
4
1
0
0
2
0
1
0
0
0
4
0
1
0
0
0
0
0
2
1
1
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
5
2
2
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
1
0
1
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
1
0
2
0
0
2
0
0
2
2
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
1
0
0
2
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
2
0
2
3
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
1
0
2
1
0
2
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
3
0
2
3
2
0
0
0
0
0
0
1
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
3
2
0
2
0
0
0
0
0
0
2
0
0
0
0
4
2
0
2
0
0
0
0
1
0
0
0
0
0
2
0
2
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
3
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
2
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
1
0
1
0
2
1
1
0
0
2
0
0
1
1
2
0
2
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
3
0
0
0
2
0
0
0
0
0
0
0
0
2
1
2
0
2
0
0
0
0
0
5
0
1
2
0
3
1
0
2
0
0
1
1
0
0
2
0
2
0
2
0
0
0
3
0
1
1
1
1
1
2
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
1
2
1
0
2
0
0
0
0
2
3
2
0
2
0
0
3
0
0
1
1
0
2
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
3
2
0
2
1
2
0
0
1
0
2
0
0
1
0
0
1
0
2
2
0
0
0
0
0
0
1
3
0
1
0
2
0
0
0
0
0
0
0
2
0
1
0
2
0
0
2
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
2
1
2
0
2
0
1
0
0
2
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
2
1
0
0
0
0
4
0
0
0
0
0
2
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
1
2
2
0
0
2
0
2
1
3
0
2
0
0
0
2
2
2
0
1
0
1
1
0
0
0
1
0
1
2
0
2
0
0
0
0
0
0
0
0
0
1
0
1
1
0
3
2
1
1
1
2
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
2
0
2
0
2
0
0
0
2
0
0
2
0
2
0
4
2
0
0
1
3
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
1
1
1
0
0
0
2
0
0
2
0
1
0
0
1
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
2
0
0
2
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
4
0
2
0
1
0
1
1
0
0
0
1
0
1
1
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
2
2
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
3
1
2
0
0
0
0
0
3
0
0
0
0
0
3
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
3
1
1
0
1
0
0
2
0
0
0
2
2
0
1
0
0
0
0
1
0
0
2
1
1
0
0
0
3
2
0
0
0
0
0
7
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
2
0
2
0
1
0
1
0
0
1
0
0
0
1
2
0
1
0
0
2
0
0
3
2
0
0
0
1
0
3
0
4
0
2
0
1
0
0
0
2
0
0
0
1
0
3
3
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
1
1
0
2
0
0
0
0
0
0
0
0
2
1
2
0
0
2
0
0
0
0
0
0
0
1
1
0
1
0
2
2
1
2
0
0
0
0
0
2
1
0
2
0
2
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
3
1
0
2
0
1
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
1
0
0
8
0
0
0
1
0
2
2
0
0
0
0
0
2
0
1
0
2
0
0
0
2
0
0
1
0
0
2
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
5
0
0
0
0
2
0
0
1
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
2
0
1
0
1
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
1
3
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
1
0
0
2
0
0
1
0
0
1
0
0
2
0
0
2
0
1
0
0
0
0
2
3
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
3
0
1
0
0
3
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
1
1
0
4
0
1
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
2
0
0
0
1
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
1
2
0
0
1
0
0
0
1
0
0
2
0
3
2
1
2
0
1
0
1
0
3
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
1
0
0
0
1
0
0
2
0
1
3
0
0
0
0
1
0
2
0
0
0
2
0
0
0
2
1
0
2
3
3
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
1
2
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
3
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
1
0
1
0
0
1
0
0
0
9
1
2
1
2
0
0
0
1
0
0
2
0
0
0
2
0
0
0
2
0
0
0
2
2
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
2
0
1
0
0
0
2
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
3
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
4
2
0
0
0
2
2
0
0
0
1
0
2
3
0
0
0
0
2
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
2
0
0
1
1
0
0
0
2
0
1
0
0
1
1
0
0
2
1
0
1
2
2
0
0
0
0
1
0
0
0
0
0
0
0
2
2
2
1
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
1
1
2
2
0
0
0
1
0
0
0
0
0
1
2
0
0
1
1
1
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
6
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
3
1
1
2
0
0
0
0
2
2
0
0
0
0
1
0
0
0
2
0
1
1
0
0
0
0
1
0
0
0
0
5
0
0
0
1
0
2
0
1
2
2
0
0
0
0
0
1
2
0
2
0
0
1
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
1
0
0
0
0
1
1
0
2
0
1
2
1
0
0
0
1
3
2
1
0
0
0
5
1
0
0
0
0
1
0
0
2
0
0
2
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
13
0
0
2
0
0
2
0
1
0
1
3
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
1
0
1
2
0
1
0
2
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
1
1
0
0
5
0
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
2
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
3
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
3
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
2
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
3
3
0
1
0
0
1
4
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
5
0
1
0
0
2
0
0
0
0
1
0
1
0
0
0
0
1
0
2
0
1
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
1
2
0
2
0
2
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
1
0
2
0
1
0
0
0
0
2
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
1
0
3
0
2
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
2
0
0
1
2
0
0
0
0
0
0
1
0
6
0
0
3
0
1
1
0
0
0
0
0
1
0
2
1
1
0
2
0
0
0
0
2
0
0
0
0
2
2
1
0
0
0
3
2
1
1
3
0
0
0
0
0
0
5
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
2
3
0
0
1
0
0
0
1
1
1
0
0
0
0
0
2
0
0
0
2
2
0
0
2
0
0
0
0
0
0
2
0
2
0
1
0
1
0
0
2
3
0
2
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
2
2
0
0
0
0
0
0
0
1
0
0
1
4
1
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
1
0
1
2
0
0
0
0
0
1
2
0
1
2
2
0
2
2
0
1
0
0
0
1
2
0
1
0
1
1
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
4
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
1
0
0
1
0
2
1
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
1
0
0
1
0
2
0
1
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
4
0
2
0
2
2
0
1
0
1
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
7
2
0
0
2
2
0
0
0
1
0
0
0
0
1
3
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
2
0
0
1
3
0
0
1
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
3
0
1
2
0
0
2
0
0
0
2
2
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
1
2
0
0
0
0
2
0
0
2
2
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
1
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
1
1
2
2
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
2
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
1
0
0
2
0
2
1
0
2
0
1
0
0
2
0
0
0
0
1
1
0
1
0
0
1
0
2
0
1
0
3
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
2
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
2
0
2
0
0
0
3
0
0
1
0
0
0
3
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
2
0
1
0
0
0
0
3
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
8
1
1
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
1
3
0
0
2
0
0
0
2
2
4
2
1
0
1
0
0
0
0
0
0
3
2
0
1
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
1
1
2
0
0
1
0
0
1
0
0
0
1
1
0
1
0
0
1
1
0
0
1
2
0
1
0
0
0
0
2
0
0
0
0
0
1
5
0
0
0
0
2
1
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
4
1
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
1
1
0
0
1
2
1
0
1
0
2
0
0
2
0
0
0
2
2
2
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
2
1
3
0
0
0
0
0
0
0
0
0
2
0
2
2
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
2
0
1
2
0
0
0
2
0
3
0
0
0
0
0
0
2
0
0
1
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
2
0
1
1
0
2
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
2
1
0
2
2
1
0
0
2
1
1
0
0
0
0
2
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
1
1
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
1
2
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
2
1
0
2
0
0
6
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
5
0
0
0
0
3
2
2
2
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
2
0
0
0
0
0
1
0
1
2
0
2
2
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
7
0
1
0
0
0
0
0
0
1
0
3
2
0
0
1
0
0
1
0
1
0
0
2
0
0
1
0
0
1
0
0
2
0
0
0
4
0
0
1
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
2
3
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
2
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
2
0
0
2
0
8
2
0
0
1
0
2
0
2
0
2
2
0
0
0
0
2
0
2
0
0
0
2
1
2
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
4
0
0
0
0
3
2
0
1
0
0
0
0
0
2
0
0
2
1
0
0
3
0
1
0
2
3
0
1
0
0
0
2
2
0
0
0
0
1
2
2
0
0
1
0
1
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
2
0
0
0
0
1
2
2
0
0
0
0
1
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
3
1
0
0
0
1
0
0
2
1
0
0
2
1
0
0
0
0
0
0
3
0
0
0
0
0
1
0
1
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
3
0
3
1
0
0
0
2
0
0
1
0
0
2
0
1
0
0
1
0
0
1
0
0
2
0
1
0
0
0
0
1
1
0
0
0
0
0
0
3
2
0
1
0
2
0
0
2
1
0
0
0
0
0
0
0
0
1
1
1
2
0
0
1
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
4
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
1
2
2
0
0
0
1
0
4
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
1
0
0
2
0
2
0
1
0
0
0
0
0
0
0
1
0
2
0
2
0
0
1
0
2
0
0
2
0
2
0
0
1
0
0
0
0
0
2
1
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
3
0
0
0
0
0
1
2
0
1
0
3
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
2
2
0
1
0
1
0
3
0
2
0
0
1
0
1
2
2
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
1
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
2
0
2
0
1
1
0
2
1
2
1
0
0
1
0
0
1
0
2
0
1
0
0
0
2
2
0
0
2
0
0
1
2
2
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
3
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
3
2
0
1
0
0
1
1
0
0
2
0
2
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
1
2
0
0
1
0
0
0
2
0
2
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
1
8
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
1
1
0
0
2
0
1
1
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
1
3
0
0
0
0
0
0
4
2
1
0
0
2
2
0
0
0
0
0
5
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
3
2
0
0
0
1
1
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
2
2
1
2
0
0
0
0
11
0
0
1
0
0
0
0
1
0
0
0
0
3
1
0
0
1
3
0
0
1
1
1
0
2
1
2
1
1
0
1
0
0
0
0
0
2
2
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
2
6
0
0
0
5
2
2
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
3
1
2
0
2
0
2
0
0
0
0
0
0
0
1
1
0
2
1
0
0
0
3
1
0
1
0
0
0
1
0
0
1
3
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
5
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
1
0
0
2
0
1
0
0
1
0
0
1
0
0
0
0
0
1
2
0
1
2
0
2
0
2
0
1
2
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
2
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
1
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
2
1
1
0
2
0
1
1
0
0
0
0
1
0
0
1
0
0
2
1
2
0
0
2
0
0
0
1
0
1
2
0
0
1
0
1
3
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
2
0
0
1
0
0
1
0
0
0
0
2
2
0
0
3
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
1
1
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
2
1
0
0
1
0
2
0
1
0
1
0
0
1
2
0
1
1
0
0
1
0
0
0
1
4
0
0
0
0
0
2
2
0
1
0
0
2
1
2
2
0
2
0
0
2
0
2
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
1
0
1
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
2
1
0
0
2
0
0
0
2
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
1
2
0
4
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
2
1
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
2
0
2
0
2
0
1
2
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
3
1
0
1
1
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
2
0
2
0
0
0
1
0
0
0
0
2
1
0
0
2
2
0
0
0
2
0
0
0
0
0
0
1
2
1
0
4
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
2
0
0
1
0
0
4
2
0
3
1
0
0
0
0
0
2
0
0
0
0
1
0
1
2
0
2
0
0
1
0
3
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
1
0
1
1
0
0
0
0
7
0
1
1
0
2
0
0
0
0
1
0
2
1
0
0
2
0
1
0
0
3
0
0
0
0
0
0
0
1
1
2
0
0
0
0
6
0
0
1
2
0
0
1
1
0
0
2
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
2
2
0
0
2
2
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
3
0
1
0
0
0
5
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
3
3
0
0
0
0
1
4
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
1
2
2
1
2
1
0
0
1
0
2
1
0
0
3
2
0
0
0
0
0
0
1
0
0
0
1
2
0
1
0
2
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
1
0
0
0
2
0
0
0
3
0
3
2
1
1
0
0
0
2
2
0
0
0
0
0
0
0
0
3
0
2
2
0
1
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
2
0
2
2
2
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
3
2
0
0
0
0
0
0
2
0
1
0
1
0
0
0
1
2
0
0
1
0
1
3
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
1
0
0
2
0
3
0
1
0
0
2
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
1
0
0
0
2
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
2
0
0
0
0
1
0
0
0
2
2
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
4
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
2
2
0
1
0
0
0
1
0
2
0
0
1
0
0
0
0
2
0
0
0
3
0
1
0
1
0
0
1
1
1
1
0
0
0
2
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
1
0
0
1
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
5
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
1
2
0
2
1
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
1
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
2
0
2
1
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
2
0
3
1
0
2
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
2
0
0
2
0
0
0
1
3
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
3
0
0
2
0
0
0
0
0
0
2
0
2
1
0
2
2
0
3
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
1
0
1
0
0
2
0
0
3
0
0
2
0
0
0
1
0
0
0
0
2
1
2
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
1
2
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
1
2
1
0
2
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
2
0
2
0
0
0
0
2
0
0
3
0
0
0
0
2
0
0
0
2
0
2
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
2
0
0
1
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
1
2
0
1
0
1
1
0
0
1
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
2
0
0
1
0
2
1
0
0
2
0
0
0
0
1
0
0
0
1
2
1
0
2
0
1
1
0
5
3
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
2
2
2
0
2
1
0
1
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
1
2
0
0
0
1
0
0
0
0
1
2
1
0
2
2
0
1
0
0
0
2
0
0
1
0
0
0
2
3
0
2
0
0
0
2
0
0
0
0
0
0
4
1
1
0
0
0
3
0
1
1
0
0
1
2
0
0
0
3
1
3
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
2
0
0
0
2
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
2
0
1
1
1
0
0
2
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
2
1
0
1
0
0
0
0
0
2
5
1
0
0
2
0
0
0
0
3
0
0
0
0
0
0
3
2
0
0
0
1
3
0
0
2
2
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
2
0
1
1
0
2
1
2
0
3
1
0
0
2
3
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
2
0
0
0
1
0
2
0
1
1
1
2
1
2
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
2
0
2
0
0
0
0
3
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
2
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
1
1
0
2
0
2
1
1
3
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
1
2
0
0
0
0
0
1
1
0
0
1
0
0
2
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
3
0
2
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
2
1
1
2
0
3
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
1
0
2
2
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
2
1
0
0
0
2
0
1
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
2
2
0
0
1
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
2
2
2
0
1
0
1
0
0
0
0
0
1
1
0
0
1
0
1
0
2
0
0
0
1
0
1
1
2
1
0
0
1
0
2
0
0
0
0
0
1
0
0
2
1
1
0
2
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
3
1
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
1
0
1
1
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
1
1
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
2
0
0
0
0
1
0
2
1
0
0
0
2
0
1
2
2
2
5
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
1
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
3
0
1
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
3
0
2
0
2
1
1
0
0
3
2
0
0
0
0
0
0
0
1
2
0
0
0
3
0
0
0
0
1
0
2
2
0
0
0
0
1
1
2
0
3
0
2
1
0
0
0
2
1
1
0
2
0
0
0
0
0
0
0
2
3
0
2
0
2
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
2
1
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
7
1
0
0
2
0
0
0
4
0
0
3
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
3
0
0
1
0
0
0
3
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
2
2
0
2
0
2
2
0
0
0
2
0
0
0
0
0
1
2
2
0
0
0
1
2
2
0
1
0
2
0
2
0
0
1
2
0
2
0
0
0
1
2
1
2
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
2
1
1
2
0
0
0
2
0
0
0
2
0
0
2
2
0
0
3
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
1
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
1
2
0
2
0
1
0
0
2
0
0
0
0
0
2
2
0
2
0
2
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
18
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
2
2
2
0
0
0
0
1
0
0
1
0
0
2
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
1
0
2
0
1
0
0
0
0
7
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
4
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
3
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
1
2
0
0
0
0
0
2
0
1
0
0
0
1
0
0
1
0
0
1
0
1
0
1
3
0
0
0
0
0
0
1
1
0
2
0
0
3
0
2
0
0
1
0
1
0
0
2
0
0
0
0
0
2
1
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
2
3
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
1
0
2
0
0
2
0
0
3
0
0
0
0
2
1
0
4
1
0
0
1
0
0
0
0
0
3
0
0
0
1
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
2
3
0
2
0
0
1
0
0
1
4
0
0
2
0
0
0
0
2
2
0
1
0
0
0
0
0
3
1
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
2
0
0
0
9
0
1
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
3
3
1
1
0
2
0
0
0
1
0
1
2
0
0
1
0
0
0
1
3
0
0
1
0
0
1
1
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
2
0
0
1
1
0
0
2
0
0
2
0
0
1
1
0
1
0
1
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
1
0
0
1
0
0
2
0
0
0
1
1
1
0
0
0
0
2
1
1
1
0
1
0
0
0
0
2
0
1
0
0
0
0
2
0
0
1
0
2
0
0
0
1
1
0
2
0
0
0
2
0
1
3
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
1
2
4
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
1
2
0
0
0
0
3
0
0
0
0
2
2
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
2
2
3
0
1
1
2
3
0
0
2
0
0
1
0
2
2
0
0
0
1
2
0
3
1
1
0
0
0
1
0
1
0
0
0
2
0
1
2
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
1
3
0
0
0
0
2
0
0
1
2
0
0
0
1
1
1
2
0
0
0
0
0
2
0
0
1
0
1
2
2
0
0
2
2
1
0
0
0
0
1
0
0
2
2
0
0
0
2
0
0
0
0
2
0
0
1
2
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
1
0
1
2
0
0
0
0
1
1
0
2
0
0
2
0
1
1
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
3
0
2
0
3
1
0
0
0
0
2
0
0
3
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
3
2
2
2
1
0
0
1
0
2
1
0
1
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
2
0
0
0
5
0
0
0
0
1
0
2
0
0
1
0
2
0
1
4
0
0
1
0
4
0
0
0
2
2
0
0
0
0
0
0
0
2
1
1
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
4
1
0
1
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
4
0
2
0
0
0
3
2
2
1
0
1
0
0
2
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
3
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
2
0
1
0
2
0
0
2
0
0
1
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
1
0
0
2
2
0
1
2
0
0
0
1
2
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
2
0
0
1
0
1
0
0
1
0
2
0
0
0
8
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
3
2
1
0
0
2
0
1
1
2
1
0
0
0
2
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
5
0
0
4
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
1
1
4
0
0
2
0
0
1
0
1
1
1
0
2
0
0
3
1
0
0
0
0
0
3
2
0
0
1
0
0
2
2
0
0
1
0
2
0
0
1
0
1
1
2
2
1
4
0
2
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
2
1
1
0
0
2
0
1
0
0
2
0
0
0
1
0
0
0
1
0
1
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
1
1
0
2
2
1
1
1
0
0
2
1
1
0
0
0
0
2
0
0
2
0
5
0
1
0
0
2
1
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
1
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
5
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
1
0
0
1
0
2
1
0
0
0
0
1
0
0
1
0
0
1
0
2
0
1
0
1
0
0
1
0
0
1
2
2
0
0
0
0
1
0
0
1
0
2
2
2
0
2
0
3
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
1
2
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
2
2
0
1
0
0
0
2
0
0
0
0
0
2
2
0
2
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
2
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
1
2
0
1
0
2
0
0
0
0
0
1
1
7
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
1
0
0
0
0
1
0
1
0
0
0
0
2
1
0
1
0
0
0
0
1
0
2
0
0
0
2
0
1
2
0
2
2
1
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
1
1
2
1
0
0
0
0
1
0
0
1
0
0
0
0
1
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
1
0
2
0
0
2
0
0
1
0
0
0
2
0
0
2
0
0
0
0
2
0
2
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
2
1
1
3
0
0
0
0
0
0
0
0
0
1
1
0
0
2
1
1
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
3
0
0
1
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
2
0
2
2
2
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
2
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
2
0
0
1
0
2
0
0
0
2
3
2
1
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
3
0
0
2
0
0
1
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
1
0
0
0
1
3
0
0
1
0
1
0
0
2
0
2
0
0
2
0
0
1
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
2
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
3
2
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
1
1
0
0
1
2
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
2
0
0
0
0
0
0
2
1
0
0
0
0
0
1
1
0
0
3
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
4
0
2
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
2
0
0
1
0
0
0
3
0
0
0
0
0
0
2
0
0
1
0
0
0
2
1
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
5
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
1
2
0
2
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
2
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
3
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
1
0
2
0
0
0
2
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
2
0
0
0
0
0
0
1
0
3
0
5
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
2
0
0
1
0
0
0
0
2
2
0
0
0
0
0
2
0
2
0
0
0
0
0
2
2
0
0
1
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
2
0
1
1
0
0
0
0
0
2
0
0
0
0
0
1
0
1
1
0
2
2
1
0
0
1
0
2
6
0
0
0
4
0
0
0
0
2
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
3
0
0
0
0
0
1
0
1
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
2
2
1
1
0
0
2
0
0
1
0
3
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
2
0
2
0
0
1
1
0
0
0
0
2
0
0
1
0
2
2
2
2
3
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
1
1
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
2
0
1
2
0
0
0
0
6
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
2
2
1
0
0
0
0
0
0
0
1
0
0
0
2
0
4
0
0
1
0
0
0
2
2
0
2
0
0
2
0
0
2
2
0
0
0
0
1
1
0
2
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
2
2
0
0
0
1
0
0
1
0
0
0
0
0
1
4
1
0
0
2
0
2
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
2
1
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
1
0
0
0
1
0
3
0
2
3
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
2
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
3
0
0
0
0
0
1
0
0
0
0
3
0
1
2
0
0
0
2
1
0
2
0
1
2
0
0
0
1
0
1
0
1
0
1
0
0
0
0
2
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
3
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
3
0
0
0
2
0
0
0
1
0
0
2
0
0
0
2
2
0
1
0
1
0
0
1
2
0
0
0
1
1
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
2
0
1
2
0
0
2
0
0
1
0
1
0
0
0
0
1
2
1
0
0
0
1
2
0
0
1
0
0
3
0
2
2
0
0
0
0
0
0
0
2
1
0
0
1
0
2
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
2
0
2
2
5
2
1
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
4
0
0
0
2
0
1
0
1
0
0
1
0
1
1
0
0
0
1
0
2
0
0
0
0
0
0
0
4
5
0
0
0
3
0
1
0
0
0
0
1
2
2
0
0
0
2
0
2
1
0
1
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
3
2
0
1
0
0
0
0
3
0
0
2
2
0
0
2
2
0
2
0
1
0
0
0
0
0
5
0
1
1
0
0
0
0
0
1
3
0
1
0
0
0
1
3
0
1
0
1
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
1
0
2
1
0
4
0
1
0
1
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
1
0
0
0
1
2
0
0
0
0
0
1
0
0
0
1
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
1
0
0
3
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
1
1
0
2
2
0
0
0
1
0
0
4
2
2
2
0
0
1
0
1
2
0
2
0
0
0
1
0
1
0
2
0
0
1
0
1
0
0
2
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
4
2
2
0
1
1
0
2
0
0
0
0
1
0
0
0
0
0
1
1
0
0
3
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
2
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
3
0
0
2
0
0
0
1
1
0
0
0
0
1
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
1
0
0
2
0
0
0
0
2
0
2
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
1
3
0
0
0
0
0
0
0
0
1
0
1
4
0
0
0
0
0
2
2
0
1
0
0
0
0
5
2
2
1
3
1
0
1
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
3
2
0
1
0
1
0
0
0
1
2
1
2
1
1
0
2
0
0
1
2
0
0
0
0
0
0
0
2
1
0
1
1
0
0
0
1
0
0
3
0
0
1
1
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
4
2
0
1
0
1
2
0
1
1
1
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
3
0
1
0
1
0
0
0
0
0
0
2
2
0
0
2
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
11
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
3
0
0
0
0
0
0
1
0
3
0
0
0
0
1
0
0
0
0
5
0
0
0
0
0
0
2
0
2
0
2
1
1
2
2
2
0
0
0
0
0
2
1
0
2
0
2
2
1
0
2
1
0
0
1
0
0
1
2
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
1
1
0
1
0
0
0
1
2
1
0
0
2
0
1
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
2
2
1
0
0
0
0
1
2
0
0
0
0
0
0
0
1
3
0
0
0
1
3
0
0
1
0
0
0
0
3
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
2
0
0
3
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
1
1
2
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
3
2
2
0
0
1
1
0
0
0
0
0
0
1
0
0
1
1
1
0
3
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
1
0
0
0
1
2
0
0
0
0
3
0
1
0
1
0
0
2
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
3
1
0
1
0
2
2
0
1
0
2
0
2
0
2
1
0
0
0
4
0
0
1
2
0
0
1
0
0
2
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
1
1
2
0
2
0
2
2
0
0
0
0
0
0
2
0
2
0
0
3
0
2
0
0
0
1
0
0
1
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
1
0
0
0
1
1
2
2
1
2
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
2
1
1
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
2
0
2
0
2
1
0
0
1
0
1
0
0
1
1
0
0
0
0
0
1
2
0
0
0
0
2
1
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
2
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
1
0
0
1
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
5
0
2
0
1
0
1
0
2
0
2
0
1
1
0
0
1
0
0
1
0
0
0
3
0
0
0
0
2
1
0
2
2
3
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
1
0
0
0
0
2
2
1
0
0
0
1
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
1
0
1
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
2
1
0
0
0
2
0
1
0
0
2
0
2
0
0
2
0
2
2
1
1
3
0
0
0
2
0
0
1
2
1
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
4
0
0
0
0
0
1
0
2
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
1
1
0
0
0
1
1
2
0
0
3
0
0
0
0
0
4
0
0
0
0
0
0
0
2
0
2
0
2
2
0
0
0
2
3
0
0
0
0
0
0
0
0
1
0
1
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
4
0
0
0
1
0
2
0
2
0
1
1
2
0
0
0
1
0
0
0
0
5
0
0
0
1
2
0
0
0
1
0
0
0
2
0
2
0
2
0
1
0
0
2
0
4
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
1
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
3
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
3
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
3
0
0
2
0
2
0
0
2
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
2
1
1
0
2
1
0
2
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
4
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
2
0
1
1
1
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
1
0
1
0
1
1
1
0
0
0
1
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
1
1
0
0
0
2
0
0
0
1
0
0
0
2
0
0
1
1
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
2
0
2
0
2
2
0
1
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
2
1
0
0
0
0
0
0
0
0
0
2
0
1
2
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
6
2
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
1
0
0
5
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
1
0
0
1
0
0
0
2
0
0
0
3
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
3
0
4
2
0
2
0
0
0
2
1
1
0
0
1
0
0
0
0
0
2
1
3
1
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
2
0
0
0
2
0
1
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
1
1
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
1
1
0
0
0
0
0
2
2
1
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
2
0
2
0
0
0
0
0
0
0
1
3
0
0
0
1
0
0
1
2
0
2
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
2
0
2
0
2
0
1
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
7
0
1
0
1
5
1
0
0
2
1
2
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
1
0
0
0
0
3
0
0
0
0
2
0
0
0
1
0
1
1
1
0
0
0
1
1
1
0
1
1
0
1
0
0
2
1
0
0
0
0
0
0
0
1
3
3
1
0
0
0
0
2
0
0
1
0
0
0
0
0
1
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
1
0
0
2
0
0
0
1
1
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
1
0
0
0
1
0
0
2
0
1
0
0
0
0
2
1
1
0
0
1
0
3
0
5
0
0
0
0
0
0
3
1
0
0
0
2
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
1
0
0
0
0
1
2
1
0
2
0
1
0
1
0
2
0
3
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
4
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
1
0
2
0
2
2
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
2
2
2
0
0
1
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
5
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
2
1
0
0
1
0
0
0
0
0
0
2
1
0
0
0
2
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
2
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
4
2
2
0
1
0
1
0
2
1
0
0
2
0
1
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
2
2
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
1
1
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
1
2
0
0
0
0
0
3
0
0
1
0
0
0
0
2
0
0
0
0
3
2
0
1
0
1
2
0
1
0
0
0
0
1
1
2
0
1
1
0
0
0
2
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
1
0
2
0
0
1
0
0
2
2
0
1
0
0
0
0
2
0
2
0
3
0
1
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
1
1
0
0
0
0
0
2
2
0
0
0
3
0
0
2
0
2
1
0
2
1
7
0
2
4
1
0
1
1
2
2
1
0
0
1
2
2
0
0
2
0
0
2
0
1
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
2
0
2
2
2
0
1
2
0
0
0
1
0
1
1
0
3
1
1
0
3
0
2
0
0
0
0
0
0
2
1
0
1
0
4
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
4
0
0
2
0
0
0
2
1
0
0
2
0
0
0
0
0
1
2
0
0
1
0
0
0
1
1
1
1
2
0
1
0
0
0
0
0
1
2
1
1
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
1
2
1
0
2
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
1
3
0
1
0
2
0
0
0
0
2
0
2
3
0
0
2
0
0
0
0
0
0
1
0
2
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
2
0
0
0
4
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
3
0
4
0
2
1
0
0
0
1
0
0
0
2
1
0
1
0
1
0
2
0
0
3
1
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
1
0
2
0
0
1
0
0
0
2
1
1
0
0
2
0
0
2
2
0
0
1
0
0
0
0
2
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
2
1
0
1
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
4
2
0
0
0
2
0
0
2
0
0
2
0
3
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
5
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
1
0
0
1
0
3
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
3
0
0
0
0
3
0
0
2
0
1
0
1
0
0
1
0
0
0
0
0
0
0
4
2
1
0
0
1
1
0
0
0
0
2
0
7
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
2
0
0
0
0
0
1
0
1
1
8
0
0
0
0
0
0
0
0
1
0
0
0
2
1
2
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
1
1
1
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
2
1
2
2
0
3
4
0
0
4
0
2
0
0
0
0
0
1
1
2
0
0
0
1
2
1
0
1
0
1
0
0
0
0
0
0
3
2
1
0
0
2
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
4
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
1
2
0
1
0
0
0
0
1
0
0
1
0
0
2
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
2
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
2
2
1
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
3
2
0
0
1
0
0
0
0
0
0
1
0
0
1
0
2
1
0
0
2
4
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
1
0
0
2
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
2
1
1
1
0
0
0
0
0
0
0
0
1
0
0
3
2
0
2
1
0
0
0
0
0
1
0
2
3
2
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
2
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
2
2
2
0
0
1
0
0
0
0
4
2
0
0
1
1
0
2
0
0
1
0
0
2
0
0
0
2
0
2
0
2
0
0
0
2
0
0
0
0
1
2
0
1
0
2
0
0
1
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
2
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
2
2
2
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
2
0
0
2
1
0
2
0
0
0
0
0
1
1
0
0
2
1
0
0
0
0
0
1
3
2
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
3
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
1
1
0
0
0
1
0
1
1
1
2
0
0
1
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
2
1
0
0
0
0
1
1
1
0
3
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
4
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
3
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
2
0
0
1
1
2
0
1
0
1
2
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
2
1
0
3
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
1
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
1
0
1
0
0
2
0
0
3
0
2
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
2
1
0
2
0
0
2
0
0
0
0
0
0
1
2
0
0
0
1
0
2
0
2
1
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
1
2
0
0
0
0
1
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
1
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
2
0
1
0
0
0
0
0
0
0
3
0
1
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
5
0
1
0
0
2
1
2
0
2
0
0
0
0
0
0
2
0
2
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
5
2
1
1
0
0
0
1
1
0
3
3
1
0
1
1
2
0
0
1
0
2
1
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
5
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
2
4
0
1
0
0
1
0
0
0
1
0
0
0
1
0
2
0
0
0
2
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
2
2
1
0
0
1
0
0
3
2
0
0
0
2
1
0
1
0
0
0
1
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
3
0
0
0
0
0
0
1
2
0
0
2
0
2
0
0
0
0
0
0
1
0
0
1
1
0
0
0
3
0
0
0
3
0
1
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
3
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
1
1
1
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
2
0
1
0
0
2
0
0
0
0
0
0
2
0
1
0
1
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
8
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
5
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
1
1
1
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
1
1
0
2
0
1
0
0
1
1
2
2
1
1
0
0
1
0
0
0
0
1
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
1
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
2
0
0
0
0
2
0
0
0
0
2
2
3
1
0
1
1
2
0
1
1
0
0
0
2
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
3
0
0
0
2
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
1
3
1
1
0
1
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
2
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
3
0
2
0
1
4
1
0
0
0
0
0
0
0
1
2
0
0
2
2
0
0
0
3
0
2
0
0
0
4
0
0
2
0
0
2
3
0
1
0
0
3
0
0
2
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
2
0
1
1
2
2
0
0
2
0
1
0
0
1
3
0
0
0
0
0
2
0
2
1
0
2
0
0
0
0
2
5
0
0
0
0
0
1
0
2
0
1
1
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
3
0
0
0
1
0
1
0
0
1
0
0
0
0
0
2
0
0
2
2
0
1
1
1
0
0
0
0
0
0
0
1
2
2
1
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
1
1
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
3
0
0
2
1
2
1
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
2
1
0
2
0
0
0
0
0
1
2
0
3
0
0
0
0
0
0
1
1
0
0
2
0
2
0
1
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
1
0
2
0
1
0
0
0
2
0
0
0
1
1
2
0
2
0
0
3
1
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
2
2
1
0
0
1
0
0
2
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
2
0
0
5
1
0
1
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
3
0
1
0
0
0
2
3
0
1
2
0
0
0
0
0
0
1
0
2
0
0
0
1
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
1
3
0
1
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
2
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
2
0
0
0
1
0
1
0
0
2
0
1
2
0
0
0
0
0
0
1
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
1
0
0
0
0
2
0
0
1
0
0
4
2
0
0
0
2
0
0
0
3
2
2
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
2
1
1
0
0
0
0
0
2
0
1
4
0
0
0
2
1
2
0
0
1
0
2
0
0
0
1
0
0
0
2
0
0
0
2
0
0
2
0
1
0
1
2
1
1
0
0
0
0
1
0
0
1
1
0
0
2
0
2
0
1
0
3
2
0
1
2
0
0
0
0
0
4
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
3
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
1
0
0
0
0
0
0
1
0
1
2
2
3
0
0
1
0
0
1
0
3
0
0
2
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
1
0
2
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
4
0
1
1
1
0
0
3
0
0
0
4
0
2
1
0
0
1
2
0
0
1
0
0
0
2
0
2
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
2
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
1
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
3
0
0
1
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
2
1
0
1
0
2
0
2
0
0
0
2
2
2
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
5
0
0
0
0
2
0
1
0
0
0
2
2
0
1
0
0
2
2
0
0
1
0
0
0
0
2
2
0
1
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
1
0
2
0
0
0
0
2
2
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
1
1
0
0
1
1
2
0
0
0
0
1
0
0
0
2
0
1
0
0
0
1
3
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
1
0
0
2
0
0
0
0
1
0
2
1
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
2
0
2
2
0
2
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
2
2
1
2
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
1
1
1
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
2
1
0
0
0
2
0
0
0
0
3
0
2
0
0
0
3
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
1
0
1
0
0
2
0
0
0
0
0
0
1
1
0
1
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
3
1
0
1
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
1
1
1
0
2
1
1
0
0
0
1
0
0
2
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
4
0
0
0
0
0
0
1
3
0
2
1
0
0
2
0
1
0
2
0
0
0
2
1
0
2
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
1
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
1
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
2
0
2
0
0
0
2
0
0
2
0
0
0
1
0
1
1
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
2
4
0
0
0
0
0
0
0
1
1
0
0
1
1
0
1
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
2
0
2
0
2
1
2
1
0
0
0
0
2
0
0
2
0
0
0
0
1
2
1
2
0
0
0
0
0
0
3
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
1
0
0
2
0
2
0
0
0
1
0
2
0
3
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
2
0
3
0
2
0
0
0
0
3
3
0
0
0
0
2
0
0
0
1
3
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
1
2
1
0
2
0
0
1
1
0
1
0
1
0
0
0
0
1
1
0
2
0
0
1
1
0
0
1
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
1
1
2
0
0
0
1
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
2
1
0
0
2
1
0
0
0
2
0
2
1
1
2
7
0
0
0
0
0
2
2
2
0
0
2
5
0
0
0
0
1
0
9
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
5
0
0
0
0
4
0
0
1
2
0
3
0
0
0
0
1
0
0
0
0
3
0
0
1
2
0
0
1
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
1
0
0
0
0
2
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
2
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
2
0
2
1
2
0
0
2
0
0
1
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
1
2
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
1
1
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
1
0
2
0
2
0
2
1
0
0
2
0
2
0
0
0
0
2
0
0
0
0
1
0
1
1
4
2
1
0
0
2
0
0
0
1
0
0
0
2
2
3
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
1
1
0
3
0
2
0
2
0
0
0
0
0
2
3
0
0
2
0
0
0
0
3
0
0
0
1
2
0
2
2
1
2
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
3
1
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
3
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
3
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
1
0
1
0
0
2
0
0
2
1
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
2
0
1
0
0
2
0
2
1
0
1
0
0
2
2
2
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
3
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
2
0
0
0
0
3
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
2
2
0
1
0
0
1
0
2
1
0
0
1
1
2
0
1
0
1
0
0
0
2
0
0
0
2
2
0
1
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
2
0
0
1
8
0
0
1
0
0
0
0
0
1
2
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
1
0
1
0
0
0
2
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
2
2
0
0
0
0
2
0
1
1
0
0
0
0
2
0
0
2
0
2
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
1
0
0
1
0
0
0
0
2
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
2
0
1
0
0
0
0
0
2
0
1
0
1
0
1
0
1
0
0
1
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
2
2
2
1
0
0
0
0
2
0
0
2
3
0
0
0
1
0
0
0
0
0
2
0
0
0
0
4
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
2
1
0
0
0
0
1
0
1
0
0
0
1
2
2
0
0
1
2
0
0
1
0
0
1
1
0
0
2
2
0
4
0
2
0
0
0
0
0
2
1
1
0
1
2
1
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
1
0
2
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
2
2
0
0
0
2
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
2
3
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
1
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
1
1
0
0
0
0
3
0
0
0
1
0
0
1
2
2
0
0
0
0
0
0
0
2
0
0
1
0
0
1
2
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
1
0
3
0
0
0
0
1
0
1
0
0
1
0
1
0
1
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
9
2
0
1
0
0
0
0
0
1
0
0
2
0
1
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
4
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
2
0
1
1
0
0
0
2
0
2
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
2
0
1
0
0
0
1
0
2
1
0
1
0
0
0
1
0
3
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
3
2
0
0
0
0
1
0
0
0
0
2
0
0
0
2
2
0
0
2
3
0
0
0
1
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
1
0
1
0
2
0
0
1
2
0
0
3
0
2
2
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
5
0
2
0
0
2
0
0
3
0
0
0
0
1
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
1
0
2
2
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
3
0
0
0
2
1
1
0
2
0
2
0
0
0
1
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
1
1
0
0
0
0
0
4
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
2
0
1
1
0
1
0
2
0
0
1
0
0
0
2
0
0
2
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
2
2
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
3
0
1
2
0
0
0
0
1
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
2
3
1
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
9
1
1
4
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
2
0
1
2
0
0
0
0
2
0
2
0
1
1
0
0
0
0
0
3
0
0
0
0
0
2
0
0
2
0
0
0
1
1
0
0
0
1
0
0
0
1
4
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
4
1
0
2
0
0
0
2
0
0
0
0
3
0
1
0
0
0
2
0
2
2
0
2
0
0
0
0
0
0
2
2
0
0
0
2
0
2
0
1
2
2
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
1
2
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
1
0
2
0
0
2
0
0
0
1
0
0
0
2
0
1
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
2
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
1
0
1
0
1
3
0
2
0
2
0
5
0
1
0
1
0
0
0
2
0
0
0
0
2
1
1
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
1
1
1
1
0
1
2
0
0
1
3
0
0
3
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
2
2
0
0
0
1
0
0
0
0
3
0
0
0
10
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
2
3
0
2
2
0
0
8
0
0
0
0
2
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
2
0
0
2
0
2
0
1
4
0
1
0
0
0
0
1
1
0
2
0
1
2
0
0
0
0
0
0
1
3
0
1
0
0
0
3
0
0
0
0
0
1
0
2
0
2
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
7
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
1
0
1
0
0
0
2
0
2
0
0
0
2
0
0
0
2
0
0
2
0
1
1
0
1
0
0
0
0
3
0
0
1
0
0
0
0
0
1
1
1
2
0
0
2
0
0
0
1
1
0
0
1
1
0
0
3
0
0
1
0
1
0
0
2
1
0
1
0
0
1
0
0
0
0
0
0
0
1
3
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
1
0
1
5
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
1
2
0
0
2
0
0
3
1
0
0
0
2
0
1
0
0
0
2
1
0
0
0
3
0
1
0
1
0
0
1
0
0
2
0
0
1
0
0
9
0
0
0
0
1
2
1
0
0
0
0
0
3
0
1
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
2
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
2
0
2
0
0
1
2
2
2
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
5
2
0
0
0
0
0
0
0
0
2
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
2
2
0
0
2
0
0
2
2
2
0
0
0
0
2
0
1
1
0
0
0
2
0
1
1
0
0
0
0
1
0
0
0
5
0
0
1
0
0
0
0
2
0
0
3
2
1
0
1
0
0
0
1
0
2
1
0
2
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
2
0
0
0
1
0
0
0
1
2
0
0
0
1
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
2
0
0
0
0
2
0
0
0
0
0
0
2
3
1
2
5
0
0
0
0
0
0
2
2
0
2
2
0
0
0
2
0
0
0
0
2
0
0
1
2
0
0
1
0
0
0
2
0
2
2
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
2
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
1
2
0
0
3
0
0
0
0
0
0
0
1
2
2
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
3
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
4
0
2
0
0
0
2
0
0
1
0
0
3
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
1
2
0
2
0
1
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
2
0
0
0
3
0
0
0
0
2
0
0
0
3
0
1
1
2
1
0
1
2
0
0
0
0
1
0
0
2
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
2
0
0
0
0
1
0
1
0
0
0
0
0
2
2
0
1
2
2
0
1
2
0
0
1
1
0
0
4
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
3
2
0
0
0
0
0
0
2
1
1
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
3
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
3
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
1
0
0
3
0
2
0
0
3
0
0
0
0
1
0
2
1
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
1
2
0
0
0
0
1
1
2
1
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
1
2
1
2
2
1
0
0
1
2
0
1
0
2
1
0
0
2
0
2
0
0
0
1
0
0
0
0
1
0
0
3
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
3
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
2
0
1
2
0
2
2
0
0
0
1
0
0
1
0
0
2
0
1
0
0
0
0
3
2
0
0
0
0
1
0
0
0
2
0
1
0
1
0
0
2
2
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
1
0
1
0
0
0
0
0
1
3
0
1
0
0
0
0
0
1
0
0
0
2
0
2
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
11
1
0
2
0
1
1
0
2
1
2
2
0
0
1
0
0
0
0
0
0
0
2
1
2
2
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
1
2
0
0
1
0
0
0
0
0
1
1
2
0
0
1
1
0
0
2
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
1
1
2
1
0
0
0
0
0
0
0
0
1
0
2
1
1
0
0
0
0
2
0
2
2
0
1
0
1
0
1
0
0
0
1
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
2
3
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
2
0
0
0
1
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
1
0
3
0
1
1
0
0
2
1
0
0
0
1
2
0
2
0
0
2
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
5
1
1
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
1
1
4
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
2
1
0
3
0
0
1
2
0
0
0
0
0
0
1
0
0
2
2
0
0
1
2
0
2
1
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
1
2
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
3
0
0
0
0
2
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
20
2
0
0
0
0
0
2
2
0
0
0
0
1
2
0
0
0
2
0
2
1
3
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
2
0
2
0
0
1
0
0
2
1
0
0
0
2
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
2
1
0
2
1
0
0
0
0
0
0
0
0
1
0
2
0
2
1
0
0
0
6
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
1
0
0
2
0
0
2
2
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
2
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
1
0
2
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
1
3
1
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
1
0
1
2
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
1
2
0
0
3
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
2
1
1
0
2
0
0
2
0
1
0
0
0
2
0
2
0
0
1
3
2
0
0
0
0
12
1
0
1
0
0
2
0
0
0
0
0
0
0
2
1
0
0
1
0
1
0
0
0
1
0
3
3
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
2
0
3
1
2
2
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
9
0
0
1
0
1
0
0
0
0
2
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
1
2
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
1
0
2
1
0
2
0
0
1
0
1
0
0
2
0
0
0
0
0
2
0
1
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
2
2
0
2
2
2
0
2
1
2
0
0
3
0
3
0
0
1
0
0
0
1
0
0
0
1
2
0
0
1
1
0
2
0
0
2
0
2
2
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
2
0
0
0
0
1
0
0
2
1
0
1
2
0
2
0
0
0
0
0
0
2
2
0
2
0
0
3
2
0
3
1
2
0
2
1
0
3
2
0
0
0
2
3
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
3
0
2
0
2
0
2
0
0
0
0
0
1
0
0
2
1
2
0
0
0
0
1
0
0
1
0
2
0
0
1
0
0
0
0
27
0
0
1
0
0
0
2
2
0
0
0
0
2
2
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
1
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
2
1
0
4
0
0
2
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
1
0
2
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
1
0
2
0
0
0
2
0
2
0
0
1
2
0
0
0
0
2
2
0
0
1
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
7
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
2
2
0
0
2
2
1
0
0
0
0
0
0
1
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
3
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
1
0
0
0
0
0
0
0
2
0
0
2
0
1
0
1
1
0
0
1
2
0
0
0
2
0
0
0
0
0
1
0
2
0
0
1
0
1
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
2
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
2
1
0
1
2
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
2
2
0
0
0
3
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
1
0
0
3
0
1
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
6
2
0
0
0
0
0
2
2
0
1
1
0
1
0
0
0
0
0
2
0
1
0
0
1
0
2
0
1
0
0
0
0
2
2
0
0
2
0
1
0
3
0
0
0
0
0
1
1
1
0
0
2
0
0
0
1
0
1
2
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
1
1
0
1
1
0
1
0
0
0
0
2
2
0
0
0
1
0
1
0
0
2
2
0
0
0
2
2
0
1
2
2
0
0
0
1
0
0
0
2
0
0
0
0
1
0
1
0
1
0
2
0
0
0
0
2
6
0
1
1
2
0
2
0
1
2
1
0
0
0
0
0
1
0
0
1
2
2
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
2
2
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
2
0
0
0
2
0
0
0
0
2
0
2
1
2
0
4
1
0
1
1
0
0
0
1
0
2
1
0
1
1
2
1
3
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
3
0
0
0
0
0
1
0
1
0
1
2
0
0
1
0
2
1
0
2
0
0
3
1
0
0
0
0
1
3
10
1
0
0
1
0
2
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
6
2
0
2
2
0
0
1
0
2
4
0
2
2
0
0
1
0
0
0
0
0
0
1
2
0
1
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
3
0
0
1
1
2
0
0
2
2
2
0
1
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
2
1
0
1
0
0
2
2
0
0
2
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
1
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
1
0
0
1
2
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
1
1
1
0
1
0
1
0
0
0
5
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
1
3
0
2
2
0
0
0
0
1
2
0
0
0
2
2
1
0
0
0
6
0
2
0
0
1
0
0
0
1
0
1
0
0
2
0
0
2
0
3
0
0
2
0
0
0
0
0
0
0
0
1
1
1
2
0
0
1
0
0
0
0
2
0
1
2
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
2
1
0
0
1
2
0
0
0
0
0
0
0
2
1
1
0
0
4
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
2
1
2
0
0
0
0
0
0
0
2
0
2
5
0
0
0
1
0
0
2
0
1
1
0
2
2
1
0
0
0
1
0
0
0
0
3
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
1
0
0
0
1
0
2
0
0
1
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
2
0
2
0
0
2
2
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
2
2
1
0
1
0
0
2
0
0
3
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
5
1
1
6
0
2
0
1
0
0
0
0
0
1
2
0
0
2
0
0
0
2
0
1
0
0
0
1
0
0
0
0
3
1
0
0
1
1
0
1
0
0
2
0
0
0
1
3
0
2
0
0
1
0
0
2
2
0
1
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
1
0
0
1
2
0
0
0
0
2
0
2
0
1
0
0
2
0
2
0
1
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
4
1
1
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
2
1
0
0
1
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
2
0
2
0
0
1
0
2
2
0
2
2
0
0
0
3
0
0
0
0
2
0
0
0
0
2
3
2
0
1
0
0
0
0
1
0
0
0
2
0
2
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
1
2
2
1
1
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
1
1
1
0
1
0
0
2
0
2
0
2
2
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
2
2
0
2
0
0
2
2
0
0
0
1
2
1
0
0
0
1
1
1
0
0
0
2
0
2
0
0
0
0
0
1
0
2
0
2
0
0
2
0
2
0
2
0
0
0
0
0
0
2
2
1
0
1
0
1
0
0
0
2
1
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
2
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
2
0
1
0
0
3
1
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
2
1
0
2
2
2
0
0
0
0
0
0
1
0
0
0
2
0
1
2
0
2
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
1
0
2
0
0
1
0
2
0
1
0
2
0
0
2
1
0
0
2
1
0
0
2
1
0
0
0
0
0
1
0
2
1
2
0
0
1
0
1
2
0
0
0
2
2
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
1
1
0
0
0
0
0
1
0
2
0
0
0
4
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
1
0
6
0
2
0
0
0
0
0
1
0
0
0
0
0
3
0
0
2
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
3
0
0
3
0
0
0
1
1
0
0
0
0
2
0
1
2
2
0
2
2
0
0
0
0
0
1
0
2
1
2
2
2
0
2
0
0
2
2
2
0
2
1
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
1
0
1
4
1
0
2
0
2
1
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
1
0
2
1
2
0
0
0
0
0
2
0
0
1
0
0
2
2
2
0
2
0
1
0
0
0
0
0
1
0
2
2
0
0
3
0
0
1
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
1
0
0
0
0
0
0
1
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
2
0
0
1
2
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
1
2
1
0
1
0
0
0
0
0
0
2
1
1
0
2
4
0
1
0
0
0
0
0
0
0
0
0
0
4
0
2
2
0
0
0
2
0
2
2
0
0
1
0
0
0
0
1
0
4
1
2
0
1
0
0
0
0
0
0
4
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
2
1
0
0
2
1
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
1
1
0
1
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
1
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
2
2
0
0
0
0
0
0
2
1
2
2
0
0
1
0
0
0
0
1
0
0
2
1
1
0
1
0
0
1
0
0
2
0
0
0
1
0
1
2
0
0
0
2
0
0
0
2
0
0
0
0
1
2
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
6
0
2
1
0
1
4
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
1
0
0
0
2
1
2
0
1
2
1
1
2
1
0
0
0
0
0
2
1
2
3
0
0
2
0
2
2
0
0
1
1
1
2
0
0
2
2
5
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
1
0
0
2
1
3
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
3
2
0
1
0
0
0
0
2
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
3
0
0
2
0
0
0
0
2
0
0
0
0
0
2
2
2
0
0
4
0
0
0
0
5
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
2
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
2
0
2
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
2
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
1
0
1
1
2
0
0
0
0
0
1
2
3
0
0
0
1
2
0
2
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
2
1
0
0
1
1
1
2
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
1
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
1
2
0
2
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
2
1
1
0
0
1
0
0
0
0
0
2
1
0
0
2
0
2
2
0
0
1
0
0
1
0
0
1
0
1
2
1
2
0
1
2
0
1
0
0
0
0
1
0
0
0
1
1
1
2
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
4
0
1
0
2
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
2
0
0
0
2
0
0
1
2
0
0
0
2
0
0
0
1
1
1
0
0
0
0
0
0
0
1
2
0
3
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
1
3
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
7
0
0
0
3
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
1
7
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
2
0
0
1
0
0
0
0
0
2
0
0
1
3
2
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
1
0
2
0
0
0
2
0
1
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
1
0
0
2
0
0
0
1
5
0
1
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
1
2
1
0
0
0
2
0
0
2
1
0
0
0
0
0
3
0
2
0
0
1
0
0
0
2
0
0
0
0
2
0
4
0
2
0
0
1
0
0
0
1
2
0
0
0
0
1
1
2
0
0
1
0
2
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
3
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
2
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
2
1
4
0
2
3
0
0
0
2
2
2
2
0
2
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
3
1
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
1
2
0
0
0
1
2
0
0
0
0
0
1
0
0
2
0
1
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
5
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
1
0
3
1
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
3
0
0
2
2
1
0
0
2
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
2
0
2
1
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
2
2
2
2
1
2
0
0
1
2
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
2
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
2
0
0
0
2
0
0
2
2
1
0
0
1
0
0
0
1
0
2
2
0
0
0
1
0
0
1
0
1
10
0
1
1
0
2
3
0
0
0
0
0
0
1
0
1
2
1
1
0
0
0
2
2
1
0
0
0
0
2
0
0
1
0
0
0
2
2
0
0
0
0
2
0
0
0
2
0
2
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
1
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
1
1
2
2
0
0
0
1
2
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
2
0
0
0
1
0
0
0
0
2
0
1
1
2
0
0
1
0
2
0
0
1
1
0
0
2
1
0
0
0
2
2
0
0
2
0
0
1
1
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
2
1
0
0
0
0
0
2
0
0
1
0
0
2
0
2
0
0
2
0
2
2
0
0
0
1
0
0
0
0
0
1
0
2
0
2
0
0
2
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
1
0
1
1
1
1
0
0
0
0
0
0
2
1
2
0
0
1
2
1
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
1
0
0
2
0
0
1
1
0
0
0
1
2
0
0
1
2
0
0
0
2
0
0
0
3
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
2
0
0
1
2
2
2
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
1
2
2
5
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
3
0
0
2
0
1
0
3
2
0
1
0
0
0
0
2
2
0
1
2
0
0
1
2
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
2
1
0
0
0
0
1
0
1
0
1
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
3
0
0
1
2
1
0
0
0
0
2
0
2
0
0
0
2
0
2
3
0
1
1
0
0
2
0
2
1
0
0
1
1
2
1
0
0
2
0
0
0
1
0
2
0
1
0
0
0
0
1
0
1
0
0
0
2
4
2
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
1
1
1
1
0
1
0
0
0
0
0
0
0
2
1
0
0
1
0
1
1
0
0
0
3
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
2
0
2
0
2
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
1
0
0
0
0
1
2
0
2
2
1
0
0
2
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
1
0
1
1
0
0
0
2
0
2
0
1
1
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
2
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
1
2
2
0
0
0
1
2
0
1
0
0
3
3
0
2
0
0
1
0
0
1
0
2
1
0
1
0
0
0
2
0
1
2
0
4
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
1
0
0
2
2
0
0
0
0
2
0
0
1
0
2
1
0
2
0
0
0
0
2
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
1
1
1
0
0
0
1
2
0
0
0
5
0
0
2
1
0
3
2
0
1
0
2
2
0
0
1
1
2
0
0
0
1
0
0
0
1
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
3
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
1
0
0
1
0
2
0
0
0
0
0
2
0
1
1
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
2
1
0
1
0
0
2
0
0
0
1
0
0
0
0
2
2
0
2
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
4
1
0
0
1
0
0
1
2
0
0
0
0
2
0
0
2
0
1
1
1
0
2
0
1
0
0
0
2
1
3
0
1
0
2
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
3
0
4
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
3
0
0
1
0
0
0
0
0
0
0
0
4
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
2
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
3
0
0
0
0
0
0
0
0
0
1
3
0
1
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
1
2
0
2
0
0
2
0
0
0
0
0
0
2
2
0
0
1
0
1
2
2
0
1
0
0
0
0
2
1
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
4
0
1
0
0
0
1
0
2
0
0
0
0
0
1
0
0
1
2
0
0
1
0
0
0
0
2
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
3
1
0
0
0
2
0
0
0
0
0
2
0
2
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
2
0
2
0
0
2
5
0
2
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
4
0
0
0
1
1
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
2
3
0
2
0
0
0
0
0
0
1
0
2
0
0
0
1
1
2
0
0
0
0
0
2
0
1
0
0
0
2
1
0
1
0
0
2
1
0
1
0
0
0
0
2
0
0
0
0
4
0
0
0
2
0
0
0
0
3
0
0
0
0
2
2
2
0
0
0
0
0
2
0
0
0
2
0
1
0
3
2
0
0
2
0
0
0
0
0
2
0
5
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
1
0
2
0
0
1
0
0
0
0
1
1
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
3
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
1
2
0
0
0
0
0
3
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
2
2
1
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
3
0
2
2
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
2
0
0
0
1
2
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
5
3
0
0
0
7
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
1
0
2
0
1
0
0
1
0
2
0
1
0
0
0
2
0
0
0
2
2
2
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
2
0
2
2
0
0
0
0
0
0
5
0
2
0
0
0
0
0
0
0
0
0
0
2
1
1
1
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
2
1
2
1
0
0
1
0
0
0
3
0
0
0
1
1
0
2
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
3
2
1
2
0
0
0
2
2
0
2
0
0
2
0
0
0
0
0
2
0
1
1
1
0
0
2
1
0
0
0
2
1
0
0
0
1
0
2
0
1
1
0
0
2
0
3
0
0
0
2
0
0
1
0
1
2
0
0
0
0
0
2
0
0
2
0
1
0
0
0
2
0
0
4
0
0
0
0
0
2
0
1
0
0
0
0
0
6
0
0
0
2
1
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
2
1
0
1
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
1
2
0
1
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
1
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
1
2
0
1
1
1
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
2
0
2
0
1
2
0
2
0
0
2
0
0
0
1
0
0
2
0
1
0
1
2
2
0
0
0
0
0
0
1
0
1
0
0
1
2
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
4
2
0
0
1
1
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
1
0
0
2
0
1
0
0
0
5
0
0
2
0
2
0
0
1
0
0
0
2
0
2
0
1
0
0
1
2
0
1
0
0
2
0
0
0
2
1
0
1
0
1
1
1
0
2
0
0
0
2
2
0
0
1
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
3
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
3
0
1
0
0
0
0
3
1
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
2
0
2
2
1
0
0
0
3
0
2
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
2
1
1
0
2
1
2
0
0
1
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
3
0
0
0
2
1
0
0
0
2
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
3
1
0
1
0
2
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
1
0
0
2
2
0
2
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
3
0
1
0
0
0
0
2
0
0
1
0
0
1
1
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
2
1
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
2
0
0
0
0
4
2
0
0
2
0
0
3
0
0
1
0
0
2
0
0
2
0
1
0
2
0
0
0
0
0
2
4
0
0
0
0
1
2
0
1
0
0
0
2
0
0
0
2
0
0
0
2
1
0
1
0
0
0
0
0
0
0
2
0
0
0
2
3
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
1
1
0
0
2
0
2
3
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
1
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
2
0
1
0
0
0
2
0
2
2
0
0
1
0
0
1
0
1
1
0
0
0
0
2
0
1
0
1
2
0
2
0
0
0
3
0
11
1
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
5
0
3
2
1
2
0
5
2
0
1
2
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
2
2
3
1
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
1
0
0
0
0
1
2
0
1
1
0
0
0
0
0
0
1
1
1
0
2
0
1
0
0
2
3
0
2
0
0
1
0
2
0
1
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
1
0
0
0
2
0
0
0
0
2
0
0
2
1
0
0
2
0
2
0
2
0
2
0
2
2
0
0
0
1
0
0
0
0
1
0
2
2
0
1
1
0
0
0
1
1
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
2
1
0
1
0
0
0
2
0
0
0
0
3
0
2
0
1
0
0
0
2
0
0
0
1
1
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
2
0
0
0
3
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
1
1
0
1
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
2
1
0
0
0
0
0
0
0
0
1
2
2
0
0
2
0
0
0
2
0
1
0
0
1
0
1
0
0
0
0
0
3
0
0
0
1
0
0
1
1
0
0
0
2
1
1
1
0
1
4
2
0
2
0
1
2
0
0
0
1
3
2
0
2
0
2
0
0
2
2
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
1
2
1
0
2
2
0
2
0
3
0
0
0
0
2
2
0
0
2
1
2
0
2
0
1
0
0
0
0
0
0
2
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
6
0
0
1
0
1
0
2
0
1
2
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
2
1
0
2
0
0
0
2
0
0
0
0
0
0
1
0
1
0
2
0
0
4
2
0
0
0
0
1
0
2
1
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
1
0
0
1
0
0
1
0
1
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
3
0
1
1
2
0
2
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
2
0
0
3
0
2
2
0
0
0
2
1
0
0
0
0
3
0
0
1
3
0
0
0
1
1
0
0
0
2
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
2
0
0
2
0
0
2
0
1
0
0
1
0
0
2
1
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
1
0
0
0
0
0
1
2
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
4
0
2
0
0
0
1
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
2
0
2
1
0
0
0
0
0
0
1
0
1
3
2
0
2
0
2
0
0
0
3
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
2
0
1
0
0
0
0
0
0
4
3
1
0
0
2
0
0
0
0
0
0
2
0
0
0
2
4
0
0
0
0
0
3
1
0
0
2
0
2
0
0
2
0
0
0
0
0
0
4
0
3
0
1
1
0
0
0
0
0
3
1
1
1
0
0
0
0
0
1
0
4
0
0
1
0
0
0
0
0
1
1
0
0
1
0
2
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
1
2
2
0
1
0
0
0
0
1
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
2
0
8
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
3
2
1
0
1
0
2
0
1
0
0
0
0
2
2
0
0
0
0
0
1
0
2
0
0
2
1
0
0
0
2
0
0
0
0
0
0
5
0
0
0
1
2
0
0
1
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
2
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
2
0
0
0
0
0
1
2
0
0
4
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
2
2
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
3
0
1
0
0
0
3
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
2
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
2
0
0
2
0
0
1
0
0
2
0
0
0
2
0
0
3
0
0
0
0
2
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
2
1
0
0
2
0
0
0
0
0
0
0
2
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
2
1
0
0
1
0
0
2
0
0
0
0
2
0
0
2
0
4
0
0
0
0
0
3
0
2
2
1
0
0
0
5
2
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
1
0
0
0
1
1
1
0
2
0
0
3
0
1
0
0
0
0
2
2
0
0
2
2
2
0
1
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
4
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
2
0
1
1
0
0
0
1
2
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
2
0
1
1
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
3
0
3
0
0
0
0
0
0
2
0
1
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
3
1
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
3
2
2
0
0
0
0
0
4
2
0
0
2
1
0
0
1
0
3
0
0
5
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
2
0
0
3
0
0
2
0
0
1
0
0
0
0
0
1
0
3
1
2
1
0
0
4
0
0
0
2
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
2
0
0
1
0
0
2
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
2
0
0
0
0
2
1
0
1
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
1
0
0
1
1
0
0
1
0
0
3
0
0
2
3
0
1
1
0
1
0
0
2
0
0
0
3
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
1
1
0
2
2
0
1
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
2
1
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
2
1
1
2
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
1
2
0
0
0
1
0
2
0
0
3
0
0
0
0
1
0
0
7
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
3
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
2
0
0
0
2
1
1
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
5
0
0
6
0
2
1
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
2
0
1
2
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
2
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
1
0
0
0
2
0
1
0
0
1
0
0
2
0
0
2
2
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
1
1
0
3
0
0
0
0
0
0
0
2
0
2
0
0
1
1
1
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
1
1
0
1
0
2
1
0
2
2
0
0
12
0
0
1
0
0
0
0
2
0
0
0
2
0
0
2
0
0
1
0
2
0
0
0
0
0
0
2
1
0
2
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
2
1
0
2
0
0
0
0
2
1
0
0
0
1
0
1
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
1
0
1
2
0
1
0
0
1
0
0
0
0
0
0
2
0
0
1
1
0
1
0
0
0
0
2
0
0
0
3
0
2
0
0
0
1
0
0
0
2
1
0
1
1
1
0
0
0
2
0
4
0
2
0
2
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
3
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
1
2
2
2
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
3
1
0
0
2
0
0
0
0
0
1
3
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
1
0
2
1
0
3
0
5
0
0
0
0
0
0
0
3
0
2
0
0
0
3
0
0
1
0
0
0
0
0
0
0
2
2
2
0
0
2
2
2
0
7
3
0
1
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
1
2
0
0
0
0
0
0
0
2
2
1
0
0
0
1
0
0
0
1
0
1
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
1
0
0
0
0
0
1
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
2
0
0
1
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
2
0
4
1
0
0
0
0
1
0
1
0
0
0
0
3
2
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
2
1
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
1
0
0
2
0
0
0
5
0
0
0
0
0
0
0
0
3
1
0
1
0
2
0
0
1
0
2
0
1
0
2
2
0
0
2
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
1
2
0
0
0
0
2
1
2
0
0
0
2
2
0
0
0
0
0
5
1
0
0
0
4
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
2
0
3
0
1
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
1
0
0
2
3
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
3
0
1
0
0
1
1
1
0
0
3
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
1
0
0
1
1
0
1
0
0
1
0
0
3
2
1
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
2
0
0
2
0
1
2
1
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
1
0
1
2
5
0
0
0
0
0
0
1
2
0
1
0
0
0
1
0
0
0
1
1
0
2
1
2
0
0
0
0
0
0
0
2
2
0
3
0
0
0
0
1
1
1
0
0
0
1
0
1
1
1
1
0
0
0
1
0
0
1
3
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
2
0
0
3
2
0
2
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
2
0
1
2
2
1
1
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
1
3
1
0
0
0
1
0
0
7
0
3
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
1
1
0
0
0
2
1
1
0
2
2
1
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
1
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
2
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
5
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
1
2
1
1
0
0
0
2
0
0
0
0
1
0
0
0
1
0
2
1
0
0
0
4
0
1
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
1
0
1
0
1
0
1
2
1
0
2
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
3
2
0
0
0
2
0
0
0
2
2
2
0
1
0
0
0
0
0
2
0
1
2
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
2
6
2
4
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
2
0
1
0
1
0
0
1
0
0
0
0
2
0
1
1
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
1
0
2
0
3
2
0
0
0
0
0
0
0
1
0
0
2
0
2
1
0
0
1
0
1
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
1
2
0
0
1
1
0
2
0
1
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
3
2
0
0
2
1
0
0
1
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
3
0
1
0
1
2
0
0
0
0
2
0
0
0
1
1
0
1
2
0
1
0
2
0
0
0
0
0
1
0
0
0
1
2
0
1
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
3
0
0
2
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
1
0
0
8
0
0
2
0
0
0
0
2
0
2
2
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
2
0
2
2
2
0
2
1
1
0
3
0
0
0
0
0
0
0
0
2
2
0
1
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
2
0
1
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
8
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
3
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
2
0
1
1
1
0
0
0
0
0
0
2
2
1
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
1
0
1
0
2
0
2
1
0
0
0
0
0
0
0
3
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
2
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
2
1
2
2
1
0
2
2
0
0
2
2
0
1
1
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
6
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
4
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
2
0
1
2
0
2
0
1
0
0
0
0
0
2
1
2
2
0
2
2
0
0
2
2
0
1
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
2
0
2
0
0
1
2
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
2
0
2
0
0
0
0
1
2
0
0
0
3
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
1
0
0
0
1
0
0
0
2
0
1
2
0
2
0
2
0
0
2
2
0
1
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
1
0
2
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
3
0
0
2
0
0
1
0
0
0
3
0
0
1
0
0
1
0
2
0
0
0
2
1
0
0
2
0
15
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
1
0
0
0
2
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
5
0
0
1
2
5
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
3
0
2
1
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
2
4
0
1
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
1
2
0
1
2
2
0
0
0
0
2
0
2
0
0
0
2
0
3
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
1
2
3
0
0
0
0
2
1
0
0
0
0
0
1
2
0
2
1
1
0
0
0
1
0
0
0
0
0
1
0
2
1
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
2
1
1
4
0
0
0
0
1
0
0
2
0
2
1
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
2
2
1
0
0
0
2
0
0
0
2
2
0
1
0
2
0
2
2
0
2
0
0
0
2
0
0
0
0
1
1
0
1
0
0
0
0
1
0
1
2
2
0
0
1
2
0
0
0
0
3
0
1
0
0
0
1
0
0
0
0
0
2
0
2
0
0
2
0
0
1
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
1
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
2
2
1
0
0
1
0
0
0
0
0
0
0
2
0
1
1
0
1
0
0
2
0
0
0
1
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
1
2
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
1
2
1
0
0
1
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
1
1
0
0
1
2
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
3
1
0
0
0
0
0
2
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
2
0
2
2
0
2
0
0
2
0
2
0
4
2
0
0
0
1
2
0
0
0
2
0
0
2
2
0
3
1
0
1
1
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
1
0
0
0
1
0
1
0
2
1
2
3
0
0
1
0
1
0
0
2
0
0
1
0
2
2
1
1
0
0
0
0
0
0
3
0
1
1
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
2
0
0
2
0
0
0
3
3
0
2
0
0
2
0
2
0
0
1
1
2
0
0
2
0
1
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
1
1
2
1
0
0
0
0
1
0
1
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
2
0
1
0
0
1
0
3
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
2
2
0
0
0
2
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
1
0
1
2
0
2
2
0
0
0
0
0
2
1
2
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
2
1
0
0
0
2
2
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
1
0
2
4
0
0
0
0
0
0
2
0
0
0
3
0
0
0
3
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
2
0
0
2
0
2
0
0
0
0
0
1
1
0
4
0
2
1
0
0
0
0
1
2
0
0
0
0
0
0
2
2
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
7
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
1
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
2
2
0
6
1
0
0
0
0
0
3
0
0
0
0
2
0
2
0
0
1
0
0
3
1
0
1
0
0
0
0
1
0
1
2
2
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
2
2
0
0
1
0
0
0
0
1
0
2
2
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
1
2
0
0
0
2
0
4
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
2
0
3
0
0
0
1
0
0
0
0
0
2
0
2
1
0
0
1
0
0
0
2
2
0
0
0
0
2
1
0
0
0
0
0
0
0
1
2
0
3
0
0
0
0
0
0
0
2
3
0
0
2
1
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
2
1
0
0
0
0
0
1
1
0
0
0
2
0
1
0
0
0
0
2
0
0
1
2
2
1
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
3
0
2
0
3
0
0
2
0
1
0
0
1
2
0
0
0
0
2
0
0
2
1
0
1
1
0
1
0
1
0
1
2
0
0
1
1
0
0
5
0
1
3
0
0
0
8
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
1
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
1
2
0
0
0
0
0
0
0
1
3
0
1
0
0
0
0
2
0
2
0
0
0
3
0
0
2
0
1
0
0
0
0
2
0
0
0
0
2
2
0
0
1
0
0
0
0
0
2
2
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
1
3
1
0
0
0
0
0
2
0
0
0
0
1
2
0
0
2
0
1
0
0
0
0
0
3
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
1
1
0
1
2
1
1
2
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
2
2
0
0
2
0
0
1
2
2
0
2
2
0
0
1
0
1
2
0
1
0
0
0
2
0
6
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
1
1
0
0
1
0
2
0
1
2
0
0
3
0
0
0
0
0
2
0
1
0
2
1
0
0
7
2
0
0
0
1
0
2
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
4
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
2
0
0
2
1
0
1
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
2
1
0
0
1
2
1
0
0
0
0
0
0
1
0
1
1
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
3
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
3
0
2
0
2
0
0
0
0
2
2
0
0
0
0
1
0
0
2
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
2
0
1
0
0
2
1
0
0
4
1
0
0
1
0
0
3
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
3
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
2
0
2
0
2
1
1
0
1
0
0
1
1
0
0
1
0
0
1
0
0
1
0
0
2
0
1
1
0
1
0
1
0
0
0
2
0
1
0
0
0
0
0
1
0
1
0
4
2
0
0
0
0
2
2
0
1
1
0
2
0
0
2
0
0
1
0
1
4
0
1
0
1
0
0
0
0
1
0
0
6
0
1
2
0
1
0
0
0
0
0
2
0
0
1
0
0
1
2
0
0
2
0
2
0
1
2
0
0
0
2
0
2
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
2
0
0
0
2
2
0
0
0
0
2
0
1
0
1
1
2
0
0
2
2
2
1
0
0
0
2
0
1
0
2
0
1
1
2
0
1
2
0
1
0
0
0
0
0
1
0
2
2
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
4
0
0
2
0
0
0
1
0
0
2
0
0
2
0
2
0
0
0
1
2
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
7
0
0
2
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
1
1
0
1
1
0
1
3
4
0
0
0
0
2
0
0
0
2
0
0
0
1
9
0
0
0
0
5
0
0
0
0
0
0
0
1
0
2
2
2
1
0
0
0
1
0
0
0
4
2
0
0
2
0
0
0
2
1
0
0
0
0
0
0
1
0
2
3
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
2
0
1
0
1
0
0
1
0
1
1
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
1
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
1
0
1
0
0
0
0
1
1
1
0
0
0
2
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
2
0
0
0
0
0
2
1
0
0
2
0
1
0
0
1
1
2
0
2
1
1
0
0
0
0
1
0
1
0
2
1
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
1
0
1
2
0
0
0
1
3
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
1
2
0
2
2
0
0
0
0
1
1
1
2
2
0
2
0
0
2
0
2
1
0
0
1
0
0
2
0
0
0
0
0
2
1
2
2
2
0
1
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
2
0
0
0
0
1
0
5
0
0
0
1
0
0
2
0
0
1
3
1
0
2
0
2
0
2
0
0
2
1
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
2
3
0
2
1
0
0
1
1
0
1
0
1
0
0
0
0
0
0
2
0
1
2
0
1
0
0
3
0
0
1
0
0
1
0
0
2
0
0
0
2
1
0
0
1
0
0
0
0
1
3
1
0
1
0
1
0
1
0
0
0
1
0
2
0
1
0
0
1
1
0
0
1
0
0
0
0
0
5
2
0
1
1
0
2
1
0
2
1
0
0
1
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
1
1
3
0
0
0
0
2
0
1
2
0
0
0
1
1
2
2
0
2
0
1
0
0
2
1
0
2
0
2
0
0
0
2
0
1
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
2
1
2
0
2
0
0
0
0
0
0
0
2
0
0
0
3
0
4
0
1
0
0
2
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
2
0
1
1
0
1
1
0
0
0
0
0
1
0
1
0
2
0
1
0
0
0
0
0
1
1
0
0
2
0
0
1
0
0
2
0
2
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
1
0
0
2
1
2
0
1
2
0
0
1
2
0
0
0
2
0
1
0
1
1
0
1
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
2
0
1
0
1
0
2
2
1
0
0
0
0
2
0
0
1
2
0
1
0
0
2
0
1
2
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
1
2
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
4
0
0
0
0
1
2
0
0
0
0
1
0
0
10
0
0
0
4
0
2
0
0
2
0
0
0
2
0
0
0
2
1
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
3
0
0
0
1
0
0
0
0
1
2
0
2
0
0
0
0
0
1
0
0
0
1
0
0
2
3
0
0
0
2
0
0
0
2
0
2
1
0
0
1
0
1
0
4
0
2
2
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
1
1
2
2
2
0
2
0
0
0
1
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
2
0
2
0
0
0
1
2
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
1
0
1
0
1
0
1
0
1
0
0
0
2
2
0
1
2
0
1
0
0
0
0
2
5
0
2
1
0
0
0
0
0
0
0
1
2
1
2
1
0
2
0
2
2
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
2
0
0
0
0
0
1
0
0
2
2
0
0
0
1
0
0
3
1
1
2
3
0
0
0
0
3
1
0
0
3
0
2
0
7
0
0
0
2
2
0
0
2
2
0
2
2
0
0
0
0
0
2
2
0
1
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
2
3
0
0
0
0
0
1
1
1
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
1
0
1
0
1
0
0
0
1
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
2
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
1
2
3
0
1
0
0
1
2
0
0
2
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
2
1
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
2
1
0
1
1
0
0
1
0
3
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
2
1
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
3
0
0
1
0
0
0
0
0
1
2
0
0
0
0
1
2
3
0
3
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
1
0
1
1
2
0
1
0
0
1
0
6
2
0
0
0
2
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
5
0
0
0
2
0
0
0
1
0
0
0
0
0
3
0
0
2
2
1
2
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
1
1
0
0
3
0
0
0
1
1
0
0
0
2
2
1
0
0
4
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
1
0
2
2
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
1
0
0
2
2
0
1
0
0
0
0
0
1
0
2
0
2
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
2
0
2
0
0
0
0
3
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
1
2
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
4
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
1
2
0
2
0
0
0
1
2
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
2
1
4
1
2
0
0
2
0
4
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
5
0
0
0
1
0
2
2
0
2
2
0
13
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
1
0
2
0
0
1
1
1
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
2
2
0
1
1
0
0
0
2
0
0
0
0
0
1
0
2
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
3
1
0
0
1
0
0
0
1
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
1
1
0
0
1
0
1
0
2
0
0
2
0
0
0
0
0
0
2
1
1
0
1
1
0
0
0
2
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
3
2
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
1
2
0
0
1
0
2
0
0
0
3
0
0
1
0
2
2
0
2
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
2
1
0
0
0
0
1
2
0
2
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
3
0
3
1
0
2
0
0
0
0
0
1
2
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
1
2
2
0
0
0
1
0
0
4
0
3
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
3
1
0
0
0
1
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
2
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
3
2
0
1
1
0
1
0
1
0
1
0
0
1
7
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
1
0
0
0
0
0
1
2
1
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
2
1
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
2
1
1
0
0
0
0
2
0
2
1
0
1
0
1
1
0
0
1
0
0
4
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
1
0
1
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
1
1
0
0
0
4
0
1
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
3
1
2
0
0
0
2
3
0
1
1
0
0
3
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
2
0
0
0
0
0
2
0
1
0
0
2
8
0
0
0
0
0
0
1
2
0
0
0
0
1
2
0
0
0
3
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
1
0
1
2
0
2
0
0
0
1
2
0
0
1
0
0
0
0
2
1
0
0
0
1
0
2
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
1
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
2
0
0
0
2
2
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
1
1
1
2
2
1
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
1
2
0
3
0
1
0
0
1
2
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
5
0
0
0
0
2
1
0
1
0
0
1
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
3
1
0
0
0
0
0
1
0
0
0
7
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
3
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
5
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
3
2
0
0
2
0
1
0
0
2
0
0
1
2
1
0
0
0
0
0
0
0
1
0
2
2
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
2
1
2
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
2
1
0
0
2
2
0
0
0
1
2
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
2
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
2
1
0
1
0
1
0
0
3
2
1
0
0
1
2
1
0
0
0
0
4
0
0
0
0
2
2
0
0
1
1
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
3
2
2
2
0
1
0
1
1
1
2
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
2
0
1
3
0
0
0
1
0
3
1
0
0
0
0
0
0
0
0
0
7
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
1
1
1
1
0
3
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
8
3
2
0
0
1
0
0
2
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
1
0
0
0
1
0
0
0
1
0
2
0
4
1
0
0
0
1
0
2
0
1
0
2
0
0
3
2
3
0
0
2
0
0
0
0
3
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
1
0
0
1
3
0
1
0
2
2
0
0
0
1
1
2
0
0
2
1
2
0
2
1
2
2
1
0
2
1
0
0
1
0
0
0
1
2
0
0
2
0
1
0
0
2
0
0
1
0
1
1
0
0
0
2
1
1
0
0
2
0
0
0
2
0
0
1
0
2
2
0
1
1
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
1
0
0
0
0
3
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
2
2
1
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
1
1
0
2
0
0
0
0
0
0
2
0
0
1
2
0
0
1
0
0
0
0
0
1
2
0
0
2
0
0
5
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
2
2
1
0
0
2
0
0
0
0
2
1
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
1
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
2
1
2
0
0
1
0
2
0
1
0
0
0
0
3
0
0
1
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
1
0
0
2
2
0
0
0
0
0
2
0
0
3
0
0
1
0
0
1
9
0
0
0
2
0
0
2
0
0
0
2
1
0
0
0
1
1
0
0
1
0
1
1
1
0
0
1
0
0
0
3
0
0
0
0
0
0
2
0
0
0
1
0
3
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
1
0
0
0
0
0
1
2
0
1
0
2
1
0
2
1
0
3
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
1
0
1
0
0
0
0
0
0
0
3
1
0
0
0
2
0
2
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
5
0
0
0
0
0
2
0
0
0
2
0
0
0
2
3
0
2
0
0
0
2
0
0
2
1
0
2
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
2
0
2
2
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
5
0
0
0
0
0
0
0
1
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
1
2
0
0
0
0
0
2
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
1
0
2
0
0
2
0
1
0
1
0
0
0
2
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
2
2
2
1
0
0
0
0
4
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
4
0
0
0
1
0
0
1
0
1
0
0
0
0
2
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
1
1
0
0
2
0
2
2
0
0
0
1
0
2
0
0
0
0
0
0
5
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
2
0
2
1
1
3
0
1
0
0
0
0
0
1
0
2
3
0
0
2
3
0
2
0
2
0
2
0
0
0
0
1
0
1
0
0
3
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
2
0
0
2
5
0
0
0
0
2
0
0
0
0
1
2
1
0
1
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
1
3
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
1
2
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
1
1
0
1
0
0
2
1
0
2
1
0
0
0
1
2
3
1
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
3
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
3
0
3
0
3
3
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
1
0
2
0
0
1
0
0
1
4
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
2
0
1
1
2
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
2
1
0
0
1
2
0
0
2
0
0
0
0
0
1
2
0
1
1
0
0
0
0
0
0
2
2
2
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
1
0
0
0
3
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
1
0
2
0
1
0
0
0
1
0
0
0
2
0
3
0
0
2
2
0
1
0
0
0
1
0
1
1
1
1
1
0
0
0
0
1
1
0
0
2
3
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
1
0
0
1
6
2
0
0
1
1
1
0
0
1
0
1
1
0
0
0
1
3
0
2
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
3
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
1
2
1
3
0
2
0
0
2
0
1
2
0
0
1
0
0
0
0
0
0
2
2
0
1
0
0
0
2
0
0
0
0
0
1
0
0
1
1
1
0
1
2
0
0
2
0
0
0
2
1
1
2
1
2
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
2
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
1
0
2
1
0
0
0
0
0
0
2
2
0
2
0
0
0
2
1
0
0
2
0
1
0
0
0
0
3
2
0
0
0
0
0
0
0
0
1
0
0
1
1
2
0
2
0
2
0
0
1
0
1
2
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
1
2
0
1
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
1
1
0
0
1
0
0
3
0
2
0
2
1
0
2
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
1
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
2
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
2
2
1
0
2
1
0
0
0
2
1
0
1
0
2
0
2
0
1
1
1
0
0
0
2
0
0
1
2
0
0
0
0
1
0
0
0
0
9
0
0
0
0
0
1
0
0
0
0
0
0
2
1
2
0
1
2
0
0
2
0
0
2
0
0
0
1
2
0
2
3
0
0
0
0
0
3
0
0
0
1
1
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
2
1
2
0
0
2
0
0
0
0
0
0
0
2
1
0
0
2
0
1
0
0
2
0
2
1
2
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
2
0
0
1
2
0
0
0
0
0
0
0
1
0
0
6
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
5
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
2
3
1
0
2
0
0
0
2
2
1
0
0
2
1
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
1
0
1
2
2
0
0
0
2
0
0
0
0
0
2
0
3
0
2
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
3
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
3
1
1
0
0
0
1
0
2
0
2
0
1
0
1
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
1
1
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
2
0
1
2
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
1
2
0
0
2
5
1
0
2
2
0
1
1
0
0
0
0
0
0
3
0
1
2
0
0
0
0
0
1
0
0
1
0
2
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
1
1
0
0
0
2
0
1
0
2
2
4
0
0
0
0
0
0
0
0
0
0
1
0
1
2
1
0
0
2
1
1
1
0
0
0
0
0
0
2
3
1
1
1
0
0
0
0
0
0
1
0
0
0
0
2
2
2
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
1
3
1
0
0
0
1
2
1
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
1
0
0
2
0
0
2
2
0
1
0
0
0
1
0
1
1
1
1
2
2
0
0
2
1
3
0
1
0
0
1
0
5
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
1
1
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
1
0
1
0
0
0
2
3
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
2
1
0
0
1
0
0
1
0
2
0
0
0
2
0
1
0
1
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
1
0
1
2
3
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
1
1
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
2
0
0
0
1
0
0
2
0
0
0
0
2
0
1
1
0
1
0
0
0
0
2
0
2
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
2
0
1
1
0
0
0
6
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
3
0
1
1
0
0
0
1
2
2
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
2
2
0
5
1
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
1
2
1
0
0
2
0
0
0
0
0
1
0
1
1
0
0
1
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
1
2
1
2
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
3
0
1
0
2
0
0
2
1
1
0
0
1
2
1
3
2
2
3
0
0
0
0
0
2
0
0
1
0
3
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
1
0
0
2
3
0
1
2
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
3
2
2
1
0
0
0
0
0
0
2
0
0
3
0
1
0
0
2
0
0
3
0
0
0
0
3
1
0
0
0
5
0
0
2
0
0
0
0
0
1
0
1
2
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
3
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
1
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
2
2
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
2
4
0
0
0
0
1
0
0
0
1
2
0
2
0
0
1
0
0
0
2
1
0
0
0
2
0
1
0
0
2
2
0
0
0
1
0
0
0
0
1
0
1
0
1
0
2
0
1
0
0
2
0
0
1
0
0
0
0
2
0
0
2
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
3
0
2
0
0
0
2
0
0
1
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
1
1
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
2
0
1
2
0
0
3
2
1
0
3
0
1
0
2
0
1
1
1
2
0
1
0
1
2
0
2
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
3
0
0
1
0
0
0
0
1
2
2
1
2
1
0
0
2
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
2
1
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
3
0
0
1
0
6
0
0
0
0
0
0
0
0
0
6
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
2
2
0
2
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
3
0
0
0
0
3
0
0
1
2
0
0
0
0
0
0
0
0
0
2
1
0
1
1
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
2
1
0
1
0
1
2
0
0
0
0
2
1
0
2
0
0
0
2
0
0
0
0
2
0
0
0
5
4
1
0
0
0
0
0
0
0
2
1
0
2
0
4
2
0
1
0
2
0
0
0
0
3
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
2
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
1
1
0
2
3
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
2
2
2
2
0
1
0
1
0
0
0
0
0
1
1
1
1
0
1
2
0
0
0
0
0
1
0
0
0
0
0
1
3
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
2
0
0
0
2
0
0
1
0
0
0
2
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
1
0
2
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
1
0
0
2
0
0
0
0
0
2
2
2
0
0
0
2
0
1
0
0
0
0
3
0
0
0
0
0
2
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
2
1
1
0
2
2
1
3
0
0
0
3
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
2
0
0
0
0
1
1
1
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
3
0
2
1
0
0
2
1
3
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
1
0
0
0
0
1
0
0
1
1
2
0
0
0
2
0
1
0
2
0
0
0
1
0
3
1
2
0
0
2
0
0
0
0
1
0
0
0
1
2
0
1
1
0
3
0
1
0
0
0
0
0
0
0
0
0
1
0
2
1
1
0
4
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
1
0
0
0
0
2
1
0
2
0
0
0
0
2
0
0
1
2
2
0
0
0
0
1
0
1
0
2
0
0
0
2
2
1
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
1
2
0
2
2
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
1
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
1
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
4
1
1
2
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
2
2
2
2
1
0
2
0
0
1
1
1
2
0
0
2
0
1
0
1
3
0
0
2
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
1
2
0
0
0
1
0
0
0
0
2
2
0
0
0
0
1
1
0
0
0
2
1
4
0
0
0
2
0
1
0
2
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
1
1
2
0
0
0
1
0
0
0
0
0
3
0
2
1
0
0
2
0
5
1
0
0
1
1
0
1
1
0
0
1
1
0
1
2
2
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
2
0
0
1
0
1
0
0
2
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
1
2
1
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
2
0
0
1
0
0
0
0
0
2
0
0
1
1
0
0
0
2
0
0
0
0
2
0
3
0
2
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
3
1
0
0
0
0
0
0
1
0
1
0
0
1
2
1
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
1
0
1
0
0
0
1
2
0
0
0
0
0
1
0
0
0
2
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
1
0
0
2
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
4
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
9
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
3
0
0
0
2
0
1
1
0
0
1
2
0
1
1
0
0
2
2
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
2
1
0
1
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
1
1
0
0
0
2
2
4
0
4
2
0
0
0
1
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
1
0
0
0
0
0
1
0
0
2
2
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
1
0
0
2
2
0
1
1
0
2
0
0
0
0
0
1
0
0
2
0
1
0
1
0
2
0
1
1
0
0
2
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
3
0
2
0
2
1
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
1
0
0
2
0
1
1
0
2
0
0
0
2
2
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
1
2
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
1
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
1
3
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
1
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
2
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
1
3
0
0
0
0
0
1
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
1
1
1
3
2
0
0
0
0
0
0
0
4
1
0
1
0
0
2
1
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
2
3
3
0
0
0
0
1
0
1
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
1
0
2
1
0
0
1
0
1
0
0
2
5
0
4
4
0
0
0
2
1
2
1
0
0
0
0
0
0
1
0
2
2
8
0
0
0
0
1
0
0
0
2
3
0
0
0
0
1
1
0
0
0
0
2
0
0
0
1
0
0
2
0
0
1
0
1
0
0
0
3
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
4
0
0
1
0
0
0
3
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
3
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
1
0
2
0
0
0
2
1
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
3
1
1
0
0
0
2
0
0
2
0
0
0
0
0
0
1
2
2
0
0
1
1
0
0
0
0
0
1
0
5
3
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
1
2
0
0
1
0
2
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
2
1
0
0
1
1
2
0
2
3
0
2
0
0
0
1
0
0
0
0
2
0
2
0
0
1
2
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
1
0
2
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
1
1
0
2
0
2
0
0
2
0
0
0
0
0
0
0
2
2
1
0
2
0
1
0
0
0
1
0
0
2
0
0
0
0
2
2
2
3
2
0
1
0
2
0
0
1
2
2
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
3
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
1
1
0
0
0
4
1
0
0
5
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
2
1
0
2
1
0
2
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
1
2
0
0
1
0
0
3
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
2
1
1
1
0
0
2
0
1
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
1
2
4
2
2
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
1
0
1
1
0
1
2
0
0
0
0
0
0
1
1
0
0
1
2
0
1
0
0
0
0
1
0
1
1
0
0
0
0
2
2
3
0
0
0
2
0
0
2
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
1
0
0
2
1
1
0
1
1
0
0
1
1
0
0
0
0
0
2
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
2
0
0
2
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
2
0
1
2
0
0
4
0
0
0
0
0
0
0
2
0
2
1
0
2
0
0
0
0
0
1
0
1
0
0
0
0
2
1
1
0
0
1
0
0
2
4
2
0
0
0
0
1
0
0
2
0
0
6
0
0
0
2
1
2
0
2
0
0
0
0
0
0
1
0
0
2
2
0
2
0
1
0
0
1
0
0
0
0
4
0
1
1
0
0
0
0
1
1
0
0
2
2
0
0
0
0
0
1
2
1
0
2
0
0
2
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
2
2
0
2
0
0
0
0
2
2
1
0
0
0
3
2
0
1
0
0
0
1
2
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
1
2
0
2
0
0
2
1
1
0
1
2
4
0
1
2
1
1
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
1
0
1
0
0
2
0
1
0
1
0
0
1
0
0
0
2
0
1
5
0
1
0
0
2
2
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
2
0
3
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
1
0
0
2
0
0
1
0
1
0
0
2
2
1
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
2
0
2
0
1
0
0
2
4
0
2
1
1
0
2
1
2
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
1
0
0
0
2
0
1
1
0
1
2
0
2
0
0
0
0
1
0
0
2
0
2
8
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
1
0
3
2
0
0
3
0
1
1
0
0
0
0
2
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
3
0
1
0
0
0
1
0
2
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
3
0
2
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
2
0
2
0
1
1
1
0
0
0
0
0
3
0
0
0
3
0
0
0
0
0
0
2
2
1
0
2
0
0
0
1
0
0
0
2
2
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
1
0
1
0
1
0
2
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
2
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
3
0
0
0
0
1
1
0
0
2
2
0
0
0
0
0
0
1
0
0
2
3
2
2
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
2
0
2
0
0
0
0
0
1
2
0
0
1
0
1
2
0
0
2
1
0
1
0
0
0
0
3
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
3
0
0
1
0
0
0
0
3
0
0
1
2
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
1
0
2
0
4
0
2
0
0
0
0
0
0
2
1
0
0
0
0
1
0
2
0
0
0
2
0
1
0
0
0
3
0
2
0
1
0
1
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
2
0
1
2
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
2
0
0
0
0
2
1
0
1
0
0
1
2
0
0
0
0
0
1
0
1
5
1
1
0
2
0
0
0
0
0
4
0
1
3
0
0
2
0
1
0
2
1
0
2
0
0
0
2
1
1
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
2
3
2
0
0
0
0
0
0
2
0
0
0
2
1
0
0
1
1
0
0
0
0
0
1
0
0
2
2
0
0
2
0
0
2
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
1
0
0
2
0
1
0
2
2
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
2
1
2
0
0
0
0
2
0
0
0
2
0
0
1
0
0
1
2
0
0
0
0
1
2
0
1
2
2
1
3
0
0
0
0
0
0
2
0
0
3
0
0
0
0
1
0
2
0
0
2
0
2
0
0
1
3
2
1
0
0
0
1
1
0
1
1
0
0
2
3
0
2
1
2
0
0
0
0
2
0
1
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
1
0
3
0
0
0
0
2
1
0
0
0
2
0
0
0
3
0
0
0
0
0
1
0
0
0
0
2
3
2
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
1
2
0
1
0
0
0
0
2
1
0
1
0
2
0
0
1
1
10
0
0
1
0
0
0
0
1
0
0
3
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
1
0
2
0
1
0
3
0
0
0
1
1
0
0
0
0
0
0
0
2
1
0
0
1
2
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
1
0
2
0
0
1
2
1
2
0
0
0
1
3
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
2
0
0
1
1
0
0
3
0
1
1
0
1
0
1
0
0
0
2
0
1
0
0
0
0
1
0
0
0
1
2
0
0
1
2
2
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
4
0
0
1
0
2
0
2
0
2
0
0
0
0
0
0
2
1
0
2
0
0
1
0
0
0
0
4
1
0
0
0
0
0
1
0
2
1
2
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
5
0
0
0
0
0
0
0
2
0
2
3
0
0
0
0
0
0
0
3
2
1
0
0
0
0
2
0
0
0
1
2
0
0
0
2
2
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
6
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
3
1
0
2
0
0
0
0
0
0
1
0
0
1
2
0
0
1
4
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
2
0
1
0
1
0
2
0
0
1
2
0
1
0
0
0
0
2
1
0
1
0
0
0
5
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
1
0
0
0
0
1
2
0
1
0
3
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
1
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
1
0
2
2
0
0
0
3
2
0
1
2
0
0
0
0
1
0
1
2
0
2
0
0
0
0
0
0
0
1
0
3
3
0
2
0
0
3
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
1
3
1
1
0
0
0
0
1
3
0
0
0
0
4
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
2
0
0
8
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
3
2
0
2
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
1
1
0
2
0
0
0
2
0
0
0
0
0
1
0
2
0
2
0
7
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
3
4
1
0
2
0
0
2
0
0
0
2
0
0
0
2
0
7
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
2
2
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
2
0
0
3
3
0
2
0
0
0
2
1
0
0
3
1
0
0
0
0
2
2
1
0
0
0
2
1
0
0
1
0
2
0
2
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
2
2
1
1
0
2
0
2
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
3
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
2
0
1
1
0
0
1
0
0
1
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
2
0
0
3
1
0
0
2
1
0
0
0
0
2
2
2
0
2
0
0
1
0
0
0
1
0
0
0
2
0
0
2
2
1
0
0
1
0
0
0
0
1
0
0
0
0
2
1
0
1
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
3
0
0
0
5
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
2
3
1
0
0
1
0
0
2
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
6
0
0
0
0
0
0
1
2
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
3
0
0
0
2
0
0
1
3
1
0
0
0
0
2
1
1
0
1
1
2
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
3
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
6
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
1
1
0
2
1
0
0
1
3
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
1
0
1
0
2
2
0
0
2
2
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
2
1
1
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
1
2
2
0
0
0
1
1
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
2
0
0
0
1
0
2
2
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
1
2
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
2
0
0
2
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
1
0
0
0
1
0
2
0
0
1
0
2
0
1
3
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
1
0
3
1
0
0
0
0
0
0
0
1
0
3
2
0
0
1
0
0
9
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
1
0
1
0
1
0
2
1
0
0
0
0
0
0
1
1
3
0
0
0
0
0
1
0
2
0
2
0
0
2
2
0
0
2
1
0
0
0
0
2
0
0
0
1
2
2
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
3
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
6
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
2
4
2
0
0
1
0
0
0
1
0
0
7
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
2
2
0
0
0
0
2
0
0
1
0
0
1
1
0
0
1
1
2
1
0
1
1
0
3
0
2
0
0
0
0
0
0
3
0
0
2
0
2
0
1
0
0
0
0
1
0
0
0
2
0
1
0
0
0
2
1
1
0
2
2
2
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
4
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
3
0
0
2
0
0
2
1
0
0
2
2
2
0
0
2
1
0
0
0
1
0
2
0
0
1
0
2
0
0
0
1
0
1
2
0
0
0
1
2
1
0
0
0
1
2
1
0
0
0
0
0
0
0
3
0
0
2
2
0
1
2
0
0
0
0
0
0
1
2
0
2
0
2
0
0
0
0
4
0
0
1
0
0
0
2
0
0
2
0
2
0
0
0
2
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
2
1
0
1
4
0
0
0
0
2
0
0
2
0
0
1
0
0
0
2
0
2
2
3
0
1
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
3
0
1
0
0
1
3
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
1
0
1
1
0
2
0
0
0
0
1
0
2
0
0
2
0
0
0
0
2
2
1
2
0
0
0
2
0
2
0
3
0
0
0
1
2
0
1
0
0
0
0
0
2
1
0
0
1
0
1
1
1
0
4
2
0
0
0
0
1
0
0
0
1
2
0
0
0
0
1
0
1
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
2
0
2
1
0
2
2
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
1
2
2
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
1
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
1
0
0
0
1
2
0
0
2
0
0
0
0
1
1
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
2
1
0
0
0
2
0
0
0
2
0
0
0
1
0
1
0
2
1
4
1
2
0
2
2
0
0
0
0
0
0
1
0
1
0
1
0
2
2
0
4
2
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
2
1
0
0
1
0
0
0
0
1
1
1
0
0
1
2
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
2
2
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
1
2
0
2
0
1
1
2
0
0
0
0
0
0
0
1
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
1
1
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
1
1
1
0
2
0
1
0
0
0
1
2
0
1
1
0
1
0
0
0
0
2
0
3
1
0
0
2
1
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
1
2
0
0
0
2
0
0
2
0
2
0
1
1
1
2
1
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
3
0
0
0
0
2
0
0
0
6
2
3
0
1
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
4
0
0
0
1
0
2
0
0
2
0
0
1
2
0
0
1
0
2
1
1
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
1
1
0
4
0
2
1
3
2
1
0
0
0
3
2
0
0
0
1
0
0
0
2
0
1
1
0
0
0
0
2
1
2
2
0
2
0
0
0
0
2
0
1
1
2
0
0
4
0
1
0
2
0
1
0
0
0
0
2
0
0
2
1
0
0
1
0
0
0
0
0
1
2
0
0
1
0
2
0
0
0
4
1
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
2
0
0
2
1
0
0
0
0
3
1
0
0
0
1
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
1
0
0
0
4
0
0
3
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
1
2
2
0
0
0
0
0
0
1
0
0
2
1
0
2
1
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
2
1
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
1
0
1
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
2
0
3
0
1
0
0
0
0
2
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
1
2
1
0
0
2
2
0
1
0
0
1
0
0
2
0
0
3
0
2
2
4
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
2
0
0
1
0
0
2
0
0
0
2
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
1
0
2
0
0
0
2
0
0
0
0
0
1
4
0
0
1
2
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
1
0
1
0
0
0
0
1
1
1
0
0
0
2
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
8
0
2
0
0
0
0
1
1
2
0
1
0
0
1
0
0
0
0
2
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
2
2
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
2
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
1
1
0
0
0
0
0
0
1
1
0
0
2
0
0
0
2
0
0
0
2
0
1
0
0
3
0
2
0
2
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
3
0
0
0
0
2
2
0
1
2
2
3
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
3
1
0
0
0
0
0
0
0
0
0
0
0
3
2
2
0
0
0
0
0
2
0
1
0
0
0
2
2
2
2
1
0
0
1
0
1
2
0
0
1
2
1
2
0
0
0
1
0
0
0
2
0
0
1
1
0
0
2
2
0
0
0
0
0
2
0
0
0
0
3
0
0
0
1
0
2
0
0
0
2
1
2
1
0
0
0
0
2
0
2
0
0
1
0
4
0
0
2
2
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
2
0
0
0
1
2
0
1
1
0
0
0
2
0
1
0
1
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
3
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
1
0
0
2
2
0
0
0
0
2
0
1
0
0
2
0
0
0
1
1
1
0
2
1
0
0
1
2
0
0
0
2
0
0
2
3
3
0
0
2
0
0
2
0
2
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
2
2
0
3
0
2
2
1
1
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
2
0
4
0
5
0
2
1
0
1
3
0
0
2
0
1
3
0
0
0
1
1
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
1
1
0
0
0
0
0
2
3
0
2
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
1
0
0
0
2
0
0
2
0
1
0
2
0
3
0
1
9
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
2
0
2
0
0
0
0
0
0
0
2
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
2
0
0
2
0
0
0
1
1
0
0
2
0
2
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
1
1
0
2
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
6
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
1
1
0
0
0
0
2
0
2
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
1
1
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
1
2
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
2
0
3
0
2
2
0
0
0
0
0
0
1
1
0
0
0
0
2
2
2
0
0
0
2
0
0
0
0
1
2
3
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
5
0
1
0
0
1
0
0
0
0
0
1
0
2
1
0
2
0
2
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
2
2
2
1
0
0
0
0
0
0
2
0
1
0
0
0
3
0
1
0
0
2
1
0
0
2
5
0
2
0
0
1
0
3
0
0
2
0
1
2
1
2
0
0
0
0
0
0
1
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
1
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
2
0
1
0
0
1
0
0
1
0
0
0
0
0
3
2
0
0
1
0
0
1
2
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
1
11
2
0
0
2
3
2
0
0
1
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
1
2
0
0
0
2
0
1
2
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
8
0
0
1
0
0
0
2
2
0
2
0
0
0
0
2
0
0
1
1
0
1
0
0
0
1
0
1
2
0
0
0
0
0
0
1
0
1
1
0
2
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
4
0
0
3
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
3
0
0
1
0
0
0
0
0
1
2
0
0
2
0
0
0
0
1
1
1
2
1
2
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
2
0
0
7
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
2
0
1
0
1
2
0
2
0
0
2
0
0
2
0
0
1
1
0
1
0
0
2
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
2
1
0
1
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
1
0
1
2
0
0
0
0
0
2
1
0
2
0
1
0
1
2
0
0
1
0
0
0
2
0
0
2
0
0
0
2
2
0
0
0
0
1
2
0
1
2
0
4
2
1
0
1
0
0
0
0
2
0
0
0
1
0
2
2
0
0
0
0
0
1
2
0
0
3
1
0
1
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
2
0
0
0
1
2
0
0
2
0
0
2
0
4
0
2
0
0
0
0
0
0
2
1
0
2
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
2
0
3
0
0
0
0
1
0
1
0
0
0
1
0
1
3
3
0
1
2
0
0
1
0
1
0
0
0
2
1
0
1
0
0
1
0
1
0
1
0
3
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
1
0
0
0
0
2
2
1
2
0
1
1
0
0
1
0
0
0
0
1
1
0
0
1
0
2
1
1
1
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
1
0
0
0
2
0
1
1
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
9
0
2
0
0
0
4
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
2
2
0
2
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
2
3
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
2
2
0
0
1
1
2
0
0
0
1
1
1
1
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
1
2
0
1
2
0
0
0
0
1
0
1
0
0
1
0
2
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
1
0
1
2
0
0
3
0
0
0
0
1
2
0
1
2
0
0
2
0
1
0
1
0
2
0
0
0
1
0
3
2
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
1
0
0
0
2
3
0
0
0
0
0
0
0
0
0
2
0
0
1
3
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
2
0
1
0
1
0
1
2
2
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
1
0
0
2
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
2
0
0
0
1
0
0
1
3
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
1
0
1
0
0
0
0
1
3
1
0
0
0
0
0
0
0
0
0
0
2
2
2
1
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
2
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
1
1
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
2
0
0
1
0
2
0
2
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
2
0
0
0
6
0
0
0
2
1
2
0
3
0
0
0
2
0
0
5
0
0
0
0
0
5
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
2
2
0
0
0
2
0
3
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
2
0
0
5
0
0
0
0
0
0
1
2
0
1
0
0
1
0
0
0
1
0
3
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
2
0
0
2
0
0
0
0
0
2
1
1
0
0
3
1
1
0
0
0
0
1
0
0
2
0
1
1
2
0
0
0
0
0
0
0
4
2
0
1
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
2
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
2
0
0
0
2
1
1
0
0
3
0
0
0
1
0
0
0
0
0
2
2
0
0
1
0
0
2
2
0
0
0
0
0
0
3
0
0
0
1
0
3
0
0
0
2
2
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
1
0
0
2
0
0
2
0
2
0
0
0
2
0
2
0
0
1
0
3
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
2
1
2
1
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
3
1
0
0
1
0
0
1
2
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
2
0
1
1
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
1
1
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
17
0
0
0
0
0
0
0
1
2
2
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
1
0
2
0
2
0
0
0
0
2
0
0
0
2
3
0
2
0
2
0
0
0
0
0
0
1
2
2
0
1
2
2
0
2
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
2
0
2
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
2
2
0
1
0
2
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
2
2
0
0
0
2
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
2
2
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
2
0
1
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
1
0
0
0
0
0
0
1
0
0
2
2
0
1
0
2
0
1
0
0
0
0
1
0
0
0
0
1
2
0
2
0
1
0
1
0
0
0
0
1
2
0
0
0
0
1
1
0
1
0
2
0
0
0
0
2
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
3
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
2
0
0
0
2
1
2
0
2
0
0
0
3
0
1
1
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
3
1
1
2
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
2
2
1
1
0
0
0
0
1
0
2
0
0
1
0
0
1
0
0
1
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
3
0
2
0
2
2
0
0
2
3
0
0
1
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
3
1
0
0
0
1
2
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
2
1
0
2
1
0
0
0
0
1
2
0
0
0
2
0
0
0
0
1
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
2
0
0
0
0
0
2
0
0
0
0
2
0
2
1
2
0
0
0
0
1
2
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
3
0
0
0
1
0
0
0
3
0
1
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
5
0
0
2
0
0
2
2
1
0
0
0
0
2
0
0
2
0
0
1
2
0
0
0
2
0
0
0
0
1
1
1
0
8
0
2
0
0
0
2
0
0
1
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
2
1
0
0
0
0
0
2
0
2
2
2
0
0
0
0
2
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
2
4
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
1
1
0
0
0
0
2
2
1
0
2
0
2
1
2
2
2
0
3
1
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
2
1
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
1
0
1
0
0
0
1
0
2
0
2
0
3
1
0
0
0
1
0
2
0
2
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
2
2
0
0
0
1
0
0
0
2
1
0
3
0
0
0
0
0
0
0
4
0
0
2
0
1
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
1
3
0
0
1
2
0
0
0
0
0
2
0
1
0
0
0
0
2
0
1
0
0
1
0
2
0
0
0
0
0
5
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
3
0
2
0
0
0
0
2
0
0
0
1
0
2
0
0
1
1
2
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
1
0
1
1
0
0
0
2
0
0
0
0
2
0
1
1
1
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
2
0
1
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
2
1
2
0
0
0
2
0
0
1
0
0
0
0
1
0
2
0
0
0
0
1
0
0
2
1
0
0
0
1
2
0
0
0
0
0
0
2
0
1
0
0
4
0
2
1
0
0
0
2
1
2
0
0
2
1
0
0
3
2
0
2
0
1
0
0
1
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
1
0
0
0
1
0
0
0
0
3
0
1
3
0
0
1
0
1
2
1
2
1
1
1
2
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
1
3
2
0
1
0
0
1
0
0
0
0
0
0
1
2
1
0
1
3
1
0
0
0
0
1
0
1
2
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
2
1
0
0
2
2
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
1
3
0
1
1
3
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
1
0
2
0
1
2
0
0
2
1
0
1
0
0
0
0
2
2
1
0
0
2
2
1
1
3
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
2
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
3
2
1
4
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
2
2
2
0
0
4
0
0
1
0
0
1
0
0
0
1
1
2
1
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
1
0
0
1
0
2
2
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
1
0
1
1
2
1
0
2
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
1
0
4
3
0
0
0
2
0
2
0
0
0
0
0
0
2
4
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
1
0
0
0
0
2
2
0
2
0
2
1
1
0
0
2
2
1
2
1
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
2
2
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
1
0
1
2
0
2
0
0
1
0
0
0
0
2
2
0
0
0
1
2
0
0
0
0
0
0
1
1
0
1
1
3
0
0
0
1
5
0
0
0
0
2
0
2
2
0
0
0
0
1
2
1
0
0
2
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
1
2
2
0
0
1
1
0
0
0
2
2
1
0
0
0
0
2
0
0
0
0
1
0
1
0
1
2
0
0
1
0
0
0
0
0
0
0
0
2
0
4
0
0
0
0
0
2
1
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
2
0
1
1
3
1
2
0
0
0
2
4
0
0
0
3
0
0
0
5
1
0
0
2
0
0
0
0
0
2
0
1
0
4
2
2
0
1
0
1
0
1
0
0
0
1
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
2
2
0
1
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
1
0
2
0
1
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
3
0
2
0
2
0
0
0
1
0
0
0
1
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
2
0
1
1
0
0
4
1
0
0
1
0
0
1
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
3
1
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
1
1
5
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
2
0
3
0
0
0
0
0
2
0
1
0
0
0
2
0
4
2
0
0
0
0
1
0
0
1
2
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
1
0
0
0
0
1
0
1
1
0
0
2
0
0
2
1
1
2
0
2
0
0
0
0
0
3
1
0
0
2
0
1
0
1
0
0
0
3
0
0
1
0
0
0
1
0
1
2
0
0
0
0
2
1
1
0
0
0
0
1
0
0
0
2
1
0
2
1
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
1
0
1
0
0
1
2
0
2
0
0
2
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
1
3
0
0
0
0
0
0
2
0
2
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
1
1
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
1
4
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
1
0
0
0
1
2
0
0
1
2
0
1
0
0
0
0
2
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
2
0
1
2
0
2
0
0
2
1
0
3
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
2
1
0
2
2
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
2
1
0
0
0
6
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
3
0
3
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
4
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
8
0
0
0
0
1
2
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
2
0
3
0
0
2
0
0
0
0
0
0
1
2
0
2
0
0
2
0
3
0
0
0
0
0
0
1
0
0
1
1
1
0
0
3
1
0
1
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
2
2
0
0
0
2
0
0
1
0
0
1
0
2
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
4
0
0
0
0
0
0
0
2
3
1
0
1
0
2
0
0
0
0
2
1
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
1
0
1
2
0
0
0
3
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
2
2
0
1
0
1
2
0
2
0
2
0
1
0
0
0
1
2
1
1
0
0
0
0
3
0
0
1
0
0
1
0
2
2
0
2
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
1
0
0
0
2
2
3
0
2
0
0
0
0
1
2
0
0
1
2
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
1
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
2
2
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
2
0
2
0
0
0
0
0
1
2
0
0
0
0
0
2
1
1
0
2
0
0
0
3
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
2
0
1
0
0
0
1
2
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
4
0
2
2
0
0
1
0
0
0
0
2
2
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
1
2
0
0
2
0
0
2
0
1
1
2
0
2
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
2
2
0
0
2
0
1
0
0
0
0
1
0
0
1
0
1
0
1
1
2
0
0
0
0
0
0
0
4
2
0
1
1
0
0
2
1
1
1
0
1
0
0
0
1
0
1
0
1
0
4
0
1
1
0
0
0
0
0
0
3
0
1
2
0
0
1
0
1
1
0
0
1
0
2
0
0
1
0
0
1
0
2
0
0
1
1
2
0
1
2
0
1
0
2
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
2
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
3
2
0
0
2
0
0
0
2
7
0
1
0
0
0
0
2
1
0
3
3
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
1
2
0
1
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
1
0
0
0
1
3
2
0
0
0
0
0
0
0
1
0
4
0
1
0
0
2
3
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
2
0
2
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
3
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
5
1
1
0
0
0
0
0
1
1
0
1
0
2
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
2
0
0
2
1
0
0
2
0
1
0
1
0
0
1
0
0
3
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
1
0
0
0
2
0
0
1
0
0
1
0
0
0
0
2
0
0
0
2
2
0
0
0
1
3
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
1
1
0
0
2
0
1
0
1
0
0
1
0
2
0
0
1
0
2
1
0
2
0
2
0
0
0
0
0
0
0
0
2
0
1
2
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
2
0
7
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
1
0
2
0
0
0
4
2
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
1
0
0
0
1
0
0
0
2
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
1
0
0
2
0
0
2
1
1
0
2
1
0
0
0
0
0
1
2
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
3
0
0
0
0
2
1
0
0
0
1
0
2
0
0
2
1
0
1
1
0
2
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
1
0
0
2
0
2
0
1
2
0
0
1
0
1
0
0
0
0
0
0
3
2
1
2
0
1
0
0
2
0
0
2
0
0
0
0
0
0
1
1
0
0
2
0
0
1
0
0
1
0
0
0
1
0
0
1
2
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
1
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
1
0
0
0
0
0
2
1
2
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
1
0
0
0
1
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
2
0
0
6
1
0
1
2
1
0
0
0
0
0
0
0
2
2
0
0
2
0
1
1
0
0
1
0
1
1
0
0
0
2
2
1
0
0
2
0
0
0
0
0
0
0
5
0
0
2
0
2
0
0
0
2
0
0
2
1
1
3
0
0
0
1
0
3
1
0
0
0
0
0
1
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
3
0
5
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
2
2
0
0
1
1
0
0
0
0
0
0
0
1
2
2
0
0
0
2
0
0
1
0
2
0
0
0
1
0
0
0
2
2
0
0
1
3
2
0
0
1
0
0
2
2
1
0
0
1
0
0
0
2
0
2
0
3
0
2
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
2
0
3
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
2
0
1
0
0
1
0
0
0
0
2
0
0
1
0
2
3
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
1
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
2
0
3
0
2
0
3
0
2
0
0
0
0
0
0
0
1
3
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
1
0
0
2
1
0
0
0
8
1
0
2
0
0
0
0
0
2
0
0
0
0
0
2
2
0
3
0
1
5
0
0
2
1
2
0
1
0
0
0
0
0
0
0
0
1
2
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
1
0
2
0
0
2
2
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
1
1
0
0
2
0
0
0
0
0
0
2
0
0
2
0
1
0
1
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
2
0
0
1
0
0
1
0
0
2
0
0
0
0
0
3
0
0
1
2
0
0
0
3
0
0
0
0
0
1
0
2
0
3
0
2
0
0
0
2
1
0
1
0
0
1
2
0
0
0
3
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
1
1
0
2
0
0
1
0
0
0
2
2
0
3
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
11
0
1
0
0
1
1
3
1
0
1
0
1
0
1
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
2
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
2
5
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
2
0
0
1
0
0
0
1
2
1
0
0
0
0
0
2
0
1
0
3
0
0
1
2
0
1
0
0
0
2
0
0
2
0
0
0
0
2
0
1
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
3
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
2
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
1
1
0
0
0
3
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
3
0
0
3
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
1
0
0
0
2
0
0
0
1
2
0
2
2
1
0
1
0
2
0
0
4
0
0
2
3
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
5
3
0
0
0
0
0
0
0
3
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
2
2
1
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
2
0
1
0
0
0
2
1
1
0
2
2
0
2
1
0
1
0
0
2
0
2
1
0
0
2
0
0
0
1
2
0
0
2
0
3
1
0
2
3
0
0
0
2
0
2
1
0
0
1
0
0
0
1
1
0
4
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
1
1
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
5
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
2
3
2
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
1
0
2
0
0
0
0
0
1
0
0
1
2
0
0
2
1
0
2
0
1
1
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
1
2
2
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
2
0
1
2
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
2
2
0
2
0
0
0
0
2
0
2
2
1
0
3
1
2
2
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
1
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
2
0
0
0
0
0
0
0
1
2
1
0
1
0
0
1
2
0
0
0
0
0
0
0
1
0
0
1
0
4
1
0
2
0
1
0
2
0
2
0
0
4
0
0
0
0
0
1
0
5
0
0
0
1
0
0
1
3
0
0
0
0
1
0
2
0
1
0
1
0
0
0
0
0
0
1
2
1
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
1
0
0
1
0
0
0
0
3
0
0
0
0
0
1
0
3
0
0
1
0
0
2
0
2
0
0
0
1
1
1
4
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
3
0
1
0
1
1
2
0
0
0
1
2
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
2
1
0
1
0
0
1
0
0
0
0
0
0
1
0
1
3
0
0
0
2
1
0
0
2
0
1
0
1
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
2
1
1
0
0
2
1
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
2
1
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
2
0
1
0
0
1
0
2
4
2
0
1
0
1
0
2
2
1
2
0
0
0
0
2
0
0
1
1
0
0
1
0
0
0
1
0
0
2
0
0
0
1
0
0
0
1
0
0
2
2
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
2
1
0
0
1
0
3
0
0
0
1
1
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
4
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
2
1
2
4
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
7
0
0
1
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
1
2
0
0
0
0
0
1
0
1
0
3
0
1
0
1
1
0
0
0
0
0
0
1
0
2
0
1
0
0
2
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
1
2
0
0
1
0
0
1
1
0
2
2
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
3
0
1
0
0
0
0
0
0
0
1
0
1
1
0
2
2
0
0
0
1
0
1
0
0
0
0
0
1
5
1
1
0
2
0
1
0
0
0
0
0
0
2
0
0
3
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
2
0
0
1
0
0
2
0
1
2
2
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
2
2
1
0
0
1
0
2
0
0
0
1
0
0
0
2
0
2
0
0
0
0
2
1
0
0
0
1
1
0
4
1
0
0
0
2
1
1
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
1
1
2
1
0
0
0
0
0
1
0
1
0
0
1
1
0
1
0
1
2
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
2
0
2
0
0
0
2
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
6
1
1
1
0
2
0
0
0
0
0
3
0
3
1
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
3
0
2
2
0
0
0
0
0
0
1
2
0
0
1
0
0
2
0
0
2
2
0
0
0
1
0
2
2
0
2
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
1
1
0
0
0
0
0
0
0
1
2
0
2
0
0
2
0
0
2
0
2
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
3
2
2
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
2
0
1
1
0
0
0
2
1
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
4
2
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
4
0
0
0
1
0
0
12
0
1
0
1
1
0
2
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
5
1
0
3
0
2
1
0
1
0
0
0
0
0
0
0
0
0
2
2
0
1
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
2
0
2
1
0
0
0
0
3
0
0
1
0
0
0
0
0
0
2
0
1
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
2
1
1
1
0
0
0
1
0
2
3
0
0
0
2
0
1
2
0
0
0
3
0
0
0
2
1
0
0
0
0
0
0
1
0
2
1
2
1
0
0
1
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
2
0
1
0
0
3
1
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
7
0
2
0
4
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
3
0
0
1
0
0
2
1
2
2
2
0
0
0
0
0
0
1
2
0
0
3
0
2
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
2
1
0
5
0
0
1
0
0
0
2
0
2
1
0
0
2
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
3
0
0
0
1
0
1
0
0
0
0
0
0
2
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
2
0
1
0
0
0
2
0
1
1
0
1
0
0
0
0
1
0
2
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
2
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
2
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
1
1
1
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
1
0
2
0
3
1
2
0
0
0
0
0
1
0
0
0
0
2
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
2
0
1
0
2
1
0
0
0
0
1
0
0
2
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
4
2
0
1
0
0
0
0
2
0
2
0
0
0
1
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
4
2
0
0
0
0
3
0
2
0
0
0
1
2
1
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
5
0
0
2
0
1
0
0
0
2
0
0
0
2
3
0
0
0
0
1
0
2
0
0
0
1
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
1
0
2
0
0
0
0
2
0
2
2
2
2
0
1
2
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
2
1
0
1
0
0
3
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
8
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
2
0
0
3
0
0
2
0
1
3
0
0
0
0
3
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
1
0
3
0
1
0
2
0
1
0
1
0
0
0
0
0
0
1
0
0
2
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
2
1
0
0
0
0
0
0
1
0
2
0
6
2
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
1
0
2
0
0
0
0
2
2
1
1
0
0
0
2
2
0
0
0
0
2
2
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
1
0
3
0
0
2
0
0
2
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
3
1
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
1
0
2
2
0
0
1
2
0
0
0
0
0
0
2
1
3
0
1
0
4
0
0
3
0
0
0
0
0
0
0
2
2
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
5
0
1
0
0
2
1
0
2
2
0
1
0
0
0
2
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
2
1
0
0
3
0
0
0
0
2
0
0
1
0
0
0
1
0
2
1
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
1
0
1
3
0
1
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
2
0
0
2
2
0
2
0
0
2
0
0
4
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
1
1
2
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
1
3
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
1
2
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
2
0
2
0
1
0
2
1
0
1
0
0
0
0
0
0
1
2
1
0
0
1
0
0
0
0
0
0
0
1
1
4
2
1
0
2
1
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
2
1
1
0
0
0
0
0
0
1
0
0
0
0
2
1
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
1
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
1
0
0
0
2
3
3
3
2
0
0
0
0
0
4
0
0
2
0
1
0
1
3
0
2
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
2
1
1
0
0
0
0
0
1
2
1
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
3
1
0
2
0
0
0
0
0
2
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
4
0
0
2
8
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
2
0
0
0
3
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
5
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
3
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
3
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
2
2
0
0
0
0
2
1
1
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
4
2
0
2
0
0
1
0
3
0
0
0
1
0
1
0
1
3
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
1
0
2
0
0
0
0
2
1
0
1
3
0
2
0
1
2
0
2
1
0
0
0
0
0
0
4
3
0
0
2
0
1
0
1
2
0
1
1
2
0
1
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
2
0
0
0
1
0
2
0
2
0
0
2
4
0
2
0
0
0
1
1
0
1
0
0
2
0
2
0
2
1
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
1
1
0
0
0
1
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
2
1
0
2
2
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
1
1
0
0
0
0
0
2
1
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
6
0
0
1
0
2
0
0
0
0
1
0
0
0
0
2
2
2
0
1
1
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
5
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
1
1
3
1
1
0
2
1
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
1
1
0
1
0
0
0
2
0
1
2
1
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
2
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
2
0
0
1
1
0
0
0
2
2
0
0
2
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
2
1
0
2
0
0
2
2
1
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
1
2
0
0
0
0
2
2
0
0
0
1
2
0
0
0
0
1
0
0
0
2
0
1
0
0
0
1
2
0
2
0
0
1
0
1
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
1
1
2
0
2
0
2
2
0
2
0
0
0
1
0
0
0
0
1
0
0
2
0
2
0
2
0
0
0
2
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
4
0
2
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
1
0
0
0
0
1
1
0
0
0
2
1
0
0
0
0
1
0
1
2
2
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
1
2
0
2
0
0
3
0
0
2
0
0
1
0
2
1
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
1
0
1
0
3
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
1
0
0
0
0
0
0
2
3
2
1
2
2
1
0
0
0
0
0
0
2
0
2
1
4
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
3
0
0
2
0
0
0
0
5
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
1
0
1
0
0
0
0
1
2
0
0
0
2
1
0
0
0
1
0
2
2
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
2
1
0
0
0
2
2
2
0
0
4
1
0
0
1
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
1
3
1
0
0
0
0
0
0
1
6
0
0
0
1
0
0
0
2
2
0
2
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
1
1
5
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
1
0
2
0
0
0
0
2
2
0
0
2
2
1
1
0
0
0
0
0
0
0
0
2
2
0
2
0
2
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
7
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
2
0
2
1
1
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
2
3
0
0
0
0
1
0
0
1
0
2
2
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
3
0
1
1
0
0
0
0
0
0
1
2
1
0
0
0
0
1
0
2
0
0
0
0
0
2
0
2
1
2
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
2
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
1
0
0
0
2
2
2
2
0
0
0
0
1
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
2
0
0
0
1
0
0
0
0
0
1
2
0
1
0
0
0
4
2
0
0
1
0
0
0
0
0
0
1
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
2
0
0
1
0
0
0
0
0
1
0
2
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
2
0
2
1
0
1
0
1
0
0
0
0
2
1
2
0
1
0
2
2
0
1
0
0
1
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
3
0
0
3
0
2
0
0
1
0
0
0
3
0
1
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
2
2
1
0
0
0
1
0
0
1
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
1
0
2
0
1
1
0
0
0
0
2
0
0
1
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
3
1
0
0
0
0
1
1
1
2
0
0
0
0
0
2
1
1
0
2
0
0
0
0
0
2
0
0
0
0
2
1
2
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
3
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
1
0
1
0
0
2
0
0
0
0
1
0
1
0
2
0
0
0
0
2
0
0
0
0
0
2
0
1
2
0
0
0
1
0
1
0
0
0
0
4
0
3
0
0
0
0
0
0
0
0
2
2
0
0
1
0
2
0
3
1
0
0
2
1
0
1
2
0
0
0
0
2
0
1
0
0
0
1
4
0
0
0
0
0
0
0
2
1
1
0
0
0
0
1
1
2
0
0
2
0
2
0
3
0
2
0
0
0
0
1
2
0
0
1
0
0
1
0
0
2
0
0
2
0
2
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
2
0
0
1
0
2
0
0
0
0
1
1
1
0
0
0
0
1
1
2
0
0
0
0
0
1
0
2
1
0
0
0
3
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
1
2
2
0
1
0
2
2
0
1
2
1
0
1
0
0
0
0
0
0
0
0
2
1
4
0
0
2
0
2
0
0
0
1
0
1
1
0
1
0
0
2
2
1
1
1
1
0
0
0
0
2
0
0
1
2
2
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
4
2
0
2
1
0
0
0
0
0
0
5
1
0
2
0
2
0
0
0
1
0
1
0
1
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
4
0
0
1
0
2
0
0
0
0
2
2
0
0
0
0
2
0
0
0
2
0
0
1
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
2
4
0
0
2
2
0
0
0
0
0
1
1
0
2
0
0
0
0
2
0
0
1
0
2
0
0
1
0
0
0
0
1
0
2
0
0
0
0
1
3
0
1
2
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
4
0
1
0
2
0
0
0
0
0
0
0
0
1
2
0
2
0
0
1
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
2
1
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
2
1
2
0
0
1
2
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
2
0
0
0
0
0
0
2
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
2
1
1
0
0
0
0
0
0
2
1
0
0
2
2
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
1
0
0
0
1
0
0
2
0
0
1
7
1
3
0
1
0
0
0
2
0
0
0
0
3
3
1
1
0
0
2
0
0
0
0
0
4
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
4
1
0
0
2
0
0
0
0
0
0
0
1
0
2
2
2
0
1
2
3
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
3
1
0
0
0
1
0
0
1
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
1
0
2
2
1
2
1
3
1
1
2
0
0
0
0
0
1
1
0
0
0
2
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
1
2
1
2
0
0
0
0
0
2
0
1
0
0
1
2
0
2
0
2
0
0
2
0
0
0
0
0
0
0
1
1
0
5
0
2
0
0
0
0
0
0
0
0
0
0
1
3
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
1
0
2
0
1
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
1
0
2
0
0
0
0
0
0
2
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
2
0
0
1
1
0
0
2
2
0
0
0
0
2
0
0
2
2
0
0
0
2
0
5
0
1
0
0
2
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
5
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
14
0
0
0
1
0
0
3
0
0
0
0
2
0
4
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
2
1
1
2
0
0
2
1
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
1
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
8
0
0
1
0
0
0
0
0
2
3
0
0
1
0
0
0
0
2
1
0
0
3
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
2
0
0
0
1
0
0
0
0
0
0
2
1
1
2
0
1
2
1
0
0
1
0
0
0
0
3
0
0
2
0
2
2
0
0
0
1
1
0
0
1
0
0
1
0
0
2
0
3
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
2
0
0
0
0
2
0
2
0
1
0
1
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
2
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
3
1
2
2
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
7
0
0
2
1
0
0
2
0
1
2
2
0
0
0
0
5
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
1
2
0
0
2
1
3
1
0
1
1
1
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
2
0
0
0
2
2
2
1
0
0
0
0
0
1
1
0
0
2
0
0
0
0
1
0
1
0
0
3
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
1
0
0
0
2
0
1
0
0
4
0
1
0
0
2
1
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
1
1
2
2
0
0
1
0
0
0
0
0
0
0
0
1
2
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
2
0
2
0
3
0
0
0
0
2
2
0
0
0
1
1
1
0
2
2
0
0
0
0
0
0
1
2
0
1
1
0
0
1
0
0
0
2
0
0
0
0
0
3
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
5
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
6
1
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
1
1
0
3
0
1
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
1
0
0
3
1
0
2
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
1
0
0
1
0
0
1
0
2
0
0
0
0
0
0
1
2
0
0
0
0
2
0
1
3
0
1
2
0
0
0
0
0
0
2
1
2
2
1
0
0
1
0
0
2
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
2
0
0
0
1
1
0
1
0
0
0
2
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
1
1
0
0
2
1
0
0
2
0
0
0
3
1
0
2
0
2
1
0
0
1
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
4
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
2
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
2
0
1
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
1
3
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
1
1
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
4
2
1
1
0
0
0
0
2
0
0
0
2
0
2
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
2
1
1
2
0
0
0
2
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
2
1
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
1
0
2
0
0
0
2
0
2
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
3
0
0
2
0
0
0
1
3
1
0
0
0
1
0
0
0
0
0
2
0
0
2
1
0
2
1
0
2
0
0
2
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
5
2
0
0
0
0
0
0
2
2
0
2
0
0
2
0
0
0
1
0
1
1
4
0
0
0
0
2
0
0
2
0
0
0
0
2
0
1
0
0
0
1
0
0
1
1
0
2
0
0
0
0
2
0
1
3
0
0
1
1
3
0
0
0
2
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
1
0
2
0
0
0
0
4
2
0
0
3
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
2
0
0
0
0
1
2
2
2
0
0
0
0
0
3
0
0
0
0
0
0
2
1
1
0
0
0
0
1
1
0
0
0
8
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
2
2
0
0
2
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
1
0
1
0
1
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
2
1
3
0
2
1
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
2
1
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
2
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
3
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
1
0
0
0
1
2
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
2
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
5
1
0
0
0
0
1
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
2
2
1
2
1
1
1
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
1
0
1
3
0
0
0
1
0
1
0
1
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
2
0
2
0
0
0
2
0
0
0
1
0
1
0
1
2
1
0
0
0
2
1
0
0
0
0
0
3
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
2
0
2
0
0
1
0
0
2
0
2
1
0
0
0
1
1
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
1
0
2
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
1
2
0
0
5
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
3
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
2
0
2
1
0
2
0
1
2
1
0
0
1
0
0
0
0
0
0
2
1
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
1
2
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
3
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
1
1
0
7
0
2
0
2
0
0
1
0
1
1
0
3
0
0
1
0
0
1
0
0
1
3
0
0
0
0
2
0
1
1
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
2
1
0
0
0
1
2
0
1
0
0
2
0
0
0
0
0
4
0
0
0
0
2
0
0
0
3
0
2
0
0
2
0
0
0
2
0
0
2
0
1
0
1
0
1
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
2
0
0
2
0
2
0
1
2
0
0
0
2
1
0
1
0
0
2
3
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
2
2
0
1
0
2
1
1
0
0
0
1
0
0
2
2
0
0
0
2
0
0
0
0
2
2
0
0
0
2
0
0
0
3
0
1
0
2
0
2
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
3
0
0
0
2
0
0
1
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
2
1
0
2
0
2
0
0
1
0
0
0
0
0
0
1
4
0
0
1
0
0
0
0
0
2
1
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
1
0
3
0
0
2
0
0
0
2
2
0
3
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
2
1
0
0
1
1
0
0
0
0
0
1
0
0
0
2
1
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
3
0
0
1
0
0
2
1
0
0
0
0
1
2
2
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
1
2
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
2
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
1
1
0
0
1
0
0
0
1
0
0
0
3
3
1
0
0
0
1
0
0
1
0
0
0
2
2
2
0
0
1
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
4
0
0
1
0
0
1
3
0
0
0
2
0
0
0
0
2
0
1
0
2
0
0
0
0
1
1
0
0
1
1
2
1
1
0
1
2
1
0
0
1
0
0
0
2
0
1
0
1
0
2
0
0
0
0
0
0
0
3
2
2
1
2
2
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
1
1
1
1
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
6
1
0
1
2
1
0
1
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
1
0
0
0
0
2
0
1
0
0
0
0
0
2
0
2
1
0
0
2
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
1
2
0
0
3
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
3
0
1
0
0
0
0
2
2
0
0
0
0
1
3
1
0
0
0
1
0
0
0
1
0
3
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
3
0
1
0
0
1
0
0
2
0
0
2
0
0
0
1
1
1
3
0
1
0
1
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
2
6
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
2
0
0
1
2
0
1
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
1
2
1
0
0
2
1
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
1
1
2
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
2
1
0
0
0
0
1
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
3
2
0
0
2
2
0
1
2
2
2
3
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
4
1
1
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
3
0
0
0
2
1
0
0
1
0
0
2
1
0
0
0
2
0
0
0
0
1
0
0
2
2
0
1
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
1
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
4
0
0
0
2
1
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
4
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
3
0
0
0
0
0
0
1
0
2
2
0
1
0
1
1
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
2
0
2
0
0
2
2
0
2
1
0
0
0
0
0
0
2
0
1
0
2
0
0
2
1
0
0
1
0
0
0
0
1
0
0
0
2
0
1
1
3
1
0
5
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
2
0
1
2
1
3
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
1
2
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
2
2
0
0
0
0
0
2
0
1
2
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
2
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
4
0
0
2
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
3
2
4
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
4
0
0
1
0
1
1
0
5
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
2
4
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
1
1
1
1
0
0
0
0
0
1
0
2
2
1
0
2
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
1
0
0
2
0
0
0
0
0
0
2
0
2
2
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
2
1
1
2
2
1
0
0
0
0
0
0
0
0
0
2
1
2
0
2
1
2
0
0
0
0
2
0
0
0
0
0
0
2
0
1
2
0
0
0
2
2
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
2
0
0
1
0
7
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
2
0
0
0
2
0
2
1
2
0
0
2
0
0
2
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
3
4
0
0
0
0
0
0
1
2
0
1
0
3
0
0
0
3
0
0
0
1
0
0
1
0
2
1
0
0
0
0
0
4
0
0
4
0
0
0
2
0
0
0
0
0
1
0
0
4
2
0
1
0
2
0
0
0
1
0
0
0
0
0
0
2
2
0
3
0
1
0
1
0
0
1
0
0
2
0
1
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
3
1
0
2
0
0
2
0
0
1
2
0
0
0
0
0
0
0
2
0
4
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
1
0
3
1
0
0
1
0
0
2
1
4
0
0
2
0
1
1
1
0
0
0
0
2
0
0
0
1
0
2
0
2
0
0
0
2
0
0
1
0
12
0
0
0
0
0
1
1
0
0
2
1
1
0
2
2
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
2
2
0
0
2
2
1
1
0
2
0
0
0
1
1
2
0
0
2
2
0
0
4
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
1
3
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
2
0
2
2
1
0
4
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
2
3
0
1
2
2
0
0
0
1
1
0
2
4
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
1
0
1
1
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
2
1
0
0
0
1
2
0
0
0
0
1
0
2
0
0
0
2
1
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
2
0
0
2
1
0
0
0
0
0
0
2
0
0
0
3
0
0
1
0
0
1
0
2
0
0
2
1
0
1
0
3
0
0
2
0
2
0
0
0
0
0
2
1
0
2
2
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
1
0
1
3
2
2
1
0
0
2
6
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
2
2
0
0
0
4
1
2
0
2
1
0
0
0
2
2
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
1
2
0
0
2
2
0
0
1
0
2
0
0
3
0
0
0
2
0
0
0
0
0
0
2
1
5
1
0
0
2
2
0
1
0
1
0
0
2
0
0
0
0
0
2
2
0
2
0
0
0
2
1
0
0
0
1
0
0
2
1
2
0
0
0
0
0
3
2
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
2
0
1
0
2
0
2
0
0
0
1
2
0
4
0
1
0
1
0
0
2
0
0
2
0
0
1
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
1
0
0
0
4
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
4
0
0
1
1
2
0
0
0
0
2
2
1
1
2
0
0
1
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
2
0
0
0
0
2
1
1
0
0
0
4
0
1
0
0
0
0
2
3
1
0
0
2
0
0
2
0
0
0
0
0
0
1
0
3
0
0
2
0
1
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
5
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
1
0
1
0
1
0
0
0
2
1
0
2
0
0
2
0
2
0
0
0
0
1
2
0
2
0
0
0
1
0
0
1
0
0
0
1
0
1
2
2
1
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
2
0
0
0
0
0
4
0
0
2
0
0
0
3
0
0
0
2
2
3
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
1
0
2
2
0
0
0
0
0
2
1
0
0
3
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
2
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
2
0
2
0
1
0
0
2
1
1
0
8
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
10
0
1
0
2
0
2
1
0
4
1
0
1
0
2
2
0
0
0
0
1
0
2
0
1
2
0
0
1
0
0
0
2
0
0
2
0
0
2
4
2
0
0
0
0
0
0
0
1
1
0
2
1
0
3
0
0
1
0
1
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
3
0
2
0
0
0
1
0
1
0
2
1
1
0
1
1
0
2
0
0
0
0
1
1
0
0
0
0
1
0
7
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
4
1
0
0
0
0
0
0
0
2
2
2
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
2
0
0
2
0
1
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
2
0
0
0
2
2
1
0
2
0
2
0
0
3
1
1
0
0
1
0
0
0
2
0
0
0
1
0
0
1
2
0
0
0
0
2
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
2
0
2
2
0
0
0
2
3
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
1
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
1
0
0
0
2
1
1
0
0
3
0
2
1
4
0
0
0
0
2
0
0
2
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
3
1
1
0
2
0
1
1
0
0
0
0
0
0
2
0
0
2
0
2
0
1
0
0
0
1
1
0
11
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
2
1
0
0
0
1
2
1
0
2
2
1
0
1
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
3
0
0
2
0
0
1
1
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
3
1
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
3
2
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
2
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
1
2
0
1
0
0
1
0
2
0
0
0
0
0
1
0
0
1
1
2
0
1
0
2
2
0
1
0
2
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
1
2
0
1
0
0
0
1
1
0
0
2
3
5
2
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
2
0
0
1
0
2
0
1
0
2
2
0
2
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
2
0
0
2
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
1
0
3
0
0
0
0
0
0
1
0
0
1
0
0
1
0
2
0
0
0
0
1
0
0
5
0
1
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
1
1
1
0
2
1
0
0
0
1
2
2
1
0
0
2
0
0
0
6
0
0
3
0
0
1
0
0
0
0
0
0
1
1
0
1
2
0
0
1
0
2
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
3
0
18
0
0
1
0
0
0
0
2
2
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
1
2
0
1
0
0
1
1
0
1
0
0
0
1
0
1
6
0
0
2
1
0
1
0
0
1
0
0
0
0
2
3
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
1
2
1
0
0
0
4
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
3
0
0
1
0
0
1
0
1
0
1
0
0
1
1
1
0
2
2
0
0
0
0
0
1
0
1
3
0
0
1
0
0
0
0
0
1
3
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
2
2
0
0
0
0
1
0
0
0
0
0
2
0
0
1
1
2
1
0
0
0
0
0
0
0
0
0
0
2
2
0
4
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
5
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
1
0
1
0
1
0
0
1
0
0
1
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
2
2
0
0
0
2
0
0
1
0
1
2
0
0
0
0
0
0
0
2
0
2
0
2
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
6
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
1
4
2
0
0
2
0
0
0
0
2
1
1
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
1
0
1
0
2
0
0
0
0
2
0
0
0
0
6
0
1
1
0
0
0
2
0
2
0
3
0
0
1
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
1
1
2
0
4
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
3
1
0
0
1
0
0
0
2
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
3
2
2
0
0
1
0
0
0
1
0
0
0
1
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
1
1
0
1
0
2
0
2
0
0
0
0
0
0
1
0
1
0
4
0
0
0
0
0
0
0
0
0
0
3
1
1
0
2
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
1
1
1
1
0
2
0
0
0
0
2
2
1
0
2
0
1
0
0
0
1
0
0
0
0
2
0
0
1
2
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
1
0
1
1
1
0
2
0
0
0
1
2
0
6
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
2
0
1
2
1
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
5
0
3
0
0
0
0
0
0
3
0
1
1
1
3
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
2
2
0
0
0
2
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
6
0
0
0
0
0
0
2
0
3
2
0
0
1
1
0
2
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
2
1
2
0
0
0
1
0
0
0
2
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
2
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
2
0
0
0
1
0
0
1
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
5
0
0
2
2
0
0
0
0
3
0
2
0
1
0
0
1
2
1
0
0
0
0
0
3
2
3
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
1
0
0
0
1
0
1
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
1
2
0
1
0
1
0
1
0
0
3
0
2
0
2
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
1
0
0
0
0
0
0
1
2
0
2
1
0
1
0
0
0
0
0
2
0
0
2
1
0
0
0
1
2
1
0
0
0
1
2
2
0
0
0
2
0
1
0
0
2
0
0
0
0
2
1
0
0
1
0
6
2
1
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
2
9
0
0
0
4
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
1
2
0
0
2
0
1
0
0
0
0
1
0
0
0
1
2
2
2
1
0
0
3
1
0
0
0
0
1
2
1
0
0
1
0
0
0
1
0
1
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
11
0
2
0
0
2
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
2
2
0
0
2
0
2
2
0
0
1
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
1
0
1
0
0
0
2
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
2
0
1
0
0
1
0
0
0
0
2
3
0
0
2
4
0
2
1
0
0
0
1
0
1
2
0
0
0
2
4
0
2
3
0
0
1
3
0
0
2
0
0
0
0
1
0
2
0
1
0
2
0
0
0
0
0
2
0
0
6
0
1
0
0
0
1
0
2
0
0
0
1
0
2
2
0
0
0
0
0
1
1
0
0
2
1
1
0
0
2
0
0
2
0
0
0
1
3
0
2
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
2
2
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
2
1
4
0
1
1
0
0
0
0
0
1
2
0
1
1
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
1
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
2
1
0
2
0
8
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
2
0
0
1
1
0
2
0
1
1
0
0
2
0
1
0
0
0
0
1
1
0
0
0
0
2
2
0
0
1
2
2
0
0
0
1
2
0
3
0
0
2
0
0
2
0
0
1
0
2
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
2
0
0
0
2
2
0
1
1
0
3
1
1
1
0
0
0
1
0
0
0
0
3
0
0
0
0
3
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
1
0
0
4
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
4
1
1
0
1
0
0
1
2
3
1
0
2
0
0
2
1
0
1
0
0
0
1
0
1
3
0
0
0
1
2
0
2
1
0
3
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
2
2
0
1
0
0
2
0
0
0
0
1
2
2
0
1
1
3
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
3
2
0
0
3
0
2
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
2
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
3
0
0
0
0
2
1
0
0
3
0
1
0
0
2
0
0
2
2
0
0
0
0
3
0
0
0
1
0
2
0
0
1
0
1
1
0
0
0
0
0
0
2
3
1
1
0
1
0
0
0
0
0
0
3
0
0
0
0
0
1
1
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
3
0
0
2
1
1
0
0
0
2
0
0
0
1
0
1
0
0
2
0
3
0
0
1
3
0
0
0
0
0
0
0
6
2
0
0
2
0
1
0
0
0
0
0
1
0
1
1
0
0
0
3
0
0
0
0
1
0
2
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
4
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
3
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
2
0
0
0
1
0
0
0
0
0
1
0
3
2
0
0
0
0
2
0
0
1
0
0
0
2
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
1
1
2
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
1
1
0
0
1
0
0
0
0
0
0
2
3
0
0
2
2
1
0
0
0
0
0
0
0
0
2
0
0
4
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
1
0
2
2
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
2
0
0
0
0
1
0
0
2
0
0
2
0
0
1
0
1
0
0
0
0
1
4
1
1
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
1
0
0
0
0
0
1
2
0
2
0
1
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
3
0
0
0
1
0
0
0
1
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
1
2
2
0
0
0
0
2
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
4
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
3
0
0
1
5
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
2
1
0
2
0
2
0
0
0
0
0
2
0
0
3
0
1
1
2
0
0
2
0
0
4
0
0
0
0
2
0
0
0
0
0
1
0
0
3
1
0
1
1
1
2
0
0
0
0
2
1
0
2
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
1
0
2
2
1
0
0
0
1
1
2
2
2
1
0
0
0
0
2
0
0
1
0
0
1
0
0
0
1
3
1
0
0
0
0
1
0
0
0
0
1
0
3
3
0
0
0
2
0
0
2
2
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
2
0
0
0
0
1
1
0
0
0
2
0
0
0
2
0
0
0
0
1
1
0
1
1
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
1
0
3
0
0
0
2
0
0
1
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
1
2
1
0
0
1
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
2
3
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
2
1
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
3
0
0
2
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
2
1
2
0
0
0
1
0
2
0
0
2
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
2
1
0
0
0
2
0
2
0
1
2
0
1
1
0
0
1
0
1
2
0
0
0
0
0
0
1
0
0
2
0
1
3
0
0
1
2
4
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
2
1
2
1
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
1
0
1
1
0
0
0
2
0
0
0
4
1
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
2
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
3
2
0
0
2
0
0
0
0
1
0
0
2
2
0
0
0
0
0
1
0
0
2
0
0
1
0
0
1
0
0
0
0
1
1
1
1
0
2
1
2
0
1
0
2
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
1
1
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
4
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
3
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
1
1
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
2
3
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
1
0
3
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
2
0
1
0
0
1
0
0
0
1
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
2
0
0
2
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
3
0
1
0
2
0
1
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
1
0
0
0
2
0
0
0
2
0
1
1
1
0
0
0
2
0
0
1
0
0
0
1
0
0
2
0
0
2
0
0
4
0
0
0
1
1
2
2
0
0
0
0
0
1
0
2
2
1
0
0
0
2
0
0
0
0
2
0
0
0
2
2
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
2
0
0
1
1
0
0
0
2
0
2
0
1
2
1
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
1
3
0
1
2
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
2
1
0
0
0
1
1
2
0
0
0
1
0
0
1
0
1
1
0
0
2
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
1
1
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
1
1
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
1
0
0
1
2
0
4
0
1
0
0
2
0
1
0
0
2
0
0
0
1
0
0
0
0
1
1
0
0
2
2
0
3
2
0
0
1
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
2
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
1
0
0
1
2
0
0
3
1
0
0
0
1
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
2
0
1
0
0
2
1
0
0
0
1
2
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
1
0
0
1
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
2
1
0
1
0
1
0
0
1
0
3
1
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
3
2
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
1
1
0
0
0
0
0
0
1
0
0
2
1
0
2
2
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
2
1
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
1
1
2
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
2
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
2
2
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
3
0
1
1
1
1
0
1
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
2
1
1
2
1
0
0
1
1
2
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
2
1
0
0
2
1
0
0
0
1
0
2
0
2
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
2
6
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
2
0
3
0
0
10
2
0
0
2
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
1
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
1
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
3
0
0
1
0
0
0
0
1
0
0
1
1
6
2
0
1
1
0
1
0
0
0
0
0
0
3
1
0
0
0
1
0
0
0
0
2
0
0
2
2
2
0
1
0
0
1
0
1
2
2
1
0
0
1
0
0
0
0
0
2
2
2
0
0
0
0
2
0
0
2
2
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
2
2
0
2
0
0
1
0
2
0
1
0
0
0
1
2
0
1
0
0
2
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
2
0
4
2
0
1
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
2
0
2
1
0
0
0
2
0
2
1
1
0
2
0
0
2
0
0
0
0
0
0
0
0
4
0
4
0
0
0
1
0
0
0
2
0
1
0
0
0
1
0
0
1
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
1
0
2
0
1
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
3
0
3
0
0
0
0
0
0
0
0
0
1
0
2
3
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
1
0
1
0
0
0
0
1
0
2
0
0
0
0
3
0
0
0
0
1
0
1
0
0
0
2
3
0
2
0
1
0
2
0
2
0
0
0
1
0
0
0
2
0
2
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
1
2
1
0
0
2
2
0
1
0
0
0
2
0
1
0
0
0
3
2
0
0
0
0
2
0
0
0
3
0
1
2
3
1
0
0
0
0
0
0
1
1
0
0
1
2
0
0
1
0
2
0
2
0
1
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
1
0
0
4
2
0
1
0
2
2
0
0
2
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
1
1
0
0
3
0
1
1
0
1
0
1
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
2
0
1
0
0
0
1
0
0
2
3
0
3
0
0
0
1
0
0
0
0
0
0
0
1
1
0
2
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
1
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
1
0
2
0
1
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
1
0
2
0
0
0
1
0
1
0
0
1
1
0
0
1
2
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
2
2
0
1
0
0
0
0
0
0
0
2
1
1
0
0
0
2
0
0
2
0
0
0
1
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
3
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
2
0
0
2
0
1
2
2
0
0
1
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
4
1
0
2
1
0
1
0
2
0
0
2
2
0
0
1
0
0
0
0
1
0
2
0
3
2
0
2
2
3
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
3
0
0
0
0
0
1
2
3
0
0
0
0
0
1
0
0
1
0
2
0
0
2
0
0
1
2
4
0
2
3
1
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
6
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
1
2
0
0
0
2
0
0
0
0
1
0
2
0
4
0
2
1
1
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
2
2
0
2
3
4
0
0
0
0
0
0
0
2
0
1
0
2
0
2
0
0
0
2
2
0
0
2
0
0
2
0
0
0
0
5
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
2
0
0
0
2
2
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
3
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
1
0
0
0
0
0
2
1
0
0
2
0
1
0
0
0
0
0
0
1
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
2
0
1
0
0
0
0
0
1
0
1
1
0
0
0
2
2
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
3
0
1
0
4
0
0
1
0
0
0
1
3
0
0
2
0
1
2
0
0
0
1
0
0
2
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
1
2
0
2
0
0
2
0
0
0
0
3
1
0
2
0
0
0
0
5
2
0
0
1
2
1
0
2
0
0
0
0
0
0
4
0
0
2
0
2
0
0
0
0
3
0
0
1
2
0
1
2
0
0
2
2
0
1
2
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
4
1
5
0
2
0
0
0
2
0
0
0
2
2
0
0
1
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
1
2
1
0
0
0
1
2
0
2
0
2
0
0
0
0
0
0
0
3
0
0
1
0
1
0
0
0
0
0
0
0
1
0
2
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
2
0
1
0
2
1
1
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
1
0
2
0
0
0
0
0
0
1
2
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
1
0
0
1
0
0
2
0
0
0
2
0
1
0
0
0
0
0
1
0
3
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
2
1
0
0
2
2
3
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
2
0
2
0
0
0
3
0
1
0
2
0
0
0
1
0
0
0
1
0
0
5
0
1
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
2
0
1
0
2
1
0
0
0
2
0
0
0
1
1
3
0
1
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
1
0
0
2
3
0
0
0
2
0
0
2
0
3
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
2
0
0
0
0
1
0
1
0
0
0
2
0
2
0
0
3
1
0
0
1
1
1
0
0
1
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
2
0
0
0
1
2
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
2
0
0
0
0
3
0
0
2
1
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
1
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
4
1
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
1
0
1
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
2
0
0
2
0
1
0
0
2
0
0
0
0
1
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
2
0
1
0
2
0
3
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
3
0
0
0
0
1
0
1
3
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
1
2
2
0
0
1
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
7
0
0
2
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
1
1
0
2
0
0
0
2
5
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
1
0
2
0
0
1
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
2
2
0
2
1
0
2
0
0
0
0
1
0
0
2
0
0
0
0
1
2
0
0
4
0
0
1
0
3
1
0
3
0
2
2
0
0
0
0
0
1
1
2
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
3
1
0
0
0
2
0
2
0
1
2
1
0
5
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
1
0
3
0
0
0
0
1
2
0
1
0
0
1
2
0
2
0
0
0
2
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
2
1
2
0
5
0
0
1
0
2
0
1
0
0
0
0
0
0
1
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
6
0
0
2
0
2
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
2
0
0
0
0
2
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
1
3
0
1
0
1
0
2
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
2
0
0
0
0
2
0
0
0
0
0
3
2
4
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
2
0
0
1
2
0
0
0
1
0
0
0
0
1
2
0
2
1
0
2
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
2
0
2
0
0
0
1
0
1
1
0
0
0
1
0
0
0
1
2
0
0
2
0
2
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
1
2
0
0
0
0
1
0
3
2
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
6
0
0
0
0
1
0
0
1
0
1
0
0
0
2
2
0
0
0
0
1
0
1
1
0
0
2
0
2
0
0
0
1
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
4
0
1
0
0
1
0
0
0
0
0
1
2
0
0
0
0
2
2
11
0
5
1
0
3
0
0
1
1
0
2
2
1
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
1
0
0
0
0
0
3
2
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
2
1
1
0
2
0
0
0
0
0
0
0
0
3
0
0
1
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
2
3
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
5
0
0
0
0
0
1
0
0
2
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
4
0
0
0
1
0
2
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
3
1
0
2
0
0
3
0
0
2
3
0
0
0
2
0
1
0
2
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
3
0
1
0
1
3
2
0
0
0
3
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
1
0
0
1
1
0
0
1
1
0
2
0
0
0
2
0
0
0
2
0
0
1
2
3
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
2
0
0
2
0
2
1
0
2
0
1
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
2
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
1
0
1
1
0
2
0
1
0
0
0
0
2
0
0
0
0
2
0
2
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
1
0
0
1
0
0
0
0
1
0
2
0
0
1
0
0
2
1
0
0
2
0
2
0
0
0
0
2
2
0
0
0
1
0
0
1
0
2
2
1
0
0
0
0
2
0
1
0
1
0
0
0
0
0
2
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
2
0
1
1
2
0
2
0
0
0
0
0
0
4
2
1
0
0
0
0
2
0
2
0
1
1
0
0
0
0
1
2
1
1
0
0
0
0
1
2
0
0
2
2
1
2
0
0
0
0
2
0
0
0
0
2
1
1
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
2
0
2
0
0
0
2
6
2
0
0
5
3
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
1
0
0
3
0
0
1
2
1
0
0
1
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
3
1
0
1
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
3
0
1
0
0
0
1
1
0
2
0
1
1
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
2
0
2
2
1
0
0
0
2
0
0
1
0
0
2
0
2
0
0
0
0
1
0
0
0
2
0
0
1
1
0
1
0
0
2
0
0
2
1
1
1
0
0
0
0
2
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
2
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
1
0
2
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
1
0
0
3
2
0
0
0
1
0
2
1
0
1
2
0
0
2
0
0
2
0
0
0
0
0
2
0
1
0
2
0
0
2
1
1
0
0
0
0
0
1
0
2
0
0
1
3
1
0
0
0
2
0
0
0
2
0
0
2
0
2
0
0
0
1
0
0
2
0
0
0
2
0
4
0
0
0
0
1
0
1
0
1
0
0
2
0
0
0
2
1
0
1
0
1
0
0
1
2
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
1
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
1
0
3
2
1
0
2
0
4
0
1
0
1
2
0
0
0
0
0
0
0
3
1
0
1
0
0
0
1
0
1
0
0
0
1
0
1
0
0
2
0
1
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
1
1
0
0
3
0
0
0
0
1
2
1
0
3
1
0
1
1
0
1
0
0
0
0
2
0
0
1
0
1
0
0
0
2
0
0
1
0
0
0
0
6
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
1
0
0
2
2
0
1
0
0
0
0
0
2
1
0
0
2
0
0
1
0
0
2
0
0
1
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
2
0
0
2
0
3
1
0
0
0
0
1
2
1
0
1
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
8
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
1
0
2
0
0
0
0
1
0
0
7
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
1
4
1
1
0
3
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
1
0
2
0
1
0
0
0
0
0
0
1
2
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
1
4
1
0
0
1
0
0
3
1
3
0
1
0
0
0
0
0
0
0
2
0
0
2
1
2
0
3
0
1
1
0
0
2
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
2
0
0
0
1
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
3
0
0
0
0
1
0
1
0
0
0
0
0
2
2
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
1
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
2
1
0
0
0
0
0
0
0
2
5
0
1
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
1
2
0
1
0
0
0
1
0
2
1
1
0
0
0
0
0
0
0
2
0
2
1
0
1
0
0
0
0
2
0
0
0
1
0
0
2
0
2
0
0
0
0
2
0
0
1
2
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
3
0
0
0
0
0
0
1
0
0
2
0
1
2
0
0
0
0
0
0
1
3
0
0
0
2
0
3
0
0
2
0
0
1
1
1
0
1
0
0
0
3
0
0
1
0
1
0
0
3
1
0
0
0
0
1
0
1
0
0
0
1
1
0
1
0
0
4
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
1
1
0
2
2
0
1
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
2
0
1
1
0
0
0
2
0
1
0
4
1
0
0
0
0
0
0
0
0
0
0
0
2
2
1
2
0
0
2
0
2
0
3
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
3
0
0
0
2
0
0
1
0
0
0
2
1
0
0
1
0
0
1
0
0
0
0
1
0
0
2
2
0
0
0
2
0
1
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
2
2
0
1
0
1
1
0
0
0
1
0
0
0
2
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
5
0
1
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
2
2
0
0
2
1
0
0
0
1
2
0
1
0
0
2
1
1
0
1
3
0
0
0
1
2
4
0
2
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
1
0
0
0
0
0
1
0
0
0
1
2
0
0
0
1
0
2
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
1
0
1
0
0
1
0
0
2
2
0
0
0
0
0
0
1
2
0
1
2
1
4
1
2
0
0
0
1
0
0
0
0
0
0
2
1
0
0
2
0
0
1
2
0
0
0
2
2
1
0
0
2
0
0
1
2
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
5
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
2
0
0
0
0
3
0
0
0
1
1
0
0
2
0
0
0
0
0
1
0
0
0
0
2
1
2
0
0
0
0
0
1
1
0
0
0
0
4
0
0
0
0
2
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
1
0
0
0
1
1
1
0
0
1
2
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
8
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
5
0
0
2
0
1
1
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
2
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
2
3
0
1
0
3
1
0
2
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
2
0
3
1
0
0
0
1
0
2
2
2
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
1
0
0
2
0
2
0
2
1
0
0
0
5
1
0
0
2
1
2
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
2
0
1
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
2
1
2
0
2
0
1
2
1
0
0
0
2
0
0
0
2
0
1
0
0
0
2
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
2
0
1
0
0
1
1
0
1
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
2
0
1
2
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
3
0
0
0
2
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
2
2
2
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
7
0
0
1
0
0
1
0
4
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
6
0
1
1
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
3
0
0
1
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
1
1
2
1
2
1
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
1
0
2
0
0
1
1
1
0
0
0
2
0
2
1
0
0
2
0
0
0
0
0
2
0
0
2
0
1
0
0
3
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
3
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
1
2
0
1
0
0
1
0
2
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
3
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
1
1
0
0
2
0
0
0
0
0
3
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
2
0
2
0
0
0
0
2
0
0
0
0
4
0
1
0
0
2
1
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
1
2
0
2
0
0
2
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
1
2
2
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
1
0
0
0
2
1
0
0
0
0
0
0
0
1
1
2
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
1
1
0
0
0
0
1
2
0
0
0
0
2
1
0
0
0
0
2
0
1
0
2
0
0
2
1
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
2
0
2
2
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
4
0
1
1
2
0
0
0
2
1
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
2
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
1
1
0
2
2
1
0
2
1
0
0
0
0
0
0
3
0
0
0
0
1
2
2
0
0
0
0
1
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
2
0
0
0
0
2
1
1
0
0
0
2
0
0
1
3
2
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
4
3
0
0
0
0
0
0
0
0
0
1
2
3
0
1
4
0
0
0
1
0
2
0
0
0
2
2
0
2
0
0
0
2
0
2
0
0
0
2
0
0
0
1
1
1
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
2
0
1
0
2
1
0
0
3
0
0
2
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
1
0
0
2
1
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
1
0
0
2
3
0
0
0
0
3
0
1
0
0
0
0
0
0
4
4
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
1
0
0
0
0
0
0
0
2
0
0
0
0
2
1
3
0
0
0
1
1
0
0
2
0
0
0
0
2
2
0
0
2
0
0
3
0
0
2
0
1
2
0
0
0
1
2
0
1
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
2
0
0
0
0
0
1
0
2
0
1
1
0
0
2
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
2
0
0
2
2
2
2
0
0
0
0
1
0
0
0
2
2
0
0
3
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
2
0
0
2
1
0
0
0
0
2
2
2
1
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
2
0
2
0
0
1
1
1
0
0
0
0
0
0
0
2
2
0
1
0
0
0
7
0
3
2
0
1
3
0
2
0
0
2
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
2
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
1
1
0
0
2
0
0
1
1
2
0
0
0
2
2
0
0
0
1
1
1
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
7
2
3
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
1
0
1
1
1
2
2
0
0
0
0
0
0
1
0
0
1
1
0
0
2
2
0
0
1
2
0
0
2
0
2
0
1
1
5
0
2
0
0
0
0
0
0
1
0
1
1
1
0
0
0
1
0
2
1
0
1
0
2
1
2
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
1
1
0
0
1
0
0
0
0
1
2
0
2
0
0
2
2
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
3
2
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
2
0
0
3
0
0
0
1
2
6
0
0
0
2
0
0
0
0
3
0
0
0
0
0
2
0
0
3
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
2
0
0
2
2
0
0
0
0
2
1
0
2
1
2
0
0
2
0
0
0
0
0
0
1
0
2
0
2
1
0
2
0
0
0
2
2
2
1
0
0
1
0
6
0
0
0
1
2
2
0
1
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
3
0
0
0
1
0
0
2
2
1
2
0
0
0
0
0
0
3
2
0
0
0
0
0
1
0
1
0
0
2
0
2
0
0
2
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
5
0
0
2
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
2
0
0
2
0
2
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
2
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
4
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
2
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
2
1
1
1
0
1
1
0
0
0
0
0
0
0
1
0
0
3
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
1
1
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
2
2
0
0
0
1
0
0
0
1
1
0
2
0
0
1
1
1
2
0
1
0
2
0
0
0
0
0
0
0
0
1
1
0
2
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
2
0
0
0
2
2
2
0
1
0
0
1
0
0
0
1
0
1
0
2
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
1
1
3
0
0
1
0
0
0
0
0
0
2
4
0
0
0
0
4
0
0
2
2
0
2
2
1
0
1
0
0
0
1
0
0
0
0
1
1
0
1
0
0
1
0
1
1
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
1
0
1
0
0
1
0
1
0
0
2
1
0
0
0
0
0
2
1
1
0
0
0
1
0
1
0
0
0
0
0
1
7
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
3
0
1
0
0
1
0
2
0
2
1
1
0
1
0
0
0
1
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
2
4
0
0
2
1
0
0
0
0
0
0
0
1
2
1
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
2
1
0
0
0
0
2
0
0
0
0
2
2
0
2
0
1
0
0
0
1
0
0
0
3
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
1
1
2
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
1
0
2
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
1
0
0
0
0
0
2
1
0
0
0
1
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
2
0
0
0
1
0
3
0
0
0
2
0
2
5
0
0
3
0
0
2
0
0
0
1
0
0
0
4
1
1
2
0
0
0
1
0
0
0
1
0
1
0
0
2
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
7
0
0
0
1
1
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
3
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
3
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
2
3
0
0
1
1
0
3
0
0
0
0
3
2
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
8
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
2
0
1
1
0
0
0
0
2
1
1
0
0
1
0
0
1
2
0
0
0
2
2
0
0
0
1
1
2
4
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
1
0
0
1
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
4
1
0
2
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
2
0
8
1
0
0
0
0
0
0
0
0
1
0
2
3
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
1
2
0
2
1
0
0
0
0
2
1
2
2
0
1
0
0
3
0
0
0
0
0
0
1
2
0
0
1
2
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
2
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
3
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
1
1
0
2
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
6
0
0
0
0
0
2
2
1
0
0
2
0
0
0
0
0
0
2
3
9
0
0
0
6
0
1
0
0
1
0
0
4
0
0
0
0
3
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
3
2
0
0
0
3
0
0
1
0
0
0
0
0
0
1
0
0
0
3
1
0
0
0
0
2
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
3
1
0
2
0
1
0
2
0
0
1
1
0
0
1
0
2
0
0
4
2
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
2
0
3
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
1
2
0
0
0
1
0
0
1
2
0
0
2
0
0
0
1
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
2
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
1
2
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
3
1
0
0
0
1
0
0
0
0
1
1
0
2
1
0
0
1
0
2
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
1
2
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
3
0
0
0
0
0
0
2
0
1
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
2
1
0
1
0
0
0
2
3
0
0
0
0
5
1
1
0
0
0
0
3
0
3
0
0
2
0
0
0
0
0
1
1
0
0
0
0
1
3
1
1
2
0
2
2
0
2
0
1
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
2
2
2
1
2
0
0
0
1
0
0
3
0
1
0
1
1
0
0
0
0
1
0
0
0
1
2
2
0
0
7
1
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
1
0
2
0
1
0
0
0
2
0
0
2
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
8
0
2
0
0
0
2
0
0
2
0
2
2
2
0
2
2
0
0
0
0
2
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
1
0
1
3
0
0
0
0
0
2
5
1
0
0
0
2
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
1
0
1
0
0
1
0
1
0
0
1
0
1
1
0
0
0
2
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
1
0
2
4
0
1
0
2
0
0
0
0
0
0
2
2
1
0
1
0
0
0
0
2
1
0
0
0
2
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
1
0
2
2
2
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
1
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
2
1
1
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
4
0
0
0
1
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
2
0
0
2
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
1
1
3
2
0
0
0
0
0
0
1
1
0
3
0
1
2
1
0
0
1
1
2
0
0
0
0
0
0
0
3
0
2
2
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
1
0
1
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
3
0
0
0
0
0
5
0
0
3
1
1
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
2
0
1
0
0
0
2
1
1
0
1
0
2
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
1
2
0
0
1
0
1
0
1
0
1
2
0
0
0
0
0
0
1
1
0
0
0
2
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
2
1
0
2
0
2
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
2
1
1
0
2
1
0
0
4
2
0
2
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
2
1
4
0
0
0
1
0
0
0
2
0
0
2
1
0
0
0
0
0
0
1
0
1
3
0
0
0
0
1
0
0
0
0
2
2
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
3
1
1
3
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
2
0
2
1
0
1
0
0
0
0
0
4
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
3
0
3
0
0
0
0
0
0
2
2
2
2
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
2
2
3
1
0
0
0
0
1
1
0
1
0
0
0
2
1
1
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
1
1
0
1
2
1
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
2
3
0
0
3
0
0
0
4
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
1
2
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
1
2
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
1
1
1
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
1
0
0
2
1
0
0
0
1
2
0
0
0
1
0
0
0
6
0
0
0
0
0
0
0
3
0
2
2
0
0
0
0
1
0
0
0
1
0
0
0
1
0
2
0
0
1
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
1
1
0
2
1
0
0
0
0
0
0
2
0
0
1
2
1
0
0
0
0
1
2
1
1
0
1
2
0
2
1
0
0
3
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
3
1
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
4
0
0
0
2
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
3
1
2
2
2
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
4
0
2
3
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
1
0
0
2
1
1
3
4
0
0
0
0
0
2
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
3
0
0
0
0
0
0
0
1
0
2
0
1
1
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
2
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
1
2
2
0
0
0
2
2
1
0
0
0
1
1
0
1
0
0
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
2
0
0
0
2
1
0
0
0
0
0
2
0
0
0
2
0
0
0
5
0
2
1
0
1
1
0
0
1
1
2
2
0
1
0
0
2
0
0
0
0
0
2
2
0
0
1
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
1
0
1
1
0
0
1
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
1
2
1
4
1
0
0
0
0
0
0
0
0
0
1
1
3
0
0
0
2
0
12
0
0
0
0
0
0
1
1
2
0
0
0
1
0
0
2
0
0
0
1
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
2
0
2
0
0
1
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
2
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
2
0
0
3
0
1
2
0
2
0
0
0
0
2
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
2
2
0
2
0
0
1
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
2
0
0
1
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
1
0
0
2
2
2
2
1
0
0
0
2
2
0
0
0
0
1
0
2
2
0
0
0
2
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
2
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
1
2
0
0
0
3
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
4
0
0
0
2
2
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
3
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
1
2
0
1
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
3
1
0
0
2
1
1
0
0
1
0
1
0
1
0
0
1
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
2
0
0
0
0
1
2
1
2
0
0
0
0
0
0
0
2
0
2
2
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
5
2
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
1
1
0
0
0
0
0
3
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
5
0
3
2
1
0
0
0
1
0
0
0
2
1
0
2
0
0
1
0
0
0
0
0
0
0
2
1
0
0
2
0
0
3
2
2
2
0
0
1
2
0
0
0
0
1
0
0
2
2
0
0
0
2
0
2
0
0
1
1
0
0
2
0
2
0
0
0
4
1
0
1
2
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
10
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
8
0
0
0
0
0
1
0
0
0
2
2
0
1
0
2
0
0
2
1
1
0
0
1
0
1
0
0
2
0
0
3
0
2
2
1
0
0
1
0
2
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
1
0
0
0
1
0
1
0
1
2
0
0
0
0
2
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
1
4
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
3
1
0
2
0
1
0
1
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
2
0
0
0
1
1
0
0
0
2
0
0
0
2
0
0
2
4
0
1
1
1
0
0
0
0
0
1
1
0
1
1
2
0
1
0
0
0
2
1
0
0
0
0
0
3
0
2
0
0
0
0
2
2
0
0
1
0
0
0
1
2
0
1
2
0
2
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
2
2
1
0
0
0
0
0
0
0
3
0
0
0
1
0
0
1
0
0
0
0
0
2
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
9
0
0
0
0
4
0
2
1
0
0
0
0
1
1
3
2
0
1
0
0
2
0
0
1
0
1
0
0
0
0
0
0
2
0
2
0
0
1
0
2
0
0
0
2
0
2
0
0
0
0
0
1
2
0
2
0
0
0
0
2
6
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
1
0
1
2
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
1
1
1
0
0
0
2
1
0
0
0
0
0
0
2
0
3
0
0
1
2
2
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
3
0
1
2
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
3
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
2
0
0
0
7
0
0
0
0
0
0
2
0
0
0
0
0
2
1
1
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
3
0
1
0
2
0
0
0
2
0
0
2
0
0
3
1
0
1
0
2
0
1
0
0
1
0
1
0
2
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
3
0
1
0
2
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
2
2
0
1
0
1
0
0
1
2
0
2
0
0
0
0
2
1
2
1
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
2
1
0
0
0
0
0
1
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
2
0
0
0
0
0
0
1
1
3
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
1
0
2
0
0
0
1
1
0
0
0
1
0
0
0
0
0
2
0
0
1
1
0
2
1
0
0
2
0
0
0
0
0
2
2
0
2
1
2
4
2
1
3
0
0
2
1
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
1
1
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
3
0
0
1
0
0
0
1
0
0
1
1
3
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
1
2
0
0
2
0
1
2
0
0
1
0
2
2
0
2
2
0
0
3
0
0
2
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
1
1
0
0
7
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
2
1
0
0
2
0
0
3
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
2
2
0
0
0
0
2
2
0
0
2
1
0
0
0
0
0
0
2
0
2
2
0
1
0
0
1
0
2
1
1
2
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
3
2
0
1
2
0
0
2
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
3
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
3
4
1
0
0
0
0
1
0
0
0
1
0
1
0
2
0
0
1
0
1
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
1
2
0
0
0
0
0
1
1
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
1
2
0
0
0
0
9
0
0
0
1
1
0
0
0
0
1
4
0
0
0
0
0
0
2
1
0
0
1
2
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
3
1
1
11
0
0
5
0
0
0
1
0
0
1
2
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
2
0
0
1
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
1
2
0
1
0
1
2
1
0
0
0
0
0
0
2
0
4
0
0
2
0
0
2
1
0
2
3
2
0
0
1
0
0
0
0
3
0
0
0
0
0
0
1
0
0
2
0
0
1
1
1
0
0
0
2
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
2
1
0
1
0
0
2
0
0
0
0
0
2
2
0
2
2
2
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
11
2
2
0
1
0
2
0
0
1
1
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
2
1
0
0
1
0
0
0
1
0
0
0
1
0
0
3
0
2
0
2
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
6
0
1
0
0
1
0
0
0
1
0
2
0
2
4
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
5
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
1
0
0
0
0
1
6
0
2
0
0
0
0
0
0
1
2
2
0
0
1
1
0
0
0
0
0
0
0
2
1
1
0
0
0
1
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
1
0
0
2
2
2
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
3
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
1
3
0
2
0
0
0
2
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
2
1
1
2
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
3
0
0
0
1
0
0
1
2
0
1
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
2
0
0
2
0
0
0
2
1
1
0
1
0
0
0
0
0
2
0
0
1
2
0
2
0
2
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
1
1
1
0
0
2
0
2
0
2
1
0
2
0
2
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
3
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
1
0
2
2
1
0
0
0
0
1
0
2
1
0
0
0
0
1
1
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
1
0
3
0
0
0
0
0
1
2
0
0
0
1
1
0
0
0
0
1
0
0
0
1
2
0
0
1
0
2
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
1
1
1
0
0
1
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
3
0
0
0
1
1
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
1
0
2
0
0
1
0
0
3
1
0
0
0
4
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
2
0
0
2
2
0
0
0
2
1
0
2
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
1
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
2
1
0
3
0
2
0
0
0
0
0
1
1
0
1
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
2
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
1
3
1
0
0
2
0
0
0
3
0
0
0
0
1
0
1
0
0
0
0
1
2
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
3
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
2
2
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
1
1
1
0
0
2
2
6
2
0
0
0
0
2
0
0
2
1
1
0
0
2
0
1
2
1
0
2
0
0
1
0
2
0
0
0
0
1
0
0
0
3
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
2
0
0
0
2
0
1
1
0
0
2
2
0
1
1
0
0
0
0
2
1
2
0
0
2
0
0
0
0
0
1
0
1
0
2
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
3
2
0
2
0
2
0
0
0
0
0
0
0
1
2
5
2
0
0
0
0
0
1
1
0
0
2
2
0
0
0
0
0
0
0
0
2
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
2
0
1
3
2
0
0
5
2
0
0
2
0
1
0
2
1
2
2
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
2
2
0
0
1
0
2
0
0
0
0
1
0
0
2
0
0
2
0
0
0
2
2
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
1
3
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
2
0
3
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
1
0
1
3
0
2
0
1
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
2
0
0
0
0
0
1
2
0
0
0
0
0
3
2
2
2
0
1
0
0
0
0
0
0
2
1
0
1
1
0
0
2
0
0
1
0
0
0
2
0
1
1
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
2
1
0
2
2
0
0
3
2
0
0
0
0
2
1
0
2
1
2
0
0
0
3
0
0
0
0
1
0
0
0
0
0
8
0
0
2
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
8
0
0
1
0
0
2
1
0
0
2
1
0
0
0
0
1
0
0
0
1
0
0
1
0
2
0
0
2
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
2
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
2
0
3
0
1
0
2
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
2
1
0
0
2
1
0
0
2
0
2
0
1
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
1
3
0
2
5
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
2
2
1
0
0
0
1
0
0
1
2
0
2
0
2
0
1
0
1
0
0
0
0
2
2
0
1
0
0
0
0
0
0
2
0
0
0
1
0
6
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
2
1
0
0
0
2
0
0
2
0
4
0
0
0
0
0
0
1
2
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
1
1
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
1
0
0
0
5
2
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
2
0
1
0
0
2
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
3
1
0
0
0
0
1
0
0
2
0
0
1
2
0
0
0
0
2
0
0
0
0
0
1
2
0
1
0
0
0
2
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
4
1
0
0
0
0
0
0
1
0
0
1
0
2
0
0
1
0
0
3
0
0
0
0
0
2
0
0
1
0
1
1
0
2
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
4
0
0
0
0
0
0
0
1
2
2
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
2
0
2
0
0
1
0
0
2
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
3
0
0
1
0
0
0
0
3
0
1
0
0
1
0
0
0
2
0
0
2
0
2
0
1
0
2
0
0
1
0
1
0
0
0
0
2
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
2
1
0
0
0
0
1
2
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
2
0
0
0
1
1
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
5
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
1
0
0
0
0
0
0
2
0
0
2
0
2
0
5
0
0
0
0
0
0
1
2
0
0
1
0
0
1
0
0
0
0
0
9
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
2
0
0
1
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
4
0
2
0
0
0
2
0
3
5
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
2
0
1
3
1
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
1
0
2
0
2
0
2
0
0
0
0
0
1
2
1
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
4
0
0
0
2
0
2
0
0
0
0
2
3
0
0
0
0
0
0
1
0
2
0
0
0
2
0
1
0
0
1
0
4
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
1
0
0
0
2
1
1
0
0
2
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
2
1
1
0
0
2
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
2
0
1
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
2
0
0
0
0
1
2
2
0
2
1
0
0
5
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
1
1
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
1
1
2
0
0
0
0
1
0
1
1
2
1
2
0
0
0
0
0
2
0
2
2
1
1
0
0
0
0
1
0
2
1
4
2
3
0
2
0
0
0
1
0
0
2
0
1
2
0
1
3
1
0
0
0
1
2
0
0
2
2
2
0
0
0
0
0
0
0
2
1
0
1
0
0
1
0
1
0
0
2
0
0
2
0
1
1
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
2
0
1
1
0
0
0
1
0
0
1
0
1
0
1
0
0
2
0
4
0
2
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
3
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
3
0
1
3
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
2
0
1
0
2
2
6
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
2
1
0
0
0
0
2
0
0
2
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
2
0
0
1
0
0
2
0
2
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
2
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
2
1
1
0
0
0
0
2
0
0
1
0
0
0
0
1
1
0
0
1
0
0
2
1
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
2
2
0
0
0
2
0
0
1
0
0
0
0
1
0
0
2
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
3
0
0
1
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
1
2
0
0
0
0
0
0
2
1
4
0
0
0
0
1
1
0
1
0
0
3
0
2
0
0
0
0
2
0
1
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
2
0
0
2
1
0
0
1
0
0
0
2
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
2
0
0
0
1
0
0
0
0
1
0
0
1
4
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
2
2
0
2
0
0
2
0
0
0
0
0
0
4
0
0
1
1
2
1
1
1
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
1
0
0
2
0
0
0
0
2
0
1
2
1
2
0
0
2
1
0
2
2
0
0
1
0
0
0
0
1
2
1
2
0
1
2
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
1
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
2
0
0
1
1
2
0
1
0
0
1
2
0
0
2
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
1
0
1
2
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
2
0
2
0
1
0
0
1
2
0
0
2
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
2
1
0
1
0
0
0
0
0
0
1
1
0
1
0
1
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
1
1
2
1
0
4
0
0
0
0
1
0
0
1
0
1
1
4
3
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
1
0
0
0
0
0
1
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
3
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
3
0
0
2
0
0
1
1
0
0
3
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
1
0
0
2
0
0
1
0
0
0
0
4
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
2
0
1
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
2
0
0
1
2
0
0
0
2
0
1
0
3
0
0
0
0
2
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
1
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
1
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
6
0
0
0
0
0
0
2
0
2
1
0
1
0
2
0
0
1
0
0
0
2
2
2
0
1
2
1
0
0
0
2
0
1
1
0
0
0
0
0
2
0
1
0
6
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
2
0
0
0
0
3
0
0
1
0
0
2
0
0
0
0
1
0
0
0
2
2
0
0
0
1
0
0
2
2
0
2
0
0
0
3
0
0
0
0
1
0
0
0
5
2
2
0
1
0
0
0
1
0
0
0
0
3
1
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
1
1
0
0
1
0
2
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
2
0
3
2
0
2
4
0
0
1
0
0
5
0
0
0
0
0
1
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
1
2
1
1
0
0
0
0
0
0
1
0
1
0
1
3
0
2
0
0
1
0
0
0
0
2
0
1
1
0
0
0
1
0
0
0
0
2
5
0
0
0
2
0
3
1
1
1
3
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
2
2
0
0
5
3
0
0
0
0
0
0
0
1
2
1
2
0
1
1
0
0
0
0
1
2
2
2
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
2
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
1
0
4
0
2
0
0
1
0
0
0
0
0
0
0
0
0
4
2
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
2
0
1
1
3
0
2
1
0
2
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
6
1
1
0
0
0
0
0
0
2
0
2
1
1
0
1
2
0
0
0
0
1
0
0
0
1
0
0
1
0
0
2
0
0
0
0
3
1
0
0
0
0
0
0
0
1
0
0
7
0
1
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
2
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
2
1
0
0
0
0
0
0
2
0
0
1
1
1
2
0
4
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
1
0
1
1
1
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
2
0
0
0
0
4
0
0
0
0
1
2
0
2
0
1
0
0
2
1
0
0
0
0
2
0
0
0
0
1
0
2
0
2
0
2
0
1
0
0
0
0
0
0
1
3
1
0
2
2
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
2
2
1
0
0
0
1
0
0
0
1
0
0
1
0
2
1
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
3
0
0
1
0
0
0
0
0
1
0
2
0
0
1
1
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
1
2
0
2
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
1
2
0
0
2
2
0
1
0
0
0
1
1
1
0
2
0
1
0
0
1
0
1
0
0
1
0
0
2
2
4
0
0
1
0
1
2
0
0
0
0
0
0
1
1
0
1
2
0
3
2
0
0
0
0
2
0
2
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
1
2
2
4
0
0
0
0
0
1
2
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
4
0
2
2
0
1
0
0
0
0
0
0
0
2
0
0
1
0
7
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
2
1
1
0
0
0
2
1
0
0
0
0
0
0
1
4
0
0
0
2
0
0
2
0
1
1
0
0
0
0
2
0
0
0
2
2
1
0
1
8
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
2
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
5
0
0
2
0
0
0
0
1
0
0
1
1
4
0
0
0
2
0
2
2
0
1
0
1
0
0
0
0
2
0
1
0
0
3
0
0
2
2
0
0
0
2
0
0
0
0
1
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
2
0
0
0
0
2
0
1
0
0
0
0
4
0
1
0
0
0
0
1
0
0
0
0
0
1
4
0
2
0
1
0
0
0
2
3
0
2
0
0
2
2
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
2
2
2
0
0
0
0
0
0
1
0
3
0
2
0
2
0
1
2
0
0
0
2
0
1
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
1
3
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
2
1
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
2
1
0
1
2
0
0
1
0
2
1
0
0
2
0
2
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
2
1
0
1
0
1
1
4
0
1
2
2
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
4
1
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
1
2
2
2
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
2
0
1
2
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
2
1
0
1
0
2
0
2
0
2
2
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
4
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
3
0
2
0
0
0
0
1
2
0
0
0
2
0
1
0
0
0
2
0
3
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
3
2
8
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
1
0
0
2
2
0
1
0
2
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
2
3
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
1
0
2
2
3
0
3
0
0
2
0
0
0
0
0
1
0
2
0
1
2
0
0
1
0
1
0
0
0
0
0
0
0
0
2
1
0
1
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
1
1
0
2
0
0
1
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
2
0
2
0
1
0
0
1
0
2
0
0
0
2
2
4
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
2
2
2
0
1
0
0
1
0
0
2
1
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
2
2
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
1
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
3
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
3
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
2
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
1
2
0
1
0
0
1
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
2
0
2
5
0
0
2
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
1
2
1
0
0
0
0
2
0
0
0
0
0
0
6
0
0
2
2
1
2
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
1
2
0
1
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
2
0
0
2
0
1
0
0
2
0
0
0
0
1
0
1
0
0
0
1
2
2
3
0
2
0
0
0
1
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
1
2
0
1
1
2
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
2
2
2
2
0
0
0
3
2
1
0
1
0
0
2
2
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
1
1
1
0
0
0
1
1
0
2
0
1
0
0
0
1
2
0
2
0
2
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
1
0
2
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
1
0
0
5
3
0
1
2
0
0
0
0
2
0
2
2
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
1
2
0
0
0
0
1
2
1
0
0
0
0
0
0
1
0
0
0
0
2
2
0
2
0
2
2
0
0
1
0
0
0
1
2
1
0
0
0
0
2
2
0
0
0
0
0
2
2
2
1
1
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
2
2
0
0
0
0
0
0
0
5
0
0
2
0
0
2
0
0
0
1
2
2
0
2
0
0
1
0
1
0
0
0
0
0
2
0
1
0
1
0
0
1
1
0
0
0
2
2
1
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
2
0
0
3
2
0
0
2
0
2
0
0
0
2
0
2
0
0
2
0
0
0
0
2
0
1
0
0
3
0
0
0
1
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
4
0
1
0
0
0
2
0
0
2
0
0
3
2
0
0
3
0
2
2
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
3
0
0
0
3
0
0
0
0
0
0
2
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
3
2
0
0
1
4
0
0
3
0
2
0
0
2
2
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
1
0
1
0
2
0
0
2
0
0
3
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
2
2
2
3
0
0
2
1
0
1
0
0
1
2
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
3
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
1
0
0
0
0
0
1
0
2
0
2
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
2
0
0
0
1
0
0
0
2
1
0
0
0
1
0
0
0
0
1
0
2
1
1
1
0
3
0
0
0
0
0
0
0
1
1
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
1
1
0
0
2
0
1
0
0
0
1
2
1
1
0
1
3
0
0
2
2
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
2
0
0
0
2
1
0
4
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
1
0
5
0
1
0
0
0
0
0
0
1
0
1
1
0
2
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
3
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
3
1
2
0
0
2
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
2
0
0
1
0
2
0
0
2
0
1
0
0
1
2
0
0
0
0
2
0
0
0
0
5
0
0
1
2
0
0
0
0
1
3
0
0
0
0
0
1
2
0
1
0
0
0
1
5
0
0
1
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
3
0
1
0
0
1
0
0
0
0
1
1
1
2
1
2
0
0
1
0
0
0
0
1
2
0
1
0
0
0
0
0
2
0
2
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
2
2
0
0
0
0
0
0
1
0
0
3
0
0
0
0
2
0
2
0
0
0
0
1
2
1
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
2
2
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
1
0
1
0
0
0
2
0
2
0
0
0
2
2
0
2
0
0
0
0
2
0
0
0
0
0
0
2
2
3
0
1
2
4
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
2
0
0
0
0
1
0
2
0
1
0
0
3
0
1
1
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
1
3
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
2
4
0
2
2
0
0
1
0
0
0
1
0
2
1
0
0
0
0
1
0
1
1
2
0
2
0
0
2
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
4
3
0
0
0
0
0
2
0
1
0
1
2
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
1
0
1
0
1
0
0
2
0
0
1
0
0
0
2
2
1
1
0
0
0
0
0
0
0
2
1
0
0
2
0
0
2
0
0
2
1
0
0
3
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
2
0
2
0
3
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
1
0
1
0
0
0
1
1
1
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
3
0
0
0
1
0
0
0
0
2
1
1
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
1
2
2
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
2
0
0
3
2
2
0
3
0
0
0
2
0
0
0
1
1
0
1
2
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
1
0
0
1
0
0
0
1
0
2
0
0
2
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
3
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
2
0
0
1
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
4
2
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
2
1
0
0
0
0
1
1
0
3
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
1
1
0
0
1
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
4
1
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
2
2
3
0
0
0
0
1
0
0
0
0
2
0
2
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
1
0
0
1
2
0
3
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
3
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
1
0
3
2
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
2
1
0
0
0
1
0
1
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
2
3
0
3
1
0
0
0
0
1
0
5
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
2
1
0
1
0
0
0
0
0
0
3
0
0
0
3
0
0
0
0
0
0
2
0
1
0
2
0
0
1
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
2
3
0
0
0
0
0
0
0
1
0
2
0
5
2
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
1
0
0
0
0
0
1
0
0
2
2
0
0
0
0
1
0
2
1
0
0
0
1
0
0
0
4
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
2
0
1
1
0
0
0
0
1
0
3
0
0
0
1
0
1
0
2
0
0
0
0
1
0
2
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
1
1
0
0
0
0
0
0
0
0
5
0
7
0
2
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
2
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
3
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
3
0
0
0
0
2
0
0
1
0
0
1
0
0
1
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
1
0
0
2
3
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
2
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
2
0
2
0
0
1
1
0
1
0
0
1
0
0
2
1
0
0
0
2
1
1
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
1
1
3
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
3
0
2
0
1
3
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
2
1
2
0
0
1
0
0
0
0
0
3
0
2
0
0
1
0
0
1
0
0
0
2
0
0
0
0
1
1
1
1
0
0
2
0
2
0
0
0
0
0
2
0
0
0
6
1
0
0
0
0
2
0
1
0
0
0
0
0
2
0
2
0
0
0
4
2
2
0
0
2
0
1
1
0
0
0
0
0
1
0
0
0
2
1
0
0
2
0
0
1
1
0
0
0
0
0
0
1
2
0
1
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
1
2
1
0
1
1
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
5
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
1
0
0
1
2
0
0
0
0
1
0
0
0
0
0
2
2
2
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
1
0
1
0
1
0
0
2
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
3
0
2
0
0
0
0
0
0
1
2
1
2
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
1
2
1
0
0
0
0
0
1
2
0
2
2
1
0
0
0
0
0
0
0
0
15
0
0
2
3
2
0
0
1
0
2
1
3
0
0
0
0
0
0
1
0
1
0
0
2
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
4
0
0
3
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
2
2
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
2
0
1
0
1
0
1
0
0
0
1
2
0
0
0
0
1
1
0
2
0
0
0
0
1
1
1
0
0
0
1
0
1
2
3
0
2
0
0
2
2
0
0
0
0
1
3
0
0
0
0
0
1
2
2
0
1
1
0
2
0
0
1
0
0
0
4
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
2
6
0
0
0
2
0
0
2
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
2
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
2
3
0
0
1
0
0
0
1
0
0
0
2
1
1
2
0
2
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
1
0
3
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
2
2
0
0
2
0
0
0
0
0
1
0
1
0
2
2
0
0
0
0
0
2
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
1
2
2
0
0
0
1
0
0
0
1
0
1
2
1
0
0
0
0
2
0
0
0
0
2
1
2
0
0
0
1
2
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
4
0
0
1
0
1
2
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
3
0
1
2
1
0
0
4
2
0
1
1
1
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
1
0
0
0
0
1
2
0
2
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
3
2
1
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
2
0
0
1
0
1
0
2
0
3
2
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
2
0
0
0
1
0
0
1
1
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
2
0
1
0
1
0
2
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
1
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
4
0
1
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
2
0
0
1
0
1
2
0
0
2
0
2
0
1
0
0
2
0
0
0
0
0
0
1
0
0
2
0
1
0
0
1
2
0
1
0
0
0
0
0
0
0
2
0
0
2
3
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
2
2
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
9
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
1
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
3
1
0
1
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
1
0
2
1
0
0
0
1
1
2
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
3
4
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
5
0
0
2
2
0
0
0
1
0
0
1
0
0
2
0
0
0
1
0
0
0
2
1
0
0
0
3
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
3
0
0
1
2
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
3
0
0
2
0
1
2
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
2
1
0
1
2
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
2
0
0
0
2
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
1
2
0
0
1
0
2
0
0
0
0
0
0
1
0
2
2
1
0
0
0
0
0
0
0
2
0
0
0
2
1
1
2
0
0
0
2
0
0
0
0
0
1
1
3
2
1
2
1
0
0
0
0
0
1
2
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
1
0
2
0
0
11
0
1
0
1
0
4
1
2
0
0
0
1
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
1
0
4
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
1
0
0
0
1
0
0
0
0
1
2
0
0
1
0
1
0
0
1
0
0
1
0
2
0
1
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
2
0
0
1
1
2
0
1
0
0
0
0
2
3
0
1
0
1
4
1
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
3
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
2
3
1
1
2
0
0
0
1
3
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
2
1
2
2
0
0
2
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
3
0
0
0
2
0
2
0
0
0
1
0
0
3
0
2
1
0
0
0
0
0
0
0
0
0
1
2
0
4
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
2
1
2
0
0
0
1
1
0
0
0
2
0
0
0
2
1
0
0
0
0
0
1
1
0
2
1
0
2
1
0
0
0
1
0
0
0
0
1
2
0
0
0
0
6
0
0
1
2
0
9
2
0
0
0
0
1
0
1
1
0
0
0
0
0
2
2
1
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
2
1
1
0
0
2
0
0
0
0
2
2
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
2
0
0
1
0
0
0
1
0
0
2
0
0
1
0
2
1
0
0
0
0
2
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
1
2
1
0
0
0
0
1
0
0
0
2
0
0
2
2
4
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
2
0
0
0
2
1
1
0
0
0
0
0
2
0
0
0
2
2
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
2
2
1
2
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
2
1
1
0
0
0
0
0
1
1
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
1
1
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
1
0
0
0
0
2
1
0
0
0
1
0
0
2
0
1
0
0
0
1
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
1
2
0
1
0
0
4
0
0
0
0
1
0
0
4
0
0
0
2
0
2
3
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
1
2
3
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
4
0
2
3
1
0
1
0
1
1
0
1
0
0
0
1
0
0
2
1
0
2
0
0
0
0
0
0
1
0
0
0
1
0
1
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
1
2
0
0
0
1
0
0
2
0
0
0
0
2
0
2
3
0
0
4
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
2
0
0
4
0
0
1
2
2
0
0
1
0
2
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
4
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
1
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
2
1
0
0
0
0
1
2
0
2
1
1
1
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
3
0
0
2
0
0
1
0
0
2
3
1
0
0
0
2
0
0
1
0
0
1
1
0
1
0
0
0
0
0
1
0
0
2
1
0
0
0
0
3
0
0
0
0
0
0
0
4
0
3
1
1
0
1
2
2
0
0
0
1
0
1
0
0
0
1
0
0
0
2
2
0
0
0
1
2
0
0
2
1
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
2
0
2
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
1
1
1
0
2
0
0
1
0
0
2
1
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
3
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
7
0
2
2
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
1
0
0
0
0
0
1
0
2
0
0
2
0
1
1
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
1
2
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
2
0
0
1
0
1
0
1
0
2
2
0
0
0
0
1
0
0
0
2
1
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
2
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
1
1
0
0
2
0
3
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
2
2
0
0
0
0
1
1
1
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
18
0
0
0
1
0
1
0
0
1
1
0
2
1
0
0
2
2
3
0
2
0
0
2
2
0
2
0
1
0
2
0
2
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
2
0
2
2
0
1
2
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
1
0
2
4
2
1
0
1
2
0
1
0
0
8
0
0
0
2
1
0
0
0
3
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
1
0
0
1
0
0
0
3
0
0
0
0
0
2
0
0
0
2
1
0
0
0
2
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
2
0
2
1
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
1
2
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
1
0
2
0
0
2
0
2
1
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
2
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
3
0
4
0
0
0
0
0
0
0
2
0
0
2
2
0
3
2
0
0
2
3
0
2
0
0
0
1
0
0
2
0
0
1
0
1
0
1
0
3
1
0
4
2
2
0
0
0
2
0
2
0
0
3
1
2
0
0
0
0
2
5
0
2
0
0
2
0
1
0
0
2
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
2
0
1
1
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
1
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
1
1
1
0
0
0
1
0
0
1
2
0
0
0
1
1
1
0
0
0
0
2
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
1
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
2
0
0
0
0
1
0
0
2
4
0
0
0
0
0
0
0
2
3
0
2
0
0
0
0
2
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
2
0
1
0
0
1
0
0
0
0
1
0
2
2
1
0
2
0
0
0
2
0
0
0
0
0
3
0
0
4
0
0
0
2
0
1
0
2
0
0
0
0
2
0
0
0
1
2
2
2
0
2
1
2
0
1
0
2
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
2
0
0
0
3
0
0
2
1
0
0
0
0
1
0
2
0
0
2
0
0
0
3
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
2
1
0
0
0
2
2
0
0
2
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
3
2
0
2
3
0
0
0
0
0
1
2
0
0
0
2
0
1
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
4
0
0
0
4
0
0
0
1
0
2
2
2
0
0
2
2
0
0
0
0
2
0
0
0
1
0
0
0
2
0
2
0
2
0
0
0
0
2
3
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
2
0
0
2
1
0
1
0
0
1
0
2
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
1
0
1
0
0
2
0
1
0
1
0
1
0
1
1
0
0
0
0
3
0
2
0
0
0
1
1
2
1
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
1
1
2
0
0
1
0
0
2
0
2
0
0
2
0
2
0
0
0
1
2
2
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
1
4
0
1
0
0
0
0
2
2
2
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
3
2
1
0
1
0
0
0
1
1
0
4
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
7
4
0
0
0
0
0
0
1
1
3
2
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
2
2
0
2
0
0
0
0
1
2
0
0
0
2
2
0
0
2
0
2
3
0
2
0
2
0
2
1
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
1
0
1
0
0
0
0
1
2
2
0
0
0
1
0
1
1
0
1
1
1
0
0
0
1
0
0
0
1
0
0
2
0
0
1
0
0
1
2
0
2
0
0
0
1
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
3
0
0
3
1
0
1
0
0
0
0
0
0
3
0
2
0
2
0
1
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
2
1
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
2
0
2
0
2
2
0
0
1
0
1
0
1
0
2
1
1
1
1
0
0
2
0
0
1
0
0
1
0
0
1
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
2
3
0
0
0
0
0
1
2
0
3
1
0
0
0
2
0
0
2
1
0
0
0
0
2
0
0
0
1
0
1
1
1
0
1
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
1
0
0
0
0
4
0
0
0
0
2
1
0
2
0
3
0
0
2
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
2
3
0
0
0
0
2
0
1
2
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
4
1
0
3
1
0
2
1
0
0
0
0
1
0
0
0
0
1
2
2
0
0
1
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
2
3
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
3
0
0
2
0
1
2
2
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
3
0
2
0
1
2
0
0
2
0
0
0
0
0
2
1
2
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
1
0
2
0
2
0
0
2
0
0
0
2
0
0
0
0
0
1
1
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
1
2
1
0
0
2
0
0
0
2
0
0
2
6
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
3
0
2
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
1
0
0
0
2
0
2
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
2
0
2
0
1
2
0
2
0
1
0
0
0
0
1
2
0
0
0
1
2
0
0
0
0
0
0
1
1
0
0
0
0
1
2
2
2
1
0
3
0
3
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
3
0
2
1
1
0
0
2
1
2
1
0
1
2
2
0
1
0
0
1
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
2
2
1
0
0
0
2
2
0
0
1
1
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
1
0
0
3
3
0
0
2
0
0
0
1
0
1
2
0
1
0
0
2
2
0
2
0
2
1
0
0
0
1
0
0
0
1
2
0
1
1
0
0
0
0
0
0
1
3
0
0
0
0
0
0
1
0
1
2
0
1
0
5
0
2
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
3
1
0
2
2
2
1
2
0
2
0
2
0
1
2
1
0
0
0
5
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
1
1
0
1
0
1
0
0
3
0
1
0
0
0
0
0
1
1
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
2
2
2
0
0
0
0
0
3
18
0
3
0
2
2
0
0
2
3
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
2
0
0
0
0
1
1
0
0
0
0
2
2
0
0
0
0
0
2
0
0
2
0
0
2
3
0
2
2
0
3
0
0
0
1
0
2
0
0
0
0
0
0
4
0
2
2
1
2
2
0
0
2
0
2
0
1
2
0
0
0
0
0
1
1
0
2
0
0
0
0
2
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
3
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
1
0
2
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
6
2
0
0
0
0
0
2
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
2
0
0
2
0
2
0
1
0
0
0
1
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
1
0
0
0
2
0
0
2
0
2
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
2
0
2
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
1
0
0
4
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
2
1
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
2
0
0
2
3
0
0
0
0
3
0
0
0
0
2
2
0
2
0
0
0
0
2
0
1
0
3
1
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
1
2
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
2
3
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
1
2
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
3
0
0
3
0
0
2
0
0
1
0
0
4
0
2
0
0
0
1
0
2
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
1
1
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
1
0
0
0
2
1
0
0
1
0
2
0
0
0
2
0
0
4
0
0
0
1
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
2
2
2
0
0
0
1
0
0
0
1
0
0
0
1
1
0
2
0
0
1
0
0
0
0
3
0
2
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
2
2
0
0
3
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
2
2
2
0
0
0
0
0
0
0
0
1
4
0
1
1
0
2
2
0
0
0
0
0
0
0
0
0
2
2
0
1
2
0
1
0
0
0
0
2
0
1
2
1
2
2
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
4
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
1
0
0
0
2
0
2
0
0
2
1
3
0
0
2
2
0
1
0
0
0
0
0
1
0
3
1
2
1
0
0
0
0
1
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
2
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
2
0
1
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
2
2
1
0
0
1
1
0
2
0
2
0
0
0
1
0
0
2
2
0
0
0
1
0
0
0
2
0
2
0
0
1
1
0
0
0
0
0
0
0
2
0
2
0
2
2
0
0
2
0
0
0
0
0
2
2
2
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
1
3
0
0
0
1
0
0
2
0
1
0
1
2
0
2
0
2
2
0
4
0
2
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
1
2
0
0
2
0
0
0
2
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
1
1
2
1
0
0
2
3
0
0
0
0
0
0
2
0
0
0
0
4
0
0
2
2
2
1
0
0
2
1
0
0
0
0
0
6
1
0
0
1
1
1
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
1
0
0
0
1
0
0
0
0
2
0
1
0
0
2
1
1
0
0
0
1
2
0
1
0
1
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
6
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
1
0
0
0
2
1
0
0
0
0
1
1
0
0
1
0
0
6
3
1
1
2
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
2
1
2
3
0
3
0
0
0
1
1
2
0
0
0
0
0
1
0
0
0
0
1
2
0
1
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
1
0
2
1
0
0
0
0
1
1
1
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
1
1
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
4
2
0
1
0
0
0
0
0
0
0
4
0
0
0
0
1
1
0
0
0
2
0
0
0
0
2
0
1
2
0
0
2
0
2
0
3
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
3
0
0
0
2
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
4
0
0
0
0
2
0
0
2
0
2
0
0
2
2
0
0
0
0
3
0
2
0
0
2
0
2
0
0
2
0
0
0
0
0
0
1
2
1
0
0
0
1
2
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
2
0
1
2
0
0
0
0
1
0
1
0
0
1
2
1
0
0
1
6
0
2
0
0
2
4
0
2
1
1
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
3
2
0
3
0
0
0
0
1
0
0
1
2
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
3
2
2
0
0
0
0
0
1
0
2
1
0
1
2
0
0
0
0
0
2
0
0
0
1
1
1
0
0
0
0
2
2
0
0
0
3
0
0
0
2
0
0
3
0
2
1
0
0
0
0
1
1
2
0
0
0
2
0
1
2
0
0
0
2
0
0
0
3
2
0
0
0
0
2
0
0
0
1
2
0
0
1
2
0
0
1
1
2
0
0
1
1
2
1
2
1
1
0
0
0
0
1
2
2
0
0
0
0
1
2
1
0
1
2
0
0
0
1
0
0
0
2
2
0
0
1
3
0
0
1
1
2
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
2
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
1
1
2
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
2
0
1
0
0
1
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
5
0
0
2
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
2
0
0
0
3
1
0
0
0
0
0
0
0
0
4
1
0
5
1
0
0
0
0
0
0
2
2
0
2
1
2
0
1
0
0
3
1
2
1
3
0
2
0
0
1
0
1
0
3
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
2
2
0
1
0
0
0
0
1
1
0
2
0
0
0
2
0
0
0
1
3
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
1
1
1
0
0
2
1
0
0
0
0
0
3
1
1
0
0
2
2
0
0
3
0
2
0
0
1
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
1
0
0
0
1
1
0
0
1
0
0
2
0
0
1
3
1
0
0
0
0
1
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
2
0
0
2
0
0
2
0
2
0
0
1
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
1
1
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
2
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
3
1
0
0
0
3
2
1
0
0
0
2
2
0
0
1
1
1
2
2
0
0
2
0
0
2
0
2
1
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
3
0
0
2
0
2
2
0
0
2
2
0
0
1
0
1
0
0
2
0
1
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
4
0
0
0
0
1
2
0
0
1
0
2
0
0
0
0
0
1
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
1
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
3
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
5
1
0
0
0
1
0
1
0
0
2
0
0
1
1
2
0
2
0
0
0
2
0
2
0
0
1
2
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
1
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
3
2
2
0
1
1
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
2
2
0
0
0
0
2
0
1
0
1
1
0
0
2
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
4
0
0
1
3
3
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
3
0
2
0
0
0
0
0
0
1
0
0
0
3
0
3
0
1
1
1
0
1
0
2
0
1
0
0
0
0
0
0
0
2
1
2
0
1
0
0
0
2
1
0
4
0
0
0
2
0
1
0
2
0
2
0
0
0
1
0
1
3
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
2
0
0
1
0
1
0
2
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
2
2
0
0
2
0
0
1
2
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
3
0
2
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
1
1
2
0
0
0
0
2
2
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
2
0
0
2
0
0
2
0
0
2
0
1
0
3
0
0
0
0
0
0
2
1
0
2
1
0
0
0
0
0
0
1
2
4
2
0
0
2
0
0
1
0
0
1
0
0
1
2
1
0
2
0
1
0
0
0
1
0
0
2
0
1
0
0
2
0
0
2
0
0
0
1
0
0
2
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
2
0
0
0
0
2
1
3
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
1
0
2
0
0
0
4
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
1
0
0
2
0
1
0
0
0
2
0
0
0
0
1
1
2
2
0
3
0
1
0
0
0
0
0
2
1
1
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
3
0
0
0
0
0
0
2
1
1
4
0
2
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
1
2
0
0
1
1
0
0
0
2
1
0
0
0
2
2
0
1
2
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
2
0
0
0
1
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
2
0
0
0
0
0
2
1
3
0
0
0
0
2
2
0
0
2
0
2
0
0
2
0
2
0
0
0
0
0
2
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
2
0
0
2
3
2
0
1
1
3
1
0
0
0
2
1
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
1
2
0
0
1
3
2
0
0
0
0
0
2
0
0
2
0
0
0
0
2
1
0
1
0
0
1
0
0
0
1
0
2
0
0
2
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
2
1
1
2
3
0
0
2
2
0
0
0
1
0
0
0
0
2
2
0
6
1
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
1
0
0
0
1
0
0
0
0
0
2
1
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
1
1
0
2
0
1
1
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
1
2
0
1
1
1
0
0
2
0
1
0
3
0
0
2
2
2
2
0
0
0
0
2
0
1
2
0
0
2
0
0
0
1
0
0
0
1
1
1
2
0
2
0
1
0
0
0
2
0
1
0
0
0
0
0
1
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
2
0
0
0
0
2
2
0
0
0
1
0
1
0
0
1
0
1
0
3
0
0
0
1
0
0
2
2
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
3
0
2
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
3
0
1
3
0
0
0
0
1
0
2
1
2
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
2
2
2
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
1
0
2
2
0
0
0
2
1
0
2
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
2
1
0
0
0
0
0
1
1
0
0
4
0
2
2
0
0
0
1
0
1
0
2
0
0
1
0
0
0
2
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
3
0
2
0
0
0
0
2
0
0
2
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
1
0
1
2
0
0
1
1
2
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
5
0
0
0
0
0
2
0
1
2
0
2
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
2
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
2
0
3
0
0
1
0
0
0
1
0
4
2
2
1
0
1
2
0
2
0
2
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
2
0
3
0
1
0
0
3
4
0
0
2
2
0
1
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
1
2
0
0
0
1
1
0
0
2
0
1
0
0
0
1
1
0
0
0
1
0
0
2
1
2
0
0
1
0
1
0
0
0
1
0
4
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
2
1
0
0
0
1
0
0
1
0
0
0
0
0
3
0
0
0
0
0
2
0
2
0
0
0
1
2
0
0
0
3
0
1
0
0
0
3
0
0
0
0
0
0
0
1
2
0
0
0
0
0
5
0
0
1
0
0
0
1
2
0
0
2
2
2
1
0
0
0
0
0
1
1
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
2
0
0
2
0
1
0
0
1
2
1
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
2
0
0
2
0
2
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
2
0
0
0
0
4
0
0
1
0
0
1
0
0
0
0
0
1
0
3
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
2
1
0
3
6
2
0
1
0
0
0
0
1
0
1
0
2
0
0
0
2
1
1
0
4
0
0
0
0
0
1
0
1
1
0
0
1
0
0
1
0
0
1
0
0
0
1
4
0
0
0
2
0
1
2
1
2
0
0
1
0
0
0
1
0
0
0
0
2
0
1
1
2
1
0
0
0
0
0
0
0
1
2
1
0
0
1
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
2
0
0
1
2
3
5
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
2
2
0
0
1
0
1
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
2
0
0
0
2
1
0
1
2
0
1
1
0
1
1
1
0
0
0
0
2
1
2
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
4
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
1
0
0
0
2
2
0
1
0
0
2
0
0
2
0
1
2
0
2
1
0
4
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
3
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
3
0
0
0
8
2
0
0
2
0
2
0
3
0
0
0
0
0
0
1
1
0
4
0
0
0
0
0
0
2
0
2
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
1
0
1
0
0
2
2
0
0
0
3
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
1
0
0
2
1
1
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
1
1
0
0
0
0
4
0
1
2
2
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
3
0
0
0
1
1
2
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
3
2
0
0
0
1
0
3
0
0
1
2
1
1
0
1
0
0
0
2
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
1
1
2
0
5
0
0
0
2
0
0
0
0
0
7
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
3
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
1
0
0
1
2
1
2
0
2
0
1
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
2
2
0
1
2
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
1
2
0
0
0
2
2
0
0
1
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
7
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
1
0
0
0
0
0
0
0
2
0
2
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
4
0
2
0
2
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
2
0
3
0
0
1
0
2
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
2
0
0
1
0
0
1
2
0
0
0
0
1
1
0
2
1
0
2
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
1
1
5
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
2
1
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
3
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
2
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
1
1
1
2
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
5
0
0
0
0
1
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
3
2
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
3
0
0
0
1
1
0
0
1
0
0
0
1
3
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
3
0
0
0
2
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
1
0
2
1
0
0
0
2
0
0
0
0
0
2
0
0
3
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
2
0
0
0
0
2
0
0
0
0
3
2
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
3
0
1
0
0
0
2
1
0
2
2
0
2
1
0
0
2
0
0
2
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
2
0
0
0
1
1
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
3
0
1
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
2
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
2
2
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
3
2
1
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
1
2
1
2
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
3
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
1
0
0
0
2
0
1
0
0
1
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
1
3
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
2
0
2
0
1
2
0
2
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
5
0
0
0
2
0
0
0
0
1
0
2
0
1
0
2
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
5
0
1
0
2
2
2
2
0
1
0
0
2
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
3
0
0
2
0
0
4
0
1
0
0
2
2
0
0
5
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
1
3
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
1
0
2
1
0
0
0
2
1
0
0
0
0
1
0
0
0
1
0
0
2
0
2
0
0
1
1
0
1
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
4
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
2
0
0
1
2
2
0
1
0
0
0
1
0
0
1
2
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
2
2
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
1
1
0
0
0
2
0
2
0
1
0
0
0
0
1
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
1
0
0
3
2
2
0
0
0
0
0
0
2
0
0
0
0
3
1
0
2
0
6
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
1
2
0
0
0
0
1
2
0
2
0
0
0
0
1
0
2
0
0
2
1
1
0
0
1
0
2
1
0
1
1
0
0
0
0
1
1
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
3
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
1
0
0
1
1
0
0
1
0
0
1
1
2
2
0
0
0
0
0
0
0
0
1
0
3
0
0
0
2
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
2
0
1
1
0
0
0
1
0
0
0
2
0
0
0
0
0
2
4
0
2
1
0
2
0
2
0
0
0
1
2
1
0
1
2
0
2
0
0
2
0
0
0
2
0
0
0
3
0
0
1
0
0
0
0
0
2
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
2
1
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
1
1
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
1
2
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
2
1
0
4
0
1
0
0
2
0
0
0
1
1
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
1
1
0
1
0
4
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
8
0
2
0
0
4
2
0
2
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
2
0
0
0
0
2
0
2
0
1
0
0
0
0
0
1
1
0
2
1
0
0
0
2
0
0
0
1
2
0
0
2
1
1
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
2
0
0
3
1
0
0
0
0
1
0
2
0
1
1
2
0
0
1
2
0
1
0
0
0
2
1
0
1
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
2
0
0
2
2
1
0
0
2
0
0
0
0
0
0
0
1
1
0
0
2
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
1
0
0
0
0
0
1
2
6
0
0
4
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
1
0
5
0
0
3
0
0
3
0
2
2
1
0
3
0
3
0
0
0
2
1
2
0
0
0
3
1
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
2
2
1
1
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
2
0
0
0
0
0
0
3
0
2
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
1
0
0
2
1
0
0
0
0
0
0
2
3
1
0
0
0
1
0
0
4
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
2
0
0
0
0
2
2
1
0
2
0
1
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
1
0
2
0
1
0
0
0
4
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
2
2
0
0
0
2
0
1
0
0
2
2
0
0
1
0
0
0
0
0
2
1
2
2
0
0
0
0
0
0
1
2
0
0
0
0
0
1
1
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
2
0
1
0
0
0
2
1
0
2
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
1
1
0
0
3
0
0
0
1
0
0
0
0
1
0
0
2
0
2
1
0
2
0
2
1
0
0
2
0
1
3
0
0
1
0
2
2
1
2
0
0
1
1
0
0
2
2
0
0
0
0
0
1
1
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
2
2
1
0
0
0
0
0
0
0
1
0
0
3
0
2
0
0
2
0
0
1
0
0
2
2
0
0
0
3
0
0
0
0
0
1
0
1
0
0
1
0
2
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
2
0
0
0
0
0
0
5
1
1
0
0
0
2
3
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
5
0
2
1
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
3
2
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
2
1
0
0
2
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
1
2
2
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
3
0
3
0
0
0
3
1
0
0
2
0
0
2
0
2
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
1
1
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
2
0
0
2
0
0
0
0
1
1
0
0
2
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
0
2
0
0
0
0
0
0
6
0
1
0
1
0
0
0
0
0
0
0
2
0
1
0
0
1
1
2
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
3
1
1
0
0
0
0
1
1
0
0
2
0
0
0
2
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
1
0
2
0
2
0
2
0
0
0
0
0
0
2
3
1
1
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
8
0
0
1
0
0
0
0
2
2
0
1
1
0
2
0
0
0
0
2
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
2
0
1
1
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
2
1
0
0
0
0
2
0
0
2
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
2
0
2
1
0
1
1
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
1
0
3
0
4
0
2
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
1
0
0
0
2
0
0
2
0
1
0
0
2
0
0
0
0
2
0
2
0
0
1
2
0
1
1
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
2
2
0
0
0
2
0
0
0
0
2
0
0
0
1
1
2
0
2
0
0
0
1
1
0
0
2
0
0
0
1
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
1
3
0
3
0
0
2
0
2
0
1
0
1
0
0
2
0
0
0
3
2
0
3
0
0
0
0
1
0
1
2
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
2
0
5
0
2
0
0
0
1
2
0
2
1
0
0
0
0
0
1
0
2
0
0
3
0
1
1
0
0
4
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
3
0
0
0
0
0
2
0
1
2
0
3
0
0
1
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
2
1
0
2
2
0
2
0
0
1
0
0
0
0
2
0
0
0
0
1
0
2
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
4
0
0
0
2
0
1
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
2
2
0
0
1
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
2
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
8
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
1
2
0
2
0
0
0
1
4
4
0
0
0
0
0
0
0
0
2
0
0
0
2
2
1
0
0
0
0
2
2
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
2
2
2
0
2
0
0
0
1
0
0
0
2
1
0
0
1
2
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
1
0
0
0
2
0
4
1
0
0
0
1
1
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
1
0
1
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
1
2
1
2
0
0
0
0
0
0
0
0
0
0
1
1
0
1
2
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
1
0
7
0
0
0
2
0
2
0
0
0
0
2
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
2
0
0
2
0
2
0
0
1
0
0
0
2
1
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
1
1
0
0
2
2
2
3
0
2
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
1
0
3
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
9
2
2
0
1
0
0
2
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
1
2
2
2
0
0
0
0
0
7
0
0
0
1
1
1
2
1
1
0
0
0
0
0
1
0
2
0
2
2
1
2
0
2
2
0
1
0
1
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
1
1
2
1
1
1
0
9
2
0
1
0
2
2
2
7
0
0
0
0
1
2
0
0
0
0
1
0
1
1
0
0
2
2
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
3
0
0
0
0
0
0
2
0
2
1
0
0
0
3
0
0
2
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
1
0
1
0
2
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
2
1
0
0
2
0
0
0
0
2
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
2
0
2
0
2
0
1
1
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
2
1
0
0
3
0
3
2
0
0
0
0
2
1
0
0
1
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
2
2
0
0
1
0
0
0
0
0
0
9
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
2
0
2
1
0
2
0
2
0
0
0
1
2
0
1
0
0
1
2
0
0
3
2
1
0
0
0
0
0
3
0
2
0
0
1
0
2
0
1
0
2
0
0
0
0
0
0
0
2
0
0
2
1
0
2
0
1
0
0
1
0
0
1
3
0
2
0
0
1
0
2
0
0
0
2
0
0
3
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
1
0
0
0
1
2
0
0
2
0
1
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
2
0
2
0
0
0
0
0
0
3
1
0
0
0
2
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
1
0
2
0
1
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
3
1
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
2
2
0
0
2
0
0
4
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
2
0
2
1
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
2
2
0
2
2
0
0
2
0
0
0
2
0
0
0
3
0
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
2
2
15
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
2
1
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
2
2
0
2
0
1
0
0
0
2
0
0
0
3
0
0
0
0
1
1
2
0
0
1
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
3
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
3
0
0
0
0
2
1
2
1
1
2
0
1
0
0
0
2
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
1
0
2
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
2
0
0
1
1
0
0
0
1
1
0
0
2
0
0
0
1
0
0
1
1
3
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
1
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
1
1
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
1
4
0
0
2
0
0
4
2
0
0
0
0
0
1
1
0
1
1
0
3
1
1
0
0
2
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
1
3
3
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
2
0
0
2
1
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
2
3
0
0
2
0
0
1
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
2
0
0
1
0
2
0
1
0
0
0
2
0
1
2
0
0
6
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
2
2
2
0
0
0
0
0
0
0
1
2
1
1
1
2
0
0
0
2
0
0
3
1
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
4
0
0
0
1
2
0
3
0
1
0
2
0
0
1
0
0
1
0
0
0
0
7
0
0
2
2
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
3
0
0
1
0
1
0
0
1
0
1
0
2
0
0
2
1
2
0
0
0
1
2
0
0
0
0
0
0
1
0
1
3
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
1
0
1
0
2
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
1
0
2
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
2
0
1
0
2
0
0
2
0
0
0
0
0
1
0
2
0
4
2
0
2
0
0
1
0
1
0
0
2
0
0
0
0
2
0
2
0
0
0
1
0
0
2
0
1
0
0
0
0
0
2
1
1
0
2
0
5
0
0
0
0
2
2
1
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
2
0
0
2
1
1
0
0
2
0
1
1
2
0
0
1
0
2
0
0
0
0
0
1
0
0
0
2
0
0
2
2
0
0
0
1
0
1
1
0
1
0
0
1
0
0
0
0
3
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
2
0
0
0
0
2
0
0
0
2
1
0
1
1
0
1
1
3
0
0
0
1
0
0
0
0
0
0
0
0
1
2
1
0
0
3
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
2
2
2
1
0
0
1
0
0
0
1
4
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
1
2
2
0
0
0
0
2
0
1
0
2
0
0
0
0
1
4
0
0
0
0
0
0
5
0
0
0
0
2
0
0
1
0
0
4
0
0
0
0
1
0
1
0
0
0
0
1
1
0
1
0
0
1
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
3
1
1
0
0
2
0
0
0
0
0
0
1
2
0
3
2
3
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
2
4
2
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
5
0
0
2
1
0
0
0
0
0
1
0
0
1
0
2
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
2
0
1
0
0
1
0
0
1
0
2
0
1
2
0
0
0
2
0
2
1
0
0
0
0
1
3
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
1
2
1
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
1
0
0
3
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
2
2
1
0
0
1
0
0
0
1
0
0
0
2
0
0
2
1
0
4
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
7
0
1
0
0
1
0
2
1
0
4
0
0
0
1
1
2
0
1
0
0
1
1
0
2
1
1
0
0
0
2
0
0
1
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
2
1
0
0
0
0
0
0
4
0
0
2
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
3
0
1
0
0
0
0
0
1
0
0
0
2
2
0
1
0
1
2
0
1
0
0
0
0
0
1
0
0
2
1
0
0
2
2
1
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
2
0
1
0
3
0
0
0
1
0
1
4
0
0
0
0
2
0
0
0
2
0
0
0
2
0
1
0
1
0
0
0
0
0
0
2
0
3
1
0
0
0
0
1
0
0
0
0
1
3
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
1
3
0
0
0
0
0
0
2
1
3
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
3
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
1
1
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
3
0
0
2
0
0
0
0
2
0
0
0
1
1
1
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
3
0
0
0
1
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
1
0
3
2
1
0
1
2
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
2
2
0
2
0
0
0
0
1
0
0
0
3
1
0
1
0
0
0
0
0
2
0
1
2
0
0
0
0
0
2
2
0
1
0
2
0
3
2
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
1
2
0
2
0
2
0
1
0
0
0
0
0
2
0
0
2
1
2
0
1
0
0
0
0
0
1
0
2
0
0
0
1
1
0
1
0
0
1
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
2
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
2
0
1
0
2
2
1
0
0
1
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
3
0
2
1
0
1
0
4
0
1
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
3
0
0
2
2
0
0
0
2
0
0
0
1
0
0
0
1
2
1
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
1
1
0
0
1
0
2
0
0
0
2
0
0
0
0
1
0
0
3
0
1
0
5
2
0
0
3
0
0
0
1
2
0
0
0
0
1
0
2
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
1
0
0
2
0
0
2
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
2
0
2
0
0
1
2
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
2
2
0
0
0
2
1
1
0
0
0
1
0
0
3
0
0
0
1
1
0
2
0
0
2
3
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
2
2
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
4
0
1
0
0
2
0
1
0
0
0
0
0
1
0
0
0
2
2
1
0
2
1
0
0
0
0
1
1
0
1
0
2
2
1
0
1
1
0
0
0
0
1
0
1
0
3
0
1
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
2
1
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
2
0
1
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
3
0
0
2
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
1
3
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
1
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
1
0
1
0
1
1
1
1
2
0
0
2
2
0
0
0
5
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
6
0
0
0
0
3
0
0
0
0
1
2
0
0
1
0
2
1
0
2
0
2
1
0
0
1
5
0
0
0
0
0
0
0
1
4
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
2
0
5
3
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
4
0
0
1
1
0
0
1
0
1
0
0
0
1
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
2
1
0
0
0
0
1
0
0
3
0
0
0
0
1
0
0
0
1
1
2
0
0
1
0
0
0
2
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
2
2
0
1
0
1
1
1
1
0
0
0
0
2
0
0
0
0
0
0
2
3
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
3
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
1
2
0
1
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
4
3
0
0
0
0
2
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
1
0
1
2
0
0
1
0
0
2
0
0
2
0
0
3
0
0
0
1
0
0
1
0
0
0
1
0
0
0
3
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
1
0
1
0
0
2
0
0
0
1
0
0
2
0
0
1
3
0
0
3
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
5
0
0
2
2
2
0
2
1
0
0
0
2
2
0
0
1
0
0
0
0
0
2
0
1
0
3
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
10
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
1
0
0
4
0
1
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
2
5
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
1
0
1
2
0
0
0
2
2
1
0
0
1
0
1
0
0
2
0
1
0
0
2
0
0
0
0
2
0
0
0
2
0
2
1
2
2
1
1
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
1
0
0
0
0
3
0
0
0
0
1
0
1
2
0
0
2
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
1
0
0
0
2
0
0
0
1
1
1
1
2
0
0
0
0
2
0
0
2
0
0
0
3
0
2
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
1
0
0
0
0
0
1
2
0
0
2
0
2
0
0
0
0
1
0
2
2
0
2
2
1
2
0
2
0
2
2
0
2
0
2
0
0
2
2
3
0
0
0
0
0
0
0
2
0
0
2
0
0
1
2
1
2
1
0
2
0
0
0
0
0
0
0
2
3
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
1
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
2
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
5
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
3
0
0
1
2
0
0
1
2
1
0
2
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
2
3
0
0
0
0
1
0
1
0
1
2
0
0
0
0
0
1
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
1
0
3
0
2
0
0
0
2
1
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
1
2
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
1
0
2
2
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
2
0
0
2
1
0
2
1
0
0
2
0
1
2
2
2
0
2
0
2
0
0
2
0
0
0
0
3
1
0
0
0
0
0
0
2
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
1
0
0
5
0
1
2
0
0
2
2
2
0
0
2
2
0
0
0
0
1
1
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
1
4
0
1
3
1
0
0
2
0
3
1
2
2
0
1
0
0
7
1
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
2
0
0
0
2
0
3
0
2
0
0
0
2
0
1
3
0
0
0
0
4
0
1
0
0
0
3
0
0
1
0
0
0
0
2
0
1
0
0
2
1
0
0
0
2
1
0
0
0
0
0
0
1
0
1
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
1
0
0
0
0
2
0
1
2
1
0
2
0
0
0
0
0
0
2
0
0
0
0
1
1
0
1
2
0
0
2
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
2
0
0
1
1
2
0
2
0
0
0
1
0
1
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
5
0
0
1
0
0
1
0
0
0
0
3
0
0
1
0
1
0
0
2
1
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
2
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
1
0
1
0
0
2
1
0
1
1
0
0
0
0
0
2
1
0
1
0
1
1
0
2
0
1
0
1
0
2
0
2
0
0
0
0
2
0
0
0
0
0
1
0
3
0
0
2
0
1
0
0
1
0
0
0
0
0
2
0
1
0
2
0
1
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
4
0
0
1
2
0
0
0
0
0
0
0
0
1
2
1
0
2
0
3
1
0
1
0
1
0
0
0
0
2
2
0
0
1
0
2
1
1
1
0
2
2
0
0
0
0
0
0
0
0
1
1
0
0
0
2
1
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
1
0
0
0
1
2
0
7
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
2
1
0
0
2
0
3
0
3
0
0
0
0
0
0
1
0
0
1
2
2
0
1
0
0
0
0
1
0
1
2
0
0
0
5
0
0
0
0
0
1
0
0
0
2
0
1
0
0
5
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
1
0
1
2
0
2
0
0
1
0
0
1
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
2
2
1
0
0
3
0
0
2
0
0
1
0
1
0
1
0
0
0
3
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
2
2
1
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
2
0
1
0
1
0
0
0
0
1
2
0
1
1
0
2
0
0
0
1
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
2
0
1
0
0
0
2
0
0
1
0
0
0
2
0
0
1
0
0
1
0
1
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
3
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
2
0
2
0
0
0
1
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
2
2
0
0
1
1
0
0
0
2
0
1
1
2
0
1
1
0
1
0
0
1
0
2
0
0
0
3
2
3
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
2
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
2
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
2
1
0
0
3
0
0
2
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
5
3
0
0
2
0
0
0
3
1
0
0
2
0
0
0
0
1
0
0
0
0
3
0
0
2
0
1
0
0
0
3
0
0
0
2
0
0
0
0
0
2
0
0
1
0
2
0
0
2
0
1
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
2
1
0
2
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
2
0
0
0
2
0
0
2
0
1
2
0
0
1
2
1
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
1
0
0
1
0
0
3
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
1
1
0
0
2
0
0
3
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
1
0
1
0
0
0
2
2
0
0
1
0
2
1
0
2
0
4
2
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
1
0
2
1
1
0
2
0
0
0
1
0
2
1
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
1
0
2
1
0
0
1
0
0
0
1
0
0
0
0
0
0
4
0
1
1
4
1
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
3
0
2
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
1
1
0
0
2
1
1
0
2
0
2
0
0
0
0
2
0
0
0
2
0
4
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
2
0
0
3
0
2
0
2
0
0
2
0
2
1
1
0
0
0
1
1
0
0
2
2
0
0
0
0
0
0
1
0
0
1
1
0
0
2
2
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
1
0
0
2
0
0
0
0
0
1
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
3
0
0
1
2
0
0
0
1
0
0
1
0
1
1
0
2
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
3
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
1
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
1
9
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
3
2
0
0
0
0
0
2
4
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
1
1
2
1
0
3
1
0
2
1
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
2
0
0
0
1
0
0
3
2
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
1
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
2
2
1
0
1
0
0
0
1
0
1
3
0
0
0
0
5
0
3
2
1
1
0
2
1
0
0
1
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
1
2
0
0
2
0
0
0
0
0
2
0
2
0
0
0
1
1
0
0
1
0
0
0
0
1
2
0
2
1
0
0
0
3
0
0
0
0
0
0
0
0
0
3
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
3
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
1
0
0
2
0
3
0
0
0
1
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
1
1
0
0
0
0
1
0
1
0
1
2
0
0
4
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
2
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
1
0
1
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
5
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
3
0
0
0
1
0
2
0
0
0
0
0
2
2
1
0
2
0
1
0
0
0
0
0
0
2
0
1
2
0
0
0
3
1
2
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
3
0
0
1
0
0
2
0
2
0
0
0
1
2
0
0
0
0
1
0
2
0
2
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
2
2
0
1
0
0
0
2
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
1
1
1
1
2
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
2
1
0
2
0
2
0
0
0
7
0
0
0
0
1
0
0
0
0
0
2
1
2
0
4
0
0
3
3
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
1
4
0
0
0
0
2
1
0
1
0
0
0
4
0
0
0
0
1
0
0
0
2
0
1
0
1
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
1
1
0
1
2
1
0
0
0
0
1
1
0
2
0
2
0
0
0
0
1
0
1
0
0
2
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
1
0
1
2
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
2
0
0
2
0
0
2
0
0
0
2
0
0
0
1
0
0
2
2
0
0
1
1
2
0
0
0
0
0
0
0
1
0
2
1
1
0
5
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
1
1
1
0
0
1
0
0
0
0
2
0
0
1
1
1
0
0
0
0
0
2
0
1
0
0
2
0
0
0
1
0
0
0
1
0
1
1
0
0
3
0
0
0
1
0
2
0
0
0
2
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
4
2
0
0
0
2
0
0
1
0
2
0
0
1
0
1
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
2
0
0
0
2
1
1
0
1
0
0
1
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
6
0
2
0
0
3
0
2
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
2
0
0
1
0
2
0
0
2
0
2
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
2
0
2
0
0
2
1
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
4
0
3
0
1
0
0
1
3
1
0
0
0
0
2
0
0
0
2
3
1
0
1
0
0
0
0
0
1
0
2
2
1
1
1
1
3
2
1
0
2
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
3
0
2
0
0
0
2
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
1
0
0
0
2
0
1
0
2
0
1
2
2
1
0
2
0
1
0
1
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
1
0
0
0
1
2
0
0
2
1
1
0
0
0
0
0
1
1
0
1
0
2
0
1
0
1
1
2
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
3
0
0
0
0
1
1
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
2
0
0
0
1
0
1
0
3
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
2
0
3
0
1
1
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
4
0
0
0
0
2
0
0
1
1
0
0
1
0
1
0
0
0
0
0
3
1
0
0
0
1
0
1
2
0
0
2
0
0
0
1
0
2
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
2
0
2
1
0
0
0
0
2
2
0
2
1
0
2
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
1
0
2
3
2
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
2
0
0
0
2
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
1
0
3
2
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
2
0
1
0
6
0
0
0
0
1
2
0
0
0
1
0
0
1
0
0
0
2
0
1
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
1
3
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
2
3
2
1
0
2
2
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
2
0
0
0
2
0
0
1
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
2
4
0
0
0
0
0
2
0
2
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
2
0
1
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
1
0
0
2
0
2
2
0
1
2
0
0
2
0
1
0
0
0
0
0
0
2
2
0
3
0
0
0
1
0
0
0
0
1
0
1
1
0
1
0
2
0
0
0
0
0
1
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
3
1
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
3
0
0
0
0
2
0
0
0
2
1
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
2
1
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
1
0
2
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
2
2
1
0
1
3
0
2
0
0
0
0
1
0
0
1
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
1
3
1
0
0
0
1
0
1
0
0
1
0
0
2
1
1
0
1
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
2
2
0
2
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
2
0
1
0
1
0
1
0
0
1
0
1
1
0
0
1
0
0
0
1
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
3
0
0
0
0
0
1
0
1
0
2
0
0
0
4
3
0
0
0
0
0
0
2
0
0
2
1
2
0
0
1
1
0
0
0
2
0
0
0
2
4
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
6
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
4
1
0
1
0
0
4
0
0
1
2
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
3
0
0
1
3
0
2
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
2
0
2
0
0
0
1
0
2
1
0
0
1
0
0
1
0
2
0
0
0
3
0
0
2
0
0
1
0
2
0
0
1
1
1
1
0
0
1
1
0
0
1
0
0
0
2
2
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
4
1
0
0
1
2
0
0
0
1
0
0
0
2
0
0
0
0
2
0
1
0
4
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
2
1
0
0
0
1
1
0
1
1
0
1
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
1
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
2
0
2
0
0
0
1
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
2
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
1
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
3
0
0
0
0
1
2
2
1
0
0
1
0
2
1
0
0
0
2
0
0
1
2
2
0
0
0
0
1
0
2
0
0
0
0
0
0
2
1
0
0
0
1
1
0
0
0
3
0
0
0
0
0
0
1
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
3
0
0
1
0
1
0
2
1
2
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
2
0
1
2
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
2
2
2
0
3
0
2
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
2
0
0
0
1
0
0
0
5
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
7
0
2
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
3
1
0
0
0
0
2
0
0
3
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
2
0
5
2
0
0
0
0
0
0
0
1
0
1
1
0
1
1
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
2
0
2
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
1
0
0
0
2
2
0
0
0
0
0
0
0
2
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
2
0
1
3
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
8
1
0
0
1
0
0
0
0
1
0
2
2
0
2
1
1
0
0
0
3
0
0
2
1
0
2
0
0
0
0
1
3
0
0
1
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
3
2
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
2
0
0
0
0
3
0
3
0
0
2
1
0
1
2
1
0
1
2
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
2
2
1
0
0
0
0
1
2
1
0
1
0
0
1
0
0
2
1
0
1
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
3
1
0
0
0
0
0
1
0
0
1
0
0
2
0
0
2
3
0
0
0
0
2
0
3
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
3
0
0
1
5
0
0
2
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
5
0
0
3
0
0
0
2
2
1
0
0
0
1
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
2
1
0
0
1
2
2
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
3
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
3
2
1
0
1
2
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
2
0
2
0
0
1
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
2
1
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
2
1
0
0
2
0
0
2
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
4
0
2
2
2
0
0
2
0
0
2
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
2
2
0
0
2
3
0
2
2
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
3
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
4
0
0
0
0
2
0
2
0
1
1
1
2
2
0
0
0
1
2
2
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
4
0
0
2
0
3
0
0
0
9
0
0
0
0
1
0
0
0
3
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
2
1
0
1
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
1
0
0
0
0
0
0
2
1
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
2
1
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
2
0
0
3
0
0
0
0
0
1
2
0
2
0
0
0
0
1
0
0
0
0
0
0
2
2
0
1
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
2
0
2
1
0
2
0
1
0
0
0
0
0
0
1
2
1
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
4
0
1
0
1
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
3
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
2
1
0
0
2
0
0
0
0
1
1
0
0
0
16
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
1
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
1
1
0
0
2
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
2
0
1
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
7
2
1
2
1
0
1
0
0
4
0
1
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
2
0
1
0
0
0
1
2
1
0
2
0
1
0
0
1
0
0
2
1
0
2
2
0
0
1
2
0
1
0
1
0
2
0
1
3
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
2
1
0
0
0
2
0
0
0
0
0
0
0
1
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
3
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
1
0
4
0
0
0
0
0
1
0
0
0
2
0
2
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
3
2
1
0
2
0
0
0
4
0
0
1
0
0
0
2
0
0
0
0
5
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
3
0
0
0
1
3
0
0
1
0
1
0
1
0
0
1
3
0
1
0
0
0
0
0
0
2
0
0
0
0
5
2
0
0
2
1
0
0
0
0
0
2
0
2
3
1
2
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
1
0
0
1
3
0
0
0
2
0
0
0
0
2
1
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
1
0
1
0
0
1
0
0
0
1
0
2
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
1
4
0
0
0
2
0
0
1
0
0
0
0
2
0
1
0
0
0
1
0
2
2
0
1
0
4
1
0
0
0
0
2
2
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
3
0
0
0
0
2
0
0
0
2
0
2
3
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
2
3
0
1
1
2
0
0
2
0
0
0
2
2
0
0
2
4
1
0
0
2
0
0
1
0
0
1
0
0
0
2
0
0
2
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
8
1
0
0
0
0
0
2
0
0
0
0
0
1
0
2
1
0
0
1
0
0
1
2
1
2
0
0
0
1
0
0
0
0
0
0
2
2
0
0
2
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
2
1
1
0
2
0
0
1
2
2
0
0
0
0
0
1
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
2
1
1
0
0
3
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
5
0
0
0
4
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
2
1
0
3
0
0
0
0
0
2
1
0
0
0
2
0
2
0
0
2
0
0
1
2
1
0
1
0
0
0
2
1
0
0
0
1
0
4
2
0
2
0
1
3
1
0
1
1
0
0
0
0
1
0
0
1
0
0
1
3
0
1
4
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
1
2
1
2
0
0
0
0
0
2
2
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
2
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
1
0
0
2
1
0
0
0
1
1
2
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
2
2
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
2
0
2
0
3
0
0
2
1
0
0
0
0
1
0
1
1
0
0
0
2
0
2
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
1
2
0
2
0
0
0
1
0
1
0
2
0
0
7
0
0
0
1
0
0
0
0
1
1
0
0
0
0
2
0
0
0
2
2
0
0
3
2
0
1
0
0
4
0
1
0
1
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
2
0
0
2
0
0
0
0
3
0
0
0
1
0
0
0
2
2
3
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
2
0
2
0
0
0
1
0
11
3
2
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
2
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
1
3
0
0
2
0
0
0
1
0
0
0
1
2
2
0
0
1
0
0
2
2
2
0
0
0
0
2
0
2
0
2
1
0
2
2
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
1
1
0
2
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
2
0
4
0
0
1
0
2
0
2
0
0
0
1
0
2
1
0
2
1
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
2
0
0
0
0
2
0
0
0
2
0
0
3
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
1
2
1
1
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
1
0
0
2
2
0
0
1
1
0
0
0
0
4
0
0
2
0
0
1
0
0
0
1
2
0
1
0
0
2
0
0
0
1
0
0
0
0
2
0
0
2
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
1
0
0
0
0
0
0
4
1
0
0
0
0
0
0
1
2
0
1
0
0
1
1
1
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
1
1
0
3
0
0
0
3
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
2
2
0
0
0
2
0
2
1
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
2
1
0
2
0
2
0
1
0
2
0
0
1
0
2
0
2
2
0
2
2
0
2
2
0
0
0
2
0
3
0
0
3
0
0
0
2
0
0
0
0
0
1
0
2
4
0
0
2
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
11
0
2
0
2
0
0
0
0
0
2
1
0
0
0
2
4
2
1
0
0
0
0
0
0
0
2
4
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
2
2
2
0
0
1
1
0
1
0
0
2
1
0
0
1
3
1
0
0
0
0
4
0
2
0
0
0
2
1
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
2
2
1
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
1
0
0
1
1
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
4
0
0
1
0
0
0
1
0
0
0
2
0
0
2
2
0
0
0
0
0
0
3
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
2
1
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
1
0
1
2
1
1
1
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
2
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
1
0
1
0
1
2
2
0
2
0
1
0
2
0
0
0
0
0
2
0
0
0
2
1
2
2
1
2
0
0
0
0
0
1
0
0
2
2
0
0
0
5
0
0
0
0
0
1
1
0
0
0
2
0
0
1
1
2
0
2
0
0
2
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
7
0
0
0
2
2
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
2
0
2
1
2
0
2
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
1
13
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
2
0
2
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
1
1
3
0
0
0
1
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
1
0
0
1
2
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
1
1
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
2
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
2
0
0
0
2
1
2
0
2
0
3
1
0
3
0
2
2
0
1
0
2
0
0
2
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
2
0
0
0
0
0
4
0
1
1
0
2
2
0
0
1
0
0
0
1
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
1
0
0
2
1
0
0
1
2
0
0
2
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
1
1
0
0
1
0
0
1
0
0
1
0
1
1
2
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
2
2
0
2
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
1
0
0
0
2
0
0
0
1
0
1
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
3
0
1
0
0
2
0
0
4
2
0
0
0
0
0
1
1
0
0
2
0
0
2
0
2
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
1
2
0
1
0
0
0
0
2
0
0
1
2
1
0
1
1
0
2
0
0
4
0
0
0
0
2
0
0
1
2
1
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
1
0
3
2
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
1
1
1
4
2
0
0
0
0
0
2
1
0
2
0
0
1
0
0
1
1
0
0
0
0
0
1
2
0
1
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
3
0
1
0
0
0
0
1
0
0
0
2
1
0
0
1
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
2
1
9
3
0
0
0
0
1
0
0
0
0
2
0
4
0
0
0
0
2
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
2
1
0
2
0
0
0
0
0
2
0
2
0
0
0
0
2
1
1
0
1
1
0
0
0
0
0
0
0
4
1
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
2
0
0
1
1
0
1
1
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
1
0
1
0
2
2
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
2
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
2
0
1
0
2
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
2
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
2
0
0
0
1
0
1
1
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
2
1
0
2
2
1
0
0
3
0
0
1
0
0
0
0
2
0
0
2
0
2
1
0
2
1
1
3
0
0
0
0
0
0
1
0
0
0
2
0
0
5
0
1
0
0
2
2
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
8
0
1
1
0
1
0
0
0
0
1
0
0
0
2
2
0
1
0
2
1
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
1
0
2
0
2
2
0
0
2
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
7
1
2
2
1
0
2
0
0
3
2
2
1
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
1
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
2
1
1
2
2
0
2
0
0
0
0
0
2
2
1
0
0
2
0
0
1
2
0
0
2
0
1
0
0
0
2
1
1
2
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
3
1
2
0
0
2
1
1
0
0
1
1
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
3
1
0
0
0
2
0
1
0
1
0
0
0
0
1
0
0
0
0
0
2
0
1
1
0
1
0
1
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
2
0
0
0
0
2
1
0
1
2
0
1
1
0
0
0
0
0
2
0
0
0
0
1
0
3
0
0
0
0
0
0
0
1
2
0
2
2
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
2
0
0
0
2
0
0
2
0
0
0
0
1
0
0
2
0
0
2
0
2
0
0
0
0
0
3
0
2
0
0
1
0
2
0
0
1
1
2
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
6
0
0
2
2
0
0
2
0
2
0
1
0
0
0
1
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
2
0
3
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
3
0
0
0
3
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
3
0
0
0
1
1
0
2
0
0
0
1
0
2
0
0
2
0
0
2
2
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
5
1
0
1
3
0
2
1
1
0
0
2
0
2
2
1
0
0
0
1
0
0
0
0
2
0
0
2
0
0
2
1
0
0
2
0
0
0
0
0
3
0
3
0
1
2
2
0
0
0
2
0
0
1
1
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
1
1
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
2
1
2
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
2
0
1
1
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
3
0
0
0
0
0
4
0
0
0
0
1
1
0
0
0
0
0
4
0
2
0
0
0
1
0
0
0
1
1
0
0
2
0
0
2
0
0
0
1
0
2
1
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
2
2
0
2
0
3
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
1
3
0
0
0
0
0
2
0
3
1
0
0
0
0
2
0
0
0
0
0
2
3
3
3
0
0
2
0
2
0
0
0
1
0
0
0
1
2
0
0
0
1
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
2
0
0
3
2
0
2
0
0
1
0
0
0
0
0
1
0
1
0
0
2
1
0
0
2
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
2
1
1
0
0
2
0
1
0
1
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
3
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
3
1
3
0
0
0
0
0
0
0
1
2
1
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
1
2
1
0
2
0
0
0
0
0
1
0
1
0
2
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
1
0
1
1
0
1
1
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
1
0
0
3
1
0
0
0
0
0
2
0
0
1
1
0
2
0
0
1
1
0
3
1
2
3
1
0
2
0
2
0
1
0
0
1
1
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
2
2
0
2
1
0
0
1
1
0
0
0
0
1
0
0
1
0
2
3
0
0
0
1
2
0
0
1
0
0
0
2
0
0
0
0
1
0
0
1
1
0
0
0
1
3
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
2
0
0
0
2
1
0
0
3
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
1
2
2
0
0
3
0
2
0
0
1
0
0
2
0
0
0
5
0
0
0
1
0
1
0
1
0
0
0
0
0
2
0
0
1
0
2
0
2
0
0
0
1
1
2
0
0
1
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
2
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
1
2
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
2
1
0
0
1
1
2
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
1
0
0
0
0
0
1
1
0
0
1
0
1
0
0
3
1
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
2
2
0
0
0
0
2
4
0
2
0
0
3
1
0
2
2
0
0
0
0
2
2
1
1
0
0
0
0
0
0
0
0
0
2
1
1
2
0
0
2
0
0
0
0
1
0
2
1
1
0
1
0
1
2
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
2
2
1
2
0
0
0
0
1
2
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
2
1
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
2
1
1
2
0
0
2
1
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
1
0
1
2
0
2
1
2
0
1
0
0
0
0
0
2
0
1
1
1
2
0
4
0
0
1
0
0
1
0
3
0
2
0
1
0
1
1
0
2
2
1
0
0
0
0
0
5
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
1
1
2
0
2
0
2
0
0
0
1
0
1
3
0
7
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
2
0
0
0
1
1
0
0
2
0
1
0
0
1
1
0
0
0
2
0
0
2
0
2
1
0
0
0
0
0
0
0
1
1
2
0
0
1
0
0
2
0
0
1
1
0
0
0
1
2
0
2
2
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
2
3
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
2
0
3
0
0
0
0
3
0
0
0
0
2
0
0
0
0
1
0
2
2
1
0
0
0
1
0
0
0
1
0
1
1
0
0
1
2
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
2
2
1
0
0
3
1
1
2
0
1
3
2
0
0
0
2
0
0
0
1
7
0
0
0
1
0
0
0
0
0
2
0
2
0
2
0
2
0
0
0
0
1
1
0
0
1
2
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
4
0
0
0
0
1
2
1
0
0
0
0
0
1
1
0
2
0
3
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
1
0
1
1
0
1
0
5
0
0
0
1
0
0
1
2
0
0
1
0
0
0
0
0
0
0
1
0
0
3
2
0
0
3
0
0
0
0
1
2
0
2
0
0
0
0
0
2
2
0
0
0
0
0
2
2
0
1
0
0
2
1
0
0
0
0
1
1
1
0
1
2
0
0
0
1
0
1
0
0
2
0
0
4
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
3
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
2
2
0
0
0
1
0
2
0
0
2
0
1
2
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
2
1
0
0
0
3
1
1
0
2
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
2
0
3
0
0
0
2
0
0
0
0
0
0
0
1
2
0
1
4
1
0
4
0
1
0
0
0
0
0
1
2
2
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
6
0
1
0
1
0
0
0
0
2
1
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
5
0
2
1
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
3
2
1
0
0
0
0
1
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
1
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
4
0
0
1
2
1
0
0
2
1
0
0
0
2
0
1
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
1
2
0
2
1
0
1
0
1
0
1
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
4
0
0
1
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
2
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
1
1
0
0
0
0
0
2
0
0
3
0
0
0
2
2
0
0
0
1
0
0
0
2
0
2
1
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
3
0
0
2
2
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
2
0
0
1
0
1
2
0
1
3
0
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
2
1
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
1
1
2
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
3
2
0
0
2
2
0
0
1
2
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
2
0
2
0
1
0
1
2
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
2
0
1
0
0
1
0
1
1
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
1
2
0
1
3
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
2
1
2
1
0
0
2
0
0
0
0
1
3
4
0
0
2
0
2
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
1
4
0
0
1
0
0
0
0
1
0
2
3
0
0
1
0
0
0
0
3
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
2
2
0
0
2
1
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
1
0
0
0
2
1
0
2
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
1
3
0
3
0
1
0
0
0
0
2
0
0
0
0
0
0
2
1
1
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
1
1
0
0
0
2
0
2
0
2
2
0
0
2
0
2
0
0
2
0
2
0
0
0
0
2
2
4
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
1
0
0
1
2
1
2
2
0
0
0
0
0
0
0
0
0
2
2
2
0
2
0
0
0
0
0
2
0
2
0
0
2
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
2
0
1
0
8
0
0
1
0
1
0
0
0
0
2
1
0
0
0
0
0
0
1
2
3
0
0
2
0
0
0
0
0
0
2
2
0
0
0
2
0
1
0
0
0
0
3
0
0
0
0
0
3
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
2
0
1
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
2
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
1
8
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
3
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
1
1
0
1
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
2
0
0
0
0
0
0
0
2
2
1
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
1
1
0
0
0
1
2
0
0
1
1
1
0
0
1
0
1
0
0
0
2
1
0
0
0
0
2
2
0
1
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
2
0
0
0
0
3
0
2
2
0
0
2
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
3
0
1
0
0
4
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
2
0
6
0
0
0
1
2
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
2
0
3
1
0
0
1
0
0
0
1
1
0
3
0
0
2
4
0
0
1
0
1
3
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
2
1
1
0
2
0
0
2
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
2
0
2
1
0
0
0
0
2
0
0
3
0
0
0
1
0
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
1
0
1
0
0
1
0
1
1
0
2
0
0
0
1
1
0
1
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
2
2
0
1
1
3
0
1
0
2
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
1
1
0
0
0
0
0
2
2
1
2
0
0
2
0
0
0
2
0
0
0
0
0
0
1
1
0
1
2
1
0
2
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
3
0
1
0
1
2
0
0
0
0
2
0
0
0
2
0
0
3
0
0
0
0
0
0
0
1
0
0
3
1
2
1
0
0
0
2
0
3
0
0
0
0
0
0
1
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
2
0
0
0
0
0
2
0
0
1
1
0
2
0
0
0
1
0
1
0
0
0
0
4
0
1
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
1
3
0
0
0
1
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
2
2
1
0
2
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
1
2
0
1
0
0
1
0
1
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
6
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
3
0
1
3
2
0
0
1
0
0
2
2
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
3
0
1
0
0
1
0
1
0
0
0
0
0
2
0
1
0
1
0
0
2
0
0
1
1
2
0
0
0
1
2
1
0
0
0
0
1
0
1
1
2
0
1
0
0
1
0
0
4
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
1
0
1
0
0
0
0
2
0
0
1
0
0
0
8
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
1
0
0
0
1
2
1
2
0
2
1
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
1
0
0
0
2
1
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
2
1
0
0
0
0
2
2
0
2
0
0
0
0
2
0
0
1
0
0
0
0
2
2
0
0
0
0
4
0
0
0
1
2
0
0
0
1
3
0
0
2
2
0
0
1
0
0
0
0
0
1
0
0
1
1
2
2
0
1
0
0
1
2
0
0
0
0
1
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
1
0
1
0
0
0
1
0
0
0
0
0
3
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
3
0
0
2
0
1
0
1
0
1
0
0
2
0
0
1
0
2
0
0
0
2
2
0
0
4
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
1
2
0
0
0
0
0
2
2
2
0
0
2
0
3
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
3
0
0
0
0
2
1
0
0
1
0
1
1
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
1
2
0
1
0
2
0
0
0
0
2
0
0
2
10
0
1
3
2
2
0
1
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
2
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
2
2
0
2
3
0
2
2
0
0
0
2
0
0
0
2
1
0
0
0
0
0
1
2
2
0
0
0
4
0
0
1
0
1
0
0
0
0
1
0
0
0
2
2
0
1
0
2
2
2
0
0
0
2
1
0
0
0
1
0
0
0
0
1
1
0
0
1
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
3
3
0
0
0
0
0
0
0
3
0
2
0
0
0
2
0
0
0
0
2
0
0
1
0
2
0
0
1
2
0
2
0
0
1
0
0
2
1
2
1
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
2
1
2
3
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
1
0
0
0
3
2
0
0
0
0
1
1
0
0
1
1
0
3
0
0
0
2
0
0
0
0
0
1
1
0
3
2
1
0
1
0
0
1
0
0
0
0
1
0
1
0
5
0
0
1
0
0
0
2
0
2
0
1
2
0
2
0
0
0
0
2
0
0
0
0
0
0
2
1
1
0
2
0
0
0
1
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
2
1
1
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
1
3
0
1
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
1
1
0
0
0
1
1
0
0
0
2
0
2
2
2
0
0
0
0
0
3
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
2
0
0
0
0
2
0
0
0
2
1
0
2
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
2
1
0
0
0
0
2
0
0
0
5
0
1
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
2
4
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
1
2
0
0
2
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
2
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
1
1
2
0
0
2
0
0
0
1
0
3
0
0
0
0
0
0
0
1
1
2
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
2
0
0
0
0
0
2
1
2
0
1
1
0
1
2
1
0
2
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
1
2
1
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
2
0
0
0
0
2
2
0
0
3
0
0
0
0
0
5
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
3
1
2
0
0
2
0
0
0
0
2
0
1
0
3
1
0
0
0
0
0
1
0
0
2
0
2
2
0
0
0
0
0
1
0
1
0
2
2
0
1
1
0
0
1
0
2
0
0
1
1
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
2
2
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
1
0
1
0
0
2
0
0
0
0
0
2
0
1
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
3
1
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
2
0
1
0
2
0
0
2
1
1
0
2
0
0
2
2
2
1
0
0
0
0
2
2
0
0
0
7
0
0
0
0
1
0
0
0
1
2
0
0
2
0
0
0
0
2
1
0
0
0
0
0
1
1
0
1
1
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
2
2
2
1
1
2
1
1
0
0
1
0
2
0
1
0
1
0
0
0
0
2
2
0
2
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
2
1
0
3
1
2
0
0
0
0
0
0
0
0
2
0
1
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
2
0
1
0
2
0
0
2
0
0
0
0
2
1
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
2
2
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
2
4
1
0
0
2
1
0
1
0
0
0
3
6
1
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
3
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
2
0
2
0
2
1
2
0
1
0
0
1
0
0
0
1
0
0
2
0
0
1
1
2
0
2
2
2
0
1
0
2
0
0
0
3
2
0
0
2
0
0
0
1
0
2
0
2
2
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
1
1
0
1
0
2
0
2
0
1
1
0
0
0
0
0
0
0
2
1
0
0
0
2
0
2
2
0
0
2
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
2
1
0
2
2
0
0
0
2
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
1
0
0
0
0
1
1
4
0
2
0
1
0
1
0
2
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
1
1
5
0
0
0
1
0
0
2
0
2
0
0
1
0
2
0
3
0
0
0
2
0
2
2
0
0
0
2
0
0
0
2
0
0
0
1
0
0
1
0
2
2
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
3
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
1
3
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
1
2
1
0
0
1
0
5
4
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
1
0
0
2
0
2
0
2
1
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
1
0
0
0
0
1
3
1
0
0
1
0
0
2
0
2
3
0
1
0
2
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
2
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
1
1
1
2
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
1
0
0
1
1
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
1
0
0
2
0
0
1
0
0
0
1
0
2
0
0
0
1
1
0
0
0
0
2
0
1
3
0
1
0
0
0
1
1
0
1
2
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
1
1
1
2
0
0
2
2
2
0
0
0
0
0
2
4
1
0
0
0
2
0
2
0
0
2
1
0
2
2
0
4
0
2
0
0
3
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
1
0
3
2
0
1
0
1
2
0
3
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
2
1
0
2
0
1
0
0
2
2
2
0
0
0
4
0
0
0
1
2
0
4
1
0
1
0
2
0
3
1
0
0
2
0
0
0
1
0
0
0
2
1
2
0
0
0
0
0
1
1
2
0
3
0
0
0
0
0
1
2
1
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
3
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
2
2
0
2
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
1
2
1
1
1
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
2
2
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
2
1
0
2
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
3
2
0
0
1
0
1
1
0
1
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
2
2
0
0
1
1
1
1
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
2
2
2
1
0
1
2
2
1
1
2
0
2
0
0
0
1
1
2
0
1
0
0
0
0
0
0
3
0
0
1
2
1
0
0
0
0
0
0
1
0
2
0
0
2
0
0
2
0
0
0
0
1
0
0
0
2
2
1
0
0
0
0
1
0
2
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
1
0
0
0
1
1
2
0
0
0
0
2
2
0
0
1
2
0
0
0
0
5
0
0
0
9
2
0
0
0
0
2
1
1
0
1
0
1
2
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
2
0
0
0
0
0
0
1
0
0
2
0
1
0
1
0
1
0
2
0
0
2
2
0
0
0
0
2
7
0
1
2
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
1
0
0
0
0
2
0
4
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
1
1
0
1
0
0
0
6
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
3
2
1
0
0
2
1
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
1
0
2
0
0
0
0
0
0
0
1
0
0
1
0
2
1
0
3
0
0
0
1
0
0
0
1
0
2
0
1
0
0
1
2
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
2
0
0
0
1
0
0
0
2
1
0
0
0
0
0
1
0
2
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
2
0
0
0
0
2
0
0
0
0
1
0
0
4
0
0
0
0
0
2
0
0
0
0
1
2
1
0
0
0
1
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
1
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
2
2
2
0
0
0
1
1
0
0
2
0
0
2
0
1
0
0
0
0
0
1
0
0
1
2
0
1
0
2
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
1
0
1
0
1
2
1
0
0
0
1
1
0
0
0
0
0
1
2
0
0
0
2
2
1
1
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
3
0
2
0
0
2
1
0
0
0
0
2
0
0
0
0
1
0
0
2
1
0
0
0
0
2
0
2
0
0
3
0
1
0
0
0
0
5
1
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
1
1
0
2
0
3
1
1
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
1
2
2
1
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
1
0
1
0
0
2
1
0
0
0
0
2
0
0
0
1
0
2
2
0
0
1
1
0
0
0
0
0
0
2
1
1
0
0
3
0
0
0
1
1
0
1
0
0
0
2
0
1
0
0
0
2
1
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
3
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
4
0
0
0
2
0
0
4
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
2
2
0
1
0
0
1
2
5
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
7
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
3
0
1
0
0
0
3
3
0
2
1
0
0
1
0
2
0
0
1
1
0
1
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
1
1
0
2
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
2
1
0
0
2
1
0
0
0
1
0
1
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
2
3
2
0
0
0
0
0
0
0
0
1
1
0
0
1
0
2
0
0
1
0
2
2
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
1
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
3
3
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
1
1
0
2
2
0
0
0
2
0
0
0
5
2
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
2
2
0
0
2
0
0
0
1
1
0
0
1
2
2
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
3
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
1
1
0
0
1
1
0
1
0
0
2
0
0
4
0
2
2
1
1
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
1
0
0
0
0
2
0
2
2
1
1
0
1
0
2
2
0
0
0
0
1
2
1
0
0
1
0
0
4
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
1
0
0
3
1
0
0
1
1
2
2
0
0
0
0
0
1
1
0
0
0
0
3
0
0
0
1
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
2
0
0
2
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
3
2
0
2
0
0
2
1
0
2
0
1
0
0
0
0
2
0
1
0
2
0
0
0
0
0
1
0
0
1
0
0
1
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
6
0
2
0
0
0
1
0
0
0
1
0
0
2
2
0
0
1
1
0
0
0
0
0
0
0
1
1
1
0
0
3
0
0
1
0
0
0
3
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
2
0
0
1
0
0
1
2
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
1
2
0
2
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
2
0
2
1
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
2
3
0
1
2
2
0
0
0
2
1
1
2
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
3
2
1
1
0
0
0
0
0
2
3
0
0
0
1
3
0
0
0
0
0
0
1
0
0
0
2
0
0
2
2
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
1
1
1
0
0
0
0
0
2
4
0
0
0
1
2
0
0
1
1
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
2
1
1
0
2
0
0
0
0
2
0
0
1
2
0
0
0
3
1
1
1
1
2
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
2
0
0
1
0
0
0
1
0
0
0
1
1
1
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
3
0
0
1
0
0
3
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
2
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
2
1
0
1
0
0
2
1
0
0
0
1
2
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
2
0
2
1
1
1
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
1
0
0
0
0
0
2
0
0
2
0
2
0
0
2
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
4
0
0
1
1
0
2
0
0
0
1
0
0
4
0
0
0
0
0
1
0
2
0
3
0
0
0
0
2
1
2
0
2
2
0
0
0
0
0
0
0
0
2
2
0
2
0
2
0
0
0
1
1
0
0
0
0
0
2
1
0
0
0
1
0
0
0
2
0
0
0
1
0
0
1
2
2
0
1
1
0
0
0
0
2
1
0
0
0
0
0
0
0
3
1
0
0
0
2
0
0
0
0
0
0
2
1
2
1
0
2
1
0
0
0
2
2
0
1
0
0
2
1
1
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
2
0
0
0
0
1
0
0
3
2
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
2
2
3
2
0
2
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
2
1
0
6
0
0
0
0
0
0
2
0
2
2
1
0
0
0
0
0
1
0
3
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
3
2
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
4
0
0
0
1
0
0
2
0
0
2
0
0
0
2
0
0
0
2
0
1
0
1
0
0
0
2
0
0
2
1
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
2
0
1
0
0
0
1
4
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
3
2
0
0
0
2
0
1
0
0
1
0
2
0
0
0
1
3
0
0
1
0
1
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
2
2
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
2
1
1
0
0
2
1
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
2
0
0
1
0
0
0
0
1
0
2
0
0
0
1
4
1
0
0
1
0
2
0
0
2
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
2
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
2
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
1
0
0
0
2
1
2
2
0
1
0
1
0
0
0
1
1
2
0
3
0
2
0
2
2
0
3
0
0
0
2
0
2
2
2
0
0
1
0
0
0
0
2
5
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
1
0
1
0
1
1
0
1
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
1
0
0
2
0
1
0
0
1
0
2
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
1
0
0
1
1
2
2
2
0
2
0
1
0
0
0
0
0
2
2
1
0
0
3
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
1
0
0
2
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
2
0
2
1
2
3
2
1
1
3
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
2
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
5
0
2
0
2
0
0
0
0
2
2
0
0
0
2
0
0
0
1
0
0
0
1
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
2
3
0
1
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
1
0
0
2
0
0
0
0
2
1
2
0
0
0
0
0
1
0
0
0
0
1
2
0
0
2
0
2
0
1
1
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
2
0
0
1
1
1
2
0
0
2
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
4
0
0
2
0
0
0
0
0
2
2
1
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
3
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
4
2
2
0
0
0
0
2
0
0
1
0
2
0
1
0
0
1
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
2
0
0
0
0
1
0
1
3
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
1
0
2
0
0
1
1
0
0
1
1
1
0
0
1
1
0
5
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
2
2
0
0
2
0
0
1
0
2
0
0
0
2
0
1
0
0
2
0
2
0
3
0
0
0
2
2
1
1
0
0
0
0
0
1
1
0
0
0
0
0
2
0
1
1
0
2
0
3
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
1
1
3
2
0
0
0
2
2
0
2
2
2
0
0
0
2
0
3
0
0
0
2
0
1
0
1
1
0
1
1
0
0
0
0
0
0
0
2
0
0
1
2
0
0
2
2
2
0
0
0
2
0
0
0
0
0
2
2
0
1
0
0
1
0
0
2
0
1
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
3
3
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
2
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
3
0
9
0
0
0
0
0
0
0
1
0
0
2
0
1
0
1
1
0
0
0
2
0
0
1
0
0
0
0
0
0
1
3
1
3
0
0
3
0
1
0
0
0
0
0
2
0
0
1
0
2
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
4
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
2
1
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
2
1
3
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
1
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
3
2
0
0
1
0
0
1
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
2
2
0
0
3
0
0
0
0
0
0
0
2
0
0
2
1
0
4
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
2
0
1
1
0
0
14
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
1
0
1
0
0
3
0
0
2
0
0
0
2
0
1
0
0
0
3
1
1
0
0
1
0
2
0
0
2
0
2
0
0
1
1
0
1
0
2
2
0
0
2
0
0
0
0
0
0
1
0
0
3
0
0
2
0
0
0
1
1
0
1
0
0
0
2
1
0
1
1
0
2
0
0
0
1
0
0
2
0
1
0
0
0
0
3
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
2
2
1
0
3
0
0
0
0
1
0
3
1
0
2
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
2
2
0
0
0
1
0
0
1
2
0
0
1
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
5
0
0
2
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
2
0
2
2
0
2
1
0
0
3
1
1
0
1
0
0
2
2
0
1
0
0
3
0
0
1
1
3
2
0
0
0
1
0
0
0
0
0
3
2
2
0
0
0
0
0
1
1
0
0
0
0
0
2
2
0
2
0
1
5
1
0
0
0
0
0
0
0
1
0
0
0
1
1
2
0
2
0
0
0
2
1
0
0
0
0
1
2
2
0
1
0
2
2
0
4
0
1
0
0
0
0
3
1
1
0
1
0
0
3
2
0
2
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
1
0
0
0
0
2
0
2
2
0
2
0
2
0
0
0
2
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
2
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
2
2
0
2
0
0
2
0
0
0
0
2
0
0
2
1
0
1
3
0
2
0
0
1
0
0
1
3
0
0
1
0
2
0
1
0
0
0
2
0
0
0
0
1
4
0
0
2
0
0
2
0
1
0
1
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
1
0
3
0
0
1
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
1
0
0
0
2
0
2
1
1
0
0
1
0
3
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
2
0
0
0
0
2
0
0
5
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
1
5
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
1
0
3
0
0
5
0
0
0
1
0
0
1
0
0
1
0
1
2
0
2
0
0
1
1
0
0
2
0
2
2
2
0
0
1
2
2
0
0
1
2
2
0
0
0
0
6
1
0
0
1
0
0
0
0
2
0
0
1
1
2
0
0
0
0
0
0
0
1
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
1
2
0
0
1
0
2
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
2
2
0
2
0
2
0
0
0
0
0
0
0
2
0
2
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
2
0
1
0
0
0
0
0
2
2
0
1
0
1
0
0
0
1
0
0
0
4
3
0
0
2
2
0
3
0
0
2
0
1
0
0
1
0
0
0
0
1
0
2
0
2
1
0
0
0
0
1
0
1
0
0
2
0
0
0
3
2
0
0
0
1
0
0
0
0
1
0
0
1
0
2
0
0
0
0
1
0
1
1
0
0
0
0
0
0
2
1
0
2
0
0
1
1
0
0
0
0
1
1
0
0
2
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
1
0
2
2
1
0
0
2
0
0
1
0
0
0
1
1
0
0
2
0
0
2
0
0
0
2
0
2
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
2
0
0
0
2
0
1
0
0
2
0
0
0
0
0
3
2
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
4
0
0
0
1
1
0
1
2
0
2
0
0
0
1
0
0
1
2
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
2
0
0
0
2
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
2
0
1
0
0
0
0
1
0
0
0
1
0
3
1
0
0
1
0
0
0
0
0
0
1
0
2
2
0
0
2
1
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
2
0
0
0
4
0
0
1
0
0
0
0
0
1
0
0
0
2
0
2
0
1
0
0
0
0
1
0
0
2
0
1
2
0
0
0
0
1
1
0
1
1
0
1
0
2
0
0
2
0
2
1
0
0
2
1
1
0
0
0
0
2
1
2
7
0
0
1
0
0
0
0
0
0
0
0
2
0
4
2
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
1
2
1
0
2
0
0
0
0
0
0
0
2
1
2
0
1
1
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
2
0
2
0
2
0
2
1
0
0
0
0
3
3
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
2
2
2
2
0
0
2
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
3
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
1
0
0
0
0
2
6
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
1
2
0
0
1
0
0
0
0
3
3
0
2
0
2
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
1
0
0
2
4
0
1
0
0
2
0
0
0
0
0
3
0
0
0
0
4
2
0
0
0
0
0
1
0
0
0
0
0
3
0
1
0
0
0
0
0
0
3
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
1
2
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
1
2
0
1
0
0
2
1
0
0
0
0
1
0
1
2
0
0
1
0
0
0
0
0
2
2
1
0
1
0
0
1
0
0
3
0
0
0
0
1
2
0
0
0
0
0
2
0
0
2
2
0
0
1
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
4
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
2
1
0
0
2
3
5
2
0
1
0
0
1
0
0
0
0
10
0
4
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
1
1
2
0
0
0
0
2
2
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
1
0
2
1
0
1
0
0
0
0
0
1
0
2
0
3
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
2
2
2
0
0
1
0
0
1
0
0
2
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
1
2
0
0
1
1
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
3
2
0
2
0
0
1
0
0
0
0
0
0
1
2
2
0
0
0
0
0
2
2
1
0
0
2
0
1
1
0
2
0
2
2
0
1
2
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
2
2
0
0
0
4
0
0
1
0
2
1
0
1
1
0
0
1
0
1
0
1
0
0
0
0
2
0
3
2
1
0
0
0
0
1
2
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
1
0
0
0
2
0
0
3
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
2
0
1
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
1
2
1
0
0
2
2
0
0
0
1
0
1
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
2
1
2
0
0
1
0
2
2
1
0
2
0
1
2
2
0
3
0
1
0
0
1
0
0
0
2
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
2
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
1
2
2
0
2
0
0
0
0
0
2
0
1
0
1
0
0
2
2
0
2
2
0
0
0
0
3
0
0
1
0
1
1
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
2
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
3
1
2
0
0
2
0
0
1
3
0
0
1
0
0
0
1
2
0
1
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
1
0
0
2
0
0
0
1
1
2
2
2
0
0
0
0
1
0
0
0
0
0
0
2
1
0
3
0
1
0
0
1
1
0
1
3
0
0
0
0
0
0
1
0
1
0
1
2
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
1
2
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
2
1
0
0
0
0
0
0
1
0
0
3
0
1
0
0
1
2
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
2
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
2
0
3
0
2
1
0
0
0
1
0
0
0
0
0
1
0
1
1
0
2
0
1
2
0
0
2
0
0
0
0
1
0
0
4
0
0
1
0
0
0
1
1
1
1
0
1
0
0
0
0
0
0
0
0
2
2
1
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
4
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
2
1
0
2
0
1
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
2
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
1
2
2
1
2
2
0
0
1
0
0
0
0
0
2
0
3
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
1
0
0
3
1
0
0
2
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
9
0
2
0
0
0
0
1
0
1
2
0
0
1
0
0
2
2
0
1
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
2
0
0
0
0
0
0
2
2
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
2
1
0
0
0
2
0
2
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
1
2
0
0
0
0
0
1
1
0
2
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
3
1
2
0
1
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
1
1
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
2
1
0
0
0
0
0
2
0
0
1
0
2
0
0
2
1
0
0
0
1
1
0
0
0
3
0
0
0
1
1
1
1
1
0
0
0
1
0
0
1
0
0
0
0
0
2
2
1
0
2
2
0
2
1
0
0
2
2
1
2
2
0
0
2
0
0
0
0
0
0
0
0
0
2
1
1
0
1
2
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
2
0
1
0
3
0
1
1
1
0
1
0
0
0
0
0
0
2
0
2
0
0
2
2
0
0
0
0
0
0
0
0
2
2
0
0
2
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
1
0
0
0
3
1
0
0
1
0
0
0
3
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
2
0
2
1
2
2
0
0
0
0
1
2
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
1
2
0
1
2
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
4
0
0
0
2
1
0
2
0
1
2
0
0
0
4
0
0
1
0
0
0
0
0
1
0
2
0
0
0
4
0
1
0
2
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
3
0
1
0
0
0
0
3
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
3
1
0
0
0
0
1
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
1
2
0
0
2
0
0
1
0
0
3
0
0
1
0
1
0
0
0
2
2
0
0
2
0
0
0
0
2
0
1
0
0
0
2
3
0
0
0
0
0
0
1
0
1
1
3
0
4
0
0
0
0
0
2
2
0
0
1
0
0
2
2
0
1
0
0
0
0
2
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
1
0
2
2
0
0
0
2
2
0
2
0
1
0
0
1
0
0
0
2
2
0
0
0
0
0
0
1
2
2
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
2
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
1
0
0
0
1
1
1
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
2
0
2
0
0
2
0
0
0
0
0
0
1
0
2
1
0
0
1
2
0
0
0
1
2
0
0
0
2
1
0
0
0
0
0
0
0
2
2
0
1
0
7
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
2
0
0
1
2
0
0
3
1
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7
2
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
1
0
3
0
3
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
3
0
1
0
0
0
2
1
1
2
3
2
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
7
2
0
2
0
0
1
0
1
0
0
2
0
0
0
0
2
0
2
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
1
4
0
0
0
2
0
0
0
1
0
1
2
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
1
0
0
0
0
2
0
0
1
0
2
0
0
1
2
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
2
1
0
0
1
2
0
0
0
0
0
0
0
4
0
2
0
2
0
0
0
0
0
0
1
1
1
0
0
0
0
6
0
0
0
1
0
0
1
0
2
1
0
1
1
0
0
0
0
0
0
3
0
0
0
2
0
0
0
1
0
0
1
0
2
2
0
2
2
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
1
0
0
2
1
0
0
1
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
2
0
0
0
0
1
0
0
1
1
0
0
1
0
0
1
1
1
1
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
1
0
0
1
0
0
0
1
3
0
0
0
1
1
0
0
1
0
2
0
1
0
1
1
2
2
0
0
2
1
0
0
0
0
0
0
0
1
0
2
0
2
0
1
1
0
1
0
0
0
0
0
2
0
0
1
0
0
1
2
0
0
2
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
1
0
0
0
1
2
0
0
1
0
3
0
0
0
0
2
0
0
1
2
0
2
1
0
1
2
0
0
0
0
1
0
0
0
0
1
0
0
0
4
0
0
0
1
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
2
2
1
0
1
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
3
2
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
5
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
1
1
0
0
0
0
0
2
0
2
0
1
0
0
0
2
1
0
0
2
0
0
0
0
1
0
0
1
1
2
2
0
0
3
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
1
4
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
1
1
4
2
0
1
0
1
0
1
1
0
2
1
0
1
0
0
1
0
0
0
1
0
0
0
1
1
0
0
1
0
0
1
1
2
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
2
2
0
1
0
1
1
1
1
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
2
2
2
0
0
0
0
0
0
3
2
0
2
0
1
1
1
2
0
2
2
0
0
1
0
0
0
2
0
0
0
2
1
0
1
0
0
0
0
0
0
3
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
2
0
0
0
1
0
1
0
0
1
3
0
0
0
1
3
0
2
2
0
0
2
1
0
0
0
0
2
2
0
0
1
0
0
4
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
2
0
1
1
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
3
0
0
0
1
0
0
0
2
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
2
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
2
3
0
0
0
0
2
0
2
0
0
0
0
2
0
2
0
5
0
1
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
7
0
1
0
0
0
1
1
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
1
0
3
0
1
0
1
0
0
2
0
0
1
2
1
2
0
1
0
0
0
0
0
0
3
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
2
0
3
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
2
0
0
0
0
0
0
0
1
2
0
1
0
1
0
0
0
1
0
0
0
3
0
0
0
2
2
0
0
2
2
0
1
0
2
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
1
0
0
0
1
1
0
2
0
0
0
0
1
2
0
1
2
1
0
0
0
0
0
1
2
2
0
3
0
0
0
0
0
0
1
0
0
1
0
0
0
1
2
3
0
1
2
0
1
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
2
2
1
4
0
1
0
1
0
0
0
0
0
0
0
0
0
2
1
1
1
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
3
2
0
0
0
1
1
0
2
0
7
2
0
0
0
2
1
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
1
0
0
0
0
0
2
0
1
0
2
1
1
0
0
0
0
0
4
2
0
0
0
0
0
2
1
0
0
1
0
2
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
1
3
0
2
0
0
2
1
0
0
0
0
0
0
2
2
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
3
1
0
0
0
0
0
0
0
0
1
1
0
0
4
0
0
0
0
0
2
2
0
0
0
0
2
1
1
2
2
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
2
1
0
0
0
1
0
0
2
0
1
0
2
0
0
0
0
0
2
0
2
0
3
0
0
3
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
1
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
2
1
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
2
0
0
0
0
1
1
1
0
0
2
2
0
0
0
0
0
0
2
0
0
2
2
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
3
2
0
0
0
0
2
2
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
10
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
1
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
3
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
3
0
0
2
1
0
0
0
0
3
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
2
0
0
0
2
2
0
0
1
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
2
6
2
4
1
3
0
0
3
0
0
0
0
2
1
0
0
0
2
0
0
0
1
0
0
0
3
0
0
1
0
0
0
0
0
2
2
2
0
0
1
0
0
1
2
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
4
0
1
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
2
0
0
2
0
2
1
0
0
0
0
0
0
1
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
5
2
2
0
0
0
0
0
0
1
0
0
0
1
0
0
1
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
2
0
1
1
0
0
3
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
2
1
0
2
0
0
0
0
1
0
0
0
0
2
0
1
0
22
0
0
1
1
0
0
0
0
0
0
0
2
0
1
0
1
2
0
4
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
2
1
1
2
0
2
4
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
3
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
3
1
0
0
3
0
0
0
0
0
0
2
2
0
0
0
1
0
1
0
0
2
0
1
2
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
2
0
0
0
3
0
1
0
0
0
0
1
0
0
1
2
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
3
0
0
1
0
0
2
0
0
0
2
0
0
2
0
0
1
0
0
0
4
0
0
2
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
2
2
0
1
1
0
0
0
0
0
0
1
2
0
0
0
0
2
0
1
0
2
2
1
0
0
2
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
2
0
2
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
2
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
2
1
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
2
0
1
0
0
0
0
0
1
1
0
1
1
1
0
0
0
2
0
0
0
0
3
2
1
0
0
1
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
2
0
0
0
2
1
0
0
0
0
0
0
4
0
0
0
0
0
0
2
2
0
2
1
0
1
0
0
0
1
0
1
0
2
0
0
0
0
1
1
0
0
0
2
0
0
0
2
0
0
0
2
0
1
0
0
0
1
1
5
1
0
0
0
0
2
0
0
1
0
2
0
0
2
0
1
1
0
1
1
0
2
0
0
0
0
0
0
0
0
0
2
1
0
2
2
1
1
0
0
0
0
0
0
1
1
0
1
0
0
2
0
1
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
1
0
1
1
1
2
2
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
1
1
0
0
0
1
2
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
5
0
0
0
2
2
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
1
1
2
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
2
0
3
0
0
1
0
0
0
0
0
1
0
0
0
2
2
0
0
1
2
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
4
0
0
0
0
1
1
3
0
3
0
1
0
0
2
0
0
0
2
0
0
2
0
0
2
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
1
0
0
2
0
0
0
0
1
0
0
0
1
0
2
2
1
2
0
0
0
2
0
0
2
0
0
0
0
0
0
10
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
4
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
2
1
0
3
0
0
0
4
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
3
0
0
0
0
0
1
0
0
1
0
2
0
0
2
0
0
2
0
1
1
0
0
0
0
2
0
2
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
2
0
0
0
2
2
0
0
3
1
0
0
1
0
0
1
0
2
2
0
0
1
0
1
2
0
0
1
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
1
1
1
0
3
2
1
2
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
4
0
0
0
0
1
0
2
1
0
0
0
2
0
0
0
0
0
2
1
0
0
1
0
0
1
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
2
1
2
0
0
0
2
0
0
1
0
4
0
0
2
4
0
0
0
1
0
2
0
1
0
1
0
0
0
2
2
2
2
0
0
0
0
0
2
2
1
0
0
0
2
1
2
2
2
1
0
2
2
0
0
0
1
0
1
3
2
0
0
0
0
1
0
0
1
1
0
0
2
0
3
0
0
0
2
0
0
0
2
1
0
0
0
2
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
1
2
0
0
3
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
5
1
2
0
0
2
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
2
2
2
1
1
0
1
0
0
2
1
2
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
1
1
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
3
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
3
0
0
2
0
0
0
0
1
0
0
2
0
0
2
0
0
0
2
3
0
0
1
0
2
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
2
0
0
0
2
0
1
0
0
0
2
1
0
2
0
0
0
0
0
2
0
1
0
0
1
0
3
0
0
1
0
0
0
0
0
1
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
3
0
0
0
2
1
0
2
0
1
0
0
0
0
0
0
2
1
0
0
0
0
1
0
1
0
1
0
0
0
1
0
2
1
0
0
2
2
0
0
0
1
0
0
0
0
1
1
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
3
1
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
1
0
1
0
0
2
3
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
2
0
0
0
1
1
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
2
2
0
0
0
1
1
0
0
0
0
2
2
0
0
0
1
0
0
1
0
0
0
0
0
2
0
1
0
3
0
1
2
0
0
0
0
1
5
1
1
0
0
0
0
2
0
0
0
0
0
2
2
2
0
0
0
0
1
0
0
2
2
0
0
0
0
2
1
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
4
2
0
0
0
0
0
4
0
1
0
2
0
0
1
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
1
4
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
6
3
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
1
1
2
1
1
1
1
1
2
0
1
0
2
0
0
0
0
1
0
0
0
0
1
0
2
0
1
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
4
0
2
0
2
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
1
0
0
2
0
0
0
2
0
0
0
2
1
0
0
1
0
0
7
0
0
0
0
0
0
0
0
1
0
2
0
0
2
2
0
2
2
0
2
1
0
3
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
1
0
0
0
2
1
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
3
0
0
2
2
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
1
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
2
0
0
0
0
2
0
1
0
2
0
2
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
2
0
1
0
0
1
2
0
2
0
0
0
0
0
1
2
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
1
0
2
2
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
2
0
0
0
0
3
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
1
3
0
1
0
1
0
0
0
0
2
0
1
0
0
1
0
1
0
0
2
1
1
2
0
0
1
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
1
0
0
2
1
0
0
0
0
0
0
0
0
1
0
2
0
2
2
0
1
2
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
3
1
2
0
1
2
0
0
0
2
0
0
3
1
0
0
0
0
2
1
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
1
0
2
2
2
0
0
1
2
3
1
2
2
2
0
0
2
3
3
2
1
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
1
0
2
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
2
1
0
1
1
0
2
0
0
0
2
0
0
1
0
2
2
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
2
0
5
0
0
0
1
0
2
2
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
3
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
2
2
0
0
0
0
0
1
2
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
1
0
2
2
2
0
1
0
0
0
0
0
5
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
3
0
0
0
1
1
0
0
0
1
2
3
1
0
0
0
0
0
2
0
0
2
2
2
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
2
0
1
0
0
2
2
0
0
2
0
1
0
0
0
0
1
2
0
0
0
0
3
2
0
0
0
0
0
2
0
1
3
0
2
0
5
1
0
0
2
0
2
0
2
0
1
0
0
0
0
2
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
1
1
0
1
0
0
0
2
0
0
0
0
3
1
0
2
2
1
0
1
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
1
1
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
4
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
1
0
2
1
0
2
1
0
0
2
0
0
2
3
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
3
1
0
2
1
2
0
1
0
2
1
0
0
2
0
1
1
0
0
0
0
1
3
0
1
0
0
0
0
0
0
0
0
3
2
0
2
1
0
0
6
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
1
0
4
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
1
4
0
3
0
0
1
0
3
2
0
1
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
3
0
2
2
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
1
0
0
0
2
0
2
0
0
2
0
0
0
1
0
1
0
0
1
1
0
1
1
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
1
1
0
1
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
6
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
1
0
2
0
0
1
0
1
3
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
1
0
0
4
1
0
0
0
1
0
3
0
0
0
0
0
0
0
0
3
1
0
1
1
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
2
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
2
1
0
1
2
0
2
0
0
0
0
0
0
2
0
0
1
0
0
2
0
1
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
1
0
2
1
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
2
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
4
0
0
0
0
0
1
0
0
0
0
1
0
1
0
2
0
3
0
2
2
1
1
0
0
0
4
0
0
0
1
1
0
0
0
2
2
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
3
0
1
0
1
0
0
0
0
2
0
0
0
2
1
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
2
4
0
0
0
2
1
2
0
0
1
0
0
0
2
2
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
3
0
1
0
0
0
0
3
0
0
2
0
0
0
1
0
0
0
5
0
0
0
0
1
1
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
2
3
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
1
1
1
1
0
0
2
0
1
0
1
0
3
1
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
1
4
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
2
2
0
0
1
0
0
1
0
0
0
0
0
0
1
2
0
2
1
2
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
2
2
0
1
1
5
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
1
0
2
1
0
1
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
2
0
1
1
3
2
1
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
1
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
1
1
0
1
0
0
1
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
7
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
1
1
0
1
0
1
0
0
0
4
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
1
2
0
0
0
0
0
3
0
1
1
0
0
0
0
0
0
2
0
2
0
0
1
0
2
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
3
0
1
0
0
0
2
0
1
0
1
1
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
1
3
0
2
2
0
2
0
0
0
3
1
1
0
0
0
2
2
1
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
1
0
5
0
0
0
0
0
0
0
0
0
2
0
0
3
0
2
0
0
2
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
2
0
0
2
2
0
0
1
1
0
2
0
0
0
0
1
0
1
2
0
2
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
2
0
1
0
1
0
1
0
0
0
0
0
0
1
0
2
1
0
1
1
0
1
0
0
0
2
0
0
7
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
2
0
1
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
2
0
0
0
0
1
0
1
0
1
0
0
2
1
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
2
1
0
0
2
0
0
1
0
0
3
0
2
2
0
1
0
0
0
4
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
2
2
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
1
0
5
0
0
2
0
0
1
0
0
6
0
0
0
0
0
2
0
0
1
2
0
0
2
0
0
0
1
0
1
0
4
0
2
0
1
0
2
0
1
1
0
0
2
0
1
0
1
2
0
2
0
1
0
2
1
0
0
0
0
0
1
2
1
0
0
2
2
2
0
0
0
0
0
0
0
0
3
0
0
0
3
1
0
0
2
1
0
3
0
2
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
2
0
0
1
2
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
1
0
2
0
1
0
0
1
0
0
0
0
2
0
0
1
0
0
0
1
0
4
1
0
0
1
0
3
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
3
0
1
0
0
2
0
0
0
0
0
0
0
2
1
0
0
2
0
2
0
0
0
0
1
2
2
0
2
0
0
0
0
0
1
0
0
0
0
0
7
1
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
2
0
1
1
2
2
0
2
0
0
0
2
0
0
0
0
2
1
0
3
0
2
1
2
1
0
0
1
0
2
3
0
1
0
2
1
2
0
0
0
0
0
0
4
0
0
1
0
1
0
0
2
0
0
0
0
0
2
1
0
2
0
2
0
0
0
0
0
0
0
1
0
2
0
1
2
0
0
0
2
0
2
0
1
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
2
1
0
0
0
1
0
0
1
0
2
0
0
1
2
3
0
1
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
2
0
1
2
0
0
1
3
1
0
1
0
0
0
3
0
0
2
0
0
0
4
1
0
0
0
0
0
0
1
0
1
0
1
3
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
3
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
1
0
0
0
2
0
0
0
0
2
0
0
0
1
2
0
1
0
1
0
0
0
0
1
1
0
0
1
3
1
2
0
0
0
4
1
0
0
0
1
1
0
0
0
0
2
2
0
2
0
0
4
0
1
0
0
0
0
0
1
1
2
1
0
0
3
0
1
0
2
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
1
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
1
4
2
2
0
0
0
3
0
0
2
0
0
1
0
0
0
0
0
1
2
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
2
0
1
0
0
2
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
3
0
2
1
0
0
0
0
0
0
0
0
1
1
0
0
1
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
2
2
0
0
0
0
0
0
0
0
1
0
4
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
1
0
2
0
2
1
0
2
0
0
0
0
1
2
0
0
1
0
0
0
0
0
2
1
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
2
6
0
5
0
0
1
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
2
2
2
0
0
0
0
2
1
0
0
2
0
1
2
0
3
0
1
0
2
1
1
0
1
0
0
0
0
0
1
0
0
0
0
1
2
2
0
2
0
0
0
0
0
2
3
0
0
1
0
0
0
0
2
2
0
0
0
0
1
0
0
1
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
1
0
1
0
0
0
3
4
0
2
0
1
0
2
0
2
1
0
0
0
0
0
2
2
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
3
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
2
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
2
1
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
3
2
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
1
3
0
0
0
4
1
0
0
0
0
0
0
1
3
1
0
2
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
2
0
0
4
0
0
0
0
0
3
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
3
0
0
0
0
2
2
0
0
2
0
0
0
3
0
0
0
1
0
0
0
0
3
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
2
1
1
0
0
0
0
0
1
0
2
0
1
0
0
1
2
0
0
0
1
1
1
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
2
5
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
1
0
2
0
1
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
1
1
0
1
2
1
1
2
0
0
0
2
1
1
0
0
0
2
3
0
1
0
0
0
0
0
1
0
0
1
3
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
1
1
2
4
1
0
0
1
0
1
0
0
0
2
0
0
1
2
0
0
3
2
0
0
0
0
2
0
0
0
2
0
0
0
1
2
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
1
0
1
2
0
0
1
0
2
1
0
0
0
2
0
0
0
1
0
0
2
0
2
0
1
2
0
0
0
0
1
1
2
0
2
1
0
0
0
0
0
1
2
2
0
2
0
0
2
0
2
0
1
2
0
0
0
2
0
2
1
2
1
0
1
0
1
3
0
0
2
0
3
0
0
0
1
3
1
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
4
0
2
0
0
0
0
2
1
0
0
0
5
0
0
1
0
1
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
3
0
0
0
1
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
1
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
1
5
0
0
0
0
0
0
0
2
0
2
0
0
0
2
1
0
1
0
0
2
2
1
0
3
0
0
0
0
0
0
1
0
0
0
0
2
3
0
2
1
0
0
0
0
0
0
1
2
0
0
0
2
0
0
2
2
0
0
1
0
2
0
1
0
1
1
1
0
2
1
0
2
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
3
0
0
0
1
0
2
0
0
2
0
2
1
1
0
2
0
1
1
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
2
1
1
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
2
1
1
0
0
0
2
2
0
0
0
4
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
1
1
0
0
1
0
1
0
0
2
0
2
0
1
1
0
0
0
1
0
0
1
6
0
3
2
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
1
0
0
0
0
0
0
2
1
1
0
1
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
2
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
2
0
0
0
1
4
0
0
0
0
2
2
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
3
2
0
2
0
0
0
0
0
1
0
1
1
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
1
0
2
1
0
0
0
0
1
0
0
0
1
1
0
0
0
3
1
0
1
1
2
0
0
0
0
1
0
0
2
3
0
0
0
0
1
0
2
0
0
0
0
0
0
2
2
1
0
1
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
2
0
1
0
2
3
0
0
0
2
0
0
0
1
2
0
0
2
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
3
0
2
0
2
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
3
0
2
0
0
0
1
0
2
0
2
2
0
1
2
0
2
0
0
3
0
0
1
4
0
1
2
0
0
0
0
2
2
1
1
1
0
0
0
2
6
0
0
2
2
0
0
0
2
0
0
2
0
2
2
2
0
0
0
0
0
0
4
1
0
0
0
4
2
2
1
0
0
0
1
0
0
0
0
0
1
0
0
1
5
0
0
2
0
2
0
2
0
0
0
0
2
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
4
0
1
0
1
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
3
0
0
0
0
0
2
1
0
0
0
0
2
0
0
3
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
2
0
0
0
0
1
1
1
4
1
0
2
0
0
0
2
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
3
0
2
0
2
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
2
2
2
2
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
5
2
1
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
2
3
0
0
2
0
0
2
0
0
1
0
1
1
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
3
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
2
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
2
0
0
0
2
0
0
1
0
0
1
0
2
0
0
0
0
2
2
1
2
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
6
2
2
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
4
1
0
1
0
1
2
0
0
0
0
2
2
0
0
1
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
5
0
1
2
2
1
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
2
0
1
2
0
0
0
0
0
2
0
0
3
0
0
1
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
2
0
0
2
0
1
0
0
0
0
0
2
6
1
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
2
1
0
0
2
3
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
2
1
1
0
1
0
0
0
0
2
2
0
0
2
2
0
0
0
1
0
0
0
0
2
0
0
1
0
2
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
3
0
0
1
2
1
3
2
2
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
1
2
0
0
0
1
0
0
0
0
3
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
1
1
3
1
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
1
1
0
0
2
0
0
1
0
0
0
0
0
3
0
1
2
0
0
0
2
2
0
0
0
0
2
0
1
0
1
1
0
0
0
0
0
0
0
0
1
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
1
2
0
0
0
0
2
1
3
0
2
0
1
0
0
0
7
0
2
1
0
0
0
1
0
0
4
0
2
0
0
0
0
0
3
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
2
0
1
0
0
1
2
0
1
0
3
0
2
0
1
0
0
0
5
2
0
0
0
2
0
0
0
2
0
2
0
0
1
0
0
0
2
2
0
0
1
0
2
0
1
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
3
0
2
0
2
0
0
1
0
1
0
0
0
0
2
1
0
2
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
2
0
0
1
2
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
1
0
3
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
2
2
0
0
0
0
1
0
0
0
0
0
0
1
1
2
0
1
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
2
1
0
0
1
0
0
0
0
1
0
2
1
0
0
2
2
1
0
0
0
1
0
0
1
0
0
1
1
0
0
2
0
2
0
0
0
3
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
3
0
2
0
0
1
0
0
1
0
1
0
0
0
3
0
0
0
0
2
0
0
0
1
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
2
1
1
0
0
0
0
0
0
1
2
1
1
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
1
2
0
0
0
0
0
0
4
0
0
0
0
0
1
1
0
2
0
0
2
0
0
1
2
0
1
0
1
0
2
2
2
1
0
2
6
0
1
2
1
0
0
2
1
2
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
5
0
1
0
1
0
4
1
0
2
2
1
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
2
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
2
1
0
3
0
1
0
0
2
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
2
3
0
0
3
1
0
0
0
0
1
1
0
0
0
1
1
3
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
4
0
1
2
0
0
0
0
2
0
3
1
0
0
1
0
0
1
1
0
2
0
0
2
0
0
0
0
9
0
0
0
0
2
0
1
2
0
0
0
1
0
1
0
1
0
2
0
1
0
0
0
0
1
0
1
0
0
0
0
0
2
0
2
0
1
1
1
2
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
3
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
2
1
0
0
0
2
0
0
0
6
1
0
0
0
1
0
0
4
0
0
2
0
2
2
0
1
0
0
0
0
1
0
1
2
0
0
7
0
0
1
0
0
1
0
1
2
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
1
0
0
0
0
0
0
4
0
1
0
2
1
0
0
0
4
0
0
0
1
1
1
0
2
0
0
0
0
0
2
0
2
0
0
1
0
2
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
2
0
2
0
0
0
0
2
2
3
0
0
0
0
1
0
2
0
0
2
0
0
1
2
0
0
0
0
0
0
0
4
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
2
0
0
1
0
0
2
2
2
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
3
0
0
0
0
0
3
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
1
1
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
2
4
0
0
0
0
3
1
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
1
0
3
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
3
0
2
0
1
2
0
0
0
1
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
1
1
0
0
0
1
0
0
0
0
1
4
2
0
2
0
0
0
1
2
0
2
0
0
0
3
0
1
0
0
2
0
0
0
2
0
0
0
0
2
0
2
0
2
0
2
0
2
0
0
0
0
0
2
3
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
2
0
2
1
0
0
0
2
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
3
0
0
4
0
0
2
0
0
0
0
0
0
0
9
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
4
6
1
0
0
0
0
0
1
0
0
2
2
2
0
0
2
0
0
0
1
1
2
0
0
1
0
0
0
1
0
2
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
1
1
2
0
0
0
0
0
0
3
0
0
1
3
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
2
2
2
0
1
0
0
0
0
0
0
0
6
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
1
1
1
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
1
0
2
0
1
0
2
0
0
0
0
1
0
2
0
4
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
2
0
0
2
1
0
0
2
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
3
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
3
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
2
0
1
0
1
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
4
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
3
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
2
2
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
1
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
2
0
2
1
1
1
0
1
0
0
0
2
0
0
0
1
0
1
2
0
0
0
1
0
1
2
1
0
1
2
0
1
0
2
0
0
0
1
1
0
0
0
0
0
1
1
2
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
2
1
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
2
0
0
0
1
2
2
0
2
0
0
1
0
0
0
1
0
0
0
1
1
0
0
1
0
1
2
0
2
0
0
0
2
4
1
2
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
1
2
2
1
0
0
0
2
2
0
0
0
0
1
0
1
0
1
2
0
1
2
0
2
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
1
3
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
1
0
2
0
0
0
1
2
0
0
0
2
0
0
0
0
1
1
0
0
0
2
2
0
0
0
0
2
0
1
2
0
2
0
0
0
0
0
2
1
1
12
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
1
2
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
1
4
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
2
1
0
0
1
0
2
0
0
0
2
0
0
0
1
0
2
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
1
0
2
0
0
0
2
0
0
2
2
0
0
2
0
0
0
0
3
0
1
0
0
2
2
1
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
1
0
0
3
1
1
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
3
2
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
2
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
1
0
0
2
0
3
0
1
1
0
0
0
0
0
2
1
0
0
0
1
0
0
0
2
2
1
0
2
0
0
0
3
0
2
1
0
1
4
0
0
0
0
0
1
1
0
1
2
0
0
1
0
0
0
1
1
0
0
0
0
0
1
2
2
0
2
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
2
1
0
0
1
2
1
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
5
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
1
0
0
2
0
0
0
2
1
0
1
1
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
2
1
2
3
0
0
0
0
0
1
1
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
2
0
0
0
1
0
0
0
1
0
2
0
0
0
1
0
0
0
2
0
0
0
2
0
0
1
1
0
0
0
2
1
2
0
0
2
0
0
0
0
0
0
0
2
0
2
1
0
0
2
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
3
1
0
0
0
2
0
5
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
1
0
1
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
2
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
9
0
0
1
2
0
0
0
2
0
0
0
6
0
0
2
0
0
1
0
1
0
1
1
0
0
0
2
0
0
0
0
2
0
0
1
0
1
0
0
2
0
0
2
2
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
2
1
0
2
0
0
0
1
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
2
1
0
0
2
2
0
1
0
0
1
0
1
0
2
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
1
0
0
3
0
0
2
0
2
2
0
2
0
0
2
1
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
2
1
0
0
0
0
0
0
0
2
0
1
2
0
0
3
0
1
0
0
0
2
1
0
0
0
0
0
1
0
2
0
1
2
0
0
2
0
0
2
1
0
0
0
0
0
0
2
0
0
1
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
2
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
2
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
2
3
0
0
0
0
0
0
0
1
0
0
2
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
2
0
0
1
0
1
0
2
0
0
0
0
0
1
2
0
0
2
0
1
0
1
1
0
0
2
0
0
0
0
0
2
0
0
3
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
12
0
0
0
0
1
1
0
0
0
1
0
2
0
0
1
0
0
0
1
0
0
0
1
0
2
1
1
0
0
0
0
2
2
2
1
2
1
0
0
0
0
2
0
0
2
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
2
2
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
2
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
2
0
2
0
0
0
3
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
1
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
2
1
0
0
2
0
0
1
2
0
0
0
1
0
1
0
1
0
0
0
4
0
1
0
1
1
0
0
0
2
2
1
2
0
0
0
0
1
0
2
0
1
2
3
0
0
1
0
0
1
0
2
0
0
0
0
2
1
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
1
0
2
0
0
1
0
0
1
0
0
0
3
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
5
0
2
0
0
0
1
2
0
0
0
1
0
2
3
0
1
0
0
3
0
0
0
0
2
0
0
2
0
0
1
8
0
0
0
4
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
3
2
0
2
0
0
1
1
0
1
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
8
0
0
2
0
0
0
0
2
0
1
2
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
1
0
0
1
3
0
2
0
9
0
0
0
0
0
1
0
2
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
3
1
0
2
0
4
0
0
0
0
0
0
0
0
1
0
2
0
0
1
2
0
0
3
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
2
2
0
1
0
2
0
0
1
2
1
0
1
1
1
0
2
0
0
2
0
0
0
1
0
1
2
1
0
0
0
3
0
0
0
0
0
2
0
0
1
0
1
0
0
2
0
0
0
0
1
1
0
0
1
0
2
0
0
0
1
0
2
1
0
2
1
0
0
0
0
0
0
2
1
0
0
0
3
0
2
2
0
1
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
2
1
0
0
1
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
3
0
2
0
0
0
0
0
0
2
0
4
1
0
0
2
0
0
1
0
0
0
2
2
1
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
4
0
2
0
0
0
0
0
1
1
0
1
0
1
0
2
3
0
0
0
0
2
1
0
1
0
0
1
0
1
2
2
2
0
0
0
0
2
0
0
0
0
0
1
3
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
4
2
0
0
0
0
2
0
0
0
1
0
0
0
0
2
1
0
1
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
1
0
1
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
1
0
0
1
3
0
0
0
1
0
0
0
2
0
1
0
0
0
0
1
4
0
0
1
0
1
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
2
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
2
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
3
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
2
1
2
2
0
2
0
1
2
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
2
0
0
2
1
2
0
0
0
0
1
0
2
0
0
0
2
0
0
1
0
0
0
1
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
1
0
0
0
2
0
0
0
0
2
0
2
0
1
0
0
0
1
0
3
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
1
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
2
0
2
0
1
0
0
0
0
0
2
0
0
0
0
2
0
3
0
0
0
1
2
3
0
0
3
0
2
2
0
0
0
0
2
2
0
0
0
0
2
0
0
0
2
1
0
0
1
1
0
0
0
2
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
1
3
0
2
0
0
0
0
2
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
3
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
2
2
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
1
0
1
0
2
0
0
0
0
2
0
2
0
0
1
0
1
1
0
0
0
1
0
1
1
0
0
1
0
0
0
0
1
2
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
2
1
2
2
0
2
2
0
1
2
0
1
0
2
0
0
0
0
0
9
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
1
0
0
0
0
0
2
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
3
0
1
0
0
1
3
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
1
0
1
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
1
0
0
2
1
0
1
1
0
0
0
1
0
0
0
0
2
0
0
0
3
1
0
0
0
0
0
2
0
0
0
0
2
1
0
0
2
0
3
0
0
2
1
0
0
1
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
1
2
0
0
2
1
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
1
1
2
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
4
0
0
0
1
0
0
4
2
2
0
1
0
13
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
2
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
2
0
1
2
0
0
0
0
1
0
2
1
1
1
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
1
0
2
2
0
0
0
2
0
0
2
2
0
2
0
2
0
0
0
0
0
0
1
2
0
0
0
0
1
0
2
0
2
0
1
1
3
1
0
1
2
0
0
0
0
2
4
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
1
0
0
2
0
0
0
0
0
1
2
0
0
1
0
0
0
0
3
0
1
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
3
0
2
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
1
2
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
3
0
0
2
1
1
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
1
0
0
2
0
1
0
2
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
1
0
0
0
2
0
4
0
0
2
1
1
2
0
0
0
1
2
0
0
0
0
0
0
0
3
1
0
0
0
2
0
0
0
1
1
0
0
2
0
1
2
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
1
1
0
0
0
0
0
0
0
2
0
2
1
0
1
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
4
1
0
0
0
0
1
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
1
1
0
2
0
0
3
0
0
0
0
0
0
0
0
0
2
8
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
5
0
0
1
0
0
2
1
1
0
1
2
1
0
0
1
4
0
0
0
1
0
0
1
0
0
0
0
2
0
1
0
2
2
0
2
0
0
0
1
0
0
0
0
1
0
1
1
0
0
2
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
1
0
3
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
2
0
0
2
3
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
3
0
0
2
0
0
0
0
2
3
0
0
0
0
0
2
1
0
1
0
0
2
0
0
0
1
0
1
3
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
2
2
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
1
0
0
2
1
2
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
1
1
0
0
4
0
3
0
0
2
1
1
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
1
0
0
1
0
0
2
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
2
2
0
2
1
1
1
2
0
1
0
0
1
1
0
2
0
0
0
2
1
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
3
1
0
3
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
2
2
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
4
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
2
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
2
1
1
0
1
0
0
0
2
0
0
1
0
1
2
1
1
0
0
2
0
0
3
0
0
1
2
0
1
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
2
0
2
0
0
1
1
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
3
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
4
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
1
1
1
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
1
0
0
0
0
1
0
0
2
3
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
3
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
2
2
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
2
0
4
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
3
2
3
0
0
0
0
1
0
2
2
0
0
1
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
5
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
2
1
1
0
2
1
1
0
2
0
0
0
0
0
1
1
2
2
0
1
0
2
0
0
0
0
0
0
0
0
2
1
0
0
2
2
1
0
3
0
0
2
0
0
1
0
0
1
0
6
2
0
2
2
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
3
0
3
0
0
0
0
0
2
2
0
1
1
0
0
1
0
0
0
2
0
2
0
0
0
0
1
2
0
0
0
1
0
2
0
0
2
1
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
2
0
0
1
0
2
0
0
1
0
2
0
0
0
0
2
0
0
0
0
1
1
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
2
1
1
0
0
0
2
0
0
0
0
2
0
1
0
0
1
0
0
1
0
2
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
2
1
2
0
0
0
0
2
1
0
0
3
0
1
0
0
0
2
1
1
0
0
1
0
1
0
1
1
1
0
0
0
2
1
0
0
1
0
0
0
0
0
0
2
0
3
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
2
0
0
0
2
1
0
3
1
0
0
5
0
2
0
0
0
0
1
0
0
0
1
0
2
0
0
1
1
0
0
1
0
0
2
2
2
0
2
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
1
0
0
1
0
0
1
2
2
2
0
0
0
1
0
0
1
0
1
3
0
0
1
2
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
1
0
2
2
0
0
0
0
0
0
2
0
2
1
0
1
2
0
1
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
2
0
0
2
0
0
2
0
0
0
1
2
0
2
2
0
0
0
2
1
0
0
0
0
2
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
1
1
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
1
4
0
0
1
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
2
1
0
0
1
0
0
1
0
0
0
1
2
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
1
0
4
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
1
0
0
1
2
0
0
1
0
0
0
1
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
2
0
0
0
2
0
2
0
2
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
3
0
0
0
0
0
2
1
0
0
0
2
3
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
2
0
0
3
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
2
0
0
0
0
4
2
2
0
1
0
0
0
0
2
1
2
0
0
1
2
1
0
0
2
0
2
1
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
2
1
1
1
0
0
1
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
1
1
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
2
0
5
0
0
1
0
0
0
1
0
0
1
1
0
0
2
2
0
0
1
0
0
1
0
1
0
2
1
2
0
1
0
0
1
0
1
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
1
0
0
0
2
0
0
2
0
0
1
0
0
2
0
0
1
1
0
0
2
2
0
0
1
0
0
2
0
0
0
2
0
0
0
2
0
0
0
1
2
0
0
0
1
0
1
1
1
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
1
1
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
2
0
0
3
2
0
0
0
0
0
0
0
1
2
1
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
3
0
0
0
2
0
2
0
0
0
0
2
2
0
3
1
0
0
0
1
0
1
0
0
2
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
1
1
1
0
0
0
0
2
0
0
2
2
0
2
0
0
0
3
0
0
3
0
2
0
0
0
0
1
2
0
1
0
0
1
0
0
2
1
0
1
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
2
1
0
2
0
2
2
0
1
0
0
2
1
1
0
2
1
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
3
0
2
2
1
1
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
1
1
0
0
2
0
2
0
0
0
0
2
2
2
0
0
0
1
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
2
0
0
2
0
0
0
0
0
2
1
1
1
2
0
1
0
0
3
0
0
0
1
0
2
1
0
5
0
0
0
1
0
0
0
0
0
0
0
2
3
0
0
1
2
2
0
0
0
0
1
0
0
1
3
0
0
0
0
0
0
1
3
1
2
0
1
0
2
0
0
1
0
0
0
0
0
1
2
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
2
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
3
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
2
2
0
0
2
0
1
0
2
0
0
0
0
1
0
1
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
2
1
1
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
1
1
0
0
1
0
0
2
0
0
1
0
0
0
1
2
0
0
1
1
0
1
0
0
0
0
1
0
1
2
1
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
1
1
2
0
2
0
0
1
0
1
0
1
2
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
1
2
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
3
0
0
3
1
0
1
0
2
0
0
0
0
0
0
2
0
0
0
2
3
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
2
2
0
0
0
2
1
3
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
2
0
1
2
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
2
0
1
0
1
0
0
1
2
2
0
0
4
0
0
2
2
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
1
0
2
2
0
0
1
0
2
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
1
0
2
0
3
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
2
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
1
0
2
1
0
0
0
0
0
2
0
0
0
1
0
1
1
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
1
2
0
0
2
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
1
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
1
0
0
2
0
1
0
2
2
1
2
0
1
2
0
0
0
0
2
0
0
0
0
0
2
1
2
1
0
0
0
0
0
0
0
2
0
2
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
3
1
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
1
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
1
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
2
2
1
0
3
0
0
0
2
1
0
0
0
2
4
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
2
0
0
0
1
0
0
0
0
0
1
0
1
0
1
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
2
0
1
0
0
1
1
2
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
3
0
3
0
0
2
0
0
4
0
1
0
1
0
0
1
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
2
0
0
0
1
4
3
0
1
0
2
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
5
0
0
2
2
0
0
1
0
0
0
2
2
0
0
0
2
2
0
0
0
0
1
0
0
2
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
1
2
2
0
2
0
1
0
0
2
2
2
1
0
0
0
0
2
0
0
2
2
0
0
2
1
0
1
0
0
1
0
0
2
0
4
0
0
0
1
0
0
1
0
1
0
1
1
1
2
0
0
0
0
0
0
0
3
0
0
0
1
0
0
3
0
1
0
6
0
0
0
0
0
2
1
0
4
2
0
1
0
1
0
2
0
0
2
0
0
0
1
2
1
0
3
2
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
1
0
2
0
0
0
0
0
1
1
0
0
1
0
0
3
0
0
0
1
0
2
0
0
0
1
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
3
2
0
0
0
0
4
2
1
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
2
0
0
0
0
1
0
1
1
1
0
0
1
0
0
1
2
0
0
1
1
4
0
2
2
2
0
0
1
0
2
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
1
0
1
2
1
2
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
2
2
1
2
0
2
0
0
0
0
0
0
0
0
3
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
2
0
0
2
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
1
0
2
0
2
0
1
1
0
0
0
0
0
2
1
1
0
0
0
3
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
6
2
1
3
0
0
0
2
1
2
0
0
1
0
1
0
2
1
0
0
0
0
0
1
1
0
0
2
0
1
0
2
0
0
0
2
0
0
0
0
1
0
0
0
2
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
3
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
2
0
2
0
0
2
0
1
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
2
0
0
0
1
1
1
2
0
0
2
0
1
0
0
2
1
2
0
0
1
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
1
0
0
2
0
0
0
1
0
2
3
2
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
1
0
0
1
0
0
2
1
1
0
2
2
0
0
0
0
2
0
1
1
4
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
3
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
1
0
1
0
2
0
0
1
0
2
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
1
1
0
0
0
1
3
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
6
0
0
0
0
0
0
1
0
0
2
0
1
0
0
2
0
3
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
1
2
1
2
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
4
1
0
0
1
0
1
2
3
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
2
1
0
0
0
1
0
0
1
0
0
1
0
0
0
1
1
0
1
1
1
0
1
0
0
1
2
0
0
2
0
0
0
1
0
0
0
2
0
0
0
1
0
1
0
1
0
1
1
1
0
0
0
1
2
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
1
1
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
3
3
0
0
0
1
2
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
8
2
0
0
0
2
0
0
0
0
5
0
0
0
0
0
1
0
2
0
0
0
0
0
1
1
0
0
0
0
1
0
2
0
0
0
0
0
3
0
0
1
0
0
0
3
1
0
0
0
0
0
2
0
1
0
2
1
0
0
0
0
0
0
0
0
4
1
2
0
0
0
0
0
1
1
0
2
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
1
0
0
0
0
1
0
2
0
1
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
1
1
2
0
0
0
0
1
1
2
2
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
1
0
0
2
0
2
1
0
2
1
1
0
0
0
0
2
0
1
2
0
0
0
0
0
1
1
0
0
1
0
2
0
0
0
4
0
3
0
0
2
0
1
0
0
0
2
0
0
2
2
0
2
1
0
1
2
2
0
1
0
0
0
0
0
0
0
1
1
2
0
0
4
0
0
0
0
0
2
0
0
0
0
3
0
1
0
0
1
1
2
3
1
0
0
0
0
2
0
2
0
0
2
2
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
2
1
1
1
0
0
4
0
0
1
1
1
0
2
0
0
0
0
0
0
0
0
4
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
1
2
2
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
2
2
0
2
3
0
1
0
0
0
0
0
2
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
1
0
0
2
5
0
1
0
2
0
1
0
0
3
0
1
0
1
0
0
0
2
3
0
0
0
0
0
0
0
0
2
0
0
1
2
0
2
0
0
0
0
1
1
0
2
0
0
0
0
2
0
0
2
4
0
2
0
2
0
4
0
1
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
3
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
1
1
0
0
0
1
0
0
3
0
0
0
0
2
0
0
0
2
1
1
0
2
0
1
1
0
0
1
6
0
1
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
1
2
1
2
2
0
0
0
2
0
0
0
0
1
0
1
0
2
0
0
0
1
0
4
1
2
2
0
0
0
0
0
2
0
0
0
0
0
1
1
2
1
0
0
0
0
0
3
3
2
2
0
0
0
0
0
0
0
2
0
0
6
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
1
0
0
2
0
0
1
0
2
0
0
0
0
1
0
3
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
2
0
1
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
1
0
0
2
0
0
2
2
0
0
0
0
0
0
0
2
2
0
1
0
0
1
0
4
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
1
1
1
0
2
0
0
1
0
0
0
1
0
0
1
2
0
0
3
0
1
0
4
3
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
2
1
0
0
0
0
0
0
2
0
0
1
0
1
1
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
4
2
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
2
1
4
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
2
1
2
0
2
1
0
2
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
2
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
1
0
1
0
0
2
0
0
1
1
0
1
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
2
0
2
0
1
0
2
0
0
0
0
2
0
2
0
0
0
0
2
0
0
1
1
2
0
0
0
0
0
0
1
1
2
1
0
0
2
0
1
1
0
1
2
0
1
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
1
3
1
0
0
0
0
0
2
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
5
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
2
1
2
0
0
0
2
0
0
0
0
0
3
2
0
2
0
3
1
0
0
2
0
0
0
0
2
0
1
2
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
1
0
0
0
0
2
0
0
1
0
1
0
0
2
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
1
0
0
0
1
2
1
1
1
1
1
2
0
0
0
2
0
0
0
5
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
2
2
0
1
0
2
3
1
1
0
1
0
0
0
1
1
0
0
1
0
0
0
1
1
1
0
0
0
2
0
0
0
0
0
0
0
2
1
2
0
0
0
0
3
1
0
0
1
0
0
0
0
2
0
0
3
0
1
0
0
2
0
0
2
0
0
1
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
5
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
2
0
1
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
6
0
0
0
0
0
0
4
0
1
0
0
0
0
3
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
2
1
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
2
1
1
0
0
0
1
0
0
0
2
2
2
0
0
0
1
2
0
0
0
0
0
0
2
0
2
2
0
0
0
0
1
0
0
2
1
0
0
1
0
0
1
0
1
0
1
1
2
0
1
0
1
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
2
2
0
0
0
2
0
0
1
2
0
0
2
1
0
1
0
0
2
0
0
3
2
3
2
0
1
0
0
2
0
1
0
0
0
0
0
2
1
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
1
0
0
2
2
0
0
0
1
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
2
1
0
2
2
0
2
2
2
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
1
2
0
0
2
1
0
4
0
0
0
2
0
0
0
4
0
0
1
0
3
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
3
3
0
1
0
0
0
0
1
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
2
0
0
2
1
0
0
0
3
0
0
2
0
0
1
0
2
0
0
0
1
0
2
0
0
0
1
0
1
0
0
0
0
0
0
2
0
2
0
0
3
0
0
2
0
0
2
0
1
1
0
0
2
0
0
1
0
3
0
0
0
1
0
1
0
0
0
1
3
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
1
0
0
1
1
0
0
0
0
0
1
2
2
0
4
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
2
1
0
1
0
0
0
1
0
0
0
1
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
2
0
1
0
0
0
0
1
0
2
2
0
0
0
0
0
2
12
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
1
2
3
1
0
0
0
2
0
0
0
0
1
2
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
2
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
1
0
0
1
0
1
2
0
1
0
0
0
0
2
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
4
0
1
2
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
1
0
0
2
0
0
2
2
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
1
4
0
0
1
2
0
0
0
0
0
0
2
0
0
1
0
0
2
0
1
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
2
0
2
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
2
1
0
0
0
2
1
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
2
0
2
0
2
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
1
2
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
2
1
1
0
1
4
0
0
0
1
2
0
2
2
0
2
0
2
2
0
1
0
0
0
2
1
1
2
1
1
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
1
3
1
0
0
2
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
3
0
1
4
2
0
0
2
0
3
0
2
2
2
0
0
1
0
0
3
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
6
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
1
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
2
0
2
2
0
0
2
1
0
0
0
0
0
0
0
1
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
12
0
2
2
0
0
0
1
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
1
0
0
1
0
0
0
0
2
0
0
2
1
0
0
2
0
0
2
0
1
1
0
0
0
2
0
0
0
0
2
1
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
2
3
3
2
0
0
0
0
0
1
2
2
2
0
0
8
1
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
3
0
1
0
0
2
0
0
0
0
0
1
0
1
1
0
1
0
0
2
0
0
0
0
0
0
1
0
1
0
2
3
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
2
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
5
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
2
2
0
1
0
0
2
0
0
0
0
2
0
0
2
0
0
1
0
0
2
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
1
0
0
1
0
0
2
2
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
3
0
2
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
2
1
0
3
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
6
2
1
0
1
1
1
0
0
0
2
1
0
0
0
0
1
0
3
0
0
2
0
0
1
1
2
0
0
0
0
2
3
0
0
0
0
0
2
1
0
0
0
1
0
0
0
2
1
4
1
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
3
0
0
0
0
0
0
1
1
0
0
2
0
2
1
2
2
1
0
0
0
2
0
0
0
0
2
0
0
2
0
1
0
0
2
1
2
0
0
2
0
0
2
2
0
1
1
0
0
0
0
1
0
0
1
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
2
1
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
1
1
0
0
1
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
3
1
0
2
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
1
0
0
3
0
2
0
1
0
1
0
0
0
0
2
0
0
0
2
0
2
0
0
3
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
2
0
0
2
1
0
0
0
0
0
0
1
3
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
2
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
6
2
1
1
1
0
0
0
1
0
1
2
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
1
0
1
0
2
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
2
0
0
0
2
0
0
0
1
0
1
0
0
0
0
1
3
0
0
0
0
0
0
1
1
0
3
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
1
2
2
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
2
2
0
3
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
2
0
1
0
0
2
0
1
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
5
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
3
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
2
0
0
1
0
0
0
0
2
1
0
0
0
2
0
0
1
0
0
2
1
2
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
1
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
3
0
0
0
0
2
0
1
0
1
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
4
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
3
0
0
1
0
0
0
2
0
1
0
1
1
2
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
1
0
0
0
1
2
0
0
0
0
0
0
1
0
0
1
0
0
1
0
3
0
0
0
1
3
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
5
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
4
0
0
0
0
0
0
2
2
1
0
0
2
0
0
1
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
2
0
0
2
0
2
0
1
0
2
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
1
0
0
0
2
0
2
0
0
2
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
3
4
0
0
1
0
0
1
0
0
0
1
0
0
1
2
0
0
3
2
0
0
0
0
2
0
0
2
2
0
2
0
0
0
2
0
0
2
2
0
1
3
2
0
0
1
0
2
0
1
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
1
0
0
0
0
1
0
0
0
0
1
0
1
1
3
0
2
0
1
2
2
0
0
0
0
0
0
0
0
2
0
3
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
3
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
4
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
2
1
2
0
0
0
0
1
0
0
2
0
0
1
0
1
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
3
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
2
1
0
1
0
1
0
0
0
1
0
2
0
0
0
1
2
2
1
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
2
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
1
0
1
1
0
0
0
0
1
1
1
1
3
2
0
0
1
0
0
0
1
2
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
2
0
2
0
0
0
5
0
0
0
0
2
0
0
0
0
1
0
2
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
1
0
2
0
0
1
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
1
3
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
1
0
2
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
1
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
1
0
0
0
0
2
2
0
0
1
0
1
0
0
2
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
1
1
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
2
0
1
0
2
0
1
0
1
0
0
0
0
2
0
4
1
0
1
1
0
2
0
0
1
0
0
0
2
0
0
0
0
2
0
0
1
0
0
2
0
0
5
0
0
0
2
0
1
1
0
2
0
0
0
2
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
2
1
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
7
0
0
1
1
0
1
0
3
0
0
2
0
0
0
0
0
0
2
2
0
1
0
0
0
0
2
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
2
0
0
1
3
1
2
2
2
1
0
0
1
0
0
1
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
3
0
1
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
4
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
4
2
1
0
0
1
0
2
0
1
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
1
2
1
1
0
0
0
0
2
0
0
1
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
2
1
1
1
0
1
0
1
0
0
0
3
0
0
2
2
0
0
1
0
1
1
0
0
0
0
0
2
0
0
2
0
0
2
0
1
0
2
0
0
0
0
2
0
1
3
0
0
2
0
0
0
2
0
1
0
0
1
0
0
0
1
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
1
0
2
1
0
0
0
0
0
2
2
0
0
0
0
0
0
7
0
1
0
0
0
0
1
2
1
2
2
0
0
0
1
0
0
0
1
0
2
1
0
2
3
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
2
0
1
2
1
0
0
0
0
0
0
1
0
2
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
1
0
1
0
0
1
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
1
0
0
0
2
2
2
0
2
2
0
0
0
3
1
1
2
1
0
0
2
0
1
0
0
1
1
0
0
1
0
0
2
0
0
0
0
1
0
2
2
0
4
2
0
0
0
0
0
0
2
0
1
0
0
2
0
0
3
3
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
1
0
2
0
0
0
0
2
0
2
0
2
0
0
0
0
2
0
0
0
0
1
0
0
2
1
0
2
2
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
3
0
3
0
0
0
1
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
1
0
0
1
0
2
0
1
0
0
0
2
2
0
0
1
0
0
2
0
0
2
0
0
0
2
0
2
0
2
2
1
2
2
2
0
0
0
0
5
1
0
2
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
2
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
1
0
0
0
2
0
2
1
0
0
0
0
0
2
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
2
2
2
0
0
2
0
0
0
1
0
0
2
1
0
0
2
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
2
0
0
3
2
1
0
0
0
2
1
1
2
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
2
2
2
2
0
1
0
0
0
0
0
1
2
0
2
1
0
0
0
0
2
0
2
0
0
1
0
0
0
0
2
0
0
0
0
2
1
0
0
1
2
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
1
3
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
3
1
0
0
1
0
0
0
0
1
0
1
0
1
1
3
0
0
0
0
2
0
1
2
2
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
2
0
2
0
0
4
0
0
0
2
1
2
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
1
0
2
0
0
0
2
3
0
0
2
1
0
0
0
1
1
2
0
1
0
1
0
0
0
0
0
2
0
1
1
0
3
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
1
2
0
0
0
1
1
0
1
0
0
3
0
1
1
0
0
2
0
0
0
1
4
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
1
4
0
0
2
0
2
0
0
1
1
0
0
0
0
0
0
3
2
0
0
2
2
0
0
2
0
0
0
1
2
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
2
1
0
0
0
0
0
1
2
1
0
2
0
1
1
0
2
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
3
1
0
0
0
0
0
0
2
0
0
2
1
2
0
0
0
3
0
0
0
0
0
0
0
3
0
1
0
0
0
0
1
2
0
0
0
2
0
1
0
0
0
4
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
2
0
2
1
0
1
0
0
1
0
0
2
0
0
0
1
0
0
2
0
0
1
1
1
0
1
0
1
0
8
0
11
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
3
1
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
1
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
4
0
0
1
1
0
0
0
1
0
1
1
0
0
0
4
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
1
0
0
1
0
0
0
0
1
3
0
0
0
0
0
2
0
1
0
0
1
0
1
0
0
1
0
2
0
0
0
3
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
2
1
1
0
1
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
2
1
0
0
0
1
0
1
3
0
0
1
0
0
1
3
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
2
1
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
4
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
3
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
3
0
0
1
0
3
0
0
2
0
0
6
0
1
0
1
1
0
4
0
1
0
0
0
1
2
0
0
0
1
0
1
0
2
0
0
1
0
0
0
1
0
2
1
0
0
0
2
0
1
0
0
0
1
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
3
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
1
1
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
2
0
2
1
0
0
2
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
2
2
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
2
1
0
1
1
1
0
0
0
2
0
0
0
2
0
0
1
0
0
0
2
0
1
0
0
0
0
0
1
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
1
2
1
0
0
0
1
2
0
0
2
0
2
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
4
0
1
0
0
0
0
0
0
0
2
1
1
1
0
2
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
4
0
3
0
0
1
0
0
1
0
0
0
3
2
2
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
1
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
2
2
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
2
0
2
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
2
1
2
2
0
0
2
0
0
2
0
1
0
1
0
2
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
1
2
2
0
0
0
2
0
3
0
0
0
0
2
0
0
0
1
0
1
2
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
3
0
1
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
2
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
2
1
1
0
0
0
1
0
0
0
1
4
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
1
1
0
0
2
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
3
0
2
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
3
0
1
0
2
2
1
0
0
0
0
0
0
1
0
0
0
0
0
4
2
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
3
1
0
1
0
0
0
0
0
1
1
2
0
0
2
0
2
0
1
0
0
0
2
5
0
0
2
0
1
0
2
1
0
0
2
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
2
0
0
0
1
1
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
10
0
0
0
0
3
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
2
0
0
1
3
0
0
0
0
0
1
0
0
2
1
0
1
0
0
2
0
0
0
0
0
0
2
0
3
0
3
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
2
1
0
0
0
0
0
0
1
0
2
0
2
0
0
1
0
0
0
0
1
1
0
0
0
2
1
0
8
0
2
0
1
0
0
2
0
0
3
1
1
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
3
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
2
2
1
0
4
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
1
2
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
1
0
2
0
3
0
2
0
1
2
0
0
2
2
0
0
3
0
1
0
1
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
1
2
2
1
0
0
1
0
0
2
0
0
0
0
1
0
1
2
2
0
0
0
0
0
0
2
0
1
0
0
0
2
0
2
0
0
0
1
0
0
1
0
0
0
0
2
0
1
2
0
2
1
2
0
4
0
2
0
0
1
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
2
2
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
2
1
3
0
2
0
0
0
1
0
0
0
0
1
0
0
2
0
0
2
1
0
0
2
0
0
0
1
0
2
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
2
1
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
1
1
1
0
0
5
0
1
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
2
0
2
0
2
0
0
0
2
0
2
0
0
2
1
3
0
0
0
1
0
0
0
0
0
1
0
2
1
0
2
3
0
1
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
3
0
0
0
0
1
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
1
0
0
7
0
0
0
0
2
4
0
0
1
2
0
1
0
0
0
0
1
2
1
2
2
0
1
0
0
2
2
2
1
0
0
0
1
0
1
1
4
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
2
0
0
2
0
0
0
0
0
0
1
2
0
2
0
0
0
0
1
2
0
2
0
0
0
3
0
2
2
0
0
0
2
0
2
0
0
2
0
0
0
1
0
0
0
1
1
0
2
0
0
0
0
1
6
0
0
2
0
0
0
0
0
2
0
2
0
1
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
2
0
1
0
1
2
0
3
1
0
0
0
2
0
2
0
0
2
0
0
0
1
0
0
1
0
1
0
2
0
0
0
2
2
0
0
0
0
2
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
2
0
0
0
1
0
0
0
0
1
0
1
1
0
0
1
0
0
3
0
0
0
0
0
0
1
1
1
0
2
0
0
0
0
2
2
0
1
1
0
2
1
1
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
2
2
0
0
1
2
0
1
0
3
4
0
1
0
0
0
1
0
0
2
2
0
0
0
0
0
2
0
1
0
4
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
2
0
2
1
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
1
0
1
0
2
1
0
3
1
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
2
0
2
0
0
0
0
0
2
0
0
5
2
1
0
0
1
0
2
0
0
2
0
0
1
1
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
5
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
2
1
0
0
0
1
0
2
0
0
0
3
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
1
2
0
0
1
1
2
1
0
0
2
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
1
0
0
0
2
2
0
0
0
2
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
4
0
1
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
2
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
2
0
0
0
0
0
1
0
1
0
2
0
2
0
0
1
0
0
0
2
0
2
1
0
1
0
0
1
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
1
2
1
0
0
1
0
1
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
2
0
0
0
2
2
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
4
0
0
0
1
2
6
1
0
4
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
2
0
0
1
5
0
0
0
8
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
1
0
1
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
1
2
0
1
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
2
2
0
0
1
0
2
0
0
0
0
1
2
0
0
1
0
0
0
1
2
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
2
0
2
2
0
1
0
1
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
2
2
0
0
0
3
2
0
0
0
1
1
2
0
0
0
0
0
2
1
2
0
2
0
0
1
0
0
0
1
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
2
2
0
0
0
0
1
1
0
2
0
0
0
2
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
3
0
0
0
0
1
1
0
0
0
1
0
0
2
2
1
0
1
2
0
0
0
0
0
1
0
2
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
1
2
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
3
0
0
0
2
0
0
0
0
0
1
3
0
2
1
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
6
0
0
0
0
0
2
0
1
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
2
0
0
0
0
2
1
1
2
0
0
2
0
0
0
2
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
1
0
0
1
0
0
0
0
0
3
0
1
2
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
1
2
1
1
2
2
2
3
0
0
0
3
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
1
1
1
0
1
0
1
0
1
2
2
1
1
2
3
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
2
1
1
0
0
0
0
1
1
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
2
0
1
1
0
1
0
2
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
1
0
1
0
2
0
1
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
1
2
2
0
0
0
2
2
0
2
1
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
3
0
0
2
0
2
2
2
0
0
0
1
0
0
0
1
0
2
0
1
2
0
0
1
0
2
0
1
1
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
1
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
2
2
0
0
0
2
1
1
0
2
1
2
0
0
0
0
1
0
3
1
0
0
0
0
1
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
1
0
3
0
0
2
0
0
0
0
0
1
1
0
2
1
1
1
0
0
0
2
0
1
0
1
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
5
0
0
2
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
3
0
0
1
2
0
2
0
0
0
0
0
0
1
1
2
0
0
0
2
0
1
1
2
0
0
3
0
0
2
0
0
1
2
1
1
0
0
0
0
3
0
0
1
1
0
0
2
2
0
2
0
0
3
0
2
2
2
2
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
2
1
0
0
1
0
1
0
0
2
0
0
1
0
2
0
0
2
0
0
0
1
1
2
0
2
0
0
1
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
1
2
0
2
0
0
1
1
0
0
0
1
0
3
0
0
1
0
0
0
1
0
1
0
0
0
1
2
1
0
0
0
0
1
0
2
0
0
0
1
0
2
1
1
0
2
0
1
0
0
0
1
0
2
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
2
0
2
2
5
0
0
3
0
1
0
0
0
2
0
1
0
0
1
2
0
0
0
0
1
0
0
2
1
0
1
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
1
2
0
0
0
2
0
1
1
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
2
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
3
1
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
1
1
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
2
0
0
0
0
0
1
0
1
0
2
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
2
0
0
0
0
1
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
3
2
0
0
2
1
0
0
1
0
2
0
0
0
0
0
2
1
0
0
0
2
2
0
0
1
0
1
0
0
0
1
2
1
0
0
2
1
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
1
0
0
1
1
0
1
1
0
0
0
0
0
1
0
2
0
0
0
1
3
0
1
1
2
0
0
0
1
1
0
2
0
0
0
2
2
1
0
0
0
2
2
0
0
0
2
0
0
1
2
0
0
0
0
0
2
2
1
0
1
0
0
0
2
1
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
2
2
4
0
0
0
1
0
0
3
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
3
1
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
1
3
0
0
0
1
0
0
0
2
2
2
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
3
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
1
1
0
0
1
0
0
0
2
0
0
0
0
3
0
0
2
0
0
0
1
0
0
0
1
3
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
2
0
1
0
2
2
0
1
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
3
0
1
2
1
2
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
1
0
2
0
2
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
1
0
0
0
0
0
0
0
1
1
3
2
1
1
0
0
2
0
2
0
2
2
3
0
3
2
0
2
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
4
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
2
0
0
0
5
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
2
2
0
0
0
0
0
3
0
0
2
0
1
0
0
0
0
2
0
0
0
0
1
2
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
2
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
1
2
0
0
1
0
2
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
2
2
0
0
0
0
0
1
2
0
2
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
2
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
1
1
1
1
0
2
0
1
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
1
1
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
1
0
2
0
0
0
0
2
1
2
3
0
0
1
0
2
2
0
0
0
0
1
0
0
0
0
2
2
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
2
0
0
2
0
2
2
2
4
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
4
5
0
0
0
0
2
2
0
0
1
0
2
0
0
0
3
2
0
0
0
1
0
0
0
2
0
0
0
0
2
1
1
1
0
1
6
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
1
0
4
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
3
0
4
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
3
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
1
5
2
0
0
0
1
2
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
1
2
0
2
0
0
2
0
8
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
2
0
0
2
0
1
2
2
0
2
1
2
0
1
2
4
0
1
2
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
2
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
1
0
11
0
0
0
0
0
1
2
1
0
2
1
0
0
0
2
0
0
0
0
3
0
1
0
0
0
0
0
0
2
2
1
0
0
0
2
0
1
0
0
0
2
0
0
0
4
0
2
3
0
0
0
0
1
1
1
2
0
0
2
1
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
2
0
0
1
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
1
0
0
0
3
0
0
2
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
1
0
2
0
0
0
1
2
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
2
2
2
0
0
1
0
2
0
6
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
2
0
0
0
0
0
2
1
0
1
0
0
0
2
0
0
0
1
0
0
0
2
2
0
0
3
0
2
0
2
0
0
0
0
2
0
0
2
1
0
0
2
0
1
0
1
2
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
1
0
2
0
0
1
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
2
2
2
0
1
2
0
1
0
0
0
0
1
0
2
2
1
1
7
0
0
0
0
0
0
0
0
0
0
1
2
0
3
0
0
1
0
0
2
2
0
2
0
0
2
0
0
0
2
1
0
1
1
0
2
0
0
1
2
0
0
0
0
0
1
0
0
2
0
0
2
0
2
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
2
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
1
0
0
1
0
2
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
2
0
0
2
0
1
0
0
3
0
1
0
2
2
0
1
0
1
0
0
0
1
0
0
0
0
2
2
2
0
0
0
0
0
0
0
1
1
0
0
1
2
1
0
1
0
0
1
1
3
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
10
0
2
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
1
0
0
6
0
0
0
1
0
0
0
0
2
0
0
0
3
0
0
2
0
1
4
0
1
0
2
2
4
0
0
2
1
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
3
1
0
0
1
1
1
0
2
1
0
0
1
1
0
2
0
0
0
0
0
0
8
0
2
0
1
0
0
1
3
5
0
2
1
0
0
0
0
0
5
0
0
0
2
0
0
0
1
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
3
1
0
0
2
2
0
0
0
2
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
2
0
0
2
1
0
1
0
2
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
1
1
0
2
0
0
0
3
0
1
1
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
1
1
0
1
0
0
2
0
0
1
0
0
0
0
1
0
0
0
2
3
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
2
0
0
1
0
0
1
2
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
1
0
4
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
1
0
0
0
2
0
0
1
1
2
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
1
0
2
0
1
2
0
0
0
5
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
2
0
0
0
2
0
1
0
0
0
0
2
0
2
0
0
1
0
0
0
0
2
0
0
0
0
1
2
2
0
0
2
0
0
2
0
2
1
0
0
0
0
0
1
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
2
0
0
3
0
0
2
0
0
1
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
4
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
2
2
0
2
0
0
0
1
1
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
2
0
0
2
0
1
2
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
2
0
2
3
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
3
0
1
0
1
2
2
7
3
0
2
0
0
2
0
0
2
0
0
0
2
0
1
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
3
0
0
0
0
0
2
1
2
2
0
0
0
1
0
0
0
0
0
0
1
0
2
0
2
0
0
1
0
0
2
0
1
0
0
2
0
1
2
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
6
2
1
0
1
0
2
3
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
2
2
0
1
0
0
0
2
0
0
0
0
0
2
0
2
0
4
1
2
0
0
0
0
0
1
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
2
0
3
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
5
0
0
0
1
0
0
0
0
2
2
0
2
2
2
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
2
1
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
3
2
0
2
0
0
2
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
1
3
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
2
0
3
0
0
2
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
1
2
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
1
0
2
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
2
0
0
1
0
0
0
2
0
1
9
2
2
0
1
2
0
1
0
2
0
3
0
0
0
0
2
0
0
0
0
1
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
1
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
1
2
2
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
2
2
0
0
0
1
2
0
0
0
0
1
0
1
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
1
3
0
0
0
0
1
2
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
6
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
3
0
0
0
0
4
0
2
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
1
1
0
1
1
0
0
0
0
0
0
3
1
0
1
1
2
1
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
1
2
2
2
2
0
0
0
0
0
0
0
2
0
2
0
1
0
1
1
0
2
0
0
2
0
0
0
0
0
0
2
2
0
1
0
0
0
1
0
0
0
1
1
2
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
1
1
0
0
3
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
1
2
0
0
0
1
0
1
0
0
2
2
1
1
0
1
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
1
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
2
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
1
0
1
0
2
0
0
0
2
0
0
0
0
0
15
0
2
1
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
1
0
2
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
1
3
0
0
0
1
0
0
0
0
0
0
1
2
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
2
2
1
0
2
1
0
2
0
0
0
2
0
1
0
0
0
0
0
1
1
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
4
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
1
2
1
0
0
1
0
1
0
0
0
2
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
3
0
2
0
0
0
0
0
2
1
2
1
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
6
0
0
0
3
0
0
0
0
0
0
1
0
0
1
3
0
0
0
1
1
1
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
1
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
2
1
0
0
0
2
0
1
1
2
0
0
1
0
0
0
0
1
0
0
0
2
1
2
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
1
2
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
1
0
1
1
2
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
4
0
0
0
2
0
0
3
0
0
2
1
2
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
3
0
1
0
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
1
0
3
0
0
0
0
1
0
0
0
0
0
1
1
1
0
1
0
0
1
0
1
0
0
0
0
2
0
0
1
2
0
2
0
0
2
0
0
0
0
0
0
1
0
0
1
1
2
0
0
2
0
0
0
7
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
3
0
0
0
2
1
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
2
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
3
1
1
0
0
0
3
1
1
2
1
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
3
0
2
0
2
0
1
1
0
0
0
0
0
0
0
1
1
0
3
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
1
0
0
4
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
2
0
2
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
2
1
0
0
0
1
0
0
1
1
0
0
1
0
0
2
0
0
0
1
0
0
0
1
0
2
0
0
2
2
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
5
2
0
0
0
0
0
1
2
0
1
0
0
0
0
2
0
2
0
0
4
1
3
2
0
0
1
0
0
0
1
0
0
0
0
0
0
2
1
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
2
1
1
0
0
2
2
0
0
0
0
0
0
0
0
2
1
0
1
2
1
0
0
0
1
0
0
1
0
0
0
0
0
2
7
1
0
2
0
0
0
2
2
0
2
0
0
0
0
2
0
0
0
2
0
1
1
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
2
1
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
3
0
0
2
0
0
0
0
1
0
0
0
1
0
1
5
0
0
0
0
0
2
1
0
2
0
2
0
0
0
0
0
0
0
1
0
2
2
0
0
0
2
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
2
0
1
0
0
1
2
0
0
0
0
2
2
0
0
2
0
0
0
2
0
1
0
0
0
5
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
1
0
0
0
0
2
2
2
1
0
0
0
2
1
2
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
2
0
0
0
0
2
0
2
2
2
1
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
1
0
0
0
0
1
0
2
2
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
2
0
1
1
0
2
0
1
2
0
0
2
0
0
0
0
2
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
2
0
1
0
0
6
0
0
0
1
0
0
0
2
0
0
1
1
0
0
0
0
0
0
2
1
0
0
0
1
0
0
2
1
0
0
2
1
1
0
0
0
1
1
2
4
0
0
0
1
2
0
0
3
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
2
0
1
0
0
0
0
4
0
0
0
2
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
5
0
0
1
0
0
0
0
1
1
0
2
0
0
1
0
0
0
0
0
2
0
1
2
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
2
1
2
0
1
0
0
0
0
0
0
3
0
0
0
1
2
0
0
0
0
1
0
1
0
0
0
2
1
0
0
0
0
0
2
0
2
1
0
0
1
0
1
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
3
1
1
0
2
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
2
0
3
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
2
2
1
2
2
5
0
0
0
3
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
2
0
2
0
2
0
2
0
0
1
1
0
0
0
0
2
0
0
2
0
0
1
0
2
0
0
0
1
0
0
0
2
0
2
0
0
2
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
5
2
0
0
2
0
0
1
1
0
2
0
0
0
0
0
1
0
0
0
4
0
0
2
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
2
1
0
0
1
1
0
0
0
0
0
0
0
0
2
1
0
3
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
4
0
0
2
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
1
0
2
0
0
1
0
0
2
2
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
1
0
0
0
1
0
0
2
0
0
1
0
0
1
0
2
0
3
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
2
0
0
0
2
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
1
2
0
0
0
1
1
2
0
0
0
0
0
2
0
0
0
1
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
2
1
0
0
0
0
0
0
0
2
0
1
1
0
0
1
0
0
0
0
0
7
0
0
0
1
2
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
1
0
2
0
2
0
0
4
0
2
2
2
0
0
0
2
0
1
1
0
1
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
1
4
0
2
0
0
0
0
1
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
2
0
0
2
0
0
0
2
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
2
0
2
2
0
1
2
1
2
1
0
1
1
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
1
0
0
0
2
2
0
2
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
1
0
1
0
1
0
3
0
0
1
2
1
2
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
1
0
1
0
0
2
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
2
1
1
0
0
2
0
0
2
0
2
0
2
2
0
0
2
1
0
2
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
1
0
0
0
2
0
9
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
1
2
0
0
0
0
0
3
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
1
2
2
0
0
0
1
0
0
1
0
0
0
1
2
0
0
3
0
0
1
2
1
0
0
0
0
0
0
0
0
1
0
1
0
2
0
2
0
1
0
0
0
0
0
0
3
0
0
0
0
1
2
0
0
0
3
0
0
0
2
0
0
0
4
0
0
2
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
1
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
1
0
0
1
0
2
0
0
0
1
0
4
2
1
0
2
0
0
0
0
0
0
0
0
0
1
2
0
1
0
2
0
0
0
0
1
1
1
0
0
0
3
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
2
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
1
0
1
0
0
1
0
1
0
0
0
0
0
2
1
0
1
0
2
1
0
0
1
3
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
1
0
1
0
3
0
1
0
2
0
1
1
2
0
0
0
1
0
0
0
0
2
0
0
0
1
0
1
0
0
2
2
0
1
0
1
2
1
2
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
2
1
0
1
1
0
1
1
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
1
0
2
2
0
0
2
3
1
0
0
1
2
0
0
2
0
0
2
0
2
0
4
0
0
0
1
0
2
0
0
0
0
0
4
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
2
0
0
0
1
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
5
0
0
0
1
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
2
1
0
0
0
0
0
0
2
1
0
0
5
1
0
2
0
0
0
0
0
0
3
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
1
0
1
2
2
3
2
0
0
0
0
0
0
0
2
3
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
2
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
2
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
1
1
0
0
0
2
0
2
0
0
0
1
0
0
1
0
0
2
1
0
0
0
0
0
2
2
0
1
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
1
0
0
1
1
0
0
1
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
2
2
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
2
0
0
0
0
1
0
0
1
1
0
0
0
0
0
2
1
0
2
0
1
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
2
2
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
2
0
0
1
6
0
1
0
1
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
6
1
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
2
0
0
1
0
2
0
0
1
2
2
0
0
0
0
1
2
0
1
0
0
0
0
0
2
2
0
1
1
0
0
0
0
0
2
2
1
1
2
0
0
0
0
2
2
1
0
0
0
0
1
0
2
0
2
1
2
1
0
0
2
0
0
0
2
0
1
0
0
1
0
0
2
0
5
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
1
0
2
2
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
2
0
0
0
0
0
0
0
0
0
0
1
3
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
1
0
0
2
0
0
0
2
0
1
1
0
0
1
0
0
0
0
1
0
0
1
1
0
0
1
0
0
2
0
1
2
1
0
2
0
0
2
0
0
0
0
0
0
2
3
1
0
0
2
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
2
0
4
0
2
0
1
1
0
0
1
0
0
0
2
0
0
2
0
0
0
1
0
2
0
1
0
0
3
0
0
0
2
0
0
0
0
2
0
0
0
2
0
2
0
0
6
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
7
0
0
0
0
1
0
0
1
0
0
0
0
2
2
1
0
0
2
2
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
5
0
0
1
0
0
0
2
3
0
1
0
0
2
0
1
0
0
2
0
0
0
0
2
0
0
2
0
2
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
3
0
0
4
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
1
1
0
0
0
2
0
1
1
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
1
0
2
2
0
0
2
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
2
1
0
0
0
2
1
0
2
0
0
3
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
2
3
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
3
0
0
0
0
2
1
0
0
0
0
1
0
4
0
0
3
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
1
1
0
0
1
0
2
0
0
1
1
1
2
0
2
2
0
1
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
1
3
2
1
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
2
0
1
1
0
2
3
0
0
0
2
0
2
0
0
2
0
0
3
2
0
5
0
0
0
0
0
0
0
0
0
3
1
0
0
0
2
0
0
0
0
1
0
1
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
3
0
1
0
0
0
2
2
0
0
1
0
9
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
2
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
3
0
0
2
0
2
0
0
0
0
0
2
0
0
1
2
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
3
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
3
0
4
0
0
0
0
3
0
2
0
0
0
0
2
0
1
0
0
2
1
0
0
0
0
0
0
2
0
2
2
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
2
0
1
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
1
1
2
0
0
1
0
0
1
0
0
2
0
0
1
1
0
7
2
0
0
0
0
0
3
1
0
0
1
0
0
0
1
0
2
0
1
2
0
2
0
0
0
0
0
0
0
1
0
0
1
4
0
3
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
1
2
0
2
0
0
0
0
0
0
0
0
0
1
2
1
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
3
0
2
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
1
2
0
0
1
2
1
0
0
0
0
2
1
2
1
1
0
1
3
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
1
0
1
0
1
2
1
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
4
0
0
1
0
2
0
0
0
4
0
0
0
2
0
2
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
1
2
3
1
0
0
0
0
0
2
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
2
2
0
0
0
0
0
0
1
0
0
0
2
0
0
5
1
1
0
0
0
1
0
0
0
2
1
0
0
0
1
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
2
0
1
1
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
3
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
1
2
0
0
1
1
0
1
0
0
2
2
3
0
0
0
2
1
1
0
0
1
0
1
1
0
1
2
0
0
1
2
0
0
1
0
3
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
5
0
2
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
1
2
0
0
0
1
1
4
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
1
0
2
1
0
0
0
0
0
0
1
0
2
0
0
2
3
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
3
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
2
3
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
1
2
0
0
0
2
0
2
1
0
2
2
0
0
0
1
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
4
3
0
0
0
0
0
1
2
0
2
0
1
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
2
1
0
2
0
2
0
0
0
1
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
3
0
1
0
0
0
0
1
4
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
2
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
4
1
0
2
2
0
0
0
0
0
0
0
1
0
2
0
1
0
0
1
0
0
0
1
1
0
1
2
2
0
2
0
0
0
0
0
2
2
2
2
0
2
0
4
0
0
0
0
0
1
2
0
0
0
0
3
2
0
0
2
0
2
0
2
1
0
1
1
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
2
0
0
3
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
2
0
0
0
0
2
1
1
0
2
1
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
1
3
1
2
0
0
0
2
0
7
0
0
0
0
0
2
0
0
1
0
0
2
2
2
0
0
0
1
2
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
1
2
0
0
0
0
1
0
2
2
0
0
0
0
0
1
0
0
0
2
0
0
0
1
1
1
0
0
0
0
1
0
0
0
2
0
1
2
0
0
0
3
0
2
2
2
0
2
0
1
2
0
0
0
1
2
0
1
0
0
0
2
0
0
1
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
2
1
2
0
0
1
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
5
0
0
0
0
2
0
0
0
3
2
2
0
2
1
0
0
0
0
1
0
0
1
0
2
0
2
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
2
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
1
2
0
1
0
0
0
2
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
2
0
0
0
1
2
0
0
1
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
1
0
0
2
0
0
2
0
0
3
1
2
1
0
0
0
1
0
2
0
0
0
2
1
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
1
0
2
0
2
2
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
1
1
0
0
0
1
0
0
0
0
1
2
2
0
0
2
2
2
0
0
0
0
0
1
0
1
2
1
0
0
0
2
0
2
0
0
4
0
2
0
2
0
0
1
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
1
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
2
2
0
0
0
0
1
1
0
2
0
1
0
1
0
0
0
1
2
0
0
0
0
1
0
3
2
0
0
2
0
0
2
0
0
0
0
2
2
0
0
1
0
2
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
4
0
1
2
0
2
0
0
0
0
0
0
0
0
0
1
1
0
1
1
1
0
0
1
0
0
0
2
0
0
0
0
0
1
1
0
0
2
0
1
0
0
1
0
1
0
0
0
0
1
0
2
2
2
0
2
0
0
0
0
1
0
2
1
0
2
2
0
2
1
0
0
2
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
2
3
0
1
0
0
0
0
0
1
0
0
12
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
2
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
1
1
0
0
0
0
0
0
0
0
0
2
0
2
0
1
1
0
0
0
0
2
0
2
1
1
2
0
0
0
0
1
0
2
2
0
2
0
0
0
0
0
0
0
2
1
2
2
1
1
0
0
0
0
2
0
0
2
0
0
2
0
0
0
1
0
1
0
2
1
0
1
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
1
2
0
2
0
0
2
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
1
0
0
0
0
0
0
3
1
2
0
0
0
1
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
2
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
2
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
1
0
1
0
2
1
0
0
0
1
0
2
0
2
0
1
0
2
0
0
0
0
0
2
1
0
0
0
0
1
0
0
2
0
1
1
1
0
3
1
0
0
1
2
0
5
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
2
0
1
0
0
0
1
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
1
0
0
0
2
0
0
2
0
2
0
2
1
0
2
0
0
1
0
5
0
0
1
1
0
0
0
1
2
2
1
0
0
1
1
0
0
0
0
1
0
1
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
1
1
0
2
0
1
0
1
0
0
2
0
0
2
0
6
0
0
1
0
0
1
0
0
0
2
0
0
2
0
3
0
0
2
0
1
1
1
1
0
0
0
0
0
0
1
3
2
0
2
0
0
0
1
0
1
0
0
0
0
2
0
3
0
3
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
1
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
1
2
0
0
2
0
2
2
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
2
1
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
4
2
2
0
2
0
1
0
0
0
1
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
1
0
2
3
1
1
2
0
1
0
0
0
0
1
0
0
0
0
1
2
0
0
2
0
0
1
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
1
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
1
1
2
0
0
2
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
2
0
2
2
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
1
1
0
0
0
2
0
0
0
0
2
2
1
2
0
0
0
0
0
2
1
0
0
1
0
0
2
0
0
0
0
2
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
3
1
2
0
0
0
2
3
0
0
1
0
0
2
0
0
0
2
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
2
0
1
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
1
1
1
1
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
3
0
0
0
1
0
0
0
1
0
2
0
0
0
4
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
1
0
0
2
0
0
0
1
1
0
1
0
0
2
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
1
0
1
0
0
0
4
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
1
0
0
0
3
2
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
2
2
0
1
0
2
0
0
0
2
0
0
0
0
2
1
1
0
1
0
0
0
0
2
0
0
1
0
2
2
0
0
0
0
0
0
2
0
0
2
0
2
0
1
0
0
0
1
3
1
0
0
0
0
1
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
1
2
0
6
0
1
2
0
1
0
1
0
0
2
0
1
2
0
3
0
0
3
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
2
0
2
2
3
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
3
0
0
0
0
2
2
0
1
1
0
0
0
0
0
1
0
0
0
2
0
0
0
1
2
0
1
0
2
0
0
1
0
3
0
0
0
2
0
0
0
0
0
1
0
2
2
0
1
0
2
0
0
2
0
0
2
0
0
0
0
1
0
3
0
0
0
0
0
0
0
1
2
2
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
3
1
1
1
0
0
0
2
1
1
1
0
2
0
2
2
0
0
3
1
0
0
2
2
0
5
2
0
2
0
0
0
0
0
0
2
3
1
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
1
0
1
0
0
0
0
2
0
0
1
0
0
2
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
2
2
0
1
0
2
3
0
0
0
0
0
4
1
0
0
2
0
2
0
0
0
0
0
0
3
0
0
1
1
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
2
0
0
0
0
0
2
0
1
1
0
2
0
2
0
0
0
1
0
0
0
0
0
1
1
2
1
1
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
9
0
2
0
0
0
2
1
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
2
1
0
1
1
0
0
0
2
0
0
1
0
2
1
0
1
0
0
0
2
0
0
0
0
0
0
0
1
1
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
1
1
3
0
1
0
1
0
0
0
0
0
2
3
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
2
1
0
1
2
0
0
0
0
0
2
1
0
0
3
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
2
0
0
2
2
0
0
0
0
0
0
3
1
0
1
0
1
3
0
0
0
0
0
1
0
0
0
1
1
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
2
0
0
1
1
2
0
2
0
2
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
2
0
0
1
0
0
2
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
2
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
4
0
1
0
2
1
0
1
0
0
0
0
2
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
2
1
2
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
2
1
0
2
1
0
0
1
0
0
0
0
0
1
0
3
0
0
0
2
0
2
2
2
0
1
0
2
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
1
0
2
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
1
0
0
0
1
0
0
0
2
0
1
0
0
1
0
0
0
1
0
4
0
1
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
3
0
0
1
2
0
0
0
1
0
0
2
1
0
2
1
3
0
0
1
0
0
0
1
1
0
0
2
0
0
2
0
2
1
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
1
0
0
2
0
0
0
1
0
1
2
0
0
0
0
3
0
0
1
1
1
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
2
0
3
0
0
0
2
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
2
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
7
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
2
2
2
0
0
0
1
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
1
2
0
1
0
0
2
1
2
0
1
2
0
0
0
0
0
0
0
2
0
2
2
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
1
2
0
0
1
2
3
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
1
0
0
0
0
2
0
2
1
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
1
0
0
2
1
0
0
0
0
0
1
2
0
0
1
0
1
0
1
1
1
0
0
0
1
2
0
1
0
0
1
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
5
0
0
0
0
2
0
2
0
0
1
1
2
0
2
0
2
2
1
0
0
0
0
0
3
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
2
0
2
0
0
0
3
0
2
0
1
0
0
1
0
2
0
0
0
2
0
2
2
0
0
1
0
1
0
0
1
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
1
0
2
2
2
1
1
0
0
0
0
0
0
0
0
2
1
3
0
0
0
0
0
0
0
2
2
0
1
0
0
0
2
1
2
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
9
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
9
0
0
0
2
2
1
0
0
1
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
1
0
2
0
0
1
1
0
0
0
0
0
0
0
1
1
2
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
3
1
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
1
1
1
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
2
0
1
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
2
1
1
0
0
2
0
0
0
0
0
0
0
0
2
1
0
1
0
0
2
2
0
1
0
0
0
1
2
1
0
0
1
0
0
6
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
2
3
0
0
1
0
0
0
0
1
4
0
0
2
1
2
6
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
3
0
4
0
0
1
0
0
1
1
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
1
0
2
1
1
0
0
5
1
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
1
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
7
2
0
0
1
1
0
0
1
1
1
0
0
0
0
0
0
2
2
2
0
0
0
0
2
0
1
2
1
1
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
1
0
1
0
0
0
3
0
0
0
2
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
4
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
2
1
3
0
0
0
2
0
2
0
0
0
0
0
0
0
2
3
0
2
2
0
2
3
0
2
0
0
0
2
2
0
0
0
0
0
1
0
0
1
2
0
0
0
1
1
1
0
0
0
0
0
0
0
2
8
0
0
2
2
0
0
0
0
2
2
0
2
0
0
0
0
0
1
2
0
2
2
0
0
0
2
0
0
0
2
0
0
0
0
2
0
2
0
0
0
1
0
0
2
0
0
0
2
0
0
1
1
0
0
0
0
2
1
0
0
0
0
1
1
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
2
0
0
0
1
1
0
0
2
0
1
0
2
0
1
0
0
0
1
0
0
0
1
3
0
0
0
0
0
2
2
0
0
1
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
3
0
0
0
0
0
0
2
0
0
0
2
3
0
1
1
0
0
0
0
0
3
2
0
0
1
1
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
2
0
3
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
3
0
0
0
0
7
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
2
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
1
0
2
1
2
2
1
1
2
0
2
0
0
0
1
1
0
1
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
1
2
0
1
0
1
0
0
0
2
0
1
0
0
2
0
2
2
0
0
0
0
0
2
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
2
0
1
1
1
2
0
0
0
0
2
2
0
0
0
1
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
1
2
0
0
0
2
1
0
0
2
0
0
1
0
0
0
0
1
5
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
2
1
0
2
0
1
0
1
0
0
0
2
0
0
1
1
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
1
0
0
1
0
0
2
2
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
2
0
0
0
0
0
2
0
0
3
0
0
2
0
0
0
0
0
1
0
0
5
0
0
0
1
3
0
0
0
0
1
0
2
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
2
0
1
0
0
3
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
2
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
2
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
3
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
1
2
2
0
2
0
1
0
1
0
0
0
0
2
0
0
2
3
0
0
0
0
2
0
2
0
0
1
0
2
2
1
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
1
2
0
2
0
1
0
2
0
0
0
1
5
1
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
1
2
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
1
2
1
0
0
1
0
0
0
1
0
0
0
1
0
0
1
1
0
1
0
2
0
2
0
2
0
0
4
0
1
0
0
2
1
0
0
0
0
1
0
0
1
0
1
0
0
0
3
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
2
0
0
0
0
1
0
0
2
0
1
3
0
0
2
3
0
0
0
0
1
3
0
0
1
0
0
0
0
2
0
0
0
1
7
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
3
1
2
0
0
1
0
0
1
0
1
3
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
2
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
1
0
0
2
0
2
0
0
2
0
1
0
0
0
2
0
11
0
1
2
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
1
2
0
0
0
1
0
0
2
2
0
3
1
1
0
0
1
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
3
0
0
3
0
0
4
1
2
1
0
1
0
2
0
1
0
0
2
1
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
2
1
2
0
0
0
3
3
0
2
0
0
0
3
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
1
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
5
4
0
0
2
1
0
1
1
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
2
0
2
1
0
1
0
0
0
0
1
0
1
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
2
0
0
2
0
0
3
2
2
2
2
1
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
7
0
0
0
1
1
0
0
0
0
0
0
0
2
0
1
2
2
0
2
0
1
2
0
0
1
0
0
2
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
2
2
0
0
1
0
0
2
0
1
2
0
1
0
0
0
0
2
1
0
0
3
0
0
0
2
1
0
0
2
0
0
0
0
0
2
2
2
0
0
0
2
0
0
2
0
0
0
0
1
0
1
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
3
0
1
0
0
0
2
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
1
1
2
2
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
2
1
0
0
0
2
0
0
0
2
1
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
2
0
1
0
0
0
0
0
2
1
0
0
3
0
2
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
1
0
0
0
0
0
3
0
0
2
0
0
0
3
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
10
0
0
0
0
0
2
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
3
0
0
1
0
0
2
0
0
0
2
2
0
0
1
0
2
1
1
0
0
0
0
0
2
0
0
0
1
0
0
1
1
0
0
0
0
0
2
0
1
0
3
0
0
0
0
1
0
1
0
1
0
2
0
0
4
1
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
1
2
0
2
0
0
0
1
0
0
1
2
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
2
0
2
0
0
0
0
2
0
0
1
1
0
0
2
0
0
0
0
1
2
0
1
0
0
0
0
2
0
0
2
0
0
0
1
2
0
0
0
0
0
2
2
0
0
2
0
0
0
2
0
1
0
0
0
0
0
2
0
2
0
1
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
5
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
2
3
0
0
0
0
1
1
7
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
1
0
0
2
0
3
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
1
0
4
2
0
2
0
3
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
3
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
1
0
2
3
2
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
2
0
1
2
2
2
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
1
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
3
1
1
0
2
0
0
0
0
2
2
0
0
0
0
0
3
0
2
0
0
0
0
1
0
1
2
0
1
1
2
0
0
0
0
1
0
5
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
3
4
0
1
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
3
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
5
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
2
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
2
0
1
0
1
2
1
1
0
1
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
1
1
2
0
3
0
0
0
1
0
4
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
1
3
1
0
2
2
0
0
0
2
0
0
2
0
2
1
0
0
2
0
2
0
0
0
2
0
0
1
1
0
0
2
0
0
0
2
0
1
0
2
0
0
0
4
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
1
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
2
0
2
0
0
1
0
0
1
2
0
0
0
0
2
1
0
0
2
0
0
0
0
1
0
0
1
0
1
0
0
2
1
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
2
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
3
2
0
0
0
0
0
0
0
2
0
0
3
0
0
1
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
4
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
2
1
1
0
3
0
0
0
2
2
0
2
2
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
3
0
1
0
0
0
0
0
1
1
0
3
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
2
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
2
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
2
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
2
1
1
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
3
0
0
0
1
0
1
2
0
0
0
0
0
0
0
1
2
3
0
0
1
1
0
0
0
1
0
0
0
2
0
0
0
4
0
3
0
0
0
1
0
1
1
0
0
2
2
0
0
1
0
3
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
3
2
0
1
0
2
0
0
0
1
0
0
0
0
2
0
0
2
0
1
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
2
2
0
0
1
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
4
0
1
2
0
0
1
4
0
0
0
0
0
0
0
0
1
0
0
0
2
3
1
2
2
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
1
0
0
1
1
0
2
2
0
0
1
0
0
0
1
0
3
0
0
0
1
1
0
2
0
0
1
1
2
1
0
0
2
0
2
2
0
0
0
0
0
1
1
1
1
2
0
0
0
1
0
0
1
0
0
0
2
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
2
2
0
2
2
2
0
1
0
2
0
2
2
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
2
1
0
0
2
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
1
1
0
1
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
4
1
2
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
2
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
1
0
2
1
1
0
0
0
1
0
0
2
2
0
2
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
2
1
0
2
2
0
2
0
0
1
2
1
2
2
0
2
0
0
0
0
0
0
3
2
0
0
2
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
2
1
0
0
1
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
2
1
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
1
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
1
0
0
2
0
1
1
0
0
2
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
2
0
0
1
1
1
1
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
2
0
0
0
0
0
2
1
0
0
1
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
2
1
0
2
1
0
0
0
0
0
0
1
0
0
1
2
4
0
3
0
2
0
0
0
1
0
0
0
0
0
0
6
0
1
2
1
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
1
0
1
0
0
0
0
2
0
1
2
0
0
3
0
1
0
1
0
0
0
1
0
0
2
0
0
0
2
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
2
0
0
1
0
0
0
0
0
1
0
1
2
0
0
0
1
1
0
0
0
0
1
0
2
0
0
0
0
0
1
1
0
3
1
0
4
1
0
1
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
1
0
0
1
0
0
3
0
0
1
0
0
0
0
2
0
0
0
0
1
0
1
1
2
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
2
0
1
0
1
0
0
0
1
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
2
2
1
0
0
0
0
0
2
1
0
1
0
0
0
1
0
1
1
0
1
0
1
1
0
0
0
1
0
0
0
0
1
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
1
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
1
2
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
1
2
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
1
0
2
1
2
0
0
1
0
0
0
0
2
0
0
2
0
0
0
1
1
2
1
0
0
0
0
0
2
0
1
0
0
2
2
0
2
0
0
0
1
2
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
1
0
4
0
0
0
2
0
0
0
0
0
1
2
0
2
0
1
0
2
2
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
1
1
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
3
0
0
0
0
2
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
2
0
2
2
0
0
2
0
0
0
0
2
0
4
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
2
0
2
0
2
1
0
0
0
2
0
0
1
0
1
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
3
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
2
0
0
2
2
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
2
0
1
0
0
0
0
0
3
0
1
1
3
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
2
1
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
2
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
1
0
6
2
1
0
0
0
2
1
1
0
0
1
0
0
0
0
0
0
0
0
2
0
4
1
0
0
0
0
0
0
0
1
1
0
0
1
1
1
2
0
0
2
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
4
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
2
0
1
0
2
0
2
0
0
0
0
0
0
2
0
0
0
2
2
2
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
4
2
0
1
0
0
0
0
0
0
0
0
2
0
1
5
3
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
2
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
4
0
0
0
1
0
0
0
2
0
1
0
0
0
0
1
2
2
1
1
1
0
0
0
2
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
2
0
0
0
1
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
1
2
1
0
0
4
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
1
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
1
0
0
0
2
2
1
1
0
0
0
0
0
0
1
2
1
0
2
0
2
0
0
2
0
0
0
2
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
1
0
0
0
0
1
0
0
2
0
0
0
2
0
1
0
2
2
0
0
1
0
2
0
2
1
0
0
0
0
0
0
0
2
0
1
1
0
0
0
2
0
0
0
1
1
0
0
0
1
0
0
0
0
0
2
0
0
3
3
0
0
0
0
0
0
0
0
2
1
0
0
0
1
1
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
1
1
1
0
2
0
0
0
2
2
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
3
1
0
0
2
1
0
1
0
0
1
0
0
2
0
1
2
0
2
0
2
2
0
0
0
0
1
0
3
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
3
0
2
1
1
2
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
5
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
3
1
0
0
1
0
1
0
1
1
0
0
1
0
2
0
0
0
0
0
0
0
0
2
2
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
2
1
1
0
0
5
0
3
2
2
0
0
0
0
0
0
1
2
2
1
0
0
1
1
2
0
0
0
1
0
0
0
0
3
2
0
0
0
0
3
0
0
0
0
0
2
2
0
1
1
1
1
0
1
0
2
0
2
0
0
1
2
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
1
0
1
2
0
0
1
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
3
0
3
0
2
0
1
2
0
2
0
0
0
0
1
1
0
0
0
0
1
2
0
0
4
0
0
3
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
2
0
0
2
0
2
0
1
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
1
1
1
0
1
0
4
0
0
2
0
2
0
2
0
1
0
0
1
2
2
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
3
0
0
5
2
0
0
2
0
0
2
0
1
0
0
0
2
0
3
0
0
1
0
1
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
2
0
0
2
0
1
2
2
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
2
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
2
2
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
1
0
2
0
0
0
2
0
0
1
0
0
0
0
0
2
2
0
0
0
2
0
0
3
2
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
2
1
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
13
1
0
0
0
2
0
0
0
0
2
2
0
2
1
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
2
1
0
0
2
0
0
0
3
5
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
5
0
3
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
1
0
0
2
1
2
0
0
0
1
0
0
0
1
0
2
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
2
1
1
1
0
0
1
1
2
1
1
1
0
1
2
0
0
0
1
1
2
1
2
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
2
1
2
0
0
2
0
0
2
0
2
2
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
5
0
0
1
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
2
0
1
1
0
2
0
0
2
0
1
0
0
2
0
0
0
1
1
1
1
0
0
0
0
0
2
0
0
0
0
1
4
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
1
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
2
0
0
2
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
2
0
0
0
0
1
0
2
0
2
0
0
2
1
0
0
0
1
0
0
0
2
2
4
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
1
1
0
0
0
2
1
1
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
5
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
1
2
0
0
0
1
0
0
0
0
0
0
1
0
2
2
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
1
0
0
2
0
1
0
0
0
0
2
2
2
1
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
1
0
3
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
1
2
0
0
1
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
3
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
5
3
1
1
0
0
0
0
0
0
0
1
0
7
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
2
2
0
0
2
0
0
0
2
1
0
1
0
1
0
0
2
1
0
0
2
1
2
0
0
1
2
0
2
2
0
1
0
0
0
2
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
3
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
2
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
2
2
1
0
1
1
2
0
1
0
0
1
1
0
2
0
0
1
0
0
0
0
0
0
0
3
0
1
0
0
2
0
0
0
2
1
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
3
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
2
0
0
0
0
0
2
1
0
2
0
2
0
0
0
0
2
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
2
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
2
0
0
0
0
0
0
0
2
0
2
0
0
2
2
1
1
2
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
1
1
0
0
0
0
0
1
0
2
0
0
0
1
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
1
0
0
0
0
1
0
2
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
4
0
3
0
0
0
2
0
1
0
5
1
0
0
0
1
0
0
2
1
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
3
0
1
0
0
1
1
0
1
0
0
0
0
0
2
0
0
0
2
0
1
2
1
0
2
0
1
0
0
0
0
1
0
0
2
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
3
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
4
0
4
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
1
0
0
0
2
0
2
2
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
4
1
0
0
3
0
0
0
0
0
0
2
0
1
0
0
1
0
0
1
0
0
0
0
7
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
3
0
0
2
0
2
0
2
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
1
4
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
3
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
1
3
1
0
0
0
2
0
0
0
2
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
2
1
0
0
0
2
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
3
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
3
0
0
0
0
0
0
2
1
0
0
3
0
0
0
0
1
2
2
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
8
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
2
1
0
0
0
0
0
0
0
3
0
0
2
0
0
1
2
0
2
0
2
0
2
2
0
0
3
0
3
0
0
0
0
1
1
0
0
1
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
1
1
0
0
0
2
1
1
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
1
0
0
0
2
1
3
0
0
0
0
0
0
2
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
2
0
0
0
1
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
2
2
1
0
3
0
1
0
2
0
0
0
1
0
0
0
0
0
4
0
2
0
1
0
0
0
3
2
2
0
0
0
0
1
0
0
1
1
0
0
3
1
0
0
2
0
0
0
0
0
1
1
0
2
0
0
2
0
0
2
2
2
0
0
1
1
2
0
0
2
0
0
1
1
0
0
4
0
2
0
1
0
0
0
2
1
0
0
2
2
0
0
2
0
0
0
0
2
0
1
1
0
0
0
0
3
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
1
1
1
0
0
0
0
3
2
0
0
0
1
0
0
0
0
0
0
9
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
11
0
0
0
0
2
1
0
0
0
0
0
0
1
0
1
1
0
0
1
0
1
0
0
1
0
0
1
1
0
2
1
0
0
0
1
0
1
2
0
0
0
0
0
1
0
1
0
1
2
0
0
0
0
0
0
1
1
0
0
0
0
1
0
2
0
0
0
1
1
0
0
0
0
0
2
1
5
0
3
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
1
4
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
3
0
0
2
0
0
0
4
2
0
0
2
2
0
0
0
1
0
0
0
1
0
2
2
0
0
4
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
2
1
2
2
0
0
0
1
1
2
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
1
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
1
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
1
0
0
0
2
0
2
0
1
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
7
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
1
3
0
0
0
0
1
0
0
0
0
0
0
0
2
2
2
1
0
0
1
0
0
0
0
0
1
9
0
0
0
0
1
0
0
0
0
1
2
2
1
0
0
0
0
2
0
2
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
2
0
3
0
0
2
0
0
1
0
1
0
0
0
0
0
2
1
1
0
1
4
0
0
0
0
2
0
0
0
1
0
1
11
0
1
0
0
0
2
0
1
2
0
1
0
0
0
1
0
1
0
0
0
2
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
1
0
2
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
2
1
2
1
0
2
2
2
0
0
0
2
1
0
0
0
0
2
0
1
1
2
0
1
0
0
2
0
0
2
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
1
0
2
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
1
2
7
1
1
0
1
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
3
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
1
0
2
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
2
1
1
0
0
0
2
0
0
0
0
1
1
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
6
1
0
0
1
0
0
0
0
0
0
0
1
1
2
2
0
1
0
1
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
4
0
0
0
1
1
0
0
2
0
1
2
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
2
0
0
0
1
0
1
0
0
1
0
0
1
0
1
0
0
1
0
0
3
0
0
0
0
1
0
1
0
2
1
2
0
1
1
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
1
2
2
0
2
1
3
0
0
0
3
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
4
0
0
0
0
1
0
2
0
1
2
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
4
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
2
0
0
2
0
0
1
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
2
0
1
0
0
0
0
0
0
2
2
0
0
2
0
0
2
0
0
0
0
2
1
0
0
0
0
2
0
0
0
2
1
0
2
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
1
2
0
0
2
1
0
2
0
2
0
0
1
0
0
0
1
0
2
0
0
0
0
0
1
0
2
0
0
0
1
2
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
2
0
0
0
0
2
1
0
2
0
0
0
0
1
1
0
2
0
2
1
2
0
0
0
0
0
0
0
2
1
2
1
0
0
0
0
1
0
2
0
0
3
0
1
0
2
2
0
1
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
1
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
1
0
0
0
1
2
1
0
0
1
0
0
0
2
1
0
0
0
1
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
3
2
0
0
0
2
0
0
1
1
0
0
0
2
2
1
0
0
0
0
2
0
2
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
3
2
1
1
0
2
0
1
2
0
0
2
0
0
0
1
0
2
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
1
0
1
0
0
1
0
1
0
1
0
0
0
2
0
2
0
0
0
1
3
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
2
2
0
0
0
0
0
2
0
0
0
0
1
0
0
2
2
0
0
0
0
0
1
1
0
0
1
1
0
1
0
0
0
0
3
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
4
0
0
0
2
0
0
2
0
1
1
0
0
0
0
0
0
0
0
1
2
1
0
5
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
3
0
1
0
2
1
0
0
0
1
0
0
0
0
3
0
0
1
0
0
0
3
0
0
0
0
0
1
0
2
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
1
0
0
0
0
2
0
1
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
1
2
0
1
0
2
0
2
0
0
0
0
1
0
1
2
0
0
0
0
0
3
0
1
3
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
2
0
0
1
3
3
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
2
4
1
0
1
2
0
0
0
0
0
1
1
1
2
0
0
0
0
2
0
0
0
0
0
2
2
1
0
2
0
0
1
3
0
2
0
0
0
0
1
1
0
0
1
0
0
1
2
0
0
0
0
0
2
0
0
0
2
1
2
1
2
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
3
5
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
2
2
1
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
3
1
1
2
3
0
2
1
0
2
0
0
0
2
2
0
0
0
0
2
0
2
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
2
2
1
1
1
0
0
0
0
0
1
2
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
1
0
2
0
2
15
0
0
0
2
0
0
1
0
2
0
1
0
1
0
0
1
3
0
0
0
0
0
0
0
2
2
0
0
2
0
0
1
1
0
0
0
1
1
0
0
0
0
2
1
0
1
0
0
0
0
1
0
0
0
0
1
1
0
1
1
0
1
0
0
0
0
0
2
0
0
0
2
1
0
0
0
2
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
1
0
1
0
0
3
0
0
0
2
1
0
0
0
0
0
6
2
0
0
0
1
3
0
0
1
0
1
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
2
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
5
1
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
2
0
1
2
0
0
2
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
7
1
0
0
0
0
0
0
0
2
1
0
0
1
0
2
0
1
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
1
1
3
0
0
0
0
0
2
0
1
2
3
0
0
0
0
0
0
0
2
0
0
1
2
1
0
0
0
0
0
0
2
2
0
2
0
0
1
0
0
2
0
2
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
2
0
0
0
0
0
2
0
0
5
1
2
2
0
4
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
1
0
0
0
0
1
1
0
2
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
2
0
1
2
0
0
0
2
0
0
2
1
0
0
0
2
0
0
2
1
0
0
2
0
0
0
0
2
0
0
0
0
2
2
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
2
10
0
1
0
1
1
0
2
0
1
1
0
0
0
0
0
1
2
1
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
2
0
2
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
1
4
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
2
0
0
0
0
0
0
2
1
0
1
2
2
0
0
1
0
5
2
0
0
0
0
1
0
0
0
1
0
2
0
1
0
0
0
0
1
0
2
0
0
1
0
3
1
0
2
1
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
2
2
7
0
0
0
2
0
2
0
0
0
0
0
2
0
2
0
1
0
0
2
0
0
0
0
0
2
0
2
1
1
0
0
0
0
0
2
0
1
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
2
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
2
3
0
0
0
1
2
2
2
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
1
8
0
0
2
0
1
0
0
2
0
0
1
0
0
0
2
0
2
0
2
0
0
0
0
2
0
0
2
1
0
0
0
0
2
0
0
2
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
1
0
0
0
0
1
2
0
0
0
3
0
0
2
0
0
0
0
0
0
2
1
0
2
1
0
2
0
0
1
0
1
0
0
0
2
0
0
0
1
0
0
2
0
2
0
0
1
0
1
1
2
0
2
0
0
0
2
2
0
1
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
4
2
0
3
0
2
1
0
0
1
0
1
0
2
0
0
0
0
0
3
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
2
1
2
0
0
1
0
0
1
0
0
0
0
2
2
1
0
0
0
0
0
0
0
1
0
0
0
3
0
2
0
0
0
1
1
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
2
0
1
2
2
0
0
0
0
0
1
2
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
2
0
1
0
0
0
0
2
0
0
1
0
2
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
2
2
2
2
0
0
0
0
0
0
0
0
7
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
2
0
1
2
0
0
2
1
0
3
0
2
0
0
0
2
2
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
3
2
0
1
0
1
0
0
0
2
0
0
0
0
0
2
1
0
0
1
1
2
1
0
0
0
2
1
1
0
0
0
1
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
1
1
2
0
0
0
0
0
2
0
0
0
0
1
0
4
3
1
1
1
0
0
0
2
0
0
1
1
1
0
0
2
0
1
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
2
0
1
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
2
1
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
1
0
1
2
0
0
0
2
1
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
1
1
0
0
0
2
0
7
0
0
1
0
0
0
0
0
0
9
0
1
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
1
1
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
3
0
0
0
1
0
0
0
2
1
0
0
2
0
0
0
0
0
1
1
0
0
0
2
1
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
3
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
3
1
0
2
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
2
0
1
0
1
0
0
0
2
0
2
0
0
1
0
0
0
2
0
0
1
0
0
0
0
2
0
1
0
1
0
0
0
0
0
2
1
0
0
6
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
3
0
3
0
0
0
0
1
2
0
1
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
1
0
0
0
0
0
2
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
2
2
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
2
0
2
0
2
0
2
0
2
1
0
0
0
3
1
0
0
0
0
1
3
0
0
0
2
0
0
0
0
0
0
2
2
0
0
2
2
1
0
0
0
2
0
0
0
0
0
0
2
3
0
1
2
3
0
0
1
0
2
0
0
3
0
0
1
1
1
0
0
1
0
2
2
0
0
0
3
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
3
0
0
2
0
1
2
2
2
0
1
0
1
0
0
2
0
0
0
0
0
1
0
1
2
0
1
2
0
0
4
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
1
0
0
0
1
2
1
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
2
0
0
0
0
0
1
2
2
1
2
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
2
4
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
2
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
2
2
0
0
2
2
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
3
2
0
0
1
0
0
2
3
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
2
0
0
0
2
1
1
0
0
2
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
1
2
0
0
0
0
0
0
0
3
1
2
0
0
2
0
0
3
1
2
0
0
0
0
1
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
1
0
1
0
0
0
0
1
2
5
0
0
1
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
1
1
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
3
0
3
0
0
0
0
2
0
0
0
1
0
0
0
2
3
0
1
0
0
1
0
1
0
0
0
0
0
0
0
2
0
1
0
1
0
2
1
0
0
0
0
0
0
3
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
1
0
6
1
0
0
0
0
2
0
1
0
0
2
0
2
0
0
1
0
0
0
1
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
1
10
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
1
3
0
0
2
2
1
0
0
2
0
0
2
0
0
1
1
0
0
2
1
0
0
2
2
0
1
0
1
0
1
2
0
0
0
3
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
3
1
2
2
3
3
2
0
2
0
0
0
1
0
1
0
0
3
0
0
0
1
0
2
0
0
0
0
2
0
0
0
3
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
2
2
2
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
1
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
1
0
0
2
0
0
0
0
0
6
0
3
0
0
1
0
2
3
1
1
2
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
1
0
2
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
3
2
0
0
0
0
0
1
0
0
1
2
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
3
1
0
0
0
2
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
1
1
0
0
0
5
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
2
0
3
0
0
0
0
1
0
0
0
2
1
0
2
2
0
0
2
2
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
2
0
1
1
0
2
0
2
0
0
0
0
0
1
2
0
2
0
3
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
3
0
0
0
0
2
1
1
0
0
1
0
2
0
0
0
0
1
1
4
0
0
0
0
0
2
0
1
2
0
0
0
1
0
2
0
2
2
1
2
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
2
0
0
0
2
0
0
1
1
0
0
0
0
0
8
0
0
0
0
2
0
0
0
0
1
2
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
1
0
2
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
3
0
0
0
0
2
2
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
4
0
1
0
0
0
0
2
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
2
4
0
0
0
0
1
2
0
0
1
0
0
0
0
0
2
0
0
2
1
1
0
1
1
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
1
2
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
2
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
1
4
2
0
0
2
1
2
0
1
0
1
0
0
1
0
0
0
3
0
0
0
1
0
0
0
1
1
2
0
0
2
0
0
1
2
1
0
0
0
0
0
0
0
0
4
0
0
3
1
0
1
0
0
0
0
0
1
1
0
2
0
0
0
0
3
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
5
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
3
0
0
1
0
0
2
2
1
0
0
2
0
0
2
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
2
3
1
0
1
2
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
1
1
2
0
2
1
0
1
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
2
0
1
4
1
2
0
0
0
0
2
0
0
0
0
1
3
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
2
0
1
1
1
0
0
0
2
0
0
0
0
0
2
2
0
0
1
0
0
1
2
0
0
0
2
1
0
2
0
0
0
0
1
0
1
2
0
0
2
0
2
1
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
5
0
0
1
2
1
0
0
1
1
0
0
0
2
2
1
0
0
0
0
0
0
0
6
0
1
2
6
2
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
1
0
0
0
0
2
0
0
1
0
0
2
0
1
0
0
0
0
2
3
0
1
1
2
0
2
2
0
0
2
0
0
0
0
0
2
2
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
2
1
2
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
1
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
3
0
0
1
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
1
1
0
2
0
0
2
0
1
0
1
0
1
1
1
2
0
2
0
0
1
0
2
2
0
0
0
0
0
2
3
0
0
3
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
2
0
2
0
2
0
2
2
0
1
0
0
0
0
0
2
0
0
1
0
1
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
5
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
1
2
0
2
0
1
0
0
2
0
0
3
2
0
2
0
0
0
0
2
2
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
3
0
0
0
0
1
0
0
0
0
0
1
3
0
0
2
0
2
0
2
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
1
3
0
2
0
2
3
1
0
0
1
0
0
0
2
0
0
2
2
0
0
2
0
0
2
0
0
0
0
3
0
0
2
0
2
0
0
1
1
0
0
1
1
0
0
0
2
0
2
0
0
0
0
0
1
0
1
0
2
2
2
2
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
1
0
1
1
3
0
7
2
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
2
0
0
0
0
0
2
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
2
0
0
0
0
2
1
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
2
1
0
0
2
0
0
2
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
1
0
2
0
0
0
0
0
1
0
0
0
2
1
0
1
1
3
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
3
0
2
0
2
3
0
0
0
2
0
0
1
2
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
3
1
3
0
0
1
0
1
0
0
0
0
2
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
3
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
2
0
2
2
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
1
0
0
1
0
2
0
0
0
0
1
0
0
0
1
0
0
1
0
2
2
0
0
0
0
0
2
0
0
0
1
1
1
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
3
3
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
2
0
1
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
1
0
0
0
2
0
0
2
0
2
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
1
0
0
0
0
2
0
1
0
0
1
2
2
0
0
0
0
0
2
1
1
1
1
0
0
0
2
1
1
0
0
0
0
2
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
3
0
0
0
2
1
0
0
0
0
1
0
2
0
0
2
1
1
0
1
2
0
0
1
2
0
0
2
3
0
0
0
1
5
0
1
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
1
1
0
0
2
2
0
0
2
2
0
0
0
1
1
1
1
1
0
0
2
0
0
0
4
1
1
0
1
2
0
0
0
0
0
0
1
0
0
2
2
1
0
0
0
0
0
0
1
0
0
0
1
0
2
0
1
1
0
0
0
0
0
0
1
0
2
1
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
1
2
5
0
0
1
0
0
1
2
0
2
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
1
2
0
2
0
0
0
0
1
0
2
1
0
1
0
1
0
1
0
1
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
2
1
1
1
0
0
0
1
0
0
0
1
2
0
0
3
1
0
2
0
0
1
2
0
0
3
0
1
1
0
2
1
1
0
0
0
1
0
0
3
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
3
0
0
2
4
2
0
2
2
0
0
0
0
2
0
0
3
0
0
0
0
0
0
1
2
2
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
2
2
0
0
1
0
2
0
0
0
0
0
3
0
0
0
0
0
1
1
2
0
2
1
0
1
0
0
2
0
0
0
0
0
1
0
2
0
1
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
1
0
0
0
0
0
2
0
0
1
2
0
0
0
3
2
1
0
0
0
2
0
0
0
0
0
0
0
0
1
2
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
2
2
0
0
2
2
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
2
0
0
0
3
3
4
1
0
3
2
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
2
1
0
1
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
3
0
0
0
0
1
0
0
1
1
3
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
2
1
0
0
2
0
0
1
1
0
1
2
1
0
0
2
2
0
2
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
3
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
3
0
0
2
0
1
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
3
0
2
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
1
2
2
0
2
2
0
0
0
1
0
0
1
0
0
1
0
1
0
1
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
2
0
0
2
1
0
1
0
0
0
1
0
0
0
3
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
1
2
0
0
1
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
1
4
1
0
0
0
2
0
2
0
0
1
3
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
1
1
2
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
1
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
1
1
2
0
0
0
0
0
2
0
0
0
0
2
2
0
2
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
2
0
0
2
0
2
1
0
0
0
0
1
0
0
2
2
0
0
2
1
0
0
0
0
0
7
0
2
4
3
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
1
0
2
0
1
0
0
0
0
0
0
0
2
2
0
0
0
1
1
0
0
0
1
2
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
1
0
1
2
0
0
0
2
0
0
0
1
3
0
0
0
2
1
0
2
0
0
0
0
0
0
3
2
0
2
2
0
2
0
0
2
2
0
0
1
0
2
0
6
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
4
0
1
2
0
1
0
0
0
2
0
0
1
3
1
1
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
1
2
0
0
0
2
0
1
1
0
0
0
0
0
1
2
0
0
1
2
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
4
0
0
1
0
1
0
0
0
0
1
1
0
0
2
1
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
1
2
2
0
0
0
2
0
0
2
0
1
1
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
2
1
0
0
2
0
1
0
0
0
2
0
0
1
2
1
0
1
0
0
0
0
2
1
0
1
0
0
1
4
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
2
0
0
2
0
0
1
0
4
2
0
0
1
0
2
2
0
0
0
0
0
0
0
0
2
0
0
2
1
0
2
1
2
0
3
0
0
0
0
0
2
0
0
1
0
0
0
2
0
2
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
1
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
2
3
0
2
2
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
2
0
0
3
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
1
0
0
1
0
2
0
0
0
1
0
0
0
7
0
1
2
0
1
1
0
0
1
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
8
0
0
0
2
0
2
2
1
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
2
0
0
0
0
5
1
3
0
0
1
0
1
1
0
0
1
0
2
1
0
2
1
2
1
0
0
1
0
0
0
0
0
3
1
0
0
2
1
1
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
1
2
1
0
0
0
1
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
1
2
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
2
0
1
1
1
2
2
0
0
1
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
1
2
1
0
0
1
0
0
0
0
0
2
2
0
0
2
1
0
1
0
1
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
1
1
0
2
0
0
0
2
3
1
0
1
0
0
2
0
0
0
1
1
0
0
1
0
0
0
0
0
2
2
0
0
0
4
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
1
1
1
1
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
1
1
1
0
0
3
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
2
1
0
0
5
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
3
0
1
1
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
1
1
0
0
0
1
2
0
0
1
0
0
1
0
0
0
0
2
0
0
3
0
2
0
2
0
0
3
0
0
0
0
0
4
0
0
2
0
0
0
1
0
0
0
0
0
1
0
2
1
0
1
0
0
1
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
2
1
0
2
6
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
2
1
0
1
0
5
0
0
0
0
3
1
0
0
0
0
0
0
0
3
0
0
0
2
2
0
0
0
3
0
0
0
2
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
1
2
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
1
2
0
0
0
1
1
2
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
3
0
0
2
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
1
1
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
2
0
1
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
3
0
0
1
0
2
0
2
0
0
0
0
1
0
0
2
2
1
0
0
0
2
0
0
0
0
0
4
0
0
2
0
2
2
0
0
1
0
0
0
0
0
0
1
0
2
1
0
4
0
0
2
2
0
0
0
0
3
1
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
2
1
0
0
0
0
1
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
1
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
6
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
2
0
0
0
4
1
1
0
0
0
2
0
0
0
2
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
1
1
0
0
0
1
2
2
1
2
0
0
1
1
1
2
0
0
1
0
0
1
2
0
0
2
0
0
0
0
0
0
2
0
0
0
2
1
0
2
0
0
0
0
0
1
0
0
0
2
0
0
2
2
0
0
1
0
0
0
1
0
0
2
3
2
0
0
0
0
0
2
1
1
0
2
1
0
1
0
14
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
1
0
1
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
2
0
0
2
0
0
2
2
1
0
1
1
0
1
0
1
2
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
2
0
1
1
1
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
3
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
1
0
2
0
0
2
0
0
2
0
1
0
0
0
1
2
0
3
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
1
0
3
2
0
0
0
0
2
3
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
4
1
0
0
0
0
0
2
1
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
4
0
1
1
7
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
2
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
1
2
3
1
1
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
1
0
0
1
0
3
1
2
0
0
0
0
0
0
3
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
2
1
1
0
0
1
0
0
0
2
1
0
0
2
1
0
0
0
0
2
1
0
0
2
0
1
2
0
1
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
2
1
0
1
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
1
0
0
0
0
0
0
3
2
0
3
0
0
0
1
0
0
2
2
3
0
0
0
2
2
0
0
0
6
0
0
1
0
0
1
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
9
0
0
0
0
0
2
0
0
0
0
1
0
0
2
1
0
0
0
0
1
0
0
1
0
0
1
1
0
2
0
2
0
1
0
2
0
0
1
0
0
2
0
0
0
0
1
0
0
0
2
2
0
2
0
0
0
0
2
0
2
2
0
0
3
0
1
6
1
1
0
0
0
0
0
0
0
1
0
2
0
0
0
2
1
0
2
0
1
0
0
3
0
0
0
2
0
0
0
2
0
1
0
1
1
2
0
1
0
2
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
2
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
1
0
2
0
0
2
1
1
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
2
0
0
0
1
0
0
0
0
2
0
0
2
2
2
0
0
3
0
2
0
0
1
0
0
0
0
2
3
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
2
0
1
1
0
0
0
1
1
0
2
2
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
3
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
2
0
0
2
0
1
0
1
0
2
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
3
2
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
4
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
1
2
0
0
0
0
0
0
0
1
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
2
2
0
2
0
1
2
0
0
1
2
0
0
0
2
0
1
1
0
0
0
1
0
0
1
1
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
1
0
0
2
1
2
0
0
0
0
1
0
0
0
0
0
0
4
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
2
1
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
2
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
1
1
1
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
1
0
2
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
1
2
2
0
5
0
3
0
0
0
1
0
0
1
0
0
0
2
1
1
1
1
0
0
0
0
0
1
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
1
0
0
2
0
1
2
0
0
0
0
0
0
1
1
2
0
0
2
0
5
0
0
1
0
0
1
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
4
0
1
0
0
1
0
2
0
0
1
1
0
0
0
0
1
0
1
0
0
2
0
0
2
0
2
0
0
0
1
0
0
0
0
0
3
3
0
0
4
0
0
0
1
0
3
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
2
1
0
0
3
0
0
0
1
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
2
0
0
0
1
1
2
0
0
1
1
2
0
0
0
0
0
0
0
0
5
0
0
0
2
0
2
0
0
3
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
4
0
0
0
0
1
1
2
1
0
1
0
0
0
0
2
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
3
0
0
0
1
2
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
1
0
1
1
0
2
2
0
0
0
0
2
0
0
0
2
1
0
0
0
0
2
3
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
2
1
0
0
1
0
0
2
1
2
0
0
1
0
0
0
2
0
0
2
0
2
0
0
0
0
1
1
0
0
3
0
0
1
1
0
0
2
0
0
0
1
1
0
2
0
0
0
1
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
4
0
1
0
1
2
2
0
0
0
0
0
2
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
1
2
3
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
1
0
0
0
0
0
1
1
0
0
0
2
1
0
0
1
0
0
2
1
0
0
0
6
2
1
0
2
0
0
0
0
0
2
0
1
2
0
0
1
1
0
0
0
1
0
0
0
0
2
1
0
0
2
0
2
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
1
0
0
0
0
0
3
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
2
0
0
3
0
1
0
0
0
0
1
1
3
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
2
2
0
2
2
0
0
0
1
0
1
2
2
0
0
0
0
0
1
0
0
0
0
1
2
1
0
0
0
0
2
0
1
0
0
0
3
0
2
1
0
0
2
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
3
1
1
1
0
0
0
2
0
1
0
0
0
0
3
0
0
0
2
0
1
0
1
1
2
1
0
0
0
0
0
2
6
0
3
3
0
2
2
0
0
1
0
0
1
2
0
2
0
0
0
3
1
0
0
0
0
0
0
4
2
0
1
0
2
0
0
1
0
1
0
0
0
0
0
4
2
0
2
0
0
3
1
0
0
0
0
0
0
2
0
2
1
0
1
2
1
0
0
1
3
0
0
1
0
0
0
1
7
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
2
0
2
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
2
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
1
2
1
1
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
2
4
0
0
1
0
0
0
0
0
0
0
1
1
1
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
4
0
0
0
0
0
0
0
1
4
0
1
1
0
0
2
0
0
0
1
1
0
1
4
1
0
0
0
3
2
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
3
1
0
0
2
0
0
2
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
2
0
2
2
0
1
0
0
0
1
3
0
1
0
0
0
2
2
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
3
0
2
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
1
0
2
0
2
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
1
0
0
0
0
1
0
1
0
2
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
2
2
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
2
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
2
0
1
0
1
0
3
0
2
1
2
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
8
3
2
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
1
1
0
2
0
2
0
2
2
0
0
1
0
0
0
2
0
0
0
1
3
0
1
0
0
0
0
0
0
1
0
0
2
1
0
1
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
3
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
3
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
1
2
0
0
0
2
0
3
0
1
0
0
0
0
0
3
2
0
0
0
1
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
2
2
0
1
0
0
0
0
0
0
0
1
3
0
1
0
0
0
3
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
2
2
0
0
1
2
0
0
3
0
1
0
2
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
1
0
2
1
0
0
2
0
0
2
0
0
0
7
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
2
0
0
0
0
2
1
0
2
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
1
0
0
1
0
0
2
0
0
0
1
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
3
2
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
4
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
1
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
2
0
3
0
0
3
1
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
1
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
1
2
0
2
0
2
0
2
0
0
2
0
0
0
0
0
2
0
0
2
0
1
2
3
0
0
2
0
1
2
0
1
1
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
2
2
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
1
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
2
2
0
0
3
0
0
2
1
1
0
2
2
2
0
0
0
0
0
0
2
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
1
2
3
1
0
0
2
0
2
1
0
2
0
0
1
0
1
0
0
0
1
0
0
0
0
0
2
0
2
0
0
1
0
0
2
1
0
5
1
0
1
1
1
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
1
2
3
0
0
0
0
0
1
2
0
1
0
0
0
0
1
0
2
0
0
0
2
0
0
2
0
2
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
1
0
1
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
3
3
0
1
3
1
2
0
0
1
2
0
1
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
2
0
0
1
0
1
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
2
0
0
2
0
5
0
2
0
0
5
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
2
2
0
0
2
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
2
0
1
0
0
0
2
0
0
2
0
0
1
0
1
0
0
1
0
2
0
0
0
0
0
6
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
1
0
0
0
1
3
0
4
1
1
0
3
0
0
0
0
0
0
2
0
0
0
1
2
1
2
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
2
0
2
0
0
1
0
0
0
2
0
0
0
0
0
1
1
1
2
0
0
0
0
3
0
0
1
1
0
1
0
2
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
10
0
0
0
0
0
1
2
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
1
1
0
0
0
0
0
2
0
0
1
0
0
0
2
0
1
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
1
0
1
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
4
0
3
0
1
0
0
0
1
0
0
1
0
0
0
0
2
0
1
0
1
2
0
1
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
5
0
0
2
1
1
0
0
0
0
0
0
0
0
2
1
2
0
0
1
0
0
0
0
0
2
2
1
0
0
2
0
0
0
0
0
0
0
1
2
2
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
3
0
3
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
2
2
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
2
3
0
0
0
4
0
0
2
0
0
2
0
1
0
0
0
0
0
2
0
0
3
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
3
2
0
0
0
1
0
0
1
1
0
1
0
0
1
2
1
0
0
2
1
0
0
0
0
0
1
2
0
0
0
0
0
0
1
4
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
3
0
0
0
3
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
2
2
0
0
0
2
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
1
0
0
0
0
1
0
0
0
1
1
2
0
3
0
0
2
0
0
1
0
0
2
0
1
0
0
0
2
0
0
1
2
2
2
0
1
0
0
6
0
1
0
0
1
1
2
0
0
0
0
0
0
2
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
4
1
1
0
2
0
2
0
0
0
0
0
0
0
0
1
3
2
1
0
0
0
2
0
1
0
0
0
1
0
0
0
1
0
2
0
2
0
0
1
1
1
0
0
0
1
3
2
1
0
1
0
0
0
0
0
0
0
2
1
2
0
0
0
0
2
1
0
1
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
3
1
0
0
1
0
0
0
0
0
0
2
0
1
0
1
2
2
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
3
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
1
2
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
4
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
3
2
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
1
1
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
3
0
0
2
0
2
0
1
0
0
1
2
2
0
0
0
1
0
2
0
0
0
1
0
4
2
0
0
3
0
0
0
0
1
0
0
1
0
2
0
1
0
0
0
0
0
0
1
0
0
0
1
4
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
1
2
0
0
0
2
0
0
2
0
1
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
2
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
2
0
0
1
1
0
0
0
2
0
0
0
0
0
7
0
0
1
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
3
0
0
2
1
0
2
0
1
2
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
2
2
2
2
0
1
2
0
0
2
0
2
0
0
0
2
2
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
2
0
0
0
0
2
0
2
0
0
0
1
0
0
2
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
2
0
0
2
0
0
1
1
2
0
0
2
1
0
0
1
4
1
0
0
0
0
0
0
0
1
0
0
3
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
1
0
0
1
0
0
0
1
0
1
1
0
2
0
0
0
0
0
2
3
2
0
0
1
0
0
2
1
0
0
2
3
1
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
2
0
1
1
0
0
0
0
2
0
1
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
3
0
0
0
0
0
0
2
1
0
0
2
0
0
1
1
1
2
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
3
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
2
0
2
0
2
0
4
0
0
0
0
0
0
1
0
0
1
0
1
9
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
6
0
0
0
3
0
1
0
0
0
2
2
0
0
0
0
0
1
0
2
0
1
0
0
2
0
0
2
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
1
0
0
2
0
1
0
1
1
0
3
0
0
0
0
2
1
0
0
1
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
2
0
1
0
2
0
0
2
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
2
0
2
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
3
0
1
0
0
0
0
2
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
8
0
0
0
3
0
0
0
0
0
0
1
0
3
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
2
0
1
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
1
3
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
1
3
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
2
2
1
0
0
2
0
0
0
0
0
1
0
2
0
2
2
1
0
0
0
0
0
1
2
0
2
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
3
1
0
0
0
3
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
3
1
5
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
3
0
0
3
5
0
0
2
0
2
0
1
0
0
0
0
2
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
1
0
3
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
1
0
0
2
0
1
0
0
0
0
1
0
1
1
1
0
0
0
0
0
2
0
0
0
0
0
2
1
0
2
0
1
0
2
1
0
0
1
0
0
0
0
2
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
2
0
1
0
0
1
0
1
0
0
0
0
0
1
0
1
0
2
1
0
0
2
0
0
0
2
0
0
1
0
2
1
0
2
0
0
0
2
0
0
0
0
0
0
2
2
2
0
0
0
1
0
1
1
2
1
2
0
1
0
0
0
2
0
0
0
0
0
1
0
1
0
1
0
1
1
2
0
0
0
3
0
0
0
5
0
1
0
0
0
0
4
0
0
1
1
1
2
0
2
2
1
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
1
0
0
7
2
0
2
0
0
0
0
2
0
1
2
1
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
2
0
0
3
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
1
0
3
0
0
1
1
0
0
3
3
0
0
0
2
0
0
0
1
0
0
1
0
1
0
2
2
0
2
2
1
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
3
0
0
1
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
2
0
0
0
5
0
2
0
0
0
0
0
0
1
0
0
0
1
0
1
2
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
1
1
2
0
0
1
0
0
0
0
0
2
1
0
0
0
0
4
0
2
2
0
0
2
0
0
0
1
0
2
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
2
3
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
3
0
0
0
0
0
2
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
1
0
0
0
1
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
1
1
0
0
3
1
0
0
0
0
1
0
0
2
3
0
0
0
0
0
0
0
1
2
1
0
0
1
2
2
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
2
2
1
0
0
0
0
0
1
1
0
0
1
1
0
0
2
0
1
2
0
0
2
0
0
0
0
2
1
3
0
2
1
1
0
0
0
0
0
2
1
0
2
2
1
2
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
2
1
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
3
0
0
0
0
1
0
2
0
0
2
0
0
0
0
3
0
1
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
2
2
1
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
1
2
0
0
2
2
0
0
0
1
0
0
0
0
1
1
1
0
0
0
2
1
0
1
0
2
0
0
0
0
3
0
0
0
1
0
2
4
2
0
3
0
0
0
0
0
0
2
1
0
0
2
0
2
0
0
2
0
0
8
0
0
0
0
0
0
0
1
0
0
0
0
1
2
1
0
0
1
0
0
0
2
1
1
1
0
3
0
0
0
0
2
0
0
0
0
0
0
0
1
6
0
0
0
0
0
0
0
0
0
0
2
0
5
0
0
2
0
4
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
1
1
0
0
0
0
0
0
2
2
2
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
1
0
0
0
0
2
2
2
2
1
1
0
0
0
0
0
0
0
1
2
0
2
3
0
0
0
2
1
1
0
0
2
0
0
0
0
1
0
0
2
0
0
0
1
2
0
0
1
0
0
0
1
0
2
0
0
1
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
1
0
0
0
0
0
1
1
2
0
1
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
3
0
0
1
1
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
2
1
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
1
0
1
2
1
2
0
0
2
0
0
0
0
0
2
3
0
0
1
0
0
1
0
0
1
0
0
1
0
3
0
0
1
0
2
2
1
0
0
2
0
1
3
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
2
0
0
0
0
1
2
0
1
0
0
0
3
1
0
0
0
1
2
0
0
1
0
0
2
0
0
3
0
0
1
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
6
1
2
2
0
0
1
0
0
0
0
2
0
0
2
0
0
2
1
0
1
0
0
0
0
0
0
0
3
0
2
0
0
0
2
0
1
0
0
0
0
0
1
0
0
2
1
0
2
0
0
0
1
0
0
0
0
0
0
2
3
0
0
2
0
2
0
0
0
0
0
2
0
1
0
0
0
0
1
1
0
2
2
1
1
1
1
1
0
1
0
0
0
2
0
0
2
0
0
0
2
0
3
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
3
2
0
1
0
0
0
0
1
1
0
0
0
1
1
1
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
3
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
1
0
0
2
0
2
0
3
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
2
0
2
0
3
0
0
0
0
1
0
1
0
1
1
1
1
1
2
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
6
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
2
1
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
1
2
2
0
2
2
4
0
0
2
0
0
0
2
0
0
0
0
0
0
1
3
1
0
0
0
0
1
0
1
0
1
1
0
0
0
0
1
2
0
0
0
0
1
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
2
1
2
0
0
0
1
0
0
0
2
2
0
0
0
0
1
1
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
3
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
1
0
4
0
0
0
0
3
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
2
1
0
2
1
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
4
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
4
0
0
6
1
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
3
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
3
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
3
0
0
2
2
0
1
0
0
0
2
1
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
1
0
1
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
1
2
2
2
0
1
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
1
0
2
0
1
0
0
0
2
0
0
1
0
0
0
2
0
0
0
1
1
0
0
0
2
0
0
0
0
0
3
1
0
0
0
2
0
2
0
0
0
2
0
0
1
2
1
0
0
0
0
1
0
0
0
0
0
1
4
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
3
0
0
1
0
0
0
0
0
3
0
0
2
2
0
1
2
2
1
0
2
1
2
0
0
0
2
1
2
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
2
0
0
0
2
0
0
0
0
1
0
0
0
1
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
4
2
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
1
0
0
1
0
2
1
0
0
0
0
0
0
2
2
0
1
1
1
0
0
2
2
2
0
0
0
0
0
2
1
2
0
0
0
0
0
0
2
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
3
0
0
0
2
0
2
2
0
0
0
0
1
0
2
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
1
0
0
0
2
1
1
1
0
1
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
3
0
0
1
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
2
0
2
0
0
2
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
3
1
2
0
0
0
0
0
0
0
0
0
4
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
2
0
0
0
0
2
1
0
2
3
0
0
4
0
0
0
0
2
0
0
0
2
0
0
1
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
3
0
1
2
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
1
1
1
0
0
0
2
0
1
0
0
0
0
2
0
0
0
2
0
2
2
0
0
0
1
0
0
0
0
0
2
4
2
2
0
2
0
0
0
0
2
3
0
2
0
2
0
0
1
0
0
0
4
0
0
0
0
0
0
2
0
0
3
0
2
1
2
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
2
2
0
0
0
0
3
2
0
1
0
1
0
0
0
0
0
0
0
3
4
2
0
0
0
0
0
0
5
2
0
0
3
0
0
2
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
1
0
0
0
0
4
0
0
0
2
0
0
0
2
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
1
2
1
0
0
0
0
1
0
2
0
2
0
0
0
0
2
0
0
1
3
2
0
0
1
1
0
3
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
1
0
1
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
2
0
0
0
0
0
1
0
1
0
0
0
1
0
0
2
0
2
0
0
1
0
1
0
2
0
0
0
0
0
0
2
2
1
0
1
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
1
2
0
1
1
0
2
0
0
0
1
1
0
0
2
0
2
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
3
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
3
0
2
0
2
1
0
0
2
0
0
0
2
0
1
0
1
0
0
0
0
0
2
0
0
0
0
6
0
0
0
0
1
0
0
0
3
2
0
0
0
1
1
2
0
0
0
0
0
0
2
2
1
0
1
0
0
2
0
0
0
0
0
0
0
0
2
1
1
2
0
2
0
0
0
0
2
0
0
0
2
0
0
3
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
2
0
0
1
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
3
0
1
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
1
0
3
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
8
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
3
0
2
1
0
1
0
0
0
0
2
1
0
0
0
0
0
1
0
1
0
0
2
2
0
2
1
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
2
0
1
1
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
1
0
0
8
0
0
0
0
2
1
0
3
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
1
0
0
0
2
1
0
1
1
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
2
2
0
0
1
0
0
2
2
0
0
0
2
0
0
3
0
3
0
0
0
0
0
1
3
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
2
2
0
2
2
1
2
2
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
4
0
0
0
3
0
3
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
2
0
0
0
0
1
0
1
1
1
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
2
0
0
1
0
2
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
2
0
1
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
3
0
2
1
2
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
2
1
2
0
0
0
0
1
0
1
1
0
1
1
0
2
3
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
1
0
2
2
0
0
2
0
0
0
0
2
1
0
0
1
0
2
0
0
3
3
2
0
1
0
0
0
0
0
1
4
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
2
0
0
0
0
2
0
1
2
0
0
0
0
3
0
2
1
2
2
0
0
1
0
2
0
0
1
1
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
1
2
2
1
0
0
1
0
1
0
2
1
2
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
2
0
0
0
1
0
2
2
0
1
0
0
0
0
1
1
0
2
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
2
7
0
0
0
0
0
1
2
2
1
0
0
0
0
0
0
0
2
2
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
2
1
1
0
0
0
5
2
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
1
1
2
0
0
1
0
0
3
2
0
0
0
0
0
1
3
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
2
0
5
0
2
0
2
1
0
0
0
4
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
2
0
0
1
1
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
2
2
0
0
0
0
0
0
2
0
0
0
0
4
3
0
0
2
0
0
2
1
1
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
2
1
0
0
1
0
0
1
3
0
1
0
0
2
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
1
1
0
2
0
0
1
1
0
0
0
0
1
2
2
1
0
0
1
0
0
0
1
0
1
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
2
1
6
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
1
0
0
0
0
1
0
0
2
2
2
0
0
0
0
1
0
2
1
2
2
0
0
1
1
0
2
0
0
0
0
0
0
1
6
0
0
4
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
1
0
0
1
0
2
1
0
0
0
1
0
0
0
0
2
0
4
0
0
1
0
0
2
0
0
0
2
2
3
1
0
0
0
2
0
0
2
3
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
3
0
0
0
2
0
0
2
2
0
0
1
2
0
0
0
2
1
1
0
0
0
1
0
2
0
1
2
0
0
4
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
1
1
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
2
2
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
2
1
0
1
0
0
0
0
1
0
2
1
2
0
2
0
0
0
0
2
1
2
0
0
0
2
0
0
0
0
0
0
0
0
3
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
1
0
0
0
0
0
0
2
0
1
0
1
2
0
0
1
0
1
0
0
0
2
2
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
1
0
1
1
0
1
0
1
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
1
2
2
1
0
0
0
4
0
0
0
0
1
0
0
0
2
0
1
2
0
2
0
0
1
0
0
2
0
0
0
2
2
0
0
2
1
2
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
2
1
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
2
0
0
1
0
2
0
0
0
1
0
0
1
1
0
0
0
0
2
0
3
0
0
0
0
1
2
0
0
2
2
2
0
0
2
4
0
2
0
0
0
1
0
1
2
1
1
2
1
0
1
0
0
0
1
0
0
1
0
2
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
2
0
0
4
0
1
0
2
0
0
0
2
0
2
0
0
2
2
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
3
3
0
0
1
1
1
2
0
0
0
0
0
2
2
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
1
1
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
2
0
0
0
1
0
2
1
0
1
0
0
2
0
0
1
3
0
0
0
0
0
0
3
0
0
0
2
0
0
1
0
2
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
2
1
1
3
1
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
6
2
1
0
2
0
0
0
2
0
1
1
1
0
0
0
0
1
0
0
2
0
0
3
0
2
1
1
0
1
1
2
1
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
2
2
0
0
0
0
1
0
0
0
0
0
0
4
0
0
2
0
0
1
0
2
0
2
0
0
0
1
2
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
2
0
0
2
0
1
0
0
0
1
1
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
2
2
0
2
0
1
0
1
0
0
0
2
0
0
1
2
0
0
0
0
2
0
0
5
1
0
2
0
2
0
2
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
1
1
2
2
2
0
1
0
0
0
0
0
0
1
2
0
2
2
1
0
0
2
0
2
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
2
3
0
2
3
0
0
0
0
2
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
1
3
1
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
2
1
0
1
2
1
2
1
0
1
0
0
0
4
2
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
2
2
1
0
1
1
2
0
0
1
1
0
0
0
1
5
2
0
0
0
2
2
0
1
1
0
0
2
0
2
0
0
1
1
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
1
0
0
0
4
0
0
2
0
1
1
0
0
0
0
2
1
0
0
0
1
0
0
0
2
0
0
0
0
1
0
2
1
0
1
2
0
0
0
2
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
2
0
0
0
0
0
0
0
0
2
2
0
0
2
1
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
2
6
0
2
2
0
4
2
0
0
0
0
0
1
1
0
1
0
0
1
2
0
0
0
0
0
0
1
2
0
4
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
2
0
1
0
0
0
0
0
0
0
2
0
1
2
1
0
1
0
2
0
1
1
0
0
0
1
0
0
0
2
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
1
1
0
0
0
0
2
1
1
2
0
0
0
2
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
2
0
0
2
2
1
0
4
2
0
0
0
2
0
0
0
5
0
0
0
0
0
0
1
0
0
0
0
1
1
1
2
0
0
0
0
0
0
2
0
2
1
0
0
0
1
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
2
2
0
0
0
0
0
2
0
1
0
0
0
1
1
1
0
0
0
1
2
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
1
0
2
2
2
0
1
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
2
0
1
2
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
1
0
1
0
0
0
1
1
2
0
0
0
1
0
0
1
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
2
0
0
7
0
2
1
0
0
0
0
2
1
0
0
0
0
1
2
0
2
0
2
0
0
1
2
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
2
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
2
0
1
0
1
2
0
2
0
2
2
0
1
1
0
0
2
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
1
0
1
0
2
1
1
0
0
3
1
0
0
1
2
0
0
0
0
2
0
2
1
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
2
0
0
2
2
1
0
0
2
0
1
0
0
0
0
2
3
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
3
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
3
1
0
0
0
0
0
2
0
0
0
1
2
2
0
0
0
1
1
0
0
0
1
0
2
2
0
1
0
0
1
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
5
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
1
1
2
0
0
0
1
1
0
0
2
2
0
3
0
0
1
0
0
0
3
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
1
0
0
0
1
2
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
2
1
0
3
0
0
0
2
1
1
2
0
0
0
0
2
3
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
2
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
1
3
1
0
0
0
0
0
0
0
1
0
1
2
0
0
2
7
2
0
0
1
2
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
3
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
1
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
1
1
1
2
0
2
1
1
0
0
0
1
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
1
2
0
0
1
1
1
0
1
2
0
0
0
2
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
3
0
0
3
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
2
0
0
1
2
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
2
0
2
2
0
0
0
0
0
0
0
0
1
0
3
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
2
0
3
1
0
0
0
0
0
0
1
1
1
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
1
0
0
0
1
0
1
1
0
1
0
0
0
0
2
1
0
3
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
2
0
1
0
2
1
0
0
0
0
2
0
0
0
0
2
0
0
1
2
0
0
0
0
0
2
1
1
0
3
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
2
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
1
0
2
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
3
2
0
0
2
0
0
0
0
0
0
1
1
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
7
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
1
0
2
0
0
1
0
0
0
2
1
3
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
1
0
1
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
1
0
0
1
2
0
0
0
1
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
3
0
0
1
0
3
0
1
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
3
0
0
1
0
0
0
0
4
1
0
0
1
0
0
0
1
0
0
0
2
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
1
2
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
1
1
0
1
3
1
0
0
2
0
1
0
0
0
0
2
0
0
4
0
0
1
2
1
0
0
2
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
2
2
0
0
0
1
1
2
2
1
1
0
0
1
0
0
1
0
2
0
0
2
1
0
3
0
0
2
0
0
0
0
1
0
2
2
0
0
4
2
1
0
2
0
0
1
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
1
0
0
0
0
2
0
0
1
2
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
1
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
2
2
0
2
0
2
0
2
0
2
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
6
2
0
0
0
7
0
1
0
1
2
4
0
0
3
2
2
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
2
0
0
2
0
0
1
0
1
4
0
2
0
0
1
0
3
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
2
0
0
1
0
10
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
3
1
0
3
0
0
0
11
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
2
2
1
2
0
0
2
0
0
0
0
2
0
0
2
2
4
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
2
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
2
0
2
0
0
1
1
0
0
1
0
0
0
1
0
0
2
0
0
0
0
2
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
2
0
1
1
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
5
0
0
0
1
0
2
0
0
0
0
0
1
0
1
0
2
0
1
0
4
0
0
0
0
0
0
0
0
1
2
0
1
1
0
0
0
1
0
0
1
0
0
1
0
1
1
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
10
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
2
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
2
0
2
0
1
2
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
2
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
1
0
3
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
1
0
0
0
0
2
2
0
0
1
1
1
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
1
2
2
0
0
0
1
0
0
0
0
0
2
0
2
0
2
1
0
1
0
1
4
2
0
0
0
0
0
0
3
0
2
0
1
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
1
0
2
0
0
4
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
2
0
2
2
0
0
0
0
0
0
1
2
2
0
0
0
6
0
0
2
0
2
3
2
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
1
2
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
1
0
0
2
1
0
0
0
2
0
0
0
0
0
0
1
1
1
2
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
2
0
5
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
3
0
0
1
0
1
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
2
0
0
5
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
1
2
0
0
0
3
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
2
0
2
1
0
2
0
2
0
0
0
0
0
0
0
1
0
2
0
0
1
1
0
0
0
0
1
0
2
0
2
0
0
0
1
0
0
0
1
1
0
0
0
2
0
0
0
0
1
0
2
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
1
0
2
0
2
2
0
0
0
0
0
2
0
0
0
1
1
2
2
0
3
0
0
0
0
0
1
2
2
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
2
1
0
1
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
3
3
0
0
2
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
5
0
0
0
2
0
0
0
0
2
0
2
0
1
0
0
0
3
2
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
2
0
1
0
2
0
0
2
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
3
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
4
0
0
2
2
0
0
0
0
0
1
0
2
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
2
0
3
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
1
0
0
0
0
0
2
2
0
2
0
0
0
1
1
0
0
0
0
1
0
1
0
3
2
1
0
0
0
2
2
1
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
2
1
0
0
1
0
1
0
1
0
0
1
2
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
2
1
1
2
0
0
0
0
0
0
3
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
2
0
1
0
0
0
0
0
0
1
2
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
5
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
1
1
0
0
1
2
0
0
0
1
0
0
2
0
0
0
3
0
2
1
2
0
0
1
0
1
2
2
0
1
0
0
1
2
1
0
0
1
0
0
0
2
0
2
0
1
0
2
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
2
0
3
0
1
0
1
0
0
1
0
1
0
5
0
2
0
2
0
0
2
0
1
1
2
0
0
0
0
0
0
3
0
0
0
1
0
0
2
0
0
0
2
0
0
2
1
2
0
1
0
0
2
0
0
0
0
3
0
1
0
0
0
0
2
0
0
0
2
0
1
0
0
0
1
1
0
0
0
0
0
0
0
8
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
3
0
2
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
1
0
3
1
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
3
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
1
0
2
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
3
0
2
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
3
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
3
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
2
0
2
3
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
1
2
0
1
0
0
1
1
2
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
2
0
1
0
0
1
4
2
0
0
0
2
1
2
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
2
0
2
0
2
0
1
1
0
0
1
0
0
0
0
0
6
0
2
2
0
2
1
2
0
0
2
0
1
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
3
0
0
0
0
5
0
0
0
0
0
0
1
1
0
0
0
2
0
0
2
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
3
1
0
2
0
4
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
2
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
2
0
0
3
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
1
1
1
2
0
4
0
0
0
0
2
0
0
1
0
0
0
0
1
2
2
0
1
2
0
0
2
0
0
0
0
2
1
2
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
2
0
2
0
0
0
0
1
0
1
2
0
1
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
1
0
1
2
0
0
0
0
2
0
1
0
0
2
1
0
2
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
1
1
2
6
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
2
2
2
0
0
0
0
0
0
0
2
0
0
1
0
0
1
2
1
0
0
0
1
0
0
2
2
0
2
1
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
2
1
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
2
1
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
1
1
4
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
2
1
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
1
1
0
1
0
1
0
4
2
1
0
0
2
0
0
0
0
0
0
1
0
1
1
0
0
2
0
0
0
1
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
2
0
0
0
0
1
0
2
0
3
2
1
0
1
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
1
1
0
2
2
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
3
0
0
3
0
1
0
0
0
0
1
0
0
0
5
1
0
2
1
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
2
3
1
1
1
1
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
1
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
10
0
1
0
0
2
0
0
0
0
2
3
0
0
0
0
3
1
0
2
0
0
2
0
0
0
0
2
2
0
1
0
2
1
0
0
1
0
0
0
2
0
1
0
1
1
0
0
0
0
1
0
0
0
2
0
1
2
2
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
3
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
1
0
1
2
0
2
0
0
0
0
0
2
2
2
0
0
1
0
1
0
0
0
1
0
0
0
0
2
4
0
0
0
0
0
0
1
2
2
0
3
2
0
0
0
3
5
0
2
0
0
0
0
1
0
0
1
1
0
2
0
0
0
0
0
1
0
1
2
0
0
0
1
0
2
0
2
0
1
1
0
0
0
1
0
1
9
0
0
0
0
2
0
1
2
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
3
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
2
0
1
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
2
1
1
0
0
0
0
1
1
0
2
0
1
0
1
1
2
2
0
0
1
0
2
0
0
1
0
1
0
0
2
0
1
2
0
4
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
1
0
0
0
2
0
2
0
2
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
3
0
1
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
2
0
1
0
0
2
2
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
2
0
1
0
4
0
2
0
0
2
5
0
1
1
0
2
1
0
0
0
0
1
2
0
0
0
0
0
1
0
1
0
2
0
0
0
0
1
0
0
1
2
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
2
0
2
0
1
2
0
0
2
4
0
0
0
0
1
2
0
0
0
2
0
3
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
2
2
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
3
2
0
0
0
3
0
0
2
3
0
0
0
2
0
0
2
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
1
1
2
1
0
0
0
0
2
0
1
2
2
0
0
0
0
1
0
0
0
2
0
0
1
1
0
0
0
0
0
2
0
3
0
1
0
0
0
2
0
3
0
0
0
0
0
3
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
2
1
0
0
2
0
0
2
0
0
1
0
0
0
2
0
2
0
0
3
0
1
0
0
1
0
0
2
0
0
1
0
0
0
1
0
2
0
0
0
0
0
2
1
2
0
0
0
1
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
2
2
0
2
1
0
2
0
0
0
0
0
2
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
3
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
2
1
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
1
0
0
0
1
0
1
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
1
0
0
0
0
0
0
1
2
0
0
2
2
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
2
0
1
0
0
0
1
1
0
1
0
0
0
0
3
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
1
0
0
0
2
0
0
2
0
1
1
0
0
1
2
0
0
1
1
0
0
2
0
1
0
1
0
0
0
1
0
0
0
0
0
0
4
0
2
0
0
1
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
3
0
0
1
0
0
0
0
0
3
0
0
2
6
0
0
1
1
0
0
1
1
0
0
0
1
2
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
2
0
0
0
0
0
2
0
1
0
0
1
0
0
2
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
1
1
2
0
0
1
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
3
0
0
0
1
1
0
2
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
10
1
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
1
1
2
2
0
0
2
1
0
2
0
0
0
0
0
2
1
0
0
0
1
2
1
0
0
0
2
0
2
0
1
0
1
0
2
0
2
1
0
0
0
2
0
1
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
10
2
2
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
8
0
0
0
0
1
0
0
2
0
1
2
0
0
3
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
1
2
1
0
1
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
2
1
0
2
2
1
2
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
3
1
0
0
1
0
0
1
0
2
0
2
0
1
0
0
2
0
0
0
0
1
1
2
1
0
0
0
2
2
2
1
1
0
2
2
0
1
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
4
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
2
1
0
0
2
0
0
0
4
0
1
0
0
0
2
0
2
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
2
0
0
0
1
0
1
1
0
1
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
2
2
1
0
0
0
1
0
0
0
0
1
0
0
2
0
3
0
0
0
2
0
2
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
1
2
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
5
1
0
0
2
0
0
0
0
2
0
0
0
1
0
1
0
0
2
0
0
0
4
1
0
1
0
0
2
0
2
0
0
1
1
0
0
2
0
0
0
0
0
0
3
0
0
0
0
2
0
1
2
0
0
0
0
0
0
1
0
2
1
0
0
1
0
0
0
1
2
0
1
0
0
0
0
1
1
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
2
3
0
0
0
0
2
0
2
2
2
0
0
0
0
0
1
0
3
0
3
3
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
4
0
0
0
0
1
1
1
3
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
1
0
2
0
1
0
0
3
0
1
0
1
0
1
0
2
0
2
0
2
0
2
0
1
1
2
2
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
1
1
0
0
1
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
2
0
1
0
0
2
0
0
0
0
0
0
0
0
2
1
0
2
1
1
0
0
2
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
1
0
1
0
1
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
3
2
0
0
0
1
0
0
0
0
0
1
2
0
1
0
0
2
2
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
1
0
2
0
0
1
0
0
0
0
0
1
0
2
0
0
2
2
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
5
0
1
0
2
0
2
1
1
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
2
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
2
0
0
0
2
0
0
0
0
0
2
1
0
5
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
1
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
2
0
4
2
0
0
0
1
0
1
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
2
2
0
0
0
2
1
2
0
0
0
1
1
0
2
1
0
2
1
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
2
2
0
2
0
1
0
1
1
0
0
2
0
0
0
0
1
0
0
0
0
0
1
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
1
0
0
0
1
0
1
0
0
0
2
1
1
0
0
2
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
1
1
1
0
0
2
0
0
2
1
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
1
2
1
0
2
1
0
0
0
0
0
3
0
0
1
2
2
0
0
0
0
0
0
1
2
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
1
0
1
0
0
2
0
0
1
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
1
2
1
0
0
1
0
0
0
3
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
1
1
2
0
0
1
3
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
2
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
2
2
1
1
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
2
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
4
0
0
2
0
0
0
3
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
2
1
0
0
0
1
0
0
1
0
2
0
2
0
0
1
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
1
0
0
2
4
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
1
0
0
2
0
0
0
1
1
0
0
1
0
2
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
1
0
2
1
0
0
0
0
0
0
6
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
3
0
2
0
0
2
0
3
0
0
0
0
0
0
1
0
2
2
1
1
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
2
0
2
3
0
0
0
0
2
2
0
0
1
0
0
0
4
2
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
2
2
0
0
0
0
2
0
1
0
0
0
1
3
0
0
0
0
1
0
0
0
1
2
0
2
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
2
0
2
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
1
0
2
0
2
2
0
0
0
1
0
3
0
1
0
5
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
2
0
0
0
0
2
0
0
0
0
0
0
2
2
0
1
0
2
1
0
0
0
0
0
0
0
1
0
3
2
0
0
0
0
0
0
0
0
0
2
2
3
0
0
1
0
0
0
0
2
1
0
0
0
3
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
2
0
0
1
0
1
0
1
0
0
2
0
0
0
3
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
1
1
2
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
2
1
0
0
0
2
1
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
1
0
0
2
0
0
0
1
4
0
0
1
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
2
0
0
1
0
2
1
0
0
0
0
1
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
2
1
0
0
0
0
0
0
2
2
0
1
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
2
2
0
0
1
0
0
4
0
0
0
0
2
0
0
0
0
0
4
2
0
2
0
0
0
1
0
1
0
2
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
4
0
1
1
1
2
0
0
2
0
0
0
1
1
2
0
2
0
0
1
0
1
0
1
0
1
0
0
1
2
1
0
0
0
5
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
3
0
0
2
0
1
0
1
2
2
1
0
0
0
0
0
0
2
0
0
3
2
0
2
2
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
2
1
1
0
1
2
2
0
0
0
0
2
0
2
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
1
1
2
0
0
0
2
2
0
1
0
0
0
0
0
2
2
1
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
4
0
1
0
1
0
0
0
0
0
0
1
3
2
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
2
0
8
1
1
0
0
1
0
0
0
0
1
1
0
2
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
7
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
1
0
1
1
4
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
1
0
0
0
2
0
0
0
0
0
0
1
0
2
0
1
2
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
7
0
0
0
0
1
1
0
1
0
0
0
0
2
0
2
0
1
0
0
0
2
0
0
2
0
0
1
0
0
1
1
0
0
1
0
1
1
0
0
2
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
1
0
1
0
1
1
0
2
0
2
0
0
0
0
2
0
0
0
3
1
2
0
0
0
2
2
0
0
0
0
1
2
0
0
0
2
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
2
0
2
2
0
2
0
0
0
0
2
2
2
0
2
0
0
0
1
1
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
1
0
2
0
0
0
1
0
2
0
1
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
5
0
0
2
0
0
2
2
0
4
0
0
0
1
0
0
0
0
9
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
4
0
2
2
0
0
0
0
0
2
3
1
1
1
0
0
0
0
0
0
0
2
0
0
1
2
2
0
0
1
1
0
2
0
0
2
0
0
0
0
0
1
2
0
3
0
0
2
0
1
0
1
1
0
2
0
0
2
0
1
0
0
0
2
2
1
0
0
1
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
2
1
0
0
2
0
1
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
2
1
1
0
0
1
0
0
2
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
2
1
0
1
0
0
0
1
1
2
0
0
2
0
2
0
0
1
0
0
0
0
2
3
0
0
1
2
0
2
0
1
0
0
0
2
0
0
1
2
1
0
1
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
1
1
0
1
2
0
0
1
2
0
0
0
1
0
2
0
1
0
1
0
2
0
3
0
1
1
0
0
1
1
1
1
0
0
1
0
1
0
2
0
0
2
0
0
2
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
2
1
0
1
0
1
2
0
2
0
0
2
0
0
0
0
1
0
2
1
0
0
0
0
0
0
1
1
0
0
0
1
0
1
1
0
2
0
1
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
2
2
2
0
2
0
1
0
0
0
0
0
0
1
0
0
0
1
1
1
1
2
0
0
0
2
0
2
0
0
0
0
2
0
2
0
0
0
0
1
2
2
2
0
0
0
2
0
1
2
0
2
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
1
0
3
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
2
2
0
0
0
2
0
1
0
0
1
0
0
2
1
0
1
1
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
1
0
1
0
1
0
0
0
2
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
3
0
2
0
1
0
0
2
0
0
0
0
0
1
0
0
0
3
0
0
0
0
1
0
2
0
0
0
1
0
0
1
0
2
0
0
0
0
2
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
3
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
1
1
1
2
0
0
0
0
0
2
0
0
1
2
0
0
0
2
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
2
1
0
0
0
1
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
2
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
3
0
1
0
0
0
0
0
1
0
0
0
2
2
2
0
1
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
2
3
2
0
0
0
2
0
0
2
0
2
0
0
1
0
0
4
0
0
0
0
0
0
0
1
0
5
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
2
0
0
0
5
1
1
1
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
1
2
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
1
1
1
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
3
0
0
0
0
3
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
5
1
2
1
0
1
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
1
1
2
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
3
0
2
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
1
1
1
1
1
0
0
0
0
0
0
2
1
0
3
1
0
0
0
0
0
0
0
2
0
0
0
0
1
2
1
0
3
1
0
2
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
1
0
1
2
0
2
0
3
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
5
5
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
2
0
0
0
1
0
6
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
2
0
1
0
0
1
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
2
0
1
0
2
0
0
2
1
1
0
0
1
2
2
0
0
0
0
0
0
2
2
1
1
0
2
0
2
0
0
0
0
0
2
3
0
0
1
1
0
1
1
0
0
0
0
0
0
1
0
0
0
2
1
0
3
0
0
0
0
2
0
1
0
0
0
1
0
2
0
0
1
2
0
0
0
2
0
1
0
0
0
0
0
0
2
2
0
2
1
0
0
0
3
0
0
0
1
0
1
0
1
0
1
1
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
1
1
2
1
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
3
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
1
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
2
2
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
5
0
0
1
0
1
4
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
2
0
1
0
0
0
0
1
1
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
2
1
0
0
2
1
0
2
8
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
1
1
0
0
0
0
2
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
2
5
2
0
1
0
0
0
0
0
2
4
0
3
0
0
6
0
0
0
0
0
0
2
0
2
0
0
1
1
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
3
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
1
1
0
0
3
0
1
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
2
1
0
1
0
0
2
2
0
0
3
1
3
3
0
0
0
1
2
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
1
0
1
3
3
0
0
1
0
0
0
0
0
2
1
2
0
0
0
2
0
0
1
0
0
0
2
2
2
2
0
0
0
2
0
1
0
1
0
0
2
0
0
1
0
0
0
1
0
0
2
2
0
0
0
0
0
2
2
0
0
2
0
0
2
3
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
1
0
2
0
0
0
0
1
1
1
0
2
0
0
0
1
0
0
0
0
0
2
0
2
1
0
0
0
2
2
2
2
2
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
2
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
3
0
2
2
2
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
1
0
2
1
2
0
0
1
0
0
0
5
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
2
0
2
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
1
0
1
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
1
5
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
2
0
0
0
1
0
0
0
1
0
1
0
0
0
3
0
0
0
2
0
0
1
1
2
0
0
0
0
0
2
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
2
0
0
0
1
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
2
0
2
0
1
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
3
0
0
0
0
0
1
0
0
1
1
3
0
0
1
1
2
1
0
2
0
0
0
0
0
2
0
2
1
1
2
0
2
0
0
1
0
0
1
0
3
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
2
4
0
0
2
0
2
0
0
0
2
0
0
0
2
2
0
0
1
0
0
0
2
2
1
0
0
1
0
1
0
1
1
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
3
0
0
0
0
2
0
0
0
0
0
1
0
1
2
0
0
0
0
2
0
0
0
0
0
2
3
3
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
2
0
2
0
0
0
0
2
0
0
0
0
1
0
0
2
2
1
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
1
0
0
0
1
0
0
1
0
1
0
0
1
0
0
1
0
2
1
2
0
0
2
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
3
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
1
0
2
0
0
2
0
0
0
0
2
2
0
0
0
2
1
2
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
2
0
2
0
0
0
0
0
2
0
2
2
0
0
1
1
2
0
0
1
1
0
2
0
1
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
2
0
1
0
0
2
0
0
0
0
2
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
1
3
1
0
3
0
2
0
2
1
0
1
0
1
0
2
0
0
0
0
0
0
3
0
1
0
0
0
0
0
1
0
1
2
2
0
0
1
1
2
0
1
2
0
2
0
0
0
0
2
6
0
0
0
0
1
0
3
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
3
0
0
2
1
3
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
3
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
1
2
2
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
2
0
2
0
0
1
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
2
0
0
0
0
0
4
1
0
2
0
0
0
0
0
0
1
0
0
0
0
1
2
2
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
1
2
0
1
0
0
1
0
2
1
0
0
0
2
0
0
0
0
0
2
1
0
0
2
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
1
2
1
5
0
2
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
1
0
0
0
1
2
0
1
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
2
1
0
0
0
0
1
2
0
0
1
2
2
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
2
0
0
2
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
4
0
0
2
2
0
0
1
2
0
0
3
0
3
4
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
2
2
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
2
2
2
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
3
0
1
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
3
0
0
0
0
0
1
2
0
2
0
1
0
0
0
4
0
1
0
0
0
0
2
1
0
0
0
0
2
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
4
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
2
0
0
2
0
0
2
1
0
0
0
0
1
2
0
1
2
2
0
0
0
0
0
2
2
0
2
0
0
0
0
0
1
0
0
2
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
2
0
0
0
0
0
0
2
0
0
1
2
0
0
0
2
0
0
0
0
1
1
0
0
0
0
2
0
0
1
2
0
2
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
3
0
0
1
2
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
2
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
1
0
1
7
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
4
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
2
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
2
2
0
1
0
0
1
0
0
0
0
0
0
0
1
0
5
1
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
2
0
0
2
0
0
0
0
0
0
0
2
2
0
1
0
0
2
2
0
0
1
1
0
0
5
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
1
2
0
0
0
1
0
0
2
0
4
0
1
1
0
0
2
3
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
1
1
1
0
0
0
0
0
2
2
1
0
1
0
2
0
0
0
0
0
0
3
1
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
1
0
0
2
0
0
1
1
0
1
0
0
2
0
0
1
0
0
0
0
2
0
7
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
1
3
0
0
2
1
2
0
0
0
1
1
2
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
2
1
0
2
2
2
0
0
2
0
2
0
0
0
0
0
0
0
2
2
0
3
0
0
0
0
0
2
0
0
0
0
0
0
2
2
1
1
0
6
0
0
0
1
0
0
0
0
0
0
0
0
5
0
0
3
0
0
0
0
1
2
0
0
1
0
0
0
1
0
0
0
0
0
2
1
0
2
0
0
2
1
2
0
0
2
0
1
0
0
2
6
0
1
2
0
4
0
1
0
0
1
0
1
2
0
1
0
0
0
0
0
2
1
1
3
0
1
1
2
1
0
0
0
1
2
0
0
1
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
1
0
0
2
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
2
2
0
0
0
2
2
1
2
0
0
0
0
0
1
1
0
0
0
0
0
9
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
2
0
0
0
0
0
1
0
0
6
0
1
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
2
0
0
0
0
0
1
0
3
0
1
0
0
0
1
2
1
1
0
0
1
0
0
2
0
0
0
2
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
2
3
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
1
1
0
0
0
1
1
5
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
1
0
2
0
0
0
0
0
0
1
0
10
0
0
0
3
0
1
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
2
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
3
0
0
1
0
0
0
0
1
1
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
3
2
0
2
2
0
0
0
0
3
0
0
0
2
0
1
0
0
2
1
2
1
0
0
0
0
1
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
2
0
2
0
2
4
0
0
0
3
0
0
1
1
0
0
2
3
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
3
1
0
2
0
0
0
2
0
0
2
2
0
2
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
1
2
0
2
0
0
7
2
0
1
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
2
1
1
0
0
0
0
1
2
2
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
2
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
2
2
1
0
0
0
1
0
1
0
0
0
2
0
1
0
0
0
1
0
0
2
0
0
2
1
3
0
0
2
1
2
0
2
0
1
0
0
0
0
1
0
0
0
1
1
0
0
1
0
1
2
2
1
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
1
0
1
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
1
2
0
3
0
0
2
0
0
0
0
2
0
2
0
0
1
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
1
2
1
2
0
2
0
3
2
0
3
0
2
1
1
1
0
0
0
2
1
0
2
0
0
1
0
2
0
0
0
0
0
2
0
0
0
2
0
2
2
0
0
5
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
2
1
3
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
2
2
1
1
0
0
0
1
0
0
2
0
2
1
2
2
0
1
1
0
2
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
1
0
0
1
0
1
0
0
1
1
0
0
2
0
1
2
1
1
0
0
0
1
0
0
1
0
2
0
0
0
0
0
1
4
0
1
0
2
2
0
0
0
0
0
3
0
0
1
0
1
0
3
0
0
0
0
0
0
0
2
0
2
1
0
1
2
0
0
0
2
1
0
0
1
0
2
0
2
0
2
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
3
0
1
0
1
0
0
0
2
4
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
1
2
1
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
1
1
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
2
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
1
0
0
0
2
0
1
0
0
2
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
1
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
2
1
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
1
0
0
0
2
0
1
0
1
1
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
3
0
2
0
2
2
4
1
2
0
0
0
0
0
1
2
2
0
1
0
0
0
0
1
0
2
0
2
0
0
1
0
0
0
2
0
2
0
0
0
0
2
0
0
0
2
2
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
5
0
0
0
0
1
0
0
1
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
2
4
0
0
1
0
2
0
0
0
0
3
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
2
1
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
1
0
2
0
0
0
0
0
2
1
1
0
0
0
0
0
0
1
0
2
2
0
1
0
0
0
0
2
0
0
0
1
3
0
1
0
0
0
0
1
0
0
0
0
1
2
0
1
0
0
0
2
0
0
0
0
3
0
0
0
0
0
2
0
1
1
1
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
2
1
0
1
0
2
2
0
1
0
0
0
0
3
2
2
0
0
0
0
0
0
0
0
1
0
7
0
0
3
0
0
2
1
0
1
0
1
0
2
0
0
2
0
0
0
0
2
0
0
1
1
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
1
0
1
0
0
2
0
0
1
0
0
0
0
4
1
0
0
1
3
0
0
0
1
0
3
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
1
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
2
0
0
2
2
0
0
0
0
0
1
0
0
1
0
1
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
2
1
2
0
0
0
2
0
0
0
0
1
0
1
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
2
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
4
0
1
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
3
2
3
0
1
2
0
1
0
0
0
1
0
2
0
0
0
0
0
1
0
2
1
2
0
0
1
3
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
1
3
0
1
3
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
4
0
2
0
0
2
0
0
2
1
0
0
0
0
2
0
0
2
0
0
1
2
0
1
0
1
0
6
2
0
1
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
1
2
0
1
0
11
4
0
2
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
2
3
1
2
1
2
2
0
0
2
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
1
0
1
0
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
3
1
1
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
2
2
0
0
0
2
2
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
1
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
2
0
0
0
1
2
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
1
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
7
0
0
0
0
0
0
1
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
2
0
0
0
2
0
1
0
0
0
2
0
0
3
0
0
0
2
1
2
0
0
0
0
0
0
1
0
2
0
0
0
1
1
2
0
0
0
0
0
2
0
0
1
1
0
0
1
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
2
0
0
0
0
1
0
3
1
1
0
0
1
1
1
0
0
2
3
0
2
0
1
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
3
2
0
0
0
1
0
0
0
3
1
0
0
4
0
0
0
1
1
1
0
2
2
1
0
2
0
0
2
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
1
0
2
1
2
1
2
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
5
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
4
0
1
0
0
0
0
0
0
1
0
1
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
2
0
0
0
0
0
2
0
2
0
0
2
0
0
3
0
3
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
1
2
2
0
0
0
1
0
3
1
0
2
0
1
0
2
0
0
0
2
1
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
3
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
2
0
3
3
0
0
0
0
0
0
0
0
7
3
0
0
1
0
1
0
2
2
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
1
0
1
0
1
0
0
1
0
2
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
1
1
0
1
0
0
0
2
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
2
3
0
0
0
0
2
1
0
2
0
2
0
0
0
3
0
0
0
0
3
0
0
2
0
0
1
2
0
0
1
0
2
1
0
0
0
2
0
0
1
0
2
0
2
0
0
0
0
0
1
3
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
1
1
1
0
0
2
0
1
1
0
2
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
2
3
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
3
1
0
0
0
0
1
1
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
2
2
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
3
2
0
0
0
0
1
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
6
0
0
0
0
1
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
2
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
4
0
2
0
1
1
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
1
0
2
0
0
2
0
2
0
0
0
1
0
3
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
2
2
0
2
0
0
0
1
0
2
0
0
0
2
0
1
0
0
1
0
1
0
1
0
1
0
1
1
0
4
0
0
0
2
0
0
1
0
0
1
0
0
2
0
0
0
2
1
0
0
0
0
3
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
2
0
1
1
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
2
2
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
2
2
0
0
0
0
2
0
0
2
2
0
2
1
0
0
0
0
2
0
1
1
0
0
2
1
0
0
2
0
0
2
0
0
2
0
1
0
0
0
1
2
0
2
2
0
0
0
2
0
0
1
0
1
2
0
0
2
0
1
0
0
0
0
2
0
0
2
0
0
0
2
0
0
1
0
0
2
2
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
2
0
0
1
1
0
0
0
1
0
1
0
1
0
2
0
1
0
0
1
0
0
0
1
2
2
0
1
3
0
0
0
0
0
0
1
0
0
2
2
0
2
1
0
4
0
0
0
2
2
0
0
3
0
0
1
0
0
2
0
0
1
0
0
0
0
0
2
2
0
0
0
1
2
0
2
1
0
0
2
0
4
0
0
2
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
2
0
0
0
1
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
1
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
1
1
0
0
2
0
0
2
0
0
0
1
0
3
1
0
8
1
2
5
1
0
1
3
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
3
2
0
0
1
2
0
0
0
1
0
0
0
3
0
1
0
0
0
0
0
0
0
2
0
1
0
1
4
0
1
1
0
1
0
2
2
0
0
0
1
0
0
2
0
0
0
0
1
2
0
1
0
0
3
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
2
0
0
1
3
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
1
1
0
2
0
0
0
0
0
2
1
0
1
0
2
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
5
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
1
3
0
2
0
0
2
0
0
0
0
3
0
0
0
0
3
0
0
0
0
2
0
2
0
0
1
0
1
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
1
3
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
2
0
1
0
0
0
0
0
0
3
0
0
1
2
2
2
1
0
0
0
0
2
1
2
3
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
2
2
0
1
2
0
2
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
2
2
0
0
2
0
1
3
2
0
1
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
3
0
0
0
2
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
3
0
4
1
0
0
2
0
2
1
1
0
0
0
0
0
0
1
0
0
2
1
1
0
2
1
0
2
0
0
0
2
1
0
0
1
0
0
0
1
2
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
2
1
0
1
0
0
0
0
1
2
1
0
0
0
0
1
0
0
2
0
0
5
0
0
0
2
0
2
0
0
2
0
0
0
2
2
2
0
0
2
1
0
0
0
2
0
0
0
0
2
2
1
0
0
0
2
0
0
1
0
0
0
1
0
0
0
1
0
2
1
2
0
0
0
0
0
2
2
2
0
0
0
0
2
0
0
0
1
2
2
0
0
0
4
9
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
2
2
0
0
0
1
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
9
2
1
0
0
1
0
0
0
1
0
0
2
1
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
2
1
0
0
3
0
0
2
2
0
2
0
0
0
0
0
1
1
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
2
0
1
1
0
0
0
0
2
0
2
2
0
0
0
1
2
0
1
2
1
0
0
1
0
0
0
2
0
1
1
1
0
0
1
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
2
0
2
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
1
0
1
0
2
0
0
0
2
2
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
3
0
0
2
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
1
0
3
0
0
1
0
0
0
0
0
4
1
0
0
1
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
1
0
1
0
0
1
0
1
0
4
0
0
0
0
1
2
0
1
2
0
0
0
2
0
0
2
2
0
0
0
0
2
0
1
0
0
0
0
0
2
0
1
3
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
6
0
3
3
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
1
0
0
1
1
0
0
0
0
0
0
1
2
2
0
0
0
0
2
3
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
1
0
2
0
0
0
2
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
2
0
1
1
3
0
0
2
0
2
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
5
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
3
0
0
1
1
1
0
0
0
0
0
3
0
0
0
0
0
0
0
2
1
3
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
2
2
0
1
0
0
0
1
0
1
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
2
0
0
2
0
0
0
0
0
1
0
0
2
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
3
2
0
1
0
0
0
1
1
4
0
0
0
0
0
0
0
1
2
1
0
0
0
0
2
1
0
0
1
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
1
0
1
0
0
2
0
1
1
2
0
0
0
2
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
4
0
1
0
0
2
0
0
3
0
0
1
0
0
1
0
1
0
0
0
2
0
1
0
0
0
1
2
0
0
0
2
1
1
2
0
0
0
3
1
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
1
0
1
0
0
0
0
2
0
0
0
0
2
1
1
2
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
1
0
1
0
0
2
1
1
0
0
2
1
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
3
1
0
3
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
1
0
2
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
1
0
1
0
1
0
0
1
0
3
0
0
0
0
1
0
0
1
1
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
1
3
2
0
0
0
0
0
0
1
0
0
2
1
0
1
0
2
0
0
0
0
0
0
1
0
1
0
0
2
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
4
1
0
0
0
2
0
1
0
0
0
0
0
0
1
1
2
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
1
1
0
0
2
0
0
0
0
0
2
0
0
0
0
2
2
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
2
1
0
0
0
1
0
0
0
2
0
0
0
2
1
0
0
2
0
0
0
2
3
1
2
0
2
0
0
1
0
2
0
1
0
0
1
0
0
0
1
2
2
0
1
0
1
0
0
0
1
0
0
0
0
1
2
0
1
0
0
2
1
0
1
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
2
1
0
0
2
1
2
0
0
1
1
0
0
0
0
2
0
0
0
0
0
2
0
1
0
1
2
1
0
2
2
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
1
1
2
0
0
1
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
2
0
0
0
1
1
2
0
0
0
2
2
0
1
0
1
0
1
2
0
0
1
11
0
0
0
0
0
0
0
0
0
1
2
1
1
0
2
0
0
0
0
0
0
0
0
7
0
0
1
2
0
1
4
1
0
0
1
4
0
0
0
0
2
0
0
2
0
2
2
2
0
0
0
2
0
2
1
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
1
2
0
0
0
2
3
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
2
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
7
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
1
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
1
2
1
0
2
0
0
0
0
0
0
0
2
0
3
0
1
1
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
2
2
0
3
0
0
1
0
0
0
0
0
0
1
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
1
1
0
1
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
2
8
0
1
0
0
1
1
1
0
0
1
0
0
0
0
2
0
0
0
0
0
1
1
1
0
0
1
0
0
1
0
2
0
0
1
2
2
1
2
0
1
2
1
1
0
0
0
1
0
0
2
1
1
0
0
2
0
1
0
0
0
3
0
1
0
2
1
1
5
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
1
0
0
2
2
1
0
0
0
0
0
0
3
0
1
0
1
0
0
0
2
0
0
2
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
2
0
0
1
0
0
0
0
1
2
0
0
0
2
0
1
0
2
3
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
2
0
4
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
2
0
0
0
2
0
2
0
0
0
2
1
18
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
2
2
0
0
1
2
0
0
1
2
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
3
0
0
0
2
0
4
1
0
0
0
2
0
2
2
1
0
0
2
0
0
0
2
2
0
0
1
2
0
0
0
2
0
0
0
2
0
2
2
2
1
0
0
0
0
0
3
0
0
0
0
0
0
0
2
1
0
0
1
2
2
0
0
0
2
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
2
0
0
1
0
3
0
1
0
0
1
2
1
0
2
0
2
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
1
0
2
0
2
0
1
1
2
0
2
0
0
0
1
0
0
3
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
2
2
2
0
0
0
0
0
2
1
0
0
0
2
0
3
0
1
2
0
1
0
0
0
0
1
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
1
2
0
0
0
1
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
3
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
3
0
1
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
3
2
0
1
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
1
1
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
4
0
0
2
1
0
0
0
0
0
1
0
2
0
1
0
0
0
1
1
0
0
2
2
0
2
0
0
0
0
0
1
2
0
0
0
2
0
1
0
0
0
3
2
0
1
0
0
0
0
0
0
3
0
0
0
0
0
1
1
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
1
0
1
0
1
0
1
1
2
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
1
0
0
3
1
0
0
0
0
2
2
1
0
2
0
0
0
3
3
0
1
0
0
0
2
2
0
1
2
1
0
0
0
0
0
0
0
4
0
2
0
0
0
0
4
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
2
1
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
2
0
0
1
0
3
0
1
3
0
1
0
1
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
2
0
0
1
0
2
2
0
0
0
2
2
2
0
0
0
0
0
0
1
0
2
1
0
1
0
0
0
0
0
3
0
0
2
0
0
1
0
0
0
0
0
0
2
1
1
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
4
0
0
0
0
0
2
0
0
1
2
2
1
0
0
0
0
0
0
0
3
0
0
1
0
0
1
1
0
1
1
0
0
0
3
0
0
0
0
0
0
2
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
2
0
0
0
0
2
2
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
2
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
2
0
1
2
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
1
1
2
0
0
2
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
2
0
0
0
1
0
1
0
0
1
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
4
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
3
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
3
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
2
0
0
2
0
0
0
0
2
0
0
1
0
2
0
1
0
1
0
2
0
0
0
1
1
0
1
2
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
2
0
1
0
0
1
0
0
2
1
2
0
2
2
0
0
2
0
0
0
1
0
0
0
0
2
0
1
0
1
0
2
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
3
3
2
0
2
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
2
0
1
2
0
2
0
0
0
0
1
1
0
0
0
0
0
1
1
2
2
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
2
2
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
1
0
2
1
0
0
0
2
0
0
0
0
2
0
2
0
2
1
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
2
1
2
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
1
1
0
0
1
0
0
2
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
2
0
1
1
2
0
0
2
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
2
0
0
1
1
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
2
0
0
0
2
0
7
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
1
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
1
1
0
2
0
0
0
2
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
1
2
0
0
0
0
0
1
0
0
1
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
2
2
0
1
0
0
2
0
0
0
0
0
0
0
0
1
2
2
0
2
1
2
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
2
2
0
1
0
0
0
2
0
0
2
1
0
0
2
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
2
0
2
0
0
1
0
0
2
0
2
2
0
0
0
2
2
0
1
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
1
0
0
0
2
2
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
1
1
0
1
0
2
0
2
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
3
2
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
2
0
4
0
2
2
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
2
1
0
0
0
0
0
1
2
0
0
0
1
0
2
0
0
0
1
3
2
0
0
0
2
0
0
2
1
2
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
1
0
0
5
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
1
0
1
1
0
2
0
0
0
5
0
1
2
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
2
0
1
0
2
0
0
2
0
1
2
0
2
0
0
1
0
2
0
0
1
2
0
0
0
0
2
3
0
2
0
2
2
0
0
0
0
0
0
2
3
3
0
0
0
2
1
0
2
2
0
0
0
0
0
1
0
2
0
1
0
0
2
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
1
0
3
1
0
0
1
6
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
3
0
8
0
0
0
0
0
1
0
3
2
0
2
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
2
3
0
0
0
0
2
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
2
2
0
0
2
0
0
1
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
6
0
0
0
2
2
0
0
0
2
0
0
0
0
1
0
0
1
4
1
2
0
2
0
0
0
0
1
0
0
2
0
2
3
0
0
0
0
1
0
1
0
1
2
0
2
2
2
0
0
0
2
2
0
0
0
0
3
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
4
1
0
0
4
2
0
1
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
2
2
0
2
0
2
0
3
0
0
2
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
2
1
0
2
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
1
2
1
0
2
0
1
1
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
3
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
2
0
1
2
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
1
0
0
0
0
0
2
2
0
0
2
2
8
1
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
1
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
1
2
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
1
0
0
3
1
0
2
0
2
0
0
0
1
2
0
2
0
0
0
0
0
1
1
0
2
0
1
2
1
2
0
0
0
1
1
1
1
1
1
0
0
0
0
1
0
1
0
2
1
2
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
1
0
1
2
1
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
1
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
2
2
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
2
2
2
2
0
0
0
0
0
2
0
0
2
2
2
0
0
0
2
1
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
2
0
0
0
0
0
0
2
0
2
1
1
0
0
0
1
0
0
0
0
0
0
0
2
2
3
2
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
2
0
0
0
1
0
2
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
1
0
4
0
1
3
0
2
0
3
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
1
0
0
0
1
0
0
0
1
0
2
2
0
1
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
3
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
1
2
1
0
0
0
0
0
0
0
0
2
1
0
4
0
2
0
0
0
1
0
0
0
2
0
0
0
0
2
1
0
0
1
0
0
1
1
0
0
0
0
1
2
0
1
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
3
0
0
0
0
1
0
2
0
0
1
1
1
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
4
1
0
0
0
0
2
2
2
0
0
0
0
1
2
0
0
1
3
2
1
0
0
3
2
0
0
2
2
0
1
0
0
0
0
0
2
0
1
7
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
1
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
2
2
0
1
0
2
0
0
2
1
1
1
2
1
1
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
3
0
0
0
0
0
1
1
0
0
0
0
0
2
1
0
0
0
0
1
0
1
0
6
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
2
0
1
0
1
0
0
0
1
0
2
0
2
2
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
6
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
2
0
3
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
3
2
2
0
0
0
0
1
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
1
0
2
0
1
0
0
2
2
0
2
0
0
0
0
5
0
1
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
1
0
1
0
2
1
0
0
1
0
2
0
1
0
0
2
0
2
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
1
2
0
0
0
1
0
0
1
2
0
0
0
0
0
1
0
1
0
0
0
0
0
3
0
0
0
0
0
1
0
1
2
0
0
0
4
0
0
0
0
2
0
2
0
1
1
1
0
2
2
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
2
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
1
1
2
0
0
0
5
0
0
1
0
0
0
3
2
2
0
0
0
2
0
0
1
0
0
0
0
0
0
3
4
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
2
2
0
2
1
1
1
0
0
0
0
0
1
0
0
2
1
0
0
0
1
0
0
1
0
0
0
0
2
1
1
1
0
0
0
4
0
0
0
0
1
0
0
0
0
2
0
0
3
0
4
0
3
0
0
0
0
4
0
1
2
2
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
3
1
0
1
0
0
1
0
0
0
1
0
0
3
0
1
2
1
0
0
0
0
2
2
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
3
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
2
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
4
3
0
1
2
1
0
0
1
0
0
2
0
1
0
0
1
0
1
2
0
0
0
0
0
1
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
4
2
0
0
0
1
0
3
4
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
2
0
0
1
0
1
0
1
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
1
0
0
0
2
2
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
1
2
2
0
0
1
0
2
1
0
0
1
0
0
0
0
0
1
1
0
2
0
0
0
3
0
0
4
1
0
2
0
0
2
0
0
0
0
0
1
3
0
1
0
2
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
2
0
2
1
2
0
0
0
2
0
2
1
0
2
1
1
2
0
1
1
0
1
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
2
0
1
2
4
1
3
0
0
0
0
2
1
0
0
0
0
0
0
2
1
0
2
0
2
0
1
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
2
1
2
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
2
0
0
0
1
0
2
2
0
0
1
0
0
2
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
2
1
0
0
1
0
2
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
2
1
0
2
2
3
0
2
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
2
0
1
1
0
1
0
1
0
0
0
0
2
2
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
2
0
0
1
0
1
0
0
2
1
0
0
0
2
1
1
0
0
0
2
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
1
0
2
0
0
0
4
0
0
0
0
1
0
0
0
1
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
7
0
2
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
1
2
0
0
0
0
0
1
1
1
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
2
1
1
0
0
3
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
1
0
1
1
0
0
0
0
0
1
0
3
1
0
4
1
0
0
2
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
2
0
2
0
0
0
4
0
0
0
0
0
0
2
0
2
0
0
2
0
1
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
1
0
1
0
0
0
1
1
0
0
0
0
2
0
0
0
2
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
4
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
3
0
2
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
1
0
0
0
2
0
0
2
3
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
2
0
0
1
2
0
1
1
1
2
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
9
0
0
0
2
0
0
0
0
0
0
0
0
1
1
2
0
2
0
0
0
2
0
0
0
2
0
0
0
0
2
0
1
2
0
0
0
1
3
0
0
0
2
0
2
0
0
2
3
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
1
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
2
0
1
1
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
3
0
0
0
0
1
0
0
2
0
0
0
2
1
1
0
1
0
0
0
0
0
0
1
2
0
1
0
0
2
0
1
0
0
0
1
0
0
0
3
0
0
1
0
0
0
2
0
1
0
0
0
2
1
1
2
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
2
0
1
1
0
0
2
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
1
2
0
1
0
0
0
0
0
0
0
0
3
1
0
2
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
2
3
0
0
2
0
2
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
3
0
2
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
2
2
0
3
1
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
3
2
0
0
2
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
1
0
1
2
2
0
1
0
0
0
0
0
0
0
0
0
0
2
2
1
1
0
0
0
0
0
0
0
2
2
1
0
0
1
0
0
0
1
1
2
1
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
2
2
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
3
2
4
0
0
1
0
2
1
2
0
0
6
0
13
0
0
1
0
0
0
0
0
0
0
0
0
19
0
0
4
1
0
1
0
0
0
0
0
1
2
0
0
0
3
2
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
3
0
0
3
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
1
0
0
0
0
0
1
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
3
3
0
0
0
0
0
0
1
1
0
0
4
0
0
0
1
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
4
0
0
1
0
3
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
1
0
1
2
1
0
1
0
1
0
1
2
0
0
2
0
0
1
0
0
2
0
0
0
0
0
2
0
1
0
0
0
2
1
0
0
0
2
1
2
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
1
0
1
0
0
2
1
0
0
2
0
0
2
0
0
1
0
2
1
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
2
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
1
2
2
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
3
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
1
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
2
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
4
0
0
1
4
0
0
0
2
0
2
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
2
1
0
0
0
0
1
2
1
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
2
0
1
0
0
0
1
0
0
2
0
0
1
0
1
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
3
0
1
2
0
2
0
1
0
0
4
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
1
1
0
0
2
0
0
1
0
0
0
0
0
1
0
0
2
0
2
0
3
2
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
3
0
0
2
0
0
2
0
0
0
0
0
10
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
1
0
0
1
1
1
0
0
0
1
0
0
0
2
0
0
0
2
0
1
0
0
1
0
3
1
0
0
1
0
1
0
0
2
0
2
0
1
0
2
0
0
0
1
2
0
1
2
0
0
0
3
2
0
0
0
0
0
2
0
1
0
2
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
1
1
0
0
4
1
0
0
0
5
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
1
4
2
2
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
2
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
2
0
0
2
0
0
0
2
0
2
0
3
0
0
0
0
0
1
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
2
1
2
0
2
0
0
3
2
4
0
0
2
0
1
1
0
1
0
0
0
2
0
0
0
2
0
0
3
0
0
0
0
0
0
2
2
0
0
0
2
2
0
0
0
0
2
0
0
2
0
0
2
0
0
2
0
0
1
0
0
0
0
2
0
0
2
0
2
2
0
1
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
1
1
0
4
0
0
0
1
0
1
0
0
2
1
0
0
0
0
0
2
0
2
0
0
0
0
2
0
2
2
0
2
0
2
1
0
1
0
0
0
0
1
1
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
1
1
0
2
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
4
0
2
0
0
1
0
2
0
0
0
3
2
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
1
0
0
1
0
1
0
0
1
2
0
0
0
1
2
0
0
1
0
2
0
0
2
0
2
1
1
2
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
2
1
2
2
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
2
1
0
2
1
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
1
0
0
0
0
2
1
0
0
0
0
1
0
1
1
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
2
1
2
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
2
0
0
0
0
1
0
0
0
0
1
2
1
0
1
1
0
0
4
1
0
2
0
0
0
0
0
2
0
0
2
0
0
2
0
2
0
0
0
2
0
0
0
4
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
2
1
0
1
0
3
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
5
1
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
2
2
1
0
0
0
1
0
0
2
2
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
1
2
1
0
0
0
0
0
1
0
1
0
0
1
0
2
0
0
2
0
0
0
2
0
2
0
0
0
1
3
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
1
0
0
1
2
0
0
0
2
0
0
0
0
1
0
2
0
1
0
0
2
2
2
0
0
0
0
2
0
0
3
0
0
1
0
0
0
1
0
3
0
2
1
0
0
0
1
0
1
2
0
0
0
1
2
3
0
0
0
0
0
0
0
0
0
1
0
0
3
0
1
1
3
0
0
0
0
2
0
0
0
0
0
0
0
2
1
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
3
0
0
1
2
0
0
0
0
0
2
5
0
0
0
3
2
0
2
1
3
0
2
0
0
0
0
1
0
8
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
2
0
0
1
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
1
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
1
1
3
0
1
0
2
2
0
1
0
1
0
0
0
0
2
0
0
1
0
0
0
2
0
0
2
2
6
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
1
2
0
0
0
0
0
3
2
0
1
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
1
0
1
0
0
1
1
0
2
0
2
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
1
2
0
2
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
5
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
1
0
0
2
0
1
0
0
0
0
2
2
2
0
0
3
0
0
0
0
1
2
0
1
0
0
2
0
0
2
0
0
0
0
2
1
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
1
2
0
0
0
0
1
0
1
1
0
2
0
0
0
0
2
0
0
1
0
0
1
0
0
1
0
0
2
2
0
0
0
2
7
2
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
1
0
2
0
0
1
0
1
0
0
1
0
2
1
0
0
5
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
2
0
1
0
0
0
1
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
2
0
0
2
0
0
1
0
1
1
0
0
1
0
1
0
0
1
2
2
0
0
1
0
0
0
1
2
0
0
1
0
0
2
0
0
3
0
0
1
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
2
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
2
2
0
0
1
2
0
0
0
2
4
2
0
0
2
0
0
1
0
0
0
3
0
1
0
0
2
0
0
0
2
0
2
1
0
0
1
0
0
0
0
1
3
0
0
3
0
0
0
2
3
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
2
2
2
0
0
0
0
1
1
0
0
3
1
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
2
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
1
2
1
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
4
2
0
0
0
0
1
0
1
0
0
0
3
0
1
1
0
0
0
0
4
0
0
0
0
4
0
0
0
0
0
1
2
0
1
1
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
1
0
1
1
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
2
2
1
1
0
0
0
0
0
0
0
2
0
0
1
0
0
3
0
0
0
0
0
1
0
1
1
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
2
0
0
1
1
0
0
1
0
2
2
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
2
0
0
0
2
0
0
0
2
1
2
0
0
0
0
1
0
0
1
1
0
1
0
1
0
1
1
0
1
1
0
0
0
0
2
1
1
0
2
0
0
2
0
1
1
1
0
2
1
0
0
2
3
0
0
2
0
0
0
0
0
0
0
0
0
2
1
3
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
2
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
1
2
1
2
0
0
0
0
0
0
0
1
0
0
9
0
3
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
2
0
1
0
0
1
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
2
0
0
2
2
2
0
0
0
0
0
2
0
2
1
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
2
0
2
1
0
0
1
2
0
1
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
2
0
2
0
1
0
0
0
0
0
1
0
0
0
4
2
0
0
0
0
0
0
0
1
1
0
1
0
2
0
0
2
0
0
0
0
0
0
2
0
0
1
2
0
1
0
2
0
0
0
2
1
0
0
0
0
0
1
0
0
2
2
2
3
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
4
2
1
0
2
0
0
0
0
0
2
0
0
1
1
2
1
0
0
0
1
6
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
1
0
1
2
2
1
0
0
3
0
0
0
2
0
0
3
1
0
0
1
0
0
0
0
1
1
1
0
0
2
0
1
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
2
0
1
1
0
0
0
2
1
0
0
0
0
0
2
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
1
3
0
0
0
0
0
0
1
1
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
1
2
0
1
0
0
0
0
0
1
0
0
0
1
0
0
2
2
0
1
0
0
0
0
2
0
2
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
2
1
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
2
0
0
0
2
0
0
0
0
1
2
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
2
1
1
0
0
0
0
1
2
1
1
0
4
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
2
0
0
1
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
1
0
2
1
2
1
3
0
0
2
0
2
0
2
3
0
0
2
0
0
0
0
3
0
1
0
0
0
3
0
0
0
3
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
1
2
0
1
0
0
0
2
0
0
0
1
0
5
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
1
2
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
1
1
0
1
0
1
1
3
1
0
1
1
2
0
2
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
3
0
2
2
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
3
0
6
0
0
0
0
0
0
0
0
2
1
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
2
1
0
2
0
0
2
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
2
0
0
0
1
0
1
0
3
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
2
0
0
3
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
2
1
0
0
1
0
0
2
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
1
0
0
0
2
1
1
1
0
0
1
0
1
0
0
0
1
1
1
0
0
1
2
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
1
0
1
0
1
0
0
0
0
1
0
0
0
0
2
2
0
0
2
0
1
0
0
1
0
0
0
1
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
3
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
1
0
2
0
0
0
0
0
0
1
0
0
0
1
1
2
1
0
0
0
0
0
0
2
1
0
0
0
0
3
1
2
0
1
0
0
0
0
0
2
0
0
0
0
3
2
0
0
0
0
0
0
1
0
2
0
0
0
1
1
0
0
0
0
0
4
0
0
0
1
2
0
2
1
0
0
0
0
2
1
0
0
0
0
0
0
0
1
1
2
0
0
0
0
1
1
0
0
1
1
0
2
3
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
1
0
2
0
2
0
0
3
2
0
0
2
0
0
0
0
0
1
0
1
1
0
0
0
2
0
0
1
2
2
2
6
0
0
0
0
0
2
0
0
0
2
2
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
2
2
2
1
2
0
0
0
0
0
1
2
0
0
1
3
4
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
1
2
2
0
2
0
0
0
1
1
0
0
3
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
2
1
0
1
0
1
0
1
1
0
0
0
3
0
2
0
2
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
2
2
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
1
0
0
0
0
2
1
0
0
1
0
2
0
0
0
4
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
1
0
0
2
1
0
2
0
0
0
1
1
0
0
0
1
1
0
0
0
0
1
1
1
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
3
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
2
2
0
0
1
0
2
0
0
0
5
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
1
2
0
0
0
2
0
0
0
1
0
0
0
0
0
1
2
0
1
0
0
3
0
0
1
1
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
2
0
1
2
0
1
0
0
0
0
0
1
0
2
0
0
0
1
0
0
1
0
3
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
4
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
2
0
1
0
1
0
0
0
2
0
0
0
0
0
2
0
1
1
0
2
0
0
0
0
0
0
1
2
0
0
0
1
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
1
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
4
0
0
1
0
0
0
0
0
0
0
0
7
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
1
0
0
0
0
1
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
1
0
2
0
0
0
0
0
0
2
3
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
1
1
1
0
0
0
0
0
2
0
2
1
0
0
2
2
2
0
1
2
0
0
0
2
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
2
0
0
3
2
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
2
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
2
3
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
1
0
0
0
2
0
1
0
1
0
0
0
0
0
3
0
2
2
0
0
0
0
0
0
0
2
4
0
0
1
0
1
2
0
0
0
0
0
1
0
0
0
2
0
0
0
3
2
0
0
3
2
1
0
0
1
2
1
1
0
0
0
0
0
2
1
0
0
0
1
0
0
1
0
0
1
3
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
2
3
0
0
0
0
0
0
0
0
1
4
1
0
4
0
0
0
1
0
0
0
1
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
1
0
2
0
1
1
0
1
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
2
0
3
0
1
0
0
0
0
2
0
4
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
2
0
0
5
1
2
0
0
0
0
0
1
0
0
0
1
0
0
2
1
0
0
0
0
1
0
2
0
1
2
0
0
1
7
0
0
0
2
2
0
0
0
0
0
0
0
1
1
0
1
0
0
1
3
1
0
0
0
2
0
0
0
0
2
0
2
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
1
1
1
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
1
0
0
2
1
0
0
1
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
4
0
0
0
0
1
0
2
0
0
0
1
1
0
0
0
4
0
0
0
0
1
0
0
2
0
2
0
0
1
0
0
2
2
3
1
0
0
0
1
2
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
1
0
2
0
2
0
2
0
0
0
0
1
0
0
0
0
0
4
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
2
1
3
1
1
0
1
0
0
0
0
0
0
0
1
0
8
0
2
1
0
2
0
3
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
2
2
0
2
1
0
2
0
2
0
2
0
0
1
0
0
0
0
2
0
0
1
2
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
1
0
0
2
1
0
0
1
0
2
0
0
1
1
0
0
0
3
0
0
0
2
0
1
0
3
1
0
2
2
0
1
0
1
0
0
0
0
0
0
0
0
0
1
5
0
0
4
2
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
1
0
0
2
1
0
0
1
0
0
0
0
0
0
1
2
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
1
0
2
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
2
2
1
0
0
0
0
1
0
0
0
0
0
0
3
1
3
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
1
1
2
1
0
0
2
0
0
1
0
0
0
0
1
0
0
1
2
1
1
0
0
1
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
2
2
1
0
0
1
1
0
2
1
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
5
0
1
5
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
1
0
1
2
3
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
2
0
0
2
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
1
0
0
2
3
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
10
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
2
1
0
0
2
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
3
0
0
1
0
1
0
0
1
0
0
1
0
2
2
0
0
0
1
2
0
0
2
1
1
2
0
0
0
0
1
0
2
0
0
1
5
0
0
2
0
0
1
0
0
0
0
0
0
1
0
2
1
1
2
0
3
0
0
1
2
0
0
0
0
0
3
2
1
1
1
0
0
0
1
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
4
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
1
0
0
1
0
0
0
1
0
0
3
0
0
2
0
0
0
0
0
2
1
0
1
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
1
2
2
1
2
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
1
0
0
2
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
1
1
0
0
0
2
2
0
0
0
0
3
0
4
0
2
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
1
0
1
0
0
2
0
2
3
0
2
0
2
0
0
2
3
2
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
1
0
0
2
0
1
0
1
0
0
0
2
2
4
0
0
0
2
0
0
0
0
0
0
0
0
1
2
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
1
1
0
0
0
2
0
2
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
2
0
0
1
0
0
0
0
0
0
0
1
0
1
2
1
2
2
0
1
1
2
0
0
3
0
4
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
3
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
2
0
2
0
1
0
5
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
2
0
0
1
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
2
0
2
2
0
3
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
2
0
0
1
0
1
1
0
0
2
0
0
0
1
0
1
2
1
0
1
0
0
6
0
0
0
3
0
2
0
2
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
2
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
4
0
0
2
1
1
0
0
2
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
3
2
0
2
0
0
0
0
0
0
0
0
2
3
1
0
0
0
0
0
2
2
0
3
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
2
2
0
0
0
0
1
0
0
1
0
1
0
2
0
0
1
2
2
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
1
2
0
0
2
0
0
0
0
2
0
0
0
0
1
0
2
0
1
3
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
2
0
0
1
2
0
1
2
0
0
0
0
0
0
1
0
2
0
0
3
0
2
0
0
0
1
0
0
2
1
0
0
0
1
2
3
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
3
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
3
0
0
3
2
0
0
0
0
1
1
2
1
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
3
0
0
0
0
0
3
2
0
0
2
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
2
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
1
1
2
1
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
2
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
1
2
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
1
0
2
3
0
0
0
3
1
0
0
1
3
0
0
1
0
0
1
0
2
1
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
3
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
3
0
0
2
0
0
11
0
0
1
1
0
0
1
1
2
0
0
0
0
1
1
2
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
1
1
2
0
0
6
0
0
3
0
2
0
0
2
0
0
0
1
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
1
0
3
0
0
0
0
2
2
0
0
0
0
0
0
1
2
1
0
0
2
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
2
2
0
0
1
0
0
1
1
1
2
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
1
2
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
2
2
0
1
0
1
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
8
0
0
0
0
0
2
0
0
0
2
0
0
2
0
3
2
0
2
1
0
0
1
0
0
0
0
1
0
0
1
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
2
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
1
1
0
0
0
0
0
1
0
2
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
3
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
1
0
0
1
2
0
0
1
1
1
1
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
1
2
0
2
5
0
0
0
0
2
0
1
0
0
0
2
1
2
0
2
0
0
2
0
0
1
0
2
2
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
2
2
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
1
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
2
0
0
0
0
2
0
2
1
0
1
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
3
0
0
5
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
4
0
2
0
0
1
2
0
0
0
2
0
1
0
0
1
0
1
0
0
1
0
1
0
0
0
2
1
0
2
0
0
2
0
2
0
0
1
0
0
0
0
0
1
0
2
0
0
1
0
0
1
0
0
2
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
2
0
0
1
0
0
0
1
2
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
1
0
0
0
2
2
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
2
0
2
1
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
1
0
0
1
0
2
0
0
2
2
1
0
0
1
0
0
0
2
2
0
2
1
0
0
0
1
0
0
3
1
0
0
1
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
1
0
2
2
2
0
1
2
0
0
1
0
0
0
0
2
1
0
0
0
1
0
0
1
1
0
2
0
0
2
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
6
0
0
2
2
2
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
2
0
2
0
1
0
3
2
0
0
0
0
0
0
2
2
0
0
3
1
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
2
2
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
1
3
0
0
0
0
0
0
0
2
0
0
0
2
1
0
9
2
0
2
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
1
0
0
2
1
0
0
2
0
0
1
0
0
0
0
1
0
0
2
1
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
2
1
0
0
0
0
0
0
0
2
2
1
2
0
0
0
1
0
0
0
2
0
0
3
0
1
0
4
0
2
0
0
0
1
0
0
0
0
0
3
0
2
2
0
0
0
0
0
0
2
0
2
0
1
1
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
2
1
0
2
0
0
0
0
0
0
3
0
0
0
1
0
1
0
1
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
8
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
3
0
0
0
2
0
0
0
1
0
0
2
0
0
0
1
1
2
0
0
0
0
0
6
0
2
0
2
0
0
2
0
1
0
1
1
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
1
2
0
0
0
0
0
2
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
2
3
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
2
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
2
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
3
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
2
1
0
0
0
0
1
1
0
2
1
0
0
1
3
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
1
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
1
3
2
3
0
0
1
0
2
2
0
2
0
0
0
0
2
0
0
0
0
2
0
2
2
1
0
0
1
1
0
0
1
2
1
0
2
1
0
2
0
1
0
1
0
1
2
0
3
0
1
1
0
0
0
0
0
4
2
0
0
0
0
2
0
0
0
0
0
2
0
2
1
0
0
0
0
0
2
0
4
0
1
1
0
0
0
2
0
0
2
0
0
0
1
0
0
1
1
1
0
0
0
2
0
2
2
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
2
2
0
0
1
0
1
0
0
0
0
0
0
0
2
0
2
0
2
0
2
0
0
0
0
0
0
0
2
0
2
2
1
1
0
0
0
3
0
0
2
2
3
0
0
0
0
0
2
0
1
0
0
2
0
2
1
0
0
1
1
0
0
1
1
0
0
0
1
0
0
2
2
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
4
0
0
0
2
1
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
2
0
2
1
1
0
0
1
3
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
2
0
2
1
1
0
0
0
1
2
2
1
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
1
0
0
0
0
1
1
1
0
1
0
1
1
0
2
0
2
0
1
1
0
1
0
0
0
0
2
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
2
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
2
0
0
0
0
1
1
0
2
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
5
0
0
1
0
0
1
1
0
0
0
0
1
0
1
2
2
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
2
0
1
0
1
0
0
2
0
1
2
0
1
0
0
1
0
0
0
2
0
1
1
0
5
0
0
0
0
0
1
0
0
4
0
0
0
1
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
3
1
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
2
0
2
0
0
2
2
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
2
1
0
0
0
1
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
4
2
0
1
0
0
5
1
2
1
0
0
0
0
2
0
0
0
0
0
0
0
2
1
2
0
1
0
0
0
0
0
0
0
5
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
2
0
0
2
0
1
0
2
0
4
3
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
3
1
3
5
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
1
1
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
1
3
0
0
0
1
0
4
1
1
1
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
3
2
0
0
0
0
0
0
2
3
0
0
2
0
2
0
2
0
1
0
1
0
0
0
0
0
2
2
1
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
1
2
0
0
0
0
1
0
0
0
1
6
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
1
0
2
0
0
2
0
1
0
0
0
2
0
0
0
1
2
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
1
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
3
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
2
0
2
0
5
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
2
0
0
0
0
1
1
0
1
1
1
0
0
1
0
2
5
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
2
3
0
0
0
0
0
0
0
2
1
0
1
0
0
0
1
2
0
2
2
1
0
1
0
0
0
2
2
1
0
0
1
0
2
0
0
0
0
2
1
2
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
2
0
0
3
1
0
1
0
0
0
0
0
2
0
2
1
0
0
0
0
2
0
0
2
0
0
0
1
2
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
3
0
0
0
1
0
0
0
0
0
3
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
1
2
1
0
2
0
0
2
0
0
0
2
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
2
0
0
1
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
2
1
0
2
0
2
2
1
0
0
0
2
0
0
0
1
0
0
1
2
0
0
0
0
0
2
0
0
0
1
0
2
0
0
3
0
2
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
1
0
1
0
1
4
0
1
0
0
1
0
1
0
2
0
0
0
1
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
2
1
0
0
1
2
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
2
1
1
3
1
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
2
1
0
0
0
1
1
1
2
0
0
0
0
4
1
0
0
2
1
2
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
2
0
2
0
0
1
0
0
2
0
1
2
2
0
0
0
0
1
0
0
0
0
0
0
2
0
4
1
0
1
0
2
2
0
0
3
0
0
1
0
1
0
0
0
0
2
0
0
0
1
2
0
0
3
2
2
0
2
0
0
0
0
0
2
6
0
2
0
0
0
1
0
0
0
0
2
0
0
2
0
0
1
0
0
3
0
0
2
0
0
0
1
0
1
0
0
2
0
0
1
0
0
2
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
1
2
2
4
2
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
1
0
3
0
0
1
2
1
1
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
2
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
2
1
1
0
0
2
0
0
1
0
0
1
1
1
1
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
1
0
0
0
8
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
1
0
0
2
0
0
3
0
1
0
1
0
2
2
0
1
2
0
0
3
0
1
0
0
1
2
1
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
1
2
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
2
4
2
0
3
0
0
0
1
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
2
0
2
2
0
0
0
0
0
1
1
0
0
1
2
1
0
0
0
0
1
0
0
2
1
1
2
0
2
0
0
1
0
2
0
0
0
0
0
0
0
2
0
1
0
0
2
2
0
0
0
1
1
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
2
0
0
2
2
2
0
0
0
0
0
0
2
2
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
2
0
0
0
0
2
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
1
4
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
1
0
0
3
0
0
1
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
2
0
0
2
0
1
1
0
0
4
0
1
2
0
0
0
0
0
0
0
0
2
0
2
0
5
0
1
0
0
2
0
0
5
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
2
2
0
0
0
2
0
2
0
0
0
0
2
0
2
0
0
1
2
2
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
2
0
3
0
0
3
2
0
0
1
0
0
1
2
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
2
0
0
2
0
1
0
0
0
0
0
0
0
0
2
2
2
0
1
0
0
0
2
0
0
0
2
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
1
0
1
1
0
1
0
0
2
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
1
0
1
0
0
0
1
1
0
2
0
0
0
0
0
0
2
0
3
0
0
1
0
0
3
0
2
3
0
0
0
2
0
1
2
0
1
2
0
0
1
1
0
0
2
0
0
0
0
0
4
0
4
2
1
2
2
0
1
0
0
0
0
0
0
2
0
0
0
2
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
4
0
1
0
2
0
2
0
0
2
2
0
2
2
0
1
0
2
2
1
0
0
0
1
0
0
0
0
0
0
0
1
0
2
2
1
0
0
1
0
0
1
0
2
2
2
0
0
0
1
1
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
1
2
0
3
2
0
0
0
1
2
0
0
0
0
0
1
0
2
2
0
2
0
0
0
1
0
0
0
1
2
1
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
1
2
0
0
2
0
0
0
1
1
0
2
0
0
0
1
1
2
0
0
0
2
0
0
0
0
0
0
1
3
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
3
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
2
0
1
0
5
14
2
0
2
1
0
0
0
2
0
0
0
0
0
0
0
1
2
1
0
4
2
0
2
0
1
2
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
2
2
0
0
0
0
1
0
2
0
0
0
1
2
3
2
1
2
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
2
1
0
0
0
0
2
0
0
2
0
2
1
0
1
2
0
0
0
0
0
0
1
0
0
0
2
3
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
2
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
1
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
2
2
0
0
0
0
2
2
0
0
0
5
0
0
1
2
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
2
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
2
4
2
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
2
1
1
0
1
2
2
0
0
0
3
1
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
2
0
0
0
2
0
1
0
0
0
2
1
0
1
0
0
0
2
1
0
2
0
0
1
0
0
0
2
0
2
2
1
0
2
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
1
0
0
1
0
0
0
2
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
1
0
1
0
0
2
0
0
0
1
0
2
0
0
0
0
2
1
0
0
2
0
0
0
0
0
2
0
0
0
0
3
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
2
0
5
0
1
0
2
0
0
1
0
1
0
0
0
0
0
1
0
0
3
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
3
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
2
2
0
0
1
0
2
0
1
0
2
0
2
0
0
0
1
0
0
0
0
1
2
0
1
0
0
0
1
0
1
0
2
0
0
0
2
0
1
0
2
0
0
2
0
0
1
2
0
1
0
12
2
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
2
2
0
2
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
2
0
0
0
0
2
0
0
1
2
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
1
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
2
0
0
0
0
0
2
1
0
0
0
1
0
2
2
2
0
0
2
1
0
0
0
0
1
0
2
0
2
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
1
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
2
1
0
0
4
0
1
2
1
0
0
2
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
2
0
0
2
0
0
0
0
0
0
2
0
0
0
3
0
1
0
0
1
0
2
0
0
0
2
2
0
0
4
2
0
0
1
0
0
0
0
0
0
2
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
2
2
2
0
0
0
1
2
0
0
0
1
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
3
1
0
0
0
0
2
0
0
0
1
1
0
0
0
1
0
2
1
0
3
0
2
2
0
2
0
0
0
0
0
2
0
0
1
1
0
3
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
1
0
2
0
0
1
0
0
0
0
0
3
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
2
0
1
0
0
0
0
1
1
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
1
4
2
0
2
1
0
0
0
0
2
2
0
0
0
0
1
2
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
2
1
0
1
0
0
0
0
5
2
0
0
0
2
0
0
0
1
0
0
2
0
1
0
2
2
2
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
1
2
2
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
1
1
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
2
3
0
0
0
2
0
0
0
0
0
2
3
0
2
1
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
1
0
0
3
2
0
0
0
0
2
2
0
0
1
0
1
0
0
0
2
0
0
0
1
0
0
2
0
2
3
0
0
0
0
0
0
0
1
2
0
1
1
3
0
2
0
0
0
0
1
1
0
0
0
2
2
0
2
0
1
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
2
0
0
0
0
1
5
2
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
2
0
1
0
0
2
0
0
0
1
2
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
2
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
5
0
2
2
0
2
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
2
1
0
0
2
2
1
2
0
0
2
0
4
5
1
1
0
0
0
0
2
0
0
2
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
3
1
2
1
0
0
2
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
2
0
2
0
0
0
0
0
0
0
2
0
1
1
0
0
1
0
2
0
3
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
3
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
1
1
1
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
1
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
2
0
0
0
1
1
0
2
0
0
0
0
0
1
0
2
0
3
1
0
3
0
0
0
0
1
0
4
0
0
0
0
1
2
0
0
0
0
3
0
1
1
1
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
2
0
0
0
1
0
0
0
0
0
2
1
1
0
0
2
2
2
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
2
1
0
0
0
2
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
2
2
0
0
0
3
0
2
1
0
2
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
1
1
3
1
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
2
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
2
0
0
0
2
0
0
0
2
1
2
0
1
0
0
0
0
2
0
0
1
0
0
0
1
0
4
0
2
2
0
0
3
0
0
0
0
2
0
2
0
2
0
1
0
0
1
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
1
0
2
4
0
2
2
0
2
1
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
4
2
1
0
0
0
1
0
2
1
0
0
1
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
5
0
0
0
0
1
0
0
0
0
2
0
0
0
2
3
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
2
0
0
1
2
0
2
1
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
1
0
0
1
0
0
0
1
1
0
2
0
2
0
0
0
0
2
0
0
0
0
0
1
2
0
2
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
1
2
0
0
1
0
0
1
1
3
0
0
0
0
0
2
0
0
1
2
7
0
0
0
1
0
0
0
0
0
3
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
2
1
2
2
0
1
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
2
0
1
0
2
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
2
1
0
0
3
0
0
1
3
4
0
0
0
1
1
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
2
2
2
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
2
1
3
2
1
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
2
0
0
2
0
2
0
2
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
1
2
0
2
1
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
1
1
0
0
1
0
0
1
0
0
0
0
3
1
0
0
0
0
0
2
3
0
0
0
0
2
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
1
3
0
0
2
2
2
0
0
0
2
0
2
0
2
2
4
2
0
1
0
0
2
0
0
0
1
0
6
0
0
2
2
0
2
1
0
1
0
2
1
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
2
2
0
0
2
0
0
1
2
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
1
0
3
0
0
0
1
0
2
1
0
0
4
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
1
0
2
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
5
1
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
3
1
2
1
0
0
0
1
0
2
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
1
0
0
1
0
0
1
5
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
3
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
2
1
0
0
0
1
1
0
2
0
0
0
0
11
2
1
0
2
1
1
0
1
0
0
0
0
0
1
0
2
1
0
0
2
0
0
1
0
0
1
1
0
2
0
0
1
0
2
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
1
2
0
1
0
0
2
2
1
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
1
0
2
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
2
2
0
3
0
0
1
0
0
0
2
0
0
2
1
0
1
0
2
1
1
2
4
0
0
1
0
0
0
0
0
2
0
0
0
3
0
2
0
2
1
1
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
3
1
0
0
2
0
0
2
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
3
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
1
1
0
0
1
0
1
0
3
0
0
0
0
0
2
0
0
0
0
2
0
0
1
1
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
2
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
4
0
0
0
2
1
0
2
0
1
0
0
1
0
0
0
0
2
0
0
1
0
0
0
1
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
1
0
0
1
0
1
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
1
2
0
1
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
2
0
0
2
0
0
0
0
0
2
0
1
0
1
2
2
3
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
2
0
0
0
2
1
0
0
2
0
1
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
3
0
2
3
2
0
0
0
1
0
0
0
0
2
0
2
0
2
1
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
2
0
2
1
2
0
0
0
5
0
0
0
0
1
0
0
2
0
2
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
2
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
3
2
0
1
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
1
2
1
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
2
0
2
0
0
1
0
0
0
2
0
1
0
0
3
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
1
2
1
0
0
0
0
0
0
0
2
2
2
0
1
0
0
0
2
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
1
3
0
0
0
0
0
2
1
0
0
2
1
2
0
0
2
0
0
0
0
0
0
0
1
2
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
3
2
1
2
0
1
0
0
0
2
0
0
2
0
0
0
2
0
1
0
1
2
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
1
2
2
2
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
2
2
0
1
0
3
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
2
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
2
2
0
0
0
3
1
0
0
0
0
1
0
4
2
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
1
2
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
1
3
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
4
0
0
3
2
0
0
1
4
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
2
0
2
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
3
0
1
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
2
1
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
1
0
2
0
0
0
0
0
0
1
0
0
0
0
2
1
0
2
0
0
2
0
0
2
2
0
1
2
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
2
0
2
2
1
0
0
1
0
0
0
2
1
1
1
0
0
0
0
2
0
2
0
0
0
2
0
0
2
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
2
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
3
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
1
3
0
0
1
0
0
0
0
0
8
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
1
1
0
0
0
0
2
0
0
2
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
1
0
0
0
1
2
2
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
1
3
2
0
0
2
0
0
0
0
0
0
0
1
0
2
1
0
0
1
0
0
0
0
1
0
0
0
0
2
0
2
3
2
1
0
3
0
0
0
0
0
0
0
0
2
0
0
0
1
2
2
0
2
0
0
0
0
2
0
2
0
1
4
2
0
0
0
0
0
0
2
0
0
3
0
3
3
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
3
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
7
1
2
2
1
5
0
0
0
0
0
2
0
0
1
0
0
0
2
2
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
2
0
1
2
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
2
3
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
3
2
0
2
0
0
0
2
0
0
0
0
1
0
0
1
2
0
2
0
1
0
0
0
0
1
0
0
2
0
1
2
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
3
0
0
0
0
2
0
0
2
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
1
0
0
1
0
0
0
2
1
3
0
1
2
1
1
0
0
0
0
0
0
2
1
0
0
0
2
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
3
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
2
0
1
2
2
0
2
2
1
0
0
0
0
0
1
0
0
2
1
1
1
0
0
8
0
0
1
0
0
0
0
2
1
0
0
0
4
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
2
0
0
0
0
0
2
0
2
0
1
0
0
0
0
5
0
0
0
0
0
0
2
2
2
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
3
0
1
0
0
0
0
0
0
1
1
2
1
1
0
0
0
0
0
2
0
0
0
1
2
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
2
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
2
1
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
1
2
1
0
0
0
0
1
0
0
1
1
0
1
0
1
0
0
2
0
0
0
0
0
2
0
1
2
2
0
0
0
0
0
1
0
0
1
2
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
2
0
0
0
0
2
0
1
2
0
0
0
0
1
1
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
1
1
2
1
0
0
0
0
0
0
0
17
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
2
0
1
0
1
0
1
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
2
1
0
0
1
0
0
0
3
1
0
1
0
1
1
0
2
0
0
0
0
0
2
1
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
1
1
1
1
2
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
1
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
4
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
1
0
2
0
0
0
1
0
0
0
0
2
1
2
0
1
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
2
0
2
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
1
1
1
1
0
1
0
3
0
0
0
1
0
0
2
0
0
1
1
0
0
0
0
2
0
1
0
0
0
0
1
2
0
0
0
4
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
3
0
2
0
0
0
0
0
0
1
1
2
0
0
0
0
0
3
2
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
3
0
0
0
0
0
0
0
0
2
0
1
0
0
2
1
0
0
0
0
1
0
0
2
0
0
2
2
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
2
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
2
2
0
1
0
3
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
2
0
0
0
1
0
2
2
2
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
1
1
0
0
1
0
0
1
0
2
1
2
2
0
1
0
0
1
2
2
1
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
1
2
0
1
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
4
0
1
0
0
0
2
0
2
0
0
1
2
2
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
1
0
2
1
0
3
2
1
0
0
1
0
0
0
3
0
1
0
0
2
1
0
0
1
1
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
2
2
0
0
2
1
1
0
2
0
1
0
0
2
0
0
0
1
0
0
0
0
0
2
2
2
0
0
0
0
1
1
0
0
2
0
0
0
0
0
2
1
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
1
3
0
0
0
1
1
0
0
1
0
1
0
3
0
2
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
2
1
2
0
0
0
1
2
0
1
0
2
0
0
0
3
0
1
0
0
0
0
0
1
0
2
2
3
0
0
0
2
0
0
1
0
0
0
0
1
1
2
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
3
2
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
1
3
0
1
2
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
1
2
0
0
2
0
0
0
0
0
1
3
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
2
2
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
1
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
3
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
1
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
2
2
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
2
0
0
1
0
0
0
1
1
0
2
0
0
1
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
2
0
1
0
0
1
0
0
0
2
0
0
0
0
0
1
0
1
0
0
2
1
0
1
0
0
1
0
2
1
0
0
2
0
3
0
2
0
0
0
0
0
0
1
0
0
1
0
2
1
2
1
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
1
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
2
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
2
1
0
0
0
0
1
1
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
2
0
1
0
0
1
0
0
0
3
0
0
0
0
0
0
1
1
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
2
0
1
1
0
0
1
0
2
0
0
1
0
0
0
2
0
0
1
0
0
3
0
3
0
0
0
0
0
1
0
0
1
0
1
0
2
4
0
0
0
0
0
0
2
1
0
1
0
0
0
2
0
0
0
0
1
7
0
0
0
0
0
0
1
0
1
1
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
2
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
5
0
0
1
0
0
0
0
0
0
2
0
1
0
1
2
0
0
0
1
1
0
3
13
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
11
1
0
0
0
0
6
0
1
2
0
3
2
0
0
0
1
0
1
2
1
2
1
1
0
0
0
0
0
3
0
0
0
3
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
7
0
0
0
2
0
0
1
2
0
0
0
0
1
0
0
0
1
0
0
0
0
1
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
2
2
0
0
2
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
3
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
1
0
2
0
0
1
0
0
0
0
0
2
1
0
2
4
0
2
0
0
0
2
0
0
1
1
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
1
10
1
0
0
0
0
2
0
0
1
0
2
0
0
0
2
0
0
0
2
0
0
0
0
1
0
1
0
0
1
2
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
2
0
0
0
4
0
0
3
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
1
2
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
1
4
0
2
0
0
0
0
0
2
0
1
0
0
0
1
0
0
4
0
0
0
0
5
0
0
2
2
0
0
0
0
3
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
1
0
0
0
2
2
0
2
3
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
3
1
0
3
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
1
2
0
2
1
0
0
0
0
0
0
0
0
2
2
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
2
0
0
2
3
0
0
0
0
0
0
1
1
1
2
2
0
2
0
0
0
1
0
0
1
0
2
2
3
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
2
2
0
12
0
1
2
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
3
0
1
0
4
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
2
0
0
2
0
0
0
0
0
3
0
2
0
0
0
0
0
0
1
0
1
0
2
0
2
0
0
2
1
1
1
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
2
4
0
0
1
0
1
0
0
2
0
0
2
1
0
0
1
0
1
4
0
0
0
0
0
2
5
1
0
0
0
0
0
0
0
0
0
1
1
2
0
1
0
0
3
1
0
0
0
0
2
2
2
0
0
0
3
2
0
0
0
0
0
0
0
3
0
0
1
0
2
0
0
0
0
0
0
2
2
0
2
1
0
0
0
0
0
0
1
1
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
1
1
2
0
2
2
0
0
1
0
0
0
2
2
4
0
0
2
0
0
0
0
0
0
2
0
2
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
1
0
1
0
1
3
0
0
0
0
0
0
0
0
1
2
3
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
3
0
0
2
0
0
2
1
2
0
1
1
0
0
2
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
3
0
0
0
0
2
0
2
1
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
2
0
1
0
1
0
0
0
0
2
0
0
0
1
1
0
3
0
0
0
2
0
1
2
2
0
0
0
0
2
0
0
1
0
2
1
0
2
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
1
2
2
0
1
0
2
0
1
0
0
2
0
0
0
2
0
0
0
0
0
2
1
2
3
0
0
1
0
0
0
0
2
0
0
0
2
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
6
2
0
0
3
0
1
0
0
1
2
0
0
0
0
0
0
2
1
0
0
2
0
2
3
2
0
0
0
0
1
0
3
1
0
0
0
0
1
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
1
0
3
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
6
0
0
0
1
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
1
2
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
1
0
0
2
2
2
0
0
2
2
0
0
1
2
0
1
2
0
3
0
2
0
0
3
1
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
2
0
0
0
2
0
0
2
0
2
1
2
0
2
1
0
0
3
0
2
0
0
1
0
1
2
0
2
0
1
0
2
7
0
0
0
0
1
0
0
2
1
0
0
0
0
0
3
1
1
0
1
2
0
1
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
2
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
5
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
2
2
1
0
0
0
0
0
1
0
0
0
2
1
1
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
2
0
0
2
2
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
1
2
0
1
0
0
1
5
0
1
0
0
0
0
0
0
0
0
1
1
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
7
1
0
0
0
0
1
2
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
1
0
2
0
0
0
2
1
1
0
2
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
1
0
0
1
1
0
1
0
0
0
1
0
0
2
1
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
2
0
1
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
1
1
0
0
1
0
0
0
0
2
2
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
2
2
1
0
1
0
0
0
0
0
0
0
0
2
2
0
1
0
1
1
0
0
1
0
4
0
2
0
0
2
1
0
0
4
0
0
0
1
0
2
2
0
0
0
0
0
0
1
0
4
0
2
0
0
0
2
0
0
0
1
0
0
2
0
2
0
0
1
0
0
1
0
8
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
1
1
0
0
1
0
0
2
0
1
2
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
2
2
1
0
0
0
1
0
0
0
2
1
0
0
2
0
3
1
0
0
1
2
2
1
0
0
0
0
0
0
2
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
1
0
2
0
2
1
2
0
2
2
0
0
0
2
0
2
0
0
1
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
2
2
0
0
0
1
2
0
0
0
0
2
1
1
0
0
1
0
0
3
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
2
1
0
0
0
0
1
2
1
3
0
0
0
0
0
0
0
0
1
0
2
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
1
3
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
4
1
0
0
2
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
2
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
1
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
2
0
0
0
0
1
0
2
0
1
0
0
0
0
1
0
2
0
1
2
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
1
1
4
3
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
1
0
0
0
0
1
0
3
0
0
0
0
0
2
2
1
1
2
0
0
1
0
0
1
0
0
0
0
0
0
3
0
0
0
2
1
1
6
0
0
2
0
0
2
1
0
1
0
0
0
1
2
0
0
2
0
1
2
0
0
0
0
2
0
1
2
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
2
2
0
0
1
0
2
0
0
0
1
2
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
2
0
0
0
2
2
0
0
0
2
0
0
0
0
0
1
0
0
1
0
2
0
2
0
1
3
2
0
2
2
2
1
1
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
2
1
0
1
0
0
1
2
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
5
0
0
1
0
0
0
2
0
2
0
0
0
2
0
3
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
2
3
0
0
2
0
1
2
0
0
1
0
1
2
0
1
1
2
0
0
2
0
0
0
2
0
0
0
2
0
0
2
0
1
3
3
0
1
0
0
0
1
0
0
0
0
0
0
3
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
2
2
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
3
1
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
1
3
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
1
0
1
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
4
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
2
2
0
0
2
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
2
0
1
0
1
0
0
2
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
2
0
1
0
2
2
0
1
0
0
0
1
0
1
1
0
0
1
0
0
3
3
0
2
0
0
1
0
1
2
0
1
0
2
2
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
4
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
5
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
2
0
1
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
3
0
0
1
0
1
0
0
0
1
0
2
1
0
0
1
2
0
0
2
0
0
0
0
1
1
0
1
1
2
1
2
0
2
2
2
1
1
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
1
1
2
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
2
0
3
2
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
1
0
1
0
2
0
2
0
2
2
0
0
0
1
0
0
0
0
0
2
1
0
0
1
1
1
0
0
0
1
0
2
0
0
0
2
0
0
1
2
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
2
0
0
0
3
1
0
1
0
0
0
0
2
2
0
0
1
0
4
0
0
0
1
2
1
0
2
0
1
1
1
2
2
0
2
0
6
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
1
1
0
0
0
2
2
1
0
0
0
0
0
0
0
1
0
4
1
0
0
2
1
0
0
0
0
0
1
2
0
2
0
0
2
0
0
2
1
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7
0
0
2
2
0
6
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
1
0
1
0
4
0
0
0
0
0
0
1
5
1
2
2
0
0
0
2
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
1
0
2
0
0
1
0
2
0
0
1
1
0
0
0
0
1
0
0
0
2
1
0
0
1
0
0
2
1
1
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
4
1
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
1
2
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
3
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
1
2
0
0
3
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
3
0
0
0
0
0
2
0
0
0
0
0
0
0
3
3
0
0
0
1
0
0
0
0
0
0
2
0
2
0
2
0
0
1
1
2
1
0
0
0
0
2
1
0
0
0
1
0
0
2
0
2
0
0
0
0
1
0
2
0
0
1
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
3
0
0
0
0
0
2
1
2
0
2
0
0
3
0
0
2
0
0
1
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
1
1
4
0
0
1
0
0
1
0
0
0
0
0
0
0
3
1
0
0
1
0
2
0
0
0
1
1
1
0
0
0
0
1
0
2
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
2
3
0
0
0
0
0
0
0
2
0
2
0
0
1
0
1
0
1
0
2
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
1
5
1
0
0
1
0
3
2
2
1
3
0
0
1
1
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
2
0
1
0
0
2
1
0
3
0
0
0
2
0
0
1
2
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
2
0
0
2
0
0
0
1
3
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
3
2
0
0
1
0
2
0
0
1
6
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
1
1
1
0
0
0
0
0
0
0
0
2
2
2
1
0
2
1
1
0
0
0
0
0
0
1
2
0
0
2
0
2
0
0
0
0
0
0
0
2
3
1
0
0
0
0
0
0
0
0
1
0
0
2
0
1
2
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
2
1
0
0
3
1
2
1
0
0
1
0
1
1
0
2
0
2
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
1
0
1
1
2
0
0
0
0
0
0
0
0
6
0
0
1
1
0
3
2
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
4
1
1
2
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
2
1
2
0
0
0
0
0
0
2
2
0
0
1
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
2
0
2
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
2
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
2
0
0
0
3
1
0
0
0
2
2
1
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
1
0
1
2
3
1
3
0
0
0
0
0
0
0
0
6
0
2
2
0
0
2
0
0
0
0
1
0
0
0
2
1
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
2
3
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
3
2
0
0
0
0
1
0
0
0
1
2
2
0
2
1
1
0
0
0
6
1
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
2
0
1
0
0
2
0
0
0
0
2
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
5
3
0
0
0
0
0
1
2
0
0
1
0
0
0
1
1
1
1
0
0
0
0
0
0
0
1
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
1
0
0
1
0
1
4
0
0
1
0
0
0
0
0
0
1
0
0
0
2
2
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
2
2
0
0
0
10
0
0
2
0
0
0
0
1
2
2
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
3
0
0
0
0
1
0
2
0
0
1
2
0
0
0
0
1
1
1
0
0
0
0
2
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
2
1
0
1
0
1
0
2
0
0
2
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
2
2
0
0
0
2
1
2
2
0
0
1
0
0
4
0
1
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
1
2
0
1
0
0
0
0
1
2
1
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
1
0
2
2
0
0
2
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
2
1
0
1
0
0
0
1
1
2
1
0
0
0
1
0
1
0
2
0
2
0
2
0
0
1
0
0
0
2
2
0
0
0
0
0
2
0
2
3
1
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
2
2
0
0
0
0
2
0
0
0
0
2
1
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
2
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
1
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
2
3
0
0
0
3
1
0
1
0
0
0
1
1
0
0
1
0
1
2
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
2
1
0
0
0
2
0
0
1
2
1
1
0
0
0
0
1
0
2
0
0
1
0
2
1
0
0
2
0
1
0
1
0
2
0
0
0
3
0
0
0
0
1
0
0
0
0
0
1
0
2
0
2
1
0
0
2
0
0
0
1
0
2
1
0
1
1
1
1
0
0
0
1
2
2
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
11
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
1
1
3
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
12
0
0
0
0
0
0
0
2
0
1
1
1
0
0
2
1
2
0
0
1
2
0
2
3
0
2
0
0
1
0
2
0
3
2
0
2
2
0
2
1
0
0
0
0
2
0
0
0
0
0
1
0
2
2
2
0
0
0
0
2
2
0
2
0
0
0
2
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
3
0
0
0
0
0
0
0
1
0
0
2
2
0
2
0
1
1
0
0
0
0
0
1
0
0
2
0
2
0
0
2
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
2
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
1
1
0
0
0
0
3
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
2
1
0
1
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
1
1
0
0
0
1
0
0
0
0
2
2
3
1
1
0
0
1
0
0
0
1
0
0
2
0
0
0
2
1
0
1
1
0
0
0
2
0
0
0
0
0
0
1
0
0
2
1
0
4
1
0
0
2
0
0
0
0
0
0
0
0
6
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
1
0
0
1
2
0
2
2
1
0
1
0
1
0
0
2
2
2
2
0
2
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
1
1
2
0
0
0
1
0
0
0
0
0
0
0
0
3
1
0
0
0
0
2
0
1
0
1
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
1
2
0
2
0
0
0
0
1
0
2
0
0
0
0
1
0
0
1
1
2
0
1
0
1
0
0
2
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
3
1
0
0
2
0
4
0
2
1
2
1
2
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
1
0
0
3
0
0
0
0
1
0
0
2
2
0
2
4
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
3
0
0
0
1
0
0
0
0
1
0
2
0
2
0
1
2
1
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
6
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
2
0
0
0
1
1
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
2
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
6
0
0
0
1
2
1
0
0
1
0
0
0
0
0
1
0
0
1
0
2
0
0
0
1
0
0
1
0
0
0
1
0
1
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
3
0
0
0
2
0
0
2
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
2
1
0
0
0
3
0
0
0
0
0
0
1
0
0
0
1
0
2
2
2
0
1
0
0
0
0
0
0
0
0
0
2
2
0
3
2
1
0
2
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
2
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
2
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
1
0
0
1
2
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
9
2
0
0
2
1
0
0
0
0
1
0
0
3
1
0
0
0
0
0
1
0
2
0
1
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
1
2
0
0
0
0
2
0
2
0
1
0
2
0
0
2
1
1
1
1
0
0
1
1
0
0
0
0
1
0
0
0
2
3
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
1
0
1
0
2
0
0
1
0
3
0
0
0
0
1
0
1
0
0
0
0
2
1
0
0
0
0
0
2
0
0
2
0
0
2
0
0
1
2
0
2
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
1
0
1
0
2
0
0
0
1
1
0
1
0
2
0
0
0
2
1
0
3
0
0
3
0
0
4
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
3
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
2
0
1
0
1
0
1
3
0
0
0
0
2
2
0
0
0
0
0
0
2
1
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
8
0
0
0
0
0
0
0
2
0
0
5
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
3
3
0
0
0
1
1
5
0
0
0
0
0
0
0
0
2
0
0
2
2
2
1
0
1
1
0
0
0
2
0
1
0
1
0
0
2
0
3
0
0
1
2
1
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
1
0
2
0
2
2
0
0
0
1
0
0
1
0
1
1
0
2
0
3
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
3
1
0
0
0
0
0
4
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
2
0
2
2
0
2
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
6
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
1
0
0
0
1
0
0
0
0
1
0
0
0
2
1
0
2
0
1
1
0
0
0
2
2
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
2
0
2
0
2
0
0
0
1
1
0
0
0
0
2
0
1
0
2
0
0
2
0
0
0
0
0
1
3
0
1
0
0
2
0
0
0
1
0
0
2
0
0
0
2
1
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
2
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
3
0
2
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
1
0
1
0
1
2
0
2
0
0
2
0
2
0
1
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
2
0
0
0
1
0
1
1
0
2
2
0
3
0
0
2
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
2
2
1
0
1
0
0
1
2
0
0
0
0
4
0
1
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
2
1
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
1
2
1
0
0
2
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
2
0
4
0
2
0
0
0
0
0
2
3
0
0
0
0
1
0
2
0
0
0
2
2
0
0
0
0
0
0
1
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
2
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
1
0
0
0
2
3
2
0
1
0
2
0
0
0
1
0
0
1
0
0
0
0
0
2
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
2
1
0
0
3
0
0
2
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
1
2
1
2
1
2
2
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
5
0
0
0
3
0
0
0
0
0
0
0
0
3
1
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
3
0
2
0
2
0
2
2
0
0
2
0
0
0
0
0
1
1
0
0
0
1
1
0
0
4
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
1
0
0
1
1
0
0
1
1
1
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
2
0
1
0
1
0
0
0
0
2
0
1
2
0
0
0
0
1
0
2
0
0
0
2
0
2
0
0
0
4
3
0
0
0
0
0
1
1
0
0
1
0
0
0
0
2
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
3
2
1
1
1
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
1
0
1
0
0
0
0
0
2
0
1
0
0
1
0
1
0
0
0
3
0
0
7
1
2
2
0
0
2
2
2
0
0
0
0
2
0
4
2
0
0
1
2
0
2
2
0
0
2
0
1
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
2
0
3
0
1
1
0
1
0
0
1
2
0
1
2
0
0
0
2
0
1
0
2
1
0
0
0
0
1
0
2
0
0
0
2
0
3
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
2
4
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
2
0
0
2
0
2
0
1
2
0
0
0
0
1
2
0
2
0
3
0
0
0
1
0
0
0
3
2
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
3
0
1
0
0
0
0
2
1
0
0
2
2
1
0
0
0
0
3
1
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
3
0
0
0
0
0
2
0
0
0
0
0
3
2
2
0
0
0
1
1
3
0
0
0
0
2
1
2
4
0
1
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
1
1
0
0
0
0
2
1
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
1
0
1
0
0
2
1
0
2
0
2
0
0
0
1
0
0
1
3
0
3
0
0
0
0
4
1
0
0
0
2
0
0
2
0
0
0
2
0
0
0
1
1
0
0
1
1
2
0
0
2
0
0
0
0
1
1
0
2
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
6
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
3
0
0
0
0
1
1
1
0
0
0
2
0
0
0
0
1
1
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
4
1
0
0
0
0
0
0
2
0
0
0
2
2
2
1
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
2
1
0
0
0
1
2
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
1
0
3
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
4
2
0
0
0
0
0
0
1
0
0
0
0
0
3
1
0
0
0
0
0
0
2
1
0
0
0
0
0
1
2
0
0
0
0
0
1
0
1
0
2
0
0
0
0
2
0
0
0
0
1
1
0
1
0
2
0
0
1
0
2
0
1
0
0
1
3
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
3
0
0
0
0
0
1
1
0
2
0
0
2
0
0
5
3
0
1
0
0
2
0
0
0
0
2
4
0
2
0
2
0
0
0
0
2
1
1
2
0
0
1
0
0
0
0
1
2
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
4
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
2
0
4
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
2
1
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
2
0
0
0
1
1
0
3
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
4
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
1
0
1
0
0
2
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
2
0
2
0
0
3
2
0
1
0
0
0
0
0
0
2
1
2
2
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
5
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
4
0
1
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
2
5
2
0
1
1
0
0
0
3
1
1
0
0
0
4
0
1
1
2
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
2
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
1
1
0
1
0
3
0
1
0
3
0
0
0
2
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
1
2
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
2
0
0
0
0
2
0
0
1
0
2
2
1
0
1
0
4
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
1
0
0
1
0
0
0
0
0
2
0
2
0
0
1
0
0
1
1
0
0
0
1
1
0
0
0
2
0
0
0
0
2
1
2
2
0
0
2
2
0
2
0
0
0
0
0
0
0
0
1
0
0
2
1
0
2
0
1
1
1
0
0
0
0
0
1
0
0
0
0
1
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
2
0
0
0
2
0
0
0
0
0
2
0
0
1
1
0
2
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
3
0
2
0
0
2
0
1
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
2
0
2
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
1
0
1
1
0
0
0
2
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
2
2
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
3
2
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
2
0
0
0
1
0
0
0
0
0
0
1
1
2
0
0
0
0
0
2
0
0
2
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
5
0
0
0
1
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
2
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
1
2
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
5
0
1
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
1
0
0
0
0
0
0
0
0
3
1
0
1
0
0
2
0
0
0
0
1
1
0
1
0
0
1
2
1
0
3
0
1
2
2
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
2
0
0
0
0
0
0
2
2
0
2
0
1
0
1
0
1
0
1
0
0
0
1
0
2
0
0
0
0
5
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
2
0
2
0
0
0
0
1
0
0
1
0
1
0
0
1
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
1
0
0
3
0
0
0
0
0
0
2
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
2
0
0
0
0
2
2
0
1
1
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
1
1
0
0
0
1
2
1
0
0
0
0
0
1
1
0
0
1
0
0
0
2
0
2
0
1
0
1
2
1
1
0
1
2
0
0
0
3
0
2
0
2
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
2
0
2
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
1
0
2
0
6
3
1
0
0
2
1
0
2
2
0
0
2
0
1
1
1
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
9
0
0
0
0
2
0
0
1
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
2
0
1
0
1
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
1
2
1
0
0
3
2
4
0
1
0
0
2
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
2
0
0
2
2
1
1
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
3
0
0
2
0
1
0
0
0
0
2
0
0
2
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
2
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
1
1
0
3
1
1
2
1
0
0
0
0
0
0
0
3
1
1
1
1
0
0
0
1
0
0
0
0
2
0
0
0
1
2
2
0
2
0
0
0
0
0
0
2
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
2
0
3
0
1
0
2
0
2
1
0
2
0
2
0
2
0
0
0
2
1
2
0
0
0
0
1
2
1
0
1
2
1
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
3
2
13
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
2
0
1
1
0
2
0
1
2
0
0
4
0
4
1
0
2
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
6
1
1
0
0
0
1
0
1
0
3
1
0
0
3
0
0
0
0
0
0
0
0
2
0
0
2
5
1
0
0
1
0
2
2
3
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
2
0
0
2
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
3
0
0
0
0
0
0
0
2
0
0
1
1
0
1
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
1
0
0
0
4
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
2
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
9
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
2
0
0
2
0
0
1
1
2
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
2
0
1
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
3
1
0
0
2
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
2
2
0
1
1
1
0
0
0
0
1
3
2
0
0
0
2
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
3
2
2
0
0
0
2
0
2
0
0
0
2
0
2
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
1
0
0
1
0
1
2
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
2
2
1
0
0
0
1
0
0
2
5
2
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
1
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
6
0
1
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
1
0
4
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
3
1
1
4
1
0
2
2
0
0
0
1
0
1
0
0
2
2
1
1
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
1
1
0
0
2
0
0
2
0
4
8
0
0
0
0
0
3
0
2
1
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
1
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
2
0
0
0
1
3
1
0
0
1
0
0
0
2
0
1
0
0
0
1
2
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
2
2
0
1
1
0
0
2
2
0
0
2
0
0
0
0
0
1
0
2
0
1
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
2
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
4
0
2
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
2
1
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
2
0
1
0
0
2
1
0
1
0
1
1
0
1
0
0
0
2
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
8
0
1
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
3
0
2
0
2
0
0
2
0
2
2
2
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
2
1
3
0
0
0
0
0
1
2
0
2
1
0
2
0
2
0
0
0
0
0
2
1
0
3
0
1
1
0
0
1
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
1
0
0
2
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
2
3
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
2
0
2
0
1
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
4
2
2
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
2
0
0
0
0
3
0
0
2
0
0
0
0
0
2
2
0
0
1
2
0
0
1
0
1
0
1
0
1
0
0
1
0
0
0
0
0
1
1
0
0
3
2
2
0
2
1
0
0
0
0
1
0
2
2
0
0
0
1
0
0
0
0
0
0
3
0
0
0
1
0
0
1
0
0
0
0
1
2
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
2
2
0
1
0
0
0
2
0
0
2
2
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
2
0
0
2
1
1
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
2
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
2
0
0
0
2
0
3
1
2
0
0
0
0
0
0
1
1
0
2
0
1
0
0
0
0
1
1
0
0
0
0
0
2
2
1
1
0
0
0
0
0
0
0
0
0
0
3
2
2
5
0
0
1
1
2
0
0
2
0
3
0
0
1
0
0
0
0
2
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
2
0
0
2
0
0
1
3
2
0
1
0
1
0
0
0
0
1
1
0
0
0
1
0
2
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
2
0
0
0
1
0
1
2
0
2
2
0
2
0
0
1
0
2
0
1
1
0
0
0
0
1
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
3
1
1
0
1
2
0
2
0
0
2
0
0
0
0
2
0
3
0
0
1
0
0
0
0
0
2
0
4
0
0
0
0
2
1
0
0
1
2
0
0
0
0
0
1
0
0
0
0
1
0
0
2
1
0
2
0
1
0
2
0
0
0
0
1
1
0
1
1
0
2
0
2
0
0
0
2
0
0
0
2
1
0
0
0
0
2
1
1
2
0
0
0
0
1
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
2
0
3
2
1
0
2
0
0
2
2
1
0
0
5
0
0
0
3
1
0
0
0
1
0
0
0
0
2
0
2
1
1
1
1
2
3
0
1
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
3
2
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
3
0
3
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
4
0
1
0
0
1
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
2
0
0
0
2
0
0
0
0
0
3
0
2
0
2
0
2
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
3
3
0
1
0
2
2
0
0
0
0
0
0
2
0
0
0
0
2
0
4
1
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
1
0
2
1
0
0
0
0
1
2
2
0
1
1
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
1
2
0
1
1
1
0
0
0
1
0
1
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
3
0
0
0
0
1
1
0
1
1
0
0
1
0
0
1
1
0
2
2
1
1
0
0
0
2
0
2
1
4
1
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
1
2
1
0
0
1
2
2
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
2
2
2
0
2
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
3
1
2
0
1
0
0
1
2
2
1
5
0
0
2
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
2
1
1
0
0
0
0
0
1
0
0
3
1
0
0
0
2
0
0
0
7
0
2
1
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
1
3
1
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
1
0
0
3
0
0
2
1
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
2
1
2
0
0
2
0
0
2
1
0
1
0
1
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
2
0
1
2
0
2
0
0
2
0
2
0
2
0
1
0
2
0
2
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
1
2
0
0
2
2
0
0
0
0
2
1
0
0
3
0
0
4
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
2
1
0
0
0
0
0
0
0
2
1
0
0
0
4
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
1
0
2
2
2
2
0
1
0
0
0
2
0
0
0
1
2
0
0
0
0
1
0
2
0
0
0
0
2
1
0
0
2
0
0
4
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
1
1
0
0
2
2
3
2
0
0
0
1
2
2
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
2
0
0
0
2
1
0
2
0
0
2
1
3
0
0
0
2
0
0
1
0
1
0
1
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
2
6
0
0
1
0
1
1
0
0
6
0
0
0
2
0
2
0
1
0
0
2
2
0
0
2
1
1
0
3
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
1
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
2
0
0
2
4
0
1
0
0
1
0
0
0
1
2
0
0
0
0
2
0
0
0
2
0
0
0
3
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
2
0
1
0
0
3
0
1
0
2
0
1
1
0
0
0
0
2
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
3
1
0
0
0
1
4
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
3
0
0
2
0
0
0
0
1
0
0
1
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
1
2
0
1
2
2
0
0
0
0
1
0
2
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
1
1
1
3
2
0
1
0
0
1
3
0
0
0
0
2
0
0
2
0
0
0
0
1
0
2
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
2
0
0
0
0
0
0
0
1
2
0
2
1
0
0
0
1
0
2
0
0
0
0
0
0
1
0
1
3
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
2
0
0
1
2
0
2
0
0
0
1
1
2
0
1
1
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
2
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
2
2
4
3
0
0
0
0
0
0
0
0
0
0
2
1
2
0
3
2
0
0
2
0
2
1
0
1
0
0
3
2
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
3
3
1
1
0
2
0
1
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
3
2
0
0
1
0
0
2
0
1
1
0
2
0
0
0
0
0
2
0
1
1
2
0
0
3
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
2
0
2
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
1
1
1
0
0
0
0
0
1
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
1
1
1
0
0
0
0
0
0
2
0
0
0
1
0
1
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
1
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
1
1
0
0
0
0
1
0
0
0
0
2
2
0
1
0
0
0
0
1
0
1
0
2
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
1
0
0
0
1
0
0
1
1
0
1
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
4
0
2
0
0
1
0
0
1
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
3
1
2
0
0
1
2
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
2
0
0
0
0
1
2
0
2
0
2
0
0
0
0
1
0
3
0
0
0
1
0
0
0
3
1
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
2
0
2
0
0
0
2
3
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
2
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
1
2
0
0
0
1
2
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
1
0
1
0
0
0
1
4
0
0
2
2
1
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
2
2
2
0
0
8
0
0
0
2
1
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
1
3
1
1
1
1
0
0
0
1
0
1
0
0
1
0
0
2
0
0
3
1
0
0
1
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
1
2
1
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
2
1
0
2
0
2
2
1
2
1
2
0
0
1
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
3
0
0
0
0
1
0
0
0
0
0
0
1
3
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
1
1
2
2
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
2
0
0
3
0
0
4
0
0
0
2
1
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
3
0
0
1
0
1
2
2
0
1
0
1
1
0
0
0
0
0
1
0
0
0
2
1
0
3
0
0
0
0
0
0
2
0
0
1
0
2
0
1
0
0
0
2
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
1
1
0
0
2
2
0
0
0
0
2
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
2
0
3
0
0
2
1
0
0
2
1
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
1
1
2
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
1
0
2
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
2
1
0
2
0
1
0
0
1
2
0
0
0
2
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
2
2
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
1
3
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
3
0
0
1
1
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
2
1
0
0
0
0
1
2
0
0
0
0
0
0
2
0
1
0
0
1
1
0
1
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
1
2
0
0
2
0
0
2
1
0
1
1
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
3
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
3
0
2
0
1
1
0
0
0
0
0
2
2
0
1
0
0
1
0
0
0
0
0
2
0
3
1
2
1
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
3
0
1
0
2
2
0
0
2
0
0
0
1
2
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
2
2
0
0
0
2
1
1
2
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
1
0
0
0
2
0
2
0
0
1
0
0
0
1
0
0
0
3
0
0
2
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
2
0
1
3
1
0
0
0
0
2
2
0
0
0
0
0
2
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
2
2
1
0
2
0
3
1
2
0
1
2
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
4
1
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
1
1
1
2
0
0
0
0
0
1
2
0
0
0
1
0
0
0
1
0
0
0
0
2
0
1
0
1
1
2
0
0
0
0
0
1
0
0
0
3
0
1
0
0
0
1
0
0
0
0
0
0
0
2
1
2
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
3
0
0
2
1
0
0
0
0
1
2
0
0
0
1
0
2
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
1
2
7
0
2
0
3
1
0
0
0
1
0
0
0
0
2
1
2
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
1
2
1
4
2
1
0
0
0
3
2
1
0
0
0
2
0
0
0
1
0
1
0
0
1
0
0
0
1
0
2
0
0
0
1
1
2
0
1
0
0
2
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
1
0
0
0
1
0
0
1
0
0
1
0
2
1
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
2
2
0
2
0
0
0
0
0
0
4
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
1
1
0
2
3
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
1
2
0
0
2
0
0
1
0
0
0
2
0
1
0
2
0
3
0
0
0
0
1
1
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
1
2
0
2
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
2
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
2
5
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
3
0
0
0
2
0
0
0
0
0
1
0
0
0
1
2
0
2
0
2
0
1
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
4
0
0
0
0
0
1
0
0
1
1
0
0
2
1
0
0
0
0
0
0
0
0
1
0
1
3
0
0
2
0
0
0
2
0
0
0
2
1
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
2
0
2
0
0
0
2
0
2
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
2
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
2
2
1
0
0
1
1
2
0
2
2
0
2
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
2
0
0
1
2
0
2
1
0
1
0
0
0
2
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
1
1
1
0
2
0
2
0
0
0
0
0
0
0
2
2
0
1
3
2
0
3
0
0
0
1
0
0
0
1
1
0
1
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
2
1
1
2
1
2
2
0
4
1
0
0
2
0
1
0
2
0
0
0
1
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
2
0
0
0
1
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
1
1
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
2
0
0
2
0
0
4
0
0
2
0
0
0
1
1
0
2
0
2
0
0
0
2
1
0
1
0
0
0
2
1
0
0
0
1
0
0
0
2
2
2
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
2
0
0
0
2
0
1
2
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
1
2
0
1
0
0
3
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
1
1
0
0
0
0
0
0
3
0
0
0
0
0
0
4
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
5
0
0
0
2
0
0
1
0
1
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
3
3
1
3
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
5
0
1
0
2
0
0
0
1
0
0
1
0
2
8
0
0
0
0
0
0
0
0
1
3
1
2
5
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
1
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
2
2
2
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
2
1
0
4
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
2
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
1
1
0
0
2
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
2
0
2
0
0
2
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
3
0
1
0
1
0
0
2
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
2
0
0
1
2
0
0
4
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
3
2
1
0
0
0
1
3
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
1
1
0
2
2
0
0
0
0
1
2
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
1
2
1
0
0
2
0
0
0
0
2
0
0
0
2
2
0
1
1
0
1
0
0
0
2
0
1
1
0
2
2
0
1
0
0
0
0
0
0
0
2
0
0
2
1
1
1
2
0
0
0
2
0
0
2
0
2
0
0
0
0
0
1
0
0
1
0
0
0
1
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
2
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
2
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
2
0
2
2
1
0
0
1
2
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
3
0
2
1
0
0
0
2
1
2
1
0
0
0
0
0
1
0
0
0
1
0
3
0
0
5
0
0
0
0
2
1
1
0
1
1
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
1
0
4
0
0
0
0
0
1
3
0
1
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
1
0
0
0
2
0
0
0
0
0
0
0
3
1
0
1
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
3
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
1
2
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
2
0
0
2
2
0
0
1
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
3
0
2
3
0
0
0
0
2
0
1
2
0
0
1
0
0
0
0
2
2
1
0
1
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
3
0
0
0
0
2
0
2
1
0
0
2
0
0
1
0
1
2
2
0
1
0
0
0
0
0
2
1
1
0
1
2
0
0
3
2
0
0
0
0
0
0
2
2
0
0
0
2
0
2
2
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
4
1
2
0
1
2
0
0
1
1
2
0
0
0
0
0
2
0
1
2
0
0
0
2
0
0
0
0
0
2
0
0
0
3
0
0
1
0
0
1
0
2
1
0
0
0
0
0
0
1
0
2
2
0
0
2
0
0
0
0
2
0
1
1
0
0
0
1
0
0
1
1
0
0
0
1
1
0
4
0
0
0
0
2
0
2
0
0
0
0
0
1
0
1
1
1
2
1
1
0
0
0
0
6
0
0
2
2
0
0
0
1
5
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
1
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
2
3
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
2
1
2
0
0
0
1
0
0
0
1
0
1
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
3
0
1
2
0
0
1
2
0
0
1
1
0
0
0
1
0
0
0
2
0
2
0
0
2
2
2
0
0
1
2
0
0
1
0
0
2
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
2
2
0
1
0
7
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
1
0
1
0
2
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
2
2
0
3
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
3
0
0
0
0
2
2
0
0
0
1
1
0
1
1
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
3
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
1
0
2
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
2
2
1
0
1
1
2
0
2
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
1
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
3
1
0
0
0
0
1
1
2
0
0
0
2
0
0
0
0
0
1
0
9
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
1
0
3
3
1
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
1
0
2
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
3
0
0
1
3
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
9
0
0
0
2
0
0
0
0
3
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
2
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
1
0
0
0
0
0
2
0
0
1
2
2
0
0
0
0
1
2
0
0
1
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
2
1
1
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
1
0
1
0
2
0
0
1
0
0
1
0
0
0
0
2
0
1
0
0
0
1
0
0
2
1
0
0
0
0
2
0
1
0
0
2
1
0
0
1
0
0
5
0
0
2
1
1
0
1
2
0
0
2
2
0
1
0
1
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
4
0
0
0
2
1
3
2
0
0
2
2
0
0
2
2
0
0
0
0
2
1
1
0
0
0
0
2
0
0
2
1
0
0
1
0
0
0
0
0
0
2
1
1
0
0
2
0
2
1
0
0
3
1
2
0
0
0
0
0
0
0
0
2
3
0
0
1
1
0
2
0
2
0
0
0
0
0
0
0
2
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
3
0
1
0
0
0
0
2
0
0
0
1
1
0
0
1
0
0
4
0
0
2
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
1
2
2
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
2
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
7
0
0
0
0
2
0
2
1
0
2
0
0
2
2
0
0
0
0
2
1
3
0
0
0
0
0
0
1
2
2
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
2
3
2
1
0
0
0
0
0
0
0
0
1
2
1
1
0
5
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
2
0
7
1
1
0
1
0
1
0
0
1
0
0
0
1
0
2
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
1
1
1
1
2
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
2
1
1
0
0
0
2
0
0
0
3
0
0
1
1
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
1
1
1
0
0
0
0
2
2
0
0
0
2
2
1
0
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
1
0
2
1
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
2
0
0
0
2
0
0
0
0
0
5
0
0
0
0
2
0
0
2
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
7
2
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
3
0
0
2
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
1
0
0
0
1
0
0
2
0
0
1
1
0
1
0
0
0
0
1
0
0
2
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
1
0
1
2
1
0
2
0
0
0
0
1
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
2
0
2
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
1
0
1
0
0
0
1
2
0
0
0
0
2
0
1
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
3
0
0
1
2
0
0
0
0
0
0
1
2
0
4
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
2
1
1
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
2
2
0
3
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
1
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
4
0
2
2
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
2
2
0
3
0
1
0
0
0
0
2
0
2
3
0
0
0
0
0
1
0
2
1
0
1
0
1
0
0
1
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
1
1
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
2
0
0
4
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
2
2
0
0
0
2
2
0
0
1
1
1
0
0
0
0
2
3
0
0
2
0
0
1
1
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
2
0
0
0
3
0
2
0
2
2
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
2
0
3
2
0
0
2
1
0
0
2
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
1
0
0
1
0
0
0
1
0
2
0
3
1
0
0
0
2
0
0
0
0
0
0
0
1
4
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
3
2
0
1
0
0
1
1
0
1
0
2
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
1
0
2
0
0
0
0
0
0
1
0
4
0
2
1
0
2
0
0
0
2
1
1
0
0
0
0
0
0
0
1
2
1
2
0
0
4
0
1
1
0
0
0
1
0
0
0
1
0
1
2
0
0
0
0
1
0
1
4
0
0
1
0
0
2
0
0
0
0
2
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
2
2
0
0
0
0
0
0
0
0
2
2
2
2
0
0
0
0
0
0
1
2
0
0
2
1
1
1
0
2
0
0
0
2
0
0
0
2
1
0
0
0
1
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
1
2
2
2
0
0
2
0
0
0
1
2
0
0
1
2
0
0
2
0
2
0
0
0
1
0
0
2
1
1
0
2
0
0
1
0
0
1
0
2
0
0
0
1
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
2
2
0
0
1
0
0
0
0
0
2
0
1
0
1
3
0
1
0
2
0
0
2
2
0
0
2
0
0
0
0
0
1
0
0
3
0
0
0
2
0
0
0
1
2
0
0
0
0
1
0
0
1
1
4
0
0
0
0
0
2
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
2
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
2
0
2
0
0
1
0
0
2
2
0
1
0
1
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
2
0
0
0
2
0
1
3
0
2
2
2
0
2
0
0
0
2
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
2
0
0
2
0
0
0
0
1
0
0
2
0
0
2
2
1
1
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
2
1
0
1
0
3
0
0
0
0
0
0
0
1
0
0
1
1
0
2
1
0
1
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
1
0
2
2
1
0
0
0
1
0
0
0
3
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
3
0
2
0
0
0
0
1
0
0
2
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
3
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
2
2
0
1
0
1
2
1
0
0
0
0
0
0
0
2
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
2
0
0
2
0
0
0
0
1
0
0
2
3
2
2
2
0
0
0
0
0
2
2
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
2
0
0
1
0
1
0
0
0
0
0
2
0
0
9
0
0
0
0
0
0
0
5
0
1
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
1
0
0
0
0
0
1
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
2
0
0
0
1
0
0
2
0
1
2
0
0
2
1
2
0
1
0
1
1
0
2
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
5
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
1
0
1
1
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
1
2
0
1
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
1
0
0
0
0
0
2
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
1
1
0
1
1
0
0
0
0
0
4
0
0
2
2
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
2
1
2
0
0
1
0
0
2
0
0
0
0
0
0
2
1
0
0
0
1
1
0
0
0
0
0
3
0
2
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
2
2
2
0
0
1
0
0
2
1
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
1
1
3
0
2
4
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
3
3
2
1
0
1
0
0
0
2
0
0
0
0
2
0
0
1
0
0
2
0
0
0
1
0
0
0
1
2
1
1
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
3
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
5
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
1
2
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
2
0
0
0
0
0
1
0
0
2
1
0
3
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
1
0
0
1
0
1
0
2
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
2
2
0
1
0
2
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
2
0
0
0
0
1
1
3
2
0
1
0
0
2
0
0
2
0
0
0
4
1
0
2
0
0
2
0
1
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
1
1
0
0
0
0
1
0
2
0
0
0
2
1
2
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
1
1
0
0
0
0
0
0
0
1
2
2
0
1
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
7
0
1
0
0
1
0
0
2
0
1
0
0
1
0
5
0
0
0
0
0
1
0
0
1
0
0
0
2
1
1
0
0
2
0
0
2
1
0
1
2
0
2
2
0
0
2
0
2
0
0
2
0
0
0
2
1
1
2
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
3
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
2
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
4
1
0
0
0
0
0
1
2
1
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
2
0
0
1
0
0
0
2
1
2
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
4
0
0
2
0
0
0
3
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
1
3
0
0
0
1
0
1
1
0
0
0
0
0
0
2
0
0
1
0
0
1
0
5
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
3
4
1
3
0
0
0
2
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
2
0
0
1
3
2
0
1
2
2
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
3
0
0
1
1
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
2
0
0
0
0
2
0
2
1
0
0
0
1
0
0
3
1
0
1
0
0
0
0
0
1
2
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
2
0
0
1
2
0
0
0
0
0
1
0
3
0
0
0
0
0
1
1
2
1
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
1
0
1
0
0
0
0
2
0
0
0
0
0
1
4
0
2
0
0
2
0
0
0
0
0
1
0
1
0
0
0
3
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
3
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
2
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
1
0
2
0
0
2
0
0
0
0
0
3
2
0
0
0
0
0
0
1
0
2
2
0
2
0
1
0
3
2
1
0
3
2
6
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
5
0
0
3
0
0
2
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
1
1
2
0
2
1
3
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
2
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
3
0
1
0
0
0
2
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
2
2
2
0
0
2
2
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
2
0
2
2
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
1
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
1
2
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
2
0
1
1
0
0
0
3
1
1
0
1
0
0
0
0
0
1
0
1
2
0
0
0
2
0
0
0
0
0
0
1
0
0
3
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
2
2
2
1
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
3
0
3
1
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
3
0
0
1
0
0
0
0
2
4
1
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
1
0
2
0
2
2
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
4
0
0
0
0
0
0
0
2
1
0
2
0
0
2
0
0
0
2
0
2
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
2
1
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
1
1
0
5
0
0
0
3
0
0
0
0
1
1
0
0
1
0
0
2
0
0
0
1
2
0
0
1
2
0
0
0
2
0
0
0
2
1
0
2
0
3
0
0
1
0
1
0
2
2
3
0
1
1
0
0
0
1
0
0
0
0
0
0
3
1
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
2
0
0
0
0
0
0
0
3
2
0
0
0
3
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
1
1
1
1
0
0
0
0
0
2
0
2
0
0
0
0
2
0
2
2
0
0
2
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
1
2
0
0
1
0
0
0
5
0
0
0
0
2
2
2
0
0
2
0
0
0
3
2
2
0
0
0
1
0
5
0
0
0
2
2
2
0
2
0
0
1
1
1
0
0
1
1
0
0
0
0
2
0
0
0
4
2
0
0
0
0
0
1
2
0
2
0
2
2
0
0
0
0
0
0
1
2
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
2
0
2
3
0
0
0
0
4
2
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
2
0
0
1
0
0
1
0
1
1
0
0
0
0
1
0
0
0
2
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
1
1
0
0
2
0
0
0
1
2
0
0
0
1
1
4
0
0
1
5
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
1
2
0
0
0
0
0
0
2
0
0
0
2
2
2
0
0
0
0
1
1
1
0
0
1
2
0
0
1
1
0
1
0
0
0
0
0
1
0
1
2
1
1
1
0
0
0
0
1
2
0
1
0
2
0
2
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
2
2
0
2
0
2
0
0
2
0
0
0
0
1
0
8
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
1
2
0
0
0
2
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
1
0
0
3
0
1
0
0
0
0
0
1
0
0
0
0
4
0
0
1
0
0
0
0
2
2
0
2
0
0
0
4
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
2
0
0
0
3
0
0
2
2
0
0
0
0
1
2
0
0
0
0
3
1
1
2
0
0
1
0
2
0
0
0
0
1
2
1
0
2
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
3
0
0
0
0
0
1
0
0
0
0
2
0
3
0
3
0
0
0
0
1
0
1
0
0
1
0
0
0
0
2
0
1
0
0
2
2
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
5
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
2
0
4
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
3
2
0
0
0
1
0
2
1
3
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
2
0
0
3
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
2
2
2
1
0
2
2
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
1
0
1
2
2
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
2
2
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
3
0
0
0
0
1
2
0
1
0
0
0
0
0
0
1
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
1
2
0
1
0
0
0
0
0
0
2
1
0
2
0
0
3
0
2
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
2
0
1
0
0
0
0
0
1
2
2
0
0
0
2
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
2
0
1
0
0
1
2
0
2
0
0
1
0
0
0
0
3
2
0
0
4
2
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
2
0
0
0
2
1
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
3
0
0
2
0
0
0
0
0
1
0
0
1
1
0
0
1
1
1
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
2
3
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
8
0
0
0
0
2
0
1
0
0
1
0
2
1
0
2
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
3
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
2
0
1
1
0
0
0
0
0
5
0
0
0
0
2
2
2
0
0
2
2
1
0
0
1
0
0
0
0
2
0
0
0
1
0
0
2
0
0
1
2
0
0
0
0
0
0
1
0
2
0
0
0
2
1
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
2
0
0
0
1
2
2
1
0
0
2
2
2
1
0
2
0
2
0
0
2
0
0
2
0
2
2
0
2
0
0
0
0
0
0
1
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
2
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
2
0
1
1
0
0
0
0
0
3
0
0
0
0
0
2
1
0
1
0
0
2
1
0
0
0
0
0
0
2
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
1
0
0
0
0
2
0
0
1
0
0
1
0
3
0
0
0
0
0
2
0
1
0
2
0
3
0
0
1
0
0
2
0
0
1
1
1
2
0
0
2
1
0
0
0
0
2
0
2
0
1
0
0
0
0
1
0
0
0
3
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
1
0
3
1
0
0
1
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
2
2
0
0
0
0
0
0
0
0
1
2
0
0
4
0
1
0
1
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
1
1
1
0
1
0
0
0
0
0
0
0
1
2
1
2
5
0
0
0
0
0
0
1
0
0
1
0
0
0
2
1
2
0
1
0
1
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
2
0
0
1
0
0
1
0
2
1
0
0
1
0
0
0
0
1
0
0
0
4
2
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
2
0
0
0
0
0
1
3
0
0
0
2
0
0
0
0
1
0
0
1
0
0
2
1
0
0
2
2
2
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
3
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
1
3
0
1
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
2
0
1
0
0
0
0
2
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
1
4
0
1
2
0
1
0
0
0
1
0
0
0
2
0
1
0
0
2
0
1
0
2
0
0
0
0
0
0
4
0
0
2
0
1
0
0
2
0
0
1
0
2
1
0
0
0
0
2
1
0
0
0
1
0
2
0
0
0
0
2
0
0
2
0
1
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
2
1
1
0
0
0
2
0
0
0
2
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
1
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
4
0
0
2
0
0
0
1
3
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
1
0
0
0
1
0
1
0
2
0
0
2
0
1
1
2
0
0
0
2
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
1
2
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
2
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
1
0
3
3
0
0
1
0
2
1
0
0
3
1
1
0
1
0
2
0
2
0
2
0
0
2
0
0
1
1
0
0
0
0
0
1
4
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
2
0
0
1
0
0
0
0
2
1
2
1
2
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
1
0
3
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
2
1
1
0
0
2
0
0
0
1
0
0
1
0
1
1
0
0
1
0
0
1
1
0
0
0
3
0
0
0
2
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
1
0
3
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
1
1
3
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
1
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
6
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
2
0
2
0
0
0
0
0
4
0
1
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
2
1
0
0
0
2
1
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
3
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
2
2
2
0
0
0
1
0
0
0
0
0
1
0
0
1
3
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
1
0
1
0
1
2
0
0
2
1
2
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
2
1
0
1
0
2
0
2
0
2
2
0
0
0
0
3
0
0
1
0
1
0
2
3
0
0
0
0
2
0
0
0
0
0
1
1
2
0
2
2
2
0
0
3
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
1
3
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
1
2
0
0
2
0
0
1
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
2
2
3
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
1
1
0
2
2
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
0
2
3
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
1
7
0
0
0
0
1
2
0
0
0
1
1
2
0
1
1
0
0
1
3
1
0
2
1
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
3
0
4
0
1
1
0
2
1
0
0
2
0
0
2
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
2
0
0
2
0
0
2
0
0
0
0
0
0
0
8
0
0
0
2
2
0
2
0
1
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
2
0
2
0
0
0
0
0
1
0
2
0
0
0
4
0
0
1
0
2
1
0
0
2
0
0
1
2
1
0
0
0
0
0
1
0
0
2
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
1
0
0
0
1
2
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
2
0
0
0
1
0
1
0
0
2
2
0
0
2
2
0
2
0
0
0
1
0
1
0
1
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
1
1
0
2
0
1
0
2
1
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
1
0
2
2
0
1
0
0
0
1
0
0
0
0
0
1
0
0
2
1
0
2
0
0
0
0
0
0
1
3
2
0
0
0
0
2
0
2
1
0
0
0
0
2
2
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
2
2
0
0
1
0
0
0
0
0
2
0
2
2
0
1
1
0
1
0
2
1
1
0
0
1
0
0
0
0
2
1
0
0
1
0
0
3
1
0
3
0
0
2
1
0
1
1
0
0
1
0
1
0
0
0
0
1
0
0
1
0
2
0
0
0
1
0
0
0
1
0
0
0
0
2
2
0
0
0
2
1
0
0
0
1
0
0
0
0
2
1
1
0
4
0
0
0
0
0
0
2
0
1
0
0
0
0
3
4
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
3
0
2
0
0
0
2
0
2
2
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
2
2
2
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
3
2
0
0
0
0
2
2
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
2
1
0
1
0
0
1
0
1
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
2
0
2
0
3
0
0
0
2
0
0
3
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
2
0
0
0
0
5
0
1
1
0
0
0
2
0
1
2
0
0
1
0
0
0
0
0
2
0
0
1
1
2
2
0
0
1
0
0
1
0
2
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
2
0
2
0
2
0
2
0
0
2
0
1
0
0
0
1
0
0
1
1
1
0
2
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
1
0
1
2
2
0
0
1
0
1
2
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
3
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
1
2
1
0
0
0
0
2
0
1
0
0
0
0
2
2
0
2
0
0
0
0
2
0
1
0
0
0
3
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
2
2
0
1
0
1
0
0
1
0
0
1
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
1
6
0
2
2
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
3
0
2
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
1
2
0
0
1
0
0
0
1
0
0
1
1
1
0
0
0
0
1
3
0
1
0
4
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
2
1
0
0
0
2
0
1
0
0
0
1
1
0
0
0
0
0
0
2
0
1
1
0
0
0
3
1
1
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
1
0
0
0
0
1
2
0
0
1
0
0
0
1
0
0
0
0
0
2
1
0
0
0
2
1
2
0
0
0
0
0
0
1
2
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
1
0
0
2
0
1
1
0
1
0
1
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
1
1
0
0
2
0
3
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
2
0
0
0
0
3
2
0
6
0
2
1
0
2
0
0
0
1
0
0
0
0
1
7
2
0
0
2
0
0
0
0
0
2
2
1
4
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
1
0
0
1
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
1
2
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
1
2
2
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
3
1
0
0
2
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
2
1
0
0
0
0
2
0
0
1
0
2
2
0
0
5
1
2
2
3
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
2
1
1
3
0
0
0
1
1
0
1
0
0
2
0
3
0
2
0
0
0
1
2
3
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
3
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
1
0
0
2
0
0
2
0
0
0
1
0
1
1
1
0
0
1
0
2
0
0
2
1
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
2
0
1
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
2
0
0
0
3
0
0
1
2
0
2
1
0
2
3
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
1
1
0
0
2
3
1
0
0
0
0
2
0
0
1
0
0
1
1
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
2
2
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
2
1
1
0
1
2
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
3
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
3
0
2
0
1
2
3
2
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
1
0
0
1
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
2
0
0
1
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
4
2
2
0
0
0
3
1
0
0
0
0
0
1
2
1
0
3
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
3
0
0
2
0
1
1
0
0
0
0
2
2
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
4
2
0
0
1
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
6
0
0
0
0
2
0
0
0
3
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
1
0
1
1
1
2
0
1
3
0
0
2
3
0
0
0
3
0
1
1
0
0
0
3
0
0
0
0
0
0
2
2
2
0
2
0
0
1
0
0
0
0
0
0
0
0
1
3
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
2
1
0
0
1
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
2
1
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
5
0
0
0
0
0
1
1
0
1
0
2
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
2
3
0
1
0
0
0
1
1
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
1
0
0
1
2
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
6
2
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
1
2
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
2
0
1
1
2
1
3
0
1
0
1
0
0
0
2
0
0
1
1
0
3
1
0
0
2
0
0
0
2
0
0
1
1
0
1
0
2
0
0
1
0
1
0
0
1
2
0
1
0
2
1
1
0
0
0
0
0
0
0
2
0
0
5
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
2
2
2
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
3
2
0
2
2
0
1
0
1
0
0
0
1
4
0
0
0
0
0
0
0
2
2
0
1
1
0
0
0
0
1
0
0
0
0
0
1
1
0
1
2
5
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
1
2
2
0
0
1
0
1
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
3
0
0
2
0
1
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
10
2
0
0
0
0
0
0
0
0
2
1
0
0
1
0
3
0
1
0
0
0
2
0
0
0
0
1
2
0
1
0
0
0
0
2
0
0
0
0
0
2
0
2
2
2
0
0
1
0
0
2
5
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
1
0
0
0
0
2
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
1
1
0
0
1
1
2
3
1
1
0
0
0
0
0
0
0
2
1
0
0
2
0
2
0
0
0
1
0
0
0
2
3
1
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
2
0
0
2
0
0
0
0
6
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
3
0
0
2
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
2
1
0
2
0
0
0
0
1
0
0
0
2
0
1
2
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
1
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
3
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
2
2
0
0
0
2
0
2
0
0
2
1
0
0
0
0
0
1
0
0
0
0
1
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
8
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
2
1
0
2
0
1
1
0
0
0
1
1
1
1
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
5
0
2
3
0
0
0
2
1
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
2
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
3
0
2
0
1
2
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
1
0
2
1
0
0
1
0
2
0
0
1
0
0
0
0
1
1
0
0
0
1
1
1
0
2
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
2
2
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
2
0
1
0
0
0
3
0
0
2
0
0
0
2
2
0
0
2
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
2
0
1
0
0
1
0
1
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
2
2
1
0
0
2
0
2
0
0
0
1
0
0
0
0
0
2
1
0
1
0
0
1
0
1
2
0
2
0
0
0
0
2
1
0
0
1
0
0
1
0
0
1
0
0
1
0
2
0
1
1
0
0
0
1
0
0
0
2
0
0
2
1
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
2
0
0
0
1
1
1
0
0
0
1
0
0
4
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
2
0
0
2
0
0
0
2
0
1
0
0
1
1
0
0
2
1
0
0
2
0
0
1
0
0
2
0
0
0
0
1
0
0
2
2
1
2
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
1
0
0
2
1
2
0
0
0
0
1
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
2
0
7
0
0
1
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
1
0
5
0
2
0
2
0
0
2
0
2
0
0
1
0
2
1
2
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
1
0
1
0
0
0
0
2
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
1
3
0
0
1
0
0
3
2
0
0
0
1
0
3
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
1
1
0
0
0
1
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
1
0
1
1
2
0
0
1
2
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
2
3
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
1
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
1
1
0
0
2
0
2
0
2
0
0
0
0
0
2
1
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
1
0
2
0
0
0
0
0
2
0
1
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
3
0
1
0
0
2
0
2
0
2
0
1
0
0
2
1
2
0
3
0
2
0
0
0
1
0
0
0
0
2
4
2
0
0
0
0
3
0
0
3
0
0
6
0
5
0
1
0
2
0
0
1
3
0
1
0
1
1
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
1
0
0
4
2
2
1
0
0
1
0
0
0
1
2
2
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
1
0
1
0
2
0
0
0
3
0
0
0
0
2
0
0
1
2
2
1
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
1
0
0
0
0
1
1
1
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
2
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
3
0
0
1
0
0
2
3
0
1
2
0
2
2
0
0
0
0
0
0
2
0
2
0
0
1
0
0
1
0
4
0
0
0
4
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
2
1
0
0
2
0
0
0
0
0
0
2
0
0
1
2
0
2
1
0
0
1
1
0
2
1
2
2
0
0
2
0
3
1
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
2
0
1
1
0
0
0
0
0
2
0
0
0
2
0
0
2
2
2
2
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
1
0
1
2
0
0
0
0
0
2
1
0
0
2
1
2
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
1
2
0
0
1
3
0
0
1
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
3
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
3
0
0
1
0
0
1
1
3
1
0
2
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
2
1
2
1
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
2
1
0
1
1
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
5
2
0
0
2
0
0
2
2
3
1
0
2
0
0
0
0
1
0
0
1
2
2
0
2
1
0
2
0
8
2
0
0
0
1
0
0
0
1
2
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
1
1
0
0
0
2
0
3
0
0
0
2
0
0
1
0
4
0
0
0
0
0
0
1
0
2
2
0
0
1
0
0
2
0
1
3
0
0
0
0
1
0
0
0
1
0
0
2
3
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
2
0
1
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
1
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
2
1
0
1
2
0
0
0
0
1
2
0
1
0
0
0
0
2
1
1
0
0
1
1
0
0
0
0
1
0
0
2
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
2
0
2
0
1
0
0
0
1
0
0
2
0
2
0
0
0
0
3
2
1
0
0
1
2
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
3
0
0
0
0
1
1
2
0
1
0
0
0
0
0
0
0
1
0
1
0
1
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
2
0
2
2
0
0
0
1
2
0
2
0
0
0
0
0
1
0
0
0
0
0
2
1
2
0
0
1
1
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
2
1
2
1
0
0
0
0
0
0
1
0
0
0
1
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
1
3
0
0
0
2
0
0
2
1
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
2
0
3
4
0
0
0
2
1
1
0
2
0
0
1
1
1
0
0
0
3
1
0
0
0
0
2
0
2
0
0
0
0
0
2
0
2
0
0
0
1
0
2
0
0
1
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
4
0
2
0
0
0
0
1
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
1
1
0
2
0
0
0
1
0
0
1
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
1
0
1
2
3
0
2
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
2
0
0
0
0
0
0
2
1
1
3
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
1
0
0
4
0
0
0
1
0
2
0
0
0
0
0
0
0
3
1
0
0
0
1
0
1
0
0
0
0
0
0
2
2
0
0
2
0
2
2
0
0
1
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
2
0
0
1
1
2
0
0
0
1
0
3
2
1
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
1
1
1
1
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
2
1
1
0
0
1
0
0
0
0
1
0
2
2
0
0
0
0
2
0
0
0
3
2
0
0
2
0
0
0
0
1
0
0
0
1
0
2
2
1
0
0
1
2
2
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
2
2
1
0
1
2
2
0
0
2
2
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
4
0
0
0
0
2
0
1
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
1
2
1
0
1
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
3
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
2
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
1
0
0
0
3
0
2
0
0
0
2
1
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
2
0
0
0
3
2
2
0
0
0
1
0
0
1
1
2
1
0
2
0
0
0
1
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
3
2
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
2
2
3
1
0
0
0
0
0
0
1
2
0
0
0
2
0
0
1
2
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
1
2
1
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
1
0
1
0
1
0
1
0
2
2
0
0
2
0
1
0
4
0
0
2
1
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
1
2
0
0
0
0
0
2
0
0
0
1
0
3
0
0
0
5
0
2
5
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
1
1
1
0
2
0
4
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
1
0
1
0
0
0
1
1
2
0
0
1
1
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
1
1
2
1
2
0
0
2
0
1
0
0
1
0
0
0
1
2
1
2
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
2
0
3
0
0
0
1
0
0
1
2
3
1
0
0
0
0
0
0
2
0
0
0
3
0
1
2
0
1
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
1
1
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
2
3
0
2
0
2
0
3
0
2
0
0
0
1
0
0
1
0
0
0
1
2
0
2
0
0
2
0
1
0
0
0
0
0
0
0
3
0
1
0
0
0
1
2
1
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
2
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
3
2
2
2
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
1
2
0
1
0
2
3
0
2
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
2
0
1
0
0
0
0
1
0
3
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
2
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
1
0
1
1
1
0
0
1
1
1
3
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
1
0
1
2
1
2
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
1
1
0
0
0
0
2
1
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
1
2
0
0
0
1
0
0
0
0
3
0
0
2
0
2
0
0
0
2
1
0
0
0
0
0
1
2
1
2
0
2
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
2
2
0
0
2
0
0
0
2
0
2
1
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
4
0
0
1
0
0
2
3
0
0
0
2
0
0
2
0
0
0
1
1
0
0
2
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
6
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
2
0
3
0
0
0
2
0
0
0
1
1
1
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
1
1
0
0
1
1
2
3
0
2
0
1
2
0
0
1
0
0
0
1
0
0
0
0
0
0
2
1
2
2
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
2
0
2
0
1
0
4
0
0
0
0
1
3
0
0
0
1
1
0
0
2
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
1
0
2
0
1
1
0
0
0
0
0
0
1
2
0
0
0
2
1
1
0
0
2
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
3
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
3
1
0
0
0
0
0
0
0
1
0
1
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
1
2
2
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
2
0
0
0
0
1
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
1
2
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
1
1
0
2
0
1
0
0
0
0
2
1
0
2
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
3
0
2
0
2
0
0
0
2
1
0
2
0
1
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
5
1
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
1
0
1
6
2
0
0
0
0
0
1
0
2
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
1
0
0
2
0
1
1
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
1
0
0
3
0
0
0
0
0
2
0
0
0
0
2
2
2
0
0
0
1
0
1
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
2
0
0
5
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
2
2
0
3
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
2
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
4
1
0
0
1
2
1
0
0
4
1
2
1
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
3
0
0
2
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
3
3
1
0
0
0
2
1
2
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
2
2
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
2
0
2
1
0
1
0
1
0
0
1
0
0
1
2
6
1
1
0
0
1
0
0
0
2
0
0
0
2
1
0
2
0
0
0
1
0
1
0
0
0
3
0
0
0
1
0
0
3
0
0
3
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
2
0
1
0
0
2
2
2
0
0
2
1
0
2
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
2
1
0
1
0
0
2
0
2
0
0
1
0
2
0
6
2
1
1
0
2
0
0
0
2
0
0
1
0
0
0
2
1
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
3
0
0
2
0
1
0
0
3
2
2
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
2
0
2
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
3
0
1
1
0
1
0
1
0
1
0
2
0
0
0
1
0
1
1
2
0
2
0
0
0
0
2
2
1
7
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
2
1
2
1
1
0
0
0
0
1
0
1
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
1
2
1
0
0
0
1
0
1
3
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
4
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
6
0
0
0
2
2
0
0
2
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
1
0
1
0
2
0
1
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
2
1
2
0
2
2
0
1
0
1
0
2
0
0
0
2
0
2
0
0
0
1
2
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
3
0
0
1
0
0
0
1
0
0
0
1
2
0
0
0
0
2
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
3
1
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
1
2
0
2
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
2
2
2
0
1
0
0
0
0
0
0
3
0
0
0
0
0
7
0
0
0
1
1
0
0
0
1
1
0
0
2
1
0
0
0
0
0
0
0
0
8
1
1
0
0
2
0
0
2
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
1
1
0
0
0
0
1
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
1
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
1
0
0
0
1
0
0
0
1
0
1
2
0
0
1
0
2
0
0
0
0
0
3
3
1
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
1
1
0
3
0
0
2
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
2
0
0
0
2
1
0
0
0
0
0
0
2
0
2
0
0
2
2
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
2
0
1
1
1
0
0
0
0
0
2
0
0
2
0
3
1
1
0
3
0
0
0
0
0
0
1
1
0
0
2
0
0
2
0
0
0
1
0
0
0
2
0
2
4
5
0
0
1
0
2
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
1
2
0
0
0
0
0
1
2
2
2
0
0
0
0
0
1
2
2
2
1
0
3
0
0
1
2
0
0
0
0
3
0
4
0
0
0
1
0
0
0
0
0
1
1
0
0
2
0
0
0
2
0
0
2
0
0
0
2
2
2
0
0
0
0
0
1
0
0
1
0
0
1
0
0
2
0
2
0
0
0
0
0
1
0
1
2
0
0
2
0
2
0
2
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
2
0
1
0
0
2
0
0
2
0
0
1
0
0
2
0
0
0
3
2
0
0
0
0
1
0
0
1
0
1
1
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
2
0
0
0
2
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
2
0
2
0
1
2
2
0
2
0
0
0
0
0
0
0
1
1
1
0
2
1
0
2
0
2
0
0
5
0
0
0
0
0
1
1
2
2
1
0
1
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
1
0
0
1
0
4
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
2
2
0
0
0
0
0
0
1
2
2
1
3
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
2
2
0
0
1
0
0
0
2
2
0
0
1
0
0
1
0
0
0
1
2
1
0
2
0
0
1
2
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
1
0
0
0
0
0
2
0
4
0
0
1
1
0
0
0
0
1
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
3
0
2
0
0
0
0
0
0
0
5
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
3
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
1
1
0
0
0
3
0
0
0
1
0
2
0
2
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
2
1
0
0
2
0
0
0
2
1
0
0
0
2
0
0
3
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
4
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
1
0
0
0
2
0
3
0
0
0
0
1
0
0
0
0
1
0
0
2
2
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
2
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
2
2
0
0
2
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
2
2
0
2
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
2
2
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
2
1
0
1
1
0
0
0
0
0
3
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
9
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
3
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
2
2
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
5
1
0
2
0
0
0
0
0
0
2
2
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
2
1
0
0
1
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
1
1
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
1
0
0
0
6
0
2
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
2
1
0
2
3
0
0
0
1
2
0
2
2
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
1
0
2
2
0
0
1
2
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
1
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
2
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
3
1
0
0
0
0
0
1
0
2
0
3
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
2
0
0
0
1
0
2
0
0
0
0
0
1
0
2
2
0
0
2
0
0
0
0
0
0
0
1
0
0
3
0
0
0
3
0
0
0
1
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
2
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
5
0
0
2
0
0
0
0
0
0
0
2
0
1
0
1
0
2
0
0
0
0
0
0
0
1
2
2
0
2
2
1
0
2
1
0
2
0
0
6
1
0
0
0
2
0
2
0
0
2
0
0
0
2
0
0
0
3
1
2
0
0
1
0
0
2
0
0
3
2
0
0
0
0
3
0
0
0
1
1
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
2
1
0
1
3
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
2
1
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
3
0
3
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
2
2
0
1
0
0
2
2
0
0
0
0
1
0
1
0
0
1
0
4
0
1
1
0
0
0
0
2
0
0
3
0
0
2
0
0
0
1
0
0
1
1
0
0
1
0
6
0
2
0
0
2
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
5
0
0
1
2
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
1
0
0
0
2
0
1
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
1
0
0
0
2
0
3
0
0
0
1
1
0
0
0
2
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
1
0
0
0
1
2
1
0
0
1
2
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
1
2
2
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
2
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
5
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
3
0
2
2
0
1
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
2
1
0
0
0
1
0
1
2
0
0
0
0
2
2
0
0
0
1
0
0
2
1
2
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
2
0
0
0
0
1
2
0
1
3
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
1
0
0
1
0
2
0
0
0
0
2
3
0
4
0
0
0
1
0
0
0
0
0
0
2
0
1
1
0
0
0
0
2
0
1
0
0
0
1
2
0
0
0
2
0
1
1
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
2
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
6
0
1
0
0
0
0
1
0
2
3
0
2
0
0
0
2
0
2
3
2
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
1
0
1
0
0
2
0
3
0
0
0
1
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
1
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
2
3
0
1
1
0
1
1
0
0
0
2
1
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
3
0
0
1
0
0
2
0
2
0
1
3
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
1
0
0
0
1
1
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
1
0
0
0
0
1
0
0
0
0
0
2
0
1
2
1
0
0
3
0
1
2
2
0
0
1
1
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
2
1
0
2
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
1
0
3
0
1
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
2
0
2
1
2
0
1
0
0
0
0
0
1
0
0
1
0
0
3
0
1
0
1
1
0
0
0
0
0
1
0
1
1
1
0
0
0
0
2
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
2
0
2
0
2
0
0
2
0
2
2
0
0
0
1
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
2
2
1
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
1
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
5
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
3
0
2
0
0
0
1
0
2
2
0
0
0
1
2
0
0
0
0
0
0
0
2
2
1
1
0
0
0
2
2
0
2
0
2
2
1
1
0
0
0
2
0
0
2
0
1
1
0
0
0
0
2
3
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
1
0
0
2
0
1
3
0
0
0
0
0
0
1
1
0
1
0
0
0
2
2
0
2
0
0
0
1
0
0
0
1
0
0
2
1
1
0
0
1
0
0
2
0
2
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
1
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
3
2
0
0
0
3
8
0
0
0
0
0
0
1
0
0
0
0
2
2
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
1
3
0
0
1
0
1
0
0
0
0
0
1
0
3
2
1
0
0
0
0
0
0
0
0
1
0
0
0
4
2
1
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
3
0
0
1
0
0
0
3
1
2
0
2
0
0
3
0
0
0
0
0
0
0
0
3
0
0
0
2
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
3
2
2
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
3
0
1
0
2
1
0
0
2
0
1
0
1
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
1
2
0
2
1
0
0
0
2
1
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
8
0
0
0
0
1
0
20
0
2
0
0
0
1
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
2
2
0
0
0
1
0
0
0
0
0
0
0
1
1
2
1
0
0
1
1
0
2
0
1
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
1
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
1
0
0
3
16
2
0
0
2
0
0
2
0
0
0
0
1
1
1
2
0
2
0
2
0
1
0
0
0
2
0
0
0
2
0
1
0
0
0
0
1
2
0
0
0
1
0
0
0
2
0
2
0
5
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
2
2
3
1
0
3
2
1
0
2
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
1
0
1
1
0
0
9
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
3
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
2
0
2
1
0
0
2
0
1
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
2
0
0
1
0
2
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
1
0
0
0
3
0
9
0
2
2
0
0
0
5
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
2
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
3
1
0
0
0
0
0
1
1
0
4
0
0
0
2
2
0
0
0
1
1
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
2
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
2
2
2
1
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
3
2
0
0
2
0
0
1
1
0
2
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
5
0
2
0
2
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
3
0
1
7
0
0
1
0
0
0
2
0
0
0
0
1
0
2
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
2
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
2
1
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
1
0
2
0
0
3
0
0
0
0
1
0
0
0
3
1
1
0
1
0
0
0
2
0
2
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
1
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
4
0
0
0
0
0
2
1
0
0
0
0
0
3
0
0
0
0
1
0
0
0
2
0
0
0
0
2
1
2
6
1
3
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
2
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
2
0
0
0
2
2
1
0
0
0
0
0
0
2
2
2
0
1
0
2
1
1
0
0
0
0
1
0
1
1
0
1
0
0
0
0
2
2
2
0
0
1
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
2
5
0
0
2
0
0
1
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
2
2
2
0
0
0
0
2
2
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
1
0
2
2
1
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
2
1
0
0
1
0
2
2
0
3
2
0
0
0
0
0
1
0
1
1
1
1
0
0
0
0
1
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
2
2
0
0
0
0
3
1
0
0
0
2
0
0
1
0
2
0
0
0
1
2
0
0
2
1
0
2
0
0
0
0
0
2
2
1
6
0
0
0
2
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
1
0
0
0
0
2
0
1
0
0
1
2
0
0
2
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
4
0
0
1
0
1
2
0
2
0
0
0
0
1
0
1
0
0
0
0
1
1
1
0
1
0
0
0
0
0
1
2
0
1
0
0
0
0
0
2
0
2
0
3
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
2
2
2
2
0
0
0
0
0
1
0
1
0
3
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
3
2
0
0
0
1
0
0
0
1
0
0
0
0
0
3
0
1
0
2
1
1
2
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
1
0
2
1
0
0
1
0
0
0
2
2
2
0
0
0
2
1
0
1
0
1
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
1
0
1
0
0
2
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
2
0
0
0
5
1
0
0
1
0
1
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
2
4
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
1
1
0
0
0
0
1
0
2
0
0
1
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
1
2
2
0
0
1
0
1
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
2
2
0
1
0
0
0
2
3
2
0
0
2
0
1
0
0
0
0
3
0
0
0
0
0
3
0
2
1
0
2
0
0
2
0
0
3
0
2
1
2
0
0
0
0
0
0
0
2
0
1
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
1
0
0
1
0
0
2
0
0
1
0
1
0
0
0
1
0
1
1
2
0
1
1
2
0
0
0
2
0
0
0
0
0
0
0
1
0
2
1
1
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
4
0
0
2
3
0
0
0
1
0
0
0
0
0
1
0
2
2
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
2
0
1
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
2
0
2
0
2
0
0
0
0
2
0
0
0
0
1
1
0
1
0
0
4
0
2
0
0
0
0
2
0
1
0
0
2
0
0
2
1
0
1
1
1
0
1
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
1
0
0
2
0
0
2
1
0
2
0
0
0
0
6
0
0
0
0
3
0
0
1
1
0
0
0
0
0
0
1
0
0
0
3
0
0
2
0
1
2
0
0
2
0
0
0
0
2
0
0
2
0
0
17
1
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
2
0
1
0
0
0
0
0
2
0
0
1
1
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
3
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
2
5
0
0
1
0
0
0
0
0
3
2
0
0
1
0
0
1
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
2
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
4
2
0
0
0
1
1
0
0
0
2
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
1
2
0
0
0
0
1
0
0
7
0
0
0
1
0
1
1
0
0
0
0
0
1
0
1
0
0
2
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
1
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
1
0
0
4
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
3
0
2
0
0
2
0
0
0
1
0
0
2
0
0
1
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
4
0
2
0
0
1
2
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
1
0
2
0
1
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
2
0
0
1
1
0
1
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
2
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
1
1
1
1
1
0
1
2
0
0
1
1
0
0
0
1
2
0
0
2
0
0
1
2
0
0
2
0
0
2
0
0
1
0
0
3
0
2
0
0
0
0
0
2
2
0
0
3
2
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
1
3
2
1
0
0
0
2
0
2
0
0
1
2
0
1
0
0
0
0
0
0
0
0
2
0
3
0
0
1
0
1
0
0
0
1
0
0
0
0
0
2
1
0
1
0
0
1
0
0
0
2
0
1
1
0
0
0
0
0
0
2
0
4
1
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
5
0
1
0
2
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
1
0
5
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
3
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
6
0
0
0
2
0
0
1
2
0
0
2
0
0
1
0
0
0
2
1
1
0
0
0
0
1
0
0
0
2
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
2
1
0
0
0
0
0
0
0
0
0
1
2
0
0
3
0
1
2
2
0
0
0
1
0
0
0
0
0
2
1
0
0
1
0
3
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
2
0
3
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
2
0
0
2
3
0
0
0
1
1
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
3
0
0
2
1
0
0
0
2
1
0
0
0
0
0
0
1
0
2
0
1
1
2
1
0
0
4
0
1
0
0
0
1
0
0
1
0
2
2
1
0
0
0
0
2
2
1
0
0
0
2
0
1
0
2
0
1
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
1
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
2
0
1
0
2
0
0
1
2
2
0
0
0
0
1
0
0
2
0
0
0
3
0
1
0
2
1
0
0
0
0
2
2
0
0
0
0
1
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
3
1
0
0
5
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
3
0
0
2
2
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
2
0
0
0
1
1
2
0
2
0
0
0
0
0
0
0
0
1
2
0
1
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
1
1
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
2
0
1
0
0
0
1
0
0
2
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
2
0
0
1
1
1
2
0
0
0
1
0
0
1
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
1
3
2
4
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
3
0
3
2
1
0
0
1
0
0
0
0
2
0
0
2
0
0
0
4
0
1
2
0
0
0
0
0
2
1
0
2
0
4
0
3
0
0
2
0
0
2
0
0
0
0
2
0
1
0
0
1
2
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
1
1
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
2
2
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
2
0
1
0
0
0
3
2
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
1
2
1
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
2
2
0
0
0
6
0
0
1
2
2
2
0
0
0
2
0
0
1
0
2
0
0
0
0
0
2
1
2
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
1
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
2
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
1
0
1
0
0
0
0
0
3
1
0
0
0
0
1
0
2
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
1
1
2
0
1
1
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
3
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
4
0
0
0
0
0
0
3
0
0
0
1
1
0
0
0
1
1
0
0
3
1
1
0
0
2
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
4
0
0
1
2
0
0
0
1
0
0
0
1
1
0
3
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
1
0
1
0
4
0
0
1
0
1
1
0
0
0
1
0
2
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
2
0
0
4
0
1
2
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
2
2
0
0
0
0
2
2
0
0
0
0
0
0
0
2
1
0
0
2
1
2
0
0
0
0
2
0
0
0
1
3
0
0
0
3
0
0
0
3
0
1
2
0
0
0
1
0
0
3
3
0
1
0
0
0
0
0
0
1
0
2
1
0
0
0
2
0
1
1
0
0
4
0
0
0
0
1
2
0
1
0
0
0
0
4
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
2
3
0
0
0
0
1
0
1
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
1
2
1
0
2
2
0
0
0
1
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
2
0
2
0
1
2
0
0
0
0
2
0
1
2
0
2
1
0
2
0
0
2
0
2
2
0
0
0
0
1
2
0
1
0
0
0
1
3
0
2
0
0
2
0
1
2
1
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
1
1
2
1
0
0
0
1
0
0
0
0
2
2
1
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
1
3
4
3
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
1
1
0
2
1
2
0
2
0
3
1
0
1
0
0
1
0
0
0
1
0
2
2
0
2
0
0
0
2
1
0
1
1
0
0
2
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
1
1
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
2
1
0
0
0
2
1
0
0
0
0
1
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
4
0
0
0
1
0
0
1
0
0
0
0
1
2
0
1
1
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
1
0
1
0
0
0
0
0
0
0
0
1
1
0
1
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
2
0
0
1
2
3
2
0
0
0
0
2
0
0
1
0
0
0
0
1
0
2
2
0
3
3
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
5
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
2
2
1
0
0
0
0
3
2
0
0
2
0
0
0
2
2
0
1
2
1
2
0
0
1
0
0
0
0
2
1
2
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
2
2
1
1
0
0
2
0
4
0
0
0
0
0
1
0
1
0
0
2
1
3
2
0
0
0
0
2
0
0
2
0
0
1
2
0
1
0
0
1
0
0
0
1
0
0
2
1
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
1
2
0
2
0
0
0
1
0
0
0
2
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
2
0
0
0
0
1
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
2
0
0
4
0
0
2
0
1
0
0
0
3
0
5
0
2
1
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
2
0
0
0
0
0
2
1
0
0
2
1
0
0
0
0
1
0
0
0
3
1
7
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
1
2
1
0
0
0
0
1
0
1
4
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
2
1
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
5
0
2
0
1
0
0
2
0
2
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
2
2
0
2
0
0
0
1
0
1
0
0
3
2
1
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
4
0
0
2
2
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
3
0
0
1
0
0
3
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
2
2
1
2
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
1
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
2
0
2
0
2
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
2
2
0
1
2
2
0
1
2
0
1
0
0
2
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
3
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
2
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
3
2
1
0
0
2
0
0
0
0
2
1
1
2
0
1
0
1
1
0
2
0
0
0
0
2
0
0
0
0
0
2
0
3
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
3
2
2
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
2
2
1
1
0
0
0
0
1
0
0
0
3
0
0
1
1
0
0
0
0
0
0
0
0
1
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
2
2
3
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
2
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
1
0
1
0
0
0
2
0
2
0
0
0
3
0
2
0
0
0
1
0
0
0
2
0
1
0
0
0
0
2
0
2
0
2
0
0
0
0
0
1
2
0
1
0
2
0
2
0
0
2
1
0
2
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
3
3
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
1
0
0
0
3
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
1
1
1
2
1
0
0
0
2
2
1
1
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
2
0
2
2
1
0
2
0
0
0
0
1
0
0
1
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
3
0
0
1
0
0
0
2
2
11
0
3
1
2
0
0
1
0
2
0
1
1
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
3
0
1
1
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
2
0
0
1
1
0
0
2
0
0
0
0
3
0
0
0
0
0
1
0
2
0
0
0
0
2
1
0
0
0
1
1
1
0
2
0
0
1
0
0
0
1
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
2
0
0
0
1
2
0
0
1
0
1
0
0
2
1
0
1
0
0
0
0
2
0
1
2
0
1
2
0
0
2
0
0
2
2
0
0
0
0
0
0
0
1
1
3
1
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
2
1
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
1
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
3
0
0
1
2
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
2
2
2
0
1
0
0
0
1
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
2
0
0
2
0
0
1
2
6
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
1
0
0
0
0
0
2
2
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
2
0
0
0
0
2
2
0
0
1
1
2
2
1
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
1
1
0
2
0
3
0
0
0
2
0
0
0
0
1
0
1
0
1
0
0
2
0
0
0
1
1
0
0
1
0
0
2
0
0
0
0
1
2
0
1
1
0
1
0
2
0
0
2
1
1
0
0
2
0
0
0
0
0
2
2
0
0
0
2
0
1
0
1
2
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
4
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
1
0
4
0
0
0
0
3
2
0
1
1
0
0
0
1
0
0
2
1
0
0
0
2
3
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
4
0
2
1
0
0
1
0
0
0
0
3
0
0
0
2
1
0
1
0
2
2
5
0
0
0
0
2
2
0
0
2
1
0
0
1
0
0
1
0
0
0
2
0
1
0
0
0
0
1
1
0
0
0
0
2
2
0
0
0
2
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
2
2
0
2
1
1
0
2
0
0
2
0
0
1
0
0
2
0
1
0
0
0
0
1
0
0
0
0
11
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
1
0
0
1
2
0
0
0
0
1
0
4
2
1
0
0
2
0
0
0
1
4
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
3
0
0
2
0
2
0
0
0
0
0
0
0
1
0
1
0
1
2
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
2
0
0
0
0
2
1
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
2
2
0
0
0
0
0
1
2
0
0
0
0
0
0
3
0
0
0
1
0
0
1
0
0
0
3
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
2
0
0
0
3
2
0
0
0
0
0
0
0
0
1
0
1
0
2
1
1
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
2
0
0
1
0
0
0
2
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
5
0
1
1
0
2
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
1
0
0
0
1
1
0
0
2
0
2
0
0
0
0
0
1
1
2
1
0
0
0
1
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
1
0
0
0
1
2
0
0
0
2
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
1
0
2
1
0
1
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
2
0
2
2
0
0
0
1
1
0
0
0
0
3
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
3
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
1
0
1
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
2
0
1
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
4
1
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
1
0
1
2
0
0
2
1
1
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
1
0
3
2
1
2
1
0
0
0
0
3
2
1
0
1
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
1
1
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
2
1
1
0
3
2
1
0
0
2
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
4
1
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
2
0
2
0
3
2
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
3
2
2
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
2
0
0
0
1
0
0
0
0
3
0
0
2
0
1
1
12
0
1
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
2
2
1
0
0
0
0
1
0
0
2
2
0
2
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
6
0
0
2
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
1
1
0
0
0
0
2
0
3
0
0
0
1
0
0
1
2
0
0
2
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
1
0
0
4
0
0
2
1
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
4
2
0
0
1
0
0
0
0
0
1
0
2
2
0
0
2
0
0
0
0
0
0
0
2
0
2
0
2
2
1
2
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
1
2
0
0
1
0
0
2
0
0
0
0
0
3
2
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
5
0
3
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
1
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
2
0
0
0
3
1
0
0
0
0
0
2
0
1
5
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
3
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
1
2
1
0
0
2
0
2
2
0
0
0
1
0
0
2
0
8
0
0
0
2
0
1
0
0
1
2
0
0
0
0
0
2
18
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
2
2
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
1
0
0
1
1
1
0
2
2
2
3
0
0
5
0
0
3
2
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
1
0
0
2
0
4
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
2
1
0
1
2
0
0
0
0
0
2
0
0
0
0
2
0
1
2
1
1
0
2
0
1
0
0
0
3
2
2
0
2
0
0
0
0
2
0
1
0
0
1
0
2
2
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
2
1
2
0
1
0
1
1
0
0
0
0
3
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
2
0
1
0
2
0
0
0
1
0
1
0
0
1
0
0
1
3
0
0
1
0
2
0
2
0
0
0
0
2
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
3
0
0
0
3
0
0
0
1
0
3
0
0
0
1
0
2
0
0
2
0
2
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
3
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
1
0
3
1
1
0
0
1
0
0
0
0
1
2
2
0
0
1
0
0
1
0
0
1
0
1
0
2
0
0
1
2
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
2
0
2
2
0
0
0
0
0
0
0
0
3
1
0
2
0
2
2
0
0
2
0
0
2
0
3
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
1
1
0
0
2
2
0
0
0
2
0
0
1
2
0
0
0
1
0
0
0
0
3
0
0
0
0
3
2
0
1
1
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
3
2
1
1
0
0
1
0
0
2
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
2
1
0
0
2
0
0
0
1
0
0
0
0
2
3
0
0
1
0
0
1
0
0
0
1
2
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
3
0
0
0
0
1
0
1
1
0
1
1
0
0
0
2
0
1
0
0
0
0
0
1
0
0
1
2
0
2
0
0
2
2
1
0
0
0
0
0
2
1
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
2
0
0
0
2
0
0
8
0
0
0
0
0
0
0
1
0
4
2
1
0
0
0
0
0
0
2
0
0
0
0
2
2
1
1
0
0
2
1
0
0
0
3
1
0
0
2
1
2
0
2
0
0
2
0
0
0
2
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
2
0
2
1
0
0
2
0
2
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
2
1
0
0
1
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
2
2
0
1
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
2
0
1
0
2
0
1
1
1
0
0
1
0
0
1
0
1
2
1
2
0
0
0
2
3
0
0
0
0
0
0
2
1
1
0
0
2
0
0
0
1
2
0
6
0
0
1
2
0
0
0
0
1
0
1
0
0
2
2
0
1
0
0
2
1
1
2
0
2
2
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
2
0
0
0
0
2
0
0
0
0
1
1
0
1
0
1
2
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
1
0
2
2
0
0
0
1
0
0
0
2
0
1
0
0
2
2
0
2
0
0
0
0
1
1
0
0
1
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
1
0
1
0
0
0
1
0
0
2
0
0
1
2
0
3
1
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
2
0
0
2
0
2
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
2
1
0
0
0
0
2
0
1
3
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
2
0
0
1
0
1
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
1
1
0
1
1
0
1
0
0
2
1
0
0
0
0
0
2
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
1
0
2
1
1
0
2
0
0
1
1
0
1
2
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
1
0
0
3
0
0
0
0
3
0
0
0
0
0
0
0
0
2
2
1
1
0
0
1
0
0
0
0
0
0
0
2
2
0
2
0
1
2
2
0
1
0
1
0
0
0
0
1
0
0
0
0
2
0
0
1
1
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
1
0
1
2
0
0
1
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
3
1
1
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
1
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
2
0
2
1
0
0
0
0
3
0
1
0
1
2
0
0
3
0
1
0
2
0
2
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
1
0
0
2
3
0
1
2
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
1
0
1
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
2
0
2
0
0
0
0
2
1
0
2
0
0
0
0
0
0
2
0
0
1
0
2
1
2
0
0
1
0
0
0
0
2
3
0
0
2
5
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
1
0
0
2
0
0
0
0
0
2
0
0
0
1
0
3
1
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
1
0
0
0
0
2
0
1
0
0
0
1
2
0
0
0
0
2
2
2
0
0
0
0
0
2
0
2
0
0
0
0
1
3
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
2
0
0
2
2
0
2
0
0
0
0
1
0
0
0
0
0
0
1
1
2
1
3
0
0
1
0
0
2
3
0
0
2
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
3
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
4
2
0
1
0
0
1
0
3
0
1
0
0
0
1
2
1
0
0
1
2
0
3
2
0
2
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
2
0
1
0
0
2
1
0
0
0
0
1
0
0
2
0
0
0
3
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
4
0
0
1
2
1
0
0
0
0
0
1
2
0
0
1
0
1
0
2
0
0
0
1
0
0
0
0
0
2
0
2
0
0
1
1
0
2
0
0
0
0
0
1
0
2
1
1
0
2
0
0
1
2
0
1
0
1
2
0
2
2
0
0
0
0
2
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
1
0
2
0
0
0
0
0
1
0
2
0
0
2
2
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
2
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
2
1
0
0
0
1
0
0
0
2
0
0
0
1
0
0
1
1
0
0
0
2
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
2
2
0
0
0
0
0
2
0
0
0
0
0
2
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
2
0
0
0
0
2
0
0
0
1
0
1
2
1
0
0
0
1
1
0
1
0
0
7
2
2
0
0
0
0
0
0
2
4
0
0
0
1
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
2
2
0
1
0
0
3
0
1
0
2
1
0
2
1
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
2
0
2
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
1
2
2
0
0
0
2
0
0
0
1
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
1
1
1
0
0
0
0
0
0
1
1
0
0
4
0
0
2
0
1
0
0
1
2
0
0
0
1
1
2
0
3
0
0
0
0
0
1
0
0
1
0
0
0
0
5
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
1
0
0
0
2
1
0
0
0
2
0
0
2
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
1
3
0
2
0
0
0
2
0
0
0
1
0
1
1
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
2
2
2
1
0
0
0
0
1
0
0
2
0
0
0
1
0
1
3
1
3
2
1
0
0
0
0
0
0
1
0
0
0
0
0
2
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
2
0
2
0
1
0
0
1
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
2
2
0
0
1
0
0
1
0
2
1
0
0
0
0
0
2
2
0
2
2
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
2
0
1
0
0
2
1
3
0
0
0
1
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
3
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
1
0
0
0
0
1
1
0
2
0
2
0
0
1
0
1
0
2
0
0
0
0
0
1
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
2
2
1
0
0
0
0
1
2
0
0
0
0
3
1
0
0
0
0
1
1
0
0
3
0
0
0
0
0
1
1
0
0
0
2
2
0
0
0
1
1
2
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
4
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
1
0
0
2
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
3
1
1
0
0
4
1
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
2
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
1
0
2
0
0
0
2
0
0
0
1
0
1
2
0
1
0
1
2
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
2
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
2
1
2
0
0
0
0
2
0
0
1
2
1
0
1
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
1
2
1
0
0
2
0
0
0
0
0
0
2
2
1
0
0
0
1
1
0
0
0
0
0
0
2
2
0
5
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
2
0
0
1
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
3
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
3
0
0
2
1
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
1
1
0
0
0
0
0
2
3
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
2
0
0
0
0
1
0
0
1
2
0
2
0
0
2
2
0
0
0
2
3
0
1
0
0
2
2
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
1
0
2
1
0
0
1
0
2
1
1
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
2
0
0
0
2
0
0
2
0
1
0
0
1
0
0
0
1
2
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
4
0
6
1
0
0
0
0
1
0
0
0
4
0
1
0
2
0
0
1
0
0
0
0
0
0
0
3
0
1
0
2
0
0
1
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
1
0
2
0
1
0
0
0
0
0
2
0
1
2
0
1
0
0
0
1
0
2
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
5
1
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
3
0
6
0
0
1
0
2
2
0
2
0
0
1
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
2
1
0
0
0
0
2
0
2
0
0
0
1
2
2
0
1
1
0
0
0
0
2
0
1
1
0
0
1
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
8
0
1
3
0
0
0
0
0
2
4
0
0
2
0
0
0
1
7
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
1
1
2
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
1
0
0
0
0
1
1
1
0
2
1
0
0
0
1
0
0
0
0
0
0
1
0
4
0
1
1
2
1
0
0
0
2
0
2
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
7
1
0
0
0
0
1
0
0
1
0
0
0
0
2
1
0
0
0
0
0
5
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
2
1
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
1
2
1
0
0
0
0
0
1
0
0
4
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
7
6
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
1
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
2
0
2
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
1
0
0
0
0
1
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
2
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
1
1
0
1
0
2
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
1
0
0
1
0
0
2
0
2
2
0
1
1
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
2
4
0
0
2
0
2
0
0
2
0
0
3
0
0
0
1
1
0
0
0
0
2
0
2
0
0
2
0
0
0
0
1
2
0
0
1
2
0
0
0
2
0
1
0
0
0
0
0
0
2
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
17
2
0
2
0
0
0
0
2
2
1
1
0
1
0
0
2
0
0
0
2
0
1
0
0
0
0
0
1
1
0
0
1
0
0
2
0
1
2
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
5
0
0
0
0
1
2
0
0
1
2
0
2
0
1
2
2
0
0
0
0
0
2
0
0
1
1
0
1
0
1
0
0
1
0
2
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
1
1
0
2
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
1
1
0
0
0
1
0
0
0
0
0
0
1
0
2
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
3
0
1
0
0
0
0
0
1
2
0
0
3
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
1
0
2
0
0
2
2
0
2
3
0
0
0
0
1
2
0
0
1
0
0
1
0
0
0
0
0
0
4
0
1
0
0
2
0
2
2
0
0
2
0
0
0
0
0
2
0
8
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
1
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
4
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
1
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
2
0
0
0
1
1
0
2
2
0
0
2
0
0
0
2
0
0
0
0
0
2
2
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
3
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
3
0
5
0
0
1
2
0
0
0
0
0
1
0
0
1
2
0
2
0
0
0
0
1
1
1
1
1
0
0
3
0
2
1
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
2
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
1
0
1
1
1
1
2
0
1
0
0
0
0
4
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
1
0
0
0
1
0
1
4
0
3
1
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
2
0
2
1
0
1
0
0
0
1
0
3
0
1
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
6
2
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
2
0
2
0
2
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
1
1
0
0
2
0
5
0
2
0
0
0
1
1
0
0
2
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
2
1
0
0
0
1
3
9
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
2
2
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
3
0
0
0
0
1
1
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
2
2
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
3
2
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
2
0
0
0
1
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
2
1
0
1
0
1
2
0
2
2
2
2
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
3
2
0
0
2
0
1
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
2
2
2
0
2
5
0
0
2
0
0
0
0
2
1
0
2
0
0
0
3
0
0
1
0
1
0
2
0
0
0
2
0
0
0
0
0
1
2
1
2
0
0
1
2
0
2
0
0
0
0
0
2
2
0
0
0
0
0
1
0
2
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
1
0
0
0
2
0
2
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
1
4
0
2
2
0
0
0
1
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
2
0
0
1
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
2
2
0
0
0
0
0
0
1
2
0
0
0
1
2
0
1
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
5
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
2
2
0
2
2
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
2
0
2
0
0
5
2
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
2
0
1
0
0
1
0
2
0
0
0
0
2
0
2
0
0
0
0
2
2
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
2
0
2
1
0
0
0
0
1
0
0
0
0
0
0
2
1
0
1
0
0
1
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
4
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
1
0
1
1
1
1
1
0
0
2
5
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
2
1
0
0
0
0
1
0
1
1
3
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
2
0
1
0
0
1
0
0
2
1
2
0
0
1
1
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
1
1
0
1
0
0
2
0
0
2
1
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
17
0
0
0
2
2
0
0
0
0
2
1
2
0
0
2
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
1
2
0
0
1
0
0
0
0
0
5
0
0
1
0
1
0
0
1
0
1
0
1
0
2
0
0
0
2
0
0
0
0
1
1
1
0
0
2
0
0
0
3
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
1
2
0
2
0
2
0
0
2
0
2
0
1
2
2
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
1
1
0
0
0
1
2
1
0
0
0
0
0
0
0
2
1
0
1
2
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
1
1
0
1
0
0
0
1
4
0
0
0
0
1
2
0
1
0
1
0
0
1
0
0
0
2
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
2
0
1
0
3
2
0
0
1
0
1
0
0
0
0
3
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
1
1
0
2
1
1
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
1
0
0
0
2
0
0
1
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
2
1
0
1
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
1
2
7
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
1
2
0
1
0
0
2
0
0
2
1
0
0
0
2
1
1
1
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
1
0
0
0
1
4
0
0
0
0
0
0
0
0
1
1
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
2
0
0
3
0
0
0
2
1
2
0
0
0
1
2
0
2
0
1
0
0
1
0
1
1
2
0
0
1
1
0
0
0
0
0
0
0
1
2
0
0
0
2
1
0
2
0
0
0
2
0
0
0
0
2
0
0
2
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
2
1
0
2
1
0
0
0
2
0
0
1
2
0
0
1
0
7
0
0
0
3
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
2
3
0
1
0
0
2
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
1
1
0
3
0
0
0
2
0
0
0
0
0
3
0
0
0
1
0
0
0
0
2
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
2
0
0
3
0
2
2
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
2
0
0
0
0
2
1
0
1
0
1
0
2
2
0
0
1
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
2
0
1
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
3
0
0
0
0
0
0
1
0
0
2
2
0
0
3
0
1
0
0
0
0
1
1
0
2
2
2
0
0
0
0
0
2
1
2
1
0
0
0
1
0
1
0
1
0
0
0
2
0
2
2
1
0
1
0
0
0
0
0
2
0
2
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
2
2
0
2
0
2
1
0
2
2
2
0
2
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
1
1
3
2
0
2
0
0
0
1
0
0
0
0
0
2
0
0
2
2
0
2
0
1
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
5
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
1
1
2
0
0
0
0
0
0
1
0
2
0
0
1
1
0
0
3
0
2
0
2
2
0
0
0
0
0
0
0
0
0
1
0
4
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
2
1
0
0
1
2
0
2
2
3
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
2
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
6
0
2
3
0
0
1
0
0
0
2
0
3
0
0
2
1
0
0
0
1
0
0
1
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
1
0
1
2
2
0
1
1
1
5
0
1
0
0
2
0
1
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
1
0
0
0
3
0
0
0
1
0
1
0
0
0
2
0
0
0
0
3
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
1
0
2
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
4
0
0
0
0
0
0
0
4
2
0
0
2
1
0
1
2
0
2
2
0
0
1
0
3
0
3
0
2
2
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
3
0
0
1
0
2
0
0
0
2
1
0
0
0
0
2
0
1
0
0
0
0
0
6
2
1
1
0
0
0
1
2
0
0
2
0
0
0
0
1
2
1
1
0
0
0
0
0
1
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
1
1
0
0
0
0
0
3
5
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
3
2
0
0
0
0
2
0
2
0
0
0
2
0
2
1
0
0
0
1
0
0
1
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
4
1
0
0
0
0
0
0
1
0
0
0
0
4
0
2
0
0
0
0
0
0
1
2
0
1
0
2
1
0
0
0
0
1
0
0
1
2
0
0
0
0
1
0
0
0
2
0
2
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
1
0
1
3
0
0
0
0
2
0
1
0
0
0
2
0
0
0
2
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
2
1
0
2
0
2
0
0
1
1
0
1
0
0
0
0
0
0
0
1
4
0
0
0
2
0
3
0
2
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
1
0
0
0
1
1
2
1
0
0
0
1
1
0
3
3
0
0
0
3
0
0
0
0
1
0
0
0
2
0
0
3
0
0
0
0
1
2
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
1
3
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
2
0
2
0
0
0
0
0
1
2
3
0
1
0
3
0
0
0
1
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
3
1
0
0
0
0
0
3
2
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
6
1
0
0
0
0
1
2
0
1
0
0
0
0
2
0
2
1
0
0
1
0
1
0
0
2
1
0
3
1
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
2
0
2
1
2
0
1
2
5
1
0
0
0
0
1
0
0
2
1
1
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
2
1
0
2
0
1
1
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
1
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
1
0
1
0
2
0
1
2
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
3
0
0
0
2
0
0
2
0
6
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
4
0
0
2
2
0
0
0
0
0
0
2
0
1
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
3
0
0
1
0
1
3
0
0
0
0
0
0
2
2
2
0
2
0
0
0
0
0
0
0
1
0
1
4
0
0
0
1
0
1
0
2
1
0
0
1
0
0
0
2
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
2
1
0
0
4
0
1
0
0
2
1
0
0
2
2
3
0
0
1
0
0
0
0
0
1
0
0
0
0
5
1
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
2
0
7
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
1
1
0
0
1
1
1
2
0
0
0
0
2
1
2
2
2
0
0
2
0
0
2
0
0
0
0
0
0
0
2
2
2
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
3
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
2
0
0
0
0
3
1
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
1
1
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
6
0
0
0
1
1
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
3
1
3
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
1
0
0
2
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
2
0
0
1
0
1
0
1
0
1
0
1
0
0
0
0
2
0
0
1
2
0
2
0
0
0
0
2
0
0
1
7
0
0
0
0
0
2
0
2
0
2
0
1
0
2
0
0
0
0
0
5
0
3
0
2
0
0
2
0
0
0
0
0
2
0
0
0
1
1
0
2
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
3
2
0
0
2
0
0
0
1
1
0
0
0
0
2
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
1
2
0
0
2
1
0
0
2
0
0
1
1
1
1
2
0
2
0
0
0
0
4
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
2
0
0
0
0
0
2
0
4
0
0
7
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
2
0
0
1
1
1
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
2
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
2
0
1
0
2
1
0
0
0
0
0
0
1
0
0
0
2
0
0
3
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
1
0
1
0
0
1
2
0
0
2
0
1
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
2
0
0
2
0
0
1
0
0
1
2
1
2
2
0
2
2
0
0
0
0
0
1
2
0
2
0
2
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
2
0
0
0
0
3
1
0
0
0
0
1
1
0
0
0
1
1
1
0
0
4
2
0
2
0
0
0
0
0
1
0
3
0
1
1
0
4
0
1
1
0
0
0
0
0
0
1
0
6
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
2
0
0
1
0
0
2
0
0
0
0
3
1
2
0
0
6
0
0
0
0
0
4
1
0
0
2
2
0
7
1
0
0
1
0
0
0
2
1
1
3
1
0
1
0
4
0
0
0
0
0
1
0
1
1
0
1
0
0
2
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
2
2
0
0
1
0
1
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
3
1
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
3
0
0
0
2
0
0
0
1
0
0
0
1
0
0
2
0
1
0
2
0
0
1
2
3
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
1
3
0
0
0
2
3
0
1
1
0
3
0
0
1
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
3
0
0
2
0
4
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
1
0
1
2
0
0
0
0
1
1
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
3
0
0
2
2
0
0
0
0
2
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
2
1
1
2
1
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
2
1
0
0
2
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
1
1
1
0
0
1
0
0
1
0
2
0
0
0
3
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
3
0
2
2
0
0
2
2
0
3
0
0
1
0
0
0
0
0
2
1
8
2
4
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
2
0
1
1
1
0
0
0
0
0
0
0
0
1
1
0
0
2
2
0
0
1
0
0
0
1
1
0
0
2
1
1
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
1
0
2
2
1
0
0
0
0
0
0
0
4
0
0
0
2
3
0
0
0
0
2
0
0
0
0
0
0
2
0
3
0
0
0
0
2
0
2
0
0
1
0
0
0
0
3
0
0
1
0
0
2
2
0
1
1
1
0
0
1
2
1
0
0
2
0
0
2
1
0
0
0
2
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
1
0
0
1
0
3
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
3
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
4
1
0
2
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
12
1
0
0
1
1
0
0
0
2
0
0
0
0
3
0
0
1
2
0
2
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
5
0
0
4
0
0
1
0
1
0
1
0
0
1
2
0
0
2
3
0
1
0
0
3
0
0
2
1
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
2
1
0
1
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
2
0
0
0
0
1
0
1
0
0
0
0
2
1
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
1
1
0
1
1
2
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
2
0
2
1
1
0
0
0
1
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
2
0
2
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
4
0
0
0
1
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
2
0
2
1
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
1
2
0
0
1
1
0
0
0
0
2
0
0
0
0
2
0
1
0
2
0
2
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
1
0
0
2
0
2
3
2
0
0
2
0
0
2
0
0
0
0
2
0
0
1
0
0
0
2
3
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
2
0
0
2
0
2
0
0
0
1
0
0
1
0
0
2
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
1
0
1
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
5
0
2
2
1
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
2
1
0
0
0
0
1
2
0
0
3
0
0
0
0
0
2
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
2
0
2
0
1
0
0
1
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
1
0
2
0
0
0
2
0
2
0
0
0
0
1
0
1
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
1
1
1
0
2
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
1
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
2
0
2
0
2
0
0
0
0
0
1
1
0
2
0
1
2
0
2
0
2
0
0
2
0
2
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
2
2
0
0
0
0
0
0
0
2
0
2
0
0
0
1
2
4
1
0
1
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
2
1
1
0
1
0
0
0
0
0
2
0
1
1
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
1
0
0
1
0
3
0
0
3
0
2
0
1
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
2
1
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
2
2
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
1
2
0
0
1
0
2
0
0
0
1
0
1
0
0
2
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
2
0
2
2
0
0
0
0
0
0
1
1
0
0
0
0
6
0
1
0
0
3
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
2
0
0
0
0
0
1
0
0
0
0
0
1
2
3
0
1
1
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
1
1
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
2
0
0
3
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
1
0
0
0
0
2
0
2
2
0
0
0
1
1
2
0
0
0
1
0
2
0
2
0
0
1
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
1
1
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
5
0
0
0
1
0
1
0
2
0
2
0
2
0
0
0
0
1
0
1
2
0
1
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
2
1
0
0
1
2
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
2
1
0
0
0
0
1
0
1
2
0
2
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
6
0
0
1
0
0
1
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
1
0
3
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
1
0
0
2
0
1
0
0
2
0
2
0
0
0
2
2
2
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
2
0
1
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
3
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
2
0
1
1
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
3
1
0
0
2
0
0
0
2
0
0
0
2
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
2
1
0
0
0
0
1
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
3
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
2
1
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
1
0
23
3
2
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
1
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
2
1
0
0
1
3
1
0
2
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
1
0
2
0
2
1
0
0
1
1
0
3
0
2
0
3
0
2
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
2
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
4
0
2
0
2
0
0
3
0
0
0
2
0
0
0
0
0
1
0
0
2
2
1
0
0
0
0
2
0
2
0
1
0
2
0
0
0
1
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
2
7
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
1
1
0
0
0
0
0
2
0
2
2
0
0
0
1
0
0
0
2
0
0
2
0
3
3
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
2
0
1
0
2
0
1
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
2
3
0
1
0
0
0
0
0
0
1
0
0
1
0
1
4
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
1
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
1
0
2
0
2
1
0
0
0
0
0
1
2
0
0
1
1
0
0
2
2
0
0
0
0
0
1
0
0
0
0
1
1
1
1
0
0
1
2
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
3
0
0
0
0
0
4
0
5
0
2
0
0
1
0
1
2
0
0
0
1
0
0
0
1
0
0
2
0
1
2
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
3
0
2
0
0
0
0
1
2
0
0
0
1
0
2
0
0
0
0
0
0
1
1
0
0
0
3
0
0
1
0
2
2
0
0
1
0
0
0
0
0
0
2
0
0
2
2
1
0
1
0
1
0
0
2
0
2
0
2
2
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
2
4
0
0
0
0
0
2
2
1
0
0
0
1
0
1
1
0
0
2
0
1
0
1
2
1
1
1
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
2
0
0
1
0
0
2
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
1
0
1
0
2
0
0
3
1
1
2
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
3
1
0
2
0
0
1
1
0
0
3
0
0
1
1
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
1
2
0
0
2
1
0
1
1
0
0
1
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
2
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
2
2
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
2
0
1
0
0
0
0
0
0
1
1
2
0
3
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
1
1
2
0
1
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
2
0
0
3
0
0
3
1
3
0
1
0
0
0
0
0
1
0
0
1
2
1
0
0
0
0
2
0
1
0
0
0
0
1
0
2
0
0
1
0
0
0
2
0
1
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
2
0
1
0
0
3
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
2
2
1
0
0
2
2
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
5
2
1
2
0
2
0
1
0
0
0
0
2
0
0
2
0
0
0
0
1
2
0
0
0
0
1
0
2
1
0
2
0
0
0
4
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
4
2
0
0
0
0
0
0
2
0
0
1
0
0
0
2
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
3
0
2
1
0
1
0
2
0
0
1
0
0
0
0
1
0
2
0
2
2
1
0
2
1
1
1
0
1
1
0
0
0
0
0
0
0
0
2
0
1
0
0
1
2
0
0
0
0
0
0
2
0
1
1
1
0
2
1
0
0
2
0
0
1
0
4
0
2
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
2
0
0
1
0
0
1
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
2
0
0
6
0
0
0
0
1
1
0
0
0
0
0
0
1
1
3
1
0
1
0
1
0
0
0
1
0
0
2
2
0
0
0
0
0
1
3
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
1
1
2
2
1
0
1
0
1
2
0
2
2
0
2
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
1
1
0
0
0
2
0
0
0
2
1
2
2
0
2
0
0
0
0
1
0
0
1
2
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
1
1
1
0
0
0
0
2
1
1
1
1
0
1
0
2
3
0
2
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
2
1
0
2
0
2
2
0
2
0
0
0
1
0
0
0
2
1
0
0
0
2
3
0
0
0
2
1
1
2
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
3
1
0
2
2
0
0
0
0
0
0
5
2
0
0
2
1
0
1
0
1
0
0
0
1
0
2
1
0
2
0
1
0
0
0
0
3
0
0
0
0
0
0
1
1
1
0
0
0
1
2
0
0
1
0
0
0
0
2
1
0
0
0
1
0
0
0
0
1
2
0
0
2
0
1
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
3
0
0
1
1
1
0
0
1
1
1
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
2
0
0
1
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
4
3
0
2
0
0
0
0
2
0
0
0
0
0
1
0
1
2
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
1
1
0
0
1
0
0
1
0
0
2
0
0
1
0
1
0
0
0
0
0
2
0
0
0
5
0
1
0
2
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
3
0
0
0
2
2
0
1
2
1
0
0
2
1
0
2
0
0
3
0
0
2
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
2
0
0
3
2
0
0
0
1
0
0
0
0
0
0
0
3
2
2
0
0
0
0
5
0
0
0
0
0
2
0
2
0
0
1
0
1
0
0
0
1
1
1
3
0
1
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
5
0
1
0
0
2
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
2
2
2
1
0
0
0
2
0
0
1
2
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
1
0
0
4
1
0
0
2
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
2
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
1
2
0
0
2
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
1
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
2
1
0
0
0
1
0
8
1
0
0
0
0
1
0
0
2
0
1
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
4
0
0
2
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
2
1
0
2
0
0
0
1
2
1
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
2
0
1
0
0
0
2
0
2
2
2
0
2
2
0
0
1
2
0
0
0
0
0
0
0
2
0
1
2
0
3
1
0
0
3
1
0
0
0
1
1
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
2
2
3
0
0
2
0
0
2
0
0
2
0
1
0
2
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
2
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
2
3
0
0
0
0
0
0
0
3
0
3
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
5
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
11
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
1
0
0
1
0
0
0
0
1
0
0
2
1
0
0
0
0
1
0
0
1
2
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
4
0
2
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
1
0
0
0
0
1
1
0
0
0
1
2
2
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
2
0
1
0
1
0
0
0
2
0
1
0
1
0
0
0
2
3
0
0
0
0
0
1
0
2
2
0
0
0
0
0
2
0
0
0
3
1
0
1
0
0
1
2
0
1
1
0
0
1
0
0
1
0
2
2
0
0
0
8
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
3
2
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
2
3
1
2
0
1
0
1
2
2
2
0
1
0
0
0
1
0
1
0
1
1
0
0
0
0
3
0
0
0
0
0
0
1
1
2
0
0
0
2
0
0
2
0
0
2
2
0
1
1
0
0
0
2
2
0
1
2
0
2
0
2
0
0
1
1
2
0
0
1
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
1
2
1
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
1
0
1
1
2
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
2
0
0
2
0
0
2
2
1
0
0
0
1
2
1
0
0
0
0
0
3
3
0
3
2
0
0
1
0
1
1
0
0
0
0
0
0
0
2
0
0
0
6
0
0
2
2
0
1
0
0
1
3
0
0
3
0
2
0
3
2
0
0
2
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
1
1
0
0
2
0
0
0
0
0
0
0
0
3
0
2
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
1
0
0
2
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
1
2
0
0
2
0
0
2
0
0
0
0
1
0
0
1
0
0
0
2
0
1
2
1
0
0
0
0
0
0
2
1
0
0
2
0
0
0
3
0
2
0
0
2
0
0
0
1
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
1
0
0
0
0
1
2
0
1
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
4
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
3
0
0
0
1
1
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
2
2
0
1
0
0
2
0
0
2
0
2
0
5
0
1
0
0
0
0
2
2
0
0
0
0
2
0
0
2
1
0
4
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
1
0
2
1
0
0
1
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
1
4
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
2
0
1
0
0
2
0
1
0
0
0
1
0
2
1
1
0
2
0
2
0
1
0
1
0
2
0
0
1
1
0
0
0
0
2
2
0
3
0
1
0
0
0
1
0
2
2
0
0
1
0
0
2
1
1
0
0
1
0
2
0
0
0
0
1
0
0
1
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
2
1
2
0
0
0
1
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
3
0
1
0
0
0
0
1
0
2
1
0
0
0
0
0
1
2
0
2
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
4
0
1
1
0
0
1
1
2
0
0
0
1
0
2
0
0
2
0
2
0
0
0
0
0
0
1
0
0
1
0
0
2
1
0
2
0
0
0
0
0
3
0
2
0
2
1
0
4
1
0
0
0
0
0
0
0
5
0
0
2
2
0
0
1
2
1
0
2
0
3
2
0
1
0
2
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
3
0
0
2
0
0
1
4
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
1
1
1
1
0
0
0
3
1
2
0
0
5
0
1
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
1
0
0
1
2
0
0
0
1
2
2
0
2
0
0
2
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
1
0
2
2
0
0
0
1
2
2
0
0
1
1
2
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
1
0
1
0
0
0
1
0
1
0
2
1
1
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
2
0
0
1
0
0
0
1
2
3
1
0
0
2
0
1
0
2
1
1
0
0
0
2
0
6
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
6
2
2
0
1
0
0
0
0
0
1
2
0
1
0
1
2
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
2
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
2
0
3
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
3
0
2
0
0
0
1
0
3
0
0
1
0
0
2
1
0
3
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
3
2
0
0
0
0
1
1
1
0
0
0
0
1
3
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
3
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
1
0
2
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
2
5
1
1
2
1
0
1
0
1
0
3
1
1
0
0
0
1
2
2
0
0
2
0
0
0
1
0
2
3
0
1
0
0
2
2
1
0
0
0
0
0
0
1
0
0
2
0
2
0
1
0
0
2
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
1
0
0
2
0
0
0
0
0
2
1
2
0
2
0
0
2
0
0
0
0
0
1
0
0
0
2
0
2
1
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
2
0
0
0
2
1
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
2
1
0
0
0
1
2
2
0
1
2
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
2
3
1
0
1
0
2
1
0
0
0
0
0
1
0
1
2
1
2
0
0
0
2
1
1
1
1
0
2
0
0
3
0
0
0
2
0
1
2
0
0
0
0
1
0
0
0
0
1
3
0
0
0
0
0
3
2
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
3
0
0
0
0
0
1
0
0
2
0
0
0
0
3
1
0
0
0
2
0
0
0
0
0
0
2
0
1
0
2
0
2
0
0
2
0
1
3
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
1
0
1
0
2
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
1
1
0
0
1
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
1
2
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
2
0
0
0
2
2
0
0
0
1
1
0
1
0
0
0
0
1
1
0
0
0
2
2
0
0
0
2
5
0
0
0
0
0
0
2
2
0
0
2
2
0
0
2
0
0
0
2
2
0
2
0
0
1
1
0
2
0
0
0
0
1
1
2
0
1
0
1
1
1
2
0
0
0
0
1
0
0
0
1
2
0
1
0
0
2
0
2
1
0
1
0
0
0
0
0
4
0
1
0
0
1
0
2
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
1
4
1
2
0
0
0
0
0
1
0
0
0
0
1
0
0
3
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
4
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
3
0
2
0
1
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
2
0
2
0
2
0
1
0
0
2
0
0
0
1
0
0
0
0
1
1
0
0
2
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
2
3
0
0
2
2
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
1
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
3
2
0
0
0
0
3
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
2
0
1
0
0
0
0
1
0
0
2
0
1
0
0
1
0
1
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
2
0
0
0
2
2
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
4
0
0
1
1
0
0
2
0
1
0
0
0
0
2
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
1
0
1
1
0
0
0
0
1
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
2
2
1
0
0
3
0
0
0
1
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
2
1
0
0
2
1
0
0
2
0
0
4
0
0
0
3
0
0
3
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
2
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
2
1
0
2
0
0
2
1
0
0
0
0
1
0
1
0
0
2
0
0
0
0
1
0
0
0
5
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
1
0
0
2
1
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
1
3
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
1
0
3
0
0
0
3
0
1
0
0
0
0
0
15
0
1
2
0
0
1
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
1
0
0
0
0
1
0
0
0
1
0
1
0
3
2
0
2
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
1
2
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
1
1
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
1
0
1
0
0
2
1
0
2
1
2
1
2
0
0
1
0
2
0
0
0
0
0
2
1
0
0
0
4
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
2
0
2
1
0
0
0
0
0
0
0
1
0
2
2
0
1
0
3
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
2
0
0
0
0
0
0
2
0
0
2
0
1
1
2
0
0
0
0
0
0
2
4
0
0
0
0
0
1
0
0
2
1
0
0
2
0
0
2
2
0
1
0
0
0
0
2
0
0
0
2
0
2
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
3
0
0
2
0
0
1
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
1
0
2
2
2
0
0
0
0
0
0
0
0
2
2
3
0
0
2
0
0
1
2
2
0
1
1
0
0
0
0
0
0
1
0
3
0
0
0
0
0
1
0
0
2
0
0
2
0
1
0
1
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
2
0
0
2
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
1
1
0
2
0
0
0
2
1
0
1
0
2
0
2
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
5
1
3
0
1
0
0
0
0
1
1
1
0
2
2
0
0
0
2
2
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
1
3
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
2
0
0
2
2
0
1
0
1
2
2
0
0
0
0
1
1
2
0
0
0
0
0
2
2
0
0
1
0
0
0
0
1
0
0
0
2
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
1
0
0
0
2
2
0
0
3
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
1
1
1
0
3
2
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
2
2
0
0
1
2
2
1
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
2
0
0
0
0
0
1
2
2
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
2
0
2
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
1
2
0
2
0
1
0
0
0
2
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
6
0
1
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
2
0
2
2
2
0
1
1
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
2
2
0
2
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
1
2
2
0
0
0
0
0
1
0
2
0
0
1
0
2
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
2
1
1
0
0
1
0
0
2
0
1
0
0
1
0
0
0
0
1
2
2
0
2
0
0
0
0
2
0
0
0
1
0
2
3
3
0
0
2
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
1
3
2
2
0
2
0
0
2
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
3
0
0
0
0
0
0
0
2
0
0
2
1
4
1
1
2
0
0
2
0
1
2
0
3
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
1
3
1
0
5
0
0
1
0
2
3
0
0
0
0
0
1
0
2
4
0
0
2
0
0
0
0
0
0
2
1
0
0
2
0
0
1
0
0
0
0
0
2
2
0
1
0
0
0
0
2
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
13
0
1
1
2
0
1
2
0
0
0
2
0
0
0
2
2
0
2
0
0
0
2
1
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
5
0
0
1
0
0
0
0
0
0
2
0
0
2
1
1
0
2
0
2
0
1
0
0
2
0
2
0
0
0
0
2
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
3
0
0
2
0
1
1
0
0
2
0
2
0
1
0
0
1
1
0
0
2
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
4
0
1
1
2
1
0
0
0
1
1
2
0
2
0
2
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
2
0
0
0
0
0
1
0
2
1
2
0
2
1
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
2
0
2
0
0
0
3
2
0
1
0
2
0
0
2
0
2
0
1
5
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
1
2
4
0
0
0
0
0
1
2
2
0
0
0
0
1
0
0
2
2
0
0
0
1
2
1
2
0
0
0
2
0
2
2
0
0
0
2
0
0
5
0
0
0
0
0
0
0
0
0
1
0
5
2
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
6
0
2
0
1
0
0
0
0
1
0
0
2
0
2
2
0
0
1
0
0
0
2
2
1
0
0
0
0
0
2
0
0
3
0
2
0
0
1
0
0
2
0
1
0
1
0
0
3
0
2
1
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
3
0
0
0
1
3
0
0
1
0
0
0
5
0
0
0
2
1
0
0
0
0
1
0
1
0
2
0
2
0
0
0
0
2
1
0
0
0
0
2
0
1
1
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
2
2
0
0
0
0
1
0
0
1
0
0
0
0
0
2
1
0
0
8
1
2
0
0
1
1
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
2
2
1
1
1
0
1
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
3
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
1
1
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
2
1
0
0
2
1
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
3
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
2
0
3
0
0
1
1
3
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
2
1
0
1
0
0
0
0
0
0
0
0
1
0
0
3
0
2
0
1
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
3
0
0
0
1
3
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
2
0
0
0
0
0
1
3
0
0
1
0
3
0
0
0
2
0
2
0
0
0
0
0
0
2
1
0
4
1
0
1
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
2
0
1
0
0
0
2
0
1
0
2
0
0
0
2
0
0
1
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
1
0
1
4
0
0
0
0
1
2
0
2
0
0
2
2
0
1
0
1
2
0
0
1
1
2
2
0
2
2
0
0
0
1
0
0
0
0
0
0
2
3
0
0
0
0
0
2
0
0
0
0
0
0
3
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
2
1
4
2
1
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
3
1
1
0
2
0
0
2
1
1
1
1
0
0
0
0
2
0
0
2
1
0
2
0
1
0
0
0
1
0
0
0
1
3
0
0
1
0
0
1
0
2
2
0
0
0
0
0
0
1
2
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
2
2
0
0
0
0
1
0
2
0
0
0
2
0
1
0
0
0
0
0
0
4
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
1
0
2
0
0
2
2
0
0
1
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
3
2
0
0
0
0
1
0
3
0
1
3
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
2
0
0
2
0
0
0
0
5
1
0
0
1
0
1
1
0
2
0
0
1
0
0
1
0
0
0
0
3
0
1
1
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
2
1
2
2
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
1
0
0
1
0
2
0
0
0
0
0
1
1
0
0
2
2
0
0
1
0
0
0
3
1
0
2
0
0
3
0
1
0
0
2
1
1
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
1
3
0
1
1
0
0
1
0
2
0
2
0
0
1
2
2
0
0
0
1
0
1
0
2
0
2
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
2
0
0
0
2
1
3
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
2
0
0
1
0
0
2
1
0
0
2
3
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
1
2
0
2
0
0
0
0
4
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
2
2
1
2
0
0
0
0
0
0
0
2
1
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
3
0
0
0
0
0
0
1
1
2
0
0
0
0
2
0
0
0
1
1
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
3
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
1
0
2
2
2
0
0
0
0
0
0
2
0
0
0
2
0
0
1
2
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
4
0
0
0
2
2
1
0
0
1
0
0
0
0
0
2
0
0
1
2
0
1
0
0
2
1
0
0
1
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
1
1
0
0
0
0
3
2
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
3
0
0
1
0
1
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
2
0
2
2
2
4
0
2
1
0
0
0
0
0
0
0
0
0
1
0
1
3
0
1
0
0
1
0
2
0
0
2
0
2
0
1
0
0
3
0
0
0
2
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
2
3
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
1
0
0
2
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
1
2
3
0
3
0
3
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
1
2
0
0
0
2
2
2
0
0
1
2
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
1
0
0
2
0
2
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
3
1
0
1
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
3
0
0
1
0
0
0
2
0
0
0
0
2
2
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
2
0
39
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
1
2
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
3
2
1
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
3
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
1
2
0
5
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
2
2
0
1
2
0
2
0
0
0
1
2
1
0
2
0
1
1
0
0
1
0
0
0
0
0
1
0
2
0
0
2
0
0
2
0
1
0
0
1
0
0
0
2
2
0
1
0
0
0
0
0
0
1
0
0
2
1
0
0
2
0
1
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
7
3
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
1
0
2
0
0
2
2
1
1
0
3
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
4
2
0
2
0
0
1
3
0
0
2
0
1
0
0
0
0
3
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
3
2
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
2
1
1
0
0
3
3
2
0
0
0
2
0
0
0
0
2
0
1
1
1
0
2
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
2
0
1
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
1
1
0
0
0
0
1
0
0
0
4
1
0
0
0
0
1
0
2
0
0
0
1
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
2
1
0
0
2
0
0
0
0
0
1
1
1
0
0
0
1
2
0
1
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
1
2
0
0
0
0
0
0
2
0
0
2
0
1
0
2
1
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
2
0
0
1
0
0
1
0
0
2
2
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
6
1
1
0
0
2
0
0
0
0
1
2
0
0
2
0
0
0
2
0
2
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
4
3
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
1
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
1
0
0
0
1
1
1
0
0
1
0
0
0
0
0
1
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
1
2
0
4
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
1
0
0
0
0
1
0
2
0
0
2
0
2
3
0
2
1
4
0
0
2
2
1
0
2
0
1
1
1
2
0
5
1
3
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
1
0
0
1
1
0
1
0
1
0
0
0
0
1
0
0
2
2
0
0
0
2
0
0
0
0
0
1
0
1
0
3
0
1
0
2
2
0
0
0
0
0
0
0
3
0
0
0
2
2
0
0
0
1
0
2
1
0
1
0
2
0
0
0
3
1
1
2
0
0
0
0
0
0
2
0
0
2
1
1
0
0
0
0
0
0
0
0
3
2
2
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
3
0
0
3
0
0
0
1
2
1
0
2
1
0
0
0
1
0
1
1
1
0
1
0
0
0
1
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
2
0
1
0
2
2
0
0
1
0
0
0
0
0
1
2
3
0
0
2
0
0
0
0
0
0
1
0
0
0
1
1
1
0
1
0
1
0
0
1
0
0
2
0
0
0
0
3
0
0
0
0
2
0
1
0
0
0
0
1
5
0
1
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
2
2
0
1
0
0
0
0
3
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
2
0
1
0
0
2
0
0
0
1
0
1
2
1
0
0
1
2
0
0
1
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
2
1
0
3
0
0
0
0
1
0
1
2
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
2
2
0
4
0
0
0
1
0
1
0
1
0
2
2
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
1
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
2
1
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
2
1
0
0
2
1
0
0
0
1
0
0
3
3
0
1
0
2
0
0
0
2
0
0
1
0
0
0
1
0
0
1
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
2
1
0
1
1
0
0
0
0
0
2
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
1
2
1
0
3
0
1
0
0
0
1
0
0
0
0
1
2
0
0
0
2
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
2
3
0
0
0
0
2
2
0
4
1
0
1
2
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
1
0
0
2
1
2
0
1
0
2
0
0
0
0
0
1
0
1
1
1
2
1
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
2
1
0
0
2
0
0
0
0
0
2
6
1
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
2
0
2
1
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
2
2
0
2
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
1
3
1
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
2
0
2
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
5
1
0
0
1
3
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
2
1
0
1
1
0
2
0
2
0
0
1
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
1
3
0
0
0
0
1
0
0
1
1
0
2
0
0
0
2
0
2
2
0
0
1
0
1
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
3
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
1
0
0
0
0
2
0
0
1
0
0
3
2
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
7
0
0
0
1
0
0
0
2
0
0
1
1
0
2
0
0
0
0
0
0
0
2
2
0
0
0
1
0
2
1
0
0
2
2
0
0
1
0
0
0
1
0
0
2
3
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
1
1
0
0
4
0
0
0
0
0
2
0
2
0
2
2
2
0
1
1
0
2
0
2
0
1
2
0
0
0
0
0
2
0
1
1
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
1
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
2
2
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
1
1
2
0
0
1
3
1
2
1
1
1
0
0
0
0
2
0
3
0
2
0
0
1
1
0
2
0
2
0
1
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
2
0
0
2
2
1
0
0
2
1
3
1
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
2
1
0
0
1
0
0
0
1
2
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
1
1
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
2
3
0
0
1
1
0
0
0
2
0
0
2
0
0
0
0
0
1
4
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
3
0
1
1
0
0
2
1
3
0
2
1
1
1
0
2
5
0
0
2
3
0
2
0
0
0
0
2
0
0
2
2
0
0
0
1
1
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
2
0
0
3
0
0
1
1
0
0
3
0
2
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
2
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
2
2
0
1
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
3
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
3
0
0
1
1
0
2
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
1
1
0
0
0
4
0
2
1
0
0
0
0
3
1
0
0
0
1
1
0
0
0
0
0
3
1
2
0
2
0
3
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
2
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
1
1
0
1
1
0
0
1
1
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
1
0
1
1
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
2
0
0
3
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
2
2
2
0
0
1
3
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
5
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
1
0
0
0
2
2
0
0
5
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
3
0
0
0
2
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
2
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
2
0
0
4
0
0
0
1
0
1
0
2
0
0
0
0
0
1
1
1
2
1
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
1
0
0
0
1
3
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
1
0
0
0
0
2
1
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
2
2
2
0
1
1
1
0
2
0
1
0
0
1
0
2
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
1
0
0
0
1
2
1
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
2
0
0
0
1
0
0
0
2
2
0
0
1
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
3
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
2
0
0
1
0
0
0
1
0
0
0
2
0
0
0
2
2
2
1
0
2
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
2
1
0
0
2
3
0
0
0
0
0
0
0
3
0
0
2
1
0
0
0
0
2
0
0
0
0
0
1
2
0
2
0
1
0
0
0
2
0
2
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
2
2
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
1
1
1
1
0
0
1
0
2
0
2
1
0
2
0
0
2
1
0
2
0
1
0
0
2
0
0
1
0
0
2
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
2
2
4
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
2
0
1
1
0
0
0
0
0
0
0
5
0
2
0
0
0
1
0
0
0
0
2
0
2
0
0
1
0
0
0
0
2
2
1
0
1
2
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
3
1
0
0
0
0
1
0
0
0
0
1
0
2
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
1
0
0
0
3
0
2
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
5
0
0
2
3
0
0
0
1
1
0
1
2
0
1
0
0
1
0
0
0
1
0
0
0
3
1
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
2
1
0
0
0
0
0
1
1
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
1
0
0
1
0
0
2
0
0
1
0
0
0
0
2
0
0
0
2
1
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
1
2
0
0
0
1
0
0
5
1
0
0
1
0
0
0
0
0
2
0
0
2
1
1
2
0
0
2
0
0
0
0
0
3
1
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
3
0
0
2
0
0
0
1
0
0
0
0
4
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
3
2
1
1
0
4
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
1
2
0
0
0
0
0
2
1
0
1
0
0
1
0
0
2
0
1
0
0
1
0
0
0
0
1
1
3
0
2
1
0
0
0
0
3
1
0
0
2
0
1
0
0
0
0
0
2
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
4
0
0
1
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
1
1
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
2
1
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
2
0
0
0
2
0
0
0
1
0
0
2
1
1
0
0
0
2
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
3
0
0
0
0
0
2
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
5
0
0
0
1
0
0
0
0
0
1
0
2
0
4
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
2
0
1
2
0
2
3
2
0
0
0
0
2
0
0
2
3
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
2
0
2
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
3
1
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
3
0
0
0
2
0
0
2
3
0
9
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
2
0
0
2
0
0
1
0
0
3
1
0
0
0
2
1
2
1
1
1
0
0
2
0
3
1
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
1
2
2
2
1
0
0
0
1
0
1
1
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
2
0
0
2
0
0
1
3
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
3
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
2
1
1
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
2
0
0
0
1
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
1
2
1
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
1
2
0
1
0
3
0
0
1
0
2
0
0
0
0
0
0
0
0
2
1
1
2
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
3
0
0
0
2
0
3
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
3
0
0
0
1
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
4
0
0
0
0
2
0
0
1
2
1
2
0
1
0
2
1
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
1
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
4
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
3
2
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
1
1
1
0
0
0
1
0
0
1
0
0
0
1
0
8
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
2
0
0
0
0
0
2
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
2
1
0
2
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
1
0
5
0
0
0
0
1
2
0
0
0
0
3
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
1
2
0
0
3
0
2
0
0
0
1
1
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
2
0
0
3
0
0
1
0
0
0
2
0
1
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
2
0
0
0
1
0
0
5
1
2
1
2
0
0
0
2
0
2
0
0
0
1
2
1
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
1
1
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
1
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
1
2
1
2
0
0
2
1
0
1
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
2
4
2
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
2
0
1
0
0
2
0
1
0
2
2
0
0
1
0
0
0
0
0
0
2
2
2
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
1
0
2
0
1
1
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
3
0
1
1
0
1
0
0
0
0
1
0
2
2
3
0
0
0
0
0
0
0
1
0
1
1
2
0
0
0
0
0
0
0
2
1
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
1
0
2
0
0
0
0
1
2
0
0
1
0
0
0
1
4
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
3
1
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
1
0
4
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
5
2
0
0
3
0
1
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
3
1
0
0
1
0
0
0
2
1
0
0
0
0
0
0
1
0
0
1
1
0
2
0
0
1
0
0
0
0
2
1
1
0
0
0
1
0
0
0
2
2
2
0
1
0
2
0
0
0
0
2
0
0
3
2
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
1
2
0
1
1
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
2
0
0
0
0
0
2
1
0
1
0
0
2
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
7
0
3
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
2
1
0
0
1
1
0
0
0
0
0
0
0
0
2
2
2
0
0
1
1
0
0
2
0
0
1
2
0
0
0
0
0
1
2
0
0
1
2
2
0
0
0
0
0
2
2
0
0
0
2
0
1
1
0
0
0
2
1
0
0
0
0
0
0
0
0
2
3
0
1
0
3
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
1
1
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
2
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
3
0
0
0
0
1
0
1
0
0
0
0
0
1
2
2
0
0
2
2
0
0
0
0
5
0
0
3
0
0
0
0
0
2
1
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
1
0
2
1
0
0
0
1
0
0
0
2
0
2
0
0
2
0
1
0
0
0
0
0
2
1
0
0
0
0
2
0
0
2
4
0
0
1
2
0
1
0
0
2
2
0
1
1
0
2
0
1
0
1
0
1
0
0
3
1
0
0
0
0
3
0
0
0
0
0
0
0
0
2
1
0
1
1
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
1
2
0
0
0
0
0
0
1
1
0
1
0
1
1
0
0
1
0
0
0
0
0
4
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
2
0
0
0
2
0
0
0
0
0
0
2
2
7
0
0
2
3
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
2
0
0
0
1
2
0
0
1
1
0
0
0
1
0
0
0
0
1
0
2
0
1
0
0
0
0
0
1
2
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
5
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
2
0
1
2
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
3
1
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
1
7
0
2
0
0
0
0
3
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
2
1
0
0
0
0
2
0
0
1
1
1
1
0
1
2
0
0
2
0
1
0
0
0
2
1
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
1
0
1
0
0
0
1
2
0
0
2
0
0
0
0
2
1
0
0
2
1
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
2
2
0
0
2
0
2
0
2
0
0
1
1
0
0
0
1
2
2
0
2
1
0
0
0
0
0
1
0
1
0
0
0
2
4
0
0
0
0
0
0
2
2
0
0
2
0
0
0
2
0
0
2
0
1
2
0
0
0
0
0
0
5
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
3
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
2
0
0
0
0
0
1
2
1
0
1
0
0
0
3
3
0
0
1
0
1
1
0
0
2
0
0
0
2
0
0
0
0
0
2
0
1
4
0
0
0
0
2
1
0
0
0
2
2
0
2
0
0
1
2
1
0
0
0
0
0
0
0
0
0
3
0
0
2
0
1
0
0
1
0
2
1
0
0
0
2
0
1
0
0
1
0
3
1
0
0
0
0
2
1
0
0
0
0
0
2
0
0
2
0
0
0
0
1
2
0
0
4
2
0
0
2
3
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
2
0
0
0
2
0
2
0
0
0
0
1
0
0
0
1
0
2
2
0
3
0
0
0
0
2
1
0
0
0
2
0
0
1
0
1
2
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
2
2
0
0
0
2
0
0
0
0
1
0
0
0
0
1
1
0
1
2
2
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
1
2
0
1
2
0
0
1
1
0
0
0
0
2
1
2
2
0
0
0
2
0
1
1
2
2
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
6
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
2
2
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
1
1
0
0
2
1
0
0
0
0
2
0
0
0
0
2
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
2
2
1
0
1
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
1
0
1
1
0
1
0
0
0
0
2
0
1
0
0
0
7
0
2
1
0
0
0
2
2
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
2
0
0
2
2
1
2
0
0
2
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
2
0
2
1
1
2
0
0
0
2
1
0
0
1
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
1
0
0
1
0
3
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
3
0
1
3
0
0
0
0
0
0
0
0
0
2
1
1
1
1
0
2
0
0
0
0
1
2
0
1
0
0
0
0
1
0
2
0
2
0
2
0
2
0
2
0
0
0
0
0
0
2
0
2
0
0
0
1
2
0
0
0
2
0
2
0
0
2
0
0
1
1
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
1
3
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
3
0
2
0
2
2
0
1
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
3
0
3
1
4
0
0
0
2
2
0
0
1
1
0
0
0
0
0
1
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
3
2
0
0
0
0
0
2
0
0
0
1
0
0
0
2
2
1
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
2
1
0
0
0
0
8
0
0
0
1
0
0
0
0
0
0
0
3
1
0
1
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
1
2
0
1
0
1
0
1
1
1
2
0
0
1
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
1
0
3
0
0
0
0
2
1
0
0
2
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
2
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
4
0
1
2
2
0
0
2
0
1
0
0
0
1
2
1
0
0
2
0
0
2
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
2
0
0
0
1
0
2
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
1
3
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
4
0
0
2
0
0
2
0
1
0
0
0
0
0
2
1
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
10
2
0
0
0
0
0
0
2
0
0
2
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
1
1
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
1
2
0
0
1
2
2
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
2
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
1
1
0
0
0
1
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
3
0
1
2
0
0
0
0
0
2
0
0
1
0
2
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
1
2
0
0
2
1
0
0
0
0
0
0
0
3
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
3
0
2
0
0
2
1
0
0
0
1
0
0
0
1
0
2
3
0
0
0
2
0
0
0
0
1
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
3
0
1
0
2
0
0
0
0
2
2
0
0
0
2
0
1
0
1
1
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
2
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
1
0
0
0
0
1
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
7
0
0
0
1
2
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
2
0
2
0
1
0
2
0
2
3
0
0
2
0
0
0
1
1
0
0
0
0
1
3
0
2
0
0
1
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
2
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
2
1
0
1
1
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
3
3
2
0
1
2
0
0
0
0
0
0
2
0
2
0
0
0
0
1
1
4
0
8
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
4
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
5
0
0
0
0
2
0
1
2
1
0
0
0
2
0
0
1
0
0
2
0
0
2
0
0
0
0
1
0
0
1
0
0
2
3
0
0
0
1
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
1
0
2
3
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
2
2
0
0
0
0
1
0
0
14
2
1
0
0
0
0
2
0
0
0
1
1
0
0
0
2
0
0
0
0
1
0
0
0
2
2
0
0
1
1
0
0
1
3
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
2
0
0
0
1
0
0
5
1
0
2
1
0
2
0
0
0
0
0
0
0
1
1
0
1
0
0
2
1
0
1
0
1
0
2
0
0
1
0
0
0
1
0
0
0
0
0
2
1
2
0
0
0
0
0
0
1
0
1
2
1
0
0
1
0
0
0
0
2
0
1
0
0
0
0
2
1
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
3
0
0
1
0
0
0
0
0
1
2
0
0
1
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
2
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
2
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
1
0
1
0
2
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
2
0
1
2
0
2
1
0
0
0
1
0
1
1
0
0
0
1
2
0
0
0
0
0
0
0
5
1
1
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
1
2
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
1
0
0
1
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
3
0
0
1
0
0
0
2
0
2
0
0
0
1
1
0
0
0
0
1
0
0
1
2
2
0
0
1
0
0
0
0
0
0
1
0
2
0
0
1
0
2
0
0
3
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
4
1
0
4
1
1
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
3
0
1
0
0
0
2
2
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
2
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
2
0
0
0
0
8
0
0
1
0
0
0
1
2
0
2
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
3
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
2
0
0
2
0
2
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
1
0
0
0
2
0
0
2
2
0
0
1
2
0
0
1
0
0
0
0
1
0
0
0
0
1
1
2
0
1
0
2
0
0
0
0
0
1
0
2
0
0
3
0
0
0
0
1
0
1
0
0
2
0
1
0
0
1
2
1
0
0
0
0
0
0
2
2
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
4
0
0
2
0
1
2
2
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
1
0
2
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
1
2
0
0
0
1
0
0
1
0
0
0
3
0
2
1
1
0
0
2
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
2
0
0
1
1
1
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
3
0
0
0
1
0
1
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
2
0
1
0
0
2
1
1
0
0
0
0
0
0
0
1
0
0
3
0
2
1
0
0
0
2
0
2
0
0
0
1
0
2
2
0
0
0
0
0
2
3
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
3
0
0
0
2
0
0
0
2
0
5
0
0
2
0
2
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
3
0
2
0
2
0
0
1
1
0
0
0
3
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
5
2
0
3
1
1
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
1
0
1
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
2
0
1
10
0
1
0
2
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
2
0
0
0
2
0
0
1
1
0
0
0
1
0
0
0
0
1
0
2
2
0
2
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
1
0
2
2
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
6
0
0
0
1
0
0
0
3
0
0
0
0
0
0
2
0
2
1
1
1
0
1
1
2
0
0
0
0
1
0
0
0
2
0
0
0
0
4
0
0
0
0
1
0
0
1
2
2
3
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
2
1
0
1
1
0
0
0
1
1
0
1
0
2
2
0
0
0
0
0
0
0
1
0
0
3
1
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
1
1
0
2
2
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
1
2
0
3
1
4
1
1
0
0
2
0
2
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
2
0
0
1
1
0
2
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
3
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
2
0
1
0
0
0
0
0
1
2
2
0
0
3
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
1
2
0
3
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
3
0
0
0
0
0
5
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
2
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
2
2
0
0
0
0
0
1
0
0
1
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
2
2
1
0
0
0
0
0
0
2
0
1
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
1
2
0
0
0
2
1
0
0
2
0
0
0
0
0
0
3
0
0
1
0
2
0
0
0
0
0
0
0
0
3
2
0
1
0
2
0
0
0
2
0
0
0
0
0
2
0
2
1
2
0
2
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
1
2
2
2
0
0
0
2
0
1
0
2
0
0
0
0
2
1
0
0
0
2
0
0
5
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
4
2
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
2
1
1
0
4
0
0
0
1
1
4
0
0
1
0
0
0
0
8
0
0
0
0
0
2
1
0
2
1
0
0
4
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
1
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
1
1
0
0
2
0
2
0
5
0
2
0
1
0
0
0
0
0
3
1
2
0
0
0
0
0
0
0
2
1
0
0
0
1
1
1
4
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
2
2
0
0
2
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
2
1
0
2
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
1
1
0
0
0
0
2
1
0
0
1
0
0
0
2
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
1
0
0
0
0
1
0
0
0
2
0
1
2
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
8
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
1
1
2
3
4
0
0
0
1
0
0
0
1
1
0
0
0
1
0
2
0
0
1
1
2
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
4
1
1
2
1
0
0
0
2
0
1
0
0
2
0
0
0
0
2
1
0
0
1
0
0
0
1
2
2
2
0
0
0
0
2
2
0
0
9
0
0
0
0
1
0
0
0
0
0
3
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
3
0
0
2
0
0
1
2
0
0
0
1
0
2
0
0
0
2
0
0
0
1
2
0
2
0
2
1
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
1
3
0
0
0
0
0
0
1
2
0
1
2
0
2
0
0
0
0
0
0
0
2
0
0
2
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
1
1
0
0
1
1
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
1
0
1
0
2
2
0
2
0
0
1
0
2
0
0
1
0
2
0
0
0
0
0
2
2
0
2
0
0
1
0
0
2
0
0
3
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
2
1
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
3
0
1
1
0
0
1
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
2
0
2
2
0
2
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
1
0
0
3
0
1
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
2
0
0
0
0
1
1
0
0
1
0
2
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
2
0
2
0
1
2
0
0
0
1
0
1
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
2
3
0
0
2
0
0
0
4
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
3
0
0
1
2
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
1
2
0
0
2
2
1
0
3
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
4
1
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
2
2
1
0
0
0
0
0
2
0
0
1
1
0
0
2
0
0
0
0
4
0
0
0
0
1
0
0
2
0
0
0
0
0
0
3
2
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
4
0
0
3
0
0
1
1
2
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
3
2
0
0
0
0
1
3
0
2
0
0
0
0
0
2
2
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
1
1
2
0
0
2
1
0
0
0
4
0
2
2
0
0
2
0
0
0
0
0
1
0
0
2
1
0
1
2
0
0
0
1
0
0
0
1
2
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
2
0
0
0
0
7
0
1
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
1
1
1
1
0
0
0
0
0
2
1
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
8
0
0
0
3
2
0
1
0
0
3
0
0
1
1
2
0
0
0
2
4
0
1
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
2
0
0
2
1
0
1
0
0
0
0
0
0
0
0
2
0
1
2
0
0
2
0
2
2
0
0
1
1
0
0
0
2
2
0
2
2
0
1
0
2
0
0
0
0
2
1
0
2
0
2
0
0
1
0
1
3
0
0
0
0
0
0
2
0
0
0
1
0
1
0
2
1
0
0
0
0
1
0
0
0
1
0
3
0
1
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
2
0
6
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
2
3
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
1
0
2
0
1
1
0
2
1
2
0
0
2
0
1
0
0
1
0
3
0
0
0
1
2
0
0
0
1
0
0
1
0
0
0
1
1
0
2
0
0
0
0
0
2
1
0
0
0
3
2
0
1
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
3
0
0
1
0
0
0
2
2
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
4
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
3
0
0
2
0
0
2
1
1
0
1
0
1
0
0
0
2
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
2
0
2
0
2
0
0
0
0
0
2
0
1
2
0
0
0
1
0
0
0
1
0
0
3
2
0
2
0
0
1
2
0
3
1
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
2
0
0
0
1
0
0
0
0
14
5
0
0
0
0
1
0
0
2
0
0
1
2
0
0
0
2
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
2
3
0
0
0
1
1
2
0
0
3
0
0
0
0
0
1
0
3
0
0
0
0
0
0
2
2
0
2
0
0
0
3
0
2
0
2
2
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
1
0
0
0
0
2
0
3
0
2
0
0
1
0
0
0
0
0
0
0
0
1
4
1
0
0
0
0
0
0
1
0
0
0
2
0
2
1
1
0
0
1
0
1
2
0
0
2
0
1
0
0
5
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
1
1
0
0
8
0
0
2
0
1
0
0
1
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
1
0
1
2
0
0
1
0
3
0
0
0
3
0
0
1
2
1
0
0
0
0
0
0
0
1
2
1
0
0
0
7
0
0
2
0
0
0
2
0
2
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
2
0
0
2
0
0
1
1
0
0
0
0
0
0
6
0
2
1
0
0
0
1
0
0
0
0
0
3
2
2
0
0
2
0
0
0
0
0
2
0
4
0
1
0
2
1
2
0
0
0
0
0
0
0
1
0
2
0
0
2
0
1
0
0
1
0
3
0
0
0
0
1
3
1
0
0
2
2
2
0
0
0
0
2
1
2
3
0
3
2
0
0
1
2
0
2
1
2
2
2
0
1
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
1
2
1
2
0
2
0
0
1
0
0
0
0
1
0
1
0
0
1
0
1
0
0
2
0
1
0
2
2
0
0
1
0
0
0
0
0
2
0
4
1
0
1
0
0
0
0
0
0
1
2
0
2
1
1
2
0
1
0
1
0
3
2
0
0
0
0
0
0
0
2
0
0
2
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
2
0
0
3
0
0
2
2
5
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
3
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
2
0
2
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
2
0
0
1
0
2
0
2
1
0
0
1
1
1
1
0
0
1
0
0
2
0
1
1
0
0
0
0
1
3
0
0
2
0
0
0
2
2
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
3
1
0
2
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
1
1
0
0
1
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
2
0
2
1
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
2
1
0
0
2
0
0
0
2
0
0
1
3
0
4
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
2
0
1
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
1
1
0
0
0
1
2
0
2
0
0
0
1
2
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
3
0
0
0
9
0
2
1
2
0
0
0
1
2
1
0
1
0
0
0
1
0
1
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
1
0
1
1
1
1
1
0
0
0
0
0
1
2
0
0
2
0
0
2
1
1
0
0
0
1
0
0
0
2
0
0
1
1
1
0
0
0
0
0
0
4
0
0
1
5
1
0
0
2
0
0
1
0
1
2
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
1
0
0
0
0
2
1
1
2
2
0
1
0
0
0
2
0
0
2
0
4
1
2
0
2
0
0
0
0
0
0
1
4
0
1
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
2
0
1
0
0
0
2
0
0
2
0
1
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
3
2
0
1
0
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
2
2
0
0
0
1
0
0
0
1
2
0
0
0
2
0
0
1
1
0
0
12
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
1
0
0
3
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
2
0
0
1
0
0
4
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
5
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
3
0
0
0
0
0
0
2
0
0
2
0
0
0
0
3
0
0
1
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
1
0
0
1
0
2
0
0
0
0
1
0
1
0
0
0
2
1
0
0
0
2
0
0
1
0
1
0
1
0
0
0
0
0
0
0
2
2
0
2
1
0
0
1
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
2
3
0
0
0
0
0
0
2
2
0
0
1
1
2
0
0
0
1
0
0
1
0
0
0
0
3
2
0
0
0
0
0
2
0
0
2
0
2
0
0
1
0
0
2
0
0
6
0
1
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
2
1
0
0
0
6
0
2
0
0
0
0
0
0
3
0
1
0
0
0
0
0
1
1
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
2
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
1
0
1
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
2
0
0
1
0
0
0
0
0
0
0
2
3
0
1
0
0
0
1
0
0
0
2
1
0
2
1
2
0
0
0
1
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
1
0
1
2
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
2
1
2
0
0
1
1
0
0
0
4
0
0
0
1
0
0
1
0
0
0
1
0
1
1
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
1
3
0
0
1
2
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
2
0
2
0
3
0
0
3
0
0
4
0
0
0
0
0
3
1
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
3
1
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
2
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
1
1
0
0
0
0
2
0
1
3
0
0
2
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
2
0
2
2
2
3
0
0
0
0
0
0
2
5
0
0
3
1
0
1
0
0
0
0
0
1
0
3
2
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
1
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
2
1
0
0
0
2
0
0
0
0
0
0
0
1
0
1
1
0
0
2
2
2
0
0
2
0
0
1
2
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
3
0
0
0
0
0
0
1
1
2
0
0
2
0
0
1
0
2
1
1
1
0
0
0
0
2
0
2
1
1
2
2
0
0
2
0
1
0
2
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
1
0
0
1
2
2
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
2
0
2
2
0
2
1
0
0
0
1
0
1
0
2
0
0
2
2
0
1
0
0
4
1
0
0
0
1
0
4
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
1
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
3
1
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
2
0
0
4
0
0
0
1
2
0
0
0
3
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
4
0
0
0
0
0
0
0
0
3
2
0
0
1
0
0
2
0
0
0
2
1
0
0
2
0
0
0
0
3
0
3
1
0
0
1
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
1
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
2
1
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
1
0
0
1
0
2
0
2
0
0
0
0
3
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
1
2
2
2
0
0
0
0
1
2
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
4
0
1
0
0
1
0
1
2
4
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
3
0
0
0
0
1
1
0
0
2
0
0
2
1
0
0
3
1
0
1
0
0
0
0
0
1
0
3
0
0
0
0
2
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
5
0
0
2
0
0
2
4
0
0
0
0
2
2
0
0
1
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
3
0
2
1
0
0
0
0
1
0
1
0
0
0
1
2
2
0
0
2
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
1
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
5
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
2
0
0
1
2
0
0
0
0
1
1
0
0
2
2
0
0
0
2
3
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
2
0
1
3
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
1
0
0
1
1
3
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
1
0
6
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
2
0
2
0
0
2
0
2
1
0
0
2
0
0
2
0
2
0
1
0
0
0
1
0
3
0
0
0
0
0
0
0
0
2
0
3
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
3
0
2
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
2
2
2
3
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
3
3
0
0
0
1
0
0
1
0
0
0
1
0
0
2
0
1
0
0
2
2
2
0
2
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
2
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
1
2
0
2
2
0
1
0
0
3
1
2
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
5
0
0
0
0
0
0
2
0
1
0
0
4
0
0
1
0
0
0
1
0
1
2
0
2
0
0
0
2
0
0
1
3
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
3
4
0
0
1
2
0
0
0
0
2
1
0
0
0
0
0
0
1
1
0
0
2
2
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
5
0
0
0
2
1
0
0
0
0
0
1
1
0
0
0
0
0
2
1
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
1
0
0
0
2
0
0
0
2
0
0
1
0
2
2
0
0
0
1
0
0
2
0
0
0
2
2
0
0
1
0
2
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
2
0
0
0
0
2
0
1
0
2
0
1
0
0
2
0
2
1
1
0
0
2
0
0
3
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
2
1
4
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
2
0
2
0
0
2
0
1
0
2
0
0
0
0
0
1
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
1
0
0
0
0
0
0
1
2
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
2
0
1
0
0
2
0
0
2
2
0
6
0
1
1
2
0
0
0
2
0
0
1
0
0
0
0
0
2
2
0
0
1
0
1
0
0
3
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
1
2
1
2
2
1
0
1
1
2
0
0
0
0
1
1
0
0
2
0
0
0
2
0
2
0
2
0
3
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
1
0
0
0
1
1
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
2
0
2
0
1
1
0
0
0
0
0
0
0
2
1
0
0
0
2
1
0
0
0
0
2
0
2
0
0
0
0
2
2
1
0
0
0
0
1
0
1
0
0
2
3
0
0
0
2
0
0
1
1
0
0
1
1
0
2
1
0
0
1
0
3
2
0
2
0
0
1
2
0
0
1
0
0
0
0
0
1
0
0
0
1
0
2
2
1
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
3
0
1
0
0
2
1
0
0
2
3
2
0
0
0
1
0
1
0
0
1
1
0
0
0
2
3
0
0
0
1
0
0
3
0
2
0
0
0
0
1
0
1
2
0
0
2
5
0
0
2
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
1
0
0
0
2
1
0
1
1
2
0
0
0
2
1
2
4
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
3
0
3
1
0
0
0
0
0
0
0
0
5
2
0
0
0
0
0
0
3
1
0
0
0
0
0
3
0
0
1
0
2
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
3
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
2
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
1
5
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
1
2
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
1
2
0
2
1
0
2
0
0
1
0
0
1
0
0
0
3
0
0
1
2
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
2
2
0
0
0
0
1
0
0
0
2
0
1
0
2
1
0
0
0
0
0
0
0
0
1
0
2
2
1
0
1
2
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
1
8
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
1
0
0
0
0
0
1
0
2
0
0
0
5
0
0
0
0
0
0
1
1
0
0
3
0
1
1
0
0
0
0
0
0
0
1
1
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
2
0
2
1
0
0
3
0
0
0
1
0
1
0
0
0
0
0
0
1
3
0
0
2
0
0
0
1
0
0
1
1
0
0
1
0
2
1
0
0
2
0
0
1
0
2
0
2
0
0
2
0
0
2
2
1
0
0
2
0
0
1
0
2
0
0
0
0
1
2
0
0
2
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
2
0
0
3
0
0
0
0
0
0
0
1
0
0
2
0
0
0
5
0
1
0
0
1
2
0
2
0
1
0
0
1
2
1
0
0
1
2
2
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
7
0
1
1
2
0
0
2
0
0
0
0
0
2
3
2
0
0
0
0
1
1
0
0
0
0
0
2
0
0
3
0
2
0
2
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
2
3
0
2
0
0
2
1
0
0
0
0
1
2
2
3
0
2
0
0
0
0
0
0
2
0
2
1
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
3
2
2
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
1
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
1
1
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
1
0
0
1
2
1
1
0
0
0
1
0
0
0
0
5
1
0
0
0
2
0
0
0
4
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
1
0
1
3
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
4
1
0
3
0
0
0
1
0
1
0
2
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
3
2
0
0
0
0
0
1
0
1
0
0
0
1
2
0
2
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
2
1
0
1
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
1
0
3
0
1
0
2
0
0
1
0
2
2
0
0
0
0
0
2
1
0
3
0
1
0
0
0
2
2
1
3
1
2
0
0
0
0
0
0
0
2
2
1
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
1
0
0
0
1
2
1
0
0
0
0
0
0
2
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
3
0
0
0
2
2
2
0
0
0
1
0
0
1
0
0
1
3
0
0
0
2
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
2
2
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
2
1
1
0
0
0
0
0
1
0
0
0
1
2
2
0
0
0
2
1
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
1
0
0
1
2
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
4
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
2
0
1
0
0
4
2
0
1
0
0
1
0
0
0
2
0
0
4
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
2
1
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
2
0
1
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
3
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
2
1
0
0
0
0
1
0
0
0
2
0
0
2
2
1
0
0
3
0
2
0
0
2
1
0
0
0
0
0
1
0
4
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
2
2
1
0
1
0
0
0
0
0
3
0
0
4
0
0
2
0
0
3
0
0
0
0
2
2
2
0
0
3
0
2
2
0
0
1
3
0
0
2
0
0
0
1
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
4
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
3
0
0
0
2
0
0
0
1
2
0
0
0
1
0
0
1
1
0
1
0
0
0
2
1
0
2
0
0
0
0
2
2
0
2
0
0
0
1
0
0
2
0
0
0
0
0
2
0
1
0
0
0
2
2
0
0
0
2
2
0
0
0
0
8
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
2
0
2
0
0
1
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
1
0
2
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
2
0
0
0
0
0
1
1
0
1
0
0
2
1
1
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
2
1
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
4
2
0
0
0
0
1
0
0
1
0
0
0
1
1
0
1
0
2
0
0
1
0
0
1
4
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
2
1
1
2
2
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
2
1
0
0
0
0
0
0
3
0
1
2
2
4
0
0
0
0
0
0
0
0
0
0
5
0
0
2
2
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
3
3
0
0
2
1
2
0
1
0
0
1
0
2
0
0
2
1
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
1
0
1
3
0
2
1
0
2
0
0
0
0
2
0
2
0
2
6
0
0
0
1
0
0
0
0
1
3
2
0
0
0
0
0
0
1
0
1
2
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
3
1
0
2
0
1
0
0
1
0
0
1
2
3
0
0
2
0
1
1
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
1
1
2
4
1
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
2
1
1
0
0
0
0
0
1
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
2
0
0
0
0
1
0
1
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
6
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
1
3
1
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
2
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
2
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
1
2
0
2
2
2
7
0
0
0
0
0
1
3
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
4
0
0
0
0
2
1
0
2
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
1
0
0
0
2
0
1
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
1
0
0
1
2
0
0
1
1
1
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
4
2
1
0
3
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
1
1
0
1
0
2
0
1
1
0
0
0
0
2
2
1
0
0
2
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
1
0
1
1
0
1
6
0
0
0
0
0
0
2
0
5
0
0
1
0
0
0
3
2
2
1
0
0
2
1
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
1
3
0
1
0
0
3
0
0
0
0
1
0
1
2
0
0
0
0
0
1
3
0
0
2
4
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
1
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
2
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
2
1
0
1
0
0
0
0
1
9
0
1
0
0
0
2
0
3
0
0
1
0
0
0
0
0
1
1
0
2
2
2
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
3
0
0
2
2
0
1
0
0
0
2
0
0
0
0
0
5
0
1
0
0
1
0
0
4
0
0
1
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
2
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
3
0
0
2
0
0
1
0
2
2
0
1
0
1
1
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
3
0
2
0
3
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
1
0
1
1
1
1
0
0
2
0
1
0
1
1
1
0
0
0
0
0
1
0
2
1
0
0
1
0
6
1
2
0
3
2
0
1
0
1
1
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
1
2
1
2
0
0
0
2
0
0
0
0
0
0
0
4
2
0
0
1
0
0
0
3
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
1
0
0
0
0
0
2
1
4
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
3
3
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
3
0
2
2
0
2
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
2
0
0
0
0
0
2
0
0
1
1
1
2
0
2
2
7
1
2
0
0
0
0
0
1
1
0
0
0
0
0
2
0
1
1
0
0
0
0
0
2
0
0
0
0
2
0
0
2
2
1
0
1
0
0
3
2
0
0
2
1
0
0
0
1
0
2
1
1
2
0
0
0
0
0
0
1
1
0
3
0
0
0
0
0
0
0
4
0
0
1
0
0
0
1
0
0
2
2
0
0
0
2
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
1
1
2
2
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
2
0
1
2
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
2
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
3
0
0
0
0
0
0
0
3
0
0
0
2
3
0
0
0
0
1
0
0
1
0
0
0
2
1
0
1
0
0
2
0
1
0
0
1
0
0
1
0
0
2
12
0
1
2
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
2
0
3
0
1
0
0
0
0
0
0
0
0
1
1
4
2
0
1
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
1
0
2
0
0
2
0
2
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
1
4
0
0
0
0
0
0
0
0
7
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
1
2
1
2
1
0
0
0
0
0
2
1
0
0
2
0
1
1
3
0
0
0
0
0
1
0
0
2
1
0
1
0
0
2
0
0
0
1
1
0
1
0
0
0
1
0
2
1
1
0
0
0
0
1
2
0
0
1
0
0
1
4
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
1
2
0
2
0
1
0
0
0
0
0
1
2
1
0
0
0
3
0
0
0
3
0
0
1
0
0
0
0
1
0
0
0
0
2
0
1
3
0
1
0
0
0
1
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
1
0
2
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
2
1
0
1
2
0
1
0
0
0
0
0
0
0
2
0
0
2
2
0
2
1
2
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
1
0
0
2
2
1
6
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
2
0
4
2
1
0
1
0
0
0
1
2
0
0
1
0
0
1
0
1
0
0
1
1
0
1
0
1
0
0
1
2
2
0
0
0
0
2
0
0
2
1
0
1
0
0
0
1
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
1
2
1
0
0
1
2
1
0
0
0
0
2
2
3
1
3
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
2
0
2
1
0
0
2
0
0
0
0
2
0
1
0
0
3
0
1
0
0
1
0
1
0
0
0
1
1
1
0
0
0
0
0
0
2
1
0
0
0
0
0
3
0
0
2
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
4
0
0
0
2
0
0
2
2
1
0
0
0
1
0
0
0
0
1
0
0
0
1
1
2
0
2
0
2
1
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
2
0
0
0
0
1
1
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
3
0
0
1
0
0
2
0
2
0
2
16
0
2
0
0
0
0
0
2
1
0
0
2
0
0
0
2
2
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
2
3
0
1
0
1
0
0
0
0
2
0
1
0
0
4
0
0
3
2
0
0
0
0
1
0
1
0
1
2
0
2
0
2
2
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
1
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
1
1
0
1
0
1
0
0
0
1
0
3
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
2
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
1
3
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
2
0
0
1
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
5
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
2
0
2
1
0
0
0
0
0
0
0
1
2
2
0
2
0
2
0
0
0
4
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
1
2
0
0
0
1
2
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
1
1
2
2
0
0
0
0
2
1
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
2
1
0
1
0
0
2
1
1
2
2
2
0
0
1
0
1
0
1
0
2
0
1
0
1
1
0
0
1
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
1
1
0
2
2
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
2
0
0
0
0
3
0
0
0
2
0
1
0
2
0
0
0
0
0
1
2
1
0
0
2
0
0
0
1
0
0
0
0
2
1
1
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
15
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
3
0
0
0
0
2
0
2
2
0
1
0
0
0
2
0
2
1
2
0
0
2
0
0
0
0
0
0
0
0
1
2
0
1
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
2
0
0
1
0
0
2
0
1
0
0
1
0
0
0
1
0
0
1
0
0
2
1
0
0
0
0
0
0
1
0
4
0
0
1
0
3
0
2
0
0
0
0
2
0
0
2
0
0
0
0
3
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
1
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
1
0
3
0
2
3
0
2
0
0
2
0
0
0
2
0
2
0
0
0
2
0
1
0
0
0
0
0
0
2
2
0
3
3
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
3
0
0
0
1
1
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
4
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
3
1
2
0
0
0
0
0
0
2
0
0
0
2
0
4
0
0
0
1
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
2
0
0
2
0
0
0
0
2
2
0
0
1
0
1
2
0
1
0
0
2
2
0
0
0
0
2
2
0
0
0
0
0
2
0
0
1
0
0
0
2
2
0
0
2
2
0
0
1
0
0
0
0
0
3
3
1
0
0
1
2
0
2
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
1
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
2
0
1
1
1
0
0
0
2
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
2
0
1
0
2
1
2
2
1
0
0
0
0
0
0
0
2
0
3
0
0
1
0
0
0
1
0
0
0
3
1
1
1
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
1
1
0
1
0
0
2
0
0
0
0
1
0
1
1
0
0
0
0
1
1
0
0
0
2
2
0
0
0
2
0
0
0
0
2
2
1
1
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
1
1
0
0
0
0
1
0
1
0
2
0
0
2
2
2
0
0
0
0
0
1
0
0
0
2
2
0
0
1
0
0
0
0
0
0
2
0
0
2
2
0
2
1
0
2
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
1
0
0
2
1
0
0
0
0
1
1
0
0
2
0
0
0
1
2
0
0
2
0
0
0
0
0
0
2
2
0
0
0
1
2
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
2
1
0
2
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
1
0
0
2
0
0
0
1
2
0
0
0
0
0
3
0
0
2
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
1
2
0
1
0
0
2
0
3
2
0
0
1
0
0
1
0
2
2
1
2
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
1
0
2
0
0
2
0
0
4
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
2
0
0
0
0
2
4
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
2
0
1
0
1
0
0
0
2
2
0
0
0
0
1
0
0
0
1
1
0
2
2
0
0
2
1
0
0
2
0
2
0
3
0
0
0
0
0
1
1
2
2
0
0
0
0
2
2
1
0
1
2
0
0
1
0
0
2
0
0
2
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
1
0
0
1
1
9
0
1
0
0
0
0
0
2
0
0
0
0
3
1
0
0
0
0
0
1
0
0
0
1
0
0
2
1
0
2
3
0
1
2
2
0
2
0
0
0
0
0
0
0
0
1
0
2
2
2
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
1
1
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
2
0
0
0
1
0
0
0
2
1
0
0
0
1
1
1
1
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
2
0
1
0
2
1
1
0
0
1
2
0
0
0
4
0
0
0
2
0
0
0
3
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
1
2
1
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
5
2
0
0
3
0
0
0
0
0
1
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
1
2
0
0
0
0
0
0
1
1
2
0
1
1
2
0
0
3
1
0
0
0
1
0
0
0
5
0
0
1
1
0
2
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
3
0
2
3
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
1
5
0
0
0
0
0
1
0
1
2
0
1
0
2
0
0
0
0
3
0
0
0
2
0
0
5
2
0
0
0
0
1
2
0
1
0
0
0
0
2
0
0
0
0
1
0
2
0
1
0
1
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
1
0
0
1
0
2
1
2
0
0
0
0
0
0
1
0
1
0
1
2
1
0
0
0
0
0
1
3
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
3
0
2
2
0
0
0
0
0
1
0
1
1
0
2
2
0
2
0
0
0
2
2
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
3
0
2
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
1
3
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
3
0
1
0
0
0
0
0
0
2
0
1
0
2
0
0
1
0
0
0
0
1
0
0
0
2
3
0
0
0
1
1
2
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
2
0
0
1
0
0
1
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
2
3
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
3
0
2
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
1
0
2
0
0
0
1
2
0
1
1
0
0
0
1
3
1
0
0
0
0
1
1
1
1
0
0
2
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
2
1
2
0
0
0
0
2
0
0
0
0
0
1
1
1
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
1
0
1
2
0
1
0
2
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
3
0
0
1
0
0
0
0
0
2
0
0
0
1
4
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
5
1
0
2
2
2
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
2
0
0
1
1
2
0
1
0
0
2
0
0
0
0
2
2
2
0
0
2
0
0
2
0
0
3
1
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
4
0
0
0
2
0
1
0
0
1
0
1
0
0
0
0
0
5
0
0
0
0
2
0
1
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
1
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
1
2
0
1
0
0
0
0
1
2
0
1
0
0
0
2
1
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
2
2
2
1
0
1
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
3
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
1
1
1
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
2
0
0
0
0
0
1
1
0
1
0
0
0
1
0
1
2
0
0
0
1
1
2
0
0
1
0
0
0
4
0
1
0
0
0
0
0
2
0
0
1
2
2
1
3
0
0
0
1
0
2
1
2
0
0
5
1
1
0
0
0
2
0
0
2
1
0
0
0
0
0
1
0
3
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
4
1
2
0
2
0
0
0
0
0
0
0
2
0
0
2
2
1
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
7
0
2
0
0
2
0
0
0
0
0
0
0
3
1
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
2
1
0
0
1
1
1
0
1
0
0
0
0
0
1
1
0
0
2
1
0
0
0
0
5
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
1
1
1
0
0
0
2
0
2
2
0
0
2
2
0
0
0
2
2
0
1
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
1
0
1
2
3
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
2
0
1
1
0
1
0
0
1
0
1
0
0
1
1
3
0
1
0
2
0
0
1
0
0
0
0
1
2
3
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
1
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
1
0
1
0
0
0
0
0
1
2
0
1
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
5
2
1
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
1
0
2
0
2
0
0
1
3
0
0
0
0
2
0
0
0
1
0
0
0
0
3
2
0
0
2
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
2
0
0
0
0
0
0
1
0
0
0
1
0
1
2
2
0
0
2
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
2
2
0
2
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
2
0
1
2
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
7
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
3
2
0
2
0
0
0
0
0
0
2
0
2
0
0
1
0
0
3
0
0
2
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
2
0
0
0
1
0
2
0
4
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
1
1
0
2
0
0
2
0
2
2
2
0
2
0
0
0
0
0
0
5
0
0
2
0
0
0
1
0
0
0
1
3
1
0
1
2
0
0
1
1
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
1
0
2
0
1
1
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
1
2
0
0
0
0
0
1
2
0
0
2
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
2
1
2
2
0
0
0
2
0
0
1
0
1
1
1
0
2
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
2
0
0
0
0
0
0
0
0
0
1
2
2
0
0
1
1
0
0
0
0
0
2
1
1
0
2
2
2
0
0
0
5
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
2
0
0
1
0
0
1
0
0
0
0
0
2
0
1
0
2
0
0
1
0
0
0
0
0
2
1
0
2
0
0
0
0
0
2
0
1
2
0
0
0
4
0
0
0
0
0
0
0
1
2
0
0
0
2
0
1
0
2
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
2
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
1
3
0
1
0
0
0
2
0
0
4
1
1
2
0
0
0
1
1
0
0
1
2
0
1
4
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
2
2
0
1
0
0
0
0
0
0
0
1
1
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
2
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
2
1
0
0
2
2
0
2
0
0
2
0
0
0
2
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
2
0
1
2
0
3
0
0
0
0
0
3
1
0
0
0
0
0
0
0
2
2
0
2
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
1
1
3
0
0
0
0
1
0
1
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
1
3
0
1
0
2
0
2
0
0
0
0
1
0
0
0
0
1
0
1
2
0
0
1
0
1
0
2
0
0
0
0
0
2
1
0
0
0
0
0
2
0
2
0
1
0
0
2
0
0
1
0
0
0
2
0
0
2
0
1
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
2
0
0
0
0
0
2
0
0
0
0
0
0
1
1
1
3
2
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
1
0
0
0
0
1
0
0
1
1
2
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
1
2
0
0
0
0
1
0
0
0
0
0
1
2
3
0
0
0
0
0
2
3
1
0
1
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
1
0
2
0
1
0
1
0
0
2
0
2
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
3
0
0
3
0
1
0
1
0
0
1
0
0
0
0
0
0
5
0
0
0
0
0
2
2
0
0
2
1
2
0
0
1
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
3
1
1
2
0
2
1
0
0
1
0
0
0
2
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
1
0
0
1
0
3
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
1
1
0
2
2
0
2
2
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
6
0
2
0
0
0
0
2
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
3
1
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
2
0
2
0
2
2
0
0
1
0
0
2
0
1
1
6
0
0
1
0
0
1
0
2
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
2
0
1
0
2
2
3
1
0
0
0
0
1
0
2
1
1
2
0
0
2
0
0
2
2
0
0
2
2
0
0
0
1
0
0
3
0
0
0
1
0
2
0
0
1
0
2
1
0
1
0
0
0
0
0
0
0
1
0
0
1
2
0
3
1
1
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
5
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
5
0
1
0
0
2
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
2
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
2
0
1
0
1
3
0
0
3
0
1
0
1
0
2
0
0
0
1
1
0
2
1
2
0
2
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
3
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
2
0
0
0
2
0
2
0
2
0
1
0
0
0
0
0
0
0
2
1
2
0
0
0
0
9
1
0
0
2
0
0
2
1
2
1
1
0
0
0
1
0
0
0
2
0
2
0
2
1
0
0
0
1
1
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
2
0
2
0
0
2
2
2
0
0
2
0
0
0
0
0
0
1
0
2
1
1
1
0
1
0
2
0
0
0
2
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
2
1
0
0
0
0
2
2
0
2
0
0
0
3
2
0
1
0
0
0
0
0
1
0
0
0
1
0
3
2
0
0
0
1
0
0
0
2
0
4
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
1
3
2
2
0
0
1
0
1
1
2
2
0
1
0
0
0
0
0
0
1
1
0
0
0
2
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
1
0
0
0
2
2
0
2
1
0
0
1
0
1
0
2
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
2
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
4
0
0
0
0
0
1
0
0
0
0
0
0
1
2
1
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
2
0
0
0
1
0
0
2
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
4
2
3
2
0
0
0
1
0
0
0
0
2
0
4
2
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
2
2
1
5
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
1
0
0
2
1
0
0
0
1
8
0
0
0
0
1
1
1
1
3
2
0
0
2
0
2
0
0
5
2
0
0
1
0
2
0
0
2
0
0
2
0
1
0
0
1
0
0
2
0
0
0
2
0
1
0
0
2
0
1
0
0
0
0
0
2
2
0
0
4
0
2
0
0
0
0
0
1
0
0
0
3
1
2
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
4
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
2
0
0
2
0
2
0
1
1
2
0
2
0
0
1
3
0
2
0
0
0
0
1
0
1
0
0
0
0
1
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
2
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
1
2
2
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
1
0
0
1
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
2
0
1
0
0
0
1
1
0
0
0
0
0
1
2
1
0
0
1
0
0
0
4
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
2
3
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
3
0
0
2
2
0
0
1
0
0
1
1
0
0
2
0
1
2
0
0
0
0
0
0
0
1
2
0
0
2
2
1
0
0
1
2
0
0
0
0
0
0
0
0
0
5
0
1
2
0
3
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
2
3
3
0
0
0
4
0
0
5
0
3
0
0
1
2
2
0
1
1
0
0
0
0
0
2
0
0
0
0
0
2
0
1
2
0
1
0
0
0
2
0
2
0
3
2
2
5
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
3
2
2
2
0
2
0
1
1
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
2
0
0
0
1
0
2
0
0
0
1
1
0
0
0
0
1
0
0
0
2
0
0
0
0
1
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
1
0
1
0
0
0
0
0
0
2
2
0
1
0
0
1
0
1
2
0
1
2
0
0
0
1
0
0
1
1
0
0
0
2
0
1
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
2
0
2
1
0
2
1
1
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
2
0
1
0
2
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
3
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
4
0
3
2
0
2
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
2
2
0
0
0
2
0
0
0
3
0
2
1
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
1
1
1
2
0
0
1
0
0
0
1
0
2
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
1
0
2
0
0
2
0
0
0
2
2
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
2
2
1
0
0
2
0
0
0
0
1
0
0
0
0
2
2
2
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
1
3
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
3
0
0
0
1
0
0
0
0
2
1
0
2
2
1
0
0
0
1
0
3
0
0
0
4
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
1
0
2
0
1
0
0
0
0
1
0
1
0
0
0
2
3
1
0
2
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
2
0
0
1
3
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
3
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
3
2
0
0
0
0
3
0
2
1
0
0
0
1
0
1
0
0
1
0
1
0
1
2
0
0
0
2
2
0
0
0
0
0
0
3
0
0
0
0
0
4
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
2
0
1
2
2
0
1
0
0
1
2
0
0
2
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
1
0
1
2
2
0
0
2
0
0
0
2
0
0
1
2
2
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
2
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
3
0
0
1
0
1
0
0
0
0
2
0
0
1
0
2
0
0
0
0
2
0
0
2
2
0
0
0
2
0
0
1
0
1
0
2
0
0
0
0
1
0
5
0
0
2
0
2
1
0
0
1
0
2
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
8
0
0
2
0
0
0
0
0
0
0
4
0
0
2
0
0
0
2
2
1
0
0
2
0
0
0
1
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
2
2
0
0
0
2
1
3
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
1
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
2
0
0
2
1
0
1
0
0
0
1
0
1
0
2
1
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
2
0
0
3
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
2
1
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
3
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
3
0
2
0
1
0
0
0
0
0
2
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
2
0
0
2
0
0
1
2
0
1
1
0
1
0
2
0
2
0
0
0
2
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
5
0
3
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
2
2
2
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
3
0
1
1
3
0
0
1
2
0
1
1
0
0
0
2
0
0
0
0
0
1
2
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
3
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
2
0
0
0
0
1
0
1
1
0
1
0
0
0
2
0
0
1
0
2
0
2
3
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
1
0
2
0
4
0
0
1
1
1
1
2
0
0
0
0
0
7
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
3
0
1
0
0
3
0
0
0
0
0
1
0
1
0
0
0
0
0
2
1
0
1
2
0
0
1
0
3
0
2
1
0
0
0
0
0
7
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
5
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
2
0
1
3
0
0
0
0
0
0
0
2
0
0
5
1
0
0
2
2
0
2
0
0
0
2
0
1
0
0
1
0
2
0
0
1
0
3
1
0
1
0
0
0
0
2
0
2
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
2
0
0
0
2
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
1
0
0
0
2
0
2
1
0
0
2
1
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
3
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
1
3
0
2
0
0
0
0
2
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
2
1
0
0
0
1
1
0
0
2
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
1
0
1
0
0
0
2
0
2
0
0
1
0
0
0
0
1
0
0
0
1
0
3
0
0
0
0
0
1
1
0
0
1
1
0
2
0
2
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
1
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
2
0
0
0
0
0
2
2
0
0
0
0
2
1
0
0
0
1
0
0
2
2
0
0
1
0
1
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
2
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
2
0
0
0
0
0
0
0
2
1
0
2
2
0
1
3
0
0
0
0
0
2
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
8
0
0
0
0
4
0
0
1
0
2
0
7
2
3
2
0
0
2
0
0
2
0
0
0
1
2
0
0
2
0
2
1
0
0
2
0
0
1
0
2
4
2
0
0
0
2
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
2
0
0
1
0
0
3
1
1
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
2
0
0
0
4
1
0
0
0
0
0
0
1
0
3
0
1
2
0
1
0
0
0
1
2
0
1
0
0
1
1
0
2
0
1
1
0
0
0
2
0
1
0
0
2
0
0
0
1
0
1
0
0
1
0
0
1
0
0
1
0
2
1
0
1
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
1
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
2
1
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
2
1
0
0
0
3
0
0
0
1
2
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
1
0
0
1
0
3
2
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
2
2
0
0
0
2
0
2
0
0
0
1
0
0
1
0
2
0
0
0
1
0
2
2
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
12
1
0
1
0
0
1
0
0
0
0
0
2
1
0
0
0
0
2
1
1
0
0
0
2
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
2
1
0
2
1
1
0
0
6
2
0
0
0
2
0
0
1
1
2
2
2
0
3
0
0
0
0
0
0
0
0
4
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
2
2
0
1
0
0
0
0
1
1
0
2
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
1
2
0
2
2
0
0
0
0
1
1
2
1
0
0
0
0
0
0
2
2
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
1
0
0
2
2
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
3
0
0
2
1
0
0
1
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
1
0
2
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
2
0
0
1
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
2
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
2
2
0
0
0
2
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
1
0
3
0
0
0
0
0
0
3
2
1
0
0
3
0
0
0
0
0
0
2
0
0
2
2
2
0
0
1
0
0
1
1
0
0
2
0
0
0
5
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
4
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
2
0
2
0
0
1
2
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
1
1
0
3
1
0
0
0
0
3
1
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
1
1
2
1
0
1
1
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
3
0
0
0
0
0
1
0
0
2
0
0
1
2
1
0
0
2
0
0
1
1
2
1
0
0
0
0
0
3
2
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
1
0
2
2
0
0
0
2
0
0
0
0
1
2
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
3
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
1
1
0
2
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
3
1
0
1
0
0
1
1
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
3
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
2
2
0
0
2
1
1
0
0
2
0
2
0
0
1
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
4
0
0
2
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
1
2
0
0
2
0
0
0
1
0
0
4
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
2
3
0
0
0
0
5
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
2
0
0
1
0
1
0
0
0
0
0
0
1
0
0
3
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
1
0
0
2
1
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
2
0
0
0
0
0
0
2
2
2
0
2
0
1
0
1
1
0
0
0
1
0
0
2
2
1
0
1
1
1
1
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
3
0
0
0
1
0
1
0
0
0
4
0
0
0
0
2
0
1
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
4
2
0
1
4
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
1
0
0
1
0
3
2
0
0
1
2
0
0
1
0
0
1
1
0
1
0
0
2
1
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
2
0
2
0
1
0
0
1
1
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
1
2
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
2
2
1
0
0
0
2
0
0
0
2
0
0
3
0
1
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
2
0
1
2
0
2
0
0
2
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
4
1
0
2
0
0
0
0
2
0
1
0
0
0
1
0
0
3
0
0
0
0
0
0
0
2
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
1
1
2
1
0
0
0
2
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
2
3
0
2
1
0
0
1
0
0
0
0
0
0
0
2
0
1
0
1
0
1
1
0
0
0
1
0
0
0
2
0
3
0
0
0
1
2
0
0
0
1
0
1
0
0
2
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
2
0
1
2
2
0
3
0
0
0
2
2
0
0
1
2
2
0
2
0
2
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
2
0
0
0
3
0
4
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
2
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
2
1
1
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
2
0
0
0
0
0
5
1
0
2
0
1
0
2
0
0
0
0
2
1
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
1
1
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
1
1
0
2
0
2
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
1
0
0
0
3
0
1
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
3
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
1
2
0
3
2
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
1
0
0
1
0
0
0
0
1
0
2
2
2
2
0
0
0
2
2
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
2
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
4
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
2
6
2
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
5
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
1
2
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
1
3
3
0
0
2
0
0
0
0
0
0
0
0
0
1
0
3
0
1
0
1
2
2
2
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
2
0
2
0
0
0
3
0
1
2
0
0
2
0
0
1
0
0
1
0
4
0
1
1
2
2
0
2
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
3
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
3
0
2
1
1
1
1
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
1
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
8
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
1
2
0
3
0
0
1
0
0
2
0
0
2
0
0
0
0
1
0
1
0
0
0
0
1
2
0
2
0
0
0
2
0
0
0
0
0
1
1
1
0
3
1
2
2
0
3
1
0
0
0
0
1
2
0
0
0
1
0
0
0
1
0
1
0
0
2
0
0
1
0
0
0
1
0
0
1
2
0
1
2
0
1
1
0
0
0
0
0
7
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
2
0
2
0
2
2
0
4
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
2
2
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
2
1
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
1
0
1
0
1
0
0
0
2
0
2
0
0
0
0
1
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
2
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
2
0
2
0
1
0
2
0
0
0
2
0
0
0
2
0
2
2
0
2
0
0
0
1
0
0
0
0
2
0
1
2
0
0
0
1
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
2
0
0
0
0
0
0
1
2
1
2
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
3
0
0
0
1
1
0
0
0
1
0
0
2
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
1
0
2
0
2
1
0
0
0
1
0
1
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
1
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
1
0
0
1
0
0
0
1
0
0
0
1
0
2
0
1
2
0
0
0
0
0
0
0
2
1
0
0
0
3
1
0
0
2
2
0
2
2
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
1
0
0
0
0
0
5
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
1
0
0
0
0
2
0
2
0
1
0
0
0
0
0
1
0
0
2
0
0
1
0
2
0
0
5
0
0
0
1
1
0
0
0
0
0
0
0
0
2
1
0
0
1
2
0
1
2
0
0
0
0
0
2
2
0
0
0
2
2
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
3
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
3
0
0
1
1
1
0
3
2
0
0
1
0
2
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
2
1
0
4
0
0
1
0
3
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
1
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
1
0
0
1
1
0
2
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
4
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
2
1
0
0
0
1
1
2
0
0
1
1
0
1
0
2
0
0
0
0
0
0
5
4
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
2
0
1
0
0
0
0
1
0
0
2
1
0
0
0
0
0
1
0
1
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
1
2
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
2
2
0
0
2
0
0
0
0
1
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
2
0
0
0
0
1
0
2
0
0
6
1
2
2
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
2
3
3
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
2
0
0
0
2
2
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
1
3
4
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
2
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
2
1
4
0
0
0
0
1
0
0
0
2
0
0
1
1
2
0
0
2
1
0
0
3
0
2
0
2
0
0
0
1
0
0
3
0
0
0
0
0
3
0
0
1
0
1
0
0
0
0
4
0
0
0
0
0
0
2
0
0
0
0
4
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
2
0
0
1
0
1
0
0
0
0
2
1
0
0
0
1
0
0
0
1
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
3
2
1
0
0
0
1
0
0
1
0
0
1
0
0
0
2
0
0
0
0
2
0
3
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
2
1
0
1
0
0
0
0
0
0
2
2
0
0
1
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
2
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
2
0
1
0
1
0
0
2
2
0
0
0
0
6
3
0
0
0
2
0
2
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
2
0
1
0
0
0
0
0
2
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
3
1
0
0
1
1
0
0
0
0
2
0
0
0
0
2
0
0
0
1
2
0
0
0
3
1
0
0
2
0
2
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
2
0
0
0
0
1
1
0
0
0
2
2
2
0
0
1
1
2
0
0
0
0
0
0
0
1
0
1
0
0
1
2
0
0
1
0
0
0
0
2
2
2
1
0
0
2
0
0
0
0
0
1
0
0
0
3
2
0
1
0
0
1
0
1
1
1
0
2
0
2
2
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
2
2
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
2
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
2
0
0
0
1
2
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
2
0
0
0
1
1
2
0
0
0
0
1
0
2
1
1
0
0
0
1
1
0
0
0
0
0
2
0
0
0
2
1
0
0
0
1
0
1
0
0
2
0
0
0
1
0
0
0
0
0
3
0
1
2
2
5
0
0
0
0
0
0
1
0
0
0
0
0
1
3
0
2
0
1
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
3
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
2
2
0
10
0
1
0
0
0
1
0
0
0
0
0
0
0
1
2
0
1
2
0
0
0
3
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
2
0
2
2
0
0
1
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
8
2
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
2
0
0
2
1
1
0
0
1
0
0
0
0
0
0
0
2
0
0
2
1
1
0
0
0
1
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
1
1
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
1
0
0
0
2
2
0
0
2
1
1
0
0
0
1
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
2
2
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
6
0
0
0
0
0
0
1
1
0
0
2
0
2
0
3
0
0
0
2
0
0
0
1
0
1
0
1
0
1
1
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
1
4
0
2
1
0
0
2
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
1
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
2
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
2
0
0
0
2
2
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
3
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
2
0
1
0
1
1
1
0
0
3
0
0
0
3
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
3
0
0
2
4
0
0
0
0
0
1
0
0
0
0
3
2
2
1
0
0
4
1
1
0
2
0
1
0
2
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
5
2
2
0
0
1
0
0
0
1
0
0
2
0
0
0
4
0
1
0
0
2
3
0
0
2
1
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
1
0
1
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
3
2
1
0
0
1
0
1
1
2
0
0
0
2
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
2
11
0
0
2
0
0
1
2
0
0
1
0
0
0
0
0
2
1
0
3
0
0
1
0
0
0
0
0
0
1
2
0
0
0
2
0
0
1
4
0
0
0
0
0
0
0
2
1
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
6
0
1
0
0
0
3
0
2
2
0
0
0
0
0
1
2
0
2
0
2
0
2
1
0
1
4
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
2
3
1
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
5
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
4
0
0
0
0
2
0
0
0
0
0
0
0
2
1
1
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
3
1
0
0
0
0
2
0
1
3
0
3
2
2
2
2
0
1
0
0
2
0
0
2
2
0
1
0
2
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
3
0
2
0
1
1
0
0
0
0
0
1
1
1
0
0
1
0
0
0
2
1
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
2
0
2
2
0
1
3
0
1
2
0
0
1
1
1
0
2
0
0
0
2
0
0
0
0
3
0
1
1
0
0
0
0
1
2
1
0
0
1
0
0
1
0
0
0
0
0
2
1
1
2
0
1
0
2
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
2
2
0
0
0
0
0
0
0
0
1
1
2
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
2
2
1
0
0
2
2
1
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
2
0
0
2
0
2
0
0
0
1
0
0
0
0
2
3
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
8
0
0
0
0
2
2
0
2
0
0
0
2
3
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
0
2
0
1
0
2
1
0
0
2
0
0
0
5
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
1
0
1
1
1
2
0
0
3
1
2
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
3
0
0
9
0
0
0
0
0
0
0
0
0
4
1
0
0
5
0
0
0
2
0
0
0
0
2
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
1
0
0
1
2
2
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
5
4
0
0
0
0
1
0
0
1
0
0
0
0
1
2
0
0
0
2
2
0
3
2
0
0
0
1
2
0
4
1
2
0
0
0
0
1
2
2
2
0
0
0
1
0
0
0
0
0
2
0
0
0
1
1
0
0
1
0
0
2
1
0
0
0
0
0
0
1
0
0
0
1
0
0
7
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
1
1
2
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
1
3
0
0
0
0
0
0
1
2
0
0
3
0
0
0
0
0
2
0
2
3
0
0
1
2
0
0
0
0
1
0
0
0
0
1
2
1
0
0
0
0
0
1
0
0
0
1
0
2
1
0
0
0
0
0
0
0
2
2
0
1
0
0
2
0
0
1
1
2
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
4
0
0
0
2
0
0
3
0
0
2
0
1
0
0
0
0
1
0
0
0
0
2
0
1
2
0
1
0
0
0
1
0
0
1
0
2
0
0
0
1
0
0
0
0
1
0
2
0
0
1
0
2
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
2
2
1
0
0
0
0
0
2
0
0
2
0
2
0
0
2
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
3
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
2
0
2
2
0
0
0
0
0
2
2
0
0
0
0
1
1
0
0
0
1
2
0
2
1
0
0
0
2
2
3
1
0
0
2
0
1
0
2
2
0
2
0
1
0
0
3
0
0
1
2
1
0
0
0
0
0
0
3
1
0
0
2
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
5
0
0
0
1
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
1
0
0
1
0
1
0
2
0
2
0
2
0
0
1
0
0
0
0
0
0
0
1
0
3
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
2
1
1
0
0
0
0
1
2
0
5
1
0
0
0
0
0
0
0
0
1
1
0
2
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
2
0
1
0
0
1
2
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
1
2
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
2
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
8
2
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
3
0
2
1
0
3
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
2
1
1
0
0
0
2
0
0
1
1
2
0
2
0
1
2
1
0
0
4
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
2
1
0
1
2
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
2
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
1
0
1
0
1
2
0
0
0
2
0
1
2
1
2
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
1
1
2
0
1
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
4
2
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
1
0
0
2
0
1
0
0
0
0
0
2
0
0
1
1
0
1
1
0
0
3
0
0
0
1
4
2
0
1
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
1
0
0
2
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
3
0
0
0
1
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
1
2
3
0
1
0
1
0
2
0
0
0
0
0
5
0
0
0
3
0
0
0
0
0
0
2
0
2
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
2
0
2
1
2
0
0
1
0
1
0
1
0
1
0
0
2
0
0
1
0
1
0
0
7
0
0
0
2
0
0
2
0
0
0
0
2
0
0
1
2
2
0
0
2
2
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
1
0
2
0
2
0
0
0
1
0
0
0
0
0
1
2
0
2
2
0
1
0
1
2
0
0
1
2
0
0
0
2
0
1
0
1
0
0
0
0
2
0
2
2
0
1
2
0
2
0
0
0
0
2
1
0
0
0
3
1
0
2
0
0
0
0
2
2
1
0
0
6
0
0
0
2
2
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
2
0
0
1
1
9
0
0
0
0
0
0
0
1
1
0
1
0
0
0
2
0
0
2
0
0
0
5
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
3
0
1
0
0
2
2
3
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
1
1
0
0
0
1
0
0
2
0
1
1
0
0
0
0
0
2
0
0
0
0
1
3
1
0
0
2
0
0
0
0
0
9
2
0
0
0
1
2
3
0
0
0
0
0
0
0
2
0
2
2
0
2
0
2
0
0
0
0
0
0
1
0
1
2
0
0
2
0
0
3
0
3
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
6
0
3
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
2
2
0
0
0
0
0
2
2
1
0
0
0
0
0
2
0
0
2
0
0
0
2
1
0
2
0
0
0
2
0
2
0
2
0
1
0
0
1
0
1
0
1
0
0
1
2
0
0
0
2
2
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
1
0
0
0
2
0
1
2
0
1
0
2
1
0
2
0
0
0
2
0
0
0
0
1
2
1
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
1
3
2
0
4
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
1
0
0
2
0
0
2
2
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
2
1
0
1
0
0
2
0
9
0
3
0
24
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
2
0
0
1
2
2
0
2
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
3
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
1
3
0
0
0
0
2
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
2
0
0
0
0
2
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
2
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
3
0
4
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
3
0
0
2
1
0
1
0
0
1
0
0
1
2
0
0
0
1
2
3
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
1
1
3
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
1
0
5
0
0
3
2
0
0
1
1
1
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
1
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
2
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
4
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
2
0
0
1
2
2
0
1
0
3
0
0
0
1
0
0
2
0
1
1
0
0
0
3
2
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
2
2
0
2
0
0
1
2
2
0
0
2
0
0
0
2
0
2
0
1
2
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
1
1
0
0
0
0
2
0
0
1
0
1
2
1
3
0
1
0
0
0
1
0
0
2
1
0
1
2
0
2
0
4
0
0
0
1
0
2
0
0
2
3
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
2
0
0
1
2
0
0
1
0
0
1
1
2
2
0
0
0
1
0
0
0
4
1
1
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
2
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
6
1
2
0
1
0
0
0
1
1
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
1
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
2
1
1
0
2
0
0
0
7
0
0
2
0
1
0
0
0
2
3
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
2
1
0
0
2
2
1
0
0
0
0
0
2
0
0
1
3
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
3
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
5
0
0
1
0
0
0
0
1
2
0
0
2
0
0
2
0
0
0
1
0
0
1
2
2
0
0
1
0
0
0
0
0
0
1
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
2
0
0
1
0
1
2
0
1
0
1
0
0
0
0
1
0
4
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
1
0
0
0
0
2
2
0
1
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
2
0
1
1
0
0
0
1
1
0
2
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
1
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
1
0
0
0
0
1
1
2
0
2
0
1
0
0
0
0
0
3
0
1
2
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
1
1
1
2
0
0
0
2
0
0
2
0
1
0
3
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
1
2
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
2
1
2
1
2
0
0
0
0
0
1
1
2
1
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
1
0
0
2
2
0
0
1
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
9
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
3
0
0
2
4
1
0
0
0
0
0
0
0
2
2
1
0
0
0
2
2
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
2
2
0
1
0
0
0
0
0
1
4
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
2
2
2
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
2
0
2
0
1
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
3
2
0
0
0
1
2
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
5
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
2
1
1
1
0
0
2
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
2
1
0
0
0
2
1
0
0
0
0
2
3
2
0
1
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
13
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
2
2
1
0
0
0
1
0
0
0
0
0
3
1
1
1
2
0
0
1
0
0
0
0
0
2
0
0
0
3
2
0
0
0
0
0
0
0
0
3
0
0
0
1
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
1
0
0
2
0
0
3
0
1
1
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
1
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
2
0
0
1
0
0
1
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
1
0
3
0
0
0
0
0
0
4
0
0
0
0
0
0
2
0
2
0
0
2
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
3
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
4
2
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
1
0
2
0
0
0
4
0
0
4
0
0
0
0
1
0
0
1
0
0
1
0
1
1
0
1
0
1
0
0
3
0
0
1
2
0
4
2
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
1
0
2
1
2
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
2
1
0
0
1
0
0
2
0
0
0
2
0
2
0
1
1
0
2
2
0
0
2
0
0
2
0
0
0
0
0
1
0
0
1
4
0
0
1
0
0
1
0
1
0
0
0
1
2
0
0
0
1
0
2
0
1
0
0
0
0
0
0
2
0
2
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
1
0
1
1
0
2
0
0
2
0
1
2
2
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
2
2
0
1
0
2
0
2
2
0
0
3
2
1
1
0
2
0
0
1
0
2
0
0
0
0
2
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
1
1
0
1
0
2
1
2
0
1
1
0
2
0
0
3
3
0
4
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
2
0
0
0
0
0
0
0
1
1
2
0
0
0
2
0
0
0
0
0
3
3
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
2
0
2
0
0
0
0
0
0
0
0
1
2
1
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
2
0
0
0
1
4
1
0
0
3
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
2
2
2
0
0
4
0
0
0
2
0
0
2
1
1
0
0
0
1
0
2
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
1
1
2
0
2
0
0
3
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
3
0
2
1
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
3
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
2
1
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
2
2
0
1
0
0
2
0
1
0
1
0
2
0
3
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
3
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
2
2
2
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
2
0
1
2
0
2
0
0
0
0
1
1
4
0
0
2
2
0
0
0
1
0
0
0
0
0
0
2
1
0
0
3
1
1
0
2
3
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
1
0
0
0
2
1
0
0
0
0
2
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
2
2
2
0
0
2
0
0
1
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
2
1
1
1
0
0
7
0
2
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
2
0
8
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
1
0
2
0
0
1
0
0
1
0
1
0
0
0
4
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
11
0
0
0
0
0
1
3
0
0
0
2
1
0
0
0
0
0
2
0
2
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
1
3
0
1
4
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
3
2
0
1
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
2
0
1
0
1
0
0
0
0
2
0
0
2
0
1
2
1
0
0
1
0
0
2
1
2
0
2
0
2
0
0
0
1
0
1
0
1
0
1
1
2
2
1
0
1
0
0
2
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
1
0
0
2
0
0
0
0
1
1
0
0
2
0
0
1
2
1
0
0
0
0
0
2
0
1
0
2
0
0
0
2
1
2
3
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
1
2
3
0
1
0
0
1
0
0
0
0
0
0
0
0
3
0
0
1
0
1
2
0
1
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
7
0
0
0
0
0
2
0
0
2
0
2
0
1
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
1
0
0
0
2
2
0
0
0
1
0
3
1
0
4
0
0
2
0
2
0
0
0
5
0
1
0
0
0
0
0
0
0
1
2
1
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
1
0
0
0
0
1
0
0
2
1
1
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
1
0
1
0
0
0
1
2
1
0
0
0
0
0
0
0
4
0
0
1
0
0
2
1
0
3
2
0
0
3
0
0
1
0
1
0
0
1
2
0
0
3
0
1
0
0
2
2
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
2
1
0
1
2
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
2
2
2
1
0
0
0
0
0
0
0
0
1
0
2
0
1
1
3
0
0
0
0
0
0
0
1
2
0
0
0
0
2
2
2
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
2
0
2
0
0
2
0
0
0
1
3
0
0
0
0
0
1
1
0
0
0
2
0
2
1
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
2
2
0
1
0
1
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
1
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
2
0
0
1
1
0
0
0
2
0
0
1
0
0
2
2
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
1
0
0
3
1
0
0
0
2
0
2
0
0
0
0
0
0
1
2
0
0
0
0
3
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
5
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
3
2
0
0
0
0
0
2
3
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
10
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
1
0
2
0
1
2
0
0
0
2
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
6
2
0
0
2
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
2
0
2
1
2
0
0
0
0
0
0
0
3
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
1
4
0
2
0
0
0
0
2
3
0
0
0
1
0
1
0
2
0
0
2
2
0
0
2
0
4
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
3
7
0
1
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
1
0
0
0
2
1
1
0
0
0
0
2
2
0
0
0
1
0
0
0
2
0
0
2
2
0
0
0
0
0
1
0
0
0
0
2
2
2
1
0
2
0
0
0
0
0
0
2
0
2
2
0
0
0
2
1
0
0
1
0
0
1
0
0
3
1
2
1
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
1
2
0
2
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
3
0
1
0
0
2
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
1
0
2
2
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
2
0
0
0
1
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
2
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
2
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
1
0
0
0
0
1
0
0
0
2
2
0
0
0
1
0
0
5
1
3
0
0
2
7
2
1
0
1
0
0
0
1
1
0
1
1
0
0
0
0
2
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
2
2
0
1
0
2
0
0
0
0
0
2
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
3
0
1
0
0
0
1
0
0
0
0
0
0
2
2
0
0
1
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
3
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
3
2
1
0
0
2
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
1
0
0
2
0
4
0
1
0
0
0
0
0
0
1
1
0
0
3
1
0
1
1
0
0
2
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
2
0
0
0
0
0
3
1
2
2
0
0
0
0
0
0
1
0
1
1
0
0
0
7
0
5
0
0
0
0
2
2
2
0
0
1
0
2
0
1
1
0
0
2
0
2
0
0
2
2
0
0
0
0
0
0
0
0
1
1
4
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
1
0
2
0
1
0
1
0
0
1
0
0
0
0
2
2
0
1
2
0
0
0
0
0
0
0
1
0
2
1
2
0
3
0
0
2
0
1
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
3
0
2
1
0
0
1
2
0
0
0
1
0
0
0
0
0
1
0
2
0
2
2
0
2
0
1
0
0
3
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
1
1
0
0
2
0
0
0
0
0
1
0
0
0
1
1
2
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
1
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
2
1
0
2
0
0
0
0
1
2
0
0
2
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
2
2
2
0
0
0
0
1
0
1
0
0
0
1
0
2
2
1
0
0
0
1
1
0
2
1
1
1
0
1
0
4
0
2
0
1
0
0
0
0
0
0
1
0
1
0
2
0
0
2
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
2
1
10
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
1
1
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
3
0
0
0
0
1
2
0
2
0
0
1
2
0
1
0
0
2
0
0
2
0
0
0
0
0
1
0
2
1
0
1
0
1
0
0
0
0
0
1
0
0
2
1
1
0
2
0
0
0
0
0
0
0
1
2
0
2
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
2
1
2
2
0
0
0
0
0
2
1
0
0
2
1
0
3
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
2
0
2
0
0
1
0
0
3
0
0
2
0
0
1
0
0
0
3
1
0
0
1
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
1
0
0
1
0
0
0
0
2
0
3
0
1
0
0
0
0
0
0
2
2
0
1
0
2
0
0
0
0
1
5
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
2
0
0
0
0
0
0
1
0
1
0
2
1
1
0
1
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
5
0
0
0
1
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
2
0
0
1
2
0
0
0
0
0
2
1
0
0
1
2
0
0
2
0
2
1
0
1
0
0
1
0
0
2
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
5
0
3
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
3
1
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
1
2
3
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
2
4
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
1
0
2
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
1
1
0
2
0
0
0
2
0
0
2
1
2
0
0
2
2
1
1
0
0
0
0
0
0
0
2
2
0
1
0
0
1
0
0
1
0
0
4
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
2
2
0
2
0
0
0
1
1
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
2
0
2
1
0
2
0
0
1
0
0
0
1
0
0
2
3
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
1
0
2
0
0
2
2
1
0
2
0
0
1
0
0
1
0
0
0
0
1
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
1
0
2
1
0
1
0
1
0
0
0
1
0
2
2
0
0
0
0
1
0
2
1
0
1
0
0
0
0
0
0
0
1
1
2
2
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
2
0
2
2
0
2
1
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
2
2
0
2
1
0
2
1
0
0
3
2
2
0
2
0
0
2
0
0
1
1
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
2
2
2
1
0
1
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
2
1
0
1
2
0
0
2
1
1
1
0
0
0
0
0
0
1
1
1
2
0
0
0
2
0
0
0
1
1
1
0
1
2
1
0
0
0
2
2
0
2
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
2
0
0
0
2
0
0
0
5
1
1
2
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
1
2
0
0
2
0
0
2
2
0
2
0
1
0
1
0
3
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
2
0
2
2
0
2
0
0
0
3
0
0
0
1
0
3
0
1
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
2
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
3
0
0
0
0
0
1
1
0
0
0
1
1
1
0
1
0
0
0
0
1
0
4
0
0
0
0
2
1
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
3
0
0
0
0
1
2
2
0
0
2
0
0
0
0
11
1
0
1
0
0
2
0
0
2
2
0
2
1
1
0
2
2
0
2
0
2
0
0
0
1
0
2
0
0
0
0
0
0
1
0
1
1
1
0
0
1
0
0
0
2
0
0
2
0
2
0
0
1
2
0
0
0
1
0
2
0
1
0
0
0
1
2
0
0
4
1
0
1
0
2
0
0
0
1
0
0
2
1
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
2
0
0
1
1
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
1
0
1
5
0
0
0
2
0
0
1
0
0
0
0
2
0
3
1
1
0
1
0
0
0
0
1
0
1
0
3
0
0
0
0
1
0
2
2
0
0
0
0
0
1
0
0
1
1
1
1
0
1
0
0
0
3
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
2
1
1
1
2
2
0
0
0
2
3
0
1
0
1
1
0
0
1
0
0
0
4
0
0
0
0
0
2
0
1
2
0
0
0
1
0
4
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
1
0
20
0
1
1
0
0
0
0
0
0
1
0
2
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
1
0
0
2
1
3
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
5
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
2
0
0
2
0
0
0
0
0
0
0
1
0
1
4
0
0
0
0
2
0
4
2
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
1
0
1
0
2
0
0
0
0
0
0
0
3
0
0
2
1
0
0
1
0
0
0
0
2
2
0
0
0
2
0
0
3
2
1
0
2
0
0
1
0
0
0
0
0
0
0
0
1
2
0
2
1
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
2
2
0
1
0
2
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
6
2
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
1
0
3
0
2
1
0
1
2
0
0
2
2
1
2
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
1
1
2
2
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
2
3
0
0
0
0
0
2
1
2
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
1
2
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
2
0
1
0
1
0
1
2
0
2
0
3
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
4
0
2
0
0
0
2
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
2
0
0
2
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
3
0
1
0
2
0
3
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
1
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
1
0
0
0
0
4
0
2
0
1
1
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
1
0
0
1
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
13
1
1
0
0
2
2
0
0
0
1
0
0
0
3
0
0
0
0
0
0
1
0
0
1
0
2
1
2
0
0
2
0
0
0
0
1
0
2
0
0
2
0
1
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
2
0
0
3
0
1
1
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
2
1
2
2
0
2
0
3
1
1
0
2
0
0
0
0
3
1
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
1
7
0
0
0
0
1
4
0
2
0
0
0
0
1
0
0
0
0
0
4
2
0
0
0
0
0
1
0
1
2
2
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
1
0
2
0
0
0
0
2
3
0
0
0
0
0
1
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
3
0
1
0
0
2
0
0
0
2
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
4
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
1
0
3
0
0
1
1
0
0
0
0
2
0
0
0
1
0
2
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
2
3
0
1
1
2
1
1
2
0
0
0
0
0
1
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
6
0
0
0
0
1
0
0
2
0
5
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
1
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
1
0
1
1
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
2
3
2
0
2
0
1
0
0
0
0
0
0
0
2
1
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
2
1
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
5
2
1
0
0
2
0
0
0
0
0
1
0
1
2
0
1
3
0
0
2
0
2
0
0
1
2
0
0
0
2
0
2
0
0
0
1
0
1
0
0
0
1
0
0
0
2
2
0
1
0
0
0
1
0
0
1
0
2
0
0
4
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
4
3
0
2
2
3
0
0
0
2
0
0
2
0
2
2
0
0
0
0
0
0
2
0
0
2
2
3
3
1
0
2
0
0
0
0
0
0
0
1
0
2
1
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
1
2
0
0
2
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
6
0
0
2
1
0
0
0
0
0
0
2
1
0
0
0
1
0
1
0
2
0
0
1
2
0
0
0
2
0
1
2
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
2
0
1
0
0
1
0
0
2
0
0
0
1
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
1
2
2
0
2
2
0
0
2
0
0
1
0
2
0
2
2
2
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
2
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
2
0
2
1
0
0
0
0
0
1
0
0
2
2
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
1
0
1
0
2
0
0
0
1
0
0
0
0
1
2
1
0
1
0
0
0
2
2
0
0
1
0
2
0
0
0
2
0
3
0
2
0
0
0
0
0
0
0
1
0
0
0
1
2
2
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
4
1
0
1
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
3
0
0
0
0
5
2
0
0
2
1
0
0
0
1
1
1
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
1
0
0
0
0
1
0
0
0
0
2
2
0
0
0
1
1
0
0
2
0
2
0
2
0
0
0
0
0
0
2
0
3
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
1
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
3
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
1
2
1
2
0
0
1
1
1
0
0
3
0
0
1
3
1
0
0
0
0
0
0
0
2
0
2
2
0
1
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
2
2
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
11
2
5
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
1
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
2
3
0
0
1
2
0
3
2
0
1
0
2
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
5
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
2
2
0
1
1
2
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
4
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
2
2
0
1
2
1
0
0
1
0
2
0
0
0
0
1
0
0
1
0
1
1
0
0
0
4
3
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
1
3
0
1
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
1
3
1
0
0
2
0
0
0
0
0
2
0
2
0
1
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
1
0
2
2
0
2
0
1
2
0
1
0
0
0
0
1
0
2
0
2
0
1
2
0
2
2
0
0
0
0
0
0
1
0
2
2
1
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
1
0
0
2
0
0
0
2
0
2
0
0
2
0
0
1
1
2
3
2
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
2
0
0
5
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
1
0
0
2
0
0
0
0
0
0
16
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
3
0
0
0
2
2
0
0
2
0
0
0
3
0
0
0
0
1
0
0
1
0
2
2
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
4
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
8
0
0
0
2
0
0
1
2
0
0
4
0
0
0
0
0
0
4
0
1
0
0
0
0
1
0
0
0
0
3
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
4
0
2
0
0
3
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
1
1
0
0
1
0
0
1
0
3
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
1
0
2
1
0
0
1
0
0
0
0
0
0
1
2
0
2
2
5
0
2
0
1
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
2
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
1
1
0
1
0
1
0
3
2
0
0
2
0
0
5
1
0
0
0
0
1
0
0
0
0
0
2
0
3
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
3
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
2
0
0
1
0
0
2
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
1
3
0
1
2
0
2
0
0
0
0
1
0
1
0
2
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
1
0
0
1
2
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
2
0
2
0
0
1
0
4
0
0
0
0
0
0
2
2
0
2
0
0
0
0
1
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
1
0
8
0
0
0
0
0
1
0
2
1
0
0
2
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
1
0
0
1
2
0
0
0
0
2
2
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
2
0
0
0
2
0
0
0
0
0
2
1
2
1
1
0
0
0
0
0
0
1
0
0
2
0
2
1
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
3
0
0
2
1
0
2
1
2
0
0
0
0
1
0
3
0
0
2
0
1
2
0
2
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
2
0
0
0
0
2
1
3
0
0
2
0
2
1
1
0
0
1
0
0
0
1
3
0
0
0
0
0
1
1
0
1
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
5
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
1
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
6
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
1
1
2
1
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
3
0
2
0
0
2
0
0
1
0
0
1
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
1
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
2
2
0
1
1
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
2
1
0
1
0
0
0
0
0
3
0
0
0
0
0
0
2
0
1
2
1
0
0
0
0
0
1
0
0
2
2
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
2
1
1
0
0
0
2
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
2
0
0
1
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
1
0
2
2
0
2
0
0
0
0
0
2
0
0
0
0
1
2
2
0
0
0
2
0
0
0
0
0
1
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
2
1
4
1
0
3
1
1
0
0
0
0
0
0
1
0
0
0
2
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
2
0
0
1
0
0
2
1
0
0
0
2
0
0
2
1
0
1
1
0
0
0
0
0
0
3
1
0
2
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
7
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
3
2
0
0
0
3
0
1
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
3
2
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
2
0
1
0
1
0
0
0
2
0
2
2
0
0
0
0
0
3
0
2
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
2
2
0
0
1
2
2
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
5
3
0
0
0
3
0
0
1
0
1
0
0
0
0
0
2
0
1
0
2
1
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
2
0
0
0
0
0
0
0
0
3
0
0
0
0
2
3
0
2
2
1
0
1
0
0
0
0
0
0
0
3
0
1
1
0
0
0
2
0
0
0
0
2
4
0
2
1
1
0
2
0
0
0
2
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
3
1
0
2
0
0
0
0
0
0
1
2
0
2
0
1
0
0
0
0
0
0
1
0
1
0
2
2
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
2
0
0
0
0
0
0
2
2
3
2
0
1
0
2
0
0
1
0
0
0
0
3
3
2
0
0
0
2
0
0
0
0
1
0
0
3
0
1
0
1
0
0
2
0
0
0
0
1
0
2
0
0
0
0
3
2
0
0
0
0
0
0
1
3
0
1
1
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
2
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
1
3
0
2
1
1
0
2
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
3
3
0
0
0
0
0
2
0
0
0
2
0
2
2
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
2
0
2
2
0
0
2
1
1
1
2
2
0
0
0
0
0
1
0
2
0
1
0
0
1
1
0
1
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
1
0
2
0
2
5
2
3
2
0
1
1
0
1
3
1
2
0
1
0
1
0
1
0
0
0
0
0
1
0
0
2
0
0
0
8
0
1
0
1
2
1
0
2
2
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
6
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
3
1
2
1
0
1
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
3
0
1
3
0
1
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
2
0
0
0
0
1
0
0
4
0
0
2
0
0
0
0
3
0
1
0
0
2
0
0
0
4
2
2
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
1
1
1
1
1
0
0
0
0
0
0
0
1
0
0
2
1
0
2
0
0
2
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
1
0
1
0
0
7
2
2
2
0
1
0
0
0
0
1
0
0
0
3
1
1
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
4
2
0
0
0
0
4
0
2
2
0
1
0
0
1
0
0
0
0
3
1
0
0
7
0
0
0
0
0
2
0
2
1
0
0
0
0
1
0
1
0
1
2
0
0
1
0
0
2
0
2
0
2
2
0
0
0
2
0
1
1
2
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
3
0
0
0
0
0
1
0
2
2
1
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
1
0
2
1
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
2
0
0
0
0
0
0
5
0
4
0
0
2
1
0
0
0
0
0
1
1
5
0
0
2
0
0
0
0
1
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
2
0
0
2
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
2
0
0
0
0
1
0
2
0
2
1
2
1
0
0
2
0
2
0
1
1
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
2
0
1
0
2
0
0
2
1
1
1
1
0
0
0
3
2
0
0
1
2
0
0
1
3
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
3
3
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
1
0
1
2
0
0
0
1
2
0
0
1
1
0
0
0
0
1
0
1
1
0
0
0
2
0
0
0
1
0
2
0
0
0
2
1
0
0
5
0
2
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
1
1
0
0
1
0
2
0
0
0
2
3
3
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
2
0
0
5
0
2
1
0
1
0
0
0
0
0
0
0
0
0
5
0
0
0
1
0
0
0
1
0
0
1
2
2
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
2
2
0
0
1
1
0
2
0
0
0
1
2
0
2
0
2
0
0
0
0
1
1
0
1
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
9
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
1
0
0
1
0
1
0
1
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
3
2
1
0
0
0
0
5
0
2
0
0
1
0
0
1
2
0
3
2
2
0
0
1
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
1
0
0
1
4
0
2
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
2
0
0
2
2
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
1
2
1
0
0
0
2
0
0
0
2
1
0
0
1
0
0
0
0
0
1
2
0
0
1
0
1
0
0
0
2
0
0
2
0
1
1
0
1
0
0
0
0
0
2
1
2
0
2
0
2
0
1
0
1
0
0
0
0
2
2
2
2
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
2
2
0
0
2
0
1
0
1
0
1
0
0
2
0
0
0
3
2
0
0
3
2
1
0
0
0
0
4
0
0
2
0
0
0
2
1
1
1
1
2
1
2
0
1
0
0
2
0
0
0
2
2
0
2
1
0
0
1
0
1
0
0
1
2
0
1
1
2
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
2
0
2
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
2
0
1
0
1
0
0
2
0
0
0
0
2
0
2
0
0
3
1
0
1
1
0
0
0
1
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
2
0
1
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
3
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
2
2
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
1
3
0
0
0
1
2
0
1
0
3
0
0
1
1
0
1
0
0
1
0
0
2
0
0
0
1
2
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
1
2
0
0
2
0
0
2
0
0
1
1
3
0
0
3
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
2
0
0
0
1
2
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
4
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
3
1
0
1
1
0
0
0
1
0
1
0
2
0
1
0
2
0
2
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
1
1
0
0
0
0
1
1
2
0
0
0
0
2
0
1
1
0
1
2
0
2
1
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
2
0
0
3
0
0
0
1
0
1
1
0
0
0
0
0
0
6
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
4
0
0
0
0
2
0
0
0
1
0
2
0
2
0
0
0
1
1
2
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
2
0
0
2
2
1
0
1
0
0
1
1
0
3
1
0
0
1
2
0
0
0
0
0
0
2
2
0
0
3
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
2
0
0
0
0
0
2
0
2
0
1
0
1
3
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
2
0
0
4
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
6
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
2
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
2
0
0
2
7
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
2
1
0
2
1
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
3
2
3
0
0
0
2
0
0
0
3
0
1
1
1
0
1
0
0
0
0
0
2
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
1
0
1
0
0
1
3
0
0
0
2
0
0
0
0
0
2
0
1
0
0
2
1
0
0
0
0
2
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
1
0
2
1
2
0
1
2
0
0
1
3
2
3
2
0
0
0
1
1
1
1
1
0
0
0
0
0
0
0
5
2
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
1
1
0
3
0
0
0
0
3
0
0
0
0
2
0
2
0
2
1
1
0
0
2
0
0
0
0
0
0
2
2
0
1
0
0
2
0
2
0
0
0
0
1
2
2
2
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
2
0
0
0
3
0
0
0
0
2
0
1
0
0
1
0
0
0
0
2
2
0
0
2
1
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
2
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
1
0
1
0
0
0
0
2
0
0
1
1
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
2
1
0
2
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
1
0
0
0
1
2
0
2
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
4
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
2
0
2
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
2
1
0
0
0
0
0
0
1
2
0
0
2
0
1
0
0
1
1
0
0
2
2
0
0
0
2
0
0
0
0
1
0
1
2
0
0
1
0
0
0
1
1
0
1
0
1
0
1
0
0
0
0
2
0
0
1
1
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
2
0
0
0
3
0
0
2
2
1
0
0
0
0
2
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
2
0
1
0
0
1
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
2
1
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
2
0
1
0
1
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
2
2
0
0
0
1
0
2
0
0
0
2
0
2
0
1
0
0
5
2
1
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
8
0
0
0
0
2
0
0
2
2
0
1
1
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
1
2
0
1
1
0
1
2
0
1
2
0
0
0
1
2
0
0
0
2
0
0
0
0
5
0
1
0
0
0
1
2
0
0
0
1
1
0
0
0
0
0
2
0
0
2
0
0
0
0
2
2
0
1
0
0
2
1
0
0
0
0
3
2
0
0
0
0
1
0
0
0
3
0
0
0
1
3
1
2
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
1
2
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
2
2
3
2
2
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
2
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
2
0
2
0
0
0
3
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
4
0
3
0
0
0
0
0
0
0
2
0
2
0
1
2
0
1
1
1
1
0
0
1
0
2
0
0
0
2
0
2
0
1
1
1
0
0
0
0
1
3
0
0
0
2
0
2
1
0
2
0
0
0
0
0
0
0
1
0
1
2
0
1
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
2
0
1
0
2
0
2
2
1
0
0
0
4
0
0
0
2
0
0
0
2
1
1
0
1
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
2
2
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
2
2
0
0
0
1
3
0
0
0
0
2
0
2
1
0
0
0
0
0
1
0
1
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
1
0
1
2
1
0
2
2
0
0
2
0
0
0
0
2
3
0
0
0
0
0
0
1
0
0
0
2
2
1
0
0
0
1
3
0
0
1
1
0
1
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
3
0
1
2
0
0
0
1
1
1
0
0
0
2
0
0
0
0
0
1
0
1
3
1
0
0
2
2
0
0
0
0
1
1
0
0
0
0
0
0
3
0
0
0
0
0
2
2
2
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
1
0
0
0
2
2
0
3
2
0
1
3
0
1
3
2
2
0
0
2
1
0
0
0
1
0
0
2
1
1
0
2
0
2
0
0
2
1
0
0
2
0
1
1
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
3
2
1
0
0
1
1
0
1
0
1
1
2
1
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
2
0
1
0
0
0
0
0
3
0
0
1
0
0
0
0
2
0
0
0
1
0
0
1
0
1
4
1
0
0
0
2
0
0
0
0
1
0
0
1
1
1
0
0
11
2
0
4
0
0
0
0
0
0
1
0
2
0
0
4
0
2
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
4
0
0
2
0
0
0
0
1
2
0
0
1
2
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
1
0
0
1
1
0
2
2
0
1
0
0
2
1
1
0
1
0
0
0
0
0
2
0
0
0
0
2
2
0
0
1
0
0
2
3
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
5
0
0
0
0
0
0
2
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
2
1
0
0
0
2
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
1
0
2
0
0
1
0
1
1
2
2
0
0
0
2
1
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
1
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
1
1
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
3
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
4
0
0
2
4
2
0
0
0
0
0
0
0
1
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
2
1
0
0
1
0
0
2
2
1
0
2
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
3
0
0
0
1
0
0
0
3
0
2
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
2
0
0
0
3
0
0
2
0
0
0
1
0
1
1
0
0
0
2
0
3
0
0
0
0
0
0
2
2
0
1
2
0
0
0
0
1
2
0
1
1
0
2
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
2
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
4
2
0
0
0
2
1
0
0
0
0
1
1
0
2
0
0
0
0
2
1
2
1
0
0
1
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
2
0
0
3
2
1
0
0
1
1
0
0
2
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
1
1
0
0
0
2
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
3
0
0
0
0
0
2
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
2
3
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
8
1
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
1
3
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
4
0
0
0
1
0
0
2
2
0
0
0
1
0
0
0
1
1
0
2
0
3
0
1
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
2
0
0
2
3
0
0
0
0
1
0
1
2
0
1
0
0
0
1
0
3
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
3
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
2
1
3
1
2
0
0
0
0
1
0
0
0
0
0
2
0
2
2
0
0
1
0
0
2
0
0
2
0
0
1
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
3
0
0
0
2
0
0
0
2
1
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
1
0
1
0
0
1
0
2
2
0
13
0
0
0
0
1
0
0
1
0
0
2
0
1
0
0
0
1
1
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
3
0
1
4
0
2
0
0
0
0
5
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
1
0
2
1
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
2
2
0
0
0
0
2
0
0
0
2
0
2
0
2
2
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
1
0
1
0
3
0
2
0
1
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
2
0
1
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
2
3
0
0
0
0
2
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
2
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
1
2
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
2
0
1
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
2
2
0
0
4
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
3
0
0
0
3
0
1
0
0
2
0
2
0
3
0
0
2
3
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
2
0
0
0
0
1
0
2
6
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
1
1
1
1
0
0
0
0
4
0
0
0
0
5
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
2
1
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
1
1
0
0
0
1
0
1
0
2
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
2
0
2
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
2
0
0
0
0
1
0
1
2
0
0
2
0
0
0
2
0
0
1
0
3
0
0
0
0
0
0
1
0
1
1
0
1
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
3
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
5
0
0
0
1
0
1
0
2
1
1
0
1
0
0
2
3
0
0
0
0
1
2
0
0
2
0
1
0
0
1
0
2
0
0
0
0
2
0
1
0
0
0
4
4
0
0
0
2
0
1
0
0
0
1
2
2
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
2
0
0
0
2
3
1
0
2
1
1
0
2
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
2
0
1
1
0
0
2
0
0
2
0
0
0
2
0
0
1
0
0
0
0
5
1
0
0
1
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
2
0
1
0
1
0
0
0
0
0
4
0
0
3
0
1
2
2
0
0
0
0
0
0
0
0
0
0
2
2
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
6
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
1
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
3
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
2
0
0
2
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
2
1
1
0
0
2
2
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
1
0
0
0
1
2
1
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
2
0
0
0
0
0
0
2
1
0
0
1
0
0
1
0
1
2
2
1
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
2
0
2
0
1
0
1
1
0
0
0
2
0
0
0
0
1
1
1
1
1
0
0
1
0
0
0
1
0
2
0
0
0
2
0
1
0
0
0
0
1
0
0
0
1
0
2
0
0
1
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
2
1
0
0
2
1
0
0
2
0
2
0
1
1
0
0
3
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
1
0
3
0
2
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
1
0
0
0
1
3
0
1
0
0
0
0
0
3
1
0
0
0
1
1
0
0
0
0
0
1
3
0
0
0
0
1
2
1
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
1
0
0
5
6
0
2
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
2
1
0
2
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
3
1
0
0
0
1
0
2
2
0
0
1
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
2
0
2
0
0
1
0
0
1
0
0
0
0
0
0
1
2
4
1
0
2
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
1
2
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
3
0
0
0
1
0
0
0
5
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
1
0
0
0
0
0
6
0
1
0
0
1
0
0
0
0
2
0
2
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
1
0
0
0
1
0
1
2
0
0
2
0
0
2
2
1
0
0
0
0
0
0
0
0
0
1
1
0
4
0
1
1
0
0
1
0
2
0
1
0
0
0
1
2
0
0
0
0
0
1
0
5
0
0
0
2
0
2
0
0
0
0
1
2
0
1
0
0
0
0
1
1
0
0
0
0
0
0
7
0
0
0
0
0
1
2
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
3
2
0
0
3
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
2
0
0
0
1
0
0
0
0
0
0
2
2
0
1
0
1
0
2
0
0
0
2
0
0
0
0
3
0
0
0
0
2
3
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
2
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
2
0
0
2
0
0
0
1
0
1
0
0
1
0
2
0
0
0
0
2
0
2
0
0
0
0
1
2
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
3
1
0
0
2
0
0
0
2
2
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
1
0
2
0
0
1
0
0
1
0
0
2
0
0
1
0
0
0
0
1
1
2
0
0
2
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
1
0
2
2
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
2
0
0
0
1
1
0
0
0
0
1
0
2
0
0
0
0
4
0
0
0
3
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
3
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
1
2
0
1
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
2
0
0
0
1
2
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
2
0
0
0
0
0
0
1
2
0
2
3
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
2
1
0
0
0
2
0
0
0
1
2
0
0
0
4
2
0
2
0
0
2
1
0
0
0
1
0
0
0
0
0
1
2
1
0
0
0
0
1
6
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
1
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
1
2
2
1
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
4
0
0
0
0
2
0
0
1
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
1
0
0
0
0
0
1
0
0
2
2
0
0
1
2
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
2
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
2
2
1
2
1
0
1
0
0
0
0
14
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
1
0
2
0
2
0
0
1
2
3
0
0
0
2
0
1
0
1
1
0
0
0
2
0
0
0
0
2
0
1
0
0
0
2
0
1
1
3
1
0
2
0
1
1
1
1
1
2
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
2
0
0
0
4
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
2
0
0
1
0
0
0
1
0
1
1
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
3
0
0
1
0
0
2
0
5
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
1
2
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
1
0
0
3
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
2
2
2
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
2
0
0
0
1
0
0
2
0
0
0
1
2
1
2
0
3
0
0
0
2
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
7
2
1
2
0
0
0
2
0
2
0
0
1
0
2
1
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
1
1
1
0
0
0
0
2
0
0
0
0
1
3
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
1
2
0
1
1
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
1
0
0
2
0
0
0
0
4
0
0
0
0
0
4
2
2
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
2
2
0
1
0
0
1
0
1
2
0
0
0
0
1
1
0
2
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
3
0
1
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
1
1
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
1
1
0
0
0
0
0
3
0
0
0
0
1
1
0
0
1
0
1
1
4
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
1
1
0
0
2
0
0
2
0
0
2
2
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
6
0
0
0
2
2
0
0
0
0
0
0
0
1
2
1
0
0
0
2
2
1
2
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
2
1
0
0
1
0
0
0
0
2
0
0
0
0
3
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
1
1
3
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
2
0
0
0
2
0
0
2
3
1
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
3
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
1
2
0
0
1
0
3
1
0
0
0
0
0
0
2
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
1
0
2
0
0
2
0
0
0
6
0
0
2
1
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
2
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
1
0
2
0
3
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
3
0
0
1
0
2
0
0
0
2
0
2
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
1
0
0
2
2
0
0
1
0
2
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
2
3
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
1
1
0
1
2
0
0
0
0
0
1
0
0
2
3
0
0
2
1
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
1
1
0
2
0
1
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
2
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
1
1
0
0
2
0
2
0
0
1
0
0
0
0
3
0
0
0
2
1
0
0
0
1
0
5
0
0
0
0
2
1
0
0
1
0
0
0
1
0
0
0
0
0
1
2
2
2
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
3
0
0
0
0
3
0
2
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
1
2
2
0
2
0
0
0
0
0
1
0
0
4
1
1
0
0
2
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
9
0
1
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
1
0
0
2
0
0
3
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
3
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
1
1
1
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
2
1
1
0
2
0
0
1
0
0
0
0
2
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
1
1
0
1
1
0
2
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
5
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
1
2
2
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
4
2
2
0
2
0
0
0
2
0
1
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
7
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
2
1
0
0
2
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
2
0
1
0
1
0
0
0
0
0
0
3
1
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
1
0
2
0
1
0
0
1
2
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
2
0
1
0
1
0
0
0
3
0
1
1
0
6
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
4
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
5
0
0
2
2
2
2
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
3
0
0
0
1
1
0
0
2
0
0
1
0
0
2
1
0
2
0
2
0
1
0
3
1
2
1
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
2
1
0
2
0
3
2
1
0
0
0
3
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
2
0
1
0
2
2
0
1
2
0
0
0
0
0
2
1
1
0
3
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
1
0
0
0
0
3
2
2
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
1
1
0
0
0
0
0
1
1
1
0
2
1
2
0
0
2
0
0
0
0
1
0
0
2
0
2
0
2
0
0
1
0
0
1
0
2
1
2
0
0
2
0
2
2
0
0
0
0
1
3
2
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
2
2
1
2
1
0
0
1
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
3
0
0
0
3
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
3
0
2
2
0
0
0
3
0
0
0
0
0
1
0
0
0
0
1
4
3
1
0
0
2
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
2
2
0
0
1
0
2
0
0
0
2
2
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
2
1
0
0
0
2
0
0
0
2
0
1
0
1
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
1
0
0
2
2
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
3
0
2
0
1
0
0
0
0
0
0
0
9
0
0
0
0
2
1
0
0
1
0
2
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
1
0
0
0
0
1
0
2
0
0
0
2
0
1
0
0
0
0
0
1
3
2
0
2
0
2
2
0
2
2
0
0
0
2
0
0
0
2
0
1
0
2
0
2
0
0
0
0
1
3
0
0
0
4
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
3
1
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
2
2
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
3
0
0
0
0
1
0
0
0
1
0
0
2
1
0
0
2
0
2
0
1
1
0
0
1
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
1
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
3
0
4
0
0
0
2
0
1
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
2
3
0
2
4
0
0
2
0
0
0
1
0
1
0
1
0
0
1
1
0
0
0
0
0
1
2
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
2
1
0
0
2
1
1
1
0
1
0
1
2
0
1
1
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
4
1
1
1
1
3
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
2
3
0
0
1
2
2
2
0
0
0
1
0
0
0
0
0
4
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
2
2
0
0
0
1
0
0
0
1
0
0
0
0
2
0
5
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
1
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
2
0
2
0
0
2
2
0
2
1
1
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
2
0
0
0
0
1
0
2
2
0
2
0
0
0
0
2
2
1
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
1
1
0
0
0
0
2
0
1
0
0
0
0
0
2
1
0
0
1
0
0
0
1
2
0
0
0
0
1
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
1
1
1
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
2
3
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
2
3
0
0
0
0
1
1
0
2
0
0
2
0
0
0
0
2
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
1
0
0
0
2
0
2
2
0
0
0
0
1
0
3
0
0
8
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
5
1
0
0
0
0
1
0
0
0
1
2
0
0
1
2
2
0
1
0
0
3
0
1
2
0
3
0
0
0
1
0
0
0
0
0
0
2
1
0
0
2
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
3
3
0
0
2
1
0
0
1
0
0
2
1
0
0
1
0
2
1
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
2
0
4
0
0
0
0
1
0
0
0
1
1
0
0
2
2
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
2
1
0
2
2
1
0
2
2
1
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
1
0
3
2
1
2
1
0
1
0
0
0
0
0
0
0
0
0
1
0
3
0
2
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
2
0
0
0
0
1
1
0
0
0
0
0
1
0
2
0
2
0
2
0
0
2
0
0
0
0
1
2
0
0
1
3
0
2
1
0
0
1
2
1
0
1
1
0
0
2
0
0
0
0
0
2
1
1
1
0
0
0
3
1
0
0
0
0
2
0
1
1
3
0
0
0
2
1
0
2
0
6
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
3
0
0
0
1
0
0
1
1
0
0
0
2
0
1
2
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
2
0
0
2
2
0
0
0
0
1
0
0
0
0
2
1
0
0
2
2
0
1
0
1
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
2
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
2
0
0
2
1
0
1
0
1
2
0
0
0
0
0
2
0
0
0
1
1
0
0
0
4
0
0
0
0
0
1
0
0
0
2
0
1
0
0
2
0
0
2
2
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
1
0
1
0
0
1
0
2
0
2
0
0
1
2
0
0
0
0
1
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
2
2
0
0
0
2
0
1
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
3
0
0
0
0
8
0
0
2
0
0
0
1
0
0
1
1
1
0
0
0
0
1
0
2
2
0
0
0
0
2
0
0
0
1
0
0
1
0
4
0
0
0
0
1
0
0
0
3
1
0
1
0
8
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
2
0
1
0
0
3
0
0
0
0
0
2
0
0
0
0
0
1
0
1
4
0
1
1
0
1
3
0
3
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
3
0
0
0
2
0
1
3
2
0
0
0
0
0
0
0
6
0
0
0
1
0
0
0
2
0
4
0
0
2
2
1
0
2
1
0
0
0
1
0
1
0
2
0
1
0
2
2
0
0
0
0
0
0
0
1
1
0
2
0
0
0
2
0
0
0
3
0
2
0
0
0
0
0
1
2
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
1
2
0
0
0
2
1
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
2
0
2
0
0
0
0
0
1
0
0
0
1
1
1
0
1
0
0
0
0
1
0
2
2
0
0
0
2
0
1
1
0
0
1
2
0
0
1
0
0
0
1
0
0
1
0
0
2
0
6
2
0
0
0
0
0
2
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
1
2
2
0
0
0
2
0
0
0
2
0
0
0
2
2
0
2
2
1
0
0
3
0
0
2
0
1
0
2
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
4
0
0
0
0
1
0
3
0
2
0
1
0
0
3
0
0
0
0
2
0
3
0
0
0
0
0
1
2
0
1
1
0
0
0
0
1
0
0
0
0
0
1
2
0
2
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
2
0
1
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
3
0
1
1
0
0
1
0
0
2
0
1
0
3
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
2
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
1
0
1
0
0
1
0
3
1
0
0
0
2
0
1
0
3
0
0
3
0
0
0
2
4
0
1
2
1
0
0
2
0
2
0
0
2
1
0
1
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
2
0
0
2
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
1
1
0
0
0
1
0
4
0
0
0
0
0
1
0
1
1
2
2
0
1
2
0
1
0
0
1
0
1
0
0
1
0
0
0
0
3
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
2
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
1
0
1
1
2
2
1
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
2
1
0
1
0
0
0
2
0
0
1
1
2
0
1
0
2
0
2
0
1
0
0
0
0
1
0
0
2
3
1
0
0
0
0
1
1
0
0
1
1
0
1
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
3
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
2
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
1
0
0
1
0
1
0
1
0
2
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
1
0
0
0
2
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
1
2
2
1
0
2
0
8
0
0
1
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
2
0
0
2
0
2
0
2
0
0
1
1
1
0
1
0
0
0
0
0
0
1
2
2
0
0
2
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
1
0
2
1
0
0
0
0
5
0
0
0
1
1
0
2
2
0
0
0
1
2
0
0
2
2
0
0
2
2
0
0
0
1
1
0
0
0
2
0
0
0
1
2
0
0
0
2
1
2
0
0
0
0
3
0
2
0
2
0
0
0
2
1
0
1
1
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
1
0
0
2
0
2
2
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
2
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
1
2
0
0
0
0
0
0
0
2
1
0
2
0
1
0
1
2
0
0
1
0
0
0
0
0
0
2
0
0
0
2
1
0
1
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
2
1
0
0
0
3
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
1
0
1
0
0
2
0
0
0
0
0
2
2
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
4
0
2
0
1
0
1
3
1
0
0
0
0
0
2
0
0
0
0
1
2
2
0
1
0
0
0
0
2
0
0
0
1
0
1
0
0
0
1
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
2
4
0
0
0
0
0
0
0
1
0
3
0
1
1
1
0
0
1
0
2
0
0
0
1
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
1
0
1
0
1
1
3
0
0
0
0
1
3
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
1
0
2
0
0
0
1
0
2
2
2
0
0
0
2
0
0
2
0
0
0
0
2
0
1
2
0
0
0
0
0
2
0
0
0
0
1
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
4
1
2
1
0
0
0
2
0
0
0
0
2
0
1
1
1
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
3
4
0
1
0
1
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
13
0
2
0
0
2
0
0
1
0
0
0
3
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
3
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
1
2
0
0
1
0
0
2
0
0
0
2
3
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
1
2
1
0
1
0
0
0
0
1
1
1
1
0
0
0
1
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
1
0
0
1
0
0
0
4
0
0
0
0
2
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
3
1
0
0
0
2
1
0
0
0
2
1
1
2
0
0
0
0
0
0
1
0
0
0
2
0
0
4
0
2
0
2
2
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
2
1
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
2
0
0
0
2
4
0
2
0
0
0
0
2
0
1
1
1
0
0
0
0
0
0
0
0
0
3
0
0
0
1
4
0
0
4
0
2
0
2
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
2
1
0
1
1
0
0
0
0
0
1
2
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
1
1
0
2
2
0
0
0
0
0
1
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
1
1
0
1
0
2
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
3
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
2
0
2
1
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
3
0
0
0
0
0
2
2
0
3
1
1
2
0
0
0
0
0
0
2
1
2
0
0
0
4
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
1
2
0
0
0
2
2
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
2
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
9
0
0
5
0
2
0
1
0
0
0
1
2
0
1
0
0
0
4
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
1
3
0
0
0
0
0
2
0
0
1
0
1
5
0
0
0
0
0
1
2
0
0
1
0
1
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
2
0
1
0
0
2
0
0
0
0
0
0
0
1
0
1
2
1
0
2
0
1
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
2
0
1
0
0
0
1
0
2
3
0
0
2
0
0
5
0
0
4
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
2
1
0
2
0
3
0
3
1
0
0
0
0
3
0
0
2
1
0
0
0
0
0
2
0
0
0
0
1
0
2
1
0
0
0
0
1
1
0
0
0
0
2
0
0
0
2
0
0
3
0
1
2
2
0
0
1
1
0
0
0
0
0
0
2
0
0
2
0
2
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
3
0
1
1
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
3
2
0
2
0
0
2
0
1
0
0
0
0
0
0
8
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
3
0
0
1
1
1
0
0
2
1
0
2
0
0
1
3
0
0
7
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
2
2
2
2
2
1
0
0
0
0
0
0
0
0
0
1
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
2
2
2
0
0
0
2
2
0
2
0
0
0
0
0
0
0
2
1
1
0
0
1
0
0
0
0
0
0
0
2
1
0
0
3
0
3
0
0
0
0
0
1
0
0
1
0
0
0
2
1
2
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
4
0
0
0
0
0
0
1
2
0
2
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
1
1
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
1
2
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
1
1
1
0
0
0
2
1
0
0
1
0
1
0
1
0
4
1
0
2
0
2
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
2
0
0
0
0
0
3
1
2
0
0
0
0
1
0
0
0
0
0
0
1
1
2
0
0
1
1
2
2
2
1
0
0
0
0
0
0
1
2
3
0
0
2
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
5
1
0
0
0
2
2
2
0
0
1
3
0
0
0
2
0
0
2
0
0
0
0
2
1
0
0
0
2
4
2
0
0
0
0
1
2
0
0
1
0
0
1
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
2
0
5
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
2
0
0
2
0
1
2
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
1
3
0
0
0
0
0
0
2
0
0
0
0
0
3
0
1
0
0
2
0
1
0
0
0
0
2
2
1
0
1
0
0
0
1
1
0
0
0
0
0
1
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
2
2
0
2
0
0
1
2
0
0
1
0
2
2
0
0
0
2
0
0
2
2
2
0
0
0
0
2
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
12
1
1
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
1
0
1
0
0
0
1
0
1
0
0
0
0
3
0
2
0
0
0
0
0
1
0
1
2
0
0
0
0
0
1
0
2
0
0
0
0
0
2
2
0
0
0
0
0
2
0
1
3
2
2
1
0
1
1
0
0
0
1
0
2
2
0
1
0
0
2
0
0
1
2
2
1
0
2
2
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
1
1
3
0
0
0
1
0
4
1
1
0
3
1
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
2
1
2
0
0
0
0
0
0
0
1
0
1
0
1
3
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
3
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
1
0
2
2
0
2
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
2
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
2
0
0
2
0
0
0
0
0
0
0
0
3
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
2
0
2
1
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
11
2
2
2
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
2
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
1
0
1
0
0
0
2
0
1
2
2
1
2
0
2
0
2
0
0
0
0
0
0
0
5
0
2
0
1
0
1
0
1
0
0
0
1
0
0
1
2
0
2
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
1
0
0
0
2
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
3
0
0
0
2
1
0
0
0
0
1
0
0
0
0
1
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
2
4
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
2
0
0
0
0
2
0
1
0
0
0
2
0
2
0
0
0
2
0
0
0
1
1
1
0
0
1
4
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
1
0
2
0
2
0
1
0
0
0
0
0
0
0
3
0
2
1
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
3
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
2
0
1
0
0
2
1
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
1
3
2
0
0
0
1
0
2
0
0
1
0
0
2
1
0
2
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
2
2
1
1
0
0
0
0
0
0
0
1
2
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
1
0
1
0
0
2
0
2
0
0
0
1
0
0
2
0
0
7
0
0
2
0
1
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
3
0
0
0
0
0
0
2
2
0
0
0
0
4
0
0
2
0
1
2
1
1
1
0
0
0
0
0
0
1
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
3
0
2
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
3
2
0
0
0
0
0
0
0
0
0
1
2
2
2
2
0
2
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
1
0
0
1
1
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
1
3
0
0
0
2
0
0
1
0
0
0
2
0
0
0
1
0
1
0
1
0
0
1
1
0
2
0
2
0
2
0
1
0
0
0
0
0
0
1
0
2
0
1
0
2
0
0
1
0
0
0
0
0
2
0
2
2
2
0
1
0
0
3
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
2
1
0
4
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
2
0
3
0
0
0
0
2
1
0
1
0
0
0
3
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
1
0
0
0
2
2
0
0
1
0
2
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
2
0
0
0
0
0
0
7
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
2
2
0
0
0
0
0
3
0
1
2
0
0
0
0
1
0
3
1
0
0
2
0
0
0
0
1
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
2
0
0
2
0
1
2
0
0
3
0
1
0
1
2
0
3
1
0
0
1
2
14
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
2
1
1
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
2
0
2
0
0
0
1
2
1
0
0
0
2
0
0
0
0
1
0
2
0
0
2
0
0
0
2
0
0
0
1
0
3
0
1
0
2
0
0
2
0
0
0
0
1
0
0
2
1
0
1
2
0
0
0
2
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
2
1
1
0
0
0
0
2
2
0
0
1
0
1
9
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
2
0
0
0
2
0
2
0
1
0
0
0
2
0
0
0
0
0
0
2
2
1
0
0
0
0
1
1
0
2
1
0
1
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
1
0
2
0
1
0
0
0
0
0
1
0
0
0
3
0
2
1
1
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
1
0
1
3
0
0
2
0
1
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
3
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
6
1
0
0
1
1
0
1
0
0
0
0
1
0
0
4
0
2
0
0
2
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
1
0
0
1
0
0
0
1
0
0
0
0
0
1
2
1
0
0
1
2
0
0
2
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
2
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
2
0
1
1
0
0
1
0
0
0
0
1
0
0
2
2
0
2
0
3
0
0
0
0
2
0
1
0
2
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
3
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
2
0
0
0
5
0
2
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
3
0
0
0
0
0
0
0
1
1
2
0
1
1
0
1
0
0
0
0
0
1
2
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
2
4
0
1
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
2
1
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
1
2
0
3
0
0
0
1
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
2
0
2
0
2
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
2
2
0
0
0
0
0
2
0
2
0
0
0
2
3
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
2
0
1
1
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
1
0
1
0
0
1
2
1
1
0
0
0
2
1
0
0
0
1
2
2
2
2
5
1
0
1
0
3
1
1
0
1
0
0
0
2
0
1
0
0
1
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
3
5
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
1
2
0
0
0
2
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
1
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
2
0
1
0
0
0
0
2
0
0
0
0
9
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
2
2
1
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
2
2
0
0
0
0
0
0
2
0
1
0
2
0
0
0
1
1
2
0
0
1
0
0
0
0
2
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
1
1
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
3
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
1
2
1
0
0
2
3
0
0
1
0
2
1
0
0
0
0
2
0
0
1
2
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
1
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
1
0
3
0
0
0
0
0
2
0
1
0
0
0
2
0
1
0
1
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
1
1
2
0
0
0
0
0
2
2
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
3
0
0
2
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
2
0
0
0
0
1
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
1
0
1
1
1
2
2
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
2
0
0
1
2
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
1
0
0
2
0
0
0
2
0
1
0
5
0
1
0
0
0
0
1
1
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
3
0
0
1
0
0
0
0
1
0
3
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
1
0
0
0
2
0
3
0
0
0
0
1
4
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
1
1
0
1
0
0
0
0
2
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
1
0
1
0
0
2
0
0
1
0
1
0
2
0
2
0
0
3
0
0
0
2
0
0
0
0
3
0
0
1
1
0
0
0
0
1
0
0
3
0
2
0
0
0
0
0
1
0
2
1
0
0
2
0
0
1
1
0
0
0
2
0
2
0
0
0
0
0
0
1
1
0
0
0
1
0
2
3
1
0
0
0
0
5
3
0
0
1
0
1
0
0
2
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
2
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
2
0
2
0
1
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
1
0
0
0
0
1
0
2
2
0
1
3
0
2
0
0
0
0
0
0
2
2
0
2
0
2
3
0
0
2
0
0
2
0
0
0
0
3
0
0
0
0
1
0
0
5
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
2
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
2
2
0
2
0
0
0
0
1
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
2
0
2
0
1
0
0
2
2
0
0
0
0
1
1
1
1
0
6
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
1
1
0
0
2
0
0
0
0
2
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
4
0
0
0
2
0
0
0
1
2
0
0
0
0
1
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
2
0
2
0
0
1
2
0
0
0
0
1
2
0
1
0
0
0
2
0
0
2
0
3
1
0
2
1
2
1
0
1
2
0
0
1
1
0
0
1
0
0
1
3
0
1
0
0
0
0
0
0
1
0
0
2
2
1
0
0
1
0
0
0
0
0
0
3
0
0
0
1
2
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
1
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
2
2
0
0
0
2
0
2
0
0
0
2
0
0
1
0
0
6
1
0
2
0
1
1
0
0
2
0
0
0
0
1
2
0
0
1
0
1
0
2
2
0
0
0
2
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
3
0
0
0
0
2
1
2
0
0
0
0
14
2
2
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
2
2
0
0
1
0
1
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
4
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
1
2
0
2
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
1
2
0
0
1
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
4
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
1
0
0
2
0
6
0
0
2
0
5
0
1
0
2
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
2
0
0
0
0
0
3
1
2
0
0
1
0
0
2
0
0
2
0
0
2
1
0
0
0
2
0
1
0
0
2
4
0
0
1
0
0
0
0
0
0
1
0
1
2
0
1
0
0
2
0
1
0
0
0
0
0
1
0
2
0
1
1
0
3
0
0
1
2
0
1
2
0
0
0
2
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
3
0
0
1
0
0
2
0
0
0
0
7
1
0
0
0
0
2
2
0
1
3
0
0
0
0
0
2
1
0
0
2
0
0
2
4
0
2
0
0
1
0
1
0
0
2
1
0
3
0
0
0
1
0
0
2
0
1
2
0
2
1
0
0
0
0
0
0
1
0
0
2
1
1
2
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
3
0
2
0
0
0
2
0
0
0
1
0
0
1
1
0
0
0
0
0
0
2
1
2
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
1
2
6
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
2
2
0
0
0
0
0
2
0
0
0
0
3
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
4
1
0
1
0
0
0
1
2
0
0
0
1
2
0
0
0
1
3
1
0
0
2
1
0
1
1
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
2
1
0
1
2
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
2
0
2
2
2
0
0
0
0
0
1
3
1
0
0
0
0
0
1
0
1
0
1
0
2
0
0
0
1
0
1
0
1
0
0
0
2
0
0
0
1
0
1
0
0
0
0
2
0
0
0
1
2
1
0
0
0
1
0
1
0
2
0
0
0
0
1
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
2
4
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
1
1
0
1
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
1
0
0
0
0
0
1
0
3
0
2
2
0
2
1
2
0
0
0
0
1
1
0
0
0
0
0
1
2
1
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
2
2
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
2
0
0
2
0
2
0
0
0
2
1
1
0
2
1
0
0
0
1
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
2
0
0
1
1
0
2
0
0
2
0
0
0
1
1
0
0
0
0
1
1
1
2
2
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
3
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
2
0
0
0
0
0
1
1
1
0
0
2
1
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
1
0
0
2
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
3
0
3
0
0
0
0
1
0
0
2
0
0
2
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
3
1
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
1
1
1
1
0
0
0
1
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
1
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
3
0
0
2
0
0
1
0
0
0
0
0
2
2
1
0
0
0
1
0
0
0
0
0
0
8
0
0
0
0
0
2
2
2
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
1
2
0
0
2
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
2
0
1
0
3
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
1
2
3
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
1
0
0
2
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
3
1
0
3
0
0
1
2
0
0
1
0
0
0
0
0
0
1
1
0
0
0
3
2
1
0
0
1
3
0
0
0
2
0
2
2
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
2
0
1
0
0
2
0
0
1
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
2
0
2
0
0
0
1
2
0
2
2
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
2
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
3
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
2
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
2
0
0
0
2
1
0
0
0
0
0
1
0
0
2
0
2
0
3
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
4
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
2
0
1
0
1
0
0
2
0
0
1
0
3
2
1
1
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
1
1
1
1
3
0
1
0
0
3
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
1
1
0
0
1
0
0
2
0
0
0
0
1
1
0
3
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
2
0
0
0
0
1
0
2
1
0
1
0
0
0
1
0
1
0
0
0
2
0
0
0
0
1
3
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
1
2
0
0
0
0
1
0
0
1
2
0
6
1
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
1
1
0
1
2
0
0
1
2
0
0
0
0
0
0
1
1
0
2
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
6
1
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
2
1
2
2
0
0
0
3
0
0
1
0
0
0
0
3
0
1
0
0
1
0
1
0
0
1
0
2
2
0
0
0
0
0
2
0
0
0
2
2
0
2
1
0
0
0
1
0
0
1
0
1
0
1
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
2
0
0
1
0
2
0
0
0
0
2
0
0
3
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
1
2
2
1
0
0
0
0
0
2
1
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
3
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
2
0
0
0
2
0
3
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
2
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
1
2
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
2
3
3
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
3
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
6
1
2
1
1
0
0
0
0
1
3
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
1
0
1
0
6
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
2
0
0
0
0
2
0
1
0
0
0
0
1
2
6
0
0
3
0
1
0
0
0
2
2
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
2
0
0
0
3
0
0
2
0
3
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
1
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
2
1
0
6
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
2
0
2
2
1
1
0
0
0
1
1
1
0
0
2
0
0
2
0
1
1
0
2
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
3
0
0
2
1
0
1
0
2
0
0
2
0
0
2
2
0
0
0
1
2
0
2
1
0
0
2
0
0
0
2
0
0
0
1
1
1
2
0
0
0
0
0
3
1
0
2
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
1
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
5
0
0
0
1
0
0
0
1
2
0
0
0
0
0
1
1
0
0
2
1
0
0
0
0
2
1
0
0
0
2
0
0
2
0
0
3
0
2
4
3
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
1
0
0
1
0
2
0
0
0
3
0
0
1
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
2
0
2
1
0
0
0
0
0
0
0
3
1
0
0
0
3
1
1
0
0
1
0
2
2
0
2
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
3
0
0
0
0
2
0
0
0
0
2
0
1
1
1
1
0
1
2
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
1
0
1
0
0
2
2
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
4
0
0
2
0
0
0
0
0
0
0
0
0
14
1
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
2
0
1
0
1
1
0
0
0
0
2
0
0
1
1
0
0
0
2
0
2
0
0
0
1
2
1
0
0
0
0
0
6
2
1
2
3
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
1
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
0
1
2
0
1
2
0
0
0
2
0
0
2
0
2
0
1
0
0
0
0
0
1
0
0
2
0
2
0
0
1
0
0
1
1
1
1
0
1
0
0
1
2
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
1
0
2
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
1
0
0
0
2
1
0
0
0
1
0
0
0
0
3
0
1
2
0
0
0
2
0
0
0
1
2
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
4
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
1
0
0
0
2
1
0
0
0
3
2
0
0
1
0
1
0
0
0
0
0
0
1
1
2
2
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
2
0
2
0
0
0
0
2
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
5
0
3
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
4
0
3
1
0
0
0
0
0
1
0
0
0
2
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
1
2
0
2
2
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
1
2
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
2
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
2
0
0
0
1
2
0
1
0
2
1
0
0
2
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
3
0
0
1
0
1
0
0
1
11
4
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
2
2
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
3
2
0
0
2
0
0
0
2
10
0
0
0
0
1
0
0
2
2
2
0
2
0
0
2
1
0
2
0
0
0
0
1
0
2
0
4
0
0
0
0
2
2
0
0
0
0
0
2
2
0
0
1
0
1
0
0
2
0
0
0
0
0
1
0
0
1
0
1
0
0
1
1
2
0
0
1
0
0
1
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
1
0
1
1
0
0
2
2
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
2
0
3
1
0
0
2
0
0
0
0
3
0
0
0
0
0
2
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
1
0
2
0
0
3
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
2
3
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
10
0
1
1
0
0
1
0
0
0
0
0
3
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
2
1
2
1
2
0
0
1
0
1
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
2
0
1
2
1
0
2
0
0
0
0
0
3
1
0
2
0
2
0
0
0
7
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
1
0
1
1
0
0
0
2
0
2
0
2
0
1
2
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
4
4
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
2
0
0
1
0
0
1
0
1
0
2
0
1
1
0
2
3
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
2
0
2
0
0
1
2
0
1
0
0
1
3
2
0
0
0
1
0
0
0
0
0
3
1
1
0
0
0
3
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
1
2
0
0
0
1
0
2
2
0
0
0
1
0
2
0
0
1
0
1
1
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
1
2
0
0
2
0
2
0
0
0
0
0
0
1
1
1
0
1
1
2
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
2
1
0
0
1
0
1
0
0
1
2
0
0
2
0
1
0
0
0
0
2
0
0
0
2
0
0
1
0
2
1
0
0
0
0
1
1
0
0
2
1
2
4
0
1
0
1
0
0
0
0
0
0
2
2
0
0
0
0
1
2
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
3
0
0
0
2
0
0
2
2
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
2
12
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
10
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
2
3
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
3
2
0
0
4
1
0
1
1
0
0
1
0
0
0
0
2
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
1
1
0
0
2
0
0
1
0
0
3
0
0
2
0
0
0
2
0
0
0
0
2
0
0
1
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
1
2
2
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
1
2
0
0
0
0
0
1
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
1
0
2
0
0
2
0
1
0
1
1
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
5
2
2
1
2
2
0
1
0
0
0
2
2
0
1
0
2
0
0
6
0
1
2
0
3
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
1
2
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
2
0
2
1
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
1
2
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
2
2
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
1
0
1
2
1
0
0
0
0
2
2
0
0
0
0
1
0
0
0
2
0
0
3
0
0
0
0
1
0
0
2
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
1
2
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
1
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
1
0
0
2
0
0
4
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
2
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
3
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
3
1
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
3
3
2
0
0
4
0
0
0
0
3
2
0
0
0
0
0
0
0
2
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
1
2
1
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
2
0
1
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
5
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
3
0
2
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
2
1
0
2
1
2
0
0
0
0
2
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
2
0
0
1
0
0
0
1
0
0
0
0
2
0
1
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
1
0
0
0
3
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
2
0
2
2
2
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
1
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
3
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
1
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
9
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
2
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
4
0
0
0
0
1
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
1
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
3
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
2
2
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
7
0
1
2
1
0
0
0
0
0
2
0
2
0
1
0
0
0
0
1
1
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
3
0
0
0
0
1
0
2
1
0
1
0
0
0
0
0
2
0
2
0
1
0
2
1
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
2
2
2
0
2
0
0
0
0
0
0
2
0
2
2
0
1
1
2
0
0
0
0
2
0
0
0
1
1
2
2
1
0
1
0
0
2
0
0
0
2
2
1
1
0
0
0
0
0
0
1
2
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
2
0
0
2
1
0
2
0
0
0
0
0
1
0
2
1
0
0
0
2
0
0
2
0
1
2
1
0
1
0
0
0
1
2
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
3
0
0
3
1
1
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
2
1
2
0
0
1
0
1
0
0
2
1
0
0
0
1
1
1
0
0
0
0
0
0
0
1
2
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
2
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
1
0
0
0
1
1
2
1
0
1
2
0
0
0
0
0
3
1
0
0
4
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
2
0
2
0
0
0
2
0
0
0
1
0
2
0
2
1
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
1
0
0
2
2
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
1
2
1
1
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
3
0
1
1
0
2
0
0
0
2
0
0
0
1
1
0
0
0
0
2
1
3
0
2
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
1
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
2
0
0
2
1
2
1
0
0
0
0
1
0
2
1
0
0
0
0
0
0
1
2
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
1
2
0
0
0
1
0
1
2
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
1
0
0
2
0
2
0
0
0
1
2
0
2
0
0
0
0
1
2
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
1
2
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
2
0
2
0
0
2
0
1
0
4
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
2
0
2
0
0
1
2
0
1
2
0
1
2
0
0
2
0
0
1
0
1
0
0
4
0
0
2
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
2
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
2
0
0
0
0
0
2
0
0
2
1
0
2
1
0
0
0
0
0
1
0
2
3
0
1
0
2
0
1
0
4
0
0
0
0
1
0
1
2
0
0
1
0
2
0
3
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
2
0
0
0
1
2
1
0
0
1
1
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
2
1
0
0
0
0
0
0
2
1
0
0
0
3
0
2
0
0
0
2
0
0
2
0
2
0
0
0
0
2
0
2
0
0
0
0
2
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
1
0
0
0
0
0
1
0
0
0
2
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
1
0
2
0
1
0
0
1
0
0
0
0
0
0
2
1
2
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
2
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
1
1
1
0
0
1
3
0
0
3
0
0
0
0
2
0
0
0
0
1
1
0
1
2
2
1
0
0
0
0
2
0
2
1
0
0
0
2
3
0
0
0
1
0
0
2
0
1
0
0
1
0
0
0
0
0
0
2
0
0
3
2
2
6
0
0
0
0
1
2
0
3
0
0
0
2
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
1
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
1
1
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
3
2
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
1
2
2
0
0
0
0
4
0
0
0
0
0
0
1
0
1
0
0
2
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
2
2
1
0
1
0
0
3
0
1
2
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
2
0
0
2
1
0
2
0
0
2
1
0
2
0
1
3
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
1
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
7
0
0
0
0
0
0
0
1
0
1
2
0
2
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
2
0
0
1
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
3
0
0
0
0
0
1
2
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
2
2
3
0
0
0
0
1
1
0
0
0
1
2
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
1
3
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
1
0
1
0
0
0
0
2
0
2
2
1
0
2
1
1
0
0
0
0
0
0
0
4
0
0
0
3
0
1
0
0
0
2
0
1
0
0
0
0
0
0
2
0
1
0
1
4
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
6
0
1
0
0
0
0
0
0
0
0
4
1
0
0
2
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
1
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
1
0
1
1
0
2
0
0
2
0
0
0
1
2
1
0
0
2
0
0
0
0
0
3
1
2
0
0
4
0
0
0
0
0
0
2
0
1
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
2
2
0
1
0
0
2
0
0
1
2
0
0
2
0
0
1
0
0
0
0
0
2
3
0
0
0
1
0
0
0
0
0
1
0
2
0
0
2
0
1
3
0
0
0
0
0
0
0
0
2
2
0
2
2
0
0
1
0
2
2
1
0
0
0
0
0
0
2
1
0
0
0
0
2
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
3
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
1
1
1
0
0
1
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
1
2
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
2
1
1
1
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
2
1
0
2
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
2
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
2
0
0
0
2
0
2
0
0
0
0
0
0
0
1
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
2
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
8
1
1
2
1
2
0
0
0
0
1
2
0
1
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
2
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
2
0
0
0
1
0
2
0
2
1
0
1
0
1
3
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
1
0
0
0
0
3
0
0
0
1
0
2
1
0
1
2
1
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
1
0
0
0
0
0
2
1
0
1
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
4
2
1
0
0
2
0
0
0
0
0
0
2
3
0
5
0
1
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
1
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
1
1
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
2
2
0
0
0
0
1
0
1
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
1
1
0
0
0
1
2
0
3
0
0
0
1
0
3
2
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
1
3
0
0
0
0
0
2
2
0
0
3
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
1
2
1
0
0
0
0
1
0
2
0
0
2
1
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
1
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
2
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
1
2
1
0
0
0
2
0
0
0
1
0
0
0
1
3
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
2
1
0
1
2
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
6
1
0
1
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
2
0
2
1
0
1
0
0
0
0
0
0
2
0
0
2
0
2
3
1
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
2
2
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
1
0
1
1
0
0
0
0
0
2
1
0
0
1
2
0
4
0
1
2
2
1
0
0
0
1
0
1
0
1
0
2
0
0
0
2
1
0
0
0
2
2
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
1
2
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
1
0
2
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
2
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
1
0
1
2
0
2
2
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
5
0
1
1
0
0
1
0
0
1
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
4
2
0
0
0
0
0
0
2
1
0
0
1
0
0
0
1
2
0
0
1
2
2
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
1
2
1
0
0
1
1
0
0
1
0
1
2
1
0
0
0
2
0
0
0
0
0
1
1
0
0
2
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
2
0
2
3
0
1
0
3
0
0
0
2
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
1
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
1
2
0
3
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
1
0
0
0
0
0
1
0
2
3
0
1
0
0
0
0
5
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
2
2
0
2
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
3
1
2
2
0
0
2
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
1
0
1
0
0
1
0
3
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
1
1
0
0
0
4
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
5
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
2
2
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
3
1
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
2
1
0
2
0
0
2
0
2
4
0
0
0
0
0
5
0
0
2
0
3
0
2
0
1
0
0
0
1
2
1
0
2
0
0
0
1
0
0
0
2
0
4
2
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
2
0
2
0
0
2
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
2
0
0
1
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
1
0
2
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
5
0
0
0
0
2
0
0
0
0
2
5
0
2
0
0
0
2
0
2
0
0
2
0
0
0
0
2
0
2
0
0
2
2
0
3
2
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
1
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
1
2
0
0
2
0
4
2
0
1
1
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
1
2
1
0
1
2
3
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
4
3
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
2
0
0
0
0
1
0
0
2
0
1
2
0
1
0
0
0
0
0
0
0
0
3
0
1
0
0
0
1
0
2
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
1
0
0
4
0
0
0
1
0
0
0
2
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
3
1
0
0
4
0
0
0
1
0
0
0
3
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
2
2
0
0
0
1
0
2
0
5
1
0
2
0
1
2
2
2
0
2
0
2
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
1
0
2
2
0
0
0
0
1
0
2
0
0
0
1
0
0
0
1
0
0
0
2
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
1
1
0
0
0
0
0
2
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
2
1
2
2
0
3
2
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
1
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
2
0
2
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
5
1
0
1
0
0
1
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
2
0
1
2
2
0
0
2
0
2
0
0
1
0
0
1
1
0
1
0
0
0
2
0
0
2
1
0
0
1
0
0
0
0
2
2
0
1
0
0
1
1
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
11
0
0
0
0
0
2
1
0
2
1
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
1
0
0
0
7
0
0
0
0
0
2
0
0
2
0
0
1
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
1
2
0
0
0
0
0
0
1
0
2
1
0
0
0
2
0
0
0
1
0
0
0
2
2
0
2
2
0
0
0
0
0
2
0
0
1
0
0
2
0
1
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
7
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
4
0
1
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
1
2
1
0
0
0
0
2
0
0
1
0
1
0
0
0
0
1
2
1
2
0
0
2
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
3
0
1
0
0
2
2
2
1
2
0
0
0
1
0
2
0
1
1
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
3
0
1
0
0
0
2
0
2
0
0
1
0
2
1
0
0
0
0
0
0
3
0
2
0
0
1
2
0
0
0
3
1
0
0
1
0
0
1
1
1
0
2
0
1
2
0
1
0
2
0
1
0
0
0
1
1
0
0
0
1
1
0
1
0
0
0
0
1
1
0
0
0
0
3
2
0
0
0
3
1
0
1
0
2
0
0
2
1
3
2
0
0
0
0
0
0
1
1
0
0
2
0
2
0
0
0
0
0
3
0
1
2
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
1
2
0
0
0
0
1
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
2
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
3
0
1
0
0
1
0
1
0
0
0
0
2
1
3
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
2
4
0
0
1
0
2
0
0
0
0
1
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
1
2
0
0
0
3
0
0
0
0
0
0
0
2
0
4
1
0
0
2
0
0
1
1
0
0
1
0
2
0
0
0
0
0
0
1
1
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
1
2
0
2
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
1
0
2
0
0
0
0
0
2
1
2
0
0
2
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
5
2
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
2
0
1
0
0
1
0
0
1
4
0
0
0
0
0
0
0
0
0
4
1
0
0
3
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
2
2
1
0
1
1
0
1
0
0
3
0
0
0
2
0
0
0
0
0
1
1
0
0
1
0
0
0
2
2
0
0
0
0
2
2
0
0
0
0
1
0
0
2
0
1
0
0
0
2
0
0
0
0
0
2
0
0
1
2
2
2
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
1
0
2
1
1
2
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
2
2
0
1
0
1
2
0
1
0
1
0
1
3
0
1
0
0
0
0
0
1
0
0
1
2
0
0
0
0
2
0
0
0
0
1
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
4
0
0
0
2
0
2
0
0
0
1
0
2
2
0
1
2
0
2
2
2
0
0
0
0
0
0
2
0
0
0
2
0
3
0
0
2
0
0
2
3
0
4
1
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
2
0
0
0
1
5
2
0
0
0
2
0
0
1
0
2
0
1
0
0
0
2
0
1
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
2
0
1
2
1
0
0
1
1
2
0
0
0
0
0
0
3
0
0
2
1
0
2
2
0
0
0
0
0
0
0
0
2
0
1
1
4
0
0
0
0
0
2
0
0
0
0
4
0
1
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
1
0
0
1
0
1
0
0
0
4
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
4
1
0
2
0
0
1
2
1
0
0
0
0
3
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
2
0
2
0
0
1
1
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
1
0
0
0
0
0
2
0
0
2
2
0
2
0
0
1
1
2
2
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
1
0
0
2
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
2
1
2
2
0
0
0
0
2
0
0
1
0
0
0
2
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
1
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
1
0
2
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
2
0
0
4
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
2
1
5
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
2
1
0
0
0
0
1
0
2
0
0
0
5
0
0
0
0
1
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
2
2
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
2
2
2
0
1
0
0
0
0
2
0
0
3
0
2
0
0
0
0
0
2
2
0
1
0
0
0
2
0
0
0
0
2
1
0
0
0
1
0
2
0
1
1
0
2
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
3
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
3
2
2
0
2
0
0
0
0
1
0
0
0
1
0
1
0
0
0
2
1
1
1
2
0
2
0
1
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
3
0
0
2
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
1
2
0
3
1
0
2
0
0
2
2
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
4
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
2
1
0
0
0
0
0
0
0
0
5
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
1
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
2
1
0
0
1
1
0
1
1
2
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
2
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
5
1
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
4
1
1
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
1
0
2
0
2
2
0
0
1
0
0
1
2
0
0
2
0
0
0
1
0
0
1
0
0
2
0
0
0
1
0
0
0
2
1
0
0
0
0
1
1
0
0
0
1
0
1
0
1
0
1
1
0
0
3
0
2
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
2
1
1
0
2
2
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
4
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
1
0
0
2
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
4
1
2
0
0
0
0
0
0
0
1
0
0
3
0
0
2
2
2
1
0
0
1
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
1
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
1
2
0
1
2
1
0
1
0
1
0
0
0
2
0
0
1
1
1
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
8
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
2
1
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
2
0
1
0
2
0
0
0
0
0
0
2
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
2
0
0
0
0
2
2
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
5
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
1
0
0
0
0
0
1
2
1
0
0
1
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
1
1
2
8
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
1
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
1
0
0
2
0
0
0
0
0
3
0
1
0
2
0
0
0
0
0
2
1
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
2
3
0
1
0
0
3
0
0
0
2
2
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
1
1
0
0
3
7
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
7
0
2
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
1
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
2
0
1
0
1
0
0
0
2
0
0
0
0
0
2
3
0
2
0
0
0
0
2
0
0
0
1
0
0
1
0
1
0
0
1
1
1
0
0
0
2
0
0
1
0
0
0
1
0
1
0
0
0
3
2
2
0
1
1
0
0
0
1
3
2
0
0
0
1
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
2
2
1
1
0
0
2
0
2
0
1
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
2
1
0
0
0
1
0
1
0
2
0
0
1
0
2
0
0
2
0
2
0
0
0
2
0
0
0
0
1
0
0
2
2
0
0
2
0
0
0
3
2
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
3
2
0
1
0
0
0
0
2
0
0
2
0
1
0
1
0
2
2
1
1
0
0
0
1
1
0
0
1
2
0
0
0
5
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
3
1
0
0
0
1
0
1
0
0
2
0
0
2
0
0
0
0
0
0
5
1
0
0
1
0
0
0
3
0
0
0
0
0
0
1
0
2
0
0
3
0
0
1
0
0
1
2
0
0
0
0
2
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
1
2
2
1
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
8
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
2
0
1
0
0
0
0
1
0
1
7
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
1
4
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
1
1
1
2
0
0
0
0
0
0
0
0
0
0
3
0
1
1
0
4
0
1
0
0
0
1
2
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
3
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
1
2
2
0
2
0
0
1
1
0
4
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
2
0
0
1
1
1
0
0
0
2
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
2
2
1
0
0
1
0
2
1
0
0
0
1
0
0
0
1
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
5
2
0
0
0
0
0
2
0
2
1
2
0
1
0
1
0
0
1
0
0
0
0
0
2
2
2
0
0
0
1
1
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
4
1
2
1
0
0
0
0
0
0
0
1
0
0
1
2
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
1
0
0
0
2
0
0
0
2
0
2
1
0
0
0
0
1
0
0
0
0
2
0
2
0
1
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
5
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
2
0
2
2
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
1
2
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
1
0
3
0
4
1
0
2
0
1
0
1
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
1
2
0
0
0
2
1
1
1
0
0
0
0
3
1
0
0
0
0
0
2
0
0
0
2
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
4
2
1
0
0
1
0
2
0
2
0
2
0
2
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
1
1
0
0
0
0
0
0
2
2
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
1
2
2
0
1
0
0
0
0
0
0
3
0
2
0
0
2
2
2
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
1
2
0
0
0
0
0
1
0
0
1
0
0
1
2
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
2
0
1
1
1
0
1
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
1
0
2
0
0
2
0
2
0
0
0
2
0
2
1
0
2
1
0
0
1
0
0
0
2
1
0
0
0
0
1
0
0
2
0
0
1
2
0
1
0
0
2
0
0
0
0
2
0
0
0
2
1
1
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
8
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
2
1
0
0
0
0
0
1
0
0
0
1
0
2
0
1
4
0
5
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
1
1
2
0
1
0
1
0
0
3
0
1
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
3
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
3
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
1
0
1
0
1
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
1
0
2
0
0
0
1
1
1
0
0
1
0
0
0
1
0
1
0
0
0
2
2
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
4
1
0
0
2
0
1
0
1
2
0
0
0
2
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
2
2
2
0
1
1
0
0
2
0
0
1
1
0
2
0
0
0
0
2
0
0
1
0
2
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
2
2
2
0
0
2
0
0
0
0
0
0
2
0
1
2
2
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
1
0
3
0
0
0
0
2
0
2
0
0
0
0
0
1
2
0
0
2
0
1
1
2
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
2
0
1
0
0
0
2
2
0
0
1
0
0
1
1
0
0
0
1
0
0
2
0
0
1
2
0
0
0
1
0
0
2
0
0
2
0
0
0
0
2
1
3
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
1
2
0
0
1
4
1
0
0
0
1
1
1
0
3
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
3
0
1
0
1
2
1
2
1
2
0
1
2
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
2
0
2
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
13
2
1
0
0
0
4
0
0
2
3
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
2
0
0
2
2
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
1
1
0
1
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
3
0
0
2
1
0
0
2
2
9
2
0
7
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
2
0
1
0
4
0
2
0
0
2
0
2
0
0
0
0
2
0
0
0
2
0
3
0
0
0
0
1
3
0
0
0
0
1
0
0
0
2
0
0
1
0
0
1
0
0
0
1
1
0
1
0
0
3
2
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
11
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
4
0
0
0
2
2
0
0
0
1
0
0
1
1
2
0
0
2
0
3
0
0
0
0
2
0
1
0
1
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
1
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
1
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
2
0
0
3
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
2
0
2
1
2
0
4
5
1
0
2
0
0
1
0
2
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
1
2
0
0
2
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
6
0
3
0
0
0
2
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
1
1
1
1
0
0
0
2
0
0
3
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
1
2
2
2
0
2
0
0
0
3
0
0
0
0
0
0
0
0
1
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
1
2
0
1
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
1
2
2
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
1
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
5
1
0
0
0
0
7
3
0
0
0
1
0
0
0
1
0
1
1
1
0
1
1
0
0
0
1
0
3
0
1
0
0
0
2
1
1
0
2
1
0
0
0
2
0
1
0
0
0
1
0
0
2
0
2
0
0
0
1
2
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
1
2
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
1
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
2
5
0
0
2
1
4
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
3
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
9
0
0
1
0
0
2
2
0
0
0
0
0
0
6
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
2
1
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
1
3
0
0
2
0
0
0
0
0
2
2
1
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
1
2
0
1
0
0
0
1
2
0
0
0
0
1
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
1
0
0
1
0
0
2
1
0
0
2
0
1
2
0
0
0
1
2
0
4
2
2
0
0
0
0
2
0
1
0
2
0
1
0
2
2
0
0
2
1
0
0
0
0
2
2
0
2
0
0
0
1
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
2
2
0
0
0
0
0
0
0
3
0
5
0
2
0
0
0
0
2
0
0
1
0
0
0
0
1
0
2
0
1
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
1
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
3
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
3
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
3
0
0
0
1
0
0
1
0
1
0
0
2
0
1
0
0
1
0
1
0
1
0
0
1
0
0
1
0
2
0
1
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
1
0
2
0
2
2
2
0
0
1
0
3
0
0
1
0
2
0
0
2
0
0
2
0
0
2
1
0
0
1
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
1
0
1
0
1
0
0
0
2
0
2
0
0
1
0
0
2
0
0
0
0
0
2
3
1
7
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
2
1
0
0
0
1
0
0
0
0
2
1
0
1
0
0
0
0
2
0
0
0
0
4
0
0
1
1
1
0
0
0
3
1
0
0
1
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
2
0
1
0
2
2
0
3
0
0
0
1
1
0
0
0
0
0
0
2
0
1
0
1
0
4
0
0
0
0
2
0
0
1
0
2
2
0
2
0
2
0
0
0
0
0
0
3
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
1
0
2
0
1
0
0
0
0
0
2
2
2
0
0
2
2
1
1
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
1
0
1
1
0
2
0
0
0
2
0
1
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
1
2
0
1
1
2
0
0
0
0
0
0
0
1
1
0
2
1
3
0
0
0
5
0
0
0
0
2
1
0
0
1
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
3
0
0
0
0
2
0
2
0
2
0
0
1
1
0
1
0
0
0
2
0
0
1
0
0
0
0
1
0
1
3
1
0
0
0
0
1
2
2
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
3
1
1
2
0
0
0
0
0
2
0
1
2
0
0
0
0
0
1
0
1
0
1
2
2
2
1
0
0
1
0
0
0
0
0
0
0
0
3
0
1
0
0
1
0
0
2
0
0
0
2
0
0
0
1
2
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
3
0
0
2
1
0
0
2
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
1
1
1
0
2
0
0
1
1
0
0
0
0
0
5
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
2
0
1
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
1
2
0
0
0
0
1
0
0
2
0
0
2
0
0
1
0
0
0
3
1
2
0
0
0
2
0
0
6
0
1
0
0
1
0
1
0
0
0
2
0
0
0
1
2
0
0
0
0
0
1
2
0
0
1
0
3
2
1
0
0
0
1
1
2
2
0
4
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
3
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
3
0
0
1
0
0
2
2
2
2
2
0
0
1
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
1
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
1
1
2
0
0
0
2
0
0
0
0
2
1
0
0
0
2
0
0
0
0
2
0
1
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
5
2
0
0
0
0
0
0
0
0
1
1
0
1
1
2
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
1
1
0
0
0
1
0
4
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
1
0
0
4
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
2
1
2
1
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
1
0
0
0
1
0
0
0
2
1
0
0
0
3
0
0
0
1
0
1
0
2
0
0
2
0
0
0
2
1
1
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
2
0
1
1
1
2
2
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
1
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
1
1
0
1
0
1
1
0
2
0
2
0
0
0
2
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
2
0
0
0
1
1
0
0
1
1
2
0
0
0
0
0
0
0
0
2
1
1
1
1
1
0
0
2
0
0
2
1
0
0
0
1
0
0
0
1
1
2
0
0
2
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
3
0
0
0
0
0
0
3
0
0
2
0
0
0
1
0
0
1
0
0
1
0
0
1
0
2
0
2
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
2
0
0
4
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
5
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
1
0
0
1
2
1
0
2
0
0
0
2
0
0
4
0
0
0
1
1
0
2
1
0
2
1
1
0
0
2
2
0
2
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
1
0
1
1
0
0
2
1
0
1
2
1
1
1
1
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
2
0
0
2
0
2
2
0
0
0
2
1
1
0
1
0
0
0
0
1
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
3
1
2
0
0
0
0
0
2
1
0
2
0
0
0
0
0
1
0
0
1
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
3
0
0
0
2
0
0
0
1
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
2
0
0
0
0
0
2
0
3
1
2
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
1
2
1
0
0
0
0
1
0
5
1
0
1
0
0
0
0
0
0
2
2
0
0
1
0
0
0
2
0
1
0
0
1
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
4
0
0
0
0
4
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
4
0
3
2
0
0
1
0
2
1
0
0
0
0
0
0
1
0
2
1
0
1
0
0
0
0
0
1
0
0
0
2
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
2
1
1
0
0
1
0
1
0
2
0
4
2
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
1
2
0
4
0
0
0
1
0
0
0
0
0
2
0
3
0
0
0
0
0
1
1
0
2
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
1
0
1
0
1
1
0
0
0
0
2
0
0
0
3
2
0
0
0
1
0
2
0
0
0
0
2
2
0
2
2
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
3
0
2
0
1
0
0
1
0
0
0
0
2
2
0
0
0
0
2
0
0
2
0
1
0
2
4
1
3
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
3
0
1
0
0
0
1
0
2
0
0
0
0
1
0
2
0
0
2
0
0
2
0
0
1
3
0
0
1
0
2
0
0
0
0
2
2
0
0
0
1
0
0
4
0
0
1
2
2
0
2
0
0
0
1
0
0
6
0
0
0
0
0
0
0
0
1
0
0
0
0
3
2
0
0
0
0
0
0
3
0
1
0
0
2
2
0
0
0
1
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
3
1
0
1
0
0
1
0
2
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
3
0
0
1
0
0
0
0
0
1
0
2
1
1
0
0
2
1
1
0
0
0
2
0
1
0
2
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
3
2
0
0
1
0
0
0
0
0
2
1
2
0
0
0
0
0
0
1
4
0
1
0
0
2
0
0
0
1
3
2
0
0
1
2
0
0
0
1
1
3
0
0
0
0
0
0
3
2
0
0
0
2
0
0
0
0
0
0
0
0
0
3
1
0
0
2
0
1
0
0
0
0
2
1
0
1
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
1
0
0
0
0
0
2
1
0
0
1
0
0
0
0
2
0
1
2
1
0
2
1
0
1
0
1
0
1
2
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
2
1
1
0
1
0
0
1
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
1
0
1
0
1
1
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
2
2
0
0
0
2
1
0
0
2
1
0
0
1
0
0
0
0
1
1
0
1
1
0
2
2
0
0
2
0
0
2
0
0
1
0
0
1
0
14
0
0
1
0
2
1
0
3
0
1
0
1
0
1
0
1
0
0
2
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
2
2
0
0
0
2
0
0
0
0
0
1
0
1
2
0
0
0
0
0
1
2
0
1
1
0
0
1
2
0
0
0
0
2
0
1
0
0
0
0
2
1
1
0
0
0
0
2
0
1
0
2
0
0
0
0
0
2
0
0
2
0
1
0
0
2
0
2
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
3
2
2
0
0
1
0
0
0
1
0
0
0
1
0
0
0
5
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
2
0
0
0
0
2
0
2
2
0
2
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
2
2
0
2
2
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
2
0
2
3
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
2
0
0
0
0
3
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
2
0
1
0
0
1
2
0
1
2
1
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
11
0
0
0
0
0
0
2
0
2
2
0
0
1
0
0
0
0
2
2
0
1
2
0
0
0
1
0
0
0
0
0
0
1
2
1
2
0
0
0
0
0
1
0
1
0
1
1
2
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
1
0
0
0
0
0
1
2
1
0
0
2
0
0
1
0
0
1
2
0
0
0
1
2
0
0
2
0
1
4
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
1
0
0
0
0
0
1
2
0
2
0
0
0
0
2
0
2
2
1
0
0
1
1
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
2
0
0
2
0
1
0
0
0
0
2
0
0
0
1
0
2
0
0
1
2
0
0
0
2
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
2
0
2
0
2
0
0
2
0
0
0
0
0
0
0
3
0
1
3
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
2
0
2
0
1
0
0
0
2
2
0
0
1
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
1
1
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
1
2
2
0
0
2
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
3
1
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
1
0
0
9
2
0
0
0
1
1
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
1
1
1
1
0
0
2
0
0
0
0
3
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
3
1
0
0
0
0
0
0
2
1
1
0
0
1
2
0
0
0
0
0
0
0
2
0
1
3
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
2
1
0
0
2
0
0
3
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
2
0
2
3
0
0
5
0
0
0
0
0
3
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
4
0
1
0
2
1
0
0
0
0
0
1
0
2
0
0
0
0
0
1
2
1
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
2
2
0
0
0
0
3
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
2
0
0
1
0
0
0
0
2
1
0
1
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
1
0
0
0
6
3
0
0
1
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
3
1
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
2
0
6
2
1
1
2
0
0
0
0
1
6
1
0
0
0
0
0
0
0
1
2
0
0
0
1
0
2
0
0
0
0
1
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
1
0
2
0
0
0
0
0
2
0
2
2
1
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
1
0
2
0
0
2
0
0
0
0
0
2
1
1
0
2
0
1
0
1
1
2
0
0
0
0
1
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
1
4
0
2
2
2
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
1
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
2
9
2
2
0
0
0
0
0
0
0
1
4
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
3
0
0
1
0
0
0
2
0
2
1
2
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
2
0
1
0
0
0
1
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
2
0
1
0
0
1
0
0
2
1
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
6
0
3
0
0
0
1
0
2
0
1
0
0
3
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
1
0
1
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
3
0
0
0
0
2
0
0
0
0
0
5
0
1
1
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
2
2
0
1
3
0
0
0
0
0
0
0
2
0
0
0
3
1
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
2
0
0
1
0
1
0
1
0
0
0
1
0
0
3
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
2
1
2
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
2
0
0
2
1
0
1
0
0
0
0
1
2
0
0
0
1
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
1
2
0
1
2
0
0
0
0
0
0
0
1
2
0
0
0
0
2
1
0
2
0
0
2
0
2
0
2
0
0
0
0
0
2
0
0
7
0
0
1
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
1
0
1
2
2
1
1
1
1
0
0
0
1
0
0
0
0
0
0
2
0
4
0
2
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
3
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
2
1
0
0
0
1
0
0
3
1
3
0
0
0
1
1
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
2
0
0
3
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
2
0
2
0
0
2
5
0
0
0
1
0
0
2
0
1
1
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
1
0
0
1
1
2
3
0
0
2
0
0
0
1
3
0
0
0
0
2
0
2
2
1
2
0
0
0
0
0
0
0
2
0
1
0
3
0
0
2
0
0
2
2
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
3
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
3
7
0
0
2
0
0
0
1
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
1
2
0
2
1
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
2
0
1
1
0
0
0
0
0
0
1
0
1
0
0
1
2
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
1
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
2
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
2
1
2
0
2
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
1
2
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
2
0
3
0
0
1
0
0
0
0
0
0
1
0
1
1
1
0
0
2
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
4
0
0
0
1
0
0
1
1
1
3
0
2
0
0
1
0
0
0
0
1
0
2
0
0
1
0
0
2
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
1
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
7
0
0
0
0
1
0
1
2
2
1
0
1
1
0
0
1
2
1
0
0
0
0
2
1
0
0
2
0
3
2
2
0
0
2
0
2
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
1
0
0
1
2
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
2
2
2
0
1
0
2
0
0
0
0
0
0
0
3
2
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
1
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
1
2
0
0
0
1
0
0
1
0
0
0
1
0
1
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
2
0
0
1
2
2
0
3
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
9
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
4
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
2
2
0
3
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
2
2
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
1
0
0
1
1
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
1
0
0
0
2
0
1
2
0
2
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
1
1
0
0
0
0
0
0
1
0
0
1
2
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
2
0
2
1
2
1
2
3
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
1
0
3
0
1
2
0
0
0
0
0
0
0
0
0
3
0
0
3
0
1
0
1
1
2
1
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
2
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
1
0
2
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
8
0
0
2
1
1
0
0
0
1
0
0
2
1
2
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
1
0
1
0
2
0
1
0
1
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
4
1
2
1
0
2
0
0
0
2
0
3
0
0
3
0
0
1
0
0
0
0
0
0
0
0
2
0
2
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
1
0
1
0
0
1
1
0
2
1
0
2
2
0
0
1
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
1
0
1
0
0
2
2
1
0
0
0
0
0
2
1
0
0
0
1
2
1
0
0
0
2
0
0
3
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
6
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
2
2
0
0
0
1
0
0
0
0
5
0
0
0
1
0
0
0
1
0
1
0
3
0
0
0
0
1
2
0
2
0
0
0
2
0
0
2
0
0
1
0
0
2
0
2
0
0
0
0
1
0
0
0
3
0
2
0
0
0
0
0
2
0
0
2
2
0
2
2
0
0
0
3
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
2
0
2
0
0
2
0
0
0
0
0
2
11
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
5
0
2
0
0
0
0
2
0
0
0
1
0
0
10
0
2
2
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
1
0
0
2
3
1
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
2
1
1
0
0
2
2
0
0
0
0
0
0
1
0
1
2
1
0
0
1
0
1
1
0
0
0
0
0
0
1
0
4
0
0
1
0
0
3
3
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
3
0
1
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
1
1
1
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
1
2
0
0
0
0
0
0
0
5
0
0
0
2
1
0
0
0
0
0
0
0
7
0
0
1
0
0
1
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
2
0
1
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
2
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
1
2
0
4
0
0
0
0
1
0
0
0
0
2
0
0
3
0
0
2
0
0
0
0
1
2
0
0
0
0
1
1
0
0
2
2
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
2
1
1
0
0
0
0
0
0
0
1
0
0
1
3
0
0
2
0
1
2
0
0
0
0
0
1
0
2
0
0
2
0
0
1
0
2
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
2
0
0
1
0
0
2
0
0
0
1
0
2
1
0
0
1
1
0
0
2
2
1
2
2
1
1
0
1
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
2
2
0
0
2
2
0
0
2
2
2
0
0
0
0
0
0
2
0
0
1
0
0
1
0
2
0
0
1
2
0
0
2
1
0
1
0
2
1
0
0
2
0
0
0
0
3
0
1
0
1
0
2
0
0
2
2
1
0
1
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
2
0
0
1
0
0
0
2
0
4
0
2
2
0
0
0
1
0
0
2
1
0
2
0
0
0
0
0
1
2
1
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
3
0
0
3
1
0
2
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
1
1
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
1
0
1
1
0
1
0
0
0
1
2
0
2
0
0
0
0
0
0
1
1
2
0
0
0
0
1
0
2
1
0
0
0
0
2
0
2
0
2
1
1
1
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
1
3
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
2
0
0
0
0
2
0
0
2
1
1
2
0
0
1
1
0
0
1
2
2
0
0
6
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
2
3
0
1
0
0
0
2
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
2
2
2
2
0
0
0
1
0
0
0
0
3
0
0
0
1
0
0
0
0
1
0
0
1
2
0
0
2
2
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
4
1
0
0
0
2
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
1
2
1
0
0
0
0
2
0
1
1
1
2
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
1
3
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
1
4
2
1
2
0
0
0
0
0
0
0
0
3
0
1
0
2
0
0
0
1
1
0
0
0
0
2
0
1
1
0
2
0
0
0
0
1
0
1
0
1
1
0
1
0
0
3
1
1
0
0
2
0
1
1
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
1
2
0
2
2
1
0
0
1
0
2
0
0
0
0
0
0
4
0
3
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
1
3
0
0
0
2
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
2
0
1
0
0
0
0
1
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
3
0
0
2
0
0
2
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
1
2
2
0
0
4
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
1
1
0
0
0
2
0
1
0
0
0
0
0
0
2
2
0
0
0
2
0
1
1
0
0
0
0
3
0
0
2
0
0
0
3
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
1
0
0
1
0
0
1
0
1
0
0
1
1
2
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
2
1
0
2
2
0
2
0
0
0
4
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
2
1
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
2
2
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
2
0
3
0
0
0
0
1
1
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
3
0
1
0
1
1
0
0
0
0
0
0
0
0
2
0
3
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
2
0
3
0
0
0
0
0
0
0
0
3
2
2
0
0
2
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
3
0
0
0
0
0
0
3
0
0
0
1
2
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
1
1
0
0
8
0
0
1
0
0
2
1
0
0
0
0
0
0
0
1
3
0
0
1
1
0
0
0
0
0
0
2
2
0
0
0
1
0
2
0
2
0
0
0
2
2
2
0
0
2
0
0
0
0
0
1
2
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
2
0
0
0
0
2
0
1
0
2
1
0
0
0
1
1
1
1
0
1
3
0
0
0
0
2
0
0
0
0
1
3
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
1
0
3
0
0
0
0
0
2
1
0
0
1
2
0
2
1
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
2
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
5
2
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
1
0
0
1
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
3
6
0
0
0
0
0
0
2
1
0
0
0
1
0
2
0
2
0
0
0
0
0
3
0
2
0
0
0
0
2
3
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
2
0
2
0
1
0
2
0
0
0
1
0
0
0
1
0
0
2
2
0
0
0
2
0
2
0
1
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
1
0
0
2
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
3
0
0
0
3
3
0
0
0
0
0
0
1
0
0
3
0
3
0
0
1
0
0
2
0
1
2
1
0
0
0
0
2
0
0
1
0
0
1
2
0
0
0
0
3
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
1
0
1
0
1
1
0
1
0
3
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
1
8
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
1
0
0
0
6
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
1
2
1
0
2
1
2
0
0
0
0
0
0
0
3
1
0
0
2
0
1
3
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
5
0
1
2
0
0
0
0
2
1
0
0
0
0
0
1
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
1
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
5
0
0
0
1
0
0
0
0
0
0
0
1
0
2
4
0
3
2
2
0
0
0
1
0
0
0
4
2
0
0
0
1
0
0
0
2
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
3
0
1
0
0
0
1
1
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
2
2
2
2
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
3
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
1
0
1
0
0
0
2
0
3
0
0
0
3
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
1
2
0
1
0
0
0
1
1
0
1
3
0
0
0
0
1
2
0
0
0
0
0
0
2
0
2
0
2
1
2
0
0
0
3
1
0
0
0
0
0
0
1
0
2
1
2
0
0
1
0
0
2
1
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
2
2
0
0
1
1
0
1
0
0
2
1
2
0
0
0
1
0
0
0
0
1
0
0
0
2
1
0
2
1
1
0
0
2
1
0
0
0
0
0
2
0
0
0
2
0
1
0
1
4
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
3
0
0
0
0
1
0
0
1
0
1
2
1
0
0
2
0
0
0
0
2
0
1
2
0
1
1
1
0
0
1
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
2
0
1
3
2
0
0
0
1
0
1
1
0
0
0
0
0
0
3
1
0
0
0
2
2
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
4
1
0
4
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
3
1
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
2
0
2
2
2
0
0
1
2
0
0
2
3
0
1
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
2
1
0
0
2
0
0
2
0
2
0
2
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
1
0
2
0
1
0
0
0
1
0
0
1
0
2
0
0
0
5
2
1
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
2
0
2
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
1
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
3
0
0
0
2
1
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
2
0
0
0
1
0
2
0
0
0
0
1
0
0
1
1
0
0
0
0
1
1
0
2
1
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
2
1
0
1
0
2
2
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
1
0
3
0
5
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
2
0
2
1
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
2
0
1
0
1
2
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
2
1
0
0
2
1
0
0
0
0
4
4
1
0
0
0
0
0
0
3
2
2
0
2
2
0
0
0
0
0
0
1
0
1
2
4
1
0
2
0
0
0
0
0
0
0
2
0
2
2
1
1
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
4
0
0
1
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
1
0
0
0
2
2
0
2
1
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
2
0
2
0
0
0
1
0
4
0
0
0
1
3
0
2
1
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
2
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
2
1
0
1
0
0
0
0
0
0
0
3
0
0
1
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
1
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
1
1
1
0
0
1
0
0
1
2
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
1
1
2
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
1
0
2
2
0
0
2
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
4
0
2
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
1
1
0
0
0
0
1
1
1
2
2
0
0
0
1
0
2
0
2
0
2
0
3
0
2
1
0
0
0
0
1
1
0
1
1
2
0
2
0
0
0
0
0
1
3
1
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
4
3
0
0
0
0
0
0
1
0
1
3
2
0
1
0
0
0
2
0
0
1
0
0
0
0
1
1
0
2
0
0
0
0
2
0
2
2
2
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
1
0
0
7
0
0
0
0
1
1
3
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
1
1
1
0
0
2
2
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
2
0
0
1
0
0
0
1
0
1
0
0
0
2
0
0
1
0
2
0
0
0
1
0
1
0
2
0
2
0
2
2
0
2
0
0
0
0
2
2
0
0
0
0
2
8
0
1
2
1
0
0
0
2
3
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
2
2
0
0
0
0
0
6
0
0
0
1
0
2
0
2
0
0
0
1
0
0
3
2
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
1
1
0
0
2
0
0
0
0
0
0
2
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
3
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
2
2
1
0
0
0
2
0
0
2
0
0
1
0
2
0
1
2
0
0
1
2
1
0
0
0
0
1
0
2
0
0
0
1
0
0
3
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
1
1
0
0
1
2
0
0
4
0
2
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
2
2
0
0
0
2
0
0
1
2
2
3
0
0
0
0
2
0
0
3
0
2
2
0
0
1
2
0
0
0
1
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
1
2
2
1
0
2
2
0
2
0
0
0
0
0
0
0
2
2
0
2
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
3
2
0
3
0
0
1
2
2
1
3
2
1
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
3
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
13
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
2
2
0
0
0
2
0
2
0
1
0
0
0
1
0
0
2
1
2
0
3
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
6
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
3
1
0
0
0
2
1
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
1
3
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
3
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
2
2
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
2
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
1
2
0
3
0
0
2
0
0
0
0
1
0
1
0
0
0
1
3
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
3
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
2
0
2
0
1
2
0
0
0
0
0
0
0
1
0
1
2
1
0
0
1
0
0
1
0
2
0
0
0
0
0
5
2
0
3
0
0
1
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
2
1
1
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
1
1
0
2
2
0
0
0
3
0
0
0
0
0
2
3
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
2
2
0
0
0
3
1
1
0
6
1
0
2
1
0
0
0
0
1
0
0
0
2
2
0
0
1
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
2
2
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
2
2
2
0
2
0
1
0
0
0
0
0
1
0
0
0
0
1
3
0
0
1
2
0
0
0
0
3
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
4
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
2
0
0
2
2
0
7
0
2
0
0
2
0
2
0
2
0
1
0
0
0
0
2
0
0
2
0
1
0
2
2
0
1
2
0
0
1
0
1
0
4
0
0
2
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
2
3
0
0
0
0
1
0
2
1
1
2
0
2
0
0
0
1
0
1
0
1
0
0
0
0
0
2
2
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
2
0
0
0
1
0
0
0
0
2
3
0
0
0
1
0
2
1
0
0
1
2
1
1
0
5
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
1
2
1
1
2
0
0
0
0
0
0
1
0
2
1
0
0
0
0
1
0
1
1
0
2
1
0
2
2
2
0
3
0
1
0
0
0
2
0
0
0
0
0
0
1
2
1
1
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
2
0
0
0
3
0
0
0
0
0
1
0
1
0
2
2
0
1
0
0
0
0
0
1
0
0
1
0
0
3
1
0
2
3
1
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
2
0
1
0
1
0
1
2
0
1
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
1
1
0
2
0
0
2
1
0
0
0
1
1
1
0
1
2
0
1
0
0
2
2
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
4
0
0
1
2
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
1
1
1
1
3
0
3
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
2
0
1
0
0
1
0
1
2
0
0
0
0
1
0
0
0
0
0
2
0
0
2
1
0
0
4
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
4
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
2
0
2
0
0
0
2
0
1
3
0
3
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
2
0
2
1
0
0
0
2
0
0
1
3
0
0
0
0
0
2
0
0
0
0
3
2
0
2
0
0
0
0
0
1
0
2
2
0
2
0
2
2
0
0
0
0
0
0
0
3
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
1
0
2
1
8
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
1
0
1
0
0
1
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
2
0
0
1
0
2
0
0
2
1
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
2
0
0
4
0
0
1
0
1
0
0
1
3
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
1
2
0
2
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
1
0
2
1
2
1
0
1
0
0
0
1
2
0
2
0
0
0
0
0
0
1
2
0
0
1
2
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
1
0
1
0
2
1
0
2
2
1
1
0
0
1
0
1
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
2
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
2
1
0
2
0
0
2
0
3
0
1
0
0
0
0
1
0
1
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
3
3
0
0
0
0
0
0
0
0
1
2
0
0
2
3
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
2
1
0
1
0
0
1
2
2
2
3
1
2
0
0
1
0
1
0
0
0
2
0
0
1
2
0
0
0
0
4
3
2
2
0
0
0
1
0
4
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
1
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
3
0
3
0
0
0
0
1
1
0
0
0
2
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
2
0
0
0
2
0
2
0
0
0
0
2
0
2
0
0
0
0
0
2
1
2
3
0
0
0
1
0
0
0
0
0
0
0
0
1
3
1
0
0
0
0
0
0
0
1
0
1
0
0
0
3
0
0
0
2
0
0
0
0
2
0
0
0
2
2
1
0
0
0
0
2
0
1
0
0
2
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
2
1
0
0
0
0
0
0
0
2
1
0
0
1
1
0
1
2
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
2
1
1
0
0
0
0
1
0
0
1
0
0
2
0
2
2
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
1
1
2
1
0
0
2
0
2
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
1
0
2
0
0
0
3
0
0
1
1
0
0
0
2
1
0
1
0
1
0
2
0
0
5
0
2
1
0
1
0
1
2
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
1
1
2
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
1
1
0
0
0
1
1
0
2
2
1
2
0
0
0
2
0
2
0
0
0
3
2
0
2
0
1
2
0
0
1
2
0
1
0
0
0
0
0
0
2
0
0
0
2
2
3
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
2
0
4
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
2
0
2
0
3
0
2
0
3
0
0
0
0
2
0
0
0
1
2
1
0
0
0
0
1
0
0
0
0
0
1
2
0
3
0
0
1
0
3
0
1
0
0
3
0
0
1
0
1
0
1
1
2
0
2
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
1
0
3
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
4
0
0
2
0
0
1
0
0
2
0
0
1
0
0
0
2
1
0
0
0
0
2
0
0
2
0
0
0
3
2
1
1
0
0
2
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
1
0
1
0
0
2
2
0
1
1
0
0
1
0
0
3
0
0
0
1
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
2
1
0
2
0
1
1
1
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
5
1
2
0
0
3
0
1
0
0
3
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
5
1
0
2
0
2
1
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
1
1
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
2
1
0
0
2
2
1
5
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
1
0
0
2
0
1
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
3
0
1
0
2
0
0
1
1
0
0
0
1
1
0
4
0
2
1
2
0
2
0
2
0
0
0
1
0
0
2
0
0
1
3
2
2
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
7
1
1
0
0
0
2
2
2
2
0
0
1
1
0
1
0
0
1
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
4
2
0
0
0
0
0
0
1
0
0
1
2
0
2
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
2
0
1
0
0
2
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
2
2
1
0
0
1
0
0
0
0
1
0
0
0
0
1
2
0
1
0
0
1
0
1
0
0
0
2
0
0
0
0
0
2
0
0
6
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
2
2
0
1
0
0
0
4
0
0
0
0
1
0
0
0
2
0
0
0
0
6
1
1
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
1
0
2
1
0
0
2
0
2
0
0
0
0
1
0
0
3
0
0
2
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
2
1
0
1
1
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
1
2
1
10
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
1
2
2
0
1
0
0
2
0
0
0
0
0
2
0
1
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
5
0
1
0
0
0
0
3
3
0
0
2
2
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
3
1
0
1
1
0
0
0
0
1
0
3
0
1
2
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
5
2
0
2
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
3
1
0
0
0
0
0
0
2
1
2
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
2
0
0
3
0
0
3
0
0
4
0
0
2
0
1
0
2
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
2
0
1
0
2
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
2
1
0
1
0
5
0
0
0
0
0
0
1
5
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
2
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
2
0
0
0
0
2
2
0
1
0
2
0
3
2
2
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
2
0
0
0
0
0
0
0
1
0
1
0
2
0
0
2
0
2
0
0
0
0
2
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
3
0
0
2
0
0
0
0
0
2
0
0
0
0
2
2
0
1
0
0
0
2
1
2
1
0
0
0
0
0
3
0
0
0
0
1
1
0
0
0
2
0
3
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
3
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
2
0
1
0
2
1
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
2
2
0
2
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
2
2
2
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
1
0
3
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
1
0
2
1
0
0
0
0
2
0
0
1
0
0
0
1
1
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
2
1
0
0
0
0
1
0
0
5
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
2
0
2
0
0
3
0
0
0
0
2
0
1
3
0
0
1
0
2
0
0
0
1
1
1
0
0
2
0
1
2
2
0
0
0
0
2
0
0
0
2
0
0
1
0
3
2
1
0
0
0
1
0
0
2
0
0
3
2
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
3
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
2
0
0
1
0
2
1
0
0
0
3
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
1
0
2
0
0
0
1
0
0
0
0
0
3
0
1
0
1
0
4
0
0
0
0
4
1
0
2
0
0
2
2
0
2
0
0
0
0
0
4
0
0
0
2
2
0
2
2
1
0
0
0
0
2
0
0
0
0
2
2
0
2
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
2
1
1
0
0
0
0
2
0
0
2
0
1
0
2
0
1
0
0
1
2
0
0
1
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
5
0
2
1
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
2
0
2
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
1
1
0
2
1
0
0
0
0
0
1
0
1
0
4
0
2
3
2
2
0
0
0
0
0
0
1
2
0
0
0
0
0
5
0
0
1
0
0
2
1
3
0
1
0
0
1
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
1
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
2
1
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
3
1
1
0
0
1
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
4
0
0
2
0
1
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
2
2
0
0
1
0
0
1
0
0
0
0
1
0
0
0
2
1
0
0
1
3
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
3
2
0
0
2
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
1
0
1
0
2
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
4
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
1
0
0
0
1
0
0
0
1
0
0
2
0
1
0
0
2
2
0
0
0
0
1
0
0
0
1
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
6
0
0
1
4
0
0
0
2
0
0
0
2
1
0
0
0
2
0
0
0
1
0
0
2
0
0
4
1
0
0
0
0
0
4
0
2
0
1
0
0
0
1
2
0
0
1
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
2
1
2
3
0
1
0
0
1
0
0
1
2
0
0
0
0
0
3
0
0
0
0
2
0
0
1
0
0
0
7
2
0
0
1
0
2
2
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
2
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
3
0
2
0
0
0
3
0
2
0
2
0
2
0
0
0
0
1
0
1
2
0
3
0
0
0
0
1
2
0
0
1
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
1
2
0
0
1
2
0
1
0
1
0
0
0
0
2
0
2
0
4
0
0
0
0
0
0
13
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
2
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
2
6
0
1
1
0
2
1
0
0
0
2
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
7
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
2
0
0
0
1
2
2
0
1
1
1
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
1
0
0
6
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
6
2
1
0
1
2
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
4
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
1
0
2
0
0
1
0
0
1
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
2
0
0
0
1
0
1
0
0
0
2
2
0
2
0
1
0
0
2
0
0
2
0
1
0
0
0
0
2
2
3
0
2
1
1
1
0
0
0
1
0
0
0
2
0
2
0
2
0
0
1
2
0
2
0
0
0
2
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
2
0
1
2
1
1
2
2
0
0
0
0
3
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
2
3
0
0
2
1
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
2
1
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
2
1
0
0
0
0
1
1
0
0
2
0
2
1
0
2
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
1
0
1
0
0
0
3
1
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
2
2
1
0
1
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
3
0
2
1
1
1
1
0
0
2
1
2
0
2
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
1
0
0
0
2
2
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
1
0
0
2
0
0
0
11
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
2
2
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
2
3
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
1
1
0
4
0
0
1
0
0
0
0
0
0
0
2
2
0
1
0
0
0
2
0
0
0
0
1
2
0
2
1
2
0
3
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
1
2
0
0
1
0
0
0
2
2
0
0
0
0
1
0
0
0
3
0
0
0
2
0
2
0
0
0
0
2
0
1
0
0
1
0
0
0
0
1
0
0
0
3
3
0
0
0
0
2
0
0
0
2
2
2
0
0
0
3
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
2
0
0
0
0
0
1
0
0
2
2
1
0
0
0
1
0
0
3
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
3
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
2
0
3
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
1
1
0
2
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
1
1
4
0
2
2
0
2
2
0
2
0
1
2
0
0
1
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
1
1
0
2
0
2
3
0
1
1
0
0
0
0
0
2
0
0
0
0
2
3
1
0
0
0
0
2
3
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
3
0
0
1
0
6
2
0
0
4
1
0
1
0
0
2
0
0
0
5
0
1
2
1
1
2
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
3
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
1
1
0
0
2
2
1
1
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
2
2
1
3
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
5
0
2
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
5
0
1
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
1
0
0
4
1
0
3
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
2
1
0
0
0
0
0
1
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
5
0
0
0
0
0
0
0
0
3
0
2
0
1
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
2
0
1
3
1
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
1
1
0
1
0
1
0
0
2
0
1
3
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
1
1
2
0
0
0
0
0
0
1
0
1
0
1
0
2
0
0
0
0
1
0
0
0
1
1
1
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
1
1
0
1
2
0
2
0
0
2
0
0
0
0
1
2
0
0
0
1
0
1
0
2
0
0
0
0
2
0
0
5
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
3
0
1
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
1
2
0
1
0
0
1
0
0
0
2
1
2
1
2
0
0
2
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
3
0
1
2
0
0
0
0
1
1
0
0
0
0
5
0
0
0
0
0
0
0
0
0
2
1
3
0
0
2
0
0
0
0
1
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
3
2
0
2
1
0
1
0
5
0
0
0
0
0
0
2
0
0
0
1
3
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
4
5
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
2
1
0
2
0
0
1
0
0
0
0
1
0
0
0
1
0
3
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
1
0
2
2
0
1
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
1
1
0
1
0
0
0
1
0
0
1
0
0
0
5
0
0
0
0
0
0
1
0
2
2
1
0
0
0
0
0
0
0
0
2
0
0
1
2
1
0
0
2
0
2
1
0
0
0
0
5
1
0
3
0
0
0
1
0
0
0
0
2
0
0
1
2
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
3
2
0
0
3
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
3
0
2
0
2
0
0
0
0
0
1
1
0
1
0
0
2
0
0
0
0
0
1
2
0
1
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
3
1
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
2
1
0
0
0
3
0
0
0
0
0
2
0
0
0
2
0
2
1
1
2
2
0
0
0
0
2
0
0
0
2
1
2
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
1
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
2
1
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
1
1
1
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
1
3
0
0
1
0
1
0
0
0
2
2
0
0
0
0
0
0
0
3
0
1
0
0
0
0
4
0
0
0
2
0
1
3
2
0
3
0
0
0
0
0
0
1
2
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
1
0
0
0
1
2
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
2
0
0
0
3
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
1
0
2
1
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
6
3
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
1
0
0
0
0
0
2
1
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
2
0
2
2
0
2
0
0
0
2
0
0
0
0
0
1
0
1
2
1
0
1
0
0
3
2
1
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
4
2
0
0
0
2
0
0
0
1
0
0
0
3
1
0
0
1
0
0
0
1
1
1
2
0
0
0
0
0
1
0
0
0
1
3
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
2
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
3
0
2
0
0
0
1
0
0
0
2
0
1
3
2
0
1
2
0
1
0
1
0
0
0
0
2
2
2
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
2
2
0
0
0
0
2
0
0
0
0
0
0
3
2
0
0
2
0
0
0
1
0
0
0
0
0
1
0
1
2
1
2
0
2
1
2
0
1
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
2
2
3
0
0
1
0
0
0
1
1
2
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
2
4
0
0
0
0
1
3
2
4
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
2
0
1
0
0
1
2
0
0
0
0
0
2
0
0
0
0
2
4
0
3
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
1
0
0
2
2
0
2
1
1
3
0
2
1
0
2
0
2
0
0
0
0
1
0
0
0
0
1
0
1
2
0
2
0
1
0
0
0
0
2
1
0
0
0
0
2
1
0
0
2
0
0
0
0
0
2
0
0
0
0
1
2
0
0
1
0
1
1
0
1
0
0
0
0
0
0
1
0
3
0
0
0
0
7
0
1
3
1
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
3
2
0
3
2
1
0
2
0
2
0
1
0
1
2
0
2
1
0
0
0
1
0
1
0
2
0
0
2
0
0
0
0
0
1
0
0
2
1
0
1
0
0
1
0
0
1
0
1
1
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
2
0
0
2
2
2
2
2
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
6
0
0
2
0
2
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
2
2
0
0
1
2
0
0
2
0
2
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
2
0
2
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
2
1
0
1
1
2
0
0
1
0
0
0
0
0
0
2
0
1
2
0
0
2
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
2
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
6
0
0
0
1
1
0
3
2
0
2
2
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
3
0
0
0
0
4
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
1
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
3
0
1
0
0
3
0
0
1
0
0
0
0
0
0
0
0
2
1
0
1
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
2
0
0
1
1
1
1
0
0
0
0
0
1
0
0
1
2
0
2
2
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
2
0
0
1
2
0
2
0
0
1
0
0
0
0
0
0
0
0
1
2
2
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
2
0
0
1
0
0
0
0
2
1
0
0
2
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
3
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
3
1
0
0
0
1
0
0
1
0
0
1
0
0
0
2
0
1
1
0
0
1
2
0
0
0
1
1
0
0
0
0
5
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
3
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
1
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
1
2
0
0
0
2
3
0
0
0
0
0
0
0
2
0
0
3
2
0
0
1
0
0
0
0
2
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
3
0
0
2
1
1
2
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
2
0
2
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
2
0
0
1
2
0
0
1
0
0
0
0
2
0
0
0
2
1
0
0
0
2
0
2
0
0
0
0
1
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
2
1
3
3
0
0
2
2
0
0
2
0
1
0
2
0
0
0
2
2
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
1
0
0
2
2
0
0
0
2
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
2
1
2
0
1
1
2
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
3
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
2
2
0
0
0
0
0
0
1
2
1
0
2
0
0
0
0
0
0
0
2
0
2
0
0
3
0
0
2
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
1
0
2
0
0
0
1
2
0
1
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
1
0
2
2
0
0
0
0
3
0
1
1
1
0
0
0
0
0
0
0
0
0
2
2
0
1
1
0
0
0
2
1
0
0
0
0
1
0
0
0
0
1
1
0
1
2
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
2
0
3
1
0
0
0
0
0
0
0
8
0
1
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
1
2
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
2
0
2
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
2
2
2
0
2
0
1
1
3
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
2
0
2
2
1
0
0
0
0
0
2
0
0
0
0
0
0
4
0
0
2
0
2
0
0
1
0
0
2
0
0
0
0
0
1
0
2
2
0
1
2
0
0
2
0
0
2
2
2
1
2
1
0
0
0
0
2
2
0
0
0
0
0
1
0
2
2
0
2
1
0
0
0
0
0
0
0
0
0
0
1
1
3
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
3
2
0
2
0
0
0
0
1
0
1
2
1
0
0
1
0
2
0
0
0
1
1
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
6
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
2
0
2
0
0
0
1
0
0
0
0
3
0
0
0
1
0
0
2
0
0
0
1
0
1
5
0
0
2
2
3
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
5
0
2
2
0
0
2
0
0
0
3
0
2
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
2
0
0
4
0
1
0
0
0
0
0
0
1
1
0
0
1
0
2
1
1
1
0
0
0
2
1
0
0
0
0
2
0
0
1
0
1
1
0
1
2
0
0
0
1
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
2
2
0
0
2
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
2
0
0
0
3
0
0
0
0
2
0
0
1
1
0
0
1
0
1
0
4
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
1
0
2
0
1
0
0
1
2
2
0
2
0
0
0
5
0
0
0
0
0
1
2
0
2
0
2
0
1
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
2
0
2
0
0
1
0
0
0
2
0
1
2
0
0
0
0
1
0
1
0
0
2
0
0
0
0
1
0
0
2
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
1
0
0
1
1
2
0
1
2
2
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
2
0
7
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
1
2
0
3
1
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
2
2
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
1
1
0
0
0
0
2
0
1
0
0
0
2
1
0
0
0
1
1
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
1
1
1
1
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
1
1
0
2
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
3
0
0
1
0
3
0
0
2
0
0
0
0
0
3
0
1
0
0
1
1
1
0
0
0
1
1
0
3
1
2
2
0
1
1
0
0
0
0
0
0
0
0
3
0
2
0
0
0
1
0
0
0
2
1
1
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
2
0
0
4
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
2
0
3
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
2
0
0
1
0
1
1
0
0
0
0
0
1
4
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
4
3
0
0
1
2
0
0
0
0
3
1
2
0
1
2
1
0
0
0
0
0
1
0
0
2
0
2
0
2
3
1
4
2
2
0
2
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
1
0
0
1
0
1
0
1
0
2
0
0
2
0
0
0
0
0
0
2
1
2
1
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
2
1
0
2
0
2
2
1
0
4
0
1
2
0
1
0
0
0
2
0
2
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
1
0
1
0
0
0
1
0
2
2
0
0
0
0
0
0
1
0
1
1
0
0
0
2
1
0
0
0
0
2
0
2
1
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
1
0
1
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
1
1
0
2
2
0
0
0
0
1
1
0
1
1
0
1
1
0
1
1
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
1
0
3
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
1
0
0
0
3
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
3
0
0
0
3
1
0
0
0
1
0
1
1
2
0
1
0
2
0
0
2
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
4
0
1
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
2
1
0
2
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
3
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
1
0
0
2
3
0
2
0
2
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
1
0
1
0
0
0
2
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
2
0
1
2
0
0
2
1
1
0
7
0
0
2
1
1
1
0
0
1
0
1
2
0
0
3
0
3
1
0
0
0
0
0
0
1
2
1
0
0
2
0
1
2
2
0
0
0
0
0
1
2
0
0
1
2
0
0
0
1
1
1
0
0
0
0
2
0
0
0
2
0
3
0
2
0
0
1
0
0
0
0
0
0
0
3
0
2
0
0
0
1
0
0
2
0
1
3
0
0
0
0
0
0
0
3
0
1
0
0
0
0
1
2
2
0
2
2
0
1
0
1
0
0
0
0
0
2
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
2
0
0
1
4
1
2
0
0
0
0
2
1
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
1
0
2
0
1
0
0
2
1
0
0
0
1
1
0
0
0
0
0
0
0
1
1
1
0
0
2
0
0
0
0
0
1
0
0
0
2
1
2
0
0
0
0
1
0
10
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
2
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
2
2
1
0
1
2
2
0
0
1
0
0
1
1
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
2
1
0
1
0
0
0
0
0
1
0
1
0
1
0
0
2
0
0
0
1
0
0
0
1
0
1
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
2
0
1
0
1
2
0
3
1
2
0
2
0
1
0
2
1
2
0
0
0
0
1
0
0
0
5
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
1
1
0
2
0
0
0
0
0
4
1
0
0
0
1
0
0
0
0
0
0
1
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
1
0
0
0
0
0
2
2
1
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
1
0
2
1
0
0
0
0
0
0
2
2
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
3
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
1
2
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
3
0
1
1
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
2
3
0
1
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
1
1
0
0
0
2
1
1
0
2
0
0
0
0
1
0
0
1
1
0
2
2
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
2
1
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
1
0
0
1
1
2
2
1
0
0
1
0
2
2
0
2
0
0
1
0
1
0
0
3
0
2
0
0
0
0
0
1
1
0
2
0
0
2
0
1
0
2
0
3
0
0
0
1
0
0
0
1
1
2
0
0
0
0
0
0
2
2
0
1
0
0
0
1
0
0
2
1
0
0
0
2
1
1
2
0
0
0
0
0
0
2
0
1
1
0
0
3
0
0
0
0
2
1
1
0
0
0
1
0
0
0
0
2
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
7
0
0
2
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
1
2
2
0
2
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
3
2
1
0
2
1
0
2
0
1
0
0
0
0
2
0
0
2
0
2
0
1
6
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
3
0
0
0
1
0
1
0
0
0
0
0
0
2
2
0
1
2
2
0
0
0
2
0
0
0
0
0
0
0
1
0
1
3
0
2
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
2
1
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
3
0
2
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
2
2
2
2
0
2
2
0
0
1
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
2
0
0
1
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
3
0
0
0
1
2
0
5
0
0
3
1
0
0
0
0
0
0
2
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
3
1
0
0
0
2
1
0
1
0
0
0
1
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
2
3
2
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
1
0
1
0
0
2
0
2
0
1
6
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
2
0
0
1
0
0
0
0
2
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
3
0
0
0
0
0
0
0
0
0
0
2
2
0
2
1
1
0
0
0
3
2
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
1
0
0
1
0
0
0
1
0
2
2
2
0
0
0
0
1
2
1
0
0
0
0
0
7
2
0
1
0
2
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
2
2
1
0
2
0
2
0
1
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
3
1
2
0
0
1
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
2
1
1
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
2
1
4
0
2
1
0
0
1
1
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
2
0
2
0
0
0
1
2
0
0
0
1
1
0
0
0
0
1
2
0
1
2
2
0
0
0
0
2
0
0
0
2
0
0
4
0
0
0
0
1
1
0
0
1
0
5
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
1
3
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
1
2
0
0
2
2
0
0
1
0
4
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
1
0
1
5
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
2
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
3
0
1
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
2
0
2
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
2
1
0
0
1
0
0
0
2
2
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
4
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
2
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
1
1
0
1
0
0
0
0
0
0
1
2
1
0
0
2
0
0
0
1
1
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
4
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
2
0
0
1
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
2
0
0
1
0
0
1
0
0
2
0
1
0
0
2
0
1
0
0
0
0
0
1
2
0
0
1
0
2
0
0
4
0
1
0
0
0
2
0
0
2
0
1
1
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
1
0
0
0
2
2
0
1
0
0
0
2
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
3
3
2
0
0
0
2
0
0
0
2
0
0
2
2
0
1
0
0
0
0
0
0
1
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
2
0
0
0
0
1
0
2
1
2
0
4
0
0
0
0
0
2
1
0
1
2
2
0
0
0
0
0
1
0
0
0
2
2
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
1
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
1
0
0
2
2
2
0
0
0
0
1
0
1
0
0
0
0
3
0
0
0
0
0
1
2
0
1
2
1
0
2
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
2
2
0
1
0
0
2
1
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
2
0
2
1
2
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
5
0
0
0
0
0
0
1
1
0
0
1
1
0
0
1
0
2
0
1
0
1
0
0
0
1
2
0
2
0
0
2
0
0
1
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
2
2
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
1
1
7
0
2
0
0
0
0
0
0
0
0
2
0
4
0
2
3
1
0
2
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
1
0
0
1
2
0
0
1
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
3
0
0
1
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
1
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
1
0
1
2
0
2
0
0
0
3
0
2
2
0
0
0
0
2
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
2
1
0
0
0
0
0
2
0
2
2
1
0
0
0
0
0
0
2
0
0
0
0
5
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
2
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
4
0
0
0
0
0
2
1
3
0
0
1
0
1
0
0
1
0
1
0
0
2
2
0
0
0
0
1
2
0
1
0
2
2
1
0
0
2
0
1
1
0
0
0
0
0
0
0
2
3
1
0
0
0
0
0
1
2
0
1
2
0
2
0
0
0
1
2
0
1
1
0
0
0
2
0
2
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
2
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
1
1
0
1
2
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
4
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
2
1
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
2
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
3
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
2
3
0
0
2
1
0
0
0
0
0
2
0
0
0
3
3
0
0
0
0
1
0
0
1
0
1
1
1
2
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
2
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
1
2
2
0
2
1
0
2
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
2
1
2
0
2
0
0
2
0
0
0
0
0
4
0
0
0
0
0
0
0
2
0
0
2
2
0
1
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
2
0
1
2
0
0
0
1
1
2
0
2
2
2
4
2
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
1
1
0
0
0
0
0
3
4
2
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
3
0
1
0
2
0
0
0
0
2
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
3
2
0
2
0
0
0
2
0
1
0
0
0
0
0
2
0
1
1
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
6
0
1
0
0
0
0
0
1
0
2
0
0
2
0
0
2
2
0
2
0
2
2
0
0
0
1
1
0
0
0
0
0
1
0
0
2
0
2
0
0
0
1
1
0
0
0
2
0
0
1
0
0
0
0
2
2
1
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
1
1
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
3
3
0
0
1
0
1
0
1
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
13
1
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
5
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
2
2
0
2
2
0
0
1
2
0
0
2
0
0
0
0
0
1
0
0
0
0
2
2
2
0
0
0
2
0
0
0
2
0
0
1
0
1
0
0
1
1
0
0
0
1
0
2
1
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
1
2
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
1
0
0
0
1
0
2
1
2
0
2
0
0
0
2
2
0
0
0
2
1
2
0
0
0
1
0
0
0
2
0
1
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
2
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
2
0
0
2
0
0
1
0
0
0
2
0
1
0
0
0
2
0
2
2
2
0
0
0
0
1
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
2
2
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
3
0
0
2
0
0
1
2
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
2
1
0
0
0
2
2
0
2
1
0
0
0
1
0
1
2
3
0
0
0
1
1
0
2
1
0
0
0
0
3
0
0
2
0
1
0
1
0
0
0
1
0
0
3
0
0
0
0
0
1
0
10
2
0
0
0
2
0
0
1
0
1
2
0
2
1
0
0
0
4
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
7
0
0
3
0
2
0
0
1
0
0
1
1
2
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
2
1
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
3
0
2
1
1
0
0
1
2
1
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
2
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
1
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
1
2
0
1
0
0
1
0
0
2
2
2
0
0
0
0
3
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
2
1
2
0
0
0
1
1
2
0
0
1
0
0
2
2
1
0
0
0
2
0
2
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
3
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
2
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
2
0
0
1
2
0
0
0
0
0
0
1
0
3
1
0
0
1
2
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
1
0
1
1
0
0
0
1
1
0
1
1
0
0
2
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
1
0
3
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
1
0
1
1
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
2
0
0
2
0
0
4
2
0
0
0
2
2
2
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
2
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
7
1
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
3
0
1
0
0
0
0
0
0
0
1
2
2
2
0
0
2
0
1
1
2
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
3
0
2
1
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
3
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
3
1
2
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
1
2
1
0
2
0
0
0
1
0
2
1
0
0
1
0
2
1
3
2
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
1
0
2
0
0
2
0
0
1
0
1
0
0
0
2
1
0
0
2
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
5
0
0
1
3
1
0
0
2
0
1
2
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
4
0
0
0
0
1
0
5
1
0
1
0
0
2
0
0
0
0
1
3
0
3
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
2
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
1
0
1
2
0
1
0
0
0
1
0
4
0
2
0
2
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
2
0
0
0
0
0
0
1
1
1
0
2
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
2
2
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
2
0
0
0
2
1
0
1
0
1
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
2
0
0
0
0
0
2
0
0
2
0
0
0
1
2
0
1
1
0
2
1
0
0
2
4
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
4
3
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
2
0
0
2
3
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
4
0
2
2
0
0
0
0
0
0
0
0
1
3
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
2
2
0
0
2
0
0
0
0
0
0
0
3
0
0
0
2
0
1
2
2
0
0
1
0
0
2
1
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
4
1
0
1
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
2
3
1
0
0
1
0
3
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
2
2
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
4
0
0
1
0
2
0
0
0
0
2
0
2
1
0
0
1
0
0
0
3
0
0
2
0
0
0
0
0
0
0
1
1
3
1
0
0
0
2
0
0
0
1
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
2
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
2
0
0
4
0
2
0
0
0
0
0
1
0
0
1
2
0
2
1
0
0
0
1
0
0
0
0
0
1
0
2
0
0
4
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
2
0
2
2
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
4
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
2
0
0
1
2
0
0
1
1
1
0
2
0
0
0
0
6
0
0
0
2
0
1
2
1
0
1
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
2
0
2
0
0
0
0
0
1
5
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
2
0
0
2
0
4
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
2
1
1
0
0
0
0
0
0
0
4
2
0
0
0
2
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
2
0
1
1
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
3
2
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
1
3
0
1
1
1
2
0
0
1
0
0
0
0
0
2
0
3
0
2
0
1
0
0
0
0
2
0
0
2
0
2
0
0
0
1
0
0
0
1
2
2
0
0
1
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
2
0
0
0
0
0
1
1
0
2
1
1
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
2
1
0
0
0
0
0
0
1
2
0
1
0
1
0
2
1
1
0
0
2
0
0
1
0
0
2
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
3
0
2
0
0
0
0
0
1
1
0
0
2
0
1
2
0
0
0
1
0
0
0
2
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
2
1
0
1
1
0
0
1
0
0
3
2
0
2
0
0
0
1
2
0
0
2
0
0
3
2
0
0
0
0
2
0
0
2
0
1
0
0
0
0
1
0
0
0
2
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
1
0
1
1
0
0
1
1
2
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
8
0
0
0
0
0
0
2
0
2
0
1
0
0
1
0
0
0
0
1
2
0
1
2
0
0
0
1
0
0
0
1
0
2
0
3
0
0
0
0
2
1
0
1
0
1
1
2
2
5
0
2
4
0
0
0
0
2
3
0
0
0
2
0
0
0
0
1
0
0
1
1
0
1
2
2
0
0
0
2
0
3
0
0
0
2
1
1
1
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
4
0
2
1
0
2
0
0
0
0
5
0
0
0
0
2
0
1
0
0
0
2
0
1
0
0
0
0
0
0
6
0
0
0
1
1
0
1
0
0
0
0
0
0
2
2
0
0
2
1
0
1
0
2
0
2
2
0
0
0
0
0
1
2
0
0
0
2
1
1
1
2
0
1
0
3
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
1
0
1
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
1
3
0
0
0
2
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
1
2
0
0
3
0
0
0
1
0
1
0
1
0
1
3
0
0
1
1
0
2
2
1
0
1
0
0
0
0
0
2
2
2
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
2
1
0
2
4
0
0
0
3
0
0
0
0
0
2
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
2
0
0
2
0
0
0
2
0
0
3
0
2
0
0
0
2
0
0
0
2
5
0
1
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
1
0
1
0
0
2
2
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
2
0
2
0
0
2
0
2
0
1
1
0
1
0
0
0
0
0
2
2
0
1
0
2
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
1
1
0
0
0
1
0
0
2
0
0
0
2
0
0
0
1
0
0
2
1
1
0
0
1
0
0
4
0
0
0
0
2
0
0
2
1
1
0
0
4
1
2
0
0
0
2
2
1
0
0
0
1
0
0
0
2
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
2
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
3
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
4
0
3
0
1
0
0
2
0
0
2
0
0
0
4
0
0
1
1
0
0
0
0
1
0
0
1
0
0
1
0
3
0
0
0
0
0
0
1
0
2
0
0
1
0
1
2
0
0
0
0
1
0
0
0
1
2
0
1
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
1
2
0
0
0
0
1
0
0
0
2
0
2
0
0
4
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
1
0
1
0
0
2
0
3
0
0
0
2
0
1
1
0
2
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
3
2
0
0
0
0
0
1
0
0
0
0
2
0
0
2
1
2
1
0
1
0
0
0
2
0
0
0
1
0
1
1
0
2
0
0
1
0
0
0
0
2
1
2
0
0
0
0
1
0
0
2
0
2
0
1
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
1
0
1
2
0
0
1
2
0
0
0
1
0
0
0
0
0
0
2
0
0
6
0
0
2
2
3
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
7
0
0
0
2
1
0
0
0
4
0
0
0
0
2
2
0
1
0
0
2
0
2
1
0
2
1
0
0
0
1
0
0
0
1
1
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
2
0
1
0
1
0
2
0
2
0
0
2
0
1
0
0
0
1
0
1
1
2
2
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
2
3
0
0
0
0
0
0
0
1
0
1
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
2
0
2
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
1
0
1
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
1
2
0
0
1
0
1
0
0
1
0
2
0
0
0
0
0
1
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
3
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
1
0
0
0
0
1
0
2
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
6
4
4
2
1
0
0
0
0
2
0
0
4
2
0
0
0
0
0
1
0
2
0
0
2
2
2
0
2
0
0
1
2
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
3
0
0
1
2
0
0
0
1
1
0
0
1
0
1
0
0
0
2
0
0
0
0
1
2
0
0
0
2
0
0
0
1
0
4
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
1
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
1
2
0
3
0
1
0
0
0
0
1
0
1
0
1
0
0
0
2
0
2
0
1
0
0
0
0
0
2
0
3
0
0
0
0
0
2
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
1
4
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
5
0
0
0
0
0
0
2
0
2
2
0
0
0
1
0
0
2
0
0
0
1
1
0
0
0
0
0
1
1
0
0
2
1
0
2
0
0
2
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
1
2
0
0
1
1
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
2
1
0
0
2
1
0
1
1
0
1
0
0
2
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
1
2
0
0
0
2
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
2
0
0
1
0
0
2
0
1
3
0
1
0
1
1
1
1
0
0
0
0
0
0
0
0
0
2
0
0
2
1
1
0
0
2
0
0
2
1
2
0
0
0
0
2
0
0
2
2
0
0
2
0
0
3
2
0
1
1
0
1
0
2
2
0
3
0
0
0
1
0
0
2
0
1
0
1
0
0
0
2
0
0
2
0
0
0
0
0
2
1
1
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
1
1
0
0
0
0
0
2
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
2
5
0
0
0
1
0
2
0
1
0
1
0
0
0
0
2
0
0
2
0
0
4
0
0
0
1
1
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
8
0
2
0
2
1
1
2
1
0
0
0
0
1
1
0
0
0
0
2
1
4
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
9
0
0
0
0
0
0
0
0
0
2
1
0
2
0
1
0
0
0
0
0
0
0
0
1
0
4
0
0
1
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
1
0
3
0
0
0
0
2
0
0
0
0
0
1
2
0
4
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
2
0
0
0
1
0
0
2
2
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
3
0
0
1
1
0
1
0
0
0
2
0
1
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
2
1
0
0
1
0
1
1
2
2
0
0
0
0
0
1
2
2
0
2
2
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
1
1
0
1
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
2
2
2
0
0
1
2
0
0
0
1
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
1
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
1
2
0
0
0
0
4
0
0
0
0
1
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
6
1
0
1
0
2
1
2
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
2
2
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
1
4
0
0
0
0
0
1
0
0
1
0
1
0
2
0
0
1
0
4
0
2
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
3
0
0
1
0
0
1
2
0
2
0
0
2
2
0
1
2
1
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
3
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
1
0
0
2
1
3
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
1
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
1
0
0
2
1
0
0
0
0
0
0
1
1
1
0
2
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
3
0
0
0
0
2
0
0
3
2
0
0
1
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
1
0
1
2
0
1
0
0
2
0
0
2
1
2
0
2
2
0
0
0
0
0
0
2
2
1
0
0
1
3
1
1
0
2
0
0
0
0
0
2
0
0
0
1
0
0
1
2
0
0
1
1
0
0
0
0
0
1
1
2
1
0
0
0
0
0
2
0
4
2
0
0
1
1
2
0
0
0
0
0
2
0
0
1
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
2
2
1
0
2
1
2
0
4
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
1
0
2
0
0
0
2
0
0
1
0
2
0
0
0
0
1
2
1
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
2
0
0
0
1
0
2
0
0
0
3
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
3
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
2
2
0
0
1
0
0
2
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
1
6
2
0
0
3
0
0
0
0
0
0
1
0
0
0
0
1
3
1
0
0
2
0
0
2
1
0
2
0
0
1
2
0
1
1
0
2
0
2
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
4
2
0
0
2
0
0
0
0
5
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
4
0
0
0
0
2
0
0
1
0
1
0
2
0
0
0
0
2
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
3
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
1
0
1
2
0
2
0
0
1
0
1
0
0
0
0
0
7
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
1
0
0
2
0
2
0
0
0
0
1
0
0
1
0
0
1
2
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
2
0
0
0
0
2
1
1
2
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
3
1
0
0
2
0
0
0
1
0
0
0
0
2
1
1
2
1
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
2
2
2
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
2
2
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
12
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
1
2
0
0
0
2
0
0
0
1
2
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
2
0
1
0
1
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
2
0
2
0
0
1
0
3
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
1
2
0
2
0
0
0
3
0
1
1
1
2
0
0
0
2
1
0
0
0
0
0
2
1
0
1
1
0
1
0
0
0
0
1
0
0
2
0
0
1
2
0
0
0
0
2
0
1
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
2
2
0
0
0
0
2
2
0
2
1
0
0
1
2
2
0
0
2
1
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
1
3
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
5
1
0
0
1
0
2
0
0
2
0
2
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
3
0
0
0
1
0
2
2
0
3
3
0
0
2
0
0
0
1
0
0
0
1
2
0
0
0
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
1
1
0
0
1
0
0
0
0
0
2
0
2
0
1
2
1
0
0
0
0
0
0
0
2
4
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
1
0
0
1
0
1
1
2
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
2
0
2
1
2
0
1
2
2
0
0
2
0
1
0
1
1
0
0
1
0
1
2
0
0
0
0
0
1
0
0
2
2
0
0
0
0
1
0
0
1
0
0
0
2
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
2
0
1
0
1
0
2
1
3
0
0
2
0
0
0
2
2
2
0
0
2
0
0
1
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
1
0
1
0
2
3
0
0
0
0
2
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
2
2
0
0
0
0
2
0
0
1
1
0
2
0
2
0
0
2
2
1
0
1
1
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
4
1
0
1
1
0
0
2
2
0
2
0
1
2
0
2
0
1
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
1
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
1
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
3
0
2
0
0
1
0
0
0
0
2
3
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
3
2
1
2
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
2
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
1
0
0
0
0
1
0
0
0
1
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
1
2
0
0
2
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
1
0
1
1
0
1
2
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
2
3
0
0
0
2
1
0
0
2
0
0
0
0
0
0
3
0
1
0
0
2
0
0
2
1
0
1
0
0
0
0
2
0
0
0
0
1
0
5
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
1
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
2
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
1
2
0
0
0
2
1
0
1
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
3
0
0
1
1
0
0
2
0
2
0
0
0
0
0
0
0
0
2
1
0
0
2
0
2
2
0
2
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
4
0
0
0
1
0
1
0
0
0
0
2
0
0
0
1
1
0
1
1
0
0
0
0
1
0
0
0
0
0
2
0
1
0
1
2
0
2
1
2
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
2
0
0
1
0
0
0
0
0
0
1
0
1
2
2
1
0
1
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
6
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
2
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
3
0
1
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
1
0
0
0
0
0
2
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
3
0
0
1
1
0
0
1
0
2
1
0
1
0
0
2
0
2
0
3
0
1
0
0
1
0
3
0
2
0
0
2
0
1
3
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
2
0
2
0
0
0
4
0
1
0
1
0
2
4
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
2
0
0
0
2
1
2
0
0
2
0
2
1
0
4
1
0
2
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
1
0
1
2
0
0
0
0
0
4
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
3
0
3
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
2
0
1
1
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
2
2
2
1
0
0
0
0
0
0
0
1
0
0
2
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
0
0
2
1
1
0
1
2
0
1
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
1
3
0
0
0
0
0
2
1
1
0
0
1
2
1
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
11
0
0
0
2
3
0
0
3
1
0
2
0
2
0
0
0
2
3
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
2
0
2
0
0
2
0
0
1
0
1
0
1
2
0
0
0
0
2
0
0
0
1
0
2
2
0
0
0
0
2
0
0
0
0
1
0
2
0
2
0
2
0
0
0
2
2
1
0
0
1
2
0
0
0
0
2
0
8
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
1
1
0
1
2
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
1
0
0
1
0
0
0
1
0
1
2
0
1
1
1
0
0
0
0
0
0
7
0
0
0
1
2
0
0
0
0
0
0
0
0
0
3
1
0
0
0
2
0
1
0
2
2
0
2
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
2
1
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
1
2
0
1
0
0
0
2
0
1
0
0
0
1
1
0
0
2
1
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
1
0
2
1
0
0
1
0
0
0
2
1
1
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
3
4
1
0
1
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
1
2
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
1
0
0
1
2
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
2
1
0
1
0
0
1
0
1
2
0
1
0
0
0
1
0
0
0
1
0
1
3
0
3
0
0
0
0
0
1
0
0
1
0
0
0
0
1
3
0
0
0
2
0
0
2
2
0
1
0
0
0
2
0
2
1
0
0
1
1
2
0
1
0
0
1
2
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
1
2
0
2
0
0
2
0
2
0
1
0
0
0
0
1
1
0
1
2
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
2
0
2
0
0
0
0
1
0
0
0
1
1
1
1
2
0
0
0
0
0
0
0
0
1
1
2
0
1
0
0
1
2
0
1
0
2
0
0
0
1
0
0
2
1
0
2
2
0
0
0
1
0
0
1
1
4
1
2
0
4
2
0
1
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
1
1
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
3
0
0
0
2
0
0
0
0
0
0
1
0
1
1
0
1
0
0
1
2
1
3
0
0
0
0
0
0
0
0
0
0
0
3
2
0
2
0
0
1
0
0
0
2
0
0
1
0
2
0
0
0
0
1
2
0
0
2
0
1
0
0
0
1
0
0
0
0
0
3
0
0
0
1
0
0
4
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
1
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
3
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
8
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
1
0
1
0
0
0
0
0
2
0
1
1
0
1
0
0
0
2
0
2
0
1
0
0
2
0
2
0
0
0
0
1
2
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
1
0
1
0
0
1
0
0
2
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
3
2
0
0
1
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
2
2
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
2
1
0
2
0
0
1
0
0
0
1
0
0
0
2
1
0
2
0
0
0
0
0
0
1
1
0
0
0
2
2
0
0
2
1
0
0
0
0
2
0
1
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
3
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
1
1
1
2
2
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
4
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
1
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
5
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
2
3
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
1
0
2
0
0
0
0
2
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
1
0
0
2
0
2
0
0
1
0
0
0
0
0
0
2
2
0
0
1
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
2
0
0
0
0
0
0
2
0
2
1
0
0
0
1
0
2
0
0
0
0
0
1
0
1
0
0
1
1
1
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
2
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
3
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
2
1
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
2
0
0
1
0
0
0
2
0
0
0
0
0
2
0
1
0
0
1
0
1
0
0
0
1
0
1
2
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
1
0
0
1
0
0
1
3
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
2
0
2
0
1
0
1
0
0
1
2
2
1
1
1
0
0
2
0
0
0
0
0
1
0
0
2
1
0
1
0
0
1
1
0
0
3
0
0
0
0
1
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
1
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
1
0
0
0
0
0
1
0
0
0
2
0
0
1
2
0
2
0
0
2
0
0
0
0
3
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
2
1
0
1
0
0
0
0
1
3
0
0
0
1
0
0
2
1
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
1
2
0
1
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
1
2
0
1
0
0
0
0
0
0
0
2
0
3
0
0
2
1
0
0
0
0
0
0
6
0
0
0
2
1
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
5
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
1
0
0
0
0
2
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
2
1
0
0
0
2
0
2
0
1
2
0
0
1
0
0
0
2
2
0
0
0
0
1
0
2
1
0
2
4
2
0
1
0
0
0
0
0
0
2
0
1
2
0
0
0
1
0
1
0
0
2
0
0
0
0
5
3
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
1
0
1
0
1
0
1
2
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
1
2
0
2
0
0
0
0
0
2
1
0
1
2
0
0
0
2
0
0
0
0
1
2
0
2
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
1
0
1
0
0
0
2
0
0
2
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
1
0
0
1
3
0
1
1
0
0
0
0
1
2
2
1
2
0
2
2
1
0
0
0
0
0
5
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
2
0
1
1
0
2
15
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
2
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
2
2
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
3
0
1
0
0
2
0
0
1
0
0
3
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
1
1
0
0
2
1
0
2
0
0
2
0
0
2
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
2
0
0
2
1
0
3
0
0
2
0
0
1
2
1
0
0
2
0
2
0
1
0
2
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
1
1
2
1
0
1
0
0
0
0
0
0
0
0
3
0
0
0
5
1
2
0
0
2
0
0
0
0
0
1
0
0
1
0
1
0
0
0
4
0
0
0
0
2
0
0
0
0
0
0
1
2
1
0
0
2
1
0
0
0
2
1
0
0
0
1
0
1
0
0
1
0
0
0
0
2
0
0
1
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
2
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
2
0
3
0
0
0
0
2
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
1
0
2
0
2
0
1
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
1
0
0
0
0
0
0
0
0
2
0
0
0
1
2
2
0
0
0
0
2
0
0
0
2
0
0
0
1
0
2
0
1
1
2
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
1
0
0
1
0
2
1
0
2
0
2
0
0
0
2
0
0
2
2
0
1
2
0
0
0
2
1
0
0
1
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
2
1
0
0
4
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
1
0
0
2
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
2
0
2
1
0
0
1
3
0
0
4
1
0
0
0
2
1
0
0
0
1
0
0
0
0
0
1
1
2
1
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
6
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
1
2
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
3
0
0
1
0
0
2
1
2
0
0
0
0
0
0
1
0
0
1
0
0
0
2
1
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
2
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
2
2
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
1
0
2
0
0
0
1
1
2
0
0
2
0
0
3
2
0
1
0
0
0
2
3
0
1
0
0
1
0
0
1
0
0
0
2
0
0
2
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
6
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
1
0
2
0
1
2
0
0
0
0
0
0
2
1
1
0
1
0
0
1
1
0
0
2
2
2
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
1
2
1
0
1
1
1
0
3
1
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
3
0
1
2
1
2
0
0
0
1
1
2
0
0
1
2
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
2
0
1
1
2
2
0
0
0
0
2
0
0
3
0
2
1
0
0
0
0
0
2
2
0
0
2
0
0
2
0
0
0
1
1
0
0
2
0
0
0
0
1
0
1
0
0
1
0
0
0
2
2
0
0
0
2
3
1
0
0
0
0
1
0
1
2
2
3
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
3
0
2
2
0
0
0
0
2
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
1
0
1
0
1
1
0
2
0
5
0
2
1
0
0
0
0
0
0
2
0
2
0
1
2
0
0
0
0
0
3
0
1
0
0
0
5
8
0
2
0
0
0
0
0
0
0
1
2
0
2
0
1
1
0
0
1
0
1
0
1
0
3
2
0
0
0
0
0
0
1
0
0
1
0
0
0
1
2
0
1
0
0
1
2
0
1
1
0
2
0
0
0
1
0
0
0
0
2
1
1
0
2
0
1
0
0
1
0
0
0
0
0
0
2
0
1
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
2
1
0
2
0
1
1
1
0
2
2
2
0
0
0
0
8
2
0
0
2
0
0
0
1
4
0
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
2
0
3
0
0
2
0
1
0
0
0
0
1
2
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
1
0
2
1
0
0
2
0
1
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
1
2
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
1
0
0
1
0
1
2
0
7
1
0
0
0
0
0
0
0
0
2
2
0
0
0
1
1
0
2
0
0
0
3
0
2
2
0
0
0
4
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
2
1
0
0
0
0
4
0
0
2
0
0
0
0
0
1
0
0
1
1
0
3
0
0
0
2
3
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
1
2
0
0
1
1
0
0
2
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
2
2
0
0
0
0
0
0
2
1
1
1
0
0
0
0
0
1
0
0
0
2
4
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
1
2
0
1
0
0
0
0
2
2
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
2
3
1
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
2
0
1
0
2
2
0
0
2
2
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
1
0
0
0
3
0
0
0
0
1
0
0
0
1
0
1
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
2
0
2
0
2
0
0
1
0
2
3
2
0
0
0
0
0
2
0
0
1
0
2
1
0
2
0
0
0
0
2
0
2
1
2
2
2
0
1
2
0
0
1
0
2
1
0
2
0
0
0
0
1
0
2
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
2
7
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
2
4
0
1
2
0
0
0
1
0
6
0
0
0
2
0
0
1
0
0
0
0
2
1
0
0
0
1
2
0
0
0
0
0
0
2
0
0
2
1
0
0
0
2
2
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
3
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
2
0
1
2
0
0
0
0
0
2
0
1
0
0
2
2
2
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
4
0
1
0
0
0
0
1
0
0
2
0
1
0
1
1
0
0
0
2
0
0
0
0
1
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
1
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
2
2
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
1
0
2
0
0
1
0
2
0
0
0
0
0
0
4
0
1
0
2
0
1
0
0
1
1
0
2
0
0
2
0
0
0
0
0
1
0
0
2
0
0
2
2
0
0
2
2
0
0
0
0
0
1
0
0
2
2
0
2
0
0
2
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
3
0
2
0
2
2
0
0
0
0
0
1
0
0
0
0
0
1
2
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
1
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
2
2
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
2
0
4
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
1
1
0
0
0
0
0
2
0
1
0
0
0
0
1
2
1
0
1
0
0
0
0
1
2
0
1
0
2
0
0
0
4
0
0
0
3
0
0
0
0
0
2
3
0
0
0
0
0
0
0
2
0
0
0
1
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
2
0
3
1
1
0
0
1
0
0
0
4
0
1
0
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
3
0
2
2
1
0
1
0
0
0
0
0
0
0
0
0
1
0
5
0
0
1
0
0
0
1
0
1
0
0
0
0
0
2
2
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
1
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
2
0
0
1
0
2
2
0
0
1
1
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
1
0
0
1
2
0
2
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
3
0
0
0
0
0
1
2
0
0
0
0
2
2
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
1
1
1
0
2
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
2
0
0
0
0
3
0
3
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
2
0
0
0
2
0
2
3
0
2
0
0
0
3
1
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
1
0
1
3
0
0
0
0
0
0
0
0
1
1
0
0
2
1
0
1
0
2
0
0
0
2
1
0
0
0
0
0
0
1
2
0
0
0
2
0
0
1
0
0
1
3
0
0
5
0
1
0
0
0
2
0
3
0
2
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
2
2
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
2
2
0
0
2
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
1
4
0
1
0
0
0
0
0
1
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
2
0
4
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
8
0
0
1
0
0
2
0
2
0
0
0
0
0
0
5
0
0
1
1
0
2
0
1
0
0
0
0
0
1
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
2
0
2
0
0
0
0
0
0
1
0
2
2
0
0
0
0
1
0
0
1
0
2
2
0
1
0
0
0
0
0
2
1
3
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
1
0
0
0
0
0
0
2
1
4
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
1
3
1
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
3
0
0
1
1
0
0
2
1
0
0
0
0
0
1
1
0
0
0
1
0
0
2
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
1
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
1
1
0
0
2
0
0
1
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
3
6
0
0
0
1
0
1
1
0
1
0
2
2
1
2
0
0
0
0
0
0
2
0
1
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
1
1
1
1
0
0
0
0
0
0
1
0
1
2
2
0
2
2
0
0
0
0
0
0
2
2
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
1
0
2
0
0
0
2
0
2
0
0
0
0
2
0
0
2
2
1
0
0
0
3
1
0
0
0
0
2
0
0
1
0
1
1
0
0
2
0
2
0
0
2
0
0
0
0
0
0
1
3
0
0
1
0
2
0
0
0
2
0
0
2
2
2
1
0
0
0
3
0
2
2
0
2
0
0
0
3
0
2
0
0
0
0
0
0
0
0
1
1
2
2
0
2
0
0
0
0
2
0
0
1
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
3
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
3
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
1
1
0
0
0
2
0
0
0
0
0
0
0
0
4
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
1
2
0
0
0
1
0
1
3
0
0
1
0
0
0
0
1
0
3
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
2
0
2
1
0
0
0
0
0
0
0
0
2
2
1
0
0
0
3
0
0
2
2
0
0
1
0
1
1
0
0
0
1
0
1
2
2
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
2
2
0
0
2
1
0
1
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
1
1
0
1
1
0
0
1
4
1
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
1
2
2
0
0
2
0
0
0
2
0
1
3
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
2
0
0
0
0
2
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
2
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
1
0
2
0
0
2
0
0
0
0
1
0
2
0
1
0
2
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
2
0
1
2
0
1
0
0
0
2
0
0
0
0
2
1
3
0
0
1
1
0
2
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
2
2
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
2
1
1
0
2
0
0
0
0
0
1
1
0
0
1
2
0
1
1
2
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
1
0
2
1
0
1
0
7
2
0
4
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
2
0
0
0
0
0
1
2
4
1
2
0
1
0
1
0
0
0
0
1
2
0
0
0
0
3
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
2
1
1
1
0
0
1
0
0
1
1
0
1
0
1
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
1
0
1
2
0
1
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
1
2
1
0
0
0
0
0
0
2
0
0
0
1
2
1
0
1
0
2
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
5
0
2
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
2
0
0
10
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
1
0
1
4
0
0
1
1
1
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
1
0
1
0
0
2
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
2
2
2
0
0
0
0
3
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
3
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
3
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
12
0
6
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
3
2
0
2
1
0
0
0
1
0
0
1
0
1
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
2
0
1
1
0
0
0
0
0
0
0
1
6
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
1
1
0
0
0
0
1
1
1
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
2
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
1
2
1
1
0
2
0
1
1
0
1
1
1
3
0
0
0
0
0
2
0
0
2
3
1
0
0
0
3
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
2
2
2
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
2
0
0
0
0
0
1
2
0
2
0
0
0
2
2
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
1
2
0
0
4
0
0
2
0
0
0
3
3
0
2
1
0
2
0
0
0
0
0
0
2
1
0
0
2
0
0
0
1
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
3
0
2
0
0
1
2
0
0
0
0
0
0
1
1
1
1
0
0
0
0
1
0
1
0
0
1
0
0
0
2
2
0
0
0
2
0
2
1
1
0
0
1
0
0
1
0
0
0
0
1
2
0
2
2
0
0
3
1
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
1
0
2
0
0
1
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
1
0
0
0
0
2
0
1
0
2
2
0
0
0
1
0
0
2
1
0
0
1
1
0
0
2
0
0
0
0
2
0
0
0
2
3
0
2
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
1
2
0
3
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
3
2
2
1
0
1
0
1
0
2
2
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
4
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
2
2
2
0
0
0
0
0
0
2
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
1
2
0
0
0
0
0
3
0
0
1
2
0
0
1
0
0
0
4
0
0
2
0
0
0
4
0
0
0
0
0
0
1
2
1
0
2
0
0
5
0
0
0
3
0
0
0
2
0
0
4
0
0
0
0
3
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
2
1
0
2
0
0
1
0
1
2
3
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
1
0
1
0
0
0
0
1
0
1
0
0
3
2
0
0
0
0
0
2
2
0
1
0
2
0
0
1
0
0
1
1
0
2
2
1
2
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
1
2
0
0
0
0
0
0
0
2
2
0
1
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
2
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
5
0
2
0
0
0
0
5
0
1
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
2
0
1
0
1
1
2
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
2
0
1
1
0
0
0
0
0
0
2
0
2
0
0
0
0
4
0
0
0
0
1
2
0
1
0
2
0
0
1
0
0
3
0
0
0
1
1
2
2
0
1
3
1
2
0
2
0
0
0
0
4
0
0
0
0
0
1
3
0
0
2
0
1
0
0
1
0
1
0
1
2
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
1
0
0
2
1
0
0
2
2
1
0
2
0
2
3
0
1
0
0
1
0
0
2
3
2
0
0
0
2
0
2
0
0
0
1
0
0
0
0
1
1
0
0
0
1
2
0
0
0
0
0
1
4
2
0
1
0
2
0
0
2
1
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
2
0
0
0
0
2
1
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
1
2
0
1
3
0
0
2
0
0
0
0
0
2
2
1
1
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
2
1
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
2
0
0
2
0
2
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
2
1
0
0
0
0
0
2
1
1
0
0
0
2
1
2
0
2
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
2
0
1
0
0
0
2
1
0
0
0
3
0
0
2
0
0
0
0
0
2
1
1
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
4
0
0
0
0
2
2
1
1
2
0
0
2
0
1
2
0
5
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
1
1
1
2
0
1
0
0
0
0
2
0
2
0
1
0
0
2
0
0
0
0
0
2
0
2
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
2
1
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
3
2
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
2
0
0
0
0
0
0
0
0
1
1
0
0
0
1
2
0
1
0
0
1
1
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
4
1
0
0
0
0
0
0
0
0
1
2
1
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
1
0
0
0
2
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
3
1
0
0
0
1
1
0
0
0
2
2
0
0
0
0
0
0
1
0
0
2
0
2
3
0
2
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
3
0
0
0
0
1
0
1
2
0
1
0
1
1
2
0
0
0
2
0
0
0
2
2
1
2
2
0
0
0
0
0
1
3
0
3
0
1
0
0
3
0
1
1
0
0
2
0
0
0
6
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
3
1
0
2
0
2
0
2
0
0
1
1
0
0
2
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
5
0
2
0
0
0
0
0
2
2
5
0
0
0
0
0
2
0
1
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
1
1
0
1
2
0
1
0
1
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
1
0
0
1
0
2
0
0
0
1
0
0
2
2
3
0
0
0
0
0
0
0
0
0
0
8
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
2
1
0
2
0
1
0
0
0
0
0
0
0
1
0
6
1
1
0
0
3
0
0
0
0
4
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
2
0
2
2
2
2
0
0
0
0
0
0
1
1
2
0
0
0
0
2
1
0
0
0
0
0
0
0
2
2
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
1
1
0
2
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
4
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
2
0
0
0
1
0
0
1
0
0
0
2
0
7
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
2
0
1
2
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
4
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
3
0
1
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
2
0
0
0
0
2
0
2
1
0
2
2
0
0
0
0
2
0
0
0
0
0
0
5
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
1
0
2
2
0
2
1
1
0
0
0
2
2
2
2
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
3
0
0
0
0
0
0
2
0
0
2
1
3
1
0
1
2
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
2
2
0
0
0
0
1
0
1
2
0
0
0
2
0
2
2
1
0
2
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
5
0
0
0
0
3
0
0
0
0
0
0
3
1
0
0
0
0
1
0
0
0
2
1
0
0
1
0
0
0
0
1
0
2
0
0
1
0
1
2
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
2
1
0
0
0
2
2
0
2
2
0
1
0
1
0
2
0
2
0
2
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
2
0
0
1
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
2
0
2
0
0
1
0
0
0
3
1
2
1
1
2
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
1
2
2
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
3
0
0
0
1
0
2
2
0
1
0
4
2
0
0
0
0
0
1
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
3
2
0
1
0
0
0
0
1
0
0
0
0
1
3
2
0
1
1
1
0
3
0
0
0
3
3
0
0
0
0
0
2
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
3
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
6
0
0
0
0
1
0
0
2
1
0
0
0
0
1
0
2
0
2
2
0
0
0
0
1
0
1
0
0
0
0
2
0
2
0
0
2
0
0
0
5
0
3
0
1
0
0
1
1
0
1
2
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
2
2
0
2
0
2
0
1
0
0
0
0
0
0
0
1
0
2
1
0
1
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
2
0
0
0
0
5
0
2
0
1
2
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
2
2
0
2
0
0
2
0
0
1
1
0
2
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
1
2
2
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
2
1
0
0
2
0
0
0
0
0
2
0
2
1
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
3
1
2
0
0
2
1
2
1
0
0
1
0
0
1
2
3
2
0
1
0
0
0
0
0
2
2
0
2
2
0
2
1
0
1
0
2
1
0
0
1
0
1
0
0
3
0
1
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
3
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
1
2
1
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
1
0
2
0
0
0
2
1
2
2
1
0
0
3
2
1
0
0
2
0
0
0
0
1
2
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
4
2
0
1
2
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
2
0
0
2
0
2
1
0
0
0
0
0
0
1
0
0
1
1
2
0
4
0
1
1
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
2
0
1
1
2
0
0
0
2
1
0
0
0
0
2
0
0
0
1
0
2
0
0
0
1
1
0
2
1
0
0
0
2
2
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
2
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
3
0
0
0
2
2
0
0
0
1
0
0
0
0
0
4
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
2
2
0
0
1
0
0
1
1
3
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
2
2
0
1
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
1
0
2
0
2
1
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
2
0
0
0
2
0
0
0
0
0
2
0
1
0
2
0
1
0
1
0
0
1
0
2
0
0
0
0
1
7
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
2
0
1
0
0
0
0
0
1
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
1
0
1
0
1
0
0
0
3
1
0
1
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
1
2
2
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
2
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
3
0
2
0
1
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
3
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
2
1
0
2
1
0
0
0
2
0
0
2
0
2
0
2
2
1
0
0
0
2
2
2
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
3
1
0
0
5
0
1
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
2
0
0
1
0
0
0
0
0
1
0
1
0
4
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
3
2
1
0
0
0
0
4
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
1
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
1
2
0
7
0
0
0
2
0
0
0
0
0
0
0
2
0
3
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
1
2
0
0
3
2
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
2
0
2
0
0
1
2
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
2
0
0
0
0
5
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
2
0
0
1
2
2
2
0
0
2
0
0
0
0
0
0
4
0
0
0
0
1
0
0
1
0
0
2
0
0
2
3
0
0
0
0
1
0
2
0
2
0
0
2
0
0
0
0
2
1
0
0
0
0
1
0
2
0
0
0
0
2
3
0
1
0
0
1
0
2
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
2
0
2
0
0
0
0
2
3
0
0
2
1
1
0
0
0
0
0
1
0
0
3
0
1
0
0
0
0
2
0
0
0
2
2
0
3
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
2
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
1
1
2
0
1
1
0
0
0
1
0
0
0
0
2
0
1
0
0
2
1
0
1
0
1
0
0
0
0
2
8
0
0
2
0
0
0
0
0
0
0
2
0
0
2
2
2
1
0
0
0
0
0
0
1
0
2
0
0
1
1
0
0
0
1
0
0
1
1
2
2
0
2
0
0
0
1
0
0
0
1
2
0
0
0
0
1
1
1
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
1
0
2
0
0
1
2
0
0
0
1
0
0
0
0
0
1
0
1
1
1
0
0
1
2
0
0
0
3
0
0
0
1
0
1
0
3
2
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
2
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
2
2
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
1
0
2
0
3
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
1
0
1
0
0
2
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
2
2
0
1
0
2
1
1
0
1
0
0
0
0
0
0
0
5
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
2
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
2
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
2
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
1
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
2
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
1
0
0
0
1
0
2
2
2
0
0
0
1
2
0
2
0
0
0
2
1
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
1
4
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
2
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
2
2
0
0
0
2
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
4
3
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
1
1
0
1
2
0
1
0
1
2
0
0
0
0
1
2
0
0
0
0
2
2
0
2
0
0
0
2
1
0
2
0
0
6
0
0
0
0
2
0
0
3
1
2
0
0
1
1
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
3
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
1
0
0
1
0
1
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
1
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
2
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
2
1
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
2
1
0
0
1
0
0
2
0
0
0
0
1
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
2
0
1
2
1
0
0
1
1
0
1
1
0
4
1
0
0
0
0
0
1
0
0
1
0
3
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
1
2
0
0
0
1
0
0
0
0
1
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
1
0
1
0
4
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
3
0
0
1
0
3
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
1
0
0
0
1
1
0
2
1
0
0
6
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
3
0
1
1
1
0
0
0
0
0
0
0
2
0
1
0
1
0
0
2
0
0
1
1
0
2
2
2
1
0
0
0
1
0
0
0
0
0
0
0
2
1
0
1
0
2
1
0
0
0
0
2
0
0
1
0
0
1
2
2
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
1
1
0
3
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
2
0
0
2
0
0
6
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
2
0
0
1
0
0
3
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
3
0
1
2
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
3
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
2
0
2
0
0
2
0
0
0
0
2
0
0
3
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
1
0
0
3
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
2
1
0
2
0
0
0
2
0
0
0
2
0
2
0
1
0
0
1
0
0
2
0
0
2
0
0
2
0
0
2
1
0
0
1
0
0
0
0
0
2
1
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
3
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
1
1
2
0
0
2
1
2
2
0
2
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
2
0
3
0
0
0
0
2
2
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
4
1
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
1
1
0
2
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
2
0
1
0
0
1
0
0
3
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
1
3
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
4
3
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
2
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
2
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
2
0
0
0
1
3
0
0
1
0
0
2
0
0
1
0
0
2
0
0
0
1
0
0
0
2
1
1
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
1
1
1
0
1
0
0
0
1
2
1
0
2
0
0
0
0
0
0
0
2
1
1
0
1
0
3
0
0
2
0
2
2
0
2
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
1
5
0
0
0
2
2
0
0
1
0
0
0
2
2
0
2
0
2
0
1
0
0
0
2
0
1
0
1
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
3
0
0
1
0
3
0
0
0
0
0
0
2
3
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
1
2
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
1
0
1
0
2
0
0
2
0
0
2
3
3
2
0
0
6
0
2
0
1
0
0
1
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
1
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
3
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
2
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
6
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
1
2
2
1
0
1
1
0
0
0
0
0
0
0
2
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
2
0
0
0
0
0
0
2
1
0
2
1
0
0
0
0
0
0
1
2
0
0
0
2
2
0
0
0
2
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
3
0
1
0
0
2
0
0
0
1
1
0
5
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
2
2
0
0
0
1
0
0
0
0
1
0
0
0
0
3
0
0
0
2
0
0
0
1
2
0
0
1
1
0
2
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
2
0
2
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
2
1
0
3
0
0
0
1
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
2
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
3
1
0
0
1
0
0
1
0
2
1
0
0
2
2
0
1
0
1
0
0
0
0
0
0
2
0
2
1
1
0
0
0
1
0
0
1
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
1
2
0
0
0
2
0
0
0
0
0
1
0
0
1
2
0
1
2
0
2
2
0
0
1
0
0
0
0
0
0
2
2
0
0
2
2
0
0
0
0
0
0
0
1
0
2
1
0
2
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
2
2
0
1
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
3
3
0
1
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
1
2
1
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
3
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
1
1
0
0
0
2
0
0
0
0
2
0
2
0
0
2
0
4
0
0
0
0
2
0
0
2
1
0
1
0
0
1
1
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
1
0
2
1
0
0
0
1
2
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
3
0
0
1
0
0
0
0
2
2
1
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
7
0
0
0
0
0
1
0
2
0
2
0
1
0
0
0
2
0
0
1
0
2
0
0
1
0
0
0
0
1
0
3
0
2
0
1
2
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
1
0
0
1
0
2
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
2
0
1
0
0
0
0
3
2
5
0
0
0
0
0
0
0
0
0
1
6
5
1
0
0
1
0
2
0
0
1
0
1
0
1
0
0
0
0
0
0
0
4
2
0
0
0
3
0
0
1
1
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
1
1
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
1
2
1
0
0
0
0
1
0
1
2
0
0
1
1
2
0
1
1
0
2
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
1
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
1
2
0
0
2
0
1
0
0
2
3
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
2
0
0
0
2
0
0
2
0
0
1
0
0
2
0
0
1
0
2
0
0
1
0
0
0
0
0
0
2
1
0
2
2
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
1
2
1
0
0
2
0
2
2
0
1
2
0
2
0
2
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
4
0
0
0
1
2
0
1
0
0
0
0
2
2
2
2
0
0
3
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
1
2
0
2
0
1
2
0
0
1
1
0
0
0
2
2
1
2
0
0
1
2
0
0
0
0
0
0
2
0
0
1
2
0
2
0
0
0
2
0
0
0
2
1
0
2
0
1
0
0
0
1
0
0
0
1
0
1
0
0
1
0
2
0
2
0
1
0
0
2
2
4
0
0
4
2
0
1
2
0
1
0
0
0
0
0
0
0
1
0
1
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
2
0
3
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
2
2
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
1
1
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
2
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
2
0
0
0
0
0
0
1
4
2
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
2
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
2
0
0
0
4
0
1
1
2
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
1
3
0
0
1
1
0
0
1
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
2
2
0
0
0
0
2
2
0
0
0
1
0
0
0
0
1
0
0
2
0
2
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
2
0
2
4
2
0
0
0
0
2
1
0
0
0
2
0
1
1
0
0
0
0
1
1
0
0
0
1
0
0
1
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
2
2
2
0
0
0
0
0
0
0
0
0
2
2
0
1
2
1
2
0
0
2
0
2
2
0
1
0
0
0
0
0
0
8
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
1
0
0
0
0
2
0
0
2
0
0
0
0
1
0
2
0
1
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
2
0
0
0
3
2
0
0
2
0
0
0
3
0
0
0
1
0
0
2
0
2
2
0
0
1
0
1
0
1
0
2
0
0
0
0
0
2
1
0
2
0
2
0
0
0
0
1
0
0
2
2
1
0
0
0
0
1
0
0
2
2
0
0
0
2
0
0
1
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
2
0
0
1
2
0
0
0
3
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
3
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
1
2
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
2
1
1
0
1
0
0
0
2
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
1
1
0
6
2
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
2
2
0
0
1
0
0
0
2
2
3
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
2
4
1
0
3
0
2
1
2
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
1
1
0
2
1
0
2
1
0
0
0
5
0
0
0
1
0
5
0
2
0
0
0
1
2
1
1
0
0
0
0
3
0
0
0
0
1
2
2
0
2
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
2
1
0
0
3
2
0
0
0
0
0
2
1
0
0
0
2
0
0
0
2
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
1
0
0
0
2
0
0
0
0
4
0
0
1
0
0
2
0
0
1
0
1
0
0
0
0
0
2
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
2
0
1
0
0
3
0
0
2
0
0
0
0
0
0
1
2
0
0
1
0
0
1
1
0
3
2
0
0
0
0
0
2
0
0
0
0
0
3
2
6
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
2
0
0
0
1
2
0
2
0
1
0
0
0
1
0
0
0
1
0
1
0
1
2
0
0
0
2
0
0
0
0
0
0
0
1
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
1
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
2
1
1
2
0
0
2
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
2
2
0
2
0
0
3
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
1
0
0
1
0
1
0
0
4
0
1
1
1
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
2
0
0
0
0
2
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
2
0
1
0
0
0
2
2
1
0
1
0
1
2
0
3
2
2
0
0
0
0
0
0
1
2
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
2
0
1
0
2
0
0
0
0
1
1
1
2
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
2
0
0
3
2
0
0
2
0
0
1
0
1
0
0
1
0
0
0
1
0
2
0
0
0
0
0
1
1
0
0
2
0
2
0
0
1
0
0
0
0
2
1
0
0
2
0
0
0
0
3
1
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
2
0
0
2
1
0
0
0
0
1
2
0
0
2
0
2
0
1
0
1
0
1
2
2
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
1
2
0
1
0
0
2
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
3
1
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
2
0
0
1
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
1
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
4
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
2
4
0
3
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
2
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
2
0
0
0
0
0
0
1
4
0
1
2
0
0
0
1
0
2
0
0
2
0
0
0
0
3
0
1
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
2
1
0
2
1
0
2
2
1
2
0
0
0
0
1
1
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
3
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7
0
2
0
2
0
1
1
1
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
1
0
0
0
0
2
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
2
2
0
0
2
1
0
1
0
0
2
0
0
3
0
0
0
0
4
1
0
0
1
0
0
0
0
2
0
0
2
0
2
0
1
0
0
2
0
1
0
0
0
0
0
0
2
0
2
1
1
1
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
1
0
1
0
0
0
2
2
3
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
1
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
2
1
2
0
0
0
2
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
3
2
0
5
2
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
2
3
0
0
0
0
3
0
0
0
0
0
2
0
2
1
0
0
2
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
4
0
1
0
0
1
0
2
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
3
0
0
0
2
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
1
0
0
0
2
2
2
0
2
0
0
0
3
0
0
1
3
0
0
0
0
0
4
0
0
3
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
2
0
0
0
0
0
4
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
4
0
1
2
0
1
0
1
3
0
0
0
0
2
0
0
2
0
0
0
0
2
3
1
0
0
0
1
0
0
0
0
2
0
0
0
0
3
0
0
2
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
1
1
0
1
1
1
0
0
0
1
0
0
1
0
0
1
0
1
2
0
2
0
2
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
3
0
0
2
2
2
0
0
0
0
0
0
1
0
2
1
0
2
0
2
0
0
0
2
0
1
2
0
0
0
1
1
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
4
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
4
2
0
0
0
1
0
0
1
0
0
0
0
3
2
3
2
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
1
0
0
0
0
0
2
0
0
0
1
0
1
0
0
2
1
0
1
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
3
1
2
0
1
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
2
1
1
0
0
0
0
0
2
1
0
1
0
2
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
2
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
2
0
0
0
0
1
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
3
1
4
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
2
0
2
1
0
0
0
1
0
0
0
1
2
1
0
0
1
0
1
0
0
0
1
0
0
0
3
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
1
2
0
0
0
3
0
0
1
0
0
0
0
0
0
1
2
2
2
1
0
0
0
0
2
1
1
0
0
2
0
1
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
1
2
0
0
3
0
0
0
0
1
1
0
0
0
12
2
1
2
2
0
0
0
0
0
0
2
1
0
0
0
1
2
0
2
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
1
0
1
2
1
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
2
0
0
0
1
1
0
0
0
0
0
2
0
1
1
0
0
2
0
0
1
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
2
0
2
0
0
2
0
0
2
1
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
3
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
3
1
0
1
1
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
1
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
1
0
0
0
0
0
0
0
2
0
3
0
0
1
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
1
2
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
1
2
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
3
0
0
1
0
0
0
0
2
1
0
2
0
0
0
1
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
1
0
1
0
0
0
2
0
0
1
0
2
0
0
3
1
0
0
1
1
0
2
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
2
0
0
0
0
1
0
0
0
0
0
0
3
1
0
0
1
0
0
0
1
0
0
0
3
0
0
0
0
1
2
0
0
0
0
1
1
1
0
0
3
0
1
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
1
0
0
2
0
0
0
0
1
0
0
0
3
2
0
0
0
2
0
0
0
1
0
0
2
0
2
0
0
0
3
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
11
0
0
0
0
2
0
0
0
0
1
0
2
0
1
0
2
0
0
1
1
2
3
2
0
0
0
1
0
0
0
2
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
1
2
0
3
0
0
0
2
0
2
0
0
0
1
3
1
0
4
0
1
2
0
0
1
0
0
0
0
0
2
3
1
0
0
0
0
2
2
0
1
0
0
3
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
1
2
0
9
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
7
0
0
0
2
0
0
0
0
0
2
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
1
1
1
0
0
1
1
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
4
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
3
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
3
0
0
2
0
4
2
0
0
1
0
2
0
0
0
2
1
2
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
11
0
0
0
0
0
1
1
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
1
2
1
2
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
2
0
2
0
0
0
2
2
1
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
1
1
0
0
2
0
0
1
0
1
0
0
0
2
1
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
5
0
1
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
1
2
0
0
0
0
0
2
0
1
2
0
0
1
0
0
0
0
0
0
1
0
0
0
2
2
0
1
0
0
0
0
1
0
0
0
0
0
1
1
2
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
2
0
0
0
0
0
0
0
0
1
1
0
0
1
0
2
0
2
0
0
1
0
2
1
1
0
0
0
0
2
0
0
0
0
4
1
0
0
0
2
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
1
0
0
0
1
0
2
0
0
2
0
0
0
0
1
2
0
1
0
2
0
0
0
2
0
2
3
1
0
2
1
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
2
0
3
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
2
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
2
0
3
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
1
0
2
2
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
3
1
2
5
0
5
0
2
0
0
0
1
2
1
0
0
0
0
2
0
0
2
0
0
0
2
1
0
0
0
2
0
0
0
1
2
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
3
1
4
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
3
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
1
2
1
0
2
0
1
0
3
0
0
0
0
2
0
0
2
0
0
0
1
0
1
2
0
0
0
1
0
0
0
2
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
2
0
0
1
4
1
0
0
0
2
0
0
0
0
2
1
0
2
0
1
0
1
1
2
0
0
2
0
0
6
2
2
3
0
0
0
0
2
0
1
0
0
0
0
0
0
1
1
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
1
0
0
0
2
1
0
2
0
0
0
2
0
2
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
1
1
0
0
2
0
1
0
0
0
0
0
0
0
1
0
1
1
1
0
1
0
0
0
0
1
0
0
0
2
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
1
0
2
0
0
1
2
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
3
0
2
2
0
0
0
0
1
2
0
1
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
2
0
1
0
1
0
0
1
2
0
1
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
2
0
1
1
0
1
0
1
0
1
1
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
2
0
3
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
2
0
0
0
2
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
4
2
1
3
2
2
0
0
2
0
0
2
0
2
0
0
0
1
0
2
0
0
0
3
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
3
2
0
0
1
0
1
2
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
2
1
0
1
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
2
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
1
1
2
0
1
1
1
0
0
0
1
2
2
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
2
0
0
0
1
1
1
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
2
0
0
0
0
1
1
2
0
0
0
2
1
0
0
1
0
0
2
5
2
0
0
0
2
0
2
2
2
0
2
1
3
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
1
0
4
0
0
0
0
2
0
0
0
0
0
1
1
1
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
1
0
0
0
0
1
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
1
0
2
0
0
1
1
2
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
1
1
0
0
2
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
3
2
0
0
0
0
0
0
1
0
2
2
0
0
0
3
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
3
1
0
1
0
1
1
0
0
0
1
0
2
0
0
0
2
1
1
0
0
0
1
0
0
0
2
0
1
0
0
1
0
0
0
1
2
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
1
4
0
0
0
1
0
1
0
1
1
0
0
1
0
2
2
0
2
0
0
1
0
8
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
1
0
0
0
0
0
1
2
2
0
0
2
0
0
0
1
0
0
1
0
2
2
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
2
0
1
0
0
2
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
1
0
2
0
0
0
0
0
2
2
0
0
2
2
0
0
0
3
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
1
0
0
0
1
0
1
0
0
0
2
0
2
0
2
0
0
0
0
3
0
1
1
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
1
1
0
2
0
0
0
2
0
0
0
0
0
0
0
1
2
0
4
0
0
0
0
0
2
1
0
0
1
2
3
0
0
1
6
0
0
0
3
0
0
0
2
0
0
0
0
1
0
0
1
0
2
2
0
2
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
1
0
1
0
1
0
2
0
0
0
0
0
1
0
0
1
0
1
2
0
0
0
0
1
3
0
1
0
0
0
1
1
0
0
0
2
0
0
1
3
0
0
1
2
1
0
0
1
1
2
0
0
1
0
0
0
0
2
0
1
0
2
0
0
1
0
1
2
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
2
1
0
2
0
0
0
0
2
0
1
2
0
2
2
0
0
0
0
0
6
0
0
0
0
0
2
0
0
0
0
1
0
1
2
0
1
0
0
0
0
2
0
0
0
4
0
0
0
1
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
2
0
0
1
2
1
2
2
0
2
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
2
0
0
0
1
1
1
0
2
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
2
1
5
0
1
0
1
0
0
0
1
0
0
6
2
0
0
0
0
0
2
0
2
0
1
0
2
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
2
2
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
3
0
0
1
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
1
0
0
0
2
1
0
0
0
1
0
0
0
0
3
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
1
2
0
0
0
2
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
1
0
0
0
2
0
0
3
0
0
2
1
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
2
1
1
0
1
1
0
0
0
2
0
0
0
0
0
0
2
0
1
2
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
1
2
1
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
2
0
1
0
0
2
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
2
1
0
0
0
1
0
2
0
1
0
2
0
2
0
0
0
2
0
2
1
2
2
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
2
2
0
2
1
0
0
0
0
1
0
0
2
0
0
1
1
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
2
0
1
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
1
0
7
0
2
2
0
0
3
1
0
0
0
0
0
2
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
2
1
2
2
0
0
0
12
0
0
0
0
0
1
1
0
0
2
2
2
2
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
3
0
2
1
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
3
7
0
0
2
2
0
0
0
0
1
0
0
3
0
1
1
0
0
2
0
0
3
0
1
0
0
0
0
0
0
3
1
0
0
0
0
0
3
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
1
0
0
0
2
1
0
2
0
1
1
1
0
0
2
0
0
0
0
0
0
0
3
1
2
0
0
0
2
0
0
0
0
0
0
0
1
1
1
0
3
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
1
0
2
0
2
1
0
0
0
1
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
3
1
1
1
0
0
0
0
3
1
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
1
3
1
0
0
1
1
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
2
1
2
2
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
2
0
2
1
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
1
2
1
0
0
2
0
2
2
2
0
0
1
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
13
0
2
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
1
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
2
2
1
0
0
0
0
1
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
3
0
3
2
0
0
0
1
2
0
2
1
0
2
0
1
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
1
3
0
0
0
0
3
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
2
1
1
2
0
0
0
4
0
0
0
2
1
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
3
0
2
1
0
0
2
1
1
2
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
4
0
0
0
0
0
0
0
0
1
0
1
2
0
0
2
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
4
0
0
0
0
2
0
0
0
0
2
1
0
0
0
2
1
0
0
0
0
0
2
0
0
0
1
0
0
0
2
1
0
0
0
1
0
0
0
0
1
0
0
0
2
2
2
0
1
0
0
1
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
3
0
0
0
2
2
0
1
2
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
5
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
1
0
2
1
0
1
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
1
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
3
2
1
1
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
1
0
1
0
0
0
4
2
0
0
0
2
0
2
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
1
0
2
0
2
0
0
2
0
0
1
0
0
0
1
1
2
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
1
2
1
2
1
0
0
0
2
1
2
0
0
0
1
0
0
0
2
1
0
2
0
0
0
0
1
2
1
0
0
0
1
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
3
4
0
0
0
3
0
0
1
0
0
0
0
0
0
1
0
2
0
1
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
3
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
3
0
0
2
0
0
2
0
0
0
0
0
0
2
2
2
0
1
2
2
0
3
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
1
1
0
0
0
0
0
0
0
1
0
2
6
0
2
0
1
0
1
0
0
0
0
1
1
0
2
1
0
0
2
2
0
2
0
0
0
0
0
2
2
0
0
0
2
0
2
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
3
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
2
0
0
0
0
2
0
4
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
5
0
3
0
4
2
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
2
0
0
1
0
1
0
1
0
2
0
2
0
1
2
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
1
0
0
1
0
2
0
0
2
0
0
0
1
2
0
0
0
0
0
2
1
0
0
0
0
2
0
0
2
2
1
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
2
0
0
9
0
0
0
0
3
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
1
1
2
0
0
0
2
0
0
1
0
0
0
0
2
0
0
5
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
4
1
1
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
2
0
0
0
1
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
2
1
2
0
0
2
1
0
2
2
0
1
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
1
0
0
0
2
3
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
1
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
2
0
2
0
0
0
0
2
0
0
3
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
1
1
0
1
0
0
0
2
0
0
0
0
0
2
2
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
1
1
0
0
0
0
0
2
0
0
0
2
0
1
0
2
0
1
0
1
0
0
1
0
0
2
0
0
1
2
0
0
0
1
0
0
0
2
2
0
0
0
1
0
5
0
0
0
0
2
0
1
0
2
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
2
0
2
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
2
1
2
0
1
0
0
0
0
0
1
0
0
1
0
1
0
2
0
1
0
0
1
0
0
1
0
0
0
0
2
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
1
0
0
1
0
1
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
2
1
0
2
0
0
0
2
0
0
0
1
0
0
0
2
0
2
0
2
0
0
1
0
2
1
3
1
0
0
0
0
0
0
1
0
0
3
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
1
0
0
0
2
0
0
0
0
3
0
0
2
0
1
0
2
2
0
3
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
2
1
2
0
0
0
0
2
0
0
1
0
0
0
1
0
0
2
0
0
1
1
0
0
0
0
0
0
0
1
0
2
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
2
1
1
0
0
1
0
0
3
0
0
1
0
2
0
0
0
1
1
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
1
0
0
2
2
1
0
0
0
0
0
0
0
3
2
2
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
2
3
0
0
0
0
1
1
2
0
0
0
1
0
0
0
0
0
1
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
1
2
1
0
1
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
2
0
1
0
0
0
0
0
1
0
2
0
0
2
0
0
0
1
2
2
2
2
2
0
0
2
1
0
0
1
0
1
0
0
2
0
0
0
0
1
1
2
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
2
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
2
0
3
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
2
1
0
0
0
2
0
1
0
3
0
0
0
1
3
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
1
0
0
1
2
0
2
0
2
0
1
0
0
0
0
2
0
1
0
0
2
1
0
0
2
0
2
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
1
0
1
2
0
0
2
0
0
0
2
0
0
1
5
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
3
0
0
3
1
1
0
3
0
0
0
0
0
0
0
0
1
0
2
2
2
0
0
2
0
0
2
1
0
0
3
0
1
0
1
0
1
0
0
0
0
0
2
3
2
2
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
1
0
2
0
1
0
0
1
0
0
0
3
0
1
0
0
0
0
0
0
3
2
0
0
2
4
0
0
3
0
0
0
2
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
1
6
0
2
0
2
0
2
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
1
0
1
4
1
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
5
0
1
2
0
0
0
0
0
0
3
0
0
1
1
1
0
0
2
0
2
0
0
0
1
0
0
1
0
0
5
1
1
0
0
2
2
0
0
1
0
0
0
1
1
0
0
2
2
0
0
0
0
2
0
0
1
0
0
1
0
0
1
0
0
0
1
0
2
0
1
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
3
2
0
2
0
0
1
2
2
0
0
0
1
0
0
2
0
2
0
0
3
0
0
0
2
2
0
2
0
0
0
0
2
3
0
2
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
4
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
2
0
0
3
0
0
2
1
0
0
3
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
2
0
0
4
0
0
1
0
0
0
2
2
0
0
2
2
1
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
2
2
2
0
0
0
1
0
0
4
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
2
2
0
2
0
0
0
2
0
0
0
0
1
0
1
2
1
0
0
0
0
0
0
1
0
0
3
2
2
0
0
0
0
2
2
0
0
0
0
3
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
1
1
2
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
2
0
0
4
0
1
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
1
1
0
1
0
0
2
4
0
0
0
0
0
0
1
2
3
2
0
0
2
0
0
9
0
0
1
2
0
0
0
0
2
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
1
3
2
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
2
0
0
2
0
3
0
1
1
1
1
0
2
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
5
0
2
0
2
0
1
0
0
1
0
2
0
1
0
1
2
2
0
0
0
0
0
0
0
0
2
2
0
4
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
2
2
1
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
2
0
2
0
0
0
1
0
0
0
4
0
0
1
0
0
2
1
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
2
2
0
0
2
0
0
0
0
0
2
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
1
1
0
2
0
0
0
1
0
0
0
1
0
2
0
2
1
2
0
2
0
0
2
0
2
1
4
1
2
0
0
0
0
2
0
1
0
2
2
0
0
2
0
0
0
0
2
1
0
2
0
0
0
0
1
0
2
0
1
2
0
0
2
0
0
0
0
0
1
1
0
0
0
1
2
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
2
2
4
3
0
0
0
21
0
1
0
0
2
0
2
0
0
0
0
1
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
2
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
1
0
0
0
3
0
1
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
3
0
0
0
1
0
1
1
2
0
4
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
2
0
2
1
0
1
0
0
0
0
0
0
3
0
1
0
0
0
0
2
0
0
0
1
0
2
0
0
0
3
1
0
0
0
1
1
2
0
0
0
0
0
0
0
0
4
0
2
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
3
0
0
1
2
2
1
1
5
0
0
0
0
0
1
2
2
0
2
2
0
2
0
0
0
0
4
0
1
0
0
2
2
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
1
1
3
0
0
0
1
0
2
0
1
0
0
1
0
0
1
1
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
2
1
2
0
0
0
0
0
3
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
1
0
2
0
1
2
0
2
2
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
2
2
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
1
0
2
0
1
0
0
0
0
0
1
1
0
0
2
2
2
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
1
2
2
0
0
0
1
2
2
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
3
0
2
0
0
4
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
2
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
2
1
0
1
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
3
3
0
3
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
1
0
2
1
0
2
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
2
0
0
0
2
0
1
0
1
0
0
0
0
0
2
1
0
1
0
0
0
1
0
0
0
1
0
2
0
0
0
0
2
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
1
2
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
2
1
2
0
0
2
0
0
0
1
1
0
0
0
2
0
0
1
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
1
2
0
0
0
0
0
1
0
0
1
0
0
2
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
7
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
1
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
3
0
0
0
2
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
1
2
2
0
0
0
0
0
0
0
2
0
0
4
2
0
2
0
10
0
1
2
2
0
0
0
3
0
0
0
1
1
0
0
0
0
2
1
2
1
0
1
0
0
1
0
0
0
2
0
2
0
0
1
2
0
0
4
0
0
2
2
6
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
1
2
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
2
1
0
0
2
0
1
0
0
0
1
0
1
0
2
0
0
0
0
0
1
0
2
0
2
6
1
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
1
0
3
0
0
2
1
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
4
0
0
1
0
0
0
1
5
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
7
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
1
1
3
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
3
0
0
0
2
2
0
2
0
0
0
0
0
1
2
0
1
1
1
0
1
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
3
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
2
0
2
0
6
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
1
0
0
0
0
2
0
0
5
0
0
1
1
0
0
0
0
0
2
0
0
0
2
1
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
3
0
0
0
0
1
2
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
2
0
4
0
0
0
1
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
3
0
1
0
0
0
2
0
0
0
0
1
0
1
2
2
2
0
0
0
0
0
2
4
0
0
2
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
2
1
2
0
1
0
0
0
2
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
2
1
2
0
2
0
1
2
0
2
0
1
0
0
2
0
2
0
0
6
0
2
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
1
0
0
0
1
0
2
1
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
1
2
0
0
0
0
2
2
1
4
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
2
0
2
0
0
0
0
0
0
2
1
1
1
0
0
0
2
0
0
0
0
2
0
1
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
1
0
2
2
0
0
0
0
1
1
0
0
2
2
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
1
2
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
3
1
0
0
2
0
0
2
2
1
0
0
0
0
4
0
0
0
2
0
1
0
0
0
2
0
0
0
0
1
0
1
0
0
0
4
0
0
0
2
0
0
1
0
0
2
1
1
0
4
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
2
0
2
2
1
0
0
0
0
0
0
0
0
1
0
0
3
0
0
3
0
1
0
0
0
0
0
2
2
0
0
2
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
1
2
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
3
0
1
2
0
0
2
1
0
0
1
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
1
0
2
0
2
2
0
1
0
0
0
0
0
0
1
0
0
3
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
3
0
1
5
1
0
0
0
0
0
0
0
3
0
0
1
2
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
2
2
0
0
0
2
2
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
1
2
0
0
0
0
0
1
2
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
3
2
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
2
2
2
0
0
0
0
2
0
0
0
2
0
1
0
1
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
2
0
1
1
0
1
0
0
0
2
0
0
2
0
0
0
4
1
0
2
0
0
2
1
0
0
0
0
0
2
0
0
3
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
1
1
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
3
1
1
2
0
0
2
2
0
0
2
2
1
0
0
1
0
0
0
2
0
0
1
1
1
0
0
0
0
1
1
0
2
0
0
2
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
1
1
0
2
2
0
0
0
1
0
1
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
2
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
2
0
0
1
0
0
1
2
0
1
2
0
0
0
0
5
2
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
4
2
1
0
0
2
0
0
1
0
2
0
0
1
0
0
0
2
0
0
0
0
0
2
2
2
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
3
0
0
0
1
0
1
0
0
0
0
2
0
0
0
1
1
2
1
0
0
1
1
0
1
2
0
1
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
2
0
0
0
0
2
0
2
1
0
1
0
0
0
1
1
0
0
1
0
1
0
0
0
2
0
2
2
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
2
0
4
1
2
0
0
0
0
0
6
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
2
0
0
1
0
1
0
0
2
0
0
0
1
0
3
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
1
0
1
2
0
0
1
0
0
0
0
0
0
1
2
0
0
1
3
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
7
1
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
2
0
0
3
2
0
2
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
3
0
2
0
0
2
0
0
3
2
0
2
0
2
0
0
2
0
0
0
0
1
2
0
4
0
2
0
3
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
6
0
0
0
2
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
2
2
4
1
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
1
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
3
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
4
0
4
0
0
0
0
0
2
0
2
1
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
2
2
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
1
2
2
2
0
0
1
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
1
2
0
0
1
0
0
0
0
0
0
1
2
0
1
2
0
0
0
1
1
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
2
1
0
2
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
1
1
0
1
0
0
1
0
2
2
0
1
0
0
0
3
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
1
0
2
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
2
0
0
0
1
1
0
0
4
1
2
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
1
1
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
3
0
0
2
0
0
0
1
2
1
0
0
0
0
0
0
0
0
2
0
0
1
5
0
0
0
1
2
0
2
0
0
0
1
0
2
0
3
0
0
1
0
0
0
0
0
1
0
0
3
0
2
0
0
0
1
0
0
0
0
0
1
0
2
2
0
0
1
0
0
0
0
0
0
2
3
2
4
2
0
0
2
1
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
2
1
0
1
0
0
0
0
0
1
1
2
0
0
0
1
0
0
1
0
0
2
0
0
2
2
2
0
5
0
0
0
0
0
0
2
0
1
0
1
0
1
0
0
0
2
1
0
0
1
0
0
2
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
4
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
1
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
2
3
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
2
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
2
0
0
2
0
0
1
0
0
1
0
0
0
2
2
1
3
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
1
0
2
0
2
1
2
0
1
0
0
0
0
3
1
2
0
0
1
0
1
0
0
0
1
0
2
0
0
0
0
0
2
2
0
2
1
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
2
2
0
0
0
2
0
0
0
0
0
2
1
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
2
1
1
1
0
0
1
1
0
2
1
0
0
0
0
0
0
2
1
0
0
2
0
0
0
1
0
1
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
5
2
0
0
0
0
0
1
0
0
1
0
0
0
0
1
3
1
0
2
0
2
0
0
0
2
1
0
2
0
0
0
2
2
0
2
0
2
0
0
1
2
0
1
0
0
0
0
0
1
0
1
0
0
2
0
1
0
0
0
0
0
2
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
4
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
2
1
0
0
2
1
2
0
2
0
2
0
0
0
1
0
0
0
0
2
4
0
0
0
0
0
0
1
0
0
1
0
4
1
0
0
1
1
2
2
0
0
0
2
0
0
3
0
0
0
0
0
1
0
0
3
0
1
1
0
0
0
0
0
2
0
0
0
0
3
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
1
0
2
0
2
0
2
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
2
1
2
0
0
0
0
0
0
0
1
0
0
0
2
1
0
2
0
1
2
0
0
0
1
0
0
0
2
1
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
1
1
1
0
2
1
1
0
0
1
2
0
2
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
2
1
0
1
0
0
0
0
1
1
2
0
1
2
0
2
0
2
1
0
0
2
0
1
1
0
0
0
1
1
1
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
1
0
2
0
1
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
2
3
0
0
0
0
0
1
1
0
1
1
2
2
0
0
0
1
0
0
0
0
0
3
0
1
0
0
0
1
0
0
0
0
0
1
3
0
0
1
0
0
0
2
0
0
2
0
0
2
0
0
1
0
0
0
1
1
0
0
0
1
0
0
3
0
4
2
0
0
0
0
0
2
2
0
0
0
0
1
1
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
3
2
1
0
0
0
0
0
0
1
4
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
1
0
0
1
4
1
0
1
2
5
0
0
0
1
7
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
2
0
0
1
0
2
0
1
0
0
0
0
3
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
1
1
0
0
1
0
0
2
0
0
0
1
0
1
2
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
1
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
2
2
0
0
2
0
0
0
3
0
2
0
0
0
0
0
0
2
1
2
0
0
0
0
2
0
2
0
0
2
0
0
0
1
2
0
2
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
2
0
0
1
2
4
0
2
0
0
4
2
1
0
0
0
1
1
3
0
1
1
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
2
0
0
0
2
1
2
0
0
0
1
2
0
2
2
1
0
0
0
3
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
1
2
0
0
0
1
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
6
0
2
0
0
0
0
0
0
1
0
2
1
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
1
0
2
0
0
1
0
1
0
0
0
0
0
1
0
1
2
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
2
1
0
0
0
1
1
0
2
0
1
1
0
0
0
2
0
0
0
1
0
0
2
0
0
1
0
2
0
0
2
0
2
2
4
0
0
0
1
2
2
2
0
0
0
0
0
1
0
0
0
1
2
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
2
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
2
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
1
5
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
2
2
2
0
0
0
1
0
0
0
0
2
2
2
1
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
1
0
1
2
0
0
2
0
1
0
0
0
0
1
0
2
0
2
1
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
3
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
2
0
2
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
1
0
0
0
1
2
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
1
1
1
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
3
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
7
0
2
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
2
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
1
0
10
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
4
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
2
1
0
0
0
0
2
2
1
0
2
0
3
0
2
1
0
3
2
2
0
0
0
0
0
0
1
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
5
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
2
1
0
0
0
2
1
0
2
0
0
2
0
1
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
3
2
0
0
0
1
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
1
0
1
2
2
2
0
1
0
3
3
0
0
2
2
0
1
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
3
0
0
0
2
0
0
1
0
2
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
7
0
0
0
0
0
2
0
0
0
0
3
2
2
0
0
0
2
0
0
0
1
0
0
0
1
0
0
4
0
0
2
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
2
2
1
0
1
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
2
0
2
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
1
2
0
0
0
1
2
0
0
0
0
0
0
2
2
0
0
0
1
2
0
0
0
0
0
1
0
0
0
2
1
0
0
1
1
0
0
0
0
0
0
1
3
0
0
0
0
2
1
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
2
1
2
0
0
1
0
0
1
0
2
0
0
3
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
2
0
0
0
2
2
2
1
1
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
2
0
0
0
1
1
3
2
0
0
2
2
2
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
3
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
4
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
1
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
3
3
1
0
0
1
0
2
0
2
0
0
0
4
0
0
0
0
0
0
2
2
0
1
1
0
0
2
0
0
0
0
0
1
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
2
0
0
2
0
0
1
2
0
0
1
0
0
0
0
1
0
0
0
2
0
0
2
3
0
0
0
0
2
2
0
2
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
1
1
2
0
0
0
1
0
1
0
0
0
0
2
0
0
0
3
0
0
0
1
0
1
0
0
2
0
0
0
0
0
2
1
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
4
0
2
4
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
2
0
0
0
1
0
3
0
1
2
0
0
0
1
0
0
1
0
1
1
0
0
2
1
0
0
0
0
0
0
2
0
1
0
3
0
2
0
1
2
0
0
0
0
0
4
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
2
1
0
2
5
1
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
2
0
0
0
3
1
0
0
0
1
0
1
0
0
0
2
0
1
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
2
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
2
1
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
2
1
4
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
3
1
0
2
0
0
0
0
0
0
2
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
1
0
0
1
1
0
2
0
0
0
2
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
2
0
3
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
3
0
2
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
2
0
1
1
0
2
2
0
0
3
0
0
3
0
1
0
1
0
2
0
1
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
1
0
0
0
0
1
0
0
0
2
0
0
2
2
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
1
0
2
0
1
1
2
0
0
3
0
0
0
1
3
0
0
0
0
0
0
0
0
2
0
0
3
0
0
2
2
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
1
2
0
0
3
1
0
0
0
1
0
0
1
0
1
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
2
0
0
2
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
2
3
0
1
0
0
0
0
1
0
0
1
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
3
0
2
4
0
0
0
0
2
0
5
0
0
3
0
0
3
0
0
0
0
0
2
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
2
1
2
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
2
2
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
2
0
2
0
1
0
0
2
0
0
1
0
1
0
2
0
0
1
0
0
1
2
0
0
1
0
0
0
0
2
0
0
0
0
1
2
1
4
2
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
1
0
0
0
0
2
0
1
2
0
0
0
0
2
0
0
0
0
2
0
0
1
1
0
2
1
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
1
2
0
0
2
3
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
1
0
0
0
1
1
4
0
0
0
0
0
1
2
1
1
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
1
0
0
0
3
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
2
1
2
0
0
0
2
2
1
0
0
0
0
0
2
0
0
2
2
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
2
0
0
2
0
1
0
0
1
1
0
1
1
0
2
3
0
2
0
1
0
2
0
0
0
0
1
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
2
0
0
2
0
0
0
0
1
2
0
0
0
0
2
2
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
1
5
1
0
0
0
1
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
2
0
2
1
0
1
2
0
0
0
0
0
2
0
1
0
0
3
1
0
1
0
0
2
0
0
1
2
1
0
2
0
1
1
0
0
0
2
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
1
0
0
0
1
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
3
0
0
0
0
0
2
0
2
1
0
0
4
1
0
0
11
2
0
2
0
0
0
1
0
2
1
0
1
0
0
0
1
0
0
1
0
0
0
0
1
2
0
1
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
2
1
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
1
0
4
0
0
2
0
2
0
0
0
0
2
0
11
0
0
0
0
0
2
1
0
1
1
0
0
0
1
1
0
1
0
4
1
0
1
0
2
1
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
3
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
3
1
0
2
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
1
1
0
0
2
3
1
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
3
0
2
1
2
0
0
0
3
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
1
2
0
0
0
0
0
0
2
0
1
1
1
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
1
0
2
2
0
1
0
0
3
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
5
0
0
0
1
0
0
1
1
0
0
0
14
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
2
2
1
2
1
1
0
2
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
3
1
0
2
0
2
1
0
2
0
0
0
1
0
0
0
0
0
0
0
1
2
1
1
1
1
0
2
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
6
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
1
0
0
0
0
0
1
0
0
0
0
2
4
2
0
1
0
2
0
1
0
0
1
3
1
0
0
2
0
0
0
0
0
4
2
2
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
3
2
0
0
1
2
1
0
0
0
0
1
0
2
0
0
0
0
4
0
0
5
0
0
0
0
0
1
1
0
0
0
0
1
1
2
1
0
0
0
0
0
2
0
2
0
2
2
0
0
0
0
0
0
1
0
0
1
0
0
1
2
0
1
0
0
0
1
0
2
1
2
3
0
0
0
0
0
0
1
0
0
2
2
0
0
1
0
0
1
2
0
1
0
2
0
2
1
0
2
1
0
0
1
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
2
0
0
0
2
1
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
4
6
2
0
1
0
1
0
0
0
3
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
3
2
0
1
0
0
0
1
0
0
0
2
3
4
0
1
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
2
0
2
0
3
0
0
0
1
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
2
1
0
1
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
1
0
0
1
0
0
1
1
0
0
1
0
1
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
1
0
3
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
2
2
0
0
1
1
1
0
0
0
0
1
1
0
0
2
0
0
0
1
1
0
0
2
1
0
0
1
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
6
0
1
2
0
0
1
0
0
4
1
2
0
0
2
0
0
0
0
0
0
2
0
0
1
1
0
3
2
0
0
0
0
2
0
0
0
2
0
1
1
1
0
0
5
1
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
2
0
1
0
0
0
0
1
0
0
1
2
0
1
0
2
0
0
4
0
0
3
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
2
0
0
0
0
0
2
2
2
0
0
0
2
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
1
2
3
0
0
1
0
0
0
1
0
0
0
0
0
3
2
0
0
2
0
0
1
0
2
0
1
0
0
0
1
0
0
0
0
0
0
1
0
2
1
0
0
2
2
0
0
1
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
9
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
2
2
0
2
1
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
2
0
0
0
1
0
0
9
3
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
2
0
2
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
1
2
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
1
2
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
2
4
1
7
1
2
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
3
0
0
2
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
2
1
0
1
0
0
0
0
0
2
2
0
0
1
0
0
3
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
1
0
2
2
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
0
4
0
1
0
0
0
0
2
2
0
1
0
0
1
4
0
1
2
0
0
2
2
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
1
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
2
0
0
2
2
2
1
0
0
4
0
0
2
0
0
0
0
0
0
0
2
1
1
1
0
0
0
4
0
2
1
1
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
3
0
1
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
2
0
0
0
2
0
0
1
0
0
0
1
0
2
0
0
0
2
2
0
0
0
0
3
0
0
0
1
2
1
0
0
0
2
6
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
1
0
0
0
2
1
0
0
1
3
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
1
0
1
0
4
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
1
0
3
0
2
0
0
2
0
0
2
0
0
0
1
0
0
1
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
1
2
0
0
0
1
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
1
2
0
0
1
1
0
0
1
0
0
0
3
0
0
2
0
0
0
0
5
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
2
0
2
0
0
2
0
1
0
2
0
2
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
2
0
2
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
2
2
0
2
0
0
0
0
1
0
0
1
0
0
0
1
0
1
2
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
2
1
0
0
2
0
0
1
0
0
0
2
2
0
0
0
1
0
0
1
2
0
1
0
0
0
0
0
1
0
3
3
1
0
0
1
3
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
1
0
1
4
2
0
2
0
2
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
8
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
2
2
2
0
0
1
0
0
1
0
2
0
3
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
3
0
2
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
1
0
3
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
1
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
1
0
0
0
0
3
1
0
0
0
0
0
2
2
2
1
0
0
2
0
1
0
1
0
3
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
2
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
5
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
2
1
2
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
1
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
1
0
1
0
0
0
0
0
1
2
0
0
0
0
0
1
3
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
2
1
0
0
1
0
2
0
0
0
0
0
1
0
1
0
0
0
0
2
0
1
0
0
3
0
0
0
0
2
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
2
1
0
2
0
0
0
0
0
2
2
1
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
2
1
1
0
2
2
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
1
0
2
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
2
0
0
0
1
0
1
0
0
2
1
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
2
2
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
1
2
0
1
0
2
0
0
0
0
0
1
0
0
2
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
5
1
1
0
2
0
1
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
3
0
1
0
0
0
0
0
4
1
0
0
0
0
0
1
1
2
0
0
0
0
1
1
0
0
0
0
2
1
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
2
2
2
0
0
0
0
0
2
0
4
0
0
2
0
2
1
0
1
2
0
1
2
1
0
0
0
0
0
2
0
2
0
0
1
0
1
1
0
1
0
0
1
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
1
0
2
3
0
0
0
0
2
2
0
0
1
0
0
0
2
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
1
2
0
1
0
3
0
1
0
1
0
0
0
0
3
0
2
2
0
3
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
4
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
2
2
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
2
2
2
0
0
0
0
0
0
0
4
0
2
0
0
0
2
0
1
1
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
2
0
0
1
0
0
2
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
2
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
4
1
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
1
1
0
0
0
0
2
0
0
1
2
0
0
4
2
0
2
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
2
0
2
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
1
1
3
0
0
1
2
0
2
2
0
0
0
1
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
1
0
0
2
1
1
0
0
1
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
2
0
1
0
0
1
0
0
1
0
2
0
0
0
0
2
0
0
0
6
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
1
0
0
1
0
0
2
0
0
1
0
2
0
2
1
0
1
0
0
0
2
1
3
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
2
0
1
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
4
0
0
2
1
0
1
0
0
0
0
0
2
0
0
2
1
2
0
0
0
0
2
0
1
0
0
0
1
0
0
2
1
0
0
1
0
1
0
3
0
2
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
2
0
2
0
1
2
0
0
0
1
0
2
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
3
0
0
0
2
1
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
3
1
0
1
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
2
1
1
3
0
0
0
0
0
1
1
1
0
0
2
5
5
0
3
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
1
2
0
2
2
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
3
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
1
2
0
0
0
1
1
0
0
0
1
2
0
0
0
0
1
0
2
1
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
2
1
2
0
0
7
0
1
0
0
4
0
2
0
0
1
1
0
1
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
3
0
2
0
0
0
0
0
0
2
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
1
2
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
4
2
2
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
1
2
0
0
1
0
2
0
0
2
0
1
2
1
0
1
2
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
4
0
0
0
2
2
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
1
0
0
0
0
0
1
1
3
0
4
0
1
0
0
1
2
1
0
0
0
0
0
0
2
0
2
2
0
0
0
2
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
1
0
2
0
3
0
0
0
1
0
2
0
0
0
0
0
0
0
0
3
0
1
0
2
1
2
0
0
2
3
1
0
1
2
1
0
0
2
0
0
0
0
2
0
2
0
0
0
2
0
2
0
0
0
0
4
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
2
0
1
1
0
0
0
1
1
0
0
0
2
0
1
1
0
2
0
0
2
0
0
1
0
2
0
0
0
0
0
2
0
0
0
2
0
0
2
0
2
2
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
1
0
0
2
0
0
0
0
0
2
0
2
1
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
2
0
0
1
0
0
0
1
0
1
0
0
2
0
2
1
2
3
1
1
4
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
5
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
1
0
0
0
3
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
5
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
1
0
0
0
0
1
2
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
1
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
2
1
0
0
0
0
2
0
0
0
1
0
0
1
2
1
2
0
0
0
0
1
3
0
1
0
1
2
0
2
0
1
0
3
0
0
2
0
0
2
0
2
0
5
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
1
2
0
0
0
0
2
0
0
0
1
0
0
1
1
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
2
0
0
2
0
0
0
0
0
3
0
1
1
0
2
2
2
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
2
0
2
0
0
3
2
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
3
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
3
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
2
2
0
7
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
1
0
0
0
0
4
2
2
0
0
0
0
0
0
3
1
2
2
0
0
0
0
1
0
0
0
0
0
0
1
2
0
1
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
1
2
0
2
0
0
2
0
1
3
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
2
2
2
0
0
2
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
6
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
1
0
0
2
1
0
0
2
0
0
0
0
1
0
0
2
5
1
0
0
0
0
2
1
0
0
0
0
1
0
2
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
2
4
0
1
0
2
2
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
2
0
0
1
1
2
0
0
0
0
0
3
1
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
1
2
0
1
1
0
2
2
1
0
0
1
0
3
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
4
0
0
0
0
1
0
0
1
0
0
1
0
0
1
1
2
0
1
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
2
0
0
0
2
1
0
1
3
0
0
2
0
3
0
0
2
0
0
0
0
0
0
0
0
2
0
1
1
1
0
0
0
0
2
1
1
0
0
0
4
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
3
2
2
2
0
0
0
0
0
1
0
0
1
0
0
2
1
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
1
0
0
2
0
2
0
0
0
1
0
0
0
0
1
1
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
1
2
0
2
0
0
0
0
0
0
2
0
1
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
2
0
2
0
0
7
0
2
2
0
0
3
0
1
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
2
1
0
0
2
0
0
0
0
0
2
2
1
2
4
0
0
0
0
0
0
2
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
3
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
7
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
2
1
0
0
0
0
0
0
0
0
1
3
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
2
2
0
0
2
0
0
0
2
0
2
0
3
0
0
0
0
1
0
2
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
2
0
2
0
1
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
3
2
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
2
1
2
0
0
2
0
0
0
1
0
1
0
0
3
0
0
0
1
0
0
0
0
2
3
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
2
3
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
1
0
0
2
0
2
0
0
1
0
0
1
2
2
0
0
0
3
1
0
0
1
0
0
5
0
0
0
2
0
0
2
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
2
1
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
2
0
4
1
0
0
0
0
0
0
2
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
2
0
1
1
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
2
0
0
0
1
2
0
0
1
0
0
0
0
0
0
1
0
0
0
4
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
3
0
3
0
0
0
0
0
2
2
0
1
2
0
0
0
0
2
2
0
0
0
1
0
0
0
0
1
1
3
0
0
0
0
0
2
0
0
0
0
1
0
0
1
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
3
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
1
1
0
0
2
0
3
0
0
0
1
0
2
0
0
0
4
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
3
0
0
0
0
0
0
0
1
2
0
0
1
1
0
0
0
0
0
0
1
0
1
0
2
0
2
1
2
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
5
0
0
0
0
0
1
0
3
0
0
0
1
0
0
0
2
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
1
0
2
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
5
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
2
0
0
2
0
0
3
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
5
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
1
6
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
2
1
2
0
1
1
1
0
0
0
1
0
0
0
0
2
0
0
2
1
1
0
1
0
1
0
0
0
0
0
0
0
0
1
2
2
0
0
1
1
0
0
2
0
0
0
0
2
1
0
0
0
0
0
1
0
2
0
0
1
2
2
0
2
0
2
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
2
1
0
2
0
0
1
0
0
0
0
0
1
1
0
0
0
0
4
0
1
0
1
0
0
1
0
2
1
0
0
2
8
1
0
0
0
0
0
0
0
3
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
1
0
2
0
0
0
2
0
0
0
0
0
0
2
1
0
0
2
1
1
3
2
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
2
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
1
2
0
2
2
1
0
0
2
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
3
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
2
1
2
0
0
0
0
2
1
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
14
0
1
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
2
0
0
0
1
1
0
0
0
0
2
1
0
0
0
0
1
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
3
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
1
2
5
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
6
0
0
1
2
0
0
0
1
0
0
0
0
0
0
1
3
0
0
0
0
0
1
2
2
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
1
0
0
1
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
2
2
0
0
0
0
0
1
0
0
1
2
1
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
3
0
2
0
6
0
0
0
2
2
0
5
0
0
1
0
3
0
2
0
0
2
1
1
0
0
0
0
2
0
0
0
0
0
0
1
3
0
2
3
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
3
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
2
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
3
0
5
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
5
1
0
0
0
0
2
0
0
0
0
1
0
2
0
0
1
0
2
1
0
0
1
0
0
0
0
0
0
2
1
2
0
0
0
0
1
1
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
1
1
1
0
2
0
0
0
0
0
2
0
0
1
0
0
2
0
1
0
0
0
0
2
0
2
0
2
0
0
0
1
1
0
0
0
0
2
1
0
0
0
0
0
0
1
0
2
2
0
0
0
2
0
3
0
0
0
2
2
0
0
0
0
0
4
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
4
3
0
3
0
1
0
0
0
2
1
0
0
0
0
1
2
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
2
0
3
1
0
0
0
0
6
1
0
0
0
1
0
0
0
1
2
0
0
0
0
0
1
4
2
0
1
0
2
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
2
0
0
1
0
0
2
1
2
0
3
1
1
0
0
0
0
2
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
2
2
0
0
0
1
1
2
0
0
0
0
2
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
1
2
0
0
2
1
2
0
0
1
0
0
1
1
0
0
0
1
0
0
2
0
0
1
0
0
0
1
0
0
2
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
2
1
2
0
0
0
1
2
0
2
0
2
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
1
1
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
2
2
0
0
0
0
1
0
0
0
0
0
1
0
0
4
0
0
2
0
0
0
0
0
0
1
0
6
1
0
0
0
1
1
1
2
0
0
0
0
0
0
0
1
0
0
1
1
3
4
0
1
0
1
1
1
0
0
8
0
0
0
2
0
0
2
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
3
0
0
0
1
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
14
0
0
0
0
0
2
0
5
0
0
1
2
0
1
1
1
0
2
2
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
1
0
1
0
0
2
1
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
2
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
3
0
1
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
2
1
1
0
1
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
2
0
8
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
3
1
0
0
0
2
0
6
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
1
2
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
1
2
1
0
0
0
2
0
0
2
2
0
1
0
0
2
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
3
0
0
0
1
0
0
1
0
1
0
1
2
0
1
0
0
2
0
0
0
0
2
2
0
0
1
0
0
0
0
0
1
1
0
1
0
0
2
0
0
0
0
1
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
1
0
1
0
0
0
0
1
0
2
0
1
2
1
2
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
1
0
2
0
2
0
0
2
5
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
4
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
1
0
0
0
1
0
1
0
1
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
1
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
1
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
8
0
0
0
0
0
2
0
0
2
1
0
0
0
1
0
1
0
0
0
2
1
2
0
0
0
2
0
0
0
0
0
0
0
1
2
0
2
0
0
2
0
0
0
2
0
0
0
3
0
1
0
2
0
0
2
1
1
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
2
0
2
2
2
2
3
1
0
0
0
2
0
0
2
1
0
0
0
1
0
0
0
0
0
0
2
0
2
0
2
0
0
0
1
2
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
4
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
11
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
10
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
1
3
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
1
0
1
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
2
1
0
0
0
2
0
2
1
1
1
0
0
0
1
0
3
0
0
0
0
0
0
1
3
1
1
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
2
1
0
0
0
0
0
4
1
0
0
0
0
4
0
0
0
1
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
2
0
0
3
2
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
3
3
0
0
0
0
1
2
0
1
0
0
1
0
0
0
2
2
0
1
2
0
0
0
0
0
0
0
0
1
0
2
0
2
0
1
0
0
1
0
1
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
2
1
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
2
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
1
1
0
1
0
0
1
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
2
0
0
1
0
2
0
0
1
0
2
0
0
1
0
2
0
0
2
0
1
0
2
0
0
2
0
0
0
0
1
2
0
0
1
0
4
0
0
0
0
0
0
1
0
1
0
1
3
2
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
2
0
0
0
0
6
1
0
0
0
2
0
0
0
0
1
2
0
2
1
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
3
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
1
0
0
2
0
0
0
1
1
0
0
1
2
2
0
0
0
0
0
0
2
0
1
0
1
0
2
0
0
0
0
1
0
0
0
1
0
2
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
1
0
0
0
0
0
0
1
0
2
0
0
2
0
0
2
0
0
0
0
1
0
0
2
3
1
1
0
0
0
0
2
1
0
0
2
0
1
0
3
0
0
0
0
0
1
2
0
2
0
0
1
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
1
2
0
0
0
1
0
0
3
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
1
0
0
0
0
1
4
2
0
1
0
0
0
0
0
0
0
2
0
0
2
4
1
0
3
0
2
0
2
0
0
0
2
0
0
0
0
2
0
2
2
0
0
0
0
0
2
4
0
0
0
0
2
0
0
2
0
0
2
0
0
2
0
2
0
1
1
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
1
2
0
2
0
1
0
2
6
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
2
0
2
1
0
0
1
1
0
0
2
0
4
1
4
2
0
0
1
0
0
0
2
4
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
2
0
0
0
0
1
0
0
1
1
0
0
2
0
3
2
0
0
0
0
0
0
4
0
0
0
2
1
0
0
0
1
1
0
0
1
0
1
2
0
0
0
0
1
0
5
1
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
1
2
0
0
1
0
2
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
1
2
0
1
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
4
1
0
0
0
2
2
2
1
0
0
0
0
0
1
0
0
2
0
3
0
0
1
0
0
0
1
0
0
0
1
0
2
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
3
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
3
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
1
1
1
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
2
1
0
1
0
0
1
2
1
0
0
0
2
0
1
0
0
0
0
2
1
1
2
1
2
0
1
2
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
1
2
1
0
1
0
0
0
0
0
0
0
1
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
3
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
2
1
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
2
1
2
2
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
3
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
3
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
1
2
0
0
2
0
0
1
0
1
0
1
2
0
0
1
0
0
1
2
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
2
1
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
2
0
0
2
2
2
0
1
0
2
0
0
4
0
0
0
0
2
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
3
0
0
0
0
2
0
2
0
1
0
0
0
0
1
1
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
3
2
0
3
2
0
1
2
0
0
2
2
0
0
1
0
0
0
1
0
1
2
2
0
0
0
0
0
2
0
0
2
0
2
0
2
1
0
1
0
0
0
1
1
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
1
3
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
2
0
0
0
2
1
2
0
2
0
0
0
0
1
1
0
1
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
2
0
0
1
1
1
0
2
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
2
2
0
0
0
0
0
0
0
0
0
2
1
2
2
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
2
0
1
2
0
0
0
0
0
0
0
1
0
2
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
1
0
1
0
3
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
3
0
0
0
1
0
0
2
0
0
1
1
0
2
0
0
1
2
0
0
0
0
0
0
3
1
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
2
0
1
1
4
0
0
0
2
0
2
0
2
0
0
0
2
0
2
0
1
1
0
2
1
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
2
0
1
0
1
0
2
0
2
0
0
2
0
0
0
2
0
2
0
0
1
1
3
1
0
0
2
0
2
0
0
2
2
0
1
0
0
2
1
0
0
0
0
0
1
1
2
0
0
1
2
1
0
0
0
0
0
0
0
0
1
0
0
0
2
3
0
1
2
1
2
2
0
0
2
1
0
0
0
3
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
1
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
1
0
1
2
0
0
1
0
2
0
0
0
1
0
2
0
0
0
0
0
1
0
5
0
1
0
2
1
0
0
1
1
2
0
1
0
2
1
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
2
3
0
0
1
2
4
0
0
0
2
0
1
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
3
0
0
0
3
0
0
0
0
1
0
0
2
0
0
1
0
2
0
2
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
1
0
0
0
3
0
0
0
2
0
0
0
2
2
0
0
1
2
0
2
2
0
0
0
1
0
2
0
2
0
2
0
0
0
0
2
0
3
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
1
1
2
0
0
0
0
0
0
0
1
0
1
2
3
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
1
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
1
1
1
0
1
1
0
0
0
2
0
0
2
0
4
3
0
0
1
1
0
2
2
0
2
0
0
0
0
2
0
0
1
0
2
0
0
1
0
0
0
0
1
0
0
0
0
2
2
0
0
3
0
0
5
1
1
0
0
0
0
5
0
0
0
0
0
2
1
3
2
0
2
0
0
0
3
0
0
0
1
2
0
2
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
4
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
2
0
1
2
3
3
0
0
0
2
0
0
3
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
1
0
0
0
0
2
0
0
0
1
0
0
0
2
0
3
0
0
2
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
2
0
2
0
2
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
2
2
1
0
0
0
1
0
0
0
2
0
0
0
0
3
0
0
0
1
0
2
0
0
0
3
1
1
0
0
0
0
0
0
2
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
2
0
2
0
2
0
0
1
0
0
0
0
0
2
1
0
0
1
0
0
1
0
0
0
0
0
2
1
2
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
2
3
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
1
1
2
3
0
0
1
0
0
0
1
3
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
2
2
0
0
2
0
2
0
0
0
0
0
0
1
1
0
0
0
2
2
0
0
0
0
0
2
0
2
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
1
4
0
0
0
1
0
4
0
0
2
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
1
0
1
1
0
1
1
1
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
3
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
2
0
1
0
3
0
4
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
2
1
1
0
2
0
0
0
0
0
2
0
2
0
0
0
3
2
0
0
0
0
0
2
1
0
0
0
0
2
0
0
1
1
0
3
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
2
1
2
0
0
0
1
0
3
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
2
0
0
0
0
0
2
1
2
0
0
0
0
0
0
2
0
0
0
3
0
0
2
1
1
0
0
2
0
2
0
1
3
0
1
0
0
2
0
2
0
2
0
0
0
2
1
0
1
0
0
0
2
1
0
0
1
1
0
0
0
0
0
2
0
0
0
0
1
2
0
1
2
0
2
0
0
0
2
0
1
0
0
0
0
2
1
0
0
0
1
0
0
1
2
2
2
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
1
1
0
1
2
0
0
0
1
0
2
0
0
1
0
0
0
2
0
1
0
0
0
0
1
0
2
2
0
2
0
2
0
0
0
0
1
0
2
0
0
0
2
0
0
0
1
0
4
0
1
1
0
1
2
0
1
0
0
1
0
0
0
0
2
2
0
0
0
0
2
9
0
0
0
1
0
2
0
0
0
2
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
1
0
0
2
0
0
0
1
0
3
1
0
1
0
1
0
0
0
1
2
1
0
2
0
0
0
0
1
1
1
1
0
2
0
0
0
0
2
2
2
1
0
0
0
0
2
0
1
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
2
1
2
0
0
2
0
0
0
0
0
0
0
0
2
0
2
2
0
0
2
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
1
0
0
0
0
0
2
0
0
0
0
2
1
4
0
0
0
2
0
2
1
0
0
0
0
2
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
3
0
0
1
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
5
0
0
1
0
0
0
0
0
1
2
1
0
0
0
5
0
0
0
1
2
0
0
1
0
0
0
0
0
2
1
1
0
2
0
0
0
0
0
0
1
2
0
1
1
3
2
0
1
0
0
0
0
0
0
0
1
0
0
3
0
0
2
1
0
0
0
0
2
2
0
0
0
0
0
0
1
5
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
1
2
0
0
0
0
1
2
1
0
0
0
1
0
1
0
2
2
0
2
0
0
0
0
0
0
0
0
1
2
2
0
0
4
3
5
0
1
0
2
0
0
0
2
0
0
0
1
0
0
0
2
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
2
0
0
0
0
0
1
0
0
0
0
0
2
2
0
1
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
1
4
0
0
0
0
0
0
1
0
0
2
0
4
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
3
1
2
0
0
2
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
1
2
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
2
1
0
1
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
3
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
2
1
0
0
0
2
3
0
1
1
0
2
0
0
0
0
0
0
0
1
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
2
0
2
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
1
2
0
0
0
0
1
2
2
1
0
0
0
0
0
0
0
2
0
1
1
0
0
5
0
1
0
0
1
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
2
0
1
0
0
1
0
0
2
0
1
0
1
1
0
0
0
0
0
2
2
0
3
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
4
2
1
0
0
0
0
0
0
0
1
0
11
0
2
0
0
0
0
0
0
0
2
0
4
0
0
0
0
2
3
0
2
0
2
0
0
0
2
0
0
0
3
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
4
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
2
4
0
2
3
0
0
0
2
0
0
0
2
0
1
0
0
0
4
2
0
0
1
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
4
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
11
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
6
1
0
1
0
2
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
4
0
0
0
0
0
1
0
1
2
0
0
0
2
0
2
0
2
0
2
0
1
0
0
2
0
0
0
0
0
2
0
1
0
1
2
0
3
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
3
0
1
0
3
0
2
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
1
0
3
0
1
0
2
0
0
2
2
0
0
2
0
1
0
1
2
1
1
2
2
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
1
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
2
1
0
2
0
0
0
2
1
0
0
0
0
0
1
2
0
0
2
0
0
0
2
1
0
2
0
2
1
0
0
2
0
0
2
0
0
0
0
2
0
2
2
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
2
1
4
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
3
0
0
0
2
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
4
0
0
0
1
2
0
2
0
2
0
0
0
0
1
2
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
3
2
0
0
0
1
0
0
0
0
0
1
0
0
2
1
0
0
1
0
1
0
1
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
1
3
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
2
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
2
1
0
2
0
2
1
1
1
0
0
0
2
0
0
1
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
2
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
2
0
2
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
1
0
0
1
1
0
0
0
0
0
1
0
0
1
1
0
3
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
3
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
1
4
0
2
2
0
1
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
1
0
2
0
0
0
2
0
0
0
2
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
1
0
2
1
0
0
0
2
0
1
0
1
0
0
0
0
0
0
1
0
2
2
0
0
2
2
0
0
3
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
2
3
0
1
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
2
1
0
0
3
0
0
0
0
0
0
1
2
0
0
1
1
1
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
2
0
1
1
0
0
0
2
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
4
3
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
2
2
0
0
1
0
0
0
0
2
1
0
0
1
0
0
0
0
0
1
0
0
0
2
1
0
0
0
2
0
0
0
0
2
1
2
1
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
1
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
3
0
1
2
0
0
2
0
2
0
0
0
0
0
0
0
0
2
5
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
3
0
2
2
0
0
0
0
2
1
0
0
2
0
0
0
3
1
0
0
0
2
8
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
1
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
2
1
2
0
0
0
1
0
1
0
2
0
1
1
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
2
2
0
0
2
1
0
0
0
0
2
0
1
2
2
0
0
0
0
1
2
0
0
0
2
2
0
0
0
0
0
0
2
0
1
2
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
2
1
0
0
0
0
0
0
3
0
0
0
1
0
2
0
2
1
0
2
0
0
0
0
0
2
0
0
2
2
1
0
2
0
1
2
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
2
0
0
0
2
1
0
2
0
0
2
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
2
1
1
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
1
0
1
0
1
2
0
2
1
1
1
0
1
1
0
0
1
0
2
0
0
0
3
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
1
0
1
0
0
0
1
2
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
1
0
0
0
0
2
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
3
0
1
0
0
1
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
5
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
1
1
0
0
0
1
1
0
0
2
0
0
3
0
0
0
1
0
1
1
0
0
1
0
1
0
2
0
0
0
0
1
2
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
9
1
0
2
0
0
0
0
2
0
0
2
0
0
2
0
0
3
2
0
2
1
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
2
1
0
0
0
0
0
2
0
0
0
0
1
2
2
0
0
1
0
0
2
1
2
0
0
0
2
0
3
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
1
1
1
0
0
2
2
1
0
0
0
0
0
0
0
0
2
1
1
0
0
2
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
8
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
3
0
0
0
2
2
1
1
0
1
0
0
0
1
1
5
2
0
1
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
3
0
1
0
0
0
0
0
2
2
0
1
1
2
2
0
0
0
2
0
0
0
1
0
0
1
0
2
0
1
0
0
1
0
0
0
0
0
4
0
2
2
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
3
0
1
2
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
1
0
1
0
0
0
0
3
2
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
1
0
1
1
1
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
2
1
0
3
0
0
0
2
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
2
2
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
2
0
2
1
1
2
2
2
1
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
1
2
1
0
1
2
1
1
0
0
1
0
0
0
0
0
0
2
1
0
1
0
0
1
0
0
0
0
2
0
0
0
0
1
1
0
0
2
0
0
0
0
1
2
0
0
1
0
0
2
0
0
0
0
1
2
0
2
0
2
1
0
0
1
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
1
1
2
0
2
0
0
1
0
2
1
0
0
2
0
0
1
0
0
0
0
0
1
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
3
0
0
1
1
0
0
2
0
0
0
1
2
0
0
3
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
3
0
1
2
0
0
1
0
0
0
0
0
0
1
2
0
1
0
0
1
8
0
2
0
0
0
0
1
2
0
2
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
1
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
1
1
0
0
0
0
1
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
5
2
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
2
0
1
0
0
0
2
2
1
2
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
2
0
0
0
0
2
3
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
3
0
0
2
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
5
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
3
1
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
3
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
1
1
0
2
0
0
0
1
4
0
0
1
2
2
0
0
3
1
0
1
0
0
2
1
0
2
0
1
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
2
1
0
0
0
0
2
0
0
0
2
0
0
3
0
0
0
0
1
0
2
0
3
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
7
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
2
0
2
0
0
0
2
0
0
0
0
0
0
1
1
0
5
0
0
3
0
1
0
0
2
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
2
0
0
1
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
2
0
1
0
0
1
0
0
0
0
2
1
0
1
0
0
1
0
1
0
0
1
0
1
1
0
1
0
1
2
1
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
2
1
0
3
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
3
1
0
0
2
0
2
0
0
1
1
0
0
3
0
0
2
0
0
0
0
1
3
0
2
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
1
0
1
2
0
0
0
0
2
0
2
0
0
2
0
0
0
0
2
4
1
0
0
2
2
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
3
0
3
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
1
2
0
0
0
0
1
0
2
0
0
0
4
2
0
0
0
0
0
0
0
3
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
1
0
2
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
1
0
0
2
0
0
0
2
0
3
0
2
0
2
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
3
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
3
0
1
0
2
0
2
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
1
1
2
0
0
0
2
0
0
0
3
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
2
0
0
1
2
1
2
0
0
1
4
1
0
0
1
0
3
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
1
2
2
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
1
0
0
0
0
2
2
1
0
0
1
0
0
0
0
0
2
0
0
0
2
2
0
2
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
1
0
1
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
2
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
2
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
1
0
1
0
0
0
2
1
1
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
1
6
0
0
2
1
0
0
2
0
0
2
1
1
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
6
0
0
0
0
0
0
1
0
2
3
0
0
2
0
0
0
0
1
2
0
0
1
0
1
0
2
0
1
2
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
3
1
0
3
0
0
0
4
0
2
0
0
2
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
2
3
0
0
0
2
0
0
0
0
1
0
2
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
2
0
1
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
1
1
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
3
2
0
0
1
0
2
1
1
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
2
0
0
2
1
0
0
0
0
1
1
0
0
0
4
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
1
0
3
0
2
0
3
2
0
1
0
1
2
0
0
0
2
2
0
0
0
1
2
0
2
0
0
0
2
0
4
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
2
0
2
0
2
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
1
3
0
2
2
1
0
0
2
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
3
1
1
0
1
1
0
0
2
2
0
0
2
0
2
0
2
0
0
2
0
0
0
2
0
0
0
2
0
2
1
0
0
0
0
0
2
0
1
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
4
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
3
0
1
2
1
0
0
1
0
2
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
2
0
0
1
0
2
0
1
1
1
2
1
1
0
0
0
0
0
0
4
0
1
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
3
0
1
1
0
2
0
0
0
2
0
0
0
2
0
2
0
0
1
0
0
0
0
1
0
0
1
3
0
0
0
0
3
1
0
0
2
1
2
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
1
2
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
1
1
0
0
1
0
0
0
2
0
0
1
0
1
1
0
0
0
0
0
0
1
2
0
0
1
0
0
0
2
0
2
0
0
1
1
0
2
1
2
0
0
1
0
0
0
2
0
0
2
0
2
2
0
0
2
0
0
2
0
2
0
1
2
0
0
0
0
0
0
16
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
4
4
0
2
2
0
0
0
0
0
0
1
0
6
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
2
0
0
0
1
2
0
2
0
3
2
0
1
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
1
2
0
2
0
0
0
1
0
0
0
0
0
2
0
0
1
2
1
1
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
2
1
1
0
0
0
0
0
0
1
0
0
3
0
0
0
2
1
0
4
0
0
0
1
0
0
2
0
2
2
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
1
0
0
2
0
2
2
1
0
0
2
0
0
0
2
0
0
0
0
0
0
3
0
0
0
1
2
0
0
0
0
0
1
0
2
0
0
0
0
1
0
1
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
1
2
0
0
0
1
2
2
0
0
3
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
1
3
0
0
0
0
2
0
0
0
9
1
0
2
0
0
0
0
0
2
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
1
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
1
2
1
0
1
2
0
0
1
0
0
3
1
1
0
0
0
1
2
3
0
0
2
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
1
1
0
2
1
0
2
1
1
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
1
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
2
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
4
0
0
1
1
3
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
2
0
0
2
0
0
1
0
0
2
1
0
0
0
0
1
0
2
0
0
3
0
2
1
2
0
0
0
1
0
0
2
0
0
2
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
2
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
1
2
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
2
2
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
2
6
0
0
2
0
1
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
2
1
0
0
1
0
0
1
2
0
1
0
0
0
2
0
0
1
0
0
0
0
1
0
0
2
2
2
0
1
1
2
1
2
0
0
0
0
1
0
1
0
2
0
0
2
0
2
0
1
2
0
0
0
0
0
0
4
1
1
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
1
0
0
1
0
0
0
0
3
0
0
2
0
0
0
2
0
0
1
0
0
0
0
4
1
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
3
0
1
0
0
2
0
1
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
2
1
0
2
0
1
0
0
0
0
1
1
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
2
1
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
1
2
1
0
0
2
2
2
0
0
0
0
0
0
0
0
2
0
2
1
1
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
2
0
1
1
0
0
2
0
2
0
2
2
0
0
0
2
1
0
2
2
0
0
0
0
0
0
2
1
0
0
0
0
5
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
1
0
2
2
0
0
2
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
4
2
2
0
0
1
2
2
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
3
0
0
2
0
2
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
3
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
2
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
2
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
1
0
2
0
1
0
0
0
0
0
2
1
0
0
0
2
0
1
0
0
1
2
0
0
0
1
0
1
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
1
1
0
1
0
2
2
2
0
3
0
0
1
0
2
1
0
0
0
0
0
2
0
1
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
1
2
0
0
0
0
0
0
2
0
2
0
2
0
0
1
0
2
0
1
0
0
0
0
2
1
0
2
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
1
1
1
2
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
2
0
1
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
2
0
0
0
2
2
0
2
8
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
6
0
0
4
0
1
1
1
0
1
0
0
0
0
2
0
0
1
2
0
0
0
1
1
1
2
0
0
0
0
0
1
1
0
1
0
0
2
0
3
0
0
2
0
1
0
1
0
0
0
2
0
2
0
0
0
0
1
0
0
2
1
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
2
1
0
1
1
1
0
0
0
2
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
3
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
1
0
0
2
1
0
1
1
1
3
2
0
0
0
2
0
0
0
3
1
0
0
0
2
2
0
0
1
0
0
0
1
0
2
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
2
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
3
2
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
3
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
1
2
1
0
3
0
0
2
0
0
1
0
2
0
0
1
0
1
0
0
0
0
1
2
0
0
0
2
0
3
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
1
0
2
1
0
0
0
1
1
1
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
8
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
5
0
0
1
0
0
2
0
2
2
0
1
1
0
1
0
0
0
1
0
0
0
2
0
3
0
0
0
0
1
2
0
0
1
0
0
0
1
1
3
0
0
0
3
0
0
0
0
0
0
2
1
0
0
0
3
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
5
0
0
0
0
1
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
3
2
1
0
1
0
0
2
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
2
1
0
1
0
0
0
0
2
0
0
0
0
1
1
0
0
0
1
0
0
0
2
0
0
0
0
0
1
2
0
1
0
1
0
2
1
0
1
0
1
1
0
0
0
1
3
0
2
0
0
1
3
1
0
0
1
0
1
1
3
2
0
0
2
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
3
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
4
0
0
0
5
1
2
1
1
0
0
0
0
2
0
1
1
1
2
0
0
2
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
1
2
0
1
0
7
0
0
0
2
0
0
2
0
0
1
2
1
0
0
0
2
0
0
0
0
0
3
3
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
4
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
3
0
0
0
0
0
1
0
0
1
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
2
0
0
2
2
2
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
2
0
0
1
0
0
0
0
0
1
0
0
2
2
0
1
0
2
1
0
0
0
0
0
1
0
1
0
2
0
2
0
1
0
2
0
1
0
0
2
0
2
0
1
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
1
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
5
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
2
0
0
1
2
2
1
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
2
0
0
0
1
0
2
0
2
0
0
0
0
1
2
0
0
0
2
1
0
0
0
0
2
0
1
0
0
2
1
3
1
0
1
2
0
1
2
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
2
0
2
1
3
0
0
0
0
1
1
0
2
0
0
1
0
3
2
0
0
0
0
2
0
1
0
0
2
2
0
0
1
0
2
2
0
0
0
1
2
0
0
0
1
0
2
3
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
1
2
2
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
3
1
0
4
0
1
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
2
2
2
0
0
1
0
0
0
0
4
0
0
0
2
1
0
0
0
0
0
0
0
0
6
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
2
2
0
0
0
0
0
0
0
0
1
2
0
3
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
2
2
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
1
0
0
1
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
2
1
0
0
2
0
0
0
0
2
0
0
0
2
0
2
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
2
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
7
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
2
1
0
1
0
0
0
4
2
0
2
0
2
0
0
0
2
1
2
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
2
2
0
3
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
2
0
0
1
0
0
2
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
7
0
0
0
0
3
2
4
4
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
2
0
2
2
1
0
2
2
0
0
0
0
0
2
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
1
0
0
0
0
1
0
2
1
0
4
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
2
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
2
0
2
0
0
0
0
0
2
0
0
1
0
2
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
2
0
0
2
0
0
7
0
1
0
1
0
0
0
1
3
2
3
1
0
0
0
0
0
5
0
1
0
0
0
1
0
2
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
3
2
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
3
1
2
0
2
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
2
1
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
3
0
1
2
2
0
1
0
0
0
6
1
0
0
2
1
0
3
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
1
2
1
0
0
0
0
2
2
1
1
0
0
2
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
2
1
3
0
1
2
0
2
2
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
1
1
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
1
2
0
1
0
0
1
0
0
1
0
0
2
0
0
1
1
0
2
2
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
1
0
1
0
0
0
0
0
0
2
9
0
0
0
0
0
0
0
1
0
0
3
0
2
0
1
0
0
2
0
0
1
2
0
1
0
0
2
0
0
0
2
0
6
0
1
1
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
3
0
0
0
0
1
1
0
2
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
1
2
3
0
2
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
1
1
0
0
1
0
0
1
3
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
1
1
0
0
3
0
0
0
0
4
1
0
5
0
0
0
0
0
0
1
0
0
1
0
0
1
0
4
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
2
1
2
0
2
0
1
0
0
0
2
0
0
0
2
0
0
0
1
0
0
1
1
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
5
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
1
1
1
0
2
0
2
0
0
0
1
0
0
0
1
0
1
2
0
1
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
1
0
0
0
2
2
0
0
0
1
2
0
0
0
1
1
0
0
0
2
0
1
0
2
0
0
1
0
0
2
0
0
0
2
4
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
2
1
0
2
0
0
0
2
0
2
2
0
1
0
0
1
1
0
1
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
2
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
2
1
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
2
0
0
1
0
1
2
2
1
0
0
0
0
0
0
1
1
0
0
1
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
1
0
2
0
1
2
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
3
0
3
1
0
0
0
0
2
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
1
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
2
0
0
0
2
2
0
0
1
0
0
0
0
0
0
1
0
0
2
1
0
0
0
2
1
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
1
2
1
0
0
0
2
0
0
0
1
0
1
0
2
0
0
3
0
0
0
0
0
2
2
2
0
1
0
1
3
1
0
0
0
0
2
0
1
1
0
0
2
0
0
0
0
0
0
0
1
3
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
1
0
2
0
0
0
3
0
1
0
0
0
1
0
2
1
1
0
2
1
1
0
0
1
1
1
0
0
0
0
0
2
0
0
0
0
0
1
1
1
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
1
0
0
0
2
0
0
0
4
3
0
0
0
1
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
2
0
1
1
0
0
2
2
1
0
3
0
0
0
0
0
2
2
2
2
0
1
1
0
0
4
2
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
2
0
2
2
0
1
2
0
1
2
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
1
1
0
2
0
2
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
2
0
0
0
0
2
2
0
2
1
0
0
0
0
0
2
2
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
9
0
0
0
1
2
0
2
0
1
0
0
1
0
2
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
1
0
0
2
0
0
0
0
0
0
0
0
2
0
3
0
0
1
3
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
3
0
1
0
1
0
0
0
0
2
0
0
0
0
0
1
1
6
0
0
4
1
1
1
0
0
0
2
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
4
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
1
0
0
2
9
0
1
0
1
0
1
0
0
0
4
0
0
0
1
0
0
0
0
0
1
0
1
0
7
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
2
0
1
0
0
0
0
0
1
1
1
1
0
0
0
1
0
0
0
0
0
1
1
0
2
0
0
0
2
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
4
0
0
0
1
2
0
2
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
2
3
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
1
0
0
1
0
0
0
2
0
0
1
2
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
2
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
3
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
2
0
0
1
1
1
0
0
0
0
2
0
2
0
1
0
2
0
0
0
2
0
0
1
0
0
0
0
0
2
0
1
0
2
0
0
0
2
0
0
0
0
0
0
1
1
2
0
0
0
0
2
0
1
0
1
0
1
0
0
2
0
0
0
0
2
0
0
0
9
1
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
2
0
1
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
2
2
0
0
1
1
0
0
0
0
2
0
0
1
1
2
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
2
1
0
1
0
0
0
0
0
0
0
0
2
1
3
1
0
0
0
0
0
0
3
0
0
0
0
1
0
2
0
0
1
0
0
3
0
0
0
2
0
0
3
0
1
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
2
2
1
1
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
1
1
1
0
0
1
0
0
0
0
0
0
2
1
2
1
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
1
0
1
0
0
0
0
0
0
0
2
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
3
2
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
2
1
0
0
0
0
0
1
0
0
2
0
0
2
0
1
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
6
0
0
0
2
0
0
0
1
0
0
0
0
2
0
1
0
2
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
2
2
2
3
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
2
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
2
0
0
0
0
1
0
0
1
1
0
1
1
2
0
0
2
2
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
1
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
5
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
3
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
4
2
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
3
0
0
2
0
5
1
0
0
0
1
2
0
0
0
0
0
0
4
0
0
0
5
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
1
0
3
2
2
0
1
2
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
3
0
0
0
1
2
0
0
1
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
1
0
1
2
0
0
0
0
3
0
0
0
0
2
0
2
1
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
3
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
1
2
0
0
0
2
0
3
0
2
0
0
0
1
2
1
0
0
0
0
0
0
2
2
2
0
0
1
0
0
1
0
0
0
0
1
0
1
0
2
0
0
5
0
0
0
0
0
2
0
2
3
0
1
0
0
0
0
0
2
1
0
0
0
1
0
1
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
1
0
0
0
0
0
0
0
4
0
3
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
4
2
4
0
0
0
0
0
1
6
2
1
0
1
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
2
0
0
2
0
0
0
2
0
2
0
0
1
0
0
0
0
2
2
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
1
0
1
3
0
0
0
2
3
0
0
2
0
1
0
0
2
1
0
0
0
0
0
2
0
0
0
0
2
0
1
1
0
2
1
0
1
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
1
1
0
2
0
0
1
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
3
2
0
0
0
0
2
0
0
2
0
0
0
3
0
0
0
0
0
0
1
0
0
0
1
2
0
2
2
0
0
0
0
1
0
4
0
0
0
0
0
0
2
0
0
0
2
1
0
1
2
0
2
0
0
2
0
0
0
2
0
0
1
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
2
0
1
0
2
1
1
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
2
0
1
0
0
0
0
3
0
2
0
0
0
2
0
0
0
0
2
1
0
12
3
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
2
0
0
0
1
0
0
0
3
1
0
0
1
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
2
0
0
0
0
1
1
0
0
2
0
0
0
1
2
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
2
2
1
0
0
2
0
0
0
1
0
0
0
1
0
1
0
0
3
0
0
1
0
1
0
2
2
0
0
1
0
2
0
2
2
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
1
0
0
0
1
0
2
0
0
0
0
2
0
0
2
0
1
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
2
0
0
2
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
5
0
0
2
0
0
2
1
1
0
0
0
0
0
1
0
0
0
0
1
0
3
0
1
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
3
0
2
0
0
0
0
1
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
1
0
2
1
0
2
0
0
0
0
0
0
2
2
0
0
0
1
0
1
1
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
2
0
0
1
0
0
0
1
0
1
0
4
0
1
0
0
0
2
0
1
0
0
0
0
0
0
5
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
6
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
2
0
2
0
3
0
1
0
0
0
0
3
3
0
0
2
0
1
0
0
5
0
0
1
0
0
1
0
2
0
1
2
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
2
2
0
1
2
0
0
0
4
1
1
0
1
0
2
0
2
5
0
0
0
1
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
2
0
1
1
0
1
1
0
0
0
1
2
0
2
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
1
0
0
2
0
1
2
0
0
0
1
0
0
0
0
2
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
2
0
1
0
5
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
1
0
0
0
1
0
0
0
0
1
0
0
2
0
3
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
1
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
2
3
0
0
1
0
0
0
2
0
0
2
0
1
2
1
0
0
0
0
1
0
0
0
0
0
0
1
2
3
0
1
0
1
2
0
0
1
0
0
2
2
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
2
0
2
0
0
0
1
1
0
1
0
3
2
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
2
2
0
1
0
0
0
0
0
1
0
2
0
0
3
0
0
0
0
2
0
1
1
0
0
0
0
1
0
0
0
1
0
2
0
0
4
0
0
3
0
1
0
0
2
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
1
0
0
0
2
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
1
2
1
0
1
2
2
1
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
2
1
0
1
2
1
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
5
1
2
0
0
1
2
0
0
0
1
0
1
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
2
2
0
0
0
0
0
0
0
2
2
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
3
0
0
0
0
0
3
0
1
1
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
3
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
1
1
0
0
0
1
0
3
0
2
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
2
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
3
0
0
2
2
0
3
2
0
1
2
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
2
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
3
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
1
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
2
2
0
1
0
1
1
2
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
2
0
0
0
1
1
0
2
0
0
0
0
0
0
3
0
3
0
3
0
0
4
0
2
1
0
1
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
8
2
1
2
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
1
0
0
0
0
3
0
0
2
2
0
2
0
0
0
1
0
0
0
0
2
0
1
4
0
0
0
2
0
0
0
2
2
1
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
1
1
0
3
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
1
2
0
0
0
0
0
2
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
1
0
0
1
2
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
8
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
2
1
0
0
0
2
0
0
0
0
1
2
0
1
1
1
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
1
0
1
0
0
0
2
2
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
2
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
2
0
0
2
3
2
0
0
0
0
0
0
2
3
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
2
2
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
3
2
0
0
0
2
1
1
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
2
1
0
2
0
1
0
5
0
0
1
2
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
1
2
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
1
0
0
1
0
1
0
0
0
2
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
1
0
0
1
2
4
1
1
0
2
0
2
0
1
2
0
2
0
0
2
2
0
0
0
0
0
2
3
0
1
0
0
0
0
0
2
0
0
1
0
0
2
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
3
2
6
1
1
1
0
0
0
0
0
0
2
0
1
0
1
0
2
0
1
0
0
3
0
0
2
0
0
2
0
0
0
2
0
0
2
0
0
0
0
3
0
2
3
1
0
0
0
2
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
1
2
2
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
7
0
0
0
0
1
0
2
0
3
1
0
0
0
1
2
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
1
2
1
0
0
1
2
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
3
0
0
0
4
2
0
0
0
0
0
0
0
0
0
2
1
0
1
2
0
0
1
2
0
0
0
1
0
0
1
3
0
0
1
0
1
0
2
0
1
1
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
1
0
0
2
1
2
0
0
1
0
0
0
3
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
3
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
2
1
1
0
0
0
1
1
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
1
4
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
1
0
0
0
2
0
1
1
0
2
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
1
1
0
0
2
0
1
0
2
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
3
1
2
1
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
3
0
3
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
3
0
0
0
3
1
2
2
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
1
2
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
1
2
0
0
1
0
1
0
1
2
0
1
0
0
0
0
0
1
0
1
0
0
0
0
2
1
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
1
1
0
0
3
0
0
1
0
2
1
1
1
1
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
2
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
1
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
3
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
1
0
2
0
0
1
1
0
0
0
1
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
1
0
0
0
2
0
2
1
0
0
0
0
0
3
0
1
0
0
2
0
2
1
2
2
2
0
0
0
0
0
0
1
0
1
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
2
1
0
1
0
0
0
0
0
0
0
0
0
0
3
1
0
5
0
0
0
1
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
2
2
2
2
3
2
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
2
1
1
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
1
0
0
0
3
0
0
0
0
2
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
3
0
0
0
1
3
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
2
2
0
0
3
0
4
0
0
0
0
0
2
0
0
13
0
0
0
0
0
0
2
0
1
0
0
0
1
2
2
0
3
2
1
0
2
0
0
1
2
0
0
0
2
0
0
0
1
0
2
0
2
0
0
2
0
0
1
0
0
1
0
1
1
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
2
1
0
0
0
0
3
0
0
0
0
0
2
1
2
0
0
2
1
2
0
0
0
0
1
2
0
1
2
0
1
1
0
0
0
0
0
2
0
0
0
0
2
0
1
2
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
2
1
0
0
0
0
0
1
1
0
4
0
0
0
2
0
0
0
2
1
1
2
0
1
0
0
0
0
2
0
0
2
1
0
0
0
2
0
0
0
0
2
2
0
1
0
0
0
0
1
2
2
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
2
5
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
1
0
2
3
0
0
0
0
0
1
1
2
0
0
0
0
0
0
2
0
1
0
1
3
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
1
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
6
1
1
0
0
0
1
0
2
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
2
2
1
3
1
0
0
1
0
0
2
2
0
0
0
2
0
1
0
0
0
1
0
3
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
7
0
0
0
0
0
2
0
0
1
2
1
0
0
0
0
0
0
1
0
1
0
0
0
2
0
3
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
1
1
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
2
0
2
0
0
3
1
0
0
0
0
0
0
0
0
0
0
5
0
1
0
0
0
0
0
0
2
1
0
1
0
2
0
3
0
0
2
0
0
2
0
1
0
1
0
0
2
0
0
1
0
0
0
2
0
1
0
0
1
2
0
0
2
1
2
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
2
0
0
6
1
0
1
2
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
2
0
0
1
0
1
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
1
2
3
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
1
2
1
2
0
0
0
0
0
1
0
2
0
0
2
0
0
0
1
2
0
1
0
0
0
0
1
0
0
0
3
0
2
3
0
0
0
0
4
2
0
2
0
0
0
0
1
2
0
2
0
0
0
0
2
0
0
0
1
2
0
1
2
0
1
0
0
0
2
2
2
0
0
0
0
1
1
0
0
0
2
0
0
1
0
0
0
0
0
2
2
1
0
1
0
0
0
0
0
2
3
1
0
1
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
2
0
2
1
0
0
1
0
0
0
0
2
1
3
0
2
0
0
0
0
6
0
0
0
1
0
0
1
0
2
0
0
0
1
0
2
2
0
2
2
1
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
1
0
0
4
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
3
1
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
1
1
1
0
0
2
1
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
3
0
0
0
0
0
1
0
1
0
2
0
0
0
1
1
2
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
2
0
1
1
0
0
0
1
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
3
0
1
0
0
1
1
0
0
0
0
0
3
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
2
1
0
1
0
3
1
0
0
0
0
0
2
0
0
0
1
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
13
0
0
2
3
0
1
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
3
0
1
1
0
0
0
0
0
0
1
0
1
1
0
1
1
0
1
0
0
1
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
1
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
1
0
0
0
2
2
2
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
1
0
0
2
0
1
0
0
2
0
0
1
1
0
1
0
0
0
1
0
0
1
0
0
0
1
0
3
0
0
0
2
0
1
0
1
2
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
5
0
0
0
0
0
2
0
0
0
2
0
0
1
1
1
0
0
0
0
1
1
0
0
0
0
2
2
0
0
0
0
0
0
2
0
1
0
2
0
0
2
1
0
1
0
0
2
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
2
0
0
1
0
0
0
0
1
0
0
3
0
0
0
0
1
0
0
0
1
0
0
0
2
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
2
2
0
0
2
0
2
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
2
0
0
2
0
2
0
1
0
0
0
0
1
0
1
1
1
0
0
0
1
1
1
0
0
0
1
1
2
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
1
1
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
3
0
0
0
1
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
1
0
2
0
1
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
2
0
1
0
2
0
0
0
1
0
0
2
0
0
3
0
2
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
1
0
1
0
0
0
0
4
0
1
0
0
0
2
1
0
0
0
1
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
2
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
3
1
0
2
0
1
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
3
1
1
0
0
2
0
0
0
0
0
2
0
2
0
1
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
3
0
1
1
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
2
0
0
1
1
0
0
2
2
0
1
0
0
0
0
0
0
0
0
2
0
0
1
3
0
2
2
0
1
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
1
0
2
0
0
2
1
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
1
0
2
0
0
0
1
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
1
0
0
2
0
0
0
0
1
0
1
0
3
0
0
0
1
2
0
0
0
2
0
2
0
0
1
0
2
0
0
0
1
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
3
1
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
2
0
2
0
1
1
0
1
0
1
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
1
0
1
0
2
0
0
0
1
0
2
1
0
0
0
0
0
1
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
3
2
0
0
0
2
0
1
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
2
0
1
0
1
1
1
0
0
4
2
0
0
0
1
1
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
3
1
0
0
4
0
0
0
0
0
0
1
2
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
3
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
2
2
1
0
0
0
0
2
0
0
0
0
0
1
0
1
0
2
2
1
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
5
0
2
1
1
0
1
0
0
0
0
1
1
0
4
0
2
0
0
1
2
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
1
0
0
2
0
0
0
0
1
0
3
0
9
0
2
0
1
2
0
1
0
2
0
0
2
0
1
2
0
1
0
0
0
0
0
0
0
0
1
3
1
0
0
1
0
0
1
0
0
0
2
0
0
2
0
0
0
4
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
2
2
1
0
0
1
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
3
0
0
1
0
0
0
0
0
0
2
1
0
0
2
0
2
2
1
0
0
0
0
1
1
0
3
1
0
1
0
0
0
2
0
1
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
2
0
0
3
0
0
2
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
1
0
0
1
0
0
1
0
0
2
0
2
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
4
0
2
0
4
0
0
0
0
0
2
0
0
0
1
0
1
0
3
0
0
0
2
0
0
0
0
0
0
1
2
0
0
1
0
0
2
1
0
1
0
0
1
0
0
0
0
0
0
2
0
1
1
0
2
0
2
0
0
0
0
2
0
0
6
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
2
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
1
0
2
2
0
2
0
0
0
0
1
2
0
0
0
0
2
0
1
1
1
0
0
0
1
0
0
0
0
4
0
0
0
2
0
0
0
0
0
2
0
0
3
0
2
2
0
0
0
0
0
3
1
0
1
0
0
0
22
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
1
0
0
0
2
3
0
0
0
0
0
0
0
2
3
1
0
0
0
3
0
0
3
0
3
0
1
0
0
0
0
0
0
0
0
1
1
0
2
0
0
2
2
1
0
0
2
4
0
2
1
0
0
2
0
0
0
0
0
1
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
4
0
0
4
0
0
0
0
2
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
3
0
0
0
0
0
2
0
0
3
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
2
1
0
0
0
1
2
1
0
0
0
2
0
0
0
1
0
0
1
0
0
1
0
2
2
0
0
1
2
0
2
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
2
0
1
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
3
0
0
0
1
0
2
1
0
0
1
0
0
0
2
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
1
0
0
2
0
0
0
0
4
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
2
1
2
0
1
0
0
0
2
0
0
1
2
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
1
1
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
2
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
2
0
1
2
0
0
0
0
0
2
3
0
0
0
0
0
0
2
0
1
1
0
0
2
0
2
0
0
2
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
2
0
3
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
2
2
0
0
1
0
2
0
0
0
3
0
0
0
0
0
1
2
0
0
1
0
0
0
1
1
2
0
0
0
0
0
1
1
0
1
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
2
0
2
2
0
0
0
0
0
1
0
0
4
0
0
0
3
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
4
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
1
0
0
2
1
3
0
0
1
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
2
0
1
2
0
6
0
2
0
0
0
0
0
0
0
0
0
0
1
2
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
2
0
2
2
0
0
1
3
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
1
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
2
0
1
0
1
0
0
0
2
0
0
0
0
0
1
2
0
2
2
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
3
0
3
1
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
1
0
1
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
3
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
2
1
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
5
0
2
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
2
0
0
1
0
0
3
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
2
2
0
0
0
0
0
0
4
0
2
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
2
0
3
0
0
1
0
2
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
2
0
0
1
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
6
0
0
1
0
1
0
0
0
0
0
2
0
0
0
3
1
0
0
2
0
2
0
2
1
1
2
1
0
0
1
2
0
0
3
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
2
2
0
0
0
1
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
3
0
2
0
0
2
1
0
0
0
0
2
2
3
9
0
0
0
0
1
1
1
1
1
0
0
0
1
0
1
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
2
0
0
1
2
1
0
0
0
1
0
0
2
2
1
0
0
0
0
3
0
1
2
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
2
1
2
0
0
2
0
0
2
0
2
4
0
1
0
0
0
0
1
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
3
0
0
3
0
0
1
0
0
0
0
2
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
1
0
2
0
2
1
0
0
0
0
1
0
1
0
0
0
0
0
0
3
0
0
0
1
0
0
1
0
2
0
0
0
0
2
0
2
0
0
0
2
2
0
0
0
1
0
0
2
5
0
0
0
0
0
0
0
2
2
0
1
0
0
0
1
0
1
0
0
3
2
0
0
0
0
0
0
0
0
0
2
1
0
0
1
1
0
1
2
2
0
1
0
5
0
0
1
0
0
2
0
2
0
1
0
0
1
0
0
0
1
2
0
0
0
2
0
0
0
2
0
0
0
0
1
2
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
2
2
1
0
0
0
0
2
0
0
0
1
2
0
1
0
1
0
0
0
0
0
0
0
4
2
0
1
2
1
0
2
4
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
1
0
0
0
0
2
2
1
2
0
0
2
0
0
0
1
2
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
1
0
0
0
1
2
1
2
0
0
4
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
7
2
0
1
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
1
2
0
0
2
2
0
1
0
0
1
0
4
0
3
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
3
0
2
0
0
0
2
0
0
0
1
0
0
0
0
2
1
0
0
1
0
2
0
2
0
2
0
0
0
1
0
3
0
0
1
1
0
0
0
0
1
1
1
0
0
1
0
4
0
1
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
3
0
0
1
0
0
0
1
0
1
2
0
0
0
0
1
0
0
0
1
0
1
0
2
0
0
0
0
1
0
1
0
0
1
0
1
1
0
0
0
0
2
0
0
2
0
0
1
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
1
2
8
0
0
0
0
0
0
0
0
2
2
1
1
1
2
0
0
3
3
2
0
2
2
0
0
2
1
0
0
1
0
1
0
0
1
0
0
0
1
0
2
0
0
1
2
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
2
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
3
2
0
0
1
0
3
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
2
1
0
0
0
0
0
0
1
1
0
0
1
1
3
1
2
0
0
0
0
0
0
2
1
0
2
0
2
0
0
0
0
0
1
0
1
1
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
2
0
3
0
0
0
0
1
0
0
0
2
0
0
2
0
1
0
0
0
2
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
1
0
2
0
1
2
0
0
1
0
0
3
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
3
0
0
4
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
3
0
0
0
0
0
0
4
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
2
0
1
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
2
0
0
0
1
0
0
0
1
0
0
0
2
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
1
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
2
0
0
1
0
2
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
2
2
0
0
1
2
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
2
0
5
0
1
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
2
0
0
1
1
0
2
0
1
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
3
1
3
1
0
0
0
0
1
0
1
2
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
1
2
2
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
2
1
0
0
0
0
0
0
1
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
6
0
4
2
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
7
2
0
0
2
2
0
0
1
0
0
0
1
0
0
0
2
0
0
2
1
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
2
2
0
0
1
0
2
0
0
0
2
0
0
2
2
0
0
0
0
0
0
2
0
0
1
0
1
0
0
2
0
0
0
0
1
0
3
0
0
2
0
0
0
2
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
4
0
0
0
2
0
0
0
2
0
0
0
0
1
0
1
0
2
2
0
0
2
0
0
0
1
0
0
0
0
0
2
0
2
1
3
0
0
0
0
0
3
0
1
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
1
2
0
0
1
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
1
0
2
0
1
0
0
0
0
3
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
1
2
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
1
0
1
2
0
1
2
0
0
1
0
2
0
0
0
2
0
0
1
0
2
0
0
0
0
2
1
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
1
0
1
0
0
0
0
3
0
2
0
2
2
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
2
1
2
1
0
0
0
2
0
2
0
2
0
0
2
0
0
0
1
2
2
2
0
2
1
0
0
4
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
3
2
0
2
0
2
0
0
0
0
0
1
0
0
1
0
2
1
2
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
3
1
0
0
1
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
4
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
1
1
1
0
2
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
2
0
0
0
2
0
0
3
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
1
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
2
1
1
0
0
1
0
1
3
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
3
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
1
0
0
0
1
2
2
2
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
7
2
2
0
3
0
0
1
1
5
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
2
2
0
3
0
0
3
0
0
0
0
0
3
0
2
1
0
0
2
0
0
0
2
0
1
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
1
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
3
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
2
0
0
0
1
0
0
0
1
0
0
0
0
2
1
3
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
1
0
0
0
0
0
0
0
0
1
3
0
2
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
1
0
7
0
0
2
1
0
0
0
0
0
0
0
0
0
0
10
0
3
1
0
1
0
0
0
0
1
1
0
0
1
1
1
1
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
5
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
2
0
2
0
2
0
1
1
0
1
0
0
0
2
4
0
0
2
1
2
0
0
0
0
0
0
0
1
0
2
1
0
0
0
1
1
0
1
0
0
1
2
0
2
0
1
0
2
0
5
0
0
0
0
0
0
2
0
1
2
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
2
0
2
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
1
1
2
0
1
0
0
2
0
0
0
2
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
2
0
1
0
0
2
1
0
0
0
0
0
2
2
1
0
0
2
0
2
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
3
0
2
2
0
0
0
0
0
0
0
2
2
0
0
0
1
1
1
0
0
0
1
2
2
0
0
0
2
0
0
0
0
0
2
2
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
1
0
5
1
0
1
0
1
0
1
0
0
0
0
0
0
1
0
1
1
1
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
3
2
2
1
0
2
0
0
1
2
0
0
2
0
0
2
0
0
4
0
2
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
2
0
2
1
2
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
1
2
0
0
0
0
1
0
0
1
0
0
0
0
0
1
2
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
2
2
1
1
0
0
2
2
1
0
0
1
1
0
0
1
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
2
0
1
1
2
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
2
0
2
0
0
1
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
3
2
1
0
0
0
0
2
0
0
0
0
0
0
1
0
2
1
0
0
1
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
6
1
0
0
2
2
0
3
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
1
0
2
0
0
2
0
0
0
0
0
2
1
0
0
0
1
0
0
0
2
0
0
0
0
2
1
0
0
0
3
0
0
1
2
4
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
2
2
0
2
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
1
0
0
4
0
2
3
0
0
0
0
0
2
0
0
1
2
0
1
0
0
4
4
0
1
0
0
1
0
0
1
1
0
2
0
0
0
0
0
0
2
0
0
0
1
2
1
2
0
0
0
0
0
0
1
2
1
2
0
1
1
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
1
0
1
0
2
0
0
0
0
2
0
0
12
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
2
0
2
0
1
0
0
1
1
1
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
2
0
2
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
2
0
0
1
0
1
2
0
1
2
2
0
0
0
0
2
0
0
0
1
0
0
0
1
0
1
0
1
1
0
0
0
0
1
3
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
2
0
1
0
2
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
2
0
2
0
1
0
0
5
0
2
2
2
2
0
0
0
4
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
1
1
1
0
2
0
0
2
1
2
5
1
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
5
0
1
1
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
2
1
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
1
0
2
2
0
0
0
0
3
0
0
1
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
3
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
2
1
1
0
1
2
0
1
2
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
1
1
1
0
0
0
1
2
0
1
0
0
2
0
1
2
0
0
0
2
0
3
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
3
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
1
1
2
0
2
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
1
2
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
1
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
1
2
0
0
0
1
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
2
0
1
2
0
0
0
0
0
3
0
1
0
0
0
0
2
1
2
2
2
2
0
0
0
1
2
0
0
2
0
0
0
0
0
1
0
0
2
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
1
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
1
2
2
0
1
0
2
0
0
0
0
1
0
1
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
3
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
2
0
1
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
4
0
0
1
3
0
0
0
0
0
0
4
4
0
0
0
0
0
2
0
0
0
0
1
2
0
4
0
0
2
0
1
0
0
1
2
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
4
0
1
2
0
0
0
0
0
0
2
1
2
2
0
0
0
5
0
0
0
2
1
0
1
0
1
0
2
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
1
2
0
2
2
0
0
0
2
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
3
2
0
1
0
1
3
1
2
1
0
1
0
0
0
0
1
0
0
0
0
2
0
1
2
1
0
1
1
2
0
0
1
0
0
0
0
0
0
0
2
2
1
0
1
0
0
0
0
2
0
1
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
2
2
1
0
0
3
0
1
1
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
5
2
1
0
0
0
0
0
0
2
0
0
1
1
0
2
3
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
2
3
0
0
0
2
0
0
0
2
0
0
0
0
0
2
3
2
1
0
1
1
0
3
1
0
0
0
1
0
0
2
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
2
0
0
0
2
1
0
0
2
0
0
0
0
0
4
0
0
0
2
0
2
1
0
0
0
0
0
0
1
0
0
0
0
1
2
1
0
2
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
2
0
1
0
0
0
0
0
2
0
0
2
0
0
3
0
1
0
2
0
0
2
0
1
2
0
0
0
2
0
0
1
1
0
0
1
0
2
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
1
0
0
2
1
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
1
0
2
2
1
0
0
0
0
3
0
0
0
0
0
2
2
2
1
0
1
0
0
0
0
1
0
2
0
0
0
2
0
3
1
2
0
4
0
0
0
1
2
0
2
0
0
0
1
1
0
0
0
0
0
4
1
0
1
0
0
0
2
0
3
0
1
1
0
0
0
0
4
0
2
1
0
1
0
2
3
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
2
0
0
1
2
0
3
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
3
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
5
2
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
3
0
0
0
0
0
1
0
0
2
0
0
0
1
2
2
0
1
0
0
0
0
1
0
1
2
0
0
3
0
3
2
1
0
0
0
0
0
0
2
0
2
1
4
1
2
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
3
2
0
2
0
1
2
0
3
1
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
1
0
2
1
0
0
1
0
0
0
2
0
0
0
0
2
1
0
0
0
2
0
0
1
0
2
4
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
3
0
0
0
2
1
1
0
3
0
0
0
0
2
0
0
0
0
2
0
3
0
2
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
2
0
0
0
0
2
0
1
0
0
0
0
2
0
0
1
2
0
0
6
2
0
0
0
0
0
0
0
1
3
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
4
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
1
0
2
1
1
1
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
2
0
0
1
2
0
0
1
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
4
9
1
0
0
0
0
2
1
0
2
2
1
3
1
1
0
0
0
0
0
0
2
3
0
0
0
0
0
0
2
1
0
2
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
4
0
0
0
0
1
1
0
0
2
0
1
2
0
0
0
2
0
0
0
0
0
0
2
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
3
0
0
1
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
1
2
0
1
1
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
2
0
0
0
0
0
0
2
2
0
0
2
0
0
2
1
4
0
2
1
2
0
3
0
0
0
0
0
0
0
1
0
2
2
0
7
2
1
0
0
0
1
0
0
2
0
0
1
0
0
0
5
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
2
0
0
0
1
1
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
1
0
0
1
0
2
0
0
1
0
2
0
0
0
0
2
0
0
0
2
0
0
1
2
0
0
2
0
2
0
1
0
0
2
5
0
0
0
1
1
0
2
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
3
0
3
0
1
0
0
0
0
1
1
0
0
2
2
1
2
0
0
0
1
1
2
0
1
2
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
3
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
1
2
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
2
2
0
1
0
0
0
0
0
0
0
0
2
0
2
0
1
1
0
0
2
0
1
0
0
0
2
0
0
0
0
4
1
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
1
2
0
2
0
1
0
2
0
0
0
0
0
0
1
0
0
1
0
2
0
2
0
0
0
2
2
0
2
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
2
0
1
0
1
0
0
2
1
1
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
3
0
2
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
2
4
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
2
0
1
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
2
0
0
0
1
1
0
1
1
0
2
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
1
0
0
0
3
1
2
0
0
1
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
2
1
0
1
0
0
0
1
0
2
0
0
0
2
1
0
0
2
0
3
2
1
0
0
0
1
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
2
0
0
0
1
0
0
3
2
2
0
0
2
0
0
2
0
1
0
1
0
0
0
0
0
2
1
2
0
0
0
0
0
1
1
0
5
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
2
1
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
1
3
0
0
0
0
0
1
0
2
0
3
2
0
2
1
0
2
2
0
0
0
0
2
0
0
0
0
2
2
0
1
0
0
2
0
0
0
2
0
0
0
0
1
0
0
1
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
1
0
0
2
2
0
0
1
0
1
0
1
0
1
0
0
0
1
0
2
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
3
0
1
0
0
0
2
0
0
0
0
1
2
0
0
0
1
0
3
0
0
1
0
1
0
2
0
2
0
0
3
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
1
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
1
2
1
2
3
2
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
2
3
0
2
0
0
0
2
0
0
1
0
0
0
0
0
2
0
3
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
2
0
1
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
1
2
3
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
1
0
1
3
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
1
2
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
3
0
0
0
0
0
0
2
0
0
3
0
0
1
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
3
0
0
0
1
2
1
1
0
0
4
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
4
1
1
2
5
2
0
0
0
2
0
0
0
1
0
2
0
0
0
1
1
0
1
1
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
1
0
0
0
1
0
0
2
0
0
0
7
1
0
2
3
1
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
2
3
2
0
1
3
0
1
1
0
0
2
0
1
0
0
0
1
1
0
2
0
0
0
1
1
0
0
0
2
0
3
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
1
2
2
1
2
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
5
0
0
0
0
0
0
2
1
0
2
1
0
0
0
0
2
4
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
2
0
1
1
0
1
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
3
2
0
1
1
1
0
0
0
0
5
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
2
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
2
1
0
0
0
0
0
0
2
0
1
0
0
0
2
0
2
1
0
0
0
0
1
2
2
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
1
0
0
2
5
0
2
0
0
2
0
0
0
0
2
1
1
0
4
0
2
0
0
2
0
1
0
0
0
1
1
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
2
1
1
0
0
0
0
2
0
1
0
0
1
0
0
1
1
0
0
0
0
1
2
2
0
0
0
0
2
3
0
0
3
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
2
1
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
4
0
0
0
2
1
0
0
0
0
1
1
1
0
0
0
2
2
2
1
0
0
1
1
2
0
4
0
0
2
2
4
0
0
1
0
0
0
2
1
2
1
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
2
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
1
1
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
2
0
2
0
1
0
2
0
0
2
2
1
2
0
0
1
0
0
0
0
0
1
0
1
2
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
7
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
1
1
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
2
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
1
0
1
1
0
1
0
0
0
0
1
0
0
0
2
0
0
0
3
0
0
0
1
0
3
2
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
3
0
0
2
2
0
0
0
0
0
1
0
0
0
7
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
4
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
1
0
1
0
1
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
2
0
0
0
0
0
1
2
0
3
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
2
2
0
0
0
0
0
0
0
0
0
3
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
1
0
1
0
1
0
1
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
1
2
0
1
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
2
2
0
0
1
0
0
1
0
0
2
0
1
1
2
0
0
0
0
1
2
1
2
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
1
0
1
1
0
0
0
1
1
0
3
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
2
0
2
0
0
0
0
1
1
2
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
2
1
0
1
2
1
2
0
3
1
0
0
0
1
0
0
0
3
0
0
1
3
0
0
0
4
0
0
1
2
2
0
1
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
2
0
0
1
3
0
2
0
0
2
0
0
1
2
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
4
0
0
2
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
2
0
0
2
0
1
0
1
0
0
0
1
0
2
0
0
2
1
0
0
1
0
0
3
0
0
0
0
0
2
2
0
0
1
0
0
0
1
0
0
0
1
0
2
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
2
1
1
2
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
3
0
2
0
1
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
2
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
5
0
2
0
0
0
0
2
2
0
2
1
2
1
0
2
0
0
0
0
0
2
2
0
3
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
2
0
0
0
1
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
1
2
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
2
0
0
2
0
2
1
0
0
0
1
0
0
0
5
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
5
0
0
0
0
0
1
1
0
0
0
0
0
3
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
3
0
0
1
2
0
0
1
0
0
0
2
2
0
0
0
2
2
0
2
0
3
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
3
1
0
0
0
0
0
0
0
1
0
1
0
0
0
2
2
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
1
0
0
0
1
3
1
0
3
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
1
0
0
3
0
2
2
0
0
0
1
2
0
0
0
0
2
0
2
2
0
1
0
0
1
0
2
1
0
2
0
0
0
0
2
2
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
3
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
2
0
0
1
1
2
0
0
1
1
0
3
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
2
2
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
1
0
1
2
0
0
0
0
0
1
0
2
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
1
0
2
1
2
0
0
2
0
0
0
1
1
0
1
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
2
4
0
0
0
0
0
1
0
2
0
2
1
0
1
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
3
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
2
0
2
0
3
0
0
1
0
0
0
0
3
0
0
1
0
0
0
2
0
1
2
0
0
0
1
1
0
2
1
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
3
1
0
1
0
1
1
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
1
1
0
0
0
3
0
0
0
0
0
0
0
0
2
3
2
1
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
2
0
0
0
0
1
0
0
0
0
2
2
0
2
0
2
0
0
0
0
0
2
2
0
0
0
0
0
1
2
2
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
1
0
2
0
0
0
0
0
0
0
1
4
0
3
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
2
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
1
0
2
0
2
0
0
0
5
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
2
1
0
0
0
0
0
0
0
0
0
0
4
0
1
2
0
2
0
0
0
1
0
0
0
0
1
0
0
2
1
2
1
0
0
0
1
0
2
0
0
2
0
1
0
4
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
1
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
2
0
1
0
0
2
2
0
1
0
0
1
0
3
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
2
0
2
1
0
1
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
3
0
1
0
2
1
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
5
0
1
0
2
0
0
2
0
0
0
2
0
1
1
2
0
0
0
0
0
0
0
2
2
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
2
0
5
0
0
2
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
5
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
1
0
2
0
0
3
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
3
0
0
0
0
1
0
0
0
0
0
1
2
3
0
0
0
0
0
0
1
0
1
1
0
0
0
0
2
0
0
0
0
0
2
1
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
1
3
2
0
0
0
1
0
0
2
0
0
0
0
0
0
1
2
2
2
1
2
2
3
0
0
2
0
0
2
0
0
1
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
3
0
0
1
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
2
2
1
2
0
2
0
0
0
2
0
6
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
3
0
2
0
0
2
0
0
0
2
1
0
0
0
0
0
0
2
0
0
2
0
2
0
2
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
2
1
0
0
0
1
1
0
0
0
3
10
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
4
2
1
0
0
0
1
2
0
0
0
0
3
0
0
0
2
0
0
2
2
0
2
1
0
0
1
0
2
0
1
0
1
1
0
0
0
0
1
0
1
0
1
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
1
0
0
1
0
0
0
2
1
0
0
0
2
0
0
2
2
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
2
1
0
0
0
0
2
0
0
0
0
2
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
2
1
2
0
0
3
1
0
0
0
0
2
0
1
0
1
0
1
0
0
3
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
1
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
1
8
0
2
0
1
2
1
0
2
0
0
0
0
0
2
3
0
0
0
0
2
1
0
1
0
0
0
1
6
2
0
0
1
0
1
2
2
0
0
0
0
0
2
6
0
2
2
0
1
1
0
1
0
0
0
0
1
0
1
2
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
2
0
4
2
0
0
0
2
1
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
1
0
2
0
0
1
0
0
0
0
1
0
1
1
4
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
2
3
3
0
0
0
0
0
3
1
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
1
0
1
0
0
0
0
0
1
1
1
1
0
1
0
0
0
0
0
0
0
2
0
1
2
1
1
0
0
0
0
2
0
0
2
0
0
1
0
0
1
0
0
2
0
0
0
0
2
1
1
0
0
0
0
2
1
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
2
2
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7
0
1
0
0
0
1
0
0
1
0
1
0
0
0
2
0
2
0
0
1
1
0
0
0
0
0
0
0
1
1
2
0
2
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
5
0
1
0
0
0
2
1
1
0
0
0
0
1
0
0
1
0
0
0
3
0
1
0
0
2
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
1
1
0
0
0
1
4
3
4
2
1
0
0
0
0
8
0
0
1
0
0
1
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
1
2
0
0
0
0
0
0
1
1
2
1
1
0
2
0
0
1
2
0
1
0
2
0
3
1
0
0
0
0
0
2
0
0
8
0
1
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
3
0
0
0
3
0
2
1
0
2
0
0
0
0
0
0
0
0
3
1
0
1
0
2
0
2
2
0
0
1
0
0
0
0
1
0
1
2
0
0
0
0
0
0
2
0
0
0
0
2
1
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
3
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
3
1
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
1
0
2
0
0
0
0
3
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
1
1
0
1
0
1
2
0
2
0
0
0
0
1
0
0
0
1
0
1
0
0
1
1
2
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
2
3
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
4
0
0
0
2
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
2
2
1
0
0
0
1
1
1
2
0
0
1
0
0
2
0
2
0
0
1
1
0
0
2
0
0
0
0
4
1
0
1
2
1
1
2
2
0
2
0
0
0
4
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
2
0
2
0
0
0
0
1
2
0
0
0
1
0
0
0
0
1
2
0
1
0
0
2
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
2
0
0
2
2
1
0
1
0
2
1
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
2
4
0
2
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
3
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
3
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
1
0
3
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
2
2
0
2
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
1
1
0
2
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
1
2
1
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
1
0
2
0
1
0
0
2
0
0
2
0
0
2
0
0
2
0
1
2
2
0
1
2
2
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
2
2
0
0
0
0
3
1
0
0
2
0
1
0
1
2
0
0
0
0
9
0
2
0
0
2
2
2
0
6
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
1
1
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
3
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
2
2
1
2
0
0
2
0
0
2
1
0
0
1
2
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
2
2
0
0
0
0
0
1
0
0
0
1
1
1
0
2
1
0
0
1
0
0
1
0
1
0
0
0
0
2
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
2
2
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
3
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
1
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
1
0
0
0
2
2
2
2
0
0
3
0
1
0
1
2
0
1
0
0
0
0
1
0
0
2
1
0
0
2
1
0
1
1
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
1
2
0
0
1
4
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
2
0
0
3
1
0
0
0
0
2
0
1
0
2
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
1
0
2
2
0
1
0
2
1
0
0
0
2
1
0
0
0
1
1
1
0
2
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
6
0
0
0
0
2
0
1
0
1
0
0
2
1
1
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
3
1
2
0
2
0
0
0
1
0
0
0
1
0
3
1
0
1
0
1
1
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
2
0
0
0
3
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
1
1
2
0
1
2
0
0
0
0
0
0
5
1
0
2
0
0
3
0
2
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
1
1
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
6
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
2
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
3
0
0
2
0
1
0
0
1
0
1
1
2
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
1
1
3
0
1
1
0
0
0
3
0
3
0
0
0
0
0
0
0
0
0
2
0
2
1
2
0
2
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
1
0
0
2
5
2
0
0
0
1
0
1
0
0
1
0
3
0
0
0
0
3
2
2
0
0
4
0
0
0
2
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
3
0
0
0
2
0
1
0
0
2
0
0
0
14
0
1
0
0
2
0
1
0
0
2
0
0
4
0
0
1
0
1
0
0
0
0
0
0
0
0
0
3
1
0
1
0
0
0
0
0
2
0
1
0
1
0
0
1
0
0
2
0
0
0
0
1
0
2
0
0
0
0
1
2
2
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
3
0
2
0
1
0
0
0
1
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
2
0
0
2
0
0
3
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
2
0
0
1
2
1
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
1
0
3
0
3
1
4
0
2
0
0
0
1
2
0
0
2
0
0
0
2
0
0
8
1
0
0
0
1
1
1
0
3
2
1
0
0
0
1
0
0
0
0
0
1
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
3
1
0
1
2
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
2
0
2
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
2
6
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
4
0
1
0
1
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
2
1
0
0
2
2
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
3
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
1
0
0
1
0
1
0
0
0
4
0
2
2
0
1
2
0
0
0
0
3
0
0
0
2
0
0
0
0
0
1
2
2
1
4
0
0
1
0
0
2
2
0
0
2
4
0
0
0
3
0
0
0
0
0
1
0
0
3
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
1
2
1
0
0
0
0
1
0
0
0
0
0
0
2
0
4
0
0
2
0
0
1
0
2
0
2
0
0
3
0
0
0
2
0
0
1
0
0
0
2
0
0
1
0
0
1
0
0
6
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
2
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
3
2
0
0
0
2
0
0
0
0
0
1
0
1
2
0
0
0
1
0
0
0
0
5
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
2
0
0
2
0
0
2
1
1
0
2
3
2
1
0
1
1
0
1
2
0
1
0
0
2
0
0
0
3
0
2
0
0
2
1
0
0
2
2
1
0
0
2
0
0
0
0
0
0
1
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
2
0
0
2
2
2
0
2
0
0
1
2
0
1
1
0
0
2
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
1
0
0
0
0
2
2
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
1
3
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
1
0
0
0
0
3
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
2
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
1
2
0
0
0
0
0
0
0
0
2
0
1
0
0
2
3
0
0
1
2
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
4
0
0
0
0
2
2
3
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
1
2
0
1
0
0
2
0
2
2
0
1
1
1
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
1
2
0
2
1
0
0
2
0
0
0
0
0
0
0
1
2
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
1
2
0
0
0
0
4
0
1
1
0
1
0
2
0
2
0
0
3
0
0
0
0
0
0
0
0
0
1
2
2
0
0
2
1
0
2
0
1
5
1
0
0
0
0
1
1
1
1
0
0
1
0
1
0
0
0
0
0
2
0
0
1
0
0
0
1
3
0
0
0
2
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
2
0
1
2
0
0
0
0
0
2
0
3
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
2
0
0
2
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
3
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
2
0
0
0
2
0
2
2
1
0
1
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
1
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
2
0
2
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
1
0
0
0
1
0
0
0
1
1
0
2
0
0
0
0
0
0
3
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
1
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
3
0
0
0
0
0
0
0
0
3
2
2
0
1
0
0
0
0
0
1
0
0
3
0
2
0
0
2
0
0
0
2
1
0
2
1
0
0
0
5
2
0
2
0
0
1
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
2
0
0
1
5
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
2
0
0
0
3
2
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
1
0
2
0
2
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
1
1
0
0
1
1
0
5
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
1
1
0
2
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
2
2
0
1
0
2
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
2
0
0
1
0
0
1
0
0
2
0
1
0
2
2
0
1
0
0
0
2
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
6
1
0
1
0
0
0
0
0
0
1
2
0
1
2
0
0
0
0
0
0
0
0
0
2
0
1
0
1
1
0
0
0
0
0
0
0
5
0
0
1
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
2
0
2
0
2
0
1
0
1
0
0
2
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
2
0
0
2
0
5
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
1
0
0
0
2
0
0
2
0
2
0
1
0
0
1
1
0
1
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
6
0
0
0
0
0
1
2
2
0
0
2
0
0
0
0
1
0
2
0
2
0
1
0
0
1
0
0
0
0
0
0
0
2
0
2
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
1
1
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
2
1
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
1
0
1
0
0
1
0
1
0
0
0
0
2
0
0
0
0
3
0
1
1
0
0
0
0
0
3
1
0
0
3
0
2
0
0
1
0
0
2
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
2
1
0
1
2
0
0
0
0
0
0
0
1
0
2
1
6
0
0
1
0
0
0
0
2
0
0
0
0
0
1
1
0
0
4
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
1
0
1
1
0
0
0
0
3
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
2
2
0
0
0
0
0
0
2
0
0
0
1
0
1
1
2
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
1
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
2
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
2
0
0
1
1
0
1
3
2
0
0
2
1
2
2
0
2
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
3
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
3
0
4
1
2
0
0
3
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
2
0
0
2
0
5
0
2
2
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
3
0
0
0
1
2
0
2
0
0
2
0
0
2
2
0
2
0
0
0
0
0
2
1
0
0
0
1
0
0
3
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
2
6
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
2
0
2
2
0
0
3
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
1
0
0
7
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
5
2
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
2
2
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
1
2
0
0
1
0
0
0
1
1
0
0
3
0
1
2
0
1
1
0
3
2
0
1
0
0
1
1
2
1
1
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
1
0
0
0
2
0
0
0
0
0
2
0
0
1
1
0
1
4
1
0
0
0
0
0
1
0
0
0
0
0
1
4
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
2
2
2
2
0
0
0
1
0
0
2
0
0
0
1
0
0
1
2
0
0
0
0
3
0
1
2
0
2
0
2
0
0
2
0
0
2
2
0
3
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
4
2
2
0
0
0
0
2
2
1
1
2
1
0
0
1
0
1
2
0
2
0
0
0
1
3
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
1
1
0
0
2
0
1
0
0
0
2
1
0
0
0
0
1
0
1
2
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
2
1
2
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
3
0
0
0
0
1
2
0
1
1
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
7
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
9
2
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
1
1
0
0
0
0
1
2
0
0
0
0
2
0
0
2
0
0
1
0
2
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
2
0
2
0
1
0
0
0
1
0
0
0
2
0
2
0
1
4
0
1
2
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
3
0
0
0
1
0
0
1
0
0
1
2
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
1
0
0
6
0
0
0
0
2
0
0
0
4
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
1
0
0
0
0
0
0
0
0
1
0
2
0
2
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
3
4
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
4
0
0
0
0
0
0
0
2
1
1
0
0
0
0
1
0
0
1
0
0
1
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
2
2
0
2
0
0
2
0
1
0
2
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
1
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
4
0
0
2
0
0
1
1
0
0
0
0
0
0
2
2
0
2
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
3
0
1
0
0
0
1
0
0
0
1
0
0
2
0
0
2
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
1
2
3
0
1
2
1
0
0
0
0
0
0
1
0
2
0
0
0
1
0
2
1
0
0
0
1
2
0
0
0
1
1
2
0
0
0
0
0
2
0
0
0
1
0
1
0
2
1
2
7
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
1
1
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
1
4
2
0
0
2
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
1
0
0
0
0
0
0
0
2
1
0
2
4
0
0
0
0
0
1
0
1
1
1
2
0
0
0
0
0
1
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
1
1
1
0
0
3
1
0
0
0
2
0
3
0
1
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
2
0
0
2
1
0
2
0
0
2
0
0
0
1
0
1
0
1
2
0
1
0
0
0
0
0
2
1
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
2
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
1
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
3
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
1
1
0
0
0
3
0
0
0
0
1
0
0
1
0
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
3
0
0
1
1
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
3
0
0
0
1
0
1
0
0
2
0
0
0
0
1
0
2
0
0
1
1
0
0
1
2
0
3
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
2
1
3
0
1
1
0
1
0
0
0
1
0
0
0
2
0
0
1
2
0
0
0
4
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
2
2
1
0
1
0
0
0
2
0
0
0
0
0
0
2
2
0
1
0
1
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
3
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
3
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
1
2
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
2
1
0
1
1
1
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
2
1
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
1
1
0
0
0
2
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
2
0
1
0
0
1
2
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
2
3
0
2
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
3
0
0
0
0
2
2
0
1
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
2
2
0
1
0
1
2
0
1
0
1
0
0
2
0
0
0
0
2
0
0
2
0
2
1
0
1
0
0
2
0
1
1
0
0
1
0
0
0
0
1
5
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
2
4
2
1
2
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
2
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
1
0
0
0
1
0
2
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
1
1
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
1
0
1
0
0
2
2
0
0
0
2
0
1
0
2
2
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
3
0
0
0
0
0
1
2
0
0
0
1
2
0
0
0
0
0
2
2
2
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
1
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
12
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
2
3
0
0
0
1
0
0
0
0
0
1
1
0
1
0
1
0
0
2
0
1
0
0
1
2
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
2
1
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
14
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
2
0
0
2
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
3
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
1
1
1
0
1
0
0
0
0
1
2
0
2
0
3
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
2
0
3
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
6
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
2
2
2
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
1
2
0
0
1
1
0
0
2
0
0
1
0
0
2
0
6
1
0
0
0
0
0
2
1
1
1
0
2
2
0
0
0
0
1
1
1
0
0
2
2
0
0
1
0
2
1
0
0
0
0
1
2
0
3
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
1
0
1
0
0
0
0
0
1
0
0
2
0
0
0
2
0
2
1
0
0
0
0
0
1
0
0
0
1
1
1
1
2
1
0
1
0
0
0
0
0
0
2
1
3
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
1
0
1
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
2
2
2
0
0
0
0
1
2
1
0
0
0
0
0
0
2
0
0
1
0
0
1
2
0
0
0
0
0
0
1
2
1
1
0
0
2
1
0
0
0
1
0
0
2
0
0
3
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
1
2
0
0
1
0
0
1
0
0
0
0
1
2
2
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
2
0
0
0
1
0
1
1
4
2
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
1
1
0
2
1
0
0
2
1
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
3
0
2
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
2
2
0
3
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
1
2
2
1
1
1
1
0
0
2
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
3
2
0
0
2
1
1
0
0
1
1
0
2
2
0
0
4
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
1
0
1
0
3
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
2
0
2
0
1
0
1
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
2
1
1
1
0
0
0
0
1
0
0
5
0
0
1
1
0
0
0
0
0
0
0
3
0
0
0
2
0
2
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
2
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
7
2
0
1
0
0
0
0
1
2
0
0
0
0
0
1
0
0
1
2
2
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
2
0
0
2
2
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
5
0
2
2
1
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
1
2
0
0
0
1
2
0
0
0
1
1
2
2
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
1
3
2
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
2
0
0
1
0
0
0
2
1
1
0
0
1
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
2
0
0
1
0
2
0
0
8
0
2
2
0
0
1
1
0
0
0
0
0
0
0
1
0
2
0
1
3
0
1
0
0
0
0
1
0
0
0
0
0
2
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
2
0
5
0
0
1
0
1
2
1
0
2
0
0
0
0
0
0
3
1
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
2
1
0
0
1
0
0
0
2
2
1
1
2
2
0
0
0
0
2
0
0
0
0
0
2
1
0
1
0
0
0
0
2
0
0
1
2
0
2
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
2
1
2
0
2
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
1
3
1
0
2
0
0
0
0
2
1
2
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
2
1
2
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
2
0
0
0
1
0
0
0
1
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
2
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
1
0
0
2
0
3
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
2
0
0
0
0
0
2
3
0
0
0
0
0
2
0
0
0
0
0
0
0
7
0
0
0
0
0
1
2
0
0
2
1
1
0
0
1
0
0
0
0
0
0
2
0
0
6
0
0
0
1
1
0
5
0
0
2
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
1
0
0
0
2
0
0
2
1
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
2
0
2
0
0
0
3
0
0
2
0
1
0
0
2
0
0
2
0
0
0
0
0
1
0
0
3
0
1
0
0
1
3
0
0
0
1
0
0
2
0
2
0
0
0
1
1
2
0
0
0
1
0
0
0
0
0
0
2
1
2
1
0
0
0
3
0
0
0
0
0
1
0
0
0
2
1
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
3
0
0
2
0
0
2
0
0
0
2
0
0
2
0
1
0
2
0
2
2
0
1
1
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
1
1
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
1
0
3
1
1
0
0
0
0
2
0
0
0
2
0
0
0
1
2
0
0
0
1
2
0
1
0
1
0
0
0
0
0
0
0
0
0
5
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
2
0
0
2
0
1
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
1
0
1
1
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
4
0
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
4
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
1
0
0
0
0
1
0
1
2
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
1
2
2
0
0
0
0
1
0
0
0
0
0
3
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
1
1
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
1
0
1
0
0
3
2
0
1
0
0
0
0
2
1
2
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
2
1
0
0
3
0
0
0
1
0
0
0
0
0
2
1
0
0
1
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
8
0
0
0
0
0
0
0
0
2
0
0
4
1
0
2
0
0
0
3
0
0
2
0
0
0
0
0
1
0
2
1
1
0
1
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
1
4
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
4
0
0
0
2
0
0
1
0
0
1
0
0
2
3
0
2
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
2
0
2
3
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
1
0
0
0
1
2
2
0
0
0
2
0
0
0
0
0
0
2
0
1
0
3
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
1
1
0
2
0
2
0
1
2
0
0
1
1
4
1
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
2
0
1
0
1
0
0
1
0
1
0
1
2
0
2
1
0
0
2
1
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
7
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
3
0
2
0
0
0
0
2
0
0
2
1
0
0
0
1
0
0
2
2
0
0
0
0
0
0
3
0
0
0
1
0
0
1
0
0
0
0
0
1
0
2
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
1
0
2
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
2
0
0
3
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
2
2
2
0
0
1
0
2
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
2
1
1
2
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
2
1
0
0
0
0
2
2
0
3
0
0
0
1
3
0
0
1
2
0
0
0
2
2
2
0
3
0
0
0
0
0
2
2
0
1
0
2
0
0
4
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
3
0
1
0
2
0
0
0
0
0
2
0
2
0
2
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
4
0
1
0
0
0
2
0
0
5
0
0
2
0
1
2
0
0
0
1
0
0
0
0
0
0
0
1
0
3
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
2
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
3
0
2
0
2
1
0
0
1
0
2
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
3
0
0
1
2
2
0
2
1
0
0
0
0
0
2
1
4
0
2
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
1
1
0
1
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
2
0
3
0
0
0
0
1
0
0
0
0
1
0
2
0
0
3
0
1
0
0
2
0
3
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
6
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
4
0
0
2
0
0
0
0
2
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
1
1
0
0
0
0
2
0
0
0
3
1
0
0
0
2
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
7
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
1
1
1
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
2
1
0
0
1
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
2
0
2
1
2
0
0
1
0
0
0
0
0
0
0
0
1
2
2
1
1
0
0
0
1
0
0
2
2
0
0
1
0
0
0
0
0
2
0
0
2
0
2
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
2
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
2
0
0
1
1
2
0
1
0
1
0
2
0
1
0
0
2
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
2
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
1
0
0
0
0
1
0
2
1
5
0
0
0
0
1
0
0
0
2
0
1
0
2
0
4
0
0
3
0
0
0
2
0
0
0
2
0
0
5
0
1
5
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
1
0
0
1
0
0
1
1
0
0
0
0
1
2
0
0
2
2
0
0
1
0
0
1
0
1
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
2
0
0
0
0
0
1
0
0
0
0
3
2
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
2
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
2
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
2
0
0
0
1
0
1
2
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
2
3
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
2
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
2
1
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
2
2
0
0
0
1
0
0
2
2
1
2
0
3
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
2
1
0
0
2
0
0
0
0
0
0
1
0
0
3
2
0
0
0
2
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
2
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
7
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
2
4
0
0
0
0
1
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
1
1
3
0
0
0
0
0
1
3
0
0
1
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
1
0
0
0
1
0
1
5
0
1
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
1
2
1
1
0
0
1
2
4
0
0
1
0
0
1
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
2
0
1
1
0
0
4
2
0
1
0
0
0
1
2
1
0
1
0
0
1
0
1
0
0
1
0
0
0
1
0
2
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
2
1
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
2
0
0
0
0
3
0
0
0
0
0
0
2
1
0
2
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
2
2
0
0
0
2
0
0
2
1
0
0
2
0
0
0
2
0
0
2
0
6
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
3
2
0
2
2
0
2
0
1
0
0
0
1
0
0
2
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
2
0
0
2
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
2
1
0
0
0
2
0
0
0
1
0
0
0
0
2
1
0
0
5
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
1
0
0
2
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
1
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
2
2
2
0
0
0
0
0
0
2
0
1
2
1
2
0
0
1
0
0
2
0
0
0
0
0
1
0
0
1
1
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
2
0
1
0
0
2
0
0
1
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
2
2
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
1
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
3
0
0
1
0
2
2
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
1
4
0
0
0
0
0
2
0
0
5
1
1
0
5
3
0
0
0
0
2
1
0
0
0
2
0
0
2
1
0
2
0
2
0
0
2
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
2
2
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
3
0
0
0
2
0
0
1
0
0
0
0
0
1
0
2
0
3
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
2
0
2
0
0
1
0
0
0
1
0
2
0
0
0
0
2
0
0
1
2
1
0
3
1
0
1
0
0
2
1
0
2
1
0
2
0
2
0
1
0
0
4
2
0
0
0
1
0
0
0
0
2
0
1
3
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
2
0
4
0
2
1
3
2
0
0
1
0
1
1
1
5
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
8
0
2
0
2
5
1
0
0
0
0
2
0
0
0
2
1
1
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
2
2
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
3
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
2
0
0
2
3
2
0
0
0
0
1
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
2
0
0
0
0
0
0
1
2
2
0
0
2
0
0
0
1
0
2
0
0
0
0
3
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
3
0
0
0
1
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
2
1
2
2
0
1
0
1
0
2
1
0
0
2
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
1
5
0
1
0
0
0
0
0
0
2
0
0
0
0
2
1
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
7
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
2
0
1
0
0
0
1
0
2
0
0
1
2
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
1
2
0
0
0
2
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
2
0
0
0
0
0
0
2
1
0
2
0
1
0
0
0
0
0
0
0
0
0
2
2
1
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
1
0
1
1
0
0
1
0
0
0
0
0
2
0
1
1
1
1
0
0
0
2
1
2
0
0
0
0
0
1
0
1
0
2
0
0
0
1
1
0
0
0
0
2
0
0
1
0
0
0
0
0
1
2
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
2
0
1
4
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
2
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
2
1
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
2
1
0
0
1
0
0
2
1
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
2
1
2
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
1
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
4
1
0
0
2
1
2
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
1
0
0
1
0
1
0
0
1
0
0
1
0
0
7
0
0
0
0
0
1
0
1
2
3
0
1
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
1
1
0
0
1
0
3
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
1
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
2
0
1
1
0
2
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
2
1
0
1
0
0
2
1
2
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
3
0
0
0
1
0
0
0
2
0
0
0
0
0
3
0
0
1
0
0
0
2
1
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
4
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
3
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
4
0
1
0
2
0
1
0
0
1
0
0
0
0
0
1
0
2
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
1
1
1
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
2
0
1
0
0
0
0
0
1
2
0
0
0
1
0
0
2
0
0
0
0
1
1
0
1
0
0
3
0
2
1
0
3
0
0
1
0
0
1
0
0
0
0
1
0
1
0
3
0
0
0
2
0
0
3
0
2
0
0
0
0
0
0
0
1
0
2
0
1
0
2
0
0
1
1
0
0
1
2
1
0
0
1
0
0
2
0
0
0
2
2
0
0
0
2
0
0
0
4
0
1
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
3
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
4
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
2
0
2
0
0
0
0
0
0
0
2
0
1
0
2
0
0
2
0
0
3
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
6
2
0
0
0
2
0
0
0
0
0
3
1
0
0
0
0
0
0
1
0
2
2
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
3
2
8
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
2
0
0
2
0
0
0
0
2
2
2
2
0
0
2
0
0
0
2
1
0
0
0
0
1
0
0
0
2
0
0
1
2
0
1
0
2
0
0
0
0
0
0
1
1
3
0
0
0
0
0
0
0
0
3
2
0
0
1
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
1
0
0
0
0
2
0
1
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
1
2
2
0
0
2
0
0
0
0
0
2
0
0
0
2
2
0
2
1
0
0
2
2
0
0
0
1
0
0
0
0
2
0
0
0
1
2
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
2
2
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
4
0
1
0
0
1
0
0
0
0
0
0
2
0
2
1
1
1
1
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
2
1
0
0
1
0
0
0
0
0
2
0
0
0
4
1
0
3
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
2
3
0
0
2
0
0
2
0
2
2
0
0
1
0
0
2
1
0
0
3
0
2
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
2
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
2
1
0
1
0
1
1
0
0
0
0
1
0
1
0
1
0
1
3
2
2
0
0
1
0
0
0
0
2
1
0
2
0
0
2
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
3
2
0
0
0
1
2
0
0
0
0
2
0
0
0
1
0
2
0
2
1
2
0
0
0
1
1
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
3
0
1
0
1
0
0
0
0
2
1
0
3
0
0
0
2
0
0
0
2
1
1
2
0
0
0
1
2
1
0
0
2
1
0
1
0
0
1
3
0
2
8
1
2
0
0
0
1
1
0
0
3
0
2
0
0
1
0
0
0
1
0
2
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
1
5
0
2
0
0
2
0
1
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
2
0
2
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
2
1
0
0
1
0
1
0
1
2
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
2
0
0
0
2
0
1
0
0
1
0
0
0
0
2
0
0
3
0
0
0
0
1
0
13
0
0
2
0
0
2
0
2
2
0
0
1
0
2
2
4
2
0
2
0
2
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
1
0
1
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
3
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
2
0
3
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
3
2
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
3
2
1
0
2
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
1
0
2
0
0
1
0
0
0
0
2
0
0
0
2
0
1
0
1
0
0
2
2
0
0
1
0
0
0
0
2
2
0
0
0
0
0
2
0
3
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
2
0
3
2
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
4
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
1
0
3
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
7
0
0
2
1
5
0
0
1
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
2
0
0
1
0
1
0
2
0
0
0
1
1
0
1
0
0
0
0
0
1
1
0
0
2
0
2
0
0
0
0
0
0
1
0
2
1
1
0
1
1
0
0
1
0
0
0
0
1
0
0
1
0
0
2
2
1
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
2
0
0
0
2
0
2
3
0
0
0
0
3
9
2
0
2
0
0
0
0
0
0
0
0
2
4
5
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
1
0
1
0
0
0
3
0
0
2
0
0
0
2
0
0
0
1
1
1
0
1
0
0
2
0
0
2
0
0
0
0
0
0
7
2
2
0
1
1
0
2
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
1
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
2
0
0
2
0
0
0
1
0
1
2
1
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
1
0
0
0
0
2
0
3
0
0
9
0
0
2
0
0
0
0
0
0
0
0
1
1
1
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
1
1
0
0
2
1
2
0
0
0
0
2
2
0
3
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
1
1
0
0
2
0
0
0
1
1
0
0
1
2
1
0
0
0
1
0
1
0
1
0
0
2
0
2
0
4
2
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
1
0
2
0
0
0
0
3
0
0
0
1
2
0
0
0
0
0
1
1
0
0
0
2
2
0
0
2
0
2
1
2
1
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
2
2
2
0
0
1
0
1
0
2
0
0
3
2
2
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
1
1
0
1
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
1
0
2
0
0
2
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
3
0
0
2
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
1
0
0
0
2
2
0
2
0
0
0
0
0
0
0
2
1
0
5
0
0
0
0
2
0
2
0
0
0
0
1
0
1
0
1
0
2
0
0
1
2
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
2
0
0
0
0
0
2
4
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
2
2
0
0
1
0
2
0
3
1
0
0
0
1
2
0
0
0
0
1
0
0
0
0
2
2
0
0
3
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
4
2
3
2
0
0
1
0
1
2
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
7
0
2
1
0
0
1
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
2
0
0
2
0
0
0
1
0
0
0
0
1
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
3
1
0
0
3
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
2
2
1
0
1
1
0
0
0
1
2
0
0
0
2
0
0
1
0
0
0
3
2
0
5
0
0
2
0
0
0
0
1
2
0
1
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
2
0
2
0
0
0
0
0
0
2
0
2
0
2
2
1
1
0
0
2
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
2
2
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
2
0
0
4
0
0
0
0
4
0
1
1
0
0
0
0
2
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
7
0
2
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
3
1
0
1
0
1
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
2
1
0
1
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
1
0
2
0
1
2
0
0
0
0
1
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
1
0
0
0
5
2
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
2
0
2
0
1
2
2
1
0
1
1
0
1
0
0
0
0
1
0
0
2
2
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
2
2
0
0
0
0
1
8
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
2
1
1
2
0
0
0
0
0
4
2
1
0
0
0
0
0
0
2
1
0
0
0
1
1
0
0
2
0
2
0
2
2
0
0
0
1
0
2
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
1
2
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
2
1
0
1
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
2
0
0
7
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
4
1
1
2
0
1
2
0
0
0
0
0
0
2
0
0
0
3
0
0
2
0
0
0
0
0
0
5
0
0
3
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
2
0
1
2
1
1
1
0
0
4
2
1
0
0
1
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
2
1
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
2
0
0
0
0
0
2
1
3
0
0
0
0
0
1
0
2
0
0
0
1
0
0
2
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
3
0
1
0
1
0
0
0
1
0
1
0
2
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
1
1
3
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
4
0
0
0
0
2
0
0
0
2
0
0
2
0
1
0
0
1
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
1
3
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
2
2
1
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
1
2
2
0
0
1
0
2
0
0
1
0
1
0
2
2
0
1
2
0
1
0
0
0
0
0
0
0
1
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
1
0
2
2
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
2
0
0
0
2
2
1
0
1
2
0
2
2
4
0
0
0
1
1
2
0
0
2
0
2
0
2
2
0
0
1
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
3
0
3
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
2
1
0
1
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
2
0
1
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
2
0
0
0
0
0
3
0
0
2
1
0
1
0
2
0
0
0
0
0
0
1
0
2
0
1
1
0
0
0
1
2
1
0
1
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
3
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
2
0
0
0
0
0
1
0
2
0
2
0
0
0
1
0
0
0
1
0
0
2
0
2
1
0
2
0
1
0
1
0
2
0
1
0
1
2
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
1
0
0
1
0
2
1
0
2
0
1
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
4
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
1
0
3
0
2
0
1
1
0
0
3
0
0
0
1
2
0
0
0
0
1
2
0
0
0
0
1
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
2
0
1
0
0
0
0
0
0
2
2
0
2
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
1
2
0
2
0
0
0
0
0
4
0
2
1
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
4
1
0
1
2
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
3
2
0
2
0
0
1
0
0
0
2
0
8
2
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
1
2
0
2
1
0
0
0
0
0
0
2
1
0
0
0
0
0
1
2
0
0
0
0
2
2
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
4
0
0
0
0
0
2
0
2
0
1
0
0
2
0
0
0
0
1
1
1
0
0
0
2
0
0
1
0
0
2
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
2
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
1
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
3
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
5
0
0
0
1
0
0
0
0
1
2
0
2
0
0
2
5
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
1
2
2
0
0
0
0
2
0
2
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
6
0
1
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
2
0
2
0
0
0
3
0
0
0
0
2
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
2
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
3
1
2
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
1
0
0
3
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
3
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
2
3
0
2
2
0
1
0
0
1
2
0
0
0
0
2
0
3
0
0
2
2
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
2
0
2
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
1
0
0
0
3
1
0
0
0
2
2
2
0
0
0
0
0
0
0
0
1
1
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
2
0
1
0
2
2
0
0
0
0
0
4
0
0
2
1
0
2
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
2
0
0
0
0
2
2
0
0
1
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
1
0
2
2
2
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
1
3
0
0
0
2
0
0
0
0
0
1
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
2
2
0
1
7
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
1
1
2
2
0
0
0
0
0
1
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
1
2
0
1
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
3
0
0
0
0
3
0
0
0
1
0
0
7
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
1
0
0
0
0
2
1
0
0
0
2
2
1
0
0
7
2
0
2
0
0
1
0
0
2
0
0
0
3
2
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
2
0
1
0
0
0
1
0
0
1
0
2
2
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
2
2
0
0
0
0
1
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
1
1
0
0
1
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
2
0
2
0
3
1
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
3
0
1
0
0
1
0
1
0
0
0
4
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
3
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
3
0
0
0
0
2
2
0
1
2
0
0
0
1
0
0
1
0
1
0
2
2
5
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
2
0
0
0
0
1
0
0
2
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
1
0
3
1
0
0
0
2
0
2
0
0
0
0
0
0
1
0
2
1
0
4
0
2
0
0
0
1
0
0
0
0
1
2
0
0
0
0
2
1
0
1
0
0
0
3
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
2
0
0
0
1
2
0
0
0
1
0
2
2
0
1
0
2
0
2
0
0
0
0
2
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
2
0
0
2
1
0
0
0
0
1
0
0
0
2
1
1
0
0
2
2
2
0
2
0
0
0
0
1
1
0
1
2
1
0
0
0
2
1
0
0
1
2
0
0
1
0
0
0
2
2
0
0
0
1
1
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
1
0
2
0
1
0
0
1
0
0
1
0
0
2
0
2
1
1
0
0
0
0
2
0
0
0
1
0
2
0
0
0
2
0
0
0
0
3
0
0
0
0
1
1
0
0
0
2
0
0
5
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
2
0
1
0
1
2
0
2
0
0
0
0
2
1
0
1
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
1
0
4
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
2
5
0
0
0
4
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
2
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
1
0
0
2
0
0
0
0
0
1
0
0
1
0
0
2
0
2
1
0
0
2
2
1
0
2
0
1
0
0
2
0
3
0
0
1
0
0
0
0
2
0
0
1
0
0
0
1
3
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
1
3
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
1
0
0
2
2
0
0
0
0
2
1
1
0
0
0
0
0
2
1
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
2
2
0
0
0
0
2
0
2
0
0
2
1
0
3
0
1
0
0
1
0
2
0
1
2
1
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
2
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
1
1
2
0
0
0
3
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
1
0
0
1
2
3
0
0
0
0
2
0
16
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
2
0
0
2
2
1
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
4
1
0
2
1
3
0
1
1
0
0
0
1
0
2
1
1
2
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
2
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
2
0
0
2
2
1
0
0
0
1
0
0
0
1
1
0
2
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
2
0
0
0
0
1
0
2
0
1
0
0
0
2
0
0
0
0
1
0
0
1
3
2
2
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
3
0
0
0
1
0
0
2
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
2
1
0
2
0
2
0
0
2
1
0
0
0
0
2
0
2
2
0
0
2
1
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
3
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
2
0
0
0
0
0
0
0
0
0
3
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
2
4
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
3
3
0
0
0
1
2
0
0
0
0
2
0
0
2
2
0
0
0
1
0
1
0
0
1
0
0
1
0
2
1
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
2
0
0
1
1
1
0
0
0
0
2
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
3
2
1
1
0
2
0
0
0
0
0
0
0
2
3
0
0
0
0
0
1
0
0
2
2
3
2
0
2
0
2
0
0
1
0
0
0
2
2
1
0
0
1
0
0
0
2
0
1
0
0
0
0
2
0
0
0
2
2
0
2
0
0
1
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
1
2
2
1
1
1
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
3
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
3
2
0
0
1
2
0
0
2
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
3
2
0
1
0
2
0
0
0
0
0
1
0
1
2
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
2
0
0
0
0
1
1
2
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
5
0
0
1
0
1
0
0
0
0
0
0
2
1
0
2
2
2
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
3
0
0
0
0
0
0
3
0
1
1
0
0
2
0
0
0
0
0
1
2
2
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
2
0
0
2
0
0
1
0
0
1
0
4
3
1
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
1
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
1
0
1
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
2
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
1
0
2
0
2
0
0
3
0
1
2
2
0
0
0
0
0
2
0
0
1
0
0
0
2
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
3
0
0
0
0
0
0
4
0
1
0
2
1
0
0
0
1
0
0
0
0
0
1
3
0
2
0
2
0
0
1
0
2
0
0
0
0
0
0
0
2
1
0
1
0
1
0
2
0
0
0
0
0
0
0
0
2
2
1
1
0
1
3
0
2
2
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
1
0
2
0
0
4
1
0
1
0
0
1
0
0
0
2
0
0
0
4
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
1
2
0
0
0
0
0
1
0
1
2
0
0
2
1
0
0
2
0
0
2
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
3
2
0
0
0
0
0
2
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
2
2
3
0
0
0
1
2
0
0
0
1
0
0
0
1
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
2
1
0
0
3
0
0
0
2
0
0
0
2
0
2
0
0
0
0
1
0
0
2
0
0
0
0
2
0
2
1
0
0
0
0
2
0
2
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
2
1
0
2
1
0
2
2
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
3
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
2
1
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
2
0
0
0
0
0
3
0
1
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
3
0
0
1
0
0
7
0
0
2
0
2
1
0
0
0
2
0
0
3
2
0
0
1
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
2
0
1
0
0
0
0
0
0
2
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
3
1
0
2
2
0
0
0
0
0
5
0
1
0
0
0
0
0
1
2
2
0
2
0
0
4
0
0
0
2
0
1
0
0
1
0
0
1
0
0
0
0
1
2
0
1
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
2
0
0
0
0
0
0
2
0
0
2
0
2
1
0
0
0
1
0
0
0
0
2
0
0
3
0
0
0
1
0
1
3
0
0
0
2
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
2
1
0
2
0
0
0
2
0
8
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
1
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
2
4
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
2
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
2
2
0
2
0
1
1
0
0
0
0
1
2
0
1
0
0
3
0
2
0
0
1
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
2
0
2
0
0
0
0
2
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
1
0
0
0
0
2
2
2
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
9
4
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
3
2
2
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
2
0
0
0
0
2
0
0
1
0
5
1
0
0
0
0
0
0
0
6
0
0
0
2
0
0
2
1
0
2
0
0
0
2
0
0
2
0
0
0
0
1
0
1
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
3
1
0
2
2
0
0
0
0
0
7
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
6
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
1
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
2
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
4
0
1
0
0
0
1
0
1
0
0
0
0
1
0
2
1
2
0
1
0
1
2
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
14
0
0
0
1
0
2
1
0
2
0
0
4
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
1
0
0
2
1
1
0
0
2
0
0
0
0
1
2
0
1
0
0
1
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
2
1
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
4
0
0
1
0
0
2
3
2
1
0
0
0
0
0
0
1
1
0
1
1
0
0
0
2
1
2
0
0
0
0
0
0
0
2
0
5
2
0
0
2
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
5
0
0
1
1
0
0
2
0
2
2
2
2
1
0
2
2
0
2
0
1
1
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
1
0
0
1
0
0
2
0
1
2
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
1
0
0
4
9
1
0
0
0
0
5
0
0
0
0
0
0
1
2
2
4
0
1
1
0
0
0
0
0
0
0
2
0
0
2
0
2
2
0
1
0
0
6
0
0
0
0
0
0
4
0
0
2
0
0
1
1
1
1
0
0
0
1
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
5
0
0
0
0
0
0
0
7
0
0
0
2
0
0
2
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
2
0
0
4
1
1
2
0
0
0
0
0
2
1
0
0
0
0
1
4
0
0
0
1
0
0
0
2
0
1
2
1
0
1
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
3
0
0
2
3
2
2
0
0
0
0
1
0
0
0
0
0
3
0
1
0
1
0
0
0
2
0
1
1
0
0
0
3
0
0
2
0
0
0
2
2
0
0
1
0
0
0
0
0
0
2
0
2
0
3
1
1
0
0
1
0
0
1
0
0
0
2
0
3
3
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
1
1
0
1
0
0
2
5
0
0
0
2
0
2
2
0
0
1
0
0
0
0
0
0
0
1
0
2
0
4
0
0
0
0
0
1
1
0
0
0
0
2
2
0
0
0
0
0
1
0
0
2
0
1
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
3
0
0
2
1
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
2
1
0
0
3
0
0
1
0
0
2
1
0
0
3
1
2
0
0
1
1
0
0
0
0
2
0
1
0
0
1
2
2
0
0
0
3
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
2
0
1
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
1
0
1
2
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
5
0
0
0
3
0
2
0
1
2
0
0
0
0
2
0
2
0
2
2
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
3
0
0
1
0
0
0
3
0
2
1
0
3
0
0
0
0
0
0
1
0
2
0
1
1
1
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
9
0
0
0
1
0
0
4
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
3
2
2
0
2
1
0
0
0
0
0
0
0
0
0
1
1
0
2
1
0
0
2
0
0
0
0
0
2
1
0
0
0
0
1
0
2
0
2
0
0
2
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
3
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
3
1
1
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
4
0
0
1
1
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
1
0
0
0
0
1
0
0
1
0
1
2
0
0
0
0
0
0
1
1
1
2
0
0
0
0
0
0
0
0
1
2
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
2
1
1
0
0
0
0
0
0
2
1
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
3
4
0
0
0
1
0
0
3
0
0
3
2
0
0
0
0
0
2
2
2
0
0
0
0
0
3
2
0
0
2
0
0
2
1
0
0
0
0
2
1
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
3
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
1
2
0
0
2
0
8
0
0
0
0
0
3
0
2
1
0
0
1
0
0
1
0
0
3
1
0
0
0
0
0
0
0
0
0
0
3
0
0
1
2
0
0
1
2
1
1
4
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
1
2
0
1
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
2
1
0
0
0
0
0
0
0
0
1
1
0
2
1
3
8
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
3
0
0
0
1
2
3
2
0
0
0
1
0
0
0
0
1
2
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
2
2
0
0
1
0
0
0
0
0
1
0
0
2
1
2
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
2
1
0
0
2
0
0
2
0
1
1
0
0
0
2
0
3
0
1
0
0
0
0
0
0
0
2
0
0
2
0
2
0
1
2
0
0
0
1
0
0
0
0
0
0
2
0
2
2
0
0
0
2
2
0
0
0
0
2
0
0
2
1
2
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
2
1
0
1
0
2
0
1
0
0
0
0
0
3
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
1
1
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
1
0
0
1
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
2
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
3
0
3
1
0
0
1
0
0
2
0
0
0
0
0
1
1
2
0
1
0
0
0
0
3
2
1
1
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
1
0
6
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
5
2
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
2
3
0
0
0
0
3
0
0
2
1
0
0
0
0
0
0
0
3
0
2
0
3
0
0
0
3
2
0
0
0
0
0
2
2
2
2
0
0
5
2
0
0
0
1
1
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
6
0
0
1
0
2
0
2
2
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
5
0
2
0
1
2
0
0
0
2
0
0
0
0
1
2
1
0
1
1
0
0
0
0
0
0
2
0
0
1
0
3
0
1
0
1
0
0
0
2
3
2
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
1
3
0
0
2
0
2
1
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
2
0
1
0
0
0
0
2
2
0
0
0
1
0
1
0
1
0
0
1
0
0
2
2
0
0
0
0
0
0
2
0
2
0
0
1
1
0
0
0
2
0
0
0
2
1
0
1
0
3
0
0
0
0
0
0
0
0
0
2
0
3
0
0
1
0
1
0
0
2
0
2
0
0
0
1
1
0
2
0
4
1
0
0
0
4
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
2
0
2
0
0
0
0
2
0
0
1
0
0
0
2
1
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
3
0
0
2
2
0
0
2
2
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
3
1
0
0
0
5
0
1
0
0
0
0
13
0
0
0
2
3
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
1
0
0
0
0
3
0
0
0
1
1
0
0
0
1
2
2
0
0
1
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
1
2
7
0
1
2
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
2
2
0
0
1
0
2
0
0
0
0
4
2
0
1
1
0
2
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
2
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
1
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
2
0
0
2
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
1
0
1
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
1
1
1
1
0
0
1
5
0
0
0
1
1
0
1
0
0
2
1
0
1
0
2
1
0
1
3
2
3
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
2
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
3
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
4
0
0
1
3
0
0
0
2
0
0
0
0
0
1
0
0
0
0
4
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
2
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
3
1
0
2
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
2
2
2
3
0
0
2
2
2
2
0
0
1
0
0
3
2
0
2
2
0
0
0
3
0
0
0
2
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
2
2
1
0
0
1
0
2
0
1
1
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
1
2
2
1
0
0
0
0
3
0
0
1
2
1
0
0
0
2
0
0
0
5
0
0
0
1
1
0
2
0
0
0
3
2
0
0
0
1
1
2
0
0
0
0
0
0
0
3
0
3
0
0
1
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
2
0
0
0
1
0
1
0
1
2
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
2
2
2
0
1
1
0
0
1
2
0
2
0
1
1
2
0
0
2
0
0
1
1
0
0
1
0
0
0
1
0
0
3
0
0
2
2
0
0
1
1
0
2
1
0
2
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
4
0
0
0
0
1
2
0
2
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
2
1
0
2
0
0
0
2
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
2
2
0
2
0
0
1
0
0
1
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
2
0
0
2
2
0
0
0
2
2
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
1
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
3
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
2
0
0
0
0
1
0
2
0
0
0
2
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
6
0
2
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
5
0
0
1
1
1
1
0
0
0
0
2
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
1
3
1
0
0
0
0
0
1
1
1
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
2
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
1
0
0
1
0
0
1
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
1
2
0
0
0
0
0
0
8
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
3
0
0
2
1
1
1
0
2
1
0
0
0
0
0
2
8
1
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
2
0
0
1
1
0
2
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
1
0
1
0
2
1
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
2
0
1
0
0
2
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
2
0
0
2
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
2
3
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
1
1
0
2
1
2
0
0
0
3
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
1
0
0
2
0
2
0
0
0
2
3
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
1
2
1
0
0
2
0
1
0
0
0
1
0
1
1
2
1
0
0
0
0
6
1
0
0
0
0
0
0
0
3
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
3
0
1
0
1
0
0
0
0
2
0
0
0
6
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
3
2
2
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
2
0
1
2
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
2
0
0
0
3
0
1
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
1
1
0
0
1
1
2
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
1
0
2
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
2
2
0
0
0
1
0
2
0
0
0
0
3
0
0
1
2
1
2
0
0
0
1
0
0
1
0
3
0
0
0
2
1
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
3
3
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
2
0
0
0
2
0
1
1
0
0
2
0
0
0
3
0
0
1
2
0
1
3
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
1
0
0
0
1
1
1
0
1
0
0
1
2
2
0
0
0
0
0
0
0
0
0
1
7
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
4
2
0
0
0
0
5
0
0
0
0
1
0
2
2
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
1
2
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
2
0
2
0
2
1
0
1
1
0
0
0
0
0
1
1
0
3
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
3
0
1
0
1
0
1
1
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
1
0
0
0
2
0
0
2
1
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
3
0
2
0
0
0
0
1
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
2
1
0
0
0
6
2
2
0
0
0
0
0
0
0
2
1
2
0
0
2
0
2
0
0
1
0
0
1
4
0
1
0
0
0
1
0
1
2
1
0
1
0
0
0
0
1
1
0
0
0
0
2
1
1
0
2
1
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
2
1
1
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
2
0
2
1
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
1
1
0
0
2
3
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
2
0
0
2
0
0
3
0
0
0
0
2
0
0
0
2
0
0
1
2
0
0
0
0
1
0
0
0
1
1
9
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
3
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
1
0
0
2
0
2
0
0
0
2
0
0
0
0
0
2
2
4
0
2
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
2
0
0
0
2
0
1
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
1
0
0
0
0
1
0
0
0
5
1
0
0
3
0
0
1
0
0
1
1
0
0
0
1
0
1
0
0
2
0
0
2
0
0
2
0
0
0
1
0
2
2
2
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
5
1
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
1
0
0
0
0
0
0
2
0
0
1
3
0
2
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
1
2
2
0
0
0
0
0
0
1
1
2
0
3
0
0
2
2
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
2
0
0
0
1
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
2
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
2
0
1
0
1
1
2
0
0
0
1
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
2
0
0
2
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
12
0
2
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
1
0
0
1
1
0
2
0
2
1
0
2
0
0
0
2
0
1
2
1
1
0
2
0
2
0
0
4
0
0
0
2
0
0
2
2
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
1
0
0
0
2
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
2
0
0
1
0
0
1
2
0
1
1
0
1
0
1
0
1
0
0
0
0
0
0
1
3
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
3
2
0
3
1
2
2
0
0
1
1
0
0
1
0
0
3
0
0
0
0
0
0
3
1
0
2
0
0
0
0
0
0
1
0
0
0
2
0
2
2
0
2
0
0
0
0
0
2
2
0
0
0
0
3
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
3
0
0
0
0
0
0
0
0
2
0
1
0
0
1
1
0
1
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
1
0
2
0
1
0
0
3
0
0
0
2
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
1
0
1
0
2
0
0
1
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
1
0
1
0
0
0
0
2
0
3
0
0
1
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
1
0
2
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
1
0
2
0
1
0
1
1
3
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
4
2
0
0
0
0
0
0
1
0
0
2
1
0
2
0
0
0
1
0
2
0
0
0
1
0
0
2
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
2
0
0
0
2
0
1
0
0
0
1
0
0
1
0
5
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
1
1
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
2
0
0
1
0
1
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
2
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
1
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
3
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
1
1
0
2
0
0
1
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
2
1
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
4
0
0
2
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
3
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
1
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
2
1
0
1
1
0
0
1
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
3
0
0
2
1
2
0
1
0
0
2
0
0
2
0
0
2
0
0
1
2
2
1
0
0
0
0
0
0
4
0
0
1
0
1
2
0
0
0
2
0
1
2
0
0
0
2
0
0
0
0
0
0
1
0
1
2
1
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
1
0
0
1
0
0
0
0
0
0
2
1
1
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
1
2
1
0
0
0
0
0
1
1
0
1
2
0
0
0
0
0
0
0
2
2
0
1
0
0
2
0
2
0
0
0
0
3
0
0
0
0
3
0
0
0
1
0
1
0
0
0
1
2
0
0
3
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
1
0
0
1
2
0
3
0
2
3
0
0
0
2
2
0
0
0
1
0
0
0
0
0
2
0
2
2
0
2
0
1
0
0
0
0
0
0
1
0
0
3
0
0
0
0
2
0
0
1
0
2
3
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
2
0
2
0
1
0
0
0
0
0
0
1
1
0
1
2
0
1
0
2
0
0
5
0
1
0
2
0
0
2
2
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
1
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
3
1
0
0
2
2
0
0
0
2
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
1
1
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
6
2
1
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
1
0
1
2
0
0
0
1
0
1
1
1
0
0
0
0
1
0
1
0
0
0
0
0
2
1
1
0
0
1
0
0
0
0
0
0
4
0
0
0
0
2
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
4
2
0
0
2
0
0
0
0
0
3
2
0
1
0
2
0
0
1
0
0
2
0
0
0
1
0
1
0
2
3
0
3
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
2
2
0
0
0
0
0
0
1
0
0
0
2
0
0
1
3
2
0
0
0
2
0
2
1
0
0
0
2
0
2
2
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
1
1
0
0
0
0
2
0
1
0
0
0
0
0
2
0
1
2
2
0
2
0
0
1
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
1
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
2
1
0
0
0
0
1
0
0
0
3
0
3
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
1
0
1
0
0
0
1
3
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
1
0
1
4
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
1
0
0
1
0
0
0
2
2
3
0
0
0
0
0
0
0
1
1
2
0
2
0
1
1
0
2
1
0
1
3
0
2
0
0
0
1
0
0
0
0
4
0
1
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
1
0
2
0
0
2
0
2
0
2
2
0
2
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
1
2
2
0
0
1
2
0
0
0
0
0
0
2
2
0
0
1
2
0
2
0
2
0
0
0
0
5
0
1
1
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
1
0
0
0
1
2
0
0
0
0
0
1
2
0
0
2
0
2
0
2
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
4
2
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
4
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
3
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
1
0
0
0
1
2
2
0
1
2
1
0
0
0
1
1
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
1
0
0
2
0
0
0
0
1
0
2
0
0
0
1
2
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
1
1
0
0
0
0
0
2
0
0
2
0
0
1
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
2
0
3
0
0
0
0
0
0
1
0
2
2
0
1
0
0
3
0
0
2
0
0
0
0
1
2
3
0
0
0
0
3
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
1
2
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
1
0
0
2
1
0
0
1
0
2
0
0
0
3
0
0
2
2
0
1
0
0
0
0
0
0
1
0
2
0
0
2
1
0
0
1
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
3
0
0
0
0
0
2
2
0
1
0
0
1
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
4
2
0
0
0
0
2
3
2
0
1
0
2
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
2
0
0
1
1
2
0
2
2
1
8
0
1
0
2
0
0
2
0
0
0
0
1
3
0
0
0
0
0
3
0
1
0
0
0
2
0
0
2
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
1
0
0
2
2
0
1
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
1
3
0
1
0
2
0
0
1
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
2
0
0
4
0
0
2
0
0
0
1
1
0
0
0
0
1
2
0
0
2
1
0
2
2
0
0
1
1
2
0
1
0
0
0
2
5
0
1
0
0
2
0
0
2
0
0
0
0
3
0
0
0
0
2
0
2
0
1
0
1
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
1
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
2
0
0
0
0
2
1
0
2
0
0
2
0
0
0
0
0
1
1
0
0
2
0
0
1
2
2
0
9
0
0
1
0
2
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
1
1
0
5
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
2
2
0
2
0
0
0
0
1
0
2
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
2
0
0
2
1
0
0
0
0
0
2
0
0
1
2
0
0
3
1
1
0
0
0
2
0
0
0
2
0
2
0
1
0
0
0
3
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
3
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
1
3
3
0
0
0
0
0
0
0
1
0
0
1
0
0
3
0
0
2
1
2
1
0
0
2
0
3
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
2
0
0
0
0
1
0
1
0
1
0
0
0
2
2
0
0
1
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
4
1
3
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
2
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
3
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
2
1
0
0
0
0
0
0
1
2
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
1
2
0
1
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
2
1
0
1
1
0
0
1
1
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
1
2
0
0
1
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
2
2
2
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
1
0
0
2
2
1
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
1
0
2
0
0
0
0
2
0
0
2
0
0
1
1
1
2
0
2
2
0
0
0
2
0
1
2
0
1
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
2
1
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
1
1
0
1
0
0
0
0
2
0
0
0
1
0
2
2
1
0
0
0
0
1
0
0
2
0
3
0
2
2
1
0
1
0
0
0
0
0
0
2
0
2
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
1
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
3
1
1
1
0
0
0
1
0
1
0
0
1
1
0
1
1
0
1
1
2
0
0
0
0
1
2
0
1
0
0
0
0
0
7
0
2
1
0
0
3
0
0
2
0
0
0
0
0
0
2
1
0
1
0
0
0
1
2
2
2
1
0
2
2
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
5
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
4
1
0
2
1
0
0
1
3
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
3
2
0
0
0
1
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
2
0
0
2
1
0
0
1
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
1
0
0
0
0
0
3
0
1
0
0
0
0
2
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
2
1
0
0
1
0
1
2
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
5
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
2
1
0
2
0
0
0
1
0
4
2
0
1
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
1
0
0
0
0
2
0
2
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
2
0
0
0
0
0
0
1
1
0
1
0
0
2
0
0
6
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
2
1
1
2
0
2
2
0
0
1
0
2
2
2
0
1
0
0
0
0
0
0
0
0
2
2
0
0
3
0
0
0
1
0
0
0
0
0
5
0
0
0
0
2
0
2
0
3
1
1
1
0
0
0
0
0
2
0
1
0
3
0
0
0
0
0
1
0
0
0
0
0
0
3
1
0
1
2
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
1
0
0
2
0
1
1
1
1
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
2
0
0
1
0
2
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
2
0
1
0
0
2
0
0
0
0
1
1
0
1
1
1
0
0
0
1
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
2
0
2
0
0
2
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
2
1
5
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
1
1
2
1
0
0
0
3
4
1
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
2
0
1
1
1
1
0
2
0
0
0
0
0
2
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
2
0
0
3
1
0
2
0
0
0
4
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
5
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
3
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
2
2
2
5
0
0
0
1
0
1
1
2
2
0
0
0
1
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
3
1
0
1
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
1
0
0
3
2
0
0
0
2
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
1
2
1
0
1
1
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
2
2
0
0
1
2
1
0
2
0
0
0
0
0
2
1
2
0
0
2
0
0
2
0
1
2
0
0
0
0
1
0
3
1
0
0
0
0
0
0
2
0
0
1
0
0
0
1
4
0
2
0
0
0
0
1
1
0
0
2
0
2
1
0
0
0
0
0
1
2
0
1
0
0
2
2
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
1
0
0
0
1
1
3
0
2
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
1
0
0
0
2
0
1
5
0
0
0
0
2
2
1
0
0
0
0
0
2
0
0
0
2
2
0
0
1
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
2
2
0
1
0
1
1
0
2
0
0
2
3
2
2
0
2
0
0
1
0
0
0
2
2
2
0
2
2
1
0
2
0
2
0
0
0
0
1
0
0
2
2
0
0
0
0
2
1
0
0
1
0
2
0
1
0
0
1
0
0
0
0
0
0
2
0
1
2
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
2
2
1
0
1
0
1
0
1
0
2
0
1
1
0
0
0
0
3
2
0
1
2
0
0
0
5
0
2
0
4
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
1
2
0
0
1
0
0
0
2
2
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
2
1
0
0
1
0
1
1
0
0
0
0
3
2
0
2
0
0
0
1
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
1
0
0
2
2
0
0
2
2
2
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
2
0
1
1
0
0
0
0
0
0
1
0
2
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
1
3
1
1
0
0
0
0
0
2
3
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
2
0
0
0
0
0
2
1
0
4
0
3
1
2
0
0
0
0
0
4
1
0
0
0
2
0
2
0
0
0
1
2
0
0
0
0
0
2
2
2
2
0
1
0
0
2
2
2
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
2
0
0
1
0
0
1
0
1
0
0
0
0
0
0
3
0
0
1
0
0
0
2
1
0
0
0
0
0
1
2
4
0
1
0
2
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
2
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
2
0
1
0
1
1
0
0
0
2
0
0
0
2
0
1
0
0
1
0
0
0
2
0
0
0
2
4
0
1
0
0
4
0
0
1
0
0
0
1
0
0
0
1
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
2
0
0
0
1
1
0
1
0
0
2
2
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
2
0
0
1
0
0
2
0
1
1
0
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
3
2
0
2
0
0
2
0
0
1
0
2
0
0
0
1
0
1
0
0
0
0
1
0
0
0
2
1
0
0
1
0
0
0
0
0
2
0
0
3
0
1
0
3
1
0
0
0
0
0
2
0
0
1
1
0
0
1
1
0
0
1
0
0
1
1
2
1
0
0
1
0
0
2
1
0
1
3
2
2
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
2
1
0
0
1
2
0
1
0
2
0
0
0
0
0
2
0
1
1
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
2
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
1
2
0
1
0
1
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
2
0
0
0
0
0
0
0
0
1
0
2
4
1
2
0
2
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
1
1
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
1
1
0
0
0
0
0
0
2
0
0
1
2
0
1
2
1
2
0
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
3
0
2
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
2
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
1
0
2
0
0
0
0
2
0
1
0
0
1
0
1
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
2
0
0
2
0
2
0
0
2
1
0
0
2
2
0
0
0
0
0
0
1
0
0
0
1
0
0
1
2
0
2
0
4
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
1
0
1
0
2
0
2
0
2
0
2
0
0
0
2
1
0
2
0
2
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
3
2
2
1
0
1
0
2
0
0
1
1
2
0
0
1
1
0
2
1
0
0
0
0
2
0
2
3
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
3
0
2
0
0
0
0
2
0
0
0
4
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
1
2
2
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
3
0
5
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
5
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
1
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
2
0
0
0
1
2
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
3
3
0
1
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
3
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
3
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
2
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
3
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
2
1
1
0
0
2
0
0
2
0
1
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
2
1
0
0
0
0
0
2
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
3
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
2
2
0
0
2
2
2
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
2
0
2
2
1
2
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
2
2
1
0
0
1
2
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
3
2
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
3
0
0
0
0
0
0
0
0
0
0
3
0
5
0
2
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
1
2
0
2
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
2
4
0
0
0
0
0
0
0
0
0
1
2
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
2
2
0
2
1
0
1
0
2
2
0
0
0
0
3
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
4
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
2
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
3
1
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
2
2
0
2
0
0
0
0
0
3
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
4
0
2
0
2
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
3
1
0
4
0
0
0
0
0
0
2
0
0
1
2
0
1
0
0
0
1
1
1
0
1
2
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
3
1
0
1
0
2
0
0
0
0
1
1
2
2
0
4
1
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
2
0
0
0
0
10
0
2
4
0
1
0
0
0
4
0
1
2
0
0
0
0
2
0
0
1
0
0
0
0
3
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
5
1
0
0
0
0
1
1
2
0
0
0
1
0
0
1
0
0
1
2
0
1
0
1
0
2
1
1
0
0
2
0
0
0
1
0
0
1
0
2
1
0
1
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
3
0
0
2
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
3
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
2
2
0
0
0
0
0
2
0
2
10
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
4
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
1
0
0
0
1
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
3
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
2
1
1
0
0
1
0
2
0
3
1
1
0
0
1
0
0
0
1
1
2
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
1
0
2
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
1
2
0
1
2
0
0
0
0
0
0
3
0
0
0
2
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
1
0
3
0
1
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
1
4
0
1
0
0
0
0
0
2
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
2
0
0
2
1
2
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
3
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
1
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
7
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
2
2
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
4
0
2
2
2
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
2
0
0
0
0
0
1
0
0
0
2
4
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
2
1
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
2
1
3
0
0
0
0
1
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
3
1
0
1
0
0
0
0
0
0
1
0
0
0
1
2
1
0
5
1
1
0
0
0
0
2
0
2
0
0
1
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
2
0
0
0
0
0
0
2
1
2
0
0
1
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
2
0
1
0
1
0
0
0
0
0
0
0
2
0
1
3
0
0
0
0
0
0
2
0
0
0
0
2
0
2
1
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
1
0
1
4
2
1
0
0
2
0
1
0
0
4
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
1
0
0
0
0
2
1
2
1
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
1
0
0
2
2
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
2
1
0
0
0
1
0
0
1
2
2
3
0
0
0
0
2
0
0
2
2
0
0
1
0
1
0
0
0
0
2
0
0
1
0
0
0
0
3
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
2
0
0
1
0
2
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
2
5
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
2
1
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
2
0
0
1
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
2
0
0
0
0
2
0
0
1
1
1
4
2
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
1
0
2
0
1
0
1
0
0
1
0
0
0
4
2
0
0
0
0
0
0
2
0
0
0
2
2
1
0
0
2
0
0
0
2
0
0
2
0
4
1
1
0
0
0
0
2
0
0
0
0
1
1
3
0
0
0
2
2
1
0
0
1
0
1
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
2
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
2
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
2
2
1
2
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
1
2
0
0
1
0
1
0
0
1
2
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
1
0
1
0
1
0
0
0
2
0
0
1
1
0
0
0
1
0
0
1
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
2
3
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
2
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
3
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
2
2
2
0
2
2
1
0
0
0
2
0
1
0
2
1
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
4
0
0
0
0
4
0
0
0
0
2
0
1
0
0
0
3
1
2
1
10
1
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
2
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
1
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
3
0
1
1
0
2
1
0
0
0
0
0
2
0
0
0
2
0
0
1
0
2
0
1
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
2
2
0
2
1
0
0
0
0
0
0
0
1
1
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
1
2
0
0
0
2
2
2
0
0
2
2
0
0
1
0
0
0
0
1
2
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
1
0
2
1
0
0
0
2
0
3
0
0
0
1
0
0
0
2
0
0
0
1
2
2
0
1
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
2
2
0
0
0
2
3
1
2
2
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
2
0
1
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
2
1
0
0
0
0
2
0
1
0
0
0
0
3
1
4
1
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
3
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
2
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
1
1
0
2
0
0
1
1
2
1
0
0
0
0
0
0
1
3
0
0
1
0
0
0
0
0
0
2
0
1
1
0
2
0
3
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
1
2
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
2
1
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
4
1
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
4
0
1
0
1
0
0
1
3
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
3
0
0
2
2
2
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
1
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
2
2
0
2
2
0
1
0
0
2
1
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
3
0
0
0
0
2
0
0
1
0
1
0
2
1
1
2
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
2
2
3
0
0
0
3
0
1
1
1
0
3
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
2
1
1
0
0
1
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
2
0
0
1
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
1
2
5
0
0
0
0
0
0
0
0
2
3
0
0
0
1
0
2
0
0
2
0
0
0
1
0
0
0
1
2
2
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
2
0
0
0
0
0
1
0
0
2
0
1
0
0
0
2
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
1
0
0
2
4
0
0
0
0
0
2
0
5
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
2
1
2
2
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
2
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
3
2
1
0
0
2
0
2
0
0
2
0
0
0
1
0
1
0
0
2
1
0
0
1
2
1
0
1
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
3
1
0
0
0
0
0
1
1
0
0
0
0
0
0
4
0
0
3
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
3
0
0
0
2
0
0
0
2
0
2
0
2
0
2
1
0
0
0
1
0
2
2
0
1
3
0
0
2
1
0
0
3
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
1
1
0
0
0
0
1
3
0
0
0
2
3
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
1
2
0
0
1
0
0
0
1
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
6
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
3
6
1
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
1
2
0
2
0
2
0
0
0
0
0
0
0
0
4
0
3
0
0
1
0
0
0
0
1
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
2
0
2
0
1
0
0
0
0
0
0
1
0
0
0
1
2
1
0
4
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
2
0
0
0
1
2
0
2
0
0
0
2
0
0
1
0
0
2
0
0
2
2
1
2
0
0
0
0
0
0
1
0
1
0
0
0
1
0
2
0
3
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
2
1
0
0
0
0
0
2
1
0
0
0
0
0
0
3
1
2
0
1
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
1
1
0
0
1
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
3
0
3
0
0
1
0
0
0
3
0
2
3
0
0
0
1
1
0
0
0
0
2
1
0
2
1
0
0
4
1
1
2
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
1
0
0
2
1
1
0
1
1
0
1
1
0
0
3
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
1
0
0
0
0
0
0
1
2
0
0
0
0
2
0
2
0
2
0
0
1
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
1
2
0
0
1
0
0
1
0
0
2
3
0
0
0
1
0
0
0
2
1
0
0
1
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
1
2
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
1
1
0
0
0
0
0
2
1
0
0
0
1
0
1
0
2
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
1
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
2
2
0
2
0
0
0
1
0
2
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
1
0
0
4
0
1
0
2
0
0
0
1
0
1
0
0
0
1
0
0
2
1
0
0
1
0
0
0
0
2
1
0
0
0
1
2
0
2
0
1
0
1
0
0
1
2
0
0
2
0
2
0
0
0
0
1
0
0
1
0
2
2
1
0
2
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
1
0
0
3
0
2
1
1
0
0
3
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
2
2
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
1
0
0
2
2
0
1
2
0
2
0
0
0
0
0
2
0
0
0
0
1
4
0
0
3
0
3
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
1
0
1
0
0
1
3
0
0
1
2
1
2
2
3
0
1
0
2
2
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
2
1
0
2
1
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
1
2
1
2
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
1
0
0
2
5
1
0
2
0
0
0
1
0
1
1
0
0
1
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
2
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
2
0
0
0
2
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
1
1
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
1
0
1
0
0
2
1
2
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
3
0
0
2
0
1
1
0
0
1
0
0
1
0
1
4
2
2
1
0
1
0
0
0
0
0
1
3
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
2
0
0
2
2
0
2
0
0
0
1
0
1
1
2
0
1
0
0
2
0
0
10
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
3
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
1
0
0
1
1
0
0
2
0
0
0
0
1
0
1
0
0
0
1
0
0
2
0
1
0
4
0
0
0
0
0
0
2
2
0
1
0
1
2
0
1
2
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
2
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
1
0
2
2
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
2
0
0
2
0
2
2
0
0
1
0
2
0
0
1
1
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
2
0
1
2
0
0
2
1
0
0
0
1
0
1
1
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
3
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
1
1
0
3
2
0
0
1
0
0
3
0
1
2
5
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
2
0
0
1
2
0
2
1
0
2
0
0
0
2
0
2
0
0
0
0
0
0
1
0
2
1
2
0
0
1
0
3
0
2
2
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
2
2
0
0
2
1
0
0
1
2
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
2
0
0
1
2
0
0
1
0
0
2
0
0
0
0
0
2
1
0
0
1
1
0
3
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
2
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
1
0
0
0
0
3
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
2
1
0
1
1
2
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
1
2
0
0
4
0
0
1
0
0
0
0
1
0
0
0
0
3
0
0
0
2
0
0
0
0
2
2
1
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
2
3
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
4
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
2
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
2
0
0
0
1
0
1
0
0
2
0
1
2
0
2
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
1
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
1
3
0
0
1
2
3
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
1
3
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
3
1
2
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
1
0
0
0
0
2
1
0
1
0
0
0
0
0
1
0
0
2
0
0
1
1
0
0
0
1
0
0
0
0
0
0
2
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
1
2
1
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
1
1
2
0
0
2
0
0
1
0
0
2
0
0
0
0
0
2
1
1
6
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
3
0
0
0
0
1
0
0
0
0
0
2
3
0
0
2
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
1
2
0
2
1
2
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
1
0
0
0
0
1
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
1
1
0
0
0
2
2
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
2
1
1
0
0
1
0
1
2
0
0
0
1
0
2
0
1
1
0
0
1
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
3
2
1
0
0
2
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
1
2
0
0
0
1
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
2
2
1
2
2
0
0
0
0
0
0
0
2
0
0
3
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
5
0
1
0
2
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
3
1
0
2
0
0
0
0
1
0
0
1
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
2
0
1
0
0
2
0
1
0
3
0
0
0
2
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
3
0
2
1
0
0
1
0
0
2
0
10
0
0
0
0
2
0
1
0
0
0
1
2
0
0
0
0
2
2
2
1
2
1
0
0
0
1
0
1
2
0
0
0
1
0
2
0
0
0
2
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
2
1
0
0
0
0
0
2
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
2
1
2
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
1
0
0
0
0
2
0
1
2
4
1
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
3
0
0
0
2
0
2
0
0
4
0
0
1
2
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
2
2
0
0
1
3
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
1
1
0
0
2
1
1
0
0
0
0
1
0
0
2
0
0
0
2
0
1
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
2
1
0
0
0
1
0
0
2
2
0
0
0
1
3
0
0
0
0
0
0
0
1
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
4
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
3
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
2
1
2
0
2
0
2
0
0
0
4
1
0
3
0
1
2
2
0
0
0
0
2
3
0
3
0
0
0
2
0
0
0
0
0
1
0
0
1
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
2
1
0
2
0
1
1
1
1
0
0
0
0
1
2
0
2
1
0
0
0
0
0
0
2
0
2
0
0
1
0
1
0
0
0
0
1
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
3
2
0
0
0
1
2
2
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
1
1
1
0
2
1
0
2
0
0
0
0
2
0
0
0
2
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
2
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
3
2
0
1
0
2
0
0
2
2
0
0
0
2
1
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
2
4
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
3
0
0
1
0
2
2
2
0
1
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
1
0
0
0
1
2
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
7
0
2
0
0
5
1
0
2
0
0
0
0
7
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
1
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
1
2
2
0
0
0
0
0
1
0
0
1
1
2
4
2
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
2
0
2
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
1
0
0
0
1
3
0
0
2
0
0
0
0
0
0
2
2
1
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
1
0
2
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
1
0
0
1
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
3
0
0
2
0
0
2
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
2
0
2
0
0
0
2
0
3
1
0
0
0
0
0
0
0
2
1
0
1
0
0
0
2
0
0
0
0
0
1
2
0
3
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
1
0
0
7
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
1
2
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
1
2
0
1
0
3
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
2
2
0
0
0
0
5
0
0
0
2
1
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
2
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
1
1
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
2
1
0
1
2
1
0
0
1
0
2
0
2
0
1
0
0
2
2
1
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
3
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
2
0
1
0
1
0
2
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
1
0
0
5
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
2
0
0
0
1
1
1
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
2
0
3
0
0
0
0
0
0
0
0
6
0
0
0
0
5
0
0
2
1
0
0
0
0
1
0
0
0
0
1
2
0
2
0
0
0
0
1
1
0
2
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
1
2
0
3
1
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
2
1
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
2
0
0
0
0
2
0
0
1
0
0
2
0
0
0
2
2
1
0
0
0
2
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
1
0
1
0
0
0
0
1
1
2
2
4
0
0
1
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
2
1
1
3
0
0
1
0
0
1
0
4
2
0
0
0
0
0
2
0
0
6
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
2
0
2
0
0
0
0
1
0
0
0
2
1
0
0
2
6
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
1
0
0
2
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
2
0
0
1
0
0
0
0
2
1
2
0
0
1
0
1
0
2
0
0
2
0
0
0
2
1
1
1
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
3
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
2
0
1
1
0
3
0
0
0
1
0
1
1
0
0
0
2
3
0
0
0
0
0
0
1
2
1
1
2
1
0
0
1
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
3
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
2
0
1
2
0
0
0
0
0
0
0
3
0
2
0
0
1
2
0
0
0
1
0
0
0
2
1
0
0
1
2
0
2
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
2
0
0
1
0
2
1
0
0
0
0
0
0
0
2
0
0
1
1
1
0
2
0
1
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
3
0
2
0
3
0
1
1
0
0
0
2
0
1
2
0
0
2
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
2
1
1
1
2
0
1
0
0
0
1
0
0
1
0
0
1
2
0
0
0
1
1
0
2
0
0
0
1
0
0
0
0
1
0
0
2
1
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
1
1
2
0
0
0
0
1
0
4
0
1
0
0
0
0
2
1
0
0
0
2
0
0
1
0
0
0
0
0
0
2
1
0
1
2
0
2
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
1
0
0
0
1
1
0
0
0
3
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
2
0
1
2
1
0
0
0
1
0
3
1
1
2
1
0
0
0
0
0
2
0
1
1
0
0
3
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
1
0
1
0
0
2
2
0
1
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
2
1
0
1
0
2
4
0
0
0
1
2
2
0
2
1
0
0
3
0
2
0
0
0
1
0
0
0
0
2
0
2
3
0
2
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
5
2
0
1
0
0
2
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
1
2
1
0
0
2
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
2
0
1
1
1
2
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
3
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
5
0
2
0
0
1
0
0
0
2
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
2
0
0
4
0
0
0
1
0
0
0
6
0
0
2
0
0
3
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
3
2
1
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
2
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
8
1
3
0
0
2
2
0
1
1
0
0
0
0
0
1
0
1
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
2
0
0
2
0
0
2
0
2
2
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
2
1
0
2
2
0
2
0
2
0
0
3
1
0
0
0
0
0
0
1
3
0
0
1
0
0
0
3
2
0
2
0
0
0
0
2
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
2
2
0
1
1
1
1
2
0
0
1
0
2
0
0
0
2
0
1
0
0
0
0
0
1
0
1
2
0
2
0
0
5
1
1
1
0
0
1
1
0
2
0
0
0
0
0
5
1
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
2
0
0
0
2
0
1
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
2
2
0
2
2
0
0
0
0
2
0
0
1
2
0
1
0
2
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
1
1
0
0
2
0
0
0
2
0
0
2
0
2
0
1
1
0
2
0
0
1
0
2
0
2
0
5
2
1
2
1
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
4
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
3
2
4
0
1
0
0
0
0
1
0
2
0
1
0
0
1
0
2
0
0
0
0
4
0
0
0
1
0
0
0
2
2
0
1
0
2
0
0
2
2
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
3
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
1
0
0
0
0
1
1
2
0
0
0
2
0
1
2
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
6
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
3
0
0
5
2
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
1
0
0
0
1
2
2
0
2
0
2
2
2
0
0
0
1
0
2
2
0
0
0
2
1
0
2
0
0
2
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
1
0
1
0
0
0
0
1
2
0
0
0
2
2
2
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
2
2
2
0
0
0
1
0
2
1
0
0
0
2
0
0
1
0
0
2
0
2
1
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
7
2
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
4
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
2
0
0
0
2
0
0
0
2
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
3
1
0
0
0
0
3
0
0
2
0
0
2
0
1
0
3
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
4
1
0
0
0
0
13
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
2
2
0
0
0
2
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
3
1
1
0
0
1
0
0
0
0
0
1
3
1
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
1
2
0
2
2
2
0
0
5
1
0
0
0
2
0
3
0
2
0
0
0
0
0
0
0
1
0
1
2
4
0
0
0
2
2
1
2
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
2
3
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
1
0
2
0
0
0
0
0
0
5
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
2
0
2
0
1
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
1
0
2
2
2
3
0
0
0
1
1
0
2
0
2
1
2
1
1
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
1
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
2
0
0
0
1
1
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
2
1
0
0
0
0
0
1
2
0
0
1
0
0
0
0
1
0
2
0
0
2
0
0
0
1
0
2
3
0
2
0
0
2
0
0
0
0
0
3
0
0
0
0
2
0
0
2
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
1
0
0
0
0
2
0
1
2
2
0
0
2
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
2
1
0
1
0
0
1
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
1
3
0
0
0
0
3
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
1
1
0
0
5
0
1
0
0
0
0
0
0
0
1
3
3
0
1
1
0
0
2
0
2
0
1
0
0
0
0
0
1
0
0
0
0
2
0
3
0
2
0
0
1
1
0
1
0
0
2
1
2
1
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
2
0
0
2
2
0
1
2
1
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
1
1
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
1
0
0
0
0
2
2
0
2
0
0
0
0
0
2
1
9
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
2
4
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
3
0
2
0
2
0
0
1
1
0
0
0
3
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
2
0
1
0
0
0
0
2
0
0
1
0
4
0
1
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
3
0
2
1
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
3
0
0
0
0
2
0
1
0
2
1
1
2
2
2
0
1
0
0
0
0
0
0
0
0
2
0
1
1
0
2
2
0
0
1
2
1
2
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
4
0
0
1
2
0
0
0
0
0
0
0
1
2
0
1
0
1
1
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
1
3
0
0
1
1
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
1
1
2
2
0
0
0
2
1
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
3
0
0
0
0
2
2
0
1
0
0
1
0
1
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
2
0
1
0
2
0
0
0
2
0
0
0
3
0
0
0
0
0
1
0
0
3
0
0
1
0
1
0
0
1
0
0
1
2
0
0
0
0
1
1
0
0
0
2
1
1
1
0
1
0
0
2
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
2
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
2
1
2
2
0
0
6
0
0
0
0
1
0
2
1
2
0
2
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
2
1
0
1
1
2
1
1
0
0
0
0
0
1
0
0
0
2
0
2
2
0
0
1
1
0
2
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
1
0
0
1
0
0
1
1
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
5
0
3
0
0
1
2
0
0
2
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
2
3
0
0
0
0
0
2
0
1
0
0
3
0
0
0
0
0
0
2
0
1
0
0
0
0
0
3
0
0
0
0
2
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
5
2
0
0
0
1
0
1
0
0
0
0
3
0
2
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
2
3
0
2
0
0
1
0
2
0
1
3
1
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
2
1
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
1
0
0
0
0
5
0
2
0
0
0
0
1
2
0
0
1
0
0
0
1
0
1
0
2
0
2
2
1
0
0
0
1
0
2
0
0
2
1
0
0
0
0
0
0
1
3
1
0
2
4
1
4
0
1
0
1
0
2
2
2
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
2
0
2
0
0
0
0
0
2
0
1
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
2
3
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
3
3
1
1
0
0
0
2
0
1
0
0
7
0
0
0
0
1
0
1
2
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
3
1
0
0
1
0
0
0
0
0
0
2
1
0
0
0
1
0
1
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
3
0
3
0
3
1
2
0
3
0
2
0
0
0
0
1
2
1
0
2
0
0
0
0
1
0
0
1
2
2
0
0
0
0
1
0
0
1
1
1
3
1
0
2
0
2
0
0
0
0
1
1
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
6
0
0
1
0
0
1
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
2
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
1
1
0
11
1
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
2
2
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
2
3
1
1
0
0
0
1
0
1
0
1
0
2
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
2
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
3
1
0
0
0
1
1
0
0
0
0
2
0
1
0
2
1
0
0
0
0
1
2
0
0
3
0
0
0
0
2
0
2
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
1
0
1
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
1
1
0
0
2
1
2
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
1
2
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
5
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
2
0
3
0
1
0
7
2
1
0
0
0
0
4
0
0
1
0
1
1
1
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
2
0
2
2
2
0
0
1
1
0
0
0
0
0
0
2
0
1
7
0
0
0
2
0
0
2
0
0
0
0
0
1
2
0
1
1
0
2
1
0
0
0
0
0
2
0
0
3
0
0
1
1
0
1
1
0
0
0
0
0
2
0
0
0
0
0
1
1
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
3
2
2
2
0
0
0
0
3
2
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
2
1
2
1
0
0
0
1
0
1
0
2
0
0
1
0
0
0
0
2
0
0
0
1
0
3
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
1
1
0
0
1
0
2
0
0
0
1
0
0
1
1
0
3
1
0
0
0
0
0
2
1
2
0
0
0
0
2
0
0
1
0
0
1
1
0
0
1
2
2
0
0
0
1
1
2
2
0
0
1
1
0
2
1
0
0
2
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
2
0
0
0
2
0
1
1
0
0
6
0
0
0
0
2
0
1
3
2
1
0
0
0
0
0
1
0
3
1
1
2
0
2
0
0
0
1
0
2
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
1
0
0
0
0
0
0
2
0
0
0
6
0
0
0
1
0
0
0
1
1
0
3
0
0
0
2
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
2
2
0
0
0
0
3
1
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
2
1
0
1
2
2
0
0
0
2
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
2
0
0
0
0
0
0
1
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
1
0
0
2
1
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
3
0
0
1
0
0
2
2
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
2
2
0
0
1
2
0
0
1
0
2
0
2
0
0
2
0
1
0
1
0
0
2
0
0
0
1
0
0
0
0
6
1
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
1
0
5
0
0
0
0
2
1
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
1
0
0
0
0
1
0
0
1
0
0
0
0
0
19
0
0
0
1
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
2
0
1
0
2
0
0
1
0
0
0
1
0
0
1
1
1
1
0
0
0
13
1
1
0
3
0
0
2
0
0
1
0
1
0
3
0
1
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
2
2
0
0
2
4
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
9
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
2
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
1
0
1
2
1
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
2
0
0
1
0
1
0
0
2
2
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
1
1
0
0
2
0
0
1
0
0
1
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
3
1
0
2
0
0
0
0
0
1
0
0
0
0
0
1
3
1
1
0
0
0
1
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
1
0
0
0
0
1
2
0
3
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
2
2
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
1
4
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
1
1
0
0
0
0
2
0
0
0
2
1
0
0
0
2
0
1
0
0
0
0
0
0
1
2
0
3
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
2
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
1
2
0
1
0
0
2
0
0
0
0
2
1
3
0
0
1
0
0
0
1
0
0
1
3
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
2
0
0
0
0
1
0
2
0
0
1
0
0
3
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
2
0
0
2
0
1
0
0
4
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
1
0
2
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
2
0
0
0
2
1
0
2
0
2
0
0
0
3
0
2
2
3
1
0
0
1
0
0
1
1
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
2
0
0
1
1
2
1
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
2
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
2
2
0
1
0
0
1
1
0
1
1
2
0
1
0
0
1
0
1
1
0
0
0
1
0
0
1
0
1
0
2
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
3
0
2
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
2
1
0
0
0
1
0
0
2
2
1
2
0
0
0
0
0
0
0
0
2
2
0
0
0
1
5
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
2
3
0
0
0
0
0
0
2
1
0
0
2
0
1
0
1
2
0
0
2
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
2
1
0
0
0
0
0
0
1
1
2
1
2
0
2
0
1
0
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
1
0
2
0
0
0
1
0
0
0
1
1
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
2
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
1
1
1
0
0
4
0
0
1
1
0
0
0
0
0
5
0
2
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
2
1
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
3
0
1
0
0
0
0
2
2
0
1
1
0
0
0
1
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
4
5
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
1
1
0
0
4
0
1
0
0
3
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
5
0
0
0
0
0
1
0
0
0
2
0
1
1
2
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
2
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
2
0
0
0
0
2
0
0
0
0
2
0
2
2
2
0
0
0
0
0
2
0
0
0
0
0
1
0
3
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
5
1
0
2
2
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
1
0
0
1
0
8
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
2
0
2
1
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
1
0
1
0
1
1
2
0
1
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
1
1
1
1
0
3
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
3
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
1
3
0
0
2
0
1
0
2
2
0
0
2
0
1
2
0
0
0
0
0
0
1
0
0
2
1
0
0
0
3
2
0
0
2
0
0
0
0
1
0
0
0
0
0
1
2
0
0
1
0
0
0
0
2
2
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
2
0
2
0
3
0
0
0
0
1
4
1
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
3
3
0
0
0
0
0
1
1
0
0
1
1
0
0
0
2
2
0
0
1
0
4
1
3
0
6
2
2
1
2
1
0
0
1
0
0
0
1
0
0
0
5
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
1
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
3
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
2
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
3
0
0
1
0
1
0
2
0
1
1
0
0
1
0
0
0
0
0
1
0
1
1
0
0
2
0
2
0
0
1
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
3
0
2
2
0
0
0
0
0
1
0
0
1
0
0
0
2
0
1
0
2
0
2
1
3
0
2
1
0
2
1
0
0
0
0
1
0
0
0
0
0
2
1
0
1
0
0
5
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
3
0
2
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
2
1
4
0
7
0
2
0
0
0
1
1
1
0
1
0
0
0
5
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
1
1
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
3
0
0
0
1
0
0
2
0
0
1
0
0
0
1
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
1
2
2
1
0
0
0
0
0
2
2
1
0
0
0
2
2
3
0
1
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
3
2
2
0
0
2
0
2
2
2
0
2
1
1
0
0
0
0
1
0
2
0
0
0
0
2
0
2
0
1
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
2
0
3
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
1
0
2
0
0
0
2
0
0
0
0
0
2
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
3
1
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
2
0
0
0
0
1
0
0
0
2
2
1
2
0
0
0
0
4
2
0
0
0
0
0
1
2
0
0
0
0
0
1
1
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
1
0
2
1
0
0
2
0
2
2
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
3
1
1
0
0
1
2
0
0
0
0
0
0
0
0
1
2
2
0
0
0
3
2
1
0
0
0
0
0
0
2
1
1
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
4
0
2
1
0
0
0
2
0
0
0
0
0
0
1
0
0
1
3
0
0
0
0
1
0
0
1
0
0
1
0
0
0
2
1
2
1
0
2
0
1
0
0
0
0
0
2
0
2
2
0
1
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
4
0
0
0
2
0
0
1
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
1
2
2
1
0
0
1
0
1
2
0
2
2
1
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
1
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
1
0
0
0
1
0
1
1
0
1
2
0
0
1
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
2
0
8
0
0
0
0
0
0
0
0
0
0
1
2
0
1
1
1
0
0
1
1
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
5
0
0
2
3
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
1
1
0
0
2
0
0
0
2
0
0
1
1
0
0
0
2
2
2
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
3
1
0
0
1
0
0
0
0
0
3
0
0
2
1
1
2
0
1
0
0
0
0
0
0
0
0
3
0
0
2
1
0
0
0
2
3
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
2
0
0
2
0
0
1
0
0
0
2
2
0
2
0
2
0
2
2
2
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
3
3
3
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
2
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
2
0
0
0
1
2
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
3
0
0
4
1
0
0
0
0
1
0
0
1
0
2
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
2
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
3
0
0
0
0
0
0
2
1
0
1
0
0
0
0
6
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
1
2
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
2
3
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
3
2
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
1
0
0
0
1
4
0
0
0
2
1
1
3
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
1
0
2
2
0
2
0
0
0
0
1
0
2
0
0
0
0
2
2
0
0
2
1
1
0
0
0
6
0
0
0
0
0
2
0
1
0
1
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
1
2
0
0
2
2
1
0
4
1
1
2
0
0
0
0
0
1
1
0
0
0
2
0
0
2
0
0
0
1
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
1
0
0
0
0
1
2
0
1
0
1
0
1
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
1
2
1
0
0
0
0
0
0
0
6
0
2
0
0
0
0
5
0
0
0
2
0
0
5
0
1
0
2
0
0
0
0
0
0
2
0
2
1
1
0
0
0
2
0
0
0
0
0
1
2
0
1
1
0
0
0
1
0
1
0
2
0
0
0
2
0
1
0
1
0
0
3
2
0
3
0
0
0
0
0
1
1
0
0
0
0
1
0
2
0
2
0
0
0
3
2
0
0
0
0
1
1
0
1
0
0
0
2
1
2
0
0
2
0
0
0
0
0
0
0
1
1
2
0
0
0
0
1
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
2
0
0
1
0
0
0
1
1
0
2
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
1
0
2
0
0
2
0
0
0
0
2
2
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
3
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
4
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
3
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
4
2
2
3
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
1
0
0
0
0
1
3
2
0
0
2
4
0
8
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
2
0
0
0
2
2
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
2
0
1
0
2
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
5
0
0
0
0
0
0
0
0
0
3
2
1
2
0
0
4
1
2
0
1
0
0
0
2
0
1
0
0
1
0
0
2
0
0
0
1
0
0
1
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
2
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
2
0
1
0
0
1
3
0
1
2
0
0
0
0
0
1
0
2
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
1
2
0
2
1
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
2
0
0
1
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
1
0
1
2
0
0
0
1
0
2
2
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
1
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
2
0
1
2
2
0
0
0
2
0
2
0
0
0
0
2
1
3
0
0
1
1
0
0
0
2
0
0
0
1
1
0
0
0
2
5
0
1
1
0
2
0
0
0
0
0
0
2
0
0
0
0
2
1
0
2
0
1
2
0
0
0
0
2
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
2
0
1
1
0
0
1
0
0
0
0
0
0
0
1
2
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
3
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
3
1
1
0
0
1
1
0
0
0
1
1
11
1
1
0
0
0
1
0
0
0
2
0
1
0
0
0
0
2
0
2
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
3
1
0
0
0
1
0
1
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
2
2
0
0
3
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
2
0
0
2
0
1
1
2
1
0
0
0
0
2
1
1
0
0
1
0
0
0
1
1
0
1
4
0
0
0
2
2
1
0
2
3
2
2
0
0
2
0
0
0
0
1
1
0
0
0
0
0
2
2
1
0
0
3
0
2
1
0
2
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
4
1
0
0
1
2
1
0
0
0
1
1
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
6
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
5
0
0
0
0
1
1
1
0
0
0
0
2
0
1
0
2
0
0
1
2
0
0
0
0
3
0
5
1
1
0
2
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
2
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
3
0
2
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
2
0
0
0
0
1
1
0
1
1
0
0
0
2
0
0
0
1
0
0
0
2
1
0
0
0
0
0
1
1
0
2
0
0
0
1
2
2
0
1
0
1
0
0
1
0
2
0
0
0
0
0
2
3
0
1
2
0
2
1
0
1
0
0
0
0
0
0
1
2
2
0
1
0
1
0
0
1
1
2
2
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
6
1
2
0
2
2
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
2
1
0
0
0
0
1
0
0
0
1
0
2
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
4
0
0
0
2
0
0
0
0
1
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
3
1
2
0
1
0
2
0
0
0
1
0
2
0
0
0
2
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
3
0
0
0
2
0
0
1
2
0
1
1
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
1
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
2
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
1
1
0
2
0
0
0
0
1
0
1
1
1
2
0
3
0
2
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
3
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
2
0
0
0
2
0
0
1
2
1
2
0
4
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
2
0
0
0
0
3
0
0
0
0
0
0
2
1
0
0
0
2
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
2
0
0
2
0
0
2
10
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
1
0
0
1
0
2
0
0
0
0
0
0
1
1
2
0
1
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
2
0
0
0
2
2
2
0
0
0
0
1
0
1
2
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
1
2
0
0
0
2
0
0
1
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
3
4
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
1
1
0
0
0
1
1
3
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
2
0
2
0
1
2
2
1
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
2
0
2
2
3
2
0
2
0
0
1
4
1
0
2
0
0
0
1
0
1
2
0
2
0
0
1
2
0
0
0
0
1
0
1
1
0
0
0
0
0
2
2
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
2
0
0
1
0
1
0
0
0
3
0
0
2
0
0
2
0
0
0
4
0
2
0
0
2
0
2
1
0
0
0
0
2
1
1
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
1
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
5
0
2
1
1
0
0
2
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
2
2
3
0
0
2
0
1
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
1
0
0
2
0
1
0
0
0
2
1
2
0
1
0
0
3
0
1
0
0
0
0
1
0
2
2
2
2
1
2
0
0
1
2
0
1
0
1
0
1
1
0
0
0
0
0
2
0
2
0
0
0
0
1
1
3
1
0
0
0
2
0
0
3
0
0
0
0
0
1
0
0
0
2
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
2
0
3
5
0
0
2
0
0
0
0
0
0
1
1
0
1
2
2
0
0
0
0
0
0
0
1
0
0
0
3
0
0
1
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
1
0
9
1
2
0
0
0
0
1
0
0
2
1
0
1
0
0
5
0
1
0
0
2
2
0
0
0
2
0
0
0
1
2
3
1
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
2
1
1
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
2
0
2
1
0
17
0
0
2
0
1
0
0
1
1
2
0
0
1
1
0
2
0
0
2
4
1
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
1
2
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
2
0
3
0
1
0
1
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
3
0
1
1
2
1
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
1
0
0
0
0
0
0
0
2
0
0
1
1
2
0
0
0
1
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
3
2
1
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
3
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
10
0
1
2
0
0
0
0
0
0
3
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
1
0
2
0
0
0
1
0
0
0
2
0
0
2
0
0
2
2
0
1
2
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
4
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
1
1
2
0
0
0
0
0
0
2
0
1
2
0
1
0
1
2
1
0
1
0
1
0
0
0
0
3
0
0
0
0
2
1
0
1
0
0
0
0
2
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
2
0
0
0
2
1
2
1
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
2
1
0
2
0
0
1
0
1
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
1
2
2
0
1
0
0
0
1
1
0
2
0
5
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
3
0
0
1
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
1
2
0
0
0
1
1
0
0
2
0
0
1
0
1
1
0
0
0
2
0
0
0
0
0
2
2
1
0
0
0
2
1
0
0
0
2
2
2
2
3
0
1
1
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
1
1
0
0
0
2
0
0
2
0
1
0
1
0
0
1
0
0
0
0
4
0
0
2
0
0
0
1
2
0
2
0
1
0
0
0
0
2
1
0
0
4
0
0
1
2
0
2
0
0
3
0
0
1
2
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
2
0
2
0
0
0
0
0
0
0
0
1
1
2
1
0
2
0
1
0
2
0
0
2
0
1
0
1
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
1
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
1
1
1
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
2
0
1
2
1
0
1
0
3
2
0
0
0
0
1
0
2
0
0
0
0
1
0
2
0
3
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
2
3
1
0
1
0
0
0
0
2
1
0
0
1
2
2
0
2
0
0
0
1
0
1
0
0
0
0
2
0
2
0
0
1
1
0
1
0
2
0
0
0
0
0
2
1
0
0
1
0
0
2
0
0
2
1
0
1
1
1
0
4
0
1
1
1
0
0
0
0
0
0
1
0
0
0
1
1
0
1
2
2
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
2
0
1
2
0
0
1
0
0
0
0
0
2
0
1
0
0
1
2
0
0
3
0
1
0
0
0
0
0
1
1
0
2
0
1
0
0
0
0
0
0
2
2
0
2
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
1
0
0
3
0
0
0
0
0
0
2
0
1
2
0
2
1
1
0
0
0
1
0
0
0
0
0
1
1
3
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
2
0
3
0
0
0
0
0
2
2
0
0
0
1
1
0
0
0
2
1
5
0
0
0
0
0
0
0
2
6
0
0
1
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
3
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
1
0
1
2
0
0
0
0
2
0
0
0
0
2
0
6
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
3
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
1
1
1
0
0
0
0
0
3
1
2
0
0
0
0
2
1
0
2
1
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
2
0
0
1
2
0
1
0
0
1
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
2
0
0
0
0
0
0
0
1
0
0
0
2
2
0
1
3
1
0
1
1
2
1
0
0
2
0
0
2
0
0
0
1
0
1
0
0
0
0
2
0
1
2
1
1
2
0
2
0
0
2
2
0
0
2
3
0
0
0
0
1
1
0
0
0
1
1
1
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
2
0
0
1
0
0
3
0
1
2
0
0
2
0
0
1
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
2
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
4
2
0
1
2
1
1
0
1
0
0
1
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
3
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
3
0
0
0
0
2
0
2
0
0
2
0
1
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
2
1
1
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
3
0
2
0
0
0
1
0
0
1
0
0
0
1
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
4
0
1
2
0
0
0
1
1
0
0
0
0
0
1
1
0
0
2
0
0
0
1
0
0
0
0
2
0
1
0
2
0
0
1
0
0
1
1
0
1
0
0
0
0
4
0
0
0
0
0
0
0
2
0
0
1
0
2
1
0
0
2
0
0
0
0
0
0
3
2
0
0
0
1
0
0
1
0
1
1
0
0
0
0
2
0
1
2
0
1
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
5
0
0
0
0
0
1
1
1
1
1
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
5
0
0
0
7
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
5
1
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
2
0
2
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
2
1
0
0
1
2
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
1
0
0
0
0
1
0
2
1
0
0
2
0
0
1
0
0
0
0
0
0
1
2
0
0
1
1
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
1
2
0
0
2
0
0
0
0
2
0
0
0
1
0
1
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
2
1
0
0
1
0
0
2
0
0
3
0
0
0
0
2
1
0
0
1
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
3
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
1
0
0
0
3
1
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
1
0
1
0
0
2
0
0
0
0
0
2
0
0
0
1
1
1
0
1
0
0
1
0
2
0
0
0
1
0
0
1
0
0
3
0
0
0
1
0
0
1
1
1
0
0
0
0
0
1
0
0
0
2
0
0
0
1
1
1
0
2
0
1
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
1
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
2
0
3
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
1
1
0
1
0
1
2
0
0
0
4
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
1
2
0
2
0
0
0
3
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
3
1
0
2
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
6
2
1
0
0
0
0
0
0
0
0
2
4
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
4
2
1
2
2
3
0
0
0
0
2
0
1
0
0
3
0
0
1
0
1
0
0
2
2
1
0
0
1
2
0
0
0
0
0
0
2
1
2
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
2
4
1
1
0
0
0
2
2
0
2
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
1
2
0
0
0
0
0
1
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
2
4
0
0
1
2
2
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
2
0
2
0
1
0
2
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
1
1
0
1
2
0
0
0
0
0
2
0
0
2
2
0
0
2
0
0
0
0
1
0
0
1
0
1
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
1
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
2
0
1
1
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
1
0
0
0
0
2
2
0
2
1
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
2
0
0
10
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
2
2
0
3
1
1
0
0
1
0
0
1
0
0
0
2
0
0
1
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
1
0
1
0
1
2
1
1
0
0
2
0
1
2
0
0
0
0
0
1
1
2
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
5
0
0
0
2
0
0
0
2
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
1
0
2
2
2
0
0
0
0
0
2
4
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
1
4
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
3
0
2
0
0
0
0
0
0
2
2
0
1
2
0
0
0
2
0
0
2
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
5
0
11
0
0
1
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
6
1
0
1
0
0
0
1
0
2
0
0
0
0
0
0
2
0
2
0
2
0
2
0
0
2
0
0
0
1
0
0
1
0
0
0
2
0
2
1
2
1
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
1
4
1
1
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
4
2
0
0
0
1
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
1
0
0
0
2
0
2
0
1
1
0
1
0
0
0
0
0
0
0
0
2
2
0
1
2
0
0
2
0
0
0
1
3
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
4
0
0
0
1
0
2
0
0
0
2
1
0
0
1
0
0
0
0
1
1
1
1
0
0
1
0
0
0
1
0
3
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
2
0
1
0
0
2
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
2
1
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
7
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
1
1
0
0
0
2
0
0
0
0
0
4
0
0
0
0
0
1
0
0
2
0
2
0
0
1
0
0
3
0
0
3
0
1
0
1
0
4
0
0
1
0
0
0
0
3
1
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
2
0
1
2
2
0
0
2
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
2
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
2
1
0
0
0
0
0
9
1
1
1
0
0
0
1
0
1
0
1
0
0
1
0
0
0
1
0
1
0
2
0
0
2
0
2
2
0
0
0
0
0
1
0
0
0
0
1
0
2
2
1
1
0
0
0
0
2
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
3
0
0
1
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
1
0
0
3
0
0
0
0
0
0
2
0
0
0
1
0
1
2
1
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
1
2
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
1
0
1
1
0
2
0
3
2
2
0
2
2
0
0
0
1
1
0
1
2
2
0
1
0
2
0
2
1
0
1
0
0
2
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
1
2
0
2
0
0
1
4
1
1
0
0
1
0
1
2
0
0
0
0
4
0
0
0
1
1
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
1
2
0
5
0
0
0
0
0
0
2
1
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
4
1
2
0
2
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7
2
1
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
12
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
1
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
3
0
1
0
2
1
2
0
0
0
2
0
0
0
0
0
2
2
0
1
0
0
1
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
3
0
0
2
0
0
0
2
0
0
0
0
2
0
1
0
1
0
0
1
2
2
2
0
1
3
2
0
0
1
0
2
0
0
1
3
0
2
1
0
2
1
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
3
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
2
1
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
1
2
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
2
1
0
0
2
0
1
1
0
0
2
0
0
0
0
3
0
0
0
6
1
0
0
1
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
1
2
1
1
0
12
3
0
0
1
1
0
0
0
0
0
0
1
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
2
0
2
0
2
0
1
2
0
4
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
1
3
0
4
2
0
2
0
2
0
0
0
0
0
1
2
2
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
1
1
0
0
2
0
0
0
0
0
2
0
1
2
2
0
1
0
0
2
0
4
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
2
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
2
0
2
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
1
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
2
0
0
1
2
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
1
0
0
0
0
1
0
0
0
2
6
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
2
1
1
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
1
1
0
1
0
1
0
0
1
0
0
3
0
0
0
0
0
2
0
0
5
1
0
0
2
0
0
0
1
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
1
1
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
2
0
0
4
0
0
0
1
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
1
2
1
1
0
0
0
2
1
1
0
0
0
1
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
2
1
0
1
0
0
0
2
0
2
0
0
0
0
2
0
1
0
0
0
0
1
1
1
2
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
4
1
0
1
0
0
0
0
1
1
0
0
2
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
1
1
0
2
1
0
2
0
3
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
2
2
0
0
0
2
3
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
4
0
0
0
2
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
1
2
1
0
0
0
2
4
0
0
1
2
0
0
0
1
0
0
0
1
0
1
0
2
1
0
0
2
0
0
0
0
0
2
1
0
0
0
0
1
0
1
0
0
0
0
2
2
0
3
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
1
2
0
2
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
2
4
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
2
1
0
0
0
0
0
1
6
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
5
0
0
4
2
1
0
0
0
0
0
0
1
0
1
1
1
1
1
1
0
0
2
0
0
1
2
2
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
2
1
0
0
2
2
0
0
0
0
2
0
0
2
0
0
0
2
2
2
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
1
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
3
1
2
0
0
1
1
2
1
2
0
2
0
0
0
1
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
2
2
0
0
2
0
0
0
1
1
1
0
0
7
0
0
0
0
1
0
2
0
1
0
0
1
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
2
0
0
0
2
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
2
3
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
2
1
0
2
0
0
0
0
0
0
1
0
1
0
1
2
2
0
0
0
0
0
1
0
2
2
2
0
1
0
2
0
2
2
0
1
2
0
0
0
0
1
0
0
0
0
0
0
4
0
2
0
0
0
0
0
2
0
0
2
1
0
0
0
2
0
0
0
0
2
2
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
2
0
2
0
2
0
1
0
2
0
0
2
3
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
2
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
2
0
0
0
1
0
0
0
1
0
2
2
1
0
0
2
1
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
3
0
0
0
0
0
1
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
3
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
2
0
3
0
2
1
1
0
0
0
1
0
2
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
1
0
0
0
1
0
0
0
4
2
0
0
0
0
0
0
0
0
2
2
0
1
0
4
0
1
0
0
0
0
0
0
0
2
0
1
0
0
2
0
2
1
0
0
3
1
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
3
0
2
0
1
2
0
0
2
0
1
1
0
1
1
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
1
0
1
0
0
0
0
2
1
0
0
7
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
7
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
2
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
1
0
2
1
1
0
0
2
0
0
1
1
0
2
0
0
1
0
0
0
2
0
0
0
0
1
2
2
3
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
2
1
0
1
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
2
2
0
2
0
0
0
0
2
2
2
0
0
2
2
2
0
0
0
0
1
0
0
2
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
1
0
0
0
0
2
0
0
0
1
0
2
0
0
0
2
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
2
0
0
2
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
5
0
0
0
2
0
0
0
2
1
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
1
1
0
0
2
2
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
2
0
2
0
2
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
3
1
0
0
0
0
2
2
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
2
0
1
2
0
1
0
2
0
0
1
0
0
3
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
3
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
4
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
2
4
0
2
0
2
2
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
2
1
0
0
0
1
1
0
3
0
0
0
0
1
0
0
2
0
0
0
0
1
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
1
1
0
2
1
0
0
0
1
0
2
0
0
0
1
0
0
2
4
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
1
0
0
0
2
1
0
0
0
0
0
0
2
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
2
3
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
2
1
1
2
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
2
1
0
0
0
0
0
0
1
2
0
1
0
0
0
2
0
0
2
0
9
0
0
1
2
0
1
0
0
0
0
0
2
0
0
1
0
1
0
2
0
1
2
1
0
0
2
1
0
1
2
0
0
2
0
0
0
1
2
2
0
1
0
2
0
3
0
0
0
0
0
1
0
0
0
2
0
0
1
0
1
0
1
0
1
0
0
0
2
0
0
0
0
0
3
2
2
1
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
3
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
2
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
2
0
3
2
1
0
2
0
0
2
0
0
0
4
0
0
0
1
0
2
3
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
2
0
0
1
0
0
1
1
0
0
0
1
1
2
0
0
0
0
1
3
0
0
0
1
0
0
0
0
0
0
1
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
2
1
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
3
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
2
0
0
0
2
1
2
0
1
0
0
1
0
2
1
0
0
2
0
0
0
0
0
0
0
3
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
4
0
1
3
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
3
0
2
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
2
0
0
1
0
0
2
2
0
0
1
0
2
1
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
2
0
0
0
2
0
1
0
0
0
2
1
0
1
0
0
1
0
1
0
0
0
9
1
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
2
0
1
0
0
2
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
1
0
2
1
0
1
2
0
2
3
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
2
2
2
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
3
0
14
2
0
0
1
0
0
0
0
0
2
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
4
0
1
2
3
0
1
2
3
0
0
0
1
0
0
0
0
0
0
0
1
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
1
0
1
0
0
0
1
1
0
0
0
1
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
2
0
1
0
0
2
0
0
2
1
0
1
2
2
2
0
0
2
0
2
1
5
2
2
0
0
0
0
0
0
2
0
1
0
0
0
1
0
3
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
5
1
0
2
3
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
2
7
0
2
0
0
0
0
0
0
0
0
0
2
2
2
0
0
1
0
0
1
0
0
0
0
0
2
0
1
0
0
2
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
3
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
2
0
2
0
0
2
0
0
3
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
2
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
2
0
4
0
0
1
0
1
0
0
0
1
0
3
2
0
0
2
0
0
0
0
0
1
0
0
0
2
2
0
0
1
1
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
3
1
2
5
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
2
0
0
0
0
2
2
1
0
0
1
0
2
1
0
2
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
3
0
0
1
1
0
0
2
0
0
0
1
0
0
0
0
1
2
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
2
0
2
0
2
0
0
0
0
1
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
2
1
2
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
1
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
2
1
2
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
1
0
0
0
0
2
0
1
2
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
1
0
0
1
2
2
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
4
2
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
2
0
0
0
0
2
1
0
1
0
0
0
0
2
0
2
2
0
0
1
0
3
0
0
0
0
0
0
2
0
0
0
3
2
0
0
0
1
0
2
0
0
1
1
0
2
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
2
2
1
0
0
1
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
3
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
2
0
2
1
0
0
0
0
0
0
0
2
0
1
0
1
1
1
2
2
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
1
0
0
0
0
2
0
0
0
0
2
0
0
2
3
0
0
2
0
3
1
0
0
0
0
0
2
2
0
0
2
0
0
2
0
0
0
0
4
0
0
0
0
0
3
0
0
0
0
1
1
1
0
2
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
2
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
2
2
0
0
1
0
2
0
1
1
0
0
0
0
0
0
0
2
1
0
2
0
4
4
0
0
1
0
0
3
0
0
0
0
0
0
1
0
1
0
0
2
1
0
1
0
0
0
10
0
0
0
0
0
2
0
1
0
2
0
2
2
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
3
1
0
0
0
0
0
0
2
0
0
2
2
2
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
2
1
0
2
0
0
0
1
0
0
1
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
1
0
0
0
1
2
0
0
3
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
4
0
7
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
5
0
0
0
2
0
3
1
0
2
0
3
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
3
2
2
0
0
0
2
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
4
1
0
0
0
4
0
2
0
0
0
0
0
1
0
1
0
2
2
2
0
2
0
0
0
1
0
0
0
2
0
4
0
0
1
0
1
0
2
2
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
1
0
0
2
0
3
0
1
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
4
2
0
4
0
0
0
1
0
0
0
0
1
0
0
0
0
2
6
0
0
2
1
0
0
2
2
0
0
0
0
2
1
1
0
0
2
2
0
2
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
2
0
0
0
2
1
0
1
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
1
0
1
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
2
0
3
0
0
1
2
0
3
1
0
0
0
1
0
0
0
3
0
0
1
0
0
0
0
0
1
0
0
0
1
1
1
0
1
1
0
1
0
0
3
0
0
0
0
0
2
0
0
0
2
1
1
0
1
0
0
0
0
0
2
0
0
0
0
0
8
0
0
0
0
2
0
2
0
3
1
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
2
1
0
2
0
0
2
1
0
1
0
0
2
0
1
0
2
2
0
0
0
0
1
0
0
2
0
0
1
0
0
0
1
2
0
2
0
0
1
1
0
0
2
1
0
2
1
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
2
0
2
0
0
2
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
1
0
1
0
0
0
0
2
2
0
1
2
0
0
0
0
0
0
0
4
0
0
1
0
0
2
1
0
2
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
8
0
0
0
0
0
0
2
1
2
1
0
1
0
2
3
2
0
0
1
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
1
0
2
1
0
0
2
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
1
0
1
0
0
2
0
0
0
0
1
1
0
3
0
0
0
0
1
0
0
2
0
2
0
0
0
0
1
0
2
1
2
0
0
1
0
0
0
1
0
2
0
0
0
0
4
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
2
0
1
0
2
0
0
0
0
2
0
2
0
2
0
2
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
1
2
1
2
0
2
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
1
0
0
0
2
0
0
0
1
0
2
1
0
0
0
0
0
2
2
0
1
0
0
0
2
0
0
0
3
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
2
2
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
1
0
2
0
0
0
2
2
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
1
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
3
0
1
0
0
0
1
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
4
0
2
0
2
0
0
2
0
2
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
3
1
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
1
2
0
0
3
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
1
2
0
0
2
0
1
2
0
1
2
0
0
0
2
0
1
1
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
3
2
4
2
0
0
2
0
0
0
0
3
0
0
0
2
0
0
0
2
0
1
0
0
0
0
1
1
2
0
1
2
0
0
0
0
0
0
0
3
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
2
0
0
0
2
0
0
2
0
0
0
2
0
0
1
1
0
1
1
0
0
1
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
1
1
1
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
3
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
1
1
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
5
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
3
0
0
2
0
0
0
1
0
0
1
1
0
2
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
4
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
5
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
3
2
0
0
0
0
1
0
0
0
2
2
0
2
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
1
0
0
0
0
3
3
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
2
0
2
0
0
0
2
1
1
1
0
0
0
1
1
0
2
2
0
0
0
0
4
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
2
1
2
2
0
2
0
0
1
2
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
2
1
0
0
1
1
0
1
2
0
1
0
1
0
0
0
0
1
1
0
0
0
1
2
1
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
2
0
2
0
0
1
0
0
2
2
0
1
0
0
0
0
1
1
1
3
1
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
5
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
2
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
2
1
1
2
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
3
1
0
0
3
2
1
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
3
0
2
0
0
0
1
0
0
2
0
2
0
0
0
0
1
0
0
0
1
0
2
1
0
1
0
0
0
1
0
0
2
1
0
0
0
0
0
1
2
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
7
1
0
1
0
0
2
1
1
0
0
0
1
0
1
0
1
0
0
0
0
1
2
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
1
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
2
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
3
2
1
1
0
0
3
1
0
0
2
1
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
2
0
0
3
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
2
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
1
3
0
2
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
2
0
3
2
0
0
0
0
3
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
1
0
0
5
1
0
0
0
0
0
1
0
1
0
3
0
0
0
0
0
0
0
0
1
0
0
0
3
0
1
0
2
0
1
2
0
0
0
0
1
1
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
3
0
0
1
0
0
0
0
2
2
0
0
2
2
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
2
0
0
0
1
2
0
0
0
2
0
0
0
1
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
3
1
0
0
2
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
1
0
1
0
2
0
0
0
1
0
0
2
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
1
0
0
2
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
2
0
3
0
0
0
0
1
0
0
0
0
2
0
1
0
1
0
0
0
3
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
2
1
0
2
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
1
0
1
0
2
1
1
0
0
0
0
0
2
3
0
0
0
1
0
3
0
0
1
1
2
0
0
2
1
1
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
2
1
0
0
0
0
0
0
3
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
2
0
0
0
1
2
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
1
0
2
0
0
1
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
2
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
2
0
0
0
0
0
0
1
2
0
1
0
1
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
2
3
0
1
0
0
0
2
1
0
0
0
0
0
1
0
0
0
1
1
0
1
0
1
0
0
3
0
0
2
0
2
0
0
0
2
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
3
0
0
4
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
7
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
1
0
1
2
2
1
0
0
2
0
2
2
2
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
1
2
0
3
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
2
2
0
0
0
1
2
0
0
0
0
1
2
0
8
0
0
0
2
0
0
2
0
2
3
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
1
0
1
1
0
0
1
1
2
2
0
0
0
0
0
5
0
2
0
0
0
0
0
0
4
0
2
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
1
1
0
1
0
1
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
2
1
0
0
2
1
0
0
0
1
0
0
0
0
0
0
2
0
0
2
2
2
3
0
1
0
0
1
0
2
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
2
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
1
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
2
0
0
0
2
0
0
1
0
1
2
0
0
0
0
0
3
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
3
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
1
0
1
0
2
1
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
2
2
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
1
0
1
0
1
2
2
0
0
0
1
0
1
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
3
0
0
0
0
1
0
0
1
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
1
2
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
1
0
2
1
0
2
0
0
0
1
0
0
0
0
0
0
1
0
3
1
0
0
0
2
0
0
0
0
2
2
0
0
0
1
0
1
1
0
0
0
0
2
0
0
0
0
1
0
0
1
2
2
1
0
0
0
2
0
0
2
0
2
0
0
1
0
0
0
1
0
1
0
0
1
0
1
2
1
0
1
1
0
0
2
2
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
1
0
1
0
0
0
0
1
0
1
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
2
0
2
1
0
0
3
0
1
1
0
1
0
0
1
1
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
3
2
0
1
0
0
0
1
0
1
0
0
2
0
2
1
2
1
0
2
1
0
0
2
0
0
0
1
1
1
0
1
0
1
1
2
0
0
0
0
0
0
0
0
2
0
2
2
0
2
0
0
0
0
0
0
0
0
3
0
2
2
1
0
0
2
1
0
0
0
0
4
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
1
0
0
0
1
2
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
1
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
1
1
0
2
0
0
5
1
0
0
1
1
0
0
0
0
0
0
2
1
0
0
0
2
3
0
0
0
0
0
0
0
0
5
1
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
2
0
2
1
1
0
0
2
1
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
2
1
2
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
2
1
1
0
0
2
0
3
2
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
2
0
2
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
3
0
2
0
2
0
0
2
2
0
0
0
0
0
0
0
1
0
2
0
0
4
0
1
0
0
0
2
0
1
0
0
2
1
0
2
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
1
0
1
0
0
0
2
0
1
0
0
0
0
0
0
3
0
0
0
0
2
0
0
1
2
2
0
0
0
0
0
0
2
2
0
0
1
0
0
2
2
0
2
0
0
0
0
0
0
2
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
1
2
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
2
0
1
1
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
17
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
3
0
2
2
0
0
0
0
0
0
0
2
0
2
0
4
0
0
0
0
0
0
0
0
1
0
0
0
2
2
1
0
0
1
1
2
0
0
0
0
1
0
0
1
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
1
2
3
0
0
0
0
0
1
0
0
0
0
2
0
0
1
2
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
2
2
2
0
2
0
0
2
1
0
0
0
0
0
2
0
0
1
3
0
0
0
2
0
3
0
0
1
0
0
0
1
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
1
1
1
1
0
1
2
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
4
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
2
6
2
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
2
0
1
2
0
0
1
0
0
0
2
3
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
1
3
1
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
5
0
0
0
0
0
1
1
0
1
2
0
0
0
0
2
0
3
0
0
0
0
0
2
0
0
0
0
0
1
0
1
2
0
1
0
0
1
4
0
0
1
0
2
0
1
0
0
0
0
0
0
0
2
0
0
5
0
0
1
0
1
3
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
2
0
0
1
0
0
0
2
1
0
0
0
0
0
3
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
3
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
3
0
3
0
0
0
0
2
1
0
1
0
0
0
0
2
2
0
2
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
2
1
2
1
0
3
0
0
0
1
2
0
0
0
0
2
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
2
0
0
1
0
0
2
2
2
0
0
0
0
1
1
1
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
1
0
0
0
1
0
0
0
0
2
1
0
0
0
0
2
0
1
2
0
1
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
2
0
0
2
0
0
1
0
2
1
0
0
0
2
2
0
0
1
1
2
0
0
1
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
2
3
0
0
3
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
8
0
0
4
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
1
0
0
0
0
1
0
2
0
0
0
0
2
2
0
1
1
1
0
1
0
2
2
1
1
0
0
4
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
1
0
1
2
0
0
0
0
2
0
0
0
1
0
1
1
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
1
1
2
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
3
2
0
0
4
0
0
1
1
0
1
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
3
4
1
0
0
2
0
0
0
2
0
0
0
1
1
2
0
0
0
0
2
0
0
1
0
0
2
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
2
1
2
2
2
0
0
0
1
0
0
0
1
1
2
0
0
3
0
0
4
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
4
0
0
0
0
0
0
2
1
0
0
0
1
0
1
0
0
2
1
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
2
0
0
1
0
0
4
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
1
0
1
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
1
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
2
0
2
0
1
0
0
0
1
0
2
0
2
1
2
2
0
0
0
0
0
0
3
0
1
0
0
0
0
0
1
0
0
1
0
0
1
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
1
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
2
2
1
2
0
0
0
0
1
1
0
1
0
0
0
0
5
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
2
0
0
0
1
0
0
0
8
0
0
0
1
0
1
2
1
3
0
0
3
2
0
0
0
2
0
0
2
1
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
2
0
0
0
0
1
1
1
0
0
0
2
0
2
3
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
5
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
1
0
2
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
2
0
0
1
1
0
0
1
0
0
2
2
0
2
0
0
2
1
0
0
0
1
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
2
0
0
2
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
4
0
0
0
0
0
1
0
0
0
1
0
2
0
0
1
0
0
2
0
0
1
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
3
0
0
1
0
0
1
1
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
4
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
2
2
0
1
4
0
0
5
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
3
0
0
2
2
0
0
0
1
2
0
0
0
2
0
1
0
1
0
0
1
0
0
0
0
0
2
0
2
0
2
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
1
2
0
0
0
1
0
0
0
0
2
0
0
0
1
2
0
1
2
0
0
0
0
0
0
1
0
0
4
0
1
0
0
0
0
1
0
0
1
1
2
2
0
0
1
2
2
0
0
0
2
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
4
0
0
1
0
1
0
0
1
2
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
5
0
2
2
0
1
2
1
0
0
0
0
0
0
3
0
0
0
0
0
2
0
1
0
0
3
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
3
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
3
0
2
0
2
0
1
0
0
0
0
1
0
0
0
2
1
0
0
2
0
0
0
0
0
2
0
0
0
0
1
1
1
0
3
0
2
0
2
1
0
0
2
2
0
2
2
2
0
0
3
2
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
1
1
0
1
2
0
0
0
0
0
4
0
0
2
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
1
0
0
0
0
2
0
0
2
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
1
1
0
1
1
1
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
2
0
1
0
0
0
1
1
0
0
1
0
0
2
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
1
0
3
0
1
1
0
1
0
2
2
0
0
2
0
1
1
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
1
1
1
1
0
0
1
0
0
2
0
1
0
3
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
2
0
0
0
2
1
1
0
0
2
3
1
0
1
0
1
0
0
0
0
2
2
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
3
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
1
2
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
2
0
2
0
0
0
0
0
0
0
0
2
0
2
0
1
0
4
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
3
0
2
0
2
0
2
0
1
0
0
0
0
0
2
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
1
1
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
2
1
1
1
1
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
3
0
0
2
0
2
0
1
0
3
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
1
2
0
0
1
1
0
3
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
2
0
0
0
2
1
0
0
1
0
1
0
0
2
0
0
0
0
1
0
1
0
1
1
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
0
3
0
4
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
1
0
2
0
0
2
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
2
0
0
0
0
2
1
0
2
2
0
0
0
0
0
2
5
0
2
0
0
0
0
1
0
0
0
0
2
2
0
1
0
0
0
2
0
0
0
2
1
0
1
0
1
1
0
2
1
0
1
0
2
1
2
0
2
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
2
1
1
1
0
0
0
0
2
2
1
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
2
3
0
0
2
1
1
0
0
2
1
0
2
0
2
0
0
0
0
1
0
0
0
0
2
1
3
0
0
0
2
0
0
0
1
1
2
0
0
0
0
0
2
1
0
0
0
1
0
0
2
2
0
2
0
0
0
0
0
1
0
0
0
1
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
2
0
0
0
0
1
1
2
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
1
0
0
0
3
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
1
2
0
0
0
3
0
0
1
0
2
0
0
0
1
1
0
0
2
2
0
0
0
0
0
0
1
0
2
2
1
2
0
0
1
2
1
0
0
2
1
0
0
0
0
1
1
2
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
2
1
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
2
2
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
1
1
0
0
1
0
1
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
1
1
0
0
2
3
0
0
0
0
0
1
0
0
0
3
0
0
1
2
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
10
0
2
2
1
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
2
0
2
1
0
1
0
0
2
0
0
2
0
0
1
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
1
0
2
0
1
1
0
3
0
1
0
1
1
0
2
1
2
1
0
0
1
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
2
0
3
0
0
1
0
0
1
0
0
0
0
2
0
0
2
0
0
2
0
1
0
0
3
0
0
0
0
0
3
0
2
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
3
0
0
0
1
0
0
0
2
0
0
0
7
0
0
1
0
1
1
0
0
0
2
2
0
0
0
0
0
0
2
2
0
1
2
0
5
0
0
2
0
0
0
0
0
0
0
2
0
1
2
0
0
0
2
0
1
0
0
0
1
0
0
1
1
0
1
0
2
0
0
2
1
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
2
0
0
2
1
0
0
1
0
1
0
0
1
0
1
0
0
2
0
0
0
1
1
0
0
2
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
3
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
3
1
0
1
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
2
0
2
0
0
2
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
6
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
2
0
0
0
0
0
0
2
0
2
0
0
0
1
0
2
0
1
1
0
0
0
0
1
2
0
0
0
0
0
2
0
2
2
0
1
0
0
1
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
1
0
4
0
2
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
3
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
3
0
2
0
0
0
0
0
0
0
1
0
1
0
0
2
4
2
3
0
2
0
0
5
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
1
0
2
0
0
0
0
0
0
2
1
0
1
2
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
8
0
2
0
0
0
0
1
0
0
0
2
0
0
1
1
0
0
0
0
1
0
0
1
3
0
0
0
0
0
1
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
2
2
2
2
0
0
0
0
1
0
0
0
2
2
2
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
2
1
4
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
4
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
2
2
1
1
1
0
2
0
0
0
0
2
0
1
2
1
0
0
1
0
0
0
0
0
2
1
0
0
1
0
0
2
1
1
6
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
1
2
1
2
0
2
2
0
2
0
0
4
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
2
0
0
2
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
1
0
0
0
2
0
1
0
0
1
1
0
0
0
0
0
1
0
0
3
0
2
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
3
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
2
0
0
2
0
0
0
2
0
0
1
2
0
0
0
2
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
3
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
1
3
0
0
2
0
1
4
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
1
0
2
0
1
0
0
3
1
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
3
2
0
2
0
0
0
0
0
0
0
0
8
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
2
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
3
2
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
5
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
1
2
0
1
0
0
1
0
0
0
1
0
2
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
1
3
0
0
0
0
0
1
0
1
0
0
1
0
3
0
0
1
1
0
0
2
0
0
1
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
2
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
3
0
2
1
0
0
1
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
4
2
1
0
0
2
0
0
0
1
2
2
1
1
0
0
0
2
0
2
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
1
1
1
0
1
1
0
0
0
0
0
2
0
0
0
1
0
2
0
0
1
0
0
1
0
0
5
1
2
0
1
2
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
2
1
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
3
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
6
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
1
1
0
0
0
0
1
1
0
1
2
2
0
0
3
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
2
1
0
0
1
0
0
0
0
0
0
2
0
2
0
2
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
3
2
2
1
1
0
1
0
0
0
0
0
2
0
2
0
2
4
0
0
0
2
0
0
2
1
1
1
2
0
0
0
0
2
1
0
1
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
1
2
0
2
1
0
0
0
1
0
0
0
0
0
2
0
1
2
0
0
0
0
0
1
0
1
1
0
0
1
0
1
2
2
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
1
6
1
0
0
0
4
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
3
0
2
2
1
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
1
0
0
2
1
4
0
1
0
1
1
0
0
0
1
0
1
0
0
0
1
0
2
1
0
0
1
2
0
0
0
1
0
0
0
2
2
0
1
0
0
1
0
0
2
2
0
0
0
1
0
0
0
2
0
0
3
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
1
0
2
0
0
0
2
1
1
0
0
2
1
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
3
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
1
0
1
1
0
0
1
0
0
0
0
2
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
1
0
2
3
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
6
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
1
2
0
0
3
0
0
0
0
0
2
0
0
0
0
1
0
0
2
2
1
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
3
1
3
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
2
2
2
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
2
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
2
0
0
1
0
1
1
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
2
2
0
2
0
2
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
2
0
0
0
2
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
0
3
0
0
0
5
1
0
0
0
2
1
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
3
0
1
0
0
0
0
1
0
0
0
0
0
0
2
1
2
0
0
0
0
2
1
0
0
2
0
0
0
0
0
2
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
4
0
0
0
1
1
0
0
0
2
1
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
3
2
2
1
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
4
1
0
0
0
2
0
2
0
0
2
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
2
0
0
0
2
0
2
2
0
1
0
0
0
2
1
0
1
3
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
1
1
0
0
2
0
2
0
2
1
2
0
0
0
2
0
0
0
1
0
2
0
1
0
1
0
2
0
0
0
0
0
0
0
0
5
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
2
0
1
0
0
0
2
0
0
3
0
0
0
0
0
0
0
3
0
0
1
0
2
0
0
0
0
0
2
0
0
1
1
0
2
0
2
0
1
0
1
1
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
1
0
0
0
0
2
2
2
0
4
2
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
3
0
0
0
0
0
3
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
4
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
2
0
2
0
1
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
3
0
0
3
2
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
4
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
1
2
1
1
2
0
0
0
0
3
0
1
1
0
0
0
1
0
0
2
1
0
1
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
1
2
1
2
0
2
2
1
0
1
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
3
0
0
0
0
2
2
0
0
2
0
1
1
0
2
0
2
1
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
11
1
0
1
2
0
2
0
3
0
0
1
0
0
0
2
2
0
1
0
0
2
0
1
4
0
0
1
0
0
0
0
2
0
0
1
0
2
3
0
2
2
1
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
1
0
2
0
0
1
0
0
2
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
1
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
2
1
2
0
0
2
0
0
1
0
0
0
0
6
8
1
2
0
0
0
1
0
2
0
1
0
0
0
0
1
1
0
0
1
0
2
0
0
1
0
0
0
0
0
2
1
0
2
0
2
1
3
0
0
0
1
0
0
1
1
0
1
0
0
0
0
2
0
0
1
0
0
2
0
2
0
0
2
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
1
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
2
0
1
0
1
1
0
0
0
0
1
0
2
3
0
1
1
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
3
0
0
0
0
0
0
0
0
2
1
0
0
2
1
2
0
0
0
2
1
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
1
0
0
4
0
0
0
0
2
1
0
0
0
2
2
0
1
0
0
0
3
0
0
2
0
0
0
1
0
0
0
2
0
2
0
0
3
0
0
0
0
0
0
1
2
2
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
1
0
0
0
0
1
1
0
0
2
0
0
0
0
2
1
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
1
0
1
0
0
1
3
0
0
0
1
1
0
0
0
3
0
0
0
1
2
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
2
0
2
0
0
0
1
2
1
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
2
0
1
0
4
0
0
0
2
0
0
0
0
1
0
0
1
0
2
0
0
2
0
0
1
0
0
4
2
1
0
0
2
0
0
0
0
0
1
0
2
0
0
0
1
2
0
2
0
0
0
1
2
0
0
0
0
0
0
0
2
0
2
2
0
1
2
1
0
2
0
0
1
0
3
0
2
0
0
0
2
0
0
3
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
2
1
0
0
0
2
1
2
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
3
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
2
0
0
1
2
2
0
2
0
0
1
0
0
0
2
1
2
0
2
1
0
3
0
0
0
3
0
0
0
1
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
2
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
2
1
2
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
1
0
0
0
1
0
0
2
2
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
1
2
0
0
0
1
0
0
3
0
2
0
2
0
1
0
0
0
0
0
1
0
0
0
0
4
2
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
2
2
1
0
0
2
1
0
0
1
0
0
0
1
0
0
1
0
1
2
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
2
0
0
0
2
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
1
0
2
1
0
1
1
1
1
0
2
0
0
0
0
0
3
1
0
0
1
0
0
0
0
1
1
0
2
3
2
0
0
1
0
3
0
2
1
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
2
2
0
0
3
0
0
2
0
0
0
1
1
1
0
1
0
1
2
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
1
0
0
1
0
0
0
2
0
1
2
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
1
0
1
0
0
1
1
0
2
1
0
0
0
1
0
0
2
2
0
0
0
0
0
2
2
0
2
2
0
0
0
0
0
0
3
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
3
2
1
0
3
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
2
0
0
1
0
2
0
1
0
0
0
2
1
0
1
0
2
1
0
2
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
4
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
3
1
0
2
0
0
0
0
1
0
0
0
0
2
1
2
0
0
1
2
0
0
2
0
0
0
4
2
1
2
0
1
0
14
0
0
3
2
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
1
0
2
0
0
0
0
0
0
0
3
1
1
0
0
3
1
1
1
0
0
0
0
0
2
4
0
0
1
1
1
0
0
0
2
0
1
0
3
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
1
0
0
1
0
0
0
0
0
2
0
0
1
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
2
0
0
2
3
0
2
1
0
0
0
0
0
2
0
0
1
0
0
0
0
2
2
1
0
0
2
0
0
0
1
1
0
1
2
0
0
2
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
3
0
0
3
0
0
0
0
1
0
0
3
0
0
0
0
0
0
2
0
1
0
0
5
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
1
0
2
0
0
0
2
0
7
0
0
0
1
2
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
2
1
1
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
2
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
2
0
0
2
0
0
1
1
0
0
0
2
1
0
0
0
0
2
0
0
0
0
2
2
0
0
0
2
0
1
0
0
0
0
0
0
0
3
0
1
0
0
1
4
0
0
0
0
0
2
2
0
1
1
0
0
1
1
2
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
1
0
2
0
0
2
2
0
0
0
1
2
0
0
0
1
2
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
1
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
2
1
0
0
0
0
1
2
1
2
1
1
0
0
2
1
0
2
0
0
2
0
0
0
6
0
1
0
1
0
1
0
0
2
0
0
0
0
0
1
1
0
0
1
0
0
0
2
0
0
0
0
0
2
3
0
0
2
0
0
2
0
0
1
2
2
0
0
0
0
1
0
0
5
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
2
0
2
0
0
2
1
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
2
0
2
1
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
2
1
0
2
1
0
1
0
0
4
0
0
2
0
2
1
0
0
0
0
2
1
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
1
1
1
0
2
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
1
2
2
0
0
0
0
2
0
0
0
0
1
0
2
0
1
2
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
1
0
0
1
0
2
0
0
0
0
1
0
0
0
2
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
3
2
0
0
0
1
0
0
2
0
0
4
0
1
0
0
0
2
2
0
2
0
0
0
1
3
1
0
1
0
0
2
4
0
0
0
0
0
1
0
0
0
0
1
0
0
2
2
0
0
0
1
0
0
0
0
1
2
2
0
1
3
0
1
1
0
0
0
0
0
1
0
0
1
2
2
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
1
4
0
0
0
0
2
0
0
0
0
2
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
2
2
0
2
1
0
0
0
2
2
1
0
2
0
0
0
0
0
0
0
2
1
1
0
0
2
0
0
2
0
0
0
2
0
1
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
3
2
1
1
1
0
3
0
0
0
0
0
0
0
2
0
1
2
0
3
1
2
0
0
0
0
0
1
0
6
2
0
2
0
0
8
0
1
0
2
1
2
0
1
0
0
0
2
1
2
2
0
0
3
1
0
1
0
0
0
0
0
2
0
0
0
0
0
1
6
0
0
0
0
0
3
0
0
2
0
0
0
2
0
0
1
0
1
0
0
0
3
0
0
1
0
2
0
0
3
0
0
0
2
0
3
0
0
0
0
0
0
0
1
0
1
8
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
2
0
1
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
1
0
2
0
0
2
2
0
0
0
1
1
0
0
0
1
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
2
1
2
1
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
4
0
1
0
0
1
0
0
0
0
0
0
1
0
2
0
0
2
0
2
0
1
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
2
2
0
2
0
0
0
0
2
0
0
0
0
0
0
2
1
1
0
0
0
4
1
0
5
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
1
3
0
0
0
0
1
1
0
0
0
2
0
0
0
0
3
0
0
2
0
2
0
1
1
0
1
0
1
0
1
0
0
2
0
0
0
0
2
0
4
0
2
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
2
1
0
0
0
2
0
1
0
0
0
0
2
0
0
0
2
0
0
0
3
2
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
1
0
1
0
0
1
2
0
0
0
2
0
1
0
0
0
0
1
0
0
0
2
0
2
1
0
0
0
0
0
0
2
0
0
2
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
2
2
0
2
3
1
2
0
2
1
0
1
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
2
0
2
1
0
0
0
0
2
1
0
0
0
1
1
0
0
0
0
1
1
0
2
0
0
2
0
0
0
0
0
1
0
0
3
0
0
1
0
0
0
3
0
1
0
1
0
0
0
0
1
0
1
0
0
0
2
2
0
1
0
0
3
0
2
0
2
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
1
0
2
0
0
1
0
1
2
0
2
1
0
0
0
0
0
1
2
0
0
2
0
0
0
2
0
1
0
1
0
0
0
2
0
1
2
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
2
1
0
0
2
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
2
0
0
0
1
0
0
1
0
1
0
0
1
0
2
0
2
1
0
0
0
0
0
0
0
1
0
0
0
1
1
2
0
0
0
0
0
3
0
2
0
2
0
0
2
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
2
5
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
3
0
0
0
0
0
0
0
1
1
2
0
2
0
1
0
1
2
0
0
0
0
0
0
2
0
0
0
0
2
4
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
2
0
2
1
0
3
0
0
0
3
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
2
0
0
1
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
1
0
3
1
0
0
3
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
1
0
2
2
0
0
0
0
1
0
0
1
0
0
1
0
1
1
0
0
1
2
2
0
0
0
0
2
0
1
0
2
0
0
0
0
2
0
0
2
1
0
2
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
2
0
0
3
1
0
0
0
4
2
0
1
3
2
1
1
0
3
0
1
0
2
0
0
1
0
0
2
0
0
2
0
0
0
2
0
0
2
1
0
1
0
0
0
3
0
0
2
0
0
2
1
0
0
0
2
4
0
0
2
2
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
4
0
0
0
0
0
0
0
0
0
0
1
2
1
1
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
2
1
1
0
2
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
5
0
2
0
2
1
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
1
0
0
1
0
1
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
1
0
0
0
0
2
0
2
0
0
0
3
1
0
0
0
0
2
0
0
1
0
1
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
4
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
1
2
0
0
0
0
0
0
0
2
1
1
0
1
0
2
0
0
1
0
0
2
0
1
0
0
0
1
0
0
0
0
2
0
0
3
0
2
2
0
0
0
0
0
1
0
2
0
2
1
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
1
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
2
0
0
2
2
0
0
0
1
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
1
1
0
1
0
0
0
6
0
0
0
2
2
3
1
0
0
0
0
0
1
1
0
0
0
0
0
3
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
3
0
0
2
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
2
2
2
2
0
1
0
2
0
0
2
0
0
2
1
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
1
1
0
0
3
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
3
0
0
0
1
1
0
0
0
0
0
2
0
0
2
0
0
3
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
3
2
0
0
0
0
2
1
1
2
0
0
1
0
1
1
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
2
0
0
1
2
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
2
0
0
0
0
0
0
1
1
0
0
0
2
0
0
1
2
0
1
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
1
0
0
0
1
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
5
1
1
4
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
4
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
2
1
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
3
2
0
0
1
0
0
0
1
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
3
1
2
0
0
0
2
0
0
0
2
0
2
0
3
0
0
3
4
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
1
1
0
2
0
0
2
0
0
1
0
0
0
0
1
0
0
0
2
0
0
7
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
2
5
1
0
0
2
0
2
0
0
0
0
2
0
0
0
1
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
2
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
2
0
2
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
2
1
1
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
1
0
0
1
0
0
2
1
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
2
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
2
2
0
0
2
0
2
0
0
2
0
1
2
1
0
0
0
0
0
0
2
1
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
3
0
0
0
0
0
2
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
1
0
1
3
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
1
0
0
1
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
2
0
0
1
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
2
0
1
0
0
0
1
1
2
0
0
0
0
0
0
0
2
2
2
0
2
3
0
0
0
1
2
1
1
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
2
1
1
0
0
3
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
4
0
0
1
2
0
0
0
0
2
2
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
2
0
1
0
0
0
0
0
1
2
0
3
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
3
0
0
0
2
0
0
1
1
0
0
0
0
1
2
1
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
2
1
0
1
0
0
0
0
2
0
1
1
0
0
0
0
3
0
0
0
0
0
2
0
0
2
0
0
2
2
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
2
0
0
2
2
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
2
0
0
0
2
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
1
0
2
0
1
0
0
0
0
6
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
2
2
0
0
0
0
2
0
0
2
0
0
2
2
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
3
0
0
2
0
0
0
2
1
0
0
0
0
1
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
1
4
0
0
0
1
0
0
0
3
2
0
0
0
1
0
0
0
0
3
2
0
0
1
0
1
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
1
1
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
2
0
0
0
2
0
0
2
0
0
0
0
0
2
0
3
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
1
2
2
0
0
2
1
0
2
0
0
0
1
0
2
0
1
0
0
2
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
2
0
0
2
0
0
1
0
0
1
0
0
0
0
0
2
2
1
0
2
1
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
5
2
0
3
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
1
1
0
2
7
0
0
0
0
1
0
1
0
2
2
0
0
1
0
2
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
2
0
2
0
0
2
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
4
1
0
1
0
0
0
0
0
3
1
1
0
0
0
2
2
0
0
0
6
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
2
1
2
0
0
0
0
0
1
2
0
0
0
0
2
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
3
2
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
1
2
0
5
0
0
2
1
1
1
0
0
0
0
0
1
0
3
2
0
0
0
0
0
0
0
0
0
2
1
0
2
0
3
0
0
1
0
1
1
1
0
0
0
0
0
0
0
5
0
0
0
3
1
0
1
1
0
0
0
1
0
0
0
1
2
0
0
0
0
2
0
1
0
1
0
0
2
1
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
3
0
1
0
0
0
0
0
0
2
2
2
2
0
2
1
0
0
11
0
0
0
0
0
0
0
0
0
2
0
1
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
1
1
2
2
0
0
2
5
1
0
1
0
0
0
0
1
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
5
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
2
2
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
3
0
0
0
2
1
2
2
0
0
0
0
2
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
1
2
0
1
3
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
3
0
2
0
0
0
0
0
0
0
2
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
2
0
2
0
0
0
0
1
0
0
0
1
3
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
6
0
2
0
0
0
1
0
0
0
0
0
2
1
1
0
0
0
0
1
0
0
0
1
0
0
0
2
1
2
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
2
2
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
1
1
0
0
2
2
2
2
2
0
1
2
2
1
0
0
0
3
0
0
0
0
1
1
0
0
0
2
0
2
0
0
2
0
0
0
0
2
0
2
0
1
1
0
0
0
0
0
1
2
0
0
0
2
0
0
2
1
0
2
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
5
1
0
3
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
1
0
0
1
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
1
0
1
0
0
2
0
0
0
0
1
0
2
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
3
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
1
2
0
0
0
1
2
0
1
2
0
0
0
0
0
0
1
1
0
0
1
0
1
1
1
1
1
0
0
0
2
0
2
0
0
1
0
1
0
0
0
0
1
0
0
1
2
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
2
2
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
3
1
0
0
0
1
0
1
2
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
2
0
0
2
1
1
0
0
0
0
1
1
0
0
0
0
3
1
0
0
0
0
0
0
1
1
0
1
1
0
2
0
1
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
1
1
2
1
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
6
0
0
0
0
0
0
2
0
2
0
2
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
2
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
5
1
0
0
0
2
0
2
1
0
0
0
0
0
1
0
0
1
0
2
2
0
1
2
0
0
0
0
0
0
0
1
1
0
0
0
0
2
2
0
2
0
0
2
0
0
1
3
0
0
0
0
0
1
0
2
0
0
0
0
3
0
0
1
0
2
0
0
0
3
0
0
0
0
0
2
0
0
1
0
0
0
1
0
2
1
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
2
1
0
0
0
0
2
0
0
0
1
0
1
0
2
1
0
0
0
0
0
0
3
2
2
0
0
1
0
0
3
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
1
0
0
3
0
1
0
0
0
2
0
0
0
0
0
1
0
1
0
0
1
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
2
1
1
0
2
0
0
0
1
0
2
3
0
0
2
0
0
1
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
2
0
0
0
0
0
1
2
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
1
0
0
1
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
2
0
2
0
0
1
0
0
0
1
1
0
0
0
0
0
1
1
0
0
3
2
0
0
0
0
0
0
0
1
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
1
1
1
1
0
2
0
2
0
0
0
0
1
3
1
0
0
0
0
0
1
2
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
2
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
1
0
1
0
0
0
0
0
0
1
5
0
0
1
0
1
0
2
1
0
0
0
0
2
1
1
0
0
0
0
0
0
1
3
0
0
0
1
1
0
0
1
0
0
0
0
0
2
0
0
1
2
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
1
0
2
0
0
0
2
1
0
1
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
2
0
2
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
1
1
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
2
0
0
0
1
2
0
2
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
2
2
0
0
0
0
0
0
1
2
0
0
2
1
0
0
0
1
0
0
0
1
2
2
3
0
2
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
2
1
0
1
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
2
2
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
1
0
0
1
0
2
0
0
2
2
0
0
0
0
1
0
0
2
1
0
0
0
3
0
0
0
3
0
0
1
2
0
0
2
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
2
1
0
0
0
0
2
2
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
2
0
0
2
0
1
0
1
0
0
1
0
1
0
1
0
0
2
0
0
0
0
1
0
2
0
1
2
0
4
1
1
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
3
0
0
0
0
2
0
0
0
2
0
2
1
0
0
1
0
1
0
2
0
0
2
0
0
0
0
0
2
0
0
1
0
1
0
3
0
0
2
4
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
4
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
2
2
0
0
1
0
2
0
0
1
2
0
1
2
2
0
0
0
0
0
1
0
0
2
1
0
0
0
2
0
0
0
1
3
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
2
0
3
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
1
0
2
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
1
0
0
0
3
0
0
0
0
0
0
0
0
1
1
3
2
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
1
0
1
0
0
0
0
9
0
0
0
0
0
0
0
2
0
4
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
2
0
2
0
1
0
0
2
0
0
0
2
1
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
1
0
1
1
0
1
2
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
1
0
0
0
1
0
2
1
2
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
2
1
0
0
0
3
0
1
2
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
3
0
2
1
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
2
0
1
0
0
0
2
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
2
2
2
0
0
0
0
2
0
1
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
1
0
1
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
2
0
0
2
1
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
3
2
0
2
0
1
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
6
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
2
3
0
0
1
0
0
1
1
1
2
2
0
1
0
1
1
2
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
2
1
1
1
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
1
0
0
1
0
2
0
0
1
0
3
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
3
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
2
0
2
1
2
0
1
0
0
0
0
2
2
2
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
2
2
0
0
0
0
0
2
2
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
1
2
0
2
0
0
0
0
0
3
0
0
1
0
2
0
14
0
0
0
0
1
2
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
2
2
0
1
0
0
2
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
7
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
2
0
2
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
2
0
0
2
1
0
1
0
1
0
0
2
0
0
0
0
1
0
0
0
1
1
0
1
1
1
0
0
0
3
0
0
0
0
0
1
3
0
0
0
2
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
2
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
2
2
0
0
0
0
0
0
1
0
0
0
0
1
2
2
0
0
0
0
2
1
0
1
0
0
0
2
0
1
0
0
0
0
0
0
2
0
1
0
2
0
1
1
2
1
4
2
1
0
2
2
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
1
2
1
0
0
1
1
0
2
0
2
0
0
0
1
0
0
2
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
1
0
0
0
1
1
2
2
5
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
1
1
2
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
3
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
3
2
1
0
0
0
1
0
0
1
1
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
3
0
0
2
1
2
0
0
2
0
0
0
1
2
0
0
0
2
0
1
2
0
0
0
2
0
0
0
2
0
2
0
2
0
0
0
1
1
1
2
1
0
0
0
0
0
3
0
2
0
0
0
0
0
2
3
0
0
2
0
0
0
0
1
1
0
2
0
3
0
1
0
0
0
1
1
0
1
2
2
2
1
3
0
0
0
0
0
0
1
2
0
0
2
0
0
0
3
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
3
2
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
1
1
0
1
0
0
2
0
2
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
2
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
1
4
0
0
0
0
0
1
0
0
2
1
2
1
0
2
0
0
0
0
0
2
1
2
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
5
0
0
0
1
2
0
0
0
1
0
1
1
2
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
2
2
0
2
0
0
1
0
2
0
0
0
2
1
0
0
0
2
0
2
0
0
0
0
1
3
0
2
2
0
0
2
0
0
0
0
1
0
3
1
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
1
2
0
1
1
0
0
0
1
1
0
0
0
0
0
1
3
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
3
0
0
0
0
0
1
0
0
2
3
2
2
2
0
0
0
1
0
6
0
0
2
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
1
0
1
0
0
0
0
1
2
1
0
2
0
0
0
2
1
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
2
0
0
1
0
2
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
1
1
0
0
0
1
0
0
0
1
1
0
1
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
5
2
1
0
0
0
0
4
1
0
2
0
1
0
0
1
0
2
2
0
0
0
2
2
0
1
1
2
0
0
2
3
0
0
1
2
0
0
1
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
1
1
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
2
0
1
0
0
1
0
0
2
2
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
2
0
0
0
2
0
2
0
1
1
0
2
0
0
0
0
0
0
2
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
2
2
3
1
0
0
1
0
2
0
1
2
2
0
0
1
0
1
0
0
0
0
0
13
0
2
0
0
0
2
0
0
2
1
1
0
0
1
0
0
0
2
1
0
1
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
1
0
0
2
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
3
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
2
2
0
0
1
2
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
1
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
1
0
0
0
1
0
0
3
1
2
0
0
4
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
1
2
2
1
0
2
0
0
2
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
2
1
2
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
1
0
0
0
0
0
0
0
3
0
0
0
2
0
1
0
1
0
0
0
0
0
1
1
0
0
3
1
2
0
0
0
2
0
0
1
2
0
0
2
0
2
1
2
0
0
0
0
2
1
0
0
1
0
0
1
0
2
1
1
0
0
0
0
1
2
1
0
0
1
1
0
0
0
0
0
2
0
2
0
0
2
2
0
1
0
0
0
0
1
1
0
1
0
0
3
0
1
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
1
0
0
0
1
2
0
2
2
1
2
0
0
0
2
0
1
0
2
0
0
1
2
2
0
0
0
0
0
0
0
0
3
1
2
0
0
1
0
2
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
3
1
0
1
0
0
2
1
2
4
3
0
2
0
0
0
0
0
1
2
2
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
2
0
2
2
0
2
1
2
0
0
1
2
0
0
0
0
1
0
1
0
2
0
1
2
2
0
2
2
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
1
0
2
0
0
2
2
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
2
0
4
1
0
0
2
1
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
3
0
0
2
0
0
0
3
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
4
0
0
0
0
0
1
1
0
2
2
0
0
0
2
0
0
0
0
0
0
0
4
0
1
2
1
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
3
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
4
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
2
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
4
0
2
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
1
0
0
0
2
1
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
3
2
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
2
0
0
2
0
0
0
0
3
0
1
1
0
0
0
2
4
0
2
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
1
0
0
0
2
0
0
2
0
0
0
2
0
0
2
0
0
1
0
0
0
1
0
0
0
0
4
1
0
0
2
0
2
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
2
0
0
0
0
0
2
0
1
0
0
0
2
1
0
0
1
2
1
2
0
0
0
1
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
2
1
0
0
0
2
0
0
2
0
0
0
0
0
1
3
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
2
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
2
1
1
1
0
2
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
1
2
0
0
0
2
2
0
0
0
0
0
0
1
2
0
2
0
2
0
0
0
2
0
1
0
4
0
0
0
1
0
2
2
0
2
3
0
0
2
0
0
0
0
0
0
0
0
2
0
3
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
2
0
0
0
1
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
2
2
1
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
1
3
0
3
0
0
0
0
0
2
2
2
0
0
0
0
1
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
1
2
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
1
0
0
0
1
4
0
0
0
2
0
0
0
0
1
2
2
0
0
0
0
0
0
1
2
1
0
0
1
0
0
2
0
0
1
0
0
0
0
0
1
0
2
1
0
0
0
1
0
0
2
0
0
1
0
0
0
0
1
1
0
2
0
0
0
3
2
1
0
0
0
1
1
1
1
0
0
0
0
2
0
0
0
0
2
0
2
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
3
0
2
0
0
0
0
0
0
1
2
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
1
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
2
2
1
0
2
2
0
0
0
0
1
2
2
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
2
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
4
0
0
0
0
0
2
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
2
2
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
1
1
0
0
0
2
0
0
0
2
2
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
2
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
1
2
1
1
0
0
0
2
0
1
0
2
0
0
0
4
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
2
2
0
0
0
2
0
0
2
0
1
0
0
2
0
2
0
0
0
1
1
3
1
0
0
0
0
2
0
1
0
1
0
1
0
0
0
1
0
12
0
0
0
1
0
0
0
2
2
0
0
2
0
3
0
0
1
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
2
0
2
2
2
1
0
1
0
0
3
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
2
0
1
0
0
1
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
1
1
0
0
0
0
2
1
0
3
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
3
1
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
2
2
0
0
1
0
0
2
0
2
0
0
0
1
0
0
1
0
0
1
2
0
0
2
2
2
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
1
1
0
0
2
1
1
0
0
1
0
0
0
0
1
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
4
0
0
0
1
2
1
2
0
0
0
0
1
2
0
1
0
0
0
0
1
2
0
2
1
1
5
0
0
0
1
0
3
1
2
0
0
2
2
2
2
1
0
2
0
0
0
0
0
0
0
0
2
1
2
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
1
1
0
1
0
0
0
2
0
0
4
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
1
0
0
1
0
1
3
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
5
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
2
0
0
0
3
0
1
0
0
0
1
1
2
0
0
1
1
0
0
0
1
1
2
0
1
0
0
0
2
5
0
0
1
1
2
2
0
0
0
0
0
2
2
0
0
1
2
0
0
1
0
0
2
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
7
0
0
1
0
0
2
0
2
0
1
2
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
1
0
0
2
2
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
1
0
0
0
2
0
2
0
2
1
1
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
1
2
1
2
0
0
1
0
0
0
0
1
1
0
0
0
2
0
0
1
1
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
3
0
6
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
1
3
0
0
1
0
0
1
0
0
1
0
0
0
1
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
1
0
1
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
2
0
0
0
0
1
0
0
0
2
1
0
2
0
0
2
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
3
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
1
1
3
0
0
0
2
1
0
0
1
2
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
1
0
2
0
1
1
0
1
0
3
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
1
1
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
2
0
0
0
0
1
0
0
0
2
0
0
0
1
0
3
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
2
2
0
3
0
1
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
3
0
1
0
0
2
2
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
1
0
0
0
2
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
2
1
0
0
2
2
0
0
1
1
0
0
2
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
3
1
0
0
0
6
0
0
2
0
0
2
2
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
1
2
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
1
0
0
0
2
0
1
0
0
0
0
1
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
1
1
2
0
0
2
0
0
0
1
2
0
2
3
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
2
0
0
0
2
1
1
2
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
3
0
0
1
0
0
0
0
1
0
2
3
0
2
2
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
2
2
0
0
0
0
0
0
3
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
2
2
2
0
0
1
0
0
2
0
4
1
0
0
0
0
0
0
0
0
0
1
2
2
0
2
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
3
0
2
1
0
2
0
1
1
1
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
2
2
0
0
0
3
0
2
0
2
0
0
0
0
0
2
0
1
0
1
0
2
0
0
2
0
0
0
2
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
2
2
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
3
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
3
2
1
0
0
0
0
1
2
2
1
0
0
0
1
1
2
0
0
0
0
2
2
0
0
0
0
0
0
0
1
1
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
3
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
2
0
0
0
4
0
0
0
0
4
0
0
0
0
0
0
2
0
0
4
0
2
0
1
1
1
1
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
2
0
0
1
2
1
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
1
0
3
0
1
6
0
0
0
0
2
10
0
2
0
2
0
0
0
2
0
0
1
2
0
1
1
0
0
0
0
2
0
0
0
0
0
0
2
0
3
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
3
0
2
2
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
1
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
1
0
1
0
0
0
3
1
1
1
0
0
0
2
2
0
1
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
2
0
1
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
1
2
1
0
0
1
2
0
0
1
2
0
4
1
2
0
0
0
0
0
0
1
2
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
3
2
0
2
0
1
0
2
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
2
0
1
0
0
1
0
2
0
1
0
2
0
3
0
0
2
2
0
0
0
1
1
2
0
1
0
1
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
3
1
0
2
0
0
2
2
0
0
0
0
0
0
0
0
1
0
1
3
2
0
4
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
2
2
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
2
0
0
1
1
1
2
2
0
1
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
1
0
0
0
1
1
0
0
0
2
0
8
0
0
2
0
0
0
0
2
1
2
0
0
0
3
0
1
0
0
1
0
0
0
1
0
0
2
0
1
0
0
2
4
1
0
0
0
1
4
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
1
0
0
0
0
0
0
3
0
2
2
0
3
0
1
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
1
0
1
0
0
2
1
0
0
3
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
2
0
0
0
0
1
1
0
3
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
1
0
0
2
1
0
1
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
1
0
1
0
2
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
6
0
1
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
1
1
2
0
1
0
2
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
1
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
2
0
1
0
3
0
0
0
1
0
2
0
2
0
0
0
0
1
0
0
0
0
2
0
3
0
2
0
0
0
0
1
0
2
0
0
1
2
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
1
0
1
1
1
0
0
0
0
2
1
0
1
0
0
0
2
0
0
0
2
0
0
0
2
2
0
0
0
1
3
0
0
0
0
0
0
2
0
0
0
0
2
1
2
0
1
0
0
0
2
0
1
0
3
0
2
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
2
1
0
0
0
2
0
0
0
3
0
0
0
0
2
0
0
1
2
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
2
1
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
2
2
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
3
2
0
1
0
0
0
0
0
0
3
0
1
0
0
0
1
2
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
5
0
0
2
0
0
0
1
0
0
0
0
2
2
0
1
2
0
0
0
0
2
2
2
0
3
0
0
0
0
0
0
0
2
2
0
2
1
2
0
1
0
0
0
0
2
2
0
1
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
2
5
0
0
0
2
1
0
2
2
0
0
1
1
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
3
1
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
1
2
0
0
1
0
0
0
2
0
0
0
0
1
0
1
1
1
0
2
1
0
0
0
0
0
2
3
0
0
2
0
1
1
0
0
1
0
3
0
0
0
0
0
1
1
2
0
0
0
3
3
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
1
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
1
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
2
0
1
1
0
0
0
1
0
0
2
0
0
0
0
0
0
5
0
2
0
0
0
1
0
0
0
0
0
3
0
1
0
1
0
0
0
0
3
0
0
0
2
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
2
0
0
0
0
0
1
0
1
0
0
2
0
1
0
0
2
1
2
0
0
1
0
0
2
1
0
2
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
2
2
0
2
1
1
0
2
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
2
2
0
0
0
4
1
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
2
0
0
0
2
2
1
1
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
4
2
0
0
0
2
0
1
1
1
2
0
2
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
2
0
0
2
0
0
2
0
0
2
2
1
0
0
3
0
2
0
0
0
2
0
0
0
2
0
1
2
4
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
1
0
1
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
3
1
2
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
1
0
2
2
0
1
0
1
0
0
3
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
1
3
1
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
3
0
1
1
0
0
0
0
0
0
1
0
1
1
0
1
0
0
3
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
4
1
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
2
1
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
3
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
1
0
0
1
0
1
0
2
0
0
1
1
0
0
1
0
1
0
0
0
0
0
2
1
0
0
0
1
0
0
0
1
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
1
2
0
1
1
0
0
1
1
2
0
0
0
0
0
0
2
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
2
2
2
0
1
1
0
0
2
0
0
0
0
1
1
0
0
1
1
2
0
0
0
0
0
2
1
2
0
1
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
2
2
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
1
0
0
2
0
2
1
2
0
1
1
0
2
0
0
0
0
0
2
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
3
1
2
0
0
1
0
2
0
2
2
3
2
0
0
0
1
2
0
0
0
0
1
1
0
0
0
0
2
3
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
1
0
3
4
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
3
2
1
0
2
0
1
2
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
1
0
2
0
0
0
1
0
0
2
0
2
0
1
1
0
0
0
1
0
0
0
3
0
0
0
0
0
2
0
0
2
0
0
0
0
2
2
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
2
0
0
0
1
0
1
0
0
0
3
2
0
1
0
0
2
0
0
2
0
2
2
3
4
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
1
0
0
0
2
1
2
0
1
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
2
2
2
0
0
0
2
0
0
1
1
2
0
0
2
0
2
0
0
0
0
2
0
0
2
2
2
1
0
0
0
0
3
1
0
0
0
0
2
0
0
1
0
0
0
0
1
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
1
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
1
1
0
0
1
1
0
0
2
0
0
1
1
1
1
0
0
2
0
0
0
0
0
1
1
0
2
0
0
1
0
1
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
1
0
1
2
0
3
0
2
0
0
1
0
1
1
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
3
1
0
1
0
0
3
2
2
1
0
0
0
2
0
1
0
0
1
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
2
0
1
0
0
1
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
2
0
0
2
2
0
0
0
1
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
3
1
0
0
2
0
1
1
1
0
1
0
0
0
0
0
1
0
0
2
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
2
0
0
0
3
2
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
1
0
3
0
2
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
2
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
3
0
3
1
2
0
0
0
0
0
2
1
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
1
0
1
0
1
2
0
2
0
0
0
0
1
0
2
0
2
2
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
2
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
2
0
0
1
4
0
0
2
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
2
0
1
1
0
0
0
0
1
3
2
0
0
0
0
0
0
1
0
0
0
0
2
1
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
6
1
0
0
0
1
3
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
2
0
0
0
2
0
1
1
1
0
0
2
0
0
0
0
2
2
0
0
1
0
0
1
3
0
0
1
0
4
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
2
2
0
0
4
1
0
0
1
1
0
1
1
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
1
0
2
1
1
0
0
0
0
1
2
1
0
0
2
0
0
2
1
0
2
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
3
0
0
1
1
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
3
0
2
1
1
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
2
0
2
0
0
0
0
1
1
0
0
0
1
0
0
0
1
1
0
0
1
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
1
0
0
2
0
0
0
0
0
1
0
0
2
1
0
0
0
0
2
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
2
0
2
0
0
0
3
0
0
0
2
1
1
2
0
2
0
0
0
0
2
0
1
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
2
2
0
0
0
2
0
1
0
0
0
2
0
0
1
0
0
0
5
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
1
0
0
2
0
0
0
0
0
1
1
0
1
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
1
0
0
2
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
2
2
0
0
2
0
0
0
1
1
0
0
2
0
0
2
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
5
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
1
1
0
0
0
0
1
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
2
1
0
2
0
0
1
0
0
2
0
1
0
0
2
1
0
0
1
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
1
1
0
2
0
0
1
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
0
0
0
0
0
8
0
0
0
2
1
2
0
2
1
2
0
0
1
0
1
0
0
0
4
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
3
0
1
0
0
3
0
0
1
4
2
2
2
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
2
0
0
1
1
0
0
1
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
1
0
0
0
1
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
2
0
2
0
1
2
3
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
2
1
2
1
0
0
0
0
1
0
0
0
2
0
1
0
0
2
0
1
2
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
1
2
0
1
0
0
0
1
0
0
0
1
2
2
0
2
0
0
1
1
0
2
0
0
0
2
0
0
0
0
2
2
0
0
0
0
1
0
0
2
0
2
3
6
0
0
0
0
0
0
2
1
2
0
0
1
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
2
1
0
2
0
2
0
0
0
3
2
0
0
0
3
0
0
1
0
0
0
2
0
1
2
0
2
2
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
4
2
0
0
1
0
0
0
0
0
0
0
0
1
0
2
2
2
0
1
1
0
2
1
0
0
2
0
2
1
1
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
1
0
0
0
2
2
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
1
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
1
1
0
2
0
1
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
4
0
2
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
1
2
1
0
2
0
0
6
2
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
1
0
2
0
1
2
0
1
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
2
1
0
0
1
0
0
0
2
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
3
2
0
0
1
0
0
0
0
2
0
0
0
0
0
3
0
1
0
0
0
3
0
0
0
0
1
0
1
0
0
0
1
0
0
1
3
2
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
1
0
2
0
1
3
1
0
0
0
0
0
1
2
1
2
0
0
3
2
1
2
0
0
2
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
3
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
3
0
2
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
2
2
2
1
2
2
0
0
0
0
0
0
0
1
1
0
0
1
2
0
0
0
0
2
1
2
0
1
1
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
1
2
0
0
0
0
0
2
2
0
0
0
1
1
0
0
0
4
0
2
0
2
2
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
2
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
3
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
3
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
1
1
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
4
1
0
2
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
2
0
1
1
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
3
0
0
1
0
0
0
0
3
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
2
1
2
1
0
0
0
0
2
1
0
0
1
2
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
4
0
0
0
0
1
0
0
0
0
0
2
0
0
2
2
1
0
0
0
3
0
2
2
1
1
0
2
0
0
2
0
0
0
0
0
1
3
0
0
1
0
0
1
0
0
0
0
1
0
0
0
2
0
0
2
1
0
0
2
0
0
1
0
0
1
0
0
0
2
0
2
0
0
0
1
0
0
0
1
0
2
2
2
1
0
4
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
2
0
0
0
0
0
4
2
0
0
1
0
0
1
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
2
1
0
0
1
0
0
1
1
0
0
0
0
0
2
0
0
0
2
1
0
1
0
2
0
0
0
2
0
0
0
0
6
0
1
0
1
0
0
0
0
0
0
0
3
1
0
0
0
1
0
1
1
2
1
0
0
0
0
1
1
0
1
0
0
0
2
1
1
0
0
0
0
0
0
1
1
0
2
0
0
0
0
5
0
2
0
1
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
1
2
0
2
2
2
0
0
2
0
0
0
0
0
1
2
0
2
1
0
2
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
4
0
2
0
2
0
0
1
0
0
3
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
7
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
4
0
2
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
1
1
0
1
1
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
2
2
0
0
0
0
1
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
1
2
0
1
0
1
1
0
4
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
2
0
0
1
1
0
0
0
0
1
1
1
3
1
0
0
1
2
0
0
0
3
0
1
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
2
0
1
2
5
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
1
0
0
0
1
0
1
0
0
1
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
2
0
3
3
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
1
0
0
0
2
2
0
0
0
0
1
3
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
2
1
1
0
0
0
0
0
0
0
0
1
1
1
0
2
0
0
0
2
0
0
0
0
0
0
1
1
2
0
4
2
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
1
0
2
0
0
0
0
2
0
2
2
1
1
2
0
0
2
0
0
0
0
0
1
1
0
0
0
0
2
1
0
0
0
2
0
0
2
0
0
0
0
0
2
0
1
0
1
2
1
2
0
0
1
0
0
0
0
0
1
1
0
0
0
2
1
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
3
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
2
0
1
4
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
2
0
1
1
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
1
2
2
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
1
0
3
0
1
0
0
5
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
1
0
0
1
1
2
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
1
1
0
0
2
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
2
2
1
0
0
0
0
2
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
2
2
2
0
2
1
0
4
0
0
0
1
0
2
0
1
0
0
0
1
0
0
1
0
1
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
3
0
1
0
0
0
1
2
0
0
0
1
1
1
3
0
0
2
0
0
2
0
0
0
2
0
0
0
2
0
0
4
2
0
0
0
0
0
0
1
0
2
2
0
0
0
2
0
2
2
1
2
2
0
1
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
1
0
0
0
1
0
0
0
1
2
0
0
0
3
0
0
0
0
2
0
0
0
0
0
1
0
0
1
1
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
2
0
1
0
0
1
0
0
2
0
0
0
0
0
0
6
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
2
0
6
2
2
0
0
0
0
0
0
0
3
0
0
2
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
1
2
0
2
1
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
4
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
2
1
0
0
7
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
2
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
2
0
0
1
0
0
2
1
1
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
1
0
2
0
0
3
0
2
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
2
0
1
2
1
0
0
0
0
2
0
2
1
0
0
1
0
2
3
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
1
0
1
1
1
1
0
1
0
0
0
0
0
0
1
0
0
1
3
1
0
1
1
0
0
0
0
0
0
0
2
1
0
0
0
2
1
2
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
2
0
2
0
0
0
1
0
0
0
0
0
1
0
2
0
1
2
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
2
2
0
0
1
1
0
0
0
0
2
0
0
0
1
0
0
2
0
2
0
0
0
0
0
1
1
0
0
2
2
2
0
2
1
0
0
0
0
2
2
0
0
0
0
0
3
0
1
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
4
0
0
0
5
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
3
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
3
0
0
0
0
2
0
1
0
0
3
0
0
0
0
0
1
0
1
1
2
0
0
1
0
1
0
0
2
0
0
1
0
2
0
3
0
0
0
3
0
1
0
1
0
0
2
0
6
0
0
2
1
0
0
0
0
2
1
1
0
0
0
2
0
0
0
2
1
1
0
0
2
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
5
2
0
1
0
0
0
0
0
2
0
0
3
0
0
2
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
2
0
2
0
0
3
0
0
0
2
0
2
0
0
0
2
0
1
0
0
1
5
2
0
1
0
0
0
0
0
2
1
0
2
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
1
0
1
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
2
1
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
1
3
1
0
0
0
2
2
2
0
0
0
0
0
1
0
1
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
2
1
0
0
0
0
1
0
1
3
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
3
1
0
0
0
2
0
0
0
2
0
0
2
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
1
0
2
2
0
0
0
1
0
1
1
3
0
0
0
0
0
0
0
0
3
0
4
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
1
0
2
0
0
1
0
0
3
5
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
2
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
3
1
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
3
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
2
0
0
0
3
1
0
0
2
0
0
0
0
2
1
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
2
0
1
2
1
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
1
0
1
1
0
0
0
3
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
2
0
0
2
0
0
0
0
0
1
2
0
1
1
0
0
2
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
2
2
2
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
2
0
3
0
0
1
0
0
0
0
0
1
0
0
1
1
3
2
2
0
1
0
2
0
0
2
0
0
0
2
1
0
1
0
0
0
0
0
0
2
2
0
2
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
2
1
1
0
0
0
0
0
0
2
1
0
3
0
0
0
1
0
0
1
0
2
1
2
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
2
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
2
2
2
1
0
0
2
0
0
0
0
2
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
3
0
0
1
0
2
0
0
1
2
0
0
2
0
0
0
0
2
0
0
2
0
0
2
0
0
2
0
2
2
2
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
3
0
0
2
2
0
0
0
0
1
0
2
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
1
1
0
0
0
2
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
1
0
0
2
0
2
0
1
2
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
1
2
0
2
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
1
5
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
1
1
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
2
0
1
1
2
2
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
3
0
0
1
0
0
0
0
1
0
0
0
2
1
0
2
0
0
0
0
0
2
0
0
0
0
1
1
0
0
1
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
4
0
0
0
0
0
0
0
2
1
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
1
0
2
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
3
0
0
1
0
2
0
0
0
0
3
0
0
0
2
0
0
0
0
0
1
1
0
2
0
2
1
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
1
1
0
4
0
0
0
0
0
1
0
1
0
0
0
0
2
0
2
0
0
0
1
0
0
5
0
0
0
1
0
1
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
1
1
0
2
0
0
0
1
0
2
0
0
0
0
1
1
0
0
2
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
1
0
0
0
1
0
0
2
0
1
0
0
0
2
0
0
1
0
0
1
0
0
1
1
0
1
0
0
0
0
1
0
1
0
0
0
0
3
0
1
1
1
0
0
0
1
0
0
3
1
0
0
0
0
3
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
1
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
2
0
2
0
0
2
1
0
0
3
1
1
1
0
0
0
0
0
1
1
1
0
0
0
0
0
2
2
0
2
0
0
0
0
2
1
0
0
1
2
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
1
0
0
0
2
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
1
0
3
1
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
3
1
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
1
1
0
0
0
1
2
0
1
1
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
1
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
3
0
0
0
1
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
3
0
0
0
1
2
0
0
0
0
0
1
0
2
0
0
0
0
1
0
1
0
2
0
0
0
0
2
0
0
1
1
0
0
1
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
2
1
1
0
0
0
1
2
0
0
0
2
1
0
0
0
0
1
3
1
0
1
0
1
0
0
0
1
0
0
2
0
0
1
0
2
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
3
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
2
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
5
0
1
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
3
0
1
0
0
0
0
2
0
1
0
1
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
2
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
1
0
1
2
0
0
0
0
1
0
2
2
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
3
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
2
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
2
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
3
0
2
1
2
2
0
0
0
0
0
1
2
0
0
0
0
1
0
0
2
2
0
0
2
1
2
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
1
1
0
1
2
2
1
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
1
0
0
2
0
1
0
2
1
1
1
1
0
2
2
0
0
0
0
1
1
0
0
1
0
0
1
0
0
2
1
0
0
0
2
2
2
0
2
0
0
2
1
0
0
0
0
0
0
2
2
0
1
0
1
1
0
2
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
2
0
2
1
0
2
0
0
1
1
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
2
2
0
1
2
0
0
0
0
0
0
0
2
0
1
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
1
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
1
2
0
0
0
0
2
0
0
0
0
0
0
0
3
0
3
1
2
0
0
0
0
0
0
0
0
1
0
4
1
0
0
0
1
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
2
1
2
0
0
0
2
1
0
1
0
1
0
0
0
0
0
0
2
0
0
2
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
3
0
0
1
0
0
0
2
0
1
1
0
2
1
1
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
1
0
1
0
0
0
1
1
0
0
1
2
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
2
0
0
0
0
1
0
0
0
1
1
2
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
3
0
0
0
1
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
4
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
1
2
0
0
0
0
1
0
0
1
0
1
0
0
0
1
1
2
2
0
0
0
0
0
0
1
1
0
0
0
2
1
0
0
2
0
5
1
2
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
2
0
0
0
0
0
2
0
0
0
2
0
0
3
0
1
0
0
1
0
1
2
0
1
0
2
0
1
0
0
2
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
1
2
2
0
0
0
0
0
3
0
0
0
0
0
0
2
2
0
0
0
1
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
3
0
1
0
0
1
0
2
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
2
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
2
0
2
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
4
1
0
0
0
0
0
0
0
1
3
0
2
0
2
3
0
1
0
2
0
1
0
0
0
3
0
0
0
0
0
5
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
1
2
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
2
1
0
2
0
0
3
2
3
0
1
2
0
2
1
1
1
0
2
0
0
0
2
0
0
1
0
3
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
2
0
1
0
2
0
0
0
0
2
3
0
0
0
0
0
0
1
0
2
0
2
1
2
0
0
0
0
0
2
2
1
0
2
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
2
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
1
0
5
2
0
0
0
2
0
0
1
0
0
2
2
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
1
1
2
0
6
0
0
0
0
0
1
0
0
2
1
0
1
2
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
2
0
1
0
0
0
3
0
0
0
0
1
0
0
1
0
1
3
0
2
0
0
0
1
0
1
2
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
1
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
2
2
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
2
0
1
1
0
0
5
0
0
1
2
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
2
0
0
1
0
7
1
0
1
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
2
1
0
2
2
0
0
1
2
0
2
2
0
1
2
0
0
1
0
2
0
0
1
0
0
1
2
0
1
3
0
1
0
0
0
0
0
1
0
0
1
0
2
0
1
1
3
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
2
0
0
2
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
2
2
0
0
4
0
0
0
2
0
0
0
2
0
1
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
1
0
0
2
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
2
1
1
1
0
0
2
3
0
0
0
0
0
2
0
0
0
0
0
2
1
2
0
0
0
0
0
1
1
2
1
0
1
0
0
0
0
0
1
0
0
0
2
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
2
0
1
2
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
3
0
2
2
0
0
1
3
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
1
3
4
2
2
0
0
2
0
2
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
2
3
1
1
0
0
0
0
0
1
0
2
0
0
2
2
0
0
2
0
0
0
1
0
0
0
0
0
3
0
0
0
2
0
1
1
0
0
0
0
0
2
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
1
1
0
2
0
0
0
1
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
2
2
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
2
1
2
0
0
0
0
0
0
0
1
0
0
0
2
0
1
2
0
2
2
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
1
0
1
2
0
1
0
0
1
0
2
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
1
5
0
0
0
1
3
2
1
1
0
0
1
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
9
1
0
0
0
2
0
0
0
1
2
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
1
2
0
0
0
1
0
0
4
2
4
0
2
1
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
2
3
0
1
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
2
2
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
2
2
3
0
1
0
2
0
1
1
0
0
2
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
4
2
0
0
0
0
0
0
0
0
0
7
2
1
2
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
2
2
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
6
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
1
0
0
2
0
0
0
4
0
2
0
2
2
0
0
0
3
2
0
1
3
0
1
0
1
2
0
2
0
1
0
0
0
1
0
0
0
1
0
0
1
3
3
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
2
2
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
5
0
4
0
0
3
2
0
0
0
2
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
1
2
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
1
0
0
0
0
0
2
0
0
1
0
1
0
1
1
1
2
0
1
0
0
2
0
0
0
0
0
1
1
2
0
2
0
0
0
2
4
2
0
0
0
0
2
2
0
0
0
0
2
1
0
3
2
0
2
0
0
0
1
0
0
0
2
2
6
0
2
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
1
0
0
1
2
0
2
1
1
0
2
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
1
0
0
0
2
0
1
0
0
0
1
0
0
0
0
1
2
1
0
0
0
0
0
0
0
4
0
2
0
0
0
2
0
1
0
0
0
0
0
4
1
1
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
1
0
1
2
1
2
0
1
1
0
0
0
1
0
0
2
3
0
0
0
0
0
2
0
0
0
0
0
0
0
3
1
1
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
2
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
2
1
2
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
1
0
0
2
0
1
0
1
1
0
1
0
0
0
0
0
0
2
0
2
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
2
2
2
0
0
0
1
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
1
1
0
4
2
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
1
0
3
2
0
0
0
1
0
0
2
0
0
0
0
0
5
2
0
0
2
0
1
0
2
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
4
0
0
1
1
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
3
2
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
2
2
1
0
0
0
0
3
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
2
0
0
1
0
1
1
0
2
0
0
2
1
1
0
0
0
2
1
1
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
3
1
2
0
2
0
2
2
0
1
0
2
0
2
0
2
2
0
0
0
0
0
2
0
1
0
0
1
1
2
0
1
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
2
0
2
0
0
2
0
2
1
2
2
1
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
2
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
1
1
0
0
0
1
0
1
0
0
1
0
0
2
3
0
5
0
0
1
0
0
1
0
0
2
0
0
4
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
1
1
0
0
1
1
0
0
0
2
0
0
2
0
0
1
0
0
0
1
0
1
0
1
0
0
0
1
1
0
2
1
0
1
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
2
0
0
1
1
0
1
0
2
0
2
0
0
0
0
0
2
3
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
2
0
0
0
0
0
2
0
3
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
1
9
0
1
0
0
1
1
0
0
0
0
0
1
2
0
1
2
0
0
2
1
0
2
0
0
1
2
0
2
0
2
0
1
2
0
0
2
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
2
0
0
0
0
1
1
0
0
0
0
0
0
0
2
1
0
1
0
0
2
0
2
0
0
2
0
0
1
1
0
0
2
0
0
0
0
0
0
0
1
2
1
0
0
1
1
0
1
0
6
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
5
0
0
2
0
0
0
2
0
0
2
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
2
2
0
3
0
1
0
2
0
0
0
2
0
0
0
1
1
1
0
0
1
0
0
0
1
0
0
1
1
0
3
0
0
0
0
2
0
2
2
2
0
0
0
0
0
0
0
0
3
0
2
0
2
1
1
0
1
1
0
2
0
0
1
2
1
0
2
0
0
0
1
0
1
0
0
0
1
0
0
2
0
1
0
0
0
7
1
0
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
1
1
0
2
0
3
0
0
0
0
0
0
1
0
0
1
0
0
7
2
0
2
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
1
0
0
2
2
0
1
0
0
1
0
2
0
0
2
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
1
0
1
0
2
0
0
0
0
2
0
0
0
1
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
2
0
1
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
3
0
0
0
1
1
0
1
3
0
0
0
0
1
0
2
8
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
4
0
3
0
2
0
0
1
2
0
1
0
1
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
8
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
3
0
1
0
0
0
0
0
0
2
2
2
2
0
0
0
0
0
0
0
0
2
0
0
2
1
0
1
0
2
1
0
0
1
0
1
0
0
2
1
0
0
0
0
2
2
1
0
0
0
1
1
0
0
2
4
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
3
0
0
0
1
2
0
2
1
1
0
0
0
1
1
0
0
0
1
0
1
1
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
1
1
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
4
0
0
0
2
0
0
2
0
1
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
3
0
2
2
0
1
1
0
0
1
0
0
0
0
1
0
0
3
0
3
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
2
0
1
0
2
0
0
0
1
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
2
0
2
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
3
0
1
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
1
0
0
1
1
0
1
0
0
0
2
0
0
0
0
3
0
2
2
0
0
1
0
2
2
1
0
1
0
0
0
0
0
0
0
2
0
1
0
2
0
3
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
1
0
2
1
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
1
7
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
1
0
0
0
1
0
1
0
0
0
3
2
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
2
2
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
2
1
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
2
0
0
2
1
2
1
0
0
2
2
0
0
1
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
2
2
2
1
0
5
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
2
1
1
0
1
1
0
0
1
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
4
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
1
0
2
0
0
2
0
2
0
0
0
2
2
0
2
0
0
0
0
3
2
0
2
0
0
2
2
1
0
0
0
0
2
2
0
2
0
1
0
0
2
2
0
0
0
0
0
0
0
1
1
0
0
3
0
0
3
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
1
2
0
0
3
1
1
0
0
0
1
1
1
2
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
1
1
2
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
4
1
2
2
0
0
0
1
0
1
1
0
0
0
3
0
2
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
9
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
1
0
0
0
2
3
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
2
2
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
2
0
0
1
0
0
3
2
1
0
2
0
0
0
0
0
1
0
1
0
2
0
0
0
1
0
0
0
0
0
1
1
1
2
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
2
0
2
0
0
2
0
0
2
0
0
2
0
0
1
0
0
2
1
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
2
0
1
1
0
0
0
0
0
0
1
2
0
0
1
0
4
0
0
0
0
2
2
0
0
0
0
1
0
0
1
0
2
0
1
3
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
1
2
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
1
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
4
0
0
1
0
2
0
0
0
2
0
0
0
0
0
7
1
2
0
0
0
0
2
2
1
1
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
1
0
2
0
0
1
0
0
0
0
0
0
2
0
1
0
0
1
0
1
1
2
0
0
0
0
0
3
0
0
1
0
0
2
2
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
1
0
0
2
0
0
0
1
2
0
0
1
1
0
0
0
0
1
0
0
0
2
1
0
2
1
0
1
0
0
2
1
0
2
0
0
0
0
0
2
1
0
0
0
0
1
1
1
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
1
2
0
0
0
0
1
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
2
2
0
2
0
0
0
0
0
1
2
1
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
3
0
0
0
0
0
0
1
0
1
0
2
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
2
4
0
0
0
0
1
0
2
0
0
2
1
0
0
0
0
0
2
1
0
2
3
0
0
0
0
0
0
3
0
7
1
1
1
1
0
0
3
1
0
3
0
0
0
0
3
0
3
0
0
0
0
2
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
2
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
1
0
1
0
1
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
3
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
2
2
0
0
0
4
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
2
2
0
0
0
1
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
2
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
1
0
6
1
0
2
0
0
1
2
0
0
0
2
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
1
0
1
2
2
0
0
0
2
0
1
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
1
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
3
0
0
0
0
1
0
0
0
0
0
0
1
0
0
3
2
0
0
0
2
0
0
0
1
0
5
1
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
1
1
0
0
0
0
1
0
2
0
0
0
0
3
0
1
1
0
0
2
1
1
0
0
0
2
0
2
0
2
0
0
0
0
0
0
2
0
1
2
0
0
0
2
1
0
0
2
0
0
3
0
2
3
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
2
1
0
2
2
1
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
9
1
1
0
2
2
1
1
0
0
0
2
2
0
0
0
1
1
0
2
2
0
0
1
0
0
0
1
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
3
0
1
0
1
0
0
0
0
0
1
1
0
2
0
2
2
0
2
0
0
2
0
0
0
0
4
0
0
0
1
2
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
3
1
1
0
1
0
3
1
0
2
0
0
3
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
1
2
1
1
2
2
0
0
0
2
2
0
5
0
0
0
0
0
1
0
2
0
0
0
2
2
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
2
0
0
2
0
2
2
0
6
0
0
1
1
0
3
2
0
0
0
2
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
3
0
2
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
3
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
2
1
2
1
0
2
0
0
1
0
0
0
0
2
1
0
0
1
0
0
3
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
2
2
2
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
1
0
0
0
0
0
1
1
0
2
1
0
0
0
0
0
2
5
0
1
1
1
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
1
2
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
1
2
0
0
0
0
0
1
1
0
0
2
0
1
1
2
1
0
0
2
0
1
0
0
2
2
0
0
0
0
0
0
1
2
0
1
2
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
1
0
6
0
3
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
2
0
2
0
0
1
0
1
0
4
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
6
3
0
0
0
0
2
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
3
0
0
0
0
2
0
1
1
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
2
0
1
0
0
1
3
0
1
0
0
1
2
0
0
0
0
3
0
0
0
0
2
0
1
0
0
0
0
0
1
0
1
2
1
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
2
1
0
0
0
0
2
0
2
1
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
1
2
1
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
3
0
0
0
0
1
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
1
0
1
0
0
0
0
0
0
0
1
1
2
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
1
0
2
0
0
2
0
0
2
0
0
0
0
1
1
1
3
0
3
0
2
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
1
1
0
0
1
2
0
0
1
0
3
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
2
0
0
4
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
2
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
1
1
3
0
3
0
0
1
1
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
3
0
2
3
2
2
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
2
2
0
0
0
3
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
1
0
0
2
0
1
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
1
0
0
0
2
1
2
0
0
0
0
2
0
0
0
3
2
0
0
0
0
2
1
0
0
0
3
2
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
2
0
0
0
0
0
1
0
1
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
2
0
1
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
3
2
2
1
0
0
0
2
0
1
2
0
2
1
0
6
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
9
0
0
2
0
4
1
1
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
1
2
0
0
0
0
2
0
0
0
0
1
0
0
2
1
0
0
0
2
0
1
0
2
0
0
1
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
1
0
2
0
0
0
0
0
0
2
2
1
0
0
0
1
0
0
0
0
0
0
0
3
2
2
0
1
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
6
0
0
1
0
1
0
0
0
0
0
0
0
0
1
3
0
0
0
2
0
2
0
0
3
0
2
1
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
2
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
1
1
1
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
2
0
2
0
3
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
1
2
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
2
2
1
0
0
0
0
1
0
1
2
0
1
1
0
1
2
2
1
0
0
0
0
3
3
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
1
1
0
0
2
2
0
0
0
0
1
1
3
0
0
1
2
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
1
0
0
0
0
1
0
2
2
0
2
3
2
2
0
2
0
1
0
0
0
0
1
1
0
0
5
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
2
2
0
0
0
1
0
1
2
0
0
0
0
2
1
0
0
0
1
0
0
0
1
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
1
0
0
1
0
0
0
1
1
0
1
0
0
0
0
1
2
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
1
0
2
0
0
3
0
0
0
0
0
0
3
0
0
0
0
2
0
1
0
0
1
0
0
0
0
2
0
0
2
0
1
0
1
2
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
1
0
0
0
0
2
0
1
2
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
1
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
1
2
2
0
1
0
0
0
0
0
1
0
0
1
1
0
0
1
0
2
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
2
2
0
3
0
0
0
0
0
2
0
0
1
0
0
2
0
0
3
0
0
2
2
1
0
0
0
1
0
2
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
2
2
0
0
0
1
0
0
0
0
0
1
1
0
1
2
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
1
1
0
1
1
1
0
0
0
3
0
0
1
0
0
2
0
3
2
0
2
0
0
0
0
0
3
0
1
0
1
2
2
0
0
0
0
0
0
0
0
0
1
2
1
0
1
4
0
0
2
1
0
0
0
5
0
0
0
0
1
0
0
0
0
0
0
1
1
2
0
1
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
1
0
0
0
3
5
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
1
1
1
0
1
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
2
1
0
0
1
0
1
1
0
2
0
0
0
0
0
0
0
0
0
1
0
2
2
2
1
0
1
0
1
2
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
1
1
0
0
1
2
1
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
1
0
2
0
1
1
2
0
3
0
0
0
0
0
0
2
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
8
2
2
0
2
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
1
2
1
2
0
1
0
0
0
0
0
2
2
0
0
2
2
1
0
0
0
0
2
0
0
0
0
0
1
0
2
1
0
0
0
1
1
2
0
0
1
1
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
1
0
1
0
0
0
0
0
2
0
1
1
1
0
3
0
0
0
0
1
4
0
0
1
1
0
0
3
0
0
1
0
1
0
0
3
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
2
0
3
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
2
2
0
0
2
1
2
0
0
0
2
3
0
0
0
0
0
2
0
0
1
3
0
0
1
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
4
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
1
0
0
1
0
0
1
3
0
2
0
0
0
1
0
4
1
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
2
1
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
1
1
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
3
0
0
0
2
0
4
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
1
0
0
1
2
1
0
2
0
1
0
0
0
2
1
0
1
0
0
0
1
0
0
0
0
0
0
0
3
2
0
0
0
0
2
0
0
0
0
0
1
0
1
2
0
0
0
1
1
2
3
0
0
0
0
1
0
0
0
0
0
1
1
2
1
0
0
0
0
0
0
1
0
2
1
3
0
1
1
0
0
1
1
0
2
0
0
3
0
2
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
1
0
2
0
1
0
0
1
0
0
0
1
2
0
0
0
1
0
2
0
2
0
1
1
0
0
3
2
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
1
2
0
0
0
0
4
0
0
0
2
2
0
0
0
0
0
0
3
0
1
2
2
0
0
0
0
0
0
0
2
2
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
1
0
1
2
0
0
0
1
0
0
5
0
0
2
0
1
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
12
0
0
2
0
1
0
0
1
0
1
0
0
0
2
0
0
1
0
1
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
2
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
2
1
2
0
0
3
0
0
0
1
0
2
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
2
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
2
1
2
0
7
0
0
0
1
2
0
2
0
2
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
1
2
0
0
0
1
0
0
0
0
0
4
0
0
0
2
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
4
0
1
0
0
2
1
0
1
0
0
0
0
0
2
2
0
0
2
0
2
0
0
0
0
1
2
0
0
1
1
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
2
0
0
2
0
0
0
2
0
1
0
0
0
2
0
0
0
1
2
0
0
0
2
0
1
0
0
3
0
1
0
0
0
1
0
2
0
0
0
0
1
2
0
2
0
0
0
1
0
0
0
0
0
2
0
1
0
2
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
3
0
3
0
1
1
1
0
0
2
2
0
2
0
0
0
1
0
0
1
1
0
0
2
0
0
0
0
1
0
0
0
1
1
3
0
2
0
0
2
0
0
2
0
2
0
0
0
0
1
0
1
2
1
1
0
3
2
0
9
0
2
3
2
0
1
0
0
1
0
0
0
1
0
0
1
0
2
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
1
5
0
1
0
0
0
1
0
0
0
0
2
0
0
3
1
0
1
1
1
0
0
2
0
2
2
1
2
0
0
1
0
0
0
0
0
0
2
0
1
1
0
0
1
5
0
0
0
0
0
2
0
0
2
2
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
2
2
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
3
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
2
0
0
5
0
0
1
1
1
1
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
1
0
1
0
0
0
0
2
1
0
1
0
0
0
2
0
2
2
0
2
0
2
1
1
2
0
0
0
0
0
0
2
1
1
1
1
0
0
0
1
0
0
2
2
0
0
0
0
0
0
1
0
1
0
2
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
1
2
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
2
0
2
2
0
0
0
1
2
0
0
1
0
0
1
0
0
0
0
2
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
1
1
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
1
0
0
1
0
1
0
0
0
2
1
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
2
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
4
2
0
1
1
0
0
1
2
0
0
2
0
0
0
0
1
2
0
1
0
0
0
1
0
0
2
2
0
0
0
0
0
2
0
0
2
2
1
1
0
0
2
0
0
0
0
0
0
0
1
1
0
1
0
1
1
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
3
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
2
1
0
2
1
0
1
0
0
0
0
6
0
1
2
1
0
0
1
0
0
0
1
0
2
0
3
2
0
3
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
2
0
0
1
1
0
2
0
2
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
3
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
3
0
0
0
2
0
1
0
0
0
1
1
3
0
0
0
2
0
3
1
2
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
3
2
2
0
2
0
0
0
0
2
1
0
0
1
0
1
0
0
0
0
0
3
2
1
0
0
0
0
0
1
6
1
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
3
0
2
4
1
0
0
0
1
0
2
0
1
0
1
1
2
0
1
0
0
2
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
2
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
1
1
0
1
0
0
2
0
2
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
1
5
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
1
0
0
0
1
0
2
1
2
2
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
4
4
2
1
0
0
0
0
0
1
2
0
1
0
0
0
0
1
1
0
2
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
2
0
1
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
2
0
2
0
0
2
0
4
2
1
0
0
0
0
0
0
1
6
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
1
0
2
0
0
0
1
0
0
3
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
2
0
0
1
3
0
3
0
0
0
0
0
0
0
0
1
2
2
0
0
2
0
0
0
0
1
4
0
0
0
1
0
0
2
0
0
0
0
0
2
0
2
0
0
2
1
0
0
0
1
0
3
0
0
0
0
0
0
0
4
0
2
1
0
0
0
0
0
3
0
0
0
2
1
2
0
0
0
0
2
0
0
2
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
2
0
2
0
1
0
2
0
3
0
2
0
1
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
1
1
0
0
1
0
0
0
0
2
1
0
1
0
0
0
0
2
0
0
1
0
1
0
2
0
1
1
0
1
2
0
2
1
1
3
0
1
0
0
0
0
0
0
0
0
0
8
0
0
0
1
1
0
0
3
1
1
0
0
2
0
2
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
1
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
2
0
2
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
1
1
0
1
0
0
4
0
1
0
1
0
0
0
2
0
0
0
0
1
0
2
0
0
2
0
0
1
0
0
0
0
2
1
0
0
0
2
0
2
4
1
0
0
0
2
1
1
1
1
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
2
6
1
0
0
0
1
0
0
1
0
2
0
1
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
1
0
2
2
0
0
2
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
2
0
1
2
0
1
0
0
0
0
1
1
0
1
2
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
3
0
0
0
3
0
0
0
2
0
4
1
1
0
1
2
2
0
0
0
0
0
0
0
0
0
0
2
1
0
1
2
0
0
1
0
0
1
0
0
1
0
0
0
2
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
2
0
0
2
2
0
0
0
2
0
0
0
1
0
2
0
1
1
0
1
1
0
0
1
2
2
0
0
0
0
0
2
2
0
0
1
2
0
0
2
1
1
0
0
0
0
0
1
0
0
0
6
0
3
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
1
0
1
0
1
3
0
1
0
1
0
1
0
2
1
0
0
1
0
2
1
0
1
1
2
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
2
0
0
0
0
2
0
0
1
0
0
0
0
1
2
0
2
1
0
0
0
2
0
2
0
0
2
0
1
0
0
1
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
5
0
0
1
0
0
0
1
2
0
2
3
1
0
0
0
0
1
0
0
2
0
0
0
0
1
0
2
0
0
1
2
0
1
0
1
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
1
1
0
0
0
0
0
2
2
1
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
1
0
0
4
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
3
2
0
2
0
0
1
1
0
2
0
0
1
0
0
0
1
0
0
2
0
0
3
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
3
3
1
0
0
0
0
0
3
0
0
0
1
2
2
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
2
1
0
2
0
1
0
2
0
0
3
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
1
0
2
3
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
2
2
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
1
2
2
2
0
0
0
0
0
1
0
0
2
0
2
0
6
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
4
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
1
1
1
1
0
0
0
0
0
1
0
0
0
4
0
0
0
2
0
0
1
0
0
0
2
0
1
3
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
1
0
0
2
2
1
1
0
0
0
1
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
6
1
0
0
3
0
0
0
0
0
0
0
2
2
0
2
0
0
0
2
2
0
0
0
0
0
2
0
0
3
0
0
0
1
2
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
2
0
1
0
0
2
1
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
5
4
2
1
0
3
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
2
0
0
0
1
0
2
0
0
0
0
0
3
0
2
0
0
0
0
0
3
0
0
0
0
1
0
2
0
2
1
1
0
0
2
1
4
2
1
0
0
0
0
1
0
0
2
0
1
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
2
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
1
1
0
0
0
1
0
2
2
0
0
0
0
0
0
1
0
1
1
1
0
2
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
3
0
0
0
0
0
1
1
3
0
0
0
0
2
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
2
0
2
0
0
0
2
0
0
0
0
1
0
2
2
0
2
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
3
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
1
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
1
0
0
0
2
0
2
2
0
0
0
0
0
1
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
3
2
0
0
0
1
0
2
0
2
0
0
0
0
0
1
0
2
2
2
0
0
2
1
2
0
0
2
0
2
0
3
0
0
1
1
0
2
0
0
0
0
2
4
0
0
0
0
1
0
1
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
2
0
3
0
0
1
0
0
0
0
0
0
2
1
4
0
0
2
0
2
0
0
2
0
0
2
1
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
4
1
1
2
0
0
0
0
0
1
2
2
1
0
0
0
0
1
1
0
0
0
0
0
0
0
2
1
0
0
1
0
1
0
1
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
9
0
0
0
0
0
2
0
3
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
1
2
2
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
1
2
0
0
0
2
0
0
2
1
0
0
1
2
0
0
0
0
1
0
0
1
0
0
2
0
2
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
2
2
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
3
0
0
0
2
0
0
2
0
1
0
2
0
2
2
2
0
0
0
0
2
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
1
0
0
0
4
2
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
2
2
0
1
2
0
0
1
1
0
0
0
2
1
2
0
1
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
3
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
2
0
2
0
2
2
0
0
0
0
3
1
1
0
2
0
0
0
0
2
0
2
0
1
0
2
0
2
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
2
2
0
0
0
1
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
6
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
2
0
0
1
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
4
0
0
2
1
6
0
1
0
0
1
0
0
0
0
0
1
0
2
0
1
2
9
3
0
1
0
0
1
0
1
0
0
0
0
0
9
0
2
0
0
1
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
3
0
1
0
1
1
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
3
1
1
0
1
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
3
3
1
1
0
0
0
0
0
0
2
1
1
0
0
2
0
0
0
0
0
0
2
2
0
0
3
4
0
0
0
1
0
1
0
4
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
1
1
0
1
1
0
2
0
0
1
0
0
0
0
0
2
0
0
0
1
2
1
1
0
0
0
0
0
0
0
0
0
3
0
0
0
2
1
0
0
2
1
0
2
0
0
1
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
1
0
3
3
0
0
1
0
1
0
2
1
0
2
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
2
0
2
2
2
2
0
0
0
0
0
0
0
0
0
2
0
1
0
2
2
0
0
2
2
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
1
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
3
0
1
3
0
0
0
2
0
10
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
3
0
1
0
0
0
0
2
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
2
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
2
0
0
2
0
0
0
0
0
6
1
0
0
0
0
2
0
1
0
1
0
1
1
2
0
0
0
2
3
0
0
0
2
0
0
0
0
0
0
0
1
2
0
1
1
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
2
0
1
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
2
0
1
0
0
0
0
1
0
0
0
0
1
1
0
2
0
0
0
1
0
1
3
5
0
2
0
0
1
0
0
0
0
0
0
5
1
0
0
2
0
0
0
3
2
0
2
0
2
0
2
0
0
1
2
0
0
0
2
2
0
1
0
2
0
0
1
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
4
0
0
0
1
2
2
0
0
0
2
0
0
2
0
0
2
0
1
0
2
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
2
2
0
2
1
2
0
1
0
0
0
0
0
0
0
1
4
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
1
1
2
2
0
3
0
2
1
0
0
3
0
2
0
1
3
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
1
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
3
0
2
1
1
0
0
0
0
2
0
2
0
0
3
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
3
0
2
0
0
1
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
1
3
0
2
1
1
0
1
0
2
0
0
0
0
2
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
3
0
1
0
2
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
3
0
2
0
0
0
2
4
3
3
1
0
1
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
1
1
0
0
2
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
1
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
2
0
1
0
2
1
0
0
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
1
0
2
0
0
3
0
2
0
1
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
3
2
0
1
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
1
3
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
8
0
0
0
0
2
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
1
1
2
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
3
0
1
0
0
0
0
0
3
1
2
2
0
0
0
0
0
2
0
3
0
1
1
2
2
1
0
0
0
1
1
1
2
0
1
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
2
1
0
1
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
1
0
0
0
1
0
0
2
2
0
0
6
0
0
0
1
1
0
0
0
1
2
1
2
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
1
1
1
1
2
0
0
0
0
0
0
4
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
2
0
2
0
0
3
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
1
0
0
1
0
1
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
3
1
0
0
1
0
0
0
0
2
0
1
0
1
0
0
0
0
0
2
0
5
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
2
0
3
1
0
0
0
1
1
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
1
1
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
2
2
0
1
0
0
0
2
0
1
0
0
0
1
0
1
0
0
0
0
1
1
0
2
0
1
1
1
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
1
0
2
0
2
0
0
1
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
3
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
2
2
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
1
0
0
0
0
0
0
0
1
0
3
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
1
0
2
2
1
1
0
2
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
3
1
1
0
0
1
0
0
0
0
2
0
0
2
0
0
1
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
1
0
0
3
0
2
0
0
0
0
0
1
0
0
0
1
0
2
2
1
2
2
0
1
1
2
0
2
3
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
3
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
5
2
4
0
2
2
0
0
1
0
1
1
4
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
1
0
1
2
0
0
0
2
4
0
0
0
0
0
1
0
0
0
0
2
6
0
1
0
1
0
0
0
0
0
0
2
2
1
1
0
0
0
0
1
2
1
0
0
0
3
0
1
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
2
1
0
0
0
1
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
1
2
2
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
1
1
0
0
0
0
2
0
0
0
2
0
0
1
2
1
0
0
0
0
0
1
3
0
0
2
1
2
2
0
0
1
2
0
3
2
0
2
0
0
0
0
3
0
0
0
0
0
0
2
2
0
3
0
0
0
0
0
6
0
0
1
0
0
0
0
3
0
0
0
2
0
0
0
3
0
0
0
0
3
2
2
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
3
0
1
1
0
0
2
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
1
1
0
2
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
1
2
0
0
0
1
0
0
2
1
2
0
1
0
2
0
0
2
0
0
0
1
0
0
0
2
0
1
0
0
2
1
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
1
0
1
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
3
2
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
1
0
2
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
2
0
2
0
0
0
0
0
0
1
1
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
1
1
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
2
0
0
0
2
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
2
1
3
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
2
1
0
4
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
1
1
0
2
2
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
1
1
2
0
1
0
0
0
0
0
0
1
0
0
1
0
2
2
2
0
0
0
3
0
0
1
0
1
0
0
1
0
0
0
0
2
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
2
10
2
2
0
0
0
1
0
1
0
0
1
1
0
0
2
1
0
1
0
1
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
1
0
3
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
1
1
0
0
2
0
0
2
0
0
2
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
2
0
1
0
0
0
1
1
0
0
2
0
0
0
0
1
2
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
2
2
0
0
0
2
2
2
0
0
0
1
0
0
0
3
1
0
0
1
0
0
3
0
0
0
1
0
0
6
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
1
1
0
2
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
3
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
1
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
5
0
1
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
1
2
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
1
0
1
0
2
1
0
0
2
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
5
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
2
1
1
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
1
0
0
0
1
0
2
2
0
0
0
2
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
4
2
0
1
0
1
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
2
1
2
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
1
2
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
5
0
2
0
0
0
1
0
0
2
0
2
3
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
1
0
0
0
0
0
0
2
0
2
3
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
1
0
0
2
0
1
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
1
0
2
0
1
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
3
2
1
0
0
0
2
2
1
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
1
0
1
0
1
0
1
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
2
2
2
0
0
0
2
0
0
1
0
0
2
0
2
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
2
0
1
0
0
0
2
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
1
2
0
0
1
0
0
2
0
0
1
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
1
0
1
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
2
0
2
0
1
1
0
2
1
0
0
0
2
0
0
0
0
3
0
0
0
0
7
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
1
0
0
0
1
2
0
2
2
2
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
5
0
0
0
0
2
0
1
0
2
0
0
0
2
2
0
1
2
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
6
0
0
2
0
0
2
0
0
0
0
1
2
1
0
0
1
0
0
0
0
0
0
2
1
0
1
2
0
0
0
0
1
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
5
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
2
0
2
0
0
0
0
1
0
0
0
0
2
2
1
0
0
2
0
2
0
0
0
2
0
0
0
2
0
2
0
2
0
0
2
2
0
0
2
0
0
0
0
3
1
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
3
0
0
2
0
0
2
2
2
0
0
2
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
1
0
3
0
0
0
2
0
2
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
1
0
3
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
1
1
0
0
0
0
1
0
1
0
0
2
2
0
1
0
1
3
0
0
0
2
0
0
0
0
0
3
0
0
0
1
0
0
0
1
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
2
2
0
0
0
2
0
1
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
2
3
0
0
0
0
0
0
0
1
1
0
0
0
1
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
1
1
0
1
2
0
0
2
0
2
0
0
0
0
0
0
1
2
0
0
0
0
2
1
2
0
0
2
0
0
1
2
0
2
0
3
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
2
1
0
0
4
1
3
6
3
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
2
1
2
0
1
1
0
0
0
1
2
0
2
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
1
2
0
2
0
6
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
1
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
1
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
1
2
0
1
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
2
0
1
0
1
0
0
0
0
1
0
2
1
0
0
0
0
0
4
1
1
2
0
2
2
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
3
1
0
0
2
1
1
0
0
2
1
0
2
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
2
4
0
1
0
0
0
1
0
0
0
0
0
1
0
2
0
2
0
3
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
1
0
1
0
0
0
1
0
2
0
3
0
0
2
1
0
0
0
1
0
0
2
2
0
2
1
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
2
1
0
4
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
3
0
0
0
0
0
0
0
3
0
0
1
3
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
1
0
0
0
2
2
2
0
0
0
2
0
1
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
2
0
2
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
3
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
1
0
2
0
0
0
0
2
0
0
0
1
2
1
0
0
0
0
0
0
0
1
2
0
1
0
1
0
0
0
0
2
2
0
1
2
0
0
1
0
0
1
2
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
2
1
0
0
0
0
2
3
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
1
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
3
0
0
0
3
0
0
1
0
1
0
0
0
0
2
1
0
0
3
0
0
0
1
1
0
1
2
0
3
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
11
0
0
1
1
0
0
0
1
2
0
1
0
0
1
0
0
1
1
3
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
2
0
0
3
0
0
2
0
0
2
0
1
3
1
0
0
0
2
0
0
2
0
0
3
1
0
0
0
2
1
0
0
0
0
0
2
2
1
0
0
2
2
0
2
1
0
1
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
2
2
0
0
1
0
0
0
1
0
2
0
0
2
2
0
1
0
0
2
0
2
0
0
0
0
0
0
0
1
2
0
0
1
1
0
0
3
0
0
0
1
0
0
2
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
1
2
0
0
2
0
0
0
0
1
2
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
2
0
0
0
1
0
1
1
1
0
1
0
1
0
0
0
0
1
2
1
0
0
2
0
0
0
0
1
0
0
1
1
0
0
0
0
2
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
2
2
2
0
0
2
0
0
0
0
0
2
0
0
0
1
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
3
0
0
0
1
1
0
2
0
1
1
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
4
2
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
4
0
2
0
0
0
0
0
0
3
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
1
0
0
0
1
2
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
1
0
2
2
2
0
0
0
0
1
2
0
3
0
0
1
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
1
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
2
0
0
0
0
1
3
0
1
1
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
1
0
0
1
0
0
0
0
0
2
0
0
1
0
2
0
0
0
1
0
0
2
0
0
0
2
0
2
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
3
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
2
1
0
2
1
3
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
1
0
2
0
0
0
0
1
2
0
0
0
2
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
3
1
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
3
4
0
0
1
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
2
1
0
1
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
2
0
5
3
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
1
0
2
0
1
2
0
0
0
0
1
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
3
0
1
0
2
0
0
1
0
1
2
3
0
0
2
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
3
0
0
0
1
0
0
2
0
2
0
1
1
0
0
0
1
1
0
0
0
2
6
2
0
1
1
1
0
0
0
0
0
0
1
0
0
1
0
1
2
0
0
1
0
1
3
0
0
0
1
0
0
2
0
0
1
0
4
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
2
1
0
0
1
1
1
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
3
0
0
2
2
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
7
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
2
0
0
1
0
0
0
3
1
0
0
3
0
1
0
0
0
0
0
0
1
0
0
1
3
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
2
1
0
1
1
0
0
0
1
0
0
0
3
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
2
2
0
0
0
1
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
3
2
1
2
2
0
0
3
1
0
0
0
1
1
0
0
0
0
0
0
2
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
1
1
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
3
0
0
0
2
0
0
0
0
3
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
6
0
1
2
0
0
0
2
0
0
0
0
0
1
1
0
0
0
2
1
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
2
2
0
1
0
0
3
3
5
0
0
0
0
2
0
0
2
2
2
0
0
1
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
2
2
0
0
0
0
0
0
1
0
2
1
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
2
2
0
0
1
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
1
1
0
0
2
2
0
0
1
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
1
1
0
0
1
4
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
2
0
1
2
1
2
0
0
1
2
2
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
1
0
0
0
0
0
0
0
2
0
2
3
0
0
0
0
0
4
2
11
0
0
0
1
0
3
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
2
0
0
4
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
1
2
0
2
2
0
1
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
4
1
0
0
0
2
0
1
0
0
0
0
0
2
0
2
0
2
0
0
0
0
2
0
2
2
0
2
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
1
0
0
0
1
1
0
0
0
2
1
0
0
0
0
0
1
0
1
0
0
0
0
0
2
2
0
1
0
0
0
0
2
2
1
1
0
0
0
0
2
0
3
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
2
0
1
0
2
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
2
2
1
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
1
2
0
0
2
2
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
1
1
0
1
0
1
0
1
0
0
0
0
1
2
0
0
0
0
0
1
2
0
0
0
0
1
2
3
0
0
2
0
1
0
0
0
4
0
2
2
0
0
2
0
0
0
0
2
0
0
0
2
0
0
1
1
0
0
0
2
2
0
0
2
0
1
2
1
1
0
1
0
0
0
0
0
0
2
1
0
0
2
2
1
2
0
0
0
0
2
0
0
0
0
0
3
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
1
0
0
0
0
4
0
3
0
0
0
1
0
0
1
0
0
0
1
2
1
0
0
0
1
0
0
1
2
0
0
0
0
2
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
6
1
0
1
2
0
0
0
1
0
1
0
0
0
1
0
0
1
2
2
0
1
0
0
0
0
1
0
0
2
2
0
0
0
3
0
0
0
1
1
0
0
0
1
2
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
1
1
1
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
1
2
2
2
0
0
2
0
0
0
0
0
0
1
2
1
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
2
0
2
1
0
0
0
0
0
2
2
0
1
0
1
1
0
0
1
0
1
0
2
1
4
0
0
0
0
0
1
1
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
2
0
2
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
1
2
0
2
0
1
1
1
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
2
3
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
2
1
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
1
2
0
0
2
1
0
0
0
0
2
1
0
2
2
0
0
0
1
7
0
1
0
0
0
0
1
0
1
0
2
0
0
3
1
0
0
0
1
0
0
0
2
0
2
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
7
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
1
1
2
1
2
0
0
0
1
0
2
0
1
0
2
0
0
0
0
1
1
0
0
0
0
0
3
1
2
0
0
2
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
2
0
0
1
0
0
0
0
0
0
0
2
0
1
3
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
2
2
0
0
3
6
2
0
1
1
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
6
2
0
0
2
0
2
0
0
0
0
1
0
0
4
0
1
0
0
2
0
1
0
2
0
0
0
2
0
0
2
0
1
4
0
0
0
0
2
2
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
1
0
1
0
2
0
0
2
0
0
3
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
1
0
0
1
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
4
0
0
2
0
2
0
0
0
0
1
0
0
0
1
4
4
0
0
0
1
0
0
0
3
0
1
1
0
0
0
1
0
2
0
0
0
0
5
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
1
0
0
3
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
9
0
0
0
0
0
1
0
0
2
2
0
3
0
0
2
2
2
0
2
0
0
1
0
1
0
1
0
2
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
1
0
1
0
2
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
2
6
1
0
0
1
0
1
0
0
1
0
2
0
0
0
0
0
0
2
1
1
1
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
1
0
2
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
1
0
0
0
0
0
0
2
2
0
0
0
0
1
2
1
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
2
3
0
0
0
0
0
0
0
2
1
2
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
2
1
0
0
0
1
0
0
1
0
2
0
0
3
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
5
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
5
2
0
1
2
0
0
0
0
0
0
2
2
0
1
0
3
0
0
0
0
0
0
1
0
0
0
0
2
2
0
2
0
0
0
1
2
2
0
1
0
0
0
0
1
0
1
0
2
0
2
1
3
0
0
0
0
0
0
1
0
0
2
0
1
0
0
3
0
2
0
2
0
0
0
3
0
0
0
0
2
1
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
1
0
1
1
1
0
0
2
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
1
1
0
0
0
0
1
0
0
2
1
0
0
0
1
0
2
0
0
0
1
0
4
0
0
0
0
1
0
2
1
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
2
0
1
0
0
1
1
2
0
0
0
0
2
0
0
2
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
2
0
0
3
0
0
0
0
0
2
1
2
0
2
0
4
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
1
2
2
0
0
0
6
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
1
1
0
0
0
1
1
2
1
0
0
2
0
0
0
2
0
0
1
0
2
1
1
0
0
0
0
2
0
2
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
2
1
0
0
3
1
0
0
0
2
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
4
1
0
0
1
1
0
0
0
3
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
3
0
0
2
1
0
0
0
2
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
4
0
1
0
0
2
0
1
0
2
1
0
0
0
0
2
2
1
1
0
0
0
0
4
2
0
1
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
1
3
2
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
1
2
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
1
1
2
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
2
0
0
1
0
0
2
0
0
2
0
0
1
0
0
0
0
0
2
0
2
0
0
1
0
4
2
0
0
0
2
0
2
0
1
0
0
1
0
0
2
0
0
2
0
1
1
1
2
1
0
0
0
1
0
0
0
2
2
0
0
0
1
0
0
2
0
3
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
2
1
0
1
2
1
1
0
1
0
0
0
2
0
0
0
0
4
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
2
0
2
0
0
0
1
0
0
0
10
0
0
0
0
6
2
2
0
0
0
0
2
1
0
0
1
1
0
0
1
0
0
2
0
1
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
1
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
2
2
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
3
0
0
0
1
2
1
0
2
0
1
0
0
2
1
0
0
0
2
1
0
2
0
2
0
0
0
0
1
1
0
0
1
0
3
0
0
0
0
1
0
0
1
0
2
0
0
0
2
1
4
1
1
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
4
0
1
0
1
0
2
2
0
2
0
0
0
1
0
0
0
1
0
0
2
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
1
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
2
2
0
3
0
0
0
0
1
0
2
2
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
1
2
0
0
1
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
2
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
2
4
1
0
0
1
0
0
1
2
1
2
0
3
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
1
2
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
1
0
0
0
2
0
2
0
0
0
0
1
1
2
0
0
0
3
2
0
0
0
0
0
2
1
0
2
2
0
0
2
0
2
2
0
0
0
1
0
0
0
1
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
1
0
0
2
2
0
0
1
0
3
0
0
0
0
1
3
1
0
2
0
2
0
2
0
0
0
0
2
0
0
2
0
1
2
0
1
2
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
1
1
0
0
1
0
0
2
0
2
0
0
0
0
0
1
1
0
2
0
2
0
0
0
1
1
1
0
0
0
0
1
0
2
2
0
0
1
0
0
1
2
0
0
1
0
2
0
3
0
0
1
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
2
1
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
3
0
2
0
1
0
2
0
2
2
0
0
2
0
0
2
1
0
3
0
0
2
0
0
2
0
0
0
4
2
0
0
0
3
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
1
1
1
0
2
1
0
2
0
0
2
0
0
0
0
0
0
1
0
1
0
2
0
1
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
4
0
0
0
0
1
0
1
0
1
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
2
1
0
1
1
0
0
0
0
0
0
0
2
0
1
0
1
0
0
3
0
1
1
0
0
2
0
2
0
0
0
0
0
1
1
0
0
2
2
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
3
1
0
0
3
2
0
1
0
0
0
2
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
2
0
1
2
0
0
0
3
0
2
0
0
0
1
0
0
0
0
0
2
0
0
2
0
4
0
0
2
0
1
1
0
0
0
2
0
0
0
1
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
2
1
3
1
1
0
0
1
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
4
0
0
2
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
1
0
2
1
0
1
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
2
0
0
0
2
2
0
2
0
8
0
0
2
0
0
0
0
0
0
2
0
0
2
0
1
1
4
0
0
0
3
1
0
3
0
0
0
0
0
2
2
2
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
1
0
2
0
0
0
2
13
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
2
2
1
2
0
0
0
0
0
0
0
2
1
1
0
1
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
2
2
1
0
0
0
2
0
0
3
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
1
1
0
1
1
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
2
1
0
0
2
0
2
0
1
0
0
3
2
0
0
0
0
0
2
0
0
4
1
2
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
2
2
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
1
0
2
1
2
0
0
2
0
2
0
0
0
0
1
0
0
1
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
2
0
0
0
2
0
0
1
1
0
2
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
2
0
1
2
1
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
2
2
0
0
2
0
1
0
10
0
1
0
0
0
2
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
8
0
0
0
0
2
0
2
0
0
2
0
2
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
1
1
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
1
2
0
0
2
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
1
2
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
3
0
1
1
0
1
0
0
0
2
0
3
1
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
4
1
2
0
0
2
2
0
0
0
1
0
0
0
1
3
3
0
0
2
0
2
3
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
7
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
2
0
0
1
0
2
0
0
4
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
1
1
2
3
0
0
1
2
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
2
0
2
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
2
0
0
1
0
1
0
2
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
2
1
1
0
0
0
2
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
4
0
0
0
0
0
0
2
0
1
0
0
0
1
0
1
0
0
1
0
1
0
0
2
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
1
1
0
2
2
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
4
0
6
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
2
1
2
3
0
4
2
0
0
0
1
0
2
0
0
0
2
0
1
0
0
0
0
1
1
0
0
0
2
4
0
2
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
1
0
0
3
0
0
0
2
0
1
0
0
0
0
0
0
4
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
1
2
2
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
1
1
0
2
0
2
0
0
0
0
0
0
0
2
1
1
0
0
0
2
0
0
0
4
2
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
1
1
1
1
2
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
2
1
0
0
1
0
1
0
1
0
0
1
0
1
0
0
1
0
3
0
1
0
0
0
0
0
0
4
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
3
0
0
0
2
0
0
0
1
0
2
0
0
0
3
0
1
0
1
0
0
2
0
0
0
2
0
0
1
0
2
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
6
2
0
0
0
0
0
2
2
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
2
0
1
2
1
0
1
0
0
0
0
0
0
0
0
2
2
0
0
1
1
2
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
7
0
1
6
0
0
0
2
0
0
1
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
4
0
2
2
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
2
1
0
1
0
0
0
0
3
2
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
2
4
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
1
0
0
2
0
0
0
0
0
1
0
0
2
1
2
0
0
3
0
2
0
0
0
1
0
0
2
0
0
0
2
2
2
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
1
0
0
0
0
4
0
0
3
1
0
1
0
1
1
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
1
0
1
0
0
1
2
0
0
0
1
0
2
0
0
0
0
1
0
0
0
1
0
2
0
1
0
1
1
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
2
0
2
1
1
1
1
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
2
0
1
0
2
2
1
0
2
2
0
0
2
0
2
2
0
0
0
0
0
2
0
3
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
1
0
0
0
0
1
0
0
1
3
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
2
0
1
0
0
1
1
0
0
0
0
0
0
1
2
1
0
0
0
2
0
1
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
2
0
0
0
3
1
0
0
2
0
0
0
0
1
2
0
1
0
4
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
2
2
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
2
0
4
2
1
0
0
0
3
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
1
0
3
0
0
3
2
2
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
1
0
1
2
2
0
0
1
1
0
0
2
0
0
0
0
1
0
2
0
1
0
0
0
1
1
0
1
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
1
0
0
0
2
1
0
1
3
1
1
1
0
1
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
1
4
0
2
2
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
1
2
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
1
0
2
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
2
0
1
0
0
0
0
1
1
0
2
0
2
2
0
2
0
1
0
2
0
0
0
1
1
0
2
1
0
1
0
0
0
2
4
0
0
1
0
2
0
2
0
1
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
2
2
3
1
0
2
3
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
4
0
1
1
1
0
2
0
0
2
1
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
3
1
1
0
1
0
0
0
0
5
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
7
1
0
0
0
1
0
0
0
1
0
0
0
1
1
0
3
0
1
1
0
0
0
0
0
0
2
1
0
0
0
2
1
0
0
0
0
1
3
3
0
1
0
0
1
0
0
0
1
2
0
2
0
0
2
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
2
0
2
0
0
1
1
1
0
3
0
0
0
0
0
0
0
0
6
1
0
2
1
2
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
2
0
2
2
0
1
0
0
0
2
1
0
0
0
0
0
0
0
1
0
2
0
0
0
3
0
2
0
0
2
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
2
0
0
1
0
0
1
1
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
2
0
1
0
0
1
1
0
2
1
0
0
3
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
2
0
0
0
0
2
0
3
3
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
1
3
0
0
0
1
2
0
1
0
5
0
0
0
0
1
2
0
0
2
0
1
0
1
0
0
0
0
0
1
1
1
2
1
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
2
2
0
2
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
10
0
0
0
2
1
3
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
2
0
2
2
0
1
2
0
2
0
0
0
0
0
0
2
1
0
0
0
1
1
0
1
0
2
0
2
2
1
0
0
1
0
0
2
2
2
1
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
4
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
3
0
0
0
0
2
0
2
0
1
0
2
2
1
2
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
2
0
0
1
0
1
0
1
1
0
0
0
0
0
4
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
3
0
0
0
0
0
2
1
1
2
0
2
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
2
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
3
0
0
0
0
0
0
1
2
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
1
1
0
0
2
0
1
1
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
2
1
0
0
1
1
0
0
1
0
1
0
0
3
0
0
0
0
0
2
0
0
1
1
0
2
0
0
0
1
2
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
2
1
0
0
0
1
0
0
0
1
3
0
1
0
0
0
0
0
3
2
2
2
0
0
1
0
1
2
0
0
0
1
0
3
0
0
5
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
2
0
0
1
0
0
2
1
0
2
1
1
2
0
0
0
0
0
0
2
0
0
1
3
0
0
1
0
0
0
2
0
0
0
2
2
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
3
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
2
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
2
2
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
3
0
1
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
3
0
0
5
0
8
2
0
1
2
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
2
0
0
0
1
0
0
1
0
0
0
0
1
0
2
1
1
0
0
0
0
0
2
0
1
0
1
2
0
1
2
0
1
2
1
0
1
0
0
0
0
0
1
2
0
0
0
0
0
2
1
0
0
2
0
1
0
0
2
2
0
0
3
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
2
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
2
1
0
0
1
2
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
3
0
1
2
0
0
0
2
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
3
0
1
1
0
0
1
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
3
2
1
0
2
0
2
0
1
0
0
2
0
3
0
2
2
0
0
0
0
0
0
0
0
1
0
2
1
1
0
0
0
2
0
0
0
2
0
0
0
2
1
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
2
0
3
1
2
0
2
0
2
0
2
0
0
3
3
0
2
2
1
0
0
1
1
0
0
2
0
1
0
2
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
1
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
3
1
0
0
0
0
0
0
0
0
1
2
2
0
0
0
2
2
1
1
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
2
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
3
0
0
2
0
2
1
0
1
0
2
3
0
0
1
0
1
1
3
0
0
0
0
2
0
1
0
1
1
1
0
0
0
2
0
0
0
0
2
0
2
1
0
0
1
0
0
2
0
0
0
0
0
0
3
4
0
0
2
0
1
0
1
0
0
0
1
0
0
0
1
0
0
2
2
2
1
0
0
0
0
0
1
0
1
2
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
2
2
1
0
0
0
1
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
1
0
0
3
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
1
1
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
2
0
0
1
0
0
0
0
1
2
0
0
2
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
1
2
1
2
1
0
0
2
2
0
2
0
0
0
0
0
1
0
0
0
0
5
1
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
1
0
3
2
0
0
0
2
0
1
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
2
1
2
0
0
2
2
1
0
0
1
0
1
1
0
0
1
0
2
0
2
3
0
0
3
1
0
0
2
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
2
0
0
1
0
3
3
0
1
0
0
4
0
0
0
0
0
1
0
0
1
2
2
1
1
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
1
2
1
1
1
0
4
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
2
0
0
0
2
1
1
0
0
1
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
1
1
0
0
2
1
1
0
0
0
2
0
0
0
1
0
2
1
0
3
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
3
3
0
0
0
0
0
0
0
2
1
0
1
0
0
2
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
2
1
0
0
0
0
2
0
2
0
2
2
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
3
2
0
2
0
1
0
0
6
1
0
0
1
0
0
1
0
1
0
0
1
1
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
1
1
0
1
3
2
0
0
2
0
0
1
0
1
0
0
0
0
2
2
1
0
0
0
0
0
0
1
0
0
0
0
1
2
0
1
0
1
0
1
0
0
0
0
1
2
0
0
1
0
3
2
3
1
0
0
2
0
0
0
0
0
0
2
2
0
0
2
1
1
0
4
0
0
2
0
0
0
0
2
0
3
0
1
8
1
0
0
1
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
2
0
1
1
3
0
2
0
0
0
0
1
1
0
0
1
0
0
0
0
2
1
1
1
2
0
0
1
0
0
0
0
1
2
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
2
0
0
0
2
0
2
0
1
1
0
0
2
0
0
2
0
1
1
0
0
2
1
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
2
1
0
0
2
0
1
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
1
0
1
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
1
0
3
1
2
0
0
0
0
8
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
2
0
1
0
2
0
0
2
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
2
6
0
0
0
0
0
0
2
1
3
2
0
0
0
0
2
3
0
0
1
0
2
0
0
0
0
0
0
0
2
0
1
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
2
1
0
1
0
1
0
0
0
0
2
0
0
1
1
0
1
0
1
1
2
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
1
1
0
0
0
2
0
0
3
2
0
0
2
0
0
0
0
2
0
6
0
0
0
0
0
1
1
0
1
0
1
2
2
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
3
2
1
0
0
3
0
0
0
0
0
0
1
3
2
2
1
0
0
1
0
2
2
0
0
2
0
1
0
0
1
0
0
0
0
0
0
2
1
0
0
0
2
0
1
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
2
0
1
2
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
2
0
2
0
0
1
2
0
0
0
2
0
0
0
0
2
4
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
2
1
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
2
2
0
0
0
0
0
2
4
0
1
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
1
0
0
1
0
0
0
2
1
2
0
0
0
0
2
1
2
0
0
0
0
0
1
1
1
0
2
1
0
0
0
2
2
0
0
0
0
2
2
0
1
2
1
0
3
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
1
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
1
1
0
0
3
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
4
0
0
0
0
0
2
1
0
0
1
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
2
1
4
0
0
0
0
0
0
1
0
0
0
1
2
1
1
2
0
0
2
2
0
2
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
2
1
0
4
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
2
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
1
2
0
0
1
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
1
0
2
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
3
2
2
1
2
1
0
3
0
2
0
2
2
0
0
0
2
0
0
0
0
0
1
0
0
0
2
1
0
1
0
2
1
0
0
0
2
0
0
0
0
0
2
1
1
0
0
0
2
2
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
3
2
1
0
2
0
0
2
0
0
0
1
1
2
0
0
0
0
0
1
0
2
0
0
2
0
0
2
2
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
1
0
1
0
0
1
0
0
0
1
0
3
2
0
0
0
0
0
1
0
0
0
2
2
2
1
2
0
0
0
0
0
0
0
0
3
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
2
0
0
0
2
0
1
0
0
0
0
2
0
0
2
0
2
0
0
3
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
1
0
0
0
0
0
3
0
2
0
0
2
0
1
0
0
1
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
3
2
0
0
0
0
0
0
0
1
0
0
2
1
0
2
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
2
0
0
2
0
0
0
2
0
1
0
0
1
0
1
1
0
0
0
0
2
2
0
0
1
0
0
0
0
0
1
2
0
0
0
1
1
2
1
1
0
0
2
2
1
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
4
0
0
2
1
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
1
0
2
1
1
0
0
2
1
1
2
2
0
0
0
1
0
3
4
0
0
1
0
0
2
0
1
0
0
2
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
4
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
1
0
0
0
2
0
1
0
0
2
1
1
1
0
1
0
1
0
0
0
0
0
3
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
4
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
1
1
0
0
0
2
0
0
1
1
1
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
2
1
1
0
2
0
0
2
2
0
0
2
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
2
1
0
0
0
2
1
0
0
0
0
2
2
0
1
0
2
0
0
0
0
0
3
0
2
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
1
0
1
2
0
0
0
2
0
0
0
0
0
2
1
1
1
1
0
1
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
2
0
1
3
0
0
0
1
1
1
0
0
0
2
0
0
1
0
1
0
1
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
1
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
1
0
0
0
0
1
0
0
0
0
1
0
1
2
2
1
2
0
0
0
2
2
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
3
2
0
1
0
0
0
2
0
0
0
1
0
0
0
1
1
0
0
2
2
0
0
0
0
0
2
1
1
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
2
0
2
0
0
0
1
2
0
0
1
2
0
0
0
1
0
2
0
0
3
0
0
0
0
2
0
1
1
1
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
2
0
0
1
1
1
2
1
0
1
0
0
1
2
1
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
3
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
1
0
4
3
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
2
0
0
2
7
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
4
2
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
2
0
0
0
2
0
1
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
2
0
0
2
0
2
0
2
1
0
2
0
0
0
0
0
3
0
2
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
2
0
0
0
0
1
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
1
2
0
2
0
0
2
0
1
0
1
2
0
1
1
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
2
2
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
3
0
0
0
2
0
0
1
1
2
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
2
0
1
0
0
1
1
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
1
0
0
0
3
0
0
1
0
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
1
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
3
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
2
1
0
1
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
1
1
0
0
0
2
0
6
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
1
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
5
0
1
0
0
0
0
2
0
0
0
1
0
1
1
0
0
0
0
0
2
0
0
0
0
3
0
0
2
0
1
0
1
1
1
0
0
0
1
2
0
0
0
2
0
1
1
0
0
0
2
0
0
0
2
2
0
0
0
0
0
3
0
1
0
2
0
0
2
1
0
0
0
0
0
1
0
1
0
1
0
2
2
1
0
0
0
0
0
0
2
2
0
8
0
2
0
0
0
1
1
0
3
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
8
0
4
2
0
1
0
1
1
0
1
0
1
1
0
2
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
1
0
2
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
2
7
0
0
0
0
0
0
0
2
3
7
0
2
2
0
0
0
0
1
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
3
1
0
2
1
1
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
1
0
0
0
0
2
0
0
0
1
1
0
0
0
1
0
3
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
1
0
1
0
0
0
0
2
0
1
2
0
1
0
0
0
0
1
1
2
0
0
0
0
2
1
0
0
1
1
2
1
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
2
2
0
3
0
2
0
0
0
1
0
0
0
0
0
0
1
1
2
0
0
0
0
0
1
0
0
0
0
0
0
2
3
3
0
2
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
3
2
1
0
0
2
0
0
2
2
0
0
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
2
2
1
0
0
0
1
2
1
0
1
0
0
0
1
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
1
0
0
3
2
0
2
0
0
0
0
0
1
1
1
0
0
2
0
0
0
2
0
0
0
0
4
0
0
5
0
0
0
0
0
0
0
2
0
3
0
2
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
3
1
1
2
0
2
2
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
2
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
3
0
0
0
0
0
1
2
0
0
0
0
4
1
0
2
0
1
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
1
0
2
4
0
1
0
2
0
2
2
1
0
0
0
0
0
3
0
1
3
1
0
2
4
0
0
0
1
0
1
2
1
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
1
0
0
1
0
2
1
1
1
0
1
2
0
0
0
0
2
0
2
0
1
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
3
0
1
0
1
0
3
2
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
3
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
3
1
1
0
0
0
0
2
0
1
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
3
1
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
2
0
0
2
0
0
0
2
0
0
0
2
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
3
0
0
0
2
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
1
0
0
1
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
1
2
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
2
2
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
2
1
0
0
2
3
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
2
0
1
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
3
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
1
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
2
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
9
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
4
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
2
0
1
0
1
1
2
0
2
2
0
1
1
2
3
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
2
0
0
2
1
1
0
2
0
0
2
0
7
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
2
1
0
0
0
0
0
0
0
0
1
2
1
0
0
1
0
0
2
0
2
2
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
2
2
0
2
3
0
0
0
0
1
2
0
0
1
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
8
2
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
3
0
0
0
3
1
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
1
0
2
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
1
2
0
0
1
1
0
2
0
0
2
0
0
1
2
0
0
0
2
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
3
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
4
2
0
3
0
2
0
0
0
0
1
0
0
2
0
0
0
1
0
1
0
0
0
2
0
0
0
2
1
0
0
1
1
0
0
2
1
2
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
1
0
0
0
0
0
9
0
0
0
2
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
6
0
1
1
0
0
2
2
0
0
3
2
0
1
3
0
2
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
3
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
3
2
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
1
1
0
2
0
0
2
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
1
0
1
2
1
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
2
3
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
1
0
0
0
2
1
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
3
1
0
0
0
0
2
3
2
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
2
2
0
0
0
0
0
2
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
2
2
0
0
0
0
2
0
0
2
0
0
0
0
0
1
1
0
0
1
0
0
0
2
0
2
1
1
0
1
1
1
0
0
1
2
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
1
0
3
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
2
1
0
0
0
2
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
2
0
0
0
2
2
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
2
1
0
0
0
1
0
0
10
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
2
0
0
3
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
1
2
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
3
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
1
3
2
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
3
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
2
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
3
0
0
1
0
1
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
1
0
1
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
40
0
3
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
9
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
2
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
2
0
0
1
0
0
1
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
2
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
2
0
0
2
0
2
0
1
0
1
0
0
0
1
1
0
2
1
0
0
2
2
0
1
0
0
1
0
0
0
0
0
0
2
1
1
1
2
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
2
1
0
0
1
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
3
0
2
0
2
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
3
0
2
0
2
2
2
0
0
1
1
0
0
2
0
1
2
2
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
1
0
1
0
0
3
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
1
2
1
0
2
0
0
1
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
2
0
0
0
0
2
0
0
0
1
0
0
0
1
2
0
1
2
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
1
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
1
0
4
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
2
1
2
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
2
0
2
0
2
0
1
0
1
0
0
0
0
2
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
2
1
2
0
0
0
0
0
0
0
0
2
0
2
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
1
3
0
0
0
6
1
0
0
0
0
2
2
0
0
3
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
2
4
0
1
0
0
0
1
0
0
2
4
0
0
0
0
2
0
0
5
0
2
0
0
1
0
0
2
0
2
0
0
0
0
0
0
1
0
0
2
0
0
1
2
4
0
3
0
0
0
1
0
1
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
5
0
0
2
0
0
0
1
0
2
0
2
0
0
1
0
0
2
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
3
2
1
0
0
2
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
2
0
0
1
0
0
0
1
0
0
2
0
0
2
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
6
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
2
0
0
0
1
2
0
2
0
0
2
0
0
0
2
0
3
1
0
0
0
0
0
0
0
1
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
10
0
0
3
0
0
0
2
0
2
1
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
2
0
1
0
0
0
2
0
0
2
0
2
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
3
0
0
2
0
0
0
2
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
1
0
0
2
3
1
0
0
2
0
0
1
0
2
0
1
0
2
0
0
0
1
1
0
2
0
1
2
0
0
2
0
1
0
0
2
0
0
0
0
0
0
2
0
1
0
0
1
1
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
2
0
0
0
0
1
0
1
2
1
1
1
0
0
0
2
1
0
1
0
0
0
0
0
1
0
1
1
0
0
1
0
2
3
0
0
0
1
0
0
3
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
1
0
2
2
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
2
1
0
1
0
1
0
1
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
2
1
0
0
0
0
2
0
4
0
0
0
1
2
0
1
0
0
0
2
2
0
0
0
1
0
1
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
2
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
2
0
1
0
0
0
2
0
2
0
2
0
3
0
0
0
0
1
0
0
0
2
1
2
0
0
0
2
0
0
0
2
2
2
0
1
0
0
1
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
2
0
0
2
0
2
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
1
0
0
2
0
0
0
3
0
0
1
0
4
1
0
0
1
2
1
0
0
0
0
0
0
2
0
3
0
1
2
1
1
0
0
0
1
0
1
0
0
1
0
0
1
2
0
2
3
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
1
0
3
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
1
2
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
1
0
1
1
0
0
0
2
0
1
0
2
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
3
0
2
2
0
3
0
2
2
2
0
3
0
0
0
0
8
0
2
0
3
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
2
2
0
0
1
0
0
2
0
0
0
2
0
0
3
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
1
0
0
1
0
0
3
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
1
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
6
0
0
0
3
0
0
0
1
0
1
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
1
1
1
0
2
0
0
0
1
0
0
1
0
0
1
2
0
0
2
3
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
1
0
0
2
1
0
1
0
1
0
0
2
0
1
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
3
0
0
1
0
0
0
0
3
1
0
0
0
1
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
2
2
2
1
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
2
2
0
1
1
1
0
0
3
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
1
0
1
0
0
0
0
0
0
1
1
2
2
3
1
1
0
2
0
0
0
0
3
0
2
0
0
0
1
0
0
2
2
0
1
2
0
0
0
1
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
2
0
0
4
0
1
0
1
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
2
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
1
0
0
1
3
0
0
0
0
2
0
0
1
0
0
2
2
0
1
0
0
2
0
0
0
0
0
0
0
0
1
2
3
0
0
2
0
0
1
0
0
0
0
0
3
0
0
2
0
0
0
2
0
0
2
0
2
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
2
0
0
1
4
0
0
2
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
2
1
0
0
0
0
1
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
7
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
2
2
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
2
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
4
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
2
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
1
0
0
0
2
0
2
1
0
11
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
4
0
0
0
1
0
0
0
0
0
0
0
2
3
0
1
0
2
2
0
0
0
0
6
0
0
1
0
0
0
0
0
1
2
0
2
0
1
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
2
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
2
1
0
2
1
0
2
0
1
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
4
1
0
0
1
0
0
1
0
0
0
2
0
0
2
0
0
0
2
0
2
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
2
0
0
1
1
0
0
0
0
1
0
0
2
2
0
0
0
0
0
9
0
2
0
1
1
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
2
2
2
0
0
0
2
0
0
0
0
0
0
0
0
1
2
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
1
0
2
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
2
1
2
1
0
0
0
0
1
1
2
0
3
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
1
2
1
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
3
0
3
1
2
0
0
0
0
2
0
0
1
0
0
0
0
0
1
1
0
1
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
2
0
0
0
0
1
2
0
0
4
0
0
0
2
2
0
2
2
1
0
0
0
0
2
0
0
0
0
3
0
2
0
1
0
0
0
1
0
0
0
0
2
0
1
2
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
2
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
1
2
0
0
0
0
2
1
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
1
0
0
2
2
0
0
0
2
0
0
0
3
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
1
2
0
0
0
2
1
0
0
0
0
1
2
0
0
0
0
0
1
0
2
0
0
0
0
1
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
1
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
1
0
0
0
1
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
1
0
1
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
1
0
0
1
0
1
0
0
2
1
0
1
1
1
0
0
3
0
0
0
2
2
1
0
1
3
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
5
2
0
0
1
0
0
0
2
0
1
1
3
1
0
1
1
0
1
0
2
0
0
2
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
1
1
0
1
0
0
2
0
0
0
0
2
1
0
3
0
0
2
3
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
1
0
0
1
0
0
2
2
0
1
2
0
0
0
0
0
0
0
0
2
0
2
0
1
2
0
0
0
0
0
0
0
2
0
2
2
2
0
0
0
0
1
0
0
0
2
0
3
0
0
0
0
0
0
1
0
1
0
2
2
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
2
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
1
1
3
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
2
2
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
1
2
1
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
2
1
0
0
0
1
4
1
1
0
1
0
2
1
2
0
0
0
0
0
0
5
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
1
4
2
0
2
2
0
0
1
0
0
0
0
0
1
1
1
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
1
0
0
0
2
3
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
1
0
0
3
0
2
0
0
2
0
0
1
0
0
1
1
0
0
0
0
1
0
6
1
1
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
1
0
0
3
0
0
2
2
0
0
0
0
0
0
0
1
3
0
0
0
0
2
1
0
1
0
0
0
0
0
2
2
0
0
4
0
0
2
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
1
0
1
0
0
0
1
2
0
0
2
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
2
2
2
0
2
2
3
0
2
0
0
0
1
0
0
2
0
0
2
0
0
0
3
1
1
1
1
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
2
1
3
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
1
3
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
1
0
0
0
2
1
2
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
2
2
0
2
0
0
0
0
0
2
2
0
0
0
0
2
1
0
2
0
0
0
2
0
0
0
0
2
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
3
0
0
2
0
3
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
3
0
0
0
0
0
0
2
2
1
0
0
1
1
0
0
0
1
0
0
0
0
1
0
1
0
2
2
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
1
0
1
1
0
0
1
0
0
1
0
1
0
2
0
0
0
1
0
3
0
0
0
0
4
0
0
0
0
0
2
0
0
0
3
0
1
0
0
1
0
0
0
2
0
3
0
0
1
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
2
0
2
0
0
0
1
0
0
0
0
1
2
1
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
1
2
0
2
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
4
0
0
0
0
1
0
0
0
0
2
0
0
0
1
1
1
3
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
2
0
2
1
0
3
1
0
0
1
1
1
0
0
0
2
2
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
1
1
0
2
5
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
1
2
0
0
2
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
1
0
0
1
1
2
0
2
0
0
1
0
0
5
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
1
0
0
1
1
0
3
0
3
1
1
0
1
2
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
4
0
1
0
0
0
1
0
0
0
1
2
0
1
0
1
0
0
2
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
2
0
0
0
1
1
0
0
1
1
1
0
4
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
2
2
0
0
2
0
1
0
0
0
2
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
1
0
3
0
0
1
2
1
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
3
1
0
0
2
1
2
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
1
4
0
1
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
1
0
3
0
2
0
2
0
0
1
0
0
1
0
2
2
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
2
1
0
1
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
2
0
2
1
1
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
3
1
3
0
1
0
1
0
1
0
1
0
0
1
1
2
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
1
0
2
0
0
1
1
0
0
1
3
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
3
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
2
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
5
0
1
0
0
2
0
0
1
0
0
0
1
0
2
0
0
1
0
0
3
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
1
3
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
5
0
1
1
0
3
1
0
1
0
0
2
2
0
2
0
0
2
0
2
0
0
2
0
0
0
1
0
1
0
0
0
0
1
4
0
0
0
0
0
2
6
2
0
0
2
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
2
0
1
0
0
0
0
2
0
1
0
0
2
0
0
0
1
0
3
0
0
0
3
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
2
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
1
1
0
1
0
1
0
0
2
2
0
0
0
0
0
1
0
2
0
0
0
1
2
0
1
0
1
0
0
0
0
0
2
0
2
0
0
0
1
2
1
0
0
2
0
0
0
0
1
2
2
0
4
0
0
1
0
0
0
2
2
0
0
0
1
1
0
1
0
2
0
1
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
2
0
0
0
2
2
0
0
1
0
1
0
0
2
1
1
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
1
2
0
0
2
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
3
1
1
0
0
0
0
0
0
2
0
2
2
1
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
2
0
0
1
0
0
2
0
0
0
0
0
1
0
0
2
1
1
2
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
3
0
3
0
2
1
0
0
2
0
1
0
0
0
1
2
0
0
0
1
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
1
0
1
0
0
1
0
0
2
3
0
1
0
1
2
0
0
0
2
0
1
0
0
0
0
0
1
1
1
1
0
0
2
0
0
1
1
0
2
1
0
0
0
0
0
0
2
0
0
2
0
2
0
0
3
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
2
0
0
1
0
0
3
0
0
1
2
0
2
1
0
1
0
2
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
1
0
0
0
1
1
0
1
0
1
0
0
2
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
1
2
8
0
0
0
0
3
0
1
0
0
1
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
2
0
0
3
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
3
1
0
0
0
0
0
2
1
0
2
2
2
0
0
1
0
0
0
0
0
0
3
2
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
2
0
0
2
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
2
1
0
0
0
2
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
2
0
2
2
1
0
4
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
2
1
0
0
0
0
1
0
0
0
2
2
0
1
1
0
0
0
0
2
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
2
2
0
1
2
2
1
0
2
0
2
2
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
1
2
0
0
0
0
1
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
2
2
0
0
0
2
1
0
0
0
0
0
0
1
2
6
0
0
0
1
0
0
2
0
0
0
0
2
2
2
0
2
0
1
0
0
1
0
2
1
0
2
0
1
2
0
1
2
0
0
0
0
2
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
1
0
0
1
0
0
1
0
1
0
1
0
0
0
0
1
1
0
0
0
2
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
3
0
2
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
2
0
0
0
2
0
1
0
1
2
1
0
0
0
0
1
2
2
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
2
1
1
0
1
0
0
2
0
0
2
0
1
0
0
0
0
2
1
0
1
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
2
0
0
0
3
0
2
0
0
0
2
1
0
1
2
0
0
2
0
2
4
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
3
1
0
1
1
0
3
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
2
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
7
0
0
3
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
3
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
3
1
0
0
0
1
1
0
0
2
0
1
1
0
0
0
0
0
0
2
0
0
0
2
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
2
0
0
0
0
1
0
0
0
1
2
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
1
0
0
0
1
1
1
0
1
1
0
0
0
2
6
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
2
0
0
2
0
1
2
0
0
0
1
6
0
0
0
0
2
2
2
0
1
0
1
0
0
1
1
0
0
0
0
3
0
2
0
0
0
0
0
1
0
0
4
1
0
0
0
0
2
0
2
0
0
0
1
0
2
0
2
0
0
5
0
1
0
0
3
0
0
1
0
0
0
0
0
0
1
0
1
2
0
0
2
0
2
1
2
0
0
0
1
0
0
2
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
1
1
0
0
0
0
1
1
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
1
1
0
1
0
1
0
0
3
0
0
0
0
2
0
2
0
0
0
0
0
0
1
2
2
2
0
0
0
1
2
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
1
2
2
2
0
0
1
0
1
0
0
2
0
4
1
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
1
1
0
1
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
5
0
0
1
0
0
0
1
0
6
0
0
0
0
0
0
2
1
0
2
0
0
0
1
2
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
3
0
1
1
0
0
0
1
2
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
3
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
2
0
1
2
0
0
0
1
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
1
0
0
3
0
1
1
0
0
0
0
0
0
1
2
0
1
1
0
0
0
2
0
1
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
1
2
1
0
0
0
0
2
1
4
1
2
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
1
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
1
1
0
0
0
0
6
0
2
0
0
0
0
0
3
2
1
2
0
2
3
0
2
0
0
0
2
0
0
1
0
3
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
2
2
0
2
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
2
0
2
0
0
0
0
0
1
0
1
0
0
0
2
0
0
1
0
0
0
0
3
0
1
0
0
2
0
0
0
4
0
1
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
2
0
1
0
0
2
1
0
0
0
0
5
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
2
3
0
3
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
3
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
2
1
0
1
0
8
0
1
0
1
0
0
1
0
1
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
1
2
0
0
2
2
0
0
0
1
2
0
0
0
1
3
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
1
2
0
0
0
0
1
0
0
0
2
0
1
0
1
2
0
2
0
0
0
0
0
4
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
3
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
3
0
0
2
1
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
2
0
1
2
0
0
0
0
3
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
1
0
2
0
0
0
2
0
2
0
0
0
0
1
1
2
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
1
0
0
0
1
2
0
0
1
0
2
0
2
0
0
2
0
0
0
0
1
0
2
2
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
2
2
0
1
0
0
0
0
2
0
0
0
2
0
1
0
1
0
0
2
3
0
1
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
3
1
0
2
2
1
1
0
0
1
0
0
0
0
1
0
0
2
1
0
0
0
2
0
0
0
0
3
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
2
0
0
0
2
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
4
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
1
0
2
0
0
0
0
2
0
1
2
1
0
3
0
2
0
0
0
0
1
0
0
0
2
0
2
0
0
0
2
0
0
0
2
0
0
5
0
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
2
2
1
0
0
1
2
0
0
0
2
2
1
0
2
0
0
1
1
0
0
0
0
2
0
1
3
0
0
0
0
1
2
0
1
0
0
1
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
3
1
0
2
0
2
0
0
0
2
0
2
1
1
0
0
0
0
2
2
0
1
2
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
2
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
3
2
0
1
0
1
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
1
0
0
2
0
1
1
0
1
1
2
0
0
0
3
2
0
0
0
2
0
2
0
0
0
0
1
1
3
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
4
0
2
2
2
0
0
1
3
2
0
0
1
0
0
0
0
0
2
0
0
2
0
1
0
0
2
2
0
0
0
2
0
0
0
3
2
0
3
0
0
2
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
2
0
0
1
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
2
1
0
0
1
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
1
0
0
0
0
1
1
0
6
0
0
0
0
0
0
0
1
1
0
0
0
0
2
1
0
0
0
0
0
0
2
0
1
0
0
0
1
0
3
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
3
0
2
2
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
2
0
0
0
1
0
4
0
1
0
0
1
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
3
1
0
1
2
0
2
2
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
3
0
0
1
0
0
0
0
1
1
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
3
0
2
0
0
0
1
0
1
0
2
1
2
0
2
0
0
0
0
0
0
1
0
0
0
2
0
2
3
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
2
3
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
1
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
1
2
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
2
1
0
0
2
0
2
0
3
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
1
0
0
3
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
2
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
2
2
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
1
1
0
2
0
2
0
0
0
0
0
0
0
0
1
0
1
2
0
2
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
3
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
1
0
1
0
0
0
0
1
0
0
0
2
0
0
0
3
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
2
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
1
1
2
0
0
0
0
0
0
0
0
1
0
0
2
3
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
1
0
0
1
0
2
0
0
0
0
1
0
2
2
0
0
0
0
0
2
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
2
0
0
0
1
0
2
2
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
4
0
0
2
0
2
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
1
1
1
0
4
2
0
1
0
0
2
0
0
0
0
0
0
1
0
1
0
6
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
1
2
1
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
3
0
0
3
0
1
0
3
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
2
1
0
0
2
0
0
1
1
2
0
0
0
1
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
2
4
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
2
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
1
1
0
0
0
0
0
2
0
0
2
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
2
0
1
0
0
0
3
0
0
0
0
1
0
0
2
0
0
1
0
2
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
2
2
0
0
2
0
0
1
0
0
2
0
0
0
0
0
4
0
0
0
0
1
0
0
0
3
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
7
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
1
2
0
0
0
0
1
0
1
0
4
2
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
3
0
0
0
0
1
0
0
3
1
0
2
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
2
0
1
1
0
0
0
0
0
3
0
2
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
2
0
2
1
0
1
0
0
3
1
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
4
1
1
0
0
0
0
2
2
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
2
1
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
7
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
2
0
0
1
0
0
3
2
0
0
0
2
1
0
2
1
0
1
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
2
0
0
0
3
1
2
2
0
0
0
0
0
0
0
1
0
1
0
0
0
2
3
1
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
1
0
0
3
0
0
0
0
0
1
0
2
4
0
1
0
2
0
0
1
1
0
1
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
1
0
2
0
0
0
0
1
2
3
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
2
2
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
2
2
0
1
0
0
2
1
2
3
0
0
1
0
0
0
2
0
0
0
0
0
0
4
0
0
0
2
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
1
0
0
2
1
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
1
0
1
1
0
0
0
2
0
1
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
1
0
0
2
0
0
0
0
1
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
1
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
1
2
2
0
0
0
0
2
0
0
2
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
3
1
0
0
0
2
0
1
0
0
2
2
2
0
0
0
0
0
2
0
2
2
1
3
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
2
6
4
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
4
0
0
1
1
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
3
0
0
2
1
0
1
1
2
2
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
5
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
7
1
0
0
0
2
0
0
1
5
0
0
0
2
0
0
0
1
0
1
0
0
2
0
1
0
4
0
0
0
2
0
0
2
0
2
0
0
0
0
1
0
0
1
2
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
2
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
4
1
2
2
0
2
0
0
0
2
5
2
0
3
0
0
0
1
0
0
1
1
0
0
0
0
0
2
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
2
0
0
0
2
0
0
0
3
0
0
0
3
0
0
0
1
2
2
0
2
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
2
2
0
0
0
0
2
0
2
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
2
0
1
0
0
0
1
0
3
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
1
0
2
0
0
0
0
3
0
0
0
2
0
0
0
0
2
0
0
0
0
0
8
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
5
0
1
0
0
1
0
0
0
0
2
0
1
2
2
0
0
0
0
1
0
2
2
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
3
0
1
0
2
0
0
2
0
0
0
2
0
2
2
0
0
0
0
1
1
1
0
0
1
0
1
1
0
3
0
0
0
1
0
0
2
0
1
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
1
0
2
1
1
2
0
0
0
0
0
1
1
0
0
0
0
0
0
3
0
0
0
2
2
5
2
0
0
2
0
1
1
2
0
1
0
0
0
1
2
0
0
3
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
2
0
0
1
0
2
0
2
0
0
0
1
0
0
2
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
1
2
0
1
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
1
0
1
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
2
0
1
1
7
0
1
4
0
0
1
1
0
1
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
2
1
0
0
0
0
0
1
0
0
0
3
1
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
2
3
0
0
0
0
1
0
0
0
0
0
2
4
0
0
0
0
1
0
1
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
1
2
0
0
0
0
2
1
1
0
1
0
0
2
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
3
1
1
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
5
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
2
1
2
0
1
1
0
1
0
0
0
0
2
0
0
0
2
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
1
2
1
0
0
0
0
2
0
2
3
0
0
1
0
0
0
0
1
3
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
2
0
0
2
0
2
1
0
0
0
0
0
1
0
2
0
1
0
1
0
0
0
4
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
4
0
2
4
0
0
0
0
1
0
0
0
0
0
0
2
1
2
0
2
0
0
0
0
1
1
2
0
0
0
2
0
0
2
2
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
2
0
0
2
4
0
0
0
0
0
2
0
0
0
0
0
3
0
0
2
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
5
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
1
0
0
0
0
0
0
0
1
0
2
2
0
0
2
0
0
3
3
0
0
0
0
1
1
0
0
0
0
0
2
2
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
1
0
0
0
2
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
2
0
0
2
0
1
0
2
0
0
2
0
2
2
2
0
0
2
0
0
0
1
0
0
3
2
1
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
2
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
5
0
0
0
0
3
2
2
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
1
0
2
2
0
0
0
2
0
1
2
2
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
1
0
1
1
2
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
2
0
2
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
2
0
1
1
0
0
3
0
0
5
0
0
4
0
2
0
0
1
0
0
1
0
1
0
0
0
0
3
0
0
0
2
2
1
0
1
2
0
1
0
1
0
0
0
2
2
0
1
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
1
0
0
1
0
2
0
2
0
0
0
0
0
1
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
3
2
1
2
0
2
0
0
0
0
0
1
6
1
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
3
0
1
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
3
0
0
0
0
0
1
2
0
0
0
2
0
0
0
1
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
3
0
1
0
0
2
0
0
1
0
0
0
0
1
0
0
2
1
2
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
1
0
0
0
0
1
0
4
0
0
0
2
0
0
0
0
0
0
0
0
1
2
2
3
2
3
0
0
1
0
2
0
0
0
2
1
0
0
2
2
0
1
1
0
0
2
1
1
0
0
0
0
0
1
2
0
0
0
2
0
3
0
0
0
2
0
2
0
0
0
0
0
0
0
2
2
0
1
1
0
0
0
1
2
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
1
0
0
0
1
0
1
0
1
1
0
1
0
0
0
0
0
2
0
0
1
2
3
1
2
2
0
2
2
0
0
0
0
2
2
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
2
0
2
1
0
0
0
4
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
2
0
2
6
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
6
0
1
2
1
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
1
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
2
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
5
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
3
2
0
0
0
0
0
0
0
1
1
0
0
0
2
2
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
1
1
0
0
2
2
0
0
0
0
2
0
0
0
0
2
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
3
1
0
2
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
3
0
0
1
0
2
2
1
2
0
0
2
0
2
0
0
1
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
1
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
2
2
2
1
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
1
2
2
0
0
0
0
0
0
0
1
2
0
1
0
1
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
3
0
0
1
0
0
0
0
2
1
1
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
5
0
0
2
0
0
2
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
4
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
1
0
4
0
1
0
0
2
0
2
0
3
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
1
1
0
2
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
4
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
1
0
1
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
1
0
0
0
2
2
1
1
0
0
0
1
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
3
5
2
0
2
0
4
0
1
0
0
1
0
0
1
0
2
0
3
0
1
0
0
0
0
0
1
0
0
0
0
5
1
0
0
2
0
2
0
0
1
0
1
0
0
2
1
2
2
0
0
0
1
0
2
0
0
0
0
2
0
3
0
0
0
0
1
1
3
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
4
0
1
0
2
0
2
0
2
0
0
0
5
0
0
2
1
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
2
0
1
0
2
0
0
0
0
0
1
1
2
0
2
1
0
2
3
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
2
1
0
0
1
2
4
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
2
5
0
0
0
0
1
1
1
0
0
2
0
0
1
2
1
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
2
1
0
1
0
1
0
0
0
0
0
1
0
0
0
3
0
0
0
0
2
1
0
0
0
1
0
0
0
1
1
1
0
0
0
2
1
0
1
0
1
0
2
0
0
0
1
0
0
0
2
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
1
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
2
0
1
0
0
0
1
0
0
1
0
1
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
2
1
0
2
2
0
2
0
0
0
0
0
2
0
0
2
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
3
1
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
2
0
1
1
0
2
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
3
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
9
0
0
0
1
0
0
1
2
2
2
0
1
2
0
0
0
2
0
0
0
1
1
0
0
2
0
2
0
0
0
0
0
1
0
0
0
1
0
3
0
1
0
0
0
2
1
1
0
0
1
0
0
0
0
1
0
1
2
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
2
0
0
2
0
2
0
1
0
0
3
0
0
0
3
0
0
0
1
2
2
0
2
3
0
0
2
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
1
1
0
1
0
1
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
1
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
3
0
0
1
0
0
2
2
2
0
1
0
0
2
0
2
0
0
0
0
0
0
2
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
2
1
0
0
1
3
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
6
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
3
0
3
0
2
0
0
0
0
1
0
0
0
0
3
0
0
1
0
0
0
0
2
0
0
0
2
2
0
0
2
0
0
0
3
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
3
2
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
1
1
2
0
0
0
1
1
0
0
0
3
2
0
2
0
0
0
0
0
0
2
2
1
2
1
0
1
0
1
0
0
2
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
1
0
0
0
0
0
1
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
3
0
0
0
2
0
1
0
0
0
0
1
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
2
0
0
0
3
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
1
0
1
0
0
0
0
0
2
0
0
0
2
2
0
0
1
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
1
0
2
0
2
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
1
1
2
3
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
1
3
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
1
6
0
0
1
0
0
1
3
1
0
0
2
0
0
2
0
2
0
0
1
0
2
0
3
0
2
0
0
5
0
0
1
0
0
2
0
2
0
2
0
2
4
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
2
1
0
2
1
0
0
0
0
0
4
2
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
2
0
2
0
0
0
2
0
0
2
1
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
7
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
3
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
2
0
0
2
0
0
2
0
2
0
1
0
1
0
2
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
1
0
0
1
0
0
2
1
0
2
0
2
0
0
1
0
0
0
0
0
1
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
2
0
3
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
3
2
0
0
1
0
0
0
0
0
0
0
0
0
0
5
1
0
0
1
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
2
1
0
0
2
0
2
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
3
0
0
1
0
0
0
1
0
0
0
2
2
0
0
0
0
0
2
0
0
2
0
0
2
1
1
2
1
2
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
2
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
2
0
2
2
0
2
0
0
2
0
2
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
2
1
0
0
5
0
2
0
0
0
0
0
2
3
3
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
1
0
3
0
0
3
2
0
0
2
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
1
0
2
2
0
0
2
0
1
0
0
2
0
0
0
1
0
1
0
0
2
0
2
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
1
1
0
1
0
2
0
3
1
2
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
2
1
0
0
0
0
2
0
2
1
1
0
0
3
0
0
1
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
4
1
1
2
1
0
0
0
1
1
0
2
0
0
0
0
2
0
0
3
0
1
0
0
0
1
0
2
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
1
3
2
3
0
0
0
0
2
1
0
1
0
1
3
0
0
0
1
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
1
0
0
2
0
2
0
1
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
1
2
0
0
1
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
2
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
1
0
1
0
0
0
2
0
0
0
1
2
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
1
0
1
0
1
2
0
0
0
0
0
3
0
1
0
0
0
2
2
1
2
0
1
0
0
0
0
1
0
2
0
0
2
0
0
2
0
0
0
0
0
0
2
0
2
0
0
2
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
1
0
0
1
1
0
1
0
0
1
0
0
0
1
0
3
0
1
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
2
1
0
2
2
2
0
0
0
2
0
2
0
0
0
1
0
0
2
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
2
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
3
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
2
0
0
0
0
2
0
0
1
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
3
2
1
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
3
3
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
2
0
1
0
0
0
0
1
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
2
0
1
4
1
0
0
0
2
0
0
0
2
0
0
2
0
1
0
2
0
0
0
0
0
0
0
2
2
0
0
2
1
0
1
0
2
1
0
1
0
2
0
0
0
0
0
1
0
0
0
0
2
0
1
2
0
2
0
2
0
0
0
0
3
1
0
0
0
0
1
2
0
2
2
2
0
0
0
0
3
0
0
2
1
0
0
3
0
0
0
0
0
1
0
2
1
1
0
1
0
0
0
2
0
0
3
0
4
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
1
1
0
0
2
0
1
0
8
1
0
0
0
1
2
2
1
0
2
0
0
0
2
0
0
0
0
6
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
6
0
0
0
0
1
0
0
0
0
0
0
2
1
2
1
1
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
2
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
1
2
2
0
0
2
0
2
0
0
0
2
2
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
1
0
2
1
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
1
1
0
2
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
1
0
2
0
1
0
0
0
0
0
0
1
0
1
2
0
0
0
1
1
2
0
0
0
2
0
1
0
1
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
2
1
0
0
0
0
0
1
0
0
1
2
0
0
1
1
0
0
0
2
0
0
0
3
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
2
0
0
0
3
2
2
1
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
6
0
0
0
3
0
2
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
1
2
2
0
1
0
2
1
0
2
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
1
0
1
0
0
1
0
2
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
1
2
2
0
2
0
0
2
1
0
2
0
0
0
0
1
0
0
1
0
1
0
0
0
2
0
1
3
0
0
0
0
2
0
0
0
2
0
0
0
2
0
2
2
0
0
0
0
2
1
0
0
3
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
2
0
3
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
2
0
0
0
2
0
1
2
0
0
0
0
2
0
0
5
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
6
3
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
1
1
0
1
0
0
0
0
2
1
2
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
2
1
0
0
0
2
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
3
1
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
1
1
1
0
0
2
2
3
0
0
0
0
2
0
2
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
1
0
1
2
0
0
2
0
1
0
1
0
1
0
0
0
0
0
0
2
0
1
0
2
0
0
2
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
2
0
1
0
0
2
3
0
0
0
0
0
0
0
2
1
2
1
0
1
0
2
0
2
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
3
2
1
0
0
0
0
1
0
0
2
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
2
2
2
1
0
0
2
0
1
1
0
2
0
0
1
1
0
2
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
2
0
0
6
0
3
0
0
0
0
0
1
1
0
1
3
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
1
1
2
0
2
2
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
2
2
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
2
0
1
2
0
0
0
0
0
2
0
0
0
2
0
2
2
2
0
1
0
0
0
0
0
1
1
0
0
0
2
0
1
2
2
0
2
1
3
0
1
2
0
1
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
3
1
0
0
0
2
0
1
0
0
1
2
0
0
0
0
1
0
0
0
1
0
0
0
0
1
4
0
0
0
0
0
1
2
0
0
2
2
0
2
2
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
2
2
1
0
1
0
2
1
0
0
0
0
0
0
5
0
0
0
0
0
2
0
0
0
1
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
2
2
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
2
1
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
2
0
0
0
1
0
0
2
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
2
0
2
0
2
0
0
0
0
0
0
0
0
2
0
2
2
1
0
0
0
0
0
1
0
0
0
3
1
0
2
0
2
0
1
0
0
0
1
0
0
2
2
1
1
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
1
2
0
0
2
0
0
0
0
1
0
0
0
0
2
0
1
0
1
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
1
0
0
0
0
0
2
0
0
0
5
0
0
0
1
1
0
0
0
1
1
0
3
0
0
2
2
0
0
0
2
2
1
2
0
2
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
2
2
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
3
1
0
0
0
0
4
1
0
0
1
0
0
0
0
0
0
2
0
2
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
3
0
0
0
0
2
3
0
0
0
0
0
1
2
0
1
1
0
0
1
0
0
2
0
0
0
0
0
3
0
0
0
0
1
0
1
1
0
0
1
2
0
1
2
0
0
0
0
0
2
0
0
0
3
2
0
0
1
0
2
2
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
1
1
1
0
1
2
1
0
1
0
1
0
2
0
2
0
2
1
2
0
0
2
0
0
2
2
0
0
0
0
3
0
1
1
2
1
0
0
0
0
0
0
0
1
1
0
2
0
0
0
1
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
2
2
2
2
0
0
0
1
0
0
4
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
2
5
1
0
0
1
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
2
0
0
0
0
2
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
3
0
2
0
0
0
0
1
1
1
0
1
0
0
1
3
0
0
0
1
1
0
1
0
1
0
3
0
0
0
0
0
0
0
0
3
0
0
0
0
3
0
0
0
2
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
6
0
2
2
3
2
0
0
0
0
3
0
0
0
0
1
1
2
2
1
0
0
1
2
0
0
0
0
0
0
3
0
2
1
0
0
0
0
0
0
1
0
2
0
1
1
0
1
0
1
1
1
1
0
0
0
0
0
3
1
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
6
1
0
0
0
1
1
0
2
2
2
1
1
0
0
1
0
0
0
1
1
0
0
1
0
1
2
0
0
0
1
0
0
0
2
1
0
0
1
0
2
2
0
0
0
0
2
7
0
0
0
0
0
2
0
0
0
3
2
2
0
0
0
0
0
0
3
0
0
0
0
0
1
0
1
0
2
0
1
0
0
0
1
0
2
1
2
0
0
0
0
0
0
2
1
1
0
1
0
0
0
0
1
0
2
0
1
0
0
2
0
0
1
0
0
0
0
0
0
2
0
2
1
1
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
4
2
1
4
0
0
0
0
0
1
0
1
2
0
0
0
0
0
3
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
9
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
1
3
0
0
1
0
1
1
2
0
1
0
0
0
0
2
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
2
1
0
2
3
0
0
0
2
2
1
0
0
0
0
1
2
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
1
0
2
0
0
0
0
1
0
1
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
2
0
2
0
2
0
1
0
1
1
1
0
0
0
1
5
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
2
1
0
0
0
0
1
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
7
0
1
0
1
0
4
0
0
0
2
0
1
2
1
4
0
0
1
0
2
0
0
2
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
1
2
0
0
1
2
1
0
0
1
2
2
2
0
2
0
0
4
1
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
2
5
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
1
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
2
0
2
2
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
1
0
0
0
0
0
1
2
0
2
0
2
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
2
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
3
0
3
0
2
2
2
0
0
0
0
0
0
0
1
0
1
0
2
2
0
0
1
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
1
6
0
0
0
0
2
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
2
0
0
1
0
0
0
0
0
3
0
0
0
1
0
2
0
0
1
0
0
0
0
2
0
0
0
2
1
7
0
0
0
0
2
0
0
0
0
5
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
2
0
1
1
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
2
1
0
2
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
1
2
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
1
5
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
2
0
2
1
2
0
0
1
1
0
0
0
0
0
0
1
0
2
2
0
1
0
0
0
0
0
2
1
0
1
0
0
1
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
5
0
4
2
0
1
0
1
0
2
0
2
1
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
1
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
1
0
0
2
0
1
0
0
1
1
0
2
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
3
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
5
0
3
0
2
0
0
4
0
0
1
0
0
2
0
0
0
2
0
3
2
0
0
2
2
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
1
6
0
0
9
0
1
0
0
0
0
1
1
2
2
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
2
1
2
0
0
2
3
0
2
1
1
1
0
0
1
0
0
2
0
0
1
1
0
1
0
1
2
0
0
0
2
0
1
1
2
2
1
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
3
0
2
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
6
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
2
3
0
0
0
0
2
0
1
1
0
1
0
0
0
0
1
2
0
0
1
2
0
2
0
0
0
1
0
0
2
0
2
0
0
2
2
0
0
1
1
0
0
1
0
0
0
1
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
2
1
0
0
0
0
0
3
2
0
0
0
2
0
2
0
0
2
0
0
1
0
0
0
2
0
2
0
1
0
2
0
0
0
0
0
3
4
0
0
1
0
0
0
0
1
1
0
3
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
1
0
2
0
0
0
0
0
0
2
1
0
2
0
2
0
2
0
2
1
0
0
2
2
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
3
2
0
2
0
2
0
1
0
2
0
0
0
1
0
0
0
1
2
0
0
2
2
0
2
0
0
0
0
2
0
0
2
2
0
0
0
1
1
2
0
2
0
0
0
0
0
0
0
2
1
1
0
2
1
1
0
0
0
2
1
0
3
0
2
0
1
0
0
0
1
0
2
3
0
1
3
1
0
0
0
0
0
1
1
0
0
2
0
2
0
2
0
3
0
1
2
0
0
0
0
0
0
0
0
1
0
2
0
1
3
1
0
0
0
1
0
2
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
1
0
0
1
0
2
3
0
0
2
0
2
0
0
0
2
0
1
0
0
1
0
0
0
0
2
0
0
5
0
1
2
10
0
0
2
2
1
0
0
0
0
2
0
0
1
2
0
0
1
0
3
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
1
0
0
0
0
2
1
1
0
0
0
2
2
0
0
1
0
2
0
2
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
1
0
0
0
3
2
0
0
0
2
3
0
0
0
1
3
0
0
0
0
0
2
2
1
0
0
2
0
0
0
0
2
1
1
1
0
0
2
0
3
0
2
0
0
0
0
0
0
2
0
2
2
0
1
0
1
0
0
0
0
2
0
2
1
2
1
1
0
0
1
0
2
2
0
0
2
0
1
0
0
0
2
0
1
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
1
0
0
1
0
1
0
0
0
1
0
0
1
1
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
3
0
1
3
2
0
5
0
0
1
2
0
1
1
0
2
2
0
0
0
1
0
0
1
0
2
1
0
1
0
2
0
1
0
1
0
0
0
0
0
0
3
0
0
0
2
2
0
0
0
0
1
0
2
1
0
0
2
2
0
1
2
2
0
0
0
1
0
0
1
1
2
1
0
0
1
0
1
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
1
1
1
0
0
0
0
2
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
1
2
0
1
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
2
0
2
0
0
2
0
1
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
1
1
0
2
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
1
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
2
0
1
0
0
0
0
2
2
0
2
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
1
1
0
0
2
3
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
3
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
3
0
0
0
0
0
2
0
2
0
0
2
0
0
2
3
0
0
0
3
0
1
0
0
0
0
1
2
2
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
2
0
1
1
0
0
1
2
2
0
0
0
3
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
2
0
2
0
0
2
2
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
2
0
1
0
5
0
0
1
4
0
0
0
0
1
0
0
3
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
1
1
0
1
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
1
1
0
0
0
1
1
2
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
2
2
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
1
1
3
0
0
0
1
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
1
0
0
0
1
0
2
1
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
3
0
2
0
2
0
0
2
2
0
0
0
0
1
0
2
1
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
3
0
3
0
0
0
1
0
0
4
2
0
2
0
2
0
1
0
1
1
0
0
0
0
0
0
0
3
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
3
1
0
0
0
0
1
3
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
2
2
0
0
0
0
0
0
0
0
2
3
0
0
0
1
2
2
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
3
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
2
0
0
2
1
1
2
0
0
0
0
0
2
0
0
2
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
8
1
0
1
3
3
0
1
0
1
0
0
2
1
0
1
1
0
0
0
1
0
0
0
1
1
2
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
2
1
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
3
3
0
2
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
1
0
4
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
2
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
5
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
1
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
1
0
0
0
2
0
0
0
0
3
0
0
0
2
2
0
0
2
1
0
0
0
1
0
1
0
0
2
2
2
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
1
0
2
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
3
0
0
0
6
0
0
0
0
0
2
2
0
1
0
0
0
1
0
0
1
2
1
0
0
0
0
0
0
0
0
0
8
0
0
0
1
0
0
0
2
2
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
3
1
1
0
0
1
0
0
0
2
1
0
0
0
0
2
2
0
0
0
0
0
1
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
2
2
0
0
1
0
1
2
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
4
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
2
0
2
0
0
0
0
1
2
1
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
1
1
3
0
0
3
2
0
1
0
0
0
2
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
1
0
0
2
0
0
2
2
0
2
1
0
0
0
0
2
2
0
0
0
2
0
0
0
0
3
3
2
0
1
3
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
1
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
1
2
0
0
2
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
2
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
2
0
0
1
2
1
0
0
0
1
0
1
0
0
1
0
2
0
0
0
0
2
0
0
3
2
1
0
0
0
1
1
1
0
0
2
0
0
2
0
2
0
0
1
0
1
2
0
1
0
2
0
0
0
2
0
0
0
2
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
2
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
1
0
0
1
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
1
2
2
0
0
0
0
1
0
1
0
2
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
2
1
0
0
3
3
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
3
0
0
0
1
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
1
0
0
0
2
0
4
2
0
0
2
0
2
0
0
2
1
0
0
2
3
0
0
1
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
2
0
1
0
0
0
4
0
1
0
0
0
3
0
0
0
1
0
1
0
0
0
0
0
4
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
2
0
1
1
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
3
0
1
1
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
1
2
0
0
0
0
0
1
0
1
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
2
2
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
2
3
0
0
2
2
0
0
0
0
0
1
2
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
4
0
2
0
0
0
2
0
2
2
0
2
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
1
2
0
2
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
3
0
6
0
0
1
0
0
0
2
0
2
0
1
2
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
4
0
0
1
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
1
1
1
0
0
0
0
1
0
0
0
2
0
1
0
1
0
2
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
3
0
2
2
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
1
0
7
0
0
0
2
2
0
0
4
0
0
0
2
1
1
2
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
1
2
2
0
1
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
1
0
0
2
1
0
0
0
0
0
1
0
0
2
0
0
0
2
1
0
0
4
0
2
0
0
2
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
2
3
0
0
2
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
2
0
2
0
1
2
0
0
0
2
0
0
3
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
2
0
0
1
2
1
0
0
0
0
1
0
0
0
0
1
2
1
0
1
0
0
2
0
0
0
2
0
0
1
0
2
0
0
1
0
2
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
4
0
0
0
1
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
3
1
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
2
2
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
1
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
8
0
1
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
1
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
1
2
2
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
1
0
1
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
1
0
0
0
0
0
3
0
0
0
0
2
2
0
0
0
0
2
0
0
3
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
1
1
0
3
0
0
1
2
0
0
0
0
2
0
0
0
0
0
2
2
1
0
0
0
1
0
0
6
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
1
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
1
2
0
0
0
0
2
0
0
0
3
0
0
0
1
1
0
2
0
1
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
1
1
0
0
3
0
2
1
2
3
1
2
2
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
3
2
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
1
0
3
1
0
1
0
0
0
1
0
0
0
0
0
0
3
1
0
2
2
0
0
0
2
0
0
0
2
0
2
2
2
0
0
0
0
0
0
0
4
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
2
0
2
0
0
1
0
1
0
0
2
0
2
0
0
0
0
0
0
0
1
0
8
0
0
2
1
2
0
2
0
0
1
0
1
0
2
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
3
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
1
2
2
2
2
0
0
2
0
0
2
0
0
2
2
2
0
0
0
0
0
0
1
2
0
2
0
1
0
0
1
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
4
2
0
1
0
0
1
0
1
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
2
0
0
0
0
2
1
3
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
2
0
1
0
3
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
1
0
0
2
2
0
0
3
0
1
1
1
1
0
0
0
0
0
2
1
1
2
1
2
0
0
0
0
0
0
0
0
0
3
2
0
3
1
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
1
1
2
0
0
0
0
0
1
0
0
1
1
0
1
2
0
1
0
1
0
0
2
0
0
0
1
0
0
0
2
2
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
1
2
2
0
0
0
0
1
0
0
0
0
1
0
0
3
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
2
2
0
1
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
2
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
1
0
0
2
4
0
0
0
1
1
2
1
0
2
0
0
1
0
2
0
0
2
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
2
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
1
1
0
0
0
0
1
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
4
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
1
1
0
2
1
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
4
0
1
1
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
2
0
1
1
1
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
2
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
1
0
0
0
1
4
3
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
2
1
2
0
0
0
0
0
0
0
2
0
0
0
3
1
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
2
2
0
1
0
0
0
0
0
5
0
0
2
1
0
1
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
1
4
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
1
2
0
0
1
0
1
0
0
0
0
1
0
2
0
0
0
0
0
1
0
1
0
3
0
0
0
0
0
1
1
2
0
2
2
0
0
0
0
0
0
3
0
0
1
1
0
1
0
0
1
0
0
0
1
0
0
0
1
0
2
1
0
1
0
0
0
2
0
0
0
0
0
0
4
0
2
0
1
0
0
2
0
0
0
0
0
1
1
0
0
1
2
0
0
0
1
0
0
0
0
0
0
1
0
2
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
3
0
1
0
0
0
0
0
0
0
0
0
2
2
2
0
2
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
1
0
1
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
2
0
0
0
1
0
0
2
0
0
0
0
2
0
1
1
2
0
0
0
0
0
3
0
0
0
0
1
2
0
0
0
0
0
1
1
0
0
2
3
0
0
0
2
0
0
0
0
2
1
2
0
0
0
1
0
0
0
3
0
2
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
5
0
1
0
0
1
0
2
0
0
2
0
0
2
0
2
0
1
0
0
0
0
0
0
0
2
1
1
2
0
0
0
1
1
0
1
2
2
0
1
0
1
0
0
2
2
0
0
0
1
0
0
0
1
0
0
0
2
0
2
0
0
0
2
0
0
2
1
0
1
0
0
0
1
0
2
0
0
2
0
2
0
2
2
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
4
0
2
0
2
2
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
2
0
2
1
0
0
0
1
1
2
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
2
1
1
0
1
0
0
0
2
0
0
1
0
0
1
0
0
2
0
0
0
0
2
1
1
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
2
0
0
2
0
0
0
0
2
0
1
0
0
2
0
0
1
0
3
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
1
1
0
1
2
0
7
0
0
1
1
0
1
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
2
0
2
0
0
1
0
0
0
2
1
0
0
1
1
0
2
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
1
0
0
0
0
0
1
0
2
0
1
2
0
0
1
1
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
1
1
0
5
0
2
0
0
0
0
0
2
3
3
0
0
1
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
1
1
2
2
3
0
0
0
0
0
1
1
5
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
1
0
0
0
1
2
0
10
1
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
3
0
2
0
1
0
1
0
0
0
0
0
2
0
0
0
2
1
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
1
2
0
4
0
1
0
0
0
2
0
0
0
0
2
0
1
2
0
0
1
0
3
0
0
2
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
2
0
0
0
0
1
0
1
2
1
0
0
0
0
0
0
2
0
0
8
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
2
0
0
2
0
2
0
3
1
0
0
0
0
0
1
0
0
0
1
0
1
2
0
0
0
0
1
0
0
2
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
2
1
2
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
2
4
0
0
0
0
0
0
2
1
0
1
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
4
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
2
2
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
2
1
0
1
0
2
0
2
1
1
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
1
0
1
6
0
0
0
0
0
1
1
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
1
1
0
0
0
2
0
0
3
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
2
1
0
0
3
0
0
2
0
0
0
0
2
1
0
2
2
1
2
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
3
0
2
1
0
2
0
1
0
2
1
0
0
0
0
2
2
0
2
0
1
0
1
2
0
0
0
0
0
2
2
1
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
1
0
0
0
2
1
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
4
0
0
1
0
0
0
2
0
0
0
1
0
1
0
0
2
0
1
0
2
0
0
0
0
2
2
0
0
0
2
0
0
0
1
0
0
1
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
1
0
0
1
0
5
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
2
1
1
0
0
1
1
0
0
1
0
0
0
3
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
1
3
0
0
0
1
0
1
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
2
1
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
1
2
0
2
1
0
0
2
4
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
7
0
4
0
0
0
1
1
0
0
2
0
0
1
1
2
0
0
0
0
0
2
0
1
0
0
0
0
1
1
1
1
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
2
2
0
0
0
0
1
0
0
0
0
0
1
0
3
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
3
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
2
2
0
1
0
2
0
0
0
0
2
0
0
2
2
0
0
0
0
0
1
0
2
1
0
0
2
0
0
0
1
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
2
2
2
0
0
2
2
0
0
3
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
2
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
1
0
2
0
0
1
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
2
1
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
6
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
1
2
0
1
0
2
0
2
0
0
0
0
2
2
2
0
0
0
1
2
0
3
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
7
0
0
0
2
0
0
0
0
1
0
0
0
0
2
2
2
0
1
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
3
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
3
0
3
0
0
0
0
0
0
1
0
2
0
0
0
0
2
1
0
2
0
0
0
0
0
0
1
0
2
0
1
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
3
0
0
2
0
0
0
2
0
4
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
3
2
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
3
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
5
0
1
1
0
0
0
0
1
1
0
0
0
1
0
4
1
1
0
2
1
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
2
0
1
0
0
0
2
0
0
0
2
0
1
0
0
0
0
1
3
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
5
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
2
1
1
0
0
0
0
0
0
0
0
0
2
2
1
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
3
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
6
2
0
0
0
0
2
0
0
2
3
0
0
0
0
0
5
2
0
0
0
0
0
1
0
1
0
0
0
2
1
2
0
1
0
0
0
0
0
1
1
1
4
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
3
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
2
0
1
0
0
0
2
1
0
1
0
0
0
4
0
0
0
1
1
0
0
2
0
1
0
0
2
0
0
0
0
0
2
1
0
0
0
1
0
1
1
0
1
2
0
2
0
1
0
0
0
0
0
2
0
3
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
1
0
2
1
1
0
2
0
0
0
0
0
2
0
0
2
1
0
0
0
0
4
2
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
2
1
0
0
0
2
0
0
0
3
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
2
4
0
0
0
0
1
0
2
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
7
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
1
2
0
0
0
0
1
0
0
1
2
0
0
0
0
1
2
2
1
0
0
0
0
1
0
0
1
0
1
0
0
0
1
1
0
0
2
1
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
2
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
1
0
0
1
1
1
0
0
0
0
3
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
1
1
0
0
2
0
1
0
3
0
2
0
0
2
0
0
0
1
2
0
0
3
1
0
2
1
3
0
2
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
2
1
2
0
0
0
0
0
0
0
1
3
0
3
2
2
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
2
3
0
0
0
0
0
0
0
1
0
0
0
2
1
0
2
2
0
1
0
0
2
0
0
1
0
0
2
0
0
2
1
1
0
0
0
0
0
0
0
2
0
0
0
0
2
4
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
2
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
3
2
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
2
0
0
1
0
1
0
2
0
0
0
0
2
3
0
2
1
3
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
3
0
0
0
0
0
0
0
1
0
1
2
3
0
2
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
1
2
0
1
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
2
4
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
2
1
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
2
0
0
1
0
0
0
1
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
1
4
1
0
3
0
0
0
2
0
0
2
1
1
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
2
0
0
0
2
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
1
0
0
0
0
0
2
0
3
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
1
2
1
0
0
1
1
1
0
1
2
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
2
0
0
0
1
0
2
0
0
0
2
0
0
0
0
2
3
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
2
2
1
0
0
0
0
0
0
0
2
1
1
0
2
2
0
1
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
4
0
0
3
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
2
1
0
4
0
0
2
0
0
0
0
0
0
1
1
1
0
2
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
1
0
0
3
0
1
0
0
0
0
1
2
0
0
0
0
0
2
2
1
0
0
1
0
0
0
0
1
1
2
0
0
0
0
2
0
0
0
5
2
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
2
0
0
0
1
0
2
1
1
0
0
0
0
0
1
1
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
1
1
0
0
3
0
0
0
0
0
0
2
0
0
0
3
3
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
1
0
0
1
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
1
2
1
2
0
0
0
2
0
1
0
0
2
0
0
2
0
0
0
5
0
0
0
0
2
1
1
0
0
2
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
1
6
0
0
1
0
0
0
0
2
0
2
0
3
1
0
0
0
2
0
0
0
1
3
2
0
0
0
0
0
0
0
1
2
0
0
0
2
2
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
2
0
1
0
15
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
1
0
0
0
0
2
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
3
1
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
2
2
2
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
3
0
0
1
0
1
1
0
2
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
2
0
1
0
0
0
1
1
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
2
0
1
2
1
0
3
0
0
0
0
2
1
1
0
0
0
1
5
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
18
0
0
2
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
1
1
0
0
0
0
0
0
1
1
0
1
2
0
1
0
1
2
0
0
0
2
2
0
2
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
3
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
2
0
0
0
3
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
3
2
0
0
1
0
2
0
0
2
0
0
1
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
3
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
1
0
0
0
4
0
0
0
2
0
0
1
2
2
1
0
0
1
0
1
0
1
0
1
0
0
0
0
5
2
2
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
3
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
5
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
1
0
2
2
2
0
0
0
0
0
3
1
0
2
0
1
3
6
3
0
1
1
0
0
0
0
0
0
1
0
2
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
4
0
1
0
0
0
0
0
0
0
4
2
2
0
0
0
2
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
2
0
0
1
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
2
0
1
0
0
3
0
1
0
2
0
0
0
1
0
0
3
0
0
0
0
0
1
0
0
3
0
1
0
0
0
2
2
0
1
0
2
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
3
2
0
0
0
3
0
2
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
1
2
2
0
0
1
0
0
0
0
0
0
0
0
4
1
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
3
0
2
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
2
1
0
2
0
0
2
0
1
0
2
2
2
0
1
2
0
0
0
0
3
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
2
0
0
1
0
0
0
2
0
1
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
3
0
1
0
2
0
0
0
0
0
0
1
0
1
0
0
1
1
2
0
1
0
0
0
0
0
0
2
2
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
2
0
2
0
0
0
1
0
2
0
0
1
1
2
0
3
0
0
0
0
1
3
0
0
0
3
0
0
1
0
2
0
1
2
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
2
1
0
0
4
2
0
0
0
0
3
0
2
0
0
1
0
2
0
3
2
0
0
0
1
0
0
0
3
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
2
0
1
0
0
0
2
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
2
1
0
0
0
0
2
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
1
1
0
0
2
1
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
1
0
0
0
0
4
0
3
0
1
1
0
0
0
0
0
0
2
0
2
0
1
0
0
2
0
2
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
1
1
0
0
0
1
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
2
0
0
2
0
1
1
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
3
1
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
2
1
2
2
2
0
2
2
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
2
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
1
2
2
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
2
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
1
0
0
0
0
0
0
2
0
1
0
1
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
1
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
2
1
0
0
2
0
1
0
0
0
0
0
0
1
2
0
0
0
4
0
0
1
0
0
0
1
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
4
0
0
0
2
0
0
1
0
1
1
3
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
1
1
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
2
1
1
0
0
2
2
0
3
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
1
1
0
3
1
0
0
1
3
0
2
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
1
0
2
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
2
2
0
1
0
0
0
0
0
2
1
1
0
0
2
0
2
0
0
0
0
1
2
0
0
1
0
1
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
3
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
2
0
0
2
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
2
0
0
3
0
0
2
0
0
0
0
0
0
1
2
0
0
2
0
0
1
0
0
1
0
0
0
1
1
0
0
0
2
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
2
0
0
2
0
0
0
0
2
0
0
0
5
1
2
1
0
0
0
0
2
2
0
0
0
2
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
2
3
0
0
2
0
0
0
0
0
1
0
1
2
2
0
1
2
0
0
0
0
2
0
0
0
0
1
0
3
0
0
1
0
1
2
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
2
0
2
0
1
0
0
0
0
0
0
1
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
5
3
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
1
1
0
0
0
0
2
0
0
0
0
0
1
2
1
0
0
1
2
0
0
2
0
0
0
1
0
2
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
3
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
2
0
2
1
0
0
2
0
0
4
0
0
0
1
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
3
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
1
0
2
0
1
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
1
1
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
2
1
0
0
2
0
1
0
1
0
0
2
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
1
0
0
0
0
2
1
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
2
1
0
2
1
1
1
0
1
2
1
4
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
4
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
1
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
1
2
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
1
1
0
2
3
0
0
1
2
0
2
1
2
0
2
0
0
0
2
0
0
2
0
0
0
2
0
0
1
0
0
0
2
0
0
0
1
0
1
0
18
0
1
0
2
0
1
3
5
0
0
0
0
0
0
0
0
0
0
0
1
2
1
2
0
0
0
0
0
2
0
2
1
0
2
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
4
0
0
0
1
3
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
2
1
0
2
4
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
1
0
0
1
3
0
1
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
2
4
0
0
1
0
0
0
0
3
0
2
0
1
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
1
0
3
0
0
1
0
1
0
2
0
0
2
0
0
0
1
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
1
0
0
3
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
7
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
2
1
0
2
0
0
0
0
2
0
0
0
0
0
2
0
1
1
0
3
0
0
0
0
0
0
0
3
1
0
0
0
3
0
2
0
0
1
0
1
0
2
0
0
0
0
0
0
0
1
1
0
1
1
1
0
0
0
1
0
1
0
0
1
0
1
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
2
2
0
0
0
2
0
0
1
0
1
0
1
0
0
0
0
0
2
1
0
0
5
1
2
0
0
1
0
0
0
0
0
1
0
0
0
1
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
2
0
2
1
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
2
0
1
1
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
3
0
0
0
0
2
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
1
0
0
2
1
0
0
1
0
0
2
0
0
2
0
0
1
0
0
0
0
0
1
1
2
2
0
2
0
0
0
0
0
2
0
0
1
1
1
0
2
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
1
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
1
0
0
2
0
1
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
1
0
2
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
2
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
2
0
0
1
4
0
0
0
0
0
0
1
0
0
0
0
3
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
3
0
2
0
0
0
0
0
1
2
0
0
0
2
0
0
0
1
0
0
0
0
1
0
1
2
0
2
1
0
0
0
0
0
1
1
0
0
1
1
0
0
0
1
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
2
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
2
2
2
0
0
0
2
0
2
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
1
1
0
2
0
0
3
1
0
0
1
0
0
2
0
0
1
0
0
0
1
2
1
0
0
2
1
0
1
0
0
0
0
0
1
0
2
0
1
1
0
0
0
0
0
0
0
2
0
1
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
2
0
1
0
0
0
0
0
0
0
0
0
3
1
0
6
2
0
0
1
0
0
1
0
0
3
4
1
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
2
2
2
0
1
0
0
1
0
0
2
0
0
0
1
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
1
1
0
2
2
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
1
0
0
1
2
1
0
2
0
3
0
0
0
1
2
0
1
0
0
0
2
2
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
3
0
0
0
1
0
4
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
1
1
0
0
0
16
0
0
0
1
0
0
1
1
0
0
0
0
2
0
0
2
0
0
0
2
0
0
1
0
0
1
0
0
0
8
0
0
0
0
2
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
1
0
1
0
0
2
0
0
0
2
0
0
2
0
1
2
0
1
2
0
0
0
0
0
0
2
3
0
2
0
0
0
2
0
2
2
6
2
0
0
2
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
2
0
1
0
1
1
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
5
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
1
2
0
0
0
0
0
1
1
0
0
0
4
2
3
1
0
0
1
2
0
2
0
0
0
0
0
0
2
2
2
0
2
0
1
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
4
1
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
1
0
0
0
2
0
0
1
0
3
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
3
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
6
0
4
1
2
2
2
2
0
2
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
2
0
2
0
1
0
0
0
1
1
2
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
2
1
1
0
0
1
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
1
3
0
0
1
1
0
0
0
0
0
2
0
0
0
0
2
9
0
0
1
1
0
1
2
0
0
0
2
0
0
0
0
2
0
2
0
0
2
0
0
1
0
2
0
0
5
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
1
0
0
0
1
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
5
0
0
1
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
6
1
0
0
1
0
2
0
1
0
2
0
0
0
0
0
0
0
1
1
0
2
0
2
2
0
0
2
0
2
0
0
0
1
0
2
0
0
1
0
0
1
0
0
0
0
0
0
2
0
3
0
1
2
0
0
0
2
1
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
3
0
0
1
0
0
2
0
0
0
0
1
1
0
1
0
0
0
2
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
4
0
0
1
2
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
2
3
1
0
0
0
2
0
0
3
1
0
0
1
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
1
2
2
2
3
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
3
2
0
0
1
0
1
0
2
0
0
0
0
0
1
1
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
2
0
1
0
0
0
0
3
0
1
2
2
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
2
1
2
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
2
1
0
2
0
2
2
0
0
3
0
0
0
0
0
0
2
0
0
0
1
0
1
0
1
1
0
0
1
2
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
2
0
2
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
1
2
0
0
0
0
0
0
2
1
0
0
2
0
1
0
0
0
0
0
0
2
1
2
2
0
0
2
0
0
0
1
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
3
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
1
0
0
3
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
3
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
3
0
0
1
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
1
0
1
2
1
1
0
0
0
1
1
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
2
0
0
1
0
0
1
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
1
1
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
2
0
0
2
2
2
0
1
0
1
0
0
1
1
0
0
0
0
1
0
0
1
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
3
2
0
0
2
0
2
0
0
0
0
1
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
2
0
0
2
0
0
1
0
0
2
0
0
2
0
0
2
1
0
0
0
0
1
0
1
0
0
0
2
0
1
0
0
1
0
0
0
2
0
2
0
1
0
1
1
0
0
0
0
2
0
0
2
0
0
1
0
0
0
1
0
0
0
1
2
1
0
0
0
0
2
0
0
0
0
1
0
1
2
0
0
0
0
0
2
0
2
0
0
3
0
1
0
0
2
0
2
0
0
0
0
1
2
0
0
1
0
0
0
0
0
2
0
1
0
0
0
2
0
1
2
1
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
1
1
0
2
2
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
2
1
0
2
0
0
0
0
1
0
0
2
0
0
0
2
0
4
0
0
3
0
0
1
0
0
1
0
1
1
2
0
2
1
0
1
0
0
1
0
0
1
0
0
0
0
0
7
0
0
2
0
1
3
0
0
0
0
1
1
2
0
0
0
0
5
0
3
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
2
0
1
0
0
0
0
2
7
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
3
2
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
2
0
1
1
0
1
1
0
0
2
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
5
0
1
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
1
1
0
0
0
1
0
0
1
0
2
1
1
2
0
1
0
0
0
0
0
1
2
0
0
0
4
0
1
0
1
2
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
4
2
1
0
1
1
1
0
2
0
1
1
2
0
1
0
0
0
2
1
2
2
0
0
2
0
0
0
1
0
0
1
0
1
0
0
0
0
0
2
0
0
2
0
0
0
3
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
1
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
1
0
1
1
0
0
2
3
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
2
0
0
1
0
2
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
2
0
0
0
0
1
0
2
0
2
1
0
7
0
1
0
1
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
1
1
0
2
0
0
0
0
0
0
1
0
0
1
2
0
0
1
0
0
1
0
1
0
0
0
0
2
0
0
2
2
0
0
2
2
1
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
3
1
2
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
2
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
2
1
0
0
0
0
2
1
0
2
0
0
2
0
0
0
2
0
0
1
0
2
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
1
2
0
0
0
0
1
0
2
0
1
2
0
0
0
2
2
0
1
0
0
0
0
2
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
1
0
0
0
1
0
0
0
1
0
0
0
1
2
0
0
3
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
1
0
0
0
2
0
1
0
0
2
3
0
2
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
3
0
0
3
0
2
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
1
0
2
0
7
1
0
7
0
0
1
0
2
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
2
0
0
1
1
0
1
0
0
2
5
1
1
0
0
2
1
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
13
10
0
0
0
2
0
2
1
0
0
0
0
0
0
2
0
0
2
1
2
0
2
0
0
2
0
0
0
1
0
0
0
8
0
3
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
2
0
0
2
2
1
0
2
0
0
1
0
2
1
0
0
2
0
1
0
5
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
1
0
0
1
1
2
0
1
2
2
0
0
0
0
0
0
1
1
1
0
0
2
2
1
2
1
0
0
0
0
2
0
0
2
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
1
0
0
0
0
0
0
0
0
3
1
0
0
0
2
0
2
0
0
2
0
0
0
0
0
4
0
0
0
2
2
0
1
2
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
1
0
2
0
0
0
6
0
2
0
0
0
0
0
0
1
3
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
1
0
0
0
2
1
0
2
0
1
0
0
2
0
0
2
1
0
0
0
0
3
3
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
2
2
0
0
2
0
0
1
0
0
0
1
2
2
0
0
0
1
0
1
1
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
3
0
0
0
0
0
0
0
1
0
1
2
0
0
0
2
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
5
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
1
2
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
1
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
3
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
1
2
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
1
0
2
0
0
0
3
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
1
2
0
0
2
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
2
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
3
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
3
0
2
1
0
0
0
0
0
0
1
0
1
2
3
1
3
0
0
5
2
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
2
0
1
0
1
0
0
0
0
0
1
0
2
0
2
0
0
0
2
0
1
0
0
0
0
1
3
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
1
0
2
2
2
0
2
1
1
0
2
1
0
0
0
2
1
0
0
0
0
1
0
0
0
1
2
0
0
1
2
0
0
1
0
0
0
1
0
0
0
0
0
0
2
1
1
1
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
3
0
0
0
0
2
0
0
0
1
3
0
0
0
0
6
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
2
1
1
0
0
0
0
0
0
1
0
2
0
1
2
1
2
0
0
0
0
0
0
1
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
2
1
0
1
0
1
0
0
0
2
0
4
0
0
0
5
0
0
1
1
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
2
1
0
2
2
2
1
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
1
0
5
0
1
0
2
1
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
1
0
0
1
0
0
1
1
0
0
1
0
1
0
1
0
0
0
1
0
2
0
3
0
4
2
0
2
0
2
0
0
0
0
1
1
2
0
1
1
1
2
0
2
1
2
4
0
0
0
0
1
1
0
2
0
0
1
0
0
1
0
0
0
0
0
2
0
1
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
3
2
0
3
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
4
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
1
1
0
0
1
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
1
2
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
2
1
0
0
0
2
1
0
0
3
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
3
0
0
1
0
0
0
2
0
1
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
2
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
2
1
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
2
1
5
0
0
0
0
0
1
2
2
0
0
1
0
0
0
2
0
0
2
2
0
0
0
1
0
1
0
0
0
1
0
5
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
1
0
2
0
2
2
3
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
1
1
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
7
1
0
0
0
0
0
1
0
0
0
2
1
0
0
2
1
1
1
0
0
0
1
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
1
1
0
0
0
1
0
2
1
1
0
0
2
0
1
1
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
3
0
0
0
1
0
3
0
0
0
3
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
1
0
0
2
0
0
3
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
1
0
0
0
0
2
1
0
2
3
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
2
1
0
1
0
0
2
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
1
3
0
0
0
0
9
0
2
0
0
2
2
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
2
2
0
1
0
0
0
4
2
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
2
0
2
0
0
0
4
0
0
1
0
0
0
1
0
0
0
0
1
1
0
2
0
0
2
0
0
0
1
0
1
3
0
3
0
0
2
0
0
2
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
3
2
0
0
0
2
0
0
0
1
0
0
0
3
0
0
3
0
0
0
0
2
0
0
0
2
2
0
0
0
2
2
0
0
0
4
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
2
1
0
2
2
2
2
3
2
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
3
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
4
0
2
0
0
0
1
0
3
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
1
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
1
0
0
0
1
0
0
3
0
0
0
4
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
1
2
2
0
2
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
2
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
3
3
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
2
3
0
0
1
0
0
0
0
2
2
8
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
1
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
1
2
0
0
1
1
0
0
0
0
2
0
0
1
2
0
0
1
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
1
0
0
0
0
3
0
2
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
4
0
0
3
0
6
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
1
0
1
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
2
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
3
0
3
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
3
1
1
0
0
0
0
0
0
2
2
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
4
0
0
0
0
2
0
0
0
2
0
0
0
1
0
1
0
1
0
0
0
0
2
2
0
0
0
0
2
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
1
0
0
0
0
2
2
0
0
0
2
2
0
0
0
0
0
1
0
2
0
2
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
7
0
1
3
0
2
0
1
0
2
0
0
0
0
2
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
1
0
2
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
1
0
0
1
0
0
0
2
0
0
2
0
2
1
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
2
3
1
0
0
0
2
0
0
0
0
2
0
1
0
2
0
0
1
0
0
0
0
0
0
5
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
1
0
1
2
0
0
3
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
4
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
2
2
0
0
2
0
0
0
0
0
3
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
1
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
2
2
0
0
0
0
2
0
2
3
0
2
0
0
0
0
0
0
0
1
0
3
1
0
3
0
0
0
0
1
0
1
0
0
0
0
1
0
2
0
1
0
0
0
0
0
1
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
2
2
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
1
1
3
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
1
0
0
0
0
2
1
0
1
0
0
0
1
0
3
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
2
0
2
0
0
3
2
0
2
1
1
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
1
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
2
0
0
1
2
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
2
1
0
0
0
1
0
0
2
2
0
0
0
0
0
2
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
1
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
2
3
2
0
0
1
0
2
2
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
3
0
0
2
0
1
0
0
0
0
2
1
0
1
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
2
2
0
0
0
4
0
0
0
0
0
3
2
0
0
0
0
0
1
2
2
0
0
0
0
0
1
0
3
1
1
0
0
0
0
1
0
3
3
0
0
0
0
0
1
0
1
1
0
2
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
2
0
1
2
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
1
1
0
0
3
0
0
1
3
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
3
0
2
0
0
0
0
1
0
0
1
2
0
0
2
0
0
2
0
0
1
0
0
0
1
0
2
0
0
0
3
0
0
0
0
0
0
0
0
1
2
3
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
2
2
0
0
1
0
0
0
2
0
0
1
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
2
0
0
0
0
3
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
2
1
1
2
2
1
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
1
0
0
1
1
0
0
0
0
0
0
0
2
0
2
0
2
1
0
0
0
0
2
0
0
1
1
0
1
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
1
4
0
0
0
0
0
0
0
2
1
0
3
0
0
0
0
0
0
0
1
0
0
0
0
1
3
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
2
0
1
0
1
0
0
0
1
1
0
0
2
0
1
0
0
0
0
1
1
1
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
2
0
2
3
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
5
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
2
2
0
0
0
0
1
0
1
1
0
0
0
1
0
0
1
2
2
1
2
2
1
0
0
2
2
0
0
0
2
0
0
0
0
0
0
4
2
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
1
0
0
0
11
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
1
0
0
2
0
0
2
0
2
1
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
1
0
2
2
2
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
1
2
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
2
0
3
0
0
0
0
0
2
2
0
0
1
2
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
1
0
0
2
0
0
1
0
2
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
2
0
1
0
0
0
1
0
0
0
2
0
1
0
2
0
2
1
0
0
1
1
0
0
0
0
0
2
0
0
0
6
1
0
0
0
0
0
1
0
1
0
0
2
0
0
1
1
1
0
0
0
4
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
2
1
0
2
1
0
0
0
2
1
0
0
0
1
0
0
0
0
2
1
2
0
0
0
0
0
7
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
1
0
3
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
1
1
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
1
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
2
0
2
0
0
0
2
2
0
2
2
0
1
0
0
0
0
0
0
1
0
1
0
0
2
1
1
1
0
5
1
0
0
4
0
0
0
1
0
0
2
2
0
0
0
1
2
0
1
2
0
2
0
1
2
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
2
0
0
2
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
2
0
3
0
2
0
0
2
0
0
1
0
2
0
1
1
1
0
0
0
2
0
1
0
3
0
1
2
0
0
0
0
1
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
6
1
0
0
0
2
1
0
0
0
0
1
1
1
0
0
0
1
0
0
3
1
0
1
0
0
0
0
0
2
0
0
0
0
1
0
3
0
0
2
0
3
0
0
0
3
1
0
0
0
0
0
0
1
0
3
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
6
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
3
1
0
0
2
2
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
2
0
2
0
1
0
1
0
0
0
0
0
1
1
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
3
0
0
0
0
2
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
2
0
0
1
0
2
0
1
0
0
0
2
0
0
0
0
0
3
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
12
0
2
0
0
0
0
1
1
0
0
0
0
0
2
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
2
0
1
0
2
0
1
2
0
0
0
1
0
0
0
0
0
0
0
3
0
1
0
1
1
0
0
0
5
0
2
0
0
3
0
0
0
2
0
0
1
0
2
0
0
4
1
0
0
2
0
2
2
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
1
0
1
0
1
0
0
1
2
0
1
0
0
2
0
1
2
0
1
0
0
0
0
1
0
0
0
0
3
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
1
0
1
3
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
1
4
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
3
2
0
0
7
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
1
0
0
0
1
2
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
2
0
2
1
2
0
0
2
2
1
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
1
0
2
0
0
0
2
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
2
0
2
0
0
1
1
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
5
2
0
0
0
0
0
6
2
0
2
1
0
0
0
0
0
0
0
1
2
0
0
2
1
2
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
1
0
0
0
2
2
0
0
3
0
0
0
4
0
2
1
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
1
0
0
1
0
0
0
1
0
0
2
0
0
1
2
0
0
0
0
1
0
0
0
1
0
0
0
2
1
0
1
1
0
0
0
2
0
2
0
0
2
2
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
1
0
1
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
2
0
0
1
0
0
2
0
0
2
0
1
0
1
2
2
0
0
2
1
0
1
1
2
1
0
2
0
0
2
0
0
0
1
0
0
0
1
0
1
0
0
3
0
0
0
4
2
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
2
2
0
0
1
1
0
0
2
1
2
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
1
2
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
2
0
2
0
0
0
1
1
2
0
2
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
2
2
2
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
3
0
0
0
3
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
1
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
3
0
0
1
0
0
0
0
4
3
0
1
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
1
1
0
2
2
0
0
8
0
0
0
1
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
1
0
0
1
1
0
0
1
0
0
0
0
0
1
3
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
2
0
0
0
1
0
0
0
0
1
2
0
3
0
4
0
0
1
0
0
0
0
0
0
3
0
0
0
2
0
1
0
2
0
0
0
0
0
0
1
0
2
1
1
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
3
0
0
0
2
0
0
1
0
0
2
0
0
0
1
6
0
0
0
9
0
0
0
0
1
2
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
3
0
2
0
0
2
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
2
0
1
4
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
1
0
0
2
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
3
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
2
0
1
0
0
0
0
0
0
2
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
5
2
2
0
0
0
0
0
0
0
2
2
0
0
2
2
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
1
1
1
0
0
0
0
1
0
0
2
0
2
0
0
2
0
0
2
1
0
0
1
0
0
2
2
0
2
0
1
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
2
1
0
0
0
0
0
0
0
1
2
1
0
0
2
2
1
0
0
0
0
2
0
3
0
0
0
0
1
2
2
0
0
0
2
0
0
0
0
0
1
1
0
0
0
1
0
0
9
0
0
2
0
0
0
0
2
0
1
2
0
2
0
1
0
0
2
0
0
0
0
3
0
4
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
2
0
3
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
8
0
2
0
0
1
0
1
0
0
0
5
0
0
1
0
0
3
0
0
2
0
0
0
0
0
1
0
0
0
0
1
2
1
0
0
0
1
0
2
0
0
0
1
0
0
1
2
1
4
0
0
0
0
3
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
2
1
0
0
1
2
0
0
0
1
2
1
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
1
0
2
0
0
2
0
2
1
1
1
0
0
0
1
0
0
2
0
2
0
0
0
0
1
2
0
0
0
0
1
2
0
1
2
1
2
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
6
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
1
0
0
0
1
0
3
0
0
1
1
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
2
2
1
0
0
0
2
0
1
2
0
0
0
0
0
2
1
1
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
2
0
0
2
1
0
0
1
0
0
0
0
0
1
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
1
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
2
0
0
1
0
0
0
1
0
2
0
1
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
2
2
1
0
0
1
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
3
0
2
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
1
1
0
0
2
0
2
0
0
0
1
0
3
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
1
1
0
1
0
2
8
0
0
2
2
0
0
0
0
0
0
1
0
0
2
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
1
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
3
0
0
0
3
0
0
2
0
2
0
0
1
0
0
0
0
1
2
0
2
1
0
0
0
2
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
2
0
2
0
2
0
0
2
2
0
0
0
0
1
1
0
5
1
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
3
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
3
2
0
2
2
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
2
1
1
0
2
0
3
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
2
0
2
0
0
2
0
2
0
1
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
2
1
1
2
3
0
0
0
2
0
2
0
0
0
0
1
0
0
2
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
2
1
0
1
0
0
2
0
2
0
0
1
2
0
1
0
0
0
0
0
0
4
0
0
0
2
0
0
1
0
0
0
2
1
0
0
0
3
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
1
0
2
0
3
0
3
0
0
2
1
0
2
0
0
0
2
0
0
1
1
1
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
2
0
0
0
1
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
2
0
0
0
0
0
1
1
2
0
0
1
0
2
0
0
0
0
2
0
1
1
0
0
0
0
0
0
2
2
0
0
0
1
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
1
0
2
2
0
0
1
0
0
2
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
1
3
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
1
0
0
0
1
0
1
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
1
0
1
1
3
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
1
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
4
2
1
0
0
0
0
2
0
2
2
0
0
1
1
0
0
0
4
0
1
1
1
0
0
2
0
0
0
0
1
0
0
1
2
0
1
2
4
0
0
1
0
0
0
0
0
1
1
0
2
2
1
0
1
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
1
2
0
0
3
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
2
0
0
0
2
1
0
2
1
2
0
1
0
0
0
0
2
0
2
2
0
2
2
0
0
0
0
2
1
2
9
1
0
2
0
0
0
3
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
3
0
0
2
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
1
1
2
0
0
2
0
0
1
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
3
1
0
1
0
0
0
2
0
2
1
1
0
0
0
0
1
0
0
1
0
0
0
2
0
1
0
0
0
0
1
0
0
2
0
2
0
2
0
0
1
0
0
0
0
0
0
0
1
0
2
1
0
1
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
2
2
2
1
1
0
0
4
0
0
0
0
0
0
0
0
2
0
0
2
2
0
1
0
0
0
1
0
1
0
3
0
1
2
0
0
0
0
0
1
0
0
2
0
0
1
0
2
0
0
0
0
1
0
1
0
0
0
0
2
0
0
1
0
0
0
2
0
1
0
0
1
0
0
0
0
0
4
1
0
1
0
2
2
0
0
2
0
0
0
2
2
0
0
0
2
0
1
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
4
0
1
0
0
2
0
0
0
0
2
2
1
0
2
1
0
0
0
2
2
0
2
0
0
0
0
2
1
0
0
0
0
0
5
0
1
0
1
1
1
2
0
2
0
1
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
1
0
1
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
1
2
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
6
1
1
0
0
1
1
0
3
1
0
0
0
2
0
0
0
0
2
2
1
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
3
1
0
0
1
1
0
0
0
0
0
0
0
2
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
4
0
0
0
0
0
4
0
0
0
0
1
0
3
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
1
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
7
0
1
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
1
1
2
0
1
1
0
0
2
0
0
0
0
0
0
2
0
1
1
1
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
1
0
2
1
1
3
0
0
1
0
0
2
0
0
1
2
0
1
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
2
1
0
0
0
1
0
0
2
2
0
0
0
0
0
2
1
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
2
0
0
1
0
2
3
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
3
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
1
0
0
1
2
0
0
0
2
0
0
0
0
2
2
1
0
0
0
2
2
0
0
2
0
0
0
2
0
1
0
0
1
2
0
1
0
0
2
0
0
1
3
0
0
0
0
2
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
2
0
0
0
0
0
0
0
2
0
4
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
2
0
1
1
0
0
0
0
2
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
1
0
0
2
0
0
0
0
0
0
1
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
1
0
2
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
1
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
2
0
1
3
0
0
0
8
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
2
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
1
0
0
0
3
0
1
0
0
1
0
2
1
2
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
2
0
0
0
1
1
0
0
0
0
0
1
0
0
0
2
0
1
0
1
0
0
1
2
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
2
2
2
2
0
0
1
2
0
2
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
4
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
4
2
3
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
1
0
2
0
0
2
2
3
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
3
2
0
0
0
0
1
2
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
5
0
2
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
1
0
0
0
2
2
2
1
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
1
2
0
0
0
2
0
0
0
2
3
2
3
0
0
0
4
0
1
0
2
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
3
0
3
0
2
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
5
0
0
2
1
1
2
0
0
0
0
0
0
1
0
0
0
0
3
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
3
0
0
0
2
0
0
0
2
4
1
0
0
1
1
0
2
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
1
2
0
1
0
1
2
2
4
2
2
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
1
0
3
1
2
0
2
0
2
1
0
0
2
2
1
1
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
2
0
0
0
0
1
1
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
4
0
0
0
0
2
0
1
0
2
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
3
0
2
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
1
0
2
1
0
2
1
0
0
0
0
2
1
0
0
0
1
0
0
2
1
1
0
0
0
0
0
0
1
0
0
0
0
0
2
4
0
0
0
1
0
0
1
0
0
1
0
0
2
1
0
0
0
0
0
2
0
1
2
0
2
1
0
0
0
0
0
0
0
0
3
0
0
1
0
0
2
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
2
1
2
1
1
0
1
2
2
0
0
0
2
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
1
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
5
0
0
1
0
0
0
1
3
0
0
1
1
0
1
0
1
0
0
2
0
0
2
0
0
0
0
0
2
0
2
0
0
0
2
0
0
1
5
0
0
0
0
0
1
1
0
1
0
0
2
0
0
2
0
0
1
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
1
1
3
0
0
0
1
0
0
0
0
2
0
0
1
2
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
3
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
4
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
1
0
1
0
0
0
2
2
0
0
4
2
2
0
0
2
2
0
0
2
3
0
2
0
0
2
0
2
2
1
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
2
0
1
0
0
2
0
2
2
0
0
1
2
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
10
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
2
0
0
1
2
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
2
0
2
0
0
0
0
0
0
1
0
1
0
3
0
0
1
0
1
0
0
0
0
0
1
2
5
2
0
0
0
2
0
0
0
0
0
1
2
0
2
0
1
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
1
2
0
2
0
2
0
1
0
2
5
0
0
2
0
0
0
0
1
1
1
0
0
0
0
0
5
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
1
0
1
2
0
8
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
4
1
2
0
2
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
2
0
1
2
0
0
1
0
3
2
0
0
2
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
1
0
0
0
0
0
2
4
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
5
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
2
0
0
0
0
1
0
0
2
0
2
0
0
1
0
0
1
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
7
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
4
0
2
2
0
0
4
0
0
0
2
0
0
1
0
0
0
2
0
0
2
0
1
0
0
0
0
1
0
2
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
1
0
2
0
2
0
0
0
3
1
0
0
0
0
2
1
1
1
0
0
0
0
2
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
1
0
0
0
1
0
0
2
0
1
0
1
0
0
1
1
0
0
0
0
0
1
0
2
0
0
1
0
1
1
0
0
0
0
0
1
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
2
0
0
1
0
0
0
0
1
1
0
0
1
0
1
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
4
1
0
0
2
0
1
1
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
3
0
0
0
0
0
0
1
2
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
2
3
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
1
2
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
3
1
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
3
2
0
0
0
2
1
0
0
0
0
3
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
2
1
2
2
0
0
0
0
1
0
0
0
2
1
0
0
0
0
1
0
1
0
1
0
0
0
1
0
1
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
2
2
2
0
2
0
1
0
0
1
3
0
2
0
0
0
2
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
5
1
0
2
0
1
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
3
0
1
0
0
2
0
0
0
1
0
2
0
1
0
0
3
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
2
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
2
1
0
0
2
0
0
1
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
2
2
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
1
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
2
1
0
0
2
2
0
0
0
0
0
0
3
1
0
1
0
0
2
0
0
2
3
1
0
1
0
0
0
0
0
11
0
0
0
3
1
0
0
0
2
0
0
2
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
1
1
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
2
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
2
0
1
1
0
2
0
0
2
2
1
0
0
0
0
2
0
2
0
0
3
0
0
0
0
0
1
0
0
3
2
4
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
2
0
3
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
1
10
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
2
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
1
1
0
2
0
2
0
0
0
0
0
2
2
1
0
2
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
2
1
0
1
2
0
1
0
1
0
2
3
0
0
2
1
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
3
0
0
0
0
2
0
0
2
0
0
0
1
0
1
0
2
0
1
0
0
1
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
3
0
0
0
0
0
2
0
0
0
0
0
2
0
2
1
0
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
2
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
12
2
2
0
0
0
0
2
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
2
2
2
0
1
2
1
0
0
0
2
1
0
0
0
0
0
1
0
3
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
1
0
2
1
1
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
6
2
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
1
0
0
0
2
1
0
0
0
0
0
1
1
0
0
0
0
0
2
0
2
0
2
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
1
0
2
1
0
0
0
0
0
2
0
0
2
0
1
0
0
1
0
1
0
0
0
2
1
0
0
0
0
1
0
0
2
0
0
1
2
3
0
0
0
0
1
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
2
0
0
1
0
0
0
0
0
2
0
0
0
3
0
0
0
0
2
0
2
3
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
1
0
3
0
0
0
1
2
1
0
2
1
3
0
0
0
2
0
0
0
1
0
2
0
1
0
2
0
3
1
0
2
2
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
2
2
1
0
0
2
2
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
1
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
2
1
0
0
1
0
0
1
1
0
0
1
0
0
2
2
0
3
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
2
0
2
1
1
3
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
1
0
0
0
0
0
2
1
1
0
0
0
0
0
1
0
0
0
0
1
1
0
1
2
1
0
1
1
0
0
0
0
0
0
0
2
1
0
0
1
0
2
0
0
0
0
1
0
0
1
0
0
0
0
2
0
1
0
2
0
0
0
2
1
0
1
0
3
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
1
0
4
1
0
2
0
0
0
0
0
0
2
1
0
0
0
0
1
0
1
1
2
0
0
1
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
2
1
0
0
1
0
0
0
0
2
1
1
1
2
0
3
0
0
0
1
0
0
0
3
0
2
0
0
0
0
0
1
0
0
0
2
0
1
2
0
1
2
1
2
0
2
2
0
0
0
0
0
0
2
0
0
0
1
1
1
0
0
0
0
2
0
0
2
0
0
0
2
1
2
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
2
2
2
0
6
0
4
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
5
2
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
1
0
0
1
0
0
0
0
1
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
1
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
2
3
0
0
0
0
2
0
0
2
0
2
0
0
3
0
2
0
2
2
1
0
0
0
0
2
0
0
2
1
0
2
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
2
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
3
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
2
2
0
0
2
0
0
0
0
3
0
0
0
0
0
2
2
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
2
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
2
0
0
0
3
0
0
1
0
0
2
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
1
0
0
3
0
0
0
0
0
0
0
0
2
1
2
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
2
0
2
2
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
4
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
2
2
1
0
0
0
2
1
0
2
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
3
0
2
0
0
0
0
0
0
0
1
0
0
2
2
0
0
1
0
4
3
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
2
2
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
3
3
2
0
0
0
0
0
2
0
0
1
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
1
0
1
0
0
2
0
2
0
0
0
0
2
0
0
0
3
0
2
4
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
3
0
0
2
2
0
0
0
0
0
1
0
0
2
1
0
0
1
2
0
1
1
0
1
0
2
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
5
2
0
0
0
0
2
0
0
0
0
2
2
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
1
1
2
0
0
2
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
1
0
0
1
0
1
1
2
3
1
2
0
4
0
0
0
0
1
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
1
0
2
2
0
2
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
3
0
1
0
0
0
0
0
0
1
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
1
0
0
3
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
3
0
1
0
0
0
0
1
0
0
0
2
1
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
3
0
3
0
0
0
0
0
0
0
0
0
3
1
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
2
0
0
2
0
2
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
2
1
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
2
2
0
0
1
0
1
3
0
0
0
0
2
0
0
0
0
1
1
3
0
0
0
0
0
0
0
0
2
0
1
2
0
1
0
1
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
1
1
1
1
0
2
0
1
1
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
1
0
0
1
0
1
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
2
0
0
0
4
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
2
1
0
0
1
0
0
1
0
0
5
0
0
2
1
2
0
0
3
2
0
0
1
0
0
0
1
0
0
0
0
0
2
0
2
0
0
2
1
0
2
2
0
1
2
0
0
0
0
0
0
0
2
1
0
2
0
0
0
2
2
0
0
0
1
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
1
0
1
1
3
1
0
0
0
0
4
0
0
2
2
0
1
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
2
2
0
2
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
6
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
2
0
0
0
0
0
1
1
1
0
0
0
0
0
2
2
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
4
2
0
0
3
3
0
0
0
1
0
0
0
0
1
2
2
0
0
0
0
2
0
0
1
1
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
1
0
0
0
1
0
0
0
1
4
2
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
2
0
3
2
1
0
0
1
0
1
0
0
2
0
0
0
0
0
0
1
3
0
0
2
0
0
0
1
0
0
0
0
3
0
2
0
0
2
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
1
0
1
0
0
0
1
1
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
2
1
0
2
0
0
1
1
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
2
3
0
1
0
0
1
0
1
0
0
0
2
0
1
2
2
0
0
0
1
0
0
3
0
0
0
1
0
0
1
0
0
1
0
4
2
2
1
1
0
2
1
0
0
0
0
0
0
2
0
0
0
0
3
0
4
2
0
0
0
0
0
4
0
1
0
0
0
0
0
2
3
0
0
0
0
1
2
0
0
1
0
1
1
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
1
0
0
1
1
0
3
0
2
0
0
1
0
1
0
0
0
3
0
0
0
2
0
2
0
0
3
0
0
0
0
1
0
0
0
0
0
2
0
0
1
2
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
1
1
1
0
3
3
0
1
0
1
2
0
1
0
1
2
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
2
0
1
0
0
2
0
0
0
2
1
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
1
0
0
0
2
0
0
0
1
0
0
2
2
2
2
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
5
0
0
0
1
0
0
2
0
0
1
0
2
1
0
2
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
2
2
0
1
3
0
0
1
2
2
0
0
0
0
0
1
0
0
1
1
2
0
0
0
2
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
1
0
1
0
0
0
2
0
2
2
0
2
0
1
0
1
0
0
0
1
0
2
2
0
2
0
2
0
0
0
0
0
0
1
2
0
1
0
0
1
0
0
0
2
0
0
2
4
0
0
0
0
0
0
4
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
2
0
0
1
0
1
0
0
2
1
0
0
0
0
0
0
0
0
4
2
2
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
2
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
2
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
2
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
1
1
2
2
0
3
1
1
0
0
0
2
1
0
0
3
1
0
1
0
0
0
1
0
0
2
0
1
1
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
2
0
1
0
2
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
4
2
0
0
0
0
2
0
0
0
0
0
1
0
1
2
1
1
0
1
3
0
1
0
0
1
0
2
2
2
0
0
0
0
0
1
1
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
1
0
3
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
2
0
0
1
0
1
0
2
0
0
2
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
1
1
1
0
0
0
1
1
0
1
0
2
2
0
2
0
0
0
0
0
0
3
0
0
2
0
0
1
0
0
1
2
2
0
1
1
0
0
2
0
0
0
0
0
2
0
0
1
0
1
0
0
0
1
2
0
0
2
0
0
2
2
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
1
0
0
0
0
1
4
0
0
0
0
0
0
0
8
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
1
0
0
0
1
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
2
0
0
0
0
1
0
0
1
2
0
0
0
2
2
0
0
0
1
0
0
0
0
0
1
0
2
0
2
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
2
1
0
0
2
1
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
1
0
2
2
0
0
2
0
0
0
2
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
1
2
8
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
3
2
0
1
0
0
0
0
2
3
0
1
0
1
0
0
0
0
0
4
1
1
0
2
1
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
1
0
1
4
0
0
0
0
0
0
2
0
1
0
0
0
2
1
1
1
0
0
0
0
0
2
0
1
0
0
3
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
2
1
0
1
0
1
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
2
0
2
1
0
0
2
2
2
0
0
2
2
0
0
0
2
2
0
1
2
2
0
0
0
3
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
1
0
0
0
0
3
1
0
2
2
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
2
0
0
3
2
0
0
0
1
0
0
2
0
0
0
0
0
1
0
2
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
2
2
0
0
0
4
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
1
0
2
0
3
0
4
2
1
0
1
0
2
2
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
2
2
2
0
2
0
0
0
1
0
0
2
2
0
0
1
2
1
0
1
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
4
0
1
0
1
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
2
0
2
2
2
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
6
0
0
0
6
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
2
0
0
1
0
1
1
0
0
2
0
0
0
0
1
0
2
0
1
2
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
2
0
0
0
1
2
0
1
1
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
2
0
0
0
2
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
1
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
1
0
2
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
4
2
0
0
3
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
1
2
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
3
0
0
1
0
0
3
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
1
1
0
0
2
1
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
2
0
2
0
0
0
3
0
0
2
1
0
0
0
0
1
0
0
0
0
2
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
2
0
0
1
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
2
0
0
1
0
0
3
0
0
0
1
2
0
0
1
0
0
0
0
0
3
2
0
0
0
1
2
0
0
0
1
2
0
0
0
0
0
0
0
2
1
0
0
3
0
0
0
1
0
0
0
1
0
2
0
0
0
0
2
0
3
0
0
0
0
1
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
3
2
1
0
2
2
2
0
0
0
2
0
0
0
0
2
2
0
2
1
0
0
0
1
2
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
1
0
2
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
1
0
0
2
0
0
2
0
1
1
1
0
0
0
0
2
1
0
0
0
0
0
0
0
3
1
0
2
2
0
0
0
4
1
0
1
0
0
0
0
4
2
0
2
0
0
0
1
2
0
2
1
0
2
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
2
0
2
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
3
1
1
0
0
0
1
0
1
0
2
1
1
0
1
0
0
0
1
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
1
0
0
0
0
2
0
0
0
1
0
3
0
1
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
1
0
1
0
0
0
0
1
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
1
0
2
0
2
0
0
3
1
0
1
2
0
0
1
0
0
1
0
1
1
1
0
0
0
1
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
1
0
1
2
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
2
1
1
0
2
0
0
0
0
0
0
1
1
0
0
0
1
1
0
1
1
2
0
0
0
0
0
0
0
1
2
0
0
1
2
0
0
0
0
2
0
2
0
0
2
0
2
1
0
0
1
0
0
0
3
2
1
0
0
0
2
0
0
1
2
0
0
0
0
1
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
2
0
2
2
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
3
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
2
0
4
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
2
1
2
0
2
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
2
1
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
4
1
0
1
3
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
3
0
0
0
0
0
0
0
0
3
0
2
0
0
1
0
2
0
1
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
2
0
2
2
2
2
0
0
0
1
1
0
2
0
0
3
0
1
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
1
1
0
0
0
1
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
2
0
1
0
0
0
0
2
0
2
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
2
2
0
1
0
2
0
0
0
1
2
0
0
1
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
12
1
0
1
0
1
0
1
2
0
0
0
1
1
0
3
0
0
1
0
2
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
2
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
4
0
2
0
2
0
2
0
0
2
0
0
0
0
2
2
2
0
0
2
0
0
0
0
1
1
0
2
6
3
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
2
0
2
1
0
0
2
2
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
3
1
0
2
0
0
0
1
0
0
1
0
2
3
1
0
0
0
0
0
0
0
1
3
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
1
1
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
3
0
0
4
0
1
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
1
0
0
1
0
2
0
0
0
0
2
0
2
0
0
2
0
1
0
0
0
0
0
0
1
1
0
0
0
2
0
0
1
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
2
1
2
0
2
1
0
2
0
0
0
2
1
2
3
3
1
0
0
0
9
0
0
0
0
0
0
0
0
1
0
0
2
2
2
0
0
0
0
0
0
1
1
0
0
2
0
2
1
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
2
0
0
0
0
0
3
0
2
3
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
2
0
3
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
4
0
0
0
2
0
2
0
0
0
0
2
0
2
0
1
0
1
0
0
0
2
0
1
0
0
0
3
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
1
1
0
0
0
2
0
0
0
0
0
0
0
1
2
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
2
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
1
1
0
0
0
1
0
1
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
3
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
1
2
0
1
0
0
0
1
0
0
2
0
0
2
0
1
1
0
0
2
0
2
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
2
5
0
0
0
0
0
0
0
0
0
1
1
0
1
0
2
0
0
0
0
0
1
0
0
2
0
0
0
2
2
4
2
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
2
0
2
0
1
1
2
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
2
0
0
0
0
3
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
5
0
2
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
1
0
2
1
0
3
0
2
0
2
2
0
0
3
0
3
0
0
0
0
0
1
2
0
0
0
0
0
0
2
6
1
0
0
0
0
2
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
2
0
0
0
0
1
0
0
0
0
1
1
2
0
0
0
0
0
0
2
7
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
2
0
0
2
0
0
0
0
1
1
1
0
2
0
2
0
0
2
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
1
1
0
2
0
0
0
1
0
1
0
0
2
0
2
3
0
1
0
0
0
0
0
1
0
1
1
0
2
2
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
1
0
2
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
3
0
1
1
0
0
2
0
2
0
0
2
0
1
1
1
2
2
0
0
2
1
0
0
0
2
0
1
0
0
1
1
0
0
0
0
2
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
1
0
0
0
0
1
0
0
2
2
0
0
0
0
1
0
2
0
0
0
0
2
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
1
1
0
0
1
0
2
1
0
2
0
0
0
0
0
2
2
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
3
1
2
0
0
1
0
0
0
2
1
2
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
1
0
1
1
1
0
0
1
1
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
2
5
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
2
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
2
3
0
0
2
0
1
0
0
0
2
0
2
0
0
1
0
1
0
2
1
0
1
0
0
2
0
0
0
2
1
2
1
0
0
1
0
0
0
0
0
4
0
0
2
0
1
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
2
0
0
0
2
0
0
0
2
0
0
1
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
1
2
0
0
2
0
0
0
2
2
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
1
0
0
1
0
0
0
1
1
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
4
0
4
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
0
0
1
1
0
1
0
0
0
0
0
0
0
0
2
0
0
4
0
0
1
2
0
0
1
0
0
0
1
0
1
0
2
1
7
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
2
0
2
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
1
1
0
0
0
0
4
2
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
2
0
1
0
1
1
2
1
0
0
0
0
1
2
0
0
0
0
0
1
0
2
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
2
1
3
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
2
2
0
0
0
0
0
0
2
2
0
0
1
1
0
0
2
3
0
0
0
0
0
2
3
0
0
0
2
1
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
2
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
2
1
0
1
1
0
0
0
0
0
2
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
1
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
3
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
2
0
2
0
1
0
0
2
0
0
0
0
0
2
0
0
1
2
0
0
1
0
0
0
0
0
1
2
2
0
1
0
0
1
0
1
0
0
0
0
0
1
0
3
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
1
0
1
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
3
3
2
0
0
2
2
1
0
1
0
4
1
0
0
0
0
0
1
0
1
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
2
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
1
0
1
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
1
1
0
0
2
0
0
2
1
0
2
0
1
2
0
0
0
0
13
0
2
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
5
2
0
0
1
1
1
1
1
0
1
0
0
2
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
3
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
2
1
1
0
0
0
2
3
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
3
0
0
0
2
0
1
0
0
0
1
3
0
0
0
1
0
0
1
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
2
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
2
0
0
0
2
1
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
2
0
0
2
0
0
0
1
0
0
3
0
0
0
1
0
0
1
2
0
0
0
0
0
2
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
1
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
3
0
0
0
1
1
0
0
0
0
0
0
3
0
1
0
0
2
1
0
1
0
0
0
0
1
0
1
0
0
0
0
3
1
0
0
0
1
0
2
1
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
1
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
2
1
2
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
2
0
0
0
2
1
0
0
1
0
2
2
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
2
0
3
2
0
0
0
1
2
0
0
0
0
0
0
0
0
2
2
1
0
0
0
2
0
1
0
0
1
1
0
0
0
0
1
2
0
0
2
0
0
1
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
1
2
1
0
2
0
2
1
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
2
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
4
0
2
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
1
0
0
2
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
3
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
2
0
1
0
0
2
1
2
0
0
0
0
0
0
1
0
1
0
0
0
1
2
0
1
0
0
0
0
3
5
0
0
0
0
0
2
0
0
7
0
0
0
0
0
0
1
0
0
0
2
1
2
0
2
0
2
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
3
0
1
1
2
0
0
0
0
0
0
0
1
0
1
0
2
3
0
1
0
0
1
0
3
0
1
0
0
0
0
1
3
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
1
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
2
0
2
2
0
0
0
2
0
0
0
0
0
0
2
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
1
2
3
0
2
0
0
1
1
2
0
0
2
0
0
0
2
2
0
0
0
1
0
1
0
0
2
2
2
0
2
0
0
1
0
1
0
0
0
2
0
0
0
1
2
0
0
0
0
1
2
0
1
0
0
0
1
2
0
0
0
0
1
0
2
0
0
0
0
0
1
2
0
0
1
2
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
2
0
1
1
0
0
0
0
0
0
2
2
2
0
2
2
1
0
0
0
0
2
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
2
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
4
0
0
0
0
1
0
2
1
0
1
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
3
0
0
1
0
2
0
0
1
0
0
0
0
0
0
2
0
2
0
1
1
0
0
0
3
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
1
2
0
1
0
0
0
3
0
1
0
1
1
1
0
0
0
3
0
0
2
1
0
0
2
0
0
1
2
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
4
0
1
1
1
2
0
2
0
0
0
0
1
1
0
0
1
1
0
0
0
1
4
0
0
2
0
2
0
0
0
2
0
0
2
2
0
0
2
0
1
0
1
2
0
0
0
0
0
0
3
0
0
0
2
1
0
0
1
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
2
0
0
1
0
1
2
0
2
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
2
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
1
2
0
2
0
2
0
0
0
0
2
0
2
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
2
0
1
0
0
0
2
0
0
1
0
0
0
2
0
0
4
1
0
0
2
2
2
0
1
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
5
0
0
0
1
0
2
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
1
0
0
0
1
1
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
3
0
1
2
0
1
1
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
1
1
2
0
1
1
3
2
3
0
0
1
1
0
2
0
0
0
0
0
0
0
3
0
3
0
0
2
0
0
0
3
1
0
1
0
0
0
0
1
2
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
1
0
0
1
0
0
1
0
2
0
0
0
0
0
2
0
1
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
2
2
0
1
0
0
0
0
2
0
0
1
2
0
2
2
7
2
0
0
0
0
0
2
0
1
1
1
0
0
0
2
0
2
0
0
0
0
0
0
2
2
1
2
0
0
0
0
1
0
2
0
2
1
0
0
0
0
0
2
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
1
1
0
2
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
2
4
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
2
0
1
1
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
1
0
0
1
0
0
0
3
2
0
0
0
0
0
1
0
2
0
2
0
0
2
0
0
0
2
0
2
0
0
0
1
0
0
0
4
0
2
0
2
1
0
0
0
0
1
0
0
1
1
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
2
4
0
0
0
0
0
0
1
0
0
0
1
0
2
1
0
0
0
0
2
1
0
0
0
1
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
10
0
2
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
2
0
0
1
1
0
0
2
0
0
0
0
0
0
2
0
0
2
2
0
2
0
1
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
3
4
1
2
0
0
0
1
1
2
2
0
0
0
1
0
3
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
1
0
0
0
0
0
0
0
3
1
2
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
2
2
1
0
0
0
1
0
0
0
1
2
0
1
0
2
1
0
0
0
2
0
0
1
0
0
0
1
0
2
2
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
2
1
2
1
0
0
0
0
2
0
0
0
0
2
0
3
0
0
0
0
2
0
0
0
0
0
2
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
2
2
2
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
1
0
1
0
0
2
0
2
0
2
0
0
2
0
0
2
3
0
0
1
0
0
0
0
2
0
2
2
0
0
0
1
0
0
2
0
0
0
0
0
2
2
0
0
1
2
2
0
0
0
0
0
2
0
0
2
0
2
0
0
1
0
0
3
0
2
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
1
1
0
0
0
0
0
0
0
0
2
0
5
0
2
0
0
2
0
0
2
0
1
0
1
1
0
0
2
2
0
0
0
2
0
2
0
0
0
2
0
1
2
2
0
1
2
0
0
0
2
1
2
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
3
0
1
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
1
2
0
2
0
1
1
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
2
0
0
1
0
0
1
0
0
0
2
0
0
0
2
0
2
2
0
1
2
0
0
0
1
0
0
2
0
0
2
2
1
0
0
0
0
0
2
4
1
2
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
1
0
0
2
1
0
0
0
0
1
2
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
4
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
1
3
0
3
1
0
0
0
0
0
2
2
1
0
0
1
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
1
0
1
0
0
2
0
3
0
0
0
0
1
0
0
3
0
0
0
1
2
2
0
1
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
2
0
2
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
3
1
0
2
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
4
0
0
0
0
0
0
2
1
0
0
0
0
1
1
0
0
0
0
1
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
2
0
2
0
0
0
0
0
0
5
2
0
0
1
1
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
1
3
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
1
0
2
1
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
1
2
0
0
0
0
0
1
0
0
2
0
0
2
0
0
2
0
1
2
1
0
1
0
1
0
0
0
0
2
0
0
0
1
1
0
0
0
0
3
1
1
2
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
1
0
2
2
0
0
1
0
2
1
0
0
0
1
0
0
1
1
0
0
0
1
1
0
1
0
0
0
2
0
0
1
0
0
0
1
1
2
1
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
1
1
0
0
0
2
0
0
0
0
0
2
0
2
3
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
2
2
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
1
0
4
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
2
1
0
2
0
0
0
0
7
0
0
0
0
2
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
2
0
0
2
0
1
0
2
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
2
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
2
0
0
0
0
0
2
2
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
1
0
2
0
0
2
0
1
1
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
1
0
0
0
1
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
2
2
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
7
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
1
0
0
0
0
0
0
0
3
0
0
3
2
0
0
2
0
2
1
0
1
2
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
3
1
2
2
3
1
0
1
0
0
5
0
2
0
0
0
0
0
0
3
0
1
2
0
1
0
0
0
0
2
1
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
1
0
2
2
1
2
0
0
0
0
0
2
2
1
2
2
0
0
8
0
0
2
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
1
7
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
2
0
0
2
0
1
1
0
0
1
2
2
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
1
1
0
1
0
0
0
0
2
3
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
3
1
0
1
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
3
0
2
2
1
0
2
3
2
1
0
0
0
0
0
0
4
0
0
0
1
2
2
0
0
0
0
0
0
0
1
0
2
0
0
1
2
0
0
2
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
3
2
0
0
1
0
2
0
0
1
0
0
0
2
0
2
0
0
2
2
0
0
0
1
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
4
0
4
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
2
2
1
0
2
0
0
0
2
0
1
1
0
0
1
0
0
0
2
0
2
2
0
0
0
1
2
0
2
1
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
1
1
2
1
0
0
0
0
0
0
1
6
0
0
2
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
2
0
2
1
0
0
0
2
0
0
0
1
0
1
0
0
0
1
2
0
0
0
0
1
0
0
0
0
1
0
0
2
0
2
0
0
1
2
0
0
1
0
0
2
0
0
0
2
3
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
3
2
2
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
1
0
0
1
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
3
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
3
0
1
2
0
0
0
0
0
3
0
0
0
0
3
1
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
1
0
0
2
0
2
1
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
3
2
0
2
0
0
3
2
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
2
1
0
0
0
0
0
1
0
0
2
0
0
0
2
1
0
3
1
1
0
0
1
0
0
1
1
1
0
1
0
0
2
1
0
0
1
0
1
3
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
3
1
2
0
0
0
0
0
1
0
3
0
0
0
0
1
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
1
0
1
4
0
0
2
0
1
0
0
4
0
1
2
0
2
0
0
0
2
2
0
0
0
2
0
0
0
1
0
0
1
1
0
2
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
2
1
0
0
0
0
0
1
3
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
1
0
0
0
2
2
0
0
2
0
2
0
1
0
0
0
0
0
1
0
0
2
1
2
0
0
0
1
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
2
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
2
0
0
0
2
0
1
2
2
0
0
0
0
0
3
0
2
0
0
0
0
1
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
1
0
1
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
2
0
0
0
1
0
0
1
0
2
0
0
2
0
0
0
2
0
0
1
1
0
1
0
0
0
0
0
2
0
0
3
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
2
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
1
0
1
0
2
0
4
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
2
4
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
1
0
0
1
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
3
0
2
0
0
1
0
0
0
0
0
3
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
1
0
0
0
0
0
0
3
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
1
0
1
0
0
0
2
3
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
2
1
0
0
1
0
2
2
0
0
0
0
0
0
1
0
0
0
0
2
3
0
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
1
1
1
1
0
0
1
2
0
1
0
0
0
0
0
0
1
0
0
2
1
2
0
1
1
0
0
0
2
0
2
1
0
0
0
2
0
1
0
0
1
0
0
0
0
0
2
0
0
1
2
0
2
0
0
0
0
0
1
0
2
0
0
1
0
4
0
1
0
0
0
0
2
0
0
0
4
1
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
1
2
4
0
1
2
0
0
0
0
0
2
0
1
0
0
0
1
0
0
2
0
0
0
0
0
2
1
0
3
0
0
0
0
0
1
2
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
2
1
0
0
0
0
1
3
2
1
1
0
0
0
0
1
1
1
1
0
0
0
1
4
0
0
0
0
0
0
0
0
0
1
0
1
0
1
2
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
3
0
0
0
3
1
1
2
0
0
3
0
0
2
0
3
0
2
0
0
1
0
0
0
0
0
2
0
0
1
0
6
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
1
0
0
0
0
1
0
2
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
4
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
2
1
0
4
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
2
1
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
2
0
2
0
0
0
2
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
1
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
2
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
3
0
0
2
0
3
1
0
0
0
1
1
0
3
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
1
1
0
0
0
0
0
0
0
2
0
2
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
2
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
2
1
1
2
0
0
1
0
0
0
2
1
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
2
0
3
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
1
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
3
2
0
2
0
0
2
0
0
0
0
0
3
0
0
0
3
1
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
2
0
0
0
1
3
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
1
2
0
2
1
2
1
3
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
1
2
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
3
1
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
1
2
0
0
0
1
0
0
0
2
0
2
2
0
0
1
0
2
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
2
2
0
2
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
1
0
3
1
0
0
2
2
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
1
0
2
2
0
0
1
0
0
0
0
3
1
2
2
3
0
1
0
0
0
2
1
0
0
1
0
0
0
2
0
0
1
0
0
0
2
0
0
0
1
0
3
1
2
2
1
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
2
1
1
0
0
0
0
0
0
3
0
0
1
0
0
0
2
2
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
2
1
1
2
2
0
0
0
1
0
0
0
0
0
0
1
2
2
2
2
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
2
0
0
2
0
0
1
1
0
0
1
2
3
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
1
2
3
0
3
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
1
1
2
0
0
0
2
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
1
5
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
9
0
2
3
0
2
1
0
1
0
1
0
0
2
0
1
2
0
1
0
0
0
1
0
0
0
2
0
2
0
0
2
1
2
0
1
0
1
0
0
2
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
1
1
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
1
0
2
0
2
0
1
0
0
2
0
0
2
3
0
0
1
0
0
0
2
0
0
0
0
0
3
2
0
0
0
0
1
0
5
1
0
1
2
1
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
1
0
0
0
0
0
2
0
2
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
2
2
0
0
0
0
2
0
2
0
2
0
0
0
1
0
0
0
0
0
0
2
2
1
2
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
2
1
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
1
0
4
0
0
0
0
1
0
0
0
1
3
0
0
1
0
0
0
0
0
0
2
1
0
1
0
2
1
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
1
2
2
0
1
0
4
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
3
0
0
1
2
0
0
0
0
0
0
1
0
0
1
6
0
0
0
0
0
0
0
0
1
0
0
3
2
1
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
1
0
1
0
3
0
1
0
3
0
0
0
2
0
0
0
0
0
1
0
1
0
2
1
0
2
0
2
1
0
0
2
0
0
2
0
0
0
0
0
1
2
2
1
0
0
0
0
0
1
1
0
0
0
0
0
8
1
0
2
2
1
0
0
2
0
1
0
1
0
0
2
0
0
3
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
2
2
0
0
0
0
1
2
0
2
2
0
0
2
0
0
0
0
0
0
3
2
0
1
0
0
0
1
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
1
2
0
1
0
0
0
0
0
0
0
1
0
2
2
0
0
2
1
2
0
1
0
1
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
2
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
2
0
1
1
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
2
0
0
1
1
0
0
2
1
0
0
0
2
1
0
0
1
0
0
0
2
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
1
0
0
0
1
0
0
0
2
0
0
1
1
1
1
0
0
0
0
0
2
2
0
1
1
1
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
1
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
2
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
4
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
2
2
0
0
0
1
0
1
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
1
1
2
0
0
0
1
0
0
2
0
0
0
0
3
0
0
0
1
0
2
1
8
0
3
0
0
3
0
0
0
0
2
0
1
0
0
0
2
8
0
2
0
0
0
0
0
0
0
2
0
0
0
2
1
1
0
1
0
1
1
2
0
1
0
1
0
0
2
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
1
0
3
1
1
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
1
0
2
0
0
0
1
2
0
1
0
0
1
0
0
0
0
0
2
1
2
1
0
1
0
2
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
2
0
0
1
0
0
1
0
1
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
2
0
2
0
1
0
0
0
2
2
0
1
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
3
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
1
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
2
0
0
1
0
0
1
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
1
0
0
0
7
0
0
2
0
0
1
0
2
0
0
1
0
0
2
0
0
0
1
0
0
1
0
0
0
0
5
0
0
0
0
1
2
2
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
3
0
1
0
1
2
0
0
0
0
1
0
2
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
2
1
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
5
0
1
0
1
0
0
0
0
3
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
2
0
1
0
0
1
0
0
2
1
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
1
0
0
0
2
1
0
0
0
1
0
2
0
0
0
1
0
0
0
2
0
8
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
6
0
1
0
2
0
0
1
0
0
0
4
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
1
2
1
0
1
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
2
1
0
0
2
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
2
0
2
0
0
2
0
2
0
0
0
0
0
2
0
2
0
2
0
0
1
0
0
0
0
1
2
0
0
1
0
0
0
2
0
0
0
1
0
0
2
1
1
0
0
0
2
1
0
0
1
0
0
2
2
0
2
0
0
2
0
0
0
2
0
0
2
3
0
0
0
0
0
0
2
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
2
1
2
1
1
0
0
2
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
1
0
2
1
3
1
0
2
0
2
0
0
2
0
0
0
3
6
0
0
0
0
0
0
0
0
0
1
2
0
0
1
1
0
1
0
4
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
2
7
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
1
1
0
2
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
4
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
5
3
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
2
1
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
6
0
0
0
0
0
0
0
5
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
2
0
1
2
0
1
0
0
3
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
1
1
2
0
0
0
0
0
0
3
0
1
0
1
1
0
0
0
0
2
0
0
0
0
0
3
3
0
0
2
2
1
2
2
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
2
1
1
0
0
2
2
0
0
0
0
1
1
0
0
0
1
1
0
2
1
0
1
1
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
3
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
1
2
0
1
2
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
5
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
2
1
0
0
1
1
0
0
0
0
2
2
0
0
0
0
0
0
1
2
0
2
2
0
0
0
1
0
0
1
0
3
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
1
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
3
0
0
0
0
1
1
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
1
0
0
0
1
0
1
0
1
1
0
0
0
0
1
0
0
0
1
0
0
3
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
2
1
0
1
1
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
2
2
2
1
0
0
1
0
0
0
1
0
1
0
3
0
3
2
0
1
1
0
0
0
0
0
5
0
0
0
0
0
0
0
0
1
1
2
5
2
0
2
2
2
0
0
1
0
2
0
0
0
1
1
0
1
0
6
0
0
2
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
1
2
0
3
0
0
3
0
2
2
1
2
0
2
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
2
0
0
2
1
3
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
2
2
0
2
1
2
0
1
1
3
0
1
1
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
2
1
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
1
0
0
2
1
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
2
0
2
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
9
0
0
0
0
3
0
0
0
0
8
0
0
0
1
0
0
0
0
2
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
2
0
0
0
0
2
1
2
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
2
0
0
3
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
7
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
3
1
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
2
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
3
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
2
0
0
0
1
0
2
1
0
0
2
0
0
0
0
0
0
1
3
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
4
0
0
1
0
1
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
3
2
1
0
1
0
0
2
0
1
0
1
2
3
0
2
2
0
3
0
2
0
0
0
4
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
1
2
0
0
1
0
2
0
0
0
0
3
3
2
2
0
1
1
0
0
0
1
0
2
1
1
2
0
0
0
0
1
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
3
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
2
1
0
1
0
0
1
1
0
0
0
1
0
0
0
0
1
1
2
2
1
0
1
2
0
1
2
0
0
1
0
1
0
0
0
1
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
1
0
0
4
0
0
0
0
0
1
0
0
0
2
1
0
0
0
1
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
3
1
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
1
3
1
0
1
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
2
2
0
2
0
0
1
1
0
0
2
1
0
0
4
1
0
0
1
2
0
0
2
0
2
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
1
2
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
3
0
2
0
0
1
0
0
2
0
2
0
0
1
0
0
0
2
0
0
0
2
1
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
1
3
0
0
0
0
2
1
1
1
1
3
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
1
0
3
2
0
0
0
2
2
0
0
0
0
1
2
2
0
0
0
3
0
1
0
0
1
0
0
0
0
2
1
0
0
0
2
0
4
0
0
0
2
0
0
1
0
2
0
0
2
0
0
0
2
0
0
0
0
2
1
0
0
0
3
0
1
0
0
0
1
0
0
2
0
0
1
2
0
1
0
0
1
0
1
0
0
1
0
0
2
0
1
2
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
2
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
2
0
3
0
0
0
0
0
0
2
0
2
1
0
0
1
0
0
0
0
0
2
2
0
3
0
0
0
5
0
0
1
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
1
0
2
0
0
1
0
0
1
1
2
2
0
2
2
0
0
0
1
2
1
1
2
0
1
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
2
2
0
1
0
3
2
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
3
0
1
0
2
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
2
0
2
0
0
2
0
2
0
2
0
1
1
0
0
0
0
0
1
0
0
0
1
2
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
5
0
0
5
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
2
0
0
1
1
0
0
0
2
2
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
2
1
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
1
0
2
2
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
2
0
1
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
3
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
5
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
2
3
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
2
1
0
2
0
0
0
0
1
2
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
1
2
1
0
3
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
2
1
0
1
0
0
2
2
0
0
0
2
2
0
0
1
0
0
0
1
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
2
0
0
0
2
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
1
0
0
0
0
0
0
0
2
3
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
2
0
2
0
0
3
2
5
0
0
4
0
1
0
2
1
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
1
2
0
0
0
1
1
0
2
2
0
0
0
2
3
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
1
2
0
1
0
0
0
0
2
2
0
0
0
2
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
2
0
2
1
2
2
0
0
0
0
0
0
0
2
1
1
0
0
0
7
1
1
0
2
0
0
3
0
2
0
0
2
0
0
1
0
1
0
0
1
0
1
0
5
0
0
0
0
0
2
1
0
1
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
1
0
0
0
2
0
0
0
0
0
1
2
0
1
1
0
0
0
0
0
0
0
0
0
0
2
2
3
0
0
2
2
0
0
2
0
2
0
0
0
1
0
0
0
2
2
2
0
0
0
2
2
0
0
0
1
1
0
0
0
1
2
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
2
0
0
3
0
0
2
0
0
2
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
2
2
0
1
0
0
0
4
0
0
5
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
2
0
1
0
0
0
0
0
0
0
1
0
1
2
0
0
1
0
0
0
0
0
0
3
3
2
0
0
0
0
0
1
0
0
2
1
1
0
1
0
0
1
2
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
1
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
1
4
3
0
2
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
2
1
2
1
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
5
1
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
2
0
1
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
2
1
0
5
0
0
0
0
2
0
0
0
1
1
0
0
0
2
2
0
2
0
2
0
0
0
1
0
2
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
3
0
0
0
0
0
2
2
1
2
0
0
0
2
1
0
0
2
0
0
1
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
2
0
3
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
2
0
0
0
3
0
2
0
1
0
0
1
0
2
0
0
0
0
0
0
2
1
0
0
0
1
0
1
0
2
2
2
0
0
0
0
0
0
0
2
0
0
3
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
1
1
0
2
1
0
1
0
0
0
0
0
0
0
3
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
9
0
3
0
0
0
1
4
0
0
2
0
1
0
1
0
2
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
1
0
1
0
0
2
1
0
0
0
1
0
0
5
0
0
0
2
0
0
0
1
0
0
4
5
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
1
2
4
3
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
1
3
0
1
1
0
0
0
0
0
1
0
1
1
1
2
1
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
2
0
1
2
0
0
0
0
0
0
0
0
0
0
7
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
1
1
1
0
2
0
0
0
0
0
0
0
1
0
2
6
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
2
0
1
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
1
0
1
0
0
1
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
1
2
2
0
0
0
0
0
1
1
0
0
0
2
1
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
2
3
0
0
0
2
0
1
1
0
0
1
0
0
1
2
0
0
0
0
0
1
0
4
0
2
0
1
0
0
0
0
0
0
0
1
0
2
1
0
2
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
1
2
0
0
0
0
0
0
1
0
0
3
0
0
1
1
3
0
2
1
0
0
1
0
1
1
0
0
0
0
0
1
2
0
0
0
2
0
2
1
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
1
2
2
0
0
0
0
1
0
0
0
0
0
1
1
0
0
2
0
1
0
1
0
2
0
0
1
0
0
1
0
2
0
0
0
0
0
2
3
0
0
0
0
3
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
1
2
1
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
2
0
0
0
1
0
0
0
2
2
0
0
2
0
0
0
0
1
1
0
0
0
3
0
2
1
0
0
0
0
0
0
0
0
2
1
2
1
1
0
3
0
2
1
0
0
0
0
2
0
2
0
0
4
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
5
0
0
0
0
3
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
1
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
2
1
0
0
1
1
0
0
1
3
3
0
0
1
0
0
0
0
0
0
2
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
1
0
0
0
2
0
0
0
2
0
0
0
0
4
0
0
1
1
2
1
0
0
0
0
0
0
0
0
2
0
0
0
3
3
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
2
0
2
1
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
1
1
1
0
2
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
2
0
0
2
1
0
0
0
0
0
0
0
1
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
2
1
0
0
1
0
0
1
0
0
2
4
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
2
0
0
0
0
1
1
2
0
3
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
1
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
1
0
2
2
2
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
1
0
0
0
5
2
0
3
2
1
1
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
1
1
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
18
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
5
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
1
2
2
0
0
0
0
0
1
2
0
1
0
0
0
0
0
1
24
0
2
0
0
0
0
2
0
1
0
0
0
1
1
0
0
0
1
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
2
0
2
2
0
0
1
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
1
1
1
0
1
1
0
0
0
0
3
2
0
0
2
0
0
0
0
2
2
0
0
0
1
1
0
0
2
0
0
6
0
0
0
1
0
0
1
2
0
2
0
1
0
1
0
2
0
0
0
0
1
1
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
1
1
1
0
0
0
0
0
0
2
2
0
2
2
0
2
3
0
0
0
2
0
0
2
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
1
0
3
0
0
0
1
0
0
0
0
0
5
0
1
0
1
0
3
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
2
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
3
0
0
2
1
2
2
0
0
0
0
0
2
0
3
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
7
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
2
3
0
0
1
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
1
2
0
1
1
0
3
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
2
1
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
3
0
2
0
1
0
2
0
0
0
0
0
1
0
1
0
1
1
0
3
0
0
0
2
0
2
3
0
3
0
0
0
0
2
1
1
0
1
2
0
1
0
1
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
2
2
1
0
2
0
0
0
0
1
0
0
1
1
0
0
3
2
0
0
0
2
2
1
2
0
0
0
0
1
0
0
0
2
0
1
0
0
0
1
0
2
3
0
0
0
0
0
1
0
0
1
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
2
2
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
1
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
2
2
0
0
0
2
1
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
2
0
1
1
0
0
0
0
0
0
0
2
0
1
0
1
1
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
2
0
2
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
5
0
0
1
0
3
2
0
2
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
2
1
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
2
1
0
0
0
0
1
0
2
2
0
1
0
0
1
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
2
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
1
2
0
0
3
0
2
2
0
0
0
2
2
0
1
0
1
0
0
0
0
2
2
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
2
0
1
0
2
0
0
0
2
0
1
0
0
2
0
0
0
0
1
0
0
0
1
1
0
2
0
0
2
0
0
0
0
0
2
1
2
0
0
1
0
1
2
0
3
0
0
0
0
1
0
0
0
0
0
1
2
1
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
1
5
2
1
0
0
2
0
0
0
0
3
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
2
0
0
0
1
2
1
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
1
0
1
2
0
0
0
2
0
4
0
1
3
2
0
2
2
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
2
1
0
1
0
0
0
1
0
0
0
2
2
1
0
2
0
2
0
0
2
0
1
0
1
0
0
1
1
0
0
0
2
0
0
0
0
0
3
0
2
1
0
0
2
0
0
0
0
1
4
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
4
2
0
0
0
0
0
0
0
0
0
0
2
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
1
0
0
0
0
2
1
1
0
2
0
0
0
0
3
0
0
0
0
0
0
1
0
1
2
0
1
0
1
0
1
0
0
2
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
2
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
2
0
0
2
0
2
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
2
2
0
0
0
1
0
0
1
0
2
0
0
0
0
1
0
2
2
0
2
0
0
2
0
1
2
2
1
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
1
2
2
2
1
0
1
0
0
0
0
0
3
0
2
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
1
0
2
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
5
0
0
2
2
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
2
1
0
0
2
0
0
0
2
1
0
2
0
4
2
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
4
0
0
0
1
0
0
0
0
2
0
2
1
0
2
0
0
0
0
0
2
0
1
0
0
1
0
1
0
1
0
2
0
0
1
1
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
3
1
0
3
0
0
0
0
2
2
2
0
0
2
0
0
0
0
0
0
1
0
0
1
0
1
2
0
3
0
0
1
3
2
0
0
3
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
2
2
0
0
1
0
0
0
1
2
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
2
0
0
0
0
0
2
2
0
2
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
1
0
3
0
1
2
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
2
1
0
0
0
0
3
2
0
0
4
0
0
0
0
0
0
2
0
2
3
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
1
0
0
1
2
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
2
2
0
2
0
0
2
0
0
0
0
1
1
2
0
0
0
0
3
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
3
0
2
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
1
0
2
0
0
0
1
3
0
3
0
0
0
0
0
1
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
2
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
4
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
4
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
2
0
0
1
0
1
2
0
0
0
0
0
0
1
2
0
0
1
2
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
1
0
2
0
0
0
2
1
2
1
0
0
0
2
0
0
5
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
2
6
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
2
4
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
2
0
2
0
0
0
2
1
2
0
0
1
0
4
1
0
4
0
0
0
2
1
0
2
2
0
0
0
0
0
2
0
2
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
2
4
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
1
1
0
0
0
0
3
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
2
1
0
0
2
0
0
0
1
0
0
1
0
1
2
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
1
2
0
0
2
2
0
0
0
0
2
0
2
0
2
0
1
0
0
0
0
0
0
8
0
1
0
0
0
2
2
0
0
1
0
0
0
1
0
2
1
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
2
1
0
1
0
0
1
0
2
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
4
1
0
1
0
0
0
0
2
0
0
0
0
5
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
2
0
0
0
0
0
1
8
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
2
2
0
1
0
0
2
0
0
2
1
3
2
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
2
0
2
0
1
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
3
1
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
1
1
0
1
2
2
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
1
2
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
1
0
0
0
2
2
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
4
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
1
0
1
2
0
0
0
0
0
0
0
0
2
1
2
0
2
0
2
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
2
0
0
2
1
1
0
1
0
1
0
0
0
1
2
0
0
0
0
0
0
0
3
5
0
0
0
0
0
0
0
2
1
2
0
0
1
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
2
0
0
1
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
3
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
1
0
2
1
0
0
0
0
0
2
0
0
0
2
0
1
0
1
0
1
2
2
0
1
0
0
0
2
1
0
0
1
1
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
1
0
0
2
0
2
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
5
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
2
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
1
2
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
1
1
0
0
0
2
0
2
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
2
0
2
0
0
0
2
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
4
1
0
3
0
0
0
0
0
0
0
1
1
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
2
1
0
0
2
1
0
0
0
0
0
1
1
2
0
0
0
2
0
0
2
0
0
0
0
0
1
2
2
0
0
2
0
0
2
0
0
0
0
0
1
0
2
0
2
0
2
0
2
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
1
1
2
1
0
0
2
2
0
0
1
0
0
0
3
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
4
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
2
2
0
2
0
0
2
0
0
0
0
2
3
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
5
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
2
0
3
1
0
0
0
0
0
1
0
2
0
0
1
2
0
0
2
0
0
2
1
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
1
0
1
0
0
1
0
3
0
0
0
0
5
1
0
2
1
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
2
0
5
0
2
0
0
2
0
0
1
0
0
0
2
0
1
0
0
0
1
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
2
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
2
1
0
0
0
2
1
0
0
0
1
0
1
0
0
2
1
1
0
0
0
0
1
0
0
7
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
1
0
1
0
2
0
0
0
1
2
0
1
2
1
0
0
0
0
1
1
0
1
0
0
0
2
0
0
1
0
0
0
3
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
6
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
1
1
0
2
0
0
0
0
0
0
2
1
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
3
0
0
0
2
0
2
0
0
0
2
0
0
2
1
2
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
1
1
0
0
1
3
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
2
0
0
0
2
1
0
0
0
0
2
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
2
0
2
1
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
1
1
2
2
2
0
0
0
0
2
0
0
1
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
3
1
2
0
2
2
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
2
0
1
2
1
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
1
0
3
0
4
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
1
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
1
0
1
1
0
1
0
3
1
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
1
0
0
0
1
0
0
1
0
2
0
0
0
0
0
1
3
2
0
1
1
1
0
0
1
1
0
1
1
0
0
2
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
3
0
1
3
0
0
2
0
2
0
0
0
0
0
2
0
0
1
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
1
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
4
3
3
0
2
3
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
1
0
0
1
0
1
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
3
0
0
0
0
0
0
3
0
0
0
2
0
0
4
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
2
0
2
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
1
0
0
0
0
1
0
2
0
1
0
1
0
2
2
1
0
0
0
1
0
2
0
0
0
0
3
1
2
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
1
1
0
1
0
0
0
0
2
0
1
2
0
5
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
2
0
0
0
0
0
1
3
2
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
1
0
2
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
2
0
2
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
2
1
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
3
0
2
0
0
0
0
0
0
0
2
0
1
2
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
2
1
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
2
0
0
0
1
0
3
0
0
2
2
0
0
1
0
3
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
1
0
2
0
0
0
0
0
0
0
4
0
0
0
1
6
0
0
1
2
3
0
0
0
3
2
0
0
0
0
2
4
1
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
3
1
1
1
0
0
0
0
0
1
0
0
0
2
1
0
0
1
0
2
1
2
0
0
0
0
0
0
1
2
2
2
0
0
1
0
0
1
0
0
1
0
0
2
0
0
0
0
4
0
0
2
2
0
0
0
0
3
0
0
0
0
0
0
2
1
0
0
1
1
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
3
0
3
1
0
0
0
0
0
0
0
0
1
0
3
0
0
1
0
0
0
0
0
0
2
0
2
1
0
0
0
1
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
2
0
2
0
0
0
1
0
0
0
1
0
0
0
2
3
0
0
0
1
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
1
0
1
0
2
0
0
1
0
0
0
0
2
2
0
0
0
1
0
0
3
0
0
2
2
1
0
0
2
0
0
1
2
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
2
0
0
0
3
0
1
0
0
0
3
0
5
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
3
0
1
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
1
0
1
0
0
0
3
1
0
0
2
0
2
0
0
0
1
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
1
0
0
0
4
0
0
3
0
0
0
0
0
2
0
0
2
3
0
0
0
0
0
0
0
1
3
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
3
0
5
0
0
0
0
0
0
0
0
0
4
0
0
2
2
0
0
0
2
0
1
0
2
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
2
1
2
0
0
2
0
2
0
0
0
0
2
0
0
1
0
0
1
0
0
0
2
2
0
0
1
0
0
0
2
0
0
2
0
0
1
0
0
0
0
2
0
0
1
0
0
2
1
1
0
0
1
0
6
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
1
1
0
2
1
0
1
1
0
0
0
0
0
0
1
2
2
0
2
0
0
0
1
1
1
0
0
0
1
0
0
1
2
0
0
2
2
0
0
0
0
0
2
1
0
0
1
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
1
0
2
7
0
0
1
0
2
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
2
0
2
0
2
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
2
0
0
0
6
0
0
2
0
0
1
1
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
2
2
0
3
1
0
0
0
0
2
1
0
0
0
0
0
2
2
0
0
2
1
0
0
0
0
1
0
0
0
0
2
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
2
2
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
1
2
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
2
0
2
0
1
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
1
1
0
2
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
2
0
0
1
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
3
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
1
0
1
1
0
2
2
0
0
2
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
4
0
0
0
1
0
0
0
1
2
0
2
0
0
0
1
1
0
0
5
1
0
0
2
0
3
0
2
0
0
0
1
0
2
0
0
3
0
0
1
0
0
0
0
0
2
2
0
4
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
1
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
1
0
1
0
0
0
0
2
2
2
0
1
1
0
0
0
0
0
2
0
1
0
1
0
0
0
2
2
2
0
0
1
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
4
1
1
10
0
1
0
0
0
0
0
0
0
3
1
1
0
0
0
2
0
2
0
0
0
0
0
0
3
0
2
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
2
3
0
1
0
0
0
2
0
1
0
0
1
0
2
0
1
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
2
1
2
3
1
0
0
2
1
0
0
0
2
2
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
2
0
0
2
0
2
2
2
1
2
3
0
1
1
0
0
2
0
0
0
1
0
0
0
2
1
2
0
1
3
0
1
1
1
0
0
2
0
1
1
6
2
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
2
0
2
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
2
1
1
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
2
0
2
1
2
0
0
0
1
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
5
0
0
2
0
2
0
4
0
0
0
0
1
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
2
0
1
2
0
0
1
0
2
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
1
1
1
2
0
1
0
0
0
0
0
0
0
1
1
0
0
2
0
0
1
0
1
1
0
2
0
0
0
0
2
1
0
0
4
0
0
0
0
0
1
0
0
2
0
0
0
1
0
2
2
0
0
2
0
2
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
1
0
0
3
0
0
1
0
2
2
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
1
0
3
0
0
0
0
0
0
1
0
0
0
3
0
0
1
2
0
0
2
0
2
1
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
1
2
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
2
1
0
0
0
3
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
2
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
2
0
3
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
1
0
1
0
1
1
1
0
0
1
0
0
0
2
0
0
0
1
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
5
2
0
1
2
0
0
1
0
2
4
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
2
0
3
0
0
0
0
0
4
1
0
0
2
0
2
0
0
1
0
0
0
0
0
0
1
1
0
2
1
0
0
4
2
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
2
2
5
3
1
2
0
0
2
2
2
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
1
0
0
2
0
3
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
2
1
0
2
2
2
0
0
0
0
0
3
1
0
2
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
1
2
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
2
0
0
0
4
0
0
2
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
1
1
0
0
2
0
0
0
1
0
2
0
1
2
0
0
0
2
3
0
0
0
1
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
1
0
0
0
2
0
0
1
0
0
1
0
0
0
1
0
0
1
1
0
1
1
0
0
1
0
1
2
0
0
0
3
0
1
0
0
0
0
2
1
0
0
1
0
0
4
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
1
2
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
2
0
1
3
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
1
1
1
1
0
0
0
2
2
1
0
0
0
0
0
2
0
1
1
0
0
2
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
2
2
0
3
0
0
1
1
2
0
1
1
2
3
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
2
0
0
0
0
0
2
0
0
0
2
0
0
1
0
4
3
0
1
0
0
0
0
1
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
2
0
1
0
1
0
1
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
3
0
2
0
2
0
0
0
2
0
0
2
0
0
0
0
2
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
2
0
3
0
0
1
0
1
0
0
7
1
1
2
1
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
2
2
2
1
0
1
0
2
0
0
1
0
0
0
0
2
0
0
0
0
2
1
0
0
1
1
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
2
0
1
0
0
0
1
1
0
0
0
0
1
0
1
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
3
1
1
11
0
1
0
2
0
2
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
3
0
3
0
2
0
0
0
0
0
1
0
0
1
3
0
0
0
0
0
0
1
2
2
0
0
0
1
0
2
2
1
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
3
0
0
0
0
0
0
1
2
2
3
1
2
0
0
0
1
1
2
1
0
1
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
4
0
0
2
0
0
3
0
0
0
0
2
1
0
2
1
0
0
0
0
0
1
2
0
0
0
1
0
1
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
3
2
0
2
1
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
1
0
1
1
3
2
2
0
2
0
0
0
0
0
0
5
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
4
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
1
2
0
3
3
3
1
1
0
0
0
1
0
2
0
0
0
4
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
1
0
2
2
0
2
1
0
0
0
0
0
2
0
0
0
1
0
2
1
0
1
1
0
2
2
2
1
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
1
0
0
0
0
2
0
0
1
2
1
1
0
2
0
2
2
0
1
2
0
0
2
0
0
0
0
0
3
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
3
0
1
3
2
0
1
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
1
2
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
4
0
0
0
0
2
0
0
0
2
2
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
2
0
0
3
0
1
2
0
2
0
0
2
0
0
0
4
0
1
1
1
0
0
1
0
0
0
0
0
1
0
2
0
2
1
0
2
0
1
0
0
4
0
0
0
0
0
2
1
1
3
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
1
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
5
0
0
0
1
0
1
0
0
3
0
0
0
0
0
0
2
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
7
1
2
0
0
1
0
0
1
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
2
1
0
2
2
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
2
2
0
7
1
0
0
1
0
1
0
0
0
2
0
0
0
1
1
0
2
0
0
3
2
0
0
0
0
2
0
0
1
0
2
0
0
2
0
0
0
0
0
1
1
2
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
1
0
0
0
1
0
0
2
2
0
0
1
2
0
0
0
2
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
3
0
3
0
1
2
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
1
1
0
0
0
0
1
0
0
0
1
0
3
0
1
0
0
2
0
9
1
0
0
0
0
0
1
0
0
2
0
2
2
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
5
0
5
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
2
3
0
1
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
2
0
0
2
1
0
3
1
0
2
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
2
0
1
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
3
0
0
0
0
0
0
1
2
0
2
1
0
0
0
0
1
0
1
0
0
2
1
2
0
0
0
2
0
0
0
0
0
3
0
0
0
2
0
0
1
1
0
0
0
0
0
1
0
0
4
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
3
0
0
0
0
0
0
2
0
2
0
0
3
0
2
0
0
0
1
1
1
1
0
0
1
2
0
2
0
2
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
1
0
0
0
0
0
0
2
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
4
1
0
0
0
2
0
0
4
0
0
0
0
1
1
0
0
0
1
0
6
0
0
0
0
0
1
1
1
1
0
0
1
1
0
0
1
2
0
3
0
0
0
0
0
2
2
2
0
0
0
2
0
0
0
0
1
1
0
1
0
0
0
0
2
0
0
3
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
2
2
0
1
0
2
1
2
1
1
0
0
0
0
4
4
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
1
1
1
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
2
0
5
0
0
0
1
1
0
0
2
0
4
1
0
0
0
1
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
2
2
0
0
0
0
1
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
1
2
0
0
1
0
1
0
0
1
0
0
2
2
0
0
0
1
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
2
0
0
0
0
2
0
2
0
0
2
0
2
0
0
0
2
3
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
1
2
0
0
1
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
6
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
2
0
2
0
0
2
6
2
1
0
0
2
0
0
0
1
0
0
0
2
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
4
0
0
1
0
1
1
0
0
0
3
0
0
4
0
1
0
1
0
2
1
0
2
0
0
0
2
1
0
2
0
0
2
1
0
0
0
0
0
1
4
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
3
0
1
0
1
0
2
0
1
1
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
5
1
0
0
2
0
0
0
0
0
0
0
2
1
2
1
0
1
2
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
2
0
0
1
0
2
1
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
2
2
2
0
0
0
0
0
2
0
1
2
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
2
2
2
1
0
0
2
2
0
0
0
3
0
0
3
2
1
2
0
2
1
2
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
1
0
2
0
0
2
0
0
0
0
1
0
0
0
0
1
2
0
0
0
2
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
3
4
2
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
1
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
3
0
0
0
0
0
1
0
0
0
0
2
0
0
3
0
0
0
4
1
0
0
0
2
0
0
0
0
1
0
0
0
1
4
1
0
1
0
0
2
1
2
0
2
0
2
0
0
1
0
0
0
1
1
0
0
0
1
1
0
0
0
1
2
0
0
2
2
0
0
1
0
0
0
2
0
0
0
1
1
0
0
0
1
0
0
0
0
2
0
2
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
1
0
0
4
0
1
0
0
0
0
0
1
1
2
0
1
2
0
0
0
2
2
0
0
0
1
1
1
0
0
0
0
1
0
0
0
2
1
0
0
0
0
1
1
0
2
1
0
0
0
0
0
1
0
0
1
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
2
0
0
0
2
2
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
2
0
0
1
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
1
0
1
0
0
2
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
2
2
0
0
2
0
0
3
1
0
0
0
1
2
0
3
0
0
1
0
0
2
0
0
0
0
0
3
0
0
0
2
0
0
3
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
1
0
0
1
2
0
0
2
0
2
0
2
0
0
2
0
0
2
0
0
2
0
0
0
1
0
1
0
2
0
0
0
0
0
0
2
0
0
0
2
1
1
0
2
0
0
0
1
0
0
2
2
2
0
0
1
1
4
0
0
2
0
0
0
2
2
0
1
1
0
2
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
3
1
0
0
0
2
0
1
0
0
2
0
0
0
0
2
2
1
1
2
0
0
2
0
1
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
2
0
2
0
0
2
0
0
1
0
0
4
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
3
0
1
0
0
0
0
0
0
0
1
0
2
2
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
2
0
1
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
1
2
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
2
0
0
3
0
0
0
0
2
1
2
1
0
1
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
2
0
1
0
1
0
0
0
0
0
0
1
0
0
0
2
1
0
0
1
0
0
2
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
2
0
0
2
2
0
2
0
0
0
1
1
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
3
2
1
0
3
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
2
0
2
1
0
0
2
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
2
0
2
1
0
1
0
0
0
0
1
4
0
0
0
0
0
0
1
0
0
0
0
1
0
3
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
2
1
0
0
0
0
0
6
0
0
0
0
0
1
0
2
0
0
0
0
2
2
0
0
1
0
0
1
0
0
0
2
1
2
1
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
2
0
1
1
0
0
0
3
2
1
0
2
0
0
0
0
0
0
0
0
2
2
0
1
2
0
0
0
1
1
2
0
0
0
0
0
0
0
2
0
0
2
0
0
2
1
0
0
1
1
0
2
0
0
2
2
0
1
2
1
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
2
1
1
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
2
1
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
1
3
0
2
0
0
0
0
0
2
0
1
0
0
0
0
1
0
2
2
0
0
0
0
2
0
1
0
0
0
0
0
1
2
0
1
0
0
1
0
0
0
0
2
0
2
0
0
0
0
3
1
0
1
0
0
3
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
1
1
0
1
0
0
1
0
4
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
5
0
1
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
1
0
0
0
0
0
0
1
0
2
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
4
0
1
0
0
0
1
0
2
0
0
2
1
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
2
0
1
2
1
2
0
0
0
0
0
1
0
0
2
2
0
2
0
0
0
2
0
0
1
0
1
3
0
0
0
0
0
0
1
5
0
1
2
0
0
1
2
0
0
0
0
0
2
0
2
0
1
0
0
0
5
0
0
1
0
2
0
0
0
0
1
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
3
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
2
1
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
3
0
1
0
0
0
0
0
0
0
3
0
0
0
2
0
1
0
0
1
2
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
3
0
1
0
0
0
0
2
0
0
0
0
1
0
0
1
0
2
2
2
0
0
2
0
0
0
0
0
0
2
1
0
1
0
2
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
1
1
1
0
1
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
2
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
1
0
0
0
1
0
0
0
1
2
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
2
0
0
1
0
0
0
0
2
0
0
1
0
0
0
1
0
3
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
2
0
0
3
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
1
0
1
2
0
0
1
1
0
0
8
2
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
3
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
3
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
5
0
2
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
4
0
0
3
0
0
0
0
0
0
1
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
1
0
2
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
3
0
2
0
0
1
2
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
5
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
1
0
1
2
0
0
2
0
0
0
1
2
2
0
0
0
0
0
0
2
0
0
0
0
2
4
2
0
1
2
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
2
2
1
0
0
0
0
3
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
1
0
2
1
1
0
0
1
2
1
0
0
1
0
0
5
0
0
2
2
0
0
0
0
0
0
3
0
1
0
0
5
1
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
1
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
3
3
0
1
1
1
1
0
0
0
2
2
0
2
2
0
0
10
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
2
1
2
0
1
0
2
2
0
0
1
0
0
0
0
1
0
0
0
0
0
2
2
0
7
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
2
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
1
0
0
1
2
2
1
2
0
0
0
1
0
0
0
0
0
0
2
1
1
0
1
0
0
0
2
0
0
3
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
3
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
1
1
0
0
0
1
0
0
0
1
0
3
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
4
0
1
0
0
0
1
9
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
2
2
2
0
0
1
0
2
0
0
0
3
1
0
0
0
2
2
0
0
0
0
0
0
1
0
1
1
1
0
0
1
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
2
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
2
2
1
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
2
2
0
0
1
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
1
0
1
0
0
3
0
0
0
0
2
0
0
0
2
0
0
0
0
3
0
0
0
2
2
1
0
3
2
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
1
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
1
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
2
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
9
0
0
0
2
1
0
0
1
0
0
0
0
1
0
2
1
0
0
0
1
2
1
1
2
0
0
0
1
2
2
1
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
2
2
0
0
0
3
2
0
0
2
2
0
0
1
0
0
1
0
0
0
0
0
0
0
2
2
1
0
1
0
0
1
0
2
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
1
0
3
0
0
1
2
0
0
0
0
2
0
4
0
1
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
1
0
2
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
4
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
2
0
1
2
0
0
2
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
3
3
0
0
2
0
0
0
0
2
0
0
2
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
1
0
1
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
1
0
2
2
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
1
0
0
0
0
2
1
0
0
0
0
2
2
0
0
2
0
1
1
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
2
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
2
0
0
0
2
0
0
0
2
0
3
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
2
2
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
2
2
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
2
0
0
2
1
0
0
0
0
1
0
1
0
0
0
0
2
0
0
2
0
2
2
2
0
0
0
0
1
2
0
0
0
0
1
0
0
2
1
0
1
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
1
3
0
1
1
1
0
0
3
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
15
1
1
2
0
0
2
0
0
0
0
1
2
1
1
0
0
0
1
0
1
0
0
0
0
0
2
0
0
1
0
0
1
0
3
0
0
2
0
0
1
1
0
0
2
2
2
0
0
0
0
0
1
0
0
0
0
0
2
4
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
10
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
2
1
0
1
1
0
1
0
0
0
0
0
1
0
0
3
0
0
1
0
4
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
2
0
2
0
2
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
1
0
0
0
0
0
0
2
1
0
0
2
0
5
0
1
0
2
0
0
1
0
0
2
0
1
1
3
1
0
1
0
0
0
0
0
0
0
3
0
2
1
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
2
0
1
0
0
0
0
0
2
0
0
0
1
0
2
1
0
3
1
0
2
2
0
0
1
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
1
2
2
0
0
0
0
0
2
2
4
1
0
0
1
3
0
0
0
0
0
0
3
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
4
2
0
0
0
1
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
2
0
2
0
1
0
2
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
1
0
1
0
0
2
0
1
0
0
0
0
2
0
0
0
1
2
1
0
0
0
0
0
1
2
0
0
1
2
0
2
0
0
0
0
1
0
0
2
1
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
1
0
1
1
0
0
0
2
1
0
0
0
2
0
0
0
2
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
5
0
0
2
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
1
0
2
0
0
0
0
0
2
0
0
2
0
2
0
0
3
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
4
0
1
3
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
2
0
1
0
0
2
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
3
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
2
2
0
2
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
1
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
2
0
0
0
1
0
2
0
1
0
0
0
1
0
1
0
1
1
1
2
0
0
0
0
2
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
2
0
0
1
0
1
0
0
1
0
0
0
2
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
2
1
1
0
0
2
1
4
0
0
0
0
1
1
2
2
0
0
0
1
0
0
1
0
0
2
2
1
0
0
0
1
0
0
1
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
2
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
2
0
0
1
1
0
0
0
0
0
0
0
5
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
1
4
2
0
0
1
0
2
0
2
2
0
0
0
0
0
0
0
1
1
3
1
0
2
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
1
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
2
0
5
1
1
0
0
2
1
1
0
1
1
0
0
2
0
0
0
0
0
2
1
2
0
1
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
1
2
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
1
1
0
1
0
0
0
0
0
1
0
2
0
0
1
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
1
3
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
2
0
1
2
0
0
0
2
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
2
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
2
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
2
0
2
0
0
2
0
1
1
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
5
2
4
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
2
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
3
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
3
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
2
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
1
0
0
0
3
0
0
0
0
2
0
1
1
0
0
0
1
0
0
0
1
0
0
1
2
1
0
0
1
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
2
1
0
2
0
0
0
2
0
0
0
0
2
7
0
0
0
1
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
4
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
2
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
4
1
1
0
2
2
0
0
0
2
0
7
0
0
0
0
2
2
5
0
0
1
0
0
2
0
0
0
0
2
0
0
0
2
2
2
0
1
0
2
0
0
0
1
0
2
0
1
0
0
2
2
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
4
0
0
3
0
2
0
0
2
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
1
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
2
1
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
1
8
0
0
0
7
0
0
0
1
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
1
2
2
0
2
1
1
0
2
1
1
0
0
0
0
2
1
0
0
0
0
2
0
0
1
2
0
0
0
0
2
0
2
0
2
0
2
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
1
1
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
3
0
0
0
0
1
2
2
0
0
0
0
0
1
0
0
0
0
1
2
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
1
0
1
0
1
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
2
0
0
0
2
0
1
0
2
2
0
0
2
0
2
0
0
0
0
0
0
1
0
0
1
1
2
0
0
0
0
0
1
0
0
0
0
2
0
2
2
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
1
2
2
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
5
0
0
0
0
0
0
0
1
2
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
2
0
0
2
1
0
1
2
0
0
0
2
0
1
0
0
0
1
0
0
2
0
1
2
0
1
2
0
1
1
0
1
0
0
0
0
2
0
2
2
0
0
4
1
0
0
0
0
0
1
1
2
2
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
1
0
4
2
0
0
0
0
0
0
0
3
0
0
0
0
0
1
2
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
2
1
2
1
0
1
0
0
0
0
0
2
0
0
0
3
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
1
0
1
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
3
0
3
0
0
0
1
3
0
0
1
1
2
0
0
0
0
0
1
0
0
1
0
0
0
2
0
1
1
2
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
1
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
1
1
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
1
0
1
0
0
2
2
0
0
0
0
2
0
0
0
1
0
3
2
0
0
0
0
0
2
2
0
0
0
3
1
2
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
4
0
0
0
9
0
2
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
2
0
0
1
2
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
1
0
1
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
2
0
0
0
2
8
4
2
0
1
0
3
1
0
0
0
2
1
0
1
0
0
1
0
0
0
1
0
0
0
2
2
0
1
0
0
0
1
1
0
0
2
0
0
0
2
0
0
0
0
2
0
1
1
0
0
0
0
0
1
2
0
0
1
2
1
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
2
4
0
0
1
0
0
0
0
0
0
0
2
16
1
0
2
0
0
0
2
2
0
0
1
0
0
0
0
2
0
1
0
0
0
2
1
0
0
5
0
0
0
0
2
2
0
2
0
0
2
0
1
0
1
2
0
0
0
0
2
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
1
1
0
2
0
2
0
2
1
1
0
2
0
5
2
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
2
1
0
0
0
1
1
2
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
2
0
0
0
0
2
1
0
0
0
2
0
2
2
0
0
2
0
1
8
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
2
0
0
1
6
0
0
0
0
0
0
2
2
0
0
0
0
0
1
1
2
0
0
0
1
0
0
0
2
1
0
0
1
1
0
2
1
0
0
0
2
0
1
0
2
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
1
0
0
0
0
2
1
2
0
1
1
0
0
0
2
0
0
0
2
1
0
0
0
2
0
2
1
0
0
0
0
2
1
0
0
0
1
2
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
1
1
0
1
1
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
2
0
2
1
1
1
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
5
0
1
0
0
1
0
2
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
2
0
2
5
0
0
0
2
1
0
1
0
0
1
0
0
0
0
0
0
6
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
2
2
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
1
2
0
2
0
2
0
0
0
0
0
0
0
3
2
0
0
0
0
1
0
1
0
1
0
0
0
4
1
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
1
0
0
0
1
0
1
0
0
0
2
0
3
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
4
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
2
0
0
0
0
0
0
2
1
0
2
0
0
0
0
1
0
2
0
2
0
1
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
2
0
1
2
0
0
2
2
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
1
3
0
0
0
0
1
4
0
2
0
0
0
2
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
5
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
1
2
2
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
1
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
2
1
0
0
0
2
0
1
0
5
0
0
0
0
0
2
3
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
4
0
2
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
4
0
0
0
1
4
2
0
0
0
2
0
0
2
0
0
0
0
1
2
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
4
1
0
0
0
2
0
2
3
0
0
2
0
1
0
0
1
0
0
2
1
3
0
0
0
2
0
0
0
1
0
1
2
0
1
0
0
2
0
2
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
3
0
0
3
0
0
0
0
0
2
2
2
0
0
0
0
1
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
4
2
0
0
0
2
0
0
5
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
2
2
2
2
5
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
4
2
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
2
0
2
1
0
1
0
0
0
1
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
3
0
0
0
2
0
0
1
1
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
5
0
0
1
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
1
1
3
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
3
0
1
2
2
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
2
0
0
0
1
0
2
0
0
1
1
0
0
0
0
0
2
2
0
0
1
0
0
0
1
0
2
2
0
0
1
1
0
2
0
1
1
0
0
1
0
0
1
0
0
8
0
0
1
0
0
0
1
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
3
2
0
0
0
0
2
0
0
0
1
1
0
1
2
2
0
2
2
1
0
2
1
0
0
0
0
2
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
2
0
0
1
6
1
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
2
0
2
0
0
0
1
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
3
2
1
0
0
2
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
1
0
0
1
1
0
1
1
0
1
1
1
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
2
0
1
2
0
2
1
0
0
0
0
8
0
2
0
2
0
2
0
0
1
0
0
2
0
0
2
0
0
1
0
2
2
1
0
0
0
0
0
2
0
2
0
0
0
2
0
0
2
0
4
1
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
1
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
3
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
3
0
1
1
1
0
2
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
2
2
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
4
1
0
0
0
2
0
0
2
0
0
0
2
1
0
2
0
1
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
3
1
0
0
2
1
0
1
0
0
0
0
1
1
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
1
1
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
2
1
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
1
1
0
2
1
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
2
0
2
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
1
0
0
2
1
0
0
0
0
0
0
1
2
0
0
0
1
1
1
1
0
1
0
0
0
1
0
0
1
0
2
2
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
4
3
1
1
2
0
0
0
1
0
1
1
0
0
0
0
3
0
0
0
1
0
0
3
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
2
1
0
2
0
0
1
1
2
0
0
0
6
0
0
0
0
0
0
0
0
2
0
0
0
1
1
1
0
0
0
0
1
0
2
2
0
0
4
2
0
2
0
0
0
0
3
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
2
4
1
1
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
1
0
2
0
0
0
1
1
1
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
1
0
1
0
2
0
0
0
2
0
0
0
1
0
0
0
1
0
3
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
1
0
0
3
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
4
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
3
5
0
0
1
0
0
0
0
0
0
0
2
4
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
2
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
2
0
2
0
2
0
0
0
0
1
1
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
2
1
2
0
2
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
4
0
2
2
0
0
2
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
2
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
2
1
0
2
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
3
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
1
2
0
2
0
0
0
2
0
1
0
0
2
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
4
0
2
0
2
0
0
2
1
0
0
0
1
2
2
0
0
3
2
0
0
2
0
1
0
0
0
2
1
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
3
0
1
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
1
0
3
0
0
0
0
0
0
0
1
1
2
0
0
1
0
2
0
0
0
0
0
0
1
2
0
0
0
0
3
1
2
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
2
0
0
1
1
0
0
2
0
1
1
1
1
0
1
0
0
1
2
0
2
0
2
0
2
0
0
0
0
0
2
0
1
2
2
0
0
2
0
1
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
1
0
0
2
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
3
0
0
0
0
2
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
5
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
7
1
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
2
1
1
0
0
0
2
1
0
1
2
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
1
0
0
2
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
6
0
0
0
1
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
4
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
4
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
2
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
4
1
0
0
0
0
2
0
0
2
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
2
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
2
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
2
1
2
0
0
0
1
3
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
1
0
1
2
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
2
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
1
0
2
2
0
0
0
0
2
1
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
2
0
0
0
0
1
0
0
1
0
0
0
2
2
0
0
0
0
0
2
0
1
0
0
1
0
2
2
0
0
0
0
0
2
2
0
2
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
1
0
0
2
0
2
0
0
0
2
2
2
0
2
1
0
0
2
1
0
1
0
0
0
2
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
4
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
2
0
0
0
1
2
0
0
2
0
0
2
0
2
0
0
0
0
0
1
1
0
3
0
1
1
0
1
0
1
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
2
0
5
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
2
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
2
0
1
0
0
0
0
0
1
0
0
1
0
3
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
2
1
0
0
0
2
0
0
0
0
3
1
0
1
1
0
0
1
1
0
3
0
2
2
0
0
0
1
0
2
0
0
0
4
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
1
0
1
1
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
1
2
1
0
2
1
2
0
11
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
1
0
1
2
1
0
0
0
0
0
0
0
14
0
0
0
0
0
0
0
0
1
1
0
1
0
1
1
2
1
0
0
5
0
1
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
5
0
0
0
1
0
0
2
0
0
2
0
0
0
1
0
1
0
0
0
2
0
3
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
1
2
0
1
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
2
1
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
2
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
2
0
2
0
0
2
0
1
0
0
0
0
0
3
0
0
4
0
0
0
0
0
2
3
0
0
0
0
0
3
0
0
1
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
2
0
0
3
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
1
0
2
0
1
2
1
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
2
0
3
0
0
2
0
2
0
0
1
3
0
0
0
0
0
0
1
2
1
2
0
0
0
1
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
3
0
1
0
0
0
0
1
0
1
1
0
0
0
0
2
0
0
1
0
1
0
0
0
0
2
1
0
0
0
2
0
3
0
0
0
0
0
1
0
2
0
1
0
0
1
0
0
1
0
0
2
0
0
2
2
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
2
0
2
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
2
2
2
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
1
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
2
0
0
0
1
1
0
0
0
2
0
2
0
0
3
2
0
0
0
0
1
0
0
0
0
1
2
0
1
0
2
0
0
0
0
0
0
3
1
0
2
0
2
2
0
0
0
2
0
0
0
1
0
0
2
0
0
0
1
1
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
2
0
0
2
2
1
0
0
0
0
3
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
1
0
0
0
1
1
0
0
1
0
1
0
2
0
0
0
0
0
0
0
1
0
0
1
2
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
3
0
0
1
3
0
0
2
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
2
2
1
1
0
2
0
0
1
0
1
1
0
2
3
0
0
0
0
2
1
0
0
1
0
0
0
0
2
0
0
1
0
3
0
0
0
0
0
2
2
5
0
1
1
0
0
3
0
1
0
0
0
1
2
0
0
0
0
0
1
4
0
0
1
0
4
0
0
0
0
1
0
0
1
0
0
1
1
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
4
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
3
0
1
2
0
0
0
0
2
2
0
0
0
0
0
1
0
2
0
1
0
0
0
0
2
2
0
2
0
0
0
1
0
0
2
0
0
2
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
1
1
1
0
0
0
0
0
3
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
2
0
0
4
0
0
2
0
0
0
1
0
1
1
0
0
0
1
0
0
1
0
0
0
0
2
0
0
1
1
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
1
0
1
0
0
1
1
0
0
3
2
1
1
0
2
0
1
0
0
2
0
2
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
2
0
0
1
1
0
0
0
0
1
0
0
2
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
3
0
3
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
2
1
1
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
2
0
2
2
0
0
0
0
2
0
0
0
2
1
0
0
0
0
1
2
1
3
0
2
0
0
3
0
1
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
2
0
0
1
0
0
2
0
1
1
0
0
0
6
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
1
0
1
0
1
0
1
0
0
2
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
2
0
2
0
1
5
1
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
2
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
3
2
1
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
3
0
0
0
0
0
0
2
0
2
1
0
1
2
1
0
2
0
0
3
0
2
0
0
2
1
1
0
0
0
1
4
0
2
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
2
1
0
6
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
1
0
2
0
1
0
2
0
0
0
0
0
2
0
0
1
0
1
0
2
0
0
0
2
0
0
0
1
0
0
1
0
0
2
1
2
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
2
1
0
2
2
0
0
0
0
0
0
1
0
2
2
0
2
0
0
0
0
0
0
2
1
0
2
3
0
2
0
2
0
0
0
3
0
0
4
1
0
1
1
0
0
0
0
0
0
0
0
0
2
0
1
3
0
0
0
0
0
0
0
0
2
0
1
0
2
2
0
1
1
0
1
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
2
1
0
1
0
1
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
2
1
0
0
0
1
0
0
0
0
1
0
0
0
0
2
3
0
0
0
0
0
1
0
0
2
1
0
0
0
0
2
3
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
2
0
0
1
0
0
0
0
1
0
0
0
1
2
0
0
0
2
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
2
0
0
1
0
0
0
2
0
0
6
1
0
1
1
2
2
2
1
0
1
0
0
2
0
0
0
2
2
0
0
0
0
0
1
1
1
5
1
0
1
0
0
1
0
0
0
5
2
0
0
2
0
0
0
0
1
0
0
0
1
2
2
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
1
2
0
0
1
2
0
0
1
0
0
0
2
0
0
2
0
2
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
1
2
1
0
0
2
2
0
0
0
0
0
1
0
0
0
2
0
1
0
2
0
0
0
0
0
1
0
2
2
0
0
0
1
0
0
1
0
4
0
0
0
1
0
3
0
0
0
0
0
2
0
0
0
2
0
0
0
4
5
0
1
0
0
3
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
3
0
0
2
2
0
3
1
0
0
1
2
0
3
0
3
0
0
0
0
0
0
2
0
1
0
1
1
0
0
0
0
2
0
0
0
3
0
0
1
0
0
0
1
1
0
0
0
0
0
2
0
1
0
0
0
5
1
0
0
0
0
0
2
0
1
1
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
2
0
0
1
2
1
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
2
0
0
0
1
0
1
0
1
3
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
2
1
0
1
0
0
0
0
0
0
0
2
1
2
0
2
0
0
0
1
2
0
1
0
2
3
0
0
0
0
0
2
0
0
0
0
0
0
1
2
4
0
0
0
2
0
0
1
0
1
0
0
2
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
3
2
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
7
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
2
0
2
2
0
0
0
0
0
1
0
3
0
2
1
0
0
0
0
0
0
1
0
1
0
0
2
0
0
1
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
2
1
0
0
0
0
0
0
0
7
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
1
1
1
1
0
2
0
1
0
0
1
1
1
0
3
0
0
0
0
0
1
2
0
0
3
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
3
0
0
0
0
0
0
0
1
0
0
0
3
0
0
1
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
2
1
0
0
2
0
0
1
0
0
0
0
2
0
3
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
2
1
1
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
2
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
2
0
0
0
0
1
2
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
2
0
1
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
2
2
0
0
0
1
0
0
2
0
1
0
2
0
2
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
2
0
0
2
1
1
0
0
0
1
0
0
0
0
0
2
0
2
1
2
0
0
0
2
2
3
0
0
0
0
0
2
0
0
0
1
0
1
0
0
2
0
0
0
0
1
0
0
0
0
2
1
0
2
0
1
1
2
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
1
1
2
0
0
0
2
0
1
0
1
0
0
0
1
1
0
2
0
0
0
0
1
1
1
0
1
1
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
3
1
0
2
0
1
0
3
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
5
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
2
0
1
1
2
0
0
0
0
0
1
2
2
2
0
0
0
0
0
1
2
0
0
1
1
0
0
0
3
0
0
0
1
0
0
1
0
3
7
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
2
0
1
1
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
2
0
3
0
1
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
3
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
1
0
0
0
1
0
1
2
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
2
0
2
1
0
1
1
0
0
0
0
0
0
0
1
0
5
0
0
2
0
0
2
0
0
0
0
0
1
0
2
0
3
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
1
0
0
0
0
0
2
2
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
2
1
0
0
0
0
0
0
0
0
3
2
0
0
0
0
6
0
0
3
0
0
0
0
2
0
1
1
0
1
0
1
1
2
0
0
0
0
3
0
1
0
0
0
0
1
2
1
0
0
0
0
1
1
1
3
0
4
0
0
0
1
0
0
0
0
1
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
1
1
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
2
0
2
2
2
0
1
2
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
1
0
1
1
1
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
4
1
1
0
2
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
2
0
1
0
0
0
0
1
0
2
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
1
1
1
1
0
0
0
3
0
0
0
2
2
0
1
0
0
3
0
1
0
1
2
2
0
1
2
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
2
0
1
0
1
0
2
0
2
0
0
0
0
0
0
1
0
3
0
0
2
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
2
1
1
2
0
0
1
2
1
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
1
0
2
1
0
0
0
2
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
1
2
2
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
3
0
0
0
0
0
0
1
0
0
0
1
1
0
2
0
4
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
2
2
1
0
1
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
1
0
0
1
2
1
0
0
0
1
3
0
0
3
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
2
1
0
2
2
0
0
0
1
0
0
0
0
2
0
0
2
3
1
0
0
0
0
0
0
0
0
2
0
0
2
1
0
2
0
1
0
1
0
0
1
0
0
2
0
0
1
3
0
1
2
0
0
0
1
0
0
0
1
0
0
2
2
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
1
1
2
2
0
0
0
2
0
0
1
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
1
0
0
2
2
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
3
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
4
1
0
0
0
0
0
2
0
1
2
0
1
0
0
0
0
0
0
0
3
0
0
0
2
0
1
0
0
0
1
1
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
5
2
3
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
8
0
0
1
0
1
0
1
1
0
1
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
1
1
0
0
0
0
3
1
0
0
0
0
0
0
0
2
3
0
0
0
1
1
0
1
2
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
1
1
2
1
0
0
0
4
0
0
1
2
0
0
0
2
0
1
2
0
1
0
0
0
2
0
0
0
0
0
0
0
2
1
1
1
2
0
0
2
0
0
0
2
0
0
0
4
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
1
1
0
0
2
0
0
0
1
1
0
0
0
0
0
0
1
0
0
2
2
0
0
0
1
0
2
0
0
1
3
0
0
0
1
0
0
1
0
0
0
1
0
0
2
2
0
1
0
1
0
2
0
0
3
1
0
2
2
0
0
0
0
0
0
2
1
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
1
0
0
0
1
2
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
3
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
3
0
1
2
0
1
1
0
1
1
0
0
0
1
0
0
1
2
1
0
0
0
0
0
1
0
0
2
0
2
0
0
0
3
2
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
1
2
0
2
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
1
0
0
0
0
3
0
2
0
2
2
3
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
1
0
4
0
2
2
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
4
0
0
1
4
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
1
2
1
0
0
0
0
0
1
2
0
0
0
3
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
1
0
0
2
2
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
2
0
1
2
2
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
3
0
0
0
1
3
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
2
2
0
0
1
2
2
0
2
0
0
0
0
0
0
0
0
0
1
0
2
2
2
2
0
0
0
0
1
1
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
2
1
0
0
0
0
2
0
0
1
1
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
2
0
0
2
1
2
0
0
0
1
0
0
1
0
0
0
0
2
0
0
2
3
0
1
0
0
1
0
0
2
1
0
0
0
0
2
0
2
1
0
0
2
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
1
0
2
1
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
2
0
2
0
3
1
1
0
0
1
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
2
1
1
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
1
3
0
0
0
1
0
1
0
1
0
0
0
2
0
1
0
0
0
1
0
0
0
3
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
2
1
0
1
0
0
0
3
0
2
0
1
2
0
0
2
0
0
0
0
0
2
0
0
0
0
1
1
1
0
0
0
0
2
0
2
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
2
0
2
5
1
0
2
1
1
0
1
2
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
2
0
3
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
1
0
0
0
0
1
2
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
3
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
1
2
0
0
1
2
0
0
0
3
2
0
1
1
0
0
1
2
1
0
0
0
0
0
2
0
1
0
4
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
2
0
0
0
2
0
1
2
0
2
0
1
0
1
0
0
3
0
0
0
0
3
0
0
0
0
1
0
0
3
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
2
1
0
0
2
0
0
1
0
2
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
1
0
0
0
1
2
1
0
0
0
2
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
2
1
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
2
0
0
0
1
1
0
0
2
0
0
0
0
1
0
2
0
3
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
1
0
0
0
2
0
2
0
1
0
0
2
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
3
0
0
1
2
1
0
0
0
0
1
0
0
1
0
2
1
0
0
0
0
0
0
0
2
0
1
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
3
0
0
1
0
0
0
2
1
0
2
0
0
0
0
2
0
0
0
2
5
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
1
0
1
0
4
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
1
2
0
0
0
0
0
2
4
0
1
0
0
1
1
2
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
2
0
2
0
0
3
2
0
0
0
0
0
1
0
2
0
0
0
0
1
2
0
0
0
1
0
0
1
0
2
0
0
0
2
0
1
1
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
2
1
2
2
0
0
0
0
0
2
2
1
0
0
0
1
3
1
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
2
2
1
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
1
0
0
1
1
0
2
2
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
1
1
2
2
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
2
0
0
1
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
1
1
2
0
1
2
0
0
0
0
1
0
0
0
0
2
1
0
2
1
0
0
0
0
2
0
0
0
1
0
1
2
0
0
0
0
3
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
2
0
1
0
1
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
1
2
1
0
0
0
0
2
0
0
2
1
1
0
0
0
1
1
2
0
0
0
1
1
1
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
3
0
2
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
6
0
0
0
0
0
0
4
1
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
2
2
2
0
0
2
0
0
2
0
2
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
3
0
0
0
0
1
0
3
0
0
0
5
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
1
1
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
4
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
2
1
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
1
0
0
1
0
0
0
0
2
2
0
1
0
1
0
3
1
1
0
1
1
0
0
0
2
0
0
0
1
0
3
0
0
2
0
0
2
0
2
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
2
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
8
0
0
0
0
0
0
0
1
0
0
0
2
0
0
3
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
1
0
0
0
2
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
2
2
2
3
0
1
0
2
3
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
2
0
0
2
0
3
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
2
2
1
0
5
0
0
0
0
0
0
0
1
0
0
5
0
0
0
0
1
1
1
2
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
2
1
0
0
0
0
0
1
0
2
0
1
0
0
0
2
0
2
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
1
2
1
3
0
0
7
0
1
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
4
0
0
2
0
2
1
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
3
0
0
2
1
0
0
2
0
0
0
1
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
3
0
0
0
0
2
0
2
0
1
1
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
3
1
0
0
0
4
0
1
0
0
0
0
1
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
2
0
1
1
0
0
0
0
2
0
0
0
2
4
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
2
0
1
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
2
0
2
0
1
1
0
0
0
1
2
0
0
0
1
0
2
0
1
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
2
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
3
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
4
0
0
1
0
0
1
0
0
0
2
3
0
0
2
0
0
1
0
0
0
1
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
2
1
1
0
2
0
0
2
1
0
0
0
3
0
1
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
5
0
2
0
1
0
2
0
3
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
2
0
0
0
0
0
0
3
2
0
5
0
0
0
0
0
2
1
0
0
2
1
0
0
1
2
2
0
2
2
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
3
1
2
0
0
0
1
0
0
0
1
0
0
0
0
1
0
2
0
1
2
0
0
0
0
2
0
0
0
0
2
0
2
1
0
0
2
0
1
0
0
0
0
2
0
2
2
2
0
2
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
2
0
0
2
0
0
0
0
1
0
2
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
1
0
3
0
0
0
0
0
1
0
0
0
2
0
1
1
0
0
1
0
0
0
0
3
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
1
0
0
1
2
0
2
0
1
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
2
0
1
0
2
0
0
1
2
0
0
0
1
1
2
0
0
0
0
0
0
1
0
0
2
0
0
3
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
2
0
1
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
2
2
2
0
3
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
3
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
1
1
1
0
2
0
0
2
1
0
2
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
2
0
0
1
0
1
0
0
0
0
2
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
5
2
1
0
5
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
1
2
0
2
0
0
0
2
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
1
1
0
2
2
1
0
1
0
0
0
0
1
0
0
1
0
2
2
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
2
1
2
0
0
0
1
1
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
4
2
0
0
0
0
2
0
1
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
2
0
0
2
0
0
2
2
0
2
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
1
0
0
0
1
0
0
0
3
2
2
0
0
0
1
0
2
0
0
0
0
0
4
0
2
2
0
0
0
1
0
0
0
2
0
12
0
0
0
1
1
0
0
1
0
0
2
0
0
0
2
0
0
1
2
0
0
2
0
2
0
0
0
1
0
1
2
0
1
0
0
0
0
0
0
0
6
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
2
2
2
0
0
0
2
0
1
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
2
2
0
0
1
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
1
1
1
2
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
2
0
0
0
0
0
1
0
0
1
1
0
1
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
1
1
0
1
0
0
0
2
1
2
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
6
0
0
0
0
0
0
0
0
2
0
2
1
0
2
0
0
1
0
0
0
2
0
1
0
0
2
0
2
0
1
0
0
2
0
0
1
0
2
1
2
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
3
0
0
0
0
2
1
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
2
1
0
0
0
2
0
2
0
0
0
0
0
2
2
0
0
0
1
0
0
0
1
1
0
1
0
0
2
0
0
1
5
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
2
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
1
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
5
0
0
1
1
0
0
0
0
0
0
1
1
1
0
2
2
0
0
0
0
4
2
2
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
4
0
2
2
0
2
0
0
1
2
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
1
2
0
0
2
0
0
0
1
0
2
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
3
0
0
1
3
0
1
1
1
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
2
1
0
3
0
0
3
0
0
0
0
3
0
1
3
2
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
1
0
1
0
0
2
0
1
0
0
1
1
1
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
3
0
0
1
0
1
0
0
0
1
0
0
4
0
4
0
1
0
2
3
1
0
1
1
0
0
0
3
0
1
0
0
0
0
0
0
1
0
1
0
0
2
2
1
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
4
0
2
1
0
5
0
0
1
0
1
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
1
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
4
0
0
1
1
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
3
0
0
0
6
0
0
0
0
0
1
0
0
2
0
0
0
3
0
0
1
0
0
1
0
0
1
2
0
2
0
0
1
1
2
0
0
0
1
0
1
0
2
0
1
0
0
0
0
1
2
0
1
0
2
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
5
1
2
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
1
0
1
3
0
0
0
0
0
3
0
1
0
1
0
1
1
2
1
0
0
1
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
3
1
0
0
0
2
1
0
2
0
1
0
0
1
0
0
0
0
2
0
0
1
1
0
0
0
1
0
0
2
0
0
1
2
0
0
0
0
2
1
1
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
1
0
2
0
0
0
0
0
1
0
0
0
0
1
2
8
0
2
0
0
0
0
0
0
0
2
2
2
0
1
0
1
2
0
3
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
4
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
2
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
3
0
3
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
3
1
2
0
2
0
0
3
0
0
0
0
0
0
1
3
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
2
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
1
2
0
2
2
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
1
1
0
1
2
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
2
3
0
2
0
0
2
2
2
0
0
2
0
0
1
0
0
2
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
1
0
0
0
0
2
0
2
0
2
0
0
1
2
0
0
0
1
3
2
0
1
2
0
0
0
2
2
0
0
0
0
0
0
0
1
2
0
1
1
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
1
0
1
0
1
0
2
0
0
0
0
2
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
2
0
2
0
2
6
0
0
0
0
1
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
3
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
5
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
3
1
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
1
0
2
2
0
0
0
0
0
0
3
2
0
3
0
2
0
0
0
0
0
0
4
0
2
0
2
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
3
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
1
0
0
0
0
0
1
2
0
3
0
0
0
0
0
0
0
1
0
0
1
2
0
1
0
0
0
1
2
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
2
1
0
1
2
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
1
0
3
0
0
0
0
0
2
0
1
0
0
0
0
2
1
0
2
3
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
3
0
2
0
1
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
3
4
4
1
2
3
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
3
1
0
0
0
0
0
0
2
0
1
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
2
1
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
3
6
0
3
0
0
1
0
0
0
2
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
2
0
0
0
2
2
0
0
0
0
0
0
0
3
1
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
5
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
2
1
0
0
1
0
2
0
0
0
0
1
0
0
3
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
3
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
2
0
0
1
0
0
2
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
1
0
0
0
2
0
2
1
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
2
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
3
0
1
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
2
0
0
1
2
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
2
1
0
0
0
0
2
2
0
2
0
2
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
2
3
0
0
0
0
1
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
2
0
0
0
0
3
0
1
0
1
0
1
1
0
0
0
1
0
2
1
0
0
0
0
1
2
0
0
0
1
0
5
0
1
1
2
0
0
2
0
0
2
1
0
0
2
0
0
1
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
1
3
0
0
0
1
0
1
0
0
0
1
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
1
2
0
0
0
0
0
0
0
1
0
0
1
2
3
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
3
1
0
1
0
0
0
0
1
0
0
0
1
3
0
3
0
0
2
2
1
0
0
0
0
0
0
0
0
1
2
0
2
0
0
2
0
0
0
0
5
0
1
1
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
2
0
0
2
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
1
2
0
0
0
0
1
0
0
0
1
0
3
0
1
2
0
0
1
0
0
0
0
0
2
0
1
0
0
2
0
0
2
0
2
0
0
0
0
1
0
0
2
0
0
3
1
2
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
4
0
2
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
3
0
0
0
2
2
0
0
0
0
0
2
1
0
1
0
2
0
0
0
0
0
2
0
0
0
0
2
0
1
2
0
0
1
0
0
0
2
1
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
1
2
0
2
0
0
0
2
1
1
2
1
0
1
0
0
4
3
0
2
0
0
0
0
0
0
0
2
1
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
2
2
2
2
2
0
1
1
0
2
1
0
1
0
0
0
2
0
0
0
0
0
1
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
1
0
1
0
0
2
2
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
4
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
2
3
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
2
2
0
0
0
2
1
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
2
0
0
1
0
0
0
1
0
0
2
0
0
0
0
2
1
0
3
0
1
0
1
2
0
3
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
1
0
1
2
0
1
0
0
6
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
1
2
0
0
2
0
0
1
1
0
3
0
2
0
1
0
0
0
0
2
0
2
0
0
0
2
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
1
0
0
3
2
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
1
0
2
1
0
0
1
1
0
0
0
0
1
3
0
1
0
0
1
2
0
0
0
0
0
0
0
0
1
0
2
0
2
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
3
0
1
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
2
1
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
3
0
0
0
1
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
1
1
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
3
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
1
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
3
2
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
1
0
0
0
1
2
0
2
0
1
0
4
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
3
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
3
1
0
0
0
1
2
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
2
0
0
0
0
4
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
5
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
3
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
2
1
0
1
0
1
3
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
4
2
0
1
1
0
0
1
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
10
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
1
1
1
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
3
0
1
0
0
2
0
0
0
0
1
3
0
0
0
0
0
0
2
0
1
0
2
0
2
1
0
2
0
2
0
1
1
0
0
0
3
0
0
2
1
0
0
0
0
2
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
9
0
1
0
0
0
2
0
1
0
0
0
0
2
1
2
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
3
2
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
1
1
0
1
1
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
5
2
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
3
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
3
0
0
0
0
0
0
2
0
0
0
1
2
0
2
0
0
2
1
3
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
2
0
0
0
0
2
0
0
0
0
1
2
0
0
2
0
0
1
1
0
0
1
0
0
0
2
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
1
1
0
0
0
0
0
1
1
0
2
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
1
0
0
0
0
2
0
1
0
0
3
2
0
1
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
1
2
0
0
2
0
1
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
1
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
2
2
0
0
2
2
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
7
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
1
0
2
1
0
2
3
0
2
0
3
2
2
1
1
1
0
0
0
0
0
0
0
0
0
0
1
5
0
0
2
1
0
0
3
2
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
3
0
1
3
0
1
1
0
0
0
1
0
0
0
0
0
2
0
1
0
0
1
0
0
2
0
1
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
2
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
5
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
3
1
0
1
0
0
3
0
0
0
0
2
1
0
0
1
0
2
0
2
0
1
1
0
0
0
0
0
1
0
0
0
0
2
1
3
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
1
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
3
0
0
0
1
0
2
2
0
2
0
2
0
2
1
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
2
2
3
2
0
0
1
0
0
0
0
0
0
1
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
2
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
4
0
0
0
2
0
1
0
0
0
1
0
0
2
1
0
0
1
0
0
0
1
0
2
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
1
1
2
0
1
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
1
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
1
0
0
0
1
2
0
2
2
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
3
0
0
2
0
1
0
0
2
1
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
3
0
4
0
0
2
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
1
2
1
0
0
0
1
0
0
0
0
2
0
1
0
0
2
0
0
0
0
1
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
1
1
2
1
0
1
0
1
0
0
0
0
0
0
2
0
0
1
1
0
1
0
0
0
0
0
0
0
1
2
0
2
0
1
0
0
0
1
0
2
0
1
0
0
0
0
2
0
0
2
1
0
2
0
4
0
0
0
2
2
0
0
0
0
2
0
0
1
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
1
0
0
0
1
0
1
2
0
0
1
0
0
0
0
0
0
0
2
0
2
3
7
0
2
0
0
1
0
3
0
0
2
0
0
0
0
1
0
0
0
0
1
4
2
0
2
1
0
0
1
0
0
0
1
0
0
0
0
2
1
0
0
1
0
0
1
0
0
0
2
0
0
0
0
2
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
1
2
0
0
2
0
0
1
0
0
0
2
0
2
0
2
0
0
1
1
0
0
2
0
0
0
2
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
3
0
0
1
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
2
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
1
0
0
1
0
0
1
2
0
0
1
2
3
0
0
0
2
2
0
0
0
2
0
0
0
0
0
1
2
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
2
2
1
0
1
1
1
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
6
0
0
2
0
0
2
0
0
0
0
0
3
0
0
0
2
0
1
1
1
0
2
0
0
1
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
3
2
0
2
0
0
0
0
2
2
3
0
0
0
0
0
1
0
0
0
0
2
0
2
2
0
0
0
0
1
0
0
3
0
2
0
2
1
2
0
0
1
1
0
0
0
1
0
1
1
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
1
3
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
3
0
2
1
0
1
2
0
1
2
2
2
0
1
0
0
2
2
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
2
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
1
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
3
1
2
0
0
0
1
0
0
0
0
3
0
5
0
1
0
0
0
0
0
0
0
0
1
1
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
3
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
2
0
1
2
0
0
0
1
0
0
0
0
0
1
1
0
0
4
2
0
2
0
0
0
0
1
0
0
0
0
2
3
0
2
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
2
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
1
3
0
2
0
2
0
0
0
0
1
1
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
1
0
0
2
0
2
0
0
0
0
0
0
2
1
0
0
0
9
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
3
1
0
0
0
1
2
3
0
1
0
3
0
0
1
0
0
0
0
1
0
1
2
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
1
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
2
2
0
0
0
0
2
2
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
1
2
1
1
0
0
0
2
1
0
1
3
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
1
0
2
2
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
2
1
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
1
1
0
0
2
0
0
0
1
0
1
0
0
3
2
0
0
0
0
0
0
1
2
0
0
0
1
0
0
2
2
0
0
1
1
2
1
0
2
0
0
0
1
1
0
0
1
0
0
0
0
1
0
4
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
3
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
3
1
0
1
0
0
4
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
2
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
1
1
1
0
0
0
1
0
0
0
1
0
1
2
0
1
0
0
0
0
0
0
0
1
2
1
0
2
2
0
0
0
1
2
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
1
3
0
2
0
0
0
0
0
0
0
1
0
0
2
0
1
1
0
0
1
0
0
0
1
2
0
0
1
2
0
0
0
2
1
1
2
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
1
2
1
0
0
0
0
0
0
0
0
2
1
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
1
0
1
0
0
2
1
0
1
0
0
0
0
0
0
0
2
0
2
2
0
1
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
2
2
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
3
1
0
0
0
2
0
0
1
0
0
3
0
0
2
0
2
0
3
0
0
0
0
1
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
3
0
0
0
0
0
0
0
0
0
2
3
1
2
2
0
2
2
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
1
0
0
0
0
0
1
0
1
0
3
0
1
1
1
0
0
0
0
0
0
1
0
2
1
0
1
0
1
0
0
0
1
2
2
0
2
0
0
0
2
0
2
0
0
0
0
0
2
0
1
1
2
0
0
1
0
0
2
1
0
0
3
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
2
2
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
4
0
2
2
2
2
0
0
0
0
0
0
1
0
1
3
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
1
2
0
0
2
0
0
0
1
0
1
2
0
0
0
0
0
2
0
0
2
3
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
3
2
7
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
5
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
2
1
0
0
5
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
3
0
1
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
1
3
0
0
1
0
2
0
0
2
0
2
2
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
3
3
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
3
0
0
0
1
0
1
1
2
0
0
3
2
1
0
2
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
1
2
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
3
2
0
1
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
3
2
0
1
0
1
2
1
6
0
0
0
0
0
2
3
0
1
0
1
2
0
0
1
2
0
0
1
0
1
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
1
0
0
1
1
0
1
0
0
2
0
1
1
1
0
0
0
0
0
2
0
2
0
0
2
0
2
2
0
0
2
0
2
0
0
4
0
0
2
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
1
0
0
1
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
3
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
1
0
0
1
0
1
0
1
0
0
0
2
1
2
0
0
0
0
1
0
0
0
0
1
0
2
0
2
1
0
0
0
2
1
3
0
2
4
0
0
0
1
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
2
4
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
1
0
0
0
0
0
1
0
0
3
2
2
0
0
1
0
0
0
0
1
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
2
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
2
0
0
1
0
0
1
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
1
0
0
0
2
0
0
10
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
2
2
0
0
0
1
0
2
0
0
0
0
3
0
0
0
0
2
0
0
1
2
0
0
0
2
0
0
0
2
0
2
0
0
0
2
0
0
0
2
0
0
2
0
0
1
0
0
1
2
0
0
3
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
1
0
1
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
1
0
0
2
1
0
0
1
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
3
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
1
0
2
0
0
0
3
2
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
2
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
5
1
1
0
0
0
0
2
0
2
0
1
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
3
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
1
0
0
0
0
0
0
1
0
1
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
1
0
2
0
0
1
0
1
0
2
0
0
0
2
0
1
0
0
1
0
1
0
0
0
2
0
2
0
0
0
0
1
0
0
0
1
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
1
2
1
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
2
0
0
1
0
1
2
0
0
0
0
2
1
0
0
0
0
0
2
0
2
0
0
0
0
2
0
2
0
2
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
2
1
0
3
2
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
1
0
0
0
0
2
1
2
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
3
1
0
1
0
0
0
0
0
2
0
1
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
2
0
0
2
1
0
0
2
2
1
0
0
0
2
2
0
1
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
1
1
0
1
0
2
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
2
1
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
2
2
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
2
0
2
2
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
4
0
2
2
0
0
0
0
0
0
1
0
0
0
1
1
0
1
1
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
2
0
3
0
0
0
2
0
0
0
0
0
2
2
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
3
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
4
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
2
1
0
2
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
1
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
3
1
0
1
0
0
0
0
0
0
1
1
0
0
7
0
0
0
0
1
1
0
1
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
1
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
2
0
1
0
1
0
2
0
0
0
1
1
3
2
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
2
0
0
1
0
2
0
0
0
1
0
0
1
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
2
0
0
2
2
0
0
0
2
0
0
1
0
2
0
0
1
1
0
0
0
3
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
3
0
2
1
0
0
0
0
0
0
0
0
1
0
0
1
2
0
1
0
1
0
0
0
2
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
4
0
2
1
2
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
1
0
1
0
2
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
3
2
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
3
0
1
0
1
2
2
0
0
0
0
1
1
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
2
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
1
1
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
2
0
9
0
4
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
6
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
3
0
2
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
3
0
0
0
2
2
0
0
2
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
6
0
0
0
2
0
0
0
1
1
0
1
0
2
0
3
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
3
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
1
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
2
0
0
0
0
4
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
2
1
1
0
0
1
0
0
0
3
0
0
0
0
0
2
0
0
2
0
2
0
0
0
2
0
4
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
1
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
2
1
0
0
2
0
0
1
2
1
0
1
0
1
1
0
0
0
0
0
0
0
7
0
2
0
0
0
1
2
1
1
0
2
0
0
0
1
1
0
1
0
0
0
0
0
0
2
0
2
0
0
3
0
0
2
2
0
3
1
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
2
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
1
2
0
0
0
2
1
0
2
2
1
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
2
2
0
3
0
2
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
2
1
2
0
0
0
2
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
1
0
0
0
0
2
0
1
1
1
1
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
2
0
0
1
0
2
0
0
1
1
0
0
0
1
1
0
0
0
1
1
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
2
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
5
2
0
1
0
1
0
1
0
0
0
9
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
2
1
0
0
2
0
2
2
0
0
0
2
2
0
0
4
1
0
1
0
0
2
0
0
0
0
0
2
0
0
0
2
0
2
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
2
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
5
1
0
0
1
0
0
0
0
0
0
1
0
3
0
0
1
1
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
3
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
2
0
1
0
1
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
1
1
2
0
0
0
1
0
1
0
1
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
2
1
0
0
0
2
0
2
2
6
2
2
0
1
0
0
1
0
4
1
2
0
0
0
4
0
2
2
0
1
0
0
0
0
0
0
1
2
2
1
0
0
0
0
0
2
0
3
0
2
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
2
1
3
0
0
0
0
1
0
0
0
0
2
0
0
3
2
0
0
9
0
2
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
3
0
0
0
1
0
1
1
0
0
0
0
2
0
1
0
0
0
3
0
0
0
1
0
2
0
0
0
2
0
2
1
0
1
2
0
1
0
0
0
2
2
0
2
0
1
1
1
0
2
0
0
1
0
0
1
2
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
2
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
2
2
0
1
1
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
1
6
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
2
2
1
2
0
0
0
0
0
1
0
2
0
0
1
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
2
2
0
0
1
3
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
1
0
0
1
1
1
0
0
1
0
0
1
0
2
0
0
0
0
0
0
2
0
3
2
2
0
0
2
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
2
0
0
1
0
1
0
0
2
2
1
0
1
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
1
2
1
2
0
2
2
2
1
0
0
2
2
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
1
2
0
0
0
2
0
0
0
0
3
2
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
1
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
1
0
0
0
0
2
2
2
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
2
0
0
2
0
0
2
7
0
0
0
0
0
1
1
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
3
0
0
1
0
0
0
0
2
0
1
0
1
0
0
1
0
0
0
0
0
2
0
1
0
0
1
1
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
2
0
3
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
3
0
1
0
0
1
0
0
1
2
3
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
1
1
0
0
0
2
1
0
0
0
1
2
0
0
0
0
2
0
0
0
0
2
1
1
2
0
0
0
0
1
3
0
0
2
0
0
0
0
0
0
1
0
2
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
2
2
1
0
0
1
0
0
1
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
1
1
2
0
0
0
0
1
0
0
0
1
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
2
0
1
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
3
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
2
0
2
0
1
1
0
0
0
1
0
0
2
1
0
0
0
0
2
2
0
0
0
2
0
0
1
0
0
2
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
1
0
8
1
2
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
1
0
1
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
3
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
2
0
0
0
0
0
1
2
0
1
0
1
0
0
1
2
0
1
0
0
2
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
1
2
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
3
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
3
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
2
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
2
0
0
0
0
2
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
1
0
1
0
1
0
0
1
0
1
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
1
0
2
0
0
0
1
1
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
2
0
1
1
0
2
0
0
0
1
0
0
1
0
0
1
1
0
2
0
0
2
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
3
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
2
0
1
0
0
0
0
2
0
0
2
0
0
1
2
0
2
0
1
0
0
2
1
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
2
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
1
0
0
2
1
0
1
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
3
0
1
0
0
1
0
2
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
1
1
0
1
0
2
0
0
0
0
0
0
1
0
0
2
4
0
0
0
0
0
0
0
0
4
1
2
0
0
0
1
0
0
3
2
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
3
0
0
1
1
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
1
0
1
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
1
0
1
0
2
1
1
0
0
1
0
0
1
0
0
1
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
1
0
1
0
0
0
2
0
0
0
2
0
1
0
1
1
0
0
0
0
1
0
0
0
3
0
0
0
0
2
0
3
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
1
1
0
0
0
2
2
1
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
3
0
0
0
0
0
1
1
1
0
0
2
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
1
0
0
0
2
0
0
0
3
1
1
0
0
0
0
2
2
0
0
2
0
1
0
1
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
2
1
0
0
1
0
0
0
2
0
3
0
0
0
0
0
4
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
3
0
0
3
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
2
0
0
0
2
0
2
1
0
2
0
2
0
0
0
1
0
1
0
0
2
0
1
0
9
1
0
1
0
2
0
0
0
1
0
0
2
1
0
1
0
0
0
1
4
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
1
0
0
0
0
0
1
0
1
0
0
2
0
0
1
0
1
0
2
0
0
1
0
0
0
0
1
0
0
0
2
0
2
3
0
0
0
0
2
2
2
2
2
2
2
0
0
0
0
0
1
0
0
1
2
1
0
2
2
2
2
0
2
0
2
1
2
0
1
2
0
1
1
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
4
0
3
1
0
3
0
0
0
0
0
1
0
0
1
0
0
3
0
0
2
2
0
2
2
1
1
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
1
3
1
0
0
0
1
2
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
2
0
1
2
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
1
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
4
0
5
0
1
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
2
2
2
0
0
0
0
1
0
0
1
3
0
0
2
0
0
0
1
0
0
2
0
0
0
0
1
2
2
0
0
0
2
0
1
0
0
0
2
0
0
1
0
0
2
0
0
2
0
0
2
2
0
1
0
2
0
0
0
0
2
0
0
0
0
2
2
2
0
0
0
0
2
1
0
0
2
2
1
0
0
2
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
2
1
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
2
0
2
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
2
1
0
1
0
2
0
0
0
2
0
2
0
0
0
1
2
2
0
2
0
2
0
0
0
2
0
0
0
0
0
0
2
2
1
1
0
0
0
0
3
0
0
0
2
0
2
0
0
0
1
2
0
2
0
0
0
1
0
3
2
2
0
0
2
1
0
9
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
1
0
1
0
0
1
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
2
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
1
0
2
0
0
0
1
1
2
0
0
0
0
0
0
3
0
0
0
1
0
1
2
0
0
0
0
4
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
1
0
1
0
0
1
1
1
2
0
0
0
0
1
1
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
1
2
1
0
0
0
0
0
0
0
1
0
0
0
2
0
1
1
1
2
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
3
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
1
1
0
1
0
0
0
0
2
0
2
3
0
1
0
0
0
2
3
1
0
1
0
2
0
2
0
0
0
0
0
0
2
0
0
4
0
0
0
0
1
0
0
2
0
1
0
0
0
0
1
2
0
0
1
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
3
0
0
1
0
0
0
0
1
0
0
2
1
0
2
5
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
1
0
2
2
1
0
0
1
2
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
2
0
1
2
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
2
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
4
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
2
2
0
3
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
3
1
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
2
1
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
1
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
2
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
2
1
2
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
1
0
2
0
2
0
1
0
1
0
0
2
0
0
2
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
3
0
2
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
2
0
0
0
0
0
0
0
0
3
2
2
0
0
0
0
1
0
0
0
2
2
0
2
0
0
1
0
0
0
2
0
1
0
1
0
1
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
2
1
2
0
0
0
0
1
0
0
0
3
0
0
0
2
1
0
2
0
0
0
0
0
2
0
0
0
3
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
2
0
2
0
0
2
2
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
2
0
1
0
0
0
0
1
2
0
2
0
1
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
2
2
1
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
2
0
0
2
3
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
1
1
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
34
0
0
0
0
4
2
0
1
0
0
4
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
2
3
0
0
0
0
0
0
0
0
2
3
0
0
1
0
1
1
0
1
0
0
1
2
2
0
0
0
0
1
0
0
0
0
0
0
6
1
1
2
0
0
1
1
0
0
4
0
0
2
0
0
1
0
1
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
4
0
1
0
1
0
2
0
0
0
3
0
2
0
1
1
0
2
0
0
0
0
1
0
2
0
0
0
2
0
1
0
2
1
0
0
0
2
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
1
1
0
1
0
0
2
0
1
1
2
2
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
5
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
3
2
0
0
0
0
0
1
1
0
0
1
1
0
1
2
0
0
2
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
3
0
0
0
0
0
1
1
0
2
1
0
0
1
0
0
2
1
0
0
0
0
0
1
6
0
0
2
0
0
1
1
0
5
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
1
0
1
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
1
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
2
0
0
0
0
3
0
1
0
0
1
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
1
1
0
0
1
0
1
2
2
1
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
2
0
2
0
3
0
0
1
5
0
0
0
0
1
0
3
0
1
2
2
0
1
2
0
0
0
0
0
0
2
0
0
2
0
3
0
0
0
0
1
0
2
0
0
1
0
0
1
0
0
1
0
2
0
0
1
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
3
0
0
0
1
0
0
0
2
0
0
0
0
2
2
2
1
0
0
2
0
0
0
0
0
0
0
0
0
2
3
0
2
0
0
0
0
2
0
2
1
0
0
0
0
4
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
1
0
2
0
0
1
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
3
0
0
0
1
1
0
0
0
1
3
0
0
1
1
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
2
1
1
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
3
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
1
2
1
0
0
0
1
2
2
2
0
0
2
0
0
1
0
0
3
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
1
1
2
1
2
2
2
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
1
0
0
1
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
2
0
0
0
1
1
0
0
0
2
0
1
6
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
2
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
2
0
2
0
2
0
0
0
2
0
0
1
0
2
0
0
0
0
1
2
3
1
1
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
2
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
1
0
2
1
0
1
0
0
0
0
0
1
0
2
2
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
2
1
2
0
0
0
0
0
0
2
0
0
0
3
0
1
0
2
1
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
2
0
0
2
1
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
1
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
3
0
1
1
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
7
0
0
1
0
0
0
1
1
0
0
2
0
0
1
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
3
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
2
0
3
0
5
0
2
1
0
0
0
0
2
3
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
1
0
1
2
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
2
2
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
2
2
0
0
0
3
0
2
0
0
0
0
0
0
0
0
2
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
2
2
2
0
0
0
0
0
1
0
0
0
0
1
0
0
2
2
0
0
2
0
1
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
1
2
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
1
0
0
0
1
0
6
0
1
0
2
0
0
0
0
0
1
2
2
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
2
0
2
1
0
0
0
0
1
2
2
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
2
2
1
0
0
2
0
0
0
0
0
2
0
0
0
2
1
1
1
2
2
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
1
2
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
1
1
2
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
1
0
2
0
0
0
0
0
3
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
24
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
1
0
0
2
2
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
2
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
1
0
0
3
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
1
2
0
1
0
2
2
0
1
0
2
1
0
1
0
0
0
0
0
0
0
1
3
0
0
0
0
2
0
2
0
0
2
0
0
1
0
0
0
1
2
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
2
0
1
2
0
2
0
2
1
0
2
0
0
0
2
0
0
0
1
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
2
3
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
3
0
2
0
0
1
2
0
0
0
0
0
2
0
3
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
2
0
1
0
0
0
0
4
1
0
0
1
0
0
0
0
0
1
2
0
0
3
0
2
0
0
2
0
0
0
0
0
2
0
0
0
2
0
2
0
1
0
2
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
1
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
2
0
2
1
0
0
0
0
1
0
2
0
0
0
1
0
2
2
2
0
0
0
2
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
1
0
2
0
0
0
0
2
0
0
0
2
4
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
1
0
1
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
3
0
0
0
2
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
1
0
1
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
5
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
1
0
2
0
2
0
0
0
2
0
0
2
0
0
1
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
1
0
0
2
0
0
0
1
0
1
0
2
0
0
2
0
2
1
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
2
0
2
0
0
1
3
2
0
0
1
1
0
0
1
0
1
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
2
1
0
2
0
0
1
0
0
0
2
1
2
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
2
0
0
0
1
0
0
2
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
2
3
0
1
0
0
1
3
0
2
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
2
1
0
0
0
0
1
0
0
0
0
1
3
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
2
1
2
0
1
8
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
1
0
3
1
0
0
0
2
1
1
0
0
1
0
0
0
0
1
0
2
2
0
0
0
1
0
0
2
2
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
1
0
0
0
0
0
0
2
2
0
1
0
0
2
0
2
0
0
0
2
2
0
1
0
0
0
2
1
0
0
0
0
0
1
0
2
0
2
2
2
0
0
0
0
0
2
0
1
0
0
0
0
3
2
0
0
0
0
2
0
2
0
0
0
2
1
0
0
1
0
0
2
1
2
1
0
2
1
0
0
3
2
0
0
0
0
3
2
0
0
0
0
2
2
2
0
0
0
2
0
1
8
0
2
0
0
1
0
0
0
0
0
0
1
0
2
1
0
1
1
1
0
0
0
0
0
0
0
1
1
2
4
0
2
1
0
0
2
0
0
2
0
0
2
2
0
0
0
1
1
0
0
0
0
2
1
0
0
0
0
0
0
0
2
2
0
1
0
0
3
2
2
2
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
2
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
1
0
0
0
2
0
2
2
1
0
0
0
2
2
0
0
0
2
0
1
1
0
1
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
2
0
3
0
0
2
1
2
0
3
2
0
0
0
0
0
1
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
1
2
4
1
0
0
0
0
0
0
0
0
0
0
1
2
1
2
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
1
0
0
0
0
0
2
0
1
0
0
1
0
2
2
0
1
0
2
0
0
0
2
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
3
1
3
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
1
1
1
0
0
0
1
1
0
0
0
0
1
0
0
3
0
0
0
0
2
1
1
0
0
0
0
0
0
0
2
0
7
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
2
1
0
3
0
0
0
0
0
0
0
2
2
1
0
0
0
1
0
0
3
0
0
0
2
0
0
0
0
0
2
0
1
3
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
3
0
0
0
1
0
2
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
2
2
0
0
2
1
0
1
0
2
0
1
0
2
2
1
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
1
1
0
0
0
0
2
3
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
3
0
0
0
0
2
0
0
0
2
0
0
0
0
1
2
0
0
3
0
1
0
1
0
2
0
0
0
0
0
2
1
3
2
1
0
1
0
1
1
0
0
2
0
2
0
0
0
1
0
0
0
0
0
2
0
2
0
1
0
2
0
0
0
0
2
0
0
0
2
0
1
0
1
0
0
0
0
2
1
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
2
2
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
9
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
1
3
0
2
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
1
0
2
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
1
2
0
1
0
0
2
0
0
2
0
0
0
1
1
0
0
0
1
2
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
2
1
1
1
0
0
0
0
0
0
1
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
3
0
3
0
0
0
0
0
6
1
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
1
4
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
2
0
0
0
0
0
0
0
1
2
2
1
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
1
0
1
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
1
0
0
0
0
1
3
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
1
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
1
1
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
1
0
0
0
5
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
1
0
2
0
1
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
1
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
2
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
2
2
1
0
2
2
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
1
1
0
2
0
5
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
1
2
2
0
0
0
2
2
0
0
1
0
1
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
1
2
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
3
0
0
0
0
1
0
0
0
2
2
0
1
0
0
0
0
1
2
1
0
3
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
2
5
1
1
4
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
2
0
0
0
0
2
1
0
0
0
0
2
0
0
3
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
2
1
2
0
0
0
0
2
0
0
0
1
2
2
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
3
0
2
0
1
1
0
1
0
2
2
0
1
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
2
2
0
2
0
2
0
2
0
0
0
0
0
1
0
0
1
0
1
2
1
0
0
1
0
0
3
1
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
1
0
0
2
0
0
0
1
1
2
2
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
1
0
0
0
0
1
0
0
0
2
1
0
1
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
1
0
0
2
1
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
1
0
0
0
0
0
2
0
0
1
0
2
2
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
3
2
1
0
0
0
0
0
1
2
1
1
2
1
0
1
0
0
0
10
0
0
2
0
0
0
0
0
2
1
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
2
1
3
2
1
2
0
0
0
0
0
1
1
0
2
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
4
2
1
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
2
1
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
4
0
2
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
2
0
1
0
0
0
1
0
0
0
1
0
2
2
1
2
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
1
0
2
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
2
0
0
1
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
1
1
3
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
1
2
0
1
0
0
1
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
4
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
2
1
2
0
0
0
0
0
2
0
0
3
0
0
0
0
2
1
0
2
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
1
0
0
2
0
0
0
2
0
1
0
1
0
0
3
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
1
2
0
0
0
0
0
1
2
0
0
2
2
0
0
1
0
0
0
0
0
0
0
2
0
3
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
1
0
2
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
4
0
2
2
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
4
0
0
0
2
0
2
0
0
0
0
0
0
2
2
2
3
0
1
1
0
0
0
0
2
1
0
1
0
0
0
0
0
1
2
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
1
4
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
1
0
2
0
1
0
1
2
0
0
0
0
0
1
0
2
0
0
1
2
2
0
0
4
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
2
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
3
0
0
0
0
6
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
8
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
2
0
1
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
2
1
3
1
0
0
0
0
0
3
0
0
1
0
0
1
2
0
0
2
0
2
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
3
0
0
0
2
1
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
1
0
2
0
0
0
2
0
2
0
5
1
2
0
2
2
0
0
0
0
0
0
0
0
1
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
2
1
2
0
0
0
0
2
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
2
0
2
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
3
0
1
0
2
0
0
1
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
2
2
0
2
2
0
1
0
0
0
1
0
0
1
2
0
2
0
2
1
1
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
2
0
0
0
1
0
0
3
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
4
2
0
2
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
4
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
2
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
3
0
0
0
2
0
0
0
0
1
0
1
0
2
3
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
2
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
1
0
0
5
0
1
0
1
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
4
0
2
0
0
0
0
3
2
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
2
1
0
3
2
0
2
0
0
2
2
2
0
1
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
2
0
0
0
2
0
0
0
0
0
0
0
3
2
1
1
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
3
0
0
2
0
2
0
0
0
0
2
2
2
0
2
1
0
2
0
0
0
2
2
0
0
2
0
0
0
0
2
0
2
2
0
0
0
0
1
0
0
0
0
0
2
0
1
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
2
1
0
0
2
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
2
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
1
2
0
0
3
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
3
0
0
0
0
2
0
1
0
2
0
2
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
1
3
0
0
0
0
2
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
2
2
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
3
1
0
0
0
0
1
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
2
2
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
2
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
5
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
2
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
1
2
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
3
0
3
2
0
0
1
1
2
2
0
2
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
1
0
1
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
3
0
0
1
0
0
0
3
1
0
0
2
0
1
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
2
1
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
1
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
2
0
0
2
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
2
0
2
0
1
1
1
0
0
0
0
0
3
0
0
0
0
1
1
1
0
0
0
0
1
1
0
0
0
1
0
2
0
0
0
0
1
2
0
0
2
0
1
0
1
1
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
3
0
1
0
0
3
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
1
0
0
2
2
0
0
0
3
2
2
0
4
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
1
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
1
0
0
0
1
0
0
1
0
0
0
1
1
0
2
0
4
2
0
0
2
0
0
0
2
2
0
0
0
2
0
0
0
0
1
1
1
2
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
2
0
0
2
0
2
0
0
0
0
2
2
3
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
2
2
0
0
0
2
0
0
0
2
1
0
0
2
3
2
0
0
1
0
0
1
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
2
0
2
1
0
0
0
0
2
2
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
2
0
2
2
0
0
0
1
0
0
0
0
1
0
1
2
0
1
0
0
0
2
0
0
0
1
0
0
0
1
0
1
2
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
2
0
2
0
0
2
2
3
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
1
2
0
5
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
3
0
0
0
1
0
2
0
0
1
0
2
2
0
0
1
0
0
1
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
2
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
2
0
1
0
0
2
0
0
0
1
0
1
11
0
0
4
0
2
2
0
0
0
1
1
0
0
0
0
2
1
0
0
0
0
0
1
0
0
1
1
2
0
0
0
1
0
0
0
0
0
3
0
0
2
0
0
2
0
2
1
0
0
0
0
0
1
1
3
2
0
0
0
0
0
1
0
0
1
5
0
0
0
0
3
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
1
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
2
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
2
3
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
3
1
0
0
0
2
0
0
0
0
0
2
0
0
0
1
2
0
1
0
4
0
0
0
0
2
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
3
0
1
0
0
1
0
0
0
2
1
0
1
2
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
1
0
1
0
0
3
0
0
0
0
0
0
2
0
0
2
3
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
2
2
0
0
0
1
0
0
0
0
0
2
0
0
1
1
1
0
2
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
1
1
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
2
0
1
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
1
0
2
2
2
1
1
2
0
2
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
1
0
0
2
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
1
4
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
2
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
9
1
2
0
0
0
0
0
1
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
1
2
0
0
2
1
2
0
0
0
0
0
0
0
2
0
1
1
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
1
0
2
0
0
0
0
1
0
2
1
1
0
0
0
1
0
0
0
0
0
3
0
0
0
0
1
1
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
3
3
2
1
1
1
0
2
0
2
0
0
0
0
0
3
0
1
0
1
0
0
0
0
3
0
0
0
1
0
0
0
1
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
6
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
9
0
0
0
0
2
0
0
2
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
1
1
1
1
0
0
0
2
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
2
0
2
2
0
0
0
2
3
10
2
0
0
0
0
2
0
2
1
0
0
0
1
0
1
0
2
0
0
0
1
0
0
2
0
3
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
2
0
0
2
1
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
2
0
2
0
0
0
2
0
2
0
0
0
0
1
0
1
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
3
0
0
3
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
3
0
0
0
0
2
0
0
0
0
0
0
2
8
0
4
0
1
2
0
0
6
0
1
0
0
7
2
0
0
0
0
1
3
0
3
2
0
0
0
0
0
0
0
0
0
1
1
1
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
2
0
0
0
0
1
1
0
0
0
0
2
6
0
0
0
1
0
1
0
2
0
0
0
0
2
0
0
0
0
2
2
0
2
0
2
0
2
2
0
0
0
2
0
0
2
0
1
1
1
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
2
0
0
0
2
0
3
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
2
0
3
0
1
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
1
0
2
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
1
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
1
3
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
3
1
0
0
0
0
2
0
0
1
0
1
0
0
0
0
2
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
3
0
0
0
1
0
1
0
0
2
0
0
0
2
0
1
0
2
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
4
1
0
2
0
2
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
1
0
0
2
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
1
2
0
1
1
2
0
1
0
0
0
1
2
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
2
3
0
2
1
0
0
2
2
3
1
1
3
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
1
0
0
4
0
0
0
2
0
0
0
2
0
0
1
0
2
2
3
0
0
0
2
0
0
0
0
2
0
2
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
3
0
0
1
1
2
0
0
1
2
1
0
0
0
6
2
0
0
0
1
1
0
0
1
1
1
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
2
1
1
0
0
2
1
2
0
0
0
0
0
0
0
2
0
0
1
0
0
1
1
1
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
2
1
0
0
0
0
2
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
1
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
2
0
1
3
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
2
0
4
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
3
0
0
0
0
0
0
1
2
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
1
0
0
3
0
1
0
2
1
0
6
0
0
0
0
0
0
0
0
0
1
1
3
0
0
1
0
0
0
1
0
0
1
0
0
1
2
1
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
3
0
2
0
0
0
0
0
0
0
3
0
0
1
0
1
0
0
3
0
1
0
0
0
0
2
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
1
0
0
1
0
1
2
0
0
0
0
1
2
0
1
2
0
0
0
3
0
0
0
3
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
2
0
0
0
3
0
0
0
0
0
0
2
0
2
0
1
3
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
2
0
0
0
0
0
0
2
1
1
1
0
0
0
0
0
0
2
1
2
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
3
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
1
0
0
1
1
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
3
0
1
0
0
0
0
0
0
0
0
0
3
0
2
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
3
2
0
0
0
2
1
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
3
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
2
0
0
0
0
1
1
0
0
1
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
1
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
1
2
0
0
1
0
0
0
2
0
2
0
0
2
0
0
2
1
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
2
0
0
1
0
0
0
1
2
0
3
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
2
0
1
0
0
0
1
1
2
0
1
3
0
1
2
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
2
2
1
0
2
0
0
3
0
6
0
1
1
0
0
4
0
0
0
0
0
0
1
1
0
4
0
0
0
1
0
0
0
2
0
0
0
1
1
0
2
0
0
0
2
0
0
0
0
0
0
4
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
1
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
3
0
0
1
0
1
2
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
2
0
1
7
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
3
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
2
2
2
0
0
0
0
0
0
0
2
0
0
3
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
5
0
2
0
0
0
0
0
2
2
2
0
1
0
1
0
0
0
3
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
3
0
0
0
2
1
0
2
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
1
3
0
0
0
1
0
0
0
1
2
3
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
4
1
0
0
2
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
1
2
0
0
1
0
2
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
2
2
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
2
1
0
1
0
0
2
0
2
0
0
1
0
0
0
0
0
1
0
0
2
0
1
0
2
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
2
0
1
1
0
1
0
2
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
2
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
1
0
0
0
2
0
0
0
0
0
1
1
2
0
0
0
0
2
0
0
0
3
0
1
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
1
0
2
0
0
0
1
1
1
0
0
0
0
0
2
0
3
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
1
2
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
2
0
1
3
1
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
1
0
1
0
2
0
1
0
3
0
0
4
0
0
0
0
0
2
0
0
3
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
2
1
1
0
0
0
0
0
0
1
0
0
0
1
2
0
0
2
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
2
1
0
0
0
0
2
0
1
0
0
1
0
0
0
0
2
0
0
0
2
2
1
1
0
0
0
0
0
0
0
2
0
2
0
0
0
3
0
3
1
0
0
2
2
0
2
2
0
0
1
0
0
0
2
0
2
0
2
2
2
0
1
3
0
1
0
1
0
0
0
0
0
2
3
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
2
2
0
8
0
2
0
0
0
2
0
0
0
0
0
0
0
2
1
0
2
0
0
2
0
2
0
0
0
0
0
1
0
2
0
0
0
0
2
2
0
0
0
2
0
0
0
2
1
0
0
0
11
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
2
0
0
1
0
0
1
1
0
0
0
2
2
0
0
0
0
1
1
0
0
0
2
1
0
2
2
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
4
0
0
1
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
2
2
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
5
0
0
0
2
1
0
3
2
0
0
0
0
2
1
3
0
0
2
0
2
0
0
1
1
0
0
0
1
2
0
2
0
0
3
0
0
1
1
0
0
1
0
0
2
1
0
0
1
1
0
1
1
1
2
0
0
2
0
0
0
0
0
0
1
2
3
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
2
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
2
1
0
0
1
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
2
2
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
2
2
2
0
0
1
1
0
0
2
0
4
0
1
2
2
0
0
1
0
1
0
2
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
2
0
0
0
0
0
2
0
1
0
7
1
0
1
0
0
0
0
2
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
1
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
2
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
1
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
4
1
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
2
0
0
0
1
0
0
0
3
0
0
0
0
1
1
3
0
0
0
2
0
2
0
9
2
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
5
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
2
1
0
0
1
0
0
0
0
0
1
2
0
2
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
1
2
0
0
0
0
1
0
2
1
0
0
0
0
2
3
1
1
3
2
0
2
1
1
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
4
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
3
0
1
0
2
0
0
0
1
1
0
0
0
2
0
0
2
0
0
0
3
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
2
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
2
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
1
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
1
2
0
0
1
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
1
1
0
0
0
0
0
2
0
0
2
0
0
0
2
2
0
0
0
1
0
0
2
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
1
0
2
1
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
1
1
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
1
0
2
0
0
0
1
1
1
0
0
2
1
0
0
0
0
2
0
2
0
0
2
0
1
0
1
1
0
0
0
0
0
2
0
0
0
0
1
0
1
2
0
0
0
2
0
2
0
0
0
0
0
2
3
0
0
3
0
0
0
0
4
1
3
3
0
0
0
0
1
4
0
0
3
0
0
2
2
1
0
1
0
2
2
0
0
0
0
2
0
1
0
0
0
1
0
2
1
0
0
3
0
0
0
0
1
0
0
0
0
0
0
2
2
0
1
0
0
0
1
0
0
0
3
1
0
0
3
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
2
0
0
0
0
0
2
0
2
1
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
2
0
0
0
0
1
2
0
0
2
0
0
0
0
0
3
0
2
1
0
1
0
0
0
0
0
4
0
3
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
1
1
0
2
0
0
0
1
0
0
0
0
1
3
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
4
0
0
2
1
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
4
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
3
0
3
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
1
0
0
1
2
0
0
1
1
0
1
0
0
2
0
2
0
2
5
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
3
0
0
1
0
0
3
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
1
1
3
0
1
2
0
2
0
2
0
2
1
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
5
0
0
6
2
0
2
0
1
0
0
0
0
1
0
0
0
0
2
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
2
0
2
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
2
1
0
0
0
0
3
2
0
2
0
1
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
2
0
2
0
2
0
0
1
0
0
0
0
0
2
0
4
0
2
0
2
1
2
0
0
2
0
0
1
0
2
1
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
2
1
0
0
0
2
0
0
0
0
0
2
2
1
2
2
0
0
2
0
0
0
0
0
3
1
0
0
0
0
0
2
0
0
1
0
0
1
2
0
0
1
0
0
0
0
0
0
1
0
0
2
0
2
1
2
1
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
3
1
0
2
0
1
0
3
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
1
2
0
0
2
3
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
4
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
4
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
1
0
0
0
1
1
0
0
0
1
1
0
1
2
0
0
1
2
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
2
0
1
1
0
0
0
0
0
1
5
0
0
0
1
1
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
3
0
3
1
0
3
1
0
1
0
0
0
0
2
2
3
0
2
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
2
0
0
2
1
0
1
0
2
0
3
1
1
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
2
0
0
0
2
0
2
0
0
0
0
0
0
1
2
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
2
0
0
0
1
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
1
0
0
0
3
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
2
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
1
0
1
2
0
4
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
1
0
2
2
0
0
1
0
1
0
0
0
2
0
2
3
0
0
0
1
0
0
0
0
1
2
0
0
2
0
0
0
0
1
0
2
0
0
2
1
0
0
0
3
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
2
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
4
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
1
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
2
2
2
0
0
1
0
0
2
0
0
2
1
2
0
0
0
0
1
0
0
0
0
0
0
2
2
0
2
0
0
1
1
0
0
0
0
0
0
0
2
1
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
1
1
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
1
0
0
1
2
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
1
2
3
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
2
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
1
2
0
1
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
3
0
0
1
2
0
0
0
2
0
1
0
0
0
1
0
0
2
0
0
0
2
0
0
2
0
0
2
0
0
0
0
2
2
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
2
0
0
0
2
0
0
0
1
0
2
0
2
0
1
0
0
1
0
0
2
1
0
0
0
0
0
1
0
0
2
1
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
1
0
0
1
2
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
3
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
1
1
2
0
1
0
4
0
0
0
3
0
1
0
2
0
1
0
2
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
5
2
0
5
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
1
0
2
1
0
0
0
1
0
0
0
1
0
0
2
3
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
2
0
1
0
0
0
1
2
0
0
2
1
0
0
1
0
0
0
1
0
0
0
0
2
0
0
2
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
1
0
2
1
0
0
1
0
1
0
0
2
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
5
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
2
1
0
0
0
0
0
3
0
2
0
0
1
0
0
0
1
2
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
4
0
3
0
0
0
0
1
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
3
0
0
0
0
2
0
1
0
0
2
1
2
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
1
0
0
1
0
2
0
2
0
2
5
0
0
0
1
1
0
0
2
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
3
1
0
0
0
2
0
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
2
1
2
4
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
2
0
0
0
1
2
0
1
1
0
0
1
2
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
2
0
0
0
0
2
0
2
1
3
2
0
0
0
1
0
0
1
2
0
1
2
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
1
0
1
3
0
2
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
4
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
2
0
0
1
0
1
0
2
0
1
0
1
0
0
0
0
0
0
2
0
0
3
0
0
0
0
2
0
0
2
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
2
2
0
2
2
0
0
0
0
2
0
0
0
2
0
0
1
0
1
0
0
0
0
0
1
2
2
0
0
1
0
3
0
0
0
0
0
2
1
0
0
0
1
0
0
0
1
0
1
0
1
0
0
1
0
0
2
2
0
0
0
0
2
0
1
2
0
2
0
2
0
1
0
2
0
0
0
1
0
2
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
2
0
0
0
0
2
2
2
0
2
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
1
2
0
0
1
0
0
0
1
0
2
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
1
0
0
0
4
0
1
0
0
3
1
1
0
1
0
1
1
2
0
2
0
0
1
2
1
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
1
0
0
3
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
2
0
2
0
2
2
0
0
2
0
0
0
3
0
2
2
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
4
2
0
2
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
2
1
0
0
0
0
0
2
2
0
2
0
0
0
1
1
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
1
0
1
2
1
2
0
0
0
0
2
0
2
0
3
3
2
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
3
1
0
1
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
2
0
0
0
0
8
2
0
2
2
0
0
2
0
5
0
2
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
7
0
1
2
1
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
2
2
0
1
0
0
0
1
0
0
2
0
0
1
0
0
1
1
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
2
1
0
0
0
2
1
0
0
0
0
0
4
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
2
0
0
3
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
2
0
0
0
1
0
1
0
2
0
0
0
0
2
0
2
0
1
0
1
1
1
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
1
0
0
2
2
0
0
0
0
1
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
2
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
1
0
0
3
0
2
0
1
2
0
0
0
0
0
0
0
10
1
0
1
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
1
0
0
2
0
3
0
7
0
0
0
0
0
3
0
0
0
0
1
0
0
3
0
0
0
0
0
0
1
0
0
2
1
0
0
0
1
2
0
2
2
3
0
0
1
2
2
3
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
1
0
0
2
0
2
0
1
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
4
0
2
2
0
0
0
0
0
2
1
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
2
1
0
0
0
2
2
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
1
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
4
1
2
1
0
2
0
0
0
0
0
0
1
1
1
0
0
0
1
0
2
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
2
0
1
2
0
0
2
1
0
0
1
2
0
0
0
0
0
3
0
0
2
0
0
0
0
1
0
0
2
2
0
0
0
0
1
0
1
0
1
0
0
2
1
2
0
0
0
0
0
0
1
0
0
0
1
0
1
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
1
1
0
0
0
0
2
0
0
1
0
0
0
3
0
1
0
0
0
0
0
0
1
1
0
1
2
0
0
0
3
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
2
1
0
0
1
1
1
1
0
2
1
1
0
1
0
0
1
0
0
0
0
3
0
0
2
1
0
0
0
0
0
0
0
2
0
2
0
0
3
0
2
0
0
2
1
1
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
2
3
0
1
0
1
0
0
1
2
0
0
1
0
0
0
1
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
2
0
1
0
0
0
0
1
0
4
1
0
1
1
0
1
0
0
2
0
0
0
0
1
0
3
1
0
0
0
2
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
2
0
2
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
1
1
2
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
3
0
0
3
2
0
2
1
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
2
1
1
0
0
0
0
0
0
1
0
3
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
2
1
0
0
0
0
2
0
0
0
1
0
0
3
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
2
0
0
1
0
0
2
0
1
0
0
2
1
2
0
0
1
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
2
4
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
2
0
2
2
0
0
1
0
1
2
0
1
1
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
3
0
2
0
0
1
0
0
0
1
0
0
0
0
2
1
1
1
0
0
0
1
2
1
0
1
0
1
0
0
1
1
0
0
1
0
0
0
0
0
1
2
1
0
0
0
1
2
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
1
0
0
1
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
11
1
0
0
2
0
0
2
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
3
3
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
2
0
0
1
0
0
1
4
2
0
3
1
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
8
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
2
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
4
4
1
2
0
0
2
0
0
0
2
1
0
1
4
0
0
0
1
0
0
1
0
0
0
4
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
1
0
0
0
1
0
0
4
0
1
0
1
0
2
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
5
4
0
0
0
0
0
0
0
2
2
1
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
2
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
2
1
0
0
0
0
0
0
2
0
2
0
9
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
1
2
0
0
2
0
0
3
0
0
0
0
1
0
0
0
1
2
0
1
1
0
0
0
1
0
1
0
0
0
0
2
2
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
1
2
1
3
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
3
1
0
5
0
0
0
0
0
0
0
0
2
1
1
1
0
11
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
2
3
0
2
0
0
2
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
4
0
2
3
1
2
1
0
2
1
1
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
5
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
2
1
1
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
3
1
1
1
0
0
0
2
1
0
0
0
4
0
0
0
0
0
1
0
2
0
0
0
1
0
2
1
0
1
1
0
0
2
0
0
2
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
5
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
1
0
2
2
2
0
3
0
0
0
1
0
0
2
2
0
1
0
0
2
1
0
1
0
0
2
0
2
4
0
0
1
0
0
0
0
0
2
2
0
0
1
2
0
0
1
0
1
0
0
2
0
3
5
0
0
0
1
1
0
0
0
0
0
0
1
0
1
3
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
2
0
0
0
0
3
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
1
1
2
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
1
0
0
2
0
1
1
0
1
0
1
0
1
0
0
0
2
1
0
0
0
0
3
0
0
2
0
0
2
0
0
0
2
0
1
5
0
0
0
0
0
0
0
2
2
0
0
2
2
4
3
0
2
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
2
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
3
0
3
0
2
0
0
0
2
2
0
0
5
0
0
0
0
0
1
4
0
2
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
1
2
3
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
4
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
2
2
0
0
1
0
1
2
0
0
1
2
0
1
0
2
0
0
2
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
2
0
0
1
1
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
2
1
0
0
0
2
2
1
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
1
1
3
0
1
0
0
0
0
2
1
0
0
0
0
0
2
3
3
0
0
2
0
0
0
0
0
0
0
2
0
0
1
3
0
0
2
0
1
0
0
0
1
0
0
1
1
2
0
1
0
0
1
0
1
0
0
0
0
3
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
2
0
1
2
0
1
1
0
1
0
0
0
0
0
2
2
0
0
1
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
2
2
0
1
0
2
0
2
1
0
3
1
0
0
0
0
2
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
2
1
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
2
2
0
0
1
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
3
2
2
1
0
0
0
1
0
2
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
3
0
0
1
1
0
0
2
0
1
1
0
0
0
0
1
0
0
1
1
1
2
0
0
0
0
1
0
3
2
0
4
0
0
1
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
1
1
0
1
0
0
0
2
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
2
2
0
2
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
1
2
1
1
0
0
0
0
2
0
0
0
0
0
3
1
2
0
0
1
0
0
0
1
2
0
0
0
1
0
0
0
2
1
3
0
0
2
1
3
0
0
0
1
2
0
1
1
0
0
0
1
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
3
0
2
0
2
2
1
1
0
2
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
1
0
2
2
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
3
0
0
0
2
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
3
1
1
0
0
0
0
2
0
1
1
1
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
1
2
0
1
0
1
0
0
0
3
0
0
1
0
1
0
2
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
1
1
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
3
1
0
1
0
0
2
5
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
1
3
0
2
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
1
1
2
0
0
0
0
0
0
0
0
1
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
7
2
0
1
1
0
0
0
1
0
0
1
0
2
0
0
0
2
0
0
0
0
0
2
0
4
1
1
1
0
0
1
0
0
0
0
1
0
8
2
0
0
0
2
0
0
2
3
0
1
0
1
2
3
2
2
0
0
0
2
0
0
0
3
0
7
0
0
1
1
0
0
1
0
0
0
2
0
0
0
0
0
2
5
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
1
0
0
2
0
0
1
0
2
0
0
0
1
0
1
0
0
2
0
0
2
0
2
0
1
2
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
2
1
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
2
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
1
6
0
0
0
0
2
0
2
1
0
1
0
0
1
1
0
1
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
2
0
0
0
0
1
2
0
0
0
0
0
0
2
2
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
2
0
0
2
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
2
2
2
0
0
0
3
0
1
0
0
2
0
2
0
2
0
0
0
2
0
0
0
0
1
0
0
4
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
2
1
1
0
0
0
0
0
2
0
0
1
0
1
2
2
2
0
1
0
0
0
1
0
2
0
0
0
0
1
0
3
2
0
2
0
2
1
0
0
0
0
0
1
0
3
2
3
0
0
1
2
0
0
0
0
1
1
0
0
0
3
0
0
0
0
0
0
0
2
1
0
0
0
1
0
2
0
1
0
0
0
0
2
0
0
0
2
1
0
0
0
1
0
0
1
0
0
0
0
2
1
0
0
0
1
0
3
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
2
0
0
1
1
0
2
0
0
1
0
2
3
4
0
3
0
0
1
1
5
0
0
1
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
2
0
1
0
1
0
1
0
0
3
0
0
0
0
0
2
0
2
2
0
5
2
3
0
0
0
0
2
2
0
0
0
0
0
1
1
2
0
0
1
0
0
3
0
0
1
1
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
2
2
0
1
0
2
0
0
1
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
1
0
0
1
2
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
1
0
0
0
0
1
1
0
2
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
2
2
0
0
0
0
0
0
0
0
0
3
0
0
3
3
2
0
0
1
0
0
0
1
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
2
0
1
0
0
0
0
2
0
1
0
0
1
6
0
0
0
2
0
0
0
2
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
2
1
0
1
0
0
1
0
2
2
0
0
1
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
7
2
0
0
3
0
0
0
0
0
0
0
1
0
0
1
0
0
2
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
1
2
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
1
2
0
2
1
0
0
0
0
0
1
2
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
2
6
3
0
0
0
3
0
0
0
1
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
2
0
0
1
0
0
1
0
0
0
0
2
4
2
1
0
0
0
0
0
1
0
2
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
2
0
0
2
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
1
5
0
0
0
1
1
3
0
0
0
0
0
0
3
0
2
0
0
0
0
3
0
0
4
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
1
1
2
0
0
1
0
0
0
2
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
6
0
1
0
0
0
0
2
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
6
0
1
1
1
2
0
0
0
0
0
0
0
1
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
3
0
2
0
0
1
0
4
0
0
0
0
2
0
0
2
0
0
0
2
1
2
0
0
0
3
2
0
0
0
1
0
0
2
0
0
2
2
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
3
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
3
0
2
2
0
2
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
2
0
0
1
2
3
0
2
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
1
0
3
0
0
2
0
0
0
1
0
0
1
1
2
0
0
0
0
0
2
0
0
0
0
3
2
0
0
0
0
0
0
2
1
0
0
0
1
1
2
0
0
0
0
0
0
0
1
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
2
1
0
0
1
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
1
0
2
0
0
1
0
2
0
3
0
0
0
0
0
0
0
0
2
1
2
1
2
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
1
3
2
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
1
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
1
0
2
0
2
0
2
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
2
0
0
0
0
1
1
0
0
2
5
0
1
1
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
2
0
0
0
3
0
0
0
0
0
0
2
0
3
0
0
0
0
0
2
1
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
3
2
1
2
0
0
0
2
0
2
2
2
2
0
0
0
0
0
0
0
0
2
0
1
0
2
0
1
0
0
0
0
0
1
0
0
1
0
1
2
0
0
2
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
1
1
2
0
1
0
0
2
0
0
1
0
0
1
2
0
0
1
0
1
2
1
0
2
0
0
0
1
0
1
1
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
1
0
0
0
1
1
0
0
2
0
1
1
0
0
1
1
0
0
0
0
0
1
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
3
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
3
0
0
0
0
1
1
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
4
3
1
0
0
1
6
1
0
1
2
0
0
1
0
0
0
0
0
0
0
3
0
0
1
2
0
0
0
1
0
2
1
0
0
0
2
0
0
0
0
1
1
0
0
1
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
2
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
2
1
2
0
0
1
0
0
1
2
0
0
0
1
2
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
2
0
0
0
1
0
0
1
0
0
1
0
0
1
2
3
0
0
0
1
2
2
0
0
0
0
0
0
2
0
0
2
1
1
1
0
0
0
0
1
4
2
0
0
0
1
1
2
2
1
0
2
0
1
0
0
1
0
0
0
0
2
0
1
1
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
2
0
0
2
0
0
2
0
0
0
2
0
0
0
2
0
0
0
2
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
1
2
0
2
0
0
0
0
0
1
0
0
0
0
3
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
2
0
0
2
0
0
0
0
2
0
0
0
0
2
7
4
1
0
0
2
2
2
1
1
0
0
0
2
0
0
0
2
0
0
1
3
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
1
1
0
1
2
0
0
0
0
2
0
0
2
0
2
0
0
2
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
1
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
3
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
4
0
0
0
0
0
1
0
0
2
0
0
0
3
2
0
0
0
0
0
1
0
1
0
2
0
0
2
1
0
0
0
0
0
0
1
0
2
0
2
2
0
0
0
3
0
0
0
1
0
1
0
3
0
0
0
3
0
2
1
0
0
1
0
2
0
0
0
2
0
2
2
0
0
1
0
0
0
1
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
3
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
2
0
0
0
1
0
0
0
1
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
3
0
3
0
0
2
0
0
0
1
0
0
1
0
1
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
2
0
0
0
2
1
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
2
2
0
0
2
0
0
2
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
16
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
4
2
0
0
1
0
0
0
0
0
0
2
2
1
0
2
0
0
2
0
2
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
1
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
2
0
1
0
7
0
0
1
0
0
2
2
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
1
0
2
0
0
0
0
3
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
2
2
0
2
0
0
0
0
0
0
0
2
0
0
0
3
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
2
0
0
0
2
1
0
1
0
2
0
0
0
0
1
0
0
2
0
1
0
0
2
0
0
0
0
2
2
1
0
0
0
1
2
2
0
2
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
8
2
2
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
1
1
2
0
0
0
0
0
0
0
0
1
2
0
0
1
0
2
0
0
0
0
0
0
1
1
0
2
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
2
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
3
1
0
0
0
0
2
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
1
2
0
0
0
0
1
0
1
1
0
0
3
0
1
0
1
0
0
0
0
0
1
2
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
3
0
1
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
8
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
1
0
0
1
1
0
2
2
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
7
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
3
1
3
2
0
1
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
1
1
0
0
0
2
1
2
2
0
1
0
2
0
0
0
0
2
1
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
2
0
0
0
2
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
1
0
0
1
2
1
0
0
0
0
0
0
0
1
0
0
0
0
4
1
0
0
0
0
3
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
2
0
2
2
0
2
0
2
0
0
1
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
1
1
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
3
0
0
0
1
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
2
0
1
2
0
0
0
0
3
0
0
0
2
0
0
1
0
0
0
1
0
0
2
0
1
0
0
0
2
1
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
1
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
2
2
0
1
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
1
1
0
0
1
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
1
2
3
1
0
0
0
2
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
3
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
2
0
0
1
0
0
0
2
2
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
2
0
0
0
0
3
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
1
2
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
2
1
2
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
1
1
1
0
1
2
2
1
0
0
0
0
0
1
0
0
0
0
0
1
1
2
0
0
0
2
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
2
0
0
0
4
3
0
1
0
1
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
2
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
3
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
5
0
0
1
0
0
1
3
0
0
2
0
2
0
0
1
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
2
0
2
0
0
2
0
0
0
0
1
0
0
0
0
4
0
2
0
0
0
0
0
0
2
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
2
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
5
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
5
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
3
0
2
0
0
1
2
0
0
0
0
2
0
0
0
0
2
0
2
0
0
2
0
2
2
0
0
2
0
0
0
2
1
2
3
0
0
0
0
0
2
1
2
1
0
0
0
1
0
0
0
0
0
3
1
0
0
0
1
0
0
2
2
2
0
1
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
2
0
0
0
2
0
1
1
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
2
1
2
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
2
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
1
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
3
0
0
1
0
1
0
0
0
0
0
3
2
0
2
0
0
0
2
0
2
1
4
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
1
0
1
2
0
0
0
0
0
0
2
0
0
0
1
0
2
0
1
0
1
0
0
0
0
2
0
1
4
0
0
0
0
2
0
1
0
0
1
0
0
3
0
0
0
0
2
0
0
1
0
1
1
0
0
2
0
0
0
0
2
0
3
0
0
0
1
1
5
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
1
0
0
3
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
1
0
1
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
3
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
4
2
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
2
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
1
0
2
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
3
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
1
0
1
2
0
0
0
0
0
2
0
2
0
2
0
0
1
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
2
2
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
4
0
2
0
0
1
2
0
2
1
0
1
0
2
0
2
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
2
2
0
0
3
3
1
2
0
0
0
0
0
2
1
0
0
0
0
0
0
7
0
0
3
1
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
4
0
0
1
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
1
1
0
2
1
0
0
2
2
0
0
2
0
0
2
0
0
0
0
0
1
0
0
2
0
2
2
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
1
1
0
0
6
0
3
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
1
0
2
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
1
0
1
2
0
1
0
0
0
1
2
0
0
0
0
2
1
1
0
0
1
2
0
0
0
1
1
2
2
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
2
2
0
0
0
0
2
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
1
0
0
2
2
0
2
0
0
1
0
0
0
1
0
2
3
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
6
0
0
0
3
0
4
0
0
1
0
2
0
0
0
0
0
0
1
0
0
2
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
1
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
2
1
0
2
0
0
0
0
0
0
2
0
0
0
2
1
2
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
3
0
2
0
0
2
3
0
1
0
0
0
1
0
0
2
0
1
1
2
1
0
1
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
1
0
1
0
0
2
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
1
0
3
0
0
0
3
2
0
0
0
0
2
0
0
0
0
0
2
3
1
0
0
0
0
0
4
0
0
2
2
1
0
0
0
0
1
0
0
0
3
0
1
0
0
0
0
0
0
2
1
1
0
1
0
0
0
0
0
2
0
0
2
0
1
0
0
2
0
0
0
0
0
0
2
2
0
0
0
2
0
0
1
0
0
1
1
0
0
0
2
0
2
0
0
2
0
1
2
1
0
0
2
0
0
0
0
0
1
1
0
0
2
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
1
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
2
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
3
0
0
0
0
2
2
0
0
0
0
2
0
1
0
0
0
0
1
0
2
0
3
0
0
1
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
2
1
1
0
0
1
2
2
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
1
0
0
3
2
0
0
0
0
0
3
0
0
0
0
1
0
1
1
2
1
0
0
0
2
2
0
0
0
0
2
0
0
1
0
0
1
1
0
0
0
0
1
1
0
0
1
2
0
0
0
0
0
0
2
1
0
0
1
0
0
1
0
2
1
0
0
2
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
2
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
1
2
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
2
2
0
3
0
0
0
0
0
0
2
0
3
0
0
1
2
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
2
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
2
0
0
3
0
0
2
0
2
2
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
1
0
0
3
1
0
0
0
4
0
1
1
0
0
0
0
2
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
1
0
2
0
1
1
0
0
0
1
1
2
0
2
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
3
0
0
0
1
2
1
0
0
0
2
2
0
2
1
0
1
1
0
0
1
1
2
2
1
0
0
0
0
2
2
1
0
5
0
0
0
0
0
0
2
0
0
0
2
0
0
0
3
1
0
0
0
1
0
2
1
0
0
0
0
0
0
0
1
1
2
1
1
1
0
0
0
0
0
2
0
1
0
0
0
1
2
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
2
2
0
1
0
0
0
0
0
2
0
0
2
0
2
0
0
0
1
0
2
0
0
1
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
2
0
2
0
2
0
0
0
2
2
2
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
1
0
2
0
0
0
0
1
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
1
0
0
0
2
0
0
0
0
1
0
1
1
0
1
1
0
1
0
0
0
1
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
1
0
1
2
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
3
1
0
0
0
2
2
0
0
5
0
1
1
0
0
0
3
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
2
2
0
2
0
0
1
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
3
2
1
0
0
0
0
0
0
2
1
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
1
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
3
0
1
0
0
1
1
0
0
2
0
1
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
2
0
0
3
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
1
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
2
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
5
0
1
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
2
0
0
0
0
2
0
0
0
0
2
0
1
2
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
1
3
0
0
2
0
3
0
2
0
1
0
2
0
1
1
0
2
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
1
0
1
0
2
0
0
0
0
0
2
0
0
0
2
0
2
0
0
2
0
0
0
1
1
0
0
0
1
0
0
0
0
1
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
4
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
2
1
0
0
1
2
0
0
0
0
0
0
0
0
1
2
0
0
1
0
1
1
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
2
2
0
1
2
0
0
0
0
0
0
0
0
2
2
2
2
1
0
2
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
2
0
0
2
2
0
0
0
1
0
1
2
0
1
0
0
2
0
0
3
0
1
0
0
0
0
1
1
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
1
2
1
0
1
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
2
1
1
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
2
2
0
0
0
0
2
1
0
0
2
0
2
0
0
0
1
2
0
0
2
0
2
0
0
1
0
0
0
2
0
1
0
0
0
2
0
0
0
0
1
0
1
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
5
1
2
0
0
2
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
1
0
4
0
0
0
1
0
2
0
0
1
0
0
0
0
2
0
2
0
2
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
3
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
2
0
0
1
0
0
1
0
0
0
1
1
0
0
1
0
0
1
2
3
0
0
0
0
0
1
0
2
1
2
0
2
0
2
0
0
2
1
2
2
1
0
1
1
0
2
0
0
1
1
0
0
2
0
2
0
0
1
0
0
0
0
0
1
1
3
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
3
0
0
0
1
0
0
0
2
1
0
1
1
0
0
1
0
1
2
2
0
0
0
1
1
0
2
0
0
3
0
0
0
1
0
1
2
1
4
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
2
1
0
1
5
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
1
2
0
0
0
0
0
4
0
0
0
0
0
1
0
1
0
1
0
0
1
2
0
2
0
0
0
1
0
1
0
0
0
2
1
0
0
2
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
1
0
0
0
4
0
0
0
2
0
0
0
0
0
0
1
0
3
0
2
0
2
0
2
1
0
0
0
0
2
0
1
0
2
0
0
0
2
2
0
0
0
0
0
0
0
1
1
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
5
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
1
0
0
0
1
0
2
0
0
0
0
0
0
1
0
1
0
0
2
0
0
2
0
0
2
3
0
2
1
2
0
2
0
2
0
3
1
0
3
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
2
3
0
0
1
1
0
1
0
1
0
2
0
0
0
1
0
2
0
0
0
0
0
0
1
0
2
1
0
0
0
2
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
2
0
1
0
0
0
0
3
2
0
0
2
2
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
1
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
2
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
1
0
3
0
2
0
2
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
2
0
0
4
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
1
1
0
0
1
1
0
0
0
0
1
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
2
2
2
0
0
0
3
0
0
0
3
9
1
0
0
2
0
1
2
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
2
1
1
1
2
0
0
0
2
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
1
0
1
0
0
1
0
0
1
0
0
2
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
7
0
0
0
7
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
1
2
1
0
0
1
0
0
0
1
0
2
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
1
2
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
2
0
0
2
1
2
0
0
0
0
0
2
0
0
1
2
0
0
1
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
2
0
1
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
1
0
1
1
0
0
1
0
1
2
0
1
0
0
0
0
0
0
0
2
2
2
0
0
0
0
1
0
1
0
0
0
0
0
2
0
2
0
1
0
1
1
0
0
4
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
2
2
1
0
6
1
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
3
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
4
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
5
2
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
2
3
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
2
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
4
0
0
0
2
0
0
2
1
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
2
1
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
1
0
3
2
0
2
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
2
0
2
1
1
0
1
0
0
2
2
1
0
0
1
0
1
1
0
0
3
0
0
0
0
1
0
2
2
2
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
2
1
0
0
0
0
0
0
0
0
2
2
0
0
2
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
2
3
0
1
0
0
2
1
0
0
0
1
0
0
1
0
1
5
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
2
0
2
2
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
3
0
0
0
0
0
1
0
0
0
3
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
1
0
1
0
2
2
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
3
2
2
0
0
0
1
0
0
3
0
0
0
0
1
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
2
1
2
2
0
0
0
0
1
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
2
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
1
0
1
1
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
3
0
0
0
0
2
1
2
1
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
1
0
1
0
0
0
0
2
0
2
0
1
6
0
0
0
0
0
1
2
0
0
0
4
2
0
0
0
0
0
0
1
1
1
2
0
0
0
0
1
0
0
0
0
2
0
0
0
7
0
2
1
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
2
0
3
0
0
0
0
0
1
0
2
0
1
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
4
1
0
0
0
0
0
0
1
0
1
0
2
2
2
0
2
0
0
0
0
0
0
0
0
2
0
2
0
1
0
1
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
2
0
1
0
0
0
0
2
0
1
0
0
0
4
0
0
0
0
1
0
1
1
1
0
0
0
0
2
3
0
0
1
1
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
3
1
0
0
0
3
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
1
0
2
0
0
0
0
0
1
2
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
2
1
2
0
0
0
0
1
0
0
0
0
2
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
2
0
0
0
0
2
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
7
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
2
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
2
0
2
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
1
1
0
1
0
2
0
1
0
0
1
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
1
2
2
0
0
2
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
2
2
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
1
2
0
2
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
2
0
0
1
0
0
2
0
0
0
0
0
3
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
3
0
0
0
0
2
1
0
1
0
0
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
3
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
1
2
0
3
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
4
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
3
0
3
1
2
1
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
2
0
0
2
0
2
0
0
2
0
1
2
0
0
0
0
0
2
0
0
1
1
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
1
0
0
2
0
2
0
0
2
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
2
2
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
2
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
1
0
0
0
0
2
0
0
1
0
1
1
0
2
0
0
0
0
0
0
2
0
1
0
1
1
3
0
0
0
0
2
0
2
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
5
2
2
0
3
0
1
0
1
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
3
1
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
3
0
0
1
2
0
0
0
2
0
0
0
2
0
2
1
0
0
0
0
2
0
0
0
2
1
0
1
2
3
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
2
2
0
0
1
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
2
2
0
0
0
2
1
0
1
2
0
0
1
0
2
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
2
1
0
0
1
0
2
0
0
2
2
0
3
0
0
2
0
2
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
2
2
0
1
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
2
0
2
0
0
0
1
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
2
0
1
0
1
0
0
2
0
2
0
1
0
1
0
0
0
2
1
2
0
1
0
0
1
0
0
1
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
4
0
0
1
0
2
0
1
0
0
2
2
0
0
0
0
0
2
0
3
1
0
0
0
0
0
1
0
2
0
0
2
0
1
0
0
0
0
0
1
0
2
0
6
2
1
0
0
0
0
0
0
0
2
0
2
2
0
2
2
0
3
0
0
0
2
3
0
0
1
1
2
0
0
0
0
2
0
1
0
2
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
2
3
0
0
0
1
3
0
0
0
0
0
0
2
3
0
1
2
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
1
2
0
0
0
2
3
0
0
0
1
2
0
0
0
0
0
1
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
2
0
0
3
1
0
2
0
0
1
0
0
0
2
0
1
0
1
0
0
3
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
3
1
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
2
2
0
2
0
2
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
2
0
0
1
0
1
3
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
2
0
0
1
0
0
1
0
5
0
0
0
2
0
0
0
1
0
1
0
2
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
2
0
0
3
0
0
0
0
1
0
2
0
0
0
3
1
0
0
0
0
0
1
0
0
0
2
0
0
0
1
1
1
2
0
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
3
3
2
0
0
0
2
1
0
0
0
1
2
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
2
0
0
2
0
1
1
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
3
0
0
0
2
0
0
1
1
0
0
1
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
1
2
1
0
0
0
0
2
0
0
0
0
5
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
2
1
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
2
0
2
0
0
0
0
0
0
4
1
1
1
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
3
3
0
0
0
0
0
0
0
2
0
1
2
1
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
2
2
1
0
1
1
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
4
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
1
0
0
0
3
0
0
0
0
0
4
0
0
1
0
0
0
0
1
0
0
2
0
1
0
0
0
0
4
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
2
0
0
0
3
2
1
2
0
2
0
0
1
0
2
0
1
0
0
0
0
1
0
0
2
2
0
2
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
2
0
1
0
1
0
0
0
1
0
1
1
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
2
0
0
0
0
1
0
2
0
2
1
0
0
0
0
2
0
1
2
0
1
1
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
2
0
0
2
2
1
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
2
1
2
1
2
2
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
1
2
0
0
1
1
0
0
0
4
0
0
0
0
0
2
0
0
1
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
1
1
2
2
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
2
0
0
0
2
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
1
1
0
0
0
2
1
0
0
0
0
0
0
0
1
2
2
0
2
0
1
1
0
0
0
0
0
0
0
0
3
0
0
1
2
3
0
0
2
0
0
2
0
0
0
0
1
0
0
5
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
2
2
0
0
0
0
1
0
0
0
2
0
0
0
0
1
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
2
0
1
0
2
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
2
6
0
1
0
0
0
1
0
0
2
0
0
0
4
3
0
2
0
0
1
0
0
0
1
2
1
0
0
2
0
0
0
0
0
0
0
0
1
1
1
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
4
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
1
0
0
0
0
1
0
0
0
0
1
2
2
0
2
0
0
2
1
0
0
0
0
0
2
0
0
0
0
5
0
0
0
1
3
2
0
0
0
1
0
0
1
1
3
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
2
0
0
3
2
0
0
2
1
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
3
2
1
2
0
0
1
1
1
0
1
0
1
0
2
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
2
0
1
0
0
1
0
0
6
0
0
0
2
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
5
1
0
0
0
0
0
0
1
1
0
2
2
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
1
0
1
1
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
5
0
0
0
1
1
0
1
0
0
1
1
0
3
0
0
0
2
0
0
1
1
0
3
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
1
2
1
0
1
0
1
0
1
0
0
1
2
2
1
0
3
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
2
0
0
0
1
2
0
0
1
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
2
2
0
0
2
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
1
0
1
0
0
0
0
0
2
2
1
0
2
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
2
1
2
0
0
0
1
1
0
0
1
0
2
1
0
0
0
1
2
0
0
0
0
0
0
1
0
1
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
6
0
0
0
2
2
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
2
0
0
0
0
0
2
0
0
1
1
2
1
2
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
2
0
0
1
0
1
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
2
2
1
0
0
0
2
0
1
0
0
2
0
0
2
1
0
0
0
1
1
2
0
1
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
4
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
2
0
1
0
0
2
1
0
0
0
0
3
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
3
1
0
0
0
1
0
0
2
1
0
0
0
0
2
2
0
0
1
0
2
0
0
1
2
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
1
1
2
1
0
0
0
1
0
0
0
0
2
0
2
1
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
2
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
1
0
0
0
0
1
3
0
3
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
2
1
0
0
2
0
1
0
0
0
2
0
2
0
0
2
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
2
0
0
0
2
0
0
0
1
0
1
0
2
0
2
0
0
0
1
0
0
1
1
1
0
2
0
2
1
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
3
0
0
1
0
0
1
0
0
2
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
2
0
0
0
0
0
2
0
1
0
0
0
3
0
0
0
1
0
2
0
2
0
1
1
0
2
0
2
0
1
0
0
0
1
1
1
0
1
1
4
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
2
1
2
0
2
0
0
0
1
0
1
0
0
1
0
0
0
2
0
0
0
0
0
2
1
0
0
2
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
3
0
5
1
0
0
0
1
0
0
0
0
0
3
0
0
0
2
0
0
1
0
0
0
2
0
0
0
1
0
0
1
0
2
1
0
1
0
1
0
0
0
2
0
0
0
0
0
2
0
1
2
1
0
0
0
0
0
0
2
0
4
1
0
2
0
0
0
2
2
0
1
2
0
2
1
1
0
2
0
0
0
1
1
0
0
1
2
1
0
1
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
2
1
2
0
0
0
6
2
0
0
0
1
0
0
0
0
2
0
0
0
2
1
1
0
3
0
1
0
0
0
1
1
0
0
0
2
2
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
3
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
2
1
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
2
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
2
2
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
3
3
0
0
2
0
0
0
0
3
0
0
0
2
0
2
1
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
2
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
1
0
0
0
3
5
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
5
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
1
2
0
1
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
1
1
2
0
0
3
0
1
0
0
3
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
2
1
2
0
0
2
0
0
0
0
2
0
0
2
0
0
0
1
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
1
0
0
2
0
0
0
0
1
4
1
1
0
0
1
0
2
0
2
0
3
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
3
0
0
0
0
1
1
0
0
0
0
0
2
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
2
0
0
0
2
1
0
1
1
0
0
0
0
1
1
0
0
2
0
1
2
0
0
0
0
4
0
0
1
0
0
1
1
0
2
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
1
1
0
0
2
0
0
1
0
1
0
0
2
0
1
0
1
0
0
0
1
0
1
0
0
0
3
2
0
0
0
2
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
3
0
2
0
1
0
1
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
1
0
1
0
0
0
2
0
0
0
0
1
0
0
1
0
0
2
0
1
0
1
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
1
0
0
1
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
6
0
0
0
0
0
0
0
0
0
0
0
0
1
0
9
1
0
0
0
0
0
0
0
2
0
0
2
0
2
0
3
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
3
2
0
2
0
0
1
0
0
0
2
0
0
0
2
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
1
0
2
0
2
0
0
0
0
1
1
0
1
0
0
0
0
4
0
0
0
2
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
1
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
1
0
3
0
0
0
0
2
2
0
0
0
0
1
1
0
0
0
0
0
2
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
2
1
1
0
1
1
0
1
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
3
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
2
0
0
0
6
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
2
0
0
5
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
2
2
0
1
0
0
2
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
3
0
0
0
2
2
1
0
2
8
0
1
0
2
1
0
0
0
0
0
1
1
1
0
0
0
2
0
1
2
0
1
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
4
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
2
1
0
1
0
2
0
0
3
0
0
0
2
0
0
2
0
0
1
1
2
1
0
2
0
0
1
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
1
2
1
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
1
0
0
0
0
1
0
0
0
4
1
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
3
2
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
2
1
0
0
2
2
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
1
2
0
0
0
0
2
1
3
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
1
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
2
0
0
0
0
2
1
0
5
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
1
0
0
0
2
0
1
1
0
0
1
1
0
1
0
2
0
1
0
2
0
0
0
0
1
2
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
1
0
2
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
2
1
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
1
0
1
2
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
3
2
2
0
0
0
0
0
0
1
2
0
0
1
0
0
2
0
5
0
1
1
0
1
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
3
0
2
2
0
0
1
0
0
0
0
0
1
2
0
0
2
0
1
0
0
1
0
2
0
0
0
1
0
0
0
2
0
0
1
0
0
2
0
0
0
0
5
0
0
0
0
0
1
1
0
2
3
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
3
0
2
3
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
1
0
0
4
0
1
0
0
0
0
2
0
2
2
0
0
0
2
0
0
0
0
0
2
0
2
0
0
1
2
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
2
0
3
0
0
0
0
0
0
3
0
0
2
0
0
0
0
2
0
0
0
1
1
2
0
0
1
0
0
0
0
1
0
0
1
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
2
1
0
0
2
1
0
0
0
2
0
0
0
0
2
2
0
0
4
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
1
1
0
0
2
2
0
0
1
1
2
0
0
0
0
3
0
0
0
1
1
0
0
4
2
1
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
1
5
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
1
1
0
0
0
2
2
0
0
0
0
9
0
1
0
2
4
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
2
2
0
2
1
2
0
2
2
2
0
1
2
0
1
4
0
1
0
0
1
1
0
0
0
0
0
0
0
0
2
1
1
1
7
0
0
1
0
2
1
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
2
2
0
3
0
0
0
2
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
7
0
2
0
0
1
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
4
0
0
0
2
1
0
2
2
0
0
0
1
0
2
0
1
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
2
0
0
0
2
2
0
0
2
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
1
2
0
0
1
2
2
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
4
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
4
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
1
0
0
1
0
3
1
0
0
0
0
0
0
0
0
0
1
3
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
3
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
15
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
1
0
0
2
1
0
2
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
2
0
0
0
0
1
0
0
1
0
2
1
2
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
2
0
0
3
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
2
0
0
0
5
0
2
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
2
0
0
2
2
0
0
0
0
1
4
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
1
0
1
0
0
2
0
0
1
1
0
2
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
2
1
0
0
0
4
2
0
1
0
0
0
0
2
4
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
2
2
1
1
0
1
0
1
0
1
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
1
0
2
0
3
0
2
0
0
2
0
0
0
0
1
1
0
3
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
2
3
0
0
0
2
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
1
0
2
0
1
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
2
0
0
0
1
0
0
1
2
0
0
0
2
0
1
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
1
0
0
0
2
1
2
0
2
0
0
0
1
1
0
2
0
1
2
1
0
0
0
0
0
0
0
0
1
3
0
0
0
1
1
1
0
0
0
0
0
0
1
1
0
0
1
2
0
0
0
2
0
0
1
0
1
1
0
1
0
0
2
0
0
0
3
2
0
0
1
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
2
0
0
0
1
2
2
4
1
0
0
0
2
3
0
2
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
1
2
0
0
0
2
3
0
0
0
0
0
6
0
1
1
0
0
0
0
1
2
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
1
1
0
2
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
3
0
0
0
0
0
2
2
0
1
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
2
0
1
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
1
0
0
0
3
2
0
1
0
0
0
0
0
0
0
0
2
1
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
1
0
2
0
1
0
0
0
1
0
2
0
0
1
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
1
1
0
5
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
4
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
1
1
0
1
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
2
1
0
0
3
2
0
0
0
2
0
0
0
2
1
0
0
0
0
3
1
0
0
0
0
3
0
0
0
0
0
3
0
0
0
0
0
0
2
1
1
0
0
2
1
0
0
1
0
1
0
1
0
2
0
0
0
0
0
0
0
1
0
0
2
2
3
0
0
0
2
0
0
1
1
0
3
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
2
0
0
0
0
0
2
0
0
2
0
0
2
0
0
1
2
0
3
0
0
2
1
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
1
2
0
1
0
1
2
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
2
0
0
2
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
1
0
0
2
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
1
0
0
1
0
2
0
0
1
2
0
0
0
2
0
2
0
0
0
0
0
0
2
0
3
0
0
0
1
0
0
0
1
0
0
0
0
0
3
2
0
0
0
0
2
0
0
2
0
0
2
0
0
2
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
3
0
0
1
0
2
0
0
0
0
0
2
1
2
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
2
0
5
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
2
0
1
0
0
0
2
0
1
0
1
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
1
0
0
2
0
2
2
2
2
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
6
0
0
0
1
0
0
1
0
0
1
2
1
4
1
0
0
0
0
0
4
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
2
1
2
2
0
0
1
0
1
0
0
0
0
0
3
2
0
0
0
0
0
0
1
0
2
0
3
1
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
1
0
2
0
0
0
3
0
0
0
2
0
2
2
2
0
0
0
0
1
2
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
8
0
2
0
2
16
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
1
0
2
2
0
0
0
2
1
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
2
2
0
0
2
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
3
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
1
0
0
5
2
0
0
0
0
1
0
0
0
0
0
0
0
4
0
2
0
1
0
1
0
1
0
1
0
0
2
0
0
0
0
0
1
1
6
2
0
1
0
1
0
0
0
1
1
0
0
4
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
1
1
1
2
0
0
0
2
0
0
0
2
1
0
0
2
0
0
3
0
0
0
0
2
0
0
0
0
2
0
0
16
2
0
0
0
0
0
0
0
3
0
0
1
1
0
0
0
0
2
0
4
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
3
0
0
0
0
0
2
1
0
1
0
0
2
0
0
0
0
2
0
1
0
0
1
1
1
0
1
0
0
0
0
0
1
0
4
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
2
0
1
0
2
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
2
0
3
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
3
0
0
0
0
0
3
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
3
1
3
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
3
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
2
2
2
0
2
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
2
0
2
1
2
0
0
0
0
2
3
2
0
2
1
2
1
1
0
0
0
0
0
2
0
0
0
0
1
0
2
0
2
1
2
0
0
0
1
0
0
1
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
2
2
0
0
1
0
1
0
2
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
1
0
2
0
0
0
1
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
1
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
1
1
0
0
0
0
0
1
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
5
1
0
1
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
1
0
2
0
0
1
0
0
0
0
1
1
0
1
0
0
4
1
1
1
0
2
0
0
0
3
1
2
0
0
0
0
0
0
0
0
0
2
2
0
5
5
0
1
0
0
3
0
1
0
0
0
1
2
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
2
0
3
0
0
0
2
0
3
2
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
9
0
1
0
0
2
1
0
0
0
1
0
0
2
1
2
0
0
2
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
2
0
0
0
5
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
1
4
0
0
1
0
0
0
0
0
3
3
4
0
0
2
0
0
1
0
1
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
2
0
1
0
0
2
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
1
1
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
1
0
0
2
1
0
0
0
2
1
0
0
0
3
1
1
0
0
0
0
2
0
4
0
0
2
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
4
0
0
0
2
0
0
1
0
0
0
0
1
0
0
1
0
2
0
1
1
0
0
0
0
1
0
0
3
0
0
0
0
0
1
5
3
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
1
2
2
2
0
0
0
0
0
2
1
0
1
0
0
0
0
1
0
1
0
2
0
2
0
2
1
0
0
0
2
0
0
2
0
0
0
0
3
3
0
0
0
3
0
0
0
0
0
4
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
1
1
2
1
0
0
0
2
2
0
2
0
2
0
4
0
3
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
2
1
0
0
2
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
1
0
0
1
0
2
0
0
3
0
0
0
1
0
0
0
2
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
3
0
0
0
0
0
0
1
2
2
0
0
1
1
0
3
0
0
0
0
0
2
2
0
2
0
0
0
2
0
0
0
0
0
0
1
2
2
0
0
0
0
1
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
2
3
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
1
0
0
1
0
0
1
1
0
0
0
1
2
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
4
0
0
1
1
1
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
2
0
0
2
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
4
1
0
0
2
1
1
2
0
1
0
0
0
0
0
0
0
1
0
2
0
2
3
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
1
1
0
2
1
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
2
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
2
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
2
0
2
0
0
2
0
0
0
0
0
0
0
1
1
0
1
0
0
2
1
0
0
0
2
0
0
1
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
4
0
2
0
3
0
0
0
1
0
0
1
2
0
0
0
0
2
0
2
0
0
0
0
1
0
0
2
0
2
0
1
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
2
0
1
0
0
1
0
1
0
0
0
0
0
0
2
2
0
1
2
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
3
2
2
0
0
1
0
1
2
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
1
1
1
0
1
0
0
0
0
0
0
0
2
1
0
0
0
3
1
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
2
0
2
0
1
2
2
0
0
0
2
0
0
0
0
1
2
0
2
0
1
1
1
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
2
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
1
0
2
0
1
0
0
0
3
0
1
2
2
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
2
1
0
0
0
0
0
0
1
0
0
3
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
7
0
0
0
1
0
0
0
2
3
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
1
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
2
0
2
0
0
0
0
0
1
0
0
1
2
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
5
1
0
0
0
0
7
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
2
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
4
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
2
0
0
0
0
2
1
0
0
0
0
1
2
0
1
0
0
1
0
0
0
0
2
1
0
0
0
3
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
4
0
0
2
0
0
0
0
1
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
1
0
2
0
1
0
0
2
0
0
0
0
3
0
2
0
0
0
1
2
0
3
2
0
2
1
0
0
0
0
1
2
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
4
0
0
1
0
0
0
0
2
0
3
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
2
0
0
0
0
2
2
0
0
2
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
1
0
0
0
2
1
1
0
0
2
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
2
0
0
0
4
0
0
0
0
0
0
0
0
5
0
1
0
0
0
0
0
0
2
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
1
0
0
4
0
0
0
0
0
0
0
0
0
2
1
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
2
3
2
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
1
0
0
2
1
0
0
1
0
1
0
0
1
1
1
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
2
1
0
1
0
0
3
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
3
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
2
1
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
3
9
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
1
0
0
1
1
0
0
0
0
0
1
2
0
0
0
1
0
0
1
0
0
0
0
1
0
2
1
0
1
2
0
0
0
1
0
0
0
0
3
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
2
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
2
0
0
1
0
0
1
2
3
0
0
0
0
0
0
2
2
0
2
0
0
1
0
1
0
2
0
0
0
4
0
0
0
0
0
2
2
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
2
0
2
2
0
0
0
0
1
0
0
0
2
0
1
0
0
0
3
1
3
0
3
0
0
0
1
1
0
0
0
2
0
0
2
0
0
4
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
2
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
2
2
0
0
1
0
0
2
0
0
1
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
1
3
0
0
0
0
0
2
0
0
0
0
0
1
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
1
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
1
0
0
1
0
0
0
2
1
0
1
0
0
0
0
0
0
1
0
0
0
0
3
3
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
3
1
5
0
0
0
1
0
0
0
0
0
0
5
0
0
0
0
2
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
2
4
2
0
2
1
0
0
0
0
1
2
0
0
1
0
0
3
0
0
0
0
0
0
3
0
0
0
2
0
2
1
1
0
2
2
1
1
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
1
2
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
3
1
1
1
1
0
0
0
2
0
0
2
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
2
0
0
0
0
1
0
0
1
0
0
2
1
0
0
0
1
0
3
0
1
0
1
0
2
0
0
1
0
0
0
0
0
0
2
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
2
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
2
4
0
0
0
0
1
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
2
0
1
0
1
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
1
0
0
0
0
1
0
1
0
0
0
2
0
0
1
0
2
0
1
1
0
0
1
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
2
1
0
0
0
0
2
0
1
3
0
0
0
0
0
0
0
1
0
0
1
1
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
2
2
1
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
1
0
0
0
2
2
0
2
1
0
0
1
1
2
1
0
0
2
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
4
0
0
2
0
0
0
0
2
0
0
0
0
0
3
0
2
1
0
0
0
0
1
2
0
0
0
0
2
2
0
2
0
2
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
1
0
0
0
0
0
3
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
1
0
2
0
0
2
0
2
2
4
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
6
2
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
2
2
0
0
0
0
0
0
1
0
1
0
1
2
1
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
2
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
2
0
2
1
0
1
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
2
2
0
2
1
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
1
2
11
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
3
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
1
0
0
3
0
2
1
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
2
1
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
1
0
1
0
1
0
2
0
0
0
2
0
0
0
2
0
2
1
0
2
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
1
0
1
0
1
2
0
1
0
2
0
0
0
2
0
0
0
0
2
1
1
2
0
0
3
1
1
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
1
0
0
0
1
0
0
1
1
0
1
0
0
0
0
2
4
2
2
0
0
0
1
0
0
2
2
0
0
0
0
0
2
2
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
2
2
0
0
0
1
2
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
3
0
0
2
0
0
1
0
1
1
0
2
0
0
0
2
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
2
0
0
1
3
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
1
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
1
0
2
0
1
0
1
0
0
1
2
2
0
0
4
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
2
1
0
2
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
3
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
1
1
3
0
2
1
2
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
1
2
0
0
2
0
3
1
0
0
5
0
0
1
0
0
2
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
3
0
2
0
0
0
1
0
2
0
0
2
0
0
0
0
1
0
2
0
2
0
0
0
0
1
2
0
2
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
1
0
0
2
2
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
2
1
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
2
0
0
0
0
2
0
0
0
0
0
2
1
0
0
2
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
2
2
0
2
0
0
0
0
0
1
2
0
2
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
2
0
0
1
0
0
2
2
0
1
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
2
2
0
0
0
0
0
2
0
0
0
3
2
0
0
0
0
1
0
0
0
1
0
2
0
0
2
0
0
2
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
2
0
0
2
1
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
2
0
0
2
0
0
0
2
0
2
0
0
0
0
2
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
1
2
3
2
0
0
0
0
0
3
0
2
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
1
1
0
0
2
3
0
0
0
0
0
0
0
1
0
0
1
3
0
0
2
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
2
2
1
1
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
4
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
3
2
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
1
2
0
1
1
0
0
0
0
0
1
0
2
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
2
2
0
0
2
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
6
0
2
0
2
0
1
0
2
0
0
1
0
0
0
0
0
4
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
3
2
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
1
0
2
0
0
0
2
1
0
0
0
0
0
0
2
1
0
1
0
0
0
1
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
1
2
0
1
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
2
0
2
0
2
0
0
1
0
1
0
0
0
0
0
0
2
2
0
1
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
2
1
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
2
1
1
1
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
8
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
3
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
3
1
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
1
0
0
0
1
0
3
0
0
1
0
0
0
2
0
0
0
2
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
2
0
1
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
1
2
1
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
2
0
0
1
0
0
0
1
0
0
2
1
2
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
2
1
1
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
2
1
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
2
3
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
2
0
2
0
0
0
0
1
0
3
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
4
2
2
0
0
2
2
0
0
0
2
0
0
2
0
0
0
0
1
1
0
0
1
0
2
2
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
4
0
0
0
3
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
3
3
0
2
2
1
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
3
0
0
0
2
1
3
0
0
0
2
2
0
0
0
0
0
1
2
0
2
0
0
0
1
2
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
2
6
0
0
0
0
0
2
0
1
1
2
1
0
0
1
0
0
1
0
1
2
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
2
0
0
0
3
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
2
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
1
0
1
1
0
0
0
0
6
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
1
0
2
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
4
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
2
3
0
1
1
0
0
0
0
2
0
2
1
0
0
2
0
1
0
0
0
0
1
0
0
0
0
2
2
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
2
4
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
3
1
0
0
1
0
0
0
0
0
1
0
2
1
0
0
0
0
1
0
2
0
0
1
0
0
2
0
0
0
1
0
1
0
2
0
0
0
2
2
0
0
1
2
2
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
1
0
0
0
6
0
0
0
2
0
1
0
0
0
2
0
1
1
0
0
0
0
4
0
0
1
0
0
0
0
0
1
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
1
0
0
3
0
0
1
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
2
2
0
1
0
1
0
0
1
0
0
0
2
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
3
2
0
1
0
0
0
0
3
0
0
1
1
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
3
0
1
0
0
0
0
0
1
2
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
4
1
0
0
1
2
1
1
1
0
0
0
0
2
0
0
0
0
0
1
0
1
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
2
1
0
0
0
0
1
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
2
0
0
1
0
1
0
0
0
1
2
1
0
2
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
1
0
4
0
0
0
0
1
0
2
1
0
0
0
1
6
0
0
0
0
1
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
2
0
2
2
0
1
0
0
2
0
2
0
0
2
0
0
0
1
2
0
0
3
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
2
1
1
0
0
0
0
0
0
2
1
0
0
1
0
0
2
1
0
0
0
0
0
0
0
2
2
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
2
0
0
0
1
0
2
0
1
0
1
0
0
2
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
3
0
2
0
0
0
0
0
0
2
0
1
0
2
2
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
1
0
2
0
1
2
1
0
0
1
1
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
2
2
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
2
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
2
3
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
1
1
0
2
0
1
0
3
0
0
0
2
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
2
2
0
7
0
0
0
0
0
1
0
2
0
0
0
0
1
2
0
1
1
2
0
0
0
0
0
2
0
1
0
0
1
0
0
0
2
2
1
3
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
3
2
2
0
2
0
1
2
2
0
0
2
2
0
0
1
1
0
1
0
0
2
1
2
0
0
0
0
0
0
1
0
3
0
1
0
2
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
2
0
0
0
1
0
3
1
0
1
4
0
1
0
0
0
0
2
0
0
2
0
2
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
2
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
1
0
2
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
2
0
2
0
0
0
0
2
0
0
0
1
0
0
2
2
0
10
0
0
0
0
0
0
0
0
0
2
2
0
3
0
0
1
0
0
0
0
0
1
0
1
0
2
0
2
1
0
2
2
2
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
2
0
1
4
0
0
1
0
0
3
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
1
0
0
3
0
0
0
0
2
0
0
0
3
0
0
2
0
0
1
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
1
2
0
0
0
0
1
0
0
1
0
0
0
2
0
2
0
0
1
1
0
2
0
0
1
0
0
0
2
0
0
0
0
0
2
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
1
0
1
3
0
0
0
1
0
2
0
0
0
1
2
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
2
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
4
0
0
2
0
2
1
0
0
0
3
3
0
1
0
0
0
2
0
1
0
1
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
1
2
0
0
0
1
0
0
2
0
1
0
0
2
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
1
0
0
3
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
1
0
0
4
1
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
3
0
0
0
1
2
2
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
2
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
2
0
0
1
1
2
0
0
0
0
0
0
2
0
3
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
2
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
2
0
0
0
0
2
3
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
3
2
0
1
0
1
0
0
0
0
0
0
0
8
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
3
1
2
0
0
0
0
0
1
0
0
0
0
5
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
2
2
0
0
0
0
0
0
2
0
0
0
0
1
0
2
2
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
3
1
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
1
1
3
2
0
0
2
0
0
0
11
0
0
1
2
0
2
0
1
1
0
1
0
0
1
1
0
0
0
0
0
0
2
1
1
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
2
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
3
0
0
2
2
0
1
0
0
0
2
0
1
0
0
2
0
1
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
5
1
0
0
0
0
2
0
0
0
0
0
2
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
2
0
0
2
2
0
0
3
0
2
0
0
0
0
0
0
0
3
0
0
2
1
0
1
0
0
0
0
0
2
0
0
0
1
1
0
2
0
0
2
0
1
3
0
0
0
0
1
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
8
0
2
0
1
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
2
0
2
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
3
1
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
7
0
2
0
0
2
0
1
2
2
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
3
0
0
0
2
1
1
2
0
0
0
0
1
0
1
0
0
0
0
0
3
2
0
0
1
0
0
2
0
0
0
0
1
2
2
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
1
1
2
2
0
0
0
1
0
0
0
0
1
0
2
1
0
5
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
5
0
2
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
1
2
0
2
0
1
0
0
0
1
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
3
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
2
0
0
0
0
1
1
0
0
0
0
2
0
0
0
1
0
2
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
1
1
1
1
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
2
0
2
0
1
0
0
0
0
1
0
0
0
3
0
0
1
2
1
0
0
2
0
0
2
0
2
0
0
2
2
1
0
3
0
0
1
1
0
0
0
0
0
1
0
0
3
0
0
1
0
0
2
1
1
1
0
2
0
0
2
2
1
0
1
2
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
2
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
3
2
0
0
0
0
1
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
2
0
2
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
2
2
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
3
1
2
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
2
1
0
2
2
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
1
0
0
0
3
3
1
0
0
0
1
1
0
0
0
0
2
0
3
0
0
0
0
2
0
7
1
0
0
0
2
2
0
0
0
0
1
3
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
3
0
1
0
1
2
1
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
2
0
2
1
2
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
3
0
0
0
2
0
0
0
2
0
2
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
3
0
0
0
1
0
2
2
3
0
1
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
1
2
2
0
0
1
0
0
0
3
0
0
2
0
2
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
1
0
0
0
0
1
0
2
3
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
2
0
0
5
0
0
1
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
2
0
3
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
3
0
2
2
2
0
1
0
2
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
3
1
0
0
0
2
0
0
0
0
0
0
2
1
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
2
1
0
1
0
0
0
0
0
1
0
1
2
3
0
1
0
0
0
0
2
2
0
1
0
0
2
0
1
0
0
2
1
0
1
1
0
0
2
0
0
0
0
0
0
2
0
1
0
2
0
1
1
0
0
1
0
0
2
0
0
0
0
0
1
0
1
0
0
3
2
1
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
1
1
2
1
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
1
0
0
0
0
5
0
1
0
0
0
2
1
0
0
0
0
0
2
1
0
0
2
2
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
5
0
0
2
0
0
0
3
0
0
0
0
0
2
0
1
0
0
1
0
1
0
0
0
1
0
1
1
2
0
1
1
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
2
0
2
1
0
0
2
0
2
0
2
0
2
0
0
0
0
0
0
0
0
4
1
2
0
1
0
0
0
0
0
4
0
0
0
1
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
1
0
0
2
2
0
2
2
0
1
0
1
0
1
0
0
1
0
0
0
1
0
1
2
0
0
0
1
0
0
1
0
0
0
0
2
0
0
2
0
0
1
0
0
0
1
0
2
2
0
0
0
0
0
0
2
0
1
0
3
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
1
2
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
2
0
0
0
2
1
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
4
0
0
0
0
0
3
0
4
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
2
2
0
0
1
0
0
0
0
0
0
2
3
0
0
0
0
0
0
1
3
0
1
0
2
0
0
2
3
0
0
1
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
2
0
1
0
0
2
0
0
2
0
0
2
0
1
0
0
0
2
0
0
0
0
3
2
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
2
2
2
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
2
0
0
2
1
1
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
1
2
0
0
0
0
2
0
2
0
0
0
2
0
0
1
2
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
2
2
0
2
0
1
1
0
0
1
0
0
0
0
1
0
0
2
0
2
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
1
0
0
2
2
0
0
0
0
6
1
0
0
0
0
0
0
0
0
1
0
0
1
0
4
0
2
0
0
1
2
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
5
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
2
0
0
2
0
0
0
0
2
0
2
0
2
0
0
2
0
0
1
1
0
0
0
2
1
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
3
0
0
0
0
0
3
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
2
0
0
0
1
2
0
3
0
1
0
0
0
1
2
0
0
0
1
0
0
2
0
0
0
0
0
2
0
2
0
2
1
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
1
0
1
2
1
0
0
1
0
2
0
2
0
0
0
0
1
1
0
2
2
0
0
0
2
0
0
0
0
0
0
0
1
2
0
1
0
0
3
0
1
2
0
0
1
2
1
3
0
0
0
1
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
2
1
1
0
1
0
0
2
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
2
0
1
0
0
0
0
3
0
0
3
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
1
0
0
0
2
0
2
0
0
1
0
0
2
1
0
0
0
1
1
0
0
2
0
2
0
0
1
0
1
0
0
1
0
2
0
0
1
1
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
8
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
3
0
0
1
2
0
0
0
1
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
2
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
2
1
2
0
1
0
0
0
0
2
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
10
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
2
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
4
2
0
0
0
0
2
1
1
1
0
0
1
0
2
1
2
3
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
3
0
0
3
0
0
0
1
0
0
0
0
1
0
0
0
2
0
1
0
0
0
1
0
0
2
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
1
4
0
0
0
0
1
0
0
0
2
0
1
2
0
1
0
0
0
2
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
4
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
1
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
4
2
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
2
1
2
0
0
1
2
0
0
2
0
0
0
0
1
2
0
0
0
1
2
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
2
2
2
2
0
1
1
0
2
1
2
0
0
0
2
0
0
0
0
0
0
0
5
0
0
2
1
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
4
2
0
1
1
0
0
0
0
1
2
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
5
0
0
0
0
2
2
2
2
0
0
1
0
3
0
2
2
1
0
0
0
0
1
2
2
0
0
0
6
2
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
4
0
0
2
2
2
0
0
0
2
0
0
1
0
0
0
2
2
0
2
0
0
0
0
1
2
0
0
1
0
0
0
1
0
0
0
0
1
0
0
2
0
2
0
0
3
0
0
1
0
0
0
1
2
0
3
0
0
2
0
0
1
0
2
2
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
4
0
0
0
0
2
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
3
0
0
0
2
2
2
1
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
1
2
1
0
0
0
1
1
0
0
1
0
1
1
2
1
1
0
1
0
0
0
0
0
2
0
1
0
2
1
1
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
1
2
1
3
0
0
0
0
0
0
0
1
1
1
0
2
0
4
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
4
2
0
0
0
1
2
0
0
0
1
0
0
2
0
5
1
3
0
1
1
1
0
0
2
4
0
0
0
0
4
1
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
3
1
0
0
2
1
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
1
2
0
2
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
3
1
2
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
2
0
1
1
1
1
1
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
1
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
10
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
2
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
2
0
0
1
2
0
0
2
0
1
0
2
2
3
0
0
0
1
0
0
1
0
2
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
3
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
1
2
0
1
0
0
0
6
2
2
0
0
0
2
0
0
1
0
2
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
3
0
0
0
0
0
0
1
0
2
0
1
0
2
1
0
0
0
0
1
0
0
0
1
0
0
2
0
1
0
2
0
0
2
0
0
2
0
2
0
0
2
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
1
0
0
2
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
2
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
4
4
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
3
0
3
0
3
0
2
0
0
2
0
2
2
1
10
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
3
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
2
0
2
0
2
0
0
0
0
0
0
2
0
2
1
0
2
0
2
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
2
0
0
0
4
2
0
0
4
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
2
0
2
0
3
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
2
0
1
0
0
1
1
0
0
0
0
2
1
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
1
0
0
0
0
0
2
1
0
0
1
1
0
1
2
1
1
2
1
3
0
1
0
1
0
0
0
0
2
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
2
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
3
0
0
2
0
1
2
1
0
2
4
0
0
0
0
0
0
1
0
2
1
0
1
0
0
0
0
0
0
0
2
0
2
0
0
1
0
2
0
0
1
2
2
0
0
0
0
0
0
1
0
2
1
0
0
0
0
1
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
2
2
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
3
1
0
0
2
0
0
0
1
0
0
0
2
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
2
1
1
0
2
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
2
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
2
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
2
1
0
0
1
1
2
0
0
0
0
0
0
0
0
1
0
2
0
2
1
2
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
4
0
0
1
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
3
0
2
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
2
0
0
0
2
0
0
0
0
1
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
2
2
1
0
0
0
0
0
1
2
0
0
0
0
0
0
2
1
0
0
3
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
2
1
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
2
1
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
4
0
1
0
0
0
0
1
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
4
2
1
1
2
2
2
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
2
0
4
0
0
0
2
1
0
2
0
0
0
0
0
0
3
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
2
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
2
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
3
0
0
0
0
2
1
0
1
0
0
0
3
2
0
0
0
0
2
0
2
2
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
5
0
2
0
0
0
0
0
0
2
0
1
0
3
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
3
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
2
0
3
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
1
1
1
0
0
0
2
0
0
0
1
1
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
2
1
1
0
2
0
2
2
0
0
3
0
3
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
2
2
0
0
2
0
1
0
0
0
0
1
0
0
0
0
1
2
0
0
2
2
0
1
0
0
0
2
0
0
0
2
1
0
2
2
0
0
0
0
1
1
0
0
1
0
0
0
0
2
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
1
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
3
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
3
0
0
2
0
2
0
0
2
0
1
0
0
2
3
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
2
0
0
1
0
1
0
1
0
0
0
3
0
0
0
2
1
0
0
1
5
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
2
0
2
0
0
0
1
1
0
0
0
1
0
0
0
2
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
4
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
2
0
1
0
0
2
2
0
0
0
1
0
0
2
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
5
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
3
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
2
1
0
0
0
2
2
0
0
0
1
1
1
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
4
0
0
0
0
1
0
0
2
0
3
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
4
2
0
0
1
0
0
2
0
0
1
0
0
0
1
0
2
0
2
0
0
2
1
1
0
1
0
1
2
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
2
1
0
2
0
1
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
1
1
2
2
0
0
0
1
3
0
0
0
0
0
1
0
1
0
0
1
1
0
1
0
2
0
0
0
4
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
2
2
0
2
0
0
0
0
0
2
0
0
1
1
2
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
3
3
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
1
0
2
1
2
0
0
0
0
1
0
1
2
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
3
0
0
2
0
0
0
2
0
0
0
0
0
2
2
2
0
0
0
0
0
1
0
0
1
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
3
2
10
0
0
0
0
0
2
0
0
0
2
2
1
1
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
4
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
2
0
3
0
1
2
2
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
2
0
0
2
0
2
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
4
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
1
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
1
1
1
0
0
0
3
2
0
0
0
0
1
1
0
0
1
0
0
2
0
1
1
0
0
2
0
1
1
2
0
0
1
0
0
0
1
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
1
0
1
0
0
0
1
0
2
0
0
0
2
0
0
0
1
0
2
0
0
0
0
3
0
0
0
1
0
0
0
2
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
1
0
1
0
2
1
0
3
0
1
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
2
0
1
1
0
0
1
0
0
2
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
2
0
0
2
1
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
3
2
0
1
2
2
0
2
1
0
0
0
0
2
0
0
0
0
2
0
0
1
1
0
1
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
7
0
0
2
1
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
1
1
0
0
0
0
0
0
1
1
2
2
2
0
1
0
0
0
2
0
1
2
0
0
1
0
1
2
0
1
1
0
2
0
0
3
0
0
2
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
3
0
4
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
1
0
1
0
0
1
0
1
2
0
2
5
0
0
3
2
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
2
0
2
0
0
2
2
0
2
0
0
0
0
0
0
2
0
4
1
0
1
1
1
1
3
1
0
0
1
2
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
1
2
0
1
0
0
0
0
2
0
0
0
0
0
2
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
2
2
0
2
0
0
0
1
0
0
0
1
1
0
1
1
0
0
0
0
2
0
0
0
0
2
2
1
0
0
0
0
2
3
0
0
2
0
1
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
4
0
2
0
1
0
0
0
1
0
0
0
1
0
0
1
2
0
0
0
0
1
2
0
1
1
0
0
0
1
0
0
0
0
3
2
0
1
0
0
0
2
2
0
0
0
0
3
0
0
0
4
0
0
2
1
0
0
1
4
0
0
0
2
2
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
1
2
0
0
2
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
1
0
1
0
0
1
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
2
1
0
0
2
2
0
0
3
0
0
0
0
0
1
1
0
1
0
0
1
1
3
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
2
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
3
3
0
0
3
2
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
2
0
2
0
0
1
1
0
0
1
0
0
1
2
0
1
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
1
0
3
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
1
2
2
1
0
0
0
1
1
1
0
0
0
0
0
0
0
2
0
5
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
2
0
2
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
2
0
0
0
0
2
0
0
0
0
0
1
1
0
1
0
3
0
1
2
1
0
0
0
0
4
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
1
0
0
1
0
0
0
2
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
7
2
0
0
0
2
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
2
0
0
0
1
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
2
0
1
0
1
0
2
0
0
0
2
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
2
0
1
0
0
0
2
1
0
1
0
0
0
0
0
2
0
0
0
0
2
2
0
0
1
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
2
1
1
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
3
0
2
0
0
0
0
0
2
0
0
1
1
0
0
0
1
1
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
1
3
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
2
1
0
4
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
3
0
0
0
0
3
1
0
2
0
0
0
0
0
0
0
2
2
4
2
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
1
2
3
2
0
0
0
0
0
0
0
0
2
0
0
1
1
2
0
0
0
6
3
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
4
0
1
0
0
2
0
2
0
3
0
1
0
1
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
3
2
0
1
0
2
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
1
0
4
0
1
0
0
1
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
2
0
2
1
0
2
0
1
0
0
0
2
1
0
0
0
1
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
2
1
0
1
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
1
0
2
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
1
0
0
0
1
0
1
1
0
0
0
0
0
4
0
2
0
1
1
0
0
0
0
0
0
0
2
2
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
4
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
2
2
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
3
0
2
0
1
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
2
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
2
2
0
2
0
2
1
0
1
0
0
0
0
0
1
0
1
0
1
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
2
1
1
0
0
0
2
0
0
2
1
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
3
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
2
0
1
2
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
2
0
1
0
2
0
2
1
0
0
0
1
0
0
0
0
3
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
1
1
0
0
0
0
3
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
2
0
0
1
0
0
0
2
1
0
0
0
0
0
3
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
2
0
0
0
6
0
0
1
1
0
0
0
0
2
0
1
0
0
0
1
0
2
0
0
2
0
0
0
0
0
2
3
3
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
1
0
0
0
3
1
0
2
1
0
0
0
0
0
0
1
0
0
2
1
0
0
1
0
2
0
0
0
1
0
1
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
3
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
1
0
0
0
0
0
2
0
1
0
1
0
1
0
1
0
0
0
0
0
4
2
0
0
3
0
0
1
1
0
0
0
0
0
2
1
1
0
0
3
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
1
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
3
4
0
1
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
2
1
1
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
4
1
1
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
1
4
3
0
0
0
0
0
2
2
2
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
5
0
0
0
1
0
2
0
0
1
0
0
0
2
0
0
2
0
1
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
3
0
0
1
3
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
1
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
2
1
0
0
0
5
0
0
0
0
0
2
0
0
1
2
0
2
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
1
0
2
0
2
0
0
2
1
2
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
1
0
1
0
0
0
0
1
0
1
1
0
0
0
0
1
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
2
2
0
0
0
0
1
0
0
1
0
0
0
1
1
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
3
1
2
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
3
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
1
0
2
0
1
0
0
2
0
0
0
2
2
0
2
1
0
1
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
4
0
0
2
0
0
0
1
0
2
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
2
0
0
0
2
0
0
0
1
0
2
0
2
0
2
2
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
3
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
5
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
2
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
3
0
0
0
0
1
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
3
0
0
0
2
0
1
0
2
2
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
1
2
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
3
5
2
0
0
0
1
0
1
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
3
0
1
0
0
0
0
0
0
0
0
2
0
3
0
0
2
0
2
1
0
0
1
0
2
1
2
0
0
0
1
0
0
0
0
1
0
0
0
0
2
1
2
2
2
0
1
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
4
1
0
0
0
1
0
0
1
2
0
1
1
1
0
1
0
1
0
1
0
2
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
2
0
0
0
0
0
2
2
0
0
0
1
0
2
0
1
0
2
0
2
0
2
0
1
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
3
0
1
0
0
1
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
1
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
2
1
0
2
0
0
6
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
2
1
0
0
0
0
1
0
0
0
3
0
4
0
0
1
1
0
3
0
1
0
1
0
2
0
0
0
1
1
0
0
2
0
2
1
0
0
1
1
0
1
0
0
2
2
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
3
0
0
0
4
0
2
0
0
2
2
0
0
3
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
2
0
0
2
0
1
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
1
0
0
1
2
0
2
0
2
0
0
1
0
0
0
0
3
2
4
0
0
1
0
2
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
2
1
0
0
0
0
2
0
0
0
3
1
2
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
2
0
0
5
0
0
1
0
0
0
2
0
0
2
1
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
10
1
0
0
2
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
1
0
0
2
2
0
2
0
2
0
0
2
0
1
1
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
3
4
0
0
0
0
0
1
1
0
0
0
0
0
1
2
0
0
4
0
0
1
1
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
2
0
1
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
4
2
0
0
0
0
1
2
0
0
2
0
0
0
1
2
0
1
2
1
2
2
1
0
1
1
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
4
2
0
0
0
0
1
3
0
0
0
3
1
0
0
0
0
0
0
0
1
0
0
0
0
1
2
2
1
0
0
0
2
0
0
0
0
2
1
0
2
0
1
0
1
1
0
0
0
0
0
0
0
2
0
0
1
0
2
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
2
2
2
0
0
0
8
0
2
2
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
2
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
1
0
0
0
1
2
0
0
4
0
0
0
0
4
0
2
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
4
0
1
0
0
0
0
3
0
1
0
3
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
1
2
0
1
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
1
2
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
1
0
3
2
0
0
1
2
0
0
0
0
0
0
2
0
0
0
2
3
2
1
0
0
1
1
0
0
1
0
0
1
1
0
2
1
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
2
14
2
0
1
2
3
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
2
0
0
0
1
1
0
1
0
0
0
0
0
0
0
2
0
2
2
1
0
0
0
0
0
1
0
0
1
0
0
4
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
2
0
2
1
1
2
2
0
0
2
1
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
3
0
0
2
0
2
1
0
0
2
2
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
1
0
0
0
0
1
3
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
1
1
1
0
2
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
1
2
1
1
2
0
2
3
0
2
0
0
2
1
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
1
3
0
0
0
0
2
0
2
0
0
2
0
0
0
1
1
1
0
0
0
2
1
0
0
0
1
0
3
0
0
0
0
0
0
2
4
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
1
1
1
0
1
0
1
0
0
0
0
2
0
0
1
0
0
0
2
0
2
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
2
0
0
0
1
2
1
0
0
1
0
4
1
0
0
0
1
1
2
0
0
0
2
0
0
0
0
4
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
2
1
0
2
4
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
1
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
1
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
2
0
0
0
1
1
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
2
1
1
0
0
0
2
0
0
1
0
0
0
0
1
1
1
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
3
0
0
0
0
1
2
0
0
3
0
0
2
0
2
2
0
0
5
0
0
0
0
1
0
0
0
0
0
3
0
0
0
2
0
2
0
0
0
0
0
0
0
1
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
1
4
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
1
3
1
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
4
0
2
0
0
0
0
2
0
0
2
0
0
1
2
0
0
1
0
0
1
0
2
0
0
1
1
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
2
1
0
0
0
1
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
1
2
0
0
2
0
0
2
0
2
0
1
0
0
2
0
0
0
0
0
2
0
1
0
0
0
1
0
0
2
0
0
0
1
0
2
0
3
5
0
0
0
0
0
0
0
2
0
0
2
0
2
3
0
0
0
2
1
1
0
6
0
2
3
0
0
1
0
0
0
0
2
1
4
0
2
1
0
2
0
0
0
0
2
0
0
0
0
0
2
0
1
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
2
2
3
0
0
1
1
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
1
1
2
0
0
0
0
1
1
0
0
3
3
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
1
0
0
2
0
1
0
2
0
2
0
3
0
1
0
2
0
0
0
0
1
2
2
0
0
1
0
0
2
0
0
4
2
0
0
0
0
0
0
1
0
0
0
0
1
2
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
1
2
0
1
1
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
3
0
2
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
2
0
2
2
0
1
3
0
0
3
0
1
0
0
0
1
0
2
0
0
0
0
1
0
3
0
0
3
0
2
0
0
1
0
0
0
0
1
1
0
0
0
1
0
1
2
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
1
0
0
0
1
0
0
2
0
0
3
2
0
0
0
0
0
4
2
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
1
0
2
1
1
0
0
1
2
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
2
0
2
0
0
1
2
0
0
0
0
2
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
1
2
0
0
0
0
2
1
1
0
0
0
0
0
1
0
0
0
2
0
0
8
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
5
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
2
0
1
1
2
2
0
4
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
2
2
0
0
0
2
3
0
2
2
0
0
0
0
1
0
0
0
1
0
1
0
0
2
3
0
1
0
1
0
1
0
0
0
2
0
0
2
1
1
2
0
0
0
1
1
0
0
0
0
2
1
1
0
0
1
1
0
0
0
1
0
0
2
0
2
0
2
0
0
0
0
0
0
1
0
2
0
2
0
0
0
2
2
0
1
0
0
2
0
0
3
2
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
2
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
2
2
0
0
1
0
0
0
2
0
0
1
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
2
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
3
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
1
2
0
2
0
0
2
0
0
1
1
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
2
2
0
3
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
2
0
0
0
1
0
2
0
0
0
0
1
4
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
1
3
0
0
0
0
0
1
1
0
0
0
0
2
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
2
0
0
0
0
0
0
1
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
1
1
0
2
0
0
3
1
0
0
1
1
0
0
0
1
0
0
0
1
11
0
0
0
2
0
1
0
0
0
0
0
2
1
2
0
0
3
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
1
0
2
2
0
0
0
2
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
2
0
0
2
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
3
1
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
1
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
2
0
1
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
1
0
2
5
1
0
0
0
1
0
0
0
4
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
2
1
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
1
1
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
5
0
0
0
2
0
1
2
2
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
1
2
2
1
0
0
1
1
0
0
0
13
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
2
1
0
0
0
0
2
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
1
1
2
4
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
1
2
1
0
0
2
0
0
0
2
1
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
2
3
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
1
0
0
0
4
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
2
2
1
2
0
0
1
0
0
1
0
1
0
0
2
1
0
0
2
0
1
1
0
0
0
1
0
1
3
0
1
0
0
0
1
0
0
0
2
0
1
1
3
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
2
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
2
0
0
1
2
1
0
5
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
3
1
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
3
2
2
2
0
0
2
1
0
1
0
1
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
2
2
2
0
1
0
0
0
0
0
2
0
1
2
0
0
0
1
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
1
0
0
1
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
2
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
2
0
3
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
6
0
0
0
0
0
0
2
1
2
0
3
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
1
0
0
0
0
0
2
1
1
0
0
0
3
0
2
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
1
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
5
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
1
0
7
1
1
0
0
0
0
0
1
2
0
0
0
0
0
0
1
1
2
2
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
1
1
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
1
0
0
0
0
3
0
0
1
0
0
2
1
0
2
0
2
0
0
0
1
0
1
2
2
0
0
1
1
0
0
2
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
1
0
2
0
0
0
1
0
3
0
1
0
1
0
0
0
2
2
1
0
0
0
0
0
0
2
0
2
2
0
2
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
2
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
1
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
1
2
0
2
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
1
0
2
0
0
2
1
1
0
1
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
1
0
0
1
4
0
2
0
0
0
0
0
1
0
0
2
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
1
2
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
1
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
1
2
0
0
2
0
0
0
2
0
2
0
2
0
0
2
1
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
1
2
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
2
0
2
2
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
1
0
3
0
2
0
0
0
0
0
0
0
1
3
0
1
0
2
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
1
0
0
0
1
0
2
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
1
1
0
0
3
1
0
1
0
2
0
2
0
0
5
1
0
0
1
0
0
0
0
0
0
0
1
0
2
2
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
3
2
2
2
3
2
0
0
0
1
2
2
1
1
0
0
1
3
0
0
0
0
4
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
1
0
0
0
0
0
0
3
0
0
1
0
2
2
3
0
0
0
0
0
0
3
0
2
0
0
0
2
0
0
2
0
0
0
0
2
0
2
0
1
0
0
0
1
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
2
2
0
0
2
0
0
0
0
0
2
1
2
0
0
0
0
1
1
0
0
0
0
2
1
0
1
0
0
0
0
1
2
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
2
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
4
0
0
0
0
3
0
0
2
0
0
1
0
2
0
0
0
0
0
0
2
0
2
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
1
1
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
1
0
0
1
0
0
2
2
1
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
6
0
0
0
1
0
2
1
0
1
3
0
0
0
0
0
1
0
2
4
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
2
0
0
2
0
1
0
0
0
0
1
1
1
0
2
2
0
2
0
2
2
2
0
1
0
0
0
0
0
3
0
5
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
1
2
1
2
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
2
2
0
1
6
0
0
0
2
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
2
0
0
2
0
1
0
0
0
2
2
2
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
5
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
2
0
2
0
1
0
2
2
1
1
1
1
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
1
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
2
1
0
3
0
0
1
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
2
0
2
0
3
0
0
2
1
0
0
0
0
0
1
3
0
1
1
0
0
0
0
0
1
2
0
1
0
0
1
2
2
0
2
0
0
0
0
0
0
0
0
2
0
2
1
0
0
1
2
0
0
0
0
0
4
1
2
0
0
2
0
0
0
0
2
0
0
1
2
0
1
0
3
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
2
1
0
0
1
0
0
2
0
2
1
0
1
0
1
0
2
0
0
2
1
0
1
0
0
0
2
0
0
0
0
0
1
0
2
0
1
1
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
1
0
0
0
1
0
6
0
2
0
1
2
0
1
2
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
1
2
1
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
2
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
3
0
1
0
0
0
0
0
0
2
0
0
0
1
0
1
0
1
1
1
0
3
0
4
0
0
0
0
1
1
0
1
0
0
0
1
2
0
0
1
0
2
0
2
0
0
1
1
1
0
0
0
0
1
0
0
2
2
0
0
0
1
0
1
0
0
0
3
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
2
0
4
2
0
0
0
0
2
0
2
2
0
0
1
0
1
0
2
0
2
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
7
0
0
2
0
0
0
0
2
1
0
0
2
0
2
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
4
1
0
0
0
0
0
0
0
0
0
0
0
1
1
3
1
2
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
2
0
1
0
2
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
2
2
0
0
0
1
0
0
1
2
0
0
0
0
0
1
0
0
2
0
0
2
0
0
2
2
0
2
0
0
0
0
0
1
1
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
3
0
2
0
3
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
2
2
1
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
2
2
0
2
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
2
0
0
1
0
0
2
1
0
0
0
0
0
0
0
2
0
1
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
2
2
0
1
2
1
0
0
0
0
0
0
1
2
0
2
0
0
0
1
0
0
0
0
2
0
0
0
1
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
2
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
3
2
2
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
1
0
0
0
0
2
0
0
2
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
2
1
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
2
0
0
0
2
1
1
0
0
0
0
1
2
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
1
1
1
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
2
0
0
2
5
0
2
0
2
4
1
0
0
0
0
0
1
2
0
0
0
1
0
0
0
1
4
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
2
0
1
1
0
0
1
0
2
0
0
0
0
1
0
2
2
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
1
1
0
4
0
0
2
6
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
3
0
0
0
0
0
0
2
0
1
1
2
0
0
0
0
0
2
0
2
0
0
3
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
2
0
0
0
0
2
1
0
1
0
0
1
0
1
0
0
1
0
0
0
0
2
1
0
1
0
0
0
2
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
1
0
0
1
1
0
2
2
0
0
0
0
3
0
1
0
2
1
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
1
2
1
2
0
2
0
0
0
0
1
0
0
1
0
2
0
0
0
0
2
0
0
0
1
1
0
0
0
2
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
3
2
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
5
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
1
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
1
1
0
0
0
3
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
3
0
0
0
0
0
0
0
2
2
0
0
0
0
1
3
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
3
0
1
2
0
3
0
1
2
0
2
2
1
0
1
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
2
0
0
0
1
0
0
2
3
0
0
0
0
0
1
0
0
1
0
2
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
3
0
0
0
0
1
0
0
1
0
1
0
0
0
0
2
0
2
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
1
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
8
0
0
0
0
0
0
0
0
0
2
1
6
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
2
0
0
1
0
0
2
0
0
1
0
0
0
0
2
1
3
0
0
1
0
1
2
0
0
4
0
0
0
0
0
18
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
3
2
1
0
0
1
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
2
0
0
0
1
0
0
1
1
1
0
1
0
0
0
0
0
0
1
1
1
0
0
0
1
0
1
2
1
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
2
0
1
2
2
0
0
0
0
0
0
1
1
0
0
1
2
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
2
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
1
0
0
0
2
0
0
0
0
4
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
1
0
1
0
0
0
2
0
0
0
1
0
0
3
2
2
0
0
0
1
2
0
1
3
0
2
0
0
5
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
3
0
2
1
0
1
1
2
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
1
0
3
0
4
2
0
0
0
0
2
0
0
1
0
2
0
0
0
1
0
2
0
2
3
0
0
0
1
0
0
3
0
1
0
2
0
1
0
0
1
0
0
0
0
1
0
2
0
0
0
1
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
5
0
5
2
0
0
2
1
0
0
0
1
0
0
1
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
1
1
1
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
2
0
2
0
0
2
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
4
0
1
0
0
0
2
0
2
2
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
2
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
6
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
1
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
2
0
4
0
2
2
0
0
0
0
0
0
2
0
3
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
2
1
0
0
2
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
3
1
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
1
0
3
2
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
1
2
0
1
0
0
1
0
0
0
3
2
0
2
0
0
1
1
0
0
0
2
2
1
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
2
0
0
4
0
0
0
0
0
0
2
0
1
2
2
0
0
0
0
0
0
4
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
4
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
1
0
0
0
2
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
2
2
2
0
2
1
0
0
3
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
2
0
1
1
3
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
1
4
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
2
0
2
3
1
0
0
3
0
2
1
2
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
3
0
0
0
2
2
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
2
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
1
1
5
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
3
1
1
0
0
0
2
0
1
0
1
0
0
0
0
0
1
0
0
2
1
0
1
2
0
2
1
0
2
0
0
0
1
0
0
0
0
1
0
1
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
2
0
1
0
2
1
0
0
1
0
0
2
2
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
3
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
1
1
2
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
2
1
0
3
0
0
0
0
0
3
0
0
2
2
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
2
2
2
1
0
0
0
1
0
2
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
2
0
0
0
2
0
1
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
9
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
1
0
1
0
0
0
1
1
3
0
0
0
0
0
0
2
0
0
5
0
0
2
2
0
0
2
10
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
4
0
0
1
1
1
0
0
0
0
0
3
2
1
0
0
2
0
0
0
1
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
15
0
0
2
1
1
3
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
1
0
2
0
5
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
1
1
0
2
1
1
0
2
1
2
1
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
3
2
1
4
2
2
0
0
1
4
1
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
2
2
1
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
3
2
1
0
0
0
1
1
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
6
1
0
0
1
0
1
0
0
0
0
0
1
0
2
0
1
0
0
4
1
0
0
1
0
0
2
2
0
1
0
0
1
0
1
0
2
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
2
0
0
0
1
0
0
1
3
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
1
0
0
1
0
0
0
0
1
0
0
0
2
1
2
0
0
0
0
2
0
0
0
0
0
4
0
0
2
1
1
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
2
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
1
0
1
0
2
1
0
0
2
0
2
0
0
2
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
2
0
2
0
2
0
0
2
2
1
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
4
0
0
1
1
2
0
0
0
1
1
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
1
2
0
2
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
1
2
0
1
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
1
4
0
1
0
0
0
3
0
2
0
0
1
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
2
2
0
0
1
0
0
0
0
2
1
2
3
0
0
0
0
1
1
0
0
0
2
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
2
2
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
1
2
1
0
0
1
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
4
0
2
0
0
0
0
1
0
1
0
0
0
1
1
1
1
0
0
0
0
0
0
1
0
2
2
2
0
1
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
3
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
2
2
1
2
1
1
0
1
0
3
0
0
0
1
1
0
2
0
0
1
0
1
0
0
1
0
0
1
0
2
2
0
0
0
0
0
0
1
0
1
0
0
1
0
1
1
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
1
2
2
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
3
0
0
0
0
1
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
4
0
1
2
2
0
1
0
0
0
0
1
0
2
1
0
0
0
0
2
0
0
2
0
2
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
2
1
0
0
0
2
0
0
3
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
3
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
2
0
1
1
0
0
3
1
1
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
1
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
1
0
0
0
2
1
0
2
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
1
0
0
2
0
2
6
0
1
1
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
1
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
1
0
0
2
0
0
0
0
2
2
0
1
0
1
3
0
0
0
0
3
0
0
1
1
2
0
0
0
0
0
0
0
0
3
0
4
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
4
0
0
1
2
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
2
2
0
2
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
1
0
0
0
0
0
2
0
2
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
3
1
0
0
0
0
2
1
0
0
0
0
1
3
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
2
3
1
0
1
0
0
1
1
0
2
10
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
2
0
0
0
2
2
0
2
0
2
0
2
2
0
2
0
2
0
1
0
1
0
1
0
0
1
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
1
0
2
0
0
0
2
0
1
2
1
0
0
0
1
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
2
1
0
0
0
0
0
0
1
1
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
3
1
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
1
2
2
0
0
2
2
3
0
0
1
0
1
0
1
1
3
0
1
0
0
0
0
1
0
0
0
0
0
2
0
1
0
1
2
0
2
0
0
2
0
0
0
0
0
1
3
0
0
1
1
1
0
0
1
1
0
0
3
0
0
1
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
1
0
2
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
1
0
2
1
2
0
0
0
2
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
1
0
0
0
2
0
2
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
1
0
2
1
0
0
0
2
0
2
0
1
0
4
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
2
0
0
2
0
2
0
0
0
0
3
1
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
6
1
0
2
2
0
0
0
0
0
2
0
0
1
0
2
2
1
0
2
0
2
0
2
0
0
0
0
0
0
0
6
0
0
1
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
1
0
2
0
2
0
2
3
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
2
0
0
2
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
3
2
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
2
0
3
0
2
0
0
1
2
2
5
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
2
0
1
0
0
2
1
0
1
0
1
0
0
0
1
1
0
0
2
0
0
2
0
1
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
2
1
3
0
0
0
0
0
1
0
0
0
1
0
2
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
2
0
0
1
0
2
0
0
0
0
0
0
2
1
0
0
2
0
2
1
1
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
1
1
0
2
1
0
1
0
2
0
0
0
0
1
0
0
0
4
0
1
0
4
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
2
0
0
0
2
0
1
0
2
2
0
0
2
0
0
2
0
1
0
1
3
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
2
1
2
0
1
0
0
0
0
2
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
6
0
1
0
0
0
2
2
1
6
1
0
0
1
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
0
0
0
0
0
1
0
0
0
3
0
0
1
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
2
0
0
0
0
1
1
2
2
0
0
0
1
0
3
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
3
0
0
0
0
0
0
2
0
1
0
1
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
3
2
2
0
0
2
0
2
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
1
2
0
2
2
2
1
10
0
0
1
0
0
0
0
1
0
1
0
1
1
0
2
2
2
2
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
2
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
3
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
1
1
1
0
0
2
1
1
1
0
0
0
0
1
0
1
0
0
6
0
0
0
0
2
0
1
3
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
3
2
0
0
2
1
2
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
2
0
0
2
2
0
0
0
1
2
0
0
2
0
0
0
1
0
0
0
2
2
2
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
3
0
0
1
2
2
0
0
0
3
1
0
1
0
0
2
0
0
0
0
0
2
2
0
0
1
3
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
2
0
4
1
2
0
0
0
0
0
0
1
2
1
1
0
0
0
1
2
1
1
1
2
2
0
1
0
0
0
0
0
0
1
1
3
0
1
3
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
1
1
0
2
1
0
0
1
1
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
4
0
1
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
1
0
2
0
0
4
2
0
2
0
0
0
2
2
0
0
2
2
0
2
0
2
0
1
2
0
0
5
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
3
0
0
1
3
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
3
0
1
0
1
1
0
0
0
0
2
0
0
0
1
0
1
3
0
0
0
0
2
0
2
0
0
2
0
1
2
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
1
2
0
2
0
0
0
0
0
1
1
0
2
1
2
1
0
0
1
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
2
0
1
0
2
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
3
0
3
0
0
0
0
0
0
1
1
2
0
1
2
0
0
0
1
0
2
0
0
0
0
0
2
1
0
3
0
0
0
1
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
2
2
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
3
0
0
0
0
1
0
0
0
1
0
0
2
0
0
1
0
1
0
0
0
1
0
0
0
2
2
0
1
1
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
4
0
0
1
0
1
0
0
2
2
0
1
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
2
0
3
0
0
0
1
2
2
1
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
1
4
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
1
2
2
0
2
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
1
0
1
0
0
0
0
1
0
2
0
2
0
0
0
0
2
0
1
0
0
0
2
0
0
0
2
0
0
0
2
0
0
2
0
0
0
2
1
0
0
1
0
0
0
2
1
0
2
0
0
4
0
0
2
0
0
1
0
1
1
0
2
0
0
2
0
0
0
0
0
1
2
2
0
0
0
2
2
2
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
1
1
0
0
1
0
1
0
0
2
2
2
0
0
0
4
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
2
0
1
0
3
0
0
0
0
0
4
0
1
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
2
1
0
0
0
2
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
3
0
0
0
0
0
2
0
2
0
2
0
2
1
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
2
2
0
1
0
1
0
0
3
2
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
2
1
0
4
2
0
0
0
0
2
0
2
0
1
0
0
2
0
0
0
0
3
1
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
1
0
0
0
0
2
1
0
1
1
0
0
0
0
0
1
0
1
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
2
1
1
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
2
0
0
1
1
2
0
1
0
1
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
2
0
1
2
10
0
0
0
0
0
0
0
5
0
0
1
0
2
0
0
0
2
3
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
1
0
2
1
3
1
0
0
1
0
2
1
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
5
0
0
1
0
6
1
0
0
0
0
0
2
0
2
0
1
0
0
1
0
0
1
1
2
0
1
0
0
0
1
0
1
0
0
2
0
0
2
2
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
2
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
1
0
0
0
0
1
1
3
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
2
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
2
0
1
0
1
0
0
1
0
2
1
0
0
0
0
3
2
0
0
0
0
2
2
0
0
0
0
1
0
2
0
0
1
0
0
0
3
0
1
0
0
0
2
0
0
5
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
1
0
2
0
0
2
0
2
0
0
2
1
0
2
0
0
2
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
2
2
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
1
3
0
0
2
2
2
2
2
1
0
1
0
0
0
2
0
0
0
0
0
1
0
2
0
1
0
0
1
0
2
2
2
0
4
0
0
0
0
5
1
1
0
2
0
2
1
0
0
3
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
1
0
1
0
2
0
0
2
0
1
2
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
1
0
0
0
2
0
0
0
0
0
2
0
0
1
0
1
0
0
2
0
0
0
0
0
2
2
3
2
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
1
1
1
0
2
1
0
0
1
0
0
2
2
0
3
2
3
0
0
3
1
0
0
0
0
2
0
0
1
1
0
0
3
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
2
1
0
2
0
1
0
0
1
0
0
0
0
0
0
1
0
0
3
0
3
0
1
0
0
0
0
2
0
0
1
0
1
0
0
1
2
1
0
2
2
2
2
1
1
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
3
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
1
1
0
0
3
0
0
0
0
2
2
2
0
0
0
0
0
3
0
0
1
0
0
0
1
2
0
0
0
2
1
0
1
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
3
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
3
0
0
2
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
3
1
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
2
0
2
0
2
0
1
0
0
0
2
0
0
0
0
1
0
2
1
2
0
2
0
4
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
2
0
0
0
1
0
1
0
0
0
0
1
2
0
1
0
1
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
2
1
0
2
3
0
2
2
2
0
0
1
2
1
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
2
0
2
0
0
0
0
1
0
0
1
2
2
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
2
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
3
0
0
1
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
1
0
0
2
2
1
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
3
0
1
0
2
0
0
2
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
1
1
1
0
1
2
0
0
1
0
0
0
0
0
1
0
2
0
0
0
1
1
2
0
0
0
2
0
0
2
0
0
1
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
1
0
1
0
2
0
0
1
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
2
0
3
0
2
1
0
0
1
0
2
0
0
0
3
2
0
0
1
0
0
0
0
2
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
2
1
0
1
0
0
0
2
0
1
8
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
2
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
2
1
0
0
0
3
0
0
0
0
0
2
0
0
1
0
1
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
3
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
3
0
1
0
0
0
1
0
1
0
0
0
0
0
0
2
6
1
1
1
0
0
1
3
0
0
2
0
1
0
0
0
1
1
0
0
0
0
1
0
0
2
5
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
2
1
0
1
0
0
1
0
0
0
2
0
0
1
0
0
0
2
2
0
0
2
2
1
0
2
0
0
2
1
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
2
0
0
2
0
1
0
0
0
0
2
2
2
0
1
2
0
0
2
2
0
1
1
0
0
2
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
8
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
1
1
0
0
0
0
0
0
3
0
0
1
0
1
0
2
1
0
1
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
2
0
0
1
0
0
0
0
0
0
1
0
0
2
2
0
0
0
1
1
1
2
0
0
2
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
2
0
0
0
0
0
0
2
0
1
0
0
2
0
2
0
0
1
0
0
0
2
2
0
1
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
1
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
2
2
0
0
2
0
0
0
0
0
1
2
0
1
2
2
0
1
0
0
0
1
0
2
1
0
1
0
1
2
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
1
0
0
1
0
2
0
2
0
0
2
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
2
0
0
2
3
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
2
0
2
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
2
0
1
0
1
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
15
0
0
4
0
0
0
2
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
6
0
1
6
2
1
0
1
0
0
0
2
2
0
1
1
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
5
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
5
0
2
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
2
0
0
0
0
0
1
1
0
1
3
0
0
0
0
0
1
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
1
0
0
0
1
1
0
2
1
0
0
0
0
0
0
1
0
4
0
1
1
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
2
0
0
4
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
3
1
0
0
0
0
2
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
1
0
0
0
2
1
13
1
0
0
2
0
0
2
0
1
0
0
0
2
1
0
2
0
0
0
0
0
2
0
0
1
0
0
3
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
4
1
0
0
0
1
0
2
0
0
0
0
0
1
3
0
0
6
0
0
0
2
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
1
2
1
0
0
2
0
0
0
0
0
0
0
0
0
7
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
2
0
3
1
0
0
0
0
3
0
0
1
0
0
1
0
2
0
1
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
6
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
2
2
0
0
0
0
2
0
0
0
1
2
0
0
0
0
1
0
2
2
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
1
2
0
0
1
2
0
0
0
1
1
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
2
1
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
2
1
1
0
0
0
0
2
0
0
1
0
0
1
1
0
0
0
2
1
0
0
3
1
0
0
5
0
0
2
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
2
0
0
9
1
1
0
0
0
2
2
1
2
0
1
2
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
1
1
2
2
0
1
0
0
0
0
0
1
1
2
0
2
0
1
1
2
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
3
0
1
0
0
3
0
2
0
0
1
0
0
0
2
0
1
0
1
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
1
0
0
0
3
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
2
2
0
0
2
0
0
0
1
1
1
0
0
0
0
0
0
1
0
3
1
1
1
0
0
3
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
6
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
1
0
1
0
0
0
3
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
4
0
1
0
2
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
1
1
0
0
2
2
0
0
0
0
0
0
0
2
1
0
0
1
0
3
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
2
1
2
2
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
1
0
0
1
3
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
2
0
1
2
0
0
0
1
0
0
0
0
0
0
0
2
1
2
0
0
3
1
2
2
0
0
1
0
2
2
0
0
2
0
1
0
4
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
1
1
0
2
2
2
0
0
2
1
0
0
0
0
0
2
2
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
2
2
1
0
2
0
1
2
0
0
0
0
0
2
1
0
2
1
0
0
2
0
2
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
1
1
0
0
0
0
2
1
1
0
1
0
0
1
0
0
2
0
0
0
0
0
2
0
0
1
2
0
0
0
3
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
3
0
3
2
0
2
1
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
2
2
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
4
3
0
0
0
0
0
0
0
3
0
0
0
3
0
0
0
2
1
0
1
2
2
0
2
0
0
0
2
1
0
2
0
0
0
0
0
0
1
2
0
0
1
0
0
1
2
2
2
0
0
2
0
0
0
1
0
0
3
2
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
3
1
0
0
2
0
0
0
1
0
0
0
0
1
1
0
0
0
0
2
0
2
0
0
0
2
1
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
2
4
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
2
0
0
0
2
1
1
0
1
0
1
0
2
0
2
2
1
2
0
0
1
0
0
2
0
1
0
1
0
1
0
0
1
0
0
1
1
1
1
0
0
0
0
0
0
1
2
0
0
2
0
0
1
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
3
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
3
0
0
1
0
0
0
2
0
0
0
2
1
0
0
0
1
2
0
0
2
1
0
2
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
2
0
1
1
2
0
0
0
0
0
0
1
2
0
0
1
0
2
0
0
0
0
0
1
2
0
2
0
1
0
1
1
2
0
1
2
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
2
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
1
2
2
0
0
0
0
0
0
0
0
2
2
0
2
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
2
2
1
0
0
2
0
0
1
0
2
2
0
2
0
0
0
2
0
0
2
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
1
0
1
2
0
1
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
1
5
0
0
1
0
0
0
0
3
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
2
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
2
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
2
2
0
0
0
0
0
1
0
2
0
3
0
0
1
0
0
1
0
0
0
1
1
2
0
0
2
0
1
0
2
0
1
1
0
0
0
0
1
0
2
0
3
1
0
0
0
0
1
0
2
0
0
0
3
0
1
2
0
1
0
1
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
5
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
2
2
0
0
0
1
0
1
2
0
0
1
2
2
0
0
2
1
0
0
0
0
0
0
1
1
0
0
0
0
1
2
0
0
0
2
0
0
0
0
2
1
0
1
0
0
0
0
0
1
0
0
0
0
3
3
1
0
0
0
0
2
0
0
0
0
1
0
1
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
2
2
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
3
0
0
3
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
2
0
1
2
0
1
0
0
1
0
2
0
0
0
0
0
0
1
2
0
0
3
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
1
0
0
2
3
0
0
0
1
1
0
0
0
0
0
0
0
2
0
1
1
0
1
0
0
0
0
0
0
1
0
1
0
2
2
0
0
0
0
1
1
0
0
2
0
0
0
0
0
2
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
2
2
1
0
1
2
1
0
1
2
0
0
0
0
0
0
0
0
0
8
0
0
0
1
1
0
2
0
0
0
3
0
0
2
0
0
0
1
1
0
2
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
2
0
1
0
5
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
1
0
0
2
0
0
0
0
1
1
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
2
2
0
0
2
0
0
0
0
0
2
0
2
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
2
1
1
0
0
0
0
0
0
2
1
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
1
1
0
3
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
3
2
2
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
2
1
1
1
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
2
0
0
0
2
0
0
0
0
0
0
2
3
2
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
2
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
2
2
2
0
0
0
0
0
1
0
3
0
0
0
1
7
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
1
1
0
0
0
0
2
0
1
0
1
2
0
0
1
0
1
0
3
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
2
0
0
0
0
1
2
2
2
3
1
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
1
1
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
3
1
0
0
0
0
2
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
2
0
1
3
1
0
0
0
3
0
2
0
0
0
0
0
1
0
0
1
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
2
0
3
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
8
0
2
1
0
0
0
2
1
1
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
1
2
0
4
0
0
0
2
0
2
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
1
2
0
0
2
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
1
0
1
2
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
1
0
1
0
1
1
1
0
0
1
0
0
1
2
0
0
0
0
0
2
0
0
1
0
0
1
0
0
1
0
0
1
0
1
0
1
0
0
2
0
2
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
2
1
0
0
0
7
0
2
0
0
0
1
0
2
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
2
0
1
0
0
0
0
1
0
2
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
2
0
0
2
0
2
0
0
1
0
0
0
0
0
2
2
0
2
1
2
0
1
1
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
1
0
0
2
2
0
0
1
0
0
0
0
1
0
2
0
0
2
2
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
2
1
0
0
2
0
1
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
3
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
5
0
1
2
0
0
2
0
1
0
0
2
2
0
0
2
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
3
0
0
0
0
6
0
0
0
0
1
1
0
0
0
0
0
1
0
2
0
3
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
2
2
0
2
0
0
0
0
3
0
0
2
1
2
1
0
2
0
0
0
1
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
3
0
0
0
1
0
9
0
0
0
1
0
2
1
2
0
0
0
0
2
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
5
0
2
0
0
1
0
2
4
0
0
2
0
0
0
3
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
1
0
0
0
3
0
1
1
0
0
0
0
0
0
2
0
0
6
1
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
1
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
2
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
2
0
0
2
3
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
2
1
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
1
0
0
0
0
0
0
2
1
1
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
1
0
0
2
0
2
0
0
0
2
0
0
0
0
1
0
2
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
2
2
1
1
2
2
0
0
0
0
1
0
2
2
0
0
0
0
0
0
3
0
0
0
0
2
1
0
2
0
0
0
2
0
0
1
1
0
0
0
0
2
0
2
1
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
2
0
0
0
2
1
2
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
2
0
0
0
1
0
2
2
0
1
0
0
0
0
2
1
1
0
0
2
0
0
0
2
1
0
0
0
3
0
0
0
0
0
0
0
1
0
2
1
0
1
2
0
0
0
0
0
0
0
0
1
2
1
1
1
2
0
3
0
0
2
1
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
1
0
0
3
2
0
0
0
1
2
3
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
2
0
1
0
0
0
0
1
0
2
0
0
0
2
0
2
0
1
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
2
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
19
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
2
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
2
1
0
1
1
2
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
1
0
2
7
0
1
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
3
0
0
0
2
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
1
0
2
2
0
3
0
0
0
1
1
2
0
0
1
0
0
0
0
2
2
0
0
0
2
2
0
2
0
0
2
2
0
1
2
0
2
0
0
1
0
0
1
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
6
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
1
0
0
0
0
4
0
0
0
0
0
0
2
0
1
0
1
0
0
2
1
0
0
0
2
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
3
3
1
0
0
0
2
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
2
0
2
2
0
0
2
1
1
0
0
0
0
0
0
2
0
2
2
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
2
0
0
3
0
0
1
0
0
0
0
1
1
2
0
0
1
2
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
2
0
0
1
0
0
0
0
2
1
0
0
0
0
0
1
0
2
0
0
0
0
0
2
2
2
0
2
0
2
0
0
0
0
0
2
0
0
1
0
0
3
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
3
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
3
0
2
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
2
5
0
0
0
3
0
0
2
0
2
0
0
0
0
0
0
2
0
2
1
0
0
0
1
1
1
2
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
3
0
0
0
3
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
6
0
0
0
0
0
0
0
2
1
0
1
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
2
2
0
0
0
2
0
1
2
0
2
0
2
2
0
6
1
0
0
2
0
5
1
2
2
0
0
2
0
1
0
0
1
0
0
0
0
0
1
2
0
0
0
1
2
0
3
0
0
0
4
2
0
0
0
0
1
0
0
1
1
1
1
3
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
4
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
4
0
0
0
0
0
0
1
2
2
0
0
6
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
1
0
2
0
0
0
0
1
0
0
0
0
0
3
0
2
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
2
0
0
1
2
0
1
2
0
1
0
0
5
0
0
0
0
3
0
1
2
0
0
2
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
1
3
0
0
0
0
0
1
0
0
3
1
2
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
1
0
2
1
0
2
1
1
0
0
0
3
0
0
2
0
0
1
0
2
1
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
1
0
0
0
1
0
3
0
2
0
0
0
2
0
0
0
0
0
0
1
2
0
1
3
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
2
0
0
3
1
0
0
0
0
2
0
0
0
0
0
2
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
2
1
0
2
0
0
0
0
0
2
3
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
2
2
2
0
0
0
0
1
0
2
0
0
0
4
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
4
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
1
1
0
0
2
0
0
3
0
0
0
0
2
2
0
2
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
2
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
1
0
2
1
0
0
0
0
0
0
1
2
2
0
0
2
1
0
0
1
0
0
0
2
0
0
0
1
0
2
0
1
0
0
0
0
1
0
0
2
0
0
0
0
2
1
2
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
1
0
0
2
0
0
0
2
1
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
2
0
0
2
0
0
0
0
0
0
1
1
0
1
1
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
1
0
0
1
2
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
2
2
0
0
0
3
0
0
1
2
2
0
0
0
1
0
0
0
0
2
0
4
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
3
0
0
2
0
0
0
0
0
0
0
0
0
1
0
3
0
0
1
0
2
0
0
2
2
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
1
2
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
2
2
2
0
1
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
2
0
2
0
0
0
0
3
0
0
0
0
0
0
1
0
1
0
1
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
1
2
1
1
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
1
0
0
2
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
2
1
0
1
2
0
0
5
0
0
0
0
1
0
1
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
1
0
2
0
1
4
2
1
0
0
0
0
2
0
0
0
0
0
1
0
3
2
0
0
0
1
2
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
2
0
0
2
2
0
1
2
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
1
0
0
0
0
2
0
0
3
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
1
3
0
2
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
4
1
0
0
0
0
0
0
0
0
0
0
3
1
0
1
0
0
0
1
0
1
0
0
0
1
0
0
2
2
2
0
0
1
0
0
0
0
0
2
2
2
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
1
0
1
0
0
0
0
0
1
1
2
2
0
0
2
2
0
0
0
1
2
0
0
1
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
2
4
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
8
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
2
2
0
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
1
1
0
0
0
1
0
0
0
0
0
1
1
1
2
2
0
3
0
0
1
1
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
4
2
2
1
2
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
1
0
0
0
1
0
1
1
0
1
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
4
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
2
0
0
0
0
3
0
0
4
2
0
0
0
0
0
0
0
0
0
0
1
4
2
0
0
0
0
0
0
0
0
0
2
0
5
0
0
1
0
0
0
0
1
0
0
3
0
2
1
2
2
0
0
0
0
0
0
0
0
0
7
0
0
2
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
6
0
0
1
0
0
0
0
1
2
0
0
0
0
0
2
0
0
3
0
6
0
0
0
0
0
0
1
1
1
2
1
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
3
1
0
2
1
0
1
0
0
0
0
0
0
0
2
0
0
2
2
0
0
3
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
2
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
2
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
1
2
1
0
1
1
0
0
0
0
2
0
0
0
0
0
0
2
0
2
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
3
0
0
1
2
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
1
2
2
0
0
2
1
1
0
2
0
0
0
0
0
0
0
1
2
2
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
1
1
0
0
2
2
0
0
0
0
2
0
0
1
0
2
0
2
2
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
2
10
0
0
2
0
0
2
1
0
0
0
2
0
0
0
0
2
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
2
0
0
0
0
2
2
1
0
0
0
0
2
0
2
2
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
1
0
0
1
2
0
1
0
1
0
0
0
2
0
0
0
0
0
1
2
0
0
2
0
0
1
2
0
0
2
0
2
1
0
0
0
0
2
1
0
0
0
0
2
2
0
0
2
2
1
0
0
0
0
0
0
2
2
2
0
1
0
2
0
1
0
0
0
1
0
1
0
0
0
0
2
4
1
2
0
0
0
0
0
0
3
0
2
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
2
0
1
0
1
1
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
2
2
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
1
0
2
1
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
2
0
0
5
0
0
0
2
0
0
0
0
0
1
2
2
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
1
2
1
0
0
2
1
0
0
0
1
2
2
2
0
0
0
0
5
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
1
2
0
0
0
1
0
0
2
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
3
0
0
0
0
0
0
7
2
1
0
2
2
0
0
2
1
0
0
0
1
1
0
2
2
1
2
0
2
0
1
4
0
2
0
0
0
2
2
0
2
0
1
3
0
0
2
0
0
0
2
0
2
0
0
1
0
0
0
2
0
0
0
0
0
2
0
1
1
2
0
0
0
0
0
0
3
0
0
2
1
0
0
0
0
0
2
3
0
2
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
1
0
2
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
3
0
0
0
1
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
5
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
8
0
1
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
9
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
1
2
0
3
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
2
2
3
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
4
2
1
0
0
0
0
0
0
0
0
0
5
2
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
4
0
0
1
0
0
1
0
2
2
0
3
0
0
2
0
0
0
0
0
0
0
0
1
2
0
1
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
1
1
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
1
0
3
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
2
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
3
0
1
0
3
1
3
0
2
2
1
0
0
0
1
3
0
2
1
0
0
0
1
3
0
0
0
2
0
2
2
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
1
2
0
1
0
0
0
0
0
0
1
3
0
2
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
2
2
0
0
0
2
2
0
2
2
0
0
2
0
0
2
1
0
2
0
2
0
0
0
2
0
0
1
0
0
8
0
1
0
0
2
0
0
2
0
2
0
0
2
1
2
2
1
0
2
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
3
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
2
0
0
0
2
2
1
0
1
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
2
4
0
1
1
1
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
2
2
2
0
0
0
0
2
0
0
0
1
0
2
0
2
1
0
0
0
1
0
0
2
0
0
0
0
1
0
2
0
0
10
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
1
0
0
2
0
2
0
1
0
2
0
0
0
2
0
2
3
0
0
3
1
0
0
0
2
0
0
0
0
0
0
0
0
1
3
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
2
0
0
0
2
0
0
0
0
1
0
0
0
1
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
2
1
0
0
0
0
0
2
0
2
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
2
0
0
2
0
1
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
2
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
3
0
2
2
0
0
0
0
1
0
0
1
0
2
0
0
0
0
1
0
0
0
1
0
2
0
2
0
0
2
2
0
0
0
1
0
1
0
2
1
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
2
0
0
1
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
1
0
0
0
2
0
0
0
2
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
3
0
0
0
0
0
0
0
6
0
0
0
0
2
1
1
0
0
0
0
0
0
1
2
0
0
0
2
2
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
2
1
0
3
1
2
2
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
2
0
2
1
0
0
1
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
3
0
0
2
2
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
2
0
0
1
0
0
2
2
0
0
0
0
0
0
4
0
0
2
2
2
0
0
1
0
0
0
3
0
0
1
2
0
2
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
4
0
1
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
1
2
0
0
2
0
1
2
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
1
0
2
2
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
2
0
0
0
0
1
0
0
1
2
2
0
3
1
1
1
0
1
0
4
0
0
1
0
0
2
0
0
3
0
0
0
1
2
0
2
2
0
1
0
2
0
2
0
0
5
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
2
0
1
0
1
0
0
0
2
0
0
1
0
2
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
2
1
0
1
0
2
0
0
0
0
3
1
0
0
0
2
2
2
1
2
0
1
0
1
4
1
0
0
3
1
0
0
1
0
2
0
1
0
0
0
0
0
1
0
2
1
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
1
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
1
2
2
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
3
0
0
0
0
0
1
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
2
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
1
1
0
1
0
1
0
1
0
3
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
3
0
0
2
0
1
4
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
2
0
0
0
2
0
0
2
1
0
3
1
2
0
0
1
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
2
1
0
0
0
0
1
0
2
1
0
1
0
0
1
0
0
0
0
2
0
0
2
0
2
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
3
0
1
0
2
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
4
2
1
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
1
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
1
4
2
0
0
1
3
0
0
0
0
0
0
0
0
2
0
2
1
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
3
1
0
0
0
0
0
1
0
0
0
0
3
0
2
0
0
0
1
2
1
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
1
1
1
0
3
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
3
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
2
0
1
3
3
0
1
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
1
2
0
0
1
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
3
4
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
7
2
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
1
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
1
0
2
2
1
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
1
0
0
1
2
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
2
0
2
2
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
1
0
7
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
2
0
0
2
0
2
0
1
1
0
0
1
0
3
0
0
2
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
2
0
1
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
4
2
0
0
1
0
0
2
0
1
1
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
2
0
0
0
2
0
1
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
2
0
0
2
1
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
2
2
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
2
0
0
0
2
2
0
0
2
2
2
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
2
3
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
2
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
1
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
2
0
2
0
0
0
0
2
6
0
0
3
0
0
1
1
2
0
1
0
0
0
0
0
2
2
0
2
0
0
2
0
0
1
2
2
0
1
3
0
0
0
1
2
1
0
0
3
0
0
0
0
0
0
2
1
2
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
1
0
3
0
1
0
5
0
2
0
0
1
0
0
0
0
0
0
3
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
1
1
1
0
2
0
0
0
0
0
0
2
0
2
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
3
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
2
2
0
1
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
1
1
1
0
0
0
0
2
1
1
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
1
0
0
0
1
2
0
0
0
2
2
0
0
0
1
5
1
0
0
0
2
3
0
0
1
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
1
2
0
1
0
0
1
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
4
0
0
2
0
2
0
1
0
0
0
0
1
0
0
1
2
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
1
0
2
0
2
0
0
0
0
0
0
0
0
3
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
2
2
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
3
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
3
0
0
0
0
0
1
2
1
0
4
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
2
0
0
1
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
1
0
0
1
0
0
0
2
2
2
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
2
0
0
0
1
0
1
4
0
0
0
0
0
2
0
1
0
0
0
0
2
2
0
0
1
0
0
0
0
1
0
0
0
0
0
3
2
1
0
0
0
0
2
0
0
0
0
1
2
0
0
2
2
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
2
0
0
0
0
0
0
0
6
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
4
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
2
1
0
1
0
0
1
0
0
0
0
1
2
2
0
0
2
0
0
1
0
2
0
0
0
2
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
2
0
0
0
1
3
1
0
0
0
0
2
0
1
0
0
0
0
0
1
0
2
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
2
0
0
0
2
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
1
0
2
1
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
2
2
0
1
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
1
0
0
2
0
3
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
1
0
0
2
2
0
0
0
2
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
4
2
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
3
0
1
0
2
0
1
0
0
0
2
1
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
2
0
0
0
1
1
0
1
0
1
1
0
0
2
0
1
0
0
0
0
0
2
2
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
1
0
3
0
2
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
1
0
1
1
0
2
0
0
0
2
0
2
0
1
1
0
0
0
0
0
1
0
0
0
3
0
1
3
0
2
0
0
0
3
2
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
1
0
1
3
0
0
1
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
5
0
2
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
1
3
2
2
2
0
1
1
0
2
1
0
0
0
0
2
1
2
0
1
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
4
2
1
0
2
2
2
2
1
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
1
0
0
1
0
0
0
0
0
1
2
0
0
0
0
1
1
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
2
0
2
0
1
1
0
2
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
1
2
0
0
1
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
2
2
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
3
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
2
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
3
2
2
0
0
0
0
0
0
0
0
0
3
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
5
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
4
1
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
2
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
1
2
0
0
0
1
0
0
0
2
1
0
0
2
2
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
3
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
2
1
0
0
0
1
2
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
2
2
0
0
1
1
0
0
2
0
0
0
1
2
0
0
0
1
1
0
0
2
1
2
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
1
0
4
0
1
1
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
2
1
0
1
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
1
0
0
0
5
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
1
2
1
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
2
0
0
2
0
0
1
3
0
0
0
4
0
0
2
0
2
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
2
0
0
1
0
0
1
0
0
0
2
0
0
1
1
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
1
2
2
0
2
0
0
0
0
3
0
0
1
0
0
2
0
0
0
0
0
0
3
1
2
2
0
1
2
0
0
1
2
2
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
3
0
0
0
0
2
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
2
1
0
0
0
2
2
0
0
0
0
0
0
1
1
0
0
2
1
0
1
1
3
0
0
3
0
0
1
0
1
0
0
0
0
0
0
1
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
5
0
1
2
0
0
0
0
0
0
0
2
3
3
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
1
2
0
0
2
1
2
0
1
1
0
2
1
0
0
1
0
1
2
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
2
0
0
0
2
0
0
0
0
0
1
2
2
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
1
0
2
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
2
1
0
2
0
0
1
0
0
0
1
0
0
1
0
0
0
1
1
2
0
0
0
0
0
0
3
1
0
0
0
1
0
0
0
0
1
0
0
0
2
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
2
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
3
1
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
1
0
0
0
1
2
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
1
2
0
0
0
0
0
1
2
0
2
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
2
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
4
1
1
0
0
2
0
2
0
1
2
0
2
2
0
0
0
0
2
0
1
1
1
0
3
1
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
3
2
0
0
1
0
0
0
0
1
1
0
0
1
2
2
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
2
1
0
0
0
0
0
3
3
0
1
2
1
0
1
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
2
0
2
1
0
0
0
1
1
0
0
2
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
2
0
0
2
0
0
0
1
0
1
1
0
0
0
0
0
2
1
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
2
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
2
1
0
0
0
1
0
2
0
1
0
1
0
0
1
0
0
0
0
1
0
2
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
1
1
2
0
0
0
2
1
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
1
1
0
0
0
2
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
1
1
2
0
0
0
0
0
0
0
1
1
1
0
0
1
1
0
1
4
0
0
0
3
0
1
1
0
0
0
2
0
0
0
0
2
0
2
2
0
0
0
2
1
2
2
2
0
0
0
0
1
0
1
0
3
0
2
0
0
2
0
0
2
0
1
0
1
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
2
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
5
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
3
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
2
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
1
0
0
2
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
8
0
1
0
0
1
0
0
0
0
2
0
2
2
2
1
2
1
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
2
0
1
0
1
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
2
0
0
2
0
0
3
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
1
0
0
0
0
0
0
2
1
0
0
3
0
2
1
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
4
4
1
0
0
0
2
2
0
0
0
0
2
0
2
0
0
0
1
1
0
1
0
2
0
0
0
0
0
0
3
0
2
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
2
1
0
1
0
0
0
0
1
2
0
0
0
2
2
0
0
0
0
0
0
1
1
0
0
2
0
0
2
0
0
1
0
4
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
3
0
0
1
2
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
3
1
0
0
0
1
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
2
1
0
1
0
1
1
0
0
0
0
0
1
0
0
1
2
2
1
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
1
1
2
0
2
2
0
0
0
0
0
0
0
0
0
0
5
0
2
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
1
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
2
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
2
0
2
0
0
2
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
2
0
0
2
0
4
0
0
1
2
0
0
0
0
0
2
0
0
2
0
2
1
0
0
0
0
1
0
2
0
0
1
0
0
0
3
1
0
2
1
1
0
0
0
0
0
0
0
1
0
2
1
2
0
1
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
1
2
0
1
0
2
0
0
2
0
0
0
1
3
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
1
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
1
3
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
2
0
0
1
1
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
2
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
2
0
2
0
2
1
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
3
0
2
2
1
5
0
0
1
1
0
1
2
0
0
0
0
0
2
1
0
0
0
0
0
3
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
1
1
0
0
0
0
0
2
2
0
2
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
2
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
1
2
0
0
0
2
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
3
0
0
3
1
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
2
0
0
1
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
1
2
1
0
0
0
1
1
0
1
1
0
0
0
0
0
3
0
0
0
1
0
0
2
0
0
0
0
0
0
4
0
3
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
2
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
2
2
0
2
0
0
0
0
2
2
0
0
0
2
0
0
1
0
2
0
3
1
2
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
4
2
0
0
0
0
7
0
0
0
0
0
1
0
1
1
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
1
2
0
1
0
0
2
3
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
2
0
1
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
1
1
0
0
2
0
1
1
0
1
0
0
2
0
0
0
0
2
0
0
1
0
0
3
0
1
0
0
2
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
2
2
1
0
0
0
0
0
0
0
2
0
0
1
0
2
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
2
2
0
0
0
2
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
3
0
0
0
1
0
0
2
0
0
3
0
0
1
0
0
1
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
3
0
1
0
0
0
2
0
2
0
0
0
1
1
1
0
0
0
0
0
0
3
0
2
3
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
1
0
0
0
1
0
2
0
0
1
0
0
0
0
1
0
1
0
0
2
2
0
2
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
3
0
2
0
0
2
1
0
0
0
0
0
0
0
2
1
0
1
0
2
0
0
0
0
2
1
0
2
2
0
2
0
1
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
1
2
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
3
0
2
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
3
2
5
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
1
5
0
0
0
1
0
1
0
0
2
1
0
2
0
0
0
0
0
0
0
0
3
0
0
1
0
0
2
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
4
0
0
1
1
0
3
0
0
0
0
0
1
2
1
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
2
1
0
2
2
0
1
0
0
1
0
1
0
0
0
2
0
1
1
2
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
1
0
0
0
0
3
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
4
0
0
0
0
0
2
0
2
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
3
2
0
1
0
0
0
0
0
0
0
1
1
0
2
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
1
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
2
0
1
2
3
0
1
0
0
0
1
1
0
0
1
0
3
0
2
1
0
1
5
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
2
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
5
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
1
0
2
0
1
2
0
0
0
0
0
0
7
1
0
0
0
0
1
1
1
0
0
0
1
1
2
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
5
1
0
4
0
1
2
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
1
3
0
0
0
2
0
0
0
0
0
3
0
1
0
2
1
0
1
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
2
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
3
0
1
0
0
2
2
1
1
0
2
0
0
0
0
0
0
2
0
1
0
1
0
0
0
1
0
0
0
0
0
1
3
0
2
2
0
0
0
0
3
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
2
1
0
0
1
0
0
1
0
0
2
2
0
0
0
0
1
0
0
0
1
0
1
0
3
0
0
0
0
1
0
1
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
3
0
0
0
0
0
0
1
6
2
0
0
2
0
0
0
0
0
0
0
0
0
3
2
0
0
1
0
1
0
0
1
2
2
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
1
2
0
0
1
0
0
0
2
0
0
2
0
3
0
0
0
0
0
0
0
1
3
0
0
2
2
0
0
0
1
0
0
2
0
0
0
0
0
0
4
1
0
0
0
2
1
2
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
2
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
1
0
1
3
0
0
2
0
2
0
0
0
0
2
2
1
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
2
2
0
0
0
2
0
2
0
0
0
1
2
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
2
2
0
0
2
0
0
0
0
0
0
0
0
2
3
0
0
0
0
2
2
2
0
0
2
0
0
0
1
0
0
12
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
3
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
1
0
0
5
1
0
0
0
1
0
0
1
0
0
0
1
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
2
2
0
1
0
0
1
1
0
3
0
0
0
0
1
0
0
0
2
1
0
1
1
2
0
1
2
0
2
0
1
0
3
6
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
5
0
0
0
0
0
1
1
0
1
2
3
0
1
0
3
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
2
3
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
1
2
0
2
0
0
0
0
1
0
1
1
2
0
2
0
0
1
0
0
0
2
1
0
0
2
0
2
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
1
0
1
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
2
1
0
0
1
0
2
0
0
0
0
2
0
2
1
0
2
1
0
0
0
0
1
0
1
0
0
0
0
3
0
2
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
1
2
0
0
1
0
0
2
0
0
1
2
0
0
0
1
0
2
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
2
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
1
0
2
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
4
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
1
0
0
1
0
0
1
1
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
3
1
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
1
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
1
4
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
2
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
2
1
0
1
0
1
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
2
0
0
0
0
0
0
1
0
3
0
1
1
2
3
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
1
0
0
2
0
0
0
2
0
3
0
0
0
1
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
1
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
1
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
3
0
2
1
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
1
1
0
0
2
0
0
0
0
2
1
0
2
0
0
1
1
0
2
0
0
0
0
1
0
1
2
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
2
1
0
0
0
1
1
0
1
1
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
2
2
1
0
0
2
0
0
0
0
0
0
6
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
2
1
1
1
0
2
1
0
0
0
0
0
0
1
0
1
0
1
0
2
0
0
0
1
1
3
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
1
0
2
0
2
0
0
0
1
0
0
0
0
0
2
2
0
0
0
4
0
0
1
0
0
0
0
0
2
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
1
0
2
2
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
2
0
2
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
3
1
1
1
0
1
0
0
1
0
0
2
1
1
0
0
0
1
7
0
1
2
0
1
1
0
0
0
2
0
0
0
2
0
0
1
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
0
2
0
0
0
1
0
3
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
2
0
2
0
0
2
0
2
2
2
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
2
2
0
1
0
0
2
0
0
1
0
0
0
2
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
3
1
3
2
1
1
0
0
0
1
2
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
3
0
2
0
0
0
0
1
1
2
1
0
0
0
1
0
1
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
2
1
2
0
2
2
0
1
0
0
1
0
0
2
2
0
0
0
0
1
0
0
2
0
3
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
2
1
0
1
2
2
0
0
0
1
3
0
1
0
0
3
0
0
0
0
0
0
1
0
0
0
2
1
0
3
1
0
0
1
0
1
0
0
0
2
0
1
0
0
2
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
2
1
0
0
0
0
1
0
2
2
1
0
0
1
0
1
0
0
0
0
0
1
0
0
3
0
0
0
0
1
2
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
1
0
0
1
2
0
3
0
1
0
0
0
0
0
1
2
0
0
0
0
0
2
0
1
2
0
0
0
0
2
0
0
2
2
2
2
1
0
0
0
0
1
0
0
0
0
0
0
0
3
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
1
0
0
2
0
1
2
0
0
1
1
0
0
2
0
0
0
2
1
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
1
1
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
3
1
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
1
0
4
1
1
2
0
0
0
0
0
0
0
0
0
2
2
2
0
1
0
0
0
0
1
1
5
0
0
0
0
0
0
1
0
1
0
1
1
0
2
1
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
1
1
0
0
1
1
0
1
1
0
0
0
0
0
2
1
0
0
0
2
3
2
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
1
2
0
0
1
0
0
1
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
2
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
8
0
1
1
0
2
0
0
0
0
1
0
2
0
0
6
0
2
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
2
0
0
3
0
0
0
2
2
2
0
0
0
0
1
0
0
1
0
1
0
4
0
1
0
0
1
0
0
1
1
0
1
2
0
0
1
0
0
0
0
0
0
0
2
2
3
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
2
0
2
0
0
1
2
0
2
0
0
0
0
2
0
0
0
0
0
0
1
1
1
0
0
1
0
0
1
0
0
0
2
0
1
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
5
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
3
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
2
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
1
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
2
2
0
1
1
0
0
0
0
0
2
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
1
0
0
1
1
0
0
0
0
0
0
0
1
2
0
0
1
0
1
2
1
0
0
0
2
4
2
0
2
0
0
2
1
1
0
0
0
1
0
0
0
0
3
0
0
2
1
0
0
0
0
2
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
1
0
0
2
1
1
2
0
0
2
1
0
0
0
0
0
0
0
0
3
1
2
0
2
0
0
0
0
0
0
5
2
1
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
2
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
2
2
0
2
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
1
0
1
0
0
2
0
2
1
2
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
9
0
2
0
0
1
0
0
0
1
0
0
0
0
2
0
0
1
0
0
1
0
0
2
1
2
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
1
0
0
2
2
0
0
0
1
0
1
1
0
0
0
0
0
0
1
3
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
4
0
0
0
2
2
0
0
0
0
1
2
0
0
0
0
0
0
2
2
0
1
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
2
0
0
1
0
0
1
0
0
1
0
0
1
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
3
0
2
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
2
1
0
2
0
2
1
0
2
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
2
2
0
1
2
0
3
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
2
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
2
0
0
1
0
2
0
1
0
0
0
1
0
2
1
0
0
0
2
1
0
0
1
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
2
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
5
1
0
0
0
3
1
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
2
2
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
2
1
0
0
0
1
0
0
2
1
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
2
0
2
0
1
0
0
1
0
0
2
1
1
0
0
1
2
1
0
0
1
0
0
0
0
0
0
2
0
2
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
3
0
0
0
0
2
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
3
2
0
0
0
1
2
0
0
1
1
0
0
1
0
0
0
1
0
1
1
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
2
3
1
2
0
0
0
0
0
0
1
2
0
2
0
0
2
0
0
0
4
0
2
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
6
0
0
3
4
0
0
0
2
0
0
1
0
0
1
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
1
2
2
2
0
1
0
0
0
0
1
0
0
0
2
0
5
0
0
1
1
3
0
0
0
0
2
0
0
1
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
1
1
2
0
1
0
1
0
0
1
3
2
0
0
0
0
2
0
2
0
0
1
1
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
1
3
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
2
0
0
0
2
1
1
0
0
2
1
0
0
0
1
0
0
0
0
5
1
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
6
0
0
3
0
1
1
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
2
2
0
0
0
1
0
1
0
0
0
0
0
1
1
2
2
0
0
0
0
2
2
0
0
1
3
2
1
0
0
0
0
3
2
0
2
0
0
2
0
0
0
0
0
2
2
0
1
0
0
0
0
2
0
0
0
0
2
0
0
2
0
2
0
0
2
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
3
1
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
1
2
0
2
2
0
1
0
2
0
2
0
1
0
0
0
0
0
2
0
0
0
0
2
0
2
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
3
0
2
0
0
0
0
0
0
2
0
0
0
0
2
1
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
1
2
1
2
0
0
0
1
1
0
0
0
0
0
0
0
0
2
2
0
3
0
0
1
3
0
2
3
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
2
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
2
0
0
0
2
0
0
1
1
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
1
2
0
0
4
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
2
5
0
0
0
0
0
2
1
0
0
0
2
1
0
2
2
0
2
0
2
0
0
1
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
1
0
0
0
0
0
0
1
0
0
2
0
1
1
0
0
2
0
2
0
0
0
1
2
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
2
0
0
0
2
2
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
4
0
0
0
2
0
1
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
1
1
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
1
0
0
3
0
0
0
2
0
0
0
1
0
0
0
1
0
2
0
0
0
0
2
0
0
0
1
0
0
1
1
0
1
1
1
1
0
1
0
3
0
2
2
0
1
1
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
3
0
1
0
1
0
0
2
0
2
1
1
0
4
0
2
0
0
0
0
0
0
0
0
2
0
1
1
0
0
2
0
0
0
4
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
1
0
3
1
3
2
2
1
0
1
0
0
0
0
0
2
0
0
1
0
0
2
1
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
2
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
2
1
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
2
0
3
2
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
1
0
3
4
1
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
1
0
3
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
1
1
1
0
0
1
2
1
0
0
0
0
11
2
1
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
2
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
3
6
0
0
0
1
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
2
0
1
1
0
3
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
1
0
0
1
2
0
2
1
1
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
1
0
0
0
1
1
0
0
0
3
0
0
2
1
2
0
2
1
0
1
0
0
0
0
0
1
0
0
0
3
0
2
0
0
0
1
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
5
0
5
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
4
1
0
8
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
1
1
1
0
0
2
2
0
0
2
0
2
2
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
2
0
1
0
3
1
2
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
3
2
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
2
1
0
2
0
0
0
0
0
1
0
2
2
2
0
0
0
0
2
0
2
0
0
1
1
0
0
0
0
0
1
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
5
2
0
2
1
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
2
0
2
2
0
2
0
0
1
1
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
5
0
2
0
0
0
0
1
0
0
0
1
0
0
0
1
2
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
1
0
1
1
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
2
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
2
0
2
0
2
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
1
1
0
1
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
1
1
0
0
0
0
2
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
1
0
2
1
0
0
2
1
0
0
2
0
1
0
0
1
0
1
0
0
0
3
0
0
2
0
0
0
0
0
2
0
2
0
0
0
1
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
1
0
2
1
2
0
0
0
1
2
1
0
2
0
0
0
1
0
0
0
1
1
0
0
0
2
0
4
0
0
0
0
0
0
0
2
0
0
2
0
2
0
2
0
0
1
2
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
2
0
0
2
1
0
1
1
0
0
0
2
2
0
2
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
2
4
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
3
0
0
1
0
2
0
1
2
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
2
0
0
1
0
0
1
2
0
0
0
1
2
0
0
0
0
0
2
0
1
3
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
1
0
1
1
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
1
0
2
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
1
1
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
2
3
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
1
0
0
0
0
0
0
5
0
0
1
0
1
3
0
0
0
0
0
0
0
0
1
2
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
4
0
0
0
0
0
2
2
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
1
3
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
1
0
2
1
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
3
2
1
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
7
1
0
0
2
0
0
1
2
2
0
0
0
0
2
0
0
0
1
0
0
3
0
0
0
0
1
0
2
0
0
1
2
0
0
2
0
0
0
4
0
0
0
3
0
2
0
0
1
2
0
0
2
2
0
0
0
0
0
1
1
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
1
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
3
0
2
0
0
1
0
0
0
0
0
2
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
1
2
0
0
0
1
1
0
2
0
1
2
2
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
1
0
0
2
0
0
1
2
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
2
0
1
0
0
1
0
0
0
0
2
0
0
0
1
1
0
1
0
2
0
0
0
2
0
0
2
0
2
0
0
0
0
0
2
0
0
0
2
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
3
0
0
0
0
1
0
0
0
1
0
3
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
3
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
2
1
1
2
0
0
1
2
0
1
0
2
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
2
2
0
0
0
2
0
0
0
2
0
0
0
4
1
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
3
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
2
2
2
0
0
0
2
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
1
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
2
1
0
0
1
0
0
0
0
2
0
1
0
0
1
2
3
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
2
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
1
0
0
1
0
0
0
0
0
0
2
0
1
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
2
2
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
2
0
0
1
0
0
0
2
0
1
2
0
1
1
4
1
0
0
2
0
2
0
5
1
1
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
2
1
1
0
2
2
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
1
0
5
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
1
0
2
0
3
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
1
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
5
0
0
0
0
0
0
0
7
0
0
2
0
0
0
0
0
2
0
1
2
2
0
0
0
0
0
0
3
0
0
0
0
2
7
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
2
1
0
0
1
0
0
0
0
0
2
3
0
0
0
8
1
1
0
1
1
0
1
0
0
0
0
1
0
1
0
0
0
2
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
1
0
1
0
1
0
8
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
4
0
0
0
0
0
0
1
2
0
2
0
2
0
0
1
0
1
0
0
0
1
2
1
0
0
0
0
0
4
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
3
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
2
0
0
0
1
1
1
0
1
0
2
0
0
0
0
0
2
0
2
3
0
0
4
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
1
0
0
0
0
0
2
2
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
3
1
0
0
0
0
0
2
1
1
1
2
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
2
0
0
1
0
1
0
0
0
1
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
1
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
2
0
0
2
5
0
2
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
5
0
0
0
0
0
0
1
0
0
0
2
0
2
2
0
1
1
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
1
0
0
0
0
0
0
1
1
3
0
0
2
0
1
2
2
0
0
0
0
1
2
1
0
0
0
0
1
0
2
0
3
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
2
2
1
0
3
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
1
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
4
2
0
1
0
0
0
0
1
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
1
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
1
2
0
0
0
1
2
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
2
2
7
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
1
2
0
2
0
0
1
2
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
2
0
1
2
0
0
0
2
0
0
0
0
0
0
0
3
1
0
0
0
0
1
2
0
0
2
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
1
1
0
0
0
0
0
2
1
0
1
1
2
0
0
0
0
0
3
0
0
0
1
0
2
1
0
0
1
0
0
1
2
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
1
0
2
2
0
0
0
2
0
0
0
0
1
2
1
0
0
2
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
1
0
2
2
1
0
1
0
1
0
0
2
0
3
0
2
0
0
2
0
0
0
0
0
0
0
2
1
2
1
0
0
0
1
0
0
1
0
2
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
4
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
2
1
0
1
0
1
0
0
0
3
0
0
2
0
0
0
0
2
0
0
0
1
2
0
1
2
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
2
0
2
0
0
1
0
2
0
2
1
0
2
0
0
0
0
0
0
0
0
1
0
2
1
0
0
2
0
0
0
0
0
1
5
0
1
0
0
0
1
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
3
1
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
2
0
0
1
0
2
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
3
0
1
0
2
0
0
2
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
3
3
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
1
0
2
0
0
0
0
0
2
0
1
0
0
2
0
2
0
2
0
0
2
0
1
0
0
0
0
2
0
0
1
2
2
0
1
0
2
0
0
0
1
0
0
2
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
2
2
3
1
0
0
2
0
0
1
0
2
0
0
0
0
1
0
0
3
3
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
1
0
0
4
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
1
3
0
0
0
1
1
0
0
3
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
4
1
2
0
0
0
0
2
0
0
0
0
0
1
1
1
0
0
4
0
0
0
0
0
8
0
1
1
0
2
0
0
3
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
1
2
0
2
1
0
0
1
0
1
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
4
0
2
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
1
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
1
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
1
0
0
2
0
0
3
1
0
0
0
1
2
0
0
0
1
0
0
0
0
2
2
0
2
2
0
0
2
0
0
1
1
0
1
3
1
2
0
0
1
1
0
0
0
2
2
0
0
4
0
0
0
0
0
0
4
3
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
2
0
0
1
0
0
1
0
1
0
2
0
0
2
0
0
1
0
0
0
0
2
0
2
1
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
1
0
1
0
1
0
2
2
1
0
3
0
1
2
0
2
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
1
1
0
0
0
1
0
2
4
0
2
0
2
0
2
0
0
1
1
1
0
1
0
2
0
0
1
0
2
0
1
1
2
0
3
0
0
2
0
0
2
2
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
4
2
0
0
0
2
1
0
1
0
0
0
0
0
2
2
1
2
0
0
0
2
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
1
0
0
0
2
0
1
2
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
2
3
0
0
0
0
0
0
0
0
0
2
2
2
0
0
1
2
0
0
0
1
1
2
0
0
0
1
0
0
0
0
1
1
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
1
1
1
1
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
2
5
0
0
0
1
0
0
2
0
0
1
0
0
2
0
2
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
1
2
3
2
0
0
0
0
0
1
2
0
0
2
0
0
0
3
2
0
0
0
0
0
0
0
2
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
2
0
0
0
1
0
1
0
0
1
0
1
0
2
0
0
1
0
1
2
3
0
0
0
3
0
1
0
2
1
0
1
0
2
2
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
2
0
0
1
0
1
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
3
0
0
2
0
1
0
3
0
0
0
0
3
1
0
0
0
0
0
0
1
0
0
1
0
2
0
0
2
0
1
0
4
0
0
0
0
0
2
0
1
0
1
0
2
0
0
1
2
1
1
2
0
0
0
0
0
1
0
0
0
0
1
1
1
3
2
0
2
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
1
0
0
2
2
1
0
0
2
2
1
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
1
0
1
1
0
0
2
0
0
0
2
0
0
0
2
0
0
1
1
0
0
0
0
0
2
0
3
0
2
0
0
0
0
0
2
1
0
0
2
3
0
1
0
0
1
2
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
2
1
1
0
0
0
2
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
2
0
1
2
2
0
0
1
0
0
0
1
0
2
1
2
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
2
1
2
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
1
2
0
0
0
2
1
2
0
2
0
2
0
2
1
2
0
2
1
0
0
1
0
2
0
1
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
2
1
1
1
0
0
3
0
0
2
0
0
0
0
1
2
0
2
0
2
0
0
0
0
0
0
2
0
2
0
0
1
0
1
0
0
0
0
0
2
2
2
0
0
2
0
0
0
0
0
0
0
1
3
2
0
0
0
2
0
1
0
0
0
0
0
0
0
2
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
2
2
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
2
1
0
0
0
1
0
4
1
2
0
0
0
0
0
0
1
0
0
2
0
2
0
1
0
0
3
2
0
3
2
0
0
0
2
0
2
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
3
0
1
0
0
0
0
0
0
1
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
1
2
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
2
1
2
0
0
0
0
1
0
0
0
2
1
0
1
0
0
0
1
0
1
2
0
0
0
0
0
0
0
2
0
2
0
0
0
2
2
1
0
0
2
1
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
1
1
1
0
2
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
1
0
0
4
1
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
4
0
0
0
0
1
2
0
0
2
0
0
0
4
0
0
0
0
0
2
1
0
0
0
0
0
0
1
2
1
1
0
0
0
0
0
2
0
1
0
0
0
0
3
0
0
2
0
0
0
0
0
0
2
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
1
2
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
2
1
0
2
5
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
6
0
0
1
2
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
1
1
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
3
0
3
0
0
0
1
0
2
1
2
0
0
0
1
0
0
0
2
0
1
0
0
1
0
2
0
0
0
1
0
0
0
0
10
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
1
0
0
0
0
0
1
0
0
0
0
2
0
1
1
0
0
2
0
0
0
2
0
0
3
0
0
0
0
0
1
1
3
0
1
0
0
0
0
0
0
0
0
0
3
2
0
0
0
2
1
0
2
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
1
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
2
0
1
0
1
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
3
3
0
2
0
0
0
0
0
2
0
1
1
0
0
2
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
2
1
1
2
2
0
1
0
0
2
0
1
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
3
2
0
0
0
0
0
0
1
0
2
1
1
0
0
3
0
1
2
0
0
0
3
1
2
0
0
0
1
2
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
1
2
0
0
0
3
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
1
1
0
0
0
1
1
0
0
0
2
1
2
1
0
0
1
0
2
0
2
1
0
2
0
0
0
2
2
0
2
0
2
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
1
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
2
0
0
1
0
1
0
1
0
0
1
2
0
0
0
0
1
0
2
3
0
0
1
0
0
0
0
1
0
1
0
3
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
3
1
1
0
0
0
2
0
3
0
2
0
0
1
3
2
0
0
1
0
0
0
0
0
2
0
1
0
0
0
1
0
0
1
0
0
1
2
1
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
2
0
0
0
2
0
0
0
1
2
0
0
0
0
2
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
3
0
1
0
0
2
0
0
0
0
0
1
2
0
0
0
2
0
0
2
1
0
0
0
0
1
0
3
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
1
0
0
0
0
0
3
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
1
0
0
1
2
0
0
0
0
0
1
1
1
0
2
0
0
0
0
0
2
1
0
1
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
2
1
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
1
2
0
1
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
2
1
0
0
1
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
2
1
1
0
0
0
0
0
0
0
0
0
2
2
0
1
0
5
0
0
0
1
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
5
0
1
2
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
2
1
1
2
2
0
0
1
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
1
0
0
2
0
0
0
0
1
1
0
1
0
1
0
0
0
2
2
1
1
1
0
1
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
1
2
1
0
0
0
1
0
0
2
0
1
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
1
2
0
0
0
1
1
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
2
2
1
0
0
0
3
2
2
0
1
0
2
0
1
0
0
0
2
0
2
0
6
0
0
0
0
0
2
0
0
0
0
0
2
0
1
2
1
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
2
0
2
0
1
2
1
0
0
0
0
0
0
0
0
4
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
2
0
2
2
0
1
0
0
1
0
0
0
0
0
1
1
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
1
1
0
1
0
2
1
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
2
0
0
0
2
1
1
1
0
0
0
0
0
1
1
3
0
3
0
0
0
0
0
2
0
2
3
0
0
0
0
9
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
1
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
1
0
0
1
1
0
0
4
0
0
0
0
0
1
0
0
1
2
1
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
2
0
2
0
2
0
2
0
0
0
1
0
0
0
0
4
0
2
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
1
0
3
0
0
0
2
1
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
1
0
2
0
1
0
1
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
1
0
1
0
0
1
2
0
1
0
0
1
1
1
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
5
0
0
2
0
1
0
0
2
1
2
0
0
0
0
0
2
0
2
1
1
0
1
0
0
0
0
2
0
0
0
0
1
0
2
1
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
2
2
1
0
0
0
0
2
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
2
1
0
1
0
0
0
0
0
12
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
1
2
0
0
0
0
0
0
1
0
1
2
0
2
0
1
0
0
0
2
0
0
0
1
3
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
1
2
0
1
0
2
0
3
0
0
0
0
2
0
0
0
2
0
0
2
0
4
1
1
1
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
1
2
0
1
0
0
2
0
0
0
0
0
4
1
0
2
0
0
0
0
1
0
2
0
0
0
0
0
1
0
2
2
0
1
2
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
1
0
2
0
0
0
2
0
1
0
2
0
0
2
1
0
0
0
0
0
0
0
1
0
0
5
3
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
2
1
0
0
0
1
0
0
1
0
1
1
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
1
2
0
1
0
1
0
0
2
1
0
0
0
0
1
0
2
0
0
0
0
4
0
0
2
0
0
0
0
1
0
3
1
0
0
2
0
1
0
0
0
0
0
0
0
2
2
0
2
1
0
0
2
1
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
1
1
1
0
1
0
1
0
0
0
3
0
0
0
2
0
0
0
0
5
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
1
0
2
0
0
0
2
2
3
0
0
0
0
0
0
0
3
2
1
0
1
2
1
0
0
0
1
0
2
0
3
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
5
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
2
2
0
0
0
2
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
2
0
2
0
3
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
2
0
0
1
0
3
0
2
1
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
1
3
0
2
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
5
1
2
0
0
0
0
0
2
0
0
3
1
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
3
1
0
0
0
1
0
1
0
0
1
0
2
0
0
0
0
0
1
0
0
2
0
0
1
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
4
1
2
0
0
1
1
0
0
4
0
0
2
1
0
2
0
0
0
0
3
2
0
0
0
0
2
1
3
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
1
0
1
0
2
6
0
0
0
0
2
3
0
2
0
2
0
0
0
0
0
0
0
0
1
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
1
1
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
3
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
2
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
1
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
6
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
1
0
0
1
1
2
0
0
2
0
1
0
2
2
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
1
2
1
0
0
0
0
2
0
0
0
0
2
2
0
3
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
2
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
2
2
0
2
2
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
1
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
3
0
2
0
0
0
0
2
3
0
1
0
0
0
1
2
0
0
0
0
2
1
0
0
0
2
1
0
2
0
0
1
0
0
0
0
0
0
2
0
1
0
0
2
0
2
0
0
3
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
2
0
0
3
1
3
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
2
0
1
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
2
0
0
3
1
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
2
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
4
2
4
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
3
1
0
0
1
0
1
1
0
0
0
0
2
0
0
2
0
0
0
0
1
2
0
0
0
0
2
2
0
2
0
1
1
0
0
1
0
0
2
0
0
0
2
0
0
2
0
0
1
0
0
0
1
2
2
0
1
2
0
0
0
0
1
1
1
0
0
2
1
0
0
0
0
3
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
2
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
2
0
1
0
5
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
2
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
5
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
2
0
0
1
0
2
0
0
0
2
0
2
0
0
1
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
2
1
0
0
1
2
0
0
2
0
2
0
2
0
0
2
2
0
1
0
2
0
2
0
2
2
0
0
0
0
1
2
1
1
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
3
0
0
1
0
0
0
0
7
0
1
0
1
0
0
0
1
1
2
0
0
0
3
0
1
0
5
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
1
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
1
2
0
1
2
0
1
3
0
0
2
0
0
0
0
0
1
0
2
0
0
3
0
0
1
0
0
0
0
0
0
2
1
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
1
0
2
2
0
0
3
1
0
2
1
0
0
4
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
2
0
0
0
0
0
3
2
1
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
1
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
1
2
0
2
0
0
0
0
0
0
0
2
0
0
3
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
1
0
0
0
1
0
0
0
3
0
1
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
1
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
3
0
0
0
0
0
0
1
2
2
0
0
1
0
0
0
1
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
2
0
0
0
1
0
0
0
2
0
2
0
0
0
0
2
5
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
1
1
0
1
2
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
4
2
1
0
0
0
0
2
1
0
0
0
0
1
2
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
3
1
0
0
0
0
0
0
2
2
1
1
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
2
0
0
0
0
1
1
0
1
0
0
0
0
0
4
0
0
0
0
3
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
2
1
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
3
0
0
4
3
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
4
1
0
1
2
0
1
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
1
2
2
0
1
0
1
1
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
3
1
0
0
0
2
1
0
2
0
0
0
0
0
1
1
0
4
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
1
0
0
0
1
0
1
1
0
0
0
0
0
2
0
0
2
0
1
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
1
2
0
2
0
1
0
0
3
0
0
0
0
0
1
0
0
0
8
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
1
0
2
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
2
0
2
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
2
2
3
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
3
1
0
1
0
2
1
1
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
2
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
2
1
0
0
0
3
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
2
1
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
2
1
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
1
0
1
2
0
0
1
1
0
0
0
0
2
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
3
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
1
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
2
0
3
0
0
1
2
0
0
2
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
7
0
0
1
1
0
0
3
0
1
0
0
9
2
1
0
0
0
0
0
1
1
0
1
1
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
1
2
0
0
0
3
0
1
2
0
0
0
0
1
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
1
0
0
0
3
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
2
1
5
0
0
0
0
2
0
0
0
1
0
0
1
2
0
0
0
0
0
0
1
1
0
2
0
0
2
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
2
0
1
0
1
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
1
0
0
1
0
0
0
0
0
0
0
2
0
0
4
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
3
2
0
0
0
0
0
2
0
0
1
0
2
0
0
1
0
0
1
1
1
0
2
0
2
0
0
0
3
0
0
0
1
1
0
0
0
0
0
1
2
0
2
0
1
0
0
0
0
1
2
1
0
1
2
0
1
5
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
5
0
0
1
0
0
0
0
0
2
0
0
2
1
1
0
0
0
0
0
0
0
3
2
0
0
0
1
1
0
0
1
1
0
1
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
1
0
0
0
0
1
0
2
0
0
0
1
0
0
1
0
1
1
0
2
2
1
2
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
2
0
0
0
1
1
0
2
3
1
0
0
0
2
0
3
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
1
1
0
0
3
0
0
2
2
2
0
0
1
1
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
2
0
1
0
1
0
0
0
0
2
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
3
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
1
1
0
0
2
0
1
0
0
1
0
0
1
1
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
1
3
0
1
0
2
0
0
0
0
1
0
0
0
1
0
1
0
2
4
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
2
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
7
0
2
0
1
0
0
2
1
2
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
2
0
0
1
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
1
1
1
0
0
0
0
0
3
0
2
0
0
0
1
0
1
0
0
0
0
11
2
1
0
1
0
0
0
0
0
0
0
2
0
0
0
2
2
0
1
0
1
0
0
0
1
0
0
1
0
2
0
0
0
2
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
1
1
1
2
1
2
0
0
0
1
0
1
0
0
0
0
0
3
0
2
0
0
0
0
0
0
2
0
0
1
0
2
2
2
0
2
0
0
0
1
1
1
2
0
0
0
0
2
0
0
2
3
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
2
2
0
2
0
0
0
0
1
0
1
1
0
1
2
0
0
1
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
3
0
1
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
3
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
1
0
3
0
1
0
0
0
0
0
0
0
0
0
0
1
0
6
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
1
1
1
2
0
1
2
0
0
1
0
1
0
0
0
1
1
0
0
0
0
1
0
2
1
2
2
0
0
2
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
1
0
0
2
0
0
1
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
2
1
1
0
1
1
0
1
2
0
1
0
2
0
1
0
0
1
0
0
0
0
2
0
2
0
0
2
0
0
0
2
0
0
0
2
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
21
1
1
0
0
7
0
1
0
1
1
0
1
1
0
0
3
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
2
1
0
0
0
3
0
0
0
0
0
1
5
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
1
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
2
0
2
0
2
0
2
0
0
0
2
0
1
1
0
0
1
0
1
2
0
0
0
0
0
1
1
4
0
1
2
0
0
0
0
0
2
1
0
1
0
0
1
0
0
2
0
0
0
0
0
5
0
0
0
0
0
3
0
2
0
0
0
1
0
1
0
2
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
3
1
0
0
0
0
0
0
0
0
0
0
5
1
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
2
0
1
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
3
0
0
1
0
0
0
0
0
0
1
2
0
0
2
0
1
5
1
2
0
0
0
6
0
3
0
2
0
3
0
0
0
0
0
2
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
2
0
0
0
0
0
2
0
0
0
0
6
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
2
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
4
2
0
0
0
0
2
0
1
2
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
4
0
0
0
1
2
0
0
0
2
0
0
1
1
0
0
1
1
2
0
0
0
1
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
3
0
1
0
2
0
0
0
0
0
4
4
0
0
0
3
0
0
1
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
1
0
1
0
0
1
0
0
2
1
0
0
2
1
1
0
0
0
2
1
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
8
0
0
2
0
0
1
2
0
0
0
0
0
2
0
2
3
0
0
0
2
0
1
0
0
0
0
0
0
0
1
1
2
2
2
2
2
1
0
2
0
2
3
0
0
1
0
0
0
2
1
0
0
1
0
0
0
0
2
1
0
1
0
0
0
0
3
0
0
1
0
0
0
0
0
0
3
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
1
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
1
11
1
0
1
2
0
2
2
0
3
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
4
1
0
0
0
0
0
1
1
0
0
0
0
2
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
2
0
2
0
1
0
0
2
0
0
2
2
1
0
0
0
0
2
0
1
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
2
2
1
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
2
0
0
3
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
6
0
0
0
0
0
1
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
2
1
1
0
0
0
1
0
0
0
2
1
3
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
1
0
1
2
1
0
2
2
0
0
0
0
3
2
0
0
0
0
1
3
1
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
2
1
1
0
0
0
4
0
1
2
1
0
2
0
0
0
1
0
1
6
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
4
2
0
1
0
1
1
0
2
0
2
0
1
0
0
0
1
1
0
1
0
1
1
0
0
1
2
2
0
0
0
3
1
0
0
7
0
3
0
0
0
0
1
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
2
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
5
0
0
2
0
1
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
2
0
0
2
1
0
0
0
2
0
0
2
0
0
1
0
0
0
1
0
0
1
0
6
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
4
0
0
0
3
0
3
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
1
0
1
0
1
2
0
0
0
0
0
0
1
2
1
0
0
0
0
2
0
0
1
1
1
0
3
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
1
0
0
0
0
1
0
2
1
0
2
0
0
0
1
3
0
3
0
0
1
0
1
0
0
0
2
3
1
0
0
0
0
0
1
1
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
2
2
0
0
0
1
2
0
1
3
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
4
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
3
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
2
0
1
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
3
1
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
2
1
0
0
1
2
0
0
0
0
2
2
0
0
0
4
0
0
0
0
1
2
0
1
0
0
0
2
0
0
1
0
2
1
0
1
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
2
1
1
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
2
1
0
0
0
0
2
0
0
0
4
1
2
0
0
1
0
0
0
2
0
0
2
1
1
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
1
2
0
0
0
0
2
1
0
0
2
0
2
2
1
0
0
1
0
0
2
0
2
0
1
1
0
2
0
0
1
0
2
0
2
0
1
0
0
1
0
0
2
1
0
0
0
1
0
0
0
0
0
2
1
2
0
0
3
0
2
2
0
0
0
1
2
0
0
0
0
2
1
1
0
0
1
2
2
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
2
1
0
2
2
0
0
0
0
1
0
0
0
0
0
5
0
0
0
2
1
0
0
0
0
0
0
5
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
3
2
0
0
0
0
0
4
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
2
2
2
0
0
0
2
0
3
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
2
0
0
3
0
0
1
0
0
0
0
0
3
0
0
2
0
0
0
0
0
1
0
1
0
0
1
1
1
0
0
0
1
1
0
1
2
0
2
0
2
0
0
0
0
0
0
3
2
0
2
0
0
1
0
2
0
0
2
2
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
2
0
0
0
2
1
0
2
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
1
0
2
0
0
0
0
0
2
2
2
0
0
1
3
0
0
1
2
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
1
0
2
1
0
0
0
0
1
1
0
0
0
3
4
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
3
0
0
0
1
0
0
0
2
0
0
1
0
2
1
0
0
2
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
3
0
0
2
0
0
0
2
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
3
0
0
1
2
0
1
1
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
1
1
0
0
0
0
1
2
0
1
0
0
1
0
0
0
1
1
1
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
1
5
2
1
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
2
0
2
0
2
0
1
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
3
0
3
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
3
1
0
1
0
0
0
0
1
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
2
1
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
1
1
1
0
0
0
0
1
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
0
0
2
0
2
6
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
1
3
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
2
0
0
1
2
3
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
3
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
2
0
2
0
0
0
0
0
0
0
1
1
0
0
0
1
1
2
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
1
0
0
0
0
2
0
0
1
0
0
2
4
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
2
2
0
0
0
0
0
2
0
1
1
0
0
1
0
0
0
1
1
0
0
0
0
1
2
0
0
0
1
0
0
2
1
2
0
2
0
0
2
0
2
0
2
1
0
0
2
2
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
2
0
1
0
0
0
0
4
0
0
0
0
1
0
0
1
0
0
2
2
0
2
0
0
0
0
1
0
0
4
0
0
1
0
0
1
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
2
0
1
0
0
2
0
0
1
2
0
0
0
0
0
0
2
2
1
2
1
0
1
0
1
0
0
0
0
0
2
1
0
1
2
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
3
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
7
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
3
0
0
0
0
1
1
0
0
0
1
1
0
0
0
2
0
0
0
0
2
0
0
2
1
0
2
0
2
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
2
0
0
2
0
2
0
1
0
0
8
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
2
1
0
0
2
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
1
0
0
0
0
0
1
2
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
2
0
1
0
0
0
0
0
1
0
1
0
1
0
3
0
0
0
0
2
1
2
2
0
0
0
1
0
0
1
2
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
2
0
0
4
0
1
0
0
0
0
0
1
0
0
0
0
5
0
1
0
0
0
2
0
2
0
2
0
0
2
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
3
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
2
0
1
0
2
0
0
1
0
0
1
0
1
0
0
0
2
0
0
2
1
1
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
1
1
3
0
0
0
0
0
0
0
3
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
1
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
2
0
2
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
2
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
4
0
1
0
0
2
2
3
0
0
0
0
1
1
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
2
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
3
0
0
0
0
0
0
0
0
1
1
0
2
0
3
0
0
2
0
0
0
0
2
1
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
1
2
2
0
2
0
0
1
0
0
1
1
0
1
3
0
0
0
1
1
0
2
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
2
2
1
2
0
1
0
2
1
2
0
0
1
0
0
0
0
0
1
0
1
0
0
0
2
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
2
0
0
2
0
0
0
3
0
0
0
0
2
2
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
1
0
1
0
1
1
0
0
2
1
0
1
0
0
0
0
2
0
0
0
0
1
1
2
0
2
0
0
0
0
0
0
0
1
0
0
1
0
2
2
0
0
2
0
0
3
2
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
3
2
2
0
0
2
0
0
0
0
0
2
0
0
0
0
2
2
3
0
0
0
0
0
0
0
0
0
2
7
0
0
0
0
0
1
0
0
0
0
1
0
3
2
2
0
0
2
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
1
0
0
0
2
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
3
0
0
1
0
0
2
1
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
1
2
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
2
0
0
0
0
3
1
1
0
0
2
0
0
0
0
0
0
1
1
2
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
3
0
1
0
0
0
0
0
0
3
1
2
0
1
0
0
0
0
0
0
0
0
0
1
1
3
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
3
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
2
1
0
1
2
0
2
1
3
0
0
1
0
0
1
1
0
2
2
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
3
6
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
9
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
3
0
0
0
0
1
2
0
0
2
1
0
0
0
0
0
2
1
0
0
0
2
0
0
0
2
0
0
1
0
0
0
2
0
0
0
1
0
0
1
0
2
2
1
0
0
0
0
0
1
0
0
0
1
3
2
0
4
2
1
1
1
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
1
0
0
2
1
2
0
0
1
0
1
0
3
0
1
0
2
0
0
2
0
1
0
0
0
2
0
0
0
0
1
2
0
1
0
1
0
3
0
0
0
0
0
0
2
0
1
1
0
0
0
1
4
1
0
0
0
1
2
0
2
0
2
0
2
0
1
0
0
1
0
0
0
0
0
2
2
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
2
2
0
2
0
1
0
1
0
0
0
0
2
0
2
0
7
0
0
0
2
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
3
0
0
1
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
3
0
1
0
0
0
1
0
0
0
0
2
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
2
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
1
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
2
0
4
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
1
0
0
0
2
0
0
1
1
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
2
1
0
0
0
0
0
1
0
1
0
0
1
0
1
3
0
2
0
2
0
0
1
0
0
0
0
0
0
2
2
0
0
1
0
2
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
1
2
2
2
5
0
0
0
0
0
0
4
2
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
1
0
0
3
0
0
0
1
2
0
1
0
0
0
2
2
0
0
0
2
6
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
3
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
3
1
0
0
1
0
1
0
0
0
2
2
2
0
0
1
0
1
0
0
0
0
0
0
0
0
1
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
2
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
1
3
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
2
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
2
0
0
2
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
1
1
0
2
0
1
0
0
0
0
1
1
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
1
2
0
1
0
1
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
1
0
0
0
0
2
2
0
0
0
2
1
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
1
2
1
0
2
0
0
2
0
0
0
1
1
0
1
0
2
1
2
0
0
0
2
1
1
1
1
0
1
0
0
1
0
2
0
0
0
2
0
0
0
0
0
2
0
2
0
1
0
0
2
1
0
0
1
2
1
0
2
2
0
0
1
0
0
0
0
2
1
1
2
0
0
1
3
2
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
2
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
1
2
1
1
0
3
0
0
4
1
0
0
0
2
1
0
1
2
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
2
0
2
2
0
0
0
2
0
3
1
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
3
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
2
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
2
0
0
2
0
0
2
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
3
1
3
0
0
1
2
2
0
0
0
0
0
0
5
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
5
1
0
0
2
0
0
0
0
0
3
0
0
2
2
0
0
0
0
0
4
2
0
0
1
0
0
0
0
0
0
0
3
1
0
2
1
0
0
0
2
0
0
0
1
1
0
0
0
2
0
1
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
2
2
2
0
0
1
0
1
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
2
2
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
1
0
1
0
0
0
0
2
1
0
2
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
2
1
0
0
0
0
0
0
3
2
0
0
0
1
0
2
0
0
2
0
1
0
2
0
0
0
0
1
0
0
0
2
0
2
2
0
2
0
0
0
0
2
0
0
0
1
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
2
0
0
1
2
1
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
3
0
0
0
0
0
1
2
1
0
0
0
3
0
0
1
0
1
0
1
0
2
1
2
0
0
0
0
0
0
0
2
0
1
0
1
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
2
0
0
0
1
7
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
1
0
0
2
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
2
0
1
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
1
0
1
1
2
2
2
0
3
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
2
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
3
0
1
1
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
3
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
2
0
0
0
0
0
0
0
5
0
0
0
0
2
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
2
0
0
0
0
1
0
0
1
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
1
0
0
0
0
0
2
1
0
0
3
1
0
0
0
0
1
0
0
2
0
1
0
1
0
1
1
0
0
0
1
0
2
1
0
2
0
3
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
2
2
0
1
1
0
0
1
4
0
2
0
0
0
0
2
1
2
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
3
0
0
0
0
0
0
1
0
0
0
1
0
0
0
5
0
0
0
2
0
0
0
0
3
1
1
1
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
4
0
0
1
0
0
0
0
0
0
1
0
4
2
2
0
0
1
1
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
2
1
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
1
0
0
0
2
1
0
2
0
0
1
0
0
2
0
0
1
0
0
0
0
2
0
0
0
2
0
2
3
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
1
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
7
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
2
1
0
0
0
1
0
0
0
0
0
2
2
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
5
0
0
0
0
0
2
1
1
1
0
0
0
0
2
0
0
1
0
0
0
0
4
0
0
0
0
0
0
1
0
8
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
1
2
0
0
0
2
0
0
0
1
0
4
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
4
0
0
1
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
4
0
0
1
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
4
0
1
2
0
2
1
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
3
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
2
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
4
0
0
0
0
5
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
1
1
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
2
0
0
0
3
0
0
0
0
0
0
0
0
2
1
0
0
2
1
0
1
0
0
2
0
0
2
0
2
0
2
0
0
0
0
0
1
0
2
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
2
0
1
1
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
2
0
2
0
6
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
1
1
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
3
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
1
0
1
1
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
3
1
0
1
1
0
0
0
1
1
2
0
0
1
0
1
1
2
1
0
1
0
1
0
1
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
1
1
1
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
2
0
1
0
0
0
0
1
0
0
3
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
3
2
0
0
0
0
3
1
1
2
0
0
0
0
0
0
0
1
1
0
0
0
1
0
2
1
1
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
2
0
0
0
4
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
1
0
0
1
1
0
0
0
2
0
1
0
0
0
0
1
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
1
0
0
0
1
3
0
1
1
0
0
0
2
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
13
0
1
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
1
1
0
0
0
2
0
0
0
1
0
2
0
2
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
1
2
1
2
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
1
2
0
2
0
0
2
0
0
2
4
4
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
2
2
0
0
0
1
0
0
0
0
0
3
2
0
3
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
4
0
0
1
0
0
1
0
0
1
0
0
2
0
1
2
0
1
0
0
1
2
0
0
0
0
0
2
1
0
1
0
0
2
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
1
1
2
1
0
0
0
1
1
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
3
0
2
0
0
0
0
0
1
1
2
1
0
0
0
0
0
0
2
0
0
4
0
0
0
0
0
1
0
0
0
1
1
2
0
0
0
1
0
1
0
0
1
0
0
1
2
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
4
1
0
0
1
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
2
0
2
0
1
0
0
1
0
0
0
0
0
0
0
1
0
2
0
2
0
1
1
1
0
1
0
0
0
0
2
0
2
0
0
0
0
1
0
1
0
0
1
1
2
0
0
0
1
0
2
1
0
0
1
0
0
0
0
0
0
1
0
2
0
2
0
1
2
0
2
0
0
0
0
0
0
0
0
3
1
0
0
0
1
1
0
5
0
0
0
0
0
2
0
0
2
0
5
2
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
1
3
1
0
0
0
0
0
2
3
1
2
0
1
2
1
0
0
0
0
1
1
0
0
1
2
0
0
0
0
0
0
0
0
2
0
1
1
1
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
7
0
0
0
3
0
0
0
3
2
0
0
0
0
0
0
0
0
1
2
1
1
1
0
0
2
0
0
0
0
0
0
1
0
0
0
4
0
2
1
0
0
1
0
0
0
0
0
0
0
0
1
3
1
0
0
0
4
0
1
0
2
0
2
3
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
3
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
1
0
0
0
2
0
2
0
2
1
0
2
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
8
0
0
0
2
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
1
2
2
1
0
2
1
0
0
0
0
1
2
0
2
0
2
5
1
0
0
1
0
0
0
1
0
1
0
0
0
2
0
1
1
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
2
0
0
0
1
0
2
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
2
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
1
0
0
0
1
1
2
2
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
1
3
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
2
0
0
3
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
1
0
0
2
0
0
1
0
0
0
0
0
2
1
0
1
0
0
1
3
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
2
0
3
2
0
2
1
1
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
1
2
0
1
0
0
2
1
0
0
3
0
0
0
0
0
1
1
1
0
1
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
1
0
2
1
0
1
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
2
1
0
0
0
0
1
1
1
0
0
2
0
0
0
0
1
0
2
0
2
1
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
1
2
0
1
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
2
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
2
0
0
1
0
1
0
0
2
1
1
0
2
0
0
0
0
0
0
0
2
2
1
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
1
1
1
0
0
2
2
0
0
0
1
2
1
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
2
2
1
0
0
1
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
1
0
0
2
2
0
0
0
0
0
2
0
0
6
0
0
1
0
1
0
1
0
2
0
1
1
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
8
0
0
3
0
0
1
1
2
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
1
1
1
0
0
0
0
0
0
0
2
1
1
2
1
2
1
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
1
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
1
0
5
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
5
0
4
0
0
0
1
2
0
1
0
0
1
0
2
0
0
2
0
0
1
0
1
1
0
0
0
0
0
1
0
0
1
2
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
2
0
0
0
2
0
0
1
1
3
0
0
0
0
2
1
0
0
1
0
0
1
1
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
4
1
1
0
0
1
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
2
0
0
2
0
0
2
0
1
0
0
0
0
1
4
0
2
1
1
0
2
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
3
2
0
0
0
0
0
0
0
2
1
0
0
1
0
2
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
3
2
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
2
0
0
1
0
1
2
0
0
0
1
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
2
2
1
1
0
0
1
2
0
0
0
2
0
1
0
2
0
2
1
0
0
0
0
2
0
0
1
2
0
0
0
0
0
1
2
0
0
1
0
0
0
2
0
1
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
1
1
11
0
0
0
0
1
1
0
0
2
2
0
0
1
0
0
0
0
0
0
0
3
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
2
0
1
0
0
0
0
3
0
1
0
0
0
1
0
0
0
0
2
1
2
0
0
0
1
0
0
2
0
0
1
0
0
0
0
1
0
2
2
2
2
0
0
0
0
2
0
0
0
0
1
1
0
0
2
0
1
2
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
5
0
0
0
2
1
0
0
1
0
0
0
0
0
2
0
1
0
1
0
0
0
2
0
1
0
0
2
3
0
0
0
1
0
0
1
2
2
0
2
0
0
0
2
2
0
0
1
1
0
0
0
0
1
0
1
2
1
0
0
2
0
0
1
0
0
2
2
1
0
0
0
0
0
3
0
0
2
2
0
0
2
0
0
1
0
0
3
2
0
1
0
0
0
1
2
0
0
1
1
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
2
1
0
0
3
0
1
0
0
0
0
0
2
0
2
0
0
0
2
2
0
0
0
1
0
2
0
0
0
0
1
0
0
1
0
0
0
0
2
0
3
2
1
0
0
0
0
2
2
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
1
2
0
0
0
3
0
0
2
0
1
0
0
2
2
0
0
0
1
1
2
0
0
0
0
1
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
1
0
3
0
0
0
1
2
0
0
0
0
3
0
0
1
0
0
0
1
1
0
3
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
1
0
2
0
0
2
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
3
0
0
2
0
0
1
0
0
1
2
0
0
1
1
1
0
0
0
0
1
1
4
1
0
0
0
1
0
0
3
0
0
1
0
0
1
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
2
1
6
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
2
2
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
2
0
1
0
0
1
0
0
1
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
3
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
1
0
2
4
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
2
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
2
0
2
0
2
1
1
0
0
0
3
1
1
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
1
0
1
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
5
2
0
2
0
0
0
0
0
0
0
1
0
0
1
1
0
2
0
2
0
0
2
1
0
3
2
0
2
0
0
0
0
0
0
1
2
0
1
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
4
0
1
1
1
0
2
0
0
0
0
0
0
0
1
2
0
2
0
2
0
0
0
2
0
0
0
0
0
2
1
0
1
0
0
2
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
1
1
0
0
0
0
0
0
0
0
1
0
0
3
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
1
2
0
1
1
0
1
0
0
1
0
0
2
5
0
0
0
2
0
1
0
0
2
0
3
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
2
0
2
0
2
0
0
0
0
0
0
1
0
2
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
9
0
0
2
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
3
1
0
2
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
2
2
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
2
1
2
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
8
0
2
2
1
2
0
0
3
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
2
0
3
0
2
0
0
0
9
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
1
1
0
0
0
0
0
0
2
0
3
1
0
0
0
2
0
0
1
0
0
0
0
0
2
0
1
2
0
2
0
0
0
1
1
1
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
8
0
1
0
0
1
1
0
0
0
0
2
1
2
0
0
1
0
0
0
0
2
0
3
2
2
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
1
1
0
0
0
0
2
0
0
0
2
3
0
0
2
2
1
1
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
1
0
0
1
0
0
2
3
1
1
1
0
2
2
0
1
0
0
0
2
2
0
1
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
1
0
0
1
0
0
0
0
3
0
0
1
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
1
5
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
3
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
2
0
0
0
0
0
1
0
2
3
0
0
0
0
0
2
0
0
1
0
0
0
0
5
0
0
1
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
3
0
1
1
0
0
0
2
0
2
0
0
0
4
1
0
1
0
2
0
0
0
2
0
1
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
2
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
1
2
0
1
0
0
0
0
1
0
0
0
2
1
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
1
0
0
0
1
0
1
0
0
0
2
1
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
1
1
0
1
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
1
2
1
2
0
2
0
0
0
0
0
0
0
2
3
0
1
1
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
2
2
3
1
0
3
2
0
0
2
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
1
0
0
1
0
2
0
0
1
0
0
1
2
0
0
0
0
1
0
0
2
2
1
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
4
0
0
0
0
0
1
0
0
1
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
1
0
0
0
2
0
2
2
1
1
2
2
2
0
0
0
1
0
0
0
0
0
0
0
2
1
0
2
1
1
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
2
0
1
0
0
2
2
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
6
0
0
0
0
0
1
0
0
2
1
0
0
2
2
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
1
1
0
0
0
0
0
0
1
0
0
2
2
1
0
0
1
0
1
0
2
0
1
0
0
0
3
0
0
0
1
0
0
0
0
1
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
2
0
1
0
2
2
0
0
1
0
3
1
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
1
1
0
0
0
0
3
0
0
0
1
2
0
0
0
2
0
0
0
4
0
0
1
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
1
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
2
0
1
0
1
0
1
2
0
1
3
0
1
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
3
2
2
0
0
0
0
0
0
0
0
0
2
0
1
2
0
3
0
1
0
0
2
2
1
0
1
2
2
0
0
0
1
0
0
0
0
0
2
3
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
1
1
0
0
1
0
0
0
0
1
0
1
0
0
2
2
0
0
0
0
1
0
4
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
2
2
0
0
0
0
0
2
0
1
4
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
2
1
0
0
0
0
1
9
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
3
3
0
0
0
4
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
2
0
0
2
0
4
0
3
0
1
1
0
0
0
1
2
0
0
0
0
0
2
0
2
1
0
0
2
0
1
0
0
0
0
1
0
0
2
0
0
0
1
0
0
1
2
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
1
0
0
2
1
0
1
0
2
1
0
1
3
0
2
1
1
1
0
2
0
0
0
0
0
0
1
0
0
0
0
3
0
1
2
0
0
0
1
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
2
0
0
0
0
0
2
0
0
0
2
0
0
0
1
2
2
1
0
1
0
0
0
1
2
0
0
2
1
0
0
0
0
1
1
0
1
0
0
2
1
0
0
0
0
2
0
0
1
2
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
4
0
0
2
0
0
0
1
1
0
1
0
0
0
0
2
0
0
0
2
0
0
0
2
1
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
3
0
1
0
1
2
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
4
0
0
2
1
0
0
0
0
0
1
1
0
0
0
2
1
0
1
0
0
0
0
0
1
0
0
2
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
1
0
0
2
2
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
4
1
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
1
0
5
2
1
4
0
0
0
0
0
2
0
0
0
0
2
0
2
3
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
4
1
0
0
2
1
0
0
0
2
0
1
0
0
0
0
0
1
0
0
2
0
1
0
2
1
0
0
2
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
2
2
1
0
2
0
0
2
1
1
0
1
0
2
2
0
1
1
0
1
1
2
1
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
5
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
2
1
2
0
0
2
0
0
0
1
0
0
1
0
0
0
1
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
2
0
2
0
0
0
0
1
1
0
0
1
0
1
0
0
1
0
4
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
1
1
1
2
2
2
0
0
0
1
2
0
0
0
0
2
2
0
0
0
0
2
0
3
0
0
0
2
0
1
0
4
0
0
1
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
1
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
1
3
0
0
0
0
2
1
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
3
0
2
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
2
1
0
1
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
1
1
0
0
2
3
0
0
0
2
1
0
2
4
1
0
0
2
0
0
5
1
0
0
0
0
0
0
0
0
1
5
0
0
2
0
0
0
1
0
2
0
0
0
2
0
0
2
0
0
1
0
0
0
0
1
1
0
0
0
6
1
1
2
0
0
0
0
0
1
2
0
0
1
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
3
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
2
0
0
2
2
3
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
3
0
0
0
0
0
2
0
2
4
0
0
2
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
3
3
0
2
0
1
2
0
1
3
0
0
2
3
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
2
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
1
0
2
0
0
2
0
0
1
0
0
1
0
0
0
2
0
0
1
2
0
1
0
1
0
0
0
0
0
1
0
0
2
0
1
0
2
0
2
0
0
0
1
2
0
0
3
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
1
4
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
2
2
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
2
1
0
0
0
1
1
2
2
0
0
2
1
3
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
1
0
0
0
7
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
1
0
0
1
0
0
0
3
0
0
1
0
0
0
0
1
2
0
2
0
2
0
0
0
0
0
0
0
0
1
3
0
0
2
1
0
1
1
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
2
0
0
0
2
0
1
0
1
1
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
4
2
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
8
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
2
0
1
0
2
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
1
1
6
2
0
2
0
0
1
0
2
1
0
0
0
0
0
3
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
2
1
0
0
1
0
0
0
0
2
3
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
2
1
0
1
0
0
2
0
0
0
0
1
0
2
0
0
2
0
2
0
1
0
0
1
0
0
0
0
0
0
0
3
0
0
0
1
0
0
3
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
6
0
0
0
2
0
1
0
2
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
2
2
2
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
1
0
2
0
1
0
3
0
0
2
1
0
1
1
1
4
3
3
1
0
0
1
1
0
2
0
2
0
1
0
0
0
0
0
2
0
1
0
0
0
2
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
3
2
0
0
0
0
0
8
0
0
0
0
0
0
0
1
0
2
4
2
2
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
2
1
0
0
0
1
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
4
0
0
0
2
0
0
0
1
0
0
2
0
1
1
0
0
0
0
0
0
0
0
1
0
1
1
2
0
0
0
0
0
0
0
0
0
2
2
2
0
2
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
2
1
0
2
0
0
0
2
1
0
0
1
0
1
1
0
0
0
0
1
0
3
0
0
1
1
2
2
0
2
0
2
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
2
2
0
0
0
2
2
1
1
0
0
2
0
0
0
0
0
0
0
3
2
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
1
2
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
1
0
0
2
2
0
2
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
1
3
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
1
0
1
2
0
0
0
7
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
2
1
3
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
3
0
0
0
0
0
4
2
0
0
0
0
0
0
0
1
0
2
1
0
1
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
3
1
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
1
2
0
0
0
0
2
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
1
0
4
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
2
0
1
3
0
1
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
1
0
2
2
0
0
0
8
2
0
2
1
0
0
0
0
5
3
0
0
0
2
0
0
2
0
0
2
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
5
0
1
2
2
0
2
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
1
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
2
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
3
2
0
1
0
0
0
0
1
1
2
1
0
0
0
2
0
0
0
2
1
0
1
0
0
0
0
1
0
0
0
2
0
1
0
0
2
0
0
0
2
0
0
3
0
0
0
0
2
0
1
0
1
2
0
0
0
0
2
3
2
1
1
1
0
1
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
2
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
4
0
0
0
1
4
0
0
0
0
0
0
0
1
1
1
13
0
1
2
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
1
2
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
2
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
3
2
2
0
0
0
2
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
6
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
3
0
0
0
0
0
1
0
1
0
1
0
2
1
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
2
0
0
0
0
0
1
2
0
0
0
0
1
0
1
0
0
0
1
0
0
2
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
3
1
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
3
0
0
2
0
0
1
0
6
0
0
2
1
2
2
3
0
0
0
0
2
2
0
1
2
1
1
0
0
0
0
4
0
0
0
0
0
3
2
0
0
0
0
2
1
2
0
0
2
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
1
2
0
2
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
1
1
0
0
0
0
2
0
1
0
2
0
0
2
3
0
0
0
1
0
0
1
0
1
0
0
2
0
0
0
0
2
0
0
1
2
0
2
0
2
1
4
0
0
0
0
1
0
2
1
0
0
0
1
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
1
1
0
2
0
0
0
0
0
0
1
1
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
2
1
0
2
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
2
0
0
0
1
0
2
0
1
0
0
2
0
0
0
0
0
0
2
2
2
0
2
0
0
0
2
0
0
0
0
0
0
0
1
3
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
1
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
1
0
0
0
2
4
0
0
0
1
0
0
0
0
0
0
5
2
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
1
1
0
0
0
0
1
0
0
3
1
0
0
0
0
0
1
0
2
0
0
2
0
1
1
0
0
1
0
0
0
0
0
0
4
0
12
0
0
0
1
0
0
2
0
0
1
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
2
0
0
0
1
2
0
0
2
0
1
3
0
0
1
2
0
0
0
1
1
1
0
0
0
2
2
0
0
0
2
0
0
0
1
0
2
0
0
2
1
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
2
0
0
0
1
0
3
0
3
1
0
0
2
1
2
0
0
1
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
1
1
2
0
1
0
0
0
0
1
0
0
0
0
2
0
0
2
2
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
2
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
2
2
2
0
1
0
0
0
1
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
1
0
1
1
1
0
1
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
1
0
0
4
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
3
0
3
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
2
0
0
1
2
0
2
0
0
0
3
0
0
0
1
0
0
0
4
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
1
0
0
0
1
4
0
0
2
0
0
0
1
0
0
0
0
0
2
0
1
2
0
0
0
0
0
4
2
0
1
0
0
0
0
0
0
0
0
3
0
1
0
0
0
1
0
0
2
0
0
0
4
4
2
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
1
0
2
2
1
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
2
2
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
1
0
1
0
1
1
0
1
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
5
2
0
1
0
1
3
3
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
2
0
1
0
0
2
1
0
0
2
0
0
0
3
0
3
0
1
0
0
1
0
0
1
0
2
0
0
0
2
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
3
0
2
0
2
2
0
2
0
0
1
1
0
0
0
1
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
2
2
0
6
0
0
0
0
5
0
0
2
0
1
0
0
0
1
0
6
2
0
0
0
0
2
0
0
0
0
0
0
2
0
2
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
12
0
0
0
4
0
2
0
1
0
1
0
3
2
2
0
2
2
0
1
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
1
1
3
0
2
2
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
3
1
0
1
0
2
1
0
0
0
0
0
0
0
2
1
0
2
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
3
0
0
0
0
0
0
0
0
1
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
2
0
0
0
0
0
0
2
0
1
0
0
0
1
2
0
0
0
0
1
1
0
2
0
0
1
1
1
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
2
0
1
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
3
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
2
0
1
2
0
0
0
0
0
0
2
0
1
1
0
0
0
0
1
1
0
0
0
2
0
0
0
1
0
2
0
0
1
1
0
1
0
1
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
2
0
2
0
0
2
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
2
0
0
0
4
0
2
0
1
0
0
0
0
2
0
0
1
0
0
0
0
2
2
0
1
3
0
0
2
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
5
0
3
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
2
0
2
3
0
0
0
0
2
1
2
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
3
2
1
1
0
2
0
2
1
0
0
0
0
0
1
0
0
3
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
1
0
0
0
2
0
0
1
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
7
0
0
0
1
2
0
2
0
2
2
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
1
0
2
2
0
0
0
0
0
2
1
0
0
0
2
0
2
3
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
1
2
0
0
0
3
1
2
0
0
0
0
0
0
1
2
0
0
1
0
0
2
0
1
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
2
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
2
0
0
2
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
4
0
0
2
0
4
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
1
1
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
2
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
1
0
1
0
1
2
0
2
1
0
0
0
2
2
2
0
0
2
0
0
0
2
0
1
0
1
2
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
1
0
0
0
2
1
1
2
0
1
0
0
0
0
0
1
2
0
0
0
0
2
0
6
0
2
0
3
0
2
3
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
3
2
2
0
0
0
0
0
1
0
0
0
3
0
2
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
1
0
2
2
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
1
0
1
1
2
0
0
0
0
0
1
0
0
0
2
0
1
2
0
0
0
0
2
0
1
0
2
0
1
0
0
2
0
0
1
0
0
0
0
0
0
2
0
1
2
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
1
0
0
0
0
2
0
0
2
0
0
0
1
2
0
3
0
0
0
0
2
2
4
0
0
2
0
0
0
0
2
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
4
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
2
2
3
0
0
1
0
0
2
0
0
1
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
1
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
2
1
0
1
0
4
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
2
0
2
2
3
1
0
2
0
2
1
0
2
1
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
2
0
0
1
1
0
0
2
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
2
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
3
2
0
1
0
0
0
0
2
1
0
0
1
0
2
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
1
0
0
0
1
1
0
2
0
1
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
1
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
4
0
0
0
0
1
0
0
0
1
0
2
0
1
0
0
0
0
0
2
1
1
0
0
1
0
0
5
0
0
0
0
0
2
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
1
2
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
3
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
2
2
0
2
0
1
2
0
2
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
2
2
0
0
0
2
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
2
1
0
0
0
0
0
2
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
4
0
1
0
0
0
0
4
0
2
0
0
0
0
1
0
1
6
0
0
2
2
0
0
1
2
0
0
0
0
0
1
1
0
1
0
2
1
0
0
2
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
8
0
0
1
0
2
0
2
2
3
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
6
0
0
0
0
1
0
0
4
1
0
0
2
2
0
0
2
2
1
0
0
2
0
1
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
2
0
2
1
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
2
0
0
0
0
2
1
0
0
2
0
0
1
0
0
0
0
0
0
0
8
1
1
0
0
0
1
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
1
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
2
0
2
1
0
0
1
0
0
2
0
0
2
0
0
1
2
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
9
0
0
2
0
0
0
1
0
0
0
1
0
0
0
2
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
2
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
1
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
1
0
2
0
0
0
2
0
0
2
0
1
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
3
2
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
4
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
3
2
0
2
1
0
0
0
0
3
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
3
2
2
0
0
0
0
1
1
1
1
1
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
1
0
2
0
1
0
1
1
0
0
0
0
3
2
2
2
0
0
0
2
0
0
0
0
3
1
0
0
1
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
1
3
0
1
0
0
1
0
2
0
1
1
0
1
0
0
0
2
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
1
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
3
0
0
3
0
0
0
2
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
3
2
1
0
0
0
0
5
2
0
0
0
1
2
0
0
3
1
3
0
3
1
2
0
0
0
1
0
0
0
1
2
3
0
0
1
2
2
0
0
1
0
0
0
3
2
0
3
1
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
2
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
2
2
0
0
2
2
0
2
0
0
1
0
0
2
0
0
0
2
1
0
2
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
1
0
1
0
4
0
0
0
0
0
0
0
1
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
2
2
1
0
0
2
2
0
0
0
0
1
1
0
0
0
0
4
0
0
4
0
0
2
0
0
2
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
3
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
1
1
0
0
1
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
1
0
1
2
0
0
2
0
0
3
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
1
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
2
0
0
2
0
1
0
0
0
1
0
1
0
1
0
0
0
0
2
1
0
2
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
2
2
0
0
0
0
0
5
3
1
0
2
0
0
0
1
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
1
3
0
1
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
2
0
1
2
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
2
0
0
0
3
0
0
1
1
2
2
1
0
2
0
0
0
2
1
0
0
1
0
1
3
0
6
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
1
0
0
3
0
0
0
2
1
0
2
0
0
0
2
1
0
2
0
2
1
0
1
0
2
2
0
2
1
0
0
0
0
0
0
0
0
2
0
1
1
0
1
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
2
1
2
0
2
0
0
2
0
1
2
0
1
0
0
0
0
0
0
0
0
4
1
0
2
1
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
1
0
0
2
0
0
0
0
0
0
1
0
0
3
4
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
1
0
0
0
0
2
0
0
0
0
1
0
1
0
0
2
0
0
0
6
1
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
3
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
5
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
2
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
3
1
0
0
0
0
0
2
0
0
0
0
2
1
0
1
2
0
0
0
1
0
0
1
0
0
1
2
0
0
1
0
0
2
0
0
0
0
0
2
0
2
1
2
0
1
1
0
0
0
0
0
0
0
0
0
3
0
0
1
0
2
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
4
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
3
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
1
0
2
0
2
0
0
0
0
1
2
4
0
0
2
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
1
0
2
1
1
2
0
0
0
0
2
0
0
0
2
2
0
2
1
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
1
0
0
0
2
3
0
2
0
4
0
0
0
1
0
2
0
0
1
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
2
2
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
2
0
2
1
2
1
0
5
0
1
0
3
0
1
3
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
2
2
1
0
0
0
0
0
1
1
1
3
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
2
1
2
0
1
2
0
0
0
2
1
0
0
1
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
3
0
0
0
1
0
2
2
0
0
0
0
0
0
1
2
0
1
0
2
0
0
0
0
1
0
0
1
0
2
3
0
0
0
0
0
0
0
0
2
0
0
3
0
0
2
0
1
0
1
0
0
0
2
1
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
2
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
1
0
2
0
1
0
0
0
0
4
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
4
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
2
0
2
0
0
0
2
0
1
0
0
2
0
0
0
1
1
0
0
2
0
0
0
0
0
5
0
0
0
1
2
2
2
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
2
0
2
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
2
0
1
0
2
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
2
0
0
1
2
2
3
0
0
0
0
0
3
1
0
0
1
0
0
2
0
0
1
1
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
6
0
2
2
1
0
1
0
2
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
3
1
0
0
0
2
0
1
0
0
2
0
2
2
0
1
0
0
0
2
1
0
0
4
0
0
3
0
0
0
0
0
0
0
2
0
2
0
1
0
2
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
1
1
0
2
2
2
0
0
0
3
0
1
10
0
2
0
0
0
0
0
0
1
1
5
0
2
0
0
2
0
0
0
0
0
0
1
1
0
0
1
0
1
0
1
1
0
0
1
2
3
0
1
0
1
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
2
1
2
0
0
0
0
1
3
1
0
0
9
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
1
0
2
0
2
1
0
0
0
0
0
2
0
0
0
3
0
0
0
2
0
3
0
0
0
0
0
0
2
0
0
2
2
0
3
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
3
2
1
2
0
3
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
2
0
2
2
0
2
0
0
0
0
0
0
0
0
0
2
9
0
2
0
1
0
0
0
1
1
0
1
2
1
1
0
0
1
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
2
0
2
0
0
0
2
2
0
1
0
3
0
0
1
2
0
1
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
2
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
1
0
3
0
1
0
2
3
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
3
0
0
2
2
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
1
0
0
0
0
1
0
0
1
1
0
2
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
2
0
2
0
2
1
0
2
2
0
0
0
1
0
2
0
0
0
0
1
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
2
0
2
2
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
3
1
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
2
2
0
0
1
0
0
0
0
0
1
0
0
2
1
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
3
1
2
0
0
0
0
0
2
0
3
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
2
2
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
5
0
0
2
0
0
0
6
0
0
0
0
0
0
1
1
0
2
0
2
0
2
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
1
2
1
0
2
2
0
0
0
2
0
0
3
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
2
0
4
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
1
0
0
1
0
3
0
0
1
0
0
1
1
0
0
2
2
0
0
0
0
0
0
0
0
0
1
2
2
1
2
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
1
0
0
0
3
0
1
2
2
1
2
1
0
1
0
0
0
0
3
1
0
1
0
0
0
2
0
1
0
1
0
0
0
0
1
2
3
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
1
2
0
0
0
0
0
1
0
2
0
1
0
0
0
2
2
0
0
0
0
2
1
0
0
0
0
1
1
0
0
0
2
2
0
0
0
0
2
0
1
1
1
0
0
0
0
0
0
0
3
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
4
0
0
2
0
0
1
2
0
0
0
0
1
0
0
1
0
0
0
0
0
2
13
0
2
1
0
0
1
0
0
0
2
0
0
1
3
0
0
1
0
0
0
0
0
0
2
0
0
2
0
2
0
2
2
0
0
3
0
1
0
0
0
0
3
1
1
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
1
2
0
0
0
0
0
0
0
0
4
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
1
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
2
1
1
0
1
0
0
1
0
0
0
0
2
2
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
2
0
0
1
0
0
2
1
0
0
0
2
0
0
1
2
2
0
0
0
0
0
3
0
0
0
0
0
0
3
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
1
2
1
0
1
0
0
2
0
0
1
0
0
2
0
0
2
0
0
0
0
1
0
0
2
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
2
1
0
0
1
0
1
0
2
3
0
2
0
0
2
1
1
0
0
0
0
2
5
1
0
2
1
0
0
0
0
0
0
2
0
3
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
2
0
2
0
0
1
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
3
0
0
0
1
0
2
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
3
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
2
3
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
2
0
1
2
0
2
1
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
1
0
2
3
0
0
1
0
1
2
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
8
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
4
1
1
0
0
0
3
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
1
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
1
1
0
2
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
2
0
0
0
0
2
0
2
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
2
1
0
1
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
6
2
0
0
1
2
0
2
2
0
0
2
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
3
0
0
0
1
2
1
2
0
0
0
0
0
0
0
0
1
0
0
1
3
1
0
0
2
0
0
0
0
1
1
2
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
3
2
0
0
0
2
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
1
0
1
3
0
0
0
1
0
2
3
1
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
1
0
2
2
2
1
0
0
0
1
0
0
2
0
0
0
1
1
0
0
1
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
1
0
0
0
0
0
0
0
0
6
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
2
1
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
4
0
1
2
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
2
0
0
0
0
1
0
0
2
0
0
2
2
2
0
0
1
0
0
0
0
0
0
1
2
0
2
0
0
0
0
1
3
0
0
0
1
0
0
3
0
0
0
2
0
0
1
0
2
1
0
0
0
1
0
0
2
0
0
0
0
1
2
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
3
0
1
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
2
0
2
0
0
0
2
0
1
2
0
6
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
1
2
1
2
0
2
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
2
0
0
1
0
1
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
1
0
4
0
1
0
0
0
1
2
0
1
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
2
0
0
0
2
2
0
0
0
2
0
2
0
1
0
0
0
0
0
1
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
2
2
1
0
2
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
2
0
2
0
2
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
4
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
2
0
0
0
0
2
0
0
0
1
0
0
1
0
1
2
1
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
1
0
0
0
2
2
0
0
0
0
2
0
0
1
0
1
2
0
0
1
0
0
0
0
0
0
2
2
1
0
2
0
1
0
2
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
3
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
1
2
0
0
0
0
0
3
3
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
8
0
0
3
0
2
2
2
2
0
1
0
1
2
0
0
1
0
0
3
2
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
1
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
1
1
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
2
2
3
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
5
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
3
0
0
1
0
2
0
0
0
0
0
0
1
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
1
0
1
0
1
0
2
0
0
0
0
1
0
0
1
0
2
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
5
0
0
3
1
0
0
0
2
0
1
0
0
1
0
0
1
0
0
0
0
2
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
2
1
0
0
2
0
3
1
0
0
0
0
0
2
0
0
3
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
3
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
3
2
0
0
0
2
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
4
1
0
5
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
2
0
0
2
0
0
1
0
1
2
0
1
0
0
0
2
0
1
0
0
0
1
1
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
1
0
0
1
0
1
1
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
3
1
2
0
2
0
0
0
0
1
2
0
2
0
1
1
3
0
0
0
0
0
0
1
0
0
0
0
3
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
2
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
2
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
4
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
1
2
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
1
1
0
0
0
2
0
0
0
0
2
0
0
0
2
2
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
4
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
4
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
2
0
1
2
1
1
1
0
0
2
1
3
0
1
2
0
0
0
3
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
3
0
0
2
1
2
1
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
2
2
0
1
2
1
0
2
2
0
0
2
0
0
0
2
0
0
2
2
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
1
0
0
0
2
2
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
1
2
3
0
0
0
2
1
0
0
2
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
2
2
1
0
0
2
0
0
1
2
2
0
0
0
1
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
2
1
0
1
1
0
0
0
0
0
0
0
0
4
1
2
0
1
2
0
0
0
1
1
0
0
1
0
0
0
0
2
1
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
1
0
2
0
0
2
2
0
0
2
0
2
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
1
0
8
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
1
6
1
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
6
1
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
2
0
1
2
0
2
0
0
2
1
0
1
0
1
1
0
0
1
0
1
0
0
1
3
1
0
1
0
2
0
0
0
0
3
1
0
1
0
1
2
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
2
1
2
0
0
1
0
1
1
0
1
2
0
0
0
0
0
0
0
1
0
0
2
0
2
2
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
1
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
2
1
0
0
0
0
1
0
0
2
0
0
2
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
2
0
2
0
2
2
0
1
9
0
1
0
2
0
0
1
0
0
0
1
1
0
0
0
6
0
1
0
0
0
0
0
0
0
1
0
1
2
2
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
2
2
1
0
0
1
2
2
0
1
1
2
4
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
4
2
0
0
0
1
1
0
3
0
2
0
0
0
0
1
0
0
0
2
1
0
0
2
0
2
1
0
0
2
2
0
0
2
0
2
0
0
0
0
2
0
0
4
2
0
2
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
1
0
1
0
1
0
0
0
1
0
0
1
0
1
0
0
3
0
2
1
0
1
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
8
2
0
0
5
0
0
0
0
0
0
1
1
2
0
0
1
1
0
0
0
1
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
4
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
2
0
2
0
3
0
0
0
0
0
0
2
2
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
4
2
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
3
0
2
0
0
2
0
0
0
0
0
0
0
1
2
0
0
3
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
2
1
0
0
2
0
1
0
1
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
3
1
2
0
0
0
0
0
0
4
2
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
2
0
2
0
0
0
0
1
0
2
1
0
2
0
0
0
0
0
0
1
0
2
3
0
1
0
0
0
0
0
1
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
5
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
1
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
2
0
0
3
1
1
0
0
1
0
1
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
2
5
0
0
0
0
3
0
0
1
1
0
0
2
0
2
0
1
0
0
0
0
1
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
1
2
0
0
0
0
3
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
2
0
2
1
1
2
2
0
1
0
3
0
0
0
1
0
1
0
0
1
1
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
2
4
0
1
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
3
0
0
2
0
0
1
0
0
0
0
3
0
1
0
1
0
0
0
0
0
1
0
0
2
1
0
0
1
1
0
1
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
1
0
4
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
2
2
0
0
0
0
2
6
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
2
2
2
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
6
2
0
0
0
1
0
1
0
2
2
0
0
0
1
0
0
0
0
1
2
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
1
0
1
0
0
0
0
1
1
1
0
0
0
0
2
1
0
0
0
5
0
0
0
0
5
0
0
1
1
0
0
1
0
0
1
2
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
1
0
0
0
0
1
2
5
0
1
0
0
0
3
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
2
1
0
0
1
2
0
0
0
0
0
0
0
0
2
4
0
1
0
1
0
2
0
1
2
0
2
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
2
0
0
2
0
0
0
1
2
0
1
0
1
1
1
1
1
2
1
0
0
0
3
0
0
0
0
2
0
0
0
0
6
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
1
0
1
0
1
2
1
0
5
1
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
1
2
0
1
1
4
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
1
0
1
0
2
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
1
0
0
1
0
0
0
3
0
1
0
0
0
0
2
1
0
1
0
1
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
2
2
0
0
2
1
0
0
0
0
2
1
1
0
0
1
0
0
0
0
1
2
3
0
1
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
2
2
1
0
1
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
1
2
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
1
0
4
2
0
1
2
1
0
1
1
4
0
0
0
1
3
0
3
0
0
0
0
1
0
2
1
0
0
0
0
0
1
1
0
2
0
0
0
0
2
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
3
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
3
2
0
2
0
0
0
0
0
1
0
0
1
2
0
0
0
0
2
0
0
1
0
4
1
2
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
1
0
2
0
0
2
0
0
0
1
1
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
2
0
0
2
0
1
2
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
1
0
1
0
0
1
0
1
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
7
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
2
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
5
3
0
0
0
0
0
1
0
2
1
0
0
2
0
0
0
0
2
2
2
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
3
0
0
1
0
1
0
0
0
0
0
2
0
1
2
2
1
2
0
2
2
0
0
2
2
0
0
2
0
0
0
2
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
1
0
0
0
2
2
0
0
2
2
0
3
0
0
1
0
0
0
1
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
2
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
3
0
0
0
2
0
0
1
0
0
0
0
2
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
2
1
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
2
2
0
1
1
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
1
1
0
0
0
0
0
2
0
2
1
0
0
0
0
2
1
0
0
0
0
0
1
3
2
0
2
2
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
3
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
1
0
2
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
10
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
2
0
2
1
0
1
0
0
0
0
0
0
0
0
2
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
1
3
0
2
0
0
0
0
2
0
0
0
1
1
2
0
0
0
0
1
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
1
0
2
1
0
2
0
4
2
0
3
0
1
0
0
0
0
0
0
0
0
0
1
2
0
1
0
2
0
1
1
0
0
1
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
2
1
0
0
2
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
2
1
1
0
0
1
0
0
2
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
13
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
1
1
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
1
1
0
3
0
0
2
0
1
0
1
0
3
0
0
2
0
0
1
0
0
0
0
0
3
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
1
0
0
2
1
0
0
0
0
0
3
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
2
0
2
2
0
3
0
0
0
0
1
2
1
0
1
2
0
0
2
1
2
0
0
0
1
0
0
0
1
0
2
0
0
12
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
1
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
5
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
11
2
0
0
0
0
6
0
0
2
0
0
0
0
0
2
0
0
1
0
2
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
3
2
0
0
0
0
2
0
0
1
0
3
1
0
0
0
0
0
1
0
0
2
0
2
1
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
5
0
0
0
0
1
2
2
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
1
0
1
0
1
1
0
0
2
0
2
2
1
0
1
0
2
0
0
0
1
0
1
0
2
1
0
0
0
0
2
3
0
0
2
0
0
0
1
0
0
0
2
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
3
2
2
0
1
0
0
0
2
0
0
0
0
2
7
0
0
0
4
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
2
0
0
0
2
1
0
0
2
0
0
1
0
2
0
0
0
1
1
2
2
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
2
2
0
2
0
2
0
0
0
0
0
1
0
0
2
0
0
1
1
0
2
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
2
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
4
1
0
0
2
0
0
4
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
2
1
1
0
0
0
0
0
2
3
0
0
1
0
0
0
1
0
0
0
0
1
0
2
0
2
0
0
0
0
1
0
0
2
0
4
2
0
0
0
2
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
2
0
3
1
2
0
0
2
0
0
3
0
1
1
3
1
0
0
0
1
2
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
2
0
3
1
0
0
0
0
0
2
0
0
2
0
0
2
1
0
0
0
0
1
2
0
2
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
1
0
0
2
0
0
2
0
2
0
2
0
0
2
0
0
2
0
0
2
0
0
0
1
2
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
5
0
2
2
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
1
0
0
0
1
0
0
1
0
0
0
0
3
0
0
1
0
1
0
0
0
0
0
1
0
1
0
1
0
2
3
1
1
0
1
1
0
0
1
0
0
2
0
0
1
0
2
0
0
0
1
2
0
0
0
2
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
3
0
0
1
1
0
3
0
0
0
2
0
1
0
0
2
0
1
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
1
0
0
0
0
0
1
0
1
3
0
0
0
0
0
2
0
4
1
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
3
1
0
0
3
2
0
0
0
3
0
0
0
3
1
1
7
0
3
0
0
0
2
1
0
0
0
0
0
1
2
0
0
1
2
2
2
1
2
0
0
0
0
0
1
0
2
2
0
0
0
0
1
0
1
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
2
0
0
0
4
0
2
0
0
1
0
0
1
0
0
0
4
0
0
0
0
0
0
1
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
3
2
0
0
3
0
0
3
1
0
0
0
0
0
0
2
1
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
2
3
1
2
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
2
0
1
0
2
2
0
0
3
0
2
1
0
0
0
0
0
2
2
5
0
0
0
2
0
0
0
2
0
2
0
2
0
0
3
0
0
0
0
0
0
0
0
0
1
1
0
3
2
0
0
0
2
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
2
0
1
2
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
2
0
0
2
2
0
1
2
0
0
1
2
0
2
0
2
0
1
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
1
2
1
0
0
0
1
0
2
0
0
0
1
2
2
0
0
0
2
1
0
0
0
2
0
0
1
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
2
0
0
0
2
0
1
2
0
0
1
1
0
1
0
1
0
0
0
0
0
0
4
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
2
0
5
1
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
2
1
2
0
0
2
1
1
2
0
2
0
0
0
0
0
0
0
2
0
0
1
0
2
2
3
1
0
0
0
1
0
1
0
2
0
0
0
0
0
4
0
1
1
0
0
0
1
0
0
0
0
4
0
0
0
0
2
0
0
1
1
1
0
1
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
2
0
1
0
0
0
1
0
2
0
0
2
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
1
2
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
2
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
1
1
1
1
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
2
2
0
1
0
0
0
0
0
2
1
2
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
2
2
0
0
0
2
1
0
4
0
0
0
0
2
0
2
0
0
2
0
0
0
0
1
0
0
0
1
2
1
0
0
0
0
0
0
3
0
1
0
0
0
2
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
2
0
7
1
2
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
11
0
0
0
0
0
0
0
1
2
2
0
0
0
5
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
1
0
0
2
0
0
2
1
1
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
2
0
1
2
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
2
2
1
1
0
1
0
5
0
0
2
2
0
2
0
0
1
0
0
0
0
2
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
2
1
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
3
0
2
1
0
3
0
0
0
2
5
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
2
0
0
0
0
0
2
1
0
2
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
1
2
1
0
2
2
1
2
0
2
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
2
0
0
1
1
0
0
0
1
2
0
0
0
0
0
3
2
0
0
2
0
2
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
2
0
0
0
0
0
0
0
1
0
1
2
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
2
0
2
0
1
0
0
0
1
0
0
0
2
3
0
0
0
0
0
0
1
2
0
1
0
2
0
0
0
0
0
2
0
0
1
0
0
0
6
0
0
0
0
2
0
0
1
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
2
0
4
0
0
0
1
1
0
0
0
0
1
0
3
0
2
1
0
0
1
0
0
0
2
0
0
0
0
0
2
0
2
0
0
1
2
0
0
0
0
0
1
0
0
3
2
0
1
0
0
0
2
1
0
2
0
1
0
0
0
0
0
2
0
1
0
1
2
1
0
1
0
0
1
0
2
0
0
2
0
0
1
0
0
0
2
0
0
0
0
1
3
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
1
2
0
0
1
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
4
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
2
2
2
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
3
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
2
1
0
2
0
0
0
0
0
0
0
1
1
2
0
0
1
0
0
0
0
0
0
0
1
2
2
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
2
0
2
0
2
1
0
2
4
1
1
0
1
0
0
0
0
0
0
1
0
1
0
1
1
2
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
2
0
2
0
0
2
2
0
0
4
2
0
0
1
2
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
1
2
2
0
2
2
0
0
1
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
3
2
4
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
1
2
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
2
0
1
0
2
0
0
0
1
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
1
1
3
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
3
0
0
0
0
1
0
2
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
1
0
0
0
1
2
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
1
0
0
2
0
2
2
0
0
3
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
2
2
0
0
0
7
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
2
2
3
0
0
3
1
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
2
4
0
0
0
0
0
2
0
0
0
2
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
1
2
0
0
0
0
1
0
0
0
1
0
1
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
2
1
0
0
0
2
2
0
0
0
0
0
3
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
2
1
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
3
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
5
0
0
0
1
0
2
0
0
1
0
2
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
2
0
1
2
0
2
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
1
1
2
0
0
2
0
0
1
1
0
2
2
0
0
1
0
0
0
0
0
1
0
0
0
0
1
2
1
0
1
1
2
0
1
0
1
0
2
1
0
0
1
0
2
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
1
1
0
1
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
1
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
2
0
3
0
0
0
2
1
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
2
2
3
2
1
0
0
1
0
1
0
2
3
0
0
0
0
0
0
1
0
1
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
3
1
0
0
0
0
2
2
2
0
0
0
3
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
1
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
0
1
2
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
1
1
2
0
2
2
0
0
3
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
1
3
0
0
1
0
2
0
0
0
2
0
0
3
1
0
2
0
0
1
1
0
1
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
2
1
0
1
0
0
0
0
1
0
1
0
1
0
1
0
2
0
1
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
1
3
0
3
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
2
0
0
1
0
0
0
1
1
1
0
0
0
0
1
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
3
0
0
0
0
0
2
0
0
0
0
2
2
1
1
0
0
1
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
2
0
0
0
0
0
1
1
3
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
2
2
0
2
0
0
4
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
2
2
0
0
0
1
3
0
4
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
1
0
0
0
1
2
0
2
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
1
1
3
0
0
0
0
2
2
0
0
0
2
0
0
0
2
0
1
1
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
2
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
1
0
1
0
0
0
0
1
0
1
0
2
1
0
2
1
1
0
0
2
0
0
0
1
1
0
2
6
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
1
0
0
0
0
0
2
0
1
0
0
2
0
0
2
0
0
0
0
3
1
2
3
0
2
0
0
0
0
0
2
2
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
2
2
0
2
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
3
0
0
1
0
2
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
1
0
0
0
2
0
1
0
0
0
1
0
0
0
1
0
2
0
2
2
1
1
1
0
0
0
0
0
2
0
0
1
1
0
0
1
0
0
2
2
1
1
1
0
2
2
0
0
0
0
0
0
0
4
1
0
0
2
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
1
0
2
0
0
1
0
0
0
0
2
2
0
1
1
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
1
2
1
0
0
0
0
1
0
1
1
0
1
0
0
2
0
3
5
3
0
0
0
0
0
0
2
0
2
1
0
2
2
2
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
2
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
1
1
2
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
2
0
0
1
0
0
0
6
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
1
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
1
3
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
3
2
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
2
0
2
0
0
0
1
1
0
0
0
0
0
0
1
2
0
0
0
1
0
5
0
0
0
0
1
0
0
0
0
2
0
0
2
1
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
2
0
0
1
2
2
0
0
0
0
2
0
2
2
0
0
0
4
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
2
0
0
1
0
0
0
0
1
1
2
1
0
0
2
0
2
0
1
0
2
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
2
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
2
1
0
0
2
0
0
0
0
2
0
2
0
0
2
0
2
0
0
0
0
0
0
0
1
2
3
0
0
1
0
0
1
3
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
2
2
0
2
0
1
0
0
2
4
1
3
0
0
1
0
1
1
2
0
0
0
0
3
0
1
0
0
2
0
0
0
1
1
0
2
0
0
2
0
1
0
1
2
0
0
0
1
0
0
1
1
0
0
2
2
0
1
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
6
0
2
0
0
2
0
1
0
1
0
1
2
1
1
1
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
1
0
2
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
3
0
2
0
0
0
1
0
0
0
1
2
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
1
1
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
1
2
0
0
0
0
2
1
3
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
2
2
0
0
0
0
0
2
1
1
2
0
0
1
0
0
0
1
0
0
0
0
0
4
0
0
0
0
2
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
1
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
1
0
1
2
0
0
0
0
0
0
0
2
0
0
0
1
0
1
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
2
0
0
0
0
1
0
1
0
0
0
1
1
0
0
1
0
0
2
1
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
3
1
2
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
4
2
0
1
0
2
0
0
1
0
0
0
3
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
2
0
2
0
0
0
0
0
1
0
2
0
2
0
0
2
1
0
1
0
2
0
1
1
0
2
1
0
0
1
0
0
0
0
3
3
1
2
2
0
0
0
1
0
2
0
1
1
0
0
0
1
1
0
0
1
0
2
0
1
0
0
1
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
2
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
2
0
0
1
0
0
2
2
0
0
0
0
1
0
4
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
2
1
1
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
1
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
2
1
2
1
0
0
0
0
2
0
1
0
1
0
0
0
0
1
2
0
1
0
0
0
0
0
0
2
0
0
0
1
0
1
3
0
0
0
2
2
0
0
0
1
0
0
1
0
2
2
0
0
0
2
1
2
0
1
0
0
2
1
0
1
0
0
1
1
2
1
4
0
1
2
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
8
2
2
0
1
0
3
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
1
0
0
0
0
2
0
2
0
1
1
0
0
0
2
0
0
1
2
1
1
0
1
0
1
0
0
0
1
0
0
0
1
2
0
0
0
0
0
2
1
0
2
0
0
2
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
2
0
0
0
1
0
0
1
1
0
0
0
0
2
1
1
1
0
0
2
1
0
0
4
0
2
0
0
0
1
0
0
0
1
2
0
0
0
0
2
1
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
1
0
3
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
1
3
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
3
1
0
0
0
0
0
2
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
1
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
3
3
0
0
2
0
0
0
2
0
1
1
0
0
2
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
3
0
0
0
1
0
0
3
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
2
2
2
0
2
1
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
1
2
0
4
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
2
3
2
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
1
3
0
0
0
0
2
0
1
0
0
1
0
0
0
0
1
2
0
1
4
0
0
2
0
1
2
0
0
4
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
1
2
0
0
0
1
0
2
0
0
0
0
1
2
2
0
2
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
1
0
1
0
1
0
0
0
1
0
3
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
1
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
2
2
0
0
0
0
0
0
2
0
2
1
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
1
1
0
0
0
0
0
2
2
4
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
3
1
0
0
0
0
1
0
0
0
1
0
2
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
2
1
1
0
2
0
0
1
0
2
0
0
0
0
3
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
1
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
8
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
2
2
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
2
0
0
0
1
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
1
0
0
0
0
2
0
3
0
1
0
0
0
1
0
0
0
2
1
0
0
1
0
0
0
3
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
3
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
3
0
0
1
1
0
0
0
0
1
2
0
0
0
2
2
0
0
1
0
0
0
0
1
0
0
0
0
0
3
1
0
0
0
2
2
2
2
0
0
1
0
2
0
0
0
1
0
2
1
1
1
0
0
0
2
0
0
1
0
0
0
0
0
6
2
2
0
0
2
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
2
0
0
2
2
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
1
1
2
1
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
1
2
1
0
0
0
3
0
0
2
0
1
0
0
3
0
0
0
1
2
0
1
0
0
2
0
8
0
0
0
0
1
2
0
2
0
0
5
0
0
0
0
0
0
0
0
0
2
0
2
1
1
0
3
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
2
0
0
0
1
2
0
0
3
1
3
2
1
0
0
0
0
0
0
2
0
0
1
0
0
2
2
0
0
0
2
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
2
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
2
0
0
0
2
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
2
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
2
0
0
0
1
0
1
1
2
2
0
1
2
1
0
0
0
0
0
0
0
0
0
2
2
2
0
0
4
2
2
0
2
0
0
0
0
2
2
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
1
1
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
2
2
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
2
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
1
1
2
0
1
0
0
0
0
0
2
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
2
2
1
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
4
0
2
0
0
0
1
0
0
1
2
3
2
1
0
2
0
0
0
0
1
0
1
0
0
1
3
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
2
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
2
0
1
2
0
2
1
0
1
0
1
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
1
2
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
2
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
2
0
0
2
1
0
1
0
0
0
0
0
0
0
1
6
0
0
0
0
0
0
0
1
1
0
2
0
0
1
0
1
2
1
2
0
1
2
0
1
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
1
3
2
9
0
0
0
1
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
1
0
0
2
0
0
3
0
0
0
2
1
0
2
0
0
3
1
0
0
1
0
0
0
0
2
1
0
0
0
0
0
1
0
3
1
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
2
0
2
0
3
2
1
0
1
0
0
0
0
2
0
2
2
0
0
1
0
0
0
3
0
0
1
0
0
1
2
0
2
0
2
0
0
0
0
0
2
1
0
0
0
0
0
1
3
0
1
0
0
1
0
1
0
0
2
0
0
0
0
1
2
1
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
2
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
1
0
1
0
0
2
0
1
0
0
0
0
0
3
0
0
2
0
0
0
1
2
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
1
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
3
0
2
0
0
0
1
0
2
1
0
0
0
2
0
0
1
2
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
1
1
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
3
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
1
2
1
2
2
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
13
0
0
1
0
1
0
1
1
0
2
0
0
0
1
2
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
2
0
1
0
7
0
0
3
2
0
2
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
1
0
1
0
2
2
0
0
0
1
1
0
0
0
0
0
0
0
2
2
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
2
0
0
2
0
1
0
1
0
0
0
0
0
2
0
0
0
0
2
2
1
0
0
0
0
0
1
0
1
0
1
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
1
1
0
0
2
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
3
0
0
0
2
0
0
1
0
0
0
0
1
1
1
0
1
5
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
7
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
1
0
0
0
0
0
0
3
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
2
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
7
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
1
0
3
1
0
0
1
3
1
0
0
1
1
0
0
1
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
7
0
0
2
0
0
1
0
0
0
5
0
0
0
0
0
0
0
0
1
2
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
2
1
0
0
0
0
0
1
5
2
2
1
1
2
0
0
0
1
0
0
1
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
1
3
1
2
0
0
1
2
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
2
2
1
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
5
0
0
0
0
0
2
1
2
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
4
1
2
0
0
0
0
1
0
0
0
0
2
2
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
2
2
0
0
0
0
0
1
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
1
1
3
0
1
0
1
0
0
1
0
0
0
2
2
0
0
3
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
1
0
1
0
0
3
2
2
1
1
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
3
0
0
1
0
0
0
0
0
0
0
2
1
2
0
0
0
2
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
2
0
2
0
0
0
1
1
1
0
0
0
0
1
0
0
0
2
0
0
2
2
0
2
0
2
0
0
1
2
0
2
0
0
0
2
2
0
3
0
0
2
1
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
1
0
1
0
1
2
0
1
0
0
1
4
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
3
0
0
1
1
0
0
0
2
0
2
0
0
1
0
0
0
2
0
2
4
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
12
4
1
2
1
7
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
2
0
0
0
0
2
0
0
1
0
1
0
0
2
0
0
0
0
0
3
0
0
0
0
1
0
1
0
0
1
0
1
2
0
0
1
0
1
0
0
1
0
0
0
2
0
2
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
3
0
0
0
1
0
0
1
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
2
0
3
0
0
0
8
0
0
2
0
0
3
2
0
0
0
2
0
0
2
2
0
2
0
0
0
2
0
0
0
1
0
1
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
2
2
1
2
0
0
1
2
0
1
0
0
0
0
0
0
0
4
2
0
1
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
2
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
2
0
0
1
0
1
1
0
2
0
0
0
2
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
2
0
1
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
3
0
2
0
2
0
1
2
0
0
2
1
2
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
4
0
0
1
0
2
0
0
0
2
0
0
4
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
3
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
2
2
0
0
0
0
0
0
2
0
2
1
1
0
0
2
0
2
2
0
0
0
2
0
0
0
3
0
2
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
1
1
0
2
0
0
2
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
1
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
5
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
3
2
0
1
0
0
0
2
1
0
0
0
0
0
0
3
0
0
1
0
0
0
0
1
0
0
1
0
1
2
0
1
0
1
0
0
0
1
0
2
0
0
2
0
2
0
1
0
2
1
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
2
0
0
0
0
0
4
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
1
2
0
0
1
0
2
1
0
2
0
2
1
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
5
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
1
2
0
1
0
2
0
0
0
0
0
2
1
0
2
0
0
0
0
1
1
0
0
0
0
2
2
0
1
0
0
0
2
2
0
0
1
0
0
2
1
0
2
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
2
2
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
2
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
2
1
0
0
0
3
2
0
1
3
2
0
1
0
0
0
0
0
1
0
0
2
0
2
0
1
2
2
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
2
0
0
0
0
0
0
2
0
3
1
0
0
0
0
2
1
0
0
0
0
1
0
0
3
2
0
0
0
0
2
2
0
3
0
2
0
1
0
1
0
0
0
2
0
1
1
2
0
1
0
0
0
0
1
0
2
0
1
2
1
2
0
1
0
0
2
0
0
2
2
0
0
1
1
1
0
2
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
2
2
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
1
2
0
2
0
0
0
1
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
3
0
2
0
0
1
0
0
0
1
0
0
0
0
1
2
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
2
2
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
4
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
1
2
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
2
1
0
4
1
0
2
0
0
0
0
0
1
0
0
2
1
0
0
2
0
0
0
0
0
0
0
2
0
0
1
4
0
2
0
0
0
2
0
3
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
11
0
0
2
0
5
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
3
2
0
0
2
1
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
3
0
2
0
0
1
0
2
1
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
3
0
2
2
0
0
0
0
0
0
1
0
0
0
2
1
2
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
1
0
2
1
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
2
3
0
0
0
0
5
0
0
3
2
0
0
1
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
2
3
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
2
2
1
0
0
2
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
1
4
0
0
1
2
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
5
2
0
2
1
0
3
2
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
4
0
0
1
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
2
2
0
1
0
2
0
0
0
0
0
0
0
1
0
0
3
0
0
2
1
2
0
1
0
0
0
1
0
2
2
1
0
0
4
0
0
1
0
1
0
1
0
2
1
0
0
2
0
2
0
0
0
1
0
0
2
0
0
2
0
0
0
2
2
2
0
0
1
0
0
0
2
0
0
1
0
2
1
0
0
0
1
0
1
0
0
2
2
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
8
0
1
0
0
0
2
2
0
0
2
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
2
1
0
2
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
2
0
2
0
0
1
2
0
0
0
2
0
2
0
0
1
2
1
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
1
5
0
1
0
2
0
0
0
2
0
0
0
0
1
1
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
1
3
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
4
1
1
2
0
0
0
2
0
0
0
0
1
0
0
3
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
2
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
2
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
1
0
0
0
5
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
3
0
2
1
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
2
1
3
1
0
0
2
1
0
1
0
0
2
0
1
0
1
3
0
2
0
1
0
1
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
3
0
0
3
1
2
2
2
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
1
0
0
0
1
2
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
6
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
2
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
1
0
0
0
2
0
1
0
0
0
0
0
3
0
0
1
0
0
1
0
2
0
0
0
0
1
0
2
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
4
0
0
0
0
1
1
0
0
1
0
0
1
2
0
0
0
0
0
4
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
1
1
2
0
0
1
0
1
2
0
3
0
5
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
2
0
1
2
1
0
2
3
3
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
1
1
0
0
2
0
2
0
0
0
1
0
0
2
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
5
0
0
1
2
1
0
2
0
1
1
0
1
0
2
1
2
1
0
0
0
2
0
0
0
0
0
0
0
0
3
2
0
0
0
1
0
1
0
1
2
0
0
0
0
0
2
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
2
0
2
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
1
3
2
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
1
0
1
0
3
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
2
0
0
2
3
0
0
2
1
0
0
2
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
2
7
0
1
0
0
0
0
0
0
1
0
4
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
2
0
3
2
0
4
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
2
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
4
2
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
2
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
1
0
1
0
0
0
2
0
0
0
1
2
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
2
1
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
3
0
1
0
0
0
0
0
0
0
2
0
0
2
1
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
2
1
2
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
2
1
0
0
0
2
0
2
2
0
3
1
2
1
0
0
1
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
2
0
1
2
0
0
0
1
0
0
0
2
1
2
0
0
0
2
1
1
1
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
1
2
1
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
3
0
3
0
0
1
0
2
0
2
0
0
0
1
0
0
0
1
0
0
0
0
1
2
0
0
1
0
0
0
0
1
1
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
2
2
0
2
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
2
0
0
1
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
4
1
0
1
0
0
1
0
2
2
0
0
0
0
0
0
0
1
0
1
0
2
3
1
2
0
0
0
0
0
3
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
2
0
2
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
5
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
1
0
1
1
0
0
3
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
1
0
0
2
0
0
1
2
1
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
1
1
2
2
2
1
0
0
2
0
0
1
0
3
2
0
1
1
2
0
0
0
0
0
2
0
2
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
2
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
1
3
2
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
4
2
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
7
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
2
2
0
7
1
1
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
1
0
0
1
0
0
0
0
0
3
2
0
0
0
0
0
1
0
2
1
2
0
1
0
2
0
1
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
5
0
0
0
2
1
0
0
0
0
2
0
0
2
0
3
0
0
0
1
0
1
0
0
0
0
2
0
2
0
1
0
0
3
0
0
0
0
0
0
0
0
1
1
0
0
0
1
3
3
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
2
1
0
0
0
2
0
0
1
0
0
0
0
0
1
0
2
0
0
0
1
0
2
0
2
0
0
2
0
0
0
1
1
0
0
1
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
1
2
0
2
0
0
1
1
2
0
1
0
0
0
0
1
2
3
0
2
0
1
0
0
0
1
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
2
1
0
0
0
0
0
0
0
0
1
3
3
2
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
1
4
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
3
0
0
1
0
1
1
1
2
0
0
0
1
0
0
0
0
2
0
1
0
0
0
2
0
0
1
0
1
1
0
2
0
0
5
0
0
1
1
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
1
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
4
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
2
2
0
0
0
0
0
0
0
2
0
0
0
1
1
0
2
0
2
0
2
0
0
2
0
0
0
0
0
2
2
0
0
1
2
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
2
0
0
2
1
1
0
0
0
0
0
2
1
1
0
0
1
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
2
2
0
0
0
0
2
1
0
1
1
0
0
0
2
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
2
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
1
1
0
1
2
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
2
0
1
0
0
1
2
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
2
1
0
2
1
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
2
0
0
0
1
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
1
1
1
6
0
0
0
1
0
0
0
0
0
0
0
1
2
1
1
0
2
0
0
1
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
1
0
1
0
2
0
2
0
0
0
3
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
1
0
0
0
1
0
0
0
0
0
0
1
1
2
0
0
1
0
1
3
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
1
0
2
0
1
0
0
0
0
5
0
1
0
0
1
0
0
0
1
1
0
0
0
4
0
2
0
1
0
0
0
2
2
0
2
0
0
0
2
0
1
2
0
0
0
0
0
0
2
1
0
1
2
0
0
0
2
0
0
0
0
0
0
0
2
1
0
1
1
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
1
2
2
0
0
2
2
2
0
0
0
1
0
2
2
0
2
0
2
0
0
0
2
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
2
0
0
0
1
2
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
3
0
0
0
0
0
0
0
0
1
1
2
2
0
0
0
1
0
0
0
2
0
0
0
6
1
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
1
0
0
0
2
0
0
0
0
0
0
3
0
1
0
0
1
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
2
1
0
0
0
0
0
0
0
0
1
0
0
1
2
1
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
2
0
2
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
2
0
0
1
3
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
4
0
2
0
0
0
3
0
0
2
0
0
2
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
3
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
2
1
2
0
1
0
0
2
2
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
1
0
3
2
0
0
0
0
0
0
0
1
4
1
1
0
2
0
0
0
0
0
2
0
0
0
2
1
1
1
0
0
1
0
2
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
2
1
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
4
0
2
0
0
0
1
0
1
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
5
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
2
2
0
0
0
0
2
0
0
1
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
2
0
5
0
2
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
6
0
0
0
1
2
0
2
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
2
2
0
2
0
0
0
0
0
0
1
1
1
0
1
2
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
4
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
2
0
0
2
1
19
0
0
0
2
0
0
0
2
0
0
0
0
2
0
2
1
0
0
0
0
2
3
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
2
2
0
0
2
0
0
0
0
2
0
1
0
0
2
0
1
0
2
0
2
2
0
0
1
1
0
2
1
0
1
4
0
0
2
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
2
1
0
1
0
2
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
2
1
2
0
0
0
1
3
0
0
0
0
1
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
2
2
0
0
0
2
2
2
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
1
0
0
0
0
1
2
0
2
2
0
0
0
0
0
0
0
0
2
0
0
2
0
3
0
2
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
4
1
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
2
0
3
2
0
0
1
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
2
1
0
1
0
0
0
0
0
0
0
0
1
0
0
2
2
1
1
0
0
0
2
0
2
2
0
0
3
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
1
2
0
2
1
0
2
0
0
2
2
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
3
0
0
0
2
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
2
3
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
1
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
4
0
1
2
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
2
2
1
0
0
1
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
2
5
1
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
1
0
0
4
0
1
1
2
0
0
0
0
0
0
0
0
0
2
0
0
2
1
2
0
0
1
0
0
0
2
0
0
0
0
0
1
0
1
0
0
1
0
0
2
0
1
0
0
2
0
0
0
0
1
2
0
2
0
0
1
2
0
1
2
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
2
0
1
1
1
0
0
0
2
0
0
2
0
2
1
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
2
2
2
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
2
0
2
0
1
0
1
0
2
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
2
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
1
0
2
0
0
0
0
0
0
2
3
0
0
0
0
0
0
2
0
1
0
0
0
1
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
3
0
0
1
2
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
2
0
0
0
2
2
0
0
2
0
1
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
1
0
2
1
0
3
0
0
1
0
0
0
0
2
0
2
1
0
2
1
0
0
0
0
1
2
0
0
0
0
0
0
1
1
2
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
1
5
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
3
1
4
0
0
0
0
0
0
0
1
0
0
2
0
0
0
3
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
6
0
0
0
1
0
0
1
0
0
0
2
2
0
0
1
0
0
2
0
0
0
1
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
2
0
1
2
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
3
2
1
0
0
1
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
2
2
0
1
0
0
2
0
0
1
0
3
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
2
2
0
0
0
2
0
0
2
1
0
0
0
0
1
0
2
2
2
2
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
1
1
6
0
0
3
1
0
0
0
1
1
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
4
1
2
1
0
1
0
2
2
0
1
0
1
1
2
0
1
0
0
0
2
0
1
0
0
2
1
2
0
0
2
2
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
2
0
0
0
0
2
0
0
0
0
2
0
0
2
1
0
0
2
0
0
0
0
0
0
2
0
0
2
0
2
0
1
0
0
1
0
1
0
0
0
0
2
0
2
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
3
1
0
0
0
0
0
1
2
0
0
2
0
0
1
0
0
0
0
1
0
1
1
0
2
0
0
0
1
0
1
2
1
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
2
0
1
2
1
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
5
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
2
1
0
0
1
0
2
0
0
0
1
0
2
0
2
0
2
0
0
0
0
0
0
1
0
0
0
1
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
2
0
1
1
0
0
1
0
0
0
1
1
0
0
0
0
2
0
0
0
1
0
1
1
0
2
0
0
6
0
0
0
0
0
0
0
0
5
3
0
0
0
0
2
2
0
0
2
0
0
0
0
0
1
0
0
2
1
0
4
0
1
2
0
2
4
0
2
0
2
0
0
0
2
0
1
0
1
0
0
1
0
0
2
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
2
2
0
2
0
0
0
0
0
0
1
0
2
0
2
1
0
0
2
0
0
0
2
1
0
0
0
2
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
1
0
2
0
1
0
0
2
0
0
2
0
0
0
0
0
3
5
2
2
0
0
0
1
0
1
0
2
1
0
0
0
2
0
0
0
1
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
1
2
0
0
0
0
0
0
2
1
0
0
0
0
1
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
3
0
1
0
1
0
1
0
0
0
1
2
0
0
0
0
2
0
2
0
0
0
2
0
2
0
2
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
1
0
0
2
3
0
1
1
0
1
1
0
0
0
0
0
0
0
0
2
2
2
2
2
0
0
2
0
0
0
0
2
0
0
0
0
1
2
0
2
2
1
0
0
5
0
0
1
1
1
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
2
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
2
0
0
1
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
1
0
1
1
1
0
4
0
0
0
0
2
1
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
1
0
1
0
0
1
2
1
0
0
1
0
0
0
0
0
0
1
1
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
3
1
0
0
2
0
0
0
1
2
0
2
0
0
0
0
0
1
0
2
0
1
0
1
0
0
2
2
0
0
0
0
0
0
0
2
6
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
4
0
0
0
5
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
2
2
2
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
4
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
2
0
2
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
1
0
3
0
1
0
0
0
2
1
0
1
1
1
1
1
0
1
0
2
0
1
0
0
0
2
0
0
1
0
1
0
0
0
2
0
2
0
0
0
1
0
2
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
2
0
1
0
0
0
0
1
2
0
1
0
0
0
0
0
1
0
0
0
2
2
0
2
0
0
0
2
1
0
2
0
1
0
0
0
0
1
0
2
2
0
1
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
1
1
0
0
0
2
0
2
0
0
2
0
1
0
5
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
2
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
1
2
2
2
0
2
0
2
2
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
2
2
2
0
1
2
0
0
0
0
0
0
0
3
0
0
0
0
0
3
0
1
0
2
0
0
0
0
1
3
0
1
0
0
1
0
1
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
3
2
0
2
0
0
2
1
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
1
6
0
0
2
0
2
0
1
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
2
0
0
1
2
0
0
1
2
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
2
0
1
2
0
3
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
3
0
1
0
2
2
0
1
0
0
2
0
0
1
0
0
2
0
2
1
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
4
0
0
0
0
1
1
0
1
2
0
2
1
0
0
0
3
1
0
1
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
4
0
0
2
2
0
2
0
0
0
1
0
0
0
0
0
1
0
1
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
3
0
0
0
0
0
3
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
4
0
0
1
0
0
0
2
1
0
0
4
1
0
0
0
2
0
0
1
1
0
2
0
0
0
0
1
0
2
2
0
0
0
0
0
1
0
1
0
2
0
1
2
0
2
0
0
0
1
0
0
0
0
0
3
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
2
0
0
1
1
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
2
0
1
0
0
0
0
0
0
3
0
0
2
0
0
2
1
1
0
2
0
0
0
1
2
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
2
1
0
1
0
0
2
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
1
0
0
2
0
1
0
0
1
0
2
1
0
0
0
2
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
3
2
0
0
2
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
2
2
0
1
1
0
0
2
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
1
1
2
1
0
0
0
0
0
0
0
2
1
1
0
0
0
1
0
0
0
2
2
0
0
0
0
0
1
0
6
0
0
0
0
0
0
0
0
0
3
0
1
1
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
2
1
3
0
1
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
1
1
0
1
0
0
0
0
0
1
0
0
0
0
2
1
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
2
2
0
2
0
0
0
1
0
0
0
0
1
1
1
1
2
11
2
0
0
1
3
0
0
0
1
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
2
1
0
1
3
0
1
0
0
0
0
0
2
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
2
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
7
1
0
0
0
3
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
1
2
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
2
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
3
1
0
0
1
0
1
1
0
1
0
2
1
0
0
0
0
2
0
0
0
0
2
2
0
0
0
1
2
0
0
0
0
1
0
1
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
4
2
0
1
0
0
4
0
2
2
0
0
0
0
0
1
0
0
0
1
0
0
2
1
0
0
1
0
1
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
2
0
1
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
2
0
0
2
0
2
0
0
1
0
1
0
0
1
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
1
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
2
1
0
0
0
1
0
0
0
0
1
0
2
2
0
2
0
0
0
2
1
0
0
0
0
1
2
4
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
4
0
1
1
0
0
0
0
0
0
4
2
1
0
0
0
0
0
0
1
0
0
0
0
0
2
3
0
0
2
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
3
0
0
0
0
1
0
2
0
0
0
2
1
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
2
3
3
0
1
0
0
0
0
0
0
1
3
0
1
0
0
0
2
2
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
2
0
0
1
0
0
1
0
0
0
0
0
2
0
3
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
2
0
0
1
0
0
1
1
0
0
0
0
1
0
0
1
0
10
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
3
0
0
0
0
0
0
0
2
0
3
2
0
0
0
2
0
0
0
1
0
0
0
0
0
1
1
0
0
2
1
0
0
0
0
3
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
1
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
5
0
0
0
0
1
0
0
0
2
1
0
0
0
0
3
0
0
0
1
2
0
0
0
0
0
0
0
3
0
2
3
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
2
2
2
2
0
2
0
1
0
1
0
2
0
0
0
0
0
3
2
2
0
0
1
0
0
2
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
1
0
0
3
0
2
1
1
1
0
5
1
1
0
1
1
0
0
0
0
0
0
0
2
2
3
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
1
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
2
0
0
0
1
0
0
0
1
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
1
0
0
0
1
0
0
0
0
0
0
2
0
2
1
0
2
0
0
2
0
2
0
2
0
2
0
2
0
0
3
0
0
0
0
0
2
0
0
2
2
1
0
2
0
2
0
0
1
0
0
0
0
3
0
0
0
0
0
2
1
0
1
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
1
0
0
1
0
0
0
4
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
3
0
0
2
0
0
0
0
1
1
0
0
2
0
0
0
4
0
0
2
0
1
2
1
0
0
0
0
0
1
2
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
1
0
5
3
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
1
0
0
0
0
0
3
0
0
1
2
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
2
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
1
2
1
2
0
2
0
0
3
3
0
0
1
0
0
0
1
2
2
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
1
2
1
0
0
0
0
0
2
1
1
0
0
2
0
9
0
1
0
0
0
1
0
1
0
0
2
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
3
0
0
2
0
0
0
0
0
0
0
0
8
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
2
0
1
3
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
1
1
2
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
2
2
0
0
2
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
2
0
0
0
1
0
0
3
0
2
2
0
0
0
0
0
0
0
0
0
2
2
0
1
0
2
0
0
2
1
1
1
1
2
1
0
0
0
0
0
0
2
0
0
3
0
0
0
0
2
0
2
2
2
0
1
0
0
0
2
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
3
0
0
0
0
0
0
1
0
2
0
3
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
3
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
2
0
0
0
0
3
2
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
1
0
0
2
2
0
0
1
2
2
1
0
0
1
1
0
0
0
0
0
0
2
1
1
0
0
0
0
2
2
1
3
0
0
1
0
0
0
0
2
1
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
2
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
1
0
0
0
2
0
1
0
0
2
0
2
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
1
0
2
0
0
0
0
0
2
0
0
2
0
1
1
1
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
1
1
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
2
0
0
3
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
2
3
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
1
1
1
0
2
2
0
0
0
0
0
2
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
1
0
0
2
0
0
2
0
1
0
1
0
0
0
0
1
2
0
0
0
0
0
2
2
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
3
0
0
0
0
0
1
0
2
2
0
0
0
0
0
2
1
0
0
0
0
6
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
2
3
0
0
0
0
0
0
0
0
1
2
0
0
0
0
3
0
3
0
0
2
2
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
1
0
0
0
1
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
1
0
0
2
2
2
0
0
1
3
0
0
0
0
0
1
0
3
0
2
0
2
0
0
0
1
0
1
2
2
0
0
0
0
0
0
0
0
2
0
1
0
3
1
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
2
1
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
3
0
2
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
2
2
0
3
1
1
0
0
0
0
0
0
0
0
0
8
1
0
0
2
1
0
0
4
0
0
0
0
0
0
0
0
2
0
2
3
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
1
1
0
2
2
0
2
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
2
0
2
0
0
0
1
0
1
2
2
2
0
0
0
0
2
0
2
0
0
1
0
3
2
1
0
0
0
1
2
0
0
1
1
1
0
1
0
0
0
2
0
0
2
0
0
1
0
0
0
0
1
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
2
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
5
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
1
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
1
1
1
0
0
0
0
2
0
2
0
1
8
0
1
0
1
0
0
0
0
0
2
0
3
2
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
2
0
0
3
0
0
2
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
3
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
2
2
2
0
0
1
3
0
1
2
0
1
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
2
1
1
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
1
0
0
0
1
0
1
1
1
2
0
1
1
1
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
4
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
1
0
2
0
1
0
0
0
0
1
0
0
0
0
0
2
2
0
2
0
0
2
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
8
0
0
0
1
1
1
0
0
0
0
1
2
0
0
0
0
0
0
1
2
0
2
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
3
0
1
0
0
3
1
0
0
0
0
0
1
0
1
0
0
2
1
3
1
0
1
0
0
0
3
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
4
0
0
1
2
0
1
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
1
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
2
1
0
2
2
0
1
0
0
0
3
1
1
2
0
2
0
1
0
0
0
2
0
0
2
0
0
0
3
2
1
0
0
0
0
1
0
0
2
0
2
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
2
0
2
1
0
0
4
0
1
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
2
1
0
0
1
0
0
0
2
0
1
0
1
0
0
0
0
0
0
1
0
0
2
0
0
3
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
2
0
0
0
1
0
0
0
1
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
2
0
0
0
2
1
0
0
2
2
0
0
0
0
1
0
2
2
0
0
1
0
2
2
0
1
0
1
1
0
0
0
1
0
1
2
0
0
2
0
0
0
3
0
0
0
0
0
2
0
0
6
1
0
2
0
0
0
0
0
0
0
0
0
0
6
1
0
0
0
0
2
0
1
2
0
0
0
0
0
1
4
2
2
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
1
0
0
0
0
1
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
1
2
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
1
0
0
2
0
0
0
2
2
0
0
2
0
1
1
1
4
0
0
2
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
2
0
0
0
0
0
1
2
0
0
0
0
1
1
0
0
0
8
0
0
2
1
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
3
0
0
2
0
1
0
0
1
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
4
1
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
2
1
0
1
0
0
0
0
0
0
0
0
0
2
4
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
6
0
0
2
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
2
2
0
1
0
0
2
0
2
2
0
1
1
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
2
0
3
3
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
2
0
0
4
2
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
3
0
0
0
2
1
0
0
0
0
1
0
0
2
0
0
0
1
2
0
2
1
2
0
0
3
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
2
0
0
1
2
0
0
0
0
1
0
1
0
1
0
0
0
0
2
2
2
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
1
2
0
0
2
2
0
0
0
0
0
0
1
0
0
0
1
0
1
0
2
0
0
0
1
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
1
1
1
0
0
0
2
0
0
0
4
0
0
0
0
1
0
0
0
1
0
0
3
0
0
2
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
3
1
1
2
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
1
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
2
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
2
0
0
1
0
0
1
2
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
4
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
3
0
0
0
0
0
1
0
2
0
0
0
4
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
3
0
0
0
1
1
0
0
0
4
1
0
0
0
0
0
2
0
0
0
1
2
2
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
3
0
0
2
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
3
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
2
0
0
1
0
4
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
2
2
0
0
1
2
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
7
1
0
0
0
0
0
1
0
0
0
1
2
2
0
1
0
0
0
0
1
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
2
0
0
0
2
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
2
0
2
0
0
0
0
0
1
0
0
1
2
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
1
1
0
0
0
0
1
0
0
0
2
0
2
0
0
1
0
0
6
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
1
0
0
2
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
2
1
0
0
1
3
0
0
0
1
0
0
0
1
2
1
0
0
0
0
0
0
2
0
0
0
3
0
0
0
2
1
2
0
0
0
0
0
2
0
1
0
0
2
0
2
0
0
0
2
0
1
0
1
2
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
2
0
2
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
3
0
1
0
0
0
0
0
0
0
3
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
4
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
1
0
0
0
0
1
1
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
1
0
1
2
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
2
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
2
0
2
0
0
1
2
0
0
0
0
0
0
3
0
1
1
0
0
0
2
0
0
1
4
0
2
1
0
0
0
0
0
0
0
0
1
2
1
1
0
1
0
0
0
0
0
0
2
1
0
1
0
0
0
2
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
2
0
1
2
0
2
0
0
0
2
0
0
1
1
0
0
1
1
0
1
0
0
2
2
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
1
0
0
0
0
0
1
3
1
0
0
1
0
0
1
1
0
1
1
0
0
0
0
2
0
0
0
1
0
0
1
0
3
0
0
0
0
1
0
0
0
0
0
2
0
1
0
1
5
2
0
1
0
1
0
2
2
0
0
1
2
2
1
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
3
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
5
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
3
0
0
0
1
0
0
0
0
1
3
0
4
3
3
0
0
2
2
0
0
0
0
0
0
2
0
0
0
4
0
1
0
2
0
0
0
3
0
0
1
0
0
0
0
0
1
0
0
2
0
0
2
2
1
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
2
0
0
0
0
2
1
0
0
0
0
2
0
0
0
1
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
1
1
2
3
0
0
0
0
0
0
2
2
0
0
1
0
0
2
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
2
1
2
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
2
2
2
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
2
2
1
0
2
1
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
2
2
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
1
0
0
0
0
0
1
0
0
2
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
2
0
0
0
0
3
0
0
0
0
0
2
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
2
2
0
0
1
2
1
0
0
3
2
2
0
1
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
1
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
2
0
0
0
1
0
0
2
0
1
0
0
1
0
0
0
0
0
4
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
1
0
0
1
1
0
1
0
0
2
2
2
0
0
0
1
0
0
0
0
2
1
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
1
1
0
1
2
0
2
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
1
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
2
0
2
1
2
0
2
0
0
0
3
0
0
7
2
0
1
0
1
0
0
0
3
0
0
1
0
1
0
0
1
0
0
0
0
0
1
1
1
0
0
1
0
0
0
3
0
0
2
1
0
0
2
1
0
0
0
0
1
1
2
0
0
2
1
2
0
1
0
0
1
0
6
0
0
0
2
0
0
0
0
1
0
0
0
0
3
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
1
0
0
2
0
0
0
2
0
1
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
2
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
1
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
2
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
1
1
0
0
1
2
0
0
0
0
0
0
0
1
2
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
1
0
1
0
0
0
2
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
2
2
1
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
2
3
2
2
1
0
0
0
0
2
0
0
1
2
1
0
1
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
1
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
2
2
2
0
0
0
0
0
0
1
1
0
0
0
2
0
1
0
1
2
0
0
0
0
2
1
1
0
0
0
1
0
0
2
4
0
0
2
2
1
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
2
1
0
0
0
2
0
0
0
6
0
1
0
0
0
1
0
0
2
0
0
0
0
1
1
0
1
2
0
0
0
0
2
0
1
0
0
2
4
0
1
0
0
0
0
0
0
1
0
2
0
0
0
2
1
0
0
0
1
2
1
0
1
0
0
2
1
2
2
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
2
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
2
3
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
4
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
1
2
0
1
1
0
2
1
0
2
0
1
2
0
0
0
2
0
0
2
0
0
1
0
2
0
0
1
0
0
0
2
0
0
2
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
2
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
3
0
0
2
0
0
0
0
0
0
2
0
4
2
0
2
1
0
2
1
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
1
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
4
1
0
0
7
0
0
1
0
0
0
0
2
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
2
0
2
0
1
0
0
0
16
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
2
0
0
2
2
1
0
0
0
0
0
1
0
0
2
0
0
1
0
3
1
2
0
2
0
0
0
1
0
2
0
0
1
0
2
0
0
0
1
3
0
0
0
1
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
3
0
0
0
0
0
0
0
0
1
0
0
0
5
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
6
2
2
0
0
0
1
2
0
0
0
2
0
0
0
0
1
1
1
0
0
0
0
0
2
0
0
0
3
1
2
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
1
0
0
0
0
0
2
0
2
2
2
0
3
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
1
0
0
1
1
2
0
0
1
2
0
1
0
0
0
1
0
0
0
0
0
0
2
0
1
0
2
2
2
0
0
1
0
0
0
1
0
0
1
2
0
2
2
1
0
7
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
3
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
1
2
0
1
0
2
1
2
0
0
0
0
0
2
1
0
5
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
2
2
0
0
0
0
1
0
0
1
0
2
3
0
0
0
0
0
0
0
2
1
0
6
0
0
0
1
0
0
1
1
2
4
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
2
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
1
1
0
0
0
0
2
1
2
2
0
1
2
0
2
0
0
0
1
0
0
1
5
0
0
0
0
0
0
0
1
3
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
2
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
1
0
0
0
2
3
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
2
0
0
0
1
1
0
0
0
0
0
0
2
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
8
0
1
0
0
0
0
0
2
0
3
0
1
0
0
3
1
0
0
0
0
0
0
2
0
4
1
0
2
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
3
3
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
3
2
0
0
0
2
0
0
0
0
1
1
1
0
0
2
1
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
2
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
2
0
1
2
1
0
5
0
0
1
2
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
2
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
2
2
1
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
2
0
0
2
0
0
2
1
0
0
2
0
0
0
2
0
0
2
0
0
0
5
0
0
0
0
3
0
2
0
0
0
0
0
0
2
0
0
2
3
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
3
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
2
1
0
1
0
1
0
9
1
0
3
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
1
2
0
0
1
0
0
1
0
0
0
1
0
0
0
3
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
1
0
2
1
2
0
0
0
0
1
0
0
2
2
0
0
2
0
2
0
0
0
2
0
3
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
2
0
1
0
2
0
0
2
2
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
3
0
0
0
1
2
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
2
1
0
1
2
0
0
1
0
0
1
0
1
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
2
2
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
3
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
1
0
2
0
0
0
0
0
0
2
0
0
1
2
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
12
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
1
2
1
0
0
0
2
0
0
1
0
1
2
0
2
0
1
0
0
2
2
0
1
0
2
0
0
0
1
2
0
0
0
2
1
1
0
1
0
0
7
0
0
0
1
0
3
0
0
0
2
2
0
2
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
3
0
2
0
0
1
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
2
1
0
0
0
0
1
3
0
0
0
1
0
1
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
1
2
1
1
0
0
0
0
2
1
0
0
2
0
0
2
1
0
1
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
3
0
1
2
0
0
0
0
2
0
0
0
2
0
0
1
2
0
0
0
0
0
1
1
1
0
2
0
0
0
0
0
0
0
2
0
0
1
0
3
0
2
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
3
1
1
0
1
0
0
0
0
2
0
0
0
0
0
1
3
0
1
0
1
0
0
1
2
0
0
0
0
0
2
0
0
2
0
2
0
0
0
1
0
0
2
0
0
0
0
0
2
0
1
0
0
0
2
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
1
0
0
2
1
1
0
0
0
0
1
0
2
1
0
1
0
0
0
0
0
1
0
1
1
0
0
1
2
0
0
1
5
0
0
0
1
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
2
4
1
1
0
0
3
0
2
0
0
0
0
0
0
2
1
0
2
1
0
0
2
1
0
2
1
0
0
0
0
0
0
0
0
0
1
0
4
1
0
0
0
1
1
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
3
2
2
0
1
2
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
2
1
0
0
0
2
0
3
0
0
0
0
1
2
0
0
1
0
0
0
2
0
0
0
1
0
2
0
0
2
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
2
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
1
0
0
11
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
2
0
2
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
3
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
6
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
2
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
4
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
2
0
2
0
0
2
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
1
1
0
0
0
0
0
1
0
1
2
2
1
0
0
0
0
0
0
0
0
2
0
2
1
0
0
1
0
0
0
0
0
4
0
2
0
0
1
0
0
0
0
0
0
1
0
0
1
2
0
0
1
0
0
2
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
2
3
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
2
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
1
0
2
0
2
0
0
0
0
0
0
5
0
0
1
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
3
0
2
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
2
2
2
0
0
0
0
2
3
0
0
0
0
0
0
0
0
1
2
2
0
2
2
0
0
1
0
3
0
2
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
2
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
1
3
0
0
0
0
0
1
1
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
2
1
0
0
0
0
0
0
0
2
0
2
0
0
3
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
1
0
2
0
0
0
0
0
2
1
0
1
0
0
2
0
0
0
3
0
0
0
0
0
3
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
4
0
2
2
1
0
0
0
2
0
2
0
0
0
0
0
0
7
2
1
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
3
0
1
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
1
1
2
2
2
1
0
0
0
0
2
0
0
1
0
0
0
0
0
1
1
2
0
0
0
0
4
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
2
0
1
0
0
2
0
2
0
0
0
1
1
4
1
0
2
0
0
2
1
2
0
0
0
0
2
0
0
0
0
0
3
5
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
2
0
0
0
2
0
0
4
2
0
0
3
0
0
0
0
3
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
2
0
2
1
0
1
0
2
0
2
2
0
0
2
0
0
2
0
0
2
2
0
1
3
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
3
0
0
1
0
2
0
0
2
0
0
0
1
3
3
0
0
1
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
1
1
2
1
2
0
2
0
1
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
2
0
1
2
0
0
2
0
0
2
1
0
0
0
0
0
0
1
3
0
2
0
0
0
2
0
5
0
0
0
2
0
0
0
0
0
0
0
0
1
0
3
2
2
2
0
0
1
0
0
2
1
0
0
0
0
0
2
2
0
0
2
0
0
1
0
0
0
0
0
0
1
0
2
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
2
0
2
0
2
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
2
2
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
2
0
1
1
2
0
2
0
0
0
1
0
3
0
1
0
1
0
1
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
2
2
1
0
0
0
0
1
0
0
0
1
0
0
2
0
1
2
1
0
0
0
2
1
1
0
0
0
1
0
2
0
1
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
4
2
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
2
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
1
1
0
0
0
0
0
2
0
1
2
1
0
1
0
0
2
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
2
0
0
0
2
0
0
3
0
0
0
2
2
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
15
0
0
0
2
2
0
0
1
2
0
2
1
4
0
0
0
0
0
0
0
0
1
3
0
0
0
1
0
0
1
1
1
1
4
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
4
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
1
0
2
2
0
0
1
0
1
3
5
0
0
2
0
2
0
0
0
2
0
0
2
0
0
0
0
1
0
1
0
0
1
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
2
0
0
1
0
0
1
0
0
2
0
0
2
0
0
0
0
0
2
1
0
0
0
0
5
2
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
1
0
3
0
6
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
2
2
0
0
0
0
2
1
0
0
2
0
0
0
0
1
0
0
2
2
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
2
0
2
1
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
1
2
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
1
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
3
1
0
0
0
0
0
0
0
0
4
0
0
0
0
1
2
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
2
2
0
1
0
0
0
0
0
0
1
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
1
0
0
0
1
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
1
0
1
4
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
1
2
0
2
0
0
0
0
1
2
0
2
0
0
0
0
0
2
1
2
0
2
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
2
0
1
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
2
0
1
0
0
0
2
0
0
1
0
0
0
1
0
2
0
0
1
0
0
1
0
0
2
0
1
0
0
2
0
5
0
2
0
0
0
0
1
1
2
0
0
0
1
0
0
0
2
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
2
3
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
1
2
0
0
0
0
1
0
0
0
1
1
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
1
1
0
0
0
1
0
2
2
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
2
0
0
2
2
0
1
1
0
0
0
5
2
0
1
0
0
1
0
0
0
0
0
0
3
2
0
0
1
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
2
1
0
0
0
0
2
0
0
1
0
0
2
2
2
2
0
0
0
0
0
0
0
0
0
1
0
0
4
0
1
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
1
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
9
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
2
0
1
0
0
0
0
0
1
1
1
2
1
2
5
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
2
0
2
1
0
1
0
0
0
2
2
1
0
0
2
0
0
0
0
0
2
0
0
3
0
2
2
0
2
2
2
0
0
0
0
1
0
0
0
2
0
0
1
0
1
1
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
1
0
1
0
0
3
0
0
1
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
3
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
1
0
3
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
2
0
0
0
0
1
0
0
2
0
0
2
0
2
0
0
1
0
2
0
0
1
1
1
0
1
0
1
1
0
1
2
0
0
0
0
0
0
1
0
2
0
0
2
0
0
3
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
1
1
0
4
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
1
0
0
0
1
2
5
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
7
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
2
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
1
0
2
0
0
1
1
2
0
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
2
1
0
0
2
0
0
2
2
1
0
4
2
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
3
0
3
0
1
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
5
1
0
0
0
1
0
0
0
2
0
0
1
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
2
1
0
0
0
1
2
1
4
0
0
2
2
1
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
6
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
4
0
0
0
2
0
0
1
2
0
0
0
0
1
1
0
0
0
0
0
2
2
0
0
0
1
1
2
0
0
0
1
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
1
0
2
0
1
0
0
2
0
0
1
1
1
0
0
0
2
2
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
1
0
0
1
0
0
0
0
1
2
0
2
0
2
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
2
2
0
0
0
1
0
0
0
1
1
1
0
0
1
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
2
1
0
2
0
3
0
0
0
1
0
3
0
2
0
0
10
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
2
0
1
0
0
0
0
0
2
1
1
2
1
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
2
1
0
0
0
0
0
0
1
0
1
2
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
3
0
1
7
0
0
1
2
3
0
0
0
1
1
0
0
2
0
0
0
0
1
0
0
0
3
2
2
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
2
0
2
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
5
0
0
1
0
2
0
0
4
2
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
3
0
0
0
0
0
0
2
1
0
0
2
0
0
2
0
0
0
0
2
0
2
0
0
0
1
0
3
1
0
0
0
0
1
2
1
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
1
0
0
0
1
2
0
0
0
0
1
0
1
0
2
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
1
2
2
2
0
1
0
1
0
0
3
0
2
2
0
2
3
0
0
0
0
1
0
0
1
0
0
0
2
1
2
0
0
0
0
0
2
0
1
2
0
2
0
0
0
0
0
0
2
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
1
0
2
1
0
0
1
0
0
0
0
0
1
1
0
0
0
3
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
2
2
0
0
2
0
1
0
3
1
0
0
0
0
0
0
0
1
0
0
2
2
1
0
0
0
0
0
1
0
2
1
2
0
2
2
2
8
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
3
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
5
0
0
0
0
0
0
2
3
0
1
1
1
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
2
0
0
1
2
0
1
1
0
0
2
0
0
0
2
0
2
0
1
0
0
0
1
0
1
0
1
2
0
0
0
0
0
0
0
0
0
4
2
0
2
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
1
1
3
0
0
0
0
0
2
0
1
2
1
0
1
0
0
0
0
0
0
0
1
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
2
1
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
1
0
1
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
2
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
2
0
3
1
1
2
0
0
0
0
7
0
1
0
0
0
1
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
1
1
2
0
2
0
0
2
0
0
0
0
0
1
2
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
7
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
1
0
1
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
3
0
0
0
1
0
1
0
1
3
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
2
0
0
0
2
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
4
2
0
2
0
0
0
0
0
0
0
1
3
0
0
0
1
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
2
1
0
2
0
0
0
0
2
0
3
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
2
0
2
1
0
0
0
1
0
0
0
0
1
0
2
6
0
0
1
2
0
0
0
0
4
0
2
0
0
0
0
0
1
2
0
0
1
0
2
1
0
1
0
1
1
0
0
0
0
2
0
0
5
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
4
0
0
2
0
0
1
3
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
3
1
0
0
0
0
1
0
0
0
0
3
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
1
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
1
1
0
1
0
0
2
1
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
2
2
0
0
1
0
2
0
0
2
0
0
1
0
0
2
0
1
1
0
0
0
0
0
2
1
1
1
1
0
0
0
0
1
0
2
0
2
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
1
2
1
0
0
0
0
0
0
1
1
1
0
0
0
1
1
5
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
4
1
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
3
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
1
2
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
1
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
1
0
0
0
2
0
1
1
0
1
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
1
0
0
1
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
2
1
2
1
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
2
0
0
0
1
1
0
0
2
1
1
1
0
0
0
2
1
0
1
0
2
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
1
1
0
3
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
2
1
0
2
0
0
0
1
0
0
0
0
0
2
4
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
1
0
1
0
0
0
2
2
0
1
1
0
1
0
0
0
1
0
0
1
2
0
0
0
0
1
0
1
1
0
0
0
1
0
0
1
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
1
2
0
0
0
0
2
1
1
0
2
0
3
0
0
0
0
0
0
0
0
3
0
4
0
0
2
0
1
0
0
1
0
0
0
2
0
0
0
3
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
2
1
0
1
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
1
2
0
1
0
0
0
1
0
2
0
0
2
0
0
0
2
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
1
0
3
0
0
1
0
0
0
0
0
3
1
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
2
1
1
2
2
1
0
0
0
2
0
0
0
0
2
0
0
2
2
2
1
0
0
1
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
1
0
0
3
0
2
1
0
1
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
1
1
3
0
2
0
0
0
0
2
0
0
2
1
0
2
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
3
1
0
0
2
0
2
0
1
2
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
2
0
1
4
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
2
0
0
2
0
1
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
1
0
0
1
2
1
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
3
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
1
0
2
0
0
1
0
0
0
4
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
2
1
0
0
1
1
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
3
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
1
0
2
0
1
0
0
1
2
0
1
1
2
0
0
0
2
0
2
0
2
0
0
1
0
0
1
4
0
0
3
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
1
0
0
3
2
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
1
1
1
0
1
3
0
0
0
1
0
0
3
0
0
1
0
0
2
0
0
0
2
0
1
0
0
0
0
2
0
2
1
0
0
1
0
0
1
3
0
0
0
0
0
0
0
0
1
1
2
0
3
0
3
0
0
1
2
1
0
1
2
2
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
5
0
3
0
0
2
0
0
0
0
1
0
1
0
1
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
3
0
0
2
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
3
2
0
0
0
0
0
0
0
0
1
0
0
2
0
2
3
0
0
2
0
6
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
2
0
2
0
1
0
1
0
0
0
0
0
0
2
0
0
2
0
0
4
2
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
3
1
0
0
0
0
1
2
0
2
0
1
1
0
0
4
2
0
0
0
1
0
0
0
1
0
0
3
1
0
0
2
1
0
0
0
1
0
0
3
2
1
1
0
2
0
0
2
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
3
0
0
0
0
2
1
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
1
0
0
1
2
0
0
0
0
0
1
2
3
0
1
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
1
0
2
0
1
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
4
1
2
0
0
1
3
0
1
2
0
1
1
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
1
0
0
3
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
1
0
2
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
3
2
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
3
1
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
2
1
1
0
1
0
2
0
0
2
0
2
0
0
2
0
2
2
0
0
0
2
2
0
2
0
0
0
0
2
3
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
1
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
3
0
2
0
0
0
1
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
1
2
0
0
0
0
1
0
0
0
1
2
0
0
0
2
3
0
0
0
0
0
0
0
0
0
1
2
1
0
0
1
0
1
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
3
0
2
1
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
4
0
1
0
0
1
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
2
2
0
0
1
0
0
0
1
1
0
0
1
0
0
0
1
2
2
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
2
1
2
0
0
0
0
0
0
1
0
1
0
2
0
1
2
0
0
0
0
0
0
3
0
2
3
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
2
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
1
0
2
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
4
2
0
0
0
1
0
0
0
0
1
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
2
0
1
0
0
2
0
0
1
0
3
0
0
4
0
1
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
2
0
1
0
1
1
1
0
0
2
1
0
0
2
3
0
0
0
0
0
2
2
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
2
1
0
0
0
2
2
0
0
0
2
0
0
0
0
1
1
1
0
0
1
2
0
0
0
1
1
2
0
0
0
0
1
0
0
1
2
1
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
2
0
1
1
0
0
2
0
0
0
0
0
0
3
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
2
0
0
1
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
1
2
0
0
1
0
4
0
0
1
0
1
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
2
2
0
1
0
0
0
0
0
2
1
0
0
1
2
0
0
0
0
1
0
0
0
0
3
0
2
0
1
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
1
1
2
0
0
0
0
0
2
0
2
0
2
2
0
0
0
2
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
2
0
1
0
0
0
0
2
0
1
0
0
1
2
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
1
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
1
0
1
2
0
2
1
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
1
0
1
2
0
0
2
5
0
2
0
0
1
0
0
0
0
0
0
0
0
4
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
1
0
1
0
1
0
2
1
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
2
0
2
0
0
0
0
4
2
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
1
0
0
0
4
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
2
0
1
0
1
0
0
0
0
6
0
0
0
0
1
0
2
2
0
0
0
0
0
0
2
1
0
2
0
0
1
2
2
0
0
1
1
0
2
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
2
0
2
1
2
0
2
0
0
0
0
0
0
0
3
0
2
0
1
2
0
1
0
1
0
0
0
1
3
0
0
1
0
0
0
0
0
0
2
0
2
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
3
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
2
0
0
2
0
0
0
2
2
0
0
0
0
1
0
2
0
2
0
2
0
0
0
0
0
0
0
2
0
2
1
0
2
0
2
2
1
0
2
2
0
2
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
2
0
2
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
1
0
0
0
2
0
0
3
0
0
0
3
0
3
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
2
1
1
1
2
0
0
0
2
0
2
0
0
0
2
1
0
2
0
0
4
0
2
1
3
0
0
1
0
1
1
0
2
1
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
2
2
0
0
0
0
0
0
0
0
1
2
0
1
2
2
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
2
2
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
1
0
2
2
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
2
0
2
0
0
0
1
0
0
1
1
1
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
2
2
0
0
0
2
0
0
0
1
2
0
0
0
0
2
0
0
0
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
0
1
3
0
0
3
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
1
0
2
0
1
0
3
2
0
0
2
0
0
1
1
0
2
0
1
1
0
0
0
0
1
0
0
2
1
0
2
1
0
0
0
0
2
0
0
1
2
1
0
0
0
0
1
0
2
0
0
0
0
5
0
4
0
0
2
6
1
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
1
3
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
2
0
1
0
0
0
0
2
4
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
1
3
0
0
0
3
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
2
2
2
1
0
2
0
0
1
0
0
0
0
0
0
2
1
2
3
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
3
0
1
0
1
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
1
2
2
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
2
1
2
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
1
0
1
0
0
1
0
0
0
0
1
0
1
0
1
2
0
1
2
2
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
3
0
0
2
0
0
1
2
1
1
0
0
0
0
0
1
2
5
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
1
0
0
0
1
2
3
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
2
0
2
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
1
0
0
2
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
2
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
3
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
2
0
0
0
0
1
0
0
1
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
3
0
0
0
0
0
3
1
0
1
0
0
5
2
2
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
1
0
0
0
1
1
2
0
0
2
0
0
0
3
0
1
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
2
2
0
2
0
0
0
0
1
0
2
0
2
0
2
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
2
0
2
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
1
2
0
2
0
0
0
0
0
0
0
2
2
0
0
0
3
0
1
2
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
2
1
0
0
3
1
0
0
2
2
0
0
0
0
1
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
2
2
2
0
0
1
2
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
1
3
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
2
3
0
0
0
0
0
0
1
0
5
0
1
0
0
2
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
1
0
0
1
1
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
1
1
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
2
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
1
2
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
1
2
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
2
0
0
0
1
0
1
2
1
1
0
0
0
2
2
0
0
0
0
0
0
2
4
0
2
2
0
0
0
0
2
2
0
0
1
2
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
2
0
0
0
0
2
2
0
0
1
0
0
0
0
0
3
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
3
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
1
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
2
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
4
3
0
0
0
1
0
1
1
2
0
0
0
1
1
0
0
0
0
1
0
0
0
0
2
0
2
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
1
2
0
0
1
0
0
1
5
0
0
0
1
0
0
2
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
2
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
2
1
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
2
1
0
1
0
0
1
0
0
0
2
0
0
0
0
2
1
3
0
2
2
0
0
0
0
0
1
0
2
2
0
0
0
0
2
3
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
1
0
1
1
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
2
1
1
0
0
2
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
5
0
0
0
3
0
1
2
0
1
0
0
0
0
2
0
0
3
2
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
1
0
0
0
0
0
3
0
0
3
0
1
0
0
0
0
0
0
0
0
2
0
0
2
3
2
0
0
0
0
2
0
0
1
0
2
0
0
1
1
0
1
0
2
1
2
0
0
0
0
1
0
0
2
1
0
0
2
0
2
0
1
0
0
0
0
0
1
0
2
0
0
1
0
1
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
3
0
0
2
0
1
0
1
2
0
2
0
0
1
2
2
0
0
2
2
0
0
0
2
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
1
2
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
3
0
1
2
1
0
0
0
0
0
0
1
2
3
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
2
0
0
0
0
3
0
1
1
1
0
0
2
3
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
3
2
0
0
0
0
0
0
1
1
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
1
0
1
2
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
1
0
1
0
0
0
0
0
1
0
4
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
1
0
0
0
0
0
0
1
2
0
0
2
0
1
0
3
2
0
1
1
1
0
0
1
0
0
0
1
0
0
2
0
1
0
3
1
0
1
0
0
0
2
0
2
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
1
0
0
0
4
0
1
0
0
0
0
0
4
1
0
0
2
2
0
0
1
1
0
0
1
0
0
0
0
1
2
0
0
1
0
0
0
0
0
2
1
0
0
0
0
2
0
1
0
0
1
0
0
8
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
2
0
1
0
0
0
0
1
0
0
0
0
0
2
2
1
2
4
1
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
2
2
0
0
0
0
0
1
1
1
0
1
0
0
2
1
0
3
0
1
0
0
0
1
2
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
0
0
4
2
0
0
0
0
1
0
3
0
1
0
1
1
0
0
1
1
2
0
2
2
0
1
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
2
1
3
0
1
0
2
0
0
0
0
0
2
0
2
0
2
2
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
1
0
0
1
2
0
0
2
1
0
0
0
0
0
0
2
2
0
2
1
2
0
0
0
2
0
0
0
0
2
0
1
0
1
2
3
0
0
1
1
0
0
2
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
1
1
2
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
2
0
0
0
4
1
2
0
0
0
2
0
0
3
0
0
2
0
0
0
1
0
1
2
0
0
0
0
0
0
2
0
1
0
0
0
1
2
2
0
4
4
2
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
1
0
1
0
1
2
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
2
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
1
1
0
2
0
0
0
0
1
1
0
0
2
3
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
1
2
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
3
0
0
1
0
0
1
1
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
3
2
5
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
2
0
0
0
0
0
0
2
0
1
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
4
0
1
3
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
2
1
0
0
0
2
0
0
0
1
1
1
2
0
0
1
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
1
0
2
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
1
1
0
0
0
0
0
0
1
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
3
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
3
0
0
0
2
6
0
0
0
1
2
0
1
0
0
0
0
1
0
0
0
0
2
0
0
5
3
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
1
0
1
0
1
0
0
0
9
0
0
0
1
0
0
0
0
0
5
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
2
2
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
2
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
2
0
0
0
2
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
1
0
0
1
0
1
0
0
0
1
0
3
0
0
1
0
3
0
1
0
0
0
0
2
0
2
1
3
0
1
0
0
2
1
0
3
0
0
3
0
0
0
1
0
2
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
2
1
0
2
0
0
0
2
0
0
0
0
1
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
2
2
0
0
1
1
2
0
2
0
1
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
3
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
3
0
1
0
0
1
0
0
0
0
0
0
1
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
2
0
2
0
0
0
0
1
0
0
0
0
0
1
0
2
1
1
0
2
0
0
0
0
2
1
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
2
0
0
1
0
1
0
2
0
0
0
0
0
2
3
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
2
0
0
1
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
2
2
0
0
0
1
0
2
1
0
0
1
0
1
0
2
0
0
0
0
0
1
1
0
0
2
1
0
2
0
2
0
0
2
0
0
0
0
1
0
0
0
2
3
1
0
0
0
0
0
0
4
0
0
1
2
0
0
1
0
0
2
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
7
0
0
3
0
0
2
0
0
1
2
1
0
0
7
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
11
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
1
1
0
2
2
0
0
0
0
0
1
2
0
0
0
0
0
3
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
2
2
3
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
5
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
5
1
0
2
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
1
3
1
0
1
0
2
0
1
0
0
0
0
2
1
2
0
3
1
0
0
2
0
0
0
0
0
0
2
0
0
0
3
0
0
0
1
0
0
1
2
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
1
2
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
2
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
2
1
0
1
7
0
0
0
0
4
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
3
1
1
0
0
0
2
0
0
0
0
1
0
0
2
1
2
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
2
0
0
0
1
2
0
0
0
0
1
0
0
2
1
0
2
0
1
0
2
0
1
0
0
0
0
0
2
0
0
0
0
2
1
2
0
0
0
1
0
2
0
0
0
1
0
1
1
2
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
3
2
0
1
0
0
1
1
0
2
1
0
2
0
0
1
0
0
0
0
0
1
4
0
0
2
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
1
0
2
0
0
0
2
0
0
1
0
0
0
0
2
1
1
2
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
2
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
2
1
2
0
0
0
0
0
0
0
0
0
3
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
5
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
2
2
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
3
3
1
2
1
1
0
0
0
0
0
0
2
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
2
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
2
2
0
0
0
2
1
0
2
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
3
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
2
0
2
2
3
3
2
0
1
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
3
0
0
2
1
2
0
0
2
0
1
0
0
0
0
0
1
0
2
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
2
2
1
0
0
0
0
5
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
1
0
2
0
0
0
0
5
0
2
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
1
1
0
2
0
0
2
1
0
1
1
1
1
0
0
0
0
2
1
1
0
0
0
0
0
0
3
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
1
2
0
0
0
0
0
3
0
2
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
7
2
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
2
0
0
0
0
0
0
1
0
0
0
3
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
2
3
0
0
0
0
1
2
2
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
2
0
2
2
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
2
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
2
1
3
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
3
0
0
2
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
5
0
2
2
2
0
1
2
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
2
0
2
0
0
0
0
0
8
0
0
3
0
0
0
0
2
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
1
0
0
0
0
0
0
1
0
0
2
0
0
2
2
0
1
0
0
0
0
1
1
2
2
0
0
1
2
1
3
0
0
0
0
1
0
0
0
1
2
0
0
0
1
2
1
2
2
0
0
0
1
0
0
0
0
0
2
0
1
2
0
0
2
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
2
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
1
0
4
0
0
2
0
1
1
0
1
2
0
2
0
2
0
1
0
0
0
0
0
0
0
1
1
0
0
0
2
1
7
0
0
0
0
0
1
0
1
1
2
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
2
2
0
0
1
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
3
0
1
0
0
0
0
1
0
0
1
0
0
0
0
2
1
0
0
0
2
0
0
2
0
0
0
2
0
0
0
2
0
3
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
2
1
0
0
2
0
0
0
1
2
2
0
0
3
1
0
1
0
0
0
0
1
0
0
0
2
2
0
4
0
1
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
1
2
2
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
2
3
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
1
0
1
0
2
0
0
0
0
0
2
0
0
0
0
1
2
0
0
1
1
0
1
0
0
1
1
0
0
2
1
0
0
1
0
0
0
0
0
0
2
0
3
0
0
1
0
0
1
0
1
0
1
0
0
1
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
2
2
0
0
2
0
0
0
1
0
3
0
0
1
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
1
0
2
0
0
0
0
3
1
0
0
2
1
0
3
0
0
1
0
0
0
1
0
2
0
1
0
2
0
2
0
0
0
1
1
0
0
0
0
1
0
1
0
2
0
0
0
2
2
1
2
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
2
0
0
0
0
1
4
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
2
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
2
3
0
1
1
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
1
0
0
2
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
2
0
0
2
1
1
0
0
0
1
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
1
0
0
2
0
0
1
0
6
0
0
0
0
2
1
0
1
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
2
2
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
2
1
0
0
1
0
2
0
0
6
1
0
0
0
0
0
2
0
0
0
1
0
0
2
1
0
0
0
2
0
0
0
1
1
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
2
0
0
2
0
0
1
1
0
0
0
0
2
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
3
0
2
1
0
0
1
1
0
0
0
1
1
0
0
2
1
0
0
1
0
0
1
0
2
0
2
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
2
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
2
0
2
0
0
0
0
0
1
0
0
1
2
2
0
0
1
2
3
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
1
0
0
0
0
0
2
3
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
1
1
0
2
1
0
0
0
0
2
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
1
2
0
0
2
0
0
0
0
0
0
1
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
3
1
0
0
2
0
0
2
3
0
0
0
0
0
2
0
2
0
0
0
2
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
3
0
0
0
0
0
0
0
2
5
0
2
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
2
1
2
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
2
0
4
0
0
4
0
2
0
0
0
2
0
2
3
0
0
0
3
2
0
0
2
0
0
0
0
2
0
0
1
0
1
0
0
1
1
1
2
0
2
1
0
3
0
2
0
0
0
2
0
0
0
1
2
0
6
0
2
0
0
2
0
0
0
0
0
2
2
2
2
1
2
0
0
0
1
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
1
3
0
0
0
0
0
1
0
0
2
0
0
0
1
0
1
0
2
0
0
0
0
4
0
0
2
0
0
2
2
1
0
0
0
0
1
2
2
0
0
2
0
1
0
0
0
0
0
0
1
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
9
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
1
0
0
0
3
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
2
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
1
0
2
1
0
0
2
0
0
0
0
0
0
0
1
0
1
2
0
0
1
0
0
0
1
0
3
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
2
0
2
0
0
0
0
3
0
3
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
2
2
0
1
0
2
0
2
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
1
1
2
2
1
0
0
0
3
0
2
1
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
2
0
1
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
2
0
2
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
3
0
0
1
2
0
0
2
0
2
3
0
0
2
0
0
2
1
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
3
0
0
0
3
0
0
0
0
0
1
0
1
1
1
1
1
0
0
1
0
2
0
0
0
0
0
0
0
1
0
8
2
2
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
1
0
1
0
0
2
2
0
0
0
0
0
1
0
1
0
0
1
0
4
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
2
0
0
3
0
0
0
0
2
1
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
1
2
2
6
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
1
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
4
0
0
0
1
0
2
0
1
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
2
1
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
2
0
0
1
0
0
0
0
0
0
2
1
0
0
2
1
5
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
2
0
3
0
3
2
0
0
0
6
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
2
2
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
2
1
0
0
2
0
2
0
0
0
0
0
0
2
1
1
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
1
0
1
1
2
1
0
0
0
0
1
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
3
0
0
2
0
1
0
0
1
4
0
0
0
0
0
0
2
0
0
1
0
0
0
3
3
0
0
0
0
0
1
2
0
2
0
0
0
0
0
1
0
3
0
0
5
0
2
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
2
1
0
0
0
0
1
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
4
2
0
0
2
0
0
1
0
7
0
0
1
0
4
1
1
0
0
0
0
0
0
1
2
1
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
2
0
0
0
2
1
2
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
3
0
0
0
0
0
3
3
0
1
0
0
0
0
0
3
0
0
1
0
2
2
0
2
0
1
2
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
9
0
0
0
0
0
0
0
0
0
4
2
0
0
0
0
0
0
0
0
2
1
0
2
0
1
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
3
0
0
0
0
0
1
0
3
0
0
1
0
0
2
2
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
2
2
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
5
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
2
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
6
0
0
0
0
0
0
2
0
1
2
2
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
1
0
1
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
1
2
0
0
1
0
0
2
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
3
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
2
1
0
2
0
0
0
0
2
0
0
1
1
0
0
2
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
2
2
2
0
0
0
0
2
0
0
1
0
2
0
1
0
0
0
0
2
2
0
0
1
1
0
0
1
0
0
0
1
0
2
0
1
0
0
1
1
0
1
2
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
2
1
0
0
0
2
0
1
0
0
1
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
2
1
0
1
1
1
0
0
0
2
0
0
0
0
0
4
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
2
0
0
0
2
1
2
0
2
0
1
1
0
0
0
0
0
2
2
0
0
7
0
2
0
1
0
2
0
0
1
0
1
0
2
0
0
0
0
1
0
0
0
0
2
2
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
1
0
0
3
0
1
3
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
1
0
0
0
0
2
0
1
1
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
2
1
2
0
1
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
1
1
0
3
0
0
0
0
0
0
1
3
0
0
2
1
0
0
0
1
2
2
1
0
0
0
2
0
0
2
0
0
2
0
0
0
1
0
0
0
2
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
1
1
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
1
0
2
0
0
0
0
2
2
1
0
0
0
0
0
1
0
1
0
0
0
0
0
2
1
0
0
1
0
2
0
0
0
0
1
2
2
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
2
0
3
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
2
2
1
0
0
2
4
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
1
1
0
1
1
2
0
0
0
2
1
2
0
0
0
0
0
2
2
0
0
0
0
2
0
2
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
1
1
1
0
0
0
2
0
0
0
2
0
2
2
0
2
1
2
4
0
0
0
0
0
0
0
0
0
0
4
0
2
1
3
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
2
0
0
0
2
0
5
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
1
0
1
2
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
4
1
0
0
0
1
0
0
1
1
1
0
0
1
0
1
0
0
1
2
0
0
0
0
1
2
0
3
0
0
2
2
2
2
0
2
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
4
1
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
2
2
0
2
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
1
2
0
2
1
4
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
2
0
0
0
0
2
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
3
0
0
1
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
3
1
2
2
2
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
1
2
1
0
0
0
1
1
0
0
0
0
0
2
1
0
0
0
2
0
2
1
0
0
0
0
0
0
2
0
1
0
0
0
2
0
1
0
0
1
0
0
5
0
0
2
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
2
0
2
0
0
2
0
0
0
1
0
0
0
1
0
0
0
1
1
0
2
0
0
2
0
0
0
0
0
0
0
1
1
2
1
0
0
0
0
0
2
0
2
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
2
0
3
0
0
2
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
2
1
0
1
3
0
0
0
2
0
1
0
2
1
0
3
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
2
0
2
3
0
2
0
0
0
2
0
0
2
0
2
2
0
0
1
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
2
0
0
0
2
2
2
0
2
0
0
0
0
0
2
0
0
1
2
1
0
0
2
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
1
0
0
0
0
0
15
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
1
3
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
2
0
3
2
0
0
0
0
1
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
2
0
1
2
0
0
1
0
0
0
2
3
0
0
1
1
0
0
1
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
2
1
2
1
3
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
1
2
0
0
2
2
2
1
2
0
1
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
5
0
0
0
0
0
2
1
0
2
0
1
0
0
0
1
0
2
0
1
0
0
0
0
1
2
2
8
2
0
0
2
0
0
0
1
0
1
0
1
1
0
1
0
0
0
0
4
2
0
3
1
0
0
2
0
2
0
0
0
2
0
0
2
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
1
0
1
0
0
1
0
1
1
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
2
0
1
1
0
0
2
0
0
0
2
0
0
1
0
0
0
0
2
0
1
0
1
0
0
1
1
3
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
3
1
8
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
1
0
2
0
2
1
2
1
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
3
0
2
1
0
0
0
1
0
2
0
1
0
0
0
1
0
0
0
0
1
0
0
2
1
0
0
0
0
2
0
0
0
1
1
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
2
1
4
0
0
0
0
0
1
4
2
0
0
2
3
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
1
2
0
0
0
1
0
0
4
1
1
0
2
0
0
2
1
2
0
0
0
0
1
5
2
1
2
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
1
0
4
0
1
0
0
0
1
0
0
1
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
5
0
0
0
0
0
0
1
0
2
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
3
2
0
0
0
0
0
1
0
2
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
3
0
2
2
1
1
0
1
1
0
0
1
0
2
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
2
3
1
1
1
0
3
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
1
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
2
5
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
1
2
1
0
0
0
2
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
13
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
2
2
0
0
2
0
0
1
0
3
0
2
0
1
0
1
0
0
1
0
2
3
0
0
0
1
0
0
0
0
1
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
2
0
1
0
2
0
0
0
0
1
0
0
8
2
1
0
2
0
0
0
0
2
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
2
1
0
4
1
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
7
0
0
0
0
0
2
0
0
0
0
0
0
2
4
1
1
0
1
2
2
0
0
0
0
2
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
1
0
2
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
2
0
2
0
0
0
0
3
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
1
2
2
0
1
1
2
0
0
0
1
2
2
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
1
1
0
1
0
0
2
1
0
0
0
1
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
2
0
0
2
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
2
0
1
0
0
0
1
0
0
0
2
0
0
0
0
1
0
1
0
0
1
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
2
2
0
1
0
1
0
0
2
0
1
0
0
1
2
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
1
2
1
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
2
2
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
2
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
2
1
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
1
0
0
1
0
1
2
2
0
0
0
0
1
0
0
0
2
2
0
1
0
0
0
0
0
0
0
2
11
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
1
0
1
0
0
2
0
2
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
4
0
1
0
2
0
1
0
0
0
3
0
1
0
0
0
1
0
2
0
1
0
2
2
0
1
2
0
0
1
2
0
2
0
2
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
2
1
0
0
0
1
0
0
1
2
0
0
2
0
1
0
0
0
1
0
0
1
0
0
2
0
1
0
1
1
0
3
2
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
2
0
0
0
0
1
1
0
0
2
0
0
0
0
0
3
0
0
0
1
0
0
0
0
1
1
0
0
1
4
0
0
0
1
0
0
0
1
0
0
0
5
1
2
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
1
1
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
2
0
0
0
0
3
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
1
2
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
4
0
0
0
0
0
1
1
1
1
0
0
2
0
0
1
0
3
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
1
0
0
0
0
0
3
0
0
1
0
0
0
2
2
1
0
0
1
0
1
0
0
0
0
2
11
0
0
0
0
1
0
1
2
0
2
0
0
0
0
0
0
0
0
0
5
1
0
2
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
4
0
3
0
2
0
0
2
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
1
6
0
3
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
5
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
4
1
0
0
0
0
0
0
1
3
0
3
2
0
0
3
0
0
0
0
0
0
0
2
0
2
0
1
0
0
1
0
0
0
2
1
1
0
0
2
0
0
0
0
0
2
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
2
1
0
0
0
2
0
0
0
2
0
2
1
0
2
0
0
0
4
0
0
0
0
1
2
2
0
0
2
1
0
0
0
1
1
2
2
0
0
0
0
0
2
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
1
0
1
1
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
2
2
0
2
0
4
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
2
2
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
2
2
0
1
1
3
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
2
0
1
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
1
0
0
0
0
3
0
2
2
3
2
0
0
0
0
0
1
1
0
1
2
2
0
0
0
2
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
4
2
0
2
0
2
0
0
0
0
0
1
1
0
1
2
1
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
2
0
0
1
3
0
0
1
0
0
1
0
1
0
0
2
0
0
1
0
1
0
1
0
2
0
0
3
0
1
0
0
1
0
0
0
0
6
0
0
0
2
2
0
0
2
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
2
0
0
2
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
1
0
1
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
2
1
4
0
0
1
1
0
0
0
1
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
6
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
1
0
0
1
0
0
2
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
2
0
2
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
5
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
6
0
0
0
0
2
1
0
0
1
0
1
2
0
0
0
1
2
0
4
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
1
1
0
1
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
2
2
0
1
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
2
0
1
0
0
1
0
0
0
2
0
2
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
2
3
2
0
0
0
2
0
0
0
2
0
4
2
0
0
2
0
1
0
0
0
0
0
0
1
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
2
0
1
3
1
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
2
2
2
0
0
0
5
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
2
2
2
0
0
0
1
0
1
0
0
1
0
1
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
1
1
0
0
0
0
3
2
0
2
0
0
0
1
1
0
0
1
0
2
0
0
0
0
0
2
0
0
4
0
2
0
0
1
2
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
1
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
2
0
0
0
3
0
2
1
0
3
0
0
0
0
2
0
0
0
2
0
1
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
2
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
3
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
1
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
1
2
0
3
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
2
0
0
2
0
0
1
3
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
1
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
1
0
0
0
6
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
2
0
4
0
0
0
0
0
1
0
1
0
0
0
2
1
0
0
1
0
1
4
0
0
0
0
1
0
0
1
2
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
1
0
0
0
2
1
0
0
0
0
2
2
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
5
0
0
2
1
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
2
0
0
2
1
0
0
0
1
0
0
2
0
1
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
2
0
0
0
2
1
1
0
0
0
1
0
2
0
3
0
1
3
0
0
0
0
2
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
1
0
0
0
1
0
4
1
1
2
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
2
1
2
0
0
0
1
0
0
0
0
0
0
2
3
0
0
0
0
1
0
1
0
0
0
2
1
2
0
1
0
0
0
0
5
0
0
0
0
2
0
0
0
3
0
1
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
2
1
0
1
1
3
3
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
3
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
1
0
1
0
1
0
2
0
0
2
0
0
4
1
0
0
1
3
0
1
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
2
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
3
1
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
1
2
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
1
0
2
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
3
0
2
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
5
1
0
1
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
2
0
2
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
1
0
0
1
2
2
0
2
0
0
0
1
1
2
1
1
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
2
2
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
6
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
2
0
1
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
3
2
0
0
0
0
0
0
0
1
0
0
2
0
2
0
1
0
0
0
3
0
1
0
0
0
1
0
4
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
2
0
0
0
3
0
2
0
0
0
0
1
2
0
2
2
0
0
1
0
0
3
0
2
0
0
2
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
1
0
2
0
0
3
0
2
0
3
0
2
1
0
0
0
2
1
0
1
1
1
2
2
0
0
0
3
0
2
0
0
1
1
1
0
1
0
1
2
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
2
0
0
2
0
0
4
1
0
0
0
0
0
3
0
1
0
0
1
0
0
0
0
0
0
2
1
0
0
0
2
0
0
2
0
0
0
1
0
0
2
0
3
1
1
0
2
0
2
2
0
1
0
0
1
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
1
1
0
0
0
0
3
2
1
0
0
4
0
0
2
1
0
1
0
3
0
1
0
1
0
1
0
0
0
1
0
0
2
1
1
0
0
0
0
0
2
0
0
1
2
0
4
0
1
0
0
1
0
0
4
0
2
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
3
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
2
0
0
0
1
1
0
2
0
0
2
0
2
0
0
0
1
0
0
0
0
1
1
1
0
1
0
2
0
0
1
0
0
0
1
0
1
0
1
0
1
0
0
0
0
1
1
1
1
0
0
0
0
1
0
0
0
0
0
2
0
2
2
0
0
0
1
0
0
0
0
8
0
0
1
0
0
1
0
0
0
0
0
0
2
0
2
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
2
0
0
0
0
3
0
0
0
0
2
4
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
3
0
0
1
0
0
0
1
0
0
0
3
0
1
3
0
2
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
2
0
0
1
1
0
1
1
0
0
0
0
0
0
1
0
3
0
4
0
1
2
0
0
0
0
0
0
1
3
0
2
2
0
2
0
0
0
2
0
2
0
0
0
0
1
0
1
0
1
0
0
2
1
0
0
0
0
0
0
0
3
0
0
0
2
0
0
1
2
0
0
0
0
0
2
2
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
3
1
0
1
2
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
3
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
1
1
0
0
2
0
1
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
3
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
1
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
5
0
0
0
2
0
1
0
1
0
1
2
0
0
1
0
0
0
0
0
2
0
3
0
0
1
0
4
0
0
0
2
0
0
0
0
0
0
3
0
0
3
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
2
3
0
3
1
0
0
2
0
0
0
2
1
0
0
0
0
0
2
1
0
0
1
2
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
1
1
1
1
1
1
1
0
1
0
0
1
0
1
1
0
0
0
1
0
0
1
2
2
1
0
0
0
0
0
0
0
0
0
1
2
0
3
0
0
0
0
3
2
0
0
0
0
0
1
0
4
0
0
0
2
0
2
0
2
0
0
0
0
2
0
0
0
2
0
0
0
1
0
1
0
0
2
2
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
8
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
2
2
1
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
2
0
0
0
1
1
0
0
4
0
1
0
2
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
5
0
1
2
0
0
1
0
0
0
1
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
1
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
2
2
0
0
1
3
1
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
2
0
0
0
0
1
0
0
0
2
0
2
0
0
1
1
4
0
0
0
1
0
2
0
0
0
0
0
1
0
0
2
1
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
1
0
2
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
2
0
0
1
0
0
0
0
0
2
0
0
0
2
3
3
0
4
0
0
2
1
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
1
0
0
0
2
0
2
1
0
0
0
0
0
2
0
0
1
1
0
0
1
0
0
0
3
0
0
1
2
1
0
2
1
2
0
0
0
0
2
0
2
0
0
2
0
0
0
0
1
0
3
1
1
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
8
0
2
0
0
0
0
1
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
1
2
0
0
0
2
0
0
2
1
0
3
0
0
0
0
1
0
0
1
0
0
0
0
2
0
1
2
0
0
0
0
3
0
0
0
0
0
0
1
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
1
0
0
2
0
0
2
0
1
0
2
0
0
0
0
1
1
0
1
1
2
0
0
0
0
0
2
0
1
0
4
0
1
0
0
0
0
0
0
2
2
1
0
0
0
1
1
0
1
0
0
6
0
0
1
0
0
1
0
0
0
0
1
0
1
0
1
0
0
2
0
0
0
0
1
1
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
2
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
2
2
2
0
0
0
1
2
0
2
0
0
0
1
0
0
0
0
0
2
1
0
1
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
1
0
2
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
3
0
2
0
0
0
1
0
0
1
2
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
2
2
0
0
0
2
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
2
0
1
0
1
0
2
0
0
1
0
0
1
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
1
0
3
0
2
0
1
0
1
0
0
0
0
2
1
4
0
0
0
0
0
0
0
1
1
0
3
0
1
0
2
0
2
0
0
1
1
0
0
0
0
0
2
2
0
0
0
3
0
0
0
1
0
1
0
0
0
0
2
0
0
1
0
1
2
0
1
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
5
2
0
0
0
2
0
1
2
0
1
0
2
2
0
2
3
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
2
2
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
6
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
2
2
0
2
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
2
2
0
2
3
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
2
0
0
0
0
1
0
0
0
0
1
10
2
0
1
0
0
0
0
0
0
1
1
0
2
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
4
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
1
2
0
0
2
0
0
0
3
1
2
0
1
1
2
2
0
0
5
1
0
0
0
0
1
0
1
0
0
0
2
4
0
0
2
0
3
0
0
0
0
1
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
1
0
3
0
0
0
0
1
0
0
1
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
2
0
1
0
0
2
0
1
1
2
0
0
0
0
2
0
1
0
0
0
2
1
0
0
0
0
0
1
0
0
4
0
0
0
0
0
2
0
1
1
0
0
0
1
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
2
0
0
0
0
1
0
0
0
1
0
2
1
1
2
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
1
1
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
2
0
2
0
3
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
2
2
0
0
2
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
1
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
1
1
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
5
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
2
2
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
1
1
1
1
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
1
0
1
1
1
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
2
0
0
2
5
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
2
2
0
1
0
0
1
0
0
1
0
2
1
2
0
0
0
0
1
2
2
0
3
0
0
0
0
0
2
0
1
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
2
2
0
1
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
1
0
2
1
1
0
0
1
1
1
0
0
0
0
0
0
2
2
1
3
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
1
0
2
0
1
0
0
0
3
0
0
0
0
2
0
0
2
0
0
1
0
2
0
2
0
0
2
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
2
2
0
1
1
0
1
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
1
3
2
0
0
0
0
1
2
0
2
0
0
0
1
2
0
2
0
0
0
2
0
1
0
0
0
0
2
0
2
0
4
0
2
0
0
2
2
1
0
0
1
0
1
0
1
0
0
3
0
1
0
0
2
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
1
0
0
2
1
0
0
0
0
0
2
0
0
0
1
0
2
1
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
1
2
3
2
0
0
0
0
1
1
0
0
0
2
1
0
0
1
0
2
0
0
0
2
16
1
2
1
0
0
0
0
2
0
6
0
0
0
1
0
0
2
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
4
0
0
0
0
0
0
3
0
0
1
0
2
0
0
2
0
0
0
2
0
1
2
0
0
0
2
0
0
0
0
0
1
0
4
0
0
3
0
0
0
0
1
0
0
3
1
0
1
1
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
5
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
11
1
1
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
3
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
2
0
1
3
0
1
0
0
1
2
2
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
3
0
0
2
1
0
0
0
2
0
2
0
0
2
0
5
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
4
0
0
2
0
0
1
0
0
0
0
0
3
0
2
0
1
0
2
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
2
0
1
0
0
3
1
0
0
0
1
1
0
0
2
0
0
0
0
0
1
3
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
2
1
2
0
2
0
0
0
0
1
0
0
2
2
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
2
2
1
0
2
2
0
0
1
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
2
1
0
0
0
0
0
0
2
0
2
1
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
3
0
2
0
2
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
3
0
0
0
0
1
2
0
0
0
0
0
2
2
0
0
2
0
1
0
0
0
0
7
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
2
2
2
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
3
1
0
0
0
0
0
0
0
0
2
2
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
1
2
0
0
0
1
0
2
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
2
2
0
0
0
1
1
0
1
0
0
2
1
0
1
1
0
0
1
0
0
2
1
1
3
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
3
0
2
0
0
2
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
4
3
2
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
3
1
0
0
0
2
0
0
0
1
0
1
0
0
1
1
2
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
2
0
0
0
0
0
1
0
2
2
1
1
2
0
0
1
3
0
3
0
0
2
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
1
0
0
1
0
0
2
0
2
0
0
2
0
2
0
2
0
0
0
0
1
0
2
2
1
1
0
3
1
3
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
1
0
0
2
0
2
0
0
0
0
3
0
2
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
3
2
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
4
2
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
1
1
0
1
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
1
2
0
2
0
0
0
1
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
2
0
0
1
0
0
0
0
2
0
2
2
0
0
1
0
1
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
3
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
2
0
0
0
0
2
0
1
2
1
1
3
2
0
5
5
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
4
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
3
1
0
0
0
0
2
0
1
3
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
2
2
0
0
2
0
1
0
0
2
0
0
0
0
0
1
1
0
0
2
0
2
1
1
1
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
1
1
0
1
0
0
0
0
0
2
0
0
1
2
0
0
4
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
2
0
1
0
0
0
2
2
2
1
2
0
0
3
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
3
0
1
0
2
0
0
0
0
1
1
1
0
2
2
0
0
0
1
1
1
0
0
0
1
2
0
2
0
0
2
0
0
0
0
0
0
1
0
2
1
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
3
0
0
0
1
2
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
2
7
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
1
0
0
2
0
2
0
2
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
3
1
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
2
0
2
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
1
0
0
1
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
2
0
0
2
0
0
3
0
0
3
1
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
1
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
4
0
1
2
1
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
4
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
2
4
0
0
0
0
0
0
2
0
1
0
0
0
1
0
1
0
0
2
2
1
0
1
0
0
2
0
0
2
0
1
0
1
0
0
1
0
1
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
1
0
1
1
0
2
0
1
0
1
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
2
0
1
1
1
0
7
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
2
0
0
3
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
2
0
2
0
0
0
0
1
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
1
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
2
0
0
2
1
1
0
1
3
0
1
0
0
0
0
0
2
2
20
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
1
0
0
0
2
2
1
1
0
0
0
0
1
0
0
0
0
0
0
0
2
2
2
0
0
0
2
0
1
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
3
0
2
0
1
0
0
0
0
0
0
0
0
2
0
1
1
2
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
3
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
2
0
3
0
0
1
0
1
0
0
4
0
0
0
0
0
2
0
0
0
0
0
2
1
0
1
1
0
1
0
0
2
0
0
0
0
2
1
0
0
2
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
1
0
0
0
1
0
0
2
1
0
0
2
1
0
0
2
0
0
0
0
2
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
2
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
3
0
1
0
1
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
2
2
0
0
2
1
1
0
0
1
0
3
2
0
0
1
0
0
2
2
0
0
0
0
1
0
0
2
2
0
3
0
2
0
1
0
1
0
0
0
0
0
1
0
0
3
0
0
3
1
0
0
1
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
2
0
1
1
1
0
0
2
0
1
1
0
0
2
0
0
0
0
1
0
3
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
2
0
1
0
0
0
2
0
0
0
0
2
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
2
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
2
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
3
0
0
0
0
1
1
2
0
2
0
0
1
2
1
2
3
0
0
0
3
1
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
1
0
0
0
0
0
1
0
2
0
1
0
2
0
1
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
1
0
0
1
0
0
1
0
0
0
1
1
0
0
2
0
0
4
2
0
0
0
0
2
1
0
0
2
0
0
0
0
0
1
0
1
2
0
1
1
0
2
0
0
1
0
0
0
0
2
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
2
0
2
0
1
0
1
0
3
1
0
3
1
1
0
0
0
0
0
0
0
1
2
2
2
0
0
0
0
0
0
0
0
2
0
0
1
1
4
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
2
0
6
1
2
1
0
1
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
1
3
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
2
1
0
1
0
0
0
1
0
0
0
0
5
0
0
0
0
0
0
0
3
1
0
4
0
1
0
0
0
0
0
1
0
1
0
1
0
0
4
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
1
2
1
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
2
0
1
0
0
0
2
0
0
0
1
0
2
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
2
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
3
0
3
3
1
0
2
1
0
2
2
0
0
0
2
0
0
1
0
0
8
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
2
0
1
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
1
0
0
1
0
2
1
0
0
0
0
0
0
1
1
2
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
10
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
1
0
1
2
0
2
1
0
0
0
0
0
2
3
0
0
5
0
0
0
0
0
1
1
0
0
0
0
0
1
0
2
0
3
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
1
1
1
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
2
2
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
1
0
2
0
2
0
2
0
0
0
1
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
4
4
2
0
0
1
0
2
0
0
0
0
0
0
2
0
0
1
0
0
1
1
0
1
2
0
1
0
1
0
2
2
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
1
1
0
0
0
2
1
0
3
0
0
0
0
2
0
0
1
1
0
2
0
0
0
1
2
2
0
0
0
1
0
0
0
2
0
0
2
0
0
1
4
1
0
0
0
0
1
0
3
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
2
1
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
1
0
1
0
1
5
0
2
1
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
2
0
0
2
1
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
3
0
1
0
0
0
0
0
0
2
2
1
0
1
0
0
0
2
1
0
0
2
0
1
0
0
0
0
0
2
0
0
2
0
0
1
1
2
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
2
0
1
0
0
2
1
1
1
0
0
1
1
0
0
0
0
0
0
2
1
0
0
0
2
4
0
0
0
0
0
0
0
3
7
2
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
3
2
0
0
4
2
0
1
0
3
0
0
0
1
1
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
3
1
0
1
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
1
0
0
0
0
0
1
0
0
0
0
0
4
0
0
1
0
0
2
1
0
0
2
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
1
0
0
4
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
3
0
0
2
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
3
0
5
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
1
0
2
0
2
0
3
0
2
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
2
2
0
2
1
0
4
0
2
2
2
1
1
2
0
1
0
2
0
0
0
0
2
1
0
1
0
0
2
2
0
0
2
0
3
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
2
0
1
2
0
0
2
0
2
2
0
2
2
0
1
0
2
0
0
1
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
2
2
0
0
0
0
2
1
1
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
2
1
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
6
1
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
2
2
2
2
0
0
1
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
1
2
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
2
0
0
3
0
0
0
0
2
0
0
1
0
1
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
1
1
0
1
2
0
1
1
2
1
0
0
0
0
0
2
0
0
2
0
1
0
0
2
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
2
0
0
2
0
0
2
0
0
0
0
0
0
2
0
3
0
2
0
0
0
0
0
0
6
0
0
0
0
3
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
2
0
0
2
0
0
1
0
0
0
0
1
0
2
1
1
0
1
2
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
2
0
3
1
1
0
2
0
0
0
0
0
3
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
1
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
2
2
0
3
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
1
1
0
1
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
3
0
0
0
1
0
0
0
0
1
1
2
0
0
0
2
0
0
0
0
1
1
0
2
0
2
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
1
1
2
1
2
1
2
0
0
0
0
0
0
2
0
2
0
2
0
0
3
0
0
0
0
0
0
3
0
2
2
0
0
0
0
0
2
2
0
2
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
1
0
0
0
0
0
1
0
0
1
2
0
0
0
2
0
0
1
0
2
2
1
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
2
0
1
2
0
0
2
0
0
2
0
0
2
1
0
0
2
1
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
2
1
0
0
0
1
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
2
1
1
2
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
1
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
2
2
0
0
2
0
0
0
2
0
0
1
0
0
0
0
1
0
1
0
0
2
1
2
2
2
0
2
0
0
2
0
0
0
2
1
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
2
0
1
0
2
0
2
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
2
0
0
0
0
0
1
2
0
0
2
1
0
1
0
5
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
1
0
1
2
0
0
1
0
0
1
0
1
2
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
3
0
0
0
0
2
0
0
0
1
1
2
0
0
2
2
0
0
2
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
6
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
1
0
0
2
0
0
0
2
0
2
0
0
0
1
0
1
0
0
0
2
3
0
0
0
2
0
1
0
0
0
2
0
0
2
0
0
0
1
0
0
0
3
0
1
0
0
2
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
2
0
3
2
0
2
1
2
2
1
0
0
0
0
0
2
2
2
0
2
0
0
0
0
0
0
1
0
2
1
0
3
0
1
1
2
2
2
0
2
0
2
0
0
0
2
0
0
1
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
2
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
2
1
0
0
0
0
1
0
2
0
0
2
6
0
0
0
0
2
0
3
0
2
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
2
0
1
0
1
2
0
1
3
0
1
2
0
0
0
0
0
0
0
0
0
0
2
1
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
5
0
2
0
3
0
0
1
2
0
0
0
0
0
0
3
0
0
0
2
0
1
2
1
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
2
0
0
1
1
0
0
0
0
0
2
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
3
0
3
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
1
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
4
1
0
0
2
2
1
2
2
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
2
1
1
2
2
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
2
1
0
0
4
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
2
0
0
1
0
0
0
1
0
0
1
0
0
0
0
2
1
1
1
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
3
2
0
1
1
3
1
0
0
0
0
0
0
3
3
0
2
1
0
0
0
0
0
0
1
1
0
2
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
2
0
1
2
0
2
0
0
1
2
2
0
2
0
0
2
0
0
0
2
1
0
0
1
1
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
5
0
1
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
2
2
1
0
0
2
0
0
2
2
0
2
0
0
0
2
1
2
0
0
0
1
1
0
0
0
0
0
0
0
0
2
4
2
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
5
0
1
2
1
0
0
2
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
1
0
1
0
0
2
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
1
0
1
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
4
0
0
0
0
2
1
1
0
0
1
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
3
0
1
2
0
0
2
1
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
2
0
0
0
0
0
6
0
2
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
2
2
0
1
2
1
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
1
1
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
1
1
1
0
1
0
0
2
2
0
0
0
0
0
1
0
2
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
3
1
4
1
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
1
1
3
1
0
0
0
0
0
1
0
0
0
2
0
1
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
1
1
0
2
0
0
1
0
0
2
2
0
2
1
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
2
0
0
1
0
0
1
1
0
0
1
0
0
0
8
1
0
1
0
0
0
0
2
1
0
0
0
0
1
2
0
0
0
0
2
0
1
0
2
0
0
1
0
0
0
2
0
0
2
0
0
4
1
0
0
0
0
1
0
0
2
0
1
0
1
0
3
0
3
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
1
1
1
4
1
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
3
0
2
2
0
0
0
2
0
0
0
3
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
1
2
0
0
4
0
0
0
6
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
2
0
0
0
0
3
1
1
0
1
0
2
2
2
0
0
0
2
0
0
0
2
2
0
0
0
0
1
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
4
2
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
1
1
0
2
0
1
0
0
1
2
0
0
0
2
0
0
3
0
2
0
3
1
0
0
1
0
2
0
0
2
1
0
0
0
0
0
0
2
1
0
0
0
3
0
1
0
0
0
3
0
2
0
0
0
0
2
0
0
0
2
1
0
2
0
0
2
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
2
0
0
1
2
0
1
0
0
2
1
1
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
3
0
0
1
1
0
0
0
3
0
0
0
0
1
0
0
0
2
1
0
0
0
0
2
0
0
1
0
2
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
2
2
1
0
0
0
0
2
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
2
3
0
0
0
0
0
2
0
0
0
2
0
1
0
1
0
0
4
0
0
2
1
2
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
1
0
0
0
0
2
2
0
0
0
0
0
0
0
1
2
0
1
0
2
2
0
0
0
0
2
1
0
0
0
0
0
1
0
0
5
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
2
0
0
0
0
2
1
0
0
0
0
2
1
1
0
0
0
2
0
1
0
0
1
2
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
3
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
1
0
2
0
1
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
7
1
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
1
2
2
2
0
1
0
0
0
0
0
1
3
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
1
2
2
0
0
1
2
0
2
0
2
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
2
1
0
3
1
0
0
0
1
0
0
1
0
2
0
0
1
2
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
3
0
1
1
2
2
2
1
0
0
0
1
0
0
1
0
0
0
2
1
2
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
4
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
1
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
2
0
1
0
0
0
1
3
2
2
1
3
0
0
2
0
0
0
1
0
0
0
2
2
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
1
0
2
0
1
0
1
0
0
0
0
0
1
1
2
2
0
1
2
0
1
0
0
0
0
1
0
1
0
1
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
2
0
0
0
2
0
0
1
0
0
0
0
0
0
2
3
3
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
3
0
0
2
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
2
2
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
2
0
2
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
1
1
0
10
0
0
1
0
0
0
0
2
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
3
0
2
0
0
0
2
0
0
1
2
0
0
0
1
0
25
0
2
0
0
0
2
1
0
0
0
2
0
0
1
0
2
0
2
1
0
0
2
3
0
0
0
0
3
2
2
1
0
0
2
2
0
0
1
0
0
0
0
0
0
1
0
2
0
2
1
0
0
0
0
0
2
0
1
0
0
0
0
1
1
1
1
0
2
0
0
3
0
0
0
0
2
2
0
0
0
1
0
2
2
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
1
1
1
2
0
1
0
0
1
0
2
0
2
2
0
1
2
0
1
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
2
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
3
0
0
0
0
1
2
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
2
0
1
2
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
1
0
1
2
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
1
0
0
0
5
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
1
0
2
0
0
0
0
1
0
2
0
2
0
0
0
0
2
0
0
0
0
0
2
2
2
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
2
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
1
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
1
1
2
4
0
0
0
0
0
2
0
0
0
1
2
0
2
0
2
1
0
0
0
0
1
1
1
1
0
2
1
2
0
1
3
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
1
2
0
2
0
2
0
0
0
2
0
0
0
2
2
1
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
1
1
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
2
0
0
1
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
2
1
2
0
0
0
2
0
0
0
2
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
1
6
3
0
2
2
1
1
0
2
0
0
0
1
1
5
0
0
2
0
0
0
1
1
0
2
0
2
0
0
0
3
0
1
0
0
0
0
2
0
1
1
2
0
0
0
0
0
0
0
0
3
1
1
1
0
0
0
2
0
0
2
2
0
0
0
1
1
0
0
0
2
0
0
0
0
1
2
0
0
0
2
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
3
2
0
1
0
0
0
0
0
0
0
0
0
1
1
2
2
2
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
1
0
0
0
2
0
1
2
0
1
2
0
0
0
0
0
0
1
0
2
0
1
0
5
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
2
1
0
0
0
0
0
0
2
1
0
2
0
0
0
0
1
0
0
0
2
0
0
0
2
0
2
0
0
2
0
2
0
0
1
0
0
0
0
1
0
0
0
1
2
0
3
0
0
2
2
0
0
0
0
2
0
0
2
0
0
0
2
2
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
2
1
1
2
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
2
0
4
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
5
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
1
2
0
0
0
2
1
3
0
1
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
3
0
2
0
0
0
0
2
2
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
2
0
0
1
1
0
0
3
1
0
2
0
0
3
0
2
0
2
0
0
2
1
1
0
0
0
0
1
2
0
2
0
0
0
0
0
0
2
0
0
1
1
2
1
0
2
0
0
0
2
0
2
1
0
1
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
1
2
4
0
0
0
0
0
0
0
0
0
1
2
0
2
0
1
0
0
0
0
0
0
0
1
2
0
0
0
2
2
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
1
0
0
1
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
4
2
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
2
1
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
2
1
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
2
0
1
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
2
2
2
0
0
1
1
1
1
1
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
4
1
2
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
3
2
2
2
1
0
1
1
0
2
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
2
1
1
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
2
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
8
0
0
1
2
0
0
1
0
0
0
2
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
1
1
0
0
0
1
2
3
2
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
3
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
1
0
2
1
1
0
0
0
0
0
0
0
0
0
3
0
1
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
1
0
2
0
0
0
0
2
2
0
1
4
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
1
0
2
0
2
2
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
3
0
0
1
1
0
0
0
0
0
1
0
0
3
0
0
0
2
0
0
0
1
0
2
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
1
0
2
1
0
0
0
1
2
0
0
0
0
2
1
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
2
2
0
0
2
0
2
0
2
2
0
0
0
0
1
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
1
0
3
2
4
0
0
0
0
0
0
0
2
0
1
1
0
2
2
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
2
0
0
1
2
2
1
1
2
2
2
0
0
1
11
0
3
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
1
2
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
1
1
0
0
1
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
2
0
0
2
0
1
0
0
0
0
2
0
0
1
0
1
1
0
0
0
0
0
2
0
3
1
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
2
1
0
1
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
1
0
1
0
1
0
0
0
0
2
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
2
0
2
2
0
2
0
0
0
0
2
0
0
2
0
2
2
0
1
2
0
0
2
0
0
1
2
0
0
0
0
0
1
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
4
1
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
2
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
2
2
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
2
0
4
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
2
0
0
0
2
0
0
1
1
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
1
0
1
1
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
1
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
5
0
0
0
1
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
2
1
2
0
1
0
3
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
2
2
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
2
0
0
1
1
0
0
0
2
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
2
2
1
2
2
0
3
0
0
3
0
0
0
0
4
0
0
1
1
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
1
1
0
0
2
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
2
0
2
2
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
2
0
3
1
0
0
0
0
0
0
2
2
0
1
0
0
3
0
0
0
0
1
0
2
1
0
0
1
0
1
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
2
0
0
3
2
0
2
0
0
0
1
0
2
0
0
2
0
1
0
2
0
0
0
2
1
0
0
2
2
0
0
0
0
0
0
0
1
2
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
2
1
2
0
1
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
2
0
1
2
0
0
0
0
2
0
0
0
1
2
0
0
1
0
0
0
0
2
0
0
0
0
2
1
2
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
3
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
3
0
0
0
0
0
3
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
2
2
0
2
2
0
0
0
3
0
0
0
1
0
2
0
2
0
0
0
1
0
0
0
2
0
0
0
2
1
0
0
2
0
1
2
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
3
0
3
0
1
1
0
0
1
0
0
1
0
0
0
2
0
2
0
1
0
2
0
0
0
1
2
0
1
0
0
0
0
2
3
2
0
0
0
0
2
0
0
2
0
0
0
1
0
2
0
0
1
0
2
2
0
2
0
2
0
0
0
2
0
1
0
0
0
1
0
2
0
0
0
1
0
2
2
0
0
0
1
0
0
0
0
1
1
0
1
1
1
0
0
1
0
2
0
1
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
2
1
0
0
0
0
0
0
4
0
1
0
0
0
1
0
0
3
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
4
0
0
0
2
0
0
0
1
2
2
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
2
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
1
2
0
0
0
2
0
1
0
0
1
0
0
0
4
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
2
2
0
1
1
0
0
0
0
1
2
1
0
0
0
2
0
0
0
2
0
1
2
1
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
2
3
0
0
1
0
0
0
0
2
0
0
0
2
0
0
10
0
0
2
1
0
1
2
0
0
0
4
0
0
2
0
0
0
0
0
4
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
2
1
0
2
0
0
0
0
0
1
1
0
4
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
2
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
2
0
0
1
0
0
3
2
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
2
0
2
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
1
6
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
5
2
0
0
0
0
0
1
0
0
0
0
1
3
0
0
1
0
0
1
1
0
0
1
0
1
0
0
2
1
2
0
1
1
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
3
0
1
1
0
2
0
2
0
0
0
3
0
0
0
2
0
2
5
0
0
2
0
2
1
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
1
0
0
2
0
0
1
2
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
2
2
2
1
2
0
0
0
0
0
2
0
2
1
0
0
0
0
0
2
0
0
1
1
0
0
0
0
2
0
0
0
1
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
2
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
6
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
1
0
0
1
1
0
1
0
1
1
2
2
0
1
0
2
0
0
0
0
0
0
1
0
0
1
0
2
0
0
3
0
1
0
1
0
0
0
1
0
0
0
0
0
2
0
2
1
0
2
0
0
0
0
0
0
0
2
1
0
2
0
2
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
2
0
0
1
0
0
1
0
1
0
0
3
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
5
0
0
2
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
3
0
0
0
2
1
0
0
0
1
0
0
2
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
2
2
0
3
0
2
3
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
9
0
0
0
0
2
0
0
1
1
0
2
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
2
0
2
1
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
2
0
1
2
0
0
0
0
1
0
0
1
1
0
0
2
2
0
2
0
0
1
2
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
4
0
2
0
0
2
0
0
1
0
0
0
1
1
0
0
0
2
0
0
0
0
0
1
0
0
0
3
0
0
0
0
2
0
0
0
0
2
0
0
1
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
4
0
2
0
0
0
1
3
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
3
2
0
1
2
1
2
0
2
0
3
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
2
0
2
2
0
1
0
0
1
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
3
2
0
2
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
2
0
1
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
2
0
3
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
2
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
3
2
2
0
0
1
1
0
0
0
0
3
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
2
3
2
0
3
0
2
1
0
0
3
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
1
0
2
0
1
1
0
0
0
0
0
2
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
1
3
0
0
1
2
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
1
1
0
0
0
1
6
0
0
0
1
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
1
1
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
2
0
0
0
1
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
2
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
1
0
0
0
1
0
0
0
1
0
0
3
0
2
0
0
1
0
2
0
0
0
0
0
0
0
2
5
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
3
0
0
0
1
0
2
4
0
0
0
1
0
0
2
0
2
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
2
2
0
2
0
0
1
0
1
0
1
0
0
0
1
0
1
2
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
11
0
0
0
3
0
0
1
0
0
0
1
0
2
0
0
0
0
0
2
1
3
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
1
2
1
3
0
1
1
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
3
2
0
0
0
1
0
0
5
2
0
0
0
0
0
0
1
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
5
2
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
2
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
3
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
2
2
1
2
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
3
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
1
1
0
2
0
0
1
2
2
1
0
0
0
0
0
4
1
0
0
2
0
2
0
0
0
0
0
2
2
2
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
1
0
2
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
1
1
0
0
2
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
4
2
0
0
0
0
2
0
2
0
2
4
0
1
0
0
1
0
2
2
0
2
0
0
0
2
1
1
0
3
1
2
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
3
0
4
0
0
0
0
1
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
3
0
0
0
1
0
0
2
0
0
0
1
2
1
1
0
0
0
0
2
1
0
0
0
0
1
0
0
2
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
1
1
2
0
0
0
3
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
2
3
2
0
3
0
1
1
2
1
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
3
1
0
4
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
1
3
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
2
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
3
0
0
1
1
2
1
0
0
0
0
2
0
2
0
1
0
0
2
0
0
0
1
0
1
0
0
0
0
3
1
0
1
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
4
0
2
0
0
1
2
0
0
0
0
0
0
0
0
2
0
1
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
1
0
2
2
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
2
0
0
1
0
0
0
2
2
0
3
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
1
1
0
2
0
0
0
2
0
0
0
0
2
1
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
1
2
0
0
0
2
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
3
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
3
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
2
0
3
0
0
1
0
0
2
0
2
0
0
2
3
1
0
0
1
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
3
0
0
0
1
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
1
2
0
0
2
0
1
1
1
0
2
0
0
1
2
0
0
0
0
1
0
2
2
2
0
2
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
2
0
0
1
0
2
2
0
0
0
0
0
0
0
2
0
1
1
0
2
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
1
0
0
3
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
2
1
2
0
0
0
0
2
0
2
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
2
2
0
0
0
1
0
2
0
0
0
0
0
7
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
1
0
0
0
9
0
0
1
0
0
2
1
3
2
0
0
0
2
0
0
0
2
4
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
1
1
0
0
2
0
0
0
0
0
0
0
1
2
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
2
0
0
0
1
1
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
2
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
1
3
0
0
1
0
0
0
0
2
1
2
0
0
1
0
1
0
3
2
0
0
0
0
0
0
0
0
1
2
2
0
0
1
2
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
2
0
1
0
3
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
2
1
0
0
3
3
0
0
0
1
0
0
1
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
2
2
0
0
0
1
1
0
0
2
0
1
5
0
1
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
1
1
0
2
2
0
1
0
0
0
0
0
2
0
2
0
1
1
1
0
1
0
0
0
0
0
2
0
0
1
0
0
1
0
2
0
0
0
0
2
0
0
0
2
0
3
2
0
0
0
0
0
0
1
1
2
2
0
0
2
0
0
0
1
0
0
1
1
5
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
3
1
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
1
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
1
1
0
2
2
0
2
0
2
2
0
1
0
0
1
0
2
0
0
1
0
0
0
0
1
0
2
0
0
0
0
2
0
0
2
0
2
0
0
0
2
0
3
0
0
0
0
0
0
0
0
4
0
1
1
0
2
1
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
2
0
0
2
2
0
1
1
1
0
0
0
1
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
2
2
3
2
0
0
2
2
2
0
0
0
0
0
2
0
0
0
2
1
0
1
1
0
0
1
0
0
1
1
0
1
0
2
0
2
1
0
1
0
0
0
1
0
0
0
2
0
0
2
0
0
0
1
0
1
2
0
0
0
0
0
0
1
0
1
2
1
0
0
2
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
1
1
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
2
0
0
2
0
1
0
0
0
0
1
1
0
1
0
2
0
0
0
0
0
1
0
0
1
0
0
0
2
1
2
2
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
2
0
2
0
0
0
0
0
4
0
0
2
1
0
2
1
0
0
1
2
0
0
1
0
2
0
0
0
2
2
0
1
2
0
0
0
0
0
0
0
0
0
2
1
1
0
0
2
0
0
2
0
1
0
0
2
2
1
0
0
0
0
3
2
0
0
1
2
0
0
2
1
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
4
0
0
2
0
2
1
0
0
0
0
0
1
2
2
0
0
2
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
8
0
2
1
0
0
1
2
0
0
1
0
2
0
0
4
2
3
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
1
0
2
1
0
0
1
1
0
0
2
0
1
0
0
0
3
0
0
0
0
0
1
0
2
1
2
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
1
0
0
0
2
0
2
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
2
1
0
0
2
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
2
1
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
1
1
0
0
2
0
3
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
3
2
0
0
7
2
0
0
0
0
1
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
9
0
0
2
0
0
0
0
1
0
1
2
0
0
3
1
0
0
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
1
0
4
0
1
1
2
0
0
0
0
0
0
2
2
0
0
0
0
1
1
1
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
2
1
2
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
2
1
0
0
0
0
2
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
2
1
0
0
0
0
1
2
0
0
2
0
0
3
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
2
1
1
0
0
0
0
0
0
0
1
2
1
0
2
0
0
0
1
0
0
0
0
2
0
1
0
0
0
2
0
0
1
1
0
0
1
1
0
1
0
0
0
3
0
0
0
0
0
2
1
1
0
0
2
0
2
0
0
0
2
0
2
0
1
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
4
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
1
0
2
0
0
1
0
0
2
0
0
0
1
2
1
0
0
0
0
1
0
1
0
0
0
0
0
3
1
0
0
0
0
0
0
0
1
0
3
0
2
0
0
1
3
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
3
0
1
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
3
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
2
0
2
0
2
0
0
1
1
2
0
2
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
3
0
2
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
1
0
1
2
1
0
0
0
0
0
1
0
0
0
0
3
2
3
0
0
2
0
0
1
1
0
2
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
1
3
0
1
0
0
3
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
2
0
2
1
1
2
0
1
0
0
0
2
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
1
2
2
1
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
5
0
0
1
0
0
0
0
4
0
0
0
0
1
0
2
0
0
2
0
1
0
2
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
2
0
2
0
1
2
0
0
0
3
2
2
0
0
0
1
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
3
1
3
0
2
0
2
2
0
0
0
2
0
0
1
0
2
0
0
0
0
1
0
1
0
0
2
0
0
1
4
2
1
2
0
0
0
0
1
0
1
0
0
0
1
0
1
0
1
1
0
0
1
0
0
1
0
0
1
0
0
0
2
0
0
0
0
2
0
1
2
0
1
0
0
0
2
1
0
2
0
1
0
0
0
0
0
2
0
0
0
0
3
0
0
0
1
2
0
0
0
0
2
1
0
2
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
2
0
1
3
0
0
2
0
2
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
2
1
0
0
3
0
0
1
1
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
3
0
0
3
0
0
0
0
1
0
0
12
0
0
0
1
0
0
2
0
3
0
0
0
3
1
2
0
0
0
2
0
1
2
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
1
2
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
2
1
2
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
3
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
1
1
0
0
2
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
2
2
0
0
0
2
2
1
0
1
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
2
0
2
0
0
1
0
3
0
2
0
1
0
0
0
2
0
0
0
0
0
2
0
0
1
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
5
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
1
1
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
1
0
1
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
3
0
0
4
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
2
0
0
1
2
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
5
8
0
0
2
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
2
1
3
0
2
0
0
2
0
2
0
2
0
3
2
5
2
1
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
2
0
0
0
1
0
0
0
1
1
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
2
0
0
2
1
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
2
0
3
1
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
1
2
0
0
1
0
2
0
2
0
0
5
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
5
3
1
0
1
0
1
2
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
4
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
3
0
0
0
1
0
0
0
2
0
0
2
1
0
0
9
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
2
0
0
1
0
0
0
0
1
2
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
1
1
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
1
1
2
0
1
2
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
5
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
1
0
0
1
0
1
2
1
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
1
2
0
0
0
1
2
2
2
1
2
2
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
1
1
1
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
2
0
0
3
0
1
0
0
1
1
2
0
0
1
0
0
0
0
1
0
0
0
0
1
2
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
1
1
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
5
0
0
0
4
1
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
1
0
1
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
3
0
2
0
2
0
0
0
0
1
1
0
0
1
0
0
2
0
0
2
0
0
0
0
2
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
1
0
0
1
0
3
0
2
0
0
2
2
1
1
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
2
2
2
0
0
0
0
0
0
4
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
2
0
0
0
0
2
0
0
0
0
0
2
2
2
0
2
2
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
1
1
1
1
0
1
0
2
2
0
0
0
1
0
1
1
1
0
0
2
0
0
0
1
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
1
0
2
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
1
0
1
2
2
1
1
0
2
0
0
0
1
3
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
2
0
0
1
1
2
0
1
0
3
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
4
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
1
0
0
0
0
2
1
0
0
0
1
0
0
1
2
0
0
2
0
2
2
0
0
1
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
1
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
3
1
1
0
0
3
1
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
3
2
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
3
0
3
0
1
0
2
0
0
0
0
0
1
2
1
0
2
1
0
0
0
0
0
3
0
1
0
0
0
0
1
2
2
0
0
0
0
0
1
0
1
2
0
0
0
1
0
0
0
0
1
1
1
0
2
0
0
2
0
2
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
2
2
0
0
4
2
1
0
0
0
2
2
2
0
0
0
2
0
0
0
0
2
1
2
0
0
0
0
1
2
0
0
0
0
0
0
2
0
6
0
2
0
3
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
2
0
1
1
1
0
0
2
0
0
1
0
0
5
0
0
0
0
0
0
1
3
2
2
1
0
0
0
0
8
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
3
0
0
1
1
1
2
0
0
2
0
1
5
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
1
0
2
2
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
3
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
3
0
3
0
0
1
0
0
0
0
0
2
0
0
0
0
1
1
0
3
3
1
1
0
0
0
3
1
0
0
0
2
0
0
2
2
1
1
0
0
0
0
0
0
2
4
0
0
0
0
1
0
2
2
0
2
0
1
0
1
0
0
1
0
0
1
2
0
2
0
0
3
0
0
2
2
0
0
0
2
0
0
0
3
0
0
2
2
0
3
0
0
1
3
2
6
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
2
0
0
0
1
3
1
0
2
0
5
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
4
1
0
1
0
0
0
0
0
0
1
0
2
1
0
0
1
1
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
2
0
1
0
2
0
0
0
0
1
0
2
1
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
1
2
0
2
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
2
0
2
3
2
0
0
2
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
1
1
1
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
1
2
0
0
2
1
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
1
0
0
0
0
0
0
3
1
0
2
0
0
0
0
0
1
0
1
1
2
0
1
0
2
0
1
0
1
0
0
0
0
0
2
2
0
0
5
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
1
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
3
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
1
0
3
0
0
0
0
0
4
2
1
2
2
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
2
2
0
1
0
0
0
2
1
1
0
0
0
0
0
0
0
2
11
0
2
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
1
2
0
0
0
1
0
1
1
0
0
0
0
3
2
0
1
0
3
0
1
0
2
1
0
0
0
1
4
0
0
2
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
1
1
3
0
2
0
5
0
2
0
0
0
0
0
0
2
1
2
0
0
1
0
2
0
0
0
2
5
0
0
0
0
0
1
0
1
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
4
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
1
0
2
2
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
5
0
0
2
0
0
0
0
0
2
1
0
0
0
1
2
1
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
4
0
2
0
0
1
0
1
1
0
0
0
0
1
0
0
1
1
0
0
2
0
0
0
0
5
1
0
0
1
0
0
1
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
2
0
0
1
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
3
2
0
0
0
2
0
0
2
1
0
0
2
1
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
2
2
1
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
1
0
0
0
2
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
2
4
0
0
0
0
3
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
2
3
1
0
0
3
0
1
0
1
1
1
1
7
2
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
1
0
6
0
0
5
0
0
1
0
0
4
2
0
0
0
1
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
7
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
1
0
1
2
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
2
2
0
0
0
0
0
0
2
0
2
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
3
0
0
1
0
1
2
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
2
0
2
2
0
0
1
0
0
0
2
0
0
2
0
0
2
2
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
3
0
2
1
0
1
0
0
0
1
1
2
0
0
0
1
0
0
0
0
0
2
2
0
0
0
3
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
2
0
0
1
1
2
1
0
0
2
2
0
0
0
0
1
0
2
0
2
0
2
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
2
2
0
0
0
0
1
1
3
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
1
0
0
0
1
0
0
3
0
0
4
0
1
0
0
1
2
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
2
1
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
3
0
2
0
1
1
0
0
0
0
2
0
0
1
0
1
2
1
0
0
0
1
0
2
0
2
0
0
0
0
2
2
0
0
1
4
0
0
0
0
0
0
2
1
2
0
1
2
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
2
2
2
0
0
2
0
0
2
0
0
0
3
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
2
0
0
2
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
3
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
1
2
0
0
1
0
2
0
1
0
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
3
2
0
4
1
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
3
1
1
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
2
2
2
1
1
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
1
1
1
0
0
0
1
1
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
2
2
2
0
0
0
0
2
0
0
0
3
0
2
4
2
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
1
0
2
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
1
3
0
0
0
0
0
0
2
0
0
1
0
0
1
0
1
0
0
0
1
10
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
1
0
1
0
0
1
0
0
1
0
3
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
3
1
1
0
0
0
1
0
0
0
4
1
0
0
0
0
2
0
0
0
0
2
1
1
2
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
1
2
2
0
0
0
2
3
0
0
0
0
0
0
3
0
0
2
1
1
0
1
1
0
0
0
0
0
0
0
1
1
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
3
2
0
2
2
1
1
0
2
0
0
0
1
1
0
0
0
0
1
0
2
0
0
0
2
0
1
0
0
0
2
0
2
1
2
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
3
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
4
0
0
0
2
0
0
1
2
1
0
3
0
0
0
0
0
2
2
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
7
0
0
2
0
1
0
1
0
6
7
2
0
0
0
2
0
2
1
1
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
1
1
1
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
1
0
0
3
0
0
2
2
0
1
0
0
0
2
0
0
0
2
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
1
2
1
2
0
0
0
2
0
5
0
0
0
0
3
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
2
0
2
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
2
0
0
1
1
0
2
0
0
0
0
1
0
0
2
0
0
0
2
1
0
0
2
1
1
0
2
1
1
3
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
0
2
2
0
2
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
2
0
0
0
1
0
1
0
0
1
2
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
1
2
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
2
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
2
0
0
0
1
0
1
0
0
0
4
0
0
0
0
0
0
0
4
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
3
0
0
3
2
0
0
0
0
0
0
2
1
0
0
2
2
0
1
0
0
0
1
0
0
0
1
0
3
0
0
0
0
0
3
0
0
3
0
1
0
0
0
1
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
1
0
0
2
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
2
0
6
0
2
2
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
1
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
3
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
2
0
2
0
0
0
0
0
0
1
0
2
2
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
5
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
2
0
2
1
4
0
0
3
0
0
1
0
0
0
0
0
0
1
0
3
0
0
1
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
2
0
0
0
1
1
0
0
0
1
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
2
2
1
2
1
3
0
2
2
0
1
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
2
0
1
0
2
0
7
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
2
0
0
1
0
1
3
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
1
1
2
0
0
0
0
1
0
0
0
2
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
2
0
5
0
0
0
0
0
0
2
0
0
2
0
0
1
2
0
0
0
0
0
2
0
0
2
2
0
1
0
0
0
0
1
0
0
2
2
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
2
0
2
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
2
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
2
3
2
0
1
0
0
0
0
1
0
0
0
0
0
2
2
0
0
1
0
1
2
0
0
1
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
3
2
0
0
0
0
0
0
1
2
2
3
2
0
1
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
3
0
2
1
9
1
0
3
2
0
0
2
0
0
3
1
2
0
0
3
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
2
0
1
3
0
1
2
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
1
1
0
0
0
4
0
0
0
0
0
0
0
2
3
0
0
1
0
1
0
0
0
2
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
1
0
0
0
2
0
0
2
2
1
0
1
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
1
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
3
1
1
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
3
2
0
0
0
1
1
0
0
2
0
0
1
2
0
0
3
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
1
0
0
0
2
0
2
0
2
0
2
0
0
0
0
2
0
0
0
0
1
0
1
1
2
0
0
2
0
2
0
0
0
0
0
3
1
0
1
0
0
0
0
0
7
0
0
0
2
0
1
1
0
0
0
2
0
2
0
0
2
0
1
1
2
2
1
3
0
0
1
0
0
0
0
2
0
1
2
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
1
3
0
0
0
0
1
0
2
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
2
0
2
2
0
3
2
0
0
1
0
0
1
0
1
0
0
0
0
1
3
2
0
0
1
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
1
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
2
0
0
2
0
1
0
0
0
0
2
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
2
0
3
0
2
2
2
0
2
2
1
0
0
2
0
1
0
0
2
0
0
0
0
2
0
0
0
1
1
0
0
0
0
1
0
0
2
0
4
0
1
0
0
2
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
1
0
1
2
0
2
0
0
0
0
0
0
0
0
1
0
2
0
2
1
0
0
0
0
1
2
4
0
0
0
0
0
0
2
0
0
0
1
0
1
2
0
2
0
6
0
1
0
1
0
0
0
2
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
1
0
0
0
0
0
1
2
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
2
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
2
0
3
0
0
2
0
0
0
0
0
0
0
0
2
6
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
2
0
2
0
0
0
0
0
1
0
0
0
1
2
0
0
2
0
1
0
2
2
1
1
0
0
0
0
0
0
2
2
0
2
0
0
1
0
0
2
0
2
0
0
0
0
0
1
1
2
0
0
2
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
2
0
0
2
0
0
2
0
1
0
0
0
0
1
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
3
0
0
1
1
0
0
2
0
0
0
1
0
0
0
0
2
0
0
2
0
1
3
4
0
0
0
0
1
2
1
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
1
5
0
0
2
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
2
0
0
0
3
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
2
0
2
1
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
2
0
0
3
0
1
0
0
0
0
0
2
1
0
2
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
3
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
3
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
1
0
0
2
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
4
1
0
1
0
2
0
3
0
0
0
0
1
2
0
0
0
0
2
0
1
7
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
2
1
0
0
0
1
0
0
0
0
0
2
0
0
0
1
2
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
2
0
0
2
2
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
2
1
0
0
0
0
1
0
0
2
0
2
0
0
0
0
2
0
2
0
0
3
0
1
2
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
1
0
1
0
0
2
1
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
1
0
0
0
3
1
0
0
0
1
2
0
0
0
1
0
0
1
1
0
1
2
0
2
0
0
0
1
0
0
0
1
0
0
2
3
0
3
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
1
1
0
2
1
0
0
0
2
0
0
0
1
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
2
0
0
6
0
1
0
0
2
0
2
2
4
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
1
0
1
0
0
0
2
0
4
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
2
1
0
2
0
0
0
0
0
0
0
1
0
2
2
1
0
1
0
0
0
0
0
0
0
0
2
1
0
2
0
0
1
1
2
1
2
0
0
2
0
1
0
2
0
0
0
0
0
0
2
4
0
1
0
2
0
0
0
0
0
0
0
1
0
1
0
0
1
0
2
1
2
0
0
0
1
1
0
0
4
0
0
0
0
0
0
3
2
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
1
1
0
1
0
1
0
2
0
1
0
0
1
0
1
0
0
0
1
2
4
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
1
0
0
0
2
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
1
0
3
2
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
5
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
4
1
0
1
3
0
0
0
0
1
2
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
2
1
1
3
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
1
1
0
0
0
1
0
1
1
0
1
0
0
0
0
0
2
0
2
0
2
0
0
0
2
0
0
0
0
0
0
1
2
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
3
2
0
0
0
0
1
0
1
1
2
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
1
0
1
0
0
3
0
0
0
1
0
0
0
0
7
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
3
0
0
0
1
0
0
2
1
2
2
0
0
0
0
0
0
0
0
1
0
1
0
0
1
2
4
1
1
2
1
0
0
0
0
0
0
1
2
4
0
0
2
0
0
2
2
0
1
0
0
0
0
1
0
0
0
1
1
0
0
1
0
1
0
0
0
1
0
3
2
2
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
6
0
0
2
0
2
0
0
0
1
0
2
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
2
0
2
0
1
0
2
0
0
1
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
2
0
1
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
2
1
4
0
1
0
2
0
0
0
1
2
1
0
1
0
0
1
0
0
1
0
1
0
2
1
1
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
2
2
0
0
0
0
0
1
0
1
1
0
1
1
0
1
1
2
2
0
0
0
2
0
3
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
3
1
2
0
0
1
0
0
3
0
0
1
0
0
0
0
0
2
1
0
1
0
0
0
2
2
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
1
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
2
0
0
0
0
2
5
0
0
0
1
2
0
0
0
0
2
0
1
0
0
2
0
0
0
0
1
0
0
1
7
0
0
2
2
0
1
0
0
0
0
1
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
1
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
1
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
3
2
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
2
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
2
10
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
1
2
0
8
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
2
3
2
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
1
0
2
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
2
1
0
0
1
3
0
2
0
0
0
1
0
0
0
2
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
1
0
0
0
4
0
2
0
0
0
0
0
0
0
2
1
2
0
0
2
2
0
2
2
0
0
1
1
0
0
1
0
1
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
4
1
1
0
0
2
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
7
0
0
0
0
0
5
0
1
0
2
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
1
0
3
0
1
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
1
0
0
0
2
0
0
1
0
1
0
0
1
0
0
0
0
0
2
1
0
0
2
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
4
0
3
1
0
0
1
0
2
0
0
0
1
0
0
0
0
0
2
0
0
3
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
1
0
2
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
3
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
3
0
1
0
0
2
2
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
2
1
0
0
0
0
2
0
0
2
3
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
4
0
1
0
0
0
0
0
1
0
1
0
1
0
3
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
2
0
0
0
1
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
3
1
0
0
0
0
2
0
0
0
0
1
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
1
1
0
0
0
1
0
0
2
2
1
0
1
0
0
3
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
7
0
0
0
0
1
1
1
1
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
2
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
1
0
2
1
0
0
2
0
0
2
2
1
4
2
0
0
0
1
0
6
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
1
0
2
0
5
0
0
0
0
0
2
2
3
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
8
0
0
2
0
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
2
0
0
0
0
3
0
3
1
1
1
0
0
0
0
0
0
0
2
3
3
1
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
1
0
0
0
0
0
1
1
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
2
0
1
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
3
0
1
2
1
0
0
0
0
0
2
0
0
1
0
1
0
3
2
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
1
1
0
2
2
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
3
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
3
2
0
1
2
2
0
0
0
2
0
0
0
0
1
1
0
0
0
1
1
0
0
2
2
0
0
2
0
0
0
1
1
0
0
0
0
1
2
0
2
0
2
0
0
0
0
1
0
1
0
0
0
3
0
3
2
0
2
0
1
2
0
2
0
2
1
0
0
1
2
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
1
0
0
0
0
0
3
1
0
0
0
2
2
0
0
0
0
0
1
0
1
0
2
2
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
1
0
0
2
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
2
0
0
1
0
1
1
0
3
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
1
0
0
2
0
0
0
0
0
3
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
3
3
0
0
0
0
0
0
1
0
0
0
0
2
3
0
2
1
0
0
0
0
0
2
0
0
0
1
1
1
0
2
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
1
2
0
0
0
0
2
0
0
0
2
0
1
0
0
0
2
0
1
0
2
0
4
0
0
1
0
0
0
1
1
0
2
0
0
0
1
2
1
2
2
0
0
0
0
0
1
0
0
0
0
0
7
1
0
0
0
1
0
0
1
0
0
1
0
0
2
2
0
0
0
0
1
1
0
0
0
0
1
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
1
1
1
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
1
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
1
2
0
0
1
0
1
2
0
0
0
3
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
2
0
1
1
0
0
0
0
1
0
1
2
0
2
0
0
0
1
0
1
2
0
0
2
1
0
0
2
0
0
0
0
2
1
0
1
1
1
0
2
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
1
2
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
2
1
2
0
1
0
1
0
2
0
0
7
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
1
0
0
0
2
0
2
0
2
0
0
0
3
0
0
0
0
2
0
0
0
2
1
0
2
1
0
1
2
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
4
0
0
2
0
3
0
2
0
0
0
0
2
0
0
0
0
2
0
0
2
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
2
1
1
0
2
0
0
0
2
0
0
2
0
2
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
2
1
1
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
1
0
0
0
1
2
0
0
1
0
0
0
2
2
1
0
0
2
0
1
0
1
0
0
0
2
1
1
0
0
0
0
0
0
0
0
1
0
0
2
0
2
1
0
0
0
0
0
1
1
0
3
0
0
0
0
0
0
0
1
0
0
0
5
1
0
2
0
0
0
0
0
2
2
0
0
1
0
0
0
1
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
6
0
0
2
8
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
3
0
0
1
2
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
2
2
0
2
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
2
0
1
0
1
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
2
0
0
1
0
0
0
0
1
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
2
0
0
0
0
0
0
2
1
0
0
2
0
2
0
0
0
0
2
1
1
0
0
2
0
0
2
2
0
2
0
0
0
0
1
2
0
0
2
0
1
3
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
3
1
0
0
2
0
0
2
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
1
0
3
0
0
1
1
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
1
0
3
2
1
0
0
0
1
0
0
0
0
1
0
1
0
0
2
0
0
0
3
1
0
0
0
0
0
0
2
0
1
1
0
1
0
0
0
0
0
1
0
2
2
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
2
0
2
0
0
0
0
1
2
0
0
2
0
0
0
2
3
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
1
0
0
0
0
0
0
0
0
2
1
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
2
6
0
1
0
0
0
2
1
0
0
2
0
0
0
0
2
2
0
0
4
0
0
0
0
0
0
0
0
0
0
1
3
3
0
0
2
0
1
0
1
1
2
0
0
1
0
0
0
0
2
2
0
0
2
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
1
0
0
0
0
1
1
1
1
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
2
2
0
2
1
2
0
1
0
0
0
2
1
1
2
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
3
1
0
0
2
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
1
2
2
1
2
0
5
0
0
0
1
3
1
0
0
0
2
2
0
0
0
2
0
1
1
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
1
0
1
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
2
0
0
2
1
0
0
0
2
0
1
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
1
0
2
0
1
0
0
0
1
2
2
0
2
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
2
1
2
0
0
0
0
0
0
1
2
1
0
1
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
2
1
0
1
0
0
0
0
0
4
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
3
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
2
0
1
1
1
2
0
2
0
0
0
0
0
0
1
0
0
1
3
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
19
0
0
0
0
0
0
0
2
0
0
2
0
0
2
3
0
2
0
8
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
1
0
2
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
2
0
1
0
0
0
3
0
0
0
0
2
0
2
2
3
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
2
0
1
0
0
1
0
0
0
3
2
1
0
0
1
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
2
1
2
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
6
0
2
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
2
0
0
1
1
3
0
0
1
0
1
2
0
0
1
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
3
0
0
0
3
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
1
0
1
0
0
0
3
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
5
0
0
0
0
0
0
0
0
2
1
0
5
0
0
0
0
0
0
4
0
3
1
0
0
0
0
0
0
2
0
1
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
2
2
2
0
1
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
3
1
0
3
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
1
0
1
0
0
2
0
2
0
0
0
0
0
1
1
0
2
2
0
1
0
0
0
1
0
0
0
0
1
0
1
2
4
1
0
0
0
0
0
0
2
0
0
1
0
1
0
2
0
0
0
0
5
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
3
1
2
2
1
0
0
0
0
0
2
0
0
1
0
0
0
1
2
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
2
3
0
0
1
0
0
0
0
2
1
0
0
0
2
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
1
1
0
0
1
0
0
0
1
0
1
0
0
2
0
0
0
2
0
2
0
0
1
0
2
0
4
1
0
2
0
0
2
0
2
0
0
1
2
0
0
2
0
2
0
2
0
0
0
1
0
0
2
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
1
2
1
0
1
1
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
3
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
2
0
0
2
4
0
0
0
1
0
1
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
2
1
0
0
0
1
1
0
0
0
0
0
0
1
2
3
2
0
0
0
0
1
0
0
0
0
1
2
0
1
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
6
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
3
0
2
0
0
0
0
2
0
0
3
0
0
0
0
2
2
0
0
1
1
3
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
2
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
1
0
2
0
2
2
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
1
0
2
1
0
0
0
3
1
0
2
0
0
0
2
0
0
0
0
0
0
1
0
2
1
3
0
0
0
0
0
0
0
3
0
0
0
2
0
0
3
0
0
0
1
1
0
0
0
0
3
0
1
1
0
0
1
0
1
0
0
1
0
0
1
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
2
0
2
0
0
1
0
1
1
0
1
0
0
2
1
0
0
0
0
0
2
0
1
0
0
2
0
1
0
0
1
1
0
0
0
0
0
0
1
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
2
0
0
0
1
0
2
0
2
0
0
2
0
0
3
2
2
0
0
0
2
2
0
0
0
0
0
0
3
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
3
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
3
0
0
2
1
2
1
0
0
1
0
0
0
2
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
5
0
0
0
2
0
7
0
1
0
0
0
1
0
0
0
1
0
0
2
0
0
2
0
2
1
1
0
0
1
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
1
2
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
2
0
1
0
0
0
2
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
2
0
1
3
0
0
0
2
0
0
0
0
0
0
8
0
0
0
0
0
0
3
1
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
1
3
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
2
2
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
3
2
0
0
1
0
2
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
1
2
0
0
0
2
1
2
0
2
0
1
2
0
0
1
0
1
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
3
2
1
0
0
0
0
0
1
1
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
5
0
2
0
0
3
0
0
0
0
0
0
0
2
1
0
2
0
0
2
1
0
2
2
6
0
3
0
1
0
0
0
0
0
0
0
1
0
0
3
1
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
1
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
1
2
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
1
0
2
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
3
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
1
0
3
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
1
2
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
1
1
0
0
0
2
2
0
0
0
2
0
0
1
0
0
0
3
2
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
2
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
1
0
0
0
3
0
0
0
2
0
0
0
0
2
0
2
0
1
0
2
0
0
1
0
0
0
2
0
0
2
0
0
0
1
0
4
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
1
0
0
0
2
2
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
1
2
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
2
2
0
0
2
1
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
4
0
2
2
0
1
0
1
2
1
0
2
0
0
0
3
2
0
1
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
1
3
0
0
0
2
2
0
0
2
0
0
1
1
2
0
0
0
2
0
1
0
0
0
2
0
0
0
1
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
2
2
1
10
0
0
1
0
0
0
0
0
0
0
0
1
5
0
2
0
0
0
1
0
1
1
1
1
1
0
0
0
2
1
2
0
6
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
4
1
0
0
2
1
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
1
0
2
0
0
0
0
5
0
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
2
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
2
0
0
2
1
0
0
0
0
2
0
0
3
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
2
2
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
1
2
1
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
6
3
1
0
0
2
0
0
1
2
0
0
0
0
2
2
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
1
0
0
0
0
2
2
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
2
2
1
2
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
4
1
1
0
0
2
2
0
1
2
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
2
3
0
0
2
0
0
0
1
0
0
1
0
2
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
2
0
1
0
0
1
1
0
1
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
1
2
2
0
0
5
0
0
0
2
0
0
3
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
1
1
0
0
3
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
2
0
0
2
4
0
0
1
0
2
0
1
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
2
1
2
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
3
0
1
1
2
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
2
1
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
3
1
2
2
0
1
1
0
0
1
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
2
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
1
0
0
0
1
2
0
2
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
3
0
0
0
0
3
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
3
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
1
2
0
0
1
0
1
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
2
0
0
3
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
2
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
2
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
1
2
2
0
0
0
0
0
1
0
2
0
2
1
0
2
0
0
1
0
0
2
0
2
0
0
1
2
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
1
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
2
2
0
0
0
0
0
1
1
0
2
0
1
1
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
1
1
2
0
0
0
0
0
0
1
0
0
0
3
1
0
0
1
0
0
3
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
2
2
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
1
1
0
0
0
2
0
1
0
0
0
1
5
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
2
0
0
2
0
1
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
3
0
2
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
3
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
2
0
0
1
2
0
1
0
0
2
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
3
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
2
0
0
0
1
0
1
0
1
1
0
0
0
0
7
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
2
0
0
1
1
2
0
0
0
0
0
0
3
0
0
0
0
2
0
1
0
0
0
2
0
0
1
0
0
0
2
1
3
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
2
2
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
4
2
0
2
0
0
0
1
0
0
1
0
0
1
1
0
0
0
1
0
0
0
2
0
0
0
0
2
1
0
0
0
0
1
0
2
1
0
3
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
2
0
1
2
0
0
0
2
1
0
0
0
0
0
1
0
1
3
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
2
1
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
2
0
4
0
0
1
1
0
0
0
1
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
2
0
2
0
0
0
0
0
2
0
2
2
0
0
1
0
0
1
0
1
2
3
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
1
0
0
3
0
0
2
0
0
1
0
0
0
1
0
2
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
3
2
2
0
2
0
0
2
0
0
0
1
1
1
0
0
0
1
0
2
0
1
1
0
0
0
0
0
2
3
0
0
0
0
2
0
0
4
1
1
2
1
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
2
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
1
0
0
1
1
1
1
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
4
0
0
1
0
3
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
1
0
3
0
0
0
1
0
0
0
2
1
0
3
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
1
2
1
3
2
1
0
2
0
0
0
0
0
0
0
2
0
0
3
0
3
0
1
2
0
0
0
1
0
2
0
1
0
2
0
0
0
0
0
0
2
0
2
0
0
2
0
2
0
2
1
0
0
0
0
1
2
0
0
1
0
0
0
0
0
2
1
0
0
2
0
0
2
0
0
0
1
2
1
0
0
0
0
1
0
0
2
0
2
0
0
0
2
2
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
2
0
2
2
2
0
2
0
0
0
0
0
2
1
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
2
0
2
1
3
0
0
0
1
1
0
1
0
0
0
5
2
0
0
1
0
0
2
2
1
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
1
5
1
0
0
0
0
1
6
2
0
0
0
0
0
0
2
3
2
0
1
0
0
0
2
1
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
2
2
1
0
0
4
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
2
2
0
0
1
0
0
2
0
2
1
2
0
0
0
4
0
0
0
2
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
2
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
2
2
0
0
4
0
0
2
1
0
1
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
3
0
0
0
0
0
0
1
2
1
0
0
0
1
1
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
3
2
1
0
0
1
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
1
0
2
3
0
0
0
0
2
0
0
2
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
1
0
0
2
0
2
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
5
0
0
0
0
1
2
0
0
0
0
1
1
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
2
0
1
0
0
2
0
0
0
1
6
0
0
0
0
0
0
0
0
1
2
0
0
1
1
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
3
0
0
0
1
0
0
0
1
0
0
0
0
2
2
0
0
1
0
0
1
2
0
1
0
0
1
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
2
0
2
4
0
2
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
1
0
0
0
2
2
1
0
0
0
0
0
0
3
2
0
1
1
0
0
3
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
2
0
0
0
3
0
0
2
0
0
0
0
0
1
2
0
2
0
0
0
0
0
1
0
0
1
0
2
0
0
2
4
0
1
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
4
1
0
0
0
0
0
1
1
0
0
0
0
1
4
1
0
0
0
3
2
2
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
3
0
0
0
1
0
0
0
0
1
0
0
2
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
1
2
0
1
0
2
0
1
1
1
0
0
0
0
1
0
3
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
2
1
0
1
0
0
0
0
2
0
0
1
2
0
2
0
0
1
2
0
1
0
2
0
0
2
0
1
0
0
0
0
3
0
0
1
0
0
2
0
1
0
2
0
2
0
1
0
0
0
0
0
1
0
2
2
0
1
0
0
2
2
1
0
2
1
0
0
0
2
1
0
2
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
1
4
0
1
0
2
0
0
1
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
4
1
0
1
1
0
0
0
0
1
1
2
0
0
0
0
2
1
2
0
0
1
4
0
1
1
2
0
0
2
2
1
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
2
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
2
0
0
0
0
0
1
0
2
1
1
2
0
2
2
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
2
2
0
2
0
0
0
2
1
0
0
2
2
0
0
1
1
0
0
0
0
0
0
0
2
1
2
1
0
0
0
0
1
0
1
0
0
5
0
0
0
0
2
0
0
0
1
2
1
0
2
0
0
0
0
2
0
0
0
5
0
0
0
0
0
1
0
0
2
1
0
0
0
0
2
0
0
2
0
1
2
1
0
2
0
0
0
0
1
0
0
2
0
0
1
0
0
1
1
0
0
2
1
0
0
0
2
0
0
0
1
2
0
0
4
0
0
0
4
0
1
0
1
0
1
1
3
0
0
0
2
0
2
0
2
0
2
0
0
2
1
0
1
1
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
1
9
0
2
0
0
2
0
2
0
0
2
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
1
0
0
0
1
1
0
0
4
0
1
0
0
1
0
0
3
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
2
0
0
1
0
2
0
0
0
0
1
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
2
0
1
0
0
0
1
2
0
0
0
0
2
2
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
1
1
2
1
0
2
2
0
3
0
0
0
0
3
0
2
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
1
2
0
0
1
2
3
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
1
1
0
2
0
12
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
3
0
0
0
0
1
2
1
0
0
0
0
0
0
0
2
0
1
0
1
2
1
0
0
0
2
0
0
1
0
0
1
0
0
2
0
0
0
1
3
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
2
0
2
0
2
2
0
2
1
1
0
0
2
2
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
1
3
1
1
0
1
0
1
0
1
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
2
0
0
2
0
0
0
1
0
0
0
2
1
0
0
1
0
0
0
2
0
0
0
2
1
0
0
0
0
2
2
2
0
0
0
0
0
4
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
2
1
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
2
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
2
0
1
0
1
2
0
0
0
0
0
3
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
3
2
0
0
0
1
1
2
2
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
4
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
2
0
0
1
0
0
1
2
0
0
0
1
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
2
2
0
2
0
0
2
1
0
0
0
2
1
0
3
1
2
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
3
2
0
1
4
0
4
0
0
0
2
0
0
2
0
0
2
0
2
0
3
1
0
6
1
2
0
0
0
2
0
0
0
0
0
1
0
0
3
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
1
0
0
2
1
1
0
0
2
1
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
2
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
2
1
2
1
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
1
2
0
0
0
2
0
0
2
0
0
0
0
0
3
0
0
0
0
1
0
0
1
0
0
0
1
1
0
2
0
0
1
3
0
0
0
0
1
0
2
0
1
0
0
2
0
0
0
1
1
1
1
0
0
1
2
0
0
0
0
3
0
0
1
2
1
0
2
0
0
0
0
2
2
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
3
1
0
2
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
2
2
2
0
0
0
1
0
0
2
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
2
2
0
0
0
0
0
3
1
0
0
2
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
1
0
2
0
0
0
1
0
0
3
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
2
1
0
0
2
0
0
0
2
0
0
0
2
2
1
0
0
1
0
0
0
0
1
0
2
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
2
1
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
1
2
0
1
0
6
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
1
0
1
0
0
1
2
0
0
2
0
0
1
0
0
0
2
2
2
0
0
2
1
0
0
0
1
0
1
1
0
0
0
0
1
1
0
1
0
0
2
0
0
2
0
1
0
0
1
2
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
1
2
1
0
0
0
0
0
1
1
1
0
0
0
0
1
2
1
0
1
0
2
0
2
2
0
2
1
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
4
1
0
0
3
1
0
0
1
2
1
0
2
0
0
0
2
0
0
1
0
0
0
0
0
1
2
2
0
0
2
0
0
0
0
0
0
0
1
0
2
1
0
0
0
1
0
2
1
0
0
0
0
9
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
2
0
0
2
0
1
1
0
0
1
1
0
0
0
0
0
0
0
1
1
0
2
0
0
0
2
0
0
0
0
1
0
0
3
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
2
0
0
0
0
1
2
1
1
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
3
0
0
0
0
7
0
0
0
0
0
1
0
2
0
1
0
0
0
1
1
2
1
0
6
0
2
0
0
0
2
2
2
3
0
0
0
2
0
0
2
0
2
0
0
1
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
2
0
0
2
1
0
0
0
1
1
1
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
2
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
3
0
1
0
0
0
1
0
2
0
1
1
0
2
4
0
0
0
2
2
0
0
0
0
0
0
1
0
0
1
1
0
2
0
0
0
0
2
0
0
0
0
2
3
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
1
0
1
1
0
1
1
0
0
0
2
2
1
0
2
6
0
0
0
0
0
0
0
0
1
0
1
1
2
1
0
2
1
0
0
0
2
3
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
1
1
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
2
3
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
2
0
0
2
2
0
2
2
0
0
1
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
2
2
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
2
1
2
0
2
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
1
1
0
0
0
2
0
1
2
2
1
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
1
0
0
1
1
1
0
2
1
0
0
0
0
0
0
0
0
1
2
2
0
0
2
0
2
0
0
0
0
2
0
1
2
0
0
0
2
0
1
2
0
0
2
2
0
0
3
0
1
2
0
0
2
2
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
2
0
0
0
0
3
0
0
0
1
0
2
2
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
2
0
2
0
0
0
2
0
1
0
1
0
2
0
0
7
0
0
2
0
0
1
0
0
2
0
2
2
0
2
0
0
1
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
3
1
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
2
2
2
2
1
0
0
1
0
0
1
0
2
0
2
2
2
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
1
4
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
1
2
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
1
1
0
1
0
0
1
2
4
0
0
0
0
0
2
0
0
1
0
1
0
1
2
1
0
0
2
0
1
0
0
2
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
2
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
2
0
1
2
2
0
1
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
5
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
3
0
0
0
1
0
0
3
0
0
0
0
0
0
0
1
0
0
2
0
0
1
1
1
0
0
2
2
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
2
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
3
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
2
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
1
1
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
2
0
0
2
0
0
2
0
0
2
0
0
2
0
0
0
1
0
1
0
0
2
0
0
0
0
0
2
0
0
0
1
0
1
0
0
1
1
0
0
0
0
3
0
0
0
0
0
3
1
1
0
2
0
0
0
0
1
0
1
0
0
0
0
0
2
3
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
2
0
0
0
1
0
1
0
1
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
3
2
0
0
0
2
1
4
0
1
1
0
1
0
1
1
0
1
2
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
1
0
2
3
0
1
0
0
0
0
0
0
0
0
2
0
4
2
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
2
0
0
0
0
0
10
1
0
0
0
2
1
3
1
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
3
0
0
0
2
1
1
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
1
0
1
0
3
2
2
2
2
1
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
3
0
0
1
0
1
0
0
0
1
0
0
0
0
1
2
0
0
0
0
2
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
1
0
2
1
0
0
0
3
1
0
0
1
0
0
1
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
1
1
1
0
0
1
1
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
3
3
0
2
0
0
0
1
1
0
2
0
0
2
2
0
0
1
2
0
2
0
1
0
0
0
0
0
0
0
2
1
1
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
2
0
0
2
0
1
0
1
0
2
0
1
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
3
2
0
0
0
2
1
0
3
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
2
3
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
2
0
0
0
1
0
2
0
0
5
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
2
0
2
0
2
0
2
0
1
0
0
0
0
0
0
6
0
2
4
0
1
1
0
0
0
0
0
1
1
1
1
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
1
2
0
0
0
1
0
0
0
0
1
2
2
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
2
0
0
2
2
2
0
1
0
0
0
2
2
1
0
2
0
0
0
0
1
2
0
0
0
1
0
1
2
0
0
2
0
0
1
0
0
0
1
1
0
0
0
0
2
0
1
0
0
0
0
0
3
1
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
3
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
7
2
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
1
1
2
0
0
1
0
0
0
0
0
0
2
2
1
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
2
0
2
1
0
0
0
0
3
0
1
0
2
1
0
0
0
0
0
2
0
0
0
0
0
2
2
2
0
1
2
0
0
0
1
0
1
0
0
0
2
2
2
1
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
1
2
1
2
2
0
1
1
1
1
2
0
0
2
0
1
1
2
2
1
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
2
0
0
0
0
1
0
2
0
2
0
0
1
0
0
2
1
0
0
0
0
0
0
0
1
0
2
2
1
4
0
1
0
1
2
0
0
3
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
1
0
0
0
2
2
0
0
1
2
1
0
1
0
2
0
2
0
0
0
0
0
1
0
1
0
2
1
0
0
2
0
0
3
1
0
2
0
0
0
1
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
1
0
2
1
0
0
0
3
2
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
6
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
3
1
0
0
0
2
1
2
1
0
0
2
0
0
0
0
0
1
1
0
2
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
3
2
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
1
3
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
4
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
1
1
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
3
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
11
0
0
0
0
0
0
1
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
1
0
8
2
0
0
0
1
0
0
1
0
2
0
1
0
0
0
0
1
1
1
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
1
2
0
0
3
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
2
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
1
0
2
0
0
2
0
0
0
2
0
1
0
1
0
2
1
0
2
0
1
0
1
1
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
2
0
0
2
0
0
2
1
0
0
2
0
1
5
0
1
1
0
0
0
2
3
3
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
3
1
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
2
0
0
0
0
3
0
0
2
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
3
0
0
2
0
1
1
1
1
0
0
0
0
0
1
0
0
2
1
0
0
1
0
1
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
2
0
2
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
1
0
1
0
2
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
2
3
0
0
0
0
2
0
1
1
2
0
1
0
0
0
2
0
0
0
1
0
1
0
1
0
0
2
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
2
0
2
1
0
0
1
0
1
0
0
3
0
0
0
1
0
0
2
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
1
0
0
0
2
2
1
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
3
1
0
2
0
0
0
0
1
1
0
2
0
0
0
2
0
0
1
2
0
0
0
2
0
2
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
1
1
0
0
1
0
1
0
0
1
0
0
0
2
0
0
1
0
1
0
2
2
2
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
2
1
0
1
2
0
1
0
0
0
3
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
2
1
0
0
0
0
0
0
1
0
2
0
0
0
2
0
2
2
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
3
1
0
2
0
1
0
1
0
0
0
0
0
3
0
0
0
0
2
2
2
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
1
3
0
0
2
3
0
0
1
0
0
0
0
3
0
2
0
0
2
1
0
1
0
1
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
1
2
1
0
2
0
2
0
3
2
0
0
0
2
2
0
1
0
1
0
0
0
0
2
1
2
0
1
3
2
0
1
0
0
2
2
0
0
0
0
2
0
1
0
0
0
1
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
1
0
0
0
0
2
2
2
0
0
0
2
0
0
0
2
0
0
0
3
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
2
0
0
2
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
4
1
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
2
0
2
0
2
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
1
2
2
2
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
2
0
1
2
1
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
1
0
1
1
0
0
0
1
1
0
0
0
0
2
0
0
1
1
0
0
0
1
0
0
0
1
0
3
0
2
0
0
0
0
0
0
7
0
2
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
1
0
0
0
0
3
0
0
0
0
2
0
0
0
1
2
1
0
1
0
2
0
0
1
0
0
0
2
0
0
0
2
2
0
0
1
0
0
0
0
1
0
0
2
2
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
1
2
0
0
4
0
1
2
0
2
4
2
0
2
0
2
1
0
1
0
2
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
2
2
3
0
0
2
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
1
2
0
1
0
0
0
10
0
0
2
2
2
0
0
0
0
2
0
0
0
0
0
0
3
0
0
1
0
0
0
2
0
0
1
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
1
0
3
0
0
0
0
0
0
0
0
4
0
2
0
1
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
6
2
0
0
0
0
0
0
2
0
1
1
0
2
1
0
0
0
2
0
0
0
2
1
2
0
1
0
2
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
2
2
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
1
2
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
3
2
0
0
1
1
0
0
1
0
0
0
2
0
2
0
0
6
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
3
1
0
2
0
0
2
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
1
2
0
1
0
1
0
0
0
1
0
1
0
1
0
0
0
0
2
2
0
0
1
2
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
5
0
0
1
1
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
2
1
3
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
2
2
0
1
0
0
0
0
2
0
0
0
2
0
0
1
2
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
2
0
0
1
3
1
1
0
0
1
1
0
4
0
0
0
1
2
0
0
0
0
1
2
0
1
0
0
0
1
0
0
0
0
0
0
2
3
0
0
0
0
2
1
0
0
0
1
0
1
1
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
1
1
1
1
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
2
1
0
0
2
0
1
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
3
1
0
0
0
2
0
0
0
1
2
0
0
0
3
1
1
0
1
3
2
0
0
0
1
0
2
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
2
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
3
2
0
0
0
1
1
2
1
0
2
0
0
0
0
0
0
0
3
0
0
0
0
2
2
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
1
3
0
2
2
0
1
0
0
0
0
2
1
1
1
0
0
0
1
1
3
0
0
0
0
2
1
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
4
2
2
0
0
1
2
1
0
0
1
0
4
0
2
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
2
0
0
3
2
0
1
2
0
1
2
0
0
2
0
1
0
1
1
0
0
0
0
0
0
1
0
0
2
2
1
0
0
1
0
3
0
2
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
1
2
0
7
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
1
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
4
3
0
1
0
0
0
0
0
0
0
0
1
1
2
0
0
0
2
0
0
0
0
0
0
0
2
2
2
0
0
1
0
0
2
0
1
1
1
0
0
0
0
1
1
0
2
0
2
0
0
0
0
0
3
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
1
0
1
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
4
0
0
0
0
2
2
0
0
1
0
0
2
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
1
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
2
0
3
0
0
0
3
3
0
0
2
0
1
0
2
0
2
0
0
0
0
0
0
3
0
0
1
3
0
0
0
1
0
0
1
1
0
2
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
2
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
1
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
4
0
1
0
0
0
0
0
0
2
1
2
1
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
3
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
1
0
2
2
0
1
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
2
0
0
0
0
2
1
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
3
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
1
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
2
0
3
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
2
0
0
2
0
0
1
0
2
1
0
0
2
0
2
0
5
0
0
0
2
0
2
0
0
1
1
0
1
0
0
0
0
0
1
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
2
2
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
4
0
0
0
1
0
0
0
2
0
1
0
0
2
0
2
0
0
0
0
0
0
1
0
0
2
3
0
0
0
1
0
2
1
0
0
2
0
1
0
0
0
2
0
2
1
1
2
0
0
0
1
0
0
0
2
0
0
0
2
0
0
2
1
0
1
0
0
2
0
2
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
3
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
7
0
1
0
3
0
0
0
0
1
1
2
1
0
0
1
1
1
0
0
3
0
2
0
1
0
2
0
1
0
0
5
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
1
0
2
0
3
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
2
1
0
0
0
0
0
2
1
0
1
0
0
0
2
0
1
0
2
0
0
0
1
0
1
0
0
0
1
0
0
1
1
2
0
0
0
0
0
2
1
3
1
3
0
0
2
0
0
1
0
2
1
0
2
0
0
0
0
0
0
0
3
0
2
1
2
2
0
0
3
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
1
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
1
0
2
0
2
0
0
2
1
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
4
0
0
0
0
0
3
0
0
0
0
0
0
2
1
1
1
2
0
2
3
1
0
0
2
0
0
0
0
0
0
2
2
0
2
0
0
2
1
2
2
1
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
1
0
0
0
0
0
2
1
0
0
1
0
1
2
0
1
0
0
0
2
1
0
0
0
0
0
2
0
0
0
6
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
1
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
2
0
1
0
0
0
2
1
0
0
0
2
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
3
0
0
1
0
2
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
7
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
3
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
3
0
0
0
0
2
0
3
1
0
0
0
2
0
1
0
2
2
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
3
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
2
0
2
0
1
0
0
0
1
0
0
0
0
0
2
0
1
0
2
0
1
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
1
2
0
0
0
0
0
0
0
1
1
2
2
0
2
0
1
0
0
0
0
0
1
0
0
2
4
0
1
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
1
0
1
1
2
0
0
0
3
0
1
2
0
0
1
0
0
0
0
0
0
0
0
7
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
1
0
1
0
0
0
2
2
0
2
0
0
0
0
0
1
0
0
2
2
1
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
1
0
0
0
0
0
4
0
1
2
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
3
1
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
1
0
2
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
3
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
3
0
0
1
1
1
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
3
0
0
0
0
0
0
0
1
0
0
0
2
1
0
3
0
1
0
0
2
0
0
0
2
0
2
0
0
0
0
1
0
0
2
2
0
0
0
0
0
1
0
2
1
0
1
0
1
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
3
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
1
1
2
0
0
0
0
1
2
0
0
2
2
2
1
2
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
1
0
2
0
1
1
0
1
0
0
0
2
0
1
0
0
0
2
2
0
1
0
0
0
0
0
1
0
1
2
0
0
6
0
2
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
3
2
1
0
0
2
0
1
2
1
1
0
0
0
0
1
0
2
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
2
1
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
2
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
2
0
0
1
3
0
1
0
0
0
5
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
1
2
1
2
1
0
0
1
2
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
1
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
1
2
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
2
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
2
0
1
0
0
0
0
1
0
1
0
0
0
1
0
2
0
0
0
2
0
1
0
0
0
0
1
0
0
1
0
0
0
2
1
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
2
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
2
1
1
0
0
0
0
1
2
2
1
0
2
2
1
0
0
2
2
2
0
1
0
1
2
0
0
1
0
0
0
1
0
3
0
2
2
0
2
3
2
1
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
2
0
1
0
0
3
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
2
0
2
0
0
1
0
0
0
1
1
2
1
0
0
2
1
0
0
0
0
0
0
0
1
0
0
2
0
2
0
2
0
0
0
2
0
2
1
2
0
0
1
2
2
0
0
2
1
0
1
0
0
2
1
0
0
0
0
0
0
2
0
0
2
2
0
2
2
0
0
1
0
0
3
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
1
0
0
0
0
1
0
0
2
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
2
1
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
1
0
0
1
0
2
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
1
0
1
0
0
0
0
1
2
0
0
0
2
0
2
3
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
4
0
0
1
0
0
1
0
1
1
1
0
0
2
0
4
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
2
1
2
0
0
1
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
1
1
4
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
1
1
0
0
0
0
2
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
1
0
1
2
0
0
0
0
0
0
0
2
0
0
3
0
0
1
2
0
0
0
0
0
0
1
2
0
0
2
0
2
1
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
1
1
0
0
2
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
1
1
0
0
2
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
2
0
0
0
2
0
0
0
0
2
2
0
0
0
2
1
0
1
0
0
4
0
2
0
0
1
0
2
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
2
0
2
1
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
4
1
1
0
2
2
0
0
2
0
0
0
1
1
0
1
0
1
0
0
2
0
0
1
0
0
2
0
0
1
0
2
0
3
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
1
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
5
0
2
1
1
0
2
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
1
2
0
0
0
0
2
0
0
0
2
2
0
0
0
2
0
0
2
2
0
2
1
0
1
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
2
3
0
1
0
1
0
0
1
1
2
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
1
0
2
0
3
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
1
0
1
0
0
0
0
0
0
2
0
0
0
4
0
2
1
2
1
0
0
0
0
0
0
1
0
0
2
0
0
2
0
2
1
2
0
0
0
1
0
0
1
0
1
1
0
0
0
0
2
0
0
0
0
5
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
2
2
0
0
1
0
0
0
0
2
0
0
2
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
4
1
0
0
0
0
0
4
2
2
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
1
3
0
0
0
2
0
2
2
0
0
2
0
0
0
4
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
2
1
0
5
0
0
2
0
2
3
0
2
0
0
0
0
0
2
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
1
2
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
2
0
1
0
1
0
0
0
0
1
2
0
0
0
1
0
0
1
0
0
2
1
1
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
1
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
1
0
0
1
1
1
1
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
2
2
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
2
0
1
0
0
1
1
0
0
0
0
1
0
2
1
2
0
1
0
0
2
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
4
0
0
1
0
0
2
0
1
2
0
0
0
0
2
0
1
1
1
1
6
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
2
0
0
2
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
3
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
1
0
1
0
2
0
1
2
0
0
0
0
2
0
1
0
0
0
0
1
2
2
2
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
1
0
0
1
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
1
3
0
0
0
2
0
0
1
0
1
0
2
0
0
4
0
0
2
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
3
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
3
1
0
6
0
0
0
2
0
0
0
0
0
0
2
0
2
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
3
0
1
0
1
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
1
1
2
0
0
1
0
3
0
3
0
0
0
0
0
0
2
1
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
2
0
3
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
1
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
1
2
0
2
2
0
0
0
0
2
0
0
1
2
2
1
0
0
1
0
0
2
1
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
1
1
0
0
2
0
0
0
2
0
2
1
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
3
2
0
0
0
0
0
1
2
0
2
0
3
1
0
2
0
0
0
0
1
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
2
1
0
0
0
1
0
4
3
0
0
0
2
0
2
0
0
0
0
2
0
0
0
2
1
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
3
1
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
2
5
1
0
0
0
0
0
0
0
1
2
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
2
0
0
0
0
1
2
0
1
0
0
1
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
2
2
0
0
0
0
2
0
0
2
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
3
2
0
2
0
0
1
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
1
0
0
0
0
0
0
0
1
0
0
1
2
2
0
0
0
3
0
0
0
1
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
2
0
2
0
1
1
2
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
1
0
0
2
0
2
5
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
2
0
2
0
2
0
3
1
0
0
0
2
0
1
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
1
0
1
0
0
0
0
1
0
5
1
0
1
0
0
2
2
0
0
2
0
0
0
1
0
0
0
1
0
2
1
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
2
1
0
0
0
0
6
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
2
0
0
1
2
2
0
0
0
2
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
1
0
1
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
4
0
0
1
0
2
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
2
3
0
2
1
0
0
0
0
0
1
0
2
0
2
0
0
0
2
1
2
4
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
2
1
0
0
0
0
1
0
1
2
0
0
0
0
2
2
0
0
0
0
0
0
2
5
3
0
0
0
0
1
0
0
1
3
0
0
0
0
1
0
2
1
0
0
0
0
3
0
0
0
3
0
2
1
1
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
4
1
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
3
1
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
3
2
3
0
0
0
3
0
3
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
1
0
0
0
2
2
0
0
0
0
1
1
2
0
0
0
0
0
0
3
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
1
0
0
2
1
0
0
2
0
0
0
1
0
0
0
2
0
0
2
1
0
0
2
1
0
0
0
2
0
0
0
0
1
0
1
1
1
0
0
0
2
0
0
0
0
0
2
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
2
1
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
1
0
0
1
0
0
0
0
0
1
0
1
1
1
0
0
0
0
1
0
0
0
1
0
1
3
0
0
2
2
0
1
0
0
0
1
1
1
1
3
0
0
1
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
1
1
0
0
2
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
3
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
3
0
1
2
0
0
0
0
0
0
0
5
0
0
1
0
0
0
2
1
0
1
0
0
2
1
0
0
0
0
4
0
0
1
0
1
2
0
0
0
1
0
1
1
0
1
0
0
0
0
0
2
0
0
0
1
1
2
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
2
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
1
3
0
0
0
0
1
0
0
2
0
3
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
2
2
2
0
0
0
4
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
3
1
0
0
0
2
0
2
0
0
2
0
1
2
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
1
0
0
0
0
1
2
1
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
2
0
2
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
6
1
2
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
2
2
2
1
0
0
0
0
0
0
1
0
1
2
0
2
0
0
0
0
0
1
1
0
2
0
3
3
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
1
2
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
6
2
2
0
0
0
0
1
2
0
0
0
2
0
2
2
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
1
0
2
0
0
0
0
1
3
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
1
0
0
0
2
0
5
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
2
0
0
0
0
3
0
1
1
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
3
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
3
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
2
0
1
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
7
2
1
0
0
1
0
0
9
0
2
0
1
0
1
0
3
1
0
0
0
1
0
0
2
0
2
0
3
0
0
2
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
1
1
0
0
0
0
1
0
1
2
0
2
0
0
2
1
0
4
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
2
0
0
1
1
0
0
1
0
0
2
2
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
1
0
1
1
0
0
0
2
1
0
0
0
2
0
1
4
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
3
0
0
1
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
2
0
2
0
2
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
2
0
0
2
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
2
1
0
2
2
0
0
0
1
0
2
0
0
0
7
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
2
0
2
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
2
3
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
2
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
4
0
0
2
0
2
1
0
1
1
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
2
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
1
1
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
2
1
2
1
0
0
0
1
4
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
2
2
0
0
1
0
2
0
0
0
1
2
0
1
1
0
0
2
0
0
0
2
0
0
0
0
0
2
4
2
0
1
2
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
5
0
0
0
0
0
1
4
0
0
0
1
0
0
1
0
0
1
0
0
5
0
0
0
0
0
0
1
0
1
1
1
2
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
1
1
0
1
0
2
0
1
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
2
1
1
1
0
0
0
0
1
3
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
2
1
0
0
0
2
0
0
0
0
0
1
0
1
4
2
1
1
3
2
2
0
1
0
0
1
2
2
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
2
1
1
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
2
1
1
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
2
1
0
0
1
0
0
2
0
1
0
0
2
2
2
0
2
0
0
1
0
0
2
0
2
0
0
0
1
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
2
0
0
2
2
1
0
0
0
0
0
1
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
2
3
0
2
1
0
0
4
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
2
0
2
1
0
0
1
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
1
0
0
3
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
2
5
0
0
0
0
0
2
1
0
0
2
1
0
0
0
0
1
0
0
2
0
1
1
1
0
1
0
1
0
0
0
0
0
2
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
2
0
0
0
1
0
0
2
2
0
0
2
0
1
1
1
0
2
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
2
0
0
0
2
0
1
0
0
0
0
2
0
2
0
0
0
2
0
1
0
0
2
2
0
3
0
0
0
2
0
1
1
0
2
0
2
0
0
5
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
2
0
0
1
0
2
1
4
0
2
0
0
0
0
1
2
0
2
0
0
1
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
1
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
2
0
1
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
1
0
0
2
2
0
1
1
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
2
0
0
0
0
2
2
0
0
0
0
0
3
2
0
1
1
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
1
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
6
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
3
0
0
0
1
0
0
0
0
0
1
2
1
0
0
2
2
2
0
1
0
0
0
0
0
2
0
2
2
0
1
0
0
0
2
0
3
1
0
1
0
1
4
0
0
1
0
1
1
2
0
1
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
3
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
2
0
0
0
2
0
1
2
0
0
0
1
0
0
0
0
1
3
0
0
0
0
3
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
1
2
0
0
0
3
1
2
0
3
0
0
0
0
0
2
1
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
2
0
2
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
3
2
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
1
1
1
0
0
0
0
0
0
4
0
0
0
1
0
0
0
1
0
1
1
0
0
2
0
2
0
0
0
0
0
0
0
1
2
1
0
0
1
2
0
0
0
1
0
1
3
0
3
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
2
0
0
0
0
3
2
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
3
2
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
3
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
2
0
0
1
0
2
0
0
0
0
0
2
0
1
0
2
0
0
1
0
0
0
0
0
0
0
2
2
2
1
0
0
1
2
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
1
2
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
5
2
0
0
0
0
0
1
0
1
1
0
0
0
1
3
0
2
2
0
0
0
0
0
1
0
2
2
0
0
1
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
2
1
1
0
1
0
2
0
0
1
0
0
0
2
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
2
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
2
0
0
2
2
0
0
0
0
0
0
1
0
1
0
1
1
0
1
2
2
0
1
1
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
2
0
1
0
0
2
1
0
1
0
0
6
0
0
0
0
0
0
2
0
0
0
0
2
0
0
4
0
3
0
2
0
0
3
0
0
0
1
0
0
0
0
0
0
1
1
2
1
0
0
1
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
2
0
0
0
2
0
2
0
0
2
2
0
0
0
3
0
0
0
1
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
1
1
0
1
1
0
0
0
3
0
1
1
0
0
0
0
0
0
1
0
0
5
0
0
0
0
0
0
2
0
2
0
0
3
0
0
0
0
1
0
1
0
0
1
0
0
0
4
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
2
0
0
0
1
2
2
0
2
2
2
0
0
0
1
4
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
2
0
0
0
3
2
0
0
3
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
2
2
4
0
0
0
0
0
1
1
0
1
2
0
0
0
0
0
2
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
2
1
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
3
0
0
1
2
0
2
0
1
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
1
1
1
2
1
0
1
0
0
0
0
0
1
2
1
2
1
1
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
2
2
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
1
1
2
0
0
0
0
0
0
0
6
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
2
0
2
2
2
0
0
0
1
0
2
2
2
2
2
0
0
1
1
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
1
1
3
0
4
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
2
0
0
0
0
1
1
0
0
0
2
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
2
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
1
2
2
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
3
0
0
0
1
0
0
0
2
1
2
0
0
2
0
0
1
0
0
2
0
0
4
0
0
0
2
0
0
0
1
2
1
0
2
0
0
1
0
0
2
0
0
0
0
2
1
2
2
0
0
0
1
0
0
4
2
0
0
0
0
2
4
2
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
1
0
0
2
0
0
0
2
0
0
0
1
0
2
0
1
0
1
2
0
0
0
0
0
2
0
0
0
0
1
0
1
0
2
2
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
1
2
1
0
0
0
0
0
0
1
1
0
1
0
0
0
1
2
2
0
0
1
0
1
2
0
0
0
2
2
2
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
1
2
0
0
0
0
0
0
1
0
0
2
0
1
0
3
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
2
0
2
0
2
0
2
3
0
0
0
0
5
0
1
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
2
1
0
0
6
0
0
1
0
2
0
0
2
2
0
0
1
2
1
2
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
2
4
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
2
0
0
0
2
0
1
2
0
0
0
0
2
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
1
0
0
2
2
0
1
0
0
0
2
0
2
0
7
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
2
0
2
2
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
2
0
1
0
1
0
0
1
0
0
1
2
0
0
1
1
0
0
1
0
1
0
0
0
0
2
1
2
0
0
1
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
2
2
0
6
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
3
1
2
0
0
0
1
3
0
0
0
2
1
1
0
2
1
0
0
0
0
2
0
0
0
0
0
2
0
0
2
2
0
0
0
0
1
0
0
0
0
1
0
0
1
2
2
1
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
4
0
0
0
0
0
1
5
0
0
0
1
1
0
0
0
0
2
2
0
0
0
0
2
2
2
0
0
1
0
0
0
1
2
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
3
1
0
0
0
0
2
0
2
0
1
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
2
0
2
0
0
0
0
0
16
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
2
0
1
0
0
0
0
0
2
1
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
2
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
1
2
0
0
0
2
0
0
3
0
0
0
0
0
0
2
0
1
2
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
2
2
0
0
0
0
1
2
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
2
4
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
2
2
1
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
2
1
0
1
1
0
0
4
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
1
0
0
0
0
0
2
0
0
0
0
0
1
1
0
1
0
0
2
0
1
0
1
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
3
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
3
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
2
0
34
0
0
0
1
0
0
0
1
0
0
0
0
1
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
8
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
2
1
0
0
0
0
0
0
2
2
1
0
0
0
0
3
0
0
2
0
0
0
0
0
0
4
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
1
0
2
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
2
2
1
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
3
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
2
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
2
0
1
2
0
1
0
1
0
2
0
0
0
0
1
0
0
0
2
2
0
0
0
2
0
2
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
2
3
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
1
1
0
0
0
0
0
0
0
2
0
0
1
2
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
2
1
0
1
0
0
2
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
1
0
0
0
0
3
1
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
1
0
0
0
1
0
0
0
3
1
2
0
2
1
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
2
0
1
0
0
0
2
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
2
1
2
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
1
0
3
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
2
0
0
1
2
0
2
0
0
0
0
2
1
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
2
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
1
3
0
1
2
0
2
0
0
0
0
0
1
2
2
0
6
0
7
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
3
1
1
0
2
0
0
0
0
0
1
0
0
0
0
2
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
1
0
2
0
0
1
0
0
0
0
0
1
2
2
0
0
1
0
0
3
0
3
1
0
1
0
2
0
0
0
1
0
1
1
0
1
3
1
1
2
0
2
1
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
1
0
0
3
2
2
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
11
0
1
0
1
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
2
2
0
0
0
1
1
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
1
0
2
0
0
1
2
1
2
0
0
2
0
1
0
0
0
1
3
0
0
0
0
0
0
1
0
0
2
1
0
1
1
1
1
0
2
2
2
2
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
2
0
0
1
0
0
0
1
2
0
3
2
2
0
2
0
0
0
1
0
0
1
2
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
5
0
0
0
0
0
0
1
1
0
0
0
0
2
1
2
0
0
0
0
0
0
0
1
1
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
2
0
0
0
0
2
0
1
1
1
1
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
1
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
1
0
0
0
0
2
0
0
0
1
0
1
1
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
5
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
3
2
0
0
4
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
3
2
0
0
0
0
0
0
0
1
1
1
0
2
0
0
0
0
0
0
3
1
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
1
0
1
1
0
0
0
0
4
0
0
2
0
0
1
0
0
0
1
0
1
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
2
1
2
0
0
1
0
0
2
0
0
0
2
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
3
1
0
0
2
2
1
2
2
0
3
1
0
0
2
2
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
2
0
4
0
3
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
2
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
1
0
2
0
2
2
1
0
2
2
0
0
0
0
0
0
1
1
0
0
0
0
1
1
1
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
2
0
0
0
1
0
1
0
0
2
2
0
0
1
0
1
0
0
0
1
0
2
0
1
0
0
0
0
0
1
1
0
0
1
2
0
0
1
0
0
0
1
1
0
0
1
0
2
0
0
0
2
1
0
0
2
0
2
1
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
1
0
2
0
0
1
1
0
0
0
1
0
5
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
1
0
2
0
0
3
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
3
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
1
0
0
0
0
2
2
1
2
0
1
2
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
2
0
0
2
0
0
0
1
0
3
1
1
0
0
0
0
0
2
2
1
0
2
0
3
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
6
0
1
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
3
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
1
1
0
0
0
1
0
3
0
0
0
1
0
2
1
0
0
0
0
0
0
1
2
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
2
1
0
0
0
2
0
0
0
0
0
2
0
1
0
2
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
2
2
0
1
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
1
2
1
0
0
0
0
1
2
1
0
0
2
0
1
2
0
0
0
2
0
0
2
0
0
0
0
2
2
0
0
1
0
0
1
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
2
0
2
0
0
0
0
2
0
1
0
0
0
0
1
0
2
0
0
3
1
2
0
0
0
0
2
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
2
2
1
1
0
1
1
2
0
4
1
2
1
1
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
1
0
2
0
2
1
0
2
3
3
0
2
0
1
0
0
0
0
0
0
0
1
0
3
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
2
0
0
6
2
0
2
0
1
8
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
2
2
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
2
2
0
1
2
1
0
0
0
0
2
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
1
0
2
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
1
2
1
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
2
1
0
2
3
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
1
1
0
2
1
0
2
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
2
0
1
1
2
0
0
0
2
0
1
2
1
0
2
0
1
1
0
2
0
0
0
0
0
5
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
1
8
2
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
2
2
0
0
0
0
0
0
2
1
0
1
0
0
0
3
2
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
2
1
0
0
2
0
1
0
0
0
0
5
0
1
2
0
0
0
2
0
0
1
0
1
2
0
0
0
0
2
0
1
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
2
2
1
3
0
0
0
2
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
2
2
4
1
0
0
4
1
0
0
1
0
0
2
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
3
0
2
1
1
0
2
2
0
0
0
0
0
0
1
0
1
2
0
1
0
1
0
0
1
0
2
0
1
0
0
4
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
1
0
0
0
1
0
1
2
0
0
0
0
0
1
0
1
0
0
0
0
0
2
1
2
3
0
0
0
1
1
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
2
2
0
0
0
0
0
2
2
0
2
0
0
0
2
0
0
1
0
0
2
0
0
2
0
1
1
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
2
0
2
0
3
0
0
0
1
2
0
0
1
0
0
0
1
1
0
2
1
0
2
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
2
0
0
0
1
3
2
2
1
0
0
0
1
0
2
1
3
1
0
1
0
1
1
1
2
1
0
0
0
0
0
0
1
0
1
2
0
0
2
1
2
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
3
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
2
0
2
1
2
2
0
0
0
1
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
4
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
3
0
0
0
1
1
0
2
2
0
0
1
1
0
2
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
3
0
0
0
2
0
0
0
2
0
0
0
2
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
2
0
0
0
2
0
0
0
0
1
0
2
1
0
0
0
0
3
0
2
2
0
0
2
6
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
2
0
1
0
0
0
0
1
1
2
0
0
0
0
3
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
12
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
3
0
1
0
0
1
0
1
0
1
0
2
2
2
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
1
1
2
1
1
3
0
1
2
1
0
0
0
1
0
2
0
0
0
0
0
3
0
2
1
0
1
0
0
2
2
0
2
0
0
0
0
0
0
2
3
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
2
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
2
0
2
0
0
1
0
0
2
0
0
1
1
1
0
0
0
0
0
0
0
2
0
3
0
0
0
1
0
1
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
2
0
0
0
0
1
1
0
0
0
2
2
1
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
3
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
1
0
0
2
1
0
0
1
1
0
0
0
0
0
0
1
1
0
2
1
0
1
0
3
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
1
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
5
1
1
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
4
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
2
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
3
0
0
1
1
0
0
0
1
0
0
1
0
0
2
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
1
0
3
2
0
0
0
2
0
0
0
0
0
0
2
1
1
1
2
0
0
1
0
0
0
2
0
2
1
0
0
0
0
0
1
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
1
1
1
0
0
1
1
2
0
2
0
2
0
0
0
0
1
1
0
0
0
0
2
0
4
0
0
2
2
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
1
0
0
0
0
0
0
0
1
0
2
0
2
0
0
2
0
0
2
0
0
1
0
0
2
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
2
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
2
2
2
0
1
0
0
0
1
0
0
0
2
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
3
2
0
2
0
1
0
2
2
0
0
2
0
0
0
0
0
2
0
0
2
3
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
2
2
0
2
0
0
3
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
4
0
2
0
0
0
0
0
0
1
0
0
1
0
1
2
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
3
3
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
1
2
0
2
0
0
0
1
0
1
2
0
0
2
2
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
2
2
3
0
1
0
0
0
0
1
0
2
0
0
0
0
0
1
0
2
0
0
0
0
1
0
3
0
0
1
0
0
2
0
0
0
1
0
1
2
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
5
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
2
3
2
2
1
0
0
0
2
0
2
0
0
1
1
1
0
0
3
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
1
1
2
0
0
0
0
0
0
0
0
0
2
0
2
2
2
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
1
2
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
3
0
0
2
0
1
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
2
1
0
1
0
0
1
0
0
2
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
1
0
0
0
3
1
0
0
2
0
0
2
1
0
0
2
0
0
8
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
1
0
0
2
3
0
0
1
3
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
2
0
1
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
3
1
0
0
0
0
2
1
0
0
0
0
0
0
5
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
4
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
1
0
0
1
0
2
0
0
0
1
0
1
0
0
0
0
1
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
2
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
3
0
0
0
0
2
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
2
0
2
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
2
1
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
3
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
1
3
1
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
2
0
2
0
1
0
0
0
0
1
2
2
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
3
0
1
0
0
0
1
0
0
0
0
3
0
1
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
3
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
2
1
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
1
2
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
1
2
0
2
2
3
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
2
0
0
2
0
0
0
2
0
2
0
0
0
0
0
1
0
2
0
0
0
1
0
0
1
4
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
2
0
0
2
0
0
0
0
0
2
0
1
0
0
1
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
2
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
1
1
0
0
0
1
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
5
0
0
0
2
1
0
0
0
0
2
0
0
2
0
1
1
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
2
5
2
1
0
0
0
2
0
0
0
0
0
2
1
1
2
1
0
1
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
2
0
2
0
0
2
2
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
2
0
0
1
0
2
0
0
1
0
2
2
1
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
3
2
0
0
2
0
0
0
0
1
1
2
0
0
0
0
0
2
0
0
2
6
0
0
0
0
1
0
0
0
3
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
2
1
0
1
0
1
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
1
0
1
2
0
0
0
4
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
1
2
1
3
1
0
0
1
0
2
0
0
3
2
0
0
2
0
2
2
0
0
0
0
0
0
0
3
0
1
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
2
2
2
0
0
0
0
0
0
1
2
0
1
1
0
0
0
1
0
0
6
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
1
2
2
0
0
1
0
0
0
1
1
0
0
2
0
0
1
3
0
0
1
0
0
0
4
0
0
0
0
0
1
0
0
3
2
0
0
0
0
2
2
0
0
2
2
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
2
0
3
0
0
0
3
0
0
0
2
0
0
0
0
1
0
2
0
0
0
2
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
6
3
2
0
0
0
1
2
0
0
0
2
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
1
0
1
1
0
0
0
0
0
0
2
1
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
3
0
0
1
2
0
1
2
0
1
0
0
0
0
2
2
1
0
1
0
2
2
1
1
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
2
1
2
0
0
0
0
0
0
0
1
2
1
1
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
3
1
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
2
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
2
1
0
0
1
0
0
1
2
0
1
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
4
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
1
0
0
0
0
0
3
0
3
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
2
0
0
0
2
1
0
0
0
0
0
1
2
0
0
1
1
0
0
0
1
0
1
0
1
1
0
0
0
2
0
2
0
0
2
0
0
2
1
2
0
0
1
0
0
1
0
0
0
0
0
1
0
2
0
0
1
0
0
3
0
0
2
1
1
0
2
0
0
0
2
0
0
0
0
0
2
2
0
0
0
1
0
1
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
1
1
1
0
0
3
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
2
2
0
0
0
2
2
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
2
0
1
0
0
0
0
2
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
2
2
0
0
0
1
3
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
3
2
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
1
3
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
4
0
0
1
2
0
1
2
2
1
2
0
0
0
0
2
0
1
1
0
0
0
1
0
0
0
1
0
0
2
0
3
0
0
2
0
0
0
3
0
2
0
0
2
1
2
2
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
2
2
0
0
2
0
5
0
0
0
0
2
0
0
0
0
0
0
0
1
1
2
0
2
0
0
2
0
1
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
1
0
2
1
1
1
0
0
0
1
2
2
0
2
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
2
2
0
2
2
2
0
1
0
0
1
2
0
1
0
1
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
3
0
6
0
2
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
1
0
2
0
1
1
2
1
0
0
3
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
5
1
1
0
1
0
0
2
0
0
2
1
2
2
0
0
0
1
0
0
1
2
1
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
1
0
1
0
0
2
0
1
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
3
2
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
2
0
0
0
0
1
1
1
2
0
1
0
0
2
2
0
1
0
0
0
0
0
1
0
0
1
2
0
1
0
0
0
0
1
0
0
0
5
1
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
1
0
1
2
2
0
0
3
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
2
0
1
0
0
0
2
0
0
0
0
2
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
2
2
0
0
0
1
0
2
0
2
0
0
0
2
1
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
5
1
0
0
2
0
0
0
0
1
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
2
2
0
1
3
1
0
2
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
4
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
2
0
2
2
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
3
0
1
0
0
0
0
2
0
0
0
0
1
7
0
0
0
4
0
0
0
0
4
0
0
1
0
2
1
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
2
0
2
2
0
0
0
2
0
0
0
0
0
1
0
1
2
0
0
0
1
1
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
1
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
3
1
0
0
0
0
4
2
0
0
0
1
0
0
3
1
2
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
2
0
0
0
3
0
0
0
1
0
1
0
2
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
1
1
0
0
0
0
0
2
0
0
0
0
2
0
0
1
1
2
0
1
1
0
1
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
2
3
0
1
3
0
0
0
0
0
1
0
3
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
1
0
1
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
3
0
0
1
0
0
0
2
0
0
1
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
2
1
0
0
0
1
0
0
2
0
0
1
0
3
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
2
0
0
0
2
0
0
0
2
1
0
0
2
1
2
0
0
1
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
1
2
2
1
1
0
1
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
2
1
0
3
2
0
0
0
2
1
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
2
0
2
3
1
0
0
0
2
0
3
1
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
2
0
3
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
2
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
2
2
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
2
2
1
2
0
0
2
0
0
0
2
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
1
0
0
0
0
1
0
2
3
0
0
2
0
2
0
0
1
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
3
0
0
0
2
0
2
1
0
0
1
0
0
0
1
0
0
1
1
0
2
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
2
1
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
2
0
2
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
2
0
0
1
0
0
0
0
0
1
1
0
0
0
2
0
2
0
2
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
1
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
4
1
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
1
0
0
1
2
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
2
2
0
0
3
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
1
0
1
0
0
0
1
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
4
1
0
2
2
0
2
2
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
2
1
2
0
0
0
2
1
0
0
0
0
0
3
0
0
0
0
0
0
2
0
2
1
0
2
0
0
1
2
2
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
1
0
2
2
2
2
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
2
3
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
1
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
9
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
2
0
1
0
0
1
0
0
2
5
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
1
2
0
1
0
0
2
1
0
2
0
1
1
0
0
0
0
2
0
1
0
0
0
0
0
2
0
1
2
0
0
0
2
0
0
0
0
0
2
0
2
0
3
0
0
1
0
2
0
3
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
1
2
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
1
0
2
0
1
1
0
2
1
0
1
3
0
1
0
8
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
2
0
1
0
0
0
1
4
0
2
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
1
5
2
0
0
0
0
0
1
0
3
0
1
0
1
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
1
1
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
2
2
0
1
0
0
2
1
0
0
1
0
2
2
0
1
2
0
0
0
0
0
1
2
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
2
2
0
0
0
1
0
2
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
2
0
0
3
2
1
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
2
1
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
5
0
0
2
0
0
2
0
0
0
2
1
0
1
0
2
0
1
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
1
2
0
1
1
0
0
0
0
0
0
2
0
1
0
0
0
0
2
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
2
1
0
0
3
0
0
0
0
1
0
0
2
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
2
0
2
0
0
0
2
0
0
2
0
0
0
0
0
1
1
0
0
1
1
0
0
2
0
0
0
0
0
0
2
2
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
7
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
2
1
0
1
0
0
0
3
0
0
0
0
0
0
0
2
3
0
1
0
0
0
1
0
2
0
0
1
2
1
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
2
0
0
1
0
3
0
0
0
0
1
3
0
0
0
0
0
1
3
0
1
0
0
0
0
0
1
2
0
1
0
0
0
0
0
2
0
0
0
1
0
0
2
1
0
0
1
0
0
0
2
0
1
1
0
0
0
0
1
0
2
0
0
0
1
0
0
0
1
0
0
0
0
2
2
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
1
0
1
4
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
3
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
1
0
0
2
1
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
2
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
1
2
0
0
0
0
2
0
0
0
1
0
0
0
1
1
0
2
0
2
0
2
0
0
2
0
0
0
0
1
1
0
1
0
0
0
2
0
0
0
0
0
1
0
2
3
1
1
0
0
0
1
2
0
0
1
0
2
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
1
1
0
0
0
1
1
0
0
1
1
0
0
0
2
1
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
2
0
0
0
7
1
0
0
0
3
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
10
0
2
0
0
2
1
2
0
1
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
4
0
0
5
0
0
0
0
0
2
0
0
3
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
1
0
0
2
0
0
1
0
0
1
0
1
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
5
0
0
1
0
1
1
0
0
0
4
0
0
2
2
0
0
0
0
0
2
0
1
0
0
1
2
0
0
2
0
0
0
0
0
0
1
0
2
0
3
2
0
3
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
2
1
1
0
1
0
0
0
2
0
2
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
3
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
1
0
0
1
9
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
4
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
2
0
0
2
0
1
2
0
0
0
0
0
0
2
1
0
0
2
0
0
0
1
0
0
2
0
2
0
1
1
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
1
1
2
1
0
0
2
1
1
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
3
0
0
0
2
2
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
1
0
0
0
2
1
0
0
0
0
0
0
0
3
0
2
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
2
0
3
0
2
0
0
0
2
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
2
1
0
0
1
0
0
2
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
3
0
2
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
4
0
0
3
3
0
2
0
3
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
2
1
1
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
3
2
0
3
0
0
1
0
1
1
0
0
0
0
0
0
8
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
2
1
0
1
0
0
0
2
0
1
0
1
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
2
2
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
2
2
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
2
2
0
0
1
0
1
1
1
0
0
0
0
0
2
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
7
0
0
0
1
0
0
2
0
4
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
3
0
0
1
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
2
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
1
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
3
1
0
1
0
0
0
0
2
2
0
0
0
0
2
2
2
0
0
0
0
5
1
0
0
0
4
0
2
1
0
3
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
2
0
0
2
0
2
2
0
1
0
2
0
2
0
0
2
2
1
0
0
0
0
2
0
0
1
1
0
0
7
1
0
1
0
1
0
0
0
2
0
0
0
0
0
0
2
0
1
1
2
0
0
1
0
0
0
0
2
0
0
0
0
2
2
0
0
2
0
0
2
0
1
0
0
1
0
0
1
0
1
0
2
2
5
1
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
1
0
1
0
2
0
1
1
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
1
0
3
0
0
1
0
2
0
2
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
3
0
0
2
3
0
0
0
0
0
1
0
1
0
0
0
5
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
2
4
0
0
2
0
0
0
1
2
0
0
0
0
0
1
0
0
2
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
1
0
1
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
2
0
0
0
1
0
3
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
3
0
0
2
0
1
2
0
1
0
0
0
0
1
0
2
1
0
0
0
0
1
0
1
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
1
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
5
1
1
0
1
1
0
0
2
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
1
0
0
1
0
0
0
0
2
1
0
2
0
0
0
0
0
0
1
0
2
1
0
0
1
0
0
0
0
2
0
0
0
1
0
0
1
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
1
3
0
0
1
0
4
0
0
0
0
0
0
4
0
0
0
1
0
0
1
0
0
0
3
0
0
0
2
0
1
0
0
0
0
1
0
0
1
3
0
0
0
1
0
1
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
2
1
2
0
0
0
0
2
0
2
1
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
1
1
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
2
0
5
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
1
0
2
1
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
1
0
2
0
0
0
0
1
2
0
0
1
1
0
3
0
0
0
0
0
1
0
0
0
0
3
0
1
0
1
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
1
0
0
0
0
0
0
0
3
2
1
0
0
0
0
0
1
0
0
0
2
2
0
0
1
0
0
0
2
0
2
0
0
0
3
0
0
0
0
0
2
1
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
2
0
4
1
2
0
0
3
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
1
2
0
0
0
2
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
3
0
1
1
0
0
2
2
0
2
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
1
1
1
3
2
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
2
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
1
0
0
0
0
2
2
0
1
1
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
1
0
1
1
0
0
1
0
3
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
2
1
0
0
3
0
0
1
0
0
0
0
0
0
0
0
2
1
0
2
1
0
0
2
1
0
1
0
2
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
2
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
2
2
0
0
2
0
0
2
0
0
0
0
3
0
1
0
0
1
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
2
0
3
0
2
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
1
2
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
1
0
3
0
1
0
0
0
0
1
2
0
0
0
2
1
0
0
0
2
0
0
1
4
0
0
4
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
2
0
0
0
2
0
1
0
0
2
1
1
0
0
0
0
13
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
3
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
3
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
4
3
0
0
0
0
0
0
0
2
0
0
3
0
1
2
0
2
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
3
0
0
1
0
3
0
0
0
1
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
2
4
0
0
0
0
0
0
1
0
2
0
2
2
0
0
0
1
0
2
6
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
2
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
1
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
1
3
1
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
3
2
2
1
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
2
1
1
2
0
0
0
5
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
2
2
0
1
0
0
0
1
0
1
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
3
0
0
0
0
2
0
0
0
0
1
2
2
0
0
0
0
2
0
1
0
0
0
1
2
3
0
0
0
2
0
0
1
0
1
4
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
4
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
4
0
0
0
0
1
0
0
0
0
0
4
0
2
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
2
3
0
2
0
0
0
1
0
0
0
0
0
4
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
4
0
0
0
2
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
1
1
0
0
1
0
2
1
0
0
0
0
0
2
2
0
2
0
0
0
0
0
2
0
1
0
2
0
0
0
0
2
3
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
2
0
2
0
2
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
2
0
2
0
0
0
2
0
5
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
2
0
3
1
0
0
2
1
5
2
0
0
0
1
2
2
0
0
0
0
0
2
0
0
2
1
0
0
0
0
2
0
0
0
1
0
1
1
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
1
0
0
0
0
2
1
0
0
0
1
0
0
0
1
0
1
0
0
1
1
0
0
0
0
2
0
0
0
0
1
1
2
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
3
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
1
0
0
0
0
0
1
0
3
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
2
1
0
0
0
0
1
0
0
2
2
2
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
2
0
0
1
1
0
3
1
0
0
1
0
0
0
0
0
2
2
0
0
0
2
0
2
0
3
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
1
1
0
0
1
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
1
1
0
1
1
1
1
0
0
0
2
2
0
0
0
1
1
0
1
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
2
0
3
0
0
1
1
0
1
2
0
1
3
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
3
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
5
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
2
2
0
1
2
0
0
0
0
0
0
2
0
0
2
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
1
2
0
1
2
0
0
0
0
2
2
0
1
1
0
0
0
0
2
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
2
3
0
2
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
3
0
2
0
0
0
0
0
0
1
0
0
0
0
0
3
0
1
0
0
0
0
2
2
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
2
0
0
1
0
2
0
0
0
0
2
0
0
0
2
0
2
0
0
1
1
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
1
2
0
0
0
1
0
0
0
1
0
0
2
0
0
1
2
1
0
0
0
0
1
0
0
2
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
8
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
1
2
0
0
0
1
0
0
0
1
1
0
1
1
0
1
1
0
3
1
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
1
0
0
2
0
0
2
2
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
5
0
1
0
0
0
0
0
0
0
0
2
2
1
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
2
1
1
1
0
0
1
0
0
0
0
0
2
0
0
0
2
0
1
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
3
0
0
0
2
0
2
0
1
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
2
0
0
0
0
2
0
0
0
0
6
1
0
0
0
1
0
0
2
0
0
1
1
0
0
1
2
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
2
3
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
2
0
0
0
0
1
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
2
0
0
3
0
0
3
0
0
2
2
2
2
1
0
0
0
0
0
0
0
0
0
1
0
2
0
5
1
0
0
1
0
2
2
0
0
0
0
0
0
0
2
2
0
0
0
1
1
1
0
0
0
1
0
0
0
2
2
0
0
1
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
2
2
1
0
0
0
0
0
0
3
2
1
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
2
1
4
0
0
2
1
0
1
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
6
1
0
0
1
2
0
0
0
1
0
0
0
3
0
1
0
0
0
0
5
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
1
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
1
0
0
0
1
1
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
1
1
0
0
1
0
1
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
1
0
0
1
2
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
1
0
0
1
0
0
2
0
0
3
0
2
0
0
0
1
2
0
0
2
1
1
5
3
1
0
1
0
0
1
0
0
2
1
0
1
0
3
0
0
0
1
0
0
2
0
0
0
1
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
2
0
0
1
2
1
0
0
1
0
1
0
0
0
0
0
1
1
0
0
3
2
0
0
0
0
1
1
2
0
0
0
0
2
2
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
3
0
0
0
1
0
1
1
3
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
1
1
1
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
2
1
2
0
0
0
1
0
0
0
0
2
1
1
1
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
1
0
3
2
2
0
3
3
0
0
0
0
0
0
2
0
5
0
0
0
0
0
0
3
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
3
0
0
0
2
2
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
3
0
0
0
0
0
1
0
1
0
1
0
0
2
2
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
1
0
3
0
0
0
0
1
0
0
0
0
0
2
1
0
1
2
0
0
0
3
2
0
0
0
2
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
1
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
3
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
7
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
3
1
0
1
0
2
0
1
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
5
0
0
2
0
2
4
0
0
1
1
1
0
0
0
2
2
0
0
1
2
1
0
0
0
0
3
0
0
0
0
0
0
1
0
2
0
0
4
2
0
2
0
0
0
0
0
2
1
0
0
0
2
3
0
0
2
0
1
3
0
1
8
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
4
0
0
0
0
0
2
0
0
0
0
2
0
2
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
1
0
0
0
2
0
3
0
4
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
2
1
0
2
0
0
0
0
3
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
4
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
1
0
0
0
1
0
1
0
2
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
1
0
0
0
0
2
0
2
2
0
2
0
2
1
0
2
2
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
3
0
0
2
1
0
0
1
0
0
2
0
0
0
0
0
0
2
2
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
1
0
1
0
0
1
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
1
0
1
0
0
1
3
0
0
0
0
0
2
2
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
1
1
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
1
2
1
0
0
0
1
2
0
0
0
2
0
0
0
1
0
1
1
1
0
1
0
0
1
2
0
0
0
0
2
1
0
0
0
0
6
2
0
2
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
2
2
0
0
0
0
2
0
0
2
2
1
0
2
0
0
0
1
0
0
1
0
0
0
1
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
2
0
2
0
0
0
0
2
0
0
1
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
2
2
1
0
0
0
2
0
0
0
0
0
0
3
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
2
2
0
0
0
0
0
0
1
3
3
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
3
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
5
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
3
0
2
0
2
1
0
0
2
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
2
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
3
1
1
0
2
0
0
0
2
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
14
2
0
2
1
0
0
0
2
0
0
1
0
0
2
0
0
2
0
0
0
0
2
2
1
0
0
1
1
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
2
0
1
0
0
0
5
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
2
2
0
2
0
0
1
0
1
2
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
7
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
2
6
0
0
0
0
0
0
0
2
0
2
2
0
0
0
1
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
1
0
0
1
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
1
2
0
1
1
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
2
3
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
2
0
0
0
0
1
0
0
0
0
1
2
0
2
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
1
1
0
0
0
0
0
0
2
1
0
1
0
0
0
2
1
0
2
0
0
0
0
0
0
2
0
0
1
1
0
0
2
1
1
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
1
0
1
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
2
0
0
4
0
0
0
2
10
0
0
3
0
2
0
0
2
0
2
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
1
0
2
2
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
3
0
0
0
1
2
1
3
0
1
0
0
0
0
0
0
1
0
2
0
1
0
0
2
0
2
0
0
0
1
1
0
1
1
0
0
0
0
9
0
2
1
0
0
2
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
3
2
0
0
2
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
4
3
0
0
1
0
0
0
0
0
0
0
0
2
1
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
1
0
2
1
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
1
0
0
0
1
3
0
1
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
2
3
0
0
2
0
0
0
0
1
1
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
1
0
0
0
2
0
2
0
1
0
0
2
1
0
2
0
0
0
0
1
0
0
0
0
2
1
1
3
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
3
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
2
0
0
0
1
0
3
0
0
0
1
0
1
2
3
0
0
0
3
0
0
0
1
0
2
0
0
0
4
1
1
0
0
2
0
0
1
0
0
2
2
0
2
0
1
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
4
0
1
0
2
0
0
0
0
2
2
1
1
0
1
0
0
0
0
2
1
0
0
1
0
1
0
0
0
0
1
1
0
2
0
0
0
1
2
0
5
0
2
0
0
0
0
0
0
0
0
2
1
1
1
0
2
2
0
0
1
0
1
0
2
0
0
0
2
1
0
0
0
1
0
2
0
1
0
1
0
0
0
0
0
0
2
0
2
1
0
0
0
2
0
1
0
0
0
0
2
0
0
0
2
2
0
0
1
0
0
0
2
1
0
1
0
0
0
2
0
0
1
0
1
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
1
0
2
0
3
0
0
2
1
0
0
2
1
0
0
0
0
1
2
0
3
0
0
0
0
3
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
1
0
3
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
1
0
1
1
0
2
2
0
1
0
1
0
0
1
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
3
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
5
0
0
0
4
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
1
0
0
4
0
0
0
0
2
2
0
2
0
1
2
1
1
0
0
3
0
1
0
0
0
1
1
0
0
1
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
1
0
2
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
3
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
1
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
4
2
0
0
0
0
0
4
0
0
1
0
1
0
2
0
0
0
0
0
0
5
0
3
1
0
0
0
0
0
2
2
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
2
2
1
0
1
0
0
0
0
0
1
0
0
0
0
1
2
1
0
0
0
0
0
10
0
0
0
0
1
0
0
0
0
1
0
0
2
2
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
8
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
3
2
0
0
1
0
0
0
0
2
1
0
0
0
2
2
0
0
0
0
1
1
0
1
0
0
1
0
0
2
0
0
1
0
0
3
0
0
0
2
0
0
0
0
2
1
2
1
2
0
0
0
1
0
0
0
0
0
1
0
0
0
2
2
0
1
0
0
1
0
0
0
3
0
0
0
1
2
2
2
0
1
2
3
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
1
0
0
2
0
2
0
0
0
0
0
0
0
0
2
3
1
0
0
0
1
2
0
1
0
2
0
2
0
2
0
0
0
1
1
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
1
2
2
0
3
2
0
0
1
0
0
2
1
0
1
2
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
8
0
0
3
0
1
0
0
0
0
0
0
1
0
2
0
0
0
1
2
0
0
2
0
1
0
1
0
0
2
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
2
1
0
1
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
2
1
0
0
2
1
0
3
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
1
1
0
0
3
1
0
0
0
0
0
0
0
1
0
0
0
0
3
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
2
2
0
0
0
0
0
1
0
0
2
0
0
0
1
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
1
0
0
1
1
0
0
0
0
2
0
0
0
2
0
2
0
2
1
1
1
2
0
0
0
1
0
0
0
0
1
0
2
1
0
0
0
0
2
0
0
1
0
0
2
2
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
1
0
0
2
0
2
0
0
2
0
0
8
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
2
0
0
0
0
1
0
1
2
0
0
1
1
0
2
0
1
2
0
2
1
0
0
0
0
0
0
0
0
1
4
0
1
0
0
2
0
0
1
0
0
1
0
0
2
0
2
2
0
1
0
2
0
1
2
0
2
2
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
1
0
0
0
2
2
0
2
0
0
1
0
2
1
2
1
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
2
0
0
0
1
0
2
2
0
1
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
5
2
0
0
0
0
2
0
0
3
0
1
2
0
1
0
0
1
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
2
0
0
2
0
4
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
1
1
0
1
0
2
0
0
0
2
1
0
0
2
2
0
0
0
0
0
0
1
1
2
0
1
0
0
0
0
2
0
0
2
0
2
2
0
0
0
2
2
2
0
0
0
1
0
1
0
2
0
0
2
0
2
0
0
0
2
1
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
1
2
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
11
2
0
1
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
3
1
0
1
0
0
2
1
0
2
0
2
0
1
2
1
1
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
3
0
3
0
0
0
1
1
0
0
0
0
2
0
0
1
0
0
0
0
3
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
3
1
0
0
0
1
0
2
0
2
0
3
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
1
1
0
0
1
2
0
1
0
1
0
0
0
2
1
0
2
0
0
2
2
0
0
0
0
0
0
0
2
1
2
0
2
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
1
2
2
0
0
2
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
2
1
1
0
0
0
0
2
0
0
0
1
3
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
4
3
0
0
0
0
0
2
0
0
2
1
0
1
0
3
0
2
2
0
2
0
0
1
0
0
0
1
0
1
0
0
1
0
0
1
1
0
0
0
0
1
2
2
0
0
1
0
0
0
1
0
0
2
0
0
5
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
9
2
1
0
2
0
0
1
2
0
0
0
0
0
1
0
0
2
0
0
0
0
2
2
0
0
0
2
2
0
3
0
0
0
0
0
0
0
0
0
1
2
0
0
0
3
0
0
0
0
0
2
2
0
0
0
0
0
2
4
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
1
0
0
2
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
3
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
2
0
1
2
0
0
2
1
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
2
0
1
1
2
0
2
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
1
0
0
3
0
0
1
0
0
0
4
2
2
0
0
0
0
2
0
1
2
1
0
0
0
0
0
0
1
0
0
5
0
0
0
0
0
0
0
0
0
0
0
3
0
1
2
0
0
0
0
0
0
1
0
1
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
1
0
2
0
2
0
0
1
0
0
1
3
0
0
2
2
0
1
2
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
1
1
0
0
0
0
0
2
0
0
2
1
0
0
0
0
2
0
0
1
1
0
0
0
0
2
0
0
0
2
0
1
0
0
1
0
0
2
0
1
0
1
0
0
0
0
2
0
2
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
1
0
0
3
0
0
1
0
0
0
0
1
0
0
1
5
0
2
0
2
2
0
0
0
0
1
0
1
0
0
0
1
0
1
1
0
2
0
0
2
0
2
0
1
0
3
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
5
0
2
0
0
0
2
1
0
2
0
2
1
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
3
0
2
0
0
0
1
0
0
0
1
1
0
0
0
2
0
0
0
1
0
3
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
3
0
1
0
0
2
2
0
2
0
0
0
0
0
0
0
4
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
4
0
0
0
3
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
2
2
0
2
0
0
2
0
0
0
2
1
1
2
0
0
0
0
0
0
1
0
0
3
0
2
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
3
0
1
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
1
0
1
0
0
1
0
0
1
0
0
0
3
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
4
0
0
2
2
0
0
1
0
0
0
0
2
0
2
0
1
2
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
4
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
1
1
0
1
0
1
0
0
3
0
2
0
0
0
2
2
0
0
1
0
0
0
4
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
2
3
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
2
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
1
0
3
0
0
0
1
0
2
0
0
2
0
0
0
0
0
1
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
1
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
2
2
0
0
0
0
0
0
2
0
0
3
1
0
1
1
0
0
1
2
0
0
2
0
0
2
0
2
2
1
0
2
0
1
0
0
2
1
0
0
0
0
2
0
0
1
2
0
1
1
0
0
0
1
0
0
0
1
0
0
0
2
0
6
0
0
0
0
0
0
0
0
2
2
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
2
0
2
0
0
0
1
0
0
0
0
0
1
1
0
2
0
0
0
3
0
0
1
1
0
1
0
0
0
0
0
0
2
0
0
2
0
0
2
2
0
0
0
0
2
0
0
1
0
1
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
2
2
0
0
0
0
0
0
0
0
2
2
1
0
0
0
1
0
2
0
1
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
2
5
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
2
0
0
1
0
1
0
0
1
0
0
2
3
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
1
2
0
0
0
0
0
0
2
1
0
2
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
1
1
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
1
0
1
4
2
2
0
0
0
0
1
2
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
1
2
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
1
2
4
2
0
0
0
1
0
0
1
2
0
2
1
0
0
1
0
0
0
1
0
4
2
0
0
0
0
2
2
0
0
2
1
0
2
0
0
0
0
2
0
0
0
0
2
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
1
1
0
1
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
3
1
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
1
2
0
2
2
1
1
0
0
1
0
0
2
0
0
0
0
2
0
2
0
0
0
2
2
0
0
1
2
0
0
0
0
0
0
0
0
8
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
2
0
5
1
0
0
4
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
1
0
1
2
0
0
0
7
1
1
0
0
0
2
1
0
0
0
0
0
0
2
2
3
0
0
4
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
3
0
0
0
0
2
2
1
2
1
0
0
0
1
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
2
1
0
2
1
0
0
2
2
1
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
2
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
2
0
0
0
3
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
2
1
0
1
0
2
2
1
0
3
0
1
0
0
0
2
0
2
0
2
1
0
0
0
0
2
0
1
0
0
2
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
2
2
0
0
0
0
1
0
0
1
0
4
1
0
2
0
0
0
0
0
1
0
2
0
1
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
2
0
0
0
1
2
0
2
0
0
1
0
0
1
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
2
1
0
0
1
0
2
0
0
4
2
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
1
0
4
2
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
3
1
2
0
4
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
2
0
2
0
0
0
3
0
0
1
0
0
0
2
0
1
0
2
0
0
1
0
0
0
0
0
2
2
0
0
2
0
0
0
1
0
0
0
0
3
0
0
1
2
0
0
0
2
0
0
0
1
3
0
1
0
1
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
4
1
0
0
2
0
3
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
3
0
0
0
2
0
2
0
0
2
0
0
0
2
0
1
2
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
2
1
0
0
0
3
1
0
1
0
0
0
1
1
2
0
1
0
0
0
2
2
0
0
3
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
1
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
2
0
1
0
0
1
1
0
0
0
0
0
1
2
0
0
0
2
2
2
0
0
0
2
1
0
1
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
1
3
1
2
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
2
2
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
1
2
0
0
0
0
2
0
0
1
2
0
0
1
0
2
0
2
2
1
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
2
2
1
2
3
0
0
0
0
0
0
0
0
2
0
0
1
2
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
2
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
1
1
2
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
2
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
2
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
2
2
4
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
3
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
4
0
0
1
1
0
2
0
0
2
2
2
1
1
0
0
0
0
2
0
0
1
0
0
1
2
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
1
0
2
0
0
1
2
3
1
1
0
0
0
0
0
1
2
0
6
0
0
0
2
0
2
0
0
0
0
0
0
2
0
1
0
0
1
1
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
2
0
0
1
1
1
0
0
0
0
2
5
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
2
1
0
0
0
0
0
0
2
0
0
1
2
0
2
1
0
2
0
0
0
0
1
2
4
0
0
1
0
0
2
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
3
3
0
0
0
2
4
0
0
4
2
0
0
2
0
0
2
0
0
0
0
0
1
0
0
2
0
0
1
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
2
1
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
2
0
0
1
2
0
0
0
0
1
0
2
3
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
1
0
0
2
1
1
0
0
0
0
0
0
2
0
0
1
0
2
0
1
0
0
0
2
0
0
0
1
0
1
1
0
1
0
1
2
0
1
0
0
0
1
0
0
0
0
2
0
2
0
0
2
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
2
1
0
0
2
2
0
0
0
0
1
3
0
1
0
0
0
0
3
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
1
1
1
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
1
2
2
3
0
3
0
2
2
1
0
2
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
2
0
1
0
2
1
0
0
0
2
1
0
0
5
0
0
1
0
0
0
0
1
0
0
0
1
2
1
0
0
0
1
0
0
3
1
0
0
0
0
1
0
0
0
0
0
1
0
2
0
2
2
0
1
2
1
2
0
1
0
0
1
3
3
2
0
1
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
2
0
0
0
0
0
0
2
2
0
0
0
0
2
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
1
2
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
5
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
2
3
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
2
3
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
3
1
0
2
2
0
0
0
3
0
1
0
0
0
0
2
2
0
1
0
1
0
2
0
1
0
0
0
0
1
3
2
0
0
0
2
3
0
0
0
2
0
2
0
0
0
1
0
1
0
1
0
0
0
0
4
2
1
0
2
0
0
1
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
3
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
1
1
2
3
0
0
0
0
1
0
1
0
0
0
0
0
2
2
0
1
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
2
1
1
0
0
0
0
0
0
0
0
2
3
1
1
1
0
0
0
1
0
0
2
1
1
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
1
2
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
4
1
1
0
0
0
0
4
0
0
0
0
1
0
1
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
3
1
0
0
2
1
0
0
0
1
3
0
0
2
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
2
2
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
4
1
0
0
0
1
0
1
0
1
0
0
0
0
0
2
0
2
0
1
0
1
0
0
2
0
0
1
0
2
0
0
0
0
2
2
0
0
2
0
1
0
1
0
0
0
0
0
0
1
2
0
0
1
2
2
2
0
2
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
2
2
0
0
1
0
0
2
0
2
3
1
2
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
1
2
0
0
2
0
0
0
0
2
0
0
0
0
0
2
2
1
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
1
0
1
0
0
5
0
1
0
1
0
2
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
2
0
1
1
0
0
1
0
1
3
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
2
2
2
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
5
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
1
1
2
0
0
0
0
2
0
0
0
1
0
0
2
0
1
0
0
2
0
1
0
1
0
0
2
1
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
2
1
0
0
2
1
2
0
0
1
0
1
0
4
0
1
0
2
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
3
2
0
0
0
1
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
1
0
1
0
0
0
0
1
0
2
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
2
1
0
0
2
1
1
2
1
0
0
1
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
2
0
0
1
0
1
0
6
0
2
0
0
1
2
0
0
0
0
3
4
0
1
0
0
1
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
1
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
1
2
0
0
0
2
0
1
0
3
0
2
0
6
0
0
1
3
2
1
0
0
2
1
0
2
1
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
1
1
0
2
0
0
2
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
2
0
1
0
1
1
0
0
0
2
0
0
0
0
0
0
5
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
1
1
1
0
2
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
2
1
3
0
0
0
3
0
1
0
1
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
1
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
3
0
0
0
1
0
0
0
0
0
0
0
3
2
0
0
2
0
0
0
0
0
0
0
2
2
0
1
2
1
2
2
0
0
0
0
0
2
0
1
0
0
0
2
0
1
0
0
0
2
2
1
1
1
0
0
0
0
1
3
0
0
2
0
1
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
1
1
2
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
2
0
0
2
0
1
2
1
0
0
0
2
0
2
0
0
3
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
3
0
3
3
1
2
0
2
0
0
0
0
0
0
2
0
2
1
0
1
2
0
0
2
0
0
0
1
1
0
1
2
0
0
1
0
0
0
2
1
0
2
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
3
0
0
0
2
1
0
0
4
0
0
0
2
1
0
0
1
0
0
2
0
0
2
2
0
0
0
0
3
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
2
2
2
1
0
0
0
1
0
2
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
7
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
2
0
1
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
3
1
2
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
2
0
4
0
3
0
0
0
0
0
0
1
0
1
2
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
1
0
0
2
0
0
0
0
0
0
1
0
1
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
2
2
2
0
0
0
2
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
2
0
0
3
0
2
0
2
0
2
0
0
1
2
0
1
0
0
0
0
0
1
0
0
0
0
3
0
1
0
1
0
2
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
2
2
0
0
0
0
0
4
1
0
0
0
1
0
0
0
2
0
1
0
2
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
2
0
0
0
2
1
0
2
0
1
0
0
0
0
0
0
2
1
1
0
0
0
4
1
2
0
1
0
0
0
0
0
0
1
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
1
0
0
0
0
0
2
4
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
2
0
0
2
0
0
1
2
0
2
0
0
0
0
2
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
1
0
1
2
0
0
2
0
0
0
0
0
0
7
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
3
1
0
0
0
0
1
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
3
0
3
0
0
0
4
0
0
0
0
0
0
0
2
0
1
0
0
0
1
1
2
0
1
0
0
0
0
1
0
0
0
0
2
0
4
0
0
0
0
0
0
2
2
0
0
0
1
0
0
1
0
0
2
0
2
0
0
0
2
0
0
0
1
2
0
0
2
0
0
0
2
1
2
0
0
0
0
2
0
2
1
2
0
0
0
1
0
2
0
0
0
0
1
1
0
0
0
2
0
2
0
0
2
0
0
1
1
0
0
0
1
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
1
0
0
3
0
0
0
0
1
0
3
0
2
0
0
0
0
2
0
0
0
2
0
0
0
1
2
1
1
0
3
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
2
2
1
2
2
0
2
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
5
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
1
1
0
0
3
0
0
0
1
0
1
2
0
0
0
2
0
1
0
0
1
0
1
0
0
4
0
0
0
0
0
9
2
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
1
2
1
2
0
1
0
3
0
4
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
6
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
3
2
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
2
0
0
0
1
1
0
1
0
0
1
0
0
2
0
0
0
0
2
1
0
2
0
0
1
0
0
1
0
2
0
0
0
0
2
0
0
1
0
5
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
1
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
2
2
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
1
0
0
0
2
0
0
1
2
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
2
1
0
0
2
0
0
2
0
2
1
0
0
0
0
0
0
2
3
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
6
0
1
0
0
0
0
0
0
2
2
1
0
2
0
2
0
1
0
0
1
0
0
0
0
0
0
2
0
0
1
1
1
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
1
2
2
1
0
2
0
0
1
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
1
0
0
2
0
0
0
2
1
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
1
3
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
2
0
37
1
0
2
6
2
0
0
0
1
0
0
0
2
0
0
0
1
0
3
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
2
1
0
0
1
0
0
0
0
2
0
1
3
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
1
1
3
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
1
0
0
3
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
2
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
2
1
0
0
0
2
0
1
0
0
0
0
1
1
2
0
1
0
0
0
0
2
2
0
0
3
0
0
2
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
6
1
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
1
1
1
2
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
2
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
3
0
0
0
0
2
0
0
0
2
0
2
0
0
0
2
0
0
2
0
1
0
2
0
0
2
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
2
2
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
4
2
2
1
0
1
0
0
0
0
0
0
1
1
1
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
1
0
1
1
0
2
0
0
0
0
2
0
0
1
0
0
0
2
0
0
1
0
2
0
2
1
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
2
0
0
0
1
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
1
0
2
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
2
2
2
0
2
0
1
1
0
2
0
0
0
0
2
0
1
0
0
4
0
2
1
0
0
0
0
0
1
0
2
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
1
5
0
1
0
0
2
2
0
0
1
0
0
0
0
0
0
1
2
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
2
1
0
1
2
1
1
5
0
0
1
0
0
2
2
0
1
0
0
3
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
4
0
2
0
0
0
0
1
3
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
3
1
0
0
2
2
0
0
2
1
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
2
0
0
0
0
1
2
0
3
0
0
0
0
1
0
0
2
1
0
0
0
0
0
2
3
2
0
0
0
0
1
0
0
1
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
1
2
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
2
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
1
0
1
0
0
1
0
0
1
0
2
2
0
0
2
0
0
0
1
0
0
0
0
0
3
1
6
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
3
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
2
0
0
0
0
0
0
1
0
0
1
0
0
2
0
2
0
0
0
0
1
0
2
0
0
2
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
1
1
1
0
2
0
2
0
0
1
0
2
2
0
0
0
0
0
2
2
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
1
1
1
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
1
2
0
0
0
0
2
2
0
0
0
0
0
2
0
0
2
0
0
1
2
0
0
1
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
2
0
0
2
0
2
0
1
2
0
0
0
2
0
0
2
1
1
0
1
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
2
0
0
1
1
1
0
1
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
1
2
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
2
0
0
3
0
0
0
5
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
9
1
0
1
0
0
0
0
0
1
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
2
0
0
1
0
0
0
0
0
0
1
2
0
1
0
0
0
0
1
2
0
1
0
2
2
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
1
1
1
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
4
1
1
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
3
4
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
1
0
1
0
0
0
2
1
2
1
0
0
2
0
0
0
0
0
0
1
1
2
0
0
2
1
1
0
0
1
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
3
2
2
0
0
2
0
0
0
1
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
2
2
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
1
2
0
0
2
1
1
0
1
0
0
0
0
0
5
0
1
0
0
0
2
0
1
0
0
0
0
0
1
1
0
0
1
2
0
0
0
0
1
0
0
0
2
2
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
1
0
6
0
2
2
1
0
1
0
1
0
0
1
0
0
0
0
0
1
0
4
0
0
0
1
2
2
2
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
1
0
0
0
1
0
0
2
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
2
0
0
0
2
0
0
2
0
0
0
0
0
1
0
1
1
5
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
2
1
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
2
0
2
0
1
0
0
6
0
0
0
0
0
0
1
0
0
0
0
1
3
1
0
2
0
3
2
0
0
0
0
0
1
0
0
0
1
0
1
0
2
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
2
0
1
2
0
0
0
1
2
0
1
0
0
0
2
0
1
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
1
4
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
1
2
1
0
0
0
2
0
1
0
0
0
0
1
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
2
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
1
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
3
2
0
1
0
0
0
1
0
0
0
1
2
0
0
0
1
0
1
0
2
0
0
0
0
3
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
2
1
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
1
3
0
1
0
0
0
0
0
0
0
0
1
2
0
0
1
1
0
0
0
0
0
1
0
6
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
2
1
2
1
1
0
0
0
0
2
0
0
0
0
1
2
5
0
0
0
0
0
0
2
0
0
1
4
1
4
0
1
2
0
2
0
0
1
0
0
0
0
0
2
0
2
0
1
2
0
0
0
0
0
0
0
1
2
1
0
1
0
2
2
1
2
0
0
0
0
0
3
0
1
0
0
2
0
1
2
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
2
2
0
0
2
0
3
0
0
3
2
0
1
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
2
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
2
2
0
2
0
2
2
0
0
1
3
0
3
0
1
0
1
2
2
3
0
3
1
0
0
0
2
0
0
0
2
0
0
1
0
0
0
1
0
0
3
0
0
0
0
2
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
1
0
0
0
1
2
0
2
0
0
1
0
0
3
0
0
0
2
0
1
2
0
0
1
0
1
0
0
0
2
2
0
1
0
2
0
0
0
0
0
0
2
0
2
2
3
1
1
0
0
0
0
1
3
0
0
2
0
2
0
2
0
0
0
0
0
1
0
2
0
1
2
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
3
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
1
2
0
0
0
1
0
1
1
2
0
0
0
0
0
0
1
0
1
0
2
1
0
0
0
0
0
0
1
0
0
0
0
1
3
0
0
1
0
0
0
1
0
0
0
1
1
2
0
2
0
0
0
0
0
0
0
0
1
0
2
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
1
0
3
0
0
1
1
0
0
0
1
3
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
2
3
0
0
1
0
0
0
2
2
2
0
0
1
0
0
0
1
1
0
0
2
5
0
1
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
2
0
0
0
0
0
1
2
0
0
3
1
1
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
2
0
0
1
2
0
1
1
0
2
0
0
2
2
0
0
0
0
0
0
2
0
0
1
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
2
2
1
0
0
1
0
2
0
0
0
2
0
0
2
0
1
0
0
0
2
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
4
0
0
2
1
0
0
0
0
2
0
2
6
0
0
0
0
0
0
2
3
2
0
1
0
0
2
0
0
2
0
1
1
0
0
0
3
0
2
0
0
0
2
2
0
0
1
0
0
2
0
2
0
1
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
1
1
2
1
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
2
1
2
0
2
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
2
0
0
1
0
0
0
0
2
2
2
0
0
2
1
1
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
1
0
2
0
0
0
0
2
0
0
3
1
2
0
2
2
1
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
3
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
2
0
0
2
1
0
3
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
1
0
0
0
0
2
1
0
1
0
2
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
2
0
1
0
0
0
3
0
1
0
2
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
1
0
2
0
0
0
0
0
2
3
0
0
0
0
2
0
1
0
0
1
1
0
2
0
0
0
0
0
2
0
1
0
3
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
1
0
0
0
0
0
1
0
6
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
1
0
0
2
1
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
1
0
0
0
0
0
0
1
0
2
1
0
1
0
0
2
0
0
1
1
3
0
0
0
0
0
0
2
2
0
0
2
0
0
3
0
1
0
0
2
2
0
2
0
0
2
1
2
0
0
1
0
0
0
0
0
0
2
0
1
1
0
0
0
2
0
2
0
1
0
0
2
2
0
0
0
2
1
0
0
2
4
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
1
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
1
1
1
0
2
0
2
0
2
4
0
0
0
0
0
0
2
0
0
0
0
2
2
1
2
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
2
0
2
2
0
0
0
2
0
1
0
2
1
0
2
0
4
0
0
1
0
1
2
0
1
0
0
0
0
0
0
1
0
0
3
0
0
0
0
1
0
1
0
5
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
1
1
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
1
0
1
0
0
1
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
10
2
0
1
0
0
1
0
2
0
0
4
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
1
0
2
0
3
0
0
0
1
0
2
2
0
1
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
1
2
0
4
1
0
0
0
0
3
1
0
2
0
0
0
2
2
0
0
0
0
2
2
1
0
0
0
0
0
0
1
0
0
2
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
3
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
7
0
0
1
0
0
3
0
0
0
0
0
0
0
2
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
3
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
4
1
1
0
0
0
0
0
2
0
0
0
0
1
2
2
0
0
0
0
2
4
0
1
1
1
2
0
1
0
0
1
0
0
1
2
0
0
1
0
0
0
0
0
3
0
0
0
2
0
0
1
0
0
0
0
2
0
1
0
0
0
0
1
0
1
2
0
0
2
0
0
0
0
0
3
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
3
0
2
0
0
0
0
2
0
0
0
2
0
0
2
1
6
0
1
2
0
0
2
3
0
0
2
1
0
1
0
0
3
0
2
0
1
2
0
1
1
0
2
0
0
0
1
0
0
0
0
1
0
2
0
3
0
0
0
0
1
0
0
0
2
2
6
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
1
0
1
1
0
0
2
0
1
1
0
1
1
2
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
2
3
0
0
1
0
4
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
3
1
0
1
0
0
0
0
4
0
0
1
0
5
0
0
0
0
0
0
2
2
0
2
0
2
1
0
1
0
3
0
0
1
3
3
0
1
0
0
0
5
0
1
0
1
4
0
0
0
0
0
1
0
1
0
0
1
1
1
0
0
1
1
0
0
2
0
0
1
0
0
0
2
1
0
0
0
1
1
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
1
2
0
0
0
0
0
3
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
2
0
0
1
1
0
2
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
2
0
1
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
6
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
2
0
1
0
1
0
1
1
0
2
0
0
0
3
0
2
0
2
0
0
1
0
0
2
2
0
0
1
1
7
2
0
2
2
0
0
2
0
2
0
2
0
0
2
1
0
1
2
0
0
0
0
3
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
2
1
0
1
0
1
1
0
0
1
0
0
0
0
2
0
2
0
0
1
6
0
0
1
0
1
0
0
0
0
2
1
0
2
2
0
2
0
0
0
0
2
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
3
0
1
2
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
2
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
2
1
0
2
0
0
0
0
1
0
0
0
0
0
2
2
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
1
0
1
3
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
1
0
2
0
1
0
0
3
0
0
0
2
0
0
0
1
0
1
0
2
0
0
0
4
0
1
0
0
0
2
2
2
2
0
0
1
0
2
0
0
0
0
0
5
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
2
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
5
0
0
1
0
0
1
0
0
0
1
0
2
0
0
0
0
0
3
2
0
2
0
0
0
0
0
1
0
2
1
0
0
0
2
2
1
0
1
0
0
0
0
1
0
0
1
0
0
0
2
0
2
1
0
0
0
0
0
1
2
0
6
2
0
0
3
0
0
0
1
0
0
0
2
0
2
1
0
0
2
2
0
0
1
1
0
0
0
0
1
0
1
2
2
0
1
0
0
0
0
0
0
3
0
2
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
1
0
1
3
2
1
0
0
0
0
1
1
0
0
2
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
2
1
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
2
0
0
3
0
0
0
1
0
0
4
0
0
2
2
0
0
0
0
0
0
1
0
1
2
0
0
1
0
1
2
2
2
2
2
0
0
0
0
0
0
0
1
1
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
3
0
0
0
0
0
0
0
2
0
0
0
1
0
3
0
0
0
0
2
0
1
2
0
1
0
0
2
2
0
1
0
0
0
2
0
1
0
0
0
0
0
2
0
0
3
0
0
0
0
0
2
1
0
2
0
0
0
1
0
2
0
0
0
1
0
2
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
3
0
2
1
0
0
3
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
2
2
0
0
1
0
0
0
0
1
0
0
0
1
1
0
1
2
0
2
1
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
1
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
2
1
0
0
1
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
2
0
2
0
0
0
2
1
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
2
1
0
2
0
0
0
0
0
2
2
2
0
2
0
3
1
0
2
0
0
0
0
0
1
1
0
0
2
0
1
0
1
0
0
0
0
0
2
0
0
0
0
2
0
2
1
0
0
0
0
2
0
0
1
0
0
0
0
3
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
3
1
0
1
0
2
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
2
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
1
1
2
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
3
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
5
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
3
2
0
1
0
0
0
0
0
2
0
2
1
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
4
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
1
1
0
0
5
0
1
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
3
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
1
0
0
0
2
1
2
0
0
2
0
1
0
1
2
0
0
1
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
2
0
2
1
0
0
0
2
0
3
0
2
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
2
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
2
0
2
0
0
1
2
5
0
0
0
0
0
1
1
0
0
0
2
0
0
2
0
0
1
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
3
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
2
0
1
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
2
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
1
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
3
0
0
0
1
0
2
0
0
0
8
0
2
2
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
3
2
0
1
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
1
0
0
1
9
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
3
2
0
2
0
2
2
3
1
0
2
0
1
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
1
2
1
0
0
1
2
1
0
0
2
0
2
2
0
0
0
1
0
0
1
0
0
0
0
0
2
1
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
3
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
1
1
0
2
0
2
0
1
0
0
2
0
1
0
2
2
0
0
2
2
1
2
0
1
1
1
0
0
3
0
0
0
0
1
1
0
0
2
1
0
0
0
1
1
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
5
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
3
0
1
0
0
0
0
1
0
0
15
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
3
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
3
0
0
1
0
0
0
0
0
1
0
0
0
0
7
1
0
0
0
1
0
1
0
1
1
1
1
1
0
0
3
1
1
0
8
1
1
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
3
0
0
0
2
2
0
0
0
2
0
2
0
1
1
2
0
0
0
0
1
0
1
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
3
0
0
1
0
2
0
2
0
4
0
2
0
0
0
2
0
1
2
0
2
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
3
2
0
2
1
0
0
1
2
2
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
2
0
2
0
1
1
2
1
0
0
1
3
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
1
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
1
0
1
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
2
3
0
2
2
1
0
1
0
0
0
2
0
0
0
3
0
0
3
2
0
1
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
2
0
1
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
2
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
1
0
2
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
5
2
1
0
2
2
0
0
0
0
0
3
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
3
0
0
0
1
0
0
2
0
0
4
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
3
0
0
0
2
2
0
2
0
0
0
1
2
1
0
0
2
1
0
1
0
2
0
0
2
0
1
0
1
0
0
2
0
0
1
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
3
0
0
2
0
0
0
1
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
3
3
5
1
3
1
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
10
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
1
1
0
1
0
0
0
0
1
0
2
1
0
0
2
0
3
2
0
2
2
2
1
0
2
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
2
0
1
0
0
4
0
0
0
0
0
2
0
0
2
2
0
0
0
5
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
2
2
2
0
0
0
0
0
2
0
0
2
2
0
1
0
2
1
0
0
0
1
1
0
1
0
1
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
1
0
1
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
2
0
0
0
0
0
1
0
0
2
1
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
1
7
0
0
2
0
0
2
3
0
0
0
0
0
0
0
0
2
2
1
0
4
0
0
0
3
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
1
0
2
2
1
0
0
0
0
2
0
0
0
1
0
0
2
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
2
0
1
0
0
0
0
0
1
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
2
0
2
0
2
0
0
0
3
0
5
0
0
1
0
1
0
0
0
2
1
2
1
2
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
1
1
1
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
1
0
3
0
1
1
2
0
0
2
0
1
0
1
2
0
0
0
0
0
0
1
4
0
2
2
4
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
2
0
1
1
0
2
0
0
0
2
0
0
0
2
2
0
3
0
0
0
2
1
0
0
3
0
2
0
0
0
0
0
1
0
1
0
0
1
2
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
7
1
0
0
0
0
2
0
1
0
1
2
1
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
2
0
1
1
0
2
0
0
2
0
1
0
2
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
2
1
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
1
0
1
0
0
0
0
0
2
0
0
0
2
2
0
0
0
3
0
0
1
0
0
0
0
0
2
1
2
0
0
0
2
2
0
2
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
2
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
2
0
0
1
0
2
0
0
0
0
0
0
1
1
1
3
0
0
1
0
0
1
0
2
0
0
0
0
0
2
2
1
0
0
0
2
2
1
1
1
0
2
0
2
1
0
0
0
0
0
0
0
0
1
0
4
0
0
1
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
1
3
0
2
3
1
4
1
0
0
0
0
2
2
0
0
0
0
0
3
1
0
2
1
1
0
0
1
0
2
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
4
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
1
0
2
0
0
0
2
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
2
2
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
8
1
0
0
0
0
0
2
0
3
2
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
4
0
0
0
0
0
1
0
1
0
1
1
0
0
2
0
0
0
0
1
0
0
0
2
0
0
4
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
3
2
0
0
1
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
2
0
1
0
0
2
0
0
0
2
0
0
0
0
1
0
4
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
2
0
2
0
0
0
0
0
1
1
3
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
5
0
0
0
1
0
0
0
0
1
1
0
3
0
1
0
0
0
0
1
0
1
0
0
1
0
1
0
0
1
0
0
1
3
0
0
1
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
3
0
1
2
0
0
2
0
0
2
0
1
0
0
2
1
0
1
0
0
1
0
2
0
2
0
1
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
1
2
0
0
0
1
0
1
2
0
0
0
0
0
0
3
2
0
0
1
0
0
2
0
0
0
2
0
0
1
1
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
7
1
2
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
1
2
0
0
0
2
0
0
0
0
0
0
0
0
2
10
0
0
0
0
0
0
2
0
0
2
1
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
1
0
0
1
3
2
1
0
0
3
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
2
2
1
0
1
0
0
1
3
3
1
0
0
0
1
0
0
1
1
2
3
1
0
0
1
0
0
0
0
0
0
0
2
2
0
0
3
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
7
1
0
0
0
0
2
1
0
0
2
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
3
0
0
0
0
0
0
0
1
1
1
2
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
1
0
2
0
0
0
0
1
0
0
0
1
1
0
0
0
0
2
0
0
1
0
0
3
0
0
0
0
0
1
1
0
1
4
0
0
1
2
0
0
1
0
0
0
0
0
0
3
0
0
0
1
2
2
1
2
0
0
0
0
0
0
0
0
0
0
2
2
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
2
0
2
0
0
1
0
0
1
0
2
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
2
0
1
0
2
0
1
0
0
0
0
0
2
0
0
0
0
2
2
2
0
2
0
2
0
1
0
0
2
0
0
1
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
2
0
0
5
0
0
4
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
1
1
1
5
0
2
1
0
0
0
0
3
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
1
0
2
0
0
0
2
0
2
0
2
1
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
2
2
1
0
0
2
0
2
1
0
0
0
2
0
2
0
0
0
1
0
1
2
0
0
0
0
0
0
0
1
2
1
3
0
2
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
3
7
0
1
0
1
2
0
0
0
1
2
0
0
0
2
1
0
0
0
0
1
4
4
0
3
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
1
2
0
2
4
2
0
2
1
1
0
0
0
0
0
0
9
0
2
0
0
0
5
0
0
0
1
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
2
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
3
0
0
2
2
0
2
2
1
0
0
5
1
0
1
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
1
2
0
0
1
0
0
1
0
0
3
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
2
0
0
0
2
0
1
1
0
0
0
0
0
0
2
1
2
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
2
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
2
2
2
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
1
1
0
0
0
0
0
0
2
0
0
2
4
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
1
1
0
2
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
2
0
0
0
0
0
0
2
3
0
0
0
3
0
0
0
2
12
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
1
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
2
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
3
1
2
0
0
0
2
1
0
0
2
0
1
0
1
0
0
2
1
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
5
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
2
3
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
2
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
3
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
2
0
1
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
3
1
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
1
0
1
0
2
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
9
0
0
0
0
1
0
2
0
0
0
0
2
0
1
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
1
1
0
0
0
0
3
0
1
0
1
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
1
0
1
0
0
0
0
0
3
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
1
1
0
1
0
0
1
0
0
0
1
0
0
0
1
1
0
0
2
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
2
2
2
0
0
2
0
0
0
0
0
4
0
0
1
2
0
1
0
0
0
0
0
2
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
1
0
0
0
1
0
0
0
0
0
3
1
1
0
3
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
4
0
1
0
0
2
0
0
0
0
0
2
0
0
2
1
0
0
0
1
0
0
2
0
2
0
0
2
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
3
0
0
1
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
2
1
0
0
0
1
2
0
0
0
0
0
1
0
0
1
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
2
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
3
0
0
0
0
2
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
3
0
0
2
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
3
1
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
1
2
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
3
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
1
1
0
1
0
0
0
0
1
0
0
1
1
2
0
0
2
0
0
3
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
5
0
2
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
2
0
0
1
1
0
0
0
1
0
0
0
0
2
2
0
0
2
0
1
0
0
0
0
2
2
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
1
1
0
0
2
0
0
0
0
0
0
1
0
2
2
2
2
2
0
0
2
1
0
0
1
0
0
0
0
2
0
0
2
2
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
1
0
0
7
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
4
0
0
2
1
1
1
0
0
0
0
1
0
0
2
1
0
0
2
0
0
1
2
1
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
2
0
0
2
0
0
1
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
2
0
1
0
0
0
0
0
0
1
0
2
2
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
4
0
0
0
0
0
0
3
3
0
0
2
1
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
2
0
0
4
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
2
2
3
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
2
2
0
0
0
0
1
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
2
0
1
0
0
0
3
0
2
0
0
0
0
0
0
0
2
0
0
1
0
8
0
0
0
0
0
0
2
2
0
3
0
1
0
2
0
3
0
2
0
0
1
0
0
0
0
0
1
1
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
2
0
3
2
0
0
0
1
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
3
0
2
0
0
0
3
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
1
0
0
1
2
0
0
0
0
2
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
2
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
2
2
0
1
0
2
1
0
2
0
2
0
0
0
3
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
3
1
0
1
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
2
1
0
0
2
0
0
2
1
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
2
0
2
0
0
2
2
0
2
0
1
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
1
0
0
0
3
1
0
2
0
0
0
1
0
0
0
1
1
0
1
1
0
0
1
0
1
0
0
0
0
0
0
2
0
2
1
2
2
0
0
0
0
0
0
0
1
0
3
0
1
1
1
2
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
2
1
2
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
1
0
0
0
0
0
1
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
1
0
0
2
0
0
1
2
0
0
0
2
0
2
0
2
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
3
0
1
0
0
0
1
1
0
0
0
0
0
2
0
2
1
3
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
2
2
2
0
0
2
0
0
1
4
0
2
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
3
0
0
4
0
2
1
2
3
0
0
0
0
0
0
2
0
1
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
1
0
2
1
0
1
0
0
0
1
2
0
0
0
0
0
0
2
1
1
1
2
1
0
0
0
3
1
0
1
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
2
1
2
2
0
0
1
0
2
2
1
2
1
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
5
1
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
3
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
3
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
1
0
1
3
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
3
0
2
3
1
0
0
0
0
2
0
0
1
2
0
0
0
0
2
2
2
0
2
0
0
0
0
2
0
2
0
0
0
0
4
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
2
1
0
0
2
0
1
0
0
5
0
0
0
0
1
0
0
0
2
17
0
0
2
0
0
0
2
0
1
0
0
0
3
0
0
0
3
2
0
0
0
0
2
0
1
1
0
0
0
2
0
0
0
0
0
4
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
1
5
1
2
0
2
0
1
0
2
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
4
0
0
0
2
1
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
3
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
2
1
2
0
0
2
3
2
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
2
0
0
1
0
0
0
1
2
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
7
0
0
1
2
0
2
0
2
0
2
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
1
2
1
0
0
0
0
2
0
0
2
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
3
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
2
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
2
1
2
0
0
0
0
0
1
0
0
0
3
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
1
0
0
3
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
3
2
0
0
1
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
1
1
0
0
0
0
2
0
1
3
0
1
0
0
2
0
0
0
0
1
0
1
1
0
0
4
0
3
0
0
0
0
1
3
0
0
0
1
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
1
4
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
1
0
0
0
1
2
2
0
0
0
2
0
0
1
0
1
1
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
2
0
1
0
2
0
0
0
2
0
0
0
0
0
1
2
0
0
0
1
0
2
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
1
1
0
0
0
0
0
0
2
4
2
0
2
0
0
1
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
1
0
1
1
1
0
0
0
0
0
0
1
1
0
0
0
2
0
0
1
1
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
6
1
0
0
0
1
1
0
0
0
1
0
0
2
0
0
2
1
0
0
1
0
1
2
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
1
2
0
2
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
1
0
0
1
0
0
0
0
2
2
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
1
0
1
2
1
0
0
1
0
0
0
0
0
2
0
0
2
0
1
1
0
0
0
0
0
0
1
2
1
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
2
0
0
0
1
0
1
0
4
0
2
0
2
0
5
0
0
0
1
0
0
0
1
3
2
0
0
0
1
0
1
0
2
0
0
5
1
0
0
2
0
0
0
0
1
0
0
1
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
2
0
1
0
1
2
0
2
1
1
0
2
2
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
1
3
0
2
1
0
0
1
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
2
0
0
2
0
2
0
0
0
0
0
0
1
0
1
0
0
0
4
2
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
2
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
2
0
0
2
1
0
0
0
1
0
0
0
2
0
2
0
1
0
0
1
0
0
1
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
1
3
0
0
0
2
0
0
3
0
2
0
0
0
1
0
0
0
1
2
1
0
0
0
1
1
1
2
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
2
0
1
1
0
0
2
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
5
0
0
1
2
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
1
0
0
0
2
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
1
1
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
1
0
0
1
0
0
1
0
3
0
3
0
0
2
0
0
1
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
1
2
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
2
0
5
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
2
0
2
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
1
3
0
0
0
1
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
2
2
0
1
0
0
0
2
0
2
2
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
1
2
2
0
1
0
0
2
0
0
1
0
2
0
1
0
0
1
0
0
0
0
0
0
2
0
2
2
0
2
0
0
0
2
0
2
2
0
1
1
1
0
2
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
1
2
0
3
0
1
1
0
0
1
0
0
0
0
0
1
0
2
2
0
0
2
0
0
0
1
3
3
0
0
0
2
0
2
0
3
0
2
0
0
1
2
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
2
2
0
0
1
0
1
0
0
2
2
1
3
0
1
2
1
0
0
0
0
2
0
1
2
0
1
0
1
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
2
0
2
1
2
0
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
1
0
0
0
3
0
2
3
0
0
0
0
0
0
1
2
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
1
1
2
0
2
0
2
1
1
0
1
1
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
1
1
1
1
2
0
0
0
0
0
2
0
0
3
1
0
0
0
0
0
0
0
2
0
2
2
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
2
0
0
1
1
0
0
0
2
0
1
0
2
0
0
1
2
0
2
0
0
1
0
0
0
2
1
0
0
0
0
0
3
0
0
0
2
0
2
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
1
0
3
2
0
0
0
1
0
1
1
0
0
2
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
3
0
0
1
0
0
0
0
0
2
0
0
0
3
0
1
1
0
1
0
0
0
0
0
0
5
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
2
1
2
1
0
0
1
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
8
0
0
0
0
1
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
4
0
1
0
1
0
0
0
0
0
0
2
1
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
1
0
0
1
1
3
1
0
1
0
0
0
2
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
1
2
2
0
0
0
0
0
2
0
0
0
1
1
0
2
0
2
0
0
0
0
2
0
1
0
2
1
1
0
0
0
0
0
0
0
1
2
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
4
1
0
1
1
0
1
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
1
1
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
2
0
0
1
0
0
0
2
0
0
2
1
0
2
2
0
0
2
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
2
0
1
0
0
0
1
1
0
0
2
1
1
0
0
0
0
2
0
0
0
4
0
0
0
1
1
0
1
0
0
2
0
1
0
1
3
0
0
0
0
0
0
1
0
0
0
3
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
1
0
3
0
0
1
0
0
0
4
2
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
1
2
0
2
0
0
0
0
0
1
1
0
0
1
2
1
2
0
0
0
0
0
0
0
3
3
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
1
2
1
0
2
0
2
0
0
2
0
0
1
1
0
0
0
0
0
0
0
1
0
0
2
2
2
0
0
0
0
1
0
0
4
0
2
1
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
1
1
2
1
1
0
2
1
0
1
0
0
2
0
0
2
2
2
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
2
0
0
0
2
1
0
1
2
2
1
0
1
0
1
2
0
0
4
1
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
1
0
0
1
0
0
1
0
0
0
2
0
1
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
2
0
0
0
2
2
1
0
0
0
2
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
3
2
0
4
1
0
0
0
0
1
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
1
2
1
0
2
0
0
0
0
1
0
0
1
2
2
1
2
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
1
2
0
0
0
0
1
1
0
0
0
0
1
0
0
2
1
2
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
2
0
0
2
0
1
0
2
1
2
0
0
1
0
1
0
0
0
2
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
1
1
0
1
0
4
0
0
0
1
0
2
0
2
0
0
0
2
0
2
0
0
0
1
0
2
0
2
0
0
0
0
0
1
1
0
2
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
1
1
2
0
1
0
2
0
0
0
0
0
0
1
7
10
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
3
5
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
2
3
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
1
0
0
2
5
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
1
2
0
2
0
0
0
1
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
2
0
1
1
0
1
0
3
0
0
0
0
0
0
0
0
0
0
2
1
1
0
1
0
3
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
3
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
2
2
0
0
1
0
0
0
0
0
0
1
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
3
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
3
2
0
3
0
0
2
0
2
1
0
0
2
0
0
3
2
0
0
0
0
2
0
1
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
3
1
2
0
0
0
0
2
0
0
1
1
2
2
2
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
1
2
0
2
1
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
1
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
3
2
0
0
0
0
0
0
0
1
0
2
1
2
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
4
0
1
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
4
2
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
1
0
0
0
2
2
2
0
1
0
2
0
0
5
0
1
1
0
0
0
0
0
2
0
0
0
0
7
0
2
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
1
0
2
0
2
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
2
0
0
2
0
1
1
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
3
1
1
2
0
0
0
0
0
2
0
0
1
1
0
0
0
2
0
0
1
2
0
0
0
0
0
0
1
0
0
4
2
1
2
0
1
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
2
0
4
0
2
0
0
2
0
0
2
2
0
0
2
0
0
3
2
0
2
2
0
0
1
0
0
0
0
0
0
0
3
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
1
1
0
0
1
0
0
1
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
2
1
0
0
0
0
1
0
2
4
0
0
0
1
1
0
0
0
2
16
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
1
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
2
0
1
0
0
0
2
0
1
2
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
3
1
1
0
0
0
2
0
1
2
1
1
0
0
1
0
1
1
2
2
0
0
1
2
0
0
2
0
2
0
1
0
0
1
0
1
1
0
0
0
0
0
0
2
1
2
0
0
1
0
1
1
0
0
0
0
1
0
1
0
3
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
2
2
1
2
0
0
1
0
2
2
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
2
1
0
3
0
0
0
0
0
2
1
0
0
0
1
0
0
4
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
3
0
0
1
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
1
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
1
0
0
0
0
2
2
2
1
0
0
0
0
0
1
2
2
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
2
1
0
1
0
2
2
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
1
1
2
0
0
0
1
0
0
0
2
2
0
2
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
1
0
2
1
2
0
4
2
2
0
0
0
0
1
2
0
0
0
0
0
1
1
0
2
1
0
0
0
0
0
2
2
0
2
2
0
0
0
1
2
0
3
0
1
0
0
1
0
0
0
0
0
1
2
1
3
3
0
0
0
0
0
0
2
0
2
0
3
1
0
0
0
0
1
2
1
3
0
0
3
0
0
0
0
1
2
0
0
0
2
0
1
1
2
2
0
0
0
2
0
0
2
1
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
1
0
0
0
0
2
0
2
0
0
0
3
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
1
2
0
2
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
3
0
1
0
0
0
0
0
0
2
0
0
1
2
0
2
2
0
0
0
0
0
0
2
0
0
0
1
1
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
1
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
2
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
2
0
0
0
2
1
0
2
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
1
0
0
1
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
1
1
2
0
0
0
1
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
1
0
0
0
2
2
2
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
2
0
1
0
1
0
0
0
1
0
0
0
1
0
1
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
1
2
0
1
1
0
0
0
0
0
0
0
2
3
0
1
9
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
1
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
3
0
0
1
0
0
0
4
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
6
0
0
0
0
0
0
0
2
2
3
0
0
0
0
0
0
0
1
0
0
0
0
0
15
0
1
2
2
0
0
0
6
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
3
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
1
2
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
2
0
0
0
1
0
1
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
3
0
0
0
0
3
0
0
1
1
1
0
0
2
0
2
0
1
0
0
0
0
1
9
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
3
0
2
0
1
0
0
0
0
0
2
1
1
0
1
2
0
0
2
0
0
2
1
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
4
0
1
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
4
2
2
3
1
2
4
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
2
2
0
0
0
0
0
0
0
1
1
0
2
1
0
2
2
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
1
0
1
2
0
0
0
0
5
0
0
0
0
0
2
1
3
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
2
0
1
0
1
0
3
0
0
2
3
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
3
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
1
2
2
0
0
0
1
0
0
0
0
1
1
0
0
1
0
2
1
1
2
0
0
7
3
1
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
1
0
1
0
2
0
2
0
0
1
0
0
2
0
0
2
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
2
0
3
0
0
0
2
2
0
1
6
0
0
3
0
1
0
0
0
1
0
0
1
0
1
0
2
0
0
1
0
0
3
0
0
1
0
0
0
0
0
2
2
0
0
1
0
1
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
1
2
0
0
5
3
1
1
0
0
0
2
0
0
0
0
1
0
1
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
2
1
2
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
2
1
0
0
2
0
0
0
1
3
0
1
0
0
2
0
0
0
0
0
3
0
2
1
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
1
0
0
0
0
2
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
2
0
2
0
0
0
0
2
3
0
0
2
0
0
0
0
1
0
0
0
2
5
0
0
0
2
0
1
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
2
0
1
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
1
0
0
3
0
1
4
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
2
0
0
1
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
2
1
2
0
0
0
1
0
0
2
1
0
2
0
0
0
1
0
0
1
2
2
0
0
0
0
1
0
0
0
0
0
1
0
4
0
1
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
2
2
0
0
0
0
0
0
0
4
0
0
1
0
0
2
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
2
0
0
1
0
1
0
0
0
1
0
0
2
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
1
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
4
0
2
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
3
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
1
0
0
3
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
4
0
0
0
2
0
0
0
1
0
0
0
0
0
5
2
0
0
0
1
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
2
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
3
2
0
0
0
0
1
0
3
0
0
0
0
5
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
1
1
0
0
0
0
0
0
1
2
0
0
0
3
0
0
2
0
0
2
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
2
0
1
0
0
0
0
0
2
1
0
0
0
1
2
2
0
1
0
1
1
1
2
0
0
1
0
2
0
1
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
1
0
2
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
2
1
0
1
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
1
5
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
1
0
0
2
0
0
2
0
1
0
2
0
1
0
2
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
1
2
0
0
2
0
0
1
0
0
0
1
0
1
4
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
1
0
0
0
2
1
0
0
0
2
0
1
2
1
2
1
0
0
0
0
2
1
0
1
0
0
0
1
2
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
1
0
0
1
2
0
0
3
0
0
1
1
2
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
3
2
0
0
2
2
0
2
0
0
1
0
1
0
0
0
0
0
2
0
0
0
3
1
0
0
2
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
1
0
2
3
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
1
0
0
2
1
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
1
0
2
0
0
0
0
1
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
2
1
1
0
0
0
3
0
0
0
1
2
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
2
1
0
0
3
0
1
0
0
1
0
0
2
0
1
2
0
0
0
0
1
2
0
0
0
0
0
1
2
0
1
0
0
4
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
1
1
1
0
0
0
0
0
2
2
2
0
0
2
0
3
2
0
0
0
0
1
0
2
0
0
0
0
1
0
3
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
3
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
2
2
2
0
1
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
1
1
2
0
2
0
0
0
1
0
1
0
0
0
0
2
1
1
0
0
0
0
1
0
0
0
0
2
1
0
1
0
0
1
0
0
0
2
0
0
2
1
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
2
0
2
1
1
0
0
1
0
0
1
0
3
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
1
0
1
1
0
0
0
0
3
0
1
1
0
1
8
0
0
0
0
2
0
0
0
2
0
3
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
2
0
0
0
0
1
1
2
1
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
4
1
1
0
2
1
2
0
1
0
1
0
1
3
0
0
2
0
0
0
1
1
0
0
0
0
0
0
1
2
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
1
0
0
1
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
1
0
0
4
0
3
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
3
0
1
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
2
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
2
0
0
2
0
2
0
0
0
2
0
1
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
3
0
1
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
3
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
2
0
2
0
2
3
1
1
0
1
2
1
0
0
0
0
0
0
0
4
0
2
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
3
0
0
2
2
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
1
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
8
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
1
0
1
1
2
2
2
0
2
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
2
0
1
1
0
0
1
0
0
1
3
1
1
1
0
0
4
0
0
0
0
2
0
0
2
0
1
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
2
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
3
0
0
0
1
2
0
1
2
0
0
0
0
1
2
0
1
0
1
0
0
3
0
0
0
1
0
0
2
0
0
0
0
1
2
0
0
1
0
0
0
0
0
1
0
0
4
0
1
0
1
0
0
1
0
4
2
0
0
0
0
0
0
4
0
1
1
2
0
0
2
0
0
0
0
0
0
0
0
3
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
1
0
1
1
0
0
0
2
0
2
2
1
2
0
3
0
0
1
2
0
0
0
4
0
0
2
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
4
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
1
0
0
0
2
0
2
0
0
2
0
0
1
0
4
0
0
1
2
0
0
2
0
2
1
0
0
0
0
0
1
0
4
3
0
0
0
0
1
0
2
0
0
0
1
0
2
0
0
0
0
3
0
3
0
0
0
2
0
1
1
0
0
2
3
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
3
2
0
0
0
2
0
0
0
2
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
2
0
0
5
0
0
0
0
0
0
0
0
2
6
0
0
1
1
0
1
0
0
0
0
0
0
1
2
0
1
1
0
1
1
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
3
2
0
0
2
0
2
2
0
0
0
0
0
0
0
2
1
0
1
1
1
0
0
1
1
0
0
2
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
1
0
2
0
2
9
1
0
2
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
1
0
0
2
0
1
1
0
0
0
4
0
0
2
0
1
2
0
4
1
1
0
2
0
0
0
4
3
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
1
0
0
0
0
3
0
0
0
2
2
0
1
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
2
3
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
1
2
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
1
1
0
3
1
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
2
0
3
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
2
0
2
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
2
3
0
1
1
1
0
3
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
2
2
0
0
0
1
0
2
0
1
0
8
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
1
0
0
0
1
11
1
0
0
4
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
1
2
0
0
1
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
4
0
0
0
0
1
1
0
1
0
0
0
1
0
2
2
0
0
2
0
0
0
0
1
1
2
0
0
0
0
0
0
2
0
0
0
6
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
1
1
0
1
1
1
0
2
0
0
1
2
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
2
0
3
0
2
0
0
0
2
2
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
4
7
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
2
0
0
2
0
0
0
0
0
2
2
0
0
0
0
1
0
0
2
3
0
0
1
0
2
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
2
0
2
3
1
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
2
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
2
1
0
0
0
0
0
2
0
0
0
1
0
3
0
2
0
0
0
0
2
0
0
0
1
2
1
2
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
2
2
2
2
2
2
0
0
0
1
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
1
2
0
1
0
0
2
0
1
0
2
0
0
0
0
1
2
1
0
0
0
0
0
1
2
0
0
2
2
0
0
0
1
1
1
0
3
1
3
2
0
0
2
3
2
0
0
0
0
0
0
0
0
0
2
0
0
3
0
1
3
3
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
1
0
0
1
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
2
0
2
0
1
0
0
0
0
2
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
3
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
2
2
1
0
0
0
1
0
1
1
1
2
0
0
1
0
2
0
3
0
0
0
0
0
0
0
0
1
2
0
2
0
1
0
0
0
2
0
0
1
2
1
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
2
3
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
1
0
0
0
0
2
0
0
2
0
2
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
1
1
0
2
0
0
0
2
0
2
0
2
0
0
1
0
0
0
2
0
2
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
1
0
1
0
0
0
0
2
2
0
0
0
1
2
2
0
0
1
0
2
0
0
0
2
0
0
5
0
0
0
0
0
0
0
0
1
3
0
0
0
5
1
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
1
0
3
0
0
1
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
6
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
1
0
1
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
2
1
0
0
4
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
2
0
2
0
0
0
0
0
1
0
0
1
0
1
2
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
2
2
0
2
0
2
2
1
1
2
2
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
1
2
2
0
0
2
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
2
0
0
2
0
0
0
0
2
0
0
0
1
2
0
0
0
1
0
0
0
0
2
2
2
2
0
2
0
0
0
3
2
0
2
0
0
0
0
0
1
0
0
2
0
0
1
3
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
2
3
0
0
0
4
1
0
0
0
0
0
2
2
0
0
1
0
0
3
0
0
1
0
2
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
1
0
1
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
3
2
1
0
0
1
0
0
1
0
0
0
0
0
2
2
0
0
1
2
1
0
1
1
0
1
0
3
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
2
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
1
0
1
0
3
0
2
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
1
0
0
1
0
0
1
0
0
0
2
0
0
0
0
3
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
1
1
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
2
4
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
2
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
1
2
1
0
0
1
0
2
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
3
0
2
1
0
0
0
0
0
0
0
1
0
2
2
0
0
0
2
1
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
2
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
1
0
0
2
1
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
2
2
0
2
0
1
0
0
1
4
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
2
0
1
0
0
2
0
0
0
2
0
2
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
2
0
1
2
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
3
0
0
0
0
0
0
0
0
0
1
0
0
2
1
1
0
1
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
2
2
0
2
0
2
0
2
0
0
2
0
0
0
0
2
0
0
2
0
0
0
2
0
0
2
0
2
2
1
2
0
0
3
1
2
0
5
0
0
1
0
0
2
0
0
2
1
2
3
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
2
0
0
0
0
3
0
2
0
1
0
0
0
2
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
1
0
3
0
2
0
0
0
0
2
11
3
2
0
0
0
2
2
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
1
0
3
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
2
1
0
2
0
2
0
0
0
1
0
0
3
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
3
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
1
2
0
1
1
0
0
2
2
0
1
3
0
1
1
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
2
1
2
0
0
0
0
2
1
0
1
0
2
0
0
0
2
1
0
0
1
0
0
1
1
1
0
1
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
3
0
2
0
0
0
0
0
2
1
1
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
2
0
2
2
1
0
0
3
0
0
1
0
0
0
0
0
1
0
0
0
1
0
2
2
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
1
0
3
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
2
1
3
0
2
0
0
0
0
2
0
0
0
0
2
0
1
1
0
0
0
0
1
0
1
0
0
2
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
7
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
3
2
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
1
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
2
1
1
3
0
0
0
0
0
0
2
0
0
0
1
2
0
0
2
0
0
0
2
1
2
0
0
1
0
1
0
0
0
2
2
1
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
2
1
0
0
2
0
2
0
0
0
1
0
1
2
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
3
0
0
0
0
1
0
1
0
0
2
2
0
0
0
1
0
0
1
0
0
0
1
2
0
1
0
0
1
1
0
0
2
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
2
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
1
0
1
0
1
1
0
0
3
0
0
0
1
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
1
1
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
1
0
3
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
1
1
0
0
0
1
1
0
1
1
2
0
0
0
0
0
0
0
2
2
0
3
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
1
1
0
1
0
2
0
0
0
1
0
0
0
4
0
2
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
2
0
1
1
2
0
0
0
0
0
1
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
3
0
3
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
2
2
0
1
0
2
0
4
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
2
0
2
0
1
2
0
0
0
1
0
0
0
2
1
1
0
0
0
0
0
0
0
1
0
1
2
0
1
1
1
0
0
0
2
1
2
0
2
0
1
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
3
0
2
2
2
0
1
0
0
0
2
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
2
0
0
1
2
0
0
0
0
6
2
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
3
0
0
0
0
0
0
0
1
1
0
0
1
1
2
5
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
1
3
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
2
0
2
0
0
0
3
2
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
1
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
3
0
1
1
1
2
0
0
0
0
1
1
0
0
2
1
0
1
0
0
0
0
1
1
0
0
0
1
0
2
0
2
0
0
0
0
0
1
1
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
5
0
0
0
1
0
0
0
0
1
0
0
2
1
1
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
3
0
0
0
2
2
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
3
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
2
1
0
0
0
0
4
2
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
6
0
0
0
1
2
0
2
0
0
0
0
0
1
0
3
2
0
0
2
0
0
0
2
2
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
2
1
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
1
0
2
4
2
0
0
2
4
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
3
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
2
0
1
2
0
1
0
1
0
0
2
0
0
0
2
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
4
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
7
0
1
6
2
0
0
2
0
0
0
2
1
0
2
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
4
2
0
0
1
3
0
1
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
1
2
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
8
0
0
2
0
0
1
1
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
1
0
1
2
1
2
0
0
0
0
1
2
0
0
2
0
2
0
0
0
0
0
2
0
0
2
0
0
2
4
0
1
1
0
0
0
0
2
0
0
2
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
1
0
2
0
0
0
1
2
0
0
0
0
0
0
2
1
2
0
2
2
0
0
2
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
2
2
0
0
1
1
0
0
0
2
0
0
0
0
1
1
0
0
0
0
1
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
2
1
0
0
2
0
2
0
0
0
1
0
2
4
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
2
0
0
0
4
0
3
0
0
2
1
0
4
0
0
0
0
0
0
2
1
0
0
0
0
3
0
0
0
0
0
0
2
0
2
0
1
1
0
1
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
2
0
1
0
3
2
0
0
0
5
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
1
0
0
0
0
1
6
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
2
2
0
1
2
0
0
0
2
0
0
0
0
1
0
0
1
0
4
0
0
0
0
0
2
2
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
1
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
1
0
0
0
0
0
1
1
0
2
2
1
0
0
0
0
0
0
2
0
0
2
0
0
2
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
1
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
4
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
2
0
0
1
0
0
0
0
1
0
0
2
0
2
0
0
0
0
2
2
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
2
0
0
3
0
0
1
0
0
2
1
0
1
0
2
0
0
2
1
0
0
2
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
1
0
4
1
2
0
0
1
0
2
0
0
1
0
1
0
0
2
1
0
2
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
7
2
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
2
4
2
0
1
2
0
0
0
1
0
1
2
0
0
1
2
0
0
0
0
0
1
0
2
0
0
0
2
0
2
0
0
0
3
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
2
2
0
1
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
2
1
0
1
0
1
2
2
0
0
0
2
0
0
0
0
2
1
0
0
0
1
1
2
0
0
0
0
1
0
0
1
2
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
2
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
1
1
2
0
0
1
2
0
0
0
1
0
0
0
1
0
0
2
1
0
2
0
0
0
0
1
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
1
0
1
0
0
2
0
0
0
1
0
2
2
1
1
7
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
1
0
2
2
2
0
0
0
1
0
0
0
2
0
0
3
0
0
1
0
1
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
2
0
0
0
2
0
1
0
1
1
0
0
0
0
0
1
0
0
1
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
3
1
0
1
0
1
0
0
0
1
2
2
2
0
0
0
1
0
1
4
0
2
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
2
1
0
0
2
0
0
12
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
1
2
0
0
2
0
0
0
1
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
1
2
0
2
2
2
0
2
1
0
0
0
1
0
3
2
0
0
2
0
0
2
2
2
0
3
0
0
2
1
0
0
0
2
0
0
0
2
0
0
2
2
0
0
0
4
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
1
1
0
1
0
2
0
1
2
0
2
0
0
2
2
0
0
2
0
0
0
0
1
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
2
0
1
0
2
0
2
0
0
2
0
1
2
0
0
0
1
0
0
2
0
1
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
2
0
2
0
0
2
1
0
0
2
0
8
0
0
0
1
2
2
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
2
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
2
2
0
0
0
0
0
2
2
0
2
1
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
1
2
0
0
0
0
2
1
0
4
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
2
0
0
4
0
1
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
1
2
0
1
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
3
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
1
0
4
0
0
0
0
0
1
0
0
0
0
1
1
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
1
2
0
2
0
0
1
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
2
1
2
2
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
5
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
1
1
0
2
0
0
0
0
1
0
0
0
0
1
2
1
0
2
0
0
0
0
0
0
1
1
3
0
0
1
0
0
0
2
0
2
3
0
0
0
1
1
2
0
0
2
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
2
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
2
3
0
0
0
2
1
1
0
2
0
0
0
0
1
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
4
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
2
2
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
2
0
5
0
0
0
0
0
0
0
0
0
1
0
3
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
1
1
0
0
0
0
0
0
1
0
0
0
1
4
0
0
2
1
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
2
0
1
0
0
0
2
0
0
2
0
0
0
2
0
0
0
2
1
1
1
0
0
2
0
1
0
0
0
2
0
1
0
2
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
1
3
0
0
0
0
1
0
6
0
1
1
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
2
0
2
0
0
1
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
2
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
1
0
0
0
0
2
0
2
0
0
1
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
6
0
0
0
2
1
1
2
0
0
0
0
0
0
0
1
0
0
2
0
0
2
2
0
0
0
0
0
2
2
2
1
0
0
2
1
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
3
2
2
0
1
0
2
0
0
1
0
0
0
2
0
0
0
0
3
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
2
0
1
0
0
0
0
1
0
2
1
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
6
0
1
1
0
1
1
2
2
0
0
0
0
2
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
3
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
1
0
2
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
1
0
0
2
1
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
2
2
0
2
0
0
0
0
0
4
0
1
0
1
2
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
2
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
5
2
2
0
0
2
0
1
2
0
2
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
1
0
1
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
1
0
5
3
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
1
0
2
2
1
0
1
1
0
0
0
1
0
0
0
2
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
1
2
0
0
0
0
1
2
0
1
3
0
0
0
2
2
1
0
1
0
1
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
1
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
2
0
0
2
0
1
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
3
0
0
0
0
0
0
0
2
0
2
1
1
2
0
0
1
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
2
1
0
1
0
2
0
2
2
0
0
0
0
0
0
0
0
0
5
2
0
0
2
0
2
0
0
1
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
1
1
1
1
0
1
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
2
1
0
2
0
1
0
0
0
2
2
3
0
0
0
1
0
1
2
0
1
0
0
1
1
0
0
2
0
0
0
0
0
0
0
1
0
4
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
1
0
1
1
2
0
0
0
0
0
0
1
0
0
1
4
0
2
0
0
0
0
0
1
0
0
0
0
2
2
0
6
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
2
1
2
0
0
1
0
0
0
0
2
2
0
0
0
0
0
2
4
0
0
0
0
0
2
2
0
2
4
0
0
4
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
2
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
1
0
1
0
2
0
0
2
0
0
0
0
0
2
0
5
2
0
0
0
0
1
2
2
0
0
2
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
3
0
0
0
2
2
1
2
0
0
1
0
0
2
0
0
0
1
0
0
0
0
1
2
0
1
2
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
2
1
0
0
1
0
0
0
2
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
2
0
0
0
1
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
2
0
3
1
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
2
0
4
1
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
1
1
0
2
0
1
2
1
0
2
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
2
0
0
0
0
2
0
3
0
0
0
0
1
2
2
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
1
1
3
1
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
2
2
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
1
0
1
0
2
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
1
2
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
1
0
2
0
3
0
0
2
0
0
2
0
1
2
0
0
0
0
2
1
0
2
2
0
2
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
3
0
2
0
0
0
0
0
1
1
0
1
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
3
0
3
1
0
0
2
0
1
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
2
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
1
0
1
2
1
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
2
0
0
1
1
1
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
4
2
2
1
0
0
0
3
1
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
3
0
1
0
0
0
0
3
0
0
0
1
2
2
0
2
0
0
2
1
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
1
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
1
0
4
0
0
1
2
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
2
0
0
0
1
0
0
0
1
0
0
0
0
0
1
3
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
2
0
2
0
0
2
0
1
0
0
0
0
4
0
1
0
0
0
1
0
0
0
0
2
0
4
2
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
2
2
1
2
5
1
0
0
0
0
0
2
0
0
0
1
0
0
1
1
1
0
0
2
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
1
2
2
1
0
0
1
2
0
0
0
1
2
0
0
3
0
0
0
4
0
0
2
2
0
0
0
2
0
2
0
3
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
1
2
1
0
0
0
0
0
0
1
0
3
0
0
0
2
2
0
2
2
0
0
0
0
0
0
0
3
1
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
1
2
0
0
3
0
2
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
1
0
0
0
2
0
3
0
0
2
1
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
1
2
0
2
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
2
4
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
2
3
0
0
0
0
3
0
0
1
0
0
0
1
0
0
1
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
1
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
4
1
0
1
1
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
5
0
0
0
1
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
2
0
0
2
0
0
3
0
1
3
2
2
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
1
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
1
0
1
0
0
2
0
3
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
1
2
0
0
0
2
2
0
3
0
0
2
1
0
0
0
3
0
2
0
2
0
1
0
0
0
0
0
2
0
1
2
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
1
1
0
0
1
1
2
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
3
0
1
0
0
0
0
0
1
0
2
0
0
0
3
1
0
0
0
1
0
0
2
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
3
0
0
0
1
0
0
0
0
0
0
2
0
0
1
2
0
0
0
2
0
0
0
1
0
5
0
1
1
0
0
0
1
4
0
0
0
0
0
2
0
1
2
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
3
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
5
0
0
0
2
0
0
0
0
0
1
2
0
0
1
0
0
0
0
2
1
2
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
1
2
1
0
2
2
0
0
0
0
0
2
1
0
2
0
0
1
1
0
0
3
0
0
0
1
1
0
1
0
0
0
2
0
0
0
5
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
1
0
0
2
0
0
0
0
2
2
2
1
0
0
0
0
2
2
0
0
2
1
0
0
0
0
1
0
2
0
1
0
0
0
0
2
0
0
0
2
0
0
1
0
2
2
0
0
0
0
0
2
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
2
0
2
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
1
1
0
0
0
0
0
2
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
2
0
0
1
1
0
0
1
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
1
0
0
3
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
2
0
3
0
0
0
0
5
2
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
1
2
7
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
1
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
3
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
3
0
2
1
0
0
0
1
0
2
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
4
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
2
1
0
0
0
4
1
2
0
2
2
1
0
0
0
1
2
1
0
1
2
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
2
0
1
0
1
2
1
0
2
1
2
2
0
0
3
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
7
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
2
1
0
0
0
2
1
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
2
1
0
1
1
0
0
0
0
1
0
2
1
1
0
0
2
0
0
0
0
1
0
0
2
0
0
0
1
1
0
1
1
0
1
0
0
1
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
1
0
2
0
0
3
4
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
3
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
2
2
2
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
2
0
3
2
0
0
0
0
2
0
0
1
0
0
0
0
2
1
0
0
1
3
2
0
3
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
2
1
5
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
2
1
0
1
2
0
0
0
1
0
0
1
0
0
2
2
1
0
0
1
0
0
2
2
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
1
2
0
2
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
1
1
0
0
0
3
0
1
3
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
8
2
0
2
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
1
3
2
0
1
0
0
0
0
1
0
1
0
0
0
0
2
0
1
0
2
0
0
0
0
0
2
0
2
0
2
0
3
0
0
0
2
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
1
0
3
0
1
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
1
3
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
2
0
2
0
1
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
1
2
0
2
0
1
0
0
0
1
2
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
3
0
0
0
1
0
0
1
0
0
0
1
2
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
1
2
1
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
1
0
0
2
0
0
1
0
0
3
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
3
0
1
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
1
2
2
2
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
2
1
2
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
2
0
1
0
0
0
3
0
0
2
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
2
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
12
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
2
0
0
2
0
1
0
0
0
2
0
0
4
0
2
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
3
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
1
2
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
1
2
0
2
0
0
0
2
0
2
0
0
2
0
2
2
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
2
0
1
0
2
0
1
0
0
0
0
0
0
1
0
2
1
0
0
2
0
0
0
0
2
2
0
0
3
1
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
2
0
0
0
0
0
0
1
1
0
2
0
0
1
2
0
0
0
0
2
0
0
2
0
0
2
1
1
0
1
0
0
4
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
2
1
0
0
0
0
0
0
2
0
0
0
1
0
0
2
1
0
0
0
0
0
0
9
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
2
2
1
0
1
0
1
0
3
0
0
0
2
2
0
2
0
0
0
0
1
1
0
2
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
1
3
0
2
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
5
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
2
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
2
0
0
0
1
0
0
0
1
0
0
1
1
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
1
0
1
0
3
3
0
0
0
0
1
0
0
2
0
0
2
0
0
1
1
0
0
0
2
0
2
0
0
0
1
0
0
0
0
3
2
0
0
0
0
1
0
0
2
0
1
0
2
0
0
3
0
0
0
2
0
0
1
1
0
0
0
0
3
0
0
0
0
1
2
0
0
2
0
0
0
2
1
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
3
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
1
0
0
0
0
6
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
2
0
0
0
1
0
1
0
4
0
1
0
0
0
0
0
0
2
0
1
1
0
0
2
0
0
0
0
0
0
2
0
0
6
0
4
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
4
0
2
2
0
0
2
0
0
0
1
2
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
1
2
0
1
1
1
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
3
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
2
0
2
0
0
0
1
2
0
0
0
0
0
0
2
2
2
0
0
1
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
3
0
1
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
2
0
0
2
0
1
1
1
0
0
0
1
0
2
0
0
2
0
0
1
1
0
0
0
0
0
0
0
2
0
2
1
0
0
2
2
1
2
0
0
0
0
0
2
1
0
2
0
0
2
0
0
2
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
2
3
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
2
1
0
0
0
2
0
1
0
0
0
2
1
0
0
1
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
2
0
2
2
0
2
0
0
1
1
0
0
3
2
0
2
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
3
1
0
3
2
0
1
0
0
1
0
0
0
4
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
1
1
1
2
0
0
0
0
2
0
0
1
2
0
0
0
1
0
2
0
1
0
0
1
0
1
0
0
2
2
1
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
2
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
1
2
0
0
1
2
0
0
0
2
0
1
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
4
2
1
2
0
0
0
2
2
0
0
2
0
0
0
0
1
0
0
2
0
2
1
0
2
0
0
2
0
1
0
0
0
3
0
0
1
2
3
5
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
2
2
1
0
2
0
1
0
0
0
0
0
0
1
0
0
0
2
0
2
2
0
0
0
0
0
2
0
0
1
0
0
9
2
0
2
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
1
0
0
0
1
0
3
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
2
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
4
0
0
2
0
0
0
0
0
0
2
1
1
0
0
0
1
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
1
2
0
0
2
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
2
0
3
1
0
1
0
1
1
0
0
2
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
2
2
1
0
0
1
0
0
1
2
2
0
1
0
0
3
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
1
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
1
2
0
1
0
0
0
0
2
0
2
2
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
2
2
2
0
0
0
0
0
1
0
0
0
0
2
0
1
1
0
0
0
2
1
0
0
0
0
1
0
1
0
0
0
0
2
0
0
2
4
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
1
0
1
2
0
0
0
0
2
0
0
0
2
3
2
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
3
0
2
0
1
0
3
0
0
0
0
0
0
2
1
0
0
0
0
3
2
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
1
2
1
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
2
2
2
0
2
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
1
0
0
2
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
3
1
1
0
0
1
0
0
2
0
1
0
2
2
3
0
2
0
0
2
1
0
0
0
0
2
0
0
0
0
1
2
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
2
1
2
1
0
0
0
0
2
2
1
0
0
2
0
1
2
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
2
1
0
1
0
0
0
2
0
0
1
0
2
2
2
0
0
0
2
0
0
0
0
0
0
3
0
0
1
0
2
2
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
1
0
1
0
1
1
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
1
1
0
2
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
1
1
0
2
0
0
0
0
1
0
1
0
0
1
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
1
2
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
1
0
0
0
2
0
0
0
2
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
2
1
2
0
0
2
4
0
0
0
0
0
2
3
2
0
1
1
2
1
0
1
0
0
1
1
0
0
2
0
0
1
2
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
2
0
0
1
2
0
3
1
0
1
0
0
0
1
0
2
0
0
2
4
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
2
2
3
0
0
2
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
2
0
0
0
0
0
0
0
4
2
1
6
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
2
1
0
0
0
2
2
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
5
0
0
2
0
1
0
3
0
0
0
0
0
0
2
1
0
0
0
3
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
2
0
1
0
0
3
2
0
0
0
0
0
3
1
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
1
2
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
2
0
1
2
0
0
0
1
0
3
0
0
0
1
1
1
0
1
0
0
0
0
1
2
0
0
0
0
0
2
1
0
1
0
0
0
0
0
4
2
0
1
0
0
0
1
3
1
0
1
0
0
0
0
0
5
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
2
2
2
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
2
0
0
3
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
1
0
1
0
2
0
0
0
0
1
0
0
1
0
0
2
2
1
1
0
0
0
0
2
0
3
2
0
2
2
0
0
0
0
2
0
2
0
1
0
0
0
1
1
1
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
2
1
1
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
2
0
0
3
0
0
0
0
1
0
2
0
1
0
2
0
0
0
0
2
1
1
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
2
0
0
1
2
1
0
0
2
0
0
2
0
2
2
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
5
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
2
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
1
0
2
1
0
0
3
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
1
0
1
0
2
0
0
1
1
0
0
0
1
0
0
1
2
0
0
0
1
0
0
0
0
1
1
2
0
3
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
4
1
0
0
0
0
2
1
0
1
2
0
1
0
0
1
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
1
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
2
2
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
1
1
0
1
0
2
2
0
0
2
0
0
0
0
0
1
0
4
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
2
0
1
0
4
2
0
0
1
0
1
0
2
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
3
0
2
2
0
1
2
2
1
0
0
2
0
0
3
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
1
0
2
0
0
2
0
11
2
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
1
1
0
0
0
0
0
0
2
0
1
0
0
2
3
0
0
0
0
2
0
0
1
2
0
0
1
0
0
2
1
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
3
0
1
2
0
0
0
0
0
0
2
0
0
0
2
0
1
2
2
0
2
1
0
2
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
1
0
2
1
4
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
1
3
2
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
1
0
0
2
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
3
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
2
0
0
1
0
0
2
2
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
3
2
1
3
0
0
2
0
2
2
0
1
2
0
0
0
0
0
1
0
0
1
2
0
0
2
0
1
0
0
0
0
0
1
1
0
2
2
0
0
0
0
0
0
0
0
0
2
2
1
2
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
2
1
0
2
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
1
0
1
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
3
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
2
0
0
1
2
0
0
0
0
2
1
2
2
0
0
2
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
1
1
0
2
0
1
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
2
1
2
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
5
0
0
0
0
0
0
1
0
0
0
1
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
1
0
0
0
0
2
1
2
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
4
2
0
0
0
0
0
2
0
0
0
1
0
1
2
0
2
2
0
2
0
0
0
0
0
0
0
0
2
0
1
3
1
0
2
0
2
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
3
0
0
1
1
0
2
0
0
0
8
0
0
1
3
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
3
0
0
0
0
0
0
2
1
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
2
0
0
0
2
1
1
0
0
2
2
0
0
3
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
2
2
0
0
0
0
0
0
2
0
0
2
2
0
2
0
0
0
2
2
0
0
0
2
0
2
0
2
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
3
0
0
0
0
1
1
0
3
0
0
0
0
0
2
2
0
1
0
2
0
1
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
2
0
0
1
0
0
0
0
0
0
1
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
1
0
3
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
1
2
0
2
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
2
0
0
0
2
1
2
0
0
2
0
1
1
1
0
0
0
0
1
0
2
0
0
4
1
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
2
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
2
1
1
0
0
0
0
2
2
0
1
0
0
0
3
0
0
0
0
1
0
0
2
2
1
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
3
2
0
0
0
0
2
1
0
0
0
0
0
0
0
1
1
0
2
0
2
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
1
0
0
3
2
1
0
0
1
0
2
0
0
0
0
0
1
0
0
0
3
0
2
2
2
0
0
3
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
3
1
0
0
1
1
0
0
2
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
2
1
2
1
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
3
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
1
0
2
3
0
1
2
0
0
2
1
0
2
0
0
0
1
0
0
0
0
2
0
0
2
1
0
0
0
0
2
2
0
0
0
0
0
2
1
0
0
0
3
2
0
0
0
0
3
0
2
0
1
0
0
0
0
0
2
0
1
0
0
0
1
2
1
2
0
0
0
0
0
0
0
0
0
0
6
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
8
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
1
1
0
2
0
0
2
2
0
0
2
2
0
3
1
0
0
0
0
2
2
0
0
0
2
0
0
0
0
4
2
1
0
7
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
2
0
2
0
0
1
0
0
1
0
2
2
0
2
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
2
2
0
0
0
0
0
2
0
0
0
1
5
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
1
1
0
1
0
0
2
0
2
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
2
1
0
0
2
0
1
1
0
1
0
0
1
0
0
1
3
0
0
0
0
2
1
0
0
0
1
2
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
1
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
1
0
0
1
2
0
0
1
2
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
2
1
1
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
2
0
1
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
3
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
3
0
0
0
0
0
0
2
1
0
1
0
0
0
1
0
2
0
0
2
0
2
0
2
0
2
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
1
3
1
1
1
2
0
0
1
0
1
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
3
1
0
1
0
0
1
0
0
0
0
0
0
0
2
2
0
2
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
2
2
0
0
0
2
0
0
0
2
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
2
0
1
0
0
1
3
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
3
0
7
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
1
0
1
0
0
0
1
0
0
0
0
1
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
5
2
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
2
1
4
0
2
0
0
0
1
2
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
1
0
2
0
0
2
1
1
0
0
0
0
1
0
1
0
2
1
0
0
2
0
0
1
0
1
1
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
1
0
0
0
1
0
0
1
0
1
3
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
3
1
0
0
0
4
1
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
2
2
0
3
0
0
0
0
2
0
2
0
1
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
4
0
0
1
0
0
0
3
2
0
2
1
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
13
2
1
0
0
1
1
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
1
2
1
2
0
0
0
2
3
0
0
0
2
0
0
2
1
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
3
1
0
0
1
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
3
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
13
2
0
4
1
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
2
2
0
3
0
1
0
0
0
0
0
0
0
1
1
0
2
0
0
0
2
0
0
0
0
1
0
3
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
3
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
2
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
1
0
1
0
0
0
1
0
0
0
0
3
0
2
0
0
0
0
0
1
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
1
0
1
0
0
0
2
1
1
1
0
0
0
0
0
0
0
0
1
2
0
1
1
0
1
0
1
2
0
0
2
7
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
2
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
1
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
1
0
1
0
0
1
0
0
0
0
2
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
4
0
0
0
0
0
0
1
1
0
0
0
0
2
2
0
3
2
0
0
0
0
0
1
0
0
0
1
0
1
1
1
0
0
0
3
0
0
1
1
0
0
0
3
1
1
0
0
0
2
2
2
0
0
1
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
2
0
3
1
1
1
0
0
0
0
0
5
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
2
0
2
0
0
3
0
1
0
2
0
0
2
2
0
3
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
2
0
0
0
1
0
2
0
1
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
2
1
1
0
0
0
4
0
2
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
1
1
2
2
1
0
0
0
1
0
1
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
1
0
1
0
0
1
4
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
1
0
3
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
3
0
0
2
1
0
2
1
0
0
0
2
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
1
0
1
1
2
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
3
2
0
2
0
0
2
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
3
0
3
0
1
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
2
2
0
2
2
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
1
0
0
0
0
7
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
3
2
1
0
0
2
0
2
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
2
0
3
0
0
0
0
0
0
0
2
1
0
0
0
2
2
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
2
0
0
1
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
2
0
0
0
0
0
2
2
0
1
0
1
6
0
1
2
0
0
0
0
0
0
3
0
0
2
0
2
0
0
1
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
2
1
0
1
5
0
1
2
1
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
2
0
0
1
0
0
1
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
1
2
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
3
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
2
0
1
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
2
0
0
2
4
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
1
2
3
1
1
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
4
0
0
0
3
0
0
0
0
0
1
1
0
1
0
0
0
0
2
1
0
1
0
1
3
3
0
0
0
0
0
0
1
0
0
0
2
4
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
3
1
0
2
0
2
2
1
0
2
1
0
0
0
0
1
4
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
1
2
1
2
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
1
0
1
2
0
0
0
0
0
1
0
0
2
0
1
1
0
2
2
0
0
0
0
3
0
1
1
2
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
1
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
2
0
2
0
0
0
1
0
0
2
0
0
0
0
1
1
0
0
2
0
0
0
0
7
1
0
0
3
0
2
1
0
2
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
1
2
0
2
0
0
0
0
0
0
1
0
2
2
0
0
0
1
0
1
0
7
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
3
1
0
0
0
0
0
0
1
0
2
0
0
0
0
7
0
1
1
0
1
1
0
0
0
1
1
0
2
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
1
0
3
1
0
0
0
0
0
0
0
0
2
0
1
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
2
2
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
2
0
1
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
3
2
0
0
1
0
0
1
0
0
0
2
1
0
0
2
0
3
0
1
1
0
1
0
0
0
0
0
0
0
0
0
2
0
2
1
2
0
2
2
0
0
0
7
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
1
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
3
1
0
0
0
0
2
3
0
0
2
0
0
0
1
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
3
0
1
1
0
2
0
0
4
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
9
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
1
1
0
2
6
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
2
3
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
3
1
2
0
0
1
0
0
5
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
2
0
0
0
2
0
1
0
3
0
2
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
1
0
2
0
2
0
0
1
1
0
0
1
1
1
1
0
0
0
0
0
0
0
4
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
3
0
0
1
1
2
1
1
0
0
1
0
2
1
0
0
0
1
2
0
0
2
0
0
0
0
0
0
1
1
2
0
2
0
0
0
0
0
0
1
0
2
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
2
2
1
0
0
2
0
1
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
1
0
0
0
1
1
0
1
0
0
2
1
0
0
0
0
0
1
4
0
2
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
3
1
0
0
0
0
0
0
0
0
1
1
1
2
0
0
2
2
2
0
0
2
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
1
0
0
0
1
0
0
0
3
0
0
2
2
2
0
1
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
2
0
0
2
0
2
2
2
0
1
1
0
0
0
0
1
0
2
0
0
0
0
0
1
0
3
0
0
0
2
2
0
0
2
0
2
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
2
1
2
0
0
2
2
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
2
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
1
0
0
4
0
0
0
2
2
1
0
0
0
0
0
1
0
1
0
0
0
5
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
2
1
0
2
2
2
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
2
1
0
2
0
0
0
1
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
6
0
0
0
0
2
1
2
0
2
0
0
0
0
0
0
1
0
0
6
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
2
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
1
2
0
0
0
1
0
0
2
0
2
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
2
0
0
0
0
1
0
2
0
2
0
0
2
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
4
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
1
1
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
2
0
0
1
0
1
2
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
2
2
2
0
0
2
0
1
0
0
0
0
1
2
0
0
0
0
2
2
0
0
0
2
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
2
0
2
0
0
2
1
0
2
1
0
0
0
2
2
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
2
3
2
2
2
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
3
0
0
3
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
2
0
1
0
1
0
0
0
3
1
0
0
0
0
0
2
0
0
0
1
2
0
0
2
2
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
1
1
3
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
2
1
0
0
0
0
0
2
0
2
1
2
2
0
3
0
1
0
0
2
0
0
0
0
0
0
2
2
0
2
0
0
0
1
0
0
0
2
1
0
2
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
1
0
1
2
3
1
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
3
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
1
0
0
3
0
1
0
0
1
0
1
0
0
0
0
0
2
1
0
0
1
0
0
0
0
2
0
2
0
1
1
1
0
0
0
2
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
5
1
0
0
2
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
2
1
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
2
1
0
1
0
1
0
0
0
0
0
2
2
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
1
0
2
7
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
3
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
2
0
1
0
1
0
1
0
1
1
0
0
0
0
1
0
0
0
0
2
0
0
1
0
1
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
2
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
2
0
0
0
0
0
5
1
2
2
0
1
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
1
0
0
0
2
0
2
2
0
0
0
0
0
0
1
0
0
4
2
2
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
2
0
1
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
1
1
0
0
1
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
1
4
2
0
0
2
0
0
0
0
1
2
0
0
1
0
0
0
0
0
3
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
2
0
2
1
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
5
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
2
0
0
0
2
0
0
1
0
0
1
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
2
0
0
3
2
0
2
0
0
1
1
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
2
0
0
2
2
2
0
0
2
0
0
0
0
0
1
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
3
0
1
0
0
0
1
0
0
1
0
2
1
0
0
1
2
0
1
0
0
2
0
0
0
2
2
1
2
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
2
1
0
2
0
0
1
0
0
0
1
0
2
1
0
0
2
1
0
0
0
0
0
2
0
1
0
1
3
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
3
0
0
2
0
1
1
0
0
0
0
1
2
0
1
0
1
2
2
2
0
0
1
0
0
0
0
2
0
0
0
0
0
3
1
0
1
0
0
0
0
0
1
0
1
0
0
3
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
1
1
0
0
2
2
0
0
2
3
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
2
0
1
0
0
2
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
1
1
0
0
1
0
0
0
0
1
2
1
1
0
0
1
2
2
0
2
0
1
0
0
2
1
0
0
0
0
0
1
1
2
2
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
2
2
0
0
2
0
0
0
2
0
1
0
0
0
2
0
2
1
0
2
0
0
0
0
0
0
1
1
0
1
2
0
0
1
0
0
0
3
0
0
0
2
2
0
0
0
0
0
0
1
0
4
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
3
0
0
2
0
0
0
3
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
2
3
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
2
0
3
1
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
2
2
0
0
1
1
0
0
1
4
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
2
0
0
0
0
0
2
2
0
0
6
0
0
0
0
0
0
1
0
0
2
3
1
0
0
0
0
0
2
0
2
0
0
0
2
1
0
0
2
0
0
1
2
0
0
0
0
1
0
0
0
1
0
2
0
1
2
0
0
0
0
1
1
0
0
1
0
0
2
0
0
1
2
1
0
3
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
3
0
0
2
0
0
1
0
1
2
1
0
0
2
0
0
1
2
1
1
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
2
0
1
1
0
0
1
1
0
0
2
1
0
0
0
0
0
2
1
0
0
0
1
0
1
0
0
3
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
2
2
0
0
0
2
2
0
1
1
1
0
1
1
1
1
0
0
0
0
0
1
0
0
0
0
1
0
2
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
3
0
0
1
2
3
1
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
1
1
0
1
0
0
0
0
1
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
3
2
2
0
0
0
1
1
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
2
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
4
0
2
0
0
0
1
0
2
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
2
2
0
0
0
2
1
0
1
0
2
0
2
0
1
0
0
0
0
0
1
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
2
1
0
0
0
0
0
0
0
0
2
1
0
0
0
2
3
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
3
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
2
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
2
2
0
0
0
0
0
2
0
1
2
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
2
0
1
1
0
0
0
1
0
0
0
0
1
1
0
2
0
0
1
2
0
3
2
2
0
0
2
2
0
0
2
0
2
0
1
0
0
0
1
0
0
0
0
3
0
0
0
0
0
2
2
5
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
7
0
0
0
0
0
0
3
0
2
0
1
0
1
0
0
1
0
2
2
0
1
1
0
0
0
0
0
0
0
3
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
1
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
1
1
0
2
0
0
2
0
2
0
1
0
0
0
0
0
0
1
0
1
0
2
2
0
1
0
0
3
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
3
0
0
0
2
2
2
1
0
0
0
2
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
2
0
1
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
2
1
0
3
0
0
0
1
0
1
2
0
0
0
1
1
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
1
2
1
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
2
1
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
1
1
0
1
1
0
1
0
0
0
0
0
2
0
0
0
1
3
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
1
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
1
0
1
0
2
0
2
0
2
1
2
0
0
0
0
1
0
0
4
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
4
0
2
0
0
0
2
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
1
1
0
0
4
0
0
0
1
0
0
0
1
0
3
0
0
1
2
0
1
0
0
0
1
0
3
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
1
0
0
0
0
2
0
1
0
0
0
0
2
0
1
1
0
0
0
1
2
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
6
2
1
1
0
2
0
1
0
1
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
1
0
0
1
0
0
0
4
0
0
1
2
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
2
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
1
0
3
0
0
0
0
0
0
2
3
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
1
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
2
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
2
0
0
0
0
2
1
1
2
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
2
0
2
1
0
0
1
0
2
0
6
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
1
1
4
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
2
2
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
2
1
3
0
0
0
0
0
0
0
2
0
2
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
1
0
0
0
1
0
0
0
1
1
1
0
2
0
0
0
0
0
1
2
0
2
0
0
0
1
0
3
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
3
3
0
2
3
0
2
0
0
0
0
0
0
0
2
0
1
3
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
1
0
1
1
2
0
1
2
0
1
0
2
0
0
2
0
0
1
0
0
0
0
1
0
1
0
3
1
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
1
2
0
0
0
0
1
1
0
0
1
0
0
2
2
2
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
1
0
0
1
0
2
0
3
1
0
1
0
0
0
0
0
0
1
4
0
2
0
0
0
3
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
1
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
3
1
1
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
2
0
0
0
0
0
0
0
1
2
1
2
0
1
0
1
0
1
0
0
0
0
2
0
0
0
2
0
1
0
0
0
1
0
0
0
0
2
3
0
0
2
1
2
1
0
0
4
0
4
0
0
0
1
0
0
0
1
2
0
0
2
0
0
0
1
2
0
2
2
0
1
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
2
0
0
0
0
0
3
2
0
0
0
0
0
0
1
0
0
1
0
0
2
1
0
0
0
2
2
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
2
1
2
0
1
0
0
2
4
0
2
0
2
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
2
2
0
0
0
0
1
0
2
1
0
1
2
0
0
0
2
1
1
1
0
0
0
0
0
2
0
1
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
1
2
0
1
0
0
1
1
1
0
0
1
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
2
6
2
2
2
0
0
0
2
0
0
1
0
0
1
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
1
1
2
2
1
0
0
0
2
1
0
0
0
0
2
2
0
0
2
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
3
2
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
1
0
0
1
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
2
0
0
2
2
3
0
0
0
0
0
0
3
1
0
2
0
0
0
2
2
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
1
2
2
0
1
0
0
0
1
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
2
1
4
0
0
1
0
1
2
0
1
0
2
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
3
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
2
3
0
1
0
0
2
0
2
0
0
1
0
1
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
5
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
1
0
0
0
2
1
1
0
0
0
2
0
0
2
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
1
2
0
0
0
2
3
2
0
0
0
0
0
0
0
1
0
0
0
1
3
2
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
2
1
0
0
1
2
1
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
2
2
4
3
2
0
0
0
0
1
2
0
1
0
1
0
1
0
2
0
0
4
1
0
1
0
0
0
1
3
0
2
1
2
0
0
2
1
2
0
0
0
0
2
1
1
0
1
0
0
2
0
0
0
0
2
2
0
2
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
2
0
2
0
1
0
0
0
0
0
0
0
2
0
1
2
0
3
0
1
1
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
2
2
0
0
2
2
0
0
0
2
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
2
5
0
2
0
2
0
0
1
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
2
0
0
0
1
0
0
0
1
0
2
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
3
0
0
1
0
0
0
0
3
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
2
0
1
0
0
0
0
0
1
2
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
4
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
1
0
0
0
0
0
3
0
1
0
1
0
2
0
0
0
0
2
0
0
0
1
0
1
0
0
2
1
2
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
1
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
2
0
2
0
1
0
2
0
0
1
0
0
0
3
1
0
0
4
0
1
0
0
4
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
2
0
1
0
0
6
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
2
2
0
0
3
1
0
0
0
0
1
3
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
1
0
0
1
1
0
1
1
0
2
2
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
2
2
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
1
0
0
1
1
3
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
1
0
0
0
0
0
1
0
2
0
1
0
0
1
1
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
3
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
1
1
1
1
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
6
0
0
0
0
0
0
2
2
1
0
1
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
1
1
0
2
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
1
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
2
0
0
0
0
0
2
2
0
0
2
0
0
1
1
0
0
0
0
1
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
1
2
2
0
0
0
0
0
0
1
1
2
0
0
3
0
0
2
0
0
0
2
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
1
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
2
0
1
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
3
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
1
3
0
0
0
0
3
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
1
7
1
0
1
0
0
0
1
2
0
2
0
2
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
1
0
3
0
0
0
1
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
1
0
0
2
2
2
0
1
0
0
0
1
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
3
0
0
1
2
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
2
0
0
2
1
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
2
1
1
0
0
0
0
0
0
1
1
1
0
0
0
3
0
0
2
0
2
1
0
0
0
0
0
3
0
2
0
1
0
0
2
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
1
2
0
0
0
2
0
1
0
0
0
0
2
2
1
1
0
0
4
0
1
0
0
2
0
0
0
3
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
2
2
1
0
1
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
2
0
0
2
0
2
1
0
0
2
2
3
2
0
2
0
0
0
0
1
0
1
0
0
1
2
0
1
0
0
1
0
0
0
0
0
2
2
1
2
0
0
0
0
0
0
0
0
0
0
2
2
1
2
0
2
0
1
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
2
0
1
1
0
0
0
0
0
0
2
0
1
2
0
0
0
2
0
0
0
2
2
1
2
2
2
0
0
0
1
2
0
1
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
1
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
2
2
0
0
0
0
2
0
1
2
0
0
0
0
0
0
2
0
2
0
2
0
0
1
0
2
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
1
0
2
0
0
0
0
0
0
0
2
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
4
0
1
0
0
0
0
0
0
0
0
1
0
3
0
1
0
0
2
1
0
0
0
1
1
2
0
0
0
0
0
1
0
1
0
0
0
0
4
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
2
2
0
0
0
2
2
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
1
0
2
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
2
2
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
2
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
2
1
1
1
0
0
0
0
0
0
1
2
3
1
0
0
0
0
0
2
1
2
0
0
2
0
2
3
0
0
2
0
1
2
0
1
1
0
0
1
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
2
4
2
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
2
1
0
0
0
3
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
2
0
3
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
3
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
1
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
5
2
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
4
0
0
0
2
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
1
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
2
2
0
0
0
0
1
1
0
3
0
0
0
1
0
0
0
0
0
0
0
2
1
1
3
0
0
7
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
1
4
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
5
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
3
0
0
2
0
0
0
0
0
0
1
2
2
0
1
0
0
1
0
0
0
0
2
0
0
0
1
0
1
1
0
0
2
0
0
1
0
1
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
8
0
0
1
0
0
2
1
0
0
1
0
1
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
1
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
2
1
1
2
0
0
0
0
3
2
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
1
0
2
2
0
0
1
0
3
1
6
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
1
0
0
2
0
2
2
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
1
3
0
0
0
0
0
0
1
2
1
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
2
0
0
0
0
0
2
0
4
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
1
0
0
0
2
0
0
1
0
0
1
0
3
2
1
0
0
1
2
2
0
2
0
0
0
0
0
0
0
1
2
0
2
1
0
1
2
1
0
1
1
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
2
0
2
0
0
0
1
0
0
2
1
0
0
0
2
0
0
3
0
1
0
0
0
0
0
0
0
0
0
3
0
0
2
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
1
2
0
2
0
1
0
1
0
1
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
3
1
0
0
0
0
0
3
0
0
0
0
5
0
1
0
1
0
2
0
0
0
0
0
2
1
0
1
0
0
1
2
2
0
0
0
0
0
2
0
0
0
0
2
1
2
0
0
2
0
0
0
0
2
2
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
2
1
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
2
3
1
0
1
2
0
1
2
0
0
0
0
0
0
2
1
3
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
2
0
1
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
1
1
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
1
2
1
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
3
0
1
0
0
0
0
0
1
0
0
0
0
0
5
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
2
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
2
0
0
0
0
0
0
0
0
3
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
3
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
3
0
1
0
0
0
0
0
1
0
0
0
0
0
2
2
1
0
1
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
1
0
2
3
0
0
4
0
0
0
0
0
0
2
0
2
0
0
1
2
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
5
0
0
1
1
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
1
2
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
3
0
1
0
0
0
0
3
2
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
1
1
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
2
3
0
2
3
2
1
0
1
7
0
0
0
2
0
0
0
0
1
0
0
0
0
1
1
0
0
0
2
0
0
0
1
0
0
3
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
2
0
0
1
0
0
2
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
4
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
2
2
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
1
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
2
2
0
2
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
2
0
0
3
2
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
2
0
3
0
0
2
0
2
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
2
0
0
0
1
0
0
0
0
0
1
2
0
0
0
2
0
0
1
0
0
0
0
3
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
2
0
0
1
1
2
0
0
2
0
0
0
0
4
0
1
2
0
2
0
0
0
2
0
2
0
0
0
2
2
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
2
0
1
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
1
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
2
0
0
2
0
1
0
0
1
0
1
0
0
1
3
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
1
0
2
0
0
1
0
0
2
0
0
1
3
0
0
0
3
1
0
0
0
1
0
0
0
0
2
0
0
0
1
2
0
0
0
3
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
2
0
1
1
0
2
1
3
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
1
0
3
0
0
0
2
0
1
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
2
0
1
0
0
1
0
3
0
0
0
1
0
0
1
2
0
0
0
0
0
1
0
1
3
1
0
1
0
0
0
0
0
2
0
3
0
2
0
1
1
1
0
0
0
0
0
0
0
2
1
1
0
4
0
0
0
0
0
0
1
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
2
1
3
1
2
0
0
2
0
1
0
0
0
2
0
1
0
0
1
2
5
0
0
0
0
0
0
0
1
1
0
0
2
2
0
0
2
0
0
0
0
0
2
3
0
0
2
2
0
1
0
0
0
0
3
1
0
0
0
0
0
0
2
1
1
2
0
0
0
0
0
0
0
1
1
0
0
0
2
3
0
0
1
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
5
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
3
2
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
1
2
0
0
0
0
0
2
3
2
0
2
0
0
2
3
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
1
2
0
0
0
2
1
0
1
0
1
2
0
0
2
1
0
0
6
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
2
2
1
1
0
1
0
0
0
0
0
0
0
0
2
0
1
0
4
1
0
0
0
0
2
0
2
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
4
1
2
0
0
0
0
0
0
0
1
0
1
3
0
0
0
1
0
0
2
0
1
1
0
0
0
2
1
0
0
2
0
0
2
2
2
1
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
2
1
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
3
1
0
0
0
2
2
1
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
1
0
2
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
1
8
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
3
0
0
1
0
0
1
1
1
0
1
0
0
0
2
2
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
5
0
1
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
2
1
0
0
0
0
0
18
0
0
2
0
0
0
2
2
0
0
2
2
0
0
1
0
0
0
0
0
1
2
0
1
3
0
3
0
1
1
1
0
2
0
0
1
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
2
0
0
2
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
2
0
1
0
0
1
0
0
1
0
2
1
1
0
3
0
0
0
4
0
2
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
1
2
2
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
2
3
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
2
1
0
2
0
0
0
2
0
2
3
0
2
0
0
1
0
1
0
0
0
0
1
0
1
0
2
0
0
2
0
2
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
2
0
2
0
1
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
2
2
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
3
0
1
0
0
2
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
3
0
2
0
0
0
0
0
0
2
0
1
0
0
2
1
0
1
0
0
1
0
0
0
4
1
0
0
0
0
2
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
10
0
0
0
6
0
3
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
2
2
0
1
2
0
0
0
2
0
3
0
0
2
2
3
0
0
0
0
2
0
1
2
1
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
3
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
2
1
0
1
0
0
0
2
0
4
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
6
0
0
0
0
2
0
1
0
0
1
2
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
2
0
0
0
0
3
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
1
0
2
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
2
0
1
0
0
1
0
0
0
0
2
0
1
0
1
0
0
0
0
1
0
0
0
0
0
2
2
0
0
1
0
0
2
0
0
0
0
3
2
0
0
0
1
0
0
0
1
2
0
1
0
0
1
3
0
2
1
0
0
0
0
0
0
1
0
0
2
1
2
0
0
2
0
0
1
1
0
0
0
0
0
2
0
0
1
0
0
3
0
2
0
1
0
0
0
0
3
0
0
1
1
0
2
0
0
0
2
0
0
1
1
0
0
1
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
3
1
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
2
0
0
0
0
2
0
0
0
1
2
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
4
2
1
0
2
2
0
0
0
0
2
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
1
1
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
5
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
2
0
2
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
5
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
1
3
2
0
0
0
0
0
1
2
0
1
0
0
2
4
1
0
0
2
0
0
0
1
2
0
0
0
2
0
0
3
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
2
2
0
0
0
1
0
1
0
1
0
0
0
1
1
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
2
0
0
0
0
1
0
1
1
2
0
0
0
3
0
2
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
2
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
3
0
0
0
0
1
0
0
2
0
0
0
4
2
1
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
1
1
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
2
2
0
2
0
0
0
2
0
0
1
2
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
1
2
0
0
1
0
1
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
1
1
0
0
0
1
1
0
0
2
1
1
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
3
1
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
2
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
1
0
2
4
0
2
1
0
1
0
1
0
0
0
2
0
1
0
0
0
0
1
0
1
3
0
0
0
0
0
1
0
2
1
0
2
0
2
2
0
0
0
0
0
4
2
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
3
1
0
1
0
0
3
1
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
3
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
3
0
0
0
1
0
3
1
0
0
1
0
0
2
0
0
0
0
2
0
0
2
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
1
2
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
2
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
1
3
0
0
0
0
0
1
0
1
1
0
0
3
0
0
0
0
0
1
0
3
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
2
0
0
0
0
1
0
2
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
2
0
0
2
0
0
0
0
1
2
0
1
0
0
1
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
2
3
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
1
2
3
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
2
2
1
2
0
0
0
0
0
1
0
0
2
1
0
1
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
3
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
1
1
0
0
1
0
1
2
0
3
0
0
0
1
0
0
1
0
0
0
0
0
0
1
5
3
0
2
0
0
0
0
0
0
0
1
0
3
0
1
0
0
2
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
2
1
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
2
2
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
1
0
1
5
0
1
0
0
1
1
1
1
2
1
0
0
0
0
2
0
2
1
0
0
0
0
2
0
2
0
2
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
2
0
2
0
2
1
2
0
2
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
2
0
0
1
1
0
0
2
3
0
1
1
0
2
0
0
0
0
1
0
0
1
1
2
9
0
0
0
1
0
0
0
2
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
2
2
0
0
2
0
2
0
0
0
3
2
0
1
0
0
0
3
1
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
2
0
1
1
0
0
0
1
0
2
0
0
1
0
3
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
1
0
0
2
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
2
0
0
2
0
0
2
0
0
0
5
0
0
0
1
0
2
0
0
0
0
0
2
2
0
0
0
0
2
0
7
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
2
0
1
0
0
2
0
2
0
0
1
0
2
1
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
2
0
1
0
0
0
0
0
1
2
0
0
1
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
5
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
1
2
0
0
2
2
0
2
1
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
4
0
0
0
0
0
2
0
0
0
2
3
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
7
0
2
6
0
1
1
0
2
0
1
0
1
0
0
0
2
2
2
0
0
0
2
0
2
2
0
2
0
0
0
0
0
1
0
2
2
0
0
0
0
0
2
0
2
2
0
0
0
0
3
0
0
0
0
0
0
2
3
0
0
1
0
0
0
0
1
0
1
1
0
0
2
0
1
0
0
0
1
2
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
2
1
0
1
1
1
0
0
2
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
2
0
2
0
1
0
0
0
0
0
0
0
5
0
1
1
0
0
0
4
0
0
0
0
2
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
1
0
2
0
0
0
0
1
0
0
0
3
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
2
2
1
1
0
0
0
0
1
0
0
0
0
4
0
0
2
0
0
2
0
0
2
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
1
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
1
0
0
2
0
0
3
0
1
0
1
0
0
1
0
0
0
1
2
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
1
0
1
2
4
0
0
0
0
0
0
0
2
0
2
0
0
2
0
2
2
0
0
0
2
0
1
0
0
0
0
1
1
1
0
0
0
0
2
0
0
0
0
2
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
2
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
1
1
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
4
2
0
0
0
0
2
0
4
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
4
0
0
0
0
2
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
2
0
2
0
9
0
1
0
0
0
0
2
0
2
0
2
0
0
0
1
2
0
2
0
0
0
0
0
0
0
7
0
0
0
2
0
2
0
0
2
1
0
2
2
1
0
0
1
0
1
2
0
0
2
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
2
1
1
0
0
2
0
0
0
2
0
3
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
2
0
2
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
1
2
0
2
2
0
1
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
2
0
0
0
0
0
1
1
1
0
0
0
0
0
2
0
2
0
0
0
0
1
1
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
3
0
2
0
1
2
0
0
0
2
0
0
2
0
1
0
0
1
0
0
2
2
1
3
0
0
1
2
0
0
0
1
4
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
2
0
0
3
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
1
0
2
0
0
1
2
0
1
0
0
0
1
0
0
1
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
3
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
1
0
0
2
2
0
0
1
0
0
0
0
0
1
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
2
0
0
2
2
0
0
1
3
1
2
0
3
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
2
2
0
1
0
0
1
2
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
2
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
5
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
3
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
1
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
1
0
0
0
0
3
0
2
0
0
0
0
0
2
2
2
0
0
2
2
0
1
0
0
0
0
0
0
1
1
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
3
1
2
2
0
1
2
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
5
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
1
0
0
0
2
0
0
0
2
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
2
0
0
0
1
4
0
0
1
0
1
0
2
0
1
0
1
1
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
4
0
1
0
0
0
1
1
0
0
0
2
3
0
1
0
3
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
2
0
1
1
0
3
2
3
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
2
0
0
0
1
3
2
1
0
4
2
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
5
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
1
0
0
0
0
0
2
0
0
0
3
0
1
0
0
0
1
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
1
0
5
0
2
0
0
2
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
1
0
0
0
1
2
0
0
2
0
0
0
0
0
2
0
4
1
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
1
2
0
3
1
2
0
0
1
1
0
0
0
0
0
2
0
0
0
0
3
0
0
2
0
0
0
0
0
0
1
0
0
0
3
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
4
0
0
0
0
0
0
2
0
1
0
0
2
0
0
2
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
4
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
2
0
0
0
0
0
2
2
1
0
0
0
2
0
3
0
0
2
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
2
0
0
5
0
0
0
0
0
0
0
0
0
1
2
0
0
1
1
0
1
2
0
0
0
2
0
1
0
0
0
0
1
1
0
2
3
1
0
0
1
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
2
0
1
1
0
2
0
4
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
2
1
0
2
0
1
0
1
0
0
1
0
0
0
2
0
1
2
1
1
1
1
3
0
0
0
0
0
0
0
1
0
3
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
2
0
0
0
0
1
3
0
0
1
0
1
0
2
0
4
0
4
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
2
1
0
4
0
0
0
3
0
0
0
0
2
0
0
3
0
0
0
0
0
0
2
0
4
0
0
0
1
1
0
0
0
0
2
0
0
2
1
0
0
0
1
1
1
2
0
0
1
2
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
3
0
2
0
0
0
0
1
0
0
0
0
0
2
2
0
0
2
0
2
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
4
0
0
1
2
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
1
1
5
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
3
2
0
1
1
0
1
0
0
1
2
0
0
0
0
2
0
0
2
0
0
0
2
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
1
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
1
1
0
0
0
0
0
2
2
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
3
2
0
3
2
0
0
0
2
0
0
0
2
0
1
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
2
1
0
0
0
0
0
1
3
0
0
0
1
2
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
2
1
2
0
2
1
0
2
2
2
0
0
0
1
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
2
1
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
4
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
6
1
0
0
0
0
0
0
3
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
2
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
3
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
2
0
1
1
2
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
6
0
0
0
1
0
0
1
0
0
0
2
2
0
2
1
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
1
0
2
1
0
0
0
2
0
0
2
1
0
0
0
2
0
1
1
0
0
0
0
1
1
1
1
0
0
2
0
0
1
0
0
0
1
1
0
0
0
1
0
1
0
1
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
4
0
0
0
1
1
2
2
0
0
2
1
0
0
2
0
0
0
0
0
4
0
0
1
2
1
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
1
0
2
0
1
1
2
0
1
1
0
2
0
0
0
0
0
2
0
0
1
0
2
0
2
0
0
3
0
0
1
0
2
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
2
0
0
0
1
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
1
1
0
2
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
2
0
0
0
2
0
2
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
2
0
0
1
0
0
2
2
0
0
0
1
2
0
0
1
0
0
0
0
2
0
2
1
0
0
1
0
2
0
0
2
2
0
0
0
0
0
1
0
1
0
0
1
0
0
0
2
2
0
0
0
1
0
0
6
0
0
2
2
0
0
2
1
0
0
0
0
1
2
0
0
0
0
2
0
3
2
0
1
2
1
2
0
0
1
2
0
0
0
0
0
2
0
1
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
5
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
1
0
0
0
0
0
0
1
0
2
0
0
1
1
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
2
0
1
0
0
2
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
2
1
0
0
2
3
1
0
0
2
0
1
2
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
2
0
1
0
0
6
0
0
0
0
0
0
0
1
1
0
1
2
0
0
0
5
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
4
0
0
0
0
3
1
0
0
0
1
0
0
2
4
0
0
0
1
0
0
2
0
0
2
0
2
0
0
0
0
0
0
1
1
0
1
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
2
0
0
3
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
4
0
0
0
1
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
1
0
0
2
1
0
0
0
0
2
0
2
1
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
1
2
1
0
0
2
2
0
0
0
1
2
0
0
2
0
0
0
1
0
0
2
1
0
3
4
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
2
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
2
0
1
0
0
1
0
0
2
0
0
0
0
0
2
2
2
0
2
2
0
0
0
0
0
2
1
1
1
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
1
0
1
0
1
0
2
0
0
0
1
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
1
0
3
0
0
0
1
0
0
0
0
0
0
1
0
0
3
0
1
0
0
1
0
2
1
1
2
0
0
1
0
3
0
0
3
0
0
2
1
0
2
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
3
0
0
1
0
1
0
0
0
0
0
1
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
1
0
6
0
0
0
0
0
2
2
0
2
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
2
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
3
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
1
0
0
1
3
0
3
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
2
0
0
0
0
0
0
0
1
0
0
0
0
2
2
1
0
0
0
0
3
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
1
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
1
0
0
0
0
2
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
2
1
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
1
4
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
1
1
1
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
1
2
1
0
0
1
2
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
3
1
0
0
1
0
2
0
0
0
0
2
0
0
1
2
0
0
0
0
0
1
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
2
14
0
2
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
6
0
0
1
2
0
2
0
1
0
0
0
1
0
1
2
1
2
2
0
2
0
0
0
0
0
1
0
0
0
0
2
0
1
3
0
0
2
2
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
1
0
0
2
2
0
1
0
1
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
1
0
2
0
2
0
0
0
1
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
7
0
0
1
0
0
2
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
2
1
0
2
1
0
0
2
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
1
0
1
1
2
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
2
0
0
2
0
4
2
0
0
0
0
2
0
0
1
2
0
2
2
0
2
0
1
0
0
3
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
7
0
6
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
4
1
0
2
0
0
0
2
0
2
2
0
0
2
0
0
0
0
3
0
1
0
2
0
1
0
0
2
1
1
2
0
2
0
0
0
0
2
0
0
0
1
2
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
3
0
0
1
1
0
0
0
1
0
0
1
0
0
0
1
2
0
0
0
2
0
1
1
0
0
2
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
2
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
1
3
1
1
2
0
0
0
0
3
0
0
0
2
0
1
0
0
0
2
0
2
3
0
0
0
0
0
1
1
0
4
0
0
1
0
0
0
0
0
3
2
0
0
0
3
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
3
0
0
0
0
0
0
2
1
1
3
0
0
0
1
2
1
0
0
0
0
0
0
1
2
0
0
1
2
0
1
0
0
0
0
0
0
3
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
2
4
0
1
0
0
0
0
3
0
0
0
2
1
1
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
3
1
0
1
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
4
1
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
2
0
1
2
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
2
0
2
0
1
0
0
2
3
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
6
0
0
0
2
0
0
0
0
0
0
2
0
0
2
2
1
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
3
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
1
1
0
0
2
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
1
1
0
0
1
3
2
2
0
0
1
0
2
2
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
1
0
0
1
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
3
0
0
0
4
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
2
2
1
0
0
0
2
0
0
1
0
3
0
0
0
0
0
2
0
3
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
2
0
0
0
1
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
1
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
1
0
2
0
1
0
0
0
0
0
2
1
0
1
2
3
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
2
1
0
0
2
0
1
0
0
0
0
2
0
0
0
0
2
1
0
1
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
2
1
0
0
1
0
2
3
2
0
0
1
0
2
2
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
1
0
0
0
1
4
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
4
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
2
0
0
3
0
4
0
0
0
0
0
2
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
2
0
0
0
4
0
0
1
0
1
0
0
0
3
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
2
1
0
2
0
1
0
0
1
1
0
2
0
0
1
0
0
0
2
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
3
1
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
1
2
0
1
0
1
1
0
4
3
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
5
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
2
0
2
0
0
0
2
3
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
1
0
4
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
1
0
0
0
1
0
1
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
4
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
1
0
2
1
0
2
0
1
0
0
2
0
2
0
0
2
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
3
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
2
0
0
0
0
0
3
1
0
0
0
0
0
0
2
0
0
2
0
2
1
0
2
0
0
2
2
2
0
0
1
0
4
0
0
0
0
2
0
0
0
0
3
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
1
1
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
9
0
0
1
0
0
0
2
1
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
2
0
0
0
0
1
0
0
0
0
0
0
1
2
0
5
0
1
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
2
1
2
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
2
1
0
2
0
0
2
1
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
2
1
0
1
1
1
1
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
2
0
0
0
0
0
0
2
0
2
2
0
0
0
0
1
1
0
0
0
3
0
0
0
1
0
0
0
0
0
1
0
2
0
1
2
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
1
0
2
0
2
0
1
0
0
2
0
2
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
2
1
0
0
2
1
3
0
0
0
2
0
2
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
1
0
0
0
0
0
0
1
1
0
0
0
0
2
0
2
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
3
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
2
2
1
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
2
2
0
0
0
0
1
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
1
1
1
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
3
2
0
0
0
1
0
0
0
3
0
0
0
1
1
5
0
0
0
0
0
3
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
4
0
2
2
0
0
1
2
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
1
1
0
3
3
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
5
2
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
1
0
1
0
1
2
1
0
1
0
0
2
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
6
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
1
1
1
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
1
2
1
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
2
1
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
1
0
0
1
0
0
0
0
2
0
0
1
2
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
3
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
2
0
0
2
2
0
1
0
0
0
1
0
2
0
0
0
2
2
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
2
2
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
1
0
1
0
2
1
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
3
0
2
3
0
0
2
2
0
0
0
0
0
1
0
0
0
1
0
2
2
1
1
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
4
2
0
0
0
2
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
2
1
0
1
1
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
3
3
0
0
2
2
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
1
0
3
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
2
1
0
0
0
0
2
0
0
2
0
1
0
0
0
2
0
0
1
0
2
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
2
1
2
0
0
0
2
0
1
0
0
2
1
0
0
0
0
0
15
4
0
0
1
2
0
0
1
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
2
0
0
0
5
0
0
1
0
1
0
0
2
1
0
1
0
0
1
0
0
2
0
0
0
3
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
3
0
2
0
0
1
0
0
5
1
0
0
2
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
2
1
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
2
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
1
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
3
0
0
0
0
3
0
2
0
0
0
1
0
1
1
1
2
1
0
0
1
0
2
3
1
0
0
0
0
0
2
0
2
0
0
1
3
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
2
0
2
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
2
0
1
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
2
0
2
1
2
2
1
0
0
0
1
0
4
2
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
2
2
4
1
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
4
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
2
0
2
0
0
0
0
0
1
0
1
0
1
1
0
0
6
0
1
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
4
4
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
1
0
0
0
0
1
4
0
0
0
2
0
2
2
0
0
9
0
1
3
1
0
1
0
2
2
0
1
0
0
1
0
2
0
1
0
3
0
0
0
0
3
2
0
0
3
0
0
3
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
4
0
1
0
0
0
2
2
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
2
0
2
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
1
0
0
0
2
0
2
2
0
0
2
2
0
0
0
1
1
2
0
0
0
1
1
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
4
0
2
2
1
0
0
4
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
3
1
0
0
0
0
1
0
0
0
1
1
3
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
4
1
0
0
2
0
0
0
1
0
0
1
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
1
0
0
1
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
2
0
1
0
2
2
0
0
1
2
2
0
0
1
0
0
2
0
0
1
0
0
0
2
0
2
0
1
0
0
0
0
0
3
0
2
0
1
0
1
0
0
0
0
0
0
2
0
0
0
4
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
2
0
1
1
1
0
0
0
2
0
0
0
0
2
0
1
0
0
0
1
0
0
2
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
2
2
0
0
0
1
1
1
1
2
2
1
0
1
0
0
0
3
0
0
0
1
0
1
0
0
2
0
6
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
2
2
0
0
1
0
0
0
2
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
2
0
0
0
0
3
0
2
1
2
0
0
1
0
1
1
0
0
2
0
3
0
1
0
0
2
0
0
0
0
1
0
2
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
0
0
0
2
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
1
0
0
0
2
0
2
0
0
2
0
2
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
2
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
2
1
0
4
0
0
1
0
0
1
0
0
0
0
2
1
1
1
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
1
3
1
0
0
0
2
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
4
0
0
8
1
0
2
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
2
0
1
0
0
1
0
0
1
0
2
0
0
0
1
2
1
1
3
0
2
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
3
2
2
0
0
0
0
0
0
2
1
1
0
2
0
0
0
0
0
1
0
0
1
0
3
0
0
0
0
0
2
2
1
0
1
1
0
0
2
0
0
0
1
1
2
1
0
0
0
0
0
1
1
1
0
1
2
0
0
0
0
0
1
1
0
1
1
0
0
1
1
2
0
2
0
0
1
0
2
0
0
2
1
0
0
0
2
0
0
1
2
0
2
2
0
0
0
6
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
1
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
3
0
0
0
0
0
0
0
0
2
2
0
3
0
0
0
0
0
0
0
2
0
1
1
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
1
0
2
0
0
0
0
2
2
0
2
1
0
2
1
2
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
2
2
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
2
2
0
0
0
2
0
0
0
2
1
5
0
0
1
0
1
1
1
0
0
0
0
0
1
0
2
0
0
0
1
0
2
0
0
2
1
0
1
1
0
0
0
1
2
1
1
0
1
0
1
1
0
0
0
7
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
1
1
1
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
1
2
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
2
2
0
0
1
1
3
0
0
0
4
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
3
0
2
0
0
0
0
0
0
4
1
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
3
0
0
0
0
1
1
0
0
0
0
1
0
0
2
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
2
1
0
0
0
0
1
0
0
0
0
0
0
2
0
3
2
2
0
1
0
0
1
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
2
0
0
2
0
1
0
1
0
1
0
0
0
0
1
0
0
1
1
3
0
1
0
0
1
2
1
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
1
2
0
0
0
0
2
0
0
2
0
0
0
2
2
0
0
0
0
0
0
2
0
0
1
0
0
0
3
0
0
2
0
2
0
0
0
0
2
0
2
2
0
0
0
0
0
1
2
3
0
0
0
1
5
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
2
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
6
1
2
2
2
0
1
0
0
0
0
1
0
0
0
0
1
2
1
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
2
1
1
0
0
2
0
0
0
1
0
2
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
2
0
7
0
0
0
0
0
0
2
0
0
1
0
0
0
1
1
1
0
0
0
0
2
1
0
2
1
0
1
0
0
2
0
0
0
0
4
0
0
0
3
0
2
4
1
1
0
0
0
1
2
0
1
1
1
1
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
2
0
0
2
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
2
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
1
0
0
0
1
0
0
2
0
0
1
0
0
0
1
0
0
2
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
2
1
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
1
1
0
1
0
0
1
0
6
0
0
1
2
1
2
2
0
0
0
0
3
1
0
0
0
0
0
0
0
1
0
0
2
0
1
3
0
2
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
4
0
3
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
3
1
0
1
0
2
0
0
0
2
0
0
0
0
0
2
3
0
0
0
0
0
1
1
0
1
0
1
1
0
0
0
1
0
0
0
1
1
2
2
0
0
0
1
1
0
2
1
2
0
0
0
0
4
0
0
0
2
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
2
2
0
0
0
0
0
3
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
2
0
0
0
1
1
1
0
0
1
0
0
0
0
1
0
1
2
0
3
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
1
1
0
0
2
0
1
2
0
0
3
0
2
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
1
0
2
2
8
2
0
0
0
0
0
0
1
0
2
0
3
1
0
1
1
0
0
1
1
0
0
0
0
1
0
0
1
0
0
1
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
2
3
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
2
0
0
2
0
2
2
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
3
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
3
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
3
0
0
2
0
0
1
0
0
1
0
1
0
2
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
2
2
0
1
0
0
0
0
0
0
1
0
1
2
0
2
2
1
0
0
0
0
1
1
1
2
3
0
2
0
0
0
0
0
0
0
1
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
13
0
0
1
0
1
0
1
0
0
2
0
2
2
0
0
0
3
0
1
0
0
1
0
2
0
2
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
5
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
5
1
0
2
2
0
0
2
0
0
2
0
1
5
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
2
4
1
0
0
3
2
0
0
0
0
0
0
3
0
0
2
1
1
0
1
0
0
0
0
1
0
0
0
0
1
2
0
0
1
0
0
0
1
1
0
0
0
0
1
0
1
0
2
0
2
0
2
1
2
0
1
0
1
0
0
1
0
0
0
2
0
0
0
0
2
2
0
0
3
0
0
1
0
0
0
0
0
0
0
1
0
1
1
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
2
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
2
1
0
0
0
2
0
0
0
0
0
0
1
0
6
0
0
0
0
1
0
1
0
2
0
0
0
0
0
2
1
0
0
1
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
1
1
1
0
0
1
0
2
0
2
0
0
0
0
1
0
1
1
1
0
2
0
0
1
0
0
1
0
0
0
0
0
1
0
5
0
1
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
2
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
1
2
0
2
0
0
1
1
0
2
0
0
0
0
1
0
0
1
0
0
1
0
1
0
1
0
3
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
6
0
0
1
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
2
0
1
2
1
0
1
1
0
0
4
2
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
2
2
0
2
0
0
0
1
0
0
2
0
0
0
0
0
1
1
2
0
0
2
3
0
0
2
0
0
4
2
0
0
0
0
0
0
0
0
1
0
0
5
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
1
0
1
0
0
0
0
2
1
2
0
1
0
0
2
1
2
0
1
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
1
0
0
2
1
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
2
2
0
0
0
2
0
3
0
0
0
0
0
0
1
2
0
2
1
0
0
0
0
1
1
0
0
0
0
0
3
0
2
0
0
0
0
0
0
2
0
0
0
1
1
0
1
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
2
1
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
1
3
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
1
1
0
0
0
2
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
2
0
0
2
0
0
0
2
0
0
1
3
0
0
1
0
2
2
0
0
0
0
1
0
2
3
0
5
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
1
2
0
2
0
0
1
0
1
1
0
0
0
4
1
0
0
0
1
1
1
2
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
1
2
0
0
0
0
0
0
2
2
2
0
0
0
0
1
0
0
0
2
3
2
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
3
0
2
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
2
0
0
2
1
0
0
0
2
0
1
4
0
1
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
2
2
0
0
0
0
1
3
0
0
0
0
0
0
3
2
0
4
0
2
0
0
0
2
0
2
0
1
0
0
0
2
0
0
2
2
0
0
0
0
0
2
1
1
0
1
0
0
2
1
1
0
0
0
2
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
1
0
2
0
1
0
0
0
0
0
0
4
0
0
2
0
0
0
0
1
0
1
2
0
0
0
0
0
1
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
5
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
2
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
2
1
0
0
0
2
0
0
2
0
1
0
0
2
1
0
0
0
0
2
0
1
0
0
0
0
0
1
2
0
0
1
6
1
0
0
0
1
2
0
1
0
1
0
0
2
1
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
2
0
2
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
2
2
0
0
0
1
0
0
1
0
0
0
2
2
1
1
0
1
0
0
3
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
1
2
0
0
0
1
0
0
1
0
1
0
2
0
0
0
3
0
1
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
2
1
0
0
1
1
0
0
3
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
2
0
3
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
2
0
0
0
0
0
2
0
2
2
0
0
0
2
1
0
1
0
0
0
0
2
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
2
1
0
0
0
1
0
0
2
2
1
0
0
0
0
0
1
0
2
0
0
0
2
2
0
0
0
0
2
0
0
0
2
1
2
0
0
0
1
0
3
2
0
0
0
0
0
0
0
0
0
0
2
2
0
1
2
0
0
4
0
0
2
1
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
2
0
2
0
0
1
2
0
0
0
2
0
1
1
2
0
0
0
0
0
1
0
2
0
0
1
0
0
2
0
0
0
0
1
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
1
2
0
1
0
1
0
1
0
0
0
0
1
2
1
2
0
0
0
0
0
0
0
0
1
2
2
2
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
3
0
2
0
0
0
1
0
0
0
4
0
0
2
1
1
0
0
0
0
0
2
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
2
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
2
0
2
2
0
0
0
1
0
1
1
2
0
2
1
1
0
0
2
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
3
0
2
0
2
0
0
1
2
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
1
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
1
2
0
0
1
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
1
2
0
2
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
1
0
1
2
0
0
1
0
0
0
2
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
4
2
2
1
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
3
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
2
1
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
1
2
2
0
0
0
0
0
2
5
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
1
2
2
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
2
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
3
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
2
0
0
1
2
2
0
0
0
2
0
1
0
0
1
0
0
6
2
0
0
0
1
2
0
1
0
0
0
2
3
0
0
1
0
1
1
0
0
0
3
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
1
1
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
10
0
0
0
0
0
2
1
0
0
0
1
0
0
0
1
0
2
0
1
1
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
2
1
2
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
1
2
1
0
1
0
0
1
0
2
1
0
2
1
2
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
1
0
2
2
0
1
0
0
0
0
4
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
1
1
0
0
2
0
0
2
0
0
0
0
2
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
5
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
1
0
1
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
1
2
0
0
1
2
1
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
1
0
1
1
0
0
0
3
0
0
0
0
1
3
0
0
0
0
2
1
0
0
0
2
0
0
1
1
2
1
0
2
0
0
2
0
0
1
3
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
1
1
0
2
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
1
2
2
2
0
0
0
0
1
1
3
2
0
0
0
0
0
0
0
0
1
0
4
0
0
0
2
0
0
2
0
0
0
0
0
0
3
0
0
2
0
0
0
0
2
0
0
0
0
2
1
1
0
1
2
3
0
2
0
1
0
0
0
2
1
1
2
0
1
0
0
2
0
1
1
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
3
0
0
0
1
0
0
2
1
0
0
2
0
0
1
0
2
0
2
0
0
0
1
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
1
2
0
0
0
0
1
2
1
1
1
2
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
2
2
0
0
1
0
1
0
0
0
2
0
2
2
0
2
0
4
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
2
2
0
2
0
0
1
3
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
1
0
0
0
0
0
2
1
1
1
0
0
0
0
0
0
1
0
0
1
3
0
3
1
0
2
0
2
0
2
1
0
4
0
0
0
0
1
1
0
2
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
5
1
1
0
2
2
0
1
1
0
2
0
0
2
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
2
1
0
0
1
0
0
2
2
1
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
4
2
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
3
1
0
2
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
1
0
1
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
3
0
2
0
0
0
0
1
0
2
0
2
0
0
2
2
2
0
0
0
3
1
2
0
0
2
0
0
0
0
3
0
0
0
0
1
0
2
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
5
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
1
0
1
2
3
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
2
0
2
3
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
1
0
1
1
0
2
0
2
0
0
0
2
2
2
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
2
3
0
2
0
2
0
0
0
0
1
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
3
0
0
1
1
0
0
0
0
2
2
0
0
2
5
1
1
0
0
1
0
1
2
0
0
0
0
0
0
0
2
2
1
0
0
0
0
1
0
3
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
1
0
0
2
0
0
1
0
1
0
0
2
2
0
2
0
0
0
0
3
2
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
1
0
0
0
0
0
0
0
1
0
0
0
4
1
0
0
0
3
0
0
0
1
0
0
0
2
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
1
2
2
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
2
0
2
2
0
0
0
0
0
1
0
1
0
0
2
0
0
1
3
2
0
4
1
0
2
0
3
0
2
0
2
0
0
0
0
0
1
0
0
0
5
0
1
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
1
0
2
0
1
1
0
1
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
2
1
1
0
1
0
0
1
0
0
0
0
1
2
0
1
1
2
1
0
2
0
2
0
0
0
0
0
4
2
0
2
1
0
1
0
0
0
0
1
0
0
0
0
0
1
2
1
0
1
1
2
2
0
2
0
0
0
0
0
0
2
0
2
0
2
2
0
0
0
0
2
2
2
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
1
0
0
3
1
0
0
1
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
1
0
2
0
0
0
0
2
2
0
0
0
2
0
0
0
4
0
5
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
1
2
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
1
0
1
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
1
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
1
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
2
0
0
0
2
0
0
0
3
0
0
0
0
3
2
2
0
0
0
0
0
0
0
2
0
2
0
0
1
3
0
0
2
1
0
0
1
1
0
0
0
0
0
2
1
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
2
2
0
0
0
0
2
0
0
2
0
0
0
0
3
2
0
0
0
0
0
0
0
2
0
2
2
0
0
0
2
1
0
0
2
0
0
0
0
2
0
0
0
3
1
2
3
0
1
0
0
0
7
0
2
0
0
0
0
2
0
0
0
0
3
2
3
4
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
2
1
2
0
0
0
0
1
0
0
1
0
2
1
1
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
1
0
0
1
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
1
1
0
1
0
0
7
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
2
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
2
2
0
0
2
1
0
2
0
0
0
0
0
2
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
2
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
1
2
0
1
0
0
2
0
0
0
2
2
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
1
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
2
0
1
2
0
0
2
0
1
0
0
0
0
0
1
0
2
0
1
1
1
0
0
0
3
0
0
0
1
1
0
1
0
0
0
2
0
0
1
0
1
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
2
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
1
0
0
0
3
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
3
1
0
0
0
2
2
0
4
0
2
1
0
2
2
0
0
0
0
3
0
3
0
0
1
0
0
0
1
3
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
1
0
0
2
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
1
0
2
0
2
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
6
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
3
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
1
0
0
0
6
2
0
0
0
0
3
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
1
0
2
0
0
0
2
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
2
1
2
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
3
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
1
0
1
0
0
3
0
0
0
0
0
0
1
0
0
4
0
0
2
0
0
0
2
2
0
0
1
2
1
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
8
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
7
1
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
6
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
3
0
0
0
0
1
2
2
4
0
0
0
0
3
0
0
0
2
5
2
0
0
0
2
2
0
0
1
1
2
0
2
2
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
3
2
0
2
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
1
0
0
1
0
2
0
1
0
0
1
0
0
0
0
3
0
0
0
0
0
4
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
1
2
0
0
0
1
0
0
1
0
1
2
0
0
2
0
5
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
1
0
0
0
1
0
1
0
1
4
0
2
1
0
0
2
0
1
0
1
2
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
2
0
0
0
2
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
2
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
2
0
2
0
0
0
0
2
0
5
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
1
0
0
1
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
2
0
2
0
2
0
1
2
0
0
0
0
2
0
2
0
0
0
0
1
2
4
0
1
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
6
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
3
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
1
0
0
2
1
0
0
2
2
0
0
0
1
1
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
1
0
1
1
1
1
0
0
0
0
0
0
1
2
0
2
0
0
1
0
0
0
0
2
0
0
1
3
2
0
0
0
0
0
2
2
1
0
0
1
1
0
0
2
1
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
3
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
3
0
0
2
2
2
0
2
0
0
0
0
1
0
0
1
2
0
0
0
0
1
2
0
2
0
1
0
1
1
0
0
0
1
0
1
0
1
0
1
1
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
2
0
1
0
0
0
1
0
1
0
0
1
1
0
0
4
0
2
1
0
0
0
0
2
0
1
2
0
1
0
1
0
0
0
4
0
1
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
2
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
1
4
0
0
5
0
0
0
0
0
2
2
2
1
0
2
0
0
4
1
0
0
1
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
2
1
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
1
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
7
0
1
0
0
0
0
0
0
2
0
0
1
0
2
0
2
0
0
0
0
0
1
0
0
0
0
1
2
2
2
1
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
2
0
0
2
1
0
4
0
1
0
0
2
0
1
0
0
1
2
0
0
0
0
0
1
0
1
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
1
0
0
1
0
3
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
1
2
0
0
0
0
2
0
2
0
0
0
0
1
0
2
0
1
0
0
1
0
1
0
0
0
0
2
1
2
0
0
2
0
2
2
0
0
0
0
0
1
1
0
0
2
0
0
0
0
1
0
5
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
3
0
0
2
0
2
0
1
2
0
1
0
1
0
1
0
0
0
0
0
0
1
0
2
0
2
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
2
1
1
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
1
0
0
0
0
2
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
2
0
0
1
0
0
2
0
0
0
0
0
5
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
2
2
0
1
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
2
3
0
0
2
2
0
0
3
0
1
0
0
1
2
0
1
0
0
3
0
0
1
0
1
0
0
0
0
1
0
0
0
0
2
0
2
0
1
0
2
0
0
0
0
0
0
8
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
1
0
1
3
0
1
0
0
0
2
1
0
0
1
0
0
1
2
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
2
0
0
0
0
0
0
2
2
0
2
0
0
0
0
1
1
2
0
1
0
0
0
0
2
0
2
6
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
2
0
1
0
2
0
2
0
2
2
0
0
3
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
2
0
0
1
0
0
0
0
2
2
0
0
0
5
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
2
1
0
0
0
2
0
0
0
2
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
1
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
1
2
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
4
0
0
0
1
1
1
0
0
0
2
0
2
1
0
2
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
3
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
2
1
0
0
0
0
3
1
0
0
0
2
0
0
0
0
2
0
0
1
0
2
0
1
0
0
0
0
0
2
1
2
0
0
0
1
0
2
0
0
0
0
2
1
2
0
0
1
0
0
0
0
1
0
2
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
4
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
1
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
1
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
1
0
7
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
1
1
2
0
0
0
0
2
0
0
0
0
0
1
1
0
0
1
0
0
2
0
0
0
0
0
1
1
0
0
2
0
2
0
2
0
0
0
0
0
0
2
0
0
3
0
0
0
0
1
0
0
0
0
2
0
0
0
4
0
0
1
0
0
0
2
0
0
2
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
3
0
0
0
0
0
0
2
0
2
0
3
2
2
0
0
0
0
2
0
0
0
0
0
4
0
0
1
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
1
0
2
0
1
0
0
3
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
1
0
2
1
0
0
1
2
0
0
2
0
2
0
1
0
0
2
0
1
0
0
1
0
0
2
2
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
1
2
1
0
1
0
2
2
1
0
7
0
0
0
0
0
0
0
0
0
0
2
0
3
0
2
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
1
1
0
0
0
0
2
2
0
2
0
0
0
2
2
0
0
0
1
1
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
1
0
2
0
1
1
0
4
0
0
1
0
0
0
0
0
0
2
2
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
3
0
2
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
2
2
2
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
1
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
2
0
0
0
0
0
1
0
0
1
0
1
0
2
0
0
1
2
0
0
3
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
2
0
0
4
1
0
0
1
0
0
0
1
2
0
0
0
0
2
0
0
0
2
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
7
1
0
0
0
2
1
1
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
2
1
0
0
1
0
0
1
0
2
2
2
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
1
0
0
0
2
0
0
1
0
0
0
2
0
1
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
1
1
0
1
0
0
0
1
0
1
0
0
4
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
1
0
2
0
0
0
3
3
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
2
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
2
1
0
2
0
0
1
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
1
0
0
2
0
0
0
0
0
1
2
1
1
0
1
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
3
2
0
1
0
0
0
0
0
2
0
0
0
3
0
0
2
0
0
0
0
0
0
10
0
0
0
0
0
1
0
0
0
2
0
2
2
0
0
1
0
2
0
0
3
0
1
3
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
7
0
0
2
0
2
0
0
0
0
2
2
2
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
2
1
0
7
0
0
0
1
1
0
0
1
0
0
0
1
0
1
3
0
4
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
4
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
1
0
2
0
0
0
0
2
0
0
0
0
0
1
0
2
0
1
0
7
0
2
0
1
0
1
1
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
3
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
5
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
2
0
0
1
0
1
0
0
0
0
0
2
1
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
1
1
1
0
3
2
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
2
0
3
0
0
0
0
2
0
0
1
1
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
3
0
0
1
0
0
0
1
0
0
0
3
0
0
0
3
0
2
4
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
2
0
0
0
3
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
5
1
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
1
1
0
2
1
0
0
2
1
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
2
1
2
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
2
2
0
0
0
0
2
0
0
4
0
0
2
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
1
0
0
0
2
2
0
1
0
0
2
0
0
0
0
1
2
0
2
0
0
0
0
1
0
3
0
0
2
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
1
2
2
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
1
3
0
0
2
1
0
1
0
1
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
2
0
0
0
1
2
0
0
1
0
0
0
0
0
0
2
0
0
2
1
3
0
1
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
2
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
2
0
0
1
1
0
0
0
0
2
0
0
2
1
0
0
0
0
1
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
1
2
0
1
0
1
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
3
1
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
1
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
2
2
0
0
0
2
3
0
0
0
1
0
2
0
5
1
0
0
2
1
2
0
1
1
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
2
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
1
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
1
2
2
0
1
0
1
0
0
0
1
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
2
0
2
0
3
0
3
0
0
2
1
0
1
0
0
1
0
0
1
0
0
3
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
2
1
0
0
0
2
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
3
2
0
0
0
2
0
1
0
2
0
0
2
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
2
3
0
2
0
0
1
0
0
2
2
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
2
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
4
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
2
2
2
4
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
2
1
2
0
0
0
2
0
2
4
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
1
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
5
0
1
1
1
0
0
0
0
0
0
0
0
2
1
1
0
1
2
0
0
0
0
0
3
1
1
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
1
1
0
0
0
0
1
0
0
2
0
2
0
2
2
2
0
0
0
2
2
0
0
0
2
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
1
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
6
0
3
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
3
3
2
1
3
0
0
1
2
2
0
1
0
0
1
0
0
0
5
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
1
2
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
1
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
2
4
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
3
0
0
2
0
0
2
0
0
0
4
2
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
1
0
2
0
5
0
0
2
1
0
0
5
0
0
0
0
0
2
0
1
0
0
0
0
2
0
1
0
0
0
0
1
2
2
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
1
2
1
1
0
0
2
0
0
0
2
0
0
1
0
0
0
1
0
2
0
0
0
0
0
3
0
2
0
2
0
0
0
1
0
2
0
2
0
2
1
0
0
1
0
0
0
0
0
0
1
0
3
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
1
0
0
1
1
0
0
0
0
4
2
1
4
2
9
1
1
0
2
0
4
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
1
1
0
1
2
0
2
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
1
0
0
2
0
1
0
0
2
0
0
0
0
1
0
1
1
0
0
0
0
0
1
1
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
2
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
1
0
3
0
0
0
0
1
0
0
0
1
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
1
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
2
0
0
2
0
1
1
0
0
0
0
0
3
0
0
1
3
0
2
0
0
0
0
2
0
0
1
2
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
1
3
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
1
2
1
0
0
1
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
5
1
2
0
3
2
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
5
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
1
2
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
1
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
2
2
0
2
0
1
1
1
0
0
0
1
0
2
1
0
0
0
1
2
0
0
0
0
2
1
1
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
2
0
1
0
1
0
0
0
0
0
0
0
1
0
4
0
1
2
0
0
0
0
0
0
0
0
1
0
3
2
1
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
1
0
2
0
0
0
0
1
0
0
1
1
0
1
0
1
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
1
2
1
1
0
1
2
0
1
2
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
1
0
2
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
2
0
0
2
2
0
0
0
0
1
0
0
0
0
1
1
0
3
0
1
0
2
0
0
0
0
2
0
0
0
0
1
2
1
1
0
1
1
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
1
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
1
0
0
0
2
0
1
0
0
3
0
0
2
0
1
0
0
1
0
0
0
1
0
1
0
1
0
0
0
1
0
0
1
1
0
1
0
2
1
0
1
0
0
0
0
2
2
0
2
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
2
0
0
1
0
2
0
0
0
0
1
0
0
0
0
1
2
0
1
0
0
0
1
0
0
0
2
0
0
0
0
2
0
1
0
0
0
2
1
2
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
1
1
0
0
5
1
1
0
1
1
2
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
1
1
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
2
0
2
0
0
0
0
2
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
3
0
0
2
0
0
0
0
4
2
0
0
1
2
0
0
2
1
2
2
2
0
2
0
0
0
0
1
0
3
1
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
1
1
0
1
0
0
1
1
0
1
2
2
0
0
2
2
1
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
5
2
0
0
0
0
2
0
0
2
0
1
0
0
1
0
1
1
0
0
1
0
1
0
1
0
0
0
1
3
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
3
2
4
0
1
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
2
0
1
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
2
0
0
1
0
2
0
0
1
2
0
0
0
0
0
0
0
1
0
0
2
1
2
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
1
0
0
0
1
1
0
1
0
2
0
0
1
0
2
0
2
0
0
2
0
0
0
0
0
0
2
0
1
0
1
2
0
2
0
2
1
2
0
2
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
2
0
0
0
1
0
1
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
1
1
0
1
0
0
0
2
0
1
3
0
0
0
0
2
0
1
0
0
0
2
0
1
1
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
4
0
0
1
0
2
2
1
0
2
2
0
1
1
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
2
0
3
0
0
0
2
0
1
2
1
0
0
3
2
2
0
0
0
0
0
0
1
0
0
0
1
0
0
2
1
1
1
0
2
2
0
0
1
2
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
3
3
2
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
2
0
2
0
0
0
0
1
0
0
3
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
2
2
0
2
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
3
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
2
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
2
2
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
2
2
0
0
1
0
0
1
0
0
0
2
0
0
0
0
1
1
2
2
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
1
0
0
2
0
0
0
1
3
1
0
0
0
0
2
0
0
0
0
2
0
0
3
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
1
0
0
0
0
0
2
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
3
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
1
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
1
2
3
2
0
0
3
0
0
1
0
0
0
0
1
0
2
2
0
0
0
1
0
0
1
0
0
1
0
1
2
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
7
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
2
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
1
1
1
1
0
0
0
0
1
2
0
0
1
1
1
2
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
3
1
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
2
1
0
1
0
2
0
0
0
0
0
1
2
2
0
1
0
3
0
1
2
0
0
0
0
0
2
0
2
1
1
0
0
0
0
2
2
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
2
0
1
0
0
3
0
4
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
1
2
0
0
1
0
1
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
3
2
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
2
2
0
0
0
0
0
0
1
0
1
0
2
2
0
0
1
0
0
0
4
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
3
1
2
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
1
0
0
1
0
0
2
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
2
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
3
0
0
1
0
0
0
0
0
2
2
0
0
1
2
0
0
2
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
2
0
0
1
1
0
0
0
1
0
4
3
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
3
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
3
0
2
0
0
0
3
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
1
2
0
0
0
0
0
1
0
0
2
1
0
0
0
2
0
0
0
0
2
2
1
0
0
0
2
2
0
1
0
0
2
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
1
0
0
2
1
2
2
2
0
0
0
0
0
0
0
0
0
0
8
0
0
0
2
0
2
0
0
4
0
0
4
0
1
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
2
0
2
0
2
0
1
0
0
0
0
0
2
0
2
0
0
3
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
1
2
0
1
0
0
0
0
0
0
0
5
2
0
0
0
0
1
0
1
0
0
0
1
2
0
2
0
2
0
2
1
0
0
0
1
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
2
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
5
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
2
1
0
1
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
3
0
0
0
0
3
1
0
0
0
1
0
1
1
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
3
0
2
0
1
0
0
0
0
2
0
2
0
2
2
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
1
4
0
2
0
1
0
8
1
0
2
8
0
0
0
2
0
1
0
0
0
2
0
0
1
1
0
1
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
1
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
1
0
0
0
1
1
1
0
1
0
0
0
1
0
0
2
0
0
0
2
0
0
1
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
1
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
2
0
0
0
4
0
0
0
0
0
1
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
2
1
0
3
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
4
0
0
0
0
3
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
1
0
2
1
0
0
0
2
0
0
3
0
0
5
2
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
1
1
0
0
3
0
2
0
0
0
2
0
2
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
1
2
1
0
1
0
0
0
1
0
1
0
1
0
0
0
1
1
1
1
0
2
0
0
0
0
0
0
2
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
3
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
5
0
0
1
2
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
5
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
3
0
2
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
1
1
1
0
0
0
0
2
0
1
0
0
0
0
0
2
2
1
0
0
1
0
1
0
1
3
2
0
0
1
0
0
0
1
1
0
0
0
0
0
0
2
0
2
1
0
0
0
0
2
0
0
1
2
0
2
2
0
2
0
0
3
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
1
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
24
0
0
0
0
0
0
0
1
2
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
4
0
2
0
0
2
1
2
0
0
2
1
0
0
0
3
1
0
0
0
0
2
0
0
0
1
1
0
0
1
2
0
0
1
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
4
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
2
2
2
0
1
0
0
0
1
1
0
0
0
0
0
3
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
2
3
0
0
0
2
0
0
3
0
0
1
2
0
0
0
0
2
1
2
0
0
0
0
0
2
0
1
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
1
0
0
0
1
0
2
0
0
0
0
0
3
0
1
0
0
0
0
0
3
0
0
0
3
0
2
0
0
2
2
0
2
1
2
0
5
0
0
0
0
0
3
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
3
13
0
0
2
0
0
0
1
2
0
0
0
0
1
0
2
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
2
2
0
0
0
1
1
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
2
0
1
2
1
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
3
1
0
0
1
2
0
0
0
2
0
0
0
0
0
2
0
0
3
0
0
1
1
2
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
2
0
0
1
2
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
1
1
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
2
2
0
0
2
1
4
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
1
2
0
2
2
1
0
1
0
0
2
0
2
1
0
0
0
0
0
1
0
1
0
1
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
3
0
0
0
0
0
2
2
0
0
1
0
0
2
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
2
0
1
0
0
3
0
0
0
0
1
0
1
1
2
1
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
1
3
3
2
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
1
0
0
0
0
2
0
1
0
0
0
0
2
0
0
2
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
1
2
0
0
0
4
1
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
1
0
1
0
2
0
0
0
0
1
1
3
0
0
0
1
0
0
0
0
0
0
1
0
0
0
3
2
0
0
2
0
2
0
0
0
0
1
2
1
0
1
0
1
2
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
1
2
0
2
1
3
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
2
0
2
0
0
7
0
2
0
0
0
2
0
0
0
2
0
5
5
2
2
2
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
3
0
0
2
2
0
1
0
0
2
0
0
0
2
0
1
2
0
0
1
1
6
0
0
2
0
0
1
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
2
0
0
0
2
0
2
0
0
4
0
0
0
1
0
0
0
0
0
0
3
0
4
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
1
0
1
0
1
0
0
0
2
0
1
0
1
0
0
0
0
0
1
0
0
1
0
6
0
1
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
1
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
3
0
2
0
0
1
0
2
1
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
1
1
0
0
0
0
0
0
1
2
0
0
0
1
0
2
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
1
0
1
0
1
0
1
2
0
1
3
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
1
0
0
0
0
5
0
0
2
0
0
0
0
0
0
0
0
0
0
5
1
1
0
1
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
1
0
2
1
0
2
0
0
4
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
2
1
0
0
0
2
4
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
1
0
2
0
0
2
1
0
0
0
0
0
0
0
0
1
1
4
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
1
0
0
0
3
0
1
0
1
2
0
2
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
3
0
0
2
2
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
1
0
0
2
0
0
1
0
1
1
0
0
0
0
0
1
1
0
0
2
1
0
0
1
0
0
1
0
0
1
4
2
2
0
0
1
0
2
2
2
0
0
0
0
1
0
0
1
2
1
0
0
0
0
0
0
0
1
2
3
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
2
0
1
0
0
0
2
0
0
1
0
0
1
1
2
2
1
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
2
1
0
0
0
2
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
1
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
3
0
1
2
0
0
0
0
0
3
0
2
1
2
0
0
2
0
2
2
2
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
1
1
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
2
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
3
1
1
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
3
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
5
0
1
0
2
0
7
0
0
0
0
2
0
1
0
0
0
0
0
6
5
0
0
1
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
3
0
2
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
1
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
1
0
0
2
0
1
0
0
3
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
3
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
1
0
1
0
0
2
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
1
0
0
1
0
2
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
5
0
0
1
0
0
2
1
0
0
2
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
2
2
2
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
2
0
2
0
1
0
1
0
1
0
0
0
3
0
0
0
0
0
0
0
0
1
2
1
1
2
3
0
0
0
0
5
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
1
2
1
0
0
0
4
0
2
2
1
0
0
0
3
0
0
0
0
1
0
0
2
2
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
2
0
0
0
1
0
0
2
0
1
0
0
1
0
2
0
1
0
0
1
0
4
3
0
1
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
2
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
2
1
2
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
2
0
0
1
0
1
2
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
2
1
0
1
0
0
0
0
2
0
0
0
1
3
0
0
0
2
0
0
2
1
1
0
3
2
0
1
3
0
4
0
0
0
0
1
0
0
0
0
0
2
0
2
0
1
0
0
0
2
0
0
4
3
2
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
2
0
1
0
0
2
0
1
2
0
2
1
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
2
2
0
0
3
1
2
0
0
1
0
2
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
1
0
3
0
2
0
0
0
0
0
0
2
0
0
1
3
2
1
0
1
1
0
1
0
2
0
4
0
0
3
2
0
1
0
0
5
0
0
0
0
0
1
0
0
1
0
0
0
1
0
2
0
1
6
0
1
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
1
0
0
0
2
2
0
0
2
0
0
0
0
2
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
1
0
1
0
2
2
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
3
1
0
2
0
0
0
0
2
6
1
0
0
0
2
2
0
0
0
2
0
2
0
1
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
2
1
0
0
0
0
2
0
0
4
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
1
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
3
2
0
0
0
0
0
0
1
0
1
0
0
0
0
2
1
0
0
1
1
0
3
0
0
1
2
2
0
1
0
0
0
0
0
0
0
0
0
1
2
0
1
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
4
2
0
2
0
0
3
0
1
1
0
0
0
0
0
0
1
0
0
6
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
6
0
0
2
0
0
2
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
1
1
0
0
2
2
0
0
1
0
0
2
0
0
2
1
0
0
0
3
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
1
2
4
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
2
7
0
1
2
0
1
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
2
2
0
0
0
2
0
0
0
0
0
2
1
2
0
0
0
0
2
1
1
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
2
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
2
1
0
0
0
0
0
0
1
2
2
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
1
1
2
2
0
1
1
0
2
2
0
2
0
1
2
0
1
0
1
0
0
0
3
0
1
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
2
0
1
3
1
1
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
1
2
0
0
0
1
0
0
2
0
0
0
1
0
2
1
0
0
0
0
0
0
2
0
0
2
1
0
1
0
0
1
3
0
0
1
0
0
0
0
1
1
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
5
0
0
0
1
2
2
0
0
0
0
0
0
1
0
0
0
0
1
2
2
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
2
0
0
0
1
2
0
0
1
0
0
0
0
1
0
1
0
2
0
1
1
0
1
0
2
0
0
0
0
0
0
0
3
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
1
0
0
2
1
0
0
0
2
0
0
0
3
2
0
0
0
0
1
0
1
0
2
2
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
3
0
2
0
1
0
0
0
0
0
1
1
0
1
1
0
0
0
0
1
2
2
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
1
0
0
1
1
0
0
0
0
2
0
0
2
2
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
3
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
2
2
1
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
2
0
0
0
0
3
0
0
0
1
2
0
0
1
0
1
0
0
0
1
1
0
0
3
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
1
6
0
0
0
0
0
1
1
0
0
0
0
0
1
0
2
0
0
1
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
1
0
2
0
0
1
1
0
0
0
1
0
0
2
0
0
0
0
0
3
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
1
2
1
0
2
2
1
0
0
0
0
0
1
0
0
0
0
0
0
2
4
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
2
0
0
0
3
0
2
0
1
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
2
0
0
3
1
1
0
0
0
2
1
0
0
0
0
0
0
0
2
0
1
0
1
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
1
0
0
0
2
0
3
1
0
0
0
0
0
0
2
1
0
2
0
2
1
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
1
0
0
2
2
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
3
0
1
4
1
0
0
2
1
0
0
2
4
1
0
0
2
1
0
0
2
0
1
0
0
0
2
0
0
2
0
0
0
0
1
1
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
1
0
4
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
5
0
0
0
1
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
3
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
5
0
3
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
2
0
0
0
0
1
2
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
2
2
1
0
0
0
0
2
0
0
1
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
2
3
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
3
0
0
2
2
0
2
0
2
0
0
0
2
1
0
1
0
0
0
1
0
0
1
1
0
0
0
0
2
2
0
0
0
0
0
2
0
1
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
2
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
2
0
2
0
2
4
0
0
0
0
0
0
0
0
2
0
4
0
0
2
0
0
2
0
0
1
0
0
0
0
7
0
2
0
0
0
0
0
1
1
1
0
0
0
8
2
1
2
1
1
2
2
1
0
0
0
0
0
0
2
1
1
1
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
2
0
0
0
1
1
0
0
2
4
1
1
2
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
2
0
1
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
2
0
0
1
1
0
0
0
0
0
0
2
1
0
0
1
0
2
0
0
0
2
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
4
2
0
0
1
1
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
2
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
1
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
2
1
2
0
0
1
2
2
0
1
1
0
0
1
0
2
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
2
1
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
2
0
0
0
0
0
1
0
2
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
1
2
0
1
0
0
0
0
0
0
0
0
1
0
0
3
2
0
0
3
1
2
0
1
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
1
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
3
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
1
0
1
0
0
1
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
2
2
2
2
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
3
0
0
0
0
0
0
0
0
1
0
1
0
1
2
1
0
0
2
0
1
0
2
1
2
0
0
0
2
2
0
0
2
3
0
0
1
0
2
2
3
0
2
0
1
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
3
0
1
2
0
0
0
2
0
0
0
0
1
0
0
3
1
0
0
0
0
1
2
0
0
0
2
1
0
0
0
0
2
2
0
1
0
2
2
0
2
0
0
0
1
0
2
0
1
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
1
4
0
0
0
0
0
2
1
2
1
1
0
0
1
0
2
0
2
0
0
1
0
0
0
2
2
0
0
1
0
0
0
0
0
0
2
2
0
2
1
0
0
0
2
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
2
0
0
3
3
0
1
0
0
0
2
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
2
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
4
2
0
0
1
0
0
0
0
0
2
2
0
0
0
0
2
0
1
2
1
0
0
1
1
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
2
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
3
2
2
3
0
0
0
2
0
0
0
0
2
0
2
0
0
2
0
0
2
0
0
0
0
1
2
2
0
1
0
0
0
0
0
1
0
1
0
2
2
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
1
2
1
0
0
3
2
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
3
0
0
0
0
0
1
1
1
0
0
2
0
0
0
0
2
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
2
2
0
0
0
0
0
2
2
1
0
0
0
0
1
0
0
0
0
2
3
0
0
0
0
1
0
0
2
2
3
2
4
0
0
2
0
1
1
0
0
0
0
0
1
0
1
0
0
3
0
0
0
0
2
0
1
0
0
4
0
0
1
0
0
0
1
2
0
2
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
1
0
2
1
2
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
2
0
1
0
0
0
0
0
0
3
0
0
0
5
0
0
2
0
2
0
0
0
1
0
0
0
0
2
0
2
1
4
1
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
1
0
0
2
0
0
2
2
0
0
0
0
1
0
0
0
1
0
2
0
1
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
2
0
2
2
0
0
4
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
1
0
0
2
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
2
1
2
2
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
1
2
2
4
0
0
0
0
1
4
0
0
0
0
1
2
0
0
0
0
0
3
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
3
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
1
2
2
0
0
3
0
0
0
0
0
0
0
1
2
2
0
1
0
2
0
7
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
1
0
0
0
5
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
3
0
0
0
2
0
0
2
2
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
1
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
2
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
3
0
2
1
0
2
0
1
0
2
1
0
0
2
0
0
0
2
0
1
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
4
1
0
0
0
0
0
0
0
3
2
0
2
0
0
0
2
0
0
0
1
1
0
1
1
4
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
4
0
2
3
1
0
1
0
2
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
1
2
0
0
1
2
0
0
0
0
0
0
0
0
3
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
2
1
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
2
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
3
0
0
0
2
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
4
0
0
0
0
3
0
0
0
2
0
0
0
2
1
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
1
2
2
0
0
0
0
0
1
2
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
1
0
0
0
2
0
0
0
4
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
5
0
5
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
2
1
0
2
6
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
1
0
0
2
2
0
0
0
0
0
2
2
0
1
0
0
2
0
2
1
0
2
0
0
0
0
0
0
5
0
2
3
1
0
2
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
3
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
2
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
2
0
1
0
1
0
0
0
1
0
0
1
0
0
0
1
2
0
2
0
0
2
0
0
0
2
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
3
2
0
0
0
0
0
0
0
2
0
0
0
1
2
2
2
0
1
0
1
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
2
4
2
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
1
0
0
2
1
0
1
2
2
2
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
2
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
1
2
0
1
1
2
0
1
0
0
0
1
1
2
0
0
2
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
2
1
1
0
1
1
0
0
0
0
0
0
0
2
0
0
1
0
0
2
2
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
4
2
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
2
0
0
0
0
0
3
0
6
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
1
0
0
1
0
1
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
3
0
0
0
0
3
2
0
0
0
0
0
1
0
3
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
1
1
2
0
0
1
0
2
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
3
0
0
2
0
0
0
2
1
0
1
0
0
0
0
0
0
3
2
0
1
0
1
2
0
0
0
2
1
0
3
0
2
0
0
0
2
1
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
5
0
0
0
0
0
3
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
1
0
0
0
0
1
0
0
1
0
1
0
0
0
2
0
0
1
2
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
1
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
2
1
0
0
1
2
0
0
0
1
2
0
0
0
1
1
0
0
2
0
0
0
0
0
2
0
0
0
0
1
2
1
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
1
0
0
0
1
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
4
0
0
2
0
0
0
0
1
2
2
0
0
0
2
0
0
3
0
0
0
5
0
4
0
1
1
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
4
0
1
1
0
0
0
2
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
1
1
0
1
0
0
2
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
1
1
0
1
0
0
2
0
1
0
1
0
0
0
2
1
0
0
0
0
2
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
1
0
0
2
0
7
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
2
0
2
0
1
0
0
2
1
0
1
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
2
1
0
3
1
0
0
0
0
0
0
0
2
0
0
2
2
1
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
1
3
1
0
0
0
0
2
2
0
2
0
0
1
0
0
0
3
0
2
0
0
0
0
0
2
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
1
1
0
1
2
0
0
0
0
3
0
0
1
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
3
0
2
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
2
1
2
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
2
0
0
1
2
0
0
0
0
0
0
1
0
0
0
2
2
0
0
1
2
0
0
4
2
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
2
0
2
0
0
0
0
2
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
2
0
0
2
1
2
0
0
0
1
0
0
0
2
1
0
0
1
0
0
6
0
0
0
0
0
0
1
0
0
0
0
1
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
6
0
0
0
1
0
0
0
0
0
1
2
0
0
0
4
0
2
0
2
0
0
0
0
0
2
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
3
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
2
0
1
0
1
2
0
2
0
3
2
0
0
1
1
0
0
1
2
1
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
1
0
4
0
0
1
1
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
3
0
1
0
0
0
0
0
0
2
0
1
0
1
0
0
3
2
0
0
0
0
0
0
0
2
2
0
0
0
2
2
0
2
0
0
2
0
0
1
2
2
1
0
1
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
2
0
1
0
0
1
2
2
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
1
0
3
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
1
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
3
0
0
0
0
0
0
0
0
3
1
1
2
1
0
2
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
2
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
4
0
0
0
0
0
3
0
0
0
2
3
0
1
1
0
0
0
1
0
0
0
2
0
1
1
1
0
0
1
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
1
0
1
0
0
2
1
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
2
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
2
1
0
0
0
2
0
0
0
2
2
2
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
1
0
2
1
0
0
0
0
3
0
0
0
0
1
1
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
2
2
1
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
5
6
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
1
0
1
2
0
0
0
0
0
0
0
2
0
1
0
0
0
1
3
0
0
2
0
0
0
0
0
0
2
0
0
3
1
1
0
0
0
8
1
1
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
2
0
0
2
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
1
1
1
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
1
2
1
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
5
0
0
0
2
1
0
0
0
2
0
0
0
0
1
2
0
1
0
0
0
0
0
0
1
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
1
0
0
2
0
0
1
0
2
0
2
2
0
2
2
0
0
0
0
1
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
3
0
0
2
0
1
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
5
0
0
2
0
1
0
0
0
0
0
1
2
0
0
2
0
0
3
0
1
0
0
1
2
0
0
0
1
0
0
0
0
0
1
2
7
0
0
1
0
2
1
2
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
4
0
0
0
0
0
0
0
0
1
1
0
2
2
0
1
0
7
0
0
1
0
1
0
0
0
0
0
1
1
0
2
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
2
0
0
0
1
1
0
2
0
1
0
2
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
1
0
2
0
0
0
0
0
1
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
2
0
0
0
0
2
1
2
0
2
0
0
1
0
0
1
0
0
0
2
0
2
2
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
5
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
3
1
0
0
2
1
0
3
0
0
2
2
1
0
0
0
0
1
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
1
0
0
1
2
0
1
2
2
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
2
1
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
3
4
0
0
1
1
1
3
2
3
0
2
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
2
0
4
0
0
2
0
0
0
0
0
3
0
1
1
1
4
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
4
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
2
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
6
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
2
2
0
0
1
0
0
0
0
4
0
0
1
0
2
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
1
0
1
0
1
0
0
0
0
3
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
3
0
1
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
3
2
0
0
0
0
0
1
0
0
0
0
1
2
0
0
2
1
2
0
2
3
1
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
1
0
2
1
2
1
0
2
2
0
1
0
0
1
0
2
0
0
0
0
0
0
4
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
3
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
3
0
1
6
0
0
0
2
2
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
1
2
2
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
2
1
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
3
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
2
0
1
0
0
1
2
0
2
0
0
0
0
0
2
4
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
1
0
0
0
0
0
1
0
1
1
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
1
0
0
1
1
0
0
0
0
1
1
0
2
0
0
0
1
0
0
0
0
1
0
0
0
9
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
2
3
0
0
0
0
0
1
2
2
1
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
1
1
0
0
1
0
0
0
0
2
0
2
0
0
1
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
1
0
1
1
0
3
0
0
0
0
1
0
3
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
1
0
0
2
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
2
0
0
2
0
2
2
1
0
0
1
1
2
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
1
0
2
1
0
2
1
1
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
3
0
2
1
0
0
0
0
0
2
0
0
2
0
1
0
0
5
1
0
1
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
2
0
2
2
1
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
1
0
0
1
0
0
2
2
0
2
0
0
1
0
0
0
0
2
1
0
2
0
0
0
0
1
0
0
0
0
0
2
4
0
1
0
0
0
0
1
0
0
3
0
0
0
0
1
2
0
1
0
0
11
0
0
0
0
0
3
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
1
1
0
0
0
0
3
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
5
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
1
1
0
2
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
2
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
2
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
3
0
2
1
0
0
0
0
0
1
0
0
2
1
0
0
1
0
0
0
1
0
3
2
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
1
0
1
1
0
0
2
0
0
1
0
1
0
2
0
0
0
2
4
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
1
2
0
0
0
1
0
2
0
0
1
2
0
2
1
0
0
1
0
1
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
1
3
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
2
2
0
2
1
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
1
0
2
1
0
0
1
0
1
0
3
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
2
2
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
2
3
0
0
0
0
0
3
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
3
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
1
0
0
0
0
2
1
2
1
0
0
0
3
0
0
0
0
0
1
3
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
3
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
1
0
0
1
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
1
1
0
7
1
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
1
2
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
2
0
1
1
1
0
0
1
0
1
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
2
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
2
1
0
0
0
2
1
0
0
0
0
0
0
0
2
1
0
2
0
0
1
2
0
0
0
0
0
2
0
1
4
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
2
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
2
0
1
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
3
2
0
0
0
0
0
2
2
3
0
0
1
6
0
2
2
0
1
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
8
0
0
0
0
0
0
2
0
0
1
2
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
3
0
5
0
0
2
0
0
4
0
0
14
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
1
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
3
2
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
2
0
0
0
2
0
2
0
0
2
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
2
0
1
0
2
0
0
2
0
2
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
3
0
1
0
1
0
0
0
2
0
0
0
0
0
0
1
0
2
2
1
0
0
0
0
2
0
0
0
0
1
2
0
2
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
2
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
1
0
2
1
0
0
2
2
2
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
3
2
0
2
0
0
0
0
2
2
0
0
2
0
2
1
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
1
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
8
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
1
2
0
0
0
1
0
2
0
0
0
3
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
2
2
0
1
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
1
0
0
2
0
0
1
1
1
0
0
0
0
0
0
0
0
0
2
2
1
2
0
0
0
1
0
0
0
2
0
0
0
1
1
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
1
2
0
1
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
2
0
0
1
2
2
1
0
0
0
0
0
0
0
0
0
2
0
0
6
2
2
0
2
1
2
0
0
0
0
2
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
2
0
0
5
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
1
1
0
4
1
1
0
0
0
0
2
8
0
0
0
0
4
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
2
0
0
0
0
2
0
1
0
0
2
0
0
1
1
0
0
4
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
1
0
0
0
0
2
0
0
2
2
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
1
0
0
3
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
5
1
0
0
2
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
1
1
2
0
0
1
0
1
0
0
1
0
0
0
0
0
2
0
2
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
2
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
1
0
0
1
1
0
0
0
1
2
2
0
1
2
2
1
1
0
1
0
1
0
1
0
1
2
4
2
1
0
1
1
2
0
2
1
0
1
0
0
0
0
0
0
2
0
1
0
2
0
0
1
0
0
2
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
2
1
7
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
4
2
0
0
0
0
1
2
2
1
2
0
7
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
2
1
0
0
1
0
0
1
2
0
0
0
1
0
0
1
0
8
0
0
0
0
0
0
0
2
0
0
1
2
0
1
2
0
0
0
0
0
1
2
0
0
1
0
1
0
1
0
0
0
0
0
0
0
2
0
2
2
1
2
0
0
0
0
0
0
0
0
0
0
2
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
2
1
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
1
0
1
0
1
0
0
0
3
0
0
2
0
1
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
1
0
1
0
0
0
0
2
1
0
0
2
0
2
0
0
2
0
0
0
0
0
0
4
2
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
4
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
1
1
2
0
0
1
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
2
0
2
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
1
0
1
1
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
3
0
1
0
0
3
0
0
0
1
2
0
0
0
0
0
0
2
1
0
1
0
1
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
1
2
0
3
0
2
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
2
0
0
1
0
1
1
0
0
0
0
0
2
0
0
1
0
1
1
1
2
0
2
0
0
0
2
1
0
2
0
2
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
2
1
2
0
0
1
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
1
2
0
0
2
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
3
0
3
0
2
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
1
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
3
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
3
0
0
1
0
2
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
4
1
0
0
0
3
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
2
1
1
1
0
0
0
3
2
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
2
0
1
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
1
0
0
0
2
0
2
1
3
0
1
2
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
1
7
0
0
1
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
5
2
0
0
0
1
0
0
2
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
3
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
1
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
3
1
2
0
0
0
0
1
1
2
1
0
1
0
0
3
0
0
1
3
1
2
0
2
0
0
1
3
0
0
0
1
1
0
0
2
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
2
0
0
0
0
0
3
0
0
1
0
1
2
1
0
0
1
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
2
2
2
3
2
2
0
1
1
0
0
0
0
0
2
2
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
2
0
2
0
0
0
0
0
0
2
1
0
0
0
1
0
1
0
0
4
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
4
1
0
0
1
0
0
2
4
0
0
1
0
1
0
0
0
0
2
2
0
0
3
0
0
1
1
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
1
0
0
2
0
2
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
5
0
0
5
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
1
1
1
0
1
0
1
2
1
0
0
0
1
1
1
2
1
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
1
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
3
0
1
2
0
1
2
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
1
1
0
0
5
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
2
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
1
3
0
0
1
1
1
0
0
0
0
0
0
0
1
1
0
0
1
1
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
2
0
0
0
0
1
1
0
0
0
3
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
2
0
0
1
1
0
2
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
2
1
1
2
0
0
0
0
0
0
4
2
1
1
2
2
0
0
0
1
0
0
2
0
2
0
0
2
2
0
0
0
0
0
0
1
1
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
1
1
0
0
0
0
0
0
0
2
2
2
0
0
0
0
1
0
0
0
0
0
0
0
2
2
1
0
6
0
0
1
4
0
0
0
2
1
2
2
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
3
1
0
0
0
2
0
0
1
0
0
0
0
0
1
2
2
2
0
1
0
1
2
2
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
3
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
1
0
1
0
0
1
3
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
2
0
1
1
0
0
1
0
0
2
1
0
0
0
2
1
0
0
1
0
2
0
0
1
1
2
0
0
0
0
0
2
0
0
0
1
2
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
5
2
0
0
1
0
0
2
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
2
0
0
0
0
3
0
1
0
1
0
0
0
1
1
2
0
0
2
1
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
2
0
1
2
0
2
0
1
0
0
0
2
2
1
0
0
0
2
0
0
0
0
2
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
2
3
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
3
1
0
2
0
0
0
0
0
0
0
0
1
2
0
2
0
0
7
2
0
0
0
0
0
0
0
3
1
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
1
0
1
0
2
0
1
0
0
0
2
0
2
0
0
2
1
0
0
2
1
2
0
0
1
0
0
0
0
0
2
1
0
0
0
3
0
0
0
0
0
0
0
1
5
0
0
2
0
0
0
2
0
1
0
2
2
0
2
0
1
0
0
0
0
0
1
0
0
4
0
0
0
2
0
0
1
0
0
0
0
2
2
0
0
0
3
0
0
2
1
2
2
1
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
5
2
5
1
0
1
0
0
0
2
0
0
0
0
1
0
2
0
1
0
2
0
0
0
1
0
2
0
1
0
2
1
0
0
0
0
2
1
0
0
0
1
0
1
0
2
0
0
0
0
1
1
0
0
0
1
0
2
2
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
1
1
0
1
0
0
1
0
0
0
1
0
2
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
2
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
2
2
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
3
0
0
1
0
0
1
2
0
0
0
2
1
0
4
0
0
2
0
0
2
0
0
0
1
0
0
0
1
0
2
0
0
1
6
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
3
2
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
2
1
2
2
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
2
2
1
1
0
0
0
1
0
0
0
0
0
2
0
0
0
1
3
0
0
0
0
1
0
0
0
5
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
1
0
2
0
3
0
5
0
0
0
0
0
1
1
0
1
2
0
0
0
1
0
0
0
2
0
0
0
0
0
2
1
1
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
2
1
0
2
0
0
2
2
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
2
2
1
4
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
5
0
0
0
2
0
1
0
0
0
0
2
0
1
2
0
0
2
3
0
1
0
1
0
0
1
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
1
1
0
0
2
0
0
1
0
2
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
2
0
1
0
2
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
2
2
1
0
0
0
0
0
2
3
1
0
0
0
0
1
0
0
0
0
0
3
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
1
0
0
1
0
0
1
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
2
1
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
0
1
0
3
0
3
0
0
1
0
0
0
2
0
1
1
0
0
0
0
2
2
0
0
2
0
2
0
0
0
1
2
0
0
1
0
1
0
2
2
0
0
0
1
0
1
0
1
0
5
0
1
1
3
1
0
1
5
0
0
0
0
1
2
0
11
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
1
5
0
7
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
2
2
0
2
0
0
0
2
2
0
0
2
0
0
0
0
0
3
0
2
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
2
1
0
2
2
2
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
2
1
2
0
0
0
0
0
0
1
0
1
2
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
2
2
0
0
2
3
0
1
0
0
0
2
1
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
2
0
2
2
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
6
0
0
0
6
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
1
0
1
2
0
0
1
0
1
1
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
1
1
0
3
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
1
1
1
0
3
0
0
0
0
0
2
0
0
1
2
1
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
4
1
1
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
1
3
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
2
2
1
0
0
0
2
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
1
3
2
0
0
2
0
1
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
3
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
4
0
0
2
0
0
0
2
0
0
2
2
1
1
2
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
2
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
1
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
2
0
1
3
0
0
0
0
0
0
0
0
0
0
0
1
0
3
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
3
0
0
0
1
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
2
4
3
1
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
4
0
0
0
0
0
0
2
1
0
2
0
1
1
0
0
0
0
2
0
1
0
0
4
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
2
3
0
2
2
0
2
0
0
0
0
0
3
2
0
5
0
0
0
0
1
3
0
1
0
0
0
1
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
3
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
3
2
0
1
6
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
5
0
0
0
2
1
0
0
0
0
0
0
0
2
0
1
0
0
1
2
0
0
0
0
0
0
1
2
0
0
1
0
1
2
0
0
0
0
0
1
1
1
0
0
0
0
0
0
3
1
0
0
0
2
1
0
1
2
0
1
1
0
2
1
0
0
2
2
1
1
0
0
0
0
2
0
2
1
0
0
2
0
0
0
2
0
0
2
0
2
0
1
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
4
0
1
0
0
1
2
0
1
2
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
1
0
0
2
0
0
0
0
2
1
0
1
0
1
0
0
1
0
2
0
0
1
0
1
2
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
3
0
1
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
8
0
0
0
0
0
0
1
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
3
1
0
0
0
0
2
0
1
0
0
2
0
0
0
3
0
0
1
2
0
2
0
0
2
0
1
0
0
1
2
0
1
2
0
0
0
0
2
2
2
0
0
0
0
0
0
2
0
0
1
0
0
2
0
1
0
0
0
2
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
5
2
1
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
5
1
2
0
0
0
0
2
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
3
0
1
0
1
0
0
0
1
2
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
3
0
2
1
0
1
2
0
1
0
0
1
0
0
0
0
0
0
0
2
1
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
1
1
0
0
0
2
0
0
1
0
0
0
0
0
2
1
0
0
0
2
0
2
0
0
2
0
1
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
4
2
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
3
0
3
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
3
1
0
1
1
0
2
0
0
0
1
1
0
0
2
0
0
2
1
0
0
6
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
1
1
0
2
0
0
1
1
2
1
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
1
3
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
1
0
0
0
8
0
1
1
1
0
1
0
0
0
2
0
5
0
0
0
2
0
0
0
0
0
1
1
2
0
0
1
2
0
0
0
0
0
0
0
1
0
1
1
0
1
0
3
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
7
1
0
0
0
2
0
1
0
1
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
1
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
2
0
1
2
0
0
1
1
0
3
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
1
0
0
1
0
0
0
0
3
2
2
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
1
0
0
2
0
0
2
2
0
0
0
3
0
0
0
0
0
1
0
0
0
1
0
0
1
2
0
0
0
2
0
2
0
0
0
0
0
0
0
1
1
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
2
0
2
0
0
2
2
0
1
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
2
0
0
0
0
0
0
2
3
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
1
0
2
2
0
0
2
0
2
0
0
1
0
0
1
1
2
1
0
0
0
0
0
3
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
1
1
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
2
0
3
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
2
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
2
0
0
2
1
0
2
0
0
0
0
4
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
1
2
0
0
0
2
0
0
0
0
0
0
0
2
1
0
2
0
1
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
2
1
0
1
0
4
0
0
0
0
0
0
1
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
11
0
0
0
0
2
1
0
0
0
2
0
0
2
0
2
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
1
0
0
2
0
0
0
5
0
0
0
1
0
0
0
0
0
1
1
1
0
1
0
1
0
2
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
2
0
2
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
1
2
0
1
0
2
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
2
0
0
0
1
2
0
0
0
0
1
2
0
0
0
2
1
0
0
1
2
0
0
0
0
2
2
0
0
2
1
0
0
0
0
2
2
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
2
2
0
0
1
0
0
2
0
3
0
0
0
0
1
2
0
2
1
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
1
0
1
0
2
1
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
2
1
2
0
0
0
0
9
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
1
0
0
0
0
0
3
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
2
0
1
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
2
1
0
1
0
0
0
1
0
1
0
1
0
0
0
3
0
1
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
1
0
0
1
0
2
1
2
1
0
2
0
0
1
0
5
0
0
2
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
3
0
0
3
0
3
0
0
0
2
0
0
0
2
0
1
0
2
1
0
0
1
0
0
2
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
2
1
0
0
1
1
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
3
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
1
0
0
1
0
2
0
0
0
0
2
0
0
0
2
0
6
0
1
0
1
0
1
0
0
1
0
0
0
0
3
0
0
0
0
0
0
2
3
3
0
0
0
0
0
2
0
0
0
0
1
1
0
0
2
2
5
0
1
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
5
0
0
2
1
0
0
0
0
0
0
0
0
2
2
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
3
1
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
2
0
0
0
1
0
0
2
0
0
0
0
1
0
0
2
0
2
0
1
2
2
1
0
0
0
2
3
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
4
1
0
0
0
1
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
1
0
0
0
1
0
0
0
0
3
0
8
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
1
0
0
0
1
1
1
0
0
2
0
2
1
1
0
0
0
1
0
0
2
1
0
0
1
0
1
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
1
0
1
0
1
1
0
0
2
0
2
2
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
2
0
1
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
1
0
0
0
0
0
3
0
4
0
0
0
1
0
1
2
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
2
0
0
3
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
3
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
3
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
1
1
4
0
0
7
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
1
2
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
1
2
0
0
0
0
0
1
0
0
0
1
3
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
1
0
8
0
1
1
2
0
0
2
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
3
2
0
0
3
0
0
0
1
0
0
0
0
0
1
0
2
0
2
1
0
0
2
1
0
0
1
0
0
0
1
2
0
1
1
0
1
0
0
0
0
0
0
0
2
2
2
0
3
2
0
2
2
0
0
0
1
0
0
0
0
2
2
0
2
1
0
0
0
2
0
0
0
1
0
0
0
0
5
0
0
0
0
0
0
0
1
1
2
0
0
0
0
2
0
0
0
2
0
2
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
6
1
0
0
0
0
0
2
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
4
0
4
0
1
0
0
0
0
0
0
2
0
0
0
1
1
0
1
0
1
0
0
0
0
2
2
0
0
0
1
0
0
1
0
1
0
1
0
0
0
2
1
1
0
0
0
0
2
0
1
0
0
0
0
1
0
2
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
1
0
2
1
0
2
2
2
0
0
0
2
0
0
1
2
1
1
1
1
0
0
0
2
2
0
0
0
2
2
0
0
1
1
1
2
0
0
0
1
0
3
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
2
2
2
0
0
0
0
2
0
1
1
1
1
0
0
2
0
0
0
1
0
0
0
2
0
0
2
0
2
1
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
1
0
0
1
2
3
0
0
0
0
1
0
0
0
0
2
1
2
0
1
0
0
0
0
1
0
0
1
0
1
0
1
2
0
0
1
2
1
4
1
1
0
0
0
0
1
0
2
1
1
1
0
2
0
0
0
1
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
4
0
1
0
1
0
0
1
0
0
1
2
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
1
2
1
1
1
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
2
0
0
0
0
0
2
0
2
0
0
2
0
2
2
1
0
3
0
0
0
0
0
1
0
0
2
0
2
0
2
0
0
1
0
2
0
0
0
0
0
0
3
1
0
0
0
2
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
1
0
0
2
2
0
1
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
1
1
0
0
2
0
0
1
0
0
3
0
0
0
0
0
0
1
0
2
0
0
0
2
7
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
1
2
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
2
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
3
0
0
0
0
0
2
1
4
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
1
0
0
2
0
2
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
1
0
3
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
2
2
1
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
3
2
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
2
0
2
2
2
2
0
0
0
0
0
0
0
0
5
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
5
0
1
0
2
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
1
0
0
0
1
0
0
0
3
0
1
0
0
0
0
0
0
0
0
1
1
1
0
2
0
3
2
1
0
0
2
1
2
0
1
0
0
0
0
0
0
2
0
1
0
0
0
2
0
1
0
2
0
0
1
0
0
1
0
2
2
1
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
1
1
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
2
0
3
0
0
0
0
1
0
0
2
2
0
1
0
1
0
0
1
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
1
2
0
0
2
0
2
0
0
0
0
0
1
0
2
1
0
0
0
1
0
1
0
1
4
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
4
3
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
1
0
0
2
0
4
0
0
2
2
0
0
0
0
0
0
0
1
2
1
2
0
1
0
1
3
0
0
0
0
0
1
0
1
2
2
0
1
0
8
0
1
2
1
0
0
1
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
4
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
1
1
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
2
1
5
2
0
3
1
0
0
0
1
0
0
0
2
0
0
3
0
2
0
0
0
0
0
2
1
0
0
0
0
1
0
2
0
2
0
0
1
2
0
0
0
4
0
1
0
0
2
0
0
0
0
0
3
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
1
2
0
0
2
0
0
0
2
9
2
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
1
1
0
4
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
2
0
1
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
2
0
0
0
0
2
0
0
1
0
2
0
0
2
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
3
0
0
1
2
0
0
0
1
0
1
1
2
2
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
3
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
3
1
2
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
3
2
0
2
2
1
1
0
0
0
0
1
0
0
3
0
0
0
0
0
0
1
0
0
1
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
2
0
1
0
2
2
0
0
0
2
0
0
1
0
1
0
0
2
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
1
0
0
2
0
0
1
1
2
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
3
0
4
0
1
1
1
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
2
2
1
2
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
9
2
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
2
0
2
0
0
1
0
0
0
1
0
0
0
0
2
0
3
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
2
2
1
1
0
2
0
0
0
3
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
2
0
1
2
0
2
0
2
0
3
0
0
1
0
0
2
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
2
2
0
0
0
2
0
1
1
0
1
0
0
0
2
2
0
0
0
0
0
0
2
0
0
2
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
2
0
0
0
1
0
0
2
1
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
1
0
1
2
0
0
0
0
0
2
2
0
2
0
0
0
0
1
0
0
3
0
0
0
2
0
0
0
0
1
0
0
0
1
2
0
0
0
0
3
0
0
0
1
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
1
2
2
4
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
2
1
0
0
0
0
2
0
1
1
0
0
2
0
2
0
0
1
2
1
0
0
0
0
1
1
0
0
2
0
0
2
0
0
2
1
0
2
1
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
1
0
0
7
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
2
0
0
0
0
1
0
2
3
0
1
0
0
0
2
0
2
1
0
1
2
0
2
1
0
0
1
1
0
0
0
0
2
4
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
1
0
0
0
1
0
0
0
1
0
0
0
3
2
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
1
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
1
1
0
2
2
0
0
1
2
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
1
0
2
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
2
0
2
0
0
0
0
0
2
2
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
2
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
1
4
1
0
0
2
1
0
1
0
0
0
2
0
0
0
0
0
0
2
2
0
0
3
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
2
1
3
0
0
1
0
0
0
0
0
1
2
0
0
0
1
1
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
8
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
1
0
0
0
3
2
1
0
0
0
0
2
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
1
2
0
0
0
0
0
1
0
1
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
1
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
3
0
2
0
1
0
0
1
0
0
1
1
0
1
1
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
3
0
2
0
0
2
0
0
0
0
0
0
0
3
0
0
2
0
0
2
0
3
2
0
1
2
0
1
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
4
2
0
0
0
0
2
0
0
2
0
0
1
0
2
0
2
0
0
0
1
2
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
1
0
0
1
2
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
1
3
1
0
0
0
0
2
0
0
1
0
2
0
2
2
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
3
2
2
0
0
0
0
0
1
0
0
1
1
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
1
1
0
2
1
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
1
0
2
0
1
0
1
1
0
0
3
0
0
0
0
2
0
2
2
0
0
2
0
0
0
0
2
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
2
1
0
0
1
0
0
1
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
1
0
1
1
1
1
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
4
0
0
7
0
0
1
0
2
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
3
0
0
0
0
0
1
0
1
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
3
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
1
0
0
2
0
0
0
0
0
3
0
2
0
0
0
2
0
0
1
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
3
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
1
0
2
0
1
0
1
0
0
0
0
1
0
0
0
0
2
1
0
7
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
13
0
0
0
2
0
0
0
0
0
1
2
0
0
1
0
2
0
2
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
1
4
2
1
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
3
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
1
0
0
2
0
0
3
0
1
2
2
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
1
2
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
2
0
0
2
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
2
1
0
1
0
0
1
0
0
0
1
0
0
0
3
0
0
0
0
1
0
0
0
0
1
3
0
1
0
2
2
1
2
1
0
0
0
0
2
0
1
2
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
3
0
0
0
0
2
0
2
0
0
0
0
0
0
1
2
0
0
1
1
0
1
0
2
0
2
0
0
1
0
0
1
0
0
0
1
1
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
2
3
2
0
0
1
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
2
0
3
0
1
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
2
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
2
0
2
0
1
1
2
4
0
0
0
0
0
0
1
0
5
1
0
1
0
0
0
3
0
2
0
0
2
1
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
1
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
1
1
1
0
0
0
1
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
2
1
0
0
2
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
2
1
1
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
1
0
3
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
3
0
0
0
1
1
1
0
0
0
3
0
2
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
2
3
0
1
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
1
0
1
0
0
2
2
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
8
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
14
0
1
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
1
0
0
0
2
1
3
0
1
0
0
2
2
0
1
0
0
0
0
0
0
0
2
3
1
0
5
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
1
1
1
0
0
0
0
0
2
0
0
1
0
1
0
0
0
2
0
0
1
2
7
2
0
0
0
0
1
1
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
2
0
0
2
1
1
0
0
1
0
0
0
1
0
0
1
2
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
2
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
2
0
2
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
9
0
0
0
0
0
0
0
0
1
0
0
0
1
3
4
1
0
2
0
2
0
0
0
0
0
2
2
0
0
1
0
0
0
1
0
0
1
0
3
0
0
1
0
2
1
2
0
5
0
0
0
0
0
0
0
1
0
1
0
1
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
2
2
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
1
1
0
0
0
2
0
0
0
0
0
2
0
1
4
0
2
4
1
0
0
1
1
0
0
0
0
0
0
0
1
0
1
2
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
5
0
0
0
1
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
1
0
1
0
1
2
0
0
2
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
2
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
1
2
0
0
0
1
1
2
1
0
0
1
0
0
1
0
2
0
2
0
0
0
0
0
0
0
2
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
3
2
0
0
0
0
0
2
1
0
1
0
2
0
0
0
0
0
0
0
2
0
1
0
1
0
2
0
2
0
3
0
0
0
3
0
0
0
0
2
1
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
2
0
0
0
1
0
0
2
0
0
1
0
0
1
0
2
0
0
0
1
2
0
0
6
0
0
1
0
0
7
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
1
0
0
1
2
0
0
0
0
2
0
0
2
0
1
0
1
0
0
0
1
2
0
0
0
0
1
0
0
1
0
0
5
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
2
1
0
0
0
2
1
0
1
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
1
0
4
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
1
2
0
1
3
0
0
2
2
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
1
0
2
1
0
2
0
0
1
2
1
0
0
0
0
1
0
0
1
0
0
0
8
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
1
1
0
0
2
1
0
2
2
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
2
0
0
0
0
2
2
2
3
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
5
0
0
0
0
2
1
0
0
0
0
0
0
1
3
0
1
4
0
0
0
2
0
0
2
1
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
1
1
0
0
0
0
0
1
1
0
1
0
0
0
0
2
0
5
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
1
4
2
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
1
2
0
0
1
2
1
0
1
2
0
0
2
2
0
0
0
1
1
0
2
0
1
0
0
2
1
1
0
0
1
2
0
0
0
1
0
0
0
0
2
2
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
1
1
0
0
2
2
0
1
0
1
1
2
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
2
1
2
2
0
0
0
0
0
0
0
0
0
2
0
0
1
2
1
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
2
0
0
0
1
1
0
0
2
2
1
0
1
0
2
0
0
0
0
1
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
1
2
0
0
1
0
0
2
1
0
2
1
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
2
0
0
0
2
2
3
0
0
1
2
0
2
0
0
0
0
0
0
2
0
0
1
0
0
1
2
0
0
2
0
1
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
1
1
2
0
0
2
3
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
3
0
0
3
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
1
1
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
4
1
2
0
1
0
0
0
0
2
0
0
0
0
0
1
2
1
0
1
0
0
0
2
0
1
0
0
1
0
0
0
0
3
0
2
2
1
0
2
0
0
0
0
0
4
0
1
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
4
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
4
0
0
0
2
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
2
1
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
2
0
0
0
2
2
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
1
0
0
0
1
2
0
0
1
4
0
0
0
1
0
1
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
1
0
0
1
2
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
3
0
0
1
1
0
2
1
2
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
3
1
1
2
0
2
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
2
2
2
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
1
0
0
3
0
0
1
0
2
1
0
2
2
0
0
0
0
0
2
0
0
0
0
2
1
0
0
1
0
2
0
0
1
2
0
0
2
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
1
0
0
1
0
0
1
3
0
2
0
0
1
0
2
0
2
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
1
0
2
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
2
0
0
0
0
0
1
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
1
0
0
0
2
0
0
2
0
1
0
0
0
0
3
2
0
1
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
2
0
0
3
0
0
1
0
0
0
0
0
1
0
2
3
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
5
0
2
0
1
0
1
1
1
1
1
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
2
2
0
0
0
0
1
2
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
3
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
3
2
0
0
0
0
0
0
0
0
4
2
0
2
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
3
2
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
1
2
0
1
0
0
0
1
0
0
0
0
0
0
0
1
2
1
0
0
0
0
2
0
0
3
1
0
0
1
0
0
4
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
1
0
1
0
3
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
2
2
0
3
0
0
0
0
2
1
0
0
2
1
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
2
2
4
0
0
2
1
1
0
0
0
0
3
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
2
1
2
0
1
0
0
0
2
0
0
0
0
0
2
0
0
1
1
0
0
0
0
6
2
1
0
0
0
0
3
0
3
0
1
0
0
1
2
1
1
0
0
0
2
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
5
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
1
0
0
0
1
0
0
0
1
2
0
0
0
3
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
3
1
0
0
1
0
0
2
2
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
1
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
2
1
0
0
0
1
1
1
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
2
0
0
2
0
1
0
0
0
0
0
10
0
0
1
1
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
1
2
2
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
1
2
0
0
0
0
2
1
0
0
0
2
1
0
1
0
1
0
0
2
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
2
0
0
1
0
2
0
0
2
0
1
0
0
1
2
0
0
2
0
1
1
0
0
0
0
0
0
5
0
0
2
2
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
1
0
6
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
3
0
0
1
0
1
0
0
2
0
1
0
0
0
2
2
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
1
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
2
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
2
0
1
0
1
0
0
1
1
0
2
0
0
0
0
3
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
2
0
0
0
0
4
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
3
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
1
1
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
1
3
1
0
0
0
0
0
1
0
1
0
0
1
0
2
0
2
0
1
0
0
2
0
2
0
0
0
0
1
1
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
1
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
2
2
1
1
0
2
2
0
0
0
0
0
0
0
2
0
1
2
0
2
0
0
1
3
0
0
2
0
0
1
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
3
0
0
1
1
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
1
0
0
0
0
0
0
1
0
2
0
0
0
1
2
0
1
2
0
0
0
0
0
0
2
1
0
0
0
3
2
0
0
0
0
0
2
1
1
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
2
0
0
2
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
1
1
0
0
0
0
2
0
2
0
1
0
2
1
0
0
0
2
0
5
6
0
1
0
0
1
0
0
1
0
2
0
0
0
0
3
2
1
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
2
0
1
1
0
0
0
0
2
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
1
0
0
0
0
2
0
0
0
1
1
0
1
2
0
0
0
0
0
0
2
1
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
3
0
2
0
3
0
1
2
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
2
1
0
0
0
2
0
2
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
2
2
2
0
0
2
2
0
0
2
0
2
0
0
2
2
0
1
3
1
0
3
0
0
0
0
0
0
2
1
0
2
0
0
6
0
3
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
5
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
2
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
2
3
1
0
1
0
0
0
0
1
2
2
0
0
1
0
3
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
1
0
0
2
2
0
0
0
2
1
1
0
0
0
0
2
0
0
1
3
0
0
0
0
0
0
0
0
0
2
2
2
0
2
2
0
0
2
0
0
0
2
0
2
0
1
2
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
2
3
1
0
0
1
1
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
1
0
2
1
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
2
1
1
2
2
0
0
2
0
0
0
2
0
0
3
0
0
0
2
1
0
0
0
1
0
2
0
0
0
0
2
2
0
1
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
1
0
0
1
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
2
2
2
0
0
0
0
2
0
0
0
0
0
4
0
0
2
1
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
1
0
2
0
0
0
2
2
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
3
0
0
3
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
3
0
1
0
1
0
0
0
1
2
1
0
0
2
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
3
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
2
0
2
0
0
0
1
0
0
2
0
2
0
2
0
2
0
0
0
2
0
2
2
0
0
0
0
2
0
1
1
0
1
0
0
0
2
0
3
0
2
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
3
0
2
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
2
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
2
2
0
0
0
2
1
0
0
0
0
2
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
2
0
2
0
0
0
0
0
3
2
0
1
1
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
2
0
2
3
0
0
0
3
3
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
1
0
0
1
2
1
1
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
2
2
0
0
1
0
1
0
1
0
0
0
0
0
1
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
2
0
1
0
0
4
0
0
0
1
0
0
1
1
1
1
0
2
0
1
0
0
0
2
4
2
2
0
0
0
2
0
1
1
1
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
3
1
0
6
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
4
2
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
2
0
0
0
1
1
0
2
0
0
2
2
2
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
2
1
0
0
0
0
2
0
0
0
1
2
0
1
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
6
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
5
0
0
1
2
0
0
0
1
0
1
0
0
2
0
2
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
1
1
0
1
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
1
2
0
0
0
2
2
0
0
2
0
0
1
2
0
2
1
0
1
0
0
1
0
2
0
0
1
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
2
2
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
4
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
6
2
2
0
0
2
1
0
3
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
1
1
0
0
2
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
2
0
3
0
0
0
2
0
0
1
0
1
0
0
2
2
0
0
1
0
0
1
0
1
0
0
0
0
2
2
0
0
0
1
0
2
1
0
0
0
0
0
2
0
1
1
0
1
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
2
2
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
1
0
1
0
5
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
1
5
0
0
0
1
0
2
2
2
1
0
2
0
0
1
2
0
2
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
1
2
0
0
0
0
0
0
0
1
2
0
0
1
2
1
2
2
1
0
0
2
0
0
2
0
0
1
2
2
0
0
0
0
2
0
0
0
0
0
7
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
2
0
3
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
2
0
0
2
3
0
0
0
0
0
3
0
2
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
3
2
0
0
0
0
0
2
0
0
2
1
1
0
0
0
0
0
1
1
0
0
1
2
1
2
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
2
0
0
1
0
0
0
1
1
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
2
2
2
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
4
1
0
0
0
0
0
0
1
2
0
0
0
1
0
0
1
0
0
0
0
4
0
0
0
0
2
0
1
0
2
0
2
0
0
2
0
0
2
1
2
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
1
3
0
0
3
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
2
2
2
0
2
0
1
1
0
1
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
1
0
1
0
0
0
0
1
0
0
0
2
4
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
2
1
1
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
1
2
0
2
2
2
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
4
1
0
1
0
0
0
0
2
0
0
0
0
0
2
2
0
0
1
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
2
0
0
2
0
2
0
0
3
0
0
0
0
2
0
0
0
0
0
1
2
1
0
0
0
2
3
2
0
0
0
0
0
0
2
1
0
0
4
1
0
0
0
1
0
2
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
2
0
0
0
3
0
2
3
0
0
0
0
2
0
0
0
0
1
0
2
1
0
0
1
0
1
0
0
0
2
0
0
0
0
1
0
2
0
1
0
0
1
0
2
0
0
0
0
0
0
2
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
5
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
2
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
4
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
1
0
0
0
1
0
3
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
3
0
0
0
0
2
0
0
1
0
0
1
0
1
5
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
1
0
0
0
1
1
0
0
0
1
3
0
0
0
0
0
3
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
1
0
0
1
0
0
2
0
0
5
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
1
0
1
0
2
1
2
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
3
2
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
1
0
0
0
0
0
0
13
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
2
0
0
2
1
0
2
1
0
1
0
1
0
0
0
0
2
0
1
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
3
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
3
0
1
1
1
2
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
2
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
1
2
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
2
2
0
0
0
0
0
2
3
0
0
0
0
0
0
3
0
2
0
2
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
2
1
0
0
1
0
2
0
0
2
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
2
0
0
2
2
0
2
1
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
1
0
1
0
4
0
2
2
1
0
2
0
0
0
0
0
0
3
1
0
0
1
0
2
0
0
2
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
1
0
0
0
0
3
0
1
0
0
1
2
0
2
0
0
2
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
2
0
0
2
0
0
0
1
0
0
1
4
1
0
0
0
0
0
0
1
2
0
1
0
2
3
0
0
0
0
0
0
2
1
1
0
1
0
0
0
0
0
0
2
2
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
2
2
0
0
1
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
2
0
0
0
3
0
0
0
0
0
1
0
0
0
0
1
2
1
0
4
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
2
0
0
0
1
0
0
1
0
2
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
2
0
0
0
0
2
0
2
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
1
0
0
3
0
2
1
1
0
0
2
2
0
0
0
0
2
0
0
1
0
2
2
1
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
1
2
0
1
0
0
2
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
1
1
1
2
1
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
2
0
0
0
0
3
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
2
1
0
0
5
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
1
0
2
0
1
0
2
0
0
0
0
0
0
2
0
0
2
1
0
1
0
2
0
0
2
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
1
1
0
1
0
0
0
0
0
0
1
0
0
2
0
2
2
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
4
0
0
0
0
2
0
0
0
0
0
3
1
0
1
0
1
1
0
0
2
0
0
2
0
2
0
0
0
6
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
1
0
3
0
0
0
0
0
0
0
2
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
3
2
1
0
2
0
0
0
0
2
0
0
2
2
0
1
0
0
1
0
0
0
5
0
0
0
1
0
0
0
0
4
0
2
2
0
1
1
0
1
0
3
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
1
1
2
1
0
0
0
0
0
4
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
1
0
1
1
2
0
0
1
0
2
0
0
1
0
0
0
2
0
5
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
1
0
0
0
0
1
0
1
0
0
0
2
0
0
2
0
2
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
2
1
0
0
0
0
2
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
2
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
2
1
0
0
2
0
3
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
2
0
0
1
2
0
0
0
3
0
0
0
2
2
0
0
0
0
0
0
1
0
1
0
2
2
0
3
0
0
2
0
2
0
0
0
0
1
0
0
0
0
1
2
0
1
2
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
2
3
1
0
1
0
0
0
0
0
0
1
2
0
0
0
2
0
2
0
1
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
3
0
1
0
2
0
0
0
0
1
0
2
0
0
0
2
1
0
0
0
2
0
0
0
0
0
2
1
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
3
0
1
0
0
1
0
0
0
2
3
0
1
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
2
0
2
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
2
0
2
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
2
0
1
0
0
2
0
3
0
0
0
0
2
2
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
1
0
0
3
0
2
0
1
0
0
1
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
1
2
0
0
3
2
2
0
1
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
3
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
5
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
3
1
0
0
0
0
0
1
1
0
0
0
1
0
1
0
2
0
0
0
2
1
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
3
0
0
0
0
2
0
0
7
5
0
0
0
0
2
0
1
0
0
1
0
0
0
1
0
3
2
0
0
0
1
0
0
0
0
0
1
0
4
1
0
1
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
2
0
1
2
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
10
4
1
0
0
3
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
1
1
0
0
0
2
2
0
0
0
2
0
0
1
0
0
1
0
2
0
0
0
8
0
1
2
1
0
0
0
0
3
1
0
0
0
0
0
3
1
2
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
6
0
0
0
3
2
0
0
2
0
0
0
0
2
2
0
0
0
3
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
3
0
2
0
0
1
0
0
0
0
2
0
0
1
0
1
0
1
0
0
3
0
2
0
2
0
0
0
0
2
2
0
0
0
0
2
0
0
3
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
1
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
3
0
0
0
0
0
1
0
2
0
6
0
0
0
0
1
0
0
0
2
1
2
0
0
1
0
2
0
0
1
0
0
6
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
1
0
0
2
1
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
2
4
0
0
0
0
2
1
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
2
2
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
1
2
0
1
0
0
0
0
0
0
4
1
0
2
0
2
1
0
0
0
1
0
0
1
0
0
2
0
2
0
0
1
2
0
2
2
2
1
1
0
0
0
1
0
0
2
1
0
1
0
0
2
2
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
2
1
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
1
1
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
2
2
0
1
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
5
0
1
0
0
2
0
0
0
1
0
0
0
1
1
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
1
1
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
2
0
0
0
2
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
1
0
1
0
3
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
1
1
0
1
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
4
0
0
0
3
0
0
0
0
0
4
1
0
0
0
0
1
1
0
0
2
2
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
2
0
0
2
0
0
1
0
0
0
2
0
1
0
0
0
0
0
2
0
2
1
1
0
0
1
2
0
1
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
4
2
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
1
5
0
0
0
2
1
0
2
1
0
1
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
2
0
2
2
2
1
0
0
0
0
0
0
1
0
1
1
2
2
0
0
0
1
0
1
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
1
0
1
0
0
0
2
0
1
1
0
0
0
0
1
0
0
0
0
0
1
2
2
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
2
0
0
2
0
0
13
2
1
0
0
0
0
6
0
0
0
0
0
0
2
0
2
1
0
0
2
0
0
0
0
0
0
0
1
0
2
2
2
0
0
0
0
0
0
2
2
2
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
1
0
2
0
1
1
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
2
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
1
0
2
0
1
1
0
0
4
1
0
2
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
1
1
0
2
2
2
2
1
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
2
0
0
5
1
1
2
1
2
0
0
0
0
0
0
0
0
0
1
3
3
0
0
1
0
0
0
0
0
3
1
0
0
0
2
0
0
0
0
0
0
1
1
2
0
0
0
0
2
0
0
0
2
0
0
5
0
1
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
1
0
0
0
1
0
0
3
0
2
0
0
1
0
0
0
1
1
0
2
0
0
0
3
2
0
0
0
0
1
0
0
0
1
0
1
1
1
0
0
0
0
0
1
2
1
0
0
1
0
0
0
1
0
1
0
0
0
2
0
2
0
0
0
0
1
0
2
2
0
1
0
1
0
0
0
0
0
0
2
0
0
1
0
1
0
0
17
1
0
2
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
1
0
2
0
1
0
2
0
0
0
0
0
2
0
0
0
1
1
0
1
0
3
0
0
0
1
0
1
0
0
0
0
2
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
2
2
1
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
3
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
3
0
2
0
0
0
0
2
1
2
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
3
0
1
0
0
0
0
1
0
1
0
0
1
2
5
0
0
0
0
0
1
1
4
0
0
0
0
2
0
2
2
0
0
0
0
0
1
0
0
2
2
0
2
0
0
2
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
3
0
0
2
0
0
1
4
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
2
0
0
0
1
0
1
2
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
1
1
0
0
0
0
0
2
0
0
3
0
1
1
1
6
0
2
1
1
0
2
0
0
2
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7
0
12
1
0
2
0
1
0
0
0
0
0
0
0
0
1
1
0
1
1
1
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
5
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
1
2
1
1
0
2
0
0
2
2
0
0
0
0
0
0
1
1
3
0
0
0
0
0
1
0
4
0
0
0
1
2
1
1
0
1
2
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
1
3
1
2
0
0
0
0
1
0
0
9
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
3
2
0
0
2
3
1
1
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
1
2
0
0
2
0
2
2
1
0
0
0
0
0
0
0
2
1
1
3
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
2
0
0
2
0
0
1
0
0
2
0
0
0
0
2
0
2
2
0
0
0
0
1
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
1
1
0
2
1
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
3
3
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
2
2
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
4
0
1
0
0
1
2
0
0
0
1
0
1
0
0
0
0
0
0
2
1
1
0
1
0
0
0
0
0
0
1
0
0
2
0
0
2
1
4
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
3
0
2
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
2
2
1
0
0
0
11
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
2
0
2
2
2
0
0
1
0
0
0
0
1
0
0
0
0
2
1
0
0
1
1
0
2
0
0
0
0
1
0
2
1
1
2
0
0
2
0
0
0
2
0
0
0
0
2
0
2
0
2
1
2
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
2
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
5
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
1
2
0
0
0
0
0
2
0
0
1
4
2
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
1
4
2
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
1
0
0
0
2
0
2
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
7
0
2
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
2
0
0
0
1
0
0
1
0
2
2
0
0
1
0
0
0
1
0
0
0
1
4
0
0
0
0
2
1
2
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
1
0
0
0
0
2
2
0
2
0
0
2
2
0
0
0
1
0
1
0
0
0
2
1
2
0
0
2
0
1
0
0
5
1
2
0
1
0
2
0
1
0
1
0
0
1
1
0
1
3
2
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
3
0
0
0
2
0
4
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
3
1
0
0
0
1
0
0
2
1
0
0
0
1
0
0
0
1
1
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
2
0
2
0
0
2
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
1
2
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
3
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
4
0
2
0
2
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
2
0
0
1
2
0
4
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
1
0
3
1
0
2
0
1
0
0
1
0
0
0
0
0
1
4
2
1
0
0
0
0
2
0
1
0
0
1
0
2
1
0
0
0
0
2
0
0
0
0
0
1
2
3
0
1
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
1
2
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
2
2
2
0
0
0
0
4
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
3
0
0
0
1
0
0
0
1
0
3
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
4
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
1
1
0
2
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
1
2
1
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
3
1
1
0
2
0
0
0
0
0
0
2
0
0
0
3
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
1
0
2
0
0
0
0
1
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
2
0
0
1
0
0
2
0
0
0
0
0
0
4
1
0
0
0
0
0
1
0
0
0
1
0
2
0
1
2
0
0
0
1
0
2
0
2
1
0
0
2
0
0
0
1
1
0
3
1
0
0
0
0
0
0
2
0
0
0
1
0
0
2
2
0
2
1
2
1
0
0
0
2
0
1
0
0
0
0
0
0
3
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
1
0
1
0
0
0
1
1
2
0
3
0
0
1
1
1
0
0
0
0
0
2
0
0
1
0
0
4
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
2
0
0
2
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
2
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
3
0
4
0
0
0
0
2
0
1
0
1
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
1
0
0
1
1
0
0
0
0
2
2
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
6
0
0
1
3
3
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
6
0
0
1
0
4
1
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
3
0
0
0
0
0
1
2
2
0
0
0
1
0
1
1
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
2
2
0
2
0
0
0
2
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
3
0
0
0
0
0
0
0
0
0
1
0
0
4
0
3
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
2
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
1
1
0
0
2
0
0
2
1
0
0
1
2
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
4
0
2
1
1
1
2
0
0
0
0
0
0
0
2
1
0
0
1
4
0
0
2
0
2
0
0
2
0
1
0
0
0
1
1
0
0
4
0
0
0
0
0
0
0
0
4
0
0
0
2
1
0
0
2
3
2
0
0
2
0
0
2
0
1
0
1
0
0
0
3
1
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
1
2
1
1
0
0
0
0
5
0
3
0
0
0
0
0
2
0
3
0
1
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
1
1
0
0
0
0
1
0
2
0
2
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
2
0
0
0
1
0
1
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
5
0
0
2
0
0
2
4
2
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
1
0
0
1
1
1
0
1
2
9
0
0
0
0
0
4
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
2
1
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
1
2
0
2
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
2
0
0
0
0
1
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
4
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
2
0
0
0
2
1
0
1
0
1
2
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
2
0
0
0
2
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
2
1
0
0
0
0
3
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
1
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
3
0
2
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
1
0
0
0
0
0
0
0
1
0
4
0
1
0
5
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
2
2
0
1
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
2
3
1
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
2
0
0
0
1
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
1
0
0
0
0
2
1
0
0
0
0
2
1
1
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
3
2
1
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
2
2
1
1
0
1
0
0
0
3
0
0
0
0
0
1
0
0
0
1
0
1
0
1
2
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
2
2
2
0
0
0
0
1
3
0
0
1
0
0
0
0
2
2
2
1
1
0
0
0
1
0
0
1
3
0
1
0
0
0
0
0
0
0
0
1
0
0
1
3
1
0
0
0
0
1
0
2
0
2
0
0
0
2
0
0
0
0
2
0
0
2
0
0
2
0
0
1
0
0
0
2
0
1
0
1
1
0
0
0
0
0
0
1
1
0
2
0
2
0
1
0
0
0
0
0
1
0
1
0
3
0
0
0
0
1
0
0
1
0
0
1
0
0
0
3
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
2
3
0
0
4
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
1
1
3
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
1
0
0
2
0
2
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
2
0
1
0
0
0
2
2
2
0
0
0
1
2
0
3
0
2
0
2
2
0
0
2
1
0
0
0
1
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
2
1
0
0
1
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
5
2
0
0
0
0
0
0
1
1
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
2
2
2
1
0
0
3
0
0
3
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
4
0
0
0
1
0
0
0
0
1
0
0
5
2
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
2
2
0
0
0
0
0
0
3
1
0
1
2
0
1
0
0
2
1
0
0
0
2
0
0
0
2
0
1
0
0
2
2
0
2
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
1
2
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
2
0
0
1
0
2
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
1
2
0
4
0
0
0
2
0
0
1
1
0
0
0
2
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
3
1
1
2
2
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
4
0
1
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
5
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
1
1
0
2
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
1
2
1
0
3
1
2
0
3
0
0
1
1
1
0
0
1
0
2
1
1
1
0
0
0
0
0
3
0
2
0
0
0
0
0
0
1
0
1
1
1
0
0
0
1
1
0
3
0
0
0
0
3
2
0
4
0
2
0
1
0
1
0
0
1
5
0
0
0
0
0
0
0
2
0
1
1
0
6
0
0
1
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
3
2
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
6
0
4
0
0
0
0
1
0
2
0
2
0
2
2
0
0
0
2
3
0
0
2
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
3
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
2
0
1
0
0
2
0
2
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
1
1
0
1
1
1
0
0
1
0
0
1
0
0
1
2
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
2
0
0
0
2
1
2
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
1
0
0
2
1
0
2
0
0
0
2
1
1
0
0
2
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
2
0
0
0
2
0
0
0
2
2
0
2
0
0
0
1
0
0
0
0
0
0
1
2
1
1
0
0
0
2
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
4
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
4
0
0
0
0
2
0
0
1
1
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
1
1
2
1
0
0
0
0
1
0
2
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
2
0
4
0
0
0
0
0
0
0
2
1
1
0
1
0
0
0
0
0
0
0
0
0
2
2
0
1
0
2
0
3
0
0
0
4
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
1
2
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
1
0
2
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
2
1
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
3
0
0
0
1
0
2
0
2
0
1
0
3
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
3
0
0
0
0
0
3
2
0
2
2
0
2
2
1
0
0
0
1
1
0
0
2
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
4
0
0
0
0
0
1
2
4
0
4
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
2
0
2
0
0
0
0
2
0
0
0
3
0
2
1
0
0
0
0
2
1
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
12
0
0
1
0
0
0
2
0
0
2
1
0
0
0
2
0
1
0
1
2
0
1
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
2
0
0
0
2
0
0
1
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
6
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
4
0
0
0
2
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
5
1
2
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
2
0
0
2
4
0
0
0
0
1
1
0
0
0
0
2
0
0
0
1
1
2
0
0
0
0
0
2
2
0
0
4
2
2
1
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
1
2
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
1
2
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
3
0
0
0
0
0
2
0
0
0
0
0
2
2
0
1
0
0
2
0
0
1
0
0
0
2
0
0
0
0
1
1
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
1
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
2
0
0
0
0
0
0
2
0
0
1
0
3
0
0
0
0
2
0
2
1
0
2
2
0
0
0
0
0
0
1
0
0
0
2
2
1
0
0
0
0
0
0
0
0
1
0
0
5
0
1
3
0
0
0
0
3
0
0
0
2
2
0
0
0
0
2
0
0
1
0
0
0
1
2
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
1
1
2
0
2
0
0
0
0
0
0
2
2
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
2
3
1
1
0
2
0
0
1
1
0
2
0
0
2
0
0
2
0
0
1
0
3
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
1
0
0
0
2
1
0
0
0
0
5
0
0
1
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
1
0
3
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
2
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
3
0
0
1
0
13
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
2
2
0
2
2
1
2
1
1
0
1
0
0
2
0
0
1
0
0
0
0
1
1
1
2
2
0
1
0
0
0
0
4
0
0
0
1
0
2
0
0
1
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
5
1
1
0
0
0
1
2
0
0
0
1
1
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
1
1
1
1
1
0
3
2
0
3
1
0
0
1
2
0
0
0
2
0
1
0
0
0
0
0
0
2
0
1
2
0
2
3
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
2
1
0
0
0
3
0
0
0
0
0
1
0
1
2
0
0
1
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
3
0
0
0
0
2
0
0
1
1
1
2
0
0
0
0
0
2
0
1
0
0
0
3
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
1
0
0
2
0
2
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
2
1
4
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
4
0
0
0
0
0
0
2
0
1
3
0
1
0
0
0
1
1
2
2
0
0
0
3
2
0
0
2
0
0
0
0
0
0
1
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
2
0
1
0
0
0
0
0
2
1
0
3
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
1
1
0
0
2
0
0
0
0
2
0
0
2
0
0
2
1
0
0
2
2
0
3
2
0
0
0
2
0
2
0
0
1
0
0
1
1
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
3
0
0
1
0
0
0
2
0
0
0
0
0
0
2
1
1
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
2
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
2
0
2
0
0
0
0
2
0
0
0
0
0
2
2
0
1
1
0
1
0
0
0
0
0
2
4
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
2
2
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
1
1
0
2
0
0
0
1
0
0
0
0
0
2
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
2
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
2
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
3
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
2
0
2
3
4
1
0
0
0
2
2
0
0
1
0
1
0
2
0
2
2
2
2
5
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
2
2
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
2
1
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
3
0
0
2
2
0
0
0
2
2
3
0
0
1
1
0
0
0
0
0
1
0
2
0
2
0
1
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
3
0
0
0
1
0
0
0
0
1
0
5
0
0
0
1
0
1
2
0
0
0
0
2
0
1
0
0
0
0
0
0
3
0
2
0
2
0
1
2
0
1
0
1
2
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
2
0
1
2
0
1
1
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
1
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
3
3
0
1
1
0
0
2
0
2
0
0
0
0
0
1
0
1
2
0
0
0
0
2
2
0
0
2
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
1
0
2
0
0
0
0
1
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
3
1
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
2
0
1
0
0
0
2
0
0
1
1
0
0
1
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
2
1
0
2
0
0
0
2
2
0
1
1
0
0
0
2
0
0
1
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
3
0
2
3
0
0
0
0
3
0
0
1
1
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
1
2
1
0
0
1
0
0
0
2
0
2
2
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
2
2
0
0
5
0
0
2
0
0
0
2
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
3
0
0
2
0
0
0
0
3
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
2
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
1
0
0
0
2
0
0
1
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
1
0
2
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
2
0
1
1
0
0
1
0
0
0
0
2
0
0
0
0
0
3
0
2
1
0
0
0
0
2
0
0
0
0
2
1
0
0
1
1
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
1
4
0
0
1
0
2
0
0
2
0
0
0
0
0
2
0
0
9
0
0
0
1
0
0
1
0
2
0
0
3
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
2
0
0
0
3
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
1
0
0
0
2
2
0
0
0
2
0
0
4
1
0
3
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
1
2
0
0
0
0
2
1
0
0
0
2
0
0
2
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
3
0
0
2
0
1
2
0
0
2
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
2
3
0
0
0
0
0
1
0
3
0
0
0
0
0
0
2
0
1
0
0
2
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
3
0
1
0
1
1
2
0
2
0
0
1
0
0
0
1
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
9
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
2
0
0
0
2
0
0
0
1
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
2
1
0
0
2
0
2
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
2
1
0
0
1
2
2
0
0
2
0
0
0
0
0
0
0
2
4
0
0
0
0
5
0
2
1
0
0
0
2
0
0
0
0
0
2
2
0
0
0
2
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
7
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
1
6
0
0
0
1
0
0
0
2
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
2
0
0
3
0
2
1
1
0
0
0
0
2
1
0
2
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
2
2
0
0
0
0
0
0
2
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
2
2
0
0
1
1
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
1
2
0
1
0
2
0
0
0
1
0
0
0
1
0
0
0
1
0
2
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
1
1
2
0
1
0
1
0
0
0
0
0
3
2
0
1
0
0
0
0
0
0
2
0
0
11
5
0
1
0
2
0
0
0
2
0
2
0
0
2
0
2
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
1
5
0
2
0
0
0
2
0
0
2
0
1
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
3
0
2
0
0
3
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
2
2
1
0
1
1
2
2
0
3
0
0
0
1
2
0
0
0
3
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
1
0
3
7
0
2
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
2
4
0
1
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
2
2
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
5
0
2
0
1
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
4
1
2
2
0
3
1
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
3
1
2
0
5
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
3
3
0
0
1
0
0
2
0
2
2
0
0
0
0
2
0
2
0
4
2
0
2
1
2
0
0
0
0
1
1
2
0
0
2
0
0
1
0
0
0
2
0
2
0
0
2
1
0
0
0
1
0
0
2
0
2
1
0
2
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
4
0
0
0
0
1
0
0
0
1
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
2
0
1
1
2
0
0
0
0
0
1
4
1
0
0
0
0
0
2
0
0
2
0
3
1
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
1
0
1
2
0
2
1
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
2
0
3
0
0
1
1
0
2
0
0
0
0
2
2
0
0
0
0
0
0
1
1
0
2
0
0
0
10
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
1
2
2
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
1
3
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
1
1
0
2
1
0
0
0
1
1
0
0
0
0
2
1
0
0
0
1
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
5
0
0
0
2
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
3
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
4
0
0
1
10
0
0
0
1
2
0
3
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
5
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
1
0
0
0
2
0
0
0
3
0
1
0
0
2
0
0
1
0
0
0
0
0
0
5
0
2
0
0
2
0
0
0
2
0
3
2
0
0
0
0
1
0
2
3
1
0
1
0
1
0
0
0
2
0
0
2
0
0
4
1
1
0
0
0
0
0
1
0
0
0
0
0
4
0
0
2
2
0
0
0
0
0
2
0
2
0
0
0
0
2
2
0
0
0
2
2
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
1
1
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
2
1
0
3
0
0
2
2
0
0
3
0
0
0
0
0
1
3
0
0
0
0
0
0
2
0
0
1
0
0
1
0
6
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
3
0
2
2
1
2
0
0
0
0
2
0
1
3
0
0
0
0
0
0
3
2
2
0
2
0
0
0
2
0
0
0
0
4
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
2
0
0
2
1
0
0
0
1
0
0
0
2
0
2
0
0
4
0
0
1
0
2
0
2
0
0
0
3
0
3
2
2
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
1
2
0
0
0
0
0
1
2
0
2
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
2
1
0
0
0
1
0
2
0
1
0
0
0
0
0
1
0
1
0
2
0
3
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
1
1
0
1
1
0
0
0
0
2
0
0
0
1
1
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
1
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
1
3
0
0
0
1
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
2
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
2
0
2
0
0
2
2
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
2
2
2
0
2
2
2
0
0
0
2
0
0
0
2
1
1
1
1
0
0
2
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
1
0
2
0
0
0
1
0
1
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
2
0
1
0
1
1
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
1
0
1
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
3
0
0
0
0
0
2
0
2
2
0
1
0
2
0
0
0
1
0
1
0
0
1
2
0
0
0
0
0
0
2
0
0
3
0
0
0
2
0
0
2
0
0
0
0
2
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
2
0
1
0
0
0
1
8
0
0
0
1
0
1
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
2
1
0
0
0
1
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
2
0
0
4
0
1
2
0
0
0
0
0
0
0
1
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
2
3
0
0
0
0
1
0
2
1
0
0
2
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
2
2
0
7
2
0
1
2
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
1
0
0
2
2
1
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
2
0
2
0
1
0
2
0
2
1
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
3
1
2
1
0
0
2
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
4
0
1
0
0
0
0
3
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
3
1
2
0
0
0
0
0
2
0
2
0
1
2
2
0
0
0
3
0
0
0
0
1
0
2
1
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
3
0
0
1
2
2
0
0
0
0
0
0
0
0
1
1
0
0
0
2
1
0
2
0
0
1
0
0
0
0
0
0
3
1
0
0
2
0
2
0
0
0
0
0
3
0
0
1
3
1
2
2
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
1
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
2
0
0
0
3
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
1
0
0
0
0
2
0
0
0
2
0
1
1
0
0
2
0
0
0
0
0
0
0
3
1
2
1
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
3
0
0
0
0
0
1
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
1
0
2
0
0
0
0
0
2
0
0
0
4
0
0
2
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
1
1
0
0
0
0
3
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
2
2
0
1
0
0
0
0
0
2
1
2
0
0
1
2
0
1
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
8
4
0
0
1
0
2
0
0
2
0
2
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
2
1
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
2
0
3
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
2
0
0
3
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
1
0
1
0
1
0
1
0
0
0
2
13
0
0
1
0
0
0
0
1
1
0
0
3
0
0
0
0
1
2
0
0
0
0
0
0
1
0
1
0
0
1
1
2
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
1
1
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
1
2
0
1
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
3
2
0
2
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
3
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
3
0
0
1
0
0
0
1
0
3
0
0
2
0
0
1
0
0
0
0
2
0
1
0
2
0
1
0
2
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
2
1
0
0
2
1
3
2
0
2
0
0
2
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
1
1
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
2
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
3
0
1
1
2
1
0
0
0
0
0
0
2
3
0
2
0
0
0
0
0
0
1
0
2
1
2
1
2
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
2
0
1
2
2
0
2
0
2
2
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
3
0
0
0
0
6
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
2
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
2
2
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
1
0
2
1
0
0
0
0
0
2
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
3
0
3
2
2
2
0
0
2
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
1
0
0
2
1
0
0
0
0
0
1
0
2
1
0
0
1
0
0
0
1
3
0
1
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
5
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
3
0
2
1
2
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
2
3
0
0
2
0
0
0
0
0
0
1
2
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
2
0
0
1
1
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
1
0
0
2
0
0
0
0
1
0
0
0
2
0
1
0
1
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
1
0
0
0
3
0
2
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
2
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
2
1
0
0
0
2
0
2
0
0
0
1
0
0
0
1
0
0
2
3
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
5
0
0
0
2
0
1
0
0
0
0
0
2
1
0
0
2
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
1
0
0
0
0
2
0
2
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
2
6
0
0
0
1
1
0
2
0
0
0
0
0
1
1
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
2
1
0
1
0
0
1
2
2
0
0
2
0
4
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
1
0
0
0
0
0
1
0
0
1
0
2
0
0
2
2
0
1
2
0
0
0
0
2
0
2
1
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
2
0
2
0
0
0
2
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
3
2
0
1
0
0
0
1
2
1
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
1
0
0
0
1
0
0
0
0
0
0
2
1
0
2
3
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
2
1
0
0
2
0
0
1
0
2
0
1
0
1
0
0
0
2
0
0
0
2
0
0
0
0
1
1
0
0
0
0
6
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
2
0
1
0
0
2
0
0
0
0
1
0
2
0
0
0
0
1
0
1
2
3
0
0
0
0
0
0
0
2
1
2
0
0
2
2
0
0
2
2
0
2
0
1
0
2
0
0
2
0
2
0
2
0
0
3
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
2
3
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
1
1
0
0
2
0
0
2
0
0
0
0
0
0
1
3
0
0
2
0
0
1
0
0
0
0
0
0
1
1
2
2
2
0
0
0
3
0
1
0
0
0
2
1
0
0
1
0
2
1
0
0
0
0
0
0
1
2
0
1
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
2
0
0
0
0
1
0
0
0
2
0
2
0
2
0
0
0
0
2
2
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
1
0
2
2
2
0
0
9
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
1
2
0
0
0
1
0
0
1
0
1
0
0
1
2
0
0
2
0
0
0
0
2
1
2
0
0
0
2
0
3
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
3
0
0
0
0
0
2
0
0
2
1
0
1
0
1
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
1
0
0
2
1
0
1
1
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
1
2
0
6
0
0
3
4
0
0
2
2
2
0
0
0
2
1
0
2
2
0
2
2
0
2
0
0
0
0
1
2
1
2
0
1
1
0
0
0
1
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
2
0
2
2
1
0
0
0
2
3
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
2
2
2
1
0
0
0
0
0
0
1
2
2
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
3
0
0
0
0
0
3
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
5
0
1
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
1
0
2
0
0
0
0
0
2
2
2
0
1
0
1
0
1
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
11
0
0
0
0
0
0
1
3
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
1
0
0
1
0
0
0
0
0
2
1
0
1
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
1
0
0
2
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
1
0
2
0
1
0
0
0
2
1
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
6
0
2
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
1
1
1
0
3
2
2
0
0
0
0
0
1
2
0
0
0
0
2
0
1
0
0
0
1
2
0
1
0
0
2
2
0
0
0
1
0
0
0
0
1
1
2
2
0
1
0
1
0
2
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
2
2
1
1
0
0
1
1
0
0
0
1
2
2
4
2
0
2
2
3
1
0
0
0
0
0
2
0
2
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
3
0
0
0
1
0
0
1
0
2
0
2
0
0
2
0
1
1
0
0
0
0
2
2
0
0
0
0
0
2
2
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
2
1
1
0
0
1
0
2
0
1
2
0
3
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
3
0
0
1
6
0
0
0
0
0
0
0
3
1
0
2
4
2
0
0
0
1
0
1
0
0
2
0
0
0
0
2
2
2
0
0
2
0
0
2
0
0
0
0
3
0
2
0
0
2
0
0
1
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
1
0
1
0
0
0
0
0
2
0
2
0
2
1
1
0
1
0
0
1
0
0
2
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
1
2
0
0
1
0
0
0
2
0
0
2
0
0
0
2
0
0
0
2
0
0
0
1
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
2
0
0
0
0
0
0
3
0
2
0
1
0
0
0
1
1
1
0
0
0
0
2
1
0
0
0
2
2
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
2
0
0
0
1
0
2
1
2
0
0
0
0
2
0
2
0
1
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
2
1
1
0
0
1
2
0
0
0
0
2
0
0
0
2
1
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
1
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
3
0
0
1
0
0
1
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
2
0
2
1
0
0
0
3
2
3
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
1
0
0
3
0
2
0
0
0
0
0
0
0
1
2
1
0
1
0
0
4
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
2
0
0
3
2
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
1
2
2
0
0
0
1
0
0
2
0
0
0
0
1
1
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
3
1
1
2
2
1
1
0
0
2
0
0
0
1
0
0
3
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
1
0
0
2
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
1
0
0
1
0
0
2
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
3
3
0
0
0
1
1
0
1
2
0
0
0
2
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
3
0
0
3
0
0
2
0
0
0
0
0
2
0
0
0
1
1
2
1
0
0
0
2
0
0
0
1
0
1
1
0
0
0
0
0
3
0
0
0
0
0
0
4
2
0
2
0
0
2
1
0
0
0
2
0
0
1
2
0
0
0
0
0
1
2
1
2
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
3
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
3
2
0
0
0
0
2
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
2
0
0
0
0
1
2
0
0
2
0
0
1
0
0
0
2
1
1
0
0
1
2
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
3
2
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
4
0
0
1
0
0
2
1
0
0
0
0
0
1
1
2
0
0
0
0
0
1
0
0
0
1
0
1
1
1
0
1
0
0
0
0
0
2
0
7
0
0
0
0
0
0
3
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
2
0
0
1
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
1
2
0
1
1
0
2
0
0
0
2
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
1
1
0
0
0
3
0
0
2
0
2
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
3
0
2
1
0
0
0
0
0
0
2
2
1
0
0
1
0
0
0
0
7
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
3
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
2
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
1
0
1
0
0
0
1
1
0
0
0
1
1
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
1
0
0
0
2
1
3
1
1
0
1
1
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
2
3
0
0
0
0
2
0
1
0
0
0
1
1
1
2
0
0
0
0
0
1
0
0
0
0
2
0
1
2
3
0
0
0
0
0
2
0
0
1
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
2
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
4
0
0
0
1
0
1
1
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
2
0
1
0
0
1
2
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
3
0
3
0
0
1
0
0
2
1
0
0
0
0
0
0
2
0
1
4
1
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
1
4
0
2
0
0
0
0
1
0
11
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
2
1
4
3
1
0
0
0
3
0
2
0
0
0
0
0
0
0
1
2
8
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
2
0
0
0
0
1
2
1
1
0
2
0
0
2
0
3
0
2
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
2
0
0
1
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
2
1
1
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
1
0
0
1
3
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
2
4
0
0
0
0
0
0
1
0
3
2
2
3
1
0
0
2
0
2
0
0
0
2
0
0
1
0
0
0
0
2
0
0
2
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
1
0
2
0
0
1
0
0
2
0
2
0
0
0
0
0
0
1
1
0
1
1
0
2
0
0
2
0
0
0
0
1
2
0
0
0
0
1
0
3
2
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
2
2
1
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
2
0
2
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
2
1
1
0
1
1
0
0
0
0
0
2
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
2
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
6
0
0
0
2
1
0
1
0
0
1
2
2
0
3
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
3
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
2
1
0
1
3
0
0
0
0
0
1
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
1
1
0
0
0
0
0
2
0
2
2
0
1
0
0
0
0
0
0
2
0
2
0
0
0
4
1
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
1
1
1
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
3
0
0
2
0
1
1
0
4
2
1
0
3
0
0
0
0
0
0
2
0
2
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
1
0
0
2
0
2
0
0
2
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
1
2
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
2
2
2
1
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
3
1
1
1
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
1
2
0
0
0
0
1
0
0
1
0
0
1
1
3
0
0
2
2
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
3
0
0
0
2
0
2
0
0
0
0
0
0
0
0
3
2
0
0
2
1
0
2
0
0
2
0
0
1
0
0
1
2
0
0
0
0
0
0
1
1
1
0
3
2
0
0
0
0
0
0
0
0
0
0
3
0
0
1
2
0
0
0
0
0
0
3
1
1
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
3
2
1
0
1
0
3
1
0
0
0
0
0
0
0
0
0
1
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
1
0
1
1
0
0
0
0
1
4
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
3
0
1
2
0
1
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
1
2
0
0
2
0
0
0
0
1
0
0
0
0
2
6
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
2
0
0
0
2
2
0
1
0
0
0
0
2
0
0
2
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
2
2
0
0
0
0
2
0
2
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
3
2
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
1
0
2
2
1
2
0
0
1
0
0
0
0
1
2
5
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
2
3
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
7
2
0
0
2
0
0
0
0
0
0
1
0
0
2
2
1
0
2
0
0
3
0
0
0
1
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
3
1
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
1
0
0
1
0
4
0
0
1
0
0
1
0
0
1
0
0
2
0
0
0
0
1
0
0
2
0
0
2
0
0
1
1
1
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
2
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
8
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
2
2
1
1
0
0
0
2
0
0
0
0
3
0
0
1
0
0
2
2
2
2
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
3
1
0
1
0
1
0
0
0
0
0
2
0
0
2
1
0
0
0
2
0
0
1
0
0
2
2
0
0
1
0
0
0
0
2
2
1
0
2
0
0
0
2
0
2
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
3
0
0
0
1
0
0
1
2
2
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
1
0
1
2
2
0
1
1
0
0
1
0
2
0
0
2
0
0
0
2
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
3
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
4
0
0
2
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
1
2
0
0
0
0
1
0
0
0
0
0
0
2
4
1
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
2
0
0
4
0
2
0
0
0
0
2
1
0
0
2
0
0
0
2
0
0
1
1
0
0
0
0
0
2
1
0
1
1
0
0
0
0
0
2
0
2
1
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
4
0
0
2
0
0
0
2
1
0
0
1
0
0
0
0
0
0
2
0
1
1
1
1
0
0
1
0
0
3
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
5
0
1
0
0
0
0
1
2
0
2
0
2
2
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
2
0
0
0
0
0
0
6
0
2
0
1
0
0
0
4
1
0
0
1
0
0
0
0
3
0
0
0
2
0
0
0
0
2
0
2
0
3
0
3
0
1
0
0
2
0
1
1
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
2
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
1
2
1
1
0
0
0
2
0
2
2
0
0
0
2
0
1
0
2
0
0
1
0
3
0
0
0
2
0
2
2
0
0
1
0
2
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
2
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
1
0
1
0
0
0
0
0
2
0
0
0
1
0
2
0
0
1
0
0
0
0
1
0
2
0
0
0
0
1
0
2
0
1
2
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
1
7
0
0
0
0
3
0
2
2
0
0
0
1
0
2
0
0
0
0
0
2
1
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
1
1
0
1
3
0
0
0
0
0
2
0
2
1
0
0
1
0
0
0
1
0
2
5
1
0
1
0
6
0
1
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
2
0
0
0
1
2
2
3
1
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
1
0
6
2
0
1
0
2
0
2
0
1
2
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
1
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
2
4
0
0
0
1
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
1
0
0
0
2
0
0
0
0
2
0
0
2
1
0
0
2
5
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
1
0
2
2
0
0
1
1
1
0
0
0
1
2
2
0
2
0
1
1
0
0
0
0
0
0
1
2
0
0
0
3
0
7
0
0
0
0
2
0
0
2
2
0
0
0
2
0
0
2
0
0
2
0
2
2
1
0
1
9
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
1
1
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
2
0
1
0
0
0
1
0
0
1
0
0
1
0
0
2
2
0
3
0
0
0
0
0
1
0
3
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
1
1
1
3
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
2
0
0
1
1
0
1
0
0
2
0
0
1
0
0
2
2
0
0
0
0
0
0
2
1
0
0
0
1
1
0
0
0
2
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
1
0
0
3
2
0
0
0
0
0
2
0
0
0
2
0
2
0
1
0
0
0
2
0
2
0
0
0
1
0
0
0
1
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
2
0
1
0
0
1
0
0
1
0
0
1
0
2
2
0
0
1
0
0
1
0
2
2
0
1
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
3
1
0
0
0
0
0
0
0
0
1
0
0
0
8
1
2
0
0
0
0
4
1
0
0
2
0
0
0
0
0
1
1
1
0
2
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
2
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
1
0
0
1
0
5
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
3
0
0
0
0
0
2
1
1
0
0
2
1
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
1
2
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
3
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
2
2
0
0
2
1
0
0
0
0
0
0
0
1
0
1
2
0
0
1
0
0
3
1
0
0
2
0
2
0
0
0
0
0
0
3
0
2
2
2
0
0
0
0
1
0
1
1
2
0
0
0
2
0
2
0
0
1
0
0
1
0
0
2
2
0
0
0
0
0
0
0
1
0
0
3
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
2
0
1
0
0
0
0
0
0
2
3
2
13
0
0
0
0
1
0
0
3
0
0
0
2
0
2
0
0
0
0
2
0
0
1
0
2
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
2
0
0
4
2
2
3
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
2
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
1
1
1
0
0
0
0
2
0
4
0
0
3
0
0
1
0
2
0
1
0
0
0
1
2
1
1
0
2
0
0
0
4
0
0
0
2
0
0
0
1
0
0
2
0
0
2
0
1
1
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
1
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
3
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
3
0
0
0
1
0
0
1
0
1
0
0
1
5
2
0
0
2
1
2
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
2
0
0
0
0
2
0
0
2
0
1
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
1
0
0
0
0
1
0
2
0
0
1
0
0
0
2
2
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
2
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
3
0
0
0
0
1
0
2
3
0
0
0
0
1
6
0
0
1
0
2
0
0
0
0
1
1
0
0
0
0
0
2
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
23
0
0
0
0
1
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
2
0
0
1
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
1
0
1
2
5
0
1
0
1
0
0
4
0
0
1
0
2
3
0
2
0
1
0
1
0
0
3
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
2
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
2
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
2
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
1
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
2
1
1
0
1
0
0
0
0
0
0
2
0
4
1
0
0
0
0
0
0
0
0
0
2
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
2
0
0
0
2
2
1
0
0
0
1
1
0
0
0
2
0
0
2
4
0
0
0
1
0
2
2
0
0
0
0
1
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
2
0
1
0
0
2
0
3
0
0
2
0
0
0
1
2
0
0
0
0
0
1
0
2
1
0
1
0
3
0
1
2
1
0
0
0
0
0
0
0
0
1
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
1
5
0
0
2
1
0
0
0
0
2
0
1
1
0
0
0
1
0
0
1
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
1
1
0
0
1
0
2
2
1
1
3
2
0
2
1
0
0
0
0
0
0
2
2
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
2
1
2
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
3
0
1
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
2
0
1
0
3
2
0
0
0
0
0
0
2
1
0
0
1
0
2
0
2
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
1
2
0
0
1
0
0
0
0
0
0
0
0
1
5
0
3
1
1
0
2
0
0
0
0
0
0
0
2
0
0
2
2
2
3
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
2
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
1
0
2
0
0
0
0
0
0
0
2
0
4
0
2
2
3
0
0
1
0
0
0
0
1
2
0
2
1
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
4
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
1
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
6
0
2
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
1
0
0
1
0
0
1
2
2
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
9
6
0
0
0
3
0
1
2
0
0
0
0
2
0
0
2
0
0
1
9
0
2
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
2
2
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
2
1
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
1
2
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
1
0
0
0
0
2
0
1
0
2
0
0
0
0
2
0
0
2
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
1
0
1
2
0
0
1
0
0
0
0
0
0
1
2
0
1
0
0
0
1
4
0
1
0
0
0
1
0
2
1
0
0
0
1
1
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
2
0
0
0
1
0
2
0
1
0
0
0
0
1
0
0
0
1
0
1
0
2
0
1
0
1
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
1
2
1
0
2
0
0
0
0
1
0
0
2
0
0
0
0
6
3
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
2
1
0
0
2
0
0
1
0
2
0
0
0
0
0
1
0
4
0
0
0
0
1
1
0
7
0
0
1
0
2
1
0
0
0
1
0
0
1
1
2
0
2
0
2
0
1
0
4
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
2
0
1
2
1
0
0
0
0
0
1
0
0
1
0
1
0
1
2
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
2
0
0
0
0
2
1
2
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
1
1
1
0
3
2
2
2
0
0
2
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
1
1
1
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
10
0
0
0
0
0
0
2
2
1
2
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
2
2
0
0
0
1
0
2
0
0
1
0
2
0
0
2
2
0
2
0
0
0
0
0
2
0
0
0
0
5
0
0
0
0
1
0
0
6
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
1
2
0
0
0
0
0
1
0
0
0
0
0
1
1
2
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
2
1
2
1
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
3
1
0
0
1
0
0
2
0
0
0
2
0
0
1
2
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
2
0
2
2
0
0
0
0
0
0
0
2
1
0
1
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
1
0
0
1
0
0
0
7
0
2
1
0
0
0
2
0
0
1
3
0
0
0
2
1
0
0
0
1
0
0
1
0
0
0
1
1
0
2
1
0
2
1
0
0
0
0
0
1
0
0
3
0
0
1
0
0
0
0
0
0
0
3
0
2
1
0
2
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
5
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
2
0
1
0
0
0
4
0
3
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
1
1
0
0
0
0
2
0
2
0
2
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
5
4
0
0
0
4
0
0
4
0
0
0
0
0
2
0
1
0
0
1
1
0
1
0
1
0
2
0
0
0
2
1
0
2
1
0
2
0
0
3
1
0
0
2
0
0
0
3
0
5
0
0
0
0
0
0
1
0
0
3
2
2
1
3
0
0
0
2
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
2
2
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
2
3
0
0
1
0
1
0
0
0
0
0
2
0
1
0
0
1
0
0
3
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
1
0
0
1
2
0
0
1
6
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
2
0
1
0
0
1
2
0
0
0
2
0
14
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
3
4
2
0
0
0
0
0
1
0
0
2
2
1
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
5
0
0
0
2
0
0
3
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
2
0
0
2
0
0
0
0
2
0
1
0
0
3
0
1
0
0
0
2
0
2
1
2
0
1
2
2
0
0
0
1
0
1
2
0
0
1
0
1
0
0
0
3
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
3
1
0
1
0
0
3
2
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
2
0
0
0
1
0
2
0
0
0
0
2
0
0
0
1
0
2
0
1
0
2
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
2
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
3
0
1
2
0
2
0
1
0
2
2
1
0
0
0
2
0
0
0
0
0
0
0
1
2
1
0
2
0
2
0
2
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
1
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
2
0
0
2
0
2
0
2
0
0
0
1
0
0
0
2
0
1
0
0
0
1
2
4
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
3
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
3
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
3
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
3
0
0
2
1
0
0
0
0
0
0
3
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
2
0
1
2
6
1
0
0
0
0
0
1
0
0
2
0
0
0
3
2
0
0
1
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
1
0
3
5
0
0
2
0
0
1
0
1
0
2
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
5
0
0
0
0
2
0
0
1
0
0
2
0
0
3
0
0
0
0
1
0
0
1
0
3
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
2
0
0
0
2
2
0
2
0
2
0
0
2
0
0
1
0
0
0
0
1
0
2
1
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
2
0
0
0
0
0
0
0
2
0
0
1
1
0
0
5
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
1
0
0
3
5
0
0
1
0
0
0
1
0
2
0
0
0
0
2
0
2
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
2
0
0
0
0
0
3
0
0
0
0
2
0
9
0
2
1
2
0
1
0
1
2
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
5
0
2
0
0
0
2
0
1
2
2
0
1
0
0
1
1
0
0
2
0
0
5
0
0
0
2
1
0
0
0
1
0
0
1
0
0
0
1
1
2
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
1
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
1
1
1
0
0
0
2
0
1
0
0
0
0
5
0
1
3
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
2
2
2
0
1
0
0
1
1
0
1
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
2
1
0
3
2
0
0
0
2
0
0
0
0
0
1
2
1
0
0
2
0
0
2
0
0
0
0
0
0
0
2
1
1
0
1
2
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
2
0
0
1
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
5
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
4
0
0
1
1
0
0
0
2
0
0
0
0
4
2
1
0
3
0
0
0
0
2
3
0
2
0
0
0
2
0
0
0
2
0
0
0
2
2
0
1
0
0
0
1
0
0
0
1
2
0
2
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
4
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
2
0
2
0
0
0
0
2
0
2
1
0
2
2
0
0
0
1
1
0
0
0
0
2
0
0
2
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
1
0
2
0
0
0
4
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
4
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
2
0
1
0
0
0
0
0
0
1
1
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
2
0
0
2
2
0
0
0
0
1
0
1
3
0
0
0
0
0
0
1
0
0
0
3
0
0
2
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
3
0
0
2
0
0
2
0
0
1
2
0
0
0
2
0
0
2
0
1
1
0
0
0
3
2
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
1
0
2
0
0
1
0
2
0
0
1
0
1
0
0
0
0
0
1
0
0
0
2
0
0
2
0
1
0
1
0
2
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
6
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
2
1
0
0
2
0
0
0
1
4
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
1
2
0
0
0
0
8
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
1
1
0
2
2
2
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
5
0
0
2
3
0
1
0
0
2
0
0
0
0
0
2
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
2
1
4
2
1
1
2
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
1
0
0
0
2
0
1
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
5
1
0
0
3
0
2
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
2
1
0
1
0
8
0
0
0
0
0
0
2
2
0
0
1
0
2
0
0
2
1
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
1
0
0
0
2
0
0
2
0
0
2
2
0
0
0
2
0
2
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
5
2
0
1
0
0
0
0
5
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
0
2
0
0
2
0
0
0
2
0
0
0
1
2
0
1
0
0
0
1
0
0
3
0
0
2
0
0
0
0
0
3
0
1
4
2
0
0
2
0
1
2
0
0
0
0
1
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
1
0
4
0
4
2
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
2
1
0
0
1
1
1
0
2
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
2
2
0
1
0
1
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
10
0
0
0
2
0
0
2
4
0
0
0
0
2
0
1
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
2
0
2
0
1
0
2
2
0
1
0
0
0
0
1
0
0
0
1
1
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
2
0
0
1
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
2
2
0
0
0
0
0
2
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
1
0
0
0
1
0
0
0
1
0
1
2
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
4
0
0
0
8
0
0
0
0
0
2
0
2
2
0
0
2
0
2
0
4
0
0
3
0
0
0
2
2
2
0
0
0
0
3
2
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
1
1
0
0
3
0
0
0
1
0
4
0
0
0
0
2
0
0
1
0
0
4
2
0
1
2
0
0
1
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
1
0
0
1
1
0
2
1
1
0
0
0
1
0
0
0
2
0
0
2
2
0
2
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
1
1
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
1
0
2
1
0
0
0
2
2
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
2
1
1
0
2
2
1
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
3
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
1
0
0
0
1
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
1
0
5
1
1
1
1
0
0
1
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
6
4
0
0
2
0
2
2
0
0
0
0
0
0
0
0
2
0
2
1
3
0
0
1
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
2
1
0
0
0
0
0
0
2
0
2
0
2
0
2
0
1
0
0
0
2
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
3
0
0
1
0
0
0
2
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
2
2
0
2
3
0
0
0
0
0
0
1
0
3
0
1
0
2
3
2
0
0
0
2
0
0
0
2
0
1
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
1
3
0
0
0
0
0
1
1
0
0
0
0
4
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
2
1
0
0
0
1
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
2
0
2
0
0
1
3
2
2
0
0
0
1
0
0
1
0
0
1
1
2
0
2
0
2
0
0
0
0
0
1
0
1
0
0
0
1
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
1
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
1
2
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
2
2
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
5
0
0
1
1
1
0
0
1
0
2
0
1
0
1
1
0
0
0
0
2
0
1
2
1
0
0
1
0
0
1
3
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
2
0
2
0
0
0
1
1
0
0
0
0
0
0
2
0
0
1
0
2
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
1
0
0
4
0
2
1
0
0
0
0
0
0
4
0
0
0
2
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
1
2
1
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
1
3
0
2
1
0
0
2
2
0
0
0
0
2
0
0
2
0
0
0
0
1
1
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
5
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
2
3
0
0
0
0
0
3
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
1
0
3
0
1
0
0
0
0
1
0
5
0
0
1
0
1
0
0
2
0
2
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
6
0
0
2
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
1
2
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
2
0
3
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
2
0
0
2
0
0
0
0
0
0
0
1
1
2
0
0
3
0
1
0
0
3
2
0
0
0
1
0
1
0
1
0
0
0
1
2
0
0
3
2
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
4
0
0
1
0
0
1
1
0
5
2
0
2
0
0
0
0
0
1
1
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
1
0
0
0
2
3
2
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
5
0
0
2
0
1
1
0
0
0
0
2
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
2
2
1
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
1
0
2
2
2
3
0
0
1
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
1
0
0
0
1
2
0
0
0
0
0
0
2
1
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
2
0
1
0
0
0
2
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
2
0
2
1
0
0
0
0
1
0
1
0
0
0
1
2
2
1
0
0
0
1
1
2
0
0
0
1
2
1
6
0
2
0
0
0
0
0
0
1
0
0
1
1
2
0
1
1
0
2
1
0
1
1
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
1
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
3
0
2
0
1
1
0
2
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
2
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
3
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
1
0
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
6
0
2
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
2
2
0
0
0
1
2
0
0
0
0
0
2
0
0
2
0
2
0
0
0
1
1
2
2
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
1
0
1
0
0
1
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
2
0
4
0
0
0
2
1
1
2
0
0
0
0
0
0
0
0
3
0
0
0
1
0
2
0
0
0
0
3
0
0
0
0
2
0
0
2
0
1
0
0
5
2
1
2
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
1
0
2
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
3
0
2
0
0
2
1
1
2
0
0
0
2
0
1
0
0
3
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
2
0
2
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
2
0
0
3
0
1
0
2
0
1
2
1
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
2
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
2
0
0
0
2
1
0
1
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
3
0
0
0
3
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
2
0
2
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
2
0
2
0
2
1
2
0
0
1
0
0
2
2
2
0
0
0
2
0
0
1
0
0
1
2
2
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
2
2
0
0
2
0
2
2
0
2
0
0
0
0
2
0
0
2
2
0
0
0
2
1
0
0
2
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
1
2
1
0
0
1
2
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
3
1
0
0
0
0
0
0
0
0
3
0
2
0
0
4
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
1
0
5
0
2
0
1
0
0
0
3
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
1
0
0
0
0
0
1
0
2
0
0
2
0
0
0
2
0
2
2
0
2
1
1
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
2
0
1
0
1
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
2
1
2
0
0
0
1
3
0
0
0
0
0
0
0
1
0
1
2
0
0
2
2
2
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
2
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
1
1
1
1
0
0
0
1
2
1
2
2
0
0
0
0
0
0
0
2
2
2
0
0
0
1
0
0
2
0
0
2
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
3
1
0
1
2
0
0
1
0
0
0
1
0
0
0
2
0
0
2
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
2
3
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
1
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
2
1
0
0
0
1
1
0
1
0
0
0
1
0
0
1
0
0
2
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
3
3
0
0
0
0
2
1
2
1
0
0
0
0
2
1
2
4
0
4
2
1
0
2
0
2
3
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
1
0
2
0
0
0
0
0
0
2
1
4
0
0
0
2
0
2
0
0
0
1
0
1
2
1
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
1
2
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
4
2
0
0
0
4
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
2
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
10
2
2
0
0
2
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
3
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
2
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
3
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
2
0
0
0
1
0
0
2
2
0
1
0
0
0
1
0
0
2
0
3
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
1
1
1
0
2
2
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
2
0
0
0
1
0
0
1
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
1
2
0
1
0
0
0
0
0
0
1
2
0
2
0
2
1
2
0
0
3
0
0
0
4
0
0
1
0
2
2
1
0
0
0
0
3
0
1
1
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
2
2
0
1
0
0
0
0
0
0
0
0
0
3
3
4
0
0
0
0
0
0
0
0
0
3
0
2
2
2
1
3
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
2
0
2
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
2
0
0
0
0
0
1
1
1
0
0
0
0
1
0
2
1
0
0
0
0
1
0
0
0
0
0
1
1
1
2
0
0
0
0
1
0
1
0
1
0
0
2
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
2
3
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
2
0
0
1
1
2
0
0
0
1
1
0
2
1
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
3
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
6
0
0
0
0
1
2
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
1
0
0
1
1
2
1
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
2
1
0
2
2
1
0
0
0
2
3
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
9
0
0
1
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
1
0
2
0
0
0
0
0
2
1
0
0
0
5
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
1
0
0
2
2
1
2
5
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
1
1
0
0
0
0
0
0
0
2
1
2
0
0
0
2
0
2
2
1
0
0
0
0
1
1
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
2
0
1
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
1
0
0
0
1
0
0
2
0
0
1
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
2
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
3
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
1
2
3
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
3
2
1
0
0
0
0
0
0
0
2
0
0
2
0
2
1
1
0
0
0
2
0
0
0
0
0
0
0
0
1
3
0
1
1
0
1
0
0
2
0
1
0
0
2
0
0
0
0
2
1
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
1
1
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
2
0
2
0
0
0
2
2
0
0
0
2
0
0
2
0
2
0
0
1
0
1
0
0
2
0
0
0
0
0
1
0
0
2
0
0
3
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
1
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
1
0
1
0
0
1
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
3
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
1
1
0
0
3
0
0
2
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
2
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
6
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
11
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
2
2
1
0
0
2
0
1
2
0
0
2
0
0
0
1
0
4
0
0
0
1
0
0
2
0
0
1
0
1
1
2
0
1
0
3
0
0
0
1
0
1
0
0
0
0
6
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
1
0
0
0
2
2
1
0
0
0
0
0
0
0
2
0
2
2
0
2
1
1
0
1
0
0
1
2
0
2
0
6
1
0
0
0
2
2
0
0
0
0
2
1
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
3
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
4
0
2
0
0
0
0
0
8
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
2
0
0
0
0
0
0
0
1
1
2
0
1
0
2
0
0
0
0
0
0
1
1
2
0
0
0
0
2
0
1
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
2
1
1
0
1
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
2
1
0
0
1
1
0
1
0
3
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
3
3
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
3
2
0
0
3
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
4
0
0
1
0
0
1
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
5
0
0
0
1
0
0
1
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
2
0
0
2
0
0
1
0
1
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
1
0
1
0
0
0
2
1
0
0
0
0
0
2
0
2
2
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
2
1
0
0
0
0
2
0
1
0
1
0
0
0
0
0
1
2
0
0
2
2
0
3
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
2
1
0
1
0
1
0
1
0
0
0
0
0
0
1
2
0
0
1
3
0
0
0
2
0
0
1
0
0
1
0
0
0
0
3
0
0
0
0
0
0
7
1
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
3
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
1
0
0
0
1
2
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
4
0
0
2
0
0
0
0
0
1
1
2
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
4
2
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
1
0
0
0
0
0
0
1
1
2
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
2
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
2
1
0
1
0
0
1
0
4
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
2
0
0
1
0
2
0
0
2
0
0
2
2
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
3
1
0
2
0
2
3
0
0
0
0
1
0
2
3
0
2
0
0
0
1
1
0
1
0
2
0
0
0
6
1
0
0
1
0
0
2
2
0
0
3
0
0
0
0
1
0
3
2
0
0
1
2
0
0
0
0
0
0
2
0
1
1
1
0
0
0
2
0
0
0
0
0
1
0
0
3
3
0
1
1
0
0
1
0
0
2
1
0
2
1
0
0
6
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
1
0
0
0
0
1
4
0
0
2
0
0
0
0
0
0
0
2
2
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
3
0
0
1
0
0
1
0
0
1
0
7
2
0
0
0
1
2
0
1
2
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
3
4
0
2
2
0
1
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
1
5
1
0
1
1
0
2
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
5
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
1
2
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
2
1
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
1
0
1
0
0
0
0
3
0
0
0
0
0
0
0
1
1
0
0
0
2
2
2
0
0
0
0
0
0
1
0
1
0
3
2
1
0
0
0
0
1
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
3
0
0
2
1
0
0
1
0
2
0
2
1
0
0
1
2
1
0
2
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
2
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
1
0
3
0
0
0
0
0
0
1
1
0
2
0
1
0
0
2
1
0
2
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
4
0
0
0
0
1
1
1
0
0
0
2
0
0
2
2
0
1
2
2
0
0
0
0
0
2
0
0
5
0
2
1
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
2
0
0
2
1
1
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
2
0
1
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
1
0
1
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
1
1
0
0
0
0
0
2
2
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
1
0
1
0
1
0
0
0
1
1
1
0
0
2
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
5
0
0
2
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
2
0
0
2
1
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
2
1
0
0
1
0
2
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
3
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
3
0
0
2
0
0
2
1
0
0
0
2
2
0
0
0
0
2
0
0
2
1
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
1
0
0
0
0
0
2
0
1
1
0
1
1
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
2
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
1
0
1
0
0
2
2
0
0
1
0
0
0
1
2
2
2
1
0
1
3
1
0
0
0
0
1
0
0
0
0
2
1
2
0
0
0
2
0
0
0
0
0
0
0
1
2
0
1
0
0
2
0
0
0
2
0
0
1
0
0
2
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
1
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
3
1
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
2
0
1
1
0
0
0
2
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
2
0
2
0
1
2
0
0
2
1
0
0
0
2
0
0
1
1
3
0
0
0
1
0
0
2
1
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
2
0
3
1
0
2
0
0
1
0
0
2
0
2
1
0
0
1
2
2
0
0
0
2
0
1
0
1
2
0
0
0
2
0
2
3
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
1
0
0
0
1
0
1
0
0
1
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
2
2
0
0
0
1
0
0
0
0
0
2
2
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
2
2
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
1
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
2
0
0
0
2
0
0
3
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
2
1
0
0
0
2
0
0
1
0
2
3
0
2
0
0
0
0
1
0
0
2
0
0
0
2
0
2
1
0
0
0
0
0
0
1
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
2
0
1
0
0
1
0
0
1
2
1
0
0
1
0
0
0
0
1
1
2
1
0
4
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
1
2
5
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
3
1
0
2
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
1
2
0
0
2
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
1
0
2
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
3
0
0
1
2
2
0
2
2
1
0
0
2
0
1
1
0
1
0
0
1
2
0
0
0
2
3
1
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
1
3
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
1
0
0
0
2
2
0
0
2
0
0
0
0
0
2
0
2
2
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
2
1
0
2
0
0
1
0
0
0
1
0
0
0
0
1
0
1
2
2
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
3
1
5
0
0
3
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
1
1
0
1
1
0
0
0
0
1
1
0
0
1
0
0
1
0
0
2
0
2
0
2
1
0
3
0
1
0
1
0
0
0
0
0
0
17
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
2
0
0
0
3
0
0
0
0
2
1
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
2
2
0
2
0
0
0
0
1
0
2
0
5
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
2
0
0
2
0
0
2
0
3
2
0
2
0
0
3
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
3
0
0
1
0
1
0
0
3
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
1
0
0
1
1
0
0
0
0
2
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
1
2
2
0
2
0
2
1
0
0
2
2
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
3
1
0
0
0
0
7
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
2
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
2
0
1
1
1
0
2
1
0
0
0
0
2
0
0
2
0
0
0
2
0
2
0
1
0
0
0
1
0
0
0
0
0
1
3
2
0
1
0
1
0
0
0
0
0
0
1
0
2
1
0
1
0
0
0
0
1
2
0
0
3
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
3
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
3
0
0
0
0
0
0
2
0
1
1
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
1
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
1
0
0
1
1
0
0
0
2
0
0
0
0
0
0
2
3
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
2
0
2
0
0
0
0
3
0
0
1
2
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
2
0
0
1
0
0
3
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
1
0
3
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
1
1
0
1
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
3
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
1
2
0
3
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
1
0
0
1
0
2
0
0
0
0
2
0
0
1
3
0
0
0
0
0
0
2
1
0
1
2
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
2
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
4
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
2
1
0
2
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
2
0
2
0
1
0
0
0
1
0
2
1
0
0
4
1
0
0
0
0
0
0
1
1
1
2
1
0
0
0
0
1
0
0
2
0
0
0
0
0
3
2
0
0
1
2
1
0
1
0
1
0
0
0
1
2
2
0
2
0
2
0
0
0
0
0
0
0
0
8
2
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
1
2
0
0
0
2
0
0
0
0
1
1
0
1
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
2
1
0
0
0
0
0
0
3
1
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
3
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
2
0
2
1
0
0
0
1
0
3
2
0
2
0
1
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
1
1
0
0
0
0
0
1
0
2
3
0
1
0
0
1
0
0
3
0
0
1
0
0
0
2
0
2
0
1
1
2
0
0
0
0
1
2
0
0
2
0
2
2
2
0
0
1
0
4
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
1
0
0
4
0
0
0
0
1
0
0
0
2
0
0
1
0
2
0
1
0
0
0
1
0
0
0
0
3
1
2
0
2
1
0
2
0
1
2
0
1
0
0
2
0
1
1
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
14
0
1
0
0
0
0
1
0
0
0
0
1
4
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
2
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
1
0
2
2
0
0
2
1
2
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
2
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
7
0
0
1
0
0
0
2
0
1
1
0
2
0
0
1
0
2
0
0
1
0
0
0
3
0
0
0
0
2
1
0
2
0
0
1
0
1
0
0
0
0
0
0
0
3
0
0
0
2
2
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
5
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
1
0
0
0
1
0
0
1
2
0
0
0
0
2
0
0
1
2
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
3
2
0
0
7
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
7
1
2
0
0
0
0
2
0
0
0
1
2
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
1
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
1
0
2
0
2
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
3
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
1
2
0
0
2
0
3
2
1
0
1
2
0
0
3
0
0
3
0
0
0
2
0
0
1
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
1
0
0
2
3
0
0
2
0
0
0
0
1
0
0
2
0
1
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
2
1
0
2
0
0
0
0
0
0
2
1
0
0
2
0
0
0
2
0
1
0
0
1
0
2
0
0
0
1
0
0
0
1
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
2
1
0
2
0
0
0
2
1
0
0
0
0
2
0
0
0
2
1
1
0
0
2
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
8
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
3
2
0
4
0
1
0
1
1
0
2
0
0
0
1
0
0
0
2
1
1
2
2
0
0
1
0
2
0
0
0
1
0
1
0
5
0
0
1
0
1
0
4
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
3
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
2
1
0
0
0
0
0
1
0
0
1
0
0
0
1
2
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
2
0
0
0
0
2
2
0
0
0
0
0
1
0
5
0
1
0
0
0
2
0
0
2
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
1
0
1
2
0
1
0
0
0
2
2
0
2
0
1
0
1
1
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
2
0
0
0
0
0
0
1
2
0
2
1
1
0
0
1
2
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
2
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
2
0
0
2
0
1
2
0
0
0
2
0
0
0
0
0
2
0
0
2
1
0
0
3
2
0
0
3
1
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
3
0
2
0
0
1
1
0
2
0
2
0
2
1
0
0
0
0
0
1
2
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
1
2
4
0
0
0
0
0
0
5
0
2
0
0
4
2
0
0
0
0
0
1
0
0
1
0
1
1
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
2
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
2
1
1
1
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
1
0
2
2
1
1
1
1
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
2
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
1
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
12
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
2
1
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
2
1
0
1
0
2
2
1
0
0
0
0
0
0
2
2
0
1
2
1
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
2
0
0
1
0
0
0
2
0
0
2
1
0
0
0
0
0
0
1
0
2
0
2
0
5
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
2
1
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
2
0
1
4
2
1
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
6
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
1
1
0
0
0
0
2
2
2
0
4
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
4
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
2
0
0
0
1
1
0
0
0
1
0
0
1
0
0
3
1
0
0
0
0
0
2
0
1
0
0
2
2
2
0
0
0
0
2
0
0
0
1
1
4
1
0
0
0
0
0
0
0
0
0
1
2
1
0
1
0
1
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
1
0
0
2
0
0
1
0
0
2
0
2
2
0
0
0
4
0
0
2
0
0
0
1
2
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
1
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
1
0
0
0
0
4
0
0
0
0
0
2
0
1
6
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
2
1
0
0
0
0
1
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
4
0
0
0
2
0
0
0
1
0
0
0
1
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
3
1
0
2
2
0
0
0
2
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
2
0
1
0
0
0
0
0
0
1
1
0
0
2
0
1
0
0
0
2
0
0
0
1
0
3
0
0
1
2
1
0
0
0
0
0
0
0
0
0
3
0
1
2
0
2
0
1
0
0
1
1
1
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
3
1
1
0
0
1
0
1
2
0
2
0
5
0
0
0
0
0
0
0
1
0
2
0
0
2
1
0
0
1
0
0
1
0
0
3
0
0
3
2
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
2
1
1
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
2
1
1
0
0
0
0
0
2
2
0
0
2
2
0
0
0
0
2
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
2
1
0
0
0
0
0
0
0
0
0
3
0
0
0
1
1
0
0
0
3
0
1
0
0
0
2
1
0
0
0
1
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
1
0
0
2
0
2
0
0
1
2
0
0
0
0
3
0
2
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
1
2
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
4
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
1
0
1
0
0
0
0
1
0
2
0
0
0
2
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
2
1
0
0
0
1
1
0
2
0
0
0
0
0
1
0
0
1
0
2
0
3
2
0
2
0
2
0
0
0
0
2
2
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
2
1
3
0
2
0
0
0
0
1
2
0
0
0
0
1
2
2
0
0
2
0
0
0
0
0
0
2
1
0
0
0
3
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
2
0
3
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
2
2
0
0
0
0
0
0
1
1
0
0
0
1
1
0
2
0
2
1
1
0
0
0
2
0
0
2
2
0
0
0
1
2
0
0
0
0
1
0
1
0
2
2
0
1
0
0
2
0
0
0
0
0
2
1
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
1
0
2
1
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
1
0
1
0
0
0
0
0
3
1
0
0
1
2
0
2
0
0
2
1
0
2
2
0
1
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
1
0
2
0
0
2
1
0
0
2
0
0
3
0
0
1
0
0
0
0
1
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
1
0
0
0
0
7
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
2
0
4
0
2
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
2
1
0
0
0
1
0
0
0
0
1
0
0
1
1
1
0
0
0
0
2
0
0
0
3
2
0
2
0
0
1
0
0
0
0
1
0
2
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
2
2
0
2
0
0
1
0
2
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
2
0
0
2
1
0
1
0
1
1
0
0
0
0
2
0
1
0
0
0
0
0
1
2
0
2
0
0
0
3
0
0
1
0
2
0
0
0
0
0
2
0
2
0
1
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
1
0
1
0
0
0
0
0
0
0
2
1
2
0
3
6
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
1
0
2
0
0
1
0
0
0
1
0
1
0
0
0
1
1
1
0
0
0
2
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
1
0
3
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
1
1
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
1
1
0
0
2
1
0
0
0
1
1
0
0
1
0
0
0
0
4
0
3
3
0
0
0
1
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
2
0
0
2
0
1
1
0
0
2
0
5
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
2
2
0
0
0
2
0
0
0
2
1
0
3
0
0
0
0
0
0
0
1
0
0
0
1
2
2
1
2
2
0
0
4
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
2
2
0
4
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
2
2
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
1
1
0
1
3
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
2
0
1
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
2
1
1
2
0
2
1
0
0
0
2
2
1
0
0
0
0
0
5
0
2
0
2
0
2
0
1
0
2
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
2
1
2
0
0
1
0
0
0
0
2
0
0
0
0
0
1
1
0
2
2
0
2
0
0
0
0
2
0
2
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
1
2
0
0
0
0
2
2
4
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
2
0
1
0
0
0
3
0
1
0
0
1
4
0
0
0
0
2
0
0
0
2
2
2
0
2
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
1
1
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
5
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
5
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
2
0
0
0
1
0
1
1
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
2
1
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
1
3
0
0
0
1
0
0
1
0
1
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
7
1
2
0
0
0
1
1
0
2
1
0
0
0
0
1
4
0
0
0
1
0
0
1
0
0
0
3
1
0
0
1
0
0
1
1
0
1
0
0
0
1
1
0
1
0
0
0
1
4
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
1
0
0
0
0
0
0
1
1
0
1
0
2
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
4
0
2
0
2
0
2
2
0
0
0
1
5
0
0
0
0
1
0
1
2
1
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
1
0
0
2
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
8
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
3
2
0
2
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
1
2
0
2
0
0
2
0
0
2
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
3
0
1
1
2
2
0
3
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
5
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
2
0
0
0
0
0
0
1
1
2
0
0
0
1
0
0
0
4
0
0
3
0
0
1
0
2
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
1
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
3
1
0
0
0
0
0
0
2
0
0
0
0
0
4
0
1
0
0
2
0
0
0
3
0
0
1
0
2
2
0
1
2
0
0
3
0
0
0
0
0
0
2
1
2
0
1
0
1
0
0
2
0
1
0
0
0
0
1
1
0
3
0
0
0
0
1
0
2
1
0
0
0
1
0
0
0
1
2
0
0
0
0
2
1
1
1
2
0
0
0
0
1
0
0
0
0
0
2
0
1
0
1
2
2
1
0
0
0
0
1
1
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
1
0
0
2
2
0
0
1
0
4
0
0
2
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
2
0
1
1
0
2
0
2
0
0
0
0
0
0
0
2
1
2
0
0
0
0
1
0
1
0
0
0
2
2
0
1
1
1
1
0
2
0
0
1
0
1
1
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
2
2
0
2
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
1
3
0
0
2
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
3
0
0
0
0
0
0
2
0
2
0
4
2
0
0
1
1
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
3
1
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
3
1
2
0
2
0
1
0
0
0
2
0
0
0
0
0
1
1
2
0
0
0
1
0
0
0
1
0
2
2
0
0
0
2
1
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
1
0
0
0
2
1
0
0
2
1
0
1
0
0
2
0
0
1
0
0
0
1
2
0
0
0
0
0
0
1
0
0
3
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
4
0
0
1
0
2
1
0
2
2
2
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
2
2
0
2
0
1
0
0
0
1
2
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
1
1
1
3
0
1
0
0
0
0
1
1
4
1
0
4
0
1
2
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
7
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
2
1
0
0
0
2
2
0
1
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
2
0
1
0
0
0
2
0
0
3
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
3
0
0
0
2
1
3
0
0
0
0
0
2
0
0
0
1
1
0
0
3
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
1
0
1
2
1
0
1
0
0
0
0
0
0
0
0
3
0
0
0
1
0
4
0
0
0
1
0
0
0
1
2
0
1
0
2
2
0
1
0
1
1
0
0
1
0
1
5
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
4
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
4
1
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
1
0
0
0
2
3
0
1
0
1
0
0
2
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
2
0
0
1
0
0
3
0
2
2
0
0
0
3
0
0
2
0
1
0
0
0
0
0
3
2
2
0
0
1
0
2
0
0
0
0
0
1
0
0
1
0
0
2
4
0
0
0
0
1
2
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
2
0
1
0
0
1
0
1
0
2
0
0
0
0
0
2
0
0
2
2
0
0
2
0
1
0
1
0
2
0
2
0
0
0
0
0
2
0
0
1
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
2
0
1
1
2
2
0
0
0
0
0
2
0
0
0
0
2
2
2
0
1
2
0
5
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
2
2
2
0
0
0
2
0
1
1
0
0
0
0
0
2
0
3
0
0
0
0
0
0
2
0
0
1
0
0
1
2
0
0
1
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
1
0
1
0
0
0
0
0
0
3
0
0
1
2
1
0
2
2
0
0
0
0
0
0
2
0
0
0
2
0
0
2
2
0
0
3
0
2
0
0
0
1
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
2
2
0
0
0
0
1
0
1
2
2
0
2
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
2
0
0
1
0
0
3
1
1
0
0
0
1
0
0
0
0
2
1
0
0
0
2
0
0
0
0
2
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
2
0
0
2
0
0
2
0
0
0
2
0
0
1
0
0
2
2
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
1
2
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
2
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
4
0
0
0
0
1
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
2
2
1
3
0
2
0
2
1
0
0
2
0
0
3
0
1
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
1
0
1
0
0
0
0
0
2
2
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
2
1
0
0
1
0
7
0
0
1
0
2
0
0
1
1
0
0
3
1
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
2
0
0
1
0
1
2
0
0
0
0
2
1
1
2
1
0
0
0
0
0
1
0
0
0
0
1
2
0
1
0
0
2
2
0
1
0
0
1
2
0
0
0
0
2
0
0
1
0
0
0
0
2
1
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
1
0
0
2
0
0
0
0
0
0
0
2
1
1
0
0
0
0
5
2
2
0
5
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
3
2
2
1
0
0
0
0
2
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
2
0
0
1
0
0
0
2
0
2
5
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
1
0
1
0
1
0
2
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
2
0
0
0
1
5
1
0
0
3
1
1
2
0
0
0
0
0
1
0
0
0
1
2
2
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
1
1
0
0
0
0
1
1
0
2
0
2
0
0
0
2
0
2
2
1
0
0
3
0
1
0
2
2
0
0
0
0
0
2
1
0
0
7
0
0
0
0
0
0
0
0
0
0
3
3
1
0
0
0
0
2
0
0
0
1
0
0
3
1
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
2
2
0
0
0
1
0
3
2
1
3
0
0
0
0
0
1
0
2
1
0
0
1
0
2
1
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
1
0
0
0
3
1
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
2
0
3
1
0
2
1
0
1
1
2
0
0
0
0
0
0
0
0
2
0
0
0
1
1
2
0
0
0
0
1
0
0
2
2
1
0
1
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
1
2
0
2
0
0
0
0
2
0
0
0
3
0
0
0
0
1
6
0
0
0
0
1
1
2
0
1
0
0
0
1
2
1
0
0
1
2
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
2
0
2
0
1
0
0
0
0
0
0
4
0
0
0
0
2
1
0
2
0
0
0
3
0
0
0
0
1
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
2
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
1
0
0
0
0
1
3
1
1
1
1
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
1
7
0
0
1
1
2
0
0
0
1
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
2
0
0
0
3
14
0
0
4
2
0
0
0
2
0
0
0
0
0
1
0
0
1
2
0
0
3
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
2
2
0
0
1
2
0
0
0
0
0
0
1
0
0
2
1
0
1
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
1
2
1
0
2
0
0
0
3
2
0
0
4
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
1
3
0
0
0
3
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
5
0
2
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
3
0
0
0
6
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
4
4
0
0
1
0
0
0
0
1
0
0
1
0
0
2
0
0
2
0
0
1
2
0
0
0
8
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
2
2
2
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
2
0
1
2
1
0
0
0
0
2
0
1
0
0
0
0
2
1
2
1
0
0
0
8
2
0
0
2
0
0
2
2
0
0
0
0
1
0
0
0
6
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
3
0
2
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
2
2
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
4
0
0
1
0
2
0
0
0
0
0
0
2
1
0
2
2
0
0
1
0
2
0
0
1
1
3
0
1
2
0
0
0
0
0
0
2
2
1
0
0
1
0
4
1
0
0
2
5
0
2
0
1
0
2
2
0
0
0
0
4
0
2
0
0
0
0
2
0
2
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
1
7
0
3
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
1
0
2
0
0
0
1
1
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
1
1
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
2
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
3
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
1
0
0
0
0
1
0
0
0
0
1
4
0
0
1
2
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
3
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
2
0
1
1
0
1
0
0
0
2
0
1
0
1
2
0
0
2
0
0
1
0
2
0
2
0
0
2
0
0
1
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
1
2
0
0
2
0
0
2
0
2
2
0
0
0
0
0
1
0
1
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
2
0
2
3
0
0
0
0
0
0
0
0
6
0
0
0
0
2
2
0
2
0
0
0
0
0
2
2
0
0
0
0
2
1
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
5
1
0
0
0
0
1
1
1
0
1
1
1
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
2
2
2
2
1
0
0
2
0
1
2
0
2
0
0
2
1
0
2
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
3
1
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
5
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
2
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
3
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
2
2
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
2
0
2
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
5
1
0
2
2
1
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
2
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
2
2
2
0
0
2
0
0
0
0
0
1
0
2
2
0
0
0
1
0
0
0
1
1
0
0
2
0
0
0
2
2
0
1
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
1
2
0
0
0
0
2
5
0
0
0
2
1
0
0
0
0
3
0
2
0
3
2
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
2
2
2
0
0
0
0
0
0
0
1
1
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
1
0
0
0
0
0
4
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
2
0
0
1
0
2
2
2
0
2
1
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
2
0
1
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
8
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
1
0
1
1
3
0
0
0
0
0
2
0
0
2
0
2
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
1
0
1
2
1
0
1
0
2
2
3
0
0
0
2
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
4
0
0
0
0
0
0
0
0
2
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
2
1
0
1
0
1
0
0
0
0
0
0
0
1
3
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
1
0
1
0
0
2
0
2
0
1
0
2
1
0
0
0
2
0
0
2
2
1
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
1
1
0
0
0
0
0
0
0
3
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
2
1
0
1
0
0
0
1
2
2
1
2
0
2
0
0
2
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
2
0
0
1
0
0
1
0
2
2
0
0
0
2
0
0
1
0
2
0
1
0
0
0
2
1
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
1
0
1
2
0
0
1
7
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
1
1
2
0
0
0
0
2
0
0
0
6
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
1
0
2
1
2
0
0
0
1
1
2
0
0
0
1
2
0
0
2
0
0
0
3
0
2
2
2
0
0
0
0
1
0
0
0
0
0
2
1
1
2
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
1
2
0
0
0
0
2
1
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
3
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
2
1
0
2
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
1
0
2
1
0
0
0
0
0
0
1
2
0
1
1
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
2
1
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
1
7
0
0
1
0
0
0
1
0
2
0
0
1
0
0
1
0
0
2
1
1
0
0
2
0
0
0
0
0
1
0
1
0
1
0
2
0
1
1
1
0
0
0
1
0
0
0
0
1
0
0
0
2
1
0
1
0
0
0
2
0
0
2
0
0
0
1
0
2
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
2
0
0
1
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
3
2
0
0
2
1
1
0
0
0
2
2
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
3
0
0
2
2
0
2
0
0
2
1
0
0
1
0
0
2
0
0
0
0
0
0
0
1
2
0
1
0
1
1
0
2
0
0
0
0
0
0
0
1
0
2
0
0
2
1
0
0
0
1
0
1
3
0
0
0
0
0
1
0
1
0
0
0
0
3
0
0
0
2
0
0
2
0
0
0
1
0
0
2
0
0
2
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
2
0
0
2
0
0
1
2
1
0
2
0
0
0
0
0
1
2
2
0
1
1
0
0
0
0
1
0
0
0
0
0
6
0
0
0
2
2
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
2
2
0
0
0
2
1
0
0
0
0
0
0
3
2
2
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
2
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
1
0
1
1
0
2
0
1
0
0
0
0
0
2
0
2
0
0
1
1
0
3
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
3
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
1
1
0
0
0
1
0
0
0
0
4
0
0
0
0
1
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
1
0
1
0
1
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
4
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
2
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
1
2
1
2
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
2
0
0
0
1
1
0
0
1
0
1
0
12
0
0
0
0
2
2
0
2
2
0
0
3
1
1
0
0
0
0
1
0
0
0
2
1
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
1
0
0
2
0
0
0
2
0
0
5
0
2
0
0
1
0
1
0
0
0
0
2
0
0
3
0
1
0
0
1
0
0
1
1
2
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
2
2
0
2
0
0
5
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
8
1
0
0
0
0
0
2
1
0
0
0
2
0
0
0
1
0
1
0
0
2
0
0
0
1
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
2
1
0
2
0
0
0
2
0
0
0
0
1
2
1
0
0
0
1
0
0
0
1
1
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
5
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
2
1
0
0
3
1
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
2
1
0
1
0
0
2
0
0
0
2
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
1
0
4
0
0
2
1
0
2
0
0
0
0
1
0
2
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
2
2
0
2
0
1
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
2
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
1
0
0
0
2
1
0
0
0
1
0
1
0
0
1
0
0
0
0
2
1
0
0
2
1
0
2
0
0
0
0
2
1
1
0
0
0
1
0
0
1
0
0
0
2
0
1
0
0
1
0
0
0
1
1
2
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
2
0
0
3
0
0
2
0
0
0
2
0
1
0
0
3
0
0
0
0
0
0
0
0
0
3
0
1
0
6
0
2
2
0
0
0
2
0
0
1
2
0
2
2
0
2
0
0
0
2
6
0
1
0
0
0
0
1
1
1
0
0
0
0
2
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
1
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
2
1
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
6
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
1
0
0
1
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
1
0
4
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
1
2
1
0
0
0
0
0
2
1
0
2
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
2
1
2
1
0
0
2
0
0
1
0
1
0
0
0
1
1
0
0
0
3
0
1
1
0
0
2
0
0
0
0
1
0
0
0
0
2
4
2
0
1
0
2
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
2
1
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
4
2
0
0
1
0
0
2
0
0
1
0
0
2
0
0
0
0
0
2
2
0
0
0
1
0
0
0
1
0
1
1
0
0
0
2
0
0
0
0
0
0
0
4
0
0
0
0
1
0
2
0
3
2
2
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
2
2
2
0
0
1
0
3
1
0
1
0
1
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
5
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
3
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
4
0
0
0
1
2
0
0
0
0
2
7
0
2
0
0
1
0
1
0
0
0
0
1
1
1
0
1
0
1
2
0
0
2
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
2
3
1
0
0
0
4
0
0
0
2
1
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
2
1
2
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
2
1
2
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
2
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
2
0
0
1
0
0
1
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
4
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
2
0
1
2
0
1
1
1
2
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
2
1
1
2
0
0
0
0
0
1
0
3
0
0
0
0
0
2
0
0
1
0
0
0
1
1
0
2
0
0
1
3
2
0
2
1
0
0
0
0
3
1
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
1
1
0
0
0
1
0
2
2
1
0
0
0
0
0
2
0
0
3
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
11
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
4
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
1
0
0
0
0
0
2
0
0
0
0
1
1
2
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
6
1
2
1
0
0
0
0
0
2
4
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
3
0
1
1
0
0
0
0
3
0
0
0
0
0
0
2
0
1
1
0
1
0
2
0
2
0
1
0
0
0
0
2
1
2
0
0
0
0
1
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
1
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
2
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
1
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
2
2
0
0
1
2
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
4
0
1
2
0
0
0
0
2
0
4
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
2
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
1
0
1
2
0
2
1
0
1
2
1
0
1
1
2
1
0
4
1
0
0
1
0
0
0
2
0
0
0
1
2
0
2
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
2
0
2
0
0
1
2
2
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
2
0
0
2
0
0
0
0
2
0
3
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
2
0
1
0
0
0
0
0
2
1
0
0
0
4
2
1
0
0
1
0
0
2
0
3
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
2
1
0
0
0
0
0
2
1
0
0
2
0
0
0
1
2
2
0
0
0
0
1
0
1
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
1
2
2
0
0
0
0
0
3
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
2
2
0
0
0
1
0
0
0
0
2
2
0
0
3
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
2
1
0
0
0
0
0
0
2
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
1
0
0
0
0
0
2
0
0
0
2
0
1
0
1
0
1
0
0
0
0
0
2
0
3
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
4
0
1
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
3
0
0
0
0
1
0
0
0
0
2
2
0
1
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
1
1
1
0
0
0
1
4
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
1
0
2
0
0
2
2
2
1
0
0
1
2
0
0
0
2
0
1
0
3
1
1
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
1
0
2
0
0
1
0
0
2
0
2
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
6
2
0
1
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
3
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
4
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
2
0
2
0
0
0
1
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
2
0
0
2
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
3
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
2
1
0
2
0
0
0
1
0
1
2
2
0
0
0
1
0
0
0
0
0
2
0
0
1
0
1
0
0
1
0
0
0
0
0
0
2
0
0
1
3
2
0
0
0
0
1
1
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
2
2
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
1
0
1
0
2
2
0
0
0
0
1
1
0
0
1
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
2
0
0
0
1
2
0
0
0
0
0
1
2
0
2
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
2
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
2
1
0
0
2
0
0
3
0
0
1
0
0
0
3
0
0
0
1
2
0
0
0
0
0
1
0
0
2
2
0
1
0
0
2
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
4
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
1
1
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
1
2
0
0
0
0
2
29
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
2
0
3
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
1
2
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
7
1
0
0
1
0
2
0
2
0
1
1
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
1
2
0
2
0
2
0
0
0
0
0
1
0
2
2
2
1
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
1
3
0
0
1
0
0
0
2
1
0
1
0
2
0
2
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
1
0
0
0
1
0
0
2
0
0
0
1
0
0
2
0
1
0
0
0
0
1
0
0
2
0
0
1
0
0
4
0
0
0
0
0
6
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
1
0
0
3
0
1
0
0
1
1
0
0
2
4
0
0
0
0
0
1
0
0
0
2
0
0
2
0
2
0
0
0
0
0
2
1
1
0
0
4
0
0
0
1
0
0
1
0
0
1
2
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
2
0
1
1
0
0
1
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
1
3
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
4
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
2
0
0
0
0
0
4
2
0
0
0
0
0
1
0
0
1
0
2
0
2
1
0
0
0
1
1
2
0
0
0
0
1
0
0
0
2
2
0
0
3
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
2
0
0
2
1
0
0
0
1
0
1
2
3
0
3
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
2
1
1
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
2
1
0
0
2
0
5
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
2
0
0
3
0
1
0
0
1
0
0
1
0
0
0
1
0
1
1
0
0
0
1
0
2
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
1
0
0
1
1
0
1
0
0
0
0
0
2
0
4
0
2
0
2
0
0
3
0
1
0
0
0
0
0
0
0
1
2
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
3
1
0
0
0
0
1
0
0
2
0
0
1
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
2
0
0
0
0
2
1
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
2
0
1
1
2
0
0
0
2
0
0
1
0
1
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
2
1
0
0
1
2
1
3
0
0
0
1
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
2
0
0
2
0
3
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
1
0
0
2
2
0
0
2
2
0
0
2
2
0
0
3
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
2
5
0
1
0
0
0
0
0
0
0
3
1
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
1
0
2
2
0
2
0
0
2
0
0
0
0
3
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
2
1
0
0
1
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
2
2
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
1
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
2
1
0
1
0
0
3
0
0
0
2
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
2
0
2
0
1
1
0
0
2
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
1
0
0
0
0
2
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
1
2
0
2
1
0
0
0
0
3
0
0
2
0
0
1
0
2
0
2
0
0
1
1
0
1
0
0
2
0
0
0
0
0
4
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
2
0
0
0
1
0
2
2
0
0
2
2
0
0
2
2
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
1
2
0
0
1
0
0
1
0
1
2
3
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
8
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
2
0
2
0
0
1
0
0
3
0
0
4
1
1
0
0
0
0
0
0
1
2
0
0
0
2
1
0
0
3
0
0
0
3
0
1
0
1
0
2
0
0
0
0
3
0
0
0
0
1
1
0
0
0
0
0
2
2
2
1
2
0
0
1
1
0
0
1
0
4
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
3
2
0
0
0
1
2
0
0
1
3
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
2
4
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
2
1
0
0
0
2
2
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
1
0
2
1
0
0
2
0
3
0
0
0
0
0
0
0
1
0
2
0
0
3
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
2
0
1
0
0
0
0
1
0
2
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
2
1
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
2
0
0
0
1
0
0
0
0
2
2
1
0
0
0
1
0
0
0
2
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
2
0
0
0
1
2
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
3
1
0
1
0
0
1
2
0
1
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
2
0
0
2
0
2
0
2
2
2
2
0
2
1
0
1
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
3
2
0
0
0
0
0
0
0
3
0
0
0
2
2
0
0
0
0
0
2
1
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
1
0
0
1
0
0
0
1
0
0
2
0
0
1
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
2
2
2
0
0
1
0
0
2
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
1
0
1
0
0
2
0
0
2
0
2
2
0
0
1
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
5
0
0
0
0
2
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
2
0
1
0
0
1
0
0
0
0
0
2
2
0
0
2
0
0
0
2
0
1
0
0
0
0
0
2
0
2
1
0
2
2
1
3
0
1
0
0
2
4
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
2
2
1
1
0
1
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
4
0
0
0
1
0
0
0
1
0
0
0
1
2
0
0
0
1
0
0
0
0
2
0
2
0
0
2
0
0
0
0
1
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
1
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
1
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
1
0
2
0
4
0
0
1
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
2
0
0
2
0
0
0
0
0
1
0
2
0
1
0
1
1
3
0
1
0
0
1
0
0
3
2
2
2
2
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
2
0
2
0
2
2
2
1
0
2
1
1
1
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
2
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
1
2
2
0
0
0
0
3
0
0
2
0
0
0
1
0
2
0
0
0
0
0
2
2
1
0
1
2
2
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
1
1
1
0
0
2
0
0
0
0
0
0
0
0
1
5
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
1
1
0
1
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
1
0
0
2
1
0
0
1
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
4
0
0
0
0
0
0
0
1
0
0
0
4
1
0
1
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
3
0
0
2
1
0
3
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
1
0
0
0
1
2
0
1
2
0
0
2
0
0
3
0
2
1
0
1
0
0
0
1
2
0
0
0
0
0
2
0
3
2
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
1
2
0
0
0
0
0
0
3
0
0
1
0
0
0
1
0
0
1
1
0
4
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
7
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
3
1
0
0
0
0
1
0
0
0
0
0
1
0
2
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
1
1
1
2
2
1
0
0
1
0
4
2
0
0
0
0
2
0
0
1
0
1
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
2
1
0
1
2
0
0
2
0
1
0
2
0
0
0
0
1
1
1
1
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
3
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
2
1
1
0
2
0
0
0
0
0
5
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
2
2
2
1
0
1
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
3
0
0
0
1
0
3
0
4
6
2
0
0
0
0
0
0
0
0
1
1
0
0
0
3
4
0
0
1
0
0
1
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
2
0
0
2
0
0
0
3
2
4
1
2
2
0
0
2
0
2
0
1
0
0
0
0
0
0
0
1
0
2
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
1
0
2
0
0
0
0
2
0
0
3
2
1
0
0
0
0
0
0
1
2
0
3
1
1
1
1
0
0
0
0
0
0
0
0
0
0
1
4
0
0
2
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
1
0
2
0
0
0
0
0
1
2
0
0
1
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
2
2
1
1
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
2
0
6
1
2
0
0
0
2
0
0
4
0
1
2
1
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
2
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
1
1
3
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
2
0
1
2
1
0
1
0
0
5
2
0
2
0
0
1
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
1
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
2
0
0
1
0
2
0
0
0
0
2
0
0
0
2
2
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
2
0
0
0
0
2
0
1
1
1
0
0
0
1
2
0
2
0
0
4
2
0
0
0
2
0
0
0
0
0
0
0
3
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
2
1
0
0
0
2
0
1
0
0
2
1
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
1
2
0
8
0
0
2
0
1
2
1
1
1
2
0
0
0
1
3
0
0
0
1
0
2
2
0
0
0
0
1
0
0
1
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
3
0
0
0
0
0
0
0
1
2
0
0
0
2
2
1
0
0
0
0
1
0
0
2
2
0
0
0
0
3
1
0
0
2
0
1
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
5
0
0
2
0
0
2
0
1
0
2
0
0
0
0
0
2
0
0
0
2
0
3
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
3
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
2
0
3
2
0
2
0
0
0
2
0
0
0
0
2
3
1
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
2
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
2
13
0
2
1
1
0
0
0
2
0
0
0
3
0
4
0
0
3
0
0
0
0
0
0
0
2
7
2
0
0
0
0
0
0
2
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
3
0
1
1
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
1
1
0
0
2
3
2
0
0
0
0
0
0
2
1
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
2
3
0
2
2
1
0
0
0
0
2
0
0
0
2
0
0
0
3
0
2
1
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
3
2
0
2
2
2
1
0
0
0
0
1
0
0
3
0
2
2
0
1
0
1
1
1
0
3
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
2
1
1
2
0
1
0
0
0
0
1
2
0
0
1
0
4
1
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
1
0
0
0
0
2
0
2
0
1
0
2
2
0
0
0
1
0
2
0
0
2
0
0
2
0
0
0
0
0
0
2
1
0
3
1
0
2
1
0
2
0
2
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
2
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
1
0
0
3
0
0
0
2
2
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
2
1
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
3
1
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
2
0
0
0
0
1
0
0
2
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
3
2
0
0
1
0
0
2
0
2
0
0
1
0
1
0
0
0
0
0
0
1
1
1
0
0
1
0
2
1
0
0
0
0
0
0
0
0
2
2
1
0
1
0
0
0
0
0
1
2
2
2
2
0
1
0
0
0
1
1
0
0
0
1
0
0
3
1
2
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
2
0
2
2
0
0
1
2
1
0
0
2
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
2
0
1
0
0
0
1
2
0
0
0
0
0
2
2
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
1
0
4
0
0
0
1
2
0
1
0
0
2
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
2
0
1
0
0
1
0
0
0
2
0
2
3
0
0
0
1
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
2
4
0
0
0
0
2
0
1
0
0
0
0
0
0
1
2
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
1
2
0
0
2
0
0
0
1
2
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
3
0
0
0
0
0
0
0
2
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
1
2
0
0
2
0
5
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
1
0
2
0
2
2
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
2
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
2
1
1
0
0
0
0
0
3
0
0
2
0
1
0
0
0
1
0
0
2
2
0
0
2
0
0
0
1
0
1
0
3
2
0
1
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
2
0
0
0
0
2
0
1
0
2
0
0
0
5
0
2
1
1
0
0
1
0
1
0
0
0
0
0
1
0
0
1
1
0
1
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
1
1
2
0
0
0
0
0
3
0
0
2
0
5
1
2
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
2
0
2
0
0
0
0
0
1
0
1
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
3
0
1
1
0
0
0
1
2
1
2
2
1
0
1
0
2
0
2
0
1
2
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
1
0
1
0
0
2
0
0
1
2
2
0
0
0
1
0
2
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
1
0
2
0
0
0
1
0
0
1
0
0
0
0
1
0
0
2
0
3
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
8
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
3
0
0
0
0
0
0
0
0
2
0
0
0
6
0
0
1
0
1
0
0
0
0
0
0
2
1
2
0
0
0
1
0
0
0
1
2
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
2
2
0
0
1
1
1
0
1
0
0
0
0
0
2
2
1
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
1
3
0
0
2
0
0
2
0
0
1
3
1
0
0
0
0
2
1
0
0
1
0
0
1
0
0
0
0
2
0
1
0
0
1
0
1
0
0
1
0
2
0
0
0
0
1
0
2
1
0
2
0
0
0
0
0
1
0
0
1
0
0
0
1
3
2
0
1
0
0
0
5
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
2
1
2
0
0
0
1
0
0
0
0
0
0
1
1
2
0
2
0
0
0
0
2
1
0
0
5
1
2
2
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
5
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
2
2
0
3
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
2
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
2
2
0
0
1
0
0
0
0
0
2
0
2
0
2
0
0
0
1
0
0
0
0
0
0
2
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
3
0
1
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
1
1
1
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
1
0
1
1
1
1
0
1
1
0
0
3
0
0
0
1
0
0
1
0
0
0
0
2
0
1
0
4
1
0
0
0
2
0
2
0
0
0
2
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
2
0
0
0
1
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
3
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
5
1
0
0
2
2
0
0
0
1
1
0
0
0
0
0
0
0
1
3
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
3
1
3
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
1
0
1
0
0
0
2
0
0
0
0
2
0
2
1
1
2
0
0
1
0
2
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
1
0
0
1
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
1
0
1
2
2
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
1
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
2
1
1
0
2
1
0
0
1
1
2
0
0
0
0
2
3
0
0
0
2
0
0
0
0
4
0
0
0
0
0
0
1
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
1
2
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
4
0
2
1
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
3
0
1
1
1
0
1
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
3
2
2
0
0
5
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
6
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
2
2
1
0
0
0
2
0
0
2
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
8
0
1
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
1
0
0
0
1
1
0
0
0
0
1
1
2
0
0
0
0
0
2
3
0
2
0
2
0
0
0
1
0
0
0
5
0
0
0
1
1
0
0
3
0
0
1
1
1
0
4
0
0
0
1
0
0
2
6
0
0
1
0
0
1
2
1
0
0
0
1
0
0
0
2
0
2
0
1
0
0
0
0
1
0
2
1
0
2
0
0
0
0
0
0
0
0
0
1
1
0
2
0
2
0
2
0
1
0
1
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
1
0
1
0
0
0
0
0
3
2
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
2
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
2
1
0
0
0
0
2
1
2
0
0
1
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
4
0
0
1
2
0
0
0
0
0
0
2
0
4
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
9
0
1
0
0
0
0
0
0
0
2
1
0
0
1
2
0
0
0
0
2
2
0
0
3
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
3
1
0
0
1
0
0
2
0
0
2
0
0
1
2
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
3
0
0
0
1
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
1
1
0
0
1
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
1
0
0
0
1
1
2
2
0
2
0
2
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
1
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
1
0
0
6
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
2
0
2
1
1
1
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
2
2
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
2
2
3
0
0
0
0
0
3
1
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
1
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
2
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
2
0
0
1
0
1
0
0
2
0
2
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
1
0
2
1
1
0
1
0
0
0
0
0
0
0
3
3
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
2
3
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
2
0
0
2
3
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
1
0
0
0
2
0
1
0
2
0
1
0
0
0
0
1
0
1
0
1
0
2
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
2
0
0
3
2
0
0
0
0
2
0
0
0
2
0
0
1
2
0
0
0
0
2
1
0
1
1
3
0
0
2
5
0
0
1
0
2
0
0
0
0
0
1
0
0
0
1
0
2
0
1
1
0
1
0
0
1
1
0
0
0
1
3
0
0
0
1
0
2
1
3
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
1
0
0
4
0
2
2
0
0
0
0
0
0
0
0
1
0
2
2
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
6
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
4
0
0
2
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
1
0
1
0
2
0
2
0
0
2
0
0
0
0
0
1
0
0
0
1
1
1
2
1
0
0
0
0
0
0
0
2
0
1
2
1
2
0
0
0
0
0
2
1
0
0
0
0
1
0
0
1
0
0
0
0
3
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
1
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
2
2
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
1
2
2
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
5
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
2
0
3
0
2
0
5
1
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
2
0
0
2
0
0
1
0
0
0
0
1
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
5
0
0
1
0
0
0
0
2
0
2
0
2
0
1
0
0
0
0
2
1
1
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
3
0
0
0
2
0
1
0
0
0
0
1
0
0
0
1
0
0
2
1
0
0
1
0
0
0
0
1
0
0
0
1
2
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
1
9
0
0
0
1
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
1
0
0
0
2
0
0
1
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
2
0
0
2
0
1
2
0
0
3
0
1
0
2
2
0
2
0
0
0
1
0
0
0
0
0
1
0
0
3
2
0
0
1
0
0
0
0
0
1
0
0
2
0
1
2
0
0
0
0
0
0
1
0
0
0
1
0
1
0
2
0
4
0
0
3
1
0
2
1
1
1
0
2
0
0
0
0
0
0
0
0
0
0
2
9
0
1
0
0
1
0
0
0
0
0
1
0
2
0
2
0
0
2
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
3
0
2
0
1
1
0
0
0
1
0
0
0
0
1
0
2
1
0
2
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
3
2
1
0
0
0
2
2
1
0
2
0
0
0
0
0
0
2
0
0
1
0
1
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
5
1
1
0
0
2
2
0
0
0
0
0
1
0
1
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
2
0
2
0
0
0
0
1
1
0
0
0
2
0
1
0
2
2
0
0
0
0
0
0
0
0
2
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
3
1
0
0
5
0
6
0
0
0
2
0
0
0
0
2
0
0
4
0
0
1
0
2
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
1
0
0
3
2
1
2
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
2
1
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
2
0
1
0
1
0
0
1
1
1
0
0
2
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
1
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
1
0
0
1
0
0
1
4
0
0
0
0
2
0
1
0
0
0
0
3
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
4
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
3
1
5
0
0
0
1
0
0
1
6
0
0
0
1
2
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
3
0
0
0
0
0
2
0
0
0
1
1
3
0
1
1
2
0
0
4
1
1
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
2
0
0
0
1
3
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
2
0
1
2
0
0
2
0
0
0
0
0
0
0
1
0
1
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
1
0
0
0
2
0
0
1
2
0
2
2
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
1
2
3
2
2
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
3
0
2
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
1
0
0
1
0
0
0
2
0
0
2
0
0
1
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
4
1
1
0
2
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
2
0
0
0
0
1
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
1
0
2
0
2
0
0
1
2
0
0
2
0
0
0
0
0
0
2
0
1
1
0
0
0
2
2
1
0
1
1
2
1
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
1
0
3
9
1
0
0
1
0
0
1
1
0
0
0
2
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
2
0
1
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
1
1
1
2
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
1
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
4
0
3
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
2
0
1
0
2
0
0
0
0
3
0
0
1
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
2
0
0
1
0
0
2
0
2
0
0
0
0
2
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
1
0
0
0
0
1
1
0
0
2
0
0
0
0
0
3
1
0
0
0
0
1
0
1
0
0
0
0
3
0
0
0
0
1
0
0
0
0
2
0
0
0
6
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
3
1
1
0
0
0
0
1
0
1
1
2
0
1
0
0
0
0
1
0
0
0
0
2
0
0
3
0
0
2
2
0
2
2
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
1
2
1
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
8
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
2
0
1
2
0
0
0
0
2
0
0
0
0
0
2
0
3
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
2
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
3
0
0
1
4
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
1
0
2
0
0
0
0
2
0
7
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
1
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
1
0
0
0
0
1
2
1
2
2
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
2
2
1
2
1
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
1
2
0
0
0
0
0
0
2
1
0
0
0
2
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
3
1
0
0
1
0
0
0
0
3
0
3
1
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
1
1
2
2
1
0
0
1
2
2
1
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
0
1
0
0
3
0
3
0
0
0
0
0
1
0
0
0
0
4
1
2
0
0
0
1
0
0
2
0
0
2
1
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
2
0
0
0
2
0
0
2
2
0
0
1
0
1
0
3
3
1
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
1
2
1
0
1
3
0
1
2
2
2
1
0
0
0
0
0
0
0
2
0
0
1
0
2
0
1
0
1
0
0
0
2
1
0
1
0
0
1
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
2
2
0
2
0
0
1
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
2
0
0
1
2
0
1
2
0
0
1
0
2
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
3
0
0
0
1
1
0
0
0
0
0
0
2
1
0
0
0
0
2
0
2
0
0
0
1
1
0
0
0
2
0
2
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
1
3
2
2
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
1
0
2
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
2
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
4
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
1
0
0
0
0
2
2
0
1
0
0
1
0
0
0
1
3
0
0
0
0
2
0
0
0
0
0
0
1
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
2
0
2
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
2
1
0
0
2
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
2
2
0
0
1
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
2
0
7
1
2
2
0
2
1
0
0
0
0
0
1
0
0
0
0
1
1
0
2
2
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
3
0
0
0
0
0
1
0
1
0
2
0
1
0
0
0
0
2
2
1
0
2
0
0
0
0
1
0
1
0
0
0
0
0
2
1
0
2
0
3
2
0
0
0
4
0
0
0
0
1
0
0
3
0
0
1
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
1
0
2
0
0
3
0
0
1
0
1
0
0
2
0
0
1
0
1
0
0
0
2
0
0
0
1
2
2
1
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
1
14
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
2
0
0
1
0
0
2
0
1
2
0
0
0
0
0
1
0
0
1
0
1
0
0
0
4
0
0
2
0
2
0
0
0
0
0
1
0
0
2
3
0
0
2
0
0
0
2
1
0
0
1
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
2
2
0
0
2
0
0
0
0
0
1
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
1
5
0
1
0
0
0
0
2
0
0
2
0
1
0
1
0
1
0
0
0
1
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
3
0
2
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
2
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
3
0
0
0
2
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
6
1
0
0
0
0
2
2
0
0
1
0
1
2
0
0
2
0
0
1
1
0
2
0
0
0
0
0
0
0
2
1
2
0
0
3
0
4
0
0
0
2
0
0
0
1
0
0
0
2
2
2
0
0
0
0
0
1
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
1
2
2
0
0
0
0
0
0
2
1
3
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
2
1
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
1
1
1
1
3
0
0
2
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
2
2
0
1
0
0
0
1
0
0
0
0
0
1
3
2
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
1
2
0
0
0
0
1
0
0
1
0
0
0
0
4
0
0
2
0
0
0
2
2
0
0
0
2
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
1
0
0
0
0
0
1
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
1
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
1
1
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
2
1
1
3
0
2
0
2
0
1
0
0
0
0
0
0
0
0
1
7
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
1
1
0
2
0
0
1
0
0
0
1
1
0
0
0
2
2
0
0
0
1
0
0
0
0
3
0
2
0
0
0
0
1
0
0
1
0
0
0
2
0
2
0
2
1
0
4
0
0
0
0
1
0
0
6
1
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
2
1
0
0
0
3
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
1
3
0
1
1
0
0
1
0
0
0
3
2
0
1
0
0
0
0
0
0
2
2
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
1
2
3
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
1
0
1
1
0
0
0
1
1
0
0
0
2
0
2
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
1
1
0
0
0
0
0
0
0
4
0
2
1
0
2
0
0
2
1
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
3
1
3
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
2
0
3
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
1
2
0
1
4
0
0
0
0
0
0
0
0
2
1
2
2
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
3
0
1
0
0
0
1
2
0
0
0
0
0
0
0
1
0
2
0
3
3
0
2
0
0
1
1
0
0
0
0
2
2
3
0
1
1
0
0
0
4
2
0
0
0
3
0
0
1
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
2
0
0
1
0
3
0
0
0
2
2
0
0
0
1
0
0
2
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
2
0
2
0
0
1
0
0
0
2
2
1
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
2
0
0
2
0
1
0
1
1
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
2
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
2
2
1
2
0
2
0
0
0
4
0
4
1
0
1
0
0
0
2
1
0
0
0
1
0
2
0
0
1
0
0
0
0
1
0
0
2
2
1
2
0
2
0
0
0
2
1
0
0
0
0
0
3
0
0
0
0
1
0
0
0
1
2
0
0
0
0
1
2
0
0
0
0
0
4
0
1
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
1
1
0
1
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
2
0
0
0
2
2
0
1
0
0
0
5
1
2
0
0
2
0
0
0
1
0
1
0
0
2
0
0
0
0
1
0
0
0
3
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
1
0
1
1
1
0
0
0
0
3
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
2
2
0
6
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
2
0
0
0
0
0
0
0
2
1
0
0
2
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
2
0
1
2
0
0
1
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
2
0
1
0
4
0
6
3
1
0
0
0
0
3
0
0
0
0
0
2
1
0
3
0
1
0
0
3
0
0
0
2
0
0
1
0
0
2
0
1
1
0
0
0
0
0
1
0
2
0
2
0
1
0
0
1
0
2
0
0
0
1
0
0
0
1
0
1
0
0
0
0
4
0
0
0
1
0
2
1
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
2
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
2
1
0
0
0
2
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
4
0
0
0
0
2
0
1
0
0
3
0
0
1
1
1
1
1
2
0
0
0
1
0
2
2
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
2
0
0
0
0
1
0
2
0
0
0
0
0
2
4
2
0
0
0
0
1
0
0
0
2
1
0
0
0
4
2
0
0
2
4
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
1
2
0
1
0
2
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
1
0
2
1
2
1
0
0
1
3
2
1
0
2
2
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
1
2
2
0
0
4
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
2
2
0
2
2
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
1
0
1
1
3
0
0
0
0
0
2
3
2
0
0
2
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
3
0
0
1
0
2
0
0
0
1
2
1
2
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
2
2
0
5
0
0
2
0
0
1
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
1
0
2
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
2
8
2
2
0
0
1
0
2
0
1
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
1
0
2
0
0
1
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
2
0
1
0
1
2
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
3
2
0
0
0
0
2
2
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
1
0
0
0
0
1
1
2
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
2
2
0
0
0
2
0
0
2
2
0
0
2
0
0
0
0
0
0
2
2
0
1
0
0
0
2
2
0
0
0
2
0
0
1
0
0
3
0
2
0
0
1
0
0
0
0
2
0
1
0
0
1
0
3
0
0
0
0
2
1
0
1
0
1
1
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
2
2
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
3
0
0
0
2
0
1
6
12
2
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
3
1
1
1
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
1
1
0
0
0
1
0
1
0
0
0
0
0
1
2
6
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
3
0
2
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
4
2
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
1
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
3
1
1
0
2
0
0
1
0
0
0
0
0
2
0
1
0
0
3
0
0
0
2
2
2
0
2
0
0
0
0
1
1
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
5
1
2
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
3
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
4
0
0
1
0
0
0
0
1
0
0
0
2
1
0
0
0
2
2
2
0
0
1
0
1
0
0
0
4
0
0
0
2
0
0
0
0
0
1
0
1
2
1
1
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
1
2
1
0
0
2
2
0
0
0
0
2
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
4
3
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
2
4
0
2
0
0
0
1
0
1
0
2
0
1
0
0
0
0
2
2
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
1
0
1
0
1
0
2
2
0
0
2
0
0
0
0
1
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
1
0
2
0
1
0
0
1
2
0
0
0
1
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
2
0
0
1
1
1
0
0
1
0
0
0
1
1
1
0
2
1
0
0
0
0
1
0
0
0
1
0
0
1
0
2
1
0
2
0
0
2
0
1
0
0
2
0
0
2
2
3
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
6
1
0
0
0
1
1
1
2
0
2
2
0
1
0
2
2
0
0
0
0
4
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
3
0
0
2
0
0
0
0
3
0
0
0
0
0
0
1
1
0
0
0
3
0
1
0
0
1
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
1
0
1
0
0
0
1
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
4
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
2
0
1
4
1
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
2
2
0
1
0
0
0
0
0
1
0
0
2
0
0
0
1
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
1
0
1
0
2
0
0
0
0
1
3
1
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
2
0
1
1
2
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
2
1
1
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
5
0
1
0
2
0
1
3
0
0
1
0
3
0
1
0
1
0
2
2
1
2
0
0
0
0
0
0
2
2
3
1
2
0
0
1
2
0
3
0
0
2
1
0
0
0
0
0
2
0
2
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
7
0
0
1
4
2
2
0
1
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
2
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
2
2
1
0
0
0
0
0
2
0
2
0
0
0
1
2
0
1
1
0
2
1
0
0
0
0
1
3
1
2
0
2
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
2
0
0
0
0
2
0
0
1
2
0
0
0
2
1
2
2
0
0
0
0
1
0
0
0
0
3
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
1
1
4
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
15
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
2
0
0
0
1
0
2
0
0
0
0
1
1
0
0
1
0
0
1
1
0
0
2
1
0
0
1
0
0
2
0
0
0
2
0
0
0
0
1
1
0
1
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
3
0
2
1
0
0
1
0
3
0
2
0
0
0
0
0
0
2
0
0
0
5
0
0
0
0
0
0
3
0
0
0
0
0
0
0
3
0
0
0
7
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
1
0
0
0
0
3
2
0
0
3
0
0
1
1
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
2
0
0
1
2
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
3
1
1
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
4
0
1
0
0
0
2
0
1
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
2
0
2
0
0
2
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
1
0
2
0
1
1
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
2
0
0
0
3
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
2
1
3
0
0
0
0
1
2
2
0
1
9
2
0
1
0
0
2
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
3
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
1
0
0
0
0
2
1
0
0
1
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
1
0
1
0
1
0
0
2
2
1
0
1
0
0
1
0
0
0
2
0
0
0
0
1
1
0
1
0
0
2
0
2
0
2
0
0
2
0
0
0
0
0
2
0
0
0
5
0
0
0
0
0
0
0
0
1
2
0
0
0
3
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
3
2
2
0
2
0
1
0
0
3
0
0
0
0
3
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
4
1
0
1
0
3
0
0
0
1
2
0
0
0
2
0
2
0
1
1
1
0
0
0
1
0
0
1
0
2
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
5
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
2
0
2
1
0
2
3
2
2
0
0
0
0
0
0
0
0
2
2
2
0
1
0
0
0
0
0
0
2
2
0
1
0
0
1
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
2
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
2
2
2
2
1
0
3
1
1
0
0
0
0
0
0
1
2
0
0
2
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
1
0
0
2
2
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
2
0
0
0
2
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
3
1
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
3
1
2
0
1
0
0
0
0
0
0
0
0
1
2
0
0
3
0
0
2
1
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
3
0
0
0
0
1
0
0
0
2
0
2
0
1
2
0
1
2
1
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
2
2
2
2
1
1
1
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
2
3
1
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
2
1
2
2
0
0
2
0
0
0
1
0
0
2
0
0
1
1
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
1
0
0
1
0
0
2
2
1
0
0
0
0
0
0
0
2
0
0
0
4
0
0
1
0
4
1
0
0
0
1
0
2
0
0
0
0
1
0
3
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
1
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
1
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
2
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
3
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
4
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
1
0
0
2
2
5
0
0
0
0
0
1
2
0
0
2
0
0
0
2
1
0
0
0
0
5
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
2
0
0
0
2
3
0
0
0
1
0
2
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
1
2
2
0
2
0
2
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
1
1
1
1
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
1
0
0
0
0
0
0
2
0
1
2
0
3
0
0
0
1
0
3
0
0
0
0
0
1
0
0
1
2
0
0
3
2
0
0
0
0
2
2
0
0
0
1
0
1
1
0
2
0
0
0
2
0
1
0
0
1
0
1
0
0
1
0
0
6
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
1
1
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
2
0
2
0
0
0
0
2
2
1
0
0
0
0
0
0
2
0
0
0
0
3
0
1
2
2
0
0
2
2
0
1
0
0
1
1
1
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
2
2
0
1
1
0
1
1
0
2
0
0
0
3
0
0
0
2
1
0
1
0
0
0
0
0
1
1
2
0
1
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
1
1
1
0
0
1
0
0
1
0
0
0
0
0
0
2
2
1
0
2
0
0
0
0
1
2
0
0
0
1
2
1
0
0
0
0
1
1
0
0
1
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
2
3
0
0
2
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
2
0
2
0
0
0
2
2
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
6
0
2
0
0
0
0
1
0
0
1
0
2
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
1
1
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
2
0
0
1
1
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
2
0
0
0
0
3
0
0
0
1
2
1
0
0
1
0
1
0
0
2
1
2
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
3
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
2
1
2
0
1
1
0
0
0
2
1
0
0
0
2
1
0
2
0
0
1
0
1
1
1
2
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
3
0
0
0
0
2
2
2
0
0
0
2
0
0
0
0
2
0
1
0
0
0
2
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
2
2
2
0
0
1
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
5
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
1
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
2
0
0
1
0
0
0
1
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
2
0
2
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
2
1
0
0
0
1
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
2
0
0
0
2
2
2
0
0
0
0
2
0
0
0
1
0
0
0
2
0
2
0
0
0
0
2
0
0
0
1
2
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
1
0
3
0
0
0
0
0
2
0
1
2
0
0
0
2
0
1
1
0
1
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
1
0
2
1
1
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
2
2
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
2
3
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
2
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
2
0
2
0
0
0
0
2
0
1
1
0
0
3
0
0
0
0
2
0
0
1
0
3
0
0
2
0
0
0
0
0
1
0
1
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
2
2
0
0
0
0
0
1
0
1
0
0
0
0
2
3
0
0
0
2
0
0
0
2
0
1
0
0
0
1
1
0
0
0
0
0
0
0
3
2
0
2
0
0
0
2
0
2
1
0
0
0
0
0
1
0
3
0
1
0
0
0
2
1
2
0
0
1
3
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
2
0
2
0
2
0
0
3
0
0
2
1
0
0
1
0
1
1
0
1
1
2
0
0
0
0
1
0
0
0
0
0
1
2
1
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
1
2
0
5
0
0
0
3
1
0
0
1
0
0
2
1
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
2
2
2
0
0
1
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
3
0
2
0
0
2
2
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
2
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
1
0
2
0
0
2
0
0
0
1
0
1
2
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
1
3
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
1
0
0
2
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
2
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
1
2
0
0
0
0
1
0
1
0
1
2
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
3
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
2
0
0
0
1
0
0
0
0
2
2
2
0
0
2
0
0
1
0
0
0
0
1
0
0
5
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
2
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
4
0
0
0
3
1
0
6
0
0
1
0
1
0
0
0
0
1
0
1
1
1
0
0
0
4
3
0
0
1
0
1
2
0
0
0
2
0
0
2
0
0
3
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
1
2
0
1
0
0
1
1
0
0
0
0
0
0
1
2
0
0
2
2
2
0
0
0
0
0
0
0
0
2
2
0
0
1
1
0
0
0
0
0
0
2
1
0
2
0
0
0
6
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
4
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
2
4
0
0
0
0
5
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
3
0
1
0
1
2
0
0
1
0
2
1
2
0
2
1
0
0
2
0
2
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
3
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
2
0
0
0
0
1
0
2
2
0
8
0
1
0
0
0
0
3
0
0
2
0
0
1
0
0
1
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
6
0
0
2
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
3
0
2
0
0
0
0
1
0
0
0
0
0
1
2
0
1
2
2
1
2
0
0
1
0
0
0
1
2
0
4
2
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
2
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
2
0
2
0
2
0
2
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
1
0
0
0
4
1
2
0
0
2
0
2
1
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
1
0
2
3
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
6
2
2
2
0
0
0
0
0
2
0
0
0
2
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
2
0
2
1
0
0
0
1
1
3
0
0
0
0
0
2
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
2
0
2
2
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
5
1
1
0
0
0
0
0
2
0
2
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
3
1
0
0
0
0
1
0
0
3
0
0
1
2
0
1
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
4
0
0
1
0
0
0
3
0
0
0
0
1
2
0
2
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
1
0
0
3
0
0
1
2
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
1
2
2
0
0
0
1
0
1
0
0
1
0
0
0
1
3
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
5
0
1
1
1
0
0
0
0
0
0
1
0
2
1
2
0
2
0
0
0
2
0
2
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
1
0
2
5
0
0
1
2
0
2
0
0
0
0
0
0
1
0
2
0
2
0
0
0
2
1
0
1
2
0
1
0
3
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
2
1
3
0
0
2
2
2
0
2
0
2
0
0
0
1
0
0
0
0
2
1
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
2
0
3
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
2
0
0
1
0
0
6
1
2
0
1
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
2
0
2
0
2
0
0
2
0
0
0
0
1
0
0
0
2
2
0
2
2
0
3
2
2
1
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
2
1
0
0
1
0
0
0
0
0
1
2
1
0
0
2
0
0
0
5
0
0
0
0
2
0
1
2
0
2
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
3
0
2
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
1
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
3
4
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
1
2
0
0
2
0
0
0
2
0
1
0
0
0
0
0
2
0
0
1
0
0
4
0
0
0
0
2
1
0
0
0
0
3
3
0
1
0
0
2
0
0
0
0
0
0
0
1
0
2
0
1
0
0
2
3
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
1
0
0
1
0
0
0
0
0
2
1
0
0
0
2
2
0
0
1
2
6
0
3
0
0
0
2
0
0
0
0
0
0
2
2
2
0
2
0
3
1
1
0
0
0
0
2
1
0
0
0
0
0
0
0
6
0
1
0
3
2
0
0
0
2
0
2
0
0
0
0
3
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
2
0
5
0
0
0
0
0
0
1
0
2
0
0
1
0
1
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
1
0
0
1
2
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
2
0
2
1
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
3
2
2
1
0
0
1
0
1
2
0
3
0
0
0
3
0
2
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
2
1
1
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
1
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
2
0
2
0
1
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
2
1
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
1
2
2
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
2
1
4
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
2
0
2
1
1
0
0
0
0
3
0
0
1
0
0
0
1
2
0
0
0
0
1
0
1
0
9
0
2
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
2
0
0
0
0
1
0
0
2
0
3
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
1
0
0
0
0
2
2
1
2
0
0
0
0
0
0
2
0
2
1
0
2
0
1
0
0
0
2
0
2
0
0
2
0
0
0
2
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
2
0
1
0
0
0
0
0
2
1
0
0
0
1
1
0
1
0
0
2
1
2
0
0
0
0
1
2
0
2
1
1
0
0
0
0
0
0
2
0
1
0
0
2
1
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
1
1
1
0
0
1
2
0
0
2
0
1
0
2
0
0
0
1
2
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
1
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
2
0
0
0
1
2
7
1
0
2
0
1
2
0
0
0
0
0
4
3
0
0
0
0
1
3
1
0
0
0
0
4
0
0
2
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
2
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
2
0
3
0
1
0
0
0
0
1
0
2
2
0
3
1
0
1
0
2
0
0
0
1
2
0
0
0
0
0
0
0
2
0
3
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
2
0
2
0
0
0
2
1
0
0
0
0
1
2
0
2
1
0
0
0
2
0
1
0
0
1
2
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
1
1
0
0
0
0
0
0
0
0
2
0
1
2
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
1
0
0
0
0
0
1
1
2
3
0
0
0
0
2
0
2
0
2
0
0
1
2
2
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
2
2
2
1
2
1
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
2
1
2
0
0
0
2
0
0
0
0
2
1
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
2
0
2
0
0
1
0
2
0
2
0
2
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
2
3
0
0
2
0
1
0
0
2
1
0
2
0
1
0
1
3
2
0
0
0
0
0
0
0
0
0
0
0
1
0
3
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
3
0
0
1
2
0
0
0
0
0
1
0
0
1
1
0
2
2
0
0
0
0
1
0
2
0
8
0
2
0
0
0
0
0
0
0
1
0
1
1
0
0
0
2
2
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
1
1
1
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
2
0
1
1
0
0
0
0
0
2
0
0
0
1
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
3
2
2
0
3
0
0
1
1
0
2
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
2
0
2
0
0
2
0
0
0
1
2
0
0
0
0
0
0
1
1
1
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
4
0
0
0
1
0
0
0
0
0
2
1
1
1
0
0
2
0
0
0
0
1
1
1
0
1
0
0
0
1
0
0
3
0
0
2
0
0
1
2
0
0
1
0
2
0
0
0
2
1
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
6
1
0
0
0
0
3
1
0
0
0
1
2
0
0
0
0
1
2
0
2
1
0
0
0
0
1
2
1
0
1
0
3
2
1
2
0
0
2
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
3
1
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
1
2
0
0
0
0
0
2
0
0
2
3
2
2
2
2
1
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
3
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
3
1
0
0
0
0
0
0
1
1
0
0
2
0
2
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
2
0
1
0
2
0
0
0
3
2
2
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
1
1
2
0
0
0
1
2
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
1
0
2
0
0
3
0
0
1
1
2
0
0
0
0
0
0
0
2
1
0
1
1
0
2
0
0
0
0
0
0
1
0
0
0
3
1
0
2
0
0
2
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
2
0
2
2
1
0
2
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
3
2
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
2
0
0
1
1
1
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
2
0
1
2
0
0
2
0
0
0
1
0
0
0
0
1
2
0
0
1
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
3
0
0
1
0
0
1
0
0
2
0
0
0
2
0
0
0
6
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
1
0
3
0
0
0
0
0
1
1
1
0
1
0
0
0
2
0
0
0
0
2
0
1
0
1
1
0
0
1
0
0
0
3
1
0
0
0
0
2
0
1
4
0
0
1
0
1
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
2
1
1
2
0
2
0
0
0
0
0
1
0
1
0
2
2
2
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
3
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
3
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
2
1
0
0
0
0
2
0
0
2
1
0
1
0
0
1
3
2
0
2
0
2
1
0
0
1
0
0
0
2
2
0
0
0
2
0
0
0
2
2
0
1
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
2
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
2
5
0
0
1
2
0
1
0
1
0
1
0
0
0
0
0
2
0
1
0
5
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
2
0
1
1
2
0
1
0
0
0
3
0
0
1
0
0
0
1
0
0
1
0
2
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
2
3
0
0
1
2
0
1
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
1
0
0
2
1
0
0
1
0
0
2
2
0
0
0
0
0
0
3
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
3
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
2
0
2
0
0
2
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
1
1
0
0
2
0
0
1
0
0
0
0
1
0
0
1
1
0
0
2
0
0
2
0
0
1
0
0
0
1
2
0
0
2
0
0
4
0
0
0
0
2
0
1
0
0
2
0
0
1
0
0
0
2
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
1
0
1
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
6
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
2
0
0
0
1
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
1
0
2
0
0
1
0
1
0
0
2
2
1
0
0
0
0
0
0
1
0
0
1
0
0
2
4
2
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
1
0
1
2
0
0
0
0
0
0
1
2
0
0
0
1
3
2
1
0
0
2
2
0
1
0
2
0
2
0
2
0
0
2
0
3
2
0
0
0
2
0
0
1
2
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
3
0
0
1
0
1
0
0
5
0
0
1
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
3
0
0
0
0
0
0
0
1
0
1
1
2
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
2
0
1
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
3
0
0
0
0
0
0
2
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
12
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
1
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
2
0
1
0
1
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
7
1
2
2
0
0
0
2
1
1
2
0
0
0
0
2
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
3
3
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
2
2
0
0
1
0
2
0
2
0
1
0
2
1
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
2
1
1
0
3
0
0
0
1
2
2
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
3
2
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
4
3
0
0
0
1
0
0
0
4
0
0
0
0
0
0
1
1
0
0
0
0
2
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
2
0
0
0
6
1
0
2
1
1
0
0
0
0
0
0
1
1
0
0
0
1
3
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
5
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
2
0
0
2
0
0
3
2
0
0
0
2
2
2
3
0
0
0
0
0
1
0
7
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
1
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
4
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
2
0
1
2
0
1
0
3
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
1
0
1
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
1
1
1
0
0
1
0
2
0
0
0
2
1
1
0
0
0
0
0
0
0
4
0
1
1
0
0
2
0
2
0
2
0
0
0
0
2
3
0
2
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
3
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
3
0
0
1
2
2
2
2
1
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
3
0
2
0
2
0
1
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
1
0
0
0
0
0
3
1
1
0
0
0
0
0
0
0
1
0
0
1
0
1
1
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
2
0
2
0
0
1
0
0
4
0
1
1
0
1
0
0
2
0
0
0
0
0
0
1
1
0
2
0
0
2
1
0
0
0
1
0
0
0
0
0
2
0
0
2
1
0
0
0
0
2
0
0
0
0
1
0
1
0
2
0
0
1
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
1
0
2
0
2
0
0
0
0
0
2
0
0
0
3
1
2
0
0
0
0
1
0
2
2
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
3
0
0
0
3
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
3
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
2
1
0
1
0
0
2
0
0
1
0
0
1
0
1
0
0
0
1
0
1
0
0
0
2
2
1
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
2
0
0
2
0
1
1
0
0
0
2
0
4
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
2
1
0
2
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
1
0
4
0
0
0
1
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
1
2
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
1
0
1
1
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
2
0
6
2
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
3
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
1
0
3
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
1
2
0
0
0
0
0
1
0
1
0
0
0
0
3
0
0
0
1
0
0
0
2
0
0
0
1
1
0
1
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7
2
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
1
0
1
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
1
2
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
2
4
0
0
0
0
0
1
0
1
1
2
2
0
0
0
0
1
0
0
1
1
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
1
0
0
1
0
0
0
0
3
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
1
2
0
5
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
2
0
1
0
1
0
0
0
0
1
0
3
1
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
2
2
0
0
0
3
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
2
0
0
0
3
0
0
0
3
0
0
0
0
0
0
0
0
4
4
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
2
0
0
0
2
0
2
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
2
2
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
1
0
1
0
1
2
0
1
0
7
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
3
0
0
0
0
2
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
1
2
0
0
1
0
0
0
0
2
2
0
2
0
0
0
1
0
0
2
0
2
1
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
5
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
2
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
2
0
0
3
0
1
0
3
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
1
2
2
0
0
2
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
2
1
0
1
1
2
0
0
1
1
0
0
0
0
0
3
0
0
0
0
0
1
0
0
2
0
0
0
2
3
0
0
0
2
0
0
0
1
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
1
0
2
1
0
1
1
2
0
1
0
0
0
1
2
0
2
0
5
1
0
2
0
2
0
0
0
0
0
3
0
0
0
2
0
0
2
0
0
2
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
8
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
1
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
2
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
7
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
2
0
0
1
0
0
0
1
1
0
0
0
1
1
1
0
0
0
0
1
1
1
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
2
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
1
0
2
1
1
0
0
0
0
1
0
0
2
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
2
0
1
0
1
0
2
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
1
2
0
0
1
0
2
0
1
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
1
1
0
0
2
2
2
0
0
0
2
0
2
0
0
3
3
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
2
1
0
3
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
4
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
1
1
1
0
0
0
2
2
0
4
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
2
2
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
1
0
1
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
1
2
0
2
1
0
0
0
3
0
1
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
4
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
2
1
0
0
0
0
2
0
0
0
3
0
0
8
0
0
0
2
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
3
1
0
3
0
0
0
0
0
2
0
2
0
1
1
1
0
0
0
0
0
2
0
2
0
2
0
1
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
1
1
0
0
2
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
1
0
0
0
1
0
0
0
0
2
2
0
1
0
2
2
2
2
2
0
0
1
0
2
1
1
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
3
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
1
0
2
0
0
1
0
2
0
0
0
0
3
2
0
0
0
2
1
0
1
2
0
1
1
0
2
1
0
1
0
7
0
0
0
0
2
0
1
0
2
2
2
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
1
1
0
0
0
0
0
2
2
0
1
0
0
0
0
2
1
0
0
1
0
0
1
1
2
0
0
2
0
0
0
0
2
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
3
1
0
1
0
0
2
0
0
0
2
1
0
2
0
0
0
3
0
0
1
1
0
0
2
0
1
2
1
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
2
0
0
1
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
2
0
1
2
0
0
0
0
0
2
0
0
3
2
2
0
1
0
2
0
0
0
0
2
2
0
0
0
7
1
2
1
0
1
1
0
0
2
0
1
0
0
0
3
0
0
2
2
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
2
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
2
2
0
0
0
0
0
2
0
0
3
1
1
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
2
2
0
2
0
1
0
2
0
0
0
2
0
0
2
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
2
0
1
0
0
2
0
0
0
1
0
0
0
2
3
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
1
1
0
4
0
0
2
0
0
0
0
0
0
1
1
2
0
1
0
0
0
2
0
2
1
1
4
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
1
2
1
0
0
3
1
0
2
1
0
0
0
1
0
0
0
1
0
0
1
0
1
4
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
1
1
2
0
0
1
0
0
0
0
2
3
0
0
0
0
0
0
0
1
2
0
0
2
0
0
4
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
1
0
1
0
0
0
1
0
0
0
1
0
1
0
1
0
2
0
1
0
1
0
1
0
1
1
2
0
5
1
2
3
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
1
3
0
0
0
0
2
0
0
0
0
0
0
0
1
0
3
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
1
0
1
0
3
0
0
0
2
0
0
2
2
1
0
0
0
0
0
0
1
0
1
0
0
0
2
2
0
0
0
0
0
0
2
0
2
1
0
0
5
0
1
2
0
2
1
2
0
0
0
0
1
0
1
1
0
0
0
0
2
2
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
3
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
2
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
1
2
0
0
2
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
2
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
1
1
0
0
1
1
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
1
0
0
0
0
2
0
0
2
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
2
2
2
0
1
1
0
0
0
2
0
0
0
1
0
0
0
2
0
2
0
2
0
0
0
0
2
0
0
0
0
1
2
0
2
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
3
1
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
1
0
2
2
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
2
2
0
2
0
0
0
0
0
2
0
0
1
0
0
0
1
0
1
0
0
1
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
1
6
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
1
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
5
0
0
0
0
0
0
0
2
0
2
0
0
1
2
0
0
2
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
3
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
2
1
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
2
0
0
0
0
0
0
8
2
4
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
2
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
2
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
1
2
0
0
3
2
0
0
2
2
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
1
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
1
3
0
0
1
0
3
4
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
2
0
2
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
1
1
0
1
0
0
2
0
0
0
2
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
5
0
1
1
0
2
0
0
0
1
0
1
0
0
1
2
1
0
2
1
1
1
0
1
0
1
0
0
3
2
0
1
0
0
0
0
2
0
1
0
1
1
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
4
0
0
0
2
0
1
0
1
0
0
1
0
0
0
0
3
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
3
0
1
2
0
0
0
2
0
1
0
0
1
1
1
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
3
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
3
0
0
1
1
0
0
0
0
0
1
2
2
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
1
1
0
1
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
1
0
1
0
1
0
1
0
1
0
0
0
0
2
0
0
2
0
2
0
0
0
2
2
1
1
0
1
1
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
1
0
2
0
2
2
0
0
2
2
2
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
2
2
0
1
0
2
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
2
2
0
0
2
1
2
0
2
2
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
2
2
0
0
1
0
0
0
0
0
1
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
2
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
2
0
2
0
2
2
0
2
2
0
0
0
2
2
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
1
2
0
0
0
1
0
2
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
1
5
0
0
0
0
0
0
0
4
1
1
0
0
0
2
2
2
0
0
0
0
0
0
1
1
3
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
2
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
2
0
0
2
0
1
0
0
2
1
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
1
8
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
2
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
1
1
2
1
0
1
0
0
0
0
0
0
1
1
0
0
0
3
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
2
5
0
1
0
0
0
0
0
0
2
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
3
0
1
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
1
1
0
0
0
1
0
1
0
0
0
1
0
0
1
1
0
0
2
1
0
1
0
2
0
0
0
0
0
0
1
0
1
1
0
1
0
1
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
4
2
0
1
0
0
1
2
0
0
0
2
0
1
0
2
0
0
0
0
0
1
0
0
2
0
1
0
0
0
2
2
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
3
0
1
0
0
2
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
2
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
2
1
2
0
0
0
1
0
0
0
0
2
0
0
2
2
0
0
2
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
5
0
0
0
0
0
0
2
0
2
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
2
2
0
0
2
2
1
0
2
0
0
0
0
1
0
24
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
1
0
0
1
0
0
0
3
0
0
1
2
2
0
0
1
2
1
1
0
0
1
0
0
1
0
2
0
0
0
0
0
1
2
0
0
0
0
2
1
0
0
0
0
1
2
0
0
2
1
2
1
0
0
0
0
1
0
0
0
2
0
1
2
0
0
4
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
1
2
0
0
1
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
2
1
0
0
0
0
0
2
2
0
0
0
1
1
2
0
0
0
1
2
0
0
0
0
2
0
0
2
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
2
2
2
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
3
0
0
0
1
0
2
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
3
0
0
2
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
3
0
0
2
1
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
3
1
0
0
0
1
0
0
2
0
2
0
2
0
2
0
4
2
0
0
0
0
0
1
5
2
0
2
1
3
0
0
4
0
0
2
0
0
1
0
0
2
0
0
2
0
0
3
0
0
0
1
0
1
0
3
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
1
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
1
0
0
0
1
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
3
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
2
2
0
0
7
0
2
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
2
0
1
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
2
1
0
0
2
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
3
2
0
1
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
2
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
2
2
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
2
2
0
0
3
2
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
5
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
3
0
0
1
0
0
0
2
1
0
0
0
0
0
0
2
1
1
1
0
0
1
2
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
8
0
0
0
0
1
1
2
0
0
0
0
1
0
0
2
0
2
2
0
1
2
1
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
2
3
0
1
0
0
2
1
0
1
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
2
5
0
0
1
0
1
1
0
1
1
0
0
0
0
0
3
2
2
0
2
1
0
2
0
0
1
0
0
0
0
2
1
1
0
1
0
0
0
0
0
0
0
0
0
3
0
0
1
1
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
2
1
0
0
0
0
0
3
0
0
0
0
1
0
0
1
2
0
2
0
3
0
0
0
0
0
10
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
1
0
0
2
2
2
0
0
2
2
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
2
1
2
2
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
1
1
1
0
0
1
0
0
0
2
1
2
0
0
0
2
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
2
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
4
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
2
1
0
2
1
0
2
0
0
0
0
0
0
0
0
1
2
0
2
2
2
0
1
1
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
1
0
0
3
0
0
0
0
0
0
0
0
1
0
0
2
1
2
0
0
0
0
0
0
3
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
2
0
0
2
0
0
0
0
0
2
0
1
1
1
0
0
0
1
0
0
0
1
0
0
0
0
2
0
2
1
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
3
0
0
0
1
2
0
0
1
1
1
0
3
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
1
2
0
1
1
1
0
2
0
0
0
2
2
0
0
0
1
2
0
0
2
0
0
0
1
0
0
3
0
0
1
0
0
7
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
3
2
0
0
1
1
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
2
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
2
1
0
0
0
0
2
2
0
2
2
2
0
0
0
0
2
0
0
1
1
2
1
0
0
0
9
0
1
0
2
0
0
5
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
1
1
1
0
0
2
0
0
0
0
0
0
1
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
1
0
0
0
0
0
2
0
0
0
1
0
2
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
2
0
0
0
2
2
2
0
0
1
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
2
3
0
0
0
2
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
1
0
2
0
0
2
0
2
0
0
2
0
2
0
0
3
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
3
0
0
2
0
1
1
0
2
0
0
0
2
0
0
0
0
3
2
0
1
0
1
1
1
0
0
1
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
2
8
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
3
0
4
0
1
2
0
1
5
0
0
2
2
2
0
0
0
0
0
0
0
0
4
0
1
2
0
0
0
0
0
2
2
1
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
4
0
0
0
1
0
0
0
2
0
0
0
1
1
0
0
0
0
2
1
2
1
0
0
0
2
2
0
0
0
0
0
0
4
3
1
0
0
2
1
0
3
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
1
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
3
0
1
0
1
0
0
2
0
0
0
2
2
0
0
1
0
0
1
0
0
2
0
1
0
0
1
2
0
0
0
0
2
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
2
1
0
3
2
0
3
0
1
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
1
2
0
2
0
0
0
0
3
2
0
0
0
0
3
0
1
0
0
0
0
1
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
2
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
4
0
0
0
0
5
0
0
1
2
0
4
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
4
0
0
0
0
0
0
2
3
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
3
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
4
0
1
0
4
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
1
2
0
0
1
0
2
1
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
1
0
0
0
6
0
0
1
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
2
0
0
2
0
0
0
0
2
2
0
0
0
0
2
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
2
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
1
0
1
5
3
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
2
0
0
1
0
0
0
0
0
0
0
1
2
0
0
1
0
1
0
0
0
0
0
1
1
0
0
2
0
0
2
0
0
0
2
0
0
0
1
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
2
1
3
2
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
1
0
2
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
3
2
0
2
1
0
0
0
3
2
0
0
0
0
0
0
2
0
0
0
0
1
1
4
1
0
1
0
0
0
0
0
0
0
0
0
5
0
2
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
2
2
2
0
3
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
6
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
2
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
3
2
0
0
2
2
0
1
0
0
1
0
1
0
0
1
0
1
2
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
2
0
1
0
0
1
0
0
0
0
0
0
0
2
0
2
1
0
2
1
0
2
0
1
0
0
2
0
0
0
1
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
1
0
0
3
0
0
0
3
0
4
3
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
2
2
0
0
0
0
0
2
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
2
1
0
0
0
0
1
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
1
1
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
3
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
1
1
1
2
0
1
0
0
0
3
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
2
0
0
1
0
2
0
0
0
1
1
0
0
1
0
0
2
0
0
2
0
3
0
0
1
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
5
0
0
0
0
1
3
0
0
0
0
0
2
0
1
1
0
0
2
0
1
0
0
0
2
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
2
1
1
0
0
0
1
0
1
1
0
0
1
0
1
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
1
0
1
1
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
2
0
1
1
0
1
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
5
0
2
2
0
0
1
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
1
0
1
0
0
0
0
2
0
0
2
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
1
1
1
1
2
2
0
0
0
0
0
5
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
1
0
1
0
0
0
1
2
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
3
2
0
0
0
2
0
2
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
2
0
2
2
0
1
1
0
0
0
0
0
0
1
0
0
0
3
2
0
1
0
2
0
2
0
0
0
1
0
0
1
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
4
1
0
1
0
4
1
3
0
0
1
3
0
0
0
2
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
1
2
0
1
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
1
0
0
2
2
0
2
0
1
0
1
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
2
0
0
0
0
2
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
3
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
2
0
1
1
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
1
0
0
5
0
2
2
0
2
2
1
1
0
0
0
2
0
0
0
0
0
0
1
0
0
3
0
1
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
3
1
0
1
2
0
0
0
1
0
0
1
0
0
0
2
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
3
0
0
1
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
3
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
2
1
2
0
0
0
1
0
0
0
0
0
2
1
1
0
0
1
0
0
0
0
1
0
0
1
0
1
2
0
0
0
0
0
0
0
2
0
0
2
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
1
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
2
0
0
1
0
2
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
2
1
1
2
0
0
0
2
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
2
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
1
0
0
2
0
2
0
0
0
2
2
1
2
1
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
3
0
0
0
0
2
1
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
3
0
0
0
2
1
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
1
7
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
2
1
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
2
1
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
1
3
0
2
0
0
0
2
2
1
0
0
0
2
0
1
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
3
1
0
1
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
1
3
2
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
3
4
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
2
2
3
0
0
1
0
0
0
0
0
0
0
3
0
1
0
0
2
1
2
0
3
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
2
2
2
0
0
1
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
3
0
0
0
2
0
1
0
1
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
1
1
2
0
0
0
0
0
0
2
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
2
0
0
2
0
0
2
0
0
2
1
0
0
0
0
0
0
3
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
2
1
0
2
2
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
1
0
0
1
0
2
0
2
1
0
0
0
2
0
0
0
1
0
1
0
0
0
2
0
1
0
0
2
0
0
3
1
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
3
0
1
0
1
2
2
2
0
0
1
0
0
0
0
1
0
0
2
0
0
1
2
1
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
1
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
2
1
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
4
2
0
0
0
0
1
0
0
1
0
1
0
0
0
0
2
0
2
0
0
0
0
3
0
0
0
0
0
1
1
0
0
0
0
1
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
1
2
1
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
1
2
2
0
2
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
2
1
0
2
0
1
0
0
0
0
0
0
0
3
0
2
0
0
0
0
2
2
0
2
0
0
0
0
2
0
0
2
0
0
0
2
0
2
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
3
0
0
0
3
0
0
1
0
2
1
1
0
0
0
1
2
2
1
0
2
0
2
3
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
2
0
1
1
1
0
0
0
0
1
0
2
0
0
1
0
0
0
0
2
0
0
2
1
0
0
0
0
0
1
1
0
0
0
0
0
6
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
2
0
1
0
0
0
9
0
1
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
3
2
4
1
2
2
0
2
0
0
0
2
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
2
2
0
2
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
3
0
2
0
0
0
0
0
3
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
1
0
0
6
2
0
0
0
0
0
2
0
0
1
0
0
0
0
3
1
1
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
7
0
0
0
2
1
0
0
0
2
0
1
0
0
0
0
1
1
0
2
2
1
0
0
0
0
3
2
0
1
2
0
0
0
0
0
0
1
0
1
0
2
2
2
4
0
0
0
2
0
0
1
2
0
0
0
0
1
3
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
3
0
0
0
0
2
1
3
0
0
0
0
0
1
1
0
1
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
3
0
0
2
0
2
0
0
0
2
0
0
1
1
0
2
1
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
2
0
0
0
0
0
1
0
0
0
0
1
2
0
0
2
1
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
2
2
0
0
2
0
0
0
1
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
3
0
1
0
4
0
1
0
0
0
0
0
2
0
5
0
0
0
0
0
0
1
2
0
0
0
2
0
2
0
1
2
0
0
0
0
2
0
0
0
2
0
0
1
2
0
0
0
0
3
2
0
0
1
0
0
0
0
2
3
3
0
0
1
2
0
0
0
0
0
3
0
2
3
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
1
0
0
0
1
0
2
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
5
0
0
0
2
2
0
1
0
2
0
0
2
3
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
1
1
0
2
0
2
0
0
2
0
0
2
0
0
0
0
0
2
0
2
2
0
0
1
0
2
0
2
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
2
2
0
1
2
0
0
0
0
0
0
1
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
1
0
2
2
0
0
0
1
1
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
2
0
1
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
2
0
0
0
1
0
0
0
0
2
0
2
0
0
0
1
1
0
0
0
0
3
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
3
1
2
2
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
2
1
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
2
0
1
2
0
0
0
1
2
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
2
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
2
2
2
0
0
0
0
2
3
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
2
0
1
2
0
0
2
1
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
1
1
0
1
1
1
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
2
0
2
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
2
0
0
0
0
0
0
2
3
0
2
0
0
0
2
0
2
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
4
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
3
1
2
3
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
2
2
0
1
0
0
1
2
0
0
1
0
0
1
1
1
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
1
2
0
0
0
0
0
1
0
1
0
0
2
0
2
0
1
0
0
0
0
0
2
0
0
1
1
2
1
0
0
0
0
0
0
0
0
2
7
0
0
0
1
2
2
0
1
0
2
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
1
0
0
0
3
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
1
0
3
0
1
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
2
0
0
0
0
0
0
2
0
1
2
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
1
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
1
1
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
2
1
0
0
0
0
2
2
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
2
1
0
2
2
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
2
0
0
0
0
0
1
0
2
0
2
1
0
0
1
0
0
2
0
0
0
1
1
0
0
2
0
2
0
1
1
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
1
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
6
1
0
0
2
1
0
0
0
0
0
0
2
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
1
1
0
0
1
2
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
3
0
2
0
0
0
1
1
0
3
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
2
1
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
3
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
1
0
5
0
0
0
0
1
0
0
0
0
1
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
2
0
2
2
0
0
2
2
0
2
0
1
0
0
0
0
0
0
0
1
1
1
0
0
2
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
2
0
0
0
1
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
1
0
0
0
2
1
0
0
1
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
1
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
1
0
1
0
1
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
3
0
0
0
0
0
2
1
0
0
0
0
1
0
0
3
1
0
0
0
0
0
2
0
0
2
1
2
0
0
0
2
0
0
2
0
0
2
0
0
1
0
2
2
2
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
1
1
1
2
1
0
0
1
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
1
1
0
2
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
1
0
0
1
0
0
2
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
4
0
0
0
0
3
2
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
3
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
1
1
0
0
0
0
2
0
2
2
2
2
0
0
2
0
1
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
2
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
2
2
0
0
0
1
0
0
0
2
1
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
1
3
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
1
0
1
0
0
0
2
0
0
0
0
1
2
0
1
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
1
0
0
0
1
0
0
0
0
2
0
2
2
0
2
0
1
2
0
1
0
0
0
2
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
2
1
0
0
2
0
0
2
0
0
0
0
2
0
2
1
0
0
0
1
1
2
3
0
1
0
0
2
2
0
2
2
2
0
2
0
2
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
1
0
3
2
0
0
0
0
0
2
0
0
0
0
0
0
0
3
2
0
2
0
0
1
2
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
3
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
4
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
2
0
0
1
0
0
3
0
0
0
2
0
2
0
0
2
2
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
2
2
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
2
0
1
0
0
0
0
0
0
3
2
2
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
1
1
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
1
1
1
1
0
2
3
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
2
0
0
1
0
1
0
0
3
2
0
0
2
0
0
0
0
0
1
2
0
2
0
5
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
2
1
0
1
3
0
0
0
0
0
0
0
2
1
2
3
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
11
0
1
2
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
2
0
0
1
0
0
0
0
1
2
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
1
2
2
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
1
3
0
0
0
0
0
0
1
0
3
0
1
2
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
3
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
3
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
1
2
2
0
0
0
2
2
1
0
2
0
2
1
4
0
1
1
0
0
0
0
0
0
0
0
1
2
1
2
0
0
0
0
2
0
0
2
1
1
2
1
2
0
1
1
0
0
0
0
0
2
1
1
2
0
0
1
1
0
2
0
1
0
2
2
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
2
2
0
0
1
0
2
1
1
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
2
0
2
0
0
0
3
1
0
1
0
2
0
0
2
0
1
2
1
0
3
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
3
1
0
0
0
1
2
2
0
1
0
0
0
2
2
1
0
0
0
1
0
2
0
2
0
0
1
0
1
0
1
2
0
2
1
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
1
0
2
1
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
7
0
2
0
0
0
0
1
0
0
0
0
3
0
0
0
0
3
2
0
0
2
0
0
0
2
0
2
2
0
0
0
0
4
0
0
0
2
0
0
0
3
0
2
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
1
0
1
0
2
0
0
0
0
0
2
0
1
0
2
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
2
2
1
0
1
1
0
0
0
1
0
0
0
1
0
0
0
1
0
4
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
1
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
1
0
0
1
2
0
2
0
0
0
0
0
2
0
0
2
0
1
0
2
1
2
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
1
0
2
1
0
0
0
0
2
0
0
0
2
2
3
0
0
0
0
0
0
1
1
0
0
0
1
0
0
2
0
0
2
0
3
2
0
2
0
0
0
0
0
0
1
0
0
2
0
1
0
1
2
0
0
0
1
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
2
0
1
2
0
0
0
0
1
0
0
0
2
1
2
0
0
2
1
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
6
0
0
0
0
0
0
1
0
0
3
0
0
0
1
2
1
0
1
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
1
1
4
0
0
2
0
8
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
1
0
0
2
1
0
1
2
0
0
0
0
2
2
0
0
1
2
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
1
1
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
2
0
0
2
0
0
0
0
0
1
0
0
1
0
3
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
1
0
1
3
0
0
0
0
0
0
0
2
1
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
1
1
0
0
0
0
2
0
2
2
1
0
0
2
0
0
1
0
0
0
1
2
2
3
0
0
0
1
2
3
1
2
0
2
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
3
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
2
0
0
0
2
2
2
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
1
0
2
0
1
0
3
0
0
0
1
0
0
1
0
1
0
0
0
2
1
0
0
0
0
1
0
1
0
2
0
1
0
0
0
0
0
3
2
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
13
2
0
1
0
1
1
0
1
0
0
0
0
0
0
1
2
0
1
0
0
0
3
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
2
0
4
0
3
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
2
1
0
2
0
1
0
0
0
0
0
2
2
0
10
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
2
0
0
0
1
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
2
0
0
3
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
1
2
2
1
0
2
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
1
1
1
0
0
0
0
1
0
0
1
1
0
0
0
2
1
2
0
1
0
0
2
0
0
2
1
0
0
2
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
4
0
1
2
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
1
2
3
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
2
1
0
2
0
0
0
1
0
1
0
0
0
1
0
0
1
0
2
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
2
0
1
0
3
3
0
1
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
1
1
0
0
0
3
0
0
0
0
2
1
2
0
0
1
0
0
2
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
1
0
2
0
0
1
0
1
2
0
2
0
0
0
1
0
0
0
2
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
2
1
0
0
2
0
0
0
0
0
1
2
2
2
0
0
2
1
0
1
2
0
0
1
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
2
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
2
0
0
1
1
0
0
0
6
0
0
0
1
3
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
1
0
2
0
1
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
1
0
3
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
2
2
0
2
2
0
1
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
2
0
1
0
0
1
1
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
1
0
0
0
0
3
0
1
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
3
0
0
2
0
0
0
0
1
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
4
0
1
3
2
0
1
1
0
0
2
0
6
2
0
3
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
2
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
2
1
0
2
3
2
0
0
0
5
0
0
0
4
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
2
0
0
5
0
0
0
0
2
0
0
0
2
1
0
2
0
0
4
1
2
0
2
0
0
3
0
0
2
1
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
2
0
1
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
2
2
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
2
0
2
0
1
2
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
2
1
2
0
0
8
0
0
0
0
6
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
1
1
0
0
2
0
0
0
1
0
2
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
3
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
1
1
0
2
2
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
3
0
0
3
4
1
2
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
2
0
0
3
3
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
1
2
0
0
1
2
0
0
0
3
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
2
11
0
0
0
0
0
0
0
0
2
0
0
1
0
2
2
1
1
0
0
1
0
2
0
2
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
1
0
0
0
0
6
0
1
0
2
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
3
1
0
0
0
1
1
2
2
0
0
3
1
0
2
2
0
0
0
0
0
0
0
0
0
0
3
0
2
0
2
0
1
0
0
2
2
0
0
0
0
2
1
0
0
0
0
0
2
0
2
0
0
0
0
2
1
0
0
0
1
0
1
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
1
2
1
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
2
0
1
2
0
0
0
1
0
0
2
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
5
0
2
1
0
0
0
1
0
1
1
0
0
0
1
0
1
2
1
0
1
2
0
1
0
0
0
2
1
0
0
0
2
0
0
2
0
0
0
0
2
1
0
0
1
1
0
0
0
0
0
1
0
0
2
0
3
0
0
0
1
0
0
0
0
0
0
0
0
2
2
2
2
0
1
2
1
0
2
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
2
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
2
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
1
2
1
3
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
2
0
2
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
2
0
4
0
3
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
4
0
2
1
0
2
1
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
3
0
1
0
1
3
0
0
0
0
1
2
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
2
1
0
0
0
0
1
0
0
0
0
1
0
2
2
0
0
0
0
2
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
2
1
2
1
3
1
0
0
2
1
1
0
0
0
0
0
2
0
0
1
2
0
0
0
2
0
0
2
0
1
0
0
0
1
1
0
0
0
0
0
0
2
1
0
0
0
0
2
2
0
3
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
1
1
2
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
1
2
4
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
1
1
1
1
0
0
0
3
0
1
0
2
0
0
0
0
1
0
0
0
0
1
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
2
1
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
1
2
0
0
0
0
1
0
0
0
0
2
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
3
3
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
3
1
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
4
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
2
0
0
0
1
0
0
0
1
0
0
1
0
0
0
2
0
0
1
1
0
0
0
1
0
2
0
2
2
0
1
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
1
2
0
0
1
1
0
0
1
0
0
0
0
1
1
2
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
1
0
3
0
2
1
0
0
0
0
0
0
0
0
2
2
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
2
1
1
0
0
0
0
0
0
3
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
2
0
2
0
1
0
0
1
0
0
1
0
0
3
2
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
2
4
0
0
0
2
0
0
0
0
2
0
2
0
0
0
4
0
0
4
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
1
1
0
0
0
0
3
0
1
0
1
0
0
2
1
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
1
1
0
0
0
1
0
0
0
0
0
0
0
2
1
2
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
1
0
2
0
0
0
2
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
2
1
0
0
1
0
0
2
2
0
0
0
0
1
2
1
0
0
0
0
1
0
1
2
2
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
1
0
1
0
1
0
0
0
0
2
0
0
0
2
0
0
1
0
0
2
2
0
0
2
1
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
1
2
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
1
1
0
1
0
0
1
0
0
1
0
0
0
0
0
2
0
1
0
0
1
0
0
2
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
8
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
6
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
3
2
2
1
1
0
0
0
1
0
1
0
0
0
0
0
2
0
2
0
0
6
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
2
4
0
0
3
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
1
1
0
2
0
0
0
0
2
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
1
2
0
3
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
1
2
0
3
2
2
0
1
0
0
0
1
1
0
2
2
1
0
0
0
0
2
0
0
1
1
0
0
0
0
1
0
3
0
0
0
0
1
0
3
0
0
0
0
0
0
2
1
0
0
4
0
0
0
2
0
0
0
1
0
0
1
0
1
3
2
0
2
0
0
1
1
1
0
0
3
2
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
2
1
0
0
2
1
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
2
1
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
3
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
5
1
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
1
1
0
6
0
0
0
0
2
3
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
2
0
0
0
0
1
0
0
1
0
0
0
2
1
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
3
0
0
0
1
0
0
1
3
0
0
1
0
5
0
0
0
4
0
0
0
2
0
1
1
2
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
3
0
2
0
0
0
0
0
0
0
2
0
4
2
0
1
0
0
1
1
2
0
0
2
2
1
0
2
1
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
0
2
2
2
0
0
1
1
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
2
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
3
0
3
0
2
0
0
0
0
0
0
0
0
2
1
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
1
1
1
1
3
0
0
1
0
0
0
1
0
2
1
0
0
0
0
0
2
1
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
1
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
1
1
0
0
1
0
0
0
1
0
1
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
3
1
0
0
2
0
2
0
0
0
1
0
2
1
0
0
1
1
0
0
1
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
1
0
1
1
1
3
1
0
1
1
0
0
0
0
0
1
0
0
1
1
0
0
0
1
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
4
0
0
2
0
4
1
0
2
2
0
0
0
0
0
1
0
0
0
3
0
2
0
0
0
0
0
2
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
1
0
0
0
0
0
1
0
2
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
7
0
0
0
0
0
0
2
1
3
0
2
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
2
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
6
0
0
0
0
0
1
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
2
1
2
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
4
0
1
0
0
0
0
1
1
0
2
0
1
0
2
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
4
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
3
0
0
0
0
1
0
1
1
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
2
1
2
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
1
2
0
2
1
4
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
1
0
2
0
0
3
0
0
0
2
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
3
0
0
0
0
1
0
0
0
0
1
2
0
2
0
0
0
0
2
0
0
2
1
3
2
0
2
0
0
1
0
0
1
0
0
1
0
1
0
2
0
0
0
1
0
1
0
0
0
0
0
3
0
0
0
0
2
1
1
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
1
0
3
2
0
0
6
1
1
2
0
0
2
2
0
0
0
1
0
0
1
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
1
2
0
2
0
4
0
0
0
1
0
0
0
1
0
0
0
0
0
1
2
1
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
2
0
1
0
1
0
0
0
0
2
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
6
0
0
2
0
0
2
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
2
2
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
1
4
1
1
0
0
0
0
2
0
0
2
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
2
1
0
1
0
0
2
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
2
0
1
1
0
0
1
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
1
0
2
0
0
0
1
1
2
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
1
0
2
2
0
0
2
2
0
0
1
0
0
0
0
0
0
1
0
2
1
1
2
0
0
2
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
6
0
0
0
2
1
0
0
2
0
0
2
0
2
0
0
0
0
0
1
2
0
0
2
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
1
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
2
1
2
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
3
0
0
0
0
0
0
2
0
0
0
0
1
0
0
4
1
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
2
2
0
2
2
0
0
6
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
1
1
0
0
0
1
0
2
0
2
2
2
0
0
3
3
0
1
0
1
0
0
1
0
0
0
0
1
0
0
1
1
2
2
0
0
1
0
0
0
0
0
0
5
1
0
2
0
0
2
2
0
0
0
1
0
0
0
3
0
0
0
0
0
0
3
1
0
0
0
0
1
1
0
0
2
0
0
0
0
0
2
0
0
3
0
0
2
2
0
2
0
0
1
0
0
0
0
1
3
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
1
0
2
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
2
1
0
0
0
0
0
1
3
0
0
0
0
0
1
2
3
2
3
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
4
0
0
0
0
0
1
0
3
2
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
2
3
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
1
0
0
0
0
0
1
0
2
2
1
0
0
0
0
0
5
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
2
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
2
0
0
0
2
0
0
3
0
2
1
2
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
2
0
0
1
2
0
1
1
0
0
1
0
2
3
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
2
2
1
0
2
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
3
0
1
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
3
0
0
0
0
2
0
2
0
0
1
0
3
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
2
0
2
0
2
1
2
2
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
2
0
1
0
0
0
0
4
0
0
2
0
0
0
2
2
1
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
1
0
1
1
0
0
0
2
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
1
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
1
1
0
2
0
0
2
2
0
0
2
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
2
0
1
0
0
1
0
0
2
1
0
0
0
3
0
0
0
2
0
1
0
0
1
0
0
1
0
0
3
1
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
1
0
2
0
0
4
0
1
1
0
0
0
0
2
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
2
1
0
0
2
0
0
0
0
3
0
0
0
2
2
0
0
0
3
0
2
3
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
1
0
0
2
1
0
0
2
1
0
0
0
0
2
2
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
2
0
0
1
0
0
0
0
2
0
3
0
0
0
1
0
0
0
0
1
0
3
0
2
0
0
2
0
0
2
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
2
2
2
1
0
2
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
4
5
0
0
2
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
1
0
2
5
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
5
0
0
0
0
0
0
0
0
0
0
2
0
2
2
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
1
1
0
1
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
2
0
2
0
1
0
3
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
2
0
5
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
3
2
0
0
2
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
1
1
0
2
0
0
0
0
0
0
0
1
2
0
1
2
1
0
0
0
2
2
1
3
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
2
0
0
1
1
0
0
0
0
0
2
2
0
0
2
0
3
1
0
0
0
0
2
1
0
0
0
0
0
0
1
0
3
0
0
0
1
1
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
3
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
2
1
0
2
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
3
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
2
2
0
1
0
3
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
1
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
7
2
0
1
1
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
1
1
0
0
2
0
1
3
0
0
0
0
0
0
0
1
1
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
2
0
0
0
0
0
6
0
3
0
0
2
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
2
0
3
0
0
0
1
2
2
0
2
0
0
0
1
0
0
0
1
0
2
2
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
3
0
0
0
1
1
2
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
3
0
2
3
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
1
0
0
0
2
1
1
0
0
2
1
0
0
0
4
0
1
1
0
0
0
0
0
1
0
1
0
2
1
2
0
0
0
0
0
0
0
5
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
2
0
0
2
0
0
0
1
0
1
0
1
0
2
2
0
0
1
1
2
2
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
2
1
0
1
2
1
0
0
0
0
2
0
0
0
2
3
0
1
0
0
2
3
1
0
0
0
2
0
0
0
1
2
2
0
0
1
1
2
0
0
2
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
1
1
0
0
0
1
2
0
4
2
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
1
0
0
1
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
1
3
0
1
0
0
1
3
0
0
0
0
0
0
3
0
1
0
1
0
2
2
4
1
0
1
0
0
0
2
1
1
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
2
0
0
2
2
0
0
0
0
0
0
2
0
3
1
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
4
2
1
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
1
0
0
0
0
0
2
4
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
8
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
2
1
1
1
4
2
0
2
0
0
1
0
0
0
0
1
0
0
1
2
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
3
0
0
0
0
0
0
2
3
2
0
0
0
0
6
0
0
0
0
2
0
1
2
2
2
1
0
2
0
1
0
3
1
0
1
0
0
0
1
0
2
0
1
1
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
5
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
1
1
1
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
1
8
0
2
4
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
1
4
0
1
0
0
2
0
0
2
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
2
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
2
0
1
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
4
2
0
0
2
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
1
1
2
0
0
0
1
2
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
3
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
2
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
3
0
0
0
2
0
0
0
1
2
1
0
0
0
0
0
0
4
0
2
1
1
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
1
0
2
0
2
2
0
0
1
1
0
0
2
0
2
0
0
0
0
0
0
0
0
5
0
1
1
1
0
0
0
0
0
0
0
4
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
1
3
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
1
0
2
0
0
0
1
0
1
0
0
0
1
0
0
0
2
0
0
3
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
2
0
1
0
2
0
0
0
0
1
1
0
2
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
3
0
1
0
1
1
1
0
0
0
0
0
3
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
1
0
0
0
2
2
0
0
2
0
0
0
2
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
1
0
0
0
7
0
2
0
0
2
0
1
0
0
2
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
2
0
1
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
2
0
0
3
0
0
1
2
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
1
0
0
1
1
2
2
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
2
0
0
0
0
0
2
0
1
1
0
0
0
1
1
2
2
0
2
0
0
0
0
0
0
2
1
0
2
1
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
2
2
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
1
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
2
0
0
3
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
1
2
0
3
2
0
2
0
0
0
0
0
0
0
0
1
1
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
2
3
1
1
0
0
2
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
1
2
2
0
0
0
0
2
2
0
0
0
0
1
0
0
0
2
0
0
3
0
0
0
1
0
0
0
1
1
2
0
0
0
0
1
1
0
1
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
4
0
0
2
0
0
1
0
0
0
0
0
0
0
2
1
3
2
2
0
1
0
1
0
0
1
2
0
2
0
0
2
2
2
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
1
5
0
0
0
0
2
0
3
1
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
2
3
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
1
1
0
0
0
2
1
0
0
0
2
1
0
2
1
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
3
0
0
0
2
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
3
0
0
0
1
0
3
0
3
0
2
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
8
0
0
0
0
0
1
1
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
1
0
0
1
0
0
0
0
3
0
0
0
2
0
0
0
0
1
1
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
2
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
1
5
0
0
0
0
3
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
1
0
0
2
0
0
0
0
1
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
6
0
1
0
0
0
0
1
1
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
2
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
2
0
0
3
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
3
0
1
0
0
0
2
1
0
1
1
2
0
1
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
1
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
2
0
0
1
1
0
0
2
0
0
1
0
0
2
0
0
3
0
1
1
0
0
0
0
4
0
0
0
0
1
1
2
0
1
0
1
0
0
2
0
0
0
3
0
2
2
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
2
2
1
1
2
0
0
0
0
0
1
2
2
0
1
0
0
0
0
2
2
0
0
4
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
4
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
6
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
2
2
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
2
1
0
2
0
2
0
0
0
2
1
0
0
1
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
1
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
1
1
1
2
0
1
1
0
0
2
0
0
1
0
0
0
0
1
0
0
1
2
0
2
0
0
0
1
0
1
1
1
0
0
0
0
2
0
0
2
0
0
0
0
1
2
0
1
0
2
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
2
2
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
2
2
0
1
2
0
1
0
1
1
0
2
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
1
0
1
0
0
0
0
2
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
2
1
0
0
3
2
0
1
0
0
0
2
1
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
1
0
0
1
0
0
3
1
0
0
0
0
2
0
0
0
3
0
0
1
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
1
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
1
0
2
0
0
2
0
0
0
2
0
1
1
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
1
0
0
1
0
1
0
0
3
0
2
2
2
3
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
3
1
0
0
3
0
1
2
0
0
0
0
0
0
1
0
2
1
0
0
0
2
0
0
1
0
0
0
0
0
2
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
2
0
0
3
0
0
0
2
1
2
2
0
1
1
0
1
2
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
2
0
1
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
1
2
0
1
0
0
0
1
1
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
1
0
1
2
0
1
0
0
2
0
1
1
0
0
0
1
0
1
0
0
0
2
1
1
0
0
0
0
0
1
1
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
2
2
0
2
1
0
0
0
0
4
2
0
0
0
0
0
0
3
0
0
0
0
1
0
0
1
0
0
0
0
0
0
4
2
0
2
2
0
2
0
1
0
0
0
0
2
0
0
2
0
3
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
3
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
2
0
0
1
0
1
2
0
0
1
1
0
0
0
0
0
0
0
2
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
2
1
0
0
0
2
3
0
0
0
1
1
0
0
1
0
0
1
0
0
1
0
0
2
0
2
0
0
0
0
1
0
2
0
0
0
0
0
2
3
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
2
1
1
0
0
2
1
0
2
2
0
0
1
1
0
1
3
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
5
2
3
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
2
0
1
0
0
1
0
0
0
0
0
0
2
2
0
0
0
1
1
0
2
2
0
0
2
0
2
1
0
1
2
0
1
0
2
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
4
0
5
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
1
1
1
2
2
0
0
0
2
0
0
0
1
0
3
0
1
0
2
0
0
0
0
0
0
11
2
3
2
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
2
2
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
2
1
2
1
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
10
0
0
0
2
0
0
0
0
2
0
1
1
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
7
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
2
1
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
5
1
0
0
0
0
0
1
0
2
3
0
0
0
0
0
0
2
0
2
2
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
2
0
0
1
0
2
1
3
3
2
0
0
2
0
1
2
1
1
0
0
1
1
0
0
1
2
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
1
4
0
0
0
0
2
0
0
2
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
4
1
0
0
0
1
0
5
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
2
0
0
2
0
0
0
0
0
1
0
1
2
0
0
2
0
0
0
0
0
0
0
1
0
1
0
4
0
0
2
0
0
1
2
0
0
0
0
2
0
0
1
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
3
0
2
2
2
4
0
0
1
0
1
0
0
0
0
0
2
0
6
0
0
0
0
2
2
0
0
1
0
3
0
0
0
0
1
0
0
0
5
0
2
0
0
4
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
1
3
0
0
0
0
2
0
0
0
0
0
2
3
0
0
0
2
0
2
0
0
0
2
2
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
2
1
0
0
2
0
0
1
0
0
0
1
0
2
0
2
1
0
0
1
0
3
1
0
0
0
0
0
0
1
0
1
1
0
0
1
2
0
0
2
0
0
0
2
0
0
0
2
3
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
1
0
2
0
0
0
1
1
1
2
0
3
1
1
0
5
2
0
0
0
0
1
0
0
0
0
1
0
1
2
1
1
0
1
0
0
0
0
4
0
0
0
0
1
0
2
0
0
0
0
0
6
0
1
0
0
1
0
0
1
0
0
0
0
2
1
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
2
1
2
3
0
2
0
0
0
1
0
0
2
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
2
0
2
0
2
2
0
1
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
3
0
1
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
2
2
0
1
0
0
0
0
2
0
1
1
0
1
1
3
0
2
0
0
0
0
0
3
0
3
1
1
0
0
7
3
2
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
2
2
1
0
0
0
0
2
2
1
2
0
2
0
0
0
0
0
2
1
0
2
2
0
0
4
0
1
0
1
1
2
0
0
0
1
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
1
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
2
0
1
3
0
0
1
0
1
2
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
2
0
2
0
0
1
0
1
0
0
0
0
0
0
3
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
2
0
2
1
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
1
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
2
0
1
0
0
0
0
0
1
0
0
0
0
2
0
1
0
1
0
0
1
0
0
0
1
0
0
2
0
2
0
0
1
0
0
0
4
1
0
2
1
1
0
2
1
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
2
2
0
0
2
0
2
0
0
2
0
0
0
0
2
0
5
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
2
0
2
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
1
0
0
0
1
0
0
2
2
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
1
2
0
0
1
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
3
1
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
4
0
0
2
0
2
0
1
1
2
0
0
1
0
0
2
0
2
2
1
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
2
0
2
1
0
2
0
0
0
0
0
0
1
0
0
1
0
0
2
6
2
0
0
0
2
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
1
0
2
0
2
0
0
0
3
1
0
1
1
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
2
1
1
0
0
2
0
0
0
0
0
4
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
2
2
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
3
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
2
2
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
2
1
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
3
2
4
0
0
3
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
2
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
1
4
0
2
0
0
0
2
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
2
0
0
1
0
0
1
0
0
0
0
2
0
2
0
0
0
1
2
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
2
2
0
0
0
0
2
2
0
0
0
1
0
0
0
4
5
0
1
0
2
0
0
2
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
2
0
0
2
2
0
0
0
2
2
0
1
1
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
1
0
0
0
2
0
1
2
0
0
0
5
1
0
0
0
0
1
0
2
0
0
0
0
2
0
0
1
0
2
0
0
0
1
0
0
2
0
0
0
0
3
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
2
1
1
1
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
2
0
0
0
2
4
5
0
1
0
0
1
2
0
0
0
0
0
0
1
0
1
2
0
2
1
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
11
0
1
0
0
0
0
3
2
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
2
0
0
1
0
0
0
0
0
0
1
2
0
0
5
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
2
0
2
2
0
0
0
3
0
0
0
0
0
2
0
1
1
0
0
0
2
0
3
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
1
1
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
1
2
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
1
0
0
0
0
2
2
0
0
0
0
1
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
2
1
1
0
2
2
0
0
0
0
0
1
0
0
0
2
0
0
1
0
2
0
1
2
0
0
2
1
0
0
0
0
2
0
2
2
0
1
0
0
0
0
2
0
0
0
3
0
2
0
0
1
0
2
0
0
0
3
0
2
0
0
2
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
3
4
0
0
2
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
1
0
0
0
0
0
2
1
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
2
0
2
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
3
3
0
0
0
0
1
1
0
0
1
0
5
0
1
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
3
2
0
0
1
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
2
2
0
0
0
2
2
0
0
0
0
1
0
0
1
0
0
0
2
0
1
0
1
0
0
1
1
3
0
2
0
0
2
1
2
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
1
0
0
3
1
2
0
0
0
0
1
0
0
0
0
2
1
1
0
0
2
1
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
3
2
1
0
0
0
0
0
0
0
0
0
2
0
2
1
1
0
1
1
0
2
0
1
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
2
0
0
1
2
0
2
0
0
0
0
0
0
1
0
2
2
0
3
0
0
0
2
0
0
0
2
0
0
1
0
0
0
1
0
0
2
2
1
0
0
3
0
0
1
0
2
0
1
0
0
2
2
1
2
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
2
0
0
3
1
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
3
1
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
6
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
3
1
2
3
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
1
0
0
3
0
6
0
0
0
0
1
1
2
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
2
2
0
0
1
0
0
2
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
1
0
0
0
0
0
3
2
0
1
0
2
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
1
0
0
1
0
0
1
0
0
1
0
1
0
2
0
0
1
0
0
2
0
1
2
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
4
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
3
0
0
0
0
2
2
1
2
1
0
0
0
0
0
0
0
2
2
0
0
2
0
2
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
2
0
1
1
0
2
1
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
2
0
1
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
1
0
0
0
0
2
0
1
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
2
1
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
1
1
0
2
0
0
0
2
0
0
0
0
0
9
0
2
0
1
0
0
0
0
0
0
0
1
0
6
2
0
0
2
0
0
0
0
0
0
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
2
0
0
1
1
0
0
1
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
1
3
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
1
0
2
0
0
0
0
0
1
0
2
0
1
0
1
2
0
0
2
0
0
0
3
2
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
2
1
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
4
0
0
0
0
0
2
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
3
0
0
2
0
1
1
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
1
2
0
0
0
3
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
3
2
2
0
1
0
2
2
2
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
3
0
1
0
1
0
0
0
1
0
9
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
1
0
1
0
2
1
0
0
0
0
0
1
0
0
2
1
1
1
0
1
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
1
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
2
0
0
1
0
1
2
0
1
0
0
1
2
3
0
3
0
4
2
1
0
0
2
0
0
0
0
1
0
0
1
0
4
1
0
0
2
0
2
0
2
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
3
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
3
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
1
1
3
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
1
0
3
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
1
4
0
1
2
0
0
2
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
3
0
2
0
2
2
0
0
0
0
0
0
0
0
1
0
0
2
0
4
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
1
2
2
0
0
0
1
0
0
0
0
0
0
0
11
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
2
0
0
2
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
2
2
0
0
0
0
0
1
0
0
1
3
2
0
2
1
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
2
0
0
0
3
2
2
0
0
0
0
0
0
9
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
2
0
0
0
2
5
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
3
1
4
0
2
0
1
0
0
0
0
0
0
1
0
0
2
0
2
2
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
2
3
1
0
0
0
0
0
1
0
0
0
5
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
2
1
2
0
0
0
1
0
0
1
1
0
0
0
1
1
1
0
0
0
1
1
0
1
2
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
1
0
2
0
0
0
1
0
1
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
5
2
0
0
0
1
0
1
0
0
0
0
8
2
2
0
0
2
0
0
0
0
0
0
3
0
1
3
3
0
0
0
0
0
2
0
0
2
0
3
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
2
0
2
0
0
2
1
0
0
0
0
0
1
0
2
0
0
0
0
0
1
2
1
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
2
0
0
0
2
2
2
7
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
1
2
2
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
2
1
1
0
0
0
1
0
0
3
0
0
0
3
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
2
0
1
1
0
0
0
1
0
0
2
6
0
0
2
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
1
0
1
0
0
2
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
2
0
0
1
0
2
0
1
0
2
2
2
0
0
2
0
0
0
0
1
1
0
0
0
1
0
1
1
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
2
1
1
2
0
0
0
0
2
0
0
1
2
1
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
2
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
1
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
1
0
0
1
0
0
3
1
0
0
1
0
0
0
2
0
0
1
2
1
0
2
0
2
0
2
0
0
1
0
0
1
0
2
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
4
0
0
2
0
2
2
0
0
0
0
0
1
0
2
0
0
1
4
0
1
0
1
16
0
0
2
2
0
0
0
2
0
0
0
1
1
2
0
2
0
0
2
2
0
1
0
0
0
2
0
1
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
3
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
2
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
2
0
0
3
0
0
2
1
0
0
1
0
0
1
2
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
3
0
1
0
0
0
0
0
2
0
0
2
0
0
1
3
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
3
2
0
0
1
0
0
0
1
0
2
0
1
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
1
0
4
0
1
0
2
0
3
0
0
0
1
0
1
2
0
0
0
2
2
1
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
2
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
2
0
2
2
1
0
0
1
0
0
0
0
1
0
0
0
0
0
2
2
0
0
3
0
0
0
0
0
2
2
2
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
2
0
0
0
2
0
1
0
2
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
5
2
0
0
0
2
0
2
0
1
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
5
2
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
2
0
1
0
0
0
0
1
0
2
0
2
0
2
0
2
0
0
0
0
1
2
0
2
0
3
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
3
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
1
0
0
2
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
1
3
0
1
0
1
0
1
0
2
1
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
2
0
4
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
1
2
4
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
1
0
4
0
2
5
1
0
0
2
0
1
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
5
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
1
2
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
6
0
0
1
1
2
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
1
2
0
2
0
0
0
0
0
1
0
2
0
1
2
0
0
0
2
0
0
0
2
0
0
0
2
2
0
0
1
0
0
0
0
0
2
0
0
0
0
2
3
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
1
1
0
2
0
2
2
0
0
0
0
0
0
0
0
3
0
1
3
2
0
1
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
1
0
0
2
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
2
3
2
2
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
3
0
0
2
1
2
0
2
0
0
0
2
0
2
2
2
0
0
1
0
0
0
0
1
1
3
0
0
2
0
2
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
1
1
0
0
2
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
2
0
0
0
0
2
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
2
2
0
0
0
0
0
1
4
3
0
0
0
0
0
2
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
2
0
1
1
2
0
2
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
2
0
0
0
1
2
0
2
0
1
0
1
0
0
0
0
1
0
0
0
1
0
5
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
2
2
1
0
0
2
0
0
0
0
2
0
0
2
0
0
0
1
1
0
1
1
1
0
0
0
1
3
0
0
1
0
3
0
0
0
1
2
3
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
1
1
3
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
2
1
2
0
0
0
0
2
0
2
2
1
1
0
0
0
0
0
2
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
2
0
0
0
2
1
0
2
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
1
0
1
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
2
3
1
1
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
2
1
0
0
0
0
0
0
1
0
0
0
2
1
0
0
1
0
2
0
0
2
1
1
2
0
0
0
2
0
0
3
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
1
0
1
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
4
1
2
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
4
4
0
0
1
1
0
0
1
0
0
0
0
1
1
0
1
0
0
1
0
0
0
1
0
0
2
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
1
0
0
0
3
0
1
0
0
0
0
2
0
0
2
2
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
1
2
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
1
0
0
1
0
0
0
0
0
3
0
0
2
0
0
1
0
0
0
2
0
2
0
0
0
2
0
2
0
0
2
0
0
0
1
0
1
0
0
0
0
1
3
0
0
3
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
1
1
0
1
0
0
0
7
0
1
0
0
0
2
1
0
0
0
0
2
1
2
1
0
0
1
0
0
2
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
2
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
3
0
1
0
0
1
1
1
2
2
1
2
0
0
1
0
1
0
0
0
0
0
1
2
0
0
1
1
0
1
2
0
2
0
0
1
1
0
0
0
2
0
1
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
1
1
0
2
2
0
0
0
2
0
0
0
1
0
0
0
1
3
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
2
0
0
1
7
2
0
0
0
1
0
0
1
0
1
0
0
0
0
0
2
0
1
0
2
2
0
0
1
0
0
0
0
0
3
1
2
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
4
3
2
0
2
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
5
1
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
4
0
3
0
0
0
0
0
1
3
0
0
1
0
1
1
0
1
0
2
0
0
1
1
1
1
1
1
1
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
2
0
0
2
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
2
1
1
3
0
0
1
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
2
1
2
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
1
2
1
0
0
0
0
0
2
0
1
0
1
0
0
1
0
1
0
0
0
0
0
1
2
0
3
1
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
1
0
2
0
0
2
2
0
0
1
2
0
1
3
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
1
0
0
0
3
2
2
1
1
0
0
4
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
6
0
0
0
1
0
0
0
0
0
2
0
3
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
2
0
0
2
1
1
0
0
1
2
0
1
2
0
0
1
0
0
1
0
0
0
0
0
2
0
2
2
0
1
0
2
0
0
0
1
0
0
0
0
1
0
0
0
1
0
2
1
0
2
0
0
0
0
2
0
1
0
2
0
0
1
0
2
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
2
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
1
0
5
1
1
0
0
0
2
0
1
0
1
1
2
0
2
0
1
0
0
0
0
0
2
0
0
2
2
3
0
0
0
0
1
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
2
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
2
9
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
1
0
4
0
0
0
0
0
0
2
0
1
0
0
1
0
2
2
0
0
0
1
0
0
0
2
4
0
1
1
0
0
1
0
0
2
0
0
0
1
0
1
0
0
3
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
3
0
2
2
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
1
3
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
2
2
2
0
0
0
1
0
1
2
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
2
0
0
2
0
0
0
0
3
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
2
1
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
4
0
2
0
0
0
0
1
0
0
2
0
0
0
1
2
0
1
0
0
2
0
3
0
0
0
1
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
2
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
1
1
0
2
0
0
0
2
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
4
1
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
1
1
1
0
1
0
0
0
2
1
3
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
4
0
0
0
2
1
1
0
0
1
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
1
1
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
3
2
0
0
0
2
0
1
2
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
1
2
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
3
2
0
0
0
1
1
0
0
0
0
0
0
2
0
0
2
1
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
1
2
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
2
0
0
1
0
0
6
0
0
0
0
0
2
1
0
0
0
0
0
0
1
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
4
1
2
0
0
0
2
2
2
2
2
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
2
2
1
1
0
2
2
0
2
1
0
0
0
2
0
0
1
0
0
0
1
0
0
1
0
2
3
0
0
0
0
2
0
1
0
0
0
0
0
2
2
0
2
0
0
0
0
0
1
0
0
3
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
3
0
1
0
2
0
0
0
0
0
0
1
0
1
1
0
0
0
2
0
0
5
0
0
2
2
0
0
2
0
0
0
1
2
0
2
0
0
1
2
1
0
0
0
1
0
2
0
2
1
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
4
0
4
0
0
1
0
0
1
1
0
0
0
1
0
0
1
0
0
2
2
2
0
1
0
1
0
1
0
0
0
1
0
2
0
0
1
0
1
0
0
0
0
1
0
0
1
1
0
2
2
0
0
0
2
0
0
0
0
0
0
2
0
2
3
0
1
3
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
2
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
3
0
2
0
0
0
2
0
0
1
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
3
2
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
1
0
0
0
0
2
1
0
2
0
0
1
1
1
2
0
2
0
0
0
3
0
0
2
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
1
1
0
2
0
0
0
0
0
0
2
2
0
0
3
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
1
2
0
0
0
1
2
0
0
0
1
0
0
2
2
0
1
2
1
0
2
0
0
1
1
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
1
1
0
2
0
2
0
2
0
2
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
1
0
2
0
0
5
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
2
0
0
0
0
0
2
0
1
0
1
1
0
0
2
3
0
2
0
0
0
0
0
4
0
0
0
2
0
0
1
0
0
0
0
2
2
0
0
0
0
1
2
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
3
0
0
1
0
0
2
2
2
2
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
2
2
2
2
0
8
0
1
0
0
0
0
0
0
1
2
0
0
2
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
3
0
0
2
3
0
0
6
0
0
1
1
0
0
0
2
0
1
2
0
2
0
2
0
0
2
1
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
3
0
0
0
4
0
0
0
0
0
0
1
0
0
0
2
1
0
0
1
0
2
0
2
0
3
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
2
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
3
1
2
0
0
0
0
1
1
2
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
1
0
0
3
0
1
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
1
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
3
0
1
1
0
0
2
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
2
3
0
0
0
2
1
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
3
0
1
1
1
0
2
1
2
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
3
2
0
0
0
2
0
2
0
0
0
1
0
2
0
0
0
0
0
2
2
0
1
1
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
1
1
0
2
0
0
0
0
1
0
0
2
1
0
1
1
0
0
0
0
0
1
1
0
1
0
0
0
1
2
0
3
0
0
0
4
0
0
0
0
0
2
0
1
1
0
0
0
0
0
1
1
0
0
0
0
2
0
1
1
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
1
0
0
0
2
0
0
0
2
0
2
0
0
0
1
0
2
0
1
0
0
2
2
2
1
0
1
2
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
3
1
1
1
1
0
0
0
1
0
0
0
0
0
8
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
2
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
3
1
2
0
0
1
2
2
0
0
2
0
0
0
0
0
0
3
0
1
1
0
0
0
0
0
1
0
0
0
2
0
2
1
0
0
0
0
1
2
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
3
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
1
0
1
1
2
1
0
0
2
0
0
0
0
0
1
0
0
0
0
4
2
3
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
10
0
3
0
1
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
2
0
2
0
0
2
0
0
0
0
0
0
2
2
2
0
1
0
3
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
4
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
4
1
0
1
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
1
1
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
2
1
3
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
2
0
1
0
0
3
0
2
0
2
2
0
0
0
0
0
0
0
0
0
1
2
2
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
4
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
1
0
2
1
0
0
1
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
2
1
1
0
2
2
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
3
0
2
1
0
2
0
0
0
2
0
0
0
0
0
0
0
1
1
1
0
0
2
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
2
0
0
1
1
0
0
0
1
0
0
0
0
2
1
0
2
1
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
1
2
1
1
0
0
0
0
1
0
0
0
0
1
1
3
0
3
1
0
0
0
0
2
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
4
1
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
2
1
0
0
0
3
2
2
0
0
0
2
2
2
0
0
1
2
0
0
1
0
1
0
0
0
7
0
0
1
0
0
0
2
2
2
0
0
0
0
0
0
2
0
0
0
5
6
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
2
0
2
3
2
0
0
0
0
0
0
0
2
0
1
2
4
0
1
0
0
2
0
0
0
2
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
1
4
0
0
2
0
0
1
0
3
0
2
3
0
1
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
2
0
0
0
0
1
2
2
0
2
0
0
1
0
0
0
0
2
2
2
6
0
1
3
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
2
1
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
2
1
0
2
1
0
2
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
2
2
2
0
2
0
1
0
0
4
0
2
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
3
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
2
1
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
1
0
0
2
0
1
0
2
0
3
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
1
0
1
0
0
3
0
2
2
0
0
1
2
1
0
2
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
2
1
0
1
1
0
2
1
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
2
0
0
2
0
0
1
2
0
0
6
0
0
0
0
2
0
1
0
2
2
0
2
0
0
1
0
0
0
0
0
0
0
0
5
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
2
1
1
0
0
1
2
0
1
0
2
1
0
0
1
0
0
0
0
2
0
0
0
1
2
0
1
0
0
0
0
0
0
1
0
1
0
1
0
7
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
3
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
5
0
0
0
0
1
0
2
4
0
2
0
1
0
0
2
2
0
0
1
0
0
0
0
1
0
0
2
0
2
1
0
0
0
0
0
0
2
2
0
0
1
0
0
0
2
0
0
1
0
0
2
0
2
0
0
0
0
0
0
1
0
1
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
2
0
0
0
2
1
2
2
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
1
2
2
0
0
0
0
1
1
0
0
0
2
2
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
1
1
0
1
0
2
0
1
0
0
1
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
1
0
2
1
0
0
1
0
0
0
0
1
0
0
2
2
2
0
0
0
1
0
2
0
1
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
3
0
0
0
0
2
0
2
0
0
0
1
0
0
0
2
0
0
0
2
1
0
2
0
6
0
1
1
0
0
0
2
0
0
2
1
0
1
1
0
2
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
3
0
2
0
0
0
0
0
0
1
2
1
0
2
2
1
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
1
0
2
1
0
0
1
1
0
0
0
0
0
0
0
3
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
1
0
4
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
1
2
0
2
1
0
0
0
0
0
0
1
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
2
0
2
0
0
2
0
0
0
0
0
0
2
2
0
2
0
0
2
1
2
1
2
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
1
0
1
0
1
0
1
0
2
2
0
0
1
2
0
0
0
1
0
0
0
1
0
2
0
0
1
0
1
0
0
0
0
0
1
2
0
2
3
1
2
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
2
2
2
0
0
0
2
2
2
1
0
0
1
0
2
0
0
0
2
0
0
2
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
5
0
0
0
2
0
2
0
2
3
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
5
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
1
2
0
0
1
0
2
0
0
0
0
1
0
0
0
0
7
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
2
0
2
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
1
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
2
0
0
2
0
0
0
3
3
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
2
2
1
5
0
1
0
1
1
2
0
0
0
1
1
2
0
0
0
0
1
2
0
0
0
1
0
2
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
3
0
0
2
2
0
1
1
0
0
2
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
1
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
3
0
0
0
2
1
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
1
0
0
0
0
7
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
1
0
2
0
0
1
0
0
0
3
2
2
0
1
0
0
0
2
0
1
3
2
2
4
0
0
1
2
2
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
2
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
2
2
0
0
0
2
1
1
0
0
1
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
3
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
3
1
0
1
0
0
0
0
1
1
0
0
1
0
1
0
0
2
0
0
0
0
2
1
0
0
1
0
0
0
2
2
0
2
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
2
1
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
2
0
0
1
2
0
0
0
2
2
0
0
0
2
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
2
1
0
0
2
0
1
0
0
0
0
2
1
0
2
0
0
0
0
2
0
2
0
2
2
0
0
0
0
0
0
0
0
0
1
2
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
0
1
2
0
0
0
0
0
0
1
2
2
0
2
2
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
4
0
1
0
0
0
2
3
0
2
0
0
0
5
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
1
0
2
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
2
0
0
2
0
0
0
0
2
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
2
1
1
0
1
0
5
0
0
2
0
0
0
0
0
2
1
0
0
1
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
1
0
2
1
0
0
0
2
1
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
1
0
2
2
0
0
0
2
0
0
0
2
2
0
0
0
0
4
3
2
0
2
0
0
0
0
0
2
1
2
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
3
0
0
0
2
2
3
0
0
0
1
0
1
3
0
2
0
0
1
0
0
0
0
1
1
0
0
3
0
0
2
2
0
0
2
2
2
0
1
0
0
0
2
0
0
0
0
1
2
0
0
0
1
0
0
0
0
2
0
0
0
1
2
1
4
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
2
0
2
0
0
2
0
1
0
2
0
0
0
1
3
0
0
0
0
0
0
0
2
1
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
1
1
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
2
0
2
0
0
0
4
0
0
0
0
0
1
1
1
1
0
0
0
3
0
0
0
0
0
3
1
0
0
0
0
0
0
0
3
0
0
0
3
0
2
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
3
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
1
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
4
0
0
2
0
0
0
2
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
5
0
0
7
0
0
0
0
0
0
0
0
1
1
1
0
0
2
0
0
1
3
0
2
0
0
1
1
1
0
1
0
1
0
0
2
0
0
0
0
0
2
2
1
0
0
1
0
2
0
0
0
0
0
4
1
0
0
0
0
1
1
0
0
0
3
0
0
2
0
0
2
0
0
0
1
0
0
0
1
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
2
0
0
0
0
1
0
1
1
3
0
0
0
5
0
0
0
0
0
2
0
0
0
0
1
0
1
2
0
2
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
1
0
0
0
0
0
1
2
2
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
3
2
2
0
2
0
1
0
1
0
1
0
1
0
0
2
0
0
0
0
0
3
2
0
0
2
4
0
0
0
1
0
2
0
0
2
0
0
2
2
0
0
0
0
0
4
0
0
3
0
2
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
1
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
2
0
2
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
4
0
0
0
2
2
1
0
0
0
2
0
0
1
0
0
1
2
2
0
0
0
0
0
0
0
0
0
2
4
1
0
2
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
1
0
1
0
0
0
0
2
0
0
0
0
0
4
0
5
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
2
0
1
0
0
0
2
0
0
1
0
3
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
5
0
0
0
0
2
0
0
0
2
0
0
0
1
6
0
1
0
0
0
0
0
0
2
0
0
1
2
0
1
0
2
0
2
0
0
0
0
1
1
1
0
0
0
0
1
1
1
0
0
0
0
2
0
2
0
0
2
0
0
0
0
1
0
0
0
2
1
0
0
0
4
0
2
0
0
2
1
0
0
0
0
0
0
2
0
2
3
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
1
1
0
0
2
0
0
0
0
0
0
0
1
1
1
1
0
2
0
2
0
0
0
1
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
3
1
0
0
0
1
0
0
0
1
0
3
2
0
1
2
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
1
0
1
0
2
3
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
2
3
0
2
0
2
2
0
2
0
0
0
0
0
0
0
2
1
0
0
2
1
0
0
1
2
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
3
0
1
0
0
0
0
2
2
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
2
0
0
2
0
2
0
0
0
0
1
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
2
2
2
0
0
0
1
1
1
5
1
0
0
0
0
0
0
1
0
0
1
0
2
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
2
1
0
0
0
1
2
0
0
2
0
0
0
2
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
1
1
0
0
2
0
0
0
1
0
0
1
0
0
2
0
0
0
0
2
1
0
2
2
0
0
1
1
0
0
0
2
0
1
0
0
2
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
1
1
0
0
0
0
1
2
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
1
2
0
2
0
2
1
0
0
0
0
0
0
2
1
1
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
1
0
0
0
2
0
0
0
0
1
0
1
1
0
0
1
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
3
0
1
0
0
1
1
0
0
0
0
2
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
2
1
3
0
0
0
3
0
1
1
0
0
0
2
0
2
0
0
0
0
1
0
0
1
0
0
0
2
1
0
0
0
2
0
3
0
1
0
0
0
1
0
2
2
0
0
0
0
1
1
1
0
0
1
0
1
0
0
0
1
2
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
1
2
0
0
2
2
1
0
0
0
0
0
1
0
0
0
1
0
0
5
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
1
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
1
3
0
0
1
1
2
0
0
0
0
1
0
2
0
0
0
0
0
1
0
1
0
0
0
3
0
1
0
0
0
0
0
0
1
3
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
1
2
2
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
1
1
0
1
0
0
1
0
1
1
0
0
0
0
0
0
1
0
2
0
0
2
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
1
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
1
1
1
1
0
1
0
0
2
2
0
0
0
0
2
0
0
0
0
0
3
0
0
8
3
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
2
0
0
1
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
2
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
2
0
1
1
0
0
0
0
2
2
0
0
0
3
0
0
2
0
0
0
0
1
2
0
2
0
0
0
0
2
2
0
0
0
0
0
1
2
0
1
0
0
2
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
1
0
2
0
0
0
0
0
2
3
2
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
2
0
3
0
0
0
0
2
0
0
1
0
0
0
1
0
1
0
0
2
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
1
0
2
0
1
1
0
0
0
2
2
1
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
4
1
3
0
0
0
0
0
3
0
2
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
4
0
1
0
0
1
0
0
2
0
0
0
0
0
0
1
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
1
2
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
3
2
2
0
0
2
0
0
0
0
0
1
2
0
0
1
0
0
3
0
0
0
0
0
0
2
2
2
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
1
0
2
0
0
0
0
0
1
10
0
0
0
0
1
0
0
8
0
0
1
0
0
1
0
0
0
0
0
1
2
1
0
0
2
0
0
0
0
0
3
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
2
0
1
0
2
3
0
0
0
0
6
1
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
1
0
0
0
0
0
0
0
3
1
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
2
0
5
2
2
0
2
0
0
2
0
0
1
2
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
2
0
1
2
0
0
0
1
1
0
3
0
0
0
0
0
4
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
1
2
0
0
2
2
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
2
0
0
0
1
1
0
0
0
0
3
0
0
0
0
1
0
2
0
3
0
0
0
0
0
0
2
0
2
1
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
2
0
1
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
1
1
0
0
0
1
2
1
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
6
0
1
2
0
2
0
2
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
6
1
1
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
1
0
4
1
0
0
1
0
2
0
1
1
0
0
0
1
1
0
0
0
0
0
0
2
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
1
3
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
1
0
4
1
0
1
0
1
1
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
3
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
2
0
0
1
0
0
1
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
2
0
2
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
3
0
3
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
13
0
0
0
2
0
0
0
0
0
0
1
0
1
0
2
0
0
2
0
0
1
1
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
2
2
0
0
1
2
0
4
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
3
0
0
1
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
2
0
0
2
0
0
0
1
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
2
1
0
0
2
0
0
2
2
1
0
2
0
1
0
2
3
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
2
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
3
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
5
0
0
2
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
1
2
0
0
0
2
0
1
0
3
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
2
0
3
2
0
0
2
2
0
1
0
3
0
0
0
0
0
2
2
0
0
2
1
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
1
0
0
7
0
0
2
0
0
0
2
1
0
0
0
0
0
2
2
0
1
2
0
2
0
1
0
2
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
3
0
2
0
2
0
1
0
0
2
1
0
0
0
2
0
0
0
0
0
0
2
1
0
2
0
2
0
0
0
0
1
1
0
0
0
2
0
2
3
1
2
2
2
0
0
0
0
0
0
0
0
0
0
1
0
2
1
2
0
0
0
0
1
0
0
0
3
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
2
1
0
0
0
0
0
0
0
2
1
2
2
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
3
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
1
0
1
0
2
3
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
1
0
0
5
0
0
0
2
0
0
3
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
4
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
1
4
0
0
0
0
0
0
0
0
1
1
1
0
2
0
2
0
2
0
2
0
0
0
1
0
0
0
0
1
0
0
0
2
1
0
0
0
3
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
1
0
0
1
0
0
0
0
0
1
3
0
0
0
0
0
0
0
2
2
3
0
0
0
0
2
1
0
1
0
2
0
2
0
0
0
2
1
1
0
0
0
1
0
2
1
2
0
0
1
1
1
0
0
3
0
0
0
0
2
0
0
0
1
2
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
6
0
0
0
0
2
2
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
1
0
0
0
0
1
0
2
1
0
0
0
0
2
2
0
0
0
0
0
2
0
1
0
0
3
0
0
0
1
1
1
0
0
0
0
2
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
2
0
1
0
0
1
0
0
6
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
2
4
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
2
1
2
0
2
0
0
2
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
3
1
0
0
0
0
1
0
2
0
0
0
0
1
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
3
0
0
1
2
0
1
0
0
2
0
0
0
0
2
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
2
2
1
2
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
2
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
2
0
1
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
2
0
2
0
1
0
2
0
1
0
2
2
0
0
0
2
1
0
0
0
0
2
1
1
0
3
0
9
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
2
0
0
2
0
0
0
4
0
2
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
2
2
1
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
2
0
0
0
0
0
1
1
1
1
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
5
1
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
1
2
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
2
0
2
0
0
0
0
3
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
2
2
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
3
1
2
2
0
1
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
2
0
0
1
0
0
2
0
1
2
0
2
0
0
2
2
0
2
0
2
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
3
0
0
4
0
0
1
0
0
3
0
0
0
1
1
0
0
2
0
0
0
0
0
2
2
1
0
2
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
2
1
0
0
0
2
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
6
0
2
0
1
0
0
1
0
0
2
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
2
2
3
0
0
0
0
0
2
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
1
1
0
3
2
1
0
2
0
0
3
0
3
1
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
2
0
0
4
1
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
2
0
0
1
1
2
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
1
1
5
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
1
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
3
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
2
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
2
1
0
2
0
0
0
0
1
0
0
2
0
0
3
0
2
2
0
1
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
1
2
1
0
1
1
0
0
0
0
2
0
2
0
0
0
0
3
0
0
0
0
0
1
2
0
1
0
0
0
1
0
0
0
0
0
1
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
3
1
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
3
1
0
4
0
0
0
3
0
2
0
0
0
0
0
1
0
0
0
2
0
3
2
0
0
1
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
1
0
3
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
1
0
0
0
2
0
2
0
0
2
0
0
2
0
2
0
1
0
0
1
0
0
0
0
2
2
0
0
0
1
2
0
3
1
0
2
2
0
0
0
0
2
0
0
0
0
0
2
4
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
4
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
2
0
2
0
0
1
1
0
1
0
1
1
0
0
0
0
0
0
0
3
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
1
0
0
0
0
1
1
0
1
1
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
1
0
0
2
0
1
2
2
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
1
1
0
4
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
2
0
0
1
0
0
0
1
3
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
2
0
2
1
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
1
3
0
0
0
0
1
0
0
0
1
0
0
1
1
1
0
0
2
0
2
4
1
0
0
2
0
0
0
1
0
0
1
0
0
1
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
11
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
2
0
0
0
1
0
0
3
2
0
3
0
0
0
0
0
0
0
2
2
0
1
0
0
0
1
1
0
0
0
0
5
2
0
2
2
0
0
0
2
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
1
1
0
2
0
2
0
2
1
2
0
0
2
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
4
0
2
0
0
1
1
2
1
1
1
0
0
0
0
1
2
1
0
1
0
0
0
0
0
2
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
2
1
0
2
1
0
0
2
1
1
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
2
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
1
0
0
0
0
0
1
1
0
2
1
1
1
2
0
0
0
0
0
5
0
0
2
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
3
1
0
0
0
2
0
1
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
2
2
0
0
0
0
0
2
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
1
2
1
0
0
0
1
0
1
0
0
0
1
1
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
1
0
0
0
2
2
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
5
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
1
2
0
0
0
0
0
0
0
1
2
0
0
2
2
0
0
0
0
0
0
2
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
1
2
0
2
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
2
2
0
0
0
2
2
0
0
0
2
1
3
0
1
2
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
2
1
0
0
0
0
0
0
1
1
1
2
0
0
3
0
0
0
1
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
1
2
0
1
0
0
0
2
2
0
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
2
0
0
2
0
0
0
1
2
0
0
1
0
2
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
1
0
1
1
0
0
0
0
0
0
3
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
2
4
0
0
1
0
0
2
0
0
2
0
0
1
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
2
0
0
1
1
2
0
0
0
2
2
0
0
0
3
0
0
2
2
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
2
2
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
2
1
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
1
0
1
0
1
0
0
1
3
0
0
1
0
0
0
0
0
1
5
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
3
1
0
1
0
2
2
3
0
1
0
2
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
1
3
0
0
0
0
0
0
0
0
1
0
0
1
2
0
1
2
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
1
0
0
0
7
0
0
2
0
0
0
3
2
1
0
0
0
0
1
0
1
0
0
0
0
0
5
0
0
0
0
1
0
2
0
0
0
2
0
0
0
1
1
1
0
0
2
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
1
1
0
2
0
0
0
2
2
2
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
3
0
0
0
0
1
0
1
1
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
2
1
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
1
2
3
0
2
0
2
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
2
0
0
4
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
2
0
2
0
0
2
0
0
2
0
1
0
0
1
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
7
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
1
1
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
2
2
0
0
0
6
1
0
0
0
1
1
0
1
0
1
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
1
3
0
0
0
1
2
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
2
0
2
2
0
0
3
0
1
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
3
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
3
0
0
0
0
2
2
0
0
0
0
2
1
0
0
1
0
2
1
0
2
0
0
0
0
4
2
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
1
2
0
0
1
0
1
0
0
1
0
0
0
0
5
0
0
0
0
2
0
3
0
1
0
0
0
0
0
1
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
2
2
0
1
1
0
2
0
0
1
1
0
0
3
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
2
2
1
1
0
0
0
1
2
0
0
4
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
3
2
0
1
0
0
1
2
1
1
0
0
0
2
8
0
0
0
2
0
0
1
2
0
1
0
0
0
0
0
2
0
2
2
0
2
0
0
3
0
0
2
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
2
2
0
0
1
0
5
0
0
1
0
1
0
0
0
1
0
0
0
0
8
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
1
1
0
1
2
0
0
0
1
0
0
0
4
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
2
3
0
2
0
3
0
0
0
0
1
2
0
2
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
3
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
1
3
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
4
0
0
1
0
1
0
0
0
2
1
0
0
1
0
2
2
1
0
0
0
0
2
0
1
2
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
3
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
3
0
1
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
3
0
0
0
2
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
3
3
0
1
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
2
0
0
0
2
0
0
0
0
1
1
0
6
0
0
2
0
1
0
2
0
0
0
1
0
0
0
1
3
0
2
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
2
2
0
0
1
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
2
0
0
3
1
1
0
0
0
2
0
1
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
1
0
0
0
2
1
1
0
1
0
0
1
0
0
2
0
0
0
1
2
0
3
1
0
0
2
0
0
0
0
0
2
0
0
0
0
1
1
1
0
0
0
2
2
2
0
0
0
1
0
0
0
0
0
2
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
2
0
2
1
1
0
0
0
0
1
0
1
0
0
0
0
2
0
5
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
1
1
1
0
2
2
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
4
0
2
0
2
1
1
0
1
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
4
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
1
0
0
0
3
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
4
0
1
0
2
2
0
0
0
0
0
2
3
0
1
0
0
0
0
2
0
0
0
0
0
3
0
0
0
1
1
2
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
2
2
0
0
0
2
0
2
0
2
1
0
0
0
1
3
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
2
0
0
1
4
2
2
1
0
0
0
0
0
1
0
1
2
0
0
0
2
2
0
0
0
1
2
1
3
0
0
0
1
0
0
1
2
1
1
0
1
2
0
1
0
0
0
2
0
0
0
0
2
1
1
0
0
0
2
1
0
0
0
0
0
0
2
0
2
0
3
0
0
2
0
0
0
2
1
0
2
2
6
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
2
1
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
1
3
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
2
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
2
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
2
0
2
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
2
0
0
1
0
0
2
0
0
1
2
2
0
0
0
0
2
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
1
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
3
0
2
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
2
0
2
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
1
1
0
2
2
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
4
0
0
2
1
0
0
0
0
5
2
0
0
2
2
0
1
0
0
0
0
2
1
0
0
1
0
2
0
1
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
3
4
0
0
0
0
2
0
0
0
0
0
1
0
2
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
2
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
2
0
1
0
1
0
0
2
0
2
0
1
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
2
1
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
2
0
1
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
4
0
0
0
0
0
0
0
1
0
2
0
0
0
2
1
0
4
0
0
2
0
2
0
0
0
0
0
1
0
2
2
2
0
0
0
2
0
1
5
0
0
0
0
1
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
3
0
0
1
0
0
0
2
5
1
1
0
2
3
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
3
2
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
3
0
2
0
2
0
0
0
1
0
2
2
0
1
0
0
2
2
0
0
0
4
0
0
0
2
2
0
0
0
0
2
0
2
0
2
2
0
0
2
0
1
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
1
0
0
0
0
0
3
0
0
0
0
2
3
2
0
0
2
0
0
0
2
1
1
0
0
0
2
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
6
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
3
2
0
0
0
0
1
0
0
0
0
2
1
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
1
2
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
2
1
0
2
0
0
1
1
0
3
2
0
0
2
2
2
0
0
0
0
2
0
1
2
0
1
1
0
0
0
2
0
0
1
0
1
0
0
0
3
2
1
0
0
1
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
2
0
2
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
2
0
0
19
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
1
2
0
3
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
1
0
0
0
0
2
0
2
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
2
0
0
1
0
1
0
0
3
0
0
0
0
0
1
0
2
0
0
0
1
0
2
2
0
0
2
0
0
2
0
0
0
0
0
0
8
1
0
0
2
0
0
1
0
0
0
1
0
1
0
0
4
4
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
2
3
0
0
0
2
0
0
0
0
10
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
1
0
1
0
2
0
0
2
0
0
0
1
2
0
0
2
0
1
0
0
0
2
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
3
1
0
0
1
1
0
0
1
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
2
0
0
3
0
2
0
0
0
0
0
0
0
1
2
0
0
0
1
4
4
0
0
1
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
5
0
0
0
0
0
0
2
0
0
1
1
0
2
1
2
0
2
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
3
0
1
0
1
0
0
0
0
1
0
0
4
0
0
1
0
0
1
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
1
0
7
0
0
0
0
0
0
2
0
0
0
0
0
0
3
2
0
2
0
0
1
5
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
2
2
0
2
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
1
2
1
3
0
0
0
2
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
5
0
0
0
3
0
0
0
6
1
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
5
2
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
4
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
3
0
1
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
1
0
2
0
1
0
1
2
0
0
0
0
0
0
0
3
0
3
1
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
2
2
2
2
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
1
0
0
3
1
0
0
7
1
1
1
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
3
2
4
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
1
0
0
2
0
2
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
4
3
0
0
1
0
3
1
0
0
0
0
0
0
1
1
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
3
2
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
1
1
1
2
0
0
2
1
2
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
2
0
0
0
0
0
2
1
0
1
2
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
10
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
3
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
4
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
2
4
1
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
1
0
3
0
0
3
1
2
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
1
1
2
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
2
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
2
0
0
2
0
0
1
1
0
0
0
0
0
0
1
2
2
0
0
2
0
0
2
0
0
0
2
0
2
1
0
0
0
0
0
2
0
2
0
0
0
2
0
1
1
0
1
0
0
1
2
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
1
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
2
0
1
3
1
0
3
0
1
0
2
0
1
0
0
0
0
1
0
1
0
0
2
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
1
0
0
2
3
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
2
1
2
1
0
1
1
0
2
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
2
2
0
0
0
2
3
1
2
6
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
1
0
0
0
1
0
1
0
2
1
0
2
0
1
1
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
4
0
3
2
0
0
0
0
1
0
0
0
0
1
0
2
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
2
0
0
4
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
5
2
0
1
0
0
1
2
0
0
0
0
0
0
0
0
3
0
1
0
0
0
1
1
2
2
0
0
0
1
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
1
3
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
2
2
0
0
0
2
0
0
3
0
0
0
0
0
0
1
5
0
0
0
0
2
0
0
2
0
0
2
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
2
0
0
1
0
2
1
0
1
0
0
0
0
0
3
1
2
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
3
0
0
3
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
2
1
0
0
0
1
5
0
0
0
0
0
0
1
0
0
0
0
9
0
0
0
0
1
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
2
0
2
0
0
2
0
0
0
3
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
2
0
0
1
0
3
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
2
0
0
1
2
0
0
2
0
0
0
2
2
0
2
0
0
1
0
0
1
0
0
2
0
0
0
0
1
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
2
0
3
1
0
0
2
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
1
3
0
0
1
0
3
1
0
0
1
0
0
1
0
1
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
5
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
1
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
0
5
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
2
1
0
0
0
0
1
0
1
0
2
0
0
0
0
0
2
2
0
0
1
2
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
2
0
0
0
2
3
1
3
0
0
0
0
2
0
5
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
1
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
2
2
0
0
0
3
1
2
0
0
1
0
2
0
2
0
2
0
0
0
0
0
0
1
0
1
0
2
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
1
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
3
1
3
3
1
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
2
0
1
2
1
0
0
0
2
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
1
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
2
0
0
0
3
3
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
1
2
1
0
0
0
3
0
0
1
0
0
0
1
0
0
0
0
1
0
2
0
0
0
3
0
2
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
1
2
0
0
1
0
0
0
1
1
2
1
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
2
0
2
0
0
0
3
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
3
0
1
0
0
2
0
0
0
0
0
1
1
0
0
1
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
1
0
0
0
0
0
0
0
1
2
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
4
0
2
1
0
0
0
5
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
2
0
1
2
1
0
1
2
2
0
6
0
0
2
0
0
1
0
0
0
0
3
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
2
2
0
1
0
5
0
2
1
2
0
0
0
3
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
7
0
2
2
0
0
0
0
1
2
0
0
1
1
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
3
0
0
2
2
0
1
0
0
0
2
0
0
0
2
2
1
0
2
0
2
2
0
2
0
2
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
1
0
0
0
2
3
0
0
0
0
1
0
0
0
1
0
2
0
0
0
1
1
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
2
0
3
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
2
0
0
2
0
0
2
1
0
0
2
0
0
2
1
0
0
0
0
0
0
0
2
0
1
2
1
0
0
0
0
1
0
0
2
1
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
2
0
0
1
0
0
0
0
2
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
2
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
2
2
3
0
1
0
2
1
0
1
0
2
0
1
0
1
0
0
1
2
0
2
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
4
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
3
0
0
0
0
1
0
0
0
2
0
2
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
2
1
2
0
0
1
3
0
0
0
1
0
0
0
0
0
0
0
0
0
3
1
0
3
0
1
0
2
0
2
1
0
0
0
2
1
0
3
2
0
0
0
0
0
0
2
0
0
4
0
1
2
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
2
1
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
3
1
0
0
0
0
1
0
0
0
3
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
4
1
0
2
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
1
0
0
0
2
1
0
3
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
3
2
0
0
0
0
0
6
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
1
2
0
0
2
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
2
1
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
1
2
1
0
0
0
1
0
3
0
0
0
0
1
0
0
2
0
0
0
0
0
1
1
2
0
2
1
0
0
0
0
0
2
1
0
1
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
2
1
0
2
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
1
0
0
0
2
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
2
0
2
0
2
2
0
0
2
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
2
0
3
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
2
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
5
0
1
0
0
1
3
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
2
0
1
0
0
0
2
3
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
3
0
2
0
1
0
0
0
0
0
0
3
0
0
0
0
1
3
0
0
0
0
0
1
0
0
0
2
0
3
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
8
0
0
0
0
3
1
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
2
0
1
0
0
0
0
0
0
1
0
9
0
0
1
0
0
1
0
1
2
0
1
0
0
1
2
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
6
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
3
0
0
0
0
0
1
0
1
0
0
0
3
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
2
1
0
1
1
2
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
2
0
3
0
0
0
0
2
2
0
0
0
2
1
0
0
2
0
2
0
0
1
0
0
1
0
0
0
2
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
2
1
2
2
2
3
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
2
0
0
1
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
5
0
0
0
0
1
2
0
1
1
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
1
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
2
0
2
0
2
0
0
2
6
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
1
2
1
0
0
0
0
0
2
1
0
0
0
0
0
3
0
0
0
0
0
1
0
1
0
0
0
1
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
1
0
0
0
0
0
2
0
0
2
0
0
0
2
1
1
1
2
0
0
0
1
0
2
0
0
0
0
0
1
0
0
1
2
0
1
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
3
1
3
0
0
0
0
0
0
0
0
1
0
2
2
0
1
0
0
2
2
2
1
4
1
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
4
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
3
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
1
0
2
0
1
3
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
1
1
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
2
2
0
0
0
0
2
2
0
5
0
1
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
2
0
2
0
0
0
1
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
1
4
0
0
1
0
1
0
2
1
0
0
0
2
2
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
2
0
2
0
0
0
3
0
0
0
0
0
2
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
3
0
0
0
0
0
2
1
1
2
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
1
1
0
0
2
0
3
0
0
1
0
2
0
0
0
0
0
2
1
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
2
2
0
3
0
0
2
0
0
0
0
0
3
0
0
1
1
1
0
2
0
0
2
0
0
2
0
0
0
0
2
0
0
0
2
0
2
0
0
1
2
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
4
2
1
2
0
0
1
0
0
1
0
2
0
0
1
0
0
0
0
0
3
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
3
0
0
1
0
0
0
2
0
0
0
0
0
2
0
1
4
0
2
2
0
2
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
3
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
1
1
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
2
1
1
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
3
2
0
0
0
0
3
1
1
1
0
3
0
0
2
3
0
0
5
1
0
0
1
2
2
0
0
0
2
2
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
2
1
0
1
1
0
0
0
0
0
0
3
1
1
0
1
0
0
0
3
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
1
2
0
1
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
2
2
0
0
1
0
0
2
2
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
1
2
0
2
2
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
2
2
2
0
1
0
0
0
0
1
0
0
2
0
0
0
2
1
2
2
1
0
0
2
0
0
0
0
0
2
1
2
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
2
0
2
1
4
2
1
0
0
0
0
0
1
0
0
0
0
2
1
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
2
2
2
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
1
0
0
1
2
0
0
3
2
0
0
2
0
2
2
0
0
0
0
1
1
1
0
0
0
1
0
1
2
1
1
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
2
0
0
0
1
0
1
0
2
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
2
3
1
0
1
1
2
0
2
1
2
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
2
3
3
0
0
0
1
1
0
0
0
0
0
2
1
1
2
0
0
1
10
0
1
0
2
0
0
2
0
0
0
0
2
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
2
0
0
1
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
2
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
1
2
2
1
2
0
1
0
1
2
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
9
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
2
2
1
0
0
0
0
0
0
1
0
1
0
2
0
0
1
1
1
0
1
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
2
1
1
0
0
0
0
0
0
0
0
0
1
2
0
0
1
2
2
8
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
1
0
3
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
2
2
0
1
0
0
2
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
2
0
1
0
1
0
0
0
0
0
0
2
1
0
0
2
2
0
0
0
0
0
1
0
0
1
0
2
2
0
0
1
0
0
0
0
1
1
0
0
0
0
1
3
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
2
0
4
0
0
2
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
1
2
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
4
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
2
1
2
0
0
2
0
0
0
0
1
0
3
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
2
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
1
1
0
0
2
0
0
0
0
4
0
0
0
0
1
0
0
0
0
3
1
0
1
1
0
2
1
1
2
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
3
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
2
1
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
3
1
1
0
0
0
0
0
0
0
0
0
3
2
1
0
0
0
0
0
2
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
1
9
0
0
0
1
0
0
0
1
2
0
1
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
1
0
1
1
1
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
2
0
1
0
0
2
0
0
1
2
2
0
0
2
2
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
2
1
1
2
0
1
2
1
0
1
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
1
0
1
2
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
3
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
2
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
2
1
0
2
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
2
0
1
2
2
0
0
0
3
3
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
2
0
0
0
0
2
0
0
1
0
1
1
0
2
0
0
1
0
0
0
2
0
2
0
0
1
2
2
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
1
0
0
3
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
3
0
2
1
0
0
1
1
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
1
0
3
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
1
3
2
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
3
0
0
0
1
0
1
0
2
5
0
0
0
0
0
0
0
2
1
1
0
0
1
2
0
1
1
0
2
0
1
0
0
1
0
1
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
2
2
0
0
1
2
0
2
0
0
6
0
2
1
0
0
0
3
0
0
2
0
2
0
0
2
3
3
0
0
0
0
0
2
0
2
0
0
0
1
1
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
4
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
1
0
1
0
0
1
1
0
0
0
0
1
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
3
0
0
1
0
0
0
0
1
0
0
0
0
4
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
1
0
2
0
0
0
1
2
0
0
0
2
1
2
0
0
0
0
0
2
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
2
1
0
2
0
1
2
0
0
0
4
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
2
0
9
0
1
2
1
0
0
1
1
0
0
4
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
2
0
2
0
1
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
2
2
0
0
0
0
0
2
0
0
1
2
1
2
0
0
0
2
0
0
0
2
0
0
0
2
0
2
0
0
2
0
1
0
2
0
0
0
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
1
2
0
1
0
1
0
0
0
2
0
0
1
0
2
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
1
0
1
0
1
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
1
2
0
0
3
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
2
0
0
0
0
0
0
2
0
2
0
0
1
2
2
0
0
0
1
0
0
0
2
0
0
1
2
2
4
0
0
0
0
0
0
0
0
2
0
2
1
0
0
1
1
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
1
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
3
0
0
1
0
0
0
2
1
1
2
3
0
0
0
1
2
1
2
0
0
0
0
0
0
0
0
0
0
0
1
2
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
1
0
1
2
0
1
0
0
0
0
0
0
0
0
1
2
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
1
2
0
2
0
0
0
1
0
0
1
2
0
0
0
7
0
0
0
1
2
2
1
2
3
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
2
1
2
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
1
2
0
1
0
0
1
0
0
3
0
0
0
0
0
0
0
0
2
1
0
0
5
2
0
0
0
0
1
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
2
0
2
1
0
1
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
2
1
0
4
0
0
0
0
2
0
3
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
2
1
3
0
0
0
0
2
0
1
1
0
2
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
2
1
0
0
2
1
1
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
3
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
1
0
0
0
0
0
0
1
0
2
1
1
0
0
0
0
0
0
1
1
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
2
0
2
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
7
0
0
0
0
0
0
0
0
0
1
1
0
1
0
4
1
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
4
1
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
3
1
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
1
1
2
3
0
0
0
0
1
4
3
0
0
2
0
0
0
2
0
2
0
0
0
0
1
0
0
0
1
1
0
1
0
0
2
0
1
0
0
0
2
0
1
0
1
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
3
1
0
2
2
1
0
0
0
0
2
2
0
0
0
0
2
0
1
0
1
3
2
0
2
0
0
0
0
0
2
2
0
0
0
1
0
1
0
0
0
0
0
0
2
0
1
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
1
0
0
3
1
2
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
2
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
2
1
0
0
0
3
1
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
3
0
2
0
0
0
0
0
0
1
0
0
0
2
1
0
0
1
0
0
1
0
0
0
0
0
0
1
4
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
2
0
0
0
0
0
3
1
3
0
0
0
1
0
3
0
0
0
1
0
0
2
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
4
0
1
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
2
0
1
0
0
0
0
1
0
0
1
0
0
0
3
0
0
1
0
0
0
0
0
0
0
5
1
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
1
0
3
0
2
1
2
0
2
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
2
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
3
0
0
0
2
0
0
0
1
0
0
2
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
1
0
1
2
1
0
0
0
2
2
0
0
0
0
0
0
2
1
1
0
1
2
0
1
0
0
3
0
0
2
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
1
2
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
2
2
2
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
2
1
2
0
0
0
0
0
1
0
5
1
0
0
1
0
0
1
1
0
0
0
0
0
2
0
3
0
2
0
2
0
0
0
1
1
0
0
0
1
2
0
0
0
3
0
0
2
0
0
0
0
0
2
0
0
2
0
2
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
1
0
0
0
0
3
0
0
2
2
0
0
2
0
0
0
0
0
3
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
2
0
0
5
3
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
1
0
0
0
1
1
0
1
1
0
0
1
0
2
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
2
0
2
0
0
3
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
1
1
1
0
2
3
0
0
0
0
1
0
0
0
0
6
0
0
0
1
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
1
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
2
0
1
1
1
0
0
1
1
2
4
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
2
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
2
2
0
2
0
0
3
0
3
2
0
1
2
0
1
2
3
1
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
1
1
1
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
5
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
3
2
0
2
0
0
0
3
2
0
1
0
0
2
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
2
0
0
1
0
0
1
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
1
0
0
2
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
1
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
2
1
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
1
0
0
0
3
0
0
2
0
0
4
0
0
0
0
0
0
3
0
2
0
1
0
0
0
1
1
0
1
0
0
2
0
2
0
0
0
1
0
0
1
0
0
0
0
2
2
0
0
2
2
1
0
0
0
2
0
1
0
0
0
2
0
0
2
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
2
2
0
0
0
0
2
7
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
3
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
4
0
1
0
2
0
0
2
2
0
0
0
0
1
0
0
0
1
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
2
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
2
1
0
0
2
0
0
2
1
0
0
0
2
2
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
1
0
1
0
0
0
0
0
0
0
0
3
0
3
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
1
0
0
0
0
3
0
0
4
2
1
0
0
0
0
2
0
1
1
0
0
2
0
0
7
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
2
0
0
2
0
2
2
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
4
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
1
1
0
3
2
0
3
0
0
0
1
1
0
0
1
0
1
0
2
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
3
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
1
0
0
0
0
4
0
8
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
4
2
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
2
0
0
0
2
2
0
2
0
0
0
2
3
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
2
0
0
0
1
0
2
0
0
1
0
1
1
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
1
2
0
2
0
2
0
0
0
1
0
0
1
0
0
1
1
0
0
0
7
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
1
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
1
0
2
1
0
0
0
0
0
2
2
0
0
1
0
1
0
0
2
0
0
1
1
0
2
0
1
0
2
1
1
0
0
1
2
0
0
1
0
1
2
0
0
1
1
0
2
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
3
0
0
0
3
0
2
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
1
0
0
0
1
1
0
0
2
0
0
0
1
0
0
1
1
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
3
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
2
0
0
0
0
1
2
0
0
0
0
0
1
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
2
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
3
0
0
0
2
0
1
0
2
0
1
0
0
0
2
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
2
0
2
1
0
0
0
0
1
2
0
1
0
2
1
0
1
0
1
3
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
2
1
0
3
1
0
2
0
0
0
0
0
0
0
2
2
1
0
1
0
2
0
0
1
0
0
0
1
0
0
1
2
0
2
0
0
0
0
2
0
0
0
0
0
0
3
1
1
1
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
3
5
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
5
0
0
1
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
1
0
0
3
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
2
0
2
1
0
2
0
3
0
1
0
0
0
0
0
0
0
0
0
1
0
2
1
0
2
0
0
1
2
0
0
0
0
0
5
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
2
0
0
2
0
1
2
2
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
4
1
0
0
0
1
0
0
2
0
0
0
4
0
0
0
1
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
1
0
0
0
1
1
0
3
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
1
0
0
0
0
0
1
3
0
0
0
1
1
0
2
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
2
0
0
0
3
0
0
0
2
1
0
0
0
1
0
0
0
1
0
3
2
0
0
0
1
0
0
0
0
1
0
0
2
1
1
0
1
1
0
2
0
2
0
0
0
2
0
0
3
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
2
13
0
2
0
2
0
1
0
1
1
2
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
1
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
2
0
0
0
1
0
0
0
0
0
2
1
0
3
0
0
2
3
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
2
2
0
6
0
0
0
0
0
2
2
1
0
0
0
0
0
0
3
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
5
4
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
2
0
0
2
1
0
0
0
0
4
0
0
1
0
0
1
0
0
0
0
0
0
4
0
0
0
1
1
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
5
0
0
0
0
1
0
2
0
0
0
0
2
1
0
0
0
0
0
1
2
0
0
2
0
2
0
0
0
0
0
1
2
2
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
2
0
1
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
1
3
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
3
0
1
1
0
0
1
0
1
0
1
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
2
3
0
0
2
0
2
1
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
6
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
8
0
1
0
0
0
0
0
0
1
1
0
0
1
2
0
0
0
1
1
0
1
0
0
0
0
0
0
3
0
0
0
1
2
2
0
0
1
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
2
1
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
1
3
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
4
2
0
0
1
2
0
2
0
0
3
0
0
2
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
2
0
0
0
0
0
0
0
0
0
0
1
2
2
0
1
0
0
0
0
0
0
0
1
0
1
2
0
0
1
0
1
0
0
0
2
2
0
0
2
1
4
1
0
1
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
3
0
0
0
2
1
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
1
1
2
1
0
0
0
0
0
3
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
2
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
4
0
0
1
0
0
0
1
0
0
3
0
0
1
1
2
0
0
2
0
1
0
0
0
2
2
1
0
1
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
2
0
0
1
1
0
2
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
3
0
0
1
0
0
0
1
0
0
0
2
2
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
2
1
0
2
1
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
2
1
0
0
0
3
0
1
2
2
0
0
1
0
0
0
2
0
0
2
0
2
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
1
1
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
5
0
0
1
0
0
2
1
0
0
0
0
1
0
0
0
0
0
3
0
0
2
2
0
0
0
0
0
1
1
0
0
1
0
2
0
1
0
0
1
2
0
1
2
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
1
1
0
2
0
0
0
0
1
2
0
0
1
0
1
0
1
1
3
2
0
0
0
5
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
2
1
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
1
2
0
0
0
1
2
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
4
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
3
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
7
1
2
0
0
0
0
0
0
1
2
0
1
0
0
1
1
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
4
2
0
2
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
1
2
1
1
2
1
6
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
2
0
2
0
0
0
0
3
0
0
0
1
2
2
0
0
0
0
1
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
2
2
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
2
1
3
0
1
0
0
2
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
2
2
2
0
0
0
0
0
0
0
0
0
1
0
1
0
1
2
0
7
0
2
0
0
1
0
0
1
2
0
1
0
0
0
2
0
0
2
1
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
5
0
0
0
0
0
2
1
2
0
1
0
2
0
3
0
0
1
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
1
0
0
2
0
1
0
0
0
2
0
1
0
0
1
2
0
0
0
0
0
0
1
0
3
0
0
1
0
0
0
0
1
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
2
2
0
0
0
0
0
3
1
0
3
0
0
2
1
2
0
1
0
0
1
0
0
1
1
0
0
0
2
0
2
0
1
0
0
0
1
0
0
0
2
0
0
1
0
2
0
1
2
0
0
0
0
1
0
0
0
1
2
2
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
4
0
1
2
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
2
3
0
0
1
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
2
0
0
6
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
3
0
0
0
2
0
0
0
0
2
2
2
0
0
0
1
0
0
0
2
1
0
0
1
0
0
0
0
0
0
2
0
1
1
1
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
2
4
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
1
0
1
2
2
1
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
1
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
1
1
2
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
2
1
0
1
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
3
1
3
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
1
0
2
0
0
0
0
1
0
0
5
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
5
0
0
0
0
2
0
0
2
0
0
0
0
0
1
1
0
2
2
3
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
7
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
2
0
1
3
0
0
0
0
3
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
2
1
0
0
2
1
0
4
4
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
2
0
0
0
3
2
1
2
1
0
0
0
0
0
2
0
2
0
0
1
2
1
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
2
1
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
2
2
0
0
0
0
1
2
0
2
0
0
1
1
0
2
0
1
0
1
2
0
1
0
5
2
1
2
0
0
0
1
0
1
0
0
0
0
2
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
1
0
0
2
0
2
1
0
1
0
2
0
0
1
0
1
0
0
0
0
0
1
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
6
2
1
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
1
1
0
1
2
0
0
0
0
1
1
0
0
0
0
2
1
1
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
1
0
0
0
0
2
0
0
0
1
3
0
0
1
2
1
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
1
1
0
0
0
0
0
0
0
2
1
3
2
0
0
1
0
2
0
0
2
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
3
0
1
0
0
2
1
0
1
0
2
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
3
0
0
0
0
0
2
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
2
0
1
0
0
1
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
1
2
0
0
0
0
1
1
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
1
1
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
3
2
0
0
0
2
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
2
1
5
1
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
2
0
0
0
0
1
2
2
2
3
0
0
0
0
1
2
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
2
0
0
0
0
2
1
0
1
1
0
0
0
0
2
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
3
1
2
0
1
0
0
0
0
0
5
0
0
0
0
1
1
2
0
0
1
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
2
0
0
3
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
1
0
6
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
2
1
0
0
1
0
1
0
0
0
0
2
1
0
0
2
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
2
1
1
0
3
0
2
6
0
0
0
0
0
0
1
0
1
2
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
1
0
0
2
0
1
0
2
0
0
0
1
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
2
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
3
0
2
0
0
0
14
0
0
2
0
0
0
0
0
1
0
2
0
2
0
8
0
0
0
0
0
1
2
2
0
0
0
1
1
0
1
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
2
0
2
0
0
1
1
0
1
1
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
2
0
0
0
2
0
1
0
0
4
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
2
1
0
0
0
0
0
0
1
2
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
1
2
0
0
0
2
0
0
2
0
0
1
0
1
1
3
0
1
0
8
0
0
0
0
0
0
1
0
1
1
0
2
0
0
0
0
2
0
1
1
1
0
0
0
0
2
0
2
0
2
0
0
2
0
0
2
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
11
0
0
0
0
1
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
2
2
0
0
0
1
1
0
2
2
1
0
0
0
0
0
0
0
3
0
0
0
4
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
1
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
2
2
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
1
0
0
2
1
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
2
2
1
0
1
0
0
0
2
0
2
0
1
0
0
1
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
2
1
0
0
2
0
2
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
2
0
0
0
0
0
1
0
1
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
3
1
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
1
2
0
0
2
0
0
0
5
0
0
0
0
0
0
1
3
0
1
0
2
0
3
2
1
0
0
0
0
0
2
2
0
2
0
0
0
1
0
2
0
0
0
2
0
0
0
1
1
0
2
0
2
1
2
0
2
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
2
0
0
0
2
2
0
0
0
2
0
0
2
2
2
0
3
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
3
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
1
0
0
0
0
0
2
0
1
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
1
0
0
2
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
3
1
1
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
1
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
2
2
0
1
1
0
1
0
0
1
1
0
0
1
0
1
0
3
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
1
2
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
1
2
0
2
1
2
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
3
2
0
0
2
0
2
0
1
0
1
1
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
2
0
3
0
0
2
1
0
0
2
0
0
1
2
0
1
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
1
1
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
2
0
1
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
1
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
1
2
1
0
0
2
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
3
0
0
1
2
0
0
0
1
0
2
0
0
1
0
0
1
0
0
0
0
2
3
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
3
1
0
0
0
2
0
0
0
0
0
0
1
1
0
2
0
1
1
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
2
0
0
2
0
0
0
0
1
2
1
0
0
1
0
2
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
2
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
2
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
1
0
0
1
0
0
0
1
1
0
0
0
1
2
2
1
1
0
0
1
0
2
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
3
0
0
3
0
1
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
3
1
0
0
1
0
0
2
0
0
0
1
0
1
0
0
0
1
0
1
2
2
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
1
0
0
0
2
1
0
0
2
0
0
0
0
5
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
2
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
2
0
1
2
0
0
0
0
0
0
0
1
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
2
0
1
3
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
2
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
3
2
0
2
0
1
0
0
0
0
0
0
2
1
2
0
0
0
1
2
1
0
2
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
1
2
3
0
1
2
0
2
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
3
3
0
1
0
0
0
0
1
0
0
0
0
4
0
0
1
0
0
0
0
2
2
0
0
2
0
0
0
0
1
2
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
1
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
2
2
0
3
0
0
0
0
0
0
1
2
0
2
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
1
0
2
1
2
2
0
0
0
1
0
0
3
0
1
0
0
0
0
0
0
1
0
1
2
0
2
0
1
0
0
0
0
4
1
3
0
0
1
0
0
3
2
0
0
1
0
0
2
0
0
0
1
0
0
0
0
1
0
2
0
0
2
0
0
2
0
0
0
3
2
0
1
1
0
0
0
2
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
3
0
0
0
0
1
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
3
1
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
1
2
0
0
1
0
1
0
0
0
0
0
1
1
1
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
4
0
0
0
1
0
1
0
0
2
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
2
0
1
0
0
0
0
0
2
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
2
2
2
0
3
0
0
1
0
3
2
0
0
0
0
2
0
2
0
2
0
0
1
0
0
0
1
0
1
0
1
0
0
0
2
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
4
0
0
0
0
3
0
0
1
0
0
0
3
2
0
1
2
0
0
0
3
0
0
2
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
1
2
0
0
0
0
0
0
1
6
1
0
0
2
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
2
1
0
0
0
0
1
0
0
1
0
0
2
2
0
2
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
1
0
2
2
0
0
0
0
1
0
1
2
0
0
0
0
0
1
1
0
0
1
1
1
1
0
0
5
0
0
2
1
2
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
4
0
1
0
0
0
1
1
0
1
0
2
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
1
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
3
2
1
0
1
1
0
0
1
1
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
2
0
0
0
1
0
0
0
0
0
6
0
2
2
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
7
0
2
2
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
1
0
1
0
2
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
2
0
0
1
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
2
0
3
0
0
0
0
2
0
2
0
1
0
1
1
0
1
2
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
1
0
2
0
0
0
0
2
3
0
0
2
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
1
3
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
3
0
1
0
2
0
0
0
1
1
0
0
0
1
0
2
2
10
1
2
0
0
0
1
3
0
0
0
0
0
0
1
0
0
0
0
2
0
1
1
0
0
5
1
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
2
0
0
1
0
4
2
1
0
0
0
0
0
1
0
1
0
0
0
0
0
2
1
2
0
1
0
2
0
0
0
0
0
0
0
0
1
2
2
3
0
0
2
0
0
0
0
2
0
1
0
2
2
2
0
0
0
0
3
0
0
0
0
0
0
2
2
1
0
0
0
0
1
0
0
3
0
1
0
0
0
0
0
1
1
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
1
2
0
0
0
0
1
0
1
1
0
0
0
0
1
0
2
0
3
0
1
1
0
0
0
3
0
0
0
1
1
0
2
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
2
0
2
1
3
2
2
1
0
1
1
2
0
0
0
0
0
0
1
0
0
0
0
1
3
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
3
0
0
0
0
0
0
2
2
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
8
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
2
0
0
3
1
0
0
0
0
0
1
0
2
0
1
0
0
0
1
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
1
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
10
0
0
0
0
0
0
0
0
0
0
0
0
5
1
6
0
0
0
0
0
0
0
1
0
0
2
0
2
4
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
1
0
0
1
0
0
0
3
0
1
2
0
0
0
0
0
0
2
0
2
0
2
0
0
0
1
0
0
0
2
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
1
0
0
0
2
0
1
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
1
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
1
2
0
0
0
2
1
3
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
2
0
2
2
2
0
0
0
0
3
0
0
1
0
1
0
0
0
0
0
2
0
0
1
0
0
0
5
0
2
0
0
0
4
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
8
0
0
0
2
0
0
2
2
0
0
1
0
0
0
0
0
0
2
1
1
0
1
2
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
2
0
2
0
0
0
1
2
2
0
0
0
1
1
1
0
1
0
0
0
0
0
1
1
0
2
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
3
1
2
0
0
10
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
6
0
1
0
1
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
1
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
3
1
0
0
2
0
0
0
0
0
1
3
0
0
0
1
0
0
0
1
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
2
0
2
5
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
1
2
2
0
0
0
0
0
1
0
0
2
0
2
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
6
0
0
0
1
0
1
0
0
0
0
0
0
1
4
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
5
0
0
2
0
3
0
0
4
2
0
1
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
3
0
0
1
0
0
0
1
0
0
0
0
2
0
1
1
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
1
0
4
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
2
0
1
0
0
2
0
0
0
1
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
1
2
1
0
2
1
1
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
3
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
3
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
3
1
0
0
0
0
0
0
0
2
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
1
2
2
0
0
0
0
2
0
0
2
1
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
2
0
6
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
3
1
0
2
0
0
0
2
2
0
0
0
0
0
0
3
0
1
0
0
1
1
1
0
2
1
0
0
3
0
1
0
1
2
0
1
4
0
2
0
1
0
0
0
1
0
0
0
0
1
4
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
3
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
2
0
0
0
0
3
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
1
1
0
2
0
0
0
1
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
2
0
1
2
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
2
0
2
0
0
2
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
2
0
3
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
1
2
0
2
1
0
0
0
0
0
1
0
0
0
2
0
0
0
6
0
0
0
0
2
0
3
0
0
3
2
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
3
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
1
1
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
9
1
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
2
0
2
1
0
1
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
2
1
0
3
0
0
0
0
0
1
0
0
1
0
0
0
3
0
0
1
0
0
1
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
2
0
1
1
0
0
1
0
0
0
0
2
1
0
0
0
0
1
0
0
2
0
0
1
1
0
1
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
1
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
1
0
1
0
0
1
0
1
0
3
2
0
0
0
0
0
3
2
0
0
0
0
0
0
0
1
2
0
1
0
2
0
0
2
0
1
0
0
0
2
0
4
2
0
0
1
2
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
1
1
0
0
0
1
0
2
0
0
0
0
0
0
0
1
1
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
1
2
2
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
5
0
2
1
0
1
0
0
1
2
0
0
0
0
2
0
2
1
2
1
1
0
0
2
0
0
2
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
1
4
0
0
0
2
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
5
1
0
2
0
0
0
2
0
1
0
1
0
0
2
1
0
0
0
1
0
2
1
0
4
0
1
0
2
0
1
2
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
3
1
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
3
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
4
0
0
0
0
0
2
0
1
1
0
0
0
0
1
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
1
0
3
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
5
1
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
6
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
2
2
0
2
1
0
0
0
1
1
0
0
1
0
1
0
1
0
1
1
2
1
0
0
0
0
0
2
2
3
0
0
0
2
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
2
0
2
2
0
0
0
0
0
0
2
0
1
0
0
0
1
2
0
4
0
0
0
0
1
0
0
0
2
1
0
2
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
2
0
2
1
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
1
2
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
3
2
0
0
0
0
0
0
1
2
0
0
0
1
0
3
3
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
1
1
0
0
2
2
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
1
0
2
2
2
0
0
0
0
2
0
0
1
0
1
0
1
0
0
0
1
1
0
2
0
0
2
0
1
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
2
0
0
0
1
0
0
0
1
0
0
2
0
0
3
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
2
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
1
2
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
2
1
1
0
0
0
2
1
0
0
2
2
0
0
2
0
1
0
1
0
2
2
3
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
2
2
3
2
0
0
3
0
1
0
1
0
0
1
3
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
3
0
0
0
0
0
4
0
1
0
0
1
2
0
0
0
2
0
0
1
0
2
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
2
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
2
0
0
1
0
0
0
1
0
4
0
0
0
0
0
2
2
1
1
0
0
0
1
0
0
0
1
0
0
3
1
0
0
0
0
1
0
0
2
0
0
1
1
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
3
1
0
7
1
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
2
0
0
0
2
0
0
0
2
0
0
0
2
2
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
2
1
1
2
0
1
0
0
0
2
0
4
0
0
2
2
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
1
0
0
0
3
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
3
2
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
1
0
0
0
1
2
2
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
4
0
1
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
2
0
0
2
0
0
1
2
0
2
0
1
4
1
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
2
0
0
0
2
0
0
0
0
2
2
0
0
2
0
0
0
2
1
3
1
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
1
3
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
2
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
1
0
2
3
0
0
0
2
1
0
0
2
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
1
0
0
2
0
1
1
0
2
0
0
0
0
0
2
0
2
0
0
0
0
3
0
0
2
0
0
2
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
1
0
0
0
8
0
0
0
3
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
1
2
0
0
0
4
1
2
0
0
0
0
0
1
2
0
2
2
0
3
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
2
1
0
1
1
0
2
1
2
0
2
1
0
2
0
0
2
3
0
0
0
0
0
0
2
0
0
0
1
0
3
0
1
2
2
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
1
0
2
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
2
0
1
0
0
0
0
0
2
0
2
0
1
1
0
0
2
0
1
1
0
0
0
0
0
0
2
0
0
2
0
0
5
0
0
0
0
0
0
3
0
1
0
1
0
0
1
0
0
0
2
0
2
1
2
0
0
0
0
0
0
0
0
1
0
2
0
2
0
2
2
2
0
1
1
2
2
0
0
0
2
0
2
3
0
0
0
0
0
0
2
1
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
1
2
0
0
1
2
1
0
0
0
0
2
0
1
0
1
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
1
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
1
2
2
0
0
0
1
0
1
2
1
2
0
0
0
0
0
2
2
0
0
0
0
1
1
0
1
0
2
0
0
0
0
2
0
2
0
0
0
0
3
0
1
0
0
0
0
0
1
0
1
0
0
3
0
0
1
0
0
0
1
0
1
0
2
0
0
0
2
0
2
2
0
0
0
0
1
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
5
0
0
1
1
2
1
0
0
0
0
0
2
0
0
1
2
1
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
2
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
1
2
0
0
0
2
0
0
2
0
0
0
0
1
1
0
0
0
0
0
1
1
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
1
0
0
0
0
2
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
1
3
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
1
0
1
0
0
0
3
0
0
2
0
0
0
0
4
1
2
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
1
0
3
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
2
2
0
2
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
1
3
0
0
2
0
2
0
0
1
0
0
0
4
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
4
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
3
1
0
2
0
1
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
2
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
3
2
0
0
0
3
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
1
0
0
2
0
0
0
1
0
2
1
2
0
0
0
2
0
0
0
2
0
0
0
0
0
1
2
0
1
0
1
1
0
0
0
0
3
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
1
2
2
0
0
1
2
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
2
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
2
0
1
0
3
0
0
0
0
0
0
0
2
0
1
0
1
2
0
2
0
0
2
0
0
1
0
0
0
1
1
1
2
1
2
0
0
0
1
0
0
0
2
0
3
0
0
0
0
1
0
0
2
0
2
0
2
0
0
2
0
0
1
1
0
0
0
0
0
0
0
1
1
0
1
1
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
1
3
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
2
2
0
2
0
3
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
3
0
1
1
2
1
0
0
0
0
0
2
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
2
0
0
0
0
3
0
2
1
0
0
0
0
1
0
2
0
0
0
2
0
0
1
1
0
2
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
1
1
1
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
2
0
0
0
0
1
2
0
2
0
2
0
1
0
0
0
1
0
0
0
2
0
0
2
0
0
1
3
0
0
0
0
1
0
0
2
0
1
0
0
2
0
1
2
0
2
1
2
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
1
0
1
0
0
1
0
0
2
0
1
3
0
1
0
1
0
0
0
0
1
0
0
0
0
2
0
1
2
0
0
1
0
0
0
1
0
2
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
2
0
1
0
0
2
2
2
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
2
0
0
1
0
0
6
1
0
2
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
2
0
1
0
1
4
0
0
1
0
0
0
0
0
0
0
6
0
1
1
1
0
0
0
0
0
0
0
1
4
0
0
0
0
1
0
1
1
0
0
2
0
0
0
0
2
0
0
1
1
1
0
0
0
1
0
0
0
0
1
0
1
0
2
1
1
0
0
1
1
2
0
0
0
7
0
2
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
4
0
0
0
0
0
0
1
0
3
0
0
0
0
1
0
0
0
0
0
0
2
1
2
0
0
2
0
0
0
0
2
5
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
2
0
2
0
2
2
6
7
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
2
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
1
0
0
0
0
0
1
0
2
0
0
2
0
2
0
0
0
0
0
1
0
1
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
3
1
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
5
2
0
0
0
4
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
1
0
0
2
0
0
0
2
2
1
3
1
1
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
3
0
0
0
1
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
3
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
3
1
1
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
2
0
2
3
2
0
0
0
0
0
0
1
0
0
0
2
0
1
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
2
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
1
2
2
0
2
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
1
2
0
0
0
1
2
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
1
0
0
2
4
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
1
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
1
3
0
1
0
0
0
0
1
3
2
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
1
2
2
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
2
6
0
0
0
1
0
1
0
0
2
2
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
3
0
0
1
0
0
2
0
0
0
0
0
0
0
4
0
0
0
2
1
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
2
0
2
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
9
0
0
0
0
0
0
0
1
0
0
4
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
1
2
3
2
0
0
0
0
1
1
2
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
2
0
2
3
1
0
0
2
2
0
0
1
0
0
0
0
2
0
2
0
2
0
0
0
0
0
5
0
0
2
0
0
0
0
1
0
0
0
0
0
2
2
1
5
2
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
2
0
1
0
0
0
0
0
5
3
0
0
1
1
1
0
1
0
0
0
1
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
2
1
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
2
0
2
2
1
3
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
1
0
5
2
0
1
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
3
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
2
2
0
0
0
0
2
0
1
1
0
2
0
0
0
1
3
1
1
0
0
0
0
6
0
1
1
2
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
1
1
0
0
0
1
1
1
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
2
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
2
0
0
0
1
0
4
0
0
0
0
0
1
0
0
2
0
0
0
1
1
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
1
0
1
0
0
0
7
0
0
0
0
0
0
2
0
2
2
2
0
1
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
1
2
0
0
2
0
0
0
1
0
1
0
3
0
0
1
1
0
2
0
0
0
0
1
0
0
1
0
0
1
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
2
0
1
0
1
1
0
0
0
0
0
2
0
1
0
0
1
0
1
1
0
0
3
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
1
0
0
0
1
0
3
0
2
0
2
0
0
0
0
2
0
2
1
3
0
0
0
0
0
2
0
1
0
0
0
0
3
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
1
0
0
1
0
2
2
2
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
2
2
2
2
1
0
1
0
2
1
0
2
0
2
0
0
2
2
0
0
1
0
3
2
0
0
0
2
0
2
2
0
0
0
0
2
0
0
1
0
1
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
1
4
0
0
4
0
0
2
2
0
1
2
0
2
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
2
0
1
2
1
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
2
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
2
0
2
2
1
0
2
1
1
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
2
1
2
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
1
0
0
0
2
0
0
2
0
2
0
0
0
1
0
2
0
1
0
3
0
0
0
0
0
0
0
1
0
1
2
1
2
2
1
0
0
2
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
2
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
2
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
2
1
0
2
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
2
3
0
2
0
2
1
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
2
1
0
0
2
0
0
2
1
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
2
0
0
1
0
2
1
1
0
0
0
0
2
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
2
2
0
3
0
1
0
1
0
0
2
1
0
0
1
0
2
0
3
1
1
0
2
0
2
2
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
2
2
0
1
1
0
0
0
0
0
0
0
2
0
2
3
1
0
2
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
1
0
2
0
0
0
0
1
0
0
3
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
5
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
2
2
1
0
0
0
0
2
0
2
0
0
1
2
0
0
0
1
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
3
0
1
2
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
1
0
2
0
0
0
0
0
2
0
2
0
0
0
2
0
0
2
0
0
1
0
0
1
0
1
0
0
2
7
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
3
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
1
0
1
2
0
0
0
3
0
0
0
1
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
1
0
0
0
0
2
3
1
0
0
0
0
1
0
2
4
0
2
0
0
0
0
0
0
0
0
0
10
4
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
5
0
0
0
0
1
1
0
1
0
2
0
0
0
0
3
1
0
0
2
0
0
2
0
2
3
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
2
2
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
2
0
2
0
0
2
0
0
0
0
0
0
0
0
8
0
0
2
0
2
0
3
0
0
0
0
0
1
2
0
0
2
0
0
3
0
0
3
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
6
0
1
0
0
0
2
0
1
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
1
2
0
0
0
3
0
0
0
0
2
1
0
0
0
0
2
2
0
0
0
2
1
0
0
0
2
0
0
0
2
0
1
2
0
0
0
0
1
2
2
0
0
0
0
0
3
2
2
0
2
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
3
1
0
0
0
0
3
2
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
1
0
0
0
2
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
2
0
0
0
0
2
0
0
4
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
1
0
0
0
1
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
4
0
0
2
1
1
0
1
1
0
0
2
2
0
1
0
0
0
0
2
0
2
1
2
0
0
0
3
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
1
4
0
1
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
3
2
0
0
0
0
0
0
0
2
0
2
2
1
2
0
3
0
2
0
0
0
0
0
1
1
6
0
1
0
0
0
0
1
1
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
3
0
1
2
3
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
2
0
0
2
0
0
0
1
0
0
0
0
2
4
2
0
0
1
6
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
1
0
2
2
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
1
0
0
2
1
0
2
0
0
0
3
0
2
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
2
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
4
2
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
1
1
0
0
0
0
1
0
1
0
2
0
0
2
0
2
0
1
0
0
0
2
0
0
0
2
1
1
0
0
1
2
2
0
0
0
1
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
2
2
0
0
2
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
3
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
2
1
0
2
0
0
0
0
2
1
0
1
1
0
0
2
0
0
0
0
1
4
0
0
0
0
0
2
2
0
0
0
0
1
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
5
0
0
1
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
2
0
1
0
0
0
1
0
1
2
0
3
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
2
1
0
1
3
0
0
0
2
0
0
1
0
2
0
2
0
0
0
0
0
0
0
2
0
0
1
0
1
1
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
2
3
1
0
0
0
0
0
0
0
2
0
1
0
0
2
2
2
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
2
0
0
1
0
0
0
0
1
2
2
1
0
0
1
0
2
0
0
0
0
0
0
0
2
1
0
2
1
1
1
2
2
0
0
0
3
0
1
0
0
0
0
0
2
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
2
0
3
0
0
3
0
0
0
0
0
2
1
0
0
0
0
1
2
0
1
2
1
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
1
2
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
1
2
0
0
0
1
0
2
0
2
0
0
0
0
2
0
0
0
0
1
0
2
2
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
2
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
2
1
3
0
0
2
0
1
0
2
0
4
2
0
0
0
1
0
2
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
4
0
1
0
0
1
0
4
0
1
0
1
0
0
2
0
1
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
1
2
0
0
0
0
1
2
1
0
0
0
0
8
0
0
1
0
0
0
2
0
1
0
0
2
1
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
3
0
0
1
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
3
0
1
2
0
0
1
0
2
1
0
0
0
2
1
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
1
2
0
0
1
2
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
2
1
0
0
0
0
0
0
0
1
0
1
0
5
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
2
0
0
0
3
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
1
0
0
2
0
1
2
0
0
2
1
0
0
0
0
0
0
0
1
0
3
1
0
2
2
0
0
2
0
0
0
0
0
2
4
0
0
1
0
0
2
0
0
0
1
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
1
1
1
0
2
1
1
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
3
1
0
0
2
2
1
1
0
6
0
0
0
2
0
2
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
3
0
0
0
0
1
0
3
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
2
2
10
0
0
0
2
2
3
2
2
0
0
0
0
0
0
2
1
2
0
3
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
2
0
2
2
0
0
2
2
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
9
1
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
2
0
0
0
2
0
1
1
0
0
1
1
0
1
0
0
0
1
0
1
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
3
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
2
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
3
1
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
1
2
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
7
0
2
3
1
2
1
2
0
3
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
2
0
1
1
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
1
0
0
0
0
1
0
0
2
0
0
2
1
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
2
0
0
2
0
1
2
1
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
1
0
1
0
0
1
0
2
0
2
0
6
0
0
2
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
3
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
6
2
0
0
0
0
0
3
0
1
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
2
2
0
2
2
0
2
3
0
0
0
0
1
0
2
2
0
0
0
3
0
0
0
0
0
2
0
2
0
0
0
5
2
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
2
0
1
2
0
2
1
2
0
0
3
0
1
1
0
0
1
0
1
0
2
2
2
0
2
0
0
2
0
0
0
2
0
0
0
0
0
2
1
1
0
0
0
0
2
2
2
0
0
1
2
0
0
1
0
0
0
0
0
0
0
2
4
0
2
0
0
0
0
0
0
0
1
0
2
0
2
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
5
1
1
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
1
0
0
0
0
0
0
1
1
1
0
1
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
2
1
0
0
1
0
0
0
0
0
1
2
1
0
1
0
0
0
2
0
0
1
1
0
0
2
1
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
2
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
2
2
2
1
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
4
1
1
2
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
3
2
0
1
1
0
2
0
1
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
1
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
2
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
3
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
1
2
0
1
2
1
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
2
2
1
0
0
0
0
1
2
3
0
1
3
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
2
3
0
1
0
0
0
4
0
1
0
0
1
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
1
0
1
0
3
1
0
0
2
0
1
0
0
1
0
0
3
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
3
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
4
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
6
0
0
0
0
0
0
0
1
2
1
4
2
0
1
0
3
2
2
0
0
2
0
2
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
1
0
0
2
1
1
0
0
1
0
0
1
0
0
1
0
1
2
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
1
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
1
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
2
5
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
2
0
2
0
0
0
1
0
0
0
0
2
2
0
0
1
0
1
0
0
0
2
2
2
0
0
0
1
0
0
2
0
0
0
0
0
1
2
0
0
2
0
1
0
0
0
0
2
0
0
0
1
0
1
0
1
0
1
1
0
0
1
2
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
3
0
0
0
0
0
2
0
0
1
0
4
0
0
1
0
0
4
0
0
0
0
0
0
0
1
1
0
2
0
1
0
0
1
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
2
0
0
0
2
0
1
0
2
1
0
0
1
0
1
0
0
2
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
2
0
3
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
2
1
1
7
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
1
2
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
3
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
11
1
2
1
2
0
0
1
2
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
2
2
0
2
0
0
2
0
1
0
1
0
0
0
0
0
0
0
1
2
1
0
2
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
5
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
1
1
2
0
0
4
0
0
0
2
0
0
0
0
0
0
2
0
5
0
0
0
0
0
2
1
2
0
0
0
0
2
0
0
0
0
0
5
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
3
2
0
0
0
2
0
0
0
1
0
2
0
0
1
1
1
1
0
0
0
0
0
1
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
1
2
0
2
0
0
0
2
0
0
0
2
0
0
2
0
1
4
0
0
0
1
0
1
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
1
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
5
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
2
0
0
2
0
2
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
1
0
1
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
2
2
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
3
0
0
0
0
0
0
1
0
2
0
0
0
2
1
1
0
0
1
0
0
0
1
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
2
1
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
1
1
0
0
1
1
0
3
0
2
0
0
7
0
0
0
2
2
2
0
0
1
2
1
0
1
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
2
0
2
0
0
0
2
1
0
0
0
0
0
2
0
0
0
1
1
1
0
2
0
0
2
0
2
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
2
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
1
1
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
1
0
0
0
1
1
1
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
5
0
0
0
3
0
0
1
0
1
2
2
0
0
0
2
1
0
0
0
2
0
1
2
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
2
2
0
0
1
1
0
3
0
1
0
2
0
0
0
0
0
0
0
0
1
2
0
2
2
0
0
0
0
2
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
1
0
3
1
0
0
1
0
0
1
0
2
0
0
0
0
0
4
0
2
0
0
0
0
0
0
2
0
1
1
2
1
2
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
3
0
1
1
0
4
0
0
0
1
2
0
1
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
3
3
0
0
0
0
1
0
0
1
0
0
0
0
2
0
1
2
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
2
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
2
1
1
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
5
1
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
1
2
0
1
1
0
0
0
0
1
2
0
0
0
0
0
0
1
1
2
2
0
0
0
0
0
1
0
2
6
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
18
0
0
0
0
0
0
0
2
0
0
1
2
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
3
2
1
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
1
2
1
1
1
0
0
0
1
0
0
0
0
2
1
0
0
1
0
1
1
0
0
0
2
0
0
0
0
0
1
0
3
1
1
2
0
0
0
3
1
0
0
2
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
3
1
0
0
0
1
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
3
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
2
2
0
1
2
0
0
0
2
0
0
3
2
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
4
0
2
0
2
0
1
1
3
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
5
0
1
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
1
0
2
0
1
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
4
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
1
0
2
1
0
1
2
0
0
0
0
0
3
0
2
0
0
0
2
1
0
2
3
0
0
0
0
0
2
2
1
2
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
5
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
1
4
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
2
2
0
0
0
0
0
0
3
0
0
2
0
2
2
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
3
0
0
2
0
0
0
4
0
0
0
1
1
0
2
0
0
0
1
2
0
0
0
2
1
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
1
2
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
3
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
1
1
0
0
0
0
0
1
1
0
0
3
0
0
2
0
0
0
0
2
0
2
0
1
0
8
0
1
0
0
0
2
0
0
0
1
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
2
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
2
2
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
3
1
1
0
0
2
0
0
0
2
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
4
1
2
0
0
2
0
2
0
1
0
0
1
1
3
0
1
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
2
2
1
0
7
0
1
0
0
0
2
0
0
2
0
0
0
2
0
2
2
2
0
2
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
2
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
4
0
0
2
0
0
0
0
2
0
0
0
1
0
2
0
1
0
2
0
0
0
1
0
0
0
0
0
2
2
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
1
1
2
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
3
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
1
0
0
4
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
2
0
0
2
4
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
2
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
1
2
0
0
0
2
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
4
0
1
1
0
0
1
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
1
0
0
2
4
1
0
0
0
0
2
0
0
0
0
0
3
0
1
1
1
0
0
0
0
0
0
3
1
0
0
0
0
2
0
0
0
2
0
5
1
0
0
2
1
0
1
0
0
0
0
0
4
0
4
0
0
0
0
2
0
3
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
2
0
2
0
0
0
0
1
0
2
0
1
0
0
2
0
0
0
0
2
2
0
0
2
2
1
2
1
0
2
0
0
2
0
0
0
1
0
0
0
0
2
0
0
1
2
0
0
0
6
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
2
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
2
2
1
0
0
2
0
1
0
2
0
0
1
0
0
0
0
0
0
2
4
0
0
0
1
0
3
0
3
0
2
0
2
0
0
0
0
0
0
1
0
2
1
2
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
1
2
0
0
0
0
0
0
1
2
0
0
1
0
0
0
2
0
0
3
1
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
2
0
1
2
0
0
1
0
1
2
2
0
0
2
0
1
0
1
0
0
1
0
2
0
1
2
0
0
0
0
0
0
1
2
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
1
4
0
3
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
1
0
1
3
0
0
0
0
0
0
0
0
1
0
1
1
0
3
1
0
0
0
0
2
0
4
0
0
0
0
0
0
0
2
5
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
2
0
1
1
2
0
0
2
2
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
3
1
0
0
0
0
1
0
0
2
0
0
2
0
0
1
2
0
0
2
0
0
0
2
5
2
0
0
0
0
1
1
0
1
0
0
1
0
0
0
1
0
3
0
0
1
0
3
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
1
5
2
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
2
0
0
2
0
2
3
1
0
0
0
0
2
0
0
1
1
2
0
0
0
2
0
0
0
2
0
0
3
0
2
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
1
2
0
0
2
0
0
2
1
2
0
0
3
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
1
0
1
0
0
2
2
0
1
0
0
0
0
0
1
2
0
1
2
0
0
0
0
1
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
2
2
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
3
0
0
0
0
2
1
0
1
1
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
3
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
1
0
0
0
2
3
1
0
0
1
0
0
0
4
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
1
0
0
2
0
1
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
2
0
0
1
2
0
0
0
0
2
0
0
2
2
0
2
0
2
0
0
0
1
0
2
0
0
0
2
1
0
0
0
2
0
0
1
1
2
0
0
2
0
0
2
0
0
0
2
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
4
2
0
0
0
1
0
2
0
1
0
1
0
0
0
1
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
2
2
0
0
0
0
1
2
0
0
0
0
3
2
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
6
3
0
0
2
1
0
0
0
2
1
0
0
0
0
2
1
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
2
0
0
0
0
0
0
1
0
0
0
2
2
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
5
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
5
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
2
0
2
0
0
0
0
1
2
0
1
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
2
3
0
0
0
0
1
2
0
0
0
0
2
0
1
0
3
0
2
3
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
2
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
1
0
0
2
0
2
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
2
0
4
3
1
0
1
2
0
1
2
2
0
0
0
0
0
1
0
0
2
1
4
0
2
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
3
1
0
0
0
0
0
2
0
0
0
0
9
0
2
0
0
0
2
0
0
3
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
3
0
0
0
0
2
0
0
1
0
2
1
0
0
1
0
2
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
1
0
0
1
1
0
0
2
1
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
2
1
0
0
0
0
2
2
0
1
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
1
0
0
0
0
3
2
0
0
0
1
0
0
0
6
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
1
0
1
2
0
1
0
1
1
0
0
0
0
1
0
0
0
1
0
0
2
0
2
0
0
0
0
1
0
0
0
2
0
2
0
0
1
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
2
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
3
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
1
0
0
0
0
1
0
4
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
2
0
0
1
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
2
0
0
0
0
1
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
3
1
0
2
2
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
7
0
0
0
0
0
0
2
0
0
0
0
0
0
2
4
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
1
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
5
0
0
2
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
2
1
0
0
2
1
0
0
0
0
2
0
2
0
0
0
1
0
1
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
2
1
0
0
0
0
2
2
0
2
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
1
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
1
2
0
0
0
1
0
0
0
2
0
0
1
2
0
2
0
2
2
0
0
2
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
2
0
1
0
1
1
0
2
0
0
0
0
1
0
0
0
2
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
1
1
0
0
0
0
2
0
0
1
0
2
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
2
0
0
0
2
0
0
0
0
1
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
2
0
1
0
0
0
0
0
1
1
0
0
0
0
2
2
2
0
1
1
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
2
0
1
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
1
0
2
2
2
0
1
0
0
2
2
0
1
0
2
0
2
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
1
3
0
0
0
2
0
0
2
0
3
0
0
2
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
2
1
0
0
0
2
2
0
1
0
0
4
0
0
0
0
0
0
0
1
0
7
0
2
0
0
2
0
1
0
0
0
0
0
0
2
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
2
0
1
0
1
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
2
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
3
0
0
0
0
2
0
0
1
0
0
0
2
1
0
0
2
0
0
0
0
2
0
0
1
0
0
0
2
0
2
0
2
0
1
1
0
0
1
0
0
0
0
2
2
2
0
0
0
0
2
3
1
0
2
0
0
0
0
0
0
1
2
0
1
0
0
4
1
2
0
3
0
0
0
0
0
0
7
2
0
1
0
0
3
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
1
2
0
1
0
0
1
0
0
0
1
0
1
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
1
0
0
0
2
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
16
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
1
1
0
3
0
0
0
0
2
0
2
1
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
2
0
0
0
1
0
2
0
0
1
1
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
3
0
2
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
1
1
0
0
1
1
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
2
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
3
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
2
0
0
1
2
1
0
0
1
2
0
0
0
0
0
0
2
1
0
1
0
2
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
3
0
2
2
0
2
2
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
3
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
2
1
1
0
0
0
2
0
1
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
1
0
2
2
0
0
0
2
0
0
0
0
0
0
0
1
2
2
0
0
2
0
0
0
2
1
0
0
0
0
2
0
1
2
2
2
0
0
0
0
0
2
0
0
0
2
1
2
0
0
0
0
1
0
1
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
1
2
0
0
0
0
3
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
1
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
4
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
5
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
2
0
1
0
1
0
0
0
0
2
2
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
4
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
8
0
1
0
2
2
2
0
0
1
0
0
0
0
1
0
0
0
1
2
2
0
2
0
2
2
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
3
0
3
0
1
1
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
1
0
0
0
1
0
0
1
0
13
2
2
0
1
0
2
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
2
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
1
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
2
0
1
3
2
1
2
0
0
0
1
0
0
2
2
0
1
1
0
0
0
0
1
0
1
3
0
0
0
0
2
0
0
2
0
0
0
4
0
1
1
0
0
0
2
0
0
0
2
0
0
5
1
0
0
0
0
2
2
0
0
1
0
0
2
2
0
0
0
0
0
2
0
0
0
2
2
4
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
3
5
0
0
0
0
0
1
0
0
1
2
2
0
2
0
2
2
0
1
1
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
5
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
2
1
0
0
0
2
2
0
0
3
3
0
0
0
0
0
0
1
2
0
1
0
1
2
0
0
0
6
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
1
1
0
1
3
1
0
0
1
0
1
0
1
0
0
0
0
1
0
1
2
2
3
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
2
0
3
0
2
0
0
5
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
1
0
0
1
0
0
0
2
0
1
0
0
0
1
1
2
0
2
0
0
0
2
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
2
0
1
0
1
0
2
1
0
0
0
3
1
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
1
1
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
3
0
0
1
0
0
0
0
1
0
0
2
1
1
0
0
0
2
0
0
0
0
3
1
1
0
0
0
1
0
1
0
0
2
0
0
0
0
2
0
4
2
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
2
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
1
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
2
2
3
0
1
0
2
0
0
1
0
0
0
0
0
0
0
2
2
0
1
0
0
0
2
1
0
0
2
2
0
0
0
0
0
1
0
1
0
1
1
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
1
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
4
0
0
0
1
0
0
0
0
0
2
1
7
1
0
0
0
0
0
0
0
0
1
2
0
0
1
2
0
0
0
0
0
0
8
2
1
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
1
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
1
0
2
0
2
0
2
0
0
1
0
0
1
0
0
1
0
1
0
2
3
0
0
1
0
0
1
0
0
0
2
1
1
2
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
1
1
0
0
0
1
0
0
3
0
0
2
1
0
0
2
1
0
0
1
2
2
0
1
1
1
1
0
0
2
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
1
0
1
3
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
1
2
1
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
1
2
0
0
1
1
0
1
0
0
2
1
1
2
0
0
2
0
0
0
0
2
2
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
2
1
0
0
1
0
0
0
0
0
0
3
0
0
2
0
0
3
2
0
1
0
0
2
1
0
0
0
0
0
0
1
0
0
0
2
0
0
5
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
3
0
0
2
0
0
2
0
3
0
1
0
0
3
0
1
0
0
2
0
0
0
2
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
1
2
0
0
0
1
0
3
2
0
2
0
0
1
0
1
0
0
1
0
2
2
0
0
1
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
2
1
2
0
0
2
0
1
0
0
0
0
0
2
0
2
0
0
1
0
0
4
0
0
0
0
0
0
1
0
0
2
1
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
2
0
0
2
0
0
9
1
0
0
0
0
0
0
0
2
4
0
1
0
1
0
0
0
0
2
0
5
1
0
2
0
0
1
1
0
0
1
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
2
1
2
0
0
0
2
0
2
0
0
2
0
0
0
0
3
0
0
0
2
1
0
0
2
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
1
2
2
1
0
2
2
2
1
1
0
0
0
1
1
1
0
1
1
1
0
0
0
0
0
2
0
5
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
4
0
0
0
0
0
2
0
1
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
2
0
0
0
0
0
0
2
0
1
2
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
3
0
0
0
2
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
2
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
2
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
2
1
1
0
2
0
0
1
1
0
0
0
0
1
1
0
0
0
0
1
2
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
2
1
0
0
0
2
1
0
2
1
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
2
0
2
0
2
0
2
1
0
1
3
6
0
0
0
1
1
0
0
2
3
0
1
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
2
2
0
2
0
0
1
0
3
0
0
0
1
0
1
2
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
4
0
0
0
0
3
0
0
0
1
0
2
0
1
0
1
0
2
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
1
2
0
0
0
1
0
2
0
0
0
2
0
3
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
3
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
2
0
1
0
0
2
3
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
1
0
1
1
0
3
0
0
0
0
0
3
0
0
0
0
3
0
2
0
0
0
4
0
0
0
0
0
0
0
2
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
2
0
1
1
0
0
0
0
0
2
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
1
2
0
4
0
0
1
1
0
0
2
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
3
2
0
0
0
0
0
0
2
1
0
5
0
1
1
0
0
0
6
0
0
1
2
0
0
2
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
1
1
0
0
3
0
1
0
0
0
0
0
1
0
0
0
0
3
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
1
0
0
0
0
5
0
2
0
0
1
0
0
3
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
2
0
2
2
0
2
2
0
3
1
0
0
1
0
0
1
0
0
0
0
0
2
1
0
1
2
3
0
0
0
0
1
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
2
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
2
0
0
3
2
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
2
0
0
3
0
2
0
1
0
0
0
2
0
1
0
0
0
0
2
1
0
2
0
1
1
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
1
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
1
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
1
2
0
0
0
0
0
6
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
1
1
0
1
2
0
4
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
3
0
0
0
0
3
2
0
0
0
0
0
0
0
2
1
2
0
2
0
0
0
0
0
2
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
2
0
2
2
1
0
0
4
2
1
0
0
2
0
0
1
0
2
0
0
2
0
0
0
2
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
7
0
0
2
0
6
0
0
1
0
0
0
2
2
1
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
1
3
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
2
0
2
0
0
0
2
4
0
0
2
0
0
0
0
0
1
0
0
1
2
0
0
0
0
1
0
0
1
0
0
1
0
3
2
0
0
1
0
1
0
3
0
1
1
0
0
0
0
1
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
2
0
0
1
0
2
0
0
1
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
2
0
4
1
0
0
0
0
0
0
0
2
0
2
0
1
1
1
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
3
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
4
1
0
1
0
0
0
0
0
1
0
2
1
3
0
3
0
0
0
0
0
0
1
0
1
3
0
1
2
0
0
0
2
0
2
2
0
1
0
2
0
1
0
0
0
0
0
2
1
0
0
2
1
0
2
0
2
0
0
1
0
1
0
1
2
1
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
2
0
1
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
1
0
1
2
0
0
0
0
1
1
1
2
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
1
0
0
0
3
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
2
0
1
0
0
2
2
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
2
0
0
0
1
0
0
2
2
0
2
0
2
1
0
0
0
0
0
2
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
2
0
2
3
0
0
0
0
0
0
0
0
2
2
0
1
0
2
0
0
0
0
0
1
0
0
0
0
2
0
1
1
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
2
0
1
0
2
0
0
0
2
3
0
0
0
2
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
1
2
0
0
2
2
0
0
0
1
3
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
2
2
0
3
0
0
0
2
0
0
0
0
0
1
1
1
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
4
2
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
1
3
0
0
0
3
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
1
2
1
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
2
3
0
0
0
1
0
0
0
0
0
0
0
0
1
2
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
1
1
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
6
1
0
0
0
0
2
0
0
1
0
2
0
0
1
7
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
2
2
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
1
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
1
1
2
0
2
0
3
2
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
1
0
0
0
0
2
1
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
1
1
0
0
0
1
0
0
1
0
0
1
1
1
0
3
0
1
0
2
0
1
0
2
0
0
0
0
0
1
0
0
0
3
0
1
0
1
1
0
0
0
0
0
0
2
0
0
0
1
1
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
2
0
0
1
0
2
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
1
1
2
0
0
0
0
0
1
0
0
2
3
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
2
0
2
0
0
1
1
0
0
0
0
0
1
1
0
2
2
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
2
0
2
2
0
3
0
0
0
0
0
0
0
0
0
2
2
0
3
0
0
0
0
1
0
4
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
2
1
2
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
2
0
0
1
2
2
2
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
1
0
1
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
2
1
1
0
0
3
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
2
1
1
2
0
0
0
1
0
1
1
1
0
0
1
0
0
2
2
0
0
4
0
0
0
0
1
0
0
3
0
1
0
1
2
0
2
2
0
2
0
1
0
2
2
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
4
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
2
2
1
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
1
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
2
0
2
2
0
3
0
0
1
0
0
3
0
2
1
0
0
0
0
0
2
0
0
0
1
0
1
0
1
0
0
0
3
2
0
1
0
0
0
0
0
1
0
0
0
0
2
1
0
1
2
1
0
0
2
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
2
0
0
0
1
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
2
0
2
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
1
2
1
1
0
0
0
2
2
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
2
1
0
0
0
0
1
0
0
0
2
1
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
2
2
3
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
1
2
0
0
0
1
0
2
2
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
2
5
0
2
0
0
0
2
0
0
1
1
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
3
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
4
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
5
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
1
0
0
1
0
2
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
2
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
2
1
0
0
0
1
0
1
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
4
0
0
0
1
0
1
2
0
3
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
2
0
0
2
4
3
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
2
1
0
0
3
0
0
0
0
2
0
0
2
0
3
0
2
0
2
1
0
0
1
0
2
0
0
0
0
0
0
0
2
2
2
0
0
2
2
2
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
1
1
1
0
0
2
1
2
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
8
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
2
1
0
0
0
0
2
0
0
2
2
0
0
0
2
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
2
1
0
2
0
0
0
1
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
3
0
2
1
0
0
0
0
2
0
0
0
1
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
2
0
0
1
0
1
1
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
1
1
0
0
2
0
0
1
2
1
2
0
0
0
0
0
0
3
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
2
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
2
3
1
2
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
2
2
3
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
1
0
5
1
0
0
2
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
2
0
2
1
0
0
0
0
1
2
0
2
0
1
0
1
0
0
0
0
0
0
1
0
0
2
0
0
2
1
0
0
0
2
0
0
2
0
0
1
0
2
0
0
0
0
1
2
1
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
9
0
0
0
0
0
0
3
0
1
1
0
0
0
0
0
3
0
0
0
1
0
0
0
2
0
0
1
5
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
2
0
1
1
0
0
2
2
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
3
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
4
2
0
0
0
0
1
0
3
2
0
0
0
1
1
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
6
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
3
2
0
1
0
0
0
0
0
2
0
2
1
0
3
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
5
1
1
0
1
0
0
0
0
0
5
0
1
0
2
0
0
0
1
3
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
3
0
0
0
1
0
0
0
0
0
1
0
0
1
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
1
1
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
1
0
0
0
2
0
0
0
1
2
0
0
0
2
1
0
1
0
0
0
0
1
0
2
0
0
0
0
1
1
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
3
0
0
1
0
1
0
0
0
0
0
1
0
2
0
2
0
2
0
0
0
1
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
2
2
0
0
0
0
1
0
0
5
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
2
0
0
2
0
3
0
0
1
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
3
0
1
0
0
0
0
0
0
1
0
1
0
0
2
0
2
0
2
0
0
2
0
3
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
2
0
2
0
0
0
0
0
1
2
0
0
2
0
1
0
1
0
0
0
0
0
0
3
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
2
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
1
3
0
0
0
2
0
2
0
0
1
0
2
4
1
0
2
0
1
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
2
1
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
2
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
3
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
2
0
4
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
3
0
2
1
0
0
0
0
0
0
0
0
2
1
0
0
1
0
1
0
0
1
0
0
0
2
0
0
0
0
2
3
2
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
1
3
0
0
0
2
0
0
0
2
0
0
0
2
0
2
1
8
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
3
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
1
2
2
0
0
0
4
0
0
1
0
2
1
0
0
0
0
0
2
0
0
0
1
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
1
2
0
1
0
0
1
1
0
0
0
0
0
2
0
2
2
0
3
1
0
0
2
0
0
0
3
0
0
0
1
0
3
0
2
1
0
2
2
0
5
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
2
0
0
1
0
2
0
2
2
0
0
0
0
0
2
1
0
0
1
3
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
1
0
1
0
0
1
1
0
1
0
3
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
2
0
0
2
1
0
3
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
9
0
0
0
0
0
0
0
0
0
1
2
2
0
2
1
1
0
0
4
0
0
0
0
0
0
1
0
0
3
0
1
2
0
0
0
1
2
0
0
0
0
0
0
4
2
0
0
2
0
5
0
2
0
2
0
0
0
0
1
1
0
0
0
0
0
0
2
0
2
1
3
2
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
2
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
1
1
2
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
1
1
0
0
2
0
0
2
0
0
0
0
1
0
0
2
0
0
1
1
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
2
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
4
0
2
1
1
0
2
0
2
0
0
0
2
1
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
2
1
0
2
0
1
1
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
1
1
0
0
0
0
0
1
0
0
0
3
0
0
2
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
4
0
0
0
0
0
0
2
0
0
0
2
0
1
2
0
0
2
1
2
0
0
2
0
0
3
0
0
2
1
0
1
0
0
0
1
2
0
1
1
0
1
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
1
3
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
2
0
0
1
3
0
0
0
0
0
0
2
1
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
2
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
1
0
0
0
1
1
0
3
0
0
0
0
0
0
0
3
1
2
1
2
0
0
0
0
0
0
0
1
1
1
0
0
3
2
0
0
0
0
0
1
1
0
0
0
2
0
0
1
1
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
1
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
1
0
1
2
0
0
0
0
0
0
0
0
3
1
1
1
1
3
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
1
2
2
0
0
2
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
2
2
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
2
2
1
0
2
0
0
0
1
0
0
2
2
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
1
1
2
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
2
2
0
2
1
0
2
1
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
2
1
0
0
1
2
0
0
0
0
0
0
0
1
2
0
0
0
2
0
1
0
0
2
0
0
0
4
0
0
0
0
0
0
0
0
3
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
3
0
0
0
0
0
2
2
0
0
0
0
0
2
3
1
0
4
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
2
0
0
2
0
2
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
3
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
1
0
0
0
0
0
1
0
0
1
0
1
0
2
0
0
2
0
0
0
1
3
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
1
2
0
1
0
0
0
2
0
0
2
1
0
0
0
1
0
1
0
1
0
0
2
0
0
0
1
0
0
0
1
3
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
1
0
2
1
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
3
1
0
1
0
0
2
0
0
2
0
0
0
6
0
0
0
0
2
0
0
0
0
0
0
3
1
1
1
0
0
2
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
4
0
0
2
0
3
1
0
1
0
0
0
0
1
2
0
1
2
0
0
0
2
1
0
0
0
1
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
3
1
2
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
3
0
0
1
0
1
0
0
2
0
0
2
0
1
2
0
1
0
1
0
1
0
0
1
2
0
0
0
0
1
0
0
0
0
2
0
0
0
1
1
0
1
0
1
0
2
0
0
0
2
1
0
0
1
0
0
1
0
0
2
0
1
2
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
2
0
0
0
2
1
0
1
0
0
0
0
1
0
2
0
1
0
2
0
1
0
0
0
0
1
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
1
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
2
1
1
0
0
0
0
4
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
4
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
3
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
1
0
2
0
0
0
0
0
1
0
0
0
1
0
2
0
0
1
0
1
0
1
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
2
2
0
0
0
2
0
1
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
2
3
2
0
1
1
4
0
2
0
0
0
0
2
0
0
0
3
0
2
0
0
0
1
0
0
0
4
0
0
0
0
0
1
0
0
2
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
1
2
1
0
0
0
1
1
0
0
5
0
0
0
2
0
3
0
0
0
1
0
0
0
0
3
0
0
2
0
2
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
2
1
0
0
2
1
0
2
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
3
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
1
2
0
2
2
0
0
1
0
1
1
0
1
0
3
0
0
2
0
3
0
0
1
0
1
2
2
1
0
0
1
0
0
0
1
2
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
2
0
1
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
3
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
0
2
3
0
0
0
0
0
1
0
0
0
0
0
0
1
2
1
2
0
0
4
0
0
0
0
2
1
0
0
0
1
0
0
0
2
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
2
0
0
0
1
1
0
0
3
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
4
0
1
1
0
1
2
0
0
0
1
2
1
0
0
0
0
1
0
1
4
0
0
0
0
3
1
1
1
0
0
2
0
2
0
0
0
1
0
2
0
1
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
1
2
0
1
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
1
0
0
0
0
3
3
1
0
2
0
0
1
0
5
0
2
0
2
1
2
2
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
2
2
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
4
0
0
0
1
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
6
0
2
1
0
0
0
0
0
2
0
0
2
6
0
2
1
0
2
0
0
1
0
0
0
0
3
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
2
0
0
0
2
1
0
0
0
0
1
0
1
1
2
0
2
0
0
1
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
1
0
0
2
1
3
0
0
1
0
3
0
0
2
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
2
0
0
1
2
0
1
0
0
0
0
0
0
0
0
1
3
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
3
0
2
2
0
0
2
0
1
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
2
2
1
0
1
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
2
0
2
1
1
0
0
18
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
10
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
2
2
0
0
5
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
4
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
2
2
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
3
0
0
0
1
1
2
1
0
0
2
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
2
0
2
1
1
0
0
1
0
0
1
0
0
0
2
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
2
0
0
0
0
2
2
0
2
1
3
0
0
0
0
0
0
0
2
1
0
2
0
0
1
0
0
2
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
2
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
1
1
1
0
0
2
0
0
2
0
0
4
2
1
0
0
0
1
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
3
0
0
0
1
0
0
1
0
0
1
0
0
0
0
4
2
0
0
0
0
3
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
1
0
1
0
0
5
1
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
2
0
0
0
1
2
1
0
0
0
0
0
2
0
0
0
2
0
1
2
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
2
1
0
1
0
1
2
0
1
0
1
0
0
1
1
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
1
1
0
0
0
3
1
1
0
2
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
2
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
2
0
1
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
2
2
1
0
0
0
0
0
2
0
2
0
0
0
0
0
1
2
0
0
0
2
0
1
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
1
3
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
1
0
0
0
2
2
0
0
1
0
0
0
0
0
0
1
2
2
0
0
0
0
1
1
0
0
1
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
2
3
0
0
0
1
0
2
0
3
0
0
0
0
2
0
0
0
0
1
2
0
2
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
1
0
0
3
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
1
0
0
1
0
6
0
0
0
0
0
0
0
3
0
0
2
0
0
1
0
0
0
0
1
1
2
2
0
0
3
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
1
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
1
3
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
8
0
1
0
0
1
0
3
0
0
0
0
2
0
0
0
1
0
1
1
0
0
2
0
3
0
0
2
0
0
0
2
0
1
0
1
2
0
0
2
0
0
0
0
1
3
0
3
0
1
3
0
0
2
0
2
0
0
2
2
8
0
0
0
0
0
0
0
2
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
5
1
0
0
0
2
0
2
0
0
2
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
2
0
0
0
0
1
2
2
0
1
0
0
0
0
0
0
0
2
0
0
2
2
0
2
0
0
0
0
1
1
0
2
1
2
0
0
2
0
0
0
0
0
0
1
1
0
0
0
1
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
2
4
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
4
0
0
0
2
0
1
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
1
4
0
0
0
0
0
2
1
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
3
0
0
2
2
0
0
0
1
1
0
0
2
1
0
0
1
2
0
0
1
3
0
1
0
0
2
0
4
0
0
0
0
0
1
0
0
2
0
0
1
2
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
2
2
0
1
0
0
0
0
0
0
2
1
0
0
0
2
1
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
3
0
1
0
0
0
1
0
0
1
0
2
0
0
2
2
1
2
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
7
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
1
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
2
2
0
0
0
1
0
0
0
0
3
0
0
0
0
0
1
9
0
1
0
0
0
1
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
9
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
2
0
2
0
4
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
2
1
0
1
5
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
1
0
0
2
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
1
2
1
0
0
0
2
0
0
0
2
0
1
0
0
3
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
1
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
2
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
2
2
1
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
2
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
2
1
2
0
0
0
1
2
0
0
1
0
0
0
1
2
0
2
1
2
0
0
0
7
1
0
1
0
2
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
2
1
0
0
2
0
0
2
2
1
1
0
2
1
2
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
1
0
0
0
0
1
1
0
1
0
1
0
0
1
0
0
2
1
0
2
0
1
0
0
3
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
1
1
3
2
1
0
0
0
0
0
0
1
2
0
0
0
0
3
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
1
0
0
0
1
1
0
2
0
0
0
2
0
0
1
2
0
4
0
1
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
2
1
2
1
2
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
1
2
1
0
0
2
1
0
0
1
0
0
0
0
1
0
2
2
0
0
3
8
2
0
1
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
1
1
1
2
2
2
1
0
1
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
3
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
2
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
1
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
1
0
0
0
0
2
0
0
2
0
0
2
0
0
0
2
0
1
0
0
1
0
0
0
0
1
0
0
0
2
0
1
0
0
1
0
0
0
2
0
0
2
0
1
1
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
2
0
1
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
2
0
0
0
0
0
0
2
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
2
0
7
0
2
0
4
0
0
0
8
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
3
0
2
0
0
2
0
1
0
0
0
0
0
3
2
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
2
0
0
2
1
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
3
3
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
1
2
0
0
0
0
2
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
1
0
5
0
0
1
2
0
0
0
0
0
3
2
1
0
0
0
0
0
0
1
0
1
0
2
0
1
2
0
0
1
0
0
0
0
2
0
2
0
0
0
1
0
0
1
0
1
2
1
0
2
0
0
0
0
1
1
0
0
1
0
2
0
0
2
1
0
0
0
0
0
5
0
0
1
0
1
2
0
0
0
0
0
0
2
1
0
2
0
0
1
1
0
0
1
0
0
2
0
1
1
2
0
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
1
0
0
2
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
3
0
0
0
0
0
0
2
1
0
0
1
0
2
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
2
0
1
3
3
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
3
1
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
1
0
0
0
0
1
0
2
0
2
2
0
0
0
0
0
2
0
0
0
0
2
0
2
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
2
0
3
1
1
0
1
1
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
1
0
4
1
0
3
2
0
0
0
0
2
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
1
2
1
0
4
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
1
1
2
0
0
0
1
0
0
0
0
0
0
2
2
0
1
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
2
1
3
0
0
2
2
0
0
1
0
2
2
0
0
0
2
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
2
0
2
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
1
0
0
3
0
1
0
1
0
0
2
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
3
0
0
1
0
0
0
0
3
1
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
1
2
0
0
3
0
2
0
0
0
1
0
0
2
0
1
0
0
0
2
2
2
0
0
0
0
0
0
1
0
1
0
9
1
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
3
0
0
1
0
1
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
4
2
0
0
1
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
1
0
0
2
0
0
2
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
1
0
0
0
3
0
0
0
0
0
0
2
1
0
0
2
1
0
0
2
0
0
0
0
0
2
2
1
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
1
2
1
0
2
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
3
0
5
0
0
0
0
0
0
2
1
2
0
0
2
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
2
0
0
0
1
4
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
3
1
0
1
0
2
0
0
3
1
0
0
0
0
0
0
0
1
0
2
0
0
0
5
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
1
1
0
0
0
0
2
0
0
4
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
1
1
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
2
0
1
2
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
2
0
1
2
0
0
0
0
0
0
1
0
2
0
0
0
1
0
2
0
2
0
1
1
0
3
0
0
2
1
2
0
0
0
0
1
1
0
1
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
1
2
0
0
1
0
1
2
1
0
1
0
0
0
0
2
1
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
2
0
0
3
0
0
0
0
0
3
1
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
2
1
2
2
0
0
0
1
0
1
1
0
0
1
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
2
2
0
0
0
2
0
0
0
0
0
0
8
0
0
2
0
0
0
0
0
2
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
5
2
0
1
0
1
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
1
0
0
2
0
2
0
1
0
0
1
0
1
0
1
0
0
1
0
0
1
2
0
0
0
1
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
1
0
0
0
0
0
2
1
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
3
0
2
2
0
1
0
2
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
1
0
0
2
2
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
4
0
0
0
1
0
0
1
0
0
2
0
0
0
2
0
1
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
1
1
2
0
0
2
0
0
0
0
2
0
0
0
0
3
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
2
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
3
2
0
0
0
0
0
1
2
2
0
0
0
1
0
0
2
0
0
2
1
2
1
0
0
0
0
0
3
0
0
0
0
1
0
0
2
0
1
0
1
0
2
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
2
1
2
2
0
0
2
2
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
2
0
0
1
3
0
0
0
1
0
2
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
2
1
0
1
0
1
0
0
3
2
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
1
2
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
2
2
0
0
1
2
0
0
0
2
0
0
1
0
0
0
2
0
0
5
0
0
0
2
2
2
1
0
0
0
0
2
1
0
0
0
0
2
0
1
1
0
0
0
0
0
0
1
1
0
3
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
2
1
0
1
1
0
0
0
0
1
1
0
0
0
2
0
2
0
0
0
1
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
1
1
2
2
0
1
0
2
0
1
1
0
1
2
0
0
0
0
0
1
3
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
3
0
0
2
0
2
0
0
2
0
0
2
0
1
0
2
0
0
0
1
0
0
2
0
0
0
2
0
0
0
2
0
0
2
1
0
0
0
0
0
1
0
0
1
0
0
0
2
1
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
1
0
0
2
0
0
0
5
0
1
2
0
0
0
2
2
0
1
2
0
1
0
0
1
2
0
0
0
0
2
0
0
0
4
0
2
0
1
0
0
0
0
1
0
0
2
2
0
0
1
2
0
0
1
0
0
0
0
0
1
1
2
2
0
6
1
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
1
0
2
2
0
2
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
1
0
2
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
2
1
2
0
2
0
0
0
0
0
0
1
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
3
0
0
0
0
0
0
0
1
0
2
0
1
0
0
2
0
1
0
0
2
0
0
0
2
1
0
1
0
0
0
2
0
2
0
0
2
1
0
0
1
1
2
1
2
2
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
1
0
5
2
2
0
0
0
4
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
2
2
0
0
0
0
2
2
1
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
1
0
2
0
1
0
1
1
0
0
0
0
2
0
2
0
0
0
1
0
2
2
2
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
2
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
2
0
1
2
0
0
2
0
2
2
0
0
0
2
2
5
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
2
0
0
2
0
1
0
2
0
0
0
1
1
2
0
0
2
1
0
2
2
2
2
0
0
2
0
0
0
5
0
0
2
0
2
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
4
0
1
1
0
0
1
0
2
0
2
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
6
0
0
0
0
0
1
0
2
1
0
3
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
2
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
1
0
0
0
0
1
0
0
2
2
0
0
0
0
1
2
0
0
0
0
0
0
2
2
0
2
1
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
1
0
0
0
2
0
0
0
0
0
5
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
2
3
0
2
0
0
0
1
0
2
1
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
1
0
0
0
2
0
1
3
2
0
2
1
0
0
0
2
0
0
0
2
2
0
1
0
0
2
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
4
1
0
0
0
1
1
0
0
0
2
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
1
0
0
0
0
7
0
0
0
0
2
1
1
0
0
0
0
0
3
0
0
0
3
0
0
0
3
0
0
0
0
0
0
0
1
0
1
0
2
0
1
0
0
0
0
0
2
0
2
1
0
1
1
0
0
0
0
0
3
1
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
1
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
5
0
1
2
0
2
2
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
2
1
0
0
2
1
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
3
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
4
1
2
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
2
1
0
0
0
1
1
1
0
0
0
0
0
0
2
0
1
1
1
0
0
0
0
0
0
1
1
0
1
1
7
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
2
0
0
1
2
0
1
0
0
1
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
1
0
2
0
0
0
1
1
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
2
0
2
0
0
0
0
0
0
2
0
2
1
2
0
1
2
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
3
2
2
0
0
0
1
3
0
0
0
1
0
0
3
1
2
0
0
1
2
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
2
0
0
0
0
0
4
0
0
0
1
0
0
2
2
0
1
0
1
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
1
0
0
0
0
1
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
8
0
0
1
0
0
2
0
0
0
0
0
1
1
0
0
2
3
0
1
0
0
0
0
0
0
4
1
0
0
0
2
1
1
3
3
2
4
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
1
0
0
3
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
2
2
0
0
2
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
3
1
0
0
1
0
2
0
0
2
0
0
1
2
2
1
1
2
0
0
0
2
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
2
0
0
0
1
0
2
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
1
1
1
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
1
2
0
0
2
0
0
1
2
0
0
0
0
2
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
2
4
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
1
0
0
0
1
0
2
0
0
2
1
1
0
0
2
2
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
1
1
1
0
1
0
0
1
3
0
0
0
2
0
0
0
0
1
0
0
0
1
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
2
2
0
1
1
0
0
1
0
0
0
0
0
1
0
0
1
2
0
2
1
1
0
1
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
3
1
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
2
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
1
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
15
2
0
0
0
2
2
1
4
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
2
2
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
1
0
0
2
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
1
0
0
1
0
1
1
0
2
0
1
0
0
0
0
0
0
2
0
1
0
0
3
0
0
1
0
0
2
3
0
2
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
2
1
0
1
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
2
2
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
3
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
2
0
2
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
1
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
1
0
0
0
3
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
3
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
3
0
1
0
2
0
1
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
2
2
0
0
1
2
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
1
3
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
2
0
1
2
2
1
0
3
0
0
1
2
3
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
1
1
0
2
0
0
0
1
3
0
1
2
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
3
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
2
0
1
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
1
5
0
0
2
2
0
0
0
2
2
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
2
2
0
1
4
0
0
0
0
0
0
0
2
0
1
0
0
2
1
3
1
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
4
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
3
0
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
2
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
1
2
0
1
1
0
0
2
0
0
1
0
0
1
0
3
2
1
0
0
0
0
2
2
0
2
0
0
1
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
2
0
2
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
3
0
0
1
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
1
1
1
1
2
0
2
0
0
3
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
5
0
1
0
0
1
1
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
1
1
0
2
0
2
0
0
2
0
0
1
0
1
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
7
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
1
1
0
1
2
0
0
0
0
0
0
0
2
1
0
0
2
0
0
2
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
2
0
0
2
2
1
1
0
2
0
1
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
4
2
0
0
1
0
1
3
2
0
0
0
0
0
1
1
0
0
2
0
0
0
0
2
0
0
1
0
1
0
4
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
2
0
0
0
0
0
2
2
1
0
0
0
0
1
0
1
0
1
0
0
2
6
0
0
1
0
2
0
2
0
1
1
0
0
0
0
0
2
0
2
2
0
0
2
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
4
2
0
0
0
0
1
0
2
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
2
0
0
0
3
0
1
1
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
1
0
1
2
0
2
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
2
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
2
2
0
1
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
3
0
0
1
0
0
0
1
0
0
0
0
1
2
2
0
2
1
0
2
2
0
0
0
2
1
1
2
0
0
0
0
1
2
0
1
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
2
0
2
0
0
2
0
1
0
0
8
0
0
1
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
2
0
0
0
0
3
0
0
1
0
0
1
1
0
0
0
2
0
2
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
1
2
1
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
1
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
2
0
0
2
1
0
2
0
1
0
2
2
1
1
0
0
2
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
3
2
0
0
0
0
2
2
2
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
1
0
1
0
1
0
0
0
3
0
0
0
0
1
0
1
0
0
0
2
0
2
0
0
0
2
0
0
0
2
1
0
0
0
0
0
2
0
0
1
0
2
0
0
1
0
2
1
1
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
2
0
4
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
1
2
0
1
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
5
2
0
1
0
2
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
2
1
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
1
0
1
0
2
1
0
0
2
0
0
2
0
0
0
0
0
0
3
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
2
0
1
0
0
0
0
0
0
1
1
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
2
2
0
0
0
0
1
1
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
1
1
2
0
2
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
1
1
1
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
2
0
1
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
2
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
2
4
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
1
0
0
0
0
1
0
0
2
0
0
0
1
0
0
1
0
9
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
2
4
1
1
3
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
2
2
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
1
0
0
1
0
0
2
0
1
0
0
0
1
0
0
1
0
0
1
0
4
1
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
4
0
0
2
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
2
0
0
0
1
0
1
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
2
0
1
0
0
1
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
1
0
2
1
0
2
1
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
2
0
1
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
3
2
0
0
0
0
2
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
2
0
1
2
1
0
0
0
0
0
1
0
0
3
0
0
1
1
2
0
0
0
0
3
0
0
1
0
0
0
0
1
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
2
0
0
0
0
1
1
0
1
0
2
0
0
0
0
0
2
0
2
1
0
1
0
2
0
1
1
0
0
2
0
2
0
0
2
2
1
2
1
0
0
0
2
0
0
0
0
0
4
2
2
0
0
0
1
0
0
0
1
0
0
0
0
2
2
2
1
0
0
0
0
1
0
0
0
2
0
0
0
1
0
1
5
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
4
0
0
2
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
3
0
1
2
0
1
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
1
1
0
0
2
0
1
0
3
0
0
0
0
1
0
0
0
0
1
2
0
1
1
0
0
1
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
4
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
1
0
1
0
0
0
1
1
1
1
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
3
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
2
0
0
1
1
2
0
2
0
0
2
3
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
2
0
0
1
1
0
0
2
0
1
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
8
2
0
1
2
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
3
0
0
3
2
0
0
1
0
1
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
5
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
1
2
1
1
2
0
0
2
0
0
1
2
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
2
0
2
0
0
0
0
1
1
1
0
0
0
2
0
0
2
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
2
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
2
0
2
0
0
0
0
3
0
0
2
2
0
1
0
0
0
2
0
3
0
0
0
0
0
3
1
0
0
0
2
0
0
2
0
1
0
0
0
0
2
1
0
3
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
2
3
0
0
0
1
1
2
1
0
0
1
2
0
0
0
0
0
2
1
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
3
1
0
1
0
3
0
1
0
0
0
0
3
3
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
2
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
5
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
3
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
1
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
1
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
1
2
1
0
1
0
2
2
0
0
0
0
0
0
0
0
1
1
3
0
0
1
0
0
0
0
0
2
0
2
2
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
2
0
0
0
0
2
0
1
0
0
2
0
1
0
1
0
0
0
0
3
0
0
0
1
1
1
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
2
0
0
1
0
9
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
1
0
0
0
0
1
2
0
0
0
0
0
0
0
1
1
0
2
1
1
0
0
0
0
0
0
0
3
0
0
1
1
0
0
2
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
2
3
1
0
2
0
0
0
4
0
0
1
0
0
0
0
0
0
0
1
0
1
2
1
1
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
2
0
0
0
1
4
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
2
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
2
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
7
0
0
0
2
0
0
0
3
0
0
0
1
0
0
0
1
1
2
0
1
1
2
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
11
0
2
2
2
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
4
2
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
1
1
1
2
2
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
3
1
2
0
2
0
0
0
0
1
0
0
3
0
2
1
0
0
0
0
0
2
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
2
3
0
1
2
2
0
0
0
1
0
0
0
0
3
1
2
0
0
3
0
0
0
0
2
0
0
1
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
3
1
0
0
2
0
1
0
0
1
0
1
1
2
0
9
2
3
0
0
1
0
1
0
0
0
0
0
0
1
2
0
0
0
0
2
2
0
0
1
6
0
2
0
0
0
0
0
0
0
1
0
0
0
1
2
0
7
1
0
0
0
0
1
0
2
0
0
3
0
0
0
0
0
2
0
0
1
0
0
1
1
0
0
1
0
1
1
0
0
0
2
0
0
2
0
0
1
0
2
0
1
0
1
3
0
0
0
0
0
1
2
0
1
2
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
2
1
0
0
0
0
2
1
0
0
0
2
1
0
0
1
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
3
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
4
0
0
0
0
0
0
2
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
2
0
2
2
0
0
2
0
0
2
0
2
3
0
0
2
0
0
2
0
0
8
0
0
2
1
1
3
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
5
0
1
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
1
0
1
0
1
1
0
1
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
2
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
4
0
1
0
0
2
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
1
0
1
0
2
0
0
0
0
0
2
2
0
0
1
0
0
0
0
2
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
2
0
2
1
1
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
1
1
0
0
0
2
0
1
2
0
0
0
5
2
0
0
0
0
1
0
0
0
0
0
0
4
0
2
2
0
0
1
0
1
0
1
0
0
1
2
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
2
0
1
0
0
2
0
0
0
2
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
2
0
0
0
0
0
2
2
0
1
0
0
1
0
0
0
2
3
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
2
1
0
2
0
0
1
2
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
2
0
0
0
1
0
0
7
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
1
2
0
0
0
0
1
0
0
2
3
0
0
0
0
1
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
4
0
0
0
0
3
2
0
0
1
1
0
0
0
0
2
1
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
1
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
2
0
0
1
2
0
0
3
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
1
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
2
1
1
0
0
0
0
2
0
0
0
2
0
2
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
1
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
4
0
0
1
0
0
0
0
0
0
1
1
2
0
0
1
1
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
3
0
0
2
1
0
1
0
0
0
2
2
0
0
0
0
2
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
4
2
0
1
1
0
0
0
0
0
1
0
0
0
0
0
3
1
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
2
1
0
0
0
1
1
1
1
0
2
2
0
2
0
0
0
1
0
1
0
0
0
0
1
2
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
1
0
2
0
1
0
0
1
0
0
0
0
1
1
0
2
0
2
1
0
0
0
1
3
1
0
0
0
0
2
0
0
5
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
3
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
2
0
0
1
2
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
3
2
0
1
0
0
1
2
0
2
1
1
0
0
2
3
0
3
0
0
2
1
0
1
0
0
0
1
0
0
2
1
0
0
2
0
0
0
3
2
0
0
0
0
1
0
0
4
1
0
0
3
2
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
3
0
1
0
2
0
3
3
4
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
3
2
0
0
0
0
0
0
1
0
0
1
0
0
0
1
2
0
0
2
1
0
0
0
1
0
2
6
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
2
2
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
2
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
2
0
0
3
0
2
0
0
0
0
0
1
2
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
3
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
2
2
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
2
2
0
1
0
0
0
0
1
2
1
1
0
0
3
0
1
0
0
1
0
0
1
0
0
1
0
0
1
2
0
2
3
0
0
0
1
1
0
2
0
0
0
0
0
0
0
3
0
0
0
1
2
0
1
2
0
0
0
0
1
1
0
4
2
0
1
0
0
0
2
0
0
0
1
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
1
1
1
0
2
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
3
0
0
0
0
2
0
3
0
0
0
2
0
0
2
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
1
0
1
0
0
2
0
0
0
0
2
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
1
1
2
0
0
3
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
7
0
0
0
0
2
1
0
0
0
0
2
3
0
0
0
2
0
4
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
2
0
1
0
0
0
1
0
0
2
0
2
0
0
1
1
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
1
1
0
2
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
1
0
0
2
2
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
2
2
0
2
0
0
0
2
1
0
4
0
0
2
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
3
0
1
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
3
0
1
0
2
0
0
1
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
3
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
1
0
2
0
0
1
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
1
1
0
1
1
0
0
0
3
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
1
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
2
0
2
0
0
0
0
2
0
0
1
0
1
0
0
2
0
0
2
2
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
1
1
1
1
0
2
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
1
0
2
3
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
1
0
0
0
2
0
0
0
0
3
1
0
0
0
0
1
0
0
1
0
1
1
1
1
0
0
0
1
0
0
0
2
1
0
0
2
0
0
0
0
1
1
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
1
0
0
2
2
2
0
1
0
0
0
0
2
0
2
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
2
0
0
0
2
0
0
1
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
5
0
0
0
3
1
0
1
0
1
0
5
0
0
2
0
0
0
1
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
1
0
1
1
0
0
0
0
2
0
1
0
1
0
0
4
2
0
0
1
0
0
0
0
0
2
2
2
0
0
0
0
0
0
2
1
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
2
0
2
1
0
0
0
1
2
1
0
0
0
0
0
1
0
0
0
0
0
0
3
2
0
0
3
1
0
0
0
0
2
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
2
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
2
1
0
1
0
1
0
1
0
4
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
4
0
0
2
0
0
0
0
0
0
2
0
2
0
2
1
0
2
3
0
1
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
2
0
0
1
0
2
0
1
0
0
0
0
2
0
2
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
3
0
2
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
4
0
0
1
0
0
0
2
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
1
2
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
9
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
2
1
2
0
0
0
2
1
0
1
0
0
2
1
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
3
0
0
3
0
0
0
2
0
0
1
0
0
0
1
2
0
0
0
1
0
2
0
0
1
1
1
0
0
0
0
3
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
2
1
0
0
0
1
0
0
0
0
0
2
2
0
0
0
1
0
1
2
0
2
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
1
0
2
0
0
0
0
1
1
2
0
2
0
0
0
2
0
0
1
2
2
0
1
0
0
1
0
2
2
0
2
1
0
0
0
0
1
0
0
0
2
0
1
1
0
0
6
0
1
1
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
4
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
1
0
0
0
2
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
1
1
2
0
0
0
0
2
2
2
2
1
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
5
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
1
0
0
2
0
0
0
0
2
1
0
1
1
0
0
0
0
0
1
0
2
0
0
3
0
0
0
0
0
1
2
1
2
0
1
0
0
1
0
0
0
0
0
1
2
0
0
0
2
0
2
2
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
2
0
0
1
0
2
2
1
3
0
0
0
0
0
2
0
1
0
0
2
0
0
0
1
2
0
0
2
0
0
1
0
2
0
1
0
2
0
2
0
0
0
1
3
1
0
0
7
0
0
0
1
0
0
0
2
2
0
0
0
1
1
0
0
0
2
0
0
0
0
1
1
1
0
1
0
0
0
1
0
0
0
2
1
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
3
0
2
0
0
3
2
1
2
0
0
0
1
2
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
2
1
2
0
1
0
0
1
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
2
0
0
2
0
0
0
0
0
2
0
2
0
2
0
2
0
0
0
0
0
0
3
2
0
2
0
0
0
0
3
0
0
1
2
0
0
0
0
0
0
1
0
0
0
1
0
0
1
2
2
0
0
0
0
0
2
2
2
0
1
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
1
0
1
0
1
0
0
0
2
2
0
2
1
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
1
2
1
2
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
2
0
2
1
0
0
0
0
2
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
2
0
3
4
2
1
2
3
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
1
0
0
0
0
1
1
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
1
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
1
0
2
0
2
1
1
5
0
1
1
0
1
2
0
0
0
0
0
0
3
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
2
0
1
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
2
1
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
1
3
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
3
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
5
0
0
0
0
0
1
0
2
2
0
0
0
0
5
0
2
0
1
2
1
0
1
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
2
0
2
2
0
0
1
2
2
0
2
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
1
0
1
2
1
2
2
0
0
0
0
0
0
0
3
0
1
0
2
0
3
5
0
0
2
0
0
0
0
0
0
0
0
3
0
2
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
4
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
5
0
0
0
3
1
0
0
0
0
0
2
2
2
0
2
0
0
0
2
0
0
0
2
2
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
5
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
1
2
0
0
0
1
0
0
0
0
0
1
1
0
0
3
0
0
0
1
0
0
1
0
2
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
2
0
1
1
0
2
0
0
0
0
1
1
2
0
0
1
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
2
0
0
0
1
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
3
0
2
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
2
0
1
0
0
0
2
1
5
0
0
1
2
0
0
0
0
1
0
3
1
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
2
0
0
1
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
1
0
2
1
0
1
1
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
1
0
3
2
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
2
0
0
2
0
0
0
1
0
0
0
3
0
1
1
0
2
6
0
2
1
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
1
1
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
1
0
0
10
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
4
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
3
2
2
0
2
0
0
0
0
0
0
0
1
1
0
1
1
0
3
0
1
0
0
0
0
0
2
0
2
0
2
2
0
0
0
0
0
4
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
1
0
0
1
0
0
0
3
0
3
0
0
0
0
0
2
0
1
0
0
0
0
0
1
3
3
1
0
0
9
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
3
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
3
5
0
0
1
0
0
0
1
0
0
0
1
2
0
0
2
0
0
0
2
0
2
1
0
0
0
1
0
2
2
0
0
1
0
1
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
3
2
0
1
0
0
1
2
1
0
0
0
1
1
0
0
0
0
0
1
4
0
4
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
2
0
0
1
0
1
0
0
0
0
0
2
5
2
0
0
0
0
0
1
0
0
1
0
0
2
2
0
0
0
0
0
0
0
3
1
2
0
2
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
1
0
0
0
10
1
0
0
2
0
0
2
0
0
5
0
0
0
0
1
0
0
0
0
0
0
0
2
0
3
0
0
2
4
2
0
0
2
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
2
0
0
0
0
0
2
1
0
0
1
5
3
2
0
0
0
0
0
0
1
1
0
1
1
2
0
3
0
1
0
0
0
2
1
0
0
2
0
0
0
0
1
3
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
2
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
1
2
1
0
1
1
3
2
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
2
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
1
2
4
0
3
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
3
0
0
0
1
3
2
0
0
0
1
2
1
0
0
2
2
0
2
0
0
0
0
2
0
0
1
2
1
1
0
0
0
0
0
0
0
2
0
0
1
1
1
1
0
0
1
2
2
1
2
0
5
2
2
0
1
0
3
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
2
0
1
0
0
0
0
1
0
0
0
2
0
1
0
2
2
1
2
1
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
2
0
0
0
0
2
0
2
0
1
0
2
2
0
1
3
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
1
0
0
2
3
0
1
0
0
2
2
0
0
1
0
0
2
2
0
1
1
2
0
0
0
0
0
0
1
0
0
0
2
1
1
0
0
0
2
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
1
1
2
0
0
0
0
0
2
2
1
1
2
0
0
0
1
0
0
0
3
0
0
1
0
0
0
1
0
0
0
1
0
3
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
1
3
2
1
0
3
0
0
0
0
2
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
1
0
0
0
0
1
2
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
2
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
1
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
1
0
1
1
0
0
0
0
0
0
1
0
2
0
1
0
0
1
0
0
0
0
2
1
0
0
0
0
0
2
2
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
1
0
2
1
0
0
0
1
1
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
2
1
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
3
0
0
0
1
0
0
0
2
0
2
2
0
1
0
0
1
3
0
1
0
0
0
0
1
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
1
3
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
24
0
2
0
0
0
7
1
1
2
0
0
0
0
0
2
0
2
0
2
0
0
0
5
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
3
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
2
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
5
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
3
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
1
0
2
0
0
0
1
0
2
2
0
0
0
0
1
0
2
1
1
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
3
1
0
1
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
1
0
2
0
1
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
2
0
0
0
1
0
2
1
1
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
1
1
0
3
2
1
1
0
1
0
0
1
0
0
0
0
1
0
3
1
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
1
0
0
2
1
0
0
0
0
1
0
1
2
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
2
0
2
0
0
2
1
0
0
0
0
0
1
0
0
0
0
2
2
1
1
0
2
1
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
2
0
0
0
1
0
0
0
0
1
1
0
0
2
0
0
2
2
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
2
0
1
0
0
2
0
0
1
0
0
3
0
0
0
2
2
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
1
0
0
0
2
6
0
0
0
1
0
2
0
0
1
0
0
2
0
11
5
0
0
0
1
0
1
0
0
1
1
0
2
0
0
1
10
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
2
4
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
2
2
0
0
0
0
1
0
0
0
0
1
2
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
3
0
0
3
0
0
0
0
2
0
2
0
0
3
0
0
0
2
0
2
3
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
1
0
0
2
2
1
0
0
0
0
3
0
0
2
0
2
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
2
1
0
2
1
1
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
1
1
0
1
0
0
0
8
0
0
1
0
0
0
0
3
0
1
0
1
0
0
0
1
2
2
0
0
0
1
2
0
1
0
0
2
0
0
1
0
1
0
0
0
0
2
1
0
1
2
0
0
0
0
0
0
0
0
1
1
2
2
0
1
1
2
0
2
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
2
0
0
1
2
0
0
2
0
2
0
2
0
0
0
0
1
0
1
1
0
0
0
0
0
1
1
4
0
0
0
0
0
1
1
2
0
0
1
0
2
0
0
0
0
1
0
0
2
0
1
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
1
0
0
1
0
2
0
1
2
0
0
0
0
0
2
2
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
1
1
2
0
0
2
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
1
0
0
3
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
1
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
2
1
0
2
0
0
0
0
0
1
1
0
2
2
0
0
0
1
2
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
1
1
1
0
2
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
2
0
0
1
0
0
2
0
3
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
1
0
8
0
2
0
1
1
1
2
0
0
0
0
3
0
0
1
0
0
0
3
1
0
0
0
0
0
3
0
0
0
0
0
1
1
0
0
2
1
0
0
1
0
1
0
2
0
0
0
0
2
0
0
0
2
1
0
3
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
2
0
0
1
0
0
0
2
0
0
2
0
4
0
0
2
0
0
2
1
0
2
0
0
0
0
0
1
2
0
0
3
0
0
0
0
1
1
1
0
0
5
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
1
1
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
3
1
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
1
0
0
0
0
1
3
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
1
0
1
0
0
0
0
3
0
2
0
0
2
0
0
2
0
0
2
0
1
0
0
0
1
0
0
2
0
0
0
2
1
0
2
0
4
0
2
0
0
0
1
0
0
0
0
2
0
1
0
0
1
2
2
2
0
0
0
2
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
2
1
2
2
0
2
0
0
2
0
0
1
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
3
2
0
2
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
2
0
2
2
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
2
1
0
1
5
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
4
1
0
0
0
0
1
0
0
0
0
2
0
1
2
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
3
0
0
2
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
3
0
1
2
2
0
0
0
2
0
0
1
0
0
0
1
2
0
1
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
4
2
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
1
1
2
0
3
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
2
3
0
1
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
3
0
2
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
1
0
0
2
0
0
2
0
0
0
5
0
0
0
0
1
2
0
1
1
0
0
0
2
0
0
0
0
2
0
2
0
0
0
1
0
0
2
0
1
0
0
0
2
0
2
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
2
1
3
0
1
1
0
0
0
0
1
2
2
0
0
1
0
0
0
0
0
0
0
0
0
4
0
2
1
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
2
1
2
0
1
1
2
0
0
2
0
0
0
2
0
2
1
0
0
2
0
0
1
0
0
1
1
1
1
0
0
0
0
0
0
1
0
2
1
0
1
2
0
1
0
1
0
0
0
5
2
1
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
2
0
0
3
0
0
0
1
0
0
2
0
0
0
2
0
0
0
1
0
0
1
0
2
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
1
2
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
1
0
0
1
0
2
0
2
0
1
1
0
2
0
0
0
2
0
0
0
3
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
1
1
0
0
3
2
0
0
0
2
2
2
0
0
1
0
0
1
0
0
2
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
1
0
2
0
0
0
0
0
0
0
4
0
3
1
0
2
2
0
3
2
1
0
0
0
1
0
2
0
0
0
0
1
0
0
1
0
2
0
2
0
0
0
2
0
3
2
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
1
0
0
0
0
1
0
0
1
2
2
0
0
0
0
0
0
0
0
0
3
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
2
2
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
2
0
1
0
0
2
0
1
0
2
0
2
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
7
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
3
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
1
0
0
0
0
2
2
0
0
0
1
5
1
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
1
0
0
0
1
1
0
0
0
0
2
0
2
0
1
4
0
2
2
0
0
0
0
0
0
0
2
0
1
2
2
0
0
0
0
1
0
0
0
0
1
3
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
1
2
0
0
1
0
0
0
0
0
4
0
2
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
2
0
0
1
2
0
0
2
0
0
0
0
0
0
0
10
0
0
1
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
2
0
1
2
0
3
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
4
2
2
2
0
1
2
1
0
0
1
0
0
1
1
0
0
3
1
0
0
0
2
0
0
0
2
1
0
0
0
2
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
1
0
2
0
3
0
2
2
2
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
2
0
0
1
1
0
0
0
0
0
2
2
2
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
1
0
2
0
1
3
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
2
1
0
2
0
3
0
2
2
0
2
2
0
1
0
2
0
2
1
0
0
1
0
0
0
0
0
0
0
1
4
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
1
0
2
0
1
0
0
0
2
1
0
0
0
0
1
0
2
1
0
0
0
0
2
0
1
0
0
0
0
1
2
0
0
2
11
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
2
0
0
3
1
0
0
1
1
0
0
0
0
2
0
0
1
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
2
0
0
0
1
2
2
0
0
0
0
0
0
0
2
6
1
1
0
1
0
0
0
5
0
0
0
1
2
0
0
1
2
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
5
0
0
1
0
2
1
0
0
0
1
0
1
0
1
2
2
0
0
2
0
3
0
0
1
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
2
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
1
2
2
1
0
2
0
0
2
2
0
0
0
1
1
0
0
0
0
2
0
2
0
0
1
0
0
1
2
0
2
1
1
5
0
0
2
2
1
0
1
0
0
1
2
4
0
0
1
1
1
1
2
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
2
1
1
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
3
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
2
0
0
2
0
2
0
1
0
0
0
3
1
2
0
1
0
2
0
0
1
0
0
1
0
0
0
0
1
0
1
0
1
1
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
2
0
0
0
2
1
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
1
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
3
0
2
0
1
0
2
1
1
0
0
0
1
0
0
2
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
2
2
0
1
0
0
0
0
0
0
1
0
2
0
0
0
2
0
1
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
1
0
0
5
2
0
0
0
0
0
0
0
4
1
0
0
0
0
2
1
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
3
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
1
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
1
2
2
1
1
1
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
1
1
1
0
0
1
0
2
1
0
0
0
0
2
0
0
0
1
2
0
1
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
2
2
0
1
0
1
0
2
1
2
0
0
0
0
0
1
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
4
5
2
3
0
0
0
2
2
0
0
0
0
0
0
2
2
1
0
0
0
0
1
0
3
0
0
0
1
1
0
0
0
2
0
0
0
0
1
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
1
0
0
0
2
0
0
2
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
2
1
2
0
3
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
6
0
1
0
0
0
3
0
0
0
0
1
1
0
0
2
0
0
1
0
0
1
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
4
0
2
2
0
0
2
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
1
0
1
1
0
0
1
2
0
2
0
0
2
0
1
0
0
0
0
0
0
0
2
3
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
2
0
0
0
0
1
0
0
1
0
2
0
0
0
0
2
0
0
0
1
0
0
2
0
3
0
0
1
0
1
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
1
0
2
0
0
0
0
2
3
5
0
0
2
2
0
0
0
0
0
0
3
2
0
1
2
0
0
2
2
0
2
0
0
2
1
0
2
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
3
1
0
1
0
0
0
0
0
0
0
0
3
0
0
1
2
0
0
3
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
1
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
4
0
1
0
0
0
0
0
0
1
2
0
2
0
0
3
0
1
0
1
2
0
1
2
2
2
0
2
0
1
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
3
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
1
1
0
1
0
0
1
0
2
0
0
1
0
3
0
0
0
0
4
0
2
0
1
0
0
0
0
0
1
1
0
0
1
0
0
3
1
2
0
0
0
0
2
4
1
0
0
0
0
0
0
0
0
0
0
0
3
0
2
2
0
0
0
1
1
0
0
2
2
0
2
2
0
2
0
0
0
0
0
2
0
1
0
2
0
0
2
0
0
0
0
0
0
8
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
2
0
0
0
1
1
0
0
0
0
0
0
4
2
0
2
4
0
0
0
2
1
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
3
2
3
0
0
0
2
2
0
0
1
1
0
0
0
0
0
0
3
0
0
0
0
2
1
0
0
0
0
1
0
0
1
2
0
0
0
2
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
1
0
2
1
0
0
0
1
0
0
0
0
1
1
1
0
2
0
3
0
0
0
0
0
3
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
2
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
1
1
2
2
0
1
0
0
1
0
0
0
1
1
1
0
0
0
0
2
0
4
1
1
0
0
2
1
1
0
0
2
0
0
0
2
0
0
2
0
1
1
0
1
1
0
0
0
0
2
2
1
2
1
2
0
2
0
2
0
0
0
0
0
1
0
2
0
0
1
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
1
0
2
0
0
0
0
0
2
0
1
0
0
2
1
0
0
0
3
0
2
0
2
2
0
0
2
0
2
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
2
1
0
0
0
0
0
2
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
4
0
0
0
1
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
1
2
1
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
4
0
4
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
3
0
0
1
0
0
0
4
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
3
0
2
0
0
1
0
2
0
2
0
1
0
0
0
1
4
0
1
0
0
0
2
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
2
0
0
0
4
0
1
0
0
0
2
0
3
2
2
0
0
0
0
2
0
2
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
4
1
0
0
2
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
1
0
0
1
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
2
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
2
0
1
0
0
0
0
0
1
0
2
1
0
0
2
0
0
3
2
1
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
1
0
2
0
1
0
1
2
0
0
1
0
1
0
2
2
0
1
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
3
0
2
0
2
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
5
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
1
0
2
1
0
0
0
1
0
0
0
0
0
2
0
0
2
0
3
0
0
2
0
0
0
0
2
0
0
0
1
0
3
0
1
2
1
1
1
0
0
2
0
0
2
0
2
0
1
1
5
1
0
2
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
2
0
0
0
5
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
2
0
0
1
1
2
1
0
2
1
2
1
2
1
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
2
0
4
2
0
0
1
0
3
0
0
0
0
0
0
0
0
2
0
1
3
0
0
0
0
0
0
0
5
1
1
0
0
0
2
1
0
1
0
1
0
3
0
1
0
0
2
0
2
0
0
0
0
2
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
6
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
2
3
2
0
0
1
1
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
2
1
2
3
0
1
0
0
0
0
0
3
0
0
2
4
0
0
0
1
0
3
2
2
5
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
4
1
0
3
2
0
0
0
1
1
1
1
0
0
0
0
0
1
2
0
1
3
5
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
1
2
4
1
0
0
3
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
2
0
0
2
0
1
2
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
1
1
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
1
0
3
1
4
1
2
1
0
0
1
0
0
3
2
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
2
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
2
0
2
2
2
0
0
1
3
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
1
0
4
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
2
0
1
0
0
1
0
0
1
0
1
0
0
2
0
1
0
2
0
0
0
2
2
0
0
0
6
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
2
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
1
0
0
1
0
2
0
4
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
3
0
1
2
0
2
2
1
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
2
1
0
0
1
0
0
0
4
1
1
0
0
0
1
1
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
4
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
1
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
2
1
0
3
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
2
0
1
0
0
0
0
1
2
0
1
3
0
0
0
0
0
0
0
2
2
1
0
2
0
3
0
0
0
0
2
0
0
0
1
0
0
0
2
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
1
2
1
1
0
0
2
0
0
0
0
1
2
1
0
0
0
5
0
0
0
0
0
0
0
0
2
0
0
1
0
3
0
2
0
1
0
0
0
1
0
0
1
2
0
1
2
0
0
2
0
1
0
2
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
3
0
0
1
0
2
0
2
0
3
2
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
3
1
0
0
0
1
0
0
0
1
0
0
0
3
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
1
1
6
0
0
0
2
2
0
0
0
0
0
0
1
2
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
1
2
0
0
2
0
0
1
0
0
0
0
1
0
0
0
1
1
0
2
0
0
1
1
1
0
0
2
1
0
0
4
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
2
0
0
0
0
2
0
3
2
0
0
1
0
2
2
0
0
4
1
3
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
3
1
0
0
0
0
10
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
2
1
0
1
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
2
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
1
4
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
2
1
0
1
0
0
0
0
0
0
0
0
1
0
0
2
1
1
2
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
1
0
0
2
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
8
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
2
0
1
0
0
2
0
1
1
1
1
0
2
0
1
0
0
0
0
0
1
0
2
2
0
0
0
0
0
1
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
4
2
0
0
0
4
1
0
3
0
0
0
1
0
0
0
0
0
0
0
4
2
2
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
1
2
1
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
1
1
0
0
2
3
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
1
2
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
2
2
0
0
1
0
0
0
3
0
1
2
0
1
0
0
1
1
0
0
0
4
0
0
0
0
0
0
2
1
0
0
0
2
0
1
1
0
0
0
3
0
2
0
0
0
1
0
0
1
0
0
0
0
1
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
3
0
0
2
0
1
0
0
0
0
0
0
1
3
0
1
2
1
0
0
0
2
0
0
0
1
0
0
0
2
1
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
1
0
2
1
0
1
1
0
1
0
0
2
0
1
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
5
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
4
0
0
1
0
1
1
0
2
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
6
1
1
0
2
0
0
0
1
2
0
0
2
1
1
1
1
1
0
0
0
0
0
3
0
2
0
5
0
2
0
0
0
1
2
2
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
3
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
1
1
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
3
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
5
0
0
1
2
0
0
4
0
0
0
1
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
1
0
2
2
2
0
0
2
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
3
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
4
0
0
0
0
0
2
0
0
1
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
6
0
1
2
0
2
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
3
0
0
0
2
0
0
2
1
0
0
0
0
1
1
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
3
1
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
2
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
1
0
1
0
0
0
1
0
0
1
0
0
5
0
0
0
0
0
0
0
2
0
1
0
0
0
1
2
0
0
2
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
1
1
0
2
1
2
0
0
1
0
0
0
0
0
2
1
0
0
1
0
2
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
4
2
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
1
1
1
0
0
0
0
0
0
1
0
3
0
0
0
0
1
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
1
1
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
2
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
6
0
0
0
0
0
1
0
2
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
2
1
0
2
1
1
0
1
0
2
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
3
0
0
0
0
1
1
0
0
0
0
1
3
2
0
0
1
0
0
0
0
2
0
2
1
0
0
2
0
0
1
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
2
0
0
0
1
0
0
1
2
1
0
2
0
1
0
0
0
1
2
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
1
3
0
2
0
1
2
0
0
2
1
0
0
0
0
1
2
0
0
0
0
0
1
1
0
3
1
2
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
1
3
1
0
0
0
0
4
0
0
0
2
0
0
0
1
0
2
0
2
2
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
1
1
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
2
0
0
0
2
2
2
0
1
0
0
0
1
2
2
0
2
0
0
0
0
1
2
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
1
0
1
1
0
1
0
0
1
0
1
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
2
0
3
2
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
2
0
0
0
0
0
2
0
0
1
0
1
0
0
0
4
0
1
0
1
0
0
0
2
0
0
1
0
0
0
0
0
1
4
1
1
1
2
2
0
2
0
5
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
2
1
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
3
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
4
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
5
2
0
0
0
1
0
0
0
1
1
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
2
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
4
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
4
2
0
1
0
1
2
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
4
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
4
1
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
2
2
1
3
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
4
0
0
1
2
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
2
0
0
0
0
0
0
2
0
0
0
2
3
1
0
1
0
2
0
1
1
0
0
0
0
0
0
0
1
0
1
1
1
0
1
2
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
1
2
0
2
0
0
0
0
0
1
0
0
1
1
2
0
0
0
0
0
0
2
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
3
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
6
1
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
4
0
2
3
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
2
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
2
0
0
0
0
1
1
0
0
0
2
0
0
0
2
0
2
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
2
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
1
1
0
1
0
0
2
0
0
0
1
2
2
0
0
0
0
0
0
1
2
1
0
0
0
1
2
0
1
0
0
0
0
1
0
2
2
0
0
0
0
0
0
1
2
1
0
0
2
0
0
2
0
0
0
1
0
0
4
1
1
0
0
2
0
0
0
2
0
0
0
2
2
0
0
0
1
0
0
0
4
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
2
3
1
0
0
2
0
1
0
0
2
0
0
0
1
2
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
5
1
1
0
2
1
0
1
0
0
5
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
5
1
0
0
2
0
1
1
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
2
0
2
1
3
0
2
4
0
2
0
1
0
0
0
0
0
2
1
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
1
0
0
2
1
1
0
1
0
0
3
0
1
1
0
1
0
2
0
1
0
3
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
2
2
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
3
2
0
2
0
0
1
2
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
1
3
1
2
1
1
0
0
0
2
2
0
0
0
0
0
0
1
2
2
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
2
0
2
0
0
0
2
1
0
0
0
0
2
0
0
1
1
0
1
2
0
0
2
1
0
0
1
0
2
0
0
0
0
0
0
2
1
2
0
0
0
0
3
0
0
0
0
0
0
2
0
2
1
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
2
0
1
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
3
0
0
2
2
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
3
1
0
0
0
0
0
0
0
0
0
1
5
0
0
2
0
2
0
0
1
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
2
0
0
1
1
0
2
0
1
0
0
0
0
1
0
0
2
1
0
2
3
0
0
0
1
0
2
0
0
0
0
0
0
4
2
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
3
0
0
2
0
0
0
0
2
3
1
0
1
2
0
0
0
1
0
0
2
3
0
0
0
0
2
0
0
0
1
2
7
0
1
0
0
0
0
0
0
2
0
0
2
1
2
3
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
3
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
2
1
0
0
1
1
0
3
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
3
1
0
1
0
1
0
0
3
1
0
2
0
0
0
2
2
1
0
0
1
1
2
0
0
0
0
0
0
1
0
0
0
1
0
2
3
0
0
0
0
0
1
1
0
0
1
1
0
2
3
0
0
0
0
2
0
0
1
0
2
0
1
0
0
2
0
1
0
0
0
0
0
0
4
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
2
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
3
0
0
0
1
0
0
0
1
0
0
0
1
0
2
2
2
2
1
0
2
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
3
0
0
1
2
0
0
0
0
0
0
2
0
1
2
2
1
3
1
0
2
0
0
0
0
0
0
0
2
0
0
1
1
0
2
1
2
0
0
0
0
1
2
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
3
0
1
0
2
0
0
0
0
0
1
0
1
0
0
0
1
0
0
3
0
0
1
0
1
0
0
0
0
2
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
2
2
0
0
0
3
2
0
0
1
0
0
0
0
1
0
1
0
0
6
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
2
0
1
0
2
0
2
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
1
0
1
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
2
0
1
0
1
0
0
0
1
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
1
0
1
0
0
2
0
0
0
1
0
1
0
0
0
0
1
0
1
0
2
1
0
0
0
0
2
0
2
0
0
2
1
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
1
1
1
2
2
0
0
1
1
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
11
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
1
2
1
0
2
0
1
0
0
0
0
0
2
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
1
1
0
3
2
1
0
0
2
2
1
0
0
0
2
0
0
3
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
3
0
0
1
1
0
1
0
1
0
0
0
2
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
6
2
2
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
3
0
5
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
2
2
1
0
0
0
2
0
0
3
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
3
1
0
0
2
0
0
0
1
0
0
0
0
0
1
0
1
0
2
1
1
0
0
1
0
1
0
0
0
0
0
1
0
3
0
0
2
0
0
0
2
0
0
0
0
0
0
2
1
0
2
1
1
0
0
0
2
0
0
2
1
0
0
0
2
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
2
0
2
0
1
0
2
2
2
0
1
0
0
0
0
0
1
2
0
0
0
1
0
2
2
1
1
0
0
0
0
3
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
2
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
3
0
0
0
0
0
3
0
0
1
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
6
0
0
0
0
0
0
2
1
0
0
0
1
0
2
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
2
0
1
0
0
0
0
1
5
0
2
2
0
2
0
2
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
2
4
2
1
0
0
2
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
1
2
0
0
1
2
2
0
0
0
2
1
0
1
0
1
0
3
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
3
0
0
0
0
0
2
0
1
1
0
1
2
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
2
0
1
0
0
0
0
0
1
0
0
1
6
0
0
0
2
0
1
0
0
0
0
0
0
5
2
0
1
2
3
0
0
0
0
0
0
0
2
0
0
2
5
0
0
2
0
0
0
1
1
0
0
0
0
1
2
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
1
11
2
0
0
0
0
0
0
2
0
2
1
0
2
2
0
0
0
0
0
0
0
0
2
0
2
2
0
0
1
0
0
0
0
0
2
0
0
1
1
1
1
0
0
0
2
0
0
0
0
2
0
0
3
0
0
0
2
1
0
1
0
1
0
0
0
2
4
1
2
0
0
0
1
0
0
0
1
0
0
0
10
0
0
0
0
0
0
0
0
2
1
0
1
2
0
0
3
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
2
1
0
0
2
0
2
1
0
1
0
0
2
1
1
1
0
0
0
0
0
0
2
1
0
1
1
0
0
2
0
0
2
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
2
1
2
2
0
0
0
2
0
2
0
1
0
2
0
0
0
0
0
0
1
0
0
1
1
0
0
2
0
0
0
0
1
0
0
0
0
1
0
3
1
0
3
0
1
2
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
2
0
2
2
0
0
0
0
1
0
0
0
0
0
0
3
0
1
2
0
0
0
0
0
0
0
2
0
0
2
1
0
0
1
1
0
1
0
0
0
2
1
0
0
1
0
1
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
3
0
3
0
0
0
2
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
1
3
0
0
2
1
1
0
0
1
0
0
0
2
0
0
2
0
0
2
0
1
1
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
1
3
0
0
0
0
0
0
3
0
0
0
0
1
2
0
0
0
0
2
2
0
0
0
0
0
3
0
0
0
0
2
0
1
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
3
2
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
2
0
0
2
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
2
2
0
0
0
0
0
1
2
0
0
0
2
0
2
0
0
1
0
0
2
0
0
2
0
0
0
2
0
0
1
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
1
1
0
0
0
2
2
0
0
4
2
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
2
1
0
0
0
0
1
2
3
0
0
0
0
1
3
0
1
1
1
0
5
0
0
0
0
3
0
0
0
0
1
1
0
1
1
0
0
1
0
1
3
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
5
0
0
0
0
1
0
0
0
0
0
2
0
0
2
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
1
0
2
1
0
1
1
0
0
2
1
0
0
0
0
0
0
0
2
0
1
0
2
0
2
0
0
1
0
0
0
1
1
1
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
1
0
1
0
1
0
0
2
1
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
5
2
0
1
2
0
0
1
0
2
0
0
0
0
0
2
1
0
1
0
2
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
1
1
0
0
0
1
0
2
0
0
2
0
0
2
2
3
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
2
0
2
2
1
2
0
0
0
0
4
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
2
1
0
1
2
0
2
0
2
0
0
3
1
0
0
0
1
2
2
0
0
0
2
2
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
2
0
0
0
0
2
0
1
2
0
1
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
1
4
2
0
0
0
0
2
0
1
0
0
0
0
0
0
3
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
2
3
0
0
0
0
0
0
1
0
1
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
2
1
0
0
3
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
1
2
0
1
1
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
2
0
2
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
4
1
1
0
0
1
1
0
0
0
0
1
3
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
1
0
0
2
0
1
1
0
1
0
0
0
0
1
0
0
0
3
2
4
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
3
0
2
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
2
2
0
0
0
1
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
1
0
0
1
1
0
0
0
0
2
0
0
0
0
1
0
2
2
0
0
0
1
0
1
3
1
4
1
1
2
1
0
0
0
1
15
1
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
2
0
4
0
0
0
2
2
1
0
0
0
0
0
2
0
0
0
2
0
0
3
0
0
2
0
0
0
0
1
0
0
0
0
0
2
1
0
2
0
0
2
0
0
0
2
0
0
0
0
2
1
0
3
3
0
0
1
0
1
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
2
0
0
0
6
0
0
1
1
0
2
0
0
0
0
1
0
0
1
1
2
2
0
2
1
0
0
0
0
2
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
2
1
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
3
0
0
0
0
0
1
0
1
1
0
2
0
1
2
0
0
1
0
0
3
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
2
2
0
0
0
0
1
0
0
0
2
0
2
0
0
0
1
1
0
2
1
0
0
0
0
2
0
2
2
0
0
0
1
0
1
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
1
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
1
2
0
1
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
2
0
0
0
4
0
0
0
0
2
0
0
0
0
2
1
2
0
1
0
1
0
0
1
0
0
1
2
0
0
0
1
0
3
2
0
6
0
0
0
0
0
2
0
0
0
0
0
3
0
0
1
0
1
2
1
0
0
0
0
2
1
3
2
0
0
0
0
1
2
0
1
0
1
0
2
0
0
2
0
1
2
0
0
0
0
1
1
0
0
0
2
0
1
2
0
0
1
0
0
0
0
0
0
3
0
0
2
0
2
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
6
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
2
1
0
0
0
0
2
1
1
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
1
0
0
0
2
0
0
0
2
0
0
0
0
0
2
9
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
1
0
0
1
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
2
1
1
0
0
0
2
0
0
0
0
1
2
1
0
0
0
0
0
0
0
1
0
2
1
0
1
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
2
0
0
1
0
0
2
1
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
1
2
2
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
2
0
0
2
0
2
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
1
0
0
4
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
2
0
1
0
0
0
0
0
1
0
1
2
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
1
1
1
1
2
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
2
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
3
0
1
0
5
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
2
0
3
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
1
1
2
1
0
1
1
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
1
1
2
1
1
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
2
1
0
0
5
0
0
2
0
2
0
0
0
0
0
3
1
0
1
0
1
1
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
1
1
1
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
1
2
2
0
1
0
2
0
2
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
4
0
1
0
1
0
2
0
0
0
1
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
1
0
0
2
2
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
4
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
2
1
0
0
2
0
0
0
0
0
2
0
0
0
1
2
0
0
5
1
0
0
2
2
0
0
0
0
0
0
2
0
1
0
0
2
0
0
1
0
0
0
0
2
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
4
0
1
0
2
0
2
1
1
0
0
0
0
0
0
2
0
1
0
1
1
0
0
2
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
2
2
0
1
2
0
0
2
0
1
0
0
0
7
1
0
2
0
0
0
1
0
0
1
1
0
0
1
1
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
2
0
2
1
0
0
0
0
1
2
0
0
1
2
0
0
0
0
0
0
0
0
2
2
0
1
0
1
1
1
0
1
0
2
0
1
0
0
0
0
0
2
2
0
0
0
0
0
3
1
0
3
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
2
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
1
0
0
0
0
1
0
3
0
0
0
0
2
0
4
0
2
2
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
2
2
4
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
2
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
2
0
1
0
1
0
0
0
2
0
0
0
2
0
1
2
0
3
0
2
0
1
0
0
0
1
0
0
1
2
0
0
2
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
1
1
2
0
2
0
0
0
0
0
0
0
3
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
2
0
0
0
3
1
0
2
0
0
0
0
0
1
0
0
0
2
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
5
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
2
1
2
0
0
0
2
5
0
0
0
0
0
0
0
0
0
3
0
0
0
0
3
0
0
0
0
2
3
0
0
2
2
0
0
1
2
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
1
2
2
1
0
0
2
1
2
0
0
2
2
2
0
0
2
0
0
0
1
2
1
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
2
1
2
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
5
0
0
0
0
0
1
2
0
0
0
1
1
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
3
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
3
0
1
0
0
2
1
0
0
0
0
1
0
0
2
1
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
3
0
0
1
0
4
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
3
0
2
1
0
0
0
1
0
0
0
0
2
0
2
0
2
0
0
0
1
0
0
2
0
0
0
2
0
0
2
5
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
10
1
0
0
1
0
1
2
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
1
2
0
1
3
0
0
0
2
1
1
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
1
2
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
2
3
0
2
0
1
2
3
0
0
0
1
0
0
0
1
0
0
2
1
2
1
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
4
0
1
0
1
1
1
0
1
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
1
0
1
1
0
0
0
3
0
0
2
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
3
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
6
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
7
2
0
1
0
0
2
0
0
0
1
0
0
0
0
4
0
2
2
0
3
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
1
1
2
0
0
3
0
0
1
0
0
0
3
2
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
3
0
2
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
2
2
2
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
2
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
2
0
2
2
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
1
0
0
2
0
3
0
1
2
1
3
0
2
0
1
0
0
0
1
0
3
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
1
1
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
4
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
1
0
0
2
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
2
3
1
0
1
2
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
1
0
0
1
0
2
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
3
0
0
2
0
0
0
0
2
0
1
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
1
1
0
3
0
0
2
0
1
0
0
0
3
0
2
1
0
0
0
2
0
0
1
0
0
0
0
0
1
2
0
2
0
0
0
2
3
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
1
0
0
0
2
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
2
0
0
0
0
0
2
0
0
0
0
0
4
0
0
0
0
1
0
2
0
3
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
1
0
1
0
0
0
2
2
0
0
0
0
8
0
2
0
1
0
2
0
0
1
0
0
0
1
0
3
1
0
0
0
0
3
0
0
0
0
0
0
3
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
1
3
2
0
2
1
1
2
0
0
0
0
0
1
0
0
2
0
1
2
0
2
1
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
4
1
1
1
0
0
0
0
0
1
0
0
0
0
1
1
0
3
2
0
0
0
0
0
2
1
0
2
0
0
1
0
2
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
3
0
2
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
1
2
0
0
0
0
0
0
0
3
0
0
2
0
1
0
0
0
1
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
2
0
0
1
0
0
0
0
0
1
0
2
0
1
6
0
0
1
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
1
2
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
1
0
2
1
2
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
3
0
0
0
0
0
0
2
1
2
0
2
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
2
1
2
2
0
0
0
3
0
0
3
0
0
0
1
0
2
0
0
0
2
0
2
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
2
2
0
0
0
1
0
0
2
0
0
0
0
1
1
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
2
2
1
0
0
2
0
0
2
1
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
1
1
0
1
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
1
0
0
2
0
0
0
0
0
0
1
3
0
0
0
1
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
3
2
2
0
1
3
0
0
0
0
0
1
2
0
0
1
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
1
0
1
2
0
2
0
0
1
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
1
0
0
0
2
0
2
0
0
2
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
2
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
1
2
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
1
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
1
1
2
0
1
0
0
0
1
0
1
0
0
1
0
1
0
0
0
1
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
3
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
2
0
0
0
1
0
1
0
1
0
0
0
0
2
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
3
0
0
2
0
0
2
3
0
2
1
1
0
2
1
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
7
2
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
2
3
1
0
0
1
0
0
0
0
0
0
3
0
0
0
4
1
0
0
0
0
0
0
0
2
0
0
1
0
0
4
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
2
0
1
0
1
0
1
0
0
1
1
0
0
0
0
0
1
2
0
1
0
0
0
1
0
0
0
0
1
2
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
2
0
6
2
3
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
2
1
3
0
0
0
2
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
1
0
3
0
0
0
1
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
2
1
0
0
0
0
1
2
1
0
0
3
2
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
1
0
0
0
1
2
3
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
4
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
4
0
0
0
2
0
0
0
0
1
1
0
0
2
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
2
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
1
0
0
0
0
0
1
0
12
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
2
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
1
1
1
0
1
1
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
2
0
2
0
0
1
0
1
2
0
0
0
0
1
0
1
2
1
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
3
0
0
2
1
1
0
0
0
0
1
0
1
0
0
1
0
0
2
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
1
0
0
1
0
0
6
0
0
2
1
0
0
0
0
0
1
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
2
0
0
0
2
0
2
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
4
0
0
0
1
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
2
0
2
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
2
1
1
0
2
0
2
1
2
1
1
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
2
0
2
0
2
2
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
1
0
1
0
3
0
1
2
0
2
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
1
0
2
1
2
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
2
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
2
0
2
0
0
0
1
2
1
1
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
2
2
0
2
1
1
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
2
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
5
0
0
0
2
2
1
0
0
2
1
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
2
0
0
1
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
4
0
0
0
2
3
2
1
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
2
0
0
1
0
2
3
1
0
1
1
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
1
1
0
0
0
0
2
1
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
1
0
0
0
0
1
1
1
0
2
2
0
0
0
2
0
1
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
2
2
2
0
0
2
0
0
0
1
0
0
0
0
0
1
0
2
2
0
0
1
1
0
0
0
1
3
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
5
0
2
5
2
0
0
6
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
1
0
1
2
0
0
0
2
0
2
1
0
1
0
0
2
2
0
1
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
1
0
1
0
0
0
2
2
0
0
0
1
0
2
1
0
0
1
1
2
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
4
0
0
0
0
2
2
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
6
0
0
0
0
0
2
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
9
0
0
0
0
1
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
2
1
0
0
0
0
2
1
2
0
2
0
0
0
0
2
0
0
0
0
2
2
2
0
0
0
1
0
1
0
0
0
0
2
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
1
0
0
2
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
1
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
1
1
0
1
5
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
1
0
0
0
1
0
1
0
0
2
2
0
0
0
0
0
0
1
0
0
1
0
0
2
2
1
0
0
1
3
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
1
2
0
2
0
1
0
0
1
0
0
0
0
1
2
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
4
1
0
0
1
4
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
1
0
5
0
0
0
0
0
2
0
0
1
0
0
0
2
2
2
0
1
0
1
0
0
0
1
0
0
1
0
0
3
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
1
0
3
0
0
0
0
10
2
1
0
0
0
1
0
1
0
0
1
0
1
0
0
0
1
0
0
0
2
2
0
0
0
2
1
0
0
0
0
1
1
0
0
1
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
3
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
3
0
0
0
0
0
5
0
0
0
2
0
0
5
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
2
2
2
0
0
2
0
2
0
3
0
2
0
1
0
0
2
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
1
0
1
0
2
0
3
1
0
2
0
0
0
0
0
0
0
0
1
1
0
4
1
0
0
0
0
4
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
2
0
1
0
0
0
0
0
0
2
1
0
2
4
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
2
3
0
0
1
0
1
5
0
1
0
0
0
0
2
2
7
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
1
1
1
0
0
2
0
1
4
0
0
0
1
0
0
2
0
1
2
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
2
0
0
2
0
0
0
2
0
0
1
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
3
0
0
2
0
0
1
3
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
2
2
0
2
0
0
0
0
2
0
0
0
2
2
1
0
1
0
2
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
1
0
1
1
0
0
2
0
2
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
3
0
1
0
0
0
1
0
0
2
2
2
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
1
0
1
0
1
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
1
0
0
1
3
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
4
1
2
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
1
4
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
4
0
0
5
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
4
0
0
1
1
0
0
0
0
0
0
0
3
0
4
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
4
0
0
1
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
2
0
0
2
0
0
0
0
2
0
0
2
0
8
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
1
0
0
0
2
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
2
0
3
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
2
0
0
1
1
2
0
0
0
0
1
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
2
0
0
0
0
0
0
2
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
4
0
0
0
0
4
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
1
3
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
2
0
0
0
0
0
1
1
0
2
0
0
0
3
0
0
0
0
1
2
0
2
0
0
1
0
0
1
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
1
0
2
0
1
0
2
0
0
1
0
0
5
2
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
2
1
0
0
1
2
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
1
0
0
1
0
0
2
0
1
0
28
0
1
0
0
0
0
1
0
0
1
0
0
0
0
2
2
0
2
0
0
0
0
0
0
1
2
2
0
0
0
2
0
0
0
1
0
0
0
0
0
3
1
0
1
2
1
0
0
1
1
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
1
0
1
0
0
0
2
0
0
0
0
0
0
2
0
1
0
1
1
1
0
0
0
0
4
0
0
1
0
2
0
0
1
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
4
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
2
0
0
0
1
0
0
0
2
0
2
0
0
1
0
2
2
2
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
4
0
0
2
4
2
0
0
0
0
0
1
0
1
0
1
0
2
0
0
1
1
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
2
0
1
2
0
0
3
1
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
2
3
0
2
0
0
0
0
0
2
0
0
0
2
0
2
0
0
3
0
2
3
1
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
2
2
1
1
0
0
2
2
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
4
3
3
0
2
2
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
2
0
1
0
0
0
0
0
1
0
0
2
1
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
1
1
0
0
0
0
2
2
1
0
1
2
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
1
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
1
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
2
0
2
0
2
2
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
3
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
3
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
1
1
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
2
1
0
0
0
1
0
0
0
1
0
0
1
0
1
2
0
0
0
2
0
2
1
0
0
0
0
2
8
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
1
1
1
7
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
2
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
1
2
1
1
1
1
2
1
2
1
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
1
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
3
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
1
0
0
3
0
0
0
0
1
2
0
0
0
1
2
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
6
0
0
0
2
0
2
0
0
0
0
0
0
2
2
2
0
0
1
2
0
3
0
0
2
0
0
0
0
2
1
2
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
2
0
0
1
0
8
0
0
2
0
0
0
2
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
3
1
1
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
3
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
1
0
0
2
0
0
0
2
1
1
0
1
0
0
0
0
0
0
0
1
2
1
0
0
2
1
1
0
0
0
0
1
0
2
1
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
2
0
1
1
0
0
2
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
3
0
2
3
0
1
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
3
0
0
1
0
0
0
0
1
1
0
0
0
1
1
0
0
0
1
1
1
2
1
0
0
2
0
2
0
0
0
0
3
0
0
0
0
0
1
2
0
0
0
1
0
2
0
0
0
0
3
0
0
0
0
0
2
0
0
2
2
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
1
0
3
7
0
0
0
0
2
0
0
0
1
0
0
1
0
1
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
2
1
1
0
1
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
2
0
0
0
0
0
1
0
0
0
1
1
0
0
2
0
0
0
2
0
0
0
2
0
0
2
1
1
0
0
2
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
1
0
0
0
2
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
2
1
0
3
0
0
0
1
0
0
0
0
0
0
0
4
0
0
2
2
2
0
2
1
1
2
0
0
0
1
0
1
0
3
0
0
0
2
0
0
2
1
0
2
0
0
0
1
0
0
0
1
0
3
2
0
2
0
0
0
2
2
2
0
0
0
2
0
2
0
0
1
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
2
0
1
0
2
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
3
2
0
0
2
0
0
4
0
0
0
0
1
0
0
1
2
0
0
0
0
0
1
0
1
0
0
3
0
0
0
1
1
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
3
0
0
1
0
0
0
1
1
0
0
0
1
1
0
1
1
0
0
0
0
0
0
1
0
2
0
0
0
0
2
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
4
0
2
2
0
3
0
0
0
0
1
0
1
1
0
0
2
3
0
0
1
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
2
0
2
3
0
0
0
0
0
0
0
1
1
2
0
0
0
3
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
2
0
0
2
0
0
0
0
0
2
1
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
2
1
1
2
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
1
0
0
2
2
2
0
0
2
1
0
0
0
3
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
6
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
2
0
2
0
2
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
2
0
0
0
6
0
0
1
0
1
2
0
0
0
0
0
0
4
0
0
0
0
1
0
1
2
1
0
2
0
0
0
0
0
0
2
1
0
1
0
1
2
0
2
1
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
11
2
0
0
0
1
0
0
1
0
0
4
1
0
0
0
2
0
0
1
0
2
0
7
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
1
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
4
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
6
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
1
0
0
3
2
0
1
0
0
0
0
0
0
4
0
2
1
0
0
0
1
0
0
1
1
2
0
0
2
2
0
5
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
2
1
2
0
0
1
0
0
0
0
0
0
0
0
0
2
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
4
2
2
1
3
0
6
0
0
2
0
0
2
2
1
0
0
0
0
0
0
0
3
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
2
0
2
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
3
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
1
0
2
0
0
0
0
2
2
2
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
3
2
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
3
0
0
0
2
0
1
0
2
0
1
0
2
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
1
0
1
0
0
2
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
3
0
0
2
0
0
0
0
0
3
0
2
0
0
1
0
0
0
0
0
0
0
0
2
4
2
0
0
1
0
1
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
2
0
2
2
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
1
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
3
0
0
0
2
0
2
1
0
0
2
0
2
0
0
0
0
0
2
3
1
0
7
0
0
2
0
0
0
0
0
2
0
0
0
4
2
0
0
3
1
2
0
0
2
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
7
1
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
2
1
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
1
1
1
1
1
0
0
0
1
0
2
0
1
1
0
0
0
1
2
0
1
1
2
0
0
0
0
0
0
2
3
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
2
1
2
0
0
0
1
2
0
0
0
0
0
0
0
2
3
0
0
0
0
0
1
0
2
0
0
3
0
0
1
0
0
1
0
0
5
0
0
0
0
0
0
0
1
0
2
0
0
3
0
0
0
0
0
0
0
1
2
0
0
0
0
2
2
0
0
0
0
0
0
3
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
1
1
0
0
0
0
2
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
2
0
0
0
0
0
2
0
0
2
0
0
0
1
0
1
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
2
1
0
2
3
0
2
0
0
0
2
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
3
0
0
0
0
0
2
0
1
0
2
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
2
2
2
0
1
1
0
1
2
0
2
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
8
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
2
0
1
0
0
0
2
1
0
0
0
2
0
0
2
0
4
0
0
0
0
0
0
2
0
0
0
0
2
0
2
2
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
2
0
2
0
1
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
3
2
1
1
2
1
0
0
0
2
0
1
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
2
0
0
2
0
0
0
1
0
0
2
0
1
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
2
0
0
0
1
0
0
2
0
0
0
2
0
0
0
2
0
2
0
1
0
0
0
1
0
1
2
0
1
0
0
0
1
0
0
0
1
1
0
2
2
0
0
0
0
0
2
0
0
0
0
1
2
0
0
1
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
1
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
2
5
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
1
0
0
0
0
1
1
1
2
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
3
2
0
2
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
2
1
0
0
0
2
5
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
3
0
0
3
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
2
1
1
0
0
1
0
0
1
1
0
0
0
0
1
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
2
1
0
3
0
0
0
1
0
0
0
2
0
0
4
0
0
0
0
2
0
0
0
0
4
1
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
3
0
2
0
0
2
0
1
2
0
0
0
2
0
1
0
0
2
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
1
0
2
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
4
0
0
1
2
2
2
0
0
0
0
2
0
0
5
0
0
2
0
0
3
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
5
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
2
1
1
0
5
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
2
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
1
1
1
2
2
0
0
0
0
0
1
0
0
2
1
0
0
0
2
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
3
0
0
0
0
1
2
2
0
0
1
0
2
2
3
0
0
1
2
0
0
0
0
0
2
2
2
2
0
0
2
0
0
2
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
2
0
1
0
0
0
0
2
0
1
0
0
0
2
1
0
0
0
0
0
0
0
2
0
1
0
1
0
1
1
0
0
0
0
0
2
1
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
4
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
3
1
1
0
0
0
0
0
0
2
0
2
0
0
1
0
1
1
2
0
0
1
2
1
0
2
0
0
0
0
2
0
0
0
1
0
0
0
3
0
0
0
0
2
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
2
0
0
0
2
0
4
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
3
2
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
1
2
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
5
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
4
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
2
0
2
0
0
0
0
0
2
3
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
1
0
0
1
1
0
0
0
0
1
0
0
1
2
4
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
1
0
0
0
1
2
1
0
1
1
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
12
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
1
3
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
2
0
2
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
1
1
0
1
0
2
0
3
0
2
0
0
1
1
0
0
0
0
0
0
0
0
2
0
2
0
0
3
0
0
0
0
0
0
5
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
2
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
2
0
1
0
1
0
0
0
2
0
0
2
0
0
1
0
0
2
0
0
0
1
4
0
2
0
0
2
2
0
0
0
0
0
0
5
0
0
0
0
1
0
0
1
0
2
0
0
0
1
1
2
2
0
0
0
0
0
0
2
2
2
2
1
2
0
0
1
0
2
0
0
2
0
0
0
2
0
0
1
0
0
0
0
1
3
1
1
0
2
0
0
0
1
0
0
6
0
1
6
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
1
0
0
0
1
2
0
2
0
0
2
0
1
0
0
4
2
1
1
1
1
0
3
1
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
1
0
2
0
2
4
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
5
0
0
0
2
0
0
0
0
1
1
0
0
0
0
1
0
0
2
0
0
1
2
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
2
1
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
2
0
0
0
0
0
2
0
2
1
0
1
1
4
0
1
0
0
1
0
0
1
0
2
0
2
2
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
2
0
0
0
2
0
0
0
4
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
1
0
0
2
1
0
1
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
1
0
0
0
2
0
0
0
0
5
0
1
0
2
2
3
1
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
1
2
0
1
0
2
0
2
0
0
0
2
0
1
0
1
0
0
3
0
0
0
0
0
0
1
0
1
0
0
0
0
0
10
0
4
0
0
2
1
0
0
0
0
0
1
0
1
0
0
2
0
0
1
2
0
2
0
2
0
0
0
0
1
1
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
1
8
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
2
0
1
0
2
0
3
0
0
1
0
0
0
1
0
0
0
0
2
3
0
0
0
9
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
3
2
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
2
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
3
1
0
0
0
0
1
0
0
0
0
0
0
0
1
3
0
0
0
0
1
0
0
0
3
1
0
0
0
1
0
0
0
0
1
0
0
0
2
2
0
3
2
0
0
1
1
0
1
0
0
2
0
2
2
0
0
2
0
2
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
4
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
2
0
0
0
0
0
0
0
2
0
1
0
1
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
1
0
2
0
0
1
2
0
2
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
2
2
1
2
0
0
2
4
0
0
0
1
1
0
0
0
0
0
3
0
0
0
1
0
0
2
2
0
0
1
0
0
0
0
1
1
0
0
1
1
2
2
0
1
0
1
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
3
1
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
3
0
1
1
2
0
0
0
0
0
4
0
2
2
0
2
0
0
2
2
0
0
0
0
2
0
0
0
1
0
0
1
0
1
3
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
1
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
1
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
2
0
1
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
2
0
0
0
1
0
0
0
1
5
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
2
0
2
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
5
0
0
1
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
1
0
3
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
1
1
2
0
1
0
0
1
0
0
2
0
1
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
2
0
2
0
2
0
2
0
0
0
2
1
0
2
0
0
0
2
0
0
0
1
0
0
2
0
2
0
0
2
1
0
0
0
0
0
0
1
0
3
3
0
0
0
2
1
0
1
2
0
0
0
0
1
0
3
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
3
0
0
2
0
0
2
0
0
2
2
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
2
0
2
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
1
1
2
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
2
2
2
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
2
2
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
3
1
0
1
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
1
2
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
3
0
0
0
0
2
2
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
4
0
0
0
2
0
2
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
1
0
2
0
0
0
1
1
0
0
2
0
4
0
0
0
0
1
2
0
0
1
0
0
2
2
0
0
0
0
0
0
1
1
0
0
2
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
5
0
0
0
0
0
2
0
0
0
0
3
0
0
2
0
0
0
0
0
1
0
0
1
2
0
1
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
2
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
2
0
0
1
1
2
1
0
2
0
2
0
2
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
1
0
0
0
0
2
0
2
1
6
0
2
2
2
0
1
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
1
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
3
0
0
1
1
0
2
0
0
0
0
2
0
4
0
0
0
0
0
0
2
0
2
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
1
2
0
0
0
0
0
2
0
0
0
1
1
0
0
0
1
1
2
4
2
0
0
0
0
2
1
0
1
0
1
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
1
0
0
0
2
0
2
0
2
1
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
2
2
0
2
0
0
1
1
0
2
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
1
1
2
0
0
2
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
1
2
0
1
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
2
0
0
2
0
1
2
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
1
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
2
1
0
0
2
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
11
2
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
5
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
1
1
0
2
0
0
0
2
0
0
1
0
0
0
1
0
1
2
0
0
2
1
0
0
0
0
1
2
2
0
0
0
0
1
0
1
0
0
4
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
2
0
0
0
1
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
4
1
0
0
1
0
2
0
3
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
2
0
2
2
0
2
2
0
0
0
2
0
2
0
2
0
0
3
0
0
0
0
2
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
2
2
0
0
3
0
0
0
0
0
2
0
0
0
1
0
2
0
2
2
1
0
0
0
2
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
1
1
0
0
2
0
1
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
5
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
3
0
0
0
2
1
2
0
1
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
1
0
0
0
5
0
2
0
2
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
2
2
2
0
0
0
1
0
0
2
2
0
0
1
0
0
0
0
1
0
1
0
0
0
2
0
2
0
3
1
1
1
2
0
0
1
2
0
0
0
1
0
0
0
0
0
0
1
2
0
0
2
2
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
2
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
5
0
1
0
4
0
2
2
0
0
0
0
0
1
0
2
0
0
0
0
1
0
1
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
2
1
2
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
2
0
2
1
0
1
5
0
2
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
2
2
1
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
3
0
3
0
0
0
0
0
0
1
0
1
2
0
0
0
0
1
0
1
0
2
2
0
0
0
2
4
1
0
0
0
0
0
0
0
1
3
0
1
0
2
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
2
1
0
0
0
0
0
2
0
3
0
0
0
0
5
0
1
2
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
2
2
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
2
0
0
0
3
0
0
1
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
3
0
0
0
1
0
0
0
3
2
0
0
0
0
0
0
0
0
1
0
0
2
0
1
1
1
0
0
0
2
0
0
0
0
1
0
3
3
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
2
0
1
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
1
0
0
0
2
0
0
0
2
0
1
0
1
2
0
1
0
0
1
0
1
1
0
0
0
0
3
2
0
0
0
0
0
0
2
1
0
2
0
1
0
0
2
2
0
0
1
0
0
0
1
0
0
2
0
0
2
0
2
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
1
3
2
0
1
0
0
0
0
0
0
0
0
2
0
1
2
0
2
0
0
2
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
2
2
1
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
2
0
3
1
1
1
0
0
1
0
7
3
2
0
0
2
2
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
3
1
1
0
0
0
0
0
0
2
0
2
0
2
1
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
3
0
2
0
2
2
2
1
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
1
2
0
2
1
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
1
0
0
0
0
2
1
1
1
2
0
0
0
2
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
2
0
1
2
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
2
0
0
2
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
1
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
2
0
1
0
0
2
1
0
0
2
1
0
0
0
0
1
2
2
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
3
0
1
0
0
1
1
1
0
2
0
0
0
0
0
0
2
1
0
0
1
0
2
0
0
1
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
1
1
1
2
0
1
0
2
0
0
0
0
2
0
9
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
2
0
3
2
0
0
2
0
2
0
1
0
1
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
4
2
1
1
1
0
1
0
0
2
2
0
0
0
0
0
2
0
2
1
1
1
0
0
0
2
2
0
0
0
0
0
0
3
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
3
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
2
1
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
4
0
0
0
1
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
3
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
1
0
0
0
5
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
3
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
1
0
0
1
0
0
5
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
2
1
0
0
0
0
2
0
0
0
2
0
0
0
1
2
0
0
2
0
0
0
1
0
0
1
3
1
0
0
0
2
0
0
0
2
0
2
0
0
0
2
0
0
0
3
0
0
2
0
0
0
0
0
0
1
1
0
1
0
0
0
0
2
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
4
0
0
0
2
0
2
3
1
0
0
0
1
0
1
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
3
1
0
0
0
0
2
0
0
1
1
0
0
0
0
5
0
0
0
0
2
0
1
1
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
2
1
0
1
0
0
1
0
0
0
0
0
2
0
1
1
0
3
0
0
0
0
0
1
2
0
2
3
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
1
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
3
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
3
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
5
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
1
0
1
0
1
0
2
0
0
0
0
2
2
0
0
0
0
0
0
2
1
0
2
0
0
0
0
3
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
1
3
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
1
0
0
0
0
0
0
0
2
0
2
0
0
2
1
2
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
2
0
0
1
2
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
2
2
2
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
1
0
0
0
0
1
1
0
0
2
2
0
0
1
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
3
0
0
0
0
0
2
1
1
1
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
2
1
0
0
0
0
3
0
0
1
0
0
0
0
2
0
1
0
0
0
5
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
1
1
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
1
17
1
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
3
1
0
0
0
1
0
2
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
3
0
0
0
0
1
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
2
0
3
0
2
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
3
1
1
0
0
0
0
2
1
4
0
0
0
1
0
0
2
3
1
0
0
2
0
0
0
0
0
1
1
1
0
0
0
1
0
0
2
1
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
2
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
2
2
2
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
2
3
0
2
0
0
1
0
0
3
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
1
0
0
2
0
0
2
0
2
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
4
1
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
2
0
2
2
1
1
0
2
0
2
0
0
0
2
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
3
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
1
2
0
2
2
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
1
0
2
2
2
0
0
0
0
0
2
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
3
0
0
0
0
1
2
0
0
0
0
4
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
6
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
2
1
0
0
0
0
0
2
0
1
4
0
0
0
0
0
2
0
1
1
0
0
0
0
1
1
1
0
0
0
0
0
0
2
0
0
0
2
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
1
1
0
0
0
0
2
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
3
1
1
0
0
2
1
0
0
0
0
1
0
2
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
1
0
1
2
0
1
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
1
0
0
0
0
3
0
2
2
0
0
0
0
2
0
0
0
0
2
0
2
2
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
2
0
2
2
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
2
3
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
3
1
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
2
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
2
1
0
0
0
0
1
0
2
0
0
0
0
0
1
2
0
2
0
0
0
0
0
1
2
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
2
0
0
1
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
6
0
1
0
0
0
0
1
2
0
0
0
0
2
3
0
0
1
0
0
1
0
0
0
3
0
0
2
0
0
1
0
0
0
1
0
0
0
0
4
2
0
1
0
0
0
0
1
1
2
2
0
0
0
0
0
1
2
0
0
2
1
0
2
0
0
1
0
1
0
0
0
0
0
0
0
1
0
2
1
2
0
2
1
0
2
2
0
2
2
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
2
0
0
0
0
3
1
0
2
0
0
0
0
0
1
0
2
1
0
2
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
4
0
0
3
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
3
2
3
0
2
0
0
2
1
0
0
2
0
1
1
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
1
0
0
0
0
0
1
1
1
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
3
0
0
0
2
2
0
2
0
3
0
0
2
2
0
1
0
0
0
0
0
3
2
0
1
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
1
1
4
0
0
0
0
0
3
1
1
0
0
0
0
0
0
1
0
0
5
0
0
0
0
1
2
0
0
1
0
1
3
3
0
0
0
0
0
0
1
0
0
0
1
3
3
0
0
2
0
1
0
1
2
1
0
1
0
0
0
0
0
2
0
0
0
4
0
0
3
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
6
1
0
2
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
1
0
2
2
0
1
0
0
0
0
1
0
1
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
1
1
0
1
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
2
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
8
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
2
2
0
0
2
0
1
2
0
0
0
0
1
3
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
1
6
0
2
0
3
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
2
0
0
0
0
2
2
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
2
0
0
0
0
2
1
0
0
0
2
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
1
2
0
0
1
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
2
0
0
1
2
0
0
0
6
0
0
0
0
0
0
0
3
1
2
3
0
0
0
0
0
0
0
0
0
0
0
2
1
1
1
0
3
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
1
0
0
0
2
2
1
0
0
1
0
1
0
0
0
0
2
1
1
0
0
1
2
0
0
1
0
0
0
2
1
2
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
1
1
1
0
0
1
0
0
0
1
1
2
0
0
0
0
0
1
0
0
2
4
2
0
0
2
2
2
1
0
0
0
0
1
0
0
0
0
0
0
2
1
2
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
1
1
1
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
2
0
1
0
1
0
0
0
1
1
0
0
0
0
2
2
0
0
1
0
2
1
1
0
0
2
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
1
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
2
0
1
0
2
0
0
2
0
1
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
1
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
2
0
0
1
0
0
3
0
2
0
1
0
0
0
0
0
0
3
0
0
0
2
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
4
0
0
0
2
0
0
0
3
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
2
1
1
0
0
0
6
1
2
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
2
0
0
0
2
0
2
0
0
1
0
0
1
0
0
3
2
0
0
0
0
0
3
0
3
0
0
0
0
0
0
1
0
0
0
0
2
0
1
2
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
2
2
2
2
0
0
0
4
0
0
0
1
0
3
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
1
0
0
0
1
0
3
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
1
0
2
0
0
1
1
1
0
4
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
2
2
0
0
0
3
7
0
0
2
0
0
0
0
0
1
0
4
0
1
0
0
0
0
2
0
3
0
1
0
1
0
0
2
0
0
0
5
1
0
0
0
3
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
3
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
4
0
2
5
3
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
1
0
2
0
2
1
0
0
2
1
0
2
0
0
0
0
2
0
2
2
0
0
0
1
0
2
0
0
1
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
2
0
0
3
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
3
1
0
0
0
1
0
0
2
0
0
1
0
0
0
0
1
2
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
1
0
1
0
0
0
2
2
0
1
0
0
0
2
0
2
0
3
1
1
0
0
0
1
0
3
0
0
0
1
0
0
0
1
0
0
0
0
2
0
1
0
0
0
2
0
2
0
1
2
0
0
0
0
1
2
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
1
1
2
0
0
0
1
0
0
0
0
1
0
0
1
0
0
3
3
0
2
1
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
5
0
2
2
0
0
0
2
0
3
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
2
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
1
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
1
1
0
1
1
0
1
0
6
0
1
0
0
5
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
1
0
0
0
1
0
0
0
1
0
2
0
0
3
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
2
1
2
0
0
0
0
0
2
2
4
0
1
0
0
1
0
0
2
0
0
0
0
2
2
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
3
0
0
1
0
2
0
0
0
0
0
1
0
0
0
1
4
0
0
1
0
0
0
2
0
0
0
0
0
1
3
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
1
0
0
0
0
6
0
3
0
0
0
1
1
0
1
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
1
0
4
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
2
0
1
0
0
0
0
0
2
0
1
0
0
7
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
1
1
2
0
1
1
0
0
2
0
0
1
2
0
0
0
1
2
1
2
0
1
0
0
3
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
2
2
3
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
3
4
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
3
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
2
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
2
0
4
0
0
0
0
0
1
2
0
1
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
2
1
0
0
0
0
0
3
0
1
0
0
0
3
0
1
1
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
2
0
0
1
0
1
0
0
0
1
0
0
0
0
0
6
2
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
2
0
0
2
0
0
1
0
0
0
0
0
2
0
0
2
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
1
0
2
0
0
0
0
2
0
1
0
0
1
1
0
1
0
0
0
0
0
0
2
0
2
2
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
1
2
0
0
1
0
0
1
2
0
2
3
0
0
2
0
0
2
0
1
1
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
2
0
0
2
0
1
2
0
0
0
0
0
0
0
0
4
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
3
1
2
0
0
0
0
0
0
0
2
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
2
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
2
0
0
0
0
0
1
0
3
0
0
2
2
0
5
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
3
0
1
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
3
0
0
0
2
0
0
2
0
5
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
1
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
2
0
0
2
0
1
0
3
1
0
0
0
1
1
0
2
0
0
0
0
0
2
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
1
0
1
2
0
0
0
0
0
0
2
2
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
1
0
0
1
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
4
0
2
2
0
0
2
0
0
2
0
1
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
2
2
0
1
0
0
0
0
2
0
0
0
0
1
5
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
3
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
4
2
0
0
0
3
1
0
1
0
1
0
1
0
0
0
2
0
2
0
0
0
2
0
2
0
1
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
5
0
0
0
0
1
2
2
0
1
0
3
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
2
0
0
2
0
1
2
0
0
0
2
0
3
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
3
0
0
0
0
1
0
0
0
0
1
2
0
0
0
1
0
0
0
2
1
0
2
2
0
2
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
3
1
0
1
0
1
0
2
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
2
1
0
0
2
1
0
2
0
0
0
3
2
0
2
0
0
0
0
1
0
0
1
6
0
0
0
2
0
2
0
0
0
0
2
4
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
1
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
1
0
0
0
0
1
0
0
1
1
0
0
0
2
0
0
4
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
2
0
0
0
2
1
0
2
2
0
0
0
0
1
1
0
0
0
0
0
2
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
3
0
0
1
1
2
0
0
0
0
0
2
1
0
0
1
0
0
2
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
2
1
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
2
0
2
2
0
0
1
2
0
2
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
1
0
0
0
0
1
0
0
2
0
0
0
1
1
0
1
0
0
2
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
3
0
2
0
4
0
2
2
0
0
0
1
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
5
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
3
0
0
0
0
6
2
0
1
2
1
0
0
1
1
0
3
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
2
0
0
0
0
0
0
1
3
0
0
0
1
0
2
1
1
2
2
3
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
2
0
0
0
0
1
1
1
1
0
0
0
2
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
5
1
0
0
0
1
0
2
0
2
0
1
1
0
0
0
0
0
0
0
2
0
0
2
0
2
1
2
1
0
0
1
2
0
0
6
1
0
0
2
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
4
1
0
0
0
0
0
1
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
3
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
3
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
2
0
0
2
0
9
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
1
2
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
1
1
2
0
0
1
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
2
1
2
0
0
0
1
0
1
0
0
0
2
2
1
0
0
0
0
2
1
2
0
0
2
0
1
0
3
1
4
0
0
0
2
2
0
0
0
0
0
0
0
0
0
4
1
0
2
0
2
0
0
1
1
0
0
3
1
0
3
0
0
0
0
0
0
1
1
1
0
2
2
2
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
2
0
0
1
0
2
2
0
0
0
0
0
0
0
1
2
0
0
0
0
2
1
0
2
2
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
2
1
0
0
1
0
0
1
2
1
0
0
0
0
2
4
0
0
1
0
0
1
0
0
1
4
0
1
0
0
0
0
0
0
2
0
0
2
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
4
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
2
0
0
1
0
1
0
0
0
1
0
0
0
3
1
0
0
1
0
0
0
0
4
0
0
0
0
2
0
0
0
1
0
0
0
0
0
3
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
3
1
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
6
0
0
2
0
2
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
2
2
0
0
2
2
0
0
1
3
2
0
2
0
0
2
3
0
1
0
0
1
1
3
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
4
0
0
1
3
2
0
1
0
0
2
0
3
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
2
3
1
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
2
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
6
0
2
1
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
1
1
0
1
0
2
0
0
2
0
0
0
0
2
2
0
0
0
3
0
2
0
0
0
2
0
0
0
0
0
2
1
1
0
0
0
2
2
0
0
0
0
0
1
0
2
0
1
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
1
0
1
0
0
2
0
2
0
4
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
2
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
2
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
5
0
1
0
0
0
0
0
1
0
0
0
0
0
0
4
0
1
28
3
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
3
0
0
1
0
0
0
0
3
0
0
1
0
2
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
13
0
0
2
1
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
1
1
2
4
1
0
0
0
0
1
1
0
0
0
0
0
2
2
1
0
1
0
0
0
0
0
0
0
0
3
1
0
0
0
1
2
0
0
0
0
0
1
0
0
2
0
0
2
0
2
2
0
1
0
0
2
1
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
1
0
2
0
2
0
0
0
0
1
3
4
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
2
0
2
0
0
2
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
2
0
1
0
0
0
0
0
0
1
1
0
0
0
0
2
3
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
4
0
1
0
0
6
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
1
2
0
3
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
2
0
2
1
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
3
2
0
0
1
0
1
0
1
2
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
3
0
0
2
0
0
1
1
0
2
0
0
0
0
0
0
1
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
3
0
2
2
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
3
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
2
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
1
0
2
1
0
0
0
1
1
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
4
2
0
0
0
1
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
4
0
1
0
0
0
1
0
3
3
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
2
1
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
4
0
3
2
0
0
1
0
0
0
0
2
1
0
0
2
0
1
0
0
0
0
0
0
1
1
2
1
0
0
0
0
2
0
5
2
0
0
1
0
2
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
4
2
0
0
0
0
3
1
0
5
0
2
0
1
0
2
2
0
0
0
0
1
2
0
0
0
0
1
0
0
2
1
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
3
2
2
0
0
0
0
1
1
2
0
0
0
0
1
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
5
0
1
0
0
2
0
0
0
0
1
0
0
3
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
2
0
2
0
0
1
0
0
0
0
0
0
1
2
0
1
1
0
1
2
0
2
0
4
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
1
3
0
0
0
1
0
2
0
3
0
0
0
0
0
0
0
4
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
2
0
2
2
0
0
3
0
1
0
0
1
1
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
1
0
2
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
4
2
2
0
2
0
3
0
0
0
0
2
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
1
1
0
2
0
0
2
0
0
0
2
0
2
1
0
2
1
3
1
0
0
0
0
2
0
1
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
2
0
3
0
3
6
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
2
2
2
2
1
0
0
0
2
3
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
1
0
0
0
0
1
2
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
2
2
0
0
2
2
0
2
1
0
0
1
0
0
2
0
0
2
2
0
0
0
2
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
1
3
0
0
0
2
2
0
0
2
0
1
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
3
0
2
0
2
3
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
1
0
0
0
1
1
0
1
1
2
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
2
2
0
0
0
3
0
0
0
0
0
1
0
0
0
1
0
1
0
2
0
1
2
0
1
0
0
2
1
2
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
3
0
0
0
1
0
1
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
3
0
4
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
2
0
1
0
0
0
2
2
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
2
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
2
1
0
0
1
0
0
4
0
0
0
0
0
0
5
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
5
0
0
0
0
1
0
0
0
2
0
0
2
0
0
1
0
2
0
0
2
2
0
1
6
2
2
0
0
1
0
0
2
1
0
0
0
1
2
0
0
0
1
0
0
0
0
0
2
5
0
1
0
1
0
2
0
0
0
3
0
1
0
0
0
1
0
1
0
0
0
0
0
1
1
1
0
0
3
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
2
3
1
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
2
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
3
0
2
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
1
0
0
0
2
0
0
0
2
1
0
1
0
1
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
1
1
0
0
0
3
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
2
0
1
2
0
0
0
2
1
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
1
0
2
0
0
1
0
0
0
0
0
0
1
0
3
2
2
1
0
1
0
2
2
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
10
1
2
0
0
0
0
0
2
0
0
0
0
0
2
0
1
3
0
0
0
2
1
0
1
2
0
0
0
0
0
0
1
0
0
2
0
1
1
1
0
0
1
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
1
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
1
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
2
1
0
2
0
0
0
2
2
1
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
1
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
2
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
1
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
6
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
1
0
2
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
1
2
1
1
0
0
2
0
0
0
0
0
1
0
0
1
0
0
2
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
3
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
1
0
0
0
1
2
2
0
0
0
1
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
1
2
2
0
0
2
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
2
2
0
0
0
1
0
0
0
1
2
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
1
0
2
0
2
1
1
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
1
0
1
2
0
0
2
1
0
1
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
6
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
2
2
0
1
0
1
2
0
0
2
0
0
0
0
0
0
2
2
1
1
1
8
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
2
2
1
1
1
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
2
1
0
2
0
0
1
0
0
0
0
4
0
1
0
1
2
1
0
0
0
0
0
0
0
0
1
0
0
2
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
1
0
0
1
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
1
1
0
0
1
2
1
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
2
0
0
0
0
0
1
2
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
2
1
7
0
0
0
0
0
3
1
0
0
0
0
0
1
0
0
1
0
0
0
2
2
0
2
2
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
1
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
2
0
2
1
0
0
0
0
0
2
0
0
1
2
1
0
0
0
0
0
0
0
2
2
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
1
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
0
1
3
2
0
1
0
2
0
4
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
1
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
3
0
0
1
0
0
1
0
1
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
2
0
0
0
2
0
0
0
0
2
1
2
0
1
0
0
1
0
1
0
1
1
0
2
0
0
0
0
0
2
1
0
0
1
0
0
0
1
1
2
0
0
0
2
1
0
0
0
0
2
0
0
0
0
1
2
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
2
2
1
0
0
1
1
2
0
0
0
2
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
2
0
1
0
2
1
0
0
2
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
2
2
0
3
0
0
0
2
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
2
2
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
2
0
1
0
3
0
0
1
2
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
4
0
0
0
0
0
0
0
0
0
4
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
1
0
0
1
3
0
0
0
1
0
0
0
1
1
1
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
2
0
2
5
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
1
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
2
2
0
1
0
0
0
2
0
0
2
0
1
0
2
1
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
2
3
0
3
0
2
0
0
4
1
1
0
0
0
0
0
2
2
2
0
0
0
2
2
1
0
0
3
0
0
0
0
0
0
2
1
0
2
0
1
0
0
0
0
1
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
2
0
2
2
0
0
0
1
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
2
0
0
1
0
0
0
0
0
0
0
2
2
0
1
1
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
1
1
3
2
0
0
0
0
0
2
0
4
3
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
1
0
0
1
0
0
3
2
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
1
1
2
0
0
0
0
1
0
0
0
0
0
1
2
0
1
0
0
1
0
0
0
2
2
0
0
0
0
0
0
2
0
2
2
0
3
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
2
1
0
1
0
0
0
1
1
0
0
1
3
2
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
1
1
0
2
0
2
0
0
0
2
0
0
0
4
0
1
2
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
1
3
3
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
1
0
0
1
2
0
0
0
2
0
3
0
1
1
1
0
0
0
0
0
1
3
0
0
0
0
0
0
2
2
0
0
0
2
1
0
0
2
0
0
0
0
0
1
0
1
0
2
0
0
0
2
0
0
0
0
0
2
2
2
0
0
0
0
0
2
0
0
0
0
2
1
0
3
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
2
0
0
2
0
0
0
0
2
0
2
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
1
0
0
0
1
0
0
0
2
2
1
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
2
0
1
2
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
1
0
0
2
1
1
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
2
0
1
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
2
0
0
1
2
0
0
2
2
0
0
0
0
1
2
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
2
1
0
1
0
1
0
0
0
0
2
1
1
3
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
2
2
0
0
0
2
0
1
0
0
0
0
0
0
2
1
0
2
0
1
3
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
1
0
0
0
0
0
0
0
0
2
0
0
0
1
1
2
1
0
0
3
1
0
1
0
1
0
1
0
0
1
0
0
2
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
3
1
0
1
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
1
0
1
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
1
1
1
1
1
0
3
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
1
1
3
0
0
0
1
0
2
1
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
1
0
1
2
1
0
0
0
0
0
1
0
0
2
0
0
3
1
0
0
0
0
3
2
0
0
0
0
1
0
0
1
1
0
2
2
2
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
1
1
0
1
2
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
2
0
0
2
0
0
0
2
1
0
2
0
0
0
1
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
3
2
3
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
1
0
2
0
2
1
2
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
3
2
0
0
0
0
2
6
2
2
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
2
2
0
0
0
1
0
0
0
0
0
0
2
1
0
0
2
1
0
3
0
1
0
2
1
2
0
1
2
0
0
1
2
0
3
2
0
0
0
2
3
0
1
0
2
1
0
2
2
0
1
0
0
2
0
2
1
0
0
0
0
0
1
0
1
0
0
2
1
1
0
0
0
0
2
2
0
0
2
1
0
0
0
2
0
0
9
0
2
0
0
1
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
2
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
2
0
0
0
3
0
0
0
2
3
0
0
0
0
0
1
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
1
0
1
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
2
0
1
0
3
1
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
2
0
0
2
0
1
0
1
2
1
0
0
0
0
1
0
0
0
0
2
0
1
2
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
3
0
2
2
2
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
4
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
2
0
1
1
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
2
1
0
0
3
0
0
1
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
3
0
0
0
3
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
5
2
0
0
1
0
0
0
1
0
0
0
1
1
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
2
0
0
2
0
0
1
0
0
0
0
1
0
0
2
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
2
1
1
2
0
0
1
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
2
2
2
0
0
1
3
0
0
2
1
0
2
0
0
1
1
0
0
0
0
0
2
2
0
0
0
0
0
1
0
1
1
0
0
2
1
1
0
1
0
2
0
0
0
2
0
0
0
0
0
0
1
1
2
1
1
3
2
0
0
0
0
0
0
0
0
0
2
3
0
2
1
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
2
0
0
1
0
2
1
0
1
0
0
0
0
1
0
1
0
1
0
4
1
2
0
0
0
0
1
2
4
0
0
1
0
1
0
0
3
0
2
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
2
2
0
1
2
1
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
12
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
2
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
2
2
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
1
0
0
0
1
1
2
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
4
2
0
0
2
3
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
2
2
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
2
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
2
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
1
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
1
1
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
1
1
0
1
0
0
2
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
2
2
2
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
3
0
1
1
2
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
4
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
2
3
0
0
2
0
1
0
1
0
0
0
0
0
2
0
0
0
2
0
2
0
4
0
3
0
0
1
0
0
2
0
0
1
0
0
0
0
0
3
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
1
0
4
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
1
3
0
2
0
0
0
0
0
0
0
0
1
0
2
1
2
0
0
0
2
4
0
2
0
2
1
0
0
0
0
2
0
1
0
1
2
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
6
0
0
1
0
0
1
0
2
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
5
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
2
0
0
2
0
0
0
1
1
0
0
0
0
0
2
0
1
0
0
0
1
0
1
2
2
0
0
0
0
0
2
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
1
9
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
2
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
1
0
0
2
2
0
0
1
4
0
0
0
2
2
0
2
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
3
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
1
0
0
0
0
2
0
0
2
1
0
0
0
1
0
0
1
2
0
0
2
0
0
1
1
2
0
0
1
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
5
0
0
0
2
2
0
0
0
0
2
0
2
0
0
2
0
0
2
1
0
0
0
4
1
0
0
1
0
0
0
0
3
1
0
0
0
2
0
1
0
0
0
2
0
0
2
0
0
1
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
3
4
0
0
11
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
2
0
0
2
0
0
0
1
2
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
2
2
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
1
2
0
1
0
0
0
1
0
1
0
0
2
0
0
0
0
0
1
0
1
0
3
0
2
0
1
0
0
3
0
0
0
0
0
0
0
0
2
0
0
1
2
0
2
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
2
11
1
0
0
0
1
0
2
1
3
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
2
0
0
0
2
0
0
2
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
1
0
3
2
0
0
0
0
0
1
0
0
0
3
0
4
1
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
2
2
0
0
1
2
0
1
0
0
0
0
0
1
1
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
2
0
1
0
1
2
0
0
1
0
0
0
2
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
3
0
0
2
0
0
0
0
0
1
0
4
0
0
1
0
0
0
0
1
0
2
0
0
0
2
0
2
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
2
0
1
0
3
1
1
2
0
0
1
0
0
0
2
0
7
0
1
0
0
0
0
2
2
1
1
1
13
1
1
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
2
1
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
3
0
1
0
0
5
0
1
0
0
1
4
0
0
0
0
2
0
2
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
4
1
3
0
0
0
3
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
3
2
1
2
2
0
0
0
0
0
0
0
4
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
3
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
1
2
0
2
1
0
0
2
1
0
0
0
0
0
1
0
0
2
1
2
0
0
0
2
0
0
1
0
2
0
0
2
5
1
0
1
0
2
0
0
2
1
1
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
2
1
1
0
4
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
3
0
0
0
2
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
1
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
1
0
0
2
1
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
2
0
3
3
0
0
0
0
0
0
1
1
0
1
0
0
0
0
2
1
0
0
0
0
0
0
2
1
2
1
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
2
2
0
1
0
0
0
4
0
1
0
2
0
4
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
1
2
0
1
0
0
0
1
0
0
0
0
0
5
0
1
0
0
0
0
0
2
0
0
0
1
1
0
1
2
0
0
0
0
0
1
0
2
0
0
2
2
0
0
0
0
0
0
2
1
0
0
0
1
1
0
0
0
0
0
0
1
0
2
0
1
0
2
1
0
0
0
0
0
2
2
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
2
3
0
1
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
2
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
1
0
0
0
5
0
0
4
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
2
0
0
0
1
0
1
0
0
2
2
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
3
0
0
3
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
1
1
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
1
1
0
0
1
0
3
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
1
0
0
2
1
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
3
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
11
0
0
0
1
2
0
0
0
9
0
0
1
0
3
0
0
3
2
0
0
0
0
1
2
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
1
3
0
0
0
0
2
1
1
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
2
0
3
0
0
2
0
2
0
0
0
0
0
0
2
0
0
2
2
0
2
1
1
1
2
0
0
2
0
0
0
0
0
2
1
0
3
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
2
0
0
0
1
0
0
0
0
0
3
1
0
0
0
1
0
0
0
1
0
0
2
2
0
1
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
2
0
1
0
0
2
0
0
3
0
2
4
0
0
0
1
0
1
2
1
0
2
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
2
2
0
0
0
1
0
1
3
0
2
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
1
0
0
0
0
5
0
0
2
1
0
0
0
0
0
2
0
2
0
0
0
2
0
3
1
0
1
0
2
0
1
0
2
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
1
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
3
0
0
0
0
3
0
1
0
2
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
3
0
1
0
1
1
0
1
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
1
0
0
0
0
1
0
2
2
0
1
0
2
2
0
2
3
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
1
2
0
0
0
1
1
0
3
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
3
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
1
1
0
0
0
0
1
0
1
1
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
2
0
0
0
0
3
0
1
1
0
1
0
1
0
0
2
0
0
1
0
0
0
9
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
1
0
0
2
2
0
0
0
0
1
0
0
0
0
3
1
0
0
0
0
0
2
0
0
1
0
2
1
0
1
0
0
0
0
2
0
1
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
3
2
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
1
0
1
0
0
0
0
0
0
1
0
0
0
0
2
2
0
3
0
2
2
1
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
4
0
3
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
2
0
2
6
0
0
1
0
0
2
1
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
1
2
3
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
2
0
0
2
0
0
1
0
0
0
1
0
2
0
4
0
0
2
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
1
1
0
0
0
2
0
0
0
0
1
2
2
1
0
0
1
0
1
4
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
1
0
1
0
0
0
1
0
0
0
3
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
2
2
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
1
2
0
0
1
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
1
1
0
3
0
2
2
0
0
0
0
0
0
3
2
1
2
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
4
0
0
0
0
2
0
0
0
2
1
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
2
0
0
0
1
2
0
0
0
1
1
0
0
1
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
2
0
2
0
1
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
8
2
0
2
0
0
0
1
3
0
0
0
0
0
0
0
1
2
0
2
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
2
0
0
2
0
1
0
1
1
0
0
0
2
1
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
3
0
1
1
1
2
0
1
1
1
0
2
0
2
1
0
0
0
0
0
0
4
0
2
0
0
0
0
0
0
2
0
1
0
2
0
0
0
1
0
0
9
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
1
1
0
0
0
0
0
0
1
0
0
2
2
0
1
0
0
4
0
0
0
0
0
0
0
0
2
2
3
2
0
1
0
0
2
0
1
0
0
0
2
1
0
0
0
0
0
0
2
2
0
2
1
1
0
1
0
0
0
0
1
1
2
0
0
0
0
0
2
0
0
0
1
0
0
2
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
2
2
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
19
2
0
1
2
2
0
0
1
0
1
0
1
1
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
3
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
1
3
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
3
1
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
2
0
0
1
1
0
2
0
1
0
0
0
1
2
0
1
0
0
0
1
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
2
0
0
1
0
0
1
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
2
1
0
1
0
0
0
0
1
1
0
2
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
3
0
4
0
0
1
1
2
2
0
0
0
0
0
0
1
1
0
0
0
0
1
2
0
0
0
1
0
0
0
0
4
3
1
0
0
0
2
1
2
0
0
0
0
2
2
0
0
0
0
2
0
0
1
0
2
1
2
0
0
1
2
0
0
0
0
0
0
0
0
1
1
0
3
0
2
0
0
0
0
0
0
3
3
3
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
4
2
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
2
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
1
0
0
0
0
2
0
0
1
1
1
0
2
2
1
1
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
2
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
1
0
1
0
0
0
0
2
0
1
0
0
0
2
0
1
0
2
2
0
2
0
0
0
1
0
0
3
0
2
0
0
3
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
2
0
0
0
0
0
0
0
0
2
2
2
0
2
0
2
0
0
0
0
2
0
0
1
0
1
1
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
6
0
0
0
0
0
0
1
2
0
0
1
0
0
0
1
0
0
0
0
2
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
2
0
0
1
0
0
0
2
0
0
0
1
2
2
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
1
0
1
2
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
3
0
0
1
0
2
0
0
0
0
0
1
2
1
0
1
1
0
1
0
0
2
0
0
0
2
0
0
0
2
0
0
2
0
0
2
0
3
0
1
2
0
0
0
0
2
0
0
0
2
1
1
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
3
0
2
0
0
1
0
0
1
2
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
1
2
0
3
0
2
0
2
1
2
0
0
0
4
0
0
0
2
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
5
0
0
0
0
0
2
0
0
0
2
1
0
2
2
0
1
0
2
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
2
0
0
0
0
1
1
0
2
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
1
2
2
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
3
0
0
0
0
0
1
0
2
0
0
0
0
2
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
3
2
0
0
1
0
0
0
0
2
2
2
0
1
0
0
1
0
0
0
0
2
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
1
6
0
0
1
1
0
0
2
1
0
0
0
8
0
0
0
1
0
1
3
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
6
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
2
0
2
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
3
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
1
5
2
0
0
2
2
1
0
0
0
0
0
0
0
1
1
0
0
2
1
0
0
0
0
1
2
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
1
2
0
5
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
3
0
0
0
1
0
1
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
3
0
2
2
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
3
1
0
0
2
0
1
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
2
1
0
0
0
1
0
0
6
0
0
1
0
0
4
0
0
0
3
0
0
0
2
1
0
0
0
0
0
0
1
1
0
0
2
0
0
2
0
0
0
0
5
1
0
0
0
1
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
1
1
2
2
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
1
0
0
0
1
1
1
0
2
0
0
0
0
0
2
2
0
4
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
2
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
4
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
3
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
6
2
0
0
0
2
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
4
1
0
1
0
0
0
0
0
0
0
2
1
2
0
2
0
0
1
1
0
0
2
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
2
0
0
0
1
0
1
2
0
0
2
1
0
0
0
0
0
2
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
2
2
2
2
1
2
0
2
0
0
1
0
0
2
1
1
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
4
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
2
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
3
0
0
0
0
0
1
0
1
0
0
0
1
1
0
1
0
2
0
0
0
0
0
1
0
0
1
2
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
1
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
2
0
2
2
0
0
0
0
0
2
0
2
0
1
0
4
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
2
0
0
1
0
0
0
0
1
0
0
0
2
0
3
0
2
0
0
0
0
0
4
0
0
0
1
0
0
2
1
0
1
1
0
0
0
0
0
0
2
0
2
1
0
1
1
0
1
0
1
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
3
1
0
0
0
0
1
2
1
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
3
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
1
2
1
0
0
0
1
0
2
2
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
1
2
0
0
2
0
0
0
0
0
0
1
0
1
1
0
0
0
0
2
0
2
1
1
0
0
0
2
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
1
1
3
5
0
1
1
0
0
0
0
0
0
2
1
2
0
0
2
0
0
0
0
0
2
0
0
1
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
2
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
2
1
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
2
0
2
2
0
0
0
1
1
1
0
0
2
2
0
1
0
0
0
0
0
0
0
1
0
2
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
2
0
0
2
1
3
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
1
2
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
1
2
0
1
0
1
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
1
0
2
0
0
0
0
2
0
0
0
1
0
1
0
2
0
0
0
0
1
0
0
0
0
0
6
0
0
0
0
0
2
2
0
0
2
0
0
0
2
0
0
0
0
2
3
1
0
2
0
2
0
0
0
0
0
2
1
0
0
2
0
0
0
2
0
0
0
0
0
0
5
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
3
0
0
0
0
1
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
2
1
0
1
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
1
2
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
1
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
6
1
0
0
2
0
2
0
0
2
0
1
0
0
1
2
0
1
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
2
0
0
0
0
2
2
0
0
6
0
1
2
0
2
0
1
0
0
0
0
1
2
2
0
0
0
0
1
1
0
0
0
0
2
0
2
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
1
1
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
1
1
0
2
1
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
3
0
2
1
2
0
0
1
1
0
0
0
0
0
0
0
0
3
0
0
1
0
0
1
2
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
2
1
0
1
3
0
0
0
0
0
1
0
1
2
0
0
2
0
0
2
0
0
0
2
2
0
0
0
0
0
1
0
0
1
1
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
3
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
1
0
2
2
1
5
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
7
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
1
0
0
0
0
0
2
0
2
3
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
2
0
0
0
2
0
1
2
0
0
0
0
2
0
0
6
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
1
2
0
0
1
0
2
0
0
1
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
2
1
1
0
3
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
2
1
1
0
0
0
0
1
1
2
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
1
3
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
1
0
3
0
0
0
0
0
1
0
2
0
4
2
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
1
0
0
1
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
1
2
2
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
2
0
0
0
3
2
0
0
1
0
2
0
0
0
0
0
1
1
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
2
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
2
0
0
1
0
1
2
0
0
1
0
2
3
1
1
0
3
1
0
0
2
0
0
0
0
3
0
0
0
0
0
3
2
0
1
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
1
0
0
0
0
2
1
2
0
1
0
0
0
0
0
3
2
1
2
0
3
0
0
0
0
0
3
0
0
0
0
0
0
2
2
0
0
0
1
2
0
2
0
2
0
0
1
0
1
0
0
0
0
0
2
0
0
0
2
0
1
1
0
0
0
3
2
0
0
0
0
1
0
0
0
4
0
2
1
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
1
2
2
0
0
6
0
3
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
1
2
0
0
0
0
0
1
2
2
1
0
2
0
0
0
1
0
0
4
2
0
2
0
0
0
0
0
2
0
1
0
2
1
0
0
0
1
0
0
2
0
0
2
0
2
0
0
1
0
1
0
1
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
2
0
2
0
1
0
1
0
3
1
1
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
1
4
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
2
2
3
0
0
0
0
0
0
0
0
0
0
2
2
0
3
0
0
0
0
1
0
0
4
0
1
0
2
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
1
1
0
0
1
3
0
0
2
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
2
0
2
0
0
1
0
2
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
5
0
2
0
1
0
0
0
0
2
0
0
2
1
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
2
0
0
0
1
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
1
0
1
1
1
0
0
0
0
5
0
0
2
1
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
3
0
0
0
0
0
0
3
0
0
0
0
0
1
0
1
1
0
0
0
0
2
0
0
0
0
0
2
0
3
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
2
2
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
5
0
2
0
0
0
0
1
2
1
2
0
0
1
1
1
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
2
1
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
1
1
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
2
0
1
0
0
0
1
0
2
2
0
0
1
0
0
3
0
1
0
0
0
0
1
2
1
0
0
0
0
2
0
0
1
0
0
1
0
0
0
2
0
2
0
0
2
0
0
0
1
2
0
0
0
2
2
0
0
0
0
1
1
2
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
1
5
0
0
0
0
1
1
0
0
0
1
0
3
2
1
1
0
0
0
0
2
1
2
1
1
1
2
0
0
0
0
0
2
0
0
1
0
0
0
2
1
0
0
0
1
2
0
0
1
1
0
0
0
0
0
0
0
0
0
3
0
4
0
0
0
3
2
0
0
0
0
2
0
0
0
0
0
0
3
1
0
0
1
0
0
0
0
0
0
0
0
1
2
1
0
2
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
2
3
0
2
0
0
0
1
0
0
0
1
2
0
0
0
1
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
3
0
2
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
2
0
1
1
0
0
2
1
3
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
1
0
0
0
6
0
0
0
0
1
0
0
0
1
0
2
0
1
0
2
0
0
0
0
0
0
1
0
2
0
2
1
0
2
2
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
1
1
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
2
1
0
0
0
0
2
0
1
0
0
2
1
2
0
1
0
1
2
0
0
0
0
7
0
0
1
0
2
0
0
0
2
1
1
0
0
1
0
1
0
2
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
1
3
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
1
2
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
3
0
1
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
1
0
1
0
0
0
1
0
1
0
2
0
0
2
0
0
0
1
0
1
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
1
0
0
0
1
1
0
2
2
0
0
0
1
1
2
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
5
0
2
0
3
0
2
0
0
1
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
1
2
2
1
0
0
0
0
1
0
0
1
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
2
2
0
1
1
2
0
0
1
0
0
5
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
2
0
2
0
0
0
1
0
2
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
1
2
1
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
2
2
1
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
2
0
0
2
0
3
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
2
2
0
2
0
0
0
0
0
3
0
0
0
0
3
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
3
0
2
0
1
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
2
2
0
0
0
0
5
1
0
4
1
0
3
0
0
0
0
0
1
1
0
0
1
2
3
1
0
0
0
0
1
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
2
0
2
2
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
2
0
0
1
0
0
1
1
0
1
0
2
0
0
0
0
0
2
2
2
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
4
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
2
0
0
0
1
0
1
1
0
2
2
0
0
0
0
1
3
0
1
0
1
0
0
5
0
0
0
0
0
0
0
0
7
0
2
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
3
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
3
0
5
2
1
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
1
2
0
0
2
0
0
1
1
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
1
0
0
0
0
0
2
1
0
0
2
0
0
0
0
1
1
1
4
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
1
1
2
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
3
1
0
2
0
0
2
0
0
0
0
0
0
2
0
1
2
2
2
0
0
0
0
2
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
1
0
0
0
1
1
0
0
0
3
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
3
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
2
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
2
0
1
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
1
2
0
0
0
0
0
0
0
1
0
6
2
1
3
0
2
0
1
0
0
0
1
2
0
0
0
2
0
0
0
1
0
0
1
0
0
0
1
2
4
0
2
2
0
0
0
2
0
0
0
0
0
0
1
1
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
2
0
1
0
2
4
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
2
1
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
2
0
2
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
2
2
1
3
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
2
2
2
0
0
2
0
0
0
1
0
2
2
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
3
0
0
0
0
0
1
0
1
0
0
0
0
4
0
0
1
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
1
0
2
0
0
0
0
0
0
1
2
0
0
0
0
1
0
2
0
3
0
0
2
0
1
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
1
0
3
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
1
2
0
0
3
0
0
0
0
0
0
0
2
1
0
0
0
0
1
1
0
0
3
6
0
0
0
0
0
2
2
0
0
0
0
2
1
0
1
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
1
2
0
0
3
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
7
2
2
0
2
0
0
1
0
0
2
1
2
2
0
0
0
0
0
0
0
1
1
2
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
2
0
1
0
1
0
0
0
0
0
0
1
0
2
0
1
0
0
1
0
0
0
3
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
3
3
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
1
0
1
2
1
0
2
0
0
0
0
0
1
0
2
3
0
0
2
0
0
0
3
0
0
0
2
0
0
0
1
0
0
2
2
1
0
0
3
0
1
3
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
1
0
1
2
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
2
0
2
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
3
0
0
0
0
1
0
0
0
1
0
1
5
2
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
2
2
0
0
1
0
1
0
3
1
0
0
0
0
2
0
0
0
0
0
0
2
2
1
0
0
0
1
1
0
0
1
1
2
0
2
0
0
0
0
1
1
2
0
0
2
0
0
0
0
0
2
2
2
0
0
0
2
0
0
0
0
0
0
5
0
0
0
0
0
3
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
3
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
2
0
3
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
1
0
2
0
1
2
0
2
1
0
0
0
0
1
2
1
1
0
0
0
1
4
1
2
0
0
0
0
0
2
0
0
1
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
3
1
0
1
0
0
2
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
2
2
1
1
0
0
2
0
0
0
0
0
0
2
0
1
0
0
2
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
3
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
3
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
2
0
2
0
0
0
2
0
0
2
2
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
2
1
0
1
0
0
0
0
0
3
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
1
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
3
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
3
2
2
0
0
0
2
0
0
0
0
0
1
1
0
2
0
0
2
0
0
0
0
2
0
2
2
0
2
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
2
1
0
2
0
1
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
1
0
0
0
0
1
0
2
2
0
0
0
2
3
1
0
3
0
0
0
2
0
0
5
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
5
0
0
0
30
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
2
2
0
2
0
2
0
0
4
0
0
0
0
2
2
0
0
0
0
0
2
0
2
2
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
1
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
1
4
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
5
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
2
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
4
0
0
0
0
1
1
0
0
0
0
2
2
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
3
0
0
0
0
2
0
2
0
3
0
1
1
2
0
2
0
0
0
0
0
0
0
0
3
2
0
1
0
0
3
0
0
0
0
0
0
0
0
0
2
2
2
1
0
0
0
0
2
0
0
0
1
0
0
2
3
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
1
1
0
0
2
0
0
3
0
0
0
2
1
1
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
2
0
0
4
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
2
1
0
1
2
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
2
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
1
2
0
1
0
0
2
1
0
2
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
1
0
0
1
0
2
1
1
1
1
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
2
2
1
0
0
1
0
0
2
2
0
3
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
5
0
0
1
0
0
0
0
1
1
1
0
6
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
2
0
0
0
1
2
0
0
0
1
0
0
1
0
1
0
0
1
0
1
0
0
1
0
0
3
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
1
0
2
0
0
0
0
2
0
1
2
3
1
2
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
3
0
3
2
0
1
0
0
3
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
7
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
1
1
1
2
1
1
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
2
4
0
1
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
1
0
2
2
0
0
4
0
0
1
1
2
1
0
0
0
0
0
0
3
0
0
0
1
2
0
1
0
0
0
1
1
0
0
0
0
2
2
0
0
0
2
0
0
0
2
1
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
1
0
2
1
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
1
0
1
0
2
0
0
0
0
1
1
0
0
1
2
0
1
0
0
0
1
0
0
2
0
0
2
0
0
0
1
1
0
1
0
0
0
2
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
2
0
2
0
2
3
1
0
3
0
1
2
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
1
0
1
2
0
4
0
2
0
3
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
1
2
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
2
0
2
0
1
0
1
0
0
2
0
2
0
1
0
0
0
2
0
1
0
0
2
0
0
0
0
2
2
1
8
0
2
0
1
1
0
0
1
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
2
0
0
0
0
2
0
2
0
1
0
2
1
0
0
2
0
1
0
2
0
0
0
1
3
0
1
2
2
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
2
0
0
2
0
1
1
0
0
0
2
0
2
0
1
0
0
1
1
0
1
1
0
1
1
0
0
0
3
0
0
0
1
0
0
2
0
0
0
0
3
2
1
1
0
0
0
2
1
3
0
0
2
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
3
0
1
0
2
0
1
0
0
0
0
1
2
0
2
2
0
0
2
0
0
0
0
0
2
0
0
0
1
1
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
3
2
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
1
2
0
1
0
0
0
1
0
0
0
0
0
0
2
1
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
2
1
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
1
2
0
0
1
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
2
1
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
3
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
3
1
0
0
0
0
2
2
1
0
0
0
0
1
0
1
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
1
2
9
0
3
0
0
0
0
0
0
0
0
3
0
3
0
0
0
2
0
1
0
0
2
0
2
0
0
0
0
0
0
2
1
0
1
2
1
0
0
0
0
2
0
0
3
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
2
0
2
1
0
0
0
0
2
0
0
2
0
0
2
2
0
0
3
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
1
0
3
0
0
3
2
0
0
0
3
0
0
0
2
0
1
0
1
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
1
1
0
0
1
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
4
0
0
0
1
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
2
4
0
1
0
1
0
0
0
0
0
0
3
0
1
0
0
0
0
2
0
1
0
2
0
0
0
0
0
1
0
2
0
5
1
0
0
0
0
0
1
0
1
1
0
0
0
1
0
1
4
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
2
0
0
2
1
0
1
0
0
0
0
0
0
0
4
0
0
0
0
3
1
2
2
1
0
1
0
0
0
0
1
2
1
0
0
0
1
0
1
1
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
1
0
0
0
2
0
1
0
1
2
1
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
2
0
0
1
0
4
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
7
0
0
0
0
2
0
0
0
1
0
0
1
0
1
0
1
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
2
1
0
1
2
1
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
2
0
1
0
0
1
0
2
0
1
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
2
2
0
2
0
2
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
1
1
1
0
0
0
0
1
0
0
0
0
2
0
0
0
4
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
2
0
1
0
2
0
0
1
0
2
0
2
0
0
1
0
2
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
1
1
0
2
2
0
1
0
0
0
1
0
0
0
3
2
0
0
1
2
2
3
0
0
3
2
0
0
0
0
1
0
0
0
0
0
2
2
1
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
1
1
2
1
1
0
2
0
0
0
0
1
0
1
0
0
0
1
5
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
2
0
0
2
0
2
1
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
3
0
0
2
0
0
0
0
1
1
0
0
2
0
0
0
0
2
1
0
0
2
0
0
0
2
0
0
0
1
0
0
2
0
0
0
1
0
1
1
0
0
0
0
0
1
0
1
0
2
0
0
2
1
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
1
0
0
0
1
3
0
0
0
0
0
0
2
0
0
0
0
8
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
2
3
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
1
1
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
2
1
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
1
0
2
0
0
2
0
1
3
0
0
0
2
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
1
2
2
0
0
2
1
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
10
0
0
1
1
2
0
0
2
0
1
4
1
0
0
2
0
0
1
2
0
0
0
1
0
1
0
1
1
2
0
0
2
0
3
0
2
0
1
0
2
0
0
1
0
2
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
1
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
1
2
0
2
0
0
2
0
0
2
0
0
0
3
0
0
1
0
2
0
0
2
0
4
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
1
0
2
0
0
0
0
2
0
0
0
1
2
0
0
0
0
3
0
1
2
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
1
0
0
0
0
2
0
0
0
0
1
0
0
1
0
1
0
0
1
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
2
0
0
0
0
0
5
0
0
0
1
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
3
0
0
0
0
0
1
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
3
2
0
0
0
0
1
1
1
1
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
2
2
0
0
0
1
0
0
0
0
0
3
0
0
4
0
0
1
0
0
0
0
3
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
2
2
2
0
1
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
1
0
0
3
0
0
0
0
1
0
0
0
1
0
0
2
1
0
0
1
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
2
0
1
0
2
0
0
2
0
2
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
3
0
1
0
0
0
1
0
0
2
0
0
0
0
0
1
1
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
4
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
2
1
0
0
1
0
0
0
0
0
2
0
0
2
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
2
2
0
0
0
0
0
0
0
1
0
2
0
2
2
0
0
1
0
0
0
0
0
2
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
2
0
0
0
0
2
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
2
1
1
0
1
2
0
0
0
0
0
0
1
2
1
0
4
0
0
0
0
0
1
0
1
0
1
0
0
2
0
0
0
1
0
0
2
0
2
1
0
0
0
0
0
8
0
0
0
0
0
2
0
1
0
0
0
2
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
3
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
1
0
1
1
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
2
2
0
1
1
0
0
0
0
0
2
1
0
3
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
1
0
2
0
0
2
0
1
0
0
0
0
0
0
2
0
2
1
0
3
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
11
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
2
4
3
0
0
2
0
0
1
0
3
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
2
1
0
2
0
0
0
0
3
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
2
0
0
0
2
0
0
1
0
1
0
0
0
0
2
2
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
3
0
2
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
3
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
3
0
3
0
2
0
0
1
2
2
0
0
0
2
0
1
2
2
0
0
0
0
0
0
0
0
0
3
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
1
2
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
0
1
0
0
0
0
0
0
2
2
2
0
0
0
2
0
0
0
2
0
2
0
1
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
2
1
0
1
0
1
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
1
0
2
0
1
0
0
2
0
1
0
0
0
0
2
1
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
2
1
2
0
0
0
0
1
3
1
2
0
2
0
0
0
0
0
0
0
3
3
0
1
0
0
2
0
0
0
8
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
1
0
2
1
1
0
0
0
0
1
2
0
0
0
2
1
0
0
1
0
1
0
0
0
1
1
2
0
0
0
0
0
0
0
0
3
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
4
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
2
0
2
1
0
0
0
2
0
1
2
0
0
1
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
1
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
1
0
2
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
1
2
2
0
0
0
3
1
0
0
0
0
0
0
0
0
0
7
2
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
1
2
1
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
1
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
2
0
0
2
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
1
0
3
1
3
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
1
2
0
0
0
0
0
2
0
0
0
4
0
0
2
0
2
1
0
0
0
0
0
1
0
2
0
0
1
0
1
0
0
2
1
6
1
0
0
1
1
1
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
1
2
0
0
1
1
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
2
0
0
0
2
0
0
1
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
3
0
2
1
0
6
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
2
0
1
0
0
0
2
0
1
0
0
1
0
1
0
2
0
0
1
0
0
0
2
2
0
0
0
1
0
0
1
0
0
2
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
2
0
2
0
3
0
0
2
0
0
0
0
0
6
0
0
0
1
0
1
1
0
1
0
3
2
0
0
3
0
0
0
1
0
0
2
1
0
0
0
1
1
0
2
0
0
0
2
0
0
0
2
1
0
0
0
3
2
0
0
0
0
1
0
0
2
0
1
0
0
2
0
0
0
2
0
0
0
0
0
2
0
3
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
1
0
1
0
10
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
2
2
2
0
2
0
2
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
2
1
0
0
0
0
0
1
0
0
0
2
2
0
0
0
1
0
1
0
0
1
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
2
0
1
1
2
0
0
2
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
3
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
2
1
1
0
0
0
0
0
5
0
0
0
1
0
0
0
0
2
0
1
1
0
0
0
1
0
0
0
0
1
2
0
2
0
0
2
0
0
0
0
2
1
0
0
1
2
0
1
0
3
1
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
2
0
0
2
0
0
0
0
0
2
5
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
2
7
0
0
0
0
0
0
0
1
0
0
0
1
2
0
2
0
0
2
1
0
0
0
0
2
0
2
0
0
0
2
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
11
1
1
0
1
0
0
0
0
1
2
0
0
0
0
0
1
1
0
0
1
0
3
2
1
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
4
1
3
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
2
1
0
1
0
2
0
1
0
2
2
0
1
0
0
0
1
0
0
3
0
1
0
2
0
2
0
0
0
3
2
0
0
0
0
1
0
0
1
0
0
1
5
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
2
1
1
0
0
0
0
1
0
2
0
0
1
0
1
0
0
0
2
0
0
2
2
0
0
2
0
2
0
2
0
0
0
0
1
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
2
2
0
2
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
1
2
0
0
3
0
0
0
0
3
1
0
0
0
0
0
0
0
2
0
0
2
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
10
0
0
0
2
2
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
1
2
0
2
1
0
2
0
0
0
0
2
0
0
2
3
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
3
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
3
2
0
1
0
0
0
0
0
1
0
2
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
1
2
0
1
0
0
2
1
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
3
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
2
0
2
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
5
0
0
1
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
2
0
2
0
0
2
0
0
0
0
0
2
2
0
0
0
0
2
2
0
0
0
0
0
1
2
1
0
0
2
0
0
0
1
0
0
0
2
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
2
2
0
0
0
2
0
0
1
1
0
0
0
2
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
2
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
2
0
0
1
0
2
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
1
2
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
2
4
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
1
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
1
2
0
0
0
2
1
2
1
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
3
0
2
1
0
1
0
1
0
2
4
0
2
0
0
0
0
0
1
0
2
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
2
0
1
0
1
0
1
1
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
3
2
0
0
2
0
0
0
2
2
0
2
0
0
0
0
0
0
2
0
0
1
0
0
5
0
1
0
1
0
0
0
0
2
1
0
2
0
2
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
2
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
3
1
0
2
0
3
0
1
0
0
0
0
3
1
0
0
3
0
0
0
5
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
2
0
2
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
2
0
2
0
1
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
1
2
1
2
0
0
0
0
1
0
0
0
0
0
0
0
4
1
0
1
1
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
1
1
0
0
0
0
0
0
1
0
2
0
0
0
2
3
0
0
0
3
1
0
2
0
2
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
3
0
1
0
3
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
3
0
0
0
0
3
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
2
0
2
2
0
0
0
0
1
2
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
2
0
0
2
0
0
6
1
0
0
0
0
0
0
2
0
1
0
0
1
2
7
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
4
0
0
0
0
0
1
0
2
2
2
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
2
0
0
4
0
0
0
0
3
3
0
1
0
2
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
2
0
3
0
0
1
1
2
0
0
0
0
0
0
0
0
2
1
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
2
2
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
2
0
2
0
1
3
0
1
2
0
1
0
0
1
0
1
1
1
0
1
1
4
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
2
1
0
1
0
0
0
2
2
0
0
0
1
0
0
0
2
3
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
1
0
0
1
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
4
0
0
1
0
0
2
2
0
0
0
0
0
1
0
2
0
2
1
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
1
0
0
0
2
2
0
2
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
2
1
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
2
1
1
0
0
0
2
0
0
1
1
0
0
1
3
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
1
2
1
2
0
2
0
0
0
0
1
0
0
2
1
0
0
0
0
1
0
0
0
2
0
1
0
0
1
0
0
0
0
0
1
1
2
2
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
2
0
1
2
0
1
0
2
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
1
1
1
2
0
2
0
0
1
5
0
0
0
0
0
4
0
0
0
2
0
1
0
0
2
2
0
1
0
0
0
1
1
0
2
0
0
3
0
0
0
0
0
1
4
1
0
0
1
0
4
0
0
0
0
2
0
0
0
1
0
1
0
0
2
0
2
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
1
2
2
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
2
1
0
0
0
2
1
2
2
0
2
1
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
3
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
2
6
1
0
0
2
3
0
0
1
0
0
1
0
0
0
0
2
3
0
0
0
0
0
0
2
0
0
0
0
1
0
8
0
0
0
2
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
2
0
1
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
1
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
5
2
0
0
0
0
0
2
0
5
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
4
0
0
0
0
3
0
0
0
0
2
0
2
2
0
0
0
0
2
0
1
0
0
0
0
2
0
0
3
0
1
0
0
2
0
0
0
1
0
2
1
2
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
4
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
1
0
2
0
0
0
0
0
0
2
2
0
0
2
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
2
2
1
0
2
0
0
0
2
0
0
1
0
0
1
0
0
0
2
0
1
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
1
2
1
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
2
0
1
3
0
0
0
0
0
2
1
2
0
2
0
0
0
2
2
2
0
0
1
3
0
2
2
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
5
0
2
1
0
0
1
0
0
1
0
0
0
5
0
0
2
0
0
0
0
3
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
3
0
0
0
0
0
0
0
0
1
0
0
2
2
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
3
0
2
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
1
1
0
1
0
0
2
0
0
2
1
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
3
0
1
2
0
0
1
0
2
0
0
0
0
1
0
0
2
1
2
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
2
2
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
2
0
0
1
0
0
0
2
0
1
2
0
2
1
0
0
2
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
1
2
0
0
1
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
2
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
1
2
0
1
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
2
0
0
0
0
1
0
3
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
1
1
1
0
0
0
0
0
0
0
2
3
2
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
7
1
0
0
1
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
1
0
1
2
0
0
0
0
4
0
0
0
0
0
0
1
0
2
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
2
0
0
1
3
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
2
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
1
0
0
0
1
1
0
2
1
0
1
2
0
4
0
0
2
0
1
0
0
1
2
0
0
0
1
0
0
2
0
1
1
2
0
1
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
6
0
1
1
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
1
0
1
0
0
0
1
3
0
0
0
0
0
1
3
0
0
0
0
2
0
0
2
0
3
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
2
1
0
1
2
0
2
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
2
0
0
7
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
1
1
0
0
2
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
2
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
1
1
2
0
0
0
0
1
1
0
0
0
2
0
0
1
1
0
0
0
1
0
0
0
2
1
0
0
1
1
0
0
0
0
2
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
2
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
3
0
0
1
0
1
2
0
1
1
0
0
2
1
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
2
0
1
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
3
2
0
1
1
1
0
1
0
1
0
0
0
0
1
2
1
2
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
2
0
0
1
1
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
1
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
3
0
1
2
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
1
2
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
6
0
0
0
0
0
1
0
1
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
3
0
0
0
0
0
1
0
2
0
0
0
2
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
1
2
0
0
2
9
0
0
0
0
0
2
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
1
0
1
1
0
1
0
0
0
0
0
0
0
0
4
1
0
0
3
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
2
1
1
0
2
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
2
0
2
2
0
2
3
0
1
0
2
0
0
0
2
4
1
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
1
2
2
0
1
4
0
2
0
0
2
0
2
0
0
3
0
0
2
0
2
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
1
7
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
3
0
0
1
2
1
0
0
0
0
1
1
0
1
0
0
2
1
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
1
0
0
2
0
0
0
0
0
0
0
2
1
0
1
0
1
0
0
2
0
0
1
0
2
0
0
3
0
0
1
0
1
4
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
1
3
0
1
1
2
0
0
0
1
0
0
0
1
0
2
0
1
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
1
1
2
0
1
1
0
0
0
0
2
0
0
0
1
0
0
0
2
1
0
3
2
0
0
0
0
0
0
0
0
0
0
0
1
6
2
0
0
1
1
0
0
2
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
1
2
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
1
1
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
4
0
2
2
0
0
3
1
2
0
0
0
1
0
2
0
7
0
0
0
0
0
0
0
0
1
0
0
0
2
2
1
0
0
0
1
2
0
0
0
1
0
1
0
0
0
2
0
0
0
0
1
0
0
0
1
0
2
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
3
0
0
1
1
2
0
0
0
0
0
0
0
1
0
0
0
1
0
2
2
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
3
1
0
0
2
0
0
1
0
0
0
0
0
0
3
0
1
0
0
0
1
0
2
0
2
2
0
0
0
1
2
0
0
0
0
1
2
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
2
1
0
2
2
0
0
0
0
0
0
1
0
1
0
1
0
2
0
0
0
1
0
0
2
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
1
1
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
1
2
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
2
0
1
0
0
0
0
0
0
0
2
2
2
2
0
0
0
0
0
0
0
1
1
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
2
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
2
0
0
2
0
2
1
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
1
0
0
0
0
1
1
0
0
1
0
2
0
2
0
0
2
1
2
0
0
0
0
0
0
0
0
3
0
0
2
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
4
1
0
0
0
0
0
3
2
0
0
0
2
2
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
2
4
3
0
1
0
0
1
1
2
2
3
2
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
3
1
0
0
0
0
0
0
0
5
0
0
0
1
0
2
0
2
0
0
0
2
0
0
0
0
1
0
0
1
0
0
2
0
2
0
0
2
2
2
0
0
0
0
0
2
0
0
0
1
0
0
1
1
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
1
2
4
0
0
0
0
0
1
0
1
0
0
0
2
0
1
0
0
3
1
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
2
0
0
0
0
0
0
1
0
2
0
3
0
0
3
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
2
0
0
1
2
0
0
0
0
3
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
1
0
0
2
0
0
0
1
0
0
0
2
0
2
0
2
1
2
2
0
0
0
0
0
1
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
2
0
1
1
2
0
3
0
0
2
1
2
0
0
0
0
4
2
0
0
0
2
2
0
0
1
0
0
0
0
1
0
0
2
0
0
0
2
0
0
3
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
1
0
0
1
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
2
1
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
2
0
2
0
0
0
0
0
0
0
1
2
0
2
0
11
0
0
2
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
1
2
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
1
0
1
0
1
1
0
0
0
0
0
2
0
0
0
0
1
0
0
2
1
0
0
0
0
0
3
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
2
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
14
0
2
0
2
0
2
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
2
1
0
2
0
0
0
0
2
2
0
1
0
1
1
2
2
0
0
0
2
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
4
0
2
1
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
3
0
0
0
3
0
0
1
0
0
0
0
0
0
0
2
0
2
0
3
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
2
0
2
0
0
2
2
0
0
1
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
3
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
3
0
2
0
0
2
1
2
1
2
0
0
0
0
2
0
0
2
1
0
0
0
0
2
0
0
0
0
1
0
0
2
1
2
0
1
0
0
0
2
0
0
0
0
3
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
2
0
0
0
1
2
1
2
1
0
2
0
1
0
2
0
6
1
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
3
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
2
0
0
2
0
1
0
0
0
0
0
3
1
0
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
2
0
2
0
0
2
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
1
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
4
0
0
0
2
0
1
0
0
1
0
2
0
3
0
0
1
0
7
0
2
0
2
1
1
0
0
0
1
5
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
4
0
0
1
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
2
0
0
0
0
0
0
0
1
0
2
1
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
1
4
0
0
2
0
0
1
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
2
0
0
1
0
0
0
2
2
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
2
2
0
0
0
0
0
2
0
0
2
0
0
0
2
4
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
1
0
0
0
0
2
3
0
2
1
1
0
0
1
0
0
0
2
1
0
0
1
0
0
0
3
1
2
0
0
0
2
0
1
0
2
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
1
0
0
2
2
1
0
0
2
3
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
3
0
0
2
1
1
0
0
0
0
1
0
0
0
3
1
0
3
1
0
1
0
2
0
0
0
1
1
1
1
0
0
1
0
2
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
1
1
1
0
1
1
2
1
3
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
1
0
0
0
0
2
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
2
2
0
0
2
0
1
0
3
1
0
1
0
0
0
2
2
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
1
1
1
0
0
0
4
1
2
0
2
0
0
0
0
2
0
0
1
1
0
2
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
2
2
3
0
2
0
0
0
5
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
2
0
0
2
0
1
1
0
2
0
0
2
0
1
2
0
4
0
2
2
2
2
0
1
0
7
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
2
2
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
1
0
1
0
0
0
2
0
0
1
1
0
0
1
0
0
0
0
0
4
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
2
1
2
0
0
0
0
1
2
0
0
1
0
2
0
2
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
2
0
2
1
1
2
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
1
2
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
1
1
2
0
0
0
0
4
0
1
0
2
0
0
0
2
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
1
0
2
0
2
1
0
0
1
0
0
2
2
0
2
0
2
1
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
1
1
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
2
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
2
2
0
0
2
0
0
0
0
0
0
2
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
1
0
0
0
0
0
2
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
5
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
2
0
2
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
3
1
2
0
0
2
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
2
0
0
1
0
1
0
2
2
0
0
0
1
0
2
2
0
0
0
2
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
2
0
0
0
2
2
1
1
0
0
0
1
0
1
1
0
0
0
0
0
0
2
0
0
0
1
1
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
3
0
1
0
0
2
0
1
0
0
1
0
0
0
0
0
0
1
0
1
2
0
1
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
2
2
2
0
0
1
0
0
0
0
2
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
2
0
1
2
0
0
0
0
1
1
0
0
0
2
2
0
1
2
0
2
0
0
2
2
0
2
0
4
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
2
0
2
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
2
0
0
3
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
2
2
2
0
3
2
2
0
0
0
0
1
0
2
1
0
1
0
0
0
0
3
0
0
0
2
0
0
0
0
0
2
1
0
0
1
0
1
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
3
0
0
2
0
1
0
2
1
0
2
0
0
0
2
4
0
1
0
0
3
0
0
0
0
0
0
0
2
0
1
0
0
2
0
2
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
1
2
0
0
0
1
1
1
1
2
2
0
1
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
2
2
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
4
1
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
1
3
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
3
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
2
1
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
2
2
2
0
0
0
1
0
1
0
0
0
0
1
0
0
0
2
0
1
0
0
0
2
0
0
0
0
5
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
2
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
2
0
0
3
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
2
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
3
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
2
0
2
0
0
1
3
0
1
2
0
0
0
0
2
0
0
0
0
2
2
1
0
0
0
0
2
0
2
1
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
1
1
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
2
0
0
0
0
0
2
0
7
0
0
1
2
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
4
1
0
0
0
1
0
0
1
0
1
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
2
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
2
0
1
0
2
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
1
0
0
0
0
2
0
0
0
1
0
3
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
4
0
1
0
0
0
0
1
1
0
0
0
2
0
0
2
0
1
0
0
0
3
4
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
1
2
2
0
0
0
2
0
0
1
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
1
0
2
0
0
0
0
0
0
2
0
1
1
0
0
4
0
0
0
2
0
2
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
3
0
2
0
0
0
0
0
0
0
0
1
2
1
0
0
2
2
0
3
2
0
1
2
0
1
0
0
0
0
0
0
0
2
1
0
0
2
2
0
1
0
0
0
2
0
0
2
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
1
2
0
2
0
0
0
1
0
0
2
0
0
0
0
3
0
0
1
0
0
0
0
3
0
0
1
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
1
0
1
2
0
2
0
0
1
0
0
0
0
1
0
0
2
1
1
0
0
0
0
0
0
0
0
0
1
1
2
0
0
2
0
1
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
2
2
0
2
0
2
0
0
2
0
0
2
0
1
0
1
0
1
2
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
17
0
0
0
0
0
0
0
3
0
0
2
0
2
1
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
1
0
0
0
2
0
2
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
4
2
0
0
0
2
0
2
0
0
0
5
0
0
1
2
2
0
0
0
1
1
1
0
2
1
2
0
0
0
0
0
0
0
1
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
2
2
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
2
1
0
1
1
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
4
0
0
1
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
2
0
1
0
1
0
0
1
0
2
0
0
0
0
2
0
0
0
0
3
1
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
1
2
0
0
0
0
2
0
1
3
0
0
0
1
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
1
1
2
2
0
2
0
0
1
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
8
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
1
1
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
1
2
0
0
0
0
0
0
0
1
2
2
0
2
0
1
2
0
5
0
0
2
2
2
1
1
0
0
0
1
0
0
1
1
0
3
2
2
0
2
1
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
1
0
1
0
0
1
0
2
1
2
1
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
1
0
0
2
1
1
0
0
1
0
1
0
0
0
0
2
0
3
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
2
1
2
1
2
0
1
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
4
0
0
2
0
0
1
0
0
0
0
3
0
2
0
0
1
1
2
0
0
2
0
1
0
1
0
1
0
1
0
0
1
1
3
0
0
1
1
0
0
2
0
0
0
2
2
0
1
0
0
0
0
0
0
0
2
0
0
0
1
3
0
0
2
0
0
0
2
0
2
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
1
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
3
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
2
0
1
1
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
2
0
0
0
0
2
0
0
2
0
1
0
0
1
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
2
7
0
2
0
0
2
2
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
3
1
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
2
0
0
1
0
0
2
0
0
1
0
1
2
2
0
1
0
0
0
0
2
2
0
2
0
1
0
0
1
1
0
0
2
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
1
0
0
0
0
3
0
1
0
0
2
0
0
1
1
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
6
0
0
0
2
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
2
1
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
2
0
2
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
2
1
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
5
0
0
0
0
3
3
2
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
1
2
0
0
1
0
0
0
0
2
1
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
1
0
2
0
0
3
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
1
3
1
1
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
2
0
1
0
2
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
2
2
1
2
2
0
0
5
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
2
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
1
0
5
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
2
0
2
0
0
0
0
0
1
0
1
0
2
2
1
0
0
2
0
4
0
0
0
2
2
0
2
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
4
0
0
0
2
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
5
0
0
0
2
0
2
0
0
0
1
0
1
0
1
0
0
1
2
0
0
0
2
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
4
0
0
0
3
3
2
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
4
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
2
3
2
0
0
0
0
0
0
0
0
0
0
0
6
0
0
1
0
0
0
0
0
0
2
0
0
2
1
0
1
0
1
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
2
0
0
0
2
2
0
2
0
0
0
3
0
0
1
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
3
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
2
1
1
1
1
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
2
0
0
1
0
0
1
0
1
2
0
2
0
0
0
2
3
0
0
0
0
0
1
2
0
0
1
0
1
0
0
2
0
2
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
1
1
0
0
2
0
2
0
0
2
1
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
2
2
0
2
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
1
0
1
0
0
0
1
0
0
2
0
0
2
0
0
2
0
1
0
0
0
0
0
0
1
1
4
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
3
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
1
2
0
0
0
0
0
0
1
0
0
0
2
1
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
2
0
0
0
2
0
0
2
0
0
0
0
0
1
2
0
0
0
0
3
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
2
1
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
1
1
3
0
0
2
1
0
0
1
0
0
0
0
2
1
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
2
1
0
2
0
1
3
0
1
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
2
0
2
0
3
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
1
1
0
0
2
0
0
0
1
0
0
0
0
0
2
1
0
0
2
0
0
2
0
0
0
1
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
2
1
0
0
0
0
2
0
0
0
4
0
0
0
0
2
2
0
1
0
0
1
0
1
0
0
0
1
0
1
1
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
3
1
0
0
0
0
0
2
3
1
0
11
0
1
0
0
0
0
2
2
0
0
0
2
0
0
0
0
2
2
1
3
0
2
0
0
1
0
0
2
2
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
4
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
3
0
0
2
0
2
0
0
0
0
0
2
0
0
1
0
0
0
1
0
1
0
0
0
0
8
0
0
0
0
1
0
0
2
1
1
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
2
0
1
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
1
2
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
1
0
2
0
4
1
0
0
0
3
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
1
0
2
1
1
2
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
2
0
0
1
0
1
0
0
1
0
2
0
1
1
2
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
3
0
3
0
0
2
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
2
0
0
2
0
0
0
0
0
2
0
0
2
0
2
0
0
1
1
1
0
2
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
1
2
1
1
0
0
3
0
2
0
0
0
0
0
0
0
0
1
0
2
2
0
0
2
0
1
0
0
0
0
0
3
0
2
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
6
0
0
0
0
0
3
0
0
0
1
0
1
4
0
1
2
2
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
1
1
0
2
0
0
0
1
0
0
2
0
0
2
0
0
0
0
1
1
2
0
0
2
0
1
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
2
0
0
0
2
1
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
2
0
0
0
0
0
1
0
0
1
2
2
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
3
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
3
0
0
1
0
2
2
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
1
0
0
1
0
1
2
0
0
0
0
0
0
1
0
0
1
2
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
2
1
1
0
0
1
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
2
0
0
0
2
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
3
0
1
0
1
1
0
0
1
0
0
2
0
2
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
2
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
3
0
1
0
0
0
0
2
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
2
0
0
0
1
1
1
0
3
1
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
1
0
0
2
1
1
0
0
1
0
0
2
2
2
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
4
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
3
1
0
0
0
0
0
0
0
0
0
0
3
0
2
1
0
0
2
0
0
0
1
0
0
3
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
1
0
0
2
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
2
2
2
0
0
0
0
0
0
1
0
0
2
1
2
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
2
0
2
0
0
0
2
1
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
4
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
3
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
1
0
0
3
1
1
2
0
3
0
0
2
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
2
0
1
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
2
0
0
0
0
0
2
0
1
0
0
0
2
0
0
6
0
2
2
0
3
0
0
0
2
0
0
0
2
0
1
1
0
0
0
2
2
0
0
1
0
0
0
0
2
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
3
2
0
1
0
1
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
2
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
6
1
2
3
1
1
0
2
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
3
1
2
0
0
0
1
0
0
0
0
2
1
0
0
2
0
2
2
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
1
1
0
0
0
6
0
0
2
0
0
1
0
0
1
0
0
4
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
2
1
0
4
1
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
1
2
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
1
0
3
2
2
0
0
1
0
2
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
6
1
2
0
0
0
1
1
0
0
0
0
0
0
2
2
1
1
0
0
0
0
0
0
0
0
0
1
3
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
4
2
0
0
2
1
1
0
0
0
0
0
0
0
0
1
0
2
0
0
3
0
0
0
0
0
0
0
0
2
0
2
0
1
2
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
2
0
0
1
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
2
1
1
0
2
0
0
0
0
0
0
2
0
2
2
0
1
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
3
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
2
2
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
1
0
3
0
1
0
0
0
0
0
0
2
1
0
0
0
1
0
0
1
0
2
2
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
1
2
0
1
0
0
1
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
1
1
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
1
2
3
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
2
0
1
0
0
0
1
3
0
0
0
2
0
1
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
3
0
0
0
0
0
0
2
0
2
1
0
3
5
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
2
0
0
1
2
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
3
0
1
1
2
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
1
0
2
0
0
9
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
2
0
0
1
1
0
0
0
0
0
1
0
0
1
2
0
0
0
0
2
2
0
2
0
0
1
1
0
1
0
0
0
1
0
1
2
2
0
2
1
2
0
0
2
0
0
1
1
2
0
2
0
0
0
0
0
0
1
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
2
0
0
0
0
1
1
0
3
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
1
0
2
1
2
0
0
0
1
0
0
0
0
1
2
1
1
0
0
0
0
0
0
1
0
3
0
0
0
0
2
3
0
0
0
1
1
0
0
0
0
2
0
0
1
1
0
0
0
6
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
2
1
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
2
2
0
0
0
0
0
0
0
1
3
0
8
2
0
0
2
2
0
2
0
1
0
2
0
0
0
1
1
0
2
0
0
0
0
0
1
1
0
0
0
2
0
0
2
0
0
0
1
1
1
1
0
0
2
0
0
1
0
2
0
0
0
0
1
2
1
2
0
1
0
0
0
1
0
1
0
1
2
0
1
0
0
2
1
2
0
3
0
1
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
1
1
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
2
0
1
1
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
2
0
3
0
1
0
0
1
0
0
0
0
0
0
2
0
0
2
0
1
0
2
0
0
0
0
1
0
0
0
0
7
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
1
2
0
2
0
9
0
0
0
2
0
0
0
0
0
0
0
2
5
0
0
0
1
0
0
0
3
2
0
0
0
3
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
3
0
3
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
2
1
0
0
0
0
1
0
0
0
2
0
2
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
2
0
0
0
0
2
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
1
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
3
2
0
2
3
2
0
0
0
0
1
0
0
1
2
0
2
0
0
0
0
0
2
0
1
1
2
2
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
3
1
0
0
0
0
0
0
3
1
0
2
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
2
2
0
2
0
0
2
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
3
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
2
4
0
2
0
0
2
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
1
2
1
0
0
0
3
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
1
0
0
1
0
2
0
0
0
0
1
0
0
2
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
1
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
1
0
0
0
0
0
0
1
0
0
1
2
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
3
1
2
0
1
1
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
2
0
0
3
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
2
2
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
2
2
1
0
0
0
2
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
1
1
3
2
0
1
0
3
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
1
9
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
2
0
1
1
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
2
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
4
0
0
2
3
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
2
1
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
1
0
2
0
4
0
0
0
0
0
3
0
0
0
0
4
0
0
1
2
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
1
0
3
2
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
2
2
1
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
1
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
2
2
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
2
1
0
2
0
0
0
0
0
0
1
1
0
0
0
2
2
0
4
0
2
0
0
2
0
0
0
0
0
1
0
3
5
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
2
0
1
0
0
0
0
1
1
0
2
0
0
1
0
0
3
0
2
0
3
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
5
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
3
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
3
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
1
0
0
0
1
0
0
0
0
2
0
0
2
0
2
0
1
0
0
0
0
0
0
3
2
0
1
0
2
2
0
0
0
0
1
0
0
8
0
2
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
3
0
1
0
0
0
1
0
2
0
2
1
0
0
0
1
0
0
2
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
2
0
0
0
0
3
1
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
1
0
2
0
0
0
2
1
0
1
0
3
0
0
2
0
0
0
0
2
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
3
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
2
2
0
0
1
0
1
0
0
1
1
4
0
1
0
0
0
2
0
0
0
2
0
0
1
0
0
2
2
0
2
0
0
1
0
0
2
1
0
2
0
0
1
0
1
3
0
0
0
2
0
0
2
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
2
0
1
2
0
0
1
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
1
2
0
0
0
1
1
0
1
1
2
2
3
0
0
0
1
0
2
0
0
0
0
0
1
0
3
1
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
3
0
0
1
2
1
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
2
0
0
5
0
0
0
0
0
1
0
0
1
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
4
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
1
0
0
2
1
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
1
2
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
5
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
2
0
2
1
0
0
1
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
3
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
2
0
2
0
0
3
2
0
2
0
0
2
0
0
0
4
0
1
0
2
2
0
0
1
0
0
1
0
0
0
0
3
1
0
1
0
0
2
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
2
2
0
1
2
0
0
0
0
0
2
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
2
0
0
2
1
0
2
1
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
6
0
0
2
0
1
0
0
0
2
0
2
0
1
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
1
3
0
0
0
0
0
0
3
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
3
0
0
0
0
4
1
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
2
0
1
0
0
0
0
0
3
2
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
2
1
0
1
0
2
2
0
0
0
0
2
2
1
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
2
3
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
2
1
0
1
0
0
1
0
1
0
2
0
1
0
2
2
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
2
0
1
0
3
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
2
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
2
2
0
0
0
3
0
0
0
1
0
0
0
2
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
2
1
0
0
0
0
2
0
3
0
0
0
2
0
0
1
0
1
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
1
0
2
0
0
0
2
2
0
2
0
2
0
2
0
0
2
1
0
0
0
2
2
0
0
0
0
0
1
1
0
0
3
0
3
0
0
0
0
2
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
3
0
2
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
1
2
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
1
1
0
2
2
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
7
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
4
1
2
1
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
1
0
0
2
1
1
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
3
2
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
3
0
1
0
1
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
1
1
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
2
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
3
0
2
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
2
0
1
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
2
0
2
0
0
0
2
0
0
0
0
0
0
3
0
0
1
0
1
0
0
0
2
0
2
1
0
0
0
0
4
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
3
0
2
0
2
0
1
0
2
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
12
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
2
0
1
0
0
4
1
0
0
0
0
0
1
0
1
1
1
0
0
2
1
0
2
0
2
1
0
0
0
0
0
2
0
1
0
0
1
1
3
1
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
1
1
0
0
0
0
0
2
0
1
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
3
0
0
1
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
3
0
2
2
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
5
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
1
0
1
1
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
1
2
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
3
0
0
0
0
0
0
0
4
1
0
1
1
0
0
6
0
1
0
0
1
0
2
0
3
0
0
0
0
0
1
3
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
1
0
1
0
0
0
2
0
1
1
2
1
1
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
2
2
0
0
0
0
0
0
1
0
1
2
2
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
2
0
1
0
0
1
0
0
1
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
1
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
2
2
0
1
0
0
0
0
0
0
0
0
0
0
1
3
3
0
1
0
0
2
0
0
1
0
1
1
1
0
2
0
0
0
1
0
0
0
2
2
1
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
2
0
0
0
0
0
1
0
2
0
1
4
2
0
0
0
0
2
2
0
1
0
1
2
0
0
0
0
1
1
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
1
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
2
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
1
1
0
0
0
0
4
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
1
0
0
1
1
0
0
0
2
2
0
0
2
2
0
2
0
0
0
2
2
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
2
1
1
0
0
0
2
0
2
1
2
0
0
0
0
2
0
0
1
2
0
0
0
3
1
0
0
0
2
1
0
0
0
0
1
1
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
4
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
2
1
0
1
0
0
0
2
0
0
0
1
7
0
1
0
0
1
2
0
0
0
0
1
2
0
0
0
2
1
0
0
1
0
0
0
0
0
5
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
2
0
3
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
2
0
0
1
1
0
1
0
2
0
0
3
0
0
2
1
6
0
1
2
0
0
0
2
0
2
4
0
0
0
0
1
0
0
3
0
0
0
2
1
1
0
0
0
2
0
0
2
2
0
0
0
0
2
0
0
2
0
2
3
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
7
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
1
1
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
5
0
0
1
1
2
0
0
0
2
2
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
1
0
0
0
1
2
2
0
2
0
0
2
1
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
3
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
2
2
0
1
1
2
0
0
1
2
0
0
0
0
1
0
0
0
2
0
2
1
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
11
2
2
0
0
0
2
0
0
5
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
2
0
6
1
0
0
0
3
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
4
2
0
2
2
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
1
2
1
2
0
0
1
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
3
0
0
3
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
2
2
2
0
1
0
2
1
2
0
1
0
0
0
1
0
0
0
0
0
1
1
2
0
0
0
0
0
0
1
0
2
3
0
1
0
0
0
0
2
0
5
0
0
0
0
2
0
0
0
0
2
2
0
0
1
0
0
1
2
0
0
0
0
4
0
1
0
0
1
0
0
1
0
0
2
0
2
0
0
0
0
0
0
2
1
0
0
0
3
0
1
3
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
1
2
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
1
0
1
0
0
0
1
0
2
0
0
0
0
1
0
0
2
0
0
0
2
1
1
3
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
2
0
1
0
1
2
0
2
1
2
1
0
0
0
0
0
3
0
1
0
0
0
0
0
0
2
0
0
0
0
3
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
3
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
1
1
4
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
2
0
0
0
0
3
0
1
0
0
2
0
2
0
1
0
0
0
0
1
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
7
0
0
2
0
0
0
0
0
0
1
2
0
1
0
1
4
0
0
0
0
0
0
3
3
1
0
0
0
0
1
0
0
2
0
2
0
0
0
0
1
1
0
0
1
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
1
2
0
0
0
2
2
1
0
2
0
2
0
0
0
0
0
1
0
1
1
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
1
1
0
0
0
1
1
0
0
1
0
0
0
10
3
1
0
0
2
1
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
5
0
0
0
0
0
0
1
0
1
0
0
0
2
1
0
0
2
0
4
2
0
0
2
0
3
1
1
0
2
0
0
1
1
0
0
0
0
0
1
0
0
2
2
0
0
0
1
1
0
11
0
0
0
6
1
1
1
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
1
0
0
1
2
1
2
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
3
2
0
0
0
0
0
0
0
0
1
1
1
0
0
0
2
1
0
2
1
1
0
0
0
0
0
2
3
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
1
0
1
1
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
3
0
2
0
0
0
1
1
0
2
0
2
0
0
0
1
1
0
0
0
0
2
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
1
1
0
0
2
0
0
0
2
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
2
0
0
0
2
1
0
0
0
4
2
0
2
2
0
0
6
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
4
0
0
0
0
0
1
0
0
0
1
0
0
1
1
3
2
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
1
0
1
0
2
0
1
0
0
2
0
1
0
0
0
2
0
0
0
1
1
0
3
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
2
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
2
0
0
0
2
0
1
0
0
0
0
2
0
0
1
0
0
5
0
0
0
0
0
1
2
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
2
0
4
1
2
2
2
0
1
0
0
0
1
1
0
2
0
2
0
0
0
0
3
1
0
0
0
1
2
0
0
2
0
1
0
0
0
0
1
1
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
2
0
2
1
0
0
0
0
0
0
0
3
0
2
0
0
0
1
0
4
2
1
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
3
5
0
0
2
0
2
0
0
0
0
1
1
0
0
0
1
0
1
0
8
0
0
0
0
0
1
0
1
1
0
1
0
7
0
1
0
0
0
0
1
0
0
0
0
1
2
0
0
2
0
0
0
0
1
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
3
0
0
0
2
0
0
2
0
0
2
0
0
8
4
2
1
0
0
1
2
0
0
0
0
1
1
0
0
2
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
3
0
1
1
0
0
0
0
0
1
0
1
0
1
5
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
6
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
1
0
2
0
2
0
0
4
0
1
0
0
0
2
1
1
1
0
0
3
0
1
1
0
1
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
2
0
2
1
0
0
0
2
2
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
8
0
0
1
0
1
0
0
0
0
3
0
0
0
0
0
0
0
2
1
2
2
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
3
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
1
1
0
2
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
3
1
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
1
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
4
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
4
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
1
0
0
0
2
3
2
2
0
2
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
2
1
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
1
0
0
0
0
1
1
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
2
0
0
0
0
1
0
5
0
0
1
0
0
0
0
0
2
0
1
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
2
0
0
3
2
0
0
0
0
2
1
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
2
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
2
1
1
0
2
1
0
0
0
1
3
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
2
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
2
2
1
0
0
1
0
0
2
0
0
2
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
5
4
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
2
3
1
0
0
4
0
0
0
0
0
1
0
0
2
0
0
2
0
2
0
1
0
0
0
0
0
1
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
2
0
1
1
0
0
25
1
1
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
5
2
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
2
1
0
0
1
0
0
2
1
3
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
3
0
0
1
0
0
1
0
0
0
2
2
0
0
0
0
5
0
2
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
1
0
1
0
0
2
0
0
0
1
0
0
0
0
0
4
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
1
1
1
2
1
4
0
0
0
4
0
0
1
0
1
0
0
0
0
0
1
0
0
0
2
0
1
2
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
2
0
2
3
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
1
2
0
0
0
0
0
1
1
0
1
1
2
1
0
0
0
1
0
0
0
0
1
0
0
2
3
2
2
0
0
0
0
1
2
0
0
1
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
2
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
3
2
1
0
0
0
0
0
0
0
0
2
0
0
0
2
5
0
0
2
0
0
1
1
0
0
0
0
0
0
1
1
2
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
3
3
0
1
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
2
2
0
0
1
1
0
2
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
2
0
0
1
1
2
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
2
0
0
0
0
1
0
0
0
0
2
2
2
0
1
2
0
0
0
2
0
1
0
0
0
0
2
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
3
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
2
1
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
1
0
0
0
2
0
1
2
0
1
1
1
0
0
0
0
0
0
4
0
0
0
0
0
2
0
3
0
2
0
0
0
0
0
1
0
1
0
0
0
0
2
0
1
0
0
2
0
2
0
0
0
0
3
0
2
1
0
1
2
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
1
1
0
0
1
0
5
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
2
0
1
0
1
3
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
2
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
7
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
5
0
1
0
0
0
1
1
0
0
1
0
0
0
1
0
1
0
1
0
2
1
1
0
2
0
2
0
0
0
1
0
0
0
2
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
1
1
0
2
2
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
4
0
2
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
1
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
1
2
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
2
0
0
0
4
1
0
0
2
1
3
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
1
0
1
0
0
2
0
1
0
0
1
0
0
1
0
2
0
1
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
2
0
1
0
0
1
0
1
0
2
1
0
2
0
0
0
0
0
0
1
1
0
0
0
1
1
1
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
1
0
0
0
0
4
1
0
0
1
0
1
0
0
0
2
0
2
2
2
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
2
1
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
1
0
0
3
0
0
0
0
9
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
2
0
2
0
0
2
0
0
0
0
2
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
2
0
2
0
0
0
1
1
0
2
0
1
0
0
0
1
0
1
0
0
0
0
0
3
0
0
0
0
2
1
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
1
0
2
2
2
0
0
0
1
1
2
0
0
0
0
1
0
0
0
1
0
2
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
2
0
0
0
0
1
2
0
0
0
1
0
2
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
2
2
0
0
1
1
0
0
0
0
0
2
0
2
2
0
0
3
0
0
0
0
2
2
0
1
0
0
1
0
2
0
0
0
0
0
2
2
0
1
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
2
2
0
0
0
0
0
0
3
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
1
2
1
2
0
0
1
2
0
0
2
0
0
1
0
0
0
2
1
0
0
2
0
0
0
2
3
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
6
2
0
2
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
2
3
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
4
0
0
1
0
1
2
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
2
3
0
2
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
1
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
3
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
2
0
0
2
2
2
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
2
0
1
0
0
2
0
2
0
0
0
0
0
0
2
1
0
2
0
0
4
0
2
1
2
0
1
0
1
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
2
0
2
2
2
0
0
1
0
0
0
2
2
0
2
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
1
2
2
0
1
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
1
2
0
0
0
2
0
0
0
0
4
0
0
0
0
13
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
5
0
5
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
1
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
5
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
3
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
4
4
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
5
0
0
0
2
1
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
3
2
1
2
0
1
0
1
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
2
0
0
1
2
0
0
0
0
0
0
0
2
1
1
1
0
0
0
0
1
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
3
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
2
0
0
0
1
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
1
0
1
2
0
2
2
2
0
0
0
1
2
0
0
0
2
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
2
2
0
1
1
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
1
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
3
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
2
2
0
1
2
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
2
0
0
0
0
0
3
2
1
0
0
0
2
0
2
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
2
2
0
0
0
2
1
0
0
0
0
0
0
1
0
0
2
0
1
2
1
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
1
1
0
0
1
0
0
0
0
1
1
0
3
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
1
0
1
1
0
1
0
0
0
2
1
0
0
2
0
1
0
0
0
0
0
2
1
1
0
2
3
2
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
2
0
0
0
0
3
1
0
0
2
0
0
1
1
0
0
0
0
2
1
2
0
0
3
0
0
0
0
1
2
0
0
1
1
0
0
0
0
2
0
0
0
3
2
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
5
1
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
3
0
2
3
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
3
2
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
2
6
0
0
0
0
1
0
0
4
0
1
0
0
0
0
0
2
1
0
0
1
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
1
2
2
0
0
0
0
2
1
1
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
2
2
1
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
3
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
1
2
0
2
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
3
3
0
1
0
1
0
1
0
2
2
0
0
0
2
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
1
1
0
2
1
0
0
0
0
0
0
0
2
0
1
3
0
1
0
0
0
1
2
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
3
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
5
0
0
0
0
3
2
0
0
2
0
0
1
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
3
1
2
0
1
0
0
1
0
4
0
0
0
2
0
0
1
2
2
1
0
2
0
3
0
0
0
5
0
0
0
0
0
6
0
0
0
0
0
1
3
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
1
0
0
2
0
0
2
1
1
0
0
1
0
2
0
0
1
0
0
0
2
1
0
0
0
0
0
1
2
1
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
5
0
0
0
0
0
1
1
0
0
0
0
0
0
2
1
2
0
0
0
1
1
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
3
0
0
0
0
2
1
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
3
0
1
1
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
2
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
2
2
0
0
0
0
0
3
2
0
0
0
0
0
0
2
1
0
0
0
2
0
1
0
0
2
0
0
0
2
0
0
0
0
1
0
0
1
1
0
0
0
0
2
0
0
2
1
2
0
0
0
0
0
2
0
1
0
0
2
8
2
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
2
0
0
3
1
0
2
0
2
0
0
0
1
0
0
0
1
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
2
1
0
0
0
2
2
0
3
2
1
2
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
1
0
0
2
0
0
0
0
0
0
0
0
4
1
0
0
0
0
1
0
1
0
1
4
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
5
0
0
1
0
0
0
0
0
1
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
3
0
0
0
1
1
0
0
0
2
0
2
0
0
0
0
0
2
0
0
1
0
0
0
5
0
0
0
0
0
0
2
2
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
3
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
2
3
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
1
2
0
0
0
0
0
1
0
2
1
0
0
1
0
0
1
0
0
0
2
1
0
1
2
0
0
1
0
0
0
0
3
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
3
2
1
0
1
0
0
1
0
0
2
0
4
0
2
0
0
1
2
1
0
0
1
1
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
1
1
0
1
0
0
0
2
1
1
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
2
0
2
0
1
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
2
2
1
0
0
0
0
2
0
0
0
0
0
0
0
1
2
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
3
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
2
2
0
0
0
0
1
0
0
0
1
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
2
0
3
1
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
2
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
2
2
1
0
0
0
0
0
0
1
1
1
2
0
0
0
0
0
0
1
1
7
0
2
2
0
0
0
0
0
0
0
1
0
0
2
2
1
1
1
3
0
0
1
1
0
1
1
1
1
0
0
2
2
0
0
1
1
2
0
0
0
0
2
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
1
2
0
0
0
0
1
1
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
3
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
1
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
1
0
0
3
0
0
0
1
1
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
4
1
0
0
1
2
1
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
1
2
1
0
1
0
0
0
4
1
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
2
2
0
2
0
1
0
0
0
0
0
0
1
1
1
0
1
2
0
3
2
0
0
2
0
3
2
2
0
0
0
1
2
0
0
2
0
0
0
5
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
4
1
4
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
2
1
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
5
0
0
0
2
0
1
0
0
0
0
2
0
2
0
0
0
2
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
2
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
3
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
3
0
1
0
0
1
0
0
0
1
0
2
1
0
1
0
1
1
0
3
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
1
1
3
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
1
0
0
0
2
1
0
1
0
0
2
0
1
2
1
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
2
0
4
0
0
0
2
0
0
0
0
0
0
10
0
1
0
2
0
1
0
0
2
1
0
0
1
0
0
2
0
0
0
0
2
0
2
0
1
2
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
1
2
0
0
1
0
0
0
0
0
0
2
1
0
0
3
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
2
0
0
0
3
0
0
1
0
1
1
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
1
1
0
0
0
0
0
2
4
1
5
0
0
0
0
0
0
1
0
0
0
0
0
0
5
0
0
0
1
0
0
4
0
0
2
2
0
0
0
0
0
3
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
2
1
0
2
1
0
0
0
0
0
0
5
1
1
3
1
0
0
2
0
0
0
0
2
1
4
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
5
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
2
0
0
0
1
2
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
1
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
2
1
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
2
2
0
0
1
0
2
3
0
0
1
0
0
0
0
0
0
2
0
2
5
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
1
1
0
1
2
4
1
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
1
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
2
2
0
4
1
1
0
0
0
0
1
4
0
0
0
2
1
0
0
0
0
1
0
1
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
1
2
0
0
2
2
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
4
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
2
0
2
3
0
0
1
0
0
3
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
3
1
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
1
3
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
1
2
2
0
1
0
0
0
0
0
0
2
2
2
1
0
0
0
1
0
0
2
2
2
2
0
0
0
1
0
3
0
0
2
0
2
1
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
3
0
0
2
2
0
1
0
0
0
0
2
2
0
1
0
0
0
0
1
0
2
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
1
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
2
0
2
0
0
1
2
0
1
0
0
0
1
0
0
0
0
0
1
0
0
2
2
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
1
0
1
1
0
1
0
0
0
1
1
1
1
2
0
0
0
1
0
2
0
1
0
0
0
0
2
0
0
0
0
0
1
1
0
0
1
0
0
2
0
0
0
2
0
2
0
2
0
1
0
2
0
0
1
0
0
0
0
0
2
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
3
0
0
0
1
0
2
0
1
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
8
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
6
0
0
0
0
0
0
0
1
0
0
1
2
0
0
2
3
0
2
3
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
1
2
0
0
2
1
0
0
1
1
0
0
0
0
1
0
1
2
0
2
0
0
0
1
0
1
1
1
2
2
1
0
0
0
1
1
0
3
0
0
2
0
4
0
0
1
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
1
2
2
0
0
0
0
1
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
2
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
1
0
1
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
2
4
1
0
2
0
0
0
0
0
0
2
0
0
1
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
7
0
0
0
5
2
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
1
0
0
0
1
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
1
0
1
0
0
2
0
2
0
2
0
0
2
2
1
1
0
0
1
1
1
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
1
2
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
3
0
7
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
1
0
1
0
2
0
1
0
0
1
0
1
0
0
2
2
1
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
3
0
0
0
0
1
1
0
0
1
0
0
0
2
0
2
0
0
0
6
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
9
0
0
1
2
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
1
2
0
0
0
6
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
1
2
0
2
0
0
0
33
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
1
2
2
0
0
1
2
0
1
1
2
2
1
0
5
0
2
0
0
1
0
0
0
0
1
0
2
0
3
0
0
0
1
0
0
2
0
0
2
2
0
0
0
1
1
1
1
1
2
0
0
2
0
2
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
2
0
0
2
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
1
1
0
0
2
0
0
2
0
0
0
2
0
0
0
0
1
0
0
1
0
2
0
1
2
0
0
1
0
0
0
0
0
0
0
3
1
0
4
0
0
0
0
1
0
0
1
2
0
0
3
0
0
1
0
1
4
2
0
0
1
0
0
1
0
0
2
0
0
0
1
0
0
1
1
0
0
0
0
3
1
0
1
0
1
0
1
1
0
0
0
0
0
0
0
2
1
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
1
0
0
0
0
1
0
0
1
1
1
0
1
0
2
0
2
0
2
1
2
0
0
4
0
1
0
0
0
2
2
0
0
3
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
1
1
1
0
0
0
0
1
1
0
4
0
0
2
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
2
0
0
0
3
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
3
1
0
0
0
0
6
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
2
0
0
2
1
0
1
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
3
0
0
0
0
0
0
1
0
1
0
0
1
3
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
3
0
2
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
2
2
1
0
0
2
2
1
0
0
0
0
0
0
1
0
4
0
2
1
0
2
4
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
3
2
2
1
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
1
0
0
2
1
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
3
0
0
0
0
2
1
0
0
0
3
0
1
2
1
0
6
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
2
0
2
3
1
2
0
5
0
0
0
0
1
1
0
0
1
1
0
2
0
1
2
0
0
2
1
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
2
5
0
0
0
0
6
0
0
0
0
0
1
0
0
2
3
0
0
1
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
2
0
0
1
1
0
0
0
0
0
0
1
1
0
0
1
2
0
0
0
0
0
2
4
0
0
2
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
2
0
0
1
1
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
3
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
1
0
0
2
3
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
2
2
1
0
0
0
1
0
2
2
2
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
1
0
0
1
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
1
0
2
1
0
0
1
0
1
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
2
0
0
2
0
0
1
1
2
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
1
0
0
2
2
0
0
4
0
0
0
0
0
0
0
3
1
0
2
0
2
0
0
3
0
0
0
0
0
1
2
0
0
4
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
2
9
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
2
1
4
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
1
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
5
2
0
1
0
4
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
3
2
2
1
0
0
0
0
1
0
0
0
1
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
2
0
0
0
0
1
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
2
2
0
2
8
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
1
0
0
1
2
0
0
0
0
0
2
0
2
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
2
2
4
0
0
0
0
0
0
5
0
0
1
0
1
0
0
0
0
0
0
0
4
2
0
2
0
0
1
4
0
3
0
0
2
0
1
3
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
3
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
1
0
0
0
0
2
1
1
2
0
0
1
2
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
2
0
0
2
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
1
0
2
1
0
0
1
1
0
0
0
1
0
0
0
0
2
0
0
0
1
2
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
2
0
0
0
0
0
0
1
0
0
2
0
0
1
1
0
0
1
0
1
0
0
1
1
0
0
2
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
3
0
2
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
3
0
1
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
1
2
0
0
2
2
0
0
2
0
0
0
0
0
0
2
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
4
0
0
0
0
2
0
1
1
0
0
0
2
1
1
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
2
0
2
0
2
0
0
2
0
0
1
0
0
2
2
0
0
0
0
2
0
0
0
3
1
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
2
0
0
0
0
2
1
0
2
0
0
1
0
0
1
0
1
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
1
0
3
2
2
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
1
2
0
2
4
0
1
0
2
0
0
2
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
2
0
2
1
1
0
0
1
2
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
2
0
0
2
3
0
1
0
2
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
2
0
2
2
0
0
2
0
0
0
0
1
0
0
0
1
0
5
1
0
0
1
0
3
1
1
0
2
0
0
1
0
0
3
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
5
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
6
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
2
0
4
0
0
1
2
0
0
2
0
2
0
0
0
1
1
3
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
4
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
2
1
3
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
1
0
1
1
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
2
1
0
5
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
7
0
1
1
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
1
2
0
0
0
0
1
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
1
0
0
1
0
2
1
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
2
1
1
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
1
0
0
2
0
1
0
0
1
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
1
0
2
5
0
0
1
0
0
0
0
0
0
0
0
4
0
2
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
2
0
3
0
2
0
0
1
2
0
2
0
0
0
0
0
0
2
0
2
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
1
0
2
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
3
1
0
2
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
2
2
0
1
1
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
3
0
2
0
0
0
2
0
2
0
1
0
0
1
2
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
1
5
0
1
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
1
0
2
1
0
4
0
0
2
1
0
1
0
2
1
2
0
1
0
2
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
2
0
0
0
2
2
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
3
0
2
3
2
0
0
2
0
3
1
2
1
0
0
0
0
1
1
1
0
0
0
0
0
2
0
0
0
0
1
0
2
0
2
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
1
0
0
1
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
2
0
0
2
0
1
0
0
1
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
3
0
2
0
2
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
1
2
0
0
0
3
2
3
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
6
0
0
0
0
1
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
1
0
2
1
2
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
3
0
2
0
0
0
0
0
2
0
0
1
0
1
0
0
2
2
0
0
0
0
1
0
0
2
0
0
0
0
0
1
2
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
1
0
1
1
0
2
0
2
0
0
4
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
3
2
3
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
3
2
0
0
1
0
0
0
1
2
0
0
0
1
2
0
0
0
0
0
1
0
0
0
3
1
0
1
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
1
1
1
0
1
0
0
0
0
1
0
2
0
0
2
0
7
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
3
2
0
4
0
0
0
2
4
3
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
2
1
0
1
0
5
2
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
1
6
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
2
0
2
0
0
0
0
0
1
0
0
1
2
0
0
0
2
1
1
0
0
0
2
1
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
1
0
2
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
2
0
1
1
0
0
0
0
0
0
2
0
0
1
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
2
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
1
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
2
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
2
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
2
1
0
1
0
0
2
2
2
1
0
1
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
6
0
0
0
1
0
0
0
1
0
6
0
0
2
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
3
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
5
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
2
0
0
1
0
0
0
1
0
0
0
2
0
2
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
2
1
1
2
1
0
1
0
0
1
0
0
0
2
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
1
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
1
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
1
2
0
2
0
2
2
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
1
3
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
2
1
1
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
2
2
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
1
2
1
0
0
0
0
0
2
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
1
0
0
2
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
1
2
0
0
0
0
0
2
0
1
0
0
4
0
0
2
2
0
0
2
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
2
0
1
0
2
0
0
0
2
0
0
0
0
0
1
0
2
2
0
1
0
0
0
0
0
1
0
3
0
0
0
0
0
1
0
2
0
2
2
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
6
1
0
0
0
1
0
2
0
2
2
3
0
0
0
0
0
0
1
0
0
2
2
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
1
0
2
0
0
2
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
1
0
1
0
0
2
0
0
1
2
0
0
1
0
0
1
0
4
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
2
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
1
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
2
0
0
2
0
1
0
1
0
0
2
0
0
0
0
0
1
3
2
0
0
2
3
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
3
1
1
2
0
0
0
2
0
0
0
2
0
2
0
1
1
0
0
1
1
0
0
1
1
3
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
1
2
0
1
0
0
1
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
2
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
2
2
0
3
2
0
0
0
2
1
0
3
0
2
0
0
5
0
1
0
0
0
0
0
2
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
1
0
0
0
0
2
2
0
0
1
0
2
1
0
1
2
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
2
1
0
1
0
0
0
3
0
0
2
0
0
1
0
0
2
0
0
0
5
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
1
0
0
0
2
1
0
2
0
1
0
0
2
4
0
0
2
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
1
1
2
0
2
0
0
0
0
1
2
0
1
0
1
1
0
0
0
0
0
0
0
0
3
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
2
2
0
0
2
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
3
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
1
2
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
1
1
0
0
1
2
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
3
0
0
2
0
0
2
1
0
0
1
0
0
0
2
1
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
1
0
1
0
0
2
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
2
0
0
0
4
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
2
0
0
1
0
0
0
0
2
0
1
0
0
0
2
3
0
0
2
0
1
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
1
2
1
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
2
0
0
0
1
0
6
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
4
0
0
3
0
0
0
0
0
0
1
1
2
0
0
0
0
0
1
1
1
0
1
0
0
0
0
1
0
0
0
0
3
0
1
0
0
0
2
1
0
0
0
1
0
1
0
1
1
1
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
1
0
1
0
0
0
3
0
2
0
0
0
1
0
0
1
0
2
0
0
2
0
0
0
0
1
2
2
1
0
0
0
4
5
0
1
0
1
0
1
0
0
0
0
0
2
0
0
2
2
0
0
0
0
3
0
0
0
0
0
0
0
0
2
4
0
0
0
1
2
2
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
1
0
0
0
1
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
1
0
0
2
2
0
0
0
2
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
2
2
0
0
0
0
0
1
0
0
0
0
1
0
0
2
2
0
4
2
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
5
0
0
0
0
0
0
3
0
1
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
7
2
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
3
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
2
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
4
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
1
0
0
0
3
3
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
2
2
0
1
0
2
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
2
3
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
1
3
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
8
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
1
0
1
1
2
0
0
1
0
4
0
0
0
0
0
0
3
0
1
5
0
0
0
1
0
0
0
1
0
2
2
1
0
0
2
0
0
2
2
0
0
0
1
2
2
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
3
0
3
0
2
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
4
2
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
1
3
1
0
1
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
2
0
0
2
1
1
2
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
2
2
2
1
0
0
0
1
4
0
0
2
0
0
0
4
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
1
2
0
3
0
0
2
0
0
0
0
0
0
0
2
0
5
2
1
0
0
0
1
1
2
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
2
2
1
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
3
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
2
0
0
1
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
1
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
2
1
2
0
0
2
14
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
1
2
0
0
0
2
0
2
2
0
1
0
0
0
0
1
0
2
0
2
0
0
2
0
0
2
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
4
1
1
0
2
1
0
1
0
0
2
0
0
0
1
0
2
0
0
0
0
3
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
3
1
3
1
1
0
0
1
0
0
0
2
0
3
1
0
0
0
0
0
2
1
0
0
2
0
0
2
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
4
0
2
0
0
0
0
0
0
1
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
3
0
0
1
0
0
0
2
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
2
2
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
2
2
0
2
0
0
2
1
0
0
0
2
0
0
0
0
1
2
1
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
2
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
2
0
0
1
1
4
0
0
0
2
2
0
2
0
0
2
0
2
0
1
0
1
0
0
0
2
0
2
0
0
3
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
5
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
3
0
0
1
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
2
2
0
0
0
1
2
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
2
1
1
2
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
2
0
1
1
1
0
0
0
0
0
2
3
2
0
0
1
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
2
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
2
0
0
2
1
2
0
0
0
1
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
2
0
0
0
1
1
0
0
0
5
1
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
1
1
1
1
1
1
0
0
0
0
2
0
0
0
0
0
4
0
0
0
3
1
0
0
0
0
0
0
1
0
0
0
0
0
3
0
3
1
0
0
2
0
0
0
2
2
1
2
0
0
0
1
0
0
3
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
3
0
1
0
1
1
0
0
2
0
0
4
1
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
3
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
1
2
3
0
0
2
2
0
0
2
0
1
0
0
3
2
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
1
0
0
0
2
0
0
1
1
2
2
1
0
0
0
0
0
4
2
0
2
0
1
2
0
0
0
2
1
0
0
2
0
0
2
3
0
0
0
2
2
0
0
1
0
0
0
1
0
0
0
2
2
2
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
3
0
2
3
0
0
1
1
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
2
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
2
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
3
0
1
2
0
0
0
0
0
0
2
0
0
3
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
1
0
0
2
0
0
2
1
0
0
3
0
0
1
0
0
0
0
0
0
1
1
0
0
7
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
2
2
0
0
1
0
1
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
5
0
2
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
4
0
0
2
0
1
1
1
1
0
0
0
0
0
1
0
0
2
0
1
0
0
2
0
1
2
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
4
0
3
2
0
0
2
0
0
2
1
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
3
0
0
1
0
0
2
0
0
0
0
0
1
0
0
3
2
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
2
1
2
4
0
0
2
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
2
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
5
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
1
0
0
0
0
1
0
2
0
0
1
1
0
0
0
0
1
0
2
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
2
0
1
0
6
2
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
3
0
2
0
0
1
7
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
2
2
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
1
1
0
0
0
1
1
0
0
2
1
4
2
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
2
4
0
0
0
0
0
0
0
0
2
1
0
0
0
1
2
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
1
0
0
4
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
3
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
2
3
0
0
0
1
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
2
0
0
1
0
0
1
0
0
1
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
2
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
4
2
2
1
0
0
0
0
0
0
2
0
0
0
1
1
2
0
0
2
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
1
1
0
2
1
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
1
2
0
0
7
2
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
2
2
0
3
0
0
0
2
0
1
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
2
0
0
0
1
0
1
1
0
2
0
1
1
2
1
0
0
2
0
1
2
1
1
8
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
7
3
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
5
1
0
0
0
0
0
0
0
0
1
1
0
2
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
2
0
1
0
0
0
1
0
0
2
0
0
0
0
1
0
1
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
2
0
1
2
0
1
0
0
2
1
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
3
1
0
1
1
0
0
0
0
0
0
2
0
1
1
0
2
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
2
0
0
1
0
5
0
0
0
5
2
0
0
0
2
0
0
1
0
0
2
0
4
0
2
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
2
0
2
0
2
0
2
0
2
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
1
2
0
0
0
0
2
5
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
1
1
4
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
1
1
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
1
2
0
0
1
1
2
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
1
0
2
0
0
3
1
0
0
0
1
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
3
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
2
3
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
2
1
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
1
0
0
0
0
0
0
0
2
0
0
1
0
3
0
0
0
4
0
0
0
0
0
0
3
0
0
2
2
2
0
0
0
0
1
0
0
1
0
0
0
0
2
0
2
2
0
0
1
0
0
2
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
1
1
0
0
1
0
1
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
3
0
2
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
2
0
0
1
3
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
2
2
0
0
0
0
0
0
0
1
0
2
0
1
0
0
1
1
3
0
0
0
0
0
0
0
4
0
0
2
0
1
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
1
2
0
3
2
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
2
2
1
0
0
0
0
0
0
2
0
2
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
1
3
0
0
2
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
1
0
2
0
1
1
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
7
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
7
0
1
0
0
0
2
2
0
1
1
0
1
1
0
1
0
0
0
0
0
7
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
2
0
2
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
2
1
2
0
2
0
0
0
0
0
1
0
0
0
2
0
2
2
0
0
0
0
2
3
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
1
0
2
1
0
1
0
1
0
1
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
3
0
1
2
0
1
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
2
3
0
0
0
0
0
2
0
8
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
3
1
1
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
2
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
2
3
0
0
0
0
0
0
0
0
2
0
0
3
0
0
2
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
4
1
0
0
0
0
0
0
2
0
0
0
2
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
2
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
2
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
2
0
0
1
2
2
2
0
1
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
2
0
0
2
1
0
1
1
2
0
0
0
2
1
1
0
0
2
0
0
2
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
1
0
2
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
1
0
0
0
0
2
0
0
3
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
3
1
0
0
2
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
2
1
0
0
2
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
1
0
0
0
2
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
1
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
2
0
2
0
1
1
0
0
0
3
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
5
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
1
4
2
0
0
0
8
0
0
1
0
1
0
0
2
0
2
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
1
0
2
0
1
0
1
0
0
0
1
0
0
0
1
0
4
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
1
0
4
2
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
3
2
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
1
1
0
0
2
3
0
2
0
1
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
2
0
0
0
0
1
0
2
2
0
2
0
0
1
0
0
1
0
0
2
1
0
0
0
0
0
3
1
1
2
0
0
1
0
0
0
0
2
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
1
0
1
0
2
1
0
2
1
0
2
0
2
0
1
0
2
0
2
1
1
0
1
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
4
0
2
0
2
1
1
2
0
1
0
0
0
0
1
1
0
2
0
1
0
0
0
1
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
1
0
1
2
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
2
1
2
1
0
1
0
0
0
0
5
0
1
0
2
1
0
0
0
0
0
2
2
0
0
2
1
0
2
3
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
4
0
2
1
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
2
0
0
3
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
2
2
0
4
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
1
0
1
2
2
0
0
0
0
0
1
2
2
0
6
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
2
0
0
1
0
1
0
3
1
1
0
0
0
0
3
0
0
1
0
0
0
1
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
1
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
3
0
0
0
0
1
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
4
0
0
0
1
0
4
0
0
0
0
1
1
0
0
1
2
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
3
3
1
0
2
2
2
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
2
0
0
1
0
0
2
2
0
0
0
0
0
0
2
0
1
0
0
0
2
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
2
2
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
5
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
2
0
0
0
2
0
0
4
0
0
0
0
2
0
1
0
3
0
2
1
2
0
0
0
4
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
1
1
0
0
0
0
0
2
1
0
3
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
1
0
1
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
5
2
2
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
3
2
0
2
0
0
3
0
0
2
0
0
5
3
0
0
2
1
0
2
0
1
0
0
0
0
0
0
0
0
4
0
0
2
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
1
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
5
0
1
0
0
0
1
0
2
2
0
1
0
0
0
0
0
2
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
3
1
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
2
0
0
2
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
1
2
2
0
0
0
2
0
3
0
0
0
1
1
2
0
0
1
0
2
0
0
0
2
0
0
1
1
0
2
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
2
3
0
4
0
0
4
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
3
0
1
0
0
0
1
0
1
1
1
1
0
1
0
1
0
0
0
2
1
0
0
1
2
0
1
0
2
0
2
0
1
0
0
0
1
0
0
0
0
0
0
3
2
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
2
2
1
0
1
0
2
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
1
5
2
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
1
0
0
0
2
0
0
0
0
1
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
1
2
0
0
0
1
2
1
2
0
0
0
1
0
0
2
2
2
0
2
0
0
2
0
0
0
1
1
0
0
0
0
0
3
0
0
2
0
0
0
0
0
2
2
0
2
2
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
3
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
4
1
0
0
0
2
0
0
1
0
1
0
1
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
2
1
0
0
0
0
0
1
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
1
0
0
2
0
0
0
0
0
1
0
2
2
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
2
0
3
0
0
0
0
0
0
4
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
3
0
1
1
0
0
2
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
2
0
2
2
0
0
2
0
0
0
1
1
0
2
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
1
1
0
1
0
0
1
0
0
0
0
0
2
0
2
0
1
1
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
4
1
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
2
0
2
2
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
1
1
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
1
2
0
2
0
0
0
0
1
2
2
0
0
0
0
2
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
2
0
3
0
0
0
0
1
0
2
0
0
0
1
2
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
2
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
1
2
2
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
2
2
0
0
0
1
2
1
0
2
0
0
0
0
0
0
5
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
2
0
1
0
1
0
0
0
0
0
1
0
0
1
0
1
0
1
3
0
0
0
0
0
0
0
2
2
0
1
1
1
0
0
0
1
1
2
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
2
2
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
2
1
2
2
0
0
0
0
0
0
0
1
0
1
0
1
3
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
1
0
1
2
0
0
1
0
0
3
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
1
0
0
3
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
3
2
1
2
1
3
1
1
2
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
1
1
0
0
0
0
1
0
1
0
1
1
0
1
0
2
1
0
0
0
1
0
0
0
2
0
0
0
0
0
4
0
0
0
3
0
1
1
0
0
0
2
0
0
0
1
2
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
2
0
5
2
0
0
1
0
2
0
1
0
0
2
2
0
0
0
0
2
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
1
1
3
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
3
0
0
0
0
0
2
0
0
0
0
5
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
1
0
1
2
0
2
2
2
1
2
0
1
1
0
0
0
2
0
0
2
1
0
4
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
2
0
2
0
2
0
1
1
0
1
0
0
1
0
0
2
0
0
0
2
0
0
0
0
3
0
1
1
1
1
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
1
0
3
1
0
0
0
0
0
1
1
0
0
1
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
1
1
0
0
0
0
0
0
0
2
1
1
0
0
0
0
1
1
0
0
1
0
1
0
0
2
0
0
0
0
0
0
1
0
2
0
3
2
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
1
0
2
0
1
2
0
0
0
1
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
2
0
2
0
0
1
0
2
0
1
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
9
0
0
2
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
3
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
2
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
1
7
2
0
0
0
1
3
1
0
0
0
3
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
1
0
0
0
0
3
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
2
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
2
0
0
1
0
2
2
0
2
0
2
0
0
0
0
2
0
3
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
5
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
1
0
2
0
0
1
0
0
0
2
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
6
2
1
0
0
0
0
0
0
0
3
2
0
0
0
1
0
0
0
1
0
0
0
3
0
1
3
2
0
1
0
0
0
0
0
2
3
1
2
0
1
0
3
1
0
0
0
1
0
2
1
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
1
2
1
0
0
2
0
2
0
1
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
2
0
0
0
0
0
0
3
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
1
1
2
0
0
0
0
0
0
2
1
0
9
2
0
0
0
0
0
1
0
2
0
0
1
1
0
0
0
3
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
1
2
0
1
1
0
0
2
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
2
1
0
9
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
1
0
0
1
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
2
3
0
2
1
0
1
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
4
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
7
0
0
0
0
0
2
1
0
0
2
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
1
0
2
1
1
0
0
0
0
0
0
0
0
0
3
0
0
0
2
2
2
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
1
0
1
0
0
2
0
0
0
0
0
2
2
0
2
0
2
2
0
2
2
0
0
0
0
1
0
1
2
0
0
2
0
0
1
0
0
1
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
3
1
0
0
0
0
0
0
1
0
2
2
1
0
3
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
1
1
0
0
0
1
2
0
0
0
0
0
2
1
3
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
1
0
2
0
0
1
1
0
1
0
1
1
0
0
1
2
0
0
0
3
1
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
2
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
1
0
2
3
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
2
2
2
0
0
2
1
2
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
2
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
4
0
0
1
0
0
0
0
1
1
0
0
0
2
0
0
0
2
3
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
1
0
0
0
0
0
1
2
0
0
0
2
0
0
1
0
1
2
0
1
0
1
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
2
2
0
0
1
0
0
0
0
1
0
0
1
0
0
0
4
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
2
0
1
0
0
0
0
2
0
0
0
0
2
0
0
2
1
0
0
1
1
3
0
1
0
0
4
0
0
0
0
2
0
0
0
1
0
1
0
0
2
2
0
0
0
4
0
1
2
0
2
2
0
2
1
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
3
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
2
0
0
0
0
0
2
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
2
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
2
2
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
2
0
5
0
0
2
1
0
0
1
0
3
0
0
1
0
0
0
0
0
1
2
0
2
0
2
2
0
0
0
2
0
1
2
0
0
0
0
0
1
0
0
0
0
0
2
2
0
2
0
0
2
0
0
0
2
0
0
0
0
0
1
0
1
2
0
0
0
1
2
2
1
0
1
1
0
0
0
0
1
0
2
2
0
0
0
0
0
1
1
2
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
2
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
1
2
2
0
0
0
2
0
0
1
0
0
0
0
1
2
3
1
1
0
0
2
0
2
1
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
1
2
0
0
1
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
3
0
1
0
0
0
0
0
1
2
0
0
0
1
0
2
2
0
2
2
1
0
0
1
1
0
0
0
1
0
0
0
1
2
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
1
4
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
1
1
2
1
0
0
0
0
2
0
1
0
0
2
0
0
2
0
2
0
0
2
0
0
0
0
1
0
0
0
2
0
0
3
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
5
1
0
1
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
4
0
0
2
0
0
0
0
2
0
0
2
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
4
0
1
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
3
2
0
0
0
0
0
1
0
4
0
0
3
0
2
1
0
0
2
0
0
0
0
0
1
0
1
0
0
2
2
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
2
0
0
0
0
3
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
2
0
1
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
3
1
1
0
0
0
0
1
0
0
0
0
3
0
0
2
0
0
0
0
0
0
2
0
0
1
0
2
1
0
2
0
2
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
2
0
1
0
0
0
2
2
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
1
1
0
0
0
0
1
0
2
3
0
0
2
0
1
0
0
0
2
0
0
0
0
0
2
0
0
2
1
1
7
0
0
0
0
2
2
0
1
0
2
2
1
0
0
0
0
1
0
1
2
0
0
0
0
0
0
2
2
0
1
0
1
0
0
1
0
0
0
0
0
5
0
0
0
2
0
0
0
0
2
0
0
2
0
0
1
0
2
0
0
1
0
1
0
0
3
2
0
1
0
0
0
2
0
0
0
0
0
0
0
1
1
2
0
0
2
0
1
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
1
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
1
0
1
0
0
0
0
0
0
2
3
0
2
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
1
0
0
0
1
0
16
0
2
3
0
1
0
0
1
0
0
0
2
0
0
0
2
0
0
2
0
2
0
1
3
4
0
0
0
1
0
0
1
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
2
1
2
0
0
1
0
1
3
0
1
1
0
0
1
2
0
2
0
2
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
1
2
0
1
0
2
0
1
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
2
0
0
1
1
1
2
0
1
0
0
0
0
2
0
2
2
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
1
2
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
2
0
0
0
1
0
1
0
1
0
1
1
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
7
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
1
0
0
0
2
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
2
1
2
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
2
0
0
0
2
0
8
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
1
0
1
3
0
0
0
2
0
0
0
0
2
1
0
0
3
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
2
2
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
2
0
1
0
0
1
0
2
0
0
0
1
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
5
0
1
0
0
0
2
0
0
0
2
0
1
0
1
2
0
0
2
0
0
0
0
1
0
0
0
0
3
0
0
3
0
2
2
1
1
1
0
0
0
0
0
1
1
0
0
0
0
1
2
1
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
1
1
1
0
0
0
2
1
0
1
0
0
0
1
0
1
0
2
1
0
0
0
0
0
1
4
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
3
0
0
0
0
0
0
0
0
2
0
2
0
2
0
1
1
0
2
0
5
0
1
0
1
1
0
0
0
0
0
0
2
0
1
0
2
3
0
0
2
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
1
2
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
2
0
0
0
1
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
2
0
0
0
1
0
0
0
2
0
0
0
0
0
1
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
2
1
0
1
0
0
0
8
0
1
0
2
0
0
4
2
2
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
1
2
1
2
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
1
0
0
2
0
0
0
0
0
0
7
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
3
2
0
0
0
2
0
2
0
2
0
0
0
0
1
0
0
2
0
0
3
0
0
1
0
1
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
3
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
1
0
0
2
1
0
1
0
0
0
0
0
0
2
3
2
1
2
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
2
2
3
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
3
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
6
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
3
0
0
0
0
0
2
2
0
2
0
1
2
2
3
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
2
0
0
2
2
0
2
0
1
0
3
0
2
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
2
0
2
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
2
1
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
1
1
1
0
0
0
0
0
2
0
0
0
3
1
0
0
0
0
0
2
1
4
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
3
0
0
1
0
2
0
0
2
0
0
0
1
0
0
0
2
0
1
5
0
0
0
0
0
2
0
0
3
0
0
4
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
1
0
0
0
5
0
0
0
0
0
0
1
1
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
1
4
0
1
0
0
1
2
2
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
1
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
3
0
0
0
3
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
5
0
0
1
1
0
0
0
1
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
3
0
0
0
0
2
1
0
0
0
0
0
1
0
2
0
0
0
2
0
0
2
0
0
0
2
2
1
0
0
1
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
1
1
0
2
0
0
3
1
0
0
2
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
2
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
9
0
0
2
0
0
2
3
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
3
3
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
4
0
1
0
0
0
0
1
1
0
0
1
1
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
3
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
2
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
4
0
2
2
0
0
0
0
0
0
4
0
1
0
0
0
0
2
1
0
0
0
0
0
0
3
0
0
0
1
1
0
0
2
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
1
3
0
0
0
0
2
1
0
0
0
4
3
0
0
0
0
1
0
2
0
0
0
2
0
0
0
1
0
0
0
0
1
2
0
1
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
2
1
0
0
0
0
1
2
0
0
1
0
0
2
1
1
0
0
1
0
0
0
1
0
2
0
0
0
2
1
2
2
0
0
0
0
0
0
3
2
0
0
4
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
1
0
0
0
0
0
0
1
2
1
0
2
1
0
0
0
0
1
1
2
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
1
6
2
0
0
1
4
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
1
2
0
0
0
0
0
0
0
2
1
0
0
1
2
2
1
0
1
0
0
0
0
0
2
1
2
0
0
0
3
2
2
2
0
0
0
0
0
1
0
1
0
0
1
2
1
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
2
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
4
0
0
0
0
0
3
1
1
0
6
0
0
0
0
0
0
0
4
0
0
0
0
1
1
1
0
0
0
2
2
0
0
2
0
3
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
1
2
0
2
0
0
3
0
2
0
0
1
0
0
1
2
1
0
0
0
1
0
2
1
0
0
0
3
0
2
0
0
2
0
0
1
4
0
0
0
2
0
0
1
0
0
1
0
0
0
0
1
0
2
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
2
0
0
3
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
2
3
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
1
0
0
0
0
0
2
0
0
0
2
0
2
0
0
2
0
1
2
2
0
0
0
1
0
0
0
0
1
0
1
0
0
1
1
0
1
0
0
0
0
0
0
2
0
1
0
0
0
1
0
1
1
1
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
3
0
1
0
1
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
1
0
0
0
2
2
0
0
2
0
1
0
0
0
0
3
0
0
1
1
0
0
0
0
2
0
2
2
2
0
0
0
0
0
0
0
0
0
0
2
5
0
0
0
2
1
1
1
0
0
0
3
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
1
0
0
0
0
1
0
2
0
0
5
0
1
2
0
2
0
0
0
0
0
0
0
2
1
5
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
1
3
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
2
2
1
1
0
1
2
2
0
0
2
0
0
0
0
0
0
2
0
2
0
1
2
0
0
1
1
0
0
0
1
0
0
2
0
1
0
0
0
0
2
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
7
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
1
0
2
0
0
0
1
0
2
0
1
2
2
1
0
0
0
0
1
0
0
0
1
1
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
2
2
0
4
2
2
0
0
3
2
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
2
0
0
0
0
1
0
2
0
6
0
0
2
0
0
0
0
1
0
1
0
2
0
0
0
0
0
6
1
0
0
0
0
0
0
0
0
0
0
8
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
1
2
0
0
0
0
1
0
0
0
2
0
3
0
1
0
0
0
0
4
0
2
0
2
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
3
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
1
0
0
0
1
0
2
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
1
0
2
0
0
0
0
1
0
0
0
0
1
0
8
0
0
1
0
0
0
0
1
3
0
1
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
2
0
0
1
0
1
0
3
0
0
0
1
0
0
0
0
3
0
0
2
0
1
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
1
0
0
0
1
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
2
2
0
2
0
0
0
0
0
0
1
0
1
0
1
0
0
0
3
0
0
1
1
0
0
0
2
0
0
0
0
2
0
0
0
0
5
0
0
0
0
0
0
0
1
2
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
2
0
1
2
0
0
0
0
0
2
0
1
0
2
1
2
0
2
2
0
0
0
0
0
2
0
0
2
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
3
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
5
2
0
0
0
1
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
2
0
3
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
1
1
1
0
0
1
0
2
2
1
0
2
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
2
2
1
0
0
2
0
0
0
0
1
2
0
0
4
2
0
0
0
1
2
0
0
2
0
0
0
0
0
1
0
0
1
0
0
2
2
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
1
0
0
1
0
2
0
0
0
0
0
2
0
0
0
2
1
3
0
0
0
0
0
0
2
0
0
2
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
1
0
0
2
0
1
1
1
0
2
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
3
0
0
0
0
2
0
1
0
0
0
0
0
1
0
1
0
1
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
1
0
0
1
0
0
2
0
7
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
1
0
2
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
3
0
2
0
2
0
1
0
0
2
0
0
2
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
3
2
2
2
0
0
0
2
0
0
2
0
2
0
0
1
0
1
0
0
2
0
0
0
0
1
2
0
0
0
2
0
2
0
1
0
0
0
2
0
2
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
3
0
0
2
0
0
0
2
2
0
0
0
0
1
0
2
0
0
3
0
0
0
0
0
0
2
1
0
1
0
0
1
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
1
1
1
2
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
2
0
0
0
0
1
2
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
2
1
1
2
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
3
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
1
0
0
3
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
1
2
0
0
0
1
0
0
0
0
0
2
2
2
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
2
0
2
0
0
1
2
0
1
0
0
0
2
4
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
1
0
1
0
0
0
0
0
0
1
0
1
5
1
0
2
0
0
1
0
1
2
3
1
0
2
0
0
0
3
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
1
1
0
0
2
0
0
2
0
2
1
0
2
0
2
0
3
0
0
0
0
0
0
0
2
1
2
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
2
2
3
2
0
0
0
0
4
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
1
1
0
0
0
1
0
0
2
0
0
5
0
1
2
3
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
2
0
0
1
0
0
0
0
2
0
0
0
1
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
2
0
0
2
1
2
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
2
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
3
0
3
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
1
2
0
1
2
0
0
1
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
2
4
0
0
0
1
2
0
0
0
0
0
0
0
1
2
0
0
2
2
0
4
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
1
0
0
0
0
1
2
0
0
0
0
1
0
0
0
2
0
2
0
2
0
1
0
0
0
1
2
0
0
0
0
0
3
1
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
1
1
1
0
0
2
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
1
0
3
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
4
0
0
0
0
0
1
1
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
1
1
0
0
1
0
2
2
0
0
0
2
0
0
4
1
0
0
0
0
0
0
0
0
0
1
1
1
2
2
0
2
0
1
0
1
0
0
2
0
2
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
2
2
0
0
0
1
0
1
0
2
2
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
1
1
0
2
0
0
0
2
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
5
0
0
0
0
0
0
0
0
1
3
0
1
0
0
0
0
2
2
1
3
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
2
0
2
0
0
1
0
0
0
1
0
3
2
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
1
0
2
0
0
1
0
1
2
0
0
3
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
3
0
0
1
2
1
0
0
0
2
0
0
0
3
1
2
0
1
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
3
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
1
1
0
0
3
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
1
1
0
0
3
1
0
0
1
0
0
2
0
0
2
0
0
0
0
0
2
0
0
1
3
0
0
0
0
4
4
0
0
0
0
2
0
2
0
0
2
0
1
0
0
0
0
2
0
3
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
2
0
0
0
0
0
0
0
1
2
1
0
1
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
1
0
2
0
1
1
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
1
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
2
0
1
0
0
0
0
1
0
0
2
0
0
1
0
0
1
0
0
1
2
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
2
0
0
2
0
0
1
1
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
1
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
2
0
0
2
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
3
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
2
0
0
0
2
0
0
2
0
1
2
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
2
0
0
1
3
2
2
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
3
0
0
1
1
0
1
0
1
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
5
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
1
0
1
1
1
2
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
1
0
0
0
0
0
1
2
0
0
2
1
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
2
0
0
0
0
0
5
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
2
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
3
0
0
0
0
0
2
0
1
2
0
0
1
0
1
1
0
0
1
5
0
0
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
1
0
1
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
2
2
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
2
2
0
2
0
0
0
1
1
0
1
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
2
0
0
0
0
0
0
1
0
0
4
0
0
2
0
0
0
0
2
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
1
1
1
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
3
1
0
0
0
0
2
0
3
0
0
0
0
0
0
0
1
5
0
0
1
0
2
0
2
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
5
1
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
4
0
0
0
1
2
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
1
5
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
2
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
2
1
0
1
0
0
1
1
0
0
2
0
0
0
1
0
2
0
0
0
0
0
2
0
1
2
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
2
2
0
0
0
1
2
0
2
0
1
2
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
3
0
1
0
1
0
0
0
0
0
0
0
2
1
2
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
5
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
1
0
0
0
0
3
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
2
1
0
0
0
2
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
1
2
5
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
1
3
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
1
1
1
0
0
0
2
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
2
0
0
0
2
0
0
1
0
0
2
0
1
1
0
0
1
1
3
0
0
0
0
0
0
0
0
2
0
0
2
0
2
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
2
1
1
0
1
2
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
1
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
3
1
2
0
1
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
1
1
0
0
0
0
0
2
1
0
1
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
2
0
0
2
1
0
0
2
0
0
0
0
1
2
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
3
2
1
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
2
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
2
0
2
0
0
0
0
0
0
1
1
0
0
1
3
1
1
0
1
0
0
2
2
1
0
0
0
0
0
0
0
3
0
0
1
2
0
0
1
0
0
0
2
2
0
0
7
2
2
0
0
0
1
2
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
2
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
1
2
0
0
0
0
0
0
0
0
0
0
1
3
2
0
0
1
0
0
0
1
0
0
0
1
0
0
2
0
1
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
1
0
2
1
2
0
0
0
0
2
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
2
4
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
2
0
2
0
0
0
3
0
0
3
0
1
0
0
2
1
0
0
0
1
2
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
1
1
0
1
2
0
0
1
1
0
0
0
1
0
0
0
2
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
1
0
2
1
2
0
0
3
0
2
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
2
0
1
0
0
2
1
0
0
2
0
3
3
0
0
0
0
0
0
0
0
2
0
0
0
2
0
3
0
0
0
0
0
0
0
0
2
1
0
0
2
1
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
5
0
0
2
0
0
0
0
0
2
0
0
1
2
0
2
1
0
1
0
0
0
0
0
0
1
2
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
2
0
2
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
3
2
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
4
0
0
0
3
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
1
0
1
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
3
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
3
0
0
2
3
0
1
0
0
0
2
2
0
0
0
0
3
0
1
0
0
0
0
2
0
0
1
0
0
0
0
1
0
1
2
2
1
0
2
2
1
0
0
4
0
0
2
1
0
0
0
2
2
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
1
0
0
2
0
0
0
3
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
1
1
0
0
0
0
1
2
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
8
1
1
2
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
1
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
2
1
0
0
0
0
0
2
2
2
0
0
2
0
1
0
0
1
0
1
0
1
1
1
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
2
0
1
0
0
0
1
0
3
0
0
5
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
2
0
0
2
0
0
0
2
2
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
3
0
2
0
0
0
0
0
0
0
0
4
0
0
0
0
2
1
0
0
1
0
0
3
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
3
0
3
0
0
0
0
0
1
0
2
1
0
4
0
0
0
2
3
0
2
0
0
0
0
1
3
0
0
1
1
0
0
0
0
2
0
3
1
1
0
0
2
3
1
1
0
0
0
1
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
4
4
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
2
0
2
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
1
1
0
2
0
0
0
0
2
0
0
2
3
0
1
0
0
1
0
2
3
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
1
0
0
0
1
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
2
2
1
0
1
0
0
1
0
2
0
0
0
1
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
4
0
0
1
1
1
0
0
2
0
0
0
1
1
1
0
0
0
0
2
0
2
0
0
1
2
0
2
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
2
0
0
1
0
0
1
1
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
2
2
0
0
0
2
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
1
0
3
6
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
1
2
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
1
1
0
2
1
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
2
1
0
0
0
0
1
1
0
1
2
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
3
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
2
0
0
0
2
0
1
0
0
0
0
0
0
2
1
1
1
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
1
1
0
1
0
0
0
1
2
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
6
0
0
1
0
2
2
0
1
1
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
1
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
2
2
0
0
3
0
2
0
0
0
0
2
0
0
1
0
0
1
0
3
2
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
1
0
0
1
3
0
0
0
0
1
0
0
0
1
0
2
0
4
2
0
1
1
0
2
1
0
2
0
0
0
2
1
1
0
0
0
0
0
4
0
0
0
0
0
2
0
0
2
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
4
0
2
0
0
0
0
0
0
3
1
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
2
1
2
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
2
1
1
1
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
3
0
1
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
3
2
0
1
0
0
0
2
0
2
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
1
0
0
2
0
1
0
0
0
0
1
1
1
0
1
1
0
0
0
0
0
0
2
2
0
0
0
1
0
1
0
2
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
1
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
2
2
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
1
0
2
2
0
0
0
3
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
2
0
0
0
0
0
3
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
3
0
0
1
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
2
2
2
0
1
1
0
0
0
0
1
0
2
0
1
0
0
0
0
2
2
0
0
1
0
0
0
0
2
0
0
1
0
1
0
0
2
0
1
0
0
1
0
2
0
0
0
0
3
2
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
1
0
1
0
0
0
2
0
1
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
1
0
0
2
1
0
2
3
0
0
0
2
2
0
2
0
1
0
0
0
4
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
2
2
2
0
2
0
0
0
0
0
0
1
2
1
0
0
0
0
0
2
1
0
1
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
2
0
0
1
0
2
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
2
2
0
3
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
1
1
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
2
1
1
0
0
0
3
0
0
0
0
0
1
2
0
0
1
3
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
3
1
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
2
1
0
2
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
2
0
0
1
1
0
0
0
0
0
6
0
0
0
0
0
0
3
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
3
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
2
0
0
0
0
1
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
1
0
1
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
5
0
2
2
0
0
0
0
2
0
0
6
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
2
1
0
1
0
2
1
0
2
0
0
0
0
2
1
0
7
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
1
0
1
0
1
0
2
0
0
0
0
9
0
0
0
1
0
0
8
0
0
0
0
0
2
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
1
1
2
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
1
2
3
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
2
1
0
0
0
0
2
3
2
4
0
1
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
1
0
0
0
0
0
2
2
0
0
0
0
6
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
1
4
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
1
1
0
0
0
2
0
2
0
0
0
0
1
2
0
0
1
0
0
1
1
0
0
0
0
0
1
3
1
0
2
1
0
1
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
1
0
0
0
1
2
0
0
0
0
0
0
0
3
1
0
0
0
0
1
0
3
0
0
0
0
0
0
3
0
0
0
2
0
0
1
2
1
0
0
0
0
0
2
0
0
0
1
2
2
0
6
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
1
0
0
3
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
2
0
0
0
3
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
1
0
0
0
3
0
0
0
0
0
2
1
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
1
1
0
0
0
1
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
1
0
0
0
0
0
2
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
3
0
0
2
2
2
0
1
3
0
0
1
0
2
0
0
0
0
1
1
2
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
2
2
3
2
2
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
3
0
0
0
1
0
2
0
0
1
0
0
0
0
1
1
0
0
0
0
3
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
2
0
0
2
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
3
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
2
0
0
1
2
0
0
1
2
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
1
2
0
0
0
0
2
0
1
0
2
0
0
1
0
0
3
2
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
2
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
1
0
0
0
0
0
3
0
0
0
0
2
0
0
0
1
1
0
0
0
2
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
3
0
0
1
0
0
0
0
0
0
1
1
1
1
0
0
0
1
1
0
0
0
0
0
2
2
2
0
1
0
0
2
0
2
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
4
0
0
0
2
2
0
1
0
0
1
0
0
0
2
0
2
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
3
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
4
0
1
0
0
0
0
0
1
2
0
3
0
3
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
2
0
1
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
1
2
3
0
1
0
1
0
0
0
0
0
0
2
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
1
0
0
0
0
0
2
0
0
2
0
0
1
2
0
0
0
0
3
1
0
0
0
0
0
1
2
2
0
1
0
0
0
0
0
1
0
1
0
3
2
17
0
0
0
0
0
0
0
0
0
0
0
1
0
1
3
0
3
0
2
0
0
1
0
0
0
0
3
0
2
0
0
0
2
0
0
0
0
0
0
0
2
2
0
4
0
0
0
0
2
3
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
3
0
0
0
0
0
1
0
1
1
2
1
0
2
0
0
2
0
2
4
2
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
2
3
0
1
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
2
0
0
0
1
1
0
0
0
0
3
2
1
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
1
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
2
2
0
0
0
2
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
3
0
0
2
0
1
0
2
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
1
2
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
2
2
0
0
0
0
1
0
0
1
1
0
2
4
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
2
0
1
0
0
1
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
4
0
0
1
1
0
0
0
0
0
2
1
0
0
0
2
0
2
2
2
0
0
0
0
0
4
1
0
0
0
0
1
0
0
1
2
2
0
0
1
0
0
1
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
4
5
1
1
0
0
2
0
1
0
0
0
0
2
0
0
2
2
1
0
0
0
2
2
3
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
1
2
0
0
1
0
0
3
0
0
0
2
2
0
2
2
0
3
0
0
0
0
0
2
2
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
2
0
1
1
1
0
0
2
3
7
0
0
0
1
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
5
0
2
1
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
2
2
0
1
0
0
0
1
2
1
2
3
1
0
0
0
1
2
0
0
2
1
0
0
2
0
7
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
2
1
0
2
2
0
0
1
0
0
0
0
0
1
2
0
1
1
0
2
2
0
0
0
1
0
0
2
0
2
1
4
0
0
0
0
2
0
1
1
0
0
0
1
0
0
3
0
0
1
0
1
0
0
0
0
0
4
0
1
0
0
1
0
0
1
2
0
0
2
1
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
1
0
2
0
0
1
0
1
3
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
4
0
0
0
0
2
0
2
1
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
1
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
3
0
0
2
0
3
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
1
1
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
3
0
2
0
0
0
1
0
1
0
0
0
1
2
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
1
0
2
1
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
2
0
0
1
5
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
2
1
1
1
2
0
2
2
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
2
0
2
0
1
2
1
0
0
0
11
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
2
0
2
0
2
0
0
0
0
0
2
2
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
2
0
1
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
2
1
0
0
1
1
0
0
2
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
2
3
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
7
0
0
2
0
1
0
5
0
0
0
0
0
0
0
0
0
0
0
4
2
0
3
1
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
2
1
0
0
0
0
1
0
0
2
2
2
2
0
0
0
0
0
2
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
2
1
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
3
0
0
4
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
2
0
2
0
0
0
3
2
0
0
0
0
2
0
0
0
0
2
0
2
1
0
0
0
0
1
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
1
4
2
0
0
0
0
0
1
1
0
0
0
2
1
1
1
0
0
0
0
0
0
1
0
0
0
0
2
0
2
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
1
6
0
0
0
1
0
0
2
3
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
3
2
1
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
2
1
3
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
4
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
3
2
0
0
0
0
1
0
0
0
0
0
0
2
0
1
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
2
1
0
0
2
0
0
2
0
1
2
0
1
0
0
2
0
0
0
0
1
1
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
1
0
1
0
0
2
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
2
3
1
1
0
0
0
0
1
1
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
1
0
2
0
0
0
4
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
2
4
2
1
2
0
0
2
0
1
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
1
0
0
4
2
1
0
0
0
0
2
3
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
2
1
0
1
0
0
0
1
2
2
2
0
0
1
1
0
0
0
0
2
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
1
0
6
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
2
0
1
1
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
2
0
4
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
2
0
2
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
2
1
0
0
2
0
0
1
2
0
1
0
0
0
1
1
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
1
1
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
3
2
0
0
0
0
1
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
2
2
0
0
0
0
1
0
1
0
0
1
0
0
0
0
2
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
2
0
0
0
0
0
0
2
2
0
2
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
3
0
0
0
1
0
3
1
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
3
0
0
2
2
0
2
0
2
1
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
2
1
0
0
0
1
2
0
1
1
0
0
0
0
1
0
0
0
0
2
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
4
0
2
2
4
0
0
2
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
2
0
1
0
1
0
0
2
3
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
1
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
1
1
0
3
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
1
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
2
0
0
1
1
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
2
0
0
1
0
2
0
0
0
0
0
0
2
1
2
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
3
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
2
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
2
2
0
0
0
0
2
2
0
1
0
1
0
0
0
0
0
2
1
0
0
0
0
3
0
1
0
0
0
0
1
0
2
0
0
1
0
0
0
0
2
0
1
2
2
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
2
0
0
2
1
0
0
0
0
1
0
3
2
0
1
0
0
2
0
1
0
0
1
0
1
0
1
0
1
2
0
0
0
0
1
0
0
0
2
2
2
0
0
0
0
1
0
0
1
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
4
0
0
0
0
0
3
2
0
2
2
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
2
2
0
0
2
1
0
0
0
2
0
0
0
2
1
1
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
1
2
1
0
3
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
2
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
2
0
2
0
0
2
0
0
0
0
2
2
0
0
2
0
0
2
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
2
0
0
0
2
1
0
0
0
3
0
1
0
0
0
0
0
0
2
0
0
1
4
0
0
0
2
0
2
0
0
0
1
0
0
0
2
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
4
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
2
2
0
0
2
0
0
0
0
3
0
1
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
2
0
1
1
1
2
0
0
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
1
0
0
2
1
0
0
0
1
1
0
1
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
2
0
0
3
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
3
1
1
0
1
0
1
1
1
0
2
0
0
0
0
2
1
1
0
1
0
0
0
0
1
0
2
1
1
0
0
1
1
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
2
1
0
1
0
1
0
0
2
0
0
2
0
3
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
3
0
0
1
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
2
0
2
0
0
1
1
0
0
0
0
0
2
0
1
0
3
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
2
1
1
0
0
0
0
0
0
1
0
2
0
0
2
0
3
0
0
0
0
0
0
1
1
0
2
1
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
5
0
2
0
3
0
0
1
1
0
0
0
2
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
2
2
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
1
0
2
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
2
0
2
2
2
0
0
1
2
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
2
0
1
4
2
0
0
0
2
0
2
1
0
0
0
1
2
0
2
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
4
0
2
2
0
1
0
0
3
0
0
1
0
1
0
0
2
4
0
2
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
1
0
0
1
0
1
1
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
3
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
9
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
3
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
7
0
0
0
0
0
0
1
0
0
0
0
1
1
2
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
4
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
2
5
0
0
3
1
0
0
0
1
1
0
0
0
0
0
0
1
1
2
2
0
0
2
0
2
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
2
0
2
1
0
2
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
2
0
0
0
2
1
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
2
0
0
1
0
1
0
2
2
2
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
2
0
0
1
0
0
2
4
0
0
0
0
0
0
0
0
2
2
2
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
10
0
3
0
0
0
1
2
0
2
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
2
0
0
1
1
3
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
2
0
0
0
0
1
3
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
2
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
2
0
0
1
1
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
2
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
3
2
0
1
2
2
2
2
0
3
5
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
2
1
2
1
0
1
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
1
1
0
0
2
0
3
4
0
0
1
0
2
0
0
0
1
1
0
0
0
0
0
2
2
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
5
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
2
0
0
2
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
2
1
0
0
0
0
0
1
2
0
1
0
2
0
1
0
0
0
0
2
1
2
0
0
0
0
0
1
2
2
2
0
0
0
1
0
0
2
2
0
1
1
0
0
0
0
5
0
1
0
2
0
2
0
2
2
0
0
0
2
0
0
0
1
0
0
1
0
0
2
2
1
0
1
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
2
3
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
3
0
0
0
1
2
0
0
0
0
1
2
0
0
1
0
2
1
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
1
0
0
0
1
0
0
2
0
2
2
1
0
0
0
1
0
1
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
2
0
0
0
2
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
1
2
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
1
0
2
2
0
0
0
0
1
0
2
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
4
0
2
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
2
1
0
1
0
2
0
0
1
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
2
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
2
1
0
1
0
1
0
1
0
3
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
3
0
0
0
2
0
0
0
0
1
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
3
0
0
0
0
0
0
0
4
0
0
0
2
1
0
0
0
2
2
0
0
0
0
0
0
0
2
1
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
2
0
0
4
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
16
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
1
0
1
1
0
0
0
1
1
0
0
0
1
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
3
0
0
1
1
2
0
0
0
1
0
0
0
0
3
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
3
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
2
2
0
0
2
0
1
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
2
0
0
2
1
0
0
2
1
1
0
0
1
0
0
0
0
0
2
1
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
2
1
1
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
3
2
2
0
1
0
0
1
0
0
2
0
2
0
0
2
0
0
1
0
0
2
0
0
0
2
0
1
0
0
1
0
0
0
1
1
0
1
0
0
1
0
1
0
1
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
3
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
3
1
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
2
7
0
1
0
0
0
0
3
2
0
0
0
3
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
3
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
3
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
2
2
0
1
0
0
0
0
1
2
1
2
0
2
0
0
1
0
0
2
1
2
1
0
0
3
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
2
5
0
0
0
0
2
1
0
2
0
0
0
0
0
1
0
1
0
0
5
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
1
1
2
2
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
2
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
2
4
0
2
0
0
0
0
1
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
1
3
0
0
0
1
0
0
3
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
8
0
0
4
2
0
0
3
0
0
0
1
0
2
0
0
0
0
2
0
0
1
0
2
0
0
0
1
0
0
0
2
0
0
2
0
0
0
2
0
2
2
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
1
0
0
2
0
0
0
0
0
3
2
0
0
0
2
0
0
0
0
0
0
0
1
0
1
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
2
1
0
0
0
0
0
0
2
0
0
0
0
6
0
0
2
0
0
0
0
2
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
2
0
0
0
0
0
1
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
3
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
1
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
2
0
0
2
2
0
0
2
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
2
2
0
0
3
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
2
0
2
0
0
0
0
1
0
1
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
2
0
1
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
2
0
2
0
0
0
4
0
0
0
0
0
3
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
1
0
2
1
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
1
0
0
2
0
0
2
1
0
2
1
0
0
1
1
0
0
2
1
0
0
0
1
2
0
0
0
0
0
2
0
2
0
0
0
0
1
0
1
0
2
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
1
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
1
0
1
0
0
1
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
2
0
2
0
0
0
0
8
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
3
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
3
3
3
2
0
0
0
3
2
0
0
1
0
5
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
1
2
0
0
2
2
0
1
1
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
1
0
0
0
0
0
1
1
2
1
1
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
1
0
0
0
1
0
0
1
0
0
1
2
0
3
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
2
0
1
1
0
0
0
0
0
0
0
0
0
2
1
0
1
3
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
1
0
2
0
1
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
2
2
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
3
0
0
0
2
0
0
1
0
0
0
0
1
3
0
0
1
0
0
0
2
5
0
0
1
0
2
2
0
1
0
0
0
0
0
0
1
2
0
2
0
0
0
0
1
0
0
1
2
2
0
1
0
2
0
0
0
1
3
0
0
0
3
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
1
0
0
2
1
0
0
2
0
0
1
0
2
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
2
2
1
2
0
0
1
0
0
0
2
1
4
0
0
1
0
0
0
1
0
2
0
0
0
2
0
1
2
0
0
0
2
0
0
0
0
0
1
2
2
0
0
0
2
0
2
0
0
0
0
0
0
0
2
1
0
1
0
1
2
0
1
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
4
0
2
0
0
1
0
0
2
0
0
0
2
0
0
0
0
1
0
1
2
2
1
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
3
1
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
1
0
1
0
0
2
0
0
0
0
1
0
1
0
0
1
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
1
2
0
0
2
0
3
0
0
0
0
4
0
1
0
0
0
0
0
0
0
3
0
0
2
3
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
2
1
1
0
0
0
1
3
0
1
0
1
2
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
3
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
4
0
0
0
3
2
0
1
1
0
0
0
1
0
0
1
0
0
2
2
0
0
2
0
0
2
0
0
0
0
0
2
0
3
1
0
0
0
0
0
1
0
2
1
2
1
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
2
4
0
1
0
2
0
0
0
0
3
0
1
0
0
0
2
0
2
0
0
2
1
1
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
3
0
0
0
1
2
1
0
0
2
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
1
0
2
0
2
1
1
0
0
1
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
0
1
1
1
0
1
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
1
2
0
0
0
0
0
2
0
2
0
1
0
0
1
1
0
5
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
1
0
0
0
0
0
1
2
0
0
0
0
3
0
2
0
0
2
0
0
1
2
0
0
0
0
0
2
1
0
0
1
1
1
0
0
1
0
0
0
0
0
0
1
0
0
2
2
2
0
0
0
0
2
0
0
2
0
1
0
2
7
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
3
0
0
3
0
0
0
0
1
2
5
0
0
0
0
2
0
0
0
1
0
2
0
1
0
1
0
2
0
0
0
1
0
2
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
1
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
2
0
1
0
0
2
0
2
0
0
0
0
4
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
1
0
2
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
1
0
0
0
1
0
1
0
1
0
0
0
1
1
2
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
2
0
0
0
2
0
2
2
0
0
0
3
0
1
0
2
0
1
0
0
2
0
0
0
0
3
3
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
3
0
2
2
0
0
0
2
2
2
0
1
0
1
0
0
0
1
0
0
2
0
1
2
0
1
0
0
2
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
3
0
2
0
1
2
0
0
2
0
0
0
6
2
0
2
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
1
1
2
0
0
0
0
1
0
2
1
0
1
1
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
2
5
2
2
0
1
0
0
1
2
1
0
1
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
3
0
1
0
2
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
2
0
0
1
2
0
0
1
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
2
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
2
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
2
2
0
1
0
2
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
3
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
1
1
0
2
0
1
0
2
0
0
2
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
2
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
11
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
2
0
0
1
0
0
0
0
1
1
0
2
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
2
0
0
2
3
0
0
0
0
2
2
2
0
1
1
0
0
0
1
0
3
0
0
2
0
1
0
0
1
0
0
0
0
0
1
0
1
2
0
0
0
0
1
0
1
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
1
1
1
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
13
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
3
4
0
1
0
0
0
1
2
2
0
0
1
0
0
0
0
0
0
1
0
0
1
2
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
2
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
12
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
4
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
1
2
2
1
0
1
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
2
0
1
2
0
0
0
2
0
0
0
0
0
0
1
0
0
12
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
1
0
1
1
0
0
0
0
0
3
0
2
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
3
0
0
1
2
1
1
1
2
0
0
0
0
2
0
2
0
0
2
1
1
0
2
0
2
0
0
0
0
0
5
0
1
0
1
1
1
0
0
0
0
0
0
0
0
2
0
0
1
2
1
2
2
3
0
5
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
4
2
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
2
0
0
2
0
2
1
0
0
0
0
0
0
0
1
0
0
0
1
2
1
3
0
2
0
0
0
1
1
1
0
2
0
0
0
1
0
1
0
0
1
0
0
1
0
0
2
0
0
2
1
2
0
0
0
0
0
0
0
1
2
0
0
0
1
1
0
0
1
0
0
0
1
0
1
2
0
0
1
0
1
0
0
0
4
0
0
3
2
0
0
0
1
0
2
0
3
1
0
0
0
1
1
0
0
0
2
1
2
0
0
0
4
0
0
0
0
2
1
0
2
2
1
0
0
0
6
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
1
1
0
0
1
2
2
0
2
1
1
0
0
1
0
0
1
0
0
1
2
0
2
0
3
1
0
0
0
2
0
0
0
0
0
3
2
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
1
7
0
1
0
0
0
3
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
1
1
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
5
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
1
3
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
3
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
2
1
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
2
0
0
0
0
2
1
1
0
1
1
6
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
2
2
0
0
0
0
1
1
0
4
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
4
2
0
0
0
0
1
2
0
0
0
0
0
0
0
2
3
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
1
0
0
1
2
2
0
2
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
1
3
0
2
3
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
6
0
0
0
0
2
0
0
0
0
1
0
0
0
0
3
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
4
0
2
1
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
3
2
1
2
0
0
0
0
2
0
0
7
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
1
0
1
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
2
0
1
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
2
3
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
1
0
1
0
2
1
0
2
0
0
0
0
0
3
1
0
2
0
0
1
2
1
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
11
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
2
1
0
1
2
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
1
2
2
0
0
3
0
1
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
1
0
0
1
0
1
0
0
0
2
0
1
0
2
1
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
2
1
0
1
0
0
0
0
2
1
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
2
1
3
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
2
2
2
0
0
1
0
2
3
0
0
0
0
0
0
0
2
1
3
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
2
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
2
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
2
0
0
0
2
1
0
0
0
1
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
2
0
2
0
0
0
0
2
4
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
2
2
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
2
0
0
1
0
2
0
2
0
0
2
0
0
1
0
0
0
1
0
0
0
2
2
0
0
1
0
0
0
0
2
2
0
0
2
1
2
0
0
0
0
0
1
1
0
0
2
2
0
2
0
2
0
3
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
2
1
0
0
2
1
1
0
0
2
0
0
2
0
0
0
0
0
0
0
3
0
4
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
2
1
0
1
2
0
0
1
0
0
0
0
2
2
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
2
0
0
1
0
0
0
5
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
3
2
0
0
0
2
0
0
2
0
1
1
1
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
4
0
2
0
0
1
0
1
0
0
0
2
0
0
0
2
0
3
0
2
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
3
0
3
0
0
2
0
1
0
1
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
1
2
0
1
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
1
4
1
0
0
0
0
2
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
2
0
1
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
2
0
2
0
1
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
1
0
2
0
2
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
2
0
2
1
0
0
0
1
1
0
0
1
0
2
0
0
0
0
0
2
0
0
0
1
0
0
1
1
0
1
2
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
3
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
4
0
0
0
2
2
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
3
0
0
0
2
0
2
0
1
0
0
0
4
2
2
0
0
0
0
0
0
0
2
0
1
0
4
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
3
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
2
1
2
0
0
0
0
0
0
0
3
0
3
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
1
2
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
1
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
1
0
0
0
1
0
4
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
2
0
2
1
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
2
2
2
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
1
0
2
0
0
0
1
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
1
2
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
1
6
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
1
0
2
0
1
0
0
0
0
1
1
0
0
0
1
2
2
0
1
0
7
0
0
1
0
0
0
0
0
0
1
1
2
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
2
0
0
1
1
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
3
0
0
0
0
1
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
2
1
3
0
0
0
0
0
2
1
4
2
0
2
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
1
4
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
2
0
0
0
0
0
0
1
2
0
0
2
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
1
0
0
0
2
0
1
0
0
1
0
0
0
4
0
0
0
2
0
2
0
0
1
0
0
0
0
3
1
0
1
1
0
1
0
2
2
0
2
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
2
0
0
1
0
1
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
2
1
0
0
1
0
0
0
0
0
0
0
2
7
2
0
0
2
1
0
0
0
0
0
0
1
6
0
5
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
2
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
3
0
1
1
0
0
0
2
0
2
0
4
0
1
0
0
0
3
2
0
2
0
0
0
2
0
2
1
1
0
1
1
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
1
2
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
1
0
0
0
1
2
1
0
3
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
2
0
0
2
0
1
3
0
0
3
0
0
0
0
0
0
0
2
2
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
2
0
0
0
0
0
2
0
0
0
4
1
0
0
0
0
3
0
0
1
0
2
0
3
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
5
0
0
2
0
0
0
0
0
0
0
3
0
2
1
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
1
0
2
0
0
1
0
0
0
0
0
1
3
1
0
1
0
0
0
0
0
0
0
2
0
1
0
0
1
2
0
1
2
0
2
0
0
0
0
0
1
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
5
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
2
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
2
0
1
0
2
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
1
0
0
0
0
1
0
0
2
1
0
0
0
1
0
2
0
0
0
0
2
0
0
2
1
0
0
1
0
2
0
0
2
0
0
1
0
0
0
3
0
0
0
0
2
2
0
0
0
0
1
0
0
0
2
0
1
0
1
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
3
2
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
2
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
1
1
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
3
1
0
1
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
2
1
2
0
0
0
0
0
2
1
0
0
1
0
0
1
2
3
0
1
0
0
0
0
2
5
0
0
1
1
0
0
0
1
2
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
2
2
2
0
0
1
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
9
0
2
0
0
0
2
0
0
0
0
0
0
0
2
2
0
2
0
2
1
0
1
2
0
0
0
2
3
0
3
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
1
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
2
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
1
1
0
0
0
2
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
1
0
1
2
0
2
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
1
1
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
1
2
0
0
1
2
0
0
0
1
0
0
0
0
0
4
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
3
0
0
0
3
0
0
2
1
0
0
0
0
0
0
0
0
0
3
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
2
0
0
0
1
0
0
0
2
0
0
1
0
0
1
0
0
1
2
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
1
2
0
0
2
0
3
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
1
2
0
1
0
0
0
3
0
7
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
1
1
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
1
2
2
0
0
0
0
0
0
1
2
0
2
0
2
0
0
0
0
1
0
1
0
0
0
3
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
2
0
0
2
0
1
1
1
1
2
0
0
0
0
2
2
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
1
0
1
2
0
0
1
2
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
2
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
2
2
0
0
2
1
0
2
2
0
0
0
0
2
0
0
0
2
0
1
0
0
2
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
2
0
0
0
1
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
3
3
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
3
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
2
0
1
2
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
1
5
0
0
1
0
1
2
0
0
0
3
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
1
0
0
0
0
2
0
0
1
0
0
1
0
0
0
1
1
2
0
2
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
8
0
0
2
0
0
0
0
0
0
2
0
0
0
2
2
0
1
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
2
3
2
0
0
0
0
2
3
0
1
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
1
0
0
0
0
0
1
0
2
0
1
0
1
1
2
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
2
0
2
0
2
0
0
0
1
1
2
0
0
0
0
0
0
1
2
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
4
0
0
0
1
1
0
1
2
0
0
2
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
3
2
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
2
2
1
1
0
0
2
0
1
0
1
0
3
0
0
2
0
0
2
2
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
2
0
1
3
0
0
0
0
1
0
0
0
1
2
0
0
2
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
1
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
2
1
2
2
0
0
0
0
1
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
5
0
4
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
5
0
0
0
0
0
2
0
0
0
1
1
0
0
1
2
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
3
0
0
3
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
2
0
2
0
0
0
5
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
2
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
1
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
5
0
0
0
1
0
2
0
1
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
1
0
2
0
2
0
0
1
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
2
0
1
0
0
2
1
1
3
0
0
0
0
2
0
0
1
0
1
2
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
2
1
1
2
1
1
0
0
2
0
0
2
0
0
1
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
1
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
1
2
0
0
0
0
0
1
0
2
0
0
0
1
0
1
0
0
0
1
0
0
3
1
1
2
0
0
0
0
1
1
0
0
0
1
0
0
2
0
0
0
2
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
1
0
0
2
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
2
0
1
0
0
0
0
0
0
0
2
1
0
2
2
0
0
0
0
0
0
0
2
0
0
3
0
0
0
1
1
0
2
0
0
0
0
0
0
0
1
5
0
0
0
1
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
1
4
2
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
11
0
0
0
0
0
0
0
0
0
1
0
1
0
2
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
1
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
2
0
1
0
2
2
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
2
0
0
0
3
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
2
0
1
1
2
0
0
0
2
0
0
0
0
1
1
2
9
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
1
0
0
1
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
1
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
1
1
0
2
2
0
0
0
3
0
0
0
2
0
0
0
2
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
2
0
1
0
1
0
0
1
0
0
1
0
1
2
0
0
0
0
5
1
0
1
0
2
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
2
2
0
2
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
2
0
2
0
0
0
2
1
0
0
1
0
0
0
4
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
1
0
0
2
0
3
0
1
1
0
1
0
0
0
0
0
0
0
2
0
2
1
0
1
0
0
2
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
1
0
0
1
5
0
0
1
0
0
1
0
4
0
2
2
2
2
0
0
0
0
0
0
1
2
0
2
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
2
0
3
1
0
0
0
2
0
0
0
0
1
0
1
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
2
0
2
0
1
0
4
0
1
2
0
0
0
0
0
1
0
0
1
1
0
2
0
0
0
2
0
1
0
2
0
0
0
1
0
0
0
2
0
2
0
0
3
0
0
0
0
0
0
0
0
2
0
3
0
1
3
0
0
2
0
0
0
1
0
1
0
1
3
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
7
0
2
0
1
0
0
0
0
0
0
2
0
1
1
0
2
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
1
2
0
0
0
1
0
2
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
1
0
2
2
0
0
1
0
0
0
0
0
1
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
2
2
3
0
2
0
0
0
4
0
2
0
1
2
1
2
0
6
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
1
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
4
1
1
0
0
0
2
2
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
1
0
2
0
0
0
0
0
2
0
1
0
0
0
2
1
0
1
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
3
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
1
0
0
3
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
1
0
0
2
1
2
0
0
0
0
0
1
0
3
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
1
2
2
0
0
2
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
3
2
0
2
1
0
0
0
0
0
1
0
0
0
2
0
0
1
5
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
2
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
2
0
0
0
0
0
0
0
0
2
0
2
1
0
1
3
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
1
2
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
2
0
2
1
2
0
1
2
0
7
0
1
0
0
1
2
0
0
0
0
0
0
0
1
2
3
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
0
2
1
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
3
0
0
0
0
0
0
8
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
1
0
0
0
0
1
0
1
2
2
0
0
0
1
0
0
1
0
0
0
2
2
0
0
3
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
1
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
1
3
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
2
2
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
3
1
0
0
1
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
1
4
0
0
1
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
2
10
0
0
1
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
1
0
0
3
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
2
2
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
1
1
2
0
0
0
1
1
2
0
0
1
0
0
0
0
1
2
0
0
0
2
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
1
0
1
1
2
0
0
0
2
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
2
2
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
2
0
1
0
1
2
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
2
0
0
1
0
1
0
0
1
0
0
0
6
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
2
2
0
1
0
0
1
2
0
2
1
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
1
0
0
1
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
3
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
2
0
0
1
0
1
0
2
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
2
0
0
0
0
1
3
0
0
0
0
2
1
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
1
1
0
1
0
0
0
2
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
1
1
1
0
0
2
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
2
2
1
2
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
1
3
1
0
1
0
2
0
0
0
0
0
0
1
2
2
3
2
2
1
0
2
2
0
0
3
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
1
0
0
1
0
1
0
0
0
0
0
0
3
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
1
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
1
1
0
2
3
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
2
2
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
1
0
2
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
1
6
0
1
0
1
0
0
0
3
1
1
0
0
0
1
0
1
2
1
0
0
0
0
0
2
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
1
2
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
1
0
0
2
1
0
0
1
1
0
0
2
0
0
0
1
0
0
0
2
2
0
0
0
0
2
0
1
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
1
0
2
0
3
0
0
2
0
0
1
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
3
0
0
1
0
2
2
1
1
1
0
2
0
0
1
0
0
0
1
2
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
1
1
0
1
0
3
2
2
0
0
0
0
0
1
3
0
2
1
1
1
0
1
0
2
0
0
2
2
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
2
0
1
3
0
0
0
0
0
0
0
1
0
0
1
1
2
0
0
2
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
5
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
2
2
0
0
0
1
0
1
0
1
2
0
0
1
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
2
2
0
0
0
1
0
1
0
0
1
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
1
2
0
0
0
0
2
0
1
0
0
0
1
0
0
3
0
0
1
1
0
0
0
2
0
0
2
0
4
0
0
0
1
0
0
1
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
2
2
0
0
1
1
2
0
0
4
0
2
0
0
2
0
1
0
0
0
0
0
2
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
5
1
0
1
2
2
0
2
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
4
2
0
0
0
3
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
1
1
1
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
2
1
1
0
0
2
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
2
0
1
0
0
0
1
0
2
0
0
1
0
0
1
1
0
1
0
2
0
0
0
0
0
2
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
3
2
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
1
2
0
0
0
1
0
2
2
0
0
0
0
1
0
0
0
3
1
2
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
3
0
2
0
0
1
0
0
0
2
1
0
2
0
1
2
0
0
0
0
2
0
1
0
2
2
0
0
0
0
0
1
2
0
0
6
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
1
1
0
0
1
0
0
0
2
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
1
0
0
0
1
0
1
3
0
0
0
0
2
0
3
0
1
0
2
0
0
2
2
0
1
5
0
0
5
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
1
2
0
0
0
1
0
3
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
2
2
2
2
0
0
1
1
0
0
1
0
0
2
1
1
0
0
0
1
0
0
0
0
2
1
1
1
0
1
0
2
0
0
0
1
0
0
1
2
0
0
0
0
2
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
3
0
0
2
2
1
0
0
2
0
0
0
0
1
0
1
2
0
0
3
0
0
2
0
0
0
2
3
1
0
0
0
0
1
0
0
0
1
1
0
2
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
2
0
0
0
2
1
0
2
0
0
0
1
1
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
1
3
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
3
0
2
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
2
0
2
1
0
0
0
2
1
0
0
2
1
0
0
0
0
0
0
0
0
1
2
0
2
0
0
1
0
0
0
0
0
1
3
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
2
0
1
0
1
0
3
0
0
1
0
0
0
0
1
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
1
1
2
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
2
1
0
1
1
0
0
0
2
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
3
1
0
0
1
2
0
1
0
0
3
0
1
0
0
1
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
2
0
0
3
0
0
0
0
2
0
0
3
0
0
1
1
0
1
0
1
0
2
0
3
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
3
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
2
0
2
0
1
1
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
2
0
0
6
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
2
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
1
2
0
0
0
0
0
0
0
1
0
0
1
0
2
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
1
2
0
0
0
2
0
0
2
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
3
1
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
9
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
4
0
0
0
1
0
1
1
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
4
0
1
0
0
0
1
0
1
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
1
0
0
2
0
0
1
0
2
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
2
1
0
1
3
0
0
0
0
0
0
0
2
0
2
0
1
1
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
2
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
3
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
3
4
0
0
0
1
0
1
2
1
0
2
0
0
2
1
0
0
2
0
2
0
0
0
0
0
1
0
0
0
2
3
3
0
1
1
2
0
1
1
2
0
0
0
0
0
0
1
0
2
0
2
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
3
0
0
0
0
0
0
2
1
4
0
2
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
3
0
1
1
0
1
0
0
2
0
0
2
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
2
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
2
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
2
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
4
0
0
1
3
2
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
3
0
0
0
0
0
0
1
0
0
0
3
0
0
1
1
2
1
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
2
0
0
0
2
0
2
0
0
2
0
0
2
2
2
0
1
1
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
2
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
2
1
2
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
2
1
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
3
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
2
0
1
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
2
2
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
2
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
1
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
2
0
0
0
2
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
1
1
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
2
0
1
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
4
0
2
0
1
0
0
0
0
0
2
2
0
0
0
2
0
0
0
2
2
0
0
1
1
1
1
0
0
0
0
0
0
5
3
0
2
2
0
0
0
2
0
0
2
0
0
0
1
0
0
2
1
0
0
2
1
0
0
0
0
0
0
1
2
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
2
0
2
1
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
4
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
2
1
0
1
5
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
1
3
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
1
1
0
0
1
0
0
2
1
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
2
2
0
1
0
0
0
0
0
0
0
0
0
0
6
1
1
0
1
0
0
0
2
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
2
0
1
0
0
0
2
1
0
0
2
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
4
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
2
2
0
0
3
1
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
1
2
0
2
1
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
4
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
1
0
1
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
1
0
0
2
0
1
0
2
0
1
0
0
0
0
0
0
0
1
1
3
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
1
2
0
0
0
0
0
0
0
3
1
0
3
0
1
1
0
0
0
0
0
2
0
1
0
0
2
0
0
0
1
0
0
2
3
0
2
0
0
0
2
0
0
2
2
0
1
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
2
0
0
0
1
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
1
0
0
0
1
0
0
0
0
0
2
1
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
3
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
2
6
0
1
0
0
0
0
1
0
2
0
1
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
4
2
0
0
2
0
0
0
2
2
0
0
0
1
0
0
0
1
0
0
1
1
0
2
0
1
1
0
2
2
2
0
0
0
0
2
0
0
0
0
1
2
0
0
2
3
0
2
0
0
1
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
3
1
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
2
0
0
2
0
1
0
0
4
0
0
0
0
1
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
1
0
0
5
0
0
1
0
0
0
0
0
1
1
2
0
2
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
2
0
2
0
0
3
0
0
0
0
1
0
0
2
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
1
0
0
2
0
2
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
1
1
1
0
1
0
0
1
0
0
0
1
0
0
0
2
0
1
0
0
0
0
2
0
0
2
0
0
0
0
4
0
2
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
5
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
1
0
1
2
2
2
1
2
2
0
0
0
0
0
0
0
3
2
0
0
2
1
1
0
0
0
0
4
1
0
0
2
0
0
2
1
0
0
1
0
0
0
2
1
0
1
0
1
0
0
1
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
1
1
0
1
2
0
3
0
1
0
1
1
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
1
0
1
2
0
0
3
0
0
0
1
0
0
0
2
1
2
0
2
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
2
3
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
3
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
2
3
0
0
0
0
0
2
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
6
2
2
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
1
2
1
0
0
0
2
3
2
0
0
0
0
0
0
0
0
0
1
3
1
0
1
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
4
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
1
2
1
0
1
1
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
1
0
2
0
0
1
0
0
0
0
0
0
1
2
0
1
3
0
0
6
2
0
1
0
1
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
1
2
0
0
0
2
0
0
0
2
1
0
0
0
0
1
1
1
0
0
0
2
0
0
1
0
0
0
0
1
2
2
0
0
0
0
2
0
1
0
0
0
0
2
0
1
12
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
4
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
1
2
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
1
2
0
1
0
2
0
0
0
0
0
0
0
0
2
1
0
2
2
1
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
1
1
0
4
1
1
0
0
2
0
1
0
0
0
0
1
1
0
0
0
0
2
1
0
0
0
0
0
1
0
0
1
2
0
0
0
2
0
2
2
0
0
0
1
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
1
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
1
3
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
2
0
1
1
0
3
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
2
0
1
2
1
0
2
0
0
0
0
5
0
0
2
0
2
0
0
0
0
0
1
1
2
0
0
2
0
0
1
0
0
2
1
0
1
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
5
0
0
0
0
0
0
1
2
2
2
4
0
0
0
3
0
0
1
0
1
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
1
0
0
1
1
0
0
2
1
0
1
0
2
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
1
0
0
0
2
0
1
2
0
0
0
2
2
0
0
2
0
0
0
1
2
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
7
0
0
2
0
2
0
0
0
5
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
3
2
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
2
0
0
0
0
2
0
3
2
1
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
5
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
3
2
0
0
0
2
2
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
1
1
0
0
0
0
0
0
0
2
1
0
3
0
2
0
0
3
0
0
1
0
0
0
0
0
2
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
2
0
0
0
0
0
2
0
2
1
5
0
2
0
0
0
1
1
2
0
0
0
3
2
1
0
0
2
0
3
0
0
0
0
0
2
0
0
0
0
5
0
0
0
0
0
0
0
0
2
0
1
0
1
2
0
1
0
0
2
0
0
0
0
2
2
2
0
0
0
1
0
0
1
1
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
1
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
1
0
0
0
1
0
4
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
3
0
0
1
0
1
0
0
0
0
2
0
0
3
0
0
0
0
2
1
0
0
0
2
0
2
0
2
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
1
0
0
0
3
0
0
3
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
2
0
0
1
1
1
0
0
0
0
1
3
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
1
1
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
4
1
1
2
1
0
1
0
0
0
0
0
0
0
2
2
0
1
2
0
0
2
3
0
0
0
0
0
2
1
1
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
1
0
0
1
0
1
1
0
0
2
0
2
0
0
0
1
1
2
0
0
0
1
0
0
0
0
0
0
2
1
2
0
1
0
2
0
1
0
0
0
1
2
2
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
3
0
1
0
0
0
2
0
0
0
2
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
1
0
0
1
1
4
1
0
0
0
0
0
1
0
0
2
0
0
0
2
1
0
2
2
2
0
0
0
2
0
0
2
1
1
0
0
0
0
0
2
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
2
0
1
0
4
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
2
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
2
2
2
2
0
0
0
1
0
0
2
0
0
0
2
2
0
1
0
1
2
0
0
0
2
0
0
0
0
0
1
0
2
0
2
0
0
0
2
0
0
1
0
1
0
0
1
0
1
8
0
1
1
2
2
2
0
1
0
2
0
2
0
0
0
0
2
2
0
0
0
0
1
0
0
1
0
0
0
2
0
0
2
0
0
0
4
2
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
2
0
2
2
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
1
1
1
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
2
1
3
0
0
0
3
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
4
0
0
0
1
1
1
0
0
0
0
0
2
2
0
0
3
1
0
0
0
0
1
1
2
1
2
0
1
0
0
0
0
0
0
0
2
0
0
0
3
0
0
2
0
1
1
1
0
0
0
0
5
1
0
2
0
0
0
0
0
2
0
2
1
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
2
0
1
0
0
1
2
1
0
0
2
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
2
1
0
1
0
0
0
1
0
1
0
0
0
3
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
5
0
0
0
0
0
0
3
2
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
3
0
0
0
0
0
0
3
0
0
2
0
0
0
2
2
1
0
2
0
1
2
0
0
0
2
0
0
0
0
0
0
3
0
1
0
0
2
0
1
0
0
0
1
0
0
1
7
0
1
0
3
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
1
0
2
2
2
0
0
0
0
2
1
1
0
0
2
0
0
1
1
0
2
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
3
2
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
2
0
0
2
0
0
2
0
0
0
4
0
2
2
2
2
0
0
0
1
0
0
1
0
0
0
0
1
0
0
2
2
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
2
3
0
2
1
2
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
2
3
0
2
1
1
1
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
1
0
4
5
1
0
0
2
3
0
0
0
0
0
1
1
2
0
0
2
0
2
0
0
2
0
0
0
0
0
2
0
0
0
1
2
0
0
1
0
1
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
2
0
0
0
1
0
0
1
2
0
2
0
0
0
1
1
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
1
1
1
0
0
0
0
3
0
0
0
0
1
2
0
0
0
0
0
3
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
2
1
2
1
0
0
0
0
0
0
3
2
2
0
0
0
2
1
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
2
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
3
3
0
0
0
0
0
0
2
5
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
7
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
3
0
0
1
0
1
0
1
1
0
1
0
0
0
2
0
2
2
0
2
0
0
2
0
0
0
2
0
0
0
2
0
1
0
0
0
1
2
0
0
2
0
0
0
0
1
0
0
0
0
0
1
3
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
1
3
1
0
2
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
1
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
3
0
0
0
0
0
2
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
9
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
1
0
1
0
0
0
1
1
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
2
0
1
0
1
0
0
1
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
1
1
2
0
0
0
0
0
5
0
0
0
2
0
1
1
0
0
1
0
0
0
1
0
2
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
1
0
0
3
0
2
2
0
2
2
0
0
1
0
0
1
0
0
0
8
0
0
0
1
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
2
0
0
1
1
0
2
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
2
0
1
0
0
0
1
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
5
0
0
2
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
2
1
1
1
0
0
0
1
0
2
0
1
0
2
1
0
0
0
0
0
0
0
0
1
1
2
1
3
1
2
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
1
0
1
0
2
0
0
1
0
0
1
0
0
0
4
0
1
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
4
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
2
0
0
2
1
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
3
2
0
0
3
0
0
2
1
1
0
2
1
0
0
2
0
0
0
2
0
1
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
2
0
1
1
2
0
0
2
0
0
0
1
0
0
0
1
0
1
2
0
0
2
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
1
3
0
1
2
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
2
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
3
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
3
0
2
0
1
2
0
0
0
1
0
1
0
0
0
1
2
0
2
0
0
0
0
0
0
4
1
0
0
3
0
0
0
3
0
0
3
0
0
2
0
0
0
4
0
0
0
2
1
0
0
2
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
2
0
0
0
1
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
1
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
5
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
3
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
1
0
0
0
1
0
0
2
0
0
2
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
2
3
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
1
2
0
2
0
0
1
6
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
2
2
2
0
0
3
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
3
2
0
1
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
2
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
5
1
1
1
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
2
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
1
3
0
0
1
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
6
2
2
0
1
0
0
0
1
0
2
0
0
2
5
0
0
0
0
2
3
1
0
1
1
0
2
0
0
0
3
0
0
2
0
1
0
2
0
0
0
2
0
2
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
2
0
0
1
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
2
2
0
1
0
0
1
1
0
1
0
0
0
2
0
0
1
0
0
0
2
2
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
7
0
0
1
2
0
0
0
1
0
0
2
0
0
0
0
0
1
0
1
2
0
0
4
0
0
3
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
4
0
0
0
0
3
0
2
0
2
1
2
0
0
2
0
0
2
0
2
5
0
0
1
0
2
1
0
0
0
1
1
0
0
1
1
1
3
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
2
0
1
0
0
0
3
0
0
0
0
0
0
0
1
2
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
1
1
0
0
0
0
1
0
1
0
0
0
1
0
0
2
0
0
5
0
0
2
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
1
1
0
0
3
0
0
0
0
0
1
0
2
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
2
0
0
2
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
3
0
0
1
2
0
1
3
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
2
2
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
4
1
0
0
0
2
1
0
0
0
2
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
3
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
2
0
1
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
4
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
2
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
3
0
0
0
0
0
0
0
1
1
1
3
1
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
3
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
2
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
3
0
2
2
2
0
2
1
0
0
1
0
0
0
1
2
0
2
0
0
2
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
3
2
0
0
2
0
1
1
2
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
4
3
0
0
0
3
2
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
3
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
4
0
2
0
1
0
3
3
0
0
0
0
2
2
0
0
1
3
2
0
1
0
0
0
0
1
0
2
2
2
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
2
0
0
0
3
0
0
0
2
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
3
0
0
0
0
0
1
0
1
1
0
0
0
0
0
2
1
0
1
0
2
1
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
2
0
2
1
0
1
0
1
2
0
2
0
0
0
1
0
2
0
0
0
2
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
2
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
2
2
2
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
2
0
0
2
0
0
1
0
0
0
1
2
0
0
0
0
0
0
2
0
0
2
0
2
0
1
0
2
1
1
2
6
0
0
1
1
0
4
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
2
2
2
0
1
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
2
1
0
0
1
2
1
2
0
0
0
0
2
0
0
0
2
0
0
0
0
2
2
0
0
2
0
0
1
1
1
0
0
0
1
2
0
0
1
0
0
2
0
0
2
0
0
0
1
0
0
0
0
3
0
1
2
2
0
0
2
0
0
2
0
0
0
1
0
0
1
1
0
2
5
0
0
0
0
1
0
0
0
0
3
0
0
2
0
0
1
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
2
2
0
0
0
0
1
0
1
2
2
0
0
0
2
0
1
0
0
2
2
1
0
0
0
0
2
0
3
1
5
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
1
0
2
0
0
0
1
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
1
0
0
3
2
0
0
0
1
0
0
1
0
1
1
0
0
0
1
0
0
2
0
0
0
1
0
0
2
0
1
0
3
0
0
0
0
1
0
1
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
2
0
0
1
0
2
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
1
0
0
1
0
2
2
0
0
2
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
2
1
1
0
0
1
4
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
1
1
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
2
3
0
0
0
2
0
0
2
0
0
0
0
1
1
1
0
2
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
1
0
3
0
0
1
0
0
0
0
2
0
1
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
1
0
0
3
2
0
0
1
2
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
2
0
0
0
2
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
3
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
1
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
2
0
0
0
1
0
0
2
0
1
1
1
1
1
0
0
0
2
0
0
0
0
0
1
1
0
2
0
0
0
0
0
1
0
0
1
0
1
1
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
1
0
3
0
0
0
0
0
0
0
0
0
2
2
2
0
0
1
0
0
0
2
0
0
4
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
2
0
0
0
1
0
2
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
1
0
0
0
0
0
0
2
0
1
1
1
0
0
2
1
0
0
2
0
3
0
0
1
1
1
0
0
0
0
0
2
1
0
1
0
0
0
0
1
2
0
0
2
0
0
0
0
1
0
0
0
0
1
1
0
1
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
2
0
2
0
0
0
0
0
0
1
0
0
1
2
0
2
0
0
2
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
10
1
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
2
0
1
1
0
0
0
0
0
0
10
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
3
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
3
1
0
0
0
1
0
0
0
0
1
2
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
2
0
2
2
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
2
1
0
0
2
0
1
0
0
4
0
0
0
0
0
0
0
2
2
0
0
7
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
3
0
0
0
0
0
1
1
0
0
0
2
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
2
0
2
0
0
0
1
0
2
0
2
0
0
1
0
2
0
4
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
1
0
0
0
0
1
0
1
1
0
0
1
1
2
0
3
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
1
2
0
1
4
0
1
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
2
0
1
1
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
2
0
2
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
2
0
2
0
2
1
0
2
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
2
0
2
0
2
2
0
0
0
0
1
1
0
1
0
1
0
2
2
0
0
1
1
0
0
0
4
0
0
3
0
0
2
0
0
0
2
0
3
0
0
0
2
0
0
0
0
1
1
0
2
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
1
0
1
0
0
0
2
0
0
0
0
1
0
1
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
1
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
2
2
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
1
2
2
2
1
0
0
2
0
2
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
3
0
1
0
0
2
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
1
0
0
1
0
0
1
2
0
0
0
2
0
1
0
0
0
0
0
2
2
0
2
1
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
1
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
1
0
0
1
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
4
0
1
0
0
0
1
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
6
0
0
1
0
0
1
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
3
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
2
0
2
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
2
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
2
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
3
2
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
2
0
0
1
1
3
0
0
2
0
0
0
0
0
9
0
0
2
3
0
0
0
0
0
0
0
3
0
0
0
0
0
1
1
2
0
1
0
0
1
2
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
2
0
0
2
1
11
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
1
2
0
2
0
0
0
1
0
0
0
2
0
1
0
0
3
0
0
1
0
1
2
0
0
0
0
0
0
2
1
2
1
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
1
2
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
3
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
1
2
0
0
2
0
0
2
0
1
1
0
0
0
0
0
1
0
1
0
1
1
0
2
0
2
0
10
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
4
0
0
0
0
0
3
1
1
2
0
0
0
0
0
0
2
2
0
1
2
0
0
0
0
2
0
1
0
3
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
2
0
0
3
0
0
0
0
1
0
1
2
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
3
3
2
0
0
0
0
0
2
0
0
1
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
3
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
3
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
1
0
2
0
0
0
1
2
0
2
1
5
2
0
1
1
0
1
0
2
0
0
1
0
0
0
0
0
0
2
2
0
1
0
0
1
0
1
1
0
0
0
0
0
2
1
0
1
2
0
0
0
0
0
1
0
1
2
0
0
0
2
0
0
0
1
0
1
3
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
4
0
0
3
0
1
0
0
1
0
0
0
1
2
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
3
0
0
0
0
2
0
0
3
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
2
2
0
2
0
0
0
2
0
0
2
1
1
2
2
1
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
1
0
2
0
0
0
0
2
1
2
1
0
0
2
0
0
0
3
0
0
0
0
1
0
1
0
0
0
0
0
0
3
0
2
0
0
0
0
0
2
0
0
2
2
0
0
1
0
2
0
0
0
0
0
0
2
0
1
1
0
0
1
1
1
0
0
0
2
0
0
1
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
2
1
0
0
1
0
0
0
0
0
4
1
0
0
0
0
0
0
0
1
0
0
0
3
1
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
8
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
10
0
1
1
3
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
5
0
0
0
1
0
0
0
0
2
0
0
0
2
3
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
2
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
3
2
0
0
0
0
3
0
0
2
0
0
0
2
1
0
0
0
0
1
0
1
0
0
0
2
0
0
1
0
1
1
0
1
3
0
0
1
0
0
0
1
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
3
0
0
2
0
1
0
0
1
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
2
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
1
0
0
1
17
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
1
1
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
2
0
0
0
0
2
1
0
0
1
2
2
0
0
1
2
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
3
0
0
0
0
1
0
0
2
0
0
0
0
0
3
0
0
0
2
0
0
0
0
2
0
0
0
1
2
0
0
2
0
2
0
0
0
0
2
1
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
5
0
0
0
0
1
0
2
0
0
0
2
3
0
0
0
0
1
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
3
0
0
0
1
0
0
0
0
1
4
0
2
0
1
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
3
0
0
0
1
0
0
0
0
2
0
0
0
2
0
1
1
10
0
0
0
0
1
0
0
0
0
0
0
1
0
1
2
0
0
1
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
2
2
0
2
2
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
1
1
2
0
2
0
0
1
0
0
0
0
0
1
0
0
0
1
1
2
2
0
1
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
1
0
0
1
0
2
1
2
0
0
1
1
0
0
2
0
0
1
0
0
3
3
2
0
0
1
2
0
2
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
1
2
0
1
1
0
1
0
1
0
0
0
1
0
0
0
2
0
1
0
0
0
0
1
0
2
0
0
0
0
2
0
2
0
0
0
0
3
0
0
0
0
0
0
0
5
0
1
1
0
2
0
1
0
0
0
3
0
1
1
0
0
1
0
0
0
0
1
2
0
0
0
0
0
1
0
0
7
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
3
3
0
0
4
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
2
2
2
0
0
0
0
1
0
0
1
0
0
2
1
3
0
0
2
1
0
2
0
0
1
0
0
0
0
0
0
1
2
0
0
0
2
1
2
2
0
0
0
0
0
1
1
0
0
0
1
0
3
2
0
0
2
1
0
0
0
0
0
0
7
0
2
0
0
0
1
0
0
1
1
2
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
2
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
1
4
0
1
0
0
1
2
1
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
5
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
7
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
2
0
0
1
0
0
0
0
3
0
1
0
0
0
1
0
4
0
0
1
0
0
7
0
1
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
3
3
1
0
2
1
2
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
1
2
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
4
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
1
0
1
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
2
0
2
1
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
2
3
0
0
0
0
1
1
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
2
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
2
2
1
4
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
2
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
7
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
2
2
0
2
0
0
0
0
0
2
0
0
0
2
1
0
0
2
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
2
0
0
2
0
2
0
5
1
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
1
0
0
2
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
1
0
2
0
0
4
0
2
0
0
0
0
2
0
0
0
0
1
2
0
1
1
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
3
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
1
1
0
0
0
1
1
0
0
1
0
0
0
0
0
2
0
0
0
0
2
1
2
0
1
1
0
1
0
0
0
1
0
2
0
0
0
2
0
0
0
0
2
0
2
0
0
0
2
2
0
0
1
2
0
2
1
0
1
0
0
0
0
0
0
1
0
2
0
0
0
2
2
0
0
0
0
0
0
1
4
0
0
0
3
0
0
0
1
0
0
0
0
2
0
1
0
1
3
1
0
0
0
0
0
0
2
1
0
0
0
1
0
0
1
1
0
0
0
1
0
2
0
1
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
5
1
0
0
0
1
0
0
0
0
1
1
1
1
0
2
0
1
0
0
0
0
0
0
1
0
1
3
0
0
0
0
0
1
3
0
0
0
0
0
1
0
2
0
1
2
0
0
2
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
2
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
2
0
0
1
1
0
2
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
3
1
0
1
0
0
0
3
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
1
0
0
1
0
0
0
0
2
1
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
1
2
0
0
0
3
0
0
0
1
0
2
0
0
0
0
0
0
2
2
1
2
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
3
0
0
0
2
0
0
1
2
1
1
0
0
0
0
0
1
0
0
3
3
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
1
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
1
2
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
4
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
3
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
1
1
0
0
0
0
1
0
0
1
1
0
0
5
0
0
0
0
1
0
0
1
2
0
1
1
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
1
3
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
2
0
4
1
4
1
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
1
3
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
2
0
2
0
0
0
1
2
0
0
4
0
0
0
3
0
0
0
2
0
3
0
1
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
9
0
0
1
0
2
3
0
0
0
0
1
1
0
1
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
5
0
0
0
0
1
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
2
2
1
0
0
1
0
0
2
0
0
0
0
0
1
0
3
1
0
0
0
1
2
0
0
0
0
0
1
4
0
8
1
0
2
2
0
0
0
0
0
2
2
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
1
0
3
2
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
1
1
2
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
2
0
2
2
1
2
0
0
0
0
0
2
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
3
3
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
2
0
2
2
0
2
1
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
3
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
2
0
2
2
1
0
2
0
1
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
2
0
2
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
2
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
4
1
0
0
3
0
0
0
0
0
1
0
0
3
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
5
2
0
0
0
1
0
0
1
3
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
2
1
0
0
0
1
0
2
0
2
2
0
0
1
0
0
0
1
0
0
0
2
2
0
2
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
1
0
0
0
0
2
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
1
0
0
2
1
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
2
1
0
0
2
0
2
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
2
2
2
0
1
0
0
1
0
2
0
2
0
0
2
0
0
2
1
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
3
0
3
0
1
0
0
0
4
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
4
1
0
0
0
0
2
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
3
0
0
1
1
0
0
0
0
0
2
3
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
2
0
2
0
0
0
0
1
1
0
0
1
1
2
2
0
1
2
0
0
0
0
1
0
3
0
0
2
0
0
1
2
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
1
0
0
2
1
0
0
0
2
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
3
2
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
1
1
2
0
0
0
0
0
3
0
2
1
1
0
0
1
1
0
1
0
2
0
0
0
0
0
0
2
1
0
1
0
0
0
2
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
10
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
1
0
2
0
2
0
0
0
0
1
0
0
2
1
0
2
0
0
0
0
0
0
1
1
0
0
0
0
2
1
0
0
0
0
2
0
0
1
2
0
0
1
0
0
2
0
0
2
0
1
0
0
0
1
2
2
0
0
0
0
0
1
0
0
1
2
0
1
2
1
1
0
0
0
0
0
2
1
2
1
0
1
0
0
0
0
2
1
3
2
0
0
1
0
3
0
2
0
0
0
0
1
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
3
0
0
0
0
2
1
2
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
2
0
0
0
2
1
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
2
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
4
0
1
1
0
0
0
0
0
2
0
0
1
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
1
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
2
2
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
3
0
0
0
0
2
2
0
0
2
0
0
3
0
0
0
0
0
0
0
0
6
0
0
1
2
0
0
0
2
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
3
0
3
0
0
0
0
0
2
1
0
1
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
3
1
2
2
0
0
0
0
0
0
0
0
8
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
1
0
1
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
3
2
0
1
0
1
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
1
0
1
1
0
0
2
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
2
1
0
0
0
1
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
1
0
3
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
3
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
3
0
0
2
1
0
0
0
1
2
0
0
0
0
0
0
2
1
0
0
0
0
4
0
0
0
1
2
0
0
1
0
0
2
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
2
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
2
1
0
1
0
0
0
2
0
0
7
0
0
2
0
0
0
1
1
2
12
3
0
0
1
0
0
2
1
2
2
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
1
1
0
0
1
1
0
2
2
0
0
1
2
2
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
1
0
0
0
0
1
2
2
0
0
0
0
2
1
0
1
5
1
1
0
0
0
0
0
1
0
0
3
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
2
0
1
0
0
2
0
0
0
2
0
1
1
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
5
0
1
0
0
0
2
2
0
0
0
1
0
0
0
1
0
0
1
1
1
2
0
0
0
3
1
0
1
2
0
2
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
4
0
2
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
2
0
2
0
0
0
2
2
1
1
0
0
0
0
0
2
0
1
1
0
0
1
0
0
0
0
2
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
1
0
0
0
3
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
2
0
0
2
1
0
1
0
1
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
1
0
0
0
2
2
0
0
0
3
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
1
1
0
0
1
0
0
3
0
0
0
0
0
0
0
0
2
0
2
0
0
2
1
1
1
2
1
0
2
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
1
2
0
0
2
0
0
1
0
0
1
0
0
0
0
1
0
1
0
1
0
0
2
0
2
0
0
2
0
2
1
0
1
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
1
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
3
1
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
2
1
2
0
1
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
6
0
0
0
2
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
1
0
0
3
3
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
2
2
11
3
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
1
1
1
0
1
0
1
3
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
1
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
2
4
0
2
0
0
2
2
0
0
1
0
0
3
2
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
1
2
0
0
0
1
0
2
0
0
2
1
1
0
0
2
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
4
0
0
1
0
1
0
1
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
2
0
1
0
0
2
3
3
2
0
0
2
0
0
0
1
2
0
0
0
0
2
0
0
1
2
1
1
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
1
3
3
2
2
2
1
0
0
1
0
0
0
2
1
0
0
0
0
0
3
0
0
2
0
1
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
3
2
0
0
3
0
2
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
4
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
2
2
0
1
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
3
0
0
2
1
0
1
1
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
3
0
0
0
1
0
2
1
0
0
2
0
1
2
1
2
0
1
0
0
0
2
0
0
2
1
0
0
0
0
0
1
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
2
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
2
0
3
0
1
1
0
0
0
2
0
1
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
2
2
1
0
0
4
1
0
0
0
2
1
2
0
0
3
0
2
0
1
0
0
1
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
4
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
3
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
1
0
0
1
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
1
1
0
0
2
0
0
1
0
0
1
0
0
0
1
0
0
2
3
0
2
0
5
0
3
0
1
0
0
2
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
2
0
1
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
1
2
1
2
0
2
0
0
0
0
0
3
2
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
5
0
0
0
2
0
0
0
1
0
3
0
1
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
3
0
0
0
0
1
0
0
1
0
1
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
2
0
0
2
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
2
0
2
0
3
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
3
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
2
2
0
0
2
0
0
2
0
0
1
2
0
0
0
0
0
0
0
4
0
1
7
0
2
2
1
2
0
8
0
0
0
0
0
2
3
2
1
0
0
0
2
0
2
0
0
0
0
0
1
3
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
6
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
2
4
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
3
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
2
0
0
0
0
0
0
1
3
2
0
0
1
0
0
0
1
0
0
0
0
0
1
2
3
2
2
0
0
0
2
2
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
1
0
1
1
0
2
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
1
0
3
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
3
1
2
1
0
0
0
1
0
0
0
2
0
0
2
3
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
2
0
0
0
2
1
0
0
2
1
1
0
1
1
2
0
0
0
0
0
2
0
3
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
2
0
1
1
0
0
2
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
3
0
0
3
0
7
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
2
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
1
0
0
0
2
2
0
0
0
0
0
0
1
0
1
0
0
1
0
0
2
0
0
0
0
1
1
0
2
0
2
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
1
2
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
1
0
1
2
0
0
2
0
0
2
5
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
1
0
0
0
2
0
0
0
0
2
0
0
0
1
1
1
1
1
2
2
0
0
0
0
0
1
1
1
3
0
2
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
2
2
0
0
0
0
0
0
2
2
0
0
1
0
0
0
3
0
0
0
0
0
0
2
0
1
1
0
0
3
2
3
0
6
0
2
0
3
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
3
2
0
1
0
2
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
4
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
2
1
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
3
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
2
0
0
1
1
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
4
0
0
2
0
0
0
0
0
2
0
0
1
0
1
0
0
1
3
0
2
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
1
1
0
0
0
2
0
2
0
0
0
0
0
0
0
1
1
0
2
0
0
1
0
0
0
0
0
0
1
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
2
0
0
2
0
0
0
1
0
0
0
0
0
0
2
9
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
3
1
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
2
0
0
0
2
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
2
2
1
2
2
0
0
0
0
0
3
0
2
0
3
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
1
0
0
0
0
0
2
2
0
0
0
0
3
0
0
0
0
0
0
3
1
0
0
1
0
0
1
0
0
0
0
1
1
0
0
2
2
0
2
0
0
1
0
0
2
2
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
2
0
2
0
0
2
0
1
0
10
2
0
0
0
1
0
0
2
1
0
2
0
0
1
0
0
0
2
0
1
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
3
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
5
1
1
0
0
1
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
1
0
2
0
0
0
0
0
1
2
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
1
3
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
1
2
0
0
0
0
4
0
0
2
0
0
1
1
3
0
0
1
0
2
0
0
0
1
1
2
2
2
3
1
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
5
1
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
7
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
2
2
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
6
0
0
2
0
0
1
0
0
0
1
1
1
1
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
3
0
0
0
3
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
1
1
0
0
1
0
1
2
2
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
3
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
2
0
0
0
2
3
2
0
0
1
0
0
1
2
0
0
1
0
1
0
0
0
0
0
0
0
0
3
2
1
0
1
0
1
2
2
0
0
0
5
0
2
1
0
0
0
0
0
2
0
0
0
0
1
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
1
0
2
1
0
4
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
1
0
1
1
0
1
0
0
0
0
2
0
1
0
0
2
0
0
0
0
3
0
1
0
0
1
1
2
0
0
0
1
0
0
0
0
2
0
0
2
0
2
0
1
2
0
0
1
2
0
0
0
1
1
0
3
0
1
0
0
0
1
0
1
0
0
0
0
0
2
0
0
4
0
0
0
2
0
0
0
0
1
0
0
1
3
2
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
3
0
0
1
0
0
2
0
0
0
0
0
2
0
2
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
4
2
0
0
0
1
0
0
0
2
1
0
0
0
1
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
2
2
0
0
0
3
2
0
3
0
0
0
1
0
0
0
2
0
1
2
0
1
0
1
0
0
0
0
2
0
1
0
0
3
1
0
0
2
2
0
0
2
0
0
4
0
1
2
0
0
0
0
0
0
2
0
1
0
1
2
1
3
0
2
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
1
0
0
0
1
2
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
3
0
1
0
1
1
2
0
2
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
2
2
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
1
0
0
0
0
0
3
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
4
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
1
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
4
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
2
2
0
0
0
2
1
0
0
2
0
2
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
1
0
0
0
1
0
0
2
2
0
5
2
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
2
0
0
2
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
2
0
0
2
0
4
0
0
0
2
0
1
2
2
4
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
1
0
5
1
1
0
2
2
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
3
0
1
0
2
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
6
0
0
2
0
0
0
1
0
0
1
0
0
2
0
0
0
0
1
0
1
2
11
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
2
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
1
1
0
3
2
1
0
0
0
4
0
0
1
0
0
0
2
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
2
0
0
1
0
0
0
4
1
0
0
2
3
0
0
2
0
1
0
3
1
0
2
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
2
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
3
0
2
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
3
0
0
0
1
0
2
0
0
0
6
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
3
0
2
5
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
4
0
0
0
0
0
1
2
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
1
1
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
2
0
1
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
1
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
2
0
2
1
0
0
0
0
1
0
2
0
0
0
0
0
0
2
2
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
1
0
0
0
1
0
0
1
1
1
0
0
0
0
8
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
1
0
0
0
0
1
0
3
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
1
0
2
2
2
0
1
1
1
0
1
0
0
2
0
0
1
0
0
0
2
2
1
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
4
2
0
0
0
2
0
0
0
0
0
3
0
0
0
0
1
0
1
0
2
0
0
0
1
0
0
5
0
0
0
2
0
0
0
1
0
0
0
2
3
0
1
0
2
0
0
1
2
1
0
1
0
1
0
0
0
0
0
0
4
0
2
0
0
0
1
0
3
0
0
0
0
1
0
0
2
0
2
0
0
1
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
36
0
0
2
0
0
2
0
1
1
0
0
0
0
0
0
2
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
3
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
1
1
0
1
1
0
2
0
0
2
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
1
2
3
0
2
0
0
2
0
0
0
0
1
1
0
0
0
0
3
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
2
0
0
2
0
0
0
2
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
3
0
3
0
0
2
1
0
0
1
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
1
0
0
2
0
0
0
0
0
7
0
1
0
0
0
0
0
3
0
0
0
2
0
0
0
1
4
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
1
4
0
0
4
0
3
0
0
0
0
0
0
1
2
1
2
2
0
0
0
1
0
2
0
2
2
0
0
0
1
0
0
1
1
0
0
2
2
0
0
0
0
2
0
0
0
0
3
0
1
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
5
0
0
0
0
0
0
2
0
0
1
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
2
4
2
0
0
0
0
0
0
0
0
1
2
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
9
0
0
2
2
0
1
2
0
0
0
0
0
1
1
0
1
1
0
0
2
0
0
1
0
0
0
1
1
0
0
1
0
1
1
0
1
2
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
1
0
0
0
0
2
2
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
2
0
0
0
2
0
0
1
0
0
1
2
2
0
2
2
0
0
0
0
0
6
0
0
2
0
0
0
0
0
0
3
0
0
2
0
0
0
2
2
0
0
2
6
0
0
1
1
2
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
3
1
1
0
0
0
0
0
0
0
2
0
2
0
0
2
2
0
0
0
0
0
1
0
0
3
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
2
1
3
2
1
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
2
1
1
2
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
4
0
0
0
1
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
4
1
1
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
1
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
3
1
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
6
1
0
0
0
0
0
0
0
3
0
2
2
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
1
0
1
3
0
0
0
2
0
2
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
5
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
2
0
0
1
0
0
2
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
2
2
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
2
0
2
0
0
0
0
0
1
2
0
6
1
0
1
0
0
1
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
2
0
1
1
0
0
0
1
0
2
0
1
2
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
3
0
0
0
2
0
0
0
0
0
0
2
2
0
0
2
0
1
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
6
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
3
0
0
1
0
0
0
1
1
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
2
1
0
0
0
0
0
0
3
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
2
1
0
2
0
0
2
0
0
1
0
0
1
0
0
1
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
3
2
1
0
0
0
0
0
3
1
1
0
0
2
0
1
2
2
1
2
1
0
0
0
0
0
0
0
1
0
0
1
2
0
0
2
3
3
0
1
0
1
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
1
0
2
0
0
0
0
2
0
1
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
2
2
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
3
0
0
0
0
2
2
0
0
2
0
0
0
2
0
0
1
4
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
1
2
0
1
0
1
1
0
0
0
1
0
0
0
0
2
0
0
1
1
0
0
0
2
2
4
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
2
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
9
3
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
2
0
0
0
1
3
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
3
0
0
0
0
2
1
1
2
2
0
0
2
0
2
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
1
1
1
0
0
2
0
0
0
2
0
1
0
0
0
1
0
2
0
0
0
0
1
0
0
0
1
0
2
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
2
0
2
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
1
2
1
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
2
3
2
0
0
2
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
1
0
0
2
2
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
1
1
1
0
1
2
0
0
1
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
2
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
2
0
1
1
0
0
2
1
1
0
0
0
0
1
0
0
2
0
0
0
0
2
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
3
0
1
0
3
2
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
1
0
2
0
1
0
0
5
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
4
3
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
2
2
0
0
0
1
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
2
0
0
0
2
1
2
0
0
0
1
0
2
0
0
0
2
0
0
1
2
0
0
1
0
0
0
0
6
1
1
0
2
2
0
0
0
0
1
2
0
0
0
1
0
1
5
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
2
0
0
2
0
0
0
1
2
0
0
0
3
0
0
2
0
0
2
0
0
0
2
0
0
0
0
7
2
0
0
2
0
0
0
2
0
0
0
0
2
1
2
2
0
2
2
0
0
3
0
0
0
0
0
1
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
3
0
0
0
1
0
0
0
0
1
2
2
0
1
3
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
2
2
0
2
0
1
0
0
0
0
2
0
0
1
0
1
0
1
1
2
0
0
1
0
1
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
1
0
0
0
0
0
0
3
0
0
2
0
0
0
4
1
0
0
1
2
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
2
0
0
0
2
0
0
5
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
1
1
2
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
5
2
2
1
0
0
0
2
1
0
0
0
1
0
0
0
2
0
0
0
0
3
0
2
0
0
0
0
0
1
2
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
2
2
0
0
0
2
0
1
0
0
0
0
0
3
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
2
0
5
0
0
1
0
1
0
0
0
0
1
0
0
2
1
3
2
0
0
2
0
3
1
0
2
2
0
0
2
0
3
1
0
2
0
1
0
2
0
1
0
0
1
0
1
0
3
1
0
2
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
4
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
1
3
0
0
0
0
2
1
0
0
1
2
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
1
0
1
0
0
2
1
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
4
0
0
2
0
1
9
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
1
2
0
2
0
0
0
0
0
2
2
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
1
3
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
2
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
4
1
0
1
0
0
1
1
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
1
1
0
0
0
2
0
0
2
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
4
0
0
0
0
0
0
2
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
1
0
0
0
1
2
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
5
0
0
1
0
0
0
1
0
0
1
0
0
1
2
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
1
1
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
0
2
2
2
1
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
4
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
2
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
1
2
1
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
2
2
0
0
0
2
1
0
0
2
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
2
0
3
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
2
1
1
0
2
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
1
0
0
2
2
2
1
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
2
0
2
0
0
1
0
0
0
2
2
1
0
0
0
0
0
0
0
3
0
1
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
2
2
0
0
0
1
0
0
1
0
2
1
1
2
2
1
0
1
0
2
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
2
0
0
0
0
3
0
2
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
2
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
2
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
1
0
2
2
1
2
0
0
2
0
0
0
0
2
2
0
0
1
1
0
0
2
0
0
0
0
0
0
1
0
0
3
0
0
0
0
2
1
0
0
0
2
0
2
2
5
0
0
0
2
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
2
0
0
2
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
3
1
0
2
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
2
1
0
2
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
1
1
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
1
2
0
0
0
2
0
3
0
1
1
2
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
3
2
4
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
3
0
0
2
0
0
0
1
2
0
0
0
0
2
2
0
0
0
1
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
2
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
1
2
0
0
2
0
0
2
0
2
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
4
1
0
0
3
0
0
0
0
2
4
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
1
0
2
0
0
0
2
1
0
2
0
5
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
4
0
0
6
0
0
1
4
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
4
0
2
2
0
1
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
2
2
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
3
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
1
0
1
0
2
0
1
0
0
0
2
0
2
0
1
0
2
0
2
0
0
0
2
1
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
1
0
1
0
1
0
1
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
1
1
3
0
2
1
0
0
1
0
3
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
1
0
1
3
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
1
1
0
0
1
1
1
0
3
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
2
0
2
1
1
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
3
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
2
0
2
0
0
2
2
0
2
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
1
3
0
0
0
2
1
0
0
0
1
0
0
0
2
0
1
0
0
1
0
2
0
1
2
0
0
0
3
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
2
0
1
2
0
1
0
1
2
1
0
0
0
2
0
2
2
1
0
0
0
0
2
1
0
1
3
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
2
0
0
2
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
1
1
0
2
1
0
1
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
4
2
0
0
0
0
0
0
2
0
0
0
0
1
1
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
4
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
2
0
2
1
1
0
0
0
0
0
1
1
2
0
0
0
0
0
2
2
0
0
0
2
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
5
0
0
1
2
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
4
1
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
5
0
0
2
0
0
1
0
2
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
5
0
0
0
0
2
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
1
0
2
0
2
2
0
0
0
1
0
0
0
0
2
1
0
1
0
0
0
1
0
0
0
1
1
2
2
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
1
1
0
1
4
2
1
0
1
0
0
0
0
1
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
2
2
4
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
3
1
0
0
0
0
2
0
0
0
3
1
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
3
0
0
0
0
0
2
0
1
0
1
0
0
0
1
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
1
0
2
1
0
0
0
0
0
0
2
0
0
0
1
1
2
0
1
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
2
0
1
0
0
0
0
1
0
0
1
0
0
5
0
1
1
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
4
0
0
0
0
0
0
4
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
1
0
0
0
3
0
0
0
0
3
0
2
0
0
1
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
1
3
2
1
0
0
0
0
0
3
1
2
0
3
0
0
2
0
0
0
0
0
1
0
0
0
0
2
2
0
1
0
0
0
1
0
1
2
1
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
1
0
1
0
2
0
4
0
0
0
0
0
0
2
0
1
3
0
3
1
0
0
1
0
2
0
1
0
1
0
0
0
2
1
2
1
0
0
2
2
1
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
2
0
3
1
0
2
0
0
0
0
3
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
1
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
2
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
1
0
1
0
2
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
2
0
0
0
0
0
4
2
0
0
2
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
3
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
6
0
1
0
1
0
0
0
0
0
0
1
0
2
0
0
0
2
2
3
0
1
2
2
0
1
0
1
0
0
2
0
0
0
7
0
0
0
0
0
2
2
0
0
0
0
1
3
0
0
2
0
0
0
6
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
3
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
2
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
2
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
2
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
1
0
0
0
0
0
2
5
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
3
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
1
1
11
1
0
2
1
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
1
0
1
0
0
1
1
0
2
0
2
0
0
0
0
0
0
1
0
0
1
0
2
2
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
4
2
0
0
2
1
1
2
0
2
0
1
0
0
1
1
0
0
1
0
0
3
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
2
0
0
1
0
2
0
0
2
0
2
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
2
0
0
0
1
0
0
1
0
0
1
0
0
3
1
0
0
0
0
0
0
2
2
1
2
2
0
1
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
2
1
2
2
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
1
1
0
2
0
1
0
0
0
2
0
0
2
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
9
1
2
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
2
0
0
0
1
0
0
2
0
4
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
1
0
1
3
0
0
2
2
1
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
2
1
2
0
1
1
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
2
0
0
0
0
0
0
1
2
2
2
0
3
2
1
0
2
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
1
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
3
0
2
0
0
2
2
2
3
1
0
1
0
0
2
0
1
2
0
0
0
0
0
2
0
2
0
2
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
1
0
2
0
1
0
1
0
0
0
2
2
1
1
2
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
3
0
0
0
0
0
2
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
2
1
2
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
1
0
1
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
3
1
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
3
1
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
2
3
0
2
2
2
0
0
0
0
1
0
0
2
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
3
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
2
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
1
0
0
1
2
1
2
0
0
0
0
0
0
0
1
1
4
0
2
1
2
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
1
0
0
0
2
0
1
1
0
0
0
1
0
2
0
0
1
0
1
0
0
0
0
0
2
3
0
0
0
0
0
2
0
0
0
0
1
2
3
0
0
0
1
0
2
0
0
2
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
1
0
0
1
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
4
0
2
0
0
0
2
0
0
0
1
0
0
0
2
0
2
1
0
0
0
0
1
0
0
0
5
2
0
0
0
0
0
1
0
1
0
0
0
2
0
1
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
2
1
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
4
2
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
4
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
3
3
0
0
0
0
0
2
2
0
0
0
0
0
0
2
1
0
0
1
2
0
0
0
2
0
2
0
2
3
2
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
2
2
0
0
1
0
0
0
0
1
0
3
0
0
0
0
2
0
0
1
0
0
1
2
0
1
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
2
0
0
1
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
3
0
0
0
2
2
0
0
1
0
0
0
1
0
2
0
0
0
2
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
2
0
0
0
0
0
2
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
3
0
2
0
2
0
1
2
2
2
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
1
0
2
1
1
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
1
2
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
1
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
3
0
0
1
2
1
2
2
0
0
0
0
0
2
1
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
2
2
1
1
0
0
1
0
0
2
1
0
2
1
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
1
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
3
2
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
2
1
0
1
0
1
0
0
0
3
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
2
0
0
0
0
2
0
0
1
0
0
1
0
2
0
1
0
1
0
1
2
2
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
5
0
2
0
1
2
0
0
0
0
2
3
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
1
3
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
2
0
1
2
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
8
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
1
2
0
0
0
0
2
0
2
2
0
0
0
0
2
0
1
1
0
2
0
2
0
2
0
0
1
0
0
0
0
2
1
0
3
0
0
0
0
1
0
0
1
1
2
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
5
2
0
0
0
1
1
0
0
0
0
0
0
4
0
1
1
2
0
0
0
0
1
0
1
0
2
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
2
0
0
1
1
1
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
1
1
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
4
0
0
1
0
2
0
0
0
0
0
0
4
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
1
0
1
1
2
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
1
0
0
2
0
0
2
0
2
0
0
0
0
3
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
3
0
0
3
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
1
0
2
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
1
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
1
2
0
1
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
1
0
2
0
0
1
1
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
1
0
2
0
0
0
2
1
0
0
0
0
1
0
1
0
0
0
0
1
2
1
0
2
0
1
0
0
0
0
0
2
0
0
0
2
0
3
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
2
1
2
1
0
0
0
3
0
1
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
2
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
1
1
0
0
0
0
0
0
2
2
1
2
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
2
2
0
0
2
0
2
0
0
0
0
0
0
0
0
4
1
0
1
2
1
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
1
0
1
0
2
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
2
2
0
0
0
0
2
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
2
1
0
0
0
2
1
1
2
0
0
0
0
0
3
3
0
0
2
0
0
0
0
0
2
1
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
0
4
0
1
0
0
2
0
2
0
0
0
0
0
1
0
0
3
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
3
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
2
1
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
1
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
2
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
1
0
2
0
0
0
0
1
2
0
0
0
2
3
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
1
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
1
2
2
0
1
0
2
0
0
0
2
1
0
2
0
3
1
0
0
1
0
2
1
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
7
0
2
2
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
3
0
0
1
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
5
2
0
0
2
1
0
0
0
0
0
2
0
0
0
0
2
1
0
1
0
1
0
0
2
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
1
2
0
2
1
0
0
0
1
0
1
0
1
0
0
0
1
0
0
1
0
1
1
2
1
0
1
1
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
1
0
1
2
1
0
0
1
1
0
0
2
0
0
2
0
0
0
0
1
0
3
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
3
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
2
2
1
1
0
0
0
0
0
0
0
0
2
3
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
6
1
0
0
1
0
0
0
0
1
0
0
0
0
2
0
1
2
0
1
2
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
2
0
0
1
3
0
0
0
2
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
1
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
2
1
0
0
1
0
0
2
0
2
2
1
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
1
0
0
0
1
3
0
1
0
0
0
0
0
2
0
0
0
3
0
0
0
2
1
0
1
0
0
0
0
0
2
3
0
0
0
0
1
1
0
0
3
0
0
0
0
0
0
0
6
0
2
0
1
0
3
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
2
2
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
1
1
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
1
0
5
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
3
2
0
0
0
0
2
2
0
0
0
1
2
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
3
0
0
1
0
0
0
0
1
3
0
0
0
2
0
3
2
0
0
0
4
0
0
0
0
1
3
0
1
0
0
0
0
0
0
1
2
0
0
0
2
2
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
3
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
1
0
4
0
0
2
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
3
0
0
0
0
1
0
0
2
0
0
0
4
0
0
0
0
1
0
1
1
2
2
1
1
2
0
0
0
3
0
2
0
0
1
2
0
1
0
0
0
0
0
0
0
2
1
2
1
0
0
0
0
5
1
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
2
0
0
0
2
0
0
0
0
2
0
3
1
0
0
0
0
0
3
0
0
1
0
0
0
0
1
0
0
0
0
1
2
0
0
1
0
0
0
0
0
1
2
0
0
2
1
0
1
0
1
0
0
2
0
3
2
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
2
0
2
1
11
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
1
0
0
0
2
0
1
2
0
0
0
0
0
0
1
0
0
0
0
2
1
2
0
2
0
0
1
3
0
1
1
0
0
0
2
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
3
0
0
1
0
3
0
0
0
2
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
3
1
2
1
0
0
0
0
0
1
2
2
0
2
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
3
0
0
0
3
0
0
0
2
0
0
0
1
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
1
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
1
2
0
0
0
0
0
0
0
0
3
1
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
3
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
2
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
1
2
0
0
3
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
2
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
3
2
0
0
0
0
3
0
0
4
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
1
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
2
0
0
0
2
2
0
2
2
0
0
1
1
0
0
2
0
0
0
1
4
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
1
1
0
2
2
0
1
1
2
0
0
1
1
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
4
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
2
0
2
0
1
0
1
0
2
0
1
1
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
1
1
2
0
1
2
0
3
1
0
0
0
0
2
0
0
1
0
0
0
1
0
0
3
0
0
0
0
1
2
0
0
0
1
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
1
1
0
2
0
0
0
0
2
2
1
1
0
0
3
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
1
2
0
0
2
1
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
2
0
0
1
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
2
0
0
0
0
0
0
2
0
0
1
0
1
0
1
0
5
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
1
0
0
0
2
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
4
2
0
2
0
0
1
3
0
1
0
0
0
0
3
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
2
0
2
0
2
0
3
0
2
2
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
7
2
0
0
0
0
0
0
1
0
2
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
2
0
2
3
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
2
0
1
2
1
0
0
1
0
2
4
0
3
1
2
0
0
1
0
1
0
1
0
2
0
0
1
4
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
1
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
8
0
0
0
0
0
0
0
2
0
0
1
1
2
0
2
0
0
0
2
0
6
0
0
0
2
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
3
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
1
2
0
9
0
1
0
2
0
1
0
0
0
0
1
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
2
0
3
2
0
2
0
0
0
0
0
2
0
0
2
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
1
0
0
1
0
1
2
1
2
0
2
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
2
3
0
2
0
2
1
0
0
1
1
0
1
2
1
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
1
0
0
1
2
0
0
0
1
0
0
0
0
1
0
2
1
0
0
0
0
0
2
0
1
1
1
0
0
0
2
0
0
0
7
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
3
0
0
1
1
0
0
0
0
0
0
3
3
4
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
2
1
0
2
2
0
3
0
0
3
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
1
3
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
3
2
0
0
0
0
0
2
0
0
2
0
2
1
1
1
0
0
0
0
0
0
0
2
1
0
1
0
0
2
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
1
0
0
0
10
0
1
2
1
1
0
1
0
1
3
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
1
0
0
2
0
2
1
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
1
0
0
3
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
2
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
4
1
1
0
2
0
2
0
0
2
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
3
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
2
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
3
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
1
2
1
1
2
0
0
0
0
0
0
2
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
1
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
1
0
0
2
0
0
0
0
0
2
2
0
2
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
2
0
0
1
1
0
0
0
2
0
0
1
0
0
0
0
0
4
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
2
0
2
3
0
1
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
1
0
0
2
0
1
2
0
0
0
0
3
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
3
0
2
0
0
0
0
0
2
2
1
1
0
0
0
2
1
0
0
7
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
6
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
1
0
0
0
1
0
1
0
0
0
0
0
2
0
0
2
0
0
0
4
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
3
0
1
0
0
2
2
3
0
0
0
0
0
0
0
0
2
0
1
2
1
1
0
0
1
0
2
0
1
0
2
0
0
0
0
0
0
0
0
1
0
2
1
1
0
0
0
3
0
0
1
0
1
1
2
0
0
0
0
0
0
2
0
0
1
0
2
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
1
1
0
0
0
2
0
9
1
0
1
0
0
1
0
2
0
0
0
0
1
0
3
0
0
3
4
0
0
0
0
0
0
0
1
5
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
3
0
6
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
1
1
0
2
0
0
1
0
2
0
2
0
1
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
1
2
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
2
2
0
0
0
0
2
3
0
0
0
0
0
1
0
0
0
2
2
2
0
0
0
1
0
0
0
0
0
0
0
1
1
2
0
0
2
1
0
0
0
0
0
1
0
0
0
0
1
0
0
3
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
2
1
0
0
2
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
1
3
0
1
0
1
0
0
3
0
0
0
2
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
1
3
0
0
2
0
0
0
0
0
2
1
0
2
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
2
0
2
0
4
2
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
5
0
0
0
4
0
0
0
0
2
0
0
0
0
0
0
10
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
1
1
2
0
0
0
0
2
0
1
0
2
0
0
1
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
2
2
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
3
0
0
0
0
0
1
4
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
2
0
2
0
0
2
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
3
1
0
2
0
0
0
0
2
0
2
0
1
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
1
2
2
0
0
0
0
0
0
0
0
2
0
1
1
0
2
1
0
0
0
0
2
2
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
3
1
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
1
0
0
0
0
2
1
0
0
2
0
0
2
1
0
0
3
0
2
0
0
0
0
0
2
0
0
1
1
1
0
0
0
0
0
1
1
2
2
0
0
0
0
0
0
0
3
1
0
0
1
2
0
0
0
1
0
0
2
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
2
0
0
1
1
0
0
0
2
0
2
2
0
2
0
0
2
2
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
2
0
1
0
0
0
3
0
0
0
0
0
1
0
0
0
0
1
2
0
1
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
3
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
2
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
1
3
0
0
0
0
1
2
0
0
0
0
1
2
0
0
0
2
0
2
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
2
0
2
1
0
1
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
1
0
0
0
0
1
0
0
0
3
0
0
2
0
0
0
0
0
1
1
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
1
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
2
2
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
1
1
0
1
0
0
2
0
2
0
1
1
0
1
0
2
1
0
2
2
0
0
1
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
2
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
2
0
0
0
2
0
3
0
1
2
0
0
0
0
2
0
0
2
0
2
0
0
0
0
2
0
2
6
0
2
0
1
0
0
0
0
0
1
0
0
3
0
1
0
0
2
2
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
2
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
2
2
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
2
0
2
0
0
1
3
0
0
0
0
0
1
0
0
0
2
2
2
2
2
0
0
2
1
0
0
0
0
0
0
0
1
2
0
0
5
1
2
0
0
0
0
0
0
0
2
1
0
0
1
2
0
0
0
0
0
0
2
1
0
1
1
2
2
0
0
1
0
3
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
2
2
3
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
1
0
1
2
0
3
0
0
0
1
0
0
2
0
2
0
2
0
0
0
0
1
1
0
1
0
2
0
0
0
3
0
0
1
2
0
2
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
3
0
0
0
0
0
0
2
0
0
0
2
2
1
0
2
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
2
0
0
0
8
0
0
2
0
1
0
0
0
2
1
0
1
0
0
1
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
2
2
0
0
3
0
1
0
0
0
0
0
2
0
0
2
2
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
2
1
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
4
0
0
0
1
0
1
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
1
0
0
1
0
2
0
1
2
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
3
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
3
0
0
0
1
0
1
0
0
0
1
2
2
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
2
0
0
0
1
0
0
2
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
1
2
2
0
1
1
2
0
0
1
0
2
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
1
0
0
1
0
3
2
0
0
0
0
0
0
0
2
0
2
2
0
0
0
1
1
4
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
1
0
0
0
0
2
2
0
0
0
1
0
6
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
1
2
0
2
0
0
2
0
2
0
0
0
0
1
0
0
0
2
0
1
0
0
2
0
2
0
2
1
0
0
1
2
1
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
2
0
0
5
0
0
0
1
0
2
0
0
1
2
0
2
2
0
0
0
3
0
0
0
1
0
1
0
0
0
0
0
0
0
2
1
0
0
0
3
0
0
0
0
3
0
1
1
0
0
0
0
0
2
0
0
3
0
2
0
0
0
0
0
0
0
3
2
0
0
1
1
4
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
1
0
2
0
0
1
0
0
2
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
1
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
3
0
0
0
0
2
2
0
2
0
0
0
0
0
0
2
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
3
1
0
0
0
1
0
2
0
0
0
0
2
0
0
0
1
0
1
0
2
0
0
0
0
0
2
1
3
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
2
0
0
2
0
0
1
0
0
0
0
1
1
0
4
0
0
1
1
0
0
0
0
0
3
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
1
4
0
0
0
0
0
0
0
2
0
0
0
0
3
2
0
0
0
2
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
1
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
2
0
1
0
1
0
1
0
1
0
1
3
3
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
3
0
4
0
2
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
4
0
0
0
0
0
0
1
0
2
0
0
0
0
2
2
2
0
0
0
2
0
0
0
2
2
0
1
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
1
1
0
0
4
0
0
0
0
2
0
0
0
0
3
1
2
0
0
2
0
0
0
1
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
1
0
0
0
3
0
0
1
0
0
0
2
0
0
0
0
0
0
3
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
6
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
2
0
0
0
0
1
0
0
1
0
1
2
0
0
1
1
1
0
0
0
1
1
0
1
0
0
2
0
3
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
2
1
0
2
0
0
0
0
3
3
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
1
2
0
0
0
2
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
1
0
0
0
2
0
0
0
0
1
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
1
0
2
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
1
2
4
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
2
2
0
2
0
0
0
0
0
0
1
0
1
0
0
0
2
1
0
0
2
0
0
0
0
0
1
0
0
1
2
2
2
0
0
2
0
1
0
1
2
0
2
1
0
1
0
1
2
0
2
1
0
2
4
0
0
0
0
2
0
0
2
0
0
0
0
1
1
0
1
0
1
0
3
0
3
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
3
0
0
0
1
1
2
2
2
0
0
1
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
1
0
1
0
0
0
0
1
1
2
0
1
0
1
0
2
0
2
1
1
2
0
1
0
2
1
0
0
0
0
0
0
2
2
0
0
2
0
0
0
2
1
0
0
0
3
0
0
1
1
0
2
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
2
0
2
3
0
1
0
0
0
2
0
1
2
0
2
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
1
2
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
2
1
2
2
0
2
0
0
2
2
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
1
2
0
0
1
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
4
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
2
0
2
0
0
2
0
1
2
0
0
0
0
0
0
0
1
2
2
0
2
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
2
0
0
0
0
0
0
0
2
2
0
0
0
2
2
0
0
0
0
0
1
2
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
2
0
0
1
3
2
0
0
1
3
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
3
2
0
0
2
0
0
0
0
2
0
3
1
0
0
2
0
1
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
3
0
1
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
1
1
0
1
3
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
6
0
2
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
2
0
0
0
1
0
0
0
0
0
2
1
0
1
0
0
0
1
2
0
0
0
0
0
0
0
2
0
1
1
0
1
0
0
0
0
0
0
1
0
2
0
1
0
2
0
0
0
2
1
0
2
0
0
0
0
1
2
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
1
0
1
0
0
0
0
2
0
4
0
0
2
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
1
0
1
1
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
1
3
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
3
0
0
1
0
0
2
1
0
0
0
0
1
2
0
0
0
0
0
0
2
1
0
0
0
0
2
1
2
0
0
0
2
2
0
0
2
0
0
0
0
0
2
1
1
0
0
0
1
0
2
1
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
6
0
0
0
0
2
0
2
0
0
2
0
2
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
5
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
2
0
0
3
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
3
4
0
2
0
0
2
2
2
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
3
0
2
2
0
0
2
0
0
0
0
0
0
0
1
0
0
2
1
2
0
0
1
1
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
3
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
1
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
2
2
0
0
2
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
5
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
1
3
0
0
0
1
2
1
0
0
0
2
0
0
2
0
0
0
0
3
0
2
1
0
0
1
0
1
0
0
0
0
0
1
1
0
2
0
0
2
0
3
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
2
0
0
1
0
2
0
0
0
1
0
0
0
0
2
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
4
1
0
1
1
0
0
1
0
0
4
0
0
3
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
3
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
1
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
1
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
2
1
2
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
2
1
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
2
0
0
2
0
1
1
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
1
1
2
0
1
3
0
0
1
2
0
0
0
0
0
1
0
0
0
5
0
0
2
0
3
0
2
0
0
0
0
1
0
0
3
0
0
1
1
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
2
0
2
1
0
0
0
0
0
1
0
0
0
0
0
4
0
0
1
0
0
0
2
0
0
2
0
0
0
0
1
0
1
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
4
0
1
0
0
1
1
2
0
0
2
1
0
0
0
1
0
1
0
0
0
1
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
2
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
3
2
0
0
4
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
4
0
0
3
0
0
1
0
0
0
0
0
3
0
1
0
0
0
2
0
0
0
0
0
1
2
0
2
2
0
0
0
0
0
1
0
0
1
1
2
0
0
0
0
1
0
0
0
0
0
0
2
2
0
1
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
2
0
0
0
0
1
2
0
0
2
0
0
1
0
2
0
4
0
0
1
0
0
1
0
0
0
1
2
2
0
0
2
0
0
0
2
0
0
1
1
2
2
0
2
0
0
0
0
0
0
5
0
0
0
1
2
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
3
0
1
0
5
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
2
0
1
0
0
2
0
0
0
1
2
1
0
0
1
0
0
0
1
0
2
2
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
1
1
1
2
0
0
2
0
2
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
3
1
0
2
0
1
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
3
1
0
0
0
3
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
2
0
0
2
0
0
0
1
2
0
0
2
1
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
1
3
2
0
1
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
2
0
0
3
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
1
0
0
2
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
1
0
2
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
5
0
0
1
2
0
0
1
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
2
1
0
3
0
3
0
2
0
0
0
0
0
1
1
3
0
2
0
0
0
4
0
1
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
2
2
0
1
0
0
0
2
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
1
2
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
1
9
1
0
0
0
1
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
1
0
1
0
0
3
0
0
0
0
0
1
0
1
0
2
1
0
3
0
0
0
2
2
0
2
0
0
1
0
0
0
1
0
7
1
0
2
1
0
0
0
1
1
0
1
1
0
0
0
0
1
0
2
2
0
1
2
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
2
0
1
0
1
0
2
0
0
0
0
2
1
0
1
0
0
2
1
2
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
3
1
2
0
2
0
0
0
3
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
1
1
1
0
0
1
0
0
0
1
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
4
0
0
1
0
1
0
0
0
1
0
0
0
0
2
0
1
0
0
1
0
0
0
0
2
0
0
2
1
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
1
0
1
1
0
4
0
0
0
0
2
1
1
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
1
0
2
0
0
0
1
1
1
0
0
0
0
1
0
0
5
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
2
1
1
0
0
0
2
2
0
1
0
0
0
0
2
2
2
0
0
0
2
0
0
0
0
0
1
1
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
2
0
2
1
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
2
2
0
2
0
0
0
2
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
3
0
0
2
2
0
1
0
0
1
0
0
0
0
2
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
1
2
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
3
2
1
2
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
1
2
0
0
0
2
0
2
0
1
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
3
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
4
1
0
0
1
1
0
0
0
0
0
1
0
2
0
0
0
0
0
2
2
1
0
1
1
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
2
0
0
1
2
4
1
2
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
1
2
2
0
1
3
0
0
0
0
2
0
0
2
0
3
0
1
2
1
1
0
1
1
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
1
2
0
0
0
1
2
0
0
0
1
0
2
5
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
2
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
3
1
0
0
4
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
1
1
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
2
0
0
1
0
0
1
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
1
0
0
1
0
2
2
0
0
0
0
0
0
0
2
1
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
3
0
2
2
0
0
0
2
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
2
2
0
2
1
0
0
0
2
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
2
0
3
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
2
0
2
0
1
2
0
1
0
0
0
0
0
1
0
2
1
0
0
0
2
2
0
0
2
1
0
0
0
0
1
1
1
0
0
2
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
2
2
1
1
0
0
0
0
0
1
1
0
1
1
0
0
0
1
0
0
0
2
0
0
0
0
0
1
2
1
0
0
0
0
2
0
2
2
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
2
0
6
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
3
0
2
2
3
0
0
0
0
0
0
1
0
0
3
0
0
1
3
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
2
0
0
0
0
0
1
1
0
2
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
3
0
0
0
1
2
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
1
1
0
0
2
0
1
0
2
2
2
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
1
0
0
1
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
1
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
3
1
0
2
0
1
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
3
0
0
0
3
1
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
2
0
0
1
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
2
1
1
0
0
1
0
0
0
0
0
0
0
2
0
3
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
2
1
1
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
2
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
4
0
2
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
2
1
0
2
0
1
0
1
0
1
0
0
1
1
0
0
2
3
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
2
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
2
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
2
0
0
0
1
1
2
2
1
5
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
2
2
0
0
0
1
2
0
0
1
0
0
0
0
0
1
0
0
2
0
1
1
0
1
1
2
1
1
1
2
1
0
0
0
0
0
0
0
0
2
1
0
4
0
1
1
0
2
0
1
2
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
2
1
2
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
3
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
1
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
2
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
3
1
0
0
0
0
0
2
0
0
1
0
0
0
0
1
1
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
4
0
0
0
1
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
1
0
0
2
0
0
0
4
0
0
2
1
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
2
0
0
0
0
3
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
8
3
1
0
0
0
2
0
0
2
11
0
0
1
1
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
1
2
0
1
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
2
2
1
1
0
0
0
0
0
2
0
1
0
0
1
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
1
3
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
2
0
2
0
1
5
0
0
0
0
0
3
0
0
0
0
0
0
1
0
2
2
0
5
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
3
1
0
0
0
1
0
0
0
0
0
0
1
1
0
2
0
0
2
1
0
2
0
0
12
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
1
0
0
1
1
0
0
1
2
0
3
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
2
0
2
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
1
1
2
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
3
0
0
0
3
0
1
0
4
2
0
0
0
1
0
0
1
2
0
0
0
0
2
0
0
2
1
0
0
2
0
0
0
0
0
0
2
0
5
0
0
0
1
7
1
2
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
3
1
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
2
2
0
0
3
0
1
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
1
0
3
0
0
1
1
0
0
0
2
0
0
1
0
0
1
0
0
0
1
2
0
0
2
0
0
1
0
1
0
0
0
2
0
0
2
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
2
0
3
0
0
2
0
2
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
2
0
0
0
3
0
0
0
2
0
0
0
0
0
3
2
1
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
2
1
0
1
0
2
1
0
2
0
0
0
0
0
0
1
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
1
0
3
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
1
1
1
1
2
0
0
2
0
2
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
1
0
2
0
4
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
2
0
1
1
0
0
0
1
0
1
1
2
1
0
0
0
5
0
2
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
2
0
2
0
2
0
1
0
0
0
2
4
0
0
1
0
0
2
0
0
0
2
0
2
0
2
0
0
2
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
1
1
1
0
0
3
0
2
0
0
0
0
0
0
0
2
2
0
0
1
1
0
0
0
0
1
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
2
4
3
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
3
0
1
1
0
0
0
0
2
0
0
0
0
0
2
4
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
4
2
1
0
0
0
0
0
0
0
0
0
1
1
2
2
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
2
1
0
0
0
2
0
1
0
0
2
2
0
0
2
0
1
1
2
0
0
0
0
0
0
1
2
0
0
0
2
2
0
3
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
4
0
1
0
0
0
0
0
1
1
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
1
2
1
4
0
0
0
3
0
0
0
0
1
0
1
2
0
1
2
2
1
1
0
0
2
0
0
1
1
2
0
0
2
1
0
0
0
0
0
4
0
0
1
0
0
1
0
0
1
0
0
1
0
0
3
2
0
0
1
0
0
0
0
0
1
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
1
0
0
0
3
0
0
0
0
3
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
2
1
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
2
0
1
4
0
0
1
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
1
1
0
4
2
0
2
4
0
0
0
0
0
2
0
0
0
0
0
2
1
0
1
0
0
1
0
0
0
1
0
2
0
1
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
2
1
0
0
1
1
1
0
0
2
2
0
0
0
0
0
1
3
0
2
0
0
0
0
0
0
1
0
0
0
0
1
1
0
2
0
0
0
1
0
0
0
2
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
2
1
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
4
1
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
3
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
1
1
0
0
0
1
0
0
1
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
2
1
1
0
3
1
0
0
0
0
0
0
0
0
0
2
0
0
0
3
1
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
1
0
2
1
1
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
2
0
0
1
0
0
0
6
1
0
0
0
0
0
0
2
0
2
0
2
0
1
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
3
1
0
0
2
0
2
1
0
0
0
2
4
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
3
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
1
2
2
0
0
1
0
0
0
0
2
0
0
0
0
2
2
0
2
3
0
0
1
1
0
0
0
1
4
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
1
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
2
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
2
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
2
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
3
1
4
0
0
2
0
1
0
3
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
5
2
0
2
0
1
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
4
2
0
0
1
2
0
0
0
0
2
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
1
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
4
2
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
1
2
0
1
0
1
0
1
2
0
0
0
0
0
1
2
2
0
0
0
0
0
3
0
3
1
0
2
3
2
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
6
0
0
2
1
1
2
0
1
3
1
0
1
0
0
0
0
0
2
1
0
3
0
0
1
3
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
2
0
0
1
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
2
0
0
0
0
0
0
1
2
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
1
1
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
3
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
3
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
2
0
0
1
0
2
0
1
0
1
1
3
0
1
0
0
0
0
1
2
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
1
0
1
0
0
7
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
5
0
0
0
3
2
0
2
10
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
5
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
2
0
0
0
1
0
0
0
0
3
5
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
2
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
16
1
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
1
1
0
0
0
2
0
2
2
2
0
1
0
2
6
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
3
0
6
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
3
0
0
0
1
0
0
0
0
0
1
0
2
0
2
1
0
0
1
0
0
0
3
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
3
3
2
1
0
0
0
1
0
0
0
2
0
0
0
2
0
2
0
0
0
2
3
0
1
0
0
0
0
0
0
0
0
0
0
2
2
1
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
4
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
2
2
0
0
0
0
1
0
1
0
0
0
0
0
0
5
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
1
0
2
0
0
0
1
0
2
0
0
1
0
0
8
1
0
0
2
2
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
2
0
3
0
2
2
0
0
2
2
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
4
2
0
0
0
1
0
0
0
1
0
1
0
0
1
0
1
3
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
1
0
2
0
0
2
0
1
2
0
0
2
1
0
0
0
0
0
1
2
0
0
1
1
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
2
2
0
1
0
2
0
1
0
0
0
1
0
0
0
1
0
2
0
0
2
0
0
0
0
1
3
2
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
3
0
0
0
0
0
2
0
0
1
0
0
1
0
2
0
2
0
2
0
0
1
0
0
0
2
1
0
0
0
2
1
2
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
1
0
2
0
1
0
2
1
0
0
1
2
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
1
1
1
3
0
1
0
0
0
0
2
0
2
1
0
0
0
2
0
0
2
0
0
0
0
2
1
1
1
0
0
1
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
4
1
0
2
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
1
0
0
0
0
4
0
0
0
1
1
0
0
0
1
3
0
0
0
0
0
0
0
2
2
0
0
2
0
0
1
0
0
0
0
0
0
3
0
8
0
1
0
0
0
0
0
1
0
0
0
0
0
2
2
2
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
3
2
0
0
0
0
1
0
0
0
4
0
0
2
0
0
0
3
0
0
0
1
2
0
2
0
0
0
0
0
0
4
0
0
0
0
3
0
1
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
1
1
0
2
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
1
2
0
0
1
0
0
2
0
0
0
2
0
1
0
2
1
1
0
0
1
0
1
1
1
2
0
1
0
4
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
2
3
0
2
0
1
0
2
0
1
6
0
2
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
4
0
0
1
1
0
1
0
0
3
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
3
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
1
2
0
0
0
0
1
1
2
0
2
1
0
0
1
1
0
0
0
0
1
0
0
0
1
1
3
0
0
0
0
1
0
1
1
0
3
1
0
1
0
2
1
2
1
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
1
0
0
0
0
0
0
4
0
0
1
5
0
1
0
0
0
0
0
0
0
2
0
0
1
2
0
2
1
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
2
0
0
1
0
0
1
1
3
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
2
0
0
0
0
0
4
0
0
2
0
2
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
2
0
0
1
1
0
0
1
0
0
1
0
0
0
2
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
3
0
1
1
0
0
0
0
0
1
0
0
0
1
0
1
1
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
2
2
2
0
0
0
0
0
0
1
2
0
0
1
0
0
2
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
2
0
0
0
0
1
1
0
1
0
0
0
2
0
0
1
2
0
2
0
2
0
0
2
0
1
0
0
0
1
2
0
0
1
0
0
1
0
4
1
0
0
1
2
0
0
0
0
0
0
2
2
0
1
0
1
1
0
0
0
1
0
2
0
0
0
2
1
0
1
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
2
0
0
1
0
3
0
0
1
0
0
0
1
1
0
0
0
0
0
0
2
0
0
2
1
0
1
0
0
0
0
0
0
1
1
2
0
0
3
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
3
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
3
2
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
1
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
2
0
0
1
0
1
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
1
0
1
0
0
0
1
2
4
1
0
0
4
2
0
1
0
2
2
0
0
0
2
0
0
1
0
0
3
0
1
0
0
1
0
4
0
0
0
1
3
0
1
0
0
0
0
0
0
0
0
0
2
0
1
1
2
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
1
0
0
2
0
0
0
0
1
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
1
2
2
0
0
2
0
1
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
2
0
0
0
0
0
2
0
0
13
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
1
0
0
1
2
0
1
0
2
0
2
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
1
2
1
0
1
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
2
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
1
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
1
0
0
0
0
1
1
0
2
2
1
0
0
0
0
0
0
2
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
2
0
0
3
0
0
0
2
0
0
2
2
0
2
0
2
2
1
0
0
0
0
0
0
0
0
0
1
4
0
2
0
0
0
0
0
0
0
1
2
0
0
4
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
6
0
0
0
2
0
0
0
2
1
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
2
0
2
2
0
1
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
2
0
2
0
0
0
0
0
3
1
0
1
0
2
0
0
2
0
2
0
0
1
2
2
0
1
0
0
0
0
0
1
0
0
0
0
0
2
1
1
0
1
0
0
0
0
0
0
0
2
1
1
0
0
1
1
0
0
1
1
0
0
0
0
1
0
0
0
0
2
0
2
1
0
0
0
0
1
2
2
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
1
2
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
2
0
1
2
0
4
0
0
1
0
0
0
2
0
0
2
2
0
0
1
1
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
2
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
1
0
1
0
0
0
0
0
3
0
2
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
2
1
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
2
0
0
0
1
0
4
3
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
2
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
2
0
0
1
2
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
2
0
3
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
2
3
0
0
0
0
2
2
2
1
0
3
0
0
0
0
0
0
2
2
0
2
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
3
0
0
0
1
2
0
0
1
1
0
0
0
3
0
0
0
0
2
2
1
0
2
0
0
2
2
0
0
1
0
0
0
2
0
0
2
0
0
0
0
1
3
1
0
0
2
0
0
0
2
0
1
0
2
0
0
0
2
2
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
1
1
1
1
0
0
0
1
0
0
1
2
0
3
0
0
0
0
0
1
2
2
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
1
2
2
2
0
0
0
0
1
0
2
0
1
0
0
0
1
0
0
2
1
0
1
0
0
2
0
0
0
2
0
0
0
0
0
1
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
7
0
2
1
0
0
0
0
0
0
0
3
0
0
0
2
2
0
1
0
2
0
0
0
0
0
0
2
0
2
0
0
2
1
0
2
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
5
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
1
0
0
0
1
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
7
0
2
0
2
0
0
2
0
0
0
0
3
0
4
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
2
2
0
0
0
0
0
2
0
1
0
0
2
0
0
2
0
0
1
0
0
0
0
1
1
0
0
0
2
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
1
0
0
0
2
3
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
2
0
0
2
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
4
0
0
1
2
0
0
0
0
2
0
3
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
2
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
7
0
2
0
0
0
0
2
1
0
1
1
2
0
1
2
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
5
0
0
0
0
3
0
0
2
0
0
1
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
1
0
2
0
3
0
2
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
1
0
2
0
0
0
0
2
0
1
0
0
0
0
1
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
1
2
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
2
0
0
0
2
2
0
0
0
0
0
2
0
1
0
0
0
2
0
0
3
1
0
0
0
2
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
2
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
1
1
1
1
0
0
1
2
0
0
0
0
2
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
1
0
1
0
2
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
2
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
2
2
0
1
0
0
0
0
2
0
0
0
1
0
0
0
2
8
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
2
1
2
0
0
0
0
0
0
0
1
0
2
1
0
1
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
3
1
0
0
1
0
0
3
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
3
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
2
2
0
0
0
0
2
0
1
2
0
4
1
2
0
0
0
0
2
0
2
0
0
0
1
0
1
0
3
0
0
0
1
0
0
0
2
2
0
0
4
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
5
0
2
1
0
1
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
1
0
3
2
0
0
1
0
0
3
0
0
0
1
2
0
3
0
2
0
0
0
1
0
2
1
0
0
0
0
2
3
0
0
0
0
1
2
0
0
2
2
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
2
0
2
0
0
0
0
1
4
0
1
1
0
0
0
3
2
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
1
2
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
2
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
2
2
2
0
8
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
1
1
1
4
1
0
0
0
2
0
1
3
0
0
4
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
1
1
2
0
0
0
1
2
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
1
0
2
0
2
0
2
0
2
0
0
2
0
0
1
1
0
0
0
2
2
1
0
0
1
0
0
1
0
0
1
2
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
2
0
0
0
1
0
0
4
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
3
0
0
0
0
0
0
2
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
1
6
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
2
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
2
0
0
2
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
1
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
1
1
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
4
0
1
1
0
1
0
0
0
0
0
0
2
0
0
1
0
0
1
1
1
2
4
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
1
0
0
0
2
1
2
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
2
2
2
1
1
1
0
2
1
0
1
0
0
2
0
0
0
0
2
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
1
2
2
1
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
2
2
0
0
0
1
5
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
3
0
0
2
0
0
0
2
0
1
0
0
0
1
1
0
0
0
2
0
0
1
0
0
1
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
1
0
1
5
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
2
0
0
2
1
1
0
0
1
0
0
0
0
1
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
5
0
0
1
0
0
1
0
0
1
0
0
0
1
2
2
0
1
1
0
0
0
0
0
0
2
0
2
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
1
0
2
2
0
1
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
2
2
0
0
0
0
2
0
0
0
1
2
2
0
1
0
0
1
0
0
1
0
0
0
0
0
3
0
0
0
0
2
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
1
0
0
0
0
2
0
1
0
0
0
1
1
0
0
0
3
2
0
0
0
0
0
1
2
0
0
0
1
0
0
0
2
0
0
1
1
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
4
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
5
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
1
2
0
2
0
0
2
3
0
0
1
0
2
1
3
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
2
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
2
0
2
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
5
0
0
3
1
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
1
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
3
0
1
0
0
1
1
0
1
0
0
0
0
0
0
3
1
3
2
0
2
0
1
2
1
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
1
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
1
0
5
2
0
0
0
0
1
0
2
0
0
5
0
1
0
0
0
2
2
0
1
1
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
1
2
0
2
0
2
2
2
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
1
2
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
2
2
1
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
3
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
1
0
2
2
0
0
2
1
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
2
0
0
0
1
5
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
1
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
2
0
0
0
0
1
2
0
1
0
1
2
0
2
2
1
0
0
1
0
0
0
0
2
1
0
0
1
2
1
0
0
0
0
0
3
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
1
0
1
2
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
1
6
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
1
1
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
3
0
2
0
0
0
0
0
0
2
3
0
0
0
2
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
2
0
0
1
0
0
1
0
0
0
0
2
0
0
1
2
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
3
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
2
0
0
3
0
2
0
0
2
0
1
0
0
1
0
0
1
1
0
1
0
0
0
0
4
0
2
0
0
1
0
1
0
0
0
2
0
0
0
0
1
1
2
0
0
0
2
1
2
0
0
0
0
0
0
2
2
0
0
6
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
1
1
0
2
1
0
0
0
0
0
0
0
0
2
0
1
0
3
0
1
0
0
0
0
0
0
2
2
0
1
0
0
0
0
2
0
0
1
2
0
0
1
0
0
2
2
1
1
0
0
1
0
2
0
0
0
2
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
2
0
0
0
0
2
1
1
2
0
0
0
0
0
0
0
0
0
2
0
2
2
0
1
1
2
0
0
0
1
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
3
0
1
0
2
0
2
2
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
1
0
1
0
1
1
0
0
2
0
0
1
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
3
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
2
2
0
0
0
1
2
0
0
2
0
0
2
0
2
1
0
0
0
0
0
0
1
0
0
3
0
0
0
1
0
1
0
0
0
2
0
0
2
0
1
1
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
1
1
0
2
1
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
1
1
0
0
0
0
2
0
2
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
1
0
1
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
1
0
2
1
0
1
0
0
0
0
2
1
0
0
1
0
0
0
2
2
0
0
2
0
1
0
2
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
3
0
0
2
3
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
2
3
0
0
1
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
1
2
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
2
0
0
1
0
0
0
2
1
0
0
0
1
0
2
0
0
2
0
2
0
1
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
4
1
2
0
2
1
0
0
3
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
3
0
0
0
1
0
0
0
1
0
0
0
2
0
1
1
0
2
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
4
2
0
0
0
1
1
0
0
3
0
2
0
0
0
0
0
2
1
0
2
1
0
0
1
0
0
2
0
0
0
2
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
2
0
0
1
0
0
0
1
0
0
2
0
1
0
0
0
0
0
3
1
2
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
1
1
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
2
0
0
2
1
0
0
2
0
0
0
1
0
2
2
0
0
0
2
3
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
2
1
2
0
0
0
0
2
0
1
1
0
0
0
3
1
0
0
0
0
0
0
0
6
0
0
1
1
0
0
0
2
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
1
0
0
0
0
2
2
1
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
3
3
1
0
0
5
0
2
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
1
1
0
2
0
0
1
0
1
0
0
2
0
2
0
2
0
0
2
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
2
2
0
0
1
2
0
0
0
0
0
2
0
1
1
0
0
1
0
0
0
0
2
0
0
1
2
0
0
0
0
1
2
1
0
0
0
2
0
4
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
2
2
2
0
0
1
0
1
0
0
0
1
2
2
0
0
0
0
2
0
0
0
0
2
1
2
0
0
0
0
3
0
0
0
3
0
1
0
0
2
0
0
1
0
2
0
0
2
0
0
0
1
0
0
1
0
0
1
0
4
1
0
0
0
2
0
4
0
2
0
0
2
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
2
0
0
0
0
0
1
0
2
1
4
0
0
0
2
0
0
0
7
2
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
1
2
2
0
0
2
0
0
2
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
2
0
1
0
1
0
0
2
0
0
0
0
2
0
2
0
0
0
1
0
0
0
2
1
0
0
1
1
0
0
1
1
1
0
0
0
0
5
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
4
0
2
3
0
0
0
0
0
0
2
1
0
0
2
1
5
2
0
2
2
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
1
2
0
0
0
1
0
0
2
2
2
0
0
0
0
2
2
0
1
0
0
1
0
1
0
0
2
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
1
1
2
2
1
1
0
1
1
2
0
1
0
0
0
2
0
0
2
0
2
0
3
0
1
0
1
1
0
0
0
0
2
4
0
0
0
0
0
0
0
2
1
0
1
2
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
1
4
0
2
1
1
0
1
0
0
0
0
0
0
2
0
2
0
0
0
2
1
0
0
0
0
0
1
0
0
1
0
1
0
1
0
3
0
0
0
0
1
2
2
1
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
8
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
1
0
0
1
0
1
0
1
0
2
0
1
1
0
0
2
0
0
1
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
1
2
0
0
0
1
1
0
0
1
0
0
0
0
0
0
5
1
1
0
0
0
0
0
1
1
2
0
1
0
1
0
0
2
1
2
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
3
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
4
2
2
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
2
0
0
0
2
2
0
3
0
2
0
1
0
0
0
0
2
0
0
0
1
0
0
1
0
2
0
0
2
0
0
1
0
0
1
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
2
0
0
0
1
0
0
2
0
0
1
0
0
0
2
0
3
0
0
0
0
0
1
0
0
1
2
5
0
2
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
3
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
2
0
1
0
0
2
0
0
0
0
1
0
1
0
1
0
2
2
2
0
0
1
0
0
0
3
2
0
0
0
0
0
1
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
2
0
0
1
0
1
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
1
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
1
1
3
1
0
0
1
0
0
2
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
1
2
0
0
0
0
1
3
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
2
0
0
2
0
0
1
1
0
1
0
0
0
0
1
1
0
2
0
2
0
0
0
2
0
0
0
0
0
2
2
2
1
0
0
0
0
0
2
0
0
0
3
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
4
2
2
0
0
0
0
3
1
0
0
0
2
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
1
0
0
2
0
0
2
0
1
1
2
1
0
0
0
0
0
3
1
2
1
0
2
0
1
1
0
0
0
0
1
3
0
0
0
0
1
2
2
0
0
0
0
0
0
2
1
0
2
1
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
1
0
0
2
0
1
0
2
0
5
2
2
0
0
0
0
2
0
0
0
0
0
2
1
0
1
1
0
0
0
0
2
0
1
0
0
0
0
0
0
2
2
0
1
0
0
3
1
0
2
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
2
1
0
0
1
0
2
1
0
1
0
0
0
0
0
1
0
0
2
0
1
5
0
0
0
2
2
0
0
1
0
0
0
0
0
1
0
1
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
3
0
1
0
0
0
1
3
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
1
0
0
2
2
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
5
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
2
0
0
0
2
1
0
1
2
2
2
2
0
4
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
2
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
2
0
0
2
0
0
0
1
0
1
0
2
2
0
5
0
2
1
2
1
0
1
0
0
0
1
2
1
0
2
0
0
0
3
0
0
2
0
0
0
0
3
0
0
0
0
1
0
0
2
2
1
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
7
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
2
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
3
2
0
0
0
0
2
2
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
2
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
1
0
0
0
1
0
0
0
3
0
1
0
0
4
0
0
0
1
1
2
0
0
0
0
2
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
3
0
0
0
0
0
2
0
0
0
4
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
1
0
0
2
0
1
0
0
0
2
0
0
0
0
2
2
0
1
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
2
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
2
0
1
0
0
0
0
0
0
2
1
0
0
0
0
1
0
2
0
4
2
1
0
1
1
0
0
0
0
1
1
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
1
0
2
1
4
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
2
0
0
3
0
0
0
0
0
0
0
5
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
1
2
0
0
1
2
0
1
0
0
0
1
0
0
2
0
2
0
0
0
0
2
0
2
0
1
0
0
0
0
1
2
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
1
0
2
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
2
1
2
0
0
6
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
1
0
1
1
1
3
0
0
1
1
0
0
0
2
0
0
1
0
2
0
0
0
0
2
0
0
0
1
0
1
0
0
2
0
2
0
0
3
1
2
1
1
0
0
0
0
0
0
3
1
0
2
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
9
4
0
0
0
0
1
0
2
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
2
1
2
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
4
2
0
1
0
0
0
1
2
0
3
0
2
1
0
0
2
0
0
2
0
0
2
2
1
0
0
0
0
0
2
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
2
0
0
0
2
0
1
0
0
0
0
2
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
2
1
1
0
0
0
0
0
0
3
0
0
0
1
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
2
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
2
0
1
2
0
0
1
1
2
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
6
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
3
0
0
2
0
0
0
0
0
1
0
2
0
0
0
1
1
0
0
0
2
1
0
0
4
0
0
0
0
0
0
2
0
2
0
0
1
4
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
2
0
0
2
0
0
0
0
3
0
0
0
2
0
0
0
1
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
2
0
5
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
1
2
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
4
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
2
1
0
2
0
6
0
0
2
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
1
0
1
8
2
2
1
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
2
4
0
0
2
3
0
0
0
0
0
2
0
1
2
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
3
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
1
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
1
1
0
0
0
0
2
0
2
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
1
2
0
2
0
0
0
0
0
0
1
0
1
2
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
4
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
2
0
1
0
0
0
0
8
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
2
0
2
3
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
1
1
0
2
3
0
0
2
0
0
0
0
1
0
2
0
0
0
2
1
0
0
0
4
0
1
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
2
0
0
0
0
1
4
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
1
0
2
0
0
0
0
1
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
4
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
1
0
0
5
0
0
0
0
0
2
2
0
0
1
3
1
0
2
0
0
0
1
1
0
2
0
3
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
6
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
2
1
1
0
0
1
0
2
0
0
0
0
0
0
0
0
2
4
0
0
1
1
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
5
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
3
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
2
0
1
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
1
2
0
0
0
2
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
15
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
2
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
1
2
0
2
0
0
0
0
1
3
0
0
0
1
0
2
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
4
0
1
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
2
0
0
0
1
0
1
0
0
0
0
0
3
2
0
0
3
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
4
2
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
1
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
1
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
1
0
0
2
0
0
0
2
0
0
2
2
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
2
1
2
1
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
1
4
3
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
1
0
2
2
0
0
0
1
0
0
2
0
3
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
2
0
2
0
0
2
1
0
2
0
1
0
0
0
0
1
1
0
0
0
3
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
2
0
2
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
3
1
1
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
2
0
2
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
1
2
0
0
0
2
0
2
0
0
0
1
2
5
0
0
0
0
0
4
0
2
0
0
0
0
1
5
0
2
0
0
2
0
1
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
1
2
2
1
0
3
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
4
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
2
1
0
0
3
0
0
0
0
1
1
0
2
0
0
1
0
0
2
0
0
1
0
2
0
0
1
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
1
0
5
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
1
0
2
0
0
2
0
0
0
4
1
0
0
0
0
0
0
0
1
0
2
0
0
2
1
0
1
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
1
0
0
0
0
0
0
2
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
4
0
1
1
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
2
2
2
0
1
2
0
0
0
0
0
0
0
2
0
0
0
2
2
0
1
2
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
1
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
3
0
0
2
2
0
0
1
3
1
0
0
0
0
0
2
2
0
1
2
0
0
1
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
3
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
2
0
0
0
2
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
1
1
0
1
0
0
0
3
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
2
0
0
0
0
1
0
0
2
0
0
0
1
0
3
1
0
1
0
0
1
0
0
0
0
3
2
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
1
1
1
0
1
2
0
2
0
2
0
0
2
0
2
0
2
3
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
2
2
0
0
0
1
2
0
0
0
2
0
0
0
0
0
1
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
2
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
3
0
1
1
0
0
0
0
1
0
2
0
1
0
0
3
1
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
2
1
0
0
0
2
0
0
1
1
1
0
0
0
2
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
2
2
0
1
0
0
2
0
0
0
1
0
1
0
0
2
0
1
0
0
0
0
2
0
2
1
0
2
0
2
1
0
0
0
0
0
0
0
0
3
1
0
1
0
1
0
0
2
0
0
0
0
0
0
3
0
0
0
1
0
2
0
2
0
0
1
0
2
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
2
1
1
0
1
0
0
0
0
0
5
0
0
2
0
0
0
3
0
0
5
0
3
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
2
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
4
1
1
1
0
0
0
0
0
0
0
2
0
2
2
0
1
0
0
0
1
0
1
4
1
0
0
0
0
1
0
0
0
0
0
0
2
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
2
0
0
0
0
0
0
1
0
4
1
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
2
0
0
0
0
0
3
0
2
0
1
0
0
2
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
2
2
1
0
0
0
1
1
1
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
4
0
0
0
0
1
0
0
0
0
1
0
0
0
1
2
0
0
2
2
0
1
0
4
0
0
0
0
0
0
2
1
0
2
0
0
1
1
0
2
3
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
2
0
0
3
4
0
0
0
0
2
0
0
0
2
0
1
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
2
2
1
2
0
0
0
0
2
1
0
1
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
1
0
1
1
0
0
0
1
0
1
4
0
0
0
0
0
0
0
1
0
2
0
0
2
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
3
2
0
1
0
0
3
0
2
0
0
0
0
1
0
0
0
3
1
0
0
0
2
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
2
0
0
2
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
1
0
1
0
0
2
0
0
1
2
3
0
3
2
0
0
2
2
0
0
0
0
0
2
2
0
0
1
2
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
3
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
3
2
2
0
0
0
1
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
2
0
1
0
1
0
0
0
6
0
1
0
3
0
2
1
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
1
9
0
0
0
0
0
2
0
0
0
0
0
0
0
0
7
1
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
4
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
1
2
1
0
0
0
1
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
2
2
0
0
2
1
1
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
1
0
0
1
0
2
0
0
0
0
0
0
0
3
0
0
1
0
0
0
3
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
3
2
0
0
0
2
2
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
2
0
0
1
0
1
0
0
0
1
0
2
0
2
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
2
1
0
1
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
2
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
1
0
2
0
0
0
0
0
1
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
1
2
1
0
0
0
0
0
0
2
1
0
2
1
0
0
6
1
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
2
0
0
0
1
1
3
0
0
2
0
2
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
5
0
1
0
1
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
1
0
3
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
3
0
0
1
0
0
0
0
2
0
0
0
1
1
2
0
0
2
0
0
0
0
0
1
0
2
2
0
0
1
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
2
1
0
0
2
0
0
0
0
1
0
2
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
2
0
1
0
0
2
0
1
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
3
1
0
0
0
0
0
2
0
2
0
0
0
2
2
0
3
0
0
0
0
0
0
2
0
0
1
3
2
1
0
2
2
0
0
2
0
0
0
2
0
0
2
1
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
1
0
0
1
2
0
0
0
0
2
2
0
2
0
1
0
0
0
0
0
0
1
0
2
0
1
0
0
0
2
3
0
0
0
1
0
0
0
1
1
0
2
0
0
0
0
0
0
0
1
2
0
2
1
0
0
1
0
2
0
0
0
0
0
6
2
0
0
0
1
0
0
0
0
5
0
0
1
0
1
1
0
0
0
0
0
0
6
2
0
1
1
0
0
1
0
1
0
2
0
0
0
2
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
2
0
0
5
6
0
0
0
0
0
2
2
0
1
0
0
0
1
1
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
1
2
0
0
1
0
2
3
0
2
1
0
0
0
2
0
2
1
0
1
0
0
0
0
2
1
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
2
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
1
1
1
2
4
0
1
0
0
0
0
0
0
0
0
0
5
0
2
0
2
0
1
0
2
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
2
2
1
0
0
0
0
2
1
0
0
0
0
0
2
0
0
2
0
0
1
0
0
1
0
2
2
1
0
2
3
0
0
0
0
1
0
0
2
0
0
1
1
2
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
10
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
2
0
0
0
0
2
1
0
1
0
0
0
1
0
0
0
0
1
0
0
2
0
0
3
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
2
0
0
0
0
3
1
0
0
0
0
2
2
2
0
0
0
0
0
1
0
2
1
0
0
0
1
0
0
0
0
0
0
0
5
0
1
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
3
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
4
0
1
0
0
2
0
1
0
0
2
0
0
0
3
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
1
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
1
0
0
4
0
1
1
1
0
0
0
0
2
0
0
1
0
0
1
0
2
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
1
1
0
0
0
2
0
0
1
0
0
0
0
1
0
2
3
2
1
0
0
0
2
0
0
2
0
2
4
0
0
2
0
1
0
0
0
1
0
0
0
1
3
0
1
1
0
0
0
0
0
1
0
0
0
3
0
0
2
0
0
0
0
0
2
1
1
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
2
0
0
1
2
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
3
2
2
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
2
2
0
0
1
2
0
1
0
2
0
0
1
1
7
0
1
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
1
0
2
0
2
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
3
0
0
2
0
1
1
0
3
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
5
1
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
2
0
1
0
1
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
1
2
0
4
0
1
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
2
0
2
0
0
0
0
0
0
0
0
2
2
0
0
1
0
2
0
0
1
2
0
0
2
2
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
2
1
4
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
3
2
3
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
3
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
2
0
0
0
0
2
0
0
0
2
1
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
3
0
1
0
0
1
2
0
0
0
2
1
0
1
1
0
1
0
0
0
0
3
0
0
3
0
0
0
0
0
1
0
0
0
0
2
1
1
0
2
4
0
2
0
2
0
0
0
1
2
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
2
0
1
1
0
0
2
3
2
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
2
2
1
0
0
0
2
2
2
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
2
2
2
2
0
0
0
2
0
1
0
0
0
1
0
0
2
2
0
0
0
2
2
0
2
0
0
0
0
2
0
0
0
1
0
2
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
4
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
1
0
0
2
0
2
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
2
1
2
2
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
2
0
4
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
3
1
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
3
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
1
0
0
2
0
1
0
1
0
0
0
0
0
0
0
2
0
3
1
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
3
0
3
0
0
0
2
0
0
0
0
2
2
1
0
2
0
2
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
1
1
0
1
0
2
1
0
1
7
2
0
0
0
2
0
1
0
0
0
1
0
0
0
1
0
0
0
2
1
1
0
1
2
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
2
2
1
0
4
0
4
0
1
0
0
0
0
2
0
0
5
0
0
0
0
0
0
0
0
0
2
2
1
2
0
1
0
0
0
0
0
4
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
2
0
0
0
1
2
0
3
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
1
1
0
2
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
1
1
0
0
2
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
1
2
1
2
0
0
0
1
1
2
3
2
0
0
1
2
0
3
0
1
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
3
0
0
0
0
2
0
0
0
1
0
0
1
2
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
3
0
0
2
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
2
0
1
3
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
1
0
1
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
2
3
0
0
0
2
0
0
0
0
0
2
0
0
0
1
1
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
2
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
1
0
0
1
1
2
4
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
3
1
0
0
0
0
2
0
2
2
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
3
2
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
7
2
0
1
0
0
0
0
0
2
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
2
0
0
6
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
2
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
2
2
0
0
2
1
0
0
14
0
3
2
1
0
2
2
0
0
1
1
0
0
1
0
0
0
2
0
0
0
2
0
0
0
2
1
0
0
4
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
1
0
0
0
0
2
0
4
1
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
2
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
2
1
2
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
2
2
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
3
1
0
0
1
0
0
0
2
0
0
1
0
2
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
2
0
2
1
0
0
3
0
0
0
0
2
0
1
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
1
0
2
0
0
0
2
0
1
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
1
0
0
0
1
0
0
2
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
3
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
3
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
2
0
0
0
0
2
0
4
0
0
2
0
0
0
2
0
1
0
0
0
2
0
2
0
0
0
0
0
2
1
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
1
0
0
1
0
0
2
0
1
0
0
0
0
2
2
2
0
0
0
0
0
0
2
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
1
2
1
0
2
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
9
1
3
1
0
4
0
0
1
0
0
0
1
0
0
0
0
1
1
1
0
1
0
2
2
0
0
1
0
2
2
2
2
0
0
0
1
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
7
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
3
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
2
0
2
0
0
0
0
1
0
2
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
1
1
0
0
2
0
1
0
1
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
2
2
0
2
0
1
0
0
2
0
0
1
0
0
0
2
0
2
0
0
0
0
2
0
0
2
2
0
1
0
0
0
0
2
2
0
0
1
0
0
2
0
1
2
0
1
1
1
0
1
0
0
2
0
5
0
0
0
0
0
1
0
1
0
0
1
0
1
2
2
0
0
2
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
2
3
0
0
0
0
2
2
0
0
0
0
2
0
0
0
1
0
0
0
2
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
2
0
2
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
1
2
1
2
0
0
0
0
0
2
0
0
0
1
2
0
0
0
2
1
0
0
0
2
0
0
0
2
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
1
0
1
1
0
0
0
0
1
0
1
3
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
5
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
1
1
1
0
1
1
0
0
0
0
1
0
2
0
2
0
0
2
0
0
2
0
0
0
0
1
0
0
0
2
5
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
5
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
5
2
0
0
0
0
0
2
0
2
2
0
3
0
0
0
3
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
3
0
0
0
0
0
1
0
1
0
0
0
1
1
1
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
3
1
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
2
1
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
1
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
2
0
1
2
0
0
1
2
0
2
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
1
0
0
1
1
0
1
0
1
1
7
0
1
0
0
1
0
0
0
2
0
0
0
2
4
0
0
2
0
0
2
2
0
0
0
0
0
0
1
1
1
0
0
0
0
0
3
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
1
2
0
1
2
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
2
0
0
0
4
2
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
1
0
0
1
0
1
0
0
0
2
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
3
0
0
0
0
2
0
0
3
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
3
2
0
0
0
1
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
2
2
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
2
3
0
1
2
0
12
0
0
2
3
0
0
0
0
0
1
0
2
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
2
4
1
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
1
0
0
1
0
1
0
2
1
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
2
2
0
0
2
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
1
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
5
1
2
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
1
7
0
2
0
0
1
2
1
0
0
0
2
0
1
0
0
2
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
2
1
0
0
2
0
0
1
0
2
0
0
0
3
0
3
2
0
0
0
2
1
1
0
1
0
0
0
0
0
0
1
0
0
1
0
2
2
0
0
3
0
1
1
2
0
2
0
0
0
1
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
1
9
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
3
1
1
1
0
0
0
0
2
4
1
2
0
0
1
0
0
0
0
2
2
2
0
0
0
0
1
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
1
1
0
3
1
0
0
2
0
0
2
0
0
0
0
1
0
2
1
0
0
2
1
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
1
0
0
0
4
1
0
0
0
0
0
3
0
1
0
1
0
1
0
0
5
2
0
0
0
2
1
0
0
0
0
0
0
2
0
0
3
0
0
0
0
1
0
0
1
0
0
1
0
2
1
0
0
0
1
0
1
0
2
1
1
1
0
0
0
0
0
0
2
0
0
1
2
0
1
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
2
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
2
4
1
1
0
0
2
1
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
1
1
2
2
0
4
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
1
0
1
0
4
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
1
1
0
0
0
0
1
3
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
3
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
3
0
0
0
0
2
0
0
2
3
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
2
0
0
2
0
0
3
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
1
2
1
0
1
2
0
0
0
0
0
1
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
1
1
1
1
2
0
0
2
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
4
0
0
2
1
2
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
5
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
1
1
0
0
1
0
0
0
1
1
2
2
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
2
0
0
0
0
1
1
1
0
0
0
0
0
0
1
2
0
0
1
0
0
0
1
0
0
1
3
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
4
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
2
0
1
4
1
1
0
0
1
0
0
0
0
1
2
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
3
0
1
0
0
2
0
0
4
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
1
2
1
0
0
0
0
0
0
2
1
3
0
0
2
0
1
2
0
0
7
1
2
1
0
2
0
1
1
0
0
0
0
0
0
0
2
1
0
2
1
0
0
0
0
0
0
0
2
1
0
2
0
1
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
2
0
1
1
0
0
2
0
2
1
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
1
0
2
0
0
2
1
0
0
0
0
1
2
2
2
2
0
2
0
0
4
0
0
2
2
0
0
6
0
2
3
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
4
0
2
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
3
0
1
5
0
0
0
0
0
2
0
0
1
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
3
2
3
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
2
1
0
0
0
1
2
0
0
0
2
0
0
1
4
1
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
1
1
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
2
0
0
2
2
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
1
0
1
1
0
1
0
1
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
2
0
0
0
1
1
0
1
0
0
1
1
0
0
0
0
7
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
2
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
1
0
0
0
3
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
1
1
0
0
0
2
1
2
0
1
0
0
0
0
1
1
0
2
0
1
1
0
0
0
0
0
0
4
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
3
2
2
1
1
0
0
0
2
2
0
0
0
0
0
0
8
2
1
0
0
0
0
0
1
2
2
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
1
0
1
0
0
1
0
0
4
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
1
1
1
0
0
0
0
1
0
0
3
0
2
0
1
1
0
0
2
3
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
2
0
0
2
0
3
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
2
0
0
0
2
0
1
0
1
0
1
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
4
0
0
1
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
1
2
2
1
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
1
1
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
1
1
0
2
0
0
1
1
0
0
2
0
0
0
0
0
1
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
2
0
1
0
1
0
0
0
0
0
0
0
6
0
0
0
0
0
0
2
3
1
1
0
0
0
1
2
1
1
0
0
1
1
0
0
1
0
3
2
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
1
0
1
0
0
0
0
2
0
0
0
4
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
7
0
0
0
0
1
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
1
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
1
2
2
2
0
1
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
1
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
10
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
1
0
1
2
1
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
1
0
1
0
2
0
1
0
0
3
0
0
1
3
0
2
1
0
0
3
0
2
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
4
1
0
0
2
0
0
0
2
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
1
2
2
0
0
0
0
1
0
1
0
2
0
0
0
0
2
2
0
0
0
0
0
0
3
2
2
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
3
0
0
0
1
2
0
0
2
0
0
2
2
0
0
0
2
0
2
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
1
2
0
1
0
1
0
0
0
1
0
0
0
6
0
0
2
0
1
0
1
0
0
0
0
2
0
0
2
2
1
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
1
0
0
0
1
0
0
2
1
2
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
2
4
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
4
0
2
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
1
2
0
0
0
0
3
0
1
2
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
2
0
2
1
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
2
2
2
0
0
0
3
1
2
0
0
0
1
2
2
2
0
0
2
2
0
1
0
0
2
0
0
2
1
0
0
0
0
0
0
0
5
0
0
0
0
0
0
1
1
0
0
0
0
1
4
2
5
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
1
3
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
2
0
0
0
2
1
0
0
0
1
0
0
0
1
0
1
0
5
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
1
3
0
1
0
0
0
0
1
0
1
1
0
1
0
1
0
0
0
0
0
1
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
1
2
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
2
0
1
1
2
0
1
0
0
2
0
1
1
0
0
0
0
0
0
1
0
2
0
3
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
2
0
1
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
2
3
0
0
2
0
0
0
0
1
1
0
2
0
0
0
2
0
1
3
2
1
0
2
0
1
0
2
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
2
1
3
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
1
1
0
1
0
0
0
0
0
1
2
0
2
0
0
2
2
0
2
0
0
0
0
1
0
2
0
0
1
1
1
3
1
0
2
0
0
2
2
2
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
1
5
2
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
1
0
0
2
3
0
0
0
2
0
4
0
0
0
2
0
4
0
1
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
4
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
2
0
1
0
0
7
0
0
0
0
0
1
1
0
0
2
1
1
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
2
1
1
0
2
0
0
0
0
1
0
0
1
0
0
0
2
5
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
2
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
1
2
0
0
0
0
0
1
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
2
2
0
0
0
0
0
0
1
0
2
0
1
0
1
0
0
0
2
0
0
2
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
1
1
0
1
2
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
2
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
2
2
2
0
1
0
0
0
0
1
0
3
0
0
2
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
1
0
2
0
0
1
0
0
1
0
2
0
2
1
2
0
0
1
0
0
4
0
0
0
2
0
1
0
0
1
3
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
1
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
4
0
0
0
0
0
0
0
0
0
2
1
1
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
1
2
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
2
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
3
0
0
1
2
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
2
2
0
0
0
1
0
0
0
2
5
0
0
2
0
0
4
0
1
3
2
2
0
0
0
0
0
0
2
0
2
1
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
2
0
1
0
2
1
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
2
0
3
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
1
1
1
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
2
0
0
0
1
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
4
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
3
1
0
2
0
2
0
0
0
2
3
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
1
2
0
0
2
0
3
0
0
3
0
1
0
0
0
0
0
0
1
0
2
0
0
2
0
0
1
1
0
0
2
0
0
1
2
1
0
2
0
0
0
0
1
0
0
1
0
0
0
2
0
0
1
1
0
1
0
0
1
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
2
0
0
2
0
2
2
0
0
0
0
1
2
0
0
1
0
3
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
1
0
0
2
2
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
1
2
0
1
1
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
1
0
0
2
1
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
2
0
0
2
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
1
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
1
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
3
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
1
1
0
0
0
4
0
0
2
9
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
2
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
3
1
0
1
0
0
3
0
3
1
0
1
0
0
0
1
0
1
0
2
0
1
2
0
0
0
1
0
0
1
3
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
2
1
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
4
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
2
2
0
0
1
0
0
0
0
1
1
1
0
1
0
1
1
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
2
0
2
2
3
0
2
1
1
0
0
1
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
3
0
2
0
2
2
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
1
1
0
0
0
0
1
5
0
0
0
0
0
0
1
0
0
1
2
0
0
0
4
0
0
2
0
0
1
0
0
1
1
0
0
2
1
3
1
0
1
0
0
2
0
2
0
1
0
0
2
0
0
2
1
1
1
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
11
0
2
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
1
3
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
1
2
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
2
0
2
0
0
2
0
3
0
0
0
0
0
0
0
3
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
2
0
1
0
1
0
0
0
2
0
0
0
2
0
0
0
0
1
1
1
0
0
0
0
0
1
2
0
0
0
2
0
2
0
2
0
2
2
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
2
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
1
0
2
2
2
0
0
2
0
2
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
1
0
2
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
1
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
1
2
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
2
2
1
2
1
0
1
0
1
2
0
2
0
0
0
0
2
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
4
1
2
0
1
0
0
0
0
2
0
0
2
1
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
1
1
0
0
1
0
1
0
0
0
0
0
1
2
1
1
2
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
2
0
2
0
0
1
1
0
0
1
0
0
0
0
1
2
0
0
2
0
2
5
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
3
0
1
0
0
2
1
0
0
0
0
2
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
1
0
0
0
1
0
0
2
0
0
2
0
1
2
0
2
1
0
0
1
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
2
2
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
2
3
1
1
2
0
2
1
2
2
1
1
0
3
0
2
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
5
1
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
2
1
0
0
0
0
0
0
1
3
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
5
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
2
2
0
1
2
0
0
1
2
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
2
2
2
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
2
0
0
0
1
2
2
0
3
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
2
0
0
0
1
0
8
0
1
0
0
2
0
0
0
0
1
0
2
0
1
0
2
0
0
3
0
0
2
0
0
2
3
0
0
2
0
1
2
0
0
2
0
0
0
2
0
1
2
0
1
8
0
0
1
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
1
0
0
2
0
0
1
0
0
2
0
0
0
2
0
2
2
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
3
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
2
1
0
0
0
0
0
2
0
1
1
2
2
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
2
0
2
0
1
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
7
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
2
0
0
2
0
2
0
1
2
2
2
0
0
1
2
1
0
0
0
0
0
2
0
0
2
1
0
0
0
2
0
0
1
1
0
2
2
0
2
2
0
0
0
1
0
0
0
0
1
0
0
1
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
1
0
0
0
0
2
0
2
0
3
1
1
1
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
2
0
0
0
3
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
2
0
2
1
1
3
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
1
1
0
2
0
0
1
0
0
0
0
0
1
2
0
0
0
3
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
2
0
0
0
1
0
2
0
0
0
0
3
1
0
2
1
0
0
0
1
0
2
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
1
2
0
2
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
2
2
0
0
0
0
0
0
1
0
1
5
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
5
2
0
0
0
0
0
0
0
0
0
2
0
1
3
1
0
0
0
0
0
0
0
0
1
0
0
0
3
2
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
4
0
0
1
1
0
0
1
0
0
0
0
0
4
2
0
0
1
0
0
0
0
0
0
1
0
7
0
1
0
0
0
1
0
1
2
0
0
1
0
1
1
1
0
1
2
0
0
1
1
0
1
0
0
0
0
1
0
6
0
0
2
2
0
0
2
0
0
1
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
1
0
0
0
2
1
0
1
1
0
1
0
0
3
2
2
2
0
0
0
0
0
0
2
0
0
0
0
2
4
2
1
1
1
0
0
2
0
1
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
3
4
1
0
0
0
0
1
0
1
0
1
0
0
1
0
1
0
1
0
2
1
0
0
0
1
0
0
0
0
3
0
0
1
3
0
0
0
0
0
0
0
2
0
9
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
2
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
2
0
0
2
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
1
1
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
1
1
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
2
1
0
3
0
0
0
5
2
0
1
0
1
0
0
1
2
0
0
2
1
0
0
0
2
0
0
0
0
0
0
5
0
0
0
0
0
2
0
1
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
1
2
0
0
0
3
0
2
0
1
0
0
0
0
1
0
0
0
0
2
1
0
1
0
0
0
3
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
2
0
2
0
10
0
0
0
0
0
0
0
2
0
4
3
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
2
2
0
0
1
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
2
0
0
1
0
1
2
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
1
0
1
2
0
0
0
1
1
2
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
1
2
0
0
0
2
2
0
2
0
2
1
1
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
1
2
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
1
0
3
0
0
0
2
0
1
0
0
0
0
0
1
2
2
0
0
2
2
2
0
2
0
0
1
1
0
0
0
1
0
1
2
0
1
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
2
2
2
0
0
1
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
4
0
0
0
0
2
0
0
0
0
0
0
2
0
1
2
0
0
2
0
1
1
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
1
2
0
1
1
2
3
0
0
1
0
1
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
2
0
0
1
2
0
1
0
1
1
0
0
2
0
0
1
0
0
0
2
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
1
0
0
0
0
1
1
0
1
0
0
0
0
1
3
0
1
0
0
2
1
0
0
0
0
1
0
0
0
2
2
0
0
2
0
1
1
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
1
0
0
0
1
0
0
0
2
0
0
0
1
0
2
0
0
0
0
2
0
0
1
1
0
0
0
4
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
2
2
1
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
4
2
0
0
1
0
0
0
0
0
0
0
0
3
1
0
0
0
1
0
0
1
1
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
1
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
2
0
1
0
2
0
1
2
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
1
0
0
0
0
2
2
0
0
0
1
0
0
1
0
0
0
3
0
2
0
1
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
3
4
0
2
0
2
1
0
2
0
2
0
0
0
2
0
2
0
0
1
0
0
0
1
0
0
0
0
0
1
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
2
0
0
2
0
2
2
0
0
1
0
0
0
0
5
2
0
1
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
0
2
0
3
0
0
1
2
0
0
0
2
0
0
2
1
0
0
0
2
0
0
0
1
0
2
2
0
0
0
0
0
0
0
2
1
0
1
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
2
0
0
1
2
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
1
1
1
0
0
2
0
0
0
1
0
1
0
2
0
0
1
1
0
1
1
1
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
2
0
0
2
1
0
1
0
0
1
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
1
1
2
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
1
2
2
2
0
0
2
5
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
2
0
0
1
1
0
0
0
1
0
0
0
1
1
1
0
1
0
0
0
0
2
2
0
0
2
0
0
0
0
0
4
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
2
1
0
2
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
3
1
0
2
0
0
0
0
0
1
0
2
2
0
0
2
6
0
0
2
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
2
1
1
0
0
0
3
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
1
0
3
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
4
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
4
0
0
0
1
0
0
1
0
1
0
1
0
2
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
1
0
0
2
0
1
1
2
2
1
0
0
2
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
2
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
3
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
2
2
0
1
0
0
0
2
2
0
0
1
2
0
13
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
3
0
1
0
0
0
0
2
0
1
0
0
1
2
0
0
1
0
1
0
2
0
0
0
0
0
3
0
0
0
0
1
0
1
2
2
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
2
1
1
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
3
0
0
0
1
2
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
1
1
3
0
0
0
2
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
1
1
1
2
0
3
0
0
0
0
0
1
0
1
0
1
0
0
1
0
2
0
2
0
0
2
0
0
0
0
0
0
3
0
0
0
0
3
0
1
0
0
0
0
2
0
0
0
0
2
0
0
6
2
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
2
0
0
0
2
2
0
2
0
0
0
0
3
0
1
4
0
0
1
2
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
1
2
0
3
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
3
0
0
0
1
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
4
0
2
0
0
0
0
1
0
1
3
0
0
0
0
0
1
1
0
1
0
0
0
2
0
0
1
0
0
0
0
0
2
3
2
0
0
2
0
0
0
1
1
0
1
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
1
0
0
0
2
2
0
0
0
2
3
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
1
0
0
4
0
0
2
0
0
0
2
0
0
1
0
0
0
2
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
1
2
3
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
1
0
0
1
0
0
0
0
0
1
1
0
2
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
1
0
0
0
0
0
2
1
2
0
1
1
0
1
3
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
1
2
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
1
0
0
0
8
0
3
0
0
0
0
0
0
0
0
0
1
0
3
0
0
1
0
0
0
1
0
1
0
0
3
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
2
0
1
2
0
0
0
0
0
0
6
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
1
0
0
0
2
0
1
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
1
1
0
2
0
0
0
4
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
1
1
0
0
0
1
0
1
0
0
1
1
4
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
2
0
0
0
0
1
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
1
0
2
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
4
1
0
0
2
1
0
3
2
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
3
0
4
1
0
2
3
0
0
0
0
0
0
0
0
0
0
2
2
0
1
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
2
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
5
1
0
0
0
0
1
0
0
1
0
2
0
0
0
1
1
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
1
0
1
1
0
0
0
0
5
0
0
0
0
0
2
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
1
0
2
0
0
1
3
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
1
0
0
2
0
0
1
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
2
0
0
0
2
2
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
2
2
2
1
0
0
0
0
0
2
2
1
0
0
0
0
0
0
1
2
1
1
0
0
0
2
0
0
2
0
0
0
1
0
3
0
0
0
0
6
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
2
0
0
0
2
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
4
1
0
0
0
2
2
0
0
0
2
0
0
0
0
2
2
0
0
1
0
0
1
0
2
0
2
0
0
2
0
0
0
0
0
3
1
0
0
0
0
1
0
0
1
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
2
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
1
1
0
2
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
2
0
1
0
1
0
1
0
3
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
3
0
0
0
1
1
2
0
1
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
1
0
1
0
2
0
1
0
0
0
2
1
0
1
1
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
3
0
0
1
2
0
3
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
2
2
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
2
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
1
2
1
0
0
0
0
2
0
0
2
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
1
1
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
1
0
0
2
0
0
0
2
2
1
0
0
0
0
0
0
0
1
3
1
0
0
2
1
2
1
0
0
0
1
0
0
2
0
0
0
0
2
0
0
1
0
0
0
2
0
0
3
0
2
2
0
0
0
0
0
2
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
1
2
0
1
0
2
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
4
0
0
0
0
0
0
1
2
0
4
0
0
2
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
5
1
0
1
0
0
0
0
2
0
0
2
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
3
0
1
1
1
0
0
0
1
0
1
0
0
0
2
2
0
0
1
0
2
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
1
1
0
0
0
0
0
0
0
0
8
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
6
9
0
0
0
0
0
0
1
0
0
3
2
0
0
0
0
2
0
2
2
2
0
2
0
0
0
0
0
1
0
0
0
3
0
1
0
0
0
0
1
4
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
1
12
1
2
1
1
3
1
0
0
0
0
0
2
2
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
1
2
1
2
0
0
0
1
0
0
0
0
0
2
0
0
3
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
1
0
2
0
0
2
2
0
2
0
1
1
1
0
0
0
1
0
0
0
1
1
0
3
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
1
0
0
8
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
6
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
4
2
0
1
0
1
0
2
1
2
0
0
2
0
1
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
2
0
0
0
0
0
0
0
1
0
1
2
0
0
0
1
0
0
0
0
2
1
2
0
0
0
0
3
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
1
0
0
1
0
4
0
0
3
1
0
0
0
0
2
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
2
0
0
2
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
4
0
0
0
0
0
2
1
0
0
0
4
3
0
0
0
0
0
1
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
3
0
1
0
0
1
0
0
0
0
0
0
0
0
7
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
2
0
0
1
0
7
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
6
2
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
3
0
0
3
2
1
0
0
0
0
2
2
0
0
0
0
1
0
2
0
0
1
1
2
0
4
0
5
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
1
1
2
0
1
0
0
0
0
0
3
0
0
0
2
0
1
0
0
1
0
2
0
0
1
3
1
2
0
0
0
2
0
1
0
0
0
2
0
0
1
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
2
1
0
1
2
0
0
0
2
1
1
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
2
2
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
1
6
3
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
1
4
5
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
1
0
2
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
1
0
0
2
0
0
2
2
0
0
0
0
0
2
1
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
2
0
5
0
2
0
0
0
0
1
0
0
0
4
0
0
0
0
1
0
1
2
1
2
0
1
2
4
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
1
0
0
0
2
0
0
0
1
1
1
0
2
1
0
0
0
2
0
0
0
0
1
0
0
1
2
0
0
2
1
0
1
0
0
0
0
0
1
0
3
1
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
2
0
0
1
0
0
0
0
2
0
0
0
2
3
0
0
1
2
2
0
0
0
1
1
0
0
0
0
1
2
1
0
0
0
2
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
2
0
2
0
1
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
9
0
1
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
5
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
2
2
0
0
1
0
2
0
0
0
0
1
1
2
0
1
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
3
2
2
0
0
1
0
0
0
0
1
1
0
2
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
3
0
0
0
5
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
1
1
3
2
0
0
0
0
3
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
3
0
1
0
1
0
0
0
0
0
0
2
0
0
1
0
1
3
0
3
0
0
0
0
0
2
0
0
1
0
2
0
1
2
0
0
2
0
0
0
0
0
0
0
2
2
2
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
2
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
3
0
2
0
0
1
2
0
1
0
0
3
0
2
0
0
2
0
0
0
0
2
1
0
3
0
1
0
1
1
2
0
2
1
0
0
2
1
0
0
2
0
0
1
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
4
0
0
1
1
2
0
0
0
2
0
1
0
2
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
2
0
1
0
0
0
1
0
0
2
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
3
0
0
0
0
0
0
0
0
1
2
0
0
3
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
1
0
0
2
0
1
2
0
0
0
0
0
0
0
0
3
0
0
0
0
6
5
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
3
0
1
1
0
1
1
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
3
0
0
1
0
1
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
4
1
0
2
0
2
0
1
0
0
0
0
2
0
0
0
1
0
2
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
2
2
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
3
0
0
0
1
0
2
0
0
0
1
0
2
1
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
2
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
1
0
0
0
1
0
3
1
1
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
2
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
1
1
1
0
0
2
2
0
0
0
0
0
0
0
0
3
0
0
0
2
1
0
0
2
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
2
0
0
1
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
2
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
2
1
2
0
0
2
0
2
0
0
3
0
1
2
0
0
0
1
0
0
0
0
2
1
2
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
4
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
2
0
2
2
1
1
1
0
0
0
1
0
0
0
1
0
0
1
2
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
3
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
4
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
1
2
0
0
0
0
0
0
1
0
2
0
0
0
2
0
1
6
0
0
0
1
0
0
1
0
0
1
0
1
0
0
3
0
0
0
0
0
0
0
0
0
1
1
0
0
3
1
0
4
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
3
0
0
1
0
2
0
0
0
0
1
2
1
1
0
2
0
0
0
0
2
2
2
2
0
0
0
1
0
2
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
2
0
1
2
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
2
1
0
0
1
0
0
1
1
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
1
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
2
0
1
0
0
1
1
2
1
0
2
0
0
0
0
2
0
0
3
0
0
2
2
0
0
0
0
3
0
2
1
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
1
0
2
0
0
1
0
0
1
0
0
0
0
0
2
0
1
0
1
2
0
0
2
0
0
1
0
0
0
0
0
0
2
1
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
4
4
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
3
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
2
0
1
3
1
0
0
0
0
0
0
0
1
0
0
0
2
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
1
0
0
1
0
2
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
1
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
3
0
1
0
2
0
2
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
3
0
0
3
0
0
1
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
3
0
2
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
2
0
0
0
0
0
2
2
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
1
2
0
0
1
0
0
0
2
0
0
0
2
1
0
1
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
1
2
0
2
0
0
0
0
2
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
1
1
0
0
2
0
0
0
5
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
2
0
0
0
0
2
0
2
0
1
0
0
1
1
0
0
3
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
1
0
1
0
0
0
0
2
2
0
2
1
1
0
0
0
0
1
0
0
1
0
3
0
0
2
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
2
0
0
0
0
2
0
0
1
4
0
0
0
0
0
0
3
0
0
4
0
0
2
1
1
0
1
0
0
3
0
0
0
1
0
2
0
2
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
1
0
2
0
1
0
0
2
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
3
0
1
2
0
0
0
0
0
1
0
2
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
2
1
0
0
0
0
1
0
0
0
3
1
0
1
2
2
1
1
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
2
0
0
0
1
1
0
0
0
2
0
0
1
2
5
0
0
0
2
0
0
0
1
0
1
1
0
0
0
0
0
1
2
0
0
0
4
2
0
4
0
1
0
2
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
1
1
0
0
0
1
0
6
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
2
0
0
0
0
3
1
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
2
1
0
0
0
0
0
2
3
4
0
2
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
7
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
2
0
1
0
0
0
1
0
0
0
2
1
0
2
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
1
2
0
2
1
1
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
2
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
2
1
2
1
0
1
1
0
0
0
0
1
1
1
0
1
2
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
2
0
0
0
0
0
0
0
2
0
2
1
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
4
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
3
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
2
0
0
1
1
0
0
2
0
0
0
8
1
1
0
1
0
0
2
0
0
1
2
0
2
0
0
3
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
1
3
0
0
2
2
3
0
1
0
0
0
0
0
0
0
3
2
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
1
0
2
0
0
0
2
0
0
0
0
2
0
0
0
1
2
0
0
2
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
3
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
2
0
0
3
0
0
0
0
3
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
1
0
0
1
0
0
0
2
1
0
1
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
2
0
0
1
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
3
1
0
2
0
0
2
0
1
0
0
2
0
0
0
0
1
0
0
3
0
0
0
5
0
2
0
0
2
0
0
0
0
0
2
0
1
0
2
1
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
1
0
0
2
0
2
0
1
0
4
0
0
0
0
0
0
1
0
2
1
0
0
0
0
1
0
0
2
0
1
0
0
2
0
1
0
1
0
0
0
1
1
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
2
0
1
0
0
0
3
0
0
0
2
1
0
1
0
0
0
2
0
4
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
4
2
1
3
0
0
0
1
1
0
0
2
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
2
2
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
3
0
0
2
0
1
1
2
0
0
1
0
0
1
0
0
0
2
0
2
0
1
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
3
0
2
0
0
2
1
0
0
0
1
0
0
0
3
0
0
0
1
0
0
0
0
1
2
0
1
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
1
2
0
0
2
0
2
0
0
0
0
0
0
1
1
2
0
0
2
0
5
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
1
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
3
2
0
1
0
1
1
0
0
0
0
0
2
0
1
0
0
1
2
0
0
0
0
0
0
2
0
1
0
0
2
2
0
0
2
0
0
0
0
2
1
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
2
1
2
0
0
1
0
1
0
0
0
5
0
0
2
0
2
1
0
0
2
1
0
1
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
2
0
2
0
3
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
2
0
0
1
2
0
2
1
1
0
0
0
0
0
0
0
0
1
0
3
1
0
1
0
0
0
1
0
1
1
0
0
2
0
0
2
0
0
0
0
1
0
0
2
0
0
0
1
1
0
0
0
0
0
2
0
0
2
0
2
0
0
0
9
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
1
1
0
1
0
1
0
0
0
1
0
0
0
2
0
0
1
0
0
2
0
0
0
2
7
0
3
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
4
0
0
1
2
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
1
2
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
3
1
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
2
0
5
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
1
0
0
2
2
3
0
0
0
1
2
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
2
2
2
2
0
0
0
2
0
3
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
1
0
4
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
1
2
2
0
0
0
1
0
0
0
0
3
0
2
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
1
0
0
0
0
0
2
1
0
0
1
0
1
0
1
0
0
2
0
0
0
0
1
2
3
0
1
0
2
0
0
0
0
2
3
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
1
0
1
0
0
0
2
3
0
2
2
0
0
1
0
0
0
2
0
0
0
2
1
0
0
0
3
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
2
0
0
0
2
0
2
0
0
2
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
2
0
1
1
0
0
0
0
0
0
3
0
0
0
2
1
0
0
1
0
0
1
1
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
2
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
3
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
1
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
2
0
0
2
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
2
0
2
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
4
2
0
1
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
2
0
0
1
0
1
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
3
1
2
0
4
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
1
0
2
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
2
2
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
4
0
0
2
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
3
0
0
3
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
2
0
1
0
1
1
2
2
0
0
0
1
1
0
0
0
1
2
0
2
0
0
0
0
0
2
1
1
0
0
0
0
1
0
0
0
0
0
1
0
2
0
1
0
0
0
1
0
2
0
3
0
0
0
1
0
1
2
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
1
0
0
0
2
0
0
2
0
2
7
2
0
3
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
2
0
2
1
0
1
0
3
3
0
0
2
0
0
2
0
3
0
0
1
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
2
1
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
1
7
0
0
0
0
0
0
1
2
4
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
1
0
0
0
0
1
0
1
0
2
0
0
1
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
2
0
0
0
0
1
1
2
0
1
0
0
0
1
0
2
0
0
0
1
1
0
0
1
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
1
2
0
0
2
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
2
0
0
1
0
0
2
2
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
5
0
0
0
0
0
0
0
0
0
2
0
0
0
3
2
0
0
1
0
0
0
0
2
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
2
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
1
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
3
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
1
0
0
0
1
0
1
3
0
0
0
0
1
0
1
2
0
0
0
0
2
0
0
0
0
2
0
0
1
2
0
0
0
0
0
1
1
0
0
2
0
0
1
0
2
1
0
0
1
0
0
0
0
2
2
2
0
1
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
2
2
0
0
0
2
0
0
2
0
1
0
0
2
2
0
0
1
1
0
0
0
1
0
5
0
2
0
1
0
1
0
1
1
0
2
0
0
1
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
3
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
2
0
1
0
0
0
0
1
0
0
2
2
0
0
0
0
0
2
2
2
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
1
0
3
0
2
1
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
3
1
2
0
0
1
0
0
1
0
0
0
0
1
1
1
0
2
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
1
2
2
0
3
0
0
1
0
0
1
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
2
2
0
0
1
2
0
2
0
0
0
1
0
0
0
0
0
0
2
0
3
0
0
0
2
2
0
0
4
0
2
0
1
1
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
1
0
0
1
2
0
0
0
1
0
0
2
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
1
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
1
0
0
1
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
3
1
0
2
0
0
0
1
2
2
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
3
1
0
0
0
0
0
2
0
0
0
0
0
1
3
0
2
0
2
0
1
0
0
0
1
2
0
0
1
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
1
2
0
0
0
0
0
1
0
0
0
1
0
0
2
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
1
0
2
1
0
1
0
2
2
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
2
0
1
0
2
1
0
0
0
0
0
1
0
3
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
1
0
0
1
1
1
0
0
0
1
0
1
0
0
0
1
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
1
0
3
0
2
2
0
0
0
0
0
2
0
2
0
1
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
1
0
3
0
2
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
2
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
2
0
0
0
0
0
1
3
0
0
0
2
0
0
0
0
0
0
2
2
0
0
2
0
0
1
0
0
1
0
0
2
0
0
1
3
1
0
1
0
2
0
2
0
0
0
0
0
1
0
0
1
0
1
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
5
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
1
1
0
0
0
0
0
2
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
2
1
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
2
3
0
0
0
1
0
0
0
2
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
1
2
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
1
0
2
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
2
2
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
4
0
1
0
3
0
0
1
0
0
0
1
0
1
3
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
2
0
0
0
1
1
0
0
0
3
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
3
1
2
2
2
0
0
0
0
0
0
0
1
0
2
3
0
0
1
0
0
0
0
2
0
1
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
1
2
2
0
0
2
0
2
1
0
0
0
0
0
2
2
1
0
0
1
1
0
1
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
2
3
0
2
0
1
2
2
0
0
0
0
0
2
1
2
0
0
0
0
4
2
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
2
0
0
2
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
2
2
2
0
0
1
2
0
0
0
0
2
2
1
0
0
0
0
2
0
0
0
0
3
2
0
2
0
3
2
0
0
0
2
0
2
0
9
0
0
2
0
0
1
5
0
0
0
0
1
0
0
0
0
3
0
2
0
0
2
1
1
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
5
1
2
0
1
0
1
0
1
1
0
2
1
0
0
2
0
0
0
0
0
0
0
0
1
2
2
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
1
1
0
0
0
1
1
0
0
0
0
0
0
1
0
2
1
0
0
2
0
0
2
2
0
2
2
0
6
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
1
0
0
1
0
1
0
2
2
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
3
0
1
0
2
0
0
0
2
0
0
0
1
3
1
0
0
0
2
0
0
0
0
0
2
1
0
0
0
1
2
0
0
0
2
0
0
1
0
0
2
1
1
1
0
0
0
0
0
0
0
0
0
2
0
2
2
2
0
0
0
1
0
1
0
0
0
0
0
0
0
2
1
5
0
3
0
0
1
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
10
1
0
0
0
2
0
2
1
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
1
0
2
2
2
0
0
0
0
0
0
0
2
0
0
0
2
2
1
0
0
1
2
2
0
0
0
0
4
0
0
0
2
0
1
2
0
2
0
0
0
0
0
1
0
2
0
0
1
1
1
0
0
2
0
2
0
2
1
0
2
0
0
0
1
0
0
0
0
0
0
3
2
0
3
0
0
0
2
0
1
2
0
0
3
0
2
0
0
2
0
0
1
0
3
0
0
0
0
1
0
0
0
0
0
2
0
1
1
0
0
0
0
2
0
0
0
0
2
1
0
2
0
0
0
1
2
0
0
0
1
2
0
2
0
0
0
0
1
2
0
1
0
2
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
2
4
0
0
3
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
1
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
1
0
0
1
2
2
0
0
0
0
2
0
2
0
0
0
0
4
0
0
2
0
0
0
1
0
0
1
0
0
0
1
1
0
0
9
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
1
4
0
0
0
1
0
1
0
1
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
7
0
0
0
3
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
2
1
0
0
0
0
0
0
0
2
1
2
1
0
0
0
2
2
0
2
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
3
2
0
0
1
2
0
0
0
0
0
0
3
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
3
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
2
2
0
3
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
4
0
0
1
0
0
1
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
2
0
0
5
0
0
1
0
1
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
2
0
0
0
3
1
0
0
1
0
0
2
1
0
0
1
1
0
0
2
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
3
0
3
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7
0
2
1
1
0
0
0
0
0
0
2
2
0
0
1
0
0
0
2
0
0
1
0
1
0
0
0
0
1
2
0
0
0
1
0
0
1
2
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
4
0
0
0
1
0
0
0
2
0
2
1
1
0
1
0
0
0
1
0
0
0
1
1
1
0
0
2
2
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
3
0
2
0
1
0
1
0
0
0
0
1
0
2
1
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
1
0
2
0
2
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
3
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
1
0
0
5
1
0
0
0
0
0
0
0
0
0
0
0
7
1
5
2
0
0
0
0
1
0
0
1
0
2
0
0
2
0
0
0
0
0
2
2
0
0
0
0
4
0
0
2
0
0
0
2
1
0
0
0
0
2
0
0
0
14
2
2
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
2
1
0
1
0
0
0
0
2
0
0
2
0
0
1
0
0
2
0
3
1
2
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
2
1
0
0
2
0
0
0
2
0
0
0
0
1
0
4
0
0
0
0
3
0
2
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
1
0
1
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
1
0
0
0
1
1
0
1
2
0
0
2
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
3
0
0
0
0
0
1
1
0
2
0
1
0
0
0
0
2
0
1
0
0
1
0
2
1
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
2
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
2
0
0
2
0
0
1
2
2
0
2
0
0
5
0
0
1
2
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
2
2
0
2
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
1
1
2
0
2
0
0
1
0
0
2
0
0
2
0
2
0
0
1
0
0
0
0
2
2
0
0
0
0
1
2
0
0
0
1
2
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
1
0
0
1
0
0
0
0
0
2
0
1
0
2
0
0
2
0
0
1
0
2
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
1
0
2
0
0
4
0
0
2
2
2
2
0
0
0
0
0
0
0
1
0
0
0
2
0
1
2
3
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
1
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
1
0
0
1
1
0
0
2
1
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
1
0
2
0
0
0
0
2
0
0
3
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
3
0
0
0
2
0
4
0
0
0
0
0
2
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
1
0
1
2
1
1
1
0
4
0
0
0
0
0
1
0
4
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
1
0
2
1
0
0
0
0
0
2
0
0
2
0
2
3
0
1
0
1
0
0
0
2
0
0
0
2
2
0
2
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
2
2
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
1
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
2
0
2
0
1
0
0
2
0
1
0
0
0
0
1
4
2
0
1
1
0
0
0
0
0
2
0
0
1
0
0
7
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
4
3
0
0
1
1
2
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
2
0
0
0
0
0
0
0
2
1
0
0
1
1
0
0
0
0
1
0
0
2
0
2
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
2
1
0
0
0
1
0
0
0
2
1
0
2
0
2
0
0
0
0
0
0
0
2
0
2
0
0
2
2
2
2
0
0
0
2
1
1
0
0
0
0
0
1
0
0
0
0
2
1
0
5
0
1
0
0
4
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
2
1
0
0
0
0
0
2
0
0
3
1
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
3
0
0
0
0
0
0
0
0
1
1
1
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
2
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
2
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
2
0
1
1
0
2
0
0
0
0
0
1
0
0
2
2
0
1
0
0
1
0
0
1
0
2
1
1
0
0
0
0
3
0
0
0
0
0
0
2
0
1
1
0
1
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
2
1
1
1
0
0
0
2
0
0
2
0
1
0
0
2
0
0
0
0
0
2
0
1
0
2
0
0
0
0
3
0
2
0
0
2
0
1
0
0
0
0
1
0
1
2
0
1
0
0
0
3
0
0
0
3
0
3
0
0
1
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
1
0
2
0
2
0
0
6
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
2
0
2
0
0
0
2
2
0
1
2
0
0
1
0
0
0
1
0
2
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
2
0
0
2
0
2
0
2
2
2
6
0
5
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
3
0
0
1
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
1
0
2
0
0
0
0
2
0
0
2
0
0
0
2
1
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
1
2
0
0
0
0
2
1
0
0
0
0
0
0
1
0
2
2
0
2
0
0
0
1
0
2
0
2
0
1
0
0
1
0
0
1
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
2
2
0
0
0
0
1
0
0
2
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
2
1
0
1
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
3
0
4
0
2
0
0
1
1
0
0
0
0
16
1
0
3
0
0
0
0
0
0
1
0
1
2
0
1
0
0
0
0
0
3
0
0
1
1
0
1
0
1
0
0
0
5
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
2
1
0
2
0
0
0
3
0
0
0
1
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
2
2
0
0
2
0
2
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
1
1
2
0
0
0
0
0
0
2
1
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
3
0
0
0
0
2
1
0
3
1
0
0
0
0
0
0
1
2
0
0
2
0
0
2
0
0
2
0
0
0
0
0
1
0
1
0
2
0
2
0
0
0
0
1
0
0
0
0
2
2
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
1
0
0
1
1
5
0
2
0
0
0
0
0
0
2
1
0
2
2
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
2
2
0
0
0
0
1
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
3
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7
4
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
2
0
2
2
0
0
0
1
0
0
1
2
2
0
2
0
1
1
1
0
0
2
1
1
0
0
0
0
3
0
1
0
0
0
2
1
0
0
0
2
0
1
2
0
5
2
0
0
3
0
0
0
0
0
0
0
0
1
1
2
2
0
0
1
2
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
1
2
0
0
0
1
0
0
0
2
0
1
0
0
0
1
2
3
3
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
2
0
0
2
0
0
3
1
1
1
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
2
1
0
3
0
0
0
1
0
0
0
0
0
1
1
0
1
0
2
1
0
0
1
1
2
1
0
0
3
0
1
0
0
2
2
2
1
1
0
0
0
1
1
2
3
1
0
0
0
1
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
3
0
2
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
1
2
2
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
2
0
0
0
3
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
2
0
0
0
1
0
1
0
0
2
0
0
0
0
0
2
0
1
0
2
1
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
1
0
0
3
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
4
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
1
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
1
2
0
0
0
0
1
1
0
0
1
2
1
0
0
0
1
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
2
2
2
0
0
0
0
3
0
1
0
0
0
2
0
0
0
0
3
0
0
1
0
2
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
7
0
0
1
0
1
0
0
0
0
0
0
2
0
0
1
0
0
2
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
3
1
0
0
1
0
0
2
0
2
3
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
2
1
0
0
0
0
2
0
0
1
2
0
1
0
0
0
3
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
2
2
2
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
1
1
0
1
0
1
1
0
0
0
0
2
0
2
0
1
0
1
0
1
0
2
0
0
0
0
0
0
1
0
2
2
1
0
0
0
0
2
0
0
1
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
1
1
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
2
0
2
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
1
0
2
0
0
0
2
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
1
2
4
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
3
0
0
2
0
0
2
0
0
0
0
2
0
2
0
0
0
0
2
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
3
0
1
2
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
2
0
2
2
0
0
0
0
7
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
6
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
2
0
4
2
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
5
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
6
0
0
1
2
1
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
1
0
0
1
1
0
0
0
0
1
1
0
2
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
1
1
0
0
0
2
0
0
1
2
0
2
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
2
2
0
0
0
2
0
0
1
0
0
1
0
0
0
3
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
2
0
1
0
0
2
3
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
2
0
2
0
0
0
0
0
0
1
0
0
2
0
2
0
1
0
0
1
3
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
2
0
4
0
0
0
0
0
1
0
0
2
0
1
0
1
0
0
1
0
2
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
1
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
3
0
0
0
1
1
0
1
2
1
0
0
1
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
3
0
0
0
0
0
1
0
0
1
0
0
0
3
0
0
0
0
2
1
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
4
2
0
0
2
0
2
0
0
0
1
2
0
0
0
0
0
3
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
4
0
2
1
2
0
0
3
1
2
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
3
0
2
0
0
0
0
2
0
1
4
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
1
0
0
0
2
2
0
0
0
2
0
0
2
1
0
1
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
2
0
0
0
2
0
1
2
0
0
2
0
0
1
0
2
1
0
0
0
0
0
1
0
0
4
0
0
0
0
1
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
6
1
2
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
3
0
2
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
2
1
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
1
1
0
4
0
0
1
2
0
0
1
1
0
0
0
0
0
0
2
0
0
2
3
1
0
2
0
0
2
2
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
2
0
1
1
2
0
0
0
0
1
0
1
1
0
0
0
2
1
2
0
0
1
0
1
1
0
0
2
0
0
0
0
1
0
1
0
0
1
0
9
0
0
0
0
2
0
0
0
0
0
0
2
2
0
2
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
4
0
3
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
1
0
6
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
1
0
2
2
0
1
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
1
3
2
0
0
0
0
0
0
0
0
1
1
0
0
2
0
1
0
0
0
0
0
0
1
0
1
0
1
1
1
2
1
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
1
0
0
0
0
3
2
0
0
0
0
2
1
0
0
0
0
0
2
0
0
1
2
2
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
3
0
0
0
2
0
0
4
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
1
0
2
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
3
0
3
0
0
0
0
2
0
0
0
0
2
1
2
0
0
0
0
2
1
0
0
0
0
0
2
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
3
0
0
1
0
1
0
0
0
0
1
2
0
0
2
0
0
0
2
0
1
0
0
0
2
2
0
0
2
0
3
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
1
0
2
0
2
2
0
0
2
0
0
0
0
3
2
0
0
2
1
0
0
2
2
0
0
0
2
0
0
3
0
2
0
0
5
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
6
0
3
0
0
0
0
0
0
6
0
0
0
0
1
0
0
0
2
0
0
0
2
1
0
0
1
0
0
0
0
1
1
0
0
0
2
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
2
0
0
2
4
0
2
2
0
0
0
0
0
3
0
0
1
0
1
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
1
0
2
1
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
1
2
0
2
2
0
0
2
0
2
0
0
0
0
0
1
0
3
0
0
0
2
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
5
1
3
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
4
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
2
1
0
1
2
0
0
0
0
0
2
2
2
2
1
2
0
0
0
2
0
0
0
0
0
2
0
2
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
2
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
1
2
0
0
0
1
0
1
0
1
2
0
0
2
0
1
1
1
2
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
2
0
1
1
0
0
0
1
2
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
3
0
0
0
2
2
0
1
0
0
0
11
2
0
0
0
0
2
0
2
0
0
3
0
3
0
0
1
2
2
0
0
0
0
0
1
0
0
2
0
0
1
1
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
3
0
2
2
0
2
2
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
2
0
0
2
0
1
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
2
1
0
1
0
0
0
2
1
0
2
0
0
0
1
3
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
1
0
0
2
1
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
2
1
0
1
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
2
1
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
2
0
2
2
0
0
0
0
0
1
1
0
2
1
3
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
1
0
1
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
2
0
3
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
3
0
0
1
0
1
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
2
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
1
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
3
0
0
2
0
0
2
1
2
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
1
0
0
0
1
2
0
1
2
0
0
1
0
0
0
0
0
2
0
0
0
0
1
1
0
1
3
0
0
0
0
1
0
6
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
3
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
1
0
1
2
0
0
0
0
2
0
0
0
0
3
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
1
0
0
1
0
2
2
0
1
0
0
2
0
0
0
2
1
0
0
2
1
0
0
1
1
0
0
0
2
0
0
2
0
2
0
0
0
0
1
0
2
0
2
0
0
2
2
2
0
2
0
0
0
0
1
0
0
0
0
3
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
3
0
1
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
1
2
0
0
0
0
1
0
2
1
0
1
1
0
0
0
0
0
5
2
0
2
2
2
2
3
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
2
2
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
1
0
0
1
2
0
2
0
0
0
1
2
0
0
0
0
1
0
1
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
1
0
0
0
0
1
1
0
1
0
0
1
1
0
2
0
0
0
0
1
0
1
0
0
1
1
2
0
1
2
0
1
0
0
2
0
2
0
0
0
0
2
2
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
1
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
1
0
2
1
2
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
10
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
2
0
0
0
0
2
2
2
1
0
0
0
0
1
0
0
0
3
0
2
0
0
0
0
1
0
1
0
2
0
1
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
4
1
0
0
1
3
0
0
0
0
1
3
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
1
0
0
0
0
1
0
1
0
1
0
1
0
0
0
1
0
0
2
0
3
0
0
2
0
0
1
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
2
1
0
2
2
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
2
0
2
0
0
2
0
0
0
1
0
0
1
1
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
2
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
2
0
1
0
0
2
1
0
1
1
1
1
1
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
2
2
2
0
0
0
0
2
1
0
0
0
1
0
2
2
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
1
2
1
0
0
1
0
0
0
0
0
0
0
1
0
0
2
2
0
1
0
1
1
0
0
1
0
1
2
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
3
2
2
0
0
0
4
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
1
0
1
1
0
2
0
0
0
0
0
0
0
0
1
0
0
4
2
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
2
0
1
0
1
0
0
0
0
2
1
0
13
1
1
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
1
0
2
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
2
1
0
2
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
2
2
1
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
2
0
3
1
0
0
0
1
0
0
1
0
1
2
0
0
6
0
0
0
0
1
0
0
0
1
0
0
0
1
2
0
0
1
2
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
3
0
0
0
0
0
2
1
2
1
0
0
1
0
1
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
1
0
1
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
2
0
0
1
4
2
1
4
0
0
0
2
1
0
2
0
1
0
0
2
28
0
0
0
0
0
0
3
0
0
0
1
2
0
1
1
0
0
1
0
0
1
0
0
2
1
3
0
0
7
0
2
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
2
6
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
2
2
2
0
0
0
1
0
1
0
0
0
1
2
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
1
1
0
0
0
0
1
2
0
0
2
2
1
1
0
0
0
1
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
2
4
2
0
0
0
0
0
2
0
0
0
3
3
0
0
0
1
1
0
2
0
0
1
0
1
0
1
0
1
2
1
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
1
0
0
0
0
0
2
0
0
1
1
0
0
0
2
0
0
0
2
5
0
0
0
1
0
4
2
0
0
0
1
1
0
0
1
0
0
0
1
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
2
1
0
1
0
0
0
2
0
1
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
2
2
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
3
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
2
0
1
2
2
0
0
0
0
1
1
0
1
0
1
2
0
0
0
0
1
2
2
0
0
0
0
2
1
0
0
2
1
0
0
0
0
0
2
0
0
0
3
0
0
0
0
2
0
0
0
2
0
1
0
0
1
0
0
3
1
0
1
0
0
0
2
0
0
0
0
1
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
2
2
3
0
0
0
0
0
0
1
0
0
0
1
0
1
2
0
0
0
1
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
2
0
6
6
0
0
0
1
1
2
0
0
2
1
0
1
0
0
0
2
0
0
1
0
0
0
0
1
4
2
0
2
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
2
1
0
0
0
2
1
0
0
1
0
0
0
2
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
1
0
2
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
1
1
1
0
0
0
1
4
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
2
0
1
0
0
1
1
2
0
1
0
0
1
0
1
0
0
0
0
2
2
0
0
0
0
0
1
2
3
0
2
1
0
0
0
0
0
0
0
0
2
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
1
0
0
2
2
0
2
0
2
0
0
0
0
2
0
0
2
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
1
1
0
0
0
2
2
0
5
2
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
2
0
0
1
0
2
0
0
0
0
2
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
1
0
0
0
0
1
3
0
1
0
2
0
0
0
0
0
4
2
2
0
0
0
0
0
2
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
1
1
3
2
3
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
3
2
2
2
1
1
0
2
1
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
2
0
0
0
1
2
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
4
1
1
0
0
0
2
0
0
0
0
2
0
2
2
1
0
0
0
1
0
0
0
2
0
0
0
1
0
0
3
0
0
0
0
1
0
1
0
0
2
1
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
1
1
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
1
0
0
1
3
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
5
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
1
0
0
3
0
0
0
1
0
0
0
0
0
0
2
2
1
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
2
0
0
1
0
3
0
0
0
0
0
0
0
2
0
0
0
0
2
1
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
3
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
2
2
0
0
1
1
1
0
2
0
0
2
3
0
0
0
0
2
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
1
0
0
0
0
2
1
1
0
2
0
1
0
2
2
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
2
0
2
0
3
1
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
2
0
1
0
0
0
0
0
2
2
2
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
1
2
1
2
0
0
0
1
0
2
0
0
0
1
2
2
1
0
1
0
0
0
0
0
0
3
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
4
0
1
0
0
0
1
0
2
0
0
0
0
1
1
0
4
2
0
1
0
4
0
0
0
0
2
0
1
1
0
2
0
1
0
0
2
2
0
0
0
0
0
1
2
0
0
0
0
0
1
2
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
4
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
4
0
1
0
0
0
2
0
1
1
0
0
0
1
0
0
3
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
3
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
2
0
0
0
0
3
1
0
0
0
0
2
0
3
0
0
0
2
2
0
2
1
0
2
0
1
1
0
0
0
0
0
0
0
2
2
0
1
0
1
0
0
0
1
2
2
1
0
2
0
1
0
1
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
3
0
1
1
0
2
0
2
0
0
2
0
0
0
3
0
1
0
0
0
1
0
0
0
2
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
2
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
1
1
0
0
0
0
1
0
1
1
3
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
3
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
2
2
0
0
1
0
0
1
0
0
2
0
0
1
1
1
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
4
0
0
1
0
0
2
0
1
1
0
0
0
0
1
1
0
0
4
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
1
2
0
1
0
1
0
1
0
1
1
1
0
0
3
1
0
0
0
0
0
1
1
1
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
1
0
2
2
0
0
0
0
0
2
0
0
0
1
0
1
0
0
2
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
3
0
2
0
2
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
2
2
1
3
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
3
0
0
0
0
0
0
2
3
1
0
0
0
1
0
2
1
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
1
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
2
0
0
0
0
2
0
0
2
0
0
0
2
0
2
0
0
1
0
0
1
0
0
0
2
0
2
2
0
0
0
0
0
0
0
1
2
2
0
0
0
0
2
2
1
0
0
2
0
0
0
1
0
0
0
1
2
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
2
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
2
0
1
0
1
0
2
0
2
0
2
0
0
1
0
0
0
1
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
4
0
0
0
0
2
1
0
0
2
1
2
1
0
0
1
0
2
0
2
6
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
1
2
0
0
0
2
0
0
0
0
2
0
0
2
2
0
0
0
0
2
1
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
1
0
0
0
0
0
0
0
1
4
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
2
0
1
0
0
1
0
0
0
0
4
0
0
2
3
0
1
2
0
2
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
3
3
0
0
2
2
0
0
0
0
0
2
1
2
0
1
0
0
2
0
0
1
0
0
2
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
2
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
5
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
1
1
0
1
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
2
0
2
2
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
1
1
0
0
0
0
1
2
0
1
0
1
0
0
0
0
0
2
0
0
2
2
0
0
2
2
0
2
0
1
0
0
0
1
0
2
3
0
1
0
1
0
1
0
3
0
2
0
2
0
1
0
0
0
0
2
1
0
0
0
0
0
0
1
5
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
1
1
0
0
0
1
0
0
1
2
0
0
3
0
0
2
0
2
0
0
0
1
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
1
2
2
0
1
2
0
0
1
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
2
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
2
0
0
0
0
0
2
1
1
0
2
2
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
1
1
2
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
2
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
1
0
0
1
2
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
1
0
2
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
2
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
3
0
0
0
3
1
0
0
1
1
0
0
1
3
0
2
0
0
0
0
0
0
0
2
0
2
0
2
0
1
1
0
0
1
2
0
0
0
0
1
0
0
2
1
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
2
0
1
2
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
3
0
2
0
1
1
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
2
1
0
2
2
1
0
0
0
0
0
2
2
2
0
0
0
2
1
2
0
0
0
0
0
2
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
8
0
0
1
0
0
2
2
0
2
0
0
1
1
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
1
0
1
3
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
1
5
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
3
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
3
0
2
0
0
1
2
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
1
2
0
0
2
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
5
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
1
0
1
2
0
0
2
0
0
1
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
2
1
1
0
1
0
1
11
0
0
0
0
2
1
0
0
0
2
1
4
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
4
0
0
3
0
0
1
2
0
1
0
0
2
0
0
0
0
0
1
4
0
0
2
0
0
2
2
0
0
3
1
0
0
6
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
1
0
2
2
1
0
0
0
0
1
0
3
1
2
0
0
0
1
0
0
1
0
2
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
1
0
2
0
0
0
0
0
1
1
0
0
3
0
2
0
1
1
2
0
0
0
0
0
0
0
0
0
0
1
2
2
2
0
1
2
0
1
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
2
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
2
0
0
2
0
0
0
0
0
0
0
5
2
1
0
0
2
0
0
2
1
0
1
0
0
0
0
0
1
1
0
0
2
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
1
0
2
0
0
2
2
0
0
1
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
2
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
2
0
0
1
0
0
1
1
0
0
0
1
2
0
0
0
2
1
0
0
0
6
0
2
2
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
2
1
0
0
0
0
0
0
1
0
0
0
1
1
1
0
1
0
0
2
0
0
0
1
0
9
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
1
0
0
0
0
3
0
0
0
0
0
1
0
0
0
1
3
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
2
0
1
0
0
2
0
1
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
2
2
1
0
0
0
0
2
1
0
3
0
0
0
2
0
2
0
0
0
0
2
0
1
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
3
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
3
0
0
0
0
0
1
0
0
0
1
0
0
0
2
2
2
0
1
0
1
0
0
0
2
0
2
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
1
0
4
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
1
0
2
0
1
0
0
2
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
4
2
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
1
3
2
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
1
2
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
3
1
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
1
0
0
0
0
0
0
0
0
2
0
2
1
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
2
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
2
0
0
0
2
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
1
2
0
0
1
0
1
1
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
1
2
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
2
2
0
0
0
0
0
0
0
0
1
0
3
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
2
0
0
0
0
0
1
0
2
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
1
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
1
2
0
0
0
4
2
2
0
3
0
1
1
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
2
0
0
1
0
1
2
0
3
0
0
0
0
0
3
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
2
0
1
0
0
1
0
1
0
0
0
0
2
0
0
0
3
0
1
0
0
1
0
0
0
0
4
0
2
0
1
2
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
1
0
0
0
2
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
2
4
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
3
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
2
0
0
0
0
0
0
5
1
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
3
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
2
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
2
2
1
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
1
0
1
0
0
1
0
0
0
2
2
0
0
0
0
0
0
2
1
2
0
2
1
1
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
3
0
0
2
2
0
1
0
0
0
2
0
1
0
7
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
2
1
2
0
0
0
0
0
2
0
2
1
0
0
0
0
1
2
3
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
1
2
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
3
1
0
2
0
0
0
0
0
3
2
0
0
0
0
1
0
2
1
2
0
0
0
2
2
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
1
1
0
1
0
0
2
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
1
1
0
0
0
1
0
0
0
1
0
0
1
2
0
0
1
0
0
2
0
0
4
5
0
1
0
1
2
0
8
0
0
0
0
1
1
0
0
0
0
2
0
1
0
1
2
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
1
1
2
1
2
0
0
2
0
0
0
2
0
0
2
2
2
0
0
0
2
0
0
0
0
0
0
0
2
1
0
1
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
1
2
0
1
0
1
0
0
0
0
4
0
0
0
0
0
0
0
1
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
2
0
2
0
1
0
0
0
0
1
0
1
1
0
0
1
0
0
2
2
1
0
0
0
1
0
0
0
1
1
0
0
0
1
0
1
0
2
0
0
1
0
0
0
1
0
0
0
2
0
0
0
1
1
2
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
1
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
1
1
4
0
2
0
2
0
0
0
0
3
2
0
1
1
1
0
0
1
1
0
2
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
3
0
6
2
0
0
1
2
0
0
0
2
0
0
1
2
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
2
1
0
0
0
1
0
0
0
2
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
3
0
0
0
1
0
2
0
0
0
3
0
0
0
1
0
1
0
2
0
0
0
0
0
2
0
3
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
1
0
1
1
0
0
0
2
0
2
1
0
2
2
2
0
0
0
2
2
1
0
0
0
4
0
0
0
0
0
0
0
2
0
2
0
2
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
1
0
2
0
0
2
0
0
1
0
0
1
0
1
0
2
0
0
2
0
2
1
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
3
0
0
0
1
2
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
4
0
0
0
1
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
3
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
1
0
0
2
2
2
4
0
1
0
1
0
0
0
0
1
2
0
0
0
1
1
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
5
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
1
0
0
3
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
1
2
1
1
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
2
0
0
2
0
2
2
0
0
0
2
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
3
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
2
0
2
2
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
1
0
0
2
0
0
0
0
1
2
1
0
1
0
0
0
0
1
0
0
0
2
0
0
2
2
0
0
0
2
0
0
2
0
1
0
0
2
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
1
1
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
2
2
0
1
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
1
0
1
0
0
1
0
0
0
0
0
2
0
1
0
2
0
0
2
0
0
0
0
2
1
0
0
0
0
2
3
0
0
2
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
2
0
0
0
2
0
1
0
1
0
0
0
0
0
0
5
3
0
2
1
0
1
0
7
0
0
1
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
4
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
3
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
1
2
0
0
1
2
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
1
3
1
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
2
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
3
4
2
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
3
0
2
0
0
0
0
0
1
0
2
2
0
0
2
1
0
0
1
0
0
1
0
0
0
2
0
1
1
1
0
0
0
0
2
1
1
0
3
0
0
0
1
1
0
0
0
0
0
0
0
3
0
0
2
2
0
0
1
2
1
0
0
2
0
2
0
0
0
2
0
2
0
0
2
0
0
0
0
0
2
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
1
3
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
1
1
0
0
0
1
0
0
0
0
0
3
3
0
0
1
0
0
0
2
2
0
0
0
0
2
0
0
0
1
0
1
3
0
1
2
0
2
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
2
1
0
2
0
0
0
1
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
4
0
0
0
0
1
0
0
1
0
0
2
0
0
2
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
3
2
0
0
0
1
2
2
0
0
2
0
0
0
0
0
0
2
0
0
1
2
0
2
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
2
0
0
2
0
0
8
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
1
1
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
1
0
0
1
0
1
3
2
1
0
0
2
0
0
2
1
2
0
2
0
0
1
0
0
0
0
0
2
1
0
2
0
2
0
0
0
1
0
1
0
0
1
2
1
0
0
0
0
0
1
0
2
0
1
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
1
0
2
0
0
2
0
2
0
0
0
2
0
0
0
0
1
0
0
0
1
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
3
0
0
1
0
0
1
0
0
2
0
0
1
1
2
1
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
3
0
2
0
1
7
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
1
1
0
0
0
0
0
4
0
1
0
0
0
0
0
0
3
0
0
1
0
2
2
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
2
0
0
0
0
1
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
3
2
2
4
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
3
0
2
0
2
0
1
2
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
3
0
0
0
0
0
1
0
0
4
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
1
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
3
0
0
3
1
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
2
0
0
1
2
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
2
0
0
0
1
0
0
2
1
1
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
2
0
3
0
0
0
1
0
0
1
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
1
2
1
2
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
1
0
1
4
0
2
0
0
0
2
0
0
0
1
0
0
2
0
1
0
2
0
1
2
0
0
0
0
0
1
3
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
1
1
0
0
0
0
0
0
2
0
2
2
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
3
2
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
1
1
2
0
0
5
0
0
0
0
0
3
2
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
3
0
0
0
0
1
0
0
2
0
0
0
2
0
0
2
0
1
0
0
2
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
2
0
0
2
0
4
1
1
0
0
1
1
1
1
1
0
0
0
2
0
0
0
0
0
0
3
0
2
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
3
0
0
0
2
1
0
0
0
0
0
1
2
0
1
0
0
4
0
0
0
0
2
1
2
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
2
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
2
3
0
0
0
1
0
0
0
2
2
0
2
0
0
1
0
0
0
2
0
0
0
0
3
0
0
1
0
2
0
2
0
0
1
0
3
0
0
0
0
0
2
0
0
0
3
0
0
0
2
0
1
0
0
0
0
2
0
0
2
2
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
1
3
0
2
1
0
0
2
0
1
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
2
0
1
0
0
0
0
0
7
0
0
0
1
0
0
0
3
0
2
2
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
1
2
0
0
1
0
0
2
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
2
0
0
2
0
0
2
0
0
1
0
1
2
0
0
2
0
0
0
0
1
1
0
0
0
1
3
0
0
1
0
0
0
2
0
0
0
0
1
0
1
0
3
0
0
2
2
2
0
0
1
0
0
0
0
0
2
0
0
1
0
0
3
0
1
0
0
1
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
1
0
0
1
1
0
1
0
2
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
2
1
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
2
0
1
0
2
0
0
1
0
0
0
1
0
2
2
0
0
0
0
1
0
0
0
1
3
1
0
0
0
0
0
0
0
0
2
0
3
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
1
1
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
1
1
0
0
0
0
2
0
2
0
2
0
2
2
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
1
0
0
0
0
1
0
0
1
0
1
2
0
2
1
2
0
1
0
0
1
1
0
0
0
0
0
0
0
2
0
1
0
2
0
7
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
2
0
0
0
2
1
0
1
2
0
0
3
1
1
0
0
0
0
1
2
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
2
0
0
0
0
1
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
4
2
1
1
1
0
0
0
0
2
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
2
3
0
2
0
1
0
2
0
1
2
0
0
0
0
0
1
0
0
1
0
1
2
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
1
0
1
0
0
0
4
0
0
0
0
0
2
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
3
0
1
3
0
0
2
1
0
0
1
1
2
0
0
2
0
0
0
0
4
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
1
2
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
3
3
0
0
0
0
1
1
1
0
0
0
0
2
2
0
0
1
0
0
0
2
3
0
1
0
0
1
0
1
0
0
0
0
0
1
0
7
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
2
0
1
0
2
2
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
2
0
1
2
0
0
0
5
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
1
2
0
0
2
0
0
0
0
0
0
0
2
2
1
2
0
0
0
0
0
0
0
2
0
0
0
0
1
2
2
0
2
0
0
0
0
0
1
0
0
1
0
0
3
0
1
1
1
0
0
2
1
2
2
0
1
0
0
0
0
2
0
2
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
6
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
4
1
0
0
0
0
0
0
2
0
0
2
1
2
0
1
2
2
0
3
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
2
1
0
2
0
1
1
0
0
2
0
2
0
2
1
0
0
0
0
0
1
0
0
0
0
1
0
2
0
1
2
0
1
0
2
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
2
0
1
0
2
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
2
0
0
0
0
2
1
2
0
4
0
0
0
0
1
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
1
4
2
10
0
0
4
1
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
0
2
0
0
1
1
0
0
17
0
0
1
0
0
0
1
0
2
0
2
0
0
0
2
0
0
0
0
0
0
2
1
0
1
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
1
1
0
0
2
3
2
0
0
0
3
2
0
0
2
0
0
0
0
0
0
2
2
0
0
2
0
2
0
0
1
0
4
0
0
0
2
0
0
0
2
0
0
0
1
0
1
0
0
0
2
0
0
2
0
2
0
0
1
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
1
0
1
1
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
2
0
2
0
0
0
0
0
2
2
0
0
1
0
1
0
2
0
1
1
1
0
0
0
0
0
2
0
1
0
0
0
0
0
3
0
0
0
0
1
0
2
0
0
2
0
0
0
0
1
0
0
1
1
0
0
0
0
2
2
0
0
1
2
2
2
0
3
0
0
0
0
1
5
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
2
0
0
0
0
1
0
0
1
3
0
0
1
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
1
1
0
0
0
1
2
2
0
0
0
0
0
0
2
0
2
0
2
0
0
1
0
0
0
0
0
0
1
0
3
0
3
1
2
0
0
2
0
2
0
0
0
0
0
0
0
1
2
0
3
0
0
0
0
3
0
0
0
0
1
0
0
0
1
0
2
1
1
0
1
0
0
0
0
0
2
0
3
1
1
1
0
0
2
2
1
2
0
0
0
0
0
1
2
1
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
1
0
2
0
0
0
0
0
5
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
2
0
2
3
1
0
0
0
0
0
7
0
1
2
2
2
0
0
1
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
2
0
0
0
0
1
0
0
2
0
0
4
0
0
0
1
1
0
0
0
0
1
1
0
2
4
0
1
0
0
1
0
0
2
0
1
0
0
1
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
4
2
2
0
3
1
0
0
0
0
2
0
0
0
2
3
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
2
0
0
2
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
3
0
0
1
0
0
2
0
0
0
2
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
4
0
1
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
3
0
0
2
0
0
0
5
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
2
0
0
0
3
2
0
0
1
0
0
4
4
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
2
0
1
0
3
2
0
0
0
1
2
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
1
1
2
0
0
0
0
4
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
3
1
1
0
0
0
0
0
0
1
0
0
0
0
3
0
1
0
2
2
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
4
1
0
0
10
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
6
1
0
0
0
0
0
2
0
0
1
0
0
1
0
0
2
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
2
2
2
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
2
0
1
0
0
0
2
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
1
0
3
0
0
3
0
0
2
2
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
1
0
0
1
2
2
0
1
2
0
0
0
0
1
0
0
1
0
0
1
1
0
0
2
0
4
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
1
0
1
0
1
2
2
0
0
2
0
3
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
2
0
0
2
0
0
3
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
2
0
2
1
0
2
0
2
0
0
0
0
0
1
8
0
0
0
2
2
0
2
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
2
0
1
0
0
0
1
0
2
0
0
0
0
2
4
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
1
1
0
2
0
2
1
0
0
1
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
3
0
2
1
0
0
0
0
0
0
0
0
2
2
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
2
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
1
0
0
2
0
1
2
1
1
0
0
0
0
1
0
0
1
0
0
0
2
1
2
0
0
0
1
1
3
0
0
0
0
2
0
0
2
1
1
0
0
0
0
0
1
0
1
3
2
0
0
0
0
0
0
1
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
1
1
2
2
0
5
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
3
1
0
1
0
0
0
0
0
0
2
3
1
0
0
0
0
0
1
2
1
0
1
0
1
0
0
1
0
1
0
0
1
0
0
0
2
0
0
0
0
1
3
1
2
1
5
1
0
0
0
0
0
0
0
0
1
0
0
2
1
0
2
0
0
0
0
0
0
1
0
3
0
1
0
7
1
0
0
7
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
3
0
2
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
2
0
0
0
0
2
0
0
1
2
1
0
0
0
0
1
0
0
2
0
0
0
0
1
0
1
0
0
0
0
2
0
1
2
0
2
0
3
0
0
0
0
1
0
0
3
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
2
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
2
0
2
2
0
3
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
1
2
1
1
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
1
1
1
2
0
0
0
0
1
2
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
1
0
1
0
0
0
2
1
0
0
0
0
2
2
1
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
2
0
0
3
1
0
0
0
4
1
0
1
0
2
0
0
1
0
1
0
0
0
0
0
3
4
0
0
0
0
0
0
0
2
0
0
3
0
0
1
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
1
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
1
0
0
2
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
2
0
2
0
0
1
1
0
0
2
0
0
2
0
1
0
0
6
0
0
0
0
2
2
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
2
1
3
0
0
2
0
0
2
0
1
0
0
1
0
0
2
1
0
0
0
0
1
0
1
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
2
1
0
0
2
1
0
0
0
0
1
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
3
0
0
1
0
0
0
2
0
2
0
2
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
1
2
2
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
1
0
1
0
2
1
2
0
0
0
1
1
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
2
2
0
0
0
0
6
0
0
0
0
2
1
2
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
1
0
1
0
0
1
2
0
2
0
0
5
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
2
2
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
2
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
1
0
3
1
0
0
0
2
1
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
1
5
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
3
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
1
2
0
0
2
1
0
0
0
2
0
0
0
0
2
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
2
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
2
1
0
1
2
0
0
0
1
2
1
0
0
0
0
0
2
0
0
0
0
0
1
2
0
1
0
0
1
0
0
0
0
2
2
1
0
0
5
1
0
0
0
0
1
0
2
1
4
0
0
0
0
2
0
0
0
0
2
2
1
0
0
0
0
0
2
0
2
0
1
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
2
1
0
3
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
3
1
6
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
2
2
0
0
0
0
2
0
0
0
0
1
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
2
1
0
1
2
0
0
0
2
2
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
1
1
2
0
1
2
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
4
0
0
0
0
2
0
0
0
0
3
1
0
2
3
0
0
0
0
0
2
0
0
0
1
0
2
0
2
0
0
1
2
2
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
7
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
2
1
2
0
0
0
0
1
0
1
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
3
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
2
0
0
5
0
0
1
3
1
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
1
0
7
0
3
0
0
0
0
0
0
2
0
0
1
0
2
0
0
1
0
2
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
1
0
1
2
0
1
0
0
0
0
1
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
3
2
0
2
0
0
0
5
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
3
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
1
0
0
0
2
0
1
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
3
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
2
0
1
0
1
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
2
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
3
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
2
0
4
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
2
2
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
6
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
1
0
0
0
5
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
3
0
0
0
0
0
0
4
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
1
2
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
2
2
0
2
3
0
2
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
4
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
4
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
1
0
9
0
1
0
0
0
3
0
0
0
2
0
2
0
0
1
2
0
2
0
1
1
1
2
0
1
0
0
0
2
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
2
0
2
0
1
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
2
3
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
1
0
0
3
0
2
0
2
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
4
2
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
7
0
0
2
0
0
1
0
1
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
1
0
0
3
0
0
1
0
0
0
0
0
2
0
1
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
2
3
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
2
0
2
1
1
0
2
0
0
0
1
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
1
2
2
0
0
2
0
0
2
0
1
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
2
1
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
3
6
2
0
0
2
0
1
1
0
0
0
1
1
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
2
0
0
1
0
2
0
0
0
2
3
2
0
2
0
2
2
1
0
0
0
0
1
0
2
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
3
1
0
2
0
0
5
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
1
3
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
1
0
0
1
0
0
0
1
1
0
1
0
3
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
1
1
0
0
0
0
1
0
2
0
1
0
0
0
2
0
1
0
0
2
0
0
0
3
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
1
1
0
0
0
0
1
0
1
0
1
0
0
2
2
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
4
0
1
2
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
2
0
2
1
0
0
0
3
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
3
0
1
3
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
2
1
1
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
2
6
1
0
0
0
1
0
0
1
0
0
0
0
1
0
2
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
2
0
2
0
2
0
3
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
2
2
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
2
0
2
0
0
0
1
2
0
1
0
0
2
0
0
0
0
2
1
0
0
1
0
2
0
2
1
0
1
0
0
2
0
0
0
0
1
2
0
0
0
0
0
1
2
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
2
0
0
0
0
0
0
3
0
0
0
2
0
5
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
3
0
1
0
0
1
0
0
0
1
1
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
3
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
2
0
0
2
2
2
0
0
0
1
0
1
0
0
0
0
0
2
0
3
0
0
0
0
0
0
1
0
4
0
0
0
2
0
0
0
0
0
2
1
2
1
0
0
0
2
0
4
1
2
0
1
0
2
2
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
2
0
0
1
2
2
0
2
2
0
0
1
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
3
0
0
0
0
0
3
2
0
2
0
0
2
0
0
2
0
0
2
3
0
0
2
2
0
1
0
1
1
0
1
2
0
0
1
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
6
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
2
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
1
0
1
0
0
2
0
0
0
2
0
0
0
2
0
0
1
0
0
2
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
3
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
1
2
0
0
3
0
0
0
0
1
0
0
2
0
2
0
0
2
0
0
0
1
0
3
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
3
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
2
1
2
0
2
0
0
0
0
0
0
0
2
1
0
0
0
2
1
2
0
3
0
0
0
0
1
2
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
6
0
0
1
2
0
0
1
0
0
2
1
0
0
2
1
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
1
2
1
0
0
2
0
0
2
2
1
2
0
0
2
0
1
0
1
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
3
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
3
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
3
0
0
0
1
1
0
2
1
0
0
0
0
0
1
0
1
2
0
0
0
3
2
5
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
6
1
1
0
1
0
0
0
4
2
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
2
2
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
2
2
0
0
0
0
1
0
2
2
0
0
0
2
1
3
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
2
0
0
2
0
2
1
3
0
2
0
0
0
1
0
2
0
0
0
0
2
0
2
0
0
0
0
2
0
2
0
0
2
0
0
2
0
0
0
0
0
1
2
2
0
0
0
2
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
6
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
6
0
0
2
0
0
0
3
2
0
2
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
4
0
0
0
1
2
0
2
1
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
1
0
3
0
2
0
0
0
0
0
0
0
0
1
0
0
2
2
2
0
2
1
0
0
2
0
0
0
0
0
2
0
2
0
2
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
2
0
0
7
0
1
0
1
0
1
0
0
0
2
0
1
0
0
0
1
0
0
0
0
1
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
1
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
3
0
0
0
2
2
0
0
0
0
0
2
2
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
4
0
0
2
1
0
1
0
1
0
1
1
0
0
2
0
2
1
1
2
0
2
0
0
0
2
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
1
0
0
0
3
0
0
1
0
2
0
2
1
1
0
1
0
0
2
1
0
0
0
0
2
0
0
1
0
4
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
3
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
1
2
0
1
3
0
1
0
0
1
0
1
2
1
0
3
0
2
0
2
2
0
0
0
0
3
0
0
0
0
0
1
2
0
0
2
2
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
2
0
0
2
1
4
0
2
0
3
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
2
2
1
1
0
0
0
1
0
0
1
0
1
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
3
2
0
0
3
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
3
1
0
0
0
0
0
0
0
0
0
1
3
0
1
2
2
0
0
0
0
0
1
0
2
1
0
0
2
2
3
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
3
0
0
2
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
3
0
0
1
2
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
1
1
2
1
1
1
0
2
0
0
3
0
1
2
0
0
0
0
0
0
2
0
0
0
2
1
0
2
0
0
2
2
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
4
0
1
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
1
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
7
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
2
2
0
0
0
0
0
0
1
0
1
0
0
0
2
0
1
0
0
4
1
0
0
0
0
2
1
0
0
0
2
1
0
0
1
0
2
0
0
0
3
0
4
0
0
1
0
0
0
0
0
0
0
0
3
0
1
0
0
1
0
0
0
2
0
2
0
1
1
0
1
1
2
0
1
2
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
2
5
0
0
0
2
0
0
0
0
1
1
0
3
0
0
2
0
2
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
3
1
0
0
0
1
0
0
4
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
1
0
2
3
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
2
1
0
2
0
1
0
2
0
2
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
1
2
0
2
0
1
0
2
0
2
0
0
0
0
1
3
0
0
2
0
0
0
0
0
0
0
0
2
4
0
1
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
11
1
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
1
1
0
0
0
1
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
3
0
1
0
0
0
1
0
2
1
0
0
0
2
0
1
0
0
0
0
3
3
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
1
1
0
1
0
0
0
0
0
2
0
1
1
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
2
1
0
0
0
0
1
3
0
0
0
0
0
2
0
2
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
2
0
0
0
2
1
6
0
0
0
0
0
1
0
1
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
5
2
0
0
0
2
0
0
0
1
2
2
0
0
0
1
0
1
0
1
0
1
4
0
0
2
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
2
0
1
1
0
0
0
0
2
3
0
0
0
0
2
0
1
0
2
0
1
2
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
3
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
2
1
0
2
2
0
1
1
0
0
0
0
0
1
0
0
0
1
0
5
1
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
1
2
1
0
0
0
0
2
2
0
0
1
0
2
0
0
2
2
0
0
0
1
0
2
0
1
0
0
2
0
0
1
0
0
2
0
0
0
0
2
1
2
0
0
2
0
0
0
2
0
2
1
1
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
3
2
0
0
2
0
0
0
1
0
0
1
0
0
0
0
4
0
2
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
1
0
0
1
0
2
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
2
0
0
0
0
0
2
1
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
1
2
1
0
1
0
2
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
1
2
2
0
0
0
0
1
0
1
1
0
0
0
3
0
0
2
0
0
0
0
1
0
4
0
0
0
1
2
1
0
0
2
2
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
2
0
1
0
1
0
2
0
0
1
0
0
0
2
1
1
1
3
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
1
3
0
0
3
0
0
1
0
1
2
2
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
1
0
0
0
2
1
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
1
0
1
0
1
0
0
2
0
1
2
2
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
2
0
1
3
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
1
0
0
1
0
0
2
0
0
0
0
2
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
2
0
3
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
2
2
0
0
2
0
5
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
1
4
1
0
0
0
0
0
0
0
2
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
1
2
2
1
0
0
0
0
2
2
0
1
0
0
3
0
0
0
3
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
3
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
1
0
0
1
1
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
1
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
1
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
2
1
0
0
0
3
0
0
0
0
0
2
1
1
2
2
0
0
0
0
2
0
2
0
2
0
0
0
3
1
0
0
1
0
0
0
5
2
0
0
2
0
0
0
0
0
2
0
1
0
1
2
0
0
2
0
0
0
0
3
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
6
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
2
1
2
0
0
1
1
0
1
0
0
0
2
2
0
0
0
0
2
0
1
0
2
1
0
0
2
1
0
0
0
0
0
0
2
0
0
2
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
2
0
0
2
0
2
1
0
0
2
0
0
0
0
0
0
2
0
4
1
2
0
0
0
1
0
1
0
0
2
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
3
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
2
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
2
1
0
3
0
0
3
0
0
3
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
5
0
0
0
1
1
0
2
2
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
4
0
0
2
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
2
0
1
1
0
2
0
1
0
1
0
0
2
2
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
2
0
2
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
1
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
2
1
0
0
0
0
2
2
2
0
0
1
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
6
2
0
0
3
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
2
6
1
0
0
2
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
4
0
0
2
1
0
1
0
0
1
0
0
1
1
2
0
0
0
0
0
3
0
0
2
0
0
1
2
0
2
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
4
1
3
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
2
1
0
2
2
0
0
0
0
1
3
0
0
2
1
0
1
0
0
0
0
2
0
1
2
1
0
1
2
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
3
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
4
0
1
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
1
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
1
0
2
0
1
0
0
0
3
1
0
1
0
0
0
1
1
0
0
0
2
2
1
0
0
2
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
6
0
0
1
2
5
0
0
0
0
0
0
3
1
0
2
1
0
1
2
0
1
0
1
1
1
0
0
1
3
0
1
0
0
2
0
1
0
0
0
0
0
0
0
4
0
0
0
0
1
0
2
1
0
2
0
1
1
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
2
2
0
0
0
2
4
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
1
0
0
1
1
0
0
0
2
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
2
3
0
3
0
1
0
1
3
0
0
0
0
0
0
0
0
1
2
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
2
0
0
0
1
0
2
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
1
2
0
0
0
2
0
2
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
1
0
2
2
0
0
0
0
0
0
1
2
1
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
2
3
1
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
1
2
0
0
1
1
2
2
1
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
1
0
0
3
0
0
0
0
4
1
1
0
2
0
1
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
2
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
1
0
0
0
2
0
0
0
0
4
0
1
1
0
0
1
0
1
2
0
1
1
0
0
0
0
0
0
0
1
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
1
0
0
0
0
0
0
0
2
0
0
1
0
0
2
1
0
2
1
2
0
0
0
1
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
1
0
0
0
0
2
0
0
0
1
0
0
0
1
2
4
0
0
0
1
0
2
1
0
0
0
2
2
1
0
0
2
0
0
1
0
0
0
0
2
1
0
3
0
2
0
2
2
0
1
0
0
0
0
2
0
2
1
2
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
3
1
2
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
2
0
2
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
3
0
2
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
1
0
4
0
1
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
1
0
2
1
1
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
2
0
2
2
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
3
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
1
2
2
0
0
1
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
1
2
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
2
0
0
0
11
1
0
2
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
2
0
1
1
2
0
1
0
2
0
0
0
0
2
0
0
1
1
1
0
0
1
0
0
1
2
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
3
0
0
2
0
0
1
0
0
1
2
1
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
2
0
1
0
1
2
1
0
0
0
0
1
0
0
2
2
0
0
0
0
1
0
0
1
2
0
1
0
0
2
2
2
1
0
2
2
0
0
1
0
0
0
0
1
2
1
1
0
0
0
1
0
0
1
0
0
0
0
2
0
0
6
2
0
0
0
2
0
0
0
0
0
1
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
1
0
0
0
0
3
0
0
0
0
2
0
0
0
1
0
0
2
0
1
0
1
0
0
0
1
0
0
0
4
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
1
0
0
2
0
0
0
2
0
0
2
0
1
0
0
0
0
0
1
0
0
1
1
0
0
1
2
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
2
1
1
2
0
0
0
2
9
0
0
2
0
0
0
0
5
0
1
1
0
0
0
1
0
0
0
0
0
0
2
1
2
0
0
0
0
0
1
0
0
0
1
0
0
2
3
0
0
0
0
0
1
3
0
0
2
1
0
2
0
0
0
2
0
1
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
1
0
0
0
1
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
2
1
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
2
0
0
0
0
0
0
2
0
2
0
1
0
0
1
0
0
0
0
2
0
1
0
2
1
0
0
0
3
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
1
1
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
3
0
1
0
0
2
1
2
1
1
0
0
1
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
3
0
2
2
0
0
2
1
2
0
0
0
2
2
2
0
1
1
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
2
4
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
2
0
2
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
1
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
1
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
2
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
2
0
2
0
0
0
1
0
0
0
0
0
1
1
2
1
1
0
0
3
2
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
1
0
0
0
1
2
0
0
3
0
3
2
0
0
0
0
2
0
2
0
2
0
0
0
0
1
0
0
1
0
0
0
2
2
0
2
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
1
0
2
0
0
5
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
6
1
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
2
0
0
0
2
2
5
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
3
0
2
0
2
1
0
0
0
0
1
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
1
0
0
0
0
2
2
0
1
1
0
2
0
0
0
0
0
0
0
2
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
2
0
0
0
0
2
0
1
2
0
0
2
1
0
2
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
2
0
2
0
0
0
1
0
0
0
0
0
1
0
0
3
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
2
1
1
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
2
0
0
3
0
2
2
0
1
3
1
3
0
0
0
0
0
2
2
0
3
0
2
0
0
0
0
0
2
0
2
2
0
1
0
0
0
0
0
1
1
0
2
0
1
0
1
0
0
1
0
2
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
3
0
0
0
0
2
0
0
0
0
1
1
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
1
0
0
3
1
0
0
0
0
0
0
0
2
3
1
4
1
2
0
0
2
2
0
0
0
1
0
0
2
0
2
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
3
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
3
0
0
2
0
0
1
0
2
1
0
1
0
0
0
2
0
1
0
0
1
2
0
0
1
5
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
2
0
1
0
0
1
0
0
0
0
1
2
0
2
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
3
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
4
0
2
0
0
0
0
0
1
0
0
0
0
2
2
0
0
2
0
1
0
2
0
0
0
0
0
2
0
0
0
0
1
7
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
3
0
0
0
1
2
2
0
1
0
1
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
1
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
1
2
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
1
1
0
0
1
1
0
0
2
0
2
0
0
0
0
0
2
0
0
1
1
0
0
0
2
0
0
0
0
1
0
0
0
3
0
0
0
1
1
1
0
0
0
0
0
0
0
0
2
0
2
0
1
0
2
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
3
0
0
0
1
0
0
2
0
0
2
0
2
2
0
0
0
0
2
0
0
1
2
0
0
1
2
0
1
0
5
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
1
2
3
0
2
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
2
0
0
0
0
1
0
1
1
0
1
2
0
0
0
0
0
0
0
1
0
5
0
0
11
0
0
0
0
0
1
0
1
0
0
0
3
0
0
0
2
0
0
0
0
0
2
0
1
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
1
2
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
3
0
0
2
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
2
1
0
0
0
3
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
2
0
1
0
1
0
2
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
1
1
0
3
0
0
1
0
0
2
0
1
0
0
0
0
0
2
1
1
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
2
2
0
2
0
0
0
0
2
0
0
0
0
0
2
1
0
2
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
3
1
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
1
0
0
2
0
0
0
1
3
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
1
0
2
1
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
1
1
0
2
2
1
0
2
2
0
0
0
0
1
0
0
2
1
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
3
2
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
1
2
0
0
0
0
2
0
0
0
0
2
0
3
0
0
0
0
0
0
1
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
3
0
2
0
3
0
1
0
1
1
2
0
2
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
2
1
1
0
1
0
0
0
1
3
2
0
0
1
1
0
0
6
0
0
0
0
2
6
0
0
0
0
0
0
0
0
0
0
3
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
2
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
4
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
2
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
2
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
3
1
0
0
2
0
1
1
2
0
0
0
0
0
1
0
2
0
1
1
0
2
0
0
0
0
1
3
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
3
0
1
0
0
0
0
3
2
1
0
0
0
1
0
2
0
2
0
1
0
4
0
1
3
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
1
0
2
0
1
0
0
2
0
0
0
0
2
2
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
1
5
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
2
0
2
4
0
0
0
0
1
2
0
2
0
0
0
1
0
0
0
0
0
6
2
2
0
0
0
1
2
0
0
2
5
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
2
2
0
0
1
0
0
1
0
0
4
0
1
0
1
0
0
0
1
0
1
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
2
0
0
0
0
1
0
0
0
0
2
0
2
0
0
2
0
1
0
1
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
1
2
1
0
1
0
1
1
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
1
2
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
1
0
0
1
2
0
2
0
0
1
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
2
0
2
0
0
1
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
1
0
0
0
0
1
3
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
4
1
0
0
0
3
1
0
2
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
2
2
0
1
0
1
0
0
2
0
0
2
0
2
1
2
1
0
0
0
2
0
1
0
0
0
0
2
1
0
2
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
2
1
0
2
0
2
0
0
0
0
1
1
2
0
2
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
2
0
1
3
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
1
0
0
4
0
1
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
3
0
1
0
0
0
1
2
2
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
1
2
1
0
2
0
2
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
2
2
0
1
0
0
0
0
1
0
1
1
0
0
1
0
1
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
1
0
3
6
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
2
1
0
0
0
0
5
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
1
0
0
0
2
2
0
0
0
2
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
1
0
1
0
3
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
2
0
2
3
0
0
0
2
0
0
2
0
1
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
2
0
0
2
2
2
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
1
1
0
0
0
2
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
1
1
0
0
0
0
1
0
0
4
0
0
5
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
2
0
1
0
2
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
2
1
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
2
0
5
0
0
0
2
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
2
1
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
1
0
0
0
1
0
2
0
3
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
3
0
3
2
0
0
2
0
0
1
0
2
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
3
0
0
0
0
0
0
2
0
0
0
4
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
2
2
1
0
0
1
0
0
0
0
0
0
0
0
2
1
1
1
0
0
0
0
0
1
0
1
1
0
1
0
2
0
0
0
1
2
0
1
0
0
2
0
1
2
0
0
0
0
0
0
0
1
0
0
1
2
1
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
2
1
2
0
2
2
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
2
8
1
2
0
1
0
0
0
2
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7
0
1
0
0
0
2
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
4
0
0
0
0
2
0
0
0
2
1
0
0
2
0
4
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
2
0
2
4
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
1
0
0
2
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
6
0
0
2
2
0
1
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
2
0
2
1
0
0
0
2
2
0
1
0
1
0
0
2
1
0
0
2
3
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
1
0
2
0
0
1
0
0
0
3
0
1
0
0
0
2
0
0
1
0
0
0
0
3
0
0
0
2
0
0
0
2
0
0
0
2
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
3
1
0
0
2
0
1
0
1
2
2
0
0
3
0
3
1
0
3
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
2
0
0
0
0
1
0
0
2
0
2
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
2
0
0
0
0
1
2
2
0
0
0
0
0
1
0
0
2
0
0
4
0
0
2
2
0
0
0
0
0
0
0
0
0
7
0
0
0
4
0
2
0
0
0
0
1
2
2
0
0
1
0
0
0
0
0
0
3
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
1
0
3
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
2
2
2
1
0
2
1
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
3
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
2
2
0
2
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
2
1
0
2
0
0
0
0
0
0
3
4
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
2
2
2
0
0
2
0
0
1
2
1
0
0
0
1
2
2
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
5
1
0
0
1
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
1
0
1
3
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
1
2
0
2
0
1
1
0
0
0
0
0
1
0
0
1
0
0
2
0
2
2
0
1
0
0
1
1
0
2
0
0
1
0
0
1
0
0
0
0
2
1
0
3
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
4
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
2
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
2
0
0
0
0
2
1
1
0
3
0
2
1
0
0
0
0
1
1
0
0
0
1
2
0
0
0
1
0
2
0
3
2
1
0
0
0
0
0
0
2
0
0
2
2
2
2
0
0
1
1
0
0
2
0
1
1
0
0
2
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
3
2
0
0
0
0
2
0
0
1
0
0
3
0
0
2
0
0
2
0
3
0
2
0
0
0
0
0
1
0
0
0
2
1
1
0
0
0
0
0
0
0
0
1
0
2
2
1
0
0
2
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
1
0
0
0
2
0
3
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
2
4
0
1
0
0
2
0
0
0
3
2
1
4
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
1
1
0
1
0
1
1
2
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
1
0
0
2
3
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
1
1
0
2
0
0
0
0
0
0
0
1
0
2
0
1
0
1
0
0
0
2
0
1
2
0
0
0
1
0
0
2
2
0
12
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
1
1
2
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
2
0
1
0
1
0
0
0
1
0
0
0
1
2
0
1
0
2
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
1
1
0
0
2
1
1
0
0
1
0
0
0
2
0
1
0
0
2
0
1
0
0
0
1
1
1
2
0
0
0
0
0
0
6
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
2
0
1
2
2
0
0
2
0
0
2
0
0
0
3
0
0
0
2
0
1
0
0
2
1
0
0
1
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
2
2
0
0
0
0
4
2
0
0
2
0
0
0
2
0
0
0
0
2
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
2
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
3
0
0
1
0
0
0
1
0
1
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
2
3
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
1
0
0
0
2
2
0
0
0
0
0
2
0
2
2
0
2
0
0
0
2
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
1
0
1
2
0
2
0
0
0
0
1
0
0
0
0
2
2
0
0
0
1
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
2
2
1
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
2
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
2
1
0
3
0
1
0
0
0
1
0
1
0
2
0
0
0
2
0
0
0
0
2
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
2
2
2
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
2
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
1
0
1
0
1
0
0
3
0
1
3
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
3
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
3
1
2
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
3
0
2
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
3
0
0
0
0
1
0
1
0
0
0
2
0
1
0
2
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
3
0
0
5
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
4
0
1
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
2
0
2
2
0
2
0
0
0
0
0
0
5
2
1
0
0
2
1
2
1
2
0
0
0
0
1
2
0
2
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
3
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
1
0
0
2
0
0
0
0
1
0
1
2
0
0
0
0
2
0
1
1
0
1
1
0
0
0
0
3
0
0
0
0
2
0
1
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
1
0
0
0
0
2
1
2
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
2
0
0
0
1
2
0
0
4
2
0
0
0
0
2
0
0
0
1
1
1
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
2
0
1
0
1
0
0
0
1
0
0
0
0
1
0
2
1
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
3
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
5
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
1
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
1
3
2
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
1
0
0
1
2
0
0
0
1
2
1
0
0
0
2
0
0
2
0
0
3
0
2
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
1
0
2
2
2
0
0
0
2
0
0
2
0
1
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
3
0
0
0
2
0
1
0
2
0
2
2
1
0
0
0
0
1
0
1
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
3
1
0
0
0
2
3
0
0
0
0
0
1
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
3
0
1
0
0
3
2
0
0
0
1
0
0
0
0
0
5
0
0
0
0
0
1
0
0
0
0
2
0
1
2
1
2
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
2
0
0
2
2
0
1
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
4
2
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
2
0
0
0
0
0
0
0
2
2
2
2
4
1
0
0
0
0
2
2
1
0
2
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
2
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
1
0
2
0
2
0
0
1
2
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
2
1
0
3
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
4
1
0
0
1
0
0
2
0
0
0
0
1
0
0
0
2
1
2
0
0
0
2
0
0
0
3
0
0
0
0
5
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
2
0
0
0
0
0
0
5
0
0
0
0
1
1
1
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
1
0
0
1
0
0
2
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
5
0
0
1
2
2
0
2
0
0
0
1
2
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
1
2
2
0
1
0
0
0
1
0
1
0
0
4
0
1
0
0
1
0
0
0
0
0
0
5
0
0
0
0
0
2
0
2
0
2
1
2
0
2
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
2
1
6
0
0
0
0
1
0
0
0
2
0
1
0
0
0
1
3
0
1
0
0
2
0
0
3
0
0
0
0
2
1
3
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
1
1
0
1
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
2
0
2
0
0
0
2
0
2
0
2
0
0
0
0
1
0
0
0
1
0
2
0
0
2
0
2
0
0
2
0
0
0
0
1
1
0
0
2
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
3
1
2
0
1
0
0
0
0
1
0
6
0
0
3
0
0
0
0
0
2
0
0
0
0
2
1
0
1
1
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
2
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
1
2
0
0
2
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
1
0
3
0
0
1
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
4
0
0
0
2
0
0
0
0
0
2
2
0
1
0
0
0
0
1
0
0
2
1
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
2
1
2
0
1
0
0
1
0
1
0
0
2
0
1
2
0
0
0
1
2
3
0
0
1
0
3
1
1
1
1
0
0
2
1
1
0
0
0
0
0
1
0
1
1
1
0
1
2
2
0
1
0
0
0
2
1
2
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
2
2
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
1
1
0
2
0
0
0
1
0
1
1
0
0
0
2
0
0
0
2
1
2
0
1
1
0
1
0
0
1
6
2
1
0
0
0
0
0
0
0
0
2
2
0
0
1
1
4
2
0
0
2
1
2
2
1
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
4
2
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
2
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
1
4
0
0
2
0
0
0
2
2
0
0
0
0
2
1
2
1
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
3
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
2
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
1
2
0
0
0
1
2
0
0
0
0
0
0
1
3
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
2
0
3
2
0
3
0
1
1
2
0
2
2
0
1
0
0
1
0
0
1
2
0
1
0
0
1
0
1
0
2
0
0
1
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
4
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
2
0
0
0
0
0
0
3
0
1
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
1
2
0
0
0
0
0
0
2
0
1
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
2
1
2
0
0
2
0
0
3
0
3
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
2
2
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
2
0
0
0
0
0
0
8
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
2
0
0
0
2
0
0
1
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
2
2
2
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
1
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
2
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
1
0
1
0
2
0
0
2
0
0
2
0
1
1
1
0
2
2
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
3
0
0
0
2
1
0
1
0
1
2
0
0
5
0
0
1
0
0
2
0
2
0
0
0
0
0
0
5
0
0
1
0
0
2
1
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
1
0
0
0
1
0
0
0
2
1
0
3
0
0
2
0
0
0
1
0
0
0
0
0
2
1
0
0
0
2
0
0
2
0
0
0
0
1
0
1
2
0
0
0
0
0
0
2
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
3
0
5
0
2
0
0
0
0
0
0
0
0
0
1
0
8
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
3
2
3
0
0
0
0
1
2
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
3
0
1
5
0
0
0
0
2
2
3
0
0
2
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
3
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
2
0
2
2
0
2
0
2
0
0
0
0
2
0
0
2
0
2
2
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
2
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
1
1
0
0
3
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
1
0
0
1
0
0
1
0
0
2
0
0
1
0
0
0
9
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
6
0
2
0
0
2
2
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
2
0
1
0
0
1
0
0
0
2
0
2
0
1
0
2
0
0
1
0
1
2
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
1
1
0
0
2
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
3
1
0
0
0
1
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
3
2
0
0
1
2
0
2
2
3
0
2
0
0
0
0
1
2
2
0
0
0
0
1
0
0
0
0
1
0
2
1
2
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
2
0
0
0
2
3
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
2
1
0
0
0
0
0
1
0
2
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
2
0
0
2
0
0
0
3
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
1
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
6
0
0
0
0
0
0
1
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
1
0
2
3
1
0
0
0
3
0
0
0
2
2
2
0
1
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
4
1
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
3
0
2
1
0
1
0
2
0
0
0
0
0
0
2
2
1
0
1
0
0
2
0
0
0
0
0
2
0
2
0
1
0
0
0
1
1
0
3
0
0
0
0
0
0
0
1
0
2
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
1
2
0
2
0
0
0
1
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
2
0
0
1
1
2
0
0
3
2
2
1
1
0
0
0
1
2
2
2
0
4
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
5
1
1
0
0
0
1
2
2
0
0
0
1
2
0
0
2
0
2
2
1
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
4
1
0
0
1
1
0
0
2
0
0
2
0
0
0
2
1
2
0
2
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
2
0
3
0
0
0
0
0
2
0
1
1
0
0
2
1
1
0
0
2
0
1
4
0
0
0
0
2
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
2
0
5
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
3
0
0
0
1
2
0
0
2
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
3
2
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
1
2
0
2
2
0
0
0
0
3
0
2
0
1
1
0
0
2
0
0
0
0
0
3
0
0
0
0
0
1
2
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
1
1
8
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
1
0
2
1
0
0
0
1
0
0
0
2
1
0
0
0
0
2
1
0
0
1
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
3
0
0
2
0
0
0
0
2
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
7
1
0
2
0
0
9
0
0
2
1
0
2
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
3
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
2
1
1
2
2
2
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
3
0
0
0
0
1
0
1
0
0
2
0
0
0
0
6
0
0
0
1
1
0
0
1
1
2
0
1
0
0
1
0
0
0
0
0
0
0
3
1
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
2
0
0
1
1
0
2
2
0
0
0
0
0
2
0
0
0
1
0
4
0
0
0
0
0
0
0
1
2
1
0
0
2
0
1
0
2
0
0
3
0
3
0
1
2
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
2
0
2
2
0
2
1
0
2
3
0
1
2
0
1
1
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
1
1
0
0
0
0
0
1
2
0
2
0
2
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
3
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
3
1
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
1
2
0
0
2
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
2
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
3
1
0
0
0
1
1
1
0
2
1
0
1
0
0
0
0
0
0
2
1
1
0
0
1
1
1
0
0
0
0
0
0
0
0
2
0
0
1
2
2
0
0
1
0
0
0
0
1
0
0
0
2
2
1
2
0
0
1
0
2
0
0
2
0
0
0
2
2
0
0
1
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
2
1
0
0
1
0
0
0
0
0
3
0
0
3
0
0
2
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
5
0
0
0
2
0
2
0
0
1
4
1
3
0
2
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
2
0
0
0
0
1
0
0
0
2
2
0
2
0
0
0
0
0
2
2
1
1
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
1
0
0
4
0
0
0
2
1
0
0
2
2
2
0
0
0
0
0
0
2
0
0
2
2
0
0
2
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
1
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
3
0
0
18
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
1
2
0
2
2
0
0
2
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
2
2
0
2
0
2
0
2
1
0
0
0
0
0
3
0
4
0
0
0
2
0
0
0
0
1
0
1
0
2
0
0
1
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
3
1
2
1
0
0
0
0
0
0
3
1
0
2
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
3
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
1
2
3
0
2
0
0
0
0
2
0
0
2
1
2
0
0
2
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
2
2
0
3
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
2
0
0
0
3
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
2
1
0
0
0
0
0
0
1
0
2
3
0
0
1
0
1
0
0
0
0
2
1
2
0
0
0
1
1
0
0
3
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
1
3
0
0
0
3
0
1
0
0
0
0
1
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
3
0
9
0
1
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
2
0
0
0
0
0
0
0
0
2
3
0
0
0
2
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
4
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
1
2
0
0
1
0
0
1
0
1
2
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
2
1
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
1
0
0
1
0
1
0
0
2
3
0
0
0
0
1
0
2
1
0
0
0
0
0
0
5
0
1
2
2
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
1
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
2
0
3
0
1
0
1
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
3
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
2
1
0
0
0
1
1
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
2
0
1
0
3
1
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
2
0
0
1
0
0
0
0
2
8
0
0
1
0
2
0
2
0
1
1
1
0
0
5
0
2
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
3
1
0
2
0
0
1
0
2
2
1
0
0
1
0
1
1
0
0
0
2
0
3
1
0
0
0
0
0
2
1
0
0
1
0
1
2
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
2
0
0
2
1
2
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
4
0
2
0
0
0
2
0
0
2
0
0
1
1
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
3
1
1
0
1
2
0
0
1
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
2
1
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
2
0
2
0
0
0
0
0
2
0
2
0
3
5
0
2
0
2
0
2
0
0
0
0
1
0
0
6
0
0
1
0
0
0
0
3
0
0
1
0
1
0
0
1
0
0
0
0
1
1
0
1
0
0
0
1
0
1
0
2
0
5
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
2
0
0
1
2
0
0
0
0
1
1
0
2
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
5
0
2
0
2
2
0
1
0
2
2
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
3
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
2
1
3
0
1
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
4
0
4
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
1
1
2
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
2
0
0
0
0
2
0
0
0
0
1
0
0
0
1
1
0
0
2
0
0
2
1
0
2
1
0
0
0
0
0
0
1
0
0
0
0
2
1
1
1
0
1
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
2
2
2
2
0
0
0
2
0
0
0
0
0
0
0
4
0
0
2
0
0
0
1
0
2
0
0
0
0
2
0
0
0
2
0
0
2
2
0
1
0
2
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
1
1
0
0
0
0
2
0
0
1
2
2
0
0
0
0
0
0
0
0
0
2
0
2
0
1
2
0
1
0
2
0
0
2
0
0
0
0
0
2
0
0
2
0
0
1
2
0
0
4
1
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
3
2
2
2
0
0
2
1
1
0
1
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
1
11
0
0
0
0
0
0
0
1
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
2
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
1
0
0
0
0
0
0
1
5
0
0
1
0
2
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
2
1
1
3
0
1
0
0
2
2
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
2
0
3
0
0
0
0
2
1
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
2
1
0
0
0
0
4
2
2
0
0
1
0
0
1
0
0
2
1
0
3
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
2
0
0
0
1
0
0
0
1
1
0
0
0
0
2
2
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
1
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
1
2
0
2
0
0
0
0
2
0
2
0
3
0
0
0
3
0
1
1
0
0
5
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
1
2
0
2
0
0
2
2
0
0
0
2
0
6
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
3
2
0
0
0
0
0
3
0
0
0
0
0
1
2
0
0
0
0
1
2
1
0
1
2
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
1
1
4
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
2
2
5
0
1
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
6
0
0
0
1
1
0
2
0
2
3
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
3
2
0
0
2
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
3
0
0
2
0
0
0
2
1
1
1
0
1
1
0
3
1
2
0
2
0
1
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
1
0
1
0
0
0
0
0
1
0
2
0
0
0
1
0
2
0
2
1
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
1
0
2
0
0
0
1
0
0
1
0
2
2
1
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
2
2
1
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
1
2
0
0
0
0
0
0
2
0
0
0
2
1
0
0
1
0
0
2
0
1
0
0
2
1
0
1
0
0
0
0
0
0
0
2
0
2
2
0
2
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
3
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
1
0
0
1
0
0
0
0
0
0
2
1
1
0
2
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
1
1
2
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
1
1
0
0
1
2
5
0
0
0
8
0
0
0
0
0
0
0
1
2
3
0
0
0
2
0
1
0
1
0
1
0
0
0
1
0
0
0
0
3
1
0
1
2
1
0
0
0
0
0
0
0
0
2
0
1
0
3
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
2
2
1
0
3
0
0
0
0
0
2
0
2
0
0
0
0
3
2
1
0
0
1
0
3
1
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
1
2
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
2
0
0
1
0
0
1
0
0
0
3
1
2
0
0
0
0
1
0
0
0
1
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
4
0
0
0
0
0
0
2
0
0
0
2
4
0
0
2
0
2
2
0
0
2
0
1
5
0
3
0
2
0
0
0
0
2
0
0
3
0
0
1
0
0
2
0
0
0
0
0
2
0
0
2
0
2
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
2
1
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
3
1
0
1
1
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
2
0
0
0
2
1
2
2
0
1
1
3
0
0
0
0
2
2
0
0
1
0
0
1
0
2
1
0
0
0
1
2
2
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
3
0
1
1
0
0
0
1
0
0
0
0
5
0
0
0
0
1
2
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
1
0
0
1
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
2
0
3
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
1
0
2
1
0
0
0
1
1
2
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
2
1
0
0
2
0
1
1
0
0
1
0
0
0
0
4
0
0
1
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
2
1
0
1
0
0
1
2
0
0
0
2
0
1
0
0
0
0
0
0
0
1
1
3
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
2
0
0
0
0
0
0
1
0
0
2
2
0
1
0
4
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
2
0
1
2
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
2
0
1
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
1
1
1
0
2
0
2
0
0
2
0
0
0
1
0
0
0
1
0
0
1
0
0
4
2
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
1
1
0
3
2
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
2
2
0
1
0
1
0
0
1
2
0
0
0
1
2
0
0
0
0
2
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
4
0
0
1
0
2
0
1
2
0
0
0
0
0
0
1
0
0
0
2
0
2
2
0
0
2
0
0
0
2
2
2
0
0
2
0
3
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
1
1
3
1
0
2
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
3
0
1
0
1
2
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
1
3
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
2
0
1
2
0
0
2
1
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
2
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
3
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
3
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
1
0
0
2
0
1
0
0
0
2
1
0
2
2
1
0
0
1
2
2
0
0
0
0
0
0
0
3
2
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
5
0
0
0
0
0
0
0
1
0
0
0
0
0
5
0
0
1
2
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
2
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
2
2
0
1
0
0
2
0
1
0
0
1
0
0
2
0
0
5
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
1
0
0
1
0
0
0
2
1
0
0
1
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
3
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
2
0
2
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
1
1
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
2
1
0
0
1
0
2
1
1
1
0
0
0
1
0
0
0
1
0
1
0
0
2
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
1
0
0
0
2
0
1
2
0
0
1
1
0
0
0
0
0
0
2
1
0
1
0
0
2
0
3
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
1
2
1
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
2
1
0
0
0
0
0
0
2
2
2
0
2
1
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
1
1
2
1
1
1
0
0
0
1
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
1
3
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
3
0
0
3
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
1
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
1
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
1
2
0
2
0
0
0
0
2
0
0
1
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
4
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
4
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
1
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
1
1
6
0
2
0
0
2
0
0
0
2
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
1
0
2
0
0
0
1
0
2
3
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
1
0
0
1
0
2
0
0
1
0
0
0
0
1
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
2
0
10
3
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
2
0
1
1
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
1
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
2
2
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
3
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
4
0
0
0
0
0
2
2
0
0
0
4
0
1
0
2
2
0
1
0
0
0
0
0
3
2
0
0
2
0
2
0
0
2
0
0
2
1
0
0
2
0
4
5
0
0
0
0
0
0
1
2
1
2
1
1
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
4
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
2
0
1
0
0
0
1
0
0
2
0
1
2
1
0
2
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
6
2
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
1
0
1
1
0
1
0
1
0
4
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
1
0
0
0
1
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
2
2
0
2
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
5
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
2
0
0
2
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
3
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
1
0
1
0
0
1
0
0
0
2
2
0
0
0
0
3
0
0
0
1
0
0
0
0
1
0
0
3
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
5
0
2
0
2
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
1
2
0
0
0
2
0
2
0
2
0
0
1
0
2
0
0
4
0
1
0
0
2
0
1
2
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
2
0
1
1
0
0
0
0
0
0
1
0
3
0
0
2
2
0
2
0
0
0
0
2
0
1
0
0
0
0
3
2
0
2
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
1
0
5
0
1
0
0
0
0
2
0
2
0
1
0
0
0
1
0
0
3
0
0
0
0
0
0
1
0
0
1
3
0
0
0
0
0
0
1
8
0
2
0
2
2
2
2
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
1
2
0
0
3
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
1
1
0
1
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
2
1
0
0
3
0
0
0
0
0
0
0
0
1
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
2
0
2
2
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
2
0
1
0
0
2
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
3
2
0
0
0
0
1
0
0
0
0
2
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
2
2
0
0
3
0
0
2
0
2
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
2
1
1
1
4
0
0
0
0
0
0
1
0
3
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
1
4
0
0
0
0
3
0
0
0
1
1
1
0
0
1
0
0
0
1
1
0
0
2
0
2
0
0
0
0
0
0
0
2
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
2
0
0
0
0
1
2
3
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
3
2
0
1
2
0
2
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
2
3
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
1
1
0
0
0
0
3
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
2
2
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
4
0
2
1
0
0
1
0
3
0
0
0
2
2
0
0
0
0
0
0
1
2
0
0
3
0
0
0
1
0
2
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
2
2
1
0
0
0
0
2
3
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
1
0
1
0
1
2
0
0
2
2
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
2
0
1
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
2
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
1
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
2
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
2
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
2
0
0
2
2
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
3
0
0
0
0
2
3
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
3
0
2
0
1
0
0
0
0
0
1
2
2
0
1
1
0
0
0
0
0
1
0
0
3
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
1
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
1
1
0
0
0
0
1
0
0
0
2
0
4
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
1
5
1
0
0
0
0
0
1
2
0
1
2
1
0
0
4
0
0
0
4
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
6
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
1
0
2
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
2
2
1
1
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
1
1
0
2
1
0
0
0
2
0
1
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
1
0
2
0
0
0
0
1
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
2
0
1
0
2
0
0
0
1
1
0
0
6
1
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
1
0
0
0
3
0
1
2
0
2
2
0
0
3
0
0
0
0
0
0
0
1
0
0
1
1
4
0
0
1
0
1
2
0
0
0
0
2
0
3
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
10
0
0
0
1
0
0
1
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
1
0
0
0
3
1
1
0
1
0
0
0
2
0
0
1
0
0
0
6
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
2
1
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
3
0
0
1
0
2
0
1
0
0
1
1
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
3
0
0
0
2
3
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
4
2
0
0
2
0
2
1
0
0
0
2
0
2
2
0
2
1
2
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
2
0
0
2
2
1
0
2
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
4
0
0
3
0
0
0
0
0
1
0
2
2
0
0
0
1
0
1
0
3
0
0
0
2
0
4
0
0
0
0
0
0
2
0
2
0
0
1
2
0
0
4
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
2
3
0
0
0
1
0
2
0
2
0
0
2
0
1
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
1
15
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
2
0
1
0
1
0
0
0
0
2
2
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
2
0
2
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
4
0
1
0
0
0
0
3
0
1
1
2
0
1
0
0
0
1
0
0
0
0
0
1
0
1
2
0
0
0
2
0
0
0
0
0
0
1
0
1
2
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
3
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
2
1
1
0
0
4
0
0
0
0
1
0
0
0
2
1
0
0
1
2
0
2
3
0
0
0
0
0
2
0
0
1
0
0
0
0
3
0
1
0
3
0
1
1
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
2
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
2
1
0
0
2
0
0
1
2
2
0
1
0
0
0
1
2
0
0
2
0
2
0
1
0
0
2
1
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
1
1
0
0
0
2
0
2
1
1
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
2
0
1
5
0
0
0
2
1
0
2
0
3
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
3
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
1
0
2
0
0
0
1
1
0
0
0
1
0
0
0
0
0
8
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
1
2
0
4
0
0
0
2
0
0
0
0
0
3
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
2
1
1
1
0
0
0
0
0
0
0
4
2
0
1
0
0
0
0
0
2
3
0
0
0
0
0
1
0
0
1
0
2
0
0
1
2
0
1
1
0
0
4
0
0
0
2
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
2
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
2
1
0
0
0
0
0
1
0
0
0
0
6
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
2
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
4
1
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
2
2
1
2
0
0
1
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
2
1
2
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
2
0
0
2
0
0
0
0
0
1
1
2
0
2
0
0
0
0
0
0
1
0
0
1
0
2
0
0
3
1
0
0
0
2
2
0
0
0
0
0
1
1
1
2
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
1
1
2
1
0
0
1
1
2
0
5
0
0
0
0
2
0
0
0
1
1
1
0
1
0
1
3
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
1
2
1
0
2
1
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
1
0
0
0
2
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
1
0
0
2
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
1
0
1
0
0
0
2
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
6
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
2
2
0
0
0
0
0
0
1
0
1
0
2
2
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
3
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
1
0
2
5
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
2
1
1
0
0
0
3
0
0
1
0
2
0
0
0
2
1
0
0
1
0
0
1
0
0
0
0
1
1
0
0
2
0
0
2
2
1
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
9
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
2
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
2
0
2
1
0
2
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
2
1
2
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
2
0
0
0
1
1
2
2
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
1
0
0
1
0
0
1
2
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
3
1
0
0
0
0
0
1
0
0
0
0
1
0
2
0
1
1
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
2
0
1
0
1
0
0
0
1
0
2
0
4
1
0
3
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
2
0
0
0
1
0
3
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
1
0
1
0
2
0
0
4
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
2
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
1
0
2
0
0
0
0
0
0
0
0
0
2
2
0
1
6
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
1
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
1
0
0
0
0
3
1
0
2
1
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
3
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
2
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
2
1
1
0
0
0
2
4
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
2
0
0
4
0
0
2
4
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
6
0
0
0
2
0
1
0
1
2
0
0
0
2
0
0
1
0
0
0
0
2
0
2
1
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
1
2
0
0
0
0
0
0
2
1
0
0
2
0
0
2
0
3
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
2
1
0
1
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
2
0
0
1
1
0
0
0
0
0
1
2
1
0
0
0
0
1
0
0
1
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
1
0
2
3
2
0
2
0
0
2
2
0
0
0
0
1
0
0
2
0
2
1
0
3
0
0
0
0
0
0
0
2
0
3
0
0
3
0
0
0
1
1
0
1
0
2
2
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
1
0
0
0
1
0
0
0
1
1
2
0
0
0
2
0
0
0
0
1
7
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
3
0
0
0
1
0
1
0
0
0
2
0
0
6
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
2
2
1
0
0
0
0
1
0
0
0
2
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
2
2
3
2
0
0
0
0
0
0
4
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
1
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
2
1
0
0
0
0
1
3
0
2
0
1
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
2
1
0
0
0
0
0
0
0
1
3
0
1
0
0
0
0
4
2
0
2
2
2
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
4
0
1
1
0
0
0
0
0
0
2
0
2
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
1
0
0
0
1
1
0
0
0
0
2
0
0
1
0
2
1
0
2
0
0
0
3
0
0
0
0
0
0
0
6
0
0
0
3
0
0
0
0
0
1
0
0
0
1
2
1
0
0
0
0
2
2
0
0
0
0
1
2
1
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
2
0
2
0
0
1
0
0
0
2
0
0
2
2
0
0
2
0
0
2
0
0
3
0
0
0
2
0
0
0
0
0
2
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
2
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
1
2
0
0
2
0
2
0
0
0
0
0
0
1
4
0
0
0
1
0
0
0
1
0
1
2
1
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
3
0
1
3
1
0
0
0
0
2
0
0
1
1
0
0
0
0
1
3
2
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
2
2
0
2
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
2
0
1
2
0
2
0
0
2
0
1
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
2
2
2
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
1
2
0
2
0
0
0
0
0
1
0
0
0
2
2
2
2
1
0
0
0
3
0
0
5
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
1
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
2
0
0
2
0
3
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
2
0
2
0
0
0
0
0
1
0
0
1
1
0
1
2
0
2
1
0
1
0
0
0
0
0
1
1
0
0
0
0
2
2
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
1
1
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
3
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
1
0
1
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
4
0
1
0
0
0
0
3
1
0
0
0
2
0
0
0
0
0
3
0
1
0
0
0
0
0
2
2
1
0
0
3
0
1
0
0
0
0
0
1
0
2
1
3
2
0
0
0
0
0
0
0
0
0
0
0
0
1
6
0
0
0
0
0
0
0
0
1
0
1
0
0
3
0
1
1
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
4
2
0
0
0
0
0
2
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
4
0
1
1
0
3
0
0
2
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
2
0
1
2
0
0
0
0
0
0
2
5
0
0
2
2
0
0
2
0
1
1
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
2
0
1
0
8
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
2
1
0
1
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
3
1
0
1
3
1
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
1
0
0
1
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
2
2
0
0
0
1
2
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
2
1
0
1
2
0
0
0
0
0
0
0
0
2
1
0
0
2
3
0
0
1
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
2
0
0
0
0
2
2
0
0
0
1
2
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
2
2
2
4
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
3
1
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
4
1
2
1
0
0
0
0
0
1
3
0
0
0
2
0
2
0
1
0
0
0
0
0
2
1
0
2
2
0
0
1
0
0
1
2
0
1
0
0
1
2
0
0
0
0
0
1
0
0
2
2
0
0
0
1
2
0
0
0
0
5
2
0
0
4
2
0
0
0
0
0
0
0
0
2
1
1
0
0
0
1
2
0
0
2
4
0
0
0
0
1
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
2
0
0
2
0
0
4
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
3
0
2
0
0
2
0
0
0
0
1
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
3
0
0
0
0
2
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
2
0
0
3
1
2
0
0
0
0
0
2
0
0
0
2
1
1
0
1
0
0
0
0
0
0
2
1
1
0
0
0
0
0
2
0
0
4
2
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
3
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
1
1
1
0
0
2
0
2
0
0
0
0
2
0
2
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
3
0
0
1
0
0
2
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
2
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
2
0
0
4
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
2
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
2
1
0
1
0
2
0
0
0
1
2
3
0
4
0
0
1
0
1
0
0
4
0
0
0
0
0
0
0
0
0
1
0
2
3
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
1
2
1
0
0
2
2
1
1
0
0
2
0
2
0
1
0
0
2
1
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
1
1
0
0
2
0
2
0
2
1
3
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
1
1
1
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
2
0
0
2
1
0
1
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
1
1
2
0
0
4
0
1
0
0
0
0
2
0
0
4
0
0
0
1
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
2
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
3
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
1
0
0
0
2
2
0
0
0
0
1
2
0
0
0
0
1
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
2
0
0
5
0
0
0
0
0
0
1
0
0
0
6
1
1
2
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
2
0
0
2
1
0
0
0
2
0
2
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
1
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
2
1
0
0
1
0
0
2
0
0
0
1
0
2
0
2
1
0
0
0
0
0
0
0
1
2
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
1
0
1
0
0
9
2
0
0
0
0
0
0
0
0
2
3
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
1
0
0
0
2
2
1
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
1
2
1
1
0
0
0
0
0
0
0
4
0
2
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
1
0
0
1
0
0
1
0
1
0
0
2
0
1
0
0
2
0
5
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
1
2
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
3
1
0
0
2
0
0
2
0
0
0
0
0
3
0
1
0
0
0
0
0
1
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
1
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
12
0
0
1
0
1
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
2
0
0
0
1
0
0
3
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
1
0
1
1
1
0
0
0
1
0
0
0
0
1
0
6
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
2
1
0
2
0
1
4
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
1
0
2
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
1
2
0
1
0
0
0
1
0
0
0
0
0
2
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
3
0
0
1
0
1
0
1
0
1
0
0
2
2
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
3
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
1
0
1
0
1
0
0
0
1
0
0
2
0
0
0
2
0
1
1
1
0
0
0
1
2
0
3
1
2
0
1
0
0
1
0
0
0
3
2
1
0
0
0
0
0
2
0
4
0
2
0
0
1
2
0
2
2
0
0
0
0
1
0
0
0
0
2
1
1
0
1
0
0
0
0
1
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
3
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
2
1
1
1
0
0
2
0
0
0
1
0
0
0
1
0
0
0
2
1
0
0
0
0
1
0
0
0
1
1
1
0
0
1
2
0
0
0
0
0
0
1
1
1
0
0
0
1
0
1
0
0
1
1
0
0
0
1
0
0
3
0
0
3
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
1
0
2
0
1
0
2
2
0
0
1
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
3
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
2
1
0
0
0
1
2
2
0
3
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
4
0
0
0
0
0
0
0
2
0
1
1
1
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
2
0
0
0
2
3
0
0
1
2
2
0
0
2
1
0
0
0
2
2
1
0
0
0
0
2
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
1
2
1
0
0
0
0
0
2
0
0
2
2
0
0
4
0
0
2
0
1
0
0
1
0
1
0
0
1
2
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
2
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
3
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
3
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
2
0
0
3
0
0
0
2
2
0
1
0
1
0
0
0
2
0
1
1
0
1
0
1
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
2
2
0
0
0
0
5
0
0
0
0
3
0
0
0
0
0
0
0
1
2
1
3
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
2
0
0
0
1
0
1
0
2
0
0
2
0
0
0
0
0
0
1
2
0
1
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
2
0
2
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
2
2
0
0
0
0
1
1
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
1
0
0
0
0
0
0
2
1
0
0
3
1
1
0
3
0
0
1
0
1
0
0
2
0
1
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
3
0
0
0
0
1
0
2
0
4
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
1
0
1
1
0
0
0
2
0
0
1
0
1
1
0
0
0
0
0
0
0
0
2
0
1
0
1
0
1
0
0
0
2
0
1
0
2
2
0
0
1
1
2
0
0
2
1
0
2
0
0
0
3
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
2
2
1
2
1
1
0
2
0
2
0
0
0
0
0
0
2
2
3
2
0
0
0
2
0
2
1
2
0
0
0
1
0
0
1
0
0
0
0
0
1
4
0
1
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
2
0
0
0
0
0
0
0
0
1
1
0
0
1
2
1
0
0
1
0
1
0
2
3
0
0
0
2
1
0
0
0
3
0
0
0
0
2
0
0
0
0
1
0
0
0
2
1
0
0
2
0
2
1
1
0
1
0
0
0
0
0
1
2
2
0
0
0
0
0
1
2
0
0
0
0
1
6
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
3
0
0
1
2
2
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
7
2
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
8
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
2
0
0
1
0
2
4
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
2
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
3
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
3
2
0
0
2
0
0
0
0
0
1
3
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
2
2
0
0
2
0
1
0
0
0
0
2
2
2
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
4
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
1
0
0
0
1
2
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
4
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
2
1
1
0
0
0
2
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
2
3
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
2
0
2
1
1
0
0
0
0
0
3
2
0
1
1
0
0
1
0
3
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
2
0
2
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
2
0
1
0
1
0
1
0
0
1
2
1
0
1
0
0
0
1
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
2
0
0
2
0
1
2
0
0
0
0
0
0
0
1
0
0
1
3
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
1
0
1
0
2
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
3
2
0
0
0
0
2
0
2
0
0
0
1
0
0
0
1
0
2
0
2
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
1
0
0
0
2
1
1
0
0
2
0
1
3
2
1
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
1
1
1
1
0
0
0
2
1
0
1
0
0
0
0
1
1
0
2
2
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
4
5
2
0
0
0
0
0
3
1
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
1
0
2
0
0
1
1
1
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
3
3
1
0
0
0
0
1
0
1
0
0
0
1
0
1
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
1
0
2
0
0
0
2
0
0
1
0
0
0
0
2
0
0
2
0
2
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
2
0
1
0
0
0
0
0
0
0
1
0
0
5
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
2
0
0
2
0
0
2
2
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
1
1
2
1
3
0
0
0
1
0
0
1
0
1
0
2
1
2
0
0
0
2
1
2
0
2
0
0
0
2
2
0
0
0
0
0
1
2
0
0
0
0
0
1
2
1
0
0
6
2
0
1
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
2
1
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
3
2
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
6
0
1
0
0
1
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
3
0
0
0
0
7
0
0
0
3
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
1
0
0
1
1
0
2
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
2
1
0
0
1
0
0
3
4
0
0
0
0
1
2
0
2
0
0
2
1
0
0
0
3
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
1
0
0
0
0
1
1
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
3
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
1
0
8
0
2
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
1
1
0
1
2
0
0
0
0
2
1
0
2
0
0
1
0
0
0
0
0
0
0
1
1
1
2
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
2
2
0
0
2
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
2
0
1
0
0
0
0
1
0
0
0
0
3
1
0
0
0
0
1
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
1
0
1
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
7
1
0
0
0
0
3
0
0
0
2
0
1
0
0
1
3
0
0
0
3
0
0
2
0
0
1
0
0
2
0
1
2
0
0
3
1
0
0
0
2
0
0
0
1
0
0
0
1
1
0
2
0
0
2
0
0
3
0
0
2
0
0
1
0
0
0
2
2
0
0
2
0
0
1
0
1
2
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
2
0
2
0
2
1
2
2
0
0
2
0
0
0
1
2
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
2
0
1
0
0
0
1
0
0
1
0
0
0
3
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
1
0
0
0
0
0
1
0
0
1
3
0
1
0
0
0
1
0
2
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
2
1
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
2
2
0
2
0
1
0
1
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
4
0
1
0
2
0
2
0
0
0
0
0
0
0
9
1
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
2
0
1
0
2
2
1
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
4
1
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
2
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
1
0
0
1
2
0
0
2
0
0
0
0
1
0
0
0
0
3
0
0
1
0
0
0
0
0
1
0
0
0
2
1
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
1
0
3
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
1
1
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
2
1
1
2
1
0
0
0
0
0
0
0
0
6
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
3
0
0
0
2
0
0
2
0
2
0
0
0
2
0
4
0
0
0
0
0
0
1
0
0
2
0
0
1
0
2
0
0
0
0
1
0
2
2
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
1
0
1
0
0
2
0
0
0
0
0
1
0
1
0
0
2
1
0
0
0
0
2
0
0
0
0
2
0
1
0
1
1
0
1
0
0
2
1
0
0
3
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
4
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
2
1
2
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
2
0
2
2
3
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
3
0
0
0
1
0
1
1
0
1
0
1
0
0
1
0
0
0
0
2
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
1
3
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
1
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
1
2
1
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
3
1
0
0
0
1
0
2
0
0
1
0
4
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
2
2
3
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
4
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
2
1
0
0
0
0
1
2
0
0
0
1
0
2
0
0
0
0
0
0
1
0
1
0
0
1
2
0
2
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
1
0
4
0
0
0
0
1
2
1
0
0
0
0
0
1
2
0
1
0
0
0
2
0
0
0
0
2
1
2
0
0
2
1
0
0
1
2
0
0
0
0
2
0
0
0
3
2
2
0
2
1
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
2
0
0
5
0
0
0
4
0
1
2
1
0
1
0
2
0
0
1
1
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
4
0
0
0
2
2
0
2
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
2
2
2
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
2
1
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
1
1
0
0
2
0
0
5
4
0
0
0
0
0
0
0
0
1
0
1
0
2
1
2
1
2
1
0
0
2
1
0
0
0
0
2
2
8
0
0
0
0
2
3
0
0
2
0
1
1
0
0
0
0
0
2
1
0
0
0
1
1
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
3
0
1
0
0
5
0
0
0
0
2
0
0
0
2
0
0
4
2
2
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
2
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
2
3
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
1
3
0
1
0
1
2
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
1
1
1
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
1
2
2
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
6
0
0
2
1
0
0
0
1
0
3
0
3
0
1
2
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
1
4
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
2
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
2
1
0
1
0
0
2
0
0
0
0
0
3
1
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
1
0
0
1
0
1
2
2
0
0
0
0
2
0
0
0
0
0
0
4
2
0
0
0
0
0
3
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
1
4
0
1
0
1
0
0
0
1
0
0
1
0
3
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
1
0
0
0
1
0
1
0
0
2
0
1
2
0
3
0
0
0
3
2
2
1
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
3
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
2
0
0
2
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
2
2
0
0
0
2
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
1
2
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
1
0
0
2
2
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
3
0
2
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
2
7
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
2
0
0
0
1
1
0
0
0
1
2
0
0
1
0
0
0
1
0
4
0
0
1
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
2
0
0
0
0
2
0
0
0
1
2
0
0
2
0
2
0
0
2
0
0
0
0
0
2
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
3
0
0
2
0
0
0
0
0
2
1
0
0
1
0
0
1
1
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
4
0
0
0
1
1
0
1
0
0
0
1
0
1
0
0
2
0
1
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
1
0
0
1
2
1
0
0
1
2
0
0
0
2
0
2
0
0
0
2
0
1
3
0
3
0
1
0
1
0
0
0
0
2
0
0
6
1
0
0
1
0
0
0
0
0
0
1
0
1
1
1
1
0
3
0
0
0
0
0
0
2
0
0
0
0
1
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
2
2
2
0
0
0
2
2
0
0
0
0
2
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
3
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
3
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
1
2
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
3
1
0
0
4
2
0
2
2
0
0
0
0
0
1
0
0
2
0
0
0
2
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
2
2
0
0
0
0
8
1
2
0
2
3
0
1
0
3
0
0
0
1
0
0
0
1
2
1
0
0
1
0
2
0
0
0
1
0
0
0
1
0
0
3
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
3
2
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
1
0
0
2
0
0
0
2
0
9
1
1
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
2
1
0
0
0
1
3
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
1
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
1
2
0
4
2
1
2
1
0
2
1
2
0
0
0
0
1
0
0
4
0
2
2
0
0
1
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
2
0
2
0
0
1
0
0
0
0
0
1
1
2
0
0
0
0
0
2
0
0
0
2
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
1
1
2
2
0
0
2
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
2
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
1
1
0
3
1
0
0
0
0
1
1
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
2
2
0
3
0
1
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
1
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
2
0
3
0
0
0
0
0
0
0
1
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
3
2
0
3
0
0
2
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
1
0
2
0
0
0
0
0
0
0
1
0
9
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
2
1
0
0
0
0
0
3
0
0
1
0
0
2
0
0
0
2
0
2
0
0
0
0
1
0
0
1
0
0
4
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
5
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
2
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
2
0
2
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
1
3
2
3
0
1
0
0
1
0
0
0
0
2
0
2
1
0
2
0
0
2
6
2
1
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
5
2
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
1
4
2
0
0
0
0
0
2
0
0
0
2
0
0
3
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
1
0
0
0
2
0
2
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
1
0
0
1
4
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
2
1
2
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
2
0
1
0
0
1
0
0
0
0
0
2
2
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
2
1
0
1
3
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
1
0
2
0
0
0
2
1
0
0
3
1
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
2
0
1
3
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
3
0
1
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
3
2
0
0
1
0
0
2
0
1
0
0
0
2
0
0
0
0
1
1
0
0
1
2
0
2
2
0
0
3
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
3
2
0
2
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
2
0
1
0
2
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
1
2
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
3
0
0
3
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
1
0
0
1
0
0
0
1
2
0
1
0
2
1
0
2
4
0
0
0
2
1
1
2
0
1
2
0
0
0
0
0
0
2
0
2
0
0
0
7
0
2
0
2
0
0
0
0
0
0
5
0
0
0
0
0
0
4
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
2
2
0
2
0
2
1
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
3
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
4
2
0
0
2
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
1
0
1
0
0
0
2
0
2
2
0
0
1
2
0
0
2
0
0
0
0
0
0
4
1
0
0
0
0
1
2
2
1
0
0
0
1
0
1
1
0
0
2
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
1
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
1
0
0
0
0
1
2
1
0
0
0
0
2
4
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
4
0
2
2
0
0
0
0
1
0
0
3
0
1
2
0
0
0
2
0
0
0
2
0
0
1
2
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
8
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
1
2
1
0
0
0
1
0
0
0
1
0
0
0
0
0
3
0
0
2
0
2
0
2
0
0
2
0
0
1
1
2
2
1
0
0
0
0
2
1
2
0
1
4
0
0
0
0
0
2
0
0
1
1
0
2
1
0
2
0
0
3
0
0
0
0
0
0
0
2
0
0
0
1
0
0
3
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
2
2
0
1
1
2
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
2
2
1
0
0
2
0
0
0
0
2
1
0
0
0
0
2
2
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
1
2
0
0
0
0
1
0
2
0
2
1
2
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
1
1
2
1
0
1
0
0
0
0
0
0
0
0
0
1
3
0
2
0
0
1
2
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
3
0
2
0
1
0
0
0
1
1
0
0
0
1
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
2
0
0
1
0
0
2
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
6
0
0
0
1
1
0
1
2
0
2
0
2
1
0
0
0
0
1
0
3
0
0
0
0
0
0
0
2
0
2
1
0
1
0
1
0
0
1
0
0
1
0
0
2
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
3
0
0
0
0
0
2
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
1
2
0
0
2
0
0
2
0
2
1
2
0
1
2
0
0
0
0
2
0
0
0
2
0
2
2
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
4
0
2
0
2
2
0
0
0
1
0
0
2
0
0
0
0
2
0
2
0
0
0
1
0
1
1
1
2
1
0
1
2
1
0
0
2
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
2
2
0
2
0
2
2
1
0
0
0
0
3
0
1
0
1
0
1
0
0
2
0
1
1
0
0
1
0
0
0
0
0
0
2
0
1
0
1
4
1
0
1
0
2
0
0
0
0
0
0
0
0
1
1
0
0
2
0
2
0
0
0
0
0
2
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
1
0
1
9
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
2
1
0
0
0
1
0
0
0
0
1
1
0
0
1
0
2
1
2
0
2
0
0
0
1
2
0
0
0
0
0
1
0
0
2
1
0
0
1
0
0
3
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
1
2
0
1
0
2
1
2
0
0
3
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
2
1
2
1
0
0
0
3
2
0
0
2
0
2
0
2
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
2
0
1
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
2
0
1
0
2
0
2
0
0
2
1
0
0
2
0
1
0
2
0
1
1
0
1
3
0
5
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
2
0
1
0
0
0
0
1
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
1
0
1
2
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
3
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
1
0
2
0
2
0
2
0
0
0
1
2
0
0
1
1
0
0
0
0
0
0
0
3
0
0
3
2
0
0
0
0
0
0
0
0
5
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
1
0
0
0
3
1
0
0
2
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
5
0
0
0
0
1
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
3
0
1
0
0
0
0
0
0
0
0
2
0
2
2
1
0
1
0
0
1
0
0
0
0
0
1
0
1
0
1
0
2
0
1
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
1
1
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
3
0
0
0
1
0
0
0
0
0
1
1
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
1
0
0
0
0
3
0
1
0
2
0
0
2
2
2
0
0
1
0
0
3
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
1
2
2
1
2
0
0
1
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
3
1
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
2
0
0
1
1
2
0
3
0
2
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
2
0
0
0
1
1
0
1
1
2
3
0
0
0
0
0
0
0
2
2
0
2
0
0
2
2
2
3
0
0
0
0
0
0
2
0
0
1
2
2
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
1
2
1
0
0
2
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
1
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
2
1
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
4
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
2
0
2
0
0
0
2
2
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
2
3
1
0
1
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
2
0
0
3
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
2
1
0
1
0
0
1
0
0
0
0
0
0
2
2
2
0
2
0
2
0
0
0
3
0
0
0
2
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
1
7
0
0
1
0
0
1
0
2
0
0
1
2
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
7
0
0
4
0
7
0
0
0
1
0
0
0
0
0
0
0
4
2
0
0
2
0
0
0
0
2
0
1
0
0
0
0
1
0
2
0
0
0
2
1
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
2
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
1
0
0
0
1
2
2
2
4
2
0
0
0
0
0
0
0
2
0
0
0
0
0
6
0
1
0
0
0
1
0
0
2
2
0
0
0
0
2
0
1
0
0
0
0
0
2
2
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
1
2
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
1
0
3
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
1
3
0
0
1
0
0
2
0
1
0
0
0
0
0
1
2
0
2
1
0
1
0
0
1
1
0
1
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
2
0
2
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
2
0
0
2
0
2
2
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
2
0
0
1
2
0
3
0
0
0
0
0
1
0
0
0
0
2
1
2
0
0
3
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
2
2
0
0
0
2
0
0
0
2
0
0
0
1
0
0
1
0
1
1
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
2
1
3
0
1
2
0
1
2
0
0
2
0
1
0
1
2
1
0
2
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
1
0
0
0
0
3
0
0
1
3
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
1
2
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
2
0
0
1
2
2
0
0
2
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
2
0
2
1
0
0
1
0
0
0
1
0
2
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
3
0
0
0
1
1
0
3
0
1
0
0
1
0
0
3
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
1
0
3
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
1
3
2
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
2
0
1
0
0
0
3
0
0
4
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
3
2
0
1
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
1
0
0
3
0
2
2
0
0
0
0
0
0
0
2
0
0
1
0
2
2
0
0
2
0
0
2
0
0
1
0
0
0
3
2
0
2
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
1
0
2
0
0
2
0
1
0
0
0
0
1
0
2
0
0
1
0
0
2
0
0
0
0
2
2
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
1
0
0
0
0
1
1
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
7
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
2
0
0
0
0
1
2
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
2
1
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
1
2
1
0
0
0
0
0
0
9
2
0
0
0
0
0
1
1
0
0
0
0
2
0
2
1
1
2
0
1
0
2
0
3
0
0
0
0
0
0
1
2
0
2
0
0
0
0
1
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
1
0
1
0
3
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
2
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
2
1
1
2
1
0
0
0
0
5
0
0
1
0
4
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
1
0
1
2
0
4
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
2
0
1
0
0
1
0
0
0
0
0
2
1
0
2
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
7
0
0
0
0
0
2
3
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
1
2
0
0
2
0
0
0
2
0
0
0
0
0
6
0
0
0
2
0
1
0
0
1
0
1
4
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
1
2
2
0
0
1
0
0
0
2
1
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
3
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
2
0
0
0
1
1
0
0
0
0
1
0
0
1
2
0
0
0
2
2
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
3
3
0
1
2
0
2
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
1
0
1
0
0
0
0
1
1
0
1
0
1
2
2
1
0
2
2
1
0
0
0
0
0
0
0
1
1
1
0
2
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
2
0
0
0
0
1
0
1
0
2
2
0
0
0
2
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
3
2
1
0
0
0
0
1
2
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
3
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
2
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
2
0
3
0
1
0
2
0
1
0
2
1
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
1
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
4
0
0
0
2
0
4
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
2
2
0
0
2
1
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
9
0
0
1
1
7
1
0
2
2
0
2
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
1
3
0
2
0
2
0
1
1
0
0
0
0
2
0
1
0
1
1
0
2
0
2
2
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
1
2
0
0
0
0
0
0
0
0
0
1
3
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
3
1
0
0
2
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
1
2
2
0
0
1
0
2
1
0
0
1
0
1
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
2
0
0
1
0
2
1
0
2
1
0
2
1
0
0
0
0
0
0
3
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
2
1
1
0
0
2
1
0
0
2
0
2
0
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
1
2
1
3
0
0
0
0
0
2
0
5
0
2
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
7
1
2
0
0
0
1
0
0
1
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
2
0
3
0
1
2
2
1
0
0
0
0
1
2
0
1
3
2
0
0
0
0
0
0
1
0
0
1
0
0
3
0
0
0
0
1
1
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
2
0
0
0
0
0
0
1
1
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
1
3
0
0
2
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
1
2
0
0
0
0
2
0
2
1
0
2
0
0
3
1
0
0
4
0
2
0
1
0
0
0
1
1
1
0
2
0
0
1
2
2
0
0
0
0
1
0
0
0
7
0
0
0
0
2
0
0
0
0
2
0
1
1
1
0
0
1
0
0
1
0
3
0
0
0
0
3
0
0
3
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
3
1
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
3
0
0
0
4
0
0
0
0
2
0
0
0
0
4
0
0
0
0
2
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
10
0
0
2
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
2
2
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
2
2
0
0
0
0
1
2
0
2
0
0
2
0
0
0
0
2
0
2
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
1
1
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
2
0
0
0
0
0
1
1
2
0
0
1
0
0
0
0
0
7
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
3
2
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
3
2
0
0
0
0
0
1
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
7
0
0
1
0
0
0
0
0
0
0
1
1
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
5
0
2
0
0
0
0
0
0
1
0
0
0
1
2
0
3
0
0
0
0
0
0
0
0
2
0
2
2
0
0
2
0
0
4
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
2
1
0
0
0
0
2
0
1
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
1
1
0
0
0
0
0
0
2
1
0
1
0
0
1
0
0
0
0
1
2
1
0
1
1
0
2
0
2
0
2
2
0
0
1
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
1
2
0
0
0
1
0
2
0
5
0
1
0
0
2
0
0
0
0
2
1
1
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
3
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
4
2
0
0
0
0
0
2
0
0
0
0
0
2
2
1
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
3
0
0
2
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
1
2
1
0
0
0
1
0
0
1
0
0
0
1
0
1
1
0
0
0
2
1
2
3
0
0
3
2
0
2
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
1
0
1
3
0
4
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
1
0
2
2
0
0
1
2
1
1
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
6
1
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
1
0
0
1
2
0
0
0
0
1
0
2
0
0
2
0
0
0
0
1
0
2
1
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
4
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
1
2
0
1
2
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
6
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
2
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
2
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
3
1
0
0
2
1
0
0
0
0
1
2
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
3
0
0
0
0
4
1
0
1
2
0
4
0
0
1
1
0
0
0
2
2
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
1
2
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
2
1
0
0
0
0
0
3
0
0
0
0
3
1
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
1
3
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
3
0
0
0
0
0
0
1
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
1
1
1
2
2
0
1
0
0
0
2
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
2
2
0
2
0
0
0
1
0
0
2
0
0
0
1
0
3
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
2
0
0
0
0
1
0
2
0
1
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
3
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
4
1
3
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
2
0
0
0
0
2
1
2
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
3
0
3
0
0
0
2
0
0
0
0
0
0
5
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
2
0
1
0
0
2
2
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
1
0
0
0
0
1
0
0
2
2
2
2
1
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
2
0
1
2
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
2
0
1
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
2
0
0
0
0
1
0
0
2
0
0
1
0
0
5
0
2
0
0
0
1
0
0
1
0
0
0
2
0
2
1
0
0
2
0
0
0
0
2
0
0
0
0
0
1
2
0
1
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
4
0
0
0
0
0
0
2
0
0
0
2
2
1
0
3
0
0
3
0
1
0
0
0
0
0
2
0
0
5
0
1
0
0
1
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
6
0
4
0
0
1
0
0
0
5
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
2
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
9
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
1
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
1
0
0
0
3
1
2
0
0
1
0
1
2
0
1
0
0
0
5
0
0
0
1
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
1
1
0
2
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
1
0
0
0
0
0
2
2
0
0
0
2
0
0
2
0
0
0
2
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
1
1
0
0
0
0
0
0
1
10
0
0
0
0
2
0
2
2
0
0
1
0
0
0
2
0
1
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
2
2
1
2
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
1
0
0
0
0
1
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
10
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
2
0
0
0
1
2
0
4
0
0
1
2
0
0
3
0
2
1
0
1
0
0
3
0
0
0
2
9
0
0
0
0
1
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
2
0
3
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
1
1
0
1
2
1
0
0
1
0
0
0
0
0
0
1
2
0
2
2
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
1
2
0
0
0
1
6
2
3
1
0
0
0
0
0
0
0
0
0
2
3
0
1
0
12
0
1
0
0
0
0
1
0
0
2
0
0
1
2
1
0
0
0
2
2
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
2
0
0
0
0
2
0
0
2
0
2
1
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
1
0
0
1
2
2
1
0
2
0
0
0
0
1
1
1
0
0
0
3
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
2
2
2
0
2
0
0
0
1
0
0
0
2
0
0
1
0
2
0
3
0
0
0
0
0
0
0
3
0
0
1
0
2
0
0
0
0
0
2
0
2
0
1
3
2
0
0
0
2
0
0
0
0
0
0
3
2
0
1
1
2
0
0
0
0
2
1
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
4
2
2
1
0
2
1
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
3
0
0
0
0
0
0
2
0
0
0
0
1
2
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
3
0
1
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
2
2
0
0
0
0
1
2
0
0
0
0
0
0
2
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
1
0
0
0
2
2
0
0
0
0
4
0
0
0
1
0
0
2
1
2
0
2
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
1
0
2
1
2
2
1
0
0
3
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
5
0
0
0
0
2
0
0
0
4
1
0
0
0
0
0
0
2
2
0
0
0
1
1
2
0
0
1
1
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
2
3
0
0
0
1
0
0
0
0
1
0
0
3
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
2
2
2
0
0
0
0
0
0
2
3
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
1
2
0
1
0
1
0
1
0
2
0
0
2
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
2
0
0
1
1
0
0
0
0
0
1
0
0
1
2
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
2
2
2
3
1
0
0
1
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
4
2
0
0
0
0
0
1
0
0
1
0
1
1
2
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
2
1
0
3
0
0
0
0
0
1
2
0
0
0
2
0
0
0
1
1
0
0
0
2
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
1
0
0
2
1
1
0
0
0
2
3
0
1
0
0
2
2
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
2
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
5
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
2
0
2
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
1
2
0
2
0
0
0
1
0
0
0
2
0
0
0
0
2
10
0
1
0
0
1
0
0
0
0
1
0
2
0
2
2
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
2
1
2
2
0
1
1
1
0
1
0
0
0
2
2
1
2
0
1
2
0
0
0
1
0
4
0
0
0
0
0
0
4
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
1
2
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
1
1
0
0
2
0
0
1
0
1
2
1
0
0
1
2
0
2
1
0
0
2
0
0
1
0
0
0
1
0
0
0
4
0
0
0
2
2
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
1
1
1
0
2
0
1
1
2
2
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
1
2
0
0
0
0
0
0
0
1
0
0
0
1
0
2
1
2
0
0
1
0
2
0
0
2
0
2
2
2
2
0
0
0
0
1
7
0
0
0
1
0
9
0
1
0
0
0
9
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
1
0
2
0
9
1
0
0
0
4
0
0
1
0
0
3
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
1
0
1
0
0
1
0
0
0
2
0
5
1
1
1
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
1
1
2
4
2
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
2
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
1
1
4
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
1
0
0
0
0
1
0
1
2
0
0
3
3
0
2
0
1
0
0
0
0
0
1
0
0
0
0
3
0
0
0
2
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
5
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
2
0
0
1
4
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
3
3
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
4
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
3
3
0
0
0
0
0
3
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
1
4
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
1
1
0
0
0
0
0
2
0
0
0
2
2
0
0
0
2
0
1
0
0
0
2
0
0
2
3
0
2
0
2
0
1
0
2
0
1
0
0
1
0
1
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
1
0
1
0
1
0
1
3
4
0
2
0
0
0
0
0
0
0
2
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
1
2
1
0
0
2
0
0
0
2
1
0
0
1
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
1
0
0
2
0
0
1
0
0
1
1
2
0
0
0
0
2
0
2
0
0
0
3
0
0
0
0
0
0
0
2
0
0
1
0
1
1
0
0
0
2
3
0
1
2
0
0
0
2
2
0
2
0
1
0
0
0
1
0
0
0
1
2
0
2
3
0
0
0
1
0
1
0
0
2
0
1
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
3
0
0
2
0
3
2
0
1
0
0
0
2
1
1
0
0
0
2
4
3
1
0
1
0
0
1
0
2
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
1
0
0
1
0
2
0
1
3
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
3
0
0
0
0
0
0
0
0
2
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
1
1
0
1
2
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
2
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
2
1
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
1
1
0
0
2
0
0
0
1
0
0
2
1
1
0
0
2
2
1
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
3
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
2
3
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
1
0
1
0
0
0
0
2
3
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
3
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
1
0
2
2
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
1
0
0
0
2
0
0
0
1
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
1
0
2
0
1
0
2
1
0
0
5
1
2
2
0
1
0
0
1
0
1
0
0
0
2
0
1
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
2
2
0
0
3
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
2
0
0
0
2
3
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
5
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
1
1
2
1
3
0
0
0
0
0
2
0
0
0
0
0
0
0
1
3
0
0
0
0
3
2
1
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
4
0
0
1
0
0
0
0
1
0
0
0
2
0
1
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
3
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
4
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
2
3
1
0
0
0
2
1
0
0
0
2
0
0
0
1
0
1
0
0
1
4
0
2
0
2
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
3
0
0
1
1
0
0
0
0
0
0
0
0
0
3
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
2
2
1
0
0
0
0
0
1
0
0
2
1
2
0
0
0
0
0
1
0
0
0
1
0
2
0
0
2
0
0
0
0
0
2
0
0
1
0
0
3
1
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
1
0
1
2
0
0
2
0
2
2
0
1
0
0
2
1
0
2
0
2
2
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
3
2
2
0
0
0
2
2
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
2
1
2
0
2
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
2
2
0
2
2
2
5
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
1
1
1
4
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
2
0
1
0
2
0
1
0
0
0
0
0
1
1
4
0
0
0
0
0
0
1
0
1
0
2
2
0
2
0
1
0
2
0
0
2
0
0
0
0
1
0
0
0
1
1
0
0
0
0
2
1
0
0
2
0
0
0
1
2
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
1
0
0
0
0
3
0
0
0
1
0
0
0
1
0
1
0
0
0
2
0
0
2
2
1
0
0
3
1
1
0
3
1
0
0
0
0
1
1
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
3
1
1
2
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
3
0
0
0
0
0
0
1
1
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
1
2
0
0
0
0
1
0
3
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
3
1
0
0
2
1
1
2
0
0
0
1
0
0
0
0
1
3
0
0
1
0
0
0
0
0
0
0
0
1
0
5
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
6
0
0
0
0
2
0
0
0
0
0
1
1
2
1
2
0
0
2
2
0
0
2
0
0
2
0
0
0
2
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
2
2
1
2
1
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
1
3
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
2
0
0
1
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
10
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
1
0
1
0
0
0
2
1
0
2
0
1
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
1
0
2
0
0
0
2
0
0
0
2
2
1
0
0
0
0
1
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
3
0
2
3
0
0
0
0
3
1
0
0
0
0
1
0
0
1
0
1
0
0
0
2
0
0
0
1
2
0
0
4
3
0
0
0
0
0
0
2
0
0
0
1
1
0
0
1
1
2
0
1
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
5
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
2
0
0
3
1
0
0
0
0
0
0
1
1
2
0
4
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
3
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
2
0
3
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
1
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
2
0
2
2
2
0
0
0
0
0
2
1
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
2
1
0
0
0
0
1
0
1
0
0
3
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
3
0
5
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
3
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
1
2
0
1
0
0
1
2
0
0
1
1
1
3
0
0
0
2
0
0
0
0
1
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
6
0
0
0
1
2
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
2
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
1
1
0
2
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
1
0
0
0
0
1
0
0
2
0
0
1
0
0
2
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
2
1
2
3
0
0
0
3
0
2
0
0
0
2
0
0
0
2
2
2
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
5
2
1
0
0
0
0
1
0
2
0
2
1
0
0
3
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
2
2
4
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
2
0
2
0
0
0
1
0
1
2
0
0
0
6
0
2
2
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
2
0
0
2
2
0
0
2
0
0
1
0
2
0
0
2
0
0
0
0
0
1
0
0
0
2
2
0
0
4
0
0
0
0
2
2
0
0
0
0
0
3
2
4
3
1
0
0
0
0
2
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
7
0
0
0
0
0
0
0
0
0
1
0
0
4
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
3
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
2
2
0
1
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
1
0
0
2
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
4
2
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
2
0
0
1
1
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
9
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
1
0
0
1
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
4
2
0
0
0
2
0
0
0
1
3
0
0
2
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
3
2
2
0
2
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
2
2
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
3
2
0
0
0
0
0
2
0
0
0
0
0
1
0
3
0
1
0
0
0
0
0
0
1
0
0
0
0
2
2
1
1
0
0
0
1
2
0
0
2
0
0
1
2
0
0
2
2
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
1
0
0
1
1
4
3
0
0
1
0
0
0
0
1
0
2
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
1
0
0
1
0
0
0
0
2
0
2
2
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
1
2
2
0
1
0
0
5
0
1
0
4
0
2
4
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
1
0
2
0
0
1
0
2
0
0
0
0
0
4
2
0
3
0
1
0
1
0
2
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
1
2
1
1
0
0
0
1
0
0
1
0
0
0
2
2
1
0
9
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
1
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
3
0
3
1
1
2
1
2
1
4
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
2
1
0
0
2
2
2
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
2
8
0
0
0
1
0
0
0
1
0
2
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
1
0
1
2
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
3
0
2
2
1
0
0
1
0
1
0
2
1
0
0
1
0
0
0
0
0
2
0
2
3
0
0
1
0
0
2
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
5
1
0
0
2
0
0
0
0
2
0
0
0
4
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
1
1
0
0
0
0
1
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
1
0
2
2
1
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
2
0
3
2
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
4
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
2
0
0
0
0
2
0
2
0
0
0
2
1
5
0
2
0
1
0
0
2
0
2
1
0
3
0
0
0
0
3
0
0
1
0
2
0
1
2
0
1
0
0
0
0
0
1
0
0
5
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
4
0
0
1
2
2
1
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
3
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
1
0
0
3
1
1
2
0
0
0
0
2
0
1
0
0
0
5
0
0
0
0
1
0
0
2
5
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
3
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
4
1
0
0
0
2
0
0
0
1
2
1
0
0
0
0
1
0
3
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
3
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
1
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
2
1
1
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
1
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
1
3
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
3
0
0
1
0
0
4
0
1
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
4
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
2
0
2
0
0
2
0
0
0
0
0
4
0
0
2
0
0
2
3
0
0
2
0
0
1
0
0
2
0
2
1
0
0
0
1
0
2
0
2
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
2
0
0
0
2
1
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
2
2
0
1
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
1
1
0
0
0
1
2
1
0
0
1
2
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
3
0
0
0
0
0
0
0
0
0
0
2
0
3
0
1
0
0
2
0
2
2
0
0
1
0
0
3
2
2
0
0
0
0
0
1
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
2
0
1
1
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
3
0
0
0
0
2
0
0
0
0
0
0
2
0
2
2
1
2
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
3
0
0
0
1
0
0
0
1
2
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
1
0
6
2
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
4
1
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
1
0
1
0
0
0
0
0
3
0
1
0
2
2
0
0
0
0
2
1
0
0
0
0
1
0
3
1
0
0
0
2
0
0
2
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
3
0
0
0
0
0
3
0
6
0
0
0
0
0
0
0
1
0
2
0
2
0
2
0
0
1
0
2
0
0
0
2
2
1
0
0
0
2
0
0
0
0
10
0
0
0
0
2
0
0
2
1
1
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
1
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
2
0
1
0
2
0
0
0
3
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
3
0
0
0
0
0
1
0
2
2
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
2
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
1
1
2
0
0
0
0
1
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
2
0
2
0
2
0
0
2
2
2
0
0
0
2
0
1
0
0
0
0
1
6
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
3
1
2
1
0
0
0
0
0
0
0
0
0
1
0
3
1
0
1
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
3
0
0
1
1
0
1
2
0
0
3
2
0
0
0
0
1
0
0
3
3
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
1
6
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
3
0
0
0
0
2
0
3
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
1
3
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
1
2
0
0
0
2
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
2
0
0
5
0
0
0
0
0
1
0
1
1
1
0
1
0
0
0
0
0
0
1
0
1
0
4
0
0
0
0
0
0
2
0
2
0
0
0
2
1
0
2
0
0
2
0
0
0
2
0
0
1
2
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
2
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
1
1
0
2
2
1
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
2
2
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
1
0
2
0
1
0
1
0
4
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
2
0
3
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
2
2
0
0
0
0
0
1
1
0
0
0
0
0
2
2
2
0
0
0
1
1
0
1
0
0
2
3
0
1
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
3
2
2
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
3
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
2
1
1
0
0
0
1
2
0
0
0
0
0
0
0
2
0
2
2
1
1
0
2
2
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
1
0
0
0
0
5
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
3
0
0
0
0
4
0
0
0
0
1
0
2
2
1
1
0
0
0
0
0
0
0
2
1
0
0
1
2
0
0
0
0
2
0
0
1
0
0
0
0
0
1
2
0
0
3
0
3
0
0
0
0
0
0
2
0
0
3
2
0
1
2
1
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
1
0
1
2
0
0
0
0
0
0
1
0
1
1
0
0
0
0
2
3
0
0
1
0
0
0
0
1
0
0
2
0
1
1
2
0
0
0
1
0
1
0
0
1
0
0
2
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
3
0
1
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
3
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
1
0
0
1
3
1
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
2
1
0
0
2
0
0
0
0
0
3
1
0
2
0
1
1
0
0
2
0
0
0
1
0
2
0
0
2
2
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
1
1
2
0
2
0
0
0
0
2
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
3
2
0
0
3
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
8
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
2
0
2
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
1
25
1
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
2
0
0
2
0
3
0
0
0
0
0
2
0
1
3
0
0
0
1
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
2
0
1
2
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
2
1
0
0
0
0
0
1
0
0
1
2
0
0
2
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
1
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
5
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
3
1
2
0
1
0
2
0
0
2
0
0
1
0
0
0
1
2
0
0
2
0
1
1
0
0
1
0
0
1
1
3
1
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
2
2
1
1
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
3
2
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
2
1
3
7
2
0
0
2
0
1
0
0
1
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
3
0
1
0
1
0
0
3
2
2
0
1
0
0
2
1
1
0
0
1
0
0
0
2
0
1
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
2
0
0
3
2
0
0
0
0
2
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
0
1
0
0
2
0
2
1
0
0
1
1
2
0
0
0
0
0
0
2
2
0
2
0
4
2
1
0
2
0
0
0
0
3
2
2
0
1
0
0
0
0
1
2
0
0
0
0
1
2
0
0
0
0
2
3
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
1
0
1
2
0
0
1
1
0
1
3
0
0
2
0
0
1
0
0
0
3
2
2
1
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
2
2
1
0
1
0
0
0
0
3
0
0
2
0
0
0
0
1
0
0
0
1
1
0
2
0
1
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
1
0
0
0
1
0
0
1
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
2
2
6
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
1
0
0
0
0
0
2
1
0
0
2
0
1
0
1
0
2
2
0
2
0
0
0
1
0
1
0
2
0
0
2
0
0
2
0
1
0
0
3
2
0
2
3
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
2
1
0
0
4
0
0
0
0
0
0
0
1
0
0
1
0
4
0
1
0
2
0
0
0
0
1
2
0
1
0
0
2
0
1
1
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
1
0
0
3
0
1
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
2
2
5
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
2
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
2
2
0
0
0
0
0
0
1
1
0
0
0
0
0
2
3
0
2
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
1
1
2
0
2
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
1
2
1
0
0
0
0
0
0
2
0
2
0
1
2
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
1
3
2
0
2
0
2
1
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
2
0
3
2
0
1
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
3
3
0
2
0
0
0
0
0
0
0
2
0
0
0
3
1
0
1
1
0
2
0
0
0
1
2
0
1
0
0
0
0
0
0
1
1
1
0
2
0
2
0
1
0
0
3
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
2
3
0
1
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
2
0
0
0
2
0
1
0
2
2
0
1
1
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
2
1
2
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
1
1
7
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
3
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
3
2
0
0
0
2
0
0
2
0
2
2
3
0
0
3
0
0
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
2
0
0
0
5
0
0
0
1
0
1
1
0
0
3
0
2
0
2
3
0
0
0
0
0
2
0
0
0
2
0
2
2
0
1
0
1
0
0
1
0
3
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
2
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
1
2
5
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
2
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
1
3
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
3
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
2
0
0
0
0
2
2
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
5
0
1
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
1
0
1
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
2
2
0
2
2
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
1
4
0
1
0
0
0
1
0
0
1
1
0
1
0
1
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
4
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
2
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
2
0
0
0
0
0
2
0
1
0
0
0
0
1
2
1
2
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
1
0
2
0
2
0
0
0
2
2
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
1
2
0
0
0
2
0
2
2
0
0
0
0
1
1
5
0
2
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
2
1
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
1
0
0
0
2
2
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
4
0
1
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
2
0
1
1
0
0
0
2
2
0
0
0
1
2
0
0
0
2
2
3
4
0
2
1
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
1
0
3
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
2
2
0
0
0
2
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
3
2
0
0
0
0
0
1
1
0
0
0
0
0
0
3
1
0
0
0
0
2
0
1
0
0
1
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
2
0
0
0
0
1
0
1
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
6
0
2
0
0
2
0
0
0
0
3
0
1
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
3
0
0
1
0
4
1
0
0
0
0
2
0
0
2
2
2
0
2
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
1
1
0
3
0
0
2
2
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
3
1
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
1
1
0
0
0
1
2
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
3
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
1
4
2
0
1
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
6
1
0
2
1
0
0
0
0
4
0
2
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
2
0
1
1
0
0
0
2
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
2
0
1
0
0
1
2
0
0
2
0
0
3
2
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
1
0
0
0
1
0
0
0
0
0
1
2
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
6
0
0
0
0
0
0
0
0
1
0
1
3
0
1
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
1
3
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
2
0
2
4
0
0
0
1
2
0
2
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
5
0
2
2
0
0
0
0
0
0
2
0
0
4
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
2
1
2
0
1
1
0
0
0
2
0
1
0
3
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
2
0
1
1
0
2
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
2
1
1
1
0
0
0
0
0
0
0
2
4
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
2
0
1
1
2
0
0
0
2
0
0
0
0
0
1
0
0
0
2
5
3
0
2
0
0
2
0
0
0
1
0
0
0
0
0
2
1
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
2
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
3
0
3
2
0
0
1
0
0
0
0
2
2
1
0
3
0
0
2
0
0
2
2
0
0
0
0
2
0
0
0
0
0
3
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
1
1
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
2
1
0
0
6
0
1
0
3
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
1
3
0
0
3
0
1
0
1
1
0
0
1
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
1
0
0
0
0
0
0
0
1
2
0
0
1
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
3
0
2
0
0
0
0
2
1
0
0
0
1
2
2
0
0
1
0
2
0
2
0
1
0
2
0
2
1
0
0
2
1
0
0
1
2
0
1
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
1
0
0
0
2
1
0
2
2
1
0
1
0
0
0
2
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
1
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
4
0
0
0
0
0
1
0
0
1
0
0
0
2
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
2
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
3
0
0
0
2
0
0
1
3
1
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
1
2
2
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
6
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
2
0
0
0
0
1
3
0
0
1
0
0
0
0
0
0
0
5
1
0
0
1
3
1
0
0
1
2
0
1
0
0
0
0
0
0
2
2
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
1
2
2
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
2
0
2
2
0
0
0
0
0
3
1
2
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
2
0
0
0
0
2
8
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
3
0
0
5
0
0
2
2
1
0
2
2
1
10
0
1
0
2
1
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
5
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
1
4
1
1
0
0
0
1
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
2
0
0
2
0
1
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
2
0
1
0
0
0
5
0
0
1
1
0
0
0
2
0
0
0
0
0
0
1
2
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
2
1
0
1
0
0
0
2
3
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
1
0
5
0
0
0
0
0
0
0
0
1
0
2
0
1
3
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
2
0
1
0
0
1
0
1
0
1
0
0
2
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
3
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
2
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
1
0
1
1
3
0
0
0
0
1
0
0
0
0
1
1
1
0
0
2
0
0
1
0
0
0
1
1
1
0
2
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
2
0
0
2
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
1
0
1
0
2
1
0
2
0
1
2
0
2
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
2
1
2
2
2
2
0
3
0
0
2
0
2
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
2
1
0
0
2
0
0
0
0
2
3
0
0
0
1
1
0
0
0
1
2
0
0
0
0
5
1
1
0
1
2
0
0
0
2
0
0
2
0
0
0
1
1
0
1
0
0
0
1
0
1
0
0
0
0
2
1
1
0
2
2
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
2
0
2
0
1
2
0
2
4
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
4
0
2
2
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
2
0
0
1
0
1
1
1
1
0
1
0
0
3
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
5
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
4
2
2
1
1
0
2
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
2
0
1
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
1
0
0
0
2
1
0
1
0
0
0
0
0
0
0
1
1
2
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
1
4
0
2
0
3
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
2
1
0
1
2
2
5
0
1
0
0
2
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
2
1
1
2
0
1
0
1
0
0
2
0
0
0
1
0
0
0
5
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
1
2
0
0
1
0
0
0
0
0
0
0
2
0
1
2
0
2
2
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
2
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
2
1
0
0
0
0
0
0
2
0
2
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
2
0
0
3
0
0
1
2
0
0
1
1
0
0
0
1
0
0
0
2
0
0
0
0
2
0
1
0
4
3
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
3
0
2
0
0
0
0
0
2
0
0
7
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
3
0
0
3
3
0
1
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
1
2
0
1
1
0
0
0
1
1
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
2
0
1
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
3
1
0
2
2
0
0
0
1
0
2
1
0
1
2
1
1
1
0
1
0
0
0
1
0
2
3
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
2
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
1
0
0
0
0
0
0
1
4
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
1
1
3
0
2
0
2
0
1
0
2
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
2
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
4
0
1
2
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
1
2
1
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
2
2
0
1
0
0
0
2
0
2
2
0
0
0
1
0
0
0
0
2
0
0
5
0
0
1
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
3
2
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
1
0
1
2
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
7
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
3
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
1
0
2
1
1
0
1
1
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
2
2
0
0
0
2
1
0
0
1
0
0
1
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
2
4
1
0
0
3
0
2
0
0
0
1
0
0
0
1
3
0
0
0
0
0
2
1
0
1
0
0
0
1
2
0
2
0
0
0
0
1
0
0
1
2
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
1
2
1
2
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
1
0
0
0
2
0
1
2
0
1
0
0
0
0
0
1
0
1
2
2
3
0
0
0
1
3
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
2
0
1
0
4
0
2
0
2
0
0
0
2
0
0
0
1
0
0
2
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
1
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
2
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
1
3
0
0
0
2
0
0
2
2
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
1
1
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
2
0
0
0
0
2
0
0
2
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
1
2
2
0
2
0
0
0
1
2
1
0
1
0
0
0
2
1
0
0
0
0
2
1
0
4
2
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
4
0
0
2
0
1
0
1
0
0
0
0
0
0
0
2
0
0
4
0
3
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
2
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
2
4
0
1
0
2
0
0
0
1
0
0
2
0
0
0
0
1
0
2
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
7
6
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
2
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
1
0
1
3
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
1
2
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
3
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
3
0
3
0
0
0
0
0
1
0
0
1
0
0
1
0
2
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
2
2
0
0
0
1
2
0
1
2
2
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
1
2
1
0
1
0
2
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
2
2
1
0
0
2
0
0
0
1
3
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
1
0
1
0
0
0
1
2
2
1
0
0
2
0
2
1
1
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
2
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
1
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
4
0
2
2
0
0
3
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
2
2
2
4
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
4
0
2
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
2
1
0
2
0
2
0
0
2
0
2
0
3
0
0
1
0
0
0
1
0
2
2
0
2
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
2
1
0
0
2
2
0
0
1
2
0
0
1
0
2
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
2
0
0
0
1
1
2
0
0
0
0
1
0
0
0
0
0
0
0
1
2
1
0
0
0
0
2
1
0
2
0
2
0
0
0
1
0
2
0
2
0
2
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
1
1
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
3
0
0
2
0
0
0
0
3
0
0
1
0
0
2
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
6
0
0
1
2
1
12
0
0
0
0
0
2
0
1
0
0
0
1
0
0
1
0
2
2
0
0
0
4
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
1
0
2
0
0
2
1
1
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
2
1
1
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
1
0
0
2
0
0
1
1
0
3
0
1
0
0
0
3
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
2
1
1
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
4
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
2
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
2
0
0
0
1
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
2
0
0
0
1
1
0
2
0
2
0
0
0
0
0
2
2
1
0
0
0
2
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
3
0
4
0
0
0
0
0
3
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
5
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
3
0
0
2
0
0
0
1
0
1
0
1
0
0
2
1
1
0
0
2
0
0
0
0
0
0
0
0
0
2
2
2
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
1
2
0
0
5
2
0
2
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
1
0
0
0
1
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
1
1
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
2
0
0
0
1
0
1
0
0
0
0
2
0
0
0
1
1
2
0
2
0
0
0
0
0
0
0
4
1
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
1
0
2
0
0
0
0
0
0
0
1
1
0
0
1
2
0
0
0
1
0
5
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
2
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
2
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
4
1
2
0
0
0
0
0
0
5
2
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
2
1
0
8
0
2
0
0
2
0
0
2
0
0
2
2
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
2
0
0
1
0
1
1
2
0
1
2
0
2
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
1
0
2
0
2
0
0
0
1
1
0
3
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
1
0
0
1
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
3
2
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
3
0
1
0
1
0
0
0
0
0
0
0
1
2
2
0
0
0
1
0
0
0
0
0
0
1
0
3
2
1
2
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
3
2
2
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
2
0
1
0
0
1
0
2
0
2
0
0
3
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
3
0
0
0
0
0
1
1
0
2
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
2
2
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
2
0
0
1
0
5
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
1
0
1
0
0
0
2
0
2
0
0
0
4
0
0
0
0
0
1
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
1
0
2
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
1
0
1
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
2
1
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
3
0
2
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
1
0
0
0
2
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
4
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
6
0
0
0
0
2
0
0
1
1
5
0
0
0
1
0
0
0
0
0
1
0
0
5
2
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
1
1
0
0
0
0
0
1
0
2
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
2
0
3
0
0
1
0
0
1
3
3
0
0
0
0
0
0
2
0
0
1
0
1
5
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
1
0
0
0
2
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
2
2
0
0
0
0
0
0
0
2
0
0
2
0
2
1
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
1
2
0
1
1
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
2
0
2
0
1
3
2
2
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
1
0
1
0
0
0
1
0
2
0
0
0
0
2
0
2
2
0
0
1
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
2
1
1
1
3
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
1
0
0
2
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
2
2
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
2
2
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
3
0
1
0
2
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
2
0
1
2
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
2
0
1
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
1
0
3
0
2
0
0
0
3
0
0
0
0
2
0
2
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
2
0
0
3
2
1
0
1
0
2
0
0
0
2
1
1
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
2
2
0
2
0
2
0
1
0
1
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
2
1
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
1
0
0
2
2
0
0
0
0
1
0
0
0
2
0
0
0
0
5
0
0
1
0
1
2
1
0
0
2
1
0
2
1
0
0
0
0
0
0
1
1
0
0
0
3
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
2
1
0
0
1
0
0
1
0
0
0
0
0
1
1
0
1
2
2
0
0
1
0
0
2
0
1
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
1
1
0
0
0
0
0
1
0
0
2
1
0
4
0
0
4
0
0
0
1
0
2
0
0
2
0
0
1
0
4
1
3
0
1
1
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
4
1
0
0
1
0
0
0
0
1
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
1
2
2
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
2
1
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
3
1
4
0
0
1
0
0
0
0
0
2
1
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
4
0
1
0
4
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
2
2
1
0
0
1
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
1
0
0
0
2
2
0
0
1
0
3
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
1
0
2
0
2
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
1
2
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
1
1
0
1
0
0
0
0
2
5
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
2
0
0
0
0
0
0
6
2
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
4
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
3
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
1
0
1
1
2
0
0
0
2
0
0
0
0
0
1
0
0
4
0
0
1
1
0
0
0
1
0
0
0
2
1
2
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
3
0
0
1
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
1
1
0
0
1
2
2
0
1
0
0
0
1
0
0
3
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
2
2
0
5
0
1
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
1
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
2
1
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
2
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
5
0
0
1
1
0
1
0
0
3
0
0
0
0
1
0
0
0
0
1
0
0
0
3
0
0
0
2
0
0
4
0
2
0
0
0
1
0
0
0
0
5
2
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
1
0
2
1
0
1
0
0
1
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
1
3
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
2
0
0
0
0
2
0
0
7
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
1
2
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
2
2
0
2
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
3
1
0
0
1
0
0
0
0
2
0
0
2
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
2
2
0
1
1
2
0
0
1
0
0
0
2
0
0
0
2
0
1
0
2
0
0
1
1
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
3
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
1
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
2
1
0
1
0
2
1
1
0
1
0
2
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
2
3
0
0
0
0
0
1
0
1
0
0
0
3
1
17
0
0
0
0
2
0
1
2
1
0
1
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
1
0
2
0
0
0
1
1
0
0
0
1
2
0
0
0
2
0
0
0
1
2
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
2
0
0
0
0
2
2
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
2
0
0
2
1
1
0
0
0
2
0
2
0
0
2
0
2
0
0
0
2
0
0
2
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
3
0
0
1
0
0
0
1
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
2
1
0
0
3
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
4
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
1
0
0
2
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
1
0
1
1
0
2
0
0
0
4
1
0
2
0
2
0
0
0
1
1
0
0
2
1
0
0
0
0
2
0
1
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
1
0
0
0
1
0
1
0
0
1
0
0
1
0
1
0
0
0
2
2
0
0
1
0
2
0
1
0
0
1
0
0
0
0
0
2
2
0
1
1
1
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
3
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
4
1
1
0
2
2
0
0
1
2
1
0
1
2
0
0
2
0
0
0
2
2
2
1
0
2
0
2
0
0
2
1
0
0
0
0
0
2
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
6
1
0
0
0
0
1
2
0
0
0
5
0
0
2
0
0
0
0
0
1
5
2
2
0
0
0
2
0
0
1
0
0
0
0
0
0
1
2
0
1
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
1
1
2
1
0
0
0
0
0
0
0
1
0
0
0
2
0
3
0
0
0
3
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
2
1
2
0
0
0
0
2
0
0
1
0
1
0
0
2
0
2
0
2
2
0
1
2
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
2
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
5
0
2
0
0
0
2
0
0
2
0
0
0
1
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
2
1
0
0
2
0
0
1
0
0
1
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
1
3
0
0
1
2
0
1
1
0
0
0
2
0
0
1
0
0
2
0
0
2
0
2
0
0
0
0
0
0
1
1
0
2
2
1
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
2
0
2
2
2
1
0
0
0
5
6
0
0
0
0
0
0
0
0
0
1
1
0
0
2
2
0
0
0
0
1
0
1
1
1
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
8
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
2
1
0
0
0
0
1
2
2
0
0
1
0
0
1
1
2
1
0
0
0
0
4
0
0
0
0
0
2
2
0
2
0
0
0
0
2
1
0
0
0
1
2
0
3
0
0
0
0
2
0
0
0
2
10
0
0
0
0
0
0
2
2
0
0
0
0
0
1
2
2
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
6
0
2
0
0
2
0
0
0
0
2
1
0
1
2
0
0
2
5
0
0
1
0
1
0
2
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
2
0
3
0
0
3
0
3
1
0
1
0
0
0
0
1
0
1
2
0
2
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
1
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
5
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
2
0
1
3
0
0
1
0
2
0
1
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
1
1
2
0
2
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
2
1
2
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
3
1
0
1
0
2
2
0
2
0
0
1
0
4
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
1
1
0
0
0
0
0
0
0
2
2
1
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
7
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
2
1
0
2
3
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
2
0
0
0
0
0
2
4
0
0
4
0
0
0
2
0
0
1
2
1
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
1
0
1
2
0
0
1
1
0
0
0
1
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
2
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
1
0
1
2
0
1
1
0
1
0
1
1
0
0
1
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
2
2
0
0
1
2
0
0
0
0
0
0
0
0
0
1
3
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
1
0
2
0
0
0
0
1
0
0
1
0
1
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
2
0
1
1
1
0
2
2
1
1
2
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
2
0
2
0
0
0
0
0
0
0
1
2
2
0
2
0
0
0
1
2
0
0
1
2
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
4
0
0
2
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
1
2
0
1
0
8
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
2
1
0
2
1
0
0
0
0
1
1
2
0
0
0
0
1
0
0
0
3
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
1
0
2
0
0
0
0
0
2
3
0
0
0
0
0
1
0
0
1
0
0
1
0
0
3
2
0
0
0
2
0
1
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
1
0
0
0
1
2
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
2
3
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
2
0
1
2
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
2
1
0
0
0
1
1
0
1
0
0
0
0
0
1
1
2
0
0
2
0
2
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
2
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
2
4
0
0
0
0
0
2
0
0
0
0
2
1
1
0
0
0
0
0
0
2
2
1
1
0
0
1
0
0
0
0
1
2
2
0
1
1
0
0
0
0
0
0
1
1
0
5
4
1
0
3
2
0
2
0
0
0
0
5
1
0
0
0
1
3
0
0
0
0
0
0
0
0
0
2
0
2
1
2
0
0
0
1
0
0
0
1
0
2
0
0
2
2
0
0
1
1
0
0
1
0
1
0
9
0
0
2
2
2
2
0
1
0
0
0
0
3
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
1
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
5
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
2
0
1
1
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
4
0
1
1
1
0
3
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
2
3
2
0
0
0
0
0
1
2
0
0
0
2
1
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
1
0
1
2
1
2
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
3
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
3
2
1
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
1
0
0
0
2
0
0
0
2
0
1
0
0
1
0
1
0
0
3
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
3
3
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
2
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
2
0
0
1
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
2
0
0
0
0
0
2
1
0
1
1
0
0
1
0
0
2
1
3
1
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
3
1
0
0
0
0
0
2
2
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
2
2
2
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
1
0
2
1
0
0
3
0
0
3
2
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
2
1
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
3
0
1
0
2
0
2
0
0
0
2
0
2
0
1
0
0
0
2
0
2
2
0
0
0
0
1
0
0
0
1
3
1
0
0
2
2
0
0
1
0
0
1
0
0
0
0
0
1
2
0
4
0
0
1
0
0
0
0
3
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
5
0
0
0
3
0
1
0
1
0
0
1
0
0
0
2
0
2
0
1
0
2
4
0
2
1
0
3
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
1
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
3
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
2
0
0
1
0
1
0
1
0
0
2
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
4
0
0
0
1
0
0
0
0
0
0
0
2
1
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
2
0
0
2
7
2
0
2
0
1
0
0
0
0
0
4
1
0
1
1
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
2
0
1
0
7
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
1
1
0
1
0
7
2
0
3
0
1
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
3
0
3
4
0
0
0
1
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
2
0
2
0
0
0
0
0
0
0
0
0
2
3
0
1
1
1
0
2
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
2
0
1
1
3
0
1
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
3
0
0
1
0
0
3
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
1
0
1
2
3
0
1
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
2
1
1
0
0
1
1
0
4
1
0
2
1
0
1
1
1
1
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
2
0
1
0
0
1
0
0
2
0
0
1
1
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
3
2
0
0
0
0
2
1
0
3
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
1
0
2
0
0
0
2
0
0
0
0
0
1
0
0
1
3
2
2
0
0
1
0
0
4
0
0
0
0
0
4
2
0
0
0
0
1
0
0
0
0
2
0
0
1
2
0
0
1
0
2
2
3
1
0
0
2
0
0
0
0
3
0
0
0
0
0
2
0
0
0
1
1
0
0
3
0
1
0
0
0
0
1
0
2
0
2
0
0
0
2
2
2
0
0
0
0
0
0
0
2
0
0
0
0
3
0
1
2
1
0
0
0
0
2
2
2
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
2
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
3
2
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
2
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
3
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
1
0
0
0
1
1
0
0
0
3
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
2
0
0
2
0
0
0
0
1
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
2
1
0
0
6
0
0
1
2
2
0
3
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
1
0
1
0
0
0
0
0
2
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
2
0
2
0
0
11
4
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
3
0
0
3
0
0
0
0
1
4
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
3
0
1
0
3
0
0
0
0
0
1
0
0
1
0
2
2
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
3
3
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
1
1
3
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
1
0
0
2
0
1
1
0
0
1
1
0
2
0
1
2
0
0
1
2
0
3
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
1
0
0
1
0
2
1
1
0
0
0
0
0
0
2
1
0
2
0
0
0
0
2
1
0
0
1
0
0
1
0
1
2
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
1
2
0
2
0
0
0
1
1
0
5
0
0
2
1
0
2
0
0
0
1
2
0
0
0
0
2
1
2
0
0
0
0
0
0
1
8
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
2
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
4
1
0
0
0
3
0
0
2
2
0
0
2
0
0
0
0
0
0
1
2
0
1
2
2
2
0
0
0
2
0
0
0
0
2
0
2
0
2
1
0
0
2
2
0
2
0
0
0
0
0
0
2
0
0
2
0
2
0
0
2
2
0
0
0
2
0
0
2
0
0
2
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
1
2
0
1
0
0
1
0
0
0
1
1
1
2
0
0
2
0
2
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
2
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
3
2
0
0
0
0
0
1
2
1
2
1
1
1
0
0
0
0
0
0
0
2
1
2
0
0
0
0
1
1
0
0
0
0
1
0
0
0
3
0
0
2
0
2
1
1
2
0
0
1
0
1
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
0
1
2
0
2
0
0
0
7
0
0
0
0
3
0
1
0
0
0
0
0
2
0
0
0
1
2
1
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
4
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
1
1
2
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
2
0
2
0
3
0
0
0
2
3
0
0
0
0
1
1
0
0
0
0
2
0
0
2
0
0
1
0
3
0
0
0
0
0
0
2
0
2
1
6
2
0
0
4
0
0
2
2
4
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
3
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
1
0
0
0
0
1
2
0
3
0
0
0
6
0
0
0
0
0
0
0
1
0
3
0
2
0
0
1
0
0
0
0
0
0
0
2
0
2
1
0
1
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
1
2
0
2
0
2
1
0
2
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
2
0
0
0
0
2
1
0
2
1
0
0
1
0
2
1
0
1
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
3
1
0
0
1
5
2
1
0
0
0
0
0
0
1
0
3
0
2
0
0
2
0
0
0
0
1
0
0
0
5
2
0
1
0
2
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
1
2
0
0
1
2
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
2
0
1
0
0
0
1
0
0
0
0
1
1
0
0
2
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
3
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
1
0
1
1
2
1
1
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
1
2
0
0
1
2
1
0
0
1
0
0
2
0
2
0
0
1
0
1
1
0
3
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
2
0
0
2
0
0
4
0
6
0
2
0
5
1
0
0
0
0
2
0
1
0
0
1
0
0
3
0
0
0
1
0
0
2
2
0
0
3
2
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
2
1
0
5
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
1
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
2
0
0
0
0
0
1
1
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
4
0
0
0
0
0
2
0
0
0
2
0
0
0
3
2
0
0
2
0
2
0
0
0
0
0
1
0
2
1
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
2
0
0
0
4
0
0
1
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
3
0
0
0
0
0
1
1
0
1
0
0
2
1
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
11
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
1
0
0
0
1
2
0
0
0
1
2
1
0
0
0
5
1
0
0
0
0
2
0
0
0
0
1
0
3
0
1
0
5
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
1
0
0
0
1
2
2
0
1
0
0
0
0
4
0
0
2
1
0
1
1
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
2
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
1
1
0
2
0
0
0
2
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
2
0
0
0
3
0
1
0
0
0
0
0
0
0
0
1
2
1
0
1
0
2
0
0
0
0
0
0
0
2
2
0
1
0
1
4
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
2
2
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
2
1
0
2
0
2
0
0
0
3
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
2
0
1
2
1
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
1
0
0
2
0
0
1
0
1
0
0
0
0
0
1
2
0
0
2
2
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
2
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
3
1
2
0
0
2
0
0
2
0
0
0
1
0
0
0
1
0
0
0
2
1
0
1
0
4
2
0
1
0
0
0
0
1
0
0
0
3
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
1
0
1
0
0
1
1
0
0
0
0
1
0
1
1
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
1
1
0
1
0
0
0
0
1
2
0
0
0
0
0
1
2
0
0
0
1
1
0
0
0
6
0
0
2
0
0
0
0
2
2
0
0
2
0
0
0
1
0
0
0
2
0
2
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
1
2
1
0
0
0
0
0
0
0
1
3
0
0
0
1
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
2
2
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
2
0
1
0
0
0
2
0
0
0
0
0
0
5
0
0
2
2
3
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
1
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
2
0
0
0
1
1
1
1
1
0
0
0
0
2
1
0
1
0
0
0
2
0
0
2
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
8
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
1
0
1
1
0
0
0
0
1
1
0
0
2
2
0
2
2
0
0
0
2
1
1
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
2
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
4
0
0
0
1
0
0
0
1
0
2
2
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
2
0
0
1
0
0
2
0
1
2
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
1
1
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
3
0
0
0
0
0
0
0
3
0
0
0
4
1
0
2
2
0
1
2
0
0
0
4
0
0
1
3
0
0
1
2
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
4
0
3
0
0
1
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
2
0
4
0
0
0
0
0
1
3
0
3
0
0
0
7
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
4
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
10
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
4
0
0
2
0
0
0
1
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
2
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
4
0
0
0
0
0
2
0
0
0
2
2
0
1
1
2
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
1
3
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
2
0
3
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
1
0
2
2
1
0
0
0
0
1
2
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
2
0
0
2
0
0
0
1
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
1
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
1
1
2
1
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
2
0
0
3
0
0
1
0
2
0
2
0
0
1
0
0
2
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
1
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
1
2
0
0
0
1
0
0
0
0
3
0
1
0
2
2
2
0
2
2
0
0
2
0
0
2
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
2
0
0
1
0
0
1
0
1
0
3
1
1
1
0
1
2
0
2
2
0
0
0
0
2
0
1
0
2
0
1
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
2
0
2
0
0
2
0
0
0
0
5
0
1
0
2
0
0
0
0
0
0
0
0
3
0
2
0
0
0
2
0
0
0
0
0
2
0
0
3
2
0
0
1
0
0
0
0
0
1
0
0
2
0
0
1
0
1
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
2
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
5
0
2
0
0
1
0
0
0
1
0
3
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
1
0
0
0
0
3
2
0
2
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
3
2
0
2
0
0
2
1
0
0
0
2
1
0
0
0
0
0
0
1
0
0
2
0
0
2
0
2
2
0
0
0
2
0
2
0
0
0
0
0
2
1
0
0
0
0
2
2
0
0
1
2
4
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
1
0
1
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
3
0
0
2
0
2
0
1
0
0
2
0
0
1
0
0
0
1
0
0
0
0
2
5
0
0
1
0
2
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
2
0
0
0
1
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
2
2
0
1
0
0
0
0
0
1
4
0
2
2
0
0
0
0
0
2
0
0
0
0
4
0
0
0
2
1
0
1
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
2
3
0
0
0
1
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
2
0
0
4
2
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
2
0
1
0
1
1
3
1
0
0
0
0
2
0
1
0
0
0
0
0
1
0
7
0
2
0
1
0
2
1
0
1
1
0
1
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
1
0
0
2
1
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
1
2
0
2
0
1
0
2
0
0
0
1
0
2
0
1
1
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
2
2
2
0
0
0
0
1
1
2
0
0
0
0
1
0
1
0
3
0
0
3
0
2
2
0
0
0
0
0
2
1
0
0
0
0
0
0
3
0
2
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
2
0
0
1
0
0
0
0
2
0
0
2
1
0
0
0
0
0
1
0
4
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
11
2
2
1
2
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
1
3
1
0
0
1
0
0
0
0
2
0
3
2
0
1
1
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
2
2
2
0
0
0
2
3
0
2
0
0
0
0
1
0
0
0
2
0
1
2
0
0
3
5
0
0
0
0
1
0
0
0
2
0
1
0
2
0
0
2
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
4
0
0
0
1
0
0
2
0
0
0
3
0
0
0
0
2
1
0
3
0
0
0
2
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
4
1
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
2
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
1
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
2
2
0
0
0
0
6
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
3
1
1
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
3
0
0
0
0
0
0
2
0
0
2
0
3
1
0
0
0
1
0
0
0
0
0
1
0
0
4
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
1
2
2
0
0
0
1
0
0
2
0
0
2
0
0
2
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
2
2
2
0
2
1
0
1
1
1
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
3
2
0
0
0
0
1
1
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
1
0
0
0
3
0
0
0
2
0
0
0
3
4
0
1
2
0
0
2
2
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
2
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
1
2
0
1
0
0
3
0
0
1
1
0
1
2
0
0
0
0
0
1
2
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
1
0
0
0
0
0
1
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
1
0
0
7
3
2
0
0
0
1
0
0
3
0
2
1
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
1
0
2
2
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
1
0
0
2
2
0
0
3
1
0
2
0
0
4
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
2
0
2
0
1
0
0
1
7
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
1
0
1
1
0
0
1
1
0
0
0
0
0
0
2
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
1
0
1
0
0
1
2
0
2
2
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
2
1
0
1
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
1
0
3
0
1
0
0
10
2
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
3
0
3
0
2
0
1
0
0
0
1
2
0
0
2
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
2
0
0
0
0
1
0
2
0
0
1
2
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
2
2
0
0
1
1
2
2
0
0
2
0
2
2
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
1
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
1
2
0
2
0
2
0
0
0
0
0
0
1
0
0
0
4
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
1
3
2
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
4
0
2
0
0
0
0
1
1
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
4
0
2
4
1
0
2
0
0
0
0
2
0
1
0
1
0
2
0
0
2
0
2
1
0
0
5
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
2
0
0
0
2
0
2
0
1
0
4
0
0
2
0
1
0
0
0
0
0
0
0
1
2
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
2
0
0
3
0
0
0
0
2
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
2
0
2
0
0
1
3
0
0
0
0
2
1
2
2
0
0
2
0
1
0
0
0
1
1
0
1
1
1
0
1
0
0
0
0
1
1
0
1
7
0
1
0
0
1
0
1
2
0
0
0
0
1
8
1
1
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
1
1
1
0
1
1
0
0
0
0
2
0
1
0
0
0
1
2
1
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
1
1
0
0
0
0
1
0
0
1
0
0
0
2
1
0
0
0
2
1
0
2
0
4
0
1
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
3
1
2
0
0
0
0
6
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
2
2
0
2
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
1
0
2
0
2
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
2
4
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
1
0
0
1
7
0
0
0
0
0
0
2
1
1
1
2
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
2
1
0
2
0
0
2
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
9
0
1
0
0
1
0
1
0
0
0
0
1
2
2
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
2
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
1
0
0
0
1
0
2
2
0
0
1
0
3
0
0
0
1
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
1
0
0
2
2
2
0
0
0
4
0
0
2
0
0
1
0
1
0
3
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
1
0
0
0
1
0
1
1
0
2
0
0
0
0
0
2
3
4
0
0
3
1
0
0
0
0
0
0
2
0
0
0
0
6
0
2
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
4
1
0
1
0
0
1
2
0
0
0
0
0
1
0
0
3
0
0
2
2
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
2
1
1
2
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
4
1
1
2
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
1
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
4
0
0
1
0
2
0
1
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
1
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
2
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
1
1
0
2
2
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
2
1
3
3
0
0
0
1
0
2
0
0
0
0
0
3
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
6
1
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
2
0
1
0
0
0
0
0
2
0
0
0
3
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
2
2
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
1
2
0
1
2
0
0
1
0
0
0
2
1
0
0
0
3
0
0
0
0
0
0
0
0
0
1
7
0
0
0
0
3
2
0
0
1
3
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
2
0
0
2
0
0
1
0
0
0
0
0
2
1
0
1
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
2
1
0
0
0
2
0
0
0
1
0
1
0
0
0
1
0
4
2
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
0
0
4
0
1
0
2
1
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
2
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
2
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
1
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
1
0
1
0
2
0
1
0
0
0
1
2
1
0
0
2
1
2
2
2
0
0
2
1
0
0
0
0
2
0
0
2
0
0
2
1
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
3
0
0
0
0
2
0
0
0
0
1
0
0
1
2
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
5
0
0
0
0
0
1
0
0
0
0
0
1
0
2
2
1
0
0
0
0
0
0
0
0
0
3
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
1
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
2
1
1
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
2
1
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
2
1
0
0
3
0
0
0
2
0
2
0
0
0
0
2
0
0
0
2
1
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
3
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
1
0
1
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
1
0
0
2
1
0
0
0
1
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
2
1
1
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
1
4
0
0
1
0
0
2
1
2
1
0
2
0
0
0
0
0
0
0
2
1
2
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
1
1
1
0
0
2
1
0
0
2
1
2
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
4
1
0
1
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
5
0
2
0
4
0
1
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
4
0
2
0
1
0
0
0
1
2
0
0
0
0
0
1
0
1
3
0
2
0
0
0
0
0
0
0
1
0
6
0
2
2
2
2
0
0
0
0
0
0
1
0
2
0
0
1
0
2
2
0
1
0
0
0
2
0
0
2
2
0
0
0
2
2
0
0
8
0
2
0
2
0
0
1
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
2
0
0
2
0
0
0
0
2
0
1
4
1
1
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
11
0
0
4
1
1
1
0
2
0
0
0
2
2
0
0
1
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
1
1
0
0
1
2
0
0
0
2
0
0
2
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
3
0
2
2
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
2
0
1
0
0
2
0
2
0
2
0
2
0
0
0
3
0
3
0
0
2
0
0
0
0
1
0
0
2
0
2
0
0
0
2
0
0
0
0
0
1
1
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
3
0
0
0
0
0
2
0
2
0
1
3
1
1
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
2
1
0
1
0
0
2
2
0
0
0
2
0
0
1
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
1
0
0
2
0
3
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
1
0
2
0
0
0
1
1
0
2
0
1
0
2
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
2
0
0
2
0
1
0
1
1
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
9
0
0
0
0
0
1
3
0
0
1
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
4
4
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
3
1
2
1
0
0
0
1
1
0
0
0
0
0
0
0
0
4
0
2
0
0
0
1
0
0
0
0
0
0
2
1
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
3
0
0
0
2
0
0
0
1
2
0
0
0
0
1
6
0
0
1
3
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
2
0
1
0
0
0
2
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
1
1
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
1
0
0
2
1
0
1
1
0
1
2
0
4
2
0
0
0
0
1
0
0
2
0
0
2
0
0
0
2
0
3
0
0
2
1
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
1
1
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
2
0
1
0
1
0
0
0
1
0
0
0
2
6
2
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
3
0
0
1
0
0
0
0
2
0
1
2
0
3
0
0
0
2
2
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
4
2
0
0
0
0
1
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
1
0
0
2
0
1
2
0
0
0
2
0
3
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
2
3
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
3
0
0
0
2
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
1
1
0
1
0
0
1
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
1
0
0
0
1
0
2
0
1
1
0
1
0
0
0
1
2
3
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
2
0
0
1
1
0
0
0
4
0
1
0
0
2
0
1
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
2
0
0
0
2
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
2
2
0
2
1
0
0
0
2
0
3
2
0
0
0
0
4
2
2
0
0
0
0
0
0
0
1
0
0
0
3
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
2
0
1
0
1
2
3
0
0
0
0
0
0
1
0
1
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
1
0
2
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
1
1
0
0
0
1
2
0
0
0
0
2
1
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
2
0
0
0
1
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
1
2
3
0
0
0
1
0
3
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
1
1
0
3
1
0
1
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
1
0
0
0
1
1
0
0
1
0
0
0
1
0
0
2
3
0
0
0
2
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
3
2
0
1
0
0
0
0
0
0
0
0
1
0
2
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
1
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
2
0
0
1
3
0
1
0
0
0
1
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
6
0
1
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
2
1
2
0
0
0
0
1
0
0
0
1
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
2
2
4
0
0
0
2
0
0
2
0
0
3
0
0
0
0
2
1
1
0
0
0
0
0
0
0
1
3
2
0
0
0
2
2
2
0
0
0
0
0
2
2
0
2
2
2
0
0
0
0
0
1
2
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
8
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
1
3
0
0
0
0
2
4
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
3
2
0
1
0
0
0
0
1
2
0
0
0
1
0
1
0
0
1
2
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
1
2
0
1
2
0
0
0
0
2
0
0
2
1
0
0
0
3
0
0
0
1
1
0
0
0
1
2
0
1
1
0
0
0
0
0
1
2
0
0
1
0
1
2
1
0
3
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
3
0
0
1
0
1
2
2
0
0
0
0
1
0
2
2
0
1
0
0
4
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
2
0
3
0
0
0
1
0
1
1
1
2
2
0
0
0
1
0
0
0
0
0
0
0
1
1
0
2
0
0
0
2
0
0
0
0
2
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
1
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
2
2
1
0
1
0
0
0
0
0
2
4
0
0
0
0
0
0
0
1
0
1
0
0
2
0
1
0
0
0
0
0
3
0
0
2
0
0
0
0
0
4
0
0
0
2
1
0
1
1
0
0
0
0
1
0
2
0
0
1
1
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
3
0
0
0
1
0
2
1
2
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
1
2
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
2
2
0
0
2
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
3
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
1
3
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
1
0
1
0
1
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
2
3
0
1
0
2
0
1
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
1
1
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
1
0
0
1
1
0
2
2
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
1
2
0
2
1
0
1
0
0
3
1
0
0
1
0
0
2
0
0
0
2
0
0
1
0
0
1
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
1
1
0
2
0
0
0
0
1
0
0
0
3
0
2
0
2
0
2
0
2
0
0
0
0
5
0
0
0
0
0
0
1
0
0
0
1
1
2
0
0
0
0
0
0
0
0
1
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
2
0
0
0
1
3
0
0
0
0
2
0
2
0
0
0
2
0
1
1
2
0
1
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
3
1
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
2
0
0
0
0
1
0
0
0
2
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
3
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
4
0
0
0
1
6
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
2
2
2
2
0
1
2
1
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
2
0
0
2
0
0
1
0
0
3
0
0
0
0
0
0
2
2
2
0
0
1
0
1
0
0
2
2
0
0
0
0
0
0
1
0
1
2
0
2
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
4
0
2
1
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
1
1
0
2
0
0
0
2
1
2
0
2
0
2
1
0
0
2
0
1
3
2
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
1
2
1
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
2
0
2
1
0
2
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
2
0
1
0
1
0
0
0
2
1
0
1
0
0
1
2
0
0
0
0
0
0
0
3
0
2
0
2
0
0
3
0
1
2
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
3
0
1
0
0
0
1
0
2
1
0
2
0
2
0
0
0
0
0
1
0
0
2
0
3
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
1
2
3
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
4
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
2
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
1
0
2
0
0
0
0
0
0
2
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
1
0
0
2
0
0
0
0
0
2
1
0
0
0
1
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
1
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
2
1
2
0
2
0
0
0
1
1
2
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
2
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
1
1
0
1
0
1
0
0
0
1
0
2
6
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
1
1
0
0
1
0
0
3
0
0
0
0
0
2
0
2
0
0
0
0
0
5
0
0
0
1
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
1
0
2
0
1
0
6
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
2
0
0
0
2
0
0
0
3
0
0
0
0
2
0
2
0
0
0
1
0
0
1
1
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
2
1
0
1
0
1
0
0
4
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
1
0
0
1
2
4
1
2
0
0
0
0
2
1
6
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
1
0
1
0
2
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
1
1
0
0
0
2
0
1
1
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
1
2
0
0
1
1
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
1
3
2
0
1
0
1
0
1
2
0
0
2
0
2
0
0
0
3
2
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
2
0
0
0
0
2
0
0
2
0
2
0
2
0
0
0
0
3
0
1
0
0
0
0
2
0
1
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
2
0
0
0
1
0
2
0
1
0
0
0
0
0
2
2
1
0
0
0
0
3
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
1
2
3
0
2
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
2
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
1
0
0
0
0
0
1
2
0
2
0
0
1
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
1
0
0
0
2
2
0
0
0
0
0
0
1
0
0
1
0
0
2
0
1
0
0
2
0
0
1
1
0
0
0
0
1
1
0
0
0
2
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
5
0
0
1
1
1
0
0
0
0
4
0
0
0
0
3
0
0
0
2
2
0
0
0
2
1
1
0
0
0
0
0
0
0
3
0
2
0
2
0
0
1
0
2
1
0
0
2
0
0
0
2
0
2
2
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
1
0
1
0
0
2
3
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
2
2
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
2
0
2
2
4
0
0
0
0
0
0
0
0
1
1
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
3
2
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
1
1
2
0
0
0
1
0
4
0
1
2
0
0
1
0
0
0
0
0
1
3
1
0
2
1
0
0
1
2
0
0
4
0
0
2
0
0
2
0
2
0
2
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
4
0
0
0
3
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
1
0
0
1
0
2
0
2
0
0
1
0
1
0
1
0
0
3
0
5
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
2
0
2
0
0
1
0
0
0
0
2
0
0
0
2
0
2
4
0
1
0
0
2
0
0
0
1
0
2
0
0
2
0
1
0
0
0
0
0
1
1
2
0
0
1
1
0
0
0
0
0
0
0
0
4
0
2
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
2
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
4
1
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
3
0
0
2
0
1
0
0
0
0
0
1
1
0
1
3
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
2
1
0
0
1
2
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
1
1
1
0
2
0
0
0
0
0
0
2
0
2
1
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
2
2
0
2
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
2
2
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
3
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
2
2
0
0
0
2
1
0
1
0
0
0
0
0
0
1
2
0
1
5
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
1
3
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
1
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
6
0
0
2
0
0
0
0
0
0
1
2
1
0
2
0
0
0
2
0
0
1
0
1
0
0
1
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
1
0
0
0
0
0
5
2
0
0
3
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
1
0
0
0
0
2
0
3
2
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
2
0
0
5
3
0
2
0
2
1
0
0
0
0
3
0
0
2
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
3
0
0
0
0
0
0
1
3
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
2
0
0
3
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
2
0
0
0
0
0
0
1
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
2
0
3
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
3
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
2
0
0
0
0
2
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
1
0
0
2
0
2
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
2
2
0
0
2
0
1
0
2
0
0
6
0
0
0
0
0
1
0
0
0
2
0
0
1
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
1
2
0
0
1
0
0
1
1
0
3
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
3
1
1
0
0
0
1
1
0
2
0
0
0
4
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
3
0
0
0
0
0
0
0
0
6
0
0
2
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
3
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
4
0
1
2
0
0
0
0
1
0
0
0
2
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
2
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
1
1
0
1
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
2
1
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
3
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
4
0
0
2
2
0
0
0
5
0
0
3
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
2
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
1
2
1
0
2
0
0
1
0
0
0
0
1
1
1
0
0
0
2
0
2
0
1
0
3
0
0
0
1
0
0
0
1
0
2
0
2
0
2
0
0
0
1
0
0
0
2
0
0
0
2
0
2
0
1
0
1
0
0
0
0
0
0
0
2
2
1
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
3
1
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
5
0
0
0
0
2
1
0
0
0
2
3
3
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
2
3
1
0
0
0
1
0
2
0
0
0
1
0
0
0
2
0
2
0
2
0
1
0
1
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
2
2
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
1
2
0
1
0
0
0
0
0
1
0
0
2
2
0
0
0
4
2
0
2
0
0
2
0
3
0
3
1
0
2
0
1
2
1
0
2
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
1
1
0
0
1
0
0
0
2
0
0
2
0
0
0
1
2
0
1
1
0
0
0
0
0
2
0
0
2
2
0
0
0
2
1
0
0
0
2
0
0
0
0
1
0
0
0
1
2
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
3
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
3
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
2
1
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
2
2
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
2
0
2
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
2
0
0
1
1
0
0
0
1
0
1
3
2
0
3
0
0
1
0
0
0
0
2
0
1
0
0
0
0
2
2
1
0
0
0
3
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
2
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
1
0
0
2
0
2
1
0
1
2
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
2
0
0
2
0
1
0
1
0
2
2
2
0
0
0
0
0
0
0
0
0
0
1
3
0
1
0
5
0
0
0
2
0
0
1
1
0
0
0
0
2
0
0
1
0
2
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
5
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
2
1
1
0
0
2
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
1
0
2
0
0
0
1
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
2
0
1
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
4
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
3
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
3
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
2
0
2
0
1
2
0
0
0
0
1
0
0
0
3
2
1
0
1
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
6
1
0
1
0
0
1
3
0
0
0
1
1
3
0
2
0
0
0
0
0
0
0
2
1
2
0
2
0
0
1
0
0
0
1
0
2
2
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
2
0
0
0
0
1
0
2
0
1
2
1
2
0
0
0
0
1
0
1
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
3
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
3
1
0
0
0
0
0
1
0
0
0
1
3
0
0
0
1
0
2
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
1
2
0
0
0
1
0
1
1
1
0
4
0
0
0
0
2
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
1
0
0
4
0
0
0
2
1
0
0
1
0
0
1
2
0
0
0
0
0
0
2
3
0
1
0
0
0
0
0
2
0
0
0
2
0
0
2
2
0
0
1
0
0
3
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
3
0
2
0
0
3
1
0
0
0
0
0
0
0
0
0
2
0
2
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
5
0
0
0
0
0
1
2
1
0
0
0
0
2
3
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
2
1
2
0
1
0
2
0
2
0
1
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
2
1
0
2
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
5
0
1
0
0
0
0
2
1
0
0
0
0
0
0
1
4
0
0
1
0
0
0
0
0
0
0
0
4
0
2
2
0
0
0
0
0
0
1
0
1
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
2
0
0
0
5
2
0
0
1
0
3
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
1
0
1
1
1
2
0
0
0
0
3
1
0
2
0
0
0
0
1
1
0
1
1
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
8
0
2
1
0
3
0
0
0
0
2
0
0
1
0
2
1
1
1
1
1
0
2
1
2
0
0
0
2
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
2
1
0
0
1
0
0
2
0
0
0
1
0
2
0
0
0
0
1
0
1
0
0
0
0
2
1
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
2
2
0
2
0
0
2
2
0
0
3
0
0
3
0
1
0
1
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
1
1
1
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
2
0
0
5
0
1
2
0
0
0
0
0
0
0
0
0
0
0
8
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
2
0
2
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
4
0
0
4
0
0
0
0
2
0
0
2
0
0
0
0
4
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
2
0
2
2
0
0
2
1
0
0
2
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
1
0
2
0
1
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
1
0
0
0
0
0
0
0
3
2
1
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
4
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
2
0
1
1
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
2
8
0
3
0
1
0
2
0
0
0
5
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
4
2
1
0
0
0
0
0
0
0
3
5
1
0
2
1
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
2
0
0
0
1
0
1
0
0
0
1
0
2
0
0
0
0
0
7
0
0
0
1
0
0
0
0
0
2
0
1
2
0
0
0
3
0
0
0
0
1
0
0
0
2
0
1
1
6
0
0
0
2
0
0
0
0
0
1
1
0
0
0
1
0
0
4
1
2
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
1
1
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
3
0
2
0
1
0
0
2
0
0
0
2
2
0
0
2
0
1
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
2
0
3
3
0
2
2
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
2
1
0
0
0
2
0
1
0
0
0
0
0
0
0
1
3
0
0
0
3
1
0
0
0
0
0
0
2
2
2
0
0
0
0
1
1
1
0
4
0
0
2
2
0
0
0
2
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
2
2
0
0
0
0
0
2
0
0
0
3
4
2
0
0
0
0
0
0
0
0
2
0
0
6
1
0
0
0
0
0
0
0
2
0
3
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
3
0
1
0
0
0
0
0
0
1
0
0
0
1
2
2
0
0
3
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
1
2
0
0
2
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
2
0
0
0
0
1
0
2
0
1
2
0
0
3
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
2
1
0
0
1
1
0
1
0
0
2
2
1
0
2
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
2
1
1
0
0
0
1
0
0
0
0
1
0
6
0
1
0
0
0
0
0
0
0
0
0
0
3
1
2
1
0
0
2
0
0
2
1
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
3
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
6
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
4
0
0
0
0
1
0
0
1
1
0
0
3
0
0
0
0
0
1
0
0
0
5
0
2
2
0
0
2
1
0
0
0
0
0
0
2
0
1
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
2
1
1
1
0
0
0
1
0
0
0
2
1
0
0
2
0
0
0
0
0
2
3
2
2
0
0
0
3
1
0
0
2
0
0
0
0
0
1
0
3
2
0
1
0
0
0
0
1
0
6
1
3
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
1
1
0
0
0
0
0
3
0
1
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
1
1
0
0
0
0
2
2
1
0
0
0
2
2
0
0
2
0
2
0
0
1
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
3
2
0
0
0
3
0
0
0
2
0
0
12
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
2
0
3
1
1
0
0
0
0
2
0
0
3
2
1
0
0
0
0
0
2
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
2
2
0
0
2
0
1
2
0
1
2
0
0
0
2
2
0
0
0
3
1
0
0
1
0
1
0
0
0
0
0
5
2
3
0
2
0
0
2
0
2
2
0
2
0
1
0
1
0
0
0
0
0
0
0
0
7
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
1
0
0
2
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
1
0
2
0
0
2
0
0
0
2
0
2
0
0
1
0
0
2
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
1
1
0
2
0
3
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
6
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
6
0
2
0
1
0
0
0
1
0
0
1
0
3
0
2
0
0
0
2
2
0
2
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
1
0
1
0
1
3
2
2
0
0
0
2
0
3
0
0
0
0
0
2
0
0
2
0
2
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
1
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
2
0
1
0
0
2
2
0
1
2
1
1
0
0
1
2
3
0
0
0
0
0
2
0
0
0
0
1
1
3
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
1
0
0
0
0
0
2
1
0
2
2
0
0
0
1
2
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
1
2
2
2
1
2
0
3
0
0
0
0
0
1
4
0
0
0
2
2
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
4
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
5
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
1
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
2
1
2
0
0
1
1
0
0
2
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
1
2
1
0
0
0
2
1
2
0
0
0
0
0
0
1
1
0
12
0
0
0
0
0
1
0
0
2
2
0
1
2
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
3
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
3
0
4
1
0
2
0
2
0
2
1
0
0
2
2
0
0
2
1
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
2
1
2
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
1
2
1
0
0
2
1
0
2
0
0
0
0
0
1
1
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
3
0
0
1
0
3
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
2
0
2
1
0
0
0
0
0
0
2
2
0
0
0
0
4
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
1
0
0
1
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
1
1
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
3
0
2
1
0
1
0
0
0
0
0
1
1
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
2
3
0
2
0
1
4
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
1
1
2
0
2
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
1
0
0
1
0
0
0
1
2
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
1
2
0
0
0
0
1
0
0
0
0
1
0
0
3
0
0
0
0
0
1
3
10
1
0
0
0
2
0
1
2
0
0
4
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
4
1
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
4
0
0
2
2
2
2
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
3
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
2
0
1
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
1
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
3
3
0
0
0
0
2
1
0
0
2
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
2
0
0
0
0
2
0
0
0
0
2
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
1
0
3
0
0
0
0
5
0
0
0
0
2
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
1
1
0
0
4
0
2
0
0
0
1
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
2
1
0
0
1
0
0
0
3
0
1
0
0
3
0
0
0
2
0
0
1
0
2
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
5
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
1
3
0
1
0
0
2
0
0
4
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
1
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
6
0
0
0
0
0
0
2
0
0
3
0
0
0
0
3
0
0
0
1
0
1
0
0
0
0
1
1
0
1
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
3
1
1
2
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
1
1
0
1
2
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
1
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
3
0
1
2
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
2
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
2
1
1
2
0
0
0
2
0
0
0
3
0
0
2
0
0
0
0
2
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
2
0
0
0
0
0
0
0
2
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
3
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
3
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
3
0
0
1
0
1
0
2
0
0
0
1
0
1
0
1
0
0
0
1
5
2
0
2
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
1
1
0
0
2
1
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
2
0
0
1
2
0
0
0
0
2
1
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
4
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
2
0
0
1
0
1
0
0
3
2
0
0
1
0
0
0
0
3
2
0
0
3
0
0
0
0
2
0
1
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
2
2
1
0
3
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
2
1
3
0
1
0
0
0
2
0
0
0
1
2
0
0
0
0
0
1
2
0
0
1
0
1
0
2
0
1
0
2
1
0
2
0
3
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
1
2
2
1
0
1
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
2
1
1
0
0
0
1
0
0
0
2
3
0
0
0
0
3
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
4
0
2
0
2
0
0
0
0
1
1
1
0
1
0
5
0
0
0
0
0
0
2
3
0
2
1
0
0
0
0
0
2
0
0
2
0
0
0
3
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
3
0
2
0
0
2
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
1
0
1
1
0
2
0
2
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
2
4
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
1
1
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
2
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
2
1
0
0
0
0
2
0
2
0
1
0
2
0
0
0
0
1
3
2
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
2
0
8
0
0
0
2
0
2
0
0
1
1
2
2
0
0
2
0
2
0
0
1
0
0
0
0
1
1
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
1
2
0
0
1
0
0
1
0
0
4
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
2
0
0
0
3
1
0
0
3
0
0
2
0
2
0
0
2
0
2
0
2
0
0
2
5
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
1
0
0
1
2
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
1
1
0
2
0
0
0
0
1
0
0
0
0
0
2
1
0
0
2
0
2
5
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
2
0
0
0
0
0
2
3
1
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
1
0
0
0
0
3
0
0
2
0
0
0
2
1
1
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
2
0
0
1
0
0
0
0
1
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
2
0
2
0
1
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
1
7
0
0
0
3
0
0
0
0
2
1
2
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
2
0
1
3
0
2
0
2
2
0
0
1
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
2
5
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
4
0
0
1
0
2
1
0
2
0
2
0
0
2
3
0
0
3
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
2
0
1
0
0
0
2
2
4
2
3
0
3
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
2
0
5
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
2
1
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
1
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
3
0
1
0
0
3
1
0
1
0
0
1
0
1
0
1
0
0
1
1
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
3
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
4
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
1
0
1
0
0
1
0
1
0
2
0
1
0
2
0
1
0
0
1
0
0
0
1
3
0
0
1
1
0
1
0
9
0
0
2
1
0
1
0
0
2
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
2
0
1
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
1
1
0
2
0
0
0
0
2
0
0
0
0
0
0
2
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
2
1
0
0
0
7
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
2
0
1
0
0
0
0
2
0
0
0
2
1
0
0
0
0
3
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
2
1
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
1
1
0
0
1
0
2
1
2
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
3
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
5
0
1
0
2
0
0
0
3
0
0
2
0
2
0
0
1
0
0
0
1
0
0
1
2
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
2
5
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
2
2
4
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
1
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
2
0
1
0
2
0
0
0
2
1
0
0
0
0
2
0
0
0
2
2
2
1
0
0
2
1
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
3
0
0
0
1
0
0
2
3
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
2
0
0
0
1
2
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
1
0
0
2
0
0
0
1
0
1
0
0
0
0
3
2
0
1
0
0
0
0
5
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
1
2
0
0
0
0
0
0
0
0
0
2
2
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
3
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
1
3
2
0
1
0
0
0
0
1
0
0
0
0
0
4
0
2
0
0
0
0
1
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
3
0
2
0
0
0
0
0
0
2
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
1
0
0
0
2
0
3
0
0
2
0
0
0
0
2
0
0
0
0
2
0
1
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
1
2
1
0
0
0
0
0
1
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
3
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
3
0
1
0
0
2
0
2
0
0
0
0
0
4
2
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
2
0
0
0
0
0
0
1
0
0
0
1
0
2
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
2
1
0
2
0
0
0
1
2
0
0
0
0
2
0
0
0
2
0
0
3
1
1
0
0
0
1
2
0
0
2
0
0
0
0
1
0
0
4
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
2
0
1
0
0
0
0
0
3
4
1
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
8
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
3
1
1
0
0
0
2
1
0
0
0
0
0
0
0
5
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
1
0
0
1
0
2
0
0
0
0
0
2
1
1
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
1
0
2
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
1
2
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
3
2
1
0
2
0
0
0
0
3
0
2
0
1
0
0
0
0
0
0
1
0
2
0
1
0
1
2
0
2
2
1
1
1
0
0
0
0
0
0
0
0
2
0
2
0
1
0
1
0
1
0
0
0
0
5
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
3
0
1
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
1
1
1
0
2
0
0
0
0
1
1
0
0
6
1
0
1
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
3
1
1
0
1
0
0
1
0
2
0
0
0
2
1
0
0
0
0
0
1
0
0
0
1
4
0
0
2
2
1
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
1
2
2
2
0
0
0
1
1
0
0
2
1
0
0
2
0
0
0
0
2
0
1
3
0
1
7
0
1
0
0
1
3
0
0
0
0
0
0
0
1
0
2
2
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
2
0
2
1
1
0
0
0
0
0
2
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
2
2
0
2
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
3
4
2
0
0
0
0
0
0
0
2
2
2
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
1
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
2
0
1
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
1
1
1
0
1
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
2
1
0
0
0
0
0
1
1
2
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
2
0
1
0
0
0
0
5
0
2
0
2
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
1
0
0
0
0
0
0
2
0
1
0
2
0
2
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
3
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
1
1
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
2
2
0
0
0
0
2
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
2
2
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
1
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
1
3
2
0
0
0
3
0
0
0
0
0
0
5
2
0
2
1
2
0
0
2
0
0
2
2
2
2
0
0
2
0
1
0
0
0
0
2
0
0
1
0
2
0
1
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
1
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
2
2
1
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
1
1
5
0
0
0
0
2
1
0
0
0
0
0
2
0
1
0
2
0
6
0
2
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
3
0
0
1
2
0
2
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
2
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
2
1
1
0
1
0
2
0
1
0
0
2
0
0
1
0
2
1
0
0
2
0
0
0
0
0
2
0
0
0
2
0
4
0
0
0
7
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
1
0
2
0
2
0
0
0
2
4
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
3
2
0
0
0
0
1
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
1
0
2
0
0
2
1
1
0
1
2
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
1
1
0
0
0
2
0
0
0
0
0
1
4
0
0
3
0
0
0
0
0
3
0
0
0
0
1
0
2
0
0
0
1
0
1
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
2
0
0
1
3
2
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
2
0
1
0
0
0
0
2
1
1
0
0
1
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
1
0
1
3
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
2
0
0
2
0
3
0
0
1
2
1
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
1
2
1
0
0
0
0
0
1
0
1
0
0
0
2
4
0
0
0
1
0
0
0
0
1
0
0
2
0
1
0
0
0
2
2
0
0
1
0
2
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
1
2
2
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
1
1
0
1
0
0
1
1
0
0
0
0
1
1
2
0
0
0
2
1
0
1
0
0
1
0
0
3
2
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
3
0
0
3
2
0
2
0
0
1
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
3
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
1
1
0
0
0
0
0
0
2
4
0
1
1
3
1
2
0
0
0
0
0
2
2
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
2
0
3
1
0
0
0
1
2
2
2
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
1
2
1
0
0
2
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
2
0
0
0
0
2
2
1
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
2
0
2
0
0
0
2
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
2
3
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
4
1
0
0
1
0
3
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
1
0
0
0
1
0
0
2
1
1
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
2
0
1
2
1
0
0
0
0
0
2
0
2
1
0
2
0
0
3
0
1
0
2
0
2
0
1
0
1
0
0
0
1
1
0
0
0
0
2
0
0
2
0
0
2
0
0
0
1
0
2
2
0
2
1
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
2
1
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
2
1
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
1
0
0
2
2
2
1
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
2
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
1
1
2
0
0
2
0
0
1
3
0
0
0
0
0
1
0
6
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
2
1
1
0
0
0
2
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
1
0
2
1
0
2
0
1
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
3
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
1
0
0
0
1
1
3
0
2
1
0
1
0
0
0
0
0
0
2
1
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
1
0
0
0
2
0
0
0
0
0
2
2
0
0
0
1
0
0
0
4
0
2
0
0
2
0
2
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
1
0
0
0
2
0
0
2
1
0
0
0
0
0
1
0
0
2
0
0
0
1
1
0
0
0
0
0
1
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
1
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
1
2
0
1
0
1
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
3
0
0
1
0
0
0
0
0
1
0
0
1
2
2
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
3
0
2
0
3
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
4
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
1
0
0
2
1
0
1
0
1
1
2
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
5
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
1
1
0
0
0
0
0
1
1
1
0
0
3
0
0
2
0
2
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
2
0
1
0
0
0
0
0
1
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
1
1
0
1
0
0
0
0
2
1
0
0
0
0
0
0
1
1
2
0
0
0
0
4
2
0
2
2
1
0
0
1
2
0
1
0
0
0
2
0
0
0
1
0
0
0
1
3
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
1
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
1
0
0
2
0
0
0
1
0
1
0
0
0
4
0
0
0
0
0
0
2
1
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
3
1
1
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
1
2
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
1
1
2
0
0
0
0
7
0
0
1
2
0
0
0
0
0
1
1
1
0
2
0
0
0
0
0
2
1
3
0
0
0
0
0
1
0
0
2
1
1
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
2
0
0
2
0
1
1
0
0
1
2
1
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
2
0
3
0
0
0
0
1
0
0
1
2
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
3
0
1
0
0
3
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
2
0
0
1
0
2
1
1
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
1
0
0
1
2
2
0
2
0
0
0
0
0
0
0
1
2
2
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
1
1
1
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
2
2
0
2
4
0
0
2
0
2
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
1
2
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
2
0
0
1
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
4
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
1
1
2
1
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
5
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
2
0
1
2
0
0
0
0
0
0
1
0
0
0
2
0
0
3
2
2
0
0
0
2
1
0
0
0
2
0
0
0
0
6
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
1
2
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
2
1
0
2
0
0
0
2
1
0
1
0
3
0
0
0
0
0
0
3
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
1
2
2
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
1
1
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
3
0
0
0
3
2
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
3
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
2
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
2
2
0
1
0
2
1
2
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
2
0
4
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
1
1
0
1
1
0
0
0
0
0
2
0
1
0
1
0
0
0
2
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
1
1
0
0
1
2
0
0
0
0
2
0
2
0
4
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
3
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
2
0
1
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
1
2
0
0
0
0
0
1
0
0
1
2
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
2
0
2
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
2
4
0
0
0
1
1
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
1
1
1
0
1
0
0
2
0
0
0
0
0
1
0
3
2
2
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
2
0
0
0
0
0
0
2
2
1
1
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
2
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
5
0
0
1
0
0
0
0
0
1
1
1
2
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
5
1
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
1
1
0
0
1
2
0
1
1
2
0
0
0
2
0
0
0
0
2
0
0
5
0
1
0
2
0
1
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
1
2
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
4
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
1
2
2
0
1
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
1
2
0
0
0
1
1
0
0
2
2
0
0
0
0
2
1
2
1
1
1
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
1
0
2
1
0
0
0
0
5
0
2
2
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
3
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
2
1
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
1
0
0
0
5
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
1
1
0
1
0
1
2
0
1
2
2
0
0
2
2
0
0
3
0
1
0
0
2
0
0
0
0
1
0
2
2
0
0
0
0
2
2
0
2
1
1
0
0
1
0
0
1
0
0
0
0
1
0
0
2
3
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
1
1
1
0
0
3
0
0
0
1
1
0
1
0
3
0
0
0
0
0
0
0
0
0
2
2
0
0
6
3
2
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
1
0
0
0
2
1
0
2
0
2
3
0
0
0
1
0
0
0
1
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
1
1
2
0
0
0
0
2
1
2
1
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
5
0
2
0
0
0
0
0
0
0
2
2
0
0
1
1
0
0
1
0
0
0
0
0
2
0
2
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
2
2
3
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
2
0
0
0
0
0
0
1
0
1
0
0
3
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
4
2
2
0
1
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
1
0
0
0
0
2
1
0
0
7
2
7
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
1
0
1
0
0
3
0
1
0
1
0
0
2
0
2
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
1
2
0
0
2
1
0
0
1
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
3
2
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
2
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
3
0
0
1
0
0
0
2
2
0
0
0
1
0
2
0
5
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
1
2
2
0
1
3
2
0
0
2
0
0
0
0
50
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
1
2
0
0
0
1
0
1
0
1
0
0
0
2
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
3
3
0
0
1
0
0
1
0
0
0
0
5
0
2
0
0
0
0
2
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
2
0
0
0
0
2
0
1
0
0
0
0
2
0
0
2
0
1
0
0
2
1
0
0
1
0
0
2
1
2
0
0
2
0
0
0
0
2
3
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
4
0
0
2
1
0
0
2
0
0
1
0
0
2
0
0
0
1
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
2
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
4
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
2
0
2
0
0
0
0
0
0
1
0
2
0
0
0
2
0
2
2
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
3
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
3
0
0
2
0
3
0
1
0
2
0
0
0
0
1
0
0
0
1
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
2
0
19
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
3
0
0
2
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
1
2
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
1
1
2
0
2
0
0
0
1
0
2
0
0
2
0
0
0
0
0
2
2
0
3
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
2
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
2
1
1
2
0
1
1
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
4
0
2
0
1
9
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
4
0
0
0
0
0
1
0
0
5
0
2
0
0
2
0
0
1
1
0
0
2
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
8
0
0
0
1
0
0
0
2
2
0
0
2
1
0
1
0
0
0
2
0
0
3
0
2
2
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
2
0
0
2
4
0
0
0
2
0
0
2
0
1
0
1
0
0
0
0
2
0
0
0
0
3
2
0
0
0
1
4
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
1
0
1
0
0
2
0
0
0
1
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
2
0
0
0
9
0
0
0
1
0
1
0
0
0
0
0
0
6
1
3
2
0
2
2
2
0
0
0
1
0
0
0
0
0
1
0
0
1
1
1
0
1
0
1
0
2
0
3
2
2
0
0
2
2
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
1
1
0
0
0
1
1
0
0
0
0
1
2
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
2
0
0
3
1
0
2
1
1
0
0
5
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
2
0
2
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
5
0
0
1
0
0
0
2
2
0
0
1
0
1
1
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
2
2
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
4
0
0
2
2
0
1
0
3
0
0
1
0
2
0
2
0
0
2
1
2
0
2
0
1
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
3
0
0
1
2
3
0
0
0
3
2
1
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
1
0
4
4
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
9
0
0
0
1
0
0
0
0
0
2
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
2
1
0
0
0
0
2
2
2
0
0
1
0
2
1
2
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
2
0
2
1
0
0
2
1
0
7
0
0
0
0
0
3
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
2
0
1
0
0
0
0
2
0
0
1
1
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
5
0
0
0
1
0
0
0
3
1
1
0
1
0
0
1
0
0
0
0
1
1
1
0
0
0
1
1
2
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
8
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
2
1
2
1
0
0
0
3
0
0
1
0
2
0
1
0
1
2
0
0
0
1
0
0
1
1
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
6
0
0
0
2
2
0
0
0
0
0
0
2
1
0
1
0
0
0
0
1
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
2
0
3
0
0
0
0
1
2
2
0
1
1
2
0
0
0
0
2
0
0
5
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
1
1
0
1
0
0
0
2
2
0
0
0
0
2
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
1
0
0
0
6
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
1
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
1
8
0
0
0
0
0
2
0
0
1
0
2
0
0
0
1
0
0
1
0
0
2
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
2
1
0
0
2
0
1
6
2
0
1
7
0
0
1
0
1
0
2
1
0
0
1
0
0
0
0
2
0
0
0
2
2
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
7
1
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
2
2
3
0
0
0
0
1
0
2
2
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
2
0
0
0
0
0
5
0
0
0
0
2
0
1
0
0
0
1
0
0
0
2
3
0
0
0
2
1
0
0
0
2
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
2
1
0
2
0
0
2
0
1
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
3
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
3
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
1
2
1
0
2
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
1
1
0
1
1
0
0
1
1
0
0
0
1
2
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
1
2
2
0
0
0
1
4
3
0
0
2
0
0
0
2
0
2
0
3
2
0
0
0
1
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
2
1
0
0
2
0
0
0
0
0
3
1
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
3
1
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
1
1
0
0
2
0
0
2
0
0
3
0
0
2
0
0
0
0
0
1
0
0
0
2
0
2
0
2
0
0
1
0
0
0
0
0
1
0
0
0
2
1
2
1
0
0
2
0
0
0
0
2
0
1
1
1
0
0
2
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
2
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
2
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
1
1
2
0
0
1
0
0
0
1
1
0
0
2
1
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
2
0
0
0
0
0
1
0
1
0
1
1
0
2
0
0
0
0
2
2
0
1
3
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
1
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
2
2
0
0
0
0
1
0
1
1
2
0
1
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
3
0
0
0
0
0
5
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
2
2
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
2
2
0
0
1
0
2
0
2
0
0
0
0
0
1
0
1
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
3
1
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
1
0
2
2
0
1
0
2
0
2
0
0
0
0
3
0
1
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
1
0
2
0
0
0
1
0
0
2
2
1
0
2
2
1
0
1
2
0
5
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
1
4
1
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
2
2
0
1
0
0
0
0
0
3
0
0
0
1
1
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
1
0
1
2
0
1
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
2
2
0
0
2
0
0
1
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
2
1
0
0
0
2
1
0
0
0
0
2
0
2
0
0
0
0
0
1
2
2
0
0
0
0
0
0
1
0
0
0
0
1
0
2
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
3
0
0
0
0
2
2
1
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
2
2
2
0
1
0
0
0
0
0
0
0
1
2
0
0
1
2
0
1
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
4
0
1
0
0
1
0
0
1
0
1
0
1
0
2
0
4
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
1
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
1
0
0
2
0
1
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
2
1
1
0
0
2
1
0
0
0
0
2
0
2
0
0
0
1
2
1
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
4
2
1
0
0
0
2
0
0
0
2
0
5
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
2
0
2
0
0
3
0
0
0
5
0
2
0
0
0
2
1
0
2
0
2
1
2
1
0
1
1
2
0
0
0
0
0
0
2
0
3
2
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
1
0
0
0
0
1
2
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
2
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
2
3
0
0
0
5
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
5
0
0
2
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
3
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
2
1
0
2
1
2
0
0
0
0
0
0
0
0
0
4
0
0
2
3
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
2
1
0
0
1
1
1
0
0
1
0
1
0
2
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
1
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
1
0
2
0
3
0
0
0
0
4
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
6
1
0
1
1
0
5
2
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
3
0
3
1
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
3
2
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
2
1
1
1
0
2
1
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
2
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
2
1
1
0
0
2
0
4
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
1
2
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
6
0
1
0
0
0
1
0
1
1
1
0
1
0
0
0
1
0
0
4
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
1
2
0
0
1
0
0
1
1
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
2
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
2
0
2
1
0
0
1
0
1
0
0
2
2
0
0
0
0
0
0
0
2
0
0
1
3
0
1
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
1
0
2
1
1
0
0
3
2
2
0
0
0
5
2
2
0
2
1
0
0
0
0
1
0
0
0
0
0
0
2
3
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
2
1
0
0
0
2
0
0
0
1
0
1
2
0
0
1
2
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
4
0
0
0
1
1
0
0
0
0
0
0
0
0
3
1
2
0
0
2
0
2
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
2
0
0
6
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
2
1
2
0
0
0
2
0
0
1
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
1
1
0
0
1
0
0
0
0
3
0
0
0
2
0
1
0
1
1
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
3
2
1
0
2
0
2
2
0
0
0
0
0
0
0
2
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
2
0
3
2
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
1
1
2
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
2
1
0
0
0
0
2
0
2
0
1
0
0
0
2
0
0
0
0
2
0
0
0
2
0
2
0
0
0
2
1
2
0
1
0
0
0
0
0
3
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
1
0
0
0
1
0
0
1
1
1
2
0
2
0
0
2
2
0
1
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
3
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
3
0
0
0
1
0
0
0
1
0
0
0
0
0
1
2
2
0
0
1
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
1
0
1
4
0
0
0
1
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
2
0
0
4
0
0
2
0
0
2
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
1
0
0
0
0
0
2
0
1
0
1
0
0
1
0
3
0
2
1
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
2
2
2
1
0
0
1
0
1
0
0
0
0
1
0
0
1
2
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
2
0
3
1
0
1
0
0
0
0
0
0
3
0
1
0
1
1
0
0
0
0
0
0
5
0
0
3
0
1
2
1
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
5
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
2
0
0
3
1
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
1
0
2
0
2
3
0
1
1
0
0
0
0
0
1
0
1
0
1
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
4
0
0
0
2
0
0
2
0
1
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
2
0
0
0
2
0
0
0
0
1
0
0
2
2
0
0
0
1
0
2
2
0
0
0
1
0
2
1
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
2
1
2
0
0
0
0
0
0
1
0
1
1
0
2
1
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
2
0
0
0
3
0
0
0
2
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
1
0
1
1
2
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
3
2
1
2
2
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
2
1
0
0
0
0
1
0
1
1
1
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
2
2
0
2
6
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
4
0
0
0
4
0
0
2
0
0
2
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
3
2
0
0
0
0
2
0
0
0
1
0
0
1
0
0
2
0
0
1
2
1
0
0
0
0
1
0
0
0
3
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
3
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
1
0
2
1
1
0
1
3
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
1
1
0
0
0
0
3
3
0
0
0
0
1
0
1
0
0
3
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
2
0
5
0
0
0
2
0
3
2
0
1
0
2
0
3
0
0
0
1
2
0
1
1
0
0
0
0
0
0
1
2
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
1
0
0
0
3
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
10
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
2
1
2
0
0
0
2
0
0
2
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
2
1
0
1
1
0
0
1
0
0
1
0
0
0
2
0
0
2
0
0
1
1
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
1
0
0
0
0
0
0
1
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
1
2
0
1
0
2
0
0
2
0
3
0
0
0
0
0
2
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
1
0
1
1
0
0
2
0
0
2
0
0
1
2
0
0
0
0
0
0
1
0
0
0
1
1
2
2
2
0
0
1
0
0
1
1
1
4
2
0
0
0
0
0
2
0
2
3
0
2
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
4
0
2
3
1
0
0
0
0
0
0
1
1
0
3
0
0
2
0
2
0
0
2
0
0
2
2
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
2
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
3
1
0
1
0
2
0
0
2
0
1
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
2
0
0
0
2
1
0
0
1
0
0
0
0
2
1
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
1
0
1
2
0
0
0
3
3
0
0
0
0
0
0
1
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
2
2
0
0
0
3
2
2
2
0
1
0
2
0
0
0
1
0
2
1
5
1
0
0
0
1
0
1
4
0
0
0
0
0
0
2
1
2
2
0
0
0
0
0
0
0
1
0
3
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
2
2
0
1
1
0
0
2
0
0
0
2
0
0
2
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
1
2
0
2
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
9
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
2
3
1
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
2
1
1
0
2
0
2
0
2
0
0
0
1
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
5
2
0
1
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
4
0
0
2
0
0
1
0
0
0
2
0
0
2
0
0
0
1
2
0
0
0
0
1
0
0
0
0
2
1
0
0
3
3
0
0
1
2
0
4
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
2
0
1
6
0
0
1
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
31
1
1
3
0
0
0
0
0
0
0
0
2
0
0
2
3
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
1
0
1
0
1
0
0
2
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
2
0
1
1
0
0
0
0
0
2
3
1
0
0
0
0
0
0
1
3
0
1
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
2
0
0
2
2
2
1
0
2
2
0
1
0
0
0
0
2
0
1
0
0
0
1
4
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
3
0
1
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
2
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
2
1
0
2
0
2
2
1
0
1
2
0
2
1
0
2
1
0
0
0
0
0
0
0
1
0
0
1
1
2
2
2
1
0
0
0
1
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
2
2
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
3
2
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
1
0
1
0
0
1
0
0
3
0
0
0
2
0
1
0
1
0
0
1
0
1
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
2
0
0
0
0
0
1
0
2
1
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
2
2
0
0
0
0
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
1
1
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
2
2
1
0
0
0
0
0
0
0
0
1
0
0
2
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
2
0
1
0
0
2
0
1
0
0
1
0
3
2
2
0
3
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
1
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
1
1
5
0
0
0
0
1
0
2
2
5
0
4
0
0
0
0
4
0
2
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
1
1
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
2
0
0
1
1
0
1
0
4
0
0
0
0
2
0
0
2
0
1
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
1
0
2
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
2
1
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
5
0
0
0
1
0
0
0
1
0
0
3
0
1
0
1
0
0
0
0
0
0
0
0
0
1
2
2
0
3
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
1
0
0
3
0
1
0
2
0
2
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
2
1
0
0
0
2
0
2
0
0
0
2
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
3
3
0
0
0
0
1
2
0
2
1
0
0
0
0
0
0
0
1
2
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
2
2
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
2
0
0
1
3
0
0
0
2
0
0
1
0
0
1
0
1
0
0
1
0
0
0
1
0
1
4
1
0
0
0
2
0
4
0
0
0
0
0
0
2
2
0
0
0
0
2
2
0
2
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
7
0
0
0
0
0
1
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
3
0
0
2
0
0
1
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
3
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
2
2
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
2
0
0
9
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
2
1
0
1
0
0
1
1
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
4
0
0
2
3
0
0
1
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
2
0
2
0
2
0
2
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
6
3
0
1
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
1
0
0
1
0
0
1
0
0
1
2
0
0
0
0
0
0
2
2
0
5
0
0
0
3
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
1
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
2
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
2
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
1
1
1
2
0
0
0
1
2
0
0
0
1
1
0
0
0
0
1
0
0
0
0
2
0
1
0
1
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
2
0
0
2
0
0
0
0
1
0
2
0
0
0
1
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
3
2
4
0
1
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
1
0
0
1
2
0
0
0
0
2
0
2
0
0
0
0
3
0
0
0
1
2
0
1
1
0
0
1
1
0
0
0
2
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
3
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
2
0
1
1
1
0
0
0
1
0
0
0
2
1
0
2
0
0
0
0
1
1
0
2
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
2
1
0
1
1
0
0
1
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
4
2
1
0
0
0
0
2
0
2
1
3
1
1
0
1
0
0
3
0
0
2
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
2
1
0
0
2
1
0
0
2
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
2
0
9
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
1
1
2
2
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
3
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
2
1
1
0
0
0
0
0
1
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
3
2
1
1
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
3
3
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
3
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
2
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
4
0
0
0
2
0
0
1
1
1
2
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
2
1
0
3
0
3
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
1
0
1
0
2
1
4
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
5
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
1
0
1
0
2
0
0
3
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
5
4
1
0
0
0
0
0
0
0
0
2
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
2
2
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
1
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
2
6
0
0
1
0
0
0
0
0
1
2
0
1
0
1
4
2
0
0
0
0
2
0
1
1
0
0
0
2
1
0
0
0
1
0
0
0
0
2
0
2
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
2
1
0
2
0
2
2
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
2
0
0
0
0
0
1
0
1
2
1
0
0
0
0
2
1
0
0
1
0
0
0
0
0
2
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
1
2
1
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
1
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
1
2
1
0
0
0
0
0
0
0
2
1
0
1
1
2
0
0
1
0
1
0
0
0
0
1
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
1
0
2
0
0
1
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
2
1
0
0
0
0
0
0
0
3
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
2
0
0
1
0
1
1
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
2
0
5
0
0
1
0
0
0
0
1
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
1
2
0
0
0
1
1
0
0
0
0
0
0
3
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
1
2
0
0
0
0
1
0
2
1
2
0
0
1
1
0
0
0
2
0
0
1
0
2
0
0
0
0
0
1
1
2
0
0
5
1
1
0
0
0
1
0
0
2
2
3
0
0
2
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
2
2
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
1
2
5
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
1
2
0
0
0
0
2
2
0
1
0
0
0
0
2
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
3
0
2
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
2
0
1
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
3
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
1
0
0
0
1
1
0
2
0
0
0
1
0
0
0
1
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
1
0
0
1
2
0
0
0
0
2
0
0
1
0
1
1
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
2
0
0
0
1
0
2
0
0
0
0
1
0
1
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
3
0
0
0
2
0
0
0
0
0
0
0
3
0
0
2
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
3
0
0
2
2
2
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
2
1
0
0
0
0
0
1
1
1
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
2
0
1
0
0
1
0
1
0
0
0
2
4
0
0
1
1
1
2
0
0
0
0
1
2
2
0
0
6
0
0
1
2
1
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
3
0
0
0
3
0
2
0
0
2
0
1
0
0
0
0
0
0
0
3
1
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
1
2
1
0
0
0
0
0
0
2
0
0
1
0
0
1
2
0
0
0
0
0
0
0
2
0
2
0
2
0
1
0
1
2
0
0
0
0
2
1
1
0
1
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
1
0
0
2
3
1
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
9
0
0
2
2
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
3
3
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
3
0
0
0
0
0
2
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
11
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
2
1
0
1
0
0
0
1
0
2
4
1
0
0
0
0
0
0
0
2
1
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
1
0
2
0
0
0
2
1
0
0
0
2
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
2
0
0
3
3
0
2
0
1
4
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
2
0
0
0
0
0
0
0
1
2
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
2
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
1
0
1
0
1
1
0
0
1
2
0
2
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
11
0
1
0
1
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
1
1
0
0
0
5
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
1
0
2
0
1
1
0
0
0
1
0
0
2
2
1
2
0
0
2
0
2
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
2
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
3
0
1
0
0
0
0
3
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
2
1
0
3
0
1
0
2
0
0
0
0
0
0
1
0
0
1
0
0
1
2
0
0
2
1
0
2
0
0
0
1
0
0
0
4
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
2
0
1
0
0
2
0
2
1
0
0
0
2
0
0
3
0
0
1
0
2
2
0
0
2
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
1
2
0
1
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
1
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
2
0
0
0
0
0
2
1
1
0
2
0
0
0
0
0
0
0
2
0
2
0
5
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
5
0
2
0
0
0
0
0
0
0
2
1
0
0
1
0
2
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
2
0
1
1
2
2
2
1
0
0
0
2
0
0
0
2
0
0
1
0
0
2
2
2
1
2
1
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
1
0
1
0
0
0
2
0
1
0
0
0
2
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
2
0
3
0
2
0
0
0
0
0
1
0
0
3
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
1
0
1
0
1
0
3
0
0
0
0
0
0
1
0
0
4
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
1
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
2
2
0
0
2
2
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
3
0
0
0
1
0
0
0
0
1
4
1
0
0
0
0
0
4
2
0
0
0
1
3
0
0
0
0
0
0
0
2
6
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
3
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
1
1
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
3
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
2
2
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
2
2
1
0
2
0
2
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
2
2
0
0
2
0
2
0
0
0
1
0
0
0
0
0
1
0
5
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
2
0
2
1
0
2
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
2
2
0
0
0
1
0
0
1
0
2
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
2
1
1
0
0
0
0
0
4
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
2
0
0
3
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
3
2
1
0
0
1
0
2
0
0
1
2
0
0
0
1
0
2
2
0
0
0
0
0
1
0
0
0
0
0
3
0
0
1
0
0
2
0
0
0
0
1
0
1
1
0
0
2
0
4
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
3
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
2
5
0
0
0
2
0
0
1
0
0
0
3
0
1
0
1
0
1
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
2
0
0
0
0
0
1
0
0
0
0
0
2
0
6
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
3
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
2
0
1
0
1
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
1
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
2
2
1
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
5
0
3
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
2
2
1
0
1
0
0
0
0
0
0
1
0
2
1
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
3
0
1
0
0
1
0
3
0
0
1
1
0
0
3
2
0
0
0
4
2
0
0
0
0
2
0
6
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
1
1
1
0
0
0
2
0
0
0
1
0
2
0
2
2
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
2
1
2
1
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
2
0
0
1
0
3
0
0
0
0
0
2
0
0
0
0
1
0
0
1
2
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
1
4
0
0
3
0
0
4
0
0
0
0
0
1
1
0
0
0
0
0
5
0
0
0
0
0
1
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
3
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
1
0
1
2
3
0
0
0
0
1
2
0
1
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
1
0
1
0
1
0
0
1
2
0
0
0
2
2
0
0
0
0
0
3
0
2
0
1
0
2
2
0
2
3
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
3
0
0
1
2
3
2
0
0
3
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
2
1
0
1
1
0
0
0
0
0
4
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
1
0
2
1
0
2
3
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
4
1
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
2
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
3
0
2
0
1
0
0
2
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
2
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
2
0
0
0
0
1
0
0
0
2
2
0
2
0
0
1
1
1
0
3
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
1
2
0
0
0
1
0
0
0
1
1
1
0
1
0
0
0
0
4
2
0
0
1
1
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
2
2
0
0
0
0
2
2
0
1
0
0
0
0
2
2
2
0
0
0
0
0
0
0
2
1
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
1
2
0
1
0
1
0
2
0
2
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
2
2
0
0
2
0
2
0
0
0
0
0
1
2
0
0
1
0
1
0
0
0
2
0
1
1
0
0
2
0
1
0
0
0
1
0
0
0
2
2
2
0
1
2
0
0
1
0
0
0
0
0
0
1
2
0
1
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
2
0
3
0
3
0
1
1
0
0
0
2
0
0
7
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
2
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
2
1
1
1
2
2
2
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
2
1
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
2
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
1
0
2
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
2
1
2
0
2
0
1
2
0
2
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
2
0
2
3
1
0
1
2
0
0
0
2
0
0
2
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
3
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
6
1
0
1
1
1
0
0
0
0
1
0
2
2
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
2
4
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
2
2
0
1
0
1
0
0
0
0
1
0
2
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
1
0
1
0
0
2
3
1
0
0
1
1
1
0
0
0
0
0
0
0
0
2
0
2
3
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
2
6
0
0
4
0
0
0
1
0
0
5
0
0
0
0
1
0
0
3
0
0
2
0
0
0
1
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
4
0
0
2
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
2
1
0
1
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
2
0
0
0
1
0
0
0
2
0
0
0
0
0
6
0
1
0
0
1
0
0
0
2
0
0
1
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
2
0
2
0
2
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
2
0
0
0
0
1
0
1
1
2
0
3
0
2
0
0
2
1
0
2
0
2
2
0
2
0
0
0
0
0
0
2
0
2
2
0
0
0
0
2
0
0
0
5
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
2
0
0
1
0
0
1
2
0
0
1
0
0
1
0
0
0
0
0
2
13
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
2
0
0
0
2
0
0
0
0
0
1
0
0
1
0
1
0
0
0
2
0
4
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
2
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
2
2
1
0
0
0
0
0
0
0
0
0
3
0
1
0
1
0
1
0
3
0
0
0
1
0
0
0
0
0
0
0
3
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
1
0
0
1
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
2
1
0
1
0
0
2
0
2
2
0
3
0
0
0
1
0
0
0
2
0
0
2
0
0
0
3
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
3
0
2
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
1
2
0
1
0
1
0
0
0
0
1
2
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
2
1
0
1
0
0
0
3
0
0
0
0
0
2
0
0
0
3
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
2
1
0
0
3
2
0
3
0
0
0
0
2
0
2
0
0
1
0
0
0
0
2
1
0
0
2
2
3
0
1
2
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
1
2
1
0
0
0
0
1
0
10
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
1
1
0
1
2
0
0
0
1
2
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
2
0
0
0
0
2
2
1
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
1
2
2
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
4
0
1
5
0
0
2
2
0
0
0
0
0
0
4
0
0
0
3
0
4
2
1
0
0
0
0
1
2
0
2
0
0
0
0
3
0
0
0
0
0
0
0
1
4
0
0
2
2
1
0
1
0
0
0
0
0
1
2
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
1
0
0
0
1
0
1
0
0
1
0
0
7
0
0
0
1
0
2
1
2
0
1
0
0
0
0
0
0
0
2
0
1
3
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
2
0
0
2
0
0
0
2
2
0
0
0
0
1
0
2
2
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
2
0
1
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
2
0
0
2
0
3
0
0
0
0
0
0
2
2
1
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
3
0
0
0
3
1
0
0
0
0
1
1
0
1
0
0
1
0
0
0
2
0
0
2
1
0
2
0
0
0
1
0
2
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
1
0
1
2
2
1
0
0
0
0
0
0
5
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
3
0
1
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
2
0
1
0
0
0
0
2
2
0
0
0
0
0
0
4
0
0
0
0
1
1
1
0
1
0
0
1
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
2
2
1
1
1
0
0
1
0
0
0
2
0
0
0
2
0
1
0
0
0
0
1
0
0
1
0
0
2
2
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
2
0
0
1
0
0
0
0
2
0
3
0
0
2
2
2
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
2
0
1
0
0
0
2
0
2
2
0
0
2
0
0
0
0
0
0
4
0
0
0
1
0
2
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
1
2
0
2
0
0
0
0
0
0
1
2
0
1
0
0
2
0
2
0
0
1
1
0
1
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
3
0
2
0
2
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
2
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
4
0
0
0
0
0
0
2
0
2
0
0
0
0
0
5
1
2
1
2
0
0
0
1
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
2
2
1
2
0
3
0
1
5
1
2
1
2
2
0
0
0
0
0
2
0
2
0
2
0
0
2
0
0
0
2
2
0
1
0
2
0
0
1
0
0
0
0
5
1
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
1
0
0
0
2
0
2
0
0
0
0
1
4
0
0
0
0
2
0
0
1
0
0
1
2
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
3
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
2
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
6
1
0
2
2
2
0
0
1
0
0
2
0
2
0
0
0
0
1
1
2
0
1
1
1
2
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
4
0
4
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
2
0
1
0
1
0
0
0
4
0
0
0
3
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
2
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
2
0
1
1
0
2
0
2
0
2
0
0
0
1
0
0
0
1
2
0
0
0
0
2
0
0
1
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
2
0
5
0
2
0
2
0
7
0
0
0
0
2
0
0
0
1
0
2
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
2
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
2
1
0
0
0
2
1
0
2
0
0
0
2
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
4
2
0
0
0
1
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
1
0
1
2
0
0
3
0
0
1
0
1
3
0
1
1
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
2
0
3
0
1
2
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
3
0
1
0
0
0
1
1
0
2
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
1
0
2
0
1
1
0
0
4
1
0
1
0
0
3
2
0
0
0
0
0
1
0
0
2
2
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
1
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
3
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
1
0
1
0
0
1
2
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
3
0
0
0
0
0
1
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
1
0
2
0
0
2
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
2
1
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
2
2
0
0
0
0
0
0
0
3
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
2
1
2
0
2
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
1
2
0
0
1
0
1
0
0
0
0
8
0
1
0
2
0
0
1
0
0
0
0
1
2
2
0
0
1
0
0
0
0
0
0
0
6
0
0
1
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
2
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
2
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
2
3
2
0
1
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
1
0
0
0
1
2
2
0
2
0
0
0
1
0
0
2
0
0
1
1
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
2
2
2
2
0
0
0
1
0
0
0
1
1
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
6
9
0
0
0
1
0
0
0
0
2
2
0
1
2
0
0
0
0
1
0
1
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
2
0
2
3
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
1
0
0
0
0
0
0
0
1
2
2
0
0
0
0
1
2
0
0
0
1
1
1
1
0
0
0
2
2
0
0
1
3
0
1
0
2
1
0
0
5
0
1
1
1
0
0
0
1
0
2
0
2
0
0
0
0
2
1
1
1
1
1
1
2
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
2
3
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
1
0
0
0
2
0
0
0
0
0
3
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
3
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
3
2
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
4
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
1
0
2
0
0
1
0
0
0
1
0
0
0
6
0
0
0
0
3
0
0
1
0
1
0
2
0
0
0
1
2
0
0
0
0
0
2
0
0
1
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
12
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
2
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
2
0
0
1
0
2
0
0
2
2
0
0
0
0
4
2
0
2
1
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
1
0
1
2
0
0
2
1
0
0
2
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
1
1
0
0
1
1
0
0
0
2
3
0
0
1
2
0
0
1
0
0
0
0
0
1
0
0
0
2
2
2
2
0
0
1
0
0
0
2
4
0
0
0
1
2
1
1
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
4
1
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
1
2
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
3
0
2
0
2
0
5
1
1
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
1
1
0
1
0
0
0
0
2
0
0
2
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
2
0
0
4
0
1
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
1
0
2
2
0
0
1
0
2
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
3
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
2
2
1
0
3
0
1
0
0
0
0
0
1
0
2
2
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
2
1
0
1
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
4
2
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
3
0
0
0
1
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
3
1
1
0
2
0
2
0
0
0
0
1
1
0
0
2
1
0
0
0
0
0
2
0
0
1
1
0
0
2
0
1
0
0
0
7
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
1
2
1
0
0
1
0
2
4
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
2
2
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
5
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
1
2
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
2
0
3
0
1
1
1
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
2
0
3
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
1
0
0
2
2
0
0
0
0
0
7
0
0
2
0
0
0
2
0
0
0
0
0
2
0
3
0
0
0
0
0
1
0
0
0
1
0
2
1
1
0
7
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
3
1
0
0
0
1
0
0
0
3
0
0
0
0
0
0
1
1
0
1
2
1
1
0
1
0
0
1
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
1
0
2
0
0
0
0
2
0
0
2
0
1
0
1
0
2
2
1
0
0
0
0
1
0
4
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
3
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
2
2
0
2
0
0
0
1
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
2
0
5
0
1
0
0
1
0
2
0
0
0
0
0
0
1
0
2
2
0
1
0
1
0
0
1
0
1
0
0
0
1
4
2
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
5
2
0
0
0
0
0
0
0
0
1
1
1
0
1
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
4
0
0
1
0
0
0
0
0
0
0
2
0
2
0
1
0
3
0
0
0
1
1
0
1
0
0
0
0
1
1
0
0
0
3
0
2
2
0
4
2
0
2
0
0
2
0
1
0
1
0
0
1
0
2
1
0
2
0
0
0
0
0
1
2
0
1
1
0
1
1
2
0
0
0
2
0
0
0
0
0
0
1
0
1
1
0
0
0
2
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
5
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
3
0
0
0
2
3
0
0
0
0
2
0
0
0
2
0
0
1
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
1
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
1
0
0
0
0
1
0
0
2
1
0
0
1
3
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
2
0
0
2
0
0
0
0
0
2
0
0
0
2
0
2
1
1
1
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
1
1
0
2
1
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
2
2
1
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
1
2
0
2
0
0
0
0
0
1
0
0
0
0
1
1
0
1
2
0
0
1
0
0
0
0
0
1
2
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
3
0
0
0
2
0
0
1
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
1
0
2
0
0
0
0
0
0
1
2
0
0
0
1
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
3
2
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
2
2
2
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
2
0
1
0
0
0
3
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
1
1
1
0
0
0
0
0
0
0
3
0
1
0
0
0
0
2
1
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
4
0
0
1
1
0
1
0
1
0
2
0
1
0
0
0
0
2
2
3
1
2
0
0
1
0
0
0
0
2
2
2
0
1
1
0
1
1
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
2
1
1
0
0
0
0
1
2
2
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
1
2
1
1
0
0
0
0
1
1
1
0
1
0
1
0
0
0
2
2
0
0
0
2
2
0
0
7
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
1
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
3
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
1
0
0
0
0
0
2
2
2
0
2
0
2
0
1
0
0
0
0
0
0
0
3
0
0
0
1
0
0
1
0
0
2
0
0
0
0
3
1
0
0
0
0
0
4
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
2
0
0
0
0
1
1
0
1
0
1
0
0
1
0
0
1
0
0
0
0
3
1
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
2
3
2
1
0
3
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
2
0
0
2
1
0
0
2
3
0
0
1
0
3
0
2
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
6
0
0
0
2
0
2
0
0
0
1
0
0
0
0
1
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
1
0
1
0
2
0
0
0
2
2
0
0
0
0
0
2
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
1
0
0
0
2
1
2
0
0
1
0
0
0
2
2
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
2
4
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
4
0
1
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
1
0
2
1
2
0
0
0
0
0
0
2
1
0
3
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
2
0
1
0
2
3
1
0
0
0
0
0
0
2
1
0
0
0
2
0
1
0
0
1
1
2
0
0
0
0
0
0
0
3
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
2
0
1
1
3
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
2
1
0
2
2
0
1
0
1
0
0
1
0
2
0
2
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
2
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
1
3
1
2
0
1
1
0
2
1
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
2
3
0
0
2
0
0
0
0
1
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
4
0
0
0
0
0
2
2
0
2
0
0
0
2
0
2
1
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
3
0
1
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
2
0
0
3
0
0
0
1
0
2
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
2
2
2
2
6
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
2
0
1
1
0
0
1
0
2
0
2
0
0
0
0
0
4
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
2
0
1
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
1
1
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
2
1
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
3
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
1
3
0
0
0
0
0
3
2
1
1
1
0
0
0
0
1
1
0
1
1
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
2
1
0
0
2
0
0
1
0
5
1
2
1
0
2
0
0
2
0
0
0
0
0
0
1
1
2
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
2
2
0
0
2
0
2
0
2
1
2
2
0
0
0
0
0
2
0
0
0
0
0
2
2
0
1
1
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
3
0
1
0
2
2
0
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
4
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
1
2
3
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
1
0
0
3
2
2
0
0
2
1
0
0
1
0
2
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
3
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
5
0
0
0
0
0
0
1
2
1
1
0
0
2
0
2
0
1
2
2
0
0
4
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
2
0
2
0
1
1
0
0
0
0
1
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
3
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
0
0
0
0
1
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
1
1
0
0
1
0
2
0
0
2
2
0
1
2
0
2
2
0
0
0
0
2
1
0
2
0
1
0
0
0
0
1
1
0
0
2
0
0
0
0
1
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
2
0
1
3
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
1
0
1
0
3
0
0
0
3
0
0
2
2
0
2
0
3
0
2
0
0
0
0
1
0
4
0
0
1
4
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
2
2
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
2
2
1
0
1
2
0
0
0
4
0
0
2
0
0
1
1
0
1
0
0
1
0
0
0
7
0
0
0
0
0
1
0
0
0
2
1
2
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
1
1
0
0
2
0
1
2
0
1
1
0
2
0
3
0
2
2
0
1
0
2
0
0
0
0
1
0
0
1
1
0
1
0
2
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
4
1
0
1
1
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
7
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
3
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
1
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
2
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
4
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
1
0
0
1
0
0
2
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
1
0
0
1
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
5
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
2
0
0
4
0
0
2
0
0
0
4
0
3
0
3
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
1
0
0
2
0
0
0
2
0
0
0
1
2
0
0
0
0
1
1
2
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
1
5
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
2
0
4
0
0
2
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
5
0
0
0
1
0
0
0
1
2
3
1
0
0
0
0
1
1
0
0
1
0
13
0
2
1
0
0
0
2
1
0
0
1
0
0
0
0
1
1
3
0
0
0
0
1
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
3
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
5
0
1
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
2
2
0
1
0
0
0
0
1
0
0
1
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
1
0
0
1
2
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
5
0
0
0
0
0
0
1
0
0
0
1
5
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
2
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
2
1
0
2
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
1
2
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
2
6
1
0
2
0
2
2
9
0
2
0
0
0
0
0
2
1
1
1
3
0
1
2
0
0
1
0
1
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
1
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
3
2
0
3
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
2
2
0
0
2
0
0
0
2
2
0
0
0
0
0
3
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
2
0
1
0
2
3
0
0
0
0
2
0
1
1
0
0
0
0
3
2
2
1
0
0
2
1
1
0
0
0
4
0
0
2
0
0
0
2
0
2
0
2
2
0
1
0
1
0
0
0
0
0
0
0
0
3
0
1
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
3
0
4
2
0
1
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
3
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
1
1
0
2
0
2
0
0
0
0
0
0
0
2
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
4
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
2
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
1
0
1
0
0
0
0
0
2
2
3
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
5
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
2
0
2
1
0
0
2
0
0
1
0
0
1
2
0
0
0
0
4
0
2
0
0
0
1
0
0
2
0
1
1
0
1
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
4
3
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
2
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
1
3
2
0
6
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
3
0
3
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
2
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
2
0
0
2
5
2
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
1
0
2
1
0
1
0
0
0
0
0
2
0
0
0
1
2
3
0
0
0
1
0
0
0
0
0
0
1
2
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
2
0
0
1
0
0
0
0
0
3
0
3
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
1
1
0
6
0
1
1
0
0
2
0
2
0
2
2
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
7
0
2
2
0
0
0
0
2
0
1
0
0
2
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
2
0
0
4
0
0
0
0
0
0
1
0
0
0
2
0
0
2
1
0
0
2
2
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
3
0
0
0
0
1
1
1
0
0
0
1
1
0
0
0
0
1
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
2
2
0
1
0
1
2
0
0
0
0
0
2
0
1
1
1
0
0
0
2
1
0
0
2
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
0
2
2
0
2
0
0
2
0
1
0
0
2
3
3
0
1
0
1
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
3
0
0
0
0
2
2
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
2
2
1
0
1
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
1
0
4
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
1
0
0
0
3
0
0
0
0
1
2
0
0
1
1
1
0
0
2
0
2
1
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
3
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
3
1
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
2
0
0
3
0
2
1
2
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
2
2
0
0
0
1
0
0
2
0
0
0
0
1
4
2
1
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
4
1
0
2
0
0
0
0
1
1
0
2
0
0
0
0
0
1
2
2
0
0
2
0
0
1
2
0
1
1
2
0
0
0
0
4
0
0
0
0
1
0
1
0
0
0
0
0
0
1
2
0
2
0
0
0
1
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
2
1
0
1
0
2
0
0
1
0
0
0
2
0
0
0
1
2
0
0
0
0
2
0
1
2
5
0
0
0
0
0
1
0
2
1
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
2
2
0
1
2
0
0
0
0
0
2
0
0
1
0
3
0
0
0
0
1
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
3
0
0
0
0
0
0
0
2
2
0
0
2
2
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
1
1
2
0
0
2
1
0
0
2
0
0
1
0
0
1
0
1
0
1
3
4
0
0
0
0
2
3
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
3
0
0
1
0
0
0
0
1
2
1
0
2
0
1
2
1
0
2
0
0
0
0
0
2
0
0
1
1
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
2
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
1
0
0
0
0
0
1
1
0
2
0
0
1
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
2
1
0
0
0
0
0
0
1
2
0
0
1
0
1
0
0
0
1
0
0
1
0
0
3
1
2
0
0
0
2
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
2
0
4
1
0
0
1
3
1
2
0
0
3
0
0
0
0
1
1
0
2
0
0
0
2
1
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
1
2
0
2
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
3
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
2
1
4
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
4
0
2
0
0
0
0
2
1
0
1
1
0
2
0
0
0
0
1
1
0
2
0
1
0
2
0
0
0
0
0
1
2
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
1
0
0
0
1
0
0
2
2
0
3
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
10
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
3
0
0
0
0
1
2
0
0
5
0
2
2
1
0
0
0
0
0
0
2
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
2
2
2
3
0
0
0
2
0
3
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
2
1
0
0
0
4
1
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
3
1
0
3
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
2
1
2
0
0
0
0
0
0
2
0
0
2
1
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
2
0
6
0
1
2
0
0
0
0
0
0
2
1
0
0
0
3
0
0
0
2
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
4
0
1
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
2
1
0
0
1
0
0
0
0
0
0
1
0
2
0
2
2
0
0
2
0
0
2
2
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
1
0
2
0
0
0
0
0
2
7
0
0
0
0
0
2
0
0
0
1
1
0
4
0
0
2
0
0
0
0
0
0
6
0
0
3
0
0
0
0
0
2
1
0
0
0
1
0
1
2
0
3
3
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
1
0
0
0
0
0
0
4
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
3
0
2
0
0
1
1
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
1
1
2
3
0
1
0
1
0
0
0
0
0
2
1
2
0
1
0
1
0
0
0
0
0
5
0
2
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
1
0
0
1
0
0
2
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
2
0
2
0
1
1
0
1
0
2
3
2
0
0
2
0
5
3
1
2
0
0
0
0
1
0
0
1
0
1
1
2
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
2
0
0
1
1
0
0
0
5
2
0
0
1
0
0
1
0
1
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
2
2
0
1
0
1
0
0
0
1
2
0
2
0
0
0
0
3
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
8
3
2
1
0
1
1
0
0
0
1
0
0
2
1
0
2
1
0
6
0
2
2
1
0
0
2
1
0
2
2
1
0
2
0
2
0
0
0
0
2
1
0
2
0
0
0
0
0
1
0
0
0
0
1
0
1
1
3
0
0
0
0
2
0
1
0
0
0
2
0
1
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
2
0
1
1
2
1
0
0
3
0
0
0
1
0
0
1
1
1
0
1
0
0
0
0
0
1
2
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
2
0
1
0
4
0
0
0
0
0
0
1
2
0
1
2
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
6
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
3
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
2
0
0
0
1
0
1
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
2
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
4
2
0
2
0
0
0
0
0
2
0
1
4
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
2
0
1
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
1
1
1
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
3
2
2
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
4
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
1
2
3
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
1
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
2
0
0
0
2
0
0
3
0
0
0
0
0
4
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
2
0
2
0
1
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
4
2
0
0
0
0
0
0
0
1
2
2
2
2
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
4
1
0
0
0
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
10
2
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
1
0
1
1
0
0
1
0
2
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
1
1
1
0
2
0
2
2
0
0
0
3
0
0
3
1
0
1
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
1
0
1
0
1
0
1
0
0
0
1
2
0
1
0
0
0
0
1
0
2
2
0
0
2
1
0
0
1
2
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
2
0
2
1
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
3
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
2
0
1
1
0
0
2
1
0
0
0
0
0
0
2
0
0
1
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
3
1
1
0
2
0
0
0
0
1
2
0
0
0
0
1
0
0
2
0
0
0
2
0
0
1
0
2
0
0
0
0
0
2
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
1
0
0
0
1
0
1
0
1
2
0
0
0
0
0
2
0
0
1
0
2
0
1
1
0
0
0
1
0
0
2
0
1
0
2
0
0
3
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
2
0
2
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
3
1
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
4
0
1
0
0
0
0
0
0
0
2
0
2
0
1
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
2
0
1
0
0
0
0
4
0
2
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
1
0
0
0
0
1
0
1
0
2
0
0
0
0
1
0
2
0
1
0
0
0
1
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
3
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
3
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
8
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
2
1
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
2
1
0
0
1
0
0
0
0
0
0
1
0
3
0
0
2
1
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
2
2
0
0
1
0
0
2
1
0
0
0
0
3
0
1
0
0
1
0
0
0
0
1
0
0
5
0
2
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
3
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
2
0
2
0
0
2
2
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
2
0
0
0
0
0
1
0
0
0
0
1
1
1
0
2
0
1
2
0
1
0
2
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
2
3
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
2
2
0
0
1
3
2
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
2
0
2
0
0
0
1
2
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
1
0
0
0
1
1
2
2
6
0
0
0
3
2
0
2
0
0
0
0
0
1
0
5
0
0
2
2
0
0
0
0
0
0
2
1
0
0
0
3
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
2
0
2
0
1
1
0
0
0
1
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
2
2
0
0
3
3
0
1
0
1
2
2
0
0
0
0
2
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
1
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
3
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
2
1
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
2
0
2
0
0
2
0
2
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
1
2
3
0
0
1
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
2
1
3
0
4
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
1
0
0
0
2
2
1
1
0
0
2
0
2
0
0
2
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
5
1
2
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
1
3
1
0
0
2
2
0
0
0
1
0
1
0
0
1
0
1
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
2
8
1
0
0
1
0
3
0
0
0
1
2
0
0
0
0
0
1
2
0
2
0
2
0
0
0
0
2
1
0
0
4
0
0
2
0
0
0
0
0
0
0
6
1
2
0
1
0
1
0
0
0
0
0
2
1
2
0
4
0
0
2
1
0
0
0
0
2
0
0
1
0
2
0
0
2
0
0
1
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
3
0
4
0
0
0
3
0
4
0
2
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
3
0
1
0
0
0
0
0
1
1
0
0
0
0
0
3
0
2
0
0
0
2
2
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
1
2
0
0
0
1
0
0
0
1
2
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
4
0
3
0
1
0
0
0
0
0
0
1
0
3
0
0
0
1
0
0
0
0
0
4
1
0
0
0
0
0
2
0
0
0
0
0
0
2
1
1
2
0
1
0
0
0
2
0
2
0
2
0
0
0
0
0
2
2
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
2
0
0
0
1
0
0
0
1
0
2
1
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
1
0
2
5
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
3
0
2
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
1
1
1
0
3
2
0
1
2
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
1
0
0
3
0
0
1
0
0
0
0
0
1
0
2
0
0
0
2
1
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
4
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
2
0
0
1
0
2
2
1
0
1
2
0
0
0
0
1
0
0
2
0
1
0
2
0
0
0
1
1
1
0
0
1
2
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
2
2
0
2
0
0
0
0
0
2
1
0
0
1
2
2
2
0
5
2
1
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
2
1
0
0
4
1
0
1
0
1
1
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
1
2
1
0
0
0
0
0
0
0
0
2
0
0
0
2
5
0
2
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
1
2
0
0
1
0
2
0
0
0
0
1
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
2
1
0
0
0
0
6
0
1
0
2
0
0
1
0
0
2
0
1
2
0
0
0
2
0
0
0
0
0
1
5
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
2
0
0
1
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
5
0
2
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
3
2
0
0
0
0
1
0
3
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
2
0
0
0
0
1
0
0
1
0
0
1
3
0
3
1
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
7
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
2
0
0
0
1
1
0
0
2
0
0
0
0
0
3
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
1
1
0
0
0
2
0
1
0
0
0
2
1
1
0
0
0
2
2
0
0
0
0
2
0
0
1
2
1
0
0
0
0
0
0
2
1
0
1
1
1
0
0
2
0
0
0
0
2
0
0
0
0
0
2
1
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
1
1
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
2
0
2
1
0
0
0
0
2
0
0
1
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
3
0
0
0
3
0
0
1
1
0
0
0
0
0
0
0
1
3
0
1
0
0
0
2
0
3
2
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
3
1
1
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
1
0
1
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
2
2
1
2
0
0
0
2
0
0
0
0
0
1
0
1
0
0
2
0
3
0
2
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
1
2
1
0
0
0
0
0
0
0
0
3
0
1
0
0
1
1
0
0
2
0
1
1
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
1
0
2
0
2
0
1
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
8
0
0
0
0
0
0
0
0
1
1
0
2
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
2
0
1
0
0
2
0
0
0
0
1
1
0
0
1
3
1
0
0
0
0
0
0
2
0
2
0
0
1
0
0
2
2
0
0
0
0
3
1
0
3
1
0
2
0
1
0
2
1
0
0
0
0
0
2
0
2
0
0
0
0
1
0
1
0
1
2
0
0
0
1
0
1
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
1
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
1
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
1
0
0
2
1
0
0
0
0
0
0
3
0
0
1
0
1
0
1
0
0
0
2
0
3
0
0
1
3
2
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
5
0
0
1
2
0
0
1
0
0
0
0
0
2
0
0
1
0
1
1
0
2
1
0
0
0
1
1
1
0
0
0
0
0
0
3
0
0
0
2
2
0
0
0
2
0
0
0
1
0
0
1
3
0
0
0
2
0
0
5
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
2
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
2
2
3
2
0
1
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
8
0
0
3
0
2
1
0
1
0
0
0
0
1
0
3
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
1
1
0
2
0
0
3
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
1
0
1
1
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
4
0
4
0
0
0
1
3
1
0
1
0
0
2
0
0
0
1
0
0
3
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
1
0
1
2
0
0
1
0
1
1
0
0
1
1
0
1
0
2
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
2
1
2
3
0
0
0
1
0
2
0
0
0
1
0
0
2
0
0
0
2
0
0
0
2
0
1
0
0
0
0
2
2
0
0
0
0
2
0
0
0
2
0
1
0
1
1
2
0
0
0
0
0
4
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
1
2
0
0
0
0
2
0
0
0
0
1
0
1
0
0
2
1
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
1
0
0
0
0
2
0
0
1
1
1
1
0
0
0
0
0
1
1
0
0
0
0
1
1
0
6
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
2
0
0
2
0
0
1
2
1
1
2
1
0
0
0
0
0
0
2
1
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
1
0
2
0
0
1
2
2
0
0
0
0
2
0
1
1
1
1
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
2
2
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
3
0
0
2
0
2
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
2
1
0
1
1
0
0
0
2
0
2
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
2
2
0
0
0
0
0
1
0
2
0
2
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
3
2
3
0
0
0
2
2
0
0
1
2
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
1
0
0
3
0
0
0
0
0
1
0
1
2
2
0
0
1
0
2
0
0
0
0
0
2
2
0
0
2
0
2
0
0
1
0
1
0
0
2
0
2
1
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
2
0
0
0
0
2
0
2
0
2
0
0
1
0
2
0
4
0
10
0
0
0
0
1
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
3
1
2
0
0
0
0
0
2
0
2
2
0
0
0
0
0
1
2
0
0
0
2
2
1
2
1
0
0
0
0
0
1
0
0
1
3
0
2
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
2
0
2
0
1
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
3
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
1
3
0
1
1
2
0
0
0
1
0
1
1
1
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
2
0
4
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
1
0
0
0
0
2
0
0
0
0
2
0
0
1
0
2
0
2
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
3
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
1
2
0
2
0
1
1
0
0
0
0
2
0
0
4
0
0
0
0
0
3
1
4
0
0
0
0
0
0
0
1
0
3
1
0
0
2
0
0
0
0
0
0
1
0
0
1
1
1
2
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
2
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
2
0
1
1
0
1
0
0
1
0
0
0
0
0
0
1
0
2
0
1
0
0
2
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
2
0
0
0
0
0
3
4
2
1
0
0
0
0
0
0
0
1
0
0
2
2
1
0
0
0
0
1
0
0
0
0
0
0
2
3
2
0
0
2
1
2
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
2
0
1
0
2
0
0
0
2
2
0
0
0
1
2
0
0
0
0
0
5
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
3
9
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
1
0
0
1
1
0
2
0
0
2
2
0
1
0
0
0
2
0
0
0
0
4
0
0
0
0
0
1
0
1
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
3
3
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
1
0
7
0
0
0
0
1
1
0
0
0
2
0
2
0
0
0
1
0
0
0
1
2
0
1
0
2
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
2
2
0
0
0
0
1
2
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
2
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
1
0
0
0
1
2
0
0
0
1
0
1
1
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
3
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
2
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
2
1
0
0
1
0
0
1
3
0
0
1
1
1
2
1
0
0
2
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
3
3
0
0
0
0
0
0
0
2
0
0
0
1
2
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
1
0
0
0
0
1
1
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
5
0
0
2
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
2
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
1
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
3
0
2
1
1
5
0
2
0
0
0
0
0
1
7
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
2
2
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
1
0
1
0
0
0
1
3
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
1
0
1
0
2
0
1
0
1
0
0
1
0
0
0
1
0
2
0
4
0
0
0
0
0
3
0
4
1
2
0
0
0
0
2
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
2
2
0
2
0
0
2
0
0
0
0
1
0
1
2
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
2
0
0
0
1
0
0
0
4
1
0
2
0
0
0
0
0
0
1
3
0
0
1
1
1
2
2
0
0
0
2
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
2
0
0
1
0
1
1
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
2
0
0
3
0
0
0
1
0
0
2
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
5
0
2
3
0
0
1
1
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
2
0
0
4
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
3
0
0
0
2
0
0
0
3
0
2
1
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
2
0
2
1
0
0
1
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
3
2
0
0
2
0
1
1
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
2
1
0
0
4
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
1
2
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
2
0
1
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
1
0
1
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
1
0
1
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
2
2
0
2
3
1
0
0
2
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
1
1
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
2
0
0
0
0
0
0
0
5
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
3
0
2
0
0
0
0
0
3
0
1
0
8
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
5
1
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
2
1
0
3
2
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
3
2
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
2
0
0
1
1
0
2
0
0
0
1
0
1
0
1
0
0
2
0
0
2
0
1
1
2
0
1
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
2
2
2
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
1
0
2
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
3
2
1
0
0
0
0
5
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
2
1
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
2
2
0
2
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
2
2
0
0
2
0
0
0
1
0
0
2
0
0
1
0
0
2
0
2
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
1
1
1
0
3
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
2
0
2
0
1
0
0
0
2
0
0
0
0
0
3
0
0
0
2
0
0
0
1
3
2
2
0
2
0
0
0
0
0
3
2
0
1
1
0
0
1
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
1
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
1
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
13
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
2
2
0
0
1
2
0
0
0
0
2
2
2
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
1
2
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
2
1
0
2
0
0
2
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
4
1
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
2
2
1
0
0
1
0
1
0
2
0
2
0
0
1
0
0
0
0
0
0
1
2
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
2
0
1
0
0
0
0
0
0
2
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
5
0
2
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
3
1
0
0
1
3
1
0
2
0
0
0
0
0
0
3
0
1
1
2
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
3
1
0
0
0
0
0
0
0
0
1
3
3
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
2
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
1
1
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
3
0
0
0
1
1
0
2
0
2
2
0
0
1
0
1
2
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
2
0
0
2
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
2
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
1
2
2
0
0
1
0
0
0
0
0
2
0
0
2
0
0
1
2
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
1
2
0
2
1
0
1
1
0
0
0
3
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
2
1
1
4
0
0
1
0
0
2
0
0
1
0
0
2
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
1
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
2
2
0
2
1
0
2
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
1
0
1
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
13
0
0
0
0
0
2
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
1
0
1
0
0
0
0
0
0
0
0
1
0
2
3
0
0
0
1
0
1
0
0
1
2
1
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
2
1
0
0
0
4
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
1
0
2
2
2
0
0
0
1
1
1
2
2
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
5
2
0
0
0
1
2
0
0
0
0
3
1
0
0
1
0
3
2
0
0
2
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
6
0
0
0
1
0
2
0
2
2
0
0
1
2
0
0
2
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
1
0
0
2
0
0
0
1
1
2
0
0
2
0
0
2
0
0
1
1
1
1
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
2
0
0
0
1
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
1
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
5
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
1
1
3
2
0
0
0
0
0
0
0
1
0
1
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
2
0
2
0
0
0
2
0
2
2
0
0
0
0
2
1
1
0
0
1
0
0
2
0
0
0
0
2
0
0
2
1
0
0
1
0
2
0
2
0
0
1
5
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
1
1
2
0
0
4
0
1
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
3
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
3
1
0
0
1
0
0
2
2
2
3
0
0
1
1
1
1
2
1
0
0
0
1
0
1
0
6
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
2
0
1
0
0
0
2
0
2
2
2
1
0
0
0
0
1
0
0
0
0
0
0
0
2
1
1
0
0
1
1
0
0
0
0
2
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
1
0
0
2
3
0
0
1
6
2
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
2
0
1
1
0
0
2
0
0
2
0
0
2
0
1
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
2
0
0
1
2
2
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
3
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
2
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
1
0
2
7
0
0
0
0
0
0
3
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
1
2
0
2
6
0
0
0
0
0
0
1
0
2
2
2
0
0
0
0
0
0
3
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
4
0
0
0
1
0
2
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
1
0
1
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
2
1
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
2
0
3
0
0
2
0
0
0
0
0
0
0
2
0
1
0
2
1
0
0
2
0
1
0
2
0
3
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
1
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
1
1
0
2
2
0
0
5
0
2
1
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
2
0
0
2
0
1
2
0
0
0
1
0
0
2
1
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
1
0
3
1
0
0
2
1
0
2
0
2
1
2
0
0
1
0
1
2
0
0
0
2
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
2
2
3
0
0
0
0
1
1
2
1
0
2
0
2
0
2
0
0
0
0
0
0
2
1
2
0
0
0
1
1
2
1
0
0
0
0
0
2
0
2
0
1
0
0
0
1
1
0
1
0
1
1
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
1
0
2
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
1
0
3
0
0
0
1
1
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
1
0
0
1
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
2
0
0
0
1
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
3
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
5
1
0
0
0
4
0
0
2
0
0
0
0
0
1
0
2
1
0
0
0
2
3
0
0
0
1
0
0
1
0
0
2
0
0
2
0
2
1
0
0
0
1
0
0
2
2
1
3
0
0
2
0
0
0
0
0
1
9
2
0
0
3
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
2
0
0
0
0
1
0
0
1
0
0
0
1
4
0
3
0
1
3
0
2
0
2
0
0
0
0
0
1
0
3
0
0
0
2
2
2
0
1
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
2
0
0
0
1
2
0
0
2
0
2
0
0
0
0
1
2
0
1
2
0
3
0
0
0
1
1
0
0
0
0
0
0
0
2
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
8
0
2
0
6
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
3
2
1
0
0
0
0
0
2
0
0
3
1
0
2
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
2
1
0
0
1
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
2
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
3
0
0
1
0
0
0
0
0
0
2
0
0
1
1
0
0
1
2
0
0
0
0
0
0
2
0
0
1
1
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
2
2
2
2
0
0
1
0
2
0
0
1
1
0
2
0
2
0
0
2
1
0
0
0
0
3
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
9
0
0
0
1
0
0
0
0
3
0
2
0
0
1
1
1
0
2
0
2
0
0
3
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
2
3
1
0
0
1
0
0
1
2
0
0
0
0
1
0
0
3
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
3
0
0
1
0
0
2
0
0
0
2
0
2
1
0
0
0
0
0
0
0
1
0
8
0
0
2
0
0
0
1
0
0
0
0
0
0
2
2
0
1
2
0
0
1
0
0
0
0
0
0
0
2
0
0
2
2
1
2
0
0
4
0
0
1
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
2
0
0
1
0
0
0
1
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
3
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
2
0
0
4
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
2
0
0
0
0
2
0
0
1
1
2
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
1
2
0
0
1
0
0
1
0
0
3
0
0
0
0
3
0
0
2
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
1
5
0
2
0
0
1
2
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
1
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
3
1
0
0
1
0
1
0
0
2
1
0
1
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
2
0
3
2
0
0
1
0
0
1
0
0
0
0
0
0
0
2
1
1
1
1
1
0
2
0
2
0
0
0
0
0
0
3
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
1
0
2
0
1
2
0
0
0
1
0
0
1
3
0
2
0
0
0
0
0
1
0
0
1
0
0
0
1
0
3
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
2
0
3
0
0
2
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
2
1
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
5
2
2
0
2
3
1
0
0
0
0
0
0
0
0
0
3
6
0
0
1
0
1
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
2
0
1
3
0
0
0
1
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
1
0
0
2
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
2
1
0
0
2
0
0
0
0
0
0
0
0
2
2
0
1
1
0
1
0
2
2
2
0
0
0
0
0
0
2
0
2
0
0
1
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
1
0
7
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
5
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
3
2
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
1
0
2
0
0
0
1
3
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
3
0
3
0
0
0
0
2
0
2
2
0
2
0
0
0
0
0
0
0
0
3
0
0
0
2
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
2
0
0
0
0
0
0
0
0
1
2
1
1
0
0
1
2
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
2
0
0
7
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
2
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
3
2
0
2
0
0
4
1
1
1
0
0
1
0
0
0
2
7
0
1
2
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
3
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
2
4
1
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
2
0
0
2
3
3
0
1
0
1
1
0
0
2
1
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
2
0
1
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
4
3
0
0
2
0
2
1
0
1
0
0
2
0
1
0
0
1
0
2
2
0
0
1
0
0
0
2
1
0
2
0
0
1
0
0
0
0
2
3
0
1
0
1
0
3
1
0
0
0
1
0
0
0
0
0
0
0
2
1
2
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
2
0
0
3
0
0
0
3
0
0
1
0
0
2
2
0
0
1
0
0
0
1
0
0
0
2
0
1
1
0
0
1
0
2
2
0
0
2
2
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
4
0
0
0
1
0
2
2
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
2
0
0
3
0
0
2
0
0
0
1
0
0
1
0
2
1
2
0
0
1
0
0
0
2
2
1
3
2
0
0
0
0
2
3
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
1
1
0
1
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
8
0
0
1
0
3
0
3
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
1
0
0
2
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
1
0
0
0
2
0
0
0
2
2
0
0
2
0
0
0
0
0
5
1
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
3
1
0
0
0
3
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
2
0
0
1
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
2
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
3
0
0
1
2
0
0
0
0
0
3
1
1
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
1
0
0
0
0
3
0
0
0
2
0
1
0
0
0
3
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
2
1
0
0
0
1
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
2
0
0
0
0
2
1
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
3
1
1
1
0
0
1
0
0
3
0
2
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
3
0
0
0
1
1
0
0
0
0
2
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
4
0
0
0
0
1
0
0
0
2
0
1
2
0
0
1
1
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
2
0
2
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
3
1
1
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
2
5
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
1
0
2
0
3
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
1
2
1
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
2
0
1
0
0
0
0
1
2
0
0
0
1
2
0
0
0
2
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
1
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
1
1
0
2
0
0
0
1
0
0
0
0
0
0
0
3
0
0
2
0
0
1
0
0
2
0
0
2
0
0
1
2
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
1
1
0
1
0
0
0
0
0
2
0
1
1
0
0
0
2
2
0
3
0
2
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
3
1
1
0
0
0
0
1
0
2
0
0
0
2
2
0
0
2
0
0
2
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
1
2
0
1
2
0
0
0
0
0
0
0
0
2
2
2
2
1
0
1
0
2
0
0
1
1
0
0
2
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
3
1
0
0
0
2
0
0
0
2
0
3
0
2
2
0
0
1
1
1
0
0
0
0
1
0
2
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
1
0
1
0
0
0
1
0
0
0
2
0
0
3
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
2
1
0
0
0
0
1
1
0
0
1
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
5
1
0
3
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
2
0
0
1
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
2
0
1
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
2
0
0
0
6
1
0
0
1
3
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
2
2
2
0
1
0
0
0
1
1
0
0
2
0
1
0
0
0
0
2
0
2
0
1
2
0
0
3
0
0
0
5
0
0
0
2
0
0
1
0
0
0
0
3
2
0
0
0
0
2
5
0
2
2
0
0
0
0
2
0
0
0
2
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
1
0
2
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
2
1
0
0
0
0
0
2
1
2
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
2
2
0
0
2
0
0
0
0
2
1
2
1
0
0
2
0
0
0
2
2
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
2
0
2
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
5
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
2
1
0
0
0
0
0
0
1
1
2
1
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
1
1
0
2
2
2
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
2
0
0
0
3
0
2
0
0
2
0
0
0
0
1
0
0
0
1
2
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
2
0
1
0
0
0
0
2
0
0
0
0
7
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
1
1
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
1
0
1
0
0
0
1
1
1
1
0
1
0
0
0
2
0
1
1
0
0
2
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
2
0
2
0
0
2
0
0
0
0
3
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
2
1
0
0
2
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
2
2
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
1
0
5
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
1
0
0
0
0
0
0
0
2
0
3
1
2
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
1
0
0
4
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
2
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
3
0
2
0
0
2
1
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
4
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
2
0
1
0
2
0
1
0
0
0
0
0
0
1
0
0
0
2
0
1
0
2
0
0
0
0
0
0
2
1
1
0
1
0
0
3
0
1
1
0
0
0
0
0
0
2
0
0
2
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
26
0
1
0
0
0
0
0
0
1
3
0
2
0
0
0
0
2
0
0
0
0
0
1
0
2
1
0
0
0
2
0
1
0
1
2
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
3
6
0
1
2
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
1
0
2
2
0
0
1
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
8
0
2
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
2
2
0
0
0
0
2
0
0
0
0
0
5
0
0
0
1
0
0
0
0
1
0
1
2
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
1
0
0
1
0
7
0
0
2
0
0
2
1
0
0
2
0
0
2
3
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
2
6
1
0
0
3
0
2
1
0
0
0
0
2
0
0
0
1
2
0
0
0
0
3
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
2
1
0
1
0
1
0
0
0
2
1
0
0
0
0
0
1
3
0
1
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
1
0
0
1
2
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
2
0
0
1
2
0
0
3
0
0
0
1
0
0
0
2
0
0
0
0
2
0
2
1
0
0
0
0
2
0
1
1
0
0
2
0
1
0
2
1
1
0
0
0
0
0
0
0
2
1
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
2
0
0
0
0
0
3
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
4
0
1
0
0
0
2
0
0
0
2
0
1
0
1
0
1
0
0
0
3
1
0
0
0
0
0
3
1
0
0
1
0
0
3
1
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
2
2
2
0
1
2
0
0
3
0
2
0
0
1
0
1
0
0
0
0
1
0
0
0
2
2
1
0
0
2
2
0
0
0
1
2
0
0
0
0
0
1
1
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
4
0
0
0
0
0
2
0
0
0
1
0
1
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
6
3
0
0
0
0
0
2
0
0
0
1
0
2
1
1
0
0
0
0
1
0
5
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
1
0
0
1
0
1
2
0
0
2
0
0
0
0
2
0
3
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
5
1
0
1
0
0
1
2
1
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
8
0
0
0
0
2
0
2
1
0
0
0
0
0
2
2
0
2
0
0
2
0
3
0
2
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
5
1
0
0
0
0
1
0
0
0
1
2
0
3
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
2
2
0
0
0
1
1
0
0
0
2
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
5
3
1
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
1
0
0
1
2
2
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
2
1
1
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
1
2
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
1
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
1
0
8
0
0
0
0
0
1
0
0
0
0
0
1
1
2
2
2
0
0
0
0
0
0
2
1
0
2
1
0
0
0
0
1
0
1
0
0
0
1
1
2
0
0
0
0
0
0
2
0
0
3
0
2
0
0
0
2
0
0
0
1
0
0
2
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
7
4
0
0
0
1
0
0
0
0
1
0
0
1
2
0
0
0
0
1
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
1
0
0
0
0
1
2
0
0
2
1
2
1
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
2
3
2
1
0
1
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
4
0
0
2
2
1
3
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
1
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
2
0
0
7
2
2
0
1
3
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
2
0
0
1
0
0
0
0
0
2
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
1
0
0
1
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
2
0
0
0
0
2
0
1
0
0
0
0
0
1
1
0
1
0
2
0
0
0
0
0
0
0
0
3
0
0
2
0
0
2
0
1
0
0
2
2
0
0
0
2
0
2
0
0
0
0
2
1
0
0
3
1
0
0
0
1
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
2
2
0
2
2
0
1
0
0
0
0
0
0
2
7
1
1
1
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
6
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
1
2
0
0
0
0
1
0
3
1
2
0
0
0
2
0
0
1
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
2
0
0
0
0
0
0
1
2
1
1
0
0
0
0
0
0
0
0
1
0
0
0
2
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
5
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
3
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
3
0
2
0
0
2
0
6
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
1
2
0
0
0
4
1
2
0
0
0
0
3
0
0
0
0
2
0
1
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
2
2
1
0
0
0
1
0
2
3
0
0
2
1
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
2
3
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
1
0
0
0
1
1
4
0
0
0
4
0
0
0
0
0
0
2
0
0
3
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
1
0
1
0
0
0
0
0
0
2
1
1
0
0
2
1
0
0
0
0
0
2
0
0
0
1
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
3
0
2
0
1
0
0
0
0
0
1
0
1
1
1
0
0
1
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
2
2
0
0
0
0
1
0
1
0
3
0
0
1
2
0
1
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
2
0
3
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
2
0
3
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
6
2
0
3
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
1
0
2
0
2
0
2
2
0
0
0
0
1
2
0
2
0
0
2
0
0
2
1
0
0
0
0
0
1
0
0
0
2
2
0
0
1
1
0
0
0
0
2
0
0
0
2
0
2
1
0
0
0
2
0
0
0
1
3
3
0
0
0
0
0
2
2
0
2
0
0
1
1
2
0
0
0
2
0
0
0
0
2
1
4
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
2
1
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
2
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
1
2
1
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
2
0
0
2
0
1
2
0
3
0
0
1
0
0
2
2
1
0
1
0
0
1
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
2
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
1
1
0
0
0
1
0
2
2
0
2
0
1
2
1
1
0
0
0
2
1
0
0
0
0
3
0
1
2
0
0
2
2
0
0
0
0
0
0
0
3
0
0
1
0
0
0
1
1
2
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
1
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
13
0
2
1
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
2
0
0
2
2
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
1
0
4
0
5
1
2
1
2
1
1
2
0
0
0
1
1
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
3
1
0
2
0
2
1
0
0
1
0
2
0
0
0
0
0
1
1
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
2
0
2
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
4
0
1
1
2
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
2
3
0
0
1
0
2
2
2
4
0
0
0
0
0
0
0
3
3
2
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
4
1
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
3
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
7
2
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
3
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
3
2
0
0
0
2
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
10
0
5
0
0
0
0
0
0
0
0
0
3
2
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
3
1
0
2
0
0
2
0
0
2
0
0
0
2
0
0
1
2
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
1
0
2
0
2
2
0
3
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
2
1
2
1
0
1
1
1
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
1
2
1
0
0
0
0
0
0
1
0
0
0
1
0
1
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
4
0
2
2
1
1
0
2
0
0
2
2
2
0
0
0
1
1
0
2
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
3
1
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
1
0
4
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
3
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
1
0
0
0
0
0
2
0
3
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
2
0
1
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
2
4
0
0
2
0
2
0
0
2
0
0
1
0
0
0
0
1
0
2
1
0
2
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
2
1
2
0
0
1
0
0
1
0
2
1
1
0
0
0
0
2
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
1
0
2
2
0
0
0
0
2
1
2
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
3
0
0
0
0
2
4
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
2
0
0
0
0
1
1
1
8
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
3
2
0
0
2
0
0
0
1
1
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
1
2
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
2
0
0
0
2
0
1
0
3
2
1
1
0
0
0
0
2
0
0
0
2
3
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
1
2
1
0
0
0
0
2
1
1
1
0
2
0
0
0
0
2
0
3
0
2
0
2
2
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
4
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
1
1
1
0
0
2
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
1
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
2
1
1
0
0
1
0
0
0
1
0
2
0
0
0
0
1
0
0
0
1
0
2
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
1
0
0
2
0
1
1
0
0
0
0
0
2
0
0
4
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
1
2
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
1
1
0
0
2
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
2
0
0
0
0
2
2
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
1
0
1
0
2
0
1
0
0
0
0
1
0
2
0
0
0
0
1
0
0
2
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
2
0
0
0
2
1
1
0
1
2
0
7
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
2
0
0
0
0
0
3
0
0
0
0
0
0
4
1
1
0
0
0
0
1
0
0
2
2
1
0
0
0
0
0
0
1
0
2
0
0
0
0
1
1
0
0
2
0
0
0
0
1
0
0
0
0
0
1
2
0
0
1
0
0
0
0
1
0
2
0
2
0
0
0
1
0
2
0
2
0
2
0
1
0
1
0
0
1
0
0
0
1
2
0
0
0
0
2
0
1
4
2
2
0
1
2
2
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
1
2
1
0
3
0
0
0
8
1
0
0
0
0
0
0
0
0
1
0
1
0
2
0
3
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
1
2
0
0
0
1
2
2
0
0
0
0
0
2
0
1
1
3
1
0
0
2
0
3
2
3
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
1
1
0
2
0
0
0
1
0
0
0
0
0
2
2
0
2
0
0
0
1
0
0
0
0
0
2
0
0
3
1
2
0
0
1
0
0
0
2
0
1
0
1
0
0
0
5
0
0
0
0
0
0
0
1
1
5
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
2
1
0
2
2
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
2
0
0
1
1
0
2
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
2
2
0
1
0
0
2
0
1
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
1
0
0
0
1
3
0
0
3
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
3
0
0
0
2
0
0
1
1
2
0
0
0
0
0
1
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
3
2
0
0
0
0
0
1
1
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
1
1
0
0
1
1
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
1
1
0
2
0
1
0
6
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
2
2
0
0
1
0
1
0
0
0
1
0
0
0
0
2
0
0
3
0
0
0
0
1
2
0
0
1
2
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
2
0
1
0
2
0
0
1
0
2
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
2
0
3
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
1
0
1
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
4
0
0
0
1
1
0
0
2
0
1
0
0
1
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
1
0
0
0
4
1
0
1
0
2
0
0
3
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
1
2
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
3
1
2
1
0
0
0
0
0
0
0
0
1
0
1
1
2
1
0
0
0
1
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
1
0
1
0
4
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
2
1
2
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
3
0
1
1
0
1
1
0
0
1
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
3
0
0
2
2
0
1
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
2
0
0
3
0
2
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
3
0
3
3
0
2
2
0
0
2
0
1
1
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
3
0
2
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
0
0
1
1
0
1
0
0
0
1
2
0
0
0
0
0
0
2
2
0
0
1
1
1
0
3
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
1
2
0
3
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
1
0
3
0
2
1
0
1
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
2
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
2
1
0
0
7
0
0
2
2
0
0
0
2
0
0
0
1
2
0
2
0
0
2
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
1
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
2
0
1
0
2
1
0
0
0
1
0
0
0
1
0
0
3
0
0
2
0
0
0
0
0
3
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
2
1
1
0
5
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
2
2
0
0
1
0
0
2
0
0
0
2
1
2
0
0
0
1
0
0
1
1
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
2
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
1
2
4
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
1
0
5
1
1
0
0
0
0
2
0
3
0
0
0
3
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
2
0
0
0
2
0
0
0
0
2
0
1
2
1
0
1
0
0
1
0
2
0
2
2
1
0
3
0
0
0
0
2
0
0
1
1
0
1
2
0
0
0
0
6
2
0
2
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
8
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
1
2
2
0
2
0
0
0
0
0
1
0
1
0
1
0
0
0
1
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
2
0
0
1
0
2
0
2
0
4
0
0
0
0
0
0
4
2
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
1
0
1
1
0
0
2
0
0
1
1
0
0
2
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
1
0
0
0
3
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
4
0
2
0
0
1
2
2
1
1
0
0
0
1
1
0
0
0
0
2
3
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
1
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
1
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
3
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
2
2
1
0
2
1
0
1
0
0
0
0
1
0
0
1
0
1
0
2
2
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
5
1
3
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
1
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
2
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
1
2
0
0
1
0
2
1
1
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
1
0
0
1
0
0
0
11
0
0
0
0
0
0
0
0
2
0
2
0
1
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
2
2
0
0
0
2
2
1
1
0
0
0
0
0
1
0
3
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
2
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
1
0
2
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
1
0
0
2
1
1
0
0
0
0
1
3
2
0
2
0
3
1
0
0
0
0
1
4
0
0
0
2
0
0
1
0
2
8
0
0
0
1
0
1
2
2
0
1
2
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
1
0
1
0
2
0
0
0
0
1
0
0
0
0
2
0
4
0
1
0
0
1
0
2
0
0
1
1
2
0
0
0
1
4
0
2
2
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
2
0
0
2
3
3
0
0
0
1
0
0
2
0
1
1
0
0
2
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
3
0
0
0
0
5
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
2
2
0
2
0
0
1
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
1
0
0
2
0
0
1
1
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
2
2
2
4
0
0
0
0
0
2
0
0
0
0
2
1
3
0
0
0
0
0
0
0
2
5
2
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
3
0
4
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
8
1
0
1
2
0
0
0
0
0
2
3
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
1
0
0
3
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
2
0
2
1
1
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
2
1
1
0
0
1
1
0
2
0
0
0
0
1
0
1
2
0
2
0
1
2
0
0
0
0
0
0
0
2
0
0
0
2
2
2
0
0
0
0
2
1
0
0
0
1
0
1
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
5
0
0
5
0
0
2
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
1
0
2
0
2
1
0
1
2
1
3
0
0
0
0
0
0
0
2
0
0
1
0
0
3
0
2
0
0
1
2
0
0
1
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
3
1
0
0
0
0
0
0
5
0
0
0
0
2
2
1
0
0
0
0
2
0
2
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
2
2
2
0
0
0
0
1
1
2
2
0
1
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
2
0
1
0
2
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
1
2
1
0
1
0
0
0
0
0
1
2
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
4
1
2
0
0
0
0
4
1
1
0
0
1
0
1
2
0
1
0
2
0
1
0
0
1
0
1
3
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
1
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
2
0
0
0
1
0
2
0
2
0
0
2
1
0
0
1
0
0
0
4
2
0
0
0
0
1
2
0
0
0
3
0
0
0
2
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
2
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
2
0
0
3
0
1
0
0
2
0
2
2
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
5
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
3
0
0
0
2
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
4
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
2
0
2
0
0
0
0
0
4
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
1
0
1
0
0
0
0
2
2
0
0
0
0
2
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
2
0
0
0
1
1
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
3
0
0
0
0
4
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
1
0
1
0
0
0
0
2
0
2
1
1
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
2
1
0
2
0
0
1
4
0
0
1
2
0
0
0
0
0
2
0
0
1
2
0
0
10
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
2
0
0
2
1
1
1
17
0
1
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
1
2
1
0
0
0
0
2
0
0
0
2
1
0
0
2
0
1
0
2
0
0
2
1
0
0
0
0
0
1
0
0
4
0
2
0
0
1
0
0
2
0
1
0
0
0
1
0
0
1
2
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
2
0
0
1
0
2
0
0
0
0
2
1
0
3
0
2
1
1
0
0
0
0
0
0
1
0
0
0
2
1
2
2
0
0
0
2
1
0
1
2
2
1
0
0
2
0
0
2
1
0
12
2
0
1
0
0
2
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
2
0
0
3
1
0
0
1
0
1
0
0
0
0
2
1
1
0
0
0
2
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
3
2
0
0
2
2
1
0
0
0
0
0
0
0
0
8
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
1
0
1
0
0
2
0
0
0
1
0
0
0
0
0
2
0
1
0
1
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
2
0
0
1
0
0
0
0
2
1
0
0
0
0
6
0
0
0
4
0
2
0
2
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
10
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
2
2
0
0
0
1
1
0
4
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
1
0
2
1
0
0
0
0
0
0
1
0
0
0
1
2
1
1
1
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
2
0
0
1
2
0
1
0
0
0
4
0
0
1
1
0
0
1
0
2
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
5
0
0
0
0
2
0
0
0
0
0
0
2
2
0
2
0
0
0
1
0
0
2
0
0
0
2
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
1
0
0
3
0
0
0
0
2
3
2
0
4
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
2
1
0
0
1
0
0
0
1
2
0
0
2
0
1
0
1
0
1
2
0
2
0
1
1
2
0
0
0
2
2
0
0
0
2
0
0
1
0
0
0
2
1
0
2
1
2
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
5
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
2
5
1
0
0
0
2
0
0
0
0
0
1
0
1
2
2
0
2
0
0
2
0
2
0
0
0
1
0
2
0
2
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
1
1
0
0
1
0
1
0
0
2
1
1
1
1
2
1
0
1
1
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
2
1
0
2
0
1
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
2
1
0
0
0
0
2
0
2
0
2
2
0
0
1
2
0
0
0
1
0
0
0
0
1
0
1
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
1
2
0
0
0
0
0
1
0
0
2
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
5
0
0
0
2
0
1
1
0
0
0
0
0
0
2
0
0
0
0
8
2
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
1
1
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
3
1
0
0
2
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
3
0
1
0
0
1
1
0
1
5
1
3
0
1
0
2
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
2
0
0
0
2
0
8
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
11
0
0
1
1
1
0
0
0
2
0
2
1
0
0
2
2
0
3
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
2
2
0
0
1
0
2
0
0
1
2
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
2
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
8
2
0
2
0
0
0
0
0
0
0
0
2
0
4
1
0
0
0
1
0
0
2
1
1
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
2
0
0
0
0
1
0
3
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
2
0
0
0
0
1
2
0
0
0
0
1
1
2
0
0
2
2
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
1
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
3
1
1
0
0
0
0
2
0
2
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
3
0
2
1
0
1
1
0
0
0
0
1
0
1
1
0
3
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
10
2
2
0
0
0
1
0
0
2
2
0
0
1
0
2
2
0
0
0
0
0
0
0
1
3
0
0
0
2
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
1
0
1
0
3
0
0
0
1
0
0
1
1
0
0
0
6
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
2
0
1
0
0
2
6
2
0
0
2
2
0
0
0
1
0
2
0
1
0
0
0
0
6
2
2
0
2
0
0
4
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
2
0
0
0
1
1
1
2
1
0
0
1
0
0
1
0
1
2
0
0
0
0
3
0
1
1
0
0
0
1
4
0
0
0
2
0
1
2
2
0
0
2
0
1
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
4
0
2
0
1
1
1
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
1
0
1
0
4
2
0
0
0
2
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
3
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
1
0
0
1
0
0
0
2
1
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
4
0
0
0
0
1
0
2
1
0
0
0
0
1
0
2
4
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
1
1
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
1
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
1
0
0
1
2
1
1
0
3
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
3
2
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
3
2
0
0
0
0
0
1
0
1
0
2
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
2
0
2
1
1
2
0
3
1
0
2
0
0
1
0
0
0
2
2
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
5
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
2
0
0
1
0
2
0
1
2
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
9
0
0
1
0
0
0
0
0
2
0
2
0
0
1
0
0
3
0
0
0
2
1
1
1
0
0
0
2
2
0
1
0
0
0
2
1
2
0
0
1
0
3
0
0
1
0
0
0
0
0
2
2
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
2
0
0
0
3
0
0
0
0
0
1
3
0
0
0
0
0
1
0
3
7
4
2
0
0
0
0
2
2
0
0
0
2
0
1
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
4
0
1
2
0
0
0
0
0
2
0
2
2
0
0
1
0
0
2
3
0
0
2
0
0
3
0
1
0
0
0
3
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
3
0
1
0
1
2
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
1
0
2
1
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
15
0
0
0
0
1
0
2
0
0
0
0
2
3
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
1
2
0
1
0
1
0
0
0
0
1
0
1
2
0
0
0
0
1
0
0
1
0
0
0
0
2
0
2
0
0
0
1
2
2
0
0
0
0
0
2
1
0
0
0
0
3
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
2
0
0
0
0
1
0
0
2
0
0
0
1
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
1
7
0
0
0
0
0
0
5
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
5
2
0
0
0
3
0
2
0
0
1
0
0
0
0
1
0
0
0
2
0
2
0
1
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
3
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
2
0
1
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
2
0
0
2
0
1
3
0
0
0
0
1
0
0
0
0
2
2
0
1
1
0
1
0
2
0
0
1
0
0
0
0
2
1
0
0
0
0
0
2
0
0
1
0
0
1
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
2
2
2
0
0
0
1
0
0
2
0
0
2
2
0
0
2
0
0
1
1
0
0
0
2
9
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
2
9
0
0
2
0
2
2
1
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
1
0
2
3
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
2
2
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
4
0
0
1
0
1
0
2
0
1
0
0
0
0
0
2
1
0
0
0
1
3
0
0
0
0
0
0
1
0
1
1
0
0
1
0
2
3
0
0
0
2
0
2
0
1
0
0
2
0
0
0
0
2
0
0
0
2
0
4
0
0
0
0
0
0
1
0
0
2
0
2
1
0
0
0
0
1
2
2
0
2
0
0
0
0
0
0
0
0
2
0
2
2
2
1
1
0
0
0
0
0
0
2
0
1
0
2
3
0
0
0
0
2
0
0
0
3
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
2
0
0
0
2
1
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
1
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
3
2
2
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
4
0
1
0
0
0
0
1
0
6
0
0
0
0
3
0
0
0
2
2
2
0
2
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
2
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
2
0
2
1
0
0
0
0
1
2
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
2
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
2
2
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
2
0
3
0
0
0
0
0
0
0
2
1
0
0
2
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
2
2
0
0
1
0
2
0
0
0
2
0
2
0
0
2
0
0
3
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
4
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
2
0
5
0
2
0
1
0
3
1
3
0
0
0
0
0
0
1
0
0
1
0
0
0
1
2
0
1
2
7
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
1
3
0
0
0
0
0
3
0
0
2
2
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
2
0
2
0
0
2
0
1
0
2
2
0
0
0
1
0
2
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
2
1
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
2
2
0
2
0
1
0
1
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
2
0
1
1
2
2
0
2
1
0
0
0
0
0
0
1
0
0
0
1
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
2
0
1
0
0
1
0
1
0
0
0
0
1
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
1
3
0
0
0
0
0
1
0
1
6
0
2
0
0
0
0
0
0
3
0
0
0
0
1
3
0
2
2
0
0
0
0
0
1
3
0
0
0
1
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
1
1
0
2
0
0
1
1
0
0
0
1
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
2
0
0
1
0
1
0
0
0
0
2
2
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
2
0
0
0
0
2
1
0
0
0
0
2
0
0
1
0
2
1
0
0
0
1
0
0
0
2
0
2
0
3
1
0
0
0
0
1
0
2
0
0
4
1
0
0
0
2
0
1
0
0
0
0
2
0
1
0
0
0
2
2
0
0
0
1
0
0
0
1
1
2
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
2
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
4
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
1
1
0
0
0
0
0
2
0
0
0
0
2
0
2
1
0
0
0
2
1
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
4
1
0
0
2
0
0
0
0
0
0
0
0
0
0
5
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
2
1
0
0
0
1
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
2
0
0
0
1
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
3
3
2
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
4
0
7
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
2
0
4
0
0
0
2
0
0
0
0
0
2
0
1
1
0
2
0
0
0
1
1
2
0
0
0
2
1
0
0
1
0
0
0
2
0
0
0
2
2
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
3
1
0
0
1
0
1
2
4
0
0
0
0
0
2
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
2
4
0
0
0
0
1
1
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
3
0
1
0
3
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
1
0
0
5
0
0
2
0
0
1
0
3
3
0
2
0
2
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
7
1
0
0
0
2
2
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
2
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
4
0
0
2
2
3
0
3
0
0
0
0
0
0
0
0
0
0
1
0
2
0
3
0
2
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
2
0
0
0
1
0
2
0
2
0
1
0
0
0
0
2
2
1
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
1
3
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
3
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
2
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
1
2
0
0
2
2
0
1
1
0
0
0
0
1
0
0
1
0
1
2
2
2
1
0
0
0
0
0
2
0
0
0
3
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
2
1
0
0
0
0
0
1
1
0
0
1
2
0
0
0
0
1
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
1
2
2
0
1
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
2
1
0
1
0
0
4
2
0
0
2
0
2
1
0
0
2
0
0
1
1
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
4
0
0
3
2
2
0
1
0
1
1
2
1
0
0
0
0
2
0
2
2
0
1
1
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
5
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
2
0
0
2
0
0
2
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
2
2
0
0
0
2
0
0
2
0
2
0
1
0
0
0
0
0
2
0
0
2
2
0
0
1
0
0
0
3
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
1
1
0
0
2
2
0
2
0
1
0
1
0
0
0
0
0
0
2
1
0
0
0
1
0
0
3
1
2
2
0
3
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
2
0
0
1
1
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
1
0
0
1
2
0
0
1
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
2
1
0
0
0
0
0
1
0
0
3
0
0
0
1
0
1
1
3
3
0
0
0
0
2
0
0
3
0
0
0
0
0
1
0
0
1
0
0
4
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
2
0
0
0
1
0
0
2
0
0
2
0
1
3
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
3
0
0
0
0
1
0
2
0
0
1
0
0
0
0
1
0
0
0
2
0
0
5
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
6
0
0
0
0
0
0
0
2
1
0
0
0
1
2
2
2
0
0
0
0
0
0
0
0
1
0
1
6
2
0
0
0
0
1
0
2
1
2
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
2
1
2
2
2
1
2
0
0
0
0
1
2
0
0
3
0
0
0
4
0
2
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
2
0
0
0
0
2
0
0
2
2
0
1
1
1
1
1
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
2
0
1
0
0
0
0
6
0
2
0
1
1
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
1
0
1
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
2
1
1
1
0
0
0
0
0
1
2
0
0
0
1
0
0
0
2
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
1
0
0
1
2
0
2
2
2
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
1
0
2
0
2
1
0
1
0
0
0
1
0
0
1
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
1
0
2
1
2
0
0
1
0
2
0
0
0
2
0
1
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
1
0
0
0
0
0
1
0
0
3
3
1
3
0
2
0
1
1
4
0
0
0
0
0
0
0
0
0
1
0
2
2
0
2
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
1
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
1
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
2
0
1
0
0
0
0
0
3
1
0
1
0
0
0
2
3
0
0
0
0
0
0
0
2
0
0
1
0
1
2
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
4
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
1
0
0
0
0
1
2
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
3
0
0
1
0
0
0
0
0
0
0
1
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
1
2
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
3
0
0
0
0
0
2
0
1
2
2
0
1
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
1
0
1
2
2
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
4
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
1
1
0
0
0
1
2
1
0
0
0
0
1
0
0
1
0
0
0
2
0
1
0
0
0
1
2
0
0
0
1
0
2
1
0
0
0
0
0
0
2
0
2
0
1
0
0
2
0
0
0
0
1
0
2
0
0
0
2
0
0
3
1
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
3
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
1
1
0
0
0
0
0
0
0
1
5
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
3
0
2
0
0
1
0
0
2
0
0
0
0
0
1
2
0
0
1
0
1
0
0
0
4
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
1
0
0
4
1
1
0
0
0
0
2
0
1
0
0
0
0
3
0
0
0
4
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
3
0
2
3
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
1
0
0
4
0
0
0
1
1
0
0
0
0
1
0
2
1
2
0
0
0
1
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
1
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
2
0
0
2
1
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
4
0
0
1
0
0
0
0
2
1
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
2
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
1
0
1
2
1
1
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
2
1
2
0
2
0
0
0
1
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
1
0
3
0
0
2
0
2
3
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
9
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
1
0
0
0
0
0
1
0
5
0
2
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
2
0
1
3
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
2
0
0
0
0
0
0
1
2
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
2
0
2
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
1
0
2
1
0
0
0
0
0
0
0
0
3
1
0
0
0
2
0
1
0
0
2
0
0
2
0
1
3
0
2
0
0
3
0
0
2
0
0
0
0
2
2
0
2
1
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
2
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
2
1
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
1
1
0
2
0
2
0
2
0
0
0
0
0
1
2
0
0
0
2
0
0
2
0
0
1
2
1
0
2
0
1
0
2
0
2
1
0
1
2
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
2
0
0
2
0
0
3
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
2
2
0
0
0
1
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
1
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
2
0
0
0
1
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
6
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
2
0
0
0
2
2
1
0
0
0
0
1
1
2
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
5
2
1
1
2
1
0
0
0
0
1
2
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
1
0
5
1
1
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
1
0
3
0
0
0
3
0
0
0
0
2
0
3
0
0
0
2
3
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
2
0
1
0
0
0
2
0
2
2
0
0
0
1
3
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
2
0
1
2
7
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
2
2
3
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
2
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
2
0
0
0
0
0
0
0
2
0
0
0
1
0
2
2
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
4
0
1
2
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
1
0
2
0
4
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
3
0
2
0
0
0
0
2
0
2
0
0
2
2
0
2
2
2
0
0
0
4
0
0
2
0
1
4
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
4
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
2
2
0
0
2
0
0
0
0
2
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
2
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
1
1
1
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
2
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
4
0
1
2
0
0
0
2
1
2
0
0
0
0
1
2
2
2
0
1
2
0
2
0
0
0
0
1
0
0
0
0
0
0
2
1
1
0
2
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
2
1
0
0
2
0
4
2
0
0
3
0
2
2
0
2
0
1
2
0
1
0
3
2
0
0
0
0
0
2
1
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
1
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
1
0
1
2
0
2
4
0
0
0
1
0
0
0
0
0
2
0
0
1
0
1
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
1
1
0
3
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
2
0
1
2
0
0
0
0
3
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
1
0
0
0
0
0
0
2
0
2
2
0
0
2
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
1
4
0
1
0
0
0
1
0
0
3
1
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
3
0
0
0
0
2
0
0
0
0
1
0
0
0
0
4
0
1
0
0
3
0
0
0
0
0
2
0
2
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
3
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
6
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
1
0
0
1
0
0
0
2
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
2
0
2
1
3
1
0
0
1
0
0
0
0
0
0
3
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
2
0
1
0
0
3
0
0
0
1
1
0
0
0
5
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
1
1
0
2
2
0
2
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
5
1
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
1
6
0
1
2
0
1
1
2
3
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
2
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
1
0
0
2
0
0
0
1
0
0
0
2
0
0
1
0
2
0
0
0
1
2
5
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
1
0
1
0
1
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
2
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
1
0
1
3
1
0
0
0
0
2
1
2
2
0
0
0
1
2
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
1
0
2
0
0
0
0
2
0
0
0
0
2
2
0
0
1
1
0
0
0
2
0
0
0
0
0
0
5
0
0
0
0
0
1
0
0
0
4
0
2
0
2
0
0
0
1
1
0
0
0
0
1
1
1
0
0
0
0
0
1
3
1
0
1
0
0
0
0
0
0
0
0
3
0
1
1
0
0
0
1
0
0
0
2
3
0
1
0
0
2
0
0
0
0
0
3
0
1
2
0
0
0
0
1
0
0
0
1
0
1
0
2
0
2
1
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
1
0
1
0
0
1
2
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
1
0
2
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
1
0
1
0
0
1
0
0
2
0
0
0
0
2
0
0
0
2
2
0
2
0
0
0
0
1
0
2
0
0
0
0
3
0
0
0
0
0
2
0
0
0
1
0
0
0
3
0
0
2
0
0
1
0
1
0
2
0
0
0
0
1
0
0
0
0
0
1
2
1
0
2
0
0
0
1
3
0
0
0
0
0
0
7
0
0
0
1
1
2
0
0
0
0
0
1
1
0
0
0
0
0
2
0
2
0
1
2
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
2
1
1
2
0
0
0
0
0
2
1
1
0
0
0
0
2
2
0
0
1
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
1
1
0
1
3
0
1
0
0
0
0
1
0
0
0
2
0
0
1
2
2
0
0
0
0
0
3
0
2
1
0
0
0
0
0
0
2
0
1
0
2
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
1
2
0
0
0
0
0
1
2
5
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
2
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
2
2
0
0
0
0
0
0
0
0
0
0
2
0
1
3
0
0
2
1
0
0
1
0
1
0
0
1
0
2
0
0
0
0
1
1
1
0
0
0
0
0
0
0
2
0
0
0
0
4
0
0
0
0
0
0
1
0
1
0
1
0
4
0
0
0
0
2
0
2
0
2
2
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
1
2
0
0
1
1
0
4
2
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
1
1
3
0
2
3
1
2
1
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
2
0
0
3
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
2
0
0
1
1
0
2
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
2
0
2
0
2
0
0
1
0
1
0
1
1
2
0
0
2
2
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
1
0
2
0
2
0
5
0
0
2
0
0
0
1
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
2
0
4
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
3
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
1
0
1
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
2
1
0
2
0
0
1
1
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
3
0
0
0
0
1
0
0
0
0
0
2
0
0
3
0
1
0
0
2
0
0
4
0
0
0
0
2
0
1
0
1
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
2
0
1
1
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
1
2
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
1
2
1
0
0
0
0
0
0
2
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
7
1
0
2
0
2
0
0
0
0
1
0
1
0
1
0
0
0
1
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
1
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
1
0
0
0
0
0
0
1
0
2
1
0
0
1
2
2
0
2
1
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
1
1
0
1
0
1
0
2
0
2
0
0
2
0
2
0
0
0
0
0
0
2
0
0
2
0
3
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
2
1
0
2
0
2
0
0
0
2
0
0
2
0
1
2
0
0
0
2
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
2
0
0
0
2
0
1
0
0
3
0
2
2
1
0
0
0
0
0
0
2
0
0
0
4
0
1
0
0
0
2
0
0
1
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
3
0
0
2
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
4
2
0
0
4
0
0
0
4
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
3
0
0
0
0
0
3
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
1
0
1
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
1
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
2
0
0
2
0
0
1
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
3
0
0
0
0
6
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
3
0
0
0
1
1
1
0
0
0
0
0
1
1
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
1
0
1
1
0
0
0
0
0
2
0
0
5
0
0
0
0
0
0
0
0
0
3
0
0
3
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
1
0
0
0
0
1
0
1
0
0
1
3
0
0
0
2
2
1
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
2
0
0
2
1
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
5
0
0
0
0
0
0
2
0
1
0
1
0
2
0
0
2
0
0
2
2
0
0
0
0
1
3
0
2
0
0
0
2
0
1
0
0
0
0
3
3
0
3
0
0
0
2
0
0
0
0
0
2
0
0
0
1
1
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
2
1
0
1
3
2
0
0
0
0
4
1
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
1
1
1
0
0
1
0
2
0
1
0
0
0
0
1
0
0
2
4
0
1
0
0
0
2
1
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
3
0
0
1
0
0
0
0
2
0
3
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
2
0
0
1
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
2
0
4
1
0
2
2
0
0
8
2
2
3
1
1
0
2
1
0
0
0
3
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
2
0
1
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
2
2
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
1
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
1
1
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
2
1
1
0
0
0
1
0
2
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
3
1
0
1
0
0
2
0
0
4
1
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
1
0
1
0
0
0
2
1
0
0
2
0
0
0
0
2
2
0
0
2
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
3
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
2
1
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
4
1
0
0
1
2
1
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
2
0
0
0
0
1
0
0
0
7
0
1
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
3
0
0
4
2
0
0
0
0
0
2
0
0
0
0
1
0
1
0
2
0
1
1
0
0
0
0
1
3
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
1
0
0
0
0
1
1
0
0
0
3
0
2
0
7
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
7
0
0
0
0
0
2
2
1
1
0
0
0
0
0
0
0
3
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
1
1
1
0
0
1
0
0
2
2
0
4
0
3
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
2
0
1
0
0
0
2
0
0
3
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
1
2
2
2
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
2
1
0
2
0
0
0
0
0
0
0
0
2
2
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
3
0
0
0
0
0
2
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
2
0
0
0
0
3
2
0
2
0
0
2
0
0
1
3
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
7
0
2
0
0
0
0
1
0
0
0
2
2
0
2
0
1
0
0
0
0
0
2
1
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
1
1
1
0
1
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
3
0
0
1
0
1
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
6
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
2
0
0
0
2
0
1
0
2
0
0
0
0
3
2
0
2
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
1
0
0
1
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
1
2
2
0
3
0
1
0
0
2
0
0
0
0
1
2
0
0
0
1
0
0
0
0
1
2
1
6
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
2
1
0
0
0
4
0
2
1
1
0
0
0
0
2
0
2
0
0
2
1
0
1
0
0
2
1
0
0
0
0
2
0
1
0
0
0
1
0
0
0
1
2
0
0
2
0
2
0
0
5
0
2
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
10
5
0
0
0
2
0
0
0
2
0
0
2
0
4
0
0
0
1
2
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
1
0
0
0
3
0
0
0
2
0
0
0
0
0
6
0
0
0
0
0
0
1
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
3
0
2
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
2
1
1
1
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
1
3
0
0
2
0
0
1
0
0
0
1
0
0
3
0
0
2
1
0
0
0
2
0
1
2
0
2
1
0
2
0
2
0
2
0
1
2
0
1
1
0
1
0
0
0
0
1
2
1
2
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
2
0
4
0
2
0
0
1
3
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
1
0
2
0
0
0
1
1
0
3
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
3
1
2
1
0
0
0
0
0
2
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
2
0
0
0
0
0
1
2
0
0
1
2
0
0
2
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
5
0
0
1
1
0
2
1
0
0
0
2
0
0
0
0
0
2
0
0
1
1
2
0
0
1
2
0
4
0
0
0
0
2
0
0
0
0
0
3
0
1
0
0
0
1
0
0
0
2
0
0
2
0
0
1
2
2
2
0
0
0
2
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
2
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
3
1
2
2
1
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
9
0
2
2
0
3
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
1
0
1
2
0
1
0
1
0
0
0
0
0
2
3
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
2
2
2
0
0
2
0
0
0
2
0
0
0
0
1
0
1
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
1
0
0
0
0
0
1
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
1
2
2
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
1
2
1
2
0
4
0
2
0
0
0
1
0
0
2
0
0
1
0
2
0
3
0
2
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
2
1
0
3
2
0
3
0
0
0
0
2
1
0
0
2
1
0
1
0
0
0
1
0
2
0
0
0
2
0
2
1
2
0
0
0
1
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
1
0
1
0
0
0
0
1
0
0
0
0
0
2
0
2
2
0
1
0
0
0
0
0
0
3
0
0
2
1
1
0
0
2
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
3
0
2
0
0
1
0
0
1
0
3
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
1
0
5
0
0
2
1
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
1
2
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
2
0
0
1
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
5
0
0
0
0
0
0
0
0
1
2
9
1
2
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
2
1
2
0
1
0
2
2
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
1
2
0
0
2
0
0
2
0
1
0
0
2
0
0
2
0
2
0
0
0
1
0
2
0
0
0
1
1
1
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
3
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
3
0
0
0
4
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
7
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
1
0
0
2
0
0
1
0
0
5
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
2
2
0
1
0
0
1
0
0
0
0
0
0
0
0
3
0
2
1
0
0
0
0
0
0
2
0
0
0
4
0
0
0
1
2
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
1
0
1
0
2
0
5
0
0
0
0
1
0
0
0
2
0
0
0
1
1
0
0
0
1
2
0
0
0
0
2
0
0
0
0
1
2
0
0
1
0
3
1
0
2
2
0
0
0
0
0
0
5
0
0
2
0
1
1
0
0
0
1
1
1
0
0
0
1
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
2
2
0
2
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
2
3
0
1
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
2
0
0
2
0
1
0
0
0
5
0
0
0
0
1
0
0
0
3
0
0
0
4
1
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
3
0
0
0
1
0
0
1
2
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
2
2
0
4
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
2
1
1
2
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
1
1
0
0
0
2
0
0
0
0
2
0
2
0
0
2
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
1
2
0
0
3
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
1
0
2
2
0
0
2
0
0
0
0
0
2
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
3
1
0
1
0
0
4
1
0
0
2
0
0
0
1
0
2
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
1
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
2
0
2
0
0
0
2
0
2
0
0
0
0
0
1
0
1
0
0
2
0
0
0
1
1
0
2
5
0
0
2
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
2
0
0
3
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
1
1
0
0
1
1
1
2
0
0
0
0
0
2
2
1
0
3
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
3
1
0
0
1
0
2
0
2
1
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
2
0
4
0
1
0
0
2
1
0
0
1
0
1
0
1
0
0
0
3
0
2
0
0
0
0
0
2
0
1
0
0
1
0
0
0
2
0
0
2
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
3
0
0
0
2
0
1
2
0
0
0
1
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
3
0
0
0
2
2
2
0
2
0
0
0
1
0
1
1
0
1
2
3
0
0
0
1
3
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
1
2
0
0
0
1
1
1
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
2
1
0
1
0
0
1
1
0
0
1
2
0
0
0
2
0
0
0
0
0
2
1
0
1
0
0
1
0
0
0
0
0
4
0
2
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
2
2
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
2
1
2
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
2
2
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
1
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
7
0
0
0
1
0
0
0
0
2
0
2
0
0
0
2
0
0
2
1
2
2
1
0
0
0
0
1
0
2
2
0
0
0
0
0
3
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
3
0
0
0
0
1
0
0
0
0
0
4
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
4
1
1
0
0
0
0
0
2
0
0
0
0
0
0
2
3
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
1
1
0
1
0
0
0
2
0
0
4
0
0
5
0
1
1
0
0
0
1
1
0
0
2
0
0
1
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
2
0
0
2
0
0
0
2
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
1
2
0
0
0
2
1
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
5
1
1
1
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
2
0
0
0
2
2
0
0
0
0
5
0
0
0
1
2
1
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
1
0
0
0
3
0
0
1
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
1
1
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
4
0
0
2
0
1
0
0
0
0
1
1
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
1
1
1
0
2
1
1
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
1
1
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
2
2
0
0
0
0
2
0
3
1
0
1
0
3
0
2
2
0
0
0
0
0
2
0
0
0
0
2
0
1
0
2
0
0
0
1
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
2
0
0
2
0
1
0
2
1
0
0
0
2
0
0
0
5
1
0
0
1
0
2
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
2
2
0
0
0
2
0
0
0
0
0
2
2
3
3
0
0
0
0
0
2
1
0
2
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
2
0
0
0
1
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
2
0
0
2
0
1
2
1
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
1
0
0
0
2
0
0
2
0
0
1
0
0
0
4
0
1
0
1
0
0
2
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
1
3
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
2
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
2
2
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
1
2
0
0
0
0
1
0
0
1
1
3
1
0
0
0
2
0
0
0
3
2
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
3
2
0
0
0
1
0
1
2
0
0
0
1
6
1
2
0
0
0
0
0
0
0
3
0
0
0
1
0
1
1
0
0
0
0
0
2
1
0
1
0
3
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
6
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
2
0
0
0
5
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
2
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
2
1
2
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
5
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
1
0
3
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
1
0
0
0
1
0
0
0
2
4
0
1
0
2
0
0
0
0
1
1
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
1
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
6
0
2
0
0
0
1
1
0
0
0
0
0
0
0
2
1
2
1
2
0
2
0
0
0
0
0
0
2
0
2
2
0
0
1
0
0
1
0
0
1
0
1
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
1
3
2
0
2
2
1
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
6
0
0
0
0
2
0
0
4
0
2
1
0
2
2
1
2
1
0
2
2
1
0
0
0
0
3
0
2
0
6
0
0
0
0
0
0
1
2
0
0
0
0
0
2
2
0
0
0
2
0
2
0
1
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
2
0
2
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
2
1
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
3
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
1
1
0
0
0
0
0
3
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
2
0
0
2
0
0
0
2
0
2
1
0
0
0
2
1
2
4
1
1
2
0
0
0
2
0
0
0
1
1
0
2
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
17
2
0
1
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
1
0
0
1
0
2
0
2
1
1
2
1
0
1
0
1
1
0
0
2
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
1
0
2
0
0
2
0
0
2
0
0
0
0
0
0
2
0
2
2
0
0
0
3
0
0
0
0
1
0
2
1
2
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
3
0
0
0
1
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
2
0
2
0
2
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
2
0
0
2
0
0
0
0
0
0
1
3
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
3
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
4
0
0
1
0
1
0
1
0
0
0
1
1
0
0
0
2
2
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
2
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
1
0
0
1
0
0
0
1
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
2
0
2
0
0
0
0
0
2
0
2
0
3
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
2
2
2
0
1
0
0
0
0
0
1
0
2
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
3
0
0
1
0
0
2
1
0
0
0
0
0
0
0
2
2
0
1
0
0
0
2
3
0
0
0
0
3
1
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
2
0
0
2
1
0
0
2
0
0
2
0
0
1
0
1
0
2
0
0
0
0
0
2
0
0
0
3
0
2
0
1
0
0
0
0
0
0
1
0
2
0
0
0
3
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
2
2
0
0
0
0
4
0
2
0
0
0
0
0
0
1
2
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
2
0
1
1
1
5
4
0
0
1
0
1
0
0
0
0
0
2
0
0
1
0
0
0
2
0
2
0
0
0
0
2
0
0
4
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
1
0
1
2
1
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
1
2
1
2
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
1
2
3
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
7
0
1
0
4
0
0
1
0
2
0
1
0
0
0
0
0
1
2
1
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
2
1
0
1
0
1
0
0
0
2
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
2
2
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
5
2
2
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
4
0
1
2
1
2
0
0
0
0
2
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
3
0
3
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
2
0
2
0
0
1
0
2
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
3
0
0
0
0
0
0
0
0
3
2
0
0
2
0
2
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
1
2
0
0
0
1
0
2
0
0
1
1
0
0
0
0
2
0
0
0
0
3
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
6
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
2
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
2
3
0
2
0
1
1
0
0
0
0
4
0
0
0
0
0
0
2
2
0
0
0
0
2
1
0
2
0
0
0
0
0
0
1
0
0
1
0
0
1
1
2
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
5
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
4
0
3
0
0
0
0
0
0
0
1
2
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
1
2
2
0
0
3
0
1
0
2
2
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
1
2
0
0
0
0
0
0
2
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
2
1
2
0
0
0
0
0
1
0
3
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
4
1
1
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
2
1
1
0
5
1
0
0
0
1
1
2
0
0
0
2
0
2
0
0
0
0
1
1
0
0
1
1
0
0
0
1
0
2
0
2
0
0
1
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
2
0
0
0
2
0
1
2
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
3
0
0
1
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
1
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
4
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
3
2
1
0
2
1
0
2
0
0
0
1
1
0
0
2
0
1
0
3
0
0
0
8
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
4
0
1
1
4
2
0
0
0
0
1
0
0
0
2
2
0
2
0
0
2
0
2
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
1
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
1
0
0
0
0
7
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
1
0
0
1
0
2
1
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
3
8
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
2
1
1
0
2
0
2
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
2
0
1
1
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
2
0
1
0
0
2
0
0
0
0
1
1
2
0
1
0
0
1
0
0
0
0
0
0
2
1
1
0
0
2
1
0
0
0
0
2
1
0
0
2
1
0
2
0
0
0
0
1
0
0
1
0
0
1
0
2
0
0
0
0
1
0
2
0
3
0
0
0
0
0
1
0
1
1
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
1
0
2
0
2
1
2
2
0
0
0
3
0
1
0
0
0
2
0
0
0
0
8
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
2
0
2
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
2
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
2
1
0
1
0
0
0
0
0
2
0
0
0
2
0
3
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
1
2
0
0
1
0
0
0
2
0
2
0
0
0
0
1
0
0
3
1
0
0
2
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
1
1
0
0
0
2
2
1
0
1
5
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
1
2
0
0
2
0
0
0
2
0
1
0
0
2
0
0
0
0
3
0
3
0
0
0
0
0
0
0
1
0
2
1
0
1
0
0
0
2
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
2
0
0
1
0
0
2
0
2
0
2
0
1
2
0
1
1
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
4
2
0
0
0
0
0
1
0
2
0
1
0
0
0
0
3
1
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
4
0
0
2
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
2
2
0
2
0
0
1
0
2
0
0
0
0
0
2
1
0
0
0
2
1
0
0
0
0
0
1
1
0
2
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
1
2
1
2
0
0
3
0
0
1
1
0
0
0
0
0
0
0
0
1
3
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
5
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
1
0
0
2
0
0
2
0
2
0
0
0
0
0
1
2
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
2
2
0
2
1
0
3
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
2
3
2
0
2
0
0
0
0
0
0
1
1
2
1
4
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
5
3
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
1
2
2
0
0
0
0
0
0
1
0
1
3
0
0
0
2
2
1
0
5
2
0
1
2
0
0
0
0
2
0
2
0
2
0
3
1
0
2
1
0
0
0
0
0
0
0
0
1
0
0
2
2
2
0
2
0
0
0
1
0
2
1
0
0
0
0
2
0
0
0
5
0
0
0
3
0
2
2
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
4
0
0
1
0
0
0
2
0
0
2
1
0
0
0
1
0
0
1
0
0
0
2
1
0
1
0
0
0
0
0
2
1
0
0
2
1
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
1
1
0
0
1
0
0
0
0
0
3
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
5
0
0
1
0
0
0
7
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
2
1
0
0
2
2
0
0
0
2
1
0
1
0
0
0
2
0
0
0
3
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
1
2
1
0
0
0
0
0
0
0
0
1
0
2
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
1
2
0
2
0
0
0
1
0
0
0
0
0
1
2
1
4
0
0
1
1
0
0
1
0
0
0
2
1
2
0
0
2
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
2
2
2
0
2
0
1
0
1
2
0
0
2
1
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
1
1
0
0
1
0
0
0
0
3
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
2
0
0
0
0
1
2
0
2
0
0
0
0
0
2
0
1
0
1
0
0
2
0
2
1
0
1
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
1
0
2
2
0
2
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
2
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
5
2
2
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
1
0
2
0
0
2
0
0
0
0
1
0
2
0
0
0
1
0
2
2
2
0
0
1
1
1
2
0
0
2
0
0
0
0
0
0
2
2
1
0
3
2
0
0
2
3
0
0
0
0
0
0
0
3
0
3
2
0
0
4
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
3
0
1
0
0
0
0
1
0
0
0
0
0
0
2
3
2
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
2
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
3
3
0
1
0
2
0
0
1
0
2
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
2
0
0
1
0
2
1
0
1
0
0
0
0
2
1
0
0
0
2
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
2
0
0
1
0
1
0
0
0
0
4
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
2
0
0
1
0
0
0
2
0
2
1
0
0
3
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
1
0
1
1
2
0
1
0
0
0
1
1
0
0
0
0
2
4
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
5
0
0
2
2
0
0
0
0
0
2
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
3
0
2
0
2
0
0
1
0
0
0
0
0
0
2
0
0
2
2
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
2
0
2
0
0
0
2
0
0
2
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
2
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
2
0
1
0
1
0
0
2
0
2
0
0
0
0
0
1
0
0
2
2
0
0
2
2
2
0
1
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
1
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
2
0
1
0
0
0
1
1
0
1
2
0
0
2
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
3
0
2
1
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
3
0
0
2
1
1
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
1
3
0
0
4
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
5
0
0
0
0
2
0
0
2
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
1
0
0
1
2
0
0
2
0
0
0
2
0
2
1
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
1
0
2
0
1
1
4
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
3
0
4
0
2
0
2
1
0
0
0
0
2
0
3
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
6
4
1
0
0
0
2
0
0
2
0
2
0
0
1
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
8
2
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
2
0
0
0
0
2
0
0
2
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
1
2
0
1
0
2
0
2
0
0
0
0
1
0
2
1
2
0
0
0
1
0
0
0
0
4
2
1
0
2
0
2
0
0
0
0
1
1
2
1
0
0
2
0
0
0
2
0
2
1
0
0
0
0
1
4
0
0
0
1
0
0
3
0
0
2
0
0
0
0
0
0
1
0
0
1
2
3
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
3
0
1
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
2
1
0
0
2
1
0
0
2
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
3
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
3
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
3
0
0
2
2
1
0
0
1
0
0
1
0
0
6
0
0
1
1
0
0
2
0
7
0
0
0
0
0
0
2
0
1
0
0
1
1
0
0
1
1
0
0
0
1
0
0
1
3
0
2
1
1
0
0
0
0
0
1
7
2
1
0
0
2
0
0
0
2
0
0
2
1
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
2
0
1
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
1
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
4
2
0
1
1
0
0
2
0
0
2
2
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
2
3
0
1
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
3
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
2
0
3
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
3
0
3
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
2
2
0
0
1
0
1
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
2
2
0
0
0
8
0
0
0
0
0
0
0
0
0
1
1
0
2
1
0
0
0
0
1
0
2
10
0
0
0
1
0
2
1
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
1
1
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
2
0
1
0
0
0
6
4
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
7
0
1
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
2
0
1
0
0
0
1
0
0
0
0
0
0
0
1
2
1
0
0
2
0
0
0
0
2
0
0
0
0
2
2
0
0
3
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
2
2
0
1
0
0
1
2
0
2
0
2
0
0
2
0
0
0
0
0
2
0
0
2
1
0
0
0
2
2
0
0
3
1
0
0
2
1
1
0
0
0
0
2
2
0
0
5
0
0
2
0
0
1
0
2
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
5
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
2
0
0
0
0
0
0
2
0
1
2
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
4
3
4
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
1
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
1
2
4
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
2
1
2
0
0
0
2
0
0
0
0
3
0
1
0
2
0
0
0
0
0
0
0
3
0
0
0
0
2
1
0
0
1
0
0
0
0
1
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
1
0
1
2
2
0
0
0
1
0
1
1
1
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
1
0
1
3
0
1
1
0
0
0
0
0
5
0
1
0
0
0
0
4
1
0
2
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
2
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
2
1
0
0
3
0
0
1
0
0
0
2
1
1
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
4
0
1
2
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
2
0
2
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
2
0
2
1
0
1
0
0
0
2
0
0
0
2
0
1
0
0
2
2
0
2
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
24
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
1
2
0
2
0
0
0
0
2
0
1
0
0
1
0
1
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
1
0
2
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
2
1
1
0
2
0
0
1
0
0
3
2
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
4
0
0
0
2
1
3
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
2
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
3
2
0
1
0
0
0
0
0
2
0
0
2
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
1
0
0
0
2
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
4
0
0
0
5
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
2
0
0
0
0
0
1
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
2
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
1
0
3
1
1
0
0
0
0
0
0
2
0
0
0
3
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
6
6
0
2
0
1
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
2
4
0
0
0
1
1
0
0
1
1
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
2
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
4
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
3
0
1
0
0
0
0
0
2
0
0
2
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
2
1
1
0
1
1
0
1
2
0
0
1
2
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
2
2
2
0
0
0
0
1
0
0
0
0
1
1
0
0
0
2
0
0
0
2
3
1
0
0
0
0
2
0
1
0
0
1
0
0
0
2
0
0
0
2
1
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
1
1
0
1
1
0
0
1
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
1
2
0
3
0
0
2
0
0
2
2
0
0
2
1
0
0
0
1
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
1
0
2
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
2
2
1
0
0
1
2
1
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
1
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
1
0
0
1
0
1
1
0
2
2
0
0
0
2
1
1
0
0
1
0
1
0
0
2
0
0
2
0
0
2
2
0
0
0
0
0
2
1
0
0
5
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
1
1
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
6
0
0
0
0
1
0
0
1
1
0
2
2
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
2
3
1
0
0
0
0
0
1
2
0
0
0
0
1
2
2
0
1
0
0
0
0
0
0
0
2
2
2
1
0
0
2
0
1
0
0
2
0
0
0
0
0
1
4
0
0
0
0
1
0
2
1
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
3
0
0
2
0
0
0
1
2
0
2
3
2
0
0
0
0
0
1
1
0
2
0
1
1
0
1
2
2
0
0
0
0
0
0
1
0
2
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
3
0
1
0
0
0
0
0
1
0
0
0
1
8
0
0
0
0
0
0
2
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
2
0
2
0
0
2
0
0
0
1
1
0
0
0
0
2
2
0
0
0
0
0
0
1
0
1
0
0
2
1
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
4
0
1
0
0
2
0
2
0
1
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
1
2
1
1
0
4
0
0
0
0
2
0
1
1
0
0
0
1
0
0
1
0
0
1
2
0
0
2
0
2
0
0
0
0
2
0
2
2
7
1
0
0
0
1
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
2
0
0
0
1
0
1
0
7
0
0
0
2
0
1
0
0
1
2
0
0
1
0
0
0
0
3
0
0
0
1
0
0
0
0
0
2
0
2
1
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
2
0
0
1
0
0
1
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
2
0
1
0
2
1
0
3
0
4
0
0
0
0
0
1
2
0
0
0
0
0
3
0
0
2
1
0
0
0
0
2
1
0
0
0
3
0
0
0
1
0
1
0
0
0
2
0
1
0
0
0
0
0
3
0
0
0
0
2
0
1
0
0
3
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
2
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
2
0
1
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
1
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
3
0
1
0
0
0
0
0
2
1
0
0
2
3
0
0
0
4
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
2
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
5
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
3
2
0
0
0
3
0
0
2
2
0
0
1
0
2
0
1
0
0
0
0
0
0
0
2
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
2
0
5
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
2
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
1
0
0
0
3
0
0
1
0
0
0
4
0
0
0
0
2
2
0
0
1
0
3
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
1
1
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
2
2
0
2
0
0
2
0
0
0
1
2
0
2
0
1
0
0
0
2
4
0
0
1
0
0
0
2
1
0
2
1
0
0
0
0
0
2
0
2
0
10
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
1
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
1
2
0
0
0
1
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
1
3
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
2
0
0
4
3
1
0
3
0
0
0
0
1
1
0
0
0
0
2
2
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
1
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
5
0
0
1
2
0
0
1
0
4
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
1
2
0
0
0
0
0
0
3
1
0
1
0
0
0
2
1
0
0
0
1
0
0
0
2
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
2
0
2
1
1
1
0
0
0
0
2
0
2
0
0
1
0
0
1
3
0
2
0
0
0
1
2
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
2
0
0
3
2
0
0
2
0
2
2
2
0
0
0
1
0
0
0
0
0
0
0
0
2
1
3
0
0
2
0
3
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
3
2
0
0
0
0
0
0
0
0
4
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
2
0
0
2
0
1
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
5
0
2
0
1
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
1
0
0
1
2
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
1
0
2
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
1
1
0
1
0
1
0
0
2
1
0
1
2
1
1
0
1
1
2
4
0
2
0
1
0
0
0
1
2
3
2
0
0
2
0
0
2
3
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
4
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
2
0
0
0
2
0
0
0
2
0
1
0
0
0
1
1
1
1
2
1
4
0
0
0
0
0
1
0
2
0
1
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
2
0
0
1
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
3
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
1
1
0
0
2
1
2
0
1
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
3
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
2
0
0
0
1
0
0
0
2
0
1
1
1
2
2
0
0
0
0
0
0
0
1
1
0
0
0
3
0
0
0
0
0
0
2
1
0
0
0
0
3
0
2
2
0
0
0
1
0
0
1
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
2
0
0
0
0
1
0
0
0
1
0
0
0
3
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
2
0
0
0
1
0
2
0
0
0
2
0
0
1
0
2
0
0
0
1
0
0
0
4
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
2
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
2
0
1
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
3
0
2
2
0
0
2
0
0
2
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
2
2
0
3
0
0
0
0
0
0
0
1
0
2
0
2
2
1
0
0
0
1
0
1
2
0
2
0
0
1
1
0
3
0
0
0
1
1
0
0
3
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
2
0
1
0
3
0
0
0
2
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
3
0
0
1
0
0
1
0
0
3
2
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
2
0
1
0
3
0
1
2
0
0
0
1
0
0
0
2
0
1
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
2
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
2
0
1
0
0
0
0
0
2
0
1
2
4
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
1
0
0
0
2
0
0
0
2
4
0
0
0
2
0
0
0
0
2
0
1
0
0
3
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
2
2
0
2
0
0
0
0
0
0
1
2
0
1
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
2
0
2
3
0
0
1
1
0
0
1
0
0
0
1
3
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
1
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
1
2
0
0
1
0
0
0
3
0
0
0
0
0
0
1
4
0
0
0
3
2
0
0
0
0
0
0
1
1
1
1
0
0
0
1
1
0
2
2
0
0
3
0
0
0
3
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
3
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
2
1
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
1
0
0
0
0
1
0
0
0
0
3
2
1
1
0
0
0
0
0
0
1
2
2
0
0
2
1
0
1
0
0
1
0
0
2
0
0
1
1
0
0
3
0
1
1
0
2
0
0
0
0
0
3
2
1
0
0
1
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
1
2
1
1
0
0
0
0
0
1
1
3
0
0
0
0
2
1
0
0
0
2
1
0
0
1
0
2
0
0
0
1
0
2
2
0
0
0
1
0
0
2
0
1
0
2
0
0
0
0
0
2
1
1
0
1
0
3
1
1
2
0
2
2
0
0
0
0
2
0
1
0
0
0
0
2
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
2
0
1
0
1
1
0
0
1
0
2
0
0
2
0
0
2
2
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
1
0
0
2
0
1
0
2
2
0
1
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
3
0
0
0
0
0
1
0
1
2
0
0
0
1
0
0
0
4
0
0
1
1
0
0
0
0
2
0
0
0
0
2
0
0
2
2
0
0
0
0
3
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
5
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
2
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
2
0
0
0
2
0
0
0
1
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
1
0
3
0
0
0
0
3
1
0
2
0
0
0
2
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
2
1
0
0
1
2
0
2
2
2
0
1
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
3
0
2
0
0
1
0
0
0
1
2
0
1
0
0
1
2
1
1
0
0
0
0
2
0
0
0
2
0
0
2
3
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
2
3
0
0
1
2
0
0
0
0
0
0
3
0
0
2
0
0
2
0
1
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
2
0
2
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
1
2
1
2
1
0
0
2
4
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
2
0
1
0
1
0
0
0
0
2
0
2
1
3
1
0
0
1
0
0
0
0
2
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
2
0
2
0
2
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
2
1
0
0
2
2
1
0
0
0
0
1
0
0
1
0
0
2
0
0
0
1
1
0
1
1
0
1
0
0
2
0
0
0
0
1
2
1
0
0
0
0
3
0
0
0
0
0
1
0
2
1
0
1
0
0
1
1
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
7
0
0
0
1
0
0
0
2
0
0
0
2
0
0
2
2
2
0
1
2
2
2
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
2
0
0
1
1
2
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
1
1
1
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
2
0
0
2
0
1
0
0
0
1
0
0
2
1
2
0
0
0
1
0
0
0
0
2
1
1
0
0
1
1
2
2
2
0
0
1
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
3
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
2
0
1
1
0
0
0
3
0
0
1
0
0
0
0
0
0
4
1
0
0
0
0
0
2
0
1
2
0
0
0
2
0
1
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
1
1
0
0
1
0
0
1
1
1
0
2
0
0
0
0
0
0
0
0
2
0
1
2
0
0
1
2
0
0
0
2
0
0
0
0
0
0
3
0
0
2
0
0
0
2
0
0
1
2
0
0
2
2
0
1
0
2
0
0
0
1
2
1
1
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
1
2
0
1
0
5
0
0
0
0
0
0
2
0
2
0
0
0
0
2
2
0
1
0
0
0
0
0
2
1
0
1
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
4
0
1
0
0
1
2
0
1
1
0
2
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
2
0
0
0
0
1
1
0
0
1
4
0
1
0
1
0
0
0
3
0
2
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
6
0
0
3
2
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
2
0
0
0
2
0
0
0
0
2
2
0
0
1
0
1
0
0
1
0
0
1
0
0
2
1
2
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
2
0
2
1
0
0
2
0
0
0
2
1
0
2
0
0
0
2
0
0
2
0
2
2
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
1
8
0
1
0
0
2
0
0
2
0
0
0
0
3
0
1
0
0
0
0
1
0
1
0
0
0
3
0
4
0
0
0
0
2
0
0
0
0
2
1
0
1
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
1
4
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
1
0
0
0
0
3
0
0
1
0
0
0
0
2
0
2
0
0
0
2
0
0
1
0
0
1
0
0
2
0
0
3
0
1
2
0
0
0
0
0
1
2
2
0
0
0
0
0
1
0
1
0
0
3
0
0
0
0
2
2
1
0
0
0
0
1
0
2
0
4
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
2
2
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
2
2
0
0
0
0
2
1
0
2
0
0
0
0
0
0
1
9
0
1
0
0
0
2
0
0
0
0
3
0
0
1
0
0
0
1
0
0
0
1
2
0
0
2
0
0
0
0
0
4
0
0
1
0
3
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
3
2
1
0
0
0
2
2
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
1
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
2
1
0
0
0
0
0
2
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
2
8
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
1
0
0
0
2
0
0
1
1
0
0
0
0
0
1
2
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
2
9
0
1
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
2
0
0
0
0
1
0
0
1
4
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
2
0
4
0
0
0
0
0
1
1
0
2
0
1
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
1
0
0
1
3
0
0
0
0
0
0
0
1
0
0
0
2
2
1
0
1
0
0
2
2
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
3
3
0
0
0
0
3
1
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
2
0
1
1
1
0
0
0
0
0
0
0
3
0
1
0
2
0
0
0
0
0
1
0
1
0
2
2
0
0
2
0
1
0
0
0
0
0
2
0
0
0
2
0
1
0
1
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
2
2
0
1
2
0
1
1
0
0
1
5
0
0
0
0
0
2
0
0
0
0
1
0
0
2
1
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
3
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
3
2
2
0
2
0
0
2
0
0
7
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
3
0
0
0
1
0
0
0
2
1
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
1
0
3
0
0
1
0
2
0
0
1
3
0
1
1
0
0
0
0
0
0
1
1
0
0
2
2
3
0
1
0
1
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
1
1
1
0
0
3
0
0
0
1
0
1
0
0
0
3
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
4
1
0
0
0
0
0
0
2
2
0
0
2
2
1
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
3
1
0
0
1
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
2
2
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
1
2
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
3
0
0
1
1
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
3
0
0
1
0
2
1
4
0
0
0
0
2
0
0
0
1
2
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
1
1
1
0
2
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
1
4
0
1
1
1
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
1
9
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
2
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
3
1
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
1
2
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
1
0
2
0
0
0
0
1
3
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
2
3
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
1
1
0
0
0
1
3
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
1
0
2
2
2
1
0
0
0
0
2
0
0
0
0
1
1
2
2
0
0
0
1
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
1
2
1
1
0
0
2
0
2
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
4
2
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
1
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
1
2
1
2
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
1
1
0
0
2
0
0
1
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
3
0
1
0
0
1
1
0
0
0
1
2
0
0
1
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
1
0
0
0
1
0
1
1
1
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
2
0
1
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
2
2
0
0
0
0
0
0
0
1
0
1
2
0
2
0
0
0
0
2
0
1
0
4
0
0
0
0
3
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
1
3
2
2
0
1
0
0
0
2
0
0
0
0
2
0
0
0
2
1
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
2
0
0
1
0
0
1
0
0
1
2
0
0
0
0
2
2
1
0
0
0
0
0
0
0
3
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
2
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
1
2
1
0
0
0
0
0
0
0
0
3
0
0
4
0
0
0
0
0
4
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
4
0
2
0
0
1
2
1
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
1
2
0
1
0
0
1
2
1
0
0
0
0
1
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
2
0
1
4
0
1
0
0
0
0
1
0
2
0
0
3
0
2
1
0
0
2
0
0
0
1
1
2
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
2
0
1
1
0
0
0
0
1
2
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
2
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
1
4
1
2
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
2
0
0
0
3
0
0
0
2
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
3
0
0
0
0
1
0
0
3
2
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
5
0
0
0
0
1
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
1
1
0
2
0
2
0
0
1
0
0
0
1
0
0
5
2
0
0
0
0
0
0
0
4
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
1
0
1
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
1
1
2
0
2
2
0
0
1
0
0
1
1
0
1
0
1
2
2
0
0
0
1
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
1
6
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
3
1
1
2
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
1
3
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
3
0
0
0
0
0
1
1
0
0
0
1
1
0
1
0
0
0
0
2
0
1
0
1
0
0
3
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
3
0
0
0
0
2
0
0
1
2
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
1
1
4
0
3
1
1
1
0
2
0
1
2
1
2
0
0
2
0
0
0
0
2
2
1
0
0
2
0
1
0
0
2
0
1
0
0
0
1
2
1
0
0
0
0
0
1
1
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
2
2
0
0
0
0
0
1
0
1
1
0
4
0
2
0
0
1
0
0
0
6
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
2
2
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
2
1
2
0
0
0
3
0
1
0
0
0
0
0
1
2
0
1
0
1
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
2
0
3
0
1
2
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
4
0
0
0
2
4
0
0
0
0
2
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
2
2
2
1
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
1
0
2
1
2
3
0
2
0
2
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
1
2
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
1
1
0
0
4
0
0
0
0
0
0
1
0
0
1
0
3
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
3
0
0
0
1
1
1
0
0
0
2
0
0
1
0
1
1
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
1
1
0
1
0
0
0
2
0
4
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
2
0
2
0
1
2
0
4
0
0
0
0
0
0
1
0
0
0
0
0
2
3
0
0
10
3
0
1
1
0
2
0
3
3
0
0
0
0
0
0
0
0
0
3
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
2
0
2
2
0
0
0
0
0
3
0
0
0
0
0
2
0
1
3
0
2
2
2
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
1
4
0
0
0
1
3
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
3
0
1
0
0
1
1
0
0
0
0
0
2
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
2
2
0
0
1
0
0
2
0
0
0
2
0
0
2
0
3
0
0
0
2
0
1
0
1
1
0
5
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
2
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
1
1
0
2
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
2
0
0
1
1
4
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
2
2
0
0
2
0
0
0
0
1
0
0
2
0
0
2
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
2
0
0
3
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
5
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
1
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
3
0
0
2
0
1
2
2
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
2
0
1
0
2
2
0
2
2
0
0
0
0
2
0
0
2
2
0
0
0
0
0
4
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
7
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
2
2
0
0
0
0
0
1
3
0
0
0
0
0
1
1
2
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
4
0
0
0
0
1
3
0
3
2
0
0
2
0
0
2
0
0
0
1
3
1
0
0
2
2
0
1
0
0
3
0
1
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
4
0
1
0
0
2
2
2
0
0
0
1
1
0
0
0
0
0
0
0
1
0
2
0
0
2
1
1
0
1
2
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
3
1
0
0
2
1
3
0
0
0
0
0
3
2
0
0
2
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
6
0
0
2
0
0
0
0
2
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
3
2
1
1
0
0
2
2
2
0
2
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
2
1
1
0
0
0
0
1
0
2
0
1
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
2
2
0
0
1
0
0
2
0
0
0
0
2
0
0
0
2
0
1
0
1
0
1
0
0
0
1
0
2
1
1
1
0
0
0
0
1
2
0
3
0
0
1
1
0
0
0
2
2
0
0
0
4
2
0
0
0
0
0
0
0
1
0
0
3
0
0
2
0
0
0
0
0
5
0
0
0
3
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
1
0
1
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
3
0
2
0
2
1
0
0
1
2
1
0
0
0
0
0
5
0
2
0
0
1
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
3
2
1
0
0
7
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
2
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
2
0
1
1
2
3
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
2
2
1
0
0
3
0
0
0
0
16
2
0
0
0
0
2
1
0
1
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
2
1
0
1
0
0
0
0
3
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
3
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
2
0
0
0
3
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
1
2
2
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
1
2
0
0
0
2
1
0
0
0
12
0
0
0
2
1
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
2
0
3
0
2
0
0
0
1
2
0
2
0
1
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
1
1
2
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
2
0
0
0
2
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
1
2
0
0
3
0
0
0
0
1
0
0
1
0
0
3
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
1
1
2
1
2
2
0
1
1
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
4
1
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
2
0
1
1
0
1
0
0
0
2
2
0
0
0
2
1
0
0
0
0
0
0
0
2
2
1
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
4
2
1
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
2
1
0
1
0
1
0
2
0
0
0
2
0
0
0
2
0
2
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
2
1
1
0
2
2
0
0
3
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
2
0
1
0
0
1
1
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
2
2
4
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
2
0
0
0
0
1
2
0
2
2
0
0
0
0
0
0
8
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
2
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
1
0
0
0
3
0
0
4
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
2
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
3
0
0
0
0
0
0
1
2
0
0
0
0
0
1
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
3
0
0
0
0
0
0
1
0
0
0
0
0
3
0
2
0
2
0
0
1
2
0
0
2
1
1
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
2
1
0
1
0
0
2
0
0
3
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
3
0
2
0
6
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
2
2
0
0
0
1
0
0
0
0
0
7
0
2
0
0
1
2
0
2
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
3
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
2
0
2
0
1
1
0
0
1
0
2
0
0
0
0
0
0
2
0
0
2
1
1
0
0
0
1
0
2
2
1
2
0
0
0
6
0
3
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
1
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
2
2
0
1
0
1
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
1
2
0
1
0
0
0
0
0
0
0
0
4
0
1
0
0
1
0
0
0
0
0
0
1
3
1
0
0
0
0
0
0
0
1
2
0
1
0
1
0
2
0
0
0
0
0
0
0
0
2
1
0
1
0
1
0
0
0
0
4
2
4
0
1
1
2
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
1
0
0
0
2
1
0
2
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
3
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
1
0
1
1
0
1
1
0
0
0
1
0
0
0
0
0
2
1
1
2
4
0
0
0
1
0
0
1
1
2
0
1
1
0
0
0
0
2
2
0
0
0
0
0
2
3
0
0
1
0
0
1
2
0
0
2
1
2
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
2
1
2
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
1
0
2
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
2
0
0
0
3
0
7
0
0
0
0
2
3
1
2
1
1
0
0
2
1
2
0
5
0
0
0
0
2
2
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
2
0
0
0
2
2
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
6
2
0
1
0
0
0
1
1
0
5
0
2
0
0
2
0
0
1
0
0
5
0
0
1
0
0
1
0
0
0
0
1
2
1
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
2
0
3
0
0
0
0
0
0
2
3
0
1
0
2
3
0
4
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
1
0
3
0
0
1
2
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
4
0
1
0
2
0
0
0
2
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
3
0
0
2
0
0
0
2
2
0
2
0
0
3
2
1
0
0
0
0
1
0
1
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
2
0
0
0
0
0
0
1
1
3
0
0
0
0
1
0
0
0
0
1
0
0
3
0
0
0
0
1
0
1
0
0
0
0
0
0
4
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
3
2
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
2
2
0
0
2
0
0
0
0
0
1
0
2
0
0
0
3
1
0
0
0
1
1
4
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
3
0
0
0
0
3
0
0
0
2
0
0
2
0
0
0
0
1
2
0
2
0
1
1
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
9
0
0
0
0
0
3
0
0
1
0
0
0
2
2
0
0
0
0
1
0
0
2
0
0
0
0
0
6
0
0
2
0
0
4
2
0
0
0
0
0
1
0
0
0
1
0
0
2
1
0
0
2
0
3
0
2
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
14
0
1
4
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
3
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
5
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
2
0
1
0
0
2
2
0
2
0
0
2
0
2
0
0
1
1
0
0
1
1
1
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
1
0
2
0
0
0
1
0
1
0
0
0
2
0
2
0
0
3
3
0
0
2
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
3
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
2
1
0
0
2
0
0
0
0
0
0
3
0
1
0
0
0
2
0
1
1
0
0
0
3
2
0
0
1
0
3
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
1
1
0
1
1
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
1
0
1
1
0
1
1
0
0
2
0
0
1
1
0
0
1
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
1
0
0
0
3
0
0
1
0
0
1
2
0
1
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
4
0
1
0
2
1
0
1
0
0
0
1
0
2
1
2
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
2
2
0
0
1
0
2
0
1
1
0
1
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
2
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
2
0
3
0
0
1
2
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
2
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
1
1
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
1
2
0
2
0
3
7
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
4
0
1
2
1
1
2
0
2
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
2
0
1
0
2
0
0
0
2
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
1
4
0
0
0
0
0
2
2
0
2
1
0
0
2
1
0
0
0
0
1
3
0
1
0
0
1
0
2
0
1
0
2
1
0
1
1
0
0
0
0
1
0
3
0
1
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
3
2
0
0
1
0
3
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
2
1
0
2
0
2
0
0
1
0
2
0
0
2
2
0
0
2
0
0
0
0
0
0
2
2
0
1
0
2
0
0
0
0
2
0
3
0
0
1
1
0
0
3
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
3
1
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
1
1
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
3
3
0
1
0
0
0
0
0
1
0
0
0
0
1
1
2
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
1
2
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
1
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
1
0
5
0
0
0
0
1
2
0
2
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
3
0
1
0
1
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
2
0
1
0
0
1
0
2
0
0
0
2
1
0
0
2
0
0
0
3
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
4
0
0
1
0
0
0
0
2
0
0
2
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
1
0
1
0
0
2
2
1
2
0
0
0
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
4
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
1
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
3
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
2
1
0
1
4
1
0
0
1
3
1
0
0
2
0
0
1
4
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
3
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
1
2
0
2
2
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
4
0
1
1
0
2
0
0
0
0
2
0
2
0
4
0
0
0
1
1
0
1
0
1
0
0
1
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
2
0
1
1
0
0
0
3
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
3
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
1
2
0
0
0
0
0
0
2
0
1
0
0
1
0
3
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
1
2
1
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
3
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
7
0
0
0
0
0
1
1
0
0
0
2
0
0
7
0
1
0
3
0
0
0
1
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
3
0
2
1
0
0
2
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
1
0
1
2
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
4
0
0
0
3
1
0
2
0
0
0
0
2
0
1
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
2
0
2
0
1
0
0
0
0
1
2
0
9
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
1
1
0
0
0
2
0
0
0
0
2
3
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
2
3
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
1
0
0
1
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
2
0
4
0
1
0
2
0
0
0
0
0
0
2
0
0
1
0
1
0
1
0
0
0
0
1
0
3
0
0
1
2
2
1
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
1
1
0
1
0
1
1
0
0
2
0
0
0
1
0
0
0
0
0
0
1
1
2
0
1
0
2
2
2
2
0
2
0
2
0
0
1
0
2
0
2
0
3
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
3
1
0
0
1
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
4
2
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
3
0
0
0
0
2
1
0
0
0
2
0
0
0
1
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
1
1
0
0
0
0
1
0
2
3
0
0
0
0
0
0
2
0
0
2
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
5
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
1
2
2
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
2
1
0
0
0
0
0
3
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
2
0
1
0
0
1
0
1
0
1
0
0
0
1
0
1
0
0
0
0
4
2
0
0
0
1
0
0
0
0
0
1
2
0
0
0
1
1
0
5
0
2
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
3
2
0
0
0
1
1
3
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
2
0
2
1
0
0
2
0
0
0
0
0
3
0
2
0
0
0
2
4
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
1
2
1
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
1
0
2
1
1
1
0
0
1
0
2
1
0
0
2
0
0
1
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
2
0
0
0
0
0
1
0
0
3
0
0
3
0
1
1
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
1
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
3
0
0
0
0
1
2
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
2
0
2
0
0
0
0
2
1
0
2
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
1
0
2
4
0
1
0
0
1
0
3
2
1
2
2
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
1
1
1
3
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
2
2
2
0
0
1
0
0
4
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
2
0
0
0
0
1
2
0
0
0
2
2
0
1
3
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
1
0
0
0
0
0
0
1
4
0
0
0
0
0
0
2
0
0
0
0
4
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
1
0
0
1
0
3
0
0
0
0
1
1
0
0
2
0
0
1
0
1
0
2
0
2
2
0
0
0
0
0
0
0
0
3
2
0
2
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
1
2
0
2
0
0
0
2
0
0
0
2
2
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
1
1
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
2
3
0
0
3
0
1
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
2
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
3
0
3
3
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
3
0
1
0
1
0
1
1
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
2
1
1
2
0
0
0
0
0
3
1
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
1
1
0
0
1
0
0
2
0
0
0
2
0
0
1
1
0
0
0
0
1
0
0
2
1
0
0
0
2
2
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
2
1
0
1
0
1
0
0
1
0
1
0
0
0
0
0
1
0
3
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
5
4
2
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
2
0
2
0
0
0
0
0
1
1
0
2
0
0
5
0
0
2
1
1
1
1
0
0
0
0
0
2
0
0
0
0
0
2
1
0
3
0
0
0
2
1
0
0
0
0
4
0
2
0
0
0
0
0
0
0
0
1
0
1
2
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
1
2
0
0
1
0
0
0
1
0
1
1
1
3
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
3
0
0
0
0
4
0
1
0
1
2
0
2
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
1
2
2
0
0
2
0
0
0
0
1
0
0
0
0
3
0
2
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
6
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
2
1
1
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
1
0
0
2
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
2
1
0
0
2
2
0
0
0
0
1
0
1
2
0
1
0
0
0
0
1
0
1
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
1
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
1
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
1
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
3
0
0
0
1
0
0
0
2
0
1
0
0
2
0
3
0
1
0
0
1
0
0
0
2
0
0
0
0
2
2
0
0
1
0
0
0
0
0
1
1
0
1
0
1
1
2
0
0
2
0
0
0
2
0
0
0
2
0
0
0
1
1
0
0
2
0
0
2
1
0
0
2
1
0
1
3
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
2
2
0
0
0
0
1
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
1
1
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
1
0
2
0
0
1
0
0
1
1
0
1
2
0
1
0
0
1
0
0
0
0
0
0
0
1
2
2
2
0
2
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
7
0
0
2
0
3
0
0
0
0
1
0
2
0
0
0
0
4
0
0
0
0
1
1
1
0
0
2
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
1
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
2
0
1
0
0
0
0
0
3
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
3
1
1
0
0
1
0
0
0
0
2
1
0
1
0
2
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
1
0
1
0
2
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
7
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
1
2
1
0
0
0
1
2
3
0
0
0
1
0
2
0
2
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
1
3
0
1
2
0
0
0
3
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
4
0
0
0
0
2
1
0
0
0
3
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
2
1
2
0
4
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
2
0
0
1
2
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
2
1
0
0
6
0
0
0
2
0
1
0
0
1
0
0
0
2
0
2
0
1
0
0
0
0
0
2
0
0
0
1
3
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
1
0
0
2
1
3
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
2
0
0
0
1
0
0
0
2
2
2
0
0
2
0
2
0
0
0
0
1
0
1
1
0
0
0
2
0
2
0
1
0
0
2
0
0
0
6
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
3
0
1
1
2
0
0
2
3
0
0
0
0
0
2
0
0
1
2
1
0
0
1
0
0
0
0
0
0
0
1
2
3
0
1
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
1
1
0
0
0
2
5
0
0
1
0
0
0
0
0
1
0
0
1
0
0
2
3
0
0
3
1
2
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
2
0
1
0
1
2
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
3
0
0
2
0
1
0
1
0
0
0
3
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
2
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
2
3
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
2
0
0
3
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
3
0
0
0
1
0
2
1
4
0
2
0
2
0
0
0
0
0
1
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
1
0
2
0
0
0
0
0
1
1
0
0
0
2
0
1
0
0
2
2
0
0
1
2
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
1
2
0
0
1
0
2
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
3
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
2
1
2
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
2
0
0
2
0
0
1
0
0
0
2
0
0
0
2
1
0
0
2
0
2
0
0
1
0
2
1
0
1
0
0
0
0
0
0
0
0
2
1
0
2
2
0
0
0
0
1
2
0
1
1
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
3
0
1
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
1
2
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
2
0
1
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
1
0
1
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
2
0
3
0
2
1
5
1
0
0
0
0
0
0
0
1
0
1
0
2
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
2
3
0
0
0
0
1
0
0
1
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
3
1
0
0
2
0
2
0
0
0
1
0
0
2
1
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
3
1
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
1
2
2
4
0
0
0
0
0
3
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
1
1
1
1
7
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
2
1
0
0
0
0
3
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
3
3
0
0
0
0
2
0
0
2
0
4
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
3
0
1
0
1
0
1
0
0
0
0
2
0
1
0
0
2
0
0
1
1
0
0
0
0
3
1
0
1
2
0
1
0
0
1
0
0
1
1
0
0
0
0
1
0
3
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
1
1
0
0
0
1
2
0
0
0
0
0
2
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
1
1
0
0
0
2
0
0
1
0
0
2
0
0
2
1
0
0
0
1
0
0
3
1
0
0
0
0
0
2
2
0
2
1
0
1
0
0
0
1
0
0
0
0
1
0
1
3
0
1
2
0
0
0
0
0
0
3
0
1
0
0
2
0
1
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
2
0
0
0
2
1
0
1
0
0
0
0
0
1
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
2
4
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
7
0
0
2
0
1
0
0
0
0
1
0
0
0
0
1
0
0
2
2
1
0
2
0
0
1
2
0
2
0
0
1
0
0
0
0
1
2
2
1
0
0
0
0
2
0
0
0
5
0
0
2
0
3
0
0
1
0
0
0
1
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
5
1
3
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
6
0
0
2
0
4
1
2
0
0
2
2
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
1
2
2
0
1
0
0
0
3
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
2
0
1
0
2
2
0
0
3
0
0
2
0
6
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
1
3
0
1
1
0
0
0
0
3
0
0
2
0
1
0
9
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
3
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
2
1
0
0
1
0
0
1
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
2
0
2
0
0
0
1
2
0
0
1
0
0
1
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
2
0
2
2
0
2
2
0
2
0
0
0
0
0
2
0
1
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
1
2
0
0
1
0
0
0
0
1
0
0
2
2
1
1
0
0
2
0
3
4
0
1
2
3
0
1
2
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
1
2
0
1
2
1
0
0
2
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
2
0
0
0
0
1
2
0
0
0
0
1
0
0
0
1
2
3
0
0
1
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
2
0
0
0
1
0
2
0
1
2
0
0
2
8
2
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
1
1
0
2
0
0
0
3
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
1
2
0
2
0
0
0
2
0
0
0
0
0
1
2
1
0
3
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
1
2
0
1
0
0
1
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
4
1
0
2
1
0
0
1
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
4
0
1
0
0
1
1
2
0
2
1
0
0
0
0
0
0
0
1
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
2
0
2
1
1
0
0
0
0
0
2
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
3
0
2
0
0
0
0
0
7
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
2
3
0
1
0
2
0
1
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
1
0
2
0
2
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
3
0
2
0
2
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
5
0
2
0
0
0
0
1
1
2
0
0
0
0
0
1
0
4
0
0
0
0
1
2
0
1
0
0
1
0
0
1
0
0
2
1
2
0
0
1
0
0
0
0
0
0
0
1
2
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
2
5
3
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
1
2
0
0
0
2
0
0
0
3
0
0
0
1
0
0
0
0
0
5
0
0
0
2
2
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
1
1
2
0
0
4
0
1
2
0
0
0
2
2
0
0
0
0
1
2
5
0
0
1
0
0
0
0
0
3
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
1
0
0
0
0
5
0
0
0
0
1
0
0
0
0
0
3
0
2
0
2
0
0
0
0
0
0
0
0
1
3
0
5
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
2
0
0
1
2
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
3
1
0
0
2
1
0
0
1
0
0
0
0
6
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
1
0
0
0
0
0
1
0
2
0
0
1
1
0
0
0
1
0
1
2
1
0
0
0
1
1
0
1
2
0
0
2
0
0
1
0
0
0
0
1
0
2
0
1
0
0
3
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
1
0
0
0
1
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
1
0
0
0
2
3
0
0
3
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
2
0
0
2
1
2
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
3
0
0
2
2
0
0
3
1
0
0
2
0
0
2
0
0
0
2
0
1
1
1
0
0
1
1
0
0
1
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
2
1
2
2
0
0
2
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
1
0
1
2
0
0
0
2
1
0
0
0
2
2
0
0
0
1
0
0
2
0
1
1
1
1
0
1
0
0
0
1
0
2
1
0
0
0
2
0
0
0
2
0
2
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
2
0
0
1
2
0
2
0
0
0
0
3
0
1
0
2
0
0
0
0
2
1
5
0
0
0
0
0
0
0
0
1
0
1
1
2
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
3
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
3
0
0
0
0
1
0
1
0
1
0
0
0
0
2
0
0
0
0
5
1
2
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
2
2
0
0
1
3
0
0
0
0
2
2
0
0
2
0
0
1
0
0
0
0
0
2
0
0
1
0
1
0
0
0
1
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
1
0
0
2
0
0
0
2
2
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
1
2
2
0
1
4
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
2
0
2
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
4
0
0
0
1
1
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
1
1
0
0
0
3
1
0
2
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
4
0
0
1
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
3
2
1
2
0
0
0
1
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
4
0
2
1
0
0
1
1
1
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
1
0
1
1
2
0
0
0
1
1
1
0
0
0
0
1
0
0
3
0
0
0
2
0
0
0
4
0
0
0
2
0
0
1
0
1
1
2
0
0
1
0
0
0
0
1
3
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
2
0
0
1
0
0
2
3
0
0
2
1
0
0
2
0
1
0
0
0
1
0
0
0
0
0
1
0
0
2
2
0
0
1
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
3
0
0
0
4
0
0
0
0
0
1
0
2
0
0
2
0
0
1
0
1
2
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
3
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
1
0
0
2
0
0
0
1
1
0
1
0
0
1
0
2
0
0
0
0
0
1
2
0
2
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
1
0
2
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
2
0
2
0
0
0
0
0
1
1
2
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
3
2
0
0
0
0
0
0
2
1
1
2
0
0
0
0
0
1
0
0
3
0
1
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
6
0
1
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
2
0
2
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
2
2
0
0
0
3
0
0
0
0
0
0
1
1
2
1
0
2
1
0
0
1
0
2
1
1
0
1
0
0
0
0
0
0
0
0
1
2
0
1
0
4
1
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
1
5
0
2
0
0
1
0
0
0
0
0
1
0
2
0
1
1
0
2
3
0
0
0
1
0
2
2
0
0
0
0
0
3
0
0
0
0
0
0
5
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
1
2
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
1
1
0
0
0
0
2
0
5
0
0
0
0
0
3
0
0
2
0
1
0
0
0
3
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
2
0
0
1
0
0
0
0
0
2
1
0
2
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
2
0
1
0
1
1
1
0
0
3
0
0
0
0
2
0
0
1
1
2
0
1
0
2
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
1
0
0
1
0
2
2
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
2
0
1
2
1
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
1
1
2
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
2
0
2
0
1
0
0
0
0
0
1
0
0
0
1
3
3
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
1
0
2
0
0
0
1
0
0
0
2
0
0
0
0
1
4
2
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
2
0
0
0
2
1
2
0
0
0
0
0
2
4
0
3
0
1
0
1
1
0
0
0
0
0
2
0
2
0
2
0
0
0
2
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
1
0
0
0
0
2
0
0
0
1
1
0
2
0
4
0
0
0
0
0
0
0
0
0
1
2
0
3
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
3
0
0
0
1
0
3
0
1
0
0
0
2
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
3
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
2
2
2
1
0
2
0
3
0
0
2
0
0
0
0
0
1
0
0
0
1
3
0
1
0
0
1
0
2
0
0
0
1
0
0
0
1
0
2
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
1
2
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
3
0
0
0
1
1
0
0
1
0
0
1
2
0
2
2
0
1
1
0
0
0
0
0
0
0
0
2
0
2
1
0
0
2
1
0
3
0
4
2
0
0
0
0
2
0
0
0
1
1
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
2
1
0
0
0
0
3
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
3
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
1
1
0
0
0
0
1
4
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
7
0
1
0
1
1
0
0
0
0
6
0
4
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
2
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
1
0
0
1
0
0
3
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
2
1
0
1
1
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
3
2
0
0
0
0
0
0
0
3
0
0
0
0
2
1
0
3
0
0
0
0
0
2
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
1
0
2
0
2
0
1
1
0
0
0
0
0
2
0
0
1
0
2
0
3
0
3
2
0
0
1
0
0
3
0
2
0
0
1
0
0
2
0
2
1
3
0
0
0
0
0
0
0
0
0
1
2
6
1
1
0
0
2
0
0
2
0
0
1
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
2
1
0
1
0
1
1
0
0
0
0
0
1
1
0
0
1
1
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
2
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
1
1
1
0
0
0
2
3
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
2
0
1
0
1
0
5
2
0
0
1
1
0
2
0
1
1
1
0
0
1
1
0
2
0
1
0
2
0
0
2
0
0
2
0
0
1
0
0
1
0
0
0
2
0
0
0
1
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
5
0
0
1
0
1
2
0
0
2
0
0
0
0
1
0
0
0
0
0
1
1
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
2
1
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
2
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
1
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
5
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
1
0
3
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
1
2
0
0
0
2
1
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
5
2
0
0
0
1
1
2
0
0
1
0
1
0
2
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
1
0
2
0
2
0
0
1
0
0
0
0
0
0
1
1
0
2
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
2
2
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
1
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
2
0
0
0
0
4
0
0
1
0
2
3
0
0
0
0
0
2
0
2
0
0
3
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
3
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
2
0
0
1
3
0
0
0
2
0
1
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
3
0
1
0
1
0
0
3
0
1
0
0
0
0
1
1
0
2
0
1
2
0
0
0
0
0
0
1
0
0
0
5
2
3
0
0
3
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
1
2
2
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
2
0
2
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
2
1
0
0
0
0
1
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
2
0
1
1
1
2
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
2
7
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
3
2
0
1
0
0
0
0
0
0
0
2
0
1
2
0
2
0
0
1
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
3
0
0
0
0
1
2
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
3
0
0
2
0
0
1
0
0
1
2
2
0
0
1
0
0
0
0
3
0
0
0
1
0
3
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
2
0
0
0
3
2
0
1
0
0
0
3
0
2
0
1
0
3
0
0
0
2
1
2
1
0
2
0
0
0
2
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
1
0
0
0
0
0
2
0
1
0
2
1
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
3
2
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
2
0
1
0
1
0
0
1
0
0
0
2
0
1
2
1
1
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
1
2
0
0
0
2
0
1
0
0
0
1
0
8
0
0
0
0
1
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
1
0
0
2
0
3
0
1
0
0
0
0
0
0
2
0
1
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
2
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
1
0
1
1
0
0
1
1
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
2
1
0
0
2
2
3
0
0
0
0
0
4
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
2
2
0
0
0
2
2
0
0
1
0
4
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
1
1
0
2
2
2
0
2
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
2
0
0
1
1
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
1
0
0
0
3
0
0
0
0
0
3
1
2
1
0
1
0
0
0
0
0
2
0
0
0
0
2
0
3
2
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
2
2
0
1
1
0
1
0
0
0
0
1
0
1
2
0
0
2
0
3
0
0
0
0
2
0
0
1
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
2
0
3
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
3
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
1
2
0
0
2
0
0
1
0
3
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
2
3
0
0
2
2
2
0
0
0
0
0
1
4
0
0
2
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
3
0
0
2
0
0
0
0
0
0
1
3
0
1
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
2
1
0
2
2
2
2
0
1
1
0
0
0
0
0
0
2
0
0
2
0
1
1
0
0
0
7
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
1
0
3
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
3
2
1
0
0
2
0
0
0
1
0
0
0
1
1
2
0
1
0
0
0
0
0
0
0
0
0
1
0
2
1
0
2
0
0
0
0
1
0
2
3
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
3
2
0
0
2
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
2
2
0
0
0
0
0
2
0
0
0
2
0
0
2
0
2
4
0
0
2
0
2
0
0
0
2
0
7
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
1
1
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
2
0
2
0
0
0
2
1
0
1
0
0
1
0
0
0
0
0
2
0
2
1
0
0
0
2
1
0
2
0
0
0
0
0
0
0
2
0
0
2
0
1
2
0
2
0
0
1
0
0
2
0
0
0
1
1
0
0
2
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
1
2
0
0
3
0
0
0
2
0
0
3
0
0
2
0
3
0
1
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
1
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
2
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
2
2
1
0
0
2
0
0
3
0
0
0
0
0
2
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
4
1
2
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
2
1
0
1
2
0
2
1
2
0
1
0
0
2
0
0
1
0
0
0
0
5
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
1
0
1
0
1
2
1
0
1
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
2
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
1
0
0
2
0
0
0
0
2
0
1
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
2
1
0
0
0
1
0
0
5
0
0
0
0
0
2
0
0
0
0
0
2
0
2
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
2
0
1
3
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
2
0
2
1
3
0
0
0
0
0
4
0
2
0
0
0
3
2
0
2
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
1
0
0
1
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
1
0
0
1
0
0
0
1
2
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
3
0
0
0
1
0
3
0
0
0
0
0
1
4
1
0
0
2
0
0
0
3
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
2
0
1
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
2
2
0
1
0
2
0
0
0
2
1
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
1
3
0
0
0
2
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
3
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
3
0
2
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
1
0
0
2
1
0
0
0
0
1
0
1
0
0
0
2
2
0
0
0
0
0
2
1
0
4
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
4
0
0
0
4
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
3
0
1
0
1
0
1
1
0
0
2
2
0
0
0
0
0
0
7
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
1
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
3
0
2
1
2
2
0
0
0
2
0
0
1
1
2
0
0
2
2
0
2
1
1
0
2
0
0
1
0
0
1
0
2
0
0
2
0
0
0
2
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
1
1
1
0
0
0
0
0
3
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
3
2
1
0
2
0
3
0
0
1
1
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
5
1
1
0
2
0
2
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
3
0
2
2
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
1
0
0
2
0
0
0
0
0
0
0
2
2
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
1
0
0
0
0
0
1
1
3
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
3
2
0
2
0
0
0
0
0
0
0
0
0
1
1
0
2
0
1
0
1
0
0
0
0
0
0
2
0
0
2
0
3
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
1
2
2
0
0
2
0
1
0
0
3
0
0
0
2
0
0
2
0
4
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
5
1
0
0
0
1
1
2
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
2
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
4
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
5
0
0
0
1
0
0
0
0
0
0
2
1
0
0
2
0
0
0
1
0
2
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
3
0
0
0
1
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
1
0
0
0
4
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
2
1
0
0
0
0
0
2
0
1
2
0
0
1
0
0
0
2
0
1
0
0
0
0
4
1
0
4
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
2
0
1
2
2
0
1
2
2
0
0
0
0
1
2
0
2
0
0
2
2
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
2
0
2
0
0
0
2
0
0
0
2
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
1
1
0
0
0
1
0
0
0
0
3
2
1
4
2
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
1
1
1
0
2
0
0
0
0
1
0
0
1
0
2
2
0
0
0
0
0
2
0
2
0
1
3
0
2
0
1
1
0
0
0
1
1
1
0
1
0
0
2
0
1
1
1
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
2
0
0
0
1
1
0
0
0
3
0
1
0
1
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
1
0
2
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
4
0
0
1
1
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
1
0
0
0
0
0
1
0
0
0
2
0
0
1
0
2
0
1
2
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
1
3
0
0
0
1
2
1
2
0
2
2
0
2
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
1
1
0
1
2
0
0
0
1
0
0
1
0
0
0
3
0
0
0
0
0
0
0
1
0
0
1
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
3
0
0
0
1
0
0
0
0
0
1
1
0
2
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
2
0
0
2
0
2
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
4
2
0
2
2
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
1
2
0
0
0
0
0
0
1
3
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
3
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
2
1
1
0
0
4
0
0
1
2
0
0
1
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
3
0
1
0
2
0
0
0
0
0
0
0
1
0
2
0
2
0
1
0
0
5
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
2
1
0
0
2
0
1
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
1
1
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
2
0
2
1
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
1
2
1
0
0
0
1
0
0
0
0
0
2
0
2
0
2
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
5
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
2
1
1
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
2
1
0
2
0
0
0
0
0
1
0
0
1
0
2
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
2
0
0
0
0
2
0
0
1
0
0
1
1
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
3
1
0
0
6
0
0
1
2
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
2
1
0
0
2
0
2
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
3
3
0
2
2
0
0
0
0
1
0
3
2
0
0
0
0
5
0
0
0
3
0
2
3
1
2
0
0
0
2
0
0
2
0
0
0
1
0
1
1
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
2
0
0
2
0
2
0
0
0
0
0
0
3
3
0
1
0
0
2
0
2
0
0
0
0
0
1
0
1
2
2
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
1
1
0
0
2
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
1
1
0
1
0
0
0
0
1
2
0
0
2
0
0
1
0
1
0
0
1
0
4
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
1
0
2
2
0
0
0
0
0
0
0
1
2
0
0
0
2
1
0
0
0
0
0
0
2
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
1
0
1
0
0
0
0
0
2
0
1
3
0
0
0
2
1
0
0
2
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
1
1
2
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
3
2
1
0
0
0
2
1
1
2
1
1
2
1
0
1
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
2
0
3
1
0
1
0
0
0
3
0
2
0
0
1
0
2
0
2
1
0
1
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
2
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
1
0
0
0
0
1
0
2
1
1
0
1
0
1
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
2
1
1
0
0
0
0
0
0
2
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
2
2
0
1
1
0
2
0
0
0
3
1
0
1
0
0
3
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
2
0
0
1
0
1
0
3
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
4
0
0
2
0
1
0
2
0
1
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
2
2
2
0
0
0
0
0
2
0
0
2
0
0
0
2
1
0
1
0
0
2
0
0
1
2
2
0
0
0
1
2
0
0
0
0
3
0
0
2
0
0
0
3
0
2
1
0
0
0
0
0
0
2
1
0
1
1
0
0
1
0
0
0
0
1
0
0
1
3
0
2
0
1
0
3
1
0
2
1
2
1
2
0
0
0
1
0
0
0
0
7
0
1
0
0
5
0
1
0
2
0
0
1
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
1
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
1
1
0
0
0
2
1
2
2
2
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
2
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
2
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
2
1
0
2
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
2
2
0
1
0
0
2
1
0
0
0
1
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
1
0
0
0
0
0
1
0
0
2
0
0
2
0
2
0
0
1
1
0
1
2
0
1
2
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
1
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
9
1
2
0
1
0
0
0
0
0
1
2
0
2
0
0
6
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
1
0
0
3
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
1
0
0
3
2
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
2
0
2
0
0
0
0
3
1
3
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
2
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
1
0
3
0
0
0
0
0
2
1
1
1
0
1
0
0
0
1
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
2
2
2
0
2
2
3
1
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
1
1
1
0
2
1
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
1
2
1
3
0
2
0
0
0
1
1
0
0
0
1
1
3
2
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
2
0
0
0
0
0
0
0
0
3
2
1
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
1
0
2
1
0
0
2
0
1
2
0
2
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
1
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
1
0
0
0
3
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
2
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
3
1
1
2
2
1
2
0
1
0
0
0
2
0
2
2
0
0
0
2
0
1
0
0
1
0
2
0
1
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
1
0
1
0
2
1
0
0
0
2
2
0
0
0
2
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
2
0
1
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
1
0
0
0
0
0
1
0
0
0
0
3
0
0
0
1
1
0
1
0
0
3
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
1
0
2
0
1
0
2
1
0
1
1
0
0
1
1
0
0
1
0
0
0
0
0
0
2
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
1
0
2
0
2
1
0
0
1
0
1
0
2
2
0
5
0
0
0
0
7
0
0
1
0
0
0
0
0
1
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
1
1
0
2
1
1
0
0
0
0
0
0
3
0
0
2
0
0
1
1
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
2
0
3
2
0
0
0
0
2
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
4
0
2
1
0
0
2
0
1
0
2
2
0
0
0
0
0
0
0
0
2
0
1
0
2
1
1
1
0
0
0
3
1
0
1
0
1
1
0
0
0
2
2
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
1
0
0
0
2
0
0
2
1
1
0
0
0
0
0
2
2
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
3
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
5
3
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
2
2
0
0
0
2
1
0
0
0
2
0
0
1
0
0
1
0
0
3
0
0
0
0
0
0
2
0
0
0
1
1
0
2
0
0
1
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
1
0
0
1
0
1
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
2
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
2
0
2
1
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
2
0
0
0
1
0
0
6
0
0
0
0
2
0
0
0
0
0
0
4
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
2
0
0
0
2
0
0
2
1
0
0
2
1
1
0
0
2
0
0
2
0
2
1
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
3
3
0
1
0
0
0
4
0
2
0
0
1
0
0
2
2
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
2
1
0
0
1
0
7
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
3
2
2
0
0
0
0
0
0
0
1
1
1
0
0
2
2
0
1
0
0
0
0
0
2
0
0
2
0
0
1
2
0
0
0
1
1
0
0
3
0
2
2
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
2
0
0
0
1
0
0
0
2
0
0
2
2
0
2
3
2
2
0
0
0
0
0
0
1
2
1
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
3
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
1
0
0
2
0
1
0
2
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
2
0
0
1
0
0
0
1
0
0
0
1
0
0
2
0
2
0
1
0
0
2
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
1
2
0
0
3
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
4
1
0
0
0
1
0
0
2
0
0
1
0
0
1
2
0
1
0
1
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
2
0
0
1
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
1
3
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
2
0
1
1
0
2
0
0
0
1
0
1
0
2
0
0
0
0
0
0
1
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
1
3
0
1
0
0
0
0
0
4
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
4
2
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
1
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
1
11
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
2
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
1
0
0
0
0
0
1
1
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
6
0
0
1
0
2
1
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
1
0
2
2
0
1
0
0
1
0
1
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
9
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
1
1
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
2
1
0
1
2
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
1
0
0
1
7
0
0
2
0
2
3
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
2
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
3
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
2
1
0
0
0
2
0
0
1
0
0
0
1
2
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
2
0
0
0
0
1
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
2
2
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
2
0
1
2
0
4
0
0
0
0
0
0
0
2
2
5
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
1
0
2
0
2
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
4
0
1
3
0
1
0
0
2
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
4
0
0
1
1
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
3
0
0
0
2
0
0
0
0
2
0
0
3
0
0
0
5
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
1
0
6
2
0
3
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
3
0
0
0
2
0
0
0
0
2
2
0
1
2
0
1
2
0
2
2
1
3
0
0
2
3
1
0
0
0
1
0
0
0
3
1
0
0
2
0
0
1
1
0
0
1
0
1
2
0
0
0
0
2
0
1
0
0
2
2
0
3
0
0
0
2
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
1
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
3
6
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
1
2
1
2
0
0
0
0
0
0
0
2
0
2
1
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
4
3
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
2
2
1
1
0
1
1
0
0
1
0
0
2
0
2
1
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
4
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
1
1
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
2
0
0
0
0
0
1
0
1
1
0
1
1
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
2
2
0
0
0
0
2
2
1
0
2
0
1
2
0
2
0
2
2
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
5
1
6
0
2
0
0
0
0
0
0
0
0
2
1
0
0
1
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
1
0
0
1
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
1
0
1
1
0
0
2
3
0
0
0
0
0
1
2
0
0
1
0
0
0
0
1
0
0
0
2
1
0
0
0
0
1
0
0
0
2
1
2
1
0
0
1
0
0
0
0
0
0
2
0
0
2
1
0
0
1
0
0
2
0
1
2
0
2
1
2
0
0
0
1
2
0
0
1
2
0
2
0
2
0
0
2
0
0
1
0
2
1
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
2
0
2
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
3
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
2
0
1
0
0
2
2
2
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
4
0
1
0
0
1
1
1
0
0
0
0
0
0
1
1
0
0
3
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
3
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
1
1
3
0
0
0
0
0
0
0
0
2
1
1
0
0
0
1
2
0
0
1
2
0
0
0
1
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
2
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
1
1
0
1
1
0
0
0
0
0
4
0
2
0
1
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
1
2
0
2
0
0
0
0
0
2
0
0
1
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
7
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
2
0
2
1
2
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
3
0
0
2
2
1
0
0
0
0
0
0
0
1
1
0
2
4
0
0
0
2
0
0
0
1
3
0
0
0
0
0
0
0
3
1
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
1
0
1
0
2
0
1
0
0
1
0
1
1
0
1
1
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
2
1
1
0
0
1
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
3
2
2
0
3
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
3
0
0
2
1
2
0
0
2
0
0
0
0
6
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
2
1
3
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
1
2
0
0
0
3
1
0
0
2
0
0
2
2
0
0
1
0
0
2
0
0
0
2
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
1
0
0
1
0
1
2
0
0
1
1
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
2
0
2
0
0
0
3
0
0
0
0
0
2
0
1
2
1
2
0
1
0
0
2
0
2
0
7
1
0
2
0
0
0
0
0
0
1
2
2
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
1
0
0
1
0
2
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
1
1
0
3
0
2
1
0
0
0
2
2
2
0
0
0
0
0
1
1
2
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
2
0
1
1
0
0
1
4
0
0
0
0
2
0
0
2
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
3
1
0
0
0
0
1
2
2
0
0
0
0
0
0
2
0
0
1
0
0
0
2
1
0
0
3
0
1
0
1
1
0
1
2
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
1
0
2
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
2
3
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
1
0
0
2
0
0
1
0
1
0
0
0
0
2
0
0
0
0
1
1
0
1
0
1
0
0
0
2
0
0
0
3
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
4
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
5
1
0
0
0
0
2
0
0
0
0
0
2
0
0
1
3
0
2
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
2
0
1
0
2
0
2
1
1
0
0
0
1
1
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
5
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
4
0
2
3
1
2
0
1
0
0
1
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
2
0
3
1
0
0
0
0
0
3
0
0
0
1
2
0
0
0
1
0
1
0
0
4
0
0
0
0
0
0
0
2
0
0
2
1
0
1
0
0
0
0
0
0
3
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
1
1
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
1
0
1
2
0
1
0
0
0
0
3
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
2
0
2
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
1
3
2
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
2
0
1
0
0
2
0
0
0
0
0
0
1
0
0
4
0
0
0
0
4
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
1
1
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
3
0
0
1
0
1
0
0
3
0
0
0
3
0
1
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
4
2
0
1
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
6
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
1
0
0
0
2
0
2
1
2
0
0
0
0
2
0
2
0
0
0
2
0
1
0
4
0
0
4
2
0
0
1
0
0
2
1
0
0
2
0
1
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
1
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
1
0
3
0
1
0
0
0
0
0
1
2
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
3
0
0
1
2
1
2
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
3
2
0
0
2
3
0
2
0
0
0
0
0
0
3
0
2
0
0
2
1
0
2
1
0
2
5
0
0
0
0
0
0
1
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
1
0
2
2
1
0
0
1
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
7
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
2
0
0
1
0
0
0
2
0
0
1
2
0
0
0
0
6
2
0
1
2
0
0
1
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
5
0
2
1
2
2
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
2
0
4
0
0
3
0
1
0
0
5
0
2
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
1
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
8
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
2
2
2
2
0
0
0
0
0
0
2
0
1
6
0
2
0
0
0
2
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
3
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
3
1
0
0
0
0
1
2
1
1
0
0
0
0
3
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
1
0
0
2
2
0
0
0
0
2
2
0
1
0
0
1
0
1
0
2
0
0
0
0
0
0
0
1
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
1
0
2
2
2
2
0
0
0
0
1
0
2
3
0
2
0
0
2
0
0
0
1
0
0
0
0
1
4
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
2
0
0
0
2
0
0
2
2
0
0
0
1
2
0
2
0
0
2
0
0
0
0
1
1
1
2
0
1
0
0
4
2
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
1
0
0
1
1
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
4
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
1
0
6
0
0
1
0
0
2
0
0
2
0
2
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
1
2
1
1
0
0
0
2
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
2
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
1
2
2
0
0
0
2
0
2
0
0
1
0
0
0
2
0
0
2
1
0
0
2
0
0
0
2
0
2
1
3
1
1
1
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
2
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
1
0
0
2
1
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
1
0
0
0
2
1
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
4
2
0
2
0
0
0
2
0
1
0
0
0
0
0
5
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
1
0
1
0
0
0
2
1
2
1
0
0
0
1
2
2
0
0
0
0
0
3
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
3
0
2
1
0
0
2
0
0
2
1
0
0
0
0
1
0
2
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
2
0
0
1
0
0
1
0
3
1
0
2
0
0
0
2
0
0
0
3
3
0
2
0
0
2
0
2
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
2
0
2
0
2
2
1
2
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
1
1
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
7
0
0
0
0
0
1
1
0
0
2
2
0
0
2
0
2
0
2
0
0
0
2
4
0
0
0
1
1
0
0
0
0
0
1
0
0
0
2
2
0
0
1
0
0
1
0
0
0
2
2
1
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
2
0
0
0
1
2
0
0
1
2
1
2
1
0
0
0
0
0
1
0
0
2
0
2
0
1
2
0
2
0
0
0
0
0
2
2
0
2
0
1
1
1
0
0
2
0
2
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
1
0
0
2
0
0
0
1
3
0
1
0
2
0
2
0
0
0
0
0
0
0
2
1
0
0
0
1
2
2
0
1
0
0
2
0
1
2
0
2
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
2
0
2
0
0
0
0
2
0
1
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
4
0
0
1
0
0
1
0
2
2
0
2
0
1
0
0
0
1
2
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
1
0
1
0
0
0
1
0
1
2
0
2
0
0
0
0
0
2
1
0
2
0
0
1
0
2
1
1
0
3
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
2
0
1
0
0
1
0
0
2
0
0
0
3
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
1
0
5
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
1
2
0
0
0
0
0
2
0
0
1
0
0
2
0
2
0
1
0
0
0
0
0
0
1
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
2
0
1
0
0
1
0
0
1
1
1
0
0
0
0
0
0
2
0
0
0
2
0
2
2
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
2
0
1
1
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
9
1
0
2
1
0
0
2
0
2
3
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
2
0
2
4
1
0
2
1
0
0
0
1
0
0
2
0
1
0
0
2
0
0
2
0
0
1
2
0
2
2
0
1
0
0
1
0
0
1
1
0
1
1
0
0
0
1
2
0
1
2
0
0
0
0
0
0
0
0
0
1
0
2
0
2
1
0
0
0
0
0
0
0
1
0
2
0
1
1
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
2
1
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
1
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
1
2
0
1
0
0
0
3
0
3
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
3
1
0
0
0
0
0
0
0
2
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
8
1
2
0
4
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
3
0
2
1
0
0
1
3
1
0
1
0
1
2
0
0
3
0
1
2
0
0
0
0
1
1
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
1
0
1
0
0
1
0
0
0
0
2
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
7
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
1
0
4
0
0
0
2
0
2
0
0
0
2
0
0
1
0
1
2
0
2
0
0
0
0
0
0
0
0
0
2
2
0
1
0
2
2
0
2
0
2
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
1
0
0
0
2
2
0
0
0
1
0
0
0
0
1
1
1
0
1
2
0
0
0
0
3
1
2
1
0
0
0
6
0
3
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
6
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
2
2
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
1
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
3
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
1
2
0
0
0
0
0
0
4
0
2
1
0
0
0
0
0
2
1
1
0
2
1
1
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
4
0
2
0
0
0
0
0
1
2
0
3
2
0
1
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
3
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
4
0
0
0
1
1
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
3
0
0
0
1
0
0
1
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
2
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
2
0
0
1
0
2
2
0
2
0
0
1
2
0
0
2
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
2
0
0
2
0
1
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
2
0
1
0
2
0
0
2
0
0
0
1
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
1
0
0
0
2
2
1
0
0
0
3
2
0
1
2
0
0
0
0
0
5
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
1
1
1
0
0
0
0
1
0
0
5
0
1
0
0
0
0
1
2
0
2
0
0
0
1
0
0
0
0
3
2
0
0
0
0
0
0
0
2
0
2
0
1
0
0
1
0
2
0
0
0
0
0
1
0
0
0
1
1
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
21
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
1
1
0
2
2
0
0
1
0
0
1
0
2
2
1
0
0
1
2
0
0
2
2
2
0
2
0
0
0
0
0
1
0
0
0
0
1
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
5
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
2
3
1
1
0
0
0
0
0
0
0
1
0
3
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
2
1
1
0
0
0
0
0
0
1
0
1
0
0
0
2
3
0
0
0
0
6
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
2
2
0
0
0
0
0
2
2
1
1
0
1
3
0
0
0
0
0
1
0
2
2
0
1
0
0
0
0
0
0
0
6
3
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
5
2
0
0
2
0
0
0
0
0
1
0
1
0
0
0
4
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
2
3
0
0
0
2
0
0
1
0
1
0
2
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
2
1
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
1
0
1
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
1
0
0
2
0
4
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
2
2
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
2
0
0
3
1
0
0
0
0
2
0
0
2
0
0
0
2
0
2
2
0
2
1
0
2
1
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
3
0
0
2
2
0
0
0
0
0
4
2
1
0
0
1
3
0
0
0
0
0
0
1
2
0
0
0
1
1
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
1
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
1
0
2
2
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
2
0
2
0
0
1
0
1
0
2
0
0
2
0
0
0
2
0
1
0
2
0
0
0
0
1
0
2
0
0
3
0
0
0
0
2
0
0
1
0
2
1
0
1
0
1
0
2
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
1
0
0
0
0
0
2
0
1
6
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
1
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
1
2
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
3
2
2
0
2
0
0
1
0
2
0
0
1
0
2
0
0
0
0
2
0
0
6
2
1
0
0
0
0
2
0
2
1
0
0
1
0
0
0
0
0
2
1
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
2
0
1
0
2
2
2
0
0
0
0
0
5
2
0
0
0
0
2
2
0
0
0
0
1
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
3
3
0
2
1
0
0
0
0
0
1
0
6
0
0
2
6
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
2
0
2
0
0
0
0
0
0
2
0
0
0
2
3
0
1
0
0
0
1
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
1
0
1
2
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
4
2
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
4
0
0
2
0
2
2
1
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
2
4
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
1
0
4
2
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
2
0
3
0
0
0
0
2
1
1
1
0
0
1
0
0
0
1
0
0
0
0
3
0
0
0
1
0
0
1
0
0
3
0
0
0
0
2
2
0
0
1
0
1
1
0
0
0
0
0
0
1
0
5
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
6
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
2
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
4
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
1
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
2
0
0
1
2
0
0
0
0
0
1
0
1
2
0
0
0
2
1
2
2
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
1
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
1
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
3
2
0
1
0
1
2
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
1
0
2
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
1
1
0
0
1
0
1
0
1
1
0
0
2
0
1
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
1
0
0
1
1
0
2
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
1
5
2
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
3
1
0
0
2
2
0
0
0
0
0
0
1
0
2
0
0
2
1
0
0
2
0
1
0
1
2
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
2
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
1
0
3
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
2
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
2
2
1
2
0
0
0
0
1
0
0
2
0
1
2
0
0
2
0
1
2
0
0
3
0
1
0
0
0
0
0
0
2
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
6
0
0
0
1
0
1
1
0
1
0
0
2
0
0
0
0
0
0
3
0
1
0
0
1
2
0
0
2
0
0
0
0
3
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
2
0
0
0
0
2
0
1
0
0
2
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
2
0
0
4
0
0
0
2
1
1
2
0
0
2
0
1
0
2
0
0
0
1
1
0
1
0
0
0
0
3
0
0
0
1
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
2
1
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
2
0
1
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
1
0
4
1
0
0
1
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
2
2
0
0
1
0
0
0
0
0
3
3
1
0
2
0
0
3
0
0
0
0
2
1
0
0
0
3
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
1
0
1
0
0
2
0
0
1
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
2
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
2
2
0
1
1
0
2
0
0
1
0
2
0
4
2
1
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
3
2
1
0
1
0
0
1
0
2
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
2
0
0
0
0
1
3
2
0
0
0
0
0
1
1
0
0
0
2
0
0
3
0
0
1
0
1
0
0
0
0
0
2
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
3
1
3
0
0
2
0
0
0
0
0
1
2
0
0
4
2
0
0
0
0
8
0
4
0
2
1
0
0
0
0
1
0
2
2
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
3
1
2
0
1
0
0
0
0
2
0
0
1
1
0
0
2
0
0
0
1
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
2
0
1
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
1
0
0
0
0
0
3
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
2
0
0
0
2
0
0
0
0
2
0
0
0
3
0
1
0
0
0
0
0
0
0
0
2
2
0
0
1
1
0
0
2
0
0
2
0
0
2
1
0
0
0
1
2
0
0
0
2
0
0
0
0
1
1
0
2
2
0
0
2
0
0
0
0
0
2
2
1
0
0
1
0
1
0
3
0
0
2
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
2
1
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
2
3
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
1
0
1
2
0
2
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
3
1
3
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
2
1
0
1
3
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
3
0
1
2
0
0
0
0
0
0
2
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
1
6
0
0
0
3
0
0
3
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
3
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
3
0
1
1
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
2
0
1
0
0
1
3
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
1
0
0
2
1
0
0
2
0
0
2
1
2
1
0
0
0
1
0
2
0
0
1
1
2
1
2
0
0
0
0
0
0
0
0
2
0
1
2
1
2
1
0
0
0
0
0
0
0
1
0
1
2
0
1
1
1
0
1
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
1
0
0
0
2
0
2
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
2
2
0
1
0
5
0
0
2
0
0
0
0
1
0
2
0
0
0
0
1
1
0
0
0
0
2
0
2
2
1
0
0
0
0
1
0
0
2
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
2
2
0
2
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
3
0
0
1
0
0
2
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
1
0
0
0
0
2
0
0
1
0
2
0
2
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
2
1
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
2
1
0
2
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
1
0
0
0
0
0
2
1
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
3
0
0
0
0
1
0
0
0
0
2
1
2
1
0
0
0
0
0
2
1
2
1
0
0
0
0
2
0
0
1
2
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
3
2
0
2
0
0
1
0
1
2
0
1
2
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
2
1
0
1
0
0
0
0
0
2
0
0
0
0
2
1
0
0
5
0
2
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
3
0
0
0
0
1
2
0
0
2
0
0
2
3
0
0
0
2
0
0
2
1
0
1
0
0
2
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
5
0
0
3
0
0
0
0
0
0
3
0
0
0
7
0
2
0
0
0
0
0
0
0
0
1
1
0
0
4
1
0
0
1
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
2
0
1
0
0
3
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
2
0
2
0
1
0
3
0
2
0
0
0
2
0
0
0
2
0
0
0
0
4
0
0
3
1
0
0
0
0
2
3
2
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
2
4
2
0
0
2
0
0
1
1
0
0
0
0
0
3
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
2
1
0
0
3
0
0
0
0
1
0
0
2
0
0
5
0
0
2
2
0
1
0
1
0
0
0
0
0
0
3
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
2
0
0
1
0
0
2
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
2
2
2
3
0
0
0
2
0
0
0
0
0
0
0
2
2
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
2
0
1
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
1
0
0
1
0
1
2
0
0
0
0
0
0
1
0
0
2
0
0
0
3
2
0
1
2
3
2
0
3
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
1
0
1
4
0
0
1
0
0
0
0
0
0
3
1
2
0
2
0
2
2
0
2
0
0
0
0
2
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
3
3
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
4
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
2
2
0
1
0
0
0
3
1
0
0
0
3
0
0
0
0
0
2
2
1
0
0
0
1
2
0
2
0
2
0
0
0
0
0
1
1
1
0
0
0
3
0
2
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
2
0
2
0
1
0
0
1
1
1
0
1
0
0
1
1
0
0
1
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
5
2
0
1
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
2
0
0
0
0
0
3
2
0
0
3
0
0
0
0
2
0
0
0
0
3
0
0
1
0
0
1
0
0
0
0
0
2
1
1
0
1
0
3
0
1
0
3
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
1
1
1
0
0
0
1
0
2
0
1
2
1
0
0
2
0
0
0
0
1
1
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
1
1
0
2
0
3
0
0
1
0
0
0
0
2
2
0
2
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
2
7
2
0
2
0
0
0
0
3
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
1
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
2
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
4
0
0
0
0
2
0
0
1
2
0
2
2
1
0
0
0
0
0
1
0
0
0
1
0
1
3
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
1
0
3
2
2
2
0
0
3
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
2
0
0
2
1
0
0
0
1
0
0
0
0
0
4
2
0
1
1
0
1
2
2
0
0
0
1
1
2
0
0
0
0
1
2
0
0
1
0
0
0
2
0
0
0
1
0
2
0
0
0
1
0
0
0
0
3
1
0
0
0
0
0
6
0
0
2
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
5
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
2
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
4
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
2
0
1
2
2
2
0
0
2
1
0
0
2
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
2
2
0
0
1
2
1
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
2
1
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
2
0
0
2
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
1
1
0
0
2
0
0
2
2
1
1
0
0
0
0
2
0
0
0
0
0
2
0
1
2
0
0
1
1
0
0
0
1
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
1
2
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
2
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
1
0
0
1
0
2
0
0
0
2
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
3
2
2
0
0
1
0
0
0
3
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
1
0
0
0
1
2
0
0
1
0
1
2
0
2
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
1
1
3
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
2
1
0
1
2
2
0
0
0
1
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
2
0
0
0
2
0
0
0
0
1
0
1
1
2
2
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
3
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
2
2
2
2
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
1
0
1
1
0
3
0
1
2
2
0
0
1
0
0
0
1
0
0
1
4
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
1
0
0
2
1
0
0
0
1
0
0
1
0
2
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
2
0
1
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
3
0
0
0
2
0
1
0
1
0
0
0
0
0
2
1
2
0
0
0
1
0
0
0
0
2
1
0
1
0
0
0
0
0
2
0
0
0
0
1
2
1
0
0
0
1
0
1
0
1
0
0
2
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
2
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
2
0
0
2
0
0
0
0
2
2
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
2
0
0
0
0
3
1
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
2
0
1
0
2
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
1
1
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
1
2
0
2
1
0
1
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
3
0
0
1
2
2
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
1
1
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
2
0
0
2
1
0
2
0
0
0
0
1
0
0
0
0
2
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
1
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
4
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
2
2
0
1
1
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
1
2
1
1
1
0
0
1
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
2
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
2
0
1
0
0
2
1
0
0
1
0
0
0
0
2
0
3
2
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
1
0
2
1
0
1
0
0
2
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
2
2
0
2
1
0
0
0
0
2
0
2
0
0
1
1
2
0
0
1
0
0
1
0
0
0
1
0
0
0
3
0
2
2
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
1
2
0
0
0
2
0
0
0
2
0
0
1
0
0
0
2
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
5
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
1
0
0
0
0
0
0
2
1
0
2
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
1
0
0
2
0
0
2
0
0
3
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
2
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
1
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
2
0
0
0
2
0
0
0
1
0
0
0
1
0
4
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
2
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
2
0
0
0
2
0
0
2
1
0
1
0
0
0
0
0
1
2
0
0
0
7
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
2
2
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
3
0
1
4
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
2
0
1
1
0
0
2
0
0
0
0
0
4
1
1
2
0
0
0
0
1
3
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
1
0
2
0
2
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
2
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
4
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
1
0
1
0
0
0
0
2
3
0
1
1
1
0
0
0
0
0
7
1
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
3
0
1
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
1
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
2
2
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
2
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
1
1
2
0
1
0
0
0
1
1
3
0
1
0
2
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
1
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
2
0
0
2
0
3
0
1
0
4
1
0
0
0
1
2
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
7
1
0
1
3
0
0
2
0
5
1
0
0
1
0
1
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
2
0
0
0
0
2
1
0
1
0
2
0
0
0
2
1
0
2
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
3
0
0
0
0
0
2
1
0
0
1
2
0
2
0
0
0
1
0
2
0
1
3
0
8
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
2
1
1
1
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
1
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
6
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
2
0
0
4
0
1
0
0
0
2
0
0
2
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
3
0
2
0
0
0
2
0
1
0
0
0
0
0
0
2
0
1
0
0
3
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
2
0
0
2
1
2
0
1
0
0
0
2
1
0
0
4
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
1
0
0
2
0
0
0
1
0
2
0
0
1
0
0
0
3
0
0
0
0
0
0
3
0
0
0
0
1
0
2
2
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
1
0
1
0
0
1
1
0
0
2
0
1
1
1
0
0
1
0
1
0
1
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
2
0
6
0
2
0
0
2
0
3
2
0
0
1
0
0
0
0
0
1
2
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
2
2
2
0
0
0
2
0
0
2
1
0
0
0
0
0
1
2
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
1
0
0
0
0
2
0
0
2
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
3
0
2
0
2
1
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
1
0
2
2
2
0
2
0
0
0
0
5
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
7
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
1
2
0
0
0
1
1
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
2
1
0
0
0
1
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
2
0
0
0
2
0
1
0
3
2
0
0
0
0
0
0
2
0
0
2
0
2
0
1
0
0
0
0
2
0
0
0
1
0
2
0
0
2
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
4
0
0
0
0
1
2
0
1
4
0
0
3
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
1
2
0
1
0
0
1
0
4
1
0
0
0
3
0
2
0
1
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
2
0
3
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
3
0
0
0
0
0
2
0
0
0
0
3
0
1
0
1
0
1
0
0
2
2
0
1
0
0
0
0
1
0
0
0
2
1
0
1
0
0
1
1
0
1
0
0
0
0
3
0
0
1
0
0
0
0
3
1
0
0
0
2
1
2
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
3
0
0
0
1
0
0
0
0
0
0
0
0
2
1
1
0
0
0
4
0
2
0
1
0
1
3
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
1
0
2
0
0
1
2
0
2
0
0
1
0
2
0
0
0
0
0
0
0
1
1
0
0
3
0
1
0
1
1
2
0
2
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
2
0
0
0
0
1
1
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
1
0
3
2
1
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
2
1
0
0
0
0
0
2
0
0
0
1
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
2
2
1
0
1
0
0
0
0
2
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
1
0
0
0
1
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
3
2
0
0
0
0
1
1
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
3
1
1
0
0
2
0
1
1
0
0
2
0
0
0
0
0
1
1
2
2
0
2
0
2
0
0
2
1
0
0
0
0
3
0
0
2
0
0
0
0
2
0
11
0
0
0
0
1
0
2
2
0
1
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
3
1
0
0
0
1
0
1
0
0
2
0
0
1
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
1
0
3
0
1
0
2
0
0
1
0
2
1
0
0
0
2
1
3
0
0
0
0
0
2
0
2
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
1
0
2
0
2
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
1
1
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
1
0
0
0
1
2
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
1
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
1
0
3
0
0
1
4
0
0
0
2
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
1
1
3
2
0
1
0
0
0
0
1
0
0
0
1
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
8
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
1
1
0
0
3
0
3
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
5
0
3
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
1
0
1
1
0
1
3
1
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
2
1
0
0
3
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
1
0
0
0
0
2
0
0
0
2
4
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
1
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
0
1
1
2
2
0
0
0
2
0
0
0
0
2
2
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
2
7
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
3
1
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
2
1
0
0
0
0
0
0
3
0
0
2
0
0
0
1
0
0
0
1
0
0
0
7
0
0
0
1
1
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
2
1
0
0
1
5
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
1
2
0
0
0
0
2
0
1
0
0
2
0
2
0
0
3
0
0
0
0
0
0
0
0
1
2
0
0
0
1
1
0
2
0
0
0
0
1
0
0
0
2
2
0
0
0
2
1
0
2
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
5
0
0
1
0
2
0
2
1
0
2
0
0
0
0
0
0
0
3
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
2
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
1
0
0
1
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
2
0
0
2
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
7
0
0
0
0
0
2
1
0
2
0
0
1
0
0
2
0
1
1
1
1
0
0
2
2
0
0
0
0
0
2
1
2
3
0
0
0
0
0
0
1
0
0
1
2
0
3
1
0
0
1
0
2
0
0
2
0
1
1
1
0
0
0
0
0
0
1
1
0
1
0
4
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
1
0
2
0
2
0
0
0
0
0
2
0
2
1
1
2
0
0
1
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
1
0
0
2
1
0
1
0
0
2
0
0
0
1
1
0
0
0
0
1
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
1
1
2
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
2
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
1
2
0
0
0
2
1
1
0
0
0
2
5
0
0
0
0
0
2
0
1
0
0
0
0
3
0
1
4
0
0
0
0
0
0
0
0
1
1
1
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
1
1
2
0
0
1
0
0
0
2
0
3
2
0
0
2
0
1
0
4
0
0
0
0
0
2
1
0
0
1
1
0
1
0
0
0
0
1
0
1
0
1
0
0
2
0
0
0
2
0
0
0
0
0
3
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
1
2
1
3
0
1
0
0
0
1
0
0
0
0
1
0
2
0
0
2
0
1
0
0
0
0
0
0
1
0
0
3
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
1
0
2
0
0
1
1
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
2
0
0
0
0
0
0
0
2
3
0
2
0
2
0
0
0
0
0
0
1
1
0
0
3
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
3
3
0
0
0
0
0
0
2
0
0
0
0
0
2
0
3
0
3
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
2
0
1
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
1
2
0
2
0
1
4
0
0
0
0
0
0
1
0
1
0
0
1
1
2
0
2
0
0
0
0
0
2
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
4
1
0
0
0
0
1
0
1
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
3
0
0
1
0
0
2
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
1
0
1
0
2
4
0
2
0
0
0
1
0
2
2
0
0
3
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
3
0
0
0
2
0
0
0
0
1
1
3
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
4
0
1
0
0
0
0
0
0
0
1
0
0
0
2
1
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
1
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
1
2
0
1
2
0
2
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
1
0
3
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
2
3
1
0
1
0
0
0
0
0
0
0
0
1
2
0
0
2
0
2
1
0
0
0
0
3
0
0
0
0
2
0
1
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
1
1
0
3
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
3
0
0
2
0
2
1
0
0
0
0
1
1
0
1
0
1
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
1
0
2
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
3
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
2
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
2
0
0
0
2
0
0
0
1
2
0
1
1
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
4
0
1
0
2
2
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
2
0
2
0
0
0
1
0
0
0
2
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
1
2
2
0
1
0
0
0
0
0
0
0
2
3
0
1
0
0
0
2
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
3
2
1
1
0
0
0
2
0
3
0
1
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
3
0
0
1
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
2
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
3
0
2
1
0
0
2
0
0
0
0
0
0
0
0
2
3
0
0
0
1
0
0
2
2
1
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
2
0
0
0
0
0
0
0
0
1
1
0
1
4
0
0
2
0
0
0
0
0
0
0
0
6
0
1
0
0
0
0
0
2
0
0
2
0
0
0
2
2
0
1
0
0
0
0
1
0
0
0
1
0
2
2
1
0
0
0
0
0
2
1
1
0
0
0
0
3
0
0
0
0
7
0
0
0
0
0
0
4
0
1
0
2
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
1
2
0
0
1
0
0
0
1
2
0
0
4
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
2
2
2
1
0
0
2
0
0
0
0
1
0
2
1
0
0
0
0
2
0
0
2
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
2
0
1
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
2
0
0
2
0
1
1
0
0
0
0
2
0
0
2
0
2
0
2
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
2
2
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
1
0
4
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
2
2
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
2
2
1
0
0
0
0
0
1
3
0
0
0
0
0
6
0
1
1
0
0
0
0
0
0
1
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
1
3
0
0
1
0
0
0
0
0
0
0
0
0
1
5
2
1
0
0
0
0
0
0
4
0
2
0
0
0
0
0
2
0
0
1
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
2
0
2
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
5
1
7
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
1
1
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
7
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
1
0
0
2
1
0
2
1
2
1
2
0
0
0
2
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
2
1
0
4
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
5
0
0
2
0
1
0
0
0
0
1
0
0
0
0
4
0
0
0
0
2
1
1
0
2
0
0
0
0
1
0
0
2
0
1
0
2
1
0
2
2
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
1
1
0
0
3
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
1
1
1
0
2
0
0
0
0
0
0
2
1
0
1
0
0
2
0
0
2
2
2
2
1
0
0
0
0
0
0
0
0
1
0
0
8
0
0
1
0
0
1
0
0
0
0
1
0
0
1
3
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
2
0
0
1
0
0
0
0
0
2
0
2
0
0
1
0
2
2
0
0
0
4
1
0
0
0
2
0
1
0
0
0
0
2
2
2
0
0
0
1
0
0
0
2
0
2
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
3
0
1
2
0
1
0
0
1
0
2
0
2
4
0
0
0
3
0
0
0
1
0
0
0
0
1
0
1
0
1
2
0
0
1
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
2
0
0
1
2
0
0
0
2
2
0
0
1
0
0
0
2
2
0
2
0
0
0
2
0
0
1
0
1
0
0
0
12
0
0
0
0
1
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
3
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
2
2
0
1
0
2
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
4
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
4
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
2
0
0
4
0
1
0
0
1
0
1
0
0
0
0
2
2
0
3
1
0
2
0
0
0
0
0
1
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
3
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
3
0
0
0
2
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
2
0
1
0
0
1
2
0
0
0
1
2
0
1
0
0
2
0
1
0
0
1
3
0
0
0
0
0
10
0
0
0
0
2
1
1
0
1
0
0
0
0
0
0
4
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
1
2
1
0
1
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
1
0
2
1
0
0
0
1
0
0
1
0
0
0
0
2
0
3
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
2
2
2
0
1
1
2
0
0
0
0
0
0
0
2
0
2
1
0
0
1
0
0
0
1
0
0
0
2
1
5
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
2
0
1
2
1
0
2
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
1
5
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
2
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
1
0
0
0
0
2
2
2
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
3
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
1
0
3
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
2
2
0
0
0
1
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
1
0
0
0
1
1
0
0
2
2
0
1
2
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
3
1
0
0
1
0
0
0
0
1
1
0
0
2
0
4
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
2
1
2
0
0
4
0
0
0
0
5
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
3
0
0
2
0
0
2
0
1
2
0
2
0
1
2
2
0
0
1
0
1
2
1
0
1
1
0
1
0
2
0
0
1
0
0
0
2
0
0
0
1
1
2
0
2
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
1
0
0
0
0
1
2
2
0
0
1
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
2
0
1
0
0
2
0
0
1
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
1
2
0
0
0
0
1
0
0
1
0
0
1
0
0
2
1
1
0
3
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
3
2
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
3
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
1
3
1
2
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
6
0
1
0
0
3
0
2
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
3
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
2
1
0
0
0
2
0
1
0
3
0
2
0
0
1
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
1
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
2
2
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
3
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
3
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
2
2
0
0
0
0
5
0
1
0
0
0
0
0
1
0
0
0
1
0
2
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
2
0
1
2
0
2
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
8
0
0
0
0
0
2
2
0
0
4
0
0
0
1
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
2
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
3
0
0
0
2
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
1
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
1
2
0
2
0
2
2
0
0
1
0
4
0
0
0
0
1
0
0
0
1
0
1
1
1
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
1
0
0
5
2
0
1
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
1
0
3
1
2
2
0
1
0
1
0
0
2
0
0
0
0
0
0
0
1
0
2
0
1
0
2
0
0
1
2
1
0
1
0
0
2
0
2
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
1
2
0
3
0
0
0
0
2
2
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
1
0
0
1
0
2
0
0
0
2
1
2
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
1
2
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
2
2
0
0
9
2
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
1
0
2
1
0
0
1
0
1
1
0
0
2
1
0
1
1
0
0
0
1
2
0
0
1
0
0
0
2
0
2
0
1
0
0
0
3
0
0
1
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
1
0
1
0
0
2
2
0
0
0
1
0
0
2
2
0
0
2
0
1
0
0
0
5
0
2
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
1
1
0
1
0
0
0
1
3
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
3
2
0
3
0
2
0
2
2
0
0
0
1
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
2
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
2
0
0
3
0
0
0
0
0
1
2
0
6
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
3
0
0
0
0
0
0
1
1
0
4
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
3
2
1
0
1
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
4
2
1
1
0
0
3
0
0
2
1
0
2
2
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
2
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
5
3
3
1
0
2
0
0
5
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
3
0
2
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
2
0
0
0
1
2
0
1
0
1
2
0
0
0
0
0
3
3
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
1
2
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
3
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
3
0
3
3
0
2
0
0
2
0
0
1
0
2
0
2
0
9
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
3
0
1
0
4
0
0
1
2
0
0
2
2
0
0
7
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
1
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
1
2
0
3
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
3
0
1
0
0
0
0
0
0
1
0
3
1
0
0
0
0
2
0
1
2
0
2
0
0
0
0
0
3
1
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
2
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
2
0
1
2
0
1
0
1
0
0
0
1
0
3
0
0
1
0
0
0
4
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
1
0
1
1
0
1
0
2
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
2
2
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
1
0
0
3
1
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
3
1
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
1
0
3
1
3
0
0
2
2
2
0
2
0
0
0
0
2
0
0
0
1
0
0
8
2
0
0
0
0
1
0
6
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
2
0
0
2
2
0
2
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
1
0
0
2
0
2
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
2
2
2
2
0
0
0
0
0
0
2
0
1
0
0
0
1
2
0
0
0
0
1
1
2
0
0
0
0
1
1
1
0
2
0
0
1
3
3
0
0
0
2
0
0
0
0
7
0
0
1
0
1
0
0
1
0
0
0
4
3
0
1
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
1
2
0
0
3
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
2
0
0
0
0
2
0
0
2
5
0
0
0
0
0
2
0
0
0
2
0
1
1
0
0
0
1
1
0
0
0
0
2
0
1
0
0
2
0
0
1
0
0
0
0
0
1
2
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
5
2
0
1
1
0
2
0
1
0
2
0
1
2
0
3
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
2
4
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
2
2
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
10
0
0
0
0
1
0
3
0
2
0
0
0
0
0
0
0
0
2
0
1
0
4
0
0
2
0
0
0
0
1
0
1
0
0
2
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
2
0
0
2
4
1
0
0
0
0
0
0
2
1
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
1
0
2
1
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
5
0
0
0
0
0
0
0
4
1
0
1
0
2
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
2
0
0
0
1
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
3
0
1
2
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
6
1
0
1
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
2
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
2
0
0
2
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
3
0
0
0
0
1
0
0
2
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
2
3
0
0
1
0
2
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
3
1
0
0
0
0
0
0
0
1
3
0
3
0
2
2
0
0
0
1
1
1
0
0
0
0
0
1
2
0
0
1
0
0
1
0
3
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
2
1
1
0
0
0
0
0
0
3
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
1
0
0
0
0
1
0
1
2
0
2
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
3
0
0
0
2
29
2
0
0
0
0
0
2
0
2
0
2
0
0
0
2
0
0
0
0
0
1
2
0
0
1
2
0
2
0
0
1
0
0
1
0
0
0
0
3
1
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
4
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
2
1
0
0
2
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
2
0
1
1
0
0
1
3
2
0
0
0
2
0
0
1
2
2
0
0
0
0
0
0
3
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
2
2
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
3
0
1
2
1
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
1
0
1
0
0
4
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
1
2
1
1
0
0
0
0
0
2
0
1
1
0
1
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
1
0
0
1
0
0
1
2
0
0
0
0
0
0
4
1
0
2
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
1
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
4
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
2
1
0
3
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
2
0
1
0
0
1
0
0
1
0
0
0
0
0
0
2
2
0
2
0
0
1
2
0
2
1
0
0
3
2
1
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
5
0
0
0
0
0
0
1
0
0
0
4
0
0
0
3
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
1
3
2
0
1
1
0
0
1
2
0
0
1
0
0
2
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
3
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
3
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
1
2
0
1
0
0
2
0
0
0
3
0
0
1
0
9
0
0
0
2
0
0
1
0
1
2
1
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
3
0
0
2
1
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
2
3
0
0
1
1
0
0
0
3
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
1
0
6
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
2
1
2
0
0
0
2
0
0
0
0
2
3
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
5
2
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
2
1
3
0
1
0
1
0
2
0
0
0
3
0
0
1
2
0
0
1
3
0
0
0
2
0
6
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
1
0
3
2
0
1
0
0
2
1
1
0
0
0
0
0
2
0
2
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
3
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
2
1
0
3
0
0
0
2
2
0
0
0
0
1
2
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
2
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
2
2
0
0
0
2
0
2
0
0
0
0
3
0
0
1
0
0
0
1
2
0
0
0
2
0
0
1
1
0
1
1
0
0
0
0
0
1
3
0
0
2
0
0
0
0
0
0
1
2
0
0
2
1
0
0
1
0
0
0
0
3
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
1
0
0
2
2
1
0
1
0
1
1
1
1
0
0
1
2
0
0
2
0
0
1
2
0
0
2
2
0
0
0
3
0
0
2
0
0
2
0
0
2
1
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
1
0
1
1
3
0
0
0
2
0
1
0
0
0
1
0
0
0
1
0
2
0
2
1
0
0
0
0
0
0
1
0
0
2
1
2
0
0
0
0
2
0
0
3
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
2
2
0
0
2
1
1
2
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
3
1
1
0
0
4
0
0
0
0
0
0
2
0
0
0
0
0
0
2
3
2
0
1
0
2
2
1
1
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
2
0
2
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
3
1
0
0
0
0
2
0
2
0
0
2
0
0
2
0
1
5
2
0
0
2
0
0
0
0
2
0
2
0
3
0
0
2
0
1
0
0
0
2
0
0
6
0
0
0
1
3
0
2
0
0
0
0
3
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
2
0
2
0
0
3
0
0
0
1
0
2
0
0
0
0
0
0
5
4
0
0
0
1
0
1
0
0
0
2
0
0
2
2
0
2
0
2
0
1
0
1
0
1
0
0
0
1
2
2
2
0
1
0
2
0
0
0
2
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
1
3
1
0
1
0
3
0
0
1
0
0
0
1
0
2
0
0
0
0
1
0
0
0
1
0
0
0
2
0
1
0
2
1
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
1
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
6
2
0
0
2
0
0
0
0
0
1
0
0
0
0
2
2
1
0
0
2
1
2
0
0
0
0
0
0
0
2
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
2
0
0
1
0
0
0
0
0
2
0
0
0
0
6
1
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
1
0
0
0
0
0
1
0
2
0
1
2
1
0
0
0
0
1
2
2
0
0
2
0
0
2
1
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
1
0
0
2
0
0
1
0
2
0
0
0
0
0
0
5
0
0
1
1
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
5
2
1
0
0
0
0
0
0
0
0
0
4
0
3
2
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
1
1
0
2
0
0
1
0
1
1
0
1
2
0
0
0
1
0
0
1
0
0
0
0
1
3
0
0
1
0
4
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
3
0
0
0
0
2
5
0
0
0
1
0
0
0
0
0
1
0
1
2
0
2
1
1
0
1
0
0
0
0
0
1
3
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
3
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
2
0
0
0
4
0
1
0
1
0
0
0
1
1
1
1
0
1
0
0
0
1
0
0
2
1
0
0
2
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
3
1
1
0
2
2
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
2
0
1
0
0
0
0
0
2
0
3
0
0
0
2
0
0
0
1
0
0
0
0
2
0
2
1
0
0
1
0
0
0
1
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
1
0
1
0
0
2
0
1
3
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
3
0
1
0
2
0
0
0
0
0
0
4
0
0
4
0
0
0
0
2
0
0
1
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
4
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
1
4
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
3
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
2
1
2
0
0
2
0
0
0
0
0
0
1
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
2
0
0
0
3
0
0
0
0
0
2
0
0
1
0
0
2
1
0
0
0
0
0
2
0
0
0
0
3
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
5
0
0
0
1
1
0
0
2
0
0
0
1
1
0
0
2
0
0
0
0
0
0
2
1
0
0
1
0
0
2
0
0
0
2
0
0
0
2
0
0
6
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
1
0
1
0
1
0
0
0
2
0
7
0
2
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
6
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
2
0
0
0
1
0
2
0
0
2
1
1
0
2
0
0
0
2
0
0
1
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
5
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
1
1
0
0
0
1
0
2
0
2
0
2
2
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
11
1
1
0
2
0
0
0
0
0
2
0
4
0
0
0
0
1
0
0
1
2
0
2
0
1
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
2
0
1
0
1
0
1
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
2
0
0
0
0
0
0
2
0
1
2
0
2
0
2
2
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
1
2
2
0
1
0
0
1
0
0
2
0
0
0
0
2
1
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
2
0
1
0
0
2
0
0
0
0
0
1
2
1
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
1
1
3
2
0
0
2
0
0
0
0
0
2
0
0
2
1
2
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
2
0
0
0
0
0
1
0
2
0
1
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
1
0
0
2
1
1
0
1
0
0
0
0
0
2
0
0
2
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
2
0
0
0
0
1
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
1
0
2
1
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
3
2
0
0
0
1
0
0
1
2
1
0
0
3
2
1
0
0
0
1
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
1
1
0
5
0
3
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
3
0
2
0
0
0
0
0
3
0
1
0
1
2
0
0
4
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
1
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
2
0
0
0
1
0
0
2
2
1
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
2
0
0
0
2
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
1
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
3
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
2
2
0
1
0
0
0
0
3
0
0
1
2
1
0
0
2
0
2
2
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
2
2
0
0
0
0
3
1
0
2
0
0
1
0
0
2
0
2
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
2
1
0
0
0
1
0
0
0
2
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
1
0
0
1
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
1
1
0
1
1
0
0
1
1
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
2
0
0
2
2
0
2
0
0
0
1
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
2
2
1
0
0
0
0
0
0
1
1
2
0
0
2
0
0
0
0
0
1
0
0
0
2
2
0
0
1
0
2
0
0
0
0
0
1
0
2
0
0
0
0
2
2
0
1
0
3
0
0
0
1
0
0
0
1
2
0
1
0
5
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
3
1
3
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
2
0
0
2
0
2
2
0
1
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
1
2
0
0
1
3
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
2
0
1
0
1
2
0
0
0
1
2
1
0
0
0
0
0
0
1
0
0
2
0
2
0
1
0
0
1
0
0
0
1
1
0
2
0
1
4
0
2
2
0
0
0
1
2
0
0
0
0
0
2
1
1
2
0
0
0
0
0
0
2
0
0
2
0
0
0
3
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
1
0
3
0
0
0
0
0
1
2
0
0
0
2
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
3
1
0
0
0
1
1
0
0
0
0
0
1
0
1
0
2
0
0
2
0
0
0
1
2
0
0
0
0
2
0
1
0
1
1
0
0
0
3
0
0
0
0
2
2
0
0
0
0
0
0
1
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
2
1
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
8
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
2
2
0
0
1
0
0
0
0
4
1
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
3
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
7
0
0
0
0
0
1
0
1
1
2
0
1
1
0
2
2
2
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
2
0
0
0
0
1
2
0
2
2
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
2
2
2
0
0
0
2
0
0
0
2
0
1
0
0
1
0
0
3
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
3
0
0
0
0
0
5
0
1
0
0
2
0
0
0
2
1
3
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
8
0
0
0
0
0
0
3
0
2
0
2
12
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
1
0
4
0
2
2
0
1
2
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
2
2
0
1
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
5
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
2
2
0
1
0
0
0
0
0
1
0
0
0
1
2
0
1
0
2
1
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
1
1
0
0
0
0
1
0
0
0
1
3
0
0
2
0
0
0
2
1
1
0
0
2
1
0
2
1
0
0
0
0
0
4
0
1
0
0
2
4
0
0
0
2
0
0
1
2
0
1
2
0
0
0
1
0
1
2
1
0
1
0
0
2
0
0
0
2
2
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
1
1
1
2
2
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
2
0
7
0
3
1
0
6
1
0
0
0
0
2
0
0
1
0
0
0
0
1
2
1
0
0
0
0
0
2
0
0
0
1
1
0
2
1
0
0
0
1
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
3
0
0
0
1
0
2
1
0
0
0
0
2
1
1
0
0
0
0
0
1
0
0
0
1
2
0
1
0
0
0
0
0
2
1
0
1
0
1
0
0
0
0
2
0
1
0
0
0
0
0
3
0
0
0
0
0
1
2
0
0
0
0
0
4
3
2
1
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
2
0
2
0
1
1
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
1
1
1
1
0
0
0
0
1
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
2
0
0
0
0
0
4
0
0
0
0
1
0
0
0
1
1
0
0
0
0
3
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
3
0
1
0
0
10
0
0
3
0
0
0
1
1
0
2
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
6
0
0
4
0
0
0
1
0
2
2
0
0
0
2
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
2
0
0
0
0
1
0
0
2
1
1
0
0
2
0
2
0
0
1
0
2
1
2
0
2
0
2
3
0
0
0
0
1
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
3
1
1
0
2
0
2
0
1
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
2
1
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
3
2
0
1
1
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
1
0
2
0
2
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
2
0
1
0
0
1
0
1
0
3
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
4
0
2
0
0
0
0
0
0
1
0
2
0
2
0
0
1
0
0
0
0
3
1
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
1
0
3
6
1
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
3
0
0
0
0
0
0
1
0
0
1
2
3
0
0
1
1
0
2
2
0
0
1
2
0
0
0
2
2
0
0
2
1
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
2
2
2
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
3
0
1
0
0
0
0
0
3
0
0
0
2
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
3
0
0
0
1
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
2
0
2
0
4
0
1
1
1
0
0
0
0
0
0
1
2
0
0
0
3
1
0
2
0
0
0
0
1
0
0
0
0
0
0
2
3
2
2
0
2
0
2
0
0
2
0
2
0
0
2
0
0
4
0
0
0
0
0
1
0
2
0
0
0
0
0
2
1
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
2
0
2
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
3
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
1
0
1
0
1
1
0
2
0
0
0
0
0
0
1
1
0
2
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
6
0
2
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
2
0
0
0
0
1
0
0
1
2
1
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
2
0
0
0
0
1
0
2
2
0
0
0
2
0
0
0
0
0
0
0
1
0
2
2
0
2
0
1
1
0
0
5
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
4
1
2
0
0
0
0
0
0
2
2
2
0
1
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
1
1
0
0
1
0
0
0
1
1
0
0
2
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
2
0
0
0
1
0
0
0
0
1
2
1
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
2
2
0
0
2
0
0
2
0
0
0
4
3
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
1
2
0
2
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
2
0
1
0
0
0
0
0
3
0
2
1
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
2
3
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
2
0
0
2
0
2
1
0
0
0
0
3
0
0
1
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
2
0
1
0
0
0
1
3
0
0
1
0
0
0
0
0
0
5
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
1
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
2
0
2
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
2
0
0
0
0
0
1
1
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
2
0
2
0
1
2
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
1
0
0
3
0
0
0
1
0
2
1
1
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
2
2
0
0
0
2
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
2
1
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
1
2
2
0
0
2
1
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
1
0
2
1
2
0
0
1
0
0
0
1
0
0
1
0
1
2
0
0
0
1
0
1
1
2
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
1
2
0
0
1
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
3
0
0
2
1
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
2
1
0
0
1
0
1
0
2
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
2
0
1
2
0
2
0
0
2
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
1
2
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
3
0
1
2
7
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
2
1
0
2
0
0
0
0
2
0
0
0
0
1
0
0
2
0
2
0
1
3
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
3
0
1
0
0
0
0
2
0
2
0
0
2
2
1
0
0
2
1
0
0
0
0
0
1
0
1
0
1
0
0
2
2
0
0
1
2
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
6
1
0
0
0
0
0
1
0
0
2
4
1
0
2
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
3
0
0
0
0
2
0
0
0
1
0
2
0
1
0
0
0
0
0
0
2
0
0
0
3
0
0
1
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
1
0
0
0
2
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
2
2
0
0
0
2
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
3
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
1
0
0
2
0
0
3
0
1
0
0
0
0
0
0
0
0
0
1
2
0
1
0
2
0
0
1
1
0
0
0
0
3
2
0
0
0
0
0
2
1
4
0
2
0
0
0
0
1
2
0
1
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
3
2
2
0
1
0
0
0
0
1
0
1
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
2
1
1
0
0
0
0
0
2
0
0
4
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
3
0
2
0
0
0
0
0
1
2
1
0
0
0
0
2
0
0
0
0
0
0
0
1
1
1
0
2
0
2
0
1
0
0
0
0
1
0
0
1
0
0
0
0
2
1
0
1
1
0
0
0
0
0
1
0
1
0
2
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
1
2
1
1
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
1
0
2
0
0
0
0
2
2
0
1
0
0
0
4
0
1
1
0
0
1
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
1
2
2
0
0
1
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
3
0
0
0
1
1
0
0
0
0
0
0
2
3
1
0
0
0
2
1
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
12
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
2
0
1
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
16
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
5
1
0
0
2
0
2
0
0
0
0
2
0
0
2
1
2
0
0
0
0
1
2
0
0
0
0
0
0
1
0
5
1
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
1
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
2
0
4
2
0
0
1
2
0
0
2
0
1
0
0
1
0
0
0
0
2
2
0
1
0
2
7
0
0
0
0
1
0
1
1
2
0
0
0
0
3
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
2
0
0
1
2
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
1
2
0
0
2
2
0
1
4
0
0
1
0
0
0
0
1
1
0
0
1
1
2
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
3
6
2
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
3
0
0
0
0
0
2
0
2
0
0
1
2
0
0
0
2
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
3
1
0
13
0
0
0
0
2
2
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
2
0
2
2
0
0
0
2
1
0
0
2
1
1
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
2
2
0
1
1
0
0
0
0
2
0
2
2
0
0
1
0
1
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
2
1
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
4
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
2
0
0
0
1
4
0
0
2
2
0
4
0
1
6
0
1
0
1
0
1
0
2
0
0
1
0
0
0
0
3
0
0
0
0
2
0
0
1
5
0
0
3
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
2
0
2
3
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
1
2
2
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
1
0
4
0
1
0
1
2
0
0
2
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
4
0
0
0
0
2
0
0
0
2
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
1
1
1
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
3
0
1
1
0
2
0
3
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
3
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
1
0
0
1
0
2
0
0
0
0
1
2
0
0
0
0
0
1
0
1
1
0
0
0
1
2
3
0
0
0
0
1
0
0
0
0
2
0
2
0
0
1
0
0
0
0
2
2
0
2
0
2
2
3
2
0
2
0
0
0
2
2
1
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
3
3
0
0
0
0
2
0
0
0
1
0
1
2
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
3
0
3
0
0
2
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
1
1
0
1
0
1
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
2
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
1
0
1
0
4
0
1
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
2
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
1
1
0
1
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
1
5
2
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
3
0
2
0
6
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
2
0
0
2
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
2
2
0
1
2
0
0
1
2
0
1
1
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
3
0
0
0
1
1
0
1
0
2
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
2
0
1
4
0
0
0
2
0
0
0
1
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
2
0
0
2
0
0
0
2
0
0
3
0
0
1
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
2
0
1
0
0
0
0
0
0
0
1
1
2
2
0
2
1
2
1
0
0
1
0
2
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
2
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
4
0
3
0
0
0
0
2
1
0
2
0
3
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
2
2
0
0
0
1
0
0
2
0
1
1
0
1
2
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
2
0
0
2
2
0
2
0
1
2
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
2
0
0
2
0
1
2
3
0
0
2
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
1
2
0
0
0
0
2
0
0
1
0
1
2
1
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
1
2
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
1
0
1
1
1
1
0
0
0
1
0
0
0
1
1
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
2
0
1
0
2
2
2
0
0
0
3
0
1
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
2
0
0
2
0
0
2
0
0
2
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
1
2
0
0
0
1
0
1
1
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
2
1
2
0
1
2
0
0
0
1
0
1
0
1
0
0
0
0
2
1
2
0
0
0
0
1
2
0
0
0
0
2
0
2
0
3
0
0
0
1
1
0
0
0
2
0
0
0
0
1
1
0
2
0
0
2
0
1
2
0
0
2
0
2
0
2
0
0
0
0
0
0
2
2
2
0
2
0
0
2
0
2
0
1
1
0
0
0
2
0
3
2
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
3
1
0
0
0
0
0
0
3
0
2
1
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
2
0
2
0
0
2
0
0
3
0
0
2
0
0
0
0
0
0
0
2
1
1
2
3
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
2
1
0
2
3
2
0
0
0
0
2
0
0
1
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
2
2
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
4
2
3
1
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
15
2
0
2
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
1
2
0
0
0
1
2
0
0
5
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
2
2
0
0
3
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
1
1
0
0
0
2
0
0
0
2
1
0
0
0
0
2
3
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
2
0
7
1
2
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
2
2
0
0
3
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
1
0
1
1
1
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
6
2
0
0
0
0
1
2
0
1
1
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
3
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
2
1
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
2
0
0
1
0
1
0
1
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
2
1
0
2
0
2
1
2
3
0
0
0
1
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
3
0
0
0
0
0
0
0
3
0
0
0
1
0
0
2
2
0
5
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
5
0
1
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
2
0
0
0
0
0
0
5
1
0
0
0
0
0
1
2
0
0
0
1
0
2
0
0
0
2
0
1
0
2
0
1
0
0
0
1
0
0
0
0
0
2
0
2
0
2
0
0
3
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
2
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
8
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
3
2
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
4
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
1
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
1
0
1
0
2
0
0
0
0
0
2
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
1
2
1
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
2
0
0
1
1
0
0
2
0
0
0
0
1
1
0
0
0
1
2
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
2
1
0
0
1
1
0
0
2
1
0
1
0
0
2
0
0
1
0
0
0
0
1
0
0
0
2
0
0
3
0
2
0
1
0
0
0
0
2
0
0
1
0
1
0
0
3
1
0
0
2
2
0
0
0
0
0
0
1
1
0
0
4
2
2
0
0
1
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
2
1
0
0
0
1
1
0
0
0
0
1
0
0
1
2
0
0
0
1
1
2
0
5
0
0
0
0
0
3
0
2
2
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
2
0
1
0
0
0
4
2
2
0
0
2
0
0
2
0
0
0
0
2
0
1
0
0
3
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
1
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
4
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
1
2
1
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
1
1
0
0
1
0
1
1
1
1
1
0
1
0
0
0
4
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
1
2
0
0
0
2
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
2
3
0
2
0
0
0
0
3
0
0
0
1
0
1
0
2
0
0
0
0
0
0
1
2
0
1
0
2
3
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
1
3
1
1
0
0
0
2
0
1
1
1
0
2
0
0
2
3
0
0
0
0
0
2
0
2
2
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
1
0
0
0
0
0
0
1
2
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
5
0
0
2
2
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
5
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
6
2
2
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
4
0
1
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
2
0
3
1
0
0
2
0
0
0
1
1
1
2
2
0
0
0
1
0
0
0
2
1
1
0
0
1
0
0
1
0
0
2
0
0
0
0
0
2
0
2
0
1
0
0
2
0
0
0
0
2
0
0
3
0
0
1
0
0
0
1
1
2
0
0
0
0
1
0
0
0
2
2
0
0
0
0
1
3
2
0
2
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
2
0
1
2
0
0
2
2
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
2
0
1
0
0
1
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
1
2
0
0
0
1
0
2
2
5
2
2
0
0
0
0
0
1
0
0
0
0
0
0
4
2
0
2
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
2
2
0
0
2
1
1
2
0
1
1
2
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
1
0
1
0
0
0
0
0
2
1
2
1
0
0
0
0
0
0
0
0
0
1
1
5
0
1
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
2
0
0
0
3
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
2
0
2
0
0
4
0
2
0
0
0
0
2
0
2
0
3
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
4
0
0
0
1
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
1
0
0
1
0
6
0
0
0
1
0
2
0
0
1
2
2
3
0
2
1
0
2
1
0
2
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
2
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
5
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
1
1
0
3
0
4
0
0
1
2
1
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
1
2
0
0
0
0
0
0
0
0
2
0
1
0
0
3
0
0
0
3
0
0
1
0
0
0
0
2
1
0
0
2
0
0
2
0
0
3
2
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
2
0
1
2
0
1
1
0
0
0
0
0
0
0
5
0
0
0
0
2
0
0
1
0
2
0
0
2
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
1
0
0
0
1
0
2
0
0
0
0
0
0
3
0
1
2
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
2
0
0
0
2
0
0
1
0
0
0
0
4
0
0
0
0
0
0
2
0
0
0
0
2
1
0
1
0
0
0
0
2
0
0
1
0
1
0
0
0
0
3
1
0
0
1
0
0
1
1
4
0
1
0
0
0
4
1
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
2
0
2
0
0
0
1
1
0
1
0
0
0
2
0
0
0
2
2
0
0
2
1
1
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
2
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
5
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
2
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
1
0
2
2
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
7
0
2
0
0
0
1
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
2
1
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
4
0
0
0
0
0
1
2
0
0
0
0
0
0
3
1
0
0
3
0
0
1
0
0
0
2
0
0
0
2
0
0
2
3
0
2
0
1
0
0
1
3
0
0
0
3
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
3
10
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
1
3
0
0
0
0
2
0
0
0
0
2
1
0
2
1
0
1
0
0
2
1
0
3
0
1
0
0
3
0
0
2
0
0
0
1
0
0
0
0
1
2
2
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
1
0
0
0
4
0
0
0
1
0
1
0
0
0
0
0
0
2
0
2
0
0
3
0
0
2
0
1
2
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
1
0
2
0
2
0
1
1
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
3
0
0
0
5
0
1
0
0
2
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
2
0
3
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
1
3
0
9
1
0
0
1
0
0
1
0
0
0
1
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
1
4
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
2
1
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
1
0
1
0
0
0
0
0
0
2
2
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
4
4
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
4
2
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
2
2
0
0
1
0
0
1
1
0
1
1
0
0
0
0
0
0
1
2
0
1
0
2
1
0
1
0
0
0
0
2
2
0
1
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
3
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
5
0
2
11
1
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
4
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
1
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
3
0
0
0
0
0
2
0
0
0
2
0
0
0
3
0
0
2
0
1
0
0
2
0
1
1
1
0
0
0
0
1
1
0
0
0
1
0
1
0
0
1
0
0
0
1
1
1
0
2
0
2
1
0
0
0
0
0
0
2
1
1
0
2
0
2
1
0
1
0
0
0
1
2
2
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
2
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
4
0
0
0
0
0
0
0
6
0
0
1
0
0
0
0
1
2
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
4
2
2
0
3
0
0
1
0
0
0
0
0
2
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
2
0
1
2
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
1
1
0
1
1
2
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
1
2
0
0
2
0
1
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
2
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
2
2
0
0
0
0
0
0
1
7
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
1
0
0
0
3
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
3
0
0
0
0
0
2
2
0
0
0
0
0
2
2
1
0
2
0
0
0
2
0
2
0
2
0
0
0
0
0
0
2
0
2
1
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
1
1
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
2
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
2
0
0
1
1
0
0
0
0
2
1
0
1
0
0
0
2
0
2
0
0
1
0
2
0
0
0
1
2
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
6
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
1
0
0
0
0
1
1
0
0
0
3
0
0
2
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
2
0
0
0
0
1
0
1
0
4
0
3
1
2
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
2
2
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
2
0
0
1
2
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
2
1
0
0
0
2
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
5
0
0
1
0
1
0
2
0
2
0
0
1
0
3
2
0
2
1
0
0
0
1
0
2
0
0
3
0
0
0
0
0
2
0
0
0
1
0
0
0
2
3
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
1
2
0
1
0
2
0
0
0
0
0
1
1
0
0
3
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
3
0
0
2
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
2
0
0
2
2
0
0
2
2
1
1
1
0
0
1
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
1
0
1
1
0
0
7
0
0
1
0
0
2
0
0
0
3
0
0
2
0
2
0
0
0
2
1
0
0
0
2
0
0
1
0
0
0
1
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
1
0
0
2
0
0
2
0
0
0
0
2
0
0
1
0
0
1
0
2
0
0
0
0
1
0
0
3
0
0
0
2
2
0
0
0
0
2
0
1
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
7
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
9
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
1
2
2
2
2
0
0
0
2
0
0
2
0
1
0
0
0
0
1
2
2
0
0
1
0
0
0
3
0
0
0
0
0
0
0
1
0
2
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
3
0
0
0
0
0
0
2
0
1
0
0
4
0
2
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
1
0
1
0
3
0
1
0
0
0
2
0
0
0
2
1
2
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
2
0
2
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
2
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
2
0
2
1
0
0
2
0
0
2
2
0
0
0
2
1
1
0
1
0
0
0
0
0
0
3
5
0
0
0
1
2
0
0
0
0
1
0
0
2
0
1
0
0
2
0
0
2
0
1
1
0
0
1
1
0
0
0
0
0
0
0
1
1
6
0
0
1
0
0
0
1
0
0
3
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
3
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
2
2
0
0
0
0
2
1
0
2
0
0
0
0
0
0
1
0
0
2
2
2
0
0
0
2
0
2
0
0
0
1
0
0
0
1
0
0
0
1
0
2
0
0
1
0
0
5
1
0
0
1
0
0
2
0
1
0
0
2
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
2
3
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
2
0
2
0
0
0
0
2
1
0
2
0
0
0
0
0
0
6
0
1
0
1
0
0
0
0
1
0
0
2
4
2
0
0
1
0
1
0
2
0
0
0
1
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
5
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
2
1
0
0
0
0
0
2
0
1
0
1
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
1
0
2
1
0
2
0
2
0
0
0
1
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
1
2
2
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
2
0
1
1
0
1
0
0
7
2
2
0
1
1
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
2
0
0
2
0
0
1
2
1
0
0
2
1
0
2
2
0
0
1
2
0
0
3
0
0
1
0
0
0
0
2
2
0
0
1
1
1
0
0
0
0
2
1
0
0
0
2
2
0
1
0
1
0
0
3
0
0
3
0
0
2
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
1
0
0
3
0
3
0
2
2
1
0
3
2
2
1
0
1
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
2
2
0
0
0
0
0
0
2
2
0
1
0
0
2
0
0
2
2
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
4
0
0
0
0
0
3
3
0
2
0
0
0
0
0
0
0
0
1
0
0
2
5
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
3
0
0
0
1
2
0
0
2
0
0
2
0
2
0
0
0
0
2
0
0
2
0
0
1
0
0
2
0
0
2
0
0
0
0
3
2
0
1
0
0
2
1
0
2
0
0
0
0
0
4
0
0
0
0
0
0
0
1
2
0
1
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
2
0
0
0
1
3
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
1
0
1
0
0
2
2
0
2
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
1
2
0
0
0
1
0
0
2
1
2
0
2
0
0
5
2
0
0
2
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
1
1
0
0
2
0
0
1
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
1
0
0
0
3
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
3
1
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
2
2
0
0
0
0
3
0
2
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
1
1
0
0
0
1
0
0
0
2
0
2
0
0
2
0
3
0
0
2
2
1
0
0
0
0
2
0
0
3
1
2
0
0
0
0
0
0
1
1
0
0
0
0
0
2
3
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
1
1
0
0
2
3
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
4
0
0
0
0
0
1
2
0
0
1
2
0
2
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
2
0
0
0
0
0
1
1
1
0
2
1
0
0
0
0
0
1
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
3
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
3
1
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
1
0
0
2
2
0
0
0
1
0
0
3
2
1
2
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
2
0
0
0
3
2
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
3
0
0
2
1
0
0
0
1
0
0
0
0
0
0
1
0
0
5
3
0
0
1
1
0
0
0
0
0
0
7
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
4
0
0
0
4
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
3
0
2
0
0
2
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
1
2
0
2
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
5
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
2
0
0
0
0
2
1
0
1
0
0
2
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
5
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
2
2
0
0
0
1
0
2
0
3
0
0
2
0
0
0
0
2
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
2
2
0
0
2
0
0
0
1
1
0
3
0
2
1
0
0
0
3
2
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
9
2
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
2
2
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
2
0
2
0
0
0
0
0
2
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
2
0
0
1
2
0
0
0
0
0
3
0
0
0
0
0
1
0
1
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
1
0
0
1
0
1
2
3
0
1
0
1
0
0
0
2
2
0
1
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
3
2
2
0
0
0
0
1
0
1
0
3
0
0
2
2
1
1
0
0
2
0
0
0
1
0
2
0
0
1
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
2
1
1
0
1
0
0
0
0
0
2
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
3
1
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
3
8
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
1
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
2
0
2
0
2
0
0
0
1
2
0
0
2
0
0
0
1
0
1
0
0
0
1
2
1
1
0
0
0
1
0
0
0
4
2
2
0
0
0
0
0
4
1
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
2
1
0
0
0
1
2
2
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
2
0
0
0
1
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
3
0
1
1
1
0
0
2
0
0
0
0
3
0
0
0
0
3
0
2
0
0
0
0
0
0
0
1
0
1
2
1
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
2
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
0
1
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
1
0
2
1
2
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
1
1
2
0
0
0
0
0
0
2
0
0
2
1
0
0
0
4
0
0
1
2
0
0
0
0
2
0
1
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
1
0
2
0
0
3
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
3
0
1
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
1
0
0
1
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
1
0
0
2
0
0
0
2
0
2
0
2
1
0
2
2
0
0
1
0
0
1
0
0
3
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
2
1
0
0
1
1
0
0
0
0
0
2
0
0
0
0
1
1
0
0
2
0
2
0
0
0
0
2
2
0
1
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
1
1
2
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
3
1
0
1
0
2
2
0
2
0
0
2
2
0
0
0
2
0
0
0
2
3
0
0
0
2
1
0
1
2
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
5
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
3
0
1
0
0
1
0
1
0
0
1
0
0
0
1
0
1
0
2
1
0
2
0
0
2
2
0
0
0
0
2
0
0
4
0
0
0
0
0
13
1
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
3
2
2
1
2
0
0
0
0
2
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
5
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
1
0
5
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
4
0
1
1
1
0
0
2
0
0
0
2
1
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
3
3
0
0
0
0
7
0
0
0
2
0
0
0
0
0
2
3
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
1
0
0
2
0
0
0
0
0
2
1
0
0
1
0
2
0
0
1
2
0
1
0
0
1
0
1
2
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
2
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
2
1
0
1
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
1
0
1
0
0
0
0
3
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
1
0
3
1
2
0
1
0
0
1
0
0
3
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
3
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
2
1
0
1
0
0
0
0
1
0
0
0
1
0
2
0
0
2
0
0
1
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
2
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
4
0
0
1
0
2
1
0
0
0
5
2
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
3
2
0
0
0
1
0
0
0
1
0
2
0
0
0
1
2
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
1
1
0
2
0
0
1
0
0
1
1
1
0
0
0
0
0
2
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
2
2
0
0
1
0
1
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
3
0
0
1
1
0
1
0
0
0
0
2
1
2
0
0
0
0
4
0
0
0
1
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
2
0
1
1
2
2
0
0
0
0
0
0
3
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
2
0
4
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
1
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
1
3
2
0
2
1
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
1
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
2
2
0
2
0
0
3
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
5
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
1
0
2
0
0
0
0
0
2
1
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
14
2
0
0
1
0
2
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
2
0
0
0
1
0
0
1
1
0
0
4
1
0
0
1
3
0
1
0
1
0
1
0
0
0
0
0
3
1
0
0
0
0
0
2
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
4
0
4
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
9
0
0
2
0
1
2
1
0
1
0
0
1
0
2
0
1
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
1
3
2
0
0
0
0
0
0
3
0
0
2
0
0
0
2
1
0
2
0
1
0
0
0
4
0
0
0
0
3
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
3
2
0
1
0
2
2
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
1
5
0
0
2
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
1
0
1
1
1
3
0
1
0
2
2
0
0
0
0
0
0
1
0
1
0
0
0
1
0
4
0
0
1
0
0
2
1
0
0
0
0
1
0
1
2
0
4
0
0
0
2
0
3
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
3
2
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
2
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
2
0
0
1
0
0
1
1
0
0
2
0
2
0
0
2
0
1
0
0
0
0
2
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
1
2
0
2
0
2
0
0
1
0
0
0
0
0
1
1
2
0
0
0
0
0
3
2
3
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
1
1
0
2
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
2
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
1
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
1
0
0
1
2
1
0
3
0
0
3
0
2
1
0
1
0
9
0
0
0
0
1
2
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
3
1
0
0
1
0
0
2
0
1
2
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
1
0
3
0
0
0
1
0
1
0
0
1
1
1
0
1
0
2
1
0
0
1
2
2
2
0
0
2
0
0
2
1
2
0
0
0
1
1
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
3
0
0
0
1
1
0
1
2
0
2
3
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
1
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
4
0
1
0
0
2
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
3
2
1
1
2
0
1
0
1
1
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
3
0
0
1
1
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
2
0
1
0
0
0
1
0
1
0
0
1
1
0
2
0
0
0
0
3
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
2
0
0
1
2
0
5
0
2
2
0
0
0
2
2
2
2
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
2
0
0
3
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
1
1
0
0
1
0
4
0
1
0
0
2
2
2
0
0
0
0
0
1
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
1
2
0
2
0
0
1
1
0
0
0
2
0
0
0
1
1
1
1
0
2
1
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
1
1
0
0
2
0
0
0
0
0
0
0
0
2
2
0
2
0
0
1
0
1
0
0
2
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
1
0
0
1
2
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
1
0
1
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
2
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
3
0
1
0
0
2
0
0
0
2
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
2
0
0
2
5
0
1
0
2
0
0
1
1
0
2
0
1
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
2
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
3
0
0
1
0
0
0
0
0
0
0
0
2
0
1
1
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
3
0
0
1
1
0
0
0
4
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
2
1
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
2
0
2
0
1
0
1
0
2
1
2
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
3
2
0
0
0
0
0
0
1
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
2
0
1
2
2
0
0
0
2
0
2
0
4
1
0
0
0
0
3
0
3
1
1
0
0
0
0
1
0
0
0
0
0
2
0
1
0
1
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
2
0
0
0
0
1
0
1
2
0
1
0
0
0
0
1
0
2
0
0
1
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
3
0
0
2
0
0
0
2
0
0
0
0
0
0
0
4
0
0
0
2
0
2
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
1
0
1
0
2
3
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
2
0
0
2
0
1
2
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
5
2
0
0
0
1
0
2
0
0
2
1
0
0
2
0
0
0
1
2
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
4
0
2
0
0
0
2
0
0
0
1
0
0
2
1
2
1
0
1
0
0
1
0
0
0
0
2
0
0
4
0
0
0
1
0
0
2
2
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
4
1
0
2
0
0
2
0
0
0
0
1
0
2
1
3
2
1
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
1
2
1
2
2
0
0
0
0
0
0
2
0
2
0
3
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
1
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
1
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
1
0
1
2
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
3
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
3
0
0
2
2
0
0
0
0
3
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
1
1
2
0
1
0
0
1
0
2
5
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
2
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
2
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
1
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
2
0
2
0
1
2
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
1
0
0
1
1
1
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
3
1
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
1
1
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
1
3
0
0
1
0
2
2
0
1
1
0
3
0
0
0
2
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
3
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
2
0
1
2
1
0
0
0
2
1
0
0
0
0
0
0
3
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
4
4
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
1
0
0
0
0
0
2
1
1
1
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
1
0
2
0
1
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
3
0
0
1
0
0
0
0
2
0
1
0
4
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
2
2
0
0
1
2
0
0
0
0
0
3
0
0
0
1
0
0
0
3
1
0
0
0
1
7
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
1
2
0
2
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
1
1
0
1
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
1
3
0
1
0
1
2
0
0
0
1
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
12
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
5
2
0
0
1
0
1
1
0
2
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
1
0
0
0
0
0
0
2
2
0
3
0
0
2
0
2
3
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
1
1
1
0
1
0
0
0
0
0
1
0
2
0
0
0
4
0
0
1
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
2
0
0
0
2
1
3
1
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
11
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
4
0
1
0
0
0
1
0
1
1
0
1
3
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
2
0
0
2
1
1
0
1
1
2
5
0
0
1
1
0
2
0
0
0
2
1
1
3
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
2
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
4
0
0
6
0
0
0
0
0
2
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
2
0
1
0
0
0
3
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
1
0
0
0
1
0
2
0
0
3
0
0
0
0
0
0
2
2
0
1
0
2
0
0
0
2
2
2
0
0
0
1
0
0
0
1
2
0
0
0
2
0
0
0
0
1
2
0
0
1
0
2
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
4
0
2
0
0
0
2
0
0
0
1
4
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
1
1
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
2
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
3
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
1
2
0
0
2
0
2
0
0
0
1
0
0
0
0
2
0
0
2
2
1
0
0
0
0
2
0
0
1
1
0
0
0
0
2
0
0
2
2
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
2
3
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
5
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
1
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
2
0
0
2
0
0
0
0
0
1
2
2
0
0
0
0
1
0
4
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
1
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
1
3
2
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
3
0
0
0
1
0
0
1
0
2
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
1
0
0
0
0
1
0
0
0
0
0
1
0
0
5
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
2
1
1
0
0
2
0
0
1
0
3
0
1
1
0
2
0
2
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
3
3
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
2
1
0
2
2
1
0
0
0
2
0
0
0
0
2
0
0
1
1
3
0
0
0
0
0
0
1
0
2
0
0
0
1
1
2
0
0
0
0
1
1
0
2
0
2
0
0
1
0
0
1
0
2
2
1
0
1
0
0
2
0
1
2
0
0
0
0
1
2
0
0
0
0
0
0
1
1
0
0
1
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
3
0
1
0
2
0
1
0
1
0
0
0
2
0
1
1
0
0
0
0
0
2
1
2
0
0
0
0
0
0
1
0
2
1
2
1
0
0
0
1
0
2
0
0
0
0
0
1
2
0
0
3
0
0
0
2
0
0
0
0
2
0
0
1
0
0
1
0
2
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
2
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
3
3
0
0
2
0
0
0
0
0
0
1
0
3
0
2
2
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
2
0
0
0
3
0
0
2
2
0
0
2
1
2
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
2
3
3
0
0
1
1
2
0
2
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
1
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
2
0
2
2
1
2
1
0
0
0
1
1
1
0
1
1
2
0
0
0
0
3
2
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
4
0
0
4
0
0
0
0
0
0
2
0
0
0
0
0
1
2
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
1
2
0
2
2
0
0
0
1
2
0
2
1
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
3
0
0
0
2
0
0
0
2
0
0
0
0
1
0
2
1
0
0
0
1
0
0
2
0
0
2
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
1
2
4
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
11
0
0
1
0
0
0
1
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
1
0
4
0
1
0
0
0
2
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
2
0
0
0
0
0
0
1
0
1
0
2
0
0
0
2
2
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
2
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
6
0
0
1
2
2
1
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
1
0
0
2
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
1
1
0
1
0
1
0
0
2
0
0
0
0
1
0
0
0
1
0
0
1
0
0
7
0
1
0
0
0
2
0
0
0
0
1
0
1
0
0
2
0
1
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
1
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
3
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
2
0
0
0
2
0
0
1
0
0
3
2
1
0
0
0
4
1
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
1
0
0
2
0
0
0
3
0
0
2
0
0
0
0
3
0
0
0
1
2
0
0
2
0
5
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
6
0
1
0
3
0
0
0
1
0
0
1
0
0
0
1
2
0
0
2
0
2
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
3
0
1
0
0
0
1
3
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
2
0
2
1
2
0
0
0
0
2
0
0
2
2
0
0
3
0
2
0
0
0
0
0
0
1
0
1
2
0
0
2
1
0
0
1
0
0
0
0
1
2
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
12
0
0
3
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
2
0
2
0
0
0
1
0
2
0
0
1
0
1
0
0
0
2
0
1
3
0
0
0
0
0
0
1
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
8
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
3
0
0
1
0
0
0
1
0
2
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
1
0
2
0
1
0
2
0
1
2
1
1
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
2
1
0
1
0
1
0
3
2
0
0
2
1
0
1
1
1
1
0
0
0
0
0
1
0
0
0
0
2
2
2
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
1
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
2
2
0
0
2
3
0
2
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
2
0
2
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
2
1
2
0
0
1
0
0
1
0
0
0
0
0
0
0
1
6
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
2
2
1
1
0
0
0
0
0
1
0
0
4
0
0
2
0
0
0
0
2
2
0
0
0
1
2
0
1
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
3
0
0
0
2
0
1
2
0
0
0
1
2
0
1
0
0
0
0
1
1
0
2
0
0
1
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
2
2
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
1
1
0
0
0
3
0
0
0
0
0
0
2
1
0
0
0
2
2
2
0
2
1
1
0
0
0
0
2
0
0
0
2
0
1
0
0
2
1
0
0
2
0
0
1
0
1
0
1
0
2
1
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
1
0
0
0
0
2
0
0
0
1
0
0
1
0
2
0
0
0
2
2
0
0
0
0
2
0
0
1
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
2
0
0
0
0
0
1
2
0
1
3
2
0
0
0
0
0
2
0
1
3
0
5
2
0
2
1
0
1
0
0
1
1
1
2
1
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
3
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
4
0
0
2
1
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
3
0
0
0
1
1
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
4
0
2
0
0
2
0
0
1
1
0
0
2
6
0
1
0
1
0
0
1
0
3
2
0
1
0
1
0
0
0
2
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
2
0
0
2
0
0
0
0
0
2
2
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
2
1
0
2
2
1
0
1
1
1
0
0
0
0
0
1
0
1
0
1
2
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
2
2
2
0
1
0
2
0
7
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
1
0
0
2
0
0
0
0
0
2
0
3
0
0
0
0
0
2
2
1
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
1
0
0
0
2
0
0
3
0
0
0
0
1
0
1
0
1
1
1
2
0
2
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
1
1
0
0
0
2
1
1
0
0
2
1
1
0
0
0
0
0
0
2
0
2
0
0
3
0
2
0
1
2
0
1
0
0
2
0
0
1
2
0
0
0
1
1
1
1
0
0
0
0
0
1
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
2
0
0
0
2
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
2
2
2
0
1
1
0
0
1
0
2
1
2
2
1
0
0
2
0
0
0
1
0
0
3
0
0
0
0
1
0
1
0
1
2
0
0
2
0
0
0
1
3
2
0
1
0
0
0
2
1
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
1
2
0
0
0
0
2
1
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
5
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
2
0
2
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
1
0
0
0
1
1
0
0
2
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
1
0
1
0
0
0
2
0
0
0
0
0
0
1
0
2
2
0
0
0
0
2
0
1
0
2
0
0
0
1
1
0
1
0
0
2
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
3
0
0
0
0
0
2
2
1
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
2
0
2
2
0
0
0
0
2
1
2
0
0
0
0
0
2
0
2
0
0
6
0
0
0
1
2
0
0
0
0
0
0
0
1
0
2
0
2
2
0
0
2
0
1
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
1
0
0
1
3
0
0
4
0
0
0
0
0
1
1
1
1
0
0
0
1
0
0
1
2
0
1
1
0
0
1
0
0
0
1
1
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
1
1
0
1
2
0
0
0
0
2
2
0
0
0
1
0
2
0
2
0
0
1
0
1
1
0
0
0
0
1
0
0
2
0
0
0
5
0
0
1
0
0
1
0
0
2
0
1
3
0
0
0
0
0
0
2
0
0
0
2
0
2
1
2
0
1
0
2
0
0
1
0
1
0
1
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
2
3
2
0
0
0
0
0
0
0
0
0
3
1
0
0
1
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
3
2
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
1
0
1
0
2
2
2
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
1
3
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
1
0
2
0
1
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
1
2
0
0
0
0
3
0
0
0
0
0
4
0
1
0
1
0
0
2
0
1
1
0
0
1
0
1
1
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
2
0
0
1
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
3
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
1
1
1
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
1
1
0
0
2
0
2
1
0
1
0
0
2
0
0
0
0
0
3
1
0
0
1
0
2
2
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
1
0
0
3
0
1
0
0
0
1
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
3
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
2
0
0
0
1
2
0
1
2
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
2
2
0
1
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
1
0
0
1
1
0
2
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
1
3
0
0
0
2
2
0
0
1
0
0
1
1
0
1
1
2
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
2
1
0
0
0
0
2
0
1
0
0
0
0
1
2
0
2
0
0
0
0
0
5
0
0
3
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
4
0
0
0
0
2
0
0
0
2
1
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
2
0
4
0
0
1
0
0
0
0
1
0
0
0
1
1
1
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
1
2
1
0
0
2
2
0
0
0
1
5
3
0
1
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
3
0
0
1
0
0
0
1
1
1
0
0
0
0
2
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
2
0
0
1
1
3
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
1
1
0
2
0
0
0
1
2
1
2
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
1
1
1
0
0
3
2
0
0
2
0
0
0
0
0
0
0
0
5
1
2
0
0
1
0
0
2
0
0
0
3
0
0
0
0
0
0
3
0
1
0
2
0
0
0
0
1
4
1
0
0
0
2
0
0
0
0
2
0
2
0
0
3
1
0
0
0
0
0
3
1
2
0
0
2
0
1
1
0
2
0
2
1
0
0
0
0
0
0
1
0
0
2
0
0
0
1
1
0
1
0
0
0
2
1
0
0
0
2
0
0
5
1
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
2
0
0
0
0
3
0
1
0
0
0
3
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
1
0
0
0
4
2
0
0
0
0
0
0
0
1
0
0
3
0
0
2
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
1
0
1
0
0
1
2
0
0
0
0
0
0
0
1
1
1
0
0
1
1
1
0
9
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
2
0
0
1
0
1
1
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
2
0
0
0
0
1
0
1
2
0
3
0
0
0
1
1
2
0
0
0
1
0
0
0
1
0
0
0
2
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
1
2
0
0
3
0
0
0
0
0
2
1
0
0
0
1
1
0
1
0
1
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
2
0
0
2
1
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
15
2
0
2
0
0
2
0
2
2
0
0
2
1
0
1
1
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
1
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
2
0
3
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
3
0
0
0
2
0
0
0
0
1
0
0
0
1
3
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
3
1
1
0
0
1
0
0
0
0
0
2
0
2
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
2
7
0
0
0
0
2
18
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
3
4
0
0
2
0
0
1
0
0
3
0
0
0
0
3
0
0
1
0
2
0
0
0
1
0
0
2
0
2
0
0
2
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
2
0
0
1
0
0
1
0
0
2
0
0
0
0
0
1
4
0
0
0
2
0
0
0
0
5
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
2
1
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
2
2
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
2
0
0
0
0
2
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
3
1
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
1
2
2
0
1
0
0
0
1
0
2
0
2
1
0
0
2
0
0
0
0
3
0
0
0
0
0
1
1
1
0
0
0
0
2
0
1
0
0
0
1
1
0
0
0
0
0
1
0
2
0
2
0
0
0
0
1
2
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
3
0
0
0
1
0
1
0
1
0
2
1
0
0
0
2
0
0
0
1
0
2
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
1
0
1
2
0
0
2
2
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
1
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
3
0
0
1
1
0
0
1
0
3
0
0
0
0
0
0
1
0
0
0
1
0
1
6
0
0
0
1
2
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
7
0
1
1
2
0
2
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
2
0
0
2
0
0
0
1
0
1
0
2
0
0
2
0
10
0
1
0
2
0
2
0
0
0
1
1
0
3
0
0
0
0
0
0
0
3
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
4
0
0
1
3
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
4
1
0
2
0
0
1
0
1
2
2
0
0
0
0
0
2
0
1
0
4
0
1
0
0
0
1
0
1
1
0
2
0
1
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
2
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
3
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
1
4
2
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
3
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
1
0
0
0
3
0
0
1
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
1
1
0
0
0
2
0
0
1
2
2
0
0
0
1
0
0
1
0
1
2
0
3
0
1
0
1
0
0
3
4
1
2
0
2
2
0
0
0
0
1
0
0
0
2
1
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
1
2
0
0
2
2
0
0
0
0
2
0
1
3
0
0
0
0
0
0
1
0
0
3
2
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
3
0
0
2
1
0
0
0
0
0
0
1
0
1
0
0
0
2
2
0
0
0
1
0
0
1
1
0
0
0
1
0
2
0
2
3
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
3
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
5
2
2
1
2
0
0
0
2
0
2
1
0
1
0
0
0
0
0
1
2
0
0
1
0
0
0
2
0
0
0
0
4
0
1
2
2
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
1
2
0
0
0
0
0
1
1
0
0
1
0
2
0
0
0
2
1
0
2
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
2
1
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
4
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
5
0
0
1
0
3
1
0
2
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
2
2
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
4
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
1
0
0
3
0
1
2
2
1
1
0
0
1
0
1
0
0
0
0
1
0
0
0
1
2
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
2
1
0
0
0
1
0
2
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
2
2
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
4
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
1
0
0
2
0
1
1
0
2
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
3
2
0
2
1
0
0
0
2
1
0
2
1
0
0
0
11
0
0
0
0
0
0
0
1
0
1
0
2
0
1
5
0
0
0
0
2
2
0
0
0
0
0
0
1
3
0
0
0
2
0
2
2
2
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
2
1
0
0
0
0
2
0
3
0
1
0
0
0
0
0
0
1
0
3
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
4
0
0
0
0
1
0
0
2
0
0
0
0
1
1
0
0
0
0
1
0
0
1
1
1
2
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
1
0
0
2
0
1
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
3
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
2
1
1
0
2
1
0
1
1
0
0
1
0
2
0
0
0
0
1
2
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
2
0
0
0
0
1
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
1
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
2
1
0
2
1
0
0
1
3
1
1
0
0
0
0
2
0
0
1
0
1
0
0
0
3
0
0
0
0
0
0
2
0
1
1
2
0
0
0
4
0
0
0
0
1
2
2
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
3
2
0
2
1
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
1
1
0
2
0
0
0
3
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
2
0
0
2
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
2
1
0
0
4
2
1
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
2
2
5
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
3
1
1
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
1
0
0
2
0
3
0
0
2
0
0
0
0
0
1
3
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
2
0
2
0
1
0
0
2
2
0
1
0
1
2
0
2
0
0
0
2
0
0
0
0
0
0
1
2
0
2
3
2
0
0
2
0
2
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
6
3
1
2
1
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
1
0
0
0
4
3
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
6
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
2
0
2
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
2
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
3
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
2
0
0
2
0
1
0
1
0
0
0
0
0
0
0
1
3
0
0
1
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
2
0
0
0
0
2
1
2
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
3
0
0
0
1
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
2
0
0
0
3
1
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
6
0
0
0
2
0
2
1
0
1
2
2
0
0
0
2
1
3
0
0
0
2
0
0
2
0
0
0
0
2
1
1
0
3
2
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
2
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
4
0
0
1
0
0
2
1
0
2
1
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
3
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
2
1
2
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
1
0
0
0
2
0
2
0
3
0
0
0
0
2
0
0
4
2
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
2
3
2
0
0
0
2
2
1
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
2
0
0
0
0
1
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
5
1
0
0
0
3
0
0
2
3
0
2
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
1
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
2
0
0
2
0
1
0
2
0
2
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
2
0
1
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
2
2
2
0
2
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
4
2
0
0
2
0
5
0
4
1
1
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
1
0
0
0
2
0
0
0
1
0
2
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
4
2
0
1
0
0
1
2
0
2
1
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
2
0
2
1
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
1
0
0
0
2
0
0
0
2
0
0
0
3
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
1
0
0
0
0
0
0
4
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
2
1
0
0
2
0
0
2
0
1
0
2
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
1
0
0
0
2
1
0
0
0
0
0
0
0
3
2
0
0
0
0
0
2
0
2
0
2
1
1
0
2
3
0
0
3
0
0
0
1
0
1
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
1
2
0
0
2
2
1
0
0
1
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
1
0
0
0
1
0
1
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
1
0
4
0
0
0
0
0
0
2
0
0
1
2
0
2
0
0
0
0
0
1
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
4
1
0
0
0
0
1
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
9
0
2
0
0
1
1
0
0
2
0
4
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
2
0
0
0
1
0
2
3
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
1
2
0
2
1
3
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
2
0
2
0
2
1
2
1
0
0
1
0
2
0
0
0
0
4
1
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
1
1
0
0
1
0
1
0
0
0
0
2
0
0
0
0
1
1
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
5
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
3
0
0
0
2
2
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
1
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
2
2
0
2
1
2
0
1
0
1
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
5
2
0
0
2
0
0
1
0
0
2
1
0
1
0
0
0
0
0
0
2
0
0
2
2
0
1
1
2
0
1
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
1
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
5
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
1
0
0
0
3
2
0
0
1
0
0
2
0
1
0
0
0
0
1
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
4
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
2
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
2
2
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
2
2
0
0
0
1
0
1
0
0
0
0
0
0
0
1
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
2
0
1
0
0
2
2
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
2
2
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
3
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
1
2
1
0
0
0
1
0
0
0
1
0
0
0
0
3
0
0
0
2
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
2
0
1
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
3
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
2
0
0
1
1
4
0
1
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
1
0
3
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
3
0
0
2
0
0
0
1
0
2
0
3
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
1
1
0
1
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
1
0
0
0
1
2
0
1
0
0
2
0
2
0
1
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
3
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
3
0
0
1
1
0
1
0
0
0
3
0
0
0
0
0
0
2
1
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
2
2
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
1
2
0
0
0
0
1
0
0
0
1
1
0
0
2
0
0
5
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
1
1
1
0
0
1
0
0
1
0
0
1
0
0
5
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
3
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
1
2
0
1
0
1
0
0
0
1
2
2
0
0
1
0
0
0
0
2
0
0
0
0
2
1
0
0
2
0
0
2
0
0
1
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
1
0
4
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
2
0
0
1
0
2
4
0
2
1
1
0
1
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
2
2
0
0
0
0
0
2
0
2
0
0
1
0
0
0
1
1
1
1
1
1
1
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
1
2
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
1
3
0
1
0
0
1
2
0
2
1
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
4
0
0
0
1
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
1
0
0
0
0
1
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
2
2
0
0
0
0
2
0
0
1
2
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
1
0
0
0
0
0
0
0
3
0
0
0
0
1
0
1
1
0
0
2
2
1
0
0
0
1
2
1
0
0
3
0
0
0
0
2
0
0
0
0
0
2
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
1
0
0
8
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
3
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
2
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
1
1
0
3
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
1
1
0
1
1
2
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
4
0
0
2
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
2
0
2
0
0
0
0
1
3
0
0
0
1
5
0
2
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
2
2
0
2
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
7
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
3
2
1
0
1
0
0
0
0
1
0
2
0
1
2
0
0
0
0
0
0
1
0
2
0
0
2
0
1
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
12
0
0
0
2
1
3
0
3
0
0
0
2
0
1
0
0
0
0
2
0
0
0
2
0
0
1
2
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
6
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
2
1
0
2
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
2
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
2
0
0
0
0
1
0
2
0
0
0
0
6
0
0
0
0
4
0
0
0
1
0
0
0
0
0
2
0
0
1
2
2
0
0
0
0
0
2
1
1
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
3
1
0
2
1
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
1
1
0
0
2
0
0
0
3
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
2
1
0
0
0
0
2
1
0
2
0
0
1
0
0
0
1
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
4
0
2
2
0
2
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
1
0
0
2
0
2
2
1
2
2
0
0
0
0
0
0
0
2
0
2
0
6
0
0
0
0
1
1
1
1
0
0
3
0
0
2
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
2
0
0
1
0
0
0
2
1
0
0
0
3
0
2
1
0
0
3
2
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
1
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
1
0
2
0
0
0
1
0
0
0
0
2
0
2
2
0
0
0
0
2
1
2
0
0
4
0
2
0
0
0
0
0
0
1
0
3
0
0
2
0
0
0
0
1
0
2
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
3
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
2
0
0
3
0
0
2
0
1
2
2
1
2
0
0
0
0
0
0
0
0
0
2
1
2
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
3
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
4
0
0
0
1
1
0
0
2
2
0
0
0
0
2
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
5
0
0
0
5
1
0
2
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
1
3
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
2
0
2
2
0
2
0
1
3
0
0
0
0
1
2
2
0
0
0
1
1
0
3
2
1
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
3
0
1
0
1
1
2
2
0
0
0
0
0
0
2
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
1
0
3
2
0
1
0
0
0
2
0
1
2
0
1
2
0
0
0
0
1
0
0
0
2
1
0
0
0
2
0
0
2
0
0
1
0
1
0
0
1
0
0
1
1
0
0
0
0
0
2
1
1
1
0
0
0
1
0
0
0
2
0
0
0
2
0
0
1
0
0
2
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
1
0
0
0
3
0
2
0
0
2
1
0
0
0
0
0
0
0
0
3
1
0
2
0
0
1
2
0
0
0
1
0
0
0
0
2
1
1
0
0
0
0
0
1
2
0
1
1
1
0
0
0
2
2
0
0
0
0
2
0
2
2
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
3
0
1
0
2
0
0
2
0
2
0
0
0
0
0
0
1
0
1
0
1
0
0
2
0
0
2
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
2
1
0
2
0
2
0
2
0
1
1
0
2
0
0
0
2
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
4
1
0
2
0
1
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
1
2
0
2
0
2
0
4
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
1
0
0
0
3
1
0
0
0
0
0
1
0
0
1
0
5
0
1
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
2
0
0
0
0
1
0
0
0
1
3
1
0
0
1
0
0
0
0
0
3
1
2
0
1
2
0
2
0
0
0
2
0
0
0
0
0
1
2
1
2
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
1
1
1
2
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
2
0
2
1
1
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
2
2
0
0
0
2
2
0
2
2
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
2
2
0
0
0
0
0
2
0
1
0
0
1
0
0
2
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
1
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
5
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
4
2
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
3
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
5
0
1
2
0
0
0
0
3
2
0
0
0
0
1
2
2
2
2
1
1
0
0
1
0
0
1
0
2
1
3
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
4
0
1
0
0
0
2
1
0
2
0
3
0
2
2
0
2
0
0
2
0
0
0
0
1
0
0
0
0
2
1
0
1
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
2
2
0
2
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
2
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
2
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
2
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
1
0
0
1
2
1
0
0
0
2
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
3
0
0
2
0
0
0
0
0
0
0
0
1
0
2
1
1
3
0
2
0
0
0
2
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
1
1
0
0
0
1
0
0
0
0
0
1
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
2
0
1
0
1
0
0
1
0
0
1
0
0
0
0
2
0
0
3
1
2
0
2
0
0
0
0
0
2
1
2
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
1
2
2
0
0
0
0
0
0
2
3
0
0
2
1
0
1
2
0
0
0
0
0
0
1
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
2
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
5
1
0
1
0
0
2
0
0
2
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
1
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
5
0
1
1
0
2
0
3
1
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
1
2
0
2
0
0
0
1
0
1
0
0
3
1
0
0
2
2
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
2
1
0
0
3
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
2
1
2
2
2
1
0
0
0
0
1
1
2
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
1
1
0
2
0
0
0
0
0
0
2
0
0
3
0
0
1
1
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
1
1
2
0
0
0
0
0
0
2
0
0
3
1
0
0
5
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
2
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
2
0
0
0
0
1
0
0
4
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
2
0
2
0
0
2
0
4
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
5
0
1
1
2
0
0
0
0
1
2
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
1
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
1
0
0
2
0
0
0
2
2
1
0
0
0
0
0
3
1
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
1
0
2
1
0
0
1
0
0
0
2
0
0
0
1
3
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
2
1
0
0
2
0
1
0
2
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
1
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
2
0
2
0
2
0
0
0
0
2
0
0
1
1
1
0
0
2
1
0
0
0
0
1
0
2
0
1
0
0
0
1
0
0
0
0
2
1
0
0
1
1
0
0
2
0
0
1
0
0
0
1
2
1
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
2
0
0
0
4
0
0
1
1
1
1
0
2
2
0
1
0
1
0
0
0
1
0
2
2
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
2
0
2
2
0
1
0
0
0
0
0
0
0
2
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
2
0
1
3
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
3
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
2
2
0
0
3
0
0
0
0
0
0
2
3
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
1
0
1
2
1
0
0
2
0
0
5
1
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
1
0
0
0
1
0
0
3
2
0
0
0
0
0
0
0
2
3
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
3
1
0
0
2
0
0
2
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
1
0
0
0
0
0
0
0
0
1
0
2
1
2
0
2
0
4
0
0
2
0
0
2
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
1
1
1
0
1
0
0
0
0
1
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
1
0
0
3
1
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
2
0
1
0
1
0
0
1
0
0
0
0
1
3
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
3
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
2
0
0
0
0
0
2
1
0
1
0
1
0
0
2
0
3
0
0
0
2
1
2
0
3
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
1
0
2
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
2
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
2
0
2
0
0
0
0
2
1
1
0
0
0
0
0
2
0
0
1
0
0
1
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
1
2
0
0
0
0
2
0
0
0
1
0
1
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
1
0
0
0
2
0
0
0
2
0
0
2
1
0
0
0
0
0
3
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
2
0
0
0
2
0
4
0
0
2
0
0
2
2
2
0
0
0
3
1
2
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
2
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
2
2
0
1
0
1
0
0
1
0
1
2
0
0
0
0
0
0
0
0
2
2
1
0
0
2
2
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
1
0
0
4
0
0
0
1
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
3
0
1
0
0
0
2
0
0
0
0
0
5
0
0
1
0
1
2
8
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
3
0
0
2
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
3
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
5
0
0
0
0
0
0
1
0
2
2
0
0
1
0
0
0
1
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
4
0
0
1
0
0
0
1
0
0
1
0
1
0
0
1
0
1
2
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
2
0
1
0
0
0
0
1
2
1
0
0
0
0
3
1
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
4
0
1
0
1
10
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
4
0
0
0
0
5
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
1
1
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
4
0
1
2
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
13
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
1
2
0
1
0
0
1
0
0
0
0
0
1
2
0
2
0
0
0
0
0
2
0
0
0
0
1
0
1
0
1
5
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
2
0
0
0
0
0
2
2
0
0
2
0
3
0
0
0
2
0
0
2
0
2
0
0
2
0
2
1
0
1
0
0
2
0
1
9
0
0
2
0
2
0
0
0
0
0
0
1
0
0
2
0
1
0
2
2
1
0
0
2
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
1
2
0
0
1
0
0
2
0
0
2
0
2
0
0
0
0
0
1
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
2
0
0
2
1
1
0
0
1
3
1
0
2
0
1
0
0
1
0
3
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
2
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
1
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
2
1
2
0
0
0
1
1
1
0
0
0
2
0
0
1
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
3
0
0
0
3
2
0
0
2
4
6
0
1
2
2
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
16
0
1
0
0
1
1
1
1
0
2
2
0
1
0
1
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
1
3
0
0
0
2
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
1
0
0
0
0
2
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
2
0
11
0
1
0
2
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
2
0
2
0
0
2
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
2
0
0
2
1
0
0
0
0
0
5
1
0
0
0
0
2
2
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
1
0
2
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
3
0
0
0
0
0
0
1
1
0
0
1
1
1
0
0
1
0
1
2
0
1
0
1
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
3
0
2
1
0
2
0
0
1
0
0
2
2
0
0
1
0
0
0
2
2
0
1
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
1
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
2
0
1
2
2
0
0
6
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
2
0
2
0
2
0
0
1
0
0
0
0
1
0
2
0
0
0
1
0
0
0
1
2
0
0
1
2
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
1
2
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
3
0
0
0
0
1
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
3
0
0
1
1
2
0
0
0
2
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
1
0
6
0
2
0
2
2
0
2
1
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
4
1
0
0
2
0
0
0
0
4
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
1
0
0
0
3
1
0
0
0
0
2
0
0
2
0
0
0
2
0
0
1
2
0
2
2
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
2
0
0
2
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
1
0
1
0
2
0
0
2
0
0
0
0
0
0
2
0
1
1
0
0
0
2
0
0
2
0
0
0
3
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
2
0
0
0
0
2
0
2
0
2
0
0
0
1
0
3
0
0
0
0
0
1
1
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
3
1
0
1
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
2
2
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
2
0
0
2
0
1
1
2
0
0
0
0
1
1
0
2
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
3
4
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
1
0
0
2
0
0
0
1
0
2
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
2
2
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
2
0
5
0
2
0
0
2
0
0
1
0
0
0
0
0
1
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
1
0
0
0
0
0
8
0
0
1
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
2
0
2
0
0
1
0
0
0
2
4
0
0
0
0
2
4
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
2
0
3
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
2
1
0
3
2
0
0
0
0
0
0
0
0
0
3
0
2
0
1
2
1
1
0
0
1
0
2
0
0
2
0
2
0
2
0
0
4
0
0
2
0
0
0
3
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
1
0
0
2
0
2
1
1
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
2
2
1
0
0
1
0
0
0
0
0
2
0
1
0
0
0
3
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
2
1
2
0
2
1
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
1
1
1
0
1
0
0
0
0
1
1
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
2
2
1
0
0
0
0
1
1
0
1
1
3
0
0
0
0
0
0
0
0
0
1
0
4
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
2
0
0
1
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
1
0
2
0
0
0
0
2
0
0
3
0
0
0
0
1
1
1
1
0
3
1
0
0
0
0
0
0
2
2
0
2
2
0
1
2
0
1
0
0
0
0
2
0
0
2
2
0
0
0
0
0
1
1
0
2
0
0
0
0
1
0
2
0
1
2
0
0
0
2
0
0
2
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
3
0
1
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
3
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
2
1
0
1
0
3
1
0
0
0
0
2
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
2
0
0
1
0
1
0
1
0
2
1
2
2
0
0
0
0
0
0
1
0
0
0
3
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
7
1
0
1
0
0
1
2
0
0
0
0
1
1
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
1
2
0
0
1
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
1
0
2
3
1
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
3
0
0
0
3
0
2
2
0
0
1
0
0
0
2
1
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
1
0
0
0
1
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
2
7
0
0
2
2
0
0
1
0
0
1
0
1
0
1
1
0
0
2
0
0
0
5
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
4
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
2
2
0
0
3
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
1
0
2
2
0
2
2
1
0
1
0
0
0
0
3
0
0
1
1
0
0
0
3
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
1
1
1
0
1
2
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
3
2
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
7
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
2
0
0
0
0
2
1
0
3
0
4
0
1
0
0
3
0
0
0
0
0
0
2
0
0
6
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
2
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
1
0
2
1
0
1
0
1
3
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
1
2
1
0
0
2
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
2
0
1
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
1
2
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
2
0
0
0
0
2
2
0
0
0
1
0
0
0
0
3
2
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
0
0
2
0
1
0
2
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
2
0
0
0
0
0
2
0
0
0
0
4
0
0
0
0
0
2
2
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
2
1
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
2
0
2
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
2
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
2
0
8
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
5
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
4
2
2
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
2
2
2
2
0
0
0
0
0
0
1
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
2
2
2
1
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
2
0
0
0
2
0
0
2
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
2
0
0
1
0
0
1
0
3
0
0
2
2
1
0
0
2
1
1
0
0
0
0
0
0
1
0
0
2
2
1
1
2
0
2
0
0
0
0
0
0
0
2
1
7
1
1
0
0
2
0
0
2
1
0
2
0
0
0
2
0
0
1
0
0
2
2
0
0
0
1
0
0
0
1
0
0
0
0
0
2
3
0
2
0
1
0
0
0
0
0
1
2
0
2
2
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
4
0
0
0
0
0
2
1
0
0
0
0
1
0
2
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
2
0
0
2
0
0
1
2
0
0
0
0
0
0
2
2
0
0
0
2
0
2
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
1
1
0
0
0
0
1
0
1
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
5
0
0
1
0
0
2
0
0
0
1
0
2
0
1
0
3
0
2
0
0
0
0
0
0
0
1
1
0
1
0
0
0
2
0
2
0
2
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
2
1
2
1
2
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
8
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
2
1
1
0
0
0
0
2
0
0
1
1
0
0
0
0
0
4
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
1
0
0
0
0
0
1
2
0
2
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
1
2
0
0
2
0
0
0
0
3
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
1
2
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
3
0
0
0
3
0
2
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
1
1
0
1
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
3
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
2
0
2
1
0
0
0
1
0
0
0
1
0
2
0
0
0
0
2
0
1
2
2
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
2
0
0
0
2
0
2
0
0
0
1
0
2
0
1
1
0
0
0
1
1
0
0
0
0
0
1
0
0
2
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
2
0
0
0
0
1
3
0
0
0
2
0
1
0
0
0
0
0
0
0
1
1
0
0
2
1
2
0
0
0
2
0
0
1
1
2
0
0
0
0
2
0
2
1
0
0
2
2
0
0
0
0
0
0
3
4
0
0
0
0
1
0
4
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
1
1
0
0
0
2
0
1
1
2
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
2
0
2
2
1
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
1
1
2
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
2
0
0
1
1
0
1
0
0
1
1
6
1
0
0
2
0
0
2
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
2
0
1
1
2
0
1
1
2
1
0
0
3
0
0
0
0
1
0
0
1
2
2
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
2
0
2
1
4
0
0
1
0
0
0
0
2
2
3
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
1
2
0
1
0
0
3
0
0
1
0
0
1
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
2
0
0
0
1
2
0
1
0
0
0
2
0
0
4
0
0
0
2
0
1
0
0
1
0
0
0
1
0
0
0
0
0
2
0
1
0
1
0
0
0
0
2
0
0
0
0
1
1
0
0
2
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
2
0
2
2
2
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
2
2
0
0
5
0
1
0
0
0
0
1
2
2
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
2
1
1
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
2
2
1
2
0
0
0
2
0
5
0
1
0
3
0
1
0
2
1
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
2
1
0
2
0
2
0
3
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
3
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
1
2
2
1
0
0
0
2
1
0
0
1
0
0
2
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
3
5
0
0
1
0
1
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
1
1
0
0
0
0
2
0
0
0
1
0
1
1
0
0
2
0
1
1
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
7
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
2
1
0
0
1
2
0
0
0
0
0
0
0
1
0
2
0
0
0
2
1
1
0
0
0
2
1
0
0
2
0
2
0
1
0
2
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
2
2
2
0
0
1
0
0
0
0
0
0
1
0
0
0
4
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
2
2
1
1
0
0
2
1
1
0
0
0
0
2
2
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
1
1
0
1
0
0
0
0
1
0
1
0
0
0
2
2
0
0
2
2
2
0
0
0
0
0
0
3
0
1
2
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
2
0
0
0
6
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
2
0
0
0
3
0
0
0
0
0
4
0
0
0
2
2
1
1
2
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
1
0
1
1
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
1
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
2
2
2
1
1
2
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
1
0
0
1
0
0
4
0
0
1
2
0
2
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
2
2
2
0
0
1
0
0
0
0
2
0
3
0
2
0
1
1
0
0
0
1
1
0
0
0
0
2
0
0
0
0
1
0
1
2
1
1
0
0
0
0
4
1
0
0
0
0
2
0
1
0
1
2
0
0
1
0
0
3
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
4
0
2
0
1
0
0
0
0
0
0
0
2
0
2
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
2
4
0
0
0
0
0
0
0
0
2
2
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
1
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
2
2
0
0
1
3
2
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
1
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
2
0
0
3
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
3
0
0
1
2
0
2
1
1
3
0
0
0
2
0
1
0
3
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
3
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
6
0
0
0
2
2
0
2
0
0
0
1
0
0
2
0
0
1
0
0
2
0
2
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
2
0
0
0
1
0
2
0
0
2
0
0
2
0
1
3
0
0
1
1
0
2
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
1
0
0
3
1
3
0
1
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
2
2
0
2
1
0
0
0
0
1
2
0
7
0
0
0
1
0
2
0
0
0
2
0
0
0
2
1
0
0
4
0
2
1
0
0
0
0
2
0
0
0
0
1
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
2
0
1
2
2
1
2
0
0
1
0
0
0
0
0
3
5
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
1
0
1
0
0
2
0
0
2
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
1
1
2
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
3
3
0
2
2
0
1
1
0
0
1
2
0
0
0
0
1
0
0
5
0
0
0
0
0
0
5
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
4
0
0
0
1
0
0
1
0
3
0
0
4
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
2
0
5
0
2
0
0
0
2
0
3
1
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
1
0
0
2
3
0
0
2
0
1
2
0
0
0
2
2
2
0
1
0
0
1
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
2
0
0
1
3
1
0
0
0
1
0
0
0
0
2
1
0
0
2
0
0
2
0
0
0
0
0
0
2
1
0
0
0
1
2
0
2
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
1
0
0
0
0
1
0
1
0
2
0
0
0
0
3
0
1
0
0
0
0
0
4
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
1
0
0
2
2
0
0
0
0
0
0
0
2
0
2
2
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
3
2
1
0
1
0
0
0
0
1
1
0
0
2
0
0
1
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
5
1
0
2
2
0
0
0
0
0
0
3
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
3
0
0
2
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
1
0
0
2
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
2
0
1
1
0
0
0
0
1
0
0
0
0
4
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
4
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
2
0
2
0
1
0
0
0
0
0
0
0
2
0
0
2
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
3
0
2
0
0
0
4
0
1
0
0
2
2
1
0
0
0
3
3
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
2
0
0
1
1
0
0
3
0
0
0
0
2
1
0
2
0
0
1
0
1
0
0
0
2
1
0
0
1
0
2
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
1
0
1
1
0
6
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
4
0
0
1
0
2
2
0
2
0
3
0
0
0
0
0
0
1
0
2
0
0
1
2
0
0
0
0
0
0
0
0
2
0
5
0
0
1
2
2
0
0
0
2
0
0
0
1
0
0
0
0
1
1
0
0
1
0
5
0
2
1
0
1
0
1
0
1
0
0
0
1
0
1
0
3
0
0
0
0
0
0
2
2
2
0
2
1
0
0
2
2
0
0
0
0
0
0
1
1
0
1
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
1
1
0
1
1
0
0
2
2
0
1
2
0
0
0
1
0
0
0
0
0
0
5
0
0
1
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
2
1
0
1
0
1
1
1
0
0
0
0
2
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
1
1
0
0
0
0
2
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
2
2
0
1
2
1
3
0
0
0
0
1
0
6
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
1
0
0
1
2
2
1
0
0
1
1
2
1
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
1
1
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
1
3
0
0
2
3
2
0
0
0
0
0
0
0
0
0
1
2
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
2
0
0
9
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
2
0
0
0
0
1
0
1
0
0
0
0
2
1
0
0
0
0
0
0
4
0
2
0
0
0
0
0
2
2
2
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
2
2
0
0
0
2
2
0
2
0
1
2
0
0
0
1
0
1
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
4
0
0
1
1
1
0
2
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
4
1
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
1
1
0
2
1
0
0
0
1
1
0
1
0
0
0
1
0
1
0
0
1
0
1
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
2
2
0
0
0
1
0
0
2
0
2
0
12
0
0
0
1
1
0
0
0
1
3
2
1
2
0
1
2
0
2
0
0
0
2
0
3
1
0
1
3
0
0
1
0
3
0
0
1
0
0
2
0
0
0
0
1
3
0
2
0
0
0
0
0
3
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
1
1
0
0
6
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
1
0
0
0
3
0
2
3
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
3
2
3
0
0
0
0
0
0
3
0
1
2
0
0
0
0
0
3
1
0
0
1
0
2
0
0
2
5
0
0
0
2
1
0
0
1
0
0
0
2
0
0
0
0
2
0
0
1
0
0
1
0
0
1
2
1
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
2
0
3
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
1
2
0
0
2
0
1
2
0
0
0
0
0
0
0
1
2
2
0
0
0
0
2
2
0
0
2
1
0
1
0
0
0
2
0
0
0
2
2
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
2
0
0
0
2
0
0
2
0
0
0
0
5
0
2
0
0
0
0
1
0
2
1
1
2
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
1
0
0
1
0
0
0
0
0
2
2
1
1
0
0
2
0
0
2
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
1
0
1
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
1
0
0
2
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
5
0
3
2
2
0
0
1
0
0
2
0
0
0
0
0
1
0
1
0
1
2
0
1
0
8
1
2
0
0
1
0
0
0
3
0
0
2
2
0
1
1
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
3
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
3
1
0
2
0
2
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
6
0
0
0
0
0
2
2
0
0
0
0
1
1
0
0
0
3
1
2
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
1
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
3
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
1
1
0
2
0
0
1
1
1
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
1
3
0
1
0
0
0
0
0
0
0
2
0
0
4
0
0
0
0
0
1
0
0
1
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
3
0
3
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
1
2
0
1
0
1
0
0
0
0
0
1
1
0
0
2
0
0
0
0
1
0
2
0
2
0
0
0
0
3
0
0
0
1
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
1
0
0
2
0
0
1
0
0
1
0
0
2
0
0
0
0
0
1
0
6
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
1
2
0
3
1
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
1
0
0
1
0
0
0
0
0
1
2
0
0
2
2
0
0
0
0
0
0
1
0
2
0
2
1
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
1
1
1
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
1
2
3
1
2
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
2
1
0
2
0
0
0
0
1
1
1
1
0
2
0
0
1
0
0
0
3
0
0
5
0
4
3
0
1
1
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
8
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
1
0
0
0
5
2
0
0
2
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
2
0
2
0
1
1
0
4
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
3
0
2
1
0
1
0
1
1
0
2
1
0
7
2
0
0
0
0
1
0
1
0
2
2
0
0
0
1
2
0
0
0
3
2
0
2
0
0
0
0
2
0
1
0
0
0
1
0
1
0
2
0
2
1
2
0
1
0
0
0
0
0
0
2
2
1
2
0
1
0
0
1
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
1
0
3
0
0
2
0
0
0
0
0
2
2
0
0
0
0
2
0
0
1
1
0
0
0
0
0
1
2
0
0
0
0
4
0
0
0
2
0
0
2
4
0
0
2
0
3
2
0
0
0
2
0
0
5
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
1
0
1
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
3
0
0
0
0
0
0
2
0
0
1
0
0
1
2
0
1
2
0
0
0
0
0
3
1
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
2
0
2
0
0
0
0
2
0
0
2
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
12
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
3
1
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
3
0
0
0
0
0
0
0
3
1
0
0
0
1
0
0
3
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
2
0
2
0
0
0
0
0
0
0
1
1
0
3
0
2
0
0
1
0
0
0
3
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
2
0
2
1
2
0
2
0
0
0
0
0
0
5
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
4
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
4
4
1
2
1
0
0
0
0
0
0
0
2
2
0
0
3
2
0
2
0
0
2
1
2
1
0
0
0
2
0
0
0
2
1
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
1
2
0
2
0
0
0
0
3
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
2
0
0
2
0
2
2
0
0
0
1
0
1
1
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
1
2
0
1
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
3
1
1
0
0
2
0
0
0
0
2
0
1
0
0
0
1
5
0
2
0
0
0
1
1
0
0
1
0
0
0
1
1
0
0
0
0
1
1
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
1
2
0
1
1
0
0
1
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
3
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
1
0
0
0
3
0
0
2
0
0
0
1
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
1
0
0
1
0
4
0
2
0
0
0
1
1
0
1
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
2
0
0
0
0
1
0
0
1
2
0
1
0
0
0
1
0
1
0
0
5
1
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
2
0
2
0
1
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
3
0
0
0
2
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
1
0
0
0
0
1
0
0
0
1
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
2
2
2
0
4
1
0
0
0
3
0
1
0
0
0
0
3
0
1
0
0
1
0
1
2
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
2
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
1
9
0
2
0
0
0
0
1
2
2
0
1
2
0
2
0
1
2
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
3
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
2
1
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
3
0
2
0
0
0
0
6
0
0
0
0
2
0
0
0
0
1
0
2
1
1
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
1
0
3
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
2
0
0
0
2
0
0
0
0
0
1
2
1
0
1
0
0
1
0
0
1
0
0
0
3
0
0
0
0
0
1
0
1
0
0
1
1
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
1
0
0
0
2
0
0
0
0
1
0
2
0
2
0
0
0
0
2
0
1
0
2
3
0
0
1
0
0
0
0
1
0
0
0
2
0
2
0
0
0
1
1
0
0
2
0
0
0
1
2
1
2
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
1
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
1
0
2
0
2
2
0
0
0
0
0
3
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
1
1
1
0
1
0
0
0
1
0
0
0
0
0
2
1
0
1
0
2
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
3
1
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
1
0
1
0
1
0
3
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
2
0
2
2
0
0
1
1
0
2
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
5
0
1
0
0
0
1
2
0
0
1
0
1
0
0
0
2
0
1
0
0
0
0
1
1
0
0
0
0
0
0
4
0
0
1
1
0
0
2
0
0
2
0
3
0
0
0
0
1
0
2
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
3
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
2
0
0
0
0
2
0
0
0
4
0
0
1
0
1
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
1
0
0
2
0
0
1
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
2
0
0
0
2
0
2
0
1
0
0
0
0
0
2
0
0
1
1
2
0
1
0
0
1
0
0
1
0
2
0
1
0
1
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
2
0
1
0
2
0
0
1
0
0
0
2
0
2
0
0
0
0
1
0
3
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
2
0
1
3
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
4
2
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
2
1
2
0
0
0
1
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
2
0
0
0
0
1
1
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
2
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
1
4
1
0
0
2
0
0
0
0
1
2
1
1
0
2
0
0
1
0
0
2
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
2
1
0
0
0
0
0
2
0
1
0
0
1
0
2
1
0
1
0
0
0
0
3
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
2
0
0
4
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
1
0
0
3
1
0
0
2
0
0
0
0
3
0
0
1
1
0
1
1
0
1
0
0
0
0
0
0
0
1
2
0
1
3
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
2
0
3
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
1
0
2
2
1
0
1
0
0
0
0
1
2
0
0
0
0
7
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
1
2
0
0
2
0
0
1
1
0
0
1
2
2
0
1
0
2
1
0
0
0
1
0
0
2
0
2
1
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
1
2
0
1
0
0
3
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
1
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
2
0
0
0
3
0
2
0
0
0
0
2
1
1
2
2
1
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
3
0
1
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
5
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
2
3
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
6
1
0
0
0
1
0
0
0
0
1
0
0
0
0
2
2
1
5
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
1
0
0
1
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
1
2
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
2
0
2
0
0
2
0
0
0
2
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
1
0
0
1
0
0
0
0
0
0
2
0
0
2
0
1
0
0
1
0
0
1
0
0
0
0
1
2
2
0
1
0
0
0
2
2
0
1
3
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
1
2
0
1
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
12
1
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
2
2
1
0
0
0
0
3
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
4
0
2
2
1
2
0
1
1
7
0
2
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
2
2
0
0
0
0
4
0
0
0
0
1
3
0
1
1
0
0
0
2
2
1
1
0
1
0
0
0
0
0
0
0
0
0
2
1
1
0
0
3
0
2
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
1
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
3
0
2
0
1
0
1
1
0
0
0
1
0
2
0
0
0
0
1
1
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
2
0
0
0
0
2
0
0
2
1
0
3
0
1
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
1
2
0
0
0
1
2
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
1
0
0
2
1
0
0
3
2
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
7
0
0
0
0
0
0
0
3
0
0
0
0
0
4
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
3
2
2
3
2
3
0
0
5
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
3
2
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
1
0
0
0
3
0
0
0
0
2
0
0
0
2
0
0
1
0
2
0
6
0
0
0
0
0
0
1
0
0
0
0
2
0
2
1
0
0
2
0
6
0
0
0
0
0
0
2
0
2
0
2
0
2
0
1
0
0
1
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
1
0
2
1
0
0
1
0
1
0
0
0
1
0
2
1
0
0
0
0
1
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
3
1
0
0
0
1
0
0
0
0
0
2
0
1
0
0
1
0
0
0
1
0
0
1
2
0
0
0
0
3
2
0
0
2
0
0
2
0
0
0
2
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
2
0
0
1
0
0
0
2
0
2
0
0
2
0
1
0
0
0
2
1
0
0
0
0
1
0
0
1
0
0
2
2
0
0
0
2
3
0
0
2
0
0
0
0
0
4
0
0
1
0
2
0
0
2
2
0
0
1
0
0
1
1
4
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
1
0
5
1
0
2
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
2
2
0
0
1
1
1
0
0
0
2
2
0
0
0
0
0
0
1
0
1
0
2
0
0
0
1
2
0
0
0
1
0
0
0
1
2
2
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
5
0
0
0
1
0
2
0
1
1
2
2
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
3
2
0
0
0
0
2
0
0
3
0
0
4
0
0
0
0
2
0
0
0
3
0
0
0
2
0
2
0
0
0
0
0
0
1
0
1
1
1
0
1
0
0
0
3
0
1
0
1
0
1
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
6
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
2
2
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
1
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
3
1
4
0
0
1
0
0
0
0
2
0
2
0
0
0
0
1
2
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
5
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
3
1
1
0
0
2
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
1
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
1
1
0
1
1
0
0
0
1
0
0
2
0
2
1
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
1
0
2
0
0
1
3
1
3
0
0
2
0
1
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
2
0
1
0
1
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
1
1
1
0
2
0
0
1
0
0
0
2
0
2
0
0
0
1
1
2
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
3
2
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
2
0
0
4
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
2
2
0
2
0
0
2
1
0
1
0
2
2
1
0
3
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
1
2
3
0
0
0
0
1
1
0
0
0
0
2
1
0
0
0
0
1
0
1
0
0
0
2
0
0
0
2
2
0
0
3
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
2
1
0
0
1
0
3
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
3
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
1
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
1
1
0
7
0
1
2
2
5
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
2
1
2
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
1
0
2
0
0
0
0
1
2
0
0
0
2
0
2
0
0
0
0
0
2
0
4
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
1
0
0
0
2
0
2
2
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
2
2
1
0
2
0
4
0
0
0
1
0
2
0
2
0
2
2
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
3
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
2
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
1
1
2
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
1
3
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
4
0
0
0
2
0
0
0
0
0
2
0
1
0
0
3
0
0
0
0
0
0
3
1
0
0
1
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
4
0
2
0
0
0
0
0
2
0
0
1
1
0
3
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
3
0
1
5
0
1
0
0
2
0
0
0
0
0
0
4
0
1
2
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
2
0
0
2
0
0
0
4
0
2
0
0
0
1
0
0
1
0
0
0
0
2
0
2
0
2
0
0
1
2
1
0
0
0
0
1
0
0
0
0
0
1
0
1
2
0
1
0
0
0
0
1
0
3
0
0
0
1
0
0
0
0
1
0
0
2
1
0
0
0
0
1
0
0
0
0
5
0
0
0
0
0
1
1
0
2
0
2
0
0
0
0
0
0
0
0
2
0
1
2
0
1
0
2
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
2
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
2
0
3
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
1
0
0
0
2
0
0
0
1
0
2
0
1
2
0
0
1
1
0
2
0
0
0
0
0
2
0
0
2
0
0
3
2
0
2
2
2
0
2
0
0
2
0
0
0
0
0
0
2
2
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
4
0
0
0
4
0
0
0
0
2
0
2
0
0
0
1
0
0
0
2
0
0
0
2
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
1
0
0
1
0
1
1
0
0
1
1
4
0
0
0
0
0
2
0
2
1
1
2
0
1
1
0
0
2
0
0
0
0
2
1
1
0
0
0
0
1
1
4
0
0
0
0
0
0
0
1
1
1
2
0
0
0
2
0
3
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
2
1
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
2
0
1
0
0
0
1
0
2
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
1
0
1
0
0
0
0
2
1
1
0
0
0
0
5
0
3
0
2
0
0
1
2
0
0
2
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
3
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
1
1
0
0
0
0
0
1
5
0
2
1
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
4
0
1
0
1
0
2
0
6
1
0
1
0
1
1
0
0
1
0
0
1
0
0
2
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
1
0
3
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
4
0
0
0
0
0
0
0
2
2
0
0
1
2
0
0
0
1
1
0
0
2
3
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
2
0
2
0
0
0
0
0
2
1
0
2
0
0
2
0
1
0
0
2
0
0
0
1
2
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
3
2
0
0
1
2
1
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
1
1
0
0
0
0
3
2
1
2
0
0
2
0
0
2
2
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
2
0
0
2
1
0
4
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
1
0
0
0
0
2
0
1
2
0
0
0
0
0
0
1
2
2
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
1
0
3
2
2
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
2
3
0
0
0
0
0
0
0
2
3
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
1
0
0
3
0
0
0
0
2
1
1
3
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
1
1
0
1
2
1
2
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
3
0
0
0
1
0
2
1
3
0
5
0
1
1
0
0
0
0
0
0
1
0
0
0
1
1
2
0
0
0
0
0
0
0
0
2
1
0
1
2
0
0
0
0
1
0
2
10
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
3
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
2
1
2
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
3
2
1
0
1
0
0
0
1
2
2
0
0
3
0
0
0
0
0
1
0
0
0
0
1
0
1
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
2
0
0
1
0
0
0
1
0
2
0
5
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
6
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
2
2
2
1
0
0
0
1
0
0
0
0
0
11
0
2
0
2
0
0
1
0
0
1
0
0
0
0
0
4
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
1
2
0
0
0
2
2
0
1
0
1
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
2
0
0
0
1
1
4
0
0
0
3
0
1
0
0
0
1
1
0
18
1
0
0
0
0
0
0
0
1
0
0
1
8
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
3
2
0
0
1
1
1
0
0
0
1
0
2
0
1
0
2
0
0
0
0
2
0
1
0
0
0
3
0
0
0
1
0
0
1
1
0
0
0
6
0
1
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
2
2
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
3
0
2
2
0
2
0
0
0
7
0
0
2
0
0
0
0
3
1
0
0
1
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
3
1
0
0
0
0
2
0
0
0
0
2
0
0
1
0
1
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
2
0
1
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
20
0
0
1
0
1
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
3
0
0
0
1
1
0
0
1
0
1
0
0
0
1
0
0
0
0
2
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
2
1
0
0
0
0
2
0
0
3
2
1
0
1
1
0
0
2
0
2
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
1
0
0
0
0
0
1
0
3
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
1
0
1
1
2
0
0
0
0
0
0
2
0
10
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
1
0
3
0
0
3
2
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
4
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
1
0
0
2
2
1
0
0
2
1
0
2
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
1
0
2
2
0
1
0
2
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
3
2
2
0
0
1
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
1
1
0
1
0
1
1
0
0
0
0
0
0
2
0
0
0
1
0
2
0
1
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
1
0
0
1
1
1
1
0
1
2
0
2
2
0
0
0
0
2
0
2
0
0
1
2
0
0
1
2
2
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
1
2
0
1
2
1
0
0
0
0
0
1
1
2
1
0
0
0
1
0
0
0
0
0
0
3
0
0
0
2
0
1
0
0
0
2
0
2
1
0
0
0
0
0
1
3
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
2
1
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
2
3
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
1
0
0
0
2
0
0
2
0
0
0
0
2
1
0
0
0
1
0
3
7
0
2
0
0
0
3
0
1
0
2
0
0
0
0
1
0
0
1
2
0
0
0
1
0
0
0
0
0
2
2
2
0
0
1
0
0
2
0
0
0
2
0
0
0
0
1
1
0
1
0
0
0
0
3
2
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
6
2
0
0
0
0
0
1
0
0
0
1
0
0
2
2
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
3
7
0
0
1
0
2
0
2
1
2
2
0
1
0
1
0
0
1
0
0
0
0
1
0
2
0
0
0
0
2
1
0
0
2
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
3
0
0
0
0
0
0
3
0
0
2
0
0
0
2
1
0
0
2
0
1
0
0
1
0
0
0
0
1
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
2
0
1
2
0
0
0
1
0
0
0
1
2
0
1
0
1
0
0
0
0
2
0
1
0
2
0
0
0
1
0
0
0
0
0
0
2
1
0
0
1
1
0
0
0
3
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
2
0
0
2
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
3
0
0
2
1
3
1
0
0
1
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
1
0
0
0
0
2
0
2
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
3
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
6
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
1
1
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
2
2
2
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
2
1
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
3
1
1
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
6
1
0
2
0
0
0
0
0
3
0
1
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
2
0
2
0
1
0
0
2
1
0
0
0
3
0
0
0
0
0
1
7
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
6
0
1
1
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
1
0
1
0
2
1
1
0
2
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
1
2
0
0
0
2
2
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
2
0
1
0
0
0
3
0
1
1
2
0
0
1
0
2
1
1
2
0
0
0
2
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
1
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
1
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
5
0
1
0
3
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
1
2
0
0
2
2
0
0
0
0
0
2
1
2
0
0
0
0
0
1
0
0
3
1
0
2
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
1
0
0
0
2
0
3
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
1
2
0
1
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
2
1
1
0
0
3
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
2
0
2
0
2
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
3
0
0
0
0
1
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
4
1
2
0
0
0
0
0
0
0
1
1
1
0
2
0
0
0
2
0
0
0
0
3
2
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
2
0
0
0
0
1
2
4
0
0
0
0
1
0
0
0
0
0
1
0
0
1
2
0
2
0
1
0
3
2
0
1
0
0
0
0
0
0
0
3
0
1
0
1
0
4
2
0
0
0
1
0
0
0
2
0
0
2
0
2
0
0
1
0
0
3
3
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
3
2
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
3
0
1
0
0
2
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
2
1
1
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
2
0
0
0
1
0
0
0
0
1
2
0
1
0
0
0
0
0
1
2
1
2
0
0
0
0
0
1
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
1
1
4
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
2
2
0
0
0
2
1
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
1
2
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
2
0
1
3
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
2
1
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
2
0
1
4
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
3
2
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
4
0
1
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
7
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
1
0
2
0
0
2
0
0
0
0
1
0
0
2
0
0
1
1
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
3
0
0
0
0
0
0
1
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
5
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
2
0
0
2
0
2
0
0
0
3
0
0
2
0
0
2
0
1
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
2
0
1
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
3
0
1
2
0
0
0
1
0
0
1
1
1
0
0
0
0
0
2
2
1
0
2
0
0
0
0
0
0
2
2
2
0
2
2
0
0
4
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
2
1
0
1
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
2
0
0
1
0
0
0
1
1
0
2
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
4
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
2
2
0
0
0
0
2
2
0
0
0
0
2
1
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
3
1
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
1
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
1
1
0
1
1
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
6
2
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
2
0
0
0
0
1
2
0
1
2
2
1
0
1
0
0
0
0
0
7
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
4
0
3
0
0
0
0
1
0
0
0
2
0
0
1
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
3
0
1
3
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
3
1
0
0
0
3
0
0
0
2
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
1
0
3
1
2
2
1
2
1
0
1
0
0
0
0
0
2
1
2
1
0
0
2
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
1
0
1
0
0
4
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
2
0
0
0
0
1
2
1
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
2
2
1
0
0
2
3
7
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
2
0
1
0
2
0
0
0
0
0
0
1
2
0
0
1
0
0
0
1
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
2
0
2
0
0
2
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
2
0
0
1
2
0
0
1
0
1
3
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
1
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
1
0
2
0
2
0
0
1
1
0
2
3
0
0
0
0
0
0
0
0
0
1
0
0
2
2
1
1
0
0
0
1
0
0
0
0
2
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
2
1
0
0
0
0
2
0
2
0
0
0
1
0
2
0
1
0
1
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
3
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
2
0
1
0
0
1
1
0
0
0
0
0
0
2
1
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
4
1
0
2
0
0
1
0
1
0
2
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
1
2
1
0
2
0
0
0
0
0
1
0
0
3
0
1
1
0
0
2
0
2
0
0
1
3
1
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
1
0
2
0
0
1
0
2
1
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
1
0
0
1
0
0
0
1
0
2
0
0
0
1
1
2
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
2
0
1
0
0
0
0
2
1
0
1
0
0
0
0
0
2
2
0
2
1
0
0
0
1
0
0
0
0
0
1
0
0
0
2
2
0
0
1
4
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
1
2
0
0
2
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
1
0
1
0
0
1
0
2
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
6
1
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
2
0
0
0
0
3
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
2
1
15
2
0
1
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
2
0
0
0
0
0
1
0
2
0
0
2
0
0
2
0
0
0
0
1
1
0
2
2
0
2
2
0
0
0
0
2
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
3
0
1
0
0
0
0
0
0
1
0
2
0
1
1
0
0
2
2
0
1
0
1
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
1
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
2
0
0
0
1
1
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
4
3
2
0
1
1
0
0
2
1
0
0
1
0
0
0
0
1
0
0
0
0
0
2
1
0
2
0
0
0
2
0
0
2
1
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
2
0
0
3
0
0
0
1
0
0
0
0
1
0
1
0
0
2
0
1
0
0
0
0
2
0
0
0
4
1
0
3
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
1
0
1
0
1
1
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
1
3
2
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
2
0
1
0
0
0
2
1
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
2
0
0
1
1
0
2
0
0
0
1
0
0
2
3
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
6
0
0
0
3
1
0
0
2
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
1
1
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
4
0
0
0
2
1
1
0
2
0
0
2
2
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
3
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
2
1
1
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
2
2
2
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
2
2
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
2
3
3
0
1
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
1
1
0
1
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
2
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
3
0
4
1
0
0
1
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
4
0
1
2
0
0
2
0
0
2
0
1
2
0
0
0
1
1
0
2
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
2
0
0
0
1
0
0
2
3
0
0
0
0
0
1
1
0
1
2
0
0
0
0
1
1
0
0
2
0
2
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
2
1
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
1
0
0
2
1
2
0
2
2
0
0
0
0
0
0
0
0
0
0
1
3
0
0
2
10
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
3
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
5
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
2
1
0
2
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
4
0
1
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
2
0
0
2
0
2
0
0
0
0
0
1
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
4
0
1
1
0
0
0
0
0
0
2
0
0
1
2
1
1
2
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
10
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
4
1
0
2
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
1
0
1
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
1
0
2
2
0
1
2
0
0
0
0
0
0
1
0
2
1
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
2
0
2
1
0
0
1
0
0
0
0
2
0
3
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
3
0
2
0
0
0
2
0
0
2
2
0
0
0
2
0
2
1
1
0
4
1
0
0
0
0
0
1
1
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
2
1
0
0
2
4
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
1
1
0
0
0
0
2
0
0
2
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
2
0
2
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
2
0
0
0
2
1
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
1
0
2
0
4
0
0
0
0
0
3
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
1
0
0
0
0
1
0
0
2
3
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
2
1
0
0
0
1
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
1
0
0
4
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
3
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
3
1
0
0
0
0
0
2
2
1
0
0
0
0
1
0
0
0
1
0
1
0
2
2
1
0
0
0
0
0
2
0
0
0
1
2
0
1
0
1
0
0
1
1
0
0
2
0
1
2
0
0
1
0
0
4
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
1
0
0
0
3
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
1
2
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
1
0
0
2
2
0
0
0
0
0
1
0
0
0
2
0
1
0
0
2
1
3
0
0
0
0
0
0
0
0
2
1
1
0
2
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
4
0
0
2
1
1
2
0
2
1
0
0
0
0
1
0
0
0
0
1
3
0
0
2
1
0
0
0
0
0
0
2
3
0
0
0
1
2
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
1
1
0
1
0
2
0
0
0
0
0
2
1
0
0
1
0
1
1
0
1
0
3
1
1
0
2
1
0
1
0
0
0
0
1
3
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
3
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
1
1
0
1
0
1
0
2
0
1
0
0
2
0
2
0
0
1
0
0
0
2
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
2
1
0
0
0
2
0
2
2
2
0
1
0
0
3
0
0
0
2
0
0
2
2
1
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
3
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
3
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
3
1
0
0
1
0
0
3
0
0
2
0
0
2
0
0
1
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
2
5
0
2
4
1
1
0
0
2
2
0
0
1
0
0
0
0
0
2
2
0
0
0
2
0
0
0
3
3
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
1
0
4
0
0
0
0
0
0
1
0
0
0
1
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
4
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
5
0
0
1
1
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
1
0
2
1
0
1
2
0
1
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
1
2
1
0
2
0
0
0
1
2
0
2
0
0
0
0
2
2
1
0
0
0
0
0
0
0
3
2
2
0
1
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
3
0
0
0
2
0
0
0
0
0
0
2
2
3
1
0
0
1
2
0
2
0
0
0
1
1
2
0
1
0
2
0
0
0
1
4
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
2
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
1
2
1
2
2
2
0
0
2
3
0
0
0
0
0
0
0
1
0
2
0
2
2
1
0
3
0
1
0
1
0
1
0
0
0
0
3
3
0
0
2
1
1
0
2
3
1
1
0
0
2
1
0
0
0
1
0
0
0
2
0
3
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
1
0
1
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
1
4
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
3
0
0
0
1
2
0
2
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
2
0
2
2
2
0
0
0
0
1
2
0
0
0
1
0
0
1
2
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
1
0
2
0
1
2
0
1
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
2
0
0
0
2
0
1
0
1
0
0
0
0
0
2
1
0
2
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
2
0
0
0
0
1
1
0
0
1
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
2
0
1
1
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
13
0
2
1
0
3
0
2
2
1
1
0
0
0
0
0
0
0
2
2
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
3
0
0
0
0
0
0
3
1
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
1
0
0
0
2
0
0
0
0
2
0
1
0
1
0
1
0
0
0
1
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
2
0
2
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
2
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
3
2
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
2
2
0
1
2
0
2
0
0
2
0
0
0
0
0
1
6
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
2
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
2
0
0
1
0
3
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
1
0
0
0
0
2
2
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
1
2
1
2
2
2
0
0
1
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
2
2
0
1
0
0
0
0
0
0
2
0
0
2
0
0
2
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
1
0
3
1
0
2
0
0
0
0
0
4
0
1
3
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
1
0
2
0
0
0
1
0
0
1
0
0
3
1
0
0
0
1
1
0
0
6
0
0
0
4
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
3
2
0
0
0
0
1
0
0
1
1
1
2
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
1
1
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
1
1
2
9
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
3
0
0
1
0
0
1
1
2
2
2
0
5
0
0
3
0
1
0
0
0
0
0
0
0
1
0
2
2
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
3
0
0
0
2
0
2
0
0
1
0
0
0
0
0
2
3
0
1
0
0
0
1
3
0
0
0
0
1
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
2
0
1
2
0
2
0
0
2
0
2
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
3
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
5
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
1
2
0
0
0
0
0
1
2
0
0
1
1
0
3
2
0
0
0
1
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
2
0
4
0
0
1
0
0
0
2
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
3
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
3
0
2
0
0
0
0
0
1
0
0
0
0
3
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
9
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
2
0
0
0
2
0
2
0
1
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
4
1
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
1
1
0
0
2
0
1
0
0
4
0
1
1
1
0
2
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
3
0
1
0
0
0
0
1
0
0
0
1
1
3
2
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
1
0
1
0
1
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
1
1
2
2
0
2
2
0
3
0
0
0
0
0
2
2
2
0
0
1
0
2
0
0
0
0
1
0
2
0
1
0
1
0
0
1
0
0
1
0
2
0
0
0
1
0
2
0
1
1
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
2
0
0
0
0
5
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
2
1
0
0
5
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
2
0
0
0
2
0
1
1
0
0
0
2
2
0
0
0
1
0
0
0
1
0
1
0
2
2
0
0
0
1
0
0
0
1
1
0
0
0
0
3
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
2
0
0
0
2
0
0
1
0
0
0
0
2
1
0
0
0
0
5
2
1
0
1
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
1
1
2
3
2
2
0
2
0
1
0
0
0
0
0
1
0
3
0
1
0
1
0
0
0
0
1
2
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
2
0
0
1
11
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
3
0
0
1
2
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
3
4
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
1
0
1
1
0
1
0
0
2
0
2
0
0
3
1
1
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
2
2
0
0
3
0
0
0
1
0
1
0
1
0
0
2
0
4
0
1
0
2
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
1
0
3
0
6
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
2
0
0
2
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
2
0
2
1
1
0
1
0
0
0
0
1
1
3
0
0
0
10
0
2
0
0
0
0
2
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
3
0
0
0
0
0
1
0
4
0
1
0
0
0
0
0
2
0
0
2
0
3
0
0
0
0
2
0
3
0
0
2
0
0
0
2
0
4
1
0
2
2
1
0
0
2
0
2
0
0
0
1
1
0
0
1
2
0
0
0
2
0
2
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
1
2
0
3
0
1
0
0
0
0
0
0
1
2
0
0
2
0
0
2
0
3
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
1
0
3
0
2
2
0
0
0
0
0
0
1
1
2
0
0
0
2
0
0
0
0
0
0
1
1
0
1
0
0
0
2
2
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
2
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
2
2
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
2
0
0
0
1
0
0
1
1
1
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
8
0
0
0
0
0
0
1
2
0
0
0
0
4
0
0
1
0
6
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
2
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
1
1
0
0
0
2
1
1
1
0
0
0
0
1
0
3
2
0
2
1
1
0
0
0
0
0
0
6
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
1
3
2
0
2
0
2
0
0
0
3
0
0
0
0
5
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
2
0
0
0
2
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
2
1
0
0
0
0
0
0
2
0
3
0
1
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
7
0
0
2
0
0
0
0
0
0
0
4
0
0
0
0
2
0
2
0
0
0
1
0
0
2
1
0
0
1
1
0
0
0
1
0
0
0
3
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
4
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
1
1
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
1
0
0
0
0
2
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
1
0
0
0
2
0
1
5
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
2
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
7
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
1
0
1
0
0
0
0
0
1
0
0
2
0
0
0
1
0
1
0
2
0
1
0
0
2
0
0
0
2
0
1
2
0
2
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
1
1
0
2
0
0
0
0
3
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
1
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
2
0
2
1
1
1
0
0
9
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
1
1
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
4
0
0
0
2
0
0
1
0
2
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
2
0
1
0
0
0
0
2
1
1
0
0
1
2
0
0
0
0
0
0
2
2
1
0
1
0
1
0
0
1
1
3
0
2
1
0
2
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
3
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
2
1
0
0
1
2
0
1
1
1
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
2
1
0
0
3
1
0
1
1
0
0
0
0
1
0
2
0
0
2
0
0
0
0
1
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
2
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
2
0
2
0
0
0
0
0
1
2
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
6
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
2
1
3
0
0
0
2
0
0
0
1
0
0
1
1
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
1
0
2
2
0
1
0
0
2
0
2
0
1
0
0
2
2
1
0
0
0
2
0
1
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
2
0
1
0
0
0
0
1
0
0
0
1
0
0
2
1
0
1
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
1
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
2
0
0
1
1
0
0
0
0
0
4
0
0
0
1
0
2
0
1
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
3
0
1
0
2
0
0
0
0
2
0
0
0
2
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
2
1
0
0
1
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
2
0
0
0
1
0
0
0
4
2
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
3
1
2
0
0
0
0
1
0
0
2
0
1
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
2
0
0
1
2
0
0
2
0
0
0
0
0
1
0
0
0
3
0
1
2
0
2
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
3
0
0
1
1
0
0
1
0
0
0
0
0
1
0
1
1
0
2
0
2
0
0
0
0
2
0
1
3
0
0
0
0
0
0
1
1
3
0
0
2
2
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
2
0
1
0
0
4
1
0
2
0
0
5
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
2
1
2
0
0
2
0
1
2
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
1
0
2
0
1
0
2
0
0
0
0
0
0
4
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
2
1
0
1
0
0
0
0
0
3
1
0
2
0
0
4
3
0
0
0
1
0
0
1
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
1
0
0
2
4
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
1
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
2
0
0
0
0
2
0
6
0
0
0
0
2
0
0
2
0
2
3
0
0
0
1
0
0
0
0
2
0
0
0
0
5
0
0
0
4
0
0
0
0
2
1
0
0
0
0
4
0
0
0
0
1
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
1
1
0
0
1
1
0
0
0
0
0
2
0
1
0
3
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
1
2
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
1
2
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
3
0
0
0
1
2
0
1
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
6
1
2
0
2
0
0
0
1
0
0
0
3
1
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
1
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
2
6
2
2
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
2
2
0
2
0
0
0
0
0
0
2
0
0
1
0
0
1
2
2
0
1
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
2
0
0
0
0
1
0
2
0
0
0
1
0
1
0
0
0
1
0
0
4
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
2
5
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
2
1
3
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
3
0
0
0
3
0
2
0
0
0
0
1
0
0
2
0
4
3
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
5
0
0
0
2
0
0
0
0
0
1
1
0
1
0
0
0
0
1
3
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
3
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
1
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
4
2
0
0
0
0
0
0
0
1
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
3
0
1
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
1
2
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
3
3
0
2
1
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
4
0
0
0
1
0
2
0
0
0
0
2
0
2
2
0
1
0
0
0
0
0
2
0
0
4
2
0
0
2
0
1
0
0
0
0
2
1
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
1
3
0
0
0
0
0
1
1
2
0
0
0
2
0
0
3
0
0
0
2
0
2
1
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
3
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
1
0
1
0
0
0
0
0
0
2
0
1
2
0
0
0
0
1
0
0
1
0
0
0
0
0
3
0
4
2
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
3
0
0
0
0
0
0
5
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
2
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
2
0
0
0
2
0
0
2
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
3
0
0
0
0
0
1
0
3
0
0
0
1
2
0
2
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
1
0
0
0
2
0
2
0
1
1
0
0
2
1
0
1
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
1
0
0
2
0
0
0
2
0
2
0
2
0
0
0
0
1
0
2
0
2
0
0
0
0
0
1
0
0
1
2
2
2
0
2
1
0
0
2
2
3
1
0
0
0
0
0
1
0
0
0
0
1
2
0
1
0
0
0
1
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
1
0
0
0
0
5
0
0
2
0
0
1
0
0
1
0
0
0
0
0
2
1
0
2
0
0
0
0
0
1
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
2
1
0
0
1
0
1
0
2
0
0
0
2
0
2
0
2
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
4
0
0
1
0
0
2
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
2
0
0
2
0
3
0
3
0
0
0
0
2
0
1
0
0
0
0
3
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
2
0
0
0
2
1
2
0
0
0
0
0
0
1
0
2
0
2
0
2
0
2
1
1
0
0
0
0
0
0
0
2
1
0
2
2
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
1
1
2
0
0
0
1
0
0
0
2
3
1
2
0
0
0
0
3
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
1
0
2
0
1
0
1
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
2
0
0
1
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
3
2
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
1
1
0
0
0
0
0
0
4
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
1
0
0
2
0
0
0
2
0
3
2
0
0
0
0
0
0
2
0
0
1
3
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
3
0
0
2
3
0
0
0
2
2
0
2
3
2
2
0
0
2
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
2
0
2
2
1
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
7
0
0
2
0
0
2
0
1
0
0
0
0
3
2
0
0
0
0
0
2
0
0
0
0
0
2
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
3
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
2
0
4
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
2
2
0
0
0
2
1
0
0
0
1
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
4
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
3
2
0
2
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
1
2
0
0
0
0
0
0
0
1
0
0
0
3
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
5
0
1
2
0
0
0
1
0
0
1
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
2
1
0
0
0
0
3
1
1
0
0
0
0
2
0
2
0
0
1
1
0
0
0
0
0
0
0
1
5
0
2
0
0
0
0
2
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
2
1
0
0
1
0
0
0
0
2
2
0
2
4
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
1
0
1
0
0
0
0
0
0
1
1
0
2
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
1
2
2
0
0
0
0
3
0
1
0
0
0
0
0
0
0
1
1
0
3
0
1
1
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
1
0
1
0
1
0
1
2
0
0
1
1
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
1
0
2
1
0
0
0
3
2
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
4
0
0
0
2
1
0
3
2
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
1
1
0
0
0
0
4
0
2
0
0
0
0
0
0
1
1
0
2
0
0
3
2
0
1
0
1
0
2
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
1
0
1
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
1
2
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
3
0
2
0
0
0
0
0
2
2
1
2
1
0
0
1
2
1
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
2
0
2
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
1
0
0
2
0
0
0
0
0
0
1
0
3
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
2
0
0
1
0
0
1
0
4
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
2
1
0
0
0
0
0
2
2
1
1
2
0
0
2
0
3
0
0
0
0
1
0
0
0
2
0
1
0
2
0
0
0
0
0
0
1
2
1
2
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
2
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
1
0
0
0
0
0
0
0
0
0
0
3
1
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
1
0
0
1
4
2
0
1
0
1
1
3
0
0
5
0
1
0
1
1
0
0
1
1
3
0
5
0
0
0
0
0
2
1
0
0
0
0
2
3
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
3
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
1
2
0
0
1
2
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
3
0
1
0
0
0
0
0
2
0
1
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
1
0
0
0
0
0
2
0
1
0
0
4
0
0
0
0
2
0
1
0
0
0
2
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
1
0
0
0
0
0
0
5
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
3
0
0
0
0
0
0
2
1
0
5
0
0
0
0
0
5
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
2
1
1
0
0
0
4
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
3
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
1
1
0
0
2
0
0
2
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
5
0
0
0
0
3
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
3
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
2
1
0
0
0
2
0
0
1
0
0
0
2
0
0
0
1
2
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
2
0
1
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
1
1
2
3
0
2
0
2
2
0
0
2
2
1
1
0
2
1
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
5
2
0
2
0
0
1
0
0
0
2
1
0
1
0
0
2
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
1
0
0
0
1
0
0
2
1
2
0
6
2
0
1
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
1
0
0
3
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
2
2
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
2
3
1
0
0
0
0
2
0
0
1
2
0
0
1
0
0
0
2
0
0
0
2
1
0
1
0
1
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
1
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
2
3
0
0
1
0
0
0
0
0
2
0
2
1
1
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
2
0
2
0
3
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
1
0
0
1
0
0
2
2
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
2
1
0
0
0
1
2
0
1
0
0
1
0
1
0
2
0
0
1
1
2
1
1
2
0
3
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
6
1
1
0
0
2
2
1
2
0
1
1
0
1
0
0
0
0
0
2
1
1
0
0
0
0
0
1
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
1
0
0
3
0
0
0
0
0
2
2
0
0
0
0
1
2
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
1
1
0
0
0
0
0
3
2
1
0
0
0
0
0
0
2
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
3
0
0
0
1
0
1
0
0
0
1
2
1
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
1
0
0
2
3
0
1
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
5
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
2
2
0
5
0
1
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
1
0
1
1
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
2
0
0
2
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
1
1
1
1
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
1
2
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
1
2
0
2
2
0
2
2
0
0
0
0
0
2
0
0
1
1
1
0
0
0
0
0
0
0
0
1
2
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
6
1
0
2
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
5
0
1
1
2
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
3
1
0
1
0
0
2
0
0
0
0
0
2
0
0
3
0
1
0
1
1
2
1
2
0
0
0
7
3
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
2
0
0
3
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
2
0
2
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
1
1
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
5
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
4
0
3
1
0
0
0
0
2
1
0
2
0
2
0
0
0
0
0
1
0
0
5
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
4
0
0
0
0
2
0
4
0
3
0
0
2
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
1
1
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
2
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
1
0
1
2
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
2
0
2
0
0
0
2
2
0
0
0
0
0
0
1
2
0
1
0
0
0
1
2
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
3
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
2
1
2
0
0
0
0
0
2
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
3
0
0
0
0
0
0
0
1
1
0
2
1
0
0
2
10
0
1
0
0
0
0
0
0
0
1
0
0
2
0
2
2
0
2
1
0
4
0
2
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
7
0
0
0
0
0
3
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
3
1
0
0
0
0
0
0
0
4
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
3
1
1
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
1
0
0
0
1
0
2
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
2
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
2
2
1
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
2
0
2
0
0
0
1
0
0
0
0
1
3
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
3
0
2
0
1
2
0
1
0
3
0
0
0
0
0
2
2
0
0
0
0
2
0
1
0
1
0
1
0
1
0
2
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
3
2
0
0
0
3
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
1
0
1
0
0
0
16
0
1
0
0
2
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
1
0
0
1
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
1
0
1
0
0
2
0
0
2
0
0
0
2
0
1
0
0
0
0
0
1
1
0
0
0
1
0
2
0
0
0
0
0
0
3
0
0
2
2
0
2
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
2
0
0
0
0
0
1
1
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
2
2
0
0
3
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
2
2
1
0
2
0
0
0
0
2
0
0
2
0
0
2
0
0
1
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
2
0
1
0
1
0
0
0
0
0
2
0
2
2
2
2
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
2
1
0
1
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
2
0
0
3
1
1
2
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
3
1
0
2
0
0
0
1
0
0
1
0
0
2
2
0
0
0
0
2
1
1
0
0
1
0
0
0
0
1
0
1
2
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
4
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
5
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
2
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
2
1
0
2
0
1
1
0
0
0
0
0
0
0
2
0
0
0
1
3
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
3
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
2
2
0
0
0
3
0
0
2
2
1
1
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
2
0
0
0
1
2
2
0
0
0
1
0
3
2
0
1
0
1
0
2
2
2
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
1
1
2
1
1
0
0
0
0
2
1
0
0
0
0
1
2
0
1
0
0
1
0
0
0
0
0
1
0
2
0
0
1
1
0
0
0
0
0
1
0
1
2
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
2
0
0
1
0
0
0
3
0
1
3
0
0
1
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
3
0
0
0
0
2
0
0
1
0
0
1
0
0
2
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
2
0
2
2
0
1
0
0
0
1
0
0
2
0
0
0
0
1
2
3
0
0
0
0
2
2
1
0
0
1
2
0
0
0
0
0
4
0
0
2
0
1
2
1
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
1
0
2
0
0
2
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
1
0
2
1
2
0
4
1
0
0
0
4
5
0
0
0
3
1
3
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
1
0
0
1
2
0
0
0
0
1
1
0
0
0
0
2
0
3
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
2
1
1
1
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
1
0
2
1
2
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
2
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
2
0
0
2
1
2
1
1
0
1
0
0
5
1
1
0
0
0
0
1
2
0
0
0
0
1
4
0
0
0
2
1
0
0
0
0
0
0
0
3
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
1
2
0
0
5
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
3
0
1
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
2
0
0
2
0
0
2
0
2
2
0
1
2
1
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
1
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
5
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
2
0
2
0
0
1
0
2
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
1
1
2
0
0
4
1
1
1
0
0
0
2
0
2
0
0
0
1
0
2
0
1
0
0
0
0
0
2
0
3
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
2
5
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
1
1
0
0
2
0
0
4
0
0
0
0
0
0
2
2
1
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
2
1
0
2
0
0
0
0
1
0
0
0
1
2
2
0
0
1
0
0
1
0
1
0
0
0
0
1
1
0
0
0
4
1
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
1
1
0
0
0
2
0
0
2
1
0
0
2
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
2
2
0
1
0
0
0
0
2
0
0
1
0
2
0
1
2
0
0
0
0
0
0
0
0
2
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
1
0
0
0
0
0
0
0
2
0
0
2
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
1
0
0
0
0
2
0
0
1
1
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
2
1
0
2
0
1
0
0
3
0
0
0
0
0
0
2
4
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
2
2
0
1
0
0
0
0
2
0
2
0
0
2
0
0
0
3
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
6
0
2
0
0
0
0
1
1
0
2
2
0
0
1
0
0
1
0
0
0
0
0
0
3
3
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
2
0
2
1
0
0
1
0
0
0
0
1
0
1
2
0
1
0
0
1
0
2
0
0
0
2
1
0
0
0
1
1
0
0
0
0
0
0
1
1
0
2
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
2
0
2
0
0
0
0
0
1
0
2
0
1
2
1
0
0
2
1
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
2
0
0
0
0
2
3
3
0
0
1
0
0
0
0
1
0
1
0
2
0
2
0
1
0
0
1
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
1
1
1
0
1
0
0
0
0
0
0
0
0
0
4
0
2
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
3
0
0
1
0
1
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
1
1
0
1
1
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
1
0
1
0
2
3
0
0
2
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
2
2
1
0
5
1
1
0
0
1
0
0
0
0
1
0
0
2
0
0
2
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
1
0
0
1
0
3
0
0
0
1
1
0
1
1
1
0
0
0
0
1
2
1
0
0
0
0
2
0
0
0
1
2
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
2
1
0
0
0
0
2
0
0
2
4
0
0
3
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
1
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
4
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
2
0
1
1
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
5
2
3
0
0
2
0
0
1
1
0
0
1
1
3
0
0
1
0
0
0
1
0
2
2
0
0
0
0
0
2
0
0
0
1
2
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
2
0
0
0
1
1
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
1
1
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
1
1
0
1
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
2
0
0
0
2
2
0
0
0
0
2
0
4
0
2
0
0
0
1
0
1
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
2
0
2
0
0
0
1
2
0
0
0
0
2
0
0
0
3
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
4
0
0
2
0
1
2
0
2
0
0
2
0
1
0
0
0
2
2
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
2
2
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
3
2
1
1
2
0
1
0
0
0
2
0
0
0
0
2
0
2
0
1
0
0
0
2
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
3
2
1
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
3
0
2
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
4
0
0
0
0
1
0
2
0
0
2
0
0
0
0
1
2
0
0
0
1
2
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
2
2
0
0
2
1
0
0
1
0
1
0
1
0
0
1
0
0
0
1
0
0
0
3
0
3
0
0
1
0
0
0
0
0
0
3
0
0
0
0
2
1
0
0
0
1
0
0
0
1
0
0
0
1
1
2
0
1
0
0
0
2
0
1
0
0
0
0
1
2
0
0
1
0
0
1
0
0
1
0
2
0
0
0
0
2
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
2
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
3
0
1
0
0
1
0
0
0
4
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
6
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
2
0
0
2
0
0
0
0
1
0
2
2
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
1
2
0
0
0
3
1
0
0
0
2
1
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
2
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
2
0
1
0
2
0
0
0
0
1
0
0
1
2
0
1
4
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
4
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
1
2
0
0
1
2
2
0
0
0
1
6
0
0
0
0
1
0
0
2
0
0
0
5
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
4
2
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
2
2
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
2
2
0
0
0
0
0
2
1
0
1
2
0
0
0
2
0
0
0
0
2
1
0
1
0
1
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
1
2
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
1
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
3
0
3
0
0
0
1
0
0
2
0
0
2
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
1
0
1
0
1
0
5
3
0
0
1
0
1
0
0
1
0
2
1
0
0
2
0
2
0
0
0
0
0
2
1
0
2
0
0
0
1
0
0
0
0
0
0
0
1
1
1
1
1
2
2
0
0
0
0
0
2
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
2
0
0
2
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
5
0
0
1
4
0
0
0
2
0
0
1
0
2
0
0
1
1
0
0
0
1
0
0
0
2
1
0
0
1
0
0
0
0
2
1
4
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
1
0
0
0
2
0
2
0
0
0
0
1
2
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
1
2
0
0
1
0
0
0
0
0
0
3
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
3
0
0
2
0
1
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
2
4
0
1
0
0
2
2
0
1
0
0
0
1
0
3
1
2
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
2
0
0
1
0
0
1
0
0
0
3
2
0
2
2
0
0
0
0
0
0
0
2
0
1
2
3
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
2
0
0
0
0
0
0
1
0
1
0
0
0
2
2
0
0
0
0
1
0
0
1
2
0
2
0
2
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
1
0
2
0
0
0
0
0
2
0
1
1
1
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
3
1
0
1
0
0
0
1
1
3
1
2
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
1
0
1
1
0
0
1
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
4
0
0
1
0
0
0
0
0
1
0
0
2
0
1
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
6
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
2
2
1
0
0
0
0
1
0
2
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
1
2
0
0
0
1
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
3
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
1
2
0
0
0
0
1
0
3
0
1
0
0
2
1
0
2
0
2
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
1
0
0
2
3
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
1
2
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
2
0
0
1
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
1
0
0
0
0
0
1
3
0
0
2
1
0
0
0
0
0
2
0
1
0
0
1
0
1
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
3
2
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
2
1
0
1
2
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
1
1
0
0
0
0
6
2
3
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
2
0
1
0
1
1
0
2
0
0
0
4
0
0
0
0
2
2
2
2
0
1
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
2
0
2
0
0
0
1
2
0
2
0
0
0
0
3
4
0
0
0
0
0
0
0
0
0
0
0
0
0
6
1
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
5
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
2
2
0
0
0
1
2
1
2
0
3
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
2
0
0
3
1
0
0
1
2
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
6
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
2
3
0
0
0
0
0
0
0
0
0
1
2
1
5
2
0
2
0
0
0
0
0
0
0
1
0
1
2
0
1
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
2
0
1
0
2
0
0
1
0
0
0
0
0
0
0
2
2
1
4
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
1
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
2
0
5
0
0
0
2
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
3
1
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
1
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
2
0
0
1
1
0
0
2
0
0
0
1
2
2
2
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
5
0
2
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
1
0
2
1
0
1
0
0
1
2
0
1
2
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
1
1
2
0
2
1
2
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
2
1
0
2
1
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
2
0
18
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
3
0
2
0
0
1
2
2
5
0
0
0
2
0
1
0
4
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
3
0
2
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
2
4
0
0
2
1
0
0
0
2
2
0
0
0
0
0
0
0
5
2
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
8
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
1
1
0
1
2
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
1
0
0
0
0
0
1
2
3
0
0
0
0
2
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
2
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
1
1
0
0
0
2
0
0
1
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
2
0
0
2
1
0
0
2
3
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
1
0
0
8
0
0
0
2
2
0
0
0
0
1
0
0
0
0
2
2
0
0
0
2
1
2
0
2
1
1
0
0
0
0
0
3
2
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
1
0
4
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
2
0
0
1
0
0
2
0
2
0
2
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
1
0
3
0
0
0
2
0
1
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
1
1
0
0
4
0
2
0
1
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
2
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
1
0
0
1
0
0
0
0
1
0
0
2
0
0
2
0
0
0
2
1
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
1
2
0
0
0
0
2
8
0
0
0
0
3
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
2
0
0
0
0
0
0
1
1
0
4
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
3
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
3
0
0
0
1
2
0
2
1
0
1
0
2
0
1
0
2
1
0
0
0
0
0
2
0
1
0
0
6
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
5
2
0
0
0
0
3
0
1
0
1
0
0
0
1
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
2
0
0
3
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
3
0
2
0
0
0
0
0
0
0
1
2
0
2
0
0
0
2
0
0
3
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
1
2
0
0
4
0
0
0
4
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
1
1
2
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
2
0
1
0
1
2
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
4
0
5
0
0
0
0
0
2
0
0
1
1
0
3
2
0
0
0
0
0
2
2
0
0
0
0
0
2
0
2
0
0
1
2
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
5
1
0
2
1
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
1
1
1
1
3
2
0
2
2
0
0
0
0
0
0
0
1
0
9
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
5
0
2
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
27
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
3
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
3
2
1
2
1
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
3
0
0
0
1
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
1
0
0
0
2
3
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
2
0
0
0
1
1
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
2
0
0
1
0
2
1
0
0
0
1
0
0
0
0
0
3
2
0
0
0
0
2
0
0
0
2
0
0
2
2
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
1
0
0
0
0
0
2
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
2
1
2
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
1
0
1
0
0
2
0
0
0
0
2
0
0
1
0
0
2
1
0
2
0
0
0
0
0
0
3
2
0
0
0
0
1
0
0
1
0
2
0
1
0
0
1
2
3
0
0
1
0
2
0
3
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
2
0
2
2
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
1
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
2
2
1
1
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
1
2
0
0
0
2
0
6
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
3
3
0
1
2
1
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
2
0
1
2
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
1
2
1
0
2
0
0
1
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
2
0
0
0
0
2
0
2
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
2
2
1
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
2
0
0
0
3
0
1
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
4
1
0
1
2
1
0
0
0
0
1
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
5
0
1
0
0
0
2
0
1
1
2
0
2
0
1
0
2
0
1
0
3
0
0
0
1
0
0
2
0
5
0
1
0
0
1
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
1
0
0
3
0
1
0
0
0
2
0
0
0
0
1
0
0
2
0
1
0
0
5
2
1
0
0
0
2
2
1
2
0
0
0
0
2
1
0
2
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
3
0
0
1
0
0
0
1
1
1
0
3
0
0
0
0
0
0
4
3
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
4
0
1
2
0
0
0
1
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
3
2
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
2
0
0
0
0
1
2
0
1
0
0
2
0
0
2
0
2
0
0
0
0
3
0
2
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
5
0
0
2
0
0
3
0
0
0
0
1
2
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
3
1
0
0
1
4
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
2
0
0
2
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
9
0
0
0
0
0
0
4
0
1
0
0
0
0
0
3
0
0
0
0
0
1
1
2
2
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
1
0
2
0
3
0
0
2
0
2
1
0
3
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
3
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
1
0
2
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
4
0
0
0
0
0
0
0
1
0
2
2
0
2
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
1
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
3
0
0
0
0
0
0
2
0
1
1
0
4
0
2
2
0
0
0
0
0
1
0
0
0
0
1
2
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
2
1
0
0
0
0
3
0
1
2
0
0
1
0
0
0
0
0
3
2
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
8
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
4
0
0
2
0
0
0
1
1
0
0
3
0
0
0
0
0
3
0
3
0
0
1
0
0
0
0
0
3
2
0
0
0
4
0
1
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
2
0
0
1
2
0
0
0
2
0
1
0
0
1
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
4
0
0
0
1
0
0
1
0
0
0
0
2
0
2
2
0
3
1
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
1
0
1
1
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
1
2
0
0
2
0
0
0
0
7
0
0
0
0
0
0
1
0
0
2
2
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
1
0
0
7
0
0
2
0
0
0
0
0
0
0
0
0
5
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
18
0
0
0
2
0
0
0
0
0
3
1
0
1
0
0
1
0
0
1
0
2
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
3
0
0
0
2
0
0
0
0
4
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
2
0
0
1
2
0
0
0
1
0
0
1
2
0
0
1
0
0
0
0
0
0
1
0
0
1
2
0
0
2
0
0
0
1
0
0
1
0
1
1
0
2
0
1
0
0
0
1
0
0
0
1
3
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
4
0
1
0
2
0
0
0
1
0
0
0
2
0
1
0
0
1
0
0
1
2
0
2
0
0
0
0
3
0
0
0
1
0
0
0
2
0
0
0
2
1
1
2
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
3
0
0
0
2
2
0
1
0
0
0
2
0
0
0
2
2
0
1
0
1
1
0
2
2
0
2
2
2
1
0
0
3
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
1
2
0
1
1
0
0
0
0
0
1
2
1
0
0
2
2
0
1
2
0
0
1
2
2
0
1
0
1
0
4
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
2
2
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
1
0
1
2
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
3
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
2
1
5
0
0
1
2
0
0
0
0
3
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
2
1
0
0
0
1
0
0
1
2
0
0
2
0
0
0
0
6
0
3
0
0
1
3
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
1
1
1
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
1
1
1
3
0
2
0
1
0
2
0
0
0
0
0
1
0
3
0
1
0
2
0
0
1
0
0
3
0
2
0
0
2
0
1
0
0
0
0
0
0
0
1
2
3
1
1
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
1
2
0
0
3
2
0
0
0
0
2
1
3
0
0
2
0
0
0
0
2
2
0
0
0
0
0
1
1
2
1
0
0
1
0
0
1
1
0
0
0
1
0
1
0
2
1
0
0
0
2
0
1
1
0
0
1
0
3
0
0
0
0
0
0
0
0
0
1
0
0
2
3
0
1
0
0
0
0
1
2
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
2
0
1
2
0
0
0
2
0
0
1
0
2
2
1
0
2
1
0
0
0
1
0
2
0
0
2
0
2
2
0
0
0
0
0
0
0
1
0
0
0
3
2
0
0
0
0
0
3
0
0
0
2
0
0
3
1
0
0
2
0
0
0
4
0
0
0
0
0
2
0
1
2
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
2
3
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
1
3
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
3
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
2
0
0
0
2
0
0
2
1
0
0
0
0
0
1
0
0
0
0
2
0
2
0
2
0
0
0
0
2
0
0
0
0
2
0
2
2
0
3
1
0
0
0
1
1
0
0
0
0
0
1
0
4
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
3
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
1
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
1
1
0
0
0
0
0
0
2
2
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
1
0
2
0
1
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
2
0
0
0
1
1
0
2
0
2
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
1
0
0
1
0
0
0
1
0
0
5
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
3
0
0
1
2
0
0
0
0
0
0
0
0
1
1
2
2
0
2
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
4
2
1
0
0
1
0
0
0
0
0
0
1
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
5
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
3
0
0
1
0
2
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
2
1
0
0
0
2
1
0
0
0
0
2
0
0
0
4
0
0
0
1
0
2
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
3
0
1
0
0
2
0
0
0
0
0
2
0
0
0
1
1
0
0
0
3
2
2
0
1
0
0
1
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
1
0
2
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
1
2
1
0
1
0
0
0
0
0
2
0
1
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
4
0
3
2
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
2
0
0
1
1
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
1
0
1
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
2
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
4
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
2
0
0
1
2
0
1
2
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
1
0
3
1
0
0
0
1
3
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
3
2
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
2
2
0
1
0
0
1
0
0
0
3
0
0
1
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
2
2
0
2
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
1
0
1
0
0
0
0
0
0
2
0
9
2
0
0
0
0
2
0
0
0
0
1
1
1
0
2
0
1
0
2
0
1
0
0
2
0
1
0
0
0
0
1
0
0
0
0
5
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
2
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
3
0
0
0
0
2
0
0
3
0
0
0
0
2
0
0
0
0
0
0
2
1
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
2
2
0
1
1
1
1
0
0
0
0
0
0
2
0
1
1
1
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
2
1
0
0
0
1
2
2
2
0
0
0
2
0
1
2
0
2
0
0
0
2
0
2
2
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
2
1
0
1
0
0
0
1
0
2
0
0
0
1
0
0
0
1
3
0
0
2
2
0
0
0
0
0
2
2
2
0
0
1
0
1
0
0
2
1
2
0
0
0
3
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
3
0
2
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
2
0
1
4
0
0
1
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
1
0
0
2
0
2
0
0
0
2
0
1
0
0
0
2
0
1
0
0
0
0
0
3
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
2
0
0
4
0
0
0
0
0
0
0
2
0
0
1
2
0
2
0
1
0
0
0
0
2
0
0
1
0
0
0
0
2
1
0
3
0
6
0
0
2
0
0
0
0
0
1
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
3
0
1
2
0
3
4
6
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
1
0
1
0
0
1
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
3
1
0
0
1
0
0
2
1
0
0
2
0
0
0
2
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
6
0
0
0
0
0
0
1
0
2
0
3
0
0
0
2
0
0
0
0
0
3
3
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
1
2
0
0
0
0
2
0
0
2
0
1
0
0
0
0
2
0
1
2
1
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
2
0
0
1
0
0
3
0
2
0
0
0
1
0
1
2
0
0
0
0
2
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
5
1
2
1
2
0
0
1
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
1
7
0
0
1
0
1
0
1
0
1
0
0
0
0
1
0
0
1
2
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
3
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
1
0
0
2
0
0
0
0
0
1
1
1
0
0
0
0
0
2
0
0
2
1
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
1
0
2
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
3
0
0
0
0
1
1
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
2
0
3
0
0
2
0
0
0
1
0
0
0
0
2
1
0
1
0
0
0
1
0
3
1
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
3
0
2
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
4
0
2
0
0
0
0
2
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
3
0
4
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
1
2
0
2
0
0
6
0
0
0
2
0
1
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
2
0
2
0
7
0
0
1
0
2
0
1
2
0
0
0
0
0
0
0
0
0
3
1
0
1
0
2
0
1
1
0
0
2
2
0
0
0
1
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
1
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
1
0
2
0
2
0
0
0
2
0
1
0
0
1
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
5
0
5
2
0
0
0
0
1
0
0
0
0
0
3
0
1
0
0
0
1
0
1
1
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
2
0
1
2
2
1
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
3
2
0
2
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
2
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
2
1
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
3
0
1
0
1
3
0
0
0
0
0
2
0
0
1
1
0
1
0
0
1
2
0
0
0
0
0
0
0
2
0
2
0
2
0
0
1
0
2
0
0
0
0
1
0
0
1
0
0
0
2
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
1
1
0
0
0
0
0
0
1
1
2
0
1
0
1
0
0
0
0
0
3
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
2
2
2
4
1
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
3
0
0
0
2
1
2
1
2
0
0
1
0
2
1
0
2
0
0
0
2
2
0
1
0
0
1
0
0
1
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
2
1
0
1
1
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
3
0
0
0
2
0
0
2
2
0
0
2
1
0
0
1
2
0
1
0
0
0
0
1
1
0
0
0
0
2
0
0
1
1
0
0
0
2
3
0
1
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
2
1
0
2
0
0
0
0
2
1
0
0
1
0
0
0
0
0
1
0
0
3
0
2
0
0
1
0
0
0
3
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
2
0
0
0
1
0
0
0
2
0
1
0
1
0
0
0
0
2
2
0
0
0
0
0
2
0
0
2
0
0
0
0
6
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
5
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
2
0
0
0
0
2
0
1
1
0
0
4
0
0
0
0
0
0
2
0
0
0
0
1
0
1
1
0
1
0
0
0
0
4
0
0
0
0
6
0
0
1
0
0
0
0
0
2
0
0
0
2
1
2
1
0
0
0
1
0
0
0
0
0
0
4
0
0
0
2
2
0
0
0
0
0
3
1
0
0
0
1
0
0
0
0
0
2
1
1
0
0
0
0
2
0
0
2
1
0
1
0
0
2
0
0
1
2
0
1
3
0
0
1
0
0
0
2
0
0
0
1
1
0
3
0
0
1
0
1
0
0
0
1
0
0
0
0
1
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
1
0
0
2
2
0
0
0
1
2
1
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
1
2
0
0
0
0
2
0
2
0
0
0
3
0
3
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
2
0
3
0
0
0
3
0
0
1
0
0
1
2
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
5
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
1
1
2
1
0
2
0
0
8
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
2
0
2
0
0
2
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
2
0
0
0
0
0
0
0
2
0
1
0
0
2
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
7
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
2
2
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
3
0
1
0
2
0
3
0
0
0
0
0
2
0
0
1
0
0
2
0
2
3
0
0
1
1
1
1
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
2
3
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
2
0
0
1
0
1
2
3
0
0
1
0
0
1
2
0
0
1
2
0
0
2
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
2
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
4
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
6
0
2
0
0
0
0
0
4
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
3
0
0
0
6
0
0
2
0
0
0
1
0
0
2
0
0
0
1
1
2
0
0
0
2
0
0
0
0
1
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
2
2
0
0
0
1
0
0
1
0
1
1
0
1
0
0
0
0
0
0
5
0
1
2
0
0
0
2
0
0
2
0
0
0
0
2
0
1
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
3
1
2
0
0
0
0
0
0
0
2
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
1
0
0
2
0
0
2
0
0
4
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
1
0
1
0
1
0
3
0
0
0
0
0
0
2
1
0
0
2
0
1
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
3
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
3
0
0
0
0
0
0
0
1
1
0
0
0
2
0
1
1
0
0
0
1
2
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
1
1
2
0
0
0
0
1
0
0
1
0
0
0
8
0
2
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
4
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
2
2
0
1
0
0
0
0
8
1
0
0
0
0
2
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
1
2
0
0
0
0
0
0
1
0
0
1
0
0
0
3
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
2
2
0
0
0
2
0
1
0
0
0
0
4
1
0
0
0
0
1
0
2
0
0
1
2
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
1
0
0
0
0
2
2
2
0
0
0
0
2
0
0
2
1
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
3
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
2
0
1
0
0
0
0
1
0
0
0
3
2
1
0
0
0
1
0
1
1
2
0
0
2
2
0
0
0
0
0
1
0
0
2
0
6
0
0
0
0
3
2
0
0
1
2
0
2
1
0
0
0
0
0
1
0
1
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
3
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
2
0
1
1
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
3
2
2
0
0
0
0
0
0
0
0
3
0
1
2
2
0
1
0
2
0
2
0
0
2
1
2
3
0
1
0
0
0
2
0
3
1
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
2
0
0
1
0
0
0
0
1
0
0
0
1
2
0
1
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
1
2
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
2
1
0
0
0
2
0
0
1
2
0
1
0
1
0
0
0
1
0
0
0
1
0
0
2
0
0
0
1
0
1
2
0
2
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
1
0
0
2
2
0
1
1
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
1
0
0
2
2
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
2
1
0
0
0
0
1
0
0
1
0
2
0
1
3
0
0
0
0
1
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
3
1
1
0
1
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
2
1
2
0
0
0
7
1
1
0
0
0
0
7
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
1
2
0
1
0
0
1
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
1
0
2
0
1
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
2
0
0
0
2
2
0
1
0
2
3
0
0
0
0
1
3
1
0
0
0
0
0
3
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
1
1
2
0
1
0
0
0
0
0
1
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
1
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
2
4
2
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
2
2
1
0
2
0
2
0
1
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
3
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
2
0
0
0
1
2
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
1
0
0
2
1
1
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
3
0
0
0
0
1
2
0
0
1
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
3
6
0
2
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
8
0
0
2
2
0
0
1
5
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
3
0
2
2
2
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
1
0
1
1
0
0
1
0
2
0
1
2
0
0
1
0
3
0
0
1
0
0
3
0
2
0
2
3
1
0
0
0
0
3
0
0
2
2
0
1
1
1
0
2
0
2
0
1
5
2
0
0
0
9
0
0
2
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
8
0
2
1
1
0
0
2
0
1
0
0
1
2
3
0
0
1
2
1
2
1
1
0
0
0
0
15
0
0
1
0
0
0
1
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
2
0
2
2
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
2
0
0
0
1
2
2
0
2
1
2
2
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
1
0
2
0
0
1
2
0
0
0
2
1
0
1
1
1
0
0
0
0
0
0
2
0
0
0
0
0
3
1
0
2
1
0
0
0
0
0
0
0
1
1
5
0
0
0
3
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
3
0
1
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
2
1
0
0
0
2
0
0
1
1
0
0
0
0
0
2
0
1
0
0
0
3
1
1
2
0
3
1
1
0
0
0
0
2
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
5
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
3
0
2
2
0
0
1
0
0
0
2
0
0
0
0
5
0
0
0
0
0
0
1
1
0
0
0
0
0
2
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
1
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
6
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
3
0
0
0
2
2
0
2
0
0
0
0
0
0
3
0
0
1
1
3
0
0
0
3
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
3
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
10
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
1
1
0
0
0
2
0
2
0
1
2
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
7
2
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
1
0
0
2
0
0
0
1
0
0
2
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
2
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
3
1
0
0
1
0
0
0
2
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
6
0
0
1
1
1
0
2
0
2
0
0
2
0
0
0
0
0
0
1
0
0
3
0
0
0
1
0
0
1
0
2
0
1
2
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
3
2
0
0
0
2
0
0
0
0
0
2
0
0
2
0
7
0
0
0
0
0
2
0
0
0
2
0
1
0
0
2
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
2
0
0
1
2
0
0
0
0
0
0
2
0
0
1
2
1
0
0
1
0
3
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
2
0
1
0
2
0
0
1
0
2
0
0
0
0
1
0
0
4
0
1
1
0
0
0
0
2
1
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
2
0
1
0
1
1
1
1
0
0
0
2
0
1
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
3
2
0
0
0
0
0
0
0
0
0
1
0
2
2
3
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
5
2
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
2
0
1
2
0
0
2
1
0
0
2
0
0
1
0
0
0
0
2
1
0
1
2
1
0
0
2
0
0
0
1
1
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
2
0
1
1
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
1
2
2
7
2
2
2
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
1
0
0
3
2
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
2
0
3
1
0
0
0
1
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
1
0
1
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
1
2
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
2
0
3
1
0
0
0
0
1
0
1
0
3
0
0
0
0
0
0
2
1
0
0
1
0
0
0
2
0
0
1
2
0
2
4
0
0
0
1
0
0
0
0
3
1
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
2
0
1
0
0
0
0
1
2
0
0
1
1
3
4
0
0
0
0
0
0
1
0
0
0
0
0
4
0
2
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
3
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
1
0
0
2
0
2
1
0
0
0
1
0
1
0
1
0
2
2
0
2
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
3
2
0
0
0
2
0
1
0
1
0
0
1
0
0
0
0
2
0
3
0
2
0
0
1
0
0
2
1
0
2
0
0
1
2
1
2
0
0
0
2
0
2
0
0
0
2
0
0
0
0
3
0
0
0
2
0
0
0
0
4
0
0
0
2
2
0
0
1
1
0
0
0
0
2
1
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
4
1
0
0
0
0
1
0
3
0
2
1
0
0
0
0
3
2
2
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
3
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
2
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
1
0
2
1
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
2
0
3
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
1
0
0
0
0
0
2
0
0
1
2
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
3
0
2
0
0
0
0
2
0
0
2
1
0
0
1
1
0
0
0
1
3
1
1
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
3
0
0
0
2
1
0
0
2
0
0
0
0
0
1
0
1
0
0
1
0
0
2
1
0
0
0
1
0
0
2
2
2
0
0
0
1
1
0
1
2
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
1
2
0
0
1
2
0
0
0
0
0
0
0
2
0
1
3
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
2
3
2
0
2
1
0
0
2
0
0
0
0
1
0
0
2
1
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
2
3
0
0
0
0
1
1
0
1
0
2
0
2
0
0
0
0
0
2
0
2
1
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
3
0
0
1
2
0
0
8
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
1
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
3
0
2
0
0
4
0
1
0
0
0
1
0
2
2
0
0
0
0
3
3
0
1
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
1
1
1
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
1
0
2
2
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
2
2
2
0
0
2
0
1
0
0
0
0
0
2
0
1
0
2
0
0
0
0
2
0
0
0
0
0
1
0
1
1
0
0
4
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
8
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
1
3
0
0
2
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
3
1
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
2
3
1
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
3
1
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
3
0
0
0
0
0
2
0
0
2
2
2
1
2
0
0
0
0
1
0
0
1
2
2
0
0
0
0
0
1
3
0
0
0
0
0
1
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
4
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
1
0
2
2
0
1
5
0
2
1
0
0
0
0
0
0
0
0
0
0
1
1
2
0
2
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
2
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
7
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
2
1
1
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
1
0
0
0
7
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
3
0
2
0
0
0
0
0
0
2
0
3
0
2
2
1
1
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
2
2
0
0
0
0
1
0
0
1
2
0
0
0
0
1
3
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
2
1
0
0
0
0
0
0
0
11
1
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
2
2
1
2
0
2
0
1
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
1
1
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
1
0
0
0
1
2
1
0
0
0
1
0
2
1
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
2
2
2
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
1
2
0
0
2
0
0
0
0
1
2
1
0
0
0
0
0
2
0
0
0
0
0
3
2
1
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
5
0
0
0
1
0
1
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
3
0
2
0
1
0
0
1
0
0
0
0
0
0
0
1
5
1
1
2
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
1
0
0
2
0
0
2
0
2
0
0
3
1
0
2
1
1
0
0
2
0
0
2
0
0
0
0
1
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
2
0
1
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
1
1
0
3
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
1
0
0
1
0
1
0
1
0
0
0
2
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
2
2
1
0
2
0
0
3
0
0
2
0
0
0
2
1
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
2
0
0
0
0
0
1
2
1
0
3
1
0
0
0
1
1
0
1
0
2
1
0
0
2
1
0
0
2
0
1
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
2
2
2
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
5
0
2
0
0
2
2
1
0
2
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
3
2
2
1
0
1
0
0
4
0
0
0
0
0
0
0
2
0
2
0
2
1
0
0
2
0
0
0
0
1
0
0
0
3
0
0
0
0
2
0
0
0
0
7
0
1
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
3
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
1
0
1
0
0
2
1
0
1
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
1
0
0
0
2
0
2
1
0
0
0
1
0
2
0
2
0
0
0
0
0
0
2
0
1
0
0
2
1
0
0
0
2
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
1
2
0
7
0
0
0
2
1
0
0
0
1
0
0
3
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
1
2
2
0
0
2
0
0
2
0
2
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
2
0
1
0
0
0
1
2
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
1
0
0
2
0
3
1
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
2
0
1
0
0
0
0
0
0
1
2
0
0
1
0
0
1
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
2
1
0
0
0
2
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
1
2
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
1
2
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
2
0
0
0
2
0
0
0
2
2
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
4
0
0
0
3
0
1
0
0
0
0
0
1
1
0
1
1
0
1
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
2
0
1
1
0
0
0
2
0
0
2
0
1
1
0
2
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
2
2
0
0
2
2
0
0
0
2
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
0
1
2
0
2
0
2
2
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
2
0
0
1
1
1
0
2
1
0
2
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
2
0
0
2
0
0
0
1
3
0
2
2
0
0
2
0
0
0
0
0
0
0
0
2
2
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
5
3
0
0
1
0
0
0
0
0
0
0
2
1
1
0
1
1
1
0
0
0
0
0
0
0
1
2
2
0
0
0
2
0
0
0
1
2
0
2
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
2
0
0
1
1
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
3
0
0
0
1
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
1
2
0
4
0
0
1
0
0
2
3
0
0
0
1
0
0
0
0
0
0
3
0
1
0
0
0
0
0
1
0
0
0
2
2
4
0
0
1
0
0
0
0
0
0
2
0
0
1
0
2
2
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
3
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
1
0
0
2
1
0
0
0
1
0
0
0
0
2
0
2
0
1
1
1
3
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
3
1
1
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
2
0
2
0
1
0
0
0
0
0
5
0
0
0
0
1
0
0
3
0
3
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
2
0
1
0
0
0
0
0
0
0
1
2
2
0
2
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
5
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
2
0
0
0
3
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
3
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
2
1
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
3
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
1
1
2
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
2
1
0
0
1
0
2
1
0
0
1
0
0
1
0
2
1
0
2
0
0
0
0
1
0
0
2
0
0
0
0
1
2
0
1
0
1
3
1
0
0
2
1
1
0
2
0
3
0
1
1
0
0
2
0
0
0
1
0
1
0
0
2
2
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
2
0
0
0
0
2
1
0
0
0
3
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
1
3
3
2
0
2
0
2
4
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
2
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
2
0
2
0
3
0
0
1
2
4
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
1
0
3
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
2
1
2
0
0
0
4
2
2
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
1
0
2
1
2
0
3
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
2
2
0
0
1
1
0
0
1
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
2
0
0
2
0
0
0
0
2
1
0
0
0
4
1
3
1
1
0
0
2
0
0
2
0
0
1
0
0
0
1
0
0
0
1
6
9
0
0
2
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
3
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
3
3
2
1
0
0
2
0
0
3
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
1
2
0
0
0
0
0
0
0
5
0
0
0
0
2
0
1
0
2
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
2
0
5
2
0
0
0
0
1
3
0
0
0
0
0
2
0
0
2
0
0
2
0
1
0
0
1
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
1
0
1
0
1
0
0
0
1
0
2
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
1
0
0
0
0
1
0
0
2
3
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
2
1
0
1
0
0
0
0
0
0
2
2
1
3
2
0
0
2
0
0
2
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
3
0
6
0
0
0
0
0
0
1
0
1
3
0
0
0
4
0
1
1
1
0
0
0
1
2
0
0
0
1
2
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
2
3
1
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
3
0
0
1
0
0
2
2
1
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
3
1
0
2
1
0
0
1
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
1
0
2
0
1
1
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
2
2
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
2
2
0
0
1
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
5
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
2
0
0
1
0
0
3
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
1
2
0
1
2
0
0
0
1
0
0
0
2
0
0
1
2
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
3
0
0
0
0
0
1
2
1
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
2
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
2
0
2
0
0
1
2
0
0
0
1
2
0
0
3
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
5
1
0
0
0
1
12
0
0
0
2
0
1
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
3
3
0
0
0
0
0
0
0
0
0
0
0
1
1
1
2
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
2
1
2
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
2
0
0
0
0
0
2
2
0
2
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
3
0
1
0
0
0
0
0
1
1
0
0
0
3
2
1
1
0
0
0
0
4
0
2
2
0
1
0
0
3
1
1
3
0
1
1
0
0
0
0
0
0
1
0
1
0
0
2
0
2
0
3
0
0
0
2
0
0
0
0
0
0
0
0
1
0
3
0
0
0
1
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
1
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
3
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
1
1
2
0
0
0
0
0
0
0
0
2
0
4
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
4
0
0
0
0
0
2
1
0
1
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
1
0
2
1
0
0
2
1
0
0
0
0
0
2
0
2
0
2
2
0
0
0
0
0
0
1
1
0
0
0
0
3
0
0
0
1
1
1
0
2
0
0
2
0
0
0
3
0
0
0
0
4
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
2
2
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
1
0
0
2
0
0
1
0
0
1
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
1
0
1
4
0
0
0
0
2
0
0
0
1
0
0
5
1
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
3
1
0
0
0
1
0
2
0
1
0
0
2
1
0
0
0
0
0
2
0
0
1
8
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
1
2
1
0
0
2
0
0
1
0
0
1
0
0
5
0
0
1
2
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
1
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
2
0
0
0
0
0
0
2
2
0
0
0
0
0
3
3
0
0
6
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
3
0
0
0
0
4
0
3
0
0
0
0
0
2
0
0
2
1
0
0
1
2
0
0
1
1
0
0
0
0
0
1
0
0
2
0
1
1
0
2
2
0
2
1
0
0
0
0
0
0
1
0
0
2
0
0
4
1
2
3
0
0
0
0
0
0
0
0
1
9
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
1
1
0
0
1
0
0
0
2
0
4
1
0
0
1
1
0
1
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
1
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
5
0
2
0
0
2
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
11
0
0
2
0
1
0
1
1
0
0
0
2
0
3
0
0
1
0
0
2
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
4
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
2
2
2
0
0
0
1
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
1
3
0
0
0
2
0
0
1
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
2
2
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
4
2
0
0
0
2
0
1
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
1
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
2
0
1
0
0
1
0
0
0
0
0
0
2
0
0
3
0
0
2
0
2
2
1
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
2
0
2
0
0
0
0
0
1
1
1
0
0
1
4
2
0
0
0
0
1
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
2
0
3
1
2
0
0
0
0
0
0
1
0
0
0
3
0
0
2
2
0
0
0
0
1
0
0
0
1
0
0
0
8
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
3
0
1
0
1
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
2
1
3
3
0
0
0
0
1
2
1
1
0
1
0
2
1
0
0
1
0
0
6
0
1
0
0
0
1
0
0
1
0
0
2
1
4
1
1
0
1
0
1
2
0
0
0
0
0
0
0
0
0
2
2
0
0
3
0
1
0
0
0
0
0
0
3
0
0
0
1
0
6
0
0
0
0
0
0
0
1
0
0
1
0
2
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
3
1
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
1
0
0
2
0
0
0
3
2
0
0
0
1
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
5
1
1
4
0
1
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
1
1
0
2
0
0
0
0
0
0
3
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
1
0
0
0
0
0
2
1
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
2
0
0
0
0
2
2
2
1
0
0
0
0
0
0
2
0
2
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
1
0
0
0
0
0
0
0
2
0
0
1
6
1
0
0
0
0
5
0
0
3
2
0
0
2
0
0
0
0
0
0
2
0
0
2
0
2
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
4
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
2
2
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
4
0
0
0
2
0
0
0
1
0
0
1
0
2
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
3
1
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
1
1
0
0
1
0
0
2
0
2
0
0
0
3
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
2
0
3
0
0
0
0
2
2
0
1
1
0
1
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
1
0
0
2
1
0
0
0
6
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
2
0
0
0
2
0
0
0
0
0
0
6
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
2
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
2
0
0
5
0
0
1
0
0
0
1
2
0
0
0
2
2
0
0
2
2
0
1
0
0
0
4
0
0
1
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
3
0
3
0
2
0
0
2
0
0
0
0
1
3
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
2
3
0
0
3
0
1
2
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
1
2
0
3
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
1
4
3
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
1
2
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
1
0
0
0
6
2
0
1
0
0
0
0
2
2
0
0
0
5
0
1
2
0
0
2
0
2
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
2
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
3
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
2
0
0
1
0
1
0
1
1
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
1
0
0
0
0
2
1
0
2
0
1
1
0
0
4
0
4
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
1
2
0
1
0
0
0
2
0
1
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
2
0
0
0
0
0
3
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
2
0
2
0
0
2
0
0
0
0
1
0
3
0
0
0
0
0
0
0
3
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
3
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
1
2
0
1
0
0
2
0
0
0
0
0
1
0
2
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
2
2
0
0
0
1
0
0
0
2
0
2
1
0
0
0
1
0
2
0
0
0
0
1
1
1
1
1
0
0
0
2
0
0
2
1
0
2
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
1
1
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
3
1
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
2
2
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
2
3
0
1
0
0
5
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
3
0
0
0
0
2
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
1
0
1
0
0
2
0
0
0
0
0
0
0
1
2
0
1
2
0
2
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
1
0
2
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
3
0
0
1
0
0
1
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
1
0
1
0
0
0
2
0
0
4
1
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
2
0
1
1
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
2
0
0
2
0
1
0
0
0
1
0
1
0
0
0
0
2
0
1
0
1
0
0
0
3
0
2
1
0
0
0
0
0
1
3
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
2
0
2
2
0
0
2
0
0
1
0
0
0
0
0
0
4
2
0
1
0
0
1
0
1
0
0
0
0
1
0
1
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
2
0
1
0
2
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
3
0
0
2
5
1
0
4
0
0
1
0
0
0
2
0
0
2
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
1
0
0
0
0
1
4
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
1
1
0
1
0
0
3
0
0
1
0
2
0
0
0
0
2
0
1
1
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
2
1
0
0
1
0
3
0
0
0
0
0
0
3
0
0
0
0
6
0
0
0
3
0
1
0
2
0
2
0
1
1
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
1
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
1
0
2
0
0
1
0
2
0
0
0
0
4
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
2
1
0
0
0
0
4
1
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
1
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
2
0
2
2
0
0
0
2
2
0
0
2
2
1
0
0
0
0
0
0
0
1
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
2
0
0
0
1
0
0
0
0
2
0
2
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
2
0
1
0
0
3
1
0
0
0
0
0
0
0
0
10
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
2
2
0
0
1
0
0
1
0
0
0
2
0
0
1
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
9
1
0
0
0
1
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
1
0
3
0
0
0
0
0
2
0
0
0
0
0
1
0
2
3
0
0
0
0
2
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
2
1
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
2
2
2
1
0
0
0
0
0
2
0
2
0
0
0
1
1
0
2
0
2
2
0
0
0
0
2
1
0
0
0
0
0
2
6
2
2
0
0
1
2
0
0
0
0
0
2
0
0
0
0
1
0
1
0
1
1
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
2
0
1
0
2
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
3
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
2
0
1
0
0
0
0
2
0
0
0
0
1
3
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
3
0
0
2
1
0
4
0
0
1
0
2
0
1
1
0
0
1
1
0
0
0
0
0
0
0
2
2
0
2
0
2
0
1
0
5
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
2
0
2
2
2
0
0
2
0
0
0
2
0
0
0
3
2
0
0
5
0
2
0
1
0
0
2
1
0
0
0
0
0
1
0
2
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
2
0
3
0
2
0
3
0
0
0
2
0
1
1
3
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
4
2
0
2
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
2
2
2
0
0
2
0
1
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
1
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
2
0
2
0
2
1
0
0
0
0
0
2
0
0
0
0
1
0
1
0
2
0
1
0
1
2
0
2
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
4
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
3
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
2
0
0
3
0
0
3
0
3
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
2
1
0
3
0
0
1
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
1
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
1
2
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
2
0
1
0
0
0
0
1
0
0
0
1
0
5
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
1
2
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
2
2
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
2
0
0
0
0
1
0
0
0
0
2
0
2
0
2
0
1
0
0
0
2
0
0
0
0
0
1
2
1
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
1
2
0
2
0
0
0
0
0
1
0
0
0
2
1
2
1
1
0
2
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
3
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
1
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
2
0
3
3
1
0
0
0
7
0
0
0
1
0
0
0
0
2
1
0
0
0
1
0
1
0
2
1
2
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
5
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
2
0
2
1
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
3
0
2
0
3
2
2
0
0
0
0
0
0
1
0
0
0
0
5
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
1
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
2
2
0
2
2
1
0
2
1
0
3
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
1
0
0
0
0
0
1
0
2
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
6
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
1
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
1
0
2
0
1
2
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
1
2
1
0
0
3
1
0
0
0
0
0
1
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
1
1
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
1
0
1
0
0
0
0
0
0
1
0
0
2
1
0
0
2
0
2
2
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
1
3
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
1
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
7
0
0
2
1
1
0
0
0
2
0
1
2
0
2
0
0
2
0
0
1
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
5
0
1
3
0
0
1
2
0
2
1
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
2
2
0
1
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
2
0
2
1
1
0
0
0
2
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
2
2
0
2
0
0
0
0
2
2
0
0
1
1
2
0
2
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
2
4
0
0
0
1
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
2
0
1
0
0
1
0
1
2
0
1
0
0
0
0
0
0
2
2
0
0
1
0
0
3
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
2
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
1
0
2
0
2
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
2
1
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
2
1
0
2
0
0
0
1
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
2
2
0
0
1
0
0
2
2
0
0
0
0
0
0
3
0
0
0
2
3
2
0
2
0
1
0
0
0
0
0
0
1
2
2
0
1
0
1
0
2
2
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
1
0
2
0
3
2
0
2
0
2
1
0
0
0
0
0
0
2
0
1
3
1
0
0
0
0
2
0
1
3
0
2
0
0
0
2
0
1
0
0
1
1
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
2
2
0
0
0
3
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
2
2
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
3
0
0
2
0
0
0
2
1
1
0
0
2
0
0
0
2
2
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
1
2
0
0
0
1
2
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
1
0
1
0
0
2
0
1
1
0
0
1
0
0
1
0
2
2
0
1
0
0
1
1
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
1
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
2
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
2
0
0
0
1
1
0
3
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
2
1
0
0
1
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
1
2
0
2
0
0
0
2
0
1
0
0
0
0
0
2
1
3
1
5
1
0
0
1
0
1
2
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
2
2
0
0
2
0
2
0
0
0
0
0
0
1
2
1
0
1
0
0
0
4
0
2
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
1
1
0
0
1
1
2
0
0
3
1
0
0
0
0
0
2
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
2
3
2
0
2
0
6
1
0
2
0
0
0
1
0
1
1
0
12
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
2
0
2
0
0
0
0
0
2
6
0
0
2
4
0
0
1
0
0
2
2
1
2
0
2
0
3
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
5
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
2
8
0
0
0
0
0
0
0
0
1
2
0
0
2
1
2
0
1
0
0
0
0
1
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
3
0
0
0
0
2
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
7
0
0
0
0
0
2
0
0
0
0
0
0
0
1
3
0
0
0
1
0
0
0
0
0
0
2
2
0
2
2
2
0
1
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
4
0
3
2
2
0
1
0
0
0
0
2
0
0
1
1
1
0
0
1
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
3
1
0
0
0
0
1
1
0
0
2
2
0
2
0
0
0
0
0
1
0
0
0
0
2
0
1
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
1
1
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
2
3
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
1
0
0
0
0
0
2
1
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
2
0
1
1
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
5
0
0
2
0
0
0
0
0
0
0
0
5
1
1
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
2
0
0
0
0
3
0
0
3
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
1
0
1
0
0
0
3
0
0
0
0
0
0
0
8
2
0
0
2
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
1
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
1
3
0
0
1
0
0
0
0
2
0
0
0
1
2
1
0
0
0
3
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
2
0
0
2
0
0
2
1
0
0
3
0
0
2
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
1
0
2
1
0
0
0
2
0
2
2
2
2
1
0
1
1
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
2
0
5
0
0
1
0
2
1
0
0
1
0
0
0
0
2
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
3
0
0
0
0
0
0
2
0
0
0
0
3
0
1
0
0
1
2
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
2
0
0
0
1
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
1
0
0
2
0
2
0
0
1
2
2
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
1
0
0
0
1
3
0
0
2
1
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
2
1
0
0
2
0
3
1
2
0
0
2
0
0
0
1
1
0
0
1
0
0
2
0
0
0
2
0
0
2
0
1
2
1
2
0
0
2
2
1
0
0
4
1
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
1
2
0
0
2
1
0
4
0
2
0
0
2
0
0
0
0
0
2
2
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
1
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
1
3
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
3
1
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
3
0
2
0
0
1
1
2
2
0
1
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
2
0
2
1
0
2
0
0
0
7
0
0
0
2
2
0
0
0
1
0
0
1
0
0
1
1
1
1
1
0
0
0
0
0
0
0
1
5
1
0
0
1
0
0
5
0
0
0
2
1
6
0
2
0
0
0
0
2
14
0
0
0
0
0
0
0
7
0
2
0
0
1
0
2
2
0
0
1
1
0
2
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
3
0
0
2
0
2
4
0
0
1
0
0
0
0
0
1
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
2
2
0
0
2
2
0
0
0
0
3
2
4
4
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
3
0
0
0
2
0
0
0
0
1
1
2
0
0
1
0
0
2
1
0
0
2
0
0
0
0
1
0
1
0
1
0
0
5
0
0
0
2
0
2
0
1
3
2
0
0
2
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
6
1
0
1
0
0
0
2
12
0
0
0
0
0
2
3
0
0
0
1
1
2
0
0
0
0
0
1
0
0
1
2
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
1
0
0
2
1
0
4
0
0
0
0
2
0
3
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
2
0
2
0
2
0
2
0
2
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
2
2
0
2
0
0
1
0
0
0
2
0
2
2
0
0
0
0
1
0
0
3
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
1
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
1
0
2
0
2
0
0
0
0
0
1
0
1
0
0
2
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
1
3
3
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
1
1
0
2
1
2
0
0
2
0
2
0
0
0
3
0
1
2
1
1
0
0
3
0
0
0
0
0
3
0
0
1
2
0
0
0
0
0
0
0
1
0
3
1
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
3
2
1
0
0
0
3
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
5
0
0
0
0
0
0
3
0
1
2
0
0
0
0
1
0
0
0
0
1
2
1
3
0
1
0
0
0
2
0
0
2
0
0
0
0
0
2
2
0
0
1
1
0
0
0
2
2
0
0
0
0
0
0
0
1
2
1
1
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
2
0
1
1
0
6
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
2
0
1
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
3
0
0
0
0
0
4
1
0
0
0
0
0
4
0
0
0
2
0
0
2
0
2
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
1
0
0
0
1
0
1
2
2
2
0
0
0
0
0
0
1
1
1
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
3
0
2
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
2
0
0
0
0
0
0
0
0
3
1
0
1
1
0
0
0
0
0
0
4
2
0
0
0
1
1
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
1
1
0
0
0
0
2
2
1
0
0
0
1
0
0
2
0
0
1
0
1
0
0
0
0
1
0
0
0
0
5
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
5
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
1
0
0
0
0
0
1
2
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
2
0
2
2
0
0
0
1
2
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
1
2
0
0
1
0
0
2
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
1
2
0
0
0
2
1
1
0
1
0
0
2
2
2
0
2
0
0
2
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
3
2
0
0
1
0
0
0
0
0
1
3
0
1
0
0
2
1
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
1
2
0
2
0
1
2
0
2
0
0
0
2
0
1
1
1
0
0
0
0
0
2
0
0
0
0
0
1
0
1
2
0
2
0
4
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
3
2
0
2
1
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
2
0
1
0
0
0
0
3
1
0
2
4
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
1
0
0
1
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
2
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
2
0
0
1
0
1
0
1
1
2
1
0
0
3
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
4
2
0
0
1
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
4
1
0
1
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
1
0
0
0
0
0
2
1
0
0
0
1
0
0
0
2
2
0
0
0
1
0
0
0
4
0
0
0
3
0
0
0
0
0
2
3
1
0
0
0
1
0
0
0
0
0
1
1
0
9
1
0
0
0
0
6
0
0
2
0
0
0
1
0
2
0
0
0
0
2
1
0
2
0
0
0
2
0
0
2
0
0
0
0
0
1
3
0
1
0
0
0
0
0
1
0
2
2
1
0
1
0
0
0
0
0
1
2
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
1
0
2
2
2
4
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
2
0
2
1
0
0
0
1
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
1
1
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
2
0
0
2
2
0
0
1
0
0
0
2
1
2
0
0
0
0
2
0
0
1
2
2
0
1
0
0
0
0
0
2
0
0
1
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
1
2
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
2
0
0
2
0
0
1
0
1
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
1
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
1
3
0
0
1
0
1
2
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
1
0
3
0
0
1
2
0
0
0
0
1
0
0
0
0
0
3
2
0
1
1
2
2
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
2
0
0
0
1
0
2
0
3
2
0
0
0
0
0
4
0
0
0
2
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
1
2
0
1
0
0
1
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
1
0
0
1
0
1
0
0
1
0
1
0
1
0
1
0
0
1
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
2
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
2
2
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
3
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
1
0
2
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
2
0
2
0
0
2
0
2
0
0
0
0
0
0
2
2
2
1
0
0
0
0
2
3
0
0
0
2
0
0
3
0
0
2
1
0
2
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
1
0
3
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
3
2
4
0
0
3
0
0
0
0
0
0
2
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
1
0
1
1
0
0
0
1
0
0
0
2
1
1
0
8
0
0
2
0
0
0
1
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
3
0
1
2
0
2
0
2
0
0
2
2
0
0
0
0
2
2
1
2
0
1
1
0
2
1
0
0
0
0
1
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
1
2
0
1
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
3
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
1
0
0
0
3
2
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
2
2
0
0
0
0
0
0
0
2
3
1
1
0
2
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
1
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
1
0
0
1
0
0
2
1
0
0
1
0
0
0
0
0
0
0
4
0
1
1
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
2
1
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
3
4
1
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
1
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
7
0
1
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
2
2
0
0
0
2
0
1
0
0
0
6
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
5
0
0
0
0
1
1
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
1
2
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
5
0
0
1
2
0
0
0
0
0
0
2
0
0
0
1
1
0
0
2
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
3
0
1
0
0
0
2
2
2
0
0
1
1
2
0
0
0
0
2
0
0
1
1
0
1
0
0
0
2
0
0
0
0
0
1
1
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
3
1
0
1
0
0
0
0
2
0
0
2
4
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
4
0
0
0
0
0
2
0
1
1
1
3
2
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
2
2
0
1
0
0
0
1
2
1
2
2
0
0
0
2
0
1
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
1
1
0
1
0
0
0
2
3
1
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
2
0
0
5
1
0
2
1
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
3
2
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
1
0
0
1
0
3
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
1
2
0
0
2
0
0
4
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
1
0
2
0
2
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
3
1
1
0
0
0
0
0
0
0
0
0
0
1
1
3
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
2
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
1
1
2
0
0
0
0
0
2
0
0
0
2
1
0
4
0
0
2
0
0
0
0
1
2
0
0
2
0
0
0
0
1
0
1
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
8
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
2
0
0
0
5
1
0
2
0
0
0
2
2
0
2
0
0
2
0
0
0
0
2
3
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
1
2
2
0
0
1
1
0
1
0
2
0
0
2
2
0
0
2
0
0
0
1
0
2
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
2
0
2
0
0
0
3
0
0
0
0
1
2
0
0
0
0
2
0
0
1
0
1
2
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
1
1
0
0
0
1
2
0
3
0
1
0
0
2
0
1
0
0
0
0
0
3
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
4
0
0
1
0
0
0
2
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
1
0
3
1
0
0
0
0
0
0
3
0
0
0
0
0
2
2
3
1
0
1
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
2
2
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
1
0
0
2
1
2
0
1
0
2
0
0
0
1
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
1
0
1
2
0
0
0
1
0
0
2
0
0
0
0
0
0
1
1
0
2
0
0
0
0
1
2
0
0
0
1
0
0
1
0
2
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
3
2
0
0
0
0
0
0
0
2
0
0
12
0
0
0
0
0
0
0
0
2
0
2
2
0
2
0
0
0
1
0
0
1
1
0
0
0
2
0
0
0
1
2
2
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
1
2
0
3
2
2
5
2
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
1
0
2
4
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
2
0
2
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
1
0
2
0
0
0
2
0
2
2
0
0
1
0
0
2
2
0
0
0
3
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
1
1
2
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
4
0
2
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
4
2
2
0
1
0
0
0
1
0
0
0
1
2
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
3
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
3
3
0
0
0
0
5
0
0
0
1
0
1
2
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
3
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
1
1
0
0
1
0
0
2
0
3
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
2
0
0
2
0
0
2
1
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
3
0
0
0
0
0
0
1
2
0
7
0
1
1
2
0
0
0
0
0
1
0
0
0
5
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
1
2
0
0
2
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
1
1
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
1
0
2
0
0
0
0
1
1
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
1
2
0
0
0
2
0
0
0
0
1
1
1
0
0
5
2
0
0
2
0
2
1
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
4
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
2
1
0
0
0
0
0
2
0
0
0
5
0
0
1
0
7
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
1
1
0
0
0
0
2
2
0
1
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
4
0
1
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
2
0
0
1
0
2
1
0
0
0
0
0
0
5
0
0
0
2
0
1
0
0
0
1
0
0
0
1
0
0
2
3
0
0
0
0
2
0
0
1
0
1
3
0
0
0
0
0
2
2
0
0
0
0
0
2
0
2
2
2
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
1
1
1
2
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
2
0
2
2
0
0
0
2
0
0
3
0
0
2
0
0
1
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
2
1
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
2
0
2
0
0
1
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
2
0
3
1
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
1
2
0
0
0
0
2
0
0
0
0
0
0
2
0
1
2
2
3
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
1
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
2
8
0
0
0
2
0
0
0
0
0
0
0
0
1
1
2
1
2
0
0
1
0
0
2
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
4
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
3
1
0
0
0
0
1
0
1
0
0
0
0
1
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
1
0
2
0
0
0
0
0
0
2
1
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
2
0
0
0
1
4
1
2
2
0
0
2
0
2
0
1
0
4
0
0
1
0
1
0
0
1
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
2
11
0
0
0
2
1
2
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
1
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
5
0
0
0
0
0
2
2
1
2
0
2
0
0
0
0
1
1
3
2
0
0
1
0
0
0
0
1
0
2
0
0
0
0
2
0
0
2
2
1
0
0
2
0
0
0
0
3
0
0
0
0
1
2
0
4
0
0
2
0
0
0
0
0
0
3
2
1
0
0
3
0
0
0
2
3
0
1
0
1
0
0
2
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
1
2
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
2
0
2
0
0
0
0
0
0
1
0
1
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
2
0
2
0
0
0
0
0
0
1
0
0
0
2
0
1
2
2
0
1
0
0
3
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
3
1
1
0
2
0
0
0
0
0
1
2
0
1
0
0
2
0
3
0
0
0
0
0
0
1
0
0
0
0
2
2
1
0
0
2
1
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
4
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
1
0
0
0
5
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
1
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
1
0
1
1
0
0
0
1
1
2
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
2
0
0
2
1
0
2
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
1
0
0
0
0
3
1
0
0
0
0
2
0
0
0
1
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
2
1
0
0
1
1
0
0
0
0
0
0
2
0
0
1
1
0
4
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
4
2
0
0
2
2
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
3
1
1
0
0
0
1
0
1
0
0
2
0
1
0
0
2
0
1
0
2
0
0
0
1
0
2
0
2
0
2
0
1
3
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
2
0
2
0
0
2
2
1
7
1
0
1
0
0
2
0
0
0
0
1
0
0
0
0
3
0
3
0
0
0
2
0
0
0
1
1
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
5
0
0
0
0
0
0
1
0
0
0
0
0
0
0
5
0
1
0
0
0
2
0
2
1
0
0
2
0
0
1
1
2
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
2
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
8
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
2
0
0
0
1
0
1
1
1
0
1
2
0
0
1
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
2
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
3
2
0
1
1
3
0
0
1
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
2
0
0
1
0
0
0
0
1
0
1
2
0
0
0
2
0
0
2
0
0
0
1
0
1
0
0
0
1
0
5
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
1
1
0
3
0
2
0
1
1
0
1
0
2
0
2
1
0
0
0
0
2
0
0
0
0
1
1
0
0
2
2
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
1
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
1
0
3
0
0
0
0
0
0
0
1
0
2
0
0
1
2
0
0
0
0
2
0
0
0
2
0
3
1
0
2
0
0
5
0
0
0
0
0
0
5
2
2
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
1
2
3
0
0
0
0
0
0
1
0
0
2
1
0
0
1
0
0
0
1
2
2
0
0
1
0
0
0
2
0
0
1
0
0
0
1
0
0
2
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
2
0
0
2
0
0
1
0
0
0
0
0
2
0
2
0
0
1
0
2
2
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
2
0
3
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
3
0
1
1
0
0
0
4
0
2
0
0
0
0
0
2
0
0
1
1
0
1
0
2
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
2
0
0
1
1
0
0
0
0
0
0
0
0
2
1
0
1
0
2
2
0
0
3
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
1
0
0
1
0
0
1
0
1
3
0
0
2
0
0
0
0
0
1
0
3
0
0
0
2
3
0
0
1
1
0
2
2
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
1
1
0
0
0
2
2
0
0
0
1
0
2
0
0
0
0
1
0
0
0
2
3
0
6
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
3
0
1
1
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
1
0
0
0
0
0
3
1
0
0
0
2
0
2
2
1
0
0
0
0
1
0
1
1
0
1
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
2
0
2
0
0
0
0
2
0
3
0
0
0
0
1
0
1
1
0
2
1
0
0
0
0
0
3
2
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
3
0
0
0
0
0
2
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
3
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
2
1
0
0
0
1
2
0
0
0
2
2
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
1
0
2
0
0
2
0
2
2
0
0
0
2
0
0
0
4
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
1
2
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
3
3
0
2
0
0
0
0
0
1
0
0
0
0
0
1
1
2
0
10
0
0
3
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
3
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
3
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
2
1
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
2
1
0
0
3
0
0
3
0
2
0
1
0
2
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
3
0
0
2
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
3
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
2
0
0
1
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
2
0
2
1
0
2
2
0
0
2
2
0
2
1
2
0
0
0
1
2
0
2
0
0
1
1
0
0
0
0
0
0
2
2
0
2
0
0
0
2
2
0
0
0
1
2
1
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
1
2
5
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
2
0
0
0
0
2
1
0
0
2
2
3
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
4
0
0
0
0
0
0
2
1
0
0
0
2
2
0
0
1
0
0
0
2
0
1
0
2
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
4
1
0
0
0
0
0
0
2
2
0
0
0
2
0
0
1
2
0
0
1
2
0
0
2
1
0
2
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
2
0
0
0
0
1
0
1
0
2
2
3
0
1
0
1
0
1
0
0
0
2
1
0
0
2
0
0
0
0
4
0
0
0
2
0
2
0
0
0
0
0
1
0
0
2
0
0
2
1
0
2
0
0
0
0
0
1
1
0
0
0
0
0
2
0
1
2
0
0
0
0
0
1
2
0
0
0
1
0
1
0
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
1
3
1
2
0
1
0
1
0
1
0
0
2
0
0
0
0
0
3
0
1
0
0
1
1
0
0
0
2
0
0
3
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
1
1
0
0
0
6
2
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
4
0
0
0
2
1
0
0
0
0
0
0
0
2
0
1
0
1
0
0
2
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
2
0
0
1
0
2
1
0
0
0
2
0
0
2
0
1
0
0
0
1
2
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
2
2
0
1
4
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
1
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
7
1
0
0
0
1
0
0
1
1
0
2
2
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
2
0
1
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
1
4
0
0
0
0
0
0
1
1
1
0
2
0
0
0
0
0
2
0
2
0
0
1
0
1
0
0
0
0
0
1
5
2
0
3
0
0
1
0
1
0
0
0
2
0
0
0
0
3
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
1
0
2
0
0
0
1
1
2
0
0
2
0
0
0
0
1
2
0
0
1
0
0
1
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
4
0
0
2
1
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
1
2
3
0
3
0
0
1
2
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
4
0
0
0
2
0
2
0
0
1
0
1
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
2
1
0
2
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
2
1
0
2
0
1
1
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
2
0
0
1
0
0
0
0
2
0
1
2
0
0
6
0
0
0
1
2
2
1
0
0
1
0
2
1
0
1
0
1
2
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
2
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
1
1
0
0
0
2
0
0
0
0
0
0
3
0
0
0
1
0
2
0
0
0
1
1
2
1
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
2
0
2
0
0
1
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
2
1
0
3
0
0
1
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
1
0
2
1
0
0
0
0
2
1
1
1
1
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
1
0
2
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
1
2
3
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
1
0
2
2
0
0
0
2
7
0
0
0
2
0
0
1
1
0
0
0
2
0
1
1
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
1
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
2
1
0
0
2
0
0
0
1
0
0
0
2
1
0
0
0
0
2
1
0
0
0
1
0
2
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
2
0
0
0
0
0
0
1
1
0
2
0
0
2
0
0
0
1
0
1
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
1
0
2
2
0
0
0
0
0
1
0
0
0
1
0
0
2
1
1
0
1
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
1
2
0
0
2
1
0
0
1
0
0
2
0
0
0
2
1
2
1
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
3
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
1
2
1
0
0
0
0
0
0
2
2
2
0
0
0
1
0
0
0
8
0
2
0
0
0
0
1
2
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
2
0
0
1
0
0
2
1
0
2
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
2
0
0
0
1
1
0
0
2
4
1
0
0
0
0
0
1
0
0
3
1
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
2
0
2
0
0
0
1
0
0
0
3
0
1
0
0
0
3
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
2
0
1
1
0
0
0
1
0
2
2
0
3
0
2
2
1
0
2
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
1
0
0
2
0
0
2
0
0
0
1
0
1
0
0
2
0
0
0
0
0
2
1
0
1
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
2
0
0
0
1
1
0
4
0
0
2
0
0
0
0
1
0
1
2
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
3
0
0
0
1
2
0
0
0
2
3
0
0
0
0
1
0
0
0
2
1
0
0
0
1
0
0
0
0
1
2
0
0
1
2
0
0
1
0
0
1
5
0
0
2
0
0
1
0
1
0
0
2
5
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
1
0
1
2
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
2
3
0
2
0
0
1
4
0
0
1
1
1
2
2
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
1
0
2
1
0
0
0
1
2
0
0
0
1
0
0
2
0
0
4
0
0
2
0
1
1
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
4
0
2
0
0
0
0
0
1
2
0
1
2
2
0
0
0
0
1
2
0
0
0
0
2
1
0
2
2
0
1
3
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
4
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
2
0
0
2
1
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
1
1
0
2
0
0
0
1
0
0
1
0
2
0
0
1
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
1
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
3
0
0
0
0
1
0
0
0
2
0
0
1
0
2
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
3
0
0
0
0
1
1
0
0
0
2
0
2
1
2
0
0
0
0
0
1
2
0
0
0
0
0
1
0
2
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
2
1
0
0
0
0
0
1
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
3
0
0
0
0
2
0
0
1
0
0
5
0
0
1
0
0
2
2
1
2
0
0
0
0
1
0
0
1
3
0
0
0
1
0
2
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
2
0
1
2
0
0
1
0
0
0
1
0
0
2
0
0
1
2
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
1
0
0
2
3
0
0
0
1
0
2
1
0
2
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
1
1
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
4
1
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
2
0
0
0
0
0
2
1
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
3
1
0
0
0
2
0
0
0
2
0
2
0
1
1
2
3
0
2
0
0
1
0
2
2
0
0
1
2
0
0
0
2
0
0
0
0
2
0
1
0
0
2
0
0
0
2
0
0
0
1
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
5
0
0
1
0
2
3
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
2
2
7
0
1
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
2
2
0
1
3
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
2
0
2
0
0
5
0
0
1
1
1
0
0
0
0
0
2
0
0
0
1
0
0
8
0
4
1
1
0
0
0
0
2
2
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
3
0
1
1
0
1
0
0
0
0
0
0
0
2
1
0
2
0
1
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
2
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
2
2
0
1
0
1
3
0
2
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
2
0
2
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
1
0
1
2
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
2
0
2
2
0
0
1
1
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
1
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
2
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
1
0
2
0
0
0
1
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
3
1
2
0
0
0
1
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
3
0
0
0
1
5
0
0
2
3
0
0
0
1
0
0
1
1
0
2
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
3
0
5
0
0
0
0
1
2
1
0
1
0
0
0
0
2
1
1
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
1
0
1
2
0
1
0
1
3
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
3
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
3
1
1
0
0
0
0
2
0
1
0
1
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
1
0
0
0
0
2
1
0
0
0
2
1
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
2
1
0
1
0
0
0
0
2
1
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
3
0
1
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
3
1
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
1
1
0
0
1
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
3
0
0
0
1
0
0
1
0
0
2
1
0
0
0
0
0
0
3
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
3
0
2
2
5
0
0
2
0
0
1
0
0
0
0
0
0
1
0
1
2
0
2
0
0
0
0
1
3
0
1
0
0
0
3
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
2
0
0
2
0
1
0
0
0
1
0
2
0
0
0
2
0
0
2
2
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
2
0
7
0
0
0
3
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
2
2
0
1
0
0
1
2
0
2
1
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
5
0
2
1
0
0
2
0
0
0
1
0
0
0
0
0
2
2
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
1
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
1
0
0
0
0
1
1
3
0
1
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
4
0
0
0
0
0
0
1
2
0
0
0
0
1
0
3
0
0
0
0
2
0
0
2
0
0
0
1
0
2
0
0
1
0
2
0
0
1
2
0
0
2
0
4
1
0
0
1
0
2
0
0
0
0
0
2
0
0
0
1
1
1
0
1
0
5
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
3
1
2
0
1
2
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
1
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
2
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
6
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
1
0
1
3
2
2
0
0
0
0
0
0
0
2
0
0
0
1
0
1
2
0
0
0
2
0
0
0
2
1
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
1
2
0
0
0
1
0
1
0
0
0
0
0
0
6
0
0
0
0
0
2
2
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
2
0
0
0
0
0
1
0
0
2
2
0
0
7
2
1
0
3
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
2
1
0
0
2
0
4
2
0
0
0
0
0
1
0
0
0
0
0
4
0
1
2
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
3
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
1
0
1
1
4
0
2
5
0
1
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
2
0
1
0
0
0
2
0
2
2
0
0
2
0
0
0
0
1
0
0
0
2
0
0
2
1
1
0
0
0
1
0
2
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
3
0
0
0
3
0
0
2
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
1
0
2
0
1
0
0
1
0
0
2
1
0
1
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
2
1
0
0
1
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
2
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
3
2
0
0
2
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
1
1
1
1
2
0
1
0
2
0
0
1
2
0
0
0
0
0
3
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
1
1
0
0
1
0
2
0
0
2
0
2
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
2
0
0
4
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
2
2
1
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
2
2
0
2
0
0
2
1
0
4
0
0
0
0
0
0
4
0
0
0
1
1
0
0
0
0
0
0
2
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
1
5
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
2
0
0
5
0
0
0
0
0
2
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
6
0
1
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
2
2
0
0
0
1
2
3
0
2
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
1
0
0
2
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
2
0
2
1
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
2
0
1
1
0
0
0
0
0
0
0
1
2
0
0
0
2
2
0
1
0
0
0
0
2
0
3
0
2
0
0
2
0
0
2
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
1
0
2
0
0
0
0
2
0
0
0
0
0
0
1
2
1
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
3
2
0
1
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
2
0
2
0
0
0
0
3
0
1
0
0
2
0
0
2
0
0
0
2
1
2
1
1
0
0
3
2
0
0
0
1
2
0
2
0
1
0
2
0
13
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
2
0
0
1
0
2
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
2
2
0
0
0
0
0
1
0
0
0
2
0
2
0
1
0
0
0
0
0
3
0
0
0
1
0
0
2
0
1
4
0
0
0
0
1
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
2
0
0
0
0
0
1
0
0
2
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
2
0
0
0
2
4
0
0
1
0
0
2
1
0
0
0
0
1
0
0
1
2
1
0
3
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
3
2
0
0
0
0
2
2
0
0
0
0
2
0
0
4
0
3
0
0
0
0
0
0
1
0
0
2
0
0
2
1
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
1
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
4
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
2
0
0
0
1
0
0
0
2
2
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
1
1
0
0
0
0
1
2
0
0
1
0
0
2
2
1
0
0
2
1
0
0
0
0
2
2
1
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
1
0
0
4
0
0
0
2
0
0
0
2
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
2
0
2
0
1
0
0
0
1
2
2
0
0
0
0
0
1
0
3
2
0
0
0
0
2
0
0
2
1
3
0
0
1
0
1
0
0
0
0
1
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
3
3
1
0
0
0
2
0
2
0
2
0
0
1
0
0
0
2
2
1
0
0
2
0
0
1
0
2
0
0
1
0
1
0
0
1
1
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
2
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
3
0
0
1
1
0
2
1
0
0
0
2
0
0
0
3
2
1
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
2
0
0
2
2
2
1
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
31
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
2
0
1
0
2
0
0
0
3
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
3
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
4
0
1
0
2
0
0
0
0
5
0
2
0
0
0
0
0
0
3
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
3
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
2
1
0
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
1
0
2
0
0
2
0
0
2
0
0
2
2
2
2
0
0
1
1
0
0
0
0
0
1
3
0
2
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
7
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
1
9
1
0
4
0
0
1
0
0
0
1
0
2
0
2
0
0
0
0
0
0
2
2
0
3
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
1
0
1
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
2
1
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
9
0
2
0
0
2
0
1
0
1
0
0
0
0
1
1
0
0
2
0
1
0
0
1
0
2
0
2
0
0
0
4
0
4
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
1
0
0
0
0
2
0
2
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
2
0
0
0
0
0
0
0
2
0
0
0
3
0
0
1
0
1
1
2
1
0
0
0
1
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
2
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
2
7
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
2
0
3
2
0
0
0
2
1
2
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
2
4
2
0
0
2
1
0
0
1
0
0
3
0
1
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
1
0
0
0
1
0
3
2
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
1
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
1
0
2
1
0
0
0
1
0
1
3
0
0
1
0
0
0
1
0
1
3
0
0
0
0
0
0
1
0
0
1
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
2
1
0
0
0
1
2
0
0
0
1
2
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
1
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
2
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
2
0
1
2
0
2
1
2
1
1
0
0
0
1
0
1
2
0
0
1
0
0
1
1
1
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
1
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
3
0
2
0
0
2
3
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
2
1
2
0
0
2
1
3
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
2
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
2
2
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
1
0
1
0
1
0
2
1
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
1
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
2
0
0
0
0
1
0
0
0
2
0
2
0
0
4
1
0
0
1
1
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
2
0
1
0
0
0
1
0
0
1
0
3
0
1
0
2
0
0
0
0
0
0
1
0
3
0
0
0
0
0
1
0
1
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
1
1
1
0
0
0
0
2
2
0
0
1
0
1
0
1
1
2
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
2
0
0
0
0
3
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
1
2
0
0
0
2
1
0
0
1
2
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
5
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
1
0
1
3
1
0
1
0
2
1
0
0
0
0
3
0
0
1
2
2
0
0
0
0
0
0
0
2
0
0
0
1
6
0
0
2
0
0
2
0
3
1
0
0
0
0
4
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
3
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
2
0
0
1
0
0
3
2
0
0
0
0
2
1
0
2
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
3
0
0
0
2
0
0
0
0
0
1
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
1
1
2
0
0
0
0
1
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
6
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
3
0
1
0
0
2
0
2
0
0
0
2
2
1
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
1
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
1
1
2
0
0
0
1
2
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
2
2
2
0
0
1
0
0
0
2
0
0
2
1
0
0
1
4
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
7
0
0
0
0
1
1
0
2
1
0
0
1
0
0
2
0
1
0
1
0
0
0
0
0
1
0
0
0
2
1
2
0
0
0
2
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
1
0
0
0
1
2
0
0
0
0
1
2
0
0
2
2
0
0
3
0
2
0
0
0
1
0
0
0
2
2
2
0
0
0
0
1
0
0
0
0
0
1
1
5
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
1
0
0
0
1
0
1
2
0
0
0
0
0
0
1
0
0
2
2
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
3
1
0
0
0
0
1
0
0
2
0
4
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
2
0
0
2
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
2
3
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
1
0
0
0
7
0
0
1
0
0
0
3
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
3
1
0
0
0
2
0
0
1
0
0
1
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
2
1
6
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
2
0
0
0
3
1
0
0
0
0
0
1
2
0
1
0
0
1
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
2
0
2
0
0
1
2
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
1
0
0
0
0
0
5
0
0
0
1
0
0
0
0
0
0
1
2
0
0
1
1
0
1
2
0
0
0
0
1
0
0
0
0
0
3
0
0
0
2
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
1
2
0
1
2
1
0
0
3
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
1
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
1
1
0
1
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
2
0
1
1
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
2
1
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
4
0
0
0
2
2
1
0
0
1
0
0
0
1
0
2
1
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
2
2
1
0
2
2
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
1
1
0
0
1
3
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
1
0
2
3
0
2
0
0
1
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
2
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
2
2
0
0
0
2
0
2
0
0
0
0
0
0
2
2
3
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
1
1
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
1
0
2
0
1
2
0
1
0
2
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
2
1
0
0
0
0
0
0
2
2
0
2
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
1
0
1
0
1
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
1
4
0
0
4
1
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
3
0
0
0
0
1
0
1
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
1
0
0
2
0
2
0
1
1
0
1
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
3
0
0
0
2
0
2
1
1
0
2
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
5
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
1
0
0
3
0
0
0
0
4
0
0
0
1
0
0
0
1
0
0
2
0
0
0
2
3
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
3
0
4
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
1
0
0
2
1
0
0
1
0
0
1
2
1
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
2
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
2
0
0
0
0
2
1
0
0
1
1
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
3
0
0
1
0
0
0
2
0
0
3
0
0
0
0
0
0
0
1
0
1
0
0
1
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
2
0
3
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
1
0
1
0
0
0
2
0
2
0
0
0
2
2
0
0
0
1
0
1
0
0
2
0
0
0
2
2
0
2
0
2
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
1
0
1
2
1
1
0
1
0
0
0
0
0
2
0
0
0
0
2
1
0
0
2
0
0
1
0
1
1
0
0
0
8
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
2
0
1
0
2
2
1
1
1
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
8
0
3
5
0
0
0
2
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
1
4
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
2
1
0
1
0
1
0
0
0
0
0
0
1
1
2
1
1
0
0
0
2
0
0
3
0
0
0
2
0
0
2
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
1
0
2
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
1
0
0
0
1
0
0
0
0
3
0
0
0
1
0
2
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
6
0
0
7
0
0
0
1
0
2
1
0
0
0
2
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
2
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
2
0
2
0
2
1
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
5
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
3
0
1
0
0
0
2
2
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
1
5
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
1
0
0
0
0
0
9
2
0
0
0
0
1
0
0
3
1
2
1
3
0
0
0
0
0
0
1
0
4
0
2
0
2
0
0
0
3
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
2
1
0
0
0
1
1
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
1
0
0
2
0
0
0
2
2
0
0
1
0
0
2
2
2
0
0
0
0
1
1
0
0
0
0
0
2
1
1
0
1
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
2
0
0
1
0
3
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
3
0
0
2
0
0
1
0
0
2
0
0
1
0
1
1
0
0
0
0
0
3
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
2
0
1
0
0
1
1
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
1
3
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
1
2
0
1
1
0
0
1
1
0
3
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
1
0
2
0
2
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
1
2
0
0
0
0
2
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
1
0
2
0
0
0
2
0
2
1
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
1
0
0
2
0
1
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
1
2
0
0
0
3
0
0
0
0
0
0
0
3
2
0
0
0
0
0
1
2
2
0
0
0
1
0
1
1
0
0
0
0
1
2
0
2
2
0
2
1
0
0
0
6
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
3
0
0
0
0
1
0
1
0
0
2
2
0
2
0
1
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
1
0
2
2
1
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
2
0
0
2
0
0
0
1
1
2
0
2
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
3
0
0
1
1
1
0
0
3
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
3
0
0
0
2
0
0
2
1
0
0
2
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
1
2
0
0
2
0
0
0
1
1
0
0
2
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
1
1
0
0
0
2
0
1
0
1
0
3
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
3
0
2
2
0
0
0
0
0
0
0
3
2
0
0
1
0
1
1
0
1
0
0
1
0
1
0
1
2
0
2
0
0
0
0
3
0
2
2
0
0
0
0
0
0
0
5
2
0
2
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
6
0
1
2
2
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
3
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
1
3
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
2
0
0
0
0
2
2
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
1
0
0
0
0
2
2
2
0
0
0
3
0
0
0
0
0
0
0
1
1
0
2
0
2
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
1
1
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
1
0
0
2
0
0
1
0
0
0
0
2
0
1
1
0
0
0
0
0
1
0
3
0
0
0
0
2
0
0
0
0
3
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
3
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
2
0
2
0
0
0
2
1
0
0
2
0
2
0
2
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
2
1
0
0
8
0
2
0
0
2
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
1
0
1
2
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
2
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
1
4
0
0
0
3
0
0
0
2
0
0
0
2
0
0
2
0
2
2
0
2
2
0
0
1
0
0
0
0
0
0
3
0
0
1
2
0
1
2
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
1
0
0
1
3
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
2
2
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
1
2
0
3
0
1
3
1
0
0
2
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
1
1
0
0
0
2
1
0
0
0
0
0
1
3
2
2
0
0
2
0
1
0
0
1
0
2
0
0
3
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
4
2
1
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
1
0
0
2
2
0
1
0
0
0
5
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
1
1
0
1
0
2
2
0
0
0
0
5
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
1
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
2
1
0
0
2
1
0
0
1
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
3
2
0
1
0
2
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
2
3
0
0
0
1
0
0
6
0
0
2
0
0
2
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
3
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
2
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
6
0
0
0
0
2
0
0
0
0
0
0
0
4
2
1
0
0
0
0
0
1
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
1
0
0
1
2
1
1
0
0
0
0
2
0
2
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
3
0
0
0
0
1
1
0
0
0
2
0
0
0
0
1
5
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
5
0
0
0
0
0
1
0
1
0
0
3
0
0
2
1
1
0
0
0
3
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
2
0
0
0
0
2
0
0
1
0
0
0
4
0
0
0
0
0
1
0
0
0
3
0
2
0
1
0
0
3
1
0
0
0
0
1
2
1
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
2
0
0
0
0
0
1
0
2
0
0
4
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
1
0
1
0
0
0
1
2
0
2
1
1
1
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
3
0
1
0
2
2
1
0
1
0
0
0
0
0
0
0
0
0
3
6
1
0
1
0
0
2
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
2
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
2
0
3
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
9
8
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
3
1
0
2
0
0
0
1
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
2
1
2
0
1
0
0
0
2
0
0
0
0
0
0
1
1
2
0
0
2
0
0
1
0
2
1
0
0
0
1
0
2
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
1
0
2
1
1
0
0
0
0
0
0
3
0
0
2
2
0
0
2
0
0
1
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
2
1
0
2
0
2
2
0
0
0
0
0
0
0
1
2
2
0
2
0
0
1
2
2
0
0
0
1
0
1
0
1
0
1
4
2
0
2
2
0
0
4
2
0
0
2
3
0
0
0
0
2
0
0
2
1
2
0
2
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
1
0
1
1
1
0
4
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
2
0
0
2
2
0
2
0
0
1
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
3
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
1
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
2
3
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
1
0
0
0
1
0
1
1
0
1
0
0
2
0
2
0
0
0
0
0
1
0
2
0
2
0
2
0
0
2
0
1
1
2
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
2
0
0
0
0
0
2
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
1
1
1
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
2
2
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
3
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
3
1
0
0
0
2
0
0
0
2
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
3
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
2
0
0
0
0
1
0
2
0
1
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
1
0
0
0
1
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
3
0
0
0
0
2
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
1
0
0
2
0
0
0
1
1
3
0
4
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
1
2
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
2
0
4
0
0
0
3
2
2
1
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
1
0
0
0
1
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
1
1
0
1
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
8
0
1
0
0
3
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
3
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
6
0
1
0
0
0
0
1
0
0
3
0
2
0
0
2
0
0
1
1
1
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
2
2
0
1
0
0
0
1
0
0
1
0
2
0
2
3
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
4
0
0
2
0
0
1
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
1
0
0
0
0
0
3
1
0
0
0
0
1
1
0
0
0
0
0
2
7
2
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
2
0
0
2
1
0
0
1
3
0
0
1
0
1
1
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
1
1
1
0
0
2
0
0
1
0
2
0
4
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
2
0
2
0
2
0
0
1
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
2
0
2
2
5
3
2
0
2
0
0
2
0
0
1
0
2
0
1
0
0
0
1
2
0
0
0
0
2
0
1
0
1
0
1
0
0
0
2
2
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
2
2
0
1
0
0
1
0
0
2
0
0
1
2
0
2
1
0
0
1
0
0
2
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
2
0
0
2
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
2
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
1
0
2
0
0
0
0
0
1
0
0
0
2
3
1
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
1
0
2
0
0
0
0
1
0
3
2
0
2
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
2
3
0
0
0
0
2
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
2
4
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
1
0
2
0
2
0
1
0
0
2
1
0
1
1
0
0
0
0
0
1
0
1
0
1
2
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
2
0
1
4
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
4
2
2
0
0
2
2
2
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
3
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
2
0
3
2
1
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
2
1
0
1
0
2
2
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
4
3
1
2
2
0
0
0
0
0
0
2
0
0
2
0
1
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
2
0
0
0
4
0
0
2
1
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
4
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
1
0
2
0
0
0
3
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
2
1
0
2
4
0
0
2
0
3
0
0
0
0
0
0
3
0
1
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
3
0
3
2
0
0
0
0
0
0
0
2
0
0
1
2
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
3
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
2
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
2
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
2
0
0
1
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
1
0
2
0
1
2
0
0
4
0
3
2
0
0
1
2
0
0
0
0
0
1
1
0
2
0
2
2
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
1
2
0
1
0
0
3
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
2
2
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
1
2
2
5
1
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
1
0
0
2
0
1
0
0
0
0
3
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
3
0
0
0
0
0
2
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
2
2
0
2
3
0
0
1
0
0
0
1
0
0
1
3
3
2
0
0
0
2
2
1
1
0
0
0
0
0
0
3
2
0
2
0
0
1
2
0
0
0
0
0
2
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
2
0
0
0
2
4
0
0
1
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
2
0
0
4
0
0
2
0
0
2
0
0
0
2
0
0
2
0
4
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
1
1
0
0
1
0
0
0
5
0
0
0
1
0
0
3
0
1
0
2
2
2
0
2
0
1
0
4
2
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
3
0
2
0
0
0
0
0
0
0
0
0
1
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
2
2
0
0
2
0
2
0
0
0
2
2
0
0
1
0
0
0
2
1
0
0
2
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
5
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
3
2
0
0
0
2
0
0
2
0
0
0
1
1
0
0
0
1
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
4
0
0
0
0
2
0
0
0
0
0
1
0
2
0
1
1
0
3
0
0
0
0
0
1
0
2
0
1
0
2
1
0
0
0
0
1
1
4
1
0
0
0
1
2
0
2
0
0
0
0
0
2
0
2
2
0
0
0
1
0
0
0
0
0
0
0
2
2
2
0
1
1
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
5
0
0
2
2
0
0
1
0
0
0
0
0
0
1
0
0
2
2
2
2
1
0
0
0
1
1
2
0
0
1
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
5
0
3
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
1
0
1
0
0
0
1
0
0
1
0
0
0
0
1
2
2
0
0
1
0
0
2
0
1
0
3
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
1
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
1
1
0
0
0
0
1
3
0
0
1
0
1
0
1
2
0
0
0
2
1
0
1
0
1
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
5
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
2
0
0
2
0
0
1
0
2
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
2
0
0
0
5
2
1
0
0
0
0
0
1
1
0
0
1
1
0
0
2
0
1
0
1
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
2
0
0
1
0
2
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
2
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
4
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
2
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
3
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
2
2
0
2
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
2
0
0
0
1
0
0
0
1
0
1
0
2
0
0
2
1
0
0
0
1
2
0
2
0
0
1
0
0
0
1
0
0
2
0
0
0
2
0
4
0
0
0
0
1
0
0
1
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
1
2
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
2
1
0
1
0
0
7
0
0
0
0
0
0
0
2
0
1
0
0
0
3
1
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
2
1
0
0
0
0
0
3
2
1
0
0
0
0
0
3
0
1
0
0
2
0
2
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
1
3
0
0
1
0
0
2
2
0
0
3
0
1
0
0
0
0
2
0
0
0
2
0
2
1
2
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
2
0
2
0
0
2
0
0
1
0
0
0
0
0
2
0
3
0
1
0
0
0
0
1
0
0
0
1
0
2
0
0
0
3
0
1
0
0
0
0
0
4
0
0
2
0
0
2
2
1
0
0
2
0
0
0
1
1
0
2
0
0
0
0
1
0
2
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
1
0
1
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
2
0
2
2
1
0
1
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
1
1
0
0
0
0
0
0
1
4
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
1
0
0
0
0
1
1
0
1
1
0
1
0
0
0
1
0
0
0
1
0
0
0
2
0
1
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
3
0
0
1
0
1
0
1
3
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
2
4
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
2
0
0
0
2
2
0
0
0
0
0
3
0
0
0
1
2
0
0
0
4
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
2
7
0
0
0
0
2
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
1
1
0
0
0
3
1
0
0
2
2
0
0
5
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
1
2
0
3
0
0
0
0
0
1
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
1
0
2
0
1
2
1
2
0
2
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
1
1
0
1
0
0
0
1
2
0
1
1
0
2
2
2
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
3
0
1
0
0
0
1
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
1
0
0
1
2
0
0
0
0
1
2
0
4
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
1
0
0
1
0
0
0
0
6
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
1
2
1
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
1
2
0
0
3
0
0
1
0
0
1
1
0
1
0
0
2
0
0
0
0
0
0
1
0
2
3
0
0
0
3
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
3
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
2
0
1
3
2
1
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
1
2
0
2
0
2
2
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
1
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
2
0
2
0
0
2
0
0
0
1
0
1
3
2
0
0
0
0
0
0
0
0
3
1
2
0
2
0
0
0
0
2
2
0
0
0
0
0
1
3
0
3
0
2
1
0
0
0
0
0
0
1
0
1
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
2
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
1
0
1
2
0
2
1
2
1
0
0
0
2
2
2
4
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
3
0
8
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
1
3
2
0
1
0
0
2
0
0
0
1
0
2
2
1
0
0
0
1
1
0
0
1
1
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
2
0
1
0
1
0
1
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
3
0
0
1
1
0
4
0
0
0
1
0
2
2
0
0
2
0
0
0
1
0
2
3
0
0
0
0
0
2
4
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
2
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
3
0
0
0
2
0
0
1
0
0
0
0
0
3
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
1
0
1
1
3
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
1
2
0
2
0
0
0
0
2
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
4
0
3
0
2
0
0
2
1
0
2
0
2
1
0
0
1
0
0
0
2
0
0
0
0
3
0
0
2
0
1
0
2
2
0
0
0
0
0
0
0
6
0
0
0
0
2
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
2
0
0
3
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
3
0
1
2
0
1
0
0
0
2
1
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
1
0
1
0
1
1
1
0
0
0
0
0
0
0
2
1
0
0
1
2
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
2
2
0
2
0
0
2
2
0
0
0
2
1
0
2
2
1
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
1
0
2
0
0
3
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
2
1
0
2
6
0
0
2
0
0
0
2
0
0
1
1
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
3
0
0
3
0
2
1
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
2
1
0
0
2
0
0
0
1
0
1
0
2
0
0
1
0
0
1
0
2
0
2
0
0
1
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
5
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
5
0
2
0
0
0
0
1
0
0
0
0
1
1
0
0
1
2
0
0
1
0
0
0
0
1
0
0
0
0
1
1
1
0
3
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
3
4
0
0
0
0
2
0
0
0
3
0
0
0
3
0
2
2
0
1
2
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
1
2
2
1
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
2
0
0
2
1
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
3
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
1
1
0
0
0
2
0
0
1
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
1
1
0
0
4
1
0
0
0
2
1
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
1
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
5
0
1
0
0
0
0
1
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
2
0
0
0
0
2
0
2
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
3
0
0
2
0
2
0
0
0
1
0
2
0
0
0
0
2
0
2
2
0
1
0
1
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
1
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
4
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
3
0
1
1
0
0
0
0
0
0
2
1
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
1
1
0
0
2
0
0
2
1
1
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
3
0
3
0
2
0
1
0
0
2
2
0
4
0
0
0
0
0
0
2
2
2
0
0
0
1
0
2
0
2
0
0
0
1
1
1
0
0
0
0
1
0
1
1
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
2
0
0
0
3
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
3
3
0
0
0
0
0
2
0
1
0
0
0
0
27
2
0
0
0
0
0
2
1
1
3
2
0
0
0
1
0
0
1
0
2
0
0
2
0
0
0
0
3
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
2
1
2
2
0
1
5
2
0
0
0
0
0
0
1
0
0
0
0
1
1
2
0
2
0
2
0
1
0
5
1
0
1
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
2
1
0
0
2
0
1
3
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
2
0
0
7
0
0
1
1
0
2
0
1
1
0
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
2
0
0
0
1
1
1
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
2
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
2
2
0
1
2
0
1
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
1
3
0
0
0
0
0
0
2
1
0
0
1
0
2
0
0
0
2
1
2
0
0
0
0
3
2
0
1
0
1
1
0
3
2
0
1
0
2
0
1
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
2
1
0
0
1
0
2
0
0
0
1
0
1
0
0
0
0
4
3
0
0
0
0
0
2
2
0
0
1
0
2
2
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
2
1
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
2
0
0
4
2
0
0
0
0
2
2
0
2
3
0
0
2
10
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
1
2
0
2
2
0
0
0
1
0
2
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
2
0
3
0
0
0
0
0
0
2
0
0
2
0
0
3
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
1
0
0
0
2
0
0
1
0
2
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
2
0
0
2
1
0
0
1
2
0
1
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
4
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
2
0
0
0
2
0
2
0
0
6
0
0
2
0
0
0
0
2
0
0
2
0
0
2
0
0
3
1
2
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
3
2
0
0
0
3
1
1
1
0
0
1
0
0
0
0
1
0
0
0
1
0
2
0
1
1
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
2
0
1
0
2
0
0
1
0
1
0
0
1
2
1
1
1
2
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
1
3
1
1
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
1
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
2
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
4
1
0
0
0
0
2
0
0
0
0
0
1
2
0
13
1
0
0
0
0
0
0
0
4
0
14
0
2
0
2
0
1
0
0
2
1
0
0
0
2
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
2
0
0
0
0
0
0
1
2
0
2
1
1
0
0
0
0
0
0
0
2
0
1
0
0
0
4
4
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
6
0
0
0
1
2
0
0
0
2
0
1
0
0
2
0
0
2
0
0
0
0
0
0
1
1
0
2
0
4
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
2
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
1
2
2
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
1
0
0
1
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
3
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
2
0
0
0
2
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
2
1
1
0
0
0
2
0
0
1
3
2
0
0
2
0
0
0
0
1
0
2
0
0
0
0
1
0
1
2
0
0
0
0
2
2
0
2
0
0
0
0
0
2
3
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
1
0
1
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
2
0
0
8
0
0
0
0
0
2
2
0
1
0
0
0
0
1
1
0
0
2
0
0
2
0
0
1
0
0
0
2
0
2
1
0
0
0
1
2
1
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
2
0
1
0
0
0
1
1
2
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
7
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
3
0
0
0
0
0
3
1
0
1
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
1
2
1
1
0
0
0
0
0
0
0
1
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
3
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
6
1
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
1
2
0
1
0
1
1
0
0
2
0
0
0
0
1
0
2
0
3
1
0
1
0
2
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
3
0
0
0
1
2
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
2
2
0
1
0
3
1
1
0
0
2
0
0
0
1
0
0
0
1
3
2
3
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
5
2
0
0
2
0
0
0
0
0
0
1
2
4
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
2
0
2
0
1
0
1
1
0
0
0
3
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
2
0
0
2
1
0
2
0
2
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
1
1
3
0
0
2
4
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
3
0
1
0
2
0
0
2
5
0
0
0
2
0
0
1
0
1
1
3
10
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
6
0
0
2
0
0
0
1
1
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
2
1
0
1
0
1
0
2
0
0
0
1
0
0
1
0
0
3
0
2
0
3
1
0
0
0
0
1
0
0
0
1
1
0
2
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
3
1
0
0
2
0
1
0
1
0
3
0
0
0
3
1
0
3
0
0
1
2
0
1
3
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
1
0
2
1
0
0
0
0
1
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
1
2
1
1
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
5
0
2
0
0
2
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
1
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
9
0
3
1
2
0
3
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
1
0
2
0
1
0
0
0
0
0
2
0
1
0
2
0
1
0
2
0
2
0
2
0
0
2
0
0
2
0
1
2
0
0
2
2
0
0
0
0
0
0
0
0
1
4
0
1
2
2
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
1
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
3
0
1
0
0
0
1
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
2
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
1
2
0
0
2
2
0
0
1
1
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
1
2
1
0
2
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
2
1
0
0
0
0
2
2
0
0
2
1
0
0
1
2
0
0
2
0
0
1
0
0
0
0
2
0
4
0
0
1
1
1
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
1
0
2
0
2
1
1
0
0
2
0
2
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
2
0
2
1
2
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
3
1
1
0
0
0
0
0
0
2
1
2
0
2
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
5
1
0
0
0
1
0
0
1
3
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
1
2
0
0
0
0
2
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
2
0
2
0
0
0
0
0
2
0
0
2
0
0
0
1
0
1
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
1
0
0
0
1
0
0
2
0
0
1
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
2
1
2
0
0
0
0
2
1
0
0
0
0
3
0
0
0
0
1
0
0
1
0
0
2
0
2
1
0
0
0
0
0
2
0
0
0
1
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
5
0
2
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
1
2
0
0
0
2
2
0
1
0
0
0
2
0
1
1
0
2
0
2
0
2
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
3
0
0
2
0
0
0
1
2
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
1
1
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
4
0
0
0
0
0
1
2
0
0
0
0
3
0
2
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
1
0
2
2
0
0
2
0
0
1
2
0
2
0
0
2
0
0
2
4
0
0
2
2
2
0
2
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
2
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
1
0
3
0
0
1
0
3
0
2
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
2
2
0
0
1
2
0
0
0
0
0
2
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
1
1
0
1
0
0
1
0
0
0
1
3
2
0
0
3
0
0
0
0
0
2
0
0
0
0
0
1
1
0
1
0
0
0
0
2
0
1
1
0
0
0
1
3
2
2
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
3
3
0
0
0
0
1
0
1
0
0
0
2
0
1
0
1
0
0
3
2
1
2
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
3
0
0
0
0
0
0
1
0
0
0
6
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
1
2
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
1
0
0
0
1
1
0
2
1
0
1
0
1
0
2
2
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
5
1
0
0
1
0
0
0
0
0
1
0
2
2
0
0
0
1
0
0
0
0
2
0
2
0
1
0
0
0
0
1
4
0
2
0
1
0
0
0
1
0
0
0
0
0
1
2
1
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
2
1
0
0
0
2
0
1
2
0
0
1
0
0
0
2
0
0
0
2
2
0
1
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
2
0
0
0
0
2
1
9
0
0
0
0
0
1
2
2
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
2
2
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
2
1
0
0
1
0
0
0
0
1
0
1
0
0
0
2
1
0
0
1
0
0
0
0
0
0
3
0
1
0
0
0
0
1
0
4
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
1
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
1
0
0
3
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
1
0
1
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
3
2
2
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
1
0
0
0
0
0
0
3
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
3
0
7
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
2
0
1
0
0
1
2
2
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
1
2
1
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
2
0
1
0
0
1
0
1
2
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
1
0
0
0
1
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
3
0
1
0
0
0
2
0
0
0
1
0
0
2
0
1
2
0
0
2
0
0
0
2
0
0
0
0
0
2
2
3
0
1
1
0
0
2
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
2
1
0
1
2
0
0
0
8
0
0
0
0
0
2
2
0
0
2
0
0
0
2
2
1
2
0
0
1
0
0
0
0
1
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
1
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
2
0
3
0
1
0
2
1
0
2
2
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
2
0
0
0
2
2
0
2
0
2
0
0
0
3
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
2
2
0
2
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
8
2
0
0
0
0
0
0
0
0
2
2
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
1
0
2
0
0
0
0
0
0
1
0
0
4
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
3
1
0
0
0
4
1
0
0
2
0
2
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
1
2
1
3
0
2
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
2
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
3
0
1
0
0
0
0
0
1
0
0
2
0
0
0
2
0
1
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
2
1
0
3
0
0
1
2
0
0
5
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
4
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
1
2
0
2
0
0
0
0
0
0
0
0
2
2
0
3
0
1
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
1
0
3
0
1
0
2
1
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
3
0
2
0
0
0
1
1
0
3
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
1
0
2
2
0
2
1
0
0
0
0
0
0
0
2
2
0
0
0
2
4
0
3
0
1
0
2
0
0
0
0
0
0
1
0
0
1
0
2
0
2
0
1
0
0
0
0
0
0
0
0
2
0
5
1
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
2
0
0
1
1
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
2
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
2
2
0
0
1
3
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
1
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
1
2
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
9
0
0
0
0
0
3
0
1
2
4
0
0
0
0
0
2
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
1
0
0
0
2
1
0
0
0
0
0
0
1
0
1
0
1
0
1
0
2
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
2
0
0
0
1
0
0
2
0
0
2
0
0
5
0
0
2
0
1
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
4
0
0
0
0
0
0
0
4
1
0
0
0
0
1
0
0
2
0
1
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
1
2
3
0
2
1
2
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
2
1
1
2
0
1
0
0
0
2
0
0
0
2
0
0
0
1
2
0
0
0
6
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
1
0
0
0
2
0
0
0
1
0
0
0
1
0
2
0
4
0
1
2
1
0
0
0
0
0
0
0
0
0
0
2
3
0
2
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
1
3
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
4
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
4
1
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
1
2
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
1
0
3
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
3
0
0
2
0
1
0
2
0
2
0
0
2
0
2
0
0
0
0
2
0
2
0
0
0
0
3
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
2
0
2
0
0
0
0
1
0
0
1
2
1
0
9
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
3
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
1
1
0
2
0
0
0
0
1
0
0
0
2
0
0
1
1
0
3
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
3
0
0
2
4
2
3
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
1
0
2
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
2
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
1
0
2
0
0
0
1
1
1
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
1
0
0
2
0
1
2
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
1
0
3
0
0
1
0
0
2
0
2
0
0
0
1
0
1
0
0
0
0
1
6
0
0
1
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
2
0
0
0
3
0
0
0
0
0
3
0
2
0
0
0
0
2
0
0
0
0
4
0
0
0
0
0
0
3
0
2
0
0
0
2
0
3
1
2
8
0
0
0
1
2
0
0
2
0
2
1
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
1
4
0
2
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
1
0
2
0
1
0
1
0
2
1
0
0
0
0
0
0
1
2
1
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
1
0
2
1
0
0
1
0
1
2
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
3
0
0
0
1
2
1
0
0
0
2
2
2
0
0
2
0
7
2
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
3
0
2
0
1
0
0
0
2
0
1
0
4
1
0
2
2
2
2
0
4
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
1
0
9
2
0
0
1
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
1
0
2
0
0
2
2
0
0
1
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
3
0
0
1
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
2
3
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
3
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
1
1
1
0
0
0
1
1
0
0
0
0
0
1
0
1
0
2
0
1
0
0
3
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
2
0
0
1
0
0
0
0
2
0
1
2
0
2
0
2
0
2
0
2
1
1
0
2
1
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
3
0
0
0
0
3
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
1
2
1
0
1
0
0
1
2
0
0
0
0
1
0
0
0
0
0
1
2
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
2
0
0
0
0
1
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
1
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
3
0
2
0
0
2
0
4
4
1
0
0
0
0
0
0
0
1
0
0
0
0
1
4
0
0
0
0
0
0
0
2
0
0
3
1
0
1
0
0
0
1
0
0
1
0
3
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
1
0
6
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
1
1
0
0
0
0
2
0
1
2
0
0
0
0
3
0
1
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
2
0
1
0
1
0
2
0
2
0
0
0
1
1
2
2
0
2
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
4
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
2
2
0
2
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
1
3
0
0
0
0
1
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
2
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
1
0
0
2
0
1
0
1
0
2
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
1
0
0
0
0
2
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
4
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
2
0
2
0
2
0
2
0
0
0
0
2
2
0
0
2
2
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
1
2
2
0
0
0
0
0
0
0
2
0
0
1
2
2
0
1
1
2
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
2
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
1
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
1
0
0
0
0
6
4
2
0
2
0
1
1
0
0
0
0
0
2
4
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
1
1
0
1
0
3
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
2
0
0
1
0
0
2
0
0
0
1
0
1
0
0
0
0
2
1
2
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
1
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
4
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
3
2
0
0
0
0
1
0
0
0
0
0
1
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
1
0
2
2
1
0
0
2
0
2
0
1
0
0
0
0
0
0
2
0
0
0
1
1
0
2
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
4
0
0
0
0
2
0
2
0
0
0
2
0
0
1
0
0
0
2
2
0
1
2
0
0
1
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
6
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
1
0
0
0
0
0
0
2
0
2
0
1
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
5
0
0
6
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
5
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
5
2
0
1
0
0
0
0
0
1
0
0
2
2
0
0
1
0
2
2
0
1
0
0
0
1
3
5
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
1
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
1
0
2
0
0
0
0
3
0
0
0
1
2
1
0
2
0
0
2
1
0
0
0
0
0
1
0
0
1
0
0
0
2
2
0
0
0
0
0
1
1
0
2
0
0
0
2
0
0
0
0
0
2
0
1
0
2
2
0
0
2
0
1
1
1
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
3
0
0
0
0
3
0
0
0
0
1
0
0
0
0
1
1
1
0
1
1
0
0
0
2
2
0
0
1
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
5
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
4
0
1
1
0
0
0
0
0
3
1
0
1
0
0
0
0
0
0
0
1
2
0
2
0
0
1
0
1
2
0
0
0
1
0
1
0
0
0
0
0
3
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
3
0
1
0
0
0
2
2
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
12
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
1
1
0
0
3
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
2
0
1
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
1
5
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
2
0
0
0
1
1
0
0
0
0
1
1
1
1
0
2
2
0
2
0
0
1
0
0
0
0
0
8
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
2
1
0
0
0
0
0
0
0
0
0
0
2
1
1
0
2
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
2
6
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
1
0
2
0
0
1
0
0
2
0
0
0
9
0
2
0
2
1
0
0
0
0
0
1
1
0
2
0
0
0
0
1
0
0
3
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
2
0
0
2
2
1
0
1
2
0
0
2
0
0
0
2
0
0
0
3
0
0
1
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
2
1
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
1
0
0
0
0
1
4
0
1
0
3
0
0
4
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
3
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
2
1
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
3
0
1
1
0
3
2
0
2
0
1
2
0
0
0
0
0
1
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
1
0
0
2
0
3
0
0
1
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
2
0
1
0
0
1
1
0
0
2
0
0
0
2
0
1
0
2
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
4
1
0
0
0
3
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
1
1
2
0
0
1
4
2
2
0
0
0
2
0
1
0
2
1
0
2
0
2
0
3
2
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
1
1
0
1
0
0
0
0
0
2
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
3
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
1
1
1
0
1
0
1
0
1
1
2
2
2
0
0
0
2
0
1
1
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
2
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
1
0
0
2
0
1
0
0
1
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
1
0
3
3
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
1
1
0
2
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
2
3
0
0
1
0
2
1
0
0
0
1
0
0
0
0
0
2
0
0
3
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
4
0
0
2
0
0
0
3
0
0
2
0
0
1
3
0
0
1
1
0
0
2
0
0
1
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
3
4
1
0
0
0
2
0
0
0
1
0
2
0
1
0
2
0
0
2
2
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
1
2
1
2
0
2
0
0
0
1
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
1
0
0
2
1
0
0
0
0
0
1
2
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
2
1
0
0
3
0
2
2
0
1
0
2
0
1
1
0
2
0
2
0
0
1
0
0
1
1
2
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
2
0
1
0
0
0
5
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
1
1
1
0
0
0
0
1
0
0
0
0
2
2
4
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
1
0
3
0
0
1
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
1
1
0
1
1
0
0
0
1
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
1
0
2
2
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
2
0
1
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
2
1
1
0
0
0
0
1
2
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
3
2
2
1
2
2
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
2
2
2
1
0
1
0
0
0
2
0
0
2
0
0
1
1
0
0
0
0
0
0
0
2
2
0
1
1
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
2
0
0
0
0
0
1
0
4
1
2
0
1
2
1
2
0
0
2
0
0
0
2
1
2
0
0
0
1
0
1
1
0
0
2
0
1
1
0
0
2
1
1
0
1
0
0
0
0
2
2
3
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
4
1
0
1
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
3
0
0
0
0
2
0
1
2
0
0
0
0
1
1
0
0
0
2
0
2
0
0
1
1
0
2
0
0
3
1
0
0
0
2
0
0
0
0
0
3
0
0
0
1
0
1
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
2
0
0
0
2
0
0
0
0
0
1
0
1
2
0
0
0
2
2
0
0
3
0
0
0
0
0
0
2
0
0
0
1
0
2
1
0
0
0
0
1
0
2
0
1
0
0
0
1
0
0
0
0
0
2
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
2
1
0
3
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
3
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
2
0
1
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
2
0
0
0
0
1
2
0
0
7
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
4
2
0
2
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
1
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
1
2
0
0
1
0
0
2
0
1
0
0
0
2
0
0
2
0
1
0
1
1
0
1
0
0
0
1
3
3
0
0
2
0
0
0
0
2
1
2
0
0
0
0
3
2
0
0
1
0
0
0
0
0
0
1
1
0
0
3
0
0
2
0
2
2
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
1
2
0
0
0
0
2
0
2
0
0
1
0
0
0
0
1
1
0
1
0
0
0
2
1
0
2
0
2
0
0
0
0
0
0
0
1
0
1
5
0
0
1
0
0
2
2
0
0
1
0
0
0
0
1
2
0
1
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
2
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
2
0
0
0
5
0
0
0
0
2
1
1
0
0
2
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
1
3
2
6
5
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
1
3
0
1
5
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
3
0
0
1
0
0
0
2
0
0
2
8
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
2
1
0
0
0
0
4
2
0
2
1
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
1
0
0
0
0
0
2
0
0
1
0
1
0
2
0
3
3
1
0
1
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
4
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
1
1
2
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
1
2
0
1
1
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
3
0
0
1
0
0
0
0
1
1
1
2
2
0
0
0
1
0
0
0
0
0
0
1
3
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
3
0
0
0
0
0
2
0
8
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
2
0
3
4
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
1
0
0
2
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
2
2
0
0
1
0
1
0
1
0
2
2
3
0
0
1
0
0
0
0
2
0
1
0
0
0
1
0
1
0
0
1
0
1
3
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
2
1
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
3
0
1
1
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
2
1
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
2
0
1
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
1
2
0
0
1
3
0
0
0
0
0
0
1
0
0
0
1
4
0
0
0
4
0
2
2
0
1
0
0
1
2
0
0
1
0
0
2
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
1
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
2
0
0
0
1
4
0
0
0
0
0
0
0
1
0
0
0
2
0
2
1
0
0
0
0
2
1
0
0
1
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
3
0
0
2
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
2
0
2
1
2
1
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
2
3
1
5
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
3
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
2
1
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
2
0
0
0
1
3
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
2
1
1
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
3
2
0
0
2
0
0
3
1
0
1
0
0
0
1
0
2
1
0
0
1
1
0
0
0
0
0
2
1
2
1
0
0
0
2
1
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
2
3
0
2
0
0
0
1
2
0
0
0
0
0
0
2
0
1
2
0
0
2
0
0
0
1
0
2
0
0
2
1
0
1
1
0
2
0
0
0
0
0
1
1
0
1
0
2
0
0
0
1
0
0
0
0
0
0
4
3
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
3
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
1
1
2
0
0
0
0
1
0
0
0
0
0
0
3
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
1
0
1
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
1
0
0
0
0
0
0
2
2
2
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
1
0
0
1
7
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
3
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
3
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
1
0
7
0
1
0
0
2
0
0
2
0
0
0
1
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
2
0
0
1
1
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
1
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
1
1
0
7
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
3
1
0
0
0
0
0
0
1
0
0
0
0
2
1
1
1
1
0
0
0
0
0
2
0
0
0
0
2
1
1
0
2
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
3
0
0
0
1
0
0
0
1
0
2
1
2
0
0
2
0
0
0
0
1
0
0
0
0
0
2
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
2
1
3
2
0
0
0
0
0
0
1
0
0
2
1
0
2
2
2
3
0
0
4
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
2
0
4
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
3
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
2
0
2
0
0
0
2
0
0
0
3
1
4
0
1
0
4
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
1
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
2
0
1
1
0
0
1
0
0
0
0
1
3
0
1
0
0
0
0
0
0
0
1
2
0
0
1
2
1
0
4
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
3
2
0
0
1
0
0
0
0
1
0
0
0
0
2
1
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
2
0
1
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
2
0
2
5
0
0
0
0
1
0
0
0
0
0
0
2
0
3
0
2
0
0
2
2
2
0
1
0
0
0
1
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
2
1
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
2
0
0
1
0
0
0
0
2
1
0
1
0
0
1
0
0
0
3
0
1
0
1
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
3
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
2
0
0
5
0
0
0
0
0
0
0
1
0
1
3
2
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
3
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
3
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
8
0
0
2
0
3
0
0
0
0
1
0
0
0
0
1
0
0
1
0
2
1
2
0
0
0
0
0
0
0
0
0
2
1
0
5
0
0
1
1
2
0
0
0
0
0
1
2
0
1
0
0
0
0
2
1
0
0
0
0
0
2
1
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
2
1
1
1
2
2
0
5
2
1
2
1
0
0
2
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
1
1
2
0
1
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
2
1
0
0
0
0
0
0
0
0
2
2
0
2
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
2
2
0
0
1
0
0
4
0
0
1
0
0
0
0
4
0
0
0
0
1
2
1
0
1
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
1
0
2
0
0
2
2
0
0
0
1
1
1
0
0
0
0
1
0
0
0
1
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
1
1
0
0
1
0
0
0
0
2
0
0
2
2
2
0
0
1
2
0
0
0
1
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
5
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
4
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
1
1
0
1
2
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
2
0
0
2
0
2
2
0
0
0
0
2
0
0
1
0
1
0
0
0
1
0
0
0
2
2
0
0
1
1
2
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
4
2
0
0
1
0
0
0
0
1
0
0
0
0
0
5
0
0
2
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
2
0
0
2
2
0
0
0
3
0
1
3
0
1
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
4
1
1
0
1
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
1
0
2
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
2
0
2
0
2
0
1
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
2
0
0
3
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
1
2
0
0
0
0
0
0
1
2
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
1
1
3
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
1
2
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
5
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
1
0
0
0
0
1
0
0
2
0
1
1
1
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
2
2
0
0
0
0
3
0
2
1
2
1
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
2
1
0
0
0
2
0
2
3
1
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
4
0
0
2
0
1
3
0
2
0
0
1
0
3
0
0
2
0
1
0
1
0
1
0
2
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
2
1
0
0
0
0
0
0
2
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
3
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
3
0
1
1
0
0
2
1
0
0
4
1
0
0
1
1
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
2
0
0
3
0
1
3
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
8
0
0
0
0
1
1
0
0
1
2
2
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
2
0
1
0
0
2
0
1
0
0
0
2
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
2
0
0
0
1
1
0
0
0
0
0
0
0
3
0
0
0
2
0
0
2
2
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
1
0
0
2
0
1
0
0
1
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
3
0
0
1
0
1
2
0
0
0
0
0
3
1
1
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
5
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
5
2
1
1
1
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
4
1
5
0
3
0
0
0
1
0
1
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
4
3
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
2
0
2
0
2
0
0
0
0
1
2
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
2
3
1
0
0
0
2
0
0
2
0
0
0
0
0
1
0
1
0
2
0
0
0
0
1
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
1
1
0
0
0
0
1
6
0
2
0
0
4
0
0
2
0
0
2
0
1
0
0
2
0
1
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
1
0
0
0
0
4
1
0
1
0
0
0
0
2
0
0
1
2
0
1
0
0
0
0
0
1
0
0
1
1
2
3
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
2
2
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
2
0
1
0
3
1
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
1
0
0
3
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
1
0
1
3
0
0
2
1
1
3
0
2
0
0
1
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
1
2
0
0
0
0
0
0
2
0
0
0
1
5
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
9
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
2
2
0
2
0
1
0
0
0
0
0
2
0
0
3
0
1
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
4
0
3
0
0
1
0
1
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
2
0
0
0
1
0
1
2
0
0
1
2
0
1
0
0
2
0
0
1
0
1
0
0
0
2
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
2
1
0
0
0
0
0
2
3
2
2
0
0
0
0
0
2
5
0
0
0
3
0
0
0
5
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
4
0
0
2
1
0
1
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
2
0
0
0
0
2
1
1
0
0
2
0
2
0
0
0
2
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
2
0
0
1
0
0
0
0
0
2
2
2
0
2
2
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
2
0
2
0
0
2
2
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
2
0
0
0
0
1
0
0
2
0
0
1
1
0
0
0
0
2
2
0
1
0
0
0
0
0
2
1
1
1
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
1
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
2
1
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
1
0
2
2
2
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
2
0
0
1
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
2
0
4
0
2
1
2
0
0
0
3
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
2
0
0
0
0
2
0
0
2
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
2
2
1
0
0
1
0
0
2
0
0
0
2
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
1
2
1
0
0
1
0
0
0
0
14
0
0
0
2
0
2
0
0
5
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
1
0
0
0
0
0
5
0
1
0
0
2
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
2
0
1
2
0
0
0
2
0
1
3
1
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
4
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
1
2
1
0
0
0
0
2
0
0
2
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
2
1
0
0
0
0
2
1
0
3
0
0
0
0
2
0
0
2
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
7
0
0
0
0
0
0
0
2
0
1
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
1
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
1
1
0
0
0
0
2
0
1
1
0
1
0
2
0
2
0
0
0
0
3
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
2
0
0
0
2
3
0
0
0
1
0
0
1
1
0
0
0
2
0
2
0
1
0
0
0
0
0
2
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
1
0
0
0
1
3
1
0
0
0
1
0
0
2
0
1
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
4
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
2
2
0
1
0
1
0
3
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
1
0
2
1
0
0
0
0
1
0
1
2
1
0
0
0
1
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
2
2
0
1
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
2
0
0
0
0
2
2
2
1
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
2
2
2
0
0
0
0
0
0
1
1
0
3
1
0
1
3
2
0
0
0
0
0
1
4
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
1
2
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
1
1
2
0
2
0
1
3
0
0
2
0
0
0
0
1
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
5
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
1
2
0
2
0
0
1
0
1
1
0
1
0
0
0
0
0
0
2
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
2
1
0
2
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
7
1
2
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
1
0
1
0
0
0
0
0
2
1
5
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
1
0
2
0
2
0
1
0
0
1
0
3
0
1
0
0
0
2
0
1
0
0
1
2
1
0
2
3
0
2
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
2
2
0
0
0
3
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
2
0
2
0
0
1
2
0
0
0
0
0
0
0
2
1
0
0
3
0
2
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
4
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
2
0
0
3
1
0
0
2
0
0
0
2
0
2
0
0
1
0
0
1
0
2
0
3
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
5
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
2
2
2
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
2
0
0
1
1
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
10
2
0
3
3
0
2
2
0
1
0
0
0
0
0
2
0
1
0
0
0
2
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
2
0
1
0
2
0
0
0
0
0
3
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
1
2
0
1
0
0
0
0
1
2
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
2
1
0
0
1
1
0
0
1
0
1
0
1
0
2
0
0
2
1
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
2
0
0
0
1
2
0
2
0
0
2
3
2
0
0
0
3
0
1
5
0
0
0
2
2
0
0
0
6
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
1
0
2
1
0
0
0
0
6
0
0
0
0
0
0
1
0
2
0
1
0
2
0
0
0
0
0
0
2
0
0
2
0
3
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
1
0
6
0
1
0
1
0
2
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
2
0
1
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
3
1
0
0
0
2
1
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
3
0
2
2
0
4
0
2
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
2
0
0
0
0
1
0
0
6
0
0
0
0
0
0
0
2
0
0
0
1
5
0
1
1
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
3
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
3
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
3
0
0
0
1
0
2
0
0
1
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
1
1
0
0
3
1
1
0
0
2
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
3
3
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
2
2
0
1
0
1
0
0
0
0
2
1
1
0
0
0
0
2
0
1
0
0
1
1
0
1
2
2
0
0
1
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
1
0
0
2
0
1
6
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
1
4
0
0
0
0
1
0
0
2
0
0
0
1
0
0
3
0
2
1
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
4
0
0
0
0
0
2
2
0
0
2
1
1
0
3
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
3
0
1
7
0
0
0
2
0
0
2
0
0
0
0
0
2
0
1
2
1
2
0
1
0
0
1
1
2
0
0
1
2
0
0
1
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
1
0
2
2
0
3
1
2
2
0
0
0
0
1
0
0
5
0
0
1
0
0
0
0
0
1
0
1
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
5
0
1
0
0
0
0
2
0
2
1
2
4
0
0
0
2
0
0
2
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
2
0
1
0
2
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
1
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
1
0
2
0
2
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
2
2
0
2
0
0
2
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
1
1
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
3
0
2
0
0
0
0
0
0
0
0
0
3
1
1
0
0
0
0
0
0
2
0
0
0
0
2
0
3
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
1
0
0
0
0
1
0
1
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
2
0
0
0
1
0
3
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
4
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
3
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
1
0
1
0
0
0
1
2
1
2
0
0
2
0
0
0
2
2
0
2
5
0
0
1
2
0
3
0
3
2
0
0
0
2
0
0
0
1
1
1
0
3
0
0
2
0
0
2
0
0
2
1
0
0
1
1
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
1
0
1
0
2
0
2
0
0
1
0
0
0
2
0
2
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
4
0
1
2
0
0
2
0
1
1
0
0
0
0
0
1
2
3
0
0
0
0
0
0
2
1
0
2
0
0
1
0
0
2
0
0
0
0
2
0
1
1
1
1
0
0
0
1
0
0
0
0
1
4
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
6
2
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
2
1
0
0
2
1
2
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
2
0
0
3
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
1
0
0
3
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
1
0
1
0
3
0
1
0
0
0
0
1
3
0
0
0
2
2
2
0
0
0
1
2
2
3
0
2
0
1
2
0
0
2
0
1
0
1
0
2
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
3
2
0
0
0
0
0
0
1
1
0
0
2
2
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
6
2
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
2
2
0
1
0
2
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
1
0
1
0
0
0
0
0
0
2
0
0
3
2
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
1
2
0
1
0
1
0
0
0
1
0
1
1
0
0
0
0
0
1
1
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
1
0
0
2
0
1
0
0
0
0
0
2
2
0
0
0
3
1
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
2
1
1
0
2
0
0
1
0
0
3
2
1
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
11
0
0
2
0
0
0
1
2
0
0
2
2
0
0
0
0
0
2
1
0
1
2
2
0
2
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
3
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
1
0
0
2
0
2
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
1
2
0
0
0
1
1
1
0
2
1
0
0
0
0
2
0
0
0
2
0
0
0
0
1
2
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
1
0
2
2
0
3
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
3
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
3
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
3
0
0
1
0
0
1
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
1
2
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
2
2
0
0
1
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
2
1
0
0
0
0
0
0
2
1
0
1
0
1
0
0
0
0
0
1
0
0
2
0
1
0
2
1
0
0
3
0
0
0
0
0
4
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
2
0
0
1
0
2
0
0
2
0
0
0
2
2
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
2
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
1
2
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
1
2
0
0
2
2
2
0
1
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
3
0
1
0
0
0
0
0
2
0
1
0
0
1
0
2
4
1
0
0
6
0
0
0
1
0
2
0
0
0
0
2
0
2
0
0
1
1
0
0
0
2
0
2
1
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
1
0
0
1
0
0
0
0
1
0
1
0
0
2
0
0
2
0
2
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
2
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
5
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
2
0
0
0
0
2
0
0
0
2
0
4
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
2
2
0
0
0
0
2
0
0
1
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
1
2
0
0
0
2
0
0
2
2
0
1
2
2
0
0
1
1
0
1
0
0
0
4
0
2
0
2
2
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
5
0
1
3
0
0
0
0
0
3
0
1
0
0
0
2
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
2
2
0
0
0
0
0
0
0
0
3
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
2
0
2
0
1
1
0
0
1
0
0
0
0
1
0
0
2
2
2
0
0
0
0
2
0
0
3
0
0
0
3
0
0
2
1
2
4
2
0
2
0
0
0
2
1
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
2
0
1
2
0
0
0
1
0
1
0
0
3
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
2
0
0
0
0
0
2
0
2
0
0
1
0
4
0
1
1
0
0
1
0
2
0
4
0
0
0
1
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
5
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
2
0
2
0
0
0
3
0
1
1
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
2
1
0
0
0
0
0
9
0
0
0
0
2
1
0
2
0
1
2
0
0
2
0
1
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
3
0
0
0
1
2
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
3
0
2
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
1
0
1
12
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
1
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
4
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
1
2
1
0
0
0
0
0
2
0
1
0
0
2
3
0
0
1
0
0
2
0
0
0
1
0
0
0
3
0
0
2
0
0
0
0
0
3
1
0
0
0
0
0
0
3
0
0
4
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
5
0
1
0
0
3
4
0
0
0
0
0
1
1
0
1
1
2
0
0
0
0
0
0
0
0
0
2
2
2
1
2
0
1
0
0
0
0
0
0
0
1
0
0
3
0
2
0
0
0
2
0
2
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
1
0
1
2
0
0
3
2
0
0
0
1
6
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
3
2
0
2
0
2
0
2
1
0
10
0
0
2
0
0
0
0
0
1
0
0
0
22
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
1
0
0
1
5
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
2
0
1
1
0
0
2
0
1
0
0
0
2
2
0
0
0
0
1
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
2
0
0
1
1
1
1
0
0
2
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
1
0
3
0
0
0
0
2
0
0
1
0
0
2
0
0
0
1
0
0
0
0
1
2
0
3
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
2
1
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
2
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
3
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
1
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
2
0
2
0
1
0
2
0
0
0
1
0
1
0
3
0
0
0
1
4
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
1
0
0
2
0
0
0
0
1
1
0
0
0
0
0
2
0
0
2
0
0
3
2
1
0
0
0
0
0
1
1
2
0
0
5
1
0
0
0
0
0
0
2
0
1
1
0
1
1
1
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
1
0
1
0
0
1
1
1
0
0
0
0
0
1
0
3
4
1
2
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
2
6
0
0
0
2
0
0
0
0
0
0
0
1
3
1
1
0
4
2
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
1
1
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
1
0
0
0
1
0
3
0
0
0
2
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
2
0
0
1
0
2
0
0
1
0
0
0
0
2
0
0
0
3
0
0
1
0
0
1
2
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
2
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
6
0
0
0
0
0
3
2
0
0
2
0
0
0
0
0
1
0
3
0
2
0
2
0
0
0
2
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
5
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
1
0
5
0
0
0
1
0
0
0
2
0
2
1
0
2
0
0
1
0
2
6
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
2
2
0
0
1
0
5
0
0
6
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
3
0
2
1
2
0
0
0
3
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
2
5
0
0
1
1
0
1
1
0
0
0
0
0
0
2
1
1
0
2
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
2
1
1
0
0
0
0
0
0
0
2
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
1
0
0
2
0
2
2
1
0
0
0
0
0
0
0
0
0
2
1
1
2
0
1
2
0
0
2
0
0
0
1
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
1
1
0
0
2
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
1
1
0
2
0
0
0
0
1
0
1
0
2
1
0
0
1
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
4
2
0
0
0
0
2
1
0
0
0
4
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
1
0
0
0
2
0
0
1
0
0
0
0
2
0
1
0
0
0
1
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
3
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
3
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
1
0
0
0
0
1
1
1
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
3
0
0
4
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
2
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
1
1
0
0
2
0
0
0
2
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
1
2
2
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
2
0
0
2
0
0
2
2
0
0
0
0
2
0
1
0
7
0
0
0
0
0
1
0
1
2
2
0
0
0
2
0
0
1
5
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
1
0
1
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
4
0
3
0
6
1
0
0
2
0
2
0
0
0
2
1
0
0
0
0
0
0
1
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
2
3
0
0
0
0
0
0
0
0
0
1
0
1
2
0
1
0
0
1
0
0
0
0
3
0
0
0
0
0
1
0
1
0
1
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
1
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
2
1
1
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
7
2
0
2
1
0
0
1
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
3
0
0
3
0
0
0
1
0
0
0
0
0
0
2
0
0
1
1
4
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
1
0
0
2
0
2
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
4
3
1
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
2
0
0
2
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
3
0
0
0
2
0
0
2
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
3
0
1
2
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
3
2
0
1
0
0
0
1
0
1
0
2
1
0
1
0
0
0
0
0
1
2
2
2
0
0
0
0
0
2
0
0
0
0
0
3
0
2
0
0
0
2
2
0
1
1
0
0
0
0
0
1
1
0
1
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
1
1
8
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
1
0
1
2
1
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
1
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
8
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
1
3
2
0
1
1
0
0
1
0
0
1
0
0
0
2
0
0
1
0
0
2
0
2
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
1
1
1
0
1
0
0
0
0
0
2
0
2
0
1
0
7
0
1
0
1
2
2
2
0
1
0
1
0
0
0
0
0
0
0
2
2
1
2
0
0
1
0
0
0
1
2
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
2
0
1
0
0
0
2
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
2
1
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
2
2
4
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
5
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
1
1
0
1
0
0
0
0
2
1
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
2
2
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
1
2
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
3
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
2
0
1
0
1
3
4
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
2
2
0
0
2
0
2
0
0
0
0
2
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
6
0
1
0
3
0
0
1
0
0
0
0
0
2
0
0
0
0
2
3
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
3
0
2
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
1
0
1
2
1
0
0
1
2
1
0
1
0
0
1
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
2
2
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
3
2
1
2
0
0
2
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
2
0
2
0
0
0
2
0
0
0
0
0
1
4
0
0
0
0
1
2
0
0
1
0
0
2
0
0
0
3
4
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
1
0
3
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
3
0
0
0
1
1
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
2
1
2
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
2
0
0
0
2
0
3
0
0
0
0
2
0
2
3
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
3
0
1
1
0
3
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
1
0
1
0
0
0
0
1
0
0
1
2
1
1
0
1
0
0
0
2
2
1
0
0
0
2
0
0
0
2
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
1
0
0
0
2
0
3
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
1
1
0
1
0
2
4
0
3
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
2
1
0
2
0
0
1
0
0
0
0
0
0
2
0
0
2
2
1
0
0
1
2
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
1
0
0
1
0
5
0
1
0
0
0
0
0
2
0
1
2
0
0
0
0
0
1
0
0
4
0
1
0
0
0
0
0
0
0
0
0
1
2
1
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
1
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
6
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
4
1
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
5
0
5
3
2
0
5
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
1
0
0
2
0
0
2
0
1
0
0
0
2
0
0
1
0
0
0
0
1
0
0
1
0
1
1
0
2
0
0
2
0
1
2
0
1
1
0
0
0
0
0
0
0
3
3
0
0
2
1
0
1
1
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
1
0
0
0
2
2
0
0
0
0
2
0
1
0
0
0
0
0
4
0
5
0
0
0
0
0
0
5
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
5
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
2
0
2
0
0
0
0
2
6
2
2
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
3
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
4
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
2
0
2
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
2
0
0
0
2
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
2
0
2
0
0
2
0
2
0
0
2
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
1
1
2
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
4
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
4
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
2
0
0
2
0
2
0
0
0
0
1
0
0
2
2
0
0
0
0
0
2
1
0
0
0
2
0
3
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
2
0
1
0
0
0
2
5
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
3
0
0
1
0
0
0
0
1
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
5
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
1
0
0
0
2
0
0
2
0
0
1
0
0
1
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
4
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
1
0
0
2
2
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
1
1
4
0
0
0
1
0
0
0
0
1
2
2
1
2
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
2
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
1
1
2
0
1
2
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
4
0
0
0
2
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
1
0
0
1
0
0
0
3
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
1
1
1
0
0
3
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
4
0
0
0
1
0
0
0
3
0
3
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
2
0
0
1
0
0
0
0
1
0
1
0
2
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
3
0
2
0
0
0
0
2
0
0
0
1
1
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
3
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
1
1
0
2
0
0
2
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
3
2
0
0
3
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
3
0
0
0
0
2
0
0
3
1
0
0
0
0
1
0
2
3
0
0
2
2
2
0
0
1
0
0
1
0
0
2
2
0
4
0
0
0
2
1
0
0
0
1
0
2
0
0
2
2
0
2
0
0
2
1
1
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
1
0
2
4
0
0
0
1
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
3
0
2
0
2
0
0
2
0
3
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
3
0
1
1
2
0
2
0
0
0
0
1
0
1
2
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
2
0
1
3
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
3
0
0
6
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
3
0
0
1
0
1
0
4
0
0
0
0
0
0
2
0
2
2
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
1
0
1
1
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
1
2
0
0
1
0
0
0
0
0
1
0
0
0
2
2
1
3
0
1
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
3
0
0
0
1
2
1
0
0
0
1
0
0
0
0
1
0
0
3
1
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
2
1
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
1
0
1
2
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
4
0
0
0
0
1
1
1
4
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
4
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
2
0
3
1
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
2
1
0
2
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
3
0
0
0
0
1
0
0
0
0
0
5
0
0
0
0
1
1
2
0
0
0
0
0
0
0
2
0
5
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
2
1
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
2
0
0
0
3
1
0
0
1
0
0
2
2
0
1
0
4
0
1
1
1
0
0
0
0
0
0
1
2
2
0
0
0
2
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
2
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
1
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
3
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
6
0
1
2
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
2
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
1
0
0
0
0
2
0
1
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
2
3
0
0
0
2
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
5
3
0
0
0
1
2
0
0
0
0
0
1
2
0
0
0
0
1
2
0
0
0
0
0
0
1
0
1
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
2
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
3
0
0
1
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
1
2
0
0
1
0
2
0
0
0
0
2
0
1
0
0
2
0
2
1
0
1
0
0
0
0
0
0
0
0
0
2
2
6
0
0
1
0
0
2
0
4
1
1
2
0
0
0
0
1
0
0
0
3
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
3
2
2
0
0
0
1
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
1
0
1
0
0
1
0
0
2
0
0
1
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
3
4
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
2
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
4
1
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
2
1
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
1
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
2
0
1
0
0
0
0
0
2
0
0
0
1
0
0
2
0
1
2
0
1
0
1
0
0
5
0
1
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
1
0
0
0
3
0
0
0
0
0
0
2
0
2
0
2
1
2
1
0
2
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
1
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
1
0
0
0
0
1
0
2
1
1
0
0
0
0
0
2
1
0
0
0
0
2
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
5
2
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
3
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
3
1
0
0
0
0
0
1
2
0
0
1
0
0
3
0
0
0
0
1
0
0
0
0
1
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
3
1
0
0
0
0
0
0
3
0
2
0
0
2
0
0
3
0
0
0
4
0
1
2
1
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
2
0
0
0
2
0
0
0
1
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
1
2
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
1
0
0
0
3
2
0
0
2
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
4
0
0
1
0
0
0
0
1
2
0
0
0
2
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
2
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
2
0
0
0
2
2
0
1
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
1
0
3
3
0
2
1
0
0
3
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
2
2
0
0
0
2
0
2
1
0
0
0
1
0
0
3
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
10
0
1
0
2
0
0
0
1
1
0
0
0
3
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
1
0
2
0
2
0
0
2
1
2
0
0
0
0
0
3
0
0
2
0
1
2
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
1
2
0
0
4
2
0
0
0
0
0
0
0
0
0
0
3
0
4
0
0
0
0
1
0
0
1
0
3
0
1
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
10
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
3
2
0
0
0
1
0
0
0
0
0
0
1
2
2
0
0
0
0
0
2
0
2
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
1
2
2
0
0
0
0
0
1
1
0
2
0
3
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
1
0
2
3
0
0
0
0
0
0
0
0
0
0
2
0
0
1
4
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
2
0
2
2
0
1
0
0
0
0
1
2
0
1
2
0
2
0
0
2
0
1
1
0
0
2
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
1
0
0
1
0
1
0
0
1
0
0
1
0
0
1
1
2
0
0
0
2
0
0
0
3
0
2
0
0
0
0
0
0
2
2
0
2
0
1
0
0
0
3
0
0
1
1
2
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
2
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
1
1
2
0
1
0
0
0
0
0
2
2
2
1
1
0
0
1
0
2
2
2
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
1
1
0
0
0
2
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
1
0
0
1
0
0
0
0
2
0
4
0
2
0
0
0
0
0
0
1
1
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
1
0
0
0
1
2
0
0
2
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
1
1
0
3
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
1
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
1
2
0
0
0
1
0
0
7
0
0
0
1
0
2
0
2
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
2
0
2
2
1
1
0
3
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
2
0
2
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
5
0
4
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
5
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
3
0
0
0
1
0
0
2
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
2
3
0
7
1
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
1
2
1
0
0
0
1
0
0
2
2
0
0
0
0
0
2
1
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
3
0
2
0
0
0
0
0
1
0
1
1
0
1
0
1
0
1
0
2
1
2
0
2
0
1
1
1
0
1
0
0
1
2
0
2
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
3
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
2
2
0
0
1
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
6
1
0
0
0
0
0
2
0
1
1
0
0
0
0
0
2
1
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
1
0
3
0
2
0
0
2
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
3
0
1
2
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
1
2
1
0
0
4
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
2
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
3
0
0
1
2
0
1
2
0
0
0
2
0
1
1
0
1
0
0
0
2
0
7
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
7
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
2
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
2
1
1
0
0
2
0
2
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
5
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
1
0
1
0
0
0
0
2
0
0
1
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
2
1
0
0
0
2
2
0
0
0
0
1
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
3
1
0
0
0
0
0
1
0
0
0
0
2
0
2
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
1
2
0
0
0
2
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
2
14
0
1
0
1
2
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
2
1
0
2
1
1
0
0
0
0
0
0
0
1
0
2
0
2
0
1
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
1
2
0
0
0
2
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
2
2
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
1
0
2
1
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
1
0
0
0
0
0
1
0
0
1
1
0
1
0
2
0
2
0
3
1
1
1
1
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
1
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
1
0
3
2
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
5
0
2
1
0
0
1
0
0
0
0
1
0
3
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
1
2
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
2
1
3
0
0
1
0
0
3
1
0
0
1
0
3
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
1
2
0
0
2
0
0
0
1
2
0
2
0
0
2
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
2
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
2
0
1
0
2
0
0
0
2
3
0
0
0
0
0
0
0
1
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
3
0
0
3
0
1
0
0
0
1
2
2
0
0
1
0
1
0
0
0
1
0
0
1
0
2
1
0
2
0
0
0
2
0
1
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
3
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
1
2
0
1
0
0
3
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
1
1
0
0
0
3
2
0
0
0
1
0
2
1
15
0
1
0
2
0
0
1
0
0
0
0
4
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
2
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
4
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
1
1
1
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
1
2
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
1
2
1
0
0
1
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
1
0
1
2
0
0
1
0
1
0
0
2
0
0
0
0
2
1
1
8
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
6
2
1
0
0
0
0
1
2
0
2
0
0
0
0
2
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
2
0
0
0
0
0
1
0
0
2
1
0
2
0
0
0
0
2
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
1
2
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
2
1
0
2
0
1
0
0
1
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
2
0
1
1
0
0
0
1
0
0
0
0
0
0
0
2
0
1
1
0
1
2
1
2
2
2
0
0
1
0
1
0
2
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
3
0
2
0
0
2
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
10
1
0
0
0
0
0
0
1
3
0
1
0
0
0
0
0
0
1
1
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
4
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
1
0
0
0
2
0
1
3
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
2
0
0
2
0
5
0
2
2
0
0
0
0
0
1
0
0
2
0
2
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
1
1
2
0
2
0
0
0
0
5
0
2
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
1
2
0
0
0
4
0
0
0
0
2
0
0
0
0
0
2
4
0
0
1
0
0
0
0
2
0
1
0
0
5
0
0
1
1
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
2
0
1
2
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
2
0
0
0
4
0
0
0
0
0
0
0
1
0
2
0
2
0
1
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
1
0
1
2
0
1
0
0
0
0
1
0
0
2
2
0
0
0
0
2
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
1
0
1
0
0
0
0
2
0
3
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
2
0
0
0
0
0
2
0
1
0
2
0
1
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
1
0
2
0
1
1
0
0
0
0
1
0
0
0
0
0
2
1
2
0
0
1
0
0
0
0
1
0
1
0
1
0
3
0
0
0
2
1
0
0
0
2
0
0
0
0
1
0
2
0
0
2
0
0
0
2
0
0
0
1
0
2
0
1
1
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
1
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
2
1
3
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
5
2
0
0
0
1
2
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
1
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
2
0
1
0
1
4
1
0
1
1
0
1
0
0
2
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
1
0
1
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
2
0
2
0
2
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
4
0
2
0
0
0
0
0
7
0
0
1
0
0
1
0
0
0
0
1
1
1
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
2
4
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
1
0
2
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
2
1
1
0
0
0
0
0
0
0
2
9
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
3
0
2
2
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
1
0
1
0
1
0
2
0
0
0
0
0
0
1
0
0
2
0
1
3
0
2
2
0
0
0
3
1
0
0
0
0
0
0
4
2
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
1
2
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
3
0
2
0
0
0
0
1
0
0
0
2
0
0
3
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
2
0
0
0
0
0
0
3
2
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
2
1
0
0
1
0
0
0
0
3
2
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
16
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
1
2
0
0
0
2
1
0
0
0
2
0
2
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
4
0
0
0
2
0
0
0
0
0
1
0
1
1
1
0
0
0
1
0
0
0
0
1
0
4
1
0
2
2
1
0
2
0
0
1
2
0
0
0
0
0
3
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
3
0
0
1
2
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
1
2
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
2
0
0
2
0
0
0
0
0
1
0
1
0
0
9
0
2
1
1
2
0
2
1
0
2
0
1
0
0
0
0
0
1
2
0
0
1
3
0
0
0
0
0
2
0
11
0
0
0
0
0
0
3
0
2
3
2
2
1
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
1
0
0
7
2
0
0
1
0
2
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
5
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
3
0
0
0
2
0
0
4
0
0
1
2
0
0
0
0
0
0
1
0
0
3
2
1
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
2
0
0
1
2
0
0
1
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
3
0
0
0
0
0
0
1
0
0
1
0
0
2
4
1
2
0
0
0
1
0
0
2
0
1
0
0
2
1
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
4
2
0
0
0
0
2
0
1
0
0
2
3
1
0
0
0
0
0
0
1
0
1
0
0
2
0
1
0
1
2
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
1
1
0
2
1
0
1
0
0
0
0
1
0
0
0
1
1
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
5
0
1
0
1
1
0
2
0
0
1
0
0
0
2
1
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
2
1
0
2
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
2
2
1
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
4
0
0
2
0
0
0
0
0
0
1
1
0
2
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
3
1
0
3
0
1
0
0
0
0
0
0
0
0
2
2
1
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
2
0
1
0
0
0
0
2
0
2
0
0
0
0
1
2
2
0
1
1
0
1
1
0
0
0
0
0
2
0
2
0
0
1
2
0
0
1
2
0
2
1
0
1
1
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
1
1
0
0
1
0
2
0
0
2
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
3
1
0
2
0
0
0
0
2
0
0
4
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
2
1
0
0
0
1
1
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
7
1
4
0
0
0
2
1
0
4
0
0
0
0
3
4
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
1
1
1
1
0
0
0
0
2
0
1
1
0
0
1
0
2
0
0
1
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
2
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
2
0
2
1
0
0
0
3
1
3
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
2
2
0
1
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
2
1
2
2
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
1
1
0
2
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
4
2
1
4
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
1
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
5
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
2
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
1
0
0
0
1
0
3
0
0
1
0
0
0
0
0
1
0
1
0
2
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
2
0
1
0
0
0
0
1
0
0
0
0
1
0
1
1
2
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
3
0
0
0
2
1
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
2
0
0
2
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
1
0
0
0
0
2
0
4
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
3
2
0
5
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
3
1
0
0
0
0
0
0
2
0
2
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
8
1
0
1
0
1
0
1
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
1
0
0
0
0
2
1
1
0
0
0
0
0
6
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
1
1
1
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
3
1
0
2
0
0
3
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
2
1
1
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
3
0
0
0
1
5
0
1
1
2
2
3
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
3
2
0
0
2
0
0
0
0
1
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
1
3
0
2
2
0
0
0
0
1
0
3
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
1
2
0
0
0
0
2
0
0
0
2
1
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
3
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
5
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
2
2
0
0
3
1
1
2
0
2
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
2
3
1
1
4
0
2
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
2
0
1
0
0
0
1
0
2
0
2
1
0
0
0
0
2
0
0
0
1
1
3
0
1
0
0
1
2
0
2
1
1
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
3
0
2
0
0
1
1
0
0
3
0
0
2
0
1
0
0
0
1
1
0
0
1
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7
1
0
1
3
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
2
1
0
0
2
3
3
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
2
1
1
0
0
2
1
0
2
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
1
0
1
0
0
0
1
2
1
0
0
3
1
0
1
0
2
2
2
0
0
0
3
0
2
0
0
0
2
2
2
0
0
0
0
0
2
1
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
3
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
1
0
0
0
0
2
0
0
0
0
0
1
0
2
2
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
3
1
1
2
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
2
0
0
2
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
2
2
0
2
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
6
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
2
1
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
1
1
0
2
0
3
0
2
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
1
0
1
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
2
0
2
0
1
0
0
1
0
1
0
0
0
0
0
0
0
3
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
2
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
1
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
2
0
3
1
0
0
0
0
0
0
0
1
0
0
0
0
4
0
1
0
0
1
2
1
0
0
1
2
0
0
1
0
0
0
0
2
0
0
1
0
0
3
1
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
2
1
0
1
1
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
1
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
2
1
0
0
0
0
0
1
2
0
2
1
0
0
0
0
2
0
1
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
1
1
1
0
0
0
2
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
1
1
0
3
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
2
1
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
1
0
1
0
0
1
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
2
1
1
0
2
8
2
0
0
2
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
1
2
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
3
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
1
1
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
1
5
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
3
3
0
0
0
0
2
1
2
0
0
0
0
2
2
0
0
2
0
2
0
0
4
0
2
0
1
0
4
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
2
2
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
2
0
1
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
3
2
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
1
0
0
0
0
2
1
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
1
0
2
0
0
0
0
0
1
0
1
0
2
1
0
2
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
4
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
1
0
2
0
1
0
2
1
0
0
0
0
0
0
0
0
1
2
0
0
1
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
2
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
4
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
1
1
0
0
1
3
0
0
0
0
2
1
0
0
0
1
0
5
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
2
1
0
0
0
1
3
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
3
0
0
2
2
0
1
2
0
0
2
0
0
0
0
0
0
0
0
2
1
2
2
0
0
0
1
0
3
0
0
1
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
1
0
0
2
0
0
2
0
1
2
0
2
0
1
0
0
1
2
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
4
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
2
2
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
1
3
4
1
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
1
2
0
1
1
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
1
2
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
2
2
2
16
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
1
1
1
0
0
2
0
0
0
1
0
1
0
0
0
1
0
2
0
2
0
0
1
0
0
2
1
1
1
0
0
1
0
0
0
2
0
0
1
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
2
1
1
2
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
5
0
4
0
0
0
0
0
0
2
1
0
2
1
0
0
0
2
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
1
1
2
1
0
0
1
2
0
0
2
0
5
1
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
2
1
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
2
0
3
0
1
0
0
1
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
2
2
0
0
1
0
0
0
1
0
3
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
3
0
0
0
0
1
1
0
0
1
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
2
1
2
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
1
0
0
2
1
0
0
2
0
0
5
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
1
1
0
0
0
0
0
0
2
0
0
2
1
0
0
0
1
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
4
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
3
0
0
0
2
0
0
0
1
0
0
1
0
0
1
1
0
2
0
0
0
2
0
2
0
0
0
1
0
0
1
0
0
1
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
1
0
0
1
1
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
3
1
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
3
1
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
1
2
2
0
0
0
0
0
0
2
0
0
1
1
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
2
3
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
2
2
0
1
2
1
1
1
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
2
0
0
1
14
2
1
0
0
2
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
3
0
1
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
3
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
2
2
1
1
0
9
0
0
0
2
0
2
0
1
0
0
0
0
0
2
0
1
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
2
0
2
0
0
0
0
0
2
0
0
0
1
0
2
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
2
1
1
0
0
1
1
0
0
0
0
2
0
0
2
0
1
0
1
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
2
0
2
1
0
0
1
0
0
0
3
2
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
3
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
1
1
0
2
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
2
3
0
0
7
0
2
2
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
2
1
0
2
0
0
0
0
0
6
0
1
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
4
0
0
0
0
1
2
0
0
5
1
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
3
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
2
2
1
0
2
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
1
2
1
0
0
0
0
0
0
0
2
0
1
0
4
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
2
0
0
1
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
5
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
1
2
1
1
0
0
0
1
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
3
0
3
0
0
3
0
0
0
0
0
1
2
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
1
2
0
0
2
1
0
0
0
2
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
2
0
0
2
0
1
0
0
0
0
1
1
0
0
0
1
1
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
2
1
0
0
0
5
2
0
0
0
0
0
1
0
0
1
2
0
0
0
1
0
1
2
2
0
1
0
0
0
0
1
2
1
0
0
0
0
0
1
0
2
0
2
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
3
0
2
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
6
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
2
1
1
0
0
0
0
1
0
2
0
0
1
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
1
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
1
2
8
0
0
0
2
0
1
1
5
0
1
0
0
2
0
0
0
2
0
2
0
0
3
1
1
3
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
1
2
0
2
0
0
2
0
2
0
2
0
0
0
0
0
1
1
0
0
0
2
3
0
0
0
0
0
0
0
3
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
2
0
1
0
0
0
0
1
2
0
0
0
0
0
3
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
4
1
0
0
0
2
0
1
1
0
2
0
0
0
1
0
0
0
2
1
0
0
0
0
1
2
2
0
0
0
0
1
1
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
2
0
0
1
0
0
0
1
0
1
0
0
0
2
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
3
1
0
0
0
3
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
2
0
0
2
0
1
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
3
0
0
4
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
5
0
0
0
2
2
0
0
3
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
2
0
0
1
2
2
2
0
2
0
0
2
0
1
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
5
1
0
2
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
3
0
2
2
0
0
2
0
1
2
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
3
0
0
1
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
3
1
0
0
0
0
0
0
0
3
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
2
0
4
0
0
1
0
0
0
1
0
1
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
5
0
1
0
0
0
0
0
1
0
1
2
0
0
0
0
2
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
2
1
0
1
1
1
0
1
1
0
0
0
1
0
0
1
0
0
2
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
2
0
0
2
1
0
0
0
0
0
0
3
1
0
0
1
1
0
0
1
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
2
0
2
3
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
5
0
0
2
0
1
0
0
0
1
0
1
5
0
0
0
0
0
1
0
2
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
1
0
0
2
2
2
0
2
2
0
0
2
1
2
0
0
0
0
1
0
0
0
2
0
0
0
1
0
1
0
1
0
1
0
2
2
2
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
1
0
1
2
0
0
2
1
3
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
1
1
0
2
2
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
1
2
2
0
1
0
0
0
0
0
0
2
0
4
0
3
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
3
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
2
0
7
1
0
0
0
1
0
5
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
3
1
0
1
0
1
0
0
2
0
0
0
0
2
0
0
0
0
3
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
14
0
0
1
2
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
2
2
0
0
0
2
2
2
0
0
0
1
0
0
0
0
3
0
0
2
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
2
0
0
0
0
1
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
2
1
0
2
1
0
2
1
2
0
0
3
1
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
1
2
0
0
0
0
1
0
0
4
0
0
1
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
1
1
1
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
3
0
0
0
2
0
0
2
0
1
0
1
1
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
1
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
1
1
2
2
0
0
0
1
0
0
0
1
0
0
0
0
0
1
4
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
2
0
0
1
0
1
1
0
0
0
0
0
0
1
3
1
2
0
0
2
0
1
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
2
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
3
2
0
3
1
6
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
1
0
0
1
0
0
0
2
0
0
3
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
2
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
3
1
0
0
2
1
1
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
2
0
2
1
2
0
0
0
3
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
2
1
0
0
0
0
1
2
0
1
0
0
0
0
2
2
2
0
0
3
0
0
0
1
2
0
0
1
0
1
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
2
0
1
0
0
0
0
0
1
0
0
0
0
1
1
2
0
0
0
2
0
0
0
1
0
1
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
3
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
3
0
0
0
0
2
0
0
1
0
1
0
2
0
0
0
11
0
1
0
1
2
0
0
0
0
0
0
0
3
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
2
0
3
2
0
0
0
0
5
0
0
0
0
0
0
2
0
2
0
0
0
1
1
1
0
0
2
2
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
2
2
2
0
2
1
2
0
2
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
2
0
1
2
0
2
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
2
1
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
8
0
0
0
0
2
0
0
0
5
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
1
0
2
2
1
0
0
1
1
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
3
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
2
0
1
1
1
2
0
0
0
0
0
2
2
2
0
0
2
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
1
1
2
0
0
0
1
0
0
0
0
0
1
2
4
0
0
0
0
0
0
0
0
1
0
1
2
2
2
2
0
0
3
4
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
1
2
0
0
3
0
1
2
0
0
1
0
2
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
2
3
0
1
0
0
2
1
0
0
0
2
0
0
0
0
1
0
0
0
3
0
0
1
0
0
0
0
0
2
0
0
1
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
1
3
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
6
3
4
0
0
0
0
0
0
0
0
1
1
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
1
1
0
2
1
0
0
0
1
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
2
0
1
0
1
0
0
0
0
2
0
0
0
2
1
2
0
1
1
2
0
2
0
0
0
1
0
0
0
0
0
0
2
4
2
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
2
0
0
2
0
1
0
0
0
0
1
0
2
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
1
1
0
0
0
1
1
1
2
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
2
0
0
0
0
2
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
2
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
1
2
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
3
0
0
1
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
2
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
2
0
0
0
1
0
0
0
1
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
1
0
0
3
0
0
0
0
0
2
0
0
0
0
2
0
0
1
2
0
0
1
0
1
2
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
3
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
5
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
2
0
0
0
0
1
0
2
0
1
0
2
0
0
0
0
0
2
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
2
0
0
3
0
0
0
2
0
2
0
0
0
1
0
0
0
0
1
2
2
0
0
0
0
0
0
0
2
0
1
0
1
3
2
0
0
1
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
2
2
0
0
0
0
0
2
0
2
0
0
1
0
0
1
2
0
1
0
1
1
1
0
0
0
3
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
2
0
0
0
4
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
2
0
0
0
2
0
0
0
3
1
0
1
0
1
0
0
0
0
0
0
1
2
0
1
0
7
1
0
0
0
2
1
0
2
0
1
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
1
3
0
0
0
1
1
2
0
2
0
0
0
2
0
1
1
1
0
0
0
0
0
1
0
2
1
1
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
2
1
0
0
0
2
0
0
0
1
0
0
0
0
4
0
0
1
0
1
0
0
0
0
0
2
0
0
0
2
0
1
0
0
2
3
2
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
1
0
1
1
2
0
2
0
1
1
0
1
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
3
2
0
0
0
0
0
0
0
1
0
0
0
1
0
3
0
0
2
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
4
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
2
0
2
0
3
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
1
0
0
0
2
0
0
0
0
0
0
2
0
2
0
2
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
2
0
0
2
0
0
1
1
1
1
1
2
0
0
0
0
0
2
1
2
0
0
1
1
0
0
0
0
0
0
0
2
0
0
1
1
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
4
0
1
0
2
0
1
0
1
1
0
0
1
0
0
0
0
2
1
0
1
0
0
0
1
1
1
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
2
0
2
3
0
2
1
0
1
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
2
0
1
0
1
0
3
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
2
0
2
0
0
0
1
0
0
0
1
0
0
0
0
3
1
0
0
0
0
0
0
2
1
0
0
0
0
0
1
2
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
2
2
0
1
0
3
0
0
0
0
0
4
5
2
0
0
1
0
0
0
0
2
0
0
0
1
0
2
0
0
1
1
1
0
2
2
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
2
2
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
2
0
2
3
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
2
0
1
0
2
0
1
0
0
0
2
0
0
1
0
1
2
0
0
0
0
0
2
0
0
0
5
2
0
3
1
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
1
0
0
0
2
2
4
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
1
1
2
0
0
1
0
0
0
3
2
0
0
0
1
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
6
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
2
0
0
1
2
0
0
0
1
3
0
0
0
1
0
0
0
0
0
0
0
0
0
2
6
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
2
0
0
0
0
0
2
0
1
1
0
0
0
1
2
0
0
0
0
2
1
2
0
1
0
0
0
1
0
0
1
0
0
4
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
3
0
2
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
2
3
0
1
0
0
2
2
1
0
0
0
2
0
1
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
2
0
0
0
0
1
0
2
0
0
2
0
1
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
1
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
1
0
2
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
3
0
0
0
0
0
1
0
0
0
1
0
0
2
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
1
0
1
2
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
3
2
0
0
3
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
1
2
3
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
1
0
1
0
1
0
1
0
3
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
5
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
1
0
0
1
0
0
1
1
1
0
0
1
0
1
0
3
0
0
0
0
0
0
2
0
0
0
0
0
1
1
2
0
1
0
1
0
0
2
3
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
3
0
2
0
2
1
0
0
0
1
2
0
2
0
0
0
3
0
2
1
2
1
0
0
0
0
1
1
2
0
0
1
1
1
0
0
2
0
0
0
0
2
0
1
4
0
4
0
0
1
0
0
0
0
1
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
2
2
0
0
1
1
0
0
0
2
2
0
0
0
0
0
2
2
0
0
0
0
1
0
0
2
3
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
6
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
1
0
1
1
2
0
2
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
1
0
0
0
1
0
1
2
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
2
1
0
0
3
0
0
0
0
0
4
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
4
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
3
0
0
0
0
1
0
0
0
1
3
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
2
1
2
1
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
1
1
0
0
0
2
1
0
2
0
0
0
0
0
2
1
0
2
0
0
0
0
0
1
1
1
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
3
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
2
0
0
1
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
3
0
0
0
0
0
0
1
1
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
2
0
0
1
2
0
0
2
0
0
2
2
3
0
0
2
0
1
0
2
0
0
1
2
0
3
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
2
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
5
2
0
0
0
1
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
3
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
2
3
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
1
0
0
0
0
0
3
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
2
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
2
3
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
1
0
0
1
0
1
1
0
0
0
0
3
0
0
1
1
0
0
0
0
2
1
0
2
0
1
2
0
12
2
0
2
0
0
0
0
0
0
4
0
2
0
0
0
2
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
2
2
3
0
0
0
1
1
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
2
0
0
2
0
0
0
0
0
0
3
1
0
1
2
0
0
0
0
0
1
0
0
0
2
2
0
0
1
0
0
2
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
2
1
0
1
0
0
1
0
1
0
0
0
0
2
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
1
0
1
1
2
0
0
0
0
0
0
0
0
1
3
3
2
0
2
0
0
0
2
0
0
2
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
1
1
2
0
2
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
2
0
0
1
0
0
0
2
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
6
0
0
1
0
0
2
0
2
0
0
2
0
0
2
0
0
0
2
2
0
0
1
2
3
1
1
1
0
0
1
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
3
0
2
0
0
0
1
1
0
1
0
0
1
1
2
0
0
3
0
0
2
1
0
0
0
0
1
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
2
1
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
5
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
2
2
0
0
2
3
1
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
10
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
3
1
0
0
1
0
2
0
0
1
0
0
0
0
2
0
0
2
2
0
0
0
0
4
0
0
0
2
0
2
2
0
0
0
0
0
1
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
2
2
0
0
0
0
1
0
0
1
0
0
3
0
0
1
0
0
0
0
1
0
0
1
0
3
0
2
0
0
2
0
2
0
0
0
2
2
1
0
0
0
0
0
1
0
3
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
2
0
0
1
0
1
2
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
3
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
2
0
0
0
0
2
0
0
0
0
2
1
0
0
0
1
2
2
2
0
0
0
0
0
0
2
5
0
0
1
0
0
2
0
2
0
0
2
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
2
0
0
4
1
0
2
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
1
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
1
0
0
0
1
0
0
0
1
2
1
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
3
0
0
0
1
0
0
0
0
1
2
3
0
0
2
0
2
0
1
1
4
1
2
0
1
0
0
0
0
2
0
2
0
1
0
0
0
0
1
0
3
0
0
0
2
0
0
1
0
2
0
0
0
0
0
2
0
3
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
1
0
1
0
0
0
3
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
2
0
2
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
1
0
0
2
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
3
0
2
0
0
0
1
0
0
0
0
0
1
0
2
0
0
2
2
2
0
0
0
0
0
0
0
0
2
0
1
1
0
0
2
0
1
0
0
2
0
1
2
0
2
3
0
0
2
0
2
1
1
0
0
0
0
0
1
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
1
0
3
0
0
0
5
1
1
1
0
0
0
1
0
0
0
2
0
0
1
0
2
0
0
0
1
1
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
2
3
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
1
0
0
1
0
2
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
1
0
0
2
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
2
1
0
0
0
2
0
0
2
0
0
2
0
0
0
2
0
1
0
0
0
0
1
2
0
0
2
0
0
2
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
3
0
0
1
2
1
0
1
0
0
0
0
0
0
1
1
3
0
0
0
0
0
1
0
2
0
0
0
0
0
0
3
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
1
2
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
2
2
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
1
0
1
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
1
2
1
2
0
0
2
2
0
0
3
0
1
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
4
1
2
0
0
0
0
0
0
0
0
1
0
2
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
3
0
1
0
0
0
0
2
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
1
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
0
1
0
0
2
0
1
0
2
0
2
2
0
0
0
0
0
0
5
4
0
2
0
0
3
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
1
0
0
0
1
0
0
0
0
1
0
1
1
3
0
0
2
0
0
2
0
0
0
0
2
2
3
0
0
1
1
0
0
1
0
0
0
2
0
0
0
0
0
1
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
2
0
0
1
0
2
0
0
0
1
0
0
2
1
0
2
0
6
0
1
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
3
0
0
0
3
1
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
3
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
1
2
0
0
1
0
0
0
0
1
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
2
0
0
0
0
2
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
3
0
1
0
2
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
11
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
2
0
4
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
2
1
0
0
2
3
0
0
1
0
1
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
2
0
4
2
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
2
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
4
0
0
1
0
0
0
0
3
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
2
1
0
0
1
0
0
0
0
0
0
0
3
0
2
0
0
2
2
0
0
16
2
1
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
2
0
1
2
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
3
0
0
3
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
2
3
0
0
0
0
0
2
1
0
0
1
0
1
0
0
0
2
1
1
0
2
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
3
0
2
0
0
2
0
0
2
1
1
0
0
1
6
0
1
0
0
0
4
0
1
1
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
3
0
0
0
0
0
0
2
2
1
0
0
0
2
2
0
0
2
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
3
0
0
1
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
1
0
2
0
0
2
4
0
0
0
1
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
2
2
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
7
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
3
0
0
1
0
1
1
1
0
1
0
0
1
2
0
1
2
0
0
1
5
0
2
1
0
1
0
0
0
0
0
3
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
1
1
0
1
1
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
1
3
0
3
0
0
0
1
1
0
0
0
1
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
1
2
0
0
0
1
0
0
0
0
2
1
1
0
2
0
2
1
0
1
0
0
0
0
0
0
1
0
2
0
4
2
1
0
0
1
0
0
1
0
2
2
1
0
1
2
0
3
0
4
1
0
1
0
0
4
0
0
3
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
1
0
2
0
1
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
3
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
3
0
1
0
2
1
1
4
2
0
3
0
0
2
0
2
0
0
0
0
2
0
1
0
0
3
2
2
0
0
0
0
1
0
0
0
0
1
0
2
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
1
0
1
3
0
3
2
1
0
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
1
1
2
0
2
0
0
1
0
0
0
2
0
0
0
1
1
2
0
2
0
0
2
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
3
0
0
2
0
0
0
1
2
2
0
0
0
1
3
0
1
0
2
0
3
3
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
7
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
8
0
0
7
0
2
0
0
2
0
0
2
1
0
0
1
0
3
0
2
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
1
0
0
1
0
1
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
1
2
0
0
2
0
0
1
0
0
0
2
0
0
2
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
3
0
0
0
0
0
0
0
5
2
1
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
5
1
3
0
0
1
0
0
1
1
0
0
2
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
1
2
0
0
0
0
0
0
2
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
1
1
0
1
5
0
0
0
0
2
0
0
0
2
0
0
1
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
2
1
0
0
0
0
2
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
2
1
1
0
1
0
3
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
3
1
0
0
0
1
0
1
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
2
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
1
0
0
0
0
0
4
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
2
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
2
0
2
2
0
1
0
1
0
1
0
0
0
0
2
0
0
2
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
4
0
1
1
0
2
0
0
0
0
1
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
3
0
0
0
2
1
0
1
2
0
0
0
0
0
3
0
0
0
0
0
1
2
0
0
2
0
0
2
0
0
0
1
1
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
2
0
1
0
0
0
1
0
1
1
0
1
0
2
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
2
0
0
0
0
2
2
0
4
0
1
0
0
1
1
0
0
3
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
1
0
0
1
0
2
1
0
0
0
0
0
2
2
1
0
0
0
1
0
0
0
1
0
1
0
1
1
0
2
0
1
1
1
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
1
2
2
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
1
0
0
0
0
0
2
0
1
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
1
2
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
2
3
2
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
1
0
0
0
1
2
0
1
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
2
0
0
0
0
0
2
0
3
1
0
2
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
3
5
0
1
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
2
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
2
0
0
1
0
3
1
0
0
2
0
0
1
0
0
0
0
1
0
0
1
2
0
0
4
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
3
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
3
2
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
1
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
2
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
1
0
1
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
3
0
2
0
0
0
2
2
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
1
0
0
0
1
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
1
1
0
1
0
1
0
0
2
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
1
5
1
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
1
0
0
0
0
1
0
2
1
2
0
2
2
0
2
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
1
0
1
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
1
0
1
0
0
2
0
0
1
3
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
2
2
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
1
3
0
1
0
0
0
1
0
0
1
1
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
2
0
0
0
2
0
0
0
0
5
0
0
1
0
0
0
2
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
2
0
1
0
0
0
0
0
2
0
2
1
0
0
0
1
0
0
0
0
0
1
0
2
0
1
2
0
0
0
0
0
0
0
0
1
0
1
0
2
1
0
0
1
0
0
0
0
1
0
0
0
1
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
1
0
0
1
2
1
0
0
0
0
3
0
0
0
0
1
0
1
0
2
1
0
2
0
0
0
0
0
0
1
0
0
0
2
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
1
2
1
1
2
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
3
0
0
1
1
0
2
0
0
0
0
1
0
0
2
1
0
0
0
0
0
2
0
2
0
0
0
2
2
1
1
0
0
1
0
1
0
0
3
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
3
0
0
1
0
0
0
0
0
0
0
0
1
2
1
0
3
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
2
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
1
0
1
0
0
0
0
0
1
0
0
1
1
0
1
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
2
0
0
0
1
0
0
0
2
2
0
0
0
0
1
0
1
2
1
0
0
0
0
3
0
0
0
1
0
0
3
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
1
0
1
1
0
0
0
0
0
1
0
6
3
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
2
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
3
1
0
0
0
0
2
0
0
0
1
0
0
1
0
1
0
1
2
0
0
0
1
2
0
0
0
5
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
1
0
1
0
0
0
0
2
0
1
0
1
0
2
2
0
3
0
2
1
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
2
0
1
0
1
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
4
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
1
0
1
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
3
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
2
2
1
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
2
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
1
2
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
2
2
2
0
0
0
2
0
1
0
0
7
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
3
0
0
2
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
3
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
2
0
0
1
0
0
0
1
0
0
1
0
3
0
0
1
0
0
0
0
0
0
0
0
3
1
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
7
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
4
0
2
0
0
1
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
1
0
0
0
2
0
3
0
0
2
0
0
0
0
2
0
0
0
0
1
0
1
1
0
0
0
2
0
0
0
0
0
1
0
0
1
0
1
1
2
0
0
2
0
2
5
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
2
2
0
0
0
0
0
0
1
0
3
0
0
2
3
0
0
2
2
4
2
0
2
0
4
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
3
2
0
0
0
0
0
0
0
0
3
2
1
0
0
0
0
0
0
4
1
0
0
1
1
0
0
0
0
4
0
1
0
0
0
0
1
2
0
0
4
2
1
0
2
0
2
1
0
0
0
0
0
0
0
0
2
1
1
0
0
0
1
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
2
1
0
1
1
0
0
0
1
0
1
0
2
2
0
1
4
0
0
0
1
2
0
0
0
2
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
1
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
1
0
2
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
1
1
0
2
0
1
0
2
0
0
2
0
2
1
1
2
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
2
0
3
0
0
1
0
0
1
2
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
2
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
6
2
1
2
0
0
2
0
0
0
0
0
0
1
2
0
2
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
3
0
0
3
0
0
1
1
1
0
0
0
0
0
0
0
1
1
0
2
0
2
4
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
1
0
2
1
0
0
2
2
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
2
0
2
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
3
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
2
0
1
0
1
0
0
2
0
0
0
3
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
1
0
1
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
4
1
0
0
0
0
1
0
8
1
1
0
2
0
0
1
0
0
2
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
2
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
3
3
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
4
2
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
2
2
0
4
0
0
1
1
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
2
2
0
1
0
0
1
0
0
0
0
0
1
0
0
0
2
0
2
2
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
3
0
0
0
1
0
0
1
2
1
2
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
3
0
0
0
0
1
3
2
1
2
1
0
0
2
0
0
1
0
0
0
2
0
0
1
0
0
2
2
0
0
0
1
0
0
0
0
0
1
2
0
0
0
2
0
2
2
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
4
0
0
2
2
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
2
0
1
0
0
0
1
0
0
0
3
0
0
0
0
1
0
0
2
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
2
0
2
0
0
1
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
1
1
0
0
0
0
1
0
0
0
0
0
2
1
2
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
1
0
2
0
1
0
2
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
1
2
0
0
2
0
2
0
0
1
0
2
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
2
0
1
0
0
2
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
1
3
0
0
0
1
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
5
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
1
1
0
0
1
0
0
2
0
2
0
0
0
0
0
0
1
0
1
3
0
1
0
0
1
1
0
1
1
0
0
2
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
2
2
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
2
2
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
2
1
0
4
0
0
0
0
0
1
0
0
0
2
0
2
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
1
0
3
0
0
0
0
1
1
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
1
2
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
2
0
1
1
1
0
0
0
2
0
0
0
5
0
0
1
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
4
0
0
3
0
0
0
2
1
0
0
0
1
2
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
2
0
0
0
3
2
0
1
2
0
1
0
0
0
2
2
0
0
0
2
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
3
0
2
1
2
0
0
0
2
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
3
0
0
0
0
0
4
2
2
2
0
2
0
2
1
0
0
0
0
0
1
2
0
0
0
1
0
2
2
0
0
0
1
0
1
0
2
0
0
0
0
0
0
1
2
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
1
2
2
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
2
2
0
0
0
0
0
0
0
0
0
1
0
2
1
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
2
0
2
5
0
3
0
0
0
1
0
0
2
0
0
2
0
0
2
0
0
2
0
0
0
0
2
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
1
1
0
0
0
2
0
0
0
0
0
0
2
0
0
2
2
0
2
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
1
2
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
4
0
0
0
1
0
0
1
1
0
0
0
2
0
0
0
0
0
0
2
0
2
1
0
0
1
0
0
0
0
0
0
1
2
0
0
1
2
2
2
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
5
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
2
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
2
0
1
1
0
0
0
1
1
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
3
0
2
4
0
0
1
2
1
0
0
2
0
0
1
0
0
2
2
0
0
2
0
0
0
0
2
0
0
0
2
1
2
0
0
4
0
0
2
0
1
2
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
1
0
0
0
0
0
2
1
1
0
2
0
2
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
5
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
2
2
0
0
0
2
0
1
0
1
0
2
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
1
0
2
0
0
0
7
0
0
2
0
0
2
2
0
1
1
0
2
0
2
0
1
0
1
0
0
0
2
0
0
1
0
3
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
2
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
2
3
0
0
0
0
0
0
2
0
0
2
6
0
2
2
0
1
0
0
0
0
1
0
0
0
2
0
3
0
4
0
1
0
0
0
0
2
0
0
2
0
2
0
1
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
1
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
2
0
1
0
2
0
0
0
0
0
0
0
1
0
0
1
5
2
0
1
0
0
2
0
0
0
2
0
0
1
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
2
2
0
0
3
0
1
0
0
0
1
3
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
2
0
0
0
0
1
0
2
0
3
1
0
1
3
0
0
0
0
1
0
0
2
3
3
2
2
0
0
1
0
0
0
2
0
0
0
0
3
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
1
0
2
0
0
1
1
0
0
1
0
0
0
0
0
1
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
1
0
0
1
2
0
0
1
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
1
1
0
0
3
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
1
0
0
0
2
0
2
0
0
3
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
4
0
2
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
1
0
2
0
1
2
0
0
2
0
0
1
0
0
2
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
1
2
0
0
0
0
0
0
1
0
2
0
2
0
1
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
1
0
0
2
1
1
0
0
2
0
1
0
1
2
2
0
1
2
1
0
2
0
0
0
0
0
2
2
0
0
2
1
0
2
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
2
0
3
0
0
2
1
2
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
3
0
5
0
1
2
2
0
0
1
0
0
2
0
3
0
0
0
1
3
0
0
2
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
3
2
0
0
0
1
2
1
0
2
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
2
0
0
0
2
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
1
0
2
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
2
0
0
0
0
1
2
0
0
0
0
2
0
2
0
0
0
2
1
0
0
1
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
3
0
0
0
2
2
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
2
1
0
1
0
0
0
1
0
0
1
1
2
0
0
2
0
0
0
0
0
0
0
2
1
0
0
3
0
0
0
1
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
3
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
1
0
1
2
0
0
0
0
0
2
0
0
1
2
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
1
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
2
1
1
2
0
0
2
0
1
0
0
3
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
2
0
0
2
2
2
0
0
1
0
0
1
8
2
0
0
1
3
0
0
3
0
3
0
1
0
0
1
0
0
2
0
0
0
0
1
0
0
0
3
0
2
0
0
2
1
1
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
1
0
0
5
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
3
0
1
0
0
1
1
3
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
1
0
2
0
2
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
2
0
0
1
1
2
2
0
0
0
2
0
0
0
1
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
1
0
2
0
0
2
0
2
0
0
2
0
0
2
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
2
1
0
1
4
0
0
0
2
1
0
1
0
0
0
0
2
2
1
2
2
0
0
0
2
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
1
4
0
1
0
1
0
2
0
0
0
0
0
0
0
0
2
1
2
0
0
1
0
0
2
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
2
0
2
0
1
1
0
0
0
0
2
0
0
0
1
0
2
0
0
1
0
2
0
0
0
3
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
1
2
0
0
2
0
1
0
0
0
0
3
0
0
0
1
3
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
3
0
2
0
2
0
0
0
0
2
0
0
0
5
3
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
1
0
2
0
0
0
0
1
0
0
2
0
0
0
1
0
0
1
0
0
0
0
2
0
2
0
0
0
1
0
2
0
1
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
2
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
2
0
1
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
3
0
0
2
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
2
0
0
1
2
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
2
5
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
2
2
0
0
1
0
1
0
2
2
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
3
1
0
0
0
0
0
0
0
0
0
2
1
0
2
3
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
3
2
0
0
1
0
0
0
0
2
2
0
0
0
0
0
4
0
2
0
0
1
0
0
2
0
0
0
1
1
3
0
0
0
0
2
0
0
0
3
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
1
1
2
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
2
2
1
0
2
0
2
0
0
3
0
0
0
0
1
2
1
1
0
0
0
0
0
0
0
2
0
0
1
1
1
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
4
1
1
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
2
3
0
4
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
2
0
2
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
6
0
0
0
1
0
0
0
0
0
2
0
0
0
3
2
0
2
3
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
3
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
1
0
2
0
0
0
0
1
0
0
0
1
0
2
0
1
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
2
0
0
1
1
2
0
1
2
2
0
0
0
0
0
0
1
2
0
1
0
0
2
0
0
2
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
2
2
0
1
0
0
0
0
2
2
0
0
2
0
0
0
2
1
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
2
1
1
0
0
2
0
1
0
0
0
0
0
3
0
0
1
0
1
6
1
2
0
2
0
0
0
1
0
1
0
0
3
0
2
1
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
1
0
2
0
1
0
2
0
1
0
2
0
1
0
1
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
3
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
2
0
0
0
2
1
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
3
0
2
0
0
7
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
2
0
1
1
0
0
0
1
0
0
0
1
1
0
0
0
2
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
2
0
3
0
2
0
0
2
1
2
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
1
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
3
3
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
4
0
1
0
0
2
0
0
2
1
0
0
0
2
2
0
0
2
0
2
2
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
1
1
0
0
1
1
0
0
0
0
0
1
0
0
1
0
1
0
2
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
1
0
1
1
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
1
2
0
3
2
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
3
0
1
0
0
0
0
0
0
0
0
2
2
4
0
0
3
0
0
1
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
2
1
0
2
0
0
1
0
0
0
2
0
2
0
2
0
0
3
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
3
1
1
4
1
1
0
0
2
0
1
0
0
0
2
0
1
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
2
0
4
0
0
3
7
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
2
0
5
0
0
0
0
1
0
0
0
1
3
0
0
0
0
0
0
2
0
0
2
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
2
0
0
0
0
0
0
5
1
2
0
1
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
2
0
0
0
0
2
1
1
5
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
3
0
0
0
1
2
0
3
0
0
0
0
2
0
0
0
1
0
1
0
1
0
1
0
2
0
0
1
4
0
0
0
0
0
1
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
1
2
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
4
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
2
0
1
1
2
0
2
0
0
1
0
0
1
2
1
0
0
0
0
0
3
0
2
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
2
0
6
2
1
0
0
1
3
0
3
1
0
0
0
2
0
2
0
0
0
0
0
0
1
0
1
0
0
0
2
2
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
2
0
0
1
3
0
0
2
0
2
0
0
0
0
2
2
0
2
10
0
0
0
2
1
2
2
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
3
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
1
0
2
2
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
1
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
3
2
0
0
0
2
0
1
0
0
0
2
2
0
1
2
0
2
1
0
0
2
2
0
0
0
1
0
2
0
2
0
0
2
2
2
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
3
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
1
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
2
2
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
1
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
2
0
0
2
0
2
1
0
1
0
0
0
1
2
0
0
0
0
0
0
1
0
0
2
0
1
0
3
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
2
8
3
1
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
2
0
0
0
2
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
1
0
0
2
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
2
0
2
2
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
4
0
0
0
2
2
0
0
2
0
0
0
2
0
1
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
4
2
0
0
0
0
0
0
0
0
2
1
0
2
1
2
2
0
2
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
3
0
0
0
1
0
0
0
0
0
0
1
3
0
2
0
2
0
0
0
0
0
2
0
7
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
1
0
0
2
2
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
1
1
1
0
1
1
1
2
0
0
0
0
0
0
0
0
3
2
0
0
1
0
0
0
0
0
0
0
1
0
0
3
0
0
2
2
0
0
0
0
0
0
2
0
0
0
2
1
0
2
0
3
0
0
0
0
0
1
1
0
1
2
1
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
4
0
0
0
0
4
2
0
1
0
1
2
0
0
2
0
0
2
3
0
0
1
0
0
2
0
0
2
0
0
3
0
0
0
0
0
1
1
0
0
0
0
1
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
2
0
1
0
0
2
0
0
1
0
0
2
0
0
0
2
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
2
0
2
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
3
0
0
0
0
2
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
1
1
0
2
1
0
0
0
0
0
0
2
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
4
0
1
4
0
2
0
0
0
0
2
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
3
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
4
0
0
0
2
0
0
2
2
0
0
2
6
0
2
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
1
0
0
1
0
1
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
3
0
1
1
0
0
2
0
0
1
0
2
0
2
2
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
2
0
2
0
0
1
0
3
0
0
0
2
0
0
0
1
0
0
0
1
2
0
0
0
2
0
0
0
1
0
0
3
0
1
0
0
2
1
0
0
2
1
0
0
0
0
0
1
3
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
3
2
0
0
2
0
2
1
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
2
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
4
2
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
1
1
1
0
2
0
2
0
0
0
0
0
0
3
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
1
0
1
0
0
2
0
1
1
1
1
0
2
1
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
1
0
0
2
0
0
0
0
2
0
2
0
0
1
1
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
4
1
1
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
2
1
0
1
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
1
0
1
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
1
1
0
1
1
0
0
0
0
4
1
0
3
0
0
1
0
0
0
0
2
1
0
0
2
5
0
0
1
1
0
0
0
0
0
1
2
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
2
0
3
0
2
0
0
0
0
0
1
0
3
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
2
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
1
0
2
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
1
1
1
0
0
0
0
0
0
0
1
0
1
0
2
2
0
0
1
0
3
1
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
2
1
2
0
1
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
2
2
0
0
3
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
4
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
2
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
1
1
0
0
2
0
1
1
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
3
0
0
2
0
2
0
1
0
0
2
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
2
2
2
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
4
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
3
0
0
0
2
0
0
2
0
0
1
0
0
0
0
2
0
1
1
2
2
0
0
0
0
0
0
1
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
1
0
0
1
3
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
1
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
2
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
2
0
2
0
0
0
1
2
2
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
1
0
1
2
0
0
0
3
0
2
2
0
0
2
0
0
2
2
0
0
0
0
1
1
0
1
0
1
0
0
0
0
2
0
0
0
0
1
0
1
1
2
0
0
0
1
1
1
0
0
0
2
3
1
2
0
0
0
0
0
0
1
1
0
0
0
2
2
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
4
2
1
1
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
2
2
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
5
0
0
3
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
2
0
0
2
0
5
0
2
1
0
1
2
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
1
2
0
0
1
0
0
0
4
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
2
0
0
1
1
2
0
2
0
0
0
0
2
0
0
0
0
0
1
0
5
0
0
0
0
0
0
0
0
2
0
0
2
1
1
0
0
1
0
0
5
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
3
1
2
1
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
3
2
0
0
0
0
0
2
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
2
1
2
2
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
2
0
0
2
2
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
7
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
1
0
0
0
4
0
0
0
0
0
1
0
1
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
2
0
0
2
0
0
0
1
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
2
1
0
0
0
1
0
0
2
0
3
0
2
1
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
1
2
0
0
0
0
1
0
1
2
0
0
0
1
0
0
0
0
1
0
2
2
0
0
2
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
6
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
3
0
2
0
1
0
0
0
0
2
0
0
0
3
3
0
2
2
1
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
2
1
0
2
0
2
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
8
0
0
2
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
2
2
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
3
0
0
2
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
1
0
0
3
0
1
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
1
3
2
1
0
0
0
1
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
2
1
0
0
0
0
0
0
2
0
0
2
1
0
2
0
0
0
0
1
0
0
0
1
2
0
1
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
3
0
0
0
0
2
0
0
0
3
0
0
3
0
0
0
4
0
0
1
2
1
1
0
4
4
0
0
0
3
2
0
2
3
0
0
0
2
2
0
1
2
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
1
1
0
1
0
2
0
1
1
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
1
2
0
2
0
2
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
1
2
0
1
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
1
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
1
0
2
2
1
0
0
1
0
0
0
0
2
0
0
0
2
1
0
1
0
1
0
0
0
0
0
0
0
0
2
0
2
3
0
0
2
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
6
0
1
0
0
0
1
0
0
0
0
0
0
1
0
2
0
1
0
2
2
1
0
1
2
0
0
1
1
0
0
0
1
2
0
0
1
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
2
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
4
0
0
1
1
0
0
0
0
2
2
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
3
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
8
0
0
1
1
2
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
8
1
0
1
0
0
0
0
1
2
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
4
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
2
2
1
0
2
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
1
1
0
0
2
1
3
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
2
1
6
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
1
0
1
1
0
0
1
2
0
0
0
0
2
0
0
1
2
2
1
0
0
0
2
3
1
0
0
0
1
1
0
0
2
0
0
0
3
2
1
0
0
1
2
0
2
4
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
2
0
1
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
3
1
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
3
1
0
0
0
4
0
2
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
2
2
1
0
0
2
0
0
1
0
0
0
0
1
0
2
0
0
1
0
0
0
2
1
1
0
0
0
11
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
3
2
0
1
1
0
0
0
1
0
2
2
0
0
0
2
0
0
1
0
0
4
0
0
0
0
1
1
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
1
1
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
2
1
0
0
0
0
0
0
0
0
1
2
1
0
0
1
0
0
2
0
0
2
0
2
2
0
1
0
2
3
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
3
4
0
0
0
0
6
0
0
2
0
1
0
2
2
0
1
1
0
0
0
2
2
2
2
2
0
0
0
1
0
0
0
2
1
0
0
0
0
4
1
1
0
2
1
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
1
0
0
2
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
2
0
0
0
1
2
0
0
0
0
0
0
2
1
0
2
0
0
2
0
1
0
1
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
1
1
3
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
5
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
2
1
0
1
0
0
0
3
2
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
1
2
0
0
0
2
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
2
0
1
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
3
0
1
0
0
0
1
0
2
2
2
0
0
1
1
0
0
0
0
0
3
0
0
0
0
0
3
0
2
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
1
5
0
0
3
0
0
0
3
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
1
0
2
0
0
2
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
2
0
0
0
4
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
1
0
0
0
0
0
0
2
0
1
0
2
0
0
0
2
0
0
0
0
1
2
0
2
0
1
1
0
0
2
0
0
0
1
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
2
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
1
2
1
0
0
0
0
0
1
0
1
2
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
3
0
0
0
1
0
1
0
0
0
0
1
0
0
2
2
0
0
0
0
0
2
0
0
0
2
0
0
3
0
0
0
1
0
2
2
0
0
1
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
2
0
0
1
0
1
0
0
2
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
1
0
4
1
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
1
1
0
0
0
1
0
1
4
0
0
0
2
0
2
0
0
0
0
1
2
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
2
2
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
2
1
0
0
0
0
1
0
1
0
1
0
2
0
0
0
0
2
0
2
0
0
0
0
0
1
0
1
1
0
2
2
0
1
0
0
1
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
1
0
2
0
1
0
1
1
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
2
2
3
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
4
1
2
1
2
0
0
1
0
1
0
0
0
1
0
0
2
0
0
0
0
0
2
3
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
2
8
0
2
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
3
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
2
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
1
0
0
3
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
2
0
1
0
0
0
0
1
0
0
0
0
0
1
5
2
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
1
1
1
0
0
1
1
0
0
0
0
1
1
2
0
0
2
0
0
1
0
0
0
1
0
0
0
2
3
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
2
1
0
0
1
0
0
0
2
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
2
2
0
0
2
1
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
1
0
1
0
0
0
0
2
0
0
0
0
2
2
0
0
1
1
0
2
2
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
2
2
2
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
2
3
2
2
0
0
0
0
0
1
7
0
0
3
1
0
1
1
1
0
3
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
3
0
2
0
0
0
0
0
0
1
0
2
0
0
0
1
0
2
0
0
0
0
2
0
0
0
2
0
1
6
0
2
2
0
0
0
0
2
0
2
0
0
0
0
2
3
0
2
9
0
1
0
2
2
0
0
0
0
0
1
2
0
2
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
3
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
4
0
0
0
1
0
1
0
0
1
0
0
0
2
0
0
0
0
0
2
0
3
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
4
1
0
0
0
0
0
2
0
1
1
0
0
2
0
2
1
0
1
0
0
0
0
2
0
1
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
2
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
1
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
2
0
2
0
1
0
0
0
0
1
0
0
2
0
0
0
2
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
1
1
0
1
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
3
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
1
0
0
2
0
1
9
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
3
0
2
2
3
0
0
0
0
0
0
0
2
1
0
0
1
0
2
0
0
2
0
0
0
2
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
1
0
0
2
1
2
0
0
0
0
0
2
0
1
0
0
1
2
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
2
3
0
2
0
0
0
0
4
2
0
0
0
0
3
0
0
2
0
2
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
1
2
0
0
3
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
1
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
1
0
2
1
0
1
4
2
2
2
0
0
1
0
0
1
2
0
0
2
0
2
0
0
1
0
0
1
0
2
2
0
0
0
0
1
1
2
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
3
0
0
0
0
0
0
0
0
0
3
0
0
0
1
2
0
0
0
0
0
0
0
0
2
1
0
0
1
0
2
2
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
6
0
2
2
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
2
3
1
0
0
2
0
1
0
0
0
0
1
5
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
3
1
0
0
0
2
0
2
0
0
0
1
2
0
0
1
2
0
0
2
0
0
0
1
1
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
2
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
2
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
2
0
0
1
2
2
0
0
2
2
1
0
2
0
0
0
2
1
3
1
0
0
0
0
0
0
2
1
2
1
0
0
2
1
1
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
2
0
0
0
2
0
1
0
0
1
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
1
2
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
2
2
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
1
2
2
0
0
2
0
0
1
2
0
0
0
1
0
0
0
1
0
2
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
2
0
0
1
0
0
1
0
1
2
0
0
0
0
2
1
0
0
3
0
0
2
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
2
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
2
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
2
0
1
2
0
0
1
0
0
0
1
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
2
5
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
3
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
1
0
1
1
0
0
2
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
1
0
2
0
0
1
0
2
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
2
1
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
3
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
2
0
2
3
0
1
0
2
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
1
1
2
0
0
1
1
1
2
0
0
0
0
0
0
0
2
2
0
0
2
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
1
2
2
0
0
0
0
0
0
0
0
4
0
1
0
1
2
0
1
1
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
2
1
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
2
1
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
3
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
2
0
2
1
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
2
1
0
0
0
0
1
0
1
1
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
3
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
2
1
0
0
3
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
2
0
1
0
0
0
0
0
0
0
2
1
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
1
2
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
2
1
0
2
0
0
3
0
0
1
0
2
0
1
1
0
0
3
2
0
2
0
0
0
0
2
3
0
1
0
0
0
0
2
1
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
2
0
0
0
2
4
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
2
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
1
1
0
1
2
0
0
0
2
0
2
0
0
1
3
0
2
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
1
2
2
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
4
1
0
0
0
1
0
3
0
2
0
0
0
0
0
2
0
6
0
2
0
2
0
0
2
0
1
2
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
2
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
1
0
0
1
2
1
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
1
0
2
2
2
0
5
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
9
1
0
4
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
3
1
0
2
0
0
0
0
0
2
3
2
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
4
2
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
2
0
2
0
1
0
0
1
0
2
2
1
1
0
0
1
0
0
0
2
2
0
1
0
2
0
0
3
2
1
2
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
1
2
0
2
0
0
0
1
0
1
2
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
1
0
0
1
1
0
0
1
4
0
0
1
0
0
1
0
2
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
3
0
0
0
0
0
3
0
0
1
0
2
2
1
0
2
1
0
0
1
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
1
0
1
2
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
2
0
0
0
2
0
0
0
0
2
3
0
0
0
0
2
0
0
1
0
0
0
4
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
3
0
2
0
1
0
0
1
2
0
0
0
0
0
0
0
3
0
1
0
2
2
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
2
2
0
2
2
0
0
1
1
0
1
2
0
0
0
0
0
0
0
1
2
2
1
2
0
0
0
0
0
0
0
1
2
2
2
0
1
0
1
0
0
0
0
3
0
4
0
0
0
0
2
0
2
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
2
0
1
0
1
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
3
0
0
1
2
0
0
0
0
2
0
0
0
0
1
4
0
0
2
0
0
2
0
3
0
1
0
0
0
0
0
3
0
3
1
1
0
0
0
2
0
0
0
0
0
0
0
5
1
0
0
0
1
2
0
2
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
1
1
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
4
0
1
0
0
2
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
1
0
2
1
0
0
1
0
2
0
2
0
2
0
1
2
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
2
1
0
0
1
0
1
1
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
2
1
0
1
0
0
0
0
1
2
0
0
0
2
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
2
0
2
0
0
0
2
0
0
1
2
2
2
0
2
0
0
0
1
0
3
0
0
0
0
0
1
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
4
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
1
2
2
0
0
1
2
0
1
0
2
1
0
0
1
0
0
1
2
0
0
0
2
0
2
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
2
2
0
1
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
3
0
2
1
0
1
3
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
2
0
0
1
2
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
1
1
0
2
0
0
1
2
1
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
2
1
1
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
5
0
2
0
0
0
1
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
3
2
5
0
0
1
0
0
1
2
0
0
2
0
0
2
0
0
0
0
1
0
0
1
1
1
3
0
0
1
0
0
2
3
0
0
0
1
0
1
2
0
0
0
1
0
1
0
0
0
0
1
1
2
0
0
0
1
1
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
1
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
1
0
3
0
0
2
3
0
1
0
0
2
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
3
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
5
0
0
0
4
0
0
0
0
0
2
2
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
2
0
2
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
2
1
0
0
1
0
0
0
0
1
0
0
2
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
1
4
0
0
0
2
1
0
2
0
1
2
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
4
1
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
3
0
1
0
1
0
1
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
1
0
4
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
1
2
0
0
2
4
0
2
0
0
0
2
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
2
0
1
2
1
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
2
2
1
0
2
0
0
1
1
0
0
2
0
1
1
0
0
1
2
0
2
0
1
0
3
0
2
0
0
4
0
0
0
0
0
0
2
2
0
1
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
1
0
1
1
3
0
3
0
1
1
0
2
0
0
2
0
2
2
2
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
1
2
0
2
3
0
0
0
0
0
0
1
0
3
0
0
2
0
0
2
2
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
1
2
0
2
1
0
1
0
2
2
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
2
2
0
1
0
0
1
1
0
0
0
0
10
2
0
0
0
0
2
0
2
0
0
0
2
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
2
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
2
0
1
1
0
0
0
0
1
0
3
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
2
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
5
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
2
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
3
2
2
2
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
1
0
2
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
1
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
3
0
2
0
0
2
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
2
0
4
2
1
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
6
0
0
2
0
0
0
0
1
1
0
1
1
0
0
0
1
0
0
0
1
0
0
2
0
0
1
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
3
0
1
0
0
1
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
3
1
0
0
0
5
0
0
0
1
0
3
0
0
1
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
3
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
5
0
0
0
0
2
0
0
0
0
1
2
2
1
0
2
0
1
0
0
1
0
0
1
1
0
0
0
0
2
0
1
1
0
2
0
0
1
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
2
1
0
0
2
0
0
1
0
0
0
0
0
0
2
0
2
2
2
0
0
0
2
0
0
1
0
1
0
0
0
2
0
0
0
0
2
0
3
3
2
0
1
0
0
2
0
0
0
3
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
1
0
0
0
2
0
0
1
1
1
2
1
0
0
2
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
2
1
2
0
0
0
0
0
0
0
0
1
3
1
0
0
3
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
1
2
0
2
2
0
1
0
0
0
0
0
0
2
1
0
1
0
2
0
0
1
3
0
2
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
3
0
1
2
0
0
1
1
0
2
2
0
2
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
1
0
1
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
2
1
3
0
0
0
3
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
2
2
0
0
0
0
0
2
1
0
2
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
7
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
2
2
0
1
0
0
0
3
5
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
2
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
4
0
2
0
0
0
0
2
4
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
1
0
2
0
2
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
1
1
0
1
0
0
1
6
0
0
1
0
0
0
3
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
6
0
0
0
0
0
2
1
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
3
0
1
0
0
1
0
0
0
2
0
0
0
2
1
0
0
0
1
0
0
2
1
0
3
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
3
0
2
2
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
2
0
0
1
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
3
2
0
2
1
0
0
0
0
1
0
0
0
6
0
1
0
2
1
0
0
0
2
2
2
0
1
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
1
1
1
0
0
0
0
0
0
2
0
0
1
1
0
2
0
0
0
1
0
0
1
2
0
0
0
1
0
0
0
2
2
0
0
1
1
2
0
0
2
0
0
2
0
0
0
0
0
1
1
0
2
3
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
2
0
0
0
0
0
0
1
1
1
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
1
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
1
1
0
2
2
0
0
1
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
1
0
0
0
1
1
2
1
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
3
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
1
0
2
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
2
1
0
0
0
0
0
0
3
0
1
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
1
2
0
0
0
0
2
2
0
2
0
2
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
1
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
2
1
1
2
2
2
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
2
2
0
0
0
1
0
0
0
4
0
2
0
0
0
2
0
2
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
3
2
2
0
0
0
1
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
2
0
1
0
1
0
0
0
1
0
0
2
1
0
0
1
0
1
2
2
0
1
0
1
1
2
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
1
2
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
2
1
0
2
4
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
4
0
1
0
0
0
0
1
2
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
2
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
1
0
0
1
0
0
0
0
0
2
1
0
0
0
2
1
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
1
1
2
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
2
2
0
2
0
0
0
0
1
2
0
0
0
0
1
1
2
0
1
0
0
0
0
0
2
0
1
0
0
2
0
1
0
0
0
0
0
3
2
0
1
0
0
0
2
0
1
0
1
4
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
2
0
0
2
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
3
1
2
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
1
9
3
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
3
1
0
0
0
2
0
2
1
1
1
2
0
0
0
1
2
2
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
6
3
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
3
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
3
0
1
0
1
1
1
1
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
2
1
0
2
0
2
2
2
0
0
0
0
2
0
2
0
0
0
0
0
0
5
0
0
0
1
2
0
1
0
0
2
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
4
0
2
0
2
2
5
2
1
0
1
0
0
0
1
3
0
1
1
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
1
0
2
2
1
0
0
0
0
0
2
0
0
0
2
0
1
0
1
2
0
1
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
3
1
2
1
0
2
0
1
0
0
1
0
2
2
0
3
0
1
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
1
0
1
0
0
2
4
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
1
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
2
0
0
1
1
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
1
0
1
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
5
2
0
0
2
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
0
1
1
0
0
1
0
0
0
0
0
0
3
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
2
3
0
0
0
5
0
0
0
0
0
0
0
0
1
0
3
0
2
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
1
0
0
0
0
2
0
2
1
0
0
0
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
1
0
1
0
0
1
15
0
3
2
0
0
1
0
0
0
2
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
1
0
2
0
0
0
3
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
1
0
0
0
1
1
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
2
2
0
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
2
0
3
0
0
1
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
2
2
1
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
4
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
2
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
7
2
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
1
2
2
2
2
0
2
0
1
0
0
0
0
1
1
0
0
0
0
0
2
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
5
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
1
1
0
1
2
0
1
0
0
0
0
0
0
1
0
0
4
0
1
0
0
2
0
1
1
0
0
0
0
1
2
1
0
2
0
1
0
0
0
2
2
0
0
0
0
0
1
0
2
0
1
0
2
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
2
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
7
0
2
0
0
0
1
0
0
0
2
0
4
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
2
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
2
0
2
0
1
0
0
2
1
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
2
2
1
0
2
0
0
0
1
0
0
2
1
1
0
0
0
0
2
0
1
0
0
0
1
0
1
0
0
2
0
0
0
1
3
4
0
0
1
0
0
0
0
0
1
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
1
2
0
0
1
1
0
1
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
1
0
0
0
1
0
0
1
7
0
1
2
0
0
0
1
0
1
0
1
2
0
1
1
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
1
0
2
0
0
2
0
0
0
0
0
2
0
1
0
2
0
0
1
0
1
1
0
1
0
0
3
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
1
2
0
1
0
0
2
0
0
0
0
0
0
0
2
2
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
3
0
0
0
0
2
2
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
2
0
0
1
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
2
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
1
2
0
0
0
0
2
2
1
1
0
0
2
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
2
1
1
0
0
0
2
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
2
1
0
0
0
0
0
0
0
1
0
0
3
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
2
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
3
1
0
0
0
0
0
0
0
0
1
2
0
1
0
1
1
0
0
0
3
0
1
2
1
0
1
0
1
0
0
0
0
0
0
0
0
1
1
4
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
1
0
3
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
11
0
1
0
0
0
0
2
0
2
3
0
2
0
0
0
8
0
0
0
1
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
2
2
0
0
0
0
0
0
1
0
0
1
0
2
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
2
2
0
0
0
2
1
2
2
0
0
2
0
0
2
0
0
1
0
0
2
0
0
0
0
2
1
1
0
0
2
5
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
1
0
0
0
0
0
0
1
1
0
0
2
0
2
2
2
0
0
0
0
1
0
2
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
2
0
1
1
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
2
0
0
0
2
0
3
1
2
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
6
0
5
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
1
0
0
0
6
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
1
0
0
0
0
3
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
2
2
2
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
2
3
0
1
1
2
2
0
0
0
1
2
0
0
0
4
0
0
0
0
0
0
0
0
1
1
3
1
0
0
0
0
0
2
2
0
0
1
4
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
2
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
2
0
0
1
1
0
2
0
0
0
0
2
0
0
0
0
0
0
4
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
1
2
0
2
2
0
0
0
0
0
2
0
1
0
0
0
2
3
0
0
2
0
1
0
2
0
0
0
0
1
1
0
0
0
1
0
2
1
0
1
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
4
0
1
1
0
1
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
2
0
0
0
0
0
1
0
0
2
0
2
0
0
1
2
0
0
0
0
0
0
0
0
3
1
1
0
0
0
0
0
4
0
0
0
0
0
1
0
1
1
1
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
1
0
2
0
0
1
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
1
0
2
0
0
0
0
1
0
0
2
2
0
1
1
1
0
1
0
0
1
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
1
0
0
0
0
1
1
0
0
0
0
2
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
2
5
0
0
1
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
2
0
0
0
0
0
0
2
0
2
0
0
0
0
1
1
0
0
0
2
3
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
5
0
1
0
0
0
1
1
1
3
0
0
0
0
0
1
0
0
0
2
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
3
0
0
0
0
3
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
1
0
0
0
1
2
0
2
0
0
0
1
1
3
2
0
2
0
0
0
1
0
1
0
0
0
1
1
1
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
1
0
0
1
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
1
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
2
2
3
0
0
2
0
0
0
0
0
2
0
4
0
1
2
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
2
0
1
0
2
0
0
0
0
0
3
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
1
2
0
2
0
0
1
0
1
0
0
0
1
2
1
0
2
0
0
0
0
0
2
0
1
0
0
0
2
2
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
2
0
0
0
0
1
0
3
1
0
0
1
1
0
0
1
1
1
0
3
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
6
0
0
0
0
2
0
1
2
2
0
0
5
1
0
0
0
0
2
0
1
1
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
2
0
0
1
0
0
1
2
0
0
0
0
0
1
0
0
0
0
2
0
0
3
1
0
2
6
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
2
2
0
0
3
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
1
0
2
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
2
2
0
0
2
0
0
0
2
4
0
1
0
0
0
0
2
1
2
0
0
0
0
1
0
0
3
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
2
2
0
0
0
0
3
0
0
1
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
2
0
3
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
2
3
1
2
1
0
0
0
0
0
0
0
0
3
1
0
0
2
0
3
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
1
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
3
0
1
2
0
2
1
2
0
0
5
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
1
1
2
0
2
0
0
0
0
0
0
0
0
3
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
2
2
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
1
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
2
0
4
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
2
0
0
2
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
1
1
0
2
0
0
0
3
0
0
2
0
0
0
1
2
0
0
0
0
1
2
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
7
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
1
0
2
0
0
0
2
2
1
0
0
0
6
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
1
0
2
0
1
0
0
0
0
0
1
2
1
1
0
2
0
0
0
0
0
1
4
1
1
2
1
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
2
1
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
1
0
2
2
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
2
0
1
1
0
0
0
6
1
2
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
1
2
5
1
1
0
2
0
0
0
0
0
2
1
0
0
0
2
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
1
1
0
0
0
1
0
1
0
0
0
0
6
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
2
1
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
2
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
2
0
2
2
2
0
2
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
2
2
1
2
2
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
2
2
0
0
0
2
0
1
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
1
0
1
0
0
0
1
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
1
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
1
0
0
1
0
2
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
1
1
0
0
1
0
1
1
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
1
2
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
2
0
1
0
1
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
1
0
0
1
0
0
2
2
0
1
0
0
0
0
0
0
0
1
0
0
2
2
2
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
2
1
2
0
0
0
2
0
1
1
3
1
0
0
0
3
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
2
0
0
2
0
4
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
2
0
0
1
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
1
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
7
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
2
1
1
1
0
2
0
0
0
1
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
1
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
4
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
2
3
3
2
1
0
1
2
0
1
2
0
0
2
0
0
0
2
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
2
0
2
0
0
0
1
0
1
0
0
0
1
0
0
0
0
2
0
2
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
3
0
0
2
0
1
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
4
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
2
2
1
0
2
0
0
2
0
0
0
1
0
0
0
5
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
6
0
1
0
0
1
0
1
0
0
0
0
2
1
0
0
0
0
1
0
2
2
0
1
2
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
2
0
2
1
0
2
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
2
2
1
2
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
5
2
1
0
1
0
0
0
1
0
0
2
0
0
0
1
0
2
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
2
2
0
0
2
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
2
2
0
1
0
0
2
0
1
0
2
1
2
0
0
0
0
0
2
0
2
1
0
0
0
0
0
6
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
1
1
0
0
1
2
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
2
2
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
3
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
1
2
0
0
0
2
0
2
0
2
8
0
1
1
0
0
0
0
2
0
0
0
1
0
0
2
2
0
1
0
1
2
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
3
0
0
0
0
1
2
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
2
0
0
0
2
1
5
1
0
0
0
0
0
0
1
0
0
0
0
0
3
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
1
0
1
0
4
2
2
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
6
1
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
3
0
0
0
0
3
0
0
1
1
2
0
3
9
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
1
2
0
0
0
2
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
1
1
0
1
2
1
0
0
2
0
0
3
0
0
0
0
0
2
0
1
0
1
1
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
4
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
3
0
0
1
0
0
0
0
0
1
1
0
0
0
0
2
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
1
2
0
0
0
0
4
0
0
0
0
0
0
0
3
2
4
0
4
2
0
2
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
2
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
1
0
2
2
0
3
0
2
0
0
0
0
0
0
2
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
1
0
0
2
0
3
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
2
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
1
0
0
2
0
0
0
0
1
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
1
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
2
0
2
0
1
0
2
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
3
1
0
1
0
6
0
2
0
1
0
1
1
0
0
0
0
3
2
0
0
1
0
5
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
2
0
0
0
2
0
0
0
0
1
0
0
1
1
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
2
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
2
0
1
1
0
0
0
1
0
2
1
0
2
1
0
0
1
2
1
0
3
0
0
2
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
1
1
2
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
1
0
2
0
1
3
0
0
0
0
0
0
0
0
1
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
1
2
0
1
0
0
0
0
0
2
1
2
0
0
2
4
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
6
0
0
0
2
0
1
0
2
0
1
0
0
0
0
1
0
0
0
5
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
2
0
2
0
2
0
0
0
1
0
0
2
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
1
3
0
0
0
0
0
1
0
0
0
0
1
1
0
0
2
0
0
1
0
2
1
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
3
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
3
1
0
2
3
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
1
0
2
0
0
0
1
0
2
0
0
0
2
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
2
2
0
1
0
0
1
2
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
4
2
1
2
0
1
0
0
0
0
0
0
2
0
1
0
0
0
3
0
0
0
1
0
3
0
2
0
2
0
2
2
0
2
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
1
3
1
1
0
0
2
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
7
0
1
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
2
0
2
1
0
0
1
0
0
0
0
1
1
0
0
0
4
2
0
1
0
0
1
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
1
2
0
2
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
2
0
0
2
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
4
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
6
1
1
1
0
2
0
0
0
3
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
2
1
0
0
0
0
0
0
1
0
1
0
0
2
1
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
2
0
2
0
1
0
1
0
2
0
1
0
0
0
0
1
0
0
2
0
2
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
2
1
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
2
0
1
0
1
0
1
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
2
2
2
4
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
1
0
2
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
2
1
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
1
0
4
0
0
1
0
0
0
1
0
2
1
0
1
0
0
1
0
0
0
1
0
1
0
0
1
0
2
1
0
0
0
2
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
2
1
1
0
0
2
0
0
0
0
1
0
2
0
0
0
0
1
0
2
1
0
0
1
3
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
6
0
0
0
0
0
0
0
0
1
0
1
0
1
0
2
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
3
2
0
2
0
1
0
0
0
0
0
0
2
0
1
0
2
0
0
0
2
2
0
1
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
3
1
0
1
1
2
0
1
0
0
0
1
2
0
0
0
1
0
0
0
2
0
1
2
0
1
1
0
0
1
0
1
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
1
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
1
1
0
0
0
0
0
0
0
1
0
2
1
0
3
1
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
3
2
0
0
2
0
0
0
1
0
0
0
2
1
0
1
1
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
2
0
1
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
1
2
0
0
0
0
3
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
2
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
1
0
0
0
0
0
0
2
0
1
0
0
3
0
1
0
0
0
0
0
1
2
0
0
2
0
0
2
1
0
2
0
0
0
0
0
2
1
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
2
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
1
1
0
0
1
2
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
1
1
0
2
1
1
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
3
2
0
1
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
2
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
2
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
2
0
0
1
0
0
0
0
1
0
0
1
0
2
1
2
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
2
0
0
2
0
0
1
0
1
1
0
0
0
0
1
0
0
0
2
0
0
2
0
1
2
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
2
3
0
0
0
1
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
1
1
0
0
2
1
0
0
0
0
1
1
2
2
1
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
3
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
3
0
1
1
0
1
0
0
2
0
0
0
0
0
3
2
2
1
0
2
2
1
0
0
0
0
3
0
0
0
0
0
0
1
2
0
2
4
0
0
0
2
2
2
2
1
0
2
0
3
1
0
0
2
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
2
1
0
3
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
2
0
0
1
1
0
0
2
2
0
1
2
1
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
1
0
0
1
0
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
2
0
2
0
0
0
0
1
0
3
0
0
0
0
0
2
0
0
1
0
0
0
0
4
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
5
1
0
0
0
0
2
2
0
0
1
2
2
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
1
0
2
2
2
0
0
1
0
0
0
1
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
3
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
2
4
2
0
2
0
0
0
1
0
0
0
1
1
0
0
0
0
0
3
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
1
0
0
2
1
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
1
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
7
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
3
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
2
0
3
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
1
0
2
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
2
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
2
1
2
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
2
0
1
0
0
0
0
0
2
1
0
1
0
2
0
0
0
0
0
2
1
1
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
2
0
0
0
1
0
0
2
0
2
3
0
0
1
0
0
3
2
0
4
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
4
1
0
0
0
0
0
0
1
0
0
0
1
2
0
3
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
1
0
1
0
2
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
2
0
2
0
0
2
0
3
0
0
0
0
2
0
0
0
0
2
2
0
0
1
0
0
1
3
2
0
1
0
1
0
0
2
0
0
0
0
1
4
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
2
0
1
0
1
2
0
0
0
0
0
0
1
2
2
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
2
0
0
2
0
0
2
0
3
1
0
2
0
0
0
0
1
0
0
0
0
1
0
0
1
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
2
4
1
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
2
0
1
1
0
1
0
2
0
1
0
0
0
1
0
0
0
1
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
2
1
0
0
0
0
0
2
1
0
0
1
0
0
4
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
1
3
0
2
4
0
0
0
0
1
0
0
1
0
6
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
2
0
4
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
2
2
1
0
2
2
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
1
0
0
0
2
1
1
1
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
2
2
0
0
3
0
0
2
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
1
0
0
0
0
0
5
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
3
0
1
1
0
0
2
0
0
1
0
0
0
0
1
0
0
1
0
1
2
0
0
1
1
2
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
2
1
1
2
0
0
0
0
0
0
0
2
0
0
1
0
1
0
1
0
0
0
0
1
2
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
2
2
0
0
0
0
3
0
1
0
0
0
0
2
0
1
1
2
0
2
2
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
1
0
0
0
2
0
0
2
2
0
0
1
1
0
2
2
0
0
0
2
2
0
0
0
0
3
0
0
0
2
0
0
2
0
0
0
0
2
1
0
0
0
0
0
3
0
0
8
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
2
3
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
1
1
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
2
3
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
1
0
3
2
0
0
2
2
0
1
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
2
1
2
1
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
2
2
0
2
0
0
2
2
0
0
0
0
0
1
2
0
0
0
1
0
0
2
2
0
1
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
3
1
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
5
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
1
0
0
0
1
2
0
2
1
0
0
0
2
0
1
2
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
2
1
1
0
1
1
0
0
2
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
2
0
1
3
0
0
0
0
0
1
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
6
0
0
0
2
0
1
2
0
0
0
0
0
2
0
0
2
0
1
0
1
0
0
0
2
0
1
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
1
0
0
1
0
1
0
0
0
1
1
0
0
1
0
2
0
1
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
1
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
3
1
0
0
2
0
1
0
3
1
0
0
0
0
0
0
2
0
0
2
0
2
0
3
1
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
1
2
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
1
0
0
0
0
1
0
2
0
0
2
0
3
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
2
2
0
2
0
0
1
0
0
0
0
0
2
2
0
1
6
0
1
1
1
2
0
1
0
2
1
0
0
0
2
4
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
6
2
0
0
0
0
1
0
1
0
1
2
0
0
0
0
1
0
1
2
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
1
0
0
2
0
2
1
0
2
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
1
1
0
0
0
0
2
0
0
1
1
0
1
0
0
1
10
2
1
8
3
1
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
1
0
1
2
0
0
2
0
3
1
0
0
0
0
1
4
0
1
0
0
0
0
2
0
2
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
2
0
0
0
2
1
0
0
1
0
0
1
3
0
3
1
0
0
0
0
0
0
1
1
0
0
1
2
2
0
0
1
1
0
1
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
2
0
0
0
2
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
2
1
0
1
2
0
0
0
1
0
0
0
1
0
0
1
1
2
0
0
0
0
1
1
0
0
0
0
2
0
3
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
4
0
0
0
0
0
0
0
3
0
0
2
0
1
0
0
0
1
1
0
1
1
2
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
5
0
0
2
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
1
0
0
2
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
1
0
1
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
3
0
0
0
0
2
0
2
0
2
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
1
0
2
1
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
1
0
1
1
0
0
0
2
0
1
5
0
2
0
0
0
0
1
0
0
4
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
2
1
0
0
2
3
0
2
2
0
0
0
2
0
1
0
2
0
0
0
0
0
0
2
11
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
2
0
1
0
0
0
0
2
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
1
0
0
0
1
0
2
0
2
0
0
1
0
0
0
0
1
2
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
2
0
0
2
1
0
2
2
0
0
0
0
0
1
0
2
0
1
2
3
0
1
0
0
1
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
2
2
1
2
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
1
0
0
0
0
0
1
2
1
3
0
0
0
2
1
2
0
0
0
0
0
0
0
1
1
2
0
0
0
0
1
0
0
1
2
2
0
4
0
0
0
1
1
2
0
0
1
0
0
2
1
0
0
0
0
1
0
0
0
1
5
0
0
2
0
1
1
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
2
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
4
0
1
0
0
0
0
0
0
0
0
4
0
2
2
0
0
1
0
0
1
1
0
0
0
2
0
0
0
1
0
0
0
0
0
7
1
0
0
2
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
3
1
2
0
2
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
4
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
2
1
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
3
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
1
1
3
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
2
0
0
2
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
2
2
0
2
1
1
0
2
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
3
0
0
0
1
0
2
0
1
5
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
1
0
0
0
1
0
0
0
2
0
2
0
4
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
2
3
0
0
0
3
6
2
0
0
0
1
2
0
2
1
0
5
0
0
1
0
0
0
0
0
0
2
0
2
0
2
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
1
0
1
3
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
4
3
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
1
0
2
0
1
2
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
3
1
0
0
4
0
0
0
2
0
0
0
1
0
0
0
0
1
3
2
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
1
2
1
0
0
2
2
0
3
0
0
2
0
2
3
0
0
0
0
0
0
0
0
2
0
0
0
2
1
1
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
2
1
0
0
2
0
0
0
2
0
0
0
0
0
1
0
1
0
2
0
0
2
2
0
0
0
0
1
2
2
3
0
1
0
0
0
1
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
2
2
0
0
2
2
1
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
1
2
1
0
1
0
0
1
0
2
0
0
1
1
2
1
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
3
0
0
0
0
1
0
0
0
2
0
0
1
3
0
1
0
0
2
0
2
2
1
0
2
0
0
0
2
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
3
1
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
1
2
0
3
0
0
1
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
1
1
1
0
0
0
2
1
0
2
0
0
2
0
1
1
0
2
1
0
1
2
0
0
0
1
0
0
6
0
0
0
3
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
2
0
1
0
1
0
0
1
2
0
0
0
0
0
2
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
1
0
0
0
0
0
2
2
0
1
0
0
1
1
3
0
0
0
0
1
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
2
0
0
0
4
0
2
0
2
0
3
0
0
0
0
0
2
0
0
0
2
4
0
0
1
0
0
3
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
4
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
3
0
2
0
0
0
1
0
0
0
2
0
0
1
2
0
1
2
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
2
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
2
0
0
2
0
1
2
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
4
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
2
1
0
0
1
0
3
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
2
0
1
2
0
1
0
2
0
0
0
0
2
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
1
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
1
1
0
0
1
0
1
1
0
0
0
2
1
2
0
1
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
5
0
0
0
1
3
0
0
0
0
0
0
0
3
0
0
1
2
0
2
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
2
0
2
2
0
2
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
2
2
2
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
1
1
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
2
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
1
1
1
0
2
0
0
0
2
2
0
0
0
3
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
1
0
2
0
0
0
0
0
1
0
0
5
0
2
3
0
0
1
0
0
0
1
1
0
0
0
2
1
0
0
0
0
0
2
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
1
1
0
2
0
0
0
0
1
2
0
0
0
1
0
0
1
0
1
0
0
0
1
1
1
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
1
1
1
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
2
0
0
0
3
0
0
0
3
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
3
0
0
0
0
2
0
2
0
0
0
0
0
2
2
0
0
1
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
3
0
0
1
0
0
0
1
0
4
0
0
0
0
1
0
3
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
2
0
0
0
1
0
2
0
1
0
2
2
0
2
1
0
0
0
1
1
0
1
1
0
2
0
1
2
0
0
0
2
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
3
0
0
2
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
3
0
0
3
0
1
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
2
0
2
0
0
0
0
0
0
2
1
0
0
1
0
0
2
0
0
0
3
0
0
1
1
1
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
2
0
1
1
0
2
0
2
1
0
0
0
0
0
2
2
0
0
5
0
3
0
3
3
3
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
1
0
0
0
2
2
0
2
0
2
0
1
0
0
2
0
0
0
0
0
1
0
1
0
0
1
0
2
1
0
0
1
0
2
1
0
0
0
4
0
4
0
1
0
0
0
0
0
0
2
0
0
0
6
1
1
0
2
2
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
10
2
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
3
0
0
0
0
1
1
0
1
2
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
3
0
0
0
0
4
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
2
2
0
0
1
0
0
0
0
0
0
0
2
0
0
2
1
1
2
0
2
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
1
0
0
0
0
2
0
0
1
0
1
0
0
1
2
0
3
0
0
0
0
2
1
3
1
0
0
0
1
0
4
2
0
1
0
0
1
0
0
0
0
1
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
1
2
0
0
2
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
2
2
1
0
0
2
8
2
0
2
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
2
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
1
2
1
0
0
0
1
1
0
0
0
0
2
1
0
3
0
0
2
1
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
2
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
2
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
1
2
0
2
0
1
1
1
0
0
0
1
0
2
1
0
0
2
0
3
0
0
0
0
0
1
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
2
1
2
0
0
2
0
0
2
0
0
0
0
0
0
0
2
5
0
0
0
4
0
0
1
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
3
0
0
0
2
0
0
0
2
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
2
0
0
1
2
2
4
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
3
0
0
0
0
0
0
2
0
0
0
0
5
2
0
0
0
2
2
2
0
2
0
0
0
0
0
2
0
1
0
3
0
0
0
1
0
0
0
0
3
0
0
0
3
0
0
1
2
0
0
0
2
0
0
0
0
2
0
1
0
1
2
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
1
0
1
2
1
0
0
1
0
0
4
3
0
0
1
0
0
0
0
1
1
0
0
0
0
0
2
1
1
0
0
2
0
1
0
0
3
0
0
0
1
1
0
2
2
0
0
2
2
0
0
0
0
0
1
1
1
0
0
1
1
0
0
0
0
0
2
0
2
0
0
1
0
1
0
0
0
1
1
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
2
0
0
1
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
3
1
0
0
2
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
2
0
0
0
2
3
0
0
0
0
0
1
0
2
0
2
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
1
0
2
2
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
1
0
3
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
3
1
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
3
0
2
0
1
0
2
0
0
0
0
2
0
2
1
2
1
0
2
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
7
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
1
1
2
2
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
1
1
1
2
0
3
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
2
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
2
4
0
1
0
0
0
1
0
0
0
0
0
0
0
0
5
0
0
2
0
1
0
3
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
3
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
1
2
0
0
0
2
0
0
0
2
0
1
1
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
2
1
0
0
1
0
0
0
1
0
0
0
0
0
2
1
0
2
0
1
0
2
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
2
0
0
1
2
0
0
0
0
3
0
0
0
1
0
0
0
1
0
1
0
0
1
2
0
1
0
0
0
0
1
0
0
2
1
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
2
0
0
1
1
0
2
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
4
3
0
0
0
0
7
0
0
0
0
1
0
2
1
1
1
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
2
0
2
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
3
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
1
0
0
0
0
0
3
1
0
1
1
0
1
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
1
1
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
1
2
0
0
0
0
0
0
1
0
1
0
0
0
2
0
2
1
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
2
0
2
1
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
3
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
1
0
1
0
0
0
0
0
1
0
2
0
3
0
2
2
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
4
0
2
0
0
2
0
2
0
0
0
0
2
0
0
0
2
0
2
0
0
1
1
1
1
2
1
2
1
0
2
0
0
0
3
1
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
2
0
2
0
0
1
2
0
1
0
2
0
1
0
0
2
3
2
0
0
0
0
0
0
0
0
0
0
0
1
2
1
2
0
0
0
0
0
6
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
4
2
2
0
0
1
0
0
0
0
0
0
0
0
2
3
0
1
0
0
0
0
2
0
0
0
0
2
2
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
2
1
0
0
1
0
0
0
0
0
2
2
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
1
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
2
0
0
1
0
0
2
1
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
2
0
0
0
0
0
3
0
0
2
1
0
0
0
3
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
2
0
0
0
3
1
0
0
0
0
0
0
0
3
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
1
0
0
4
0
3
1
0
0
0
0
2
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
5
1
2
0
2
0
0
2
2
0
0
0
1
0
1
0
0
0
0
1
1
1
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
1
0
4
0
1
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
1
0
3
0
1
1
0
0
0
0
1
1
0
0
0
3
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
2
0
0
0
2
0
1
1
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
1
0
1
1
0
1
0
0
0
0
1
2
0
2
0
0
2
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
7
0
0
0
0
0
0
2
0
0
0
3
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
1
1
0
0
0
0
1
0
1
0
0
0
0
1
2
0
0
0
2
1
0
2
1
5
2
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
2
1
0
0
1
0
0
2
3
2
0
0
0
0
0
0
2
1
0
2
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
1
2
3
0
0
0
0
1
0
0
0
0
0
2
2
2
0
1
1
1
0
0
0
0
2
2
0
0
2
0
0
0
0
1
0
0
4
0
0
0
1
0
2
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
1
1
0
0
1
2
0
0
0
0
2
0
4
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
4
0
2
0
2
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
2
0
0
2
1
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
2
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
2
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
7
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
1
0
0
3
0
0
0
0
0
0
1
0
2
0
2
0
0
1
1
2
0
0
2
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
2
0
0
2
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
5
2
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
2
0
1
2
0
0
0
0
0
0
0
0
0
1
2
0
0
4
1
1
0
0
0
0
0
1
0
1
1
0
0
0
2
2
0
1
0
0
0
0
0
0
0
1
1
2
0
3
0
0
1
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
3
2
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
1
1
0
2
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
2
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
2
3
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
6
0
0
0
0
2
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
3
0
0
2
1
0
0
0
1
0
0
4
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
2
2
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
2
0
2
0
0
1
0
0
0
0
0
3
2
0
0
1
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
3
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
1
0
2
3
2
1
2
2
1
0
0
2
2
0
0
2
0
1
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
1
0
2
0
0
1
2
1
0
0
1
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
1
0
0
0
2
2
0
0
0
2
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
1
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
1
0
6
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
3
1
2
0
3
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
2
0
0
1
0
0
0
0
0
1
0
0
0
2
1
1
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
1
1
0
1
2
4
0
0
0
1
2
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
2
0
2
0
0
3
1
0
0
0
0
2
2
0
2
2
1
0
0
1
2
0
2
0
1
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
1
0
1
0
2
0
0
1
2
0
0
2
0
2
0
0
4
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
6
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
3
0
0
0
0
0
2
1
3
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
1
0
0
4
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
2
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
3
0
0
2
1
0
2
0
0
0
2
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
5
0
1
0
1
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
2
2
1
2
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
1
1
0
4
1
7
0
0
0
0
0
2
2
1
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
2
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
3
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
5
0
2
0
0
1
0
0
1
0
0
2
1
0
2
0
0
0
1
0
1
2
0
0
0
0
0
0
1
0
0
0
0
2
0
1
1
0
0
0
0
2
1
0
0
0
3
0
1
0
1
1
0
0
3
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
1
0
2
0
1
4
0
0
1
2
0
0
1
1
1
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
2
1
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
3
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
2
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
5
2
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
2
0
0
0
0
0
0
0
1
0
2
1
1
0
0
0
0
1
2
1
2
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
7
2
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
1
0
0
6
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
2
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
3
2
2
0
2
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
1
1
0
1
3
0
0
1
0
2
0
0
0
0
1
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
2
0
3
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
1
0
0
1
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
2
0
1
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
2
0
0
1
2
0
1
0
1
2
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
3
2
1
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
3
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
3
0
0
1
0
0
0
0
5
0
2
1
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
1
0
2
0
1
1
0
2
0
1
0
0
0
1
0
0
2
2
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
1
0
0
0
0
0
2
0
1
3
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
1
1
0
0
1
0
2
0
2
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
2
0
0
2
1
2
0
0
0
0
0
0
1
0
0
3
4
0
0
0
0
0
2
3
0
0
1
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
1
0
2
0
0
2
0
1
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
2
2
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
4
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
2
0
0
0
1
1
0
0
2
0
2
0
2
2
0
6
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
4
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
1
0
0
0
0
1
2
2
0
0
0
0
2
0
2
0
2
0
2
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
2
0
1
0
0
3
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
1
9
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
1
0
0
2
3
1
2
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
3
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
3
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
2
0
0
0
0
1
0
1
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
1
2
0
0
0
1
1
0
1
0
2
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
3
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
2
4
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
3
1
0
0
1
0
0
0
0
0
0
2
2
0
1
5
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
2
2
2
3
2
0
0
0
0
0
0
3
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
3
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
4
2
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
1
0
2
1
0
0
0
3
0
0
0
0
1
0
0
1
2
0
0
1
1
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
2
1
0
1
0
0
1
1
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
2
0
0
0
2
0
1
0
2
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
1
0
0
0
2
1
0
0
10
0
0
0
0
2
0
0
0
2
2
2
0
0
0
2
0
0
0
2
3
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
1
0
0
2
3
0
2
0
0
1
0
2
0
0
3
0
0
2
0
2
0
2
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
2
1
0
2
0
0
2
0
0
0
2
0
0
0
0
0
3
0
1
0
0
2
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
1
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
1
0
1
1
2
0
0
0
2
0
0
2
2
2
0
0
0
2
0
0
0
3
1
0
0
0
1
0
1
2
2
0
0
1
0
0
0
0
0
3
0
0
0
2
2
0
0
3
0
0
0
0
0
0
0
1
0
0
0
2
2
1
0
1
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
3
1
4
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
2
0
0
0
2
2
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
2
0
2
1
0
0
2
0
2
0
2
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
2
1
0
0
1
0
1
0
2
0
0
2
0
0
0
0
1
0
2
2
2
1
2
2
0
2
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
2
0
1
1
0
0
2
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
1
0
0
0
0
2
1
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
1
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
2
0
0
0
1
1
0
0
0
1
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
1
1
0
0
1
0
0
3
0
1
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
2
0
0
5
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
1
0
0
2
0
2
0
0
0
1
2
0
0
0
0
4
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
5
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
2
0
1
0
3
1
0
2
1
0
0
2
2
0
0
0
0
0
0
0
1
1
0
0
2
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
2
0
0
0
0
2
1
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
2
0
1
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
3
0
0
2
0
0
2
2
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
3
0
0
0
0
2
0
2
0
0
0
0
2
2
0
0
0
0
2
0
0
0
1
0
0
0
0
2
2
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
3
0
1
3
0
0
0
1
0
0
0
0
0
1
0
2
2
0
0
1
1
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
1
1
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
2
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
3
2
1
1
1
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
3
3
0
0
0
1
2
0
0
0
0
3
0
0
0
0
1
1
0
0
1
0
0
2
0
1
0
0
2
2
0
2
1
0
0
0
0
0
2
0
0
1
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
3
2
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
1
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
1
2
1
0
0
0
1
0
0
1
0
1
2
1
0
0
1
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
3
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
2
1
1
0
2
0
0
0
1
2
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
3
1
0
0
0
2
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
2
1
0
1
0
5
0
0
0
0
0
2
0
0
1
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
3
0
0
2
2
0
0
0
0
0
0
0
3
0
0
0
3
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
2
0
3
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
2
0
2
0
0
2
0
0
0
0
0
0
3
0
2
0
0
0
1
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
4
0
0
0
0
0
0
1
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
3
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
2
1
0
3
0
0
1
2
0
0
0
2
0
0
0
0
0
1
1
1
2
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
3
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
2
0
0
0
1
0
0
0
3
0
0
1
0
0
1
0
0
0
0
1
0
0
0
2
2
0
0
0
2
0
1
0
0
0
3
4
3
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
8
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
2
1
0
2
0
0
1
0
0
2
0
2
3
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
2
1
0
2
0
1
0
0
0
1
2
0
0
1
0
2
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
2
1
2
2
0
1
1
1
0
0
0
0
0
1
0
0
0
2
0
1
0
1
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
2
2
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
1
0
0
2
1
0
0
2
0
0
1
11
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
1
0
3
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
1
0
2
1
1
0
2
0
0
0
1
0
0
0
2
0
4
0
0
0
0
0
0
0
0
2
0
1
1
2
0
1
2
0
0
1
2
3
0
0
4
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
1
2
0
0
1
0
2
0
2
0
0
7
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
1
0
1
0
2
0
0
3
2
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
2
0
0
1
2
1
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
2
2
0
0
0
1
2
0
0
0
0
0
2
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
1
2
0
2
0
1
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
1
2
0
0
0
1
0
0
2
1
0
0
0
0
0
3
0
4
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
2
2
1
0
2
0
0
0
2
2
1
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
1
7
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
1
0
1
2
0
1
3
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
1
0
0
0
2
0
0
0
0
1
1
0
1
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
3
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
3
0
1
0
0
2
0
0
0
0
2
3
1
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
1
2
0
0
0
1
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
1
1
0
2
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
2
0
0
1
1
0
1
2
4
2
0
0
0
0
0
1
0
0
2
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
3
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
3
1
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
2
2
1
0
2
0
0
0
0
0
1
1
0
4
0
2
14
0
0
2
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
1
0
1
0
0
3
0
2
0
0
0
0
0
0
0
2
1
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
7
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
1
0
0
2
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
4
0
4
0
0
0
0
0
0
2
2
0
0
0
0
0
4
0
0
0
0
0
2
3
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
1
2
2
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
2
1
1
0
0
2
1
2
0
2
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
2
1
0
0
0
0
1
0
3
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
1
1
0
2
1
0
0
2
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
2
1
1
0
0
1
0
0
1
2
0
0
0
0
1
0
0
0
2
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
1
0
0
0
0
2
0
1
0
0
3
0
1
0
0
0
0
3
0
0
0
0
1
0
0
0
0
2
0
1
1
0
1
1
3
0
0
0
2
3
0
1
0
1
0
0
1
0
0
0
0
2
1
0
3
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
3
0
1
0
0
0
0
2
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
3
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
2
0
0
1
0
0
0
2
1
0
0
2
0
0
0
0
1
0
2
0
0
0
5
0
0
1
1
1
1
2
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
2
1
0
0
0
3
0
0
1
0
0
2
1
5
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
6
0
0
0
0
0
0
1
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
13
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
2
0
0
0
1
0
1
0
0
0
1
0
0
1
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
2
0
0
2
0
2
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
2
0
0
1
0
1
2
0
0
0
0
1
1
0
0
1
0
1
0
0
0
1
0
1
0
2
2
0
0
0
0
0
0
2
1
0
3
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
2
0
2
0
0
4
0
2
0
0
0
0
0
0
0
1
0
2
2
1
0
0
0
0
1
0
1
0
2
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
3
1
2
1
0
3
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
2
1
0
2
2
0
0
0
0
2
0
0
0
0
0
0
2
1
1
2
0
0
0
0
1
0
0
0
0
1
1
0
2
0
0
0
0
0
3
2
0
0
0
0
5
0
0
2
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
1
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
2
1
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
2
0
1
2
1
3
0
0
0
0
0
0
0
3
1
0
0
0
0
2
1
0
0
2
0
0
0
2
1
0
0
1
1
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
3
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
1
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
2
0
0
1
0
2
0
3
0
0
1
0
1
0
0
0
0
1
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
3
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
1
2
0
0
0
1
1
0
1
1
0
0
0
0
0
0
2
2
2
3
0
1
1
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
1
0
0
0
0
0
1
1
2
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
1
0
1
0
0
0
2
4
0
0
0
1
0
1
3
1
2
0
0
3
0
0
1
1
1
1
0
2
2
3
0
0
2
0
0
2
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
2
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
1
2
0
0
0
2
2
0
0
0
1
0
0
0
5
0
0
0
3
2
0
0
0
2
2
0
1
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
1
0
1
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
1
0
0
0
5
0
2
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
3
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
2
0
1
2
1
0
0
0
0
3
0
0
1
0
1
1
0
0
2
2
0
5
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
3
0
0
0
1
0
2
0
0
3
0
0
0
0
0
0
0
2
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
5
2
1
0
0
0
0
2
0
3
2
0
0
0
0
1
2
0
0
0
1
1
0
2
0
0
0
0
2
1
0
0
0
0
0
2
0
0
2
0
0
1
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
2
2
0
0
0
2
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
5
2
1
0
0
1
0
0
2
0
1
0
0
0
1
0
0
0
2
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
1
2
0
2
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
1
2
1
0
2
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
3
2
0
0
0
1
2
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
2
0
0
0
2
3
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
2
1
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
1
4
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
2
0
0
1
2
0
2
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
5
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
1
0
0
0
0
0
2
2
2
0
0
0
0
1
0
0
2
2
2
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
2
0
1
0
0
0
2
0
0
0
1
2
2
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
2
2
2
0
0
1
1
0
0
1
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
3
0
1
1
0
0
2
0
0
0
1
1
0
3
0
0
0
0
0
1
0
0
2
0
1
0
2
0
0
2
0
0
0
3
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
2
0
1
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
2
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
1
1
1
3
0
0
0
0
3
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
4
1
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
3
0
0
1
0
0
0
0
1
0
2
0
0
0
0
1
0
1
0
2
0
1
2
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
2
0
2
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
1
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
2
3
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
2
0
0
1
0
1
0
0
1
2
0
0
0
2
1
1
2
1
0
0
1
0
0
0
0
2
0
0
0
3
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
2
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
4
0
1
0
1
1
0
0
3
1
1
2
0
0
0
0
0
0
0
2
0
0
4
0
0
0
0
2
0
0
0
0
4
0
3
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
1
2
0
0
1
0
2
0
0
0
2
0
0
2
0
0
2
0
2
1
1
0
0
0
0
2
0
0
0
1
3
0
0
2
0
1
0
2
2
4
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
1
1
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
1
0
0
2
0
0
0
0
2
2
0
0
0
0
1
3
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
2
0
0
2
1
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
3
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
6
0
2
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
2
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
1
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
1
2
3
0
0
1
0
0
0
2
0
1
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
1
2
0
1
3
2
0
2
0
12
0
1
1
1
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
2
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
1
6
0
0
0
0
0
1
0
3
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
2
1
0
0
0
0
0
0
1
3
0
2
0
0
0
0
5
0
0
2
0
0
0
1
0
0
0
0
2
0
2
0
1
0
1
0
1
0
1
2
0
0
1
11
0
0
0
2
0
1
1
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
4
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
2
2
0
0
0
3
1
0
0
0
0
0
0
1
0
0
2
2
1
1
0
0
0
0
2
1
2
2
0
0
2
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
2
3
0
0
2
0
0
0
0
0
1
2
0
1
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
6
0
0
0
1
0
1
0
0
1
0
2
0
0
0
1
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
2
2
0
0
2
0
0
2
0
0
0
0
0
1
0
1
2
1
2
0
0
1
0
0
0
0
2
0
3
0
2
0
0
0
0
1
0
0
2
0
1
0
0
0
0
1
0
1
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
2
0
2
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
2
1
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
4
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
2
0
0
0
0
1
3
2
0
2
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
4
0
0
0
2
0
3
0
0
0
1
0
0
2
3
0
0
0
0
0
2
2
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
2
0
1
0
2
1
0
0
1
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
7
3
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
3
0
0
0
0
1
0
0
3
0
0
0
2
2
2
0
1
0
0
1
2
1
2
0
0
0
0
0
1
0
1
0
0
2
0
1
0
0
1
2
0
0
3
0
0
1
0
0
0
0
0
0
0
1
2
1
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
7
0
2
0
0
1
0
0
1
0
3
2
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
1
4
0
0
0
0
0
1
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
2
1
1
2
3
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
1
2
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
2
0
2
0
0
0
0
0
2
2
0
0
0
0
0
2
2
0
0
0
2
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
3
0
0
1
0
0
0
0
0
0
0
2
2
2
1
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
12
0
1
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
3
2
0
0
0
0
0
1
1
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
2
2
0
1
0
1
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
4
2
2
0
0
1
0
0
0
0
0
0
2
1
1
0
0
0
0
0
3
0
0
0
0
0
1
1
1
0
1
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
1
2
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
4
0
2
0
1
2
0
0
0
0
1
3
0
0
0
1
2
2
0
0
0
3
0
0
0
0
0
0
1
0
0
4
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
4
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
11
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
1
0
0
0
2
0
0
2
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
2
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
2
2
0
2
0
0
2
3
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
3
2
0
0
0
0
0
0
0
0
2
0
2
0
4
0
0
0
0
0
0
3
0
2
2
0
0
0
0
0
0
0
1
2
0
0
0
1
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
2
0
0
3
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
1
0
0
0
1
0
0
2
0
1
0
2
0
0
1
0
0
0
0
0
2
0
0
1
3
0
0
0
0
1
0
0
0
0
0
3
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
2
1
0
3
0
0
1
0
1
1
0
0
0
2
2
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
2
0
0
3
0
0
2
0
0
0
0
0
2
13
0
1
1
0
1
0
0
1
1
0
0
2
1
0
2
0
0
0
0
1
0
2
0
1
1
0
0
1
0
1
0
0
0
2
0
0
0
0
0
1
1
0
0
0
2
2
0
0
2
0
2
2
2
0
0
0
0
0
0
2
0
0
0
3
0
0
3
0
0
0
2
0
0
0
2
2
0
0
0
1
0
2
0
0
0
2
4
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
4
0
2
0
1
0
0
0
4
2
1
0
2
0
0
1
2
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
2
5
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
3
0
1
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
2
0
0
0
2
0
0
2
0
1
0
0
1
0
0
0
0
0
0
1
0
3
1
0
2
0
0
2
0
0
1
2
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
8
0
0
0
0
1
0
0
2
3
0
0
3
0
4
0
0
5
1
1
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
4
0
2
3
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
3
3
0
0
0
0
0
0
0
2
0
1
0
0
1
3
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
1
0
0
0
2
0
0
1
0
2
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
2
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
3
2
1
1
0
0
0
1
1
2
2
0
2
0
0
1
0
0
0
1
1
2
0
0
0
2
1
0
5
0
0
0
0
0
0
2
0
0
0
0
0
1
0
3
0
1
0
2
1
0
0
0
1
2
0
2
1
0
0
1
2
0
0
0
0
1
0
0
2
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
2
0
1
0
1
1
3
0
0
0
0
0
0
2
1
0
0
2
2
1
0
0
2
0
1
0
0
0
0
0
1
0
0
0
3
0
0
4
2
2
3
1
0
1
0
1
1
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
2
0
0
0
3
0
0
0
0
0
0
2
2
1
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
3
0
0
2
1
2
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
1
2
0
0
3
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
2
1
2
0
0
0
3
2
0
1
0
0
0
1
1
0
0
0
0
2
2
2
1
0
0
0
0
2
0
1
2
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
1
0
0
0
1
1
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
1
0
2
0
0
0
4
0
0
0
0
0
2
0
0
1
1
2
0
0
0
0
0
0
2
0
0
1
0
0
0
1
2
2
2
0
2
1
2
3
1
0
0
0
1
1
0
1
1
2
0
1
0
0
1
0
0
2
3
0
2
0
0
0
0
0
0
0
0
1
0
3
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
2
2
2
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
2
0
0
0
2
0
1
2
2
0
0
0
0
2
2
0
1
0
2
1
0
1
1
0
0
0
0
1
0
0
0
0
5
0
0
0
0
0
2
2
2
0
0
1
0
0
0
0
0
0
0
0
1
0
6
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
2
0
0
3
1
2
0
1
0
0
0
2
0
0
0
4
0
0
2
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
1
0
1
2
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
2
0
0
0
2
2
1
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
2
9
2
2
2
0
3
0
0
0
0
0
1
0
0
0
2
0
0
2
1
0
1
0
1
0
2
0
0
0
0
3
0
1
0
0
2
0
0
2
2
0
1
0
0
2
0
0
1
0
0
1
0
2
0
0
0
0
0
1
2
0
0
0
2
0
2
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
3
1
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
2
0
0
0
1
0
1
0
2
0
4
0
0
0
0
0
1
0
0
3
0
0
0
2
1
2
2
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
2
0
0
0
0
0
0
2
0
0
1
1
0
0
0
1
9
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
3
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
1
0
0
0
0
0
2
0
0
1
0
2
0
0
2
3
0
0
1
1
0
0
2
0
0
0
2
0
0
1
1
0
1
0
0
1
0
2
0
0
0
4
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
4
0
1
0
0
0
3
0
0
2
0
1
1
0
0
2
0
0
0
0
0
0
0
2
0
2
2
0
2
0
0
0
0
22
0
1
0
0
0
0
1
1
0
1
0
0
0
1
1
0
0
0
3
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
2
2
0
2
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
3
0
2
0
2
0
1
0
1
0
0
0
0
0
0
0
1
2
0
4
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
3
0
0
2
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
3
1
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
2
1
1
0
2
0
2
1
0
2
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
4
1
0
0
0
0
2
0
0
0
1
0
1
0
0
1
1
0
0
0
3
0
0
2
1
2
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
1
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
6
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
2
0
1
0
2
0
1
0
0
2
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
4
2
1
0
0
4
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
1
0
1
2
2
0
3
0
0
2
0
1
0
2
1
0
0
0
0
2
0
1
2
0
0
2
0
0
0
0
2
0
2
1
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
4
2
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
2
0
0
0
1
3
2
0
0
0
0
0
1
2
0
0
2
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
2
0
0
1
0
0
0
0
1
3
0
0
0
1
0
2
0
0
3
0
1
0
2
0
0
0
1
2
3
0
0
0
0
2
1
0
0
0
0
2
0
1
0
2
2
0
2
0
1
1
1
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
1
0
2
0
0
0
0
3
0
0
0
1
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
4
0
0
2
0
0
3
1
0
0
0
0
1
0
0
0
0
0
4
2
0
0
0
2
1
0
1
0
1
0
0
0
0
0
0
0
1
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
1
0
1
2
2
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
1
0
0
0
2
0
0
0
0
1
1
2
0
0
0
0
0
2
0
3
1
0
0
0
0
0
1
0
0
1
2
3
0
0
0
0
3
0
0
0
3
0
0
0
0
1
0
2
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
1
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
1
1
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
5
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
3
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
12
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
2
3
1
1
2
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
2
0
2
1
0
0
2
0
1
0
1
1
0
0
2
0
0
1
1
2
0
0
0
0
0
1
0
2
0
2
0
0
3
1
0
0
0
0
0
0
0
0
0
1
4
0
0
2
0
1
1
0
1
0
0
0
0
0
0
2
0
2
0
2
2
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
1
2
2
0
0
0
0
2
0
2
0
0
1
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
2
1
0
0
0
0
1
1
0
0
1
2
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
2
0
2
3
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
6
2
0
1
0
0
0
1
2
0
0
2
0
0
0
2
0
2
0
3
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
1
1
0
0
2
1
1
0
0
0
0
1
1
2
0
0
0
0
1
0
0
0
11
0
0
0
2
0
2
1
0
0
0
2
0
0
0
1
0
1
0
3
0
0
0
0
0
0
1
0
0
0
1
2
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
1
0
0
0
2
0
0
2
2
1
1
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
2
0
2
0
0
0
2
1
1
0
1
0
0
0
0
0
2
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
2
2
0
0
0
1
0
0
0
2
0
2
2
0
0
0
0
0
2
0
0
0
0
0
4
2
0
5
2
0
0
0
0
2
0
0
2
0
0
0
0
1
1
0
2
0
2
1
5
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
3
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
2
1
1
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
2
0
0
2
0
2
0
0
2
4
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
3
0
1
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
1
1
0
0
1
1
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
2
0
2
0
0
0
0
0
0
2
0
0
0
0
2
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
3
8
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
2
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
5
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
1
1
0
2
1
1
0
3
0
0
0
0
1
2
0
0
0
0
0
1
0
3
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
1
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
3
0
0
0
0
1
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
1
0
0
1
1
1
0
1
1
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
2
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
1
0
0
0
2
1
1
2
0
3
0
0
0
0
3
0
0
0
1
1
0
0
2
0
0
0
1
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
1
1
2
0
0
2
0
0
0
0
2
0
2
0
0
0
2
0
1
0
2
0
0
0
0
0
2
6
0
0
2
1
1
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
1
1
0
0
2
1
1
0
1
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
1
0
1
1
0
1
2
2
0
2
9
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
2
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
1
2
0
1
0
2
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
1
1
1
1
0
0
0
0
2
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
4
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
1
0
2
0
0
3
0
0
0
0
0
2
0
1
0
1
3
2
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
1
0
0
0
0
3
1
0
0
0
2
0
2
1
0
0
2
1
0
0
0
1
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
4
0
1
0
0
0
0
2
0
0
1
2
1
1
1
0
0
2
0
0
0
0
0
0
0
2
3
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
5
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
1
0
2
0
1
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
5
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
1
2
0
0
0
0
0
5
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
3
0
0
3
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
2
0
2
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
1
0
0
0
0
2
2
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
5
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
4
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
5
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
5
2
0
0
1
0
2
0
2
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
1
0
2
1
5
0
1
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
1
0
2
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
5
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
2
2
4
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
7
0
0
0
1
1
0
1
0
0
2
2
1
0
0
2
0
0
3
0
0
0
0
0
1
0
1
2
1
0
0
0
1
2
0
0
0
0
0
0
0
2
2
2
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
1
4
0
0
0
2
0
0
0
0
0
3
3
0
0
0
1
0
0
0
0
0
0
0
0
1
2
1
1
3
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
3
0
0
2
1
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
1
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
1
0
1
1
1
0
0
0
0
0
3
0
0
0
0
0
0
0
3
0
0
0
0
2
2
3
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
1
0
3
0
0
1
0
0
3
1
1
0
0
2
0
0
0
1
0
0
1
6
2
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
2
0
1
0
0
3
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
2
0
1
0
0
0
0
1
2
0
2
2
1
1
0
0
0
0
0
0
0
1
0
1
2
0
0
1
0
2
0
0
2
0
0
0
0
0
1
0
1
0
0
2
0
0
1
0
0
2
2
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
4
1
1
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
2
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
3
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
2
1
0
0
0
0
3
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
2
0
0
3
1
0
0
0
2
1
0
0
0
4
0
1
0
0
2
0
1
0
0
0
0
1
2
2
0
0
0
0
2
0
0
0
1
1
2
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
3
0
0
0
0
1
3
0
0
0
2
0
0
2
0
0
3
0
0
0
0
3
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
1
0
2
0
0
0
0
0
2
0
3
0
0
0
0
0
1
2
0
1
2
0
2
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
2
2
0
0
1
0
2
0
1
0
0
1
0
2
0
0
0
0
1
0
0
0
0
2
0
0
4
2
0
0
0
0
1
0
0
0
0
0
2
0
2
0
1
1
3
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
3
2
2
0
0
2
0
1
0
0
0
1
0
0
0
1
1
1
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
3
4
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
2
0
2
0
0
0
0
1
1
0
1
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
2
1
0
0
0
0
0
2
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
6
0
3
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
1
1
0
3
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
1
0
0
1
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
1
1
0
0
0
1
1
0
2
0
0
0
0
0
1
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
1
2
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
1
1
0
2
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
1
0
1
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
4
2
1
0
0
0
0
0
1
0
4
2
1
2
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
1
0
1
0
0
1
2
1
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
1
0
0
7
0
0
0
0
0
4
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
2
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
1
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
1
2
0
0
0
0
2
0
0
2
0
0
1
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
1
2
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
4
2
2
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
1
2
1
0
1
0
3
0
0
0
0
1
0
0
0
3
2
0
0
1
0
0
0
0
1
2
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
3
0
0
1
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
2
0
0
0
0
1
0
1
2
0
2
0
0
0
0
0
0
0
0
0
2
0
3
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
3
0
0
2
0
0
9
0
1
0
0
1
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
2
3
0
0
0
0
1
1
0
1
0
0
0
2
0
0
0
3
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
1
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
4
0
0
1
1
0
1
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
4
0
2
0
4
2
0
0
0
0
3
0
0
0
0
0
1
0
1
0
0
3
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
1
2
0
0
0
0
0
1
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
2
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
2
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
2
0
0
0
1
0
2
2
0
0
1
1
0
0
2
2
0
0
0
0
0
0
3
0
2
0
4
0
0
0
0
4
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
2
0
2
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
2
2
0
3
1
2
0
5
0
0
1
2
0
2
0
2
0
0
1
2
0
2
2
0
0
0
0
2
1
2
1
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
1
1
0
0
0
0
0
0
15
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
4
0
0
0
0
0
0
0
0
0
2
1
0
8
0
0
1
0
1
1
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
1
0
1
2
2
0
0
1
0
0
0
0
0
1
0
0
0
0
3
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
1
1
0
0
0
0
1
0
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
1
0
2
0
0
0
1
0
0
1
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
1
2
1
0
0
0
1
0
0
1
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
1
0
2
0
0
0
0
2
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
1
0
3
2
1
0
0
1
0
0
0
2
0
3
0
0
0
0
0
0
1
0
2
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
2
0
0
0
0
1
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
2
2
2
2
2
0
0
1
0
1
1
0
0
0
0
1
0
0
1
0
0
2
1
0
0
0
0
0
1
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
2
0
0
0
0
0
2
0
0
2
1
1
1
0
0
1
1
0
1
0
1
2
0
2
0
0
2
0
0
1
0
0
2
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
3
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
5
0
7
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
1
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
1
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
1
2
0
0
0
1
0
2
1
2
2
0
2
0
0
1
2
1
0
0
0
0
0
2
0
0
0
0
1
1
1
2
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
4
0
2
0
1
6
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
3
0
0
6
0
0
0
0
0
2
0
2
0
2
1
0
2
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
1
0
0
0
0
1
2
0
0
1
1
0
0
0
0
0
1
2
0
0
2
2
0
0
2
0
0
0
0
1
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
2
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
2
2
1
0
3
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
1
2
0
0
2
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
2
0
2
0
2
0
0
2
0
0
0
0
0
0
1
1
0
0
0
1
2
1
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
1
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
2
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
2
1
0
0
3
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
1
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
1
2
1
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
1
1
2
0
0
1
3
2
0
0
0
0
4
0
1
0
1
0
0
0
0
0
0
0
1
4
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
3
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
3
0
2
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
1
1
0
0
0
0
1
1
0
2
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
1
0
0
0
2
1
1
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
4
0
2
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
5
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
2
0
0
0
1
0
2
0
0
0
2
0
0
0
1
0
0
0
1
0
0
3
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
4
0
2
0
0
0
2
0
2
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
3
0
0
2
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
3
1
0
0
1
0
0
1
2
0
2
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
3
0
2
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
2
0
1
1
0
0
0
1
0
0
2
0
0
4
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
7
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
1
0
2
0
0
0
2
0
0
0
0
0
2
2
0
0
1
0
0
0
1
0
0
1
2
0
0
1
0
1
2
0
1
0
0
0
0
1
1
0
0
2
0
0
1
5
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
4
0
0
1
1
0
0
2
0
2
0
3
0
0
0
1
0
0
0
0
1
0
0
0
2
0
2
2
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
7
0
0
1
0
1
0
1
0
2
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
1
1
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
2
1
0
0
0
2
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
5
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
1
0
0
0
3
1
5
0
2
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
2
0
1
2
0
0
1
0
0
1
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
3
0
0
2
0
1
2
0
0
0
0
4
0
1
0
1
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
3
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
6
0
0
0
0
1
0
3
1
1
0
1
1
0
0
2
0
0
0
0
2
0
0
3
0
0
0
0
1
1
0
0
0
0
0
0
0
1
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
2
2
0
0
4
2
2
0
0
0
1
0
0
0
2
4
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
14
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
2
0
1
1
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
3
0
0
0
0
0
3
3
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
5
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
3
1
3
2
1
0
1
0
0
0
0
0
3
0
0
1
0
0
0
0
2
2
0
1
1
0
0
0
0
0
2
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
3
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
5
0
1
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
2
1
0
1
0
0
1
1
0
0
0
0
2
2
2
1
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
1
6
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
2
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
1
0
1
2
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
2
1
0
2
0
1
0
1
2
0
0
2
0
0
1
0
0
0
3
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
1
1
0
0
0
1
0
2
2
0
0
0
1
1
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
1
1
0
0
0
0
3
0
0
0
1
2
0
0
1
0
0
0
0
1
0
0
2
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
2
0
2
3
0
0
0
0
0
2
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
1
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
1
2
2
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
1
2
0
2
1
0
1
0
0
8
2
0
4
1
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
2
0
0
0
0
2
0
1
0
0
0
4
1
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
3
0
0
0
2
0
0
0
0
0
1
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
1
1
0
0
0
0
1
0
2
0
0
0
2
0
1
0
0
2
5
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
1
2
2
1
0
2
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
1
1
0
1
0
1
0
0
0
2
2
2
0
0
2
1
0
1
1
1
0
2
0
0
0
0
0
3
0
1
0
2
1
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
1
0
2
0
0
0
0
0
2
0
0
2
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
2
1
7
1
1
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
3
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
1
4
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
2
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
2
0
0
0
0
0
0
0
1
3
0
0
0
1
0
1
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
4
2
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
2
0
0
0
2
1
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
1
0
0
0
0
0
1
0
1
0
0
1
1
0
0
1
0
0
1
2
0
0
0
1
0
0
0
1
0
0
0
2
2
0
0
2
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
2
0
1
2
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
1
0
1
0
0
0
0
0
2
1
0
0
4
0
1
2
1
0
0
0
3
0
0
3
0
0
2
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
2
2
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
3
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
3
1
2
0
0
1
2
2
3
1
0
1
2
1
0
0
0
1
2
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
1
0
2
1
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
2
0
0
1
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
1
0
0
0
1
1
1
0
2
0
2
2
0
1
0
1
0
0
0
0
0
0
0
2
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
2
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
1
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
3
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
1
1
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
2
0
2
0
3
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
1
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
2
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
2
0
2
1
0
2
0
0
2
0
0
0
0
0
0
1
0
2
0
1
2
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
2
0
0
0
0
0
2
0
1
0
2
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
1
0
0
2
2
0
0
0
0
1
1
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
1
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
2
2
0
1
1
0
2
1
0
1
1
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
2
0
0
0
0
0
2
0
0
2
1
0
1
2
1
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
2
2
2
0
1
0
0
1
0
1
2
0
0
0
2
0
0
0
1
0
1
0
0
2
0
1
0
1
0
0
0
0
0
2
0
0
0
1
0
4
0
2
0
0
1
0
0
2
0
0
2
0
0
1
0
0
0
0
1
0
0
0
3
5
0
3
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
1
0
0
0
0
0
2
0
2
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
4
0
2
2
0
0
0
0
0
0
0
2
2
0
0
3
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
2
0
2
0
0
0
0
1
2
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
2
0
0
0
2
1
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
2
2
0
0
0
0
1
0
1
2
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
4
0
0
0
0
2
0
2
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
4
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
1
2
2
0
1
2
0
1
2
0
2
0
0
2
0
0
0
2
2
0
0
0
2
0
0
0
3
3
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
2
0
0
1
0
0
0
1
2
0
1
0
0
0
2
1
1
3
2
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
1
0
0
1
0
3
0
0
0
1
0
0
0
0
0
3
0
1
0
0
1
1
1
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
6
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
2
1
0
0
2
2
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
6
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
3
0
1
0
1
0
0
2
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
1
1
0
2
0
3
1
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
1
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
2
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
2
0
1
1
0
0
0
0
5
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
1
0
2
1
0
0
2
1
0
0
1
1
0
1
2
0
2
0
2
0
0
0
3
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
1
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
4
1
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
2
0
0
1
2
0
0
0
1
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
5
0
0
0
0
0
2
0
0
0
0
0
1
2
0
1
0
0
0
0
0
1
2
0
0
0
0
3
0
0
0
1
0
0
0
1
1
0
0
0
2
0
5
1
0
0
0
0
0
1
0
0
1
0
2
1
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
2
2
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
3
0
0
0
1
2
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
2
0
1
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
2
2
2
1
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
2
1
0
2
0
0
0
0
0
0
0
1
0
0
4
0
2
0
1
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
1
0
0
4
0
2
0
2
0
0
0
0
0
0
0
2
2
1
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
3
2
0
0
0
0
0
0
0
5
1
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
1
0
2
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
1
0
0
0
2
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
2
2
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
2
0
0
0
1
0
1
0
0
0
1
0
2
2
1
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
1
1
1
0
0
2
0
0
1
0
0
0
2
0
1
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
3
0
0
2
0
0
0
0
3
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
2
1
0
2
0
2
0
1
2
0
0
0
2
0
0
0
0
0
8
0
0
1
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
1
2
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
1
2
0
2
2
0
2
1
0
0
0
0
1
0
0
0
2
2
0
2
1
0
0
2
0
1
2
0
0
0
0
0
2
0
0
0
3
2
1
0
0
0
0
0
0
3
0
1
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
1
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
3
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
3
0
0
1
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
3
0
0
0
1
0
0
0
0
0
4
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
1
0
2
0
0
0
0
2
1
0
0
3
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
2
1
0
2
0
0
2
2
0
0
0
1
1
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
13
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
1
0
2
0
1
0
1
3
0
0
1
0
0
3
0
2
0
0
0
0
0
0
0
0
0
1
1
0
4
0
1
0
3
0
0
0
0
1
0
0
2
1
1
0
0
0
1
0
2
1
0
0
2
2
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
1
2
4
0
0
0
1
0
0
0
1
2
0
1
0
2
0
1
1
0
2
1
0
0
0
0
3
0
0
0
0
0
2
0
0
1
0
1
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
6
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
2
2
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
3
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
2
0
3
6
0
2
0
0
1
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
2
2
0
1
1
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
2
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
1
1
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
1
1
0
1
2
0
0
0
0
0
0
0
0
2
3
3
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
2
0
0
0
3
0
1
0
0
3
0
2
1
0
0
0
2
0
2
0
1
0
0
0
0
4
2
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
5
0
0
0
0
0
2
1
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
9
0
0
0
0
0
0
2
0
0
2
0
0
0
1
2
0
0
3
2
0
2
3
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
1
0
2
0
1
2
2
0
0
3
0
2
0
0
0
0
0
0
2
1
1
1
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
1
1
0
0
1
0
2
2
1
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
3
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
5
0
0
0
0
0
0
1
1
0
0
2
1
3
2
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
1
0
0
0
2
2
0
3
0
0
0
2
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
1
1
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
2
0
0
0
0
1
0
0
1
0
0
0
1
0
2
2
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
2
1
0
0
1
2
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
1
0
1
0
0
0
3
0
0
2
0
0
2
0
2
0
2
0
0
2
2
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
3
3
0
0
0
0
0
2
0
0
2
0
1
0
0
0
2
0
1
0
0
0
1
6
0
0
2
0
0
1
0
0
0
0
1
0
0
3
0
0
1
1
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
1
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
1
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
1
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
2
1
3
0
0
0
0
0
1
0
1
0
0
0
0
0
2
7
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
1
2
1
1
1
0
2
0
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
5
2
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
1
2
2
0
1
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
1
1
0
0
0
0
2
0
1
1
1
0
0
0
1
0
0
0
0
2
2
1
0
1
0
0
3
0
0
0
0
0
0
3
0
2
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
1
2
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
1
1
0
1
0
0
2
0
0
1
0
0
3
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
2
0
0
0
2
2
0
0
2
0
0
1
3
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
2
2
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
3
2
1
0
2
2
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
2
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
1
2
0
0
3
0
3
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
3
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
2
0
0
0
0
1
1
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
1
0
1
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
3
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
1
3
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
1
0
0
2
1
1
1
2
0
0
0
0
1
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
9
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
1
0
2
0
0
0
0
1
0
0
0
3
0
0
0
1
0
0
0
1
0
0
0
1
0
2
0
2
0
2
1
0
4
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
6
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
5
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
6
1
2
0
1
1
0
1
1
0
0
1
0
0
4
1
2
0
0
0
2
0
0
0
4
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
2
0
0
2
0
2
0
2
0
1
2
0
0
0
0
0
2
0
0
0
1
0
2
0
3
0
0
2
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
1
0
1
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
1
0
0
0
2
0
2
0
0
0
0
0
0
2
2
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
5
0
0
1
0
0
0
0
0
1
0
0
2
0
2
0
2
1
7
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
2
0
0
0
3
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
2
1
1
0
0
0
0
2
0
2
0
1
1
0
0
1
0
0
1
2
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
3
0
1
1
0
0
2
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
4
1
1
0
2
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
2
0
0
2
0
0
2
0
0
1
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
3
0
1
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
2
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
3
0
1
3
1
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
2
2
0
0
0
2
0
0
0
0
0
2
4
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
1
0
0
5
0
0
2
4
0
0
1
0
0
2
0
0
2
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
5
1
0
0
0
0
0
0
0
0
0
0
5
2
0
1
0
2
1
0
0
0
1
2
2
0
2
0
0
0
0
0
2
1
12
0
0
0
1
2
0
1
2
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
2
0
1
0
1
0
0
2
0
0
2
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
1
0
3
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
3
0
1
4
1
0
2
2
0
0
0
1
0
0
0
4
1
0
0
0
0
0
0
0
5
2
0
0
0
6
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
2
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
2
0
0
0
1
0
1
2
0
2
0
2
0
0
0
0
0
2
0
1
1
0
1
0
1
0
0
1
0
0
2
1
1
0
0
0
1
0
0
0
0
1
1
1
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
3
0
3
0
0
0
0
0
2
3
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
2
1
2
1
0
0
2
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
2
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
2
2
0
0
0
0
1
1
0
0
2
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
1
0
0
4
1
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
2
2
0
0
0
0
1
0
1
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
2
0
0
0
1
0
0
0
2
1
0
0
0
2
0
4
0
0
0
0
4
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
1
1
0
0
0
0
0
0
0
0
2
1
2
0
0
2
0
1
1
1
0
2
0
1
0
2
0
0
0
0
2
0
0
2
3
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
2
1
1
0
1
0
0
0
2
0
2
0
0
2
1
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
2
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
3
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
1
0
1
0
0
3
0
0
0
0
2
0
2
1
0
2
0
1
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
2
0
0
3
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
1
1
3
0
0
0
1
0
3
0
2
1
0
0
0
1
1
0
1
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
1
2
0
0
0
1
0
0
1
2
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
1
1
0
0
2
0
2
2
0
0
1
0
1
4
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
1
2
0
2
0
1
1
0
0
0
0
1
0
2
0
0
2
2
0
0
0
0
0
0
0
0
1
1
0
4
0
1
0
0
1
0
2
0
0
3
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
3
1
0
0
1
2
0
0
0
0
0
2
0
0
0
1
0
0
1
1
2
0
1
0
1
1
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
1
2
0
0
0
2
0
0
1
0
0
2
0
1
0
0
0
1
2
0
0
0
0
0
4
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
1
0
0
0
1
1
0
0
0
2
0
0
2
0
0
0
1
1
0
0
0
2
2
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
2
0
0
0
1
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
1
0
2
0
0
1
2
0
0
1
0
0
2
3
0
0
2
0
3
0
2
1
0
0
1
0
0
0
0
3
1
0
2
0
2
1
0
0
0
0
1
0
1
0
0
2
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
2
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
2
2
0
0
2
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
2
3
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
4
0
2
0
1
1
1
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
3
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
3
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
2
1
0
0
2
0
2
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
2
2
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
4
0
1
2
0
3
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
2
0
2
0
0
0
1
0
0
0
0
2
0
0
0
1
1
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
1
0
3
0
1
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
2
1
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
3
0
0
0
0
2
0
0
2
0
0
1
0
0
0
2
0
1
0
0
0
2
0
0
1
0
0
1
0
2
0
0
2
0
2
6
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
1
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
11
1
0
0
0
2
5
0
1
0
0
2
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
3
3
2
0
0
3
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
1
0
1
0
0
0
2
0
0
0
2
0
2
3
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
2
3
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
15
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
7
1
2
0
1
0
2
0
2
0
2
2
0
0
0
0
1
2
0
0
2
0
0
2
1
0
0
0
3
0
0
0
0
0
1
0
0
2
0
0
0
0
3
0
0
0
0
1
0
1
3
2
0
3
1
3
1
0
0
0
2
0
0
2
0
1
0
0
0
0
1
0
0
1
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
2
2
0
2
0
0
0
2
2
0
0
0
1
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
7
0
0
0
0
0
0
3
0
2
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
2
0
0
0
2
2
0
0
1
0
2
0
0
0
0
2
0
5
0
2
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
3
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
1
0
0
0
0
0
0
3
0
2
0
0
3
0
0
5
0
0
0
0
0
0
0
1
0
0
0
1
2
0
2
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
1
0
0
0
2
2
1
0
0
0
0
1
2
2
1
0
1
8
0
0
0
1
0
0
0
0
1
2
0
1
1
0
0
1
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
2
0
1
0
1
0
0
0
0
2
1
2
0
1
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
2
1
0
1
2
0
0
3
0
1
0
2
1
1
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
2
2
2
2
0
0
2
1
0
2
1
0
1
0
2
2
2
0
0
2
0
0
1
0
0
0
0
0
0
1
2
0
1
0
0
0
0
1
0
0
0
0
7
0
0
0
0
0
0
0
2
3
2
2
1
0
0
0
1
2
0
3
0
1
0
0
1
2
2
0
0
0
2
0
0
0
3
0
0
0
1
0
2
0
0
1
2
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
3
0
0
1
0
0
2
0
1
0
0
1
0
0
0
2
0
0
0
0
0
1
6
2
0
2
0
0
1
0
0
0
0
0
3
2
2
1
0
0
1
0
0
2
0
0
1
0
0
0
1
0
0
0
3
0
0
2
0
0
0
0
4
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
2
0
0
2
0
1
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
3
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
3
0
0
0
0
2
0
0
0
0
1
2
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
3
2
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
1
1
1
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
3
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
3
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
3
1
1
0
0
0
0
0
0
0
2
1
2
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
7
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
3
0
0
1
0
0
1
2
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
3
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
1
0
0
0
2
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
5
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
3
1
0
0
0
0
4
0
0
2
0
0
0
1
0
2
0
0
4
0
1
0
0
0
0
0
5
0
0
0
2
1
0
1
0
2
1
0
3
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
2
0
3
0
4
0
2
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
1
0
0
0
0
1
0
1
0
1
0
0
0
3
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
3
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
3
0
0
0
0
0
3
0
0
0
1
0
0
0
0
2
2
0
0
0
2
1
2
1
0
0
0
0
0
2
7
1
0
0
1
0
0
0
2
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
1
1
0
0
0
2
1
2
0
1
0
0
0
4
2
1
0
0
0
0
1
0
0
2
0
0
0
0
0
4
0
0
0
0
0
2
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
3
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
2
0
4
0
0
0
0
2
0
0
1
10
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
1
0
2
1
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
1
0
0
0
2
0
2
0
2
0
0
0
0
0
1
0
0
0
0
4
2
0
1
0
0
0
1
0
1
4
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
3
0
2
1
0
1
2
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
2
0
2
0
0
1
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
2
0
0
1
0
0
1
0
0
2
1
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
1
0
0
0
2
0
1
0
1
2
0
1
2
0
0
2
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
2
0
0
0
1
1
0
2
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
2
2
1
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
3
1
0
0
2
1
0
1
0
0
0
0
2
0
0
0
0
0
0
3
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
4
4
0
1
0
1
0
5
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
1
0
0
1
0
0
0
0
2
0
0
0
1
0
0
1
1
6
0
4
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
1
0
0
2
1
0
0
0
2
0
0
2
0
0
0
0
0
0
2
1
2
0
1
0
3
0
0
1
0
1
0
1
2
0
0
0
0
0
2
0
0
0
2
0
3
2
0
2
0
0
0
2
2
0
0
2
0
0
0
0
1
1
0
0
0
0
0
2
0
3
6
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
1
0
2
0
1
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
2
0
0
1
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
2
0
0
2
0
0
1
2
0
1
0
0
2
0
2
0
2
3
1
0
0
2
1
0
2
0
0
0
0
3
0
0
1
4
2
1
1
0
2
0
2
0
0
0
0
2
2
4
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
1
2
5
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
2
1
4
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
1
2
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
1
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
2
4
0
0
0
0
0
1
1
0
5
0
0
0
0
0
0
1
3
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
2
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
1
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
1
1
0
0
0
2
0
0
1
0
0
0
0
3
2
0
4
2
0
0
1
0
0
0
2
0
0
5
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
3
0
2
1
0
0
2
3
0
0
0
0
1
3
0
0
1
0
2
0
0
0
0
1
2
0
0
3
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
2
2
1
0
1
0
0
0
0
0
0
1
2
3
0
4
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
4
0
1
1
1
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
7
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
2
0
0
2
1
0
1
0
0
1
0
1
1
0
2
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
7
0
0
0
0
0
1
0
0
9
0
0
0
0
0
1
0
0
3
0
1
0
2
0
0
1
0
0
3
0
1
0
0
0
1
0
0
2
1
0
0
1
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
1
0
0
1
0
1
0
1
0
0
2
8
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
3
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
2
0
0
1
0
0
0
1
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
1
0
5
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
1
3
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
2
2
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
6
0
0
0
0
0
2
0
2
0
0
1
0
0
0
2
2
1
2
1
0
0
0
0
0
2
0
0
0
0
0
4
0
0
0
2
0
2
0
3
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
2
2
1
0
0
2
0
0
0
0
1
0
0
0
1
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
1
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
7
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
4
0
0
3
0
2
2
0
0
0
0
0
0
0
0
0
2
0
1
1
2
0
0
0
0
1
1
0
0
2
0
1
0
1
2
0
2
0
0
0
0
0
0
2
2
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
1
1
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
1
1
0
1
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
3
0
0
0
1
1
6
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
3
0
0
0
0
0
1
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
2
0
3
1
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
2
0
0
0
1
1
1
0
1
0
0
2
0
0
2
0
2
1
0
0
5
2
0
0
0
1
0
2
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
2
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
2
2
0
0
0
1
1
0
0
0
0
2
0
2
0
0
0
2
0
2
0
0
3
0
0
0
0
0
0
4
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
3
1
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
3
1
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
2
1
2
2
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
4
2
2
0
0
1
0
0
0
1
0
3
0
0
0
0
2
0
1
1
0
0
0
5
0
0
0
0
0
0
0
2
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
3
1
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
3
0
0
3
5
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
1
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
6
2
0
0
0
0
3
0
1
0
0
0
3
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
3
0
0
0
0
0
0
2
3
0
0
3
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
2
1
0
0
0
0
2
2
0
2
0
0
0
0
0
2
0
0
1
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
2
0
0
0
1
2
0
2
1
0
0
3
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
3
4
0
0
1
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
2
0
2
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
1
2
1
0
2
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
4
0
0
0
0
0
0
2
0
4
2
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
2
0
0
0
0
0
2
0
0
1
1
0
1
0
2
0
2
0
1
0
0
1
1
2
2
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
1
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
2
0
0
1
1
0
1
0
0
1
0
2
1
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
2
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
2
4
0
0
1
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
2
0
0
2
2
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
2
0
0
2
2
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
1
0
0
0
0
2
2
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
3
2
1
1
0
0
0
0
0
0
2
0
0
7
1
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
1
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
2
0
0
0
3
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
2
3
0
2
0
2
1
0
0
0
1
0
2
2
0
0
0
0
0
0
8
3
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
1
0
0
2
2
1
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
1
0
0
0
2
3
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
2
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
5
0
3
0
0
0
1
0
0
0
0
0
4
0
1
0
0
2
0
0
1
0
0
2
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
2
2
1
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
2
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
1
0
1
1
0
0
2
0
2
2
0
1
0
0
1
0
0
3
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
1
0
2
1
0
0
0
0
0
0
0
1
0
3
0
0
0
0
1
0
1
0
0
0
0
4
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
3
2
0
0
0
0
1
0
2
0
0
0
30
0
1
0
0
0
0
0
0
3
0
1
0
2
0
0
1
0
0
0
0
0
2
0
1
0
0
0
2
0
1
0
0
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
1
0
0
0
0
0
5
0
0
1
0
0
3
0
0
0
13
1
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
2
0
0
0
0
2
0
1
0
1
0
0
1
2
2
0
0
0
0
0
2
1
1
0
0
0
0
0
0
1
0
0
3
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
2
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
1
0
0
0
1
0
0
2
0
2
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
5
0
26
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
2
0
3
3
0
1
0
0
1
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
1
2
0
0
0
1
0
0
2
1
0
1
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
1
2
0
0
0
2
0
0
0
3
1
0
0
1
0
0
0
2
0
0
0
0
2
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
4
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
1
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
2
2
0
2
0
0
0
0
2
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
3
0
0
3
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
3
0
0
0
2
0
0
1
0
0
0
0
0
3
0
0
2
0
3
0
1
0
0
0
0
0
0
0
2
0
2
1
2
0
0
0
0
0
2
0
5
0
0
0
0
1
0
2
0
2
0
2
1
0
1
1
3
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
2
0
2
1
0
1
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
2
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
3
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
3
1
1
0
0
0
1
0
0
0
0
2
0
2
3
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
5
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
2
2
2
1
0
0
0
0
0
0
2
0
0
2
5
0
0
0
2
0
0
0
1
0
0
2
0
2
0
0
0
1
0
0
1
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
2
0
2
0
0
1
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
3
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
4
0
2
0
0
2
0
0
0
0
0
2
0
2
0
0
0
2
1
0
0
2
2
1
0
0
0
0
1
0
0
2
0
0
3
0
1
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
1
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
3
6
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
2
0
1
0
1
0
1
0
0
0
0
0
0
0
0
2
2
2
0
0
1
0
0
0
0
1
0
0
0
0
2
3
0
0
0
2
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
2
0
0
0
1
0
0
0
3
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
4
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
0
0
0
1
0
0
2
0
2
0
0
6
0
0
0
2
0
0
0
1
0
0
0
0
1
0
2
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
2
0
1
0
0
0
0
1
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
1
0
0
0
0
2
2
0
0
1
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
4
0
0
0
3
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
7
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
1
2
0
0
0
0
1
2
0
0
0
2
0
0
0
0
1
0
0
0
0
1
2
1
0
0
0
0
2
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
2
0
2
0
1
1
1
1
0
0
1
0
2
0
0
0
0
0
3
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
3
0
1
0
1
2
0
2
0
2
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
2
0
0
0
2
0
0
2
0
0
1
2
0
1
0
2
2
0
0
0
2
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
3
0
0
1
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
3
1
0
4
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
1
0
0
2
0
2
1
0
1
0
0
0
0
0
1
0
0
1
4
0
0
0
0
1
1
0
0
2
0
2
0
0
0
2
2
2
0
1
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
3
0
0
0
0
3
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
17
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
1
2
2
2
0
0
0
0
0
3
0
3
2
0
1
0
1
0
0
0
0
0
0
0
1
0
2
0
2
0
0
2
1
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
2
0
3
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
8
0
0
0
1
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
1
5
1
1
3
0
2
0
1
0
0
0
1
0
0
0
1
2
1
0
0
0
0
1
0
0
5
0
0
3
0
0
2
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
3
0
3
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
3
2
2
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
1
1
1
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
2
3
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
2
0
0
0
2
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
2
4
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
8
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
1
2
0
0
1
0
0
0
3
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
5
2
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
6
5
0
0
1
0
0
0
0
0
1
0
1
1
1
0
0
2
1
0
2
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
4
0
0
3
3
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
3
0
0
0
0
1
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
3
1
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
3
1
0
1
0
0
1
0
2
0
0
3
2
2
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
2
1
1
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
2
2
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
3
0
1
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
5
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
2
1
0
1
0
0
0
3
0
0
0
2
0
2
0
1
0
1
0
3
0
2
0
1
0
0
0
0
2
0
0
1
0
0
8
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
2
1
0
0
6
0
0
2
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
2
0
0
0
0
3
0
0
2
1
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
2
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
1
2
3
0
0
2
0
0
0
1
0
0
1
0
0
2
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
1
3
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
2
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
3
0
0
0
0
0
2
2
0
2
0
2
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
2
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
2
2
0
0
2
0
0
0
0
1
0
0
4
0
4
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
2
0
0
0
1
2
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
2
2
2
0
2
0
0
0
0
0
3
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
1
0
0
2
1
0
0
0
0
0
0
2
0
0
1
0
3
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
3
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
4
1
0
0
0
0
2
0
0
1
2
0
0
0
2
1
0
0
0
0
0
5
0
0
0
3
0
0
2
1
0
0
1
0
0
1
0
0
0
0
5
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
2
1
1
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
2
0
0
0
0
0
0
0
1
0
3
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
2
0
0
0
3
0
0
0
2
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
1
0
0
2
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
2
0
1
2
0
0
0
0
2
2
0
0
2
1
1
1
0
0
0
1
0
0
0
0
0
2
2
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
2
2
0
0
1
0
0
0
0
1
0
0
1
2
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
3
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
2
1
0
0
0
3
2
0
2
0
0
0
0
0
3
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
2
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
3
0
0
0
1
0
1
0
0
1
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
3
2
0
0
0
2
1
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
2
2
0
0
0
2
0
0
0
1
0
0
1
1
0
1
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
1
2
0
2
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
2
1
0
1
0
0
0
10
0
0
2
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
2
0
0
1
1
0
0
0
0
0
1
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
3
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
1
2
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
3
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
1
0
2
0
0
2
0
0
1
0
2
0
1
2
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
3
0
1
0
0
2
2
0
2
0
1
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
8
0
0
0
1
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
1
0
0
0
2
0
1
1
0
5
0
3
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
2
0
3
1
0
2
0
0
0
1
2
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
3
0
0
0
2
1
0
0
0
0
1
0
1
0
2
0
2
0
0
0
0
0
0
0
0
1
2
1
0
0
4
1
2
2
0
2
0
0
0
2
2
0
0
1
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
2
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
2
2
0
0
0
0
3
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
1
0
0
2
2
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
4
1
0
0
0
2
1
1
0
0
0
0
1
1
2
0
0
1
0
0
2
1
0
0
0
0
2
1
0
0
0
1
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
1
1
1
0
3
0
0
0
0
0
0
0
1
0
0
0
0
3
3
0
0
0
0
0
0
0
0
0
0
2
1
0
2
1
0
0
2
1
0
2
0
0
0
2
2
0
0
2
0
0
1
0
0
2
0
0
1
2
0
0
1
2
0
0
0
3
0
0
1
2
0
0
0
0
0
0
0
1
0
0
1
2
0
2
0
1
0
0
0
1
0
0
3
2
0
1
2
2
0
0
2
1
0
0
0
2
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
6
1
0
2
0
2
2
1
2
1
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
1
2
3
2
0
0
1
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
1
3
0
1
0
0
1
0
0
2
2
0
0
0
0
0
0
0
1
0
1
2
3
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
1
1
2
0
1
1
0
0
0
0
0
2
0
1
0
1
1
0
0
0
0
0
0
2
1
0
0
1
2
0
1
0
2
0
0
0
1
0
0
1
0
0
1
3
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
2
0
0
0
2
0
3
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
2
1
0
2
1
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
5
0
0
2
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
2
3
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
5
0
1
2
0
0
0
1
1
2
1
0
0
2
2
0
0
0
1
0
2
2
2
0
0
0
0
0
1
0
0
0
1
0
1
0
2
3
0
0
1
0
0
0
2
0
1
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
2
0
1
0
1
0
0
0
0
2
0
1
2
3
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
2
1
2
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
2
0
0
1
2
0
0
0
0
0
1
0
2
1
0
0
0
1
1
3
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
4
1
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
3
0
2
2
0
0
0
1
0
1
0
1
2
0
2
0
0
3
0
0
0
0
0
1
0
1
1
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
3
2
0
0
0
0
0
0
2
0
1
2
0
0
2
0
0
3
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
1
3
0
0
2
0
0
0
0
1
1
0
0
0
0
0
3
0
1
0
0
0
1
1
0
0
0
2
1
1
0
0
0
2
0
2
1
1
0
0
0
0
2
0
0
0
3
0
0
4
0
0
0
2
1
0
0
0
0
0
1
2
1
0
0
0
0
1
2
0
1
0
0
1
0
1
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
4
0
0
1
1
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
2
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
2
0
0
0
0
1
1
0
2
0
0
1
1
2
0
0
1
2
1
0
0
0
0
1
1
0
0
0
0
0
2
0
1
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
3
0
0
1
0
0
2
2
0
0
0
0
1
0
0
0
1
0
3
0
0
0
0
1
2
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
3
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
5
0
0
2
0
2
0
0
0
0
2
0
0
0
2
1
0
2
0
1
0
0
3
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
4
0
0
1
0
0
0
3
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
3
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
4
2
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
1
0
0
0
0
1
2
0
0
0
0
1
0
0
0
2
3
0
2
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
2
2
0
1
2
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
1
1
2
0
1
0
0
0
0
0
1
0
0
1
0
0
0
4
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
2
1
0
0
1
0
0
0
0
0
0
1
0
2
0
1
1
3
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
2
0
0
1
0
0
0
2
2
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
3
0
0
0
0
1
2
6
0
3
0
0
0
0
0
1
0
1
1
1
0
0
1
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
8
2
1
0
0
0
0
0
1
0
0
0
3
0
0
2
1
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
2
0
1
0
2
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
1
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
2
0
0
0
1
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
4
0
1
0
1
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
3
1
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
2
0
1
1
1
0
2
0
0
0
0
0
0
2
0
3
0
1
0
0
0
1
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
1
2
0
0
0
0
0
2
2
0
0
0
0
0
1
0
2
1
0
1
0
2
0
0
0
0
1
2
0
0
2
0
1
2
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
2
0
1
1
0
0
0
0
2
1
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
2
0
2
1
0
0
2
0
1
1
0
0
0
0
2
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
2
2
0
3
0
0
0
0
2
0
0
0
0
0
0
2
0
2
1
0
4
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
2
0
0
0
0
2
0
0
1
0
2
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
2
0
4
3
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
1
0
3
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
4
5
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
1
1
1
1
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
2
0
2
0
0
2
2
1
0
0
1
0
0
0
0
1
0
0
1
2
0
0
2
0
0
2
0
1
0
0
0
2
0
0
0
0
2
2
0
0
3
0
1
0
0
0
0
0
2
1
0
0
0
2
0
2
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
1
2
0
0
0
3
0
0
0
0
0
1
0
3
0
3
0
0
1
0
2
0
0
0
2
0
0
0
2
0
1
0
0
0
1
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
2
0
2
1
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
3
0
1
0
2
1
0
0
0
2
2
0
2
1
0
0
0
2
0
1
0
1
0
0
0
0
2
0
0
0
1
1
1
1
0
0
0
2
0
0
0
1
2
0
0
0
0
2
0
0
0
0
1
0
0
1
2
1
0
0
0
3
0
0
2
0
0
2
2
2
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
1
0
0
0
5
0
0
0
0
1
3
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
5
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
7
0
0
0
1
0
0
2
1
0
0
0
2
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
3
0
0
2
1
1
0
0
0
0
4
0
1
2
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
2
2
1
0
2
0
0
0
0
0
4
0
2
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
2
0
0
0
1
0
0
1
0
0
0
2
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
1
1
1
2
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
2
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
1
3
1
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7
0
0
2
2
0
0
1
0
1
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
2
0
0
1
0
2
0
0
0
0
1
0
1
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
2
0
0
4
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
3
1
1
0
1
2
1
2
0
0
0
0
5
2
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
1
0
3
0
0
1
1
0
0
1
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
4
2
0
0
1
0
0
0
0
0
2
0
0
1
2
2
2
0
0
0
2
0
1
0
0
2
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
5
0
0
1
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
1
2
2
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
2
0
3
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
2
0
2
0
0
1
0
0
0
1
0
0
0
2
0
1
1
0
2
0
1
0
0
1
2
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
2
0
0
0
2
2
0
0
0
0
0
0
2
0
0
2
2
0
0
2
0
1
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
3
0
0
4
0
0
1
1
5
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
1
1
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
3
2
0
0
0
1
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
1
1
0
0
0
0
0
0
2
2
0
1
0
0
0
0
1
0
0
3
0
0
0
1
1
0
0
2
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
2
2
3
1
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
1
2
2
0
0
0
1
1
0
0
3
0
4
2
6
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
1
0
2
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
1
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
2
0
0
0
5
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
1
0
2
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
2
1
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
2
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
3
0
2
0
0
1
0
0
0
2
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
2
1
1
0
2
0
0
1
0
0
0
2
0
0
0
0
1
2
2
2
2
2
2
1
0
0
0
0
0
0
0
3
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
1
2
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
3
1
0
0
0
0
1
1
0
1
0
0
0
0
2
0
0
0
0
0
2
0
2
0
2
0
1
0
1
0
2
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
1
0
0
2
0
0
2
0
0
0
0
1
2
0
2
0
0
1
0
0
2
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
1
3
2
3
1
0
0
0
3
2
0
0
0
0
0
1
0
0
0
2
1
0
0
0
2
1
0
2
0
0
0
1
0
2
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
2
2
0
1
1
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
1
0
0
0
1
0
4
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
1
0
0
0
0
1
1
0
2
0
0
0
0
0
0
2
2
0
1
1
3
0
0
0
0
0
2
0
0
0
0
1
0
3
0
0
0
1
0
0
0
0
1
2
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
1
1
0
2
1
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
2
0
2
0
0
1
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
2
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
2
4
0
1
1
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
2
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
1
0
4
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
3
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
3
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
1
0
0
2
0
0
0
1
2
2
0
2
0
0
1
0
0
0
1
0
0
0
0
0
1
0
2
0
2
2
0
0
0
2
0
0
0
2
1
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
0
2
0
3
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
2
0
0
1
0
0
0
0
2
0
2
0
0
0
1
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
2
2
2
0
0
0
1
1
1
0
1
0
0
0
2
0
0
0
1
0
0
0
2
0
2
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
1
1
2
0
0
0
0
2
0
0
0
0
1
0
2
2
0
1
1
0
0
0
2
0
0
1
0
1
0
0
2
1
0
0
0
2
0
1
0
0
0
0
2
1
0
1
0
0
0
0
1
0
1
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
2
0
0
0
0
0
1
2
0
1
0
0
2
0
2
1
2
2
0
0
5
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
1
2
0
0
1
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
1
0
1
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
2
0
2
0
0
1
2
1
0
0
2
0
1
0
0
0
1
2
1
0
0
2
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
1
4
0
0
0
0
0
0
2
2
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
3
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
4
0
0
0
0
0
1
1
1
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
1
0
2
0
1
1
0
4
0
0
0
0
0
2
0
0
0
5
0
0
0
0
0
0
4
0
0
0
4
0
0
0
2
0
2
1
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
2
1
0
2
1
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
1
0
2
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
1
0
2
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
3
0
3
2
2
2
0
0
2
1
2
0
1
1
0
0
0
0
0
2
0
1
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
1
0
2
1
0
0
1
2
2
0
0
0
0
0
0
2
2
0
0
2
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
2
2
0
1
0
0
2
0
0
0
1
0
3
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
5
2
0
6
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
2
0
0
2
0
2
0
0
0
1
0
0
1
1
0
0
0
0
0
0
2
0
0
1
4
0
0
1
1
1
1
1
1
0
0
1
0
1
2
21
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
5
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
2
0
1
1
1
0
5
0
0
0
1
0
0
1
0
0
2
0
1
0
0
0
0
2
0
0
0
1
0
0
0
3
1
0
1
0
0
0
0
0
0
0
0
1
2
0
0
2
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
2
1
3
2
0
3
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
2
0
3
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
2
0
2
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
3
0
0
1
0
0
1
2
2
1
0
0
2
1
0
2
1
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
1
1
0
1
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
1
2
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
4
0
1
0
0
0
0
1
0
0
4
0
0
0
0
0
1
17
0
1
1
0
0
0
0
0
0
0
0
0
2
1
0
0
2
2
0
0
1
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
1
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
2
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
4
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
1
0
0
1
1
0
0
0
2
0
0
0
1
0
0
0
0
0
1
2
0
0
2
0
0
1
0
1
0
2
2
0
0
0
1
0
0
0
0
0
0
2
1
0
0
2
0
0
4
1
2
0
0
1
0
0
0
0
2
2
0
1
0
0
1
0
0
0
0
0
0
0
2
1
2
0
0
0
1
1
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
2
2
0
0
1
1
0
1
0
2
0
0
0
0
0
2
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
2
0
0
2
0
3
1
0
0
2
1
1
3
0
2
0
14
2
0
0
0
0
0
0
2
0
1
0
0
2
0
2
0
2
1
0
0
2
0
0
2
0
0
2
0
0
0
3
0
0
2
0
0
0
0
0
2
0
0
4
0
0
2
0
2
0
1
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
2
0
0
0
0
0
2
0
2
0
0
2
0
0
1
0
0
2
0
1
0
0
2
0
0
0
0
2
3
1
1
0
0
1
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
4
0
0
0
3
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
2
0
2
0
2
0
4
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
2
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
3
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
1
0
0
0
3
0
4
0
0
0
0
0
0
5
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
4
3
0
0
1
0
0
1
0
0
0
0
4
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
1
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
1
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
8
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
3
0
1
0
3
0
2
0
1
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
1
2
0
0
1
0
0
0
0
1
0
0
0
5
0
0
1
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
3
2
1
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
2
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
1
0
0
0
0
1
1
0
1
2
1
0
1
0
1
0
2
1
2
0
3
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
2
0
2
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
1
0
1
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
2
0
0
0
0
2
3
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
6
0
0
2
2
0
0
0
0
0
0
0
0
3
2
2
0
0
0
0
2
0
1
1
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
1
1
0
0
0
0
0
1
0
2
0
2
1
0
1
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
2
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
2
0
0
0
2
0
0
1
1
1
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
2
2
0
0
1
1
0
1
0
0
0
0
0
0
0
0
2
0
0
2
1
0
3
0
0
0
0
2
1
0
1
4
0
0
0
0
0
3
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
1
0
2
0
0
0
0
0
2
1
0
0
1
3
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
2
0
1
0
0
1
0
0
0
0
3
0
2
0
0
2
0
0
0
2
4
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
2
1
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
4
0
0
0
0
2
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
2
1
0
0
0
0
0
0
0
6
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
1
0
1
3
2
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
1
0
0
0
1
2
0
0
0
2
0
0
0
2
0
0
2
4
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
3
1
0
1
2
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
3
0
0
1
0
0
2
0
0
0
0
1
3
0
0
0
3
1
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
5
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
2
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
2
0
2
0
1
1
0
0
0
1
1
0
1
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
3
2
0
0
0
0
0
2
4
0
0
2
0
0
0
3
0
0
0
2
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
2
3
0
1
0
2
0
2
0
1
2
0
0
0
2
2
0
0
0
2
0
0
0
0
0
1
2
1
1
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
1
2
1
2
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
2
2
0
0
0
0
1
0
1
0
9
0
1
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
2
0
0
0
0
1
2
0
0
0
3
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
4
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
2
3
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
1
4
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
3
0
0
2
0
0
0
1
2
2
2
0
1
1
0
1
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
3
0
2
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
2
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
2
0
2
1
0
0
0
0
2
0
2
0
0
3
0
1
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
2
0
0
0
0
2
0
0
0
2
0
0
1
0
2
0
2
0
2
2
2
1
1
0
1
0
1
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
1
0
0
0
0
2
0
0
0
0
4
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
1
2
0
2
1
0
0
0
0
0
1
2
0
2
0
5
5
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
2
2
0
2
2
0
0
0
2
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
3
0
0
2
5
0
0
2
0
0
3
2
0
1
0
0
0
1
0
0
1
0
1
3
2
1
0
1
0
0
2
3
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
2
0
0
0
2
0
0
0
3
0
2
1
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
7
0
1
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
3
0
1
2
0
0
0
2
0
2
0
0
0
0
1
1
0
3
0
0
0
3
1
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
2
0
2
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
2
2
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
2
0
2
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
2
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
2
0
0
2
2
0
0
0
0
1
0
0
1
2
0
0
0
1
2
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
3
2
0
0
0
0
2
1
0
2
0
2
0
0
0
1
0
0
2
2
2
0
0
2
0
0
0
0
0
0
0
2
0
1
0
2
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
2
0
0
0
0
1
2
0
0
2
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
1
2
0
0
0
2
2
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
3
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
3
0
0
0
2
0
2
0
0
1
0
3
0
0
0
0
2
2
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
2
2
2
2
0
1
0
0
1
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
2
1
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
2
1
0
0
0
0
0
1
2
0
2
0
0
1
1
0
0
0
0
2
0
0
0
1
0
0
1
0
2
0
0
2
0
0
0
0
2
0
1
1
0
1
1
2
1
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
2
0
1
2
0
3
0
0
0
1
0
2
1
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
1
2
1
0
1
0
1
2
0
0
0
0
1
0
0
0
1
2
0
1
0
0
0
1
2
0
0
0
1
1
1
1
0
2
0
1
0
1
1
0
0
1
0
0
1
2
0
0
1
1
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
3
3
0
0
0
0
0
0
1
0
0
0
2
0
2
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
2
0
2
1
0
0
2
0
0
0
1
2
0
0
0
0
0
1
1
2
0
1
0
0
0
2
1
1
0
0
0
1
0
0
0
0
1
0
2
0
7
1
0
0
0
1
0
1
2
1
0
1
0
0
0
0
2
0
0
0
0
0
0
2
1
0
3
1
4
0
0
0
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
1
0
0
0
2
2
0
0
2
0
2
2
0
0
0
0
0
2
1
0
0
1
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
3
2
0
1
0
0
0
0
1
1
1
0
2
0
0
0
2
0
1
0
0
2
1
0
1
2
0
0
1
1
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
2
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
3
0
0
1
2
0
0
0
0
2
1
0
1
0
1
0
0
0
2
2
0
0
3
2
0
0
0
1
6
2
2
0
1
0
1
0
0
1
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
2
0
0
2
0
0
1
0
0
0
0
2
1
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7
0
0
2
0
0
1
0
1
2
0
2
2
0
0
0
0
3
0
0
0
1
0
0
0
2
0
0
0
0
0
4
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
1
0
0
5
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
2
2
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
1
2
0
2
1
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
1
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
2
2
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
3
0
3
1
0
2
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
1
2
0
0
1
0
0
0
0
0
0
1
0
0
2
4
2
0
0
2
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
5
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
2
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
3
0
0
0
0
0
0
0
2
2
0
0
0
2
0
7
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
1
0
0
0
0
1
0
0
0
2
0
2
4
0
2
3
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
1
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
1
0
1
0
0
2
2
3
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
1
5
0
1
0
0
2
0
0
0
0
0
0
4
0
1
3
0
0
2
0
2
0
0
1
2
0
1
0
0
2
0
0
0
2
18
1
2
0
0
2
1
0
3
0
2
2
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
4
1
0
0
2
1
0
0
3
0
0
0
0
0
0
1
2
2
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
1
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
1
0
0
0
0
1
0
0
0
0
0
1
1
0
4
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
1
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
2
0
0
1
0
1
3
0
2
0
1
0
0
0
0
2
0
2
0
0
1
0
0
2
2
1
0
0
1
1
0
2
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
2
2
0
0
1
0
2
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
1
0
1
0
1
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
5
0
1
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
1
0
0
1
0
0
3
0
0
1
0
1
1
0
0
0
2
0
0
0
2
1
0
0
0
2
0
1
0
0
1
0
1
0
0
0
0
0
1
1
0
0
1
0
2
0
0
0
0
2
0
0
3
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
1
2
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
3
0
2
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
1
0
1
1
0
0
1
3
0
0
0
0
0
0
1
0
0
2
0
1
1
0
0
0
1
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
4
0
0
0
0
0
4
1
8
0
0
0
0
0
3
0
0
1
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
2
1
0
2
0
0
0
0
0
2
0
0
1
2
0
0
1
0
0
0
0
0
1
1
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
2
3
0
2
1
2
2
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
2
0
1
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
4
2
0
0
0
0
3
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
2
0
1
0
0
0
1
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
5
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
4
1
2
0
0
0
0
2
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
1
2
0
0
0
2
0
5
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
2
0
0
1
0
2
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
2
2
0
2
0
3
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
4
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
5
0
1
1
0
0
0
2
2
1
0
0
0
0
0
0
1
0
1
0
1
1
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
1
0
0
2
1
0
0
0
0
2
0
0
0
0
1
2
0
0
2
2
0
2
0
0
2
0
1
0
2
2
2
0
0
2
0
0
2
2
1
0
0
1
0
0
2
0
0
2
0
1
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
3
0
1
0
0
0
1
0
1
0
0
2
0
1
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
10
0
1
0
0
0
0
0
2
1
0
0
0
1
0
0
2
2
0
1
0
0
0
1
0
0
2
0
1
0
0
2
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
2
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
3
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
6
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
2
0
1
0
0
1
1
0
2
2
0
2
0
2
1
0
2
4
0
0
0
0
2
0
2
1
0
0
3
0
0
0
2
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
3
1
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
2
1
0
0
0
0
1
0
1
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
1
1
0
3
1
0
0
0
0
0
0
0
0
2
1
0
2
0
0
1
1
0
1
0
0
1
1
1
0
0
2
1
1
0
0
2
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
2
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
1
2
0
0
0
2
2
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
2
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
2
0
1
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
2
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
1
0
0
0
1
0
0
1
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
2
2
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
1
0
4
0
0
2
0
0
0
0
0
2
0
0
1
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
1
0
0
0
0
2
0
0
1
0
0
0
0
2
2
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
3
0
1
0
1
0
2
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
4
0
0
1
0
0
0
0
0
0
1
0
2
0
1
0
0
0
3
0
1
0
0
2
0
0
3
0
0
0
2
2
0
1
2
1
0
0
0
1
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
1
1
0
1
0
0
0
0
2
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
2
2
1
0
2
0
0
1
0
0
2
1
0
0
0
2
0
1
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
2
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
1
1
0
0
1
4
1
2
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
1
0
2
0
0
0
0
3
2
0
2
1
0
0
0
0
0
0
2
0
0
0
2
4
0
0
0
0
0
2
0
0
2
1
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
1
2
0
0
0
0
2
0
0
0
0
2
1
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
1
2
0
0
0
0
5
1
0
0
0
2
0
0
0
0
0
0
2
0
2
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
1
1
2
1
0
2
0
0
0
1
0
1
2
1
0
2
2
0
0
1
0
0
2
0
2
1
1
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
1
0
2
2
0
2
0
0
1
0
0
2
3
1
0
5
0
0
1
0
0
0
0
0
0
0
1
0
2
1
1
0
1
0
0
0
1
0
1
2
3
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
1
2
2
0
0
0
3
2
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
3
2
0
0
0
0
1
2
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
1
0
0
0
3
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
2
0
1
0
0
0
3
0
0
0
2
0
0
1
0
0
0
3
0
2
0
0
0
0
0
2
0
0
0
1
0
0
2
1
2
0
0
0
0
0
7
0
0
1
0
0
0
0
1
0
1
0
0
0
0
3
0
0
0
1
2
1
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
1
1
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
2
0
7
0
2
1
0
2
1
0
2
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
4
0
0
0
3
1
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
1
2
1
2
2
0
2
0
0
1
0
0
0
7
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
2
0
0
0
10
0
2
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
2
0
1
0
0
0
1
0
2
0
0
1
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
2
0
2
2
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
2
1
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
1
2
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
1
1
0
1
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
3
1
0
0
0
1
1
0
1
0
4
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
3
0
2
2
0
0
0
0
0
0
0
3
3
0
0
0
0
1
0
0
0
0
0
5
1
0
0
0
4
0
0
0
0
0
0
0
1
2
1
2
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
9
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
2
0
1
0
0
1
0
0
0
1
1
1
0
3
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
4
0
0
3
0
0
0
1
1
1
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
2
4
2
0
0
0
0
0
0
2
0
0
0
0
0
0
5
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
5
0
0
1
2
0
2
1
2
2
0
1
0
0
0
0
0
0
1
0
0
1
2
0
1
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
2
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
2
0
1
0
2
1
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
2
0
0
2
1
0
1
1
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
1
0
0
0
0
1
0
1
1
1
0
0
0
0
0
1
0
0
0
3
2
2
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
2
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
6
0
0
0
1
2
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
1
2
0
0
2
2
3
2
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
4
0
1
0
2
2
0
0
2
0
0
0
0
0
0
0
3
0
2
1
1
0
2
0
10
1
0
1
0
0
0
2
2
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
2
0
0
0
0
2
4
4
3
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
3
0
1
1
0
2
0
0
0
0
0
2
2
0
0
4
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
2
2
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
1
0
1
2
0
0
2
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
2
0
0
6
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
1
0
3
0
2
0
1
0
1
2
0
0
1
0
0
0
2
0
1
2
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
4
0
0
0
0
1
2
0
0
4
0
0
1
0
1
1
0
1
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
2
1
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
6
1
0
1
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
3
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
1
0
0
1
0
2
0
0
2
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
4
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
2
1
0
0
0
1
0
0
2
2
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
1
0
2
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
3
0
1
0
0
5
4
0
0
0
0
0
1
1
2
3
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
1
0
0
2
0
1
0
0
0
0
1
0
0
0
0
3
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
1
0
0
2
1
0
0
0
1
0
0
0
0
3
0
0
0
1
0
0
2
0
0
0
0
2
0
4
0
1
0
1
0
0
0
1
0
0
2
1
0
1
7
1
0
0
2
1
0
1
0
3
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
2
0
0
2
0
2
0
2
1
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
3
0
2
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
3
2
0
0
2
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
1
0
0
0
0
2
2
0
1
1
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
2
0
0
2
0
2
0
0
0
2
0
2
0
1
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
2
0
0
0
2
0
0
0
1
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
1
1
0
0
2
0
0
1
0
2
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
2
0
0
8
1
0
1
0
0
0
0
1
0
0
0
1
0
2
0
1
1
1
2
2
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
1
1
2
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
1
0
0
0
1
0
0
0
1
4
0
0
0
0
0
3
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
3
1
0
0
0
0
0
0
0
1
0
0
1
0
2
0
1
2
0
0
0
1
1
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
3
0
0
0
0
2
0
2
1
0
0
1
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
3
0
1
2
2
1
2
0
0
0
0
1
0
1
2
0
0
3
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
2
0
0
2
0
0
1
0
0
3
0
0
0
0
1
0
2
2
0
0
0
0
0
0
1
1
2
0
0
0
2
0
0
0
0
2
0
0
2
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
1
0
0
1
2
0
0
1
0
2
0
0
1
1
0
0
1
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
7
3
0
1
0
0
2
0
1
2
0
0
2
2
0
2
0
0
0
0
1
1
0
0
5
0
0
0
0
1
5
2
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
4
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
3
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
2
0
0
0
1
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
2
1
0
2
1
0
0
0
2
0
0
0
1
1
0
5
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
1
0
1
2
0
2
0
2
0
0
0
1
2
0
0
0
0
4
1
2
1
0
2
0
0
0
0
0
1
0
1
1
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
2
0
2
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
1
1
1
0
0
0
2
2
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
2
1
0
0
1
2
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
2
0
0
1
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
1
1
0
0
0
1
0
1
0
1
0
0
0
5
0
0
0
0
0
1
0
0
2
0
0
0
0
1
2
2
0
1
0
0
0
0
1
2
2
0
0
0
0
0
0
2
2
0
2
0
0
0
3
0
0
0
0
4
0
1
0
0
0
0
2
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
2
0
0
0
0
1
0
0
0
0
0
8
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
1
1
2
1
0
2
2
0
0
1
0
0
0
0
0
2
1
0
2
2
1
0
1
0
0
0
0
0
1
0
2
1
1
0
0
1
0
0
3
0
0
0
2
1
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
3
0
0
1
0
2
2
0
0
0
0
1
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
1
0
0
2
0
0
0
0
1
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
3
1
0
0
2
0
0
0
1
1
1
0
0
0
0
0
1
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
2
0
4
0
2
0
2
0
0
0
2
1
3
0
0
0
0
0
0
1
2
2
0
0
0
0
2
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
2
0
2
0
0
0
4
0
0
2
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
2
3
2
0
1
0
0
0
0
1
0
2
0
5
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
2
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
3
1
0
0
0
0
0
2
0
0
0
0
0
2
0
13
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
2
0
2
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
2
0
2
1
2
1
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
1
4
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
3
0
0
0
0
0
2
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
1
2
1
0
0
0
1
0
0
0
0
1
0
0
1
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
3
0
1
0
1
1
0
0
1
0
0
3
1
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
2
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
3
0
2
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
6
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
1
2
2
3
0
0
1
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
1
1
0
0
0
1
1
3
0
1
0
0
2
1
0
0
1
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
3
0
0
1
2
2
0
0
0
0
0
0
0
3
0
1
0
2
0
0
0
1
0
0
1
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
1
2
2
0
0
1
0
0
1
0
0
0
0
2
0
0
1
2
2
1
0
0
0
1
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
1
2
0
2
2
0
0
0
0
2
0
0
0
3
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
1
0
0
0
2
0
1
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
1
1
0
3
2
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
2
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
1
1
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
1
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
2
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
1
2
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
1
2
0
2
0
0
0
0
2
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
2
0
2
0
0
0
0
1
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
4
0
1
1
0
3
4
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
3
0
1
0
0
0
0
1
0
0
0
0
0
1
4
0
0
2
0
1
0
2
0
0
3
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
3
0
0
0
2
0
0
0
1
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
3
0
0
3
0
0
1
2
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
3
0
0
0
0
0
1
0
0
1
1
0
0
2
0
2
3
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
2
3
0
0
0
0
0
0
0
0
6
2
0
1
2
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
2
0
1
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
3
0
0
0
0
2
1
1
0
0
0
0
1
0
0
0
0
1
0
0
2
0
1
0
1
0
0
0
2
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
5
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
3
0
1
0
0
1
0
0
0
2
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
1
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
2
3
1
2
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
1
0
0
3
2
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
3
0
2
0
1
0
0
0
0
1
0
0
2
1
1
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
1
0
3
2
0
0
1
0
1
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
1
0
0
0
0
0
1
0
7
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
4
0
0
1
1
0
2
0
1
3
2
0
1
2
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
2
0
2
0
0
0
0
2
0
0
0
0
3
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
1
0
1
0
0
3
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
1
4
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
1
3
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
3
0
1
0
0
2
1
0
1
0
2
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
1
0
2
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
2
0
0
0
0
0
0
0
0
2
0
9
2
0
0
0
1
0
0
2
1
2
0
2
0
0
2
0
0
0
0
2
3
0
0
0
0
0
0
2
0
0
1
0
0
2
2
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
2
0
1
0
0
0
1
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
1
0
3
0
0
2
1
0
0
1
0
0
2
0
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
7
2
2
0
0
0
1
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
2
0
2
0
2
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
2
2
0
0
0
1
0
1
0
3
0
0
2
1
0
0
1
0
0
1
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
2
0
1
0
0
2
2
0
3
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
1
1
2
0
0
1
0
0
0
0
0
0
2
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
1
1
2
1
1
0
0
0
1
0
0
3
1
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
0
2
0
0
0
1
2
2
4
0
0
2
1
0
0
0
1
1
0
1
0
0
0
2
0
1
2
0
0
2
2
0
0
0
2
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
9
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
2
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
1
3
2
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
3
2
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
2
0
1
2
1
0
0
1
0
0
0
1
1
2
0
0
1
0
0
0
2
0
0
2
0
0
1
0
0
2
0
0
0
0
1
1
2
0
0
0
0
0
0
1
3
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
1
2
0
0
0
0
1
0
0
0
0
0
0
2
0
3
0
2
0
0
0
0
0
0
0
2
1
0
0
2
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
1
2
0
2
0
2
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
1
2
1
0
0
0
0
0
2
0
0
1
0
1
0
2
0
0
1
0
1
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
1
0
0
1
1
2
2
0
3
0
0
0
1
0
0
0
0
0
2
0
1
4
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
1
0
1
0
2
0
0
0
0
0
2
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
9
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
2
1
0
2
2
0
0
0
4
0
0
0
0
0
0
1
0
0
0
1
2
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
2
0
0
0
2
0
1
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
3
1
0
0
0
0
0
3
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
2
2
2
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
3
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
1
6
0
0
3
0
1
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
1
1
0
0
1
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
3
2
0
0
1
0
0
0
3
0
0
0
1
0
1
1
2
0
0
0
0
1
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
10
0
1
2
1
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
2
0
0
2
0
0
0
3
2
1
0
0
0
0
0
0
2
2
1
0
1
2
0
0
1
0
1
0
0
0
0
2
0
0
2
0
0
0
2
0
1
0
1
0
0
0
0
0
0
1
0
0
2
0
0
2
0
1
0
0
0
2
0
3
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
1
0
2
0
0
1
0
0
1
1
0
0
0
0
0
2
2
0
0
0
0
0
0
3
2
2
0
1
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
3
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
3
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
1
1
0
1
0
0
0
0
2
2
0
0
0
0
0
8
0
0
0
0
3
1
0
1
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
5
0
0
0
0
0
2
0
0
0
0
3
0
2
0
0
2
1
1
0
0
2
0
0
1
1
0
0
0
0
0
0
0
3
1
2
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
3
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
2
1
2
1
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
1
0
0
1
0
0
5
2
1
0
0
2
0
3
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
1
0
1
0
0
0
0
3
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
1
0
2
0
0
0
0
2
2
0
0
0
3
0
0
0
0
0
0
0
1
2
1
0
0
0
0
4
5
0
0
2
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
2
2
0
0
0
1
0
5
2
0
0
0
0
2
1
0
0
2
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
4
0
1
0
0
0
1
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
2
0
0
0
1
0
2
0
2
1
0
2
0
0
0
0
0
0
0
2
0
1
0
0
3
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
2
0
2
0
0
0
0
2
0
1
1
1
0
0
0
0
0
0
0
0
0
2
0
1
1
1
2
0
1
0
0
2
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
1
0
2
0
0
0
2
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
2
0
1
0
1
0
0
0
1
0
5
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
4
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
1
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
1
0
0
1
1
2
0
0
0
0
0
0
0
0
0
2
0
2
3
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
1
0
0
2
0
0
1
1
1
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
1
0
0
0
0
0
0
2
0
0
0
0
1
3
2
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
2
2
3
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
2
0
0
1
0
1
3
0
0
0
1
0
0
0
2
1
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
2
1
3
2
0
0
0
1
0
2
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
1
2
1
0
0
2
0
0
2
2
0
2
0
0
0
0
0
0
0
1
0
2
2
1
0
0
0
0
0
4
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
4
0
0
0
0
2
0
0
0
0
0
0
0
1
2
3
2
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
1
0
1
2
0
0
4
0
2
3
0
1
0
0
0
0
2
0
1
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
3
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
2
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
2
2
0
2
1
1
0
0
0
0
2
1
1
1
0
0
2
0
0
2
0
0
0
0
0
8
0
1
0
1
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
3
0
0
0
0
1
0
0
0
0
2
0
0
1
0
3
0
1
0
1
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
3
0
1
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
3
0
2
0
0
0
2
0
0
2
1
0
2
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
8
0
2
2
0
0
0
0
0
0
2
1
1
0
0
0
2
0
0
2
0
2
0
2
0
0
1
2
3
0
1
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
3
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
1
2
0
1
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
1
2
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
3
2
1
2
0
1
2
2
0
0
0
0
0
0
0
0
0
0
1
0
1
2
1
0
0
1
0
0
0
0
0
1
0
2
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
3
2
0
0
1
1
2
0
0
0
0
0
4
0
0
1
1
0
0
2
0
0
2
2
0
0
2
0
0
0
4
0
2
0
1
1
0
1
2
0
0
0
2
0
2
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
1
0
2
1
0
0
0
0
1
0
1
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
2
1
0
0
0
2
1
1
0
2
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
1
0
0
0
5
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
1
0
0
1
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
1
0
0
0
3
0
0
0
0
0
0
0
0
3
1
0
0
0
2
0
0
1
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
1
0
1
3
0
0
1
2
0
0
2
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
3
1
1
1
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
6
0
0
0
1
0
0
1
0
3
0
1
0
0
0
0
1
4
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
3
0
0
3
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
3
2
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
2
0
1
1
0
0
1
1
0
0
0
0
0
0
2
3
0
0
1
0
0
0
0
0
2
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
4
2
0
0
1
0
0
0
2
0
0
0
0
0
0
2
1
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
2
0
1
2
0
1
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
1
0
1
0
2
0
0
1
0
0
0
0
0
2
1
0
2
2
0
0
0
1
0
0
2
0
0
0
2
0
1
0
0
1
1
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
5
1
0
2
3
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
1
0
2
2
2
0
0
1
0
2
2
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
2
2
0
0
2
0
0
0
1
2
0
0
2
0
0
1
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
1
2
1
1
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
2
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
2
1
0
1
0
0
0
2
1
0
1
0
0
0
1
1
0
2
2
0
1
0
0
2
3
0
2
0
0
2
1
3
0
0
0
1
0
0
0
0
0
1
2
1
2
1
0
2
0
2
0
0
0
0
1
0
0
1
0
0
1
0
0
0
2
0
1
0
2
0
0
1
0
1
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
2
1
0
1
0
2
0
0
0
2
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
2
0
1
0
0
0
0
2
1
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
3
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
2
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
1
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
1
1
0
0
0
3
0
2
0
1
0
1
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
2
3
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
3
1
2
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
2
0
0
2
1
1
0
0
0
2
2
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
2
0
1
0
0
0
0
0
0
1
1
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
3
0
0
0
0
2
3
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
3
0
1
0
0
0
0
1
1
0
2
4
0
0
2
0
0
0
0
0
2
0
0
2
1
2
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
3
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
2
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
4
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
3
0
3
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
1
2
0
0
1
0
0
1
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
2
2
0
0
1
0
0
0
1
2
0
0
0
0
0
0
4
0
2
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
3
0
0
2
1
0
0
0
2
0
0
5
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
2
1
2
2
0
2
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
1
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
5
2
0
2
2
0
0
3
0
0
0
0
0
2
1
0
1
0
2
0
0
0
0
1
0
1
0
0
0
0
0
2
2
1
2
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
3
0
0
0
0
2
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
1
0
0
0
0
0
1
4
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
2
5
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
1
0
2
2
3
2
1
3
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
1
0
0
1
5
0
1
0
0
2
0
0
0
0
3
0
1
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
1
0
0
0
0
0
2
0
2
0
0
1
1
0
0
0
0
2
0
0
0
2
3
1
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
1
4
0
0
0
1
2
0
0
0
0
1
0
1
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
3
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
2
0
1
2
1
0
0
0
0
0
1
0
0
0
0
2
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
2
1
2
0
0
0
0
2
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
2
1
0
1
2
0
0
0
0
2
0
0
2
0
0
2
1
0
1
0
0
3
0
0
0
0
0
0
3
0
0
0
0
3
1
1
3
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
2
0
0
0
0
1
2
0
1
1
0
0
0
0
0
5
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
1
0
0
2
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
1
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
1
0
0
1
3
0
0
2
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
1
1
0
2
0
0
2
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
1
2
0
3
0
1
0
0
1
0
0
0
1
0
1
0
2
0
0
0
1
0
0
2
0
2
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
2
0
2
2
1
0
1
0
2
1
1
0
0
2
0
0
1
2
0
0
0
1
1
1
1
0
1
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
3
2
2
1
0
0
0
0
0
5
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
3
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
2
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
2
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
2
0
0
0
1
3
1
2
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
2
2
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
1
2
0
2
0
0
0
0
0
0
2
0
3
0
2
0
2
0
2
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
2
0
2
1
0
0
0
1
0
0
0
1
0
0
2
1
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
2
1
0
2
3
2
1
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
1
0
0
2
0
0
1
0
0
0
0
2
1
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
2
0
2
0
0
0
0
4
0
0
0
2
0
1
0
0
4
0
0
0
0
0
1
2
1
0
0
2
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
3
2
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
4
0
2
0
0
0
0
0
0
0
0
0
1
3
0
0
2
0
0
0
0
0
0
1
0
0
0
2
2
0
1
2
3
0
0
0
0
0
0
1
1
0
0
0
1
2
0
0
5
0
0
1
1
0
0
0
0
0
0
2
0
0
0
1
0
0
2
2
0
0
0
0
1
0
0
0
0
3
0
0
2
0
0
1
0
2
2
0
0
0
0
0
0
0
3
0
3
0
0
0
0
0
0
1
1
0
0
2
0
0
1
2
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
1
0
0
0
0
1
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
2
1
0
0
0
0
1
1
0
0
0
0
1
2
1
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
2
1
0
1
0
1
0
1
1
0
0
0
0
0
2
1
1
1
0
0
0
0
0
0
2
2
2
0
2
0
0
5
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
4
0
0
0
0
1
1
0
1
0
1
2
2
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
3
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
2
0
0
2
0
0
5
0
0
0
0
0
0
0
0
0
1
0
0
1
1
3
2
0
0
0
0
0
0
2
0
3
0
0
2
0
0
2
0
1
2
0
0
0
2
0
0
0
0
1
0
1
1
0
0
2
1
0
0
0
3
0
2
0
0
0
0
2
0
2
2
0
1
0
0
2
3
0
0
0
2
2
1
0
0
0
0
1
0
0
0
0
0
0
2
0
1
1
0
2
0
1
0
1
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
2
0
0
2
2
3
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
2
0
9
2
0
0
0
0
1
0
0
1
0
1
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
1
0
1
0
0
0
0
2
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
2
2
5
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
4
1
0
0
0
2
0
1
2
0
1
0
0
1
1
0
0
0
2
0
0
0
0
2
5
0
0
1
1
0
1
0
0
0
0
0
0
0
1
2
1
1
0
0
0
0
1
2
0
0
0
2
0
0
2
1
2
0
0
1
0
0
0
0
2
0
1
0
0
0
1
2
1
0
0
0
2
2
1
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
2
1
0
1
0
0
1
3
1
0
0
0
0
2
1
0
0
0
0
2
0
0
1
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
1
2
2
1
2
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
2
0
0
2
1
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
2
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
2
0
0
0
0
2
2
2
2
2
2
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
2
0
2
0
1
1
1
0
1
1
0
0
0
3
0
0
0
0
0
17
1
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
1
2
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
2
0
0
2
3
5
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
1
0
1
0
2
0
0
1
1
0
0
0
1
2
0
0
0
0
2
0
0
1
1
0
0
0
0
1
0
1
3
2
0
0
1
0
2
0
0
0
0
0
1
0
5
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
2
2
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
1
0
0
0
2
0
0
0
2
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
9
1
0
0
0
5
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
7
1
0
3
0
2
0
2
0
0
2
0
0
0
1
0
1
0
0
2
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
4
0
0
0
0
0
0
0
2
0
0
1
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
3
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
2
0
3
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
2
0
0
1
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
2
0
0
0
3
0
0
2
1
1
2
1
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
3
0
2
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
3
0
0
2
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
2
0
0
2
2
1
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
3
0
0
4
1
0
0
1
3
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
2
2
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
2
0
1
1
2
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
2
0
0
0
1
0
0
0
1
0
0
1
1
0
2
2
0
0
1
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
1
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
2
0
0
1
2
2
0
0
0
0
1
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
2
1
0
0
0
1
2
0
1
2
1
0
2
0
0
0
0
0
0
0
2
1
0
0
0
2
0
1
0
0
0
0
0
1
3
0
0
0
0
2
2
1
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
2
0
1
1
0
1
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
3
0
2
0
1
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
1
2
0
0
0
0
0
1
1
2
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
8
0
3
0
0
0
1
1
0
2
0
0
0
0
0
0
2
0
0
0
0
5
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
3
2
0
1
2
0
5
0
0
0
1
5
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
1
2
0
0
0
0
2
0
1
3
0
0
0
0
1
0
0
2
0
2
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
1
0
0
2
1
0
2
0
4
0
0
0
0
0
0
0
1
1
0
2
0
2
0
0
2
0
2
1
2
0
1
2
0
0
0
2
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
3
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
2
0
1
0
0
0
1
2
0
2
0
1
1
0
0
0
0
0
0
0
0
0
9
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
2
1
0
0
1
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
2
1
0
0
0
0
2
0
0
0
3
0
0
2
0
1
0
0
0
0
2
2
2
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
1
0
0
1
1
0
0
0
0
0
0
2
1
0
0
0
1
0
0
3
0
0
1
0
0
0
0
2
0
0
2
0
1
1
0
1
0
0
0
0
0
0
0
1
1
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
1
1
0
0
0
0
0
1
0
0
0
2
0
0
0
2
2
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
8
0
2
0
0
1
0
1
0
0
2
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
1
2
0
0
0
0
0
0
0
13
0
0
0
0
0
0
2
0
0
0
0
1
0
2
2
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
2
0
2
0
0
0
3
0
0
0
0
0
1
0
0
0
0
1
1
0
3
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
0
3
1
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
6
0
0
0
2
1
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
1
6
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
2
0
0
1
0
0
0
0
1
0
2
0
1
2
0
2
2
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
1
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
1
2
0
0
0
0
0
0
0
0
1
3
0
0
2
1
0
1
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
0
1
3
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
3
0
0
2
0
2
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
1
1
0
0
0
2
0
0
2
0
0
0
1
1
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
3
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
1
0
2
0
4
4
0
0
5
0
1
1
0
2
0
0
1
0
7
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
2
2
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
2
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
1
2
1
1
0
2
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
2
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
1
2
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
2
4
0
1
1
0
1
1
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
2
1
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
1
1
0
3
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
3
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
1
0
0
0
3
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
1
2
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
2
1
2
0
4
0
0
1
0
2
2
2
0
0
2
2
1
0
1
1
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
1
2
1
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
2
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
2
2
1
1
0
0
0
0
0
1
2
0
0
0
1
1
0
0
0
0
1
2
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
8
0
0
0
0
0
1
0
1
0
2
2
0
0
0
0
1
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
2
0
0
1
0
0
0
1
1
0
0
0
3
0
0
1
1
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
1
1
0
0
0
0
0
0
0
1
3
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
1
1
0
0
0
0
2
0
0
1
0
0
0
0
3
0
1
0
0
2
0
0
2
0
0
0
0
0
0
1
0
1
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
1
0
0
0
1
0
2
1
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
2
0
0
1
0
0
0
0
0
2
0
1
0
1
0
1
0
0
0
0
0
1
0
2
0
0
0
1
0
0
1
1
0
0
0
0
2
2
2
3
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
1
1
0
2
0
0
0
0
0
0
1
1
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
6
0
4
0
2
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
2
1
2
0
1
0
4
0
0
0
5
0
0
0
0
1
2
5
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
2
0
0
2
0
1
0
1
0
1
1
0
3
1
1
1
0
1
0
0
0
0
2
0
0
0
0
1
0
2
0
1
0
0
2
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
2
0
1
0
0
1
0
1
0
0
2
0
0
0
2
0
0
0
0
1
1
1
2
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
4
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
3
0
7
1
0
0
0
0
0
0
0
2
0
0
0
0
1
1
1
0
0
0
1
1
1
0
0
0
0
1
1
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
2
1
1
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
1
2
2
0
2
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
2
0
0
1
0
2
0
0
0
0
0
1
0
0
0
4
0
1
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
2
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
1
0
1
0
2
0
0
0
2
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
1
0
0
2
0
0
0
3
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
2
1
2
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
3
2
0
1
0
0
0
0
0
0
0
0
0
2
1
1
1
1
0
0
0
0
2
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
2
2
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
1
0
2
1
3
0
0
2
0
0
0
0
0
2
2
0
0
0
3
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
1
0
4
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
2
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
2
0
1
0
0
0
0
2
2
2
0
5
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
1
2
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
2
1
2
0
1
0
1
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
1
0
2
2
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
3
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
1
1
0
0
0
1
0
3
2
0
0
0
0
0
0
2
4
0
0
2
0
0
0
0
0
0
2
0
0
0
0
3
0
0
2
1
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
5
2
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
2
0
1
1
0
0
0
3
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
2
0
0
0
0
1
2
0
0
0
1
0
0
0
2
0
0
4
1
0
2
0
0
0
0
0
2
1
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
5
0
0
0
0
2
0
0
0
0
7
8
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
2
2
2
0
0
1
0
0
2
0
0
0
0
0
1
0
1
1
1
0
0
2
2
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
2
1
0
1
0
0
2
0
3
0
0
3
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
3
0
0
1
2
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
2
0
3
1
0
0
2
0
0
1
3
0
0
1
0
0
0
0
3
2
0
1
2
0
0
2
0
2
1
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
2
0
0
1
0
1
0
2
0
2
1
1
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
5
1
0
0
0
0
0
0
0
5
3
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
1
1
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
1
0
0
0
0
0
1
2
1
3
0
1
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
1
3
0
0
1
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
3
0
0
0
2
0
0
0
2
0
2
3
1
2
0
1
0
0
0
0
1
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
2
1
0
0
0
0
0
0
2
4
0
1
0
0
0
1
0
2
0
0
0
1
1
0
2
0
0
0
0
0
0
0
4
0
0
0
0
1
0
2
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
3
2
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
4
0
2
0
0
2
0
0
0
0
1
3
0
0
2
0
0
3
1
1
0
0
0
0
1
0
0
0
0
0
0
0
2
3
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
5
0
0
0
0
0
6
0
3
0
1
0
1
2
0
2
0
0
0
2
4
0
0
0
0
4
0
0
0
0
0
0
6
1
0
1
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
2
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
3
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
3
0
0
2
0
1
0
3
1
0
2
0
2
0
2
0
0
2
0
0
2
2
0
0
2
7
0
0
2
2
1
0
0
1
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
6
0
0
0
0
0
0
0
0
5
1
0
0
1
1
2
0
0
4
0
0
0
0
2
0
1
1
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
7
1
0
0
0
0
2
0
1
0
0
0
0
0
0
2
1
0
0
1
1
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
1
1
0
1
0
1
0
0
0
0
6
3
0
0
3
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
5
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
2
0
1
2
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
2
0
0
0
0
0
0
1
1
0
2
0
0
0
0
2
2
0
0
0
0
0
1
1
0
1
0
1
2
3
1
0
0
0
0
0
2
0
0
2
0
2
2
0
0
0
0
0
3
0
0
0
0
0
0
3
0
0
2
0
0
2
0
0
1
0
1
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
3
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
4
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
1
0
0
2
2
0
0
0
1
0
1
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
3
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
1
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
1
1
0
4
0
0
0
0
0
2
1
0
0
1
2
0
0
0
2
0
1
0
0
2
0
0
1
0
0
0
2
1
0
1
2
0
0
1
1
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
5
2
0
0
2
1
0
0
1
2
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
3
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
2
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
2
0
0
0
1
0
0
0
2
1
0
0
0
0
6
2
2
0
1
0
0
0
0
0
0
0
2
0
0
1
1
2
0
0
0
0
1
0
0
1
0
0
0
0
1
2
0
1
2
0
0
0
0
0
1
0
0
0
2
0
3
0
0
0
2
0
0
5
0
1
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
2
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
2
2
1
0
2
0
0
1
1
0
1
0
0
0
0
3
0
3
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
2
2
0
0
0
0
1
0
0
0
1
0
2
0
0
1
4
0
0
1
2
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
2
0
0
1
0
4
0
1
0
2
0
0
0
0
0
0
1
0
1
1
2
1
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
1
1
1
0
0
2
0
0
0
2
0
0
0
4
0
0
0
0
2
0
0
0
1
0
2
1
0
0
1
0
1
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
7
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
3
1
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
1
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
3
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
2
0
0
0
1
2
0
0
1
0
1
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
2
1
0
1
2
0
0
0
0
0
1
0
0
1
1
0
4
0
0
1
0
0
0
1
0
2
0
0
0
1
0
0
0
0
1
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
1
0
2
0
0
0
0
0
1
0
0
1
0
0
3
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
1
0
0
0
1
0
2
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
2
0
2
4
2
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
2
0
2
0
0
1
1
0
1
0
2
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
1
0
2
0
3
0
2
0
0
0
0
0
2
0
2
2
1
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
4
0
0
2
0
0
0
0
1
0
0
2
2
2
0
0
1
0
0
0
0
0
0
0
0
0
1
2
1
1
0
1
0
0
0
0
0
2
0
0
4
0
0
1
0
0
0
0
0
0
0
0
1
0
0
3
0
2
0
3
0
0
0
0
2
0
0
0
1
2
0
0
1
1
0
0
0
0
0
0
2
1
1
0
2
0
0
0
7
0
0
1
0
1
0
0
0
2
0
5
0
1
1
1
0
0
0
0
2
0
1
1
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
3
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
2
0
0
3
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
14
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
3
1
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
5
0
2
0
0
0
2
2
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
1
0
4
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
5
0
0
0
0
0
2
0
1
0
1
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
2
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
1
0
1
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
3
0
2
0
1
0
0
1
2
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
2
0
1
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
6
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
2
0
1
0
1
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
1
0
2
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
4
2
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
2
2
2
0
2
0
1
0
1
0
0
1
1
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
2
1
1
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
2
1
0
0
0
2
1
0
0
0
0
1
0
2
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
4
1
0
0
0
0
1
0
1
3
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
2
0
2
0
0
0
0
2
0
4
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
1
0
1
6
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
2
0
0
2
0
2
0
0
3
1
0
0
0
0
0
2
0
0
1
2
0
0
0
0
1
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
1
0
0
2
0
0
0
1
0
1
0
0
2
2
0
0
1
0
0
0
0
0
0
2
2
1
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
1
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
1
2
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
4
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
1
0
1
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
2
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
2
3
0
0
0
0
0
2
2
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
6
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
2
0
2
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
2
2
0
0
0
0
0
1
2
0
0
0
0
1
0
3
2
0
0
4
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
3
1
0
0
0
0
4
0
0
1
2
0
0
0
2
0
0
2
0
1
1
0
2
1
0
0
0
0
1
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
1
1
1
0
0
0
3
2
0
0
0
0
2
0
0
0
0
0
1
0
6
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
6
2
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
1
0
0
2
0
0
2
0
0
0
0
3
2
0
3
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
2
1
0
0
0
0
2
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
4
0
1
0
1
0
0
0
0
0
0
5
2
2
0
0
0
0
0
0
0
0
2
0
0
0
1
1
1
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
2
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
2
1
0
0
0
0
2
2
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
7
0
0
3
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
2
0
3
0
1
0
0
0
2
2
0
0
0
0
0
0
1
2
0
1
2
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
3
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
5
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
2
0
2
0
2
0
0
0
0
3
2
0
2
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
1
11
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
3
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
4
0
0
3
0
0
1
0
0
2
0
1
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
1
0
0
3
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
2
1
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
1
0
1
0
0
0
0
0
1
0
2
0
0
0
1
0
2
0
0
0
0
1
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
1
1
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
5
0
1
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
2
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
1
1
0
2
2
2
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
2
0
1
3
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
2
0
2
0
0
1
0
2
3
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
5
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
1
2
0
0
1
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
2
1
0
2
0
0
0
0
0
0
3
2
0
0
0
0
0
0
1
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
3
2
2
2
2
0
2
0
0
1
1
0
0
2
0
0
2
0
0
0
0
1
0
0
2
1
0
0
0
0
1
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
2
0
0
1
2
0
0
0
1
1
0
2
0
0
0
1
0
0
1
2
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
2
0
0
0
2
0
0
2
0
0
2
0
0
0
0
2
1
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
3
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
1
0
0
0
2
0
4
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
2
0
0
0
0
1
0
4
1
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
2
0
0
0
2
2
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
5
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
3
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
1
1
2
0
2
0
1
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
3
0
0
0
0
7
0
2
2
0
3
0
0
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
2
0
0
2
0
0
0
1
0
0
2
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
1
0
0
1
2
0
0
0
0
2
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
2
0
2
0
1
0
1
3
0
0
2
2
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
15
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
1
1
0
3
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
2
0
0
0
0
0
0
2
0
2
0
0
1
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
2
0
1
0
0
1
0
0
1
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
1
0
1
0
1
0
1
0
0
0
2
0
0
0
0
1
0
1
2
0
0
0
0
0
2
0
2
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
1
2
0
0
0
2
0
2
2
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
4
1
0
0
0
2
1
0
0
0
3
2
0
1
0
0
2
2
1
0
2
0
0
0
0
0
1
1
0
2
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
2
2
0
0
2
1
0
0
1
0
2
2
2
1
0
0
1
0
2
0
0
1
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
1
0
2
0
0
0
0
2
0
0
2
0
0
1
0
3
0
0
0
1
1
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
1
0
0
3
4
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
2
3
0
0
0
0
0
3
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
2
5
0
1
1
2
1
0
1
1
3
0
0
0
0
2
0
0
0
0
4
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
1
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
2
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
1
0
1
1
3
0
0
0
0
0
0
1
0
0
1
0
1
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
1
2
2
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
1
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
3
0
0
1
3
0
1
1
0
0
0
0
0
0
4
0
0
0
2
0
0
0
2
0
1
1
0
0
2
2
0
0
0
2
1
1
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
5
1
1
0
1
0
1
1
1
0
0
0
0
2
0
0
0
0
0
2
3
0
2
0
0
2
2
0
3
2
0
0
1
0
0
2
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
2
0
1
1
1
0
4
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
2
0
0
1
0
1
0
1
0
0
2
1
1
1
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
2
1
0
0
0
0
0
0
0
0
0
1
0
1
0
2
1
0
2
0
0
1
0
0
3
0
0
0
0
3
0
1
0
1
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
1
0
0
2
3
1
0
0
0
0
0
0
2
2
1
0
0
1
0
2
2
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
1
1
2
0
1
0
0
2
0
0
4
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
1
0
1
1
2
0
3
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
3
0
0
1
1
0
0
3
0
0
2
3
0
0
0
0
0
1
0
5
0
0
1
0
2
1
0
1
0
2
0
0
0
0
2
0
0
0
0
0
1
1
5
0
5
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
2
0
2
0
2
1
0
2
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
1
0
3
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
4
0
3
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
1
1
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
3
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
5
0
0
3
0
2
0
0
0
1
2
0
2
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
6
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
3
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
5
0
0
0
0
2
0
0
0
0
3
0
0
0
0
3
1
0
3
1
2
0
3
0
0
2
1
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
2
3
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
2
1
0
0
3
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
7
0
0
0
1
0
2
0
1
2
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
2
0
0
0
2
2
0
0
0
0
0
1
2
0
0
0
0
0
1
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
5
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
3
0
0
0
2
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
2
2
1
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
1
0
3
0
0
2
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
2
0
0
0
1
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
1
0
2
0
0
0
2
1
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
2
2
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
1
0
1
0
1
1
1
0
0
0
0
0
1
1
0
3
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
2
0
1
0
0
0
0
0
2
0
0
1
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
2
1
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
4
0
0
2
0
0
0
0
0
0
2
0
0
1
3
0
2
2
0
0
1
0
0
0
0
0
1
0
0
0
3
0
0
1
5
0
3
0
0
0
0
0
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
2
0
0
2
0
1
0
2
0
0
0
1
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
4
0
0
0
2
0
2
2
0
0
0
2
0
0
2
1
2
0
0
0
0
0
0
1
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
1
0
2
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
5
0
0
0
0
0
1
2
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
1
0
0
0
1
0
0
0
0
0
2
0
5
0
0
0
1
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
2
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
1
0
0
3
0
1
0
0
0
0
2
0
1
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
2
2
2
0
1
1
0
0
0
2
2
1
0
0
0
3
2
0
0
0
2
0
0
1
0
2
0
0
0
1
2
0
0
0
0
2
0
2
0
0
0
3
4
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
3
0
5
0
0
0
0
0
2
0
2
0
0
3
0
0
0
0
0
2
0
2
0
0
3
0
0
0
0
2
1
2
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
4
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
1
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
2
1
0
0
0
2
2
0
0
0
0
2
0
0
0
4
0
0
0
2
0
0
4
1
0
1
1
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
5
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
2
0
0
0
1
2
2
0
0
1
1
0
0
0
0
2
0
1
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
2
2
1
0
0
0
0
0
0
0
1
0
6
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
1
0
0
7
0
0
1
0
0
0
0
0
0
0
2
1
0
0
1
0
1
0
0
0
0
2
0
0
0
3
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
1
1
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
2
1
3
0
0
0
1
2
0
0
0
0
2
0
0
0
2
1
2
0
0
0
0
2
0
2
2
2
0
0
0
0
0
0
0
1
2
2
1
0
0
0
0
2
0
0
0
2
0
0
2
1
0
0
0
0
1
0
0
0
0
1
2
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
2
1
2
0
2
0
1
2
0
0
1
0
0
6
1
3
0
2
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
2
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
3
0
2
1
0
3
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
1
1
1
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
2
1
0
0
1
0
0
2
0
1
2
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
1
3
0
0
1
0
1
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
3
0
0
0
2
0
0
1
0
0
1
0
3
0
1
0
0
0
0
2
3
1
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
3
0
0
0
1
0
0
0
3
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
5
0
2
2
0
0
0
0
3
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
8
0
2
0
2
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
2
0
0
0
0
1
2
0
0
2
0
0
0
0
2
0
0
0
3
1
2
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
4
0
2
2
0
0
1
3
1
0
0
1
1
0
1
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
3
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
1
0
0
0
0
1
1
4
0
0
0
0
0
2
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
2
1
0
0
3
0
2
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
1
0
0
0
1
0
1
2
1
0
3
2
0
1
0
0
0
0
0
0
0
1
3
0
0
3
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
1
0
0
2
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
2
1
0
2
0
0
0
0
2
0
0
0
1
0
1
2
0
1
1
0
0
0
1
0
1
2
0
0
1
1
0
0
0
2
0
0
0
1
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
2
0
4
2
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
4
0
2
0
2
1
0
0
1
2
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
1
0
1
1
1
0
0
4
0
0
0
0
2
0
0
0
1
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
3
0
2
0
1
0
1
0
1
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
1
0
2
2
0
1
1
1
0
0
0
0
0
0
0
2
0
2
2
0
2
0
0
2
0
1
2
0
0
0
1
0
0
0
0
0
1
0
2
1
1
1
2
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
2
2
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
6
0
1
0
0
0
0
0
0
2
0
0
0
1
0
2
0
1
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
2
0
2
0
0
1
2
0
0
2
2
0
0
1
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
2
2
0
0
0
4
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
2
0
0
0
0
21
0
0
2
0
0
0
0
1
0
0
2
2
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
4
1
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
4
0
2
0
0
0
1
2
0
1
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
2
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
2
4
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
5
2
0
1
0
1
2
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
3
0
0
2
0
6
3
0
0
0
3
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
2
0
0
0
2
0
0
0
2
0
1
0
0
0
0
1
0
0
0
4
0
0
2
0
2
0
1
3
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
4
0
1
2
0
2
1
0
0
0
0
1
0
0
2
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
2
0
1
0
0
0
0
0
1
5
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
3
0
0
2
0
2
0
1
0
0
0
0
2
0
1
0
2
2
0
2
0
0
0
0
1
6
2
0
0
0
0
3
0
0
0
1
2
1
3
0
0
0
0
1
0
2
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
2
0
0
1
0
0
0
2
1
0
0
0
2
1
1
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
3
1
0
0
8
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
3
0
3
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
2
0
1
1
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
2
3
0
2
0
0
0
0
2
0
0
0
0
4
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
1
1
0
0
0
1
0
0
2
0
2
0
0
0
0
0
2
1
0
3
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
3
1
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
1
0
0
2
1
0
0
1
2
0
0
0
0
0
0
0
2
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
4
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
2
0
0
1
0
2
0
0
1
0
0
1
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
2
0
2
2
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
4
0
1
0
0
2
1
0
0
0
0
0
1
2
2
0
0
0
2
1
1
3
0
2
0
0
1
0
0
0
1
0
0
0
0
2
2
0
0
2
0
2
0
2
0
2
0
1
2
0
0
0
1
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
2
2
0
2
0
0
0
1
0
0
1
1
0
0
0
1
0
0
1
0
1
0
3
0
2
0
2
0
4
0
0
0
0
1
2
0
0
0
1
0
0
1
0
0
0
1
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
2
0
0
1
0
0
2
0
1
1
2
0
0
0
0
0
0
0
3
0
1
0
0
2
0
0
0
3
1
1
2
0
0
0
0
0
5
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
3
0
0
0
0
1
0
1
1
1
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
2
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
1
0
0
0
0
0
0
2
1
1
0
1
2
1
0
0
0
1
0
0
1
0
0
0
2
0
0
0
2
0
8
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
3
0
0
2
0
0
0
2
0
0
1
1
1
0
0
1
0
2
0
1
0
0
1
0
0
0
0
0
7
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
1
0
0
2
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
2
0
0
4
0
2
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
2
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
1
0
0
1
0
1
1
0
2
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
3
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
9
0
0
0
0
0
1
0
0
1
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
1
0
0
3
1
0
0
2
2
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
1
0
0
0
0
2
0
0
1
2
2
0
0
0
0
0
0
2
0
2
0
0
0
1
0
2
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
5
0
2
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
1
2
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
2
1
2
1
0
0
1
0
0
1
1
0
0
0
3
2
1
1
2
4
1
0
8
0
0
0
0
0
0
0
0
2
2
0
0
0
4
0
0
1
0
0
1
0
0
2
0
1
2
0
0
0
0
0
0
2
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
2
0
0
1
0
2
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
4
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
1
0
0
0
2
0
1
0
0
1
0
1
0
2
0
1
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
1
0
0
0
1
2
0
0
0
7
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
2
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
2
0
1
2
0
0
0
1
0
0
0
2
1
3
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
1
2
0
2
0
3
0
0
0
0
0
0
2
4
2
1
0
2
0
0
2
2
0
2
0
0
2
0
0
0
1
0
0
2
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
5
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
3
0
1
0
1
0
1
1
0
0
0
0
1
2
2
0
0
2
8
0
0
0
2
0
0
0
0
0
0
0
0
0
3
2
0
2
0
1
7
0
0
1
4
1
0
0
1
0
1
0
0
1
0
0
0
0
2
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
1
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
1
0
1
2
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
3
0
1
3
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
1
2
6
4
0
0
0
0
0
0
0
1
1
0
1
2
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
1
2
1
4
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
2
1
0
0
0
0
0
0
0
1
2
0
1
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
2
1
0
0
0
2
2
0
0
0
1
0
0
0
7
5
0
0
0
3
0
2
2
1
0
1
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
1
0
0
1
1
0
0
1
0
0
2
0
0
3
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
1
0
0
3
1
0
0
1
0
0
1
1
0
1
2
1
0
0
0
2
0
2
0
0
0
0
0
1
1
1
2
3
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
5
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
2
0
0
0
1
0
1
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
5
3
4
0
0
1
0
0
2
0
3
0
2
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
4
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
1
2
1
0
0
0
1
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
2
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
2
0
1
0
0
1
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
1
0
0
0
1
0
0
2
0
0
2
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
1
2
1
1
0
0
0
1
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
2
2
4
1
0
0
2
0
0
2
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
2
1
0
2
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
3
0
2
0
0
4
0
0
0
0
3
0
1
1
0
2
0
0
0
3
0
0
8
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
3
0
1
2
1
0
2
1
1
1
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
4
0
0
1
3
1
2
0
2
0
0
0
1
0
0
0
0
2
1
0
2
0
3
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
2
1
1
0
3
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
1
0
0
0
0
0
0
1
0
2
0
2
0
2
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
2
0
0
1
0
0
0
0
0
0
0
2
2
0
2
1
0
2
0
0
0
0
2
0
0
1
0
1
1
0
0
2
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
4
1
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
2
3
2
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
4
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
2
0
1
0
0
3
0
1
1
0
0
3
0
0
0
0
0
0
3
1
1
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
1
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
2
2
4
2
0
0
13
2
0
0
0
0
0
0
2
2
0
0
2
0
2
1
0
0
2
0
0
0
1
2
0
0
0
0
0
0
2
2
2
0
0
5
0
1
0
1
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
4
2
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
2
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
1
2
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
8
3
0
0
0
2
0
0
1
0
0
0
0
2
0
2
0
0
2
0
0
2
0
2
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
1
1
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
2
0
1
0
2
0
0
0
0
1
0
4
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
1
0
0
0
0
2
4
1
2
0
0
2
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
10
1
1
0
1
0
0
0
0
1
0
1
0
0
3
2
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
2
0
0
0
0
0
0
2
1
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
3
2
0
0
2
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
1
0
0
2
0
2
1
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
1
0
2
2
2
0
0
0
0
0
0
4
1
1
0
0
1
0
1
0
4
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
3
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
1
0
1
0
0
0
2
0
2
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
4
0
0
0
3
1
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
1
0
2
0
0
0
0
0
1
2
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
1
0
1
0
2
2
0
2
4
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
3
4
0
0
0
0
0
0
0
1
0
0
0
1
0
2
1
1
2
1
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
2
0
0
2
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
3
0
2
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
3
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
2
0
1
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
5
1
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
1
1
1
2
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
1
1
3
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
1
0
2
1
0
2
0
0
1
1
0
2
2
0
1
0
0
1
0
0
2
0
0
0
0
0
3
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
4
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
3
0
1
0
1
0
0
1
0
4
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
2
0
1
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
2
0
0
2
0
0
0
0
2
2
2
0
0
0
0
0
0
2
2
0
0
4
0
0
0
2
0
1
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
2
0
2
2
1
2
0
4
0
0
0
0
0
0
3
0
0
0
2
0
0
2
1
0
1
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
2
2
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
1
1
0
0
1
3
0
0
2
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
6
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
1
2
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
2
0
0
2
2
1
2
0
0
0
0
0
0
0
1
0
0
0
3
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
2
0
2
0
3
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
1
0
0
1
2
2
2
0
0
3
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
1
0
1
0
2
0
1
2
1
0
1
0
0
0
3
2
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
4
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
2
0
2
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
2
0
0
2
0
0
0
1
0
2
0
0
0
0
1
1
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
3
0
0
0
0
0
0
2
6
0
1
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
1
0
2
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
4
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
5
0
2
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
2
2
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
1
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
3
2
0
0
0
0
0
2
0
0
0
2
2
1
1
1
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
3
0
0
0
1
2
0
0
0
0
0
1
2
0
0
3
1
0
1
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
2
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
1
0
1
0
0
0
0
2
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
1
1
2
1
1
0
3
0
0
1
0
2
2
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
10
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
2
0
1
0
2
0
1
3
0
2
0
0
0
1
0
1
1
3
0
0
2
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
3
0
0
0
0
0
0
0
0
2
1
1
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
1
0
0
2
0
0
1
2
1
1
0
1
0
1
2
0
1
0
0
0
1
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
1
0
1
0
0
2
0
1
1
0
0
0
0
0
2
0
4
0
0
2
1
0
0
7
0
0
0
1
0
0
3
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
5
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
1
0
1
0
0
0
0
2
2
2
0
1
2
2
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
4
0
0
0
1
0
0
0
0
1
0
2
0
1
1
2
0
1
0
0
2
0
0
0
0
0
0
4
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
3
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
4
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
3
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
2
0
2
2
0
0
0
0
1
1
2
1
1
0
0
0
0
3
0
2
0
0
1
0
2
2
0
0
2
0
0
2
1
0
0
2
2
1
1
1
0
0
0
0
2
0
2
0
0
0
8
0
0
0
0
0
0
0
0
0
0
0
3
0
1
2
0
1
0
3
0
0
0
2
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
1
1
0
2
0
1
0
0
0
0
6
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
2
0
0
3
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
1
0
2
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
3
2
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
2
0
0
2
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
5
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
1
0
1
1
0
0
2
3
1
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
1
0
0
0
0
0
0
0
3
0
2
0
0
1
2
0
1
0
0
0
0
5
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
2
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
2
2
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
3
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
2
0
1
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
3
0
0
0
2
0
0
1
0
0
1
2
2
0
0
0
0
1
0
3
0
0
0
0
0
0
1
0
0
1
3
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
1
1
0
0
0
3
1
1
0
0
0
0
2
0
0
2
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
6
1
2
1
2
0
2
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
1
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
2
1
2
0
0
0
1
2
5
0
2
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
2
1
0
0
0
3
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
2
8
0
0
3
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
2
2
0
0
2
2
0
0
0
0
0
0
0
0
0
2
3
0
0
0
1
2
0
0
0
0
1
0
0
0
0
1
0
1
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
6
1
2
0
0
1
0
1
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
1
0
0
1
2
5
4
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
2
0
3
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
2
0
1
0
0
0
0
1
0
1
0
2
0
2
0
0
0
0
0
2
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
1
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
5
0
0
0
0
1
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
3
2
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
1
2
0
1
0
0
0
0
1
2
1
2
0
2
1
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
3
0
0
2
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
2
0
1
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
1
0
0
0
2
1
0
0
0
0
0
2
1
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
3
0
1
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
1
1
1
1
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
3
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
1
0
1
0
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
2
2
0
0
0
0
0
1
0
1
1
2
0
1
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
5
0
0
1
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
3
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
2
2
19
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
6
0
5
2
0
0
0
2
0
0
0
0
0
0
2
1
0
2
0
1
0
0
0
0
1
0
3
5
2
2
0
1
0
3
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
3
3
0
0
3
2
1
0
2
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
2
2
0
0
0
0
0
0
0
0
0
1
0
1
1
2
2
1
0
0
0
1
1
1
0
8
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
9
0
0
3
0
1
0
0
0
0
0
0
2
2
1
0
1
0
0
0
0
2
2
0
2
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
2
0
0
5
2
0
0
2
0
0
2
5
0
0
0
1
0
0
1
2
1
2
0
0
0
0
0
0
2
1
1
0
0
1
1
0
0
0
0
0
0
2
0
1
1
2
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
1
0
2
0
1
1
0
2
0
0
2
0
0
0
0
0
0
0
1
2
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
3
2
0
1
0
0
0
0
0
0
0
0
2
2
0
2
0
0
2
0
0
1
0
0
0
2
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
11
0
1
0
2
1
2
2
0
0
0
0
0
0
0
0
1
0
0
0
3
2
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
1
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
1
0
0
2
0
0
0
2
1
0
0
1
1
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
2
1
1
1
0
0
0
0
0
0
0
0
3
0
0
0
1
3
3
0
0
0
0
0
0
0
4
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
1
0
0
0
2
0
1
0
0
4
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
3
0
0
0
0
2
0
0
0
1
0
0
1
0
1
3
0
0
0
0
1
0
0
2
0
0
0
0
1
0
2
1
0
2
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
2
0
0
0
0
0
0
0
1
2
1
0
0
0
1
1
0
0
0
0
0
2
0
1
0
0
2
2
0
0
0
0
2
1
0
0
1
0
2
0
0
0
0
2
0
0
5
0
0
0
0
2
0
0
0
0
0
1
1
1
2
0
0
0
0
0
2
2
0
0
2
0
0
0
3
2
0
2
0
0
2
2
0
0
0
0
1
0
0
0
0
0
1
1
4
2
0
0
1
3
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
1
1
0
0
2
2
2
2
0
1
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
3
0
0
2
1
0
0
1
0
5
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
2
1
1
2
0
0
2
0
1
4
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
1
0
0
1
0
0
0
2
2
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
2
0
0
1
0
0
1
2
0
1
2
0
0
1
0
0
0
0
1
0
1
1
0
2
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
2
2
0
0
0
2
6
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
2
0
2
0
0
0
0
0
1
0
0
1
2
2
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
3
0
0
2
0
5
0
1
0
2
2
2
0
3
0
0
1
0
0
0
0
0
1
0
2
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
9
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
1
1
1
0
0
3
0
1
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
3
0
0
1
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
2
0
2
0
0
0
0
2
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
2
2
0
0
0
0
2
0
1
4
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
4
0
1
1
0
1
0
0
0
0
0
0
0
0
0
5
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
1
0
0
0
0
0
0
0
1
0
2
1
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
2
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
1
3
2
0
0
0
0
0
0
0
0
1
2
3
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
3
1
0
2
0
0
1
1
0
0
1
0
2
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
4
1
0
1
0
0
0
0
2
2
0
1
1
0
0
1
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
2
0
0
0
1
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
2
0
0
2
0
1
0
0
1
2
0
2
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
1
0
3
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
1
0
4
0
0
0
0
2
0
0
0
1
0
0
3
0
0
0
0
1
2
1
0
0
0
2
0
2
0
2
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
3
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
2
0
2
1
0
0
0
0
0
0
0
1
0
0
1
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
2
0
2
0
3
0
2
0
0
5
0
0
0
0
0
0
1
0
0
0
2
0
0
1
1
3
0
2
0
2
1
1
0
0
0
0
0
2
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
3
2
0
0
1
1
0
0
0
0
3
0
2
0
0
0
0
0
0
0
2
0
3
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
3
2
2
0
0
2
0
3
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
3
0
0
0
1
0
1
1
0
0
0
2
1
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
1
0
0
0
1
0
1
0
2
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
2
1
16
0
3
0
0
2
0
1
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
1
0
1
0
0
1
1
0
2
2
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
2
3
0
0
0
2
0
0
2
0
0
0
1
0
0
0
1
0
1
2
0
0
2
2
0
0
2
0
0
0
0
1
0
0
1
2
0
0
0
0
0
1
0
1
2
0
0
0
0
1
1
2
5
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
2
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
1
1
2
2
1
0
0
0
0
0
0
2
5
0
1
0
1
5
0
0
0
0
2
0
2
0
0
0
0
2
0
1
0
0
2
0
1
0
0
0
0
0
1
0
2
2
0
0
0
0
0
3
0
0
2
0
1
0
0
0
2
0
0
0
1
0
1
1
1
2
0
0
1
2
0
0
1
0
0
0
3
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
4
0
0
0
0
1
2
2
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
2
0
0
1
2
1
0
0
0
0
0
0
0
7
0
0
0
3
3
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
1
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
1
0
1
2
0
0
2
0
0
3
0
0
0
0
2
0
0
1
0
0
6
0
0
0
0
0
0
0
1
2
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
3
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
6
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
3
2
0
0
0
0
0
0
1
0
2
0
0
7
0
0
1
0
0
2
0
1
0
0
2
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
3
0
2
0
0
1
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
3
0
2
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
2
1
0
4
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
1
0
2
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
2
0
0
0
1
2
0
0
5
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
1
2
1
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
5
2
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
6
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
2
0
0
0
2
0
0
2
4
0
0
2
6
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
1
0
2
0
0
0
0
2
1
0
0
3
0
1
2
3
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
2
1
1
0
0
0
1
0
2
0
0
0
4
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
5
1
0
0
0
0
2
1
0
0
0
2
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
2
0
0
1
2
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
1
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
2
0
0
0
0
4
2
0
0
0
0
2
1
0
2
0
0
0
0
1
2
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
1
0
0
0
6
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
1
0
1
1
0
2
0
0
0
9
0
0
1
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
2
0
0
0
1
2
1
0
3
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
2
0
0
1
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
1
1
0
5
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
1
0
0
0
1
3
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
2
0
0
1
1
1
2
0
0
0
0
2
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
3
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
3
0
0
0
3
0
1
1
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
1
1
0
2
1
0
0
0
1
0
0
0
0
1
2
4
0
1
2
1
0
0
0
0
1
3
0
0
0
0
1
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
2
0
1
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
2
3
0
0
1
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
3
1
1
0
1
0
2
0
0
0
0
2
3
1
0
0
0
1
1
0
0
0
0
1
0
2
0
1
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
2
3
0
0
0
0
0
0
0
3
2
0
0
0
0
1
0
2
0
0
0
2
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
2
2
0
0
1
0
3
2
1
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
3
0
0
0
0
0
0
1
0
0
2
0
0
1
1
0
0
0
0
0
0
1
0
2
1
0
2
0
1
0
3
2
0
0
12
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
2
2
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
1
1
0
0
0
0
1
0
2
0
1
2
0
0
1
0
0
1
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
4
0
0
0
2
0
0
0
2
0
0
0
4
0
0
0
0
0
0
2
0
0
0
3
2
1
0
0
0
0
0
0
1
0
3
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
1
2
0
0
0
0
0
2
1
0
0
1
0
0
2
1
0
0
0
0
4
3
0
0
0
3
2
0
0
0
0
0
2
0
0
0
2
1
3
0
0
5
0
1
0
2
0
2
0
2
0
0
1
1
2
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
1
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
1
1
2
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
2
0
2
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
3
2
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
4
0
1
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
4
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
1
0
0
0
3
2
0
0
0
2
2
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
2
3
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
3
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
1
2
0
1
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
2
2
0
1
0
0
0
0
1
0
0
2
0
0
4
0
2
0
3
1
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
1
3
0
0
1
2
2
0
0
3
0
1
2
0
0
1
2
0
0
3
0
0
1
0
0
1
0
2
1
0
0
0
1
2
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
2
1
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
2
0
0
2
0
1
1
0
1
0
1
1
0
0
2
1
0
0
0
2
0
0
2
0
2
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
1
2
1
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
1
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
1
2
0
0
3
0
0
2
0
1
0
0
0
0
1
0
0
1
0
0
0
6
2
2
6
2
0
0
2
1
2
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
2
3
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
2
0
1
0
0
1
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
3
1
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
1
2
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
1
0
6
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
2
2
1
0
0
0
1
0
2
3
2
0
1
3
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
4
0
0
2
2
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
6
0
0
2
0
0
0
0
1
2
1
2
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
4
1
0
0
0
0
0
0
1
1
0
0
2
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
1
0
1
2
0
0
0
1
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
3
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
2
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
5
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
1
0
1
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
2
1
0
0
0
1
2
0
0
0
0
0
3
0
0
4
1
2
0
0
1
0
0
1
0
0
0
0
0
0
0
2
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
2
2
1
0
0
0
0
0
0
1
0
1
0
0
1
0
2
0
4
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
1
0
0
7
1
0
0
0
3
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
2
0
2
2
0
0
0
1
0
0
0
0
0
0
0
1
2
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
1
0
0
0
0
0
2
2
0
0
1
2
2
0
0
0
3
2
0
0
0
0
1
0
1
0
0
0
0
4
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
6
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
2
0
0
1
2
0
0
0
0
2
0
0
2
2
0
1
0
0
0
0
2
2
1
0
0
0
0
4
1
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
1
4
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
11
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
1
0
1
0
0
5
2
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
1
1
0
0
2
2
2
0
1
0
0
2
0
0
0
0
0
2
0
0
0
1
0
2
0
3
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
3
0
3
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
1
6
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
3
1
0
1
0
0
0
2
0
0
0
0
0
2
0
1
0
2
0
1
2
0
0
0
0
3
0
0
0
0
0
0
0
2
0
2
0
2
0
0
2
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
2
0
0
2
0
0
3
0
2
2
1
0
0
0
0
1
0
2
0
2
2
0
0
0
0
1
0
0
2
0
0
0
2
1
0
1
2
0
0
2
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
4
0
1
0
0
1
0
0
3
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
1
0
0
0
2
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
2
1
2
0
0
3
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
1
1
1
0
0
0
0
0
0
2
0
0
0
0
6
1
0
0
0
2
0
0
1
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
2
0
0
0
1
0
2
0
1
0
0
0
0
1
0
2
1
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
2
0
0
0
2
2
0
2
3
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
1
5
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
2
1
2
0
1
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
2
2
5
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
1
0
0
0
0
2
0
0
0
0
0
2
1
0
1
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
1
0
2
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
2
0
0
2
0
2
0
0
1
0
3
0
0
2
0
0
0
0
2
0
2
0
1
3
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
3
0
0
2
3
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
1
0
1
1
0
0
0
0
0
2
1
2
0
0
0
1
2
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
1
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
1
2
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
2
0
0
2
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
4
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
1
3
1
0
0
0
2
0
0
3
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
3
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
2
0
0
4
0
0
0
1
1
0
6
0
0
0
0
0
0
2
2
0
0
0
2
1
0
0
0
3
0
1
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
3
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
1
1
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
1
3
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
1
1
1
0
0
2
1
0
0
8
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
4
2
1
0
0
0
0
1
0
2
0
2
2
0
0
0
0
0
1
0
0
0
3
5
6
0
5
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
3
0
2
2
2
0
0
0
0
0
1
0
0
0
3
0
2
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
2
0
2
1
0
1
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
1
7
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
9
0
0
0
1
0
2
0
0
0
2
0
0
1
0
0
1
0
2
0
0
0
1
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
2
0
2
0
0
1
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
3
1
0
1
0
2
0
0
1
1
0
0
2
2
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
1
0
0
0
0
1
1
1
2
1
0
1
1
0
2
1
2
0
0
0
1
0
0
0
0
5
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
4
1
2
2
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
2
0
1
2
0
0
0
0
2
0
2
5
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
2
0
2
2
0
1
1
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
2
2
0
1
0
1
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
1
2
1
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
1
0
5
2
0
0
6
2
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
1
0
1
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
2
1
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
2
0
0
6
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
2
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
3
0
7
0
0
3
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
2
1
5
0
0
0
0
1
3
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
5
0
0
0
0
0
0
2
0
0
2
0
0
2
6
0
0
0
0
1
3
0
0
2
0
3
0
0
2
0
3
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
3
0
1
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
2
2
0
0
0
1
0
1
1
0
0
0
1
0
0
0
3
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
3
2
1
1
2
0
1
0
5
0
0
1
3
0
0
1
0
0
1
0
2
3
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
1
0
0
0
0
2
0
2
0
0
0
2
0
2
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
4
1
2
0
1
0
0
3
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
7
0
0
0
0
2
1
0
0
0
3
0
0
0
0
0
2
0
0
3
0
2
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
3
1
1
2
1
0
1
0
0
2
0
0
0
0
0
1
0
0
2
2
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
3
2
0
0
0
1
0
0
0
2
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
4
1
0
0
0
1
0
0
0
1
0
0
0
0
0
2
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
4
1
1
2
1
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
2
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
3
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
2
0
1
2
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
3
2
1
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
3
0
0
2
1
2
2
0
0
3
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
1
0
2
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
2
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
4
1
0
1
0
0
0
0
0
0
1
2
0
2
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
4
0
2
0
0
0
5
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
7
1
2
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
5
0
2
0
0
0
0
0
0
16
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
10
1
0
1
2
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
2
0
1
1
0
0
0
3
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
2
0
1
0
1
2
0
0
2
2
0
1
0
0
0
2
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
2
0
1
3
0
0
1
1
0
1
0
0
3
1
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
3
0
0
0
0
3
0
0
1
0
2
0
0
1
1
0
0
2
0
0
0
0
0
0
1
2
1
7
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
4
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
1
0
0
2
2
1
0
0
0
2
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
2
0
0
0
0
1
2
1
0
0
0
0
0
1
0
0
0
0
1
2
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
2
1
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
4
0
0
0
0
1
0
3
0
3
0
0
6
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
1
0
0
0
0
0
0
2
0
0
0
0
0
2
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
1
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
2
0
1
1
1
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
1
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
2
0
2
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
2
0
1
0
2
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
2
3
1
0
1
7
1
0
1
0
0
0
2
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
4
2
1
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
2
0
0
0
0
0
1
2
3
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
2
0
0
2
0
1
0
0
2
0
1
1
1
1
0
2
0
0
0
0
1
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
1
0
4
1
2
2
2
0
2
0
0
1
2
0
0
0
0
1
0
0
2
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
2
1
2
1
2
2
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
2
0
0
0
1
0
1
2
0
0
0
0
0
1
0
1
0
0
2
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
3
0
0
1
2
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
1
0
0
0
2
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
1
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
1
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
7
0
3
2
1
0
2
0
0
0
2
0
2
0
0
0
0
0
1
2
1
0
1
0
0
2
0
1
0
1
0
0
0
1
2
0
1
0
1
0
0
0
0
2
0
0
0
1
2
1
2
0
0
0
0
1
1
1
0
2
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
1
2
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
3
0
0
0
0
0
2
0
0
0
0
0
5
0
0
0
0
0
0
2
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
1
2
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
2
0
0
1
0
1
0
1
0
0
0
0
2
0
0
2
0
2
0
1
0
0
0
0
3
0
1
1
0
0
5
0
1
0
0
2
0
0
0
0
0
0
5
0
1
1
2
0
1
0
2
1
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
1
0
2
1
2
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
2
0
2
0
1
2
0
2
0
0
1
2
0
0
1
2
1
0
0
0
0
2
0
0
0
0
0
0
1
2
0
2
0
0
1
0
0
0
0
0
2
0
0
1
3
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
2
1
2
2
0
0
0
0
0
0
0
0
0
1
0
1
1
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
1
1
0
2
1
2
0
0
0
0
0
0
3
2
0
0
0
0
0
1
2
0
0
1
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
1
2
0
2
1
0
0
0
0
1
0
0
0
1
2
0
0
0
0
3
0
1
0
0
0
0
0
3
0
0
2
2
0
2
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
1
1
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
2
1
3
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
2
1
2
2
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
3
0
0
2
2
0
0
2
0
0
0
0
2
0
0
0
0
2
2
0
0
1
0
0
2
3
0
0
1
0
4
1
1
0
1
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
2
0
1
2
2
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
1
0
3
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
3
0
5
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
2
0
2
0
0
2
0
2
0
1
0
1
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
2
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
1
0
0
0
2
0
0
0
9
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
2
2
0
2
0
0
2
2
0
3
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
2
1
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
1
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
2
1
0
2
0
1
0
0
0
2
0
3
1
0
2
0
0
2
2
0
0
1
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
4
0
0
0
1
2
0
2
0
0
0
0
1
0
0
0
0
0
0
6
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
2
0
0
0
2
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
3
0
1
0
1
0
1
1
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
1
1
1
0
0
0
0
1
3
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
1
1
4
0
1
0
0
0
0
0
0
0
1
3
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
2
0
0
0
0
1
1
0
2
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
2
0
0
0
1
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
3
0
1
0
0
0
0
0
1
0
0
0
0
0
0
3
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
1
4
2
0
0
2
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
2
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
2
2
3
0
0
0
2
2
0
0
0
1
0
0
0
0
0
2
3
2
0
2
0
0
2
0
0
0
1
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
1
2
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
4
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
1
2
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
3
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
6
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
1
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
1
2
0
0
0
3
0
2
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
3
0
3
3
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
2
0
0
2
0
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
1
0
1
2
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
5
0
0
0
0
0
1
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
1
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
2
1
0
0
2
0
0
0
0
0
0
2
1
0
0
1
0
0
0
2
3
0
2
1
0
2
0
2
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
4
0
0
0
0
2
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
1
0
2
1
0
0
2
5
0
0
0
0
0
1
0
2
0
1
0
0
2
0
1
0
0
0
0
2
2
0
0
0
0
0
1
1
3
2
0
0
0
0
0
0
0
2
0
1
0
0
2
1
0
0
0
0
2
0
0
0
0
1
0
2
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
3
0
2
0
2
0
0
0
0
0
3
1
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
3
0
0
1
0
0
1
1
0
0
1
1
0
2
2
0
0
0
2
0
0
0
1
0
0
3
1
0
2
2
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
2
2
2
0
0
0
0
1
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
2
0
0
0
0
0
0
0
1
2
0
1
0
0
2
1
2
0
1
0
0
0
3
0
0
0
0
0
0
2
0
0
3
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
7
3
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
1
2
0
0
2
0
0
0
0
2
3
0
0
0
0
1
4
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
4
2
1
0
2
0
3
0
0
0
0
0
0
0
1
0
0
2
0
3
0
0
0
1
0
0
0
2
0
0
0
0
0
5
3
2
0
0
0
0
2
0
4
0
0
0
0
0
0
2
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
1
2
2
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
2
0
6
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
1
0
0
2
1
1
0
4
1
1
0
0
0
0
0
0
1
0
0
2
0
0
1
1
0
0
0
3
0
0
2
2
0
0
1
0
0
2
0
1
3
1
0
0
0
2
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
2
2
0
0
2
0
0
0
0
0
1
0
0
1
2
0
1
0
0
0
2
0
0
0
0
1
0
0
0
2
0
2
0
0
1
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
2
2
0
0
1
1
0
0
1
0
1
0
2
0
0
0
2
1
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
3
1
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
1
2
0
0
0
2
0
2
0
0
3
0
0
1
0
0
0
1
4
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
1
2
0
3
0
0
0
1
7
0
0
8
1
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
4
2
2
0
0
0
0
2
0
0
2
0
2
0
0
2
0
4
2
1
0
0
1
0
1
1
1
0
2
0
0
0
0
2
0
0
0
0
0
4
0
0
0
0
0
2
1
0
0
1
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
2
0
0
1
1
0
0
0
0
0
2
1
0
1
1
0
0
0
2
0
0
2
1
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
8
3
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
1
0
1
2
2
0
2
0
1
0
1
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
1
0
0
1
0
2
0
2
0
0
1
0
0
0
0
0
0
0
4
3
1
0
0
2
0
0
0
0
0
0
0
4
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
1
0
0
1
0
1
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
9
0
0
1
0
0
3
0
0
1
0
3
0
0
1
2
0
0
0
0
0
0
1
2
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
2
0
1
3
1
0
0
1
0
2
1
1
0
0
2
0
0
2
0
0
0
0
0
2
0
0
2
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
3
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
2
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
2
0
0
0
3
2
0
0
0
1
0
0
2
2
0
0
2
0
2
0
0
0
0
0
2
0
0
1
0
1
0
1
0
0
2
0
2
0
0
0
0
1
1
0
0
0
0
1
0
0
4
6
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
2
2
0
2
1
0
0
0
0
2
0
0
0
0
0
0
1
1
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
1
0
1
0
0
0
2
3
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
2
0
0
0
1
0
2
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
2
0
0
0
3
0
0
0
1
0
0
0
0
1
0
0
0
0
2
1
1
0
2
3
1
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
1
0
0
0
0
0
1
0
0
2
1
0
2
2
0
0
0
0
2
0
0
1
1
0
0
2
2
0
0
2
0
0
0
0
1
1
0
0
0
1
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
2
0
1
0
2
0
0
0
1
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
2
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
4
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
2
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
3
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
1
0
2
0
0
0
1
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
2
0
2
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
1
1
0
1
0
0
0
1
0
6
0
0
3
0
0
0
2
0
0
0
3
2
0
0
0
1
0
0
2
0
2
0
0
2
0
1
0
0
1
2
0
0
2
0
2
2
0
0
0
1
0
3
0
1
0
2
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
1
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
2
1
0
2
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
5
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
2
1
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
3
2
2
0
2
1
0
1
0
0
1
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
1
2
0
1
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
2
1
1
0
0
1
1
0
0
2
2
1
2
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
1
0
2
1
0
3
0
1
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
2
0
1
0
0
0
1
0
0
0
4
1
0
0
0
0
2
0
0
2
0
0
1
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
2
1
2
1
0
1
0
0
0
2
0
0
0
3
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
1
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
4
0
1
0
0
0
1
1
0
0
0
2
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
1
1
2
2
1
0
2
0
0
1
0
2
1
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
1
9
0
1
0
0
0
0
1
0
1
0
1
1
2
0
0
0
4
0
0
0
1
0
4
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
1
0
1
2
2
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
2
0
0
0
1
1
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
2
2
4
0
1
0
0
0
0
0
0
4
0
0
3
0
0
0
1
0
0
2
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
4
0
0
0
5
0
0
1
0
0
0
1
0
1
0
0
1
0
0
2
0
0
0
2
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
1
0
0
1
0
0
1
1
0
1
2
0
2
0
0
0
0
1
3
1
2
1
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
4
0
0
1
2
0
1
0
2
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
2
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
2
0
0
1
2
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
2
0
0
2
2
0
0
0
0
0
0
2
3
0
0
3
0
2
0
0
0
0
0
1
0
0
2
0
0
0
1
1
2
4
2
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
6
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
2
1
1
0
0
0
3
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
3
1
1
2
1
0
0
12
0
0
0
1
0
0
0
1
1
1
0
0
2
0
2
0
0
2
0
1
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
3
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
3
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
2
0
0
0
2
1
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
1
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
2
0
1
0
1
0
2
1
0
0
0
0
2
0
0
0
2
0
2
0
0
0
1
0
0
0
1
0
0
1
0
0
0
2
0
1
1
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
2
2
0
3
0
0
2
1
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
2
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
2
1
0
3
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
1
0
0
2
0
1
0
0
0
0
3
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
2
0
0
0
1
1
4
0
0
1
0
0
0
1
3
1
0
0
1
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
4
0
0
2
0
0
3
0
0
2
3
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
2
2
0
0
2
1
0
1
0
0
2
1
0
1
0
1
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
4
0
0
0
1
0
0
0
0
0
2
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
1
0
0
0
2
2
1
0
1
0
1
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
2
0
1
0
4
0
0
2
0
0
1
1
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
1
1
0
2
0
0
0
3
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
1
0
0
0
0
0
5
0
0
0
2
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
2
7
3
0
0
2
0
0
0
0
2
0
1
2
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
2
0
6
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
12
0
0
2
0
2
3
0
1
0
1
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
2
0
0
0
0
0
1
0
0
0
1
0
1
1
2
0
0
0
1
0
0
0
3
0
2
1
0
0
2
1
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
1
2
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
3
0
3
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
3
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
3
0
0
0
0
1
0
0
2
0
2
3
0
0
0
0
0
0
0
0
2
0
0
0
0
3
2
0
0
0
1
0
0
0
2
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
1
2
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
7
0
0
0
2
1
1
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
3
2
0
0
0
0
0
2
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
2
1
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
2
0
0
0
0
1
0
1
1
2
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
2
0
2
0
1
0
1
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
2
0
0
0
1
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
1
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
1
0
2
0
3
0
2
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
3
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
2
0
0
1
0
0
0
2
0
2
1
1
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
3
0
1
0
0
1
0
0
0
1
0
0
1
1
0
0
5
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
2
0
1
0
0
1
1
0
0
1
0
0
0
3
0
0
0
0
0
1
1
2
0
0
1
0
2
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
3
0
2
0
3
0
0
0
1
2
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
2
1
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
2
0
3
1
2
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
3
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
3
0
0
0
1
0
1
0
0
0
0
0
0
2
3
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
1
0
1
0
1
2
0
0
0
3
0
0
0
0
1
0
1
0
0
2
1
0
2
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
2
0
2
0
0
0
0
0
0
0
1
1
0
1
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
1
2
2
0
0
0
0
0
0
2
1
0
0
0
0
0
1
1
1
2
0
2
0
3
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
2
0
3
0
0
0
0
1
3
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
4
0
1
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
6
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
2
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
3
0
3
1
0
2
0
0
0
0
0
0
0
2
0
1
0
0
1
2
0
0
2
0
1
0
0
0
0
1
0
2
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
2
3
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
1
0
3
0
0
0
1
0
0
0
0
0
2
2
0
0
1
0
0
3
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
6
0
0
0
2
0
4
0
2
0
0
2
0
0
0
0
1
0
0
1
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
2
6
1
0
1
0
0
0
0
2
0
0
0
0
0
1
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
1
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
2
2
1
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
1
2
1
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
1
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
4
1
0
1
2
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
1
0
2
0
2
1
0
0
1
0
0
0
0
0
0
2
3
1
2
2
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
1
0
2
0
5
0
0
0
0
1
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
3
0
0
0
1
0
2
0
1
2
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
2
0
1
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
3
1
0
1
3
0
0
0
1
1
0
2
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
5
0
0
1
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
2
0
4
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
3
0
1
3
0
0
0
0
0
2
3
1
0
0
2
2
0
3
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
2
0
0
3
0
0
0
1
0
0
0
0
0
0
2
1
2
0
0
0
0
2
0
0
10
0
0
0
0
0
2
0
0
0
1
2
0
0
3
0
1
0
1
1
0
1
0
0
0
3
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
1
0
0
4
0
0
2
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
1
0
0
2
0
1
0
0
2
0
0
4
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
2
2
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
1
0
0
0
3
0
0
1
2
1
0
0
0
0
0
0
3
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
3
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
3
0
2
1
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
1
0
0
0
4
1
1
0
0
0
2
21
2
0
0
2
1
0
0
0
0
2
0
0
1
1
0
0
0
0
1
0
0
2
0
1
0
0
1
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
2
0
2
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
1
0
1
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
2
2
2
0
0
0
0
0
0
1
6
0
0
1
0
0
0
2
0
2
0
0
0
2
2
0
0
0
0
1
0
3
0
7
1
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
2
1
0
0
4
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
4
1
1
0
2
0
0
0
0
0
2
2
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
1
0
0
3
1
0
2
3
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
2
1
0
2
1
1
1
0
0
0
0
1
3
1
0
2
0
1
0
2
0
0
0
0
0
1
1
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
3
0
0
1
0
0
0
0
2
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
4
0
0
0
0
1
0
2
0
4
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
6
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
4
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
1
0
1
0
0
0
4
1
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
1
1
0
0
2
2
2
0
0
0
0
0
0
1
1
0
3
2
0
1
0
2
0
1
2
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
4
1
0
0
0
2
0
0
0
0
1
1
0
1
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
1
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
2
0
1
1
1
2
0
1
0
1
0
2
0
0
0
0
0
1
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
1
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
2
0
4
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
2
2
1
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
2
2
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
3
0
0
1
0
0
0
0
0
0
0
2
1
1
0
0
0
0
3
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
3
0
0
1
0
3
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
1
0
1
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
1
0
0
0
0
1
1
0
0
0
2
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
4
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
3
0
0
0
1
0
0
0
1
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
5
1
0
0
0
2
0
0
1
1
1
0
0
0
1
0
0
0
0
1
0
4
0
0
0
0
2
1
1
0
4
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
3
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
1
0
1
0
2
3
0
2
2
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
4
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
1
2
0
1
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
1
0
0
0
0
0
1
4
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
1
1
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
1
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
5
2
0
2
1
0
2
0
2
0
0
0
1
1
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
2
0
2
0
1
0
2
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
2
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
1
1
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
2
2
0
1
2
0
1
0
5
0
0
0
0
0
1
0
0
1
0
0
1
0
1
1
2
0
3
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
1
1
0
0
0
0
1
0
0
1
1
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
2
2
0
0
0
0
0
1
2
0
1
0
0
2
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
2
0
1
0
0
1
1
2
0
0
2
0
0
1
0
0
1
0
0
1
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
2
0
0
0
1
2
0
2
0
0
0
1
0
3
2
0
0
0
0
3
0
0
0
0
0
2
0
0
0
4
0
0
2
0
0
0
0
0
0
0
0
2
5
0
1
1
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
1
2
0
0
1
2
0
2
2
1
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
1
1
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
1
0
0
0
6
0
1
4
0
0
0
0
0
0
1
1
0
0
0
0
2
1
0
0
2
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
1
1
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
6
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
2
0
0
0
0
0
0
2
0
1
0
1
0
2
0
2
0
0
0
3
2
0
0
0
2
2
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
1
0
0
0
0
0
0
3
0
0
0
2
0
0
2
0
0
0
1
0
0
0
1
0
3
2
0
1
2
2
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
2
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
1
0
3
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
3
0
1
2
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
3
2
3
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
6
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
3
1
0
2
1
1
1
0
0
0
0
2
0
0
0
0
2
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
3
0
2
0
0
0
2
0
0
1
0
1
0
0
2
0
2
0
1
0
0
0
2
0
1
0
0
0
0
0
1
1
1
1
0
3
0
1
2
0
0
2
0
0
2
1
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
2
0
1
0
2
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
1
2
2
0
0
0
0
0
1
1
1
2
0
0
1
1
0
0
0
1
0
0
0
0
0
3
2
0
0
0
0
0
0
2
1
0
0
0
0
2
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
3
1
0
0
0
1
0
2
2
0
1
0
0
0
0
0
1
0
2
1
0
0
0
1
0
0
1
0
0
4
1
0
1
0
2
0
0
0
0
0
3
2
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
3
0
0
1
0
0
0
0
0
1
0
1
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
2
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
3
0
0
0
1
0
2
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
2
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
3
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
1
8
0
0
2
0
0
0
0
0
0
2
2
2
4
0
0
1
0
3
0
2
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
1
3
1
0
0
0
0
0
0
0
1
2
0
0
1
0
0
2
0
0
0
1
4
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
6
0
1
0
0
1
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
2
0
2
2
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
1
0
0
1
0
1
0
1
0
0
0
2
2
2
0
0
0
3
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
1
1
0
0
0
0
2
0
2
4
1
0
0
0
1
0
0
0
2
0
0
0
2
0
0
3
2
0
1
0
0
0
0
0
2
0
0
0
6
0
0
2
0
1
0
0
0
0
1
0
5
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
3
1
0
0
0
0
0
0
0
2
0
2
1
0
1
0
0
0
0
0
0
2
2
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
1
2
2
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
1
2
0
1
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
2
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
3
0
2
0
0
0
2
0
1
0
0
2
0
0
1
1
0
0
0
3
1
1
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
1
0
1
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
2
0
0
1
1
2
0
0
0
1
2
1
0
0
3
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
2
0
3
2
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
3
0
0
2
0
0
0
0
0
0
2
6
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
3
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
4
0
2
0
2
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
2
0
1
0
1
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
2
0
0
0
0
3
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
1
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
2
0
0
1
1
0
0
2
0
0
0
1
3
2
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
1
1
1
2
2
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
2
0
0
2
0
0
0
0
4
0
0
1
0
0
0
0
0
0
1
0
1
0
4
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
2
0
0
2
0
0
0
0
0
0
1
1
2
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
2
2
0
2
2
0
2
0
0
0
0
0
2
0
3
0
0
0
0
1
1
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
1
1
0
0
0
2
3
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
5
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
1
1
0
0
1
0
2
2
0
0
0
1
1
0
0
2
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
2
4
0
2
0
1
1
3
0
0
0
0
1
1
1
1
2
0
1
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
3
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
2
2
0
1
0
2
2
0
2
0
1
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
14
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
2
0
1
0
2
0
0
4
0
0
1
0
2
2
0
3
0
2
0
0
0
1
0
0
0
0
2
0
0
4
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
1
0
1
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
2
0
0
0
1
0
0
0
0
0
1
2
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
5
1
0
3
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
2
1
0
0
2
0
2
0
1
0
0
1
0
4
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
5
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
5
0
0
0
2
2
0
0
0
2
0
1
0
2
1
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
1
0
0
0
2
0
0
0
0
2
1
0
2
1
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
2
0
3
0
0
0
0
0
2
0
1
0
0
0
0
0
2
1
2
0
0
0
0
1
0
0
1
0
0
1
0
0
0
2
2
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
2
0
3
0
0
0
0
2
2
2
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
1
1
0
2
0
0
0
0
0
0
1
1
0
0
0
0
1
0
2
2
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
3
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
3
0
2
1
2
0
2
0
2
0
0
0
2
0
4
0
2
0
1
0
0
3
1
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
3
0
2
0
4
0
2
0
2
0
1
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
2
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
2
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
2
0
4
2
0
0
0
0
0
0
1
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
1
0
0
2
0
0
0
0
0
0
2
1
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
4
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
2
0
0
1
0
0
0
0
2
1
0
0
0
0
1
0
1
0
0
2
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
2
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
1
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
1
0
1
0
0
2
0
3
2
0
1
1
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
2
1
0
1
0
1
0
0
0
10
1
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
4
2
0
0
0
0
0
2
2
2
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
1
1
3
2
8
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
5
0
3
0
2
0
0
0
2
0
0
0
0
0
0
0
1
2
2
1
0
2
2
0
2
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
2
1
0
2
0
0
1
0
1
0
2
0
0
1
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
3
2
0
0
0
0
1
0
0
0
0
3
1
0
0
1
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
4
0
1
2
0
0
0
0
4
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
4
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
3
0
0
1
0
2
0
0
2
0
1
0
2
0
1
0
0
1
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
2
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
2
0
0
2
0
2
1
2
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
3
0
2
0
2
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
2
0
0
0
1
0
2
0
0
2
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
1
3
0
0
0
0
0
2
2
4
0
0
1
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
3
0
1
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
1
2
0
1
0
0
0
0
2
1
0
0
0
0
0
0
6
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
2
0
2
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
2
0
0
2
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
2
0
0
2
3
0
1
0
0
0
1
2
0
0
0
2
0
0
2
0
0
0
0
0
1
0
3
0
0
2
2
1
2
2
0
0
0
0
0
2
0
0
1
0
0
0
0
4
0
3
0
2
2
0
2
1
2
0
0
1
0
0
2
1
3
0
0
0
2
0
2
0
1
1
0
0
0
1
0
0
2
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
2
1
0
0
1
1
0
0
0
0
0
2
0
0
0
1
0
0
2
3
0
1
0
0
0
2
1
1
1
0
2
0
1
0
3
0
1
0
0
0
0
1
0
1
0
0
1
2
0
0
3
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
1
0
0
0
3
0
0
2
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
2
2
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
2
2
0
2
1
1
1
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
15
2
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
1
0
0
2
0
1
0
0
0
1
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
3
0
0
2
0
0
0
0
4
0
0
2
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
2
0
0
0
3
0
0
0
0
0
0
7
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
1
0
0
3
0
2
0
0
0
0
1
0
1
0
0
2
0
0
1
0
0
0
0
2
0
0
0
3
0
0
0
1
0
0
0
1
0
0
3
2
0
0
2
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
5
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
1
0
0
2
0
2
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
1
3
0
0
0
0
3
2
0
7
0
1
0
0
1
2
0
1
0
0
0
0
2
2
1
0
0
0
0
1
2
1
0
2
0
0
3
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
1
0
2
0
0
2
1
0
0
0
0
2
2
1
0
0
1
1
2
2
0
1
1
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
1
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
2
3
0
0
0
0
3
0
1
0
0
0
2
2
1
0
1
1
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
1
0
1
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
1
0
2
2
1
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
1
0
1
0
2
2
0
0
0
1
2
1
1
4
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
2
0
1
1
1
0
0
0
0
2
0
0
1
1
2
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
4
2
0
0
1
0
0
2
0
0
0
2
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
2
2
0
0
0
2
0
0
1
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
3
0
1
0
0
0
0
1
0
2
2
0
0
0
2
0
5
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
2
0
1
2
4
0
2
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
1
0
1
1
0
0
2
1
1
0
3
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
6
0
3
0
2
0
0
2
0
1
0
0
0
2
0
1
2
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
2
0
2
0
1
0
0
2
0
0
0
1
0
0
3
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
1
0
2
0
1
1
2
0
0
0
1
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
3
2
2
0
0
0
0
0
0
0
1
1
0
0
2
0
2
0
0
4
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
1
2
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
1
2
0
1
0
0
0
0
0
2
1
3
2
0
0
0
0
0
1
0
2
0
2
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
3
0
1
2
1
0
0
0
0
1
1
0
0
2
0
1
1
0
0
0
1
2
1
0
1
1
0
1
0
0
3
2
1
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
3
1
0
4
0
0
0
0
2
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
1
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
2
3
2
0
0
0
2
0
0
0
1
3
0
0
0
2
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
2
2
0
2
1
0
0
0
0
0
1
0
1
1
0
0
2
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
1
0
2
0
0
1
1
0
0
0
0
0
0
0
3
0
1
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
3
1
0
0
0
1
0
0
0
0
2
0
0
1
0
2
3
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
5
0
1
0
1
0
0
0
0
2
0
0
1
0
0
0
0
1
0
2
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
12
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
2
0
0
0
1
0
0
0
0
2
0
0
1
0
1
0
5
0
0
0
1
0
2
0
1
2
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
1
0
2
1
1
0
0
0
0
0
0
2
1
0
1
2
2
0
2
0
5
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
2
1
0
0
0
2
0
1
1
2
0
0
0
0
2
1
0
0
0
0
5
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
2
0
0
3
0
4
0
0
0
0
2
0
0
1
2
2
0
0
2
0
0
0
0
0
0
2
0
0
2
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
6
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
2
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
1
0
1
1
0
0
0
1
1
2
0
0
2
0
0
1
0
3
1
1
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
1
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
2
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
1
0
2
0
0
1
1
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
1
2
0
0
1
0
6
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
1
0
0
0
0
2
1
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
2
0
0
1
0
1
0
1
0
0
1
1
0
0
0
0
2
0
0
0
0
1
0
2
0
0
1
2
0
0
0
0
0
2
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
9
0
0
0
0
2
1
0
1
0
0
2
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
1
2
0
0
1
0
2
0
0
0
0
0
0
2
2
0
0
0
1
1
1
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
1
2
1
0
1
0
0
0
0
0
2
3
1
2
0
0
3
0
0
1
2
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
1
1
1
0
1
0
0
2
0
1
2
1
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
11
0
0
0
0
0
0
1
7
0
0
0
1
1
0
1
2
0
0
0
0
0
0
3
0
0
0
0
1
0
2
0
0
0
1
4
1
0
0
0
0
0
0
0
2
0
2
0
0
1
0
2
0
0
0
2
2
0
1
2
0
0
1
0
0
0
1
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
3
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
2
1
0
0
0
0
0
1
1
0
1
0
0
1
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
2
0
0
0
0
0
1
0
0
1
1
1
2
0
0
0
0
0
2
0
0
0
0
1
2
0
1
0
2
0
0
1
1
0
2
0
0
0
0
0
0
0
0
1
0
2
0
3
0
2
2
0
1
0
1
1
0
2
0
2
0
0
0
0
2
1
1
0
0
1
0
0
2
1
3
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
2
0
0
0
4
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
2
0
3
0
0
0
2
1
3
2
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
2
1
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
6
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
1
0
0
2
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
5
0
1
0
0
0
0
1
0
0
0
0
0
1
2
3
0
2
3
1
0
0
0
2
0
0
0
1
0
2
0
1
1
0
0
0
2
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
2
2
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
3
1
2
0
0
3
0
0
0
0
0
1
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
1
4
2
1
1
0
1
2
0
0
3
1
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
1
0
0
1
0
0
0
1
0
1
2
0
2
2
1
0
0
1
2
0
0
0
0
1
0
0
2
1
1
0
0
1
0
0
2
0
0
1
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
2
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
3
2
0
2
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
2
0
1
3
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
4
0
0
5
0
0
2
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
1
3
0
0
2
1
2
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
1
1
0
2
0
1
0
0
0
0
0
1
2
0
0
0
0
2
0
2
2
0
1
0
0
0
0
0
3
0
2
0
0
0
0
0
2
0
0
2
2
1
0
0
0
0
2
0
0
2
0
0
0
0
0
6
0
0
7
0
0
0
0
1
0
0
0
0
2
2
0
2
0
2
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
1
0
2
0
1
1
0
1
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
5
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
1
1
0
0
3
0
0
1
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
4
0
0
2
0
1
0
0
1
0
2
0
0
0
0
1
3
1
0
0
0
0
1
0
0
1
0
0
2
0
0
1
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
2
2
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
2
0
2
0
0
1
0
1
0
1
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
1
2
0
0
0
0
1
0
2
0
1
0
0
0
2
0
1
2
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
1
0
1
2
0
1
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
1
0
0
0
3
0
0
3
0
0
0
3
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
2
1
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
2
2
0
0
0
0
0
2
0
2
1
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
3
2
0
1
0
1
0
2
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
2
1
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
1
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
6
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
1
0
0
0
0
2
2
2
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
2
2
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
2
1
3
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
5
0
0
0
0
2
0
0
0
0
1
2
0
0
1
0
0
1
0
0
1
2
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
1
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
1
1
0
0
0
2
1
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
3
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
1
2
0
0
0
3
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
1
0
2
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
1
0
0
1
0
0
1
2
0
0
0
2
0
1
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
3
2
1
0
0
1
0
1
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
2
0
1
1
0
0
0
0
1
0
0
1
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
3
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
2
0
1
0
0
2
1
1
0
0
2
1
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
1
1
1
0
1
0
0
0
1
0
0
1
0
0
0
1
0
2
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
1
0
0
0
2
2
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
4
1
0
0
0
0
0
0
0
1
0
2
0
1
0
0
2
0
2
0
1
0
0
0
0
0
1
0
2
0
2
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
1
1
2
0
0
2
0
0
0
1
0
0
0
0
0
2
1
0
2
0
0
0
2
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
2
3
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
5
0
0
0
0
0
1
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
2
0
0
0
2
0
1
1
0
2
0
0
0
0
0
0
0
3
0
0
0
2
2
0
0
3
0
0
0
2
0
0
0
0
0
2
2
0
0
1
0
2
2
0
0
0
0
0
0
4
0
0
0
0
0
0
2
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
2
1
0
0
0
2
2
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
4
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
1
2
0
1
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
3
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
1
0
1
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
3
2
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
3
2
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
2
0
1
0
1
0
0
2
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
2
0
0
2
5
0
0
1
0
0
3
0
3
0
0
0
0
1
0
0
3
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
4
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
3
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
1
2
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
2
0
2
1
2
0
0
1
0
2
0
0
0
2
0
0
0
0
0
2
0
2
0
1
1
0
1
1
0
0
0
1
1
0
0
2
0
8
0
0
0
0
0
2
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
2
0
2
0
2
0
0
0
2
0
1
0
0
0
0
1
3
0
0
0
0
0
1
2
0
0
0
1
2
2
0
0
0
0
2
2
0
0
0
0
1
0
0
0
1
1
0
1
0
0
1
0
0
2
0
0
2
0
0
0
0
2
0
0
0
2
1
0
0
0
0
1
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
1
0
0
0
2
0
0
0
0
2
0
1
2
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
1
1
0
1
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
2
0
2
2
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
2
1
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
2
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
2
0
0
0
2
2
0
2
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
7
2
0
0
0
0
1
0
0
0
1
1
0
2
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
2
1
2
4
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
2
0
1
1
1
1
2
2
1
0
0
1
0
0
0
1
0
0
3
1
0
0
0
0
0
0
0
0
0
0
1
3
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
4
0
0
2
0
0
0
0
4
0
1
0
0
2
0
1
0
0
0
0
0
0
1
0
1
0
2
0
0
0
2
0
1
0
1
1
0
1
1
2
1
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
2
0
1
0
0
2
0
0
0
0
1
1
0
0
0
0
0
2
0
0
2
0
2
0
2
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
18
0
0
2
0
0
0
0
2
2
1
0
2
0
0
0
0
3
3
2
0
1
0
0
0
3
0
1
0
0
2
4
2
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
1
0
0
4
0
0
0
0
0
1
1
0
2
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
4
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
2
0
0
0
2
0
0
0
1
0
0
0
0
2
2
0
0
0
1
1
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
1
1
2
0
0
0
2
1
0
1
0
2
0
0
2
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
1
0
2
2
2
2
0
1
0
0
1
0
0
0
1
0
2
0
0
0
0
0
2
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
5
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
2
0
0
0
0
17
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
2
0
2
0
0
1
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
4
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
1
1
0
0
1
0
0
1
0
0
2
2
2
2
2
1
0
2
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
2
0
0
0
1
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
5
0
0
0
2
0
0
0
0
0
0
1
3
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
5
0
0
0
0
2
3
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
3
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
2
2
1
4
0
1
0
2
2
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
3
1
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
2
2
1
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
4
2
2
0
0
0
0
0
2
0
0
1
3
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
2
0
4
2
0
0
0
2
1
3
2
0
3
0
0
0
0
0
4
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
8
0
0
0
3
0
2
1
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
2
1
1
4
1
0
0
1
1
3
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
1
0
2
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
3
0
0
2
1
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
2
3
0
0
0
1
0
0
2
0
0
0
0
1
1
1
0
1
0
3
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
4
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
5
0
3
0
0
2
0
2
1
0
0
1
0
0
0
2
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
2
0
1
1
0
0
0
0
1
1
0
0
0
0
1
4
2
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
1
1
1
0
0
1
0
0
3
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
3
0
2
1
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
3
0
1
0
1
0
0
1
0
0
0
2
1
0
0
2
0
1
1
1
0
0
0
0
1
1
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
2
1
3
1
0
1
0
0
0
0
0
1
1
1
0
0
2
1
0
0
1
0
1
0
3
0
1
0
1
0
0
4
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
2
0
0
0
0
2
2
0
5
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
1
0
3
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
1
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
1
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
2
1
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
2
0
0
0
0
0
2
0
1
0
0
0
2
2
0
3
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
1
1
2
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
2
1
0
0
0
0
1
0
1
0
1
2
1
2
1
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
3
0
0
0
0
1
0
0
1
0
1
1
0
0
0
1
3
0
1
0
3
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
1
0
0
0
2
0
6
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
1
0
0
1
2
2
4
2
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
4
0
0
0
2
0
1
0
0
0
0
2
1
1
1
0
3
0
0
0
0
0
0
2
0
0
0
2
0
1
2
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
2
1
0
2
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
1
0
0
0
0
2
0
0
1
0
2
0
0
0
1
1
0
1
2
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
4
2
1
0
0
1
2
2
0
0
2
2
0
0
0
1
0
2
1
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
3
0
0
0
1
3
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
1
0
2
0
2
1
0
0
0
0
0
2
3
1
0
1
0
0
0
0
0
0
0
4
2
0
0
0
1
0
0
1
4
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
2
0
1
0
0
2
2
0
1
0
0
0
0
0
0
0
0
2
2
0
0
2
3
1
3
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
2
0
0
1
3
0
2
0
0
2
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
3
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
2
0
0
1
2
1
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
1
0
2
1
0
1
0
0
2
0
2
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
4
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
1
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
3
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
1
0
0
0
2
2
0
1
1
0
0
0
2
0
0
0
0
2
0
3
0
2
0
1
0
0
0
0
0
0
2
0
0
0
1
2
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
5
2
2
0
0
0
0
0
0
0
2
0
0
0
0
1
3
1
1
0
0
0
0
0
2
0
0
0
0
0
2
2
0
1
0
0
2
0
0
1
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
3
0
2
0
0
0
0
0
0
0
0
1
0
2
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
2
0
0
0
0
4
0
0
0
0
1
2
0
1
0
0
4
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
1
0
3
0
1
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
2
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
2
1
3
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
2
0
1
1
0
0
3
1
0
0
2
1
1
0
2
0
0
0
0
2
0
0
0
2
0
0
2
2
0
1
0
0
2
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
4
0
1
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
2
2
0
0
0
1
2
0
0
0
0
0
0
1
2
0
0
0
2
2
2
0
1
0
0
1
1
0
0
0
4
4
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
2
0
0
0
1
1
0
0
0
0
0
1
0
1
3
0
0
0
2
0
1
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
4
0
1
1
0
0
0
0
0
0
2
2
0
0
0
1
0
0
1
0
0
2
0
1
0
3
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
2
0
0
3
1
2
0
1
0
1
2
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
1
4
0
0
0
2
0
1
3
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
2
3
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
3
0
2
0
0
0
0
0
0
0
0
19
0
3
0
0
0
1
0
1
2
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
1
0
2
0
0
0
1
0
0
0
2
1
2
2
0
0
0
0
0
0
0
0
0
0
0
3
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
1
0
2
0
2
0
3
0
0
0
0
0
0
0
0
0
2
0
3
0
0
4
0
0
1
0
2
1
0
0
3
1
0
0
0
0
0
0
4
1
0
3
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
5
0
0
1
0
0
0
1
0
0
0
0
0
3
0
0
0
2
1
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
7
1
0
0
0
5
3
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
6
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
1
0
0
0
0
0
0
1
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
1
1
2
1
0
0
0
0
1
4
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
6
0
0
0
0
2
0
5
0
0
0
3
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
2
0
0
3
2
0
1
0
0
2
0
0
0
0
3
1
2
2
2
0
0
2
0
0
0
1
0
1
0
0
2
1
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
1
2
0
0
0
2
0
0
2
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
3
0
0
0
1
0
0
0
0
2
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
1
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
1
1
0
0
0
0
1
0
0
2
1
0
2
0
0
0
0
0
1
2
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
1
0
4
1
4
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
1
0
0
2
0
0
0
1
3
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
1
4
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
7
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
2
2
0
0
0
0
0
0
0
0
2
2
2
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
2
1
0
0
0
1
2
1
0
0
0
0
1
2
0
1
1
0
2
2
1
0
0
0
0
4
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
2
0
2
1
0
1
0
0
1
0
0
1
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
2
0
0
0
0
0
0
1
1
5
1
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
4
0
0
1
0
0
1
0
1
1
0
0
0
2
0
1
0
2
0
0
2
0
0
1
2
0
0
0
0
0
0
1
0
0
0
1
1
0
2
0
1
0
0
0
0
1
1
1
0
1
1
0
0
2
2
1
0
0
0
0
0
1
0
0
0
0
0
2
1
0
1
0
0
0
0
1
2
3
2
0
0
0
0
0
0
2
0
2
1
2
1
2
0
1
0
0
2
0
0
1
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
1
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
5
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
3
1
2
0
0
1
0
2
1
2
0
0
6
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
2
0
2
0
2
0
0
0
2
2
0
0
0
0
0
0
3
0
1
2
0
2
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
2
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
4
0
0
0
2
1
0
0
0
0
2
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
1
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
1
0
0
0
0
1
1
0
1
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
2
3
1
2
0
0
0
1
0
0
0
0
0
1
2
0
0
0
2
0
1
2
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
1
0
0
0
0
2
0
2
3
0
0
1
0
0
0
0
0
0
1
5
2
0
0
2
0
0
0
0
0
0
2
2
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
2
1
0
1
0
0
1
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
2
0
1
1
0
0
1
1
2
2
0
3
1
0
0
0
0
0
3
0
0
0
0
2
0
0
0
1
0
9
0
0
0
2
0
0
0
0
0
0
1
0
2
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
1
1
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
3
2
0
0
0
3
1
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
3
2
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
2
0
0
0
0
0
3
1
0
0
2
0
0
0
2
1
0
0
0
1
1
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
2
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
1
1
1
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
1
0
0
0
0
3
0
0
0
0
0
0
1
2
2
0
0
1
0
0
1
0
0
1
2
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
2
1
2
0
0
0
0
1
0
0
0
0
2
0
2
0
0
1
0
1
0
1
0
2
0
1
0
0
0
0
0
0
0
0
3
0
0
1
4
0
0
0
0
0
0
1
0
1
0
0
0
2
0
1
0
2
1
1
0
1
2
0
0
0
0
1
0
0
1
2
2
1
0
0
0
0
2
0
0
0
2
0
1
0
2
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
3
2
0
1
0
0
0
2
2
0
2
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
2
0
2
2
0
0
0
0
0
3
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
2
4
0
2
2
0
2
0
1
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
2
2
0
0
0
1
2
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
2
1
0
0
0
0
1
0
1
0
3
0
0
0
0
1
0
0
0
0
2
0
4
0
2
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
2
0
2
1
0
0
1
0
1
1
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
1
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
3
0
1
0
0
1
1
0
1
1
0
0
2
0
0
2
2
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
1
0
1
0
1
2
2
2
0
0
0
0
0
0
1
0
2
0
0
2
0
0
1
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
2
2
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
2
1
0
1
0
0
0
2
0
0
2
0
0
3
3
0
0
0
0
2
0
0
1
0
2
3
0
0
0
2
0
1
1
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
2
1
0
0
3
0
0
0
1
1
0
0
0
2
0
0
0
2
0
0
1
0
3
0
0
0
0
1
1
2
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
1
0
3
0
0
0
0
0
0
2
0
0
1
0
1
1
0
1
2
2
0
0
1
0
1
0
0
0
1
1
1
0
0
2
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
2
1
0
2
0
0
2
3
0
2
0
0
3
1
0
0
2
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
2
0
1
0
0
0
2
0
3
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
1
0
0
0
0
1
0
0
0
0
2
1
0
1
0
0
2
1
1
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
3
0
0
0
2
0
0
0
0
1
0
1
1
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
2
0
1
2
0
1
2
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
1
2
2
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
4
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
2
0
1
2
1
0
0
0
0
1
0
0
0
1
4
0
0
2
0
3
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
1
0
0
2
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
3
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
2
0
1
0
1
0
6
0
0
0
0
0
2
1
0
2
1
0
1
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
1
1
4
0
0
2
0
2
2
0
1
0
0
0
1
1
0
0
0
0
0
10
0
2
1
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
1
0
0
0
7
0
0
1
0
0
0
0
3
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
2
0
1
2
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
2
0
2
0
0
0
4
0
2
0
0
4
0
1
0
0
1
1
0
0
0
0
2
0
0
1
0
0
1
0
0
1
2
1
2
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
3
0
2
0
0
2
0
0
0
0
1
0
0
0
1
4
0
2
0
0
0
0
1
0
0
0
0
2
0
0
2
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
7
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
5
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
1
0
0
1
3
0
0
0
2
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
1
0
2
0
0
0
2
0
0
3
0
2
1
0
1
0
2
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
1
0
2
1
0
0
0
2
0
0
0
1
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
1
1
0
2
0
2
0
0
0
0
3
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
1
0
2
0
0
2
0
1
0
0
0
0
2
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
4
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
3
2
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
8
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
3
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
2
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
3
0
0
3
0
0
0
1
1
0
0
2
1
2
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
1
0
0
1
0
0
2
0
0
1
0
0
6
0
0
0
0
0
0
0
1
0
0
0
0
1
0
5
0
0
0
0
0
1
0
0
2
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
1
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
4
0
0
2
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
5
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
2
2
2
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
1
1
0
1
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
2
0
0
4
1
2
2
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
2
1
0
2
0
0
1
1
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
3
0
0
0
0
0
2
0
0
2
2
1
2
0
0
0
1
0
2
0
0
0
0
0
1
0
0
2
0
3
5
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
1
1
0
1
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
1
0
1
0
1
1
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
2
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
5
0
0
0
8
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
9
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
4
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
2
0
2
0
1
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
2
0
2
0
0
0
0
0
8
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
1
2
0
0
0
2
0
0
2
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
5
0
2
2
0
0
1
0
1
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
2
0
1
2
0
0
0
2
0
0
2
0
0
0
4
2
0
0
0
0
1
2
0
7
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
1
1
2
1
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
1
1
1
5
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
3
0
0
2
0
0
0
2
0
1
1
2
2
4
1
0
2
0
6
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
4
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
11
0
0
0
2
0
0
0
2
1
3
0
0
1
0
0
0
0
0
0
1
0
0
2
2
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
7
1
2
0
2
1
6
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
1
2
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
2
0
0
0
1
0
0
0
0
0
1
1
0
5
0
0
0
1
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
2
1
0
1
0
2
0
0
0
1
2
0
0
0
0
2
0
2
0
2
0
2
1
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
1
1
3
2
1
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
2
0
2
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
2
1
0
0
0
0
0
0
3
1
1
0
0
0
0
0
1
0
0
0
2
2
2
0
1
0
1
0
1
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
2
1
2
0
2
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
4
2
0
2
0
0
1
0
0
1
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
2
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
2
0
0
0
1
0
2
0
0
0
0
2
0
0
2
0
0
0
2
0
0
1
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
2
2
0
0
0
0
1
1
0
0
2
2
0
0
2
0
0
0
1
0
0
0
2
0
0
2
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
2
1
2
1
0
2
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
4
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
1
0
0
0
2
2
0
2
1
0
0
0
1
0
2
0
0
0
0
0
1
3
0
2
1
0
0
1
0
0
0
0
0
1
0
0
0
0
2
5
3
1
0
0
0
0
0
1
1
0
1
1
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
1
1
0
1
2
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
1
0
0
2
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
2
1
0
1
0
0
1
0
0
2
0
1
1
0
2
2
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
2
0
5
0
0
3
2
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
1
0
3
2
0
1
0
0
0
0
0
0
0
2
0
0
2
0
4
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
3
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
1
0
0
0
1
2
2
2
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
2
1
2
0
2
0
0
1
1
0
1
0
0
0
0
0
0
4
0
3
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
2
0
0
2
0
2
2
0
0
1
0
0
0
0
0
1
2
2
2
0
0
0
2
3
0
0
0
0
2
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
2
0
1
0
0
0
2
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
1
0
1
3
0
0
0
0
3
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
2
0
2
0
0
0
0
0
1
0
2
0
1
0
1
0
0
0
0
2
0
1
0
0
1
1
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
3
0
1
0
0
0
0
0
0
3
0
0
0
0
4
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
5
0
1
0
2
0
1
2
0
0
0
0
2
0
1
2
0
0
0
0
2
2
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
3
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
1
0
1
0
0
0
3
0
0
0
0
0
2
0
1
0
0
0
2
0
2
0
0
0
0
2
0
0
1
0
1
0
0
2
0
2
0
0
3
0
0
0
0
2
0
1
1
0
0
0
0
2
4
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
1
0
1
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
2
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
3
0
1
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
1
0
3
0
1
0
0
0
1
2
0
0
0
4
0
0
0
1
0
0
2
0
0
2
0
4
0
1
0
0
3
0
0
0
0
2
0
3
0
0
0
2
3
0
2
0
0
0
4
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
2
1
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
2
1
2
0
2
2
0
0
1
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
2
1
0
0
0
1
0
2
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
5
0
0
2
30
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
1
1
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
1
0
0
0
0
2
0
0
1
0
1
0
0
1
0
0
0
0
2
2
0
0
0
0
0
3
2
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
4
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
2
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
4
1
0
0
0
0
2
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
2
0
0
1
2
0
0
2
0
0
1
2
0
0
0
0
0
1
0
2
3
0
0
0
0
0
2
0
0
3
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
2
3
0
2
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
4
0
0
0
0
1
2
0
2
0
0
0
1
0
1
2
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
1
1
0
0
1
3
0
3
2
0
0
0
0
1
0
0
0
3
0
0
0
0
2
4
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
1
0
1
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
3
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
1
1
2
0
0
0
0
2
0
0
0
0
12
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
2
0
0
2
0
3
2
0
0
0
0
2
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
1
0
0
3
0
0
1
2
0
1
0
1
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
2
0
1
0
2
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
1
2
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
1
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
3
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
1
0
1
2
0
1
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
1
4
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
2
1
0
2
0
1
0
2
1
0
2
1
0
1
2
0
0
0
2
0
1
1
1
0
0
0
0
0
0
3
1
0
0
0
2
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
3
0
0
4
0
4
0
0
0
2
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
1
1
0
0
0
0
0
1
0
2
0
0
0
0
0
1
1
0
2
2
0
0
0
2
0
0
0
1
1
0
0
1
1
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
3
0
1
2
0
0
0
0
0
0
1
2
0
0
0
2
1
0
0
0
0
2
0
0
2
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
2
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
1
0
0
0
0
0
2
1
0
0
0
0
1
0
0
2
1
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
6
0
0
0
0
0
0
1
0
1
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
3
1
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
5
0
1
0
2
0
0
0
2
0
4
0
0
2
2
0
0
0
1
0
0
1
0
0
0
1
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
1
0
0
2
0
0
0
2
0
0
0
0
1
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
1
0
0
0
2
1
0
0
0
0
1
0
0
0
0
5
0
2
0
0
2
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
2
0
1
0
2
0
0
0
2
1
0
0
3
0
3
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
3
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
1
0
0
0
0
1
0
0
1
0
0
3
0
1
0
3
0
1
2
2
2
0
0
0
0
0
2
0
0
0
0
0
2
0
1
2
0
2
0
0
0
2
0
0
1
0
1
0
0
0
0
0
1
0
0
3
1
0
1
0
0
0
0
2
0
0
2
2
0
0
0
0
1
0
0
3
0
0
2
0
0
0
3
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
1
0
0
0
0
2
2
1
1
0
3
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
2
1
0
2
0
0
1
5
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
2
0
2
0
0
0
1
0
2
2
0
2
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
7
5
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
1
3
4
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
1
0
0
0
1
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
2
2
4
0
0
3
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
2
0
1
0
2
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
2
2
1
0
0
0
0
1
0
0
4
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
3
0
0
1
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
1
0
0
1
2
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
2
2
0
0
2
0
0
0
2
2
2
0
0
1
0
0
0
1
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
2
0
0
1
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
3
0
0
2
0
0
0
0
0
2
2
0
0
2
0
2
0
1
2
0
0
0
0
0
1
1
0
0
0
2
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
1
0
0
2
2
2
0
1
0
1
0
0
0
0
0
0
0
0
1
2
0
2
1
0
0
0
0
2
0
0
2
0
2
0
0
1
0
1
0
0
0
2
0
0
0
0
1
0
2
0
2
2
0
5
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
1
0
2
3
2
0
0
3
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
2
0
0
1
2
2
1
0
0
0
0
1
1
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
3
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
2
2
0
2
0
0
0
6
1
1
0
0
0
0
2
1
0
0
0
1
0
0
0
0
1
1
0
2
0
0
2
0
0
0
0
2
1
2
2
2
2
2
2
2
0
0
0
0
0
0
0
0
4
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
2
1
0
1
2
0
0
0
0
0
0
2
0
2
2
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
1
0
0
0
2
1
0
0
0
0
0
0
0
0
2
2
2
2
1
0
1
0
2
5
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
1
1
0
1
0
0
0
1
2
1
10
0
2
0
0
0
0
1
0
0
1
0
0
0
0
2
0
1
0
0
0
1
2
1
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
1
0
0
2
0
2
2
0
0
0
0
0
0
0
0
1
2
1
1
1
2
0
0
0
0
2
0
0
1
2
0
0
0
0
0
2
1
2
0
0
1
0
1
1
1
0
2
1
2
0
0
0
2
1
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
1
0
0
0
0
2
1
0
0
1
0
0
0
0
0
1
3
1
0
1
0
0
0
2
2
0
1
2
0
0
2
0
0
0
1
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
2
1
0
0
1
0
0
0
0
0
3
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
3
0
0
2
0
0
2
0
0
1
2
1
1
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
2
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
1
2
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
5
3
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
7
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
1
3
0
0
1
0
0
0
0
3
0
0
0
1
2
0
0
0
0
2
0
1
0
1
0
0
1
3
0
1
0
0
2
0
0
0
0
1
2
0
0
0
0
2
0
1
0
0
0
4
0
0
0
1
0
0
3
0
1
0
0
0
1
0
1
3
0
0
0
3
0
0
0
0
2
0
1
2
0
0
0
0
1
0
0
1
2
2
0
1
0
0
3
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
3
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
2
0
2
0
0
2
0
0
2
0
2
0
0
0
0
0
2
0
0
0
8
2
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
3
0
0
0
1
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
2
0
0
1
0
1
0
2
2
1
0
0
0
0
1
3
2
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
1
2
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
6
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
2
1
0
0
0
2
0
2
0
0
0
0
3
0
3
0
0
3
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
4
2
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
2
0
0
1
0
0
0
0
2
3
1
2
3
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
2
2
0
2
0
0
0
2
0
0
0
1
0
0
0
5
0
0
0
0
2
0
0
0
0
1
0
1
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
1
0
0
0
0
3
0
0
0
0
1
2
1
0
2
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
2
1
2
1
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
3
2
0
1
1
2
0
0
1
4
0
2
2
0
3
0
2
0
2
1
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
1
0
0
1
2
2
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
2
1
1
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
2
0
0
0
1
2
0
1
2
0
0
0
1
0
0
0
1
0
0
1
0
2
1
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
2
0
1
1
0
2
0
0
0
2
0
0
0
0
0
0
1
0
8
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
2
1
1
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
1
0
2
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
2
0
1
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
2
1
1
0
0
0
0
0
0
4
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
1
0
2
0
0
1
3
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
1
0
0
1
0
0
2
0
0
0
1
5
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
6
0
1
0
0
1
2
0
2
0
1
4
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
2
1
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
2
1
1
0
2
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
2
0
0
0
0
3
2
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
3
0
0
0
1
0
0
2
0
0
2
0
0
0
2
0
0
0
1
2
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
2
2
0
3
0
0
0
2
0
1
0
0
1
2
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
2
0
0
0
3
2
2
0
0
2
0
0
0
0
0
0
1
0
2
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
4
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
1
1
1
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
2
0
3
0
1
0
0
1
0
0
0
0
0
0
1
0
2
0
1
0
0
2
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
1
0
0
2
2
0
0
0
0
0
2
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
3
1
0
2
3
0
1
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
3
0
0
0
1
0
0
2
0
2
1
0
0
0
0
2
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
6
0
0
0
7
0
0
2
0
2
2
0
0
0
0
0
1
0
1
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
1
1
0
1
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
4
2
0
0
0
0
2
0
0
0
0
3
1
0
0
2
2
0
2
0
2
0
2
0
0
0
0
1
0
0
1
6
0
1
0
1
0
0
1
0
1
0
0
0
4
0
0
0
0
0
2
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
3
0
3
0
0
1
3
1
3
0
2
0
0
5
0
2
0
0
1
0
0
0
0
1
0
1
0
1
0
0
1
1
0
0
2
0
0
1
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
2
0
0
0
2
0
1
0
1
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
3
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
1
0
2
2
0
0
0
1
0
0
0
0
0
2
0
1
0
1
1
0
0
0
0
1
0
0
0
0
2
0
2
6
0
0
0
0
0
0
2
0
2
0
0
0
0
4
0
0
0
0
2
1
2
1
0
0
2
0
0
2
0
2
0
0
0
2
0
0
0
1
0
0
0
1
0
5
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
6
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
2
1
0
0
0
2
1
2
0
2
0
0
1
2
0
0
2
0
1
0
0
1
0
2
1
1
0
0
0
0
0
0
0
0
0
1
0
2
1
0
2
2
0
11
1
0
2
0
0
0
0
0
5
0
0
2
2
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
1
1
0
2
0
0
2
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
6
0
0
1
0
1
0
0
0
0
2
0
0
1
0
0
0
1
1
1
2
1
0
0
1
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
1
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
2
0
0
1
2
0
0
5
0
0
1
0
0
0
0
0
2
1
0
0
0
0
2
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
2
0
0
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
1
1
0
0
0
3
2
0
0
0
0
0
1
0
1
0
0
3
0
3
0
1
0
2
0
0
3
0
0
2
1
1
0
0
2
0
0
2
2
1
0
0
0
0
2
0
2
0
0
3
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
3
0
2
0
0
0
0
0
0
0
0
0
8
1
2
1
2
0
0
0
1
2
1
0
0
4
1
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
5
1
0
2
0
0
0
0
0
0
0
1
1
0
0
2
1
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
2
1
0
0
0
0
6
0
0
0
0
2
0
2
2
0
1
1
2
0
0
0
2
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
2
0
1
2
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
5
2
1
2
0
0
0
2
0
0
0
0
2
0
0
1
0
1
0
0
0
3
0
0
0
0
0
0
0
2
0
0
2
0
3
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
2
3
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
1
2
2
0
1
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
1
0
0
2
0
0
0
4
2
0
0
0
0
2
2
0
0
2
1
1
1
0
0
0
0
0
1
0
1
0
0
1
2
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
2
0
0
2
0
0
3
0
0
1
1
4
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
2
1
0
1
0
0
0
0
2
0
2
0
1
1
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
1
0
0
0
0
3
1
4
0
0
1
0
1
0
3
2
0
2
0
0
1
0
0
0
2
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
7
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
1
3
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
2
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
2
1
0
1
0
0
0
0
0
0
0
4
0
3
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
2
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
4
0
0
0
1
0
0
1
1
0
2
0
0
2
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
1
0
0
0
2
0
0
0
0
0
7
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
2
1
0
0
0
2
0
3
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
1
1
1
1
0
0
2
1
0
0
0
2
0
0
1
1
2
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
1
0
0
1
0
0
0
0
1
0
2
0
0
0
2
1
0
2
0
0
1
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
2
3
0
3
0
0
0
0
0
0
0
8
1
0
0
0
5
0
0
1
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
2
0
1
1
3
4
0
0
4
1
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
2
0
0
2
2
1
0
0
1
0
1
0
0
0
0
0
2
1
2
0
0
0
2
0
2
0
0
1
0
0
0
2
2
0
0
1
0
0
0
0
0
1
4
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
3
0
0
0
1
0
1
2
0
2
0
2
0
2
0
0
0
2
2
0
0
0
0
0
4
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
5
9
2
1
0
0
0
0
0
1
0
0
2
0
2
0
0
1
0
0
0
2
0
0
0
0
3
0
0
0
0
0
1
5
0
2
0
2
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
1
2
0
0
0
0
0
2
0
1
0
0
0
1
0
1
1
2
1
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
1
1
0
0
2
0
2
0
0
0
0
2
2
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
1
0
0
0
0
1
0
0
2
0
0
2
1
0
0
0
0
3
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
6
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
5
0
1
1
3
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
1
0
2
0
0
0
6
4
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
2
1
4
0
0
0
2
0
0
1
0
0
0
1
3
1
0
0
1
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
1
2
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
1
0
0
0
2
1
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
1
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
6
0
1
0
0
0
2
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
1
1
0
0
1
0
1
0
2
0
0
0
1
2
1
0
0
0
0
0
1
1
0
0
0
0
0
2
2
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
3
0
2
0
0
0
1
0
1
0
2
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
3
0
0
2
0
0
0
2
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
2
0
0
0
1
2
2
2
2
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
1
3
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
1
2
0
2
2
0
1
0
0
0
2
2
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
1
2
0
2
0
0
0
2
0
2
0
0
2
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
2
3
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
3
0
0
0
3
0
0
0
0
1
3
0
1
1
0
0
3
0
0
0
2
1
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
3
2
0
2
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
2
0
2
0
1
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
2
0
0
1
0
0
1
0
0
1
2
0
0
0
0
0
2
1
0
4
0
0
2
0
2
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
3
0
0
0
0
0
2
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
3
0
0
0
0
3
1
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
1
0
0
3
1
0
0
0
0
0
0
0
2
0
0
1
3
0
0
0
0
2
0
0
0
0
1
2
4
0
2
2
0
2
3
0
2
0
0
0
0
1
0
0
0
0
3
0
0
3
0
2
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
1
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
2
0
1
1
0
2
0
0
0
0
1
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
2
0
0
2
1
1
0
2
0
0
0
0
0
0
2
0
0
0
0
1
2
2
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
8
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
2
0
3
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
2
0
0
0
0
0
5
0
1
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
2
2
0
0
1
0
1
0
0
0
0
2
0
0
1
0
1
0
1
0
0
0
0
0
0
0
2
1
1
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
4
5
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
3
0
0
0
0
0
0
2
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
1
1
0
1
0
4
1
1
0
2
0
0
0
0
2
0
0
0
1
0
4
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
2
1
1
0
0
1
0
0
0
0
0
0
0
0
2
2
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
4
0
1
0
0
0
0
1
0
0
0
0
0
1
0
2
0
2
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
1
0
0
3
0
0
1
1
1
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
3
0
0
0
0
1
0
0
1
0
0
0
0
0
0
3
0
0
2
0
2
0
1
3
3
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
3
1
1
0
0
2
0
2
0
0
0
1
1
1
0
2
0
0
2
0
0
0
0
0
1
1
0
1
1
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
1
2
0
0
1
0
0
0
1
1
0
0
0
0
2
0
2
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
2
2
0
1
0
0
0
0
3
0
0
0
0
2
4
0
0
0
1
0
0
1
0
1
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
1
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
5
0
1
0
0
4
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
2
0
1
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
2
1
2
2
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
4
1
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
2
0
5
0
1
0
0
0
0
0
0
3
1
0
0
0
0
2
3
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
1
0
2
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
2
0
1
0
0
2
0
0
2
0
0
2
0
0
1
2
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
2
0
0
0
5
0
0
0
0
0
2
2
0
0
0
0
0
2
0
1
0
3
0
2
0
0
1
0
0
0
2
0
0
0
0
0
3
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
1
0
1
0
0
1
0
0
0
2
1
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
2
2
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
2
3
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
2
0
0
0
1
0
1
2
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
2
1
3
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
1
0
1
2
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
1
1
0
1
1
2
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
1
0
1
0
0
2
2
0
0
0
0
0
2
1
2
1
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
1
1
0
0
1
0
2
1
0
0
0
5
0
1
2
0
1
0
0
2
0
2
0
0
5
0
0
2
0
0
0
0
0
0
0
0
3
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
3
0
1
0
0
2
0
0
0
2
0
0
1
0
0
0
4
0
1
2
0
0
2
0
0
0
0
0
0
3
0
0
1
0
2
0
0
2
2
0
0
0
0
1
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
1
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
3
0
3
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
6
0
0
2
0
0
2
1
0
1
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
2
1
0
2
0
0
1
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
1
0
2
0
3
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
1
2
2
2
0
0
0
0
0
1
0
0
2
1
0
2
0
1
0
0
3
0
1
0
0
1
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
4
0
0
0
0
1
0
2
1
0
0
1
1
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
2
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
2
2
0
0
1
0
1
0
2
3
0
0
3
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
3
5
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
1
2
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
6
1
0
2
0
0
0
2
0
0
0
0
1
2
0
0
0
2
2
0
0
0
0
1
0
0
0
0
1
3
0
0
0
0
0
1
0
0
0
0
1
1
0
2
0
0
0
2
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
1
1
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
1
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
1
2
1
0
0
0
0
0
0
0
0
0
9
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
4
2
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
1
0
2
0
1
0
0
0
0
3
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
1
2
0
2
0
0
1
0
2
0
0
0
4
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
2
2
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
5
2
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
1
2
0
0
1
1
0
0
0
0
0
0
4
0
0
0
1
0
0
0
2
0
0
2
2
0
1
2
0
0
0
1
0
2
1
0
0
2
1
1
1
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
1
0
3
1
0
0
0
2
0
0
0
0
0
5
0
1
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
2
0
0
2
0
2
1
0
0
1
0
0
0
0
0
0
0
3
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
1
4
0
2
0
4
1
1
0
1
5
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
2
1
0
0
0
0
0
2
0
0
4
0
0
0
0
0
1
0
0
0
0
0
2
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
0
0
0
2
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
4
0
0
2
0
2
1
2
1
0
1
2
2
0
0
0
0
1
0
0
0
0
2
0
1
0
1
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
2
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
1
1
2
1
0
0
0
1
0
0
0
0
0
1
2
0
4
0
0
0
1
0
1
1
0
0
2
1
0
1
3
0
0
0
1
0
0
0
0
0
0
0
2
2
1
0
1
2
0
0
0
0
0
3
0
0
0
2
2
2
0
0
2
0
0
0
0
1
0
0
0
0
1
1
2
2
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
3
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
1
1
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
1
9
2
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
3
0
0
1
0
2
0
0
0
0
0
0
3
0
0
0
1
2
1
0
2
0
0
0
1
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
2
0
2
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
3
4
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
4
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
2
1
1
1
2
8
0
0
1
0
1
0
1
0
0
0
0
0
0
2
1
2
0
0
0
2
0
0
0
2
1
0
0
3
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
4
1
2
0
0
0
2
2
2
0
0
2
1
0
0
1
0
0
0
0
0
3
0
3
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
5
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
2
1
2
0
1
2
0
0
0
0
0
0
1
0
0
1
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
5
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
2
1
1
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
2
0
0
1
0
0
0
2
0
8
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
2
0
1
1
0
1
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
1
1
2
0
0
0
2
1
0
0
1
0
0
0
0
0
2
0
0
0
3
2
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
2
2
2
2
0
0
1
0
0
0
0
1
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
3
0
0
0
0
0
1
0
7
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
2
0
0
2
3
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
4
0
0
2
0
0
2
0
0
0
1
2
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
1
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
4
0
0
0
2
1
0
0
0
0
2
0
1
1
0
1
0
0
2
1
1
0
0
0
0
0
2
0
0
0
2
0
0
0
2
1
0
0
0
2
0
0
2
0
0
0
2
0
1
0
1
2
0
1
0
1
0
1
0
0
0
0
0
1
0
3
1
0
6
0
0
0
0
0
0
6
0
0
0
2
0
0
0
0
0
0
0
1
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
2
0
0
2
2
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
2
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
3
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
5
0
0
0
0
0
3
0
0
3
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
2
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
1
0
0
2
0
2
0
0
1
0
0
0
0
1
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
2
0
0
0
3
0
2
0
0
3
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
2
0
1
0
4
1
0
0
1
1
0
0
0
0
0
7
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
3
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
1
0
0
0
0
2
2
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
2
1
0
0
0
1
0
0
0
2
0
0
0
0
3
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
2
0
1
2
0
0
0
0
0
0
4
2
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
2
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
4
0
1
0
1
0
0
2
0
0
0
1
2
0
4
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
2
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
1
2
0
1
0
0
2
1
0
0
0
0
0
0
0
0
1
0
1
2
0
0
2
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
3
0
0
2
0
0
0
0
2
0
0
2
0
2
0
0
0
2
0
0
0
0
0
1
1
1
0
0
2
2
0
1
0
2
0
1
1
0
0
0
0
2
0
2
0
0
1
0
0
0
1
2
0
0
0
2
0
0
0
1
0
2
2
0
7
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
3
0
0
0
0
1
0
0
0
0
1
2
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
2
4
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
2
0
0
0
3
0
0
0
1
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
2
3
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
2
0
0
1
1
0
3
3
2
0
1
0
0
0
0
0
2
0
2
0
0
2
1
0
1
0
4
0
1
0
0
2
0
5
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
2
2
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
1
1
0
2
0
0
0
2
0
0
1
2
0
0
1
0
0
4
3
0
0
1
0
0
0
1
0
0
0
2
2
0
6
1
2
0
0
2
0
0
2
0
0
0
1
3
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
2
0
0
2
0
0
0
2
2
4
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
4
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
3
2
0
0
0
2
0
0
2
0
3
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
2
2
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
1
2
4
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
2
0
0
0
0
3
0
0
0
2
0
0
0
2
0
0
0
0
2
2
1
1
0
0
2
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
2
2
4
0
2
0
0
0
0
0
2
0
0
6
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
2
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
2
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
2
0
1
0
1
0
0
0
0
3
0
0
0
0
0
1
0
2
1
0
1
0
0
0
1
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
1
1
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
3
0
0
0
0
2
2
0
0
1
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
2
2
0
2
0
0
0
1
0
1
0
1
2
2
0
1
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
3
1
0
0
0
6
0
0
0
0
0
1
2
2
2
0
0
2
0
0
0
2
0
0
0
0
6
0
1
0
0
0
1
1
0
0
1
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
1
1
2
0
0
2
1
3
2
0
2
0
0
2
2
0
0
1
0
2
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
3
0
0
2
0
1
2
1
0
0
1
2
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
1
1
0
1
2
0
0
0
3
0
0
0
2
0
0
0
2
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
2
1
0
2
0
0
0
0
1
2
0
2
0
1
0
2
0
2
2
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
5
0
0
3
3
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
2
0
0
0
2
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
3
2
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
2
1
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
5
0
1
1
0
0
0
2
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
2
1
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
4
0
12
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
2
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
1
0
0
2
0
0
0
1
0
2
0
0
0
0
3
0
0
1
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
1
3
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
1
0
1
1
1
1
1
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
1
1
0
0
1
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
5
0
2
0
1
2
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
2
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
1
1
0
0
2
0
0
0
1
0
2
1
1
0
0
0
0
0
0
0
1
2
0
1
2
2
1
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
2
3
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
3
0
2
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
2
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
3
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
1
2
2
2
2
2
0
0
1
0
3
0
0
0
2
0
0
0
0
0
3
0
1
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
1
0
3
0
0
0
1
0
0
0
0
0
0
0
1
2
0
3
1
0
0
1
3
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
4
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
3
0
0
2
2
1
0
0
0
0
0
0
2
1
2
1
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
7
0
2
0
0
0
2
0
2
1
0
1
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
4
0
0
0
0
0
2
3
1
0
0
2
2
0
0
2
0
0
2
1
1
0
0
2
0
0
0
0
0
0
0
6
2
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
1
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
2
0
0
0
0
1
1
0
0
0
1
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
2
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
3
2
1
0
0
0
1
0
1
0
0
0
0
3
0
0
0
0
1
2
0
0
2
0
0
0
1
0
0
0
2
1
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
1
2
2
0
0
0
0
1
0
0
0
0
2
0
2
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
5
0
2
0
0
2
1
1
2
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
2
0
4
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
2
3
0
1
0
1
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
2
0
1
0
0
1
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
2
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
1
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
2
0
1
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
2
0
0
1
0
0
0
0
0
0
2
0
1
1
0
2
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
5
0
0
0
3
0
0
0
0
0
2
0
4
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
1
0
0
0
1
0
0
2
0
0
3
0
0
2
0
0
4
0
1
1
0
0
0
0
2
0
2
0
0
0
2
2
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
3
1
0
0
1
2
0
0
3
0
1
1
0
2
0
0
0
0
0
0
0
1
2
0
0
1
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
2
1
0
1
1
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
2
0
0
1
1
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
4
0
2
0
1
0
0
0
0
0
1
0
0
0
1
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
2
2
0
0
1
0
0
0
2
0
0
0
0
2
0
1
0
0
0
1
1
0
0
1
0
0
2
1
0
0
0
0
0
2
1
2
0
0
0
0
2
0
3
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
2
0
1
1
0
2
0
1
3
0
0
0
0
0
0
0
0
3
0
0
1
1
1
0
0
0
2
1
2
0
1
0
0
0
0
1
0
1
0
0
0
0
2
0
1
1
1
2
0
0
2
2
1
0
2
0
0
0
0
0
0
0
0
0
1
3
0
2
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
1
2
0
0
0
1
0
0
0
0
0
0
0
2
1
0
3
0
0
2
2
2
1
1
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
1
0
0
2
1
0
0
1
0
0
2
0
2
0
0
0
0
1
1
0
2
0
0
3
0
0
0
2
0
0
0
0
2
5
0
0
4
2
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
1
0
0
0
0
1
0
2
0
0
1
0
1
0
0
0
1
2
1
1
2
2
0
0
0
0
0
0
2
0
0
0
0
2
2
1
1
0
2
2
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
1
1
0
2
4
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
1
0
2
1
0
0
0
0
0
0
0
0
1
0
0
1
0
2
1
0
0
1
0
0
0
0
2
0
3
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
2
0
2
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
4
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
2
0
0
0
0
1
0
1
0
0
2
0
0
2
1
0
0
1
0
0
2
0
0
0
0
0
1
0
1
1
2
0
0
0
1
0
0
2
0
0
3
3
0
0
0
0
2
2
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
3
2
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
6
2
0
1
0
0
1
0
0
2
2
0
0
0
0
0
0
3
0
0
0
0
2
2
0
0
0
0
0
0
0
2
1
0
0
3
0
0
0
2
1
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
1
2
0
0
0
2
2
0
0
2
1
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
1
0
1
1
0
1
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
4
0
3
2
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
8
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
1
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
5
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
1
2
2
1
2
1
0
0
0
0
2
2
2
0
0
2
0
0
8
0
0
2
2
0
3
0
0
0
2
1
1
0
0
0
2
0
0
0
3
2
0
0
1
2
0
1
2
0
0
0
0
1
0
2
1
2
0
2
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
2
0
1
0
0
2
0
0
0
1
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
3
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
1
0
0
1
2
0
0
0
0
0
0
0
0
1
0
2
0
1
1
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
4
0
0
0
0
2
2
0
0
0
0
0
1
2
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
3
1
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
2
0
2
0
0
0
0
2
0
1
3
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
3
0
0
1
1
1
0
0
0
2
0
1
1
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
2
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
2
1
3
0
0
1
0
0
3
0
0
2
0
1
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
2
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
3
0
1
1
0
0
0
0
2
0
0
2
1
2
0
0
0
1
1
0
0
0
2
0
3
0
0
0
1
2
0
0
0
0
0
0
1
2
3
0
0
0
1
0
3
0
2
0
0
0
0
0
1
1
0
4
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
2
0
0
0
2
0
0
0
3
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
3
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
3
0
0
0
1
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
3
2
0
0
0
0
4
1
0
1
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
3
0
0
0
0
0
0
0
2
2
0
2
0
0
0
2
0
0
2
1
2
2
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
2
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
2
1
0
0
0
1
2
1
0
0
0
0
0
1
1
0
0
0
0
2
0
2
0
0
0
3
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
2
0
0
0
0
1
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
1
0
1
2
0
0
0
0
1
1
0
1
0
0
0
0
1
0
1
2
0
0
0
0
0
0
2
1
0
0
1
0
0
2
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
1
3
0
0
0
0
0
1
0
2
2
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
1
1
3
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
3
0
2
0
0
0
0
0
1
3
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
2
1
0
0
1
0
0
0
1
0
0
0
1
0
0
2
0
1
2
0
0
0
0
2
1
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
6
0
0
1
2
0
0
6
1
0
0
0
0
0
0
0
0
2
1
1
0
0
0
4
0
2
0
0
0
0
0
0
2
2
0
0
1
0
1
0
0
2
1
2
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
2
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
4
2
0
0
0
1
1
1
0
0
0
0
1
0
2
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
3
1
0
0
3
0
1
0
0
0
0
0
2
1
2
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
1
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
4
0
0
0
0
0
2
0
1
0
0
0
1
0
0
1
0
1
0
2
2
0
0
0
0
0
3
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
3
0
0
2
0
0
0
3
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
2
0
0
1
0
0
2
2
0
0
0
0
1
0
2
0
0
0
2
1
1
1
3
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
2
2
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
2
0
0
0
0
0
0
0
2
2
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
1
3
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
2
1
0
0
2
1
2
0
0
0
4
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
2
2
1
0
1
0
1
0
0
0
0
0
2
4
0
0
2
0
0
0
0
0
0
4
0
0
0
0
3
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
1
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
1
0
1
0
0
1
0
3
0
0
0
0
2
1
0
0
0
0
3
2
0
0
1
0
1
0
0
1
0
0
0
0
1
0
2
0
2
0
0
1
0
0
1
0
0
2
0
1
0
0
1
0
0
2
0
0
0
1
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
2
0
0
0
0
2
2
2
1
0
1
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
2
0
1
2
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
1
0
0
0
1
2
0
0
1
0
0
0
1
3
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
1
0
1
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
2
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
2
2
6
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
1
0
1
0
0
4
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
2
4
0
0
1
0
0
0
0
0
0
0
0
1
0
1
2
0
2
0
1
0
0
2
2
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
3
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
2
1
0
0
0
0
0
1
0
0
0
2
2
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
2
3
1
1
0
0
2
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
3
0
0
3
3
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
1
2
2
0
1
0
0
0
0
1
0
1
0
0
0
2
0
0
0
1
0
0
0
2
2
0
0
1
4
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
3
0
1
1
1
0
1
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
3
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
1
0
2
1
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
1
2
1
1
0
0
0
3
0
1
0
3
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
6
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
4
2
0
0
1
0
0
1
0
0
0
0
0
2
0
2
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
2
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
2
0
2
0
1
0
0
0
2
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
3
2
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
3
0
0
0
0
1
1
0
0
2
1
0
1
0
1
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
3
0
0
1
1
2
1
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
3
0
2
2
0
2
0
1
0
0
0
1
1
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7
0
1
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
1
2
0
0
0
1
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
4
2
2
0
0
3
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
1
1
0
0
0
1
0
0
0
4
0
4
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
2
0
0
0
2
0
0
2
0
1
0
2
3
0
0
2
0
0
0
0
0
0
2
0
0
3
1
1
1
2
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
5
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
1
0
0
2
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
2
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
1
0
2
1
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
2
0
0
0
3
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
3
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
1
0
0
2
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
1
0
0
0
0
0
0
0
0
2
0
2
2
0
2
3
0
1
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
4
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
3
1
0
5
1
3
0
3
0
2
0
0
2
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
4
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
4
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
2
0
2
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
1
2
0
0
0
0
1
2
0
3
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
3
4
0
0
0
0
0
0
0
2
0
5
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
4
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
1
0
3
0
0
0
0
1
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
2
2
1
1
0
2
0
0
0
1
0
1
0
1
0
0
1
0
0
1
0
2
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
1
0
0
5
0
0
1
6
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
3
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
3
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
2
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
2
0
2
2
1
0
2
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
2
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
1
2
2
4
0
0
0
0
1
0
0
0
0
1
0
0
0
2
2
0
2
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
2
2
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
1
0
0
0
3
0
2
0
0
0
0
0
0
0
2
0
1
0
0
2
0
1
2
0
0
0
0
2
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
8
0
1
0
0
0
2
1
0
1
1
0
0
0
0
0
0
1
0
0
0
2
1
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
1
0
3
2
1
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
3
0
0
0
0
0
2
0
1
0
0
0
1
0
2
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
1
0
0
0
0
1
0
2
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
3
2
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
3
0
0
3
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
2
0
0
0
1
2
3
0
0
0
0
0
0
0
1
2
1
0
1
1
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
2
2
0
2
1
0
1
2
0
0
2
0
3
0
1
0
0
0
0
2
0
0
0
2
4
0
0
0
0
0
2
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
3
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
3
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
1
0
1
0
0
2
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
4
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
4
0
0
0
0
0
2
0
2
1
2
1
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
2
3
0
0
2
0
0
0
0
2
1
0
0
0
0
1
1
2
0
0
0
0
2
0
0
0
3
2
2
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
3
0
4
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
4
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
2
0
0
1
3
2
0
2
2
2
0
0
1
1
2
0
2
0
2
2
3
2
0
0
0
2
2
2
0
0
3
0
2
0
0
1
0
0
5
2
1
0
0
0
0
1
0
0
1
0
1
0
0
0
2
0
0
2
0
0
1
0
1
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
2
2
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
1
0
0
0
2
1
1
1
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
1
1
1
0
1
0
0
0
1
0
0
0
0
0
1
0
2
2
1
0
0
1
0
0
0
2
0
0
1
0
0
1
0
0
2
2
0
1
0
0
0
1
1
0
0
0
0
2
0
0
3
2
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
1
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
1
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7
0
0
0
0
2
0
0
2
1
1
0
1
2
1
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
2
0
2
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
2
0
0
3
0
0
0
2
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
2
0
0
2
0
0
2
0
1
2
2
1
3
0
2
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
1
0
1
0
0
0
0
0
0
1
2
1
2
0
0
1
0
0
1
0
0
1
1
0
0
0
1
0
0
2
0
2
0
0
0
2
0
0
0
1
0
2
0
0
0
1
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
2
2
1
0
2
0
2
1
0
2
1
1
1
0
1
0
2
0
0
1
1
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
3
0
0
0
0
1
1
1
1
0
0
1
0
0
0
2
0
0
2
0
0
0
0
2
1
2
0
1
2
0
0
0
2
0
0
0
2
1
2
0
0
0
2
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
2
0
2
3
2
0
0
0
2
0
0
1
0
0
0
0
0
2
0
1
5
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
1
2
0
2
2
0
2
0
0
4
0
0
0
1
0
0
0
9
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
3
0
1
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
2
0
0
0
2
0
3
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
2
0
0
1
0
3
0
2
1
2
0
0
2
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
2
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
3
1
0
2
3
1
0
0
0
0
1
0
2
0
0
0
2
0
0
0
2
0
2
0
0
1
0
0
0
2
0
1
0
0
0
0
3
0
1
2
0
3
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
2
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
4
0
0
0
0
2
2
0
0
0
1
0
0
0
0
1
0
0
2
2
0
0
0
2
2
0
0
2
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
2
0
3
0
0
0
0
0
1
0
2
0
0
0
1
0
1
2
1
0
2
0
0
1
0
0
1
0
1
2
2
0
2
0
0
0
2
1
0
3
0
0
0
1
9
0
0
2
1
0
1
3
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
1
2
0
0
1
2
0
0
0
0
2
0
0
0
0
2
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
1
0
1
1
2
0
1
0
1
0
1
1
0
0
0
1
0
0
1
1
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
2
0
1
0
0
2
2
0
0
0
2
0
0
1
0
0
0
2
0
0
1
0
0
0
2
0
0
0
3
0
0
1
0
0
1
0
0
1
0
0
0
0
1
1
3
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
8
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
2
0
1
0
0
2
0
3
0
0
2
0
0
0
1
0
0
0
1
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
1
2
2
0
2
2
0
0
0
0
2
0
2
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
3
0
2
2
0
0
0
1
1
2
0
2
0
0
1
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
1
0
0
2
0
0
0
2
0
1
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
2
0
2
2
0
0
0
0
7
1
0
0
0
0
1
0
0
0
0
2
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
3
2
0
0
1
2
0
0
0
0
0
1
0
1
2
3
0
0
0
0
2
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
2
0
0
0
2
1
1
0
0
2
0
2
0
0
0
2
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
3
2
1
2
1
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
4
0
3
0
3
0
0
0
1
0
0
1
1
0
0
0
1
0
0
2
1
1
0
0
0
2
2
2
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
1
0
0
1
0
0
0
0
0
3
1
1
0
1
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
6
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
3
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
12
0
0
0
0
0
0
0
0
0
2
1
1
0
2
2
3
0
1
1
2
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
2
0
0
0
2
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
2
0
0
2
2
0
0
3
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
2
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
2
1
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
4
2
0
1
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
2
1
0
0
0
1
0
0
1
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
1
0
0
2
3
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
4
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
2
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
2
0
1
1
2
0
3
1
0
0
0
0
0
0
1
0
0
2
1
1
0
0
0
1
0
0
0
0
2
1
0
0
1
2
0
0
2
1
1
0
0
0
0
0
0
3
0
0
3
1
0
2
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
3
1
0
0
0
2
0
2
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
2
5
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
1
0
0
2
0
0
0
2
0
2
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
1
0
2
0
2
0
0
0
0
0
0
1
1
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
1
0
3
0
0
0
0
0
0
0
1
1
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
2
0
2
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
3
0
0
1
0
0
3
0
0
1
0
0
0
0
2
2
0
0
2
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
2
0
0
0
2
1
0
0
2
0
2
1
0
3
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
2
2
0
1
0
2
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
1
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
2
0
1
0
0
0
2
0
0
0
2
2
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
2
0
1
0
2
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
2
0
0
2
2
2
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
1
1
2
1
2
0
1
2
1
1
1
0
1
0
0
1
2
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
3
0
0
0
0
1
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
3
1
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
2
0
1
2
0
0
2
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
2
1
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
3
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
3
0
0
0
1
2
0
1
4
0
0
1
1
1
0
0
1
1
0
0
0
0
0
0
0
1
0
2
2
0
2
2
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
2
0
0
0
3
0
0
1
0
1
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
1
2
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
1
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
1
2
1
0
0
0
0
2
0
0
0
0
0
1
2
1
2
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
2
1
1
0
0
1
1
0
0
0
5
0
0
2
2
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
1
0
0
2
4
0
1
0
0
1
1
0
0
1
1
2
1
0
0
0
0
2
0
0
0
0
1
1
0
2
0
0
4
0
4
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
7
1
1
2
0
0
1
0
0
0
0
1
0
0
2
1
0
2
0
0
0
0
0
0
1
0
0
0
3
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
1
0
2
2
2
1
0
0
0
1
0
0
1
0
3
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
1
3
0
1
0
2
0
1
0
0
0
2
0
0
0
1
0
1
0
2
0
1
1
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
3
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
2
0
0
0
1
0
1
0
2
2
1
1
0
0
3
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
2
0
1
0
0
0
2
0
0
0
1
0
2
0
0
0
0
2
0
0
3
0
0
2
0
1
1
0
1
0
0
0
1
2
0
0
0
0
2
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
3
3
2
0
0
0
0
0
4
1
0
0
0
2
0
0
0
0
0
0
2
0
2
0
2
0
5
0
0
0
0
1
0
0
0
0
0
1
0
2
1
1
0
0
1
0
2
0
1
0
0
0
0
0
1
0
2
0
0
0
0
8
1
2
0
2
2
2
0
0
2
0
2
1
0
0
0
0
0
0
0
2
1
1
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
2
0
0
2
1
0
0
2
0
0
2
2
3
0
0
0
2
0
0
1
0
0
0
0
1
1
0
1
0
0
1
2
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
2
0
2
1
0
3
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
2
2
1
1
1
0
1
1
0
0
0
0
1
0
2
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
2
0
2
1
0
1
0
0
0
0
0
2
0
2
1
0
0
0
2
0
0
1
0
0
2
2
0
0
0
2
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
1
2
0
0
0
0
0
0
2
6
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
2
0
0
2
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
1
1
2
1
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
1
0
2
0
0
0
0
0
1
1
0
2
0
2
0
0
2
2
0
1
0
2
3
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
1
1
0
3
0
0
0
0
0
2
1
0
0
1
0
0
2
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
3
0
0
1
0
0
2
0
0
1
0
1
0
0
0
0
1
1
0
0
1
0
2
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
3
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
3
1
0
0
2
0
0
2
0
0
1
0
0
2
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
1
0
2
1
0
0
0
2
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
2
0
0
2
0
1
0
0
5
0
0
0
0
2
1
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
3
0
0
1
0
0
0
1
2
2
0
0
0
0
0
0
1
2
0
1
3
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
3
0
0
3
0
0
2
0
0
1
0
1
0
2
1
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
2
0
1
0
1
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
1
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
1
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
2
3
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
3
0
1
1
0
0
0
2
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
2
2
0
0
0
2
0
0
0
1
0
0
2
0
2
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
1
0
1
1
2
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
2
0
0
2
1
0
1
0
0
0
0
0
3
0
0
0
0
0
5
0
0
0
0
1
0
0
2
0
1
0
0
2
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
2
2
0
0
3
0
0
0
0
0
0
2
1
0
2
2
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
3
0
3
0
1
2
0
0
0
0
0
0
0
0
1
1
0
0
2
6
2
2
0
2
1
2
0
5
1
0
0
0
0
0
0
1
0
0
1
0
1
1
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
5
1
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
2
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
1
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
2
0
3
1
1
0
0
0
4
0
0
0
0
3
0
0
1
0
4
2
0
2
0
2
0
0
0
2
0
0
0
0
0
2
1
0
2
1
2
0
0
0
0
0
0
0
12
0
0
0
0
0
0
0
0
3
0
3
0
0
0
0
2
2
0
0
0
0
1
0
0
0
1
1
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
1
3
3
0
1
0
0
1
0
1
0
2
0
0
0
0
0
1
3
0
0
0
0
2
0
0
1
0
0
0
0
3
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
2
1
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
2
0
0
0
0
2
0
0
0
0
2
0
2
1
0
3
0
0
0
0
3
0
2
0
2
0
0
0
1
0
0
1
0
0
2
0
2
0
2
0
2
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
1
0
0
1
0
2
3
0
0
2
0
1
0
0
1
0
0
0
0
0
1
2
1
2
0
0
0
0
2
1
0
1
3
2
0
1
0
0
0
0
2
1
1
0
0
0
0
1
2
0
0
2
0
0
0
0
1
0
2
0
0
1
3
0
0
0
2
0
0
0
2
0
0
0
0
0
1
1
3
1
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
2
0
0
0
5
0
1
0
1
1
2
0
0
0
0
0
0
1
0
8
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
1
1
0
2
1
2
0
0
0
0
1
3
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
2
0
2
0
2
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
1
0
1
2
1
0
0
0
0
2
0
0
2
0
2
0
0
0
1
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
1
2
1
2
0
0
0
1
3
0
0
1
0
0
1
0
0
2
2
0
2
8
0
0
0
0
1
0
1
2
0
0
1
0
2
2
1
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
1
0
2
1
0
0
2
0
1
2
0
0
0
0
0
2
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
1
1
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
1
2
0
2
0
0
2
1
0
1
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
1
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
3
2
0
1
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
2
0
0
1
0
1
0
1
2
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
2
1
0
0
0
1
0
0
0
1
1
0
0
0
0
2
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
2
0
3
0
0
1
2
1
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
5
0
2
1
1
0
1
0
2
0
0
0
0
0
2
0
0
1
0
0
2
0
1
0
0
2
0
2
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
1
0
2
1
1
0
0
0
0
1
1
0
0
2
0
2
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
1
0
0
0
2
0
0
1
0
3
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
2
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
4
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
1
0
1
2
0
0
0
3
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
2
2
0
0
0
2
2
1
0
1
0
0
2
0
2
0
2
0
0
2
0
2
0
0
0
0
0
0
3
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
2
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
2
3
0
1
1
0
0
2
0
0
1
1
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
1
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
3
0
0
0
0
0
0
0
0
0
4
0
2
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
2
1
0
2
0
4
0
1
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
2
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
2
3
2
0
1
0
0
0
0
0
2
1
0
0
1
2
1
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
1
0
0
0
0
0
0
1
2
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
1
2
0
0
0
3
1
1
0
0
2
0
1
0
0
3
0
0
0
0
0
0
1
0
0
0
5
0
0
1
0
0
0
2
0
2
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
2
0
2
0
0
2
0
2
0
2
0
0
2
0
0
2
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
2
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
1
2
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
3
0
0
1
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
2
0
0
11
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
2
2
2
1
0
1
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
3
0
0
0
1
0
0
1
2
0
0
2
0
0
0
1
0
0
0
0
0
1
0
2
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
1
2
0
0
0
2
2
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
4
3
0
2
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
2
0
0
1
0
2
1
0
0
0
0
5
1
0
0
1
1
0
2
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
1
2
4
0
0
4
0
0
0
1
2
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
2
2
0
0
1
0
0
1
0
2
0
0
1
2
0
0
2
0
0
0
0
0
1
1
0
3
0
0
0
1
0
2
0
1
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
2
0
2
0
0
0
2
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
1
0
9
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
2
1
1
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
2
0
0
0
1
2
1
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
2
0
0
1
2
2
1
0
2
0
0
0
1
2
2
2
0
0
0
0
2
2
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
1
3
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
6
0
0
0
0
0
0
1
0
2
0
1
1
0
0
0
0
0
0
3
1
0
1
2
0
2
2
0
0
0
0
3
2
1
1
0
2
1
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
2
0
0
0
1
0
0
0
2
2
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
2
0
0
1
1
0
0
0
2
0
0
0
0
1
0
0
0
3
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
2
0
0
0
0
0
5
0
1
1
0
0
0
0
2
1
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
1
1
0
0
0
1
0
1
2
0
0
0
0
2
0
1
0
0
0
0
0
2
1
0
2
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
1
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
3
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
1
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
2
2
0
0
0
0
0
1
0
1
0
0
2
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
2
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
3
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
2
1
0
2
1
2
0
1
0
2
2
0
2
2
0
0
0
3
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
2
2
0
2
17
0
0
3
0
0
0
0
6
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
1
1
2
0
0
0
1
0
2
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
2
0
0
0
3
0
3
0
0
0
4
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
1
2
0
1
1
0
2
0
6
0
0
0
0
1
1
0
0
0
0
0
0
0
0
3
2
0
3
0
0
1
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
2
0
1
0
2
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
2
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
1
1
2
1
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
2
0
0
1
0
0
0
2
0
0
0
0
1
0
1
0
1
3
0
2
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
2
0
1
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
1
0
3
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
2
2
0
1
0
1
0
0
0
0
1
0
0
0
0
4
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
2
0
0
4
0
2
0
0
0
1
0
2
1
1
3
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
1
0
2
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
2
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
1
0
0
2
0
0
0
0
2
0
3
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
1
0
0
3
0
2
2
0
0
0
0
0
2
2
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
1
0
0
2
1
2
0
1
0
0
2
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
2
2
0
0
0
0
0
1
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
2
0
1
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
1
1
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
2
1
0
0
0
2
0
2
0
0
0
2
6
0
0
0
0
0
0
0
5
3
0
1
0
0
0
0
0
1
1
0
2
0
0
2
0
2
3
0
0
0
0
0
0
0
0
1
2
1
0
0
0
1
0
0
2
2
0
1
2
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
4
0
2
4
0
0
0
0
1
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
2
0
2
2
0
3
0
0
1
2
0
0
0
0
0
0
1
0
0
2
1
1
0
1
0
1
0
0
0
2
0
0
0
0
2
0
1
1
0
1
0
0
0
2
0
0
3
1
0
0
0
0
0
0
0
2
2
2
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
2
0
2
0
0
3
2
0
0
0
0
0
0
0
4
0
0
0
0
0
2
2
0
4
0
0
2
1
0
1
0
1
0
2
0
0
2
0
1
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
2
0
4
1
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
4
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
2
2
0
0
0
0
3
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
2
0
0
1
1
1
0
0
1
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
2
0
1
2
1
0
0
0
0
3
0
1
0
0
2
2
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
2
1
0
2
1
0
0
1
0
0
0
0
2
0
0
0
0
0
1
1
1
2
0
0
0
0
0
1
1
4
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
1
0
1
1
2
0
0
0
2
0
0
2
2
0
0
2
0
2
2
1
0
0
0
0
0
4
1
0
0
0
0
2
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
2
4
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
2
2
1
0
0
2
5
1
2
0
0
0
0
0
0
1
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
2
2
2
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
2
0
1
0
2
1
1
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
2
0
0
2
1
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
4
0
0
1
0
0
0
2
0
2
1
2
0
0
2
0
2
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
2
2
0
0
0
1
1
0
0
0
0
1
2
2
0
0
0
0
0
2
0
0
0
0
1
1
2
0
0
1
1
1
2
2
0
0
0
2
0
1
2
0
0
0
2
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
4
0
0
1
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
3
0
1
2
0
3
0
2
0
0
3
2
0
0
1
0
0
2
0
2
2
2
0
0
0
0
0
2
0
2
0
0
0
1
2
1
0
0
0
1
2
0
0
0
0
0
0
2
0
0
2
1
2
0
3
0
0
2
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
1
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
2
0
1
0
0
0
0
0
0
1
0
0
2
4
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
1
0
0
1
0
0
0
0
2
0
0
2
0
1
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
3
0
0
0
0
1
0
2
0
0
0
0
2
2
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
1
1
1
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
2
0
1
0
0
0
2
0
2
2
0
0
0
2
1
0
0
0
0
0
0
1
0
0
2
0
0
5
0
0
0
2
0
2
0
0
0
0
1
0
2
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
2
3
0
0
0
0
0
2
0
2
0
0
0
1
2
0
2
0
0
2
0
4
2
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
1
8
0
1
0
2
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
2
1
1
3
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
1
2
0
0
0
3
0
0
1
2
1
0
0
2
0
0
0
0
0
4
0
2
0
0
1
0
0
0
2
0
0
0
0
1
0
0
3
0
0
2
2
0
0
0
0
0
0
0
0
0
3
0
1
1
0
0
0
0
0
0
0
0
2
0
1
0
1
0
2
0
0
0
0
0
0
1
0
0
0
3
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
1
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
2
0
0
0
2
0
0
0
1
0
1
2
2
0
0
0
1
1
2
0
1
0
0
2
0
0
2
0
0
0
1
3
0
0
1
0
1
0
0
0
0
0
2
0
0
1
0
1
3
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
1
0
3
0
2
2
0
0
2
0
0
0
0
0
2
2
1
0
0
0
0
0
1
0
0
2
0
0
0
1
0
1
0
0
1
2
0
0
0
2
1
0
2
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
4
0
0
0
2
0
0
0
0
1
0
0
0
0
2
1
1
0
0
0
1
0
2
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
1
0
3
0
0
0
0
0
1
0
0
0
1
2
0
0
0
1
0
0
1
0
0
0
0
1
0
2
1
0
1
0
1
0
2
0
1
0
0
0
0
0
0
8
1
1
0
0
0
2
0
2
0
2
0
0
1
1
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
2
0
2
0
0
0
1
0
0
0
0
2
0
0
3
0
0
2
0
0
2
0
2
0
1
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
3
0
0
0
0
0
3
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
2
1
1
0
0
0
0
1
2
1
0
0
0
0
2
3
0
0
0
0
0
0
4
0
0
0
0
0
0
0
2
0
0
4
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
2
1
2
0
0
0
0
0
0
0
0
3
1
0
0
1
0
0
0
0
0
0
0
2
2
0
0
1
1
0
0
0
1
0
0
0
0
0
2
1
2
0
0
0
0
0
1
1
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
0
1
1
0
0
0
0
0
1
2
0
1
1
0
0
0
2
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
2
1
0
0
1
2
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
1
0
1
2
2
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
1
2
0
1
0
0
0
2
0
0
1
0
0
0
1
0
0
0
3
0
1
6
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
2
0
1
2
0
0
0
0
0
0
0
3
0
0
0
2
0
1
0
0
0
0
0
0
1
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
1
0
4
0
0
1
0
0
0
0
1
0
1
1
0
1
0
0
0
1
0
0
2
0
2
2
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
1
0
2
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
1
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
2
0
2
0
3
2
2
0
2
3
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
2
0
2
0
0
4
0
2
0
0
2
0
1
2
1
0
0
0
0
0
1
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
1
2
0
1
2
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
2
2
2
0
2
0
2
0
0
0
0
1
0
0
0
1
0
0
3
0
0
0
0
0
0
1
1
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
1
3
2
0
3
1
0
1
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
2
0
1
1
0
1
0
0
3
2
0
2
0
0
0
1
1
0
0
2
0
0
0
0
0
0
3
0
1
1
1
0
3
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
1
0
1
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
2
0
1
0
0
1
0
0
1
0
0
2
1
0
0
0
2
0
0
0
1
0
0
4
0
0
1
0
0
0
0
1
0
0
0
1
0
2
0
0
2
1
0
2
0
0
1
0
0
2
0
0
0
0
0
2
0
0
1
0
4
1
0
1
0
1
0
0
2
0
0
0
0
2
1
0
2
0
0
0
0
0
0
1
2
0
1
2
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
2
0
0
0
0
2
0
4
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
1
1
0
3
1
0
2
0
0
0
0
2
0
0
0
1
0
0
1
0
1
0
0
0
1
1
0
1
0
0
0
2
0
1
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
2
0
0
0
7
0
0
5
0
2
0
2
0
0
1
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
2
0
2
2
0
1
0
0
0
0
0
0
2
0
2
0
0
2
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
2
2
0
0
0
2
0
0
0
0
0
4
2
0
1
1
0
2
0
0
0
0
0
0
0
1
1
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
2
1
1
2
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
2
1
4
0
0
0
1
0
1
2
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
2
0
0
0
0
1
1
0
1
1
0
0
3
0
0
1
0
0
0
2
0
2
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
1
0
2
0
2
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
2
3
0
0
2
0
0
0
2
0
2
0
0
2
1
1
0
0
2
0
0
0
1
1
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
3
0
0
1
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
3
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
3
0
0
0
2
0
1
2
1
1
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
2
1
2
0
0
0
0
0
0
2
2
0
1
2
1
0
2
1
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
2
0
1
2
0
0
0
0
0
2
0
1
2
0
0
0
1
0
0
1
0
2
2
2
0
1
0
1
0
0
0
0
0
1
0
0
1
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
3
2
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
3
0
0
0
0
1
1
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
1
2
0
1
0
0
0
1
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
3
1
0
0
1
0
0
0
0
1
0
2
0
2
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
2
0
0
1
0
0
1
0
3
0
0
0
2
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
2
1
1
0
0
0
2
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
2
1
0
2
0
0
3
0
2
0
0
0
1
0
0
0
0
0
0
0
0
4
1
0
3
2
2
0
0
1
0
2
2
0
0
0
0
2
2
7
0
0
0
0
2
2
2
0
0
0
1
0
0
1
4
0
1
1
0
0
0
0
0
1
2
0
2
1
0
0
0
0
0
2
0
0
0
2
0
3
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
2
0
0
1
0
0
2
0
0
0
2
2
0
0
0
0
0
2
2
0
1
0
0
0
2
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
1
3
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
2
2
2
0
0
1
0
2
1
2
1
2
0
1
0
0
0
0
0
0
0
5
0
1
0
0
0
1
1
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
1
2
2
0
2
0
3
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
2
3
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
1
0
2
0
1
2
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
3
0
0
2
0
0
0
0
3
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
1
0
0
0
3
3
0
0
2
2
0
0
1
1
0
0
2
0
2
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
2
0
1
2
1
0
0
0
0
2
0
2
1
0
1
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
2
3
0
0
0
1
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
2
5
0
0
0
0
0
1
0
4
0
0
0
0
0
0
2
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
3
4
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
4
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
3
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
1
2
3
0
0
0
0
1
0
0
2
0
0
0
3
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
3
0
0
0
0
0
2
0
0
0
1
0
1
0
2
2
2
0
2
0
2
0
0
4
0
0
0
0
0
0
0
0
5
0
2
1
0
0
0
3
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
1
2
0
0
0
0
1
0
1
0
0
0
0
2
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
4
0
0
0
2
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
5
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
2
1
2
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
2
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
1
2
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
4
0
0
0
0
1
0
1
0
1
1
2
0
0
2
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
4
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
3
0
1
0
1
0
1
0
0
1
0
2
0
0
0
1
0
0
1
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
2
0
5
0
0
0
2
0
1
0
0
0
2
1
0
0
2
0
0
0
2
2
0
1
0
1
0
2
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
2
0
0
0
7
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
2
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
1
2
0
3
0
0
0
1
0
0
4
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
1
0
1
0
1
0
0
0
1
1
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
5
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
2
0
0
2
0
0
2
2
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
1
0
0
0
2
1
2
2
0
2
2
2
0
0
3
0
0
0
0
0
1
0
1
0
0
2
0
2
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
1
0
2
0
1
0
2
0
0
0
0
0
1
1
0
0
1
0
0
2
0
3
1
0
0
0
1
2
0
0
0
1
2
0
0
2
2
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
6
0
0
0
0
0
0
0
3
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
2
1
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
1
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
5
0
0
0
1
0
1
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
5
0
2
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
2
0
2
0
0
0
0
0
0
0
1
0
1
1
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
1
0
0
0
0
3
0
1
0
0
1
0
0
2
0
0
1
0
0
5
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
2
1
0
0
0
2
2
0
1
0
0
0
0
2
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
1
0
0
1
1
2
0
2
1
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
3
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
2
0
1
0
0
0
2
1
1
0
0
2
0
1
0
0
0
3
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
1
2
0
0
0
0
3
0
1
0
1
2
0
0
0
1
0
0
1
2
0
0
1
0
0
1
0
2
2
2
1
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
2
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
2
1
0
0
2
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
2
3
0
1
1
0
0
2
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
1
2
0
3
2
0
2
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
1
1
0
1
1
0
2
2
0
0
0
1
1
0
0
0
2
0
0
1
0
0
0
1
0
3
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
1
1
2
0
0
0
0
2
0
2
0
0
0
1
0
0
1
0
0
0
0
0
1
2
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
2
4
0
0
0
2
0
0
0
0
1
0
2
0
1
0
0
1
0
1
0
0
0
0
1
0
2
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
2
1
0
2
0
0
0
0
0
1
0
0
1
2
0
0
0
0
1
0
1
1
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
3
0
0
3
0
0
1
0
4
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
2
1
2
2
0
0
0
0
2
1
0
0
2
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
3
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
1
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
3
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
2
2
0
1
0
2
2
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
2
2
0
0
0
2
1
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
1
2
0
0
0
0
1
2
0
1
1
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
3
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
2
0
0
2
2
0
0
0
2
0
1
0
4
0
0
2
3
1
1
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
1
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
1
0
1
0
0
0
3
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
2
0
0
0
1
0
0
4
0
0
1
1
2
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
2
3
1
0
0
0
1
5
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
2
0
2
0
0
0
2
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
2
1
3
0
0
0
3
0
0
0
0
2
1
0
0
0
0
2
0
2
0
1
2
0
0
4
0
1
0
0
0
0
8
1
3
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
3
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
2
0
2
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
3
1
0
0
0
0
1
2
2
0
3
0
0
1
0
0
3
0
4
1
2
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
2
0
2
0
0
0
0
1
3
0
1
0
1
0
1
2
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
3
0
0
2
2
1
2
0
0
0
0
0
4
1
0
1
0
0
2
1
0
0
0
1
0
0
0
0
4
2
0
2
0
2
0
0
1
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
1
0
0
3
1
0
0
1
3
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
2
0
0
1
0
0
0
1
1
0
0
0
0
0
0
2
0
5
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
3
0
0
0
1
0
0
0
1
0
0
1
0
0
1
2
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
6
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
1
2
0
0
0
0
0
0
0
2
2
2
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
2
0
0
1
0
0
0
3
1
1
0
2
0
0
1
0
0
0
0
0
0
0
1
1
0
0
3
0
1
2
1
0
1
1
0
0
0
1
0
0
1
0
0
0
1
1
0
2
0
0
0
0
1
0
1
3
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
2
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
3
0
0
1
1
1
0
0
0
0
0
0
1
0
1
2
0
5
3
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
1
0
0
1
1
1
2
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
2
1
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
2
3
1
0
0
0
0
0
0
0
1
1
0
2
0
3
0
0
0
0
1
0
0
0
0
1
2
1
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
2
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
4
1
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
2
2
1
0
1
0
0
3
2
0
0
0
0
0
2
0
1
0
0
0
1
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
1
4
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
1
2
0
0
2
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
2
0
2
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
1
1
1
2
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
2
0
2
0
0
3
0
1
2
0
4
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
3
2
1
0
0
0
0
0
1
0
0
0
2
2
0
2
0
0
0
3
0
1
1
0
0
0
2
0
2
0
0
1
2
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
4
2
0
3
0
0
0
0
0
1
1
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
2
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
2
1
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
5
2
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
1
1
0
0
0
2
0
0
1
2
0
0
1
2
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
4
1
2
0
0
0
1
0
0
0
1
0
1
0
1
0
2
0
0
0
0
2
0
0
2
1
0
0
1
1
0
0
0
2
0
0
0
2
0
0
0
0
2
2
0
1
2
0
0
2
1
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
2
2
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
2
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
3
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
6
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
3
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
2
0
0
0
2
1
3
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
2
0
0
1
1
0
0
0
3
0
1
0
2
0
3
2
1
0
1
3
0
0
2
0
1
2
0
2
0
0
2
0
1
2
0
0
0
2
0
0
0
0
0
0
2
0
2
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
3
0
1
0
0
0
3
0
0
0
0
1
0
1
0
2
2
2
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
2
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
2
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
1
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
3
1
1
2
0
0
0
0
17
0
0
0
1
0
0
1
2
2
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
3
0
0
0
0
2
0
0
2
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
1
1
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
1
0
0
0
2
3
2
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
1
0
0
0
5
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
5
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
3
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
3
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
3
0
0
1
2
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
8
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
4
0
0
0
2
2
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
2
0
0
0
2
0
0
2
0
2
0
0
0
1
0
2
2
0
0
0
0
0
0
3
0
1
1
0
0
1
0
0
3
1
0
1
0
1
1
0
0
0
2
2
0
0
0
2
0
1
0
0
0
1
0
1
0
0
3
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
1
0
4
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
1
2
0
0
0
0
0
3
0
0
0
0
1
0
2
0
0
0
0
0
0
3
0
0
1
1
0
0
2
2
0
1
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
3
0
0
2
0
1
1
1
3
1
3
0
1
1
0
0
0
1
0
0
0
0
0
0
2
2
0
4
0
0
1
0
0
0
2
0
0
0
1
0
0
3
0
1
0
2
0
0
0
0
2
0
0
1
0
0
1
0
2
2
2
0
1
0
0
2
0
1
2
1
0
0
0
0
0
1
2
2
0
0
0
0
1
1
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
2
0
0
1
1
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
3
1
0
0
0
0
0
0
1
0
2
0
0
0
2
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
1
3
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
2
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
4
0
0
2
0
2
0
1
0
0
1
1
0
0
0
2
0
0
2
2
0
2
0
0
0
3
2
0
0
2
0
0
0
0
1
0
4
0
1
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
1
2
0
1
0
0
0
1
0
0
0
1
1
1
2
2
0
0
0
0
2
1
0
0
0
0
2
3
0
0
0
0
0
0
0
2
0
2
1
1
0
3
0
3
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
2
0
2
0
0
1
0
0
0
0
1
3
0
0
0
0
0
1
0
0
1
0
2
0
2
0
2
0
0
1
2
0
0
0
0
0
1
2
2
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
2
1
0
0
0
0
2
0
0
0
1
2
2
0
0
2
2
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
2
0
1
2
1
0
2
0
2
0
0
0
0
0
0
0
0
3
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
1
2
2
1
8
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
2
2
0
1
0
0
0
1
0
0
2
0
1
2
2
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
1
6
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
3
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
2
2
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
1
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
3
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
1
0
0
3
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
4
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
2
1
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
2
2
0
0
0
5
0
1
0
0
0
1
0
0
3
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
1
2
0
2
1
0
0
0
1
2
0
1
0
0
1
1
0
0
1
1
0
2
1
0
0
0
2
0
2
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
2
0
2
1
0
0
0
2
3
2
0
0
0
0
2
0
0
2
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
1
0
0
1
2
0
0
1
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
2
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
8
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
2
0
3
0
0
0
0
2
1
2
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
2
0
0
1
2
1
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
1
0
2
0
1
0
0
0
0
0
3
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
2
0
0
0
0
1
0
0
1
2
1
4
0
0
0
2
0
0
2
0
0
0
0
0
2
6
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
2
2
0
2
1
1
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
2
2
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
1
0
1
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
2
0
1
1
3
0
0
0
2
0
1
0
2
1
2
0
1
0
2
0
2
0
0
2
0
3
2
1
0
0
0
2
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
1
1
0
0
1
4
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
1
0
1
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
2
0
1
1
0
0
3
1
1
0
0
2
0
1
2
0
0
0
0
0
0
0
2
0
0
2
2
6
0
1
0
0
0
2
2
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
2
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
1
2
0
1
0
0
2
0
0
0
0
0
1
2
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
3
0
0
1
2
0
0
0
2
0
2
2
0
0
0
0
2
0
2
0
0
2
0
0
0
2
0
0
2
1
0
0
0
1
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
2
0
0
1
2
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
7
0
0
0
0
0
0
0
2
3
0
5
0
0
2
0
0
2
0
0
0
2
1
0
0
0
2
2
0
0
0
1
0
0
0
2
0
3
1
0
0
0
2
1
0
0
0
1
1
0
0
0
0
1
0
1
1
0
3
0
2
0
0
1
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
2
0
1
2
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
1
4
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
4
0
2
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
3
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
1
0
4
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
1
1
1
0
0
0
1
0
2
0
1
0
0
0
0
1
0
1
0
0
0
0
0
4
0
1
0
0
0
3
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
3
0
0
0
2
0
0
0
2
0
1
0
2
0
0
1
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
5
3
0
1
0
0
0
1
0
1
1
0
1
0
0
0
0
1
0
0
0
1
0
2
0
2
0
0
1
2
0
1
0
2
0
3
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
1
0
2
0
0
0
0
2
0
1
3
1
0
0
0
0
0
1
0
0
1
0
2
1
0
0
0
2
0
2
1
0
0
1
0
0
3
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
3
0
0
1
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
3
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
3
1
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
3
0
1
0
2
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
3
2
0
0
4
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
3
0
2
0
0
0
2
0
0
0
0
1
2
0
0
0
0
3
0
0
1
0
0
2
2
1
0
5
0
0
0
0
0
1
0
0
0
0
1
5
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
1
0
0
0
5
0
0
0
1
1
0
2
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
1
3
0
0
0
1
0
0
2
5
0
2
0
0
2
0
1
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
2
0
1
0
0
2
0
0
0
0
1
1
1
0
0
0
0
0
2
0
0
0
1
1
2
1
6
3
1
0
0
1
0
0
1
0
0
2
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
1
0
0
0
2
0
0
0
0
0
0
2
1
0
2
0
1
0
1
0
0
1
0
0
0
0
0
2
0
0
2
0
0
1
0
1
1
0
0
0
0
0
5
0
2
1
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
5
0
0
0
0
0
0
0
0
2
0
0
3
2
0
0
1
0
0
0
0
1
2
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
1
1
2
0
2
0
2
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
2
0
1
0
0
1
1
1
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
4
2
0
0
0
1
0
1
0
0
0
0
2
0
2
0
1
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
1
1
0
1
0
0
0
0
0
0
1
0
1
1
1
0
1
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
1
0
0
1
0
0
2
0
0
0
0
0
1
0
2
2
2
0
2
1
2
0
0
0
0
4
0
0
0
0
1
2
3
1
0
0
2
0
0
0
0
4
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
1
0
1
1
0
1
0
0
0
0
0
0
0
1
2
1
4
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
1
0
1
2
0
0
1
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
2
1
0
0
0
0
0
1
1
1
2
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
2
1
0
0
2
1
2
0
0
0
0
3
2
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
2
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
3
0
2
0
0
1
1
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
3
0
0
0
0
1
0
0
0
1
0
0
2
1
2
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
2
0
5
0
0
1
0
1
0
1
2
0
0
0
0
2
0
1
0
0
0
0
0
1
0
1
0
2
0
0
4
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
3
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
2
1
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
2
2
2
0
0
0
3
0
1
0
0
1
0
0
0
0
0
0
1
0
5
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
3
0
2
2
0
0
0
0
0
0
0
1
2
0
1
0
1
0
1
2
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
6
2
3
0
0
0
0
0
0
0
0
0
0
0
1
0
3
2
1
0
0
0
0
1
0
0
2
0
2
0
0
0
0
1
2
0
0
0
2
0
2
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
3
1
0
1
2
1
0
2
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
2
0
10
0
0
2
2
0
0
0
1
0
1
0
2
0
0
2
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
2
2
0
6
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
1
2
0
2
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
1
0
0
2
0
0
2
0
0
1
0
3
0
0
4
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
2
0
2
0
0
0
1
2
2
0
0
0
0
0
0
0
1
0
1
2
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
3
0
0
0
1
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
2
0
2
2
1
0
0
0
3
1
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
1
0
0
2
0
2
0
0
1
7
0
2
0
0
0
0
2
0
0
1
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
1
1
0
0
0
1
0
2
2
0
0
0
2
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
5
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
3
1
2
0
3
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
1
0
2
0
0
1
2
2
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
2
0
0
0
0
0
2
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
1
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
2
0
0
0
0
1
1
3
0
0
0
2
0
3
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
3
2
2
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
1
1
1
0
0
2
0
0
1
0
0
1
0
3
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
2
0
0
2
0
0
2
4
0
0
0
0
0
1
0
0
2
0
1
0
0
1
2
0
1
2
1
0
0
0
0
2
0
0
2
1
0
2
0
2
0
1
0
1
1
2
2
0
0
0
0
1
2
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
2
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
2
0
1
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
3
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
2
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
2
1
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
2
2
2
1
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
2
0
0
3
0
0
1
0
0
1
0
0
0
0
0
2
0
3
0
0
0
2
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
1
3
0
1
2
1
1
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
3
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
1
0
1
2
2
1
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
2
0
0
0
2
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
4
2
1
1
0
0
1
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
2
3
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
1
2
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
1
0
1
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
1
0
0
0
0
2
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
4
2
2
0
1
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
1
2
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
1
2
0
2
1
0
0
0
0
3
0
8
0
2
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
9
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
2
1
0
0
0
1
0
2
0
1
0
0
2
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
3
2
0
0
0
2
4
0
0
0
0
0
2
2
0
0
1
1
1
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
4
0
1
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
2
0
0
0
2
0
0
0
0
0
8
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
2
0
0
0
0
1
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
1
1
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
2
0
2
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
2
2
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
3
0
0
2
0
3
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
2
0
1
0
0
4
0
0
1
0
1
2
0
2
0
0
0
0
1
2
0
0
0
1
1
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
3
0
0
2
0
2
1
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
1
0
0
0
0
0
0
0
0
0
1
4
0
3
0
0
0
3
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
2
1
1
0
1
2
0
0
5
0
0
0
0
0
0
2
0
0
2
2
0
0
0
2
0
0
0
0
0
5
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
8
0
4
0
1
6
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
4
2
2
0
3
1
0
1
0
0
0
3
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
1
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
1
0
0
3
2
2
0
2
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
3
0
1
0
0
4
0
0
2
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
2
2
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
3
1
1
4
0
2
0
0
0
2
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
7
0
0
1
0
0
2
0
1
2
0
3
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
1
2
0
1
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
2
0
1
0
0
0
1
0
0
2
1
1
0
3
0
0
0
0
1
0
1
0
0
0
4
0
0
0
0
1
0
1
0
1
0
1
1
3
3
5
1
0
2
1
0
2
0
1
0
0
0
1
0
1
4
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
1
0
2
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
1
2
1
0
5
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
7
1
1
0
0
0
0
0
1
0
0
0
1
2
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
1
0
0
0
1
1
1
0
1
1
0
2
0
1
0
0
0
0
1
1
0
0
0
0
2
0
1
0
0
0
1
1
0
0
1
2
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
1
0
2
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
7
0
0
0
3
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
3
1
0
0
0
0
1
3
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
1
3
0
0
1
0
0
1
0
0
1
0
0
2
0
0
0
0
1
3
1
0
5
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
3
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
2
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
5
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
2
0
0
0
0
0
2
0
2
1
0
0
0
2
0
0
0
0
0
0
3
1
0
1
0
0
2
1
0
0
0
1
0
0
2
0
1
0
2
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
2
0
1
2
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
2
3
0
0
1
0
0
1
0
5
0
0
2
0
1
2
1
1
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
2
2
0
0
0
0
1
2
2
1
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
2
0
0
0
2
0
0
0
0
0
1
1
2
2
2
0
4
0
0
0
0
1
0
2
0
0
1
2
2
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
2
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
2
0
0
0
0
0
1
3
0
0
0
0
0
0
0
3
1
0
0
0
0
2
0
2
0
1
0
0
0
1
1
0
0
2
0
0
2
1
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
1
2
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
1
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
1
1
0
1
1
0
1
0
0
0
2
1
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
1
1
0
1
2
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
3
2
0
2
0
2
0
0
0
1
0
1
0
0
2
0
2
1
0
4
2
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
1
1
0
1
2
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
7
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
3
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
2
2
0
2
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
1
0
2
2
0
0
0
0
0
2
0
0
0
2
0
0
0
2
2
2
0
0
0
0
0
0
0
2
2
1
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
2
1
2
0
3
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
2
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
2
1
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
1
1
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
7
0
0
0
1
2
0
1
3
2
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
3
0
0
2
0
0
0
2
0
0
0
1
3
0
0
3
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
3
2
0
0
1
0
0
4
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
3
2
0
0
0
2
0
1
1
0
0
0
0
0
0
0
1
1
0
0
1
0
1
2
0
2
2
0
1
2
0
0
2
1
2
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
6
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
1
0
0
0
1
2
0
0
0
3
0
1
0
0
0
0
0
2
0
0
0
10
0
0
1
0
2
0
0
2
0
4
2
1
1
2
0
1
1
1
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
3
1
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
1
0
1
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
2
0
0
2
0
0
2
0
4
1
0
0
0
1
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
3
0
0
1
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
2
1
2
0
0
1
1
3
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
3
0
1
2
0
0
0
0
3
0
0
0
2
0
0
1
1
1
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
4
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
3
0
1
0
0
0
4
0
0
1
0
0
0
3
0
1
1
2
0
0
1
0
0
0
0
1
2
0
1
3
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
2
1
1
0
0
2
2
0
2
0
0
0
2
1
3
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
2
0
0
0
1
1
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
4
2
0
2
1
0
4
0
0
2
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
1
0
1
0
0
0
0
1
0
0
1
0
1
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
5
0
0
0
0
1
0
2
0
0
2
0
2
0
0
0
0
0
0
1
3
2
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
2
0
0
0
0
2
3
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
1
0
0
1
1
2
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
2
0
0
0
3
2
0
1
2
2
1
2
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
3
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
2
0
2
1
1
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
3
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
2
1
0
0
0
0
2
0
2
0
2
0
0
2
0
1
0
0
0
1
0
0
0
3
0
0
0
1
2
0
3
0
1
0
0
0
0
0
1
0
0
2
2
4
0
2
2
1
0
2
0
2
1
0
0
1
2
0
1
0
0
0
0
2
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
1
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
1
1
1
0
0
2
3
1
0
1
0
0
3
3
0
0
0
0
2
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
1
0
6
0
1
1
1
0
2
0
0
0
3
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
1
0
2
0
0
0
0
2
0
0
0
0
2
5
2
0
0
6
3
0
0
0
1
0
0
2
0
0
1
0
0
0
1
0
0
1
0
1
0
0
1
0
0
1
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
1
0
3
1
0
1
0
0
0
2
0
1
0
0
1
0
0
0
0
0
1
0
2
0
0
1
0
0
1
1
2
0
0
1
2
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
1
0
1
2
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
5
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
2
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
11
0
0
1
0
2
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
2
2
1
0
2
0
0
2
4
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
2
0
1
0
2
0
0
0
0
0
2
0
1
0
0
1
0
1
0
0
0
0
0
0
4
0
0
0
0
1
0
0
2
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
2
2
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
4
0
0
3
0
0
0
0
0
2
0
0
2
0
0
2
2
2
0
0
0
1
0
0
0
0
2
2
0
0
0
7
0
1
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
2
2
0
1
2
0
0
0
2
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
2
1
2
1
0
2
3
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
1
0
0
1
0
1
1
0
0
2
0
2
0
1
0
2
0
2
0
0
0
0
1
2
0
0
0
0
0
0
2
0
1
0
0
0
1
0
2
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
3
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
3
0
0
2
0
2
2
0
1
2
0
0
0
3
0
0
1
0
5
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
3
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
1
2
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
10
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
2
0
1
3
2
2
0
1
0
0
1
2
0
0
1
0
1
0
0
1
0
1
0
0
2
1
2
1
1
2
3
0
0
0
1
0
2
5
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
2
0
0
0
0
0
0
0
1
2
0
2
0
0
2
0
0
1
0
0
0
0
0
1
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
1
2
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
2
0
5
2
2
0
0
0
0
0
0
0
1
1
3
1
0
0
0
0
0
2
2
0
2
0
4
0
0
0
0
0
0
0
2
1
0
0
1
1
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
2
2
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
2
6
0
0
2
2
0
0
0
0
1
0
2
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
1
0
1
1
2
0
2
0
0
0
0
0
0
0
0
0
0
1
1
1
4
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
1
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
2
0
1
0
0
0
1
2
0
0
0
1
2
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
4
0
0
0
0
0
0
1
0
0
1
0
2
2
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
1
2
0
0
0
0
0
1
3
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
1
2
0
2
0
0
0
0
2
1
1
0
0
0
3
0
0
1
2
0
1
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
2
0
0
3
0
0
0
2
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
3
2
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
1
0
1
3
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
1
1
2
2
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
2
0
1
2
0
2
0
1
5
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
1
0
0
0
0
1
0
0
0
0
5
0
1
1
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
2
0
0
2
0
0
0
3
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
2
1
0
1
4
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
2
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
2
1
0
0
1
4
0
0
0
7
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
5
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
1
0
0
2
0
0
0
1
0
1
1
0
1
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
2
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
1
3
0
0
0
5
2
0
0
0
11
0
0
0
0
1
0
0
1
2
2
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
1
3
0
0
1
0
0
0
1
2
1
1
0
1
4
0
0
0
0
0
2
3
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
1
2
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
6
0
0
1
1
0
2
0
0
1
0
2
1
0
0
1
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
2
2
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
6
0
1
0
0
1
0
1
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
8
0
3
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
3
0
0
0
0
2
1
0
0
0
0
4
0
0
1
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
1
0
1
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
3
2
0
0
0
1
1
2
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
1
2
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
2
0
1
0
0
1
0
0
0
0
4
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
3
1
1
0
0
1
0
0
0
1
2
1
0
0
0
0
0
0
1
2
2
0
0
0
0
0
5
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
1
1
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
1
0
2
2
0
1
0
0
0
3
2
0
0
0
1
2
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
2
0
2
0
0
0
2
0
0
2
1
2
2
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
2
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
3
0
2
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
1
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
2
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
1
0
0
1
1
0
1
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
3
0
1
0
0
0
0
2
2
2
0
3
0
0
0
1
0
0
0
0
2
0
0
0
2
0
1
0
0
0
1
0
0
0
0
2
2
2
1
1
2
0
0
0
0
0
2
0
0
3
0
1
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
2
1
2
0
0
2
1
0
0
1
0
3
1
0
0
0
0
0
0
2
0
0
1
1
0
3
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
3
0
0
0
1
0
1
0
0
0
5
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
2
2
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
1
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
2
1
1
0
0
1
0
0
2
2
3
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
1
0
2
0
0
0
1
1
0
1
0
0
0
0
0
3
1
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
2
1
0
0
0
2
1
0
0
0
1
1
0
0
0
0
2
1
2
0
2
0
1
0
0
0
0
0
3
0
2
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
1
1
2
2
1
0
0
0
0
0
0
0
0
1
0
1
2
0
2
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
3
4
0
0
2
0
0
2
1
7
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
2
2
0
0
1
0
0
3
0
0
0
0
0
0
2
0
0
1
4
0
1
0
0
1
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
1
0
0
2
2
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
2
0
0
0
0
1
0
3
1
2
2
0
0
0
0
0
1
2
0
0
0
1
1
0
1
0
0
0
0
0
0
2
2
9
0
0
1
2
2
0
0
2
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
4
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
2
2
0
0
0
0
2
1
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
1
2
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
1
0
0
0
0
0
2
3
0
0
0
0
2
0
2
0
0
0
1
0
0
4
0
0
0
0
1
1
0
0
0
0
0
1
2
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
2
0
1
0
0
1
1
0
1
0
0
0
0
2
0
1
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
1
0
0
0
3
1
1
2
1
0
0
2
5
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
2
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
2
0
1
0
0
2
0
2
1
0
0
1
2
0
0
2
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
4
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
8
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
1
0
0
1
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
1
0
3
0
2
1
0
0
0
0
3
0
0
0
0
1
1
1
0
0
0
0
0
2
0
0
0
0
1
2
1
2
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
2
1
0
0
0
0
0
2
0
0
0
1
1
2
0
1
1
0
0
2
0
1
0
0
2
0
2
2
1
2
0
2
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
1
0
0
2
0
5
0
0
0
1
0
1
0
1
0
1
3
0
3
0
0
0
2
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
1
6
0
0
0
0
0
2
0
0
2
0
0
2
2
0
2
0
2
0
0
2
0
0
0
0
1
0
1
1
0
0
2
0
0
1
0
0
0
0
0
1
0
1
0
0
2
0
0
0
1
1
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
3
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
3
0
0
0
0
3
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
2
0
0
0
3
0
0
0
0
0
4
0
0
2
0
0
0
0
1
0
0
1
0
1
1
0
2
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
1
0
3
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
5
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
2
1
0
1
0
0
2
0
0
0
0
0
2
0
2
0
0
0
3
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
1
0
0
2
0
0
0
0
1
0
0
0
1
0
1
0
1
0
2
0
0
2
1
0
0
1
3
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
2
0
0
3
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
2
1
1
0
2
2
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
2
0
0
0
3
3
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
2
0
0
0
0
2
0
0
0
3
0
2
0
1
0
1
0
0
0
0
1
2
6
2
2
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
2
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
2
0
0
1
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
2
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
3
0
0
1
2
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
4
2
0
1
2
0
0
0
0
2
1
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
1
0
0
0
1
0
3
0
3
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
2
1
0
1
0
0
0
0
0
0
1
0
7
0
0
1
0
0
0
2
0
0
0
0
0
0
2
1
0
0
1
2
0
1
2
0
0
1
0
1
0
2
0
4
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
2
0
3
0
0
1
0
2
0
0
0
0
0
2
0
0
0
2
2
0
0
0
2
0
1
0
1
1
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
2
0
0
0
0
0
3
0
2
0
3
1
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
1
2
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
4
1
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
1
2
0
2
2
2
1
0
1
0
0
1
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
1
1
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
2
0
1
2
0
0
0
0
0
1
0
2
0
0
1
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
3
2
0
0
2
2
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
1
0
0
2
0
2
3
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
1
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
4
1
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
3
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
2
0
2
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
2
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
3
0
2
0
2
2
0
0
0
1
2
0
3
2
1
0
2
1
1
0
0
2
0
0
0
2
2
0
3
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
3
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
3
1
0
0
1
2
0
0
1
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
1
1
0
0
1
1
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
1
1
3
2
0
0
1
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
2
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
2
2
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
3
0
0
0
0
0
0
1
0
0
3
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
3
2
2
0
0
0
2
0
2
0
0
0
1
2
0
1
0
0
0
0
1
1
2
0
0
1
1
0
0
0
1
0
1
3
0
0
2
1
0
0
0
0
0
0
1
0
0
2
0
1
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
2
14
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
2
0
0
0
0
2
0
2
0
0
4
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
3
0
0
1
2
1
0
3
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
2
1
3
0
1
1
0
0
0
0
0
1
0
8
2
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
4
0
2
0
0
0
0
0
3
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
2
2
0
1
1
1
0
2
0
0
0
1
1
0
1
2
0
0
0
0
2
0
0
0
0
2
0
0
2
0
8
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
2
4
0
0
2
0
1
1
0
1
2
0
1
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
2
1
0
2
0
1
0
0
0
0
0
2
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
4
0
0
2
0
0
2
0
1
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
6
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
9
2
0
0
0
1
0
1
0
0
0
3
0
1
1
1
2
0
2
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
2
2
0
0
0
2
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
1
3
0
1
0
0
2
0
0
0
0
2
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
2
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
3
2
0
0
0
0
4
0
1
0
0
0
0
0
11
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
2
0
0
0
0
0
0
2
1
0
0
0
1
0
2
8
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
1
2
0
0
1
0
0
1
0
0
0
0
0
0
1
2
0
4
1
0
0
1
0
0
0
2
2
0
1
1
1
0
1
2
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
3
0
0
0
0
2
0
0
3
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
2
0
1
2
2
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
3
2
1
0
0
0
0
0
0
0
0
0
3
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
2
0
0
12
2
2
1
0
0
0
1
0
2
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
2
0
0
0
1
0
0
0
2
1
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
2
0
2
0
0
0
2
1
0
2
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
2
2
0
0
2
0
0
2
2
0
0
0
2
0
1
0
3
0
1
0
0
2
0
0
2
0
2
3
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
1
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
3
0
0
0
1
1
0
0
0
0
0
0
0
0
0
6
0
0
0
1
0
3
2
0
1
3
5
0
0
0
2
2
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
1
0
1
0
0
0
1
0
1
2
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
3
0
1
0
0
0
3
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
3
0
2
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
1
0
2
0
0
0
0
1
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
1
0
1
0
0
0
0
1
3
0
0
0
0
0
1
1
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
9
0
2
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
2
0
2
1
2
1
1
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
2
1
1
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
1
0
1
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
4
2
0
0
1
0
0
2
1
0
2
2
0
0
0
0
0
1
2
4
0
0
1
0
2
3
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
2
0
1
0
0
0
0
1
0
2
0
2
2
0
0
3
0
0
0
0
0
3
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
3
1
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
3
0
0
2
0
0
1
0
2
1
0
0
2
0
0
1
1
0
1
0
2
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
1
0
0
1
1
0
1
0
4
0
0
0
0
1
0
0
0
1
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
2
0
0
0
0
0
1
0
0
0
2
0
2
0
1
0
0
0
0
0
0
1
2
0
0
0
2
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
2
0
2
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
3
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
2
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
2
2
0
0
0
0
1
1
0
1
0
0
0
2
1
0
0
1
0
0
0
1
0
2
0
0
0
0
2
0
0
4
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
1
0
0
0
1
0
0
1
2
1
0
2
0
3
0
0
0
0
2
2
0
0
0
0
0
2
1
0
7
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
2
0
1
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
2
0
1
0
0
0
0
1
0
0
0
0
0
5
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
2
0
1
2
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
1
2
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
6
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
1
0
1
0
1
2
4
2
0
1
1
0
0
2
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
1
0
2
1
1
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
2
1
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
2
0
0
1
2
5
0
0
0
0
2
0
2
0
3
2
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
2
1
0
0
1
1
0
0
0
0
0
1
2
0
0
1
0
0
1
2
0
1
4
0
2
0
0
3
0
0
0
0
0
6
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
1
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
1
0
1
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
2
2
1
0
2
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
1
2
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
2
1
0
0
0
0
1
0
1
0
2
0
0
0
1
0
0
0
2
0
0
0
0
1
0
2
0
2
0
2
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
2
0
0
2
0
0
1
0
0
0
0
2
0
3
2
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
1
1
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
1
3
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
4
2
0
0
0
0
0
2
0
2
0
2
2
0
0
0
0
0
0
0
0
0
1
4
0
1
1
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
2
0
3
0
1
1
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
3
0
2
2
0
2
1
0
2
0
1
0
0
1
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
3
2
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
2
0
0
1
2
0
0
2
0
0
1
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
6
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
3
0
2
0
3
1
0
0
0
0
1
0
0
2
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
1
0
2
0
2
1
0
0
2
1
0
2
1
0
2
2
0
2
0
0
2
1
0
0
3
0
0
0
0
0
0
1
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
3
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
1
0
3
0
0
0
2
2
0
0
1
0
1
2
1
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
2
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
1
7
0
0
2
2
2
0
4
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
1
0
2
1
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
2
0
0
1
0
0
2
0
0
0
1
0
2
0
0
1
0
0
2
2
0
2
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
1
0
0
0
0
0
3
0
0
0
2
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
1
2
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
1
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
1
0
0
2
0
1
1
0
1
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
2
2
2
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
2
0
1
0
0
1
0
0
0
2
2
0
0
2
0
2
0
0
2
1
0
0
1
0
2
1
0
0
0
0
0
0
0
3
1
0
0
1
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
2
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
2
0
0
2
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
1
0
2
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
1
0
1
0
1
0
2
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
1
2
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
1
0
1
0
1
2
3
0
0
0
0
0
2
1
0
0
3
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
2
4
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
3
0
2
0
0
0
1
0
4
0
1
3
0
2
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
4
1
1
0
0
0
1
0
0
1
4
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
2
5
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
2
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
2
0
0
0
0
3
0
0
0
0
0
1
2
0
2
0
1
0
0
0
0
0
0
0
2
4
0
0
0
0
2
2
4
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
1
2
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
2
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
2
0
1
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
8
1
0
2
1
0
0
1
2
2
0
1
2
0
0
0
0
0
1
1
1
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
4
0
2
0
0
0
0
2
2
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
3
0
0
0
0
0
0
0
1
0
5
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
3
2
2
0
1
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
1
1
0
1
0
2
0
0
0
0
0
0
0
0
5
1
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
2
2
1
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
1
1
0
0
0
0
0
5
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
2
2
2
0
0
2
0
0
0
0
2
0
7
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
1
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
1
0
1
1
0
0
0
0
0
0
0
0
8
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
7
3
0
0
0
0
1
2
2
2
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
1
2
0
0
1
0
2
0
0
1
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
5
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
1
2
0
2
0
0
0
2
0
3
0
0
0
0
1
0
0
1
1
0
0
0
3
0
0
0
1
0
0
0
0
3
0
0
0
0
1
0
1
0
0
0
2
0
0
3
0
0
0
0
3
0
0
2
1
0
0
0
2
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
2
0
1
0
0
2
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
5
0
0
0
0
0
0
0
0
1
1
1
2
0
2
0
0
2
0
1
0
0
2
0
2
2
1
0
0
0
0
3
0
0
1
0
1
0
2
0
0
0
2
2
0
0
2
0
1
0
0
1
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
4
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
1
1
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
1
1
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
2
3
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
3
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
2
0
0
2
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
1
0
0
0
2
2
0
2
0
0
0
0
2
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
2
0
1
0
1
0
0
2
0
1
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
1
1
1
0
0
2
1
0
1
2
0
4
1
2
0
1
2
1
2
0
0
0
3
0
0
5
0
0
2
0
1
1
0
2
1
3
2
0
1
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
1
1
0
0
0
3
2
0
0
0
0
2
0
0
2
3
0
1
1
0
1
0
2
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
1
0
1
2
2
1
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
2
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
3
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
2
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
3
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
2
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
3
2
0
0
0
0
1
0
0
1
0
0
0
0
0
4
1
0
2
0
0
0
0
1
2
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
4
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
1
1
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
1
0
3
0
0
1
0
0
2
0
0
0
0
3
0
0
0
0
2
0
0
2
0
2
0
0
3
2
2
0
0
2
0
3
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
3
2
1
2
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
3
1
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
3
1
4
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
1
2
0
0
2
0
2
0
0
2
0
0
1
0
0
0
2
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
3
0
1
0
0
2
2
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
2
1
0
2
0
0
0
0
1
1
1
0
1
2
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
1
2
0
0
0
0
0
1
1
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
2
1
0
0
0
0
2
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
2
2
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
2
0
2
0
0
1
3
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
1
6
1
0
1
1
0
2
1
0
0
2
0
0
0
0
1
0
2
1
0
0
1
0
1
0
0
0
1
1
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
3
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
2
0
3
0
0
0
0
0
1
0
0
1
2
2
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
4
2
2
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
1
0
5
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
1
2
2
0
1
0
0
2
0
0
0
0
0
0
0
3
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
6
0
0
0
0
1
1
0
1
0
1
2
2
0
1
1
1
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
1
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
2
2
0
1
0
2
1
0
0
3
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
4
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
1
0
1
0
0
2
0
1
0
0
0
1
0
0
0
1
0
0
2
0
0
0
1
0
0
0
2
3
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
3
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
2
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
6
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
2
1
0
2
0
0
1
0
2
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
1
0
0
4
0
0
0
0
0
0
2
0
0
0
0
0
0
1
4
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
10
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
2
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
1
2
0
3
0
1
0
1
2
0
0
1
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
2
0
2
0
0
0
0
0
0
0
2
2
0
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
2
1
2
0
0
0
1
2
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
3
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
1
2
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
1
0
2
0
1
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
3
1
1
0
0
0
0
1
1
0
0
0
0
2
1
0
0
0
0
0
0
0
1
2
2
0
0
2
0
0
0
0
0
2
0
0
2
5
0
2
3
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
2
1
0
0
0
0
0
1
0
6
0
1
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
2
2
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
3
2
0
0
0
1
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
1
0
1
0
0
0
4
0
2
0
1
1
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
1
3
0
0
0
0
0
2
0
0
0
0
0
4
0
0
2
0
0
0
6
2
1
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
1
0
0
0
3
0
0
0
2
0
2
1
3
0
3
0
0
2
2
4
1
2
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
1
2
0
1
0
1
0
0
0
1
0
0
0
0
2
1
1
0
0
0
0
0
0
0
10
0
0
2
0
2
2
2
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
3
0
1
0
3
0
0
0
0
0
0
0
1
0
2
2
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
1
1
0
2
0
1
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
3
2
0
1
0
2
0
2
4
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
4
0
1
2
0
0
0
0
0
1
2
0
0
0
0
0
2
2
0
0
0
0
0
0
1
1
0
0
0
0
2
1
0
0
1
0
0
0
1
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
3
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
4
0
1
2
2
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
1
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
2
1
1
0
0
0
6
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
3
0
2
0
0
2
0
0
2
0
0
0
0
1
0
1
0
0
1
0
0
2
0
0
0
1
2
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
2
2
0
2
1
0
2
2
1
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
1
0
1
0
1
0
2
0
0
0
1
0
1
0
1
0
1
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
2
0
1
0
2
3
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
1
5
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
6
8
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
2
3
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
2
0
0
0
0
2
0
2
1
0
0
2
1
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
2
0
0
0
2
0
0
3
1
0
1
0
0
0
2
0
2
0
0
0
2
0
0
1
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
2
0
2
0
1
0
3
0
2
0
0
3
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
2
0
0
0
0
2
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
2
1
0
0
3
1
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
3
1
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
3
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
2
0
0
12
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
2
2
0
2
0
0
0
0
0
2
0
0
0
0
2
1
1
2
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
2
0
0
0
1
2
0
0
0
0
1
1
0
1
0
0
1
0
1
1
1
0
0
0
0
2
0
0
2
0
2
1
0
2
1
0
0
0
0
2
0
0
3
0
0
6
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
3
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
1
0
3
1
0
1
0
0
1
1
1
1
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
1
3
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
3
0
0
5
2
2
2
6
0
0
0
0
0
3
0
0
0
4
2
2
2
2
0
1
2
0
0
1
2
0
2
0
0
1
0
2
0
0
0
1
0
0
0
0
0
1
2
1
0
0
0
2
0
2
0
0
3
0
0
0
0
3
0
0
0
0
0
2
0
1
0
4
1
0
3
2
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
2
0
2
0
0
2
0
0
0
1
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
1
0
2
0
2
0
2
0
3
0
0
0
2
0
0
0
2
0
1
2
0
0
0
3
14
0
0
3
2
0
2
0
0
2
2
1
0
0
1
0
1
0
0
2
0
2
0
0
2
0
1
0
0
0
0
4
1
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
2
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
3
2
0
1
0
2
0
0
0
1
0
0
0
2
1
0
3
0
0
0
0
1
2
1
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
2
0
0
1
2
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
3
0
1
0
1
0
1
1
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
2
1
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
3
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
2
1
0
0
0
0
3
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
1
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
2
0
2
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
1
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
2
3
0
1
0
0
2
0
1
0
5
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
5
0
0
1
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
2
1
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
6
1
3
1
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
3
1
0
0
0
0
0
6
0
0
0
1
1
0
0
0
0
1
0
2
0
0
0
3
0
0
0
0
0
0
4
1
2
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
4
1
0
0
2
1
0
0
1
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
7
0
0
0
2
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
1
0
0
0
1
0
2
0
0
2
0
0
0
2
1
0
0
2
2
2
0
1
0
0
0
1
0
0
2
0
0
0
0
0
3
1
0
0
0
2
0
2
0
2
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
1
2
0
0
0
1
0
0
0
0
2
2
1
0
0
0
3
3
1
1
1
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
1
2
0
1
0
2
0
1
0
0
2
0
0
0
0
2
0
0
3
0
0
0
2
2
1
0
0
2
0
0
0
0
2
0
3
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
2
2
1
0
0
0
1
1
3
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
1
2
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
2
2
0
0
0
0
0
0
1
0
0
0
0
4
1
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
2
0
2
1
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
3
0
1
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
2
0
2
2
1
0
0
0
2
0
0
0
2
2
0
0
0
1
0
0
0
1
3
0
0
0
1
0
0
0
1
1
1
0
1
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
3
1
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
1
0
3
0
0
1
2
0
0
0
0
0
0
0
1
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
2
0
0
0
0
0
3
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
2
0
1
0
0
0
2
0
0
0
1
7
2
0
0
0
0
0
2
0
0
0
3
1
2
0
0
0
1
2
2
0
2
0
3
2
0
0
0
0
1
0
9
0
0
0
0
1
1
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
4
0
0
1
2
0
0
3
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
2
2
0
0
0
1
0
0
0
2
0
0
0
12
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
1
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
2
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
1
0
2
0
0
0
0
0
0
1
0
3
0
0
1
0
0
0
0
0
2
0
2
3
0
0
0
1
0
1
0
1
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
1
1
0
0
0
0
1
0
0
1
0
1
2
2
0
0
3
1
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
5
2
0
0
0
3
0
0
0
1
1
2
0
1
3
0
0
0
1
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
1
0
0
0
0
3
4
0
0
0
1
0
2
0
0
2
3
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
1
0
1
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
4
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
1
0
2
0
0
0
1
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
1
2
0
4
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
2
1
1
0
0
7
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
1
6
2
0
2
1
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
2
1
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
1
0
0
1
2
2
0
0
2
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
3
0
2
1
1
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
2
0
3
0
0
0
1
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
3
0
1
0
1
1
0
0
0
0
0
1
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
1
0
0
1
0
0
0
1
2
0
3
0
0
0
0
0
0
0
0
2
0
0
0
1
0
4
2
0
1
0
0
0
0
3
0
1
0
0
0
1
1
1
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
6
0
2
0
1
2
0
0
0
1
3
0
0
0
0
1
0
0
0
0
0
0
2
1
0
1
2
0
0
1
0
0
0
0
0
0
0
0
1
1
0
6
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
8
0
0
0
2
0
0
3
0
1
0
0
0
2
2
0
0
0
0
0
2
3
2
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
2
19
2
3
2
0
0
0
0
1
0
0
0
2
1
0
0
3
0
0
2
0
0
0
2
0
0
0
0
0
1
2
1
2
0
0
2
0
1
0
0
0
2
2
0
3
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
3
1
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
3
0
2
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
2
1
0
0
0
0
0
1
2
0
0
1
0
2
0
1
2
2
0
2
0
0
0
0
2
0
0
1
1
0
4
0
0
1
0
2
1
0
0
1
0
1
0
2
0
0
0
2
0
2
0
2
1
0
0
1
0
0
1
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
2
0
0
0
1
2
6
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
1
1
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
2
2
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
3
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
2
0
0
0
0
2
0
1
3
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
2
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
1
1
0
0
0
0
0
0
0
0
2
3
0
0
0
0
2
2
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
1
0
0
0
2
1
0
1
3
0
0
0
2
0
1
0
2
2
0
0
0
0
0
1
0
2
2
0
3
0
0
0
1
0
1
2
0
1
2
0
0
0
0
0
0
1
4
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
2
0
0
1
2
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
2
0
3
0
0
0
1
0
0
1
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
2
3
0
0
0
0
0
0
2
0
0
0
2
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
3
0
0
6
0
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
2
0
0
0
2
1
2
0
0
0
0
0
1
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
3
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
1
0
4
0
0
0
2
0
0
1
0
2
1
0
2
0
3
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
3
1
0
2
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
2
2
2
0
0
1
0
6
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
2
0
0
1
0
0
1
0
0
0
0
0
2
1
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
1
11
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
1
1
0
0
0
2
2
0
2
0
0
1
0
0
1
1
0
1
0
0
0
0
2
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
1
2
1
0
0
1
0
0
0
0
1
2
0
2
1
0
0
0
0
1
1
0
1
0
0
0
0
1
1
1
0
1
0
1
0
1
2
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
2
2
2
0
0
1
0
1
0
0
0
2
0
0
0
2
0
0
1
2
0
0
0
3
0
0
0
2
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
2
0
2
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
4
2
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
2
0
0
0
3
0
1
1
0
0
0
0
2
3
0
0
0
0
2
0
0
1
0
1
0
3
0
1
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
3
4
0
1
0
2
0
0
1
3
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
2
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
2
1
0
0
1
0
2
0
0
0
1
1
0
0
0
2
2
0
0
0
2
1
0
1
0
0
0
0
0
0
0
2
1
0
2
0
1
2
0
0
0
2
2
1
0
0
0
0
0
2
0
0
3
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
3
0
0
0
1
0
0
1
1
0
0
1
0
0
2
2
0
0
1
0
0
3
0
2
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
1
0
2
0
3
0
0
0
0
2
4
0
0
0
0
0
0
0
2
0
0
0
0
4
0
0
0
0
1
1
0
1
1
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
2
0
0
0
4
2
0
2
0
1
1
0
0
1
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
3
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
1
1
0
0
0
0
0
1
2
0
0
1
3
2
2
1
0
1
0
0
2
0
0
0
2
2
0
0
0
1
0
0
0
0
1
0
0
2
1
0
0
1
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
3
0
0
0
0
0
0
1
3
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
1
0
0
0
2
1
0
0
1
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
2
0
0
0
1
0
1
1
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
1
2
1
2
1
1
0
0
0
0
0
0
1
0
1
0
2
0
0
1
0
0
6
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
2
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
2
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
2
0
0
0
0
1
0
0
0
1
0
1
0
2
0
3
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
2
2
1
0
0
0
2
0
0
0
2
1
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
3
1
0
0
0
0
1
0
0
2
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
1
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
2
1
2
0
1
1
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
3
1
0
0
2
5
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
2
1
2
0
0
0
0
0
3
0
0
1
0
0
0
0
0
2
1
2
0
0
2
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
5
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
2
2
0
0
2
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
1
2
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
2
0
2
0
0
0
0
1
1
0
2
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
1
0
0
0
1
0
1
1
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
1
0
2
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
1
0
2
1
0
0
3
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
2
1
2
1
0
2
0
0
0
1
2
0
0
2
0
2
0
0
1
0
0
0
2
2
0
0
1
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
1
0
0
2
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
1
1
1
2
1
0
0
2
1
2
3
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
3
0
0
0
0
0
0
2
1
1
1
2
1
0
1
0
0
0
3
0
0
1
0
2
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
2
2
1
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
2
5
0
0
0
0
2
0
0
0
2
0
0
0
3
0
0
2
0
0
1
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
2
1
0
0
0
0
1
2
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
1
0
0
1
1
0
1
0
0
2
0
0
1
0
0
0
2
0
2
2
2
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
2
2
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
1
3
0
0
0
1
0
0
0
0
4
1
2
0
0
0
1
0
0
0
0
2
0
0
0
0
1
1
2
0
0
0
0
0
0
1
3
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
5
0
0
0
0
0
0
2
0
1
0
1
0
0
3
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
1
0
0
0
0
0
1
2
0
1
0
0
1
0
2
0
0
2
2
0
0
1
0
0
0
0
0
3
0
0
2
0
0
0
1
0
1
2
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
3
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
1
2
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
1
0
2
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
1
0
0
0
0
0
3
1
0
0
2
3
0
0
1
0
0
0
2
1
0
0
2
1
0
0
0
0
0
2
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
2
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
1
0
0
0
0
2
0
3
0
0
2
0
3
2
0
0
1
0
0
1
0
0
1
0
0
1
1
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
2
0
0
1
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
4
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
3
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
3
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
2
3
0
0
0
0
1
0
0
1
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
1
0
0
0
2
3
0
2
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
2
3
1
2
1
0
2
1
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
3
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
2
1
3
0
0
2
2
2
0
0
0
1
1
0
0
1
0
0
1
2
2
0
0
0
0
3
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
4
1
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
1
1
3
0
0
0
0
0
3
1
0
0
0
0
0
0
0
1
0
2
0
0
1
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
1
0
0
1
0
0
0
2
0
1
2
0
0
0
2
2
0
2
1
0
0
0
1
0
2
0
0
1
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
3
0
3
0
0
0
7
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
2
0
0
0
1
0
0
2
0
1
0
0
1
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
1
0
6
0
0
2
0
1
0
0
0
1
0
0
0
0
0
2
0
2
0
0
1
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
2
0
0
0
1
0
0
1
1
0
0
0
2
0
1
0
1
2
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
7
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
1
7
0
0
1
0
3
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
2
0
1
1
0
0
2
0
0
3
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
1
0
0
0
2
2
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
2
0
0
1
0
0
1
1
0
0
0
0
0
2
0
2
0
0
1
1
0
0
0
0
0
2
7
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
2
1
0
0
2
2
0
0
0
0
1
0
1
1
2
0
1
3
0
0
1
1
0
0
0
0
0
0
0
0
2
0
1
2
3
0
0
5
0
0
1
0
0
1
0
0
0
3
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
1
4
1
1
0
0
1
1
2
0
0
0
0
0
0
0
0
2
0
5
3
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
1
2
0
0
1
0
0
0
3
0
2
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
2
0
2
2
0
0
1
0
0
2
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
1
0
0
2
2
0
0
0
0
0
1
0
0
1
2
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
2
0
0
2
0
0
0
2
6
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
8
0
1
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
6
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
1
0
0
2
1
0
0
0
0
1
0
0
0
2
0
1
0
0
0
2
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
2
2
0
4
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
2
1
0
0
0
0
1
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
1
2
0
1
0
2
0
2
2
0
0
0
1
0
0
0
0
2
0
1
0
0
2
0
2
0
0
0
0
2
2
0
1
0
0
0
2
0
0
0
1
1
0
0
0
2
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
3
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
3
0
0
0
0
1
0
0
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
2
0
1
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
2
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
2
0
0
1
0
2
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
2
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
2
1
0
2
0
1
0
0
0
0
0
0
4
0
1
0
0
2
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
1
0
0
2
0
0
0
0
0
1
1
2
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
1
0
1
1
0
0
2
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
2
0
0
0
0
0
1
0
0
4
2
0
0
1
5
1
0
3
2
2
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
5
0
0
8
0
0
1
0
1
0
0
2
0
0
0
0
1
0
0
2
0
2
2
0
1
0
0
0
1
1
2
0
0
1
0
0
1
0
1
0
2
2
0
2
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
1
0
2
0
2
2
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
1
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
3
0
0
0
0
0
0
0
0
2
0
0
0
0
3
1
0
1
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
1
0
1
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
1
1
0
0
0
2
1
0
0
0
0
0
0
1
0
1
0
0
0
2
2
1
0
0
0
2
1
0
0
0
0
0
1
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
1
0
2
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
2
2
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
4
0
1
2
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
3
0
2
2
1
0
0
0
1
0
1
2
0
2
2
0
2
0
0
0
0
0
1
1
2
0
2
0
0
0
0
0
3
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
1
0
2
0
2
1
0
0
0
0
0
1
0
15
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
1
0
0
0
0
0
0
1
1
2
0
1
0
0
1
0
2
1
0
0
0
0
0
1
0
0
2
0
2
0
0
0
1
0
1
1
2
0
1
0
0
2
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
1
0
0
0
0
0
4
0
0
1
0
0
1
0
1
0
1
0
1
0
0
1
1
0
0
0
0
2
3
2
1
0
0
0
0
0
2
1
0
0
4
3
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
1
0
0
2
1
2
0
0
4
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
1
0
2
0
0
0
2
1
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
3
0
0
1
0
1
0
0
0
1
0
0
0
1
3
0
0
0
2
1
0
0
0
1
0
0
1
1
0
1
0
0
0
1
0
0
0
0
1
1
1
1
0
0
1
0
1
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
2
0
0
0
1
0
17
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
4
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
3
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
1
1
1
0
0
0
0
2
0
1
1
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
2
1
0
2
0
0
0
0
2
1
0
6
2
0
0
0
0
0
0
3
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
2
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
2
0
0
2
0
0
0
0
1
1
0
1
0
0
1
1
0
3
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
1
0
0
5
1
0
0
0
0
2
0
0
1
0
0
0
0
2
3
0
2
2
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
2
1
2
0
0
3
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
3
1
0
1
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
3
0
0
0
0
2
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
4
0
0
2
1
0
0
0
0
1
0
0
0
1
0
2
1
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
2
5
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
4
1
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
2
0
1
2
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
2
3
0
2
0
0
1
0
1
0
0
2
0
1
1
1
1
0
0
0
0
0
0
0
2
0
0
0
0
4
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
1
1
0
0
0
0
0
2
2
0
1
3
0
0
2
2
0
0
2
0
2
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
1
0
0
0
0
3
0
0
1
0
0
1
0
0
0
2
0
0
5
0
0
1
0
2
1
0
0
0
0
0
0
0
2
0
4
0
0
0
2
0
0
0
1
0
1
0
0
2
0
0
2
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
1
0
1
2
0
0
1
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
2
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
2
1
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
3
1
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
2
0
1
0
1
0
0
0
0
2
1
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
2
0
0
0
2
2
0
0
0
0
1
0
0
2
1
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
3
4
0
0
1
2
0
0
0
0
0
0
2
0
0
2
0
1
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
1
2
2
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
3
2
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
1
2
2
0
1
0
0
1
0
0
0
0
0
0
1
0
2
0
0
1
1
0
0
0
0
0
1
6
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
2
2
0
0
0
1
1
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
2
2
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
2
2
2
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
7
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
1
2
0
0
0
3
0
0
0
0
2
2
0
0
0
0
2
0
0
1
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
2
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
2
2
1
0
0
0
0
0
3
0
0
0
0
0
1
0
0
1
1
0
1
0
1
2
1
2
2
0
0
0
0
0
0
0
1
0
1
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
3
1
0
0
2
1
2
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
2
1
0
0
0
0
0
2
0
0
3
0
2
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
1
2
2
0
1
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
2
2
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
2
3
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
1
2
2
0
0
0
0
0
2
0
0
0
0
0
0
1
1
1
3
2
0
0
0
5
0
0
0
0
0
5
0
0
2
1
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
3
0
1
1
2
0
0
0
2
0
2
2
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
2
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
1
2
0
1
0
1
0
0
0
0
2
1
2
0
2
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
1
3
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
1
2
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
3
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
2
1
0
0
1
1
1
2
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
1
0
1
0
1
3
0
0
1
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
2
0
0
1
0
0
2
0
0
0
0
1
2
0
0
2
1
1
0
2
0
2
1
0
0
0
0
0
0
0
0
3
1
1
2
1
0
0
0
0
1
0
2
0
0
0
0
1
2
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
1
1
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
2
1
0
0
0
4
0
0
2
2
0
0
0
2
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
2
0
2
0
0
0
0
2
0
1
0
3
0
0
0
3
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
2
1
0
0
2
2
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
1
1
0
2
0
4
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
1
1
0
2
1
1
2
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
3
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
2
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
1
0
0
0
0
2
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
1
0
0
3
0
1
2
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
1
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
1
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
2
1
1
0
4
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
3
0
1
0
0
0
1
0
0
0
2
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
2
1
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
7
0
0
1
1
1
0
0
0
0
0
0
0
1
4
0
0
2
4
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
2
0
0
1
0
0
3
1
3
2
1
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
1
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
3
0
0
1
2
1
0
0
0
7
3
1
0
0
0
0
0
0
0
1
0
3
0
0
0
0
2
0
1
1
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
1
0
1
0
0
0
0
0
2
0
0
3
0
0
0
0
0
2
0
1
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
3
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
4
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
1
0
2
0
0
2
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
2
0
1
0
1
0
1
0
2
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
2
1
3
5
0
0
2
2
0
1
3
0
1
1
1
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
2
0
2
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
2
1
1
0
0
0
1
0
0
0
0
0
4
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
6
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
1
1
0
0
0
0
0
2
0
0
0
0
0
2
2
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
1
1
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
2
3
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
2
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
4
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
2
3
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
2
0
0
0
0
1
0
0
0
1
2
1
0
0
0
0
0
0
2
1
1
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
1
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
2
0
0
0
0
0
1
0
0
2
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
3
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
5
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
1
1
3
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
1
2
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
2
2
0
0
0
0
2
0
0
0
0
1
1
0
2
0
0
0
0
0
0
1
3
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
2
2
0
2
0
0
3
1
5
0
2
2
3
1
2
1
2
0
1
2
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
1
2
0
1
1
0
0
0
0
2
3
1
0
1
0
0
0
3
0
0
0
2
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
2
0
0
1
2
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
8
0
0
0
2
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
1
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
2
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
2
0
0
3
2
0
0
0
1
0
2
0
0
1
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
1
2
1
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
1
0
2
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
2
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
3
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
1
0
0
0
1
0
1
3
3
0
2
2
1
0
0
0
0
0
1
0
0
2
2
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
3
1
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
1
3
0
2
0
0
0
2
0
0
2
0
0
0
0
1
0
0
2
1
0
0
0
2
0
0
1
1
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
4
0
2
0
0
0
0
2
0
2
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
2
0
0
0
0
2
2
0
0
0
1
3
0
0
0
0
0
2
0
0
0
0
3
0
2
0
1
2
0
0
0
0
1
0
0
0
2
0
0
0
2
1
1
0
0
0
0
0
2
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
2
1
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
1
1
1
2
1
0
0
2
0
0
1
0
0
4
3
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
3
3
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
3
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
4
1
1
0
0
0
0
0
0
0
1
0
0
7
2
0
0
0
1
2
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
3
1
1
1
0
0
0
0
0
0
0
1
0
0
2
1
2
0
0
0
0
0
1
0
0
2
2
0
0
0
0
1
2
2
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
2
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
3
2
0
0
1
0
1
1
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
2
0
0
0
0
1
0
1
0
0
0
2
0
1
1
0
0
1
1
0
2
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
2
0
0
0
0
1
4
0
0
0
0
2
0
7
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
3
0
5
2
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
2
2
0
0
2
1
2
3
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
2
0
0
1
0
2
1
0
0
0
0
0
1
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
2
1
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
3
0
0
0
0
1
1
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
2
1
2
0
3
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
4
0
0
1
0
0
0
1
0
0
3
3
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
1
0
2
2
0
1
3
2
0
1
0
0
1
0
2
0
1
0
0
0
0
2
0
1
2
2
0
0
4
0
0
0
1
2
2
0
0
2
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
2
0
0
9
1
0
0
0
0
0
0
0
0
0
1
0
1
3
0
0
0
0
2
0
1
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
3
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
4
0
3
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
21
0
1
0
1
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
1
0
0
0
2
0
2
2
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
1
3
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
4
1
1
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
2
2
0
1
0
0
0
0
0
1
0
1
2
0
1
0
0
0
1
3
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
2
2
0
0
2
1
0
0
0
1
1
0
0
0
0
1
0
2
0
0
0
1
2
0
2
1
1
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
3
0
1
2
0
0
1
0
0
2
2
2
1
7
0
3
0
2
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
2
0
0
1
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
3
0
0
0
3
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
2
4
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
2
0
0
1
0
0
0
0
2
0
1
2
0
0
0
1
0
2
0
1
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
1
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
3
2
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
1
0
0
0
0
1
0
0
0
1
0
1
0
0
1
2
2
0
2
1
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
2
0
0
2
0
0
4
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
3
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
3
1
0
2
0
0
2
2
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
3
2
0
7
0
1
0
0
1
0
5
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
2
3
0
1
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
2
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
1
0
1
1
1
1
0
0
0
0
0
0
11
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
2
0
0
0
8
0
0
0
0
0
0
1
3
0
0
0
2
1
0
0
0
0
2
0
2
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
3
2
0
1
0
0
0
0
1
0
0
1
1
2
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
1
0
1
3
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
2
0
1
2
2
0
0
0
1
2
0
0
0
3
1
0
0
1
1
2
0
1
0
0
0
0
0
0
0
0
5
0
0
1
0
2
7
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
2
2
0
0
2
0
0
0
0
0
3
0
0
0
0
2
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
1
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
4
0
2
0
0
2
0
3
0
0
0
0
0
1
0
0
1
0
0
2
2
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
1
0
1
0
0
0
1
3
0
1
2
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
2
0
1
0
3
0
0
0
0
1
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
4
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
2
1
0
1
1
0
2
0
0
1
0
0
0
0
1
2
0
0
0
0
2
3
0
0
0
0
0
0
0
1
0
1
1
0
2
0
0
1
0
0
0
1
0
1
0
0
2
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
9
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
1
0
0
3
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
2
0
2
0
2
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
1
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
1
0
2
0
0
1
2
0
0
0
0
0
1
1
0
0
1
1
2
1
0
4
0
0
0
1
0
1
0
0
0
0
0
0
5
0
0
0
0
0
0
4
0
0
2
0
0
0
0
0
1
0
1
5
0
0
0
4
0
0
0
2
0
0
2
0
0
0
0
0
0
3
2
1
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
6
0
1
0
2
0
4
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
5
0
0
0
1
0
0
0
2
3
1
0
0
2
0
0
3
1
0
2
2
0
0
1
0
2
0
2
0
0
3
0
2
0
0
0
0
2
0
0
1
2
0
1
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
2
1
0
4
0
1
0
1
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
1
1
0
0
2
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
2
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
3
0
1
0
1
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
2
0
0
0
0
0
1
2
0
0
1
0
0
0
1
1
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
2
0
2
1
3
0
1
0
0
0
0
1
0
2
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
1
0
0
1
0
0
1
0
0
0
2
0
0
1
0
2
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
1
0
4
0
1
0
0
0
1
1
2
0
0
0
0
1
0
0
0
0
0
1
0
2
1
1
0
0
0
0
0
2
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
1
1
1
0
1
1
0
2
0
0
1
0
0
0
2
0
2
2
0
0
3
0
2
2
2
2
2
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
3
3
1
0
3
2
2
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
2
3
0
0
2
2
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
2
1
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
1
0
0
0
0
0
1
2
1
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
2
2
0
1
0
0
1
0
0
0
0
1
0
0
4
3
1
0
1
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
2
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
1
2
1
0
1
0
0
0
3
0
0
2
0
0
2
1
1
0
0
0
0
0
1
1
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
9
0
0
2
0
2
1
0
0
0
0
0
0
1
0
0
2
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
4
1
0
0
2
0
0
0
0
0
0
1
2
0
0
0
1
1
0
0
0
2
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
3
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
2
2
0
0
0
2
0
2
0
0
0
0
0
1
1
0
0
0
1
1
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
2
0
0
0
2
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
2
0
0
0
3
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
9
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
8
0
0
2
2
2
0
0
0
1
0
0
3
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
2
0
0
0
6
0
1
0
2
0
1
0
5
2
1
0
1
0
0
0
0
0
1
0
0
0
2
2
0
1
0
2
0
0
2
0
2
3
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
4
0
0
2
0
3
0
0
2
0
0
0
7
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
4
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
1
0
0
3
0
0
0
1
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
1
2
0
0
1
2
1
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
2
0
0
1
0
1
1
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
2
0
0
2
4
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
1
0
0
7
0
2
0
0
2
0
0
2
0
2
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
1
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
5
0
0
2
0
2
0
2
0
2
0
0
0
0
0
2
0
0
0
4
3
0
2
0
0
0
0
0
0
0
3
0
0
2
2
0
0
1
1
0
0
0
0
0
1
0
1
0
2
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
2
0
2
0
4
0
0
0
0
0
0
0
1
1
4
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
2
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
1
2
1
2
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
2
0
0
2
1
0
0
0
0
0
0
0
3
0
0
0
1
0
2
0
0
3
0
0
3
0
2
0
1
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
1
0
2
0
1
0
0
0
0
1
0
1
0
0
2
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
3
1
0
1
0
0
1
0
1
0
0
0
0
4
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
3
0
2
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
3
0
0
0
1
0
0
2
3
1
0
2
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
2
0
3
2
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
1
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
3
0
0
1
3
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
2
2
2
0
0
0
0
0
1
3
0
0
0
0
0
1
4
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
2
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
3
2
0
0
1
0
0
2
0
2
1
0
0
0
2
0
1
1
0
1
0
0
1
1
0
0
2
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
1
1
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
2
2
0
0
1
0
0
0
0
2
2
0
0
0
1
1
0
2
0
0
1
0
0
1
1
0
0
0
0
0
6
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
1
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
2
2
0
0
0
0
1
0
0
1
0
3
0
0
1
0
0
1
0
0
0
2
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
5
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
1
2
0
0
1
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
4
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
4
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
2
0
2
0
0
0
0
0
2
0
0
2
0
0
0
2
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
1
1
0
2
2
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
1
0
0
1
0
2
0
0
0
0
1
0
0
0
3
0
0
5
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
3
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
1
3
0
0
1
2
3
0
0
0
0
0
0
0
2
0
2
0
3
0
0
2
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
8
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
4
0
2
2
0
0
0
0
8
2
0
0
0
0
2
0
0
0
4
0
1
0
0
0
1
0
0
0
0
3
1
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
2
0
1
2
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
3
0
0
0
1
1
0
0
0
0
0
0
5
1
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
2
2
0
0
0
1
0
1
0
0
2
1
0
0
0
1
2
0
1
0
0
2
0
0
0
1
2
0
0
1
7
0
2
2
0
0
2
0
0
0
0
2
2
4
7
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
1
4
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
2
0
0
0
2
3
0
0
0
2
0
0
1
2
4
0
0
0
0
1
2
0
0
3
0
0
0
0
1
0
0
4
1
0
2
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
2
1
2
0
0
0
0
0
0
0
0
1
0
1
1
0
4
0
0
0
0
0
0
0
0
2
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
4
0
0
0
1
0
2
0
2
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
3
0
0
2
0
4
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
2
2
1
0
0
0
0
0
1
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
4
1
1
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
3
0
0
0
1
0
0
2
0
0
0
3
0
0
0
1
1
0
1
2
2
0
2
0
0
1
0
2
1
0
0
0
0
0
0
0
0
2
0
0
1
0
2
2
2
1
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
1
2
1
0
0
0
0
1
0
0
1
0
0
1
0
2
0
1
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
2
2
6
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
1
0
0
1
0
0
0
0
2
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
1
0
2
4
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
2
2
3
3
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
2
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
7
0
0
0
0
2
0
0
5
0
3
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
2
0
0
0
3
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
2
0
2
0
0
1
0
0
0
0
1
0
1
0
0
0
5
1
0
1
2
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
3
1
0
0
2
0
2
0
3
0
0
2
0
1
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
1
2
2
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
8
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
2
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
1
0
1
0
1
0
2
3
4
0
0
0
0
0
3
0
0
2
1
3
0
0
0
8
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
2
0
2
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
2
0
2
0
0
2
1
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
2
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
3
2
0
0
0
1
0
0
1
0
3
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
2
0
1
0
0
3
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
1
0
0
2
0
0
1
0
2
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
4
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
2
2
0
0
1
1
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
1
0
2
1
3
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
2
4
0
0
1
0
0
2
1
0
0
3
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
1
0
3
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
4
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
3
1
0
0
0
0
1
0
0
1
1
0
2
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
4
1
0
1
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
4
0
1
0
1
0
0
2
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
5
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
2
0
1
1
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
2
0
1
0
0
0
0
1
0
0
2
0
0
0
3
0
0
0
0
0
0
0
1
2
2
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
2
0
2
0
0
2
0
2
2
0
4
0
0
0
2
0
0
0
1
2
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
2
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
2
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
2
0
0
4
0
0
1
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
2
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
4
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
1
1
0
1
0
1
0
0
0
4
0
0
0
0
2
0
0
1
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
1
0
0
0
2
0
0
0
1
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
2
0
0
1
2
2
0
0
0
0
0
0
0
2
0
0
2
0
0
2
1
2
0
0
0
2
3
0
0
0
0
0
0
0
2
1
2
0
1
2
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
2
0
0
4
0
0
0
1
2
1
0
2
0
2
1
0
1
0
0
0
1
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
4
0
0
0
0
2
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
3
0
0
1
0
0
0
0
0
1
2
0
0
2
0
1
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
2
2
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
3
0
2
0
0
0
1
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
2
0
0
2
2
1
0
0
0
2
0
1
0
2
0
6
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
2
1
0
0
0
0
1
0
0
1
0
0
1
0
1
1
2
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
1
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
3
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
1
0
1
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
1
2
0
0
0
1
0
2
0
0
1
3
2
0
0
1
0
0
1
2
1
0
0
0
2
0
0
0
5
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
1
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
2
0
2
2
0
2
0
2
1
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
5
0
0
1
0
0
2
0
2
0
0
0
2
0
0
0
0
0
3
2
0
3
2
0
0
1
1
0
0
0
1
0
3
2
0
2
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
4
0
2
0
0
0
0
1
2
0
0
0
2
1
0
2
0
1
0
3
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
2
0
2
0
1
2
0
0
0
0
1
0
1
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
2
0
1
0
2
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
3
0
1
0
4
1
0
2
1
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
2
0
0
0
0
0
1
2
2
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
2
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
1
2
0
0
1
2
2
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
2
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
1
1
0
0
0
0
0
1
2
1
0
0
0
0
0
1
2
0
1
0
2
1
0
0
1
0
0
2
0
0
0
0
1
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
2
2
2
0
0
1
1
0
0
1
0
1
0
2
0
0
0
2
0
0
0
2
0
3
1
0
0
2
2
3
0
0
0
0
2
1
0
0
2
0
0
0
0
3
5
0
0
0
2
0
0
0
2
2
0
0
1
2
1
4
0
0
1
1
0
1
2
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
3
2
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
1
1
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
1
2
0
2
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
2
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
3
0
0
0
0
0
1
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
3
0
1
0
0
0
1
0
0
1
0
0
0
1
0
3
0
0
0
0
0
0
0
1
0
0
2
1
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
2
2
2
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
1
0
0
1
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
6
1
0
0
0
0
0
0
2
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
2
1
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
3
0
1
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
2
0
0
0
1
0
0
0
2
2
1
0
1
0
2
1
0
2
0
1
1
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
2
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
2
0
0
2
4
2
0
0
0
0
0
0
6
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
1
1
2
0
2
1
0
0
0
2
0
0
0
0
0
0
0
1
0
1
2
0
0
2
0
0
0
0
0
1
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
3
0
2
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
1
0
0
0
0
0
3
0
0
0
2
0
1
0
2
0
0
0
0
0
1
0
0
1
1
1
0
0
0
2
0
0
4
0
0
0
7
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
3
1
1
0
0
2
1
0
1
0
2
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
4
2
0
0
1
2
0
3
0
1
0
0
1
0
1
0
0
2
0
2
1
0
0
0
0
1
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
2
2
2
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
1
2
0
0
0
0
1
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
2
0
0
0
2
1
1
0
1
0
1
0
0
1
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
2
2
2
2
0
0
2
2
0
0
0
0
0
1
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
3
0
1
0
0
1
0
0
1
0
2
0
0
0
2
0
1
0
0
0
0
0
1
1
4
1
0
0
0
0
0
1
0
0
0
6
1
0
0
1
0
0
0
2
1
2
0
0
2
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
3
0
2
0
0
1
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
2
0
2
2
1
0
0
0
3
0
1
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
2
2
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
3
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
1
1
0
2
2
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
2
0
0
0
1
1
0
1
2
0
0
4
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
2
1
0
0
1
1
0
2
1
0
0
0
2
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
2
0
0
0
1
0
0
0
2
0
0
0
2
1
2
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
3
0
2
0
0
0
0
0
0
3
0
0
0
0
1
2
3
1
0
0
0
2
0
1
0
0
2
0
0
0
1
0
1
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
2
0
1
0
0
0
2
0
1
0
0
0
0
1
0
0
0
1
3
0
0
0
0
0
0
0
1
0
4
0
4
0
1
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
2
0
2
3
0
0
0
0
0
2
1
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
2
2
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
2
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
2
1
0
0
0
0
0
1
0
1
2
2
0
1
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
1
0
0
2
0
0
0
1
1
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
1
0
0
2
0
1
0
1
2
0
0
2
0
2
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
1
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
3
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
2
0
2
0
2
0
0
0
0
1
0
0
2
0
1
0
0
5
1
1
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
1
3
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
1
0
0
0
2
1
0
0
2
0
1
1
2
1
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
2
1
0
2
4
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
3
0
0
0
0
0
0
0
2
1
0
0
0
1
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
1
0
5
0
3
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
3
1
0
0
0
2
2
1
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
2
1
2
0
0
1
1
0
0
0
2
2
0
1
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
2
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
1
2
0
0
0
1
2
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
2
1
0
2
0
0
0
0
1
1
0
0
2
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
2
0
1
0
1
0
0
3
0
0
0
1
0
0
0
0
0
0
0
7
0
0
0
0
6
0
2
0
0
0
0
0
0
1
3
0
2
0
0
0
0
0
0
0
0
0
0
0
1
3
2
2
0
0
1
0
1
0
0
1
0
0
3
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
1
0
0
1
0
0
0
0
0
0
5
0
3
2
0
0
0
0
0
1
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
11
0
0
0
0
3
0
0
0
0
2
0
0
0
0
1
1
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
2
0
1
0
0
4
0
2
0
1
0
0
2
1
0
0
0
4
1
0
0
0
0
0
0
0
6
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
2
0
0
0
0
0
0
1
0
2
0
4
0
0
0
0
1
2
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
1
0
1
0
0
1
0
2
0
0
2
0
0
0
0
2
1
2
2
2
0
0
4
0
1
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
5
1
0
0
0
1
2
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
2
0
1
0
0
0
0
6
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
1
0
0
2
0
2
0
1
0
1
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
2
0
2
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
2
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
2
8
0
0
0
1
0
0
2
1
0
0
1
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
3
0
3
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
2
0
0
0
0
0
4
0
0
0
0
0
0
4
0
0
0
1
0
5
0
0
2
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
2
0
0
3
1
1
2
0
0
2
0
0
1
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
2
2
2
2
1
0
0
0
0
2
2
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
1
1
0
0
0
0
2
1
2
0
0
1
0
0
0
1
0
1
0
1
3
2
0
0
2
1
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
1
0
1
0
0
1
0
0
2
0
0
0
1
2
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
1
0
0
3
0
0
0
2
1
0
0
0
0
2
0
1
0
4
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
3
0
0
2
0
0
0
1
1
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
3
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
1
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
8
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
4
0
2
0
0
0
0
0
2
0
0
1
0
1
0
0
1
2
2
1
0
1
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
2
0
0
0
1
0
2
0
0
4
0
0
1
2
0
0
0
0
1
0
0
0
2
0
2
0
2
0
0
0
2
0
2
0
3
0
0
0
0
0
2
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
2
2
0
4
2
2
0
2
8
2
0
0
1
1
0
0
0
1
1
0
0
0
0
2
0
0
2
1
0
0
0
0
1
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
2
3
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
3
3
0
0
0
1
2
0
0
2
2
2
3
2
0
0
0
0
0
0
1
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
3
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
2
3
0
0
0
0
2
0
0
0
2
0
1
0
0
0
2
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
2
1
0
0
0
0
0
1
0
3
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
10
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
1
0
2
0
2
0
0
5
1
2
2
0
2
2
0
2
0
0
0
3
0
0
0
0
0
0
1
5
0
1
2
1
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
2
2
2
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
2
0
0
2
0
0
0
0
0
1
0
2
2
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
1
0
0
0
0
1
3
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
7
0
0
0
0
0
0
0
2
0
0
1
0
1
2
0
0
0
0
0
2
2
3
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
2
0
3
2
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
5
0
0
0
0
0
0
1
0
2
1
2
0
2
2
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
2
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
4
0
0
1
0
0
1
0
0
0
3
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
1
2
2
0
0
0
0
0
0
0
0
1
3
0
5
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
2
0
2
0
0
0
1
0
0
0
0
5
2
0
0
2
0
1
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
1
2
1
0
1
0
2
2
0
0
0
2
3
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
2
0
0
2
0
0
6
2
0
0
0
0
2
2
1
0
2
2
0
3
0
1
0
0
0
1
0
0
0
0
2
0
1
0
1
0
0
0
3
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
1
3
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
2
1
0
2
0
0
2
1
2
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
4
0
0
1
0
0
0
0
0
0
0
1
0
2
1
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
3
2
3
3
0
0
0
0
0
2
0
0
1
0
0
0
2
2
2
0
0
2
1
0
0
0
0
0
0
1
1
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
3
1
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
1
2
2
0
2
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
4
1
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
1
1
0
0
0
0
1
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
1
0
0
0
1
0
1
2
0
2
6
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
2
1
0
0
5
0
3
1
1
0
0
0
2
0
0
0
0
0
2
2
2
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
2
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
4
1
1
0
2
0
0
0
0
0
1
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
3
0
1
0
2
0
0
0
2
3
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
2
2
0
0
0
0
1
7
2
0
0
2
0
0
0
0
1
1
1
0
0
0
2
0
0
3
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
1
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
2
0
0
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
1
0
5
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
1
0
1
0
1
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
1
2
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
1
0
1
0
0
0
1
2
0
1
0
0
0
2
0
0
0
0
0
2
2
2
0
2
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
5
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
2
0
0
0
2
0
0
2
3
1
0
0
1
2
0
1
1
0
0
0
1
0
0
0
0
1
0
0
2
0
2
1
0
2
2
1
0
1
0
0
2
0
1
0
1
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
5
2
0
0
0
0
0
1
1
2
0
2
0
0
0
0
0
1
1
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
3
1
0
1
0
0
0
0
3
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
3
2
0
1
0
0
2
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
1
1
1
0
0
3
0
0
0
0
2
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
1
0
1
0
2
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
1
2
0
0
0
1
0
0
0
0
2
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
2
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
1
2
0
0
0
0
1
0
0
0
2
1
0
0
0
0
2
0
0
0
1
2
0
0
0
0
1
2
0
1
0
0
2
0
1
5
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
1
0
0
0
0
1
0
0
2
4
0
4
0
1
2
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
1
0
0
0
6
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
5
0
0
1
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
1
2
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
3
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
2
0
3
0
1
0
0
3
1
0
1
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
2
1
1
0
0
0
0
0
1
0
1
0
0
4
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
1
0
3
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
1
0
2
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
2
2
0
1
0
1
0
1
0
0
0
2
2
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
1
0
0
1
0
1
0
0
0
2
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
4
2
2
0
1
0
0
7
0
0
0
0
1
0
3
0
3
0
0
0
2
1
2
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
1
0
3
0
1
0
0
0
2
0
0
0
2
2
2
0
2
0
0
3
0
0
0
0
3
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
2
0
3
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
2
1
1
0
2
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
2
0
1
1
0
2
1
0
0
4
0
0
1
1
0
2
0
0
0
0
2
0
2
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
2
0
3
1
0
0
2
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
1
0
3
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
1
0
2
2
0
0
0
1
0
0
0
0
1
3
0
2
0
2
2
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
3
0
2
0
0
0
2
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
3
2
2
0
0
0
0
0
2
0
0
0
0
0
0
5
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
2
2
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
1
0
2
0
2
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
2
1
0
0
0
0
1
1
0
2
0
1
0
0
0
2
2
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
2
0
2
2
0
2
2
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
2
2
2
0
0
0
4
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
2
0
3
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
1
0
0
0
0
0
2
0
2
1
0
0
0
1
2
2
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
1
0
3
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
1
0
0
0
5
0
0
2
0
0
1
1
2
0
0
0
3
0
2
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
1
0
0
0
3
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
1
0
2
0
1
2
0
0
2
1
0
2
0
0
2
3
0
0
0
2
0
0
0
2
0
0
0
0
0
0
4
0
0
1
1
0
0
1
2
0
0
0
0
0
0
0
0
1
2
1
0
1
2
0
0
0
0
0
3
0
1
0
0
0
1
0
3
0
2
2
0
0
0
0
0
2
0
0
0
0
2
0
0
2
2
0
0
0
1
0
2
0
1
0
0
0
2
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
1
0
0
1
0
2
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
1
1
0
1
4
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
3
1
0
0
2
2
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
2
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
1
2
4
2
4
2
0
1
2
0
0
2
2
0
1
0
0
0
0
0
0
0
1
0
1
1
2
0
2
1
0
0
1
2
0
2
0
2
1
0
0
0
2
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
3
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
3
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
2
2
0
0
0
2
1
0
0
1
2
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
2
1
0
2
0
2
0
2
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
2
0
0
0
2
0
2
0
0
0
0
1
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
2
0
0
2
2
0
0
0
0
2
2
2
0
0
2
1
0
2
1
1
0
2
0
0
2
0
0
0
2
0
1
0
2
0
1
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
2
1
1
0
0
0
0
1
0
0
1
0
0
2
0
0
0
2
0
0
2
1
0
0
0
0
4
1
2
0
0
0
0
1
0
0
0
0
0
1
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
1
0
0
0
2
2
2
0
1
2
0
0
0
0
1
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
3
0
0
0
1
1
2
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
3
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
3
1
0
0
0
0
0
0
0
2
0
2
2
0
2
0
2
2
0
0
1
0
4
0
2
0
1
0
1
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
1
0
2
0
3
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
6
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
2
3
0
0
0
1
0
1
0
1
0
0
0
2
1
1
1
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
3
0
1
2
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
3
0
1
0
5
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
3
0
2
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
2
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
3
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
1
1
1
0
1
0
0
0
4
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
2
0
3
2
0
0
0
0
1
1
0
2
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
1
0
3
2
0
1
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
2
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
1
0
1
0
0
1
0
1
0
2
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
2
0
2
1
0
2
0
0
0
0
0
1
2
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
1
0
3
0
4
0
0
0
0
1
0
1
0
0
0
0
2
1
0
0
0
0
2
0
1
0
0
0
1
2
0
1
0
2
0
3
0
0
0
0
0
2
2
2
0
1
0
0
0
0
0
1
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
3
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
2
0
2
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
2
0
2
0
1
1
3
0
3
0
0
0
1
2
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
1
1
2
0
9
0
0
0
2
3
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
2
0
5
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
3
0
0
0
3
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
2
1
0
1
0
2
0
1
1
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
1
0
2
0
2
1
0
0
2
0
1
0
0
0
1
1
2
2
0
0
0
2
0
0
0
2
1
2
3
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
3
1
2
0
1
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
1
0
0
0
2
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
2
0
0
0
1
1
0
0
0
1
0
2
1
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
2
2
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
2
1
2
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
3
0
2
0
0
0
0
0
2
1
1
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
1
5
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
1
0
0
2
3
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
2
1
0
2
0
1
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
1
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
1
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
3
0
1
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
1
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
3
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
2
1
0
1
0
1
1
0
0
0
1
0
0
0
0
0
1
0
1
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
3
0
0
0
3
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
3
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
2
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
1
0
1
0
0
0
0
4
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
1
0
1
2
2
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
1
0
0
0
1
0
2
0
1
1
0
0
3
0
0
0
1
0
1
0
0
0
0
0
0
0
3
0
2
0
0
0
2
3
0
0
1
0
2
0
3
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
2
0
0
2
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
2
2
4
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
1
2
0
0
0
1
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
2
2
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
2
0
5
1
0
1
2
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
3
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
2
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
2
0
0
0
0
0
0
2
0
0
0
1
0
2
0
2
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
1
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
2
0
1
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
2
0
0
1
1
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
2
1
0
0
0
2
0
0
0
2
0
0
0
0
2
0
1
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
2
1
1
0
0
1
0
2
0
0
0
2
0
0
0
1
0
0
5
0
0
0
0
1
0
0
0
1
2
0
0
1
0
2
2
0
0
0
1
2
0
0
0
1
2
0
0
0
0
0
0
1
2
0
0
2
0
1
0
0
0
0
0
0
0
1
1
1
0
1
2
0
2
0
0
2
0
0
0
0
1
0
2
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
2
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
3
0
0
0
0
1
0
2
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
5
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
2
1
0
0
2
3
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
3
0
0
0
0
0
2
2
2
0
0
3
0
1
1
0
1
2
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
1
1
1
0
2
0
0
0
0
2
2
2
0
0
1
1
2
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
3
0
0
0
4
2
0
0
0
0
2
1
0
0
1
0
1
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
2
2
0
0
0
1
0
0
0
0
0
0
1
2
0
1
2
0
0
0
2
0
0
0
0
0
0
0
1
1
0
1
0
1
1
1
0
0
0
0
0
2
0
1
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
2
1
0
2
1
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
2
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
4
0
0
1
0
1
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
1
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
1
2
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
2
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
2
0
1
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
3
0
0
0
0
0
1
0
0
1
2
4
1
0
0
0
0
3
0
0
0
0
0
0
4
1
0
0
0
3
2
0
0
1
1
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
2
0
0
1
0
0
2
0
0
0
1
1
0
0
1
1
2
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
2
0
0
0
0
1
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
1
1
0
0
0
0
0
0
1
0
2
2
0
0
5
1
0
1
0
0
0
0
1
3
0
0
2
1
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
2
3
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
1
2
1
0
0
0
0
0
0
0
1
1
3
1
0
1
0
2
2
0
4
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
1
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
2
1
1
1
0
1
0
0
0
0
1
2
0
1
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
1
1
2
0
0
0
1
0
0
0
0
0
1
1
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
3
0
0
0
0
0
2
2
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
2
0
0
0
2
0
2
0
0
1
0
0
0
0
0
1
3
0
0
1
1
1
1
0
0
0
0
1
0
1
0
0
1
0
2
0
1
0
2
0
0
1
0
1
0
0
0
0
2
0
0
2
0
2
0
3
0
0
3
3
0
0
0
0
5
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
1
0
0
1
2
0
2
0
0
1
0
1
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
2
0
0
0
2
1
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
2
0
1
6
2
0
1
0
0
2
0
0
0
0
0
2
0
0
2
0
1
0
0
0
1
0
0
0
2
1
1
0
0
0
0
2
0
1
0
2
0
2
0
0
0
0
1
0
3
0
0
1
0
0
1
1
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
8
0
0
2
0
1
2
0
0
0
0
3
1
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
3
0
0
0
0
1
0
0
0
0
1
0
0
0
3
1
0
0
0
0
1
3
1
1
0
0
0
0
0
0
0
6
0
0
0
2
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
2
1
2
10
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
3
0
0
0
2
0
2
0
0
1
0
0
0
2
0
0
0
3
0
0
0
1
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
3
0
1
0
2
0
1
2
0
0
0
1
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
2
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
1
1
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
2
0
1
0
0
0
2
0
0
0
0
0
1
2
0
1
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
1
1
0
7
0
0
2
1
0
0
0
2
1
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
2
2
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
3
0
0
2
0
0
0
0
2
0
2
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
8
1
0
1
0
0
2
1
0
0
0
0
0
0
0
1
2
1
0
2
1
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
1
2
1
0
0
0
0
7
0
0
1
2
0
2
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
4
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
1
0
0
0
1
3
0
0
0
0
1
0
0
2
0
2
2
0
2
0
0
0
1
1
2
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
1
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
1
0
1
2
0
0
0
0
0
0
0
0
2
1
0
2
0
0
1
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
2
0
0
0
2
0
0
1
2
0
0
0
1
0
0
0
0
2
1
1
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
1
1
0
6
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
2
4
2
0
0
0
0
0
0
1
2
0
0
2
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
1
1
0
1
0
6
0
0
0
0
1
0
2
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
2
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
3
1
0
0
0
3
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
1
1
0
1
0
0
1
3
0
4
0
2
0
1
0
2
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
2
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
2
1
0
0
0
1
1
0
0
1
0
0
2
1
1
0
2
0
0
2
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
1
1
6
2
0
0
0
0
2
0
0
1
2
1
0
0
0
0
2
0
2
4
0
0
1
0
1
1
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
2
0
1
0
0
0
0
5
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
1
0
0
2
1
5
0
1
0
0
2
0
0
1
0
0
2
0
0
2
0
3
1
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
2
1
0
0
4
2
1
1
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
1
0
2
0
1
2
0
0
0
0
0
0
3
0
2
5
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
3
0
0
2
1
0
0
0
0
0
1
3
2
0
2
0
4
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
1
4
0
6
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
1
0
0
0
0
0
3
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
3
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
2
0
2
0
2
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
5
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
1
1
0
0
1
0
0
2
1
0
3
0
0
0
0
0
1
0
0
0
3
0
0
0
5
0
0
0
4
0
2
0
0
1
0
0
0
0
0
0
4
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
2
0
0
2
1
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
1
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
3
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
2
2
2
0
0
0
2
0
0
2
0
0
2
0
2
0
0
0
0
0
2
1
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
2
0
0
2
2
0
0
0
2
0
1
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
5
0
0
0
0
0
0
0
0
2
0
1
0
0
4
0
0
0
1
2
0
1
0
0
0
0
0
0
2
0
1
0
0
0
1
2
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
2
0
0
1
2
0
0
0
0
0
0
2
1
0
0
0
1
5
5
0
2
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
3
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
2
1
1
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
4
2
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
1
0
1
0
1
0
0
2
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
4
3
0
1
1
0
0
0
0
1
2
1
0
0
0
0
0
0
0
3
0
0
0
0
0
1
2
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
1
0
2
0
0
0
2
0
0
1
0
0
0
0
2
0
2
0
2
2
0
0
1
0
0
0
0
2
2
1
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
1
2
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
5
0
1
1
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
1
0
0
0
0
1
3
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
1
0
0
0
1
2
0
1
0
0
3
0
0
0
0
0
0
2
0
0
0
1
0
2
0
1
2
0
0
0
0
0
0
3
0
0
1
0
1
1
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
1
2
0
0
1
0
0
0
2
0
1
0
0
0
2
2
0
1
0
1
0
0
0
1
0
1
1
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
1
1
0
1
4
0
0
0
0
0
0
0
1
0
0
0
2
2
1
0
2
0
0
0
0
2
2
0
2
4
0
1
1
0
2
0
0
0
0
2
2
0
1
3
0
1
0
0
0
0
0
0
1
1
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
2
1
0
0
0
0
1
3
0
0
1
0
0
0
0
0
2
0
2
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
4
0
8
0
2
0
0
0
0
1
2
2
0
0
0
0
1
0
1
2
0
0
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
5
3
2
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
1
2
2
2
0
2
3
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
1
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
1
0
0
1
2
0
0
1
0
0
2
0
0
0
0
0
7
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
1
0
2
0
1
0
0
2
0
0
0
0
1
0
0
1
0
0
2
0
0
1
0
0
0
0
0
3
1
2
0
2
0
0
0
0
2
0
0
0
0
3
0
0
0
2
0
2
0
0
1
0
0
1
1
0
0
3
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
3
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
1
1
1
0
0
0
0
0
0
1
1
0
4
0
2
0
2
0
0
0
0
2
1
0
0
0
0
0
2
2
0
0
0
0
2
0
2
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
3
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
6
0
1
0
0
2
1
0
0
1
2
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
2
1
1
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
1
1
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
9
2
0
0
0
0
0
1
0
0
2
1
0
1
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
2
1
0
1
0
0
0
0
0
1
0
0
0
2
0
1
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
2
0
1
0
0
0
1
0
0
3
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
2
2
0
0
1
0
0
0
2
1
0
2
0
0
0
0
0
1
1
2
3
2
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
2
1
0
0
0
0
0
0
0
1
2
1
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
1
1
0
0
0
0
1
1
0
2
1
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
5
0
0
1
0
0
1
0
0
4
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
3
0
1
0
0
1
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
5
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
1
0
0
0
1
0
0
0
1
1
0
2
0
1
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
1
0
2
0
0
1
0
0
1
0
0
0
0
0
1
1
1
0
2
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
2
2
1
1
0
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
2
2
1
0
0
1
0
0
0
0
0
1
1
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
2
0
2
0
2
2
0
1
0
2
0
0
0
2
2
0
0
0
0
0
0
1
1
0
0
0
2
0
2
0
1
1
1
2
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
2
1
0
0
1
2
0
2
0
1
1
0
0
0
0
0
0
2
0
0
1
3
0
0
0
1
0
0
3
1
0
2
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
3
1
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
2
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
7
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
1
0
0
2
0
1
0
0
1
0
0
3
0
0
3
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
2
0
2
3
0
0
0
2
1
1
0
0
0
1
0
0
1
0
1
0
0
0
1
2
0
0
0
0
8
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
1
2
0
1
0
0
2
0
2
1
0
1
2
0
0
2
1
0
1
0
0
2
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
2
3
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
3
0
0
8
0
2
1
0
0
0
1
0
0
2
1
0
0
0
2
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
2
0
0
3
0
0
2
1
0
0
0
1
0
0
2
0
2
0
0
1
0
0
1
0
0
0
1
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
4
0
0
0
0
2
0
2
0
0
0
0
0
1
4
0
2
1
0
0
2
0
1
2
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
2
0
2
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
3
1
0
3
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
2
0
2
0
0
1
0
0
6
0
0
1
0
0
0
1
2
0
0
0
1
0
0
1
0
0
0
0
2
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
3
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
3
3
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
3
0
1
0
0
0
0
1
0
0
1
0
0
0
0
8
0
0
0
0
0
0
1
0
0
0
3
0
0
0
2
0
0
2
0
0
0
1
2
0
0
0
1
0
0
0
0
0
3
0
0
3
0
1
0
0
2
0
0
0
1
2
0
1
0
0
0
1
1
0
0
0
4
1
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
2
1
1
1
2
1
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
4
0
0
0
2
0
1
0
0
3
4
0
0
4
0
0
1
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
2
2
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
4
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
3
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
2
2
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
1
1
1
0
0
1
0
0
2
0
1
1
0
1
2
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
4
0
1
0
0
0
0
0
1
3
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
1
1
0
0
2
1
0
6
0
0
0
0
0
0
0
2
1
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
2
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
2
0
0
1
1
0
2
0
1
0
0
0
2
4
0
0
0
0
1
2
0
0
0
1
0
1
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
3
0
1
0
0
2
1
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
1
0
2
1
0
1
0
0
0
0
0
1
0
2
3
2
0
0
0
1
1
0
1
3
0
1
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
1
1
4
1
0
2
1
2
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
2
3
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
3
0
1
0
2
0
0
0
1
0
0
0
0
2
2
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
1
2
0
0
2
1
0
0
0
0
0
0
0
2
0
2
1
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
2
1
0
1
2
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
1
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
2
2
1
2
0
0
0
1
0
2
1
2
2
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
2
0
5
0
1
1
0
0
0
2
0
0
0
0
0
0
0
2
0
3
0
0
2
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
1
0
0
2
2
0
2
0
0
0
0
0
1
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
2
0
0
1
0
0
0
0
2
0
2
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
3
1
1
1
0
0
0
1
0
2
0
13
0
2
0
1
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
2
0
2
0
0
0
2
1
1
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
1
0
4
1
1
0
2
0
0
0
0
0
0
1
0
2
0
0
1
3
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
8
0
0
0
2
0
0
0
0
2
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
2
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
2
3
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
1
0
1
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
9
1
0
0
0
2
0
3
0
0
0
1
0
0
0
0
1
0
2
0
2
1
2
0
0
0
0
0
2
0
0
0
0
1
0
0
3
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
2
0
0
1
0
0
1
0
2
1
0
0
0
0
1
0
0
1
2
0
0
0
2
0
1
0
1
0
0
0
0
2
0
1
1
0
0
0
2
5
1
0
0
0
0
0
0
0
0
0
0
2
1
0
6
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
1
0
0
0
2
2
2
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
1
4
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
2
3
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
4
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
1
0
0
0
0
0
4
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
2
0
0
0
1
1
0
0
1
0
2
0
0
1
2
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
3
0
0
0
0
0
0
2
0
0
1
0
0
2
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
7
0
0
0
20
0
1
0
0
0
0
2
2
2
0
0
2
0
0
0
0
1
2
1
0
0
1
0
3
0
2
1
0
0
0
0
2
0
0
3
0
2
0
1
0
0
3
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
2
2
0
0
0
2
0
0
1
1
6
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
1
0
1
0
1
1
0
0
0
0
0
0
2
2
0
3
0
0
2
0
0
0
0
0
2
1
0
0
0
0
2
2
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
1
2
2
0
3
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
2
0
0
0
0
1
0
2
0
0
1
0
0
0
1
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
2
0
2
0
0
2
0
0
0
0
0
1
6
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
1
3
0
0
2
1
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
1
0
2
0
1
1
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
2
0
3
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
15
3
0
3
0
2
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
2
0
2
0
0
0
2
2
0
0
0
1
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
2
0
1
0
3
2
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
1
0
1
0
1
2
0
0
0
0
0
0
1
4
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
1
1
0
0
3
3
0
0
0
0
0
1
1
0
0
0
0
0
0
12
0
0
2
0
3
0
0
1
1
3
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
3
2
0
0
0
0
0
0
0
1
0
2
4
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
1
0
0
0
4
1
3
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
3
0
2
0
0
3
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
1
0
0
1
0
0
3
1
0
2
0
0
0
0
2
0
0
0
0
1
0
4
0
0
0
0
0
0
0
3
1
0
0
1
0
2
0
1
0
1
2
0
0
0
2
0
0
2
1
1
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
2
7
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
1
0
5
0
0
2
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
1
2
2
1
1
1
0
2
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
2
0
2
0
1
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
3
0
0
0
0
0
0
2
1
0
0
0
1
0
0
5
2
0
0
0
0
0
3
2
0
0
4
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
1
0
2
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
3
0
0
0
0
2
0
2
0
2
0
0
0
0
2
2
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
3
0
2
0
3
0
0
0
0
0
0
0
0
1
1
1
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
1
0
0
1
0
2
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
4
1
0
1
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
2
2
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
2
3
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
2
0
0
0
2
2
2
0
2
0
2
1
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
1
3
0
0
0
0
2
1
1
2
0
1
0
0
0
0
0
2
0
0
0
0
0
2
2
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
2
2
0
0
4
0
1
0
1
6
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
3
0
2
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
2
1
1
0
0
0
0
5
0
0
1
1
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
2
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
1
1
0
0
0
1
1
2
2
0
0
0
0
0
1
0
2
1
0
0
0
0
0
1
0
1
3
0
2
0
0
0
0
5
2
0
1
2
0
0
0
0
1
1
0
0
0
1
0
0
0
0
2
0
0
2
0
0
1
1
1
0
0
0
2
0
0
0
3
0
1
0
0
0
0
0
0
0
0
1
1
2
2
0
0
0
0
0
0
1
1
0
0
1
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
3
2
2
0
0
0
2
3
0
0
0
0
2
0
0
0
0
2
2
1
0
0
0
3
0
0
0
0
2
1
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
2
0
2
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
2
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
2
0
2
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
2
2
1
7
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
6
2
0
0
2
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
2
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
4
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
1
0
0
0
0
0
2
0
0
2
1
0
1
0
2
2
0
0
0
0
0
1
0
1
1
0
0
0
0
3
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
2
0
0
0
0
1
1
0
0
0
0
2
0
0
0
1
1
0
0
0
0
6
2
0
2
1
0
0
0
0
0
2
2
3
0
0
0
0
0
2
0
1
1
0
1
1
2
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
2
0
0
1
0
2
0
0
2
4
1
1
0
0
2
0
1
0
2
0
2
0
0
0
0
2
2
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
2
1
0
0
0
2
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
6
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
1
0
0
0
0
0
6
0
2
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
2
0
0
1
0
2
2
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
3
0
0
1
2
0
0
0
2
1
0
0
0
0
0
1
1
1
0
1
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
1
2
0
2
2
0
0
0
2
3
0
0
0
2
1
9
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
2
0
0
2
1
1
2
2
0
0
0
1
0
0
1
3
0
0
0
0
2
0
2
3
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
1
0
0
0
0
1
2
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
1
5
4
0
0
0
3
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
2
0
0
2
0
1
0
0
0
1
0
0
2
0
1
0
0
0
0
0
3
3
0
0
0
0
1
0
0
1
0
0
0
0
2
2
0
0
0
0
0
2
2
0
0
0
2
0
0
1
2
1
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
1
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
1
0
0
1
2
1
1
2
0
0
1
1
0
1
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
3
1
0
0
2
0
0
2
0
0
0
1
0
1
0
0
0
0
3
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
4
1
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
1
2
1
0
1
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
2
2
0
0
0
0
1
2
0
0
2
0
2
1
0
0
0
0
0
1
2
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
2
1
3
0
0
2
1
2
0
0
0
2
0
2
0
2
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
1
1
0
3
2
0
2
1
0
3
2
0
0
0
1
0
0
0
2
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
1
2
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
1
1
2
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
1
2
0
1
2
0
2
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
3
0
3
0
0
0
1
0
1
0
0
0
1
0
3
0
0
0
0
0
0
0
0
2
1
0
3
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
4
1
2
0
0
0
0
2
0
5
0
0
3
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
2
0
0
1
2
0
0
0
1
0
2
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
1
3
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
3
5
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
2
0
0
1
0
0
1
1
3
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
3
2
1
0
0
0
0
0
0
1
0
0
0
0
0
4
1
0
0
0
0
0
1
1
0
0
0
0
1
4
0
1
0
0
0
0
0
0
0
0
2
0
2
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
5
0
0
0
1
0
0
0
0
0
2
0
1
0
0
2
0
1
0
0
0
2
1
1
0
0
0
0
0
0
1
3
0
0
0
1
0
0
0
1
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
3
0
0
4
0
0
0
0
2
3
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
1
2
0
0
0
0
1
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
6
1
3
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
3
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
1
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
7
0
2
2
1
2
0
0
0
0
2
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
3
1
0
0
0
0
0
0
0
0
2
0
2
1
0
0
1
0
0
0
0
0
9
0
2
0
0
5
2
0
0
0
0
1
0
2
6
9
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
2
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
4
0
0
1
1
0
0
0
0
2
2
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
2
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
3
2
0
0
0
0
0
2
1
0
0
8
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
3
0
3
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
2
0
2
1
0
0
0
0
0
0
1
2
3
2
3
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
3
0
0
1
1
0
0
0
1
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
1
1
2
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
1
3
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
1
0
2
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
3
0
1
0
0
1
0
2
0
1
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
1
0
2
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
3
0
1
4
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
1
0
0
0
0
1
3
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
1
1
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
3
0
0
0
2
2
2
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
1
0
2
0
3
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
2
0
1
0
0
0
0
1
0
1
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
1
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
1
2
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
1
0
2
1
0
2
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
2
0
2
0
0
0
2
2
1
0
0
2
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
3
0
0
2
0
0
0
2
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
3
0
0
2
0
0
2
0
0
2
0
1
0
1
2
0
0
0
2
0
0
0
0
0
0
0
6
0
1
2
0
0
2
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
9
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
2
1
1
0
0
0
0
2
2
1
2
2
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
3
3
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
2
0
0
0
0
0
3
0
0
1
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
1
1
1
0
1
2
0
0
1
2
1
0
3
1
1
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
2
0
2
2
0
1
0
0
0
0
1
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
1
2
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
1
1
2
0
0
1
0
0
0
0
0
0
0
6
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
1
0
1
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
1
0
0
0
1
0
2
0
1
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
2
1
0
1
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
1
1
0
0
1
0
2
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
5
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
2
0
3
2
1
0
0
1
1
0
0
1
0
0
0
0
0
1
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
1
0
0
0
2
0
0
2
0
0
0
3
0
1
0
0
0
1
4
0
0
1
1
0
1
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
2
2
2
2
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
1
2
0
0
1
2
0
1
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
2
0
0
0
0
0
0
0
1
3
0
0
3
0
0
0
1
2
1
0
0
1
1
0
0
0
1
0
0
0
0
1
2
0
0
0
1
2
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
1
2
0
2
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
5
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
5
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
1
0
1
1
2
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
2
2
0
2
2
2
0
0
2
2
0
0
2
1
0
1
0
1
0
0
2
0
7
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
1
0
0
0
2
0
0
0
3
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
1
0
0
1
0
0
0
2
0
0
2
1
1
2
2
0
2
0
0
2
0
0
0
0
3
1
0
0
0
0
2
0
0
0
0
1
2
2
0
0
3
0
0
0
2
1
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
3
0
0
0
0
1
0
0
0
0
3
0
0
2
0
0
0
0
0
1
0
0
0
1
0
3
0
1
2
0
2
2
0
8
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
2
0
0
2
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
3
0
0
0
5
2
4
2
2
0
0
0
0
0
1
0
1
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
1
2
0
0
0
1
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
6
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
3
0
0
0
2
0
0
0
1
2
2
0
0
0
0
0
2
0
0
2
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
2
2
0
0
0
0
0
2
0
0
4
2
0
2
0
2
0
1
0
0
2
1
0
1
0
0
2
0
0
0
5
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
1
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
2
1
0
2
2
0
1
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
2
0
1
0
0
2
1
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
2
0
1
0
2
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
6
0
0
1
1
1
0
0
2
0
0
0
0
1
1
2
0
2
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
2
0
0
0
0
1
1
2
2
0
1
0
0
1
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
3
1
0
0
0
1
0
0
1
3
1
1
0
1
1
0
0
0
2
0
1
1
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
3
1
1
0
2
0
0
0
0
2
0
2
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
2
1
0
2
0
0
0
2
0
1
0
0
0
2
1
0
5
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
1
2
0
0
0
1
0
0
1
0
1
0
0
0
1
2
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
1
1
0
1
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
2
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
2
0
3
1
2
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
2
3
0
2
2
1
3
0
0
0
0
1
2
0
0
3
0
2
2
0
7
0
0
0
0
0
0
0
0
1
0
2
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
4
3
2
2
0
0
0
1
2
1
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
1
0
2
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
1
0
1
3
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
5
0
2
0
1
2
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
2
1
1
0
0
1
0
1
0
3
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
1
0
4
0
3
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
2
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
3
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
2
1
0
2
0
0
0
1
1
0
1
0
2
1
1
1
0
5
0
0
2
0
1
4
0
0
0
0
0
0
2
1
0
0
2
2
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
4
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
2
1
3
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
3
2
0
2
1
0
0
0
1
3
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
1
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
2
1
0
0
1
0
0
0
0
0
0
2
1
2
2
2
2
3
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
1
0
1
0
0
2
0
2
1
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
4
0
2
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
5
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
2
1
2
2
0
2
2
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
1
1
0
0
1
0
1
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
1
0
2
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
1
4
1
0
0
5
0
0
0
0
1
0
0
1
2
0
0
0
2
1
0
2
0
1
0
0
0
2
2
0
1
0
0
1
0
2
0
0
3
0
0
0
1
1
3
0
0
0
1
4
0
0
0
0
0
1
0
0
1
0
1
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
8
3
2
0
0
0
0
2
0
0
0
0
2
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
5
3
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
2
3
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
1
2
0
0
0
1
0
2
0
0
0
0
0
2
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
1
0
0
0
2
0
0
0
3
0
0
3
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
3
0
0
1
0
0
0
4
2
0
0
2
0
2
0
0
0
0
1
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
2
2
0
0
1
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
3
2
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
1
2
0
0
0
0
0
0
2
0
2
0
0
3
0
3
0
0
1
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
1
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
3
1
0
2
0
0
2
1
0
0
0
0
0
1
1
0
0
0
2
0
0
3
0
2
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
2
0
0
1
0
0
3
0
0
0
2
0
0
1
0
0
0
0
2
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
3
0
0
0
0
0
0
2
0
2
0
0
0
0
4
0
0
0
3
0
0
0
0
0
0
1
2
0
0
1
2
0
0
3
0
1
0
0
0
0
0
0
2
0
0
0
0
0
3
1
0
0
0
1
2
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
3
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
1
2
0
2
2
1
0
0
0
1
3
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
2
0
0
1
1
0
0
0
0
2
1
0
0
0
2
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
6
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
2
1
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
3
0
0
0
0
0
3
0
0
2
0
0
0
0
1
0
1
0
0
0
0
1
1
1
0
0
1
0
1
2
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
2
0
2
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
2
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
2
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
1
1
0
0
2
1
3
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
2
0
1
0
0
0
0
0
2
2
0
0
2
0
0
1
0
0
1
1
1
2
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
3
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
1
0
1
0
0
7
0
0
0
0
3
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
1
1
0
0
2
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
2
2
0
3
0
1
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
1
0
1
2
0
2
0
1
0
0
2
0
2
1
0
0
0
0
1
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
1
0
2
1
0
2
3
2
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
2
1
0
0
1
0
0
0
1
0
0
2
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
2
0
1
2
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
2
0
2
0
1
2
0
0
1
1
0
0
0
0
1
0
0
2
1
0
0
1
0
0
1
2
0
0
0
3
0
0
0
0
0
2
0
0
0
2
1
0
1
0
0
0
0
0
0
0
1
1
2
0
1
1
0
0
0
1
0
0
1
0
0
0
0
2
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
2
0
2
0
0
0
3
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
1
0
0
0
0
0
3
0
1
0
0
2
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
2
3
0
0
0
1
0
0
0
1
0
0
1
0
0
2
0
1
0
0
1
1
3
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
1
0
1
1
1
2
3
1
0
2
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
2
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
3
0
0
2
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
4
0
0
0
0
0
2
2
1
0
2
1
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
2
0
2
0
0
0
0
5
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
2
1
2
2
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
2
0
2
2
1
2
0
1
1
3
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
2
0
0
4
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
1
1
0
2
0
0
0
1
1
0
0
0
0
2
0
0
1
0
0
0
2
0
1
0
2
2
0
0
2
0
0
0
0
0
0
2
1
1
1
0
2
0
2
0
0
2
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
3
2
0
2
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
2
1
0
0
0
2
0
0
0
2
1
0
0
0
0
2
0
2
0
2
0
0
0
0
1
0
0
0
2
0
0
0
4
2
0
0
0
0
0
0
0
0
0
0
0
3
3
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
2
4
0
1
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
2
0
0
0
1
0
2
0
0
0
1
0
2
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
2
0
0
1
0
0
0
1
0
0
0
2
0
0
0
2
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
2
0
0
0
2
0
0
2
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
2
1
0
0
0
2
0
0
0
0
3
0
0
0
3
0
0
0
0
0
0
0
1
3
0
0
0
2
0
0
0
4
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
1
0
0
0
1
1
0
3
0
2
1
2
2
0
1
1
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
1
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
5
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
1
2
2
0
2
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
2
0
0
1
2
0
1
0
0
1
0
0
0
3
0
0
0
0
1
1
0
0
0
0
3
0
0
0
0
0
0
0
0
2
2
0
2
0
2
0
2
0
2
0
0
0
1
0
1
0
0
3
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
2
1
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
2
1
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
1
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
2
2
2
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
3
0
1
0
0
1
0
2
0
0
0
0
2
0
1
0
0
0
2
1
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
2
0
2
0
1
0
0
1
1
0
2
2
2
1
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
2
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
1
0
2
0
2
0
0
0
2
0
0
2
1
2
0
0
0
1
0
0
2
0
0
2
0
3
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
2
3
0
0
0
0
1
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
1
2
1
0
0
2
0
0
0
0
0
2
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
2
2
0
2
0
1
1
2
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
2
1
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
4
2
0
0
0
0
0
0
4
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
1
0
2
2
0
0
2
0
0
0
10
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
1
0
0
0
0
0
0
0
2
0
12
3
0
1
1
2
0
0
2
0
0
0
0
0
2
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
1
0
0
0
0
0
1
0
2
0
1
2
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
2
1
0
1
0
0
2
0
0
0
0
0
0
0
1
1
3
0
0
0
0
0
0
3
0
0
2
0
0
0
0
2
0
2
0
1
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
1
2
0
0
1
0
2
0
0
0
2
0
1
0
1
0
1
2
0
0
1
3
0
2
1
0
1
0
0
0
0
0
4
0
0
0
0
0
1
2
0
2
0
0
0
1
0
0
0
0
0
0
1
2
19
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
4
0
1
0
1
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
2
2
2
2
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
2
0
1
0
0
2
2
1
4
0
0
0
0
0
0
0
3
0
0
0
2
2
0
1
0
0
0
0
0
1
0
2
2
0
0
0
1
0
0
3
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
1
0
1
1
0
0
0
0
1
0
0
1
0
1
0
0
2
0
0
1
2
2
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
2
1
2
6
0
3
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
2
0
0
0
0
1
0
0
0
5
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
2
0
2
0
2
0
0
1
3
2
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
2
2
0
1
0
0
0
0
1
0
0
0
0
2
0
2
0
0
1
2
0
0
0
0
0
0
5
0
4
1
0
0
0
1
0
2
1
0
0
1
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
2
1
0
0
0
0
2
0
0
0
0
4
2
1
1
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
2
2
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
3
2
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
1
1
0
0
0
0
0
0
1
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
5
0
0
2
1
0
1
0
0
0
3
0
1
1
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
3
0
2
1
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
2
3
0
0
0
1
1
2
0
2
2
0
0
1
1
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
2
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
2
2
0
2
0
0
0
2
0
1
0
1
0
0
0
1
0
0
1
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
5
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
3
0
0
0
2
0
1
2
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
2
1
0
1
1
1
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
2
1
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
1
1
0
2
1
0
0
0
0
2
0
0
2
2
3
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
2
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
2
1
0
3
2
0
0
0
0
2
2
2
0
0
0
1
0
1
0
0
0
2
7
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
2
0
1
0
2
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
2
0
1
0
0
0
0
0
2
4
0
2
0
1
0
0
0
0
1
0
0
1
0
1
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
3
0
1
1
0
4
0
0
0
4
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
2
0
0
0
1
0
2
0
0
3
0
1
0
0
0
2
0
0
2
1
1
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
4
3
0
0
1
1
0
0
0
0
0
4
0
0
6
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
1
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
1
0
0
1
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
4
2
1
1
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
1
1
0
0
1
0
2
2
1
0
0
0
0
0
0
1
0
1
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
1
0
0
0
5
0
0
1
1
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
4
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
1
0
0
5
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
2
2
2
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
2
0
1
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
4
0
0
1
1
2
0
3
0
2
0
0
0
0
0
1
2
0
1
0
0
2
1
0
1
0
1
0
3
0
0
0
3
0
0
1
0
0
0
0
0
3
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
4
1
0
3
0
2
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
4
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
2
0
0
0
1
0
0
1
0
2
0
2
0
0
0
0
0
2
0
2
1
0
4
0
0
0
0
3
0
2
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
2
2
0
0
0
0
1
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
2
1
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
1
0
0
2
0
0
2
0
2
0
1
0
0
5
0
0
0
1
3
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
3
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
2
0
1
1
2
0
1
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
1
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
3
1
2
2
0
1
0
3
1
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
3
0
0
2
0
1
0
2
1
1
0
0
2
1
0
2
0
1
0
1
0
1
0
0
0
0
2
0
0
3
0
0
0
0
1
0
0
0
0
0
0
2
2
2
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
2
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
2
0
0
0
2
1
1
2
0
1
0
0
0
0
0
0
1
0
0
0
2
6
0
0
0
0
0
0
1
1
1
3
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
2
1
2
0
2
2
0
0
0
0
0
0
2
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
3
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
2
0
2
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
3
0
0
0
1
0
2
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
3
1
2
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
4
1
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
2
1
2
0
1
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
2
2
0
0
0
1
0
0
0
2
0
1
0
2
2
1
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
3
2
2
1
1
0
0
2
1
2
0
0
0
0
2
0
0
0
0
3
1
0
2
0
3
0
0
2
1
0
1
0
0
2
0
1
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
1
0
1
6
0
0
0
0
0
3
0
0
1
0
0
0
0
0
3
2
0
1
0
0
0
0
9
0
0
2
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
1
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
2
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
3
0
0
2
2
1
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
1
0
0
3
1
0
0
1
0
2
0
0
3
1
2
0
0
1
0
0
2
2
2
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
2
2
0
3
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
2
0
2
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
1
0
0
0
0
2
2
0
0
2
4
0
0
0
0
3
0
0
0
0
2
0
2
0
2
0
0
0
0
0
1
2
0
0
0
1
2
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
3
2
0
0
0
2
0
0
0
3
0
0
1
0
0
0
1
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
2
0
1
0
2
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
2
4
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
2
0
0
2
2
0
0
1
3
1
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
2
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
1
1
0
0
0
3
0
1
0
0
0
1
1
0
0
0
0
0
2
1
1
0
2
0
2
0
1
2
2
0
0
0
1
0
3
0
2
1
0
2
2
0
0
0
2
0
2
0
0
1
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
1
0
2
1
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
2
0
0
0
0
0
2
2
3
0
1
0
0
0
0
0
3
0
0
0
0
2
0
0
1
1
1
0
0
2
0
2
0
2
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
3
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
2
0
1
0
0
0
0
3
0
1
2
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
2
0
1
0
0
2
4
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
1
0
2
2
0
0
2
0
0
1
2
0
0
0
1
1
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
2
0
1
3
1
0
2
2
0
2
0
0
0
2
0
1
3
0
0
0
1
0
0
0
0
0
0
2
3
1
0
0
0
0
0
0
2
1
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
3
0
0
6
0
2
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
1
1
2
0
0
1
0
2
0
1
1
0
0
1
0
0
1
0
1
2
0
1
0
1
0
0
2
0
0
0
0
3
2
1
3
0
0
2
0
0
1
0
2
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
3
0
0
2
1
0
0
2
1
0
1
0
0
0
0
0
0
1
4
0
0
2
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
1
2
1
0
0
0
0
1
0
2
0
0
1
0
0
1
0
2
0
2
2
2
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
3
0
0
1
0
1
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
2
1
0
0
0
2
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
2
1
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
2
0
0
0
2
0
0
0
0
0
2
2
3
0
1
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
2
0
1
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
1
1
0
2
0
1
0
0
0
0
0
0
0
3
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
3
1
0
1
0
0
1
2
0
0
2
0
0
1
0
0
0
0
1
0
2
0
1
0
1
0
2
0
0
2
0
1
2
0
0
1
0
0
0
0
1
1
0
3
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
3
1
1
0
0
0
0
0
0
2
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
3
1
0
0
0
0
0
0
0
1
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
3
0
1
0
0
0
1
0
0
1
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
2
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
4
4
0
2
1
0
0
0
0
1
3
3
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
2
2
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
2
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
2
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
1
1
0
1
2
0
0
0
9
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
2
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
2
0
0
0
0
2
0
0
0
1
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
3
0
1
0
0
0
3
4
0
1
0
0
1
0
1
0
2
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
2
0
0
1
2
0
0
1
1
0
4
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
2
1
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
1
0
0
1
0
2
4
0
2
0
0
0
4
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
2
0
0
1
0
2
0
0
0
3
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
1
1
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
4
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
6
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
1
0
0
0
2
0
0
3
0
1
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
1
0
1
0
0
1
0
3
0
0
0
2
0
0
1
0
0
0
0
1
0
1
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
2
2
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
3
0
0
0
1
0
0
0
0
0
0
3
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
2
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
3
0
0
4
2
0
0
0
3
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
2
2
0
2
0
0
0
0
0
2
2
1
0
0
0
0
1
0
0
2
0
3
0
2
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
2
1
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
2
6
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
2
2
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
1
2
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
1
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
1
0
0
1
1
0
0
0
2
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
4
1
1
0
1
2
1
1
1
1
2
0
0
0
0
1
1
2
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
2
0
1
1
0
0
2
0
0
0
0
0
0
1
1
0
0
0
1
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
2
0
2
1
0
0
0
0
2
2
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
3
0
0
1
0
0
0
2
0
0
0
0
0
2
0
1
0
2
0
0
0
0
3
0
1
0
2
0
0
0
4
1
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
2
0
0
4
0
0
0
2
0
0
2
1
0
0
3
4
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
2
0
0
1
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
2
2
0
2
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
2
0
2
1
1
0
1
1
0
0
3
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
2
0
0
3
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
1
2
0
3
0
3
0
1
0
0
2
0
0
0
1
0
0
0
2
0
0
0
2
1
0
0
1
0
3
0
2
0
0
0
0
4
0
0
0
4
0
0
0
0
2
0
2
0
0
2
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
1
0
1
0
0
1
0
2
0
0
0
2
0
0
0
1
0
0
1
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
1
0
1
0
1
3
0
0
0
0
0
2
0
1
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
1
0
0
0
0
2
2
0
1
1
0
0
2
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
2
1
0
0
0
4
0
0
0
2
0
0
2
0
0
0
0
0
0
2
2
0
0
2
3
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
1
2
1
2
3
2
1
0
3
0
0
0
2
0
0
2
0
1
0
0
1
0
0
0
0
0
0
2
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
1
4
8
0
0
0
0
0
1
1
0
0
0
0
3
0
0
0
0
1
0
2
2
1
0
8
0
1
0
1
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
3
2
0
0
2
0
0
1
0
0
1
1
0
0
0
0
1
0
1
0
0
1
0
0
0
2
0
0
2
0
0
0
2
2
1
3
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
1
2
0
1
0
1
0
2
0
0
0
0
0
3
0
0
1
1
2
0
0
0
0
0
0
1
0
0
0
1
1
0
2
2
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
2
4
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
1
2
1
2
0
0
0
2
0
0
0
1
0
3
0
1
0
0
0
0
2
1
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
3
1
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
2
0
0
0
0
1
0
0
2
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
2
1
0
0
0
0
2
0
0
1
5
0
0
0
0
1
0
0
2
1
0
0
1
0
0
0
0
3
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
2
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
1
0
1
0
1
0
0
1
0
0
0
1
1
0
0
0
2
2
2
1
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
4
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
2
2
0
2
0
1
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
2
2
0
1
0
0
5
1
2
0
0
0
2
2
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
5
0
0
0
0
0
0
0
0
1
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
2
0
2
0
1
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
2
0
1
0
0
0
2
2
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
3
0
1
0
2
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
1
3
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
1
0
1
0
0
1
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
3
2
0
1
0
1
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
2
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
1
1
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
6
0
0
2
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
3
0
0
0
4
0
2
0
2
0
0
1
0
0
0
0
0
1
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
3
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
1
2
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
2
2
0
0
0
1
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
1
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
1
2
1
0
4
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
3
0
4
2
2
0
0
0
0
2
0
2
1
0
0
0
0
1
0
0
0
0
0
0
4
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
3
2
0
0
0
0
0
2
2
0
0
0
1
0
2
0
0
0
0
0
2
2
0
1
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
3
7
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
2
1
0
4
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
5
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
1
0
0
1
0
0
0
2
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
3
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
1
2
1
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
4
0
3
0
0
0
0
0
1
1
0
0
1
1
0
0
2
1
0
0
0
0
2
0
2
0
0
0
0
2
4
1
2
1
0
0
1
0
3
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
2
0
0
0
1
0
0
2
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
1
2
0
0
2
0
0
0
0
2
3
0
0
2
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
1
0
2
0
0
1
0
0
0
0
1
3
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
3
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
3
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
1
0
0
0
2
0
0
1
0
0
0
1
0
2
4
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
2
1
2
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
2
4
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
1
0
3
1
0
0
2
0
0
0
2
0
2
2
1
2
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
1
2
1
0
2
0
0
0
0
2
2
0
1
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
3
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
1
2
1
0
2
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
2
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
2
0
0
0
0
1
1
0
2
0
0
0
0
1
0
0
0
0
2
0
0
1
0
1
0
0
4
0
0
0
0
0
1
0
1
2
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
2
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
3
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
2
3
0
0
0
0
2
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
1
0
4
0
0
0
2
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
3
6
0
0
1
1
0
0
0
0
0
0
0
1
2
0
1
0
0
3
0
0
0
0
0
0
2
0
0
0
1
0
0
1
1
2
1
0
1
4
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
6
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
3
0
1
1
1
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
3
0
1
0
0
0
0
1
0
2
0
0
2
2
0
2
1
0
1
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
2
2
4
0
1
2
0
1
0
0
2
1
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
5
0
0
0
0
0
0
0
0
0
1
0
3
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
2
4
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
4
0
0
0
0
0
0
2
0
2
2
0
0
0
2
0
0
0
1
0
0
2
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
3
1
0
0
0
0
0
2
0
1
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
2
1
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
1
0
1
0
2
0
0
1
1
2
0
0
0
0
1
0
2
0
0
0
0
2
0
0
2
2
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
1
0
1
2
1
0
0
0
0
0
0
1
1
1
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
2
1
0
0
0
0
0
1
0
2
2
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
3
2
0
0
4
2
0
0
0
1
2
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
2
2
0
0
0
2
0
1
1
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
5
0
0
0
1
2
1
0
2
2
0
0
0
1
0
1
2
0
2
2
1
0
1
0
0
0
2
0
1
0
0
3
1
4
0
3
1
0
0
2
0
1
0
1
0
3
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
1
0
0
0
2
0
0
1
0
2
0
1
0
0
0
2
0
0
1
1
0
0
0
1
1
0
0
0
0
2
2
2
3
0
0
0
0
0
0
0
0
0
1
1
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
2
3
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
2
1
2
3
0
0
2
0
2
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
2
0
1
0
0
0
0
1
1
1
0
0
2
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
2
2
0
0
0
0
0
6
0
2
0
0
1
1
2
0
0
0
0
0
2
2
0
2
0
0
2
0
0
0
1
0
0
2
2
2
0
2
0
3
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
2
0
0
1
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
1
0
2
2
1
0
2
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
5
2
0
3
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
2
2
0
2
1
1
0
0
0
0
0
2
0
0
0
0
0
1
0
2
1
0
1
0
0
0
0
1
0
1
0
0
2
0
1
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
1
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
3
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
4
0
2
0
0
0
0
0
0
0
3
0
1
0
0
1
2
0
0
1
0
0
2
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
2
2
0
0
0
0
0
0
2
0
2
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
2
0
1
3
0
0
0
0
1
0
0
0
2
0
9
2
0
0
2
1
0
0
1
1
0
0
0
0
0
1
1
2
0
0
0
0
1
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
3
2
0
0
0
1
0
0
0
0
2
3
1
0
0
0
0
0
5
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
3
0
0
4
2
0
2
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
1
1
0
0
0
0
2
0
1
0
0
0
0
0
3
0
0
1
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
2
0
1
0
0
1
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
1
0
1
1
0
0
0
0
0
0
2
2
2
0
0
0
0
0
2
0
2
2
1
1
2
1
2
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
1
2
0
0
0
2
3
0
0
0
1
0
0
0
0
1
1
0
0
0
5
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
1
0
0
2
0
0
0
1
2
1
0
2
1
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
1
2
0
1
0
0
0
0
0
3
0
0
0
2
0
0
1
0
0
0
0
0
0
2
2
0
4
1
2
0
0
2
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
2
3
0
0
1
0
1
0
0
2
0
0
0
0
2
5
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
3
0
0
0
0
2
2
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
4
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
2
0
0
0
1
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
2
0
2
0
0
0
2
0
0
0
0
2
1
1
2
0
0
1
1
0
0
0
2
0
0
2
0
0
0
0
1
0
1
1
0
0
0
0
1
0
2
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
2
1
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
3
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
1
0
0
0
1
2
0
1
0
0
2
1
0
0
2
1
0
0
1
2
0
0
2
0
2
0
1
0
2
3
0
0
2
1
1
3
0
0
0
0
0
2
0
1
1
0
1
0
3
0
2
1
0
0
0
0
0
0
0
1
0
0
1
0
0
3
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
2
0
1
0
0
2
0
0
2
1
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
2
0
0
0
1
0
2
1
0
0
0
0
2
0
0
2
0
2
0
0
2
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
1
3
0
1
2
0
4
0
0
0
2
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
2
0
2
3
0
0
0
1
1
0
0
0
8
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
2
0
0
0
0
1
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
4
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
1
0
0
3
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
4
2
0
0
0
0
0
0
1
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
1
0
1
2
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
1
0
2
0
0
0
2
0
0
0
2
0
0
3
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
1
1
3
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
3
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
1
1
0
0
1
2
0
1
1
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
2
0
0
0
1
0
3
0
2
0
0
0
1
1
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
1
0
1
4
0
0
2
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
2
4
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
1
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
2
0
0
0
1
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
2
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
2
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
2
3
0
2
0
0
0
0
0
1
1
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
2
2
2
2
0
2
1
1
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
1
1
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
10
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
1
1
0
0
0
0
1
0
0
0
2
2
1
0
0
2
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
2
2
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
1
1
1
0
0
0
2
0
2
0
2
0
0
0
0
3
0
8
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
1
2
0
0
0
2
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
2
0
0
0
2
3
0
0
0
0
0
0
0
2
0
0
0
3
2
2
0
0
0
1
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
5
0
0
0
1
0
0
1
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
1
2
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
2
0
0
2
3
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
2
0
3
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
3
0
0
0
2
1
0
0
0
0
0
2
0
0
1
0
1
2
0
0
0
0
0
0
0
1
0
3
2
0
1
1
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
1
1
0
0
1
2
2
0
0
0
0
1
2
0
1
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
2
1
0
0
3
2
0
0
0
0
0
0
2
1
2
1
0
0
1
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
2
2
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
1
1
0
0
2
0
2
1
0
3
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
1
0
3
0
0
0
0
1
1
1
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
1
2
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
2
0
0
0
0
1
0
0
1
1
0
2
2
0
2
0
0
0
2
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
2
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
1
0
0
0
0
0
0
2
2
0
0
0
2
1
2
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
5
0
2
2
2
1
0
2
1
1
1
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
2
0
0
0
0
2
2
0
0
2
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
7
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
2
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
1
0
0
3
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
3
0
3
0
2
0
0
0
1
1
0
0
0
0
1
1
0
0
0
2
2
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
1
1
1
0
0
1
0
0
0
3
0
0
0
2
0
0
2
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
2
2
0
0
0
1
2
1
2
0
0
1
0
0
0
0
0
2
0
2
3
0
2
0
0
1
0
0
1
2
0
2
0
0
5
0
0
0
4
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
2
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
2
3
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
4
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
2
0
0
2
0
1
0
0
0
1
0
1
0
0
0
2
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
2
0
0
3
6
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
6
0
0
1
0
0
0
0
0
0
2
1
1
0
1
0
2
0
0
0
0
2
0
1
1
1
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
3
0
0
1
2
0
0
2
0
1
0
0
2
1
0
1
0
0
0
0
12
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
1
0
2
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
3
0
0
0
1
2
2
1
1
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
1
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
1
2
1
1
0
1
0
0
0
0
2
0
0
2
1
2
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
3
0
0
1
0
0
1
0
2
0
0
2
1
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
1
0
0
1
2
0
0
2
0
0
2
2
0
1
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
2
1
0
0
3
0
0
0
0
0
1
0
2
2
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
1
0
0
0
2
0
2
2
0
3
0
0
0
0
0
0
2
0
0
0
0
0
4
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
2
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
3
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
1
0
2
1
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
1
2
0
1
1
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
3
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
3
0
2
2
0
2
0
1
0
0
0
2
0
2
2
1
2
0
0
0
2
2
0
0
2
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
1
1
0
0
1
0
2
1
0
0
1
1
1
0
1
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
1
0
0
0
0
1
2
1
0
0
0
1
0
0
0
0
0
2
4
1
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
2
0
1
0
5
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
1
0
2
2
0
0
1
1
0
1
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
1
0
2
0
2
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
2
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
5
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
2
0
2
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
1
2
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
2
1
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
4
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
1
2
1
2
1
1
0
0
0
0
2
3
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
1
1
0
0
0
0
0
0
2
0
0
0
2
0
1
0
3
0
0
0
0
3
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
1
2
2
0
0
1
1
0
2
2
0
0
0
2
0
0
0
0
0
1
0
1
0
1
1
1
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
2
0
2
1
0
0
0
0
1
0
1
0
0
2
3
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
1
0
1
0
2
0
0
1
1
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
1
0
0
1
0
1
0
1
1
0
0
0
0
3
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
2
1
0
0
2
0
0
1
7
1
1
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
2
1
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
2
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
1
0
1
0
2
0
0
3
0
1
3
0
0
0
0
2
0
1
1
0
0
0
1
0
0
0
1
0
3
0
0
3
5
0
0
2
0
0
0
1
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
1
1
0
2
0
2
0
1
2
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
1
2
0
0
2
0
0
0
0
0
2
4
0
2
2
2
0
0
1
0
0
0
0
3
0
0
0
0
1
0
0
2
2
0
1
1
2
0
0
0
0
1
0
1
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
1
0
1
0
0
2
0
0
0
1
0
2
2
1
2
0
0
0
3
0
0
0
0
1
0
0
0
0
4
0
1
0
3
0
0
0
3
0
0
0
0
0
0
1
2
0
2
2
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
7
0
0
0
0
0
1
2
0
2
0
2
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
6
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
4
1
0
0
2
2
0
0
1
0
1
2
0
0
0
0
2
0
0
0
0
0
0
1
0
2
2
0
3
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
4
2
0
0
0
0
2
1
0
0
0
0
0
0
1
0
2
1
0
0
0
2
0
0
0
0
2
3
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
1
0
0
0
0
2
0
0
0
0
0
5
3
0
1
0
0
0
2
0
0
0
0
2
0
0
0
1
1
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
3
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
2
0
0
0
1
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
2
0
0
2
1
0
0
3
1
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
2
1
3
0
1
0
2
0
0
1
1
2
0
0
0
1
0
0
0
0
1
0
1
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
2
0
0
1
0
0
2
0
2
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
4
0
1
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
3
1
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
1
0
0
0
0
2
0
2
1
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
5
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
1
2
0
1
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
4
0
0
2
1
1
0
1
0
1
0
2
0
0
4
1
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
2
0
0
0
0
0
2
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
2
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
8
0
2
0
1
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
2
0
2
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
2
0
1
2
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
2
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
6
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
2
0
0
0
3
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
4
2
1
0
0
0
0
1
1
1
2
0
0
0
0
0
0
0
2
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
2
1
2
1
0
0
1
0
2
2
0
3
0
0
0
0
2
0
0
1
0
2
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
5
0
0
0
1
0
0
1
2
0
1
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
2
0
0
0
0
2
2
3
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
1
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
2
1
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
3
2
2
0
1
0
0
0
0
0
0
1
0
0
3
0
2
0
0
0
0
0
0
0
2
1
1
0
0
0
1
0
0
1
0
0
19
4
3
0
0
2
2
3
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
4
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
1
0
1
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
2
2
0
0
0
4
0
0
0
0
0
4
1
0
0
0
4
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
2
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
3
0
0
0
0
1
2
1
1
0
2
0
2
0
1
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
1
2
0
2
2
0
0
0
0
0
0
0
0
0
2
0
2
1
1
2
0
0
0
1
0
0
1
1
0
4
0
0
2
0
0
3
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
3
1
2
0
1
0
0
0
0
0
0
2
0
2
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
4
2
0
0
0
2
2
0
0
1
0
3
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
1
2
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
1
0
2
0
2
0
0
2
0
0
0
1
2
2
0
0
0
0
0
4
0
0
2
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
2
0
2
0
0
0
0
2
0
1
3
0
2
0
2
0
0
2
0
2
0
0
4
1
0
0
0
1
3
2
0
5
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
9
0
2
1
0
2
0
0
0
0
0
0
0
0
2
0
2
1
0
3
3
3
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
1
2
1
4
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
3
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
1
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
1
1
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
2
2
0
0
0
0
0
2
0
1
3
2
0
0
2
2
0
0
0
1
0
0
2
0
2
0
0
0
0
1
1
1
0
1
0
0
0
0
0
2
0
0
0
5
2
1
2
0
0
0
0
0
0
0
0
3
2
0
1
0
0
0
3
0
0
2
2
0
1
0
0
1
0
0
0
1
0
0
0
0
3
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
9
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
3
2
2
1
0
0
1
0
0
2
6
0
0
0
2
2
0
0
0
0
0
2
3
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
3
0
0
2
0
0
1
2
1
0
0
0
2
2
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
3
0
2
2
0
0
1
0
0
0
2
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
2
0
1
0
1
0
2
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
2
2
1
0
1
1
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
1
0
1
1
0
0
1
2
0
0
1
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
2
0
2
1
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
3
0
0
0
0
0
2
3
0
0
1
2
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
2
0
0
3
1
0
2
0
0
0
0
2
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
1
0
0
1
0
0
0
1
4
0
0
0
0
0
0
1
1
1
0
1
0
0
1
0
0
2
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
1
2
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
2
0
2
2
0
2
0
0
0
0
0
0
0
0
0
5
0
0
2
2
0
2
0
0
0
0
0
0
0
1
1
0
2
2
2
1
0
2
0
0
0
2
0
0
0
0
2
0
0
2
1
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
2
0
4
0
2
3
2
0
0
0
1
1
1
1
0
0
0
3
0
1
0
1
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
3
0
0
0
1
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
4
1
0
0
0
0
0
0
0
0
9
0
0
0
0
0
0
1
0
3
2
1
1
0
0
1
1
1
0
0
1
3
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
1
1
7
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
8
0
0
0
2
0
0
0
0
0
0
1
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
4
2
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
3
2
0
0
1
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
3
0
0
0
0
0
2
1
1
0
3
2
0
1
0
0
0
0
1
0
0
1
1
0
1
0
2
0
2
0
1
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
1
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
1
2
0
7
0
0
0
0
0
0
2
0
0
4
0
0
0
0
0
6
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
2
0
0
0
0
1
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
2
1
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
1
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
5
1
0
0
0
1
0
0
3
2
0
2
4
0
0
2
0
0
0
0
1
2
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
2
1
0
1
0
0
2
3
1
2
1
2
0
0
0
1
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
6
0
0
1
1
0
0
1
0
0
0
1
0
0
2
2
0
2
0
2
0
0
2
0
0
0
0
0
0
0
3
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
5
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
2
2
0
0
0
0
1
0
1
0
2
0
0
0
0
2
2
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
2
0
1
0
0
2
2
1
0
0
0
0
0
0
0
4
0
3
0
0
0
3
1
2
0
0
2
0
0
1
0
0
0
0
3
2
0
0
2
0
2
0
0
1
0
0
0
2
0
2
0
0
1
2
0
0
0
2
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
4
0
1
0
0
0
0
1
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
3
0
0
2
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
2
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
2
2
0
0
0
2
2
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
4
0
1
0
2
0
0
1
0
0
0
3
1
3
0
0
3
0
1
0
2
0
0
1
0
1
0
1
0
0
0
0
2
2
2
0
2
0
2
1
1
0
0
0
0
0
6
0
0
0
1
2
0
0
2
0
1
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
2
0
3
0
1
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
2
2
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
1
1
2
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
1
3
2
0
0
0
0
0
0
1
0
1
0
0
0
1
2
0
2
0
2
0
1
0
0
0
1
0
0
0
0
1
0
0
0
2
2
2
1
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
1
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
6
0
0
2
0
1
0
0
1
2
0
0
0
10
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
6
0
0
3
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
3
0
2
2
0
1
0
4
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
1
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
1
0
3
0
0
0
0
0
0
2
0
0
2
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
1
2
2
1
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
2
2
0
0
0
0
1
2
0
0
0
3
0
0
2
2
0
2
2
0
0
3
0
0
0
4
0
0
0
0
0
0
0
0
1
2
0
1
0
0
3
3
0
0
0
2
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
1
0
1
2
2
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
2
2
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
2
1
2
0
0
1
0
0
0
1
0
0
0
0
1
0
2
0
0
8
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
1
0
2
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
2
0
0
0
1
0
0
2
1
0
1
0
0
0
1
0
0
0
0
1
0
0
2
2
0
0
0
1
0
1
0
1
0
0
0
1
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
4
0
0
1
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
1
0
0
0
2
2
0
0
2
0
0
0
2
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
2
0
0
0
2
1
0
1
0
0
0
0
0
0
1
2
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
3
0
2
1
2
1
0
0
3
0
0
0
1
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
2
0
0
2
2
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
3
1
0
0
0
0
1
0
0
0
2
2
1
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
2
0
0
0
1
0
2
0
0
0
0
4
0
2
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
2
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
3
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
3
2
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
2
0
1
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
2
0
0
0
0
1
5
0
0
0
0
0
0
4
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
2
0
0
0
1
0
0
2
4
5
0
0
1
1
0
0
0
0
0
0
0
2
3
1
0
2
0
1
1
0
0
0
0
0
0
1
0
1
1
0
0
2
1
0
1
0
0
1
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
1
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
2
0
0
0
1
0
0
2
0
0
0
1
3
2
2
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
3
0
0
1
2
0
3
0
0
0
0
1
0
0
2
0
1
0
2
1
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
1
2
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
4
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
1
1
0
1
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
1
0
1
1
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
2
7
2
0
0
1
0
0
0
0
0
0
0
0
7
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
1
1
2
3
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
2
0
2
0
1
0
0
2
0
1
0
1
0
0
5
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
1
3
1
0
0
1
0
2
0
1
0
2
0
0
0
2
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
3
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
7
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
2
0
2
0
1
0
0
0
0
0
1
0
0
2
0
0
2
0
0
1
0
2
0
0
0
0
0
0
1
0
0
1
2
2
1
0
0
2
2
2
4
0
3
0
0
0
0
0
0
0
0
1
0
2
0
0
1
2
2
0
0
0
0
0
2
0
2
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
2
3
0
2
0
0
0
1
0
1
0
0
2
2
0
0
1
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
2
4
0
5
1
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
2
0
0
1
0
0
1
1
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
3
0
0
1
0
0
3
0
0
0
0
1
2
3
2
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
2
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
2
0
0
0
0
6
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
1
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
1
0
2
2
0
0
0
0
0
1
2
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
1
1
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
1
0
3
0
0
0
0
1
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
3
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
3
0
0
0
1
0
2
0
0
0
0
1
0
0
0
1
2
0
2
0
2
2
0
0
4
0
2
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
1
2
2
0
2
1
1
0
0
0
0
0
0
2
1
0
0
2
2
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
1
2
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
3
1
0
0
1
1
0
2
0
0
2
0
0
0
0
1
2
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
5
1
0
0
0
0
0
2
0
1
0
2
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
3
4
3
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
5
0
0
1
1
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
3
0
6
1
1
0
2
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
5
0
1
0
0
0
0
5
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
3
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
2
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
2
1
1
0
5
0
2
0
5
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
2
1
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
5
0
2
0
0
0
1
0
2
0
2
0
0
2
2
3
2
2
1
1
0
2
0
0
0
0
0
0
2
0
0
0
2
0
6
0
0
0
0
4
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
3
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
1
0
2
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
2
0
1
0
2
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
1
0
2
0
0
1
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
2
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
1
0
0
2
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
2
0
2
0
3
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
1
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
3
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
4
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
4
1
0
0
3
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
3
0
3
0
0
2
0
0
0
0
0
0
1
1
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
5
1
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
1
0
2
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
1
3
0
1
0
0
2
0
0
1
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
2
2
0
1
0
0
1
2
0
2
1
0
0
0
2
0
0
2
0
0
3
0
0
2
0
2
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
2
0
2
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
1
0
0
2
0
0
2
2
0
0
2
0
2
1
1
1
4
0
0
3
0
0
0
0
1
0
2
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
1
1
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
2
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
1
1
0
3
0
2
1
0
0
0
1
1
0
0
2
0
0
0
1
0
2
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
1
0
0
0
0
0
0
1
2
0
0
0
2
0
0
1
1
0
0
4
1
0
0
0
0
2
0
0
0
2
2
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
2
3
0
2
0
0
0
2
1
1
0
0
2
0
0
0
0
0
0
0
3
1
0
0
0
1
0
1
0
0
0
0
0
0
1
1
3
0
0
1
0
2
1
0
1
1
1
2
0
0
2
0
2
2
0
0
0
1
0
1
0
0
2
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
2
0
0
0
0
1
0
2
2
1
0
0
3
1
0
0
0
0
1
0
4
1
0
0
5
1
0
0
0
0
2
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
2
3
0
3
0
1
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
9
0
0
0
2
0
0
0
3
0
0
2
0
1
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
3
0
0
5
0
0
0
0
0
2
2
0
0
3
0
0
0
0
1
0
0
0
1
1
0
2
2
0
0
1
0
0
0
0
0
0
0
0
1
2
0
5
0
1
1
0
0
2
0
2
0
0
0
0
0
2
0
3
0
0
0
0
0
1
1
0
2
0
0
0
2
1
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
3
0
2
0
1
0
0
0
0
0
0
8
0
0
3
1
2
0
0
0
1
0
7
0
0
2
0
0
0
0
0
1
3
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
1
0
0
0
3
1
0
1
0
1
2
1
0
2
0
0
0
0
0
0
2
0
2
0
0
0
3
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
3
0
0
0
2
0
2
0
0
9
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
2
2
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
1
2
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
2
1
0
1
1
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
2
0
1
1
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
2
0
4
1
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
2
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
3
0
0
0
0
0
0
2
1
1
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
2
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
1
0
0
0
0
0
0
0
2
1
1
1
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
2
2
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
3
0
0
0
0
2
1
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
2
0
0
2
0
1
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
1
1
0
3
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
2
0
0
0
0
0
0
10
0
0
2
0
0
0
0
2
0
0
2
1
0
2
0
0
0
0
0
1
2
1
0
8
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
4
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
2
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
1
0
0
0
2
2
0
1
0
2
1
0
0
2
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
4
0
0
2
0
2
0
0
2
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
1
0
0
0
0
0
0
2
2
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
2
0
0
1
0
1
1
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
2
2
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
6
1
1
0
2
0
0
2
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
2
0
0
0
1
2
0
1
0
0
3
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
2
4
0
0
2
1
0
0
0
1
0
2
1
0
1
0
0
2
2
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
3
1
3
1
0
2
0
0
0
2
0
0
0
0
0
1
0
1
1
1
0
2
0
0
0
1
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
9
1
2
1
0
0
1
0
1
0
0
0
1
0
0
0
0
2
2
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
4
0
0
1
0
0
0
0
0
4
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
2
0
0
0
2
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
1
2
0
0
3
0
0
0
0
2
0
1
2
0
2
0
0
1
1
2
0
0
0
0
0
1
0
1
0
0
4
0
1
0
0
0
2
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
2
2
0
1
0
1
0
3
3
1
0
1
2
0
0
0
1
1
2
2
0
0
1
2
1
6
0
0
3
0
2
2
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
1
1
0
0
0
2
0
2
0
2
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
2
0
1
0
0
3
1
0
0
0
0
0
0
0
1
0
2
0
1
6
2
1
0
0
0
1
0
0
0
0
0
0
3
0
2
0
2
0
0
1
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
2
1
2
0
2
0
0
0
0
1
1
0
2
0
0
1
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
2
6
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
8
0
0
3
0
2
0
2
1
0
0
1
0
0
0
1
0
0
0
2
2
0
0
1
0
2
1
5
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
2
0
1
2
0
0
0
2
0
0
0
0
0
1
2
1
1
0
0
1
0
2
0
0
0
2
0
0
0
0
2
2
0
0
1
0
0
0
0
0
1
0
2
3
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
1
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
1
1
0
3
0
0
1
0
0
0
0
1
0
0
1
0
1
3
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
4
1
0
1
0
0
1
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
2
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
2
1
0
1
2
0
3
0
1
0
0
1
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
3
0
0
1
0
2
0
1
1
0
2
4
0
0
2
0
0
0
0
0
0
0
1
0
0
2
1
0
1
0
0
2
0
2
1
0
0
0
1
2
0
0
0
2
4
2
3
0
2
0
2
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
1
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
1
2
1
0
0
1
0
2
0
2
2
0
0
1
0
2
0
0
0
0
0
0
0
1
0
1
0
0
2
0
1
0
0
0
0
0
2
2
0
2
0
0
0
1
0
0
3
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
2
2
1
0
0
0
0
1
2
0
1
0
0
0
4
1
3
0
1
0
2
0
0
0
0
0
0
1
2
2
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
1
0
0
3
0
0
2
3
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
3
1
3
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
2
2
0
0
2
0
0
1
3
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
3
0
1
2
0
0
0
0
0
0
0
0
3
1
2
0
0
0
0
0
0
2
1
2
2
0
0
0
0
2
2
1
1
2
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
2
0
2
0
1
5
0
0
2
0
2
2
3
2
0
2
1
2
3
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
1
0
0
4
1
1
0
0
0
1
0
1
2
1
2
1
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
2
2
0
0
0
1
2
2
0
0
1
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
2
0
1
4
0
1
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
2
3
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
1
0
2
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
3
0
2
2
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
4
1
0
0
0
3
0
0
2
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
1
2
2
5
0
1
0
0
0
0
0
0
1
0
1
0
1
5
0
1
0
0
2
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
1
1
0
0
2
0
2
0
0
0
2
2
1
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
2
1
0
0
0
1
0
0
0
1
0
2
0
3
0
5
0
0
2
0
0
2
0
1
0
0
0
1
0
0
2
1
0
0
10
0
0
0
2
2
0
0
0
0
1
0
1
1
0
0
1
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
3
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
1
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
3
0
2
0
0
1
1
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
2
1
2
1
0
0
0
2
2
0
0
1
0
1
2
0
2
1
3
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
2
1
0
0
1
0
0
0
0
1
0
0
0
2
0
3
0
0
0
0
0
0
1
0
0
0
2
5
0
0
0
0
0
0
1
0
0
0
0
3
0
1
2
1
0
0
0
0
2
2
2
1
0
1
0
1
0
2
0
1
0
0
0
1
0
1
1
0
0
1
2
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
3
0
0
0
4
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
7
0
0
3
0
1
0
0
0
2
2
0
2
2
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
2
2
0
0
3
1
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
2
2
0
2
0
0
1
0
1
0
0
0
0
0
0
2
2
2
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
1
0
0
1
0
1
0
0
0
1
0
0
2
0
1
1
0
0
2
2
3
0
0
2
0
0
0
2
1
0
0
2
1
0
0
0
3
0
0
0
0
0
0
0
2
3
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
1
0
0
2
1
0
0
0
1
0
0
2
0
0
1
1
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
1
1
2
0
0
1
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
2
0
2
0
0
0
2
1
0
0
0
0
1
0
0
0
1
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
1
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
3
0
1
2
2
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
1
3
0
0
2
0
2
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
1
0
1
2
1
2
0
0
0
0
0
0
2
0
3
1
2
0
2
1
0
3
0
0
0
0
0
0
2
0
0
1
0
3
0
2
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
2
2
2
2
1
2
0
0
2
0
0
0
0
0
0
0
3
1
2
0
0
0
0
0
1
0
0
2
0
0
1
1
0
2
5
2
0
0
1
2
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
1
2
0
1
2
3
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
1
2
3
2
0
0
0
2
0
0
1
0
0
0
2
0
0
2
0
8
0
0
2
0
0
0
1
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
3
0
4
0
2
2
0
0
0
2
0
2
1
0
1
0
3
2
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
2
2
0
2
0
0
0
0
0
1
2
1
0
2
0
0
0
0
2
0
0
2
0
0
1
3
2
3
0
0
0
1
0
0
0
1
0
1
1
0
2
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
1
0
2
0
1
0
2
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
4
0
0
0
0
0
0
0
0
1
0
0
0
1
0
3
0
0
1
0
0
1
0
0
0
0
0
0
0
2
1
2
0
0
0
3
0
1
1
1
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
2
0
0
2
1
0
0
0
0
2
0
2
0
0
0
0
2
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
2
0
0
2
3
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
1
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
3
3
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
2
0
0
0
0
3
0
0
0
0
0
0
4
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
5
0
1
0
0
2
2
0
0
1
0
0
0
0
0
0
0
1
2
0
0
2
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
2
2
2
1
0
1
0
4
0
0
0
0
1
0
2
0
0
0
3
0
2
0
0
2
0
2
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
2
0
0
2
1
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
4
1
0
1
0
0
0
0
1
1
0
0
1
4
1
2
0
0
0
1
0
1
1
0
2
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
3
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
2
0
0
3
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
3
0
0
0
2
0
0
1
0
0
0
1
2
1
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
3
0
0
0
0
2
2
1
0
0
0
2
2
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
1
0
0
2
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
5
0
0
0
0
0
1
0
0
0
2
0
0
0
2
1
1
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
1
2
0
4
0
2
0
0
0
0
4
1
0
2
0
2
0
0
0
3
0
0
0
3
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
2
0
0
0
2
2
1
0
0
0
2
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
1
0
0
2
0
3
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
8
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
1
1
2
0
0
1
0
0
0
1
0
2
3
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
2
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
2
2
1
0
0
0
0
0
0
2
1
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
2
1
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
2
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
1
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
2
0
2
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
2
0
1
2
0
1
0
0
0
0
2
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
1
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
4
0
0
3
0
0
0
4
0
2
0
2
2
1
2
0
2
0
2
2
2
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
2
3
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
2
0
2
0
1
1
0
0
1
1
0
1
1
0
0
2
3
2
0
0
0
1
0
0
0
0
1
0
0
1
2
1
0
2
0
0
0
1
3
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
4
0
0
0
1
0
0
0
2
0
2
0
0
0
0
7
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
1
0
0
0
0
2
1
0
0
0
0
1
0
0
2
1
0
1
2
0
0
0
2
0
0
2
2
0
0
0
0
2
1
7
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
2
0
0
1
3
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
1
0
1
0
0
0
1
0
1
0
1
0
2
1
0
0
0
0
0
1
0
0
1
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
2
0
0
12
0
0
0
1
0
3
2
0
0
2
0
0
0
1
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
3
2
0
0
0
0
1
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
1
0
0
3
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
3
2
0
0
0
1
0
1
0
0
0
0
1
2
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
1
0
2
0
2
0
0
1
0
1
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
5
0
0
0
2
0
0
2
0
1
1
2
0
0
0
0
0
0
0
1
0
0
0
0
1
1
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
2
0
4
1
0
0
0
0
0
0
0
0
1
2
0
0
2
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
2
0
16
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
1
0
0
2
0
0
0
2
1
2
0
2
0
2
0
0
1
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
3
2
3
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
3
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
2
0
0
0
2
0
0
0
1
0
3
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
1
2
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
2
0
2
4
0
2
1
0
0
0
0
0
0
0
1
0
3
0
0
1
0
0
1
0
3
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
1
1
0
2
2
0
0
0
0
0
2
2
1
0
0
8
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
2
0
1
0
0
1
5
1
0
0
2
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
2
2
0
2
3
0
0
0
0
0
0
0
3
1
0
0
0
0
2
6
0
0
1
1
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
1
0
1
0
0
0
1
0
0
4
0
0
1
0
1
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
13
0
0
0
0
0
1
0
3
0
0
1
2
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
1
0
2
1
0
0
0
0
0
0
1
4
0
0
1
0
1
1
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
1
0
4
0
2
0
2
0
1
0
0
0
0
0
2
0
0
0
0
8
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
1
2
0
0
0
0
0
1
0
1
0
0
0
3
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
1
4
0
2
1
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
1
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
1
0
0
3
0
2
0
0
0
0
0
2
3
1
0
0
2
0
0
0
0
0
2
0
0
2
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
3
0
0
0
1
0
0
4
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
2
3
0
0
2
0
0
1
0
1
1
1
0
1
1
0
3
0
0
0
0
0
0
1
0
0
2
1
0
0
0
1
0
1
0
0
1
0
1
4
2
2
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
5
2
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
1
3
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
1
2
0
2
0
0
0
0
0
1
1
2
2
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
2
0
0
0
2
0
0
2
0
2
0
0
0
2
1
3
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
2
2
2
1
3
2
0
0
0
0
0
2
0
0
0
1
0
2
1
0
0
3
0
1
0
0
1
0
0
0
3
2
1
0
2
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
2
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
1
0
0
0
2
0
0
0
0
0
2
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
2
2
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
1
1
0
2
0
2
0
2
2
1
0
0
0
2
0
0
0
3
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
1
0
0
1
3
0
2
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
1
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
4
0
0
0
0
0
0
1
0
0
0
0
1
0
2
1
1
0
1
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
3
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
1
1
1
0
0
1
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
1
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
2
0
2
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
3
1
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
1
0
1
0
3
0
0
1
1
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
2
0
1
0
0
0
0
1
0
0
2
0
2
1
0
1
0
2
0
1
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
2
0
0
0
0
1
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
3
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
2
2
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
2
1
0
0
2
1
3
1
0
0
1
0
2
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
1
0
1
0
1
0
0
0
1
0
0
0
3
0
2
0
0
0
0
0
2
2
1
2
0
0
0
2
0
1
2
0
1
4
0
0
1
0
2
1
0
0
2
0
3
2
1
0
0
0
2
1
0
0
1
0
0
2
2
0
1
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
6
1
1
0
2
0
2
0
0
0
2
0
0
4
2
0
1
2
1
0
0
0
2
0
2
0
0
2
1
0
2
1
0
0
2
3
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
2
0
0
2
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
1
2
0
2
1
1
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
1
0
0
0
0
2
2
2
0
0
0
1
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
2
0
2
0
0
0
0
0
0
1
1
0
3
0
0
0
0
0
0
0
0
0
0
0
4
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
2
3
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
2
2
0
2
1
1
0
0
0
1
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
2
0
2
1
0
1
0
1
0
2
1
0
0
0
0
0
0
1
0
0
0
0
2
0
2
2
1
0
3
0
1
2
0
0
1
0
0
0
0
0
0
1
0
0
0
3
3
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
2
2
2
3
0
0
1
2
0
0
0
0
2
0
0
2
0
0
0
0
2
1
2
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
1
0
0
0
0
2
0
2
0
0
2
0
0
0
1
0
0
0
2
0
0
1
0
0
0
1
2
0
0
0
3
0
0
0
0
0
0
0
2
2
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
3
0
0
0
1
0
0
0
2
1
0
2
0
0
0
0
0
2
0
0
2
0
0
0
3
0
1
2
0
0
0
0
0
2
0
3
1
0
0
0
0
0
2
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
2
0
0
3
1
0
2
0
0
0
0
0
1
2
0
0
0
1
0
0
6
0
0
0
0
0
0
0
4
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
1
1
0
2
0
1
0
1
0
0
0
0
0
0
1
0
1
4
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
1
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
2
1
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
2
1
0
0
0
0
11
0
1
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
1
0
0
0
7
0
0
1
0
0
2
4
0
0
0
0
0
0
0
0
1
0
0
1
2
2
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
1
0
4
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
2
1
0
0
2
0
0
0
1
0
2
0
0
0
0
0
3
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
1
5
1
0
1
2
0
0
0
1
0
0
0
0
3
0
0
1
10
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
1
0
1
0
0
2
2
0
1
2
0
1
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
2
1
0
0
0
0
0
0
1
0
0
0
1
1
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
2
0
2
0
3
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
1
5
11
1
0
0
0
0
0
0
1
0
2
1
2
0
0
1
0
0
0
0
0
2
1
0
1
2
1
0
1
0
0
1
0
3
1
0
0
0
4
0
0
0
1
0
0
0
2
0
2
0
1
0
1
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
4
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
2
0
1
0
3
0
0
0
2
3
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
1
1
1
1
0
2
0
0
3
0
0
1
5
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
1
1
0
0
1
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
2
0
0
0
1
1
0
2
0
0
0
0
10
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
1
0
0
0
0
0
0
2
0
0
2
2
0
0
0
1
1
0
4
2
3
0
1
0
2
3
0
0
0
0
2
0
2
1
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
3
0
1
0
0
0
3
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
5
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
1
0
1
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
2
2
0
0
1
0
0
0
1
0
1
0
1
2
0
0
0
2
0
0
1
2
1
0
0
1
1
1
0
0
2
1
0
0
0
1
0
0
2
1
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
3
1
1
0
0
0
2
1
0
3
0
0
0
0
3
0
1
0
1
0
0
1
0
2
1
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
2
0
0
2
2
0
0
0
0
2
0
2
2
2
0
0
0
0
2
0
0
0
0
2
1
1
0
0
0
0
2
0
0
3
0
2
0
2
0
6
0
0
0
0
0
0
0
0
0
3
2
0
0
2
0
0
0
0
3
0
0
0
0
1
0
1
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
5
0
2
3
0
0
0
1
2
0
0
0
0
0
3
0
0
1
2
0
0
1
0
0
0
0
0
0
0
2
2
0
2
3
0
0
0
1
0
0
2
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
2
0
1
0
0
1
0
0
0
0
1
0
1
0
1
0
1
2
1
0
1
0
0
2
1
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
5
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
2
0
0
2
0
1
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
3
0
0
0
0
0
1
2
0
0
1
1
6
1
0
0
0
2
0
1
0
3
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
2
2
0
0
0
2
0
0
2
4
2
1
0
0
0
0
1
0
0
0
0
3
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
1
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
4
2
0
1
0
0
0
1
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
2
0
1
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
1
0
0
0
0
2
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
2
0
0
0
2
0
1
3
0
0
0
0
0
2
0
1
0
2
1
0
2
0
1
2
0
2
0
2
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
1
2
0
2
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
1
0
0
0
0
1
0
0
2
1
2
2
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
2
0
2
0
2
2
0
1
0
0
2
2
3
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
1
1
0
2
3
0
2
0
1
0
0
0
0
0
2
0
0
0
2
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
1
0
0
0
0
0
0
0
0
1
2
0
0
1
1
0
0
0
0
0
0
0
0
1
0
3
0
2
0
1
0
4
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
1
0
1
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
1
1
0
1
1
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
3
0
1
0
1
0
0
0
1
2
0
2
2
0
0
0
2
0
0
2
0
0
0
2
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
1
1
0
0
2
0
0
0
1
0
2
0
2
2
0
0
0
2
1
2
2
1
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
2
0
1
0
0
0
0
5
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
2
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
2
4
0
0
0
0
0
2
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
2
0
2
2
0
0
0
0
0
0
1
1
2
0
1
1
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
1
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
2
0
2
0
0
1
0
1
0
0
0
1
0
0
0
4
2
0
2
2
0
0
2
0
0
1
0
0
0
0
0
2
0
2
1
0
2
2
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
3
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
1
0
0
0
2
0
2
2
0
0
0
0
0
0
0
2
0
0
1
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
5
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
1
2
0
0
0
0
0
0
0
0
1
0
1
2
2
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
6
1
2
0
2
0
0
2
2
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
1
2
0
0
1
1
0
0
0
3
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
3
0
0
0
0
0
1
0
0
1
0
2
0
0
0
3
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
3
0
0
1
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
3
0
0
2
0
1
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
2
0
0
1
0
0
0
1
3
1
1
2
0
2
2
0
0
0
4
0
1
0
2
1
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
1
0
2
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
5
0
1
0
0
1
2
2
2
0
0
0
0
0
0
0
1
0
0
0
0
2
1
2
0
0
0
0
0
2
0
0
2
0
0
0
0
2
1
0
1
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
1
0
0
1
0
1
0
0
0
2
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
2
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
2
0
2
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
1
2
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
1
0
2
0
1
2
1
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
1
0
2
0
1
0
1
4
0
2
0
0
0
0
1
2
0
0
0
0
2
0
2
1
2
0
0
0
0
0
0
0
0
2
3
0
1
0
0
0
0
0
2
0
0
4
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
2
0
2
1
0
0
0
1
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
4
0
0
1
1
1
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
2
0
1
0
1
4
0
0
0
0
0
1
0
1
3
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
2
1
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
4
0
1
0
0
4
2
0
0
2
1
2
0
3
0
2
0
0
0
2
2
0
2
0
0
0
2
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
0
1
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
1
0
3
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
2
0
1
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
1
0
2
1
0
1
0
0
0
0
1
0
0
0
0
2
1
1
0
2
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
1
2
2
0
0
2
0
0
0
0
0
2
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
2
0
0
0
2
0
2
0
0
0
5
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
2
0
0
0
0
0
2
1
0
0
2
0
1
1
2
0
0
0
0
0
1
0
1
0
0
0
0
2
4
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
1
0
3
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
1
1
0
0
1
0
0
0
0
2
4
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
4
4
0
3
0
0
1
2
0
0
0
0
2
2
0
1
0
0
2
0
1
0
1
0
0
0
0
2
1
0
4
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
1
0
2
1
0
1
0
1
0
0
0
2
0
0
2
0
0
1
0
0
1
0
0
0
7
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
1
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
2
3
0
0
2
0
0
1
0
0
0
0
2
0
0
2
0
2
0
0
0
1
0
1
0
0
0
0
1
0
0
0
2
1
0
0
2
0
0
0
0
0
0
1
0
2
1
2
0
0
0
1
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
5
0
0
0
0
5
0
1
5
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
1
0
2
0
0
0
0
2
2
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
2
1
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
1
2
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
3
0
0
2
2
0
0
0
0
0
1
0
0
0
2
1
3
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
1
0
0
0
3
0
2
0
3
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
3
0
0
0
0
0
0
1
0
0
0
1
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
1
1
0
0
0
3
0
2
0
0
0
0
1
0
0
1
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
2
0
0
0
1
0
0
0
0
2
1
0
0
2
0
0
0
1
0
0
2
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
4
1
0
0
0
1
0
0
0
0
0
0
3
2
6
0
0
1
0
2
1
0
0
0
2
4
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
2
0
0
0
3
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
2
1
0
1
1
0
0
0
0
0
0
0
1
2
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
3
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
1
1
1
0
1
0
0
0
0
1
1
0
0
2
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
3
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
3
2
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
3
1
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
1
2
2
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
1
0
0
0
1
0
0
0
1
1
1
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
2
2
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
1
0
3
0
2
0
0
1
0
0
1
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
3
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
2
0
0
0
2
3
0
2
1
0
1
0
0
0
2
0
2
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
2
0
2
4
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
1
0
2
0
1
0
0
2
1
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
2
0
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
1
0
0
1
0
0
2
1
0
0
1
0
4
0
0
1
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
2
0
1
0
0
2
0
0
0
0
1
0
0
1
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
1
2
0
0
0
0
0
4
0
1
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
1
2
0
0
0
1
0
1
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
1
1
0
2
0
0
0
0
0
1
2
3
0
0
0
0
0
0
1
2
2
1
0
0
0
4
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
2
1
0
0
0
0
0
0
1
2
0
0
0
2
1
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
1
2
0
0
0
0
1
0
0
0
2
1
0
0
2
0
1
0
0
0
4
1
0
3
0
1
0
1
0
0
2
0
0
0
2
0
1
0
1
0
1
3
0
0
2
0
1
1
1
1
0
0
5
0
0
0
0
0
1
0
0
3
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
2
0
0
0
0
1
0
0
0
0
0
1
2
1
0
2
2
2
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
1
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
2
0
3
1
0
0
0
1
0
1
0
2
2
2
0
3
0
0
1
0
2
2
0
0
5
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
4
0
0
2
0
0
4
2
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
2
2
0
0
0
2
2
0
0
0
0
1
1
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
3
0
0
0
1
0
0
0
1
0
1
1
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
2
2
1
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
2
1
0
2
0
0
0
0
0
2
1
1
0
0
2
2
0
0
0
1
1
0
2
0
0
2
1
0
2
0
0
0
0
0
0
2
0
0
0
3
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
4
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
2
2
0
1
0
0
0
0
2
1
0
0
1
0
2
0
0
0
2
0
0
1
0
0
0
1
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
2
0
2
0
0
0
2
0
2
0
0
2
7
2
0
0
0
0
2
0
0
0
0
0
0
0
1
3
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
1
2
0
0
1
3
1
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
1
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
2
0
1
2
0
0
2
1
0
0
0
2
0
5
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
2
0
0
0
3
2
2
0
0
0
0
0
1
0
0
2
2
1
1
5
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
2
0
0
0
1
0
0
3
0
0
0
0
0
1
2
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
2
0
0
2
1
0
1
2
2
0
0
2
1
0
1
2
0
0
0
0
0
0
4
0
0
2
1
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
2
1
0
0
1
0
2
0
0
0
1
0
2
0
0
2
0
0
0
0
0
1
4
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
2
0
0
0
0
0
2
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
2
1
0
0
0
2
1
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
1
3
0
0
0
0
0
5
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
1
2
0
0
0
0
0
0
2
0
0
0
3
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
3
0
0
2
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
2
1
1
2
2
0
2
1
0
0
0
0
1
1
3
0
2
1
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
2
0
2
0
0
0
0
2
0
2
0
1
2
1
0
0
2
0
1
2
0
1
0
0
0
0
2
0
0
2
0
0
0
2
1
0
4
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
3
2
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
1
0
2
0
0
2
1
0
0
0
0
0
0
1
2
0
1
0
0
2
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
1
0
0
0
0
1
0
0
2
0
0
1
0
3
0
0
1
3
0
0
0
0
0
0
0
0
0
3
0
1
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
1
1
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
2
0
3
0
0
2
0
3
2
0
0
0
2
0
0
0
0
0
0
4
1
0
1
1
1
2
0
0
0
2
0
0
0
1
0
3
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
2
5
1
0
0
0
0
2
0
2
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
3
0
1
0
0
0
0
1
0
0
0
2
0
1
0
2
0
2
2
4
0
1
2
0
0
0
0
0
0
0
2
1
0
2
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
3
4
1
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
8
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
2
1
1
0
0
1
0
0
1
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
6
2
0
0
3
1
2
0
0
0
1
0
0
2
0
1
0
2
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
2
0
3
0
0
2
2
0
0
0
1
0
4
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
2
0
2
0
0
0
1
0
0
0
3
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
1
1
0
0
0
1
0
0
1
2
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
3
3
2
1
0
2
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
3
0
1
0
2
0
2
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
3
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
2
1
2
2
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
2
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
2
0
0
1
0
0
1
0
0
3
0
2
0
1
0
2
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
3
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
1
3
0
2
0
0
0
2
1
1
0
0
1
0
2
0
0
1
0
0
1
1
0
0
2
0
2
0
0
1
0
0
0
0
0
0
1
2
0
0
1
0
1
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
4
1
0
1
0
1
1
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
2
0
0
0
0
3
0
0
0
1
1
0
0
0
0
1
4
0
0
2
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
3
0
1
0
2
0
1
4
0
0
0
0
0
0
0
1
1
0
0
2
2
0
2
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
1
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
1
2
0
0
0
0
0
0
1
0
0
2
1
1
0
0
0
0
0
0
1
0
1
0
3
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
1
1
0
0
0
0
1
0
3
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
1
0
0
0
2
1
0
0
0
2
1
2
2
0
2
0
0
1
0
0
0
0
3
1
0
0
1
0
0
0
2
0
3
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
2
0
3
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
2
0
0
0
3
2
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
2
2
1
2
0
0
2
2
1
1
0
0
0
0
0
0
0
0
2
0
0
1
1
3
0
2
0
0
0
3
0
1
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
3
0
1
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
1
3
1
2
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
2
1
0
3
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
1
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
2
2
0
2
0
1
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
3
0
0
1
2
0
2
0
0
1
0
2
0
0
0
0
0
2
0
2
2
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
2
0
0
1
0
1
0
0
2
0
0
0
0
0
0
1
0
2
0
0
1
1
0
2
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
2
3
0
0
0
1
1
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
3
0
0
2
0
0
0
2
0
0
3
0
1
0
0
0
0
0
1
4
0
1
0
0
0
0
0
0
0
0
0
0
1
3
3
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
2
2
0
0
0
1
1
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
4
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
4
1
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
2
2
2
0
0
0
0
1
0
0
0
1
0
2
2
3
1
0
0
0
0
2
0
0
2
0
0
2
1
0
0
0
1
0
1
0
1
2
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
1
0
2
2
0
2
2
0
0
0
0
1
0
0
0
1
2
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
2
0
2
0
0
3
0
0
1
0
0
0
1
1
0
0
0
2
0
0
0
0
2
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
2
0
0
0
1
0
0
2
1
0
0
1
0
0
0
2
3
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
2
1
0
0
0
1
0
0
0
0
0
2
1
1
0
0
0
1
0
0
0
2
0
0
1
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
2
0
1
2
0
0
0
0
0
0
2
0
2
1
0
1
0
0
2
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
3
2
5
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
2
0
0
1
1
0
2
0
0
1
0
1
0
1
4
2
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
2
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
0
2
0
0
0
0
0
1
3
0
0
0
0
1
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
1
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
3
5
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
2
2
1
1
0
0
0
0
2
0
1
0
0
0
2
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
9
2
2
0
0
0
2
1
1
0
0
3
1
1
0
0
0
0
0
0
0
0
0
1
0
1
2
0
2
4
3
1
0
1
0
2
2
0
0
0
2
0
0
0
1
3
1
0
1
0
2
0
2
0
0
0
1
0
0
0
0
0
2
1
1
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
2
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
3
0
0
0
0
0
0
3
0
1
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
8
0
0
0
0
2
0
0
2
2
0
0
2
0
0
0
1
2
0
3
0
0
4
2
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
3
0
2
0
1
0
0
0
1
0
0
0
0
2
0
0
2
0
0
6
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
2
0
4
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
1
1
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
2
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
1
2
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
1
0
3
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
4
0
0
0
1
1
1
0
0
0
0
0
0
2
0
1
2
1
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
1
0
0
0
2
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
1
5
0
2
0
1
0
1
0
1
7
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
5
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
2
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
1
2
0
2
2
0
0
1
0
2
2
0
2
0
0
1
0
1
0
0
0
1
1
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
1
2
2
0
2
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
1
2
1
3
2
1
1
0
3
0
0
4
0
0
0
0
0
0
2
3
0
2
2
1
0
0
1
2
0
0
0
0
2
0
0
0
1
1
1
0
0
0
0
1
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
3
0
1
0
0
0
0
0
2
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
2
0
0
0
3
0
1
2
0
0
0
0
0
1
2
0
0
1
0
1
0
0
0
0
1
1
2
0
0
1
0
2
0
0
0
0
0
2
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
2
0
0
2
0
0
0
0
1
0
1
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
1
0
2
0
1
1
0
0
2
1
1
1
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
2
0
0
0
1
1
2
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
1
0
0
1
0
1
0
3
0
1
2
3
2
2
0
0
1
0
0
0
2
3
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
1
0
0
1
0
1
1
0
1
6
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
1
2
0
1
1
0
3
0
1
0
0
0
1
0
0
0
1
0
0
0
0
2
0
1
0
0
0
1
0
0
2
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
2
2
2
0
0
0
0
1
0
2
0
0
2
1
0
0
0
1
0
0
0
0
0
2
2
1
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
1
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
5
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
6
0
0
0
1
0
3
0
0
0
0
0
0
1
1
0
0
1
1
8
1
0
0
0
1
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
4
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
3
0
1
0
0
0
0
0
1
3
2
0
0
1
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
1
1
2
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
1
2
0
1
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
3
3
2
0
0
0
2
0
1
2
0
2
0
0
1
0
0
0
2
2
1
2
2
2
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
1
0
1
0
0
6
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
5
3
0
0
0
0
8
0
1
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
2
1
2
0
0
1
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
6
1
0
2
0
1
3
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
1
0
0
0
1
0
0
0
2
0
2
0
5
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
3
0
0
0
1
0
0
0
0
2
2
2
2
0
0
0
0
0
0
0
2
2
3
0
2
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
2
0
2
0
2
0
1
2
2
2
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
2
0
0
0
0
1
1
0
0
2
0
0
0
1
0
0
1
0
2
1
1
0
2
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
3
0
0
0
0
0
1
1
0
3
0
0
2
0
0
0
0
1
2
0
0
0
2
2
0
3
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
2
0
1
1
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
2
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
2
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
3
0
0
2
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
2
1
0
1
1
0
0
4
1
0
0
2
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
3
0
0
0
0
1
0
0
2
0
2
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
2
1
0
2
0
0
0
0
0
0
0
2
1
0
2
0
0
1
0
1
0
1
2
0
0
3
0
0
1
0
0
0
1
0
0
0
2
0
0
1
0
0
0
1
2
0
1
0
0
1
1
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
2
0
0
0
2
0
0
0
0
4
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
3
0
1
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
1
1
0
0
0
0
0
0
2
0
0
0
0
0
1
4
0
0
0
0
0
2
2
0
0
1
2
1
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
1
1
3
0
0
0
0
0
1
0
0
0
0
0
0
1
0
3
6
0
1
2
3
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
6
0
1
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
1
0
2
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
1
0
2
2
1
0
2
0
2
0
2
0
1
0
1
0
0
1
0
0
0
0
1
0
1
1
0
1
2
1
0
0
1
0
3
1
2
2
2
2
2
1
0
0
0
0
0
1
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
1
0
0
0
0
3
2
0
1
0
0
0
0
0
2
3
2
0
0
0
0
0
3
0
0
1
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
2
0
0
1
0
0
0
2
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
3
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
3
0
1
0
1
2
2
0
0
1
0
1
1
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
3
2
0
1
1
2
0
2
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
1
0
0
1
0
2
0
1
0
2
0
2
0
0
0
0
0
0
0
0
2
1
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
4
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
3
1
0
4
0
0
1
0
2
0
0
1
0
2
0
0
2
2
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
1
0
0
0
2
3
0
3
0
0
0
2
2
8
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
1
0
0
1
0
0
0
2
0
2
1
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
1
0
1
0
0
1
1
0
0
0
1
2
0
0
0
0
0
2
0
2
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
1
0
2
1
1
2
0
0
2
0
2
0
0
7
2
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
2
2
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
2
2
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
3
2
0
0
0
0
0
1
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
2
1
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
2
0
1
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
1
1
0
12
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
1
2
1
0
0
0
2
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
2
1
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
2
0
2
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
1
2
0
0
2
0
0
0
0
2
0
3
1
2
0
2
2
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
1
0
0
2
0
1
0
2
0
0
1
0
1
0
0
0
0
0
0
2
2
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
1
2
0
3
0
0
0
0
0
1
2
1
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
1
0
0
0
1
2
2
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
4
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
4
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
2
1
0
0
4
1
0
1
0
0
2
0
2
0
0
0
1
0
0
0
0
3
0
1
0
0
0
0
0
0
0
7
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
2
2
1
0
2
0
2
1
1
1
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
3
0
0
0
0
1
0
0
0
0
0
0
0
0
1
6
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
2
0
0
0
0
2
0
1
0
0
0
1
0
2
0
0
0
0
0
2
1
0
3
0
0
2
0
0
2
0
0
2
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
1
0
1
2
0
0
0
0
1
1
0
1
0
0
2
0
0
1
0
0
2
0
0
0
1
0
2
0
1
0
0
1
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
2
3
0
0
2
0
0
1
5
0
2
0
0
2
1
0
0
1
0
0
2
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
3
0
0
0
0
2
1
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
4
1
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
1
0
0
0
0
2
2
2
0
0
3
0
4
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
1
0
0
0
1
0
3
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
2
2
5
2
0
0
0
0
0
0
1
0
1
1
0
3
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
1
0
1
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
5
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
1
0
0
0
3
0
1
0
2
0
0
0
0
3
0
0
0
2
1
0
0
0
2
0
2
3
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
2
1
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
2
0
1
2
0
0
0
2
0
0
0
2
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
1
0
0
1
0
1
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
1
0
1
2
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
1
0
0
0
0
2
0
0
0
0
2
0
0
1
0
2
0
1
1
0
0
0
0
0
0
0
0
3
2
0
2
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
2
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
5
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
2
0
0
0
1
0
0
0
0
2
0
0
2
0
0
1
0
0
0
2
0
1
0
0
0
1
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
2
0
1
2
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
1
1
0
0
0
3
2
0
0
0
1
2
0
0
1
3
0
0
0
0
0
0
1
0
2
0
5
2
0
0
0
2
1
0
4
0
1
3
0
2
0
0
0
1
3
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
1
0
2
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
1
0
2
0
0
2
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
2
1
3
2
0
0
0
0
0
6
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
2
0
1
1
0
0
2
0
0
0
2
3
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
1
0
0
2
1
0
0
1
1
0
2
2
2
0
0
0
3
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
1
2
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
2
0
0
2
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
1
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
5
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
6
0
0
1
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
1
0
2
0
2
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
1
1
0
1
0
3
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
1
1
0
1
0
0
2
0
0
0
1
3
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
1
1
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
2
0
1
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
2
0
0
0
0
0
0
1
3
1
2
1
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
3
0
0
0
0
2
2
2
0
0
0
0
0
0
0
2
3
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
3
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
1
2
0
0
4
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
2
1
0
0
0
2
0
2
0
0
0
0
0
0
0
2
1
1
0
0
1
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
2
1
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
2
0
0
0
3
0
0
2
1
0
0
1
0
1
0
0
1
0
3
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
2
0
3
0
2
1
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
2
1
0
2
2
0
0
0
0
0
0
0
0
1
1
0
0
0
2
5
0
0
0
0
2
2
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
22
0
1
0
2
2
0
1
2
0
0
0
0
0
0
0
2
1
2
0
10
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
2
2
0
0
0
0
0
1
0
2
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
2
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
5
0
0
0
0
0
0
7
2
0
2
0
1
0
1
0
0
0
0
0
1
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
1
0
1
0
0
1
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
2
1
1
2
0
0
1
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
5
0
0
0
2
2
0
2
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
2
1
2
0
0
0
0
0
0
1
1
2
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
2
0
3
0
0
0
2
0
0
0
1
0
2
0
1
0
2
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
1
0
0
0
0
5
0
0
0
0
2
0
0
1
0
0
0
4
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
3
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
3
1
0
0
0
0
0
0
0
4
1
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
1
0
0
2
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
1
0
1
0
2
1
0
0
0
2
2
0
2
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
1
0
2
0
0
1
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
1
0
2
0
0
0
0
1
0
3
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
1
0
1
1
1
0
0
0
0
0
1
2
0
0
0
0
1
2
0
2
0
2
0
3
0
1
0
2
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
2
1
0
0
0
0
0
0
2
0
0
2
0
3
0
0
0
1
0
0
2
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
2
0
1
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
3
3
2
2
0
0
0
0
1
0
1
0
2
0
0
0
2
0
0
1
2
0
0
0
0
2
1
0
2
0
3
0
1
0
0
2
0
0
1
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
1
0
1
2
0
3
0
0
0
0
2
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
3
1
0
2
0
0
1
0
0
0
0
0
0
3
0
0
0
2
1
0
0
2
2
0
1
1
3
1
2
0
0
0
0
0
2
0
0
0
0
0
2
1
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
3
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
2
0
2
0
0
0
0
1
0
1
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
2
0
2
0
0
0
0
1
0
0
0
0
1
2
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
1
0
2
0
0
0
0
0
0
1
1
2
0
1
0
1
0
1
0
0
1
1
0
0
7
0
0
0
0
2
0
0
0
1
2
2
0
0
0
0
0
1
0
2
0
0
2
0
1
1
1
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
1
1
0
2
0
0
0
1
1
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
2
1
2
0
0
0
0
2
1
0
0
2
0
1
0
0
2
0
2
3
0
0
0
2
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
4
0
1
0
0
1
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
4
0
3
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
2
0
1
0
0
0
1
1
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
2
2
0
1
2
0
0
0
0
1
0
0
0
0
1
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
3
2
0
2
0
0
1
0
2
0
0
1
2
0
0
2
1
0
0
0
3
2
0
0
0
0
0
2
2
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
1
0
1
3
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
5
0
2
0
1
0
1
0
1
0
0
1
0
2
0
0
2
0
0
0
0
0
0
4
1
0
2
1
3
0
0
0
0
0
1
2
0
1
0
0
0
2
0
0
0
0
0
1
2
0
1
1
0
0
0
0
1
0
1
2
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
2
1
2
0
2
8
2
0
0
0
0
0
0
1
2
0
2
2
1
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
3
0
2
1
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
1
1
2
0
2
1
1
2
1
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
2
0
1
0
0
2
0
1
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
1
0
3
2
0
0
1
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
3
3
2
5
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
1
0
0
2
2
0
0
0
0
0
2
0
0
0
2
0
1
1
0
0
0
0
2
0
0
2
0
3
0
0
2
2
2
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
3
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
1
0
0
4
0
0
0
3
0
0
1
0
0
0
0
2
0
0
2
2
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
2
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
2
0
1
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
2
1
0
0
2
0
0
2
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
2
2
0
1
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
1
1
3
0
0
0
1
0
1
0
1
2
0
0
0
3
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
3
2
2
0
0
2
2
0
2
0
0
2
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
2
1
0
0
0
2
0
0
0
1
0
2
2
16
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
2
2
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
3
2
0
0
0
4
0
2
0
0
0
2
2
2
0
0
0
0
0
3
0
9
0
0
0
0
0
1
1
0
0
0
0
0
0
1
2
0
0
0
0
0
3
2
0
0
0
0
2
0
0
0
0
0
2
0
1
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
2
2
1
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
4
0
0
0
0
0
0
0
0
1
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
2
0
0
8
0
0
0
6
2
0
0
0
1
1
0
2
0
0
0
2
0
0
1
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
1
1
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
2
0
2
0
2
1
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
2
2
0
2
1
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
1
1
0
0
0
0
1
0
2
0
0
0
0
0
2
1
1
0
0
2
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
1
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
1
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
3
0
0
0
1
0
0
0
0
1
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
5
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
1
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
5
0
0
0
0
0
0
2
0
0
1
3
0
0
0
1
1
1
0
0
0
2
2
0
0
1
0
0
0
2
0
0
2
0
2
1
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
1
2
2
3
0
0
0
0
0
2
0
0
2
2
0
0
2
0
0
0
3
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
1
0
0
0
3
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
3
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
2
0
0
0
2
0
0
0
1
0
0
0
1
4
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
1
0
0
1
0
1
0
0
2
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
5
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
1
1
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
1
0
0
0
2
0
0
3
1
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
1
0
0
0
0
0
1
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
4
1
1
1
1
0
7
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
2
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
2
2
2
0
2
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
2
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
2
2
0
1
0
0
2
0
0
0
2
1
0
1
1
0
2
0
0
0
0
0
0
0
0
0
1
2
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
2
2
1
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
5
2
0
0
0
4
2
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
6
0
1
0
0
0
0
0
0
0
0
2
1
4
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
1
0
0
2
2
0
0
1
0
0
1
0
0
0
0
2
0
1
0
1
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
2
1
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
1
2
0
0
0
3
0
0
0
1
0
0
1
2
0
0
2
1
0
0
0
0
2
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
3
0
0
1
0
0
3
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
1
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
2
0
0
0
0
2
0
0
1
0
2
1
0
0
0
0
1
2
2
1
5
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
2
0
0
1
0
2
2
0
1
3
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
1
0
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
2
2
0
0
1
0
0
0
2
0
1
2
0
0
0
0
0
1
2
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
1
0
0
1
0
0
2
0
0
0
2
1
0
0
0
0
2
0
0
0
2
0
0
0
1
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
3
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
1
0
0
0
0
1
0
2
0
4
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
2
2
0
0
0
2
0
0
0
1
1
0
0
1
0
0
0
0
2
0
0
0
1
1
0
4
1
0
2
1
0
1
1
0
0
0
0
4
0
2
1
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
3
0
1
2
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
1
2
2
0
0
0
2
1
0
0
2
0
0
0
0
0
2
0
0
1
2
0
1
0
0
1
0
0
2
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
2
0
0
3
0
2
1
0
0
0
0
2
0
1
0
0
0
0
0
0
1
1
0
0
0
0
2
0
2
0
0
0
0
1
2
0
0
0
0
0
0
1
0
2
1
2
0
0
0
2
0
0
0
2
0
5
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
1
0
0
2
2
0
0
0
4
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
1
0
0
2
0
0
2
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
1
10
0
0
2
0
0
1
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
3
0
0
0
0
0
2
4
1
0
0
0
1
0
0
0
0
0
0
1
0
2
0
2
0
0
1
1
0
2
0
0
0
1
0
2
0
0
2
0
0
0
2
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
3
0
2
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
1
0
0
0
1
2
0
0
2
1
0
1
0
0
0
0
0
0
0
1
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
10
1
1
0
1
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
1
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
4
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
2
7
0
0
0
0
0
1
0
3
0
1
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
1
1
0
1
0
0
0
0
0
0
3
2
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
3
0
2
3
1
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
4
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
1
1
0
0
1
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
2
2
0
1
0
0
0
0
2
3
0
0
2
0
0
0
2
1
0
0
0
0
0
0
1
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
1
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
2
0
1
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
3
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
11
0
1
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
1
1
0
0
0
1
3
0
3
0
0
0
0
0
0
2
1
2
0
0
2
0
1
0
2
0
2
0
0
0
0
0
2
0
2
1
0
1
0
2
2
0
1
0
0
0
1
0
0
2
1
0
0
0
2
2
1
3
0
0
2
0
0
0
3
0
0
0
2
0
1
0
2
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
1
0
1
0
0
0
4
1
0
0
3
0
0
0
0
0
0
2
1
0
2
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
3
0
1
1
1
0
0
0
0
0
2
2
0
2
2
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
3
0
2
2
0
0
0
0
0
0
2
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
2
2
1
0
0
0
0
0
0
2
1
0
0
2
0
2
0
1
0
2
0
1
0
1
0
0
1
0
0
1
3
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
4
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
1
0
0
0
0
0
2
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
1
0
0
0
5
2
5
0
0
2
3
0
0
2
0
0
0
3
0
0
1
0
2
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
3
0
3
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
1
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
3
1
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
2
0
0
0
2
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
1
2
0
0
0
0
2
0
0
0
2
0
2
0
2
2
0
0
0
2
2
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
3
0
2
0
0
2
0
2
1
0
0
2
1
0
0
1
0
0
0
0
1
1
2
0
0
0
0
1
1
0
0
2
2
2
0
0
0
0
0
0
2
1
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
1
0
0
2
0
0
3
2
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
2
0
2
0
0
0
2
1
0
1
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
2
0
0
0
1
2
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
1
3
0
0
1
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
2
0
3
0
0
0
1
0
4
0
0
2
1
0
1
0
1
0
0
2
0
3
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
4
0
1
0
0
1
2
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
3
0
0
2
0
0
0
1
2
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
2
3
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
7
3
0
0
3
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
6
0
0
0
0
0
1
0
2
0
2
1
0
0
0
0
0
0
2
0
0
2
0
0
2
5
0
1
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
1
2
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
11
0
0
1
3
0
0
0
0
1
0
0
3
1
0
2
1
2
0
0
0
0
1
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
2
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
2
0
2
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
1
3
2
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
1
1
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
1
3
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
3
0
2
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
2
0
1
0
0
0
0
0
2
0
2
1
0
0
2
2
0
1
0
2
0
1
0
0
2
0
0
0
0
0
1
0
0
0
2
0
2
1
0
2
0
2
0
0
2
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
1
2
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
1
0
2
2
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
3
0
0
2
2
0
0
0
1
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
2
0
0
1
0
0
0
0
2
2
0
0
0
0
1
3
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
1
7
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
2
0
1
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
4
1
0
0
0
0
0
0
0
0
1
1
0
2
0
2
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
3
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
5
1
1
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
2
0
2
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
3
0
0
0
0
0
3
2
0
0
0
0
0
0
1
0
1
0
3
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
2
1
0
3
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
2
1
1
0
0
0
0
0
0
0
2
0
0
4
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
3
0
1
1
0
0
0
2
0
2
2
0
2
0
0
1
0
0
0
1
0
0
0
1
0
0
0
2
2
2
0
0
0
1
2
0
1
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
2
0
1
1
3
0
1
0
1
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
2
0
2
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
2
0
2
0
2
0
0
1
0
0
2
0
0
2
2
0
0
2
1
0
1
1
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
1
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
1
1
0
1
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
1
1
2
1
1
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
3
1
0
0
0
0
1
1
0
0
0
0
0
1
1
0
3
0
1
0
2
0
0
3
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
2
0
1
0
0
0
1
0
2
0
0
2
2
0
0
0
0
0
1
0
0
3
1
0
3
1
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
3
1
0
0
0
0
0
2
0
2
3
0
0
0
0
1
0
0
0
0
0
0
0
0
4
1
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
3
0
0
1
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
2
1
2
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
3
0
0
1
0
0
0
0
2
0
2
0
0
1
2
0
0
0
0
2
0
0
1
0
3
0
0
0
2
0
0
1
1
0
0
0
0
2
0
0
0
2
0
0
2
0
2
0
2
0
2
0
1
1
0
2
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
5
1
0
1
0
1
0
0
0
1
3
1
0
0
2
0
0
0
0
1
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
4
4
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
1
0
3
0
0
0
0
0
2
0
1
0
1
0
0
1
0
0
0
2
0
0
0
2
0
2
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
1
0
0
0
3
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
2
2
0
0
0
0
0
0
2
1
1
0
0
1
1
0
0
0
1
1
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
2
1
0
0
1
1
0
0
0
2
2
1
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
2
0
0
2
2
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
6
0
0
2
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
2
0
0
2
0
0
2
0
1
0
0
1
0
0
0
0
1
2
0
1
0
1
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
1
0
2
2
0
0
0
2
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
1
0
0
0
0
1
1
0
0
0
0
0
1
1
1
0
0
0
0
1
12
0
0
0
0
0
0
0
4
1
0
0
0
0
2
0
2
0
1
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
3
1
1
0
0
2
3
0
1
0
0
2
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
2
2
0
0
0
1
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
2
0
0
1
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
2
2
0
2
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
1
0
2
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
1
0
0
0
2
2
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
2
0
2
1
0
0
0
2
1
1
0
0
0
0
0
0
1
0
0
2
2
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
1
0
0
0
1
3
1
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
3
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
2
2
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
2
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
2
1
0
1
2
2
0
0
2
0
0
1
3
0
4
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
3
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
1
1
0
0
0
1
0
1
2
5
2
0
3
1
0
0
0
2
0
1
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
2
3
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
3
2
0
0
1
0
0
0
0
0
2
3
0
1
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
2
0
0
2
0
4
0
2
2
1
0
0
0
0
0
0
2
0
1
2
2
0
0
0
2
0
0
2
0
2
2
0
0
0
0
0
0
0
0
2
0
1
0
0
2
2
1
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
1
0
2
0
0
1
0
0
0
0
0
0
0
0
1
2
1
2
0
2
0
0
0
1
0
0
0
1
2
0
0
2
0
0
0
0
1
3
4
0
1
0
0
0
0
0
3
1
0
0
0
1
2
2
0
0
1
0
3
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
2
0
0
2
0
0
0
0
0
0
4
1
0
1
0
1
0
0
5
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
4
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
1
0
0
2
0
1
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
8
0
0
1
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
1
0
0
1
0
0
0
2
1
0
1
0
0
2
1
1
0
0
0
0
0
0
0
2
1
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
1
1
0
1
0
0
0
1
1
0
2
0
0
2
0
0
0
0
1
0
0
0
0
2
2
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
2
0
0
1
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
2
0
2
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
2
1
0
0
2
0
0
2
0
0
0
0
2
1
0
3
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
2
1
0
0
1
2
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
3
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
3
0
0
3
0
0
0
0
0
2
1
2
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
2
2
0
0
0
1
0
1
0
0
0
1
0
0
0
2
0
0
0
1
1
0
1
2
0
0
0
2
0
0
0
0
0
0
4
1
0
0
0
0
1
0
2
0
0
2
2
1
0
2
0
0
0
0
0
0
0
0
2
0
5
2
0
0
0
0
1
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
1
0
1
3
3
2
0
0
0
0
1
0
0
0
0
0
0
0
2
1
3
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
3
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
8
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
1
0
2
1
1
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
1
2
2
2
0
1
2
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
2
0
0
2
0
0
0
0
0
2
1
0
0
2
1
2
1
0
1
0
0
2
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
3
0
4
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
2
1
0
0
2
0
2
0
2
0
2
0
2
0
0
0
0
2
0
0
1
1
0
0
0
1
0
0
1
2
0
0
1
0
0
0
0
0
0
6
0
0
0
0
0
2
0
0
0
1
0
0
0
2
1
0
4
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
2
0
2
0
0
2
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
2
0
0
1
0
0
1
1
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
2
1
1
0
0
0
0
0
1
0
3
0
0
2
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
1
0
0
1
0
0
3
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
4
2
1
0
0
4
0
0
0
0
0
0
1
3
1
2
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
2
0
0
3
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
1
1
0
2
4
1
0
0
1
1
0
2
0
0
0
0
0
1
0
0
0
3
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
2
0
2
0
0
4
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
2
1
0
2
1
0
0
0
0
0
0
1
0
2
1
0
1
1
0
0
2
0
0
1
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
2
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
1
0
1
0
1
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
1
0
0
8
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
2
0
0
0
1
0
3
0
0
0
1
0
0
8
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
3
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
1
0
0
0
1
3
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
2
1
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
2
1
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
2
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
1
1
0
0
6
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
1
0
0
0
7
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
7
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
2
0
0
0
0
0
0
2
2
0
0
0
0
2
0
2
0
0
2
2
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
1
2
0
0
0
0
0
1
0
0
0
0
0
1
2
2
1
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
2
0
2
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
4
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
1
1
2
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
2
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
3
1
2
0
2
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
2
1
0
1
0
0
2
0
0
0
0
1
1
3
1
0
0
1
2
2
1
0
0
0
0
0
0
1
2
1
0
0
0
0
2
2
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
1
0
1
0
0
2
0
2
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
1
1
1
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
1
2
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
2
0
2
0
2
0
0
2
0
1
0
2
0
0
0
2
0
2
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
1
0
1
1
0
0
0
1
2
0
1
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
1
2
3
0
0
0
2
3
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
3
2
0
0
0
1
0
0
5
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
1
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
4
1
0
0
1
0
0
2
0
2
3
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
3
0
0
0
4
0
0
1
0
0
2
0
0
0
1
0
0
1
1
0
1
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
2
2
1
1
0
2
2
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
1
0
0
1
0
0
2
0
0
4
1
0
0
0
3
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
1
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
3
0
0
0
0
2
0
0
0
2
0
2
2
0
1
0
0
0
0
2
0
0
5
2
0
1
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
2
0
2
0
0
0
1
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
4
2
0
0
0
0
1
0
0
0
0
0
0
0
1
4
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
1
0
1
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
3
0
1
2
0
0
0
2
0
0
1
3
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
3
0
1
2
0
0
2
0
0
1
0
0
2
3
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
3
1
0
0
0
1
0
0
0
1
0
1
3
2
1
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
2
0
0
0
1
0
0
2
0
1
0
0
0
0
0
1
2
1
0
0
0
0
5
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
3
2
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
1
0
0
1
0
0
0
0
0
0
1
4
0
0
0
0
2
0
1
0
6
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
1
0
1
0
2
0
0
0
0
0
0
2
0
0
2
1
0
0
2
0
2
0
0
2
2
0
1
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
2
1
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
3
0
0
0
0
3
0
0
1
0
1
0
0
0
2
0
0
2
0
2
0
1
1
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
1
1
0
0
3
0
0
0
0
0
0
0
0
0
1
1
0
0
3
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
1
3
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
2
2
1
0
0
0
0
1
1
4
1
0
4
2
1
0
2
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
2
7
0
1
0
0
2
1
1
0
0
1
2
0
0
1
0
0
0
2
1
4
1
0
0
0
0
0
0
0
0
0
0
2
1
2
1
0
6
2
1
1
0
0
2
0
0
5
1
0
0
2
1
0
1
0
0
0
0
0
2
0
0
0
2
0
0
3
0
1
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
3
0
0
0
0
1
2
0
0
1
2
0
2
0
0
0
2
1
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
2
0
0
2
0
0
1
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
1
0
1
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
2
0
2
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
5
1
0
0
0
2
0
1
0
2
2
0
0
0
0
0
1
0
2
2
1
0
1
2
0
2
0
2
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
1
1
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
2
0
0
1
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
3
1
0
1
2
1
0
1
0
0
0
1
0
1
2
2
0
0
2
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
2
1
0
0
0
6
0
0
1
0
0
0
0
0
3
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
2
0
2
2
1
1
0
0
0
0
0
1
0
2
0
0
0
1
1
1
1
1
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
2
0
2
0
1
3
0
2
1
0
0
1
1
2
2
1
2
0
0
0
0
0
1
3
2
0
0
1
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
2
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
2
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
3
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
3
0
0
0
1
0
0
0
0
1
2
0
2
0
2
0
4
0
0
3
1
0
0
0
0
1
2
0
0
0
0
1
0
1
0
0
0
0
2
2
0
0
0
0
0
3
0
0
0
3
0
0
0
0
1
0
0
1
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
1
4
2
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
4
0
0
0
1
1
1
0
0
0
4
1
0
0
0
0
0
3
2
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
2
3
0
0
0
0
0
2
4
0
0
0
2
2
1
0
0
0
2
2
0
0
2
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
3
1
2
0
0
0
0
1
0
0
0
0
3
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
1
2
0
1
1
0
0
0
1
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
1
0
1
2
0
0
0
0
1
0
0
1
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
7
0
2
0
0
0
1
0
0
0
0
2
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
1
1
0
2
1
0
1
1
0
0
0
0
0
2
0
0
5
2
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
1
2
0
0
0
3
2
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
1
0
0
0
0
0
1
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
1
0
0
1
0
0
0
0
0
0
2
0
2
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
2
1
6
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
6
0
0
0
0
0
4
0
0
1
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
4
2
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
2
0
0
2
0
0
0
1
1
0
1
2
0
0
0
3
1
2
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
3
0
2
1
0
0
0
0
0
0
0
0
1
0
0
1
0
5
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
3
2
0
1
0
2
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
3
0
2
2
0
0
0
3
0
1
0
0
1
0
0
2
0
0
0
1
0
0
0
2
0
2
0
0
3
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
3
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
1
2
0
1
0
0
0
1
1
0
0
0
0
1
2
0
0
0
0
0
0
1
0
2
0
2
0
0
0
2
0
0
0
2
2
0
0
0
0
2
0
0
0
1
2
1
2
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
3
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
3
4
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
1
0
0
1
2
0
0
1
0
2
0
0
0
0
0
1
0
2
1
0
1
0
7
0
0
1
0
2
0
0
2
0
1
0
0
1
0
0
0
0
3
0
1
0
0
0
2
0
2
3
0
0
0
0
0
0
0
1
1
1
0
0
0
1
1
0
0
1
0
2
0
0
0
2
1
0
0
0
0
0
1
0
0
2
0
0
2
1
0
0
2
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
5
0
0
0
1
0
0
2
0
0
0
1
2
1
0
0
0
0
0
1
0
0
1
2
0
1
1
3
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
3
0
0
0
0
0
0
0
2
1
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
1
1
3
0
2
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
3
0
1
0
0
1
2
1
0
0
1
2
0
1
0
2
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
2
2
2
0
2
0
2
2
2
0
0
1
1
0
0
0
0
0
0
0
0
1
0
3
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
7
1
1
1
1
0
0
0
0
0
0
0
1
0
0
0
3
0
1
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
2
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
1
0
0
0
2
0
0
4
0
0
0
0
0
0
3
2
0
0
3
0
0
0
0
0
0
1
0
0
0
2
2
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
1
2
1
0
0
0
1
0
1
2
3
0
0
0
0
0
0
2
1
0
3
1
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
1
0
0
0
0
1
0
3
0
0
0
3
0
2
0
0
1
0
0
0
0
1
0
2
3
0
0
0
0
4
0
0
0
2
0
1
0
0
2
2
0
0
0
2
2
0
0
0
0
0
0
0
0
6
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
2
0
1
2
0
0
2
0
0
1
0
3
0
1
0
0
0
2
0
0
2
0
0
0
0
0
2
1
4
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
2
0
0
2
0
2
2
1
0
0
0
2
1
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
8
0
2
0
0
0
0
2
0
1
0
0
0
0
0
1
0
2
2
0
1
0
0
0
0
1
0
0
0
3
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
3
1
0
0
2
0
0
0
2
4
0
1
0
4
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
2
3
0
0
0
2
0
1
2
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
1
0
0
2
0
2
0
0
0
0
0
1
0
0
1
0
2
0
0
0
1
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
2
0
0
1
1
0
1
0
2
1
0
0
0
0
2
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
3
0
0
1
1
0
0
0
1
0
2
0
3
0
0
1
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
2
1
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
4
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
2
1
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
2
0
0
0
0
0
0
1
1
0
2
2
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
2
1
0
0
2
0
0
1
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
5
0
0
0
0
0
1
0
2
0
2
0
2
0
2
0
0
2
0
0
0
2
2
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
2
1
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
3
0
1
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
2
1
0
1
0
0
1
2
0
1
0
0
0
0
1
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
6
0
0
0
4
0
0
0
2
0
0
0
3
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
4
0
0
2
2
0
1
0
1
0
0
0
0
2
0
0
1
0
0
1
0
0
2
2
0
0
0
0
0
0
0
1
3
0
2
0
0
0
0
0
0
1
0
0
1
0
2
4
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
1
2
0
0
0
1
5
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
5
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
6
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
2
0
2
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
6
2
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
1
2
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
2
0
1
0
0
1
0
2
0
0
0
0
4
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
2
2
3
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
1
0
0
1
0
0
0
0
4
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
5
0
0
2
2
0
0
0
0
1
0
1
0
2
0
0
0
0
1
0
2
0
2
0
2
0
0
0
1
1
0
0
0
0
0
2
0
2
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
1
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
2
1
0
0
2
0
2
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
2
0
0
1
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
4
0
1
0
0
0
1
1
0
0
1
0
0
1
0
1
0
1
2
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
3
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
1
0
0
1
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
3
2
0
0
2
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
3
0
0
0
2
0
0
3
0
2
0
2
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
2
1
0
2
1
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
1
2
1
0
2
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
2
0
2
1
1
2
0
0
0
0
0
2
1
0
1
0
0
0
0
0
1
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
2
1
0
1
0
2
1
0
1
1
2
0
2
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
3
0
0
0
2
5
1
0
0
2
0
2
0
0
2
0
0
2
0
2
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
3
0
0
0
2
1
3
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
1
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
3
2
0
2
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
1
4
1
0
2
0
0
0
0
2
0
2
0
0
0
1
2
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
3
0
2
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
6
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
2
0
1
0
2
0
0
0
0
2
1
2
1
0
0
0
3
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
3
0
0
0
0
1
0
0
0
1
0
0
0
4
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
4
0
0
3
0
0
1
0
1
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
4
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
1
0
1
2
0
2
0
0
0
0
0
0
0
2
0
0
1
1
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
2
0
0
0
0
1
0
0
0
2
0
0
0
3
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
1
1
0
0
0
3
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
3
0
0
1
0
1
1
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
3
0
0
0
1
0
0
1
0
0
0
1
1
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
2
1
1
0
2
1
0
0
0
2
2
1
0
0
0
0
1
0
0
1
0
0
2
1
2
0
0
0
0
0
0
0
0
1
0
0
2
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
2
0
0
1
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
1
0
2
0
1
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
3
0
1
1
2
0
2
0
0
2
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
1
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
1
2
3
0
0
0
0
0
0
3
2
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
3
2
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
13
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
4
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
1
0
1
0
1
2
0
1
2
0
0
0
0
0
0
0
2
2
0
0
2
0
0
2
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
1
2
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
2
1
0
0
2
2
2
0
0
0
1
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
1
0
2
0
2
2
2
3
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
2
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
2
0
1
2
0
2
2
0
1
0
0
0
0
2
0
0
1
0
2
1
3
0
3
0
0
0
2
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
2
0
2
1
1
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
2
1
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
1
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
2
0
7
0
0
3
0
2
0
0
0
0
1
2
0
1
0
2
0
0
5
0
0
0
0
0
1
0
1
0
0
5
0
1
2
2
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
1
0
0
0
2
0
2
0
0
0
2
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
1
1
0
2
0
1
2
0
0
1
0
0
0
1
2
0
0
2
2
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
1
0
0
0
2
0
2
0
0
0
2
0
0
4
0
0
0
2
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
1
1
0
0
0
0
1
2
0
0
0
0
0
2
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
4
0
2
0
0
1
0
1
0
0
0
0
1
0
3
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
1
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
1
0
2
0
0
1
1
1
0
0
0
0
0
0
0
5
0
2
0
0
0
0
4
0
0
0
2
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
1
0
0
2
0
0
7
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
3
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
2
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
3
2
3
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
4
2
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
2
2
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
2
2
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
4
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
2
0
0
0
0
1
2
0
2
0
0
0
0
1
0
1
0
0
0
0
1
0
2
0
0
0
3
3
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
1
2
0
1
2
0
0
0
2
0
1
0
0
1
0
1
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
3
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
1
0
3
0
0
0
0
2
0
0
0
2
0
0
0
0
2
1
0
2
2
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
2
0
0
1
0
5
0
0
0
1
1
1
0
0
0
0
0
3
0
1
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
1
0
2
0
2
0
0
0
1
0
2
0
0
2
1
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
3
7
0
0
2
0
0
2
0
0
0
0
0
1
0
4
0
0
1
0
0
2
0
2
0
0
2
0
0
3
0
2
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
2
3
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
2
3
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
2
2
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
1
0
0
0
0
0
1
1
0
1
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
3
0
0
0
2
0
2
1
0
2
4
0
0
1
0
0
0
0
2
4
0
0
0
0
0
0
1
0
0
0
2
0
0
1
1
2
0
1
1
0
0
0
2
0
2
1
0
2
1
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
1
0
0
0
0
2
0
1
0
1
0
2
0
4
0
5
0
0
1
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
2
0
0
2
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
1
2
0
1
0
0
0
0
1
1
0
0
0
1
0
0
2
1
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
1
1
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
4
3
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
2
1
0
0
2
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
1
2
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
2
0
0
3
0
0
0
0
0
0
0
3
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
3
1
2
0
0
2
0
0
1
0
0
2
0
2
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
1
1
0
1
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
4
0
1
0
0
2
2
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
2
0
1
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
1
0
2
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
1
0
6
0
0
1
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
2
0
3
0
0
0
0
0
1
0
2
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
1
1
0
1
0
0
4
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
2
0
0
2
2
2
0
0
2
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
2
0
1
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
3
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
7
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
2
1
2
0
2
0
0
0
0
0
1
2
1
0
3
1
0
0
1
0
0
0
0
0
0
2
1
0
1
0
0
2
0
0
2
0
0
0
2
0
1
1
2
1
0
2
0
0
2
0
7
0
0
1
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
3
2
2
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
2
0
0
0
1
0
2
1
0
0
2
0
2
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
1
4
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
1
0
1
0
0
0
2
0
0
0
0
0
7
2
1
0
0
0
0
0
0
3
0
1
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
3
2
0
0
0
2
4
1
0
0
0
0
0
0
0
0
4
0
1
2
0
0
2
3
0
0
0
0
0
0
2
1
1
0
0
0
0
2
0
0
1
0
0
0
2
0
0
1
0
0
0
1
2
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
1
0
2
1
0
0
0
2
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
2
0
2
2
0
0
0
0
0
0
1
0
1
0
0
0
0
1
2
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
3
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
2
1
0
0
0
0
0
0
1
0
0
1
0
0
2
1
0
0
1
2
0
0
2
0
0
2
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
3
0
3
0
2
1
0
0
1
0
2
0
0
2
0
0
0
2
2
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
2
2
0
0
0
0
2
3
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
1
0
4
0
1
1
0
1
0
2
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
3
1
0
1
0
0
1
0
0
2
0
3
2
0
2
1
2
1
2
0
0
0
1
0
2
0
0
2
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
1
2
0
0
0
2
2
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
2
1
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
4
0
0
0
4
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
1
0
2
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
3
0
5
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
2
1
0
1
1
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
2
0
0
2
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
0
0
0
3
1
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
4
2
0
1
0
2
0
0
0
1
0
2
0
0
1
0
1
0
0
0
0
0
2
0
2
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
2
0
1
0
0
1
0
0
1
0
0
1
0
1
0
0
3
0
0
4
2
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
4
1
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
4
0
0
0
0
0
0
1
0
1
0
0
1
0
1
1
0
0
0
0
0
5
2
0
0
0
2
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
2
2
2
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
1
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
3
2
0
0
1
3
1
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
1
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
1
2
0
2
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
2
0
0
3
0
0
0
0
0
1
0
1
1
0
2
2
1
0
0
3
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
1
0
0
0
1
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
4
0
1
1
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
2
0
0
2
0
0
1
0
0
2
0
1
3
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
3
2
1
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
2
0
0
0
0
1
1
0
0
0
0
0
2
0
0
2
0
0
2
2
0
0
1
0
0
1
0
4
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
2
0
0
0
0
0
0
1
0
2
1
2
0
0
0
2
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
1
0
1
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
2
3
0
0
1
0
0
0
2
0
2
0
0
0
4
0
0
0
2
0
0
2
0
0
1
1
0
1
0
0
0
0
0
0
2
1
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
2
3
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
1
1
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
6
0
0
2
0
0
2
0
1
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
2
1
2
1
1
1
2
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
1
0
2
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
1
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
3
0
2
1
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
1
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
1
0
0
0
2
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
3
0
0
1
2
2
2
1
2
0
4
0
0
0
0
0
1
0
3
1
0
0
0
2
0
0
0
0
0
0
2
0
0
4
0
0
2
0
2
0
1
2
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
1
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
3
2
2
0
0
0
8
1
2
3
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
1
1
0
0
1
5
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
3
0
3
2
2
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
2
0
0
1
2
0
3
1
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
2
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
2
0
2
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
2
0
0
0
0
0
0
0
0
2
0
10
0
1
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
2
1
1
0
0
0
2
0
1
1
1
1
0
0
2
0
2
0
0
0
2
0
0
0
0
3
0
0
0
0
2
0
0
0
0
4
1
1
0
1
0
0
2
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
1
0
0
2
1
1
0
0
0
0
1
0
0
0
3
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
1
0
0
0
4
1
0
0
1
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
1
2
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
2
4
0
0
0
2
0
1
0
2
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
3
0
0
0
0
1
2
1
0
1
0
1
0
2
0
0
0
1
5
0
0
0
1
2
0
0
1
2
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
1
0
0
0
2
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
1
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
2
2
2
0
1
0
0
4
0
0
2
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
2
1
0
2
0
3
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
3
1
0
3
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
2
0
0
0
0
0
0
0
2
0
0
1
0
0
5
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
1
0
1
1
0
0
1
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
4
0
0
2
0
0
0
0
2
2
0
0
0
0
1
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
2
0
0
1
2
0
0
0
2
2
2
2
0
2
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
8
0
0
1
1
0
4
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
1
0
0
0
1
3
0
0
0
2
1
2
0
0
0
0
0
2
0
2
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
2
5
0
0
0
1
0
1
0
0
2
0
0
0
2
2
0
0
0
1
0
0
0
0
1
2
0
3
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
2
0
2
0
0
2
2
0
0
2
0
0
0
0
0
2
0
0
2
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
1
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
1
0
0
1
0
0
1
0
1
0
1
0
0
0
3
0
0
0
4
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
1
1
2
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
2
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
2
0
0
1
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
2
0
0
2
0
0
0
1
0
0
1
0
0
1
0
0
2
2
1
0
0
0
0
0
0
0
0
3
0
0
0
0
2
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
2
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
2
1
1
0
1
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
2
0
1
0
0
1
0
1
0
2
1
0
0
0
1
0
1
2
0
0
0
0
0
1
1
0
0
2
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
2
3
0
1
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
2
2
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
9
0
0
0
1
1
0
0
1
2
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
2
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
5
0
0
0
2
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
2
2
0
0
0
0
0
1
0
2
1
0
0
0
2
0
1
0
1
0
1
0
0
0
0
0
0
2
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
3
2
0
1
0
0
0
0
0
0
0
0
0
2
1
2
0
2
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
1
2
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
2
0
1
0
1
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
2
0
0
1
2
2
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
2
0
1
2
2
2
0
1
3
0
1
0
0
0
0
2
2
0
0
0
2
0
1
2
0
2
1
0
0
0
0
0
1
0
0
0
0
1
1
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
2
1
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
3
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
3
2
2
0
0
1
0
2
0
1
0
0
0
2
2
3
0
0
0
0
0
2
0
0
1
0
0
0
3
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
3
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
2
0
1
0
0
0
0
2
0
0
2
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
1
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
1
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
2
0
1
0
2
2
1
0
0
0
1
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
4
1
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
2
0
0
1
3
0
2
0
0
0
2
0
0
0
2
3
0
0
1
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
1
0
1
0
0
2
0
0
7
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
8
0
2
0
0
0
0
0
0
2
1
0
1
0
0
1
0
0
0
0
0
0
3
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
2
0
0
0
2
0
0
2
0
1
4
2
0
3
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
1
3
0
0
8
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
2
0
0
1
0
0
0
0
2
0
1
0
2
0
0
0
0
0
2
0
0
1
0
1
0
1
0
2
0
0
0
2
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
1
0
2
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
2
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
2
2
0
3
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
1
3
1
2
0
0
0
2
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
1
0
1
2
1
2
0
0
2
1
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
2
1
0
0
0
0
2
0
1
0
0
2
0
0
1
0
0
2
0
1
0
0
0
0
1
3
2
2
0
0
0
0
0
2
0
0
2
0
0
4
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
2
0
2
1
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
4
0
1
0
0
2
2
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
2
0
2
0
0
0
2
0
2
2
0
0
0
0
0
1
0
0
0
1
0
2
0
1
0
2
0
2
0
0
0
0
1
0
0
0
1
0
2
2
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
1
2
0
1
0
0
1
1
0
1
0
0
0
1
0
0
2
0
0
0
0
1
1
1
0
2
0
0
0
0
0
0
1
3
0
0
0
0
2
2
4
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
3
0
2
0
0
1
0
0
2
0
2
0
0
1
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
1
2
1
1
0
0
0
1
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
3
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
1
0
1
3
2
0
0
2
1
2
0
0
0
0
0
1
1
0
0
2
1
0
0
0
1
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
3
0
2
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
1
1
1
2
3
0
0
0
1
1
0
0
0
3
0
0
0
0
0
0
1
0
2
1
0
0
0
2
0
1
0
0
0
2
4
0
0
4
1
0
0
1
0
0
2
0
0
0
1
0
0
0
1
0
0
3
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
1
2
0
0
1
0
0
0
0
0
0
1
2
1
2
1
0
0
0
1
2
0
0
0
0
0
2
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
3
0
0
0
2
2
0
0
0
1
0
1
0
0
1
0
0
0
1
0
1
0
0
0
1
1
0
1
0
0
1
1
0
0
0
2
1
1
2
0
0
7
1
4
0
0
0
0
1
0
0
0
0
4
2
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
1
0
0
1
1
1
0
0
0
0
2
1
1
0
2
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
2
0
2
12
0
2
1
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
2
2
2
0
2
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
2
0
0
0
0
2
1
2
0
0
1
1
0
0
0
0
0
2
0
0
3
0
0
2
0
0
0
1
0
1
0
2
0
1
0
1
0
0
0
0
0
1
1
0
0
1
0
2
0
3
2
0
1
2
2
1
2
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
1
2
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
6
0
0
0
0
0
0
2
1
0
1
1
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
3
0
0
1
0
0
0
1
1
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
2
0
1
0
0
0
1
0
1
0
1
0
0
0
0
1
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
3
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
3
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
3
0
1
0
0
0
1
0
0
0
0
0
1
0
2
0
1
1
2
0
0
2
0
0
1
0
0
2
1
0
1
5
0
1
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
2
1
1
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
3
0
0
2
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
3
0
0
4
0
0
0
1
2
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
2
0
2
1
2
0
0
0
5
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
4
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
2
0
0
2
3
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
3
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
2
0
0
0
0
0
0
0
1
0
0
0
1
2
1
0
0
1
0
9
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
2
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
2
0
2
0
0
0
0
0
0
0
1
0
4
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
1
0
0
0
0
2
0
1
0
0
1
0
2
1
2
1
0
0
0
0
0
1
3
2
0
2
2
0
0
0
0
0
0
0
1
2
0
0
0
1
1
0
0
0
0
0
0
0
1
2
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
3
0
0
0
1
3
0
0
3
2
0
1
0
2
0
1
1
1
0
2
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
4
0
0
3
0
0
0
2
0
0
1
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
1
0
0
0
0
0
0
3
0
0
0
0
0
0
3
1
2
0
2
0
0
2
0
0
3
0
1
0
0
1
0
0
0
2
1
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
1
2
0
0
0
1
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
1
0
2
3
3
2
0
4
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
3
0
2
0
0
0
0
0
0
0
0
1
0
1
2
0
1
1
2
0
0
0
0
5
0
0
0
0
1
0
0
5
0
0
0
0
0
0
1
3
0
1
2
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
1
0
0
2
0
0
1
0
1
2
0
1
0
0
0
0
2
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
1
1
0
0
1
1
0
0
0
1
0
2
0
0
3
0
0
2
0
0
1
0
1
0
1
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
5
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
1
0
2
0
2
2
0
0
0
0
0
0
2
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
5
0
0
0
1
0
0
0
1
1
0
2
1
0
0
2
4
0
0
0
1
0
1
0
1
0
1
0
1
0
0
2
0
0
0
2
0
0
0
1
0
0
2
0
0
2
0
0
0
0
1
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
4
0
0
0
2
1
3
0
1
0
1
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
2
0
0
0
0
2
0
0
0
1
0
2
1
0
0
2
3
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
2
2
0
0
0
2
0
0
0
1
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
2
2
1
0
0
0
0
4
0
0
1
2
0
1
0
0
0
0
2
0
2
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
3
1
0
0
0
0
2
0
0
2
2
0
0
0
1
0
0
0
1
1
2
0
0
0
0
1
0
0
0
3
0
0
2
0
0
0
0
0
2
0
2
2
0
2
0
4
0
1
0
0
2
0
1
0
0
0
0
0
2
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
3
2
2
2
0
0
1
0
0
0
0
0
0
0
0
1
2
1
0
0
0
2
0
0
0
0
2
0
3
0
1
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
5
1
0
0
0
0
3
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
2
2
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
2
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
2
2
2
0
1
0
0
0
1
0
0
0
1
0
2
0
0
0
0
2
1
0
0
2
0
0
0
1
0
0
0
0
0
0
3
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
3
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
2
2
0
0
0
0
0
2
0
0
2
0
0
0
3
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
4
0
0
0
1
0
0
0
0
0
0
2
3
1
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
1
2
0
0
0
2
0
0
2
0
0
3
0
0
0
3
2
0
1
0
0
0
0
0
1
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
2
2
2
2
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
1
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
5
0
3
0
0
0
1
0
1
0
2
0
0
0
0
0
0
2
0
1
2
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
3
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
2
1
0
0
1
0
2
0
1
1
0
0
3
0
1
1
0
0
0
0
0
0
2
5
0
0
0
0
1
0
0
0
1
0
1
1
0
0
1
0
1
0
2
1
0
0
0
2
0
0
1
0
0
0
2
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
1
2
0
0
2
1
2
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
2
0
1
1
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
2
4
1
0
0
0
0
1
0
1
0
2
0
2
0
0
0
2
2
0
1
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
1
1
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
4
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
2
2
0
2
0
1
0
0
0
0
0
0
0
0
1
1
3
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
1
2
0
0
0
1
0
0
1
0
0
0
3
2
0
2
0
0
7
1
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
2
0
1
0
0
0
0
2
0
1
1
0
0
2
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
2
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
2
1
2
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
2
1
0
0
0
0
2
1
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
2
1
3
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
1
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
1
0
0
2
3
0
1
0
0
0
0
0
0
0
1
2
2
2
2
1
0
0
0
0
0
0
0
2
0
1
0
6
0
0
0
0
2
1
0
0
0
0
0
0
0
1
4
0
1
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
5
0
0
1
1
0
0
0
3
1
2
0
0
0
0
0
0
0
0
2
0
2
0
2
1
0
2
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
1
1
1
0
0
2
1
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
1
2
0
0
0
0
0
1
1
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
5
0
0
2
0
0
0
0
0
5
0
0
1
2
2
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
1
2
1
0
0
0
1
2
2
1
0
0
0
0
4
0
1
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
1
1
0
0
1
0
0
0
0
0
0
1
2
1
1
0
0
0
0
2
0
0
0
1
3
0
0
0
2
0
1
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
4
0
0
0
0
2
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
1
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
3
0
1
0
0
0
1
0
1
0
0
1
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
2
2
0
0
2
0
1
0
0
0
0
0
0
2
0
2
0
0
1
0
2
0
1
1
0
0
0
0
1
1
0
2
0
2
0
0
0
3
0
1
2
2
1
0
0
0
1
0
0
1
0
0
0
0
0
1
1
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
3
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
2
2
0
1
0
0
1
0
0
0
0
2
0
0
0
3
0
0
1
0
2
0
0
0
0
0
2
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
2
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
2
0
2
0
3
1
0
1
0
2
0
0
2
3
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
5
2
0
2
0
0
0
0
1
0
1
0
0
0
0
1
0
0
3
1
0
0
0
2
0
1
0
0
3
1
2
2
1
1
0
2
0
1
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
3
0
0
0
2
2
0
1
0
2
0
0
4
0
0
1
0
0
0
2
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
1
1
0
1
0
2
0
0
2
0
0
0
0
0
2
0
1
3
0
0
0
0
0
1
0
0
2
0
1
0
0
0
2
0
1
1
3
0
0
2
0
0
0
1
0
0
0
2
1
0
1
0
0
0
2
0
0
0
3
0
0
0
1
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
2
0
0
0
3
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
3
0
0
3
0
0
0
3
0
1
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
2
4
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
2
2
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
3
0
0
0
0
0
2
0
2
1
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
2
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
7
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
3
2
0
0
2
3
0
1
0
2
0
1
0
0
2
0
0
0
0
0
0
0
1
0
7
0
0
0
2
0
0
0
0
0
0
2
2
0
0
1
2
0
0
0
2
0
1
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
1
1
1
1
0
0
1
0
2
1
0
0
0
2
1
0
1
2
0
1
0
1
0
1
0
7
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
2
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
1
2
0
0
0
2
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
4
0
0
0
0
1
0
1
0
0
2
1
1
2
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
3
0
0
0
2
0
1
0
0
2
1
0
2
0
0
0
0
0
1
0
0
0
1
0
0
4
2
2
2
0
0
2
0
2
0
0
0
1
0
0
0
0
2
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
2
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
1
2
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
6
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
2
0
1
0
0
0
0
2
0
0
2
0
1
1
2
0
1
1
0
2
0
1
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
2
0
0
0
0
0
1
0
3
1
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
3
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
3
1
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
1
0
2
0
0
0
2
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
3
2
1
2
2
0
0
1
0
1
0
0
1
0
0
0
0
0
2
0
1
0
3
0
0
0
2
0
0
0
2
0
1
0
1
0
1
0
2
3
0
0
1
0
0
0
1
2
0
0
0
3
1
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
4
0
2
0
0
2
0
0
0
1
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
1
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
1
1
0
1
0
0
2
0
3
0
1
0
1
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
3
0
1
2
0
0
0
1
1
3
2
0
0
0
2
0
0
2
0
2
0
0
0
1
0
0
2
0
0
2
0
0
1
0
1
1
0
0
0
0
2
2
0
1
1
2
0
1
1
2
2
0
2
0
1
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
2
1
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
3
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
3
0
1
0
0
0
1
0
0
0
0
0
2
4
0
2
0
0
0
0
0
0
0
3
1
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
1
0
0
2
0
0
0
0
0
2
2
3
1
0
1
0
0
0
0
0
0
1
0
3
0
1
5
1
0
0
0
0
1
0
0
1
0
0
0
2
2
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
1
2
0
2
0
0
2
0
0
0
2
1
1
0
0
2
0
0
0
2
0
0
2
0
0
2
0
2
0
0
0
2
0
1
0
1
2
0
0
0
0
0
3
0
0
0
2
2
0
0
0
1
0
1
1
2
1
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
3
0
0
0
1
0
0
0
1
0
0
0
0
2
0
1
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
2
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
2
1
5
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
1
1
0
0
0
1
0
0
0
1
2
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
3
2
1
0
2
0
1
0
0
0
0
1
0
2
0
2
2
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
1
0
2
0
0
1
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
1
0
5
0
1
0
0
0
1
3
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
5
0
0
2
0
0
2
0
0
0
1
0
0
1
2
0
0
0
0
0
0
1
0
0
2
0
5
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
1
0
3
1
1
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
2
0
1
0
1
0
0
0
1
0
4
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
1
1
1
0
0
1
0
1
0
2
0
8
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
1
1
2
0
0
0
0
0
0
1
1
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
2
2
0
3
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
4
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
4
1
0
0
0
0
0
2
0
0
0
1
0
2
0
4
2
2
1
3
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
3
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
8
0
0
1
0
0
0
0
3
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
1
0
0
3
0
0
0
3
0
0
0
0
0
0
1
0
0
1
1
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
3
0
2
0
0
0
0
0
1
2
0
0
3
0
0
1
0
0
2
0
0
0
1
0
0
1
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
3
3
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
1
0
0
1
2
1
0
0
0
4
0
0
0
0
0
3
0
0
0
0
1
1
1
1
1
1
0
0
3
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
3
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
3
1
2
0
0
0
0
2
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
3
1
0
0
0
2
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
3
1
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
2
0
2
1
0
0
5
1
0
0
0
0
1
0
1
2
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
7
2
0
0
0
2
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
2
0
0
1
1
0
1
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
1
1
1
0
0
1
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
7
1
2
0
0
2
2
1
0
1
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
1
2
0
0
0
0
0
1
0
0
0
0
0
3
1
2
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
3
3
0
0
0
0
0
2
0
1
0
3
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
1
1
2
1
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
1
2
0
2
2
0
0
0
2
1
0
0
0
0
2
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
1
0
0
0
2
2
0
0
0
0
0
0
4
1
2
2
0
0
0
0
2
0
0
1
2
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
3
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
1
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
3
0
2
2
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
3
0
0
0
0
1
0
0
1
0
0
1
0
0
0
2
2
0
0
2
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
3
3
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
1
0
0
2
3
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
2
1
0
0
1
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
4
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
2
0
0
0
1
0
1
1
1
2
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
2
0
0
0
2
3
1
0
0
1
0
0
0
0
1
1
2
0
0
0
0
0
0
4
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
4
1
1
8
1
2
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
1
0
0
0
1
5
0
1
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
2
0
0
0
0
2
1
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
2
1
0
0
1
0
0
0
4
0
1
0
0
2
0
1
2
0
0
1
0
1
0
0
0
0
0
0
0
7
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
8
0
0
0
0
2
0
1
1
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
3
0
0
1
6
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
2
0
1
1
1
0
0
0
1
1
0
3
2
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
2
2
0
0
1
0
0
2
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
2
0
0
0
0
1
1
0
0
0
1
0
0
1
2
0
0
0
0
1
4
0
1
1
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
3
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
2
2
0
0
0
0
2
1
0
1
2
0
5
1
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
2
0
1
0
0
0
0
3
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
1
0
0
1
2
0
1
1
0
0
2
0
0
0
0
0
2
0
0
2
0
2
0
0
1
0
0
0
0
0
0
2
1
1
0
0
0
0
1
0
2
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
2
2
0
0
0
0
1
2
2
0
1
0
0
4
0
0
0
2
0
0
0
2
0
0
2
0
2
1
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
3
0
0
1
0
2
0
1
0
1
0
0
2
0
0
3
5
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
3
0
0
3
0
0
0
0
0
1
0
1
3
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
2
0
2
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
4
2
0
0
0
1
0
0
0
2
2
0
0
0
2
0
0
0
1
2
0
1
1
0
0
2
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
2
1
0
0
0
0
2
0
3
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
5
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
1
2
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
4
0
1
2
0
0
2
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
3
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
1
1
0
3
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
2
1
1
2
0
0
1
2
3
0
1
1
0
1
2
1
1
2
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
5
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
2
0
2
1
3
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
3
0
0
0
0
0
0
0
0
1
2
2
0
0
1
0
0
0
0
2
2
2
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
1
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
3
0
0
2
0
1
2
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
2
0
2
0
0
0
2
1
0
0
0
2
0
0
0
0
0
1
0
3
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
1
0
2
0
1
2
0
2
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
2
0
3
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
1
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
2
0
0
1
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
1
0
1
2
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
1
1
0
2
2
0
2
1
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
4
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
2
0
2
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
1
2
0
2
0
3
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
2
1
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
2
2
0
0
0
1
0
0
1
0
1
2
0
1
0
0
2
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
2
2
0
0
0
1
0
0
0
0
2
0
0
2
0
1
4
0
0
0
2
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
2
0
0
1
0
0
3
0
2
0
0
0
2
0
0
0
0
2
2
2
0
1
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
1
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
1
2
0
0
1
1
0
0
0
0
2
0
4
1
0
0
0
0
0
2
1
1
0
0
0
0
0
1
2
2
0
0
2
0
0
1
0
1
0
0
0
0
0
0
3
0
0
2
0
1
2
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
2
0
1
1
1
1
0
0
0
0
0
0
0
0
1
2
0
0
1
1
0
0
0
0
0
0
3
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
1
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
3
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
2
0
0
0
0
0
1
0
0
0
0
1
4
0
0
2
0
0
2
0
0
4
1
0
0
0
1
0
1
1
0
4
0
0
2
0
0
0
0
1
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
1
0
0
0
0
0
2
2
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
2
2
1
0
0
0
0
0
1
1
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
1
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
3
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
6
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
3
0
0
0
4
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
2
1
2
1
2
0
0
0
1
1
2
1
1
0
0
0
0
0
2
0
0
2
0
1
0
1
7
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
1
1
0
0
0
0
0
0
0
5
0
0
2
0
2
0
0
4
0
0
1
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
2
3
0
2
1
0
0
2
0
1
0
2
1
2
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
1
0
2
0
0
0
0
2
0
2
0
0
0
0
1
1
1
1
0
3
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
1
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
4
0
0
0
0
1
0
9
4
0
0
0
0
0
1
1
3
0
0
0
0
0
0
0
0
3
0
1
0
2
0
0
0
1
1
1
0
2
0
0
0
0
2
2
0
0
1
0
2
1
0
2
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
1
0
2
1
0
0
0
1
0
0
0
1
1
0
0
2
1
0
0
3
1
1
0
2
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
2
0
0
0
0
2
0
0
0
2
2
1
0
2
0
2
2
0
0
2
0
1
0
0
0
1
0
1
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
4
0
0
0
0
2
0
0
2
2
0
0
0
0
0
1
0
0
1
0
0
2
1
1
0
0
0
1
0
0
0
1
2
1
0
0
0
0
1
0
2
2
1
2
0
0
1
0
0
0
0
0
0
5
0
1
0
0
2
2
0
0
0
0
0
0
0
1
2
0
2
2
2
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
1
0
0
2
0
2
0
0
0
3
2
0
0
0
0
1
0
0
0
0
0
2
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
1
0
0
1
0
2
0
0
0
3
1
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
1
1
0
0
0
0
6
0
0
2
0
0
0
0
3
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
4
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
1
0
2
0
1
4
0
0
0
2
2
0
0
0
0
0
0
0
1
0
1
0
1
0
2
0
0
0
1
0
0
0
0
0
2
1
2
0
1
0
1
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
2
1
2
1
0
1
0
0
1
0
0
0
1
0
0
1
0
2
0
0
0
0
0
2
1
0
0
0
2
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
1
0
0
1
2
0
0
0
2
0
0
0
0
2
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
1
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
2
0
2
0
0
0
0
0
0
3
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
2
6
1
0
0
0
1
0
2
1
0
2
0
0
1
0
2
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
1
0
1
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
2
0
0
0
0
2
3
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
1
0
2
0
3
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
3
2
0
2
0
0
5
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
2
0
1
1
0
0
0
2
0
1
3
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
1
0
1
0
0
1
1
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
3
0
0
0
0
0
0
2
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
4
0
2
1
0
2
0
0
1
1
0
1
1
0
0
0
1
0
0
2
2
0
0
0
0
0
2
0
1
0
2
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
3
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
2
0
0
0
6
0
1
0
1
2
0
2
1
2
1
1
5
2
0
0
2
2
0
2
2
1
0
0
0
1
0
0
0
2
0
2
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
3
0
0
0
1
2
2
2
1
4
1
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
2
0
0
0
0
1
0
3
0
0
0
0
0
0
1
2
1
0
0
3
0
0
2
0
2
3
2
1
2
2
0
0
0
0
1
3
0
0
0
0
0
1
0
0
0
0
0
1
1
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
2
4
0
2
0
0
1
0
1
0
0
0
0
4
0
0
2
1
1
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
1
1
0
1
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
2
0
0
0
0
2
2
0
0
1
2
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
3
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
1
0
1
0
0
0
1
0
2
0
0
1
0
0
1
0
0
0
0
0
2
0
1
0
0
0
2
3
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
3
0
1
0
0
0
1
0
0
2
2
3
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
4
0
1
1
0
0
0
0
2
1
0
2
0
0
0
2
2
0
0
0
3
0
1
2
0
0
2
0
0
0
1
0
0
0
2
0
0
0
1
2
2
0
1
0
0
0
0
0
3
2
0
0
0
1
0
0
0
0
0
2
0
0
0
2
1
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
2
2
2
0
2
2
3
0
1
0
3
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
2
1
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
2
0
3
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
4
2
0
1
0
1
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
1
0
2
0
1
2
0
1
0
2
0
0
2
0
0
2
0
0
1
2
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
8
0
0
1
0
2
2
2
0
2
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
1
1
0
0
0
2
0
1
1
2
0
0
1
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
1
0
1
0
2
0
1
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
1
0
0
1
0
2
2
2
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
2
3
2
2
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
1
2
0
3
0
0
1
0
1
1
1
1
0
1
0
2
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
1
2
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
1
1
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
3
0
1
0
1
1
1
0
2
0
1
2
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
1
0
0
0
3
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
6
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
1
0
1
0
2
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
1
1
0
0
1
3
0
1
0
0
2
0
1
0
1
0
2
0
0
0
0
0
0
0
2
0
0
2
3
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
1
0
0
1
2
0
0
0
0
0
1
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
8
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
1
0
0
0
2
2
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
1
2
0
2
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
1
2
2
1
2
0
1
0
0
0
0
0
1
0
2
0
0
2
0
1
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
1
1
2
0
0
0
3
0
0
0
0
0
2
0
1
0
0
0
2
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
2
0
1
1
0
0
0
2
2
0
2
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
3
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
8
0
0
1
0
2
3
0
0
1
0
1
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
2
0
0
0
1
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
2
0
4
0
1
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
7
0
2
0
2
0
2
2
2
0
0
1
0
0
0
0
2
0
0
0
1
0
3
0
0
0
0
0
0
2
0
0
0
1
0
0
1
1
0
3
1
0
0
0
1
1
0
2
1
0
1
1
2
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
1
1
1
0
0
0
1
0
1
0
1
1
3
1
0
0
0
2
0
0
0
0
0
2
2
0
1
0
0
0
2
1
1
2
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
3
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
1
0
0
2
3
0
1
0
0
2
0
0
0
0
2
1
1
0
1
0
1
0
0
0
0
0
0
0
5
0
0
0
2
0
2
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
2
2
1
0
3
0
0
0
2
0
1
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
2
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
4
0
2
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
1
0
1
2
0
3
0
0
0
1
0
2
1
0
0
1
1
0
0
1
0
0
4
0
0
0
0
0
0
3
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
3
0
7
2
0
0
0
0
1
0
0
0
0
2
1
0
1
0
1
0
2
0
1
2
2
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
1
4
0
0
0
2
0
4
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
2
0
0
0
0
2
0
2
2
0
0
0
0
1
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
2
0
0
1
2
0
2
0
0
0
0
1
0
0
0
0
4
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
2
1
0
0
5
0
1
4
0
0
0
0
2
0
0
0
0
2
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
2
0
0
0
1
0
3
1
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
3
2
0
0
0
0
0
0
2
1
1
0
0
0
0
3
0
4
0
2
0
1
2
2
2
0
0
0
0
4
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
4
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
1
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
2
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
4
2
0
1
0
0
0
0
0
0
1
2
0
1
1
0
2
0
0
0
0
0
0
1
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
1
1
0
0
0
2
0
0
0
0
2
0
0
1
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
2
3
0
0
0
0
2
2
0
0
0
1
0
0
2
0
2
1
0
0
0
0
2
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
2
0
2
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
3
4
1
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
2
0
1
0
0
0
2
0
0
0
0
0
2
0
0
1
1
2
0
0
0
1
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
4
1
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
3
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
1
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
1
0
0
4
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
2
0
3
0
0
0
0
3
0
0
0
0
0
0
0
2
2
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
1
1
1
1
2
0
0
1
0
0
2
2
0
1
2
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
1
0
0
1
0
0
0
1
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
2
1
1
1
2
0
0
0
0
0
3
0
0
0
0
2
0
0
0
2
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
2
2
0
0
0
0
0
1
1
0
0
0
0
1
2
0
4
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
1
0
2
2
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
1
0
1
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
2
2
0
0
2
0
0
2
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
3
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
1
0
1
2
0
0
2
0
0
1
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
2
0
0
0
0
1
3
2
1
1
0
0
0
0
0
0
0
0
1
0
0
0
3
1
0
0
0
0
0
0
0
2
0
1
2
0
2
0
0
1
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
1
2
2
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
1
1
0
2
1
2
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
3
1
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
4
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
1
2
2
1
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
2
1
0
2
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
1
4
0
0
0
0
1
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
2
0
2
2
0
0
0
1
1
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
15
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
1
0
0
1
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
2
0
1
1
0
0
1
0
0
0
2
0
0
1
3
0
2
0
2
1
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
3
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
1
2
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
1
0
0
1
1
3
0
1
0
0
0
0
2
0
0
3
0
0
0
0
1
0
0
0
3
1
3
0
0
1
1
1
1
1
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
3
0
0
0
2
0
2
0
0
0
0
1
0
1
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
2
1
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
4
1
2
1
0
1
0
1
2
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
1
0
2
0
0
0
1
0
1
0
0
0
2
0
2
0
0
0
2
0
1
0
0
2
0
0
0
0
0
1
0
7
0
0
0
0
0
2
2
0
0
0
6
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
2
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
4
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
2
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
4
0
0
3
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
3
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
2
2
2
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
1
2
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
3
1
2
0
2
1
0
0
1
0
0
0
0
1
1
0
0
0
0
3
0
2
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
1
0
2
2
0
0
2
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
1
1
0
0
0
1
0
0
0
0
0
0
4
0
2
0
0
5
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
3
0
0
3
0
0
0
0
3
2
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
2
0
0
0
3
0
0
2
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
1
1
0
0
0
0
0
0
2
0
0
0
1
2
0
0
1
1
3
1
0
0
0
2
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
3
0
0
0
2
2
1
12
0
0
0
0
0
0
0
0
0
0
0
1
1
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
1
0
3
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
4
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
3
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
2
3
0
2
0
0
0
0
0
0
2
1
0
0
2
0
1
0
0
1
0
1
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
1
3
0
0
1
0
0
0
2
0
0
2
1
1
1
2
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
2
0
2
0
2
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
2
2
1
0
2
0
0
2
0
2
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
3
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
1
0
2
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
2
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
6
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
1
1
0
2
1
3
0
0
2
1
0
0
5
1
2
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
2
0
0
1
0
0
0
0
1
0
2
0
0
0
0
3
2
2
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
1
0
0
2
1
0
0
1
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
1
0
2
0
0
0
1
0
0
0
0
0
0
1
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
2
1
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
4
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
2
1
0
1
1
0
0
1
0
0
0
0
2
2
0
0
0
0
0
2
2
1
0
1
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
2
2
0
0
1
0
0
0
0
2
1
1
0
0
2
2
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
1
0
0
0
0
1
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
2
0
3
3
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
2
0
0
2
0
0
0
0
0
0
1
0
1
2
2
0
0
0
0
0
0
0
2
0
4
1
0
0
0
0
1
2
0
1
0
0
0
2
3
0
1
0
0
1
0
0
2
0
0
0
0
0
2
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
5
0
2
0
5
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
1
0
1
0
0
1
1
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
1
2
0
0
0
3
0
0
1
1
0
0
0
0
1
0
2
0
0
0
0
0
0
1
6
0
0
1
2
3
0
0
0
2
0
2
0
0
0
0
1
2
2
1
0
1
0
0
0
1
0
0
0
0
0
2
1
0
1
2
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
1
0
0
0
2
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
5
0
0
1
0
0
0
2
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
3
1
0
2
1
2
0
0
0
0
0
1
0
0
2
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
1
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
3
0
0
3
1
0
2
2
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
2
0
2
2
0
2
1
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
2
0
0
0
0
0
0
3
2
0
0
0
4
0
2
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
2
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
1
0
0
0
1
2
2
1
0
0
2
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
1
0
0
0
2
0
0
3
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
4
2
0
0
2
0
0
0
0
0
0
0
0
2
0
1
2
1
2
0
0
0
0
2
0
0
0
2
0
2
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
2
2
0
0
2
2
4
0
1
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
3
0
0
0
1
0
0
3
1
0
1
0
0
0
2
1
1
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
4
1
0
0
0
0
0
0
1
0
0
0
2
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
3
0
0
2
0
0
4
0
0
0
0
0
0
1
2
0
0
0
1
0
2
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
1
0
1
0
0
2
2
0
3
0
0
0
0
0
0
0
0
0
0
1
3
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
1
0
0
0
4
0
0
0
2
0
0
1
0
1
0
0
0
0
2
0
0
0
2
0
2
0
1
0
0
0
1
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
2
2
0
0
1
0
0
0
0
0
21
0
0
0
2
1
0
0
0
0
0
0
2
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
8
0
0
0
0
0
0
1
0
1
0
1
1
0
0
1
0
2
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
1
0
0
1
1
2
0
1
0
4
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
5
3
0
0
3
2
1
0
0
0
0
0
0
2
0
0
0
7
0
0
0
0
0
0
1
0
0
0
0
1
4
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
4
0
0
3
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
2
0
2
0
0
0
0
2
3
1
2
0
0
0
1
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
4
0
1
1
2
0
1
2
0
0
0
0
0
0
0
1
0
1
1
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
2
0
0
2
1
2
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
6
2
0
0
3
0
2
0
0
0
1
0
0
2
2
0
0
0
2
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
2
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
2
0
0
2
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
2
0
2
0
2
2
0
0
2
0
0
0
0
0
2
0
2
0
1
2
0
2
0
0
2
2
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
2
3
1
0
0
0
0
2
0
2
1
0
2
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
2
0
4
0
0
1
2
0
1
0
0
0
0
2
0
0
2
0
1
0
0
3
0
0
0
0
0
0
2
1
0
2
0
0
1
3
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
1
0
0
0
1
1
2
0
0
3
2
0
2
1
0
0
1
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
1
0
0
0
0
2
2
0
0
1
0
2
0
2
8
0
0
0
0
3
3
1
0
1
0
0
0
1
3
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
2
2
0
0
0
1
0
0
3
2
0
0
0
1
0
0
1
0
2
9
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
1
1
0
0
0
1
0
2
0
0
0
2
0
2
0
1
2
1
0
0
2
0
0
0
1
5
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
2
2
0
0
2
2
0
0
0
0
0
0
0
0
2
1
0
2
2
0
0
0
0
2
0
0
0
0
2
0
0
2
1
0
0
1
0
2
1
2
0
0
0
0
0
0
2
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
3
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
2
1
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
2
0
0
0
0
1
0
0
2
1
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
1
0
1
1
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
2
1
0
2
3
3
0
0
3
0
0
2
0
0
0
0
0
0
0
1
0
0
1
1
2
1
2
4
2
1
0
0
1
0
2
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
2
2
0
0
1
0
3
0
0
0
1
0
0
1
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
1
3
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
4
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
2
2
0
0
0
2
1
2
2
0
0
0
1
2
0
2
3
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
1
0
0
0
1
0
0
0
1
3
2
0
0
0
0
0
0
3
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
4
0
0
0
1
1
0
0
0
0
4
2
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
6
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
2
3
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
2
0
0
0
0
2
1
2
0
0
1
0
0
0
0
0
0
0
1
1
0
0
2
0
0
1
1
2
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
3
2
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
2
2
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
2
0
2
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
2
0
1
0
2
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
2
1
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
6
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
2
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
2
0
0
0
3
0
0
1
0
1
0
1
0
0
0
0
0
2
0
0
0
0
2
5
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
1
1
0
0
2
0
0
0
0
0
1
0
2
3
0
2
1
0
0
0
0
2
2
0
0
0
0
0
1
1
0
2
0
0
1
1
0
1
0
2
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
2
0
4
0
1
3
0
0
0
1
0
0
1
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
1
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
1
0
0
3
2
0
1
0
0
0
0
0
0
3
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
2
0
0
0
1
0
2
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
4
0
0
3
2
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
2
0
2
1
2
2
2
1
0
0
0
0
2
2
1
0
0
0
0
2
0
2
0
0
0
0
2
0
0
1
0
2
0
0
0
1
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
12
0
2
0
1
2
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
2
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
1
2
0
0
0
0
0
1
0
1
0
0
0
0
3
3
1
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
1
0
0
1
2
0
0
1
0
0
2
0
0
0
0
0
0
0
3
1
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
9
0
1
0
0
1
0
2
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
6
0
0
0
0
0
1
3
0
1
0
0
0
0
3
0
0
0
0
0
0
0
2
0
2
2
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
1
0
0
1
2
0
2
0
0
0
2
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
2
0
0
2
0
2
0
0
0
0
3
0
0
0
2
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
2
0
0
1
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
2
1
0
1
0
1
0
0
2
0
0
2
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
3
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
3
0
1
0
0
4
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
1
0
2
1
0
0
0
3
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
2
0
2
2
0
2
0
1
2
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
1
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
1
0
2
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
2
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
3
0
1
2
0
0
0
1
2
1
0
0
5
1
2
0
1
2
0
0
0
2
0
0
0
0
0
1
0
0
2
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
2
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
3
0
2
0
1
0
0
0
2
0
0
2
1
0
0
1
0
0
0
2
0
0
0
0
0
5
0
1
0
0
0
0
6
0
2
0
0
0
0
1
0
3
1
2
0
2
1
0
3
3
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
1
0
1
1
2
0
2
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
1
2
1
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
1
1
0
1
0
0
2
0
2
0
0
0
0
0
0
1
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
3
0
0
3
0
0
1
2
0
0
0
0
0
1
0
1
1
0
2
0
0
0
0
0
1
0
0
0
0
2
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
2
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
2
0
0
0
0
1
0
0
1
0
0
0
1
0
3
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
2
0
0
3
2
0
0
3
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
4
1
3
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
2
0
0
0
1
1
2
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
3
2
1
0
0
0
0
0
1
7
0
1
0
0
0
1
0
2
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
2
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
1
0
2
0
0
0
0
0
4
1
0
0
1
0
0
0
0
1
0
1
0
4
0
0
0
0
1
0
1
0
1
0
2
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
3
1
0
1
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
2
2
0
0
1
2
0
1
0
0
0
0
0
0
1
2
0
2
0
1
0
0
0
0
0
1
0
0
2
0
0
2
3
0
2
0
1
0
0
1
0
3
0
1
0
0
0
0
0
1
0
1
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
3
0
1
0
0
0
1
1
0
0
2
0
0
0
2
0
0
0
1
0
2
2
0
0
0
0
0
0
0
5
0
2
0
0
0
0
1
2
2
0
0
2
2
0
0
0
0
0
1
1
0
0
0
1
0
1
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
1
0
1
0
0
0
1
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
2
0
0
2
0
1
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
1
0
2
0
0
0
0
0
0
2
0
0
2
1
0
3
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
1
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
2
0
0
0
2
0
1
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
1
1
1
0
0
2
0
0
0
0
2
0
0
1
0
2
1
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
1
0
0
1
0
2
0
0
0
0
0
0
3
0
0
0
1
2
0
2
0
0
0
0
0
0
0
2
1
2
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
3
0
0
2
0
0
0
0
3
0
0
1
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
2
2
2
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
4
2
0
2
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
2
0
3
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
1
0
3
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
3
0
0
1
0
0
0
0
2
1
0
0
1
0
3
0
0
2
3
0
0
0
0
1
0
1
1
0
1
0
1
2
0
2
2
0
1
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
2
1
0
0
0
1
0
0
0
0
3
1
0
0
0
2
0
0
0
0
1
0
0
0
1
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
6
1
0
0
1
0
0
0
2
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
2
0
0
0
0
0
3
0
1
2
0
0
2
1
0
1
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
2
0
0
0
0
0
1
0
3
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
2
3
0
0
8
1
0
0
0
0
1
2
0
0
0
0
2
0
2
0
1
2
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
2
0
0
0
0
2
0
5
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
1
0
0
0
2
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
1
2
0
0
0
0
1
0
0
0
0
1
0
0
2
1
0
0
0
1
0
0
2
2
1
0
0
2
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
3
0
0
0
1
0
0
0
0
5
0
0
0
0
0
0
0
3
0
0
0
2
0
0
1
1
0
0
0
2
2
0
0
0
0
0
3
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
5
2
2
2
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
4
0
0
0
2
0
3
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
1
2
0
0
1
0
0
3
2
2
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
3
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
5
0
1
0
0
2
0
0
3
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
2
1
0
0
2
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
1
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
1
0
2
2
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
6
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
2
1
2
2
0
0
1
0
7
0
1
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
2
0
0
0
0
0
0
0
1
1
1
1
4
0
0
1
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
2
1
0
1
0
0
0
0
2
0
0
0
0
1
0
1
0
0
4
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
2
2
0
0
0
0
3
1
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
5
1
1
1
0
0
0
2
0
1
0
0
0
0
5
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
1
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
1
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
2
0
0
1
0
0
0
1
0
0
1
2
0
0
0
1
0
0
0
0
0
2
2
1
1
0
0
0
0
0
0
2
0
1
0
0
1
2
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
2
1
0
0
6
1
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
5
0
2
1
0
3
1
0
0
2
0
0
0
0
0
3
0
2
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
2
0
0
1
2
2
2
1
0
0
2
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
4
0
1
0
0
0
3
2
0
0
0
0
0
2
0
0
0
1
0
0
2
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
4
0
0
0
0
0
2
0
0
1
0
2
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
8
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
5
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
2
2
0
0
0
0
0
2
1
1
0
0
2
0
0
0
0
3
0
0
0
2
1
0
1
0
1
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
1
1
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
4
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
4
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
2
2
0
0
1
2
0
2
0
2
0
0
0
1
0
1
0
0
2
0
0
0
1
0
0
2
0
2
0
3
2
0
6
2
0
0
0
0
2
2
0
2
0
2
2
3
3
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
3
0
0
2
0
0
2
0
0
1
0
0
0
3
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
2
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
1
0
2
0
2
0
1
0
2
0
0
2
0
0
1
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
2
0
0
2
0
0
0
1
0
0
0
0
2
1
0
2
0
0
1
2
0
0
0
0
2
0
0
0
0
0
1
2
1
0
0
1
2
0
0
0
0
0
1
1
1
1
0
0
1
0
0
0
0
0
0
0
2
1
1
0
0
0
6
1
0
1
0
0
0
1
1
0
0
0
0
1
0
1
0
2
3
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
2
0
0
0
0
1
0
0
2
3
0
0
1
0
0
0
0
1
0
0
0
0
3
2
0
0
0
3
2
3
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
1
0
0
2
0
2
0
1
2
0
2
0
1
0
1
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
3
0
2
0
1
0
2
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
1
0
0
0
2
0
1
0
0
0
0
5
2
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
2
0
0
0
3
1
4
1
0
3
0
0
0
0
1
2
0
0
0
0
0
1
0
0
3
1
0
0
0
0
0
0
0
0
2
2
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
1
1
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
1
0
0
0
0
2
0
0
1
3
0
1
1
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
4
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
1
1
0
1
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
1
1
0
0
3
2
1
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
3
0
0
2
1
0
0
0
1
0
0
1
2
0
0
0
0
0
2
0
1
0
0
0
1
0
3
0
1
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
1
0
0
1
1
0
1
3
0
0
1
0
0
2
1
0
0
0
0
0
2
1
1
2
0
0
0
2
0
0
0
0
2
1
0
0
0
0
2
0
4
2
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
4
0
0
0
2
2
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
2
0
1
0
0
0
3
2
0
0
0
0
0
0
2
0
0
1
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
2
0
0
0
3
0
0
1
0
0
1
0
0
0
0
2
1
0
0
0
1
0
1
2
0
0
0
0
0
0
0
1
2
0
1
0
0
0
2
0
1
2
0
0
0
0
2
0
0
0
1
0
1
1
0
3
1
0
1
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
1
2
0
2
0
2
0
0
0
1
0
1
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
2
2
1
0
0
0
0
0
0
0
1
2
0
1
0
0
2
0
0
2
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
2
1
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
1
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
9
0
1
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
1
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
3
1
0
0
0
3
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
5
1
0
1
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
3
0
2
2
0
0
1
0
2
0
0
0
0
2
0
0
0
0
2
3
0
2
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
1
0
0
0
3
0
0
0
0
0
0
2
0
0
2
2
6
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
2
1
0
0
0
1
0
0
1
2
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
3
2
1
0
0
0
0
0
2
2
0
0
0
1
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
1
1
2
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
5
1
0
0
1
0
0
2
0
0
2
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
4
0
0
0
0
0
0
3
0
0
2
1
0
0
0
2
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
1
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
1
1
1
0
0
0
0
9
1
0
0
0
0
1
1
0
0
0
1
3
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
3
0
1
0
0
0
1
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
3
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
3
0
0
0
1
1
0
0
0
0
0
2
0
0
0
2
0
0
0
1
2
1
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
1
0
0
3
0
0
1
0
0
3
0
0
0
2
4
0
0
0
1
0
0
2
0
0
2
0
0
3
0
1
3
2
1
2
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
2
0
1
0
0
1
0
0
0
0
2
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
3
0
1
1
0
0
1
2
0
0
0
0
3
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
2
1
2
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
2
0
1
0
0
0
0
0
2
0
0
0
2
0
3
0
0
1
0
0
1
2
0
0
0
0
0
2
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
6
0
0
0
1
1
0
1
0
2
2
0
0
0
2
3
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
1
0
0
0
2
3
2
0
0
5
2
2
0
0
1
0
0
0
1
1
2
0
0
0
0
1
0
0
2
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
2
0
2
0
0
2
0
1
0
0
0
2
0
0
0
4
0
2
0
0
7
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
1
0
2
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
2
0
0
2
0
4
1
0
0
0
1
0
0
0
3
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
11
0
0
1
0
5
0
1
0
0
0
0
0
0
4
0
1
0
5
0
0
2
0
0
2
2
2
0
1
0
1
0
1
0
2
0
1
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
2
3
2
0
0
0
0
0
2
1
1
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
1
0
3
0
0
3
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
2
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
2
3
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
1
0
0
2
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
5
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
2
0
1
0
1
1
0
1
0
0
0
0
0
2
0
0
2
3
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
3
0
2
1
0
0
0
0
0
0
0
0
2
1
0
1
0
2
2
0
2
2
2
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
1
2
0
0
2
0
4
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
2
1
0
2
0
0
3
0
1
0
0
0
1
3
0
0
0
0
2
1
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
10
0
0
1
0
0
0
0
2
1
0
0
2
0
1
0
1
0
0
2
0
2
0
0
0
3
2
0
0
0
0
1
2
0
0
1
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
2
3
2
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
1
3
2
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
2
2
1
0
1
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
2
2
0
0
0
0
1
0
0
2
0
2
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
2
1
1
0
0
2
1
0
0
2
4
1
2
2
0
0
0
0
5
0
1
0
1
0
1
0
0
0
0
0
2
0
2
0
0
1
0
1
0
1
0
0
6
2
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
1
0
0
1
0
0
2
2
0
0
2
0
0
0
2
0
0
1
0
0
1
0
3
0
0
0
0
0
1
0
0
0
0
2
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
2
1
0
0
0
0
2
1
2
0
1
2
0
1
0
1
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
1
1
0
0
0
2
1
0
0
1
0
0
0
2
2
2
1
2
0
0
0
1
3
0
1
0
0
0
1
2
0
1
1
0
1
0
1
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
2
0
0
1
0
0
0
1
0
0
0
3
0
1
1
0
0
2
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
1
1
0
2
0
0
1
2
2
0
1
1
0
3
1
1
2
0
0
1
3
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
2
0
2
0
0
2
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
2
3
0
2
0
2
0
0
0
2
2
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
5
0
1
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
1
0
2
1
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
2
0
1
0
2
2
0
1
1
1
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
3
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
1
2
0
0
0
1
0
0
1
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
3
1
4
0
1
0
0
0
1
1
1
0
0
0
2
2
1
0
1
0
0
1
0
0
0
0
0
1
5
0
0
0
2
0
1
2
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
1
0
0
1
0
0
0
2
2
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
2
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
1
0
1
3
1
0
0
0
0
2
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
1
0
2
1
1
2
0
0
0
0
2
0
0
2
0
0
0
0
1
0
1
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
2
0
0
0
3
2
2
1
1
0
0
0
0
3
1
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
3
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
2
0
0
2
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
2
0
3
0
2
0
0
0
1
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
2
0
1
0
2
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
1
0
4
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
2
0
1
2
0
2
0
0
0
2
1
0
0
3
1
0
0
0
2
2
2
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
1
3
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
2
0
0
2
0
0
0
1
1
1
2
0
0
0
0
0
0
0
2
2
3
0
0
2
0
0
5
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
2
3
0
2
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
1
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
2
0
0
2
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
1
1
1
0
0
0
0
0
0
1
1
0
3
1
0
2
0
0
0
2
0
0
0
1
1
2
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
2
1
1
0
0
1
0
4
1
0
3
0
1
1
0
0
0
1
10
0
0
1
0
0
2
1
0
0
0
0
1
0
0
0
2
0
1
0
2
0
2
0
0
0
2
2
0
0
0
1
0
0
0
1
1
2
0
0
0
1
0
0
0
0
0
0
0
2
1
0
2
0
2
0
0
1
2
2
0
0
1
2
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
2
2
0
1
0
3
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
3
3
0
0
2
1
0
0
0
0
0
1
0
1
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
1
1
0
0
0
0
2
2
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
12
0
2
1
2
0
0
0
0
2
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
1
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
1
0
0
1
2
0
0
3
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
3
0
0
0
0
0
0
0
3
0
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
12
0
0
0
0
0
2
2
2
0
0
2
1
0
0
0
0
0
0
0
1
1
0
0
2
2
0
0
0
0
3
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
2
0
2
0
0
0
2
0
2
1
2
2
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
1
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
1
0
0
3
4
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
1
1
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
1
0
0
2
1
2
0
0
3
1
1
0
1
1
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
4
2
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
3
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
2
1
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
1
2
0
0
0
0
2
0
1
0
1
2
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
3
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
1
0
0
2
0
1
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
1
0
1
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
1
2
0
0
0
0
0
2
0
4
0
0
0
2
0
1
2
6
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
2
1
0
0
0
1
0
0
0
2
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
3
2
0
1
0
0
0
2
1
0
0
1
1
0
0
0
0
2
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
3
2
0
0
0
1
0
0
0
0
1
0
1
2
2
0
0
1
2
2
0
0
0
14
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
5
2
0
0
0
1
0
0
1
0
2
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
4
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
2
1
0
0
0
1
4
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
2
0
0
1
0
0
1
0
0
3
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
2
3
0
0
0
0
2
0
0
2
0
0
4
2
5
0
0
0
0
1
0
0
0
4
0
0
0
0
2
0
1
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
1
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
7
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
4
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
4
0
0
0
0
0
1
1
0
3
0
0
1
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
1
0
0
4
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
1
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
7
0
0
0
3
0
0
0
0
0
1
0
1
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
7
0
0
0
2
0
2
1
0
2
0
0
0
0
0
0
0
1
2
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
3
0
0
2
0
0
0
2
2
0
0
0
1
1
0
0
2
0
0
0
0
1
2
0
0
5
1
2
2
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
1
2
2
0
0
0
0
0
0
1
0
0
4
1
0
2
0
2
1
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
9
0
1
0
0
0
2
1
0
0
0
0
1
0
1
0
0
0
0
0
0
5
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
3
0
1
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
11
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
2
0
1
0
0
0
0
1
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
4
0
0
0
0
0
2
0
0
0
1
0
2
4
1
1
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
1
0
2
2
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
5
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
3
0
0
2
1
2
0
2
0
1
2
2
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
2
2
3
0
0
0
2
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
1
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
2
1
2
0
0
0
1
1
0
0
0
0
0
1
0
5
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
3
0
2
0
2
0
0
0
0
0
0
3
0
0
5
0
0
0
0
0
0
2
0
0
2
2
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
8
0
0
1
0
0
1
0
1
1
0
2
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
2
1
0
1
0
1
2
0
0
0
2
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
2
0
0
0
0
2
1
1
0
2
0
0
0
0
0
0
1
7
0
0
0
2
0
1
0
0
0
0
0
2
0
8
0
0
0
0
0
0
1
0
0
0
1
3
0
1
2
0
0
0
0
0
0
3
2
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
1
5
2
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
1
2
0
3
0
0
0
0
0
0
0
1
0
6
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
3
0
1
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
2
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
2
2
0
1
2
0
0
3
0
0
0
0
0
2
2
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
2
0
2
0
0
0
0
0
2
0
7
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
2
1
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
2
0
1
0
2
2
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
3
1
1
0
0
0
0
0
2
0
0
0
2
1
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
4
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
1
2
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
3
2
0
0
0
3
0
0
0
0
1
0
0
1
0
1
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
2
0
0
1
2
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
1
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
3
2
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
3
0
0
0
0
0
1
0
0
8
0
0
1
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
2
2
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
2
2
1
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
3
2
2
0
1
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
3
0
0
0
0
2
0
0
2
2
0
2
1
0
0
0
2
0
0
0
0
0
0
2
0
1
0
1
1
0
0
1
0
0
0
0
0
2
0
2
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
2
3
0
0
0
0
0
0
1
2
0
0
2
0
0
0
1
1
0
1
0
0
0
0
0
1
2
0
1
1
0
2
0
2
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
2
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
2
0
0
0
6
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
1
2
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
3
0
2
0
1
0
0
0
0
0
1
0
0
3
0
1
0
0
0
0
0
1
0
0
0
2
1
0
0
3
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
5
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
4
0
2
2
0
3
0
0
0
0
0
0
0
1
4
1
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
3
0
0
0
1
0
0
0
0
1
0
0
2
3
1
0
0
0
0
1
0
0
0
0
1
1
3
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
4
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
3
0
0
0
1
2
0
0
1
1
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
3
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
1
0
0
0
0
1
2
0
0
0
2
0
0
0
0
2
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
2
1
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
1
1
3
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
2
0
1
0
0
0
0
0
2
1
0
1
0
0
1
0
1
1
1
0
2
0
0
0
1
0
0
3
0
0
0
2
2
0
0
1
0
0
0
0
2
0
0
4
0
1
0
0
1
0
1
0
2
0
1
0
2
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
1
2
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
5
1
0
0
0
0
0
0
0
2
0
1
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
1
0
1
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
4
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
1
0
5
7
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
2
0
0
0
2
0
0
1
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
6
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
3
2
4
0
2
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
6
0
0
0
0
1
0
1
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
3
1
0
0
0
1
2
2
0
0
1
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
1
0
1
0
0
0
2
0
2
1
2
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
2
0
0
0
2
2
0
0
0
1
1
0
2
2
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
2
1
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
3
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
1
1
0
2
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
2
0
0
0
1
1
0
0
2
1
0
0
2
0
2
0
1
0
0
2
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
1
0
4
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
1
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
2
0
0
1
0
14
0
2
1
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
3
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
2
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
2
2
2
2
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
2
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
1
1
0
3
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
4
0
1
1
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
1
0
1
0
0
2
1
2
0
0
0
0
2
1
1
0
0
0
0
0
1
0
0
0
0
2
1
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
1
0
0
0
0
1
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
10
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
2
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
2
0
1
1
0
0
0
0
0
0
1
0
2
0
1
1
0
2
0
0
0
0
2
0
4
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
3
1
0
0
0
2
0
0
0
1
0
0
2
0
0
1
0
0
1
0
1
0
3
1
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
4
2
1
0
0
0
0
2
0
1
0
0
0
0
1
0
0
15
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
2
0
3
0
0
0
0
0
0
0
0
1
0
6
0
0
0
0
3
2
1
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
1
1
0
0
1
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
4
0
1
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
2
0
1
0
2
0
0
0
1
2
1
1
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
1
1
0
0
0
1
0
0
0
0
0
2
2
4
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
2
1
0
0
2
2
1
0
0
0
1
0
0
0
0
0
1
2
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
2
0
0
2
0
2
0
0
2
1
0
0
0
0
0
0
0
0
1
4
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
2
2
0
0
0
2
2
0
2
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
9
0
1
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
1
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
1
1
0
6
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
1
0
2
0
0
0
0
0
1
0
0
1
0
0
1
12
0
2
0
2
0
2
0
0
0
1
1
1
0
3
0
0
2
0
0
2
0
0
2
0
0
2
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
3
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
1
0
2
1
2
2
0
1
0
0
0
2
0
3
0
2
2
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
1
1
0
2
1
0
0
0
0
0
0
1
0
2
7
0
1
2
3
0
2
1
0
0
1
2
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
1
1
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
8
0
0
2
0
0
0
0
0
0
0
5
0
0
0
1
0
1
0
0
0
0
1
0
1
0
1
0
1
0
0
1
1
0
0
1
0
1
0
1
0
0
0
0
2
1
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
3
1
0
2
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
10
0
0
0
3
0
0
2
1
1
0
0
1
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
1
0
0
2
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
1
1
2
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
2
0
0
0
5
0
0
0
0
2
2
1
0
2
1
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
2
0
2
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
1
2
0
0
1
0
1
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
2
0
0
2
0
0
0
2
2
5
0
0
2
0
0
2
0
0
2
0
2
2
0
0
0
0
0
0
0
1
1
2
1
0
0
0
0
2
3
0
0
0
0
0
0
2
0
2
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
2
2
0
0
0
2
0
0
2
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
3
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
1
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
2
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
2
2
0
0
2
2
2
2
0
2
0
2
0
0
0
3
0
0
0
0
0
0
0
1
0
1
0
2
2
0
0
0
2
1
1
0
0
0
0
0
0
0
0
2
0
1
0
0
2
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
2
0
2
3
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
3
1
0
2
1
2
0
0
1
1
5
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
2
2
1
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
5
0
1
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
2
0
4
0
2
1
2
0
1
0
0
0
0
5
0
0
0
0
0
0
1
0
3
3
1
2
0
1
0
0
0
2
0
0
0
0
0
0
0
1
2
2
3
0
2
0
2
2
0
2
0
0
0
0
1
0
0
0
0
0
3
1
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
5
0
2
0
0
0
0
1
0
0
0
1
2
0
2
0
2
0
0
0
0
0
0
0
5
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
5
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
2
1
0
1
0
0
0
2
0
0
0
0
1
2
1
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
4
0
0
0
0
0
0
0
0
2
0
5
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
4
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
5
0
0
2
3
1
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
1
2
0
0
1
0
0
0
0
3
0
1
0
0
1
4
0
0
2
0
1
4
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
1
0
2
1
0
1
0
0
0
0
0
0
4
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
2
2
0
1
2
0
2
1
0
3
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
4
1
0
0
0
0
2
0
0
1
2
0
3
2
0
0
0
0
1
0
0
2
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
2
0
0
1
2
5
0
0
0
3
0
2
0
0
0
0
0
0
0
0
1
1
1
1
2
0
1
0
1
1
0
0
0
0
0
0
2
1
0
0
2
0
0
0
3
2
0
0
0
0
2
0
2
1
0
0
1
1
0
0
1
1
0
1
0
1
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
1
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
1
2
0
2
1
2
0
1
4
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
1
1
1
1
0
0
0
0
1
0
0
0
0
0
2
1
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
3
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
1
2
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
2
3
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
1
0
2
0
0
1
0
0
0
6
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
1
2
1
2
0
3
1
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
1
0
0
1
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
3
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
4
0
1
0
1
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
3
0
0
0
1
0
0
2
1
0
0
0
0
2
0
0
1
0
0
3
0
0
0
2
2
0
0
2
0
3
1
0
2
0
1
1
0
2
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
2
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
2
0
1
0
0
0
2
13
0
0
0
2
2
0
0
1
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
1
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
4
1
0
0
2
0
2
0
0
0
2
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
2
0
1
0
0
1
1
0
0
0
0
2
1
0
0
1
0
0
1
0
0
0
0
3
2
0
1
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
2
0
0
1
0
0
0
0
3
0
0
3
0
3
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
3
0
2
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
2
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
3
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
2
1
0
0
0
2
0
0
2
0
0
2
0
0
1
0
1
0
0
0
0
0
2
0
1
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
2
1
0
0
1
0
0
0
1
2
0
1
0
0
1
0
0
4
1
2
0
1
0
0
0
1
0
0
0
0
6
0
0
0
2
0
0
1
0
3
0
0
1
0
1
0
0
0
0
0
0
0
0
5
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
3
1
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
2
0
0
1
1
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
2
0
1
1
2
0
1
0
2
0
0
0
0
2
0
0
0
1
0
0
2
1
1
1
0
0
0
2
1
0
0
0
0
1
0
0
0
3
2
0
0
0
1
0
0
2
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
1
0
7
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
1
0
1
2
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
2
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
2
0
0
0
1
0
1
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
2
1
0
2
2
0
0
0
0
0
2
2
0
1
5
0
2
0
0
2
0
0
0
0
4
0
1
0
0
1
0
1
0
2
3
1
0
1
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
3
2
0
1
2
0
2
0
0
0
2
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
5
0
0
0
1
0
3
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
1
1
2
0
0
0
0
0
1
0
4
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
1
2
3
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
4
0
0
1
0
0
0
0
3
0
0
1
0
1
0
0
0
0
0
3
0
0
2
0
0
0
0
0
1
0
0
2
0
1
0
2
0
0
0
2
0
0
0
1
0
0
0
2
2
0
0
2
0
0
0
0
1
0
0
0
2
1
0
0
0
1
0
0
2
0
0
1
0
0
0
0
2
0
0
1
2
1
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
2
1
2
0
2
0
0
0
0
1
0
0
2
2
2
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
2
0
0
1
2
0
0
0
0
0
1
1
1
0
0
0
3
1
1
0
0
0
2
1
0
2
0
0
0
1
1
0
0
2
0
1
1
0
3
2
2
0
0
3
0
0
0
1
1
1
0
1
2
2
0
3
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
3
0
1
0
0
0
0
1
1
1
1
2
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
2
0
0
1
0
0
0
1
0
0
0
2
0
1
0
0
2
0
2
2
0
0
0
1
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
2
0
2
1
2
0
0
1
0
0
0
2
0
0
0
0
0
2
5
0
5
0
0
0
0
0
0
2
0
1
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
1
0
0
0
2
1
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
2
1
1
1
0
1
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
2
0
0
0
1
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
4
2
0
1
0
0
0
2
2
0
2
0
0
2
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
1
0
0
0
4
0
0
0
1
0
0
0
0
1
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
2
2
0
0
0
0
2
0
1
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
2
2
1
2
0
0
0
2
1
2
1
2
1
0
0
0
2
0
1
0
0
0
0
0
1
1
1
0
0
3
2
0
0
1
0
0
0
2
2
2
0
0
1
0
0
2
1
0
0
3
0
0
3
0
2
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
2
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
4
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
2
0
0
1
1
0
1
0
0
1
3
0
0
0
3
1
0
0
0
1
0
0
0
2
0
1
0
0
1
3
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
2
0
4
1
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
2
3
1
2
1
2
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
1
1
0
0
0
0
0
0
1
0
3
2
0
0
0
0
1
1
0
0
0
0
0
1
0
0
2
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
2
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
3
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
2
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
2
0
0
1
0
3
2
0
0
3
1
1
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
2
0
2
0
2
0
0
2
1
0
2
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
1
1
1
1
1
0
2
0
2
2
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
14
1
0
0
0
0
0
0
0
2
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
1
0
0
1
0
0
2
0
1
0
0
0
0
1
2
0
2
0
0
0
2
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
2
0
0
0
1
4
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
2
0
2
1
0
0
0
0
0
8
0
0
0
0
2
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
3
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
2
0
0
2
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
1
1
0
0
2
0
1
1
1
0
0
1
0
2
0
0
0
0
0
0
0
0
3
0
2
0
0
0
1
0
0
0
0
0
5
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
1
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
3
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
1
0
0
0
3
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
1
0
0
2
0
0
0
0
0
1
2
2
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
1
0
0
0
0
1
2
0
2
0
1
0
2
0
0
0
4
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
1
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
1
3
3
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
1
0
2
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
2
2
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
1
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
3
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
1
2
1
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
2
0
2
1
1
0
0
0
2
0
1
1
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
2
3
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
4
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
3
0
0
2
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
2
0
0
2
1
0
2
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
3
0
2
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
1
1
0
0
0
0
0
1
1
1
4
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
2
5
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
1
0
3
0
0
4
0
0
2
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
3
0
2
0
3
2
1
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
2
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
8
0
1
0
0
0
0
0
0
0
3
2
0
0
1
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
2
0
1
0
0
1
1
2
0
2
1
2
0
0
2
1
1
0
0
0
0
4
0
3
0
1
0
0
2
0
0
0
0
0
0
0
0
1
1
0
1
1
0
1
1
0
0
1
0
0
0
0
0
0
0
2
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
5
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
1
0
0
0
0
5
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
1
1
0
0
0
1
0
2
0
2
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
1
1
0
1
0
0
2
0
0
1
0
0
0
0
0
3
0
0
1
1
1
2
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
1
2
0
1
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
2
3
1
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
2
0
1
0
1
0
1
3
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
1
2
2
0
0
0
6
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
1
1
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
2
0
0
0
0
2
0
1
1
2
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
2
2
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
3
0
2
0
0
0
0
2
0
0
0
1
2
0
0
0
0
3
0
0
0
0
0
0
2
2
1
1
3
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
1
0
1
1
1
1
0
0
0
0
0
3
2
4
0
0
1
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
2
0
0
2
0
2
0
0
0
2
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
2
0
3
0
0
0
4
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
4
1
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
2
3
0
3
2
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
3
1
0
0
1
0
1
1
2
0
2
2
0
1
0
0
2
0
2
0
1
0
0
0
0
0
0
2
1
1
3
0
4
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
3
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
1
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
2
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
3
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
4
2
4
2
0
0
1
0
0
3
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
2
0
0
2
1
2
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
1
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
1
2
0
2
1
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
1
0
2
0
0
0
0
0
1
0
1
0
0
2
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
2
0
1
0
0
1
0
1
0
0
1
2
2
0
0
2
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
2
1
1
1
0
0
0
0
2
0
0
2
0
0
1
0
0
7
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
3
1
2
1
1
2
2
0
2
0
0
0
0
0
0
0
2
0
1
0
0
2
1
1
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
2
1
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
3
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
4
0
0
0
0
1
0
0
2
0
1
0
0
2
6
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
5
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
2
2
0
2
0
1
0
0
0
0
2
1
0
2
0
0
0
2
1
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
5
1
0
4
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
3
0
1
0
0
0
2
1
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
2
0
0
4
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
2
1
1
2
0
1
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
1
1
0
0
2
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
2
1
0
1
0
0
2
0
0
2
0
1
0
0
1
2
0
0
0
0
1
1
0
0
0
0
3
0
0
0
2
0
0
0
1
0
1
0
0
0
0
1
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
3
0
0
0
0
0
2
0
5
2
0
1
1
0
0
1
0
0
0
0
0
0
0
0
2
2
0
3
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
2
2
0
2
0
1
0
0
0
1
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
2
1
0
0
0
0
0
0
0
2
2
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
5
0
2
0
0
2
1
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
2
1
0
0
2
0
3
0
2
0
0
0
0
5
1
1
0
0
0
0
0
2
0
0
1
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
1
0
1
0
1
0
2
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
1
2
0
1
0
0
2
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
1
2
0
2
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
2
1
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
1
0
0
0
2
0
0
0
0
1
0
0
2
2
0
2
2
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
1
0
4
0
0
0
0
0
2
1
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
5
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
2
0
0
1
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
8
0
1
0
0
1
0
0
0
0
0
1
0
2
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
2
0
0
0
3
0
2
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
2
2
5
1
0
0
2
2
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
5
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
2
0
0
0
0
0
3
2
2
0
0
0
0
0
0
0
0
0
2
0
0
4
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
3
5
0
0
3
2
0
4
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
1
0
1
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
6
1
5
2
1
1
0
2
0
1
0
0
1
0
0
2
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
1
0
0
2
0
0
1
2
1
1
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
2
0
2
0
2
2
0
0
0
2
1
0
0
0
1
0
0
0
0
0
2
2
0
1
0
0
1
1
0
0
1
5
0
2
0
2
2
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
2
0
0
0
2
2
2
0
1
1
1
0
0
0
0
0
0
2
2
0
0
0
2
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
1
1
0
0
0
0
0
2
0
1
2
2
2
0
1
2
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
3
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
2
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
2
1
0
0
0
0
2
2
0
0
0
1
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
2
0
0
0
0
3
2
3
3
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
1
0
3
1
0
2
0
0
2
2
0
0
0
4
0
0
1
0
0
0
0
0
1
0
0
3
0
0
0
0
1
0
0
1
0
0
1
2
0
0
2
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
3
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
2
0
3
0
0
1
1
0
2
0
0
0
3
0
1
0
0
0
0
0
2
0
1
0
2
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
6
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
1
0
2
0
0
1
0
3
0
1
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
3
1
0
2
0
0
0
0
2
0
0
1
1
0
0
2
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
3
0
0
0
0
0
0
0
0
1
0
6
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
2
0
0
0
4
0
0
1
0
1
0
0
0
0
0
0
0
1
2
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
1
2
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
1
0
0
0
1
0
0
2
0
1
0
0
1
1
0
0
3
0
2
1
0
0
1
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
5
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
2
0
2
2
0
0
0
0
1
0
1
2
1
0
0
2
0
0
0
0
0
1
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
1
0
0
2
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
5
0
2
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
2
0
0
1
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
2
0
0
0
1
0
3
0
2
0
0
0
1
0
0
0
0
2
0
1
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
2
0
0
0
1
2
1
0
1
3
0
0
2
2
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
2
0
0
0
0
2
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
7
0
1
0
0
1
0
0
0
3
0
0
1
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
2
0
0
0
2
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
2
3
1
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
2
2
0
0
3
0
2
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
4
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
1
0
0
2
0
0
2
0
0
2
1
1
2
2
0
3
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
1
2
2
0
0
0
0
1
1
0
0
0
0
0
2
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
2
0
3
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
2
0
2
0
2
2
2
0
2
2
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
2
0
1
1
1
2
0
0
0
1
0
0
0
0
0
0
0
1
2
0
2
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
4
0
2
2
0
0
0
0
0
0
2
0
0
2
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
2
1
3
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
2
1
0
0
0
0
1
1
2
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
3
0
0
0
0
0
1
0
2
0
2
1
0
0
0
0
2
0
0
1
2
0
0
0
0
0
2
0
0
1
0
1
0
0
0
2
2
0
0
0
0
0
2
1
0
0
0
3
0
0
1
2
0
3
0
0
0
0
2
1
0
2
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
2
0
0
2
0
0
2
2
0
2
2
0
0
0
1
0
0
0
2
0
1
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
3
0
0
0
0
1
0
0
0
0
2
0
0
9
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
1
1
0
1
0
1
2
0
0
0
2
2
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
3
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
5
1
0
1
6
0
2
3
0
1
0
1
0
2
0
0
2
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
2
4
0
0
0
2
0
0
0
0
0
0
4
0
0
0
1
0
0
0
3
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
2
2
0
0
0
1
2
0
2
0
3
0
0
0
0
0
0
2
3
0
1
0
1
1
3
1
0
0
3
0
0
0
0
0
0
0
2
0
1
0
0
0
3
1
0
4
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
2
1
2
0
0
0
0
0
0
5
0
0
0
4
0
1
0
0
1
3
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
2
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
2
0
0
1
0
0
2
2
2
1
0
0
0
3
0
0
0
0
1
3
1
0
0
2
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
3
0
0
0
0
2
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
1
2
2
0
0
0
0
0
0
1
2
0
0
0
0
0
1
1
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
5
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
3
0
0
0
0
2
0
0
0
2
5
0
2
0
0
0
1
1
0
0
0
0
2
0
4
0
0
0
2
0
0
0
0
2
0
3
1
1
0
0
2
2
0
1
0
2
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
10
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
3
0
0
5
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
1
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
2
0
0
2
0
0
2
0
0
0
3
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
2
1
2
2
4
0
1
2
0
0
0
1
2
0
0
1
1
1
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
2
2
1
0
0
0
0
2
0
1
2
0
2
0
0
1
0
0
0
2
0
0
2
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
4
0
0
0
0
2
2
0
0
0
0
1
0
0
0
3
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
4
1
0
2
0
1
1
0
0
0
1
1
3
0
0
0
0
1
1
0
0
2
0
0
0
2
0
2
0
0
2
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
2
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
2
0
0
0
0
2
3
0
0
1
2
9
0
2
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
5
0
1
2
0
2
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
1
0
0
2
0
1
0
0
0
0
2
0
3
0
0
0
0
0
1
0
0
0
1
3
0
0
0
0
1
0
1
0
0
4
0
0
1
0
0
0
0
0
0
1
1
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
3
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
2
0
3
0
2
0
0
0
1
2
0
0
0
2
1
0
1
0
1
6
0
1
0
2
3
0
3
2
0
1
0
0
1
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
3
0
2
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
3
1
0
1
2
0
0
1
3
0
1
0
0
1
0
0
2
0
2
1
0
0
0
0
0
0
3
2
2
3
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
1
0
1
0
0
0
2
2
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
3
8
0
2
1
0
0
0
0
0
0
0
0
0
2
4
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
5
1
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
2
1
0
0
0
0
2
0
2
2
0
0
0
0
0
1
0
1
1
1
0
0
2
0
0
0
0
1
0
0
0
2
1
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
2
0
0
2
0
0
0
1
0
1
0
1
0
0
1
0
0
2
2
0
0
6
2
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
2
0
0
3
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
2
1
0
1
0
0
0
0
2
0
2
1
0
1
0
1
0
0
0
0
0
2
0
0
0
1
0
1
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
1
1
0
3
0
0
0
0
2
0
0
0
6
0
0
0
0
1
1
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
2
2
2
0
1
0
2
0
0
0
0
0
0
0
1
0
1
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
3
0
0
0
3
0
0
2
0
0
0
2
2
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
2
2
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
2
0
1
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
2
1
2
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
5
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
21
1
0
0
0
0
0
3
2
0
0
0
0
2
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
4
2
0
0
0
2
0
1
0
0
2
0
0
5
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
3
0
0
5
0
0
0
3
0
0
0
1
2
2
1
4
0
2
0
0
0
0
0
0
2
0
1
0
0
1
2
2
1
1
4
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
2
0
0
1
1
0
0
0
0
0
2
0
0
0
2
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
4
0
0
2
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
6
3
0
0
0
0
0
0
2
1
3
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
2
2
1
0
0
1
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
2
0
0
0
3
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
3
0
1
0
0
1
0
0
0
2
0
0
0
0
1
1
0
0
4
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
1
1
2
0
0
0
0
2
1
2
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
3
0
0
0
2
1
0
1
0
0
0
0
0
1
0
0
1
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
2
0
1
0
0
0
0
3
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
4
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
2
1
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
2
0
1
0
0
0
5
0
1
0
0
1
0
2
0
0
0
0
0
1
0
7
0
2
0
0
0
0
2
0
0
0
2
0
2
0
2
3
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
3
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
3
3
0
2
1
0
0
0
0
2
1
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
2
0
0
2
0
2
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
1
0
4
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
2
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
1
1
0
0
1
0
2
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
2
1
1
0
0
0
0
1
0
0
0
0
0
0
2
3
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
3
0
2
0
0
0
0
0
0
3
0
0
1
1
0
1
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
2
0
3
0
1
0
0
0
0
0
3
2
0
0
0
0
0
2
2
0
0
0
1
2
0
0
2
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
3
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
5
2
0
0
0
2
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
2
1
0
0
0
2
0
1
1
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
3
0
1
3
1
1
0
0
0
1
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
2
2
0
1
1
0
0
0
0
7
0
0
3
0
0
0
0
0
1
0
0
0
0
0
3
2
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
2
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
1
0
1
0
0
0
1
0
2
1
0
4
0
0
0
0
0
2
1
0
0
1
1
2
0
2
2
0
2
0
0
0
0
0
0
1
0
0
3
0
0
0
0
1
3
1
0
1
0
0
0
2
1
0
0
0
1
2
0
0
0
3
0
0
0
0
5
0
2
0
0
0
1
0
1
0
0
1
2
0
0
0
2
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
4
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
4
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
2
2
0
0
2
2
0
0
2
2
1
2
0
0
2
2
0
0
0
0
0
0
0
8
0
0
0
0
0
0
0
2
2
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
2
1
2
0
0
0
1
2
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
2
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
3
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
2
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
2
0
0
1
0
0
0
0
0
2
1
0
0
3
1
0
0
1
5
2
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
3
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
4
0
0
3
0
0
0
1
0
0
1
0
0
0
0
2
2
1
2
0
0
0
1
1
1
0
0
2
0
5
0
2
0
0
0
0
0
0
7
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
2
0
0
2
0
0
1
0
0
1
0
0
0
0
2
0
0
0
1
1
0
0
3
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
1
1
0
0
2
0
0
0
0
2
0
2
2
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
1
5
0
1
1
0
0
0
0
0
2
0
0
3
0
0
2
0
1
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
3
0
0
1
2
0
1
1
2
0
0
1
0
1
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
1
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
3
0
1
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
1
2
1
1
0
0
0
0
2
0
0
0
0
0
0
2
0
1
1
2
0
0
0
2
2
0
0
0
1
2
0
0
1
0
0
2
0
1
2
3
0
3
0
1
2
0
0
0
0
2
0
0
0
0
0
1
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
4
1
0
0
1
1
0
1
0
0
1
1
0
0
1
1
1
1
0
0
0
2
0
0
0
0
2
0
0
0
2
4
0
1
0
0
0
2
0
0
2
1
0
2
0
0
0
2
0
2
0
0
0
0
0
2
2
0
2
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
1
0
0
0
1
0
1
0
0
0
5
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
3
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
1
0
0
0
0
3
0
0
5
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
4
0
2
0
2
2
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
2
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
2
1
0
2
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
1
2
2
2
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
1
0
1
2
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
1
3
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
1
0
0
0
0
2
1
0
0
1
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
3
0
1
0
0
0
0
0
0
12
2
3
0
0
0
0
0
0
0
2
1
0
2
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
2
1
2
1
0
1
0
1
2
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
1
0
1
0
0
1
2
0
2
0
1
0
3
2
0
2
0
0
1
0
0
3
0
1
0
1
0
3
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
2
2
0
2
0
0
3
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
8
0
0
1
0
2
0
0
2
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
1
2
0
0
0
2
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
1
2
0
0
0
2
0
0
1
0
0
0
0
0
3
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
2
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
1
1
0
0
2
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
1
0
0
0
1
2
3
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
2
1
0
0
1
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
1
1
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
2
1
0
0
2
0
2
0
0
0
0
2
1
0
1
0
0
0
1
0
0
1
2
0
0
0
0
0
0
3
0
1
1
0
0
0
0
0
0
0
1
0
3
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
2
0
0
0
0
1
0
0
2
0
1
2
0
0
0
1
0
0
2
1
0
0
0
0
1
4
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
2
1
0
1
0
0
1
0
0
0
2
0
1
2
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
5
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
1
0
3
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
1
0
2
0
1
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
1
5
0
0
2
2
2
0
0
1
0
1
0
0
2
0
0
0
1
0
0
0
0
0
2
1
0
2
1
0
0
0
0
2
2
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
2
0
0
0
1
2
0
0
0
1
0
0
0
0
1
2
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
2
0
0
0
1
0
0
0
0
2
0
0
0
1
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
1
0
0
0
0
3
0
0
0
0
0
0
2
1
2
0
0
1
1
0
0
3
0
0
2
0
0
0
0
0
0
0
0
2
0
3
0
1
2
0
0
1
0
0
3
0
0
0
0
5
1
0
1
2
0
1
0
1
0
2
1
0
0
2
0
1
0
0
0
0
0
2
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
3
1
0
0
0
0
0
2
2
0
2
1
2
0
0
2
0
0
2
0
2
2
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
2
0
0
1
4
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
2
1
0
2
0
0
0
2
2
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
1
0
1
0
0
0
0
1
2
0
2
0
0
2
2
0
0
2
0
1
1
3
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
1
1
0
0
2
0
0
0
0
0
1
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
3
0
1
0
0
0
0
0
0
1
0
0
0
1
2
1
1
2
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
1
0
2
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
1
0
1
2
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
2
0
0
0
0
1
0
0
3
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
1
1
0
0
0
1
0
3
0
0
0
2
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
1
3
0
0
2
2
0
2
0
2
0
0
0
0
1
0
1
0
1
0
0
0
0
2
0
0
0
1
2
3
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
1
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
3
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
1
1
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
1
0
3
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
3
0
1
0
3
1
0
0
0
0
0
0
2
0
1
1
1
0
0
0
2
1
2
0
5
0
0
2
0
0
0
0
0
1
2
0
2
0
0
0
1
0
1
2
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
3
3
2
0
0
0
0
0
0
0
2
1
0
1
2
1
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
2
1
1
0
0
0
0
0
0
2
0
3
0
0
0
2
0
0
0
2
0
2
2
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
9
0
0
2
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
1
0
0
3
0
0
0
0
0
0
1
0
4
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
2
0
0
1
0
2
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
6
0
0
0
0
1
0
0
1
1
0
0
0
2
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
1
0
0
0
0
0
0
0
1
1
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
2
4
0
0
2
0
0
0
2
0
0
0
3
1
0
0
0
0
0
0
0
2
0
2
0
2
0
1
2
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
1
1
2
0
2
0
0
0
2
0
0
1
0
0
2
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
1
1
1
0
0
0
2
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
3
1
1
0
1
0
0
0
0
0
0
1
2
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
3
1
0
0
0
2
1
1
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
5
2
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
2
2
1
0
0
6
0
2
0
0
0
0
0
0
1
0
2
2
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
2
2
0
0
0
0
2
3
0
1
2
3
0
2
0
2
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
6
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
1
0
0
2
2
0
1
0
0
0
2
0
0
0
0
0
0
3
3
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
3
2
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
2
0
0
0
0
2
0
0
0
1
2
0
1
0
0
0
4
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
2
2
0
3
2
0
1
0
1
0
2
0
0
2
2
0
0
0
0
0
3
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
2
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
2
2
1
0
1
2
0
1
0
1
0
2
0
1
6
0
1
0
0
3
2
0
1
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
2
1
0
0
2
1
0
1
2
0
1
1
0
0
0
2
0
0
2
0
0
0
0
0
3
0
1
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
1
2
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
6
0
1
1
1
0
0
0
1
0
2
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
2
0
0
0
2
0
0
0
0
0
2
0
0
2
0
3
1
0
1
0
0
1
0
0
0
1
0
0
0
3
0
0
1
0
0
0
1
1
0
2
0
1
0
0
2
0
3
1
0
0
1
0
1
0
2
0
0
0
1
0
0
0
0
2
0
1
0
2
2
0
0
0
0
0
0
5
1
0
1
0
5
0
1
0
1
1
0
0
0
0
0
0
2
1
0
2
1
2
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
2
0
0
3
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
7
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
7
0
1
0
0
1
2
0
0
2
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
3
0
0
1
0
1
0
0
0
3
0
0
0
2
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
1
1
0
1
0
0
0
0
0
0
3
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
2
2
1
1
0
0
0
2
0
1
0
0
0
0
0
1
0
2
1
0
0
2
0
0
0
0
1
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
1
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
4
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
3
0
2
0
1
0
0
2
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
3
0
0
2
0
2
2
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
2
1
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
1
0
2
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
3
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
6
1
0
2
0
0
0
2
2
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
11
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
1
2
0
0
0
0
0
0
1
1
1
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
1
2
0
1
0
0
0
2
1
0
0
0
0
1
0
1
2
0
0
1
0
2
2
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
2
0
0
0
1
0
2
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
2
1
0
0
0
1
1
2
3
1
0
1
0
0
0
0
1
0
0
0
0
2
0
3
3
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
1
1
2
2
1
0
1
1
0
1
1
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
4
0
2
0
0
2
0
0
0
0
2
0
5
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
2
0
1
0
0
2
0
0
0
3
0
0
0
0
0
0
0
3
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
1
2
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
3
0
0
1
0
2
0
2
0
2
0
1
3
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
2
0
0
1
0
0
0
2
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
1
2
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
1
0
0
1
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
3
3
0
1
0
1
0
2
0
0
1
1
0
0
0
1
2
2
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
3
0
0
6
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
2
0
0
0
2
0
0
0
0
2
2
1
0
1
0
0
0
3
0
2
0
0
0
0
0
1
1
0
0
0
0
3
0
0
0
1
1
0
0
0
1
3
0
1
0
0
0
0
0
0
2
0
0
2
2
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
1
1
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
1
2
0
0
1
2
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
11
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
1
2
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
3
0
0
0
1
0
1
0
2
0
0
0
1
3
0
0
0
1
3
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
2
3
0
0
0
0
0
1
0
1
0
0
1
0
1
1
0
0
0
0
0
0
2
0
0
3
0
0
1
0
4
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
1
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
2
0
1
0
2
0
0
0
2
0
0
0
0
0
0
2
0
1
0
2
0
0
4
0
0
0
3
0
0
0
0
0
1
0
3
0
0
0
0
0
0
2
2
0
2
0
0
2
0
0
2
2
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
1
2
1
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
2
0
1
0
0
0
0
1
0
2
0
0
2
0
0
0
0
2
2
0
0
0
1
2
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
3
2
0
0
0
1
0
0
1
0
2
0
2
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
2
2
3
1
2
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
2
0
1
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
2
0
0
0
1
0
2
0
0
2
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
3
2
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
2
0
3
1
0
0
2
1
0
0
1
0
0
0
0
0
2
0
0
1
3
0
2
1
1
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
1
0
2
0
6
0
0
2
0
0
0
0
0
0
0
1
0
2
0
1
0
0
1
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
2
10
0
0
0
0
0
0
0
7
0
0
2
2
0
0
1
2
0
0
0
2
3
0
0
0
1
0
0
0
0
0
0
0
0
1
4
2
0
0
0
0
0
1
1
0
2
0
0
2
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
2
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
1
1
2
0
2
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
1
0
1
0
0
0
0
3
0
0
0
1
0
0
3
0
2
0
3
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
6
0
0
0
1
0
0
1
4
0
0
0
2
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
2
2
3
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
1
1
0
1
0
0
0
2
0
0
0
1
0
0
2
0
0
2
1
0
0
0
2
0
0
1
0
0
1
0
1
0
0
0
2
1
0
1
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
2
0
5
0
0
0
0
1
0
1
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
1
0
0
2
2
0
0
2
3
0
2
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
3
1
1
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
1
4
0
0
2
0
2
2
0
1
3
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
3
2
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
2
0
2
0
0
0
0
3
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
1
1
0
0
1
0
0
0
0
1
1
0
0
3
0
2
0
0
0
2
2
0
1
0
2
0
0
0
1
2
0
0
0
0
0
0
1
1
0
0
0
0
2
0
2
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
2
0
2
2
0
1
1
1
0
0
1
1
0
2
2
0
0
2
0
1
0
1
2
0
0
2
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
1
2
0
2
2
1
1
0
2
1
1
1
0
0
1
0
9
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
2
1
1
1
0
0
0
2
1
2
2
2
0
1
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
2
1
0
0
1
0
0
0
0
1
2
0
2
2
0
3
0
1
0
2
0
0
1
2
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
2
1
0
2
0
0
0
0
3
0
1
2
1
2
0
2
0
0
0
0
0
1
1
0
0
2
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
1
0
2
0
3
2
0
0
0
0
0
0
2
1
0
0
1
0
0
0
2
0
1
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
7
0
2
1
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
4
0
0
2
0
2
5
2
0
0
2
3
0
0
0
0
0
0
0
1
1
0
0
2
0
0
1
2
0
0
2
1
1
3
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
3
2
0
1
1
0
1
0
1
0
0
0
0
0
1
0
0
4
0
2
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
1
1
0
0
1
0
0
0
0
0
2
2
0
0
0
0
2
2
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
2
1
0
0
1
0
0
1
2
0
2
1
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
2
2
0
0
0
0
0
0
0
0
3
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
2
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
3
1
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
2
1
0
0
2
0
0
0
0
0
0
0
1
0
3
0
0
1
0
2
0
1
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
2
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
3
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
3
0
4
1
1
0
2
0
0
1
0
2
2
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
1
1
0
0
0
1
0
1
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
1
0
2
1
2
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
1
0
2
0
0
0
0
0
0
1
1
0
0
5
1
0
0
0
0
0
2
1
0
0
1
0
0
2
0
0
0
0
0
2
0
2
1
1
0
0
1
1
0
0
2
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
2
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
2
0
0
1
1
0
0
2
0
0
0
1
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
2
0
2
0
2
0
1
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
1
0
0
0
0
1
1
0
2
0
0
1
0
0
0
1
0
2
2
0
2
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
2
1
0
0
1
0
0
0
0
0
1
2
1
0
3
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
2
0
0
1
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
1
2
1
0
0
0
0
1
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
2
7
0
0
0
0
1
2
0
0
1
0
2
0
0
0
0
0
0
0
1
2
0
0
0
2
1
3
0
0
0
2
1
0
0
0
0
2
1
0
2
3
2
2
0
0
0
0
1
1
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
3
0
0
0
0
1
0
0
1
2
0
0
0
2
0
1
0
1
1
0
0
0
2
2
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
2
0
0
2
2
2
1
0
1
0
4
1
0
0
0
0
0
0
0
2
3
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
2
2
0
2
1
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
2
2
0
0
0
0
1
0
0
5
3
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
2
2
0
0
0
3
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
3
0
3
0
0
0
0
0
1
0
2
0
1
1
0
0
3
3
0
0
1
0
1
0
1
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
2
0
0
3
2
2
0
3
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
2
0
0
1
0
2
2
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
4
1
0
0
2
2
4
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
2
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
3
1
0
0
1
2
0
1
0
0
0
1
0
4
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
1
1
0
1
0
1
0
0
0
0
0
1
1
0
0
1
0
0
1
0
1
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
5
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
3
0
3
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
1
0
1
1
0
0
2
2
0
0
0
1
0
2
0
0
0
1
0
0
2
0
0
0
0
0
2
0
1
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
1
0
1
2
0
2
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
2
1
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
3
0
0
3
0
0
0
0
1
0
5
0
0
0
0
0
4
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
2
0
2
2
0
1
0
0
2
0
0
0
0
0
0
0
0
2
7
0
2
0
0
2
0
4
0
2
2
2
3
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
3
0
1
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
1
0
1
0
0
0
2
0
0
0
0
3
0
0
0
1
0
0
1
0
0
0
0
0
0
4
0
0
5
3
0
2
0
1
0
0
0
0
0
2
0
0
0
1
3
0
2
0
0
0
1
2
0
0
0
2
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
6
0
1
0
3
3
0
0
0
0
0
0
2
0
0
0
3
0
0
0
1
1
5
0
0
2
0
0
0
3
0
0
0
0
2
0
2
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
2
6
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
2
1
1
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
3
0
2
0
0
0
0
1
1
0
0
2
2
0
0
0
0
0
1
1
0
0
0
0
1
1
0
2
0
0
0
0
0
1
0
1
0
0
2
0
1
1
0
0
1
0
2
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
1
0
0
0
0
0
0
1
2
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
3
1
0
0
3
0
0
0
1
0
2
0
1
0
0
0
2
0
0
0
0
2
2
2
0
1
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
4
2
1
1
2
0
0
1
0
2
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
1
1
2
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
2
1
0
0
0
0
0
0
2
1
2
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
5
0
0
0
0
0
0
0
0
1
2
2
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
1
0
0
2
0
0
2
2
0
0
0
0
1
1
1
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
3
0
0
0
2
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
1
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
1
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
1
1
2
0
0
0
0
0
2
1
0
0
0
2
1
0
2
2
2
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
2
0
2
2
2
2
0
3
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
5
0
0
0
1
2
1
0
0
0
0
0
0
0
0
1
0
5
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
3
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
4
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
2
1
2
0
2
5
0
2
0
1
0
1
1
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
1
0
0
2
2
2
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
2
1
1
2
1
3
0
0
0
0
1
0
2
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
3
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
3
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
2
0
0
0
2
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
1
0
2
0
0
0
0
0
0
0
2
2
0
0
0
1
1
0
0
0
3
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
1
0
2
2
3
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
2
0
0
2
0
1
0
0
0
0
0
0
3
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
2
0
0
0
0
1
0
0
3
0
0
0
0
2
0
0
0
2
1
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
3
0
0
0
0
2
2
1
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
4
0
1
3
1
0
0
1
0
1
0
1
0
1
1
0
0
0
2
0
1
1
0
3
0
2
2
1
0
0
2
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
2
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
2
2
2
0
0
0
1
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
1
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
1
0
0
0
1
1
1
0
1
0
0
0
1
0
0
0
2
1
0
2
0
0
0
0
3
0
0
0
0
1
0
0
2
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
7
0
0
1
0
0
0
2
4
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
2
1
0
1
0
0
2
0
1
0
1
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
4
0
1
1
0
0
0
0
0
0
0
0
0
1
2
1
0
1
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
1
0
0
2
1
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
1
0
0
2
0
0
0
0
0
5
0
1
0
2
2
1
1
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
1
0
2
0
2
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
1
0
0
0
0
0
0
2
1
0
0
2
1
0
3
0
0
0
1
0
2
3
0
0
0
2
0
1
2
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
4
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
3
1
0
2
0
0
1
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
2
0
0
0
0
2
2
0
1
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
2
2
2
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
1
1
1
0
0
0
1
2
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
3
0
0
2
0
2
0
1
0
0
1
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
3
1
0
0
0
0
0
0
1
0
2
0
0
0
1
1
0
2
2
0
0
1
0
0
1
0
1
1
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
3
2
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
3
0
0
0
3
0
0
0
0
0
1
5
0
0
0
0
0
2
0
0
10
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
1
2
0
1
1
0
0
0
1
0
2
2
0
0
1
0
6
0
0
1
0
2
0
0
0
0
0
1
2
1
0
0
0
0
2
1
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
1
2
1
0
0
0
1
0
1
0
0
0
1
0
3
0
1
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
1
2
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
3
0
0
1
0
0
2
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
1
1
0
0
0
3
0
0
0
2
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
2
0
0
0
0
0
0
8
0
0
0
1
1
0
0
1
0
0
0
0
2
0
0
2
0
2
0
0
0
1
2
1
2
0
0
0
0
0
0
0
1
1
3
1
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
1
0
1
0
1
1
1
0
0
3
0
0
0
0
0
0
0
1
3
1
0
0
2
0
0
0
5
1
3
1
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
3
1
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
3
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
3
1
0
1
0
0
2
0
0
3
2
0
1
2
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
6
0
0
1
0
0
5
1
0
3
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
2
0
0
1
0
2
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
4
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
1
1
0
2
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
5
0
0
1
0
0
3
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
0
0
1
1
0
0
0
0
0
0
0
0
0
1
2
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
2
1
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
1
2
0
2
3
1
2
0
0
0
0
0
0
0
3
0
1
0
0
0
1
1
0
2
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
4
0
0
6
0
0
0
2
0
0
0
2
0
0
0
0
0
1
1
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
2
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
2
1
1
0
0
0
0
3
0
0
0
2
0
2
0
0
0
2
1
2
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
2
0
1
0
0
1
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
3
0
0
0
1
0
0
0
0
3
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
2
0
2
0
0
0
0
1
0
0
1
0
2
0
0
0
0
4
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
2
2
0
0
0
0
1
0
2
4
0
0
0
0
1
0
1
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
2
2
0
0
1
4
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
1
0
2
0
0
2
0
1
0
0
0
2
0
0
0
2
2
0
0
0
0
1
0
5
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
1
3
0
0
0
0
1
1
1
1
0
0
0
0
2
1
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
3
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
5
0
0
0
1
0
0
1
0
0
2
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
2
0
1
0
0
0
2
0
0
0
1
1
1
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
1
0
2
0
0
0
1
0
0
1
0
4
0
1
0
2
2
1
0
0
2
2
0
1
0
2
0
1
0
0
0
0
0
0
2
2
3
2
2
0
0
0
1
0
0
1
0
0
0
1
0
0
0
2
0
0
0
1
2
0
2
0
0
4
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
0
0
1
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
2
2
1
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
3
0
2
0
0
0
1
0
0
2
1
0
1
0
0
0
1
0
0
3
1
0
1
0
2
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
1
2
1
2
0
0
1
0
0
1
2
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
3
0
0
0
0
1
1
2
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
3
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
2
0
0
1
0
0
0
1
0
0
1
1
1
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
3
0
1
0
0
0
0
1
2
0
0
0
0
0
4
0
2
0
0
3
1
0
0
0
0
0
0
2
0
0
1
2
2
2
0
0
0
0
0
0
0
0
0
0
2
1
1
2
0
2
1
0
0
0
0
1
0
2
1
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
5
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
1
0
0
1
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
2
0
2
3
2
0
1
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
1
2
2
1
0
1
0
1
0
0
0
1
1
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
3
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
3
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
4
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
1
0
2
0
0
0
0
2
0
0
0
2
1
1
1
0
2
0
2
0
1
0
0
0
0
0
0
0
1
1
0
0
0
5
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
1
2
2
2
1
0
0
0
1
0
0
0
2
0
0
0
1
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
2
0
0
0
1
0
2
1
0
0
0
0
1
0
0
1
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
1
3
2
0
0
0
1
0
2
0
1
0
0
1
0
2
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
3
0
0
0
2
0
1
0
2
2
0
0
0
0
2
0
0
2
0
0
3
2
0
2
0
2
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
1
1
0
4
1
2
0
0
0
0
2
2
2
0
0
2
0
0
2
0
0
0
0
0
0
2
2
0
2
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
2
1
1
0
1
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
1
3
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
3
0
0
2
1
2
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
1
2
0
0
0
0
2
0
0
0
1
1
2
0
1
0
2
0
1
0
0
0
0
0
0
2
0
0
0
1
1
1
0
2
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
2
0
0
1
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
2
0
1
0
1
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
1
0
0
0
0
2
4
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
1
0
0
0
1
0
0
0
2
5
3
0
0
0
0
0
0
2
1
0
2
0
0
0
2
0
5
0
0
0
0
2
0
0
1
1
0
0
0
0
8
0
0
1
2
0
0
3
2
0
0
0
1
0
0
0
2
2
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
5
0
1
0
0
0
1
1
1
0
0
1
0
0
1
2
0
0
0
2
0
3
0
0
0
1
0
0
0
0
0
1
0
0
1
2
0
0
2
0
0
0
0
3
1
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
5
0
0
0
0
0
2
2
0
1
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
2
0
1
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
2
0
0
0
3
0
0
0
0
3
0
3
0
1
0
0
0
0
0
0
2
2
3
2
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
6
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
3
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
1
0
0
1
0
0
0
1
0
0
3
0
0
0
0
0
1
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
3
2
0
0
0
3
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
5
0
1
0
2
2
1
2
0
0
0
2
0
2
0
0
0
1
0
0
1
0
0
2
0
1
1
0
0
0
0
0
0
0
1
2
2
1
0
2
0
0
0
0
0
0
2
1
0
0
1
0
1
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
1
0
0
1
0
1
0
1
0
0
1
2
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
1
1
2
0
0
0
0
0
0
1
0
2
1
0
0
0
0
3
0
0
2
0
0
0
0
0
2
1
0
0
0
0
1
0
3
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
2
0
0
1
0
3
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
2
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
2
1
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
1
0
2
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
3
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
1
0
3
3
1
0
1
0
1
0
0
0
0
1
0
1
0
0
1
1
1
0
2
0
4
0
0
1
2
0
0
1
0
0
2
0
0
2
1
0
1
0
0
0
0
0
0
0
0
1
2
1
1
0
2
0
0
0
0
2
0
1
0
2
0
2
0
0
0
0
1
1
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
5
0
0
0
0
0
0
0
0
0
2
0
3
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
1
0
0
0
2
2
0
0
2
0
0
0
2
0
0
2
0
2
1
0
1
0
2
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
2
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
2
1
2
2
0
0
6
3
0
0
1
0
0
2
0
0
1
0
0
0
0
4
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
1
0
1
1
0
0
0
7
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
0
2
1
1
0
0
2
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
1
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
12
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
3
2
0
0
0
0
2
0
0
0
0
1
1
4
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
2
0
0
0
1
1
0
1
0
1
2
0
0
1
0
0
2
2
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
3
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
1
0
8
0
0
0
2
2
0
0
1
0
0
2
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
2
0
0
2
1
0
0
3
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
1
1
1
0
2
0
0
0
0
2
1
1
0
0
0
0
0
0
3
0
0
2
0
0
2
2
1
1
1
1
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
4
2
1
2
0
0
0
0
0
0
2
0
0
3
0
0
1
0
0
0
2
0
0
0
1
0
0
2
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
1
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
1
0
0
0
2
2
5
0
6
0
1
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
2
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
1
0
2
1
0
0
2
0
0
2
2
0
1
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
2
2
2
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
1
0
0
0
0
2
0
0
2
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
3
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
2
2
0
0
0
3
0
0
0
1
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
2
2
4
0
1
0
0
0
1
2
0
0
0
0
0
0
2
0
2
0
0
2
0
0
2
1
0
1
0
0
1
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
2
0
0
0
2
2
0
2
0
0
0
0
2
2
0
0
1
2
2
3
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
4
0
1
0
0
1
1
0
0
0
0
0
5
0
0
0
1
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
1
0
0
0
0
1
1
1
1
0
5
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
2
1
0
2
0
0
0
0
2
2
0
5
1
0
0
3
2
0
0
1
0
0
0
0
0
1
0
3
0
0
0
1
0
0
0
1
2
0
0
0
0
0
1
2
2
0
0
1
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
1
2
2
1
0
1
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
3
0
0
0
0
4
1
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
1
1
0
0
1
0
0
0
2
0
0
1
0
0
2
1
0
0
0
1
0
1
1
0
1
1
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
1
0
0
0
1
2
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
3
2
0
0
9
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
2
1
0
0
0
1
1
4
0
0
0
2
2
0
1
0
0
0
0
2
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
1
4
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
2
0
2
0
0
1
0
0
0
0
2
0
0
0
1
0
0
1
0
0
1
0
1
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
1
0
1
0
0
1
0
1
0
2
0
2
0
2
2
0
1
0
0
0
0
0
2
1
0
1
0
0
0
2
0
0
0
0
1
1
1
0
0
0
0
0
0
0
2
2
1
0
2
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
3
0
0
2
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
1
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
2
1
0
2
0
2
0
0
2
0
3
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
2
1
0
0
2
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
0
0
2
4
2
0
0
0
0
0
0
2
0
0
2
0
1
2
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
2
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
3
0
0
3
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
2
2
2
0
1
1
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
3
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
2
0
2
0
0
1
0
1
2
0
0
2
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
1
0
1
2
0
0
2
0
0
3
3
0
2
0
0
2
0
0
0
0
1
0
0
2
0
0
1
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
3
1
0
2
0
0
0
0
1
1
0
2
0
1
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
4
0
2
2
1
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
1
1
1
0
0
0
0
2
9
1
0
0
0
0
2
0
0
2
3
0
0
0
0
0
0
2
0
0
0
0
1
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
2
1
2
0
4
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
3
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
2
0
0
2
1
0
0
0
0
0
2
3
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
5
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
1
0
0
2
0
0
0
2
0
1
0
1
0
0
2
0
0
6
2
0
0
0
0
0
0
0
2
1
0
0
1
0
2
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
2
1
2
0
1
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
3
1
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
1
1
0
0
1
0
0
0
0
7
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
1
0
4
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
5
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
5
0
0
0
2
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
2
0
2
1
1
0
0
0
2
0
1
0
2
2
1
0
0
1
0
1
0
2
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
2
4
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
1
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
2
1
1
0
0
1
0
1
1
0
0
0
5
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
7
0
2
1
1
0
1
0
2
0
0
0
0
0
1
0
0
0
0
3
0
2
0
1
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
3
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
2
0
1
0
2
0
1
0
0
2
1
0
0
0
0
0
1
2
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
2
0
0
0
0
0
0
0
2
0
0
2
2
2
0
1
0
0
0
0
0
2
5
2
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
1
0
2
0
0
2
3
1
0
0
0
0
0
1
2
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
2
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
3
2
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
2
0
1
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
2
1
2
0
0
0
2
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
1
1
2
2
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
2
0
0
1
2
0
0
2
0
2
2
0
1
0
0
3
2
0
0
0
0
0
0
0
2
4
0
2
0
0
1
0
0
0
0
0
1
0
1
2
0
1
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
2
0
0
0
2
0
2
2
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
2
0
1
2
0
2
0
1
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
1
2
0
0
2
0
0
0
0
0
0
1
1
0
1
0
2
0
0
0
0
0
1
0
0
0
4
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
4
1
3
0
0
0
1
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
3
0
1
0
1
0
2
2
2
0
0
5
0
0
0
0
1
0
0
0
0
0
0
0
2
2
2
0
1
2
1
0
0
0
0
0
1
1
0
0
0
0
1
3
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
1
1
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
1
0
2
0
2
0
0
0
0
0
1
0
2
0
0
1
0
3
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
2
1
0
0
0
0
0
2
0
0
1
0
1
0
1
0
0
0
1
0
2
0
0
0
0
2
0
0
1
0
2
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
2
0
0
1
0
1
1
0
0
0
1
0
2
2
2
2
0
0
0
0
1
0
2
1
1
0
0
0
0
2
0
2
0
1
2
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
3
0
1
2
3
0
0
0
1
1
0
0
0
0
2
1
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
3
0
0
1
0
3
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
2
1
2
0
0
2
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
2
1
0
2
0
0
0
0
0
4
0
2
0
1
2
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
1
0
1
0
2
1
2
0
1
7
0
0
0
1
1
0
0
0
0
0
0
3
0
2
0
0
0
2
0
0
0
0
1
0
0
0
1
0
2
2
0
0
2
0
1
3
2
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
5
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
2
1
0
0
3
0
0
2
0
0
0
1
0
1
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
3
2
0
0
0
0
1
0
0
2
0
0
1
0
0
0
1
1
2
0
0
0
0
0
0
0
2
0
0
1
2
0
0
2
0
0
0
2
1
0
1
0
0
1
2
0
0
0
1
2
2
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
2
2
1
2
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
3
0
0
2
0
0
0
0
1
1
0
0
0
0
2
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
3
0
0
0
0
2
0
2
0
0
0
2
2
0
0
0
0
1
7
2
1
0
0
4
0
0
3
1
1
1
3
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
1
0
1
5
0
0
2
1
0
0
1
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
3
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
1
0
2
0
2
0
0
0
0
0
2
0
4
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
1
0
0
0
2
0
2
0
0
0
2
0
0
2
0
0
2
0
0
0
1
0
0
0
1
2
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
1
1
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
1
0
1
0
1
0
0
1
1
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
2
0
2
0
0
1
0
0
0
0
2
2
0
1
0
0
0
0
0
2
1
1
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
1
0
0
0
3
0
0
2
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
2
1
1
0
0
2
0
4
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
2
0
1
0
0
2
0
0
4
0
0
1
0
0
0
0
0
1
2
0
1
3
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
2
2
0
0
0
2
0
0
1
0
0
0
1
1
2
2
0
0
0
0
0
3
0
1
0
0
0
0
2
0
2
0
0
0
2
0
1
2
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
4
0
0
1
0
2
0
0
0
0
3
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
2
0
0
2
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
2
2
0
0
0
0
2
1
1
0
0
0
0
0
0
0
1
2
3
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
5
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
5
0
0
2
0
2
0
0
1
0
2
0
0
4
0
0
1
0
0
0
0
0
2
0
1
0
0
1
0
0
2
0
1
4
0
0
0
0
0
0
0
6
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
3
0
0
0
1
6
0
0
1
0
1
0
0
0
0
0
0
0
1
0
2
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
1
2
2
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
4
0
0
0
0
0
1
0
1
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
5
0
1
0
1
1
2
0
2
0
2
0
0
0
1
0
2
0
0
0
2
2
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
3
0
1
0
4
0
0
0
2
0
0
0
2
1
0
2
0
0
2
0
2
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
1
0
2
1
0
0
0
1
1
0
0
2
0
0
4
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
1
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
1
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
3
2
0
2
0
0
2
2
0
0
0
2
1
0
0
0
2
0
0
0
0
2
1
1
1
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
1
0
1
0
0
0
0
0
5
1
6
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
2
0
0
0
0
0
0
3
0
0
2
2
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
3
2
0
0
0
0
0
1
0
0
0
0
0
3
4
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
2
0
0
0
1
0
4
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
3
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
5
0
4
0
0
0
0
0
0
0
1
3
0
2
1
0
1
2
0
11
0
3
6
0
0
0
2
0
2
2
0
0
2
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
1
0
2
0
0
1
0
0
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
1
0
0
0
0
2
0
0
2
1
1
0
2
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
1
0
0
0
0
0
0
2
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
4
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
2
0
4
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
3
0
2
0
0
0
0
1
0
0
0
1
2
1
1
1
1
0
0
0
0
4
0
0
2
0
0
2
0
0
0
4
0
0
0
0
1
0
0
1
0
0
3
2
0
0
2
0
0
0
0
0
0
2
1
2
0
2
0
0
0
0
1
2
1
1
0
3
0
0
2
4
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
1
0
0
2
1
1
2
1
1
0
0
4
1
0
1
0
3
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
2
0
0
2
1
3
0
2
1
0
0
1
0
0
2
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
2
2
0
2
1
0
0
0
0
0
0
1
1
0
1
0
0
2
0
0
2
1
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
1
0
0
0
2
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
1
2
0
1
0
0
1
0
0
0
0
0
1
0
1
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
1
0
0
0
1
0
1
1
0
0
0
2
0
3
0
0
0
0
1
0
0
3
0
0
2
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
1
0
0
2
0
0
2
1
0
2
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
3
1
0
1
0
0
0
1
0
0
0
0
0
0
1
2
0
0
3
0
0
1
0
0
0
1
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
2
3
2
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
4
0
4
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
1
1
2
0
0
0
0
0
0
0
0
4
0
0
1
0
2
0
0
1
0
0
1
0
0
0
0
1
0
1
0
1
2
3
0
0
2
0
0
1
1
0
0
1
0
0
1
2
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
0
0
0
0
5
0
0
1
0
0
2
2
0
2
0
0
0
0
1
1
0
0
0
0
0
2
0
0
2
0
1
0
1
0
2
2
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
2
4
0
0
0
0
0
2
1
2
1
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
1
2
0
1
0
1
0
0
0
0
0
0
2
1
0
0
1
0
1
2
0
0
0
0
0
2
0
0
0
2
1
1
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
3
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
2
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
2
2
0
0
0
3
0
0
1
0
0
0
0
1
2
0
0
0
2
0
0
1
0
2
0
0
0
2
0
0
0
0
2
0
0
1
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
2
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
1
1
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
2
0
0
1
0
1
2
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
1
2
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
2
0
2
0
1
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
1
0
0
2
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
2
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
1
2
0
3
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
2
1
0
1
0
0
2
1
2
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
2
1
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
2
2
0
0
0
0
1
0
2
0
0
0
0
0
0
3
7
0
0
0
2
0
1
0
1
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
2
1
1
2
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
1
0
1
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
2
0
2
0
0
2
0
2
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
5
0
1
0
0
1
0
0
0
0
0
1
0
0
2
1
0
0
0
0
2
0
0
1
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
2
0
1
0
2
1
0
2
0
2
0
0
0
2
1
2
0
0
2
0
3
0
0
0
3
2
1
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
2
2
0
2
0
0
1
0
0
1
0
3
0
0
0
0
0
2
0
0
0
2
3
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
2
0
1
0
0
2
0
4
3
0
1
0
0
0
0
1
2
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
4
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
1
2
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
3
0
0
0
2
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
1
1
0
2
1
2
0
0
1
4
0
0
3
0
1
0
0
1
3
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
1
0
0
2
1
1
2
0
0
2
0
0
2
0
0
0
2
3
0
0
0
0
0
0
0
1
0
2
1
0
0
0
1
0
0
0
0
2
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
1
0
0
1
0
0
0
1
0
2
0
0
3
1
4
0
0
0
1
0
0
2
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
2
0
0
0
0
0
1
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
3
1
0
0
3
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
2
0
0
0
2
0
0
0
1
1
0
1
0
0
1
0
0
1
2
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
1
0
0
0
1
1
2
0
1
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
1
1
2
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
2
0
2
0
1
0
0
0
4
0
0
0
2
1
2
2
0
0
0
2
0
2
0
3
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
3
0
0
0
1
0
0
1
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
2
0
0
0
0
1
1
1
1
0
0
3
0
0
0
0
1
0
1
2
0
1
0
0
2
1
0
1
0
0
0
2
0
2
0
0
5
2
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
2
0
0
0
0
2
2
1
0
2
0
1
2
2
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
2
0
0
0
0
0
0
4
0
0
0
0
2
2
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
2
0
2
0
0
0
1
0
3
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
2
0
0
1
0
0
0
0
0
1
2
2
0
0
0
3
2
0
0
1
0
0
1
0
1
0
0
0
0
0
0
2
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
4
0
0
5
0
1
0
0
0
2
0
1
2
2
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
3
0
0
0
0
1
2
2
2
1
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
7
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
2
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
3
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
1
0
0
1
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
3
0
2
1
0
1
0
1
2
0
1
1
0
1
2
0
5
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
4
2
0
1
0
0
0
0
1
1
0
0
0
1
1
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
1
0
0
2
2
2
0
2
0
0
0
0
3
0
0
0
2
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
1
2
0
1
0
0
0
2
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
2
0
2
0
0
0
1
2
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
1
1
2
1
0
0
0
2
0
1
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
7
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
1
2
0
0
2
0
0
1
0
0
0
0
2
0
2
2
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
1
0
2
3
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
1
2
0
0
1
0
3
0
0
2
0
0
0
0
0
0
2
3
0
0
0
1
0
0
0
1
0
1
0
2
0
1
0
0
2
0
0
0
2
0
0
2
0
1
0
0
0
0
2
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
1
2
3
0
0
1
0
1
1
0
0
0
0
2
2
0
2
0
1
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
3
1
0
0
2
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
3
2
0
0
0
0
2
0
1
0
1
0
0
1
0
0
2
0
1
0
0
4
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
1
0
2
0
2
0
2
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
7
0
2
0
2
0
0
1
0
0
0
0
1
0
0
1
0
2
0
0
0
0
1
0
0
0
1
1
0
10
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
2
0
0
1
0
2
0
2
0
1
0
0
0
0
1
1
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
2
1
2
0
1
3
0
1
0
0
0
0
0
0
2
0
0
2
0
3
0
1
0
0
0
0
0
0
2
2
0
0
3
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
4
0
2
2
0
1
1
0
0
0
0
0
0
0
0
1
0
2
0
3
0
2
2
0
0
1
1
0
3
1
0
0
0
1
0
0
2
2
0
1
0
0
0
2
1
1
0
2
0
0
1
0
0
1
0
0
0
3
0
0
0
0
1
0
0
2
0
0
8
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
3
0
2
0
2
0
0
0
0
0
3
0
0
0
0
0
0
2
0
1
2
2
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
3
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
2
2
0
0
2
0
0
2
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
5
0
0
2
0
0
1
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
2
1
2
0
2
2
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
3
1
1
2
1
1
0
0
0
2
0
0
5
1
0
0
0
2
0
0
1
0
0
2
0
0
0
1
0
0
0
2
1
0
1
1
0
0
0
2
2
1
1
0
2
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
1
0
2
0
1
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
1
2
1
1
0
2
0
0
0
0
0
0
0
1
0
0
2
2
1
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
2
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
2
0
3
0
2
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
1
0
2
0
0
0
0
0
0
0
0
0
4
2
0
0
0
0
0
3
0
0
3
0
0
0
2
0
0
0
0
0
1
0
0
0
4
0
2
1
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
2
2
0
0
0
1
3
1
1
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
1
0
3
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
4
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
2
0
0
0
0
0
0
0
0
0
0
3
2
0
0
1
0
0
2
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
5
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
1
0
0
2
2
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
2
1
1
1
0
0
1
0
1
0
0
0
3
0
2
0
0
0
1
0
2
0
0
0
2
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
5
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
2
0
2
0
4
2
0
2
0
0
0
0
2
0
0
1
0
0
2
0
0
0
2
1
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
2
0
0
0
4
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
3
0
0
0
0
0
1
0
0
0
0
4
2
0
2
0
2
2
1
0
0
0
0
3
0
0
0
2
0
1
0
0
6
0
0
1
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
1
2
0
0
4
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
1
0
1
0
0
0
2
0
2
2
0
0
0
1
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
2
0
0
1
0
0
1
0
0
0
0
0
0
2
2
1
0
0
0
2
0
2
0
0
1
0
0
0
0
2
0
1
0
2
2
1
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
1
2
0
1
0
0
2
0
0
2
4
0
4
4
0
0
1
0
0
3
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
3
0
0
0
1
0
1
3
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
2
2
2
0
0
0
2
1
4
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
3
1
0
0
1
0
0
0
0
1
0
3
0
1
0
0
2
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
1
1
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
1
2
1
0
2
1
1
0
0
0
0
2
0
2
0
0
0
0
0
0
5
0
0
0
0
1
2
0
1
0
2
0
0
1
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
1
2
2
2
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
1
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
3
0
1
0
0
2
0
0
1
1
0
0
0
0
0
1
2
0
0
0
0
0
2
1
0
1
2
0
1
0
1
2
2
0
1
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
2
1
1
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
5
2
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
2
1
0
1
0
1
0
2
0
0
0
2
0
0
2
2
0
0
0
0
0
2
0
0
1
0
0
1
1
1
0
0
4
0
1
0
0
3
2
0
2
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
1
1
1
0
0
2
0
0
0
0
3
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
3
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
2
2
0
1
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
7
0
0
1
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
1
0
3
0
0
0
0
0
0
1
2
0
0
0
0
0
3
2
0
1
0
0
0
0
0
2
0
0
2
1
1
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
1
0
0
1
0
0
0
2
0
0
2
0
0
0
0
2
1
0
0
2
2
2
0
0
2
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
5
0
2
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
1
0
0
2
1
0
1
0
0
0
2
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
2
1
1
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
8
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
3
0
0
2
0
0
0
1
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
1
1
1
0
1
1
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
2
1
1
0
0
0
0
0
2
3
1
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
2
0
0
1
2
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
2
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
2
0
0
0
1
1
0
0
1
1
0
2
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
1
1
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
2
1
2
2
1
0
0
0
1
0
0
2
0
2
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
2
0
2
0
0
0
3
1
0
2
2
0
0
2
1
0
0
0
0
0
2
2
0
2
0
1
0
0
0
1
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
3
1
2
0
0
0
0
2
0
0
1
0
0
0
0
3
0
1
0
0
1
0
0
1
1
2
4
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
4
0
0
1
0
0
2
0
0
0
0
0
0
0
5
0
1
0
0
0
0
0
4
1
1
2
0
3
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
3
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
2
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
1
0
1
1
2
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
1
0
0
0
2
0
1
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
3
1
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
6
0
0
0
2
0
0
0
2
0
3
2
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
3
0
0
0
1
1
0
2
2
0
0
2
1
3
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
3
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
4
2
0
0
0
0
2
0
0
2
1
0
1
0
0
0
0
0
0
0
2
2
2
0
0
2
0
0
2
0
0
4
2
0
2
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
1
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
2
0
0
0
0
0
2
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
2
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
2
0
0
1
0
1
0
0
1
1
2
0
2
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
1
5
0
1
1
2
2
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
5
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
2
1
1
0
5
0
1
0
0
0
0
0
0
2
0
2
1
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
3
3
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
2
0
0
0
0
0
2
0
1
2
0
0
1
0
0
2
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
1
0
0
0
1
2
0
0
2
0
0
0
0
0
0
5
0
0
1
0
1
0
0
1
2
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
1
1
0
0
2
0
1
0
1
0
1
0
0
2
3
0
0
3
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
4
2
0
0
0
0
0
0
0
0
2
0
0
4
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
3
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
3
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
2
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
6
0
1
0
5
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
1
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
2
2
0
0
2
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
2
1
2
0
4
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
5
0
3
1
0
0
2
0
0
0
2
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
1
0
0
2
0
0
0
1
0
1
0
0
0
1
2
0
0
0
0
0
2
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
2
0
2
2
2
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
1
0
0
1
0
0
1
1
0
0
1
1
0
0
2
0
0
1
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
3
0
0
0
2
0
0
2
0
0
0
0
1
3
0
0
1
0
2
1
0
0
0
3
0
1
0
3
0
0
2
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
2
2
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
2
0
1
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
3
0
1
2
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
1
1
0
0
0
1
0
1
0
0
2
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
2
0
0
3
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
2
3
0
0
3
2
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
2
0
1
0
0
2
0
2
0
0
0
0
0
0
0
1
0
1
1
0
1
1
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
2
4
0
0
0
0
0
1
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
2
0
3
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
2
0
1
0
0
3
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
4
0
2
0
0
0
0
0
2
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
2
1
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
2
2
0
0
0
2
0
2
0
1
0
0
2
0
0
0
0
0
1
0
0
0
3
3
0
2
0
3
1
0
0
0
0
0
1
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
1
0
0
2
0
2
1
0
1
0
1
0
2
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
2
0
0
1
0
0
0
2
0
1
10
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
2
0
1
0
3
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
1
3
0
0
1
2
0
1
0
2
0
1
0
0
3
0
0
1
0
0
0
2
6
0
1
0
2
8
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
2
1
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
2
0
1
1
0
1
0
2
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
3
0
1
2
0
3
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
4
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
1
1
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
1
0
0
0
0
2
0
1
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
5
0
0
1
0
0
2
0
0
0
0
0
2
2
1
0
0
1
0
0
0
2
0
2
0
0
0
0
1
0
0
0
1
3
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
2
0
2
0
1
0
0
0
1
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
6
0
0
0
0
2
1
1
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
2
0
0
0
3
0
0
0
0
2
0
0
0
0
1
0
0
2
1
0
0
0
0
1
0
0
3
1
0
0
0
0
3
0
0
0
1
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
1
2
0
3
0
0
0
0
1
0
0
0
0
0
0
3
0
1
0
1
1
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
1
1
0
1
2
0
0
0
1
3
1
0
0
0
1
0
2
0
2
2
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
1
0
0
0
0
0
0
3
0
0
1
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
2
3
0
0
1
0
3
0
0
0
0
0
2
0
0
0
1
0
2
0
1
1
0
0
0
0
0
0
1
0
4
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
2
0
0
0
1
0
0
1
0
0
0
1
1
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
2
1
0
0
0
2
0
2
1
0
0
2
2
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
4
0
0
0
0
0
2
0
2
0
0
0
0
1
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
3
0
0
2
0
0
0
1
0
1
0
0
2
0
0
1
1
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
3
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
6
0
0
1
0
0
2
0
0
2
0
2
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
2
0
1
0
1
0
0
0
0
0
1
2
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
4
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
2
1
0
0
0
0
0
2
2
0
2
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
1
0
0
0
1
1
2
3
1
0
0
0
0
2
0
0
0
1
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
4
0
0
3
0
2
0
1
0
0
0
2
2
1
0
1
0
0
0
1
2
0
0
0
0
1
1
1
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
1
2
0
0
1
1
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
1
1
2
0
0
0
2
0
2
0
0
0
0
0
1
2
0
0
0
0
0
2
0
2
2
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
6
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
2
0
1
0
1
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
6
0
0
0
1
0
2
0
0
0
0
1
1
0
1
0
0
0
2
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
1
1
0
2
0
0
1
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
1
0
0
2
1
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
1
0
1
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
3
0
0
0
1
2
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
2
2
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
2
0
2
1
0
2
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
4
2
0
0
0
2
1
0
0
0
0
0
1
0
0
1
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
2
1
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
1
0
0
0
0
1
0
1
2
0
0
1
0
2
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
1
0
1
0
0
1
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
1
0
0
2
0
0
2
0
0
2
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
2
1
0
0
1
0
2
0
0
0
0
0
1
0
1
1
0
0
0
2
0
0
0
0
0
0
0
2
2
1
1
0
0
0
0
0
0
0
2
0
0
0
1
10
0
6
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
3
0
0
0
0
2
0
0
0
0
1
4
0
0
2
2
2
0
4
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
6
0
0
5
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
3
1
0
0
2
0
0
0
3
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
3
2
2
1
0
0
1
0
4
0
4
0
0
0
0
0
0
0
3
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
1
2
2
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
2
1
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
3
2
0
0
1
0
0
2
0
0
2
0
0
1
0
0
0
4
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
2
1
0
0
0
2
0
2
0
0
0
2
2
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
1
1
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
1
0
0
0
0
0
1
2
0
0
1
0
0
0
1
1
0
0
0
0
0
2
0
0
1
0
1
2
2
0
0
2
0
2
0
0
0
2
0
0
0
2
2
0
0
0
2
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
4
2
0
1
1
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
1
1
0
0
0
0
0
0
1
2
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
3
0
0
1
2
0
0
0
4
1
0
1
0
1
0
0
0
1
2
0
0
3
0
0
3
2
1
0
0
0
2
0
2
0
2
0
0
0
2
0
1
0
0
0
0
0
2
0
0
2
2
0
0
0
2
0
0
2
0
0
1
4
0
0
0
0
0
0
0
1
2
0
2
0
1
0
0
0
0
1
0
1
0
1
2
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
3
2
0
0
2
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
2
0
2
0
0
0
0
2
0
0
2
1
0
0
0
0
0
4
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
2
1
0
0
0
3
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
4
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
1
4
1
0
0
0
1
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
1
2
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
2
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
2
1
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
2
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
3
0
0
3
1
0
0
0
0
0
2
1
0
0
2
1
0
0
0
0
1
0
0
3
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
3
2
0
2
1
0
0
0
0
0
0
0
1
3
2
0
0
0
0
2
0
0
3
0
0
2
0
0
0
1
1
2
0
1
0
0
2
0
0
4
0
0
0
0
2
1
2
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
1
1
2
0
1
0
0
0
1
0
0
1
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
1
0
0
3
0
1
0
1
0
0
0
1
1
3
2
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
8
3
0
0
0
0
1
2
2
0
0
1
2
0
2
0
0
0
1
1
1
2
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
2
1
0
0
0
2
0
0
0
0
1
0
0
3
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
4
0
0
1
0
1
0
0
0
0
2
0
1
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
2
2
3
0
1
1
1
0
0
1
0
0
2
2
0
0
0
0
1
2
0
0
0
1
2
0
0
2
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
3
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
4
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
2
0
2
0
0
2
0
1
0
2
0
0
2
1
0
0
0
0
0
2
0
0
0
1
2
0
0
2
0
0
1
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
2
0
0
1
0
0
2
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
2
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
4
0
2
2
2
0
0
2
0
1
0
2
2
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
4
0
2
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
3
0
3
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
3
0
1
0
2
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
1
2
2
0
0
0
0
1
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
1
0
0
0
0
1
0
1
0
0
2
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
2
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
1
0
0
0
4
0
0
0
0
2
0
2
1
0
0
1
0
0
1
2
0
0
0
1
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
2
4
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
2
0
1
2
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
2
0
1
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
1
0
2
2
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
1
1
2
0
0
1
0
2
0
1
0
3
2
1
2
1
1
0
0
1
1
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
2
2
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
2
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
11
0
1
2
0
2
0
0
0
0
0
3
2
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
1
0
2
0
0
0
0
3
0
1
0
0
2
0
0
1
0
2
1
0
0
1
1
0
0
1
0
0
0
4
0
0
2
0
0
0
0
0
1
2
4
0
1
2
0
2
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
6
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
2
0
1
2
0
2
2
0
2
1
0
0
0
0
0
0
1
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
3
2
2
0
2
0
0
0
2
0
2
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
1
2
2
2
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
3
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
3
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
1
2
0
0
0
2
0
0
1
0
1
2
0
1
0
2
2
0
0
2
2
0
0
3
0
0
0
1
1
0
2
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
1
0
0
2
1
0
2
0
0
0
1
0
1
0
2
0
2
0
3
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
2
1
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
3
0
2
0
0
0
0
2
2
1
0
1
1
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
3
0
2
1
0
2
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
2
0
1
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
2
2
0
0
0
1
1
7
0
0
0
0
0
1
0
1
0
0
0
0
2
1
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
2
3
0
1
1
0
0
0
2
0
0
1
0
0
2
0
1
0
1
2
0
0
0
2
1
0
0
0
2
0
0
0
1
0
0
2
0
0
2
3
0
0
1
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
3
0
0
1
0
0
0
0
0
0
1
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
1
1
0
0
0
0
2
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
1
0
0
1
1
0
1
0
0
0
2
2
2
0
0
0
0
0
0
3
1
0
0
0
0
0
0
3
3
0
0
0
2
0
2
0
0
0
0
0
0
0
3
0
0
2
0
2
1
0
0
0
2
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
3
0
3
1
0
2
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
1
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
1
1
2
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
3
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
4
0
0
0
0
2
0
2
0
0
0
1
1
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
3
0
1
0
1
2
6
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
2
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
2
0
1
0
0
0
2
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
2
0
1
0
3
1
2
0
0
0
0
0
2
0
0
0
0
2
3
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
6
0
1
0
0
0
2
0
0
2
0
2
0
0
1
0
0
2
1
0
0
0
0
4
1
1
5
0
2
0
3
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
1
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
1
0
0
2
0
2
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
5
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
3
1
2
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
2
6
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
3
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
2
0
0
0
0
1
0
1
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
1
2
1
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
3
2
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
2
0
2
1
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
2
0
0
0
0
1
1
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
6
0
0
0
0
2
1
2
2
2
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
3
1
0
1
0
0
0
0
3
0
0
0
0
0
1
3
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
1
0
0
0
2
2
1
0
0
4
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
3
0
0
0
3
0
2
0
0
0
1
0
1
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
1
2
0
1
0
0
0
2
0
0
0
0
0
2
0
0
5
0
0
0
0
0
1
0
0
3
0
0
1
0
0
1
0
1
2
0
1
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
1
2
6
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
3
1
0
3
0
0
1
0
0
0
0
4
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
2
1
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
1
0
2
0
2
2
0
0
2
2
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
1
0
1
0
3
1
2
2
0
0
0
2
0
2
0
0
0
0
2
1
2
0
1
0
0
0
1
0
2
0
2
0
0
0
1
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
2
0
1
0
2
1
0
0
2
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
1
2
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
6
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
2
2
2
0
1
0
2
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
2
0
2
2
0
0
0
1
0
0
0
0
2
0
3
2
2
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
2
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
3
1
0
0
2
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
2
2
0
1
0
0
0
2
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
2
2
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
1
2
2
0
0
1
0
0
2
3
0
0
0
2
0
0
0
1
0
1
3
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
4
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
1
0
2
0
1
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
3
0
0
0
2
0
0
0
2
0
2
0
0
2
0
2
0
0
1
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
2
2
0
0
0
1
1
1
0
0
0
0
0
0
1
0
1
0
0
0
2
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
1
0
0
0
0
2
0
1
0
1
0
0
1
0
1
3
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
1
0
2
0
0
0
1
3
0
0
0
0
0
1
3
1
3
0
3
1
0
2
0
0
0
2
0
1
0
0
5
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
2
1
0
2
1
0
0
0
0
1
0
0
0
0
1
0
0
2
1
0
0
0
4
3
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
2
0
2
0
0
2
0
0
5
0
0
3
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
8
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
1
2
0
1
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
2
0
3
0
0
0
0
2
2
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
1
0
0
0
0
0
0
2
0
4
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
2
0
2
2
0
0
1
0
0
0
0
2
0
1
2
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
4
0
1
2
0
0
0
1
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
2
0
0
2
2
0
0
0
1
0
0
1
0
1
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
2
2
0
0
2
8
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
2
0
1
0
1
0
0
0
1
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
1
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
1
8
0
0
0
0
0
0
2
0
0
2
0
1
2
0
1
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
1
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
3
0
2
0
0
1
2
1
0
2
0
0
0
0
0
0
0
0
0
2
1
1
0
2
0
0
0
0
2
0
0
2
2
0
0
1
0
0
0
0
0
0
2
0
2
0
0
2
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
2
0
0
0
1
2
0
0
1
0
0
1
0
7
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
3
0
0
0
0
1
2
0
0
0
2
1
1
0
1
0
0
0
0
0
0
1
0
1
0
2
0
3
2
0
0
3
0
0
0
0
0
0
2
0
0
1
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
3
0
1
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
7
0
0
0
2
0
0
0
2
0
0
2
1
1
2
0
0
0
2
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
2
0
1
0
3
0
0
0
0
3
2
0
1
2
0
0
0
3
1
0
1
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
2
0
0
1
2
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
1
0
0
0
0
1
0
9
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
1
0
0
2
0
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
2
0
1
1
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
1
0
1
1
1
1
0
0
0
0
0
0
2
0
0
2
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
1
2
0
0
0
1
2
1
0
3
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
2
0
0
3
2
0
0
2
0
0
0
0
0
0
1
0
1
0
3
0
1
0
0
0
2
0
0
0
2
0
0
0
2
2
0
0
0
0
0
3
0
0
1
0
1
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
1
1
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
2
0
1
0
2
2
0
2
0
2
0
0
1
2
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
1
0
2
0
0
0
0
2
1
0
0
0
0
1
0
1
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
7
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
2
0
1
0
0
0
0
0
0
0
1
1
0
2
2
2
0
0
3
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
2
0
0
0
0
1
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
2
1
0
2
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
3
0
0
0
2
0
2
0
0
2
0
0
2
0
2
1
2
0
4
0
0
0
0
2
1
1
0
0
0
0
0
0
2
0
0
3
1
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
4
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
4
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
1
1
0
0
0
1
1
0
0
0
0
2
2
2
0
0
1
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
3
2
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
1
2
0
0
2
0
0
0
0
0
0
0
4
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
1
1
0
0
0
1
1
0
1
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
3
4
2
0
0
0
1
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
3
1
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
4
0
2
2
2
2
0
0
0
2
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
1
2
0
0
0
9
0
0
0
0
2
6
0
0
1
0
0
0
1
0
0
0
0
2
0
2
1
1
1
0
4
1
2
1
0
0
1
0
0
0
3
0
0
0
0
2
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
2
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
2
0
0
0
3
0
0
0
2
0
1
0
0
0
0
1
0
2
0
0
0
0
1
0
0
1
2
0
1
1
0
0
0
0
3
2
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
5
2
0
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
4
2
0
0
2
0
0
0
0
0
1
1
0
0
0
0
1
0
2
1
0
0
1
3
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
1
0
1
2
0
0
0
0
0
0
0
1
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
6
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
1
2
1
1
0
0
2
0
1
0
1
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
1
0
2
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
5
1
1
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
1
0
0
0
0
0
0
2
0
0
3
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
1
1
0
0
3
0
2
0
1
0
0
1
3
0
0
0
0
0
2
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
2
2
2
0
0
0
0
0
3
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
1
1
0
2
1
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
3
1
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
1
0
0
3
0
0
0
3
0
0
0
0
0
0
1
1
0
0
1
2
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
1
0
2
0
1
2
0
0
1
1
0
0
0
1
0
0
0
0
0
3
4
2
0
0
0
1
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
3
1
0
0
1
0
1
1
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
4
0
0
2
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
1
0
0
0
2
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
4
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
1
1
2
0
0
2
0
2
0
0
0
1
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
1
0
0
0
0
1
3
0
0
0
1
2
2
0
2
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
1
0
1
1
1
0
1
0
0
3
1
0
0
0
0
0
0
0
5
0
0
0
1
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
1
0
2
2
0
2
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
2
0
0
2
0
1
1
2
3
1
0
0
0
0
0
0
2
1
0
2
0
0
0
1
0
0
0
0
2
2
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
1
1
0
3
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
2
0
0
0
2
0
0
1
0
1
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
1
0
1
2
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
1
1
0
0
0
0
0
0
0
2
2
0
8
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
2
0
0
2
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
2
0
2
0
1
1
0
0
0
0
0
1
2
0
0
1
0
1
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
1
3
0
0
0
0
2
1
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
2
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
2
0
0
0
1
2
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
5
0
0
0
0
2
2
1
1
0
0
0
0
0
0
0
0
0
0
2
3
0
0
1
0
0
0
1
0
0
0
0
0
0
2
1
0
1
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
3
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
2
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
2
0
3
0
0
0
0
0
1
0
0
0
0
0
8
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
2
3
0
0
0
0
2
2
0
0
0
1
1
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
7
0
1
1
0
0
3
1
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
2
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
5
0
1
1
3
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
2
3
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
2
0
1
1
0
0
1
2
1
3
0
0
2
0
2
0
0
0
0
2
1
0
0
0
0
1
1
0
0
0
1
2
1
0
0
0
2
0
1
0
1
0
1
0
2
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
1
0
3
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
4
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
2
1
0
0
0
0
1
1
0
0
0
1
0
2
0
0
1
0
0
0
5
0
0
0
0
0
2
2
1
2
0
0
0
1
2
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
5
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
3
7
6
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
1
0
2
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
2
0
2
1
3
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
1
1
3
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
3
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
5
0
0
0
0
1
1
0
0
0
0
0
0
0
0
3
1
0
0
0
1
0
1
2
0
0
2
0
2
0
0
1
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
21
0
3
0
0
0
0
0
0
0
2
0
0
1
0
2
0
1
0
0
0
0
0
2
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
2
0
1
1
0
0
0
3
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
2
0
2
6
2
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
2
1
0
0
1
2
0
0
0
0
0
1
1
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
2
1
2
0
0
2
0
0
0
0
2
1
2
0
0
0
0
2
1
0
0
0
2
1
0
0
0
1
0
0
0
0
2
0
1
0
0
2
0
2
2
0
2
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
2
0
5
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
4
0
0
0
1
0
7
0
0
0
0
7
0
0
0
2
1
0
0
2
0
1
0
0
1
0
3
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
2
0
0
0
0
0
0
0
0
3
0
0
0
1
0
2
0
2
0
2
0
0
0
0
0
0
0
1
0
4
0
2
2
0
0
0
13
0
0
1
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
2
0
2
0
0
1
0
0
1
1
0
0
1
2
0
1
0
0
0
0
2
0
1
2
1
0
0
0
1
0
0
0
0
1
0
2
0
0
0
2
0
1
2
0
0
0
0
1
2
0
0
0
2
0
0
1
0
0
0
2
1
0
0
0
0
0
3
0
2
0
0
1
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
1
1
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
2
1
0
0
0
0
0
0
0
1
1
0
2
0
0
0
2
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
3
4
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
3
0
0
4
0
0
0
0
0
5
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
1
0
0
1
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
1
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
3
2
0
2
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
2
0
0
3
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
1
0
2
2
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
1
1
2
0
0
0
0
0
2
2
1
0
0
1
0
0
0
0
2
0
0
1
2
0
0
0
1
1
2
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
2
0
1
2
0
0
2
0
0
0
0
0
0
1
3
0
0
0
0
0
2
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
1
0
0
0
0
0
0
2
0
1
0
2
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
2
1
2
2
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
1
3
0
0
1
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
4
0
2
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
5
2
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
1
1
1
0
2
0
0
0
2
0
0
2
2
0
1
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
2
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
2
0
2
0
0
0
1
1
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
1
0
0
1
0
3
0
1
0
0
0
0
0
1
1
0
0
0
2
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
2
0
0
0
0
0
1
0
3
0
0
1
1
0
0
0
0
2
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
1
1
0
2
1
4
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
2
1
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
2
3
0
0
0
0
0
0
0
0
0
1
0
2
3
0
0
1
0
0
2
1
0
0
0
0
0
0
2
0
1
0
1
0
0
1
0
1
2
0
2
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
2
2
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
3
0
0
3
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
2
0
0
0
0
2
0
0
0
1
0
0
0
0
2
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
1
0
1
3
0
2
0
0
0
0
2
1
0
0
2
3
0
1
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
2
0
1
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
2
0
0
1
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
2
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
3
0
0
0
1
4
2
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
2
1
0
0
0
1
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
2
3
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
5
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
1
1
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
2
0
0
3
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
2
1
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
1
1
0
2
0
2
1
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
2
0
1
0
2
0
0
1
0
1
2
0
0
0
0
2
1
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
3
0
0
0
4
0
1
0
2
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
1
0
2
0
1
0
0
2
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
1
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
3
2
2
0
2
0
0
2
0
2
0
0
1
0
0
0
0
0
3
1
0
0
0
0
0
1
2
1
2
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
1
2
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
2
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
2
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
1
0
0
0
1
0
3
0
0
0
0
0
2
0
0
1
0
0
2
1
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
1
0
0
2
2
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
3
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
3
0
2
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
3
4
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
1
3
0
0
0
3
2
1
1
0
5
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
4
1
4
0
0
0
2
0
0
0
3
0
1
0
0
2
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
4
2
0
0
0
0
2
0
0
0
0
1
0
0
2
1
0
0
0
2
0
0
0
0
1
2
0
2
4
0
0
0
0
0
0
0
0
0
3
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
2
0
0
2
0
0
1
0
3
0
2
0
0
1
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
4
0
0
1
2
2
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
2
1
2
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
2
0
1
3
0
2
3
1
1
1
1
0
0
0
0
2
0
0
0
0
2
0
0
3
1
0
0
0
0
0
1
0
0
3
0
0
0
0
2
1
0
0
0
0
5
0
1
1
3
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
3
1
0
0
0
0
0
2
0
0
1
1
0
0
0
1
0
0
0
1
1
0
2
0
2
1
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
1
0
2
1
2
2
0
0
1
0
0
0
0
1
0
1
4
0
3
0
0
4
0
0
0
3
0
0
1
0
0
2
0
0
2
0
0
1
0
0
6
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
1
0
1
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
1
0
1
0
0
0
4
0
0
0
1
0
0
0
2
0
0
1
2
0
0
0
0
4
0
0
2
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
2
0
2
0
0
1
2
0
0
0
0
2
3
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
1
1
0
0
0
0
0
2
0
0
0
1
1
0
7
1
2
0
0
1
0
0
2
0
1
0
0
1
0
1
2
2
0
0
0
0
0
1
0
2
0
0
0
1
2
0
0
0
3
0
0
0
0
0
0
0
0
2
2
1
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
1
0
3
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
3
1
1
0
0
0
0
0
0
0
1
2
1
10
0
1
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
2
1
0
3
0
0
0
1
0
2
0
3
0
0
3
1
1
0
0
1
0
2
0
0
2
0
4
2
0
2
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
1
0
0
0
0
9
0
0
0
2
0
0
0
1
3
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
8
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
1
5
0
0
0
0
2
1
0
0
0
0
2
0
1
0
2
0
1
0
0
0
0
0
0
0
0
2
1
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
1
0
2
0
0
0
0
0
1
2
0
0
1
0
0
3
0
0
0
2
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
6
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
2
0
0
0
2
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
1
0
0
0
0
2
2
0
0
4
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
1
0
1
0
0
2
3
1
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
1
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
2
0
0
0
0
0
8
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
1
0
0
1
0
0
0
2
0
0
0
0
2
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
1
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
1
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
2
1
2
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
3
2
0
0
3
0
1
2
2
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
2
0
0
4
0
2
1
1
2
0
2
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
1
0
0
0
0
0
0
5
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
1
0
3
0
0
13
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
4
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
2
3
2
2
0
0
1
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
2
0
0
3
0
0
0
0
0
0
0
0
2
1
2
0
1
0
1
0
2
0
1
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
3
2
1
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
3
0
0
0
0
3
3
1
0
0
0
2
0
0
0
2
0
0
1
1
0
3
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
1
1
0
0
4
1
0
0
0
0
1
0
5
1
0
1
0
1
0
0
1
0
0
0
0
2
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
4
0
2
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
4
1
0
0
0
1
0
0
0
1
2
0
1
0
6
1
0
5
0
2
0
0
1
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
3
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
1
2
0
0
0
0
3
0
1
2
0
0
0
0
1
0
0
0
2
1
0
1
0
1
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
2
0
2
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
1
0
0
0
1
0
0
0
1
0
2
0
0
0
0
7
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
3
0
2
1
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
1
0
6
0
0
0
1
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
1
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
1
0
1
2
0
1
2
0
0
0
0
0
0
0
1
1
0
0
0
2
0
1
2
2
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
3
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
2
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
2
0
0
0
2
0
3
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
2
0
0
3
1
0
0
1
2
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
2
3
1
0
1
2
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
2
0
0
0
0
2
0
0
0
0
3
0
3
0
0
2
1
0
2
0
0
1
0
2
1
1
0
0
0
5
0
1
0
1
2
1
0
0
0
0
0
0
0
2
2
0
1
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
1
0
2
0
0
0
0
0
0
0
0
1
0
1
4
2
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
2
2
0
0
2
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
2
2
0
0
0
0
2
0
0
0
0
1
2
0
3
1
0
0
2
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
4
0
0
0
0
0
0
1
0
2
0
1
0
2
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
2
1
0
1
0
1
0
1
1
0
2
0
0
0
1
0
0
0
0
0
2
1
0
1
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
2
0
1
0
0
0
1
0
0
1
0
1
0
0
0
1
2
2
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
2
0
4
0
0
0
0
0
2
1
0
0
0
1
1
0
0
1
0
0
0
0
0
2
0
1
0
2
0
1
0
0
0
0
0
2
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
1
4
0
3
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
2
0
0
2
0
1
1
3
0
0
0
0
0
0
0
2
0
0
0
3
0
1
1
0
0
0
0
0
0
2
0
0
2
0
0
3
0
0
0
0
0
0
0
0
7
1
0
0
0
3
0
2
1
0
0
2
0
1
0
4
0
0
2
0
0
1
0
2
0
0
2
0
0
0
0
2
0
0
3
2
0
1
1
2
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
2
0
0
0
0
3
1
0
0
0
0
0
0
1
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
1
0
0
0
1
1
0
2
0
0
1
1
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
1
1
0
2
0
0
0
3
0
2
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
2
0
0
3
1
2
0
2
0
1
2
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
2
0
1
0
1
0
2
2
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
1
3
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
2
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
3
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
7
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
3
2
3
0
1
0
0
0
0
0
2
0
0
1
0
0
0
2
1
1
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
2
1
0
0
0
0
2
1
2
0
1
1
1
0
2
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
3
0
0
0
2
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
2
0
0
1
2
2
0
0
1
2
0
0
0
1
0
0
1
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
7
0
1
2
0
0
0
2
0
0
1
0
0
1
1
1
0
0
0
1
1
0
0
1
0
0
2
0
2
0
2
1
0
0
2
0
0
1
3
0
1
0
0
0
1
0
0
0
0
2
0
1
2
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
3
0
0
2
0
0
0
2
0
1
0
0
0
0
0
2
1
0
0
1
0
1
0
0
1
0
1
0
0
1
0
0
0
2
0
0
0
1
2
0
1
2
0
1
0
1
1
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
1
0
1
0
0
0
1
1
2
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
2
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
2
0
2
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
1
0
2
0
0
1
4
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
3
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
2
0
0
3
0
0
0
1
2
0
0
1
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
3
1
0
0
0
0
3
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
3
1
1
0
0
2
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
3
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
2
0
2
0
0
0
0
1
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
2
0
0
0
1
0
0
0
0
0
2
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
3
2
0
0
2
0
0
0
0
0
1
0
0
1
0
0
2
0
0
2
1
0
2
0
1
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
1
0
0
0
2
2
0
5
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
2
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
1
0
1
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
2
1
0
0
2
0
1
1
0
0
2
1
0
2
0
0
2
1
0
0
1
0
1
0
1
0
0
0
0
0
3
0
3
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
3
2
0
2
1
0
0
0
1
0
1
0
0
0
1
0
0
0
2
2
0
0
3
1
0
1
0
0
0
0
2
0
2
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
7
1
0
0
1
0
0
0
0
0
3
0
0
1
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
2
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
1
0
2
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
1
1
0
0
3
0
0
0
1
0
1
0
3
0
2
0
0
0
4
0
0
0
0
2
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
3
3
0
0
0
1
0
0
1
0
2
1
3
0
0
3
0
0
2
0
1
0
0
1
0
2
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
2
0
0
1
0
0
0
0
8
0
1
0
0
0
1
2
0
1
0
0
1
0
0
0
6
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
6
3
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
2
0
0
1
2
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
4
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
6
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
2
0
1
2
1
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
9
0
0
1
0
0
0
0
1
0
0
1
0
3
0
0
1
0
2
0
0
3
2
5
2
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
1
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
4
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
3
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
1
1
0
1
0
0
0
0
1
2
1
1
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
2
0
0
1
2
1
0
0
0
2
0
0
0
1
2
0
0
1
0
0
0
0
3
0
1
1
1
0
0
1
0
0
6
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
2
0
1
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
1
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
3
0
0
0
4
0
0
2
1
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
4
0
0
2
1
1
0
0
0
2
0
0
0
4
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
3
2
0
0
0
0
2
2
0
0
1
0
3
1
0
0
1
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
1
0
1
1
1
0
0
0
0
0
0
2
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
2
2
0
0
0
0
0
1
2
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
2
2
0
0
0
0
4
0
0
0
1
0
0
0
0
2
0
0
2
1
0
0
0
0
1
3
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
2
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
5
0
0
0
1
1
0
0
0
0
0
0
1
2
0
0
2
1
2
2
0
0
0
0
0
0
2
1
0
0
1
1
0
2
0
0
0
0
1
0
0
0
0
0
4
0
0
0
1
0
2
2
0
0
0
1
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
2
0
1
0
0
2
1
0
0
0
0
1
3
0
0
1
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
2
2
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
2
5
0
0
0
2
0
0
2
0
2
0
0
0
1
0
0
0
0
2
2
0
0
0
0
1
2
0
1
0
0
0
0
2
0
0
0
2
1
0
0
1
2
0
2
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
2
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
1
2
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
1
0
0
0
0
2
2
3
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
2
1
3
0
2
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
1
1
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
2
2
0
0
1
1
0
0
2
1
2
0
0
2
0
0
0
1
2
1
0
1
0
0
0
1
0
1
2
0
0
1
0
1
0
0
0
1
0
0
4
1
1
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
1
2
0
0
4
1
3
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
3
0
0
0
0
0
0
0
0
1
0
2
2
0
1
0
0
0
2
0
0
0
4
0
0
0
1
0
0
2
1
0
0
0
2
0
0
0
4
0
0
2
2
2
0
0
0
2
0
0
0
0
2
1
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
3
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
3
0
2
0
0
0
1
0
2
1
0
0
0
0
2
0
0
1
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
3
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
2
0
0
0
0
1
0
2
0
0
1
0
1
5
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
2
0
0
0
2
0
2
1
2
1
1
1
1
2
0
0
0
1
2
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
3
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
2
0
3
0
0
0
1
0
0
1
0
2
0
0
0
0
0
2
0
0
1
2
3
2
0
0
0
2
0
1
0
0
0
0
0
0
1
0
3
0
0
0
0
2
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
5
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
2
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
2
2
0
0
0
0
1
0
0
3
0
0
0
0
1
0
0
0
2
0
1
0
1
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
3
0
0
0
0
1
0
0
1
3
0
0
2
0
0
0
0
0
1
1
0
1
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
2
0
2
0
0
2
0
0
0
2
0
5
0
0
2
3
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
2
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
2
0
0
0
1
1
0
0
0
0
0
2
0
1
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
5
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
1
0
2
5
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
1
0
0
0
0
2
0
0
0
0
2
2
2
0
0
0
2
0
0
1
1
0
2
2
0
0
0
4
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
3
0
0
1
0
0
0
1
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
1
2
0
2
0
0
1
0
0
1
1
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
0
2
0
0
0
2
0
1
1
0
0
0
2
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
1
0
0
0
3
0
2
1
0
0
2
0
2
0
2
0
0
0
3
0
0
0
0
0
1
1
0
0
0
1
0
2
0
0
2
2
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
3
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
2
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
7
0
0
0
0
2
0
1
0
3
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
5
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
3
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
1
1
0
0
0
0
0
0
1
2
0
0
0
0
0
4
0
0
0
0
0
2
1
1
0
2
0
0
0
1
0
1
0
4
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
2
3
0
0
0
0
1
0
0
0
0
2
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
1
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
3
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
4
0
0
2
5
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
2
0
0
1
0
1
0
0
0
0
1
0
0
0
2
0
2
1
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
1
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
2
4
0
1
0
0
0
0
0
0
0
0
5
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
1
1
2
0
0
1
0
2
0
0
2
2
0
0
2
1
1
1
3
2
0
2
0
3
0
0
0
0
0
1
2
0
0
0
0
0
1
4
0
0
0
2
0
0
2
0
0
0
1
2
2
0
0
0
0
1
0
2
1
0
1
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
3
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
3
2
1
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
1
0
0
1
1
0
0
0
1
0
2
0
2
0
0
1
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
3
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
2
1
2
0
1
0
0
0
0
0
0
0
1
0
0
3
2
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
1
2
1
0
0
1
0
0
2
0
1
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
2
0
2
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
1
0
2
3
0
0
0
0
3
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
2
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
2
3
0
4
0
2
0
0
2
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
2
1
3
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
2
2
0
0
1
1
0
1
1
0
0
0
0
0
1
0
2
2
1
0
0
0
0
0
2
0
1
1
0
6
0
2
0
0
2
0
0
0
1
0
0
0
0
0
1
1
0
2
0
0
0
1
0
0
0
1
0
0
3
0
3
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
2
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
3
0
0
0
1
0
1
0
0
2
0
0
1
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
1
2
2
0
0
0
0
0
0
4
0
0
0
0
3
0
2
0
1
0
4
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
2
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
3
2
2
0
0
1
0
0
0
0
0
2
0
0
2
0
4
2
0
0
0
2
1
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
2
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
2
1
0
2
1
0
0
1
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
2
0
2
0
0
0
0
0
1
0
0
0
3
0
0
2
1
0
0
0
0
0
0
0
0
3
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
2
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
2
0
0
3
0
0
0
1
1
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
3
0
0
1
1
0
0
0
2
1
0
1
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
2
0
2
0
2
0
1
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
2
1
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
1
2
0
2
1
2
2
0
1
0
0
0
1
0
0
0
0
1
2
2
1
1
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
1
0
2
2
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
2
1
6
2
0
2
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
2
0
0
0
2
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
2
0
0
2
1
0
3
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
2
1
2
3
2
0
2
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
5
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
3
2
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
2
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
4
0
0
0
0
0
2
0
0
0
0
0
0
3
0
7
2
0
0
0
1
0
2
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
3
0
1
0
0
1
0
0
1
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
3
0
2
0
0
6
0
0
0
0
0
0
4
2
0
0
0
0
2
0
0
0
0
0
2
1
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
2
0
0
0
0
0
0
0
0
4
2
0
0
0
0
0
0
1
0
0
8
2
0
0
1
1
0
0
0
2
1
1
0
0
1
0
0
1
2
2
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
1
4
2
0
0
2
0
0
2
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
2
2
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
3
1
0
0
0
0
1
0
0
0
4
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
1
0
1
2
0
0
0
0
2
0
0
0
0
2
0
0
5
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
4
2
0
1
0
2
1
0
1
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
1
0
0
1
1
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
2
0
3
1
0
0
0
0
2
0
0
0
0
3
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
1
0
0
1
1
0
0
0
0
2
5
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
1
1
2
0
0
0
0
0
0
1
0
0
0
0
0
3
2
0
0
3
0
0
0
1
0
1
0
2
1
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
2
1
2
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
1
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
2
0
1
1
0
1
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
5
0
2
0
0
0
0
1
0
0
0
0
0
2
0
3
2
0
0
0
0
0
2
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
5
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
2
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
6
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
2
2
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
1
0
0
0
0
2
0
0
2
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
1
2
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
2
0
0
2
0
1
2
0
0
2
0
0
2
0
2
2
2
0
0
0
0
3
2
3
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
1
0
1
3
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
3
0
0
1
0
0
0
2
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
1
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
2
3
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
3
1
0
10
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
3
0
0
0
2
0
1
2
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
1
2
0
0
0
0
0
0
2
0
0
1
2
2
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
1
2
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
1
1
0
0
0
0
2
2
0
1
0
0
0
0
3
1
0
2
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
2
1
0
4
0
0
0
2
0
0
2
0
0
0
0
1
0
1
4
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
2
0
0
0
0
1
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
1
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
2
0
1
0
4
0
0
0
0
0
0
0
2
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
4
0
0
0
0
1
0
0
0
0
1
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
4
0
0
1
1
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
2
0
2
1
0
0
1
0
0
2
4
0
0
0
0
0
0
0
0
0
4
0
0
2
0
2
0
0
0
0
1
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
4
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
1
0
0
2
0
0
0
0
0
2
0
3
0
0
0
2
0
0
0
6
0
0
0
0
0
2
1
0
0
2
1
1
0
0
0
0
0
2
0
3
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
2
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
2
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
2
3
2
0
0
0
2
0
0
0
0
0
0
2
0
0
1
2
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
2
0
0
1
0
0
0
0
0
0
0
0
0
0
4
2
0
0
4
2
1
0
15
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
3
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
2
1
6
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
3
0
1
0
0
0
2
0
0
2
0
0
2
1
2
1
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
3
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
4
0
0
1
3
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
1
1
0
2
0
0
2
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
2
0
0
0
0
1
2
0
0
2
0
0
3
0
0
0
0
1
0
2
2
0
0
0
1
0
0
2
0
0
0
2
0
1
0
0
0
0
2
2
0
0
2
1
2
0
0
2
0
0
0
0
1
2
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
7
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
2
1
0
2
0
0
1
0
2
0
0
0
0
0
0
0
1
3
2
0
0
0
0
0
0
0
0
0
6
1
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
1
0
8
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
2
0
2
0
2
0
4
0
2
2
0
0
0
0
2
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
4
0
1
0
1
2
0
1
1
0
1
2
0
0
0
0
2
0
1
0
0
0
2
3
0
0
0
0
2
1
0
0
0
0
3
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
1
0
3
0
2
1
0
3
3
2
0
0
0
0
1
0
1
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
2
1
0
2
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
3
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
2
0
0
1
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
3
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
1
2
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
1
0
1
2
0
1
1
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
2
0
1
0
2
0
0
1
0
0
0
1
0
0
0
2
0
0
0
3
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
3
0
0
3
0
1
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
6
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
1
0
3
0
1
2
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
1
0
2
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
3
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
3
0
0
2
0
0
0
0
0
2
2
0
0
1
0
2
0
0
3
0
1
0
0
1
0
0
0
2
1
0
0
0
0
1
2
1
0
2
2
0
2
0
1
2
0
1
1
0
0
0
0
2
0
0
0
0
1
0
1
0
1
0
0
1
0
2
0
0
0
0
1
0
0
0
0
2
0
2
0
0
2
2
1
2
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
2
0
0
0
0
2
0
1
0
2
0
0
2
0
0
0
0
2
0
2
0
0
0
0
1
0
0
1
0
0
2
4
3
0
0
0
0
0
0
2
0
0
0
0
3
0
2
2
1
2
0
0
0
0
2
1
2
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
1
0
0
0
1
0
0
0
0
2
0
0
2
0
1
0
0
0
1
2
0
0
0
1
2
0
0
0
2
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
1
0
1
2
0
1
0
1
0
0
2
0
0
0
0
0
2
0
6
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
2
0
1
2
1
0
2
0
2
0
2
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
6
0
0
0
2
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
7
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
2
0
1
0
0
0
0
1
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
2
1
1
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
3
0
0
1
1
0
0
0
0
1
0
2
0
2
0
0
3
1
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
2
0
2
1
1
2
0
0
2
0
1
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
2
0
2
0
1
1
1
1
0
1
0
2
0
0
0
0
0
1
0
0
0
2
1
0
0
0
1
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
1
0
0
0
0
0
0
2
0
0
3
0
2
0
0
0
1
1
1
0
0
0
2
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
5
0
0
0
1
0
0
0
3
0
3
2
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
2
0
0
0
2
2
0
0
2
0
0
0
2
0
1
0
2
0
0
0
0
4
0
0
0
0
1
1
0
0
2
0
0
1
0
1
0
0
0
0
0
2
0
1
2
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
2
0
0
0
2
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
6
0
2
0
0
0
1
1
0
0
0
0
2
0
2
2
0
0
1
0
0
0
0
2
1
0
4
0
0
0
0
0
0
1
0
4
0
0
0
0
0
3
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
3
0
3
0
0
4
0
0
0
1
0
1
2
0
2
0
0
0
0
0
0
2
2
2
0
4
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
3
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
1
0
0
2
0
0
2
0
1
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
3
0
0
0
0
0
0
0
2
0
2
2
0
5
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
2
0
0
0
0
1
0
1
0
0
2
2
0
0
0
0
0
0
1
4
0
0
0
0
2
0
0
2
1
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
2
2
0
1
3
0
1
0
0
1
0
0
2
0
0
0
0
0
3
0
0
0
1
1
1
0
1
1
0
2
1
0
0
0
2
0
0
1
0
0
1
0
0
2
0
2
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
1
1
0
0
0
1
0
0
0
0
3
0
0
1
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
2
1
0
2
1
0
0
0
2
1
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
1
2
3
1
0
3
0
1
0
2
0
2
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
1
0
2
1
0
0
2
1
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
1
0
0
1
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
1
2
0
1
0
2
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
2
0
0
2
2
0
1
0
0
0
0
2
0
2
0
0
0
1
1
0
2
0
2
2
0
0
0
0
0
0
2
1
0
0
0
7
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
1
0
0
0
0
0
2
1
0
2
1
0
0
0
0
1
0
0
1
0
0
0
2
1
0
1
0
0
0
0
1
1
0
2
0
0
0
0
0
0
2
1
0
0
0
0
1
0
1
0
0
0
2
1
2
0
0
0
0
1
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
3
2
0
0
0
0
0
0
0
1
0
2
0
0
2
1
0
0
2
0
1
2
0
0
0
3
1
0
0
0
0
1
13
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
3
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
2
0
2
0
4
0
2
2
0
2
1
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
2
1
0
0
0
0
1
0
0
2
0
2
0
0
1
0
0
2
0
1
0
0
0
2
0
0
0
1
0
2
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
7
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
2
3
1
0
0
1
3
0
0
0
0
0
0
2
0
2
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
1
2
1
0
1
0
2
2
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
2
2
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
3
1
0
0
0
0
0
1
0
0
2
0
0
2
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
4
0
0
1
0
1
0
0
0
0
3
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
2
1
1
1
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
1
2
1
2
2
3
0
0
0
0
0
0
1
0
2
0
0
6
0
0
0
1
0
0
1
0
0
1
0
0
0
0
2
0
2
0
5
2
0
0
1
1
0
0
2
2
0
0
2
0
0
1
0
0
2
1
0
0
1
0
0
0
0
0
2
0
0
0
1
2
0
0
3
2
2
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
4
2
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
2
2
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
3
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
1
0
0
0
0
0
1
1
0
0
1
0
4
0
0
0
2
0
3
0
0
0
0
1
0
3
0
2
2
0
0
0
0
0
1
1
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
2
1
1
1
0
0
0
1
2
2
2
0
0
0
0
3
0
2
0
0
0
0
2
0
0
7
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
1
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
1
3
1
0
0
0
1
3
0
0
5
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
3
1
1
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
2
0
2
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
2
0
2
2
0
0
2
0
4
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
1
0
2
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
1
1
0
0
1
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
2
1
1
2
0
0
3
2
0
0
0
2
3
0
2
0
0
0
0
0
0
6
1
0
0
1
0
0
1
0
0
0
0
2
0
3
0
0
2
1
0
0
0
0
1
3
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
2
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
2
0
1
0
0
1
0
0
0
1
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
3
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
6
0
1
2
1
0
4
0
0
1
1
1
3
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
2
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
2
0
1
1
0
0
0
0
0
2
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
2
0
0
0
0
1
1
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
1
0
1
0
1
0
0
3
0
1
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
7
0
2
0
0
0
0
0
2
0
0
0
0
3
0
0
1
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
1
0
2
1
2
0
0
1
3
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
1
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
1
0
1
1
0
2
0
1
1
3
4
0
1
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
1
0
0
1
0
2
0
0
0
2
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
3
0
1
0
0
2
3
1
2
0
1
0
1
1
3
0
0
0
1
2
0
2
4
0
0
0
1
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
3
0
0
0
1
2
0
0
0
0
0
0
1
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
3
2
2
0
2
0
2
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
1
0
0
0
0
2
0
0
1
1
0
0
0
0
4
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
2
0
0
1
4
0
0
0
0
0
1
0
1
0
0
0
2
2
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
1
0
0
2
1
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
2
1
3
0
0
2
2
0
0
0
0
1
0
1
2
0
0
0
0
2
0
0
0
5
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
1
3
0
0
0
2
1
1
0
1
2
0
2
0
0
0
0
0
1
0
0
0
1
2
0
1
2
1
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
3
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
4
0
3
0
0
0
0
0
0
0
4
0
0
0
0
0
3
0
0
0
0
0
4
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
1
1
0
2
0
0
0
2
2
1
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
15
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
2
0
0
0
1
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
5
0
0
0
1
2
0
2
0
1
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
2
1
0
2
0
0
0
1
0
0
1
0
1
0
0
0
0
0
2
1
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
3
0
3
8
0
0
0
0
0
2
0
0
2
0
1
0
0
0
1
0
0
0
0
1
3
2
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
6
0
4
2
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
4
0
0
1
0
0
0
0
1
0
0
2
0
1
0
0
0
1
0
0
1
0
1
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
1
0
1
0
2
0
0
0
1
2
0
1
0
1
0
0
0
0
1
1
0
2
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
7
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
2
2
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
2
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
5
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
2
0
0
0
0
0
1
2
0
0
2
0
0
1
0
1
4
1
2
0
0
1
0
0
2
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
6
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
2
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
2
0
1
0
0
0
0
3
0
0
0
0
2
3
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
3
0
0
0
0
0
3
2
0
2
0
0
0
1
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
2
0
0
0
0
0
1
0
2
2
2
0
1
2
0
0
0
0
5
0
4
1
0
1
0
0
0
0
0
0
2
0
0
2
2
1
2
0
1
0
0
1
0
0
1
0
0
0
1
0
4
1
0
0
0
2
0
1
0
0
1
0
2
0
0
2
0
0
2
0
0
0
0
2
1
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
1
2
0
0
2
0
1
2
0
0
0
0
0
0
3
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
1
1
0
2
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
2
3
2
1
0
0
0
2
0
0
0
0
2
0
2
1
2
0
1
0
0
0
2
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
2
3
1
0
0
0
0
0
0
0
0
0
1
0
2
2
0
1
4
1
2
2
1
1
0
0
0
0
1
2
0
0
0
2
0
2
1
4
1
2
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
2
1
0
0
0
2
0
0
2
0
5
0
0
0
0
0
0
2
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
1
2
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
7
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
3
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
4
3
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
2
2
0
0
0
0
1
1
0
0
2
2
0
0
3
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
1
0
0
0
0
2
1
2
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
1
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
2
0
2
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
2
0
0
1
5
1
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
1
0
0
0
0
3
0
1
2
2
0
2
3
0
0
0
0
2
2
1
0
0
1
0
1
0
0
0
4
0
2
0
1
2
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
3
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
1
0
0
1
2
0
0
0
0
1
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
3
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
1
1
0
0
1
1
0
1
0
1
0
0
2
0
0
0
0
0
1
1
1
0
0
2
0
1
0
2
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
1
0
0
0
0
0
1
1
0
0
0
0
2
0
0
2
1
2
0
0
0
2
0
0
2
0
0
1
0
0
0
2
0
3
1
3
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
1
0
0
0
0
1
0
1
0
0
0
1
1
0
2
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
1
0
0
2
0
0
1
0
0
2
4
0
0
0
0
2
1
0
0
0
3
0
0
0
5
0
0
0
0
0
2
1
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
1
3
0
0
0
2
0
0
0
0
0
0
4
0
1
0
0
0
1
0
2
2
0
0
0
2
0
3
0
0
1
0
0
1
0
0
0
1
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
3
0
0
3
0
0
0
0
0
0
0
0
0
1
1
0
2
0
2
0
2
0
2
0
0
0
5
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
2
3
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
4
2
1
3
0
1
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
2
13
0
1
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
2
1
3
1
0
0
1
0
0
0
2
0
2
2
0
0
0
2
0
0
0
0
1
2
0
0
0
0
2
2
4
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
1
2
1
1
1
1
0
1
2
1
0
0
1
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
3
2
0
0
0
2
1
0
0
0
0
1
2
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
2
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
2
3
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
1
3
0
0
0
1
0
0
1
2
2
2
0
0
1
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
2
0
0
0
0
0
0
1
0
0
1
2
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
7
0
0
0
0
1
0
3
0
1
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
2
0
0
1
0
2
0
0
0
0
0
1
2
1
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
2
1
0
2
0
0
0
0
0
3
0
2
0
1
0
0
0
0
1
0
1
0
1
1
2
0
0
0
0
1
0
0
0
0
0
2
0
2
0
2
1
1
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
2
2
1
0
0
0
0
1
3
1
0
2
0
1
0
2
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
1
0
3
0
0
0
0
0
3
1
2
0
0
1
0
0
1
0
0
5
3
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
2
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
4
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
2
3
1
0
0
0
2
0
0
1
0
0
0
0
2
0
2
0
0
0
0
4
0
1
1
0
0
3
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
3
1
0
0
1
0
0
0
0
0
0
3
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
1
0
2
0
2
0
0
0
0
2
1
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
3
1
0
0
0
1
0
0
0
0
2
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
1
0
1
2
0
0
2
0
0
0
0
0
0
0
0
2
3
0
0
0
1
2
1
0
0
0
1
0
1
1
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
4
2
1
0
2
0
0
0
0
2
0
2
0
2
1
0
0
0
0
0
4
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
2
0
0
0
0
0
1
0
0
1
2
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
1
0
2
0
0
0
0
0
0
2
0
0
0
5
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
2
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
2
0
1
0
0
1
1
0
0
0
0
2
0
0
3
3
0
0
0
0
2
0
1
0
1
1
0
0
2
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
1
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
2
1
2
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
2
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
2
0
0
1
0
0
2
0
1
1
3
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
3
0
1
2
0
2
0
0
0
0
1
0
0
0
0
2
1
2
0
2
0
1
2
0
2
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
3
0
3
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
1
0
1
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
4
0
0
1
2
0
0
0
0
2
1
2
0
1
2
0
0
0
0
2
0
1
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
2
5
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
1
4
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
1
1
0
0
1
0
0
1
0
0
0
0
0
2
5
2
0
0
0
0
0
2
0
1
0
2
5
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
1
1
2
2
0
0
0
0
1
0
0
1
0
2
2
0
1
0
2
0
2
2
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
1
2
0
0
0
2
0
0
0
0
0
1
2
2
0
0
0
0
0
3
0
0
0
0
0
1
2
0
2
0
2
2
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
1
1
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
1
3
0
0
0
2
0
0
0
0
0
2
0
0
5
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
2
3
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
2
0
0
0
2
0
0
0
0
1
0
2
0
0
3
0
2
1
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
1
2
0
0
0
1
1
1
0
0
0
0
2
1
0
2
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
2
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
1
1
2
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
1
0
0
0
0
0
2
0
0
0
0
1
0
1
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
2
0
2
3
0
0
0
0
0
0
3
0
1
0
0
0
0
0
2
6
0
2
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
1
2
4
1
5
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
2
2
2
1
0
1
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
6
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
4
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
4
4
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
6
1
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
1
1
0
0
1
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
2
1
1
1
0
0
0
1
0
0
2
0
0
0
0
2
0
0
2
1
0
0
3
0
1
1
0
2
1
2
2
2
0
1
0
0
4
0
0
0
1
0
1
0
4
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
1
0
0
0
6
1
0
1
1
0
0
0
1
0
0
1
0
3
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
3
0
0
0
3
0
0
1
0
0
0
0
0
1
0
1
0
0
0
2
0
2
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
2
0
0
1
2
0
1
2
2
0
1
0
1
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
1
3
0
0
0
1
3
0
1
0
0
0
0
0
0
0
0
0
1
1
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
2
1
1
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
1
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
17
0
3
1
0
0
0
0
2
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
1
0
0
4
0
0
0
0
0
0
1
3
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
1
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
2
0
1
1
0
1
9
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
4
2
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
4
0
0
0
0
0
0
1
1
0
0
1
0
0
2
1
0
2
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
1
1
2
0
0
0
3
1
0
0
0
3
2
0
0
3
0
0
0
2
2
1
0
2
0
0
2
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
1
0
3
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
1
1
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
4
2
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
2
0
4
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
2
0
0
2
1
0
0
0
0
0
0
2
2
2
0
2
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
1
2
0
2
0
0
2
2
0
2
0
0
1
0
0
1
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
4
0
2
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
5
0
2
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
2
2
0
2
0
0
1
0
2
0
0
1
0
0
0
0
2
1
1
2
0
0
1
0
0
0
0
1
3
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
1
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
2
5
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
1
0
0
2
1
1
0
0
0
0
1
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
1
1
0
4
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
5
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
1
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
3
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
3
0
2
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
1
1
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
1
0
0
0
0
3
0
0
2
2
0
0
0
0
1
1
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
2
2
3
0
0
0
1
1
2
0
0
0
0
0
1
0
0
1
0
1
0
0
0
2
0
0
0
2
0
0
2
0
0
1
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
1
2
0
1
1
0
0
0
0
1
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
3
1
0
0
1
1
2
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
2
3
0
0
2
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
2
0
0
0
3
0
2
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
6
0
3
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
3
1
2
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
4
2
0
1
0
1
1
1
0
0
3
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
1
0
1
2
0
3
0
0
0
6
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
3
0
2
2
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
1
0
2
3
2
4
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
1
2
0
0
0
0
0
0
2
1
0
0
0
0
0
3
0
1
0
0
0
2
0
1
1
0
0
0
0
0
2
1
3
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
2
1
0
0
1
0
0
0
2
0
2
0
0
1
0
0
1
0
1
1
0
1
0
0
0
0
0
0
3
0
0
1
0
0
2
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
2
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
3
1
0
0
0
2
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
4
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
1
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
2
1
0
0
0
0
0
0
2
2
0
1
1
0
0
0
0
1
0
0
1
0
0
2
2
2
0
0
1
2
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
4
0
1
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
2
0
0
4
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
1
0
0
2
1
0
0
1
0
0
0
2
2
0
0
0
3
0
0
0
0
0
0
1
2
2
0
0
2
0
0
0
0
2
0
2
6
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
1
1
0
1
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
2
0
0
2
2
6
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
2
0
2
2
1
2
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
2
0
0
0
0
1
8
0
2
2
1
0
1
0
1
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
1
0
0
0
2
1
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
2
0
1
0
0
0
1
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
1
0
1
7
0
0
0
0
0
0
0
2
0
2
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
2
1
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
2
1
1
0
2
0
1
0
1
2
0
0
0
0
0
2
1
0
1
1
0
0
0
2
0
2
0
2
0
2
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
2
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
2
2
1
2
0
0
1
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
2
1
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
1
0
1
2
0
0
0
0
2
0
2
0
2
0
2
2
2
4
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
1
0
4
0
1
2
0
3
0
0
1
0
0
2
0
0
0
1
3
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
2
0
0
1
2
0
0
2
0
0
0
0
1
0
0
1
0
4
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
5
0
0
0
1
0
0
1
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
8
0
0
2
1
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
8
0
0
0
0
2
0
0
0
0
0
2
2
2
3
0
0
0
0
0
2
3
2
1
0
1
0
3
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
1
2
2
0
0
2
0
0
0
3
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
3
1
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
2
3
0
0
2
0
0
1
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
1
0
1
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
2
0
2
0
0
2
2
0
2
2
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
1
0
0
0
0
1
0
2
1
1
0
0
0
0
0
0
0
0
0
2
3
0
0
1
0
0
1
0
0
2
0
2
0
0
0
1
0
3
0
1
0
0
0
2
0
0
0
2
0
0
0
1
2
0
2
0
0
0
0
1
0
0
2
1
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
3
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
2
0
1
0
2
2
0
0
0
0
0
0
0
2
0
0
0
2
0
1
1
0
1
0
0
2
0
1
0
0
0
1
1
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
3
1
0
0
0
0
0
0
2
1
0
0
3
0
0
2
0
0
2
0
0
0
2
0
1
1
1
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
1
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
3
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
2
3
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
2
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
5
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
1
3
0
0
1
0
0
1
0
2
1
0
0
0
4
3
1
0
0
0
0
0
0
1
0
0
0
5
1
3
0
1
0
0
0
0
1
1
0
0
0
1
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
2
2
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
2
1
0
0
1
0
0
2
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
3
0
0
0
0
0
0
1
0
0
3
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
2
1
1
0
2
0
0
0
0
0
1
1
0
0
2
2
0
2
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
1
0
0
0
2
1
0
0
2
4
0
0
0
1
2
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
2
1
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
1
0
2
0
1
3
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
3
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
4
0
2
0
1
1
1
1
3
1
0
0
1
0
6
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
10
0
0
0
0
1
0
0
2
0
0
0
0
2
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
2
2
1
0
0
0
1
0
0
0
1
0
0
2
1
1
1
2
2
1
0
2
0
0
2
0
0
0
2
2
0
0
2
0
5
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
3
1
0
0
0
1
0
1
2
0
2
1
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
1
0
0
6
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
2
1
0
0
2
0
0
2
0
0
0
0
3
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
2
0
0
1
2
1
0
1
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
2
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
9
0
2
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
1
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
1
0
1
0
0
0
0
0
2
0
0
0
1
1
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
10
2
0
0
2
2
0
0
0
1
0
1
0
0
3
2
0
0
1
2
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
4
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
2
0
1
1
0
2
2
1
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
2
0
0
1
0
0
2
5
2
3
3
0
0
0
2
1
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
1
3
0
0
1
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
1
1
0
0
1
1
0
1
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
11
1
0
0
0
0
2
0
0
0
0
0
1
0
0
1
1
2
0
0
0
0
0
1
1
0
0
0
0
1
0
1
2
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
1
0
4
0
0
0
1
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
1
2
4
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
2
0
2
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
2
0
2
0
2
1
0
2
0
1
9
1
2
0
0
0
1
1
0
1
0
0
2
0
0
0
0
3
0
0
1
0
0
0
0
0
1
0
2
0
0
1
2
1
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
1
0
2
0
1
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
2
2
0
1
0
2
0
0
0
0
2
0
2
0
0
0
1
0
2
1
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
1
3
0
0
0
0
0
0
0
0
0
1
0
1
3
0
2
1
2
0
1
0
2
0
2
0
2
0
0
0
0
0
0
0
0
1
0
1
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
2
1
0
0
1
1
0
0
0
1
0
0
2
1
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
3
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
2
0
1
2
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
5
3
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
2
1
0
2
0
0
0
0
0
8
1
0
0
0
2
0
0
0
0
0
2
1
0
0
1
2
0
1
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
2
2
1
0
0
1
2
14
1
2
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
2
1
0
0
2
0
0
0
0
3
0
1
0
1
0
0
0
4
1
0
0
0
2
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
1
0
0
2
2
1
3
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
1
0
0
0
0
4
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
5
1
0
2
0
0
0
1
2
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
3
0
0
2
1
0
0
2
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
1
0
0
0
0
2
0
0
0
2
0
0
1
0
0
1
0
0
1
0
0
0
0
2
0
0
1
0
0
1
2
0
0
0
0
0
0
2
1
0
0
2
1
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
3
0
1
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
2
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
1
0
0
2
0
1
1
0
0
0
0
0
2
0
0
0
0
1
2
0
1
0
0
5
2
0
0
0
0
2
0
0
2
0
0
2
5
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
1
1
2
3
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
1
1
0
2
0
0
0
0
0
0
2
0
3
0
0
0
0
0
2
1
2
0
2
0
2
0
0
0
0
0
1
0
0
10
0
0
0
2
0
2
0
0
2
1
0
1
0
0
1
2
0
0
2
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
1
1
3
0
1
1
3
1
0
1
0
2
2
1
2
0
4
2
0
0
0
0
2
0
0
0
1
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
1
0
0
2
0
2
0
0
1
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
1
0
0
0
2
0
0
0
0
0
0
0
0
6
0
0
0
0
1
0
0
0
2
2
0
5
0
2
1
0
0
0
0
1
1
0
0
0
0
3
0
2
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
2
0
0
0
1
1
0
1
1
0
0
0
2
0
0
2
0
0
0
0
0
3
1
2
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
1
2
3
1
0
3
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
1
3
0
0
0
0
0
1
0
0
0
0
0
2
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
2
1
0
1
0
0
0
2
0
1
0
0
3
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
2
0
1
1
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
6
0
0
1
1
0
1
1
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
7
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
4
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
4
0
0
0
2
0
0
0
3
0
0
0
5
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
2
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
1
1
0
0
0
0
1
0
2
0
0
0
1
0
0
1
0
0
0
1
1
0
0
1
3
0
2
1
2
0
0
0
0
0
0
1
0
1
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
2
1
1
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
2
0
3
0
0
0
0
2
2
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
1
0
1
0
0
1
2
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
1
2
0
3
1
1
0
0
0
0
2
0
0
2
1
0
0
2
3
0
2
1
2
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
3
0
0
0
0
0
1
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
6
0
0
0
0
0
0
2
5
1
2
0
2
0
0
0
0
0
1
2
2
0
0
0
1
1
0
0
0
0
1
2
0
0
1
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
1
0
1
0
0
2
1
0
0
0
0
0
0
1
0
0
2
0
3
0
0
0
0
0
0
0
0
2
0
1
2
2
0
0
0
0
1
2
0
2
0
0
1
0
0
0
0
0
2
0
1
0
1
0
0
2
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
2
0
0
1
0
0
0
2
3
0
2
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
3
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
2
0
1
1
0
0
0
2
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
3
0
0
0
0
0
0
1
0
1
0
2
0
1
2
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
1
0
0
0
2
1
4
1
0
0
2
0
0
0
2
0
1
0
0
0
1
0
2
0
1
0
1
0
0
0
0
1
0
0
1
2
0
0
2
0
6
2
0
0
0
0
2
0
2
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
2
1
0
0
0
0
2
0
0
0
0
2
0
0
0
3
0
0
1
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
2
0
1
2
3
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
1
0
0
1
0
0
1
0
0
1
0
0
2
0
1
0
0
2
1
0
0
0
0
1
0
0
3
0
0
0
2
2
1
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
4
0
0
0
0
3
2
0
1
2
2
4
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
1
0
0
0
0
2
0
0
1
0
3
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
4
2
0
0
0
0
1
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
2
0
1
2
1
1
0
1
0
0
0
0
0
3
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
1
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
1
2
1
0
0
2
1
0
0
0
2
0
1
1
0
2
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
2
0
1
0
1
0
0
0
2
2
0
0
0
0
0
1
0
0
0
1
1
0
2
0
0
1
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
1
0
6
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
2
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
1
1
0
2
0
0
0
1
0
0
0
0
0
4
0
2
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
1
0
0
0
2
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
4
2
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
6
2
1
0
0
0
0
2
1
0
0
2
0
0
1
0
0
0
2
0
0
0
1
1
0
0
2
0
1
0
0
1
0
0
0
0
0
0
2
0
1
1
1
2
0
3
0
3
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
2
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
2
1
2
0
0
0
0
0
0
1
0
1
2
0
1
0
2
0
0
0
0
1
0
0
0
0
3
1
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
2
1
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
3
0
4
1
1
2
0
0
0
0
0
0
0
2
0
2
1
1
0
0
0
0
0
0
5
3
2
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
2
1
0
0
0
0
0
1
1
0
0
0
0
2
0
0
1
0
0
2
2
2
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
2
0
0
0
2
2
2
0
0
0
0
1
0
0
1
1
0
2
2
0
0
0
0
0
3
0
1
0
2
0
3
0
0
2
0
0
1
0
0
0
0
0
0
3
0
2
0
0
0
0
1
0
0
3
0
1
0
0
0
2
0
0
0
3
0
2
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
1
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
2
2
1
0
0
0
0
4
0
0
0
0
2
2
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
1
7
0
0
2
0
0
1
0
1
0
1
0
1
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
2
0
0
1
0
1
6
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
2
1
1
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
1
2
2
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
3
3
0
0
0
0
0
0
1
2
0
0
0
5
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
2
0
1
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
1
2
2
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
1
0
2
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
1
0
1
1
2
0
3
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
2
0
0
3
2
2
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
2
2
0
0
4
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
2
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
3
0
0
0
2
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
2
3
0
0
1
2
1
1
0
0
0
0
0
0
2
3
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
1
0
0
0
0
1
2
0
0
0
0
0
3
1
0
2
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
3
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
2
0
1
0
0
0
0
0
1
2
1
0
0
0
2
1
0
0
0
0
2
1
0
0
1
0
1
0
2
0
2
0
2
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
2
1
0
2
0
0
0
2
0
0
0
1
0
0
0
2
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
2
2
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
2
1
1
0
2
2
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
21
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
1
0
3
1
0
0
2
0
1
1
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
6
0
0
3
0
0
0
0
2
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
1
1
0
0
0
2
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
2
0
0
0
4
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
2
0
0
0
0
0
1
1
0
0
0
0
2
0
2
1
0
0
0
2
5
1
2
0
1
0
0
0
3
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
1
0
1
0
2
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
2
0
0
2
0
1
1
2
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
2
1
0
0
0
2
1
0
1
0
0
2
0
0
2
0
0
0
0
0
4
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
1
2
1
2
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
1
1
0
0
2
0
0
3
0
0
1
2
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
1
0
0
2
1
4
0
1
1
0
0
0
1
0
0
0
0
0
0
2
1
0
0
3
2
0
1
0
0
1
0
0
0
0
0
0
0
2
1
0
2
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
3
0
0
0
0
0
0
3
0
0
0
3
1
0
2
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
4
1
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
2
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
2
2
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
3
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
1
0
0
0
2
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
2
0
0
1
2
0
0
2
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
3
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
2
2
0
0
0
1
1
0
1
0
1
0
0
1
2
1
2
0
1
0
0
0
0
1
0
0
0
0
0
0
2
1
1
2
2
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
3
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
1
0
2
1
1
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
1
0
1
3
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
1
0
2
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
1
0
0
1
0
0
1
2
0
2
0
2
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
3
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
3
0
0
3
1
0
1
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
1
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
3
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
3
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
2
1
1
1
0
0
0
4
1
1
0
1
0
0
0
2
0
0
0
0
0
0
1
2
0
0
2
2
0
3
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
2
0
0
2
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
2
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
7
1
0
0
0
0
1
0
1
0
3
0
0
2
0
2
0
1
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
5
0
1
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
3
0
2
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
2
0
2
0
0
0
1
1
2
8
1
2
0
0
1
1
0
0
1
2
0
1
1
0
2
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
2
2
0
1
2
2
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
3
0
2
0
3
1
0
0
0
0
2
1
0
0
2
0
0
0
0
1
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
7
0
5
1
0
1
0
0
0
0
0
1
0
0
0
2
1
2
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
1
0
0
3
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
2
0
2
0
1
0
0
2
1
0
3
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
1
0
3
0
2
0
0
1
0
0
0
0
1
0
1
2
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
6
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
4
0
1
0
0
0
0
1
0
2
0
0
2
1
0
0
1
2
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
3
0
0
1
0
0
0
2
0
0
6
1
0
1
0
0
0
1
0
2
0
3
0
0
0
2
0
0
0
0
1
0
0
1
2
0
2
2
0
0
0
0
0
1
2
0
2
1
0
0
0
0
0
0
1
0
0
0
2
0
0
1
1
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
2
1
0
0
0
1
0
0
1
2
2
0
0
0
0
0
0
0
2
0
0
3
1
0
0
0
1
5
1
3
4
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
1
0
2
0
1
0
3
0
2
1
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
3
0
2
2
0
0
0
1
2
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
6
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
2
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
1
3
0
0
0
2
1
2
0
0
2
2
0
0
0
2
2
0
0
1
0
1
0
2
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
2
0
0
3
0
1
1
0
0
0
0
2
0
1
0
0
0
0
0
1
1
0
0
0
2
1
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
1
2
0
0
0
0
0
0
0
3
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
1
2
0
1
0
0
0
0
0
0
0
0
0
0
3
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
1
1
1
1
1
0
1
0
0
2
1
0
2
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
1
0
0
2
0
3
0
0
0
0
1
0
0
2
0
1
0
0
1
1
2
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
10
0
0
1
0
1
0
0
0
1
2
0
2
0
0
0
0
2
1
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
2
1
3
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
10
0
0
1
2
2
1
2
2
0
0
0
0
0
2
0
0
1
2
3
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
2
0
2
2
0
0
0
0
0
2
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
5
0
0
0
0
0
0
0
5
0
0
0
1
0
0
0
1
0
0
1
0
1
2
0
0
1
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
2
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
3
2
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
2
0
0
1
2
0
0
0
0
4
0
0
0
0
2
0
1
0
8
0
0
0
0
1
0
0
2
0
0
0
0
0
1
1
0
0
1
0
0
0
1
2
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
1
0
0
2
2
2
0
0
0
0
1
0
0
0
0
0
0
4
0
0
1
0
0
0
2
0
0
2
2
0
1
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
2
0
2
0
2
0
1
3
0
0
1
0
1
0
2
0
0
0
1
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
2
2
0
0
2
1
0
0
2
0
0
1
1
0
0
0
0
0
0
2
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
3
1
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
1
2
1
2
0
1
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
10
0
0
0
0
0
0
0
1
3
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
7
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
3
0
1
0
3
1
1
0
0
0
0
0
2
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
2
1
0
0
2
1
0
3
2
2
0
0
2
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
2
6
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
3
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
2
0
0
2
0
2
0
1
2
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
2
3
0
0
0
0
0
0
1
0
0
2
0
1
0
0
1
0
2
1
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
7
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
4
0
0
0
1
0
0
1
2
0
2
0
0
0
1
0
0
0
0
1
1
0
0
1
2
0
0
2
0
3
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
2
2
0
0
1
2
0
1
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
2
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
2
0
0
0
1
0
1
0
1
0
2
2
1
3
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
1
2
2
2
0
0
0
1
0
0
0
0
4
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
1
0
1
0
0
0
2
0
5
0
1
1
0
0
0
1
0
0
2
1
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
2
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
1
2
2
0
0
0
2
0
0
0
3
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
1
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
2
2
1
0
2
1
2
1
0
2
0
2
0
1
0
2
0
1
2
2
0
2
1
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
2
0
0
2
0
0
2
2
1
0
1
2
1
0
3
0
0
0
2
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
6
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
2
0
0
2
0
0
0
1
0
0
2
0
0
2
0
0
1
0
0
1
0
0
0
0
0
2
0
1
0
1
0
0
0
1
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
3
0
0
0
0
0
0
0
0
1
0
1
3
1
1
0
2
0
2
0
0
0
0
0
0
0
0
2
3
0
2
0
0
3
2
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
2
0
1
3
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
1
0
1
0
0
2
0
2
2
0
0
0
0
0
0
0
2
1
0
0
1
0
4
0
0
0
0
3
0
0
1
0
1
0
0
0
3
0
0
0
2
0
0
1
2
0
2
0
0
0
0
1
0
0
0
1
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
2
1
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
10
0
2
0
0
0
0
1
1
0
3
0
0
0
0
2
2
0
0
0
0
0
0
2
1
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
2
2
0
0
0
1
0
2
0
2
2
0
0
1
1
2
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
4
0
0
0
0
2
0
2
2
0
0
2
0
0
0
0
1
0
1
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
1
2
0
3
0
0
2
1
1
0
0
0
0
0
0
1
0
1
1
0
0
3
0
0
0
0
0
0
0
0
0
0
3
0
0
3
3
0
0
0
1
1
1
0
0
0
1
0
2
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
3
1
0
1
0
0
0
3
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
1
0
0
2
0
0
2
0
2
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
2
0
3
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
1
2
0
1
0
0
0
2
0
0
1
0
0
1
0
1
0
1
0
2
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
1
2
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
3
0
0
0
0
1
0
0
0
0
1
2
0
1
0
0
0
0
1
2
0
1
0
0
0
0
0
2
2
0
0
1
1
0
1
2
0
0
0
0
1
2
5
0
2
1
0
0
2
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
7
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
2
0
0
2
2
1
0
0
0
0
0
1
0
1
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
1
0
0
0
0
2
3
0
4
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
1
1
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
2
0
0
0
0
1
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
2
1
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
4
2
0
0
1
1
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
1
1
0
0
0
2
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
1
0
7
0
0
0
0
0
0
2
0
0
0
0
2
2
0
1
0
0
2
0
0
0
0
0
1
0
0
1
0
0
3
0
1
0
1
0
3
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
1
0
0
0
0
0
2
0
1
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
4
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
2
1
0
0
1
0
0
7
0
0
1
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
1
1
0
0
0
0
0
1
0
2
0
0
0
2
2
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
5
3
1
1
2
0
0
0
0
1
2
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
2
2
0
0
2
0
0
0
1
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
5
0
2
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
4
0
0
0
0
2
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
2
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
2
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
1
1
0
0
0
1
0
0
0
2
0
0
0
0
6
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
1
2
0
2
1
3
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
2
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
2
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
16
0
0
0
2
2
0
0
2
2
0
2
2
0
0
0
2
2
1
0
0
2
0
0
0
4
3
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
1
2
0
0
0
0
1
0
0
0
0
2
0
0
7
0
2
0
1
0
1
0
0
0
0
0
2
0
0
0
4
3
0
3
0
0
2
4
1
0
0
0
0
0
0
0
0
1
2
0
2
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
2
0
1
0
1
0
0
0
0
1
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
1
2
3
0
0
0
1
0
0
0
0
0
2
2
3
0
0
2
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
1
0
6
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
4
0
0
2
0
2
0
0
0
0
13
0
0
0
0
1
0
1
3
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
2
2
0
0
0
0
3
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
3
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
2
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
1
0
2
1
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
2
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
3
0
0
0
2
1
0
0
0
0
6
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
1
0
0
2
0
0
0
1
0
0
0
0
2
0
1
2
0
0
0
2
0
0
0
1
0
1
0
0
0
0
4
2
0
0
1
0
0
2
0
0
2
4
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
1
0
0
0
0
4
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
1
1
0
0
3
0
0
0
0
0
0
4
0
0
0
0
0
1
1
2
0
0
0
0
0
2
2
0
0
2
0
0
3
0
0
0
2
0
1
0
2
2
2
0
0
3
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
6
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
1
0
0
0
0
2
3
0
1
1
0
0
0
0
0
0
2
0
0
0
3
1
2
1
0
1
0
0
1
0
0
0
0
1
2
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
1
0
1
0
0
0
0
0
1
0
0
6
0
0
3
3
1
2
0
0
3
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
5
0
0
0
1
0
2
0
0
2
4
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
1
1
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
2
0
0
3
0
0
1
0
0
0
2
2
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
1
0
1
1
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
1
0
0
0
0
2
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
2
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
1
1
0
0
0
2
0
0
0
2
3
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
3
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
2
0
2
1
0
1
0
0
0
2
0
0
0
1
0
0
2
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
1
1
0
1
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
1
0
1
2
0
0
0
2
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
1
1
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
1
0
1
0
0
0
2
0
0
2
0
0
0
0
0
3
0
0
0
0
3
0
0
0
0
0
1
0
1
2
3
0
0
0
3
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
3
0
1
0
0
1
1
2
0
2
0
0
1
0
0
2
0
2
0
0
0
0
0
2
3
2
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
2
0
2
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
2
2
1
5
0
2
0
0
0
0
3
6
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
2
4
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
2
1
2
2
0
0
0
0
0
1
2
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
1
3
0
0
4
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
4
0
1
0
0
0
0
0
2
1
0
0
0
0
1
2
0
0
1
0
1
0
2
2
0
2
2
1
0
1
0
4
0
0
0
0
0
0
2
0
0
1
0
1
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
1
0
0
0
2
1
0
0
0
0
0
0
0
0
3
2
0
0
1
0
2
0
3
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
4
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
8
2
0
0
0
1
1
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
1
2
0
0
1
0
3
0
1
0
0
0
1
0
1
0
1
0
1
0
2
0
0
0
0
0
0
0
2
0
1
0
1
0
4
0
0
1
0
1
0
0
0
0
0
1
2
0
0
3
0
0
0
0
0
0
2
0
1
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
3
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
2
1
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
3
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
1
0
0
3
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
1
0
0
0
0
0
2
2
0
1
2
0
0
0
0
0
5
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
1
0
1
2
1
0
2
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
2
1
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
1
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
1
0
1
0
2
0
0
0
0
0
0
1
0
0
0
3
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
3
0
0
0
2
0
2
0
0
0
1
0
0
0
1
3
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
2
0
2
1
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
1
0
0
2
3
0
0
0
0
0
3
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
3
3
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
1
2
0
0
2
2
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
4
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
1
0
2
0
0
0
5
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
2
1
1
2
2
2
0
0
0
0
0
3
0
0
2
2
1
0
0
0
0
2
2
1
0
0
0
0
1
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
2
0
0
0
0
0
0
2
0
2
2
0
0
2
2
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
1
1
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
2
0
3
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
2
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
2
0
2
0
0
0
2
0
0
2
0
1
0
0
0
0
1
0
1
0
2
0
1
0
1
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
3
1
4
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
2
1
0
1
0
0
0
4
2
0
0
0
2
1
0
0
1
0
2
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
6
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
1
1
2
2
0
1
0
0
0
0
0
0
0
2
2
1
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
2
0
0
2
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
2
0
0
0
2
0
0
2
0
0
1
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
1
0
0
2
1
3
0
0
0
0
0
2
3
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
2
0
2
0
1
0
0
0
0
0
4
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
15
0
0
1
0
0
2
1
0
0
0
2
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
1
1
2
0
0
1
2
0
0
0
0
1
2
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
6
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
8
0
0
0
2
0
0
0
0
3
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
2
0
0
2
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
2
4
3
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
1
0
0
0
0
1
0
2
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
1
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
2
2
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
2
0
1
1
1
0
1
0
0
0
0
1
0
0
1
0
2
0
0
1
0
1
2
1
0
0
0
0
0
2
0
0
0
1
2
2
0
0
1
0
3
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
1
0
0
1
4
1
0
0
0
0
0
0
0
3
3
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
2
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
4
0
0
0
0
2
2
0
2
0
2
0
0
0
0
2
2
0
0
2
2
0
1
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
3
0
0
3
1
2
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
1
1
2
5
0
1
0
1
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
1
0
5
0
0
2
2
0
3
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
1
0
1
0
0
0
2
1
0
4
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
1
0
0
0
1
1
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
3
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
1
1
0
0
0
1
3
0
0
0
0
0
0
0
0
0
2
0
2
0
2
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
2
0
4
2
0
0
0
2
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
2
0
0
0
1
2
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
3
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
1
2
0
0
0
0
1
0
0
1
0
1
1
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
2
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
4
1
0
0
0
1
0
0
0
0
2
2
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
3
0
1
0
0
2
2
2
1
1
0
1
0
0
0
0
1
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
5
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
2
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
2
0
0
0
1
0
1
2
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
3
1
0
0
0
0
0
0
0
2
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
2
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
1
1
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
2
0
0
1
2
0
0
2
2
0
0
2
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
1
0
0
0
1
0
1
0
0
0
3
0
0
1
0
1
0
2
0
1
2
1
1
0
0
1
0
0
2
0
2
2
0
0
0
1
1
0
0
3
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
2
0
0
0
4
0
0
0
0
0
1
0
0
0
2
2
0
0
0
2
0
0
1
0
0
0
2
1
2
3
2
0
0
0
2
1
0
2
0
2
0
0
0
1
0
1
0
1
1
0
0
0
0
3
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
3
3
0
2
0
0
2
0
1
0
2
0
1
0
0
0
0
2
0
2
0
2
0
0
0
2
0
0
0
0
2
0
1
1
0
4
0
0
0
0
2
0
0
0
0
0
0
3
0
0
1
0
0
1
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
2
1
0
0
2
1
4
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
2
2
0
0
1
0
1
0
0
4
1
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
2
0
2
2
2
0
0
0
3
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
1
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
2
1
0
1
0
0
0
0
0
2
0
5
0
1
0
1
1
0
0
0
0
3
0
0
0
1
0
1
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
3
2
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
1
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
1
0
1
0
0
0
1
0
0
1
0
0
1
1
0
0
1
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
2
0
1
2
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
2
0
0
2
1
0
0
0
0
0
1
0
0
0
2
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
4
2
1
0
0
1
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
2
0
0
0
2
1
1
0
0
0
0
0
1
2
0
1
0
0
0
2
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
1
0
0
0
3
0
4
2
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
4
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
1
0
0
0
0
0
1
1
0
1
1
0
0
0
2
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
1
0
0
1
0
3
0
0
0
0
0
0
1
2
0
0
2
0
1
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
6
0
0
0
0
0
0
0
0
0
3
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
2
0
0
0
1
0
1
0
2
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
2
2
0
2
0
1
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
1
1
1
0
0
2
0
0
2
0
2
0
2
2
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
1
1
0
0
1
1
4
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
2
1
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
1
1
0
0
2
2
0
0
2
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
4
0
2
0
0
2
0
0
1
0
0
0
0
1
0
2
5
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
2
2
0
0
0
0
0
1
0
0
0
1
0
4
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
6
2
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
3
0
1
7
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
2
1
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
5
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
1
0
0
2
2
0
1
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
3
0
0
0
0
0
0
1
2
3
2
1
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
3
0
1
0
2
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
1
0
0
0
0
8
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
1
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
1
2
1
2
0
1
0
0
1
1
0
1
0
0
0
1
0
1
0
1
0
0
0
2
2
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
1
0
2
0
1
0
0
0
0
2
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
1
1
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
4
0
0
0
2
0
1
0
2
0
2
0
0
1
2
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
3
0
1
0
0
2
0
1
2
2
1
1
0
1
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
2
0
0
2
0
0
2
1
2
0
2
0
2
0
1
0
0
0
0
2
2
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
3
0
0
2
0
0
1
0
0
0
0
0
2
0
2
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
2
6
0
3
0
0
0
1
2
1
0
0
3
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
2
2
0
0
0
0
0
1
0
0
0
2
1
0
0
1
0
2
0
0
0
0
0
0
0
0
7
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
9
2
2
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
1
0
0
0
0
1
0
2
0
0
1
1
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
4
0
0
2
0
1
1
1
0
0
0
0
1
0
0
0
0
0
2
3
0
0
1
0
0
0
0
0
5
0
0
0
0
0
4
0
0
0
0
0
0
0
2
2
0
0
1
0
2
0
0
5
2
2
0
0
0
2
0
0
0
2
0
2
1
0
2
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
2
2
0
2
2
3
0
0
0
0
0
2
0
1
0
1
0
2
0
1
0
0
0
0
0
0
0
0
2
3
0
2
0
1
0
2
0
1
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
3
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
2
0
0
1
0
0
0
2
0
0
1
0
2
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
5
2
2
1
0
1
0
0
1
1
5
0
0
0
0
0
1
4
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
6
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
4
0
1
2
0
1
2
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
1
1
0
0
1
0
0
0
2
2
0
0
0
0
1
0
0
0
0
1
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
1
2
0
0
2
0
0
1
0
0
0
2
1
0
0
1
0
0
1
0
0
0
3
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
2
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
2
0
0
2
2
0
0
1
2
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
2
0
0
0
0
1
2
1
1
6
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
2
1
0
0
1
1
0
0
0
0
0
0
0
0
4
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
6
0
0
0
0
0
0
1
0
0
1
0
1
2
0
1
0
0
0
1
1
2
0
0
0
2
1
0
1
0
0
0
0
0
0
2
0
0
0
0
1
1
3
2
0
1
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
1
0
4
2
0
2
0
0
1
0
0
0
0
1
2
2
0
0
0
2
3
0
0
0
0
0
0
1
0
0
0
2
2
4
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
2
2
0
0
0
1
0
1
0
0
0
0
3
0
0
0
2
0
1
0
0
0
0
0
1
2
0
0
0
0
2
0
2
1
2
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
1
2
1
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
1
1
4
1
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
3
1
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
2
0
0
0
2
1
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
1
0
0
2
1
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
2
0
0
0
0
0
2
0
0
0
4
0
2
0
2
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
2
1
0
0
0
3
0
0
0
1
2
2
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
2
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
4
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
1
0
2
0
0
2
0
0
1
1
0
0
0
1
3
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
1
2
1
0
0
0
1
1
4
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
2
1
0
0
1
6
0
0
0
0
2
0
0
2
0
0
1
0
0
1
0
2
0
0
0
2
3
0
0
2
0
1
2
0
0
0
1
2
0
1
0
0
2
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
1
31
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
8
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
2
0
0
0
0
1
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
1
0
0
1
0
0
2
0
0
0
0
1
0
0
0
4
0
0
0
1
0
2
0
1
0
1
1
0
0
7
0
2
2
0
0
0
0
0
0
0
1
0
0
0
3
0
0
1
5
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
2
2
0
1
0
2
4
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
3
0
0
0
1
0
1
0
0
0
0
3
2
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
4
2
0
0
2
0
3
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
1
2
0
1
0
0
0
1
0
2
0
0
2
0
0
0
2
0
2
2
0
0
2
0
1
0
0
0
0
0
1
0
0
0
1
2
1
2
1
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
3
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
4
0
0
0
0
0
0
0
0
2
0
2
0
1
0
3
0
0
1
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
1
0
1
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
2
0
0
1
0
0
1
0
0
2
1
7
0
0
0
0
0
0
2
0
0
0
0
2
1
2
0
2
0
2
0
0
0
2
1
0
0
7
0
0
2
1
1
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
2
2
0
0
0
0
2
0
2
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
2
0
0
6
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
2
2
0
2
2
0
2
0
2
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
1
0
0
0
0
1
0
2
0
0
1
0
0
0
1
2
0
0
0
1
0
0
0
0
2
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
2
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
4
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
1
0
0
1
0
0
0
0
1
1
1
0
1
0
2
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
1
0
4
0
0
0
0
1
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
3
3
0
2
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
1
1
0
0
1
0
0
0
2
2
1
0
0
0
0
0
0
0
2
0
2
0
3
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
2
0
0
0
0
0
2
0
1
4
0
1
0
0
1
0
2
2
2
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
1
0
2
0
2
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
1
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
2
1
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
3
2
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
1
0
1
2
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
3
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
3
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
7
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
3
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
3
3
2
0
1
0
0
0
0
0
0
1
0
0
0
6
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
2
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
1
0
1
0
0
2
1
0
0
0
2
0
3
2
0
0
0
0
1
0
1
0
3
0
1
0
2
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
1
0
0
0
0
0
5
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
2
1
2
1
0
0
0
1
0
0
0
0
1
1
0
0
0
2
0
0
0
0
1
3
0
0
3
0
1
0
0
1
0
0
3
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
3
3
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
1
2
1
3
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
2
0
1
0
2
1
0
0
0
1
0
0
0
1
0
0
0
2
0
0
1
2
3
0
0
1
0
1
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
1
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
3
0
2
3
0
0
0
0
1
0
0
0
1
0
0
1
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
2
1
0
1
1
0
0
2
2
0
0
0
0
0
5
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
2
1
0
0
1
1
0
3
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
4
0
0
0
0
1
2
3
3
1
1
0
0
0
0
0
1
0
0
3
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
1
0
2
2
0
1
0
0
1
0
2
2
2
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
3
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
1
0
2
0
3
2
0
0
0
0
0
1
2
0
0
0
1
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
2
0
0
2
0
2
2
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
4
0
0
0
0
1
1
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
3
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
2
0
0
0
0
5
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
1
4
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
0
2
0
2
0
0
0
3
0
0
0
0
1
0
2
0
0
0
0
1
2
0
0
0
0
0
0
3
0
1
2
0
0
0
1
2
3
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
3
0
1
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
3
1
0
0
0
0
5
0
0
0
2
1
0
0
0
1
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
1
0
0
1
0
2
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
1
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
3
0
1
1
0
0
0
2
0
0
0
0
0
2
0
0
1
1
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
1
0
0
1
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
2
3
0
0
0
0
0
1
6
0
0
0
5
0
2
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
1
0
0
1
0
0
0
0
0
4
0
1
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
2
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
2
0
0
2
0
1
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
3
0
2
1
2
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
1
2
0
2
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
4
0
0
0
1
5
0
0
0
0
0
0
1
0
0
0
1
0
2
2
0
2
0
2
0
1
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
2
0
0
2
0
0
2
0
2
2
0
2
0
0
0
0
0
0
0
0
3
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
5
2
0
0
1
0
2
1
2
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
1
1
1
2
3
1
2
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
6
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
1
1
0
0
0
1
1
0
0
4
0
0
0
0
1
0
0
0
0
0
0
3
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
8
0
0
0
1
1
0
1
0
0
0
2
0
2
0
1
1
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
1
0
2
0
1
2
0
0
0
0
0
2
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
2
2
0
0
2
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
2
0
0
0
2
0
0
3
0
0
0
2
0
0
0
0
0
1
0
1
0
2
0
1
0
0
2
0
2
0
0
0
2
2
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
2
0
0
0
0
1
2
0
2
0
0
0
0
1
0
2
0
0
2
0
0
1
2
0
2
0
1
1
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
4
1
0
0
1
0
0
4
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
1
0
0
0
0
0
3
0
0
3
0
2
2
0
1
0
1
2
0
2
1
0
0
0
1
2
1
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
3
0
1
0
1
0
0
0
1
0
0
2
0
0
1
0
2
0
0
1
1
0
0
0
2
1
0
2
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
3
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
4
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
2
0
0
0
2
0
0
0
1
0
1
0
0
0
2
0
0
0
1
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
2
2
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
2
0
0
1
0
1
0
0
2
0
1
2
0
0
0
1
0
2
1
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
1
0
0
2
1
0
1
1
0
0
0
1
0
0
0
0
5
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
1
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
7
0
0
0
0
0
1
0
0
0
2
0
0
2
1
0
2
0
0
0
0
0
0
1
2
0
1
0
0
0
1
0
0
2
3
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
4
0
1
0
2
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
2
5
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
3
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
1
0
0
0
2
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
1
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
1
1
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
1
0
2
2
0
0
0
1
0
0
0
1
0
2
3
3
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
1
1
4
0
3
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
1
0
0
0
2
1
0
2
0
0
0
0
0
0
1
0
2
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
1
3
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
1
1
0
1
0
0
0
1
1
0
2
2
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
1
1
0
1
0
0
1
0
5
0
0
1
0
0
0
2
8
0
1
2
0
0
0
0
2
0
2
0
0
0
2
1
1
2
0
1
0
1
0
2
1
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
2
0
2
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
3
1
2
0
0
4
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
3
0
0
2
1
0
0
2
0
0
1
1
2
0
0
0
1
0
0
0
4
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
4
0
0
2
1
0
0
2
0
0
0
2
0
0
0
3
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
1
2
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
1
0
1
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
2
2
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
6
1
0
0
0
0
0
0
0
0
2
0
1
0
2
3
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
1
0
3
0
0
3
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
2
0
2
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
2
0
0
0
0
2
2
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
3
1
0
0
2
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
2
0
0
0
5
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
3
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
7
0
0
0
2
0
2
0
0
2
2
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
3
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
1
1
0
2
0
0
1
1
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
1
2
0
2
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
1
2
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
2
1
0
0
0
3
2
0
1
1
0
0
0
0
0
0
0
2
1
2
0
2
0
2
2
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
1
0
0
0
0
0
1
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
2
0
2
2
2
0
0
1
1
0
1
0
0
0
0
0
0
0
2
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
1
2
0
0
0
2
1
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
5
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
1
2
0
0
0
2
0
0
0
2
1
2
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
2
2
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
2
0
0
2
0
1
2
0
0
0
1
1
0
1
0
0
0
0
0
2
0
1
0
1
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
3
0
0
2
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
1
0
0
0
1
1
0
0
2
0
0
0
0
1
1
0
0
0
0
1
0
0
2
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
1
2
0
0
1
0
1
0
0
0
0
0
2
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
2
2
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
2
1
0
0
7
2
0
1
0
0
0
1
0
0
2
0
0
2
0
1
0
2
0
0
0
0
6
0
2
1
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
2
0
0
1
0
2
0
1
0
0
0
1
0
4
0
0
2
0
0
0
0
0
0
0
4
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
1
0
2
1
3
0
0
0
0
0
0
0
1
0
2
2
2
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
2
0
0
2
0
1
0
0
0
2
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
2
0
2
1
0
0
0
1
2
0
2
0
0
0
0
3
1
1
1
0
0
0
0
0
0
1
0
3
0
0
0
1
0
0
0
1
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
2
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
2
0
0
1
0
2
0
0
0
0
1
2
0
0
0
0
1
0
0
1
0
2
4
0
0
0
0
0
0
4
1
0
0
0
0
0
3
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
1
4
2
0
1
1
1
1
0
1
0
0
0
0
2
1
0
0
0
2
0
0
1
2
0
1
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
2
0
0
2
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
2
1
1
2
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
1
0
0
0
0
0
1
0
11
1
0
0
0
0
0
2
0
2
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
2
0
0
0
6
0
0
2
1
0
0
2
0
0
3
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
3
0
1
0
1
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
1
1
0
1
0
0
0
0
0
2
1
0
0
2
0
0
0
2
0
0
1
0
0
2
0
0
2
1
0
0
0
2
0
1
0
0
0
0
0
3
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
2
1
0
2
0
0
0
0
0
1
2
0
1
1
0
0
2
2
2
2
0
0
0
2
0
0
0
0
2
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
2
0
0
0
5
0
1
0
1
0
4
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
2
1
0
2
0
2
0
0
2
2
0
0
0
0
2
0
0
1
1
0
0
1
0
0
0
2
3
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
2
2
0
1
0
0
0
0
1
1
1
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
2
0
0
2
2
0
0
1
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
2
0
0
0
2
1
0
1
2
1
0
1
0
0
0
0
0
0
2
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
2
7
0
0
2
1
2
0
0
2
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
2
0
0
0
0
2
2
1
0
0
2
0
1
0
2
3
1
0
0
0
0
0
0
0
0
0
6
0
1
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
2
1
1
0
1
0
0
0
0
2
1
0
2
0
1
0
0
2
0
0
2
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
2
2
0
1
2
0
0
0
0
0
2
0
2
0
0
0
0
0
2
2
1
0
0
1
2
0
0
0
0
0
3
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
2
1
0
0
2
1
0
0
0
1
0
1
0
3
0
0
0
0
0
2
1
1
2
0
0
0
0
0
0
0
2
2
0
4
2
0
0
2
0
0
0
1
0
1
0
3
2
0
2
1
1
0
0
1
0
0
2
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
1
2
1
1
0
0
0
0
2
1
0
0
2
0
0
0
2
3
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
1
2
2
0
0
4
0
2
0
0
0
0
0
1
0
0
0
3
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
3
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
2
0
1
3
0
4
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
1
2
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
1
0
3
0
0
0
1
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
2
1
1
0
0
0
0
2
0
0
0
4
0
1
0
0
1
0
0
0
2
2
0
2
0
0
0
0
0
0
2
0
0
0
2
1
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
2
4
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
2
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
1
1
0
0
2
0
2
0
2
2
0
0
2
0
2
0
1
2
0
0
4
0
0
1
0
0
0
1
0
3
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
1
0
0
2
0
4
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
1
1
0
0
1
0
0
2
0
1
2
0
0
2
2
2
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
2
0
1
1
0
0
1
0
0
1
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
1
2
0
0
0
1
0
1
0
0
0
1
0
0
2
0
0
0
1
1
0
3
1
2
0
2
0
0
0
1
2
0
0
0
1
2
0
2
0
0
1
0
0
1
2
0
0
0
0
0
0
0
2
1
1
3
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
1
0
1
0
2
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
1
1
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
2
0
0
1
0
0
7
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
3
0
0
0
2
0
0
1
0
0
0
5
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
1
0
0
0
3
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
2
0
2
0
2
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
6
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
3
2
0
1
0
0
0
0
0
0
0
3
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
2
0
2
0
0
0
0
2
0
0
0
0
0
3
0
0
2
0
0
0
1
0
0
0
0
0
2
3
0
4
2
3
0
1
0
1
2
2
1
0
0
0
0
0
1
0
0
1
0
1
2
0
4
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
2
1
0
0
0
2
1
0
0
1
2
3
0
0
6
0
0
1
0
0
0
3
0
0
2
1
0
0
0
0
0
1
2
1
0
0
0
0
0
0
1
0
0
0
3
0
1
0
0
0
1
0
2
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
2
2
1
0
0
0
0
2
0
0
1
0
1
0
0
0
0
5
0
0
1
0
0
0
0
2
0
0
2
2
1
2
0
0
0
2
2
0
0
1
0
0
1
0
0
1
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
5
0
0
0
0
0
1
0
1
0
0
0
0
2
1
0
0
0
0
1
0
2
0
0
0
2
0
1
0
0
0
0
0
1
2
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
2
0
2
2
0
1
0
1
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
3
0
0
1
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
2
0
0
0
1
0
0
2
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
5
0
0
0
0
2
1
1
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
1
0
0
7
3
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
1
2
1
1
0
1
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
1
2
2
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
1
1
0
0
1
1
1
0
0
0
0
0
2
0
0
0
0
0
2
0
1
2
0
1
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
2
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
1
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
2
1
0
0
0
0
0
2
2
0
0
1
0
1
0
0
0
0
0
2
1
2
0
0
0
0
0
3
0
0
0
0
2
2
0
0
0
0
0
1
4
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
2
1
1
1
0
0
1
0
3
3
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
2
0
0
2
1
0
2
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
2
0
0
1
0
0
0
0
3
0
0
0
0
0
1
1
0
0
0
0
0
1
0
3
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
2
0
0
0
1
0
0
1
1
2
2
0
0
0
0
0
0
0
0
1
2
1
3
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
2
0
0
4
1
0
0
0
0
1
0
2
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
1
0
1
0
1
0
0
0
1
1
0
0
0
0
0
1
1
0
2
0
0
0
6
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
5
0
0
0
0
0
2
0
0
1
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
1
2
1
2
0
0
0
0
0
0
0
0
0
3
0
0
3
0
1
1
0
1
0
3
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
3
0
0
0
0
0
0
2
0
1
0
0
3
0
0
1
0
1
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
2
1
0
0
0
0
4
0
0
0
2
1
1
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
1
0
0
0
1
2
0
0
0
2
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
2
0
1
2
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
6
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
2
3
0
5
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
2
0
2
0
0
0
6
0
1
0
0
0
0
0
2
0
2
0
0
0
5
0
0
0
1
2
0
2
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
1
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
3
0
0
1
0
1
0
0
2
0
0
1
2
0
1
0
7
1
0
0
0
0
0
0
0
0
0
0
4
0
2
0
0
2
0
0
2
3
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
2
0
1
1
0
0
0
0
0
2
0
0
0
0
1
1
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
1
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
2
0
0
3
1
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
2
0
5
2
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
4
0
0
0
0
3
0
1
0
0
1
0
1
3
0
1
0
0
0
2
2
0
0
0
2
0
0
2
0
1
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
3
0
0
0
0
0
2
0
3
0
0
0
1
0
0
2
1
0
0
3
0
0
2
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
1
0
3
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
4
3
0
0
2
0
1
0
0
0
1
0
0
0
2
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
2
0
13
1
0
0
2
2
0
0
0
0
0
3
0
2
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
1
0
2
3
2
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
7
0
0
0
1
0
2
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
2
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
2
0
0
0
1
0
2
0
2
1
0
0
0
0
1
0
0
0
0
2
0
1
4
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
2
0
0
2
2
1
2
0
0
3
1
0
0
2
0
0
0
0
0
0
2
3
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
5
2
0
3
0
0
0
1
0
0
0
2
1
0
0
1
0
1
2
2
2
2
0
0
0
0
0
0
2
2
0
0
2
0
0
0
1
0
0
0
0
1
0
0
1
3
0
0
0
0
10
0
0
0
1
0
0
2
0
0
4
0
0
0
0
0
1
0
0
1
3
0
0
0
3
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
4
0
2
0
2
2
0
0
0
0
0
1
0
1
0
0
1
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
2
0
0
0
2
1
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
2
1
0
2
0
0
2
0
0
0
0
2
8
1
0
0
2
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
1
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
4
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
1
3
0
0
2
2
2
0
0
4
0
0
0
0
0
1
2
1
1
0
0
2
1
0
0
2
0
1
0
2
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
3
0
0
2
0
1
0
0
2
0
2
0
2
0
0
2
0
2
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
2
2
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
3
3
0
2
0
0
1
0
1
2
0
1
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
4
0
0
0
0
1
0
2
0
0
0
0
0
1
1
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
2
0
0
0
2
0
2
2
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
1
0
2
0
1
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
3
0
0
0
0
2
0
0
0
2
0
0
1
0
0
2
2
1
2
0
1
0
0
0
3
0
1
0
2
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
1
0
0
0
2
0
3
2
0
0
3
0
1
1
0
0
1
0
0
0
0
2
0
1
1
2
0
1
0
0
1
0
0
0
4
0
0
1
1
0
0
0
0
1
0
0
0
0
1
2
0
0
0
1
0
1
2
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
1
0
0
0
2
2
0
0
0
1
0
1
0
0
0
0
0
2
0
0
3
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
1
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
1
2
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
3
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
2
4
0
1
0
1
1
0
0
0
2
0
0
2
2
0
1
0
0
0
3
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
1
0
0
3
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
1
0
2
0
0
0
1
0
0
3
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
2
0
1
0
0
0
0
3
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
2
2
0
1
0
1
0
0
1
0
0
1
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
3
0
3
1
0
1
1
0
0
0
1
0
0
0
2
0
1
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
1
0
0
2
0
0
0
1
2
0
1
0
2
1
2
0
0
0
0
0
0
0
2
1
1
0
0
3
0
0
2
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
1
2
0
2
2
0
1
0
0
0
0
0
2
3
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
4
0
2
0
0
1
0
0
1
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
1
0
2
0
0
0
1
1
1
0
0
0
0
2
1
1
2
0
0
1
0
0
2
2
0
0
0
0
0
1
2
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
3
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
2
2
0
0
0
0
0
4
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
2
1
0
0
2
0
2
0
1
0
0
2
0
0
0
1
2
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
1
2
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
2
1
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
1
1
0
0
2
1
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
1
2
0
2
1
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
1
2
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
1
0
1
1
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
2
0
2
0
2
2
0
0
0
0
0
0
0
0
1
0
0
5
0
1
0
2
1
0
1
0
0
0
0
0
1
2
0
0
5
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
6
1
2
0
0
0
0
2
0
0
0
0
0
2
1
2
0
0
0
0
2
2
0
0
2
0
1
0
0
2
0
0
0
1
3
0
0
0
1
2
0
0
0
0
1
0
2
1
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
1
0
0
0
2
1
2
0
2
3
0
0
0
0
0
0
0
0
0
0
5
0
0
1
3
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
17
0
0
0
0
0
0
0
0
0
2
0
0
0
0
5
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
2
0
3
0
0
0
0
2
0
2
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
3
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
3
1
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
1
0
0
1
3
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
6
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
4
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
1
0
4
0
0
0
2
0
1
2
0
0
0
1
0
0
0
3
4
1
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
3
0
1
0
0
0
2
0
2
0
0
0
1
0
0
2
0
0
1
0
0
1
0
0
0
0
0
2
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
1
0
1
0
0
1
2
0
0
1
0
0
0
2
0
2
0
1
1
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
1
1
2
0
1
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
2
4
0
1
0
0
1
0
0
0
5
4
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
1
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
2
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
2
0
2
0
0
0
0
2
0
0
2
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
1
1
0
5
1
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
1
0
0
1
2
0
0
0
2
0
0
2
3
3
0
1
0
0
2
5
0
4
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
1
2
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
1
0
0
1
0
2
1
0
1
0
0
0
0
0
0
1
0
0
0
3
0
1
0
0
1
0
1
0
2
0
0
2
0
0
1
0
1
0
2
0
2
1
3
0
1
0
1
2
0
0
0
0
2
0
2
0
0
1
1
0
0
1
0
0
0
0
2
2
3
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
3
5
0
1
0
0
2
0
1
1
2
1
0
3
2
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
1
1
0
0
0
2
0
0
0
2
0
4
0
0
0
0
0
0
2
1
0
0
1
0
0
2
0
0
0
2
2
1
0
2
0
0
0
0
0
0
1
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
3
0
1
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
2
1
2
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
3
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
2
2
0
0
0
1
0
1
0
0
1
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
2
3
0
0
0
0
0
0
0
0
0
7
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
1
2
2
0
0
0
0
0
2
2
0
0
1
2
0
2
0
0
1
2
0
2
2
0
0
1
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
3
0
0
2
0
2
0
0
0
0
0
0
0
3
0
0
0
0
2
0
1
0
0
0
0
1
0
2
0
2
0
0
0
0
0
2
4
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
1
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
1
0
1
0
0
2
0
1
0
0
3
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
2
0
2
0
0
2
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
2
1
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
1
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
2
1
0
0
0
0
3
0
0
0
1
1
2
2
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
2
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
1
1
2
2
0
0
0
2
0
2
0
0
0
0
0
3
0
0
1
2
0
0
0
0
2
0
3
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
3
0
0
0
0
3
0
0
2
3
1
0
0
0
0
0
0
0
2
0
0
0
1
6
3
0
2
0
2
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
1
1
2
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
2
4
3
0
0
4
0
1
2
0
0
0
1
0
0
3
4
0
0
0
0
0
0
2
0
1
0
3
1
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
1
1
0
0
2
1
3
0
0
2
0
2
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
1
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
1
0
2
0
0
1
0
5
0
0
0
0
0
6
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
1
2
0
0
1
0
0
2
0
2
1
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
5
0
0
0
0
2
0
0
0
1
0
0
0
2
3
2
2
0
0
0
0
2
0
0
0
2
0
0
2
0
1
1
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
1
0
0
0
2
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
2
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
3
0
0
0
0
0
0
1
0
1
0
0
0
1
2
0
0
0
0
0
2
0
2
1
0
0
0
2
0
0
11
0
0
2
1
2
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
2
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
1
0
2
0
0
0
0
2
0
0
0
0
8
0
0
0
0
2
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
4
0
2
0
0
0
0
0
3
0
0
0
0
0
0
2
0
2
2
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
1
0
2
2
0
1
1
0
0
0
1
0
0
0
3
1
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
3
1
0
2
0
0
0
0
0
0
0
1
2
1
0
1
0
0
0
2
0
0
0
0
1
2
0
1
0
1
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
3
0
1
0
1
1
0
0
1
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
3
0
1
2
0
0
0
0
0
0
0
2
3
0
0
1
2
0
0
0
0
0
1
0
0
2
0
1
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
2
1
0
1
1
0
0
1
0
1
0
0
0
2
0
0
2
0
0
1
0
4
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
8
1
0
0
1
0
0
0
0
0
0
0
0
2
0
1
1
0
0
2
0
1
0
0
1
0
0
0
2
2
0
0
0
0
0
0
2
0
1
0
0
0
1
0
1
0
0
0
0
3
0
0
0
1
3
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
2
2
1
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
5
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
3
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
2
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
2
0
0
0
1
0
0
0
1
0
0
2
0
0
1
2
1
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
1
0
0
2
0
0
2
0
0
1
0
1
0
0
0
0
0
0
1
0
2
0
1
0
2
1
1
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
2
3
0
0
0
0
1
0
1
0
1
0
1
0
2
0
4
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
2
0
0
1
2
0
2
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
1
3
1
1
1
0
1
0
0
5
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
1
1
0
0
0
0
2
0
2
0
2
0
0
0
0
1
2
0
0
1
2
1
0
2
0
0
2
13
0
0
4
0
0
0
1
0
0
1
0
2
0
1
0
0
0
0
0
0
2
2
0
2
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
2
0
2
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
4
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
4
2
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
2
0
1
2
0
0
0
3
1
2
0
2
1
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
1
2
1
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
4
0
2
2
1
2
0
1
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
1
0
1
0
0
0
0
1
4
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
2
2
0
2
0
0
0
1
0
1
0
0
0
0
0
0
1
1
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
1
0
0
0
2
0
2
1
0
1
2
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
2
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
2
0
0
0
0
2
1
0
2
0
2
0
0
0
0
0
2
0
1
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
2
0
0
0
2
0
1
1
0
2
0
0
8
0
0
0
0
0
0
0
3
0
0
2
0
3
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
2
1
0
0
0
0
0
1
0
0
1
0
2
2
0
0
0
0
2
0
2
0
0
0
0
2
0
0
2
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
2
3
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
2
0
0
0
0
0
0
3
0
0
0
0
2
0
1
0
1
0
0
0
0
0
2
1
0
2
0
0
0
2
2
0
0
0
1
0
0
2
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
1
0
2
0
0
2
0
3
0
0
0
1
1
0
0
0
0
1
2
0
0
0
0
2
1
1
0
2
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
3
1
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
6
0
0
0
0
0
1
0
1
0
1
2
1
0
0
0
0
0
0
0
0
0
6
0
0
2
0
0
0
0
0
1
1
0
0
0
3
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
1
0
0
2
0
1
1
0
0
1
0
0
0
1
0
0
0
1
1
0
1
0
1
0
1
0
1
0
0
0
1
2
1
0
0
1
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
2
0
2
3
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
1
2
1
0
0
3
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
3
0
0
1
0
0
0
2
0
0
0
0
0
1
0
1
0
0
1
4
1
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
2
2
1
2
0
0
0
2
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
1
1
2
1
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
3
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
1
1
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
3
2
0
0
0
0
1
0
0
0
3
0
2
1
1
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
1
2
0
4
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
3
1
2
0
2
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
1
0
0
2
5
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
1
1
2
0
0
0
3
1
2
1
0
2
1
0
0
0
0
1
0
1
2
0
2
0
0
0
3
0
0
2
0
0
1
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
2
1
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
2
0
2
0
1
0
0
1
0
0
0
0
2
1
0
1
1
0
0
0
0
0
0
0
3
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
2
0
0
0
0
2
0
5
0
0
2
2
2
0
0
1
0
2
1
1
1
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
1
0
2
0
0
0
3
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
4
1
0
2
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
3
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
1
0
0
0
1
0
0
0
0
1
0
1
3
0
0
0
0
0
0
0
3
2
1
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
1
2
0
0
0
1
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
2
2
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
3
0
2
2
0
2
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
2
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
5
0
0
2
2
0
1
5
0
0
0
0
6
0
0
0
0
2
2
0
2
0
1
1
0
2
0
0
0
1
2
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
1
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
3
2
0
0
0
0
0
0
1
0
0
0
1
1
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
2
1
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
2
2
0
0
2
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
3
0
0
0
2
0
0
0
0
2
1
0
0
0
1
0
2
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
2
1
0
0
2
1
0
0
0
0
1
2
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
2
1
0
2
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
2
2
1
0
1
0
0
0
2
0
0
0
0
3
4
3
0
2
0
0
0
1
1
0
0
3
1
0
2
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
3
0
2
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
1
0
0
0
0
1
0
5
0
0
0
0
2
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
1
0
0
2
0
0
0
0
2
0
1
1
0
0
0
0
0
0
3
0
0
1
0
0
1
0
0
0
0
1
1
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
1
0
0
1
1
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
2
4
0
1
0
0
0
3
2
2
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
16
0
1
0
0
0
0
2
4
1
0
0
0
0
1
1
0
2
0
0
2
0
0
1
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
1
0
0
0
0
1
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
4
2
3
2
2
0
1
0
0
0
0
1
0
0
0
1
0
0
1
2
0
0
0
0
0
2
0
1
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
3
0
1
0
2
0
0
0
0
0
0
2
0
2
0
0
3
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
2
2
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
3
0
1
0
0
0
0
0
0
1
3
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
1
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
1
1
2
0
1
0
0
2
0
0
1
0
1
1
1
0
1
0
1
2
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
2
0
0
0
1
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
2
1
1
0
1
2
0
2
0
0
1
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
1
1
0
0
0
0
0
0
0
0
2
2
0
0
0
4
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
1
0
0
0
1
3
0
2
0
0
2
0
0
0
0
1
0
0
0
2
0
1
0
0
0
1
0
0
0
1
0
0
2
0
0
0
1
0
0
2
0
2
1
0
1
0
0
0
0
0
0
0
0
3
0
0
1
1
2
0
0
0
0
0
0
0
3
0
1
5
0
0
2
2
0
1
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
2
0
0
0
1
0
0
0
1
1
2
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
2
0
2
0
0
0
0
0
0
1
0
1
1
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
1
2
0
1
2
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
1
0
1
2
0
0
0
0
1
1
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
4
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
1
0
0
0
0
2
2
0
2
0
0
0
0
0
0
2
0
1
0
2
0
2
0
0
2
0
0
1
0
0
0
0
0
0
3
0
0
0
1
2
1
2
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
1
1
0
1
0
0
0
2
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
7
0
0
2
0
0
0
0
0
1
1
2
0
0
2
0
0
2
0
2
0
0
0
1
0
0
1
0
0
0
2
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
3
2
1
0
0
1
0
1
1
1
0
0
3
0
0
0
8
0
0
1
0
1
0
0
1
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
7
0
0
2
1
0
1
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
3
0
0
1
0
4
2
0
0
0
0
0
0
1
0
2
2
2
1
4
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
2
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
2
2
0
2
2
0
0
0
2
0
1
3
0
2
0
0
1
1
1
2
0
0
1
0
0
2
0
1
2
0
2
2
0
0
0
2
0
3
0
2
0
2
0
2
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
1
0
0
0
1
1
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
1
2
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
2
0
2
2
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
1
2
1
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
1
0
1
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
2
4
0
0
0
0
0
1
0
0
0
8
0
0
2
0
0
0
0
0
0
1
0
0
0
2
1
2
0
2
0
1
0
0
1
2
0
0
0
0
2
0
1
1
0
1
0
0
0
0
0
2
0
0
2
0
1
1
0
0
0
2
1
0
2
0
2
0
0
0
1
3
0
3
0
0
0
0
1
0
0
2
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
1
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
5
0
0
0
0
3
2
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
1
0
0
0
1
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
1
1
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
1
0
0
0
3
2
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
1
2
0
1
1
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
3
0
0
0
1
0
2
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
5
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
6
0
0
2
0
0
0
1
0
0
0
2
2
0
4
0
0
2
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
1
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
5
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
2
0
2
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
1
3
1
0
0
0
0
0
2
0
0
0
0
0
0
0
4
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
2
0
0
1
2
0
0
4
2
3
0
0
0
1
1
1
0
0
5
0
2
0
3
0
0
0
1
1
1
0
2
0
7
1
0
0
0
0
0
2
1
0
0
2
0
0
0
0
2
2
0
3
2
0
3
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
3
2
2
0
1
0
0
2
0
0
0
1
0
1
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
1
0
2
0
0
0
1
0
0
0
0
3
0
0
0
0
1
1
0
0
0
1
2
0
0
3
0
2
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
2
0
2
0
0
2
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
1
0
0
0
3
0
1
0
0
0
0
0
0
2
1
0
0
2
0
1
2
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
2
0
1
0
0
0
1
0
0
0
6
0
1
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
1
0
2
0
1
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
10
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
4
0
0
0
0
0
0
0
0
2
0
0
2
2
1
0
0
0
2
2
0
0
0
1
1
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
2
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
1
0
1
0
0
2
0
2
2
0
0
0
0
0
0
1
1
1
0
1
2
3
0
2
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
2
2
0
0
2
1
1
2
0
2
7
0
2
0
0
2
0
1
0
0
0
1
0
0
2
0
0
0
0
2
1
0
2
0
0
1
0
0
2
0
0
0
0
1
0
1
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
1
0
4
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
5
0
0
1
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
2
0
2
2
0
0
0
0
0
1
1
0
1
2
0
0
1
1
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
9
0
1
3
0
0
0
0
1
1
0
0
2
2
0
0
0
0
0
2
0
0
2
3
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
2
0
0
0
1
0
2
0
0
1
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
2
0
2
2
0
1
0
1
1
0
0
0
0
8
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
3
2
0
1
0
0
0
0
0
0
0
2
2
0
1
1
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
2
0
1
0
1
0
1
0
0
2
2
2
0
2
0
3
0
0
0
0
0
0
2
0
1
0
1
0
0
1
2
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
2
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
1
0
2
0
0
0
0
1
0
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
4
2
0
0
0
0
0
0
1
1
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
4
0
2
0
0
2
0
2
0
1
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
2
3
3
0
0
0
0
2
0
0
0
3
0
1
1
0
0
2
0
0
2
0
0
0
0
0
0
0
3
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
1
1
1
0
0
2
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
1
2
2
0
0
0
2
3
0
0
0
1
0
0
0
0
5
2
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
3
0
0
0
0
2
0
0
0
1
0
2
1
1
0
0
0
2
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
2
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
3
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
1
0
0
0
1
0
1
3
0
0
0
0
0
0
2
0
4
1
0
0
0
0
3
0
0
0
0
0
1
0
0
0
3
0
2
0
0
5
0
1
0
0
0
0
0
0
0
0
1
0
2
2
1
0
0
0
0
0
2
0
0
1
3
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
2
0
0
2
0
0
3
2
3
0
0
0
0
7
2
1
0
0
0
0
0
0
0
2
1
0
2
0
2
0
0
0
0
1
1
0
0
0
0
0
0
1
1
1
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
3
1
0
1
0
0
0
0
0
5
1
0
0
3
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
1
1
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
2
0
2
0
0
0
0
0
0
1
0
2
1
0
1
0
0
0
0
0
2
0
2
0
2
2
0
0
0
0
2
1
0
0
0
0
1
3
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
2
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
1
2
0
2
2
1
2
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
1
0
0
2
0
1
0
0
0
2
0
0
0
0
1
1
2
0
2
0
0
0
0
0
0
0
0
2
0
2
4
0
0
0
0
2
0
2
1
2
0
0
4
0
2
2
3
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
3
0
0
0
0
0
0
3
0
0
0
3
2
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
4
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
2
0
1
0
2
2
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
2
1
0
0
1
1
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
2
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
3
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
1
0
0
0
0
0
1
1
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
2
0
2
0
2
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
3
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
2
2
1
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
3
1
2
0
0
0
0
0
1
2
0
0
0
2
0
0
2
0
0
2
4
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
3
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
2
1
0
1
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
6
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
3
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
1
0
2
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
1
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
4
0
0
0
0
0
2
0
0
0
1
2
0
0
2
0
4
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
1
0
0
1
1
0
0
1
0
0
0
2
1
0
2
1
1
1
2
2
3
0
2
1
0
0
0
0
1
0
1
0
0
2
2
2
0
0
2
0
0
0
1
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
2
0
1
1
0
0
2
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
3
0
1
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
2
1
2
0
2
1
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
1
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
2
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
3
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
2
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
1
4
0
0
1
5
0
0
2
0
0
0
1
0
1
0
1
1
0
1
0
0
1
1
0
0
0
0
0
1
0
2
1
1
0
0
2
0
0
0
1
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
2
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
2
1
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
4
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
4
1
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
2
0
0
7
0
0
0
2
2
0
0
2
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
3
0
0
0
2
0
0
1
1
0
1
2
0
0
0
0
0
0
0
2
1
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
2
3
0
0
2
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
5
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
1
0
1
1
0
0
0
0
2
0
2
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
5
0
1
0
0
3
0
0
2
1
0
1
0
0
0
0
1
0
2
3
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
2
2
2
0
0
0
0
0
0
1
0
2
0
0
2
0
2
0
0
0
0
2
1
2
1
0
0
0
0
1
2
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
1
0
0
1
0
0
0
2
2
1
0
0
0
0
0
0
0
0
2
0
0
0
1
2
2
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
2
3
0
0
0
1
0
0
0
0
0
0
0
4
0
1
0
0
0
0
1
0
1
2
0
0
1
0
0
1
0
0
2
0
0
2
0
0
1
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
2
0
0
0
1
0
2
0
2
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
1
4
3
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
2
0
1
2
1
0
0
0
0
6
0
0
0
0
0
0
0
1
2
0
1
2
2
0
2
0
0
1
0
0
3
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
2
2
1
2
0
0
2
3
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
1
0
2
0
1
0
0
1
1
2
0
0
2
1
0
0
0
0
0
0
2
1
0
1
0
0
0
1
5
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
2
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
1
0
0
1
0
0
2
0
0
0
0
1
0
0
2
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
3
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
1
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
1
0
1
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
1
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
1
0
3
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
1
0
2
2
0
0
2
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
3
0
0
1
1
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
3
0
0
0
2
2
1
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
2
0
1
0
0
1
0
0
2
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
1
0
2
2
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
3
0
0
1
0
0
0
6
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
3
2
0
0
0
2
1
0
0
0
0
0
0
0
1
0
4
0
2
0
1
1
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
1
0
2
0
3
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
2
0
0
2
1
0
0
2
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
5
1
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
1
0
1
0
2
1
1
2
0
2
0
0
0
0
0
0
1
0
0
1
2
0
1
1
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
2
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
2
0
2
1
1
0
1
0
1
0
0
0
1
3
3
0
0
2
0
2
2
0
0
0
2
0
0
2
0
3
1
0
0
0
0
0
2
2
0
2
2
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
3
0
0
0
2
0
0
0
2
2
0
3
1
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
1
1
0
0
1
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
4
0
2
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
2
0
2
0
3
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
2
0
2
0
0
2
1
0
0
2
0
0
0
3
0
1
0
2
0
0
0
0
2
4
1
0
0
2
0
0
2
0
4
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
3
0
0
1
0
0
1
2
0
0
4
1
0
1
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
1
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
1
2
0
0
3
2
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
2
3
0
1
0
1
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
1
0
0
6
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
2
2
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
2
0
1
1
1
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
2
0
1
0
0
0
0
0
0
0
1
2
1
0
0
0
2
0
0
2
0
0
0
3
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
11
0
0
0
0
4
0
1
2
0
0
4
0
0
1
0
0
3
0
0
1
0
1
0
0
0
0
0
0
1
1
0
1
1
0
2
0
1
0
0
2
1
1
2
0
3
0
1
0
0
2
0
0
1
0
0
1
0
0
0
7
0
0
0
0
2
0
0
0
0
0
0
0
0
5
0
0
1
0
0
0
4
0
0
2
1
0
0
0
0
1
0
0
4
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
2
0
4
0
2
1
0
0
0
2
2
1
0
0
2
0
0
0
0
0
1
0
0
2
1
2
0
2
0
0
0
2
0
0
0
0
0
0
2
3
2
0
3
0
1
0
0
4
0
0
1
0
1
0
2
0
1
1
2
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
1
1
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
3
0
0
1
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
2
1
2
1
0
0
0
0
0
0
3
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
1
1
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
2
0
0
0
0
2
0
0
2
1
0
0
0
0
1
2
2
0
1
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
2
0
7
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
3
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
2
0
2
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
4
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
1
0
2
0
1
0
5
1
0
0
0
0
1
1
0
2
1
0
0
2
0
0
1
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
1
0
0
0
0
1
1
0
0
7
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
2
2
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
2
0
2
0
0
2
0
0
1
4
0
1
0
0
1
3
0
0
0
3
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
3
0
1
0
14
0
0
0
0
0
0
2
1
0
1
0
0
0
2
0
0
1
0
0
2
0
1
0
3
0
0
0
2
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
1
2
0
0
1
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
3
0
0
2
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
2
0
2
0
1
0
2
1
2
0
0
0
0
1
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
1
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
3
0
2
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
2
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
1
1
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
3
0
2
0
0
2
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
1
1
0
2
1
2
0
0
0
0
0
0
2
3
0
0
0
0
1
0
0
1
0
1
0
0
0
0
2
0
5
0
1
0
0
0
0
0
1
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
2
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
1
4
0
3
0
2
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
4
3
0
1
2
1
0
2
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
1
1
0
0
0
1
0
1
1
0
1
2
1
2
0
1
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
1
5
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
2
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
1
2
1
2
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
3
0
0
1
1
0
1
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
1
0
2
0
2
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
1
0
1
0
0
0
0
2
0
0
0
4
0
0
0
2
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
8
1
0
1
2
2
1
0
1
1
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
1
2
0
0
0
0
0
1
0
0
0
1
2
0
1
0
0
0
0
0
0
0
1
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
2
2
0
0
0
0
0
2
1
2
0
0
3
0
0
1
1
0
0
0
6
0
0
2
0
0
1
0
0
0
2
0
0
5
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
3
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
2
2
0
0
0
0
0
1
1
1
0
0
0
0
2
0
0
0
0
0
2
3
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
2
1
2
0
2
0
0
1
0
0
0
0
2
0
2
0
2
0
1
2
0
1
1
2
0
0
0
1
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
2
2
2
4
2
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
2
0
0
0
0
2
0
1
0
1
0
2
0
0
0
3
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
3
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
2
0
0
2
1
2
0
1
0
0
1
2
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
3
0
4
0
0
4
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
3
0
0
1
0
0
0
1
1
0
0
0
1
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
2
1
1
1
2
0
0
0
0
1
0
0
0
0
1
0
0
2
1
3
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
1
0
0
0
0
0
2
0
2
2
0
0
1
0
0
2
0
1
0
0
0
0
0
4
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
2
0
1
2
2
0
3
1
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
2
0
0
1
2
0
1
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
3
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
2
0
0
1
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
2
0
0
2
0
0
5
0
1
0
3
0
0
0
2
1
2
1
0
0
0
0
0
2
3
0
0
3
0
2
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
2
1
0
1
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
2
2
0
1
0
0
3
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
2
0
2
0
2
3
1
0
2
1
1
0
1
0
0
0
0
0
0
0
0
1
1
1
5
0
2
0
1
0
1
0
0
0
2
1
2
0
1
0
0
0
0
0
0
0
2
1
0
2
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
1
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
2
0
0
4
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
6
1
0
1
0
0
0
1
0
0
2
0
0
0
1
0
0
0
1
0
2
4
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
2
1
0
0
0
0
2
5
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
1
3
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
2
0
2
0
0
3
0
2
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
2
0
1
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
1
0
0
2
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
1
0
2
0
1
0
0
0
0
2
2
2
0
0
0
0
0
0
2
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
2
0
0
0
4
0
0
0
1
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
1
2
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
1
0
2
0
2
0
1
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
2
0
2
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
2
2
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
3
0
0
2
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
1
0
0
0
2
1
0
0
0
0
0
2
0
0
0
1
0
0
3
0
0
0
1
1
0
2
1
2
0
1
0
2
0
0
1
0
0
0
0
2
0
2
2
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
3
0
0
0
1
1
1
0
0
1
1
1
0
0
0
0
2
0
0
0
2
2
0
0
0
0
2
0
1
0
0
2
1
0
0
1
1
2
1
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
1
2
0
1
1
0
0
0
3
0
2
1
2
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
4
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
2
0
1
0
0
0
0
0
2
0
0
0
2
0
0
3
2
1
0
0
0
3
0
0
0
0
0
0
0
0
2
0
1
0
2
0
2
0
0
1
1
1
1
0
0
1
0
0
0
0
0
0
0
1
2
0
2
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
3
0
1
0
0
0
1
0
0
0
0
0
0
2
0
2
1
0
0
2
1
0
0
0
0
5
0
0
1
0
1
1
0
0
0
0
2
1
0
0
0
0
0
3
2
0
0
3
3
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
3
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
4
2
0
2
0
1
0
0
2
0
0
0
2
0
0
0
0
1
2
0
0
1
2
0
0
2
3
0
0
2
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
1
2
1
1
0
5
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
1
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
1
1
1
0
3
1
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
2
2
0
0
0
0
0
0
0
1
0
0
0
2
2
1
0
2
0
0
0
0
0
0
0
1
2
0
0
0
1
0
1
0
2
1
0
2
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
2
0
0
1
0
2
0
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
3
0
0
0
0
0
0
4
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
2
0
0
0
0
1
0
2
2
3
1
2
0
0
2
0
1
0
0
0
0
0
0
0
0
3
2
0
1
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
3
0
0
2
0
0
0
0
0
2
0
0
7
5
1
0
0
0
0
1
0
2
0
0
2
0
3
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
1
2
0
1
3
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
1
10
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
2
2
0
0
1
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
4
0
0
1
0
3
0
1
0
0
0
0
1
2
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
5
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
1
2
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
1
0
0
3
0
0
0
0
1
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
2
2
0
2
0
1
0
0
1
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
4
0
1
0
0
1
0
2
0
2
0
2
0
0
2
1
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
2
0
0
1
0
0
2
2
0
0
3
0
1
0
0
2
0
1
0
0
0
0
0
1
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
1
0
0
1
2
0
0
0
0
0
0
0
2
1
0
0
0
0
1
1
0
0
1
0
0
2
0
0
0
1
1
1
1
2
0
0
2
1
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
3
3
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
2
2
0
0
0
0
0
0
3
0
0
1
1
0
0
0
1
2
1
0
0
2
3
0
0
0
0
2
1
0
0
0
0
0
0
1
1
0
0
0
0
1
1
2
0
0
2
0
0
0
1
0
0
2
0
0
1
0
0
0
0
1
0
2
0
0
1
0
0
1
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
1
2
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
3
0
2
1
0
0
3
0
1
4
0
0
2
4
0
0
2
2
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
3
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
1
0
2
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
1
0
0
0
1
0
0
0
3
1
0
0
0
0
0
0
0
2
0
3
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
3
1
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
1
0
2
1
0
9
0
0
1
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
2
0
2
0
0
1
2
1
0
0
2
0
0
0
0
0
2
3
0
0
0
2
0
0
1
2
2
0
0
0
0
0
0
1
0
1
0
2
1
2
0
0
0
0
0
0
0
0
2
0
2
1
0
6
0
0
0
2
0
2
1
1
0
1
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
7
1
0
2
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
2
1
1
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
3
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
3
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
2
0
1
0
0
0
0
2
0
2
1
0
0
0
0
0
2
0
0
7
0
0
0
5
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
2
0
0
0
0
0
0
2
1
1
3
0
0
0
8
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
1
2
2
0
0
2
0
2
0
0
0
2
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
2
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
1
0
1
0
2
2
1
0
2
0
0
0
0
3
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
1
0
0
1
0
2
3
0
0
0
0
0
0
1
1
3
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
1
0
0
0
0
0
5
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
2
1
2
0
1
1
0
0
0
1
0
0
0
1
0
1
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
1
0
2
2
0
0
1
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
1
0
3
1
0
0
0
1
0
0
0
0
0
2
0
1
0
0
1
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
2
1
0
0
0
0
0
0
3
0
0
0
0
0
7
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
3
0
0
1
0
2
0
0
0
1
0
2
1
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
3
2
1
2
3
0
1
2
2
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
4
0
2
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
2
0
1
0
2
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
2
0
0
0
1
0
0
0
1
1
2
0
1
0
0
2
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
1
4
2
1
0
0
0
2
0
0
0
0
0
3
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
6
0
0
0
0
2
0
0
1
0
2
0
2
0
0
0
0
2
1
0
0
0
0
2
1
0
0
1
0
2
0
0
1
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
14
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
6
0
2
0
1
4
3
1
1
0
0
1
1
0
0
1
2
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
2
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
3
1
0
0
1
0
0
1
0
0
1
0
0
3
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
4
1
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
2
0
1
1
1
3
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
3
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
1
0
0
0
1
1
1
0
0
0
0
0
0
2
1
0
0
2
0
2
0
0
2
0
0
0
1
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
1
2
0
0
0
0
1
0
1
1
0
2
0
2
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
1
0
2
0
0
2
0
0
0
1
0
0
0
0
1
0
0
2
1
2
0
2
0
2
0
2
2
0
0
0
0
1
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
6
0
0
0
1
0
0
3
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
4
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
1
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
1
1
0
0
1
0
0
2
0
1
0
0
2
0
0
2
0
0
1
7
0
0
2
5
2
0
0
2
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
1
2
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
1
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
1
2
2
0
0
0
0
0
0
1
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
1
1
2
0
0
0
0
2
3
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
1
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
1
2
0
0
0
2
0
2
0
2
0
3
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
2
1
0
0
0
2
2
0
0
1
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
1
0
1
2
0
0
0
0
0
0
1
1
1
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
3
2
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
2
0
0
2
1
2
0
2
1
2
0
0
2
0
0
0
1
1
0
0
2
2
0
0
0
0
0
3
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
3
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
3
1
0
0
0
0
1
0
0
0
0
0
3
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
2
0
2
0
0
0
1
1
0
0
1
0
1
0
0
0
2
0
0
1
0
0
2
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
4
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
2
0
1
0
2
0
0
0
0
0
0
1
0
1
0
2
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
4
3
0
0
0
0
0
0
3
2
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
2
0
0
1
1
0
0
7
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
2
0
0
0
0
1
1
0
0
1
0
2
3
0
2
1
2
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
2
2
3
1
0
1
0
1
0
0
2
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
2
3
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
5
0
0
0
0
0
0
2
0
1
1
2
0
1
2
0
2
0
1
0
1
0
0
1
0
0
0
0
0
1
2
3
0
0
1
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
3
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
2
1
0
3
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
1
0
0
0
1
0
0
0
0
2
1
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
1
1
2
0
2
2
0
0
0
0
0
2
0
2
0
2
2
0
0
0
3
0
0
0
0
2
0
0
1
0
1
0
0
1
0
2
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
3
0
0
0
1
0
0
0
1
2
2
1
0
0
0
1
0
0
0
2
0
0
1
0
2
0
0
1
0
1
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
3
0
1
4
0
0
0
0
1
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
3
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
1
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
2
1
0
0
0
2
1
0
1
0
1
0
0
0
0
0
0
0
4
0
0
2
0
0
0
1
0
0
0
3
0
1
2
0
0
0
0
2
0
1
0
0
0
1
0
1
0
2
0
0
2
0
0
0
0
1
0
2
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
2
0
0
0
0
1
1
0
1
0
0
0
1
2
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
3
2
0
0
0
2
2
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
1
1
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
2
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
1
2
0
0
0
0
2
1
2
1
1
0
0
0
0
1
0
1
0
1
2
0
1
2
2
0
0
0
1
2
0
0
2
2
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
1
0
0
1
0
0
0
3
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
4
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
3
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
2
0
0
0
0
0
0
2
0
0
1
1
3
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
1
3
0
0
0
0
2
4
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
3
0
1
3
0
0
3
1
0
0
1
0
0
0
1
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
2
0
2
2
2
0
0
0
0
1
0
2
2
2
0
0
0
0
0
2
0
1
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
3
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
2
0
2
2
0
0
3
1
1
1
0
0
3
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
2
2
1
0
0
0
3
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
1
0
2
0
0
0
0
1
2
0
0
0
1
4
2
0
0
0
1
1
1
0
0
0
2
3
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
1
0
0
2
0
2
1
0
2
0
0
0
0
0
1
0
0
0
2
0
1
2
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
5
4
0
1
0
0
0
0
0
2
1
0
0
1
2
0
0
0
0
1
2
0
0
0
0
0
2
2
2
0
0
0
0
2
0
0
1
0
0
0
0
1
0
2
0
1
0
0
0
2
0
2
2
1
0
2
0
0
0
0
0
2
3
0
1
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
1
0
0
1
0
0
0
2
0
1
2
2
0
0
0
0
0
0
1
0
1
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
2
2
2
1
0
0
1
0
1
0
0
1
0
2
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
2
1
0
1
1
0
0
0
2
1
0
1
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
2
2
0
0
0
0
2
0
0
0
2
2
0
2
0
0
0
0
3
0
0
1
2
2
0
9
0
0
0
0
0
2
0
2
2
0
0
2
0
0
0
1
0
0
2
1
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
1
1
1
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
2
0
1
0
0
2
0
0
0
2
0
0
1
3
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
1
1
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
1
0
0
1
0
1
2
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
2
2
0
1
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
1
0
0
0
2
0
0
0
0
2
1
0
0
0
0
3
0
1
0
2
2
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
1
0
2
0
0
0
2
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
3
0
0
3
0
1
0
0
2
0
2
0
0
0
0
2
0
2
0
0
2
0
0
0
0
3
2
2
0
0
3
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
1
0
1
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
2
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
2
0
2
0
0
0
0
0
1
0
0
0
2
2
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
3
2
0
2
0
0
0
1
0
2
2
2
2
0
2
0
1
0
0
0
0
0
0
1
0
2
0
0
3
0
2
0
0
0
1
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
2
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
4
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
2
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
1
0
0
0
1
4
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
3
1
2
0
0
0
0
2
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
1
0
0
0
0
0
2
0
0
1
1
0
0
3
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
1
0
0
0
0
2
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
2
0
1
0
2
0
0
1
0
0
0
0
0
1
0
0
2
0
1
2
3
2
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
1
1
0
0
0
0
0
1
0
0
2
0
0
0
0
2
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
3
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
2
0
0
2
1
1
1
0
0
0
0
2
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
2
0
2
1
0
0
1
0
0
0
0
0
1
0
0
4
0
2
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
2
1
1
0
0
0
0
0
2
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
2
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
1
0
0
0
1
0
1
0
0
0
1
0
0
2
0
0
1
0
0
2
0
1
0
0
0
2
0
0
3
0
2
1
3
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
1
0
2
1
1
0
2
2
0
0
0
0
3
0
0
0
2
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
2
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
1
1
2
5
0
0
0
1
0
1
0
2
0
3
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
4
1
0
1
4
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
1
0
2
2
0
1
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
1
3
2
0
0
2
0
2
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
1
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
1
0
0
2
0
0
0
1
1
0
0
0
0
1
4
0
2
0
0
0
0
0
0
0
0
1
0
2
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
1
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
3
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
1
0
2
0
2
0
2
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
2
0
0
2
0
1
0
0
0
2
0
0
2
0
0
2
0
0
3
0
2
0
0
0
1
0
0
1
1
0
0
0
1
1
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
1
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
9
0
0
0
1
0
0
1
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
4
0
1
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
2
0
0
1
0
2
0
0
0
3
1
0
0
0
0
0
0
3
0
1
1
0
0
0
1
1
0
0
0
0
0
2
2
0
0
2
0
0
0
2
0
0
0
1
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
6
0
0
2
0
0
0
1
1
0
0
2
0
0
0
4
0
0
1
2
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
1
0
3
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
1
0
2
1
3
0
0
0
2
0
1
0
0
0
0
0
0
1
2
1
3
0
1
0
0
0
6
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
2
0
0
2
0
2
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
1
2
1
0
0
1
2
0
0
0
1
1
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
2
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
1
0
0
2
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
2
2
0
0
2
0
0
0
0
1
0
0
0
0
3
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
4
1
2
0
2
1
1
0
0
0
0
1
0
1
0
2
0
0
0
0
1
1
0
0
0
0
0
0
1
1
2
0
0
0
0
2
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
1
0
0
0
1
0
0
1
1
2
0
0
0
1
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
1
2
0
2
0
1
0
0
1
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
6
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
1
0
2
0
0
0
0
1
1
0
2
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
2
0
0
0
0
2
0
0
2
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
1
0
1
0
2
0
0
0
0
1
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
3
0
2
1
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
1
3
0
1
0
0
1
0
0
0
0
3
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
4
3
0
0
0
0
3
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
1
1
1
0
0
3
0
1
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
2
1
0
0
0
2
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
2
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
1
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
2
2
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
3
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
4
0
2
2
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
2
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
5
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
4
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
1
4
0
1
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
2
2
0
2
0
0
1
0
1
0
2
0
0
0
0
0
0
0
2
2
0
2
0
1
5
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
3
4
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
1
0
1
0
1
2
0
0
0
0
0
0
1
0
0
4
2
0
0
2
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
2
0
1
1
0
0
1
0
0
0
0
0
0
1
0
2
0
1
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
4
1
2
0
1
1
5
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
1
1
1
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
2
0
0
2
2
0
0
0
3
1
0
0
0
0
1
2
0
0
0
3
1
1
1
0
1
0
0
1
0
1
0
0
0
0
2
0
1
0
2
0
0
0
0
1
2
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
1
1
3
2
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
9
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
1
0
0
0
1
0
0
2
1
0
3
0
0
0
0
1
0
0
0
0
1
0
1
0
0
2
1
0
0
0
1
1
0
0
0
0
1
0
0
0
3
0
1
0
0
0
1
2
0
0
1
0
0
0
2
2
1
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
2
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
6
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
1
1
2
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
2
0
2
0
0
0
0
2
0
1
1
0
0
1
0
2
2
0
2
0
0
2
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
1
0
2
1
3
1
0
0
5
1
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
2
0
1
0
0
2
0
0
2
2
1
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
1
0
0
0
0
0
0
0
0
1
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
1
0
0
1
0
0
0
0
0
0
2
0
2
0
1
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
2
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
2
0
0
0
0
0
2
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
1
0
1
1
0
0
2
0
1
2
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
3
2
1
0
0
2
1
1
0
2
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
2
0
2
0
1
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
2
2
0
0
0
0
1
0
1
0
2
3
0
2
4
0
1
0
0
0
0
2
0
0
0
1
0
2
1
0
0
1
0
2
0
0
3
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
2
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
1
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
2
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
2
0
1
0
0
1
0
1
1
1
0
0
0
1
0
4
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
5
0
0
1
0
2
0
3
0
0
0
7
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
3
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
2
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
3
0
0
0
0
0
2
0
1
0
0
2
0
0
1
1
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
2
0
0
0
9
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
3
1
0
0
2
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
2
0
0
2
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
2
0
0
3
0
1
1
0
1
0
1
0
0
0
0
0
0
1
0
1
2
1
0
2
1
0
0
5
1
1
1
0
0
0
0
0
1
1
0
0
0
0
2
1
0
0
0
3
1
0
0
2
0
0
0
3
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
2
1
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
1
0
0
0
5
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
2
3
2
1
0
0
2
0
0
1
0
2
0
1
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
3
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
4
3
1
1
1
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
2
2
1
5
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
4
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
1
3
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
2
1
0
2
0
0
5
0
0
1
0
0
0
2
7
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
2
0
0
0
2
0
2
0
2
1
2
0
0
0
1
0
1
1
0
2
0
0
1
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
1
0
0
0
2
2
2
0
0
2
0
3
1
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
2
0
0
0
0
0
0
2
2
0
0
3
0
0
0
0
2
3
0
0
1
2
0
0
2
0
2
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
2
0
6
0
0
0
0
0
2
1
2
0
3
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
1
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
3
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
2
0
1
0
0
0
1
2
0
0
2
0
0
2
0
1
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
3
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
2
0
2
0
0
0
0
0
2
0
1
1
0
4
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
6
0
0
0
1
1
1
0
3
0
0
0
0
0
2
2
0
1
0
0
0
0
0
2
0
0
1
2
2
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
1
0
2
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
1
1
2
0
0
0
0
0
0
0
3
0
2
1
0
0
2
0
0
1
0
1
0
4
0
0
1
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
4
2
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
2
0
0
0
0
2
6
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
1
0
2
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
2
0
2
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
2
3
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
1
0
3
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
1
0
2
0
1
0
1
0
2
1
1
0
0
0
0
0
0
0
0
0
2
0
0
1
1
2
0
0
2
0
0
1
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
10
0
2
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
1
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
2
0
2
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
4
3
0
2
2
0
0
0
0
0
1
1
1
0
2
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
1
0
2
1
0
1
1
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
2
2
2
0
0
0
0
0
1
1
0
1
0
2
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
4
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
1
1
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
2
0
0
2
0
0
0
3
0
0
0
0
1
0
0
0
2
0
2
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
3
1
0
0
0
0
0
1
0
0
0
0
0
1
2
2
2
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
1
0
0
1
2
1
0
0
0
0
0
0
0
2
0
0
0
5
2
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
3
0
0
0
0
0
0
2
2
3
0
3
0
0
2
0
0
1
0
3
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
1
0
5
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
1
2
0
4
0
0
4
0
0
0
0
0
0
0
1
0
0
2
0
1
1
0
1
0
0
0
1
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
1
0
2
0
2
0
2
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
2
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
3
2
1
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
3
0
0
3
4
0
0
0
0
0
1
0
0
0
0
1
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
2
0
4
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
3
0
0
0
0
0
0
2
0
3
1
0
0
0
2
0
3
2
0
0
2
0
2
0
2
0
0
0
2
1
0
2
0
1
0
0
0
0
2
0
2
2
2
0
0
0
5
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
1
0
0
0
2
2
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
2
1
0
0
3
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
1
0
2
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
1
9
0
1
3
0
2
3
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
1
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
1
1
3
4
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
2
12
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
1
0
2
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
3
0
0
0
0
2
0
0
0
0
0
4
0
1
2
0
0
0
0
2
3
0
1
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
3
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
3
1
2
0
0
0
0
0
1
4
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
2
0
1
0
0
0
0
2
0
0
0
0
3
1
3
0
0
0
2
2
0
2
2
2
0
2
0
0
0
0
1
2
0
0
0
3
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
3
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
2
0
1
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
1
1
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
1
0
2
0
0
1
1
2
0
1
0
2
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
1
0
0
0
0
0
2
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
1
0
1
0
2
2
0
0
2
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
2
0
1
2
0
0
3
2
1
2
1
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
1
2
3
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
2
0
2
0
0
1
2
0
0
0
2
0
2
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
1
2
2
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
2
3
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
5
0
0
6
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
2
0
1
0
0
2
1
0
0
0
0
0
0
0
0
3
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
3
2
0
0
1
0
2
0
2
0
1
0
0
0
0
0
0
2
1
1
0
0
0
1
2
0
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
2
5
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
7
0
3
2
0
2
0
0
2
0
2
0
1
1
1
2
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
4
0
0
0
4
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
1
2
0
2
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
1
0
0
1
1
2
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
1
2
2
0
1
1
0
2
2
4
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
3
0
0
0
2
0
0
1
1
1
0
0
0
2
0
0
0
2
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
4
0
0
1
0
3
0
1
0
0
3
1
1
2
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
2
0
0
2
2
0
4
0
0
0
4
2
0
1
0
0
0
0
1
0
0
0
0
0
4
2
0
1
0
2
0
3
0
1
0
0
0
0
3
0
0
0
0
2
0
0
0
3
0
1
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
1
0
0
0
2
0
0
3
1
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
1
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
6
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
5
1
1
0
1
2
0
0
1
2
0
1
0
2
0
0
0
0
0
2
0
3
0
0
2
0
0
2
0
1
0
0
0
0
2
0
0
0
2
0
0
2
1
0
2
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
2
2
0
2
0
0
1
0
0
0
0
0
0
3
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
3
1
0
0
1
2
1
2
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
1
0
3
2
0
1
0
0
0
0
0
0
0
5
0
0
2
7
0
0
2
2
0
0
0
0
1
1
0
0
0
1
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
2
2
0
1
0
0
1
0
0
0
0
0
2
2
0
0
0
0
2
2
1
2
1
2
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
2
2
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
2
0
2
0
0
0
0
0
1
0
0
2
0
2
0
0
1
0
0
0
1
0
0
2
0
0
0
0
1
2
1
0
0
0
0
2
0
0
1
1
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
2
0
0
0
1
2
0
0
0
1
1
0
0
2
0
0
2
0
0
0
3
2
1
0
0
0
3
2
0
0
1
0
0
0
0
2
0
3
0
2
0
2
0
0
0
2
0
0
0
0
0
0
3
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
3
1
1
0
1
1
0
1
2
0
2
1
0
0
0
1
0
0
1
2
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
2
0
0
1
1
0
0
2
0
1
0
0
1
0
0
0
0
0
2
2
0
0
0
1
0
0
2
0
2
1
0
0
1
2
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
1
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
1
2
2
0
0
1
0
0
1
0
1
1
0
0
0
0
3
0
0
1
2
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
1
2
2
0
4
1
0
0
1
0
2
0
0
1
3
2
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
3
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
2
2
0
1
0
0
6
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
2
1
0
0
0
0
1
0
0
4
0
0
0
0
4
2
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
7
1
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
1
0
1
3
0
0
1
0
0
0
1
6
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
2
2
0
0
0
0
0
2
0
1
0
2
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
2
0
0
1
2
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
2
0
1
0
0
0
0
2
0
2
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
2
1
1
2
0
0
0
2
0
2
0
2
0
0
0
2
0
0
1
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
2
4
1
0
0
0
0
1
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
6
1
0
0
0
2
4
0
0
0
0
0
0
0
1
2
2
0
2
0
0
0
0
0
0
0
0
0
0
3
0
2
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
2
0
0
2
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
3
0
5
2
0
0
0
0
0
3
0
1
1
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
3
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
2
0
0
3
0
1
0
0
0
0
1
0
0
0
0
6
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
4
0
1
2
0
0
0
3
0
0
0
0
0
1
3
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
1
0
0
0
0
1
0
2
2
0
1
1
2
0
0
1
2
0
0
1
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
1
5
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
1
0
0
0
3
0
0
0
0
0
1
0
0
0
0
6
2
0
2
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
2
0
0
11
0
3
4
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
3
0
0
0
2
0
0
0
0
1
0
0
0
2
0
4
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
2
0
2
2
1
0
0
0
1
2
0
0
0
0
0
0
0
0
2
1
0
1
0
2
2
2
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
1
3
2
0
0
0
0
0
2
3
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
2
0
2
0
1
2
0
2
2
0
1
1
2
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
3
1
0
0
0
1
1
0
0
0
2
0
0
1
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
2
0
4
2
0
0
0
1
2
1
0
0
0
0
0
0
4
2
1
0
4
1
0
0
1
7
0
0
0
1
0
0
0
0
0
2
0
0
4
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
2
2
2
0
2
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
3
2
0
6
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
1
0
2
1
0
1
0
3
1
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
1
0
0
0
0
3
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
2
0
1
3
0
0
0
0
0
2
0
0
0
2
0
0
1
0
1
3
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
2
1
0
0
0
2
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
1
1
0
0
3
2
1
0
0
0
0
0
0
0
1
3
0
2
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
1
0
0
0
0
1
0
0
1
1
2
1
1
0
0
1
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
2
0
1
1
0
0
2
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
2
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
1
2
0
2
1
1
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
2
0
0
0
1
1
0
2
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
3
2
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
1
0
0
2
0
0
0
0
1
0
1
0
0
0
1
1
0
0
2
0
1
4
0
0
0
1
4
0
0
0
0
0
0
3
0
1
0
0
2
0
4
0
0
1
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
2
2
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
2
1
0
2
0
0
2
0
0
2
0
2
0
0
0
2
0
0
1
0
0
0
2
2
1
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
3
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
2
0
0
1
0
0
0
2
0
0
0
0
1
2
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
3
0
0
4
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
2
0
0
0
0
2
2
0
0
0
2
1
0
3
0
2
0
0
0
0
1
0
4
2
0
0
0
1
0
0
0
3
0
0
0
2
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
1
2
2
1
0
0
0
1
0
0
1
2
1
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
4
0
0
0
0
1
0
0
4
0
2
0
0
0
1
0
5
0
0
0
0
1
1
1
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
2
0
0
6
0
0
0
0
2
2
2
1
0
1
0
1
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
2
1
2
1
0
1
2
3
2
0
0
0
0
1
1
0
0
1
0
3
0
0
0
4
2
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
2
1
0
0
1
2
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
2
1
0
1
0
2
0
0
0
0
0
0
1
0
1
0
2
0
0
2
0
2
0
1
0
0
0
0
2
2
0
0
0
0
1
0
0
2
0
2
2
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
1
2
0
0
2
1
0
0
0
0
0
0
1
0
0
2
6
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
2
1
0
2
0
2
0
0
0
3
0
0
0
2
1
0
0
0
1
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
1
0
5
0
0
0
0
1
0
0
0
0
0
1
2
0
0
2
2
0
0
0
0
0
1
0
2
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
1
0
1
0
0
0
1
2
1
2
0
1
0
0
2
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
2
2
0
0
0
1
0
2
0
2
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
2
0
1
2
0
0
1
2
0
0
0
0
2
0
1
1
0
0
2
2
1
0
3
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
3
0
0
2
1
0
3
2
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
2
1
0
0
1
0
0
0
0
0
1
0
0
0
0
2
3
1
1
3
0
1
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
1
1
1
2
0
0
0
1
0
0
2
0
0
1
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
2
0
1
2
0
2
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
3
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
2
0
0
0
1
0
2
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
2
0
2
0
3
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
2
6
0
0
0
1
2
1
2
0
2
0
1
1
0
0
2
0
1
1
2
0
2
2
0
0
0
0
3
2
3
0
0
0
0
0
0
0
0
0
1
0
1
1
2
0
0
1
0
0
0
0
0
0
2
3
0
0
0
0
0
2
0
0
0
0
1
3
0
0
2
0
0
2
1
1
5
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
2
0
2
0
0
2
0
0
0
0
2
0
2
2
0
2
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
2
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
1
0
0
1
3
0
0
0
3
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
2
0
0
0
2
1
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
1
2
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
1
0
2
2
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
2
3
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
2
2
0
2
0
0
0
0
0
0
2
0
2
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
1
1
0
2
1
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
3
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
9
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
4
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
3
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
5
0
2
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
1
1
0
1
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
2
0
1
1
0
0
2
0
0
0
3
0
0
0
0
1
1
0
2
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
7
0
1
0
0
3
0
0
2
0
0
0
0
0
1
0
0
0
0
3
2
0
0
1
1
0
0
2
0
5
0
1
3
0
0
0
0
0
0
0
0
0
1
0
5
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
1
0
2
0
4
2
0
2
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
1
1
0
0
0
0
0
0
0
1
2
0
0
2
0
4
0
0
0
0
0
2
0
0
0
1
2
2
2
0
1
0
0
6
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
1
0
2
0
2
0
2
1
0
2
2
1
1
0
0
4
1
0
1
0
2
4
0
0
2
0
1
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
2
0
2
0
0
0
0
0
1
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
1
0
2
1
0
1
0
3
0
0
1
0
3
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
2
2
0
0
1
1
0
0
0
2
0
0
2
0
1
0
0
0
1
0
0
0
0
3
0
0
0
0
2
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
2
0
0
0
1
0
1
0
0
2
1
0
0
0
1
0
1
2
0
0
1
0
0
0
0
0
0
2
1
0
0
1
0
0
4
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
2
0
0
0
2
2
0
0
0
0
2
1
0
0
1
0
1
1
0
2
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
3
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
1
2
2
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
1
1
1
0
0
4
0
0
0
0
3
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
2
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
2
2
0
0
0
1
0
1
1
1
0
0
0
2
0
0
0
0
0
0
1
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
1
0
0
2
0
0
0
2
0
2
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
7
0
0
1
0
0
3
0
4
1
0
1
0
2
1
0
0
0
0
0
0
0
1
0
0
1
0
3
0
1
0
0
1
2
0
0
0
3
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
1
0
0
1
0
0
2
1
0
0
0
2
0
0
0
2
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
1
1
0
0
3
0
0
1
4
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
1
0
0
0
0
0
0
0
1
1
0
1
1
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
1
0
2
0
0
0
0
0
0
1
0
0
0
2
3
0
1
0
1
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
3
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
1
0
0
2
0
1
0
2
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
1
2
0
0
0
3
0
1
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
3
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
3
0
0
0
0
0
4
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
1
0
1
0
2
2
0
0
0
2
0
1
0
0
0
0
0
0
0
1
2
0
0
2
0
2
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
2
1
2
1
0
0
0
0
0
1
1
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
2
0
0
0
0
3
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
1
0
0
0
2
0
1
3
0
0
0
1
0
0
0
2
1
1
2
2
2
0
0
0
0
0
0
0
0
5
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
4
2
1
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
3
1
0
0
0
0
0
0
0
0
0
3
0
2
0
1
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
1
0
0
2
3
0
0
0
0
0
0
0
2
0
1
3
0
2
0
1
0
0
0
3
1
2
0
0
0
0
0
0
0
0
9
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
8
1
0
3
2
0
0
0
0
0
0
0
5
1
3
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
4
0
0
0
2
1
2
0
0
0
0
0
0
1
0
0
1
0
0
2
0
2
1
1
2
0
0
0
0
0
2
0
0
2
0
0
1
1
0
2
0
1
0
1
0
0
1
1
1
1
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
3
2
0
0
1
0
0
0
0
1
2
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
2
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
4
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
2
0
0
2
2
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
1
0
0
0
1
1
0
0
0
2
0
1
0
0
0
0
0
2
0
1
0
1
0
0
2
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
2
0
1
0
1
0
1
0
1
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
2
1
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
2
0
0
2
0
0
0
1
1
0
2
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
4
0
0
2
2
0
0
0
0
0
0
2
2
0
2
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
2
0
0
0
0
1
1
0
0
0
2
2
0
1
0
0
0
0
0
0
1
0
1
0
0
1
2
2
0
0
0
1
1
2
0
0
0
1
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
2
0
2
4
0
0
0
2
0
0
2
0
3
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
5
1
0
0
0
2
0
1
0
1
0
0
0
2
0
0
1
2
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
2
0
2
0
0
3
6
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
3
0
0
1
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
1
0
2
0
0
0
0
2
1
0
1
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
2
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
2
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
4
0
0
0
3
0
0
0
0
2
0
0
2
0
0
2
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
2
0
1
1
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
2
1
1
0
0
0
2
0
0
0
0
1
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
2
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
1
2
0
1
0
5
0
0
0
0
0
2
0
0
1
0
0
1
2
0
1
2
4
2
0
0
0
2
0
0
0
0
2
1
0
1
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
2
0
0
4
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
3
0
0
0
0
0
2
5
2
2
1
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
2
0
3
0
0
0
0
0
2
0
3
2
2
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
1
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
2
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
2
1
0
0
2
0
0
0
0
0
0
4
0
0
1
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
1
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
5
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
2
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
9
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
3
0
3
4
0
0
0
0
0
0
0
1
1
2
2
2
0
0
0
3
2
1
1
1
0
2
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
1
0
2
3
0
0
0
0
1
0
0
1
2
0
0
1
0
0
3
0
0
0
2
2
0
0
1
0
0
0
2
1
1
0
2
0
0
0
0
2
0
0
0
2
0
12
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
1
0
0
2
0
1
2
2
0
0
0
0
1
0
1
0
2
3
1
0
0
0
0
0
1
0
0
0
1
0
2
0
2
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
1
0
0
0
0
3
0
0
1
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
1
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
1
0
2
1
0
0
1
0
0
0
0
0
0
0
1
2
1
0
0
0
2
0
0
2
0
0
4
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
2
2
0
0
0
1
0
2
2
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
2
0
2
2
1
4
1
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
2
2
0
0
1
1
0
1
0
0
2
0
0
0
0
2
0
0
0
1
2
0
0
2
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
1
3
0
1
0
2
1
0
2
0
0
0
0
0
2
0
2
0
3
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
2
2
1
0
0
2
2
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
1
2
3
0
0
0
0
0
0
0
0
8
8
1
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
5
1
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
3
2
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
2
5
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
2
3
0
0
1
1
1
1
1
0
2
0
0
1
0
0
0
1
1
1
0
0
0
2
0
2
3
0
0
0
0
0
0
0
0
4
0
2
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
5
0
1
2
0
0
2
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
2
0
2
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
3
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
5
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
1
0
0
0
2
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
1
2
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
2
0
0
0
0
2
0
0
0
0
0
2
0
3
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
1
1
0
0
1
0
1
0
0
2
0
0
0
0
2
0
0
0
2
3
2
2
2
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
6
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
2
2
0
2
0
1
0
1
0
0
0
0
0
1
0
2
1
0
1
6
1
2
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
5
0
1
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
5
0
1
0
0
1
0
0
1
0
0
0
0
3
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
4
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
1
1
0
0
1
0
1
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
1
1
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
4
0
0
1
1
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
6
1
0
0
0
0
0
0
2
0
1
0
0
0
0
4
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
3
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
3
1
1
2
0
0
0
0
2
0
2
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
3
0
1
0
0
1
0
0
0
2
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
1
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
8
0
0
1
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
5
0
3
0
2
1
1
0
0
1
0
1
0
0
2
1
0
0
2
0
0
0
3
0
1
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
2
0
0
0
0
0
1
1
3
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
2
2
0
0
0
2
1
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
2
0
0
0
0
2
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
6
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
2
2
1
2
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
2
1
0
2
2
1
0
0
0
0
0
7
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
4
0
2
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
2
2
0
0
0
0
0
0
0
2
2
0
1
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
2
1
0
1
0
0
0
2
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
4
0
1
0
0
0
4
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
1
0
0
0
0
2
0
3
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
3
0
0
2
1
0
2
0
0
1
0
2
0
0
0
0
1
0
0
1
0
1
0
1
0
0
2
2
0
0
2
0
0
0
1
0
0
2
1
0
4
2
0
0
0
1
3
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
2
1
0
1
0
0
2
3
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
2
2
0
2
2
0
0
0
1
0
1
2
1
0
2
0
2
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
5
0
0
0
1
2
0
0
0
2
0
0
2
0
1
0
0
0
2
0
3
0
1
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
1
0
0
1
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
8
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
2
0
1
0
0
0
0
2
0
0
0
2
2
0
0
0
0
2
1
2
0
0
0
0
0
0
2
0
0
2
0
1
0
0
2
0
0
1
0
1
1
0
0
2
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
4
0
2
1
0
1
1
1
2
3
1
0
2
1
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
1
2
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
1
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
3
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
1
0
2
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
2
3
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
1
0
0
0
0
0
2
0
1
0
0
0
0
0
4
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
1
0
0
0
0
1
1
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
1
0
0
2
0
0
2
0
0
0
3
0
0
0
0
0
0
1
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
1
0
0
0
1
0
2
0
0
0
0
1
1
0
1
2
1
0
0
4
0
0
3
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
3
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
2
0
0
2
1
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
2
0
3
0
2
0
0
0
0
0
0
2
2
0
1
1
0
0
0
0
0
1
0
0
1
2
1
0
2
0
0
0
2
0
3
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
1
0
2
0
0
1
0
0
2
0
0
0
2
0
0
0
2
0
0
2
0
2
0
0
3
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
2
7
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
1
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
1
1
0
0
0
0
0
3
1
2
0
4
0
0
2
0
0
0
0
3
0
0
0
1
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
3
2
0
0
1
0
1
0
3
2
0
1
1
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
1
0
0
0
2
2
0
2
0
0
0
0
3
0
0
1
0
0
0
0
0
2
0
0
1
0
2
0
2
4
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
4
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
3
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
5
1
0
2
0
0
0
0
0
0
7
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
4
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
1
0
4
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
1
2
0
3
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
1
0
2
1
0
0
0
0
3
0
0
0
0
0
0
0
2
1
2
0
0
0
1
0
0
1
1
1
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
5
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
7
0
0
0
1
1
0
0
3
0
0
1
0
2
0
0
0
2
0
0
0
0
0
2
1
0
1
1
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
3
2
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
2
0
0
0
2
0
1
1
1
0
0
0
0
1
0
2
0
0
2
1
0
0
2
2
0
0
0
1
0
0
1
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
13
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
2
0
0
2
2
3
0
0
0
0
0
0
1
4
0
0
0
2
1
0
8
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
1
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
2
0
0
0
4
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
2
2
0
0
0
1
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
3
0
0
1
1
1
0
0
4
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
2
0
1
0
0
1
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
2
2
2
0
3
0
0
0
1
0
0
1
0
0
0
0
5
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
2
1
0
1
0
2
0
0
2
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
2
0
0
0
2
0
0
1
0
0
1
0
3
0
0
1
1
1
0
0
2
0
1
1
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
2
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
5
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
2
1
2
0
0
2
0
0
1
0
2
0
0
2
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
1
1
1
0
0
2
0
0
0
0
2
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
4
1
0
0
0
0
1
3
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
2
2
0
1
0
2
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
1
0
0
2
0
1
0
1
0
0
0
0
0
0
2
0
0
0
1
4
0
0
1
0
0
3
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
1
0
2
0
1
0
2
0
0
0
0
2
0
3
0
0
0
2
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
1
1
2
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
2
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
1
2
0
0
2
0
0
1
6
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
2
0
0
2
2
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
4
0
0
4
1
0
0
1
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
1
0
2
2
0
3
1
0
2
0
0
2
2
0
2
1
0
1
0
0
0
0
0
0
0
3
0
0
0
2
0
1
0
0
0
0
0
1
0
0
1
3
0
0
2
1
0
2
0
0
0
0
0
0
1
0
0
1
1
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
1
1
0
2
0
0
0
0
0
1
1
2
1
0
4
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
2
0
0
3
2
0
1
1
1
0
2
1
2
0
0
2
0
0
0
0
1
1
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
3
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
2
0
1
0
0
1
2
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
1
0
0
2
1
2
2
0
3
0
0
0
0
0
2
0
0
0
0
0
1
0
4
2
0
0
0
2
2
2
1
0
0
0
0
0
2
2
0
1
0
1
0
0
0
2
3
0
0
0
0
2
0
0
0
0
1
0
1
1
0
0
0
0
0
4
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
1
0
0
4
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
2
2
0
1
0
0
1
0
0
0
0
2
2
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
3
1
1
0
2
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
3
0
0
1
1
0
2
0
0
0
4
0
0
0
1
0
0
2
0
0
0
0
2
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
1
0
0
1
1
0
0
1
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
2
0
0
2
2
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
8
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
2
3
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
1
1
0
0
2
1
0
2
6
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
2
0
2
0
1
0
1
0
0
1
2
0
0
0
0
0
0
2
1
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
3
0
0
0
0
1
0
0
2
0
4
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
2
0
2
0
0
0
0
3
0
0
0
1
0
2
1
0
0
0
0
2
0
0
1
1
3
0
0
0
1
0
2
0
2
0
0
0
0
0
1
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
3
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
2
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
3
1
2
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
7
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
4
2
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
2
0
0
2
0
3
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
2
0
0
2
0
0
0
0
0
0
0
1
1
2
1
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
2
1
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
3
1
1
1
0
0
0
2
2
0
1
0
0
1
2
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
3
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
1
2
0
0
1
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
1
2
2
0
2
0
5
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
2
0
2
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
3
0
1
0
0
3
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
1
0
0
4
0
2
1
0
0
1
0
2
0
2
0
0
1
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
1
3
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
1
0
2
0
1
0
0
0
3
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
1
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
2
0
0
0
1
0
4
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
2
3
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
1
0
0
2
1
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
2
1
0
0
0
0
0
0
0
3
0
1
0
2
2
0
0
0
1
0
0
0
1
2
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
2
2
2
0
0
2
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
2
0
0
0
1
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
3
0
0
0
0
1
0
2
1
1
0
2
0
0
0
0
1
1
0
0
0
5
0
1
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
1
4
0
0
0
3
3
0
0
1
2
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
4
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
2
0
0
2
2
0
1
0
0
0
0
0
0
0
2
0
0
2
0
1
0
1
1
2
1
0
2
0
1
0
0
0
0
0
0
2
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
2
0
0
0
2
0
1
0
1
0
0
0
0
0
1
0
4
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
4
1
0
2
2
1
0
1
0
1
0
0
0
0
0
1
0
0
2
0
0
2
0
2
0
0
0
1
0
1
0
0
0
0
1
1
0
0
1
2
3
0
1
1
0
1
0
0
0
0
0
2
0
0
2
1
1
1
0
0
0
2
2
0
0
0
0
1
2
1
0
0
2
3
3
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
3
2
0
0
0
1
0
0
0
0
0
2
0
0
1
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
2
1
2
0
0
0
8
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
1
0
2
0
0
2
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
5
0
0
0
0
0
2
1
0
0
1
2
0
0
0
0
0
1
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
1
0
2
1
0
0
0
0
0
0
2
2
2
0
0
1
1
0
1
0
1
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
1
0
6
0
0
0
0
0
3
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
1
0
0
0
0
0
2
0
1
0
7
0
0
0
2
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
7
1
0
0
0
0
0
0
1
0
0
0
0
0
9
0
2
0
0
0
5
0
0
2
0
0
2
2
2
0
0
0
0
1
0
0
0
0
2
1
0
2
0
0
2
0
0
0
2
0
0
0
2
1
0
0
1
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
1
0
2
0
0
0
2
0
1
0
2
0
0
1
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
1
0
0
0
1
0
2
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
1
2
0
3
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
2
2
0
0
2
0
2
2
0
0
0
1
1
3
0
0
0
0
2
3
0
0
0
0
2
2
2
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
1
3
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
2
1
0
0
0
0
1
0
2
0
0
0
3
0
0
0
2
0
1
0
1
2
0
0
1
0
0
0
1
0
5
1
2
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
2
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
1
2
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
3
0
1
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
1
0
0
0
1
0
1
0
2
0
2
0
0
0
0
0
1
1
1
5
1
1
0
0
2
2
0
0
1
0
2
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
3
0
0
0
0
1
1
3
0
0
0
0
1
0
0
0
0
2
0
1
2
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
3
0
0
0
4
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
1
0
2
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
1
0
0
0
2
3
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
4
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
2
1
0
0
2
0
3
0
0
0
1
2
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
4
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
2
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
5
2
0
1
0
0
1
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
2
2
0
2
0
0
2
0
2
0
0
0
1
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
2
0
0
2
0
0
0
2
0
2
0
0
0
1
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
2
2
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
2
6
0
3
4
0
2
0
0
0
1
1
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
4
0
1
0
0
0
0
0
0
1
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
1
0
0
0
0
0
2
2
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
4
0
0
3
0
1
2
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
4
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
6
2
1
0
2
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
2
1
0
0
0
0
0
2
1
1
0
1
1
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
1
3
4
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
1
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
1
1
2
0
8
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
1
2
1
0
0
0
0
1
1
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
1
0
3
0
0
1
0
1
2
0
0
0
2
0
0
0
1
0
0
0
1
0
1
0
2
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
3
2
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
3
0
1
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
2
2
0
0
0
1
1
0
2
1
0
0
0
0
1
0
0
0
2
1
0
0
0
0
1
0
0
0
1
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
2
0
1
0
1
1
3
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
2
1
1
0
0
0
1
0
3
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
2
3
0
3
0
0
2
0
0
0
0
0
0
1
2
0
1
0
0
1
0
1
1
3
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
2
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
2
1
0
2
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
3
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
2
0
0
0
0
4
0
1
2
0
0
0
0
2
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
2
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
1
1
1
1
0
1
0
0
1
1
0
0
2
1
0
0
0
0
0
0
0
0
1
1
2
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
2
2
0
0
2
0
0
2
0
1
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
3
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
3
1
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
2
0
0
0
0
2
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
1
0
0
0
1
0
2
0
0
0
2
0
1
2
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
2
0
2
0
0
5
0
0
1
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
2
3
1
0
0
0
0
2
0
0
5
1
2
0
0
0
2
0
0
0
2
0
0
0
2
2
3
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
1
1
0
0
3
2
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
3
0
1
0
0
0
0
1
0
1
1
0
0
1
0
0
0
1
0
0
0
2
1
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
1
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
4
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
8
1
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
1
0
0
0
3
0
0
0
1
2
1
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
9
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
5
0
0
0
2
0
2
4
0
0
0
0
0
2
0
0
2
1
0
3
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
2
2
0
0
0
0
1
3
0
0
0
0
7
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
1
0
1
0
3
0
3
0
0
0
1
2
3
2
0
0
0
0
1
0
0
1
0
0
0
2
1
2
0
1
0
0
0
0
0
1
0
0
0
1
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
1
1
5
0
2
0
0
0
0
0
0
0
2
0
2
0
2
2
1
0
0
0
0
0
1
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
2
0
0
1
1
0
2
0
2
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
2
0
2
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
2
2
0
0
14
0
1
0
0
0
0
0
1
0
0
0
0
5
0
1
0
1
1
0
0
0
2
0
1
0
1
0
2
0
0
1
2
0
0
2
0
0
0
0
2
0
1
0
3
1
2
2
0
0
0
0
0
1
0
0
0
1
0
1
2
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
3
0
0
0
2
0
2
1
0
0
0
2
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
1
1
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
4
2
0
1
2
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
5
0
2
0
1
0
0
2
2
0
0
0
0
0
0
2
0
2
0
2
0
0
0
2
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
3
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
2
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
3
0
0
0
0
1
0
0
0
1
3
2
0
0
1
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
2
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
10
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
3
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
2
2
0
0
1
0
0
0
2
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
3
1
0
0
0
0
2
2
0
0
0
0
0
0
0
1
2
1
0
0
0
0
1
2
0
0
2
0
0
0
2
2
0
4
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
2
2
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
1
2
3
0
1
0
0
0
0
1
0
0
0
1
0
0
2
0
0
2
0
0
0
0
2
0
2
0
3
0
1
0
2
0
0
0
0
0
1
3
2
8
1
0
0
1
0
4
1
0
0
0
0
2
0
0
0
0
1
1
2
0
1
0
0
0
0
2
0
1
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
1
1
0
1
2
0
0
0
0
0
0
0
0
3
1
0
0
2
1
0
1
0
0
0
0
2
0
0
1
1
2
0
0
0
0
3
2
0
0
0
0
2
0
2
2
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
5
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
4
1
0
0
2
0
2
0
0
0
2
0
2
0
2
0
0
0
2
0
0
1
0
1
0
2
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
3
2
2
0
0
0
0
0
2
1
2
0
1
0
0
5
0
2
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
1
0
1
0
0
3
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
1
3
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
1
2
0
0
1
0
1
1
2
1
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
2
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
1
0
0
0
2
0
0
0
0
0
1
1
2
0
1
2
0
3
0
1
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
2
0
2
0
0
2
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
4
2
0
2
1
0
0
1
0
0
1
0
2
0
0
1
0
0
0
1
2
2
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
2
0
0
1
0
0
0
2
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
1
0
2
0
1
0
0
2
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
1
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
2
2
3
0
0
0
0
0
0
2
0
5
3
0
1
2
1
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
1
0
0
1
1
0
0
0
1
0
1
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
2
2
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
2
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
2
4
0
0
2
0
0
0
0
0
2
0
0
4
0
0
2
0
2
2
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
2
0
0
2
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
3
5
2
0
0
0
0
0
0
4
0
0
0
0
3
0
0
2
3
0
0
0
0
0
0
1
0
2
1
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
2
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
1
0
5
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
2
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
4
2
0
0
2
1
0
0
0
2
1
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
3
0
4
0
0
0
1
0
0
0
0
2
0
3
2
0
0
0
0
0
1
0
0
1
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
1
1
2
0
2
0
1
2
0
2
1
0
0
0
0
0
1
4
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
5
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
3
0
0
2
2
0
0
1
1
2
0
1
0
0
1
0
1
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
3
0
0
5
0
0
1
1
0
1
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
1
0
0
2
0
0
4
0
0
0
1
0
0
0
2
0
0
0
0
1
0
7
0
2
2
2
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
2
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
1
2
0
0
2
0
0
0
0
0
0
0
0
2
3
0
0
0
3
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
2
0
1
0
2
0
1
0
0
0
0
1
0
0
1
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
2
1
0
0
0
0
0
1
0
0
2
0
1
0
1
0
0
0
0
0
0
0
5
2
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
2
0
0
0
0
0
0
0
1
2
0
0
0
1
0
1
5
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
3
0
0
2
0
0
0
0
0
0
3
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
1
0
0
0
5
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
3
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
1
0
2
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
3
0
1
0
5
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
3
1
2
0
0
1
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
2
4
0
0
0
4
0
0
0
1
0
0
3
0
7
0
0
0
0
2
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
1
0
2
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
5
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
2
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
2
1
0
0
1
0
1
0
2
2
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
1
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
3
1
0
2
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
2
0
1
0
1
2
0
0
1
0
0
1
0
0
2
0
0
0
2
0
1
1
0
0
0
0
0
2
0
0
0
3
0
2
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
2
3
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
1
0
3
0
3
1
0
0
0
0
0
0
6
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
6
0
1
0
0
0
0
0
0
0
0
0
0
3
1
0
2
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
2
0
0
0
0
3
2
0
0
0
2
1
0
0
0
0
1
2
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
2
0
0
2
0
0
0
0
3
0
0
0
0
1
0
0
1
0
2
0
2
0
1
0
0
0
0
2
0
1
1
1
0
0
0
1
0
2
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
2
1
0
0
0
1
2
0
1
1
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
8
2
0
0
0
0
2
0
1
0
0
2
2
0
0
1
0
0
1
1
2
0
1
1
0
0
2
0
0
2
0
0
2
0
0
4
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
3
0
1
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
1
3
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
1
0
0
1
1
2
0
0
0
0
0
2
2
0
0
0
0
1
3
0
0
0
0
4
3
1
0
0
0
0
2
2
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
4
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
2
0
0
0
0
3
0
0
0
3
0
0
1
0
1
2
0
0
0
0
2
1
0
3
0
0
1
0
0
0
1
0
0
0
0
2
1
1
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
1
0
1
3
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
3
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
2
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
2
2
0
0
1
0
1
0
0
0
0
3
0
0
0
2
0
6
0
0
5
0
0
2
0
0
0
0
0
0
0
3
2
0
0
0
1
1
0
0
0
0
0
1
0
2
2
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
2
2
0
3
0
1
0
0
3
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
4
1
0
0
0
0
0
1
2
1
1
0
0
0
0
5
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
2
0
0
4
2
0
2
0
0
2
3
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
3
0
0
0
2
2
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
1
0
0
2
1
0
0
3
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
8
0
0
0
0
2
0
1
0
0
0
2
0
0
3
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
2
2
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
2
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
2
0
0
0
2
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
1
0
1
2
0
0
1
0
0
1
3
0
0
2
2
0
0
2
0
0
1
1
0
0
0
1
0
0
2
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
1
0
1
0
0
2
0
0
0
0
1
0
0
0
2
2
1
0
0
1
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
5
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
1
0
2
0
0
0
1
0
0
0
1
0
2
1
2
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
3
0
0
0
3
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
2
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
2
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
1
0
0
0
0
0
1
2
1
2
0
1
0
0
0
2
1
1
0
0
1
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
2
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
1
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
3
1
2
2
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
3
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
1
0
0
0
2
0
0
0
0
2
0
0
2
0
1
0
1
1
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
2
2
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
1
1
0
4
0
0
2
2
0
1
0
0
0
0
1
0
0
0
0
2
2
7
3
0
2
1
2
0
2
3
0
0
0
0
0
4
2
0
0
2
2
2
0
0
0
2
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
2
1
0
0
0
0
2
1
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
1
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
2
0
2
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
3
0
2
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
3
1
2
0
1
0
0
0
1
0
1
1
0
0
0
0
0
2
2
2
0
0
0
0
0
1
0
0
0
2
2
0
0
0
3
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
4
1
2
0
1
0
0
1
0
3
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
1
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
1
1
0
3
0
0
1
1
0
1
0
8
1
1
1
0
0
0
0
2
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
3
0
1
2
1
0
1
0
0
0
0
0
0
0
0
3
2
2
2
1
0
1
0
2
1
0
2
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
1
0
0
1
0
0
0
2
0
0
0
2
2
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
2
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
2
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
1
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
2
1
0
1
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
1
0
0
0
0
0
0
0
1
0
2
1
0
2
2
0
0
0
8
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
2
1
0
2
0
1
0
0
2
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
3
0
0
0
0
0
1
2
2
0
0
2
0
0
0
1
2
0
3
2
0
0
0
0
3
0
0
0
0
1
0
0
0
2
2
0
0
0
0
1
1
1
1
0
0
0
0
2
0
0
1
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
10
2
0
2
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
5
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
2
0
2
1
1
2
0
0
0
0
1
0
1
0
0
5
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
1
0
0
1
2
0
0
2
1
2
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
3
0
0
0
0
1
0
0
1
0
1
0
1
2
0
0
0
0
5
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
1
0
0
0
0
0
2
0
0
0
2
2
0
0
2
0
0
0
0
0
0
2
2
1
3
0
0
0
1
0
2
1
2
0
0
0
0
0
3
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
3
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
1
0
0
1
1
0
0
0
0
3
0
1
0
0
2
0
0
0
0
1
1
0
0
2
0
0
0
2
1
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
2
0
3
0
0
2
0
0
1
1
0
0
0
0
0
0
2
1
0
0
2
0
0
2
2
1
0
0
0
0
0
0
0
1
1
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
2
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
2
2
1
0
2
0
0
0
0
2
0
0
1
0
4
0
0
0
1
0
0
0
0
1
1
1
0
0
1
1
1
0
1
0
0
0
2
0
2
0
0
0
3
1
0
0
1
1
2
2
0
3
0
0
0
0
0
0
0
2
0
0
2
2
2
1
0
2
0
2
3
1
1
0
0
0
1
0
2
0
0
0
2
0
0
0
2
0
0
1
2
1
0
0
1
0
2
0
0
0
1
0
3
0
2
1
0
1
0
0
0
0
0
5
0
0
0
0
0
2
1
0
0
1
1
2
0
4
1
0
2
2
0
0
2
0
0
0
0
0
2
1
2
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
1
0
2
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
2
0
0
1
2
0
0
0
1
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
2
2
0
0
1
2
2
0
0
1
1
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
2
0
1
0
0
0
2
0
0
1
0
0
0
1
2
0
2
0
0
1
0
1
0
0
0
0
0
2
0
0
0
1
0
2
0
0
1
0
0
0
1
1
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
3
0
0
1
2
1
0
1
0
3
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
1
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
1
0
1
1
0
0
0
1
0
1
0
2
0
0
0
0
2
0
1
0
1
0
0
0
2
2
3
0
0
0
1
0
1
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
4
0
0
0
9
1
0
0
0
0
0
2
0
1
2
0
1
1
0
1
0
0
2
1
2
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
4
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
3
2
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
2
0
2
2
0
0
1
0
2
0
1
2
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
1
4
0
2
0
0
0
2
0
1
0
2
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
3
0
0
0
2
1
0
0
0
0
0
0
0
0
1
2
3
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
1
2
1
0
0
1
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
2
0
1
0
2
2
2
2
0
8
1
0
0
1
1
0
1
0
1
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
2
0
0
2
0
3
0
1
0
1
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
4
0
1
0
0
1
0
0
0
2
2
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
2
2
0
1
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
2
2
0
0
0
0
1
0
0
2
0
1
0
0
0
2
0
0
0
2
0
1
1
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
3
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
3
0
0
0
9
1
0
0
2
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
3
0
1
0
0
2
1
1
0
0
0
0
0
0
1
0
3
0
0
0
1
0
0
0
1
0
0
1
0
0
0
3
0
0
0
0
0
1
0
2
1
0
2
1
8
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
1
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
3
0
0
0
1
1
0
0
0
0
0
0
3
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
5
4
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
3
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
1
2
0
10
0
2
0
0
1
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
1
0
0
1
4
1
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
2
0
0
0
1
0
0
0
0
3
1
0
2
0
0
0
1
0
0
0
0
7
1
1
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
1
0
0
0
1
1
0
0
1
0
0
2
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
3
0
0
0
0
0
2
1
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
2
0
0
0
0
0
0
5
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
2
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
1
2
2
0
3
2
0
2
1
0
0
0
3
0
0
2
2
1
2
0
0
0
1
0
3
0
0
1
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
2
2
0
2
0
0
2
0
0
0
1
2
1
7
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
4
0
0
2
0
0
1
0
0
1
0
0
2
0
0
0
1
3
1
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
2
1
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
3
0
0
0
0
6
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
2
2
0
2
0
1
0
0
2
0
0
0
0
0
0
0
2
2
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
1
2
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
2
1
0
0
0
2
2
0
0
0
0
0
0
0
4
2
0
2
0
0
2
2
0
2
0
0
0
1
0
3
0
0
0
0
1
1
0
1
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
3
3
0
0
1
0
4
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
2
0
0
2
0
2
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
2
0
0
0
0
1
0
1
0
0
1
0
0
0
2
1
0
1
0
2
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
2
0
0
2
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
7
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
2
0
0
1
2
1
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
2
2
6
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
2
0
2
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
1
1
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
1
0
0
2
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
3
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
2
1
0
0
0
0
1
0
3
0
2
0
2
2
2
0
2
2
1
2
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
2
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
2
1
0
0
0
0
2
0
0
0
0
1
1
0
5
2
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
1
1
0
1
0
0
2
0
0
1
0
2
0
0
1
0
3
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
1
1
0
1
0
0
1
0
2
1
0
1
0
0
0
0
5
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
2
2
0
2
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
2
0
0
0
0
0
2
0
1
1
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
1
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
2
0
1
0
0
1
3
1
2
0
1
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
2
0
1
2
0
4
0
0
0
0
0
1
0
2
0
0
0
1
0
0
1
1
0
0
0
2
0
0
0
0
0
1
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
2
0
2
0
0
2
0
2
0
0
0
1
0
3
0
3
1
0
1
1
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
4
0
3
0
0
0
0
0
2
2
3
1
0
2
0
1
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
1
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
1
2
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
1
0
1
2
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
1
0
1
1
2
0
0
1
2
0
0
1
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
2
0
2
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
6
0
0
0
0
0
0
2
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
2
3
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
3
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
3
0
0
0
2
0
0
0
0
0
2
0
0
0
2
2
0
0
2
0
2
0
0
0
0
0
3
2
2
2
0
2
0
0
0
1
4
2
0
0
0
2
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
1
1
2
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
3
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
2
1
0
0
2
0
2
1
0
0
0
0
2
2
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
5
0
0
0
3
0
2
1
0
0
0
0
0
0
1
3
0
0
0
0
0
0
2
0
0
0
0
0
4
0
0
0
1
0
0
0
0
1
0
0
1
2
0
0
1
2
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
3
1
0
2
0
2
1
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
1
1
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
2
4
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
2
0
3
0
2
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
2
1
2
0
1
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
1
2
0
0
1
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
2
0
0
0
1
0
2
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
1
0
0
4
0
0
0
0
0
1
0
0
1
0
5
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
2
0
1
2
0
2
0
2
0
0
4
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
2
0
2
2
2
0
0
1
0
2
3
1
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
2
0
0
0
0
1
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
2
1
0
3
0
0
0
1
1
0
2
1
0
1
0
0
0
0
0
0
0
0
0
6
1
2
0
0
0
3
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
2
1
0
0
2
1
0
2
2
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
1
0
2
6
0
0
0
0
2
2
0
2
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
2
0
0
0
2
2
2
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
2
0
1
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
2
0
0
0
1
0
1
4
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
1
0
0
7
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
1
0
1
0
0
2
0
1
0
1
0
0
0
2
0
0
0
1
0
2
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
2
0
0
1
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
1
0
2
0
0
0
1
2
0
0
0
2
1
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
2
0
2
0
1
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
4
1
0
1
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
4
0
1
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
5
0
0
1
0
0
0
0
1
0
0
0
0
0
2
2
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
3
0
1
7
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
3
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
2
1
0
2
0
1
1
0
0
2
0
1
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
1
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
2
0
1
0
3
1
0
0
0
2
0
0
0
0
1
2
2
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
2
0
2
0
1
0
0
2
0
0
2
1
1
0
0
1
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
3
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
2
3
0
0
0
0
0
0
0
1
2
1
0
0
1
0
3
0
0
1
0
0
3
0
2
1
0
0
0
0
0
1
0
0
3
0
0
0
1
0
2
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
2
0
0
0
0
0
0
0
2
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
4
0
0
0
0
1
1
0
0
0
0
0
0
6
0
0
1
3
0
0
1
0
0
1
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
1
1
1
0
0
2
1
0
0
0
1
0
2
1
0
0
0
0
1
0
2
0
0
0
3
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
2
0
0
0
1
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
1
2
0
0
0
3
0
0
1
2
0
2
0
0
0
4
0
0
0
0
1
0
0
0
0
1
0
2
0
0
1
0
0
0
1
0
0
2
1
0
0
0
0
2
1
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
2
0
0
2
2
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
1
0
2
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
1
3
1
1
0
0
2
0
2
0
0
0
3
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
2
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
2
4
0
0
3
0
0
0
0
3
0
0
0
1
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
2
0
0
0
2
0
1
1
1
1
1
0
0
2
1
2
3
0
0
1
2
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
2
0
3
0
0
1
2
3
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
2
3
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
2
0
1
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
1
0
0
0
1
2
1
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
1
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
2
2
0
0
2
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
1
3
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
1
0
2
0
0
0
0
0
5
0
0
1
0
0
0
2
0
0
0
0
3
2
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
2
1
0
0
0
1
1
0
2
1
4
0
1
2
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
3
1
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
2
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
1
1
0
0
2
0
0
0
1
3
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
2
2
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
5
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
4
0
0
0
0
2
1
0
0
0
0
10
0
0
0
0
0
0
0
0
0
0
2
0
2
0
5
0
3
0
0
0
3
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
2
1
2
0
1
2
0
0
2
1
0
2
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
1
2
3
0
1
1
0
0
0
0
0
0
1
0
0
2
0
1
2
1
0
2
1
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
2
0
0
4
0
0
1
0
0
0
0
2
0
0
0
3
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
4
0
0
0
4
0
0
4
0
0
1
0
2
0
2
1
0
0
0
0
0
0
1
0
1
0
0
0
5
1
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
4
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
2
3
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
5
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
2
0
1
0
1
0
0
1
0
0
1
0
0
0
2
0
2
1
0
0
2
0
0
0
0
0
0
0
0
2
1
1
1
2
1
0
0
0
0
0
0
1
0
1
0
2
0
0
3
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
2
0
1
1
0
0
0
1
0
0
0
2
0
0
0
2
1
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
3
0
0
1
0
1
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
3
0
4
0
0
5
1
0
0
0
2
3
0
0
1
0
1
0
1
0
2
0
1
0
2
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
2
2
0
2
0
0
2
0
1
1
0
1
1
0
0
0
0
2
0
0
0
0
0
2
0
0
7
2
0
0
0
0
2
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
3
0
0
0
0
0
0
1
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
1
0
1
0
1
0
0
0
0
0
0
0
2
1
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
5
1
0
0
0
0
1
0
1
0
0
0
0
2
0
0
1
1
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
3
0
0
2
0
0
2
2
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
3
1
1
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
1
0
3
2
0
0
0
0
2
0
1
1
0
0
0
0
0
1
0
0
0
0
8
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
3
0
0
0
0
0
2
0
4
0
0
2
0
2
2
0
1
0
0
0
1
0
0
0
1
2
2
0
0
0
2
0
1
2
0
0
0
0
1
0
0
0
2
0
1
0
2
2
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
2
0
0
3
0
2
0
0
0
0
1
1
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
2
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
2
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
6
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
2
0
1
0
1
0
1
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
1
1
1
2
0
0
2
5
0
2
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
4
0
2
1
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
1
3
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
2
2
1
1
0
0
1
1
1
0
0
0
0
0
0
0
1
0
1
2
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
2
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
1
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
1
0
0
0
2
0
1
0
0
2
0
1
1
0
2
0
0
4
0
1
0
0
4
0
0
3
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
3
0
1
0
4
1
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
4
0
1
0
0
0
1
2
1
0
0
1
0
0
0
0
2
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
2
0
0
0
3
2
0
5
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
1
0
0
0
0
0
0
0
0
0
1
0
2
0
3
1
0
0
0
0
2
0
1
1
0
2
2
0
0
0
2
0
0
0
1
2
2
0
1
0
2
0
0
0
0
0
0
0
1
2
2
0
1
0
3
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
2
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
2
0
4
1
2
0
1
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
1
1
0
1
0
0
2
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
1
0
5
0
1
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
2
1
4
0
0
0
2
0
0
0
0
0
0
1
1
2
0
0
0
0
0
2
0
0
0
0
4
0
0
0
0
2
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
3
1
0
0
1
2
0
0
0
0
0
0
0
4
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
7
0
0
3
1
0
0
1
0
0
0
0
0
0
0
6
2
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
1
2
1
2
0
0
0
1
0
0
3
0
0
0
1
0
0
0
0
0
0
1
0
1
2
0
0
5
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
2
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
6
1
0
2
0
0
0
5
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
3
0
2
0
0
1
2
0
0
2
1
0
0
0
0
0
1
0
6
1
1
0
0
2
0
2
0
0
0
0
2
0
2
2
0
0
0
2
2
0
0
0
2
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
3
0
1
0
2
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
2
2
0
1
2
0
0
1
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
2
0
0
1
0
0
1
1
0
3
0
0
2
0
0
0
0
1
0
1
1
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
1
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
2
1
0
1
0
2
0
0
3
1
0
0
1
0
2
1
1
0
0
0
0
0
0
5
1
0
1
0
0
0
0
0
2
3
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
3
1
0
2
0
2
0
1
0
0
1
0
0
2
0
0
2
2
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
3
1
0
0
0
0
5
1
2
0
0
0
1
4
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
7
0
0
1
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
1
0
2
0
1
0
0
0
2
0
0
0
0
0
2
4
2
2
0
2
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
1
2
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
2
0
1
0
1
0
1
2
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
3
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
1
0
0
3
1
0
2
0
0
1
0
0
1
2
0
0
0
1
0
0
0
0
0
2
2
0
3
0
0
0
0
2
0
0
0
0
2
4
0
1
2
0
0
0
2
0
0
0
0
2
2
0
0
0
2
0
0
2
0
2
2
6
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
2
0
2
0
0
1
0
0
0
0
0
1
0
3
3
0
0
0
0
0
0
2
3
0
2
0
0
3
2
0
2
1
0
0
1
0
0
0
1
0
2
0
1
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
3
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
1
0
2
0
1
0
1
1
0
0
2
0
0
0
2
3
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
3
0
0
0
2
3
6
0
0
0
2
1
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
2
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
1
1
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
2
2
2
0
0
1
0
1
0
0
1
0
2
0
1
2
0
0
0
0
0
1
0
0
0
0
3
1
0
0
1
0
0
0
0
0
1
1
0
0
2
0
0
2
1
0
0
0
0
1
0
0
2
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
1
0
1
0
1
0
0
2
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
1
2
2
0
0
4
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
1
1
2
0
0
0
2
0
0
0
2
0
0
2
0
2
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
2
0
2
0
0
0
2
0
0
3
0
0
0
0
1
3
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
1
2
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
2
0
2
2
0
2
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
3
1
0
3
0
2
0
0
2
2
0
0
0
0
2
1
1
2
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
1
1
2
0
0
0
1
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
1
2
0
2
0
3
0
0
2
1
0
0
0
0
1
1
0
0
0
1
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
3
2
1
0
0
3
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
6
0
0
1
0
0
0
0
0
0
1
1
1
0
0
2
0
0
1
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
1
0
0
0
1
2
0
1
2
0
0
0
2
0
0
0
0
2
0
0
0
2
0
1
2
0
2
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
2
1
2
0
2
1
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
1
0
1
0
1
0
2
0
0
0
3
0
0
0
1
2
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
4
0
0
0
1
0
1
0
2
2
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
3
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
2
0
0
1
1
0
0
0
2
2
0
1
0
1
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
2
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
1
0
0
3
0
0
0
0
0
2
0
2
1
0
0
2
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
2
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
4
2
2
0
0
0
0
1
3
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
2
0
2
0
0
2
0
2
0
0
0
1
0
0
3
2
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
1
0
1
1
2
0
0
0
0
2
0
1
0
2
0
0
2
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
1
0
1
0
0
3
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
2
0
0
1
0
1
0
0
1
0
0
0
0
4
1
2
1
0
1
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
2
0
1
0
0
0
0
1
0
0
0
3
0
2
0
3
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
8
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
3
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
5
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
3
0
2
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
3
0
0
3
0
0
0
0
3
0
0
0
0
0
5
0
0
0
0
0
1
0
0
0
2
1
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
3
0
0
1
2
0
1
0
1
2
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
1
0
1
0
1
0
2
1
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
3
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
1
1
1
0
0
0
0
0
2
0
0
0
2
2
1
0
2
0
0
0
0
2
2
0
0
0
1
0
0
2
0
0
2
1
0
1
0
0
0
1
0
2
0
0
3
0
0
0
0
0
4
0
0
0
0
2
0
0
0
1
0
0
2
0
1
0
0
1
2
0
1
0
2
0
3
0
0
2
0
0
0
0
2
0
1
0
0
2
0
0
0
4
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
2
0
0
0
0
0
2
3
0
0
0
0
1
0
0
1
0
2
0
0
0
1
2
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
1
0
2
2
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
1
4
0
0
0
0
2
2
1
0
0
3
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
4
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
2
0
1
1
0
0
0
0
2
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
3
0
0
0
1
0
1
3
1
0
2
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
4
2
0
4
0
0
0
1
0
0
0
1
0
0
0
0
3
0
0
0
0
1
3
0
1
1
0
0
0
0
0
1
0
0
0
0
4
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
1
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
2
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
2
1
0
2
0
1
0
0
2
0
0
0
0
0
1
0
1
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
1
1
0
0
2
0
0
2
1
2
0
3
0
0
0
4
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
1
0
3
1
0
1
1
0
0
2
2
0
0
0
0
2
0
2
1
1
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
1
0
0
1
0
0
0
3
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
3
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
2
2
2
1
0
0
0
3
0
0
0
0
0
5
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
1
2
0
0
1
0
0
1
1
0
0
3
0
1
2
2
0
1
0
0
3
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
3
0
0
1
1
0
0
1
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
2
2
0
2
0
3
0
3
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
5
0
0
0
0
2
3
0
0
0
2
1
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
1
1
1
0
1
2
0
0
0
0
0
0
2
2
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
1
0
0
2
0
1
2
2
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
1
0
2
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
4
1
0
0
3
1
2
1
0
0
0
1
0
1
0
0
0
0
0
2
0
0
1
3
0
0
0
0
0
0
0
0
0
0
1
1
1
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
13
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
4
0
0
0
7
0
0
1
2
2
0
0
0
0
2
1
1
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
2
0
0
0
2
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
1
0
1
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
3
0
0
0
1
0
1
0
0
2
1
0
0
2
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
2
1
1
1
2
1
1
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
2
0
0
0
2
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
4
0
1
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
2
0
6
2
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
2
4
0
1
4
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
2
0
1
1
0
0
1
2
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
2
2
2
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
2
0
2
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
1
0
1
6
0
1
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
1
0
2
1
0
0
2
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
2
2
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
1
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
1
1
0
0
0
0
0
1
2
1
3
0
0
0
1
0
0
0
2
0
0
3
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
2
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
2
2
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
1
2
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
2
0
0
0
0
2
1
0
2
0
0
0
2
0
1
0
0
0
0
0
1
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
1
3
0
0
1
2
1
1
0
1
0
0
0
0
0
0
0
0
0
1
1
2
2
1
0
0
1
0
0
2
0
0
3
0
0
0
0
1
2
1
0
0
1
0
2
1
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
3
0
3
0
0
1
0
0
0
0
1
0
0
0
0
2
0
1
0
1
0
1
0
0
2
0
1
0
0
1
4
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
3
1
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
5
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
2
0
0
0
2
2
0
3
0
0
0
0
0
2
0
0
1
0
0
0
0
2
2
1
2
2
1
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
1
0
0
0
0
1
4
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
3
0
0
0
3
2
0
0
1
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
4
0
2
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
2
1
0
0
0
2
0
2
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
2
1
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
3
0
2
1
0
1
0
0
0
1
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
7
0
2
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
2
1
2
2
0
0
0
0
2
0
0
0
1
1
0
1
0
0
3
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
2
0
0
1
0
1
0
0
0
0
5
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
1
1
1
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
3
2
1
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
1
0
1
2
0
0
2
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
1
1
1
0
0
0
0
2
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
1
1
2
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
2
0
1
0
0
0
2
0
0
2
0
2
0
0
0
1
0
2
0
0
2
0
1
0
0
0
0
0
7
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
2
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
1
1
0
0
2
2
0
2
0
0
2
0
0
0
0
2
0
1
1
1
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
1
0
1
0
0
2
0
1
0
1
0
0
0
3
2
1
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
1
0
4
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
1
0
2
1
0
0
0
0
0
0
1
0
0
1
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
2
2
1
0
3
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
5
1
1
1
4
0
0
0
2
1
0
0
0
0
0
2
2
0
0
2
0
0
0
0
1
0
0
2
0
0
0
1
2
0
0
1
0
0
0
1
1
0
0
0
1
0
2
0
0
0
0
0
2
3
1
2
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
1
0
0
7
0
0
2
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
4
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
2
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
3
0
0
0
0
0
2
0
2
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
1
0
1
0
0
0
0
0
2
1
0
0
2
0
0
0
1
1
2
1
2
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
9
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
2
0
2
0
0
2
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
4
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
5
2
0
0
0
0
0
0
1
0
1
0
0
1
1
1
1
0
1
0
2
0
2
1
0
0
0
2
0
0
1
0
0
0
0
0
1
1
3
0
0
2
1
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
3
0
2
1
0
0
0
0
1
1
0
1
0
0
0
0
0
1
7
1
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
1
2
0
0
0
0
1
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
2
0
0
1
0
7
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
1
1
0
0
2
0
2
0
0
1
2
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
2
1
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
1
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
5
0
1
0
0
2
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
2
2
0
0
3
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
1
1
0
2
0
0
0
0
0
0
3
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
3
0
0
0
5
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
2
0
0
2
0
0
1
0
0
1
0
0
2
0
2
1
0
1
1
2
0
0
2
0
0
2
1
0
0
0
1
2
0
0
0
0
1
0
1
0
1
0
3
2
1
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
1
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
4
0
2
0
0
0
0
2
0
0
0
2
0
2
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
2
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
1
3
0
0
0
0
2
0
0
2
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
1
2
0
0
0
2
0
0
0
2
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
3
2
0
0
1
0
0
0
0
0
2
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
2
2
0
0
1
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
1
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
1
0
0
1
1
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
1
2
0
0
0
0
0
2
0
1
1
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
3
0
0
0
1
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
1
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
2
1
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
4
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
1
0
0
0
0
2
0
0
2
0
1
0
0
0
0
4
2
2
0
1
0
0
0
1
0
0
0
0
1
0
0
1
2
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
1
2
0
2
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
1
0
1
1
2
3
0
0
2
0
0
0
0
1
0
0
0
2
2
0
0
1
0
0
0
1
1
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
1
0
1
2
0
0
0
0
2
4
1
0
0
0
0
0
0
0
1
0
0
3
0
1
2
3
0
0
4
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
4
0
0
2
0
0
1
0
1
0
0
0
2
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
2
0
0
0
2
0
0
2
0
2
0
0
2
0
0
1
0
0
1
0
1
0
2
0
0
0
6
0
1
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
4
1
0
3
1
0
0
0
3
0
0
0
1
0
0
0
2
1
0
0
0
1
0
0
1
1
3
0
1
3
2
0
0
2
3
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
3
0
2
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
2
0
0
1
2
0
0
0
1
1
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
1
0
0
1
1
1
0
1
0
0
0
0
1
0
5
1
0
0
1
0
2
0
0
2
0
2
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
5
2
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
1
0
1
2
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
3
0
2
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
2
4
0
0
0
0
0
0
0
2
1
0
12
2
2
0
0
1
2
2
0
1
0
1
0
0
0
4
0
0
0
0
0
0
5
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
3
0
0
7
2
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
4
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
2
9
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
2
0
2
1
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
2
4
0
1
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
2
2
0
0
0
3
6
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
1
2
0
2
2
1
0
1
0
1
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
2
1
2
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
1
2
0
6
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
1
0
0
1
2
0
0
0
0
1
1
0
0
2
0
1
1
0
0
1
0
2
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
10
0
1
0
2
0
2
0
0
1
0
2
0
1
1
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
2
0
0
0
0
2
2
0
1
2
0
0
0
0
0
1
1
2
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
2
3
0
0
2
0
1
1
0
1
0
0
0
0
3
0
0
2
0
1
5
0
0
0
0
1
0
1
0
0
0
0
2
0
1
0
0
0
1
0
1
0
0
0
0
3
0
5
0
0
0
0
1
3
0
2
0
0
0
0
0
0
0
1
2
0
2
0
2
0
0
0
0
1
0
2
1
0
0
2
0
1
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
2
3
0
0
0
1
0
0
0
0
0
0
0
0
0
2
3
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
1
5
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
2
1
0
1
0
1
0
0
0
0
0
1
0
1
2
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
2
2
0
0
1
2
1
0
1
0
0
1
0
0
0
0
0
0
3
1
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
1
0
0
0
0
0
3
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
1
4
0
0
0
0
0
0
1
2
0
0
1
2
3
0
0
0
0
0
3
6
1
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
5
2
0
0
0
1
2
1
0
0
0
0
0
2
2
0
0
1
0
1
0
0
1
1
0
1
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
2
1
0
0
0
0
1
0
0
0
0
0
1
3
0
0
2
1
1
0
0
2
0
0
1
0
1
0
0
0
1
0
0
1
0
1
1
0
1
0
0
0
0
0
0
1
1
0
1
0
1
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
1
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
1
0
2
0
1
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
2
0
0
0
1
0
0
2
0
1
1
1
0
2
0
0
0
0
3
0
0
0
1
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
3
0
0
2
0
2
0
0
0
0
0
0
8
1
0
0
0
0
0
0
0
1
0
1
0
0
0
2
1
1
0
0
0
0
1
0
2
1
4
2
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
1
2
0
0
0
2
0
0
2
1
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
4
2
0
0
2
2
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
1
0
0
1
1
0
0
2
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
4
0
11
0
0
0
0
2
1
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
1
0
0
0
2
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
1
4
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
6
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
2
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
2
0
1
3
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
2
1
2
0
0
0
2
0
2
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
2
0
0
1
2
0
0
2
0
2
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
2
0
2
1
2
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
1
2
0
1
1
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
3
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
1
0
1
0
0
1
0
2
1
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
1
0
0
1
0
0
2
0
1
0
2
0
0
2
1
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
3
2
0
0
2
2
0
0
0
1
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
1
1
1
0
1
1
0
0
0
0
5
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
1
1
0
4
0
0
0
1
0
0
0
2
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
3
1
0
0
1
0
0
0
0
0
2
1
0
0
0
0
1
1
0
2
0
2
0
1
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
1
0
0
0
2
0
1
2
0
1
3
0
0
1
2
0
3
2
0
0
0
0
0
0
0
0
0
1
0
1
1
0
6
0
0
1
0
0
0
2
0
0
2
0
1
0
1
1
0
0
0
0
3
1
0
0
0
0
0
0
0
0
2
2
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
3
2
2
1
0
0
0
0
1
1
0
0
2
0
0
0
0
1
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
1
2
0
1
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
2
0
1
2
0
0
1
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
2
0
1
0
1
3
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
2
0
3
1
0
1
0
2
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
2
0
1
0
0
1
0
2
2
0
0
0
0
0
1
1
0
0
0
0
0
0
1
3
0
0
0
0
3
0
0
3
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
1
0
0
2
1
0
0
0
0
0
1
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
1
0
3
0
0
0
0
8
0
0
1
0
0
0
2
0
2
0
1
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
2
1
0
1
0
0
0
0
0
0
2
1
2
0
0
1
0
0
0
0
2
4
0
0
0
0
0
0
0
0
3
0
1
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
2
0
0
0
4
1
0
0
0
2
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
1
0
1
1
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
1
0
0
1
0
0
1
0
0
0
0
0
0
2
0
3
0
0
1
0
0
1
1
0
0
0
2
0
0
1
2
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
3
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
1
0
0
1
2
0
0
0
0
1
0
1
0
0
0
1
0
2
0
0
0
0
0
2
0
1
3
0
2
0
2
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
3
11
2
1
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
3
0
0
0
0
3
0
0
0
3
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
2
0
2
0
0
0
1
2
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
4
1
0
0
0
2
0
0
0
0
0
0
1
3
0
1
2
2
0
7
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
2
3
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
3
1
0
0
0
0
0
0
0
1
2
0
2
0
2
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
4
0
1
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
1
0
2
0
3
3
1
0
0
0
1
1
2
0
0
0
0
0
1
0
2
0
1
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
7
3
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
1
1
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
3
0
0
0
1
0
1
0
1
0
2
0
0
0
1
0
0
0
0
2
1
0
0
0
0
1
0
0
2
0
0
0
1
3
0
0
0
1
1
1
4
1
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
2
0
0
1
0
4
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
3
2
0
2
0
0
0
0
0
0
0
0
0
1
0
2
2
0
3
0
0
1
1
0
0
0
0
0
3
0
0
2
0
0
0
2
0
0
0
0
0
0
4
0
3
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
5
1
0
0
0
2
2
0
1
0
0
0
0
0
0
2
0
1
0
1
0
0
1
2
1
0
0
0
0
0
2
0
2
2
0
0
0
0
2
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
1
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
2
0
0
1
0
0
3
0
6
0
0
0
1
0
0
2
5
0
0
0
0
1
0
1
0
0
0
0
0
2
2
0
0
0
0
2
0
1
0
2
0
0
0
0
2
0
0
1
0
1
0
0
0
0
1
0
0
2
0
0
0
0
2
3
2
1
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
4
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
3
1
0
0
0
0
3
1
2
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
2
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
1
1
0
4
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
2
1
0
3
2
0
0
1
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
2
3
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
2
0
1
1
2
0
1
2
2
2
2
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
2
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
3
1
1
1
0
0
0
0
0
0
0
0
0
1
2
4
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
2
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
1
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
2
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
1
0
2
1
0
0
0
1
0
0
0
0
5
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
3
2
3
0
2
0
2
0
1
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
2
1
1
2
0
2
3
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
2
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
2
0
1
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
1
0
2
0
2
0
1
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
1
0
0
2
0
0
0
2
0
2
1
3
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
1
0
0
0
0
2
1
0
1
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
2
2
1
0
0
0
2
2
0
0
0
0
1
0
0
0
1
0
0
0
2
1
0
0
0
0
0
1
0
1
2
0
0
0
0
0
1
1
0
0
2
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
2
2
1
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
2
0
0
0
2
2
0
0
0
2
0
0
0
0
1
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
1
0
0
2
1
0
0
0
0
0
2
1
2
0
0
1
0
0
0
2
0
2
0
0
0
0
2
1
0
1
2
0
0
0
2
0
1
0
0
0
0
0
2
1
2
2
1
2
1
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
6
0
0
0
0
1
0
0
0
0
2
0
1
0
2
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
2
0
0
3
2
0
0
0
5
0
1
0
1
0
2
2
1
0
1
2
0
0
2
0
0
0
0
0
0
0
3
0
0
1
0
2
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
1
0
0
1
0
2
2
2
0
0
0
0
2
2
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
2
0
1
0
0
0
1
3
0
0
0
0
0
2
2
0
0
4
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
3
0
0
0
0
3
0
2
1
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
1
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
2
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
1
1
1
0
1
0
0
1
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
3
1
0
0
0
0
2
0
0
0
1
0
0
0
2
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
2
0
1
1
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
1
0
3
3
3
0
0
0
0
1
0
1
0
0
1
0
0
0
2
0
0
0
1
0
1
0
0
0
2
0
0
1
0
7
3
0
0
0
0
1
0
0
0
1
4
0
1
0
1
2
2
0
0
0
0
0
0
0
0
2
1
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
2
2
1
0
0
0
0
0
1
0
0
0
3
0
1
2
0
0
0
0
0
0
0
2
0
1
0
0
1
3
0
2
0
0
2
0
0
1
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
11
0
0
1
0
0
0
0
0
0
1
0
0
0
0
5
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
7
0
0
0
1
2
0
0
0
0
2
0
1
0
2
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
2
0
1
3
1
0
0
1
0
0
2
0
0
0
0
0
2
4
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
1
1
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
1
5
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
2
2
1
0
0
2
0
0
1
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
2
0
0
1
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
3
1
0
0
2
0
0
0
0
0
0
1
0
2
0
1
1
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
3
0
0
1
2
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
1
3
0
1
0
0
4
0
0
0
1
2
0
0
0
4
0
0
0
1
0
0
0
0
0
1
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
1
1
3
2
0
0
0
1
1
0
0
0
0
1
0
1
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
2
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
2
1
0
1
0
0
2
2
0
0
0
1
0
1
0
1
0
5
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
2
1
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
4
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
2
0
0
0
0
0
1
1
1
0
1
0
2
0
0
0
0
0
0
1
2
0
0
0
3
0
2
0
0
2
0
0
0
0
1
1
0
1
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
3
1
1
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
1
0
0
1
0
0
0
1
0
0
0
0
2
0
0
4
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
1
1
2
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
1
0
0
4
0
13
0
0
0
0
0
1
0
0
0
1
1
0
0
2
0
0
1
0
2
1
0
1
3
2
0
2
0
0
1
0
0
0
1
0
0
1
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
1
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
1
0
0
2
0
0
1
0
0
0
0
0
0
4
0
0
0
0
1
1
2
1
0
2
0
0
0
0
0
1
2
2
1
1
1
2
0
0
3
1
0
0
0
0
0
0
0
3
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
6
0
0
0
3
0
1
0
0
0
0
0
1
0
0
0
1
0
2
0
1
2
0
1
1
0
0
1
2
2
2
0
0
0
0
0
1
0
0
0
0
2
0
1
0
1
0
0
0
0
3
0
0
0
0
0
2
1
0
0
1
0
0
1
0
0
0
2
0
1
0
2
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
2
0
0
0
2
0
0
1
0
0
3
1
0
3
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
2
0
0
1
0
2
0
0
2
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
2
0
0
1
0
2
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
2
0
4
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
1
0
1
0
2
0
1
2
0
0
3
0
2
0
0
0
2
0
0
1
1
0
0
0
0
2
0
0
0
0
2
0
2
2
0
1
2
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
1
2
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
1
0
2
2
0
0
2
1
0
0
0
2
0
0
0
1
0
0
0
0
2
0
1
1
0
0
1
0
0
0
0
0
5
2
1
0
1
2
0
0
0
0
0
3
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
1
2
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
3
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
2
0
0
0
0
0
0
2
2
0
1
1
0
0
0
2
0
0
0
1
3
1
0
0
2
0
0
0
5
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
1
2
0
0
1
2
1
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
2
1
0
1
0
2
5
6
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
3
0
0
0
2
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
1
0
2
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
4
1
0
2
0
3
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
3
0
1
1
0
0
0
1
0
0
0
1
0
0
1
2
0
0
1
0
0
2
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
2
0
0
0
2
0
0
2
0
0
1
0
2
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
3
0
1
0
1
1
0
0
0
2
1
3
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
1
0
2
0
0
0
1
0
2
0
0
1
0
4
0
0
1
0
0
3
0
0
0
1
0
2
0
0
0
4
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
2
0
0
0
0
0
2
5
0
0
0
0
0
2
0
0
1
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
1
2
1
1
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
3
0
0
3
0
0
0
0
0
0
0
0
2
1
0
2
0
0
1
0
0
1
2
2
0
0
0
0
2
0
1
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
1
0
2
0
0
0
0
0
2
2
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
5
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
4
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
8
3
0
0
0
1
1
3
0
0
0
0
0
1
0
0
0
2
2
4
1
1
1
1
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
1
0
0
5
0
0
0
0
0
2
0
0
0
2
1
0
0
0
2
0
0
0
1
0
0
0
1
0
2
0
1
0
1
0
3
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
2
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
2
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
2
3
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
3
0
0
0
1
2
2
0
0
1
2
0
0
1
0
2
0
1
0
0
0
0
2
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
1
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
2
0
0
1
1
0
0
0
0
1
3
0
2
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
2
1
1
0
0
2
0
0
2
0
0
1
0
0
0
0
1
0
0
1
0
2
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
2
0
1
0
1
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
1
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
1
2
0
0
0
1
0
2
0
0
2
0
12
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
2
0
1
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
3
0
2
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
2
0
1
1
2
0
1
2
3
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
1
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
1
0
0
1
0
0
0
0
0
3
0
0
1
2
0
0
0
0
0
2
0
1
0
0
0
0
0
2
1
0
0
0
0
0
9
0
0
0
0
2
0
0
1
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
1
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
1
0
0
0
2
2
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
2
1
2
0
0
1
0
0
0
0
2
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
2
5
1
0
0
0
1
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
3
1
2
0
0
0
1
1
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
1
0
0
0
2
2
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
3
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
7
2
2
0
0
0
0
0
1
2
0
2
0
0
0
1
0
0
0
2
1
1
0
0
0
0
2
1
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
2
0
0
0
0
1
0
0
2
0
0
0
0
1
0
1
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
2
1
2
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
3
0
0
2
0
2
0
0
2
0
3
0
0
0
0
0
1
0
0
0
1
0
1
1
0
6
1
0
1
1
0
0
0
0
0
1
0
1
2
0
1
1
0
0
0
0
0
2
2
0
1
1
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
2
0
0
0
2
2
0
2
0
0
2
2
0
0
2
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
1
3
1
0
0
0
0
1
2
0
0
2
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
2
0
2
1
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
1
0
2
2
0
0
0
0
0
1
7
0
2
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
1
2
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
1
0
0
0
1
0
0
2
0
2
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
3
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
2
0
1
2
0
0
0
1
2
0
1
4
0
1
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
2
0
0
0
2
0
0
0
3
1
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
8
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
2
0
0
3
2
3
0
1
0
2
0
1
0
0
0
0
1
0
0
0
0
1
3
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
2
1
0
0
0
1
0
1
0
2
0
2
3
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
2
2
0
2
1
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
2
0
0
7
4
1
0
0
0
0
0
0
0
3
2
0
3
1
0
0
0
2
3
1
0
0
1
1
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
2
1
0
3
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
5
0
0
0
0
3
0
0
0
0
1
2
2
0
0
0
0
3
0
0
0
0
0
1
0
2
0
2
0
0
2
0
3
0
0
0
1
1
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
2
0
0
0
0
1
4
0
0
0
0
0
0
3
0
2
0
1
0
1
0
0
0
0
2
0
0
0
2
0
2
0
1
0
2
0
2
0
0
2
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
2
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
2
1
3
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
3
2
0
0
0
0
1
0
2
0
0
0
2
2
1
0
0
0
0
0
0
2
0
0
2
0
1
0
1
1
1
2
0
0
0
4
0
0
2
0
0
1
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
1
1
3
0
1
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
5
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
1
0
0
0
1
0
2
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
1
0
0
0
2
0
2
2
0
1
1
2
0
0
0
0
0
1
1
0
1
2
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
3
0
0
2
1
2
0
2
0
0
1
2
0
0
0
1
0
1
0
0
1
0
0
0
2
0
1
0
0
3
0
0
1
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
3
0
0
0
3
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
1
1
0
1
0
0
0
0
2
0
0
1
0
0
2
1
1
0
2
1
2
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
1
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
1
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
1
0
2
0
3
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
2
1
0
0
2
1
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
3
1
0
1
0
0
2
0
0
2
1
0
1
0
0
1
0
1
1
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
3
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
1
0
0
0
0
2
3
0
0
0
0
0
0
0
1
1
3
1
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
2
3
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
4
0
0
0
0
2
1
0
0
1
0
0
0
1
0
0
0
0
2
0
1
0
2
1
0
2
2
0
0
0
1
0
2
2
0
1
0
0
0
0
0
3
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
3
2
0
0
0
2
1
0
0
2
0
0
1
0
0
0
0
1
0
1
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
3
0
0
0
2
2
1
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
1
2
0
0
1
0
0
1
2
0
0
0
0
1
3
0
0
0
2
0
1
0
0
1
0
0
3
0
0
0
2
0
0
0
2
0
2
0
0
0
2
3
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
1
3
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
6
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
1
0
0
4
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
3
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
1
0
2
0
0
3
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
3
0
0
0
0
0
1
4
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
1
2
0
0
3
0
0
0
1
1
0
1
0
0
2
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
1
0
0
2
0
0
0
0
2
0
0
1
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
2
3
2
0
3
0
0
1
0
0
0
2
0
1
2
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
4
0
2
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
2
0
0
0
0
1
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
5
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
1
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
2
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
2
1
0
1
3
0
0
0
2
0
1
0
1
1
0
2
0
3
1
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
3
0
0
0
0
1
2
0
0
0
0
0
3
2
2
0
0
0
0
3
0
0
0
0
0
1
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
2
2
0
1
0
0
0
0
0
0
0
0
0
2
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
2
0
0
0
0
0
1
0
0
2
0
2
0
0
2
0
0
0
1
0
1
0
2
0
0
2
0
2
2
0
1
2
3
0
2
0
1
2
2
0
0
2
0
0
0
0
0
2
3
0
0
1
0
1
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
1
0
0
2
1
1
2
1
0
0
0
0
1
0
3
0
1
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
1
2
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
1
0
0
0
0
2
0
1
0
1
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
1
0
1
2
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
1
2
0
1
0
0
0
0
2
0
0
0
2
0
3
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
2
2
2
0
0
0
0
2
1
0
0
8
0
0
1
0
0
0
2
0
2
0
0
0
1
0
1
1
0
0
0
1
1
0
0
0
1
1
6
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
3
0
0
1
2
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
2
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
5
0
0
4
0
6
2
0
0
0
0
0
0
2
3
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
1
0
0
0
0
2
2
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
2
0
2
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
1
0
0
0
0
2
2
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
5
0
0
0
0
0
3
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
11
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
4
1
1
2
0
0
0
0
0
1
0
0
2
2
0
0
0
1
0
1
0
0
3
0
0
0
0
0
0
1
2
0
0
0
0
1
2
0
0
2
0
2
1
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
3
0
0
2
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
2
2
0
2
0
0
0
3
0
2
0
1
0
2
1
2
0
0
2
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
8
0
0
0
0
0
0
1
1
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
3
2
0
2
0
0
1
0
0
2
0
0
0
1
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
3
2
0
0
1
0
0
3
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
2
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
3
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
2
0
0
3
0
0
0
0
0
0
2
2
0
0
0
2
2
0
0
0
0
0
0
2
0
3
0
0
0
0
0
3
1
2
0
0
1
0
0
3
0
0
2
2
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
4
0
0
0
1
0
0
1
0
0
0
1
0
1
1
2
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
2
0
0
2
0
0
0
0
0
3
0
0
1
0
1
0
2
0
0
0
1
0
0
1
0
0
0
0
0
2
0
2
2
0
0
2
0
1
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
4
0
0
0
2
0
1
0
0
0
0
2
1
0
1
0
0
0
0
0
2
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
2
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
2
0
0
3
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
3
0
2
1
0
2
0
0
0
0
1
0
0
0
1
1
0
0
5
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
3
1
0
0
3
0
0
0
1
2
1
0
0
0
1
0
0
3
1
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
2
0
0
0
0
3
0
2
3
0
0
0
0
2
2
2
0
1
0
0
0
0
0
2
1
0
0
3
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
2
3
2
0
0
1
0
0
3
0
0
0
0
0
1
3
1
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
2
0
1
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
1
1
0
0
0
2
0
0
0
1
2
2
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
2
2
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
3
0
1
2
5
0
0
0
1
0
0
2
0
0
1
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
2
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
3
0
0
2
0
1
0
0
0
1
1
2
0
1
1
0
0
0
0
0
1
2
0
2
0
2
0
1
0
0
1
0
0
0
0
0
2
1
0
0
0
1
0
2
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
3
2
2
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
1
1
0
4
0
0
0
0
0
0
2
0
2
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
2
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
2
0
1
0
0
0
2
0
0
2
1
0
1
1
2
0
0
0
0
1
1
2
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
1
0
2
1
0
0
0
2
3
1
0
0
4
0
2
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
2
2
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
2
0
0
2
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
2
1
2
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
1
0
0
2
1
0
0
1
0
0
0
0
0
2
1
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
3
0
1
0
2
1
1
2
0
0
0
2
0
2
0
0
0
2
0
0
1
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
2
4
2
0
0
0
0
0
2
2
0
0
1
1
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
1
0
1
0
0
0
2
0
0
2
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
4
0
1
1
2
0
0
0
0
0
3
0
4
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
1
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
2
2
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
2
0
0
2
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
1
0
0
2
0
0
0
1
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
3
0
2
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
2
3
0
0
0
1
0
1
0
0
0
2
0
2
1
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
2
0
1
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
2
1
0
0
2
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
2
0
1
2
0
0
0
0
2
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
7
4
0
0
2
1
0
1
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
9
0
0
0
0
6
0
0
0
2
0
0
0
0
1
1
0
8
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
3
0
1
0
0
0
0
1
0
1
1
1
0
0
2
0
2
2
0
1
1
0
0
0
0
0
0
0
0
1
2
2
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
1
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
3
0
0
2
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
2
1
2
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
2
0
0
0
2
1
2
1
0
0
0
0
2
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
2
0
2
0
1
1
0
0
2
1
0
0
1
0
2
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
2
3
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
1
1
0
2
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
2
3
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
2
0
2
0
0
0
0
2
0
0
0
0
2
0
0
1
0
2
2
2
0
0
0
0
0
0
2
1
0
0
1
2
0
0
0
0
0
0
1
0
0
0
4
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
2
1
0
2
0
2
0
1
1
1
0
0
0
0
1
0
4
0
0
1
1
0
0
0
0
1
0
2
0
0
1
1
2
0
0
0
2
1
0
0
0
0
2
0
1
1
0
2
0
0
0
0
0
0
0
1
2
1
0
0
1
0
2
1
0
1
2
1
0
0
0
0
0
2
5
2
0
5
0
5
3
0
1
2
0
1
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
2
2
2
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
1
0
4
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
2
2
0
0
0
3
0
1
2
2
0
2
0
0
0
2
0
0
0
2
2
1
4
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
3
0
1
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
2
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
2
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
3
0
3
0
2
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
2
0
0
3
2
0
0
0
2
1
2
0
0
2
2
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
4
0
0
0
0
1
0
1
1
3
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
3
0
0
0
0
0
1
0
2
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
1
2
2
0
0
0
1
2
0
0
0
0
0
1
1
0
0
1
0
0
6
0
1
0
0
0
0
0
0
3
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
2
3
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
4
3
0
1
0
0
1
0
0
0
0
3
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
1
1
0
0
0
0
0
2
0
1
0
1
0
0
2
0
1
0
0
0
0
0
0
2
0
0
2
2
0
0
2
0
1
2
0
0
0
2
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
3
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
2
4
0
0
1
0
0
0
1
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
2
1
0
0
1
0
0
0
2
2
0
0
0
0
2
1
0
1
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
1
0
2
0
0
0
0
0
2
0
1
0
1
0
0
5
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
2
0
2
0
1
0
1
0
0
0
2
1
0
2
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
2
2
0
0
1
1
0
0
0
0
6
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
1
6
0
1
0
0
0
0
2
1
1
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
3
0
0
1
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
1
0
3
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
1
0
1
0
0
2
0
0
1
0
0
0
1
2
0
0
2
0
0
0
2
0
2
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
2
4
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
1
0
0
0
1
1
0
0
2
0
0
0
1
0
0
2
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7
2
0
0
0
0
0
1
0
0
4
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
3
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
1
2
1
2
0
0
0
0
0
1
0
1
0
0
1
0
0
2
0
1
0
0
0
0
0
0
2
0
0
1
1
0
0
0
2
2
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
2
2
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
3
0
0
1
0
2
3
2
0
0
1
0
1
2
0
0
0
0
2
2
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
2
0
1
0
0
0
2
0
0
1
0
0
0
1
0
1
2
0
0
1
0
0
0
3
0
3
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
2
1
0
0
0
0
3
0
0
2
0
0
0
0
0
2
0
0
0
2
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
2
0
0
1
0
1
2
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
2
0
1
0
0
0
1
0
2
1
1
2
0
0
0
0
0
1
0
4
2
0
0
0
0
1
2
1
0
2
1
0
0
0
0
0
1
0
0
2
1
2
0
0
1
0
2
0
0
1
1
2
0
0
0
0
0
1
0
1
3
0
0
1
1
2
1
2
0
0
0
1
0
0
2
1
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
3
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
1
0
1
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
6
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
2
0
4
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
2
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
1
0
1
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
1
1
0
0
2
0
1
2
0
0
0
1
1
0
3
0
0
1
0
0
2
0
0
1
0
2
0
4
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
2
0
2
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
4
0
3
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
4
1
2
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
5
2
0
0
4
0
0
0
3
1
2
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
2
3
0
0
1
0
1
2
2
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
2
2
0
0
2
0
0
0
0
0
5
0
0
1
0
1
0
0
0
1
0
0
0
1
4
1
0
2
0
1
0
0
1
0
1
0
2
1
0
2
0
0
0
0
1
0
0
0
1
3
0
1
0
0
0
0
0
0
1
0
1
0
0
0
2
0
1
0
1
0
1
0
0
3
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
3
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
4
1
2
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
3
0
2
0
0
0
3
0
1
0
0
1
5
1
0
2
0
0
0
0
0
2
1
0
0
0
4
0
0
2
1
0
2
0
0
0
0
2
0
0
2
0
0
3
2
0
3
1
0
0
1
1
0
0
0
1
0
0
0
1
1
0
2
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
2
2
0
0
0
1
0
0
2
0
0
2
0
0
3
1
0
0
0
0
2
0
2
0
0
0
1
2
0
2
0
0
0
3
3
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
4
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
5
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
1
2
0
1
0
0
0
2
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
1
0
2
2
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
1
0
1
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
2
1
0
0
0
2
1
0
0
2
0
0
1
0
3
0
0
1
2
0
2
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
2
0
0
0
0
0
1
0
0
2
0
0
3
3
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
2
0
2
0
0
5
0
1
0
0
0
0
1
0
7
0
0
1
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
2
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
5
0
0
0
0
0
0
0
0
1
0
0
0
2
1
2
0
0
1
0
0
2
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
2
0
0
0
1
0
0
2
0
0
1
0
0
0
0
2
2
2
0
2
0
0
0
1
0
0
1
0
2
2
4
0
1
0
0
2
0
0
0
4
2
0
1
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
4
0
0
2
0
0
1
2
0
1
0
0
1
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
1
0
0
2
0
0
0
0
0
3
0
10
0
2
0
1
0
0
0
1
0
0
2
0
0
0
1
0
2
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
2
0
0
2
0
0
1
0
0
0
2
0
0
0
0
1
0
2
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
3
0
1
0
3
1
0
0
0
0
1
0
2
0
0
0
2
1
0
0
2
0
1
0
2
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
3
0
1
0
0
2
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
1
0
2
2
0
2
0
0
0
2
2
0
0
2
0
2
0
0
1
0
3
2
0
0
1
0
0
1
0
0
1
0
1
0
0
3
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
2
0
0
2
1
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
3
0
0
2
0
0
0
1
0
1
0
0
0
1
2
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
2
0
0
0
0
0
1
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
1
2
2
0
0
0
2
0
0
0
0
0
1
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
1
0
2
0
0
2
2
0
0
0
4
0
2
0
0
0
1
0
0
2
0
1
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
1
6
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
2
1
0
0
2
0
1
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
1
2
0
0
2
0
3
2
0
0
0
2
1
0
2
0
0
1
0
0
0
2
0
1
0
1
0
4
0
2
0
1
1
0
1
0
0
1
0
0
0
0
1
0
2
1
0
4
0
0
0
1
2
0
0
0
2
0
0
0
1
1
2
2
0
0
0
0
0
1
2
2
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
3
0
0
2
0
1
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
2
0
0
0
1
1
2
1
0
0
0
1
0
0
3
0
2
0
0
0
1
0
0
0
0
0
0
5
5
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
2
0
2
4
0
4
0
3
0
0
0
0
1
0
1
0
0
2
0
0
0
0
2
0
0
1
2
0
0
1
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
4
0
0
4
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
1
3
0
1
0
0
2
0
0
0
1
0
0
2
2
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
2
0
0
0
2
1
2
0
2
0
0
0
2
0
0
0
1
0
1
2
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
2
0
2
0
2
2
0
2
0
3
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
2
2
0
2
0
1
0
1
1
0
0
0
0
0
1
0
0
1
1
1
1
2
0
2
0
0
1
2
1
0
0
0
0
0
1
0
2
2
0
3
0
0
2
0
0
2
0
0
0
0
0
0
0
0
3
1
1
0
0
0
0
0
1
0
0
1
1
0
1
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
3
2
0
0
0
0
0
0
2
0
0
2
1
0
2
0
0
0
0
1
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
3
0
0
2
0
2
3
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
2
0
3
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
2
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
4
0
0
0
1
1
0
0
0
2
2
0
1
2
0
3
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
1
2
1
2
0
0
0
0
0
1
1
0
0
1
3
0
3
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
4
2
1
0
1
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
2
0
2
0
1
0
0
0
0
1
8
1
0
0
1
2
0
0
3
1
0
0
0
0
0
0
2
0
1
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
3
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
4
1
0
3
0
0
0
0
0
0
0
1
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
5
1
2
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
4
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
3
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
5
0
1
1
0
1
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
1
1
0
0
0
0
0
0
2
2
2
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
1
2
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
2
3
0
1
1
0
0
0
0
0
0
1
0
0
0
1
2
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
1
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
1
0
0
0
2
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
1
1
0
0
2
0
0
0
0
3
1
0
0
0
0
0
1
0
0
4
0
0
2
0
0
0
0
0
0
1
0
3
0
2
1
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
1
2
1
0
1
0
1
0
1
2
0
0
0
0
1
0
1
0
0
2
0
2
0
2
0
0
1
0
1
2
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
2
2
0
1
2
0
0
2
0
3
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
3
0
2
1
1
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
5
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
7
1
2
0
1
0
0
0
0
0
0
4
1
0
0
0
0
1
0
2
3
0
0
1
2
0
1
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
1
0
2
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
2
3
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
2
1
1
0
1
1
0
2
0
2
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
1
0
0
2
0
0
2
0
0
2
0
1
2
3
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
2
2
0
0
0
0
1
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
2
1
0
2
0
0
2
0
2
0
0
2
0
0
0
3
0
2
2
2
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
3
1
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
3
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
1
2
1
0
0
0
0
1
0
1
0
0
2
0
0
0
1
3
0
1
1
0
0
1
0
0
0
1
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
1
3
0
0
2
0
0
0
2
0
0
0
1
0
1
0
0
0
0
1
2
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
4
0
0
1
0
0
1
0
0
0
1
2
0
2
0
0
0
0
0
0
0
1
2
0
0
1
0
1
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
1
0
1
0
2
1
0
0
3
0
1
0
0
0
1
0
0
2
0
0
3
2
2
0
0
0
2
0
0
0
1
0
0
2
0
0
0
2
1
0
0
0
0
0
3
1
0
0
2
1
0
1
0
0
0
0
1
2
0
0
0
0
1
0
1
1
1
0
0
0
3
0
1
1
0
3
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
1
0
1
0
0
0
0
2
0
0
2
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
1
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
2
0
1
2
0
0
1
1
0
0
0
0
0
0
0
1
2
0
0
0
1
2
0
2
1
0
2
0
0
0
3
0
0
1
0
0
1
0
0
2
0
3
2
2
0
0
0
0
0
3
2
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
2
0
0
0
2
0
2
0
0
0
1
2
1
0
2
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
1
0
0
1
2
1
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
1
2
0
0
1
1
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
2
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
3
0
0
0
2
0
0
0
2
0
1
1
0
0
0
0
0
0
0
1
0
2
1
1
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
2
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
3
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
1
1
1
0
0
0
0
0
0
2
0
0
0
0
2
2
0
1
2
0
0
0
0
0
1
0
0
2
1
5
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
1
0
2
0
1
0
0
0
0
1
0
4
0
0
0
0
2
1
1
0
2
0
1
0
1
1
0
0
1
0
0
1
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
3
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
2
1
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
2
1
0
4
1
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
2
1
0
1
3
0
0
0
0
0
1
0
3
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
3
4
0
0
4
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
2
2
2
0
0
0
0
2
0
0
0
1
0
0
2
0
1
2
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
7
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
1
1
0
1
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
2
0
2
0
2
2
0
0
0
2
0
3
0
0
1
1
1
0
0
0
0
0
0
1
2
0
0
2
0
2
0
0
0
1
0
2
0
0
0
0
2
3
0
2
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
1
0
2
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
3
0
2
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
4
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
1
0
0
0
0
1
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
2
2
0
0
1
0
0
0
3
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
3
0
3
0
0
0
3
0
0
0
0
0
1
1
0
0
2
0
0
3
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
2
0
0
0
2
2
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
1
2
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
2
2
2
0
0
2
3
1
0
1
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
2
0
2
1
0
0
0
0
0
0
2
0
0
0
0
3
0
2
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
1
0
0
0
1
0
2
0
0
0
0
1
0
0
0
2
0
0
1
2
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
1
0
1
1
0
2
0
0
0
4
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
1
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
2
0
2
0
2
0
0
0
0
0
2
0
0
0
2
0
2
0
2
0
0
0
0
2
0
0
0
0
2
0
2
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
1
2
2
0
0
0
0
0
1
0
0
1
0
0
0
1
5
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
2
4
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
3
1
1
0
0
0
2
0
0
0
0
9
0
0
3
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
2
0
0
0
2
0
0
1
0
5
0
1
1
0
2
0
0
0
0
0
3
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
2
3
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
2
0
3
1
0
2
0
0
0
2
0
0
0
0
3
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
2
0
1
0
0
1
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
3
0
1
1
0
0
0
0
1
1
0
0
0
0
1
1
2
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
1
1
1
0
0
0
0
0
0
0
0
2
2
1
0
0
1
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
2
5
2
0
2
0
0
0
0
0
0
2
4
0
0
0
1
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
6
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
1
0
0
0
0
2
2
0
0
2
0
0
0
0
4
0
0
2
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
3
0
0
0
0
1
0
0
2
2
1
1
0
1
2
1
2
0
1
0
0
3
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
3
0
1
0
0
7
0
0
0
0
0
2
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
1
0
0
1
0
2
0
0
0
2
2
0
0
0
2
2
3
0
3
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
2
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
1
0
1
1
0
0
0
0
4
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
2
1
0
1
0
0
3
0
0
2
0
0
0
0
0
0
1
1
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
9
0
0
0
2
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
2
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
1
0
3
0
0
1
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
3
0
0
0
0
2
0
0
1
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
3
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
4
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
1
0
2
0
2
0
0
2
1
2
0
0
2
5
2
0
2
0
0
0
2
0
2
2
0
0
0
0
1
2
0
0
0
2
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
3
2
0
0
0
0
0
0
0
0
0
4
0
0
1
0
1
1
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
1
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
3
0
0
0
0
1
0
2
3
0
0
3
0
2
0
0
0
0
1
6
1
1
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
6
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
2
1
2
0
0
0
0
0
0
2
0
0
0
2
1
1
0
0
1
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
4
0
0
1
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
1
2
2
0
3
0
0
0
0
0
0
0
1
0
0
7
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
1
0
0
1
1
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
1
2
2
0
2
0
1
3
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
2
2
1
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
1
0
0
2
0
0
0
1
0
3
0
0
0
0
2
0
1
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
1
0
3
0
1
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
1
2
0
1
0
0
2
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
4
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
4
0
0
0
2
0
1
0
0
8
0
0
0
0
0
2
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
2
0
0
1
0
1
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
3
0
0
0
1
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
3
2
0
2
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
1
0
1
0
0
2
0
1
0
1
3
0
2
0
0
0
2
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
3
1
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
2
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
5
2
1
5
1
1
0
0
0
0
0
0
0
0
0
1
0
2
0
1
2
2
0
0
2
0
0
0
1
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
4
2
0
0
0
0
0
0
0
1
6
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
6
1
2
0
0
4
1
1
1
0
0
1
0
0
2
0
0
0
0
0
2
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
2
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
1
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
1
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
2
1
1
0
0
0
3
2
0
0
0
0
0
0
0
0
0
1
2
4
0
2
0
3
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
1
1
0
1
0
2
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
3
0
2
0
0
0
0
0
1
1
0
0
0
1
2
1
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
6
0
0
0
0
0
0
0
1
3
0
2
1
2
1
2
0
0
2
2
0
1
2
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
1
0
2
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
1
0
0
1
0
4
1
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
5
0
0
2
0
0
0
1
2
0
0
0
1
2
0
1
0
0
0
0
2
0
0
2
0
1
2
0
0
0
0
2
1
0
3
0
2
0
3
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
3
0
2
3
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
1
1
0
0
0
2
0
0
0
0
0
2
1
0
1
0
0
0
1
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
2
0
1
0
1
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
3
1
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
3
1
0
2
0
1
0
0
0
0
0
2
2
0
2
0
0
2
1
2
3
0
0
0
0
2
0
0
0
0
0
0
5
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
2
3
0
0
0
3
1
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
7
0
0
0
5
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
2
2
0
0
1
0
0
0
1
0
0
0
3
0
0
1
2
0
2
0
0
2
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
3
0
0
2
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
1
0
0
2
0
0
1
0
2
1
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
1
0
4
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
1
2
0
0
2
0
3
1
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
2
3
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
2
0
0
1
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
3
2
0
1
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
1
0
2
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
1
0
1
1
0
0
1
1
1
2
0
0
1
0
0
2
0
0
2
2
0
0
2
0
0
0
2
0
0
1
0
0
1
2
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
6
2
0
0
1
0
0
0
0
0
0
2
2
0
2
1
0
0
2
0
0
0
0
0
0
1
1
2
0
1
0
0
0
0
0
6
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
1
3
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
2
1
0
0
0
2
0
0
1
0
0
1
1
3
0
0
2
1
2
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
4
0
0
0
4
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
2
4
0
0
0
0
4
0
0
0
0
0
0
1
0
0
2
2
1
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
2
3
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
1
0
0
2
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
4
0
0
0
0
0
0
0
0
3
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
3
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
1
1
0
0
3
0
0
0
0
2
0
0
0
0
0
1
2
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
1
0
0
0
0
6
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
2
0
0
1
1
0
0
0
0
4
3
2
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
2
1
0
0
0
2
2
0
1
2
0
0
0
0
1
0
0
0
0
2
0
2
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
1
2
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
3
0
2
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
1
1
0
0
2
0
1
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
1
0
0
0
0
3
1
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
4
0
1
3
1
0
0
0
0
2
0
0
0
2
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
2
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
1
0
2
0
0
0
0
2
0
0
0
1
0
0
2
2
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
2
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
2
2
1
0
1
0
2
2
0
0
1
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
6
0
0
1
0
0
0
1
1
0
2
0
1
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
3
0
0
0
0
2
0
1
0
0
0
2
0
0
0
2
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
4
0
0
0
2
0
0
0
0
1
0
0
0
0
2
1
2
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
1
2
0
0
0
0
1
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
1
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
1
1
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
2
2
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
2
1
0
1
0
0
0
0
1
3
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
1
1
0
0
0
2
0
0
0
2
0
0
1
0
0
5
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
2
1
0
0
0
0
2
2
1
0
2
1
2
1
2
0
0
0
0
0
0
0
0
0
5
2
0
0
0
0
2
0
2
0
0
1
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
3
2
0
1
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
6
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
2
0
0
0
1
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
2
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
1
0
1
0
0
3
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
17
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
1
0
1
1
0
0
1
0
5
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
1
1
0
0
0
0
5
0
0
2
0
1
0
1
2
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
1
0
2
1
1
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
1
0
0
0
1
2
0
1
0
2
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
2
1
1
7
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
2
1
1
0
0
1
0
0
1
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
1
0
2
0
1
0
0
0
1
0
1
0
1
2
0
0
0
0
0
1
0
11
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
3
0
0
0
0
0
1
0
1
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
3
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
3
0
2
1
0
1
0
0
0
6
1
0
0
0
1
0
0
0
1
0
0
0
2
1
1
0
2
0
0
0
3
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
2
0
2
1
0
1
0
1
0
0
0
0
0
2
0
0
2
0
0
4
0
0
1
1
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
1
0
0
1
0
2
0
2
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
2
3
1
0
1
0
1
0
0
0
0
0
0
2
2
2
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
1
2
2
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
3
2
0
2
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
3
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
2
2
0
0
2
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
1
0
0
2
0
1
0
2
0
0
0
0
0
0
1
1
0
0
1
2
0
1
0
0
2
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
2
0
0
2
0
0
0
0
0
2
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
6
0
0
2
0
0
1
1
0
0
0
0
1
1
1
0
0
0
2
0
0
0
1
0
1
0
1
2
1
0
2
2
0
0
0
0
0
0
2
0
2
1
0
0
0
0
1
1
1
1
0
2
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
8
0
2
0
0
2
0
0
0
2
0
0
2
0
0
5
0
0
0
0
0
0
5
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
2
0
0
0
1
0
0
0
1
2
0
1
0
2
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
1
2
0
0
2
0
0
1
0
0
3
0
0
1
1
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
2
1
0
2
2
0
3
0
0
0
1
0
9
2
5
0
0
0
1
1
0
0
0
0
2
9
0
1
0
0
0
0
0
2
3
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
3
0
2
4
0
2
0
0
0
1
1
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
3
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
3
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
1
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
1
1
2
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
2
12
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
2
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
2
0
2
1
0
0
0
0
2
0
0
0
0
0
0
1
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
1
2
2
2
0
0
2
2
0
0
0
0
0
2
0
2
0
0
2
0
1
1
0
2
2
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
1
0
1
0
0
0
3
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
4
0
0
0
4
1
0
4
0
0
0
0
0
1
3
0
0
0
0
0
0
0
4
0
2
0
1
3
0
3
0
0
0
1
0
1
0
2
1
1
0
2
0
0
0
0
0
2
1
0
4
1
0
0
0
0
0
0
0
1
0
0
0
5
0
0
1
0
1
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
1
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
3
0
0
0
1
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
3
0
1
0
6
2
1
2
2
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
2
0
1
1
0
0
2
0
0
2
0
6
0
0
0
1
3
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
2
0
2
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
2
1
0
0
2
0
1
0
0
0
0
2
0
0
1
0
0
2
1
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
1
1
0
1
3
1
0
1
0
0
0
0
0
0
0
1
0
3
0
0
0
0
2
2
2
0
2
0
0
0
0
0
3
0
0
1
2
0
0
0
0
0
0
1
2
2
0
0
0
0
3
1
0
0
0
0
0
0
2
0
0
0
2
0
0
3
0
1
0
0
0
0
0
2
0
0
1
2
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
1
0
0
2
0
0
0
2
1
1
0
0
0
1
0
2
0
2
2
0
1
0
0
0
0
0
0
2
0
0
0
0
1
1
2
1
0
0
0
0
1
0
2
0
2
0
1
0
1
0
0
0
1
2
0
0
1
0
0
3
0
0
2
1
0
4
0
1
0
1
0
0
0
0
4
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
4
2
2
0
0
0
2
0
3
0
0
0
0
0
0
2
0
2
0
0
2
0
4
0
0
0
0
0
0
0
2
0
0
1
0
2
1
0
0
1
0
1
0
0
0
0
0
3
0
2
1
0
2
1
0
0
0
0
0
2
0
2
0
0
2
0
1
1
0
0
1
0
2
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
1
2
2
1
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
2
2
0
0
0
0
0
0
0
0
1
2
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
3
2
1
3
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
3
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
2
1
0
0
1
1
0
3
1
1
0
1
0
1
0
0
0
2
1
0
2
0
0
0
0
0
0
1
2
0
0
0
3
0
0
0
1
0
0
0
2
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
3
1
5
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
1
1
0
1
0
0
1
0
0
2
0
1
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
1
0
2
3
0
0
1
0
0
0
0
0
0
1
0
0
1
2
0
0
0
2
1
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
1
0
1
2
0
0
0
0
0
0
1
0
0
1
0
0
1
1
1
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
2
2
1
2
0
1
1
2
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
5
0
2
0
0
0
0
0
0
2
2
0
1
1
0
3
1
1
0
0
0
0
2
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
1
2
0
0
0
0
3
0
2
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
1
0
7
2
0
0
1
1
2
2
0
0
0
0
0
4
1
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
2
0
1
0
1
0
0
2
0
0
4
0
0
0
1
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
6
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
2
2
1
0
0
4
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
2
1
1
0
2
0
1
0
0
0
0
0
0
0
2
2
0
0
2
0
0
7
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
3
0
0
0
1
1
0
0
0
0
0
0
1
0
2
0
1
0
1
2
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
2
1
1
2
0
0
0
2
0
2
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
1
0
2
0
0
1
0
2
0
1
0
1
2
0
0
0
0
0
2
3
0
2
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
2
0
1
0
0
0
3
0
2
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
2
3
0
0
2
0
0
1
1
0
0
0
1
1
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
3
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
5
1
2
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
2
1
0
0
1
0
0
0
0
3
0
0
2
0
1
0
0
1
0
0
0
0
0
0
3
2
0
0
0
0
0
2
2
2
2
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
5
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
1
1
0
0
0
0
0
2
2
0
3
0
1
0
0
0
2
0
0
0
1
2
0
1
0
0
1
1
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
3
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
2
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
3
1
0
0
0
0
1
0
2
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
1
0
2
0
0
0
3
0
1
0
2
0
0
0
0
2
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
3
2
1
4
0
0
2
0
0
0
0
0
0
0
0
2
0
2
2
2
0
3
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
1
1
0
2
1
1
0
0
0
1
0
0
1
1
1
0
0
0
1
0
2
2
0
0
2
0
0
0
5
2
0
0
2
0
0
2
0
0
0
1
0
1
1
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
3
2
1
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
2
0
0
2
2
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
1
0
1
1
0
2
0
2
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
2
0
0
2
0
0
1
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
2
1
4
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
2
0
1
0
0
5
0
0
0
0
2
6
0
1
2
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
3
2
0
0
0
1
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
1
0
0
1
2
1
0
1
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
1
0
2
0
0
1
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
1
2
0
0
1
0
0
0
0
0
1
0
0
0
0
4
0
3
0
0
0
0
1
0
1
0
0
1
0
1
0
2
2
4
0
0
0
0
0
1
0
2
0
1
2
0
0
3
0
4
0
0
1
0
1
1
2
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
2
0
0
1
2
2
0
1
0
0
0
0
0
2
0
0
1
0
0
0
5
2
0
0
2
1
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
1
0
4
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
2
2
1
0
0
1
0
1
0
0
0
2
1
0
0
2
0
4
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
3
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
2
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
1
2
0
0
1
1
0
0
2
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
2
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
1
2
1
0
0
0
0
0
0
0
0
0
2
0
0
3
2
0
0
0
0
2
0
0
1
2
0
1
0
0
0
0
0
0
0
2
1
2
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
1
0
0
0
1
0
1
0
2
0
0
0
1
2
0
0
0
2
2
0
1
0
0
2
0
1
1
1
3
0
0
0
1
0
0
0
0
0
0
1
2
0
1
0
0
0
2
0
0
0
2
0
2
1
0
0
0
0
0
0
1
0
0
0
2
0
1
2
0
3
0
0
0
2
3
1
1
2
0
1
0
0
0
0
0
2
0
0
0
2
1
1
0
3
2
0
0
1
0
0
0
2
0
0
0
3
0
0
0
2
3
0
0
2
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
4
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
1
0
3
0
1
0
0
1
1
0
1
1
0
0
1
0
0
0
0
1
0
1
0
2
0
0
0
0
0
2
0
1
2
0
3
1
0
1
1
0
0
0
0
0
0
0
1
2
0
1
0
2
0
0
0
1
0
8
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
5
0
0
0
1
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
2
0
3
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
3
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
2
0
2
0
0
0
2
0
0
1
0
0
0
0
2
0
2
0
0
0
0
1
1
0
1
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
1
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
3
1
0
0
0
0
0
0
1
0
0
0
0
3
2
0
2
0
0
1
0
0
0
2
2
1
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
3
0
0
0
0
2
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
3
0
0
0
0
0
4
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
4
0
0
3
0
0
0
1
1
1
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
4
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
1
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
1
2
0
0
0
2
0
1
0
0
0
0
1
0
1
2
0
0
2
0
1
0
0
0
4
1
0
3
1
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
2
3
1
0
0
0
0
0
0
0
0
0
1
0
1
0
2
1
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
1
0
0
0
2
0
2
0
1
1
1
0
0
0
0
0
0
0
0
3
0
1
0
1
0
0
0
0
1
3
0
1
1
0
1
0
0
0
3
0
0
0
0
1
1
1
0
0
0
0
2
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
2
0
0
0
0
2
1
0
2
0
0
0
0
0
2
2
2
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
1
1
2
0
0
1
0
1
2
0
0
0
1
5
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
4
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
5
0
0
1
0
0
0
0
0
0
1
0
0
0
3
1
0
0
0
0
0
0
1
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
1
2
0
5
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
1
0
2
2
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
2
2
0
0
0
0
0
2
0
1
0
1
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
2
2
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
2
0
0
0
0
0
3
0
0
4
0
0
1
0
2
1
0
0
2
1
0
0
0
0
0
2
0
0
2
2
0
0
1
0
0
1
2
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
2
0
0
0
0
2
2
1
1
0
0
0
2
0
0
0
0
2
1
1
0
2
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
2
3
0
0
0
8
0
1
0
4
0
0
1
2
0
0
1
3
0
0
0
1
0
0
6
1
0
2
0
1
2
3
1
0
1
0
0
0
0
2
0
2
0
0
0
1
0
0
0
1
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
2
1
1
1
0
0
0
1
2
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
3
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
6
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
1
0
0
0
0
1
0
2
0
0
1
2
0
0
2
1
0
0
1
0
0
0
0
1
3
0
0
1
0
0
1
2
0
0
0
0
3
2
0
0
3
0
1
0
0
1
0
0
2
0
1
0
0
0
2
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
1
0
1
0
1
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
2
2
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
3
0
1
0
0
0
0
4
2
0
0
0
0
1
0
0
1
0
0
0
0
0
1
2
8
1
0
2
0
0
0
0
0
0
2
0
0
0
0
1
2
2
0
0
0
0
0
0
1
0
1
1
1
0
1
0
0
1
1
2
0
1
0
2
0
1
0
0
0
0
0
0
2
2
1
0
0
2
0
0
0
2
1
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
1
0
0
0
2
0
0
1
2
0
0
0
0
2
0
3
2
0
0
0
0
0
0
2
1
1
0
0
0
2
0
0
0
2
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
3
1
0
1
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
2
0
0
0
0
2
0
0
0
1
2
1
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
1
0
0
2
0
3
2
1
0
0
0
0
0
2
1
1
0
0
0
0
3
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
4
0
1
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
2
0
0
2
1
0
2
0
0
0
0
0
2
0
0
0
1
0
2
0
2
0
0
0
2
0
0
0
0
0
3
0
1
0
1
1
0
0
0
3
0
0
0
0
0
1
1
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
6
1
2
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
1
2
0
0
2
1
0
0
2
0
0
1
0
0
0
0
0
0
5
2
0
3
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
2
2
0
0
0
2
0
0
1
0
0
0
1
0
1
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
3
0
0
0
1
0
0
3
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
1
0
0
3
0
0
0
0
0
2
2
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
2
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
2
0
0
2
1
0
1
2
1
0
0
0
1
0
0
6
0
0
0
0
0
0
0
0
0
0
2
4
0
0
0
2
0
6
0
0
1
7
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
3
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
1
0
1
0
0
0
0
0
0
2
0
2
0
2
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
2
0
1
0
0
1
4
0
2
2
2
0
0
0
0
0
1
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
3
0
0
1
0
1
0
1
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
1
0
0
3
0
1
1
0
0
0
0
0
0
3
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
2
0
2
3
2
0
0
0
0
3
0
0
0
0
0
0
1
0
1
0
1
1
0
1
1
0
0
0
0
0
1
0
0
0
2
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
6
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
2
2
0
0
0
1
1
0
2
0
0
0
0
0
4
0
0
0
0
0
1
0
1
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
3
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
3
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
1
0
2
0
0
3
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
3
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
4
3
2
0
2
0
0
0
0
1
2
0
0
0
0
0
2
0
1
0
0
0
0
1
0
1
1
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
4
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
2
2
3
0
4
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
2
1
0
1
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
1
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
3
0
0
0
0
2
0
2
0
2
1
0
0
0
1
0
2
2
0
2
0
2
0
1
0
0
0
0
0
3
0
1
1
0
0
0
0
2
0
2
0
0
2
1
0
0
0
0
0
0
0
0
2
1
2
1
2
0
0
5
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
4
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
1
1
0
2
2
0
0
0
0
0
0
0
1
0
1
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
2
0
1
0
0
0
2
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
6
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
5
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
3
0
0
3
2
0
2
0
0
1
2
0
2
3
3
0
0
0
0
0
2
0
2
7
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
2
1
0
0
0
0
0
2
0
1
0
2
0
1
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
1
0
1
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
3
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
2
1
1
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
1
2
0
0
0
0
1
2
0
0
0
1
1
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
1
0
0
2
0
0
2
0
0
0
2
0
0
1
0
0
3
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
4
0
1
1
0
1
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
2
0
0
1
1
0
0
0
0
0
0
0
1
0
5
0
0
3
0
0
1
1
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
1
0
0
0
0
3
2
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
1
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
2
0
0
0
0
0
1
0
0
0
2
1
0
0
0
2
1
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
3
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
1
0
2
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
2
0
0
0
2
0
0
0
2
0
0
1
1
0
0
1
0
0
0
0
0
1
0
2
0
0
0
3
0
0
0
0
1
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
2
0
1
0
1
1
0
0
5
0
0
0
0
0
0
2
0
1
2
0
0
0
1
0
0
0
0
0
2
0
1
2
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
1
2
0
0
1
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
3
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
2
3
5
0
0
0
3
0
0
0
5
2
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
3
0
0
0
1
0
2
0
0
0
4
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
2
1
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
2
0
0
1
0
1
0
0
3
0
0
2
0
1
0
0
0
2
0
0
0
2
2
2
0
2
0
2
2
1
0
2
0
0
2
0
0
6
0
0
3
1
2
0
0
0
2
0
0
0
2
2
2
0
2
0
1
0
2
2
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
3
0
0
0
0
0
0
1
2
4
0
2
0
0
0
1
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
2
1
0
3
0
2
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
1
0
1
1
0
2
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
1
1
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
2
0
0
1
3
1
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
3
1
0
0
5
0
2
0
0
0
2
2
1
0
0
0
0
0
0
2
2
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
2
0
2
0
1
0
0
1
0
0
0
2
2
0
0
0
1
0
2
0
0
0
0
0
2
0
2
0
0
0
2
0
1
1
3
0
0
1
1
0
0
0
1
0
2
0
0
0
1
0
0
1
2
2
0
0
0
1
10
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
4
0
0
4
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
2
0
0
0
0
2
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
3
2
1
1
0
2
0
0
0
0
0
0
1
1
0
0
4
0
4
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
3
1
1
0
1
0
0
2
1
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
1
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
2
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
5
1
0
1
0
0
0
0
0
1
0
0
0
1
0
1
2
0
0
1
0
0
0
0
2
0
4
1
0
2
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
1
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
1
5
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
2
0
1
0
3
0
0
0
0
0
0
3
2
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
3
0
0
0
0
0
0
1
0
0
7
0
1
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
2
0
1
2
2
0
0
2
0
1
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
5
0
0
0
0
1
0
0
2
0
0
0
1
2
0
0
2
0
0
2
0
0
0
0
0
0
5
1
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
2
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
2
0
1
0
0
0
0
0
2
2
0
0
0
0
1
0
0
1
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
2
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
2
0
0
0
5
2
2
0
0
0
0
0
1
0
0
0
0
0
4
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
2
2
0
0
1
0
3
0
0
0
0
0
0
2
0
2
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
3
0
0
2
0
0
0
2
0
0
1
0
0
1
0
1
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
1
1
1
1
1
0
2
0
0
1
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
2
2
2
2
1
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
2
2
1
0
1
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
1
0
0
0
1
0
0
3
0
0
0
0
0
2
0
2
2
2
1
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
1
1
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
2
0
2
0
0
0
0
2
2
0
0
0
2
0
2
0
2
0
2
0
0
0
0
2
2
1
0
0
0
0
2
6
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
4
0
0
0
1
3
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
3
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
2
1
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
3
0
2
0
0
0
0
1
0
0
2
0
0
2
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
2
0
0
0
1
0
2
0
0
0
0
0
2
2
0
0
0
2
0
2
0
4
0
0
0
0
2
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
2
2
0
0
3
0
0
2
1
1
0
0
0
0
0
1
2
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
1
2
0
0
2
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
4
2
1
2
0
0
2
1
2
2
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
2
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
2
0
0
0
0
2
2
0
0
0
2
0
0
0
2
2
0
1
0
3
0
0
1
0
0
0
2
2
0
0
1
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
3
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
7
0
1
0
0
0
0
0
4
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
1
2
0
0
1
0
0
0
1
1
2
0
0
0
2
0
1
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
1
0
0
0
1
0
2
0
2
2
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
2
2
0
0
0
2
1
0
0
0
0
0
1
2
2
0
0
2
0
2
2
0
0
0
2
1
0
2
0
0
0
1
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
1
0
0
0
1
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
1
0
2
0
2
0
0
2
0
0
0
0
0
0
2
0
0
2
2
0
0
2
0
0
0
0
1
0
0
0
0
1
0
2
2
2
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
1
0
1
0
0
0
0
1
0
0
1
1
3
0
0
1
1
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
2
0
2
0
2
0
0
1
2
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
3
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
1
0
0
0
0
2
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
1
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
1
1
0
1
0
2
1
2
1
0
0
0
1
0
2
0
0
2
0
0
0
1
0
0
0
0
2
1
0
0
0
1
0
0
2
0
2
0
0
0
1
1
0
0
2
0
2
1
0
4
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
4
1
1
0
0
0
0
0
0
1
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
5
0
0
0
0
2
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
2
0
0
2
2
2
0
1
0
0
0
0
0
0
7
2
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
1
0
0
0
2
2
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
2
0
0
0
0
1
0
0
0
2
1
0
2
3
2
2
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
2
1
2
0
0
0
0
2
0
1
0
0
1
0
2
1
0
2
2
2
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
2
4
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
1
2
1
1
1
0
2
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
2
0
0
2
0
0
0
0
1
1
0
3
0
0
0
0
0
1
1
1
2
2
0
2
1
0
1
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
2
3
2
0
1
0
2
0
2
1
0
0
0
0
1
0
0
9
0
0
1
2
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
1
0
0
0
1
2
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
2
0
2
0
1
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
1
1
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
2
0
0
2
0
0
2
1
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
2
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
3
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
3
0
0
0
3
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
3
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
1
0
2
0
2
2
2
0
2
0
0
0
0
1
0
0
0
0
5
2
0
0
2
0
2
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
3
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
2
2
2
2
3
1
0
2
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
3
0
0
0
2
0
2
1
1
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
1
1
0
0
0
2
0
0
0
3
0
0
2
0
3
0
0
0
0
0
2
0
0
1
0
3
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
4
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
2
0
3
0
0
1
0
0
0
1
1
1
0
1
3
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
2
1
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
5
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
1
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
2
2
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
2
0
0
0
2
0
0
1
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
2
0
0
0
2
0
0
0
1
0
1
0
0
2
2
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
3
0
2
0
0
1
2
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
3
0
0
1
2
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
2
1
2
1
1
0
0
2
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
1
1
0
0
1
0
0
0
0
0
3
0
1
0
0
0
0
1
0
1
2
0
2
0
2
0
0
0
1
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
3
0
1
2
2
0
0
3
1
2
0
2
0
0
0
0
0
0
2
1
0
0
0
1
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
1
0
0
2
0
1
0
0
1
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
1
1
0
0
2
0
0
0
1
0
2
1
0
2
3
0
0
0
0
0
1
0
0
0
1
2
0
0
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
1
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
2
0
1
0
0
0
2
1
1
0
0
0
0
3
1
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
1
4
1
0
0
0
0
0
1
2
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
1
2
2
4
0
0
0
0
0
1
0
0
0
2
4
0
2
0
0
3
0
2
0
0
2
0
0
0
4
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
3
2
1
3
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
2
0
2
0
1
0
0
0
0
0
0
2
0
0
2
0
1
0
1
2
3
1
0
1
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
2
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
3
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
6
1
0
0
0
0
0
0
7
0
1
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
7
1
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
2
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
3
1
0
0
0
1
0
0
0
0
0
0
5
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
1
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
4
0
0
2
2
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
5
0
0
1
1
0
0
0
2
0
0
0
2
0
0
0
2
0
0
2
0
0
2
0
0
1
0
0
3
2
2
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
3
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
4
0
0
0
0
0
0
2
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
1
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
3
1
0
1
1
2
1
1
2
1
0
2
0
0
1
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
1
2
0
0
1
0
7
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
3
0
2
0
0
1
2
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
2
2
3
0
0
0
0
0
1
0
0
0
0
0
1
0
0
6
1
0
0
0
1
0
0
0
0
0
0
0
2
0
3
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
2
1
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
1
0
0
2
0
0
0
0
4
0
0
0
0
0
2
3
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
2
0
0
0
2
0
2
0
0
0
0
2
0
0
1
0
0
1
0
1
0
0
2
2
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
2
0
2
1
0
0
0
0
0
0
0
1
0
2
1
0
1
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
1
1
0
0
0
2
2
2
0
0
2
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
1
1
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
1
0
1
0
0
0
2
0
4
0
0
1
4
0
0
0
0
0
0
0
1
1
0
0
0
2
1
2
1
0
1
0
7
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
3
2
0
0
0
0
0
0
2
1
1
0
0
2
2
0
0
0
0
0
2
1
1
2
0
1
0
1
0
0
0
0
1
0
0
1
0
0
3
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
1
2
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
3
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
1
1
0
0
2
0
0
0
2
0
0
1
0
0
0
0
2
0
0
2
0
2
2
5
0
3
0
1
0
0
1
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
2
0
1
1
3
1
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
3
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
2
0
0
0
2
1
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
2
0
2
2
1
0
0
1
4
2
0
0
0
0
0
1
0
1
0
0
0
0
1
2
0
0
1
0
0
0
0
0
1
2
1
1
0
0
0
0
7
0
0
1
3
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
2
0
0
2
0
0
1
2
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
2
1
1
1
0
0
0
0
0
0
3
0
0
5
0
0
0
0
1
2
0
0
0
0
0
2
0
1
0
2
0
1
0
2
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
2
0
0
3
2
0
0
1
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
1
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
4
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
1
2
2
0
0
0
0
0
0
0
2
0
0
0
3
2
2
0
0
3
0
0
0
0
0
0
1
2
1
0
0
0
0
0
2
1
1
0
0
0
2
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
2
2
2
0
0
0
0
0
0
0
0
4
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
5
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
20
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
2
4
0
1
0
1
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
4
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
1
2
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
2
0
0
2
1
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
2
0
1
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
2
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
7
0
0
0
0
2
0
0
2
1
0
2
0
0
0
0
0
0
2
4
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
1
0
2
2
0
0
0
0
1
2
0
0
1
0
0
0
2
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
6
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
3
1
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
3
0
0
0
0
2
2
0
0
2
0
0
0
0
2
0
0
0
1
0
4
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
1
0
0
2
0
0
0
0
1
1
0
0
1
0
1
0
0
0
2
0
0
2
0
2
6
2
0
1
0
1
0
0
2
0
2
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
1
3
0
2
0
0
2
0
0
0
0
1
2
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
1
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
1
1
0
0
2
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
3
2
0
0
1
0
0
1
0
0
0
0
2
0
6
2
1
0
1
0
1
0
0
0
2
0
0
0
0
0
1
0
0
1
0
1
0
2
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
1
0
0
1
0
2
0
1
0
0
2
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
1
0
0
0
1
0
0
2
1
0
2
0
0
0
1
0
0
0
2
1
1
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
1
2
0
0
0
2
0
1
2
2
1
0
2
0
0
0
2
1
2
0
0
2
0
0
0
0
3
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
1
0
5
2
0
2
2
0
0
0
1
2
0
0
1
0
0
1
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
1
1
2
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
1
2
0
2
1
4
2
0
0
0
1
0
1
0
0
0
2
2
0
3
2
0
0
0
1
3
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
2
0
2
2
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
2
0
0
0
0
0
0
4
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
3
1
0
0
0
1
0
0
3
0
0
0
0
0
0
2
0
1
1
0
0
0
5
1
0
0
0
0
0
0
2
3
1
0
0
0
0
2
2
0
0
0
0
0
0
2
1
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
2
0
1
3
0
0
0
0
0
2
2
2
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
2
0
0
1
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
2
1
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
3
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
3
2
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
2
0
1
0
0
0
0
2
0
1
1
0
2
0
0
1
0
0
0
2
1
0
0
0
1
0
0
0
0
1
1
0
0
1
1
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
2
0
1
0
0
2
2
3
0
0
0
1
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
2
2
0
0
0
0
0
2
0
0
2
1
0
2
0
0
2
1
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
4
1
0
1
0
4
0
0
0
0
0
1
0
0
0
0
1
0
2
0
1
0
0
2
2
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
2
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
3
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
1
0
0
2
2
1
0
2
0
2
0
0
2
0
0
0
2
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
1
1
0
3
0
1
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
1
0
2
2
0
0
1
2
0
1
0
0
0
0
0
0
2
0
2
3
0
0
0
0
2
1
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
2
0
0
2
0
0
1
0
2
1
1
0
0
0
0
2
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
7
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
2
2
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
1
0
0
0
0
0
2
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
2
1
0
0
0
0
1
0
0
0
2
1
2
0
1
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
4
0
0
0
0
2
3
0
0
2
0
0
0
0
0
1
2
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
1
2
0
2
0
0
0
0
0
0
1
0
1
0
1
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
3
0
1
0
0
0
2
0
1
0
0
1
0
0
0
2
0
1
0
0
1
6
2
0
0
1
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
1
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
1
2
0
0
2
2
0
2
0
1
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
1
0
1
0
0
2
0
3
0
2
0
0
1
0
1
0
0
1
0
2
1
0
2
0
2
0
0
1
0
0
0
2
2
0
0
0
0
0
0
3
1
0
2
0
0
2
2
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
2
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
1
0
1
0
2
0
0
0
1
0
0
1
1
2
0
1
0
0
1
0
1
0
0
0
2
0
0
0
0
0
1
1
0
2
0
0
2
0
2
0
0
0
1
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
1
2
0
2
0
0
0
1
0
0
0
0
0
1
7
0
0
0
1
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
4
1
0
0
0
7
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
3
0
0
0
0
2
0
0
2
3
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
1
0
1
0
1
4
0
8
0
0
0
4
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
2
0
1
0
0
0
1
0
4
0
0
0
0
0
1
2
2
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
5
1
2
0
2
0
0
0
0
0
2
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
1
0
0
2
3
0
0
0
0
0
0
1
0
0
0
2
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
2
2
0
0
0
0
2
0
0
5
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
1
1
1
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
1
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
3
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
1
1
4
2
2
0
0
0
0
2
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
2
0
0
0
0
2
0
0
2
1
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
4
0
1
1
0
0
2
0
0
0
0
1
0
0
3
0
0
0
0
0
2
2
0
0
2
3
0
0
2
0
0
2
0
0
0
0
2
0
2
0
1
1
0
2
2
0
0
0
2
2
0
0
0
0
2
1
0
0
0
0
1
4
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
2
2
0
2
2
1
0
2
0
3
1
0
0
0
0
0
1
0
0
6
0
0
2
1
0
1
1
1
1
0
2
2
0
0
0
0
0
0
0
2
0
0
0
6
0
0
0
0
0
2
0
0
0
1
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
3
0
0
3
2
2
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
2
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
3
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
2
2
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
3
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
2
0
3
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
6
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
2
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
2
2
1
0
0
2
2
0
0
1
0
1
0
0
0
0
0
2
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
1
0
0
2
0
0
1
1
1
0
0
0
2
0
0
1
0
0
2
0
1
0
0
1
2
2
1
1
0
0
0
0
0
0
4
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
1
2
1
0
0
1
0
0
2
0
0
0
0
0
1
1
0
0
0
2
1
0
2
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
9
2
2
1
0
0
0
0
2
0
0
0
0
1
0
0
2
3
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
4
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
3
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
2
0
0
0
1
0
4
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
1
0
0
2
0
3
1
0
0
0
1
0
2
3
0
0
0
2
0
2
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
1
0
2
1
0
4
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
3
0
1
1
0
0
0
0
0
0
0
3
0
0
3
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
11
2
0
1
1
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
1
3
0
0
0
0
2
1
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
3
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
1
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
3
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
2
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
1
6
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
1
0
2
1
1
0
2
1
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
1
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
2
0
1
1
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
2
0
0
2
2
0
0
0
0
0
0
0
2
1
1
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
2
1
2
0
2
0
0
1
1
0
1
0
0
1
0
0
1
0
1
2
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
2
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
1
1
1
2
0
0
0
1
0
0
4
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
2
7
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
1
0
0
1
3
2
0
2
0
1
0
1
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
1
2
4
0
0
0
0
0
2
2
0
1
0
0
1
0
0
2
1
1
0
0
0
0
1
0
1
0
0
0
0
0
3
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
1
0
2
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
1
0
0
2
0
0
0
2
0
0
1
0
0
0
0
2
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
3
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
6
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
1
2
3
0
0
0
0
0
0
0
0
3
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
2
1
2
0
0
0
1
0
0
2
0
0
0
0
1
0
3
0
0
0
2
0
1
0
0
1
1
1
0
0
0
0
0
0
0
2
0
1
1
0
0
1
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
2
2
0
0
2
0
1
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
10
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
1
1
1
0
0
0
0
0
2
0
0
1
0
0
0
0
6
1
2
0
2
0
0
2
1
0
0
0
0
0
0
3
0
0
2
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
1
0
0
0
0
3
2
0
1
0
0
2
0
0
0
0
0
0
1
0
0
2
0
1
2
0
0
0
0
0
0
0
1
0
0
1
2
0
0
3
0
2
0
2
1
2
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
1
1
2
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
2
0
0
2
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
2
0
1
0
0
1
0
2
0
2
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
2
0
0
0
0
2
1
0
1
0
0
2
0
1
0
0
3
0
0
0
2
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
2
0
3
0
0
0
2
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
2
0
0
1
1
2
0
0
0
0
0
1
0
0
2
2
0
1
0
0
0
1
0
0
1
0
0
2
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
2
0
2
2
2
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
2
0
1
0
0
2
0
0
0
0
0
2
1
0
0
5
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
2
1
0
2
0
1
0
1
1
2
0
0
2
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
2
0
0
0
0
0
0
2
4
0
0
2
0
0
0
2
3
0
0
0
2
2
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
2
0
0
1
0
0
0
0
0
2
1
1
1
0
0
0
0
0
0
3
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
2
0
5
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
2
0
2
0
0
2
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
2
0
0
2
1
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
7
6
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
2
1
0
4
0
0
0
0
2
2
0
0
0
2
2
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
3
3
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
2
0
0
0
0
0
2
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
3
0
2
0
2
2
0
0
0
0
1
0
0
0
2
0
1
0
0
0
3
0
0
0
0
0
0
2
4
0
0
2
0
0
0
1
0
0
0
0
2
2
2
0
0
2
0
0
4
0
2
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
6
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
1
0
0
3
0
2
0
1
1
0
0
0
0
0
0
0
1
3
0
0
0
2
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
2
0
0
3
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
2
2
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
2
2
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
1
0
0
0
0
2
2
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
2
2
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
6
0
0
2
0
1
0
0
2
1
1
1
0
2
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
9
0
1
1
0
0
2
0
0
0
0
0
0
0
0
1
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
3
0
0
0
0
0
0
1
0
0
1
2
2
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
2
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
1
0
2
0
2
0
1
0
0
0
0
0
1
0
3
0
0
0
0
2
0
0
0
0
0
0
2
2
1
0
0
1
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
3
0
0
0
7
0
0
0
0
0
0
0
0
0
7
0
0
2
0
0
1
3
0
1
4
0
0
0
0
6
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
2
0
0
0
1
4
2
0
2
0
0
0
2
0
0
0
2
2
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
5
0
0
0
0
0
0
2
0
1
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
3
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
2
0
0
1
0
0
0
0
0
2
0
0
1
0
2
3
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
1
0
2
0
0
0
1
0
2
2
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
1
0
1
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
3
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
1
2
1
2
0
0
0
0
0
0
0
0
0
0
2
0
1
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
3
0
0
0
0
1
2
0
0
0
2
0
0
0
0
1
0
2
0
0
1
1
1
3
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
1
0
1
0
1
0
0
0
2
0
0
1
0
0
0
0
4
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
2
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
3
0
1
0
0
0
0
0
0
1
0
0
0
0
2
2
2
0
0
0
0
0
0
1
0
0
0
0
1
0
1
2
1
0
0
0
3
0
2
0
1
0
2
2
1
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
2
0
1
0
0
0
0
0
0
1
1
0
2
0
0
2
0
2
0
1
0
0
3
0
0
0
0
0
3
0
2
0
2
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
1
1
0
1
0
0
0
2
2
0
0
0
0
0
1
0
2
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
1
0
2
0
0
0
2
2
1
0
0
1
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
1
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
1
0
0
1
1
0
2
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
5
0
0
4
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
2
1
0
0
0
0
2
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
1
0
1
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
2
0
2
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
2
0
1
0
2
0
2
2
2
0
1
0
2
1
0
1
0
0
1
0
2
0
0
0
1
1
0
0
0
0
0
4
1
0
0
0
0
0
2
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
2
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
2
2
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
4
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
2
0
2
0
0
2
0
0
0
0
0
0
1
1
0
0
3
0
0
0
0
0
1
2
0
0
2
1
0
0
1
1
1
0
0
0
2
0
0
1
1
2
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
1
0
0
0
0
0
0
2
1
0
0
2
0
1
2
0
1
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
2
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
1
0
0
0
1
0
0
1
0
1
2
0
1
1
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
1
2
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
3
0
0
0
0
0
1
3
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
3
1
0
2
0
0
0
0
0
2
1
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
1
1
3
2
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
1
2
2
0
0
0
1
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
2
1
2
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
2
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
2
0
2
0
1
2
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
2
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
1
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
1
0
1
0
2
0
0
2
0
0
0
1
0
1
0
0
2
0
2
1
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
1
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
5
2
0
0
0
3
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
1
0
2
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
1
1
0
0
2
0
0
1
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
4
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
2
2
0
0
0
3
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
1
1
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
2
0
0
0
1
0
0
0
1
1
2
0
0
0
3
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
1
0
3
2
1
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
3
2
0
0
0
0
0
0
2
0
2
1
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
3
2
2
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
3
0
0
1
1
0
0
3
1
4
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
2
2
0
1
2
0
1
2
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
1
3
0
2
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
3
0
0
0
0
0
0
2
2
2
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
1
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
1
3
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
8
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
1
0
0
0
2
2
0
0
0
0
2
0
0
2
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
2
2
0
0
0
2
0
0
0
3
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
3
0
4
0
2
0
0
1
0
0
2
0
1
0
0
2
1
2
0
3
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
6
0
2
0
2
0
0
2
1
0
0
2
0
6
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
1
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
2
2
0
0
0
0
2
0
1
0
3
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
2
1
2
2
0
1
0
0
0
0
0
0
0
0
8
0
1
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
1
0
3
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
2
0
2
0
3
0
0
0
1
0
2
0
0
0
0
0
0
3
0
1
2
0
1
0
1
0
0
0
0
2
0
0
1
0
0
2
2
2
0
0
1
0
0
0
0
0
0
0
1
2
0
2
0
0
0
2
2
0
0
0
2
0
0
0
2
3
0
0
3
0
0
1
0
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
0
0
2
3
0
0
0
0
2
0
2
0
0
0
0
0
0
5
0
2
1
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
2
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
6
2
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
4
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
6
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
1
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
2
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
2
2
0
0
0
0
2
0
2
1
0
0
1
0
0
2
0
0
1
0
0
0
2
1
0
0
1
0
0
1
3
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
1
0
0
2
0
1
0
0
0
0
0
2
0
1
2
0
3
0
0
0
0
0
0
0
1
1
0
0
0
2
1
0
0
0
2
0
0
0
0
1
0
0
1
2
0
0
0
2
2
0
0
0
0
1
0
0
2
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
1
7
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
2
2
2
4
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
3
2
0
0
0
0
0
3
2
0
1
0
2
1
1
0
0
0
2
0
1
0
2
0
0
4
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
1
3
2
2
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
2
1
0
0
3
0
0
0
0
1
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
2
1
0
0
2
2
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
1
2
0
0
0
0
0
0
0
1
0
0
3
0
2
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
4
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
2
0
1
2
0
0
1
1
0
0
2
0
1
3
0
0
0
0
1
0
0
0
2
0
1
3
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
1
1
1
0
0
0
0
2
0
1
0
2
0
1
0
15
0
2
0
1
1
2
0
0
0
0
1
2
0
2
0
0
2
0
2
2
1
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
4
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
4
0
1
2
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
2
2
0
0
2
0
0
0
4
0
0
0
0
0
0
0
2
4
3
1
0
1
5
0
2
0
2
0
0
0
2
2
1
1
0
1
0
1
0
0
2
0
0
0
0
0
0
0
1
2
1
2
0
1
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
1
0
0
0
1
2
0
5
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
1
0
0
0
0
2
0
1
0
0
0
1
2
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
2
0
1
0
0
1
0
0
0
0
2
0
0
0
1
6
0
2
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
1
0
0
2
0
1
0
0
0
1
0
2
0
0
0
1
0
1
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
11
4
3
0
0
0
0
1
0
0
0
0
3
3
1
1
0
0
0
3
0
0
0
0
0
0
3
0
0
0
0
0
0
0
4
0
2
0
0
0
0
2
0
1
1
0
2
0
0
0
1
0
0
0
3
0
0
1
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
1
0
0
1
0
2
0
3
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
14
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
1
1
0
1
0
1
0
0
0
0
2
0
0
0
0
0
3
1
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
1
0
1
0
5
0
0
0
1
0
0
2
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
7
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
1
0
0
2
2
2
1
0
0
0
1
0
0
0
2
0
3
1
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
2
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
2
2
0
1
0
2
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
3
0
1
1
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
2
0
0
1
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
2
0
0
1
0
4
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
2
0
6
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
3
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
5
0
0
0
3
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
4
5
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
5
1
0
1
1
0
1
0
0
0
0
3
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
2
1
0
0
0
1
2
0
0
0
0
0
2
1
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
1
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
5
2
1
1
0
2
0
0
0
2
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
2
1
1
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
1
2
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
5
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
2
1
2
2
0
1
0
5
1
0
0
1
2
1
0
0
0
0
0
0
0
0
1
0
1
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
1
0
2
0
2
0
0
0
0
6
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
3
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
1
0
0
1
0
0
0
2
1
0
0
1
1
0
0
0
0
0
0
1
1
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
2
2
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
2
2
1
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
1
0
1
2
0
3
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
2
2
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
1
0
0
0
0
0
1
2
2
1
0
2
0
0
0
0
0
0
0
1
0
0
0
1
2
0
1
0
0
0
0
2
0
2
7
0
0
0
0
1
1
2
0
0
1
2
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
2
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
1
0
3
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
2
0
2
0
0
1
0
0
3
1
2
1
1
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
2
0
0
1
0
0
1
0
2
2
0
0
0
0
0
2
0
0
1
0
0
1
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
2
0
0
0
3
0
0
0
0
0
2
1
0
1
0
1
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
8
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
1
0
2
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
3
2
1
0
2
0
0
0
2
0
0
0
0
0
4
0
2
1
0
1
0
0
0
1
2
0
1
2
0
0
0
0
1
0
0
0
2
2
2
0
1
0
0
0
1
1
0
0
0
1
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
7
6
1
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
1
0
2
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
2
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
4
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
5
1
0
0
0
0
0
0
3
0
0
1
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
1
0
0
0
1
0
3
0
0
0
2
0
0
0
2
0
0
0
1
1
0
0
2
0
3
0
0
1
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
1
1
2
0
0
0
0
1
1
0
0
1
3
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
3
1
1
2
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
4
2
0
0
0
1
0
1
0
1
0
1
0
2
1
2
0
0
0
0
0
0
0
1
0
1
0
1
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
1
3
0
0
0
1
0
0
0
0
0
0
0
0
1
3
4
2
1
0
1
0
0
0
1
0
2
1
0
0
5
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
1
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
1
1
0
1
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
2
2
1
0
0
0
0
0
0
0
1
3
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
2
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
1
4
0
0
0
0
0
1
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
2
0
0
3
0
0
0
0
0
0
1
0
0
0
1
1
1
4
1
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
2
0
2
1
3
1
2
2
0
0
0
0
1
1
0
3
0
0
0
1
1
0
1
3
0
3
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
1
0
0
2
0
4
0
0
0
0
0
0
0
0
2
0
1
7
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
1
2
0
0
4
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
2
0
0
0
1
2
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
6
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
3
0
1
2
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
1
0
0
2
0
1
0
0
1
0
0
1
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
5
2
0
0
0
1
2
0
1
2
2
2
0
0
1
0
0
0
3
0
2
0
2
0
1
1
0
0
0
1
0
0
2
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
1
0
3
2
0
1
0
4
0
0
0
0
1
0
0
0
0
0
1
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
1
2
0
1
0
0
0
0
2
2
0
1
0
0
0
0
2
0
0
0
0
0
0
1
1
0
1
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
2
0
3
0
0
1
1
2
2
0
6
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
2
2
0
0
0
2
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
1
2
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
3
4
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
2
2
0
1
2
2
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
3
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
2
0
1
0
2
1
0
2
2
1
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
3
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
3
0
0
2
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
1
1
0
2
2
3
1
0
0
0
0
0
3
1
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
1
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
1
0
0
1
0
2
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
2
0
0
0
2
1
0
0
0
4
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
3
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
2
0
0
0
0
0
1
0
0
0
0
4
0
1
1
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
6
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
1
2
2
0
0
0
0
0
0
0
1
0
0
0
0
1
4
0
1
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
1
0
0
4
0
0
0
1
0
2
1
0
0
1
0
1
0
2
0
0
0
0
2
0
2
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
1
0
3
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
1
3
0
3
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
1
0
0
1
1
0
3
0
0
0
0
0
0
1
4
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
1
0
4
1
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
3
0
0
1
0
0
1
1
0
0
0
0
3
0
0
0
0
0
0
6
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
2
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
1
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
4
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
2
1
0
2
0
1
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
1
0
0
1
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
2
2
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
2
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
3
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
2
0
2
0
1
1
0
0
0
0
0
0
0
0
2
2
3
0
0
0
2
0
0
2
2
0
0
0
0
0
0
1
0
2
1
0
0
0
0
1
0
0
0
1
0
0
2
3
0
0
0
0
0
3
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
1
2
0
0
2
0
0
0
2
0
1
0
2
0
1
0
0
1
0
2
0
1
2
0
2
1
1
0
0
2
0
0
0
0
1
0
0
6
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
2
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
2
2
0
0
0
0
0
2
0
0
0
4
2
0
2
0
1
2
0
0
0
0
2
0
0
1
0
0
0
1
1
2
2
0
0
0
2
0
0
0
0
1
3
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
3
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
2
0
5
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
2
1
0
0
0
0
4
0
2
0
0
2
0
3
0
1
0
1
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
1
1
0
0
2
0
2
0
0
0
0
3
1
0
0
0
1
0
0
0
2
0
3
0
2
1
0
0
0
2
0
0
0
1
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
3
0
0
0
2
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
2
1
0
5
1
1
0
1
0
0
1
0
0
9
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
1
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
4
0
0
0
1
0
1
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
5
1
0
0
1
2
0
2
0
0
0
0
1
1
1
0
1
0
0
0
0
0
2
1
0
2
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
2
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
1
0
0
1
0
1
0
0
2
0
2
0
2
0
0
0
0
2
0
0
0
0
2
1
0
1
3
0
0
0
0
1
0
0
0
0
2
0
2
2
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
2
0
1
1
3
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
1
4
0
2
0
2
0
3
0
0
0
1
0
0
0
0
0
0
2
0
0
1
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
1
0
0
2
0
0
0
2
0
0
2
1
0
0
0
3
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
2
0
0
0
3
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
1
0
2
0
0
0
2
0
0
1
0
1
0
0
1
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
2
1
1
0
0
2
0
0
0
0
0
2
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
1
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
1
0
0
1
1
0
0
1
0
3
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
1
4
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
2
3
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
1
2
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
3
0
0
0
0
0
0
1
0
0
0
3
2
1
0
1
1
0
0
5
3
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
4
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
5
0
0
0
0
0
0
0
0
2
0
0
0
2
4
0
1
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
1
2
1
0
0
1
2
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
2
0
0
2
0
0
0
2
0
0
2
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
3
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
3
0
0
1
0
0
1
0
0
0
1
0
2
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
2
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
3
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
1
2
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
2
0
0
1
3
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
1
0
1
1
0
2
0
0
0
1
0
0
7
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
2
0
0
0
1
0
6
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
5
0
0
0
7
0
0
0
0
2
0
0
2
2
2
0
2
0
1
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
5
0
1
0
1
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
2
0
1
0
0
0
0
0
1
1
2
2
1
0
0
0
0
1
1
0
0
0
0
0
1
3
1
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
2
0
0
0
2
0
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
1
0
0
0
1
0
1
0
0
1
4
0
1
1
2
1
1
0
1
0
0
2
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
2
0
1
0
2
0
1
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
1
0
0
0
0
0
0
1
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
1
2
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
2
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
1
0
2
1
0
0
2
0
0
0
1
0
2
0
0
0
1
1
0
0
0
0
2
0
0
2
0
2
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
4
6
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
2
0
0
2
0
0
0
0
0
0
3
9
1
0
0
3
0
0
1
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
3
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
2
0
0
3
0
1
0
0
0
0
0
0
2
0
0
2
1
0
0
0
2
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
1
1
4
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
3
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
2
0
0
2
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
1
0
3
0
0
0
0
0
2
0
0
1
1
0
1
1
0
0
0
2
0
0
0
0
1
2
0
3
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
2
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
7
0
0
0
0
0
0
0
0
1
0
0
0
4
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
3
1
0
0
1
2
1
2
1
2
2
1
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
6
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
3
0
0
0
0
0
0
1
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
1
0
1
0
2
0
0
2
3
0
0
0
1
2
1
0
0
0
0
0
0
1
0
0
0
0
0
5
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
5
2
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
3
2
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
1
2
1
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
1
1
2
0
0
3
1
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
3
0
2
0
1
1
0
1
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
3
0
0
0
1
2
0
0
0
0
0
0
1
3
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
2
1
0
0
3
0
0
0
1
1
2
0
2
0
2
2
14
1
0
0
0
1
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
2
4
0
0
2
0
1
0
1
2
0
0
0
0
0
0
0
1
0
2
0
1
0
2
0
0
0
0
9
1
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
1
2
0
0
0
2
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
1
0
3
0
0
0
1
2
0
0
1
1
0
0
0
2
0
0
1
0
0
2
0
0
2
0
0
1
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
3
1
0
0
1
1
4
1
0
0
0
0
0
2
1
0
0
2
0
0
2
0
0
1
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
2
1
0
0
2
0
0
2
2
0
1
2
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
7
3
1
0
0
0
0
0
0
1
1
0
3
0
0
0
2
0
1
0
0
0
0
0
0
0
3
0
0
1
2
0
0
3
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
2
4
0
0
0
0
0
0
2
0
1
0
2
1
0
1
0
1
0
0
0
0
3
0
1
1
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
3
0
1
0
0
0
0
0
0
0
0
0
1
2
0
4
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
2
0
0
1
2
0
1
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
1
0
2
2
0
0
1
0
1
1
0
0
0
1
3
0
0
0
2
0
0
0
0
0
0
0
0
0
9
0
0
0
0
0
2
0
0
0
1
1
0
0
0
1
0
0
0
0
0
2
0
2
0
2
2
4
0
0
0
3
0
0
2
1
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
1
0
0
0
0
1
2
0
0
1
0
1
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
3
1
0
2
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
7
0
1
0
1
0
1
1
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
1
3
0
0
0
0
1
0
2
0
0
3
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
3
0
0
0
2
1
0
1
0
0
1
1
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
1
0
2
0
0
0
2
0
0
0
0
0
2
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
2
0
0
2
1
0
2
3
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
1
2
0
2
0
0
0
2
0
0
0
1
1
2
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
1
0
2
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
1
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
2
2
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
2
0
2
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
7
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
1
2
0
1
0
1
0
4
0
0
0
0
0
0
1
1
0
0
0
0
1
2
1
0
0
0
0
0
0
7
0
2
0
0
0
0
0
2
0
0
1
1
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
2
1
0
0
2
3
0
0
0
2
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
2
0
1
0
0
0
2
1
0
0
0
0
2
1
0
0
0
0
1
1
1
0
1
0
0
0
2
0
1
1
3
0
2
2
0
0
0
6
0
0
0
2
0
1
0
0
2
0
1
0
4
0
0
0
2
7
0
0
0
0
0
0
1
0
0
0
1
1
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
3
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
1
0
1
0
0
0
1
1
1
0
0
0
0
0
3
2
0
0
0
0
2
2
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
2
1
3
0
1
0
0
2
0
1
2
0
0
0
4
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
2
0
0
0
1
0
1
0
0
0
2
0
0
1
1
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
3
1
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
3
0
1
1
0
0
1
0
0
0
2
0
1
2
1
0
1
2
2
0
0
0
0
0
0
2
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
3
0
0
2
0
2
0
2
1
0
0
0
5
0
0
0
1
0
0
2
1
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
1
1
2
0
2
0
0
0
0
1
0
1
2
0
0
0
1
1
1
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
2
2
0
0
3
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
3
1
0
2
0
0
0
0
3
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
1
0
2
1
0
0
0
0
2
2
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
3
1
0
0
0
0
0
0
2
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
1
0
0
1
0
0
0
1
0
0
0
1
1
0
3
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
1
0
2
2
0
0
0
1
0
0
2
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
2
1
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
2
2
0
0
2
2
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
3
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
2
2
0
0
0
0
1
2
2
10
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
1
0
0
3
2
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
10
2
2
0
0
0
1
0
0
2
0
1
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
1
0
1
2
0
0
0
2
0
1
0
1
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
6
2
0
2
1
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
2
0
0
4
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
2
2
0
0
0
0
2
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
2
0
1
0
0
2
0
1
0
0
0
1
0
0
2
1
2
0
1
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
3
3
1
0
0
0
0
0
3
1
0
0
0
1
0
0
0
3
2
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
2
0
2
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
2
0
0
2
1
2
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
5
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
2
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
1
0
2
0
1
0
0
2
2
0
1
0
0
2
2
0
0
0
2
2
0
0
1
1
1
0
0
1
0
0
0
1
0
0
2
1
0
0
0
0
2
0
3
0
0
0
0
1
1
0
1
1
2
0
0
1
1
2
0
2
0
1
3
0
1
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
3
2
0
0
0
4
0
0
0
0
0
0
0
1
0
0
2
2
1
1
0
2
0
0
0
0
0
0
0
0
0
6
0
2
0
0
1
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
1
0
0
4
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
2
0
2
0
1
0
1
0
0
0
0
2
0
0
0
1
0
4
0
0
0
4
0
0
0
0
0
0
2
0
1
0
1
0
1
1
0
1
1
2
2
0
2
0
0
0
0
0
4
0
2
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
2
1
0
1
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
1
1
0
1
1
0
2
1
0
0
0
0
0
1
0
0
0
2
1
0
1
0
3
0
0
1
0
0
0
2
1
0
0
0
2
2
0
0
0
0
0
0
1
1
0
0
0
0
0
2
1
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
3
0
1
0
0
0
2
0
0
1
0
1
0
1
0
0
1
0
2
0
1
2
1
1
1
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
3
0
1
0
2
2
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
2
0
2
1
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
1
0
0
3
2
0
1
0
1
0
0
1
0
0
2
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
2
1
2
0
2
1
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
3
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
2
0
2
1
0
0
1
0
0
0
2
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
3
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
2
2
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
2
0
1
0
0
2
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
2
0
0
0
1
0
4
1
0
0
2
0
1
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
2
2
3
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
9
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
4
2
2
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
1
3
2
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
1
0
0
2
1
1
0
2
0
0
1
1
0
0
0
0
0
0
0
2
0
0
2
0
5
2
0
1
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
2
1
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
2
2
2
0
2
0
0
0
0
0
0
0
0
0
0
3
1
0
0
1
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
1
0
1
2
0
0
0
1
0
0
0
0
2
0
0
1
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
1
2
1
0
0
1
1
3
0
0
0
0
2
0
2
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
2
3
0
0
2
0
0
2
0
0
0
0
4
1
0
0
0
1
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
2
1
0
0
0
2
1
2
2
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
1
0
2
0
0
2
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
3
0
0
2
0
0
2
2
0
0
0
1
0
2
0
0
0
0
0
2
0
1
0
2
0
0
1
0
0
0
1
1
0
2
1
2
0
0
0
0
0
0
2
0
3
0
2
0
0
0
0
0
0
2
1
0
1
0
0
2
0
1
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
1
0
1
2
0
0
0
4
0
1
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
1
1
2
0
0
0
0
0
2
0
0
3
0
2
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
2
0
8
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
2
0
1
2
0
0
0
3
0
0
0
0
0
2
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
2
0
1
0
1
2
0
0
2
0
1
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
2
1
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
1
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
2
1
1
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
2
0
0
0
3
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
3
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
1
0
2
0
1
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
1
1
0
0
1
0
0
0
0
2
2
0
0
1
0
1
0
0
0
0
2
0
0
1
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
3
0
0
2
0
0
1
0
0
0
1
0
0
0
7
1
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
1
0
2
0
0
1
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
2
2
1
0
0
2
0
0
0
0
1
2
0
0
0
0
3
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
4
0
0
0
0
0
0
0
2
0
2
0
0
5
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
4
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
2
0
0
0
2
0
0
0
3
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
2
0
2
1
0
0
0
1
0
0
0
0
0
2
0
0
2
2
2
0
0
2
0
0
2
0
2
0
0
0
0
0
5
0
0
0
2
0
0
0
1
2
0
0
0
1
0
2
2
2
0
0
0
2
0
0
0
0
0
1
0
0
2
2
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
1
0
0
2
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
3
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
7
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
2
2
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
1
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
2
0
0
1
1
0
0
0
0
0
2
1
2
0
2
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
9
0
0
0
1
0
0
0
0
0
2
0
0
1
3
0
2
0
0
0
2
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
4
0
2
0
1
1
0
0
2
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
1
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
1
1
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
1
1
0
0
7
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
2
0
0
2
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
1
2
0
0
1
0
0
2
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
2
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
1
0
0
2
0
0
0
2
2
0
0
2
0
0
0
2
0
1
2
0
0
0
0
2
0
1
4
0
1
0
0
1
0
2
0
2
1
0
0
0
0
0
0
2
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
1
0
2
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
2
2
0
0
2
1
2
0
3
0
0
0
0
0
0
0
2
1
1
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
1
0
0
2
0
1
3
0
0
0
0
0
2
0
0
0
2
1
4
2
0
0
3
0
1
1
1
0
0
2
0
0
2
2
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
2
1
1
0
0
0
2
0
2
0
1
1
0
2
0
0
2
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
3
0
1
0
0
0
0
0
0
0
2
0
1
0
1
0
0
5
2
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
2
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
1
0
1
2
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
1
0
1
0
0
4
2
1
0
0
0
1
0
0
2
0
1
0
0
0
0
1
0
1
0
1
2
0
0
0
0
0
2
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
6
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
2
1
4
0
0
0
0
0
0
0
1
0
1
0
0
6
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
7
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
3
1
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
12
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
3
0
0
1
2
2
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
1
2
0
2
0
0
0
0
4
0
1
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
1
0
0
1
3
0
0
0
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
3
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
1
0
0
1
0
0
0
2
2
0
0
1
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
2
1
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
2
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
1
0
2
0
2
0
0
0
1
1
1
1
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
2
1
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
2
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
2
3
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
1
3
0
0
0
2
1
1
0
0
1
0
0
1
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
2
0
1
0
0
2
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
2
1
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
1
1
2
0
0
0
0
0
1
1
2
1
1
0
0
0
0
0
0
2
0
0
0
3
1
0
0
0
2
0
0
2
0
0
0
2
0
1
1
0
1
0
0
0
2
1
0
2
0
0
0
0
2
0
0
0
0
0
0
1
2
2
1
0
0
0
0
0
1
0
1
1
2
0
0
0
0
0
1
0
0
0
0
2
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
2
0
0
1
0
3
0
0
0
1
1
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
7
1
0
0
0
0
1
1
1
0
0
0
0
1
2
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
2
1
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
2
2
2
0
1
0
2
0
1
0
2
0
2
0
0
0
0
1
0
3
0
2
0
0
0
0
1
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
3
0
2
0
0
0
0
0
1
0
0
3
0
0
2
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
2
4
0
0
0
0
0
1
0
0
2
2
0
1
0
1
0
0
0
0
0
1
0
0
1
2
0
0
0
1
0
2
2
0
0
1
1
3
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
2
2
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
3
2
1
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
2
2
0
0
1
2
0
0
2
0
0
2
0
1
3
1
2
0
0
1
0
1
0
1
0
2
0
2
0
0
0
0
2
0
0
0
0
3
1
0
1
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
3
1
0
1
0
0
0
2
1
0
0
0
0
2
0
1
3
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
3
1
0
2
7
0
2
1
0
0
2
2
0
0
0
1
2
0
0
0
1
1
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
1
0
1
0
0
0
3
2
1
0
0
0
0
0
1
1
0
0
0
2
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
2
0
2
0
3
2
0
3
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
3
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
2
1
0
3
0
0
1
0
0
0
2
0
1
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
2
0
1
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
6
0
0
1
0
3
0
0
1
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
5
2
2
0
2
0
0
0
0
0
0
0
1
0
0
5
0
0
0
1
0
0
0
2
1
0
0
0
0
1
0
3
0
0
1
1
2
0
0
0
1
0
0
1
0
0
0
0
1
0
0
2
2
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
4
0
4
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
1
1
1
0
1
2
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
9
2
0
2
0
0
0
0
1
0
2
1
1
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
1
0
2
0
0
6
0
2
0
1
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
1
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
2
0
2
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
2
1
1
0
2
0
0
1
0
1
0
1
2
0
2
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
1
0
1
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
2
0
0
0
1
0
1
0
2
0
0
0
1
2
1
0
0
1
0
0
1
0
2
0
0
2
2
0
2
0
0
0
1
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
4
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
2
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
2
3
0
0
2
0
0
0
0
0
1
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
3
0
0
1
1
0
0
1
0
1
0
2
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
3
0
0
0
0
0
3
0
0
2
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
2
4
0
0
0
0
0
0
1
3
0
2
0
2
3
1
3
0
0
2
2
0
0
0
2
1
0
0
0
2
1
0
0
0
0
1
0
1
2
0
0
1
1
2
4
4
0
0
0
0
0
0
2
0
1
0
0
1
1
0
2
0
0
0
0
0
0
2
0
1
0
0
3
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
1
0
0
1
1
0
2
0
0
0
0
0
1
0
5
0
0
1
0
0
0
4
0
0
0
1
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
2
1
2
0
2
1
1
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
1
1
0
6
1
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
1
0
0
1
0
1
0
0
0
5
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
2
2
0
0
3
0
0
0
0
0
0
1
0
0
0
0
2
0
0
5
0
1
0
0
0
0
3
0
1
0
1
0
2
1
0
0
0
1
2
1
0
0
0
0
0
0
3
0
0
2
2
0
2
0
0
2
2
1
0
0
0
2
0
0
0
0
0
2
0
0
1
1
0
1
0
0
0
2
0
0
1
0
1
2
0
2
0
0
0
0
0
1
1
3
1
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
3
2
2
0
0
1
3
1
0
0
0
1
0
2
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
3
0
1
5
0
0
1
0
0
2
0
1
2
0
1
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
1
1
0
0
6
0
2
2
0
0
0
1
0
0
0
0
0
2
1
0
2
1
0
2
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
2
2
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
1
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
2
2
0
1
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
1
0
0
1
2
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
1
0
0
2
2
0
0
0
0
2
0
2
0
0
0
0
0
0
2
1
0
0
2
1
0
0
1
0
2
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
8
0
0
0
0
0
1
0
3
1
0
0
0
0
0
2
0
0
0
0
2
1
2
0
0
0
0
0
0
0
1
3
0
1
1
0
0
0
1
1
2
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
1
0
0
0
1
0
0
2
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
1
0
1
0
2
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
1
0
0
0
1
0
0
2
0
8
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
1
1
0
0
1
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
3
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
6
0
0
0
2
0
0
1
1
4
0
0
1
1
0
2
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
1
0
0
2
0
2
2
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
3
0
2
0
0
3
0
2
0
2
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
2
0
1
0
0
0
1
0
2
2
0
0
2
0
1
0
0
1
1
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
9
1
0
0
1
1
1
2
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
3
1
1
0
0
0
0
0
0
0
1
0
3
0
0
0
0
1
0
0
1
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
2
1
0
0
1
0
0
2
0
0
5
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
1
2
2
0
1
2
1
1
0
0
0
0
0
1
0
0
3
2
0
0
1
0
5
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
1
1
0
0
0
0
0
2
0
0
0
6
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
1
0
1
0
0
0
0
0
0
0
2
2
0
0
0
3
0
0
0
2
2
1
0
2
1
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
2
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
1
1
2
0
3
0
0
0
1
0
0
0
0
4
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
1
1
0
2
0
1
1
0
2
0
0
0
2
2
0
2
0
0
0
0
3
0
0
4
0
2
0
0
1
0
0
1
0
3
0
1
1
2
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
1
2
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
3
1
3
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
1
0
2
1
1
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
8
0
0
2
0
0
0
0
1
3
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
7
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
3
1
2
0
0
1
2
0
2
0
0
1
2
0
0
0
1
2
0
0
0
0
0
3
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
3
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
3
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
2
2
2
0
1
0
0
3
1
0
0
2
0
0
1
1
0
0
0
0
1
0
1
1
0
0
0
0
3
1
1
1
0
0
0
0
0
0
2
0
0
0
1
1
0
1
0
0
1
1
0
2
0
2
0
0
0
0
0
5
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
5
2
0
0
7
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
7
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
1
0
0
1
0
0
3
0
0
0
2
0
0
1
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
2
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
3
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
5
0
0
0
0
2
1
0
0
1
0
2
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
2
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
1
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
3
0
0
3
1
1
0
1
1
0
0
0
0
0
2
2
0
1
1
0
0
1
4
1
0
0
0
0
1
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
2
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
1
2
4
0
1
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
2
1
0
0
0
2
0
0
1
0
0
0
0
0
0
1
1
0
2
1
0
1
0
0
2
0
3
0
2
0
1
0
0
0
2
0
0
0
0
1
2
1
0
0
2
0
1
0
0
0
0
0
0
0
0
1
2
0
0
3
2
0
0
1
0
0
0
0
0
0
2
0
0
0
2
2
0
2
1
0
0
0
0
0
2
0
1
2
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
3
0
0
0
3
0
2
2
2
0
7
0
0
0
0
0
1
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
3
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
2
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
4
0
0
2
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
3
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
2
0
2
0
2
0
0
0
0
1
2
0
0
2
0
0
2
0
0
0
0
0
0
6
0
0
0
1
0
0
2
0
0
1
0
0
1
0
0
0
0
3
0
0
1
0
1
2
0
0
0
0
2
2
0
0
0
1
0
0
0
1
0
3
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
1
0
0
4
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
2
0
0
0
0
0
1
1
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
3
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
2
2
3
0
6
0
0
2
0
0
1
3
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
1
0
2
0
0
2
0
0
2
1
0
0
0
0
1
0
0
1
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
3
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
2
0
0
0
1
2
2
1
0
1
0
0
0
0
0
0
0
0
2
0
1
2
1
2
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
3
0
0
0
0
0
1
1
1
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
2
3
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
5
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
3
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
2
0
0
3
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
2
0
0
0
0
2
2
0
0
2
0
0
0
1
0
0
0
0
1
2
1
1
2
0
0
1
0
0
0
0
3
0
2
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
2
1
0
0
0
2
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
3
0
1
0
1
2
0
0
0
1
0
6
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
1
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
2
2
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
2
1
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
5
0
0
0
2
0
0
1
0
3
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
2
2
1
2
0
2
0
2
2
0
0
2
1
0
0
0
2
0
0
0
1
0
2
1
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
2
2
0
0
0
2
0
0
1
1
0
0
0
0
2
3
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
2
1
0
0
3
0
0
2
0
0
0
0
0
0
1
3
1
0
0
0
0
1
0
0
0
4
0
2
0
0
1
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
1
0
2
0
0
0
0
3
0
0
0
0
2
0
0
1
2
0
2
0
0
0
0
0
0
4
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
5
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
2
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
1
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
1
0
0
0
3
1
0
0
0
2
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
1
1
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
5
2
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
2
1
0
3
0
0
1
0
0
1
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
3
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
3
0
0
0
0
1
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
1
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
4
1
1
0
0
1
0
3
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
1
0
0
1
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
1
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
1
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
3
0
1
0
0
0
2
1
0
1
0
0
1
1
0
0
0
0
0
0
0
2
1
0
0
3
0
0
1
0
1
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
5
0
0
1
0
0
0
2
3
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
2
2
0
0
0
0
1
0
0
5
0
0
6
0
0
0
1
3
0
0
1
0
1
0
2
0
2
0
0
2
1
0
0
5
0
0
0
3
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
4
2
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
2
1
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
2
0
1
0
0
0
0
2
0
0
1
0
1
1
0
0
0
0
1
0
0
0
1
1
0
0
1
0
2
0
0
0
0
2
2
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
3
2
5
1
0
0
2
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
2
0
1
1
0
0
2
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
3
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
2
0
0
0
0
0
1
0
2
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
2
0
2
0
0
2
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
3
0
0
0
0
0
0
2
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
3
0
0
1
0
1
0
2
0
0
0
2
0
3
0
0
0
0
2
0
2
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
2
3
0
3
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
2
0
0
2
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
2
1
1
2
0
0
0
0
0
1
0
0
0
0
0
3
0
2
1
2
0
0
2
0
0
2
0
0
0
0
1
1
1
0
1
0
2
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
3
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
4
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
1
7
2
0
1
0
1
0
0
0
2
0
0
0
1
0
1
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
2
0
2
0
0
0
1
3
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
3
4
0
0
3
0
0
2
0
2
0
0
0
0
0
1
1
2
0
1
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
2
0
1
0
0
1
0
0
0
0
0
2
2
0
2
0
0
1
0
0
0
0
1
2
0
0
3
1
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
1
0
2
0
2
0
1
0
1
1
2
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
1
0
3
0
3
1
1
0
1
0
2
0
0
0
0
0
1
0
0
2
0
3
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
2
1
4
0
0
0
0
0
0
2
0
0
2
2
0
2
0
2
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
1
0
2
0
0
0
0
3
0
0
0
1
2
0
0
0
0
0
2
1
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
4
0
0
0
0
0
0
1
2
0
2
0
5
0
0
1
2
0
3
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
1
0
0
0
2
0
0
0
0
0
6
0
1
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
4
0
1
1
0
0
1
0
1
0
3
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
1
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
3
0
0
0
0
0
2
0
0
0
0
0
1
2
2
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
2
1
0
0
0
0
0
4
0
0
0
2
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
2
1
1
2
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
4
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
1
2
2
4
2
0
0
0
0
2
2
2
2
0
0
0
3
0
0
0
1
2
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
2
0
0
0
1
0
2
1
2
0
0
0
1
2
0
0
0
0
0
0
1
1
0
2
0
0
1
1
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
2
1
1
1
0
2
2
1
2
1
0
0
0
0
0
3
0
1
0
0
0
1
0
2
0
0
0
1
2
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
2
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
2
0
5
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
1
2
2
1
1
0
0
1
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
1
0
1
0
0
0
0
2
0
0
1
0
0
0
2
0
4
0
0
2
1
0
2
0
0
0
0
2
1
0
1
0
0
0
0
2
1
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
1
0
0
0
0
2
0
1
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
5
0
0
0
0
2
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
4
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
1
2
2
0
0
0
0
2
0
0
0
0
0
0
0
1
3
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
4
0
1
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
5
1
1
0
0
2
0
0
0
0
1
0
1
0
0
0
2
2
0
2
0
2
0
0
0
0
0
0
0
3
3
1
0
1
1
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
2
5
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
1
0
0
1
0
0
0
0
1
0
0
1
2
0
0
0
2
0
0
1
0
1
0
0
0
1
0
0
0
0
3
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
3
0
3
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
4
0
0
0
1
6
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
7
0
0
0
1
0
0
0
1
0
0
0
0
2
0
2
0
0
0
2
0
0
1
0
1
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
1
0
1
1
0
0
1
0
0
0
0
2
2
2
6
0
0
0
4
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
1
0
0
1
0
0
2
1
0
1
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
2
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
2
1
0
1
0
2
0
0
2
1
0
1
0
0
0
0
0
3
0
0
0
0
3
0
1
0
1
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
1
2
0
0
2
2
1
0
0
0
0
0
0
0
2
0
0
2
1
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
2
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
2
1
3
1
0
0
2
0
0
2
2
0
1
0
0
0
2
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
1
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
1
0
1
2
0
1
0
0
1
2
0
0
0
0
0
0
0
0
2
1
3
1
0
0
0
0
1
0
2
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
1
0
2
0
0
0
2
1
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
2
0
1
0
0
2
0
0
1
0
0
2
0
0
0
2
1
0
0
2
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
2
3
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
1
1
1
0
0
2
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
1
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
2
2
0
0
2
0
0
1
1
0
0
0
2
0
2
0
0
2
1
0
0
0
0
2
0
2
0
1
0
0
0
2
3
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
2
0
0
4
0
0
0
0
0
1
0
1
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
4
0
1
4
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
1
0
0
0
2
3
0
0
0
1
1
2
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
2
2
4
0
0
0
0
0
0
0
0
1
2
3
0
0
1
0
0
0
2
1
1
0
1
0
0
0
0
0
1
2
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
2
2
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
1
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
2
0
2
0
3
0
0
0
0
2
1
0
0
0
0
0
0
2
0
4
1
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
6
0
0
1
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
2
0
2
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
2
1
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
2
0
2
0
2
0
0
0
0
1
1
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
2
0
2
0
0
0
1
0
1
0
2
0
1
0
0
1
0
0
1
1
2
0
0
3
0
0
0
0
0
0
0
0
1
1
1
3
0
2
0
1
0
2
0
0
0
0
1
0
1
0
0
0
3
0
0
1
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
5
2
1
0
0
0
2
0
1
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
1
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
2
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
3
2
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
1
0
0
1
1
0
0
0
0
0
0
1
2
0
0
2
0
0
0
2
0
1
0
0
2
0
0
0
4
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
8
0
0
1
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
4
1
2
0
0
3
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
2
3
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
2
2
0
2
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
2
0
1
0
1
0
0
0
0
0
1
0
2
0
2
0
0
2
0
0
2
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
3
0
0
0
0
0
0
0
1
0
0
6
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
3
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
1
2
3
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
3
0
2
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
1
1
2
0
1
0
0
0
0
1
2
0
2
0
1
0
0
0
5
0
0
1
2
0
2
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
2
3
0
0
0
3
1
0
0
0
1
0
0
0
0
0
2
0
0
2
0
1
0
1
0
0
1
2
0
0
0
0
0
0
2
0
0
3
0
0
1
1
0
0
4
0
0
0
0
2
0
0
2
0
0
0
0
4
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
1
3
0
0
2
0
0
1
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
2
2
0
0
1
1
0
1
0
2
0
0
0
0
0
0
3
0
0
2
2
0
0
0
0
2
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
1
0
0
0
0
2
2
2
0
0
0
1
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
2
4
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
3
1
2
1
0
2
0
0
0
0
1
0
0
0
0
2
0
0
1
0
1
0
0
1
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
2
2
3
5
0
0
0
0
0
0
3
1
1
0
0
1
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
5
2
2
3
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
1
2
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
3
0
0
3
0
1
0
0
0
1
0
0
1
0
0
1
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
2
0
0
1
0
0
0
0
0
2
2
2
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
1
0
2
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
7
2
0
1
0
0
0
0
0
3
0
1
2
0
0
0
0
1
0
4
0
1
1
0
0
1
0
2
0
1
2
0
2
0
0
1
1
2
2
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
3
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
2
1
0
2
0
1
0
0
0
1
2
0
0
2
0
0
1
0
0
1
0
0
0
2
0
0
2
2
0
0
0
0
0
0
2
0
0
0
3
0
0
0
2
1
2
0
0
1
1
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
3
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
3
2
1
0
0
0
0
0
1
0
2
0
0
0
1
0
0
3
1
0
0
0
0
1
0
0
1
2
0
0
0
0
0
2
1
0
0
1
0
0
0
4
1
0
0
0
0
2
0
0
0
0
0
0
1
0
3
0
0
0
1
0
2
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
4
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
2
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
4
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
2
0
0
2
0
3
2
1
0
0
0
0
0
0
4
0
0
0
0
0
0
3
0
0
0
0
2
1
0
0
1
2
0
0
1
2
0
3
2
2
0
0
3
0
0
0
1
1
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
3
0
5
0
4
0
2
0
0
0
0
1
2
0
1
1
0
0
0
0
0
0
2
0
0
1
0
0
0
2
1
3
0
0
2
1
0
0
1
0
2
0
2
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
2
0
0
1
1
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
3
2
2
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
8
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
3
0
0
0
0
2
0
0
0
1
1
1
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
1
0
1
0
7
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
1
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
2
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
1
0
0
1
3
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
2
0
3
0
0
0
0
1
0
1
0
0
0
1
0
0
0
2
1
2
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
4
3
2
0
0
0
0
0
0
1
0
2
0
0
2
0
0
2
0
6
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
4
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
5
2
0
0
0
1
0
2
0
0
1
1
0
0
0
2
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
3
1
0
1
0
0
0
1
0
1
2
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
4
0
2
0
0
0
0
1
1
1
0
0
3
0
0
0
0
0
2
0
0
1
1
0
0
0
1
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
2
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
5
0
0
1
0
2
0
0
0
1
1
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
5
2
0
1
0
0
0
1
0
1
0
0
0
0
0
1
2
0
1
2
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
2
0
0
2
2
1
0
2
0
0
2
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
2
3
2
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
1
1
0
2
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
2
1
1
0
0
1
0
1
0
0
1
0
0
2
0
1
0
0
2
0
0
2
0
0
0
0
1
0
2
0
0
0
4
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
2
2
4
0
0
1
1
0
0
0
1
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
1
0
0
0
2
0
2
2
1
1
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
2
0
0
0
0
1
0
0
3
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
2
0
0
2
0
0
1
1
0
0
0
1
0
0
1
2
2
2
0
0
1
0
3
0
0
2
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
2
1
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
3
1
4
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
5
0
0
0
0
0
0
1
0
0
2
0
0
2
2
0
0
0
0
0
1
2
0
0
4
0
2
0
2
0
0
0
0
0
0
2
1
0
2
0
0
2
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
2
1
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
3
2
1
0
0
0
2
0
2
0
0
2
0
2
0
0
0
1
0
5
0
2
0
2
0
0
0
1
2
0
1
0
0
0
0
0
0
2
0
1
1
0
0
1
0
0
2
0
1
1
0
0
0
0
2
1
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
3
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
2
0
2
0
2
0
0
0
1
0
0
0
2
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
1
0
5
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
3
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
4
1
0
1
2
0
2
0
0
1
2
0
5
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
3
0
0
0
1
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
1
1
1
2
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
2
2
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
1
0
0
0
1
1
0
0
0
0
2
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
2
2
1
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
2
2
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
3
0
0
0
2
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
2
2
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
3
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
2
0
1
0
1
0
0
0
0
0
1
1
0
0
0
2
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
8
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
2
3
3
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
3
0
2
0
0
0
0
5
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
2
0
1
0
0
0
2
1
0
0
0
0
0
0
0
1
1
0
1
1
0
0
2
0
2
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
2
0
0
1
1
1
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
1
3
0
0
0
0
2
1
0
1
1
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
2
0
1
1
0
3
0
0
0
1
1
0
0
0
1
0
2
0
1
0
1
0
2
0
2
0
2
0
0
0
0
0
0
2
0
0
2
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
2
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
3
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
1
0
1
0
0
0
0
1
0
0
0
0
1
1
0
2
1
0
0
0
0
2
0
0
2
0
0
0
0
2
1
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
2
0
0
2
0
1
0
3
2
2
0
0
0
0
2
2
0
1
0
3
1
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
2
0
0
0
7
4
1
0
1
0
0
0
1
1
0
1
0
0
0
1
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
1
0
0
0
1
1
1
1
0
1
0
0
1
0
0
2
0
2
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
2
0
6
0
0
1
0
0
0
3
1
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
2
0
0
1
0
2
2
1
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
2
1
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
1
1
0
0
2
2
2
0
0
0
1
0
0
0
0
9
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
5
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
2
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
4
1
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
2
2
0
2
0
2
1
0
0
2
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
3
0
0
0
1
0
0
2
0
0
0
0
2
0
1
0
0
1
0
1
0
0
1
1
1
0
2
1
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
1
0
0
2
1
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
2
0
0
0
0
2
2
0
1
0
2
1
3
1
1
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
2
0
2
0
0
2
0
0
0
1
0
0
1
1
0
0
0
5
0
1
0
0
0
2
0
0
1
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
2
2
0
0
0
0
0
2
2
0
0
0
2
1
0
2
0
0
0
1
0
2
0
0
0
0
7
0
0
0
2
2
1
0
1
0
0
4
0
0
0
0
2
0
0
0
2
1
0
2
1
0
0
0
0
0
1
0
2
0
1
1
0
0
0
0
0
0
0
1
1
0
1
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
1
0
0
0
0
4
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
3
0
2
0
0
0
0
1
0
0
2
2
0
0
1
0
1
1
0
0
4
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
1
1
0
0
1
2
0
0
0
0
1
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
2
1
0
1
0
0
0
1
1
2
2
0
0
0
0
0
0
0
0
3
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
4
0
0
0
1
2
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
1
0
1
2
1
0
0
2
0
0
3
2
2
0
0
0
0
0
0
0
0
1
2
1
0
2
0
2
0
0
2
0
0
0
1
0
0
0
0
1
2
0
0
0
2
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
1
0
0
0
1
0
0
2
0
2
0
2
0
1
0
0
0
0
0
5
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
5
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
2
0
0
0
0
3
0
0
0
0
0
1
1
1
2
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
3
2
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
3
0
0
0
0
0
0
2
1
0
1
1
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
2
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
1
1
0
1
2
2
2
0
2
1
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
2
0
1
0
1
2
0
0
0
2
2
0
3
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
2
0
0
0
1
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
1
2
2
0
1
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
1
2
0
0
1
0
0
0
0
1
2
0
1
0
1
1
1
0
1
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
3
1
0
0
0
0
0
0
3
0
3
0
2
0
2
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
3
0
0
0
2
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
1
0
1
2
0
2
0
0
0
0
0
2
0
5
2
0
0
0
0
1
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
2
0
0
2
0
0
0
1
2
3
1
0
0
1
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
3
0
0
0
1
0
2
0
0
1
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
1
2
1
1
2
0
0
2
0
1
0
1
0
2
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
2
0
1
1
0
0
0
2
0
0
0
0
2
0
1
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
1
2
1
0
2
0
0
0
0
3
0
0
1
0
0
0
1
1
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
2
2
1
0
0
2
1
0
1
0
0
0
0
0
0
1
0
0
0
2
2
3
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
2
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
3
1
0
0
0
2
1
0
1
0
2
0
2
0
1
0
0
0
0
0
0
0
1
4
2
0
2
0
0
0
1
2
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
1
1
0
1
0
2
4
0
2
0
0
0
0
0
0
0
3
0
5
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
1
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
3
5
2
0
0
2
1
3
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
2
0
1
1
2
0
2
0
0
1
2
0
0
0
0
0
2
0
0
0
0
2
0
0
3
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
2
0
2
0
0
2
2
0
3
0
0
1
2
0
0
0
1
0
2
0
0
0
0
0
0
0
3
2
0
1
0
0
1
0
0
0
0
2
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
5
2
0
0
2
1
0
1
2
0
2
0
0
1
2
0
0
1
0
0
1
0
2
0
0
2
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
5
0
2
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
1
0
0
0
1
0
0
1
0
0
3
1
0
2
0
1
1
0
0
1
1
1
0
0
0
2
0
0
2
0
0
0
0
2
2
3
3
0
0
3
0
0
0
2
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
3
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
4
2
0
0
1
0
0
2
0
0
0
3
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
2
0
1
0
2
0
0
1
0
2
1
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
1
2
1
1
0
0
0
1
0
2
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
2
4
1
0
0
1
0
2
2
0
1
0
1
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
2
5
0
2
0
1
0
0
0
0
4
0
0
0
0
0
4
0
0
0
1
0
0
1
0
2
2
1
1
0
0
0
1
2
0
1
2
0
3
2
0
2
0
0
0
2
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
1
1
1
0
0
0
1
1
0
0
0
0
0
0
0
3
0
3
1
0
0
0
2
0
2
0
2
0
0
2
0
0
0
1
1
0
0
0
1
5
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
1
1
0
0
0
4
0
0
0
0
0
0
2
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
2
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
2
0
1
0
0
1
0
0
0
0
1
0
0
0
0
3
1
1
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
1
1
0
0
0
0
1
2
1
0
0
0
1
0
0
3
0
0
0
0
0
0
2
0
2
0
0
1
0
0
2
0
0
0
0
0
2
1
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
2
1
0
2
0
0
0
2
1
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
3
0
0
0
0
0
0
2
0
0
1
0
2
0
2
1
0
0
0
2
0
1
0
2
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
3
0
0
0
0
0
0
0
3
2
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
2
0
1
1
0
5
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
1
0
0
0
1
3
0
0
0
0
2
0
0
0
0
2
0
3
1
0
0
0
2
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
2
1
0
0
1
0
1
0
0
0
1
1
1
1
2
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
2
2
0
0
0
2
0
1
0
0
2
0
1
0
0
0
0
0
0
0
3
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
5
3
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
2
0
2
1
0
4
2
0
0
1
0
0
3
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
6
0
1
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
1
1
0
0
1
2
0
0
0
7
1
0
0
1
0
0
3
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
2
0
1
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
1
1
0
1
0
3
0
2
0
0
2
0
0
0
1
0
3
0
2
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
5
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
2
1
0
2
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
1
0
0
1
1
0
0
0
0
0
4
0
0
2
3
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
2
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
2
0
0
2
0
0
0
2
2
0
0
2
0
0
0
2
1
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
1
0
0
2
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
2
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
1
1
0
1
0
1
1
1
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
2
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
1
0
1
0
1
0
3
0
0
3
0
0
1
0
0
0
2
0
0
0
7
0
2
0
0
2
0
0
0
10
1
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
2
0
0
0
2
3
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
1
6
0
2
0
0
2
0
0
0
3
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
2
0
1
0
0
2
0
0
0
0
1
1
0
2
0
0
0
0
0
1
0
0
0
0
1
0
4
0
0
0
2
0
2
2
0
0
2
0
1
0
0
0
1
2
0
0
1
0
1
0
2
0
0
3
0
0
0
0
0
0
0
0
1
0
0
1
2
2
2
0
1
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
1
0
1
0
0
1
0
2
0
0
1
0
0
0
0
1
0
2
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
1
1
0
0
0
1
0
0
2
0
0
1
0
0
0
3
0
0
1
0
1
0
0
0
0
0
2
0
2
1
0
2
0
1
1
0
0
1
3
0
0
0
0
0
0
1
0
2
2
0
1
0
2
1
1
0
0
2
0
0
0
2
0
0
0
0
1
2
3
0
1
0
1
0
0
0
0
0
0
1
0
0
3
0
0
1
0
0
3
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
1
0
0
0
0
0
0
0
14
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
3
0
0
7
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
5
0
1
0
0
0
1
0
0
0
0
0
3
0
0
0
1
1
0
0
1
5
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
1
0
0
0
0
0
0
2
0
1
0
2
2
0
0
0
0
0
2
0
1
0
0
2
1
3
0
0
2
0
0
0
0
3
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
3
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
3
0
0
2
0
8
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
2
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
1
7
0
0
4
1
1
0
0
2
0
2
4
1
0
0
1
0
1
1
2
0
2
0
0
1
0
0
0
0
2
0
1
0
2
2
0
0
0
0
0
0
2
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
9
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
3
1
0
2
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
1
0
1
2
0
0
0
0
1
2
0
2
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
2
0
0
1
1
0
0
1
0
1
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
4
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
1
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
1
0
0
1
1
1
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
1
0
0
2
0
0
0
2
2
0
0
0
2
1
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
4
0
0
1
2
0
0
1
0
0
1
1
2
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
2
0
1
2
4
0
0
0
1
0
1
0
1
0
1
2
1
0
1
1
0
0
1
1
2
0
0
0
2
0
0
0
0
0
3
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
4
1
2
0
0
0
0
0
2
0
0
0
0
0
2
0
3
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
1
0
0
1
0
0
2
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
2
1
2
1
0
0
1
1
0
0
0
0
2
0
1
0
1
0
0
1
0
0
0
0
0
2
2
0
0
0
0
3
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
2
0
2
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
1
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
2
0
0
0
1
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
2
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
1
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
1
2
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
1
0
0
1
1
1
2
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
1
0
0
1
0
0
0
0
0
6
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
2
0
0
1
0
2
2
0
1
0
0
3
0
0
0
0
0
0
0
2
1
4
1
1
0
0
2
2
2
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
2
0
0
3
0
0
0
0
2
2
2
0
0
2
1
0
0
0
0
1
2
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
2
0
0
0
0
0
2
2
1
1
0
2
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
1
0
0
0
5
0
0
0
0
2
0
0
0
0
2
0
0
1
0
1
1
0
0
0
2
1
0
1
0
0
1
2
0
0
0
0
0
0
1
0
1
1
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
1
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
5
2
0
0
0
2
0
0
2
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
4
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
1
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
2
0
0
0
3
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
2
3
0
0
0
0
1
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
1
0
1
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
1
0
3
2
1
0
0
3
1
0
2
1
0
1
0
0
1
0
0
1
0
1
0
0
0
0
2
2
1
0
0
0
0
2
1
0
0
2
0
0
0
2
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
5
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
1
1
3
0
0
0
0
0
2
0
1
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
5
0
1
1
0
2
2
0
0
2
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
7
0
0
1
2
4
0
1
5
0
0
0
0
0
0
1
0
2
1
0
0
3
0
0
0
2
1
0
2
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
1
2
0
0
3
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
3
0
1
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
1
0
1
0
2
1
1
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
1
0
0
0
0
2
0
1
1
2
0
0
0
0
0
0
1
0
0
0
2
2
2
0
2
2
1
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
2
2
1
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
1
0
0
0
2
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
3
0
0
1
2
0
1
0
0
0
0
0
1
0
0
0
0
5
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
3
0
1
0
0
0
0
2
0
2
0
2
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
1
0
2
1
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
8
2
1
0
0
0
1
1
0
0
0
5
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
2
0
0
3
0
0
0
0
0
2
0
2
0
0
2
0
1
0
0
5
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
1
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
2
0
2
0
3
1
0
0
0
1
0
0
0
0
4
1
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
1
2
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
1
0
2
1
0
0
0
2
0
0
0
0
0
2
2
0
2
1
0
0
0
2
0
1
2
0
0
0
2
2
0
7
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
3
1
1
0
0
1
0
0
0
6
0
1
0
3
0
0
0
0
2
2
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
3
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
2
1
0
0
3
0
1
0
2
6
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
1
6
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
2
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
1
3
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
2
7
2
0
0
0
2
2
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
2
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
2
0
0
0
1
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
1
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
2
0
3
0
0
1
0
0
0
0
2
0
0
0
0
0
2
2
0
1
1
1
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
16
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
3
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
4
0
0
1
2
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
2
1
0
0
2
0
0
0
0
0
2
0
2
2
0
0
0
0
0
2
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
2
4
2
0
0
0
0
0
0
0
3
0
0
0
0
1
0
1
0
3
0
2
0
1
6
0
0
0
0
1
2
1
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
1
1
0
7
0
0
0
0
3
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
3
1
0
2
0
2
1
0
2
0
0
0
1
2
2
0
1
0
0
0
0
1
0
2
0
0
1
4
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
3
0
0
3
0
1
2
3
0
1
1
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
10
0
6
0
0
0
0
1
0
1
0
0
4
0
1
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
1
0
0
1
1
0
0
1
0
0
1
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
3
0
0
0
1
0
0
2
0
0
1
2
0
0
1
0
0
0
2
1
2
2
0
0
1
1
0
1
0
0
0
1
0
0
0
0
1
0
3
0
1
0
2
1
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
2
1
2
0
0
3
0
0
2
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
4
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
1
1
2
0
0
1
2
2
0
0
0
0
0
0
1
1
0
0
0
0
1
2
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
2
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
3
2
0
0
0
0
0
0
2
2
0
1
2
0
2
0
1
0
0
3
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
1
0
0
0
2
2
0
0
0
0
0
2
0
0
2
1
2
0
0
0
0
0
0
0
0
3
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
1
2
0
2
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
4
0
0
0
1
0
1
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
3
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
1
0
0
0
2
1
0
3
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
2
2
2
0
1
1
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
2
1
1
0
2
0
0
0
1
0
0
2
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
2
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
2
0
0
0
1
0
0
0
2
0
1
0
0
2
0
2
0
0
0
0
0
0
15
3
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
2
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
2
0
2
2
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
1
1
0
1
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
2
0
1
1
4
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
3
2
1
0
0
1
0
1
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
2
0
0
0
1
2
1
1
0
0
0
1
0
0
0
4
0
0
0
0
2
0
0
1
0
3
1
1
0
0
1
0
3
1
0
0
0
1
0
0
0
1
0
0
0
0
4
0
2
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
1
0
4
0
1
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
1
3
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
2
0
0
0
4
0
2
0
2
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
2
1
0
0
1
0
0
0
1
0
0
2
0
0
2
2
0
0
0
0
0
0
0
1
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
2
1
0
2
0
1
1
0
2
1
1
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
1
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
1
0
1
0
0
2
2
0
2
0
4
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
3
0
2
0
0
0
0
0
3
0
1
0
0
1
0
0
1
0
0
0
2
1
2
0
0
0
2
0
0
0
1
2
0
0
2
2
2
0
1
0
0
0
0
0
0
0
1
0
0
1
3
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
1
0
4
0
0
0
2
0
1
0
0
0
0
0
0
1
2
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
5
1
2
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
1
2
0
2
0
0
2
0
0
2
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
1
0
0
0
0
2
1
0
0
2
0
1
0
0
0
0
0
0
1
1
0
0
3
0
0
1
0
0
0
1
0
3
2
0
0
2
0
1
2
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
3
0
0
0
0
1
2
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
2
0
0
0
5
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
1
0
2
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
1
0
2
4
0
0
0
1
0
2
0
0
0
0
0
0
1
0
2
2
0
0
1
0
0
0
1
0
0
0
0
0
0
2
1
0
2
0
0
1
0
2
0
3
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
2
1
0
0
0
2
0
1
0
0
2
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
2
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
3
0
0
0
1
0
0
0
2
0
0
1
0
2
0
0
0
0
4
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
1
0
0
0
2
0
4
0
1
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
2
2
3
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
2
0
0
2
0
0
3
0
2
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
2
0
1
0
0
0
1
1
0
0
0
0
1
2
0
0
0
1
0
0
0
2
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
10
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
3
1
0
0
2
0
0
1
0
0
1
0
1
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
2
0
0
0
0
0
0
2
0
1
0
1
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
2
2
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
3
0
0
0
0
0
0
2
2
0
0
2
2
0
0
0
0
0
4
2
3
0
0
0
0
2
0
1
0
0
2
0
2
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
1
1
3
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
3
2
0
1
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
1
2
0
0
1
0
1
0
3
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
3
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
9
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
3
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
1
1
0
2
0
2
0
0
1
2
2
1
0
1
0
0
2
0
0
2
2
0
1
2
2
0
2
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
2
0
3
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
4
1
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
3
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
2
0
3
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
2
0
1
0
2
0
7
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
1
0
1
0
0
2
0
1
1
0
2
2
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
1
0
0
0
2
0
1
1
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
1
0
0
2
0
1
0
1
0
0
0
0
1
0
1
2
0
1
2
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
2
0
0
0
0
0
0
1
0
1
0
1
2
0
0
0
0
0
1
1
1
1
0
1
0
0
1
2
2
0
1
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
6
11
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
2
1
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
3
0
1
0
0
0
3
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
1
0
2
0
1
1
2
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
2
0
1
0
2
0
2
5
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
1
0
0
1
0
0
0
2
3
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
3
0
0
0
0
0
2
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
2
0
2
0
0
0
0
2
2
1
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
3
2
0
0
0
1
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
1
0
1
0
0
1
0
2
5
0
0
1
0
0
2
2
1
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
2
0
0
1
0
0
3
0
0
0
0
1
2
0
0
2
0
0
0
0
1
0
1
2
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
1
0
1
0
1
0
2
0
0
2
0
0
1
3
0
0
0
0
0
0
0
1
2
2
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
6
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
2
1
2
0
0
0
0
2
1
1
2
0
0
0
4
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
6
2
0
0
1
2
0
1
0
0
2
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
1
0
0
2
2
0
0
0
0
0
2
2
0
1
0
0
2
0
0
0
0
0
1
1
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
2
1
0
0
0
0
0
2
1
0
2
2
1
0
0
0
0
1
0
1
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
2
0
0
1
0
0
0
0
0
5
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
1
1
0
2
0
2
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
1
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
2
0
0
2
0
0
1
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
1
2
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
3
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
2
0
2
0
3
0
1
0
0
0
0
2
0
0
1
0
0
1
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
4
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
2
0
1
2
6
0
0
0
0
1
0
1
0
0
0
0
0
3
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
4
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
1
0
0
0
0
0
0
0
3
1
0
0
1
2
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
1
0
2
0
0
0
0
0
6
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
1
3
1
0
0
2
1
2
0
2
0
2
0
0
0
1
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
3
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
3
2
0
2
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
1
0
0
0
2
0
0
0
0
0
0
2
2
0
1
2
0
0
0
0
2
0
1
0
0
0
0
2
1
0
1
2
0
0
0
0
2
0
2
2
0
0
2
0
0
1
1
0
0
2
1
1
0
0
0
0
0
2
0
0
0
0
3
0
1
0
0
1
0
0
0
1
0
0
0
1
2
2
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
2
0
0
0
0
1
0
0
1
0
0
2
0
2
0
2
0
0
2
0
0
0
0
1
2
0
0
0
0
3
2
1
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
4
0
2
0
1
3
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
2
1
0
2
0
1
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
2
0
1
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
1
0
1
1
1
0
1
0
2
0
0
2
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
3
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
2
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
2
1
0
3
2
0
0
1
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
2
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
2
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
3
1
0
0
1
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
3
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
2
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
3
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
2
0
1
1
0
0
0
0
1
0
2
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
1
2
0
0
1
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
1
0
1
2
0
0
1
0
0
2
0
0
1
0
2
0
0
0
1
1
0
0
0
0
1
2
0
1
3
0
0
0
1
1
0
3
0
0
0
0
1
2
0
0
0
0
1
2
1
2
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
1
2
4
1
0
0
0
0
3
1
2
0
1
0
2
1
0
0
0
0
0
0
1
0
0
0
0
4
1
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
1
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
3
0
2
1
0
1
0
0
4
0
0
0
1
0
0
2
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
2
2
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
2
0
2
1
1
2
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
1
1
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
3
0
0
0
0
0
13
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
1
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
2
0
2
0
0
0
3
0
0
0
0
0
2
0
2
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
1
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
1
0
0
0
0
2
1
0
0
0
2
1
0
0
0
2
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
4
1
0
1
0
0
0
0
1
0
0
0
3
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
1
0
1
0
1
0
0
0
1
2
0
0
0
2
2
2
3
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
2
2
1
0
1
2
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
1
1
0
0
2
0
0
0
0
1
0
0
1
0
0
2
0
0
2
0
0
0
1
2
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
1
0
0
2
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
2
1
2
8
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
3
0
2
0
0
0
1
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
3
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
3
0
0
0
0
0
0
2
0
1
0
1
1
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
1
0
0
2
0
1
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
2
0
2
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
2
0
3
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
4
0
2
0
1
1
0
2
1
2
0
0
1
1
0
0
0
0
1
0
2
0
0
0
0
0
2
0
1
1
2
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
2
3
3
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
1
0
2
2
3
0
2
0
0
0
0
0
2
0
0
1
0
0
2
0
3
0
0
0
0
0
1
0
1
0
0
1
2
0
0
2
0
0
0
0
4
0
0
4
1
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
7
0
0
1
0
3
0
0
0
0
0
0
0
0
1
0
0
3
0
1
0
2
0
1
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
1
0
0
0
2
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
3
0
0
0
1
0
1
3
0
0
0
0
0
2
0
1
2
3
1
0
0
0
0
1
0
1
2
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
1
0
2
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
1
1
0
3
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
2
0
1
0
0
0
0
0
0
0
0
0
8
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
2
2
4
0
1
2
0
4
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
6
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
2
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
1
0
2
0
3
1
1
0
0
0
2
0
0
2
0
2
0
0
0
0
2
0
0
3
2
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
3
1
1
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
3
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
1
0
0
0
1
2
0
0
2
0
0
0
0
2
0
0
0
4
0
1
1
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
3
0
1
0
2
0
0
0
1
0
0
0
0
0
0
1
1
2
2
0
1
0
0
0
0
0
1
0
0
0
0
0
3
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
1
0
3
0
0
2
0
1
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
3
0
0
0
0
2
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
1
0
0
0
0
0
3
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
3
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
6
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
1
1
2
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
1
0
2
1
1
2
0
0
0
2
2
1
0
0
2
0
0
1
0
5
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
3
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
6
0
0
0
0
0
5
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
3
0
0
0
1
0
0
0
1
2
0
0
0
3
1
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
2
0
3
0
1
0
2
0
2
0
1
1
0
0
0
0
2
1
0
0
0
0
2
0
0
1
0
1
0
0
1
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
2
0
2
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
6
0
1
1
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
2
1
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
1
1
0
0
1
0
1
0
3
0
0
0
1
0
3
0
2
0
0
0
0
0
0
3
0
1
0
1
0
0
0
0
2
0
0
0
1
0
0
9
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
1
1
0
0
0
0
2
0
0
1
0
0
1
0
1
2
0
0
1
0
2
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
3
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
4
2
2
0
0
2
0
0
0
2
2
0
0
0
1
0
0
2
3
0
0
0
0
0
0
0
2
0
3
0
1
0
3
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
2
0
1
0
0
1
0
0
0
0
0
0
1
2
0
1
0
0
0
2
1
0
0
0
0
3
1
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
2
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
3
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
2
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
1
1
1
0
0
2
1
0
0
0
0
0
1
0
2
0
0
0
2
2
0
2
0
0
1
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
2
0
1
5
0
0
0
0
0
0
0
1
1
2
0
0
0
1
2
0
0
0
1
0
0
0
0
0
2
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
3
1
0
2
2
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
2
2
0
2
0
0
0
1
0
0
0
1
2
2
0
0
2
0
1
4
0
0
2
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
2
0
0
0
2
0
4
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
1
0
0
2
0
1
0
1
0
1
2
0
0
0
0
0
0
0
0
2
2
0
0
1
1
0
0
0
0
1
0
2
2
1
2
0
0
2
0
0
1
3
0
0
0
0
0
1
0
2
1
0
1
0
0
1
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
4
1
0
0
0
1
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
1
0
0
0
3
0
0
0
0
2
0
0
1
0
2
1
0
0
2
3
0
1
0
0
0
0
0
2
1
1
0
0
0
2
0
3
0
0
0
0
0
2
0
2
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
9
1
0
0
0
0
0
0
0
0
2
0
0
3
2
0
0
0
0
2
0
0
2
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
2
2
1
0
0
0
0
1
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
1
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
3
2
0
0
1
0
0
0
2
0
0
3
0
1
0
0
1
0
0
0
0
0
2
0
2
0
0
4
0
0
0
2
0
0
0
0
2
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
3
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
2
0
0
1
0
0
2
0
1
3
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
1
4
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
3
0
0
2
3
0
0
1
0
0
2
0
0
2
2
0
0
2
0
0
1
2
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
2
2
0
0
2
0
0
1
0
1
2
2
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
1
0
0
0
0
2
1
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
2
1
5
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
14
2
0
0
0
1
0
1
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
1
0
0
0
0
1
0
2
1
0
0
0
0
0
0
1
0
1
2
0
0
0
1
0
0
0
1
0
0
2
0
0
2
0
1
0
0
0
0
1
0
2
3
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
3
0
0
0
0
0
0
0
0
1
0
1
2
2
0
0
2
0
0
0
1
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
1
2
1
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
2
1
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
1
0
2
0
0
0
2
0
0
2
0
0
0
0
1
3
0
1
0
0
0
1
0
2
0
1
0
0
0
0
0
2
0
0
0
2
2
4
1
0
0
0
0
0
2
3
2
0
0
0
0
1
0
0
9
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
1
2
0
0
0
0
0
0
2
3
0
0
0
1
0
3
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
2
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
6
1
1
2
2
0
0
0
0
1
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
4
1
0
0
0
0
2
0
0
1
0
0
0
0
2
1
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
1
0
1
0
0
0
2
0
0
1
2
2
1
0
0
0
3
0
1
1
0
2
0
0
0
0
2
0
0
0
5
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
4
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
1
0
0
2
0
0
0
3
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
3
1
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
2
0
0
0
0
0
1
1
0
3
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
1
0
0
0
0
2
2
2
0
0
3
1
2
0
0
0
2
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
2
0
1
0
2
0
0
3
0
0
0
1
0
2
0
0
0
0
0
1
2
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
1
2
2
0
0
0
0
2
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
0
0
2
0
1
0
0
0
1
0
0
1
0
1
2
0
0
0
0
1
1
0
1
1
0
0
3
0
0
0
0
0
2
0
2
0
2
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
1
0
2
0
0
0
2
0
0
1
2
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
3
0
1
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
1
0
1
0
0
2
0
0
0
0
0
0
0
2
3
0
0
9
0
0
0
0
1
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
2
0
1
0
0
0
1
0
0
1
2
0
1
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
2
2
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
3
2
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
2
1
2
0
0
1
3
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
2
2
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
4
1
0
0
0
0
1
0
0
2
0
0
0
1
0
2
0
4
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
2
1
0
0
0
0
3
0
0
0
0
2
2
0
0
2
0
1
2
1
0
0
2
0
0
2
3
0
2
0
1
0
0
2
0
0
2
0
0
0
2
0
0
0
1
1
0
0
1
0
0
0
0
1
3
0
0
0
3
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
2
0
0
0
0
0
1
2
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
4
8
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
1
1
2
0
0
0
0
0
0
0
2
0
0
0
0
3
0
2
1
0
0
0
3
0
0
0
0
2
0
1
1
0
1
0
0
2
0
0
0
0
4
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
2
0
0
1
0
2
0
3
0
0
0
2
1
2
0
1
0
2
0
0
2
1
2
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
2
0
0
1
0
0
0
1
2
0
0
1
2
0
0
0
0
2
0
0
0
0
2
0
0
1
0
1
0
0
1
0
0
2
0
0
0
0
1
0
0
0
2
0
0
2
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
2
1
0
3
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
2
1
0
0
0
0
1
1
2
0
0
8
0
0
2
2
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
3
0
1
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
1
3
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
2
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
3
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
2
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
1
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
1
1
2
2
1
0
0
0
0
2
1
0
0
3
0
0
0
1
0
1
0
1
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
1
2
1
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
2
0
2
0
1
0
1
1
0
0
0
3
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
1
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
2
2
0
0
0
0
2
1
0
0
0
2
0
0
1
1
0
2
3
0
2
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
4
0
1
0
0
3
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
2
0
2
1
0
0
2
0
0
1
0
3
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
1
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
3
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
1
0
0
1
0
0
0
1
2
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
1
0
4
0
0
2
1
0
0
1
0
0
1
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
2
1
0
1
0
0
0
1
1
5
1
0
0
0
0
0
0
2
0
0
0
1
3
0
1
0
0
0
0
0
2
0
0
0
2
0
0
1
2
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
2
0
3
0
0
2
0
0
0
0
0
7
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
1
4
2
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
2
0
1
1
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
3
1
0
0
0
2
1
2
1
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
2
1
0
2
3
0
0
2
3
0
0
0
0
1
0
0
0
2
0
0
0
10
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
6
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
1
1
2
0
0
0
0
0
2
0
0
0
1
0
1
0
2
0
1
0
1
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
4
0
2
1
2
2
8
0
0
0
1
1
1
3
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
4
1
2
0
2
0
0
1
1
0
0
2
1
0
0
1
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
1
0
2
0
0
0
0
0
0
0
5
0
2
0
0
0
0
0
0
1
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
9
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
1
2
0
2
0
0
0
0
0
1
0
0
0
2
0
6
0
0
0
1
3
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
2
4
0
2
0
0
0
0
7
0
0
0
0
0
0
3
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
1
0
0
0
0
4
0
0
0
3
0
0
0
0
0
0
0
2
0
2
0
0
2
0
1
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
2
1
0
0
1
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
2
3
0
1
0
0
0
0
2
1
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
1
1
0
2
0
0
0
1
0
1
0
0
2
0
0
0
0
0
2
2
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
2
0
0
0
0
1
0
2
3
0
1
0
2
0
0
2
0
1
0
0
0
0
2
0
2
2
1
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
3
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
3
0
2
0
3
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
2
1
0
1
1
0
1
0
0
0
1
0
0
0
0
1
1
0
1
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
1
0
0
3
0
0
0
0
0
2
0
0
1
0
0
1
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
9
1
0
0
0
2
0
1
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
1
0
1
3
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
3
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
2
1
2
0
0
1
0
0
0
0
1
1
2
0
0
0
0
3
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
1
2
0
0
3
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
8
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
9
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
2
1
4
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
1
2
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
2
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
1
3
0
3
0
1
0
1
1
0
2
0
2
0
0
0
3
0
0
0
0
1
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
1
2
0
1
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
2
1
0
1
0
0
1
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
1
0
0
2
1
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
1
2
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
3
1
0
0
0
0
1
2
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
3
0
1
0
1
2
0
0
0
0
0
0
0
0
0
1
2
2
0
2
0
0
0
0
2
1
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
3
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
3
0
0
1
1
0
0
3
3
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
2
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
2
0
4
0
0
0
0
0
0
3
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
3
4
4
5
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
1
0
0
0
2
0
2
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
2
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
1
0
0
0
0
2
0
2
0
0
2
1
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
1
1
0
0
0
0
2
0
0
1
3
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
2
0
2
0
1
0
0
1
0
1
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
3
0
1
0
0
2
1
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
2
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
5
0
0
0
0
0
2
1
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
1
2
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
3
0
2
0
0
0
1
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
2
2
1
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
1
1
0
0
0
0
2
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
1
1
2
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
1
2
1
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
2
1
3
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
1
2
0
1
1
0
0
0
1
0
0
0
2
0
0
2
0
1
2
0
2
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
1
2
0
0
2
0
2
0
0
0
0
0
7
0
1
0
1
0
4
1
0
0
0
0
0
1
0
2
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
2
0
0
1
0
0
0
2
0
1
0
1
0
0
0
0
2
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
1
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
2
0
0
0
0
2
0
1
0
0
0
3
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
3
0
0
2
1
0
0
2
2
0
0
6
0
1
1
2
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
4
1
1
0
0
0
0
0
0
0
1
0
0
0
3
0
2
0
0
0
2
0
0
0
0
0
0
2
2
0
2
0
3
2
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
2
1
1
2
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
4
1
0
0
0
2
2
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
4
2
0
3
0
2
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
6
1
0
0
0
0
6
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
2
1
0
2
0
0
0
0
1
0
0
2
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
1
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
2
1
0
0
0
0
0
1
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
1
2
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
4
1
2
0
0
0
0
1
0
2
2
1
3
0
0
3
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
3
1
0
0
1
0
0
2
1
0
0
0
0
2
0
0
0
2
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
5
0
1
2
0
1
0
2
0
0
0
0
0
0
1
0
0
0
5
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
4
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
1
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
8
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
1
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
4
1
0
0
0
1
0
0
0
0
0
0
0
4
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
7
2
0
1
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
1
0
2
2
1
0
2
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
2
0
4
0
0
0
0
0
2
0
0
2
1
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
1
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
1
0
0
0
4
0
2
0
0
0
0
2
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
4
0
1
0
2
2
0
0
1
1
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
2
0
0
2
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
2
1
0
0
2
0
1
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
2
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
1
0
1
2
0
1
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
2
0
0
1
2
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
2
0
0
2
3
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
1
0
1
2
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
2
0
5
0
0
0
1
1
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
1
0
1
0
2
0
0
0
1
1
0
0
0
1
0
0
0
0
1
2
2
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
2
0
0
1
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
9
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
1
0
0
1
2
0
2
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
3
0
2
0
0
0
0
0
0
1
0
0
2
2
1
2
0
1
0
0
4
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
2
1
1
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
3
2
0
2
0
0
0
0
2
2
1
0
0
0
0
0
0
3
1
3
0
0
0
0
2
0
0
3
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
1
0
0
1
0
2
1
1
0
0
0
0
2
0
0
0
2
2
0
1
0
3
0
0
0
0
1
0
1
0
0
0
0
0
2
1
0
0
0
7
2
0
0
0
1
0
0
0
0
1
1
0
0
0
0
2
0
2
0
0
0
0
0
1
0
2
1
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
2
2
0
1
0
0
2
1
2
0
1
0
0
0
0
0
2
3
0
0
2
0
1
2
0
0
2
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
4
0
1
0
3
0
1
0
0
0
1
0
0
1
2
0
1
0
0
0
0
0
0
0
2
1
1
2
0
0
2
1
0
0
0
0
0
0
1
0
1
2
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
1
0
0
0
0
0
1
0
0
0
2
0
1
2
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
2
0
0
1
0
1
0
0
0
0
2
0
2
1
1
2
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
2
0
2
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
3
0
0
0
4
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
1
0
0
0
0
0
0
1
0
1
4
2
0
0
1
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
1
0
0
2
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
2
3
0
0
0
0
0
0
0
1
1
0
0
0
2
1
0
3
0
2
0
3
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
5
2
3
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
1
0
2
0
2
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
2
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
2
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
7
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
3
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
2
2
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
1
1
0
0
1
0
3
0
0
0
0
2
2
0
3
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
1
2
0
0
0
2
3
0
0
1
0
0
0
1
2
2
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
1
0
0
1
2
0
1
2
0
3
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
3
0
2
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
3
0
0
0
1
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
1
0
3
2
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
3
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
2
0
2
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
2
0
1
0
0
1
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
2
0
0
2
0
2
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
1
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
3
0
0
2
0
1
0
0
0
0
0
0
3
0
0
0
3
2
0
0
0
0
2
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
1
2
0
2
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
1
0
0
0
0
2
0
2
2
0
1
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
1
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
2
0
2
2
0
1
1
1
0
1
2
3
0
0
0
1
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
2
0
0
0
1
1
0
2
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
2
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
2
3
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
1
4
2
2
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
3
0
1
0
0
0
0
0
0
1
0
0
1
0
1
2
2
1
1
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
3
1
0
0
0
3
0
2
0
0
0
1
0
0
0
0
1
0
0
2
0
2
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
2
0
0
2
0
0
0
0
1
0
0
2
2
0
2
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
3
0
0
2
2
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
2
3
0
0
1
0
0
0
0
0
0
1
0
2
0
0
2
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
1
2
0
0
1
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
3
1
2
0
0
0
0
0
0
0
3
0
1
0
0
0
0
3
1
0
1
3
2
2
0
0
0
3
0
0
2
0
1
2
0
0
0
0
1
0
0
2
1
2
2
1
0
0
3
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
2
0
0
0
0
2
0
0
2
0
0
0
2
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
2
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
3
0
1
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
5
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
1
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
1
0
2
0
0
0
0
2
0
0
0
1
0
0
1
0
0
3
1
1
0
0
0
0
2
0
2
0
0
0
2
1
2
1
0
0
0
2
0
1
0
0
0
0
0
2
3
0
0
0
0
0
0
1
2
2
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
2
2
0
4
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
3
0
0
0
0
0
1
0
0
0
0
1
2
0
2
0
0
0
2
0
1
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
3
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
2
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
2
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
2
2
0
0
0
0
0
1
0
2
0
0
3
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
1
0
0
1
0
0
2
0
3
2
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
1
1
1
1
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
2
0
3
0
0
2
0
0
0
0
0
0
1
0
2
0
3
2
1
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
1
0
0
2
0
0
2
2
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
2
0
0
1
2
0
2
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
1
0
3
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
2
1
0
0
0
2
1
0
0
0
0
0
2
2
0
1
1
1
0
2
0
0
1
0
1
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
2
1
0
2
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
2
0
1
0
0
1
0
0
0
0
0
0
2
2
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
2
2
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
8
0
0
0
0
0
0
2
0
0
2
3
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
2
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
1
0
0
0
3
0
0
1
0
0
0
0
2
2
2
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
3
1
0
0
0
0
0
0
0
0
2
3
0
2
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
2
0
1
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
2
0
0
1
0
0
0
0
0
0
2
2
0
0
2
2
0
0
0
0
3
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
2
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
1
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
2
4
0
0
0
0
3
0
0
0
0
0
3
0
0
2
0
1
0
0
0
0
2
2
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
3
0
0
0
0
5
1
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
2
2
0
0
1
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
1
0
0
2
1
0
1
3
0
0
0
0
1
0
1
1
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
2
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
1
1
0
3
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
3
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
1
0
2
2
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
2
0
1
2
2
0
0
1
0
0
3
0
2
1
0
1
0
2
2
0
1
0
0
0
1
1
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
3
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
1
1
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
4
1
0
0
0
0
0
0
1
0
0
0
0
5
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
9
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
2
0
1
2
0
2
1
2
0
3
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
3
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
4
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
1
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
5
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
2
0
3
1
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
2
0
0
0
0
1
0
3
0
0
1
0
2
0
0
0
0
1
0
0
0
1
0
2
0
2
1
0
2
0
0
0
0
0
0
2
1
2
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
3
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
3
2
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
1
0
0
0
2
0
0
1
2
0
0
0
0
1
0
3
0
3
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
3
1
1
1
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
2
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
2
0
0
2
0
0
2
0
0
1
0
0
2
0
0
0
0
1
2
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
2
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
1
0
2
1
0
0
0
0
1
0
0
3
0
3
0
0
0
0
0
1
2
0
0
0
0
0
2
0
1
0
4
2
1
0
0
0
1
1
2
0
0
5
2
1
1
2
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
7
0
2
0
0
2
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
1
0
2
0
0
3
0
0
0
0
0
0
0
1
0
0
1
0
2
0
2
1
0
2
0
2
0
0
0
0
0
0
1
0
0
1
3
1
0
2
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
2
0
0
3
0
0
1
0
0
0
2
1
0
0
0
0
0
1
3
2
2
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
1
7
1
0
0
1
2
0
0
0
1
2
0
2
0
2
0
4
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
2
0
1
3
2
0
2
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
3
0
2
0
0
2
0
0
0
0
1
0
0
2
1
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
5
0
2
2
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
1
1
2
0
0
2
0
2
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
1
0
0
2
0
0
0
2
1
0
1
2
0
1
2
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
1
1
0
0
2
1
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
1
1
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
2
2
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
2
1
1
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
1
0
0
0
0
1
0
0
1
1
0
0
0
2
0
0
0
0
2
1
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
2
0
2
0
1
2
0
0
1
1
2
0
0
2
1
0
0
0
0
4
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
2
0
9
0
2
0
2
2
0
0
0
2
2
2
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
2
0
0
0
0
0
2
3
0
1
0
1
0
0
0
0
0
0
3
1
0
0
7
0
0
1
0
0
0
2
0
0
0
0
0
3
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
13
0
0
0
0
2
0
0
1
1
0
0
2
0
2
0
1
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
3
0
0
0
0
2
2
0
0
1
2
1
1
1
0
0
0
2
0
3
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
1
2
0
2
0
1
0
0
0
0
2
2
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
2
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
1
1
0
0
1
0
0
2
3
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
1
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
5
1
2
0
2
2
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
2
5
0
0
0
0
0
1
0
0
0
0
2
0
0
1
2
0
0
0
0
2
2
0
0
0
0
4
0
0
1
1
2
2
0
1
0
0
0
2
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
1
0
2
0
0
0
0
2
0
1
0
0
0
0
0
3
1
0
0
1
0
0
3
0
1
1
0
2
0
0
2
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
3
0
0
0
1
0
0
0
0
1
2
0
2
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
1
0
0
3
0
0
0
0
0
0
0
4
1
0
0
1
0
0
1
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
2
0
2
0
0
0
0
0
2
0
0
0
0
0
1
2
0
1
2
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
1
0
4
0
0
0
0
4
0
0
0
0
2
0
2
0
3
0
0
1
0
2
0
0
2
1
1
2
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
3
0
0
0
0
3
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
2
0
3
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
2
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
1
0
2
0
2
0
1
2
0
0
0
0
1
0
0
0
0
3
2
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
5
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
1
2
0
1
0
0
0
2
2
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
1
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
4
0
0
3
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
2
3
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
5
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
5
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
4
2
0
0
2
2
1
0
0
1
1
0
0
2
0
0
0
0
0
0
0
1
2
1
0
0
1
0
0
2
3
1
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
2
2
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
1
1
0
1
0
0
2
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
2
1
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
3
0
0
1
3
0
1
0
0
0
0
0
2
0
1
0
1
0
0
2
0
0
0
0
1
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
1
0
1
0
0
5
2
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
8
4
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
3
0
2
2
0
1
1
0
3
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
2
0
0
0
1
0
0
0
0
0
1
7
2
0
1
0
1
0
0
2
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
2
2
0
0
1
2
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
1
3
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
1
3
0
0
0
0
0
0
0
0
0
2
2
1
2
0
0
0
2
0
2
0
0
0
2
2
0
0
0
0
2
0
2
1
0
1
0
3
0
0
0
0
0
4
0
0
0
2
2
0
0
0
2
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
3
2
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
1
1
0
0
2
0
0
0
2
0
2
1
0
0
2
0
0
0
1
0
0
0
5
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
2
1
0
0
1
1
0
0
2
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
2
1
0
0
1
0
0
0
0
0
0
1
0
2
2
0
3
0
2
0
1
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
2
1
0
0
1
1
1
0
0
0
0
0
0
1
0
0
3
0
1
0
1
0
0
0
1
1
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
2
0
2
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
1
2
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
1
0
1
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
1
1
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
4
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
4
3
0
1
1
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
4
3
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
2
2
1
0
0
0
0
0
0
3
0
1
0
1
3
0
2
0
0
2
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
1
0
4
0
0
0
1
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
5
0
0
0
0
0
2
2
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
3
0
0
0
1
2
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
6
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
1
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
2
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
1
0
0
2
2
0
0
0
0
3
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
1
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
4
0
0
0
1
0
0
1
0
2
0
0
2
1
0
0
0
0
0
0
0
0
1
2
0
3
0
0
2
1
0
0
0
1
0
0
0
0
2
0
2
3
0
0
1
2
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
4
0
3
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
2
1
0
1
0
1
2
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
3
0
1
0
0
1
0
1
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
3
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
1
0
0
0
0
3
0
2
2
2
1
0
1
0
1
3
0
0
0
0
0
0
2
0
2
0
0
0
0
4
0
0
0
0
0
0
0
4
4
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
2
0
0
0
1
1
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
1
1
1
0
0
0
1
0
1
0
0
1
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
1
0
2
1
0
0
1
0
1
2
2
0
2
0
0
0
0
1
0
0
2
0
1
0
0
2
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
1
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
3
2
0
2
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
2
2
2
1
0
0
0
1
0
0
0
2
1
2
0
0
0
0
2
0
0
0
0
3
0
0
0
0
1
0
0
0
2
0
0
0
2
2
0
0
0
0
0
2
1
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
3
1
0
1
0
0
1
2
0
0
0
0
2
0
0
0
0
1
0
2
1
0
2
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
1
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
1
1
0
1
0
0
0
1
0
0
2
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
2
0
0
1
1
0
0
0
0
1
0
0
0
0
4
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
1
0
1
1
2
0
0
0
0
2
0
0
0
2
0
1
1
0
1
1
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
2
1
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
2
1
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
2
3
0
0
2
0
2
2
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
1
0
2
0
0
0
2
0
0
0
1
0
1
0
0
1
0
2
0
0
0
2
5
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
2
0
0
3
0
2
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
1
0
0
0
0
4
0
0
0
0
0
0
1
0
0
2
0
1
3
0
1
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
2
2
0
3
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
2
0
4
1
0
0
1
0
0
2
2
0
0
0
0
0
0
1
0
4
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
1
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
2
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
1
3
0
2
0
0
2
4
0
0
2
0
0
0
0
1
0
4
2
1
1
2
0
2
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
3
1
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
2
1
0
0
0
0
2
2
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
1
2
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
1
2
0
0
0
0
0
2
0
1
2
2
0
2
2
0
0
0
0
2
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
3
0
0
0
0
0
0
2
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
2
1
0
0
0
0
0
0
3
0
0
2
1
0
0
3
2
0
0
2
0
1
0
0
0
2
0
0
0
0
1
1
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
2
2
1
0
0
0
0
1
1
0
0
2
0
1
0
0
0
0
3
0
1
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
1
0
0
0
0
0
2
1
2
0
0
3
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
1
1
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
3
1
0
0
0
0
0
1
0
0
1
0
0
0
2
3
0
0
0
0
0
0
2
1
0
1
2
2
0
1
0
1
5
0
1
0
2
0
0
1
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
6
0
3
0
0
1
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
2
0
0
0
1
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
5
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
2
0
1
0
1
0
4
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
4
0
2
0
1
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
3
2
1
0
0
1
1
0
1
0
3
1
4
0
2
2
2
0
0
1
1
0
0
2
0
0
0
2
0
0
0
0
0
2
2
1
2
1
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
3
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
3
0
0
1
0
0
0
1
0
0
0
2
1
3
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
2
0
2
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
2
2
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
1
1
2
0
0
0
1
0
1
0
0
0
0
3
2
0
0
0
2
0
0
2
3
0
0
0
0
1
0
0
2
0
0
2
1
0
1
3
0
0
4
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
1
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
6
0
0
1
0
1
3
2
0
0
0
0
3
0
0
1
1
0
2
0
0
3
0
0
0
0
1
1
0
1
0
0
2
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
2
1
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
2
2
1
2
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
1
0
1
0
0
0
0
0
1
0
2
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
1
1
0
0
2
1
0
0
0
0
1
0
0
0
0
1
0
0
2
0
1
0
3
0
0
2
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
2
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
3
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
2
0
0
0
0
2
2
0
0
0
0
1
0
1
1
0
1
2
0
0
0
1
2
0
0
0
1
1
0
0
2
2
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
3
0
1
0
0
1
1
0
0
1
2
2
2
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
1
2
0
1
0
0
2
0
0
0
0
0
1
0
0
1
0
2
0
1
0
0
2
0
0
1
0
0
0
0
1
0
0
0
3
0
0
0
1
0
0
4
3
2
0
2
2
0
1
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
0
2
1
0
2
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
2
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
1
0
2
0
0
2
0
1
1
0
0
0
1
1
1
0
0
0
0
0
2
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
1
0
2
0
1
0
0
0
3
1
0
2
0
0
3
0
0
0
1
0
1
1
2
1
0
0
2
0
2
0
0
1
1
0
0
2
0
0
1
0
0
0
1
0
2
1
1
0
0
0
0
0
2
1
1
0
2
0
2
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
2
3
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
2
4
0
0
0
0
0
0
0
0
2
5
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
3
0
0
3
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
2
0
1
0
0
0
0
1
1
0
0
0
1
0
0
1
3
0
0
0
0
0
0
2
0
0
2
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
2
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
2
0
0
3
1
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
1
1
2
2
0
0
0
0
0
2
3
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
1
0
0
0
0
0
0
0
2
1
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
1
0
4
0
0
3
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
3
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
3
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
1
0
2
0
2
0
0
0
0
0
1
2
3
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
4
0
0
0
0
0
5
0
2
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
3
0
1
0
0
0
1
0
1
0
1
0
0
0
2
0
0
2
2
0
0
0
1
1
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
4
0
0
0
0
0
0
3
0
2
0
0
0
0
2
0
1
0
1
0
2
0
2
2
0
0
1
0
0
0
0
4
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
1
2
0
0
2
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
1
2
0
0
1
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
5
0
2
0
0
0
0
0
0
0
2
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
2
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
3
1
0
2
0
0
2
0
2
0
0
2
1
2
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
1
2
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
1
0
0
0
0
0
2
1
0
0
2
1
0
0
0
2
0
2
1
0
2
0
1
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
1
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
2
0
0
0
0
1
2
0
0
0
1
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
3
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
3
2
0
2
1
0
0
0
2
2
2
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
1
0
1
0
1
0
0
0
1
0
4
0
1
0
1
0
0
1
0
2
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
1
1
0
0
7
1
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
1
1
14
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
3
1
0
0
0
0
0
1
0
1
0
2
0
0
0
0
1
1
0
0
0
2
0
0
0
0
1
0
0
1
0
0
1
2
0
2
0
0
0
0
0
1
3
1
0
0
0
0
0
3
0
0
2
3
0
1
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
2
0
1
0
0
0
0
1
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
2
0
12
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
2
0
2
0
1
1
1
0
0
2
1
1
0
1
0
1
0
1
0
2
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
2
2
2
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
2
2
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
1
1
0
0
2
1
0
0
0
0
0
0
0
3
1
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
1
0
0
3
2
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
2
0
0
0
0
1
2
0
0
1
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
2
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
4
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
1
3
0
1
0
0
0
0
3
0
2
1
2
0
0
0
0
0
0
0
1
2
1
1
0
0
0
0
0
2
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
1
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
2
2
2
1
2
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
3
0
1
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
3
1
0
2
2
0
0
0
0
0
0
1
1
0
2
0
0
0
0
4
0
1
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
1
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
1
2
1
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
1
1
2
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
2
1
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
2
0
1
3
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
1
1
0
5
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
1
2
1
2
1
0
0
0
0
1
3
2
0
0
0
1
0
0
0
0
2
1
3
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
1
0
1
2
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
1
2
0
0
0
0
0
2
0
0
0
2
0
3
0
1
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
1
2
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
3
0
2
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
1
0
2
1
0
2
0
0
0
0
0
0
0
0
0
2
3
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
1
0
0
0
1
3
0
0
0
0
0
0
2
0
0
2
0
0
8
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
1
2
0
0
0
2
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
3
0
1
2
0
0
0
0
0
2
1
0
0
0
3
0
0
0
0
0
0
1
1
0
0
0
2
0
2
0
2
0
1
0
1
0
0
0
1
0
0
0
2
0
0
0
0
3
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
2
2
1
0
2
0
0
2
1
0
0
0
0
2
2
5
0
0
1
2
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
1
0
0
2
0
0
2
0
2
0
0
1
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
2
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
3
0
0
0
1
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
2
0
0
0
1
1
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
2
0
0
0
5
2
0
2
0
0
3
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
1
1
0
0
6
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
2
0
1
1
4
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
1
1
5
1
0
0
0
3
3
0
0
0
0
0
1
2
0
3
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
1
1
2
0
2
1
0
0
0
2
0
2
0
0
1
0
0
0
1
0
3
0
0
0
3
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
2
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
3
0
2
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
1
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
4
0
0
1
2
0
1
0
1
2
2
2
1
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
4
0
5
1
2
0
0
1
1
0
0
0
2
0
0
0
2
1
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
3
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
3
2
1
0
0
0
0
1
2
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
1
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
2
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
1
0
0
1
2
0
0
0
0
0
0
0
0
1
2
2
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
1
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
2
1
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
9
6
0
2
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
2
1
0
0
1
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
1
0
2
0
0
0
0
5
2
0
2
0
0
1
2
0
0
0
4
0
2
0
0
0
2
1
0
0
0
0
2
1
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
2
1
0
1
0
0
0
0
0
0
0
0
1
0
2
0
2
2
0
1
0
0
0
0
0
3
0
1
0
0
1
0
1
0
1
1
0
0
2
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
1
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
1
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
5
2
2
3
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
3
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
3
1
0
1
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
4
0
1
0
1
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
7
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
2
1
0
0
2
0
0
0
1
0
2
1
0
0
2
0
0
2
0
2
1
0
0
0
0
1
0
0
1
0
0
0
6
0
0
0
0
1
1
0
0
2
0
0
0
0
0
1
0
0
0
5
0
0
0
0
0
0
1
0
1
0
2
3
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
1
1
2
0
0
0
1
0
0
2
0
0
0
2
0
1
1
0
1
0
2
2
2
0
0
0
0
0
2
1
0
0
0
0
0
4
0
2
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
2
0
2
2
0
0
1
0
0
0
0
1
0
0
1
2
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
1
1
0
0
1
1
0
1
0
2
1
0
0
0
0
0
1
0
1
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
1
0
0
1
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
3
2
0
0
2
0
0
0
1
2
1
0
0
0
2
3
0
0
0
3
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
1
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
2
0
1
2
2
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
2
0
2
0
2
0
0
3
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
2
0
2
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
2
0
0
2
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
1
1
0
1
0
2
0
0
0
0
2
0
1
0
0
1
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
3
0
0
0
0
0
0
3
0
2
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
3
1
0
0
2
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
4
0
0
1
1
5
0
0
0
0
2
0
0
0
0
0
2
0
4
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
1
0
2
0
1
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
6
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
5
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
2
0
1
2
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
1
1
2
0
0
0
3
0
0
0
0
0
2
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
1
1
2
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
2
0
0
2
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
2
0
2
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
3
0
0
0
0
0
1
1
0
0
2
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
2
0
1
1
1
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
2
0
1
0
0
2
0
0
0
0
1
1
0
0
1
0
1
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
1
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
2
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
2
2
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
2
0
0
0
0
0
1
0
0
2
2
2
0
0
0
0
0
0
0
0
2
0
0
8
2
1
0
0
1
0
0
0
1
0
0
4
0
0
0
0
0
2
1
0
0
0
1
0
2
0
0
1
3
1
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
3
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
1
0
1
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
3
0
0
1
0
0
3
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
1
2
2
0
2
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
1
1
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
3
0
0
0
0
0
2
0
1
0
0
2
0
1
0
0
2
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
4
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
1
0
0
1
0
0
0
0
1
2
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
1
2
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
2
1
1
1
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
1
1
3
0
1
0
0
3
2
0
0
0
1
2
0
1
0
0
0
1
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
4
0
0
0
2
2
0
0
0
0
2
1
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
3
0
0
2
0
0
0
0
0
0
0
0
2
2
2
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
3
1
0
0
0
2
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
3
0
0
0
0
2
2
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
3
2
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
5
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
2
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
2
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
1
1
0
0
3
2
0
0
0
3
1
0
0
2
0
2
0
3
0
0
0
2
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
1
0
2
0
0
0
0
0
0
0
2
3
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
2
0
0
2
2
0
0
2
1
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
6
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
8
2
0
0
0
0
1
0
1
0
0
0
0
1
2
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
1
0
1
0
0
1
0
2
2
0
0
0
2
0
0
0
1
4
1
1
0
0
2
0
0
0
0
2
1
1
1
0
0
0
2
0
0
1
0
1
0
2
0
1
0
0
1
0
1
0
0
0
2
2
2
1
1
0
0
2
0
1
0
2
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
1
2
0
1
0
0
0
1
0
0
0
0
1
1
2
0
0
0
0
0
0
1
0
2
0
1
0
0
0
2
0
1
2
0
0
1
0
0
0
0
0
2
1
0
0
1
0
1
0
0
0
0
0
0
0
2
1
0
1
2
0
2
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
3
1
0
0
0
2
0
0
0
0
2
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
2
0
0
0
2
0
1
2
0
0
0
2
0
1
0
1
0
0
0
0
2
2
1
0
0
0
0
0
2
0
2
2
0
0
2
0
0
0
0
0
0
2
2
2
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
1
0
0
2
1
1
0
2
0
0
2
0
2
2
2
2
0
0
0
0
0
2
0
2
0
4
0
0
0
2
1
0
2
0
0
0
2
0
0
1
0
0
2
2
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
4
4
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
1
2
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
1
1
0
0
2
0
0
1
0
2
2
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
3
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
2
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
7
1
0
0
0
2
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
3
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
1
0
2
0
0
0
0
1
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
2
2
0
0
0
1
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
6
0
0
0
1
0
1
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
3
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
3
0
3
0
0
0
0
3
0
0
3
0
2
0
0
0
0
0
0
0
1
2
0
0
2
2
0
0
0
0
0
1
2
1
0
1
0
0
0
0
1
1
0
3
0
2
2
0
1
0
0
1
1
1
3
0
0
0
0
0
2
3
2
0
0
2
0
1
0
0
0
0
0
2
0
2
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
2
0
0
0
0
0
0
1
1
0
3
0
3
0
0
0
0
1
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
1
0
0
0
0
2
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
1
0
1
1
0
0
0
1
2
0
0
1
1
4
0
2
0
1
0
1
0
0
0
1
0
0
1
1
0
0
0
0
1
1
0
0
2
0
0
0
3
0
3
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
1
1
3
0
0
1
0
0
0
1
1
0
0
0
1
2
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
2
1
0
0
1
0
2
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
2
0
3
1
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
1
0
0
1
0
0
0
0
0
2
0
0
1
0
1
2
1
0
1
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
2
0
0
1
0
0
0
0
2
1
0
0
1
0
0
1
0
2
1
0
0
0
2
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
3
5
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
1
2
2
0
0
0
0
0
0
0
1
0
0
1
1
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
1
0
2
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
1
2
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
2
2
0
0
0
3
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
2
1
1
1
2
2
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
2
0
1
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
1
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
3
0
1
0
1
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
8
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
7
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
3
0
0
0
1
0
2
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
1
0
2
0
0
0
1
0
0
0
1
0
0
0
1
0
2
0
0
0
2
0
2
0
1
0
0
0
0
2
0
0
0
1
0
1
0
0
1
0
0
1
0
0
1
2
0
2
2
0
0
1
0
0
0
0
2
1
2
0
0
1
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
2
2
0
0
3
0
0
0
0
2
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
2
0
0
3
0
0
1
2
0
0
0
2
2
0
0
0
0
2
0
0
1
0
0
0
0
2
0
1
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
1
0
2
0
0
0
2
2
0
0
0
0
2
1
0
0
0
1
0
0
0
1
0
0
0
2
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
3
0
0
2
0
0
0
0
0
0
1
0
0
2
2
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
3
0
0
1
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
1
2
3
2
0
2
3
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
2
0
0
4
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
2
9
0
0
0
0
0
3
0
0
0
0
2
0
3
0
0
3
0
0
0
0
2
0
4
0
0
1
0
2
1
2
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
2
1
1
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
2
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
2
1
0
1
0
0
0
1
0
1
1
0
0
0
0
2
0
0
7
0
0
0
3
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
1
2
2
0
1
0
1
3
0
0
1
0
0
0
0
2
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
2
0
0
0
0
0
0
0
1
0
0
3
3
2
0
0
0
0
2
1
2
2
0
0
1
2
0
0
0
0
3
3
0
0
1
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
1
0
1
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
1
0
3
0
0
0
0
1
1
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
2
4
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
5
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
1
1
2
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
6
0
0
2
2
0
0
1
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
1
2
2
0
0
2
0
0
0
1
1
0
0
2
2
2
1
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
2
2
0
0
0
1
0
0
0
0
0
0
2
0
3
1
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
1
1
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
6
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
1
0
2
0
1
1
2
0
0
2
0
0
0
0
0
0
0
2
2
0
2
2
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
3
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
2
0
0
1
1
0
0
0
0
2
0
0
0
0
1
0
1
2
0
2
0
0
0
0
1
2
0
2
0
0
2
2
0
1
0
0
0
0
2
0
0
0
0
0
0
3
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
5
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
2
2
0
2
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
1
0
4
0
2
0
0
0
0
0
0
1
2
0
2
0
0
0
2
0
0
3
0
2
0
0
2
0
0
0
0
0
0
1
0
2
2
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
4
0
0
0
0
0
0
3
2
2
1
1
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
1
2
6
1
0
1
0
1
3
1
0
1
2
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
1
1
0
0
3
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
2
0
0
0
1
2
0
0
2
0
1
0
0
0
1
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
1
2
0
0
1
3
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
2
1
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
2
0
0
0
2
0
3
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
3
1
1
2
0
0
0
0
1
0
2
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
3
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
3
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
3
1
0
1
0
0
0
1
0
2
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
2
0
0
0
5
0
0
0
0
0
0
0
0
1
2
2
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
2
0
1
0
1
0
0
0
1
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
2
1
0
1
2
2
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
1
0
0
2
1
1
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
2
0
1
1
0
0
0
0
2
0
0
3
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
2
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
4
2
0
0
2
2
0
1
0
0
0
0
0
0
2
0
0
0
2
0
1
0
2
1
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
2
2
0
0
0
0
2
1
1
0
0
4
1
1
0
0
0
0
0
0
2
5
0
0
2
0
0
0
0
2
2
0
1
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
3
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
2
0
0
1
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
1
0
0
0
3
1
0
0
0
5
0
0
2
0
1
0
0
2
1
0
0
2
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
2
0
0
2
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
1
0
1
4
2
0
0
2
0
2
2
0
5
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
2
0
0
1
4
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
3
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
2
2
1
0
0
0
3
0
1
0
0
0
0
3
2
0
2
0
3
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
2
2
0
1
2
3
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
2
0
1
1
0
0
0
0
0
1
2
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
2
1
0
0
0
1
1
2
1
0
3
0
6
0
0
2
1
3
0
0
0
1
0
2
0
0
0
0
0
1
3
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
2
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
3
1
1
0
0
2
0
2
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
2
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
1
0
1
0
0
0
0
1
2
0
2
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
2
2
1
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
2
0
0
2
1
4
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
5
0
1
0
0
1
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
3
0
0
0
0
2
1
0
1
0
0
2
1
1
1
0
0
0
0
2
1
0
1
0
0
0
2
0
0
1
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
3
2
0
0
1
0
2
1
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
1
0
2
0
0
5
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
1
0
0
5
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
4
0
0
0
0
2
0
0
3
2
0
2
1
2
2
0
0
0
3
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
5
0
0
3
1
0
0
0
0
1
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
4
0
1
0
0
0
0
2
0
0
1
0
0
0
1
0
1
0
1
0
0
2
0
0
0
0
2
0
0
0
1
1
0
0
0
3
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
2
0
0
1
0
0
0
0
2
1
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
2
1
3
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
1
2
2
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
1
3
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
2
1
2
3
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
2
1
0
0
0
1
1
0
0
0
2
2
1
0
0
1
0
0
0
0
1
0
0
0
0
2
0
1
1
0
0
0
3
0
0
2
0
0
0
1
4
0
0
1
0
0
0
2
0
0
0
0
0
2
0
3
0
0
0
0
0
0
1
0
2
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
1
0
2
2
0
0
0
1
2
2
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
1
0
2
0
2
0
2
0
0
0
0
2
0
0
1
0
0
1
0
1
0
0
0
0
2
1
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
1
0
2
1
0
0
1
0
1
2
1
1
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
2
2
4
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
7
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
2
0
0
2
0
1
0
4
2
0
0
2
1
2
0
2
0
5
0
0
0
0
0
1
0
0
2
1
2
0
0
3
0
3
0
0
0
1
0
7
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
2
0
0
0
0
2
1
0
0
2
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
3
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
1
1
0
0
2
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
3
0
2
0
0
0
0
0
0
0
3
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
1
4
2
3
2
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
3
0
0
1
2
0
1
0
0
0
0
0
2
0
2
2
1
0
2
0
1
0
0
0
0
0
0
1
0
0
1
0
0
3
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
3
0
0
3
3
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
3
1
1
3
1
0
0
1
4
2
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
3
0
1
2
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
2
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
2
0
1
0
0
0
0
0
1
0
2
0
0
1
2
2
1
0
0
1
2
0
0
0
0
0
1
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
4
0
1
0
2
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
2
0
0
1
1
0
0
2
1
0
0
2
0
0
0
0
0
0
1
2
0
0
2
0
0
0
3
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
6
0
1
1
1
2
0
0
0
0
0
0
2
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
3
1
0
0
2
0
0
0
0
2
0
2
0
0
0
0
2
0
1
3
0
0
0
0
0
1
2
0
0
2
2
0
1
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
3
0
0
3
2
0
0
0
1
0
1
1
0
2
0
2
0
0
0
3
0
1
3
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
1
1
0
0
0
2
1
0
0
2
2
0
2
0
0
4
0
1
0
0
1
0
1
0
0
0
0
0
3
2
0
2
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
3
3
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
1
0
4
0
0
0
0
0
0
2
0
0
2
0
1
3
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
2
0
3
0
1
3
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
3
0
0
0
0
0
2
2
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
3
2
0
3
0
0
0
2
0
0
0
0
2
0
0
0
0
2
1
1
0
0
1
0
1
0
1
0
0
0
0
0
2
1
2
2
0
0
1
0
0
0
0
1
0
0
1
1
0
2
0
0
1
0
0
3
0
0
0
2
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
2
0
2
0
0
0
4
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
4
0
0
0
0
0
0
0
0
1
3
2
2
0
0
1
0
0
0
3
0
1
0
0
0
0
2
0
1
0
0
2
0
0
0
0
1
0
0
1
1
2
2
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
1
1
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
1
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
2
0
0
1
0
1
0
0
0
1
2
0
0
1
0
0
0
0
0
0
4
0
0
3
4
1
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
1
2
0
1
1
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
2
1
2
1
0
1
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
4
0
2
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
1
4
0
0
2
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
1
2
2
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
1
1
0
0
2
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
1
2
0
0
0
0
0
0
0
0
1
2
0
2
0
0
1
2
0
0
0
1
0
1
0
4
0
0
0
2
0
1
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
2
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
1
6
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
1
0
0
0
1
1
2
1
0
0
0
1
0
2
1
0
2
0
0
0
1
0
0
0
0
6
0
2
0
0
0
1
3
0
0
0
0
0
0
1
0
0
0
0
0
2
1
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
2
0
2
0
1
0
2
3
0
0
3
0
0
0
1
2
0
0
0
2
0
2
0
0
0
0
0
2
1
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
2
1
1
0
0
0
0
0
0
2
0
1
0
0
2
0
2
3
1
1
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
3
1
0
2
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
1
2
0
0
0
4
2
0
2
1
0
0
0
2
0
2
1
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
3
2
0
0
0
0
1
0
0
0
3
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
2
2
0
0
0
0
2
1
1
0
2
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
2
1
0
0
0
2
1
0
0
0
0
3
0
0
0
0
0
0
0
2
1
0
1
0
0
0
2
0
1
0
0
0
1
1
0
0
0
2
8
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
1
1
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
1
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
4
1
0
2
0
0
1
0
1
2
0
0
0
0
1
0
0
1
2
2
0
0
0
0
0
0
0
0
2
0
1
1
0
0
1
1
0
0
0
0
0
2
2
0
0
0
0
0
2
0
1
0
0
3
0
0
0
0
1
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
1
1
0
0
0
0
0
0
0
0
7
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
2
0
0
1
2
0
0
0
0
1
2
0
1
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
2
1
2
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
3
2
0
1
1
0
0
0
0
2
1
0
0
0
1
2
1
0
0
2
0
0
0
0
1
0
0
0
1
0
0
3
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
3
1
0
0
2
1
0
0
1
2
1
0
1
0
2
0
2
0
0
1
2
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
3
1
1
0
1
1
0
0
0
0
1
2
0
1
2
0
0
2
1
0
0
0
0
0
0
3
2
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
1
2
0
2
0
0
2
0
0
6
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
2
0
2
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
2
0
2
0
0
2
1
2
0
0
0
0
0
0
0
2
0
0
4
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
2
0
3
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
3
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
1
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
1
0
0
0
0
2
1
2
1
0
0
2
1
0
0
0
1
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
3
1
2
2
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
3
2
0
0
1
0
0
0
2
1
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
2
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
1
1
0
0
1
0
0
2
0
0
0
0
8
0
0
2
0
0
0
2
0
0
1
2
0
0
1
1
0
0
0
0
1
2
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
2
0
0
1
0
4
0
1
0
0
0
0
0
1
2
0
0
5
2
0
0
0
1
0
0
0
0
0
2
0
0
2
3
0
2
0
0
1
3
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
2
0
2
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
3
2
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
1
0
0
3
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
1
0
0
0
0
1
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
1
3
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
2
0
0
0
0
3
2
0
0
0
0
0
5
2
0
0
0
2
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
1
1
0
2
0
0
2
0
2
0
0
2
0
0
1
0
1
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
1
1
2
1
0
3
0
0
0
0
2
0
0
0
3
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
2
2
0
0
2
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
2
1
1
3
2
0
2
2
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
2
2
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
1
0
0
1
1
0
0
2
0
3
0
0
0
1
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
1
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
2
0
0
1
0
0
4
0
0
2
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
2
0
0
3
0
2
0
0
2
2
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
1
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
2
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
2
1
2
0
0
1
0
1
2
1
1
3
0
0
2
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
4
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
2
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
2
0
4
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
1
0
2
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
2
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
2
0
0
0
2
0
4
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
6
0
0
0
0
1
2
0
0
2
0
0
0
0
6
1
3
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
2
0
0
2
0
0
0
1
1
3
0
0
3
3
0
0
0
2
2
0
1
2
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
1
0
0
0
0
1
0
0
0
2
0
0
1
0
3
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
3
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
2
4
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
3
2
2
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
2
0
0
1
0
3
0
0
0
2
0
0
0
3
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
1
2
0
1
0
0
0
1
0
3
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
2
0
1
0
0
3
0
2
0
0
0
1
2
0
0
0
8
0
1
1
0
0
1
0
2
0
0
3
2
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
3
2
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
2
0
0
0
1
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
3
1
0
0
0
0
12
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
2
0
0
1
0
1
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
4
1
0
0
0
0
1
0
2
2
1
1
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
1
0
1
0
0
0
0
2
4
0
2
1
0
1
0
0
2
0
0
2
0
0
0
0
2
0
0
0
2
0
0
2
2
0
1
0
0
0
0
0
1
3
0
2
2
3
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
3
0
0
2
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
3
1
0
2
1
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
2
0
0
2
0
0
0
1
2
0
0
2
0
3
2
0
0
6
0
2
1
0
0
0
1
0
0
2
0
0
1
2
0
2
0
0
0
3
0
0
1
2
0
0
0
1
0
0
0
0
0
1
1
3
1
0
2
0
2
0
1
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
1
1
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
3
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
1
3
1
0
0
0
2
0
0
0
0
0
0
0
1
1
2
0
0
0
2
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
2
1
1
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
1
0
1
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
1
0
2
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
1
0
0
0
1
1
0
0
4
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
2
0
0
0
0
2
0
0
2
0
0
1
3
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
2
0
0
0
3
2
0
0
2
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
4
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
1
2
1
0
0
0
0
0
0
3
0
0
0
2
0
0
1
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
1
0
0
0
1
0
3
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
1
1
0
1
0
0
1
0
2
7
0
1
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
3
2
0
2
0
2
2
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
1
0
1
0
2
0
0
1
2
0
0
0
0
0
0
0
0
3
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
4
1
0
2
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
2
2
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
2
0
0
1
0
0
0
1
0
4
1
0
0
2
0
0
0
0
0
1
0
0
0
0
2
1
0
9
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
2
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
3
2
1
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
3
0
0
2
0
0
0
0
0
0
0
0
2
0
2
2
3
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
2
0
1
0
0
0
1
1
2
3
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
2
0
2
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
3
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
6
0
1
1
1
0
0
0
2
0
1
2
0
0
0
0
0
0
2
1
2
0
1
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
1
0
1
0
0
0
2
0
0
0
0
6
1
0
0
1
0
0
0
1
3
2
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
5
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
3
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
3
0
2
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
1
2
0
0
0
0
0
1
0
0
0
1
1
0
0
2
0
0
0
0
2
0
0
0
0
1
3
0
0
0
0
0
0
0
4
0
0
0
2
1
0
2
2
0
2
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
2
0
0
2
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
2
1
0
0
0
1
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
1
2
0
0
0
1
0
7
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
3
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
1
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
2
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
3
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
1
1
0
0
0
1
1
1
2
0
0
0
0
0
3
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
1
0
3
1
0
2
1
0
0
1
0
0
0
0
2
0
0
2
3
0
0
0
0
0
4
2
0
2
2
2
3
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
2
1
0
0
0
7
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
2
0
0
2
0
1
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
5
0
0
0
0
3
0
0
0
1
2
0
0
0
0
1
0
1
1
0
2
0
0
0
1
0
2
0
2
0
0
0
0
2
2
0
0
0
1
0
0
0
0
2
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
2
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
5
1
0
7
1
0
1
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
1
0
4
1
0
0
2
2
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
2
0
2
0
1
1
0
0
0
5
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
3
0
0
0
0
2
0
0
0
3
0
0
3
1
0
0
0
0
0
0
0
5
0
0
2
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
2
0
0
0
0
2
0
1
2
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
2
0
1
2
0
0
0
7
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
1
2
0
1
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
2
4
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
1
1
0
0
0
0
1
0
2
2
0
1
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
1
0
0
0
2
0
0
0
1
1
2
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
3
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
2
1
0
1
0
0
0
2
2
0
0
0
1
2
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
3
1
0
1
0
0
0
1
0
0
0
0
1
0
0
1
2
0
0
1
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
6
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
2
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
2
0
2
0
0
0
1
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
3
0
1
2
1
0
0
0
0
0
2
2
2
0
1
0
2
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
2
2
0
0
7
0
0
6
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
1
0
1
0
0
0
1
0
1
2
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
6
0
0
0
0
0
1
1
0
0
2
0
0
0
2
0
2
0
0
0
0
2
2
1
3
0
0
0
0
1
2
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
2
1
0
1
1
0
0
2
0
0
0
0
5
0
0
1
2
0
0
0
0
0
0
0
1
1
0
1
1
0
1
2
0
2
0
0
0
2
1
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
2
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
3
1
0
1
0
0
2
0
1
0
2
0
1
0
0
0
1
2
0
0
0
2
0
0
3
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
2
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
1
1
1
3
4
3
1
0
0
0
3
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
3
0
0
0
4
0
0
0
2
0
0
0
0
1
2
0
0
0
0
2
0
0
2
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
3
0
0
2
1
0
0
0
0
0
0
0
2
0
0
3
1
2
0
0
0
1
0
0
4
1
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
1
1
2
0
0
1
0
0
0
0
0
1
2
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
1
1
0
0
1
5
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
5
5
0
0
2
0
0
0
3
0
0
0
0
0
0
5
0
0
0
0
0
1
0
2
0
1
0
0
0
0
2
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
2
2
0
0
1
0
0
1
1
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
2
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
2
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
1
0
2
0
1
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
2
0
1
2
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
3
0
1
0
5
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
2
0
0
2
0
0
2
0
0
0
0
0
1
0
0
1
2
0
0
1
0
0
0
7
0
2
0
0
1
0
0
0
1
0
0
0
2
0
2
0
0
1
1
2
1
0
2
2
0
0
0
1
0
0
0
1
11
0
0
0
0
2
0
2
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
3
1
0
0
0
0
0
3
1
0
0
0
0
0
0
0
2
0
0
2
0
0
2
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
2
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
3
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
2
0
5
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
1
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
2
4
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
3
0
0
0
0
0
2
0
6
0
0
0
1
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
2
2
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
3
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
9
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
1
0
1
0
0
0
0
0
0
2
2
0
0
0
0
5
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
2
0
0
2
1
0
0
0
0
0
3
0
0
0
1
0
0
0
1
0
2
0
1
0
0
1
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
1
1
1
0
0
1
0
0
0
0
0
0
0
0
2
2
1
0
0
0
1
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
2
5
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
2
0
0
0
2
0
0
2
2
0
0
0
2
0
1
0
0
0
1
0
0
1
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
2
0
1
2
2
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
2
0
3
2
4
0
2
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
2
0
0
0
2
4
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
1
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
2
2
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
1
1
0
0
0
1
0
0
0
0
0
1
0
1
0
4
1
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
3
1
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
3
0
1
0
0
0
0
1
0
1
0
0
0
4
0
2
0
0
2
1
1
2
0
0
1
1
1
1
2
0
0
0
1
2
0
0
2
0
0
2
2
0
0
0
0
1
2
0
0
0
1
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
2
1
0
1
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
1
1
2
1
2
0
0
2
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
3
1
0
1
0
0
0
0
0
1
0
2
0
0
0
0
2
0
2
0
0
1
0
2
0
0
2
0
0
0
0
0
2
0
0
1
1
0
2
0
0
1
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
1
0
1
0
2
0
3
0
0
0
0
1
0
3
2
0
1
0
1
0
1
2
0
0
4
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
2
2
1
1
0
0
2
0
1
2
0
0
0
0
0
0
0
4
1
1
0
0
2
2
0
0
2
2
0
0
2
0
0
0
1
0
0
1
0
0
0
1
0
1
3
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
2
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
1
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
2
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
2
5
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
1
2
1
0
0
0
0
3
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
5
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
1
0
3
0
0
0
0
1
0
0
0
1
1
0
0
2
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
2
2
1
0
1
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
2
3
0
0
0
0
0
0
4
0
0
0
0
0
1
1
2
0
0
0
0
0
1
0
0
0
1
1
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
2
1
0
1
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
4
0
0
1
0
0
0
0
2
2
0
0
2
0
1
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
3
0
0
0
0
0
7
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
1
1
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
3
0
3
2
2
0
0
0
1
1
0
0
2
0
1
0
1
0
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
2
1
0
0
2
0
0
0
0
1
0
1
0
0
0
0
1
1
3
1
1
0
0
0
0
2
0
3
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
3
2
0
2
3
0
2
0
2
0
1
0
0
1
1
1
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
1
2
0
0
2
0
0
0
0
0
1
0
1
2
0
1
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
0
2
1
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
2
1
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
4
0
2
0
0
1
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
1
0
0
1
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
3
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
2
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
1
1
0
1
0
0
3
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
1
2
0
0
0
0
0
0
2
1
0
0
2
0
0
2
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
0
1
0
1
0
3
0
2
2
1
0
0
0
2
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
1
1
0
2
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
1
2
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
2
0
0
0
2
0
1
0
1
1
0
2
1
0
1
4
2
0
0
0
0
1
0
0
3
1
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
1
1
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
2
1
0
2
0
1
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
1
3
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
3
2
0
1
0
2
0
0
0
0
2
0
0
0
0
0
5
3
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
2
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
3
0
0
0
0
1
0
0
0
2
0
0
0
0
1
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
4
0
3
1
0
0
0
0
1
0
0
0
0
0
3
1
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
1
2
2
0
0
0
0
3
0
0
0
1
3
0
1
2
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
2
0
0
0
0
0
0
0
0
0
0
1
3
0
2
0
0
0
0
0
0
2
3
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
1
2
2
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
1
0
0
2
0
0
0
0
0
1
1
0
1
3
1
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
1
2
0
0
0
1
0
0
2
0
1
0
0
0
0
0
1
0
0
2
2
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
6
0
1
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
2
1
6
0
2
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
1
2
0
0
1
0
0
1
0
0
2
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
1
2
0
2
0
4
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
3
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
2
2
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
3
0
0
2
1
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
3
2
0
0
0
1
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
4
3
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
1
0
0
0
0
0
0
3
0
3
0
1
2
0
1
0
0
1
0
1
0
0
2
0
0
2
1
0
0
1
1
0
1
2
1
0
1
0
2
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
1
0
1
0
0
0
2
0
3
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
3
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
2
0
0
0
0
3
0
1
0
0
0
0
1
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
2
0
0
1
0
0
2
0
0
0
0
1
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
1
1
2
2
0
0
2
1
1
0
0
0
0
3
0
3
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
11
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
1
0
2
0
0
2
0
0
2
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
1
2
1
0
3
0
0
0
0
0
5
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
3
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
1
0
1
1
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
1
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
1
2
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
2
2
0
0
0
1
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
3
0
0
2
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
7
0
2
0
0
0
0
0
3
0
1
0
0
0
0
1
2
0
0
0
2
0
0
2
0
0
0
2
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
2
0
2
0
0
1
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
2
0
0
0
1
1
0
2
0
1
1
0
1
0
0
0
1
1
0
2
1
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
1
3
3
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
2
0
0
0
6
0
2
0
1
0
0
1
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
2
1
0
0
0
0
2
3
0
0
1
0
0
2
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
2
2
0
3
0
0
0
2
0
2
0
0
0
1
0
1
0
0
0
1
0
0
2
0
1
0
0
1
1
0
1
0
0
0
0
1
4
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
7
1
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
3
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
2
5
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
4
2
0
0
1
0
7
0
0
3
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
1
0
0
1
0
0
1
1
0
0
0
0
2
2
0
2
1
1
0
5
0
0
0
0
0
0
0
3
0
2
0
0
0
1
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
2
0
2
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
1
1
2
0
2
0
0
1
0
0
0
2
0
1
0
1
2
2
0
1
0
1
0
1
2
0
0
0
0
1
0
0
0
0
0
1
2
1
0
0
0
0
0
3
2
0
2
2
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
1
2
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
5
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
3
0
2
1
0
2
1
0
0
1
2
0
1
0
2
0
0
1
0
0
0
0
2
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
3
0
0
0
1
2
1
1
0
0
0
4
0
2
0
0
1
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
1
0
0
2
0
3
0
0
1
1
0
0
0
0
0
2
1
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
1
3
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
1
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
1
0
0
1
0
0
2
0
0
0
0
0
0
0
2
1
0
2
2
1
0
2
0
2
0
0
0
2
0
0
1
0
2
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
1
0
1
0
0
2
2
0
0
0
2
2
0
0
0
0
1
2
0
0
0
1
2
2
2
0
0
2
1
0
2
0
0
0
0
0
2
1
0
0
0
0
0
2
2
0
0
0
2
0
0
1
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
2
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
1
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
2
0
1
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
2
0
0
4
2
1
0
0
0
0
0
0
2
0
2
1
2
1
0
0
0
3
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
2
1
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
2
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
3
0
0
0
2
2
0
0
0
2
2
0
0
2
0
1
0
0
0
0
2
0
0
2
1
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
7
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
3
3
0
4
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
3
1
2
0
0
0
1
2
0
1
2
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
2
0
0
2
0
0
2
1
0
0
0
0
1
1
2
0
0
0
0
4
0
1
1
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
2
3
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
2
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
1
0
0
2
0
0
1
2
0
0
0
0
0
0
14
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
1
1
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
1
1
3
0
0
0
0
0
1
2
1
0
0
2
0
0
1
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
1
0
0
0
0
1
1
2
0
0
1
0
0
0
1
2
0
2
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
3
0
2
3
0
0
0
1
0
0
0
0
4
0
0
0
4
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
2
2
0
0
2
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
3
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
2
2
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
3
0
2
0
1
0
0
0
3
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
2
0
1
0
1
0
1
2
0
1
1
0
0
0
0
0
2
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
2
3
0
1
0
2
1
2
0
0
0
0
0
2
2
0
0
1
0
0
0
0
2
0
0
0
2
0
0
1
0
0
1
0
2
0
7
0
2
0
0
0
2
1
0
1
0
1
2
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
1
0
2
0
2
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
2
0
0
1
2
0
0
2
0
2
2
0
0
1
2
0
0
0
0
0
0
0
0
2
1
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
2
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
3
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
3
2
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
5
0
0
2
0
0
0
0
0
0
0
0
0
3
2
2
0
0
0
1
1
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
2
1
0
0
2
1
0
2
1
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
2
1
2
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
2
0
1
3
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
2
0
2
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
2
2
2
0
1
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
2
0
4
1
0
0
1
1
0
0
1
2
1
0
0
0
1
1
0
0
0
0
1
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
4
2
0
0
2
0
0
0
0
4
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
2
2
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
1
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
3
2
0
1
0
0
2
2
0
0
3
0
0
0
2
0
0
0
0
2
0
0
1
3
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
2
1
1
0
0
1
2
0
0
0
1
0
2
1
0
0
0
3
0
1
0
0
2
3
0
0
0
1
0
0
0
0
3
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
2
0
0
0
1
0
2
0
0
1
3
1
0
1
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
1
2
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
2
0
0
1
0
0
0
2
0
0
0
2
0
2
4
0
0
0
0
0
0
2
0
3
0
0
0
0
0
1
1
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
2
0
1
0
0
0
2
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
6
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
3
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
1
0
0
0
2
0
2
0
2
0
0
0
0
0
3
0
0
0
0
0
0
1
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
3
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
4
0
0
0
2
2
0
0
2
0
0
0
0
0
0
2
0
0
0
4
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
2
0
2
3
0
1
2
0
2
0
0
0
0
0
0
2
1
1
2
1
0
0
1
2
2
0
0
0
1
0
1
0
0
0
0
1
0
0
2
0
0
2
2
0
2
0
0
0
0
1
0
0
0
0
3
0
3
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
3
0
0
1
0
1
0
1
2
0
2
1
0
0
0
0
0
0
0
0
1
3
1
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
1
0
0
2
3
0
0
0
0
3
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
1
0
0
1
0
2
0
0
0
0
2
3
0
0
0
0
2
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
2
0
0
0
2
0
0
2
1
0
0
0
0
1
2
1
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
1
0
0
0
2
0
0
0
1
1
2
0
0
1
0
0
0
0
4
2
0
0
0
0
2
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
2
2
1
2
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
2
1
0
0
0
1
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
13
0
0
0
0
4
0
1
0
0
0
3
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
1
1
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
2
0
0
1
0
0
0
0
2
1
0
2
0
0
0
0
0
2
0
2
3
0
0
1
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
1
2
1
0
2
2
0
0
0
0
2
0
4
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
1
1
3
0
0
0
0
0
0
1
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
1
2
0
0
1
1
1
1
0
0
0
0
3
0
0
0
0
1
0
0
0
2
0
2
1
2
0
0
3
0
3
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
4
0
0
0
0
0
0
2
0
1
0
0
6
0
0
0
0
0
2
1
2
0
0
2
1
0
2
1
0
2
0
1
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
2
0
2
0
0
1
2
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
5
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
3
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
2
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
2
0
2
0
1
3
0
0
0
1
4
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
2
0
2
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
3
0
0
3
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
2
0
0
0
0
0
0
1
0
2
1
0
1
0
0
0
0
0
1
0
1
0
0
2
0
0
3
0
0
0
2
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
4
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
7
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
3
0
0
0
0
2
0
0
0
0
7
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
1
1
0
1
0
0
0
0
2
0
1
2
0
0
1
2
1
0
1
0
0
0
2
0
0
0
1
0
1
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
4
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
1
0
1
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
9
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
2
0
4
2
1
0
0
7
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
2
0
0
0
2
1
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
2
2
0
0
0
0
1
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
7
0
2
2
0
0
3
0
0
0
0
0
2
0
0
1
0
0
0
1
1
3
1
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
2
0
1
4
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
2
1
0
0
1
0
0
0
0
0
5
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
2
0
2
0
1
2
2
0
0
0
0
0
0
3
0
0
0
2
0
0
0
1
0
2
0
0
0
0
3
2
2
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
2
2
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
1
0
0
1
0
1
2
0
0
0
0
2
0
1
1
6
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
2
2
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
1
2
1
1
0
0
0
2
0
1
1
2
0
0
0
2
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
1
2
0
0
0
0
1
0
0
3
0
0
0
0
0
1
2
1
0
0
2
2
0
1
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
1
0
0
1
2
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
1
2
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
1
1
2
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
2
0
0
1
0
0
0
2
0
2
1
0
5
0
1
0
0
1
2
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
1
1
0
3
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
3
1
0
1
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
2
2
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
3
6
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
2
0
0
0
0
2
1
0
0
2
0
1
0
3
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
1
1
1
0
0
2
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
3
3
0
0
0
2
1
1
0
0
1
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
1
0
2
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
2
0
0
0
2
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
2
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
1
2
2
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
2
0
1
0
2
0
0
1
2
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
7
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
1
0
0
0
0
0
1
0
0
2
1
0
0
0
1
0
0
1
0
0
2
0
0
3
2
0
0
0
3
1
0
0
0
0
0
3
0
0
2
0
1
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
1
0
0
0
0
2
1
1
2
0
0
0
0
0
0
0
3
0
1
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
2
5
2
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
2
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
3
0
0
2
0
2
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
1
2
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
1
3
2
0
2
0
2
0
0
0
3
0
0
0
2
2
0
0
0
1
0
0
0
0
1
2
0
1
1
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
3
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
1
0
0
0
0
0
1
0
2
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
2
2
1
2
1
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
1
0
0
1
2
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
1
1
0
0
0
0
0
0
0
7
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
1
0
1
2
0
0
0
2
0
2
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
3
0
0
1
2
0
0
1
0
0
0
0
1
0
0
0
0
1
1
1
0
1
2
0
0
0
2
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
3
0
0
0
0
4
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
1
0
2
0
2
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
3
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
3
2
0
2
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
2
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
3
2
1
1
0
0
0
0
2
0
0
0
2
0
0
0
0
1
1
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
1
2
1
3
0
3
0
1
0
0
0
0
1
0
0
1
0
0
3
0
0
0
0
0
2
0
1
1
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
2
0
2
0
2
0
0
0
2
0
0
2
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
1
1
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
2
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
3
0
0
0
0
1
0
1
0
0
0
2
2
0
0
2
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
4
0
0
2
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
2
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
2
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
1
1
0
0
2
2
0
0
0
0
2
0
1
0
0
1
0
1
0
0
0
0
0
2
2
2
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
1
0
0
5
1
0
0
0
1
0
0
0
1
0
0
0
2
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
1
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
1
2
1
0
0
0
1
0
0
0
2
0
0
2
1
1
0
0
0
1
0
2
0
0
0
0
2
2
0
0
0
1
0
0
0
0
2
0
2
1
0
0
0
0
2
0
0
0
0
2
3
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
1
3
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
3
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
1
2
0
0
2
2
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
1
0
0
2
1
0
0
0
2
0
4
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
1
0
2
0
0
1
0
0
0
0
1
0
1
1
0
2
0
2
2
0
0
0
0
0
5
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
1
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
2
0
0
0
3
2
0
0
0
0
0
3
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
2
0
1
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
2
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
2
0
0
2
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
3
0
0
0
0
0
2
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
1
2
1
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
2
2
0
0
2
1
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
2
1
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
1
0
1
0
0
1
3
0
0
2
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
3
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
3
0
1
0
0
0
1
0
0
0
1
0
0
0
0
5
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
4
0
0
0
1
2
0
0
0
2
0
2
0
0
0
1
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
2
0
0
1
0
0
0
2
0
2
1
0
0
2
0
0
0
2
0
4
0
0
0
2
1
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
5
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
2
4
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
2
0
0
0
0
2
0
0
2
1
0
2
2
1
2
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
1
0
2
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
3
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
2
0
1
1
0
1
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
2
0
0
0
0
0
1
5
0
0
2
0
0
0
2
2
1
2
0
0
0
0
1
0
2
0
0
0
2
1
0
0
0
0
1
0
0
0
2
2
0
1
1
2
0
0
7
1
0
0
0
2
0
0
0
0
0
0
1
0
1
2
0
2
4
0
0
1
2
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
2
0
2
0
1
0
0
0
3
0
0
2
2
0
0
2
1
2
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
1
0
0
1
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
2
1
0
0
0
0
0
0
0
1
0
3
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
4
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
3
2
1
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
2
0
5
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
1
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
4
1
0
0
2
2
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
3
0
1
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
2
3
0
0
2
0
0
1
0
0
1
0
0
0
0
1
1
2
0
0
0
0
1
0
0
2
0
0
2
1
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
2
2
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
2
1
5
2
0
3
2
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
3
0
0
0
1
0
3
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
6
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
2
1
2
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
3
0
1
0
0
0
3
1
0
0
0
1
0
0
0
3
0
1
1
0
0
0
0
0
0
0
0
0
0
3
2
1
0
2
0
0
1
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
2
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
2
0
0
0
3
0
2
1
2
0
0
1
2
0
0
0
1
2
0
0
0
0
1
0
0
0
2
2
0
3
2
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
4
1
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
2
0
0
0
0
0
0
1
2
1
0
0
1
1
0
0
0
2
0
2
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
5
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
1
4
2
0
0
2
0
0
2
0
0
0
0
2
1
0
0
2
1
0
1
1
2
0
0
0
0
1
2
0
0
0
2
2
0
0
0
0
0
1
1
1
2
0
0
0
2
0
0
0
0
2
0
1
1
0
0
0
0
2
0
0
0
0
3
0
1
0
0
0
0
2
0
0
0
0
0
1
1
0
0
3
0
1
3
0
0
0
0
2
0
0
0
4
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
1
2
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
2
0
1
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
3
0
2
0
0
1
0
0
2
0
3
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
1
2
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
2
0
0
1
0
2
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
1
3
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
3
0
0
0
2
0
0
2
0
0
2
1
3
1
0
0
1
2
0
0
0
1
2
0
0
2
0
0
0
0
0
1
0
2
2
0
0
0
0
2
0
0
1
0
0
1
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
2
3
2
0
1
0
0
1
0
2
0
0
1
0
0
0
0
0
0
1
2
0
0
2
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
1
0
1
10
0
1
0
1
0
0
2
0
1
0
1
2
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
1
0
0
0
0
2
1
0
0
0
0
1
1
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
2
2
0
0
1
0
0
0
1
0
0
0
0
1
1
0
1
0
0
2
0
3
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
2
2
1
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
2
0
0
0
1
0
1
4
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
3
2
0
0
0
0
2
1
0
2
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
2
0
0
1
2
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
4
0
1
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
3
0
0
2
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
2
0
0
1
0
2
0
1
0
4
0
0
3
0
0
2
2
0
0
0
0
0
4
0
0
1
2
0
0
1
0
2
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
2
0
0
2
0
0
0
1
2
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
6
4
0
1
1
0
0
0
1
0
0
2
0
3
0
0
0
0
1
1
2
0
0
0
0
0
0
1
3
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
1
0
2
2
2
3
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
1
0
1
0
0
2
2
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
1
0
0
0
0
1
0
0
1
2
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
2
0
0
0
0
0
0
3
0
1
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
2
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
2
1
0
0
1
1
0
2
0
0
0
0
0
3
0
0
1
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
3
3
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
1
0
2
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
6
1
0
0
1
2
2
2
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
1
2
0
0
0
1
0
0
2
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
4
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
1
0
1
1
1
1
0
0
3
0
0
0
0
0
0
2
0
2
0
2
2
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
2
2
0
0
0
2
0
2
2
1
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
1
0
4
2
0
0
1
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
1
2
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
1
0
1
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
3
2
0
0
2
0
0
2
0
2
0
0
0
1
0
0
3
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
1
2
0
2
0
0
2
0
0
0
0
0
0
2
0
2
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
1
0
1
2
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
5
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
3
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
2
1
0
0
0
1
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
1
0
2
0
0
0
0
1
2
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
1
2
0
2
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
3
0
0
2
5
1
0
0
1
0
0
2
0
1
0
2
2
0
0
2
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
3
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
1
0
0
0
1
0
0
0
2
0
0
0
2
1
0
0
4
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
1
0
0
2
0
2
0
0
0
0
0
2
0
0
1
0
0
2
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
2
2
3
0
0
3
2
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
1
0
0
0
0
0
2
0
2
0
1
2
0
0
0
2
2
0
2
0
0
0
0
0
0
1
0
6
0
0
1
0
0
1
0
0
1
1
0
0
3
0
0
1
1
2
1
3
0
0
2
0
0
2
2
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
2
4
0
0
1
2
0
0
0
2
0
0
2
0
2
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
3
0
3
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
2
0
0
3
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
3
0
2
2
1
0
0
1
2
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
3
0
0
2
1
0
0
1
0
0
0
1
0
1
1
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
2
0
2
5
0
1
0
0
0
2
2
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
1
0
2
0
0
1
0
0
0
0
0
3
2
0
0
0
2
0
0
0
0
0
0
1
1
1
0
3
2
0
1
0
0
0
2
0
1
1
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
2
0
0
0
4
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
2
0
0
2
0
0
0
0
0
2
0
4
0
7
0
0
1
0
3
0
1
0
0
0
0
0
0
1
0
0
1
0
2
0
0
1
0
0
0
2
1
0
0
1
0
0
0
1
0
0
0
2
1
6
0
0
0
0
0
2
0
2
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
1
2
2
0
0
0
1
0
2
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
1
0
1
0
1
0
0
0
1
0
0
2
0
0
0
2
0
0
3
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
1
0
0
0
2
0
2
0
0
2
1
0
0
0
0
1
0
0
2
0
0
0
1
1
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
2
0
1
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
2
0
0
0
0
0
1
0
0
2
0
1
0
1
0
0
2
0
2
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
1
0
0
0
1
0
0
2
0
2
0
0
0
0
0
3
2
1
0
0
0
0
1
1
0
1
0
0
2
0
0
2
1
1
0
2
1
0
1
1
0
0
0
0
0
0
0
0
0
0
5
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
5
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
2
0
0
0
4
0
0
4
0
0
1
0
1
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
6
1
1
0
0
2
1
0
0
2
0
0
0
1
1
0
1
0
0
0
0
3
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
3
0
0
2
0
1
0
2
2
0
0
0
0
0
0
0
0
0
5
0
2
0
0
1
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
3
1
0
0
2
0
0
1
0
0
0
0
1
1
0
0
0
1
2
1
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
2
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
5
1
0
1
0
0
0
0
2
0
0
1
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
3
0
0
2
0
0
2
0
2
0
2
1
2
0
2
0
0
3
1
1
0
0
3
2
1
0
1
0
2
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
2
1
0
0
0
0
2
0
0
0
2
0
1
1
0
0
1
0
0
1
0
0
0
1
0
1
0
0
1
2
0
0
0
0
0
2
0
0
0
0
4
0
0
1
0
2
0
7
0
1
0
0
0
0
1
2
0
0
0
1
2
0
1
1
0
0
0
0
0
0
1
0
2
2
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
2
0
1
0
1
0
2
2
0
0
1
0
3
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
1
0
2
2
0
0
1
0
0
0
0
0
2
1
3
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
1
0
2
1
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
2
0
2
2
0
0
0
2
0
0
2
0
0
0
0
1
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
1
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
3
0
0
0
0
0
2
0
2
0
2
0
1
0
0
0
0
0
2
0
2
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
2
0
0
0
0
1
2
0
0
0
1
0
0
1
1
0
0
2
2
0
0
1
0
0
2
0
1
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
4
2
1
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
2
2
1
1
0
0
10
0
0
0
3
0
0
0
2
0
0
0
0
0
0
2
0
1
2
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
1
0
1
2
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
2
0
0
0
0
2
1
0
0
0
0
0
0
3
0
0
1
0
2
1
0
0
0
2
2
0
0
0
1
0
2
1
0
2
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
4
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
8
0
1
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
1
0
0
3
0
6
0
0
0
0
1
2
0
3
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
2
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
1
0
0
2
0
0
0
2
1
1
0
0
0
1
0
0
2
0
0
2
2
0
1
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
3
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
1
0
0
0
0
1
0
0
0
0
0
1
3
2
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
2
0
0
0
1
0
0
0
1
0
0
2
0
1
0
3
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
5
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
3
0
2
1
1
1
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
1
0
2
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
1
0
2
0
2
1
0
0
0
0
2
0
0
2
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
1
2
0
0
0
0
2
0
0
1
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
2
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
1
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
1
2
0
0
0
0
0
1
1
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
2
1
0
2
1
0
0
2
0
0
1
2
0
0
0
0
1
1
1
0
0
1
0
0
2
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
4
0
0
0
0
3
0
0
0
1
0
0
2
2
0
0
0
2
1
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
2
4
0
0
0
0
0
1
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
1
0
2
2
0
0
1
2
1
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
3
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
1
1
0
1
0
0
6
2
10
0
1
0
1
0
2
2
0
0
0
0
2
0
0
0
1
1
0
0
1
0
0
0
3
0
0
0
0
0
0
2
0
0
0
1
0
1
2
2
0
0
0
1
1
2
0
0
0
0
0
0
0
0
4
0
0
0
3
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
1
2
1
0
0
1
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
4
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
1
0
1
0
2
1
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
2
0
1
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
1
2
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
2
2
0
0
2
0
2
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
1
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
7
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
2
0
0
0
1
0
0
0
0
2
0
10
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
3
3
0
0
0
0
3
0
2
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
2
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
1
1
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
2
1
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
3
0
0
2
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
1
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
1
0
0
0
0
2
0
1
0
0
1
0
1
0
0
0
0
0
2
0
0
0
3
1
0
2
2
0
0
0
0
0
0
0
2
0
0
3
0
0
2
0
0
1
0
1
1
0
0
0
0
2
1
0
1
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
3
0
0
2
2
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
2
0
0
0
1
0
0
0
2
0
1
0
0
2
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
3
0
2
0
0
0
0
1
0
0
1
0
0
0
2
0
2
0
2
1
2
1
2
0
0
0
1
3
1
0
0
0
2
0
1
0
2
0
4
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
6
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
2
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
2
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
2
0
0
2
0
1
0
0
2
1
2
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
3
0
2
0
0
0
2
0
3
0
0
0
0
0
2
0
0
1
0
2
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
2
0
2
0
3
0
2
2
0
2
0
0
1
0
2
3
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
1
0
0
0
0
0
6
2
0
0
0
1
0
0
0
0
2
0
2
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
2
0
2
0
0
0
0
1
0
0
0
0
4
0
0
0
0
2
2
1
1
0
0
2
0
0
2
0
2
2
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
3
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
1
2
2
0
0
0
0
1
4
0
1
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
5
0
0
0
0
0
0
0
1
0
2
0
0
1
0
1
3
0
0
0
0
2
0
0
0
0
0
5
0
0
0
1
0
0
0
0
3
2
0
1
2
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
1
1
0
0
0
1
0
0
2
2
2
2
2
0
0
2
0
0
0
0
2
2
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
1
0
0
0
0
0
2
2
0
4
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
5
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
2
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
2
0
1
4
0
1
2
0
0
1
0
0
1
0
0
0
0
0
2
0
1
0
0
0
2
2
0
0
0
3
0
0
0
2
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
1
1
2
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
4
0
0
3
0
0
2
0
0
0
2
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
3
2
0
0
0
2
0
0
3
0
0
0
2
0
0
0
2
1
0
0
1
0
2
0
0
3
1
0
0
1
2
0
0
0
0
0
1
0
0
0
0
3
0
1
1
0
0
0
1
0
2
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
1
0
0
3
2
0
0
0
0
0
1
0
1
3
0
0
0
0
1
0
0
0
0
0
2
1
0
0
2
0
0
1
2
0
1
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
2
0
0
0
2
2
0
2
0
1
0
0
0
1
1
0
0
0
7
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
1
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
1
0
3
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
3
0
0
0
0
0
2
0
0
0
2
2
2
2
0
0
0
0
2
0
0
0
0
4
0
0
2
0
0
0
1
0
0
0
0
1
0
2
2
0
1
0
1
0
1
2
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
1
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
2
1
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
4
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
2
0
1
1
1
0
0
0
0
0
2
0
0
3
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
1
0
0
0
1
0
0
0
3
0
0
1
3
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
2
0
0
1
0
0
1
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
2
2
0
0
1
0
2
0
0
2
0
0
0
0
1
0
0
0
0
3
3
0
1
0
0
0
2
1
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
2
0
0
3
1
2
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
2
0
4
2
0
0
0
0
0
1
0
1
0
0
0
3
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
2
0
0
2
2
3
2
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
1
0
0
1
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
1
3
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
1
0
1
2
1
0
0
0
0
0
1
0
0
1
0
0
2
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
1
2
0
0
2
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
1
3
0
1
2
0
0
1
9
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
1
1
2
0
0
0
0
0
0
1
2
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
3
0
2
0
0
0
0
0
3
0
0
0
0
4
4
0
0
3
0
0
0
0
0
0
2
2
0
0
0
0
1
0
1
0
2
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
2
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
2
2
0
0
0
0
3
0
4
1
0
0
0
0
1
0
0
2
0
0
2
0
1
1
0
0
0
2
0
0
1
0
1
0
1
0
0
2
0
3
0
2
0
0
0
0
0
0
0
1
7
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
2
0
1
1
0
0
1
0
2
0
2
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
1
2
0
2
0
1
2
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
5
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
1
2
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
1
0
1
3
3
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
1
0
0
0
2
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
3
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
2
0
3
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
3
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
3
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
2
0
1
0
2
2
0
4
0
0
0
1
1
0
0
0
0
0
0
1
2
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
1
0
2
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
1
0
0
2
2
0
2
0
0
1
0
0
1
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
6
0
0
0
0
0
0
2
0
1
0
0
2
0
1
1
0
0
0
0
0
0
0
2
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
1
0
0
0
1
0
2
0
0
3
0
2
0
0
1
1
1
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
2
0
2
0
3
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
3
1
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
2
1
0
0
0
1
1
0
1
0
0
2
0
0
0
0
0
1
0
0
3
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
1
0
2
2
0
2
0
0
0
2
0
3
2
2
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
1
0
0
0
0
0
1
0
0
0
2
0
2
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
2
0
0
0
1
0
1
1
0
2
3
0
0
0
0
0
2
0
0
1
4
2
2
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
9
3
0
0
0
0
0
6
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
2
0
0
0
0
2
1
0
1
0
5
0
1
0
0
0
1
0
0
1
1
1
0
0
0
1
3
0
0
2
0
0
0
2
0
0
2
0
0
1
2
1
0
4
0
0
4
1
2
0
0
0
1
2
2
1
0
2
0
0
0
0
3
0
2
0
0
0
0
0
4
7
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
2
0
0
1
2
0
1
2
0
1
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
2
0
1
0
0
0
0
0
0
0
2
0
4
0
0
0
0
1
2
0
1
0
0
2
0
0
0
1
2
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
2
1
1
0
2
0
2
0
1
0
2
0
0
1
0
0
0
1
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
3
0
1
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
1
0
0
2
2
2
2
2
1
0
0
0
0
0
3
0
0
1
0
0
2
3
1
0
1
0
2
1
0
0
0
1
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
3
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
2
4
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
1
0
1
0
0
2
2
0
0
0
0
0
0
1
0
0
0
1
1
2
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
3
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
3
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
3
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
2
1
0
0
1
2
0
2
1
0
0
0
0
0
0
0
2
2
0
0
5
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
4
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
4
2
1
2
0
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
2
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
3
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
1
3
0
2
1
2
0
1
0
2
0
1
0
0
2
0
3
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
6
0
0
2
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
2
0
0
0
0
3
0
0
0
0
9
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
5
1
0
4
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
2
1
1
0
0
0
0
2
0
2
0
0
1
5
1
3
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
1
0
0
0
3
0
0
0
2
0
0
1
0
1
0
0
4
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
2
0
0
0
1
0
0
1
2
1
0
2
1
0
0
0
0
1
1
0
0
2
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
1
1
5
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
2
1
2
0
0
0
0
0
0
2
0
2
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
2
0
2
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
2
1
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
2
1
0
0
1
0
0
1
2
1
0
0
0
0
0
0
2
1
1
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
1
0
0
0
0
1
1
0
0
0
0
2
1
0
0
0
1
0
0
0
2
0
0
0
1
0
2
0
0
0
1
4
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
1
0
0
0
3
0
0
0
1
0
0
2
0
1
1
2
3
0
0
0
0
0
0
0
0
0
1
0
0
0
2
5
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
1
0
2
0
1
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
2
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
3
2
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
2
0
2
1
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
2
0
0
0
1
0
2
4
0
1
0
1
0
1
4
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
1
0
2
0
1
0
0
1
0
0
2
0
1
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
4
0
1
2
0
0
0
0
1
0
0
0
0
1
0
0
1
0
3
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
2
0
1
0
2
0
1
0
0
0
0
2
0
0
0
0
2
0
1
2
0
0
3
1
0
0
2
2
0
0
2
0
0
0
0
1
0
1
3
0
0
0
0
0
0
2
0
0
2
0
0
1
2
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
1
0
1
0
1
3
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
5
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
2
1
3
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
3
1
0
2
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
7
0
2
1
0
0
0
1
0
0
0
0
0
2
0
0
2
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
1
0
0
0
0
0
0
0
0
0
4
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
2
0
0
2
3
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
6
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
5
0
0
0
1
0
0
0
3
0
0
0
1
0
0
0
0
3
2
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
1
0
0
0
0
1
0
2
1
0
0
0
0
1
0
2
0
1
0
2
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
5
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
1
2
2
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
2
2
0
0
1
1
0
5
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
2
0
0
0
0
1
2
0
0
2
1
0
0
0
0
0
0
0
2
0
1
2
0
1
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
3
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
2
5
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
3
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
2
1
0
1
2
1
0
1
0
2
0
0
0
0
0
0
1
0
1
0
0
2
0
2
0
0
0
0
0
0
0
3
2
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
4
3
0
0
1
0
0
0
2
0
1
0
3
2
0
0
1
1
0
2
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
4
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
4
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
2
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
2
0
1
0
0
0
0
1
0
0
1
0
0
3
3
1
0
0
0
0
0
1
0
0
0
0
0
0
3
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
2
1
0
0
0
2
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
1
0
0
2
1
0
0
0
1
1
2
0
0
0
4
0
0
0
0
2
0
1
0
0
2
0
2
0
0
2
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
1
1
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
1
1
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
3
0
0
0
2
0
0
1
0
0
0
3
0
0
2
0
1
0
0
0
1
0
0
0
2
1
0
0
3
0
1
0
2
0
0
0
2
0
0
0
5
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
3
0
0
2
0
0
0
1
1
2
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
2
0
0
0
0
0
0
1
1
1
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
1
2
0
0
0
0
1
0
1
0
2
0
0
2
0
0
2
0
3
0
0
0
2
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
3
1
1
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
2
2
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
3
2
1
0
0
0
0
0
0
2
1
0
1
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
3
2
0
0
0
0
0
1
0
1
0
0
1
0
1
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
2
1
0
0
0
1
0
1
2
2
0
0
0
1
0
0
2
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
3
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
1
2
1
2
0
0
1
0
2
1
0
2
0
0
0
1
2
0
2
2
2
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
2
1
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
5
0
3
0
0
1
0
2
0
0
0
2
0
0
0
4
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
1
1
1
0
0
8
1
1
0
0
0
1
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
7
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
2
1
2
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
2
0
2
2
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
3
0
2
0
4
2
3
0
0
0
0
0
2
0
1
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
1
2
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
2
0
3
0
2
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
2
2
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
2
1
0
0
0
2
2
0
3
2
1
0
1
3
0
0
1
0
0
0
0
2
0
0
11
2
0
2
0
0
0
0
6
0
3
0
0
2
0
2
1
1
0
2
2
0
0
0
2
1
0
0
1
2
0
0
0
0
0
4
0
0
3
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
2
1
1
0
0
0
2
0
0
0
0
1
3
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
5
1
1
0
3
2
0
0
0
0
2
4
1
4
0
0
0
0
1
0
0
1
0
0
0
4
0
0
2
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
3
0
1
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
3
0
0
0
0
2
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
1
1
0
0
1
0
0
0
5
0
0
0
0
0
0
2
0
1
3
0
1
0
3
0
0
0
1
4
0
2
1
0
0
2
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
4
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
4
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
3
0
0
0
5
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
1
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
1
0
0
0
2
0
1
4
1
0
0
0
0
0
0
3
1
0
2
2
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
1
2
1
0
2
0
6
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
3
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
2
2
1
0
0
0
0
1
0
0
2
0
1
2
0
2
0
1
0
1
0
0
0
4
2
1
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
2
1
2
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
2
0
2
2
2
1
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
1
2
0
1
3
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
2
0
0
1
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
2
1
0
1
0
0
0
1
0
4
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
2
2
0
0
0
3
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
2
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
3
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
2
1
0
1
0
0
0
1
2
0
0
2
1
0
2
2
0
0
0
0
0
1
0
0
0
2
0
0
2
2
0
0
0
0
1
0
0
3
0
1
0
0
0
0
2
0
0
0
0
2
0
0
1
1
2
0
0
0
1
1
0
2
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
6
0
2
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
2
0
0
1
0
0
4
0
0
1
0
5
0
2
1
0
0
0
0
0
2
2
2
0
0
2
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
2
2
6
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
2
1
0
0
0
2
0
0
5
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
2
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
2
0
0
2
1
2
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
1
1
2
0
0
2
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
5
0
1
0
0
0
0
0
0
3
0
0
1
0
0
1
0
0
0
2
0
0
0
0
1
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
1
2
0
6
0
0
0
0
0
3
0
2
0
2
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
2
0
0
2
0
0
0
3
0
0
0
0
0
2
1
1
0
1
0
0
5
0
3
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
1
0
1
9
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
2
1
0
2
0
1
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
2
0
1
1
2
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
1
0
2
0
0
2
0
2
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
3
0
0
0
0
0
1
0
0
0
0
0
0
10
0
0
0
0
3
2
0
9
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
2
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
2
0
1
0
0
0
0
0
2
1
0
0
0
5
1
0
1
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
2
1
1
0
1
0
2
0
0
0
2
2
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
3
0
0
0
0
0
1
2
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
1
2
2
0
0
0
2
0
0
0
2
2
0
0
0
2
1
2
1
0
0
0
2
0
0
0
2
1
2
0
0
0
2
0
2
0
0
2
0
0
0
1
0
1
0
1
0
0
0
0
2
0
0
0
0
1
0
2
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
2
0
1
1
3
0
0
2
0
2
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
1
1
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
1
0
0
0
0
2
0
0
0
2
1
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
2
2
0
0
3
0
0
2
0
0
1
1
0
0
1
0
0
0
1
0
0
0
2
0
0
1
0
0
0
2
0
1
2
0
2
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
1
1
0
0
2
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
2
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
2
0
0
3
0
0
0
0
0
0
2
0
6
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
4
0
0
2
0
0
0
0
0
0
3
0
0
2
2
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
3
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
2
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
1
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
1
0
0
2
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
3
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
1
0
2
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
2
0
0
4
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
2
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
1
0
0
0
0
3
2
0
0
0
1
0
0
0
1
0
0
3
0
0
0
0
0
0
2
2
0
1
1
0
0
0
0
0
2
2
2
0
2
0
0
0
0
0
0
1
0
0
2
0
2
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
2
2
0
0
0
3
4
0
0
0
2
0
0
2
3
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
1
2
1
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
3
0
1
0
0
0
0
0
2
0
0
4
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
3
1
1
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
2
0
0
0
2
0
0
3
0
0
0
1
2
0
0
0
0
2
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
2
1
3
0
0
0
0
1
0
0
1
0
0
1
0
2
0
0
0
0
2
1
1
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
1
0
2
2
2
0
0
0
0
2
1
0
0
0
1
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
1
0
0
0
1
2
0
0
0
0
0
0
7
0
0
0
2
0
0
1
2
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
4
1
0
0
1
2
0
2
0
2
0
1
0
2
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
1
0
0
0
1
0
0
2
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
3
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
2
2
2
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
3
0
0
0
0
0
1
1
5
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
1
0
2
0
2
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
3
0
2
1
0
0
0
0
1
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
2
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
2
2
1
0
0
1
2
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
2
1
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
2
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
9
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
2
2
2
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
1
1
1
0
0
1
0
1
0
0
0
0
2
0
0
0
1
0
0
0
2
1
0
0
2
0
1
0
2
2
0
1
0
0
2
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
2
1
0
0
2
0
2
0
0
0
2
2
0
0
1
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
3
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
2
0
0
2
0
0
0
0
0
0
1
2
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
5
0
0
3
0
0
0
0
0
0
0
2
0
0
3
1
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
1
2
3
0
0
0
0
1
4
0
1
2
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
4
0
2
0
0
0
0
2
0
0
0
41
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
1
1
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
1
0
0
0
1
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
1
0
0
0
0
0
2
0
0
0
2
0
1
0
2
0
0
0
0
3
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
2
2
1
1
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
2
0
0
0
2
2
0
1
2
2
1
4
0
0
0
0
0
0
2
0
0
1
3
0
2
0
2
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
1
1
0
2
2
0
0
0
0
0
0
0
2
1
0
0
0
1
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
2
0
0
3
0
3
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
1
2
2
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
3
0
1
0
0
0
2
1
0
0
2
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
2
1
0
0
0
1
1
0
2
0
1
0
0
0
1
0
1
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
2
0
0
0
3
2
0
2
0
0
1
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
2
3
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
2
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
4
0
0
1
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
1
1
0
2
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
1
0
0
2
3
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
1
0
0
2
1
0
0
0
0
0
1
3
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
1
0
2
0
7
0
5
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
2
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
1
2
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
4
1
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
1
2
0
0
0
1
1
3
0
2
0
0
2
0
2
0
0
0
0
3
0
0
0
3
1
0
0
0
0
0
1
2
1
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
1
0
10
0
0
0
0
0
2
0
2
3
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
1
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
9
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
2
2
0
0
0
0
0
4
9
0
0
1
0
0
2
1
2
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
4
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
1
0
1
5
0
0
0
1
0
0
0
0
0
0
4
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
1
1
0
0
0
1
0
0
2
2
0
0
0
0
1
1
2
0
0
2
0
2
0
2
0
0
0
2
0
0
1
0
0
0
0
0
2
1
0
1
0
0
1
1
0
2
2
2
0
2
1
2
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
1
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
3
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
2
2
0
0
1
0
0
2
1
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
7
0
0
0
2
0
0
2
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
2
2
0
1
0
3
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
2
0
0
0
0
2
0
0
0
0
0
0
1
2
0
2
0
1
0
0
1
0
0
0
0
5
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
2
0
0
0
0
1
0
2
1
0
0
0
4
1
0
0
0
1
3
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
2
0
0
1
1
0
0
1
1
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
1
0
2
1
0
1
0
2
1
1
1
2
0
0
0
0
0
0
2
0
3
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
6
0
0
0
0
1
5
1
0
0
3
0
0
2
0
0
0
0
0
1
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
3
0
0
1
0
2
0
0
0
0
0
0
1
2
2
2
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
1
2
0
0
0
0
1
0
2
0
2
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
1
0
2
0
2
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
2
0
0
0
0
3
1
0
1
1
0
0
0
2
1
0
2
1
1
1
1
3
0
0
0
0
2
0
0
2
0
1
1
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
3
2
0
0
0
0
0
1
0
2
1
1
0
2
0
2
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
2
1
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
3
0
2
0
2
0
0
2
0
0
0
1
0
0
1
2
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
1
0
2
0
3
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
1
0
0
0
0
1
0
0
0
1
0
2
0
2
0
0
1
0
0
0
1
0
0
0
0
5
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
3
2
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
1
2
0
0
0
0
0
0
1
0
0
1
0
2
1
0
1
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
2
0
0
1
1
0
0
1
2
2
2
0
0
1
0
0
2
1
3
1
4
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
1
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
1
1
0
0
0
1
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
2
0
2
0
1
0
0
3
0
0
0
0
2
0
0
0
1
0
2
4
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
2
1
2
1
0
0
3
0
2
0
0
0
0
0
0
0
0
5
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
3
0
0
0
0
1
0
2
0
0
1
9
0
0
2
0
1
0
0
1
0
0
0
0
3
2
0
0
0
1
1
2
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
2
0
0
0
1
0
0
0
0
0
0
1
0
0
3
1
0
0
0
0
0
1
0
2
1
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
1
4
2
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
4
2
2
0
0
1
2
0
1
4
0
1
1
0
2
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
2
0
1
0
2
0
1
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
3
0
0
0
1
0
0
0
0
0
0
0
2
4
0
0
1
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
1
2
0
2
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
2
2
0
0
0
2
0
2
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
2
1
0
2
1
0
0
0
0
3
0
0
1
1
0
1
1
0
5
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
1
2
0
2
2
3
0
0
2
0
0
0
0
0
1
2
0
1
2
0
1
0
2
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
2
1
0
0
0
0
0
1
0
2
2
1
0
0
1
2
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
5
3
0
0
0
2
0
0
0
0
0
1
1
1
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
2
0
0
2
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
3
1
2
0
0
0
0
0
0
0
0
0
1
2
2
2
0
0
0
1
0
1
0
0
0
1
0
0
0
1
3
0
0
0
1
0
0
0
0
0
2
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
1
1
1
0
0
0
0
0
3
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
7
2
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
1
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
6
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
2
0
2
0
0
0
1
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
1
0
2
0
0
0
0
3
1
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
1
0
2
0
0
0
0
0
0
1
0
1
0
3
0
0
1
0
0
2
0
0
0
0
0
1
0
0
1
0
1
0
0
1
2
0
2
0
0
1
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
12
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
15
0
0
0
1
0
0
0
0
1
0
2
0
0
0
3
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
4
1
0
2
1
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
17
0
0
0
0
0
2
0
0
4
0
0
1
1
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
1
1
1
0
2
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
2
2
1
1
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
1
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
2
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
1
0
2
0
3
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
2
0
2
1
0
0
0
0
0
0
15
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
3
0
1
0
1
2
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
1
1
0
0
1
1
0
0
0
2
1
0
0
2
2
0
2
1
0
2
0
0
0
0
1
1
1
2
1
0
0
1
0
0
1
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
2
4
0
0
1
0
0
0
2
0
1
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
0
0
0
0
2
3
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
3
4
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
1
0
0
7
1
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
3
0
0
3
0
0
0
0
0
2
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
1
0
2
1
0
0
0
2
0
3
0
2
1
0
2
0
1
2
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
2
0
2
0
2
0
2
1
0
1
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
3
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
7
0
0
0
0
0
0
0
0
0
0
2
2
1
3
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
2
1
1
1
1
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
3
0
1
0
2
0
0
0
0
2
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
3
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
5
0
0
0
3
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
3
0
0
0
1
0
1
1
1
2
5
0
0
2
0
0
0
0
0
0
0
6
2
0
0
2
0
2
0
1
0
3
2
0
0
0
1
0
0
1
1
2
0
0
0
1
0
1
0
0
0
0
2
0
2
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
2
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
1
0
0
1
1
0
2
2
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
2
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
8
0
0
0
0
0
1
1
0
1
2
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
2
1
0
0
1
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
4
0
1
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
3
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
2
2
0
1
0
0
0
0
1
0
0
1
0
1
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
1
0
0
0
1
0
0
0
1
0
2
0
0
0
0
3
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
1
1
0
0
0
0
3
1
0
1
0
1
1
0
0
14
0
1
0
0
0
1
0
0
0
0
0
2
0
2
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
1
1
2
0
0
0
0
4
0
0
0
2
1
0
0
1
0
0
2
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
3
1
1
0
0
2
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
2
2
1
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
3
1
0
1
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
2
0
2
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
7
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
2
0
0
0
0
1
2
0
0
0
1
0
1
8
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
3
1
3
0
0
0
2
0
0
0
2
2
2
0
1
3
1
0
0
0
0
0
0
0
0
2
1
0
2
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
1
0
0
0
1
0
2
0
0
0
2
0
0
0
0
1
2
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
1
2
0
1
1
0
3
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
3
3
2
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
1
2
2
2
0
0
2
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
3
0
0
0
0
2
0
0
1
0
0
0
0
3
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
2
0
1
0
1
0
1
0
0
4
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
3
1
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
1
2
0
1
0
0
0
0
0
0
1
0
0
5
0
0
0
0
1
0
0
2
1
2
0
0
1
0
0
2
0
0
2
0
1
0
0
0
2
1
0
1
0
1
1
3
0
0
0
0
1
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
2
0
0
0
0
0
0
3
0
0
0
2
0
1
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
3
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
1
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
4
0
0
0
0
1
0
0
1
0
1
0
0
1
2
0
2
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
2
1
0
2
0
0
1
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
3
0
0
2
0
0
0
1
0
0
0
0
3
1
2
1
0
0
0
2
0
0
0
0
5
0
0
6
1
0
2
0
0
0
2
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
1
1
0
2
0
0
2
0
0
0
0
1
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
2
1
1
0
1
0
0
2
0
0
4
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
2
1
2
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
3
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
4
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
1
2
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
1
3
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
3
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
2
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
2
0
1
1
1
2
0
2
0
0
0
0
0
1
0
2
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
3
0
4
0
0
0
1
0
0
0
1
1
1
0
0
0
2
2
0
1
0
0
0
0
1
2
0
0
0
2
0
1
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
2
1
0
0
0
1
0
0
0
0
0
0
0
0
2
2
1
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
1
1
0
3
2
0
2
0
0
2
0
1
1
0
0
0
0
2
0
0
2
0
0
0
1
0
0
2
0
3
0
1
0
2
2
0
0
0
1
2
0
1
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
3
0
0
3
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
2
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
2
2
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
3
0
1
2
0
0
0
0
2
1
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
2
1
0
3
0
0
0
2
0
0
1
0
2
0
3
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
5
0
2
0
1
2
0
0
1
0
1
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
2
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
3
0
1
0
0
0
0
1
0
0
0
0
1
3
0
0
0
2
4
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
3
0
2
0
0
0
0
0
1
0
4
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
1
0
1
0
0
2
2
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
2
2
1
0
0
0
2
0
0
0
0
0
2
1
2
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
1
0
1
2
1
0
0
1
0
0
0
0
0
2
0
0
0
1
1
0
0
0
2
0
1
0
2
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
1
0
0
0
0
0
3
1
0
0
0
2
0
0
0
0
2
2
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
1
2
1
0
0
0
0
0
0
0
1
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
2
0
0
0
2
0
0
0
1
1
0
0
1
0
3
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
2
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
2
2
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
1
2
0
2
0
0
0
2
0
2
0
0
2
1
2
2
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
2
2
0
0
0
0
2
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
8
1
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
2
0
2
0
1
0
0
1
2
0
0
0
2
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
1
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
2
1
1
2
1
1
0
2
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
2
1
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
1
0
0
0
0
1
1
2
0
2
0
2
0
1
0
2
0
0
0
0
0
0
2
1
0
0
0
1
0
1
2
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
3
2
0
0
1
0
2
1
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
3
0
0
1
0
0
3
0
0
8
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
2
0
0
0
0
1
1
0
0
0
1
0
0
0
2
0
0
0
0
2
1
0
0
0
1
0
2
0
1
0
0
0
0
0
1
1
0
0
1
0
0
1
0
2
1
1
0
0
1
0
0
0
1
2
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
1
0
0
0
0
0
1
1
0
7
0
0
0
2
0
0
0
0
2
2
0
0
0
4
0
0
0
2
0
0
0
0
0
0
1
0
0
4
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
2
1
0
0
4
0
0
0
0
0
2
1
2
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
1
1
2
0
2
0
0
0
7
4
0
1
0
0
0
2
1
0
1
1
0
0
2
2
0
0
2
1
1
0
0
0
0
1
0
0
0
0
2
0
0
0
2
2
1
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
1
3
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
3
0
0
1
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
1
5
0
0
0
0
2
2
0
0
3
0
5
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
1
1
0
0
5
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
2
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
1
1
0
1
2
2
0
3
2
3
0
1
0
0
2
0
0
1
0
0
1
0
0
2
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
2
8
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
3
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
1
0
2
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
1
0
0
1
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
5
0
0
2
0
0
1
0
0
0
0
0
3
0
2
0
2
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
2
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
2
3
0
1
0
0
0
0
2
1
0
0
0
1
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
8
1
0
0
0
3
0
0
0
0
0
5
0
0
0
5
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
3
0
1
0
0
1
2
0
0
0
0
0
2
0
0
1
0
1
0
0
1
0
0
1
2
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
3
0
0
0
0
0
0
0
0
3
2
1
1
1
0
1
0
0
2
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
2
2
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
1
0
1
3
0
0
0
0
0
0
0
0
0
2
0
2
2
1
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
3
0
2
2
0
0
1
2
0
1
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
4
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
10
1
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
1
1
2
0
0
0
0
0
0
0
0
0
0
3
2
0
2
0
0
0
0
0
1
1
0
0
6
2
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
4
1
0
0
0
0
0
1
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
3
1
0
0
2
0
2
0
0
1
0
0
0
0
1
0
0
3
0
0
2
2
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
1
0
0
0
1
1
2
0
0
0
1
0
0
1
4
0
0
0
0
1
1
5
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
1
2
0
0
0
0
1
0
0
2
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
2
1
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
2
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
2
0
2
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
2
0
3
0
0
0
0
2
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
1
0
0
2
0
0
1
0
1
0
0
0
2
0
0
0
2
2
1
0
0
0
0
0
0
2
0
2
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
1
0
1
1
0
0
0
4
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
1
5
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
4
0
0
0
1
0
0
2
0
0
0
0
0
0
5
0
0
0
0
1
1
0
5
1
2
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
1
0
1
0
0
0
2
0
0
3
0
0
5
1
1
0
2
0
1
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
1
0
0
2
2
2
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
2
1
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
1
0
0
1
0
2
2
0
0
0
0
0
0
0
2
1
0
0
0
0
2
1
1
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
2
0
0
0
3
0
0
2
0
0
0
0
1
0
2
0
1
0
2
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
2
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
2
0
0
2
0
1
2
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
2
0
2
2
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
1
0
2
0
0
0
2
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
3
1
0
0
3
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
2
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
1
0
1
0
1
0
1
0
2
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
4
0
0
1
2
0
0
0
1
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
2
0
0
0
2
0
0
0
1
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
1
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
3
0
0
2
0
1
0
2
0
0
3
2
1
1
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
3
2
0
2
1
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
1
0
0
0
0
0
0
0
2
1
2
0
0
0
0
2
2
0
1
1
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
1
3
0
0
1
0
0
2
1
2
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
2
0
0
0
0
0
2
1
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
2
0
0
0
3
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
3
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
2
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
1
6
1
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
6
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
4
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
3
0
1
0
0
0
2
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
2
1
2
0
1
0
2
1
0
1
0
2
0
0
0
7
2
0
0
0
0
0
0
0
4
0
0
0
0
5
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
3
2
1
2
0
0
0
0
0
0
0
0
1
0
0
1
0
2
1
0
0
0
0
0
1
0
0
0
6
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
1
0
0
0
0
0
0
0
0
2
3
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
1
0
2
0
0
0
0
1
0
0
0
4
0
0
2
0
2
3
0
0
0
0
0
0
0
0
0
2
2
1
2
2
0
0
0
0
2
0
0
2
0
0
2
0
1
0
0
2
0
0
0
2
2
0
1
0
0
2
0
0
0
2
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
2
1
0
2
0
1
0
0
1
0
0
0
0
0
0
0
5
2
0
0
1
0
0
2
0
0
0
0
0
1
0
2
0
3
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
1
0
1
0
0
2
1
0
0
0
0
0
0
0
1
2
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
9
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
1
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
2
6
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
2
2
2
0
1
0
1
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
1
0
2
0
0
2
0
0
0
0
0
1
0
0
1
0
1
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
4
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
1
0
0
0
1
0
0
0
3
0
1
0
0
0
0
0
0
1
1
0
1
0
2
0
0
0
0
2
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
3
0
2
0
1
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
2
2
3
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
1
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
1
1
2
3
0
0
2
1
0
0
1
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
1
0
0
0
4
1
0
0
1
0
1
0
0
0
2
0
0
2
2
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
5
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
2
0
0
5
1
0
0
2
0
0
0
1
1
0
0
0
1
0
0
0
0
2
1
1
8
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
1
1
0
0
0
2
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
2
1
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
3
0
0
0
3
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
1
1
0
0
1
0
0
0
3
2
0
0
0
2
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
1
1
0
6
1
1
0
2
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
2
3
0
0
0
0
5
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
8
0
0
0
0
0
0
0
1
0
2
2
0
0
0
2
0
1
0
3
0
0
0
6
0
2
0
3
2
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
5
0
2
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
1
0
0
1
0
0
1
0
0
0
1
2
2
3
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
2
1
0
0
2
0
0
0
0
2
0
0
0
0
1
3
0
1
2
3
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
1
1
1
1
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
2
0
0
1
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
1
3
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
2
0
1
3
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
1
1
0
0
2
2
2
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
3
2
0
2
2
0
0
2
0
1
2
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
1
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
2
0
1
0
2
0
0
1
0
0
0
0
0
0
1
1
1
0
1
0
1
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
1
0
2
2
2
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
2
0
1
1
0
0
0
1
1
2
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
8
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
1
1
0
0
2
0
2
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
2
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
2
1
0
2
0
0
1
4
2
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
4
1
0
2
1
0
2
0
0
0
0
2
2
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
1
0
2
2
0
3
0
0
0
0
1
4
0
0
0
3
0
1
0
2
0
2
0
0
2
0
2
1
3
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
1
0
1
1
2
0
0
0
0
0
2
0
0
0
1
0
2
0
2
1
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
3
1
0
1
2
1
0
0
0
0
0
0
0
0
2
1
1
1
0
0
0
0
0
3
0
0
2
0
0
0
1
0
0
2
0
3
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
2
1
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
3
0
2
2
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
3
0
0
0
3
0
0
0
0
0
0
2
0
0
3
2
2
0
0
2
2
3
0
0
0
0
2
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
2
0
0
0
2
0
1
3
0
0
0
0
0
1
0
0
2
1
0
0
0
1
2
1
0
0
0
3
0
0
0
0
0
0
1
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
2
2
0
0
0
2
0
3
0
0
1
0
0
0
1
1
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
4
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
1
0
0
8
0
0
0
0
0
2
2
0
2
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
2
1
0
0
0
0
0
0
1
0
1
3
0
1
1
1
0
0
1
3
2
0
1
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
2
2
0
1
2
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
3
0
0
0
0
4
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
1
0
0
0
0
2
2
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
8
2
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
1
2
1
0
0
0
0
1
0
0
0
0
1
0
2
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
3
2
0
2
0
0
1
0
0
0
0
0
0
2
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
1
0
0
0
1
5
0
0
0
2
0
11
0
0
0
0
0
0
2
2
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
1
2
2
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
2
2
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
1
0
1
2
1
1
1
2
0
0
0
0
2
0
0
3
0
0
0
1
1
1
0
0
1
0
0
3
0
0
0
0
0
0
0
2
1
2
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
1
0
0
0
1
0
2
0
2
0
3
0
0
0
0
0
0
0
3
1
0
1
0
1
0
0
0
0
5
4
2
0
1
0
0
1
0
0
1
6
0
0
0
0
0
0
2
1
2
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
2
0
0
2
1
0
1
0
0
1
0
0
0
1
1
2
1
1
0
0
0
1
3
0
0
0
1
1
2
2
0
2
0
0
0
0
4
0
0
2
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
6
0
1
2
0
0
1
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
4
0
0
0
0
0
0
0
0
1
0
4
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
1
0
0
0
0
0
2
2
0
1
0
0
0
1
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
2
0
0
0
17
1
2
0
0
0
2
0
0
1
1
0
0
1
0
0
0
0
2
2
0
1
2
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
1
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
5
0
1
2
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
2
2
0
0
0
1
0
1
0
0
0
0
0
0
0
5
0
0
1
0
3
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
2
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
1
0
2
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
2
0
1
2
0
1
0
0
0
2
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
3
0
0
0
0
0
0
1
0
2
1
0
0
0
1
0
0
1
6
0
1
0
0
2
1
2
0
0
0
1
0
0
0
0
0
0
1
2
1
0
0
0
0
1
0
1
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
2
1
0
0
1
3
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
1
1
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
3
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
3
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
2
2
0
0
2
0
0
0
0
0
5
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
1
0
1
0
0
1
1
1
0
2
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
5
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
1
1
0
2
0
0
1
1
0
0
0
0
2
2
0
1
0
2
2
0
1
2
0
0
0
0
3
3
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
5
1
0
0
1
0
0
0
0
1
0
0
0
4
0
2
4
0
1
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
4
0
1
0
0
0
2
0
0
0
1
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
3
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
4
1
0
2
0
0
0
0
0
0
0
3
0
0
0
0
3
0
1
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
4
0
0
0
0
1
0
0
0
0
0
1
1
2
0
0
0
1
0
0
0
1
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
4
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
1
0
0
1
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
3
2
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
2
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
7
0
1
0
0
0
0
1
0
1
0
2
0
1
0
0
0
0
0
0
0
2
0
2
0
2
0
0
3
0
2
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
2
1
0
1
2
0
0
0
0
1
2
0
0
0
0
2
0
0
1
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
1
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
1
0
0
0
1
1
2
0
2
0
0
0
2
0
0
0
2
0
0
2
0
3
0
0
1
1
8
0
0
0
0
1
0
7
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
5
2
0
0
0
0
0
2
0
0
0
0
4
0
0
0
3
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
1
0
0
2
1
1
2
0
0
0
1
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
1
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
1
2
0
2
0
0
2
1
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
2
5
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
1
0
2
0
1
1
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
2
0
0
0
0
3
0
0
2
2
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
2
2
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
3
3
1
0
2
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
5
2
0
0
0
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
4
0
0
1
0
0
0
2
7
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
1
0
1
0
1
0
0
2
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
2
2
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
1
0
0
0
0
1
0
1
0
0
4
0
2
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
3
2
0
1
0
0
0
1
1
1
0
0
1
0
0
0
0
0
2
2
0
0
0
2
0
2
0
2
0
0
0
0
0
1
0
0
0
0
1
0
1
0
2
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
2
0
0
1
0
1
0
0
0
0
2
0
0
0
2
0
2
0
4
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
3
0
2
0
1
1
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
2
0
0
0
0
2
1
0
1
1
0
0
0
0
1
0
2
0
1
2
0
0
0
0
1
0
1
0
2
0
0
2
2
0
0
3
0
0
0
2
0
0
2
1
2
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
2
2
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
10
0
0
0
0
0
0
0
1
1
0
0
1
0
0
2
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
2
2
2
0
0
2
1
0
0
0
0
0
0
0
0
2
1
0
0
3
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
3
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
1
1
0
1
0
2
1
0
0
0
2
2
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
1
1
0
0
2
0
0
0
0
2
1
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
3
0
0
0
1
0
0
2
5
2
0
2
0
0
1
1
2
1
0
1
0
0
0
0
0
0
2
1
2
0
0
2
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
3
0
1
0
0
0
1
0
1
0
0
0
1
3
1
0
0
0
1
0
2
3
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
5
2
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
1
0
0
3
0
0
0
6
0
0
0
1
0
0
0
0
2
1
1
2
0
2
0
0
0
0
1
0
2
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
2
3
1
0
2
0
2
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
3
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
2
0
1
0
1
0
1
1
1
2
0
0
1
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
1
4
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
1
2
0
0
0
0
2
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
3
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
1
0
0
2
0
1
1
2
0
0
0
0
0
1
0
4
0
0
0
0
0
1
0
0
1
4
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
2
3
0
0
1
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
3
0
0
0
0
0
1
2
0
0
2
1
2
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
2
0
0
0
0
1
0
0
0
0
2
0
1
0
2
0
3
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
3
0
1
2
4
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
1
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
3
1
0
0
0
0
2
0
0
3
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
2
0
2
0
1
0
1
2
0
0
0
0
0
1
0
0
1
2
0
0
3
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
3
0
0
0
1
2
0
0
0
0
2
2
1
0
0
0
2
0
1
1
1
0
0
0
0
2
0
0
2
7
0
0
0
2
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
3
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
4
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
1
0
0
4
1
0
0
2
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
2
3
1
0
0
1
2
0
1
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
3
2
0
1
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
2
0
0
1
1
0
1
0
1
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
1
1
0
0
2
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
2
0
0
0
2
0
1
0
1
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
2
0
3
0
1
0
1
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
2
0
0
2
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
5
0
0
0
0
0
2
2
0
0
0
0
1
0
0
2
2
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
3
1
0
0
0
0
1
0
0
0
2
1
0
0
0
0
1
0
3
3
4
0
0
1
0
0
0
2
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
1
0
0
2
2
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
2
2
0
0
0
2
2
2
0
0
0
0
2
0
0
0
1
2
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
3
0
0
2
1
1
2
0
0
1
0
0
2
0
0
1
0
0
0
2
2
0
0
2
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
2
3
0
1
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
3
2
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
1
0
2
0
1
1
2
0
0
2
2
3
2
1
0
2
0
0
0
0
2
0
1
0
4
0
2
1
0
0
0
1
0
0
0
0
0
0
0
20
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
3
2
0
1
0
0
0
0
0
0
0
1
0
4
0
2
0
0
1
0
1
0
0
1
0
0
0
0
0
2
0
0
2
0
0
3
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
2
2
3
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
3
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
2
0
0
0
2
0
1
2
0
0
2
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
2
3
1
1
0
0
0
1
0
0
0
0
0
3
0
1
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
1
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
3
2
1
2
1
0
1
0
0
0
0
1
2
0
3
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
1
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
3
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
2
0
0
0
0
2
0
0
3
0
0
1
0
0
1
0
0
0
0
3
0
0
0
2
0
1
0
0
0
1
0
0
2
0
0
2
0
0
0
2
0
1
0
0
1
0
0
1
3
2
0
2
0
0
0
0
0
2
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
1
1
0
0
1
2
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
2
2
0
1
0
0
1
0
0
0
1
0
2
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
2
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
2
0
2
0
0
0
0
2
0
0
0
0
3
2
0
1
0
0
1
0
1
0
0
0
0
2
0
2
0
2
1
0
0
0
2
0
3
0
2
1
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
2
2
0
0
1
0
0
1
0
2
2
2
1
2
0
0
2
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
3
0
2
0
0
1
1
2
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
2
0
5
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
1
1
0
0
1
2
1
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
2
0
0
0
2
0
1
0
3
0
0
0
0
1
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
1
0
2
0
2
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
2
0
2
0
0
2
2
0
3
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
2
5
0
2
1
0
0
0
0
0
0
2
0
0
1
0
2
0
0
1
0
0
0
0
0
3
0
0
0
0
1
2
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
2
2
2
0
2
2
1
2
2
0
1
1
0
0
0
0
1
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
3
0
0
0
0
0
0
0
0
0
1
0
5
0
2
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
5
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
2
0
1
0
0
0
1
1
0
0
0
0
0
0
1
1
0
2
4
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
2
1
0
0
2
2
2
2
4
4
0
3
0
0
0
0
0
2
0
3
0
2
0
0
0
0
0
0
2
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
3
0
1
0
0
0
0
1
2
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
4
0
0
0
1
0
0
1
0
1
1
0
1
1
1
2
0
0
0
0
0
1
0
0
0
0
3
1
0
2
0
0
1
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
2
0
0
0
0
0
0
0
0
3
2
1
0
0
0
0
0
0
1
6
2
0
1
0
0
0
0
2
0
1
1
1
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
3
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
7
0
0
0
0
0
0
1
0
0
1
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
1
0
0
1
0
2
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
2
0
0
1
0
0
0
1
1
0
0
0
2
0
0
1
0
0
0
0
1
1
0
1
0
0
2
0
0
0
0
0
0
6
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
2
0
0
0
2
0
0
1
0
1
1
0
0
3
0
2
0
2
0
1
1
0
0
2
0
2
0
0
0
0
0
3
0
0
1
0
0
0
1
0
0
1
3
0
1
0
2
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
3
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
3
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
1
0
1
1
1
0
0
0
0
0
0
0
0
2
2
0
0
0
3
0
0
0
0
0
4
0
1
0
0
1
0
1
0
2
0
6
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
2
3
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
2
2
0
6
0
0
0
0
1
0
0
0
0
1
2
1
0
1
1
0
0
0
0
1
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
1
1
0
0
0
1
1
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
3
1
2
1
1
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
3
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
1
0
1
0
0
2
1
0
0
0
1
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
5
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
2
0
2
0
0
0
0
2
0
1
2
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
1
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
8
0
0
0
0
0
0
0
1
0
2
0
1
0
0
1
0
0
2
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
2
1
0
0
0
0
1
3
0
2
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
4
0
2
0
2
3
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
2
1
0
2
0
2
1
0
2
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
2
6
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
4
3
0
0
0
1
0
0
0
1
2
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
2
0
2
0
0
0
1
0
0
3
0
0
0
1
0
0
1
0
0
2
0
1
0
0
0
1
2
1
0
0
0
0
0
0
2
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
1
1
0
0
0
1
2
0
0
1
0
2
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
3
2
0
2
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
1
0
2
0
1
0
2
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
1
2
0
0
0
2
1
0
0
0
1
0
3
1
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
2
0
0
2
0
3
0
0
0
0
0
2
1
0
0
0
2
0
2
1
2
2
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
3
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
4
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
1
2
2
2
2
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
3
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
1
0
0
2
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
3
2
0
1
2
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
3
0
2
0
1
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
1
0
2
2
0
0
2
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
3
0
1
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
2
0
0
0
0
0
4
0
0
1
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
2
0
0
2
0
0
0
1
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
2
0
1
1
2
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
2
1
0
0
2
0
0
0
0
1
0
0
2
0
0
1
0
1
0
0
1
0
2
0
3
0
0
1
1
0
0
1
0
0
2
0
1
0
3
0
0
0
0
0
0
0
3
0
0
1
0
0
0
4
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
1
3
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
1
4
2
0
2
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
1
2
1
1
0
1
1
0
0
0
3
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
1
0
0
2
0
3
0
0
0
0
1
0
1
1
0
0
1
1
0
0
2
2
0
0
2
0
0
6
0
0
0
0
3
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
3
0
0
0
1
2
3
0
0
1
0
0
3
4
0
0
1
0
1
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
4
1
0
0
0
1
0
0
2
2
0
0
1
0
0
0
0
1
1
0
0
1
0
2
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
1
0
0
0
0
3
0
0
0
0
1
2
0
2
0
1
2
0
2
1
0
0
2
0
3
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
1
0
0
0
2
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
2
0
1
3
0
0
0
2
0
0
0
0
0
0
1
0
3
1
4
0
0
0
0
0
2
1
0
2
2
0
4
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
4
0
2
0
2
0
0
1
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
1
0
1
1
0
0
1
1
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
11
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
2
1
1
4
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
3
0
0
2
0
3
0
0
0
0
0
1
1
4
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
2
0
1
0
1
2
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
1
0
0
1
0
1
2
0
2
0
0
0
2
0
1
0
1
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
2
1
0
1
0
0
0
1
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
2
3
0
0
0
0
3
0
1
0
0
0
0
0
1
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
2
0
1
2
0
2
0
0
2
0
1
0
0
2
0
5
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
3
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
1
0
0
0
0
2
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
4
4
1
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
3
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
2
3
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
3
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
4
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
1
1
3
1
0
0
0
0
0
2
0
0
0
0
0
2
2
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
1
0
0
0
0
0
7
2
0
0
0
0
0
2
0
0
2
4
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
1
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
1
0
1
0
0
2
1
0
3
2
0
3
3
0
0
0
0
0
0
2
0
2
5
2
0
0
0
0
2
2
0
1
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
1
1
0
0
1
0
0
3
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
1
0
0
0
2
3
2
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
1
0
1
3
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
3
3
0
0
0
0
0
1
0
3
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
1
0
3
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
3
2
2
2
0
0
1
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
0
2
2
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
1
0
3
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
1
0
1
1
2
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
1
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
1
0
0
2
0
2
1
2
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
1
0
2
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
2
1
0
2
0
0
1
1
0
1
2
0
0
2
0
0
0
2
3
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
7
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
2
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
6
0
0
1
2
0
0
0
0
0
1
0
2
2
0
0
1
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
2
2
0
2
1
0
2
0
1
2
0
0
1
0
0
0
0
0
1
2
1
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
1
1
0
0
7
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
2
0
1
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
2
2
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
3
0
0
0
2
0
0
0
0
6
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
1
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
1
0
0
3
0
0
0
0
3
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
1
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
1
0
0
0
0
2
1
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
2
2
0
0
2
0
2
2
0
0
0
0
0
2
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
3
0
1
0
0
0
0
0
2
0
0
1
0
0
1
0
2
1
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
2
0
0
1
0
0
0
0
1
2
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
1
1
0
0
0
1
0
0
0
1
0
2
0
0
0
0
1
0
0
0
2
2
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
2
1
0
2
0
2
3
0
0
0
0
1
0
2
0
2
0
0
0
1
0
0
1
1
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
4
0
2
0
0
0
0
0
0
6
0
0
1
0
0
0
0
1
0
0
1
2
0
0
0
1
0
0
0
0
2
2
0
2
6
0
2
0
0
2
0
2
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
1
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
1
0
0
2
0
1
0
1
2
0
0
0
0
1
1
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
2
2
0
0
2
2
3
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
3
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
1
2
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
1
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
1
0
0
1
0
0
0
0
0
1
0
1
0
2
0
0
0
2
2
0
0
0
0
1
0
3
0
1
0
2
0
0
0
0
0
2
0
2
0
0
2
0
0
1
0
1
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
2
0
1
0
0
0
0
0
0
1
2
1
0
0
0
1
2
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
1
0
2
1
0
0
0
1
0
0
0
2
0
1
1
0
2
0
1
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
2
1
0
0
0
3
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
2
0
0
0
0
0
0
2
2
1
0
6
0
1
0
0
3
3
0
2
0
0
1
0
1
2
0
0
0
4
0
3
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
1
2
0
1
1
0
0
0
0
1
2
0
1
0
4
1
0
0
0
0
0
2
0
0
1
0
3
0
1
0
1
0
0
0
1
1
1
0
2
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
1
2
0
0
0
1
0
0
0
1
2
0
1
0
0
0
3
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
1
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
3
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
1
0
1
1
0
0
2
0
0
0
0
0
0
0
1
2
0
1
2
0
4
0
0
1
0
1
2
0
0
0
0
1
2
0
0
3
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
4
0
2
0
0
0
1
2
0
0
0
0
3
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
2
0
2
0
0
2
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
1
0
1
3
0
2
1
0
0
0
0
0
5
0
2
1
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
3
2
0
0
0
1
0
0
1
0
0
1
0
1
2
1
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
5
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
1
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
2
3
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
7
0
0
0
1
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
3
0
0
0
0
1
0
0
0
0
0
0
2
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
2
3
0
0
0
0
2
1
0
1
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
2
1
0
0
3
2
1
1
0
0
1
0
3
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
2
2
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
1
2
2
0
4
1
0
0
1
0
0
2
2
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
1
1
1
0
0
0
7
1
2
2
0
0
0
0
0
0
0
0
0
0
0
1
2
2
1
0
0
0
1
0
0
1
2
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
2
0
0
0
3
0
0
0
0
0
2
0
0
0
0
2
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
2
2
0
0
0
2
1
0
0
0
1
0
1
2
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
1
0
0
0
3
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
2
0
0
0
2
0
1
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
3
0
0
0
0
1
2
0
5
2
0
0
0
0
2
0
0
0
1
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
5
0
0
0
2
0
2
0
5
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
1
0
1
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
2
0
0
0
0
0
0
0
0
2
4
2
0
0
3
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
3
0
0
0
2
1
0
1
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
2
0
0
0
2
0
0
1
0
0
1
0
1
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
1
0
0
2
1
0
0
1
1
2
0
3
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
3
1
0
0
1
2
0
0
0
0
1
2
0
0
1
0
3
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
2
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
1
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
3
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
1
0
0
2
0
0
0
0
0
0
2
1
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
2
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
2
1
0
2
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
1
1
4
0
1
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
2
0
1
0
2
0
0
2
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
1
1
1
0
3
1
0
1
0
0
0
0
0
1
0
0
2
1
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
4
1
0
1
1
0
1
0
2
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
2
0
0
0
1
0
2
0
0
0
0
0
1
0
0
2
1
0
2
1
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
2
0
1
0
2
1
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
4
0
4
0
2
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
2
0
3
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
3
1
0
0
2
0
0
0
2
0
0
3
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
2
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
1
0
0
2
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
1
0
0
1
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
1
1
0
0
0
1
0
1
0
0
0
1
0
2
0
0
1
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
2
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
1
0
0
2
0
1
2
0
1
0
0
0
0
1
1
0
0
4
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
1
1
0
1
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
1
2
0
6
0
3
1
0
0
0
0
0
0
3
0
4
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
3
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
3
0
2
0
0
0
0
0
3
0
0
1
1
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
1
0
2
0
0
0
2
1
2
0
0
0
0
6
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
1
1
0
2
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
2
0
0
1
0
2
1
1
1
0
0
0
1
0
1
0
0
2
2
0
10
2
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
2
0
1
0
2
0
2
0
0
0
0
0
0
0
6
1
2
0
0
0
0
0
2
0
2
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
3
2
0
0
0
2
0
0
0
2
2
2
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
2
2
0
0
0
2
0
0
0
0
0
2
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
2
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
2
0
0
0
3
1
0
2
1
0
0
0
0
1
0
0
0
2
0
0
0
4
0
0
1
1
0
0
0
1
0
0
0
0
0
0
3
0
0
0
1
2
1
0
0
1
0
0
0
0
2
1
2
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
2
0
1
0
0
0
1
0
0
0
1
2
2
4
1
2
0
0
1
0
0
0
3
0
1
0
0
0
0
2
2
0
0
0
0
2
1
0
1
0
0
0
0
0
0
3
0
1
2
2
2
0
0
1
0
0
2
0
0
2
0
0
0
1
1
0
1
0
0
2
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
2
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
4
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
2
0
0
1
0
0
3
0
0
1
0
0
0
4
0
0
0
0
2
1
2
0
2
0
2
0
0
0
0
0
2
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
1
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
1
0
0
2
0
1
0
0
2
2
0
0
0
0
1
0
0
2
0
2
1
2
0
0
0
2
0
2
0
0
0
0
1
0
1
0
1
3
1
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
3
0
0
3
0
2
0
2
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
1
3
0
0
0
2
1
0
0
0
0
1
0
0
0
3
1
0
2
1
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
3
0
2
1
0
2
0
0
0
0
0
0
6
0
0
0
0
1
0
0
0
3
4
0
0
0
2
1
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
4
0
2
0
0
0
0
0
2
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
2
2
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
2
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
1
11
1
1
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
3
0
0
1
3
0
2
2
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
5
0
0
0
1
1
0
0
0
2
0
1
2
0
2
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
1
2
0
0
2
6
0
0
1
0
0
0
0
1
1
0
2
0
2
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
2
0
1
0
0
0
1
0
1
0
1
2
0
0
0
1
1
0
1
0
0
1
0
0
2
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
2
0
0
2
0
0
3
1
0
0
2
0
0
1
0
4
0
1
0
2
0
0
2
0
0
0
0
3
0
0
0
0
2
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
1
0
0
1
0
0
0
2
0
0
0
0
0
2
0
2
0
1
1
2
0
2
1
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
2
0
0
1
3
2
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
0
0
0
1
0
0
0
2
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
4
1
2
1
0
1
0
2
1
0
0
0
0
0
3
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
2
2
0
0
3
0
0
1
0
0
1
0
0
0
0
0
1
0
2
1
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
6
0
2
0
0
0
0
0
1
0
1
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
4
0
0
0
1
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
2
0
0
2
0
1
0
0
1
0
1
0
3
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
1
2
0
12
1
3
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
1
0
0
1
2
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
3
0
0
1
1
0
3
0
4
0
2
1
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
1
0
0
1
0
2
0
1
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
2
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
1
2
0
0
0
0
0
1
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
1
0
0
0
2
2
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
2
0
2
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
2
1
1
1
0
1
0
0
0
0
0
2
3
0
0
0
2
0
0
2
1
0
0
1
0
0
2
0
0
1
0
0
0
0
2
1
0
0
8
0
0
1
0
3
2
0
0
0
0
0
1
0
2
0
2
0
0
3
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
4
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
2
1
1
2
0
3
0
0
0
0
0
0
1
2
0
0
3
0
0
1
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
1
0
0
0
1
1
0
0
1
0
3
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
1
2
0
0
0
1
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
3
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
2
1
0
0
0
1
0
0
1
0
1
3
0
0
0
0
0
1
2
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
4
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
1
1
1
1
0
0
0
1
0
0
0
1
1
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
2
4
0
0
2
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
4
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
2
2
1
0
0
3
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
2
1
0
4
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
1
0
2
1
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
3
0
0
0
0
0
0
2
0
0
2
0
2
0
1
0
0
0
0
0
1
1
0
2
2
1
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
3
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
3
0
0
0
2
0
0
0
1
1
1
0
0
0
0
0
2
0
1
0
2
2
0
0
0
0
12
0
0
0
0
0
0
0
2
0
1
0
0
1
0
2
2
0
0
2
0
0
1
1
2
1
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
2
0
0
0
1
0
0
0
2
0
0
0
3
1
0
0
2
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
1
0
0
2
0
0
0
2
0
2
0
0
1
0
2
1
0
0
2
0
1
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
5
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
1
0
1
1
0
1
0
0
0
2
1
0
0
0
0
0
0
1
1
0
0
2
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
1
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
1
2
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
1
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
3
2
0
2
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
5
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
4
0
0
0
1
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
3
1
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
1
0
0
9
0
0
1
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
1
3
0
0
0
3
1
0
0
0
0
1
1
0
0
2
1
0
2
1
0
2
0
0
2
0
2
0
1
0
0
0
1
1
0
1
0
2
0
1
0
1
0
0
0
0
0
1
2
0
2
0
4
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
2
0
0
2
2
0
0
0
0
1
0
0
2
0
2
0
2
2
0
2
4
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
1
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
3
0
2
0
0
0
1
0
0
0
2
2
0
0
0
0
2
1
0
2
0
0
2
0
0
0
2
0
3
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
3
0
0
0
2
0
0
0
0
0
0
1
1
1
1
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
6
0
1
0
2
0
0
0
0
0
2
1
0
1
3
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
2
1
0
1
0
0
2
2
0
0
0
0
0
0
0
2
0
0
1
1
0
1
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
2
3
0
0
1
0
2
2
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
2
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
2
1
0
2
0
2
0
0
1
1
0
0
0
0
3
0
0
0
0
2
0
2
1
0
0
0
0
0
3
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
2
1
0
1
0
1
1
0
0
0
1
0
2
2
0
0
2
0
2
0
1
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
4
0
2
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
2
0
1
0
2
0
0
1
0
1
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
1
0
0
0
0
2
0
0
0
3
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
1
1
0
2
0
0
1
0
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
1
0
0
2
1
0
2
0
1
0
2
0
1
1
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
1
1
0
0
1
0
1
0
0
0
1
0
2
0
2
2
0
1
0
1
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
1
1
1
0
0
0
2
0
1
0
1
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
2
1
1
1
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
3
0
2
0
0
2
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
2
0
2
0
4
1
3
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
2
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
6
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
2
0
0
0
0
2
0
3
0
0
2
0
0
0
0
0
0
0
2
0
0
0
3
0
0
1
0
2
0
1
0
0
1
0
2
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
2
1
0
0
0
0
0
2
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
1
0
1
0
1
0
2
0
2
0
0
0
0
0
1
2
3
0
2
0
1
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
3
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
2
0
1
1
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
1
2
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
4
0
1
0
0
2
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
1
3
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
1
1
0
0
0
3
1
0
1
0
0
0
0
0
2
0
2
0
0
1
0
2
2
2
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
5
0
0
1
0
0
0
0
0
0
0
0
2
1
4
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
1
0
2
0
0
0
0
0
0
0
1
0
1
2
0
3
0
0
0
0
1
0
2
1
0
0
1
0
0
0
3
0
2
0
0
0
0
0
0
0
0
7
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
1
2
2
1
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
2
2
2
0
0
0
3
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
1
0
0
0
0
2
1
0
0
0
0
0
0
2
1
0
1
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
3
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
3
0
1
2
0
0
2
1
0
0
0
0
1
0
0
0
1
0
0
0
1
2
2
0
1
0
3
1
0
0
0
0
0
0
1
2
0
0
0
3
1
0
0
1
0
0
0
0
0
0
0
2
2
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
1
0
3
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
2
2
0
0
1
0
0
1
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
1
0
0
2
0
0
2
0
0
0
0
2
0
1
1
0
1
0
0
1
0
3
0
0
0
0
1
1
0
0
0
0
2
1
0
0
2
0
2
0
1
1
0
0
3
0
0
0
0
2
0
0
2
0
2
0
0
1
0
1
6
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
2
2
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
4
0
0
0
0
0
1
0
1
2
1
0
0
2
0
2
0
1
0
0
0
0
0
0
0
2
2
0
0
0
2
0
2
1
0
0
0
0
2
0
2
0
1
0
1
0
1
2
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
2
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
2
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
1
0
2
0
1
0
1
0
2
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
2
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
1
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
1
2
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
2
0
1
2
0
1
2
0
0
0
0
0
0
3
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
1
3
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
1
0
0
0
1
2
0
0
1
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
3
6
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
3
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
1
4
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
4
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
3
0
0
1
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
2
0
0
1
1
0
0
1
0
0
0
0
2
0
0
3
0
0
0
0
1
0
0
0
0
0
1
0
0
6
0
0
2
0
2
0
0
0
3
2
0
0
1
0
0
0
0
0
2
0
1
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
2
0
0
0
3
0
1
0
3
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
3
1
0
0
0
0
1
0
0
4
0
0
3
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
2
0
1
0
0
0
0
0
3
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
2
0
2
3
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
7
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
2
1
1
0
0
2
2
0
0
0
0
0
0
2
0
2
1
0
0
0
0
2
0
2
0
1
0
0
2
0
5
0
0
0
0
1
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
1
0
2
2
0
2
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
4
0
1
1
0
2
0
2
1
0
0
0
1
0
0
0
0
1
0
1
3
0
0
0
0
0
0
0
0
8
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
1
0
0
4
0
0
1
0
2
1
0
2
0
3
2
0
1
0
0
0
0
0
0
0
0
0
3
0
2
2
0
0
0
1
0
0
0
4
2
0
0
0
0
2
0
2
0
0
0
1
0
0
3
0
2
0
0
3
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
1
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
1
0
0
0
0
0
0
0
1
1
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
2
0
1
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
2
1
0
0
3
1
0
0
0
0
2
5
0
1
0
0
0
0
1
0
0
2
0
1
2
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
2
0
0
0
2
0
0
2
2
2
0
0
0
1
0
0
0
0
0
2
1
0
0
2
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
1
2
0
2
0
2
0
2
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
3
0
0
3
0
3
0
0
4
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
1
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
1
0
0
0
2
0
2
0
0
0
1
0
1
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
2
0
0
1
0
1
0
0
0
0
1
2
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
3
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
1
2
1
0
0
0
0
0
0
0
0
2
2
0
0
3
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
1
0
2
0
0
0
1
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
2
1
1
0
0
2
0
0
2
0
0
0
1
1
0
1
0
5
2
1
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
1
1
2
0
2
0
0
0
0
0
0
0
2
1
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
4
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
1
2
0
1
0
0
1
0
0
1
0
1
0
0
5
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
2
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
1
0
2
0
0
2
1
1
0
0
0
1
1
0
0
0
1
0
0
1
1
0
0
2
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
3
0
2
2
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
2
0
2
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
1
1
0
1
2
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
1
0
0
2
0
0
0
1
0
0
0
1
0
0
2
0
0
2
0
0
0
0
1
0
2
1
1
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
2
0
0
1
0
5
0
3
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
2
0
4
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
3
0
0
0
0
1
2
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
3
0
0
0
1
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
3
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
8
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
2
0
2
0
3
0
0
0
0
0
2
0
2
0
0
0
2
3
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
1
2
0
0
1
1
0
0
1
0
0
0
0
0
0
2
0
0
2
2
1
0
2
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
3
0
0
0
0
0
0
2
0
2
0
2
0
3
0
0
0
0
0
0
2
1
1
0
0
0
0
1
0
3
2
0
2
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
2
0
0
0
2
0
2
2
1
0
2
0
0
0
0
0
1
0
1
0
1
0
0
0
2
1
0
0
0
0
0
0
2
0
2
0
2
0
2
0
0
0
0
0
0
1
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
3
0
2
0
0
0
3
0
0
2
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
1
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
2
1
0
1
0
0
0
1
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
2
1
2
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
7
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
4
0
0
0
3
0
1
0
0
3
2
1
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
1
0
1
0
2
2
0
0
0
0
0
0
0
1
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
2
2
0
2
0
1
0
1
1
0
0
2
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
2
0
2
3
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
2
1
2
0
0
0
2
2
0
0
0
0
0
3
2
0
0
0
0
2
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
6
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
5
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
2
2
0
0
0
0
3
2
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
2
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
1
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
6
2
0
0
0
0
1
0
2
0
0
0
1
2
1
0
1
0
0
0
1
0
1
0
0
0
0
2
0
5
0
0
0
0
0
1
2
0
0
0
0
0
0
1
2
0
0
1
1
3
0
0
0
0
2
0
0
0
0
1
3
0
0
0
0
0
0
1
0
0
0
0
3
0
1
0
1
0
2
0
0
0
0
3
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
1
1
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
3
1
2
0
0
0
0
0
0
0
0
2
2
0
3
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
1
0
0
0
0
1
0
1
0
0
3
0
0
0
0
0
0
0
0
3
1
0
0
0
1
0
1
2
0
0
0
0
0
2
2
0
0
0
0
0
3
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
3
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
1
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
2
0
0
0
0
4
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
1
0
3
0
0
0
0
0
0
0
0
2
0
1
2
0
0
1
0
0
5
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
3
0
2
1
0
0
0
3
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
3
1
1
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
1
0
1
0
0
1
2
0
0
0
0
0
2
1
0
1
0
2
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
2
0
1
0
2
0
0
0
0
2
0
2
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
8
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
3
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
4
0
0
0
0
0
0
1
1
0
2
2
0
0
2
2
0
1
0
2
3
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
2
0
1
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
3
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
4
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
2
1
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
3
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
2
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
1
0
0
0
2
0
1
0
2
2
1
0
0
3
0
1
0
0
4
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
1
0
0
2
0
0
3
0
1
1
0
0
0
0
2
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
6
0
0
1
0
0
0
2
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
1
0
0
0
1
1
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
3
0
0
1
0
1
2
2
0
0
0
2
0
0
0
1
0
1
1
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
2
3
0
0
1
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
1
0
0
1
0
0
0
2
3
0
0
0
2
2
1
0
2
0
0
1
0
1
0
0
0
0
3
2
0
0
2
0
0
0
0
0
0
2
1
0
0
2
0
0
3
0
4
0
1
1
1
2
2
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
2
2
3
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
3
0
0
0
0
1
0
0
0
0
1
2
1
0
0
2
0
2
0
0
2
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
2
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
1
0
0
0
0
1
0
0
0
0
0
1
2
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
4
1
1
0
3
0
1
0
2
2
1
0
0
2
0
0
0
0
0
3
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
3
4
0
0
2
0
0
0
0
0
2
0
2
0
2
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
3
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
2
1
0
0
0
2
1
0
2
1
2
0
0
2
0
0
1
0
0
1
0
0
1
2
0
1
0
0
0
0
0
0
1
0
2
0
1
0
2
0
0
2
0
0
0
0
1
1
0
2
0
0
0
1
1
1
1
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
1
0
0
2
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
1
2
1
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
2
0
0
0
1
0
0
1
1
0
0
0
0
3
1
0
0
1
0
1
3
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
2
0
1
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
5
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
2
1
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
1
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
3
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
1
1
0
0
0
0
1
0
6
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
5
0
3
2
2
0
2
1
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
2
2
1
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
8
2
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
1
0
0
1
0
0
1
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
1
2
0
1
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
2
3
0
0
0
0
0
0
0
0
2
0
1
0
6
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
1
0
2
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
2
0
2
0
0
0
4
0
0
2
0
0
0
2
0
0
1
0
2
0
0
1
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
2
2
0
0
0
2
0
1
0
3
0
0
0
0
1
0
1
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
1
3
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
2
0
2
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
1
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
2
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
2
2
0
0
0
3
0
1
0
0
1
1
0
1
0
1
1
0
0
1
0
0
1
0
0
0
0
0
2
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
2
2
1
2
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
2
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
2
1
2
0
0
0
0
0
2
0
2
1
0
4
0
0
1
0
0
5
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
1
0
2
0
2
0
0
0
1
0
0
3
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
5
0
1
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
1
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
1
0
0
1
0
0
0
1
0
0
11
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
2
2
0
0
0
0
1
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
1
0
0
2
2
0
1
2
0
0
0
0
0
1
0
5
0
1
0
0
0
0
0
0
2
1
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
1
0
4
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
3
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
1
1
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
12
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
3
0
0
2
0
0
0
0
0
0
0
0
0
1
1
1
1
1
0
0
0
0
0
1
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
7
0
0
0
0
0
5
1
0
0
0
0
1
2
0
4
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
3
3
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
2
0
0
1
2
0
0
2
0
1
0
0
4
1
0
0
0
1
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
2
1
1
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
3
0
1
0
2
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
2
1
0
0
0
0
0
2
0
0
0
0
0
0
4
0
1
0
2
0
0
0
0
0
0
0
2
0
1
0
0
1
4
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
3
0
0
0
2
0
0
1
0
1
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
3
2
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
2
1
0
0
0
0
1
0
0
0
0
3
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
1
3
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
2
1
0
2
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
1
0
0
0
0
0
1
0
0
1
0
2
0
0
1
0
7
1
0
1
0
0
0
0
0
2
0
0
0
0
1
3
0
0
0
0
1
0
0
1
0
0
2
0
1
0
2
0
0
0
1
0
1
0
0
1
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
1
0
0
1
0
0
2
2
2
0
0
0
0
1
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
3
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
1
5
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
6
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
2
2
2
1
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
3
0
1
3
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
2
0
1
1
0
0
0
1
2
0
0
0
0
1
0
0
2
0
0
0
0
1
0
2
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
6
2
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
1
1
0
1
0
1
0
2
1
0
0
0
0
1
0
0
0
2
0
1
0
1
2
0
5
0
0
0
0
1
0
0
0
0
1
0
0
2
5
0
0
0
2
0
0
0
5
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
3
4
1
0
0
0
0
0
0
0
1
2
0
0
4
1
0
2
6
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
2
3
1
0
0
0
0
0
2
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
1
2
1
0
0
0
2
0
0
0
2
0
0
0
0
1
0
2
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
3
2
0
0
0
0
0
0
0
2
0
2
0
2
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
1
0
0
2
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
3
0
0
0
0
0
0
0
1
0
0
0
2
5
0
1
0
0
0
2
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
2
0
0
0
0
0
2
0
0
1
1
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
2
0
0
0
0
2
0
1
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
1
2
2
1
0
3
0
2
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
4
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
5
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
2
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
3
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
2
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
1
2
0
3
0
1
0
0
0
0
2
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
2
0
0
2
1
0
0
1
0
0
0
2
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
3
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
1
5
0
0
2
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
3
1
2
1
2
1
0
0
0
2
0
0
2
0
0
0
0
0
0
2
2
0
0
0
2
0
1
1
0
0
1
1
6
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
8
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
2
2
1
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
2
4
0
1
0
2
0
0
0
3
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
3
2
0
2
0
1
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
2
0
0
2
1
0
0
2
0
1
2
0
0
1
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
5
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
5
0
2
0
0
0
2
0
0
0
2
0
2
2
0
2
2
0
0
2
0
0
0
1
0
2
0
0
0
2
0
0
0
0
1
0
1
2
0
0
0
0
3
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
2
1
0
2
0
2
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
1
2
1
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
3
2
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
2
2
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
3
0
1
2
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
4
0
1
0
1
1
0
0
3
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
2
0
2
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
3
1
3
0
0
2
0
0
2
0
2
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
2
1
1
0
0
0
1
0
0
0
0
0
1
1
2
4
1
0
0
0
0
0
2
0
1
0
1
0
2
0
1
0
2
0
0
0
0
0
0
2
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
3
0
0
0
0
2
1
0
0
0
3
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
2
0
0
0
0
0
2
2
1
0
0
0
1
0
2
0
0
0
0
0
0
5
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
2
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
4
2
1
1
0
0
1
2
1
0
0
0
0
0
0
3
0
0
0
0
0
0
2
3
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
2
2
0
1
0
0
0
0
1
0
0
0
1
2
0
2
1
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
2
2
2
1
0
1
0
0
0
1
0
0
1
0
1
0
2
1
0
0
0
0
0
2
1
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
3
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
1
0
2
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
1
1
0
2
1
0
0
1
5
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
1
0
0
1
0
4
0
1
0
0
0
1
0
2
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
2
2
3
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
3
1
0
0
0
0
1
2
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
1
0
1
0
0
0
0
7
1
0
4
0
3
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
3
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
3
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
2
0
0
0
0
1
3
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
1
1
2
0
0
1
0
0
0
2
2
2
1
2
0
0
0
1
0
0
1
0
0
0
0
0
2
0
1
0
0
1
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
1
0
0
0
2
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
2
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
3
0
1
0
0
0
2
2
0
2
0
0
0
0
0
2
0
0
1
0
0
1
3
0
2
0
0
0
4
0
1
0
1
0
0
2
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
1
0
2
0
0
0
0
2
0
0
1
1
0
0
1
1
0
2
0
2
2
1
0
0
2
2
0
0
0
0
0
0
2
2
1
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
3
0
1
0
0
0
2
0
3
0
0
2
1
0
1
0
0
0
0
1
3
0
0
0
0
0
0
0
2
0
2
0
0
0
0
4
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
1
0
0
0
0
0
0
4
0
2
2
0
0
1
0
0
0
0
2
0
0
0
0
0
1
2
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
5
2
0
0
0
0
0
0
3
0
0
0
1
0
0
1
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
1
2
0
0
0
4
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
3
0
0
1
0
0
3
1
1
0
0
0
3
1
0
0
2
0
0
2
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
1
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
2
2
1
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
4
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
1
0
0
1
1
0
2
1
0
0
0
4
0
0
0
0
2
1
3
0
0
0
0
0
0
2
3
2
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
1
0
4
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
1
0
0
0
1
1
2
0
1
0
0
0
3
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
3
1
0
0
2
0
0
0
0
2
0
3
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
1
1
2
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
1
0
0
1
0
0
0
7
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
1
0
0
0
2
1
2
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
1
1
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
2
0
1
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
2
2
0
0
2
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
3
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
2
1
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
2
1
0
0
1
0
0
0
1
0
1
0
2
0
0
2
0
0
1
0
2
0
1
0
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
2
0
0
1
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
2
0
0
0
2
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
1
0
2
2
0
1
3
0
0
0
0
0
1
0
0
2
0
0
2
2
1
0
0
0
0
0
0
0
0
6
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
2
0
0
0
1
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
2
1
0
0
2
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
2
7
0
3
0
0
0
2
0
0
2
0
0
0
2
0
0
3
2
0
0
0
2
0
0
0
2
5
2
0
0
0
1
0
0
0
0
0
1
0
0
0
2
1
0
1
0
2
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
4
1
0
1
1
0
0
0
0
0
1
0
0
3
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
2
2
0
2
0
0
1
0
0
1
0
0
0
2
2
0
2
0
0
5
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
3
0
1
1
0
0
2
0
0
0
2
1
0
0
0
0
1
2
0
0
0
0
0
3
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
1
0
0
2
0
1
0
1
0
1
2
0
0
2
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
3
0
0
1
0
0
0
0
0
2
0
3
5
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
1
0
0
0
0
0
2
1
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
2
2
0
0
0
2
0
0
11
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
2
1
0
0
0
1
2
1
0
0
2
0
2
0
0
1
3
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
1
3
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
6
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
2
1
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
1
2
0
0
0
1
1
1
0
1
0
0
3
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
3
0
0
2
0
0
1
2
1
2
7
0
0
0
0
0
2
0
0
2
0
0
0
3
0
0
2
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
3
1
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
2
2
0
0
1
2
0
1
0
0
1
1
1
0
0
0
3
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
3
0
0
0
1
0
0
6
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
1
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
2
0
0
0
2
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
4
1
2
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
2
4
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
3
0
1
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
2
1
5
0
0
0
1
2
1
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
1
2
0
0
2
0
2
2
0
0
2
1
1
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
2
1
0
0
2
0
0
0
2
0
1
1
0
0
0
0
0
2
1
0
0
0
2
0
2
2
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
2
0
2
0
0
1
0
2
0
0
0
0
0
2
0
2
0
0
0
2
0
1
0
0
1
2
2
1
0
0
0
0
0
3
0
2
3
0
2
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
1
2
0
0
0
0
0
1
0
2
0
2
1
2
0
0
2
0
0
2
3
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
2
1
0
2
1
0
0
0
1
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
2
1
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
2
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
1
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
1
1
0
8
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
3
0
0
2
0
0
0
0
2
2
2
0
0
0
1
2
0
0
0
0
6
1
2
0
0
2
0
2
0
0
0
0
0
3
1
1
0
0
2
2
0
0
0
0
3
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
3
0
2
1
0
1
0
6
1
0
0
0
1
2
0
3
0
1
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
1
0
0
1
1
0
0
0
0
0
0
3
0
0
0
0
1
0
2
0
0
0
0
0
0
3
2
0
0
0
0
0
1
0
2
1
1
0
2
0
2
0
0
0
2
0
0
1
0
0
0
2
0
2
0
1
0
0
0
2
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
2
0
2
0
0
2
0
1
2
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
2
0
1
0
0
2
2
0
0
0
1
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
3
0
3
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
8
0
0
0
1
1
0
3
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
3
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
3
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
1
2
0
1
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
1
2
0
0
0
0
1
0
1
1
0
0
1
0
7
1
0
2
1
1
0
0
0
1
0
0
2
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
1
0
1
0
1
0
0
0
0
2
0
0
0
0
0
4
0
1
2
0
0
1
0
2
0
0
0
2
0
1
0
1
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
1
2
1
0
0
1
0
0
0
0
3
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
2
0
1
2
0
0
0
0
0
0
2
1
0
2
0
0
2
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
2
0
1
0
0
1
0
1
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
1
0
0
2
0
1
0
0
0
0
0
0
2
0
2
1
0
0
2
0
0
0
1
0
0
0
1
0
1
1
0
2
1
0
0
0
2
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
2
0
3
0
1
0
1
0
1
0
0
0
0
0
2
11
1
1
1
0
0
0
1
1
0
0
0
0
2
0
0
0
0
2
12
0
1
2
0
0
2
0
0
0
2
0
0
0
2
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
3
0
0
0
0
0
1
2
0
0
2
1
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
2
0
4
2
0
0
0
1
0
0
0
0
3
0
0
0
2
2
0
0
0
0
2
0
0
2
1
0
2
0
2
0
0
0
3
0
0
1
2
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
1
2
0
0
0
2
0
2
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
2
1
3
0
0
0
0
0
0
1
0
0
1
5
0
0
0
0
0
0
1
0
1
0
1
1
1
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
2
0
0
1
6
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
5
0
2
0
0
5
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
2
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
1
0
1
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
2
1
1
0
1
1
0
0
1
1
1
0
0
1
2
0
1
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
2
0
0
1
0
1
0
0
0
0
0
1
0
1
2
0
0
0
0
1
0
0
2
0
0
0
2
0
0
2
1
0
0
10
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
2
0
1
2
3
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
1
1
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
3
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
1
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
2
2
0
0
1
0
2
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
4
0
1
0
0
3
0
2
1
2
1
2
0
0
0
1
2
0
0
0
0
0
0
2
1
0
0
0
2
2
1
0
0
0
3
0
1
0
0
3
1
0
0
0
0
0
1
0
2
0
0
0
0
0
1
1
1
0
1
2
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
5
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
2
0
1
0
0
2
1
2
0
1
0
0
1
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
3
0
1
3
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
3
0
0
0
2
0
0
0
1
2
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
1
0
2
0
3
2
0
0
0
2
0
1
0
0
1
2
2
0
0
0
2
0
0
0
4
0
0
3
2
0
4
0
2
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
1
1
2
0
0
0
0
0
0
1
0
2
0
0
0
3
0
1
0
0
0
0
2
0
2
2
0
0
0
0
0
2
2
0
0
0
2
0
0
0
1
2
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
2
2
1
0
0
2
0
0
2
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
3
1
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
5
2
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
2
0
0
0
0
5
1
0
2
0
0
0
1
3
0
2
0
0
0
1
0
1
1
1
0
0
0
0
0
0
2
0
1
0
2
0
2
0
4
0
0
2
0
3
0
1
0
0
0
0
1
0
0
3
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
1
0
0
0
0
3
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
2
0
0
0
0
2
6
0
1
0
2
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
2
0
2
1
0
0
0
0
2
4
0
0
1
0
0
0
1
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
7
0
0
0
2
0
0
0
2
0
0
0
3
2
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
2
0
1
0
0
0
0
1
0
1
0
0
0
1
2
0
0
0
0
2
0
0
0
1
0
0
0
1
1
1
2
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
3
2
0
0
0
0
1
0
0
1
0
4
0
0
0
0
2
0
1
0
0
2
0
0
2
0
0
1
2
1
0
0
4
0
0
0
2
0
1
0
2
0
0
1
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
3
2
0
0
4
0
2
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
4
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
3
0
0
2
0
0
0
0
1
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
6
0
2
0
1
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
4
0
2
0
0
0
0
0
0
3
0
1
1
0
1
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
2
0
2
1
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
5
0
0
5
0
0
2
3
0
1
0
0
0
2
0
0
1
0
3
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
2
0
0
3
1
2
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
2
2
0
2
2
0
0
0
2
2
2
0
0
4
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
2
2
0
2
0
2
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
2
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
3
0
1
0
0
0
1
2
0
1
2
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
3
2
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
2
0
2
0
0
4
0
0
2
1
0
3
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
1
2
0
1
0
0
1
2
0
0
1
0
0
0
2
2
0
1
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
3
0
0
0
1
0
0
1
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
4
0
0
3
0
0
1
1
0
0
0
2
1
2
0
0
1
0
0
0
1
1
0
0
0
0
1
2
0
0
2
1
0
0
0
0
1
2
1
0
0
0
1
0
0
0
0
0
2
0
0
0
4
0
0
1
2
1
1
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
2
0
4
0
0
1
0
1
0
0
1
1
0
6
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
3
2
1
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
8
0
1
1
0
1
0
2
0
0
0
0
0
0
0
1
1
0
0
2
2
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
3
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
8
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
2
1
2
0
0
0
0
0
0
0
1
0
6
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
1
2
0
0
1
2
0
2
0
2
0
0
0
0
0
0
0
0
3
0
0
1
2
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
1
0
0
0
2
0
0
4
0
0
0
0
0
2
0
0
2
0
1
1
0
0
0
0
1
0
4
0
0
0
0
0
1
3
0
0
0
2
0
1
2
0
2
2
2
0
1
1
0
2
3
0
1
1
0
1
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
3
1
0
0
1
0
2
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
2
2
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
4
0
0
2
0
0
2
0
1
2
0
1
0
0
2
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
1
2
1
2
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
1
0
3
0
0
0
0
0
0
3
2
0
0
3
2
0
3
0
0
0
2
0
0
2
0
1
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
2
0
3
2
0
0
0
1
0
0
0
3
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
2
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
1
1
2
0
1
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
2
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
3
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
1
0
0
3
1
0
0
2
0
2
0
0
0
0
1
0
0
0
1
0
2
0
0
0
2
0
0
3
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
3
1
0
2
0
0
0
2
2
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
1
1
2
0
1
0
2
0
2
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
3
2
1
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
3
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
2
0
0
2
1
1
2
0
0
0
0
0
0
1
8
0
0
0
8
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
1
1
0
2
2
0
0
0
2
0
0
0
0
0
0
3
2
0
2
1
1
0
3
0
0
0
2
0
0
1
0
0
0
0
0
3
0
0
1
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
2
2
1
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
2
0
1
1
0
0
0
0
0
2
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
1
0
0
4
0
0
2
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
1
0
2
0
2
0
1
0
0
0
1
0
2
0
0
0
1
0
1
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
2
0
0
0
3
0
0
2
2
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
1
2
2
2
1
0
0
2
1
1
1
1
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
2
2
0
0
3
0
2
0
0
2
2
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
1
1
0
0
0
2
0
1
0
0
1
0
2
0
0
0
0
2
0
0
0
1
0
0
2
1
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
6
2
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
3
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
1
2
0
0
0
1
1
0
0
0
2
0
0
0
0
0
2
1
0
1
0
0
1
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
2
0
0
3
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
2
0
0
2
1
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
3
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
3
0
0
1
0
1
2
2
1
0
0
0
0
0
1
1
0
2
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
7
0
0
0
0
2
0
2
0
0
0
1
1
0
0
0
2
0
0
2
2
1
0
0
0
0
0
0
0
0
2
6
2
0
0
0
1
0
0
0
2
0
0
0
5
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
2
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
4
0
0
0
5
1
0
0
2
0
0
2
0
0
0
0
0
0
1
3
0
0
0
0
1
0
0
0
0
0
0
1
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
8
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
1
1
3
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
3
1
2
0
0
1
1
0
0
0
0
0
1
1
0
0
2
2
0
0
1
0
0
0
0
2
2
0
0
0
1
0
1
0
0
0
2
0
2
1
0
2
0
0
2
2
0
1
0
0
1
0
4
0
0
0
0
0
0
0
0
1
2
0
2
0
0
1
2
0
1
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
3
0
1
0
0
0
0
1
0
2
0
1
0
0
2
3
0
0
0
0
3
0
0
2
0
0
0
0
2
0
2
0
2
1
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
3
0
0
0
1
0
0
0
1
0
0
0
3
0
2
0
0
0
0
2
0
0
1
2
0
0
0
2
0
1
0
0
0
1
1
0
0
1
0
0
0
0
2
0
2
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
2
0
0
4
0
0
0
1
0
0
0
0
0
1
1
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
1
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
3
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
4
2
2
2
0
0
0
0
4
0
0
0
0
2
2
0
0
0
0
1
7
0
0
0
2
0
0
0
0
0
0
2
2
1
0
0
0
3
1
1
1
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
2
0
0
0
0
0
0
1
1
0
2
0
1
1
0
0
0
1
0
1
0
1
0
0
1
1
0
0
0
0
9
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
2
2
0
0
0
1
0
2
0
2
2
0
1
0
5
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
2
1
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
2
0
5
0
0
0
0
0
0
0
0
0
0
0
3
2
1
0
2
0
0
0
2
0
0
1
0
1
0
2
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
1
2
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
3
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
2
1
2
1
0
2
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
2
2
0
0
0
1
0
0
0
0
0
0
0
10
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
3
0
0
0
0
2
0
0
1
0
0
1
0
2
0
0
1
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
2
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
1
0
1
4
0
2
0
0
0
0
0
0
0
2
0
0
0
1
2
0
1
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
1
0
2
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
3
2
0
0
0
1
2
0
2
0
0
2
0
2
2
0
0
0
2
0
0
2
0
2
1
0
2
0
1
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
3
0
0
1
1
0
0
3
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
2
1
0
1
0
0
1
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
2
2
0
0
1
0
0
1
0
0
1
1
0
1
2
0
2
0
0
2
0
0
0
4
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
3
1
0
9
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
2
0
2
0
1
2
0
0
0
0
0
0
2
0
1
0
1
0
0
2
0
2
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
3
2
2
2
2
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
2
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
3
0
0
0
2
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
3
2
1
2
0
0
2
0
1
0
0
0
1
1
0
0
0
0
0
1
2
0
1
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
5
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
2
0
1
2
0
0
2
2
0
0
0
0
1
0
2
0
2
0
0
0
3
0
2
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
1
1
0
0
0
2
0
0
2
0
2
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
2
2
0
1
0
0
1
0
1
0
0
0
0
0
0
1
2
0
0
0
0
2
0
5
0
1
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
1
2
0
0
0
0
0
0
4
0
2
2
2
0
0
0
5
2
0
0
0
2
0
2
1
0
0
0
0
0
0
2
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
2
4
0
0
0
0
3
0
0
1
0
0
0
0
1
0
0
1
0
0
2
0
0
1
0
4
0
2
0
0
2
2
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
2
1
4
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
1
1
0
1
0
2
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
2
0
0
0
2
0
0
3
0
0
0
0
1
0
0
1
0
1
2
0
0
0
0
2
0
0
2
0
0
0
0
2
2
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
1
2
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
2
0
0
0
0
0
2
0
2
0
0
2
5
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
5
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
7
0
2
0
1
0
0
0
2
0
2
0
0
1
0
2
4
0
0
2
0
1
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
2
1
1
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
1
0
0
2
0
0
0
2
2
0
0
0
0
2
0
1
0
2
2
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
3
1
1
1
0
0
2
0
2
7
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
3
0
1
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
2
6
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
2
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
2
0
0
1
1
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
1
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
1
2
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
3
5
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
3
2
1
0
0
0
0
2
1
0
0
2
0
1
0
0
0
0
2
0
0
0
0
1
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
2
0
3
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
2
2
0
1
0
0
0
2
1
3
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
1
2
4
0
1
0
0
0
0
2
0
0
9
0
4
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
2
2
2
0
0
1
2
0
0
0
0
0
0
0
3
0
0
3
0
0
0
0
0
1
0
1
0
0
0
1
2
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
1
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
5
0
0
0
0
0
2
0
0
0
0
4
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
2
1
0
0
0
0
2
0
1
1
0
3
2
0
0
1
2
0
0
1
1
0
0
1
0
0
2
2
3
0
0
0
1
0
0
2
4
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
2
0
1
2
0
0
0
1
3
0
0
2
0
1
0
0
0
0
0
0
0
0
0
3
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
5
1
2
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
2
0
0
1
0
0
0
1
1
0
0
2
1
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
2
0
2
1
0
0
1
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
1
2
0
1
2
2
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
2
0
7
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
2
1
0
1
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
7
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
5
0
0
3
0
0
2
2
0
3
2
2
1
0
0
0
0
0
0
2
1
0
2
0
0
1
0
1
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
1
0
0
2
0
9
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
4
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
2
0
2
1
0
0
1
0
0
1
1
0
0
0
2
0
0
0
3
1
0
1
0
0
0
1
0
2
0
3
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
1
0
0
1
2
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
3
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
1
2
1
0
0
3
3
0
0
0
1
0
2
0
0
0
0
2
0
2
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
3
3
0
5
0
0
2
0
0
1
1
0
0
0
2
0
0
0
1
0
1
1
0
0
0
0
2
0
0
1
2
0
2
0
2
0
5
0
0
1
0
0
0
1
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
2
1
0
0
0
1
0
2
0
0
0
0
0
0
3
0
0
0
0
1
2
0
0
2
0
0
1
1
0
0
0
0
2
0
0
0
0
3
0
0
0
0
1
1
0
0
0
0
0
2
0
0
2
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
4
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
2
1
2
0
1
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
2
1
0
0
0
0
0
1
0
1
2
2
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
2
1
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
9
2
0
0
1
0
0
2
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
2
1
0
5
0
2
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
3
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
3
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
7
1
0
0
2
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
5
0
0
2
0
7
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
2
0
2
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
2
0
3
0
1
0
0
0
1
2
2
0
0
0
0
0
5
0
0
0
0
2
0
0
0
4
0
1
0
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
4
0
3
0
0
2
0
0
1
0
0
0
0
0
2
0
1
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
2
0
1
0
2
0
2
0
0
0
0
0
0
1
2
1
0
0
0
0
1
0
2
2
0
1
0
0
0
1
0
4
3
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
1
0
2
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
1
2
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
1
2
0
0
0
0
1
0
0
1
2
0
0
0
0
1
0
1
2
0
0
0
0
1
0
0
2
0
2
0
3
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
1
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
2
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
1
1
0
1
0
2
0
0
0
0
0
0
1
3
0
2
0
0
1
0
0
3
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
2
0
1
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
10
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
2
4
0
0
0
1
0
0
2
1
0
0
0
3
0
1
0
0
0
2
1
2
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
3
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
3
0
0
1
0
6
0
0
2
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
2
0
2
0
2
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
2
1
1
0
0
0
0
0
0
1
0
0
0
0
1
2
0
3
1
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
3
0
1
0
0
0
0
0
0
2
0
3
0
0
0
0
1
0
0
0
0
0
0
3
2
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
2
5
3
0
0
0
0
2
0
0
1
0
3
2
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
3
1
1
0
0
0
2
1
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
1
0
0
0
1
0
1
0
3
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
3
0
3
0
0
0
0
0
2
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
4
0
0
0
0
0
1
0
3
0
0
3
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
3
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
2
0
0
1
2
0
0
1
0
1
0
1
1
2
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
2
0
1
0
0
1
0
0
0
2
1
0
0
0
0
2
0
0
0
2
0
2
0
0
0
1
1
0
0
0
0
0
2
0
0
1
6
0
0
0
0
0
1
0
0
0
0
2
0
2
2
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
2
0
0
0
2
0
0
0
0
0
2
0
1
0
0
2
0
0
2
0
0
0
0
0
0
3
0
3
0
0
0
4
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
2
2
0
3
0
3
1
1
0
0
0
2
0
0
0
1
1
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
2
1
2
0
0
2
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
2
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
5
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
9
0
0
2
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
1
0
6
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
2
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
3
0
0
0
2
0
1
0
3
2
0
0
1
1
0
0
0
0
2
2
0
0
1
0
0
2
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
3
0
0
0
3
0
0
0
1
0
1
0
1
0
1
1
0
0
2
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
1
0
1
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
2
0
2
0
0
1
0
1
0
2
1
0
0
0
0
4
0
0
0
0
0
0
1
4
0
0
0
0
0
0
1
1
0
0
0
2
0
1
1
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
3
0
0
0
0
2
0
2
2
0
1
0
2
0
2
0
0
0
0
0
13
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
2
0
1
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
3
0
0
0
0
0
2
0
0
0
0
0
0
1
1
1
2
1
0
0
0
2
2
0
0
1
2
2
0
0
0
0
0
1
0
2
2
0
0
0
1
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
1
1
0
2
1
0
0
0
0
0
1
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
1
2
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
6
0
0
0
0
0
0
0
0
1
2
1
0
0
1
0
0
2
8
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
1
0
1
0
0
1
0
3
0
2
0
0
2
0
0
0
0
2
2
0
0
0
0
3
0
0
0
2
0
0
0
1
0
0
0
0
0
1
1
0
0
0
2
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
2
1
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
1
1
1
0
1
0
1
0
0
6
0
0
0
0
0
0
0
0
0
0
1
0
3
2
2
0
2
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
1
0
1
2
2
3
0
0
0
0
2
1
0
0
0
0
0
0
1
2
0
2
0
0
0
0
3
0
0
0
1
0
0
2
0
2
1
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
5
0
0
0
0
0
2
2
0
0
0
2
0
0
0
2
2
0
0
1
1
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
2
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
2
0
0
1
0
0
2
0
0
0
0
1
0
0
1
0
2
0
0
2
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
2
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
4
2
0
0
0
0
0
0
0
0
3
2
2
2
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
3
0
1
0
0
0
0
2
0
0
1
0
1
0
0
0
0
1
0
0
2
1
1
0
1
0
0
2
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
3
0
0
1
1
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
5
2
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
1
2
0
0
0
0
2
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
2
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
1
3
1
0
1
0
0
0
0
1
0
0
0
0
0
0
2
3
3
1
0
0
0
1
0
0
2
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
1
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
3
0
1
0
0
0
2
1
0
2
0
0
2
1
0
0
1
1
0
0
0
2
0
0
0
2
2
0
2
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
5
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
1
2
0
0
0
0
5
0
0
1
1
0
0
2
0
0
0
0
1
0
2
0
1
0
0
1
2
0
0
2
0
0
0
0
0
2
2
0
0
1
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
1
0
0
1
0
1
0
0
1
0
0
0
0
1
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
3
0
0
0
2
0
6
2
0
1
2
0
2
0
1
0
0
0
0
0
4
0
0
0
0
0
1
1
0
2
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
2
2
0
0
0
1
2
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
1
3
0
0
2
0
0
0
2
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
1
1
0
0
1
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
1
0
0
1
0
2
0
0
2
0
0
0
0
0
0
1
1
2
0
0
0
0
2
0
0
0
0
3
0
2
0
1
0
0
1
2
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
3
0
1
1
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
1
0
0
0
2
0
0
0
0
6
0
0
0
1
0
0
1
0
0
0
2
0
0
2
0
0
0
1
2
0
0
3
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
3
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
2
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
5
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
2
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
1
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
4
0
0
0
2
1
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
8
0
2
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
1
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
1
2
0
1
0
0
0
0
0
4
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
1
4
0
0
0
0
2
0
3
0
0
0
0
0
2
1
0
1
1
0
0
1
0
2
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
2
0
1
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
1
0
3
2
0
0
1
0
0
2
0
0
2
0
0
0
2
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
1
0
0
0
0
2
0
0
0
0
0
1
0
0
3
1
1
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
5
1
2
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
3
0
0
0
0
1
1
1
1
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
3
0
0
0
2
1
0
1
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
2
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
3
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
5
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
5
0
0
0
0
2
0
2
0
0
0
0
0
2
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
4
0
0
0
0
6
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
1
0
0
2
0
3
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
2
2
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
1
1
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
3
0
1
0
0
0
0
0
1
0
0
0
2
0
2
1
1
1
1
0
0
0
0
2
0
0
1
0
1
1
0
1
0
0
0
2
0
0
2
0
0
0
3
0
0
0
0
1
0
0
1
2
0
0
0
0
0
1
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
1
0
2
0
1
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
5
0
2
0
1
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
2
8
0
2
2
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
7
0
0
0
2
0
2
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
2
1
0
0
0
1
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
1
0
2
0
0
0
1
0
1
0
1
11
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
7
0
0
2
0
0
3
0
0
1
0
0
0
0
0
1
0
1
8
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
3
5
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
3
0
0
0
0
0
2
2
1
0
0
2
0
0
0
0
0
2
2
1
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
1
0
2
0
0
0
1
0
1
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
1
1
0
1
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
2
0
0
2
0
0
0
0
0
2
0
0
1
0
1
0
0
0
2
0
0
0
2
0
3
0
0
0
0
0
1
0
2
0
0
0
2
2
0
0
2
0
0
0
2
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
1
2
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
3
0
0
0
0
2
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
2
3
0
1
0
0
0
0
0
3
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
1
0
0
0
2
1
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
2
0
0
2
0
0
0
0
0
1
1
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
3
0
1
0
7
0
0
0
0
0
1
0
0
0
2
0
1
1
0
1
0
0
1
12
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
3
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
2
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
1
0
0
0
0
6
0
0
0
0
2
0
0
0
1
0
0
1
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
2
0
0
0
1
0
0
2
0
0
1
2
0
2
0
0
0
1
1
2
0
0
1
0
1
0
0
2
0
0
0
2
2
0
0
0
1
0
2
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
1
0
0
0
3
1
0
0
0
0
0
0
1
1
0
2
1
0
0
0
0
1
0
0
0
0
2
0
2
1
0
1
0
1
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
1
1
0
0
0
0
0
0
2
0
1
1
0
1
2
0
2
0
0
0
2
0
0
0
0
0
0
0
3
0
2
0
2
0
1
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
1
2
2
0
2
0
0
2
0
2
0
0
0
2
0
0
0
0
1
1
2
0
0
0
0
0
1
1
0
0
2
0
1
0
2
0
0
0
0
2
2
0
0
0
1
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
1
2
0
2
0
1
2
1
0
1
1
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
1
0
0
0
3
2
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
4
2
0
0
0
0
1
0
1
0
0
2
1
0
0
0
1
2
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
2
3
0
0
0
0
2
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
1
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
2
2
2
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
4
0
0
4
0
1
0
0
2
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
3
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
3
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
4
0
1
0
1
0
0
2
0
2
4
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
1
2
2
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
1
0
0
2
0
2
0
0
3
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
1
1
2
0
0
0
0
0
0
0
0
2
0
0
5
0
2
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
1
0
2
1
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
1
1
2
0
2
0
0
0
0
2
0
2
0
0
1
1
0
1
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
4
1
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
26
0
0
0
0
1
1
0
0
0
3
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
2
0
0
0
1
1
0
0
2
0
1
0
0
0
1
0
0
1
0
3
0
0
0
0
1
0
0
5
0
2
0
2
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
1
0
0
0
1
0
2
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
3
0
0
0
0
0
0
2
1
0
0
1
0
1
1
0
0
0
0
0
1
1
1
0
0
0
2
0
0
1
0
0
0
0
1
2
0
0
0
2
0
2
1
0
0
2
0
0
0
2
2
0
0
0
0
1
0
0
2
0
2
0
2
0
0
0
0
1
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
2
3
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
1
0
0
0
1
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
1
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
1
1
0
1
0
0
0
3
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
2
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
0
1
0
0
0
0
0
3
2
1
0
0
0
0
2
0
1
1
0
1
2
1
0
0
1
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
3
0
0
0
0
1
0
0
2
2
0
0
0
1
0
1
0
0
0
1
0
2
2
2
0
2
0
4
0
2
0
2
2
1
0
0
0
0
1
1
0
0
0
3
0
0
0
4
0
0
1
1
1
0
0
0
0
1
0
0
2
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
2
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
1
2
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
2
2
2
0
0
0
2
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
3
2
0
3
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
3
0
0
0
0
0
3
1
0
0
1
0
1
0
0
0
0
1
0
0
0
2
0
1
0
0
2
4
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
2
1
0
0
0
1
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
2
2
0
0
2
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
6
0
0
1
2
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
2
0
0
2
0
0
0
0
1
2
0
1
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
1
1
0
0
1
0
2
0
2
0
1
0
0
0
0
0
0
2
0
0
5
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
1
0
2
0
0
1
0
0
1
3
4
1
0
0
0
0
3
0
0
0
1
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
2
0
1
2
2
2
1
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
5
0
0
3
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
12
4
0
1
1
0
0
3
0
0
1
0
1
1
0
2
0
2
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
2
1
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
2
2
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
1
1
0
0
0
1
0
3
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
1
1
2
1
0
0
0
1
1
0
2
0
0
0
0
0
0
0
1
1
2
0
0
1
0
2
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
2
0
2
1
0
0
2
2
0
0
1
0
1
0
0
0
0
1
0
0
2
2
0
1
0
1
0
0
0
0
0
0
2
0
2
0
0
0
5
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
1
1
0
0
2
1
3
0
0
0
0
3
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
1
0
2
2
0
0
0
0
0
1
0
3
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
1
2
1
0
0
1
0
0
0
0
0
3
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
2
1
1
2
1
1
0
1
0
0
1
0
0
2
0
0
3
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
10
1
0
1
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
5
0
0
0
0
1
0
2
1
1
3
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
1
1
3
2
0
2
0
0
0
0
0
0
2
0
4
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
3
1
2
0
1
0
0
0
0
3
0
0
0
0
1
0
0
0
2
0
0
0
2
4
0
0
0
0
2
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
2
1
1
0
0
0
0
2
2
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
2
0
0
1
0
0
1
1
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
5
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
2
0
0
0
0
1
0
0
2
2
0
2
0
2
0
1
1
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
2
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
3
0
1
0
0
0
1
0
0
0
0
1
2
1
2
0
1
2
0
0
0
1
0
0
1
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
3
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
15
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
2
0
0
0
1
0
1
0
0
1
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
6
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
1
1
0
0
3
0
0
0
0
2
0
2
0
1
0
0
0
2
5
0
0
0
2
3
2
0
0
0
1
1
2
1
0
1
2
0
0
0
0
2
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
2
4
1
2
0
0
0
2
2
2
0
0
0
1
0
2
2
0
0
0
0
0
3
0
0
0
2
0
4
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
2
10
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
1
0
0
2
0
1
0
1
1
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
1
0
2
0
3
0
2
0
0
2
0
0
2
0
1
0
0
2
2
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
3
0
0
0
3
2
0
1
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
1
1
2
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
2
2
2
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
2
2
1
0
2
0
2
0
0
0
2
1
0
2
0
0
1
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
1
0
2
0
0
2
1
0
3
0
1
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
1
0
0
0
1
0
0
0
1
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
1
0
0
2
0
1
1
0
0
2
5
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
2
0
1
0
0
0
1
2
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
2
2
2
0
2
0
0
0
0
3
0
2
0
0
1
2
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
2
0
2
2
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
3
1
0
0
1
1
2
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
2
0
2
0
1
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
1
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
3
0
1
0
0
0
2
0
2
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
3
1
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
2
0
2
1
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
1
0
0
0
1
2
0
0
0
2
2
1
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
1
0
2
2
0
0
0
0
2
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
1
4
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
3
2
0
0
0
0
0
0
0
0
2
2
0
0
0
4
0
0
0
0
2
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
3
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
4
0
0
1
0
5
0
1
0
0
2
0
0
1
0
0
2
0
0
2
0
1
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
2
0
1
1
0
0
0
1
0
1
0
1
3
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
3
0
3
0
1
0
0
0
1
0
2
2
0
0
1
0
0
2
0
0
0
0
2
0
1
0
1
1
0
2
2
0
0
2
2
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
2
0
1
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
4
2
1
0
1
0
0
1
0
0
0
0
2
2
0
2
0
0
0
4
2
2
2
3
0
0
2
0
0
0
0
0
0
3
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
3
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
1
3
0
0
0
2
1
0
0
0
2
0
2
0
0
0
0
2
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
1
2
1
0
0
0
1
2
3
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
2
0
0
0
0
3
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
2
2
0
0
2
1
1
0
5
2
0
0
0
0
0
2
4
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
3
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
3
0
1
0
2
0
2
0
0
0
0
2
0
0
0
2
2
0
0
0
1
1
0
0
1
1
0
0
1
0
1
0
0
1
2
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
1
0
2
0
1
1
0
0
0
2
1
1
0
0
0
0
0
0
1
0
0
0
0
2
2
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
5
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
3
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
1
2
0
1
0
0
2
1
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
1
1
2
0
0
0
2
0
0
0
2
0
0
0
2
0
1
0
2
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
1
0
0
2
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
1
1
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
3
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
5
2
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
2
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
2
2
0
0
1
0
1
2
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
1
1
0
1
0
0
0
1
0
1
0
0
3
0
1
2
1
1
0
0
1
0
2
0
0
1
2
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
1
2
0
4
0
0
0
0
0
0
0
0
0
0
0
2
2
3
0
0
0
0
0
0
0
1
1
1
2
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
5
0
0
2
0
1
2
0
0
0
1
0
2
0
0
1
0
0
0
0
1
0
0
0
1
0
4
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
1
1
0
1
3
2
0
0
0
1
0
0
0
0
2
2
6
0
0
5
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
1
0
0
5
1
0
0
2
0
2
1
2
2
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
2
4
0
0
3
0
0
0
0
1
0
0
0
1
1
0
0
0
0
4
0
0
1
0
0
0
0
0
1
2
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
2
1
0
0
3
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
1
0
3
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
2
4
2
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
2
2
0
0
1
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
1
1
2
0
1
2
2
0
0
0
0
0
0
1
0
4
0
0
1
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
1
1
0
0
0
2
0
2
2
0
0
0
0
1
4
0
0
1
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
2
1
0
0
1
0
0
0
0
2
0
0
1
0
4
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
1
0
2
0
0
1
0
0
0
0
0
0
0
2
0
2
1
0
0
1
2
0
2
0
0
0
0
2
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
18
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
2
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
1
0
0
4
0
0
0
2
0
0
0
1
1
0
2
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
1
2
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
2
0
0
0
1
2
2
2
0
0
0
0
1
0
0
0
0
0
1
1
0
0
2
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
2
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
2
2
0
0
0
2
0
0
3
0
0
1
1
2
0
1
0
0
0
1
2
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
4
2
0
2
1
2
0
0
0
1
3
2
2
0
2
2
0
0
2
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
2
0
0
2
0
0
2
1
0
0
1
1
3
3
0
0
0
0
0
0
0
0
2
2
1
0
0
0
1
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
1
1
0
0
0
0
0
2
1
1
0
0
1
0
0
0
0
4
0
0
1
0
0
0
0
2
0
1
0
1
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
1
2
0
1
5
0
1
0
1
2
1
0
0
0
0
0
0
1
1
0
3
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
2
0
0
0
0
5
0
0
0
0
0
0
0
8
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
1
3
4
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
1
0
0
0
1
2
0
0
0
0
1
0
0
0
0
5
2
2
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
2
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
3
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
3
1
1
0
0
0
0
0
0
0
0
0
0
1
0
2
2
2
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
1
2
0
1
0
1
0
0
3
0
0
0
1
2
1
1
2
0
1
0
2
0
0
2
0
0
0
0
0
1
0
4
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
3
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
2
0
0
0
0
3
1
1
0
0
0
0
1
0
0
4
0
0
2
1
0
0
0
2
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
1
0
3
2
1
0
0
2
0
0
1
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
4
0
0
0
2
2
0
0
0
0
0
1
2
0
2
2
2
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
3
2
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
2
2
0
0
2
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
4
0
3
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
4
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
3
0
0
1
0
0
4
0
0
1
1
0
0
1
0
0
0
0
0
2
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
2
1
0
0
0
0
2
0
4
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
1
0
2
2
0
0
0
2
0
2
0
0
0
0
2
2
0
0
1
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
2
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
1
1
0
0
2
2
0
0
0
0
1
1
0
0
0
1
0
2
0
1
0
0
0
0
0
2
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
1
0
0
0
0
2
0
2
0
0
0
0
4
0
0
1
2
2
0
0
0
0
0
2
0
0
0
1
1
1
0
0
0
2
0
1
0
1
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
1
0
1
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
2
0
0
3
0
0
3
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
2
2
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
2
0
0
0
2
1
0
2
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
3
0
0
0
0
1
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
6
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
7
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
2
1
6
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
2
1
0
0
0
8
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
1
0
0
0
0
0
2
3
0
0
2
0
1
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
1
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
1
1
0
1
2
1
0
1
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
2
0
2
0
0
0
1
0
1
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
2
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
3
0
0
0
2
1
0
2
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
1
2
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
1
0
0
0
1
3
2
1
0
0
1
0
0
1
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
2
0
1
1
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
4
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
4
0
0
1
1
0
1
0
4
1
0
0
2
1
0
2
1
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
5
0
0
2
0
0
0
1
0
2
0
0
1
1
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
2
2
1
0
0
0
2
0
2
2
0
0
0
0
0
0
0
2
0
2
0
1
2
2
0
0
0
0
2
0
2
0
0
0
1
1
1
2
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
2
0
0
2
0
2
0
0
12
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
3
0
1
3
2
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
2
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
4
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
1
3
0
2
1
1
0
0
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
1
1
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
3
1
0
0
2
1
0
0
2
1
0
0
2
2
1
0
0
0
0
1
0
2
0
0
0
2
4
1
1
0
2
0
0
0
2
0
2
0
0
0
0
2
0
0
9
0
0
0
0
0
1
0
1
0
0
2
0
0
1
0
2
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
3
0
1
0
0
1
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
1
0
0
0
0
0
0
1
2
4
0
0
0
0
0
0
2
0
0
0
0
0
1
0
3
0
0
1
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
1
2
2
0
0
0
3
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
1
0
1
2
0
1
1
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
2
0
1
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
3
0
0
2
0
0
2
0
0
5
0
0
0
2
0
0
0
0
0
2
0
3
0
0
0
0
0
2
0
2
2
2
2
1
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
1
2
1
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
3
0
2
0
3
2
0
0
2
0
0
0
0
0
0
0
0
1
0
2
2
3
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
2
0
0
1
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
3
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
1
2
2
1
0
0
0
0
1
0
1
0
0
0
1
0
4
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
2
2
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
3
2
2
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
2
1
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
1
2
2
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
3
0
1
0
0
0
3
0
1
0
0
0
2
0
0
0
0
5
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
1
2
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
3
1
0
0
0
1
2
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
2
0
1
0
0
0
0
2
3
0
2
0
1
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
2
2
0
0
1
0
0
1
0
0
0
0
0
3
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
3
0
0
2
0
1
0
0
2
1
2
0
0
0
1
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
2
2
2
0
0
2
1
2
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
3
1
0
7
0
1
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
1
0
0
0
4
0
2
2
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
4
1
0
4
0
0
0
0
0
0
0
0
0
0
2
2
1
2
0
3
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
2
0
0
0
0
0
2
1
0
2
2
0
0
2
0
0
0
0
0
0
0
0
1
3
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
1
2
4
0
1
0
2
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
5
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
3
0
0
0
0
1
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
1
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
2
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
4
1
2
0
0
0
0
3
0
2
0
0
1
0
0
1
2
0
0
0
1
0
1
0
0
1
3
0
0
0
0
1
0
0
0
1
1
2
0
0
1
1
1
1
1
0
1
0
5
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
2
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
1
3
1
0
2
2
0
1
0
0
1
0
1
0
1
1
0
1
0
0
0
0
4
0
0
0
0
0
0
2
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
3
3
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
1
0
0
0
3
1
0
2
0
1
0
0
0
1
0
0
0
0
3
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
1
0
1
2
0
1
0
0
0
0
3
0
2
1
1
2
0
0
4
0
1
0
0
0
2
0
0
0
2
2
2
2
2
0
2
0
0
0
0
2
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
2
3
0
1
0
0
0
0
0
1
0
0
0
0
2
0
1
0
2
1
2
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
3
1
0
0
0
0
0
1
2
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
3
2
0
1
0
0
0
1
0
2
4
2
0
0
0
3
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
2
0
0
2
1
2
2
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
5
2
0
2
0
0
0
0
3
0
1
0
3
3
0
0
4
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
4
0
0
0
1
2
0
0
0
0
0
0
1
0
1
2
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
1
0
1
0
0
0
0
1
0
0
6
2
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
2
1
0
2
0
0
1
0
0
0
0
0
0
2
0
0
1
1
0
1
0
0
0
0
0
2
0
0
0
2
1
0
1
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
5
2
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
2
0
0
0
3
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
1
7
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
1
0
0
2
0
0
0
2
0
0
0
1
2
0
1
1
0
0
0
0
0
1
1
0
0
2
0
0
0
0
1
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
1
0
0
0
2
0
0
2
1
0
0
1
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
2
0
2
0
0
0
0
0
0
1
0
0
0
1
5
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
1
2
2
0
0
2
0
0
2
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
3
2
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
5
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
1
2
3
2
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
2
0
0
0
0
1
0
1
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
2
1
0
0
2
0
0
0
0
0
0
0
4
2
0
4
0
1
5
0
0
1
0
0
0
3
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
7
0
0
2
0
0
0
2
4
0
0
0
3
2
0
0
0
0
0
6
0
2
1
2
0
2
2
0
6
1
0
0
2
1
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
1
1
0
2
0
1
0
0
0
2
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
2
0
0
2
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
2
0
1
0
1
0
0
2
2
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
2
5
0
2
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
1
2
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
1
0
2
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
7
1
0
3
2
0
0
3
0
1
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
2
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
5
1
0
0
0
1
1
0
1
0
3
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
3
2
0
1
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
6
0
0
0
0
0
0
1
1
2
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
1
0
1
0
0
2
1
0
0
0
2
2
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
2
0
0
1
0
2
0
0
0
0
1
0
0
1
0
0
0
2
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
1
0
0
1
0
0
2
0
1
0
0
2
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
2
0
2
0
0
1
2
1
0
0
0
0
0
2
0
0
0
0
0
2
0
1
4
0
0
0
1
0
0
0
3
2
1
0
1
0
0
0
3
2
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
1
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
9
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
2
0
2
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
4
0
0
1
0
0
0
0
1
2
0
0
0
0
0
1
1
2
0
0
0
2
0
1
0
1
0
2
0
2
0
0
0
1
0
2
0
0
2
1
0
0
3
0
0
5
1
2
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
1
0
2
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
2
1
0
0
0
0
2
0
1
0
1
0
0
0
1
1
1
0
2
0
0
0
0
2
0
0
2
0
0
1
1
1
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
2
0
3
0
0
0
0
0
1
0
2
0
0
0
2
0
2
2
0
0
0
0
0
1
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
2
2
0
0
2
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
2
3
1
0
0
1
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
3
1
0
1
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
2
0
0
2
2
0
0
3
0
0
0
0
0
0
0
0
1
0
0
3
1
0
4
0
0
0
2
0
1
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
1
0
0
0
0
2
1
1
2
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
2
1
2
0
0
1
0
0
0
0
0
2
0
2
0
2
0
0
2
1
0
2
0
0
2
0
0
0
0
2
2
3
1
0
0
0
1
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
5
3
1
0
0
0
0
0
0
0
0
0
0
2
2
1
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
2
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
6
0
0
2
0
0
0
1
0
0
2
7
1
1
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
1
2
0
0
1
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
1
1
1
0
0
3
0
0
0
0
0
2
0
1
0
0
0
0
1
1
0
0
3
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
2
0
0
0
0
0
2
0
0
1
0
0
2
0
2
0
0
0
0
1
0
2
0
0
0
1
3
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
2
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
2
1
0
0
0
1
0
0
0
2
2
0
0
1
0
0
0
0
3
0
0
2
0
0
0
0
0
1
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
1
0
5
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
1
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
1
0
2
2
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
2
1
4
1
3
0
0
2
0
1
0
1
1
1
3
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
1
2
1
2
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
3
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
11
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
1
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
2
0
0
0
0
0
0
2
0
0
1
0
2
0
0
2
2
0
0
2
0
0
2
1
2
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
1
2
1
0
2
0
0
1
1
0
0
0
0
0
1
1
1
2
0
0
0
0
0
0
3
0
1
0
0
0
0
2
2
0
1
2
0
0
1
0
0
0
0
2
0
2
0
3
0
1
2
1
0
0
0
0
0
0
0
0
6
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
3
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
1
4
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
5
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
4
0
1
2
0
0
0
3
2
2
0
0
0
2
0
0
2
1
0
0
0
0
1
0
4
0
0
1
1
0
0
1
2
0
3
0
2
1
1
0
0
0
1
0
1
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
5
1
0
1
0
0
0
0
0
3
0
1
0
2
0
0
0
0
1
1
0
0
0
0
2
2
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
1
1
5
0
0
0
2
0
1
0
0
0
0
0
2
1
2
0
1
0
0
1
0
0
3
2
0
0
1
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
1
2
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
2
1
0
1
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
2
5
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
1
2
0
0
0
2
0
1
1
1
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
2
0
2
0
1
2
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
2
0
0
2
1
0
0
0
0
0
2
0
3
0
0
0
1
0
1
0
2
0
0
1
0
0
0
0
0
2
0
0
0
7
5
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
2
1
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
1
1
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
2
1
0
0
0
0
6
0
0
1
0
14
0
0
0
1
0
0
0
0
1
1
0
0
1
2
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
1
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
1
0
0
0
1
0
1
2
2
1
1
1
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
2
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
3
0
1
2
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
2
5
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
2
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
2
2
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
2
1
1
0
0
2
2
0
1
0
2
2
0
0
0
1
0
1
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
3
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
4
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
1
1
0
3
0
0
0
0
0
0
0
1
1
0
0
0
3
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
4
0
0
0
2
0
0
0
0
1
0
1
0
3
0
0
0
0
0
0
0
2
0
0
0
3
0
1
0
0
1
0
0
2
0
2
0
3
0
0
0
0
0
2
2
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
2
2
0
0
0
1
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
4
0
2
0
0
0
0
0
2
0
0
2
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
1
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
3
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
3
2
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
2
0
0
2
0
1
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
1
0
0
2
2
0
0
0
0
1
0
1
0
0
0
0
0
0
2
2
0
0
0
2
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
2
0
4
0
1
1
0
2
0
2
0
1
0
1
0
0
2
0
0
0
1
1
0
0
0
1
2
1
0
0
0
0
0
0
1
0
2
0
0
2
2
1
0
0
1
0
0
0
0
1
0
0
1
2
0
1
0
2
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
3
0
1
0
0
3
1
0
0
2
0
0
1
0
0
1
0
1
1
0
0
2
1
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
1
9
0
0
0
0
2
0
1
1
0
0
2
0
0
1
0
4
5
0
1
0
0
1
1
1
0
0
0
1
0
0
0
0
0
2
1
0
2
0
0
1
2
1
0
2
0
0
0
1
1
0
2
0
0
0
1
1
0
0
0
2
0
0
0
1
2
2
0
1
0
0
0
0
0
1
0
0
2
2
0
2
0
1
0
2
0
0
0
0
2
0
0
0
1
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
3
2
0
2
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
1
0
1
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
6
0
0
0
0
1
0
1
1
0
0
0
0
3
0
2
2
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
2
0
0
0
0
1
0
0
2
0
1
2
0
0
2
0
0
0
1
0
0
1
0
0
0
0
3
0
0
0
0
0
1
0
0
1
0
0
0
2
1
0
0
2
1
0
0
2
0
0
3
0
0
0
1
0
0
0
3
0
1
2
0
0
0
0
0
0
0
2
1
0
0
0
0
1
2
0
0
3
0
0
1
0
2
0
0
0
3
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
3
0
2
0
0
0
0
0
0
0
0
1
2
0
2
2
1
0
0
1
1
0
1
1
0
2
1
0
2
0
1
0
1
0
1
1
0
1
2
0
2
0
0
0
0
2
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
1
2
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
2
1
1
0
0
2
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
1
0
0
0
4
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
2
2
0
0
0
0
1
0
0
0
4
0
1
0
3
0
0
0
0
2
3
3
0
2
0
0
0
0
1
2
0
0
0
0
2
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
4
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
2
0
2
0
1
0
2
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
4
0
0
2
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
2
2
0
0
2
0
0
0
5
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
2
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
1
0
6
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
2
0
0
1
4
0
2
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
2
1
0
0
0
0
2
0
0
2
1
0
1
0
2
0
0
0
2
0
1
0
0
0
3
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
3
0
2
0
2
1
2
0
0
1
2
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
1
2
0
1
1
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
2
1
0
3
0
0
2
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
5
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
1
4
2
0
0
0
0
0
0
3
0
0
0
0
0
0
3
0
2
1
6
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
2
0
2
0
2
0
0
1
0
5
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
2
0
1
0
1
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
4
0
0
1
0
0
0
0
0
0
2
0
0
1
3
0
0
1
0
0
0
0
0
2
0
3
0
1
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
1
0
1
0
0
2
1
0
0
1
0
0
3
0
1
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
1
1
0
0
1
0
0
0
3
1
2
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
1
2
0
0
2
1
0
0
0
0
0
2
1
0
2
0
0
0
1
1
1
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
1
0
1
1
0
0
2
1
2
1
2
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
3
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
5
0
0
0
2
0
0
1
2
2
0
3
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
3
2
0
0
0
0
0
3
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
3
0
0
2
0
0
4
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
3
1
0
1
1
2
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
3
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
1
0
4
0
0
0
0
0
5
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
1
0
0
2
0
0
2
0
0
2
0
1
0
0
0
0
0
2
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
5
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
1
2
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
2
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
2
0
2
0
0
0
3
0
0
0
0
0
1
0
0
1
1
1
0
1
0
6
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
1
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
3
1
0
3
1
0
1
0
0
0
4
2
0
3
0
0
0
0
1
0
4
0
0
2
2
0
0
1
0
1
0
0
2
0
0
0
1
0
0
0
3
0
1
0
1
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
2
0
4
2
0
0
2
0
0
0
0
2
2
0
0
0
0
1
0
0
1
2
0
0
0
2
0
0
0
0
2
0
1
0
0
0
2
2
1
0
2
1
0
0
2
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
1
6
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
2
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
8
0
0
0
0
0
0
0
0
1
2
1
0
2
0
0
0
2
1
1
3
0
0
1
0
0
2
0
0
1
0
0
2
0
0
2
3
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
3
0
1
0
0
0
3
0
0
0
0
2
0
1
2
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
4
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
4
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
1
3
2
0
1
0
0
0
0
4
3
2
0
2
0
0
2
0
0
0
0
0
0
0
3
0
0
1
0
1
0
0
0
0
0
0
0
2
0
2
2
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
2
4
0
0
0
1
0
2
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
2
1
0
0
1
0
2
0
3
0
1
0
2
0
0
0
0
2
0
0
0
0
0
5
0
0
0
0
0
0
8
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
1
2
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
1
1
0
0
0
0
1
0
0
0
1
0
0
0
2
1
1
0
0
2
0
0
0
0
0
0
3
0
0
1
2
1
2
1
0
1
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
2
1
0
3
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
2
0
0
3
0
1
0
2
2
0
1
2
2
0
0
2
1
0
0
2
0
0
0
0
1
1
2
0
0
0
0
1
1
0
0
0
0
0
1
0
1
1
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
3
0
1
0
1
1
2
0
0
0
0
0
1
2
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
5
2
1
0
0
0
1
0
0
2
2
1
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
1
1
0
0
2
0
0
2
1
1
0
1
0
0
2
2
0
0
0
0
1
0
2
0
1
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
2
5
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
1
0
0
2
1
2
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
1
3
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
1
0
0
0
1
0
0
1
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
2
0
1
3
0
1
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
1
0
0
0
2
1
0
0
1
0
1
0
1
0
0
0
0
0
2
0
0
0
4
0
0
0
0
2
1
0
0
0
0
0
0
0
2
3
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
5
0
0
1
0
0
0
0
0
2
0
2
2
0
0
0
2
0
0
0
0
0
0
0
2
2
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
1
0
1
0
0
1
0
2
0
0
0
0
8
0
0
0
2
1
1
0
3
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
1
3
0
0
0
0
0
1
0
1
0
1
0
0
2
1
0
4
2
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
3
0
0
0
3
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
2
0
0
2
0
3
1
1
0
2
0
0
2
1
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
1
2
1
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
2
2
0
0
2
0
0
0
1
2
4
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
3
0
0
0
0
0
0
0
0
4
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
2
0
0
2
0
0
2
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
2
0
2
4
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
1
1
2
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
6
0
2
4
2
1
0
0
1
0
0
0
0
1
0
0
0
2
0
0
1
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
2
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
2
4
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
4
0
0
0
2
0
1
2
0
0
0
0
0
2
2
0
2
0
2
0
0
2
0
1
2
0
0
0
0
0
2
0
2
1
0
0
0
4
0
0
0
1
2
0
1
0
0
1
0
2
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
2
2
0
2
1
0
0
0
0
0
0
0
0
0
2
1
1
1
0
2
0
0
1
0
1
0
0
0
0
2
0
0
3
0
0
1
1
2
0
0
0
0
0
0
0
1
2
2
0
4
2
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
1
0
2
2
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
1
2
0
0
0
1
2
0
0
2
1
0
1
0
0
1
0
0
0
2
0
1
1
2
0
0
0
2
0
1
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
2
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
4
0
2
0
0
0
2
1
0
1
2
0
0
0
3
0
0
0
1
0
0
0
2
2
0
0
2
0
0
4
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
2
3
0
0
0
0
0
0
0
0
0
5
0
0
0
2
2
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
2
3
0
0
2
0
2
2
0
0
1
0
0
0
2
7
0
0
0
0
0
0
0
3
0
2
1
0
2
2
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
2
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
3
2
0
1
0
2
0
0
2
0
0
1
2
0
0
2
1
0
2
0
0
0
1
0
0
2
5
0
2
0
1
1
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
3
0
0
0
0
0
1
0
0
1
2
0
0
0
1
0
4
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
2
0
5
0
0
2
1
0
1
0
0
0
1
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
4
1
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
2
0
1
0
3
0
0
0
2
3
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
3
0
1
0
0
2
0
1
2
0
0
1
0
5
0
0
0
2
0
0
0
0
0
2
0
0
2
0
8
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
4
3
0
0
0
0
0
0
1
1
1
1
0
0
1
0
0
0
2
0
2
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
2
1
0
0
0
2
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
4
0
0
2
0
1
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
2
1
5
3
0
0
0
1
0
1
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
2
8
0
0
1
0
1
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
2
1
2
0
2
2
1
1
0
1
0
0
1
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
22
2
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
3
3
2
0
1
1
2
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
5
2
3
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
1
0
0
2
0
0
0
1
0
0
1
0
0
3
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
6
0
0
0
0
0
1
0
0
0
2
0
1
0
1
0
1
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
2
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
3
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
2
3
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
3
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
1
0
0
0
2
0
1
0
1
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
5
0
0
0
0
2
0
0
1
0
0
1
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
1
2
0
0
1
0
4
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
1
0
3
0
0
0
2
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
1
2
1
2
0
4
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
1
0
1
1
0
0
3
0
0
0
0
2
0
0
1
0
0
0
6
0
0
0
0
0
6
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
2
0
0
6
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
4
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
1
0
0
0
0
0
0
5
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
2
1
1
1
0
0
1
3
0
0
0
0
0
2
0
1
0
2
0
1
3
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
3
0
2
0
0
2
0
1
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
5
0
2
0
0
1
0
2
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
2
0
2
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
2
0
0
0
0
4
0
0
0
2
1
2
1
2
0
2
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
3
0
2
1
0
1
1
2
0
0
0
1
0
0
0
0
0
1
2
2
0
3
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
3
2
0
0
4
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
1
0
0
0
0
0
3
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
2
0
0
3
0
3
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
1
0
2
1
2
1
1
0
1
0
2
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
1
0
2
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
2
0
2
2
0
0
0
2
2
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
1
6
4
0
1
1
0
0
2
0
0
0
0
0
1
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
3
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
2
0
0
0
0
1
0
2
0
0
1
5
0
2
0
0
0
3
2
0
0
0
3
0
0
0
0
0
0
2
0
0
2
0
1
1
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
3
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
1
2
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
1
0
0
0
0
0
3
0
0
0
0
0
2
0
2
0
3
0
0
1
1
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
2
0
1
0
0
2
2
0
2
1
0
0
0
0
0
0
0
0
2
0
1
0
1
1
1
0
2
2
4
0
2
0
2
0
0
0
2
3
0
0
0
1
0
1
0
2
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
1
0
1
2
2
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
1
3
2
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
1
1
0
0
0
0
2
0
1
1
2
0
3
1
1
0
0
1
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
1
0
0
0
1
0
2
0
0
2
0
0
0
2
0
0
0
0
1
3
2
0
3
0
0
0
2
2
1
1
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
1
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
2
1
0
0
0
0
5
0
0
0
0
0
1
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
3
0
4
0
0
0
0
0
1
0
1
1
0
0
2
4
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
2
2
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
1
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
2
1
1
0
0
0
1
0
0
2
2
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
3
0
1
1
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
1
0
2
2
0
0
0
0
2
0
0
2
1
0
0
3
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
4
2
2
1
1
0
0
0
0
0
0
0
0
2
5
1
0
0
1
1
0
0
2
0
0
2
0
0
0
0
0
0
2
1
0
1
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
3
0
2
0
0
0
0
0
1
2
0
0
6
0
0
0
3
1
0
2
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
1
1
0
0
0
0
1
0
2
0
0
0
2
0
0
0
1
2
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
1
1
1
0
1
1
0
2
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
4
0
0
0
0
1
0
0
2
0
0
0
0
1
3
0
0
1
2
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
4
0
0
0
2
0
0
3
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
3
0
1
7
1
0
0
0
2
1
0
0
0
2
0
0
2
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
3
0
0
2
1
0
0
0
0
0
0
3
1
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
1
0
0
0
6
0
0
2
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
1
2
0
0
1
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
2
0
0
0
1
1
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
3
2
1
0
1
0
0
0
1
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
2
0
2
1
0
0
1
0
1
0
4
0
0
0
0
2
4
0
0
0
0
1
0
2
2
0
0
3
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
1
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
1
0
0
5
3
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
1
2
0
0
0
0
0
0
0
2
2
0
1
0
0
1
2
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
2
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
1
0
1
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
2
0
1
0
1
0
0
0
1
1
0
1
0
0
0
2
2
0
1
0
0
1
0
5
0
2
1
1
0
0
1
2
2
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
2
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
1
1
1
0
0
0
2
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
5
5
0
0
1
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
6
0
0
0
0
0
3
0
0
0
2
0
2
2
0
0
3
0
1
1
0
1
0
1
2
2
0
2
1
0
0
3
0
0
1
2
0
0
0
2
2
0
0
1
0
0
0
2
1
2
2
0
3
0
0
0
0
1
1
0
3
0
0
0
0
0
0
2
0
0
1
2
0
0
2
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
3
0
0
0
2
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
2
1
0
0
0
4
0
2
0
0
1
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
2
1
2
1
0
0
1
0
0
0
3
0
0
0
0
1
0
0
0
1
1
0
0
0
0
2
0
1
0
0
3
1
0
0
0
0
0
1
0
2
0
0
2
12
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
1
1
2
2
2
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
3
0
1
2
1
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
7
1
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
2
1
0
3
0
0
0
0
1
0
1
0
1
0
0
1
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
3
1
0
0
0
2
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
1
1
0
1
0
0
2
0
1
2
0
0
3
1
0
0
0
0
0
0
0
0
0
3
0
1
0
0
1
0
0
3
0
0
0
0
1
3
0
2
0
0
0
2
2
1
0
0
1
0
0
1
0
0
0
2
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
2
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
1
0
0
0
0
0
2
0
0
0
1
2
0
1
3
0
3
0
3
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
4
2
0
1
0
0
0
0
2
0
0
0
1
0
1
2
0
2
2
0
0
0
0
1
2
0
2
1
0
0
0
0
1
3
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
7
0
0
0
0
2
0
1
0
0
0
0
1
0
2
0
0
0
0
1
0
0
2
1
0
0
0
2
2
0
0
0
0
1
0
0
0
1
0
1
2
2
0
0
0
0
0
4
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
1
0
1
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
2
1
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
1
2
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
2
2
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
2
0
0
2
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
5
0
2
2
1
0
1
0
0
0
2
0
0
0
2
0
0
0
3
1
1
3
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
2
1
0
0
1
3
1
0
2
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
5
0
0
2
2
0
2
0
0
0
0
0
0
1
0
2
0
0
0
1
0
1
1
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
3
0
0
0
0
0
1
0
1
0
6
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
1
0
0
3
0
1
0
0
0
2
0
0
1
2
0
0
0
1
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
3
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
3
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
4
0
0
0
1
2
0
1
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
1
0
0
0
0
2
1
2
0
0
0
2
1
0
2
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
3
1
0
0
1
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
1
0
0
0
0
2
0
1
2
0
1
2
0
0
0
1
0
4
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
1
1
0
0
0
1
1
0
0
1
0
1
0
0
0
2
1
0
2
1
1
2
1
0
1
0
0
0
0
3
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
1
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
1
2
0
2
0
2
2
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
2
0
1
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
3
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
7
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
2
1
2
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
2
0
0
0
0
0
1
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
1
0
1
0
2
2
2
0
6
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
3
1
0
1
0
0
4
0
0
0
1
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
1
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
4
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
1
0
2
0
2
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
3
1
2
0
2
0
0
2
1
2
0
1
1
0
2
1
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
2
2
2
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
3
0
1
0
1
0
0
0
0
1
0
1
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
2
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
2
0
2
0
1
2
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
4
0
2
2
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
1
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
1
0
3
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
2
0
2
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
1
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
1
2
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
2
2
0
0
0
1
0
2
0
0
2
0
0
0
1
0
0
2
1
1
0
1
3
0
0
1
0
0
0
0
0
0
1
0
2
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
8
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
1
0
0
0
2
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
2
0
0
1
2
0
1
0
0
0
0
2
0
0
0
0
5
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
1
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
2
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
2
0
0
2
2
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
2
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
1
0
0
2
0
0
0
0
2
2
0
0
2
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
1
2
0
0
1
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
3
0
1
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
2
4
0
0
2
0
0
0
1
1
1
1
0
4
0
2
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
7
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
2
0
1
2
1
0
0
1
0
0
0
0
2
0
0
1
0
0
3
3
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
5
2
2
1
0
2
0
0
0
0
1
0
1
0
0
1
1
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
2
1
0
2
1
0
0
0
0
0
4
0
2
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
2
0
2
0
1
0
2
3
4
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
1
1
0
2
1
1
0
0
0
1
2
0
0
0
0
3
2
1
0
0
2
0
0
1
2
1
0
0
0
2
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
2
0
1
3
2
2
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
4
0
0
0
0
0
2
2
1
0
0
1
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
1
0
1
0
0
0
0
2
0
6
0
1
0
0
0
1
1
0
0
0
2
0
0
2
0
2
2
0
0
0
0
0
0
0
5
0
1
0
0
0
1
2
0
0
0
0
0
0
2
2
1
0
0
0
0
3
0
0
0
0
2
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
3
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
2
0
0
0
1
0
0
1
1
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
2
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
2
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
2
1
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
3
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
2
0
2
2
0
0
0
0
0
1
0
2
0
0
2
1
0
2
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
2
0
1
3
0
0
5
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
2
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
2
0
0
0
0
2
1
0
0
1
0
0
2
1
0
0
2
0
2
0
2
2
0
0
1
0
0
0
2
1
1
1
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
5
0
0
3
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
3
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
1
1
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
2
0
3
1
0
0
1
0
0
0
2
0
1
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
1
2
0
0
0
2
2
2
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
1
0
0
0
0
2
0
1
0
0
1
0
0
1
0
1
0
0
0
2
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
3
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
3
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
4
0
0
2
2
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
3
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
3
0
2
2
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
3
4
2
1
0
0
1
0
2
0
2
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
2
0
4
2
0
0
0
1
0
0
0
0
1
2
0
0
2
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
1
2
2
0
2
1
0
0
0
0
0
0
0
2
0
3
0
2
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
1
1
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
4
2
2
0
2
0
2
2
2
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
5
0
0
0
1
0
0
0
0
0
0
4
1
0
0
2
0
0
1
0
0
0
0
4
0
0
0
1
0
1
0
2
2
0
2
0
0
0
0
0
0
0
2
2
0
1
0
0
1
0
1
1
0
1
0
0
3
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
1
0
2
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
2
0
0
2
0
0
0
1
2
0
2
0
5
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
1
2
0
0
0
0
0
0
1
0
0
1
5
2
1
0
1
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
3
1
0
2
0
0
0
1
2
1
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
3
0
0
0
0
0
2
0
0
1
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
1
0
2
0
0
0
3
4
0
0
6
0
1
2
2
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
3
0
2
0
0
2
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
2
0
1
0
0
2
0
2
0
2
0
0
0
2
1
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
7
0
0
2
0
0
0
0
1
1
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
3
0
0
0
0
0
0
4
0
1
0
2
2
0
2
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
3
0
0
0
0
2
0
2
0
0
0
0
2
0
1
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
1
2
1
0
0
1
0
2
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
3
0
0
4
0
0
0
0
5
0
0
2
0
0
0
0
2
0
0
1
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
1
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
1
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
3
1
1
0
2
2
0
1
0
1
0
1
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
4
0
0
3
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
1
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
1
1
2
0
7
0
2
2
1
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
1
0
0
0
0
0
4
0
0
0
0
2
0
1
0
2
0
0
2
0
1
0
2
0
0
0
0
0
3
1
2
2
2
0
2
0
2
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
2
0
0
1
0
0
7
0
0
1
0
1
1
2
0
0
0
2
1
0
0
0
0
2
3
0
0
0
0
1
1
0
1
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
1
2
0
0
0
2
2
0
3
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
10
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
3
0
1
2
1
0
0
1
0
0
0
1
0
0
0
3
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
3
1
0
0
0
0
0
1
0
1
0
2
1
0
0
0
0
0
1
4
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
2
2
0
0
0
1
1
2
0
0
5
2
0
0
0
0
0
1
0
1
0
1
2
0
0
0
0
5
2
1
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
1
0
3
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
4
0
1
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
5
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
1
0
1
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
2
1
0
0
2
0
2
0
0
1
1
0
0
2
0
2
1
10
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
2
0
3
0
0
0
0
0
1
0
0
0
1
2
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
2
0
2
0
0
1
0
0
0
0
2
0
0
0
2
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
1
1
0
0
0
0
0
1
1
0
0
0
1
2
0
0
0
1
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
1
0
0
0
2
2
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
1
0
0
1
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
1
0
5
0
0
0
0
0
1
0
1
3
0
0
0
0
0
0
4
0
0
0
0
2
0
0
1
2
1
0
1
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
1
0
2
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
2
1
2
0
2
0
0
0
0
0
0
0
3
0
0
0
0
1
0
2
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
3
0
3
0
1
0
1
0
0
0
1
0
0
2
2
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
5
0
5
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
3
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
1
0
1
3
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
3
0
0
2
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
2
1
1
0
2
0
0
0
2
0
1
2
0
0
1
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
5
1
2
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
2
0
0
1
0
0
1
1
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
1
2
0
2
1
0
0
1
0
2
0
0
0
2
0
0
0
2
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
4
0
0
1
0
0
0
0
0
4
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
3
2
0
2
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
3
2
1
0
1
0
0
3
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
3
1
2
0
0
0
0
0
0
0
1
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
1
1
2
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
2
0
0
2
0
3
0
2
1
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
1
0
1
1
0
2
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
3
0
0
0
2
0
0
1
0
1
0
0
0
0
1
0
0
0
4
0
0
1
0
0
2
1
0
0
0
0
0
2
3
2
0
0
0
0
0
0
2
0
0
2
0
0
1
0
1
0
4
2
0
0
1
0
0
0
0
0
0
2
0
0
1
1
0
2
0
2
2
0
0
0
0
0
0
0
0
0
2
3
0
1
1
0
0
0
0
0
0
0
0
0
3
0
1
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
3
1
1
0
0
3
0
2
0
0
0
0
0
0
0
2
0
1
0
2
2
0
2
2
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
3
0
0
1
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
1
0
2
0
0
0
0
0
0
4
0
2
0
0
0
0
0
2
0
0
0
2
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
3
0
1
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
2
0
3
0
0
0
0
0
0
0
2
0
2
0
1
2
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
2
0
0
4
1
1
0
0
0
0
0
0
0
0
0
1
0
4
0
1
0
0
2
0
0
0
1
0
2
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
1
1
0
0
2
0
1
0
0
0
0
0
0
1
1
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
1
0
1
0
2
0
2
2
0
0
1
0
0
0
1
0
0
0
0
1
0
2
0
1
1
0
1
0
0
2
2
0
2
0
1
0
0
0
0
1
0
1
2
0
1
0
2
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
4
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
1
0
0
1
2
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
2
1
0
0
0
1
0
0
0
0
0
2
0
2
0
1
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
2
2
0
0
1
0
1
0
1
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
1
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
2
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
2
0
0
2
0
0
2
1
1
0
4
0
0
2
0
0
4
0
0
2
0
0
0
2
0
0
0
1
0
2
0
0
1
0
0
0
0
1
0
0
0
1
0
2
2
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
3
4
0
0
0
2
0
2
0
1
0
0
0
0
1
2
1
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
2
0
1
1
0
1
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
1
1
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
1
2
0
0
0
2
0
0
2
0
0
3
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
2
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
3
0
0
0
2
0
0
0
0
0
0
0
1
1
0
1
2
0
0
2
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
2
0
1
2
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
2
5
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
2
1
0
0
1
0
0
3
1
0
0
0
0
0
0
0
1
0
3
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
3
0
0
0
0
1
0
0
1
1
0
0
0
2
0
0
3
2
4
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
1
2
0
0
2
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
1
0
1
0
0
1
0
2
0
0
0
0
0
2
0
0
1
0
1
2
0
0
0
2
0
2
0
0
0
2
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
2
0
2
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
3
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
6
2
0
1
2
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
5
0
0
2
0
0
0
1
1
2
1
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
3
2
2
2
0
0
0
0
2
1
2
2
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
3
0
2
2
0
0
4
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
1
0
0
1
0
4
0
1
0
2
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
2
0
0
0
1
1
0
0
1
0
0
0
1
1
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
1
0
0
1
0
0
1
0
0
1
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
4
0
2
1
0
0
2
0
0
5
0
2
0
0
0
1
0
0
0
0
2
0
0
1
0
0
2
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
2
6
1
2
1
0
0
0
1
0
0
0
2
0
0
2
0
0
1
0
2
0
0
1
0
0
0
0
0
1
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
1
0
1
0
0
0
0
0
0
1
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
3
0
0
0
0
1
6
0
2
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
3
0
0
0
0
0
2
0
0
0
2
0
2
1
0
0
2
0
0
1
0
2
0
0
0
0
4
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
1
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
3
3
0
2
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
2
0
1
1
1
0
0
0
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
2
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
2
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
1
2
3
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
3
0
0
1
2
2
0
0
2
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
1
0
2
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
2
0
0
4
0
0
0
2
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
2
2
0
0
0
0
0
1
2
0
2
0
1
0
0
0
0
2
1
0
0
0
1
0
0
0
2
1
0
0
2
2
0
0
0
1
0
0
0
0
2
0
1
0
0
0
2
2
10
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
2
2
2
0
0
0
0
1
0
3
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
1
0
0
1
2
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
4
2
0
2
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
2
0
2
0
0
1
2
1
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
1
0
1
1
0
0
0
0
0
0
2
0
3
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
1
0
2
0
0
1
0
4
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
2
0
1
0
0
0
2
1
2
0
0
0
0
2
0
0
0
0
1
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
1
0
0
0
2
0
0
2
2
0
1
0
1
6
0
0
2
0
0
0
0
2
0
1
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
1
0
1
0
1
0
0
0
0
0
2
2
0
2
2
0
2
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
3
0
2
0
0
0
0
0
0
0
2
2
0
2
2
0
1
1
0
2
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
2
2
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
5
0
0
0
0
0
0
0
0
3
1
0
0
0
2
0
0
0
2
0
0
0
0
1
0
1
6
4
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
2
2
0
1
0
0
0
0
2
2
0
2
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
3
0
0
1
2
0
0
0
0
0
5
0
2
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
3
2
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
8
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
1
0
2
1
1
0
2
0
0
0
0
0
1
0
0
0
2
0
2
1
0
1
0
0
0
0
0
2
2
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
1
0
1
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
2
1
0
1
0
1
0
0
0
0
1
0
1
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
2
0
0
1
0
1
0
2
0
2
0
2
1
0
0
2
1
1
0
0
3
3
0
0
2
0
1
0
0
0
0
2
0
0
3
0
0
0
0
1
7
0
0
1
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
2
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
2
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
1
0
0
0
3
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
3
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
2
4
0
0
2
0
0
0
0
0
0
1
0
2
0
0
3
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
2
0
0
1
1
0
0
0
0
0
4
0
0
0
0
1
0
1
1
0
2
0
0
0
0
0
1
1
0
0
2
0
0
2
0
0
0
0
2
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
7
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
2
0
3
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
1
6
0
0
2
0
0
1
2
0
0
0
0
0
0
0
1
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
2
4
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
1
0
1
0
0
2
0
0
4
0
0
0
0
0
0
0
2
1
0
0
0
1
0
1
0
1
0
2
3
2
1
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
3
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
2
0
1
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
3
1
3
2
1
0
0
0
0
1
0
0
0
6
2
2
0
0
0
1
0
0
0
0
0
2
2
0
0
0
1
0
0
1
0
3
0
0
1
2
3
1
0
0
0
2
0
2
0
2
0
0
0
2
0
0
2
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
4
0
2
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
1
2
0
1
0
2
0
0
0
0
0
2
6
0
0
0
0
0
0
1
5
1
0
0
1
2
1
0
0
1
0
0
0
0
1
0
0
4
1
0
0
0
0
0
0
2
1
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
1
0
0
0
2
0
1
0
1
2
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
2
0
1
4
0
0
3
3
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
2
0
0
2
0
0
0
0
0
3
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
1
0
3
0
0
2
0
2
0
1
1
0
0
2
2
0
2
0
0
0
0
0
0
2
1
0
1
2
2
0
2
0
2
0
0
0
0
0
1
0
0
1
2
0
0
0
1
2
2
0
2
0
0
1
0
0
0
2
0
1
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
2
2
2
0
0
0
2
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
2
4
0
2
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
4
0
0
0
1
0
2
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
1
0
0
0
0
0
1
0
2
0
2
0
0
2
1
1
0
3
0
0
0
0
0
0
2
2
0
0
0
0
0
3
0
0
0
0
0
0
1
0
2
0
2
0
1
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
2
3
0
0
0
0
3
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
2
1
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
3
0
1
3
0
2
1
0
0
0
0
0
2
0
6
0
0
0
0
0
1
1
0
2
0
0
0
0
2
0
0
0
0
0
4
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
3
0
0
0
2
0
1
0
0
2
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
2
0
0
3
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
4
0
0
0
0
2
2
0
1
0
3
2
0
0
0
0
0
3
0
1
1
0
0
0
0
1
1
1
0
0
0
1
0
0
0
1
1
0
0
0
0
2
0
0
2
2
3
0
0
0
2
0
0
3
0
0
0
0
0
1
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
1
0
0
1
0
2
1
0
2
1
1
0
0
0
0
0
2
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
1
0
0
0
0
2
0
2
0
0
2
0
1
0
2
1
0
1
1
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
3
0
0
0
1
1
0
0
1
1
0
4
0
3
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
1
2
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
3
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
2
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
3
1
2
3
0
0
0
0
1
0
0
2
3
2
1
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
1
1
0
0
0
3
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
6
0
0
1
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
2
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
3
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
2
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
2
2
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
2
0
0
0
1
0
0
1
2
0
1
0
0
1
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
21
1
1
0
0
3
2
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
1
2
0
0
2
3
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
2
0
0
1
0
2
0
0
0
0
2
1
1
2
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
3
2
0
0
0
0
0
2
3
0
0
2
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
2
2
0
2
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
6
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
1
0
8
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
1
0
1
0
1
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
2
0
0
0
0
1
5
0
0
1
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
2
1
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
6
1
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
7
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
3
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
2
0
0
3
0
2
0
0
1
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
4
2
0
0
0
0
0
2
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
1
0
2
0
2
0
1
2
0
2
0
0
0
0
0
2
0
0
0
0
0
6
1
2
0
0
0
0
0
1
0
0
0
1
3
0
0
1
0
1
2
0
1
3
0
0
3
0
2
2
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
9
2
0
1
1
0
0
2
2
0
0
2
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
1
1
0
2
2
0
0
0
0
0
2
2
0
0
0
0
1
2
0
2
0
0
1
2
4
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
5
0
0
0
0
2
1
0
0
1
0
0
2
0
0
0
0
1
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
3
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
3
2
0
0
0
0
0
1
0
0
0
0
0
0
3
1
0
0
1
1
0
0
0
0
0
0
0
0
3
0
0
3
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
1
0
0
0
2
0
0
3
1
0
2
0
0
0
0
2
0
0
3
0
1
1
0
0
0
3
1
0
1
0
0
2
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
3
1
0
2
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
2
2
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
1
2
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
3
0
0
0
0
0
0
0
0
3
1
1
2
1
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
1
0
3
0
2
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
1
0
1
1
0
2
2
0
0
0
0
0
2
2
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
3
0
0
0
0
0
3
1
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
2
3
2
0
0
0
0
2
1
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
1
2
1
2
1
0
1
0
1
0
0
1
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
1
2
0
0
0
0
2
0
0
0
0
1
0
2
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
1
0
0
0
1
0
3
0
0
0
1
0
0
2
1
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
1
0
0
2
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
2
0
0
0
0
2
2
0
2
0
0
4
0
0
0
0
0
2
1
0
0
2
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
3
0
0
0
1
3
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
2
1
0
0
2
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
1
0
0
0
3
0
0
0
2
0
0
0
0
0
2
2
1
0
0
1
0
0
2
0
0
0
0
1
0
1
2
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
1
2
0
2
1
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
3
1
0
2
0
0
0
0
0
0
0
3
2
0
2
0
2
0
1
2
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
1
0
2
1
0
2
0
0
0
0
1
1
0
1
0
0
0
2
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
2
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
1
0
1
0
0
0
1
0
0
1
2
2
1
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
2
0
1
0
0
3
0
1
0
0
0
0
0
1
1
0
2
0
0
0
2
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
2
4
2
1
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
2
2
1
0
0
0
2
0
0
1
0
1
1
3
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
1
0
2
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
2
0
0
2
0
1
0
0
0
1
1
4
1
0
1
0
0
0
0
1
1
0
2
0
2
2
1
0
1
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
2
0
1
0
0
0
0
1
0
0
0
0
0
2
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
3
0
0
0
2
0
2
0
0
2
1
3
0
0
0
2
1
1
2
0
0
0
2
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
5
2
0
1
0
0
0
2
2
2
1
0
0
0
0
0
3
0
1
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
2
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
3
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
1
0
0
0
0
1
0
0
1
3
0
0
0
0
0
1
0
0
0
1
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
2
0
0
1
0
0
0
2
2
2
2
1
0
0
1
0
2
2
1
2
0
0
2
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
3
0
0
2
2
0
3
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
3
2
1
2
1
0
0
1
0
2
0
1
0
0
0
0
2
0
0
2
0
1
0
1
2
0
2
0
2
1
1
2
0
2
0
1
0
0
0
0
0
1
4
0
0
1
0
0
0
0
1
0
1
1
0
2
0
1
0
0
0
0
1
1
0
0
2
4
0
2
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
3
2
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
1
0
0
0
3
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
1
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
4
0
0
1
0
0
0
0
1
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
1
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
2
2
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
8
0
0
0
1
0
0
0
0
0
1
2
0
2
0
0
0
0
0
2
2
0
2
0
0
0
2
2
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
1
0
0
1
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
9
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
2
2
2
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
2
1
0
2
1
0
0
0
2
2
2
0
0
0
0
0
0
0
0
2
1
0
6
0
0
0
0
3
1
0
1
0
4
1
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
3
0
0
0
0
0
2
0
0
1
2
1
0
6
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
3
1
0
0
1
0
0
1
1
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
1
0
1
3
1
0
0
0
0
1
2
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
3
2
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
2
2
0
2
2
0
0
0
0
2
0
1
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
1
0
2
2
0
0
0
0
2
1
2
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
2
1
0
2
0
1
2
1
2
0
0
0
2
0
0
0
0
0
0
0
3
0
1
0
0
0
0
1
2
0
1
0
0
0
0
2
2
2
0
0
0
0
1
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
3
0
2
1
3
0
1
0
0
2
0
3
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
5
2
2
1
1
0
2
1
0
1
0
0
0
0
1
0
0
2
0
1
2
0
0
0
2
0
0
2
0
9
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
5
0
0
3
0
0
0
0
2
0
3
1
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
2
2
0
2
2
0
0
1
0
0
3
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
1
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
2
2
3
0
3
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
3
0
0
3
0
0
1
1
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
5
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
1
0
0
1
3
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
1
3
2
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
1
2
1
0
0
2
0
1
0
2
0
0
0
0
0
2
2
2
2
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
4
2
0
0
0
0
0
0
0
2
0
2
0
0
1
0
2
0
0
0
2
0
1
1
0
1
0
0
0
1
0
2
0
0
2
2
2
4
1
0
1
0
0
0
3
0
1
0
0
0
0
0
1
0
0
0
2
2
0
0
0
2
0
0
0
0
3
0
0
0
0
2
3
0
2
0
0
2
0
0
2
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
3
1
0
2
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
2
0
0
2
0
2
1
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
2
1
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
2
2
0
0
1
0
0
0
0
0
0
0
1
0
2
0
1
2
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
3
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
1
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
1
1
2
1
2
0
1
0
0
0
0
0
0
0
1
0
2
2
2
0
0
3
0
0
0
0
0
1
0
0
0
1
1
0
0
0
3
0
2
0
0
1
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
2
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
3
1
0
0
0
0
1
0
2
0
0
0
0
0
2
1
0
0
3
9
1
0
0
0
1
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
1
2
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
5
0
0
0
0
1
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
2
0
2
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
4
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
3
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
2
1
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
2
2
0
0
0
2
0
0
0
0
1
0
0
1
3
2
0
1
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
1
0
0
2
0
1
1
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
3
0
0
0
0
0
0
4
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
1
5
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
3
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
3
1
1
0
0
0
1
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
1
0
1
0
0
1
0
2
0
0
2
1
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
2
0
0
1
0
0
0
0
1
2
0
1
0
0
0
1
2
1
0
0
0
0
0
1
0
0
0
0
0
4
1
0
0
0
2
2
2
0
0
0
3
0
0
0
0
0
1
1
0
1
0
1
2
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
3
0
2
0
0
0
0
0
0
6
0
0
0
0
0
3
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
2
0
1
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
5
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
3
0
0
0
2
1
2
0
6
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
1
0
0
0
1
0
0
0
1
0
0
0
3
0
0
0
1
0
0
0
1
0
0
0
0
2
1
1
0
0
1
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
2
6
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
2
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
1
0
0
1
0
1
0
3
0
1
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
3
2
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
11
3
0
1
1
0
3
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
3
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
2
2
0
0
0
2
0
4
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
1
0
0
1
0
2
0
3
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
2
0
1
1
0
0
0
2
0
0
0
0
0
1
2
1
0
1
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
1
0
1
2
0
0
0
2
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
2
2
0
1
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
1
0
1
0
2
0
0
2
1
0
1
0
0
0
2
0
1
0
0
0
3
0
0
0
0
0
0
1
0
1
2
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
2
0
1
1
0
0
0
1
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
4
0
0
2
0
0
4
2
0
1
0
0
0
1
0
0
1
0
1
0
0
0
4
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
2
0
4
0
0
0
0
0
2
1
2
0
1
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
1
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
1
0
5
0
0
0
0
0
3
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
1
2
0
1
0
1
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
4
0
3
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
1
0
3
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
4
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
1
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
1
2
2
2
0
2
0
0
0
1
0
2
2
1
1
0
2
0
0
0
2
1
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
2
0
0
1
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
4
0
0
2
1
2
1
0
0
0
0
0
2
0
0
0
0
0
6
0
2
0
0
3
0
0
3
0
0
0
2
1
0
0
0
1
0
0
1
2
1
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
2
0
0
0
2
0
0
0
0
2
2
2
2
0
0
0
0
0
4
0
0
0
0
2
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
1
0
0
0
7
2
0
0
0
1
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
1
0
0
0
0
0
0
3
0
2
0
0
1
0
4
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
4
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
2
1
0
0
0
0
0
0
0
0
0
2
3
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
3
0
0
0
0
0
0
0
3
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
2
1
0
0
2
2
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
2
0
1
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
1
2
0
0
1
0
0
2
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
3
0
0
2
0
0
0
1
0
0
2
1
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
1
0
1
2
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7
0
0
0
2
2
0
0
0
0
0
0
1
0
3
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
1
0
2
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
3
1
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
1
1
2
2
2
0
1
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
1
0
1
4
1
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
2
0
0
0
3
0
2
0
2
4
0
0
1
1
0
3
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
3
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
1
0
1
0
1
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
6
0
0
1
8
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
5
0
0
0
3
0
0
0
3
1
0
0
2
0
0
2
0
2
1
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
2
1
0
0
0
0
0
0
2
1
0
0
0
1
0
3
0
0
1
0
0
1
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
1
0
0
1
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
2
2
0
2
0
0
0
0
0
2
1
1
0
0
1
0
2
0
2
0
0
2
2
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
2
1
0
1
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
3
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
3
0
2
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
1
3
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
1
1
0
1
1
0
0
0
4
0
0
0
0
0
1
1
0
5
0
0
0
2
0
1
0
0
0
0
2
0
1
0
1
1
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
2
0
0
0
0
5
4
0
0
0
1
2
1
1
0
0
0
0
1
0
3
0
0
0
0
4
0
0
0
0
2
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
3
0
0
0
0
0
0
3
1
0
0
0
0
2
0
0
0
0
0
2
0
1
0
1
0
2
0
0
4
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
1
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
7
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
2
2
2
0
0
0
3
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
1
0
0
0
1
1
0
1
0
0
4
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
3
1
0
0
0
2
2
0
0
1
0
0
1
0
2
0
2
0
0
1
7
2
2
0
0
1
0
0
0
0
1
0
1
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
2
2
2
0
1
2
0
0
0
0
0
0
0
1
2
0
1
0
2
1
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
2
0
0
1
1
0
0
2
0
0
0
1
0
2
1
2
2
0
2
0
0
0
2
2
0
0
0
1
1
0
2
0
0
1
0
1
0
1
2
0
0
2
0
2
5
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
3
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
2
0
2
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
1
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
1
0
1
0
0
1
1
2
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
3
0
0
0
1
0
1
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
1
0
2
0
0
0
3
0
2
0
2
0
0
3
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
2
0
0
1
0
1
0
0
3
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
2
0
6
0
0
2
1
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
1
2
0
0
1
0
0
1
1
0
1
1
0
0
2
0
1
0
3
2
0
2
0
0
0
0
0
2
0
0
0
1
0
2
3
0
0
0
0
0
1
0
0
0
4
0
0
2
0
2
0
0
0
0
0
2
5
0
0
0
0
2
2
8
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
1
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
2
0
2
0
0
0
1
1
1
0
0
4
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
3
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
2
1
0
0
2
0
0
4
0
0
0
0
1
0
0
0
1
2
0
0
1
0
0
1
0
1
0
0
0
2
2
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
2
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
3
3
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
2
0
0
2
0
2
2
0
4
0
1
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
2
0
0
1
0
0
2
2
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
2
1
0
0
0
4
0
0
0
1
0
0
1
0
0
1
0
0
2
0
2
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
2
0
2
1
2
1
0
1
0
0
0
0
1
0
2
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
1
2
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
5
0
0
0
0
3
2
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
2
0
0
0
0
2
2
0
0
2
1
0
0
4
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
1
2
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
1
0
0
1
0
0
0
0
2
0
1
0
2
0
0
1
0
0
2
2
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
3
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
1
0
2
0
0
0
0
0
0
2
2
0
1
1
2
0
0
0
2
0
0
0
0
0
1
1
1
0
0
2
1
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
3
0
0
0
2
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
1
0
0
1
0
2
0
0
0
1
3
0
3
0
0
0
0
0
0
0
2
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
2
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
3
1
0
5
1
0
2
1
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
1
1
0
0
2
1
0
1
0
0
0
0
0
1
0
4
0
0
0
1
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
1
0
2
0
2
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
8
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
1
2
1
0
0
3
0
0
0
0
0
0
3
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
2
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
1
2
1
0
0
0
1
1
0
0
0
0
0
0
2
0
0
1
0
6
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
2
1
0
0
0
2
0
0
0
0
1
2
1
0
0
0
2
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
1
1
0
0
2
1
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
1
0
0
0
5
0
0
0
0
2
3
0
3
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
1
1
1
2
3
1
0
2
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
1
4
0
0
2
2
1
0
0
0
1
0
2
2
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
2
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
3
2
0
0
2
0
0
2
2
1
2
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
1
2
0
0
1
0
0
0
0
0
3
0
0
2
4
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
2
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
1
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
2
0
0
0
0
0
1
0
1
2
0
1
0
0
1
2
2
0
0
1
0
0
1
0
2
0
2
0
0
0
2
1
2
0
1
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
3
1
0
1
0
2
0
0
0
0
0
0
0
0
2
2
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
1
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
2
2
0
0
4
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
1
1
0
0
0
0
0
3
0
0
0
1
0
1
3
0
1
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
1
1
0
0
0
2
0
2
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
5
0
1
0
0
0
0
0
0
3
2
0
0
4
1
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
2
0
4
0
1
0
0
0
0
0
7
0
0
0
2
0
0
1
2
0
1
1
3
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
2
2
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
3
0
2
0
0
0
0
0
2
1
1
0
0
0
0
0
3
0
0
1
0
0
0
0
0
1
2
2
0
0
0
2
1
1
1
0
0
1
0
2
2
0
0
0
0
0
1
0
0
2
1
0
0
0
0
2
1
0
0
0
1
1
0
0
1
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
2
0
0
2
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
2
2
0
1
0
0
1
0
2
0
1
2
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
3
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
1
0
2
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
1
1
2
0
2
1
0
1
0
1
0
2
0
1
0
0
0
0
0
0
1
0
0
1
2
0
0
0
1
0
0
2
0
1
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
1
0
0
0
0
0
1
1
0
2
0
0
0
0
2
0
2
0
1
0
0
0
1
0
0
2
0
1
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
4
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
4
0
0
0
1
1
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
2
2
2
0
4
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
4
0
0
2
0
0
2
0
1
0
5
0
2
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
2
2
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
3
0
1
0
0
0
0
1
0
1
1
0
0
2
0
0
0
1
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
3
0
1
7
0
1
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
3
2
0
0
3
0
2
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
3
0
0
0
2
2
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
2
1
2
0
2
2
1
0
0
0
0
0
1
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
3
0
2
0
2
2
0
2
0
0
2
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
1
0
3
0
0
0
0
0
0
0
3
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
3
0
1
4
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
2
0
2
0
3
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
1
2
0
0
2
3
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
2
2
2
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
3
1
0
0
0
0
0
0
0
4
0
1
0
0
0
0
1
2
0
0
0
0
0
0
1
0
2
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
2
0
0
1
1
0
0
0
0
3
0
2
0
2
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
2
0
0
3
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
1
0
2
1
0
0
0
0
0
0
1
1
0
0
3
0
2
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
5
1
0
0
4
2
0
0
0
2
0
0
0
0
0
0
0
3
0
0
2
2
0
0
2
0
0
0
0
2
0
1
0
0
0
0
1
0
0
2
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
3
0
0
0
3
0
3
0
2
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
1
0
0
3
2
0
0
0
0
0
0
0
1
0
0
0
6
4
0
0
2
0
0
2
0
0
0
3
0
3
2
0
0
2
2
0
1
0
0
0
0
2
0
0
1
1
0
1
0
0
0
2
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
3
2
0
1
0
0
0
0
0
0
0
3
1
0
0
0
1
2
0
0
0
0
1
0
0
5
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
1
0
1
1
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
1
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
2
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
4
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
2
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
1
0
2
8
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
2
1
0
0
0
0
1
0
0
2
1
0
0
0
2
1
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
1
1
0
0
2
0
1
1
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
4
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
2
1
0
0
2
0
0
0
1
0
0
0
2
2
2
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
3
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
3
0
1
1
0
0
0
2
0
0
0
0
2
5
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
2
2
2
0
2
2
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
2
0
1
0
0
2
0
0
0
3
0
0
2
0
1
2
2
0
0
1
0
2
0
0
2
10
1
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
4
2
0
0
2
1
2
2
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
1
0
2
0
0
0
0
0
0
0
0
0
3
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
1
0
0
0
0
1
0
2
2
0
0
0
0
2
2
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
3
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
1
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
2
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
3
0
1
0
1
0
0
2
2
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
2
1
0
0
1
1
0
0
1
2
0
0
0
0
1
1
15
0
2
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
2
2
1
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
2
2
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
3
0
0
1
2
0
0
0
1
0
4
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
1
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
2
1
0
0
0
0
0
2
0
0
0
2
1
0
0
0
2
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
2
2
3
1
0
0
0
0
2
0
0
0
0
1
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
2
0
3
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
3
2
3
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
1
0
2
0
1
0
1
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
3
0
0
0
2
0
0
0
4
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
1
1
0
0
2
0
0
0
0
0
2
6
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
1
0
2
2
3
2
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
2
2
0
1
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
3
3
0
2
1
0
0
1
0
0
2
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
2
0
1
1
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
4
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
1
0
2
0
0
1
1
1
2
0
1
0
0
1
0
0
2
2
0
0
0
0
1
0
3
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
6
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
2
0
1
0
0
0
0
1
0
3
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
1
1
0
0
1
0
2
0
0
0
0
0
0
0
4
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
3
1
2
0
0
1
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
1
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
2
1
1
0
0
0
2
2
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
3
0
1
1
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
2
1
1
2
1
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
2
2
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
8
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
3
1
1
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
1
0
3
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
1
0
2
0
2
0
2
0
0
1
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
2
2
1
0
1
0
0
2
0
0
2
0
0
0
1
0
0
2
0
0
1
2
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
3
1
0
0
0
2
0
0
0
3
0
3
0
0
2
1
0
1
0
0
0
0
0
0
0
2
1
4
0
2
2
2
0
0
0
0
1
0
1
0
0
2
2
0
0
0
0
1
2
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
3
0
0
0
0
1
1
0
0
0
0
0
1
2
0
0
3
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
1
0
2
0
2
0
0
0
0
1
0
1
0
0
3
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
2
0
0
2
0
1
1
2
0
2
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
3
0
0
2
0
0
0
0
0
0
1
0
0
2
1
0
0
2
0
0
2
0
1
0
0
0
0
1
0
0
0
2
1
0
0
1
0
0
1
0
0
2
1
4
0
0
2
0
0
0
2
0
2
0
2
0
0
2
0
2
0
0
0
0
0
0
0
2
2
0
1
0
3
2
2
0
5
0
0
3
0
0
2
0
0
1
0
0
1
0
2
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
5
0
4
0
0
1
0
0
0
0
1
0
0
0
0
2
4
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
1
0
2
0
1
1
1
0
2
0
0
2
0
1
0
0
0
0
0
0
2
2
0
1
0
0
2
0
2
1
1
1
0
0
0
1
2
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
1
0
1
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
3
0
1
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
2
0
0
0
2
2
0
2
0
0
0
2
1
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
1
1
1
1
1
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
2
1
0
0
3
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
8
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
2
0
0
3
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
2
2
1
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
1
0
3
0
0
0
1
1
2
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
2
0
1
0
0
0
0
1
0
1
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
2
3
1
0
2
0
1
0
0
1
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
3
3
0
1
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
2
0
0
0
1
2
0
7
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
4
0
1
0
0
1
0
0
2
0
0
0
1
0
0
0
2
0
4
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
2
0
0
0
0
0
2
2
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
1
0
0
0
1
0
1
0
0
0
4
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
3
3
0
1
0
2
0
0
0
0
0
0
0
0
1
1
2
0
0
2
0
0
0
0
0
1
4
1
0
0
0
3
0
0
0
0
0
0
0
2
2
0
2
0
1
0
1
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
1
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
3
2
0
0
0
0
0
2
0
0
1
0
2
0
1
0
1
1
0
0
0
1
0
0
1
0
0
0
2
0
3
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
1
1
1
1
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
3
0
0
0
2
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
2
2
0
0
0
0
2
1
0
4
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
2
0
1
1
2
0
1
1
0
0
2
0
0
0
2
2
0
0
0
0
2
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
3
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
1
1
2
1
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
3
2
0
0
0
4
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
2
2
1
0
2
0
3
0
4
0
1
1
2
0
0
0
0
0
0
0
0
0
2
0
2
1
0
1
0
2
2
0
1
0
2
2
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
2
2
0
0
2
0
0
0
1
0
0
0
0
3
0
1
0
1
1
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
2
3
0
1
2
1
3
4
0
0
3
0
0
0
2
0
1
2
0
0
0
0
2
0
0
0
2
1
0
0
0
3
2
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
2
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
2
1
0
1
0
0
0
0
0
0
2
0
0
0
2
4
1
0
0
2
0
0
2
1
0
0
2
0
0
1
0
0
2
0
2
2
0
0
0
0
3
0
0
3
2
0
0
0
1
2
2
3
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
3
1
0
0
0
4
1
0
0
1
1
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
1
1
0
0
1
0
1
0
2
0
0
0
0
0
1
1
3
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
1
0
0
0
0
1
3
0
0
1
0
1
2
2
1
0
0
2
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
2
0
2
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
3
0
0
0
0
1
0
0
0
1
0
0
0
0
2
1
0
1
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
2
0
0
1
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
2
0
2
1
0
1
0
0
2
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
2
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
1
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
3
0
1
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
2
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
1
2
1
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
1
2
0
0
3
0
0
0
0
2
0
2
0
0
2
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
3
1
2
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
2
3
0
2
1
1
2
0
0
1
2
1
0
0
6
2
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
2
3
0
1
0
0
1
3
0
0
0
1
0
2
0
0
0
1
0
2
0
0
0
2
0
0
1
0
0
1
4
0
0
3
0
0
0
2
0
3
0
0
0
0
1
0
0
0
4
1
1
2
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
1
0
1
2
0
0
0
0
0
0
2
0
0
1
1
1
0
1
0
2
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
4
0
1
0
0
0
0
0
1
3
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
2
0
2
2
2
0
0
0
0
0
2
0
1
0
0
0
2
0
0
2
2
0
1
0
0
0
4
0
1
1
0
3
0
0
1
0
0
0
0
0
2
3
0
0
0
0
5
0
2
0
2
3
0
0
0
0
1
0
1
0
1
0
2
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
7
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
2
2
2
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
1
0
3
0
3
0
2
0
0
0
0
0
2
2
3
0
2
5
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
4
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
1
0
0
3
0
2
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
1
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
4
0
3
2
2
0
0
0
2
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
1
3
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
2
0
0
0
2
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
2
1
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
2
1
0
1
2
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
1
0
1
0
0
0
1
0
1
1
1
2
0
0
0
1
0
0
0
0
0
2
1
0
0
3
0
0
0
0
0
0
0
0
2
4
0
0
3
0
0
0
0
1
0
0
0
2
0
2
2
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
1
1
2
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
2
1
0
2
0
0
0
2
0
1
0
0
0
1
0
0
2
0
0
2
0
0
2
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
1
1
0
0
0
2
0
2
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
6
1
1
0
0
1
0
2
1
0
2
0
1
0
0
0
0
2
1
0
0
2
1
0
2
0
0
0
0
1
0
3
0
1
0
0
3
0
0
4
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
2
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
2
2
1
2
2
0
1
0
0
0
1
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
2
0
3
0
0
1
2
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
1
0
1
0
3
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
1
2
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
1
1
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
3
0
0
0
0
2
0
0
2
0
2
2
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
2
0
0
1
1
0
1
2
0
2
0
2
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
3
1
0
0
0
1
2
1
0
0
1
0
1
0
0
1
0
0
0
2
0
2
0
2
0
0
0
0
2
0
0
2
0
1
0
0
4
1
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
3
0
0
0
0
0
0
0
0
0
2
0
0
2
1
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
2
2
0
0
1
2
0
0
0
2
0
2
0
0
0
0
0
3
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
3
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
2
0
2
0
0
0
1
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
2
2
4
0
0
0
1
0
1
3
2
0
0
1
0
0
2
3
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
2
0
0
1
0
0
2
0
0
0
1
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
2
2
2
1
1
0
0
2
1
0
0
7
0
0
0
2
2
2
0
0
1
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
1
6
2
0
0
1
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
1
2
0
0
1
1
0
1
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
2
1
0
0
0
0
1
0
0
0
1
1
0
0
2
0
0
0
0
2
1
2
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
1
0
0
2
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
5
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
4
2
0
4
0
1
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
1
1
1
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
7
0
1
0
0
1
0
0
0
1
2
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
3
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
3
0
0
1
0
0
0
0
0
0
0
0
6
5
2
0
1
0
0
0
0
0
2
2
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
2
3
0
0
3
0
2
0
0
0
0
1
1
2
0
0
0
0
2
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
3
0
0
1
2
0
2
0
0
0
0
2
2
2
2
0
2
0
0
0
1
0
0
1
0
2
0
0
2
1
0
0
0
1
0
2
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
1
1
2
0
1
0
0
2
0
0
1
0
0
0
2
1
0
0
0
0
0
2
0
2
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
3
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
2
0
0
3
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
2
0
0
0
2
1
0
1
0
0
0
0
0
0
2
3
1
0
1
0
0
0
0
4
0
1
0
0
0
0
0
2
0
1
0
0
2
0
0
5
0
0
0
2
0
0
2
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
1
5
1
0
0
0
0
0
0
0
1
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
1
0
2
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
3
0
0
0
1
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
6
2
0
0
2
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
1
0
1
0
2
0
0
2
0
2
0
2
0
0
0
2
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
2
0
2
2
0
2
2
0
0
0
0
4
1
0
0
1
0
0
0
0
0
0
0
2
0
2
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
2
1
0
0
1
2
1
0
0
0
0
1
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
2
0
1
0
1
0
0
0
1
0
1
0
1
3
0
1
1
0
0
0
0
0
0
0
0
4
0
0
2
0
2
0
13
0
4
0
1
1
0
2
0
0
0
0
0
0
0
2
0
1
0
0
2
1
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
2
3
0
0
0
3
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
1
3
4
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
2
0
1
1
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
2
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
1
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
2
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
1
1
2
0
0
0
1
0
1
0
0
1
2
0
2
0
2
2
0
1
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
3
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
2
2
0
1
0
0
0
2
1
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
2
0
1
0
3
0
0
0
0
1
0
1
0
0
1
2
1
2
0
0
1
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
2
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
1
2
1
3
1
0
0
0
0
1
0
2
2
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
1
1
0
1
0
0
2
0
0
0
0
2
3
0
0
0
0
0
1
0
1
0
1
4
0
0
1
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
2
1
1
0
1
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
10
0
0
0
0
2
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
3
1
2
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
2
2
0
0
2
0
0
0
0
0
3
0
0
2
0
0
1
2
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
3
0
0
0
0
0
0
2
0
1
2
1
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
1
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
1
0
1
0
0
1
4
0
0
1
0
0
0
0
0
0
1
1
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
1
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
1
0
2
2
0
1
0
1
0
1
0
0
0
3
0
1
1
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
2
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
2
1
0
0
0
2
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
4
0
1
0
1
0
0
0
2
2
0
1
0
0
0
3
0
2
0
2
1
0
0
1
1
0
0
0
1
0
0
1
2
0
2
2
0
0
1
0
2
0
2
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
2
0
0
1
0
0
0
0
1
0
0
0
2
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
1
0
0
0
4
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
5
1
0
0
0
0
0
0
0
0
0
0
1
0
2
2
1
0
0
0
0
0
0
0
0
2
0
0
0
2
4
0
0
0
0
0
2
3
0
2
0
0
0
2
1
0
0
0
0
2
1
0
0
0
0
2
0
1
0
2
0
0
1
1
0
0
0
0
1
0
1
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
3
0
0
2
2
1
3
0
0
0
0
4
0
0
2
0
0
0
0
0
0
2
0
0
0
1
3
0
2
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
1
1
0
2
3
0
0
0
2
0
2
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
5
0
0
2
0
0
0
0
0
2
1
0
3
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
2
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
3
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
3
0
0
0
2
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
1
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
3
6
0
0
0
0
0
1
0
2
0
0
1
0
2
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
1
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
1
0
0
2
0
2
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
1
0
2
1
2
2
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
1
3
1
2
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
2
3
0
2
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
3
0
0
2
0
1
0
0
2
1
0
4
0
1
0
0
0
0
0
2
0
0
1
1
0
2
1
0
0
0
0
0
0
0
1
1
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
4
0
0
4
0
0
0
0
0
1
0
0
2
2
3
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
3
2
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
2
0
2
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
1
0
0
2
0
2
0
0
0
0
4
0
2
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
2
2
0
0
2
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
2
1
0
0
0
0
0
0
2
0
2
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
3
0
0
0
0
0
0
1
3
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
1
2
2
0
2
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
3
2
1
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
3
2
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
6
0
0
1
0
1
0
1
0
0
0
2
3
0
0
0
0
1
3
1
2
0
0
0
0
0
0
0
0
0
2
0
2
3
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
1
0
0
1
0
2
2
5
0
2
1
0
0
0
0
0
5
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
6
0
2
0
0
0
0
0
0
0
2
0
0
0
2
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
3
0
2
3
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
1
1
1
2
0
0
0
2
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
2
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
1
0
2
0
0
0
0
2
0
1
2
2
2
2
0
1
0
0
0
1
0
0
1
0
1
0
1
0
2
6
1
2
0
0
1
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
5
0
3
0
0
2
2
0
0
0
0
0
1
0
1
1
0
0
2
0
0
1
2
0
1
3
1
0
0
0
0
0
1
3
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
1
2
0
0
0
0
0
1
0
0
2
2
2
0
0
0
0
0
1
0
1
0
0
0
2
0
0
2
0
1
0
0
0
2
0
1
2
1
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
2
0
2
1
1
1
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
2
1
2
2
0
2
1
0
0
0
2
0
2
0
2
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
3
0
0
0
0
0
0
2
1
0
0
0
0
1
2
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
2
2
0
1
1
2
0
0
0
1
0
0
1
0
2
2
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
2
1
0
0
0
0
0
0
0
0
2
4
0
0
1
0
0
0
2
1
0
0
1
0
0
0
0
1
0
0
2
1
0
0
0
2
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
1
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
1
0
0
0
2
0
0
0
2
1
0
0
2
0
2
2
1
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
2
1
0
0
0
2
3
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
1
1
0
0
0
0
2
0
0
2
2
0
0
2
2
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
4
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
2
1
0
0
2
0
0
0
1
1
1
1
0
2
0
0
0
0
0
0
3
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
2
1
0
0
8
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
2
0
0
2
0
0
0
2
0
2
0
1
0
0
1
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
1
0
0
3
0
0
0
2
2
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
2
0
1
0
0
2
0
1
0
3
2
0
0
0
0
1
1
1
0
0
0
0
1
1
0
2
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
1
0
0
0
2
2
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
1
2
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
3
0
0
2
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
2
0
2
2
2
0
0
1
0
0
2
0
0
2
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
1
0
1
0
0
3
0
0
0
1
0
0
1
0
1
1
2
1
2
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
2
2
0
0
1
0
1
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
3
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
8
0
0
0
0
0
0
0
0
4
0
0
0
0
5
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
2
0
0
0
1
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
1
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
4
0
1
0
2
0
3
0
0
0
0
2
2
0
1
0
2
1
0
1
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
1
0
2
2
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
1
4
0
0
1
0
0
0
0
2
1
2
0
0
0
0
1
0
2
2
0
2
0
1
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
2
2
0
1
1
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
2
1
0
0
0
0
1
0
0
3
0
1
0
0
2
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
4
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
3
0
3
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
2
1
2
0
1
0
0
2
0
0
0
0
0
1
0
0
2
0
2
0
0
0
2
0
0
1
2
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
1
2
1
0
0
2
3
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
2
0
0
0
1
0
3
0
0
0
0
0
0
0
0
4
0
1
0
0
2
0
0
1
0
4
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
1
2
0
0
0
3
0
0
0
1
2
2
0
0
0
1
0
0
0
0
0
0
1
0
2
0
2
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
2
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
3
1
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
3
3
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
1
2
0
0
0
0
1
0
0
1
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
2
0
0
0
2
0
0
0
1
2
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
1
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
5
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
1
0
0
2
0
2
1
1
0
0
0
1
1
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
2
1
0
1
1
0
2
0
2
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
6
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
1
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
3
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
1
0
3
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
5
0
0
0
0
0
3
1
0
0
0
1
2
0
0
2
0
0
2
2
2
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
4
1
0
0
0
1
1
0
0
2
0
0
0
1
0
0
0
2
0
0
0
2
2
0
0
0
3
0
2
0
0
0
1
0
1
0
0
0
2
1
4
0
0
0
0
0
0
0
2
1
2
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
3
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
3
0
0
0
0
2
0
0
0
0
2
2
0
2
2
0
0
0
0
1
0
0
0
0
3
1
1
1
0
0
0
0
1
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
2
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
3
1
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
2
2
0
0
0
3
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
6
1
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
3
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
2
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
3
0
0
0
0
0
0
3
1
0
0
0
0
0
0
2
0
0
1
0
0
6
0
0
0
1
0
0
0
1
0
3
0
0
0
0
0
0
0
4
1
0
0
1
1
0
0
0
1
1
1
0
0
0
1
3
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
1
0
2
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
2
0
0
0
2
1
0
1
0
0
0
2
3
0
0
0
0
0
0
0
0
2
1
3
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
1
0
1
4
1
0
0
2
0
0
2
0
0
0
0
2
4
1
0
0
0
0
0
1
1
2
4
0
0
0
2
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
2
0
0
1
0
7
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
3
0
0
1
0
1
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
2
0
2
2
0
0
0
0
0
1
2
1
0
3
2
3
0
0
1
0
0
0
0
0
0
0
0
0
0
3
2
0
1
0
0
0
0
0
0
0
0
1
0
2
0
2
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
1
3
0
0
0
2
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
3
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
2
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
4
1
0
1
0
0
0
0
2
0
1
2
0
0
0
0
0
2
0
2
0
3
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
3
0
0
0
0
1
4
0
2
0
1
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
3
1
0
0
4
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
3
1
0
1
0
0
1
0
0
3
0
0
3
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
3
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
2
0
0
0
0
0
0
0
2
0
0
3
1
0
0
0
0
1
2
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
4
0
2
0
2
3
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
3
0
2
1
0
0
2
0
0
0
2
1
0
0
0
2
0
0
1
0
0
2
1
0
0
0
0
2
1
0
0
0
1
2
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
1
2
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
1
0
1
0
1
0
0
0
4
0
0
2
0
0
0
0
0
2
4
2
0
1
0
2
0
1
0
0
0
1
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
2
0
0
1
0
4
1
1
0
0
0
2
1
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
2
0
2
0
0
0
0
0
0
2
1
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
2
0
0
0
2
0
0
2
0
2
1
0
1
0
2
1
1
1
0
0
0
0
1
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
2
0
0
2
0
0
1
0
2
0
0
1
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
1
0
0
0
2
2
0
2
0
0
1
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
3
0
1
0
0
0
0
1
1
0
2
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
4
0
1
1
0
2
0
0
0
0
0
1
0
9
0
0
0
0
0
2
0
0
0
2
1
0
6
0
0
1
0
1
0
2
0
1
0
0
0
1
0
0
0
0
2
1
0
0
2
1
0
0
2
0
0
2
0
3
0
0
0
0
0
1
0
0
0
0
0
1
0
3
0
1
0
0
1
0
0
2
0
0
3
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
4
0
0
1
0
0
1
0
1
0
1
1
4
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
4
1
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
1
1
0
0
0
3
0
0
0
2
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
1
2
0
0
0
0
2
0
0
0
0
1
0
0
0
1
2
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
2
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
2
2
1
0
0
2
2
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
2
1
0
2
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
2
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
1
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
2
0
1
0
0
0
2
2
2
2
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
9
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
2
1
0
0
2
4
0
0
1
0
2
0
2
1
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
4
0
0
2
1
2
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
2
0
2
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
1
1
3
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
2
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
2
0
0
0
0
2
0
0
1
0
0
0
2
0
2
1
0
0
0
0
2
0
0
0
0
0
2
3
1
2
0
0
0
2
0
0
1
0
3
0
1
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
2
2
0
1
0
2
0
0
0
2
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
2
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
2
2
1
0
2
0
0
0
0
3
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
2
0
0
2
0
2
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
2
1
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
3
3
0
0
1
0
0
2
0
2
0
0
1
0
0
0
1
0
3
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
3
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
1
2
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
2
0
1
0
2
0
2
0
0
2
0
0
0
2
1
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
1
2
2
0
0
0
0
0
2
1
0
0
2
0
0
0
1
0
1
0
0
2
1
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
1
0
0
1
1
1
0
0
1
0
2
0
0
0
3
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
2
1
0
2
0
2
1
0
2
1
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
2
1
0
0
0
0
0
0
0
1
0
2
1
0
1
0
0
0
0
0
0
0
2
3
0
0
2
0
1
0
0
1
0
3
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
1
0
1
2
0
2
1
0
7
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
1
0
2
0
2
0
0
0
1
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
2
2
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
1
2
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
3
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
3
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
5
0
1
0
1
0
2
2
0
0
0
1
2
2
2
0
2
0
0
0
0
0
0
0
0
2
0
0
2
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
2
0
2
0
1
0
3
0
0
0
0
2
0
1
2
1
0
0
0
0
0
6
1
2
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
1
3
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
1
2
3
1
0
0
4
2
0
2
0
0
0
2
0
0
0
0
0
0
4
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
2
1
0
1
0
2
0
0
0
0
2
0
0
2
0
0
1
4
0
0
2
1
0
1
1
0
0
2
0
1
0
0
0
2
2
0
1
2
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
2
0
0
2
0
2
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
2
1
0
1
1
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
1
2
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
4
0
0
1
2
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
2
1
0
1
2
0
0
0
1
0
2
0
0
0
0
4
1
0
0
1
0
0
0
0
1
0
1
0
1
0
0
4
1
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
2
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
1
0
0
1
0
0
0
3
1
0
2
0
1
0
0
0
0
0
1
2
0
0
0
0
0
1
0
1
0
0
2
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
2
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
1
1
0
0
1
0
0
1
0
2
0
0
0
0
1
1
0
0
0
1
0
0
0
1
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
2
1
0
1
3
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
1
3
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
2
2
0
0
0
0
1
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
3
2
0
0
0
0
0
0
0
1
2
6
0
0
0
0
0
1
0
0
2
0
0
2
0
0
1
2
1
0
1
0
0
3
0
0
1
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
1
1
0
2
1
0
0
3
0
0
0
0
2
0
0
2
0
0
0
1
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
1
2
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
2
0
0
1
0
2
0
0
2
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
1
0
2
1
0
1
0
3
0
1
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
1
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
3
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
3
0
0
0
0
4
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
2
0
0
0
0
10
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
2
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
2
0
0
0
0
0
2
0
0
1
0
2
2
0
1
0
0
0
6
0
1
1
0
0
0
0
3
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
2
2
0
3
2
0
0
1
0
0
2
3
0
1
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
1
0
0
0
1
0
0
3
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
2
0
0
1
2
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
2
0
0
0
0
3
0
0
0
8
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
5
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
4
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
2
1
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
3
0
0
0
0
0
1
0
2
0
2
0
2
0
0
0
0
0
4
0
0
1
0
1
0
1
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
3
0
0
0
4
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
5
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
2
1
1
1
0
0
3
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
3
0
0
0
1
0
4
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
2
0
0
1
1
0
0
1
2
0
0
2
0
0
1
0
0
0
0
2
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
5
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
1
0
0
1
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
1
2
0
2
0
2
0
0
1
1
0
1
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
3
1
0
0
0
2
0
0
0
2
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
4
2
0
0
0
0
2
0
1
0
2
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
2
1
3
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
1
0
0
0
1
0
1
1
2
1
0
0
2
2
0
0
2
2
0
0
0
0
0
2
0
0
6
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
3
1
0
1
0
0
0
2
2
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
2
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
2
2
0
0
1
0
2
1
0
0
0
0
0
0
0
0
1
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
1
0
2
1
0
1
1
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
3
0
0
0
0
0
2
2
1
2
0
0
0
2
1
1
0
2
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
1
0
0
1
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
2
0
0
2
2
0
2
2
0
0
0
0
2
2
0
1
2
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
2
0
0
0
2
0
0
0
2
0
0
0
1
0
0
1
3
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
3
1
0
0
1
1
0
0
0
0
1
0
0
0
1
2
0
2
0
0
0
2
0
0
1
0
2
2
2
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
4
0
0
1
0
0
1
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
3
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
1
1
1
0
0
0
2
0
1
0
1
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
2
0
1
2
0
0
3
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
2
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
1
1
2
0
0
0
0
2
0
1
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
1
2
0
0
0
2
1
0
0
0
0
0
1
2
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
5
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
1
2
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
1
5
0
1
0
0
0
0
0
3
1
0
0
3
0
0
0
0
2
0
2
0
0
1
0
0
3
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
1
1
0
2
0
0
3
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
1
2
3
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
3
0
3
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
3
1
0
0
0
0
1
0
1
0
2
0
0
0
0
0
1
1
0
2
0
0
2
0
0
0
1
0
0
0
0
3
1
0
1
0
0
1
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
1
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
5
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
3
2
0
0
0
1
2
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
3
2
3
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
2
0
0
0
1
1
0
0
0
3
0
4
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
2
0
1
0
2
0
0
0
0
1
0
2
2
0
1
0
0
0
0
2
0
0
2
1
0
0
1
0
0
1
0
0
0
0
0
2
2
0
3
0
1
1
0
0
0
3
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
2
0
0
2
0
1
0
0
0
0
1
0
0
2
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
1
2
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
2
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
2
0
0
0
0
1
0
0
0
0
1
0
3
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
2
2
2
0
0
2
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
2
0
2
2
0
2
0
2
0
1
0
2
0
0
1
1
0
2
0
0
2
0
0
0
0
0
0
1
2
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
5
0
0
0
1
0
0
0
1
1
2
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
2
0
3
0
0
0
2
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
2
0
1
1
0
1
0
0
0
0
1
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
1
2
0
2
0
0
3
0
2
1
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
2
0
1
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
1
3
0
0
0
4
1
1
2
1
0
1
0
0
3
0
0
0
0
0
2
0
0
0
2
0
1
0
0
1
0
0
0
0
2
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
1
0
0
0
0
1
0
1
0
2
1
0
0
2
0
0
0
3
0
1
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
19
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
2
1
2
0
2
0
0
0
3
2
0
0
0
0
1
0
0
0
0
3
1
0
1
0
2
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
1
0
2
0
3
0
0
0
0
0
0
0
0
0
7
0
0
0
0
1
0
0
1
0
0
0
0
1
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
3
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
3
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
3
1
6
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
1
0
1
1
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
1
0
1
0
2
2
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
2
1
0
0
0
0
0
1
1
0
2
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
2
2
0
1
1
0
0
1
2
2
2
2
0
2
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
2
1
0
0
3
2
2
0
0
0
0
0
0
0
1
0
0
6
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
3
0
0
0
2
1
0
1
4
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
3
0
0
0
3
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
2
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
2
0
3
1
0
0
0
1
2
0
1
1
3
0
0
0
0
1
0
0
0
0
0
0
0
0
5
0
0
0
1
3
0
0
1
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
1
0
2
4
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
1
1
0
0
0
0
0
0
2
1
0
2
2
2
0
0
4
1
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
2
2
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
1
0
0
1
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
2
4
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
4
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
2
0
0
2
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
2
2
0
0
0
0
0
0
1
1
0
1
0
0
1
2
3
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
1
0
3
0
0
2
0
0
1
1
0
0
0
0
0
0
0
5
1
0
0
1
0
0
3
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
2
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
2
1
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
3
0
1
0
0
0
1
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
4
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
4
0
2
1
0
0
0
1
2
0
0
0
0
2
0
2
0
0
1
2
0
0
0
0
1
0
2
1
2
0
0
0
0
0
0
1
1
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
4
2
0
0
0
0
3
0
1
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
2
1
0
0
2
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
3
0
0
4
5
0
0
1
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
3
2
0
0
1
0
3
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
4
0
0
0
0
1
0
1
0
0
4
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
2
1
1
0
2
0
2
1
2
2
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
2
1
0
0
1
0
2
1
0
0
0
3
0
0
0
1
0
1
2
1
1
0
0
0
0
0
0
0
0
2
0
4
0
0
0
0
3
0
1
0
2
0
0
1
1
1
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
1
0
0
0
1
2
2
0
0
0
0
1
0
0
2
0
1
0
0
0
1
0
3
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
3
0
0
0
0
0
2
1
0
0
0
2
1
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
2
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
2
0
0
0
0
1
2
0
0
2
0
0
0
1
0
4
0
0
0
0
2
0
0
0
1
1
0
2
0
0
0
0
1
0
0
3
2
0
0
0
3
0
1
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
1
2
0
2
0
5
1
1
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
3
0
1
0
2
0
0
3
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
5
1
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
2
1
1
0
0
0
0
0
0
0
2
3
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
2
1
2
0
0
0
0
3
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
2
0
0
2
1
0
0
0
0
1
1
0
3
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
5
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
1
2
0
0
0
1
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
1
0
0
2
0
4
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
2
1
0
0
0
0
0
2
1
1
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
2
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
2
0
2
0
0
1
0
0
0
0
3
0
0
0
3
2
1
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
2
2
0
3
1
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
2
2
0
0
0
2
0
1
0
2
0
1
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
3
0
2
0
0
4
1
0
0
2
0
0
0
2
1
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
5
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
3
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
1
0
2
1
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
2
0
3
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
4
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
2
0
0
1
2
0
0
0
1
0
0
1
4
0
0
0
0
2
2
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
1
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
3
0
6
0
0
0
0
2
0
2
2
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
5
0
1
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
3
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
2
1
0
0
1
0
0
0
0
1
3
0
0
1
3
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
3
0
0
0
2
0
1
2
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
1
0
0
1
2
0
0
0
0
0
0
1
1
0
0
1
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
2
0
1
0
2
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
2
2
0
0
1
0
0
2
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
5
0
2
1
2
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
2
0
2
0
2
2
0
1
0
2
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
1
1
0
0
0
0
2
2
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
2
1
0
0
2
2
0
0
0
2
0
1
3
0
1
0
0
2
0
2
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
1
2
1
0
0
0
1
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
1
1
0
3
1
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
2
2
0
0
1
1
0
1
0
1
0
2
0
0
0
0
1
0
1
3
0
2
1
0
0
0
1
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
1
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
2
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
2
0
1
0
0
0
1
0
0
0
2
0
0
0
0
1
2
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
4
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
1
2
0
0
1
0
3
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
2
0
1
0
4
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
2
0
0
0
0
1
1
0
0
1
0
0
1
0
0
2
0
0
2
0
0
0
0
1
0
2
0
1
2
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
2
0
0
1
0
0
2
0
1
0
0
3
2
0
1
0
2
0
0
0
0
1
0
2
1
2
0
1
2
0
0
0
0
0
2
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
2
0
0
2
0
2
0
0
5
0
0
0
0
3
3
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
2
1
2
2
0
1
1
0
0
0
0
1
0
0
0
0
1
2
1
1
0
0
0
1
1
2
0
0
0
0
1
2
0
0
0
2
0
0
0
2
0
0
0
1
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
4
0
0
3
0
1
0
0
0
0
2
0
0
0
1
0
0
2
0
0
2
0
0
0
2
0
0
0
0
1
0
0
2
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
2
0
1
0
0
1
0
0
2
1
0
0
0
0
0
0
2
0
0
1
0
1
2
0
0
2
0
0
1
2
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
4
0
2
0
0
0
0
0
3
0
2
0
0
0
4
0
0
0
2
0
0
0
0
2
1
0
2
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
2
1
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
4
0
0
1
2
0
0
0
0
0
0
0
0
7
2
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
2
0
0
3
0
1
2
0
0
0
2
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
3
0
0
5
0
0
0
1
0
1
0
2
0
2
1
1
2
0
0
0
0
0
2
0
3
0
2
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
2
0
2
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
2
2
0
1
0
0
0
0
0
0
0
0
2
0
0
2
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
1
0
3
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
1
1
0
2
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
3
0
0
1
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
3
2
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
2
0
2
1
1
0
0
0
0
1
0
0
1
0
0
3
0
0
0
0
0
2
0
0
2
2
0
0
0
1
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
3
0
0
1
0
2
0
1
1
0
0
0
0
0
0
0
2
0
3
0
2
0
0
3
0
1
0
0
2
1
1
0
2
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
2
2
1
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
1
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
1
1
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
2
2
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
8
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
2
0
0
0
1
4
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
5
0
0
0
0
2
0
2
0
0
2
0
0
0
0
1
0
3
0
0
2
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
2
0
1
0
1
0
0
0
1
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
1
0
1
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
1
0
0
3
0
0
0
0
0
3
0
0
0
0
1
2
0
0
0
2
0
1
0
2
0
0
1
0
0
0
0
0
0
0
1
0
2
0
3
0
0
2
0
0
0
0
1
1
0
0
0
0
0
2
0
4
0
0
2
0
0
0
0
0
0
1
0
2
0
2
0
1
0
0
2
2
2
1
0
1
1
0
1
0
0
0
1
0
0
2
1
2
0
0
0
2
0
0
0
0
1
0
0
3
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
3
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
2
0
5
0
1
0
2
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
2
2
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
2
0
3
0
0
0
4
0
2
1
0
0
0
0
0
0
0
0
2
0
2
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
4
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
4
0
0
2
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
6
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
1
2
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
1
0
0
3
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
1
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
2
1
0
0
0
0
2
0
0
0
3
0
0
1
0
2
0
0
2
0
0
3
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
1
2
0
4
0
0
0
0
0
0
1
0
2
0
0
1
1
0
0
0
0
0
0
0
1
5
1
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
2
0
7
0
1
0
0
1
2
1
0
0
0
0
1
1
0
0
2
2
0
0
1
0
0
1
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
3
2
0
0
0
0
1
0
0
1
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
2
0
0
2
0
0
0
0
0
4
0
0
1
0
0
0
0
0
1
3
0
0
0
0
0
0
0
3
1
0
2
1
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
2
0
0
0
1
0
0
0
2
0
2
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
1
3
0
1
3
0
0
2
0
0
0
2
0
0
0
1
0
2
0
0
0
1
0
0
0
0
2
0
0
2
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
1
0
0
0
2
1
0
2
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
4
0
0
0
1
0
2
0
0
0
0
5
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
2
1
2
1
0
0
0
0
2
1
0
4
2
0
2
1
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
2
3
1
0
0
0
0
0
1
0
1
1
0
0
0
1
0
2
0
0
1
0
0
0
1
2
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
3
1
0
0
5
0
0
0
2
0
1
0
1
0
2
0
0
2
0
0
0
1
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
3
0
0
1
0
1
0
0
3
2
0
0
0
0
0
0
3
2
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
1
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
1
0
0
2
2
2
0
2
2
0
1
0
1
0
0
0
0
2
0
0
3
0
2
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
2
0
0
0
2
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
3
1
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
2
0
0
0
1
0
1
0
0
0
1
1
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
3
0
0
0
5
0
0
0
0
0
0
0
3
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
3
0
1
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
2
0
2
0
0
1
0
1
0
0
0
0
0
0
2
2
0
1
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
4
0
0
2
2
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
3
2
2
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
1
1
0
0
0
0
2
2
0
0
1
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
7
0
0
3
0
0
0
1
0
1
0
0
0
1
0
1
0
2
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
3
0
0
1
0
0
2
0
0
0
2
3
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
2
2
0
1
0
1
0
2
0
0
0
2
0
0
0
0
3
2
1
0
2
1
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
2
2
1
0
1
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
4
1
0
0
0
0
0
0
4
0
1
2
0
0
2
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
5
0
1
0
0
0
0
0
0
1
1
0
0
0
1
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
1
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
5
0
0
0
2
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
1
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
4
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
2
1
2
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
3
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
2
1
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
1
2
0
0
0
2
0
0
0
0
0
2
0
0
3
0
0
0
2
0
0
0
0
0
1
4
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
2
0
0
0
3
0
0
2
0
0
0
0
2
0
2
2
2
0
0
1
1
0
2
0
1
0
0
1
0
0
0
0
0
2
1
1
0
0
2
0
1
0
0
2
0
0
0
1
1
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
2
1
0
1
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
3
1
0
0
0
0
5
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
2
0
0
0
2
2
0
2
0
0
0
0
4
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
1
3
2
0
1
0
1
1
0
2
0
2
1
2
2
1
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
3
1
0
1
0
2
0
0
2
0
0
0
2
2
2
0
0
1
0
0
0
0
0
0
0
1
0
0
3
2
0
0
3
2
0
0
0
2
3
0
1
0
0
1
1
0
1
0
0
2
1
1
0
1
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
1
0
0
0
1
0
0
0
2
0
2
0
0
1
0
1
2
3
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
3
0
0
2
0
2
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
1
1
0
2
0
0
1
0
1
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
1
0
0
2
0
0
0
0
0
2
0
0
2
2
0
0
1
1
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
3
1
0
3
0
2
3
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
1
2
0
1
1
2
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
1
0
0
0
4
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
3
1
0
0
2
0
0
0
0
0
0
0
0
1
0
1
2
0
0
2
0
0
0
0
1
0
4
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
2
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
1
0
0
1
0
0
0
0
0
2
0
3
0
0
7
0
0
0
0
2
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
1
2
0
0
0
0
2
1
2
2
0
2
0
0
0
2
0
0
1
0
0
3
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
1
1
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
5
2
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
1
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
2
0
0
1
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
1
1
0
0
0
0
1
1
1
0
3
1
1
0
3
1
0
0
0
0
2
1
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
2
0
1
1
0
1
2
1
0
0
0
0
0
2
1
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
1
0
0
0
2
0
0
0
2
0
1
0
0
0
1
0
3
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
2
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
2
2
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
1
2
0
0
0
0
2
0
1
3
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
1
5
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
4
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
1
0
0
1
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
3
0
0
0
0
2
0
2
1
0
0
0
0
1
0
3
0
0
0
0
2
1
0
0
0
6
0
0
0
0
0
3
0
0
1
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
2
0
0
1
0
0
2
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
2
2
1
0
0
1
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
1
2
0
1
0
2
0
0
4
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
2
1
2
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
2
1
2
2
0
2
0
0
3
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
3
1
1
0
1
0
2
0
0
0
0
0
0
0
0
2
0
1
0
2
1
0
3
0
1
0
0
3
0
0
0
0
0
6
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
3
2
2
0
0
0
0
0
6
2
0
1
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
1
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
4
0
0
0
1
0
0
1
2
1
4
2
0
0
0
0
2
0
0
0
0
2
0
2
2
0
0
0
1
2
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
2
1
0
0
2
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
2
1
0
2
0
1
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
4
0
0
0
1
2
0
0
0
0
0
0
0
0
1
5
0
1
0
2
0
0
2
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
3
1
1
0
0
0
2
0
1
0
0
0
0
0
0
0
4
0
0
1
0
0
0
1
0
0
0
2
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
3
2
0
1
0
1
1
1
0
0
0
1
0
0
0
2
0
0
0
2
2
2
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
3
0
0
0
1
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
1
0
1
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
2
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
5
1
0
0
2
0
1
0
3
0
0
1
0
0
0
0
0
0
1
9
0
0
0
0
0
0
0
2
2
0
2
0
0
1
0
0
0
0
2
0
1
1
1
0
0
1
0
0
0
0
0
2
0
0
0
2
2
0
0
0
4
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
1
5
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
4
0
2
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
1
0
0
1
1
1
0
0
2
0
0
0
1
0
0
1
2
0
1
1
0
2
0
0
0
2
1
0
0
0
0
0
1
0
0
0
2
3
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
1
2
0
0
0
0
0
0
0
3
0
1
4
0
0
0
0
1
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
2
0
1
0
2
0
0
0
2
2
0
0
0
2
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
4
2
0
0
0
0
0
2
2
2
1
0
0
1
0
0
1
0
0
0
2
0
2
0
0
0
0
1
1
0
0
0
0
0
1
2
0
0
2
0
0
1
1
0
0
0
1
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
3
0
0
0
0
0
1
0
2
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
4
1
0
0
0
1
0
0
0
0
0
2
0
2
0
0
4
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
2
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
4
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
2
0
0
1
1
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
2
1
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
2
5
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
1
0
0
0
2
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
2
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
4
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
2
2
0
0
0
2
2
0
0
0
0
0
2
0
1
0
0
0
2
1
2
0
0
0
0
0
0
2
0
0
0
2
1
0
0
2
0
0
0
0
2
1
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
1
1
0
0
1
0
0
1
0
0
0
0
2
0
3
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
4
1
0
1
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
1
1
0
1
2
0
2
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
3
1
2
0
0
0
0
2
0
0
0
1
0
1
6
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
1
0
0
1
0
0
0
2
1
0
0
0
0
0
0
1
0
0
2
0
0
2
0
2
0
0
0
0
0
4
0
0
1
0
0
0
0
4
0
1
0
0
0
1
0
2
2
3
2
0
1
1
0
0
2
3
1
2
1
0
0
0
1
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
1
2
0
0
0
1
0
0
0
0
4
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
1
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
1
1
1
0
0
0
2
0
0
0
1
2
0
0
0
1
0
1
0
0
2
0
0
3
0
0
0
1
0
2
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
2
1
1
0
2
0
0
0
0
2
0
0
2
0
0
0
0
1
1
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
2
0
0
0
0
1
1
0
1
0
0
1
0
0
1
4
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
2
0
0
0
1
2
0
1
1
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
3
1
2
0
0
2
0
0
3
0
1
2
1
0
0
0
1
0
0
1
2
2
0
0
2
1
0
1
1
3
1
0
2
2
0
0
0
0
4
0
0
0
0
0
3
0
2
0
0
0
0
0
0
5
0
1
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
2
3
0
0
0
1
0
0
1
0
2
0
0
0
2
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
3
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
1
2
0
2
2
1
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
2
0
0
0
0
0
0
2
2
3
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
2
1
0
1
2
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
1
1
2
2
0
0
1
0
0
2
0
0
0
0
2
0
0
0
3
1
0
0
0
0
0
0
0
3
3
0
0
0
0
0
1
2
0
0
1
0
0
2
0
0
0
0
0
2
0
2
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
2
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
2
0
3
0
0
0
0
0
1
0
1
0
0
0
0
3
1
2
2
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
2
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
2
2
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
2
1
0
2
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
1
1
0
0
0
0
0
0
0
2
2
1
0
0
0
0
2
2
2
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
1
2
2
1
2
0
1
0
0
3
0
0
0
1
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
1
2
2
0
0
1
2
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
1
1
1
0
3
1
0
0
2
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
1
0
0
0
2
0
0
0
0
2
0
2
0
1
0
2
0
0
1
0
0
0
0
1
0
1
2
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
4
0
0
0
1
0
0
2
4
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
3
0
0
0
0
2
2
1
0
0
0
0
0
3
0
2
2
0
0
2
0
2
1
0
2
0
2
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
7
0
0
0
1
0
1
0
0
1
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
1
1
0
0
2
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
3
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
1
1
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
2
2
0
2
0
1
0
1
0
2
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
1
2
0
0
0
1
0
1
0
0
1
0
0
0
0
0
2
0
0
0
1
1
0
0
0
3
0
2
1
1
2
0
0
0
0
0
0
0
0
1
0
0
0
2
1
2
0
2
2
3
0
1
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
1
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
4
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
2
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
1
0
0
2
0
0
0
2
1
2
1
0
2
0
4
2
0
0
1
0
0
1
0
0
1
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
1
0
2
2
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
1
2
0
1
0
0
0
0
1
1
0
1
0
3
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
1
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
1
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
1
2
1
0
2
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
8
0
0
2
0
1
0
0
0
0
2
2
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
1
0
1
0
1
0
0
2
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
4
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
2
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
3
2
0
0
1
0
0
1
0
0
1
1
0
0
1
0
0
1
0
0
1
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
7
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
2
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
2
0
1
0
0
0
0
1
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
2
2
1
2
0
0
1
1
0
1
0
0
0
1
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
4
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
4
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
1
1
0
1
1
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
8
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
2
1
0
0
0
0
0
1
2
0
1
2
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
4
0
1
0
0
0
0
0
1
0
0
2
0
1
2
0
3
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
2
2
0
0
0
0
0
0
0
0
2
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
5
0
0
0
0
0
0
1
0
3
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
1
0
4
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
1
1
2
0
2
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
1
0
0
2
1
0
0
0
2
0
1
1
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
1
2
0
0
2
0
0
3
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
1
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
3
0
2
2
2
0
0
1
0
3
1
0
0
2
1
0
0
0
0
0
0
0
1
0
0
3
0
1
0
0
1
0
2
0
0
0
2
0
1
0
0
1
0
0
0
0
1
1
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
2
0
3
0
0
0
0
2
0
0
0
0
0
0
1
0
2
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
1
1
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
3
0
1
0
2
0
0
0
0
1
0
0
2
2
1
0
0
3
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
1
1
2
0
0
0
0
0
2
0
1
0
0
0
0
1
0
2
0
0
1
0
1
2
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
4
0
0
0
2
0
0
0
2
0
4
0
1
3
0
0
0
0
0
0
2
0
2
0
1
2
0
0
0
0
0
0
0
2
0
0
0
1
1
4
0
0
0
1
1
2
1
1
2
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
2
3
0
0
0
0
0
0
0
0
0
2
0
2
2
1
1
0
0
0
0
0
0
0
0
2
2
0
1
0
0
4
0
0
0
0
4
0
4
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
3
3
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
7
0
0
2
1
1
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
2
0
0
0
0
0
0
1
2
1
0
2
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
2
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
2
0
1
0
0
2
2
0
0
1
2
3
0
2
0
2
0
0
3
0
0
0
1
0
2
0
0
0
1
1
2
0
2
2
2
1
0
0
0
1
0
2
0
0
0
0
2
2
2
0
1
1
0
0
2
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
0
2
3
1
0
0
0
1
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
2
0
0
2
0
1
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
2
0
0
1
8
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
3
2
0
2
0
1
3
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
1
1
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
3
0
0
1
1
1
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
2
1
1
0
0
2
0
0
1
0
1
1
0
0
1
0
0
0
0
0
3
0
0
2
0
0
1
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
8
1
0
0
2
0
0
0
3
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
3
3
0
0
0
0
0
0
2
1
1
2
0
0
1
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
1
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
1
1
0
4
1
1
0
1
0
0
0
2
0
2
0
1
2
0
0
0
0
0
0
2
1
2
0
0
0
1
2
1
0
0
0
1
0
2
0
0
2
0
0
0
0
2
1
0
0
0
0
0
1
0
2
0
0
0
0
0
3
2
0
0
0
0
0
0
0
2
0
0
0
0
2
1
1
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
1
3
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
1
0
2
0
3
0
0
2
0
0
0
0
2
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
3
0
0
2
0
0
0
0
0
0
2
0
3
3
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
2
0
1
0
1
0
1
0
0
1
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
3
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
3
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
1
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
2
2
1
0
1
1
0
0
0
0
0
0
3
0
0
0
2
0
0
0
1
1
0
0
5
0
0
0
0
0
2
1
0
2
0
0
0
2
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
3
2
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
4
2
2
3
1
0
0
0
1
0
0
0
0
0
2
1
0
0
0
1
0
0
1
0
0
0
2
4
0
3
0
1
0
0
0
0
2
2
4
1
0
0
0
0
0
2
1
2
0
0
0
3
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
1
1
0
0
4
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
4
0
0
1
1
1
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
4
0
0
0
0
0
0
1
0
2
0
5
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
1
0
0
2
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
9
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
2
3
0
0
2
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
2
2
0
2
2
1
2
0
0
0
2
0
0
0
0
0
1
2
0
4
0
1
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
3
1
1
1
0
0
0
1
1
1
0
0
0
0
0
0
1
2
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
3
0
0
0
0
2
0
0
0
1
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
1
1
0
1
0
1
1
3
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
1
0
2
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
2
0
2
1
0
4
2
0
0
0
0
0
1
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
1
2
0
0
1
0
0
2
0
0
1
2
0
1
1
1
0
0
2
0
0
0
0
2
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
2
0
2
0
2
0
1
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
2
2
0
0
0
3
0
0
0
0
0
2
0
4
0
0
0
0
2
0
0
1
0
0
3
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
3
0
0
1
2
0
0
0
3
2
0
0
0
0
0
1
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
2
0
0
0
0
0
0
2
2
2
0
0
0
0
1
0
0
0
2
0
0
2
0
0
1
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
3
0
2
2
0
0
0
0
0
0
1
0
0
0
1
1
0
0
2
0
0
3
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
3
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
2
1
2
0
0
0
2
1
1
1
1
0
0
0
0
1
0
2
0
0
2
2
0
0
0
1
0
2
0
0
0
0
0
0
3
2
0
2
0
2
0
0
0
0
2
0
1
2
0
0
0
1
0
1
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
2
0
1
1
0
1
0
2
0
0
0
0
0
0
1
2
1
0
2
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
4
0
0
2
0
1
0
1
2
0
0
2
0
0
4
0
2
0
2
1
0
0
0
0
0
0
0
1
1
0
2
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
1
1
0
0
1
0
2
0
0
0
0
1
0
4
2
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
1
0
2
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
1
1
1
1
0
2
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
2
0
4
0
0
0
6
0
0
1
2
0
0
0
0
0
1
0
3
0
0
1
0
0
0
1
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
4
2
0
0
0
0
2
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
3
1
2
0
0
0
0
0
0
2
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
2
2
1
0
0
1
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
2
0
0
2
0
1
2
2
0
0
0
2
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
2
0
0
0
0
0
0
0
0
1
0
1
0
0
1
2
0
0
0
0
1
0
3
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
1
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
3
5
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
1
1
0
1
0
1
2
1
0
0
0
2
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
2
0
1
0
3
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
3
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
2
1
0
0
0
3
0
0
2
0
0
2
3
2
0
0
0
2
1
0
0
2
1
1
0
0
2
2
1
2
2
1
0
2
0
0
0
0
0
0
1
0
1
0
2
2
1
0
1
0
0
2
0
0
0
0
0
4
0
0
2
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
6
0
0
2
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
4
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
1
0
0
0
2
0
0
2
2
0
0
0
0
4
0
1
1
2
0
2
0
0
1
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
1
0
0
2
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
2
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
1
0
0
0
0
1
2
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
2
0
0
3
0
0
0
0
0
0
0
2
0
1
2
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
1
2
0
3
1
0
0
3
0
0
1
0
0
0
1
0
0
0
0
0
0
2
1
0
0
2
1
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
1
0
2
0
5
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
2
1
2
2
0
0
1
2
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
8
0
0
0
0
2
0
0
1
2
0
2
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
7
0
2
0
0
0
0
0
0
0
0
2
0
1
0
1
0
1
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
3
7
1
0
0
0
0
0
0
1
0
1
0
1
0
0
2
0
1
0
0
0
0
0
2
1
0
0
1
1
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
1
3
3
0
0
0
2
0
0
1
1
1
0
0
1
1
0
0
0
0
0
1
0
2
1
0
0
1
2
0
0
0
0
0
0
2
2
0
3
1
1
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
1
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
1
0
0
2
0
2
0
0
1
2
0
0
2
0
0
2
0
2
0
0
5
0
0
1
0
0
1
0
1
0
1
0
0
1
0
0
0
1
0
1
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
1
1
0
2
0
0
0
4
0
3
1
0
0
2
0
2
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
2
1
2
0
1
0
1
0
2
0
3
0
0
0
0
0
0
0
0
1
0
0
3
1
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
7
0
0
0
0
0
1
1
0
0
2
2
1
2
0
1
0
4
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
3
2
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
2
0
1
0
0
0
1
2
1
1
0
1
0
5
0
0
1
2
2
0
2
2
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
2
0
1
0
0
0
1
0
0
0
1
0
0
0
8
0
0
0
0
1
0
1
1
0
0
3
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
1
0
0
3
0
0
2
1
0
0
0
0
2
2
0
0
2
2
0
2
0
1
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
1
2
0
0
2
0
2
0
0
3
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
2
0
1
0
1
0
0
0
2
0
0
1
2
0
5
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
2
1
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
2
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
1
0
0
1
1
0
0
2
4
0
0
2
0
0
0
2
1
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
12
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
2
1
1
1
0
0
0
0
2
2
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
2
0
2
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
1
0
1
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
2
0
0
1
0
1
0
0
0
0
1
0
4
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
1
0
2
1
1
0
3
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
2
0
0
2
0
0
0
1
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
2
1
0
1
0
0
0
0
0
0
0
2
0
2
1
0
0
0
2
0
1
0
0
0
0
2
2
1
0
3
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
5
2
0
0
0
0
0
0
3
2
0
1
0
3
2
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
2
0
0
2
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
4
0
1
0
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
1
0
1
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
2
0
1
0
0
0
0
1
2
0
2
0
0
0
0
0
1
0
0
0
1
2
0
2
0
4
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
4
0
0
0
0
0
0
3
0
1
0
0
0
0
0
2
1
0
2
0
0
6
1
0
0
0
0
0
0
2
0
0
1
2
0
1
0
0
1
2
0
0
0
1
1
0
0
0
0
0
0
0
6
2
0
0
0
0
2
0
0
1
0
0
0
2
0
1
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
2
0
2
1
2
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
3
0
1
0
0
0
3
0
0
0
0
0
1
3
0
0
0
0
1
1
1
0
2
1
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
1
11
2
2
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
3
0
0
1
0
1
1
1
0
1
0
0
3
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
1
0
1
2
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
4
0
0
1
2
1
2
2
0
0
1
2
0
1
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
1
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
1
1
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
3
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
1
1
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
2
2
2
0
1
0
0
1
0
0
0
7
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
2
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
3
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
2
3
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
1
0
2
1
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
3
1
0
2
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
1
2
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
2
2
1
0
1
1
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
1
1
0
0
0
1
0
6
1
0
1
0
0
0
0
0
1
2
1
1
1
1
0
0
0
1
0
0
2
0
0
1
0
0
0
0
2
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
2
1
2
0
0
0
1
0
0
3
0
0
0
0
0
0
0
2
0
1
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
1
2
1
1
0
3
0
0
0
1
0
0
0
0
1
1
1
3
2
3
2
0
1
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
3
1
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
13
2
0
2
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
2
1
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
2
0
0
1
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
4
0
0
1
2
1
0
2
0
1
2
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
5
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
1
2
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
1
1
0
2
0
1
1
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
2
0
3
0
2
0
2
1
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
2
2
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
2
2
2
0
0
2
0
0
0
1
1
0
0
1
2
0
0
0
0
2
0
0
0
0
1
3
0
0
0
0
0
1
0
0
0
0
0
2
1
0
2
0
0
0
0
0
2
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
3
1
1
2
1
1
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
1
0
0
2
0
1
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
5
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
2
3
0
0
0
1
0
0
0
1
0
2
2
0
0
2
0
0
0
0
3
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
2
0
0
1
1
1
1
0
0
1
2
0
0
0
0
0
3
1
0
0
0
0
0
0
1
0
4
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
1
2
1
0
2
0
0
0
3
0
3
1
1
1
2
1
0
1
0
0
0
0
2
0
0
2
2
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
1
2
0
0
0
0
0
0
0
0
0
3
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
1
0
1
1
1
0
4
0
1
1
0
2
1
0
0
0
1
0
0
2
0
0
2
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
1
1
0
0
0
0
0
1
1
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
3
0
0
1
7
0
0
0
0
0
0
0
0
0
1
0
2
0
1
6
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
1
2
2
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
1
0
4
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
2
0
2
2
1
0
1
0
0
3
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
1
1
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
4
0
0
2
0
0
1
3
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
2
1
0
0
0
0
0
1
2
2
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
2
3
0
0
0
0
0
4
0
1
0
0
0
1
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
1
0
2
0
0
2
0
0
1
1
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
1
2
2
0
5
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
3
0
0
0
0
1
1
1
2
1
1
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
2
2
0
1
0
2
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
3
0
0
2
1
0
1
0
2
0
0
1
3
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
1
0
0
3
1
0
1
0
2
0
0
3
0
0
0
0
1
0
0
0
2
2
0
0
1
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
3
0
0
0
0
1
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
2
0
0
2
2
0
0
0
4
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
1
0
2
0
0
1
0
0
0
1
0
0
1
0
2
1
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
5
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
2
0
5
0
1
0
1
1
2
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
5
0
0
2
2
1
2
0
0
3
2
0
1
0
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
2
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
2
2
2
1
1
0
0
0
2
1
0
0
0
0
0
0
3
0
0
0
0
1
0
2
0
0
0
1
0
0
2
0
0
0
0
0
2
1
0
1
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
4
0
1
0
0
0
0
0
0
4
0
0
0
2
0
1
0
0
0
3
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
3
0
1
0
0
0
2
0
2
0
0
0
0
1
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
2
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
1
0
1
0
1
0
0
0
2
2
0
0
2
0
0
0
2
0
0
0
0
0
0
3
1
0
2
0
0
1
0
1
1
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
2
1
0
0
0
1
1
0
2
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
6
0
0
0
3
0
0
2
0
0
0
0
1
0
1
0
1
0
1
0
0
0
1
1
0
0
2
0
0
0
0
0
0
2
0
0
0
2
3
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
2
0
1
3
0
0
4
3
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
2
1
0
0
1
0
0
0
1
1
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
2
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
1
1
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
2
0
1
0
2
0
0
1
0
4
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
5
4
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
6
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
8
0
2
1
0
0
0
4
0
0
1
0
1
0
0
0
0
2
1
6
0
0
0
0
1
0
1
0
7
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
2
0
2
0
0
0
0
0
0
0
1
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
5
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
2
1
0
0
1
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
9
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
3
0
2
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
1
1
0
0
0
0
0
0
2
2
4
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
1
0
1
2
0
0
3
2
1
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
3
0
0
0
3
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
2
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
1
0
1
1
1
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
1
1
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
3
0
0
3
0
3
0
0
0
1
0
0
1
0
0
1
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
1
2
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
1
1
1
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
2
1
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
3
0
1
0
0
0
0
0
0
2
1
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
2
1
2
1
0
0
1
0
2
1
1
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
2
0
1
0
2
0
0
0
0
2
1
0
3
0
2
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
3
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
1
0
2
0
0
2
1
0
0
1
0
3
0
0
0
2
1
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
2
0
1
0
0
2
1
0
0
0
0
0
0
1
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
2
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
1
0
2
2
0
0
0
0
1
1
0
0
0
1
0
2
0
0
2
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
2
2
0
0
0
0
0
2
0
0
4
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
1
1
0
1
0
2
3
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
3
1
0
0
0
0
0
2
2
0
2
0
0
0
1
1
0
3
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
2
2
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
3
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
2
0
0
0
0
1
0
1
3
0
1
2
0
2
0
0
0
2
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
1
2
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
2
0
0
1
0
1
2
1
0
0
0
1
0
0
2
0
3
0
0
0
2
0
2
0
0
0
2
2
1
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
3
0
0
0
1
1
2
0
0
1
0
0
1
0
0
0
0
2
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
2
2
0
1
2
2
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
1
0
3
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
1
0
0
2
1
0
0
0
0
0
0
1
2
6
0
1
0
4
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
3
1
0
0
0
0
2
1
0
0
0
0
0
2
0
1
0
1
2
0
0
2
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
2
1
0
0
0
0
0
1
0
0
1
0
0
0
2
2
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
2
0
1
0
0
0
1
6
2
0
0
1
0
2
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
1
0
0
1
0
1
2
0
0
2
0
0
0
2
0
0
2
0
0
1
1
0
0
0
0
4
0
0
0
1
0
2
1
0
0
0
0
0
1
0
0
0
0
3
1
0
0
0
0
0
2
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
3
0
1
0
1
0
1
1
0
0
1
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
1
0
0
4
0
0
0
0
2
0
0
1
0
2
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
1
0
0
0
0
0
0
1
0
0
1
1
1
2
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
1
2
0
0
0
2
2
3
0
1
0
1
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
1
1
0
0
0
0
0
1
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
2
0
1
0
0
2
0
0
0
10
0
2
0
0
0
2
1
1
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
4
0
3
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
3
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
1
2
0
0
2
2
0
0
1
0
0
0
2
0
0
0
1
1
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
2
0
0
0
1
2
0
0
1
0
0
2
0
0
0
0
0
0
2
1
1
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
2
0
0
0
0
4
2
0
1
0
0
2
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
2
2
0
1
0
0
5
0
0
0
1
0
1
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
2
1
0
0
0
2
2
2
0
1
1
0
0
2
0
1
0
0
0
0
0
1
3
1
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
1
3
0
2
1
0
2
0
0
0
0
1
7
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
4
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
2
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
2
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
2
1
0
1
1
0
0
2
2
0
0
2
1
0
0
0
2
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
2
0
1
0
1
1
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
10
0
1
0
1
0
1
2
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
1
0
1
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
2
0
0
3
0
6
2
2
1
0
0
0
0
0
1
0
0
0
0
0
4
0
2
0
2
0
0
0
2
0
1
0
0
1
0
2
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
1
0
0
1
2
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
2
0
0
0
1
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
3
0
0
2
2
1
0
0
0
0
1
1
0
2
0
2
0
1
1
1
2
0
0
1
0
1
0
1
2
1
1
1
0
1
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
2
2
0
0
1
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
7
1
2
0
2
0
3
1
0
0
1
1
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
5
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
1
2
1
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
3
0
1
1
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
2
0
0
0
2
0
0
0
0
0
1
0
1
0
0
1
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
1
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
3
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
2
0
4
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
4
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
1
0
2
1
0
0
0
1
2
0
0
0
0
1
0
1
1
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
2
3
0
0
0
2
1
0
0
1
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
2
1
1
0
2
2
0
0
2
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
6
0
2
2
0
2
0
0
0
0
0
0
2
0
0
0
0
1
3
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
1
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
3
0
0
2
1
0
0
0
0
0
4
1
1
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
4
0
0
2
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
1
1
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
2
2
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
3
2
2
0
0
0
2
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
4
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
3
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
1
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
1
1
1
0
2
0
2
0
0
0
1
0
0
0
3
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
2
0
0
0
1
2
1
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
3
5
1
0
3
0
0
0
0
0
0
3
1
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
3
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
1
1
0
0
0
0
2
1
0
0
2
0
0
2
0
0
0
0
0
2
2
0
1
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
1
0
1
0
0
2
2
0
2
0
0
0
3
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
2
0
0
1
0
1
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
4
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
2
1
0
2
0
0
2
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
13
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
4
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
8
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
3
0
2
0
2
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
8
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
1
0
2
2
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
2
0
2
3
0
0
1
0
0
0
1
0
2
0
0
1
1
0
1
0
0
0
0
0
0
0
1
1
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
1
0
6
0
0
0
0
0
0
0
0
5
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
1
0
1
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
2
1
1
0
0
2
0
0
1
0
0
0
2
0
0
0
1
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
1
0
0
1
0
0
0
1
0
0
0
2
1
0
1
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
2
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
5
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
2
2
0
0
1
0
1
3
0
2
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
1
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
1
2
0
2
2
0
0
2
0
0
1
0
0
0
0
4
0
0
0
1
0
0
0
3
0
0
0
1
8
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
1
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
1
0
0
0
0
0
0
0
1
1
0
3
0
0
1
0
0
0
0
0
0
0
6
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
2
0
0
0
0
0
0
0
1
1
1
2
0
0
0
0
0
0
2
0
1
2
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
1
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
3
0
0
0
1
2
1
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
3
0
1
1
0
0
2
0
2
1
0
2
2
0
1
0
3
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
2
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
2
0
0
0
0
0
2
0
0
1
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
2
0
2
0
0
0
2
0
0
0
0
2
1
2
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
1
0
0
2
1
1
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
2
1
0
0
4
1
0
0
0
2
1
0
0
2
0
1
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
2
0
2
0
2
2
1
0
0
0
2
0
5
2
0
0
0
0
0
0
2
0
1
3
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
2
1
0
0
0
0
0
0
0
3
2
1
0
1
1
1
2
0
2
0
0
0
0
0
2
0
2
0
1
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
2
0
0
2
0
0
2
0
0
0
2
0
0
2
2
1
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
5
0
0
0
0
0
1
4
2
0
0
1
0
3
0
2
5
0
0
0
4
3
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
3
1
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
1
2
0
0
0
3
0
0
0
0
0
1
0
1
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
2
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
2
0
0
0
2
0
0
0
0
2
1
0
0
0
1
0
1
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
1
2
2
0
0
0
0
2
0
2
0
1
0
0
0
2
3
2
0
1
0
0
0
2
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
1
0
2
1
3
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
2
1
0
0
1
0
0
2
0
0
0
0
3
0
2
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
2
3
0
0
2
4
0
0
0
1
0
0
0
0
1
0
0
0
0
0
9
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
4
0
0
0
0
2
2
0
1
0
0
0
0
2
2
1
0
0
0
0
0
2
2
3
1
1
0
0
2
0
0
0
0
0
1
0
0
0
0
3
1
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
1
2
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
3
0
0
0
0
2
1
0
0
0
0
0
0
1
2
0
0
2
0
1
1
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
2
0
3
0
0
0
0
1
3
0
0
0
3
3
0
0
0
0
0
0
0
0
1
0
1
2
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
1
1
0
0
0
2
2
2
0
0
0
1
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
2
0
0
0
2
0
0
0
2
0
0
0
0
1
0
2
0
1
0
0
0
1
0
0
1
2
1
0
0
0
2
0
3
0
1
0
0
0
4
0
0
0
2
1
1
0
1
1
1
0
0
0
0
0
8
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
1
0
0
0
0
1
0
0
0
2
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
4
0
0
3
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
5
1
0
0
0
2
1
0
0
0
0
1
0
4
0
2
0
1
2
0
0
0
0
0
0
0
2
0
0
1
2
1
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
6
0
0
0
0
2
0
0
0
2
0
0
0
2
4
1
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
2
2
0
0
2
1
0
0
2
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
2
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
2
0
2
1
0
0
0
1
0
3
0
0
0
0
0
2
0
2
0
1
0
0
0
0
1
2
0
3
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
2
0
1
0
0
1
2
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
2
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
1
1
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
1
0
1
0
0
0
2
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
2
2
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
2
0
0
0
0
4
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
5
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
1
0
0
2
0
2
0
0
1
0
0
0
3
1
4
1
3
3
2
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
1
0
0
0
0
0
0
0
2
1
1
1
0
0
0
2
0
0
0
2
0
0
0
1
0
0
1
2
1
0
0
1
2
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
1
0
2
2
1
0
0
0
0
1
0
0
0
0
3
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
1
0
0
0
0
0
0
2
2
0
4
0
0
0
0
2
0
1
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
2
1
1
0
0
1
2
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
2
2
0
0
0
0
0
2
1
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
2
0
0
1
0
0
0
0
2
1
0
0
0
2
2
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
2
2
1
2
2
0
0
0
0
1
0
0
0
3
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
3
0
1
0
0
4
2
0
0
2
0
0
1
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
1
0
0
2
0
2
1
0
0
0
0
0
2
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
5
1
0
2
0
2
0
2
0
0
4
0
4
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
2
1
0
0
0
4
1
0
1
1
0
0
0
0
0
2
1
0
0
0
0
0
2
0
2
3
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
1
0
0
2
0
3
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
1
2
0
1
0
0
2
0
1
2
0
0
0
0
0
0
0
0
1
0
2
1
0
1
2
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
2
2
0
0
0
0
0
2
0
0
0
0
0
1
2
0
1
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
3
0
0
0
0
0
2
2
2
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
1
1
1
4
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
1
1
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
1
1
0
0
0
3
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
1
0
3
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
2
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
3
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
1
2
1
1
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
1
0
0
0
3
2
0
1
2
0
0
0
0
0
0
3
0
2
0
1
0
1
0
0
0
0
0
1
0
2
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
1
1
0
1
0
0
1
0
0
0
0
3
0
0
0
0
0
2
1
2
0
0
0
3
0
1
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
3
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
3
0
1
0
1
0
1
0
0
4
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
2
0
0
2
2
2
0
1
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
1
2
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
1
2
0
0
0
0
0
0
3
0
1
2
0
1
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
4
0
0
1
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
2
2
0
0
0
1
0
2
0
0
0
1
0
2
0
0
2
2
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
3
3
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
3
1
3
0
0
0
0
2
0
1
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
4
0
0
2
0
0
1
0
0
0
0
2
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
2
1
1
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
2
0
1
0
0
3
0
0
0
2
0
2
0
1
2
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
2
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
3
2
3
0
0
0
0
2
2
3
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
5
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
3
0
6
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
3
0
1
0
4
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
1
0
1
2
0
0
5
0
0
6
0
0
0
0
0
0
5
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
1
0
2
0
0
4
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
3
2
1
2
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
1
0
2
0
0
0
0
0
2
0
0
1
1
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
2
0
0
0
1
2
0
0
1
0
4
2
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
1
1
0
0
1
2
0
1
0
0
2
0
0
0
0
0
4
0
0
0
1
0
1
0
2
0
0
0
0
0
2
0
3
0
1
0
1
0
0
0
0
0
2
2
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
1
1
0
0
0
0
0
1
2
0
3
0
0
3
2
0
0
0
0
0
0
2
0
0
0
2
2
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
2
0
0
0
2
0
0
0
0
0
2
0
2
0
2
2
2
0
2
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
2
9
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
3
2
0
1
2
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
1
0
0
0
0
0
3
0
0
1
0
0
5
0
0
2
1
0
2
1
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
1
0
0
1
1
4
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
1
0
2
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
2
0
1
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
2
2
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
1
0
1
0
0
0
0
2
2
0
0
0
2
0
1
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
2
0
1
0
0
0
0
0
0
0
1
3
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
2
0
0
0
4
0
0
2
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
10
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
4
0
1
0
0
0
0
6
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
1
0
5
0
1
0
2
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
4
2
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
2
1
0
0
0
0
0
3
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
3
0
0
0
0
0
2
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
2
0
0
0
0
0
4
0
0
0
1
1
0
0
0
0
0
2
0
0
0
2
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
1
0
3
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
2
0
3
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
2
1
0
0
1
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
2
0
0
2
3
2
1
3
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
0
0
2
0
2
0
1
3
0
0
2
1
0
0
0
0
1
0
0
0
0
1
2
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
2
2
0
4
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
3
2
2
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
1
0
0
2
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
2
4
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
1
0
1
2
2
1
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
1
1
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
2
2
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
3
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
4
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
1
2
0
1
0
0
1
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
1
0
1
0
2
5
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
4
1
0
0
1
0
1
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
1
0
0
0
0
0
1
0
0
5
0
1
0
1
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
2
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
2
2
1
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
3
0
2
2
1
0
0
1
0
0
0
1
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
7
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
2
0
2
0
3
0
0
1
1
1
0
0
0
1
0
0
2
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
4
0
2
0
1
0
0
2
0
2
0
0
0
0
0
0
2
0
0
2
0
0
1
2
0
0
0
0
1
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
3
0
0
1
2
0
0
0
2
1
0
0
0
1
0
0
0
2
1
1
0
0
0
0
1
0
0
0
0
2
0
1
0
1
3
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
2
2
0
2
1
0
0
1
0
0
3
1
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
1
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
2
0
1
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
1
0
0
0
4
0
2
1
0
0
1
0
1
0
0
0
0
0
2
2
0
0
0
0
2
0
2
2
1
1
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
1
0
3
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
6
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
2
0
2
0
0
0
2
1
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
3
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
1
2
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
3
0
1
0
0
1
0
1
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
2
1
0
0
0
0
0
1
0
1
0
0
0
0
2
0
2
0
0
2
0
3
2
0
2
2
2
0
0
2
0
0
0
0
0
1
0
1
1
2
0
2
0
0
0
2
0
0
0
0
1
0
0
2
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
3
2
1
0
0
0
0
2
1
1
1
0
0
0
0
0
2
0
0
0
0
0
2
0
2
1
0
0
2
0
1
0
0
0
0
1
1
3
0
0
0
0
2
1
1
0
0
0
1
0
0
1
0
1
2
0
1
1
0
0
0
3
0
1
0
2
1
0
0
0
0
1
0
0
3
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
1
2
2
0
0
0
1
3
1
0
0
3
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
4
2
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
2
1
2
0
2
3
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
2
0
1
2
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
1
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
1
2
2
0
0
0
0
1
0
0
1
0
1
0
0
0
0
2
1
0
2
2
0
1
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
1
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
1
0
0
0
0
1
0
0
3
0
0
0
7
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
1
2
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
1
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
1
3
0
0
1
0
0
4
0
0
0
0
0
1
6
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
5
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
3
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
1
0
2
0
2
2
0
0
0
1
0
2
1
0
2
1
0
0
3
2
0
2
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
1
2
1
0
0
0
1
0
1
0
0
1
2
0
3
0
0
0
0
0
2
1
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
2
0
1
0
0
2
1
0
0
0
0
3
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
4
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
3
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
2
4
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
1
1
5
1
0
0
1
0
0
0
3
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
3
0
1
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
2
2
0
4
0
2
0
1
0
0
0
4
0
0
3
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
3
0
0
0
2
1
1
2
4
1
0
0
0
0
0
2
2
0
2
0
2
0
0
0
0
2
2
0
0
0
0
2
0
4
2
0
2
0
7
0
0
0
0
0
1
0
0
2
0
3
0
0
2
0
0
3
0
0
1
2
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
3
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
2
1
1
0
2
0
2
0
0
1
1
0
0
2
0
0
2
0
0
1
1
0
0
0
0
1
0
0
2
1
0
0
0
0
11
0
0
1
1
2
0
1
2
0
0
1
0
0
0
0
1
0
2
0
1
2
0
3
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
2
1
0
2
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
8
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
3
0
0
0
2
2
3
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
5
0
0
0
0
0
0
1
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
3
0
0
2
0
0
1
2
2
0
0
1
0
1
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
1
0
0
2
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
2
2
0
0
1
2
1
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
2
2
1
0
0
0
2
1
0
0
1
0
0
0
1
0
1
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
1
2
0
1
1
2
2
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
1
0
0
0
0
2
1
0
0
0
0
2
0
0
0
2
2
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
2
0
1
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
3
2
0
0
0
3
0
1
0
1
1
0
1
0
0
0
0
1
0
0
2
1
0
2
1
0
0
0
2
1
0
0
0
1
0
0
3
0
0
0
1
0
2
0
1
0
0
2
1
0
0
0
0
0
3
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
1
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
1
0
0
0
7
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
1
0
1
0
0
2
0
0
1
0
0
0
0
0
2
5
0
1
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
1
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
3
3
0
0
0
0
0
0
0
0
2
0
1
0
1
5
0
0
0
0
2
0
2
2
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
3
0
0
0
0
1
1
2
0
0
0
0
2
1
0
0
0
0
0
2
0
2
1
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
1
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
2
2
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
1
0
0
1
2
3
0
1
0
0
0
0
0
0
0
3
0
1
0
0
1
0
0
2
0
0
0
0
0
1
2
0
0
0
0
3
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
3
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
1
7
1
0
2
1
0
0
2
0
0
0
1
0
0
2
0
1
0
0
0
0
0
2
2
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
14
0
0
4
1
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
4
0
1
0
2
0
0
2
0
2
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
1
1
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
1
0
2
0
2
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
2
0
0
0
0
1
0
2
2
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
1
1
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
6
0
1
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
2
0
1
0
1
0
4
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
1
2
0
0
1
0
0
0
2
0
0
1
0
2
0
5
0
0
0
1
0
0
1
0
1
0
1
1
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
2
0
0
1
0
0
0
0
2
0
0
2
0
3
0
1
0
0
0
2
0
2
1
0
0
0
0
0
0
2
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
5
1
0
1
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
4
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
2
3
5
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
4
2
0
0
0
1
0
0
0
0
0
0
3
0
1
0
2
1
0
0
0
0
0
2
0
0
1
1
1
0
0
0
0
0
0
3
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
1
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
2
2
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
3
0
0
4
0
0
0
0
2
2
0
0
0
0
2
2
2
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
4
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
3
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
2
0
3
0
0
0
0
0
6
0
0
0
0
0
0
2
0
0
2
3
2
0
2
0
0
0
1
0
0
0
1
0
2
0
3
0
0
0
0
0
1
0
0
0
2
0
2
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
2
1
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
2
4
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
2
1
0
0
0
1
1
2
0
5
0
0
0
0
0
5
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
2
1
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
2
0
0
0
1
1
0
0
2
0
0
0
0
0
1
0
0
0
1
0
2
2
0
0
0
0
2
0
1
2
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
2
2
2
0
1
0
0
0
0
4
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
3
0
0
0
2
0
0
3
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
2
0
2
0
0
2
2
0
0
2
0
0
2
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
1
0
0
0
0
0
0
1
1
1
2
0
0
0
0
0
2
5
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
1
0
2
0
0
1
0
0
0
2
0
0
0
5
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
2
0
1
0
0
0
0
0
2
1
2
0
0
0
2
0
1
0
0
2
0
2
2
0
2
2
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
3
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
1
2
0
1
0
0
0
1
0
0
0
0
2
2
2
0
0
0
1
1
2
0
1
0
0
1
0
2
0
0
0
2
0
0
2
0
3
0
0
0
2
0
0
4
0
0
3
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
2
0
0
3
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
1
0
1
0
1
3
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
2
3
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
1
2
0
0
0
0
2
0
0
0
0
0
2
0
1
1
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
2
2
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
1
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
2
5
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
2
2
1
0
0
2
0
0
0
1
0
1
0
2
0
0
2
0
1
0
0
1
0
2
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
2
0
1
0
0
0
2
0
0
0
0
1
0
0
0
5
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
2
2
0
0
0
3
0
0
0
0
2
0
0
1
0
2
0
1
0
0
0
2
0
0
0
0
0
1
0
0
5
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
3
0
1
0
2
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
1
0
0
0
0
0
0
3
1
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
1
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
4
0
0
2
0
0
2
0
4
0
1
0
0
0
0
0
0
0
0
1
0
1
0
2
1
0
1
0
0
1
0
0
0
0
0
0
2
1
2
0
0
0
2
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
2
0
0
0
0
1
0
1
2
0
1
0
1
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
2
1
4
0
0
0
3
1
1
0
0
1
0
0
0
0
0
0
2
0
0
5
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
1
0
0
1
0
0
0
2
0
0
0
3
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
1
2
0
0
0
3
2
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
2
0
3
2
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
6
0
0
0
0
4
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
2
0
1
0
2
0
1
0
1
1
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
1
2
1
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
7
0
1
2
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
1
2
2
2
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
6
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
1
0
2
0
0
2
0
0
1
0
1
1
0
1
0
0
0
0
0
1
0
2
0
0
2
0
0
1
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
1
0
0
0
2
0
0
2
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
3
2
0
2
0
0
0
1
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
4
0
0
2
0
2
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
2
3
0
0
0
0
0
2
1
0
3
0
0
0
0
2
1
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
3
2
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
8
1
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
1
0
2
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
2
2
2
0
0
0
2
0
1
0
0
0
0
0
1
3
0
0
0
0
0
1
2
0
2
3
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
2
1
0
0
2
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
2
0
6
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
1
0
0
0
0
1
1
0
0
2
0
0
0
1
0
0
0
1
0
3
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
2
1
0
0
0
2
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
3
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
3
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
2
0
0
0
2
2
0
0
0
0
0
0
1
0
2
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
1
0
0
1
0
1
0
1
2
0
0
0
1
0
1
0
0
0
0
2
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
1
3
2
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
3
0
2
0
0
1
0
2
0
2
1
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
1
2
1
0
0
0
2
0
0
0
1
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
2
1
2
0
0
0
0
1
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
2
2
2
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
1
0
0
2
0
2
2
1
0
0
1
0
3
0
0
0
0
0
0
2
2
1
0
0
2
1
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
1
0
0
2
1
1
2
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
1
1
0
1
1
4
0
0
0
0
0
2
4
0
0
1
0
2
0
1
2
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
2
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
1
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
2
2
3
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
1
4
0
0
0
0
0
4
1
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
1
0
0
0
2
0
2
0
0
1
0
0
1
0
0
0
0
0
2
0
1
0
2
0
0
2
0
2
0
2
2
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
1
1
0
0
0
0
1
0
1
0
2
0
1
1
0
2
0
0
0
1
0
0
0
1
0
0
0
0
1
2
2
0
2
0
0
0
0
0
1
0
4
0
0
2
1
0
0
1
1
1
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
2
0
2
0
0
0
0
1
0
0
2
0
1
0
0
2
0
0
8
0
0
0
0
2
0
0
0
4
0
0
1
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
2
0
2
4
2
0
0
0
1
2
1
0
0
2
2
0
0
2
0
0
0
0
2
0
0
1
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
1
1
0
2
0
0
0
0
0
3
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
2
0
0
2
0
2
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
2
0
0
0
2
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
4
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
2
0
0
0
2
0
1
1
0
3
0
3
0
2
0
0
1
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
2
0
1
1
1
1
0
0
0
0
2
0
2
0
1
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
3
1
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
1
0
1
0
1
4
0
0
0
0
0
3
2
0
0
0
2
0
0
0
0
1
2
0
0
0
2
0
1
0
0
1
0
1
0
0
1
0
3
0
2
2
2
0
3
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
3
0
1
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
3
2
0
0
2
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
4
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
4
0
0
0
1
2
2
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
4
0
2
0
1
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
5
2
0
0
2
0
0
0
1
0
0
0
3
0
1
0
0
0
0
0
2
2
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
2
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
3
0
0
0
0
2
0
0
0
0
0
2
0
1
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
2
0
0
2
0
0
0
2
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
2
0
0
0
0
0
3
1
1
0
0
0
0
0
2
0
1
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
2
2
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
1
0
1
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
1
1
0
3
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
1
5
0
2
0
2
0
0
3
0
0
0
0
1
0
0
0
2
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
1
1
0
0
2
0
0
0
1
0
0
0
0
2
0
2
0
1
1
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
1
0
0
0
2
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
3
0
0
2
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
2
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
3
3
0
1
0
0
1
1
0
0
1
0
0
0
0
2
0
0
1
1
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
1
0
1
0
5
0
1
0
0
0
0
1
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
2
0
0
2
0
0
0
0
0
2
1
0
0
2
2
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
1
0
2
2
0
1
0
0
0
0
0
0
0
1
2
0
1
0
0
0
2
0
1
1
0
0
0
0
0
0
1
1
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
4
0
1
1
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
1
1
0
0
0
0
0
2
0
0
1
1
3
0
0
0
0
0
2
0
0
0
2
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
6
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
1
0
0
0
1
0
0
3
1
2
0
0
3
0
2
0
0
0
0
1
0
0
0
0
1
0
4
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
1
0
0
3
0
0
0
1
0
1
0
0
0
1
0
1
0
3
0
0
0
0
0
1
1
0
0
2
3
2
1
0
0
1
1
1
0
0
0
2
0
1
0
2
0
0
1
0
0
6
0
0
0
0
0
0
0
1
0
2
1
1
0
0
0
0
0
3
2
0
0
0
0
4
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
2
1
0
1
2
0
0
1
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
1
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
0
2
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
2
1
0
0
2
0
1
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
5
3
0
1
0
0
0
0
0
1
0
0
0
3
2
0
2
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
2
0
0
2
1
0
1
0
4
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
2
2
0
2
0
0
0
1
0
0
2
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
2
0
1
0
0
1
2
0
3
0
0
1
2
0
1
0
0
1
1
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
1
0
0
2
1
0
1
0
0
0
0
0
0
1
2
0
0
0
0
1
2
0
0
0
0
1
2
1
0
0
0
0
0
0
2
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
5
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
1
0
0
1
0
0
0
1
0
0
3
0
0
0
0
2
0
3
0
0
0
2
0
0
1
0
1
2
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
1
2
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
7
0
2
0
2
0
0
0
2
0
0
0
1
0
0
1
2
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
2
2
0
0
2
0
0
2
0
0
0
2
2
0
1
0
2
1
0
0
1
1
0
0
0
1
1
2
1
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
2
0
0
0
1
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
4
1
0
0
0
0
0
0
0
2
3
0
0
0
4
0
0
1
2
0
0
0
0
0
0
2
1
0
0
0
1
0
2
2
1
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
1
1
1
0
2
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
2
0
0
2
2
0
0
3
0
0
0
0
0
2
0
0
0
3
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
3
0
0
0
0
1
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
7
0
1
2
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
3
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
3
2
1
2
0
0
1
1
0
0
1
0
0
0
0
0
0
2
1
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
1
0
2
2
1
0
2
0
1
0
0
0
0
2
0
0
0
1
0
1
3
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
1
0
1
0
2
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
2
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
2
2
2
0
0
2
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
1
0
2
2
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
1
2
2
1
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
3
0
2
0
0
0
2
0
0
0
0
3
0
0
0
5
0
0
0
1
0
0
2
0
0
0
2
2
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
2
0
0
0
3
0
0
1
1
0
1
0
2
0
1
0
0
0
2
0
0
0
0
0
3
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
1
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
1
0
2
0
0
1
1
0
0
0
0
3
0
0
0
3
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
2
0
2
1
0
1
0
0
2
0
2
2
0
0
0
0
0
0
1
0
2
0
0
0
3
0
0
0
1
3
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
2
2
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
2
2
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
3
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
1
0
0
0
1
2
0
2
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
2
0
2
2
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
2
0
0
0
2
0
1
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
2
3
2
0
0
1
0
0
0
0
1
0
0
1
1
0
2
0
1
2
1
0
0
2
2
0
0
0
0
0
0
0
3
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
1
1
0
1
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
3
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
2
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
2
0
0
0
0
2
0
2
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
1
1
0
2
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
3
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
2
0
0
1
1
0
0
0
0
0
2
0
0
0
0
1
0
5
0
2
0
0
0
0
1
1
2
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
1
4
0
0
0
0
2
0
0
0
0
1
0
0
0
1
2
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
2
0
0
1
0
2
4
0
1
0
2
0
0
0
0
0
0
2
0
3
2
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
2
0
1
0
0
4
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
7
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
3
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
2
9
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
3
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
2
2
0
0
2
1
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
4
1
3
0
0
0
0
0
4
0
2
0
2
2
0
0
0
0
0
0
2
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
2
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
10
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
1
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
3
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
2
2
0
0
0
2
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
1
0
0
0
1
1
4
0
0
0
0
1
0
0
0
3
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
3
2
0
0
2
1
1
2
1
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
3
0
2
1
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
2
2
0
2
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
2
0
4
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
2
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
3
0
0
0
1
0
0
0
0
3
2
1
0
0
1
0
2
0
3
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
1
0
1
1
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
2
0
1
0
0
0
2
0
0
4
0
0
0
3
0
2
0
0
0
0
0
2
0
1
1
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
2
0
2
0
0
0
3
0
0
2
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
3
0
0
0
1
0
1
3
0
0
0
0
0
1
0
0
2
0
2
0
0
1
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
1
0
1
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
2
0
2
2
0
0
2
0
2
3
0
1
0
0
0
1
0
3
0
0
0
2
0
3
0
0
2
0
0
1
0
0
0
1
0
1
1
0
0
0
0
1
0
1
0
0
0
3
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
2
2
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
5
0
0
0
0
0
0
2
1
0
0
0
1
1
2
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
13
1
0
0
2
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
4
0
0
0
0
1
0
0
2
0
1
1
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
2
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
1
0
0
3
0
0
1
1
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
2
0
1
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
3
0
3
0
0
1
0
0
0
0
1
0
0
0
2
0
1
0
1
0
0
1
0
2
0
2
0
2
0
1
0
0
0
0
0
0
3
3
1
2
0
0
0
0
1
0
0
0
0
0
0
0
2
2
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
3
0
2
0
0
4
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
2
0
0
0
0
2
0
1
0
0
5
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
2
0
2
1
2
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
2
1
0
0
2
0
1
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
1
3
0
0
0
1
1
0
2
0
0
0
0
1
2
1
7
2
0
0
2
0
0
0
0
0
1
0
3
1
1
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
3
3
0
0
0
1
1
0
2
0
1
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
4
0
0
0
3
1
0
0
2
2
0
1
3
3
0
0
0
0
4
1
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
5
0
1
0
0
0
0
0
0
0
2
0
1
1
1
0
0
0
2
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
6
0
0
3
3
0
0
0
1
0
2
0
0
0
2
0
0
1
0
0
2
0
0
2
0
2
0
1
0
0
2
0
1
0
0
0
3
2
0
0
0
0
2
2
0
0
0
2
0
1
0
0
2
4
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
2
1
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
1
1
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
1
2
2
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
2
2
2
0
2
2
1
2
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
2
0
0
2
0
0
0
3
0
0
0
0
1
0
1
0
0
7
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
1
2
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
6
0
0
0
0
0
0
2
0
0
2
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
3
1
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
2
5
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
1
0
2
1
0
2
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
1
2
0
1
0
0
1
1
0
0
0
2
1
2
0
6
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
1
2
0
1
0
0
3
1
0
0
4
0
0
0
0
0
0
0
7
0
0
1
0
0
0
0
2
1
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
2
0
0
1
0
0
0
2
0
1
1
2
1
1
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
2
0
9
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
5
1
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
2
0
0
1
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
2
2
3
2
0
0
0
2
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
2
0
0
1
0
0
0
0
0
0
2
0
2
0
2
0
2
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
3
0
0
0
0
0
1
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
2
0
0
0
0
0
0
0
1
0
1
2
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
1
0
2
1
1
0
0
0
1
2
1
0
0
2
0
1
0
0
0
0
0
0
0
2
0
1
0
0
2
1
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
3
0
0
0
1
0
0
0
0
0
0
5
0
0
0
0
0
1
0
0
0
0
2
2
0
1
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
2
0
0
0
1
0
2
0
0
0
0
4
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
2
0
0
0
2
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
4
1
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
2
0
1
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
1
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
2
1
0
1
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
1
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
1
2
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
4
0
2
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
1
1
0
0
5
1
0
0
1
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
6
1
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
5
0
0
0
0
0
3
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
1
1
1
0
1
0
0
1
0
0
0
0
0
0
3
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
1
2
0
1
0
0
0
0
0
3
0
0
0
0
2
2
0
1
0
2
0
2
0
0
0
1
2
2
0
0
0
0
0
1
1
3
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
2
1
0
2
1
0
0
0
0
2
1
0
0
2
0
0
0
0
0
2
2
0
0
4
0
0
0
0
0
1
0
0
0
1
0
0
2
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
3
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
4
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
3
0
0
0
0
3
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
3
1
0
0
2
2
2
2
0
1
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
2
1
0
0
0
2
0
1
0
0
0
0
1
2
0
0
1
1
0
0
0
0
1
2
4
0
0
0
0
3
1
1
0
0
0
0
0
0
2
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
7
0
0
0
2
0
0
0
1
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
1
1
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
1
1
0
0
2
0
0
0
0
0
7
0
0
0
0
0
2
7
0
0
0
1
2
0
1
0
2
0
0
1
0
0
1
0
0
2
3
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
2
2
0
2
1
3
1
1
2
1
0
0
0
2
2
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
4
0
0
2
0
0
0
0
0
0
1
2
0
1
0
0
0
0
1
0
0
0
0
0
5
0
2
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
1
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
2
1
2
0
0
3
0
0
0
0
0
1
1
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
5
0
0
0
0
0
0
2
0
0
0
1
1
2
0
0
0
2
0
2
0
0
1
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
1
2
0
1
1
0
0
0
0
2
0
0
4
0
0
1
0
0
0
0
0
0
0
2
0
2
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
1
0
2
0
1
0
0
0
1
0
2
0
0
0
0
3
3
0
0
0
0
0
1
0
3
0
0
0
0
1
0
0
1
0
1
2
0
0
2
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
1
0
1
0
1
1
2
0
0
0
0
0
2
0
2
1
0
0
0
0
2
0
0
0
2
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
1
0
2
2
0
0
0
0
0
0
1
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
6
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
1
1
0
0
1
1
0
0
3
2
0
0
1
1
2
0
0
2
0
0
0
0
0
0
0
0
2
1
0
3
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
2
0
1
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
3
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
1
0
0
2
2
2
0
1
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
1
0
0
2
0
6
0
1
0
0
2
2
0
3
2
0
0
0
0
0
2
0
0
0
2
1
0
1
1
1
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
3
1
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
3
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
3
0
2
0
0
0
1
0
2
1
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
2
1
2
0
0
0
0
4
0
0
0
0
0
4
1
1
1
1
2
0
0
0
1
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
6
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
2
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
2
2
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
1
0
2
0
5
0
0
0
1
2
0
1
0
1
0
0
1
0
1
1
0
2
0
0
0
2
1
1
0
0
0
0
2
1
0
0
2
1
0
2
1
0
0
0
2
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
2
2
0
0
1
0
0
0
2
0
0
0
0
1
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
3
0
0
0
0
1
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
2
0
0
0
1
1
2
0
0
0
0
1
0
2
0
1
0
13
0
0
5
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
2
1
0
1
0
0
0
2
0
4
1
0
0
0
0
1
0
0
1
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
2
1
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
1
0
1
2
1
0
0
0
0
3
0
0
0
0
1
4
1
0
0
0
3
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
6
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
2
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
1
2
0
0
0
0
2
0
1
0
1
0
0
2
1
0
1
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
1
0
2
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
3
0
0
2
0
1
0
0
0
0
1
0
0
0
0
2
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
1
0
0
1
0
2
0
3
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
3
0
0
0
2
2
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
2
0
0
0
2
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
1
0
0
0
0
2
0
1
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
3
1
0
3
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
2
2
2
2
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
3
3
0
0
0
0
0
0
1
0
1
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
3
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
1
0
1
0
0
0
1
0
4
1
0
0
1
1
0
0
1
3
2
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
2
0
0
0
0
1
0
0
1
0
0
0
1
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
3
0
2
0
0
0
2
0
0
2
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
1
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
2
2
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
3
0
2
0
0
0
0
1
0
0
2
0
0
0
0
2
2
1
1
2
0
0
0
0
0
2
0
2
1
0
1
0
0
0
2
0
0
0
0
0
1
2
0
1
0
0
2
0
0
0
0
0
2
0
0
3
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
2
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
2
0
0
2
0
0
1
0
2
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
2
0
0
0
1
0
0
0
0
0
1
1
2
0
2
1
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
1
5
0
0
0
0
0
0
0
0
7
0
0
0
0
1
0
0
3
0
5
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
1
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
8
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
1
0
5
0
0
1
0
1
0
0
0
0
0
2
0
0
1
0
0
2
1
2
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
2
0
0
0
1
0
1
0
1
2
0
1
0
0
6
0
2
0
0
0
0
2
0
1
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
3
2
0
2
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
3
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
3
1
1
3
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
3
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
16
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
6
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
1
3
0
0
0
0
0
0
2
0
1
0
0
1
0
1
0
0
0
1
1
0
0
1
0
0
0
0
2
0
0
0
4
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
2
0
1
1
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
3
0
1
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
2
1
2
1
2
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
3
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
1
0
0
0
1
0
0
0
7
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
1
1
0
2
0
0
0
0
0
0
0
1
2
1
0
0
0
2
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
3
0
0
0
0
1
0
1
0
0
4
1
0
1
1
0
0
0
0
2
3
4
0
0
2
0
0
2
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
1
0
0
1
1
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
2
0
0
0
4
0
0
0
2
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
1
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
1
2
0
0
0
2
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
2
0
0
0
0
0
1
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
4
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
1
0
2
0
0
1
0
2
2
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
2
0
0
3
1
0
0
0
2
1
0
0
1
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
1
0
0
2
0
0
2
0
0
1
0
0
0
0
0
1
1
0
2
1
0
2
0
0
0
0
0
0
0
1
0
4
0
0
1
1
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
1
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
5
0
1
1
0
0
3
0
0
0
0
3
0
0
0
0
1
0
0
0
3
0
2
2
0
2
0
0
0
0
0
0
0
0
0
5
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
4
1
0
1
1
0
2
0
1
0
2
0
0
1
0
0
0
0
2
0
2
1
0
0
2
1
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
3
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
1
2
0
4
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
2
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
3
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
1
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
1
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
1
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
1
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
2
0
0
0
2
0
0
1
1
1
2
2
0
2
0
0
2
0
0
0
2
2
0
0
0
1
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
1
0
1
0
0
1
1
2
0
4
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
3
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
1
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
2
1
2
0
1
0
0
0
0
0
0
0
0
1
0
0
3
1
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
2
2
1
0
2
2
2
0
0
0
0
0
4
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
3
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
3
0
2
0
0
0
1
0
0
2
1
0
0
1
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
2
5
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
1
0
0
2
0
0
0
0
1
1
0
0
0
2
0
0
2
0
0
0
3
0
2
2
1
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
2
1
0
0
0
0
1
1
0
1
0
0
2
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
3
2
0
0
0
2
2
0
0
0
2
0
0
2
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
4
0
1
0
0
3
0
1
0
0
3
0
0
0
0
2
1
0
2
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
2
1
0
3
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
1
2
1
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
3
0
0
0
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
1
1
0
0
0
1
0
1
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
3
0
3
0
0
0
0
0
0
0
1
0
0
1
1
1
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
3
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
2
0
0
2
2
2
2
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
3
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
2
0
3
2
4
3
1
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
2
0
2
0
0
1
0
1
2
0
1
0
0
0
1
0
4
0
1
1
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
3
0
0
2
1
0
0
0
3
3
0
2
0
1
0
1
3
0
1
2
0
0
1
0
5
0
0
0
1
0
0
0
0
0
1
2
0
1
2
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
2
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
6
0
2
0
2
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
1
1
0
0
2
2
0
0
0
1
1
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
1
0
0
0
0
2
2
0
0
0
2
0
0
0
1
2
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
10
0
0
0
0
0
0
0
2
1
2
0
0
0
1
0
0
0
0
0
0
0
2
0
1
3
0
0
0
0
0
0
2
0
0
2
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
1
0
1
0
0
0
2
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
31
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
3
1
0
1
1
0
0
0
0
0
1
0
0
1
0
2
0
0
0
1
1
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
2
1
0
0
0
0
0
2
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
2
4
0
1
1
2
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
3
2
0
1
1
0
0
0
0
0
1
0
0
0
1
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
3
0
0
2
1
0
1
2
0
0
0
0
0
0
1
0
1
0
1
0
2
2
0
2
0
0
0
2
1
0
2
0
0
0
2
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
2
0
0
0
0
2
0
1
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
4
1
1
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
2
0
1
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
3
1
0
1
0
2
0
0
0
0
0
0
1
0
1
4
1
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
2
0
2
0
2
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
1
0
2
2
0
0
0
0
0
0
1
2
5
3
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
7
0
0
3
1
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
2
0
0
0
1
2
1
3
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
3
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
2
1
1
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
2
5
0
0
0
0
0
0
0
0
0
0
7
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
3
0
2
0
0
0
0
5
0
0
0
3
1
0
0
0
0
2
3
0
1
1
0
1
0
0
1
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
3
0
0
2
0
0
1
0
1
0
0
0
0
3
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
3
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
1
0
1
3
0
0
2
0
1
0
0
1
0
2
1
0
0
0
2
0
1
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
2
1
0
1
0
2
0
1
0
2
1
0
0
1
0
0
2
0
0
0
1
0
1
0
2
0
0
0
2
0
2
0
0
0
2
0
3
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
2
0
0
0
0
2
3
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
1
1
0
0
0
1
0
1
1
0
0
0
3
0
0
0
1
0
2
0
0
0
0
2
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
4
0
0
7
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
3
0
1
0
0
0
2
1
3
0
0
0
0
1
0
0
0
0
0
0
3
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
2
0
0
0
0
2
0
0
2
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
8
0
0
0
2
0
1
1
0
2
0
0
0
2
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
1
0
3
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
2
2
0
0
3
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
1
0
0
0
0
1
0
0
2
0
0
0
0
3
0
0
1
2
2
0
1
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
2
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
1
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
6
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
1
2
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
4
0
0
1
0
0
2
2
0
1
0
0
0
2
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
2
2
0
2
0
0
0
13
0
0
2
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
3
0
2
0
1
0
2
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
2
0
0
0
0
1
0
0
0
0
0
0
1
1
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
1
2
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
2
2
2
0
0
0
0
2
1
1
1
0
0
0
1
0
2
0
1
0
0
0
2
0
0
0
0
2
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
2
0
3
0
0
0
1
0
1
5
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
2
0
0
0
1
0
3
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
4
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
2
0
1
0
2
1
0
1
0
0
11
0
0
1
0
3
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
1
0
1
3
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
2
0
0
2
0
0
2
0
1
0
0
0
0
1
0
0
0
0
1
1
0
1
0
2
0
2
0
0
0
4
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
2
2
0
0
0
1
1
1
0
5
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
4
1
0
0
0
2
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
1
2
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
3
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
2
0
0
0
0
0
1
0
1
4
0
0
0
0
0
0
5
0
0
0
0
1
0
2
0
0
0
2
2
0
0
0
0
0
1
2
1
0
0
2
0
0
0
1
0
2
0
0
0
2
0
1
0
0
0
0
0
0
2
2
0
0
0
1
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
2
0
1
0
0
0
2
1
0
0
0
2
0
2
0
0
0
0
0
0
0
2
2
0
0
1
0
3
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
2
2
0
0
1
0
0
0
0
0
1
0
1
0
2
0
2
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
2
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
1
0
0
0
0
2
2
0
1
0
2
2
2
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
1
0
1
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
3
0
0
0
1
1
3
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
3
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
1
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
1
1
0
1
0
0
0
0
0
0
0
0
0
1
1
1
2
0
1
0
0
2
0
0
0
0
0
0
1
0
1
1
0
0
1
10
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
12
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
2
0
0
1
0
0
0
2
4
2
0
1
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
1
0
0
0
0
0
1
0
2
0
0
0
3
0
2
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
3
2
0
0
1
0
0
0
0
0
2
2
0
1
0
0
0
3
0
0
0
0
0
0
0
1
1
1
0
2
0
0
0
0
0
0
5
0
0
0
1
2
2
2
0
0
0
1
0
0
2
0
1
0
1
0
0
0
0
0
1
0
2
0
0
1
1
0
1
0
0
2
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
2
0
1
2
0
0
1
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
3
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
2
0
2
0
0
0
2
1
0
0
0
0
1
0
0
3
0
1
0
0
2
1
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
5
2
0
0
0
0
1
0
0
0
2
0
0
0
2
3
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
1
1
0
2
0
1
0
0
0
1
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
3
2
0
1
0
0
1
0
0
1
0
2
0
0
2
0
0
0
0
2
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
1
0
0
0
0
0
2
1
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
7
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
3
2
1
0
1
0
0
4
2
2
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
1
0
0
9
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
1
0
2
0
0
0
0
1
0
1
1
1
0
0
3
3
0
0
0
0
0
3
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
2
0
0
0
3
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
1
2
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
2
0
1
0
1
0
0
1
0
0
5
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
1
0
2
0
1
1
0
0
0
3
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
1
0
1
2
0
3
0
0
0
2
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
2
1
2
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
6
0
0
0
1
0
0
0
1
0
0
1
0
0
0
2
2
2
0
2
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
2
1
1
0
0
1
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
3
2
0
0
0
0
0
1
0
0
2
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
6
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
4
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
2
0
0
1
0
0
4
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
4
0
0
0
0
0
0
0
1
0
0
0
0
2
2
2
0
0
0
2
2
1
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
1
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
1
2
0
2
0
0
0
0
0
0
2
0
0
0
4
1
0
0
0
3
0
0
0
1
1
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
2
0
0
1
0
0
0
0
0
2
3
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
2
0
0
2
2
0
1
2
0
0
1
0
0
1
0
1
0
0
0
0
1
0
2
1
0
1
0
0
0
0
2
1
0
0
3
0
0
2
0
7
0
0
0
0
0
0
0
0
0
1
0
7
1
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
4
2
2
0
2
0
0
0
2
6
0
0
0
0
1
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
7
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
8
1
0
0
0
0
1
0
2
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
2
0
1
0
2
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
3
3
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
1
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
4
2
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
2
4
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
7
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
1
0
0
0
3
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
3
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
3
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
2
0
2
0
2
0
0
2
0
3
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
2
0
0
1
3
0
0
1
0
4
0
0
2
0
0
0
0
0
1
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
2
1
0
1
0
1
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
1
0
2
0
0
0
1
0
4
0
0
1
0
0
6
0
1
2
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
3
1
0
1
0
0
0
3
0
0
0
0
1
0
0
1
0
0
0
0
1
0
3
0
0
0
0
0
2
0
2
0
1
0
1
0
0
0
1
0
2
1
1
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
1
0
2
1
0
2
0
0
0
0
0
0
7
2
1
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
3
0
0
0
3
0
1
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
1
0
0
1
0
1
0
0
2
0
0
0
0
2
1
3
1
2
0
0
0
0
2
0
1
2
3
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
2
1
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
1
0
2
0
0
4
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
5
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
2
2
0
2
2
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
1
0
0
0
1
2
0
0
1
1
0
1
1
0
0
1
0
0
2
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
5
1
0
3
1
0
0
2
1
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
1
0
0
2
2
1
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
2
1
0
0
0
2
1
0
0
1
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
3
0
0
2
2
3
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
2
2
1
0
1
0
0
0
2
0
0
0
0
4
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
3
0
2
1
0
0
0
0
1
0
0
0
0
1
0
3
0
0
0
2
0
1
0
0
0
1
0
0
1
0
0
0
0
2
1
1
0
0
0
1
0
0
0
1
3
0
2
0
2
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
1
2
0
1
0
0
0
1
3
2
0
1
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
2
1
0
1
0
0
0
0
1
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
2
2
0
0
0
0
0
0
0
3
0
1
0
1
0
1
0
2
2
0
0
0
0
2
0
0
1
0
0
0
2
2
1
0
0
0
0
2
0
0
0
1
1
0
0
0
2
0
2
0
1
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
2
1
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
2
0
0
0
0
0
0
1
0
1
1
0
0
0
0
2
2
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
6
0
0
0
0
1
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
2
0
0
0
2
0
1
0
0
0
0
0
0
2
0
1
0
0
2
1
0
0
0
0
0
6
1
2
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
2
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
1
0
0
0
0
0
1
0
1
3
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
1
0
6
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
2
0
0
0
0
3
0
3
1
0
0
0
1
0
1
1
0
1
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
1
0
0
1
0
0
1
0
1
3
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
1
1
0
2
0
1
0
0
0
3
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
2
0
0
0
2
4
0
0
0
0
1
0
0
2
0
0
2
0
2
0
0
0
2
0
0
0
0
0
2
0
1
1
0
0
0
2
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
1
2
0
0
0
0
2
0
2
0
1
0
0
0
2
0
0
1
0
2
0
2
0
3
0
0
0
0
0
1
0
0
0
0
0
2
2
1
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
2
0
1
0
0
3
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
2
2
2
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
2
0
0
0
0
1
0
1
0
2
0
0
1
1
0
1
0
2
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
2
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
1
2
1
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
2
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
6
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
2
0
2
0
0
0
0
5
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
1
2
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
2
0
2
0
1
0
0
0
2
0
2
2
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
2
0
0
1
0
0
2
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
1
0
1
2
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
2
1
1
0
0
2
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
2
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
2
2
0
0
2
2
0
0
2
0
1
0
2
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
4
0
1
2
0
0
0
2
0
0
0
1
0
0
1
2
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
6
2
0
0
1
0
0
2
0
0
0
2
0
0
2
2
3
0
0
2
0
0
2
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
3
0
0
0
2
0
0
2
0
0
0
0
0
2
1
0
2
0
1
0
0
0
1
0
2
0
0
2
0
2
1
0
1
0
0
2
0
0
0
0
2
0
6
2
1
0
0
0
0
0
0
2
0
2
0
0
2
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
2
0
2
0
0
1
0
0
0
3
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
3
1
3
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
2
1
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
1
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
2
2
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
2
2
1
0
0
0
1
0
0
0
0
0
2
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
1
0
1
1
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
1
3
0
3
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
2
0
1
5
1
0
0
0
0
0
1
0
0
1
2
2
0
0
0
0
3
2
0
0
1
0
3
0
0
1
2
0
0
0
2
1
0
2
1
0
0
9
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
2
2
0
0
2
0
2
0
1
0
1
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
1
0
0
2
1
1
1
1
0
0
0
0
0
0
1
0
0
0
0
4
1
0
0
3
0
3
0
0
1
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
3
0
0
0
1
1
0
3
0
2
0
0
0
2
0
0
0
0
0
2
2
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
1
0
3
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
2
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
2
0
0
0
3
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
1
0
0
0
0
0
0
1
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
2
0
0
1
0
2
0
2
0
0
0
1
0
1
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
9
0
0
2
1
0
1
0
0
1
0
0
0
2
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
2
0
2
1
0
1
0
0
1
0
2
0
0
1
2
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
2
0
0
0
0
0
0
0
1
1
0
3
0
0
0
2
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
2
0
0
0
1
1
0
0
2
0
0
1
6
2
0
0
0
0
0
0
0
1
1
0
2
0
0
2
3
0
1
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
2
0
0
4
1
0
5
0
0
0
0
1
1
0
0
0
2
1
2
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
1
0
2
0
0
1
0
0
0
0
0
2
0
0
2
1
0
0
2
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
2
0
0
1
2
0
2
1
0
1
1
0
1
0
3
0
0
0
1
0
0
0
0
4
0
2
0
4
0
0
1
2
1
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
2
0
0
0
1
0
0
11
0
2
2
0
0
1
0
2
1
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
4
0
0
0
2
0
2
2
1
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
1
0
0
3
0
0
0
0
0
0
2
3
1
0
0
0
4
0
0
0
2
0
0
0
0
0
0
1
0
2
1
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
2
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
3
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
3
2
0
0
0
0
2
1
0
1
0
0
0
0
1
0
2
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
2
1
1
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
2
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
2
1
0
0
0
0
2
0
1
0
0
0
2
2
0
3
0
3
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
2
1
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
3
0
0
0
1
0
0
2
1
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
2
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
2
0
2
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
2
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
1
0
0
0
1
0
1
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
1
0
3
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
2
0
0
0
0
0
2
1
0
1
1
1
1
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
2
2
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
1
0
2
0
0
0
0
3
0
0
0
0
0
3
0
0
0
0
1
0
0
2
0
0
0
1
2
0
0
0
1
0
0
0
2
2
2
0
0
0
0
0
0
2
2
0
0
1
1
0
0
1
0
1
0
0
2
0
1
0
0
0
0
0
0
0
3
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
4
0
1
0
1
0
0
0
1
0
0
1
0
0
0
3
0
0
0
0
0
0
0
2
2
0
1
2
0
0
2
2
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
3
2
0
0
1
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
2
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
2
9
0
0
1
1
0
0
0
0
0
0
0
2
0
1
0
3
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
2
0
0
1
2
2
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
2
1
0
0
2
1
2
0
0
0
0
0
0
1
0
0
1
0
0
0
1
2
8
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
2
0
0
0
0
0
0
0
1
1
0
5
1
1
0
2
2
1
0
0
2
2
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
1
2
0
1
0
0
1
1
0
0
3
0
0
0
0
0
0
0
1
4
0
1
0
0
1
0
3
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
1
1
0
0
2
0
0
1
0
2
0
0
2
0
0
0
2
0
0
2
0
2
1
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
5
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
5
0
2
0
1
0
0
1
0
1
1
0
2
0
0
7
0
0
0
0
1
0
3
0
2
0
1
2
0
0
0
0
3
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
8
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
1
3
0
2
0
0
0
0
7
0
0
2
0
0
4
0
2
0
3
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
2
0
2
1
0
0
0
1
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
3
0
0
2
0
0
0
0
0
0
2
0
1
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
3
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
2
0
2
1
0
0
0
0
1
0
0
2
1
0
1
0
0
0
0
2
0
0
3
1
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
4
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
1
0
1
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
1
0
0
2
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
2
0
0
2
0
2
1
0
0
0
0
0
1
0
0
2
0
1
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
3
0
0
0
0
0
2
0
0
1
0
0
2
0
2
0
1
0
0
0
0
0
0
2
2
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
1
0
0
2
3
0
0
1
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
1
1
1
0
0
0
0
0
2
2
0
0
0
0
0
2
4
2
0
0
0
2
0
0
2
2
2
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
2
1
1
0
1
0
0
1
3
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
3
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
10
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
2
0
1
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
2
0
4
0
0
0
0
1
2
0
0
0
0
0
0
2
0
2
0
0
0
2
1
1
2
0
1
0
1
1
1
0
2
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
3
3
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
1
1
1
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
5
0
0
0
0
2
0
2
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
1
2
1
0
0
2
0
0
0
0
0
2
2
1
0
3
0
0
3
0
0
0
0
0
1
0
0
1
0
0
0
0
4
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
3
0
0
0
0
2
0
0
0
0
0
0
3
2
0
2
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
1
0
2
1
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
2
1
1
0
0
0
0
0
2
0
1
0
3
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
4
0
0
0
0
1
0
0
3
0
2
0
0
1
2
0
0
1
0
0
2
0
0
0
3
1
2
0
0
0
2
0
1
0
0
0
0
3
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
3
0
0
0
2
3
1
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
1
3
0
0
0
0
0
0
0
1
2
0
2
1
0
0
0
2
0
1
2
0
0
1
1
2
0
0
0
2
0
0
0
0
0
0
1
2
2
0
1
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
5
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
2
1
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
1
1
0
0
2
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
2
2
1
1
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
1
2
9
0
0
2
0
0
1
1
2
0
1
0
0
10
0
0
1
2
0
2
0
1
3
6
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
3
0
1
2
0
0
0
0
0
1
0
0
0
0
0
1
1
2
2
0
0
0
0
0
1
0
1
1
0
2
1
0
0
0
0
2
0
0
0
2
1
0
0
1
0
0
0
0
1
0
1
0
0
4
0
0
0
1
0
0
1
0
0
2
0
1
0
2
0
1
2
0
1
1
0
1
0
1
0
3
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
2
0
2
1
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
2
0
2
1
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
2
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
5
2
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
2
0
2
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
1
0
0
0
2
1
0
0
0
0
0
0
5
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
1
2
0
0
1
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
3
0
0
1
0
0
0
2
2
0
1
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
1
0
1
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
2
2
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
2
3
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
3
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
2
0
2
0
2
2
7
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
1
0
0
2
0
1
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
3
1
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
2
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
3
0
0
1
0
0
0
1
0
0
1
2
0
1
0
0
0
0
0
0
0
0
1
0
2
1
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
3
1
1
1
0
0
1
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
2
1
0
2
0
0
1
0
0
0
0
0
0
0
1
2
1
0
0
1
2
2
0
0
1
0
0
2
0
0
1
1
2
1
0
0
0
0
0
1
0
0
0
0
0
1
2
1
0
4
1
2
2
2
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
3
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
1
2
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
1
0
2
0
2
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
1
1
0
0
1
0
0
0
1
2
2
0
0
0
0
8
1
0
0
0
0
0
0
1
0
1
2
0
0
0
1
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
1
0
0
2
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
1
1
2
2
0
1
0
3
0
0
3
0
1
0
0
0
0
1
0
0
3
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
3
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
2
0
0
0
0
0
5
0
2
0
0
0
2
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
1
2
2
5
1
0
0
0
0
2
1
0
0
0
1
2
0
0
0
0
0
3
1
1
0
0
0
2
0
1
2
4
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
3
0
0
2
1
0
0
0
1
0
0
0
0
6
2
3
2
0
0
0
0
1
0
0
0
1
0
0
0
0
2
1
1
0
0
2
2
3
0
0
0
0
0
1
0
0
0
0
2
0
1
2
1
0
0
1
0
0
0
0
0
1
1
3
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
2
1
2
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
3
0
0
0
3
2
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
1
1
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
1
0
0
2
4
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
1
0
2
0
0
0
0
0
2
2
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
2
0
1
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
1
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
1
3
3
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
3
0
0
0
0
1
2
0
0
9
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
4
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
6
0
1
1
0
0
0
0
0
0
0
0
0
2
0
2
0
2
2
0
0
0
1
0
2
0
0
0
0
0
0
0
2
2
0
1
2
0
2
0
2
0
0
2
1
1
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
2
0
1
2
0
1
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
4
0
4
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
2
0
1
2
0
0
2
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
2
2
0
0
1
0
0
0
0
2
2
0
3
0
0
2
0
4
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
2
0
0
1
0
2
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
3
2
2
0
2
0
0
0
0
0
0
1
2
2
0
0
2
2
0
1
0
0
0
3
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
3
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
4
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
1
0
0
2
0
1
0
2
1
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
2
0
0
1
1
0
0
0
2
2
0
1
0
0
0
0
0
1
0
2
0
1
1
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
1
1
1
1
0
1
0
0
0
0
0
0
2
1
0
1
0
1
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
2
2
1
0
0
0
1
1
0
1
0
0
0
2
0
0
0
1
0
0
2
0
1
2
0
0
0
0
1
0
0
0
0
0
10
0
0
3
0
0
0
2
0
0
0
2
0
0
0
0
0
2
2
2
0
1
0
0
0
2
0
2
0
0
0
1
0
2
3
3
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
5
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
1
0
0
1
0
0
1
0
2
0
0
0
1
0
0
0
0
1
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
2
1
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
1
0
0
2
1
1
0
0
2
0
0
1
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
2
6
0
0
0
0
2
0
0
0
1
0
2
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
1
2
0
0
1
1
0
0
0
0
1
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
5
0
0
0
2
0
0
0
0
1
2
3
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
2
1
2
1
0
0
1
0
0
0
0
0
0
1
0
2
1
0
2
0
2
0
2
0
0
0
0
0
2
2
0
0
0
0
2
0
1
0
0
0
0
0
4
1
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
2
0
0
0
2
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
2
0
0
0
0
5
0
0
0
0
0
0
0
0
0
1
2
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
1
2
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
1
0
3
2
0
0
0
0
0
0
2
0
0
0
4
0
0
2
0
0
4
0
0
2
0
0
0
0
1
2
0
1
0
2
0
1
2
0
2
0
0
2
1
0
2
0
1
0
2
0
2
0
1
0
0
1
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
13
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
5
1
0
2
2
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
2
0
0
5
0
1
0
0
0
0
1
0
0
0
0
2
4
0
2
0
1
0
4
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
2
0
2
2
0
1
0
0
0
0
1
1
0
0
0
0
0
2
4
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
1
0
2
1
1
2
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
2
1
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
11
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
2
2
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
3
0
2
0
3
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
3
0
0
0
0
0
0
1
0
0
1
0
2
0
0
2
0
0
0
0
0
2
0
0
2
0
0
4
0
1
0
2
2
0
0
0
0
0
0
2
0
2
2
0
1
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
1
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
1
0
0
1
0
0
1
0
2
1
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
1
5
2
0
0
1
0
0
0
1
2
0
1
0
0
0
2
0
2
0
0
0
0
2
0
2
0
6
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
2
2
1
0
0
0
0
0
0
1
0
1
2
2
1
0
0
1
2
0
2
0
0
3
0
0
1
3
0
0
0
1
0
0
1
0
1
2
0
0
0
2
1
0
0
1
0
3
0
0
0
2
1
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
1
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
2
2
2
0
4
0
2
0
0
0
0
0
0
0
0
2
1
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
3
2
0
1
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
4
1
0
1
0
0
0
0
0
2
0
0
3
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
2
0
0
1
2
0
1
1
0
0
0
0
2
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
6
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
4
0
1
0
0
2
0
0
0
2
0
0
0
3
0
3
0
0
1
0
1
0
0
3
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
4
0
0
2
0
0
0
1
0
0
0
0
2
1
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
5
0
1
0
1
0
0
1
0
0
2
0
0
0
1
0
0
2
1
0
1
0
0
1
0
0
0
0
3
1
0
2
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
10
1
1
2
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
8
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
1
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
2
0
2
3
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
2
2
5
0
0
0
0
0
0
0
0
0
0
0
0
1
1
3
1
0
0
0
2
1
0
0
2
2
0
0
0
0
0
2
0
0
0
1
2
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
1
0
0
1
2
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
3
0
0
0
0
0
2
0
6
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
3
0
0
0
1
0
4
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
2
0
0
0
0
0
1
0
0
0
0
1
1
2
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
2
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
1
0
0
1
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
1
2
2
0
0
0
0
1
0
1
0
1
2
0
0
0
2
0
2
0
0
2
0
0
0
0
0
8
0
0
2
2
0
2
2
0
2
0
2
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
2
0
2
1
0
0
0
0
0
0
1
2
2
0
0
0
0
0
3
0
0
0
0
2
0
0
1
1
0
7
0
0
2
0
0
0
1
0
1
0
0
0
0
1
0
0
4
0
0
1
0
0
1
1
0
1
0
0
1
0
0
0
0
2
0
0
0
1
2
1
0
0
0
2
0
1
1
1
0
0
0
0
0
0
3
2
0
0
2
0
0
1
0
0
1
0
3
0
0
0
1
0
0
0
0
0
0
12
0
0
2
0
1
0
2
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
1
0
0
0
0
1
2
4
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
1
0
0
2
0
4
0
2
1
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
1
2
0
0
0
1
0
0
2
0
2
0
0
2
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
1
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
1
1
0
2
1
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
2
0
0
0
0
1
1
0
1
0
3
0
0
2
0
0
0
0
2
5
0
0
0
2
2
0
0
0
1
0
1
0
2
2
0
0
3
0
0
0
2
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
2
0
2
2
0
0
1
0
1
0
0
2
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
1
0
1
0
0
2
0
0
2
0
0
2
0
2
0
2
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
2
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
2
0
0
2
1
0
0
1
0
0
0
0
2
0
0
1
0
0
1
0
2
0
2
0
0
0
1
0
0
0
0
2
0
1
0
0
1
0
0
2
6
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
3
0
0
2
0
0
0
0
1
0
1
1
0
0
0
2
0
9
0
0
0
1
0
0
1
2
0
0
0
2
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
3
0
3
1
2
0
0
0
1
0
0
0
0
2
1
0
0
0
1
2
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
2
1
0
0
0
0
1
4
0
2
0
0
0
1
0
0
0
1
0
2
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
3
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
4
2
2
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
2
0
1
2
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
1
0
3
0
2
1
0
0
1
0
1
0
0
0
2
0
2
0
0
0
1
0
2
0
0
2
0
0
4
1
0
0
0
5
0
0
0
0
0
1
0
0
0
3
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
2
0
4
0
0
1
0
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
2
0
1
1
0
1
2
0
0
0
0
2
0
0
1
0
1
0
1
7
0
0
0
0
2
1
1
1
0
0
0
0
0
2
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
2
0
1
0
0
0
0
2
2
0
0
0
1
0
2
0
0
0
0
0
1
1
0
0
0
0
0
1
1
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
8
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
1
0
0
2
0
2
0
2
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
1
2
0
2
0
0
0
0
0
2
0
2
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
1
1
0
0
1
0
0
0
3
1
2
1
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
1
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
2
1
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
4
0
2
1
0
1
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
2
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
1
0
5
0
0
0
2
0
0
1
0
0
3
0
0
2
0
2
0
1
1
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
1
1
0
0
1
0
2
0
2
0
2
1
5
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
1
0
0
0
2
1
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
6
0
0
0
0
1
1
0
0
2
0
0
0
0
1
7
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
3
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
3
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
3
0
0
0
1
0
2
0
0
0
0
0
0
0
4
0
2
2
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
2
0
0
2
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
2
0
1
2
0
3
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
4
0
2
1
0
2
0
0
0
0
0
0
0
2
1
0
1
0
2
2
1
0
0
0
0
0
0
0
0
2
2
0
0
0
3
0
0
0
2
0
3
0
0
0
0
0
2
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
7
1
1
1
2
0
0
0
2
0
1
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
1
5
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
2
0
0
0
0
0
1
1
2
0
0
2
0
0
0
0
0
1
5
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
6
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
1
0
1
1
0
3
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
3
1
0
0
1
1
0
2
0
0
0
0
1
3
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
1
2
5
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
1
2
0
0
2
0
0
2
0
0
0
1
1
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
1
0
0
0
0
1
3
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
1
2
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
3
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
1
0
0
1
1
1
0
2
0
0
0
1
0
0
0
0
0
1
2
0
0
0
1
0
2
0
0
0
0
0
2
2
0
0
0
1
0
0
0
4
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
1
2
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
1
0
0
0
2
0
2
0
0
3
0
0
0
0
1
0
3
0
0
2
0
1
0
1
1
2
2
0
0
0
0
1
0
0
2
2
0
0
3
0
0
2
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
2
0
0
0
2
0
2
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
2
0
2
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
1
0
0
0
1
0
2
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
2
2
0
0
1
0
1
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
2
0
0
0
1
0
2
2
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
1
0
1
0
2
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
1
0
2
0
0
0
0
0
1
0
2
0
0
0
2
0
0
1
0
4
0
0
0
1
0
0
1
0
0
0
2
3
0
0
1
1
0
1
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
1
2
0
0
0
0
2
0
0
2
0
0
2
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
2
2
0
3
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
2
0
0
0
0
0
3
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
2
0
0
0
4
0
0
1
0
0
0
2
2
0
2
0
0
1
0
0
0
0
0
1
1
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
4
0
0
1
0
2
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
1
0
2
0
1
0
0
1
2
0
0
2
0
0
1
3
0
2
1
1
0
5
0
0
0
2
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
2
0
0
2
0
3
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
3
0
5
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
1
2
0
2
0
2
0
0
0
0
1
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
1
0
0
2
0
0
0
2
1
0
0
0
0
2
0
0
1
2
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
13
0
0
0
1
3
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
2
0
0
1
0
0
2
1
2
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
3
0
0
0
0
0
0
4
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
3
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
3
0
3
1
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
1
1
1
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
4
2
0
0
2
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
3
0
3
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
3
0
2
1
0
0
0
3
0
0
0
0
0
0
4
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
1
0
1
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
5
0
1
1
0
0
1
0
0
0
0
0
0
3
0
2
0
0
0
0
0
4
0
0
2
2
0
0
2
0
2
1
6
0
0
2
0
0
0
0
1
0
2
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
3
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
3
1
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
1
0
0
0
0
0
0
2
0
0
2
2
1
0
2
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
1
2
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
1
0
2
0
0
0
0
0
8
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
3
1
0
2
0
0
1
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
2
1
5
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
3
1
3
0
0
0
0
0
0
1
0
0
0
0
2
0
2
2
1
2
1
0
0
0
0
1
1
0
0
0
0
3
2
0
1
2
0
0
0
0
0
0
0
2
3
2
0
1
0
0
3
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
3
0
0
0
1
0
1
0
0
0
8
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
3
0
2
0
0
1
0
0
4
0
2
0
0
0
0
2
0
2
0
0
0
1
3
0
1
2
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
3
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
3
4
2
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
1
2
0
1
0
2
0
0
0
0
5
3
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
3
1
0
0
0
3
0
2
0
0
0
1
0
0
2
0
1
1
0
0
6
0
0
0
2
0
0
0
0
0
0
0
4
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
4
0
0
1
0
2
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
3
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
5
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
1
0
0
2
0
0
0
0
0
0
1
3
0
1
0
0
0
0
0
3
1
0
0
2
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
2
1
0
1
0
0
0
0
0
1
3
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
3
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
3
1
1
0
0
1
0
0
0
0
1
0
0
0
0
4
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
2
1
1
0
0
1
0
2
0
0
0
0
0
0
2
0
0
1
4
2
0
1
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
2
1
0
0
0
3
0
0
0
0
0
1
0
0
0
8
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
3
1
0
0
1
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
4
0
2
1
2
0
0
0
3
0
0
0
0
1
0
1
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
1
1
6
0
0
0
0
0
0
1
0
1
2
0
1
1
0
0
1
0
0
0
0
0
1
0
2
1
0
0
0
0
0
2
0
1
0
2
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
0
2
1
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
1
1
0
3
1
0
0
0
0
0
2
2
1
0
0
2
0
0
0
2
2
2
0
0
1
0
0
0
0
0
2
6
1
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
1
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
2
1
0
0
0
0
0
0
1
2
0
0
1
3
0
0
1
0
1
0
0
2
2
0
0
0
0
0
0
2
1
0
0
0
1
0
2
0
1
1
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
2
0
0
4
0
1
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
2
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
1
0
0
0
0
2
0
0
0
2
0
2
0
1
2
0
0
0
1
0
0
0
0
0
0
0
2
1
1
0
0
0
4
1
0
0
0
0
2
0
3
1
0
0
0
0
0
0
1
2
1
1
0
0
0
0
0
2
0
2
0
0
0
0
1
2
1
2
0
0
0
0
0
0
0
5
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
1
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
2
0
0
0
0
0
1
2
0
0
0
0
0
0
3
0
2
0
2
0
2
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
1
0
2
0
0
1
0
1
1
0
1
0
0
1
0
0
1
2
0
3
0
1
0
2
2
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
2
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
2
0
0
1
0
1
1
2
0
0
1
0
0
0
0
0
1
0
0
5
0
1
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
1
0
0
0
0
0
2
0
1
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
4
0
0
2
1
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
3
0
0
0
0
0
2
1
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
4
1
0
0
0
0
3
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
1
1
0
0
0
0
5
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
1
0
1
0
0
0
0
0
0
1
1
0
1
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
2
0
1
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
2
1
0
0
1
0
2
3
0
0
0
0
0
0
0
2
0
0
2
0
2
0
3
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
3
1
0
0
1
0
0
0
1
1
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
4
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
4
0
2
0
0
0
0
0
3
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
1
2
0
0
0
0
0
0
2
0
0
1
1
0
0
2
0
2
1
0
0
0
0
0
0
0
0
2
1
2
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
1
1
0
2
0
0
0
0
1
2
2
0
0
0
2
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
3
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
1
0
0
0
0
1
0
1
0
0
0
3
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
2
1
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
3
0
0
0
1
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
2
0
0
0
0
0
0
2
0
0
0
1
5
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
1
2
2
1
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
1
1
2
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
1
0
1
0
2
1
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
10
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
1
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
2
1
0
2
0
1
0
2
0
0
0
0
0
0
0
1
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
1
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
1
3
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
1
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
2
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
2
0
0
0
0
1
0
2
1
1
0
1
1
0
2
0
1
3
2
0
3
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
3
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
2
0
1
1
3
0
0
0
0
1
0
0
0
0
1
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
2
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
1
1
0
0
1
0
1
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
1
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
4
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
2
1
0
0
6
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
1
0
0
0
0
0
0
1
2
2
0
0
1
0
0
0
0
0
0
0
0
3
2
0
0
0
2
2
1
0
0
0
0
1
0
0
0
1
1
1
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
1
0
0
1
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
2
1
0
0
2
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
2
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
3
0
1
0
0
0
0
2
1
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
2
2
0
1
0
0
0
0
1
1
0
0
0
0
2
3
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
1
3
0
0
0
2
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
3
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
2
1
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
1
0
2
2
0
0
0
0
0
1
0
0
1
2
2
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
2
1
0
0
0
2
1
1
0
0
0
0
0
0
0
0
2
1
0
2
1
3
0
0
2
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
3
0
1
0
0
0
1
3
0
0
2
0
0
0
2
0
0
0
0
0
1
2
2
0
0
2
0
2
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
1
0
1
0
0
1
0
0
0
0
0
1
1
0
2
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
4
0
0
0
0
1
2
0
1
0
0
0
2
0
0
0
0
0
1
0
5
0
2
0
2
0
0
0
1
1
0
0
2
1
0
4
0
0
0
0
5
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
5
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
2
0
0
0
0
2
2
0
0
0
1
0
0
0
1
1
2
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
1
2
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
2
0
2
0
0
2
0
0
0
0
0
0
2
0
0
2
2
0
0
3
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
1
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
2
1
0
0
0
0
2
2
1
0
0
2
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
1
0
1
0
2
0
1
0
0
0
0
0
0
3
0
0
2
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
5
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
3
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
2
0
0
2
0
0
0
2
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
1
0
0
0
0
2
0
0
0
0
0
2
0
1
0
1
2
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
1
2
0
0
0
0
1
0
0
0
0
2
0
2
0
1
1
0
1
0
3
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
3
3
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
1
1
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
2
1
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
2
1
0
0
0
3
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
2
1
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
2
2
0
2
0
2
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
7
2
0
2
0
1
0
0
0
0
0
1
0
0
0
2
0
1
1
2
1
1
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
3
0
0
0
0
2
1
0
0
1
0
2
2
0
0
0
0
2
3
0
1
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
1
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
2
1
5
2
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
7
0
3
0
2
2
0
1
0
0
0
0
0
0
0
3
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
1
1
1
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
1
1
1
2
0
2
0
2
0
0
0
0
1
1
0
1
0
0
0
0
4
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
3
1
0
0
1
0
0
0
2
2
2
0
2
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
2
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
3
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
4
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
3
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
3
0
0
0
0
0
0
2
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
2
2
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
6
0
0
2
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
2
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
3
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
1
4
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
1
0
0
1
2
0
2
3
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
3
1
0
2
1
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
2
0
0
1
1
0
0
2
0
0
1
0
0
2
0
0
0
0
1
0
0
0
1
1
2
0
0
1
0
0
0
2
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
1
0
2
0
0
0
2
3
1
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
1
0
2
1
0
0
0
3
0
0
0
0
0
2
0
0
1
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
4
0
0
1
2
0
0
0
0
0
0
0
0
0
6
0
1
3
1
1
0
0
0
0
1
1
0
2
0
0
0
3
0
0
1
0
0
0
2
0
0
1
1
2
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
3
1
0
1
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
4
2
0
0
0
1
0
0
1
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
1
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
3
1
2
1
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
2
2
0
2
0
2
2
1
0
0
0
1
0
3
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
2
0
0
1
0
1
0
1
0
0
1
0
0
2
0
0
1
0
1
1
0
1
1
0
1
2
0
2
1
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
1
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
2
0
1
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
2
0
0
1
0
0
0
0
0
1
4
0
0
0
0
0
1
0
2
0
0
1
0
0
0
2
0
0
2
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
3
0
0
1
0
0
2
0
0
1
0
2
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
2
2
2
2
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
2
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
2
0
0
3
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
2
0
1
2
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
1
2
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
3
0
0
2
0
2
0
0
0
0
0
0
3
2
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
1
2
0
0
2
0
0
0
0
0
0
0
1
0
0
2
1
0
0
1
0
0
0
0
0
1
0
0
0
0
6
0
1
1
0
1
4
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
4
0
3
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
1
2
8
4
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
2
0
2
0
1
0
1
0
1
0
0
0
0
0
0
1
2
0
0
0
1
1
0
0
3
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
1
0
0
0
4
0
0
1
1
0
0
0
0
0
1
0
0
2
0
1
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
4
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
2
1
1
0
0
2
0
1
0
0
0
2
0
0
0
2
0
1
0
6
0
0
0
0
0
0
5
0
0
0
0
0
0
3
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
3
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
1
0
0
1
2
2
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
1
0
2
0
0
1
0
0
0
0
7
0
2
0
0
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
4
0
0
0
0
2
0
0
0
0
0
0
2
2
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
2
2
1
1
0
0
0
2
0
2
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
2
0
1
0
2
0
1
0
0
0
0
2
0
0
2
2
2
1
0
0
1
0
2
2
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
1
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
3
2
0
0
0
1
0
1
1
0
0
0
0
0
0
0
5
0
0
1
2
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
1
0
1
2
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
1
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
3
1
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
1
1
0
2
2
1
0
0
0
1
0
2
0
0
0
0
0
1
0
0
7
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
1
0
2
1
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
2
1
1
0
0
0
0
1
0
2
2
2
0
0
0
5
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
2
0
0
0
0
1
1
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
2
0
0
4
2
0
1
0
0
0
1
1
0
0
0
0
0
1
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
4
1
1
0
0
0
1
2
3
0
0
0
4
0
0
0
9
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
1
2
0
0
3
0
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
2
2
0
0
0
0
0
1
0
2
0
0
1
2
0
0
0
0
0
1
0
0
1
1
0
1
0
0
1
0
2
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
2
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
1
0
1
2
0
2
0
0
1
3
0
1
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
1
3
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
1
0
1
1
2
1
0
0
0
1
0
0
0
2
0
0
2
0
0
1
0
1
0
0
0
0
1
0
4
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
5
0
2
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
5
0
2
1
1
2
0
2
1
1
0
0
0
0
0
1
0
0
3
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
2
0
0
0
1
1
0
0
3
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
1
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
6
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
1
0
0
1
0
2
2
2
1
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
2
1
0
2
1
0
0
0
1
0
0
0
2
0
2
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
1
0
2
0
0
2
1
0
0
0
1
0
0
2
2
1
0
0
0
0
0
1
0
2
0
1
0
2
0
0
0
0
0
1
1
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
2
1
1
1
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
1
0
1
1
0
0
0
0
3
2
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
1
2
0
2
0
0
0
1
2
2
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
1
0
0
0
2
0
0
0
0
0
0
2
1
0
0
1
0
0
0
2
0
2
2
0
0
2
1
2
0
0
1
0
0
0
0
0
1
3
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
2
1
0
0
0
1
3
0
2
0
1
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
1
2
2
0
3
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
3
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
4
0
0
3
0
0
1
2
2
1
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
1
0
0
1
1
0
0
0
0
0
1
0
1
2
0
1
0
0
0
0
1
0
0
2
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
1
0
0
0
0
2
1
0
0
1
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
1
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
2
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
1
0
0
0
0
1
0
1
0
3
0
0
0
0
9
0
0
0
0
1
0
2
0
1
0
0
1
0
0
1
2
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
3
0
0
1
2
0
0
0
3
0
0
1
0
2
0
0
0
0
0
0
0
1
2
1
0
0
0
2
1
0
0
0
1
0
0
0
0
2
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
3
0
0
0
1
3
2
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
6
0
1
0
1
0
0
0
0
4
0
0
2
2
1
0
0
0
0
0
1
1
2
0
0
1
0
0
0
3
0
0
0
0
0
3
0
5
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
1
0
3
2
1
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
1
2
0
1
0
1
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
2
0
1
1
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
12
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
1
3
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
1
2
0
1
2
0
0
0
0
2
0
0
0
2
0
0
0
0
3
2
0
0
0
3
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
2
0
0
1
0
1
0
0
1
0
0
0
1
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
2
0
0
0
3
0
3
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
3
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
1
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
1
0
3
2
0
2
0
0
2
2
2
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
2
0
0
0
0
2
0
1
0
2
0
0
0
1
0
0
0
0
1
2
2
0
3
0
0
0
0
0
0
0
0
0
1
3
2
2
0
2
0
0
0
1
0
0
1
1
0
0
2
2
1
0
2
2
2
1
0
0
0
1
1
0
1
1
0
0
1
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
1
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
2
0
1
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
1
0
1
2
0
2
0
0
2
0
1
0
0
0
1
2
1
0
0
0
0
0
0
0
7
1
0
0
1
1
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
5
0
0
0
3
3
1
2
1
3
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
3
0
1
1
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
1
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
2
0
0
0
0
0
1
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
1
0
0
0
1
0
0
0
0
2
2
1
0
2
1
2
0
0
0
0
0
0
0
0
1
0
0
0
3
0
1
0
2
0
0
1
1
0
1
2
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
2
0
0
0
2
2
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
2
0
0
0
0
0
1
0
0
6
0
3
0
0
0
0
0
0
0
0
1
0
1
0
1
2
0
1
2
0
0
0
2
3
2
0
0
0
2
2
0
0
0
0
1
1
1
0
0
1
1
0
0
0
2
0
0
1
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
9
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
2
0
1
0
2
0
1
0
0
2
1
0
1
0
2
0
0
1
0
1
0
0
0
1
2
1
0
0
4
0
2
1
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
3
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
2
2
0
0
0
2
0
0
0
0
1
2
0
1
0
2
1
0
0
0
0
0
0
0
0
5
1
0
0
0
2
2
1
1
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
1
2
2
2
4
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
1
0
1
4
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
1
0
0
1
0
2
0
0
2
2
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
2
2
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
2
0
1
0
0
2
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
2
0
0
0
1
0
0
2
2
2
0
0
0
0
1
0
0
0
1
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
2
1
0
1
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
1
1
0
0
0
0
2
0
1
1
1
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
1
2
6
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
1
1
0
0
2
0
0
0
0
0
0
1
0
0
4
1
0
0
0
0
2
0
2
0
2
3
0
0
0
0
4
0
0
2
0
0
0
0
0
0
3
1
0
0
2
0
0
1
2
0
1
0
0
0
0
2
0
0
2
0
0
2
2
1
0
3
1
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
3
0
0
0
2
1
0
0
0
0
0
0
0
1
1
0
0
3
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
3
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
1
0
0
0
1
0
1
1
0
0
4
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
2
1
0
0
0
0
0
0
7
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
3
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
1
0
2
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
2
0
1
2
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
2
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
3
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
1
6
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
1
3
0
0
0
0
0
3
1
0
0
0
2
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
2
0
0
2
0
4
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
2
0
0
2
1
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
2
0
0
2
1
2
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
2
0
1
0
2
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
1
1
0
0
0
0
0
2
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
2
0
1
1
2
0
3
0
1
0
0
0
0
0
7
2
1
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
2
1
1
2
0
0
1
1
0
0
0
0
1
1
0
0
0
1
2
0
0
0
2
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
1
1
2
2
0
0
0
0
1
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
3
1
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
1
0
0
0
0
0
0
0
0
2
1
1
0
0
2
0
0
0
1
1
1
1
0
0
0
0
0
2
0
1
2
0
0
3
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
3
0
2
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
2
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
1
0
0
0
0
0
3
2
0
3
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
3
0
2
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
2
0
0
2
0
1
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
1
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
2
1
2
0
0
1
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
1
0
2
0
0
1
0
0
1
0
0
0
0
2
0
1
0
1
0
0
0
2
1
0
0
1
0
0
1
0
0
0
0
2
2
0
0
0
1
2
1
3
7
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
3
0
0
0
0
0
8
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
1
1
1
0
0
2
0
3
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
1
0
1
0
0
2
0
0
5
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
2
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
2
1
7
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
2
1
0
0
0
0
1
3
0
0
0
1
0
0
0
0
0
2
0
2
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
3
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
3
0
0
1
0
0
2
2
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
2
0
2
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
2
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
1
1
1
0
2
2
1
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
2
0
3
0
0
0
0
0
1
2
1
0
1
1
0
2
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
1
2
2
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
2
2
0
0
1
1
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
1
1
0
2
0
0
2
0
0
0
0
1
0
1
1
0
0
1
0
2
1
1
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
3
2
0
0
0
0
1
2
2
0
0
0
0
0
0
1
0
0
2
0
0
1
2
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
2
3
0
2
1
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
1
0
0
2
0
0
0
4
2
2
0
0
2
0
1
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
1
2
0
0
0
2
0
0
2
0
0
2
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
2
1
0
0
1
0
0
1
0
0
1
0
0
2
0
1
2
1
0
0
0
0
0
1
0
0
2
0
2
2
0
3
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
2
0
1
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
6
0
2
0
0
0
0
2
0
0
2
0
3
0
0
0
0
1
1
3
2
6
0
0
0
1
0
2
0
2
3
0
0
0
2
1
0
0
0
0
2
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
4
2
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
2
1
2
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
2
2
0
1
2
0
0
0
0
0
0
0
0
4
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
2
11
1
1
0
0
0
0
2
1
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
1
1
0
1
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
2
1
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
2
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
2
2
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
2
0
2
0
0
1
0
0
0
0
4
0
2
0
0
0
0
0
4
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
3
2
0
0
1
0
0
0
0
1
0
0
2
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
1
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
2
0
2
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
1
0
0
1
0
0
0
0
0
0
3
0
0
0
1
0
1
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
1
1
2
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
3
0
1
0
0
0
0
0
0
3
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
1
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
1
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
2
3
2
0
0
0
0
0
2
0
2
0
6
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
1
3
1
4
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
2
4
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
2
0
2
0
0
0
2
0
0
1
2
0
2
2
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
3
2
0
0
2
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
1
0
2
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
1
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
2
1
0
0
1
0
2
0
1
0
1
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
1
0
0
0
0
0
2
0
1
1
0
0
0
1
0
0
0
0
0
0
3
1
1
0
0
10
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
1
1
2
0
2
0
0
0
1
0
2
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
3
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
2
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
4
1
1
0
0
0
0
1
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
1
0
0
2
2
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
2
0
2
0
0
3
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
8
0
0
0
0
1
1
1
0
0
0
2
1
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
3
1
0
0
0
1
1
0
0
0
1
2
0
1
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
3
0
0
0
1
0
0
2
0
0
1
1
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
2
0
0
0
0
2
2
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
4
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
2
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
2
2
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
4
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
3
0
0
0
0
0
0
3
0
0
1
2
0
0
2
0
1
0
0
0
0
1
0
0
1
0
0
1
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
2
2
0
0
1
3
0
2
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
2
0
0
0
3
2
2
1
1
0
2
2
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
2
0
2
0
5
1
0
2
0
0
2
0
0
0
0
3
0
0
0
0
1
2
2
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
2
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
2
0
0
0
1
0
4
0
2
1
1
0
2
1
2
0
1
0
0
0
0
0
0
0
0
2
2
2
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
3
0
1
1
2
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
2
0
2
0
0
3
0
6
0
0
0
0
0
0
0
1
0
0
0
0
3
1
1
0
0
2
0
2
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
2
1
0
0
1
0
0
2
4
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
2
2
1
0
1
0
0
0
0
2
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
2
1
2
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
2
0
1
1
0
0
2
0
1
0
0
4
2
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
4
0
0
1
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
4
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
3
3
0
0
0
1
3
0
2
0
0
0
2
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
4
0
0
3
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
2
0
0
0
0
0
0
3
2
0
0
1
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
1
0
0
0
1
1
0
0
2
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
2
0
0
0
0
0
2
0
4
0
0
2
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
2
0
1
1
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
1
0
0
5
0
0
0
0
0
1
1
0
0
1
0
0
2
0
0
0
0
2
0
2
0
0
1
0
2
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
3
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
2
0
1
0
0
1
1
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
3
1
0
0
0
0
0
1
2
0
1
3
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
1
2
0
0
0
0
2
3
4
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
5
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
1
0
0
1
1
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
1
1
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
2
1
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
3
0
3
0
0
0
2
0
0
1
0
2
0
0
0
2
0
0
0
0
0
3
1
0
1
1
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
2
1
0
0
2
0
2
1
2
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
2
1
0
1
2
0
1
0
2
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
1
0
0
0
1
0
0
2
1
0
0
0
0
2
4
0
3
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
1
1
0
1
0
2
0
0
0
0
0
0
0
1
0
0
3
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
1
1
1
2
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
4
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
1
1
1
2
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
1
0
0
0
3
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
3
2
0
0
0
0
2
0
0
0
3
0
0
3
0
0
0
3
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
5
0
0
2
1
0
0
0
5
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
3
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
2
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
1
0
1
0
0
0
2
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
1
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
3
0
0
2
0
0
2
1
1
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
1
0
0
2
0
2
1
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
2
0
1
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
2
0
1
3
0
3
0
0
0
1
0
0
0
0
1
0
0
3
0
2
0
0
1
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
1
0
1
0
2
0
0
0
0
1
0
1
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
2
1
3
2
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
1
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
1
1
0
2
0
0
0
0
1
1
0
2
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
3
0
0
0
0
1
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
5
0
0
0
0
4
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
3
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
4
0
0
0
1
0
0
0
0
0
2
1
0
0
3
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
3
1
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
1
1
2
3
3
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
2
0
6
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
1
0
0
3
0
2
0
1
0
2
0
0
0
0
0
0
0
0
2
1
2
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
3
3
0
0
0
0
0
0
0
0
0
0
0
1
2
0
3
0
0
1
1
0
1
0
0
0
0
0
0
0
0
2
0
3
1
0
0
0
1
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
1
2
0
1
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
3
0
1
2
0
2
1
0
2
3
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
2
1
0
0
1
0
0
0
1
0
1
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
1
2
0
0
0
1
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
1
0
2
0
0
2
3
1
0
0
1
1
1
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
1
0
0
0
1
2
0
0
0
0
1
0
0
1
0
1
0
1
1
0
0
0
1
0
0
0
0
3
0
0
0
1
0
0
0
0
4
0
1
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
4
1
0
0
3
0
0
0
0
2
1
0
0
0
2
1
0
0
2
0
0
0
0
0
0
3
0
0
0
1
0
2
0
1
0
0
0
2
0
0
0
0
4
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
3
0
1
1
0
0
2
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
2
0
3
2
0
1
1
0
0
2
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
2
1
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
2
0
1
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
1
0
2
0
0
3
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
4
0
0
0
0
3
0
0
2
0
0
0
1
0
2
1
0
0
1
0
0
1
2
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
3
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
3
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
3
0
1
0
1
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
2
0
0
1
0
0
2
1
3
0
1
10
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
3
0
1
0
1
0
0
2
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
2
4
1
1
0
0
0
0
1
0
0
1
3
0
0
0
0
1
0
0
1
0
1
0
0
2
0
1
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
1
0
0
2
0
1
0
0
1
0
1
2
2
0
2
0
0
0
0
0
0
2
3
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
2
0
0
0
6
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
1
1
1
0
0
0
0
0
0
0
2
2
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
1
1
1
2
0
0
1
0
0
0
0
0
1
0
1
0
1
2
2
3
1
0
0
2
1
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
1
0
2
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
2
0
1
0
1
0
4
0
1
1
0
0
1
1
2
0
0
2
1
0
0
0
2
0
1
0
1
1
2
3
0
0
1
0
2
0
2
0
0
0
2
0
0
2
0
0
0
0
2
0
1
0
0
2
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
2
0
0
3
0
0
2
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
5
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
1
2
0
0
0
1
0
0
0
2
0
0
1
2
0
0
0
0
1
0
2
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
1
0
2
0
2
0
0
1
2
2
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
2
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
2
2
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
2
1
0
1
0
0
0
0
0
0
0
2
0
5
0
1
1
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
2
0
1
3
0
0
0
0
0
3
0
2
0
0
1
0
0
1
0
0
0
0
2
1
0
3
0
0
0
0
0
1
0
0
1
0
0
2
7
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
2
0
0
0
1
1
0
0
3
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
2
3
4
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
1
1
2
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
1
0
1
1
0
2
0
3
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
1
0
3
0
1
2
1
0
0
0
0
2
0
0
1
1
2
0
0
3
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
2
0
0
2
0
0
0
0
0
1
1
0
0
0
2
0
0
2
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
2
2
0
1
0
0
0
3
0
0
0
0
0
0
4
0
0
1
0
4
0
0
4
0
0
2
0
0
0
0
8
0
1
0
0
0
2
0
0
0
0
0
0
1
1
0
0
1
2
1
0
0
0
0
0
2
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
2
2
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
1
1
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
2
1
0
0
0
2
0
0
0
0
2
0
1
0
0
0
1
0
1
2
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
2
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
3
0
0
0
1
2
2
2
0
0
0
0
1
0
2
1
1
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
1
3
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
3
0
1
0
0
0
0
0
0
0
0
1
0
0
5
4
0
0
0
0
0
2
0
0
0
0
8
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
3
3
0
2
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
6
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
1
0
0
3
0
0
0
2
0
0
0
0
0
1
3
1
0
0
2
0
0
0
2
2
2
0
0
1
0
0
2
0
0
0
1
0
0
1
0
0
2
7
0
0
0
2
1
0
0
2
0
0
2
0
0
0
0
2
1
0
0
0
0
2
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
3
1
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
2
0
2
0
0
0
1
0
0
1
0
0
0
0
1
0
1
1
0
1
1
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
5
0
0
0
3
0
0
0
0
1
0
0
0
0
0
3
0
0
2
0
2
2
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
1
0
0
0
6
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
6
0
0
0
2
0
1
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
2
1
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
1
3
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
1
0
0
2
0
0
1
0
0
2
1
2
0
2
1
0
1
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
2
0
0
0
1
0
2
1
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
8
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
3
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
2
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
1
0
0
0
0
0
0
0
0
3
2
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
3
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
8
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
1
0
0
0
1
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
2
3
2
0
0
0
2
0
0
0
0
1
0
2
2
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
2
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
3
2
0
0
4
2
0
2
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
2
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
3
4
2
0
0
0
1
1
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
2
2
0
0
0
1
0
1
0
0
0
2
0
0
3
0
3
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
2
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
2
0
1
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
4
0
0
0
0
0
0
2
0
2
0
2
0
0
0
2
2
1
0
0
0
2
0
2
4
0
3
0
1
0
0
0
0
1
2
3
0
0
0
1
0
0
0
3
0
1
0
0
2
2
0
4
1
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
10
1
0
1
2
0
0
1
0
0
4
0
1
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
2
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
2
1
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
2
0
0
0
0
0
1
2
0
1
0
0
0
4
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
2
2
0
2
0
2
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
3
2
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
2
0
2
0
0
2
0
2
2
0
0
0
0
1
1
1
0
0
1
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
3
1
0
2
0
0
0
0
0
0
0
2
0
0
1
3
0
1
2
0
0
0
2
2
0
0
0
2
0
0
0
0
2
0
0
1
0
2
0
0
3
2
0
0
0
0
0
0
0
4
0
0
0
1
2
2
1
0
0
0
0
2
0
0
2
0
0
0
0
2
2
1
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
2
0
1
1
2
0
0
0
0
3
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
2
0
0
0
1
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
1
3
0
0
0
2
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
2
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
2
3
1
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
2
3
1
0
0
0
1
0
0
1
2
0
2
0
2
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
3
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
2
0
2
0
0
1
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
5
0
0
1
1
3
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
1
0
2
0
1
1
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
1
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
1
2
0
1
0
0
0
0
1
0
0
0
2
0
2
0
0
2
0
2
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
2
2
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
1
0
0
0
1
0
0
2
0
0
2
0
0
2
0
0
0
0
0
2
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
1
2
0
3
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
3
0
0
1
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
1
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
2
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
1
0
2
0
3
1
2
0
0
1
0
0
1
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
3
0
0
1
0
0
0
0
2
2
0
0
7
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
1
1
1
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
3
2
0
3
1
2
0
0
0
0
0
0
1
0
0
0
0
1
2
2
0
2
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
5
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
3
0
1
0
0
0
0
2
0
3
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
1
0
3
1
0
0
0
0
0
0
0
0
0
1
0
0
6
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
3
1
2
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
2
0
0
0
0
0
0
2
0
0
2
1
0
2
1
0
0
0
0
0
9
0
0
0
2
2
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
1
0
0
0
1
0
2
0
0
0
0
1
0
0
2
2
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
2
0
3
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
3
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
2
0
1
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
2
0
1
3
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
2
0
0
2
2
0
1
2
0
0
2
2
0
0
0
0
0
1
0
7
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
2
2
0
2
2
0
0
2
2
1
1
0
0
4
0
0
2
2
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
2
1
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
3
1
0
2
1
0
0
0
0
0
0
1
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
2
0
0
1
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
1
0
2
0
0
0
0
1
1
0
1
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
2
0
1
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
6
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
1
0
0
0
0
0
0
3
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
5
0
2
2
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
4
0
1
2
0
0
0
0
0
0
0
0
3
7
0
1
2
2
0
0
0
0
1
2
0
0
1
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
4
0
0
0
2
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
2
0
2
0
2
0
0
0
0
0
0
0
1
13
2
0
1
0
1
0
0
1
0
2
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
2
2
0
2
4
0
0
0
1
0
3
0
0
0
0
2
0
5
3
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
3
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
1
0
0
0
0
0
0
0
0
0
1
6
0
0
0
0
0
0
0
2
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
2
0
0
0
0
0
0
0
0
0
6
0
1
0
0
0
2
2
2
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
3
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
1
0
0
1
0
0
0
0
4
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
2
0
1
0
0
2
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
1
2
1
2
0
0
0
0
0
0
1
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
1
0
2
2
1
0
0
0
0
1
0
0
0
0
4
0
1
0
2
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
1
2
0
2
0
2
1
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
4
0
0
0
1
0
0
0
0
0
1
0
2
0
0
3
1
0
0
0
2
1
0
0
0
0
0
0
0
4
0
2
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
2
2
1
0
0
0
0
0
3
0
0
0
2
0
1
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
2
0
0
0
2
2
1
0
0
1
0
2
0
0
4
0
0
0
0
0
0
0
0
2
0
1
0
1
0
2
1
0
1
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
3
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
1
1
2
0
1
0
3
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
1
1
0
0
1
1
4
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
2
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
2
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
3
0
0
0
1
1
0
2
2
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
2
0
0
1
0
0
1
0
1
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
2
2
0
1
0
0
1
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
1
0
3
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
1
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
1
0
1
0
0
0
1
1
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
3
0
2
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
5
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
3
0
4
1
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
3
2
0
0
1
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
2
0
0
3
0
1
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
2
1
2
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
2
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
1
0
0
1
0
0
0
0
0
0
2
1
2
2
0
0
2
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
1
2
0
0
0
0
1
0
0
1
0
0
2
1
0
1
0
1
0
0
0
0
1
0
2
0
0
1
0
0
0
0
1
1
1
1
0
2
0
2
0
0
2
0
1
0
1
0
1
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
2
2
1
2
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
2
0
1
2
2
0
6
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
1
0
2
1
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
1
0
0
1
0
0
0
2
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
4
0
2
2
0
1
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
2
0
0
0
0
1
0
0
0
1
2
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
1
0
0
0
0
0
0
0
0
0
1
3
0
0
0
9
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
2
0
2
0
1
1
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
1
0
1
0
0
0
0
0
0
2
1
2
0
0
0
1
0
1
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
1
0
0
0
0
0
5
0
0
0
3
0
2
0
0
0
0
0
2
2
0
2
0
2
0
0
0
0
2
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
3
0
2
0
1
0
1
2
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
4
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
3
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
3
0
3
0
0
0
0
0
0
2
0
0
1
2
0
2
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
2
0
3
0
1
0
2
2
0
1
1
1
0
0
0
0
0
0
0
0
2
1
2
2
0
0
0
0
0
0
0
0
0
1
0
2
1
2
0
1
0
1
0
0
0
0
0
0
0
6
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
2
0
0
0
1
4
0
2
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
3
0
0
0
0
1
0
1
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
4
0
0
0
1
5
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
2
0
0
2
2
0
0
1
0
0
0
1
0
0
0
3
0
0
0
0
1
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
1
4
1
0
1
2
3
3
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
1
2
2
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
3
0
0
2
0
0
1
0
1
2
0
2
2
0
2
0
0
2
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
1
1
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
1
0
3
0
0
0
0
1
0
0
0
0
3
2
2
3
2
0
2
0
6
1
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
4
0
0
0
0
1
2
0
0
0
0
0
0
1
0
1
4
0
1
0
0
0
0
4
0
1
0
0
0
0
2
0
0
1
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
1
0
0
3
0
1
0
0
0
2
4
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
4
0
0
0
1
0
0
2
0
0
0
0
2
2
0
0
3
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
1
0
0
0
2
2
0
1
1
0
0
1
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
2
3
1
3
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
1
0
0
0
0
2
0
0
0
0
3
0
1
0
0
0
2
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
2
1
0
0
0
1
0
0
0
0
0
1
3
2
1
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
3
0
0
0
0
3
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
2
6
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
1
2
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
3
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
3
0
0
1
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
2
0
0
0
0
2
0
2
0
0
0
0
1
1
0
0
2
0
0
0
1
2
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
2
4
0
0
2
3
3
4
0
1
0
0
0
2
0
1
0
0
2
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
2
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
1
0
2
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
1
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
1
1
0
0
3
13
0
1
1
0
2
0
1
0
0
0
1
1
0
2
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
2
2
0
0
0
0
1
2
0
0
2
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
1
0
0
2
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
2
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
1
1
0
1
1
0
0
0
0
2
0
0
0
0
0
0
4
0
1
0
1
0
0
2
0
2
1
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
3
2
0
2
0
0
0
3
0
3
0
0
0
0
0
0
1
2
1
0
0
0
1
0
0
0
1
0
2
0
0
0
2
0
0
0
0
2
0
1
2
2
0
0
0
1
0
0
0
2
2
1
0
1
0
0
0
0
0
1
0
0
1
0
0
2
1
2
0
0
0
0
0
1
0
1
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
2
3
0
0
0
1
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
1
1
0
1
0
2
2
0
0
0
1
0
0
1
2
0
0
0
2
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
1
0
0
0
1
0
1
0
1
0
1
0
0
1
2
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
5
0
0
0
0
2
0
0
1
2
1
0
2
1
0
0
1
0
0
0
0
0
0
0
0
2
2
2
1
0
1
0
1
0
0
0
0
0
0
3
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
3
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
3
0
0
0
0
0
2
0
0
0
4
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
1
1
2
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
1
0
2
1
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
2
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
3
1
0
2
0
3
0
1
0
1
0
0
0
0
0
2
1
0
2
2
0
2
0
0
0
0
0
0
2
0
1
1
0
1
0
1
0
0
0
2
0
0
2
0
4
0
0
2
2
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
3
0
0
0
0
0
0
0
2
0
0
0
0
3
2
0
0
0
0
0
0
0
2
0
0
0
1
4
0
0
0
0
2
1
0
0
1
1
0
0
0
0
1
5
0
0
0
0
0
1
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
4
1
2
0
0
0
0
0
1
0
0
2
3
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
3
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
3
0
0
0
0
1
0
1
2
0
1
0
1
0
0
0
0
0
0
0
0
0
2
3
0
3
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
2
0
2
2
0
0
1
4
0
0
2
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
2
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
2
1
0
1
0
0
0
0
0
0
3
0
2
2
0
1
0
0
3
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
3
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
5
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
2
2
0
0
2
0
0
2
0
0
1
0
0
0
0
0
7
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
1
0
0
1
0
2
0
0
0
1
0
3
0
0
1
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
6
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
1
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
2
0
2
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
1
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
2
2
1
0
0
0
3
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
2
0
2
0
0
1
2
0
0
0
0
1
0
0
0
0
3
0
0
1
0
0
0
0
0
0
1
1
0
0
4
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
2
0
0
1
0
1
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
1
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
2
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
2
2
0
0
2
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
5
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
1
0
1
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
1
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
2
2
1
2
0
1
2
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
3
0
2
2
1
0
3
0
0
0
0
0
2
0
0
2
0
0
2
0
2
0
0
0
2
1
0
1
0
0
1
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
3
0
2
3
0
0
0
0
2
2
0
1
3
0
1
0
0
1
1
0
0
0
0
0
0
2
1
0
1
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
2
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
2
2
3
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
2
0
0
1
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
1
0
1
0
2
0
0
1
0
1
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
4
3
0
0
0
1
0
0
0
3
0
0
1
1
4
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
3
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
3
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
1
0
0
0
2
0
0
2
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
1
1
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
1
2
0
0
0
1
0
2
2
1
0
0
0
4
2
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
1
0
0
2
0
0
2
0
1
2
0
0
0
0
1
0
0
2
0
0
0
0
1
1
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
2
0
0
0
0
1
1
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
1
0
2
3
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
5
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
2
0
1
0
0
2
3
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
2
2
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
2
0
2
1
0
0
0
0
1
2
0
1
0
0
0
0
5
0
1
0
0
1
0
0
1
0
0
3
1
0
0
9
2
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
2
0
0
0
1
0
2
1
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
2
0
2
2
0
0
1
0
0
2
1
0
0
0
2
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
1
1
2
0
0
0
1
0
0
0
2
3
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
4
0
0
0
0
0
0
1
1
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
1
0
0
0
3
0
2
0
3
0
0
0
2
1
0
2
0
2
6
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
6
0
0
0
1
0
0
0
2
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
1
0
0
1
0
0
2
0
3
0
1
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
5
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
2
0
4
0
0
4
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
2
4
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
2
2
0
1
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
2
0
2
1
0
0
2
0
0
0
0
2
1
2
0
0
3
3
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
2
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
1
0
0
0
0
3
1
0
1
0
0
1
0
1
4
0
0
0
0
2
0
0
0
1
2
0
0
1
0
0
0
2
0
2
1
0
0
1
1
2
0
0
0
2
1
1
0
0
0
0
0
0
1
5
2
2
0
0
0
0
0
0
0
2
3
0
0
0
1
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
2
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
2
1
0
0
2
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
3
2
1
0
0
1
0
3
0
0
1
5
0
2
2
0
0
0
2
1
2
0
1
0
0
0
0
2
1
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
3
0
0
0
0
2
2
0
0
0
0
0
0
0
3
0
2
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
1
0
1
2
0
2
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
1
0
0
4
0
1
2
0
0
2
3
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
4
0
2
2
2
0
0
0
2
0
0
0
0
1
0
1
0
0
1
0
2
0
0
2
4
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
3
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
2
0
0
2
0
1
2
0
0
0
0
0
3
1
0
0
0
2
0
1
1
1
2
3
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
1
0
3
1
0
2
0
0
0
0
0
2
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
2
0
2
1
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
3
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
2
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
1
2
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
3
1
0
0
0
1
0
2
0
0
2
3
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
1
0
0
2
0
0
0
0
2
0
0
0
0
1
1
1
0
1
1
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
2
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
3
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
3
0
0
1
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
3
3
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
1
0
3
1
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
4
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
1
0
0
0
2
2
4
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
1
0
2
1
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
2
0
3
1
0
1
0
2
0
0
0
11
0
0
0
0
2
2
1
2
0
0
6
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
3
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
1
1
0
5
0
0
0
0
2
2
0
0
0
0
1
0
0
0
1
0
0
1
0
2
4
1
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
3
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
2
1
0
1
1
2
0
0
0
2
5
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
2
1
2
0
0
2
0
1
4
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
1
0
1
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
3
0
2
0
0
0
0
0
0
2
0
0
0
1
0
2
1
0
0
0
0
0
0
0
1
0
1
0
2
1
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
1
2
2
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
1
0
4
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
3
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
3
1
1
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
2
0
3
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
3
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
2
0
3
0
0
1
0
2
0
0
0
0
0
2
2
0
1
0
1
0
0
0
0
1
2
0
2
2
0
0
0
0
0
0
0
0
0
0
2
1
0
4
1
0
0
2
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
2
0
1
0
2
1
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
7
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
2
1
0
0
4
0
1
0
0
1
2
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
1
2
4
2
0
0
0
0
1
0
2
0
0
2
0
0
0
1
0
2
2
2
0
0
0
0
2
0
0
0
4
0
2
0
0
0
6
0
0
0
1
0
0
2
0
0
1
0
1
0
1
0
2
0
0
0
0
1
0
1
0
0
2
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
1
1
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
2
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
1
1
0
0
0
0
0
2
0
1
0
0
3
2
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
3
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
5
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
2
0
0
0
0
0
0
1
0
3
0
0
1
2
0
0
0
0
2
5
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
2
0
0
0
1
0
1
1
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
2
3
0
0
0
2
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
3
1
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
1
1
1
0
0
2
4
2
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
1
2
1
1
0
0
0
1
0
2
0
1
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
2
0
0
2
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
3
0
0
0
0
0
6
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
1
0
1
2
1
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
1
1
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
2
1
0
0
1
1
1
1
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
2
2
0
0
0
0
0
1
0
0
2
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
2
2
2
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
2
0
2
0
1
2
2
0
0
0
2
2
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
2
4
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
2
3
0
0
2
0
0
0
0
0
2
3
1
0
0
2
2
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
1
0
1
1
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
2
2
1
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
2
1
2
0
0
0
0
1
2
2
0
2
2
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
5
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
2
1
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
3
0
0
7
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
2
1
0
0
0
0
0
2
0
0
2
0
2
3
0
0
0
0
0
0
1
2
0
0
0
0
0
1
2
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
4
0
0
0
0
1
1
0
1
0
0
0
0
1
2
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
3
0
0
7
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
2
1
0
1
0
0
0
0
0
0
10
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
3
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
1
0
2
0
0
1
0
1
2
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
2
1
0
2
0
0
2
0
0
0
1
0
0
0
2
3
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
1
2
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
3
0
0
1
0
0
0
0
0
0
1
1
1
2
1
0
0
0
4
1
2
0
2
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
1
0
0
0
1
0
0
3
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
2
2
0
0
0
0
0
0
0
2
2
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
4
1
0
0
0
0
0
0
0
3
0
0
0
0
2
0
2
2
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
1
5
0
0
1
0
0
0
2
2
0
0
0
0
0
1
1
1
0
0
0
0
2
0
0
0
1
2
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
1
1
0
4
0
0
0
0
0
0
2
0
0
1
0
0
0
0
3
0
6
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
1
0
0
0
2
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
1
0
1
2
0
2
0
2
1
0
0
0
0
0
0
0
0
2
2
0
1
0
1
1
0
0
1
1
0
2
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
4
2
2
0
0
0
0
0
0
0
1
2
0
0
2
0
9
0
4
1
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
2
0
0
1
0
2
0
0
0
0
1
0
2
0
0
0
3
0
1
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
1
0
2
1
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
1
2
1
0
2
1
2
1
0
0
2
1
1
2
0
0
0
2
0
0
0
0
0
1
0
0
0
2
2
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
2
2
0
0
0
0
0
1
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
1
0
6
0
0
0
0
0
0
3
1
0
0
2
0
0
1
0
1
0
0
0
0
1
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
3
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
2
2
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
2
0
0
0
2
0
0
1
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
1
0
0
0
1
2
3
2
0
0
1
2
2
0
0
1
0
3
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
3
0
0
2
0
2
1
1
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
1
4
0
1
0
0
2
1
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
1
0
0
2
0
2
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
2
1
0
0
0
1
0
0
0
1
0
1
1
0
1
0
0
0
1
0
0
0
0
2
1
0
0
1
0
0
1
4
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
3
1
0
0
0
0
1
0
2
0
2
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
3
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
1
0
0
0
1
0
2
0
0
0
0
0
2
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
3
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
2
0
1
0
2
0
2
0
0
0
0
0
0
0
2
0
2
0
0
1
1
2
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
1
2
0
0
0
1
0
1
1
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
2
0
1
5
0
0
2
0
1
0
0
0
0
2
0
0
0
1
0
2
0
2
0
0
1
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
6
1
1
1
1
0
0
0
2
3
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
1
0
0
2
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
3
0
0
2
0
0
1
0
0
0
0
4
0
0
0
0
0
2
1
0
1
0
0
3
0
0
0
2
2
0
0
0
1
0
0
2
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
2
0
1
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
2
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
2
2
0
0
0
0
0
2
0
0
0
0
0
1
1
2
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
1
0
1
0
0
0
0
2
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
4
0
1
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
2
0
1
1
0
2
0
0
0
0
0
1
3
1
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
1
1
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
6
0
0
0
0
0
3
0
0
0
0
0
1
2
3
0
0
0
0
0
0
0
5
0
0
2
1
1
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
1
0
3
0
1
0
0
0
0
0
2
0
0
0
2
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
2
1
0
0
2
1
0
0
0
2
1
2
3
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
1
1
2
2
0
2
0
0
0
0
0
0
3
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
5
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
1
0
2
1
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
1
3
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
2
0
4
2
0
0
0
3
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
1
5
3
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
5
1
0
1
0
1
1
3
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
1
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
4
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
3
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
2
7
0
2
2
0
0
3
0
1
1
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
2
8
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
5
0
0
1
0
0
1
0
0
0
0
0
0
0
3
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
2
2
0
0
0
3
2
0
0
2
0
0
0
0
2
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
3
1
0
0
1
1
2
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
2
0
1
0
0
0
0
3
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
2
4
0
0
0
0
0
1
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
2
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
3
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
2
0
2
0
1
1
0
0
0
2
2
1
2
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
1
0
0
2
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
1
0
1
0
0
2
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
1
0
0
4
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
2
0
1
0
0
0
0
3
2
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
2
0
1
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
2
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
2
1
1
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
1
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
4
0
0
0
1
2
0
0
2
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
1
1
1
0
0
2
0
0
3
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
1
0
4
0
6
0
0
0
0
0
0
0
1
2
1
0
2
1
0
2
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
7
2
0
2
0
0
1
3
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
4
1
2
0
1
0
0
0
1
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
2
2
0
2
0
1
0
2
3
2
1
0
0
0
1
0
0
0
2
1
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
2
0
0
2
2
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
2
1
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
1
0
1
0
1
1
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
4
0
3
0
0
0
2
2
0
0
0
0
1
0
0
0
1
0
1
1
0
4
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
1
0
2
0
0
0
1
0
0
0
0
0
3
0
0
0
2
0
2
0
0
0
0
2
3
0
0
2
0
2
1
0
1
0
0
1
0
1
1
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
1
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
2
0
0
0
0
1
2
0
1
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
1
0
1
0
1
2
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
2
2
0
0
1
0
0
0
2
0
0
2
1
1
2
0
1
2
0
1
3
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
3
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
4
1
0
0
0
0
1
1
2
2
0
0
0
1
0
3
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
1
1
0
0
0
1
0
0
0
1
2
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
3
0
0
0
4
0
0
0
1
0
3
0
0
4
0
0
1
0
0
0
0
0
0
2
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
2
1
1
1
2
0
0
0
0
2
1
2
0
1
0
0
0
0
0
0
0
0
8
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
2
1
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
1
1
0
0
0
0
0
0
0
1
2
3
1
0
0
2
0
0
1
1
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
2
2
0
3
0
0
1
0
0
0
0
0
1
1
4
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
1
0
1
0
3
0
2
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
2
1
0
0
2
0
0
1
0
2
0
2
0
2
0
1
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
1
0
1
2
0
0
0
0
0
0
1
1
3
0
0
0
1
2
2
1
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
3
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
5
0
0
0
0
2
0
2
0
0
0
0
0
2
1
0
1
0
0
0
1
0
1
1
0
0
0
1
0
2
1
1
1
0
0
0
0
0
0
1
0
0
2
2
0
1
0
0
0
0
0
0
2
2
0
0
0
2
0
0
2
0
0
0
3
0
0
0
1
1
0
1
0
1
0
0
2
0
1
0
0
0
0
0
2
0
1
0
2
0
0
1
0
0
2
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
1
2
0
0
3
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
2
0
0
1
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
1
2
0
0
0
0
3
1
0
0
0
0
0
2
0
2
0
0
0
0
2
0
1
0
0
0
0
0
2
1
0
0
1
0
0
0
1
2
0
0
0
0
3
0
0
2
1
0
0
1
0
0
0
1
0
4
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
2
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
2
0
0
2
0
0
3
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
1
2
0
0
0
0
1
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
1
0
2
0
2
0
0
3
0
0
0
0
1
2
2
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
1
0
2
0
0
0
2
0
2
1
1
0
0
2
2
0
0
0
0
2
1
0
2
1
0
1
0
0
2
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
3
0
1
0
0
0
1
1
1
1
1
0
0
2
0
2
1
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
2
4
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
1
0
0
0
0
0
2
2
0
0
2
0
1
0
0
0
3
2
0
2
0
2
0
0
1
1
0
0
0
2
0
0
1
0
4
0
1
0
2
0
0
0
2
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
2
2
2
2
0
0
0
2
0
1
0
1
0
0
2
1
2
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
2
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
1
3
2
0
0
0
2
0
0
3
0
3
0
0
3
0
0
0
0
1
0
0
2
1
1
0
2
0
0
3
0
0
0
0
1
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
1
1
0
0
0
0
4
2
0
0
2
2
1
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
2
0
0
0
1
0
0
1
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
1
2
0
1
0
1
1
0
0
0
0
0
0
2
4
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
1
0
0
2
0
0
0
0
0
3
0
0
0
0
6
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
4
0
2
1
0
2
0
1
1
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
3
0
0
2
0
1
0
0
0
0
1
2
0
1
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
3
3
1
0
0
2
0
0
0
0
0
2
0
1
1
0
0
0
0
2
3
0
1
0
0
2
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
1
0
0
0
0
0
4
0
0
0
0
0
1
2
0
0
2
1
0
1
0
0
1
2
0
1
0
0
3
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
2
0
0
0
3
2
0
2
0
1
3
0
0
0
1
3
0
2
0
0
0
0
0
1
0
0
0
1
3
0
2
0
0
0
0
1
0
0
0
2
0
1
1
3
1
0
0
3
0
0
0
0
2
0
0
1
4
0
0
0
0
0
1
0
0
2
0
2
0
0
0
2
0
0
2
2
0
1
2
0
0
3
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
2
2
0
1
3
0
0
0
1
0
0
0
2
0
0
2
0
0
1
1
1
0
0
1
0
0
0
2
0
1
1
2
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
3
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
4
0
1
0
0
1
1
0
0
0
0
0
4
3
0
0
2
0
0
0
0
1
2
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
2
1
1
0
0
0
1
0
0
0
2
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
1
0
0
0
1
0
2
0
0
2
0
0
0
2
1
1
4
1
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
7
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
4
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
3
0
2
0
0
0
1
2
0
3
1
2
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
4
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
1
0
0
0
1
0
0
2
0
0
2
2
1
0
0
0
1
0
0
0
0
2
0
0
4
0
0
0
0
2
0
0
0
0
1
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
2
0
0
1
0
0
1
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
1
0
1
0
1
0
0
0
1
0
0
1
0
2
0
0
2
0
1
0
0
1
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
2
0
1
0
0
1
2
0
1
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
2
1
0
0
0
0
0
5
1
0
0
1
0
0
0
2
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
2
0
2
0
2
0
0
2
0
0
3
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
1
2
0
1
2
2
0
0
0
2
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
3
0
2
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
1
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
1
0
0
1
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
1
2
2
0
1
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
2
0
2
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
2
3
0
0
1
0
0
0
0
0
2
0
1
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
2
0
1
2
0
2
0
1
0
0
2
0
0
1
1
1
0
0
1
2
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
2
1
1
0
0
0
0
0
0
3
0
0
1
1
0
0
0
0
0
2
0
0
0
3
0
0
0
1
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
2
1
2
0
0
1
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
2
0
3
0
0
0
0
0
1
0
1
0
0
1
0
0
6
0
0
5
0
0
0
2
4
0
0
0
0
0
0
1
0
0
3
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
2
2
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
3
1
1
0
3
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
1
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
3
1
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
2
2
1
0
0
0
0
0
1
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
1
2
0
0
2
0
3
0
1
1
0
0
0
0
1
0
0
0
0
3
0
0
0
1
0
3
1
2
1
0
0
0
0
0
0
1
3
1
1
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
1
1
0
2
0
2
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
2
0
0
0
2
3
0
4
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
1
0
2
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
2
0
0
6
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
2
0
0
2
0
1
0
0
10
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
1
0
0
0
1
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
1
0
2
1
1
0
0
0
0
0
0
2
1
0
2
0
4
1
0
1
2
0
0
0
0
0
1
2
2
0
0
0
2
2
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
4
0
3
0
2
0
0
1
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
5
0
0
0
2
0
0
0
2
2
0
1
2
0
0
0
0
2
0
0
1
0
0
0
0
1
2
2
3
0
0
0
0
4
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
3
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
2
0
0
0
1
0
0
2
0
1
0
0
1
2
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
3
2
0
0
0
1
0
3
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
1
3
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
10
0
1
0
2
0
2
1
0
0
2
1
0
3
0
0
0
1
2
0
1
0
0
0
0
6
0
2
0
0
0
0
0
1
1
0
0
0
0
0
3
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
1
0
0
0
1
2
0
3
2
1
1
4
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
2
1
2
2
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
2
0
4
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
2
2
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
2
0
3
0
0
1
3
0
0
1
1
2
0
0
2
0
0
0
3
0
0
0
0
2
0
0
1
0
4
2
2
0
0
0
1
0
0
0
2
0
0
0
0
1
2
0
0
2
2
0
0
0
0
0
2
0
0
1
0
1
0
2
1
0
2
1
0
0
0
2
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
2
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
2
1
1
0
1
0
0
0
0
0
1
2
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
3
1
1
2
0
0
0
0
0
0
0
2
0
0
2
2
1
0
0
0
2
0
2
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
2
0
2
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
3
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
2
0
2
0
1
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
1
2
0
0
0
0
1
1
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
2
1
0
1
0
0
0
1
1
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
1
2
1
0
0
0
2
0
0
0
0
0
0
0
0
3
0
2
5
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
2
0
0
2
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
2
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
1
1
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
1
0
0
1
0
1
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
2
0
2
1
0
0
0
1
2
0
0
0
1
0
2
0
1
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
3
0
0
2
0
0
1
1
0
0
2
0
1
0
2
0
0
0
0
0
1
2
0
0
0
1
1
2
1
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
2
1
2
2
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
2
1
0
0
2
0
0
0
2
0
0
0
0
1
0
0
1
0
0
2
0
2
2
0
0
3
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
4
0
0
0
0
0
0
2
0
0
0
1
1
1
0
1
0
0
0
2
0
0
0
0
1
0
1
0
2
0
3
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
2
2
0
1
0
3
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
3
2
0
0
1
2
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
4
0
1
0
1
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
5
1
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
3
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
2
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
1
0
3
0
0
2
1
0
0
2
2
0
0
1
0
0
0
3
0
0
0
0
0
1
0
1
1
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
3
2
0
0
0
0
0
3
3
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
1
0
1
0
0
4
0
0
2
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
3
0
2
0
0
0
4
0
0
3
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
2
0
2
2
0
0
0
0
0
0
0
0
2
0
2
0
1
1
4
0
0
0
1
0
2
0
0
0
0
0
1
0
0
1
0
2
0
0
0
4
0
1
0
2
1
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
2
0
0
0
2
0
1
3
0
2
1
0
2
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
1
0
1
0
0
0
2
1
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
2
1
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
2
1
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
3
6
2
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
1
0
1
2
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
3
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
4
1
0
0
0
1
1
0
1
2
0
0
0
0
0
0
2
0
2
0
0
1
0
0
1
0
1
0
0
1
0
2
2
0
2
0
0
0
2
0
0
0
2
0
3
0
0
0
0
0
2
0
1
0
2
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
2
0
1
0
1
0
2
0
0
0
2
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
3
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
6
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
3
1
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
3
0
0
0
0
0
0
4
0
0
1
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
1
1
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
4
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
6
0
0
0
0
2
0
1
1
0
0
1
0
0
2
0
2
2
0
2
2
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
2
0
2
0
0
0
0
0
2
2
0
0
0
0
4
0
0
1
0
0
0
0
0
2
0
1
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
4
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
3
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
2
0
2
0
1
0
0
0
1
0
0
0
1
2
1
0
0
1
0
0
0
1
4
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
2
1
1
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
3
2
2
0
0
0
0
1
1
0
2
2
0
2
1
0
0
0
0
0
0
0
0
0
0
1
1
2
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
2
0
0
1
0
0
1
0
0
0
0
0
2
0
0
3
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
2
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
2
1
0
2
1
0
0
1
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
1
3
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
2
0
2
0
3
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
1
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
2
0
1
0
0
2
0
3
4
0
0
0
1
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
1
0
0
1
0
0
2
0
0
0
0
1
5
0
2
0
2
0
0
0
0
0
2
3
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
1
2
0
5
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
2
1
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
2
1
1
0
0
0
1
1
1
0
0
0
1
2
0
0
1
0
3
0
0
0
0
0
0
3
0
0
0
6
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
1
1
1
0
2
1
0
0
0
0
0
1
0
0
0
0
1
1
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
3
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
2
0
0
1
0
3
0
0
2
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
3
0
0
0
0
1
1
0
0
2
0
0
0
0
0
2
1
2
0
2
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
3
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
2
0
1
2
2
0
0
0
2
0
0
1
0
0
2
0
0
0
3
4
0
0
0
1
2
0
1
2
0
0
0
0
6
0
0
1
1
0
2
0
0
2
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
4
3
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
2
0
0
0
1
0
3
1
0
0
0
0
4
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
1
0
0
0
2
0
0
0
2
0
2
2
1
0
0
0
0
0
0
0
0
2
0
1
4
0
1
0
0
0
8
0
0
0
0
4
1
1
0
0
0
0
2
0
0
0
0
0
0
2
2
1
0
2
4
0
2
0
3
3
0
2
1
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
1
0
0
0
0
2
1
0
0
0
0
0
1
4
0
0
2
0
0
0
0
2
1
0
1
0
2
2
0
0
0
2
0
0
2
0
0
0
2
0
0
0
2
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
5
2
1
0
0
0
0
1
1
0
2
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
1
0
0
0
1
0
0
0
1
0
2
0
0
2
0
2
0
0
2
0
0
3
2
0
1
1
0
3
0
0
0
0
0
0
0
0
2
0
5
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
2
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
1
3
0
0
0
2
0
1
0
1
2
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
5
5
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
3
0
2
0
2
1
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
1
0
0
0
2
1
0
0
11
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
2
2
0
2
2
1
0
0
0
0
2
1
2
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
1
4
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
1
2
0
2
0
0
0
0
0
0
1
0
3
0
0
0
0
2
0
1
1
1
2
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
1
1
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
1
3
1
0
0
0
0
0
2
2
0
0
1
2
1
1
1
0
0
0
0
0
2
2
0
0
0
0
0
1
0
5
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
4
1
2
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
1
2
2
0
2
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
4
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
7
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
1
0
1
0
0
1
0
0
0
2
0
5
1
0
1
0
0
0
0
1
0
0
2
0
2
0
0
0
2
1
0
0
0
0
0
0
2
0
0
3
0
0
0
0
2
1
0
2
0
0
0
1
0
0
0
1
0
0
0
12
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
7
1
0
3
0
0
2
0
0
1
0
0
0
2
0
0
0
0
2
2
2
0
1
0
0
0
0
0
4
2
1
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
3
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
1
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
3
0
3
0
2
0
0
1
1
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
2
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
8
0
1
0
0
0
0
0
0
0
0
4
3
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
1
3
0
1
0
0
0
2
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
43
0
0
0
0
1
0
0
1
0
0
0
4
0
0
0
0
2
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
5
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
2
0
0
0
1
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
1
1
0
0
0
0
2
1
0
0
1
0
0
1
0
0
0
0
0
1
0
2
0
2
0
1
0
0
4
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
2
1
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
3
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
1
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
2
2
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
1
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
2
2
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
2
1
1
0
0
0
0
0
0
1
0
0
2
2
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
2
0
0
1
1
1
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
1
0
1
2
0
0
1
0
0
0
0
0
0
3
0
0
1
0
0
2
0
0
0
0
0
0
0
0
3
0
2
0
2
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
1
1
0
3
2
4
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
2
0
1
0
0
0
1
0
0
1
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
3
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
3
0
0
1
3
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
1
0
0
0
0
2
0
2
1
1
2
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
4
0
1
1
2
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
3
0
0
0
0
0
0
2
0
2
1
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
2
1
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
1
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
4
0
2
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
1
0
0
2
2
0
0
0
0
0
2
2
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
3
0
0
3
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
2
0
0
2
1
0
0
4
0
1
1
3
3
1
0
3
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
2
2
0
0
1
3
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
1
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
1
0
10
2
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
2
0
3
0
0
2
0
0
0
3
0
2
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
2
1
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
1
1
1
9
2
2
0
0
10
2
0
0
2
0
2
0
0
0
0
2
0
0
1
0
0
3
0
1
0
0
0
0
0
0
0
1
0
0
0
3
0
0
2
0
0
0
0
1
2
0
0
2
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
3
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
1
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
3
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
2
0
0
2
0
0
2
0
1
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
1
0
2
0
1
0
0
2
0
0
0
0
0
2
0
2
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
2
0
2
2
2
0
0
0
0
0
1
0
2
1
1
1
0
0
0
0
0
0
0
1
4
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
5
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
1
2
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
2
1
0
0
0
0
0
0
2
0
0
0
3
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
5
2
0
0
0
0
0
1
0
0
0
0
2
2
4
0
0
0
0
1
1
0
0
2
2
0
2
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
1
2
1
0
2
1
2
0
2
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
4
0
1
0
0
0
3
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
3
2
0
0
3
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
4
1
0
2
0
3
2
0
0
0
0
0
0
0
0
1
0
0
0
1
2
2
0
0
0
0
0
1
0
0
0
2
0
1
2
0
2
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
6
1
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
3
0
0
0
2
0
2
2
0
0
1
0
0
1
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
3
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
2
0
0
0
2
0
0
3
2
3
0
0
0
1
0
0
0
0
1
0
0
2
1
0
0
0
4
0
0
0
0
0
1
0
0
3
0
0
0
0
2
0
2
0
2
0
1
0
0
0
1
2
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
2
0
1
0
3
0
1
0
0
1
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
2
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
2
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
2
3
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
6
2
0
0
0
0
1
2
3
0
0
0
0
0
0
0
0
2
0
1
2
0
0
1
0
0
2
0
2
2
2
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
1
2
0
2
0
0
3
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
4
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
6
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
2
2
0
2
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
1
2
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
2
0
0
4
0
0
3
0
0
0
0
0
2
0
1
0
1
0
0
1
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
1
2
2
2
2
2
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
2
0
2
0
0
0
0
0
2
3
1
0
1
0
2
0
0
1
0
0
0
2
0
0
4
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
3
0
1
0
2
0
2
0
0
0
1
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
2
1
2
1
0
2
0
1
0
0
0
6
1
1
0
1
0
1
0
0
0
0
0
0
0
2
2
0
1
0
0
0
1
2
1
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
2
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
2
2
4
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
3
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
9
0
0
0
1
1
0
0
0
0
0
2
0
1
0
2
0
0
0
0
1
0
0
0
0
0
7
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
1
0
1
0
1
0
0
2
0
0
0
0
1
6
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
2
1
1
0
1
0
2
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
9
0
0
1
2
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
1
1
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
2
0
1
0
0
0
1
1
0
2
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
6
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
1
2
0
2
2
0
0
0
0
0
2
0
0
0
0
0
1
0
1
2
1
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
3
0
2
3
0
0
1
0
0
0
0
0
0
2
0
1
2
0
0
0
2
0
1
1
5
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
3
0
0
0
0
1
0
1
0
0
6
0
0
2
0
0
0
0
0
1
0
0
0
1
0
2
0
0
1
0
0
0
2
0
0
2
0
0
1
0
0
0
0
2
0
0
0
1
1
0
1
0
0
1
1
0
0
0
2
0
0
2
0
0
1
1
0
0
4
0
1
1
0
0
0
0
0
0
0
0
0
0
10
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
1
1
0
0
2
2
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
3
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
5
1
0
0
0
1
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
1
0
0
3
0
2
0
0
0
0
2
0
0
2
0
0
0
0
1
3
0
0
0
0
2
0
0
0
0
0
2
0
1
0
2
0
0
0
1
0
0
1
0
0
2
0
3
0
0
6
0
2
0
0
0
0
0
0
1
0
0
2
1
1
2
2
0
0
0
1
0
15
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
4
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
1
2
0
0
0
1
0
1
1
0
1
0
1
2
2
0
2
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
2
1
0
0
1
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
2
0
4
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
3
0
0
3
1
0
2
0
0
1
0
0
0
2
1
1
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
1
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
4
0
0
0
0
1
2
0
0
0
0
1
1
0
0
0
0
0
1
0
2
0
0
0
1
1
3
2
0
0
1
0
3
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
1
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
3
0
0
1
2
2
0
0
5
0
0
0
2
0
1
0
0
0
4
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
1
2
0
0
1
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
1
2
0
0
0
0
0
0
1
0
3
1
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
3
2
0
0
0
0
1
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
2
0
2
0
0
0
0
0
0
2
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
4
0
1
1
0
0
0
0
2
2
0
0
0
2
2
5
4
0
2
1
3
0
0
0
1
0
0
4
2
0
0
0
0
0
0
2
0
2
3
0
0
0
1
0
1
0
0
2
3
0
0
0
0
2
1
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
2
2
1
1
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
2
0
0
0
0
0
1
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
2
0
0
0
0
2
0
0
0
0
0
2
0
2
1
0
0
0
0
1
0
2
2
0
0
1
1
0
0
0
1
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
3
0
0
0
3
2
3
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
3
1
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
4
0
0
0
0
0
1
2
0
0
1
0
0
1
1
1
0
0
2
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
3
0
2
1
3
0
0
1
0
0
2
0
0
0
1
2
8
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
3
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
3
0
2
0
0
0
2
0
0
0
1
1
0
0
0
2
0
0
0
1
1
1
0
0
1
0
0
0
1
0
0
2
0
0
1
1
0
0
0
0
1
0
1
0
2
0
0
2
0
0
1
0
2
0
2
2
0
0
0
0
0
1
2
2
2
0
3
0
0
0
2
0
0
1
2
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
2
1
0
1
7
0
0
0
2
0
0
1
2
0
0
1
0
0
0
0
0
0
1
0
0
3
0
2
0
0
1
0
0
0
0
0
3
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
0
1
0
2
0
2
4
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
4
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
2
11
2
1
0
0
0
0
0
0
0
1
1
0
2
6
1
0
2
0
2
1
0
1
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
2
0
0
0
0
0
0
2
0
0
0
3
1
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
6
0
1
1
2
0
0
1
0
0
0
1
0
1
2
0
0
0
0
1
0
0
1
0
1
0
1
0
0
2
2
0
0
2
3
2
0
0
1
1
1
1
0
0
2
1
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
3
0
0
0
2
0
1
2
2
0
1
0
0
1
2
1
0
0
0
0
0
0
0
0
2
4
0
0
1
0
0
0
0
1
0
0
0
0
1
2
2
2
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
3
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
2
0
0
0
0
0
2
0
2
0
0
0
1
0
0
1
0
1
0
2
0
0
2
0
2
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
1
0
0
0
0
0
0
0
0
0
2
1
1
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
1
0
0
1
0
0
1
0
2
0
0
0
2
0
1
0
3
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
1
0
0
0
2
0
0
0
2
0
0
1
4
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
2
2
2
0
0
0
0
2
0
0
1
0
3
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
1
2
0
3
1
0
0
0
2
0
2
0
0
0
3
0
0
1
0
0
0
0
3
2
0
0
1
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
2
2
0
0
0
1
0
0
0
0
0
3
0
2
0
0
0
0
1
1
0
0
0
2
0
0
0
0
6
2
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
1
0
4
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
1
0
2
2
0
1
0
0
1
0
0
0
3
2
0
1
2
0
1
0
0
0
0
0
0
2
4
2
0
0
0
3
1
0
0
3
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
1
0
0
5
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
5
0
0
2
2
0
2
0
0
2
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
3
0
0
0
0
0
0
0
1
0
0
0
2
0
1
1
0
0
1
0
2
0
1
2
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
4
0
1
0
1
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
2
2
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
1
0
3
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
3
0
1
3
0
13
0
0
0
1
2
3
0
1
0
0
0
0
2
1
0
1
0
0
1
2
0
0
1
0
0
0
2
4
0
0
0
3
0
0
2
0
0
0
3
0
1
2
0
0
1
0
0
1
0
0
0
3
0
0
0
0
2
0
0
1
0
1
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
2
0
0
0
4
1
0
0
0
0
1
2
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
1
0
0
1
0
0
1
0
0
0
1
2
0
0
2
0
0
0
0
0
0
1
0
3
0
0
1
0
1
0
0
2
1
0
0
1
0
1
0
2
0
0
0
2
1
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
1
1
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
2
1
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
1
0
1
1
2
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
2
0
0
0
1
0
1
1
0
1
0
0
1
2
4
1
0
1
0
0
2
2
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
1
2
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
1
0
1
0
2
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
2
2
0
1
0
0
0
3
1
0
0
0
1
2
4
3
2
0
0
2
0
2
0
0
0
1
0
0
2
0
0
0
0
1
1
2
0
0
1
2
2
0
1
1
0
0
0
1
0
0
0
0
0
0
2
0
1
0
1
2
0
2
2
0
0
2
0
0
0
2
1
1
0
0
2
0
2
0
0
0
0
1
0
0
2
0
2
0
0
1
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
2
0
1
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
4
0
2
0
0
0
0
0
0
4
2
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
5
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
2
0
1
0
1
0
2
0
2
0
0
0
0
1
0
3
0
1
1
0
0
0
3
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
3
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
3
1
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
7
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
3
0
1
0
0
0
0
2
3
0
0
0
0
3
0
0
0
2
0
0
0
0
1
1
0
0
0
0
5
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
2
0
2
0
3
0
0
0
0
2
0
3
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
2
0
0
0
1
2
0
0
0
2
0
1
0
3
1
1
2
0
0
1
1
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
2
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
4
1
0
0
2
0
0
0
3
0
0
0
0
0
3
1
0
0
0
3
3
0
0
0
0
0
2
1
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
3
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
9
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
2
0
0
0
0
2
1
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
2
0
0
0
1
1
0
0
1
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
6
0
1
1
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
2
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
3
0
3
1
0
3
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
1
0
1
0
0
1
0
0
2
1
0
1
0
1
1
0
0
0
0
1
1
0
0
0
0
1
0
1
1
0
0
0
0
1
2
0
0
3
0
1
0
0
1
0
1
2
1
0
0
0
1
0
0
0
0
0
0
5
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
2
0
5
0
0
0
2
0
0
0
0
1
0
0
2
0
0
2
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
2
0
0
2
0
0
9
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
2
1
0
0
2
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
2
0
1
0
2
0
6
0
0
2
0
0
3
0
0
0
0
1
1
1
0
0
0
0
0
2
0
1
2
0
0
1
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
2
0
2
3
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
1
1
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
5
4
0
0
0
2
0
0
0
2
0
0
1
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
1
0
3
0
1
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
2
2
1
2
4
0
1
0
2
0
0
0
1
2
0
0
0
0
1
2
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
2
0
2
1
0
0
0
0
1
0
0
2
0
1
0
3
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
1
0
2
3
0
1
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
2
2
0
0
1
2
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
3
0
0
0
0
1
2
0
0
0
1
0
0
0
3
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
3
1
0
0
0
0
0
1
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
2
0
1
0
1
0
0
3
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
3
0
0
2
0
0
0
0
0
0
0
0
3
0
0
2
0
0
1
1
1
0
0
1
3
1
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
2
0
1
1
1
2
0
2
0
0
1
0
0
0
2
0
0
2
0
2
0
0
1
2
0
0
0
0
1
0
0
4
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
2
0
0
0
3
2
0
0
0
1
0
2
0
0
2
2
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
1
1
0
0
0
1
0
0
5
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
1
4
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
4
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
2
0
1
1
0
0
0
0
2
3
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
1
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
2
2
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
2
2
0
2
0
0
2
0
0
2
0
1
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
2
2
0
0
2
2
2
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
3
0
0
0
0
2
0
0
0
0
1
3
0
2
1
2
1
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
5
2
2
0
0
0
0
0
0
0
0
0
0
0
3
1
1
2
2
1
0
0
1
3
0
0
0
1
0
0
0
1
2
0
2
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
2
0
0
2
0
2
0
0
2
0
0
0
2
1
4
0
0
3
0
0
0
2
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
1
0
0
2
2
2
0
0
0
0
2
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
2
3
1
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
2
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
1
2
0
1
0
1
2
1
1
0
0
0
2
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
2
0
0
1
3
1
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
2
1
0
0
0
1
2
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
2
0
0
3
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
4
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
3
1
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
2
5
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
2
1
3
0
1
2
1
3
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
2
2
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
2
1
0
0
2
0
2
0
0
1
0
0
0
1
3
0
0
0
0
0
1
0
0
0
1
0
0
1
0
2
1
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
3
0
3
2
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
2
3
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
3
0
0
2
1
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
1
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
2
0
1
1
0
0
0
0
0
2
0
2
1
0
2
0
0
1
1
2
1
1
2
0
0
0
2
2
1
0
1
0
0
1
1
0
0
2
0
0
0
0
0
0
8
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
3
0
3
1
0
3
0
2
0
2
0
0
0
0
1
0
2
2
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
2
2
2
0
0
0
0
0
0
8
0
0
0
1
2
0
0
0
0
0
4
0
0
0
0
2
0
0
0
2
0
0
3
0
0
0
0
0
2
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
2
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
2
1
1
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
4
0
0
1
1
0
0
1
0
0
0
0
0
0
1
3
0
0
1
0
2
0
0
0
0
1
1
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
10
0
2
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
1
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
2
0
0
0
0
0
0
1
1
0
2
0
1
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
2
1
2
0
1
0
0
0
0
2
0
0
0
0
0
1
2
0
1
0
0
1
0
0
3
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
1
0
0
1
0
1
0
1
1
0
1
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
1
1
2
5
1
1
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
4
0
0
0
0
1
0
0
2
1
3
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
1
0
2
0
2
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
3
1
0
0
2
1
0
0
0
2
2
1
0
0
0
0
2
4
0
2
0
1
0
0
0
3
0
1
0
1
0
0
1
0
0
0
2
2
0
0
1
0
0
1
0
0
0
0
0
2
0
0
2
0
2
0
1
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
1
0
0
0
2
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
12
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
1
3
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
3
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
5
1
0
1
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
3
0
2
0
0
0
0
1
0
2
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
2
0
3
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
2
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
2
0
1
0
0
0
0
0
2
0
0
3
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
2
1
1
0
0
0
1
0
1
0
2
0
0
0
0
0
0
2
2
0
0
1
0
1
2
1
1
0
1
0
0
0
0
1
2
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
3
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
2
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
7
0
2
0
2
0
1
0
0
0
0
1
0
1
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
1
0
1
2
0
0
1
2
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
3
2
2
5
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
1
0
1
2
0
0
1
0
0
0
3
1
2
0
6
2
2
0
3
0
0
1
0
0
2
0
0
0
3
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
1
0
0
3
0
2
0
3
0
2
0
0
1
0
0
0
0
0
2
0
0
0
1
2
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
1
2
0
1
0
1
2
0
0
0
1
2
0
0
2
0
0
2
0
1
0
3
0
0
0
2
0
0
1
0
1
1
0
1
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
3
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
2
0
3
2
1
0
0
0
0
0
0
0
0
0
2
0
1
2
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
3
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
1
8
0
0
0
2
0
1
0
0
0
3
1
1
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
1
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
2
0
0
0
1
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
6
0
0
0
0
0
0
2
0
0
1
0
0
0
1
2
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
3
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
1
0
0
0
0
0
1
1
0
0
0
3
0
2
0
2
0
0
1
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
2
0
2
0
0
0
0
0
1
3
1
2
1
0
0
0
0
1
0
0
1
0
0
2
2
0
0
1
2
0
0
0
0
0
6
0
0
0
0
1
0
1
2
1
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
2
0
4
0
0
0
2
1
0
0
0
2
0
0
0
1
2
0
1
0
0
0
2
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
2
0
0
1
0
0
0
0
2
0
0
0
0
2
1
0
1
1
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
2
0
2
1
0
2
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
1
2
2
2
1
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
3
0
0
0
1
0
1
2
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
2
1
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
2
0
0
2
1
2
0
0
0
0
0
0
0
0
1
2
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
2
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
1
1
0
0
0
0
2
1
1
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
7
0
5
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
2
0
1
1
1
0
0
0
0
2
1
1
0
0
1
2
0
1
0
0
1
1
0
2
1
3
0
0
2
0
0
0
0
0
0
5
0
2
5
0
0
0
0
0
2
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
1
0
0
2
2
2
0
0
0
1
0
1
0
1
0
0
0
0
2
0
0
1
0
3
0
0
0
2
0
2
1
1
0
0
0
0
1
3
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
1
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
1
0
1
0
0
0
2
0
0
0
0
0
0
1
1
0
1
1
2
0
0
0
0
2
0
2
1
0
0
1
0
0
2
0
1
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
1
3
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
1
0
0
0
1
0
0
0
1
0
2
0
1
0
0
2
0
0
3
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
4
0
0
0
0
0
2
0
0
0
0
2
1
1
0
2
0
0
2
2
0
2
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
1
1
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
1
1
2
0
0
0
0
1
0
2
0
0
0
0
0
0
3
2
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
2
1
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
2
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
5
2
0
0
1
1
0
0
0
0
1
0
0
0
0
2
0
0
3
1
2
0
0
0
1
0
0
1
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
4
1
2
2
0
2
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
2
0
1
0
0
1
0
0
2
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
8
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
3
0
0
0
2
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
3
0
0
2
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
2
0
0
2
1
0
6
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
1
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
2
0
0
0
0
0
1
1
4
5
0
2
0
0
0
0
2
0
0
0
0
3
0
0
3
0
0
0
3
0
0
0
0
1
0
0
0
0
2
0
0
3
2
0
0
0
0
0
0
1
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
3
1
2
1
0
0
3
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
3
0
2
0
0
0
2
0
0
1
0
0
0
1
1
0
2
0
0
0
2
0
2
0
1
1
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
1
1
0
0
0
0
2
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
2
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
2
0
2
1
2
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
1
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
2
0
0
2
0
0
1
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
3
6
0
0
3
0
1
0
0
0
0
0
1
0
0
0
0
1
1
1
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
6
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
1
0
1
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
2
0
1
0
0
0
0
0
0
0
1
2
0
2
0
1
0
0
0
3
0
1
0
0
1
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
4
2
0
2
0
0
0
1
0
1
0
0
1
0
0
0
0
2
1
0
0
2
0
0
0
2
0
0
0
0
0
1
2
0
2
0
0
3
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
2
0
1
5
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
4
1
0
1
2
0
1
0
0
0
0
1
0
0
0
2
0
2
0
0
0
1
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
2
2
0
2
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
3
0
0
1
2
0
0
0
2
0
0
3
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
4
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
2
0
0
0
1
2
0
0
1
0
1
0
0
0
0
0
2
0
0
1
0
1
1
0
0
0
0
3
0
0
2
0
0
0
0
0
0
1
0
0
3
0
0
1
0
0
3
0
0
2
0
1
0
0
0
2
0
0
0
0
3
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
6
1
0
2
1
0
0
0
0
2
0
1
0
0
0
3
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
2
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
2
2
0
1
1
0
2
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
4
2
2
1
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
3
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
2
2
0
0
1
0
0
1
0
0
0
3
0
0
0
10
0
0
0
0
1
1
0
2
1
0
0
2
0
0
2
2
0
1
0
0
0
1
0
5
0
0
0
3
0
2
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
3
0
0
0
1
0
0
0
0
1
0
1
0
4
2
2
0
2
0
4
0
3
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
1
0
0
2
0
0
0
0
0
1
0
1
1
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
1
0
0
1
1
3
0
0
0
0
0
0
0
0
0
0
0
5
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
2
0
0
0
2
0
1
2
4
0
2
1
0
3
1
0
0
2
6
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
2
0
2
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
2
1
0
0
1
0
0
0
0
0
2
0
0
0
2
5
1
1
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
3
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
3
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
3
1
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
1
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
2
0
2
0
1
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
4
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
1
2
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
2
2
0
1
0
2
0
2
0
0
1
2
0
4
0
0
2
1
0
0
0
0
3
2
0
2
2
0
1
0
1
0
0
0
1
0
0
0
2
0
0
1
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
1
0
1
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
1
2
0
0
1
2
0
0
0
0
0
2
1
2
0
1
0
1
0
2
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
1
2
3
0
0
0
0
0
0
0
2
0
1
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
2
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
3
0
0
0
5
0
3
0
0
0
0
1
0
0
1
0
0
2
1
0
0
1
0
0
1
0
0
1
2
0
0
2
0
1
0
0
2
0
1
1
0
3
0
2
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
2
2
0
0
0
0
1
0
0
0
2
2
0
1
1
0
0
0
3
0
0
0
1
1
2
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
3
1
0
0
0
0
0
0
0
2
0
2
2
0
1
2
0
0
0
0
0
2
1
1
6
0
0
0
0
3
2
1
1
0
0
1
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
5
0
0
0
2
0
2
0
1
2
1
1
3
0
0
0
1
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
3
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
2
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
3
2
0
1
0
0
0
0
0
5
1
0
0
2
0
2
0
1
0
1
1
0
0
0
1
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
2
1
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
1
1
1
0
0
0
1
0
3
0
0
0
0
0
1
0
0
4
0
0
0
1
2
0
0
0
0
3
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
5
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
1
0
2
0
2
0
0
0
0
0
2
0
0
0
2
2
0
0
2
0
0
2
2
0
1
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
3
0
0
0
1
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
2
2
0
0
0
0
0
1
1
2
1
0
0
0
0
0
0
0
0
0
0
1
0
6
0
0
0
0
0
0
1
0
0
5
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
2
6
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
2
0
4
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
1
2
0
0
0
0
3
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
2
2
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
1
0
2
3
0
0
0
0
2
1
0
0
1
1
0
0
0
0
0
0
6
0
2
0
1
2
1
0
0
0
0
1
1
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
1
0
0
0
0
0
0
2
0
0
1
0
1
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
1
0
0
0
0
2
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
1
0
0
0
2
2
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
7
0
1
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
1
2
0
0
2
0
0
0
3
0
0
1
1
0
1
0
2
0
0
1
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
2
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
3
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
3
1
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
1
1
1
0
0
0
0
1
3
2
0
0
2
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
8
2
0
0
1
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
2
0
1
0
2
0
0
2
2
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
3
0
0
0
0
0
0
0
0
3
2
0
0
0
1
0
0
0
0
0
1
2
0
0
1
0
2
2
0
0
0
0
1
0
0
1
0
2
0
0
0
0
3
0
0
0
2
2
0
0
1
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
6
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
4
1
1
2
0
0
0
0
1
0
0
1
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
7
0
0
0
0
1
2
0
0
2
2
2
0
0
0
0
0
0
0
0
2
0
0
0
2
2
3
0
0
0
0
1
2
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
4
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
1
3
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
3
1
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
3
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
2
2
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
2
1
1
0
0
0
1
0
0
0
0
0
0
3
0
1
5
0
0
0
0
1
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
2
2
0
3
2
1
1
0
2
0
1
0
0
0
0
0
0
0
0
1
1
2
2
0
0
0
2
4
0
1
0
0
3
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
3
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
2
1
2
0
1
0
0
0
0
1
0
0
1
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
5
0
1
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
2
0
0
1
0
1
3
0
0
0
1
0
0
3
0
0
0
0
1
0
0
1
6
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
1
2
0
0
4
2
0
0
3
1
2
0
0
0
0
4
0
0
1
4
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
11
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
2
0
0
2
0
0
1
0
0
0
2
1
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
3
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
1
0
0
0
1
2
0
0
0
0
0
1
2
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
3
1
1
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
2
3
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
1
1
2
0
2
0
0
0
1
0
1
0
0
0
0
1
3
0
0
1
1
1
0
0
1
0
0
5
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
5
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
4
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
3
1
1
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
2
2
0
0
2
0
0
0
0
0
3
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
2
0
2
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
3
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
2
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
3
1
1
2
7
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
2
1
0
0
0
0
3
0
0
0
0
3
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
1
2
0
0
0
0
1
0
1
3
0
1
2
2
0
1
0
1
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
1
1
3
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
2
1
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
1
1
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
2
0
1
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
1
0
2
1
0
1
2
0
0
1
1
0
0
2
0
1
0
2
0
0
0
2
0
0
0
0
0
1
0
1
0
0
2
2
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
1
2
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
2
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
3
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
2
1
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
2
0
2
0
2
1
2
3
0
2
2
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
3
0
1
0
0
1
1
0
1
1
2
0
1
0
0
0
0
1
0
0
2
1
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
3
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
3
2
1
1
1
1
0
1
2
2
0
0
2
0
0
0
0
0
1
1
3
0
0
0
2
3
0
0
2
0
0
0
0
2
0
0
3
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
1
3
0
0
0
3
0
0
2
1
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
7
0
0
2
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
4
1
0
0
0
3
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
1
0
0
2
4
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
2
1
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
2
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
1
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
5
0
1
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
1
2
1
0
0
0
0
0
0
0
0
6
2
2
0
2
1
2
0
1
0
1
1
0
0
0
0
2
2
0
0
0
3
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
2
0
3
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
2
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
4
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
2
2
0
0
0
0
1
0
0
0
0
3
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
2
0
1
0
1
1
0
0
1
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
1
1
3
1
1
0
0
2
0
0
2
0
1
0
2
0
0
0
0
0
2
0
2
0
0
0
2
1
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
1
2
0
0
0
0
0
1
1
0
0
2
2
0
0
1
3
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
3
0
0
2
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
2
0
1
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
2
1
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
3
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
1
0
0
1
0
1
0
0
2
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
2
1
0
2
0
3
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
1
0
1
2
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
3
0
0
1
1
0
0
0
3
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
3
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
5
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
8
2
0
1
0
0
1
1
0
1
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
3
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
2
1
0
0
1
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
1
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
3
0
0
2
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
6
2
1
2
0
0
1
1
0
2
0
0
3
2
0
2
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
1
2
0
0
0
0
1
0
2
0
1
2
0
0
0
1
1
0
0
0
3
1
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
2
0
0
0
1
0
2
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
2
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
3
1
1
0
0
0
0
0
0
2
0
1
0
0
0
2
0
1
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
2
0
3
0
0
0
1
0
0
0
2
1
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
1
0
3
0
1
0
0
0
1
0
0
4
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
2
0
1
0
2
0
1
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
1
7
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
1
0
0
0
0
1
0
0
1
0
2
2
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
2
2
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
2
1
1
1
2
0
0
0
0
3
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
6
4
0
0
0
0
0
0
0
3
1
0
1
0
0
0
3
3
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
2
0
0
2
2
0
4
0
0
0
0
0
1
0
1
0
0
2
0
3
0
1
0
2
2
0
0
1
3
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
2
2
0
0
2
0
0
0
2
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
7
0
2
2
0
0
0
0
1
0
1
0
2
0
0
1
1
0
1
0
0
0
0
3
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
5
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
1
1
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
1
2
2
0
0
1
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
4
0
0
0
0
1
0
2
2
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
2
1
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
2
2
1
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
3
0
2
0
1
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
1
0
1
1
0
0
0
2
0
0
2
0
0
0
0
1
0
2
0
0
2
0
0
1
2
0
0
0
0
2
0
0
4
2
0
1
1
0
0
1
0
2
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
3
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
2
2
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
4
0
0
0
1
2
2
1
2
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
5
2
0
0
2
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
2
0
3
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
1
3
1
1
0
1
0
0
0
0
1
0
0
0
0
3
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
6
1
0
0
2
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
2
1
0
0
1
0
0
2
0
0
1
0
0
0
0
2
1
1
0
2
1
0
1
0
0
0
1
0
0
2
1
0
0
0
2
0
0
0
0
2
0
3
3
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
2
0
0
2
1
2
0
2
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
1
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
1
2
2
0
1
0
0
0
2
2
0
0
2
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
1
2
0
0
0
0
0
2
2
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
1
2
0
0
2
2
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
2
1
0
0
0
1
0
2
0
0
0
1
0
0
0
0
2
1
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
4
0
0
0
0
1
0
0
0
0
1
0
1
4
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
2
0
2
0
0
5
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
1
0
0
1
0
0
0
0
2
2
1
1
0
1
0
0
1
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
2
0
2
0
0
4
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
1
2
2
0
0
0
0
1
0
0
0
1
0
1
1
2
1
0
1
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
3
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
2
0
0
0
0
3
0
1
2
0
0
0
0
2
0
0
0
0
2
0
1
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
4
0
2
2
0
1
0
1
0
0
1
0
0
2
2
0
1
2
0
0
2
2
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
3
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
1
0
1
2
0
0
0
2
0
1
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
1
0
1
0
0
0
2
2
0
1
0
0
1
1
0
0
0
0
4
0
0
1
0
0
1
0
0
0
4
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
3
0
1
0
1
0
0
0
0
0
0
3
0
2
1
2
0
0
0
0
2
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
1
0
2
2
1
4
0
0
0
0
2
0
0
2
2
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
1
1
0
1
2
0
1
0
0
0
0
0
0
1
0
0
1
0
0
2
3
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
3
0
0
0
4
0
0
0
0
2
0
2
0
1
2
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
2
2
1
0
1
0
0
2
1
1
0
0
1
2
1
2
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
1
0
3
1
0
0
0
0
2
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
3
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
2
1
2
0
1
0
1
0
2
0
2
0
0
0
3
0
2
1
0
0
0
4
0
1
0
0
1
0
0
0
0
3
0
0
2
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
4
1
0
0
0
1
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
2
0
0
2
0
6
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
2
2
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
3
2
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
2
0
3
0
0
0
0
1
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
1
2
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
2
2
0
4
0
0
0
0
1
0
0
2
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
2
0
0
2
2
0
0
0
0
6
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
1
0
8
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
5
0
1
2
0
0
0
0
0
0
0
0
0
2
3
0
0
2
1
0
2
0
0
8
0
0
0
0
3
2
0
0
0
0
1
0
0
0
2
0
2
0
2
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
3
2
0
0
8
0
0
0
2
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
2
0
0
3
0
0
0
0
0
0
1
2
0
0
1
0
0
2
0
1
0
0
0
0
0
0
1
0
0
1
0
0
3
1
2
2
0
0
3
0
0
0
0
0
2
0
0
1
0
0
6
0
0
0
4
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
1
0
1
0
1
0
0
1
2
0
0
0
0
0
2
2
0
0
1
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
2
1
0
0
0
2
0
0
0
0
1
0
1
0
1
0
0
0
1
0
2
1
0
0
0
0
1
2
0
1
0
1
0
2
2
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
2
0
0
4
1
0
1
0
0
0
0
0
0
2
0
3
0
0
0
0
0
1
1
0
0
0
0
0
2
2
0
0
0
0
0
1
5
1
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
2
0
0
0
0
0
0
0
0
3
2
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
3
1
2
0
0
2
0
0
1
1
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
1
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
1
0
1
1
0
0
0
0
3
1
0
0
1
0
2
0
1
0
1
2
0
2
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
1
0
0
0
0
0
3
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
2
0
0
1
1
6
0
0
0
0
0
1
1
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
1
1
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
4
2
2
2
1
0
0
0
0
1
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
1
2
0
0
0
1
2
0
2
0
0
0
2
1
0
0
0
0
0
0
2
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
1
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
2
2
0
0
0
0
0
0
2
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
4
3
0
0
0
0
0
1
0
0
2
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
4
0
2
2
0
0
1
1
0
1
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
2
0
1
6
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
1
0
0
1
2
0
2
0
0
0
0
1
0
1
2
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
2
0
0
0
3
0
0
0
1
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
3
0
2
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
2
1
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
2
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
2
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
2
1
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
1
0
1
0
0
0
2
2
0
0
4
0
0
0
0
3
0
3
1
0
0
1
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
3
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
2
2
0
0
0
1
1
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
3
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
4
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
2
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
2
1
0
0
1
0
0
0
0
0
3
0
2
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
3
0
0
1
2
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
2
0
0
2
0
2
0
0
0
2
0
0
0
1
2
0
0
2
0
0
0
2
2
0
0
0
1
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
1
0
1
1
4
0
0
1
1
0
0
0
0
0
2
0
1
3
1
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
1
0
0
0
0
0
2
2
0
0
0
2
0
0
0
4
1
2
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
1
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
2
0
0
2
0
0
0
0
0
3
2
1
0
0
1
1
0
0
0
0
0
0
1
2
2
3
0
0
1
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
1
1
2
0
0
0
2
0
2
0
2
1
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
2
1
0
0
0
2
1
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
1
2
1
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
2
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
2
0
0
0
1
0
0
0
0
1
0
0
1
0
2
1
0
4
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
2
0
0
1
1
2
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
7
0
2
0
4
1
2
1
0
0
1
1
2
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
2
0
0
0
1
0
0
0
0
4
0
0
0
2
0
0
2
2
0
0
0
0
0
3
0
0
1
0
2
0
0
1
0
0
0
4
0
1
0
0
0
0
4
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
3
1
0
0
0
0
0
1
0
2
1
2
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
1
0
2
0
2
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
3
2
0
0
0
4
0
0
0
0
1
1
0
2
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
2
0
0
1
1
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
2
1
0
0
0
0
0
0
0
1
0
2
0
2
0
1
0
1
0
0
0
1
0
0
3
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
3
0
1
0
3
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
2
0
2
0
0
1
0
1
1
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
1
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
2
0
0
0
2
3
0
0
0
0
0
0
2
2
0
0
1
0
1
0
0
0
0
0
0
1
2
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
2
0
0
2
0
0
1
0
1
1
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
2
1
3
1
0
0
1
0
0
3
1
0
3
0
2
0
0
1
0
2
0
2
2
3
0
0
1
1
0
0
1
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
5
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
1
1
2
0
1
0
3
1
0
2
1
0
0
1
0
0
0
0
0
0
2
2
0
0
1
0
1
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
5
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
2
0
2
0
3
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
2
1
0
0
1
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
6
1
0
0
0
1
0
2
1
2
0
2
0
1
0
2
0
0
0
0
0
3
0
0
1
0
2
0
0
2
2
0
0
0
0
0
2
2
0
0
0
0
0
0
2
1
0
2
0
0
2
0
0
0
1
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
2
1
1
0
0
0
0
1
0
0
1
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
2
1
1
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
2
0
0
0
0
1
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
3
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
1
0
0
0
1
0
2
2
0
0
2
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
1
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
5
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
3
0
1
2
0
1
0
2
0
1
0
0
0
1
0
2
0
0
0
1
0
2
0
0
1
0
0
0
2
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
3
1
1
2
0
0
0
0
3
0
0
0
2
0
0
1
0
0
1
0
0
0
1
2
0
0
1
0
0
0
2
1
0
0
1
1
0
0
0
0
0
2
2
0
0
2
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
2
0
0
0
0
1
0
2
0
0
0
1
0
1
0
0
0
0
0
5
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
1
0
0
1
0
1
0
1
0
4
0
0
0
0
0
2
0
0
0
1
3
0
0
0
1
1
0
0
0
2
0
0
0
0
2
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
3
1
0
0
0
0
0
1
0
0
0
0
1
5
0
1
0
0
0
0
1
0
0
3
0
0
3
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
6
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
1
1
1
0
0
0
0
2
0
0
0
5
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
2
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
1
0
1
2
2
0
0
0
0
0
0
2
0
0
0
1
2
0
1
0
0
2
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
3
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
4
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
2
2
1
0
1
2
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
3
0
0
1
2
1
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
1
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
1
2
0
0
0
0
2
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
1
0
0
2
0
0
0
1
0
0
0
0
1
3
2
0
3
0
0
0
1
0
0
0
1
0
1
0
0
1
0
1
0
0
1
0
1
1
0
1
2
0
0
0
1
0
3
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
2
1
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
3
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
1
0
0
3
0
0
0
1
0
0
2
2
0
0
0
0
2
0
0
2
0
1
0
0
2
0
0
1
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
2
0
0
1
2
0
2
2
0
2
2
2
0
6
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
2
0
0
1
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
3
0
0
3
0
0
2
0
1
2
1
0
0
0
0
0
2
0
0
0
1
2
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
1
0
2
0
0
2
0
0
2
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
1
1
0
0
0
0
0
0
0
0
3
0
1
2
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
2
0
0
0
2
1
1
2
0
0
0
1
1
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
1
1
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
2
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
2
0
2
0
0
0
0
0
0
2
0
2
2
0
0
1
0
0
0
2
0
1
3
5
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
4
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
4
0
2
3
0
0
0
0
0
0
0
3
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
4
2
0
0
1
1
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
1
2
0
2
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
1
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
3
2
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
4
0
2
0
0
0
0
1
0
0
2
0
0
0
0
6
0
0
1
3
0
2
2
0
0
2
3
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
1
0
0
0
2
2
0
2
3
0
0
0
0
0
0
0
1
2
0
2
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
2
0
2
2
1
0
0
2
2
0
0
2
0
1
0
0
0
2
2
0
1
2
1
0
0
0
5
0
0
0
0
3
2
0
0
3
2
0
2
0
1
0
1
0
0
0
3
0
0
0
2
1
0
0
0
2
1
0
0
0
2
0
0
0
0
0
2
0
0
1
0
1
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
4
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
1
1
2
3
0
0
0
0
1
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
1
2
3
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
2
1
0
1
0
0
0
0
2
0
0
1
1
2
0
0
1
1
0
2
0
0
2
0
1
1
2
1
2
1
0
2
0
0
0
3
0
0
1
0
1
0
0
0
3
0
0
0
0
0
0
0
2
0
8
8
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
3
0
0
2
0
2
0
0
2
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
2
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
4
1
0
2
2
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
3
0
0
0
0
0
2
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
4
0
1
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
2
0
2
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
3
0
2
0
1
0
0
0
0
0
0
1
1
3
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
9
5
0
0
0
2
0
2
2
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
2
0
2
3
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
2
1
0
0
0
1
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
1
1
1
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
1
2
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
1
0
1
2
0
0
0
0
0
0
1
0
3
0
0
1
0
0
0
0
0
0
0
2
0
1
1
0
0
2
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
2
0
2
0
2
2
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
2
2
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
5
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
1
2
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
2
2
0
0
1
1
1
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
2
0
0
1
2
0
0
4
2
0
0
0
0
0
0
0
1
0
1
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
1
0
1
0
0
0
1
2
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
3
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
4
1
0
1
0
0
0
2
0
0
0
2
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
1
2
2
0
2
0
0
0
0
0
0
0
0
1
0
3
1
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
1
1
0
2
0
0
0
1
0
1
0
0
0
0
0
1
1
0
1
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
2
2
2
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
2
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
1
0
1
0
1
0
0
0
0
0
0
0
3
0
0
0
2
0
1
2
2
0
2
0
2
0
0
0
0
0
1
1
0
4
0
0
1
0
0
0
2
0
0
0
2
1
0
0
0
3
1
0
0
0
0
1
2
2
0
0
2
0
2
0
0
4
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
3
0
0
2
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
4
0
0
4
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
3
1
0
1
0
0
0
1
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
2
1
0
0
1
2
0
1
0
2
1
0
0
2
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
1
0
0
0
2
0
0
0
3
0
0
1
0
2
0
2
0
0
4
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
0
1
0
2
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
2
0
2
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
5
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
2
0
0
2
0
1
2
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
1
0
1
3
0
0
0
2
0
0
1
2
1
0
4
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
3
2
0
2
0
0
0
2
1
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
2
1
1
1
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
2
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
2
3
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
1
0
1
0
1
0
0
2
0
2
0
0
0
1
0
5
1
0
0
0
0
0
0
2
0
0
2
0
1
0
2
0
0
0
0
0
1
2
0
0
1
0
2
0
0
0
1
1
0
0
1
0
0
0
0
2
0
1
0
1
0
0
0
0
2
2
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
1
2
2
0
0
2
2
0
1
0
1
0
2
0
0
1
0
2
0
1
0
2
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
2
0
0
1
2
2
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
1
0
0
2
0
4
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
3
1
0
0
0
2
0
1
2
1
0
1
0
0
0
0
2
0
0
0
0
4
0
1
2
0
0
0
0
1
0
0
0
0
1
0
2
1
1
0
0
0
0
0
0
1
2
1
0
0
0
0
1
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
5
1
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
1
2
0
0
0
1
0
1
0
2
0
4
0
0
0
0
3
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
1
0
0
2
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
1
1
0
0
0
1
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
2
0
0
2
0
0
0
1
0
0
0
1
1
0
0
0
3
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
6
0
0
0
0
0
0
0
1
0
2
2
0
0
0
1
1
0
0
0
0
1
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
2
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
1
1
1
1
0
0
2
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
2
0
2
0
3
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
2
0
0
2
0
0
0
3
4
0
0
2
0
0
1
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
1
1
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
1
0
0
2
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
2
0
1
1
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
2
4
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
2
1
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
1
1
0
0
4
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
2
1
0
0
0
0
1
0
0
2
0
0
2
1
0
1
0
0
0
0
0
0
1
0
1
2
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
3
0
0
0
0
0
4
1
0
1
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
2
1
2
0
1
0
0
0
1
1
0
0
2
1
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
2
0
2
6
0
0
0
0
0
0
0
2
0
0
0
0
1
3
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
2
1
0
0
2
2
0
0
0
2
3
0
0
1
2
0
0
0
0
1
0
0
0
1
0
2
0
0
0
1
0
0
1
2
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
2
0
1
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
2
1
0
2
0
1
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
1
1
0
0
0
3
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
4
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
2
0
0
0
0
0
0
2
0
2
1
0
0
2
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
2
2
0
3
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
3
0
0
0
2
1
1
0
0
0
0
2
0
0
2
2
0
2
0
0
1
0
3
2
0
0
0
0
0
0
0
0
2
0
1
0
2
0
2
1
0
0
0
2
0
0
0
2
1
0
0
0
0
0
2
0
3
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
2
1
0
0
0
1
1
0
1
0
0
0
2
0
2
2
2
0
0
0
2
3
0
0
0
0
0
1
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
1
1
0
0
3
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
3
0
0
0
0
1
0
2
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
2
2
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
1
0
0
1
0
1
0
0
0
2
0
1
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
4
0
0
0
0
0
2
0
0
0
6
0
0
1
0
0
0
0
0
1
2
0
0
0
2
0
2
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
1
0
2
0
1
0
0
0
0
0
0
0
1
10
0
0
0
0
0
0
0
2
0
0
1
0
2
1
0
0
0
0
0
0
1
0
0
0
0
1
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
3
1
0
0
0
1
0
2
0
0
0
0
0
1
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
3
1
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
3
2
2
2
2
0
0
0
0
1
0
2
0
0
2
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
2
1
0
0
0
1
0
0
0
2
0
2
0
3
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
1
0
0
0
1
1
3
2
1
1
0
2
0
0
0
1
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
2
0
0
0
0
2
2
0
0
3
0
0
1
0
1
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
2
0
1
1
0
4
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
2
0
0
1
1
0
0
0
0
0
0
4
0
0
1
0
0
0
0
2
0
3
1
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
1
4
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
1
1
0
0
0
2
0
0
0
1
0
0
2
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
11
0
2
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
2
4
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
3
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
2
2
1
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
1
1
2
0
2
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
1
0
1
0
0
3
0
0
0
0
1
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
3
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
3
3
0
0
0
0
3
2
0
0
0
0
0
0
1
0
0
3
0
0
1
0
0
2
2
0
0
1
0
0
3
0
0
2
2
0
0
0
0
1
0
0
0
1
2
0
0
2
0
2
0
0
2
2
0
1
2
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
1
1
1
0
3
0
0
0
0
0
0
0
0
1
0
1
0
1
2
0
0
2
0
1
2
0
0
0
2
0
0
0
1
0
1
2
1
0
2
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
2
2
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
1
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
1
2
0
2
2
1
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
1
0
1
1
0
0
0
0
0
4
0
0
2
0
0
0
2
0
0
0
0
0
1
1
0
1
0
2
0
0
0
1
0
1
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
3
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
2
1
0
0
0
0
0
0
0
1
0
3
0
0
2
0
0
2
0
2
0
0
1
0
0
0
0
0
0
2
1
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
2
2
1
0
2
1
0
0
0
0
0
1
0
1
0
2
0
0
1
0
0
0
4
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
1
0
2
0
0
0
2
0
0
2
2
0
1
0
2
0
0
0
1
0
0
0
0
4
0
1
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
5
0
1
0
0
2
1
0
0
0
0
0
1
6
0
2
0
0
0
1
1
2
1
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
1
0
0
2
0
0
0
0
1
3
2
0
0
1
0
0
3
0
0
0
2
2
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
3
2
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
1
2
0
0
1
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
1
1
0
0
2
0
13
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
2
0
0
4
0
2
0
2
0
0
2
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
2
0
2
0
0
1
0
0
0
0
3
1
0
0
0
0
2
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
4
2
0
0
0
0
0
0
0
1
1
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
3
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
1
1
0
4
0
0
1
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
1
0
1
0
1
0
0
0
2
3
0
1
0
0
0
1
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
2
0
2
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
1
0
2
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
12
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
5
2
0
0
0
3
1
0
0
0
0
4
0
1
2
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
1
2
1
1
0
0
0
0
1
0
2
0
0
0
0
0
1
2
1
0
0
5
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
3
0
0
0
0
0
0
0
2
0
0
2
0
2
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
1
0
0
2
0
0
0
0
0
0
0
2
1
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
2
0
0
0
2
0
1
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
1
0
1
0
0
1
0
2
0
3
1
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
2
1
0
0
2
2
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
3
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
2
2
0
0
3
3
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
2
1
0
0
0
1
0
0
0
0
0
0
1
2
0
1
0
2
5
0
0
3
0
0
0
1
0
5
0
0
0
2
0
0
0
2
0
0
0
1
2
2
0
3
1
0
2
0
0
0
0
0
2
0
1
2
0
0
1
0
0
1
0
0
0
0
3
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
3
0
0
0
2
0
0
0
0
0
2
0
3
0
1
0
0
2
0
0
1
0
0
0
1
2
1
0
2
1
0
1
0
3
0
0
0
1
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
1
0
1
0
2
0
0
0
0
0
1
0
0
3
0
2
0
0
1
0
0
1
2
0
1
3
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
2
0
2
0
0
2
0
1
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
2
3
2
0
0
1
1
6
0
2
0
0
0
1
0
2
0
0
0
2
0
1
0
0
0
0
3
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
4
1
1
0
3
1
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
1
0
0
0
0
1
1
2
0
0
0
0
0
1
0
0
0
0
3
0
0
4
0
1
0
0
0
0
0
0
0
4
2
0
1
0
0
0
2
1
0
0
1
2
0
0
0
0
0
1
2
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
1
0
0
3
2
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
1
0
1
2
0
0
0
1
0
0
0
1
0
0
0
1
2
0
1
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
1
2
0
2
1
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
2
0
0
2
0
1
3
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
2
0
1
2
0
0
0
0
1
1
1
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
6
0
0
0
0
0
0
0
1
0
2
0
4
0
0
0
0
2
1
0
1
0
1
7
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
5
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
1
1
0
1
0
0
0
0
3
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
3
0
0
1
0
2
1
0
0
1
1
0
0
0
0
1
1
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
2
1
0
0
0
0
0
1
0
1
1
2
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
3
0
1
0
0
2
0
0
0
3
0
2
0
0
2
2
1
0
0
2
0
0
0
2
0
0
1
1
2
0
0
3
0
0
0
0
0
0
0
0
2
0
0
3
0
2
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
5
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
1
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
9
0
0
0
0
1
0
2
0
2
0
0
1
0
0
2
0
2
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
2
1
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
1
2
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
1
0
0
0
0
2
2
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
3
0
3
2
0
2
2
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
1
1
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
1
2
0
0
0
0
0
2
0
0
0
0
2
1
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
2
1
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
1
2
3
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
5
1
0
0
1
0
3
0
0
2
0
0
0
1
0
0
0
1
2
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
1
2
0
0
3
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
3
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
2
0
0
0
0
0
1
1
0
1
1
0
0
1
0
0
0
0
0
1
1
0
1
0
0
1
0
2
2
0
0
1
0
0
2
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
3
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
3
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
2
0
1
0
1
0
1
2
0
4
0
0
0
2
0
0
0
0
0
1
0
1
4
2
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
1
0
2
2
0
0
0
3
0
0
0
1
0
0
2
0
0
0
0
1
0
1
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
1
3
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
2
0
0
0
1
0
0
0
0
0
2
0
0
2
1
1
0
0
2
0
0
0
4
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
13
0
1
0
0
0
0
1
0
2
0
2
0
0
0
0
1
0
1
0
2
0
0
2
0
1
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
1
2
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
2
2
1
3
0
0
6
0
3
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
3
0
0
0
0
1
0
3
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
2
1
0
0
0
2
0
2
2
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
1
0
0
2
2
2
0
0
0
2
4
0
0
1
1
0
0
0
0
0
0
0
2
1
0
0
2
1
2
0
0
2
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
2
1
2
3
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
1
0
0
0
0
0
3
0
0
2
1
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
4
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
2
0
1
0
3
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
1
1
0
1
0
0
1
2
0
0
0
1
1
2
0
0
0
1
1
0
0
0
1
1
2
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
2
0
2
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
3
0
4
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
2
0
2
0
0
0
5
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
2
1
0
0
0
1
1
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
1
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
3
0
2
0
1
0
0
0
0
0
0
0
2
0
1
0
2
0
0
1
0
0
0
2
1
0
0
0
0
2
1
0
0
0
3
4
0
0
0
0
1
3
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
2
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
2
0
1
1
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
1
2
0
0
1
0
0
3
2
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
1
2
0
0
0
4
1
0
2
1
1
0
2
0
0
1
0
0
0
3
0
0
0
1
0
7
0
0
1
0
0
0
0
1
0
0
0
1
0
0
4
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
1
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
3
0
0
4
2
0
2
0
0
0
1
0
2
0
0
2
0
2
1
0
0
0
0
3
0
2
0
1
0
0
0
2
0
1
1
0
0
0
0
0
3
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
2
0
1
0
3
0
0
3
0
2
1
0
0
0
0
0
3
2
0
0
1
0
0
0
3
1
0
2
0
2
0
1
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
1
0
1
3
0
0
0
1
0
0
1
0
2
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
2
3
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
2
1
1
0
0
0
0
1
0
1
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
1
0
2
1
2
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
5
1
0
0
0
0
1
1
2
0
2
0
0
0
1
1
0
0
2
1
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
2
0
2
1
0
1
3
0
1
0
1
1
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
3
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
3
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
1
1
1
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
5
0
0
2
0
0
2
0
2
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
4
1
2
2
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
1
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
3
2
0
2
0
0
2
0
1
0
0
0
0
0
0
0
2
0
2
0
2
2
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
1
2
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
2
0
0
0
3
0
0
0
0
0
1
0
2
0
0
2
2
1
0
0
0
0
0
0
2
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
1
0
0
2
1
1
1
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
11
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
3
2
0
0
0
0
1
0
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
2
1
2
3
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
2
1
0
0
1
0
0
1
1
0
0
0
0
2
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
2
0
1
0
0
0
2
0
0
0
0
0
1
0
0
1
2
4
2
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
2
1
0
0
2
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
4
0
0
0
1
0
1
0
0
0
4
2
0
0
1
3
2
0
0
0
1
1
0
0
1
4
0
0
0
0
0
0
0
0
0
1
4
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
2
0
0
0
0
0
1
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
1
1
0
0
0
1
1
1
3
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
2
2
2
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
3
0
2
0
1
0
0
2
0
0
2
0
4
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
1
0
0
2
0
0
2
0
3
0
0
1
0
2
0
2
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
2
2
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
2
2
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
2
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
1
0
1
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
4
0
2
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
3
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
1
2
1
0
3
0
3
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
2
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
3
1
0
1
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
2
0
1
2
2
0
0
0
0
0
0
0
2
0
0
2
3
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
1
3
1
0
0
0
3
0
1
0
0
0
2
0
1
0
2
0
0
0
1
2
0
0
0
1
0
0
0
1
1
0
0
0
0
1
1
0
0
1
0
1
1
2
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
2
0
2
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
3
0
0
0
0
0
2
2
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
5
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
2
0
0
1
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
1
3
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
2
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
2
0
1
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
1
0
0
1
2
1
0
0
2
2
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
3
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
1
0
2
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
2
0
2
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
2
0
0
2
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
6
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
2
3
0
2
0
0
1
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
2
0
0
1
1
0
0
1
0
0
0
0
0
2
2
0
0
1
0
0
0
0
2
1
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
2
0
0
0
1
1
2
0
0
1
0
0
1
2
0
2
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
2
0
0
0
0
1
0
0
5
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
3
0
1
1
0
0
2
5
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
3
1
0
0
0
0
0
2
0
0
0
0
0
2
2
3
2
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
2
0
0
0
0
2
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
1
4
0
0
1
6
0
2
1
1
0
2
1
0
0
0
0
4
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
1
0
2
0
2
0
2
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
4
1
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
7
0
1
0
2
0
0
0
2
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
1
0
0
1
0
3
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
1
0
0
1
0
0
0
1
0
0
0
1
1
1
1
1
4
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
2
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
2
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
5
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
2
0
0
1
0
0
0
0
2
1
0
0
1
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
5
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
3
0
1
0
0
0
0
0
1
2
1
0
0
0
1
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
2
2
0
1
0
1
0
0
0
0
2
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
1
1
0
0
3
0
0
3
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
2
0
0
0
2
0
0
0
3
1
0
0
0
0
0
1
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
1
2
3
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
3
2
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
9
0
1
0
0
2
0
0
1
0
4
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
3
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
1
0
1
0
2
1
0
1
1
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
4
0
0
0
0
0
0
0
0
2
2
2
0
2
0
2
0
0
1
2
0
1
1
0
0
1
0
0
0
0
2
3
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
1
0
0
0
0
0
0
1
1
2
0
1
1
2
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
1
0
0
0
0
0
2
0
2
2
0
0
0
1
1
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
3
0
2
0
5
0
0
2
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
6
0
2
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
1
0
3
2
1
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
2
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
4
0
3
0
0
0
1
0
0
3
0
0
0
0
0
0
0
1
0
1
1
2
2
0
0
0
0
0
1
0
0
1
0
1
3
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
5
0
2
0
2
0
0
0
0
0
0
1
1
0
0
0
2
1
1
0
2
3
0
0
0
0
0
1
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
3
1
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
2
1
0
0
0
0
5
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
3
0
0
0
1
0
7
0
4
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
3
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
1
0
1
0
1
0
0
0
1
2
1
1
0
0
2
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
5
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
1
1
0
0
0
0
0
0
0
3
0
0
0
0
5
2
0
0
0
2
1
0
0
2
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
1
0
2
0
0
1
0
1
0
0
0
0
1
0
0
1
2
0
2
1
0
0
1
2
0
0
0
2
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
4
0
2
0
3
2
1
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
4
0
0
1
0
0
0
0
0
1
2
2
0
1
2
1
0
0
0
5
2
0
0
2
1
1
1
0
0
0
0
4
1
1
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
3
0
2
0
0
2
0
0
2
2
0
2
2
0
0
2
0
0
0
0
0
0
0
3
0
0
1
1
0
0
2
0
0
1
0
2
0
1
0
3
0
0
0
0
2
0
0
2
0
2
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
2
1
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
1
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
2
1
0
2
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
4
0
0
2
0
0
0
0
0
2
0
1
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
1
1
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
10
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
1
2
0
2
0
0
0
0
1
1
3
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
5
0
0
0
0
1
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
3
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
3
0
1
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
1
1
0
0
0
0
0
1
2
1
1
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
2
1
3
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
2
4
2
0
2
0
2
1
0
0
0
0
0
3
1
0
2
4
0
2
0
0
0
1
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
3
0
0
3
0
1
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
1
0
0
0
3
0
0
2
2
0
2
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
4
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
4
0
0
0
0
2
0
1
1
0
0
2
2
0
0
2
2
2
0
0
2
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
3
1
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
1
0
2
3
2
0
0
0
0
2
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
1
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
1
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
2
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
3
0
3
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
12
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
1
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
1
2
0
1
0
3
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
1
0
0
3
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
1
1
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
3
2
0
0
0
0
2
0
0
2
0
2
0
0
0
2
2
0
1
0
0
0
2
0
1
0
0
0
0
0
0
2
0
1
2
0
2
0
0
1
1
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
1
2
0
5
0
2
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
3
0
2
1
0
0
0
0
0
0
0
2
0
0
2
1
0
1
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
2
10
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
1
3
0
0
0
0
0
0
2
2
2
0
1
0
0
0
1
1
0
0
0
2
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
4
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
1
0
1
2
0
0
0
2
0
0
1
4
2
0
0
1
0
0
0
0
0
0
1
1
0
3
0
1
2
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
3
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
1
1
0
0
0
0
0
1
1
0
1
2
1
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
2
0
2
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
2
2
3
1
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
2
0
2
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
4
1
1
0
0
0
0
2
0
0
4
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
3
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
3
2
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
3
1
2
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
2
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
2
0
1
0
1
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
2
1
0
1
2
0
0
1
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
2
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
1
0
1
0
1
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
3
0
0
0
0
0
3
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
2
1
0
0
0
1
0
2
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
3
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
1
0
2
0
2
2
0
0
0
0
0
2
0
0
0
2
1
0
1
0
0
2
0
0
0
0
0
0
0
0
6
0
0
2
6
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
1
0
0
0
0
0
0
0
0
3
0
2
0
0
0
1
0
1
0
2
0
0
0
0
0
3
0
0
2
0
0
0
0
1
0
0
1
0
0
2
0
0
0
1
0
0
0
1
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
4
2
0
0
0
0
0
0
1
0
2
0
2
1
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
3
1
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
3
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
5
1
0
1
2
2
0
1
0
0
0
0
0
2
0
0
0
4
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
4
0
2
0
0
0
1
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
2
1
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
3
0
0
1
0
0
0
2
0
0
1
3
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
1
0
1
1
2
0
0
2
0
0
2
0
0
0
0
2
0
0
1
1
0
0
0
1
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
2
1
0
0
0
0
0
1
1
0
0
3
0
4
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
2
2
0
0
0
0
0
1
0
2
0
2
0
0
0
0
2
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
1
3
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
2
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
3
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
2
3
1
0
0
0
0
0
2
2
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
3
0
0
0
2
2
0
0
0
2
0
0
1
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
1
0
1
0
0
2
0
3
0
0
2
1
0
0
1
0
0
0
1
0
4
0
0
0
0
0
0
2
0
0
0
0
0
1
2
1
0
1
0
2
2
0
0
2
2
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
1
0
0
1
2
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
2
1
0
0
0
0
2
13
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
4
0
2
0
1
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
1
2
3
0
0
2
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
4
1
0
2
0
0
3
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
2
0
0
2
0
0
0
8
1
0
0
3
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
2
1
2
0
0
0
1
0
2
0
0
0
0
0
2
0
1
2
0
0
0
1
4
1
0
0
1
0
0
0
1
0
0
0
2
1
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
4
4
0
1
0
0
0
2
0
0
1
0
1
0
1
1
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
2
0
0
1
2
2
1
0
0
0
0
0
0
0
1
2
0
1
0
0
0
1
0
2
0
1
0
0
1
0
0
0
0
1
0
1
1
0
0
4
2
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
6
2
0
0
1
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
1
2
0
0
2
0
2
0
0
2
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
4
2
0
0
0
2
0
0
0
1
0
0
0
0
1
0
1
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
8
0
1
0
0
0
0
2
0
0
0
0
2
3
0
1
0
1
0
4
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
1
0
1
2
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
1
2
1
0
3
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
3
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
1
0
1
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
2
1
0
0
0
0
2
1
1
0
0
0
0
0
1
2
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
5
0
0
2
0
0
0
2
2
0
1
2
2
0
0
0
6
0
0
2
1
0
0
0
1
0
0
0
0
1
0
0
1
4
1
0
0
2
0
2
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
1
3
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
2
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
1
0
3
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
1
1
0
1
0
0
0
2
0
2
0
0
2
0
0
0
0
1
2
0
0
0
1
0
0
2
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
1
0
0
1
4
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
1
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
2
1
0
2
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
2
1
0
0
0
0
0
3
3
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
1
1
0
0
0
2
0
0
0
0
0
0
0
3
3
0
2
0
0
0
0
0
0
1
1
0
0
0
1
0
2
0
0
0
2
0
0
0
1
0
0
1
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
1
0
0
2
2
1
0
2
2
2
5
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
5
0
0
1
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
2
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
15
0
1
0
0
0
2
0
0
0
2
0
1
0
0
2
0
1
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
2
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
1
2
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
1
2
3
0
0
0
0
0
1
0
0
0
4
0
0
2
1
0
0
1
2
0
0
0
1
0
0
0
0
0
3
0
3
0
0
1
0
1
0
0
0
0
1
2
3
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
3
0
0
2
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
3
0
0
0
0
0
1
2
0
1
2
0
2
1
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
2
1
6
1
0
0
3
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
2
0
2
1
2
0
1
1
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
1
0
1
2
0
5
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
2
0
0
1
3
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
3
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
3
0
0
0
0
2
0
2
1
0
0
0
0
1
0
0
0
0
0
0
1
2
4
0
1
1
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
1
0
0
2
0
1
1
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
5
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
6
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
1
0
0
0
0
2
0
1
0
0
2
0
0
2
2
0
4
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
1
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
2
3
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
3
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
1
1
0
0
6
2
0
3
0
0
0
0
0
4
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
2
0
0
1
0
0
0
0
0
0
5
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
1
1
0
2
0
1
2
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
2
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
4
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
2
0
0
0
0
5
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
2
0
0
0
0
1
1
0
1
5
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
2
0
2
2
2
0
0
2
1
0
0
2
1
1
0
0
0
0
1
0
2
0
1
0
0
0
0
1
3
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
4
0
0
0
0
2
2
2
0
0
2
0
0
3
3
0
0
0
2
0
0
0
0
1
2
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
1
0
2
1
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
3
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
2
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
4
1
2
2
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
3
1
2
0
0
0
0
0
0
0
0
2
4
0
0
0
2
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
1
0
1
0
0
0
0
0
2
0
2
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
2
0
3
0
2
0
0
0
0
3
1
0
1
0
0
0
0
2
0
1
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
1
2
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
1
0
0
1
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
2
0
2
0
2
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
4
0
2
0
2
0
0
0
2
0
0
2
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
2
0
0
4
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
3
2
1
0
4
0
0
0
0
2
1
0
0
1
0
2
0
1
0
1
0
0
0
2
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
2
2
0
1
0
0
0
2
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
3
0
1
0
0
0
0
2
1
0
4
1
2
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
2
0
0
0
1
0
1
0
0
0
0
1
5
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
1
1
1
2
0
0
2
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
5
0
0
0
0
0
0
1
0
1
1
0
2
1
2
2
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
1
0
1
0
2
0
7
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
2
1
0
0
0
1
0
0
0
0
0
2
0
1
0
2
0
2
0
0
2
1
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
2
1
2
1
0
2
0
0
0
0
0
1
0
0
0
2
0
0
7
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
1
0
2
0
0
2
0
0
0
0
0
0
0
2
0
1
0
4
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
4
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
3
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
3
0
1
2
0
0
0
1
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
4
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
1
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
4
2
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
1
0
0
1
0
0
1
0
0
0
2
0
0
1
0
0
1
0
5
0
0
2
0
0
0
0
4
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
1
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
2
0
1
2
0
1
1
0
0
0
1
0
1
0
2
0
2
1
2
0
0
2
0
0
0
0
1
0
0
1
1
3
0
0
0
0
2
1
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
3
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
3
0
3
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
3
1
0
0
0
0
0
1
0
1
0
2
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
1
0
2
0
0
2
0
0
0
2
1
0
2
2
0
2
0
2
0
0
1
2
2
0
0
2
0
0
0
0
0
0
0
12
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
3
0
1
4
1
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
2
1
0
1
2
0
0
1
2
0
2
0
2
2
0
3
0
1
0
0
1
2
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
2
0
2
1
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
2
0
0
0
1
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
4
0
2
0
2
2
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
6
0
0
0
0
0
0
2
0
2
3
0
0
0
2
0
0
0
2
0
0
2
0
1
0
0
0
1
2
1
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
2
1
1
0
0
0
2
3
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
5
1
1
0
0
1
2
0
0
0
2
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
1
0
0
0
0
2
1
2
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
2
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
2
0
0
3
2
0
1
0
0
3
0
0
0
2
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
2
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
2
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
2
0
0
2
0
3
0
0
1
0
0
2
0
1
1
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
2
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
3
0
0
3
0
0
0
0
2
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
3
0
0
2
1
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
2
1
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
1
0
1
0
0
2
0
0
1
3
3
0
0
0
0
0
0
1
0
0
0
0
2
3
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
1
0
2
0
0
0
2
0
4
0
0
0
1
0
0
3
2
0
0
0
2
1
0
0
0
0
6
0
2
0
2
0
0
0
4
5
2
0
0
0
0
0
4
0
0
0
0
2
2
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
1
0
0
0
1
0
0
0
2
0
0
0
1
0
2
0
4
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
2
1
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
2
3
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
8
1
2
2
0
1
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
5
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
1
3
0
2
0
0
0
0
3
0
0
1
0
2
2
0
0
0
0
0
2
0
1
1
0
1
2
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
1
0
0
0
1
0
1
0
2
3
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
1
0
0
2
2
4
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
2
0
0
1
0
0
1
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
3
0
0
1
2
0
0
0
1
0
0
0
0
0
1
0
1
0
2
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
2
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
3
0
0
1
0
1
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
2
0
1
0
1
3
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
2
0
3
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
3
2
0
0
2
0
1
0
0
0
0
1
0
0
0
0
5
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
2
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
10
1
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
3
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
1
2
0
0
14
0
0
0
0
1
0
0
1
2
0
3
0
1
0
0
0
0
1
0
1
2
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
2
2
0
1
3
2
1
0
0
0
0
2
2
0
0
0
1
0
0
2
0
2
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
1
2
0
0
3
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
3
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
1
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
2
2
0
2
0
0
2
0
0
0
2
1
2
0
0
0
1
0
0
0
1
0
3
1
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
1
0
0
1
0
2
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
3
0
0
1
0
2
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
2
0
1
0
0
1
0
0
0
8
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
2
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
3
2
0
0
2
0
0
0
0
1
0
0
1
0
0
1
2
2
0
0
4
2
2
0
1
1
0
0
0
0
0
0
1
1
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
2
0
0
1
0
3
0
0
0
1
0
0
1
2
0
0
2
1
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
2
1
2
0
0
0
0
0
0
1
0
0
0
3
0
0
1
9
0
2
0
2
0
0
0
2
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
1
1
3
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
1
0
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
1
1
1
4
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
3
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
2
0
2
0
0
2
0
2
2
0
2
0
3
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
2
0
2
0
1
0
1
0
0
0
0
0
0
1
0
4
1
0
0
0
0
0
0
0
1
1
1
0
2
0
2
0
2
0
0
1
2
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
1
1
1
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
6
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
1
0
0
2
0
1
0
1
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
1
3
0
0
0
0
0
0
2
0
0
0
0
0
4
1
1
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
1
2
1
0
0
1
0
2
0
0
0
1
0
1
1
0
0
0
0
2
0
3
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
1
0
1
1
0
0
0
1
0
2
1
0
0
1
0
0
0
0
3
2
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
2
0
0
0
0
2
2
2
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
3
0
2
0
0
0
0
3
3
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
3
1
0
0
2
2
0
6
0
0
2
0
0
0
1
1
0
1
0
2
0
0
0
0
0
3
0
0
1
0
1
0
2
0
1
0
19
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
2
3
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
2
0
2
1
0
0
0
1
1
0
0
0
0
2
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
3
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
2
1
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
1
0
0
2
0
2
0
0
1
1
0
0
0
3
2
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
1
5
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
4
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
4
3
1
1
0
0
2
0
0
0
0
0
0
0
3
2
2
0
0
3
0
0
0
0
2
2
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
2
2
0
0
2
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
1
2
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
2
0
0
1
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
13
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
2
0
2
0
1
0
1
0
4
0
0
0
0
0
0
2
2
0
0
2
0
3
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
2
1
0
0
1
2
1
0
0
0
1
0
0
0
0
1
0
2
2
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
1
0
2
0
1
0
1
2
0
0
0
1
0
1
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
1
2
0
1
0
0
1
0
0
0
0
2
0
2
0
0
0
1
0
3
1
2
2
0
1
0
0
0
0
1
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
1
0
3
0
0
0
2
0
0
0
2
0
0
0
1
0
2
0
1
0
3
0
0
1
0
1
0
0
0
0
1
4
0
2
0
1
2
1
1
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
2
0
0
1
1
0
0
1
0
1
5
1
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
6
0
0
0
5
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
2
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
2
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
2
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
2
0
2
0
0
2
1
7
0
0
0
2
0
0
0
2
0
2
0
0
0
0
2
1
0
0
0
0
3
0
0
2
1
0
0
0
2
0
3
2
0
0
2
0
0
1
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
1
0
0
1
0
2
0
1
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
2
2
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
3
0
2
0
0
0
2
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
1
0
0
2
3
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
2
0
2
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
2
0
1
1
0
1
0
2
0
0
0
0
4
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
2
2
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
2
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
5
2
0
2
0
0
0
0
2
0
3
2
0
4
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
3
2
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
1
0
0
0
2
4
0
0
0
0
2
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
3
0
2
0
0
0
0
2
0
0
0
0
0
0
0
3
0
1
0
0
0
1
0
0
0
1
0
0
0
0
2
1
0
0
0
1
1
1
0
0
0
0
0
2
0
0
0
0
0
0
3
3
1
0
1
0
1
0
0
0
0
0
1
0
1
1
0
0
0
3
0
0
1
0
2
0
0
0
0
0
0
2
0
3
2
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
2
4
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
7
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
1
0
1
1
1
0
0
0
2
0
0
1
2
1
0
0
2
0
0
0
0
0
0
0
2
5
2
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
7
0
2
0
0
2
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
5
1
0
0
1
0
0
2
0
1
3
0
2
0
0
0
0
0
0
3
0
3
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
5
0
0
1
1
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
2
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
1
2
0
0
2
0
0
0
0
0
0
1
2
0
2
2
0
0
3
1
0
0
0
4
0
0
1
2
0
0
0
0
2
0
0
0
0
0
1
0
3
3
0
2
0
0
1
0
0
0
2
0
0
0
0
2
1
0
2
0
0
0
0
0
0
3
0
0
2
2
0
1
0
0
0
0
0
1
0
1
0
3
1
2
0
0
1
0
0
3
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
1
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
1
0
1
1
0
2
1
0
0
0
2
0
0
0
2
2
0
0
1
1
1
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
3
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
2
0
1
2
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
1
0
0
0
1
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
1
0
0
0
1
0
2
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
7
0
0
1
7
1
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
1
2
1
2
0
0
0
1
0
0
0
0
0
0
0
2
3
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
1
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
1
0
2
1
0
1
0
0
0
1
0
0
2
0
0
2
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
1
1
4
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
1
2
0
0
2
1
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
1
0
1
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
2
3
0
2
0
0
5
0
0
0
0
0
1
0
3
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
1
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
2
2
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
2
1
0
0
0
2
1
1
1
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
3
0
0
0
0
3
0
0
0
2
0
0
3
3
3
1
0
0
0
0
0
0
0
1
2
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
1
0
2
0
2
0
0
0
0
3
0
2
3
0
2
0
2
0
2
2
1
1
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
1
0
0
1
0
4
0
0
2
0
0
0
0
0
2
1
0
2
0
0
1
0
0
0
0
0
0
2
0
2
2
0
0
2
0
0
0
2
0
0
0
0
1
0
2
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
2
0
0
0
0
1
0
0
1
0
2
1
0
0
0
1
0
0
0
1
0
0
2
1
2
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
2
0
2
0
0
0
2
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
2
0
0
1
0
0
0
3
2
0
1
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
2
0
1
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
5
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
1
0
0
2
5
0
3
2
0
0
0
1
2
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
2
0
2
0
1
2
0
1
0
1
0
0
1
1
0
0
0
1
0
2
0
1
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
2
0
2
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
2
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
1
1
2
0
3
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
1
2
0
1
0
2
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
5
0
0
1
0
0
0
1
2
0
0
0
0
0
4
1
0
1
0
0
2
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
1
0
2
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
2
2
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
1
1
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
2
1
0
0
1
2
1
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
3
0
4
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
1
2
0
0
1
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
6
2
0
0
0
0
2
2
0
0
2
2
0
1
2
0
0
3
0
0
0
2
0
0
0
0
0
0
4
2
2
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
2
2
0
0
0
0
1
2
0
1
2
0
1
0
0
1
2
0
0
0
0
8
0
1
2
0
0
0
0
0
1
2
0
0
0
0
0
1
1
0
0
2
0
1
0
0
0
2
0
2
0
1
0
0
0
2
0
0
0
0
1
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
1
0
0
0
1
0
6
0
0
0
0
1
1
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
1
1
2
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
2
1
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
1
0
0
1
0
2
1
0
0
0
0
0
2
0
1
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
1
5
0
0
1
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
2
2
1
0
0
2
2
0
0
0
2
0
0
0
1
1
2
0
0
1
1
1
0
0
0
0
0
0
2
0
1
0
0
0
2
0
2
2
0
0
0
0
2
2
1
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
2
0
2
0
3
0
0
0
1
3
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
1
0
0
0
2
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
2
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
2
1
0
0
0
0
1
1
2
0
0
1
0
1
2
0
0
0
0
6
0
0
0
0
0
0
2
1
2
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
2
0
1
0
0
2
1
0
1
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
2
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
2
1
0
0
0
2
0
0
0
1
1
0
4
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
3
0
1
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
7
0
1
0
0
2
0
3
0
2
0
2
0
0
2
2
0
0
0
0
0
1
0
2
1
1
0
2
1
0
0
0
0
0
0
1
0
0
1
0
0
2
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
3
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
3
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
10
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
1
1
0
2
0
0
1
2
0
0
0
0
1
3
2
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
2
0
0
1
0
0
0
1
0
0
0
2
1
1
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
2
2
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
1
0
1
2
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
3
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
2
0
0
0
0
0
0
2
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
2
0
2
0
0
0
2
1
0
2
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
2
0
0
1
3
0
0
2
0
2
0
1
0
2
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
1
0
0
1
2
0
0
0
0
1
2
1
2
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
2
1
0
1
0
3
0
0
0
0
1
0
0
0
2
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
1
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
3
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
3
1
3
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
2
0
0
2
2
0
0
0
4
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
11
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
3
0
0
0
0
2
0
0
1
0
0
2
0
0
2
1
0
0
2
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
2
0
0
3
0
0
0
3
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
5
0
0
0
0
0
1
0
3
0
1
5
1
0
0
0
0
0
0
1
1
0
0
0
1
0
2
0
0
1
0
0
3
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
1
1
1
0
0
3
1
0
0
0
2
0
0
0
3
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
3
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
1
0
0
0
1
2
2
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
1
0
0
0
3
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
3
0
0
0
0
0
0
1
0
1
4
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
1
2
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
2
2
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
4
0
0
0
0
6
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
3
0
1
0
1
4
0
0
3
0
0
0
5
0
2
2
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
3
0
0
0
0
2
0
0
0
0
0
0
0
3
1
1
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
1
1
1
0
1
0
0
1
0
1
0
0
2
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
3
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
3
3
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
7
2
0
0
0
1
0
0
0
0
5
0
2
2
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
1
0
3
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
2
1
2
0
0
0
0
0
0
7
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
1
1
0
0
4
0
0
0
1
3
0
0
0
0
2
1
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
5
2
2
3
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
1
0
0
2
0
2
1
2
0
0
0
2
0
0
2
0
1
0
1
0
1
0
0
1
0
0
0
2
0
1
4
0
0
0
2
1
2
2
4
0
1
0
0
0
0
0
1
3
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
3
0
1
0
0
6
3
0
0
0
0
0
0
0
4
1
1
0
0
0
2
0
0
0
1
0
0
0
2
1
5
0
0
0
0
2
0
0
0
1
2
0
1
0
0
0
4
2
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
1
0
0
2
1
3
0
0
1
0
1
0
0
0
0
2
0
1
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
3
2
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
1
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
2
0
0
2
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
5
0
2
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
1
0
0
2
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
2
1
0
0
1
0
3
2
2
3
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
1
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
2
2
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
3
0
0
0
0
1
0
0
0
0
2
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
1
0
0
4
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
1
0
0
0
0
0
2
0
2
0
0
3
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
1
2
0
0
1
0
0
1
0
0
1
2
0
1
2
0
0
0
0
0
1
1
0
0
1
0
1
0
1
2
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
2
0
2
0
0
7
1
0
1
0
0
2
0
0
0
1
0
0
1
0
0
0
3
0
1
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
1
1
2
2
3
0
0
2
0
2
0
2
0
2
0
0
1
0
2
0
0
0
0
1
2
0
1
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
2
0
2
0
0
0
0
0
1
0
2
2
0
1
0
0
1
0
0
1
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
5
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
3
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
2
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
1
0
3
0
1
0
0
10
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
1
0
2
0
0
0
0
2
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
2
2
1
5
0
1
0
0
0
2
0
0
0
0
1
0
1
2
0
0
0
0
2
2
1
1
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
2
0
0
0
0
1
0
1
0
0
0
0
0
2
0
2
1
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
1
4
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
2
2
0
1
4
2
0
0
0
0
0
0
0
2
0
0
2
0
0
4
0
0
1
1
1
0
0
0
1
0
0
6
0
0
2
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
4
0
0
0
0
0
0
2
1
0
2
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
4
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
2
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
1
1
0
2
0
1
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
2
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
3
0
0
1
2
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
3
0
0
0
0
1
0
0
0
1
0
1
2
1
0
0
0
0
2
3
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
1
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
5
1
0
2
1
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
2
0
0
0
0
0
0
1
0
0
2
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
1
2
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
1
2
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
2
2
0
0
0
0
2
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
2
1
0
0
0
0
0
2
0
1
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
2
0
0
2
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
1
0
0
0
0
0
0
0
2
0
4
2
0
0
1
3
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
3
0
0
2
1
0
2
2
2
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
1
4
0
0
0
2
0
2
2
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
3
0
2
0
2
0
1
1
3
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
3
0
2
0
6
0
0
0
0
0
0
1
2
2
0
2
0
1
0
0
1
0
0
1
2
0
0
0
0
2
0
0
0
0
3
0
0
0
0
1
1
0
0
0
1
0
0
0
0
2
0
0
0
1
0
1
0
1
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
13
2
0
0
0
0
1
3
0
0
0
0
0
0
0
0
1
0
2
0
0
0
4
2
1
2
0
0
0
0
0
0
1
2
0
0
2
0
0
0
1
0
2
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
5
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
2
1
0
0
0
0
1
0
0
2
1
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
2
0
0
0
0
1
1
2
0
1
2
3
0
0
0
0
0
1
1
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
5
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
1
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
4
1
3
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
1
0
0
1
0
0
0
1
0
1
0
4
0
0
1
2
1
0
0
0
0
0
0
2
0
0
1
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
3
0
2
0
0
1
2
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
1
2
0
2
0
0
0
1
0
0
0
1
1
0
0
0
3
0
2
0
0
0
1
0
0
3
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
1
2
3
1
6
0
1
0
1
0
2
0
0
0
0
0
0
0
1
0
2
0
3
0
0
1
0
0
0
1
0
0
0
2
0
9
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
1
17
0
0
0
0
0
0
2
4
0
0
0
0
0
0
2
1
0
0
0
2
0
1
0
0
1
0
1
0
0
0
0
2
5
0
0
1
2
0
0
0
0
1
1
0
1
0
0
0
1
0
0
2
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
1
0
1
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
2
2
0
0
2
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
1
1
4
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
3
0
1
1
2
1
0
0
2
0
2
0
2
0
0
0
2
2
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
2
0
2
0
1
0
0
0
1
0
0
0
0
0
0
1
0
2
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
3
0
0
2
0
2
0
2
0
0
2
0
1
0
0
1
0
2
2
0
0
0
0
3
0
0
1
0
0
0
0
1
2
0
2
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
3
1
2
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
2
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
2
0
1
0
0
1
0
3
2
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
3
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
2
0
1
1
0
0
0
0
0
6
0
3
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
1
0
0
0
0
0
0
0
1
2
3
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
5
1
0
0
2
1
0
0
1
0
6
2
0
0
0
2
0
0
0
1
0
0
1
0
1
0
2
0
3
0
0
0
0
7
0
0
2
1
0
2
0
0
2
2
0
0
2
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
2
0
3
0
0
0
2
0
2
0
0
0
1
1
0
0
0
0
0
0
8
0
0
8
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
2
1
0
0
1
0
0
0
1
1
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
1
0
0
0
1
1
2
2
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
6
0
0
0
0
3
0
0
0
0
1
0
2
0
1
3
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
1
0
0
0
1
0
2
0
0
0
0
1
1
0
0
1
0
0
2
1
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
3
0
0
1
0
1
0
2
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
3
2
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
4
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
1
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
3
0
0
0
0
0
0
1
2
0
5
0
0
0
0
0
0
0
2
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
3
0
0
1
2
1
0
1
2
0
0
0
0
0
0
1
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
1
3
1
2
0
0
0
2
0
0
0
2
0
0
5
0
1
0
1
0
0
1
0
0
0
0
1
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
12
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
3
2
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
2
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
1
5
1
2
0
2
0
0
0
0
0
0
0
2
0
2
1
3
0
2
0
0
0
0
0
1
0
3
0
0
0
1
0
0
0
0
0
0
3
0
3
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
2
0
0
0
2
0
0
0
4
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
1
0
1
0
0
0
7
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
3
0
3
0
0
0
0
1
0
1
0
0
0
0
0
2
0
2
0
0
2
2
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
1
1
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
2
0
0
0
0
0
2
3
0
0
1
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
1
4
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
2
1
1
0
0
3
0
0
1
1
0
4
0
0
0
2
0
2
0
2
0
0
0
1
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
2
0
0
0
0
1
1
0
0
0
1
2
0
1
0
2
0
0
0
1
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
2
0
0
2
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
4
0
2
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
5
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
3
0
4
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
2
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
2
0
1
0
0
1
1
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
2
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
3
1
0
1
1
2
0
1
0
0
0
2
4
0
0
0
0
0
0
0
0
4
3
1
0
1
0
0
0
0
0
0
0
0
0
1
0
3
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
2
3
0
0
0
0
2
0
2
2
0
0
0
0
0
2
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
1
1
0
2
0
0
0
0
0
4
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
2
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
2
4
1
0
0
0
0
0
0
0
1
1
1
1
0
0
1
0
3
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
5
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
1
4
2
2
0
0
0
4
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
2
3
6
1
2
0
0
1
0
0
0
0
1
3
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
5
1
1
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
2
2
1
0
2
0
1
0
0
2
0
0
0
0
0
0
0
1
0
2
2
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
3
2
0
2
0
0
0
0
2
2
1
1
1
2
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
6
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
2
0
0
0
2
0
0
0
0
1
0
1
2
0
0
0
2
4
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
2
5
0
2
0
1
0
0
0
0
0
0
0
0
0
3
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
1
1
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
5
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
1
1
3
0
0
0
0
0
0
0
1
1
0
2
0
1
0
2
0
0
1
0
2
0
0
0
0
1
1
0
0
2
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
1
0
1
0
1
0
0
0
0
0
0
0
2
2
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
1
0
2
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
4
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
2
3
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
1
0
0
2
2
0
0
3
0
0
0
0
0
2
4
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
1
0
1
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
1
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
3
2
0
0
0
0
1
0
1
0
0
0
1
0
2
0
0
0
1
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
1
0
0
0
2
0
0
2
0
0
0
1
0
0
2
1
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
2
0
0
3
2
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
1
0
0
3
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
2
0
3
0
0
2
0
0
0
0
2
0
0
0
1
2
0
1
0
0
1
0
0
1
0
0
0
2
2
0
1
1
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
1
0
0
1
0
7
0
0
2
0
1
0
2
0
0
2
0
0
2
0
0
0
2
2
0
0
2
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
2
0
1
1
0
0
1
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
5
1
0
0
0
1
0
0
0
2
0
0
3
0
2
2
2
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
1
0
0
1
1
1
1
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
1
0
2
0
2
1
0
0
2
1
0
2
0
0
0
1
2
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
2
0
0
0
0
0
2
1
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
1
0
0
2
0
0
1
0
0
0
1
0
3
0
0
2
0
3
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
1
1
0
0
2
1
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
1
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
1
3
0
0
1
0
0
0
0
2
2
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
2
0
0
2
0
0
3
2
0
0
2
0
0
1
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
2
2
0
0
8
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
5
0
0
0
0
1
0
3
0
0
2
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
2
0
3
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
6
0
2
0
1
3
0
0
0
0
0
1
0
3
0
0
0
3
0
1
0
0
0
3
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
10
0
1
0
0
3
1
2
0
2
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
1
2
0
1
0
2
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
2
0
0
2
0
0
2
3
2
0
0
0
1
2
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
1
2
0
0
0
0
1
1
0
0
0
0
0
0
1
0
2
1
0
0
0
1
0
1
0
0
3
0
0
2
1
1
0
0
0
1
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
2
2
1
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
3
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
1
3
1
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
2
0
0
1
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
1
4
0
0
0
0
0
0
0
1
0
0
1
2
8
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
3
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
1
0
6
0
1
2
0
0
0
0
0
1
0
1
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
4
0
6
0
0
0
2
0
1
0
0
0
0
1
0
1
2
4
0
1
1
0
0
0
0
0
0
0
2
0
0
3
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
2
2
1
1
1
2
0
0
1
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
1
2
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
3
4
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
2
0
0
1
0
0
3
0
0
2
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
4
0
0
0
2
0
0
0
0
0
0
2
2
1
0
0
0
0
2
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
2
1
0
0
0
1
0
0
2
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
1
1
0
0
0
2
0
1
0
0
0
0
2
1
1
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
1
1
0
2
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
2
2
0
0
1
0
2
0
0
0
1
0
1
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
1
0
0
0
1
2
0
1
0
0
0
1
0
0
2
0
0
3
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
6
0
0
0
1
0
1
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
3
0
0
2
1
0
0
1
1
0
1
0
0
0
0
0
2
0
1
0
4
2
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
1
0
3
0
0
0
2
1
0
0
2
0
0
0
2
0
2
0
1
0
3
0
0
0
3
0
0
2
0
0
0
2
0
0
2
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
1
1
2
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
3
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
2
0
0
1
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
2
0
1
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
2
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
2
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
1
0
0
0
2
0
0
0
3
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
2
1
0
2
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
3
0
0
3
0
1
0
0
0
0
0
0
0
0
3
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
5
0
3
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
1
2
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
2
0
0
0
2
0
0
2
4
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
2
0
2
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
2
2
0
2
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
2
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
1
3
2
0
0
0
2
0
4
2
0
1
0
0
0
0
0
0
0
4
0
0
0
2
1
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
3
0
0
0
0
2
0
0
0
0
0
1
0
0
1
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
6
1
0
1
0
0
0
0
0
1
0
2
0
2
0
0
0
0
1
4
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
3
1
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
2
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
2
0
2
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
2
1
1
0
1
0
0
0
1
0
0
1
2
0
0
3
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
1
0
0
0
3
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
1
2
0
3
0
0
0
0
0
0
0
0
2
0
3
3
1
0
1
0
0
6
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
3
2
0
1
0
0
0
0
1
0
0
0
1
1
0
2
2
0
0
0
0
0
0
0
0
0
0
2
1
0
1
1
1
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
4
0
1
0
0
0
0
0
0
1
1
0
2
0
0
0
0
2
1
0
0
1
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
2
0
0
0
0
0
1
0
2
0
0
0
0
0
2
2
2
0
0
1
2
0
2
9
2
1
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
2
1
2
0
0
2
0
0
0
0
2
2
0
0
0
1
0
0
0
0
1
1
1
0
0
1
2
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
3
0
0
2
0
4
0
0
0
3
0
1
0
0
0
1
6
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
9
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
5
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
3
0
2
0
0
0
0
2
1
2
0
0
2
0
0
2
1
0
0
0
2
4
1
0
0
0
0
0
0
4
0
0
2
2
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
2
0
1
0
0
0
2
3
0
2
0
2
0
0
0
0
1
1
1
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
3
1
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
1
2
0
2
0
2
0
0
0
0
1
0
0
2
0
2
2
0
0
1
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
5
0
0
2
0
4
0
0
0
0
1
0
0
0
0
2
0
0
0
1
2
0
1
2
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
2
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
1
3
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
8
1
0
0
0
0
0
0
0
11
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
3
1
0
0
0
3
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
1
0
0
4
0
0
0
2
0
0
2
0
0
0
1
2
0
1
0
0
0
1
0
0
2
0
0
2
0
0
0
1
2
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
4
0
0
5
0
0
0
2
0
0
2
0
0
1
0
4
0
2
0
0
0
0
0
0
1
0
1
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
1
0
0
1
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
1
0
0
1
0
0
1
2
0
0
0
0
0
1
4
2
2
0
0
0
3
0
0
0
1
0
1
0
2
0
0
0
0
0
1
2
0
3
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
7
1
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
1
0
1
0
0
0
1
2
1
0
0
0
0
0
0
2
0
1
2
2
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
1
0
2
4
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
5
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
1
0
0
1
0
0
2
0
0
0
2
0
2
0
0
0
0
1
0
0
2
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
3
2
2
0
1
1
0
0
0
0
0
0
1
0
0
3
0
3
0
1
0
0
0
0
1
1
0
0
0
0
0
2
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
2
0
1
0
0
0
0
0
1
0
0
0
2
2
0
2
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
4
15
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
3
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
1
1
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
3
2
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
1
0
0
0
2
0
1
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
1
0
1
0
3
0
0
1
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
2
2
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
1
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
1
1
0
1
0
0
0
0
0
0
4
0
0
1
3
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
2
0
0
0
0
1
2
1
2
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
2
3
0
2
1
0
0
0
0
2
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
2
5
0
0
3
2
1
0
0
0
0
0
0
0
0
0
0
2
0
1
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
2
0
0
0
2
0
3
1
2
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
1
1
0
0
2
1
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
14
0
0
0
0
1
2
2
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
2
0
2
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
1
1
2
0
0
1
0
1
0
0
2
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
6
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
4
1
0
0
2
1
1
2
0
0
1
0
0
1
2
0
2
0
0
0
0
3
0
0
1
0
5
1
0
0
2
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
3
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
4
1
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
3
1
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
2
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
6
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
5
0
1
0
0
0
0
0
2
0
2
0
1
0
0
2
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
1
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
2
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
7
2
0
0
0
0
1
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
2
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
2
1
0
0
0
0
0
2
2
0
0
0
0
3
0
0
2
0
0
0
0
1
0
0
2
0
0
1
1
0
2
2
0
0
0
0
1
2
0
0
0
0
0
0
1
0
2
0
4
0
4
0
0
0
1
0
0
0
1
0
2
1
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
1
4
0
0
2
0
2
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
2
1
0
2
0
0
0
0
1
0
0
2
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
7
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
3
0
0
0
1
2
2
3
0
0
2
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
1
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
4
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
1
0
0
6
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
2
2
1
2
0
0
0
0
1
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
1
0
1
2
2
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
2
0
1
3
2
0
1
0
0
0
0
0
0
3
2
0
1
0
0
2
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
2
1
1
0
0
0
0
0
2
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
1
2
1
0
0
1
0
0
0
0
2
2
1
0
0
0
0
1
0
1
0
0
1
0
0
2
2
0
0
2
0
2
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
1
2
0
0
1
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
6
3
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
2
2
1
0
0
0
1
0
0
0
0
1
0
0
0
2
0
1
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
2
1
0
9
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
7
0
0
1
0
0
0
0
1
0
0
1
1
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
1
1
0
1
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
1
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
3
2
0
1
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
2
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
2
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
2
2
0
0
0
0
0
0
0
2
0
0
0
2
0
3
0
0
0
1
0
0
0
0
0
2
0
0
0
0
12
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
1
2
0
0
0
1
1
0
0
0
2
0
0
0
2
1
2
0
1
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
5
0
0
1
0
0
0
0
0
1
0
0
0
0
4
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
1
0
0
2
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
2
0
0
0
1
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
2
3
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
1
0
0
1
0
0
0
0
1
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
3
1
1
0
0
0
0
0
2
1
0
0
0
1
0
1
1
0
2
0
2
1
0
0
0
0
2
0
0
0
4
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
3
0
0
0
2
0
0
0
0
0
0
1
0
0
0
3
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
2
0
1
0
0
0
1
0
0
2
4
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
1
1
4
0
0
0
0
2
1
0
2
0
2
0
1
0
0
0
0
2
0
1
0
1
0
0
0
1
0
0
2
0
1
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
3
0
0
1
1
0
0
1
0
3
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
2
2
0
2
0
0
3
0
0
2
0
0
0
1
1
0
0
1
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
3
1
1
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
1
0
0
2
0
0
1
0
2
0
0
2
2
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
2
3
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
3
4
1
1
0
0
2
0
1
0
1
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
1
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
2
0
0
2
0
1
0
1
0
0
1
2
2
1
0
0
0
0
1
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
2
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
2
0
2
1
2
0
1
1
0
1
0
2
0
0
0
0
0
1
2
0
0
4
2
0
0
0
2
0
0
0
0
2
0
2
1
2
10
2
0
1
2
1
2
1
0
0
0
0
2
0
1
0
2
0
0
0
0
0
1
0
1
2
0
0
3
0
1
0
1
0
1
2
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
3
0
0
8
4
0
0
0
2
0
1
0
0
0
2
0
1
0
0
1
0
0
2
1
0
0
0
1
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
2
0
2
0
0
1
1
0
0
0
0
0
0
2
0
0
2
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
2
1
0
0
0
2
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
1
0
0
2
2
0
0
2
0
0
3
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
2
0
1
0
0
0
3
4
1
0
0
0
2
0
0
0
2
2
2
0
0
0
1
0
0
0
0
0
3
2
0
0
2
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
1
2
0
0
2
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
4
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
2
0
1
0
1
1
1
1
0
0
1
0
0
2
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
2
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
1
0
0
1
1
1
0
1
0
0
0
0
0
0
0
3
1
0
0
0
0
0
2
1
0
1
0
1
0
0
0
0
0
1
2
2
1
0
0
0
0
0
0
0
0
0
1
4
0
1
3
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
1
1
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
2
0
0
0
0
1
2
1
0
0
0
0
0
1
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
3
0
0
0
1
1
0
0
0
0
1
6
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
1
6
0
0
0
2
1
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
1
2
0
0
2
0
0
0
0
0
0
1
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
3
2
0
0
0
0
0
0
1
0
9
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
2
0
1
0
0
0
0
0
0
2
0
0
2
1
0
3
0
8
2
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
3
0
0
0
2
0
0
1
0
0
1
0
0
0
1
2
0
0
0
0
2
5
1
0
0
0
3
1
0
0
0
1
0
2
0
0
0
0
1
1
0
0
1
2
0
0
1
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
3
1
1
0
0
2
1
0
2
2
0
1
0
0
2
2
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
3
0
0
0
0
0
0
2
4
1
0
0
0
0
0
0
4
0
3
0
0
0
0
0
0
0
0
0
0
1
1
0
2
1
0
0
1
0
0
0
2
1
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
2
0
1
0
0
0
0
1
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
2
0
0
1
0
0
0
0
0
2
2
0
1
2
2
6
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
3
0
0
0
0
1
0
0
2
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
1
0
0
0
0
0
0
1
2
0
0
0
1
0
0
2
0
1
0
1
3
0
0
0
0
0
0
1
1
2
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
2
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
1
0
0
0
1
2
0
1
1
0
0
2
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
1
1
2
0
0
2
0
0
2
0
0
0
8
0
2
0
0
0
0
2
0
0
1
2
1
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
1
0
0
0
0
0
0
2
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
1
2
1
0
1
0
0
1
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
2
0
0
0
3
0
1
1
1
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
1
1
2
1
3
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
2
1
3
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
2
3
0
0
0
1
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
2
2
0
0
0
0
2
1
2
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
1
0
3
0
0
0
0
4
0
0
0
0
0
3
2
0
2
0
0
0
0
2
0
0
0
1
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
2
1
1
0
0
0
0
0
2
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
4
2
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
6
1
0
0
0
0
0
1
3
0
0
0
0
3
0
2
0
0
2
0
0
0
0
0
3
2
0
1
0
0
2
0
3
0
0
0
2
0
0
0
0
0
0
1
3
0
2
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
1
0
0
0
1
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
2
0
0
0
2
0
1
2
0
1
0
0
0
0
0
2
0
2
0
2
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
1
2
2
0
0
2
0
2
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
3
1
1
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
2
0
2
0
0
2
0
1
0
0
2
1
2
0
2
1
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
2
1
0
1
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
1
2
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
1
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
1
0
0
0
0
0
3
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
3
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
3
1
0
0
0
2
0
0
0
0
0
1
0
0
6
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
2
1
1
1
0
0
1
0
0
1
2
1
2
1
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
2
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
4
0
0
0
0
2
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
2
2
0
1
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
1
1
1
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
1
1
0
0
0
2
0
1
3
0
0
0
0
0
2
2
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
3
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
2
10
0
0
2
0
0
0
0
0
1
0
5
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
1
0
0
0
0
0
1
0
0
1
2
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
1
2
0
0
1
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
3
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
3
0
0
0
2
3
1
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
4
0
1
0
0
0
1
0
7
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
2
3
0
2
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
1
0
0
1
0
0
2
0
0
0
2
0
2
0
0
0
0
2
1
0
0
0
3
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
1
2
0
0
0
2
0
0
0
0
0
1
2
2
0
0
0
0
0
0
1
0
2
1
2
2
0
0
0
2
0
2
0
0
0
0
0
1
0
0
1
0
2
0
2
1
0
0
0
1
1
2
2
0
1
0
0
0
0
0
0
0
0
0
1
1
0
2
1
0
0
0
0
2
0
2
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
2
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
1
1
1
1
0
0
0
0
0
1
1
0
2
0
0
0
0
0
1
1
2
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
1
0
0
0
4
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
2
2
1
0
0
2
0
2
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
2
1
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
1
0
1
0
0
0
8
0
0
1
0
0
4
0
0
1
1
2
2
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
2
0
0
0
0
1
0
1
0
4
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
2
3
4
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
3
0
1
0
0
2
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
1
0
0
3
0
0
0
0
0
0
4
0
0
1
0
0
2
0
1
0
0
0
2
0
1
1
0
0
0
0
2
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
7
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
1
1
3
0
0
0
2
0
1
1
0
0
0
2
0
0
0
0
1
2
0
2
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
1
0
0
6
1
1
0
0
1
1
1
0
0
1
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
3
1
1
2
0
2
1
1
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
3
1
0
0
1
0
0
2
0
0
0
1
0
0
0
0
2
0
0
1
0
0
7
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
3
3
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
2
0
2
0
0
2
0
0
0
4
0
2
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
2
0
0
0
1
0
1
2
1
0
0
0
2
0
0
0
0
4
0
0
0
0
0
1
2
1
0
1
0
2
2
0
0
0
3
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
1
3
0
2
1
2
0
1
0
0
0
0
0
0
0
1
3
0
0
1
2
0
0
0
0
0
0
1
0
1
2
0
0
1
0
0
2
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
2
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
1
0
0
0
2
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
3
0
0
2
0
0
0
0
0
1
2
0
3
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
3
0
2
1
0
0
2
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
1
3
0
0
1
0
0
1
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
1
0
2
1
0
0
3
0
0
2
0
0
0
0
2
0
0
0
1
0
0
3
0
0
6
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
1
0
0
1
2
2
0
0
0
1
0
0
1
0
0
0
2
3
0
1
0
0
0
0
1
0
1
1
0
2
0
0
1
0
0
0
3
0
0
0
2
0
0
1
0
2
0
0
0
1
0
0
2
0
0
0
4
0
0
0
0
0
2
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
2
2
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
2
1
0
2
0
0
0
1
13
0
0
0
0
2
0
1
0
2
0
2
0
0
0
0
1
2
0
0
2
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
2
0
0
2
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
3
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
1
1
0
0
0
0
1
0
1
2
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
2
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
2
0
3
0
1
0
0
0
2
0
1
2
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
2
1
0
0
0
2
0
2
0
2
0
0
2
0
0
0
1
2
2
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
2
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
2
1
0
0
0
2
0
2
2
2
0
0
0
0
0
1
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
1
0
0
0
0
0
1
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
2
0
1
0
2
0
0
1
0
0
0
1
0
0
0
1
1
0
1
0
0
1
0
0
0
1
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
3
0
0
0
2
1
0
0
3
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
2
0
0
0
3
1
1
0
0
2
0
0
0
1
0
0
0
0
0
3
0
0
2
0
0
0
0
2
0
0
0
4
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
1
1
0
0
0
0
0
4
0
0
1
1
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
3
3
1
2
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
2
2
0
4
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
3
1
0
2
0
0
0
2
0
2
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
9
0
0
0
0
2
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
1
2
0
0
1
0
0
0
1
0
0
0
0
2
0
2
0
0
0
1
1
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
5
0
0
0
0
0
0
0
3
0
3
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
1
0
0
0
2
0
1
1
0
1
0
0
3
0
0
2
1
0
1
2
1
0
0
0
1
0
0
0
2
0
0
3
0
1
0
0
0
0
0
0
4
2
0
0
0
1
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
2
0
0
0
0
2
0
0
2
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
1
3
2
2
0
0
1
0
0
1
0
0
2
2
0
2
0
2
0
2
0
0
7
0
0
0
0
0
0
4
0
0
1
2
0
0
0
0
2
0
1
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
1
0
0
2
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
1
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
2
2
2
0
0
2
5
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
3
0
8
0
0
1
0
0
0
8
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
1
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
1
0
0
0
0
2
2
3
0
0
0
0
2
1
0
2
0
0
0
1
3
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
2
0
0
0
0
3
0
0
1
1
0
5
0
0
0
1
0
0
0
1
1
0
0
0
0
0
4
0
0
0
2
2
1
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
1
0
0
0
1
3
0
2
0
0
1
0
0
0
1
1
0
0
0
3
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
1
1
0
0
0
0
0
3
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
3
0
0
0
0
1
3
2
0
0
0
0
1
0
0
0
0
2
0
1
1
0
0
2
0
1
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
3
0
0
0
2
0
0
0
0
0
0
1
0
1
0
3
1
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
6
0
1
0
2
1
0
0
0
1
2
0
0
0
0
0
0
2
1
0
0
2
2
0
0
3
0
1
0
0
0
0
1
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
2
0
2
1
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
1
0
0
2
0
1
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
1
0
0
2
2
1
0
0
0
0
2
0
0
0
0
1
0
0
0
2
4
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
1
0
0
0
1
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
9
0
2
0
2
2
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
2
0
1
1
0
0
0
2
0
0
2
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
1
0
0
2
0
0
0
2
0
1
0
2
0
2
0
0
0
0
0
1
0
0
0
2
0
1
0
2
0
0
0
2
0
0
0
0
0
4
0
0
1
1
2
1
0
4
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
3
1
0
0
2
0
0
2
2
0
0
2
0
1
0
0
0
0
5
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
1
0
0
2
0
0
1
0
1
0
4
0
0
4
0
2
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
2
0
0
1
2
2
1
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
2
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
1
1
0
1
0
0
2
0
0
1
0
0
0
0
0
2
0
0
3
2
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
3
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
1
0
1
1
2
0
1
1
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
3
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
2
1
1
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
2
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
5
0
0
1
0
2
0
0
0
0
1
0
1
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
2
11
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
1
0
0
0
2
4
2
0
1
0
0
0
2
0
0
0
0
0
4
0
0
0
1
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
2
0
2
0
1
0
2
3
1
0
0
1
0
0
0
0
3
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
1
0
2
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
2
0
2
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
1
2
2
0
0
0
2
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
1
1
2
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
2
1
2
1
0
0
0
2
0
0
0
2
0
1
0
2
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
1
1
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
1
0
2
0
1
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
1
0
2
0
1
0
0
2
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
7
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
2
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
3
0
2
1
0
1
1
0
0
0
0
0
0
2
1
2
1
3
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
2
1
0
1
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
1
0
2
0
0
1
1
0
2
2
3
0
0
1
2
1
0
0
1
0
1
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
1
1
0
0
0
0
0
3
0
0
2
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
8
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
1
1
2
1
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
1
0
1
0
2
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
2
0
1
3
0
0
0
1
1
0
0
1
0
0
0
0
0
1
1
0
3
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
2
0
0
0
4
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
1
0
1
1
2
0
0
0
2
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
2
0
0
1
0
1
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
1
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
4
0
0
2
2
3
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
2
0
0
1
0
1
2
0
1
0
0
0
0
2
4
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
2
0
0
2
0
0
0
1
0
1
0
5
0
0
0
0
0
0
0
0
4
0
2
0
0
0
0
0
0
1
3
0
0
0
2
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
2
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
2
1
0
4
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
1
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
6
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
1
0
0
0
2
0
1
2
1
5
2
0
1
1
0
1
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
2
1
2
0
0
1
0
0
0
2
0
1
0
0
0
1
0
1
2
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
2
0
0
2
2
1
2
0
0
1
0
0
0
0
1
0
0
0
2
1
1
0
2
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
4
0
0
2
2
1
2
0
0
0
0
3
0
0
0
0
1
0
2
2
0
0
0
0
0
2
0
0
5
2
1
0
0
0
0
0
2
2
0
1
0
1
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
1
2
0
3
0
0
0
0
0
0
1
1
0
0
0
1
2
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
2
4
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
2
0
1
1
0
2
1
0
1
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
1
2
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
2
0
1
1
3
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
1
1
0
3
1
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
1
1
0
2
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
2
1
2
0
0
0
0
0
0
2
0
2
0
1
0
2
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
2
2
2
0
0
2
0
1
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
12
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
3
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
2
0
2
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
1
0
2
0
0
0
2
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
3
3
0
0
1
2
0
0
0
1
0
3
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
2
1
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
1
0
0
9
0
0
0
0
0
0
1
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
2
3
0
3
0
0
0
0
0
6
0
0
2
2
2
0
0
2
0
2
0
0
0
0
0
1
2
3
1
0
0
0
0
2
0
0
3
1
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
2
0
1
0
0
0
0
0
0
0
0
2
0
1
2
0
3
0
0
0
2
1
0
0
0
0
0
2
2
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
1
0
0
2
0
0
0
2
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
2
0
0
4
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
5
1
2
2
0
1
0
3
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
3
0
0
2
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
5
0
0
0
0
0
0
0
0
4
0
2
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
3
2
0
0
0
1
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
2
0
0
2
0
3
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
2
1
0
0
0
2
0
0
0
0
2
2
1
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
3
0
0
0
0
2
3
0
0
1
0
2
0
0
0
0
1
1
0
0
0
3
0
0
0
2
0
0
2
2
2
0
0
0
0
0
2
2
2
0
1
0
0
0
2
0
1
0
3
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
1
1
3
0
0
0
2
2
0
0
2
2
0
1
2
0
0
0
0
0
1
0
1
2
0
0
0
0
2
0
0
3
0
1
0
0
0
1
2
0
0
0
0
0
0
2
0
2
2
1
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
2
3
0
0
0
0
0
0
0
4
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
3
0
0
0
1
1
0
1
0
0
0
0
1
0
0
4
0
2
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
1
0
1
0
0
0
0
0
2
2
0
2
0
0
0
2
0
0
2
0
2
0
0
0
0
3
1
0
0
0
0
0
2
2
0
1
0
0
0
2
0
0
0
2
0
1
1
0
0
2
0
1
0
2
0
0
0
0
3
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
1
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
1
0
5
3
0
0
0
2
0
0
0
1
0
0
0
0
0
2
3
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
4
0
0
2
0
3
0
0
0
0
0
0
0
0
1
3
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
1
2
0
0
2
2
0
0
1
0
0
0
0
0
0
1
2
0
2
0
0
0
1
6
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
2
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
3
0
0
0
2
0
0
1
0
0
0
2
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
1
0
0
2
0
0
2
1
1
1
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
4
0
4
0
0
0
0
0
0
0
0
0
4
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
1
1
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
1
0
0
2
2
3
1
0
0
0
0
1
0
4
0
0
0
0
0
0
1
1
0
2
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
2
0
0
0
0
0
0
0
0
0
1
2
2
1
0
0
0
7
1
0
1
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
1
0
1
0
0
0
0
0
0
0
2
3
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
3
0
2
0
0
0
2
11
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
1
1
2
0
2
0
0
5
0
2
0
0
0
0
1
1
0
0
2
1
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
3
2
1
1
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
2
0
2
1
0
0
1
1
0
0
0
0
1
2
0
0
0
0
2
0
2
1
0
1
0
0
0
0
3
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
1
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
2
0
0
1
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
2
1
2
0
1
2
0
0
1
0
0
1
2
2
1
1
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
1
0
0
2
1
0
2
1
0
0
0
1
0
0
0
0
0
0
0
3
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
2
2
2
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
1
1
2
2
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
3
0
0
2
0
0
0
0
0
0
2
0
0
0
0
3
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
2
0
0
0
1
2
0
0
0
0
1
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
1
0
0
0
2
0
0
0
1
0
0
0
1
2
1
0
0
2
3
0
1
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
3
0
1
0
1
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
2
0
0
1
2
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
2
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
1
0
1
0
8
3
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
3
0
0
1
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
1
0
0
1
2
0
0
2
0
0
0
2
4
0
0
0
0
2
0
0
0
0
0
0
2
2
3
0
0
0
1
0
0
2
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
1
2
1
0
0
3
0
0
1
2
0
0
0
1
2
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
1
1
2
1
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
2
0
0
0
1
1
0
0
0
1
0
2
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
1
0
0
1
0
2
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
1
2
0
0
0
0
2
0
2
0
0
1
0
1
0
0
0
1
5
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
4
0
1
1
2
0
2
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
1
0
0
0
3
0
2
2
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
1
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
3
2
2
2
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
1
0
2
0
1
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
2
2
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
1
0
2
0
0
0
0
0
2
2
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
1
1
1
2
1
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
2
1
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
1
2
1
5
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
1
0
2
1
0
0
0
2
0
0
0
1
2
1
0
0
0
0
1
0
0
2
1
0
3
0
0
0
2
0
0
0
1
0
0
3
0
0
0
2
0
0
2
0
1
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
2
0
2
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
3
0
1
2
0
4
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
2
2
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
2
0
2
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
1
3
0
4
0
0
1
2
0
0
3
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
3
1
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
2
0
0
0
0
1
2
0
0
1
0
0
0
0
0
3
0
1
0
2
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
2
1
1
0
1
0
0
1
0
1
0
0
0
0
0
4
0
0
3
2
0
0
0
0
0
0
1
0
2
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
2
1
0
2
0
0
0
0
0
0
1
0
3
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
3
0
1
0
0
3
2
0
0
0
4
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
2
1
0
1
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
5
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
2
0
2
0
2
0
0
2
0
2
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
1
0
0
0
2
0
0
0
2
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
1
1
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
3
0
2
1
2
0
0
0
2
1
0
0
3
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
2
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
1
0
0
0
0
2
2
0
0
0
0
0
3
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
2
2
0
1
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
12
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
3
0
0
0
2
2
0
0
2
0
0
0
1
0
0
0
0
1
1
0
2
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
1
2
0
2
2
2
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
2
2
5
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
1
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
2
3
4
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
6
2
6
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
2
1
0
0
0
2
3
0
0
0
4
1
0
0
0
0
0
0
0
2
0
2
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
6
2
0
0
1
1
3
0
1
0
0
0
2
1
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
2
0
1
0
1
1
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
1
1
0
0
1
2
2
0
0
1
0
0
0
2
0
0
2
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
2
0
2
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
3
1
2
0
0
0
1
1
3
0
0
0
0
2
0
2
1
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
2
2
1
0
1
2
0
0
0
1
0
0
1
1
2
1
0
0
0
2
2
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
5
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
3
2
2
1
0
0
0
0
1
0
2
2
0
0
0
2
0
1
1
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
4
2
1
2
0
1
1
1
0
0
0
1
0
1
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
1
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
2
3
0
0
4
0
0
1
2
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
2
0
1
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
2
0
1
0
0
0
0
0
2
2
0
0
0
0
0
2
2
0
0
0
0
0
2
2
0
2
0
0
0
4
0
1
2
2
1
2
0
2
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
3
0
1
1
1
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
1
0
0
0
1
2
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
1
2
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
2
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7
0
0
1
0
0
0
2
0
1
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
7
0
0
2
3
0
0
0
2
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
1
0
2
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
2
1
0
0
2
0
0
0
0
0
0
0
2
0
0
1
2
0
2
0
0
1
0
0
0
0
0
0
2
0
2
0
1
0
0
2
0
1
0
0
2
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
1
2
1
0
0
3
2
0
0
1
1
0
4
0
0
0
3
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
3
0
2
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
3
0
0
0
0
0
0
3
2
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
2
0
0
0
0
1
0
0
0
3
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
2
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
2
2
0
0
0
0
2
2
2
2
0
0
0
0
0
0
0
0
0
2
2
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
3
2
0
0
0
0
0
0
2
0
0
0
2
1
1
0
0
1
0
0
2
0
0
0
0
1
6
0
0
0
0
0
0
1
0
0
1
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
1
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
2
0
0
0
0
2
0
2
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
3
2
0
0
0
0
2
0
0
2
2
0
0
0
2
2
0
0
0
0
1
0
1
0
0
0
0
0
1
0
2
0
1
5
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
1
2
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
1
0
0
0
0
2
0
0
1
0
0
0
0
1
0
1
0
2
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
1
1
0
0
0
0
0
0
0
0
1
1
1
2
2
0
1
0
0
1
0
0
0
0
0
0
0
3
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
2
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
1
0
2
0
2
0
0
0
0
2
0
0
1
1
10
0
0
0
2
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
3
0
0
1
0
0
0
2
6
0
2
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
1
1
0
1
5
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
2
0
0
0
1
0
0
0
3
0
0
2
0
4
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
3
0
2
0
0
0
0
2
0
1
1
0
0
0
0
1
3
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
18
0
0
0
0
0
1
0
1
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
3
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
2
0
0
0
0
0
1
0
2
2
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
3
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
4
0
0
0
0
3
1
1
0
0
0
0
0
0
3
2
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
1
1
2
0
0
0
0
0
0
2
3
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
2
2
0
0
0
0
3
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
1
2
2
1
0
0
0
0
5
2
1
0
0
0
0
2
1
2
0
0
5
0
0
0
0
1
0
1
0
0
2
1
1
0
0
0
2
0
1
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
3
1
1
0
2
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
1
0
0
1
0
0
0
0
2
0
0
1
0
2
0
0
0
0
1
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
11
0
0
0
0
0
2
6
1
2
0
0
0
1
0
0
1
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
2
0
0
3
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
3
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
2
0
0
0
2
0
0
0
0
4
0
0
0
0
2
0
0
2
1
0
6
0
0
0
0
0
1
3
2
0
1
0
5
0
0
0
0
0
2
0
2
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
7
0
0
0
0
1
0
2
2
0
1
0
1
1
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
2
0
0
0
1
0
0
2
2
2
2
0
0
0
2
0
0
0
0
0
0
0
3
0
1
0
0
0
0
2
0
0
0
0
0
3
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
4
2
0
3
1
2
3
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
2
0
0
0
2
0
0
0
1
2
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
3
0
2
0
0
0
2
0
3
1
0
0
1
1
1
1
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
5
0
0
0
2
0
3
0
2
0
0
0
1
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
2
0
2
0
1
0
0
0
1
0
4
2
0
2
0
0
1
0
0
1
0
2
0
0
0
0
0
0
1
0
3
0
4
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
3
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
2
0
0
0
1
1
2
1
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
4
0
0
2
0
2
1
0
2
1
0
0
0
1
0
2
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
2
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
2
1
0
0
0
0
2
0
0
2
2
0
2
0
0
0
0
0
0
0
0
1
0
0
2
2
0
2
0
0
0
0
3
0
1
0
0
0
0
0
0
0
1
2
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
5
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
3
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
1
2
0
0
1
0
2
0
2
0
0
0
1
3
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
3
0
0
0
0
2
0
0
0
1
0
0
0
1
0
2
1
0
0
0
0
1
1
0
0
2
1
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
2
0
0
2
0
0
0
1
2
0
0
0
0
3
2
0
0
1
0
0
2
1
0
0
0
2
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
2
3
1
0
0
0
0
1
5
0
0
2
2
0
0
0
0
0
1
3
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
3
0
0
2
0
2
2
0
0
0
1
1
2
2
0
0
3
0
0
0
0
1
1
1
0
0
2
3
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
4
1
0
1
2
1
0
0
2
0
1
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
1
1
0
2
0
0
0
0
1
0
0
0
2
1
0
0
2
1
0
0
2
1
0
0
0
0
2
0
0
0
2
3
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
1
4
0
0
2
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
2
0
2
1
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
1
0
0
0
2
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
4
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
2
0
1
0
2
0
0
2
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
3
0
2
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
2
0
1
0
0
0
0
0
1
0
0
2
1
0
0
1
0
2
2
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
1
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
1
7
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
2
1
2
0
1
0
0
0
0
1
0
0
0
2
0
2
0
0
3
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
2
1
2
1
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
2
1
1
2
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
1
2
0
0
0
0
4
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
1
0
2
0
1
2
1
1
1
0
0
0
0
0
0
2
0
1
0
0
0
1
1
1
3
0
0
1
0
2
0
0
0
0
2
0
0
1
0
0
0
1
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
4
0
0
1
0
0
2
1
0
0
4
0
0
0
1
0
1
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
2
0
2
0
0
0
0
0
0
0
2
0
1
2
1
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
5
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
3
0
0
0
0
0
1
5
0
0
0
0
2
0
0
0
1
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
2
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
2
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
2
1
0
0
0
0
0
0
2
1
1
0
0
0
0
2
0
2
0
0
1
0
0
0
1
0
1
0
1
0
0
2
2
0
0
1
0
0
1
1
2
3
0
1
2
0
2
0
0
1
0
2
0
2
0
0
0
0
0
1
2
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
1
2
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
2
1
0
1
0
0
2
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
3
0
2
0
0
0
1
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
4
2
2
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
2
1
0
0
3
0
0
0
0
1
2
1
0
0
0
0
2
0
0
1
0
2
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
1
1
0
0
0
0
0
1
2
0
0
0
1
2
0
1
0
2
1
0
2
0
0
3
0
0
0
0
0
0
0
2
1
1
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
2
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
2
0
0
0
0
0
6
1
0
0
3
0
2
0
0
4
0
0
2
0
0
0
0
0
0
1
1
0
0
0
1
0
3
0
1
0
0
0
0
0
0
3
1
0
1
0
1
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
2
0
1
1
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
2
0
2
1
0
0
0
1
0
0
2
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
4
1
0
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
2
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
1
0
2
1
0
2
0
0
0
0
0
2
0
0
0
3
0
0
0
1
0
2
1
0
1
0
0
0
0
0
0
0
0
3
0
0
2
2
0
0
0
0
0
0
0
0
0
5
0
0
1
2
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
1
1
1
3
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
4
0
2
0
0
0
0
0
0
2
2
0
0
1
0
0
1
0
1
1
0
2
0
0
0
0
1
1
0
1
0
0
0
0
1
0
2
0
0
0
0
0
1
0
1
2
0
0
0
0
1
0
0
0
0
2
2
0
0
0
2
0
0
2
0
0
0
2
0
0
0
1
0
2
0
0
0
1
2
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
1
1
1
0
0
0
0
0
0
1
0
0
2
0
0
3
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
6
0
5
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
2
0
2
0
0
0
2
0
2
0
0
0
2
1
0
2
2
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
2
2
1
2
0
1
1
0
1
2
0
0
0
1
0
0
0
3
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
2
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
3
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
1
0
0
1
2
0
0
0
0
1
0
1
0
0
1
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
2
0
0
0
0
0
0
2
3
0
0
0
0
2
0
0
2
1
1
0
0
2
0
0
1
0
0
0
0
1
2
0
0
1
0
1
0
1
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
1
0
0
2
2
3
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
1
0
0
0
2
4
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
4
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
2
0
0
1
1
0
2
0
0
2
0
0
0
0
2
0
0
0
2
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
3
0
0
1
2
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
0
3
0
0
1
0
1
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
1
3
0
0
0
1
0
0
0
0
1
1
1
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
1
0
0
3
2
1
0
0
0
0
0
0
0
1
0
2
0
2
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
3
0
2
0
2
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
1
0
3
0
0
0
0
1
2
0
0
2
0
0
2
0
0
0
0
0
0
1
0
1
0
0
2
0
0
1
0
2
0
3
0
0
0
0
1
0
0
0
2
1
0
4
1
0
0
3
2
0
0
0
2
2
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
21
0
1
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
3
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
2
2
0
0
0
3
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
1
0
2
0
0
1
1
0
6
0
0
0
2
1
0
0
3
0
2
0
0
0
2
0
0
0
0
0
0
4
2
0
0
0
0
0
0
0
0
2
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
1
1
1
0
1
1
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
3
2
0
0
0
1
1
3
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
9
1
0
1
4
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
1
0
2
0
0
0
2
1
0
0
2
0
1
0
0
2
1
0
0
0
0
0
0
0
1
0
1
0
0
0
2
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
3
2
0
0
0
0
6
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
1
0
0
0
1
0
0
2
0
2
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
3
0
0
0
0
1
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
1
0
0
1
1
1
0
0
0
0
3
0
2
13
0
0
0
0
0
0
0
3
1
2
1
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
1
2
1
0
0
0
0
0
0
1
1
0
2
0
0
0
1
0
0
0
2
0
2
1
1
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
1
0
1
0
1
0
0
0
2
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
5
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
2
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
6
0
0
0
0
1
1
0
0
2
1
1
0
0
0
1
0
1
4
0
0
0
2
0
2
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
6
2
0
0
1
0
0
0
0
2
0
5
2
2
1
0
0
2
0
2
0
1
0
0
0
0
0
0
0
2
0
0
1
0
3
0
0
0
0
1
5
0
0
0
1
0
0
2
0
0
0
0
2
0
0
1
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
2
0
2
2
0
2
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
2
1
0
1
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
2
2
2
0
0
2
0
0
0
0
0
2
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
3
2
0
0
0
0
0
0
1
0
0
2
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
3
1
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
1
0
0
1
2
1
0
0
0
0
0
0
2
2
0
0
0
0
3
0
0
3
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
3
0
0
0
0
0
2
0
0
2
2
0
0
0
0
1
0
3
0
0
1
2
2
0
8
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
1
4
0
0
2
0
0
2
0
2
0
0
0
2
0
0
1
0
0
0
1
0
0
1
1
0
1
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
3
0
0
2
0
0
0
0
4
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
2
1
2
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
4
2
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
2
0
1
0
0
1
1
0
0
0
0
2
0
0
0
1
2
1
1
2
0
0
0
0
2
0
0
1
1
0
1
0
0
0
0
2
0
0
0
3
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
2
3
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
1
2
1
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
5
1
1
0
0
0
0
0
0
0
0
0
5
4
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
2
0
0
3
0
0
0
0
2
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
2
0
2
0
0
0
3
0
2
1
2
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
2
1
0
0
1
3
1
0
0
1
1
0
0
0
1
0
0
3
0
1
0
2
0
1
0
0
0
2
0
2
0
2
0
0
0
0
0
2
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
2
0
0
1
0
7
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
4
3
0
2
0
0
0
2
0
2
0
3
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
1
1
0
2
0
0
2
0
1
0
1
0
1
0
0
2
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
5
0
2
1
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
1
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
2
1
0
0
0
0
0
0
0
0
0
2
2
1
0
0
1
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
1
0
0
0
0
2
0
0
1
2
0
1
0
0
0
0
0
1
0
2
2
1
0
0
0
1
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
1
2
0
0
0
0
0
2
2
1
1
0
0
2
0
1
1
0
2
0
0
1
0
0
0
2
1
0
0
0
0
2
0
0
3
2
0
2
0
0
0
0
0
0
0
0
3
0
1
2
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
2
0
2
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
1
0
0
1
0
1
0
0
1
1
0
1
1
0
1
0
0
0
0
1
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
2
1
0
0
2
1
2
0
0
0
0
0
2
0
2
0
0
0
1
0
1
0
1
1
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
1
0
0
0
2
2
1
0
2
0
3
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
3
2
0
0
1
0
0
2
0
0
0
0
3
0
2
0
1
0
1
0
3
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
2
0
0
1
3
0
2
0
0
0
0
2
1
0
0
0
0
2
0
2
0
0
1
1
0
0
0
1
0
0
1
1
0
0
1
0
1
1
2
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
4
0
1
1
0
0
0
2
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
2
1
0
0
0
0
2
0
2
1
0
1
0
1
0
0
0
0
0
0
5
0
2
2
0
0
2
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
1
0
2
6
2
0
0
2
2
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
1
0
0
3
2
2
0
0
1
0
2
0
3
0
3
3
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
2
0
0
0
0
3
0
2
0
0
0
0
1
0
0
0
2
0
0
0
1
2
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
3
1
0
3
1
0
0
0
2
0
0
0
5
0
1
0
3
3
0
0
1
2
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
1
2
1
0
0
2
0
2
2
0
0
0
0
1
0
0
1
0
0
1
0
2
0
0
0
0
0
1
0
1
5
0
4
0
1
0
0
0
0
0
0
0
0
0
1
0
3
1
1
0
0
0
0
0
0
0
2
0
1
2
0
2
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
2
0
0
1
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
1
0
0
0
2
1
0
2
1
0
0
3
0
2
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
3
0
1
2
1
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
2
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
2
2
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
2
0
0
0
0
1
0
0
2
0
2
0
1
2
0
2
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
1
0
2
2
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
2
0
0
1
3
0
0
3
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
3
0
0
1
0
0
3
0
1
3
0
0
0
1
2
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
1
1
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
2
0
0
2
2
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
2
5
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
2
0
0
2
0
0
0
0
0
0
1
0
1
0
2
1
2
0
0
5
0
2
0
2
0
0
0
0
1
2
0
0
0
1
0
0
0
3
0
2
0
0
0
3
1
0
1
0
0
0
1
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
2
2
0
0
0
0
0
0
1
0
2
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
7
1
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
2
0
1
2
0
0
1
1
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
2
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
2
2
1
2
0
2
1
0
2
0
7
0
0
0
0
1
0
0
0
0
0
1
1
0
2
2
2
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
2
0
2
0
0
0
0
4
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
1
1
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
1
0
1
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
4
0
0
0
0
3
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
2
0
0
0
2
0
0
0
3
0
0
0
0
0
3
0
0
0
2
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
5
0
1
1
0
0
0
0
0
0
2
0
0
0
1
0
0
3
0
0
2
0
0
0
1
1
1
0
1
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
2
2
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
1
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
7
0
0
0
1
4
2
0
0
0
3
0
0
6
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
1
1
0
3
0
0
0
1
0
1
0
0
1
0
0
0
1
2
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
11
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
4
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
2
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
7
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
2
0
2
0
0
2
1
0
0
2
0
1
0
0
0
0
1
2
0
2
0
0
1
0
0
0
0
0
0
1
0
2
0
2
0
4
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
1
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
1
2
0
2
0
0
0
0
1
0
2
0
0
1
0
0
0
0
1
1
0
0
0
2
1
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
1
0
2
0
0
0
2
0
0
0
0
0
1
2
0
0
0
2
1
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
1
1
1
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
5
1
0
3
0
0
0
0
5
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
2
0
4
0
1
1
0
0
0
0
2
0
0
2
1
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
1
3
0
0
0
0
0
1
0
0
2
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
2
2
0
0
1
0
0
2
3
0
0
0
0
1
0
0
2
0
0
0
3
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
1
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
1
3
0
0
2
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
3
0
0
3
0
3
0
7
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
2
2
0
0
0
0
1
0
1
0
5
0
0
0
0
1
3
0
0
2
0
0
0
0
1
0
1
0
1
0
1
0
3
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
3
0
2
0
0
1
0
0
1
0
0
0
0
0
1
0
3
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
3
1
0
0
0
2
0
0
0
1
2
0
1
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
1
0
2
0
0
0
0
2
1
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
3
0
0
1
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
1
0
0
0
3
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
2
0
1
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
5
1
2
0
0
1
0
0
0
0
0
0
0
2
0
0
3
0
2
0
0
0
0
2
0
0
0
0
0
3
3
1
0
1
0
3
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
2
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
3
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
1
0
0
0
2
1
1
0
0
0
3
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
2
0
0
0
1
2
2
1
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
2
1
1
0
0
0
0
2
0
0
0
5
0
1
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
2
2
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
1
2
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
3
0
0
1
0
0
2
1
3
2
0
1
0
0
0
0
3
0
0
0
0
1
2
0
0
0
0
2
1
0
0
0
1
0
0
2
0
0
2
1
0
0
0
0
0
0
2
0
0
3
0
0
0
0
2
2
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
2
3
0
1
0
0
0
1
2
0
2
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
1
1
0
0
2
0
0
1
1
1
0
1
1
7
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
1
0
0
1
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
4
0
1
0
0
0
0
0
0
0
0
0
9
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
3
2
1
0
0
0
0
1
0
0
1
2
0
0
0
0
1
0
0
2
1
0
0
0
1
0
2
0
2
2
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
2
0
2
0
2
1
0
0
2
0
0
0
0
0
0
0
1
1
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
1
0
1
0
1
2
0
0
0
0
2
0
0
0
9
0
1
0
0
0
8
0
2
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
3
1
0
0
0
0
0
0
6
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
1
0
0
0
0
2
1
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
2
1
1
0
0
0
1
0
2
0
0
1
0
0
0
1
4
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
2
2
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
4
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
3
0
3
0
1
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
1
2
0
2
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
1
0
0
0
3
0
0
0
0
1
3
0
0
2
0
0
0
0
1
1
0
2
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
1
2
0
0
0
0
1
0
1
0
0
0
0
0
1
5
0
0
2
0
1
0
2
0
2
0
0
0
0
0
0
0
2
0
1
1
1
0
0
0
0
0
0
1
0
2
0
0
0
1
1
0
0
0
0
2
2
0
0
0
0
0
2
0
2
0
0
2
0
2
0
0
2
2
1
0
0
0
0
0
3
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
5
0
0
0
0
0
2
0
0
2
1
0
1
1
0
2
0
1
0
1
0
0
0
0
2
0
0
0
1
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
4
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
1
0
1
1
0
1
0
0
2
2
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
3
0
0
1
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
2
2
0
3
0
0
2
0
0
1
0
0
0
1
0
0
1
2
2
2
0
0
1
0
2
1
0
1
0
0
2
2
0
2
0
0
0
0
0
1
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
1
2
0
1
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
3
3
1
3
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
3
0
0
2
0
0
0
0
0
0
1
0
1
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
6
2
0
0
0
0
1
0
5
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
4
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
3
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
4
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
1
2
3
0
0
0
1
2
0
0
0
1
0
0
2
3
2
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
1
0
0
0
4
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
2
0
0
0
1
2
0
0
0
2
0
0
6
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
1
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
3
0
0
1
3
2
1
1
0
0
0
0
0
0
0
1
1
3
0
2
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
2
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
1
2
1
0
0
0
2
0
1
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
2
0
0
0
0
1
1
2
0
0
1
0
0
2
0
1
0
0
0
1
0
0
3
4
0
0
0
0
0
0
2
1
0
0
0
0
2
1
1
0
1
2
0
0
0
0
1
0
0
0
0
2
1
3
0
0
0
1
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
2
1
0
1
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
2
2
2
2
1
0
2
4
0
0
0
0
0
0
0
2
1
0
2
0
2
0
2
0
1
0
2
2
1
0
0
1
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
4
0
0
2
0
0
3
1
0
1
2
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
4
0
0
1
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
5
0
0
0
0
0
0
0
2
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
7
0
3
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
1
0
8
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
3
0
2
0
0
2
2
0
1
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
2
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
2
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
1
1
0
2
0
0
0
0
1
1
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
1
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
1
0
0
0
1
2
0
1
0
1
0
0
1
0
0
0
1
0
0
3
0
2
2
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
2
2
0
0
0
2
1
2
0
0
0
0
0
2
1
0
0
1
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
2
0
0
0
2
0
2
0
0
0
0
0
1
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
1
0
0
0
1
0
0
2
3
0
0
0
2
0
0
0
0
0
0
2
2
0
1
0
0
0
1
2
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
10
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
5
0
0
3
0
0
0
2
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
2
0
4
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
10
2
0
0
1
0
0
2
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
2
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
1
1
2
0
0
0
0
3
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
1
2
0
0
1
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
3
0
0
0
2
0
0
2
0
0
0
0
0
1
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
2
1
2
1
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
2
0
0
0
3
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
3
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
5
2
3
1
0
0
0
0
1
0
1
2
0
1
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
2
0
1
1
0
2
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
1
3
0
0
0
1
2
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
2
0
2
1
1
0
0
0
0
3
0
0
1
1
0
0
0
2
0
1
0
1
0
0
1
0
0
4
0
1
0
0
0
2
2
0
0
2
0
2
0
0
0
0
0
0
0
2
2
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
2
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
6
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
4
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
6
0
0
2
0
0
1
0
0
0
0
0
1
0
2
0
1
0
1
0
2
0
0
0
1
0
1
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
2
0
0
0
1
2
0
0
0
0
0
0
0
1
1
0
2
0
0
2
0
2
0
0
1
0
2
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
1
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
2
0
1
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
3
0
3
1
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
6
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
1
0
0
1
1
0
0
2
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
1
0
0
0
0
1
0
2
2
0
2
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
2
0
0
0
0
1
0
1
0
0
5
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
1
3
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
3
0
0
0
0
0
2
2
0
1
0
0
0
1
0
0
0
3
1
0
2
0
4
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
1
0
2
0
2
0
1
2
2
0
0
0
1
2
0
0
0
1
2
0
0
0
2
1
2
3
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
3
2
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
2
2
7
0
0
0
0
0
1
0
0
1
0
0
0
0
7
0
2
0
1
0
0
0
2
2
0
0
0
0
0
1
1
2
0
0
1
0
3
1
3
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
3
7
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
2
1
1
0
1
0
2
1
2
2
0
0
0
0
0
1
0
0
2
1
2
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
1
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
2
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
2
0
2
0
0
0
1
3
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
6
0
0
2
0
0
2
0
1
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
1
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
1
2
0
1
0
0
0
2
0
1
0
0
0
0
0
1
0
4
0
0
0
0
1
0
0
0
2
2
3
2
1
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
2
0
1
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
1
0
1
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
1
2
0
0
0
0
2
2
2
3
0
0
0
0
0
0
0
0
1
0
3
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
1
2
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
2
2
0
2
0
0
3
0
0
0
0
0
3
0
0
0
0
2
1
0
0
0
0
1
0
0
0
1
1
3
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
2
2
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
1
3
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
2
2
0
3
1
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
1
0
0
1
0
0
6
1
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
4
3
0
3
0
0
3
5
0
0
2
0
0
1
0
2
0
0
2
2
0
0
0
0
0
0
0
0
1
2
0
2
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
2
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
2
0
0
0
2
0
1
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
3
0
0
0
0
2
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
3
0
0
0
2
2
2
0
0
0
0
1
1
2
0
2
0
0
1
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
5
0
0
0
0
9
0
2
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
1
0
2
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
1
0
0
0
1
3
0
0
0
0
0
2
1
1
1
0
1
0
0
0
1
1
1
0
1
0
1
0
0
0
0
1
0
0
6
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
3
0
0
2
0
3
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
1
0
0
0
0
1
0
0
0
2
0
0
2
0
0
2
0
2
1
0
2
1
0
1
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
1
0
0
0
0
4
0
2
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
2
0
2
1
2
0
0
0
0
1
0
0
0
2
0
2
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
1
0
1
0
1
1
0
0
1
0
0
0
0
0
4
0
0
0
1
0
0
4
0
1
0
1
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
2
0
2
2
1
1
0
0
0
1
3
2
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
1
2
0
0
0
0
1
0
3
1
0
2
1
0
2
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
3
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
2
0
0
0
0
1
2
2
0
0
0
1
0
0
0
1
0
0
0
2
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
2
3
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
2
1
1
0
0
0
1
0
0
0
2
0
0
0
0
1
0
2
0
2
0
0
0
1
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
2
0
0
0
0
2
0
1
2
2
0
0
0
0
0
0
0
1
0
0
0
1
1
1
1
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
1
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
6
4
1
0
0
0
0
0
1
0
2
0
0
0
2
0
1
1
0
2
0
1
2
1
2
0
0
0
1
0
0
1
2
1
0
0
0
2
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
1
0
2
4
0
0
0
2
1
0
0
0
1
0
0
0
0
2
2
0
1
0
0
1
0
0
0
0
1
0
0
2
1
2
0
2
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
1
0
1
1
0
0
0
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
1
0
0
2
0
0
1
0
1
2
0
2
0
0
0
0
0
0
0
2
1
1
2
0
0
0
1
0
1
0
0
1
1
1
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
10
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
3
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
1
0
0
5
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
1
0
0
2
0
4
0
0
2
0
0
1
1
0
0
0
0
1
1
0
0
0
5
0
0
0
3
0
1
0
0
0
0
0
2
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
3
0
0
2
2
6
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
1
4
0
0
1
1
0
0
0
0
0
0
2
0
0
2
0
0
2
0
1
1
0
0
0
0
0
1
0
0
2
1
3
0
0
1
0
4
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
1
2
1
1
0
0
0
0
0
6
0
0
0
1
1
0
2
0
0
1
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
2
2
0
0
1
0
0
0
1
0
0
0
1
1
0
0
3
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
1
0
1
1
0
2
0
0
0
2
2
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
2
1
12
0
0
2
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
2
1
0
0
0
0
2
0
2
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
3
2
0
1
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
2
0
6
3
0
0
1
3
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
1
4
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
1
0
0
0
1
0
2
0
2
1
2
0
0
0
0
0
0
9
1
0
0
0
0
1
0
0
0
2
2
0
1
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
6
0
0
0
0
2
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
2
0
0
0
0
2
0
1
0
0
0
2
1
1
1
0
0
0
2
0
2
3
1
0
0
2
1
1
0
0
0
0
1
0
3
0
0
0
0
0
2
1
0
0
2
0
0
0
2
1
2
1
0
2
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
1
0
0
0
0
2
0
2
0
2
2
1
0
0
2
1
0
0
0
2
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
1
0
0
3
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
1
2
0
0
3
1
1
0
0
2
0
3
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
2
0
0
3
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
1
1
0
2
1
0
0
1
0
0
0
0
1
1
2
0
0
0
4
2
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
1
0
2
1
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
1
2
1
0
0
1
1
0
1
0
0
0
0
0
2
1
2
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
1
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
1
3
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
3
0
0
1
1
0
0
0
0
0
2
0
0
2
0
0
0
1
0
2
0
0
2
0
0
0
0
0
5
0
0
4
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
1
2
0
0
2
0
3
2
0
0
3
0
0
0
1
0
0
2
0
2
1
0
0
0
2
0
0
2
0
2
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
1
2
0
3
0
0
0
2
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
2
1
0
1
0
0
0
0
0
2
4
0
0
0
1
0
0
0
0
0
0
0
1
0
2
3
0
2
0
0
0
1
0
0
0
0
0
0
0
1
3
0
0
0
0
2
0
1
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
2
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
2
1
0
0
1
0
0
1
0
4
3
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
2
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
3
1
0
0
0
0
3
0
0
0
0
7
0
2
0
0
0
0
8
0
1
0
2
0
0
3
0
0
2
0
1
0
0
0
0
1
0
1
2
2
0
0
2
0
0
0
0
0
0
2
0
1
0
1
0
0
1
0
0
0
2
0
0
1
0
1
1
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
2
0
2
1
2
0
0
0
0
2
0
0
0
0
0
2
1
1
2
1
0
1
0
0
1
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
2
1
0
0
0
2
0
1
0
0
0
0
0
2
0
1
1
2
0
0
0
0
0
1
0
1
0
0
0
1
3
0
2
0
0
0
3
2
0
2
2
0
0
1
1
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
2
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
3
0
4
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
2
1
0
0
1
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
1
0
0
0
0
0
0
2
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
11
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
5
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
3
0
1
3
2
1
0
0
2
0
2
0
0
1
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
3
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
2
0
0
1
0
1
0
2
1
0
0
0
1
1
0
0
0
0
1
0
0
1
2
1
0
2
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
2
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
2
0
1
1
0
2
3
0
2
2
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
1
2
0
3
0
0
0
2
0
0
2
0
0
0
0
0
1
1
2
0
0
0
0
4
0
0
0
1
0
0
0
3
2
1
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
2
0
1
1
0
0
0
3
0
0
0
0
0
0
0
4
5
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
2
2
0
0
0
4
0
3
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
2
0
0
0
0
0
2
0
0
1
0
1
1
1
0
0
0
1
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
1
1
5
0
0
0
2
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
2
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
4
0
0
1
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
4
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
1
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
4
0
1
0
0
0
1
0
0
2
1
1
0
2
0
1
0
0
0
2
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
2
0
2
2
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
1
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
3
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
3
1
0
1
0
0
6
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
3
0
3
0
3
0
0
0
2
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
1
1
2
0
1
1
0
2
0
1
0
3
0
1
0
3
0
2
0
2
1
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
1
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
1
2
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
1
1
0
0
0
0
0
0
1
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
1
2
0
0
1
0
1
1
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
3
0
1
0
0
0
0
0
5
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
4
0
0
0
0
0
1
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
1
2
0
0
3
0
0
0
0
0
0
0
2
1
2
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
5
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
2
2
0
0
3
0
0
0
0
0
0
0
2
0
3
0
0
0
2
1
1
1
0
0
0
1
3
0
0
0
0
0
0
0
0
1
0
2
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
4
0
1
0
0
0
1
0
1
3
0
0
0
4
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
4
2
0
0
3
0
1
0
0
0
0
2
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
4
0
0
2
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
2
1
0
2
2
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
2
1
0
0
0
0
0
2
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
2
0
0
2
0
0
1
1
2
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
2
3
0
0
0
4
0
0
0
0
0
0
5
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
1
2
1
0
0
0
0
1
2
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
1
1
4
1
0
0
0
0
1
2
0
0
0
2
1
0
0
0
0
1
3
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
2
2
0
0
0
0
0
2
0
3
0
2
0
0
1
1
0
0
0
2
0
0
0
0
0
0
1
2
2
0
0
0
0
1
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
6
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
1
0
0
0
0
0
2
1
0
2
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
1
1
1
0
0
0
0
0
3
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
11
1
0
0
2
2
0
0
2
1
0
0
2
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
1
3
0
0
0
0
0
0
2
0
2
2
0
0
2
0
0
1
0
1
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
2
1
1
0
1
1
0
0
0
0
0
0
0
2
0
0
4
0
0
1
0
2
1
0
1
0
0
0
1
0
2
0
0
1
2
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
2
1
0
0
0
0
0
0
0
2
0
0
0
1
3
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
1
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
4
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
2
0
0
2
2
1
2
0
0
1
5
0
1
1
0
0
2
0
0
0
1
0
2
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
2
3
0
2
4
0
0
0
0
2
0
0
4
2
0
0
4
0
2
0
1
0
0
0
0
0
0
0
2
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
2
0
0
1
0
1
3
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
3
0
0
2
1
2
0
0
0
0
1
0
2
0
0
2
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
3
0
2
0
0
0
0
0
3
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
3
0
0
2
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
1
0
2
1
0
0
0
3
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
3
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
6
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
2
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
1
3
0
0
0
1
1
1
0
3
2
0
0
3
0
2
0
2
1
0
1
0
1
0
0
1
8
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
2
0
0
0
3
0
2
0
0
1
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
1
2
0
0
4
0
0
1
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
2
0
2
0
1
0
1
0
0
2
0
0
0
0
0
0
2
0
2
0
0
1
0
0
2
0
1
2
0
0
0
0
0
2
5
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
2
2
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
2
0
2
0
1
0
2
0
1
0
1
1
0
0
1
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
1
2
2
0
0
0
0
0
1
1
0
11
0
1
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
1
0
0
2
2
0
0
2
0
2
3
1
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
2
0
0
0
1
1
2
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
1
0
1
0
2
0
1
0
0
0
1
0
0
0
0
2
0
1
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
1
0
2
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
1
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
1
0
2
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
5
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
2
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
2
1
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
1
0
1
0
0
3
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
2
0
1
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
2
1
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
1
2
1
2
0
2
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
2
0
0
0
0
0
0
4
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
3
1
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
1
1
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
2
3
0
2
2
0
0
0
0
0
4
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
2
0
0
4
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
1
1
0
0
0
0
2
0
2
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
2
1
0
0
0
0
0
2
3
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
2
2
0
2
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
3
0
0
0
2
0
1
0
2
0
0
0
4
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
6
1
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
2
0
0
0
0
2
0
0
2
0
2
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
1
1
0
0
2
0
0
0
2
2
1
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
3
4
1
0
0
0
0
0
0
0
1
0
1
4
0
0
0
0
0
0
0
0
1
1
2
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
2
3
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
3
1
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
2
0
0
2
0
1
0
0
0
1
0
4
0
0
0
0
2
0
0
0
0
0
1
1
0
0
1
0
0
1
2
0
0
0
0
2
0
0
1
0
0
2
1
0
0
1
1
0
1
0
2
4
2
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
1
0
0
2
0
1
0
3
0
0
1
0
0
0
0
0
0
3
0
3
2
1
2
0
0
1
1
1
2
1
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
3
3
0
2
0
1
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
1
2
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
3
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
1
0
0
0
1
5
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
3
2
1
0
3
1
0
0
0
0
0
0
0
1
0
0
2
0
0
1
1
0
2
0
0
2
0
1
0
2
2
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
1
0
1
3
2
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
1
0
0
0
0
0
2
1
0
1
0
0
2
0
0
0
0
2
0
0
2
0
0
0
3
1
1
2
1
0
1
0
1
0
1
0
1
0
0
3
1
2
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
3
0
2
0
2
0
0
0
0
2
2
0
0
0
0
3
0
0
0
1
2
0
0
0
0
0
1
0
0
1
0
0
0
2
4
0
2
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
1
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
2
7
0
0
0
2
1
0
1
0
0
0
0
1
1
2
0
0
0
0
0
1
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
1
2
0
0
0
1
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
5
0
0
2
0
0
0
0
1
0
0
1
0
2
2
0
0
2
0
0
1
0
0
0
0
1
0
2
0
1
0
0
0
1
0
2
0
0
0
0
0
0
1
3
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
3
0
4
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
4
2
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
1
0
1
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
3
2
0
0
1
0
0
2
1
3
2
0
2
2
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
1
0
1
0
1
0
0
3
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
10
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
1
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
3
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
3
1
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
4
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
1
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
2
0
2
2
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
1
0
0
2
0
2
0
1
2
0
0
0
0
2
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
2
1
1
0
0
0
0
0
0
0
2
0
2
0
1
0
0
1
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
5
1
0
0
2
1
0
0
0
1
0
3
0
0
0
0
0
1
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
1
0
2
0
2
0
8
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
3
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
2
2
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
2
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
3
1
1
1
0
1
1
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
2
2
0
0
0
2
1
2
0
0
0
0
6
0
0
0
0
0
1
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
2
0
0
0
0
0
1
0
0
4
0
0
0
2
0
0
0
1
0
0
1
0
1
0
1
0
0
0
1
1
0
1
1
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
2
1
2
0
1
10
0
0
1
0
0
0
1
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
4
0
0
0
0
1
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
1
0
0
2
0
0
0
0
2
1
2
0
0
2
0
0
0
2
0
1
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
3
0
0
1
0
0
0
1
0
0
0
4
0
2
0
2
0
0
0
0
4
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
1
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
12
0
1
0
0
0
1
0
0
2
0
0
0
0
0
3
0
0
0
0
2
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
1
0
0
1
1
0
2
1
0
0
2
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
1
0
0
0
1
0
0
3
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
1
0
0
3
0
0
4
0
0
1
2
0
0
0
0
1
0
0
0
1
0
1
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
1
1
0
0
1
1
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
2
0
0
0
2
0
1
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
3
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
1
0
1
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
2
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
1
2
1
0
4
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
2
0
0
1
0
1
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
6
0
2
0
1
0
0
1
0
0
0
1
0
1
1
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
1
0
0
0
2
0
0
0
0
0
1
1
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
3
0
0
1
0
0
2
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
1
0
0
0
1
2
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
2
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
1
0
0
3
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
1
0
2
1
0
0
0
0
0
3
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
2
0
2
2
0
0
1
2
2
0
0
0
0
1
0
0
0
0
0
2
0
1
0
1
1
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
1
0
0
0
0
2
3
0
0
0
0
0
1
0
1
0
0
0
0
2
0
2
0
0
0
2
2
0
3
1
1
0
0
4
0
0
2
0
2
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
1
1
0
0
2
0
0
3
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
1
0
3
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
6
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
2
0
0
0
0
0
2
3
0
2
0
0
0
0
4
0
1
0
0
0
0
0
2
0
0
1
0
2
0
2
2
2
0
1
0
1
0
0
0
0
0
2
0
0
0
2
0
0
2
0
1
0
1
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
4
0
0
3
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
2
1
0
2
0
1
0
0
0
2
0
0
0
0
1
2
0
0
1
0
0
0
0
1
2
0
0
0
0
1
0
0
2
1
1
0
0
0
0
1
0
0
2
0
0
0
2
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
3
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
3
0
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
2
0
0
0
0
0
0
4
1
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
2
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
1
0
0
1
0
0
0
0
1
2
0
0
1
4
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
2
0
2
2
0
0
3
0
0
0
0
0
0
2
0
2
1
0
0
0
3
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
2
0
2
0
0
1
0
2
0
0
0
0
3
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
2
0
2
0
0
3
0
1
0
1
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
4
0
2
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
2
0
1
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
1
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
3
0
0
2
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
3
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
1
2
0
0
1
0
2
0
0
2
0
0
2
0
0
0
1
0
0
0
0
2
0
2
2
0
0
0
1
0
5
0
1
0
2
0
0
1
0
2
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
1
1
1
0
0
2
1
1
0
0
0
1
0
2
0
0
0
0
0
0
3
0
3
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
1
4
0
0
0
1
3
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
1
0
1
0
0
0
2
1
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
1
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
11
1
0
0
0
0
0
1
0
2
1
0
0
0
0
0
1
0
1
0
1
0
1
2
0
1
1
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
2
0
1
3
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
3
0
0
0
0
0
1
0
0
0
0
1
2
0
0
1
2
0
0
2
0
0
0
0
1
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
3
1
1
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
3
2
5
0
0
0
1
0
0
2
0
0
0
0
1
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
2
1
0
2
0
0
2
1
3
2
0
0
0
0
1
0
0
1
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
2
1
1
1
0
0
0
2
0
0
1
5
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
1
0
0
0
1
1
3
2
0
2
0
0
0
5
1
2
0
2
1
1
0
2
0
0
0
1
0
3
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
2
1
1
2
0
0
1
1
0
0
0
0
0
2
1
0
0
1
2
2
2
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
1
2
0
0
2
0
1
1
0
0
2
0
0
1
0
0
0
0
2
3
0
0
0
1
0
2
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
1
1
0
0
0
1
0
1
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
2
1
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
2
0
0
1
1
1
0
0
2
0
1
2
0
0
0
0
2
3
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
3
1
0
0
2
0
0
0
0
0
6
1
0
1
0
0
1
1
2
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
5
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
2
0
1
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
2
0
1
2
0
0
2
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
1
0
0
0
1
1
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
2
2
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
8
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
3
2
0
2
0
3
0
0
1
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
2
0
0
0
0
1
0
0
2
0
0
2
2
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
4
1
2
0
0
0
0
0
1
1
1
0
1
2
1
0
0
0
0
0
0
0
0
0
3
0
1
2
0
1
2
2
0
1
1
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
1
0
2
0
0
1
0
1
0
0
2
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
3
0
0
0
0
0
0
0
2
1
0
0
2
0
0
1
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
3
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
1
4
2
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
8
2
1
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
2
0
0
0
0
0
0
3
1
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
2
1
1
0
3
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
1
1
0
0
0
0
0
0
0
0
2
0
0
4
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
1
0
0
2
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
2
1
1
0
3
0
3
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
3
0
0
2
0
0
1
0
0
0
0
0
2
0
1
0
0
0
2
0
1
1
0
2
2
0
0
1
0
0
0
0
0
1
0
0
2
2
3
1
1
0
0
0
0
0
1
2
0
0
0
0
0
2
2
0
0
3
0
0
0
0
1
0
1
2
0
1
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
2
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
2
0
2
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
2
2
2
0
0
0
2
2
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
2
2
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
3
3
0
0
0
0
0
0
1
1
0
0
0
0
0
4
0
0
0
1
0
0
0
2
0
1
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
3
2
0
0
1
0
0
0
0
0
0
1
0
0
0
1
4
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
1
3
0
0
0
3
3
1
0
0
0
1
0
0
0
0
1
0
0
0
0
5
0
0
0
0
0
1
0
4
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
3
0
0
2
1
0
0
2
0
3
0
0
0
1
0
0
1
0
2
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
2
0
0
0
1
0
1
1
0
0
1
0
0
0
8
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
3
1
0
0
0
2
0
0
0
0
0
2
1
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
4
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
1
0
0
0
1
0
0
0
0
1
2
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
2
1
0
2
2
1
0
0
0
0
6
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
3
0
0
0
2
0
0
0
0
1
1
3
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
1
0
2
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
5
0
4
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
1
2
1
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
1
2
0
0
0
2
2
0
0
0
0
0
2
1
0
0
2
0
0
0
0
2
0
0
2
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
3
0
1
0
0
0
5
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
2
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
1
0
0
1
0
2
0
0
2
0
1
1
0
0
3
2
0
0
0
0
1
2
2
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
3
0
0
2
0
0
2
2
0
0
0
0
1
0
0
3
1
0
0
0
0
0
0
0
0
1
2
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
2
0
0
0
2
2
1
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
1
2
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
3
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
2
1
1
2
1
0
0
0
0
0
2
2
0
1
0
2
0
1
0
0
2
0
7
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
8
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
1
0
2
0
1
0
0
0
1
4
0
0
2
0
0
0
0
0
0
0
1
2
1
0
0
0
1
0
0
2
0
0
0
0
0
3
0
0
0
1
2
0
2
0
0
0
2
0
0
0
0
1
0
1
0
0
0
3
0
0
1
1
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
3
0
0
0
1
0
2
2
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
1
2
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
2
4
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
2
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
2
0
0
0
0
0
0
0
1
0
2
1
0
0
0
1
0
0
1
0
2
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
2
0
0
0
1
0
0
1
0
0
3
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
2
2
1
1
0
1
0
0
0
0
0
2
2
2
0
0
1
1
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
9
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
2
1
0
1
0
0
1
1
0
1
0
0
0
1
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
2
0
0
6
2
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
2
2
0
0
1
3
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
2
0
1
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
3
0
0
0
0
0
1
0
1
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
7
1
0
0
0
0
1
0
0
0
4
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
2
0
0
0
3
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
3
2
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
2
0
2
0
0
0
0
2
0
1
0
0
1
0
0
0
2
0
0
1
0
0
1
0
2
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
3
0
1
2
0
2
1
0
0
2
0
0
1
0
0
1
0
0
2
2
0
1
1
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
2
3
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
1
0
0
0
0
2
1
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
6
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
2
1
0
2
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
2
1
0
0
2
0
0
0
0
0
1
0
0
2
0
2
6
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
4
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
2
2
0
0
0
0
1
2
1
0
0
2
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
2
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
1
2
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
3
1
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
2
2
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
5
0
0
0
0
2
2
0
0
0
0
1
2
0
0
0
0
0
0
2
2
0
0
1
0
2
0
0
3
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
2
0
0
0
1
1
3
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
2
0
0
1
7
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
1
0
0
0
0
0
0
8
0
0
1
0
0
0
4
0
2
0
0
1
0
0
3
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
3
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
1
2
0
0
2
0
0
0
3
0
0
2
2
0
0
0
0
4
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
2
0
1
2
1
0
0
2
0
1
2
0
0
1
2
1
0
0
6
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
1
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
4
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
1
1
0
3
0
0
2
0
2
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
8
2
0
0
2
2
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
3
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
4
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
1
2
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
1
0
0
2
0
1
2
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
2
2
2
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
4
0
2
2
0
1
0
0
0
0
0
0
2
0
0
0
0
4
1
1
1
0
4
0
0
0
0
0
0
0
1
2
0
2
0
1
0
0
0
2
1
0
5
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
3
3
2
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
5
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
2
0
1
1
1
0
1
0
0
0
2
2
0
0
1
3
2
0
0
2
1
1
0
0
2
2
0
0
0
0
0
0
0
1
0
2
0
2
1
1
3
0
1
1
2
1
2
2
1
0
0
0
2
2
0
0
2
0
1
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
2
1
0
2
0
0
1
0
0
0
3
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
2
0
1
0
0
0
0
1
4
0
0
0
0
1
2
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
8
0
0
2
3
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
1
0
1
0
0
0
2
1
0
0
0
2
0
0
2
0
2
0
0
0
1
0
2
2
0
1
2
2
1
0
0
12
1
0
0
0
0
0
0
0
1
0
0
0
0
1
7
0
0
2
0
0
1
0
0
0
1
0
0
3
0
0
0
2
0
0
0
1
0
0
0
0
1
0
2
0
0
2
3
0
1
1
0
0
1
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
4
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
1
0
2
0
2
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
2
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
1
0
4
3
1
0
0
1
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
2
1
0
2
0
0
2
0
1
0
0
0
0
0
1
2
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
1
0
2
4
0
1
0
0
1
0
0
2
1
0
0
0
1
0
1
0
0
0
0
0
0
3
0
2
2
0
0
0
0
2
0
0
1
0
0
5
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
2
0
1
0
0
0
2
3
2
1
0
2
0
0
0
0
11
0
0
0
0
0
2
0
0
0
0
1
0
0
1
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
1
2
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
2
0
0
0
4
0
1
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
3
0
0
0
0
0
1
0
0
0
0
2
0
7
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
1
0
1
0
1
0
0
1
0
0
4
5
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
2
0
0
4
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
6
2
0
0
0
0
6
0
2
0
0
2
0
1
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
1
3
0
1
0
0
0
2
3
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
8
1
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
2
0
1
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
2
0
0
3
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
1
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
2
1
0
0
3
0
0
0
1
0
0
0
0
0
0
0
3
0
2
0
0
1
0
1
1
0
0
0
0
2
0
0
0
0
2
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
4
0
1
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
1
0
0
0
5
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
1
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
1
0
0
4
0
1
0
0
2
2
1
0
0
0
0
0
1
2
0
2
0
0
1
0
1
0
0
0
0
2
0
0
0
1
2
2
1
0
1
0
1
0
0
0
0
0
1
0
2
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
17
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
1
0
2
1
0
4
0
0
0
0
0
1
3
3
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
3
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
3
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
1
1
0
1
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
1
0
1
2
0
3
1
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
1
0
0
2
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
2
0
0
1
0
0
2
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
2
1
0
0
0
0
1
1
0
0
1
3
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
2
0
1
0
0
0
0
0
1
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
2
0
0
1
0
1
0
0
0
0
0
0
1
0
0
2
1
1
0
0
0
0
3
0
0
0
0
1
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
3
0
0
0
0
3
0
0
1
0
2
0
0
0
1
0
0
0
0
2
0
2
1
1
2
0
1
0
0
2
0
0
0
0
0
2
0
2
0
0
3
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
1
0
0
2
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
2
2
0
0
0
0
0
2
0
3
0
0
0
2
2
0
0
0
2
1
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
2
1
1
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
1
0
0
1
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
2
1
0
0
1
1
0
0
0
0
0
2
2
0
1
0
2
0
4
1
0
0
0
0
2
0
2
0
2
3
0
0
2
0
2
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
3
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
2
2
0
0
1
0
0
0
0
0
4
0
2
0
0
0
2
2
0
2
0
2
0
0
0
0
0
2
1
0
2
0
0
1
0
0
0
2
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
3
0
1
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
2
0
1
2
2
0
0
2
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
1
2
0
2
2
0
0
1
1
1
2
2
0
0
1
3
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
3
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
3
0
0
1
0
0
0
0
1
2
0
0
0
1
1
2
0
0
0
0
0
1
0
2
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
2
1
0
2
0
2
0
0
2
0
0
2
0
4
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
3
0
2
3
2
2
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
3
0
0
0
0
0
3
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
1
1
1
0
0
5
0
0
2
1
0
0
1
0
0
0
2
0
0
2
0
0
1
0
1
1
0
0
0
0
1
0
1
2
0
0
0
0
4
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
2
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
2
1
2
0
0
0
0
2
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
3
2
0
0
0
2
1
1
1
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
1
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
1
0
2
0
0
0
0
2
0
0
0
0
0
1
2
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
1
0
0
0
3
1
2
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
2
0
3
0
0
0
0
0
2
0
0
0
0
0
0
1
2
2
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
3
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
1
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
2
0
2
0
1
0
1
0
0
0
0
2
0
0
1
0
10
0
0
0
2
1
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
4
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
1
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
1
0
0
0
0
0
0
0
0
2
3
0
0
3
0
1
0
0
1
0
0
3
0
0
0
0
0
0
0
2
3
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
1
0
0
0
0
0
3
0
0
0
0
1
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
4
0
0
0
1
0
0
1
0
1
0
0
0
2
1
4
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
3
0
0
1
0
1
0
2
0
0
2
0
0
0
1
1
1
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
1
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
1
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
5
0
0
2
0
6
0
0
0
2
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
2
5
0
0
0
4
3
0
0
0
0
1
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
2
0
1
0
0
2
2
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
5
0
3
1
0
1
0
1
0
0
0
0
1
0
0
0
0
2
2
2
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
1
2
3
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
2
1
0
0
0
1
0
0
2
0
2
2
0
3
0
0
0
1
0
0
0
0
0
1
0
0
2
2
0
0
1
2
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
1
2
2
0
0
1
0
0
0
0
0
2
0
0
3
0
1
0
1
0
5
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
1
2
0
2
0
3
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
1
0
0
0
0
0
1
0
2
0
2
0
0
0
0
2
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
2
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
3
1
0
0
0
1
2
0
0
1
3
0
0
4
0
1
0
0
0
0
0
2
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
2
1
0
2
0
3
0
0
0
0
0
11
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
3
0
2
0
0
0
1
0
1
3
0
1
0
0
0
0
0
4
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
2
1
0
1
0
0
2
0
0
0
2
0
0
0
2
0
0
1
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
1
0
0
0
0
1
1
2
0
0
0
2
0
1
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
1
0
0
0
1
0
1
1
0
1
2
0
0
0
0
0
0
2
5
0
0
0
0
0
2
0
0
0
1
0
0
1
0
3
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
3
0
0
1
0
2
0
2
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
4
2
1
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
1
0
0
0
2
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
6
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
3
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
1
2
0
0
3
0
0
5
0
0
2
1
0
0
0
1
0
0
0
0
1
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
1
0
0
5
3
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
1
0
1
0
0
1
1
0
0
1
0
0
0
1
3
0
0
0
1
0
0
0
1
0
1
0
0
0
3
0
0
1
1
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
1
2
0
0
0
3
3
0
1
0
0
0
1
2
2
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
4
0
0
0
0
0
2
2
1
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
2
9
0
0
0
1
0
3
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
1
1
2
0
0
0
1
0
0
0
0
3
1
3
0
0
2
0
0
0
1
2
0
0
2
2
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
1
0
0
0
0
1
2
0
0
0
4
2
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
3
2
0
0
0
6
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
3
0
3
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
1
2
0
0
0
0
2
0
0
2
0
0
0
0
4
0
0
0
4
3
0
0
2
0
0
0
0
0
0
0
2
0
2
1
0
0
0
1
2
0
0
5
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
1
0
0
0
2
2
1
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
2
0
2
0
2
0
0
1
1
0
0
0
0
0
0
5
1
1
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
1
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
1
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
1
1
6
0
0
0
1
0
1
3
2
0
0
0
0
0
2
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
8
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
3
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
2
3
0
0
0
0
2
0
0
0
4
2
0
2
1
1
0
0
0
0
0
2
3
0
0
1
0
0
2
0
2
5
0
2
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
2
1
0
0
3
0
0
0
10
0
3
1
0
0
1
2
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
2
0
1
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
3
0
0
1
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
2
0
0
2
0
0
4
0
2
0
3
1
0
0
0
2
0
4
2
2
1
0
0
0
0
4
0
2
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
4
1
2
0
0
0
1
1
2
15
0
2
0
1
0
1
2
2
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
1
0
0
1
1
0
2
0
0
0
0
0
1
1
0
0
0
1
0
0
0
2
1
2
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
8
0
0
0
0
0
3
0
2
0
0
0
1
0
0
0
1
1
0
0
2
0
0
7
2
0
2
0
0
0
0
0
1
0
0
2
2
0
0
1
0
0
0
1
0
0
0
2
1
0
2
0
1
0
2
0
0
0
0
2
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
3
0
0
2
0
1
0
0
0
0
0
3
0
0
0
0
4
0
0
0
0
0
1
2
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
2
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
1
0
0
0
0
0
0
0
2
1
0
0
3
0
2
1
0
0
0
2
0
0
0
0
2
0
1
2
0
0
2
1
0
0
0
0
0
0
4
0
2
0
0
0
0
3
0
0
0
1
0
3
0
0
1
2
10
0
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
2
2
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
1
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
2
7
0
1
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
1
0
0
0
0
0
2
0
0
1
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
2
2
2
0
0
1
1
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
1
0
0
1
0
2
2
0
0
1
0
1
0
2
5
2
0
0
0
0
1
0
0
0
0
2
0
1
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
4
0
2
4
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
2
2
0
2
0
1
2
2
2
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
2
0
0
1
1
1
0
0
0
3
0
0
0
2
0
0
0
0
2
1
0
1
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
4
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
1
0
0
1
0
0
0
0
0
2
0
0
2
2
0
0
1
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
4
0
0
0
0
2
0
0
0
2
2
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
2
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
2
2
0
0
2
0
0
0
2
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
1
0
0
0
1
0
0
2
6
0
0
0
0
0
0
2
0
0
0
0
2
1
1
0
0
1
0
0
0
2
0
3
0
0
0
1
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
1
0
0
0
1
2
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
2
1
0
0
0
2
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
2
1
3
0
0
1
1
0
1
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
3
1
0
1
2
2
0
0
0
1
0
0
0
2
3
0
1
0
1
0
0
1
0
0
0
0
0
0
3
0
0
2
0
0
2
0
3
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
4
0
2
1
0
2
0
0
0
0
0
2
0
1
2
0
0
4
0
0
2
0
0
2
0
2
1
0
1
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
1
2
0
0
0
1
0
0
0
3
0
0
3
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
4
3
2
2
0
0
2
1
0
0
2
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
2
0
3
0
0
4
0
0
2
0
0
0
0
0
2
0
2
0
3
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
5
1
0
1
0
0
1
2
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
6
0
2
0
3
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
2
1
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
2
0
15
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
2
1
0
1
0
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
2
0
3
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
2
1
0
3
6
0
0
0
1
0
0
0
1
3
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
2
0
2
1
0
0
0
0
0
0
1
0
1
0
0
1
2
0
4
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
2
1
0
0
1
0
0
1
1
0
0
1
0
0
0
0
2
0
1
0
1
0
0
9
0
0
0
3
0
0
0
0
0
1
2
0
0
1
0
0
0
0
2
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
3
1
2
0
2
0
0
1
0
1
0
0
0
0
0
3
0
0
1
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
3
5
0
0
2
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
4
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
6
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
3
1
1
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
3
0
0
0
2
0
0
0
2
2
3
0
0
0
2
1
0
2
0
0
0
1
2
0
0
0
1
2
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
3
1
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
1
2
0
0
2
0
0
0
0
1
2
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
1
0
2
1
1
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
3
0
1
0
0
0
0
0
1
0
0
2
0
2
2
0
3
2
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
2
1
0
1
4
0
2
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
2
0
2
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
3
2
0
0
0
0
6
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
3
0
0
0
0
1
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
1
0
8
1
2
4
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
2
2
0
1
0
3
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
5
0
0
0
1
1
0
2
0
0
2
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
2
0
1
2
1
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
3
0
0
0
0
0
1
0
2
0
0
0
0
0
6
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
1
3
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
1
0
2
0
0
0
1
2
0
0
0
1
0
0
0
0
0
3
1
0
0
1
0
0
0
3
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
3
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
1
0
1
0
2
0
0
1
1
1
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
1
2
1
0
0
0
0
1
0
0
0
3
0
0
1
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
2
0
0
2
2
0
0
0
1
2
0
2
0
1
0
0
1
0
4
0
1
0
0
1
0
1
0
0
0
2
1
0
0
3
1
0
0
0
1
0
0
0
1
0
2
1
2
1
1
0
2
2
6
0
3
2
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
2
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
1
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
3
2
0
1
2
0
0
0
0
0
0
0
2
0
0
5
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
1
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
2
2
0
0
0
0
0
1
0
3
0
1
0
2
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
3
0
3
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
2
1
0
2
0
0
0
2
0
0
2
1
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
2
0
0
1
0
3
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
1
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
3
0
0
0
0
0
1
1
2
0
0
1
0
1
0
0
1
0
2
2
0
1
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
2
0
1
1
0
0
2
1
0
2
0
1
1
0
0
2
0
1
2
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
1
0
0
2
0
3
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
2
0
0
0
2
0
0
0
0
1
2
0
0
1
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
1
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
4
0
2
1
0
0
2
0
0
0
0
0
1
2
1
0
0
0
0
0
0
2
1
1
0
4
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
2
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
5
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
1
0
0
1
2
2
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
5
1
0
2
0
0
1
2
0
0
0
2
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
4
0
0
2
2
0
0
0
0
0
0
0
0
1
0
2
0
1
0
2
0
2
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
9
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
1
5
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
2
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
4
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
1
1
0
0
0
0
1
1
0
0
1
0
0
0
1
0
3
1
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
3
0
2
2
1
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
4
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
4
0
0
1
2
0
1
1
1
0
0
0
0
0
0
0
0
0
1
3
2
2
0
0
0
1
1
0
0
0
1
0
1
0
0
0
1
4
0
0
0
2
0
0
1
1
0
0
2
2
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
1
0
0
1
0
0
2
1
1
0
0
3
0
0
0
2
1
0
0
0
0
1
0
2
1
0
2
0
0
0
0
0
1
1
0
0
0
4
0
2
2
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
4
0
0
1
2
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
3
1
0
2
2
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
2
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
2
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
2
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
3
1
1
0
2
0
0
1
0
0
0
5
0
0
2
2
2
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
8
0
0
0
4
0
1
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
4
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
1
0
0
1
0
0
2
0
2
1
0
2
0
1
0
1
0
1
0
2
0
0
0
0
0
0
0
1
0
0
3
0
0
2
0
0
0
2
0
0
2
0
0
0
2
0
0
3
0
1
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
1
1
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
1
0
0
2
1
1
2
0
2
0
0
0
0
2
1
0
0
0
0
1
0
0
0
1
1
4
0
0
0
0
0
0
1
0
0
0
0
4
0
1
0
1
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
2
0
0
1
0
0
1
1
0
2
0
1
3
1
0
0
2
0
0
0
0
0
2
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
3
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
2
0
0
0
4
0
1
0
0
0
0
0
0
0
2
2
0
0
0
3
0
0
0
0
0
1
1
0
0
0
0
0
2
0
2
1
0
4
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
3
0
2
0
0
1
0
4
0
4
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
1
0
2
0
2
1
0
0
0
0
0
0
0
0
0
2
2
1
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
4
0
0
1
0
0
1
0
0
3
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
3
1
0
1
0
0
2
0
0
1
1
0
2
0
0
0
0
0
1
0
2
1
0
0
0
0
0
4
0
2
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
1
0
3
0
0
4
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
2
1
3
1
0
2
0
0
0
7
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
1
2
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
2
2
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
2
0
0
0
2
1
0
0
0
2
0
0
1
0
0
0
0
0
9
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
2
2
0
0
1
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
2
0
4
0
0
0
5
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
6
0
0
0
1
1
0
0
0
0
0
2
2
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
1
1
3
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
2
0
1
1
0
0
0
0
0
2
2
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
3
0
1
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
1
0
1
2
1
0
0
2
0
0
0
0
1
1
0
2
0
0
0
2
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
2
0
0
2
4
0
1
5
0
0
0
0
5
0
0
2
0
2
0
0
0
0
0
2
0
0
3
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
2
2
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
1
2
2
0
1
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
1
2
0
10
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
3
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
1
2
0
0
2
0
0
2
0
1
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
1
1
0
0
0
0
7
2
2
0
0
0
0
0
0
3
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
3
0
0
2
2
5
0
1
0
0
2
0
0
0
0
0
0
0
1
1
0
4
0
1
0
0
0
0
0
0
0
1
1
3
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
2
1
0
0
0
0
0
1
0
0
1
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
1
1
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
1
1
0
0
1
0
1
4
1
0
0
2
1
0
0
0
2
0
0
2
1
3
2
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
3
0
2
0
0
2
0
2
2
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
5
2
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
2
0
0
1
0
2
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
6
0
0
0
0
1
2
0
0
0
1
2
1
0
0
1
2
2
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
2
0
0
0
1
0
0
1
0
0
0
0
0
3
0
0
4
2
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
1
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
1
0
3
1
2
0
0
0
0
0
1
0
2
0
0
0
0
1
2
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
4
2
3
0
1
0
0
0
3
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
5
0
0
0
0
0
0
0
0
0
0
2
1
2
0
1
0
0
1
0
1
0
2
0
1
0
0
0
0
0
0
2
3
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
4
0
0
3
0
0
2
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
4
1
1
0
2
0
0
1
0
2
0
0
0
0
0
1
1
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
1
2
0
0
3
2
0
1
1
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
6
0
1
0
0
1
0
1
2
1
0
0
0
0
2
0
0
0
0
2
0
2
0
1
0
0
0
2
1
0
1
2
1
0
2
2
0
2
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
2
2
0
0
2
0
0
1
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
1
0
0
2
0
0
0
4
2
2
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
2
0
1
0
0
0
3
2
0
0
2
2
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
1
2
0
0
0
0
1
0
0
2
0
3
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
2
1
2
1
0
2
0
0
0
1
1
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
1
0
0
1
3
1
1
0
0
0
0
0
2
0
2
0
1
0
2
0
2
0
0
0
0
0
0
2
0
0
1
1
0
1
0
0
0
2
1
3
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
1
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
2
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
3
3
1
0
0
0
1
0
0
1
0
0
2
0
0
2
0
3
0
0
0
0
0
0
2
0
0
0
1
0
0
1
1
0
0
0
0
0
2
0
1
3
2
0
0
0
0
1
0
0
1
0
0
2
2
2
1
0
2
0
0
0
0
2
0
1
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
3
0
2
2
0
0
2
0
1
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
1
1
1
0
6
0
0
0
0
2
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
2
2
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
1
0
0
4
0
5
3
0
2
0
0
0
1
0
0
2
1
2
0
0
0
0
0
0
1
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
2
0
0
1
0
0
1
3
0
0
0
1
0
0
0
1
0
2
0
2
3
1
1
1
0
0
0
0
0
2
0
2
0
1
0
0
0
1
0
2
1
0
0
2
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
2
0
0
2
3
1
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
2
2
1
0
0
1
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
2
0
0
1
0
0
0
3
0
2
0
2
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
7
2
0
0
1
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
2
2
0
0
0
0
2
1
0
0
0
0
0
1
4
0
2
0
3
0
2
0
0
0
2
0
1
1
0
0
2
1
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
2
0
0
2
2
2
2
0
0
0
2
0
2
2
0
1
0
0
0
1
0
0
0
2
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
1
0
2
1
0
1
0
0
4
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
3
0
0
0
1
0
0
0
0
0
2
0
2
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
3
0
0
0
0
0
2
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
1
0
1
0
1
0
0
0
0
0
1
0
1
0
0
2
1
0
0
0
2
0
1
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
2
2
2
0
1
0
1
0
0
2
0
1
0
0
1
2
1
0
0
0
0
0
7
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
2
1
0
2
1
0
0
2
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
5
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
3
0
0
1
0
2
0
0
2
0
1
3
0
1
0
3
2
0
1
0
2
1
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
2
0
2
0
2
0
1
0
0
0
0
0
2
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
2
1
0
0
0
0
1
0
0
1
1
1
2
0
0
0
0
0
0
1
1
0
2
1
0
1
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
1
2
0
0
0
0
2
2
1
0
2
0
0
1
3
0
0
0
0
4
0
2
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
1
0
0
0
1
0
0
2
0
0
0
2
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
3
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
7
0
0
0
2
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
4
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
1
0
0
0
2
2
0
0
0
0
0
0
1
2
1
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
3
2
0
0
0
2
0
0
0
0
1
0
0
0
2
0
2
0
0
2
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
3
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
2
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
2
1
2
0
0
5
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
2
2
0
1
1
2
0
0
1
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
2
1
0
0
0
0
1
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
2
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
2
0
0
1
1
0
2
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
1
0
1
0
0
0
1
0
2
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
2
1
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
1
3
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
1
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
5
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
2
1
2
0
0
0
0
0
1
0
0
0
2
0
0
2
0
1
0
1
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
6
0
0
0
0
2
0
2
2
0
2
0
0
0
0
2
1
2
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
2
2
2
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
2
4
0
0
0
0
1
0
0
1
0
2
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
1
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
2
0
0
0
0
0
0
0
0
3
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
2
0
0
2
0
0
2
0
0
4
0
0
1
0
1
4
0
1
0
1
0
0
0
0
3
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
2
2
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
3
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
1
0
2
0
0
2
0
0
0
4
0
1
0
0
2
1
0
0
0
2
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
2
0
0
2
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
5
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
1
0
0
1
0
0
3
1
2
2
0
0
0
1
0
0
0
2
0
1
0
0
1
0
0
1
1
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
2
3
1
0
0
3
0
0
1
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
3
0
0
0
0
0
0
1
1
0
3
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
2
0
1
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
9
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
4
2
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
2
0
0
1
0
0
1
1
1
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
8
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
1
0
0
0
1
0
2
0
1
0
0
2
1
0
0
1
0
0
0
2
0
2
0
0
0
0
0
1
0
0
3
0
0
3
0
0
0
0
0
2
0
0
0
1
0
0
0
4
0
0
3
0
0
0
0
0
5
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
2
0
0
1
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
1
0
0
2
0
0
2
0
0
0
0
0
1
0
2
3
4
0
0
0
2
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
2
2
0
1
0
0
2
2
0
0
0
0
0
0
0
1
2
0
1
1
2
1
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
1
1
1
2
2
0
0
2
0
2
0
0
0
0
0
8
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
2
0
0
0
7
0
0
0
0
0
0
0
0
0
0
3
1
0
0
1
0
0
1
0
0
0
0
3
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
3
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
1
0
0
0
0
0
1
1
0
0
0
0
2
3
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
4
0
0
0
0
2
0
0
0
0
0
1
0
1
0
2
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
1
0
0
0
0
0
6
0
0
1
2
1
0
2
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
3
0
1
0
2
0
0
0
0
1
0
1
0
0
7
0
0
3
0
0
1
0
0
0
0
0
0
3
0
8
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
3
0
0
2
0
0
0
1
1
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
3
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
3
0
0
3
0
0
2
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
2
0
1
0
0
2
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
1
3
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
1
1
0
0
0
0
2
0
0
1
0
0
0
1
2
3
2
0
1
0
0
1
0
0
0
0
1
2
2
0
1
1
0
0
1
0
0
0
0
0
2
0
2
2
0
0
0
0
0
2
0
2
1
1
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
4
0
0
0
0
2
0
2
0
2
0
0
0
0
0
1
0
0
0
3
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
1
0
2
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
6
3
0
0
0
0
0
0
2
1
0
0
1
0
0
0
1
2
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
3
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
5
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
3
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
1
0
5
2
0
3
0
0
0
1
0
0
1
0
1
1
0
3
1
1
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
3
0
2
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
2
2
0
0
0
2
0
0
0
1
0
7
0
0
1
0
0
0
0
0
0
2
4
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
1
0
0
0
0
0
1
2
6
2
1
0
0
0
0
1
0
1
0
0
0
0
2
0
1
2
2
0
3
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
2
0
0
0
0
1
0
1
0
0
0
1
0
2
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
2
0
2
0
0
0
0
2
0
4
0
3
0
3
0
1
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
2
0
0
0
0
3
1
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
2
0
0
0
2
2
0
0
6
1
0
0
0
0
0
3
0
2
0
0
0
2
0
0
1
2
2
0
0
1
0
0
0
0
0
0
2
2
2
1
0
0
0
0
0
0
0
3
3
0
1
0
0
0
0
1
0
2
1
2
0
2
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
3
2
0
1
5
2
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
1
2
2
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
3
0
0
0
0
2
7
2
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
2
0
0
0
0
9
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
6
0
0
3
0
0
2
0
0
0
2
0
0
2
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
2
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
4
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
2
0
3
0
0
0
0
0
6
1
0
1
2
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
5
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
1
1
1
1
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
1
2
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
5
1
0
0
0
0
0
0
0
0
1
2
2
1
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
3
0
0
0
0
0
0
0
0
2
0
1
3
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
2
0
0
3
0
0
0
0
0
0
1
0
3
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
1
1
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
2
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
2
0
0
1
1
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
2
0
0
0
0
3
2
1
0
0
2
0
0
0
0
1
0
1
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
1
0
0
0
3
0
2
0
4
0
0
0
0
0
1
2
0
0
2
1
0
0
0
5
0
0
0
0
1
0
0
0
2
4
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
1
1
1
0
2
1
0
0
0
0
0
0
0
0
4
0
0
0
1
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
3
0
1
1
1
0
0
1
0
1
0
0
0
0
1
0
1
3
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
2
2
1
0
0
0
0
0
0
2
0
0
4
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
1
0
4
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
3
0
0
1
0
1
0
0
0
2
0
0
0
0
2
0
3
2
0
0
0
0
0
1
2
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
3
0
2
1
0
0
0
0
2
0
2
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
2
0
4
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
2
0
0
1
2
0
0
1
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
2
2
0
0
0
0
3
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
2
0
0
0
1
0
0
0
0
0
2
0
1
0
2
2
0
2
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
2
0
0
3
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
10
0
0
0
2
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
2
2
0
0
0
2
1
1
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
2
0
2
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
1
3
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
1
2
2
0
0
1
0
1
0
0
2
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
3
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
2
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
1
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
3
0
4
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
1
1
0
1
6
1
1
0
1
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
1
3
0
2
0
4
0
1
0
0
0
1
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
2
0
0
0
0
0
0
1
0
1
0
2
0
2
1
0
4
6
1
0
0
2
0
0
2
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
2
0
1
2
0
2
0
1
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
2
1
3
0
2
0
6
2
0
1
1
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
2
0
0
0
2
0
1
1
0
1
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
1
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
1
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
2
0
0
2
11
0
0
2
1
3
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
2
2
2
0
0
0
2
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
2
2
0
0
0
0
0
1
0
0
0
2
0
1
0
1
0
3
0
0
2
0
0
2
2
1
8
3
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
3
0
1
0
1
2
3
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
2
2
0
0
0
0
0
3
0
2
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
3
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
2
0
2
0
0
0
0
0
2
0
2
0
0
0
1
0
0
2
3
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
3
0
0
2
3
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
1
2
0
0
0
1
0
1
2
0
0
0
0
0
1
1
2
0
0
1
3
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
2
0
3
1
0
0
0
1
2
0
0
3
0
0
0
0
0
0
0
0
0
0
2
4
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
0
0
0
3
1
2
0
0
0
0
1
0
2
0
0
0
0
0
1
2
0
3
1
5
0
0
0
0
0
0
0
0
2
0
0
0
0
2
5
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
3
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
2
0
0
0
1
1
0
0
0
2
0
0
1
0
0
2
0
1
0
2
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
2
0
1
0
1
0
0
0
0
6
0
0
1
0
1
1
0
0
4
0
0
1
2
0
0
0
0
0
2
0
1
0
0
0
0
1
1
0
2
0
0
0
1
0
2
0
0
0
0
2
1
0
0
1
1
0
0
0
0
1
0
1
2
1
2
0
1
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
4
0
0
0
0
1
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
2
1
0
1
0
5
0
0
0
0
1
0
0
1
0
0
0
0
1
2
0
0
0
2
0
0
1
0
0
0
2
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
1
2
0
1
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
3
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
1
0
2
5
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
2
0
1
4
0
0
0
3
0
0
0
0
3
0
0
0
1
1
0
1
0
1
0
2
2
2
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
2
3
3
0
0
2
0
0
0
2
1
0
0
2
0
0
0
0
2
5
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
3
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
2
1
0
0
0
0
0
0
2
2
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
3
0
4
0
0
0
0
0
0
2
0
3
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
1
0
0
0
0
1
2
0
2
1
1
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
1
0
1
0
0
2
2
0
0
0
0
2
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
3
0
0
2
0
1
0
0
2
0
2
2
0
0
0
0
2
0
0
1
2
1
0
0
4
0
1
2
0
0
2
6
0
0
2
0
0
0
2
1
1
2
0
0
0
0
2
2
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
5
2
1
1
0
1
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
1
0
2
2
0
1
1
0
0
0
0
0
2
0
2
0
0
1
0
0
0
2
2
2
0
0
2
1
0
0
2
0
0
0
0
0
1
1
0
0
1
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
1
0
1
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
3
2
0
0
2
0
0
0
2
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
2
0
2
0
0
2
1
0
2
2
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
2
0
1
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
3
2
0
2
2
0
0
0
0
0
0
0
1
0
0
1
0
2
0
2
0
0
1
2
0
1
0
2
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
2
0
0
2
0
0
1
1
2
2
0
1
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
3
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
10
1
0
0
0
2
0
0
0
0
3
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
1
0
0
0
1
2
1
0
1
0
1
0
1
0
0
0
1
1
0
3
0
2
0
0
0
0
0
1
1
0
0
1
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
2
3
0
2
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
2
0
0
3
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
1
2
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
2
0
0
0
0
2
0
0
0
0
1
0
2
1
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
2
1
0
1
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
5
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
2
0
2
0
2
0
2
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
1
2
0
0
0
0
0
0
2
1
0
0
0
1
2
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
2
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
1
0
0
2
1
1
0
1
2
0
1
0
0
0
2
0
0
0
0
1
3
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
1
0
0
4
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
8
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
1
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
3
0
2
0
0
1
0
3
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
1
1
2
0
0
2
0
0
3
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
2
2
0
3
0
1
2
3
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
2
2
0
0
1
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
1
4
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
1
0
1
0
2
0
2
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
3
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
2
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
1
0
1
0
0
1
0
0
1
1
0
0
0
1
0
1
0
2
0
0
0
0
0
0
2
1
0
0
0
2
2
0
0
1
0
0
0
0
0
1
1
0
1
1
0
0
2
0
1
2
1
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
5
0
0
2
0
2
1
1
0
0
0
2
0
0
2
1
4
0
2
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
2
1
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
1
1
0
0
0
4
1
0
0
3
0
0
0
0
0
0
2
1
0
0
0
0
2
2
0
0
2
0
0
0
1
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
2
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
2
0
1
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
4
1
0
0
1
0
1
0
0
0
0
1
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
3
2
0
0
1
2
2
2
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
1
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
2
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
3
0
1
0
1
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
3
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
3
0
0
1
0
0
0
0
1
0
0
1
0
2
0
0
0
1
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
1
0
1
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
2
0
0
0
0
0
2
0
1
1
4
0
0
0
2
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
2
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
5
0
2
6
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
5
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
1
0
2
2
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
2
0
0
2
0
0
0
2
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
2
0
0
2
2
1
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
6
0
1
0
1
2
0
0
3
1
0
0
0
0
1
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
1
0
1
2
0
0
2
0
2
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
2
3
0
0
0
2
0
0
0
0
0
2
4
0
1
0
1
0
2
3
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
4
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
1
0
1
1
1
0
0
0
0
1
0
0
0
1
0
2
0
2
1
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
3
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
4
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
3
2
3
3
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
2
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
2
3
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
0
1
3
2
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
3
1
0
2
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
4
0
0
2
1
3
0
0
0
0
0
0
1
0
3
4
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
6
0
0
3
2
2
0
0
0
0
2
0
1
2
0
1
0
0
1
1
0
0
0
2
0
0
2
0
0
0
0
0
0
2
1
0
0
2
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
1
2
0
0
0
0
1
1
1
0
0
1
0
2
2
0
0
6
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
2
0
1
0
2
0
0
0
0
2
0
2
0
1
0
0
0
1
2
3
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
4
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
2
0
4
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
2
2
0
0
0
0
0
0
0
0
0
1
1
2
0
0
5
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
2
2
0
0
3
0
0
0
0
1
2
0
0
0
0
1
0
1
0
0
0
1
2
0
3
0
0
0
3
0
2
1
0
0
2
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
2
0
0
0
0
1
0
0
0
2
1
2
1
0
2
0
1
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
2
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
1
0
0
0
0
0
0
1
2
1
0
0
0
0
0
1
0
0
0
1
0
0
2
0
2
1
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
1
0
3
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
3
0
2
0
0
2
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
1
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
2
0
3
0
0
0
0
0
0
0
1
0
2
6
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
2
0
1
0
0
1
0
0
2
0
2
4
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
2
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
2
0
2
0
1
1
0
2
1
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
3
0
2
0
0
0
0
0
1
0
1
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
2
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
1
0
2
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
2
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
5
0
3
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
1
0
0
1
0
0
0
0
1
0
0
2
0
1
1
4
1
0
0
0
0
1
0
0
1
1
1
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
1
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
3
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
1
0
2
1
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
3
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
2
2
0
0
0
0
0
0
3
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
3
0
0
0
2
0
0
0
3
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
7
1
2
0
0
1
0
0
2
0
0
3
0
1
0
0
0
0
2
0
0
3
0
0
1
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
2
0
1
1
1
0
0
2
0
1
0
0
0
0
0
1
0
0
1
1
2
1
3
2
0
0
2
0
0
0
3
0
1
1
2
0
1
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
1
0
0
0
1
2
0
2
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
2
0
0
0
0
0
1
2
0
0
2
2
2
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
3
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
3
0
0
0
2
0
0
0
2
0
4
0
0
0
4
0
0
0
3
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
1
0
1
2
7
0
2
1
0
1
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
1
0
1
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
3
0
2
0
0
0
3
0
0
2
2
2
0
0
0
2
2
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
2
0
0
0
1
0
0
3
0
0
2
0
0
2
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
2
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
2
0
0
0
1
0
2
2
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
4
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
2
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
1
0
0
2
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
1
0
3
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
3
1
2
2
0
3
0
0
0
3
0
1
2
0
4
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
7
0
0
0
0
0
20
0
0
2
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
1
0
0
1
0
1
0
0
2
0
3
0
1
0
2
2
3
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
1
2
1
0
0
0
0
0
2
9
0
1
0
0
2
3
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
3
0
0
0
2
0
0
0
0
2
0
0
2
0
0
2
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
3
1
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
2
3
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
1
7
2
2
0
2
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
3
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
2
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
1
1
0
2
0
2
1
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
1
3
0
0
0
2
2
0
0
0
0
0
1
0
0
0
1
0
1
0
0
2
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
2
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
6
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
2
1
0
2
1
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
1
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
1
0
0
0
2
2
0
0
1
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
2
1
0
0
0
2
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
2
1
0
0
0
1
0
0
1
0
0
2
1
0
0
0
2
0
0
0
5
0
1
0
0
0
0
0
0
0
1
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
5
2
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
2
1
2
1
0
0
0
0
3
1
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
3
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
1
1
0
1
3
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
1
1
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
3
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
5
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
1
0
2
0
0
0
1
0
0
0
4
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
2
1
0
1
0
0
1
0
0
0
0
2
1
1
0
0
0
0
1
3
1
2
0
7
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
17
0
1
0
0
2
0
1
1
1
0
1
0
0
0
0
1
0
1
1
0
0
6
0
0
0
0
0
3
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
2
0
0
5
0
0
0
0
0
1
0
0
0
4
0
0
0
3
0
1
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
6
3
0
0
2
0
0
0
0
0
4
0
0
0
0
4
0
1
2
0
0
0
2
0
0
0
2
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
2
1
1
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
1
0
3
1
0
1
0
1
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
3
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
1
0
1
3
0
0
2
0
0
0
3
1
1
2
0
0
0
0
0
0
1
2
0
1
2
0
0
0
1
5
0
0
1
3
1
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
1
1
0
0
1
0
0
0
0
0
2
0
0
0
0
2
1
0
0
2
1
0
0
1
0
0
0
1
0
3
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
4
0
1
0
0
2
0
0
0
0
1
0
2
0
1
0
0
0
3
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
2
1
1
2
1
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
1
0
0
0
5
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
3
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
1
0
0
2
2
0
1
0
1
2
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
2
2
0
1
2
1
0
1
0
2
2
0
0
0
0
0
4
0
1
1
0
0
1
1
0
1
0
1
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
1
0
1
2
0
0
0
0
2
0
0
4
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
1
0
0
0
1
0
1
0
1
2
1
2
1
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
1
3
1
0
0
2
1
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
3
0
0
0
2
0
0
0
2
0
0
0
0
0
1
2
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
1
2
0
0
2
0
2
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
1
0
1
0
0
0
2
2
1
1
4
2
1
0
0
0
0
4
0
0
0
0
0
2
0
0
0
2
0
2
1
0
3
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
1
0
0
1
2
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
1
0
0
0
0
4
0
2
5
0
3
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
2
2
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
2
0
0
0
2
1
2
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
1
2
2
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
2
2
0
1
0
0
2
0
0
2
0
0
1
0
0
3
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
3
0
0
0
2
0
0
2
1
2
0
4
0
0
0
0
1
1
0
2
2
1
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
1
0
1
0
0
0
4
3
0
0
0
0
0
2
0
0
0
0
0
0
0
3
3
3
1
0
0
1
0
1
1
0
0
0
3
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
1
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
3
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
1
0
2
1
0
2
0
0
1
0
0
0
2
0
0
1
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
6
0
1
5
2
0
2
2
0
0
0
0
0
0
1
0
0
0
1
0
0
2
2
0
1
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
4
1
2
1
0
2
0
0
0
0
0
0
2
2
1
0
2
2
3
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
2
2
0
1
0
0
0
0
1
0
0
2
0
0
3
0
2
0
0
0
0
0
0
0
1
0
1
0
2
0
1
0
2
2
0
2
0
0
2
0
0
0
0
0
0
1
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
7
0
2
2
0
0
0
0
0
1
0
1
0
0
1
2
0
0
0
0
0
2
0
0
0
2
0
3
0
0
0
0
0
0
2
0
0
0
0
3
0
0
1
1
0
2
0
2
0
2
0
0
1
0
2
0
2
0
0
0
0
2
0
2
2
1
0
0
0
0
1
0
0
0
0
0
0
2
3
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
2
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
2
1
1
2
2
2
1
1
1
0
0
0
2
0
1
2
0
0
0
2
0
1
0
1
0
0
0
2
0
2
1
0
2
0
0
0
2
2
1
0
0
0
0
0
0
0
1
2
0
0
0
0
2
1
0
0
0
0
0
1
0
7
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
2
1
0
1
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
1
0
2
1
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
2
1
0
0
0
0
0
0
0
0
2
0
6
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
2
0
2
2
0
0
0
0
0
0
3
0
0
2
0
1
0
1
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
2
0
0
1
2
0
0
0
0
0
2
1
8
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
4
1
0
1
1
1
0
2
0
0
0
0
2
0
0
1
2
0
2
2
0
0
0
0
0
0
1
0
1
0
2
0
2
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
1
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
1
0
2
0
1
0
1
0
2
0
1
0
0
0
0
2
0
0
1
2
0
3
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
3
0
0
2
1
0
0
1
2
0
0
0
0
0
0
2
0
3
0
0
0
0
0
1
0
0
1
2
1
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
3
0
0
0
2
0
0
2
1
0
1
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
2
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
1
1
2
1
2
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
1
0
1
0
0
0
2
2
0
1
0
2
0
1
0
0
0
0
2
2
0
0
2
1
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
3
2
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
4
0
0
0
3
0
0
0
0
2
0
6
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
2
1
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
4
0
0
2
0
0
0
1
0
0
3
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
2
0
0
0
2
1
0
0
4
0
0
2
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
1
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
3
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
6
1
0
2
0
0
2
2
1
0
0
0
0
2
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
2
1
2
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
2
0
1
0
0
1
0
0
0
2
0
2
0
0
2
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
2
2
0
0
0
2
4
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
2
0
2
0
1
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
2
0
2
0
0
0
0
0
1
0
0
0
2
3
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
1
1
1
1
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
2
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
1
2
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
2
0
0
0
0
0
2
1
1
0
0
0
1
0
0
2
0
0
2
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
2
0
0
2
0
0
2
2
0
5
0
0
1
0
0
0
0
1
1
1
0
0
0
3
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
2
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
2
2
0
0
0
0
0
1
0
2
0
1
0
0
2
0
2
0
2
0
3
0
0
0
0
1
2
2
0
0
1
0
0
1
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
2
1
2
0
0
0
0
0
0
0
3
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
3
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
8
1
0
2
2
0
2
1
0
2
2
2
0
3
0
0
1
2
0
0
0
0
1
0
1
2
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
4
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
2
0
0
1
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
1
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
2
4
0
0
2
0
1
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
2
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
1
0
0
3
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
1
0
1
3
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
1
2
0
2
4
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
1
0
0
0
0
3
0
0
3
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
2
0
0
0
0
2
1
2
0
1
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
2
2
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
1
0
0
0
0
0
1
0
0
0
0
0
3
0
2
0
0
0
0
2
2
0
1
0
0
0
3
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
3
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
1
0
0
2
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
1
0
0
0
1
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
1
2
0
2
0
0
0
0
0
0
0
0
1
1
0
3
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
1
2
0
2
0
0
0
1
0
0
1
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
2
0
0
3
0
0
1
0
0
2
0
0
4
2
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
2
1
0
1
1
2
0
2
0
1
0
1
2
0
0
0
2
2
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
2
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
1
2
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
2
0
2
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
2
0
1
1
0
4
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
14
1
0
0
0
0
0
1
0
1
0
1
1
0
2
2
1
0
2
0
2
0
2
2
0
0
1
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
2
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
3
0
0
0
0
0
2
2
0
2
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
1
1
1
0
0
1
1
0
0
0
1
3
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
4
0
2
0
0
0
0
2
2
0
2
0
0
1
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
2
3
2
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
2
0
0
2
2
1
1
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
2
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
1
2
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
1
0
0
0
1
3
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
1
0
5
2
0
2
0
0
0
0
2
0
2
1
0
0
0
2
0
0
0
0
1
0
0
6
0
2
0
0
0
0
2
0
0
0
0
2
0
2
2
0
1
2
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
3
0
2
0
0
0
0
0
0
0
4
0
2
0
2
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
3
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
2
0
0
0
0
2
0
0
0
1
0
0
0
1
1
1
1
0
0
1
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
1
2
1
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
1
0
2
2
0
0
1
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
2
0
3
1
2
0
2
0
0
0
2
0
2
1
0
0
0
0
2
1
1
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
3
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
1
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
1
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
2
0
0
0
1
0
2
2
0
0
0
7
0
0
0
0
0
2
0
0
1
0
3
0
1
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
1
1
3
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
1
1
1
1
0
0
0
2
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
1
0
1
0
0
2
0
2
0
0
0
1
1
0
0
3
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
1
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
1
0
2
0
0
2
0
0
0
0
0
1
2
0
0
0
1
0
0
2
0
0
1
0
1
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
2
0
0
0
0
1
2
1
0
0
0
2
2
0
2
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
2
0
0
1
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
6
0
0
2
0
2
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
2
2
1
1
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
2
1
0
0
0
0
2
0
0
0
1
0
1
0
4
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
3
0
0
0
1
0
0
1
0
0
2
1
0
3
0
0
2
1
0
0
2
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
2
0
0
0
0
3
0
2
1
0
0
0
2
4
1
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
3
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
3
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
2
1
0
0
0
0
0
2
1
0
0
1
0
0
0
1
1
1
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
4
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
3
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
1
0
2
0
0
0
0
0
1
2
0
0
1
0
0
3
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
1
1
0
0
2
0
3
0
0
0
0
0
2
1
3
0
0
2
0
0
0
1
0
0
4
0
1
2
1
0
0
1
0
0
0
1
2
0
0
0
0
1
1
0
0
0
1
0
1
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
1
1
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
2
2
0
2
0
0
2
0
0
0
0
0
4
0
0
3
1
0
0
0
0
0
0
0
0
1
0
0
5
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
5
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
2
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
3
0
2
2
0
2
0
0
0
0
1
2
0
0
0
0
0
2
0
1
0
0
0
2
1
0
0
1
0
1
0
0
2
1
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
4
0
0
1
13
0
0
0
0
0
0
2
4
2
1
1
2
0
4
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
1
0
1
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
2
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
3
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
2
0
1
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
4
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
4
1
2
0
2
1
0
0
1
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
3
0
0
0
1
1
0
0
0
1
0
0
3
1
2
2
0
2
0
0
2
0
1
0
0
0
0
0
0
4
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
1
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
1
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
1
2
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
4
0
1
0
2
0
0
0
1
1
0
2
0
0
0
3
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
1
0
1
2
0
0
0
0
1
0
0
0
2
0
0
0
2
2
0
0
2
0
6
1
0
0
0
0
0
0
0
0
0
1
3
0
0
1
0
2
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
3
0
0
1
0
0
5
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
3
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
2
0
1
0
1
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
3
0
0
0
0
2
0
0
0
0
2
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
5
1
3
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
3
0
1
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
1
0
2
1
2
0
0
1
0
0
2
0
2
2
2
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
1
1
0
0
0
3
0
0
0
0
0
0
0
2
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
2
0
0
4
1
0
0
0
1
0
1
0
0
1
0
0
0
2
0
0
6
0
2
0
1
1
0
3
1
1
0
0
0
2
3
2
1
0
0
2
0
0
1
0
0
2
0
2
0
0
0
0
0
0
4
0
2
0
1
0
0
0
0
1
0
0
0
4
0
0
0
0
0
2
0
2
0
1
1
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
2
0
2
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
2
0
0
2
0
0
0
0
2
0
0
1
0
2
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
8
2
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
3
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
2
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
8
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
1
1
8
0
0
0
1
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
2
0
1
0
3
0
0
0
0
1
0
2
1
2
0
0
1
0
1
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
2
1
0
2
1
1
2
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
2
0
0
1
0
0
0
1
2
1
1
0
0
0
0
3
2
0
3
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
2
1
0
0
1
1
0
0
0
3
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
5
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
10
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
4
0
2
0
8
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
1
1
2
2
0
0
0
0
0
0
1
0
0
0
0
0
1
5
0
0
0
0
0
1
1
0
0
0
0
0
1
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
1
2
2
1
0
0
0
0
2
4
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
1
0
0
0
0
1
1
0
2
0
0
1
0
0
0
1
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
2
1
1
1
1
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
2
1
0
1
0
0
0
0
0
0
0
1
2
1
2
0
1
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
2
1
0
0
0
3
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
1
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
1
1
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
3
0
1
0
0
0
0
0
0
0
0
2
2
0
0
2
1
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
1
0
1
0
0
1
0
1
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
5
1
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
5
0
0
2
0
1
4
0
2
0
0
0
0
0
0
0
0
4
0
3
2
0
0
5
0
0
0
0
1
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
6
0
0
1
0
2
1
1
1
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
1
2
0
2
0
2
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
2
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
2
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
5
0
2
2
3
0
1
0
2
1
0
2
3
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
1
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
3
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
5
0
0
0
0
2
0
2
0
1
0
2
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
2
1
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
1
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
2
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
1
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
2
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
2
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
2
1
0
0
1
2
0
0
0
0
0
0
0
0
0
2
2
4
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
2
2
0
1
0
1
0
0
1
0
0
0
0
1
1
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
3
0
0
0
5
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
1
0
2
0
0
0
0
0
3
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
4
0
1
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
2
3
0
0
1
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
4
0
0
2
3
0
0
0
2
0
0
0
2
3
1
1
0
0
2
0
0
1
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
3
2
0
0
2
0
2
0
1
0
0
0
3
0
0
0
0
2
0
0
2
1
0
0
0
5
0
2
0
0
1
0
0
0
2
0
0
0
1
0
1
0
1
3
0
1
0
0
1
0
0
2
3
0
1
0
2
1
0
3
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
7
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
1
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
2
0
1
0
1
0
2
3
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
4
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
2
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
2
0
0
3
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
3
2
0
0
0
1
2
2
0
2
0
0
1
1
0
1
2
0
0
1
2
0
0
1
0
0
0
1
2
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
3
2
0
0
0
0
1
0
1
1
1
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
2
2
3
1
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
2
2
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
1
0
0
0
0
3
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
2
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
6
0
0
2
0
5
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
3
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
3
0
2
0
0
0
0
1
0
0
1
0
0
0
0
2
0
2
0
3
1
0
0
0
0
0
3
0
1
1
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
3
0
0
0
0
0
3
1
3
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
1
2
1
0
0
0
1
0
9
0
1
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
3
0
2
0
1
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
3
0
0
2
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
5
0
1
0
0
0
0
1
0
3
0
0
0
3
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
1
0
0
0
0
0
3
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
1
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
1
2
0
0
0
2
7
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
2
1
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
3
0
1
0
0
0
0
0
3
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
1
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
3
0
2
3
1
0
0
3
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
1
0
0
2
0
0
0
0
2
0
2
3
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
1
1
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
2
2
2
0
0
1
0
0
0
0
1
0
0
0
2
2
0
0
4
0
0
0
0
1
0
0
0
0
0
3
0
2
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
2
1
1
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
3
0
1
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
3
2
1
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
2
0
0
2
0
0
0
0
3
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
3
2
0
3
1
1
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
2
0
1
1
0
0
0
0
0
0
0
2
0
1
1
0
0
0
1
1
0
5
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
3
0
0
2
0
0
5
0
0
0
0
2
0
1
0
2
3
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
4
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
3
0
1
0
0
2
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
4
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
1
2
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
3
0
1
1
0
3
0
0
4
1
0
0
0
2
1
0
0
0
0
1
0
3
0
0
0
0
0
2
1
0
0
3
0
8
0
0
0
2
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
1
0
0
0
0
1
0
0
1
0
0
0
2
0
0
1
2
2
0
0
0
0
2
0
2
0
0
1
1
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
1
0
0
0
1
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
1
2
0
2
0
0
1
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
2
1
0
0
0
1
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
2
0
3
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
1
0
0
0
0
1
1
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
1
0
0
1
1
2
0
0
0
0
2
1
0
0
1
0
2
3
2
3
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
2
0
0
1
0
0
0
1
1
0
0
0
1
0
1
2
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
2
2
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
3
0
2
1
0
2
0
1
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
2
2
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
2
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
5
3
2
0
1
0
0
0
0
0
0
0
0
0
1
5
2
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
5
0
0
2
0
0
2
0
0
0
0
2
1
0
1
0
0
3
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
4
0
2
1
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
1
0
2
2
0
2
3
2
2
0
0
0
0
0
0
0
0
0
15
0
0
0
0
0
0
2
0
1
2
0
0
0
1
0
2
0
1
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
2
1
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
2
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
2
0
1
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
2
1
0
0
0
0
0
0
0
0
1
2
0
0
1
0
2
0
3
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
2
0
2
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
3
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
1
0
2
1
0
0
0
0
2
0
0
0
3
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
2
0
2
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
4
0
0
0
2
3
1
1
0
0
0
2
0
0
1
3
0
0
0
0
1
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
2
0
3
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
3
1
0
0
0
0
0
0
0
3
0
0
0
0
0
5
1
0
0
0
0
0
0
0
0
3
5
0
3
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
1
0
2
2
0
2
0
3
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
2
1
0
0
0
1
0
0
0
2
2
0
1
0
0
0
0
0
0
2
2
0
1
0
0
0
0
2
0
2
0
1
3
0
2
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
1
1
0
0
0
0
2
2
0
0
0
3
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
5
0
0
0
2
0
2
0
0
1
1
0
2
0
1
0
0
0
0
0
1
2
1
0
0
0
2
0
0
0
3
0
0
0
2
0
0
0
0
0
2
2
0
1
0
1
2
0
3
2
0
2
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
1
0
2
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
3
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
1
0
2
0
1
0
0
8
0
0
0
2
0
0
0
0
1
0
0
4
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
1
2
0
0
0
2
0
0
1
0
0
2
0
0
1
0
1
0
0
0
0
1
0
0
2
0
0
0
2
0
0
2
0
1
1
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
5
0
2
0
1
1
0
0
1
0
0
0
0
0
2
1
0
0
0
0
1
2
2
0
0
0
1
1
0
0
0
0
0
1
3
2
0
0
0
0
0
0
1
0
0
0
0
0
3
0
1
3
0
0
0
0
2
0
0
2
0
2
0
1
1
0
2
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
1
2
0
0
0
0
2
0
0
1
0
5
2
0
2
0
2
0
0
2
0
2
0
0
2
0
0
1
0
2
0
0
1
0
0
1
2
2
0
1
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
3
0
2
0
2
1
1
2
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
3
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
2
0
1
2
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
1
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
1
0
2
2
0
1
0
0
2
0
0
1
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
2
1
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
1
2
0
1
0
0
3
2
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
3
0
0
0
2
0
0
2
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
1
0
0
3
0
2
0
0
0
0
0
0
4
0
0
0
2
0
1
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
1
1
0
0
5
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
2
0
0
0
0
1
0
0
0
0
0
1
1
4
0
0
1
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
2
0
1
1
0
0
2
1
1
2
0
0
0
6
0
0
0
0
2
0
0
0
0
1
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
4
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
2
1
0
0
1
0
2
0
0
0
1
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
2
2
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
2
2
0
0
1
0
0
0
0
0
0
1
2
0
2
1
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
2
0
0
3
0
0
0
0
2
0
1
0
0
0
2
0
1
0
2
0
0
0
0
1
0
0
1
0
0
2
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
1
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
4
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
2
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
2
0
0
0
2
0
0
0
1
1
2
0
1
1
0
0
0
0
0
0
2
0
0
0
7
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
3
2
2
0
0
0
2
1
0
2
0
0
1
0
0
0
0
0
0
6
0
3
0
0
0
1
2
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
3
0
1
0
2
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
3
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
1
0
1
0
0
5
0
0
0
0
0
2
1
2
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
2
1
0
0
2
0
2
0
0
2
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
3
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
3
0
0
14
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
1
0
1
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
5
0
0
0
2
0
0
2
1
0
1
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
4
2
0
0
2
0
0
0
11
0
0
1
0
0
0
0
1
0
2
0
2
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
2
1
2
2
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
2
1
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
3
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
2
1
0
0
0
0
0
0
1
3
1
0
0
0
0
2
0
0
0
1
1
0
3
3
2
0
0
0
0
0
0
1
0
0
1
0
0
2
0
3
2
0
0
0
1
0
0
2
1
0
4
0
0
2
0
1
0
2
1
0
0
0
0
0
0
1
0
0
3
0
0
1
3
0
2
0
0
0
1
2
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
3
0
1
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
2
0
0
0
2
0
0
0
0
0
0
0
3
0
1
2
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
2
0
2
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
3
0
1
3
1
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
4
0
1
1
0
0
0
0
1
0
1
0
2
0
1
1
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
2
2
1
0
0
0
1
0
0
1
3
2
0
0
2
0
1
0
1
0
2
7
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
2
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
3
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
2
0
0
2
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
2
3
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
2
0
0
0
3
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
1
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
2
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
2
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
4
0
0
1
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
2
2
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
1
0
0
0
0
0
1
2
2
0
2
0
2
0
0
2
0
0
1
1
1
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
1
0
0
0
1
2
0
1
0
0
0
2
2
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
1
0
2
0
0
0
1
0
2
0
0
0
2
3
0
0
0
3
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
3
0
1
1
0
0
2
0
2
1
0
0
0
0
0
0
1
1
0
0
2
0
0
0
2
0
0
0
0
1
2
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
2
0
0
0
2
0
1
2
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
2
0
2
2
0
0
2
1
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
2
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
3
0
1
1
0
0
0
0
0
0
1
1
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
2
0
0
4
0
2
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
3
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
1
0
2
0
0
0
1
0
0
0
0
1
0
0
2
2
0
0
0
0
0
1
1
0
0
0
0
0
2
0
1
0
0
0
0
2
1
0
0
1
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
3
0
0
0
0
0
1
0
1
1
6
0
0
0
1
2
3
1
0
0
0
0
0
0
2
1
0
1
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
3
0
0
0
0
0
3
0
1
0
2
0
0
0
2
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
4
0
0
0
2
0
5
0
0
2
0
0
0
0
0
1
0
1
2
2
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
3
0
0
0
2
0
0
0
0
0
1
0
2
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
1
2
2
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
2
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
1
1
1
0
0
2
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
1
0
1
0
0
1
0
1
0
13
2
0
0
0
2
0
2
0
0
0
0
2
0
0
0
1
0
2
0
2
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
3
2
0
0
1
0
0
2
2
0
0
2
0
2
2
0
2
0
3
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
3
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
2
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
2
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
2
1
0
2
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
3
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
2
2
1
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
2
0
0
0
1
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
2
0
0
2
1
0
0
0
0
1
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
2
0
0
2
0
0
0
0
0
0
0
2
3
0
2
2
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
1
0
0
2
1
2
0
2
2
0
0
2
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
1
0
0
2
0
0
2
0
0
0
1
1
1
0
1
0
2
3
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
2
2
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
1
0
0
0
2
0
1
0
3
0
2
1
1
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
5
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
1
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
3
0
0
0
1
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
2
0
0
2
0
1
0
0
0
0
0
2
1
0
1
0
2
2
0
2
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
2
0
2
2
2
1
0
0
4
1
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
4
0
0
1
0
0
0
1
0
0
0
0
0
2
1
2
1
0
0
0
0
0
2
0
0
0
3
6
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
3
1
0
3
0
0
2
1
0
6
0
0
0
0
8
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
4
0
0
0
0
2
0
0
0
0
3
2
2
0
0
0
2
1
0
0
0
0
2
0
0
2
0
3
0
2
0
0
0
1
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
1
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
1
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
2
0
2
0
0
1
0
0
1
0
2
0
2
0
1
0
0
0
2
0
1
0
0
1
0
1
0
0
0
1
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
1
0
1
0
0
1
0
0
0
0
1
1
1
0
0
0
2
0
0
2
2
2
1
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
2
0
0
0
2
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
2
6
0
0
0
0
1
0
0
0
3
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
1
0
0
1
2
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
3
0
0
0
0
0
0
0
2
2
0
0
0
1
2
1
0
2
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
2
2
0
0
4
0
4
0
0
1
2
1
0
0
0
0
1
0
1
0
2
0
9
0
1
0
0
0
2
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
3
0
3
0
0
1
1
0
1
0
1
0
0
0
2
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
2
2
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
2
1
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
1
0
2
1
0
0
0
1
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
2
1
0
0
2
0
0
2
1
1
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
2
0
1
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
5
0
0
2
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
2
5
0
0
0
2
0
1
1
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
11
1
2
0
0
1
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
2
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
1
0
0
0
1
0
0
2
0
6
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
2
2
2
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
2
0
2
0
0
2
0
2
0
0
0
0
2
1
0
0
0
0
0
0
1
0
1
1
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
2
2
0
0
1
2
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
2
0
1
0
0
0
0
1
0
0
0
0
2
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
2
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
4
0
0
0
0
0
0
2
0
0
1
0
0
2
1
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
3
0
2
1
0
0
0
0
2
0
2
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
1
1
2
0
0
1
0
0
0
0
0
1
1
4
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
2
0
0
0
1
2
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
2
2
1
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
3
0
0
0
0
0
1
0
0
5
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
2
1
1
0
0
1
0
0
0
2
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
3
1
0
0
0
0
0
0
2
0
2
1
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
10
0
1
0
0
0
0
0
0
0
4
1
1
0
3
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
1
2
1
0
1
0
0
1
1
0
2
0
0
0
1
0
2
0
2
1
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
3
0
2
0
1
2
0
0
0
0
0
0
1
0
0
0
0
1
0
3
1
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
1
0
1
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
3
0
1
0
0
0
0
2
0
2
0
0
0
0
0
1
0
2
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
1
6
2
2
0
2
0
0
0
0
0
0
0
2
0
2
3
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
1
2
2
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
3
0
0
0
0
0
2
0
0
1
2
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
3
0
0
0
0
0
1
0
2
0
0
1
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
2
2
0
1
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
1
1
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
1
2
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
5
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
1
1
2
0
0
0
0
0
1
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
1
2
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
1
0
2
0
0
0
2
0
0
2
0
1
8
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
1
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
3
1
0
2
0
1
0
1
0
1
0
2
1
0
0
2
2
2
0
2
0
0
0
1
2
0
0
0
1
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
2
1
0
0
0
0
0
0
0
2
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
1
0
2
0
0
2
0
1
7
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
1
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
4
0
2
0
2
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
3
0
1
1
0
0
0
0
2
3
0
0
0
0
2
0
1
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
1
0
0
1
0
0
2
2
0
0
0
1
0
0
2
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
1
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
6
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
2
4
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
1
1
1
0
0
0
0
1
1
2
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
2
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
2
0
0
7
2
1
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
1
2
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
3
0
0
0
4
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
2
1
0
1
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
2
2
0
4
0
0
0
0
0
1
1
0
0
0
1
0
0
0
2
2
0
0
0
0
1
0
1
1
3
1
0
0
1
0
0
0
0
2
1
0
0
0
0
0
4
0
0
0
3
0
0
0
1
0
0
0
0
1
5
0
1
0
0
0
3
0
0
0
1
0
0
0
1
0
0
0
7
1
0
1
1
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
5
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
5
0
2
0
1
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
3
0
3
0
3
0
0
2
0
2
0
0
0
0
0
3
0
0
0
2
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
1
0
4
0
2
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
1
0
0
1
0
0
1
0
0
2
1
3
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
5
0
2
2
1
0
0
2
0
0
0
2
1
2
0
1
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
5
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
4
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
2
1
2
0
0
0
0
0
0
0
2
1
1
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
2
2
1
0
1
1
0
1
1
0
0
2
0
0
0
0
1
2
0
0
0
2
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
2
3
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
1
2
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
2
0
0
0
0
1
0
1
0
0
4
1
1
1
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
1
2
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
3
0
0
0
0
0
3
0
2
1
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
2
1
0
0
0
2
2
0
0
0
4
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
2
0
2
5
0
0
0
0
2
0
2
0
0
2
2
0
1
0
2
1
0
0
2
0
0
0
0
4
0
7
0
0
0
1
2
0
1
0
2
0
2
2
1
1
0
0
0
2
0
0
0
1
0
1
0
0
2
0
0
0
0
1
1
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
13
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
2
1
0
0
1
2
1
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
1
2
0
1
0
0
1
0
1
2
0
0
1
1
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
2
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
1
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
2
0
8
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
2
1
0
2
0
0
1
0
2
2
0
2
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
3
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
3
0
0
2
1
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
1
0
0
1
0
0
2
2
0
0
0
1
0
0
0
0
3
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
7
1
4
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
2
0
0
1
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
3
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
3
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
8
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
1
2
0
1
0
1
1
0
1
0
0
5
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
3
0
0
0
2
2
0
0
1
6
0
1
0
0
0
0
1
0
0
0
5
0
2
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
5
1
0
0
0
2
1
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
1
1
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
2
1
3
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
6
0
0
0
1
0
1
0
2
0
0
0
1
1
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
3
0
1
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
6
0
0
0
0
0
2
2
0
0
0
0
2
3
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
1
2
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
1
2
1
1
0
0
2
0
0
2
0
2
0
0
0
1
2
0
0
2
0
0
1
1
0
0
0
1
0
3
0
0
2
1
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
1
0
3
0
0
1
2
0
0
0
0
0
1
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
7
1
0
0
0
0
0
2
0
2
0
0
0
0
0
2
1
0
1
0
2
0
0
0
2
0
0
0
0
0
2
0
0
1
0
1
2
0
0
0
7
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
1
0
0
0
0
0
1
0
2
0
2
0
1
0
2
0
0
0
0
2
2
0
2
0
0
2
1
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
10
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
5
1
1
0
2
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
3
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
2
1
2
0
0
0
0
0
1
2
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
2
0
0
0
0
0
1
0
2
3
0
2
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
5
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
1
1
0
0
1
0
1
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
1
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
2
1
0
2
0
1
1
0
0
0
3
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
2
0
0
0
0
0
0
2
0
1
0
2
1
3
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
2
2
0
0
2
0
5
0
0
0
0
3
2
0
0
0
0
0
0
1
1
0
0
1
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
3
0
0
0
0
2
0
0
2
0
0
1
2
3
0
0
0
0
0
1
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
2
1
1
0
0
0
0
0
0
1
0
1
0
1
1
1
0
1
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
2
2
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
4
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
1
2
1
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
3
1
0
1
0
0
1
0
0
2
0
0
1
1
1
0
0
0
1
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
6
2
3
0
2
0
0
0
0
0
0
4
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
2
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
2
1
2
0
2
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
1
0
0
0
0
2
0
0
0
0
1
0
0
0
1
2
2
2
0
0
0
0
3
2
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
2
0
2
0
0
2
2
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
2
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
2
0
0
0
1
0
0
2
0
0
2
0
3
0
0
1
2
2
1
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
1
0
1
0
2
0
0
0
0
0
0
2
0
2
0
0
0
1
3
3
0
0
0
0
0
1
0
0
2
0
1
0
0
0
1
0
0
0
0
1
0
0
0
6
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
1
0
0
2
0
0
1
0
1
0
0
2
2
2
0
0
3
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
1
3
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
2
2
0
0
0
2
0
0
2
0
0
0
2
0
0
2
2
1
2
1
0
2
0
0
0
0
0
0
0
0
2
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
1
0
0
1
0
1
0
6
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
1
1
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
1
2
0
0
0
0
1
1
0
0
2
0
0
0
2
0
6
0
0
0
2
0
2
1
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
4
0
2
0
0
0
0
0
3
0
2
0
0
0
0
0
1
0
0
1
1
0
2
0
0
1
0
1
0
1
1
2
1
0
1
0
1
0
0
2
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
3
1
0
0
0
1
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
8
4
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
2
0
0
0
2
0
1
2
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
1
1
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
1
0
1
1
2
2
0
0
2
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
2
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
1
1
0
1
0
2
0
0
0
1
0
1
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
1
0
0
2
2
2
0
0
0
0
0
1
0
0
0
0
3
0
0
0
2
0
1
0
2
0
0
0
1
0
0
0
0
1
2
0
1
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
2
2
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
9
1
0
0
0
1
0
1
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
3
0
2
0
0
1
0
0
1
0
0
0
2
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
2
2
1
0
2
0
0
1
1
0
0
1
2
2
0
0
0
0
0
0
2
2
2
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
3
2
1
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
2
1
1
1
1
1
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
4
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
1
2
0
0
0
0
0
2
4
0
0
0
0
0
2
1
0
1
0
2
0
0
0
0
2
2
0
1
0
0
0
0
3
0
0
0
0
1
0
1
0
2
0
0
2
1
2
2
0
0
0
3
2
0
0
0
0
0
0
0
1
0
0
1
1
2
0
0
0
1
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
2
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
1
2
3
0
0
2
0
0
0
0
2
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
2
0
3
0
2
0
0
2
1
1
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
1
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
1
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
1
0
0
2
0
0
2
2
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
3
2
0
1
0
0
0
0
0
1
0
2
0
1
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
7
0
0
1
1
0
0
0
0
1
1
1
0
1
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
3
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
3
0
0
0
1
1
1
0
0
0
0
1
0
2
0
3
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
3
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
2
0
2
0
0
0
2
8
0
2
0
0
0
0
0
0
1
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
8
4
0
0
0
1
0
0
1
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
2
1
0
0
0
1
0
0
0
0
0
2
0
1
0
1
0
0
0
0
2
0
0
0
0
2
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
3
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
1
0
2
0
0
1
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
2
0
0
0
0
0
1
0
0
2
0
2
0
0
0
1
2
0
0
4
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
4
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
3
0
0
0
3
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
3
1
0
0
1
0
4
0
0
0
1
0
0
0
0
0
6
2
0
0
0
0
0
1
0
0
2
0
0
0
1
1
0
11
4
0
0
0
1
0
0
1
1
0
2
1
2
1
0
0
0
3
0
0
0
0
0
0
0
0
0
1
3
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
2
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
1
2
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
1
1
2
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
1
1
1
1
0
1
0
0
2
1
2
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
2
0
1
0
0
2
9
0
0
0
1
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
2
0
0
4
0
6
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
1
1
1
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
2
0
0
0
2
0
1
0
6
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
1
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
1
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
1
2
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
1
0
0
1
0
1
0
0
2
0
0
0
0
1
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
2
1
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
4
0
0
3
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
3
1
0
1
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
2
0
2
1
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
1
0
2
2
1
0
0
0
10
1
0
1
0
0
0
0
0
0
0
0
0
1
2
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
1
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
3
0
0
0
0
3
0
0
0
0
0
3
0
0
2
0
0
0
1
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
2
1
0
0
4
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
2
0
0
0
1
0
0
0
1
0
0
0
1
0
2
0
3
0
1
0
0
0
0
0
1
0
2
0
0
0
0
1
1
0
0
0
0
0
1
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
3
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
1
0
0
0
1
0
2
1
0
5
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
4
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
2
7
0
0
2
2
0
1
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
1
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
2
1
0
0
1
0
0
0
0
0
0
1
2
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
1
0
1
0
0
0
0
3
0
1
0
2
0
0
0
2
0
0
0
0
0
1
2
0
1
0
0
0
0
3
2
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
2
3
0
0
1
0
0
2
2
0
0
0
1
0
2
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
3
0
1
4
0
2
4
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
3
0
0
1
2
3
1
0
1
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
3
0
1
0
0
0
0
4
0
0
2
0
0
0
0
0
0
2
1
0
2
0
0
3
0
0
2
0
0
2
1
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
2
0
0
0
2
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
5
0
2
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
2
0
1
0
0
0
2
0
0
0
0
2
0
0
0
1
0
1
3
0
0
0
0
2
3
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
1
1
1
1
1
0
1
0
0
0
0
0
1
2
0
0
1
0
0
0
1
0
0
0
0
0
0
5
0
0
0
0
0
0
3
1
0
0
0
2
0
0
1
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
1
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
6
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
1
1
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
3
0
0
0
1
0
0
0
1
1
1
0
0
1
0
3
0
0
3
0
0
1
0
3
2
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
1
3
0
0
1
0
0
0
4
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
1
2
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
2
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
4
5
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
3
3
0
1
2
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
2
0
0
0
0
2
0
1
0
0
0
0
0
0
2
1
2
2
0
1
0
0
0
0
2
0
2
0
0
0
0
2
0
1
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
2
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
2
0
1
0
0
0
0
1
1
0
0
1
0
1
2
1
0
0
0
0
0
0
2
0
0
0
0
2
2
1
0
1
0
0
0
0
4
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
1
0
1
0
0
0
1
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
2
0
2
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
2
0
0
0
2
1
0
2
0
0
0
0
1
1
0
0
0
0
3
0
0
0
0
0
0
1
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
5
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
6
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
2
1
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
1
0
4
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
1
0
2
0
0
0
0
0
1
1
0
0
0
0
0
4
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
2
0
2
0
3
0
3
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
2
0
2
0
0
0
2
0
1
2
2
0
0
1
1
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
1
5
1
0
0
2
9
2
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
3
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
2
0
1
0
2
1
3
0
0
2
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
1
2
1
0
2
0
0
0
1
4
0
1
0
1
0
0
0
1
0
0
0
0
0
0
2
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
4
0
0
0
2
0
0
0
4
0
0
0
0
0
2
0
1
0
1
0
2
1
0
0
0
0
2
0
0
2
0
2
0
2
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
2
2
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
5
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
2
2
1
0
0
3
0
0
0
0
1
2
0
2
0
0
0
0
1
4
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
3
0
0
0
2
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
2
0
1
0
0
0
0
4
1
0
0
0
1
0
0
2
0
3
3
0
0
0
0
0
0
0
0
0
1
2
1
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
1
2
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
2
1
0
0
0
2
1
1
0
0
2
0
1
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
2
2
0
1
1
0
0
0
0
0
0
1
2
0
0
1
0
0
2
0
0
0
0
2
0
0
1
4
0
0
0
0
0
0
1
1
2
2
0
2
1
1
0
0
0
0
0
0
2
0
1
0
0
0
4
0
2
2
0
0
2
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
1
2
0
2
0
0
2
0
0
0
0
3
3
0
0
0
0
0
0
1
0
0
2
0
0
1
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
2
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
1
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
2
1
1
2
2
0
0
0
2
0
0
1
1
2
2
0
1
0
4
0
1
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
1
2
0
0
0
0
2
0
0
0
2
1
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
2
0
0
1
0
2
1
0
0
2
1
0
2
0
2
3
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
3
1
0
1
0
1
0
0
0
0
2
0
0
0
4
0
0
0
0
1
2
2
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
3
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
3
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
2
0
0
0
4
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
1
5
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
3
0
0
0
0
0
2
1
0
0
0
0
1
1
0
2
0
0
1
1
0
0
3
0
1
0
2
0
0
0
2
1
0
0
0
0
0
0
2
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
1
1
0
1
0
0
1
0
0
0
0
1
1
1
0
0
0
2
0
0
0
0
1
1
0
1
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
3
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
2
2
1
0
0
2
0
1
0
0
1
1
2
2
2
1
0
1
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
2
0
0
0
0
2
0
0
1
2
0
0
2
0
0
1
0
1
2
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
2
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
2
2
0
1
0
2
2
2
0
0
0
0
0
2
0
0
0
2
1
0
2
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
2
0
1
0
0
0
0
1
1
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
3
0
2
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
1
1
0
2
0
2
1
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
2
0
0
1
2
0
1
0
0
0
2
2
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
2
0
1
2
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
1
8
2
1
2
0
0
0
0
2
0
0
2
0
0
0
0
2
1
0
0
2
0
2
1
2
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
3
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
3
1
0
0
2
0
0
0
0
0
0
2
2
2
0
0
0
0
0
1
1
0
0
0
0
2
0
0
1
0
0
3
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
3
0
0
5
0
0
1
0
1
2
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
1
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
2
0
1
1
2
2
0
1
2
0
4
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
2
0
0
0
2
5
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
2
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
2
2
0
2
0
4
0
1
0
0
0
0
0
1
0
0
2
3
0
0
2
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
1
0
4
0
0
0
0
1
0
3
1
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
2
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
3
4
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
2
1
0
0
0
1
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
1
1
0
0
2
0
0
2
0
0
1
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
3
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
4
2
0
1
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
3
0
2
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
2
2
0
0
1
2
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
2
0
0
3
0
0
2
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
2
0
0
1
0
0
0
0
2
0
2
0
0
0
2
0
0
2
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
3
0
1
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
2
1
0
1
2
0
1
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
3
2
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
3
0
0
0
2
0
0
0
0
1
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
1
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
1
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
2
0
0
1
2
0
1
0
3
0
2
1
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
1
0
2
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
1
1
0
0
0
2
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
2
0
0
0
0
2
1
0
1
0
1
2
2
0
2
0
0
1
0
0
0
0
0
3
2
0
0
0
0
0
1
0
3
1
0
0
0
0
2
0
0
0
0
5
0
2
0
0
1
0
2
0
0
3
0
0
1
1
2
0
1
0
3
0
0
1
2
0
1
0
0
2
1
1
0
1
0
1
0
0
0
0
0
2
0
0
4
0
1
0
0
0
4
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
1
0
2
2
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
1
1
2
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
1
2
0
0
1
1
1
1
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
3
1
0
2
0
0
2
0
0
1
0
0
1
0
0
2
0
0
0
1
0
0
2
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
2
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
3
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
1
0
3
0
0
0
2
0
0
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
1
0
0
0
2
0
1
2
0
0
3
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
1
0
1
0
0
3
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
4
0
2
0
0
0
2
0
0
0
0
2
0
1
1
0
2
1
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
1
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
2
1
0
1
0
2
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
1
1
1
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
2
0
1
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
2
0
3
0
0
0
1
0
2
0
0
0
2
0
0
0
5
0
1
0
6
0
0
0
2
0
0
0
0
1
0
0
0
0
0
3
1
0
2
0
1
2
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
3
2
0
5
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
2
3
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
2
2
1
0
1
0
0
2
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
2
0
0
0
2
0
2
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
2
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
4
0
0
1
1
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
1
0
0
2
0
1
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
8
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
2
2
1
2
0
1
0
0
0
0
0
3
2
0
2
0
0
0
0
1
1
2
0
0
2
0
0
0
0
1
2
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
2
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
2
0
0
1
3
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
3
0
0
2
1
0
0
0
1
0
2
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
4
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
2
2
1
0
1
1
0
2
0
2
2
0
3
2
0
1
2
0
0
0
0
1
0
2
0
0
2
0
1
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
5
0
2
0
0
0
0
1
0
1
0
0
0
1
0
1
3
0
2
2
0
0
3
0
0
0
0
4
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
4
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
1
0
0
1
0
0
1
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
2
1
0
0
0
1
1
0
0
0
0
0
2
1
0
0
0
0
2
0
0
3
0
0
2
0
0
0
1
1
0
3
2
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
2
2
0
1
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
2
0
1
0
1
2
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
2
0
0
0
3
0
0
0
0
0
1
3
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
1
0
1
0
2
0
0
0
2
0
2
0
3
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
1
0
0
0
2
2
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
1
1
0
0
0
0
1
0
5
0
2
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
2
0
2
0
0
0
1
1
0
0
1
1
0
0
0
2
0
1
0
2
1
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
3
0
0
0
0
2
0
0
3
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
2
0
2
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
2
1
0
0
0
2
3
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
1
2
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
2
0
0
0
3
0
0
0
0
2
0
0
0
0
1
2
4
0
3
0
2
0
0
1
0
0
0
0
0
0
2
0
2
1
0
0
0
0
1
2
1
0
0
0
0
1
2
0
0
0
1
0
2
0
0
2
0
1
0
1
1
0
2
0
0
1
0
0
1
2
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
1
0
0
0
2
1
1
0
3
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
2
1
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
1
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
2
2
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
1
1
0
0
0
0
2
0
0
0
1
2
2
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
1
0
1
0
3
0
0
0
0
0
1
0
0
1
0
0
1
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
2
0
0
1
0
0
1
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
2
0
0
0
0
2
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
3
2
1
0
0
1
0
0
1
0
2
0
0
0
0
2
2
0
1
0
2
0
0
1
0
3
0
3
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
6
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
3
4
0
0
0
0
0
0
1
0
2
1
2
0
0
1
0
0
2
0
0
2
0
0
0
3
0
0
2
7
0
0
0
1
0
0
0
0
0
0
1
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
4
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
2
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
4
2
3
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
1
2
0
0
5
3
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
2
0
0
3
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
1
0
1
0
5
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
5
3
0
1
0
4
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
3
1
3
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
2
0
1
3
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
18
0
0
2
0
0
2
0
0
2
2
0
1
0
0
0
0
0
0
2
2
0
0
0
0
1
2
0
0
2
0
0
0
1
1
1
2
0
0
0
0
1
0
0
2
0
0
0
1
0
1
2
2
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
3
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
2
1
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
2
0
3
2
0
0
0
2
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
4
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
4
0
1
1
0
1
1
0
3
0
0
2
0
1
2
2
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
1
1
0
0
1
0
0
0
0
0
0
1
2
3
0
0
0
0
0
2
4
0
0
2
2
0
0
0
0
0
0
0
2
0
0
1
0
3
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
1
1
0
2
0
0
0
3
0
0
0
1
2
0
0
0
0
0
4
0
1
0
0
0
0
0
0
2
0
0
0
0
0
4
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
2
1
0
0
2
3
2
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
1
2
0
0
1
1
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
2
3
1
0
3
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
1
0
0
2
0
2
1
0
0
0
2
0
5
0
2
1
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
6
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
5
0
0
0
0
0
0
2
0
1
0
0
3
0
0
0
0
0
2
0
0
0
0
0
2
1
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
1
0
2
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
2
0
2
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
2
1
1
1
0
2
0
0
0
0
0
0
0
11
2
0
1
4
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
1
0
0
1
2
0
2
1
1
0
0
0
0
0
0
0
0
0
2
0
0
2
2
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
2
1
1
0
0
0
1
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
2
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
1
0
2
0
0
0
0
0
7
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
2
1
0
2
0
0
2
2
2
0
5
0
0
0
0
0
2
1
0
2
2
1
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
2
1
3
0
2
0
1
0
0
0
0
0
0
2
0
0
0
3
9
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
1
2
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
2
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
2
1
2
0
0
0
1
0
4
1
0
0
1
0
0
2
0
0
0
0
0
1
0
3
0
2
0
0
4
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
3
0
0
2
1
3
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
4
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
1
2
2
0
0
1
0
0
0
0
0
0
1
0
4
0
2
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
2
2
1
0
0
0
1
2
0
0
0
2
0
0
0
2
1
2
0
1
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
3
0
0
0
2
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
4
1
0
0
0
1
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
1
0
2
3
0
1
0
0
2
0
0
0
0
2
2
1
2
0
0
0
0
0
0
1
0
0
1
1
1
0
2
2
0
0
0
0
0
0
0
0
0
1
0
1
0
2
3
0
0
0
2
1
0
4
0
0
0
0
0
2
0
1
8
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
1
1
0
2
0
0
2
0
1
0
2
0
1
0
2
2
0
0
0
2
0
1
0
0
1
0
1
0
0
0
0
1
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
6
1
2
0
2
0
2
1
1
0
0
0
2
1
0
0
3
0
2
0
0
0
0
1
0
2
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
2
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
1
1
0
0
0
1
1
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
3
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
1
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
1
0
2
0
0
2
0
2
0
0
2
0
0
0
0
2
2
3
0
2
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
3
0
1
0
0
6
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
1
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
6
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
1
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
3
1
0
0
0
0
2
3
0
0
0
1
0
0
1
1
1
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
2
1
0
0
2
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
1
0
1
0
0
1
1
2
0
0
0
0
0
2
0
0
0
4
0
0
2
0
0
2
2
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
2
1
0
0
2
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
1
2
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
2
1
2
0
0
7
0
0
0
0
0
2
3
0
0
0
0
0
1
2
0
0
1
2
0
0
0
0
0
0
2
1
0
0
0
0
0
1
1
1
0
2
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
4
0
0
2
0
0
3
0
0
0
0
0
2
0
0
3
0
0
2
1
0
1
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
3
2
0
0
0
0
2
0
0
0
1
0
0
2
3
2
0
1
2
0
0
0
2
0
0
1
0
0
0
0
1
0
1
0
0
0
4
1
0
0
2
1
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
1
4
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
2
0
1
0
2
2
0
0
1
1
0
0
0
0
0
0
0
2
0
2
0
3
0
0
0
0
2
0
0
0
4
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
2
5
0
0
0
0
0
0
1
2
0
0
1
1
2
1
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
2
1
0
0
0
2
0
0
0
1
0
0
0
1
0
3
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
4
0
0
0
0
0
0
2
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
1
2
0
0
0
0
1
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
2
1
1
0
0
5
0
1
2
2
0
2
0
0
2
0
0
0
2
3
0
0
1
0
0
0
3
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
1
0
2
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
2
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
2
1
2
0
1
0
1
2
0
1
0
0
0
3
0
0
1
0
0
2
4
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
2
1
0
0
1
0
6
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
4
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
2
0
0
0
4
0
0
2
2
1
0
0
2
0
0
0
0
0
0
1
0
0
2
1
0
0
0
2
2
2
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
3
1
2
0
0
0
0
2
0
0
1
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
2
0
1
0
0
2
0
0
0
2
1
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
2
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
4
0
0
0
0
0
0
0
1
0
0
0
0
3
0
1
0
0
0
0
0
0
0
4
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
1
0
2
3
0
0
0
3
0
0
0
0
0
0
2
3
0
0
0
0
0
0
2
0
0
1
2
0
0
0
2
0
0
0
1
0
1
2
2
0
1
0
0
1
0
2
0
0
1
0
0
1
0
0
0
0
2
0
0
0
4
0
0
0
0
0
1
3
0
0
1
2
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
1
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
3
0
0
2
0
1
3
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
1
1
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
7
0
0
0
0
0
2
0
0
0
0
0
0
2
1
1
0
0
1
0
0
0
0
0
0
2
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
2
1
2
0
0
0
0
3
0
2
0
0
3
2
0
0
1
0
0
0
0
6
2
0
2
1
0
2
0
1
0
0
1
0
5
2
0
0
0
0
4
0
0
0
1
0
2
0
2
1
0
0
0
2
0
0
1
0
0
1
0
2
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
1
3
1
0
2
0
0
1
0
2
0
2
2
0
0
2
0
0
0
3
0
1
0
0
0
0
2
0
1
0
0
2
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
1
0
2
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
1
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
2
1
0
0
0
2
1
0
1
2
0
2
2
1
1
0
0
0
1
0
0
0
0
1
0
0
1
1
3
3
0
2
2
0
0
4
0
0
0
0
3
0
1
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
1
0
0
1
0
2
0
0
0
0
1
2
1
0
0
1
0
0
0
0
2
1
3
2
0
3
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
1
2
1
0
1
0
0
0
0
0
1
1
0
8
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
2
1
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
2
1
0
1
0
0
0
0
1
0
2
5
1
2
2
0
0
2
3
0
0
3
0
0
0
0
0
2
0
0
0
2
1
0
2
0
2
0
0
0
0
3
0
0
0
1
0
2
0
0
0
0
1
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
1
0
1
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
1
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
1
1
0
1
1
0
0
0
0
0
3
0
1
0
0
0
0
2
0
0
0
3
2
0
0
1
0
0
0
0
0
0
5
2
0
0
0
2
0
1
0
2
0
1
1
1
0
0
2
0
0
0
0
4
2
1
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
1
2
0
2
0
0
0
0
0
0
0
0
1
1
0
1
0
4
2
0
0
0
0
0
6
0
0
1
0
0
0
0
1
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
10
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
2
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
1
1
0
0
2
0
0
1
3
0
3
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
2
0
1
0
4
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
2
2
0
0
0
0
0
2
2
0
0
0
0
0
1
4
1
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
1
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
2
0
0
1
0
0
1
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
2
2
1
2
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
2
3
0
0
2
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
3
0
0
2
4
3
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
1
0
2
0
8
0
0
0
1
0
0
0
0
1
1
2
2
0
0
0
2
0
2
2
0
1
0
0
0
2
4
1
0
0
2
2
0
0
0
0
0
0
1
1
0
5
0
0
0
0
4
1
0
0
2
0
0
0
1
2
1
0
0
0
0
2
0
1
6
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
2
0
2
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
2
0
2
0
0
0
0
2
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
2
0
1
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
3
0
2
0
0
0
0
0
0
0
1
0
1
1
0
1
0
2
0
3
0
0
0
0
1
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
1
2
2
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
2
1
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
1
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
1
2
0
0
1
1
1
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
1
0
2
0
1
0
0
0
1
1
0
0
0
0
0
1
2
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
2
0
2
0
0
1
0
1
0
0
0
2
0
1
2
0
0
0
0
4
4
0
0
0
2
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
2
0
2
0
0
0
1
0
0
1
0
1
0
2
4
0
0
0
1
0
1
0
0
4
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
1
1
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
2
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
5
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
2
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
1
0
0
2
0
3
2
0
0
0
0
0
2
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
1
1
1
2
0
0
0
1
0
0
2
0
0
2
0
0
0
0
2
0
0
0
2
1
0
0
1
0
0
0
0
1
0
2
0
0
0
2
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
3
2
1
0
0
0
3
0
2
0
2
0
1
2
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
2
0
3
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
1
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
5
1
0
0
0
0
0
1
1
0
0
1
0
1
0
0
1
0
2
2
0
1
0
3
0
0
0
0
7
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
2
0
0
1
2
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
1
3
0
0
0
0
0
0
0
0
2
0
0
0
1
0
6
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
3
0
0
0
1
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
2
1
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
1
3
0
1
0
2
0
2
1
0
2
0
2
0
0
0
1
0
0
2
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
4
0
2
0
1
0
1
0
1
0
0
0
1
3
3
0
0
0
0
0
2
0
1
2
0
1
2
1
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
1
0
0
3
0
0
0
0
0
0
0
0
0
0
7
0
0
2
0
0
0
2
0
0
1
1
0
3
1
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
8
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
1
1
0
0
0
0
4
1
0
0
2
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
2
0
2
0
0
0
0
2
0
2
0
0
0
0
5
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
2
2
0
2
0
0
2
0
0
0
0
3
0
2
2
0
0
0
0
0
0
0
5
2
0
0
0
1
0
2
0
3
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
1
0
1
1
0
1
0
0
1
0
2
3
2
0
0
1
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
1
1
1
2
0
0
0
0
2
0
0
2
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
2
1
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
3
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
10
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
3
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
2
1
0
2
0
0
0
2
0
2
1
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
2
0
0
0
2
2
0
2
4
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
1
0
1
2
0
0
2
0
0
3
0
0
4
1
0
2
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
3
2
1
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
2
0
0
1
0
4
0
0
1
1
0
0
0
0
0
1
0
2
1
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
1
1
2
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
4
0
1
1
1
0
0
0
1
0
0
0
2
0
0
2
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
3
0
0
0
3
0
0
1
0
0
0
0
2
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
2
0
0
1
0
2
0
0
0
2
0
2
0
2
2
0
1
2
1
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
4
0
0
0
4
0
0
0
0
0
2
1
0
1
0
2
0
2
3
2
0
0
0
0
0
0
1
0
0
0
0
1
2
0
2
0
2
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
2
2
7
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
7
0
2
1
0
2
3
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
3
1
0
0
0
0
1
2
0
0
2
2
0
3
0
0
0
0
0
1
1
2
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
3
2
0
0
0
0
3
0
2
0
2
0
1
0
1
0
0
2
0
2
0
1
0
0
2
0
0
0
0
0
0
1
2
2
2
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
3
0
0
1
0
0
0
6
2
0
2
0
0
4
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
4
3
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
1
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
5
1
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
1
0
0
0
2
1
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
2
3
2
2
4
0
0
0
0
0
1
0
0
1
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
1
2
0
0
0
1
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
1
3
0
0
0
0
0
0
0
2
1
2
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
2
0
3
0
0
0
0
0
0
0
6
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
1
0
1
1
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
1
2
0
0
0
2
0
0
0
1
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
3
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
5
0
0
0
0
0
0
0
0
1
3
0
0
0
1
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
2
1
0
0
1
0
1
1
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
1
1
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
3
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
1
2
2
0
0
0
0
2
1
0
0
0
0
1
0
5
0
1
2
5
0
2
0
3
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
7
0
0
0
1
0
0
0
0
0
1
1
1
0
2
0
1
0
2
1
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
2
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
3
1
2
0
0
2
1
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
2
0
2
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
3
0
2
1
0
2
0
1
0
0
2
1
0
0
0
0
2
1
2
0
2
0
0
1
0
0
0
0
1
0
0
2
0
0
7
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
1
2
0
2
0
0
0
0
4
0
0
0
4
0
0
0
0
3
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
3
1
2
2
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
4
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
6
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
3
3
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
3
0
0
2
0
1
0
2
3
2
3
0
0
0
0
2
0
0
0
1
1
1
0
0
0
2
0
2
1
0
2
0
0
0
0
0
0
3
0
2
0
0
0
4
0
0
0
0
3
0
0
2
1
4
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
2
0
0
0
0
6
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
1
0
0
3
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
2
1
1
2
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
0
1
2
1
0
0
0
0
1
1
0
1
0
2
0
0
0
1
0
0
0
0
0
1
0
1
0
10
0
1
0
0
0
2
0
0
0
1
0
0
4
7
2
0
0
0
0
0
0
0
0
0
0
0
4
4
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
1
3
2
2
0
1
0
0
2
0
0
1
2
0
0
0
2
1
0
0
0
0
0
0
2
0
2
0
0
0
1
1
1
2
0
0
0
0
2
1
2
0
0
0
0
0
0
0
1
0
1
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
1
0
1
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
2
0
1
0
2
3
0
1
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
2
0
0
0
0
3
1
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
1
0
2
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
2
0
1
0
3
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
2
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
1
0
7
0
1
0
1
1
0
0
1
0
0
0
0
0
2
0
0
1
0
0
1
0
1
2
0
0
0
2
0
0
2
1
0
0
0
0
0
1
1
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
1
1
6
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
3
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
2
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
5
0
0
0
0
2
0
0
0
3
0
0
0
3
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
1
0
1
2
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
2
2
2
0
0
2
0
0
0
0
2
0
0
2
0
0
0
3
0
0
0
0
1
0
0
0
3
0
0
1
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
2
1
1
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
1
2
0
0
2
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
2
1
0
0
3
0
0
1
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
1
0
1
1
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
2
1
2
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
1
0
2
0
0
0
3
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
3
1
0
0
0
0
1
0
0
1
0
2
2
1
2
1
2
1
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
4
0
0
2
0
0
0
1
2
0
2
1
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
2
1
0
0
2
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
2
0
1
0
3
2
0
0
0
0
0
0
0
2
2
4
2
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
3
0
0
2
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
4
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
4
2
0
0
0
0
0
0
1
0
2
0
2
1
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
2
0
0
0
2
0
0
1
1
0
0
1
0
1
0
2
0
0
1
0
0
0
0
0
0
1
0
2
0
0
2
2
0
0
0
3
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
2
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
5
1
0
0
0
0
1
0
0
2
2
0
0
2
2
2
1
1
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
2
1
0
0
3
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
1
1
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
2
2
1
2
0
0
1
0
0
0
0
0
2
2
1
0
5
0
0
0
0
0
0
3
2
2
0
0
2
0
0
0
0
3
0
0
0
0
2
0
0
0
2
0
1
0
2
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
2
1
0
0
0
1
0
0
0
0
2
0
3
0
0
0
0
0
1
2
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
2
0
2
1
1
0
2
0
0
0
2
0
0
0
0
1
1
0
1
0
0
0
0
2
0
0
0
1
2
0
0
0
0
1
1
1
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
5
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
1
0
0
0
0
0
3
0
2
0
0
1
0
0
0
0
1
2
1
0
0
0
1
1
0
0
0
0
1
0
0
2
0
2
0
0
0
0
1
1
0
0
0
1
0
0
0
1
2
0
1
0
1
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
1
2
0
1
0
0
5
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
2
1
2
1
0
0
0
0
2
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
2
0
4
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
1
2
1
1
0
0
0
2
0
1
1
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
2
1
3
0
0
0
0
1
2
2
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
2
0
2
0
1
0
2
0
0
2
3
0
5
0
0
1
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
2
0
0
0
1
3
0
0
1
0
0
0
1
0
0
0
0
0
0
1
5
0
1
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
1
0
2
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
1
1
1
0
1
0
1
0
1
3
0
2
3
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
3
3
2
3
0
0
0
0
0
0
0
0
2
2
1
2
2
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
1
0
3
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
5
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
2
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
1
0
0
0
2
0
0
0
1
3
1
0
0
0
0
0
2
1
0
0
0
0
1
3
1
1
0
0
2
0
0
0
0
2
2
2
2
0
2
0
0
0
1
0
0
2
0
0
0
0
1
1
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
1
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
3
0
0
0
0
0
0
4
0
1
1
0
0
0
2
0
0
0
1
1
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
1
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
5
1
0
2
0
1
4
0
0
2
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
1
2
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
1
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
1
0
1
0
1
0
2
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
2
1
1
0
2
0
0
3
1
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
3
0
0
1
0
2
0
2
0
0
0
1
0
2
0
0
1
0
0
0
1
3
1
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
2
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
2
1
1
0
1
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
14
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
6
0
0
2
1
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
2
0
1
1
0
0
2
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
3
0
2
0
0
0
0
2
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
2
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
2
1
1
2
1
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
1
0
1
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
4
0
0
2
3
2
0
0
0
0
0
0
1
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
2
0
0
1
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
3
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
3
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
1
2
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
2
1
0
0
2
0
0
2
1
0
0
0
0
0
0
2
1
0
0
0
2
0
0
2
0
0
0
2
0
0
0
1
0
0
0
2
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
1
0
1
0
0
0
5
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
1
0
0
3
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
2
0
1
1
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
2
0
0
0
3
0
1
0
0
0
0
1
0
1
0
13
2
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
2
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
2
0
0
2
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
1
1
0
2
2
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
1
1
0
4
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
2
0
1
2
1
1
1
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
5
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
2
3
0
0
0
2
1
1
0
0
1
2
0
0
2
0
0
2
0
0
0
0
0
0
1
4
0
0
2
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
5
0
0
0
0
0
0
2
1
1
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
4
0
0
0
0
2
0
0
1
7
0
0
0
1
2
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
1
0
0
0
0
3
2
2
2
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
1
0
0
0
0
2
0
2
0
5
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
3
1
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
2
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
3
0
0
0
2
2
0
1
0
0
0
0
0
2
2
1
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
2
1
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
2
0
0
0
2
1
0
0
1
0
0
0
0
0
3
0
1
0
0
0
2
0
0
0
0
0
3
0
0
0
1
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
2
0
0
0
1
1
1
0
0
0
0
0
1
0
1
1
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
1
0
0
1
2
0
0
0
0
0
3
2
0
1
0
0
2
0
1
3
0
1
1
2
0
0
0
0
2
0
0
2
0
0
2
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
7
2
0
0
0
1
0
0
0
1
0
0
0
2
1
1
0
0
3
0
0
2
0
3
0
0
0
0
1
0
2
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
2
0
0
0
0
0
0
1
0
0
0
1
0
2
2
2
0
1
0
1
0
0
1
1
0
0
0
0
2
0
0
0
3
0
2
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
3
0
2
0
2
0
0
1
0
1
0
2
0
0
0
2
0
0
0
0
0
0
1
2
0
1
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
2
1
0
0
0
1
0
2
1
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
7
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
1
0
0
0
0
2
0
0
0
0
0
2
1
1
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
5
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
1
2
2
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
1
0
2
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
5
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
2
0
1
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
2
1
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
2
0
2
1
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
1
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
5
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
2
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
2
0
0
0
0
1
0
0
2
0
1
2
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
2
0
2
0
0
2
0
0
0
1
3
0
0
0
0
0
1
0
2
1
0
0
2
2
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
4
0
0
0
2
1
0
0
0
0
1
2
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
3
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
3
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
11
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
3
0
0
0
0
2
2
1
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
2
0
0
1
0
2
0
1
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
3
2
1
0
0
2
0
1
0
1
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
1
1
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
1
2
2
2
0
2
2
0
0
0
1
0
1
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
1
0
0
0
0
2
1
0
0
0
0
2
2
0
0
0
0
0
0
1
0
2
0
0
0
8
0
0
0
2
1
0
1
0
0
0
0
1
2
2
0
1
0
0
0
0
2
1
0
0
1
0
3
2
0
0
1
1
0
2
1
0
0
0
0
2
0
2
0
0
0
3
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
1
0
2
2
0
0
2
0
0
0
2
1
0
0
0
3
2
0
0
0
3
0
0
2
0
0
0
1
0
0
1
0
1
0
4
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
2
1
0
1
0
0
2
0
0
1
0
1
1
0
0
0
0
2
0
1
0
0
0
0
0
3
0
0
0
0
0
0
1
2
0
0
1
2
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
3
1
0
0
2
0
2
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
2
0
3
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
1
1
0
0
0
0
0
1
0
1
2
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
1
0
3
0
1
1
2
0
0
0
0
0
0
3
0
1
2
2
0
2
0
0
1
0
0
2
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
2
2
2
0
0
0
1
0
1
0
0
1
0
1
1
2
1
0
2
0
0
1
0
0
2
2
0
0
5
0
0
2
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
3
3
0
0
0
2
0
0
1
0
0
2
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
1
0
1
0
6
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
2
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
2
1
2
1
0
0
3
0
1
10
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
2
1
0
0
3
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
2
0
1
0
0
0
1
2
2
0
0
2
2
0
0
0
0
0
1
1
0
0
0
1
0
0
1
1
0
0
3
0
2
2
0
1
0
0
0
0
0
1
0
2
1
2
2
2
0
1
0
0
0
2
0
0
0
0
0
0
3
2
0
0
1
0
1
0
0
5
0
1
2
0
1
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
2
0
0
0
0
3
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
2
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
3
0
1
0
0
0
1
0
0
0
0
1
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
9
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
2
0
0
1
2
0
0
0
2
0
2
0
0
0
0
0
1
3
0
9
0
0
0
0
0
0
0
1
0
1
1
2
2
0
2
1
0
1
0
0
0
1
0
1
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
3
0
0
0
0
0
0
0
1
0
1
1
2
0
0
0
0
0
2
1
0
0
0
1
0
0
0
3
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
2
1
0
0
0
2
0
2
0
2
0
0
0
0
4
0
0
0
0
0
1
1
2
0
0
0
1
0
0
0
0
3
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
2
2
0
1
1
2
0
0
2
1
0
0
4
2
0
0
0
0
0
0
0
0
1
2
0
1
0
1
0
0
0
1
0
0
0
3
0
0
4
3
0
2
0
0
1
0
0
0
1
0
0
2
2
0
2
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
1
0
2
0
2
1
1
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
3
0
1
1
0
0
2
1
0
0
0
0
2
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
1
0
1
0
0
0
2
0
3
0
2
0
0
0
1
0
0
1
0
0
0
0
0
3
1
0
2
0
0
0
2
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
6
0
2
0
1
0
0
1
0
1
2
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
2
0
0
1
0
1
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
2
1
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
1
0
0
0
0
0
0
2
3
2
0
2
1
2
0
0
0
0
2
2
0
0
0
1
0
1
0
0
0
0
2
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
1
0
1
0
1
0
2
0
1
0
1
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
2
2
0
0
2
1
0
1
2
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
1
0
1
1
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
2
1
0
3
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
8
0
0
0
2
0
0
0
0
0
0
0
0
0
1
3
0
0
2
0
0
1
0
0
0
3
0
0
1
0
1
0
0
4
1
2
0
1
0
1
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
1
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
4
2
0
2
1
0
0
0
0
0
0
1
0
0
0
0
4
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
3
0
2
1
0
0
2
0
0
1
2
0
0
1
2
0
0
1
0
2
2
0
0
0
0
0
0
1
2
0
0
0
1
0
2
2
2
1
1
2
0
1
4
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
2
0
2
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
2
2
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
2
2
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
1
0
2
0
3
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
2
0
0
0
2
0
2
0
2
1
0
0
0
2
0
2
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
1
3
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
2
1
2
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
4
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
2
2
0
0
0
0
0
1
0
0
2
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
8
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
5
0
1
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
2
0
0
0
4
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
2
1
0
0
1
2
0
2
0
0
0
2
0
0
1
0
1
1
0
2
2
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
2
0
1
0
0
0
5
0
0
1
0
1
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
1
0
2
0
0
0
1
1
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
1
2
2
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
1
0
1
1
1
0
0
0
2
0
0
0
2
0
3
1
0
0
0
2
0
0
2
0
3
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
2
2
3
0
0
0
1
0
0
0
0
2
0
0
0
1
0
1
3
0
0
0
0
0
2
0
2
0
1
0
0
0
0
2
0
1
1
2
0
2
0
1
0
0
3
1
0
0
0
2
0
2
0
0
0
0
2
0
4
3
0
0
0
0
0
0
0
0
1
0
2
0
0
0
8
0
0
0
2
0
0
1
0
0
0
1
0
0
0
1
0
1
1
0
1
0
0
1
0
0
1
0
2
2
1
0
0
2
0
0
1
0
0
2
0
0
0
1
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
4
0
1
0
0
2
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
3
4
0
2
1
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
3
0
2
0
1
2
0
0
0
0
2
0
2
1
2
0
1
0
0
0
1
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
3
0
0
0
2
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
3
0
0
2
1
0
1
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
1
2
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
3
1
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
2
2
0
0
0
0
1
0
0
2
0
2
1
0
0
1
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
1
0
3
0
0
0
1
2
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
1
2
0
0
0
5
1
1
0
1
0
0
1
1
0
0
0
0
1
0
0
2
1
2
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
4
1
0
0
0
3
0
0
0
0
1
1
2
0
0
0
0
1
2
0
2
0
0
1
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
1
0
0
1
0
0
0
2
1
0
2
2
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
3
0
0
1
0
0
0
0
2
0
0
5
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
2
2
0
0
0
0
0
0
0
2
0
2
0
0
2
0
1
1
0
1
0
0
0
0
1
0
0
0
1
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
1
0
3
0
1
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
3
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
2
0
0
0
1
0
0
0
0
2
2
2
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
1
2
0
1
0
0
1
0
0
0
0
2
1
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
3
0
1
2
1
1
0
0
0
2
0
1
0
1
0
0
0
0
1
0
0
2
2
3
4
1
2
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
2
0
0
0
0
2
0
4
0
0
1
0
0
0
0
1
0
1
0
2
0
0
2
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
5
0
0
1
0
1
0
0
5
0
0
0
0
1
0
0
0
1
0
1
2
0
3
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
2
0
1
0
0
0
2
0
0
0
0
0
0
0
3
0
2
0
0
0
0
1
2
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
6
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
3
2
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
3
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
2
3
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
1
0
2
3
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
3
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
1
2
1
0
0
1
0
0
0
0
0
1
1
0
2
0
0
0
3
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
4
0
0
0
0
0
0
0
2
3
2
0
1
2
0
1
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
2
0
0
0
1
0
2
0
0
0
0
2
0
2
0
0
0
0
2
1
0
2
2
0
7
0
1
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
3
0
2
2
0
0
2
1
0
0
0
0
0
0
0
2
0
0
1
3
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
3
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
4
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
2
0
2
0
0
2
0
0
0
0
0
2
7
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
4
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
2
0
3
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
3
1
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
1
0
1
1
2
0
2
2
0
4
0
0
0
1
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
1
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
3
2
0
2
0
0
0
1
0
2
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
3
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
2
0
0
2
0
1
1
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
6
1
2
0
2
0
1
0
0
1
0
0
0
0
0
0
0
1
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
3
0
3
0
0
2
0
0
1
0
0
0
0
0
1
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
2
1
1
0
0
0
0
0
0
3
0
1
0
0
0
1
0
1
0
0
1
0
1
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
7
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
1
0
2
0
0
0
0
0
2
4
0
0
3
1
0
1
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
2
0
0
0
0
2
0
0
2
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
2
0
1
0
0
1
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
1
1
2
0
0
1
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
1
0
2
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
4
0
3
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
3
0
2
0
2
0
0
2
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
2
0
2
2
0
0
0
0
1
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
3
2
2
0
0
0
0
1
0
0
0
2
1
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
3
0
0
0
0
0
0
1
0
0
0
2
0
0
0
3
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
1
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
3
0
2
0
0
3
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
2
0
0
1
1
0
3
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
11
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
2
0
1
0
2
0
2
0
1
1
1
0
0
0
0
0
1
0
2
0
0
0
2
0
0
1
0
0
2
0
0
0
2
0
0
2
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
3
0
3
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
3
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
5
2
0
0
0
0
0
0
0
2
0
0
2
2
0
0
1
1
1
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
1
0
0
3
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
2
0
4
0
1
1
0
6
2
0
0
0
0
0
0
2
1
0
0
1
1
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
5
1
1
1
2
0
1
0
3
2
0
1
0
0
0
0
2
2
1
0
0
2
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
2
0
2
4
2
0
0
2
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
2
0
0
2
0
0
0
1
0
2
0
2
1
0
0
2
0
0
0
2
3
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
2
0
2
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
3
0
0
0
0
2
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
2
0
0
2
0
2
1
0
0
2
1
0
0
1
0
2
0
4
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
2
0
3
0
0
0
0
0
0
2
0
0
2
1
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
6
1
0
0
0
0
0
0
1
6
2
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
1
0
2
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
2
1
0
2
0
1
0
0
2
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
2
2
1
0
0
0
0
0
0
0
0
0
10
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
2
0
0
2
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
2
0
0
2
0
1
2
0
4
0
0
0
0
0
0
7
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
2
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
2
0
0
0
0
1
1
0
4
0
0
0
1
2
1
1
0
0
0
3
0
0
0
1
0
0
1
1
0
0
1
0
1
1
1
0
1
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
2
2
0
0
1
1
0
0
0
2
2
1
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
2
2
0
0
1
0
0
1
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
1
1
2
0
0
0
2
0
0
0
0
0
2
0
0
2
0
2
0
1
0
0
0
2
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
2
2
0
1
2
1
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
2
0
1
1
0
0
1
0
0
2
0
0
13
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
3
1
0
0
0
2
0
0
0
0
1
2
0
2
1
0
1
0
1
1
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
1
1
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
3
0
0
2
0
2
7
2
0
0
1
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
2
0
0
0
35
0
2
0
0
0
0
2
0
3
0
0
0
2
2
0
0
4
1
0
0
0
0
0
2
0
2
3
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
1
1
1
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
1
1
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
2
1
0
0
2
0
3
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
1
0
2
1
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
2
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
2
1
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
1
2
1
1
0
0
0
2
0
1
0
0
2
1
0
1
0
0
0
0
0
2
0
2
0
2
2
0
2
0
0
0
0
3
1
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
3
2
2
0
0
1
0
0
0
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
2
2
0
0
0
2
0
1
0
1
0
0
0
2
0
0
0
3
0
0
0
0
0
2
0
0
0
0
1
1
1
0
0
0
2
0
2
5
0
2
0
1
0
0
0
1
0
0
0
1
2
0
0
3
0
3
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
3
0
1
1
0
0
0
1
1
0
2
0
0
0
0
1
0
0
2
2
1
1
0
0
2
0
0
2
2
0
5
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
1
0
3
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
2
1
0
0
1
0
0
0
0
0
0
1
2
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
2
1
3
1
0
0
0
2
0
2
1
0
2
2
2
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
3
0
0
1
0
0
2
1
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
2
0
0
0
0
1
0
2
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
3
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
6
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
2
0
0
5
0
0
0
0
0
2
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
1
2
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
1
0
0
0
1
2
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
1
0
0
0
1
1
3
0
2
0
0
0
0
0
1
0
3
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
4
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
1
3
1
2
0
0
0
0
0
2
0
0
0
0
3
0
0
2
0
0
0
0
2
2
2
0
0
1
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
2
0
0
0
2
2
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
1
1
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
1
2
2
1
2
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
4
0
0
2
0
1
2
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
4
0
0
1
3
2
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
2
2
0
0
0
0
0
1
1
2
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
2
2
2
0
3
0
0
2
2
0
0
2
0
0
0
0
2
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
2
1
0
0
3
0
0
0
1
0
0
1
0
0
0
0
0
0
2
3
1
0
0
2
0
1
1
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
5
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
1
0
0
0
2
0
0
0
0
0
1
1
0
0
1
0
2
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
2
3
0
0
1
0
0
0
2
0
0
2
0
3
0
0
0
0
2
2
0
1
2
0
0
0
2
0
0
0
0
0
0
5
0
2
0
2
0
0
0
0
4
0
0
0
2
1
0
0
2
2
0
0
0
0
3
0
0
0
0
2
1
0
2
0
1
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
3
0
2
2
0
0
0
2
0
0
0
0
0
1
0
0
0
3
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
2
2
0
0
0
1
0
0
3
0
0
1
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
1
5
0
1
0
3
1
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
5
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
2
2
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
1
0
0
2
1
0
0
2
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
1
1
0
2
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
3
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
1
0
0
0
0
3
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
1
3
0
0
1
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
1
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
3
1
5
0
0
0
1
0
0
1
0
0
0
0
1
0
2
0
0
1
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
1
0
2
2
0
0
0
2
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
3
0
2
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
3
0
0
0
0
0
2
0
0
0
0
2
1
1
2
0
0
1
0
3
0
0
0
0
0
2
0
1
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
3
0
0
1
0
0
0
3
0
2
0
0
4
0
0
1
0
0
2
0
0
2
0
2
2
2
0
0
0
2
0
3
2
0
0
1
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
1
2
0
2
0
1
0
2
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
2
0
0
2
0
1
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
2
2
0
0
0
2
0
2
0
0
0
0
0
0
1
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
4
1
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
3
1
5
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
2
0
2
1
0
1
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
2
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
2
2
0
1
1
0
2
0
0
0
1
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
1
0
0
3
1
2
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
2
0
1
0
0
1
0
0
0
2
2
0
0
0
0
0
0
2
0
0
2
0
7
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
4
0
0
0
0
0
0
2
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
1
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
2
0
0
0
0
0
0
1
1
0
0
1
2
0
2
0
1
0
3
0
2
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
3
2
2
0
0
0
0
0
2
0
2
2
0
0
1
0
2
1
0
0
0
0
3
2
0
0
1
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
2
2
0
0
0
1
2
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
1
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
2
0
0
0
0
0
0
3
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
4
0
0
0
0
0
2
2
0
0
0
0
0
3
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
2
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
3
0
0
0
0
2
1
0
0
0
0
0
0
2
0
2
0
0
2
1
0
0
0
0
0
3
0
0
0
1
0
0
2
2
1
0
0
0
0
1
0
2
3
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
1
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
1
0
1
3
0
0
0
0
0
0
0
4
1
2
0
0
0
0
1
0
1
3
1
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
2
0
2
0
0
0
0
0
0
0
3
2
0
1
3
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
1
1
0
0
0
3
0
0
0
0
0
5
0
0
0
0
3
1
0
0
0
0
0
2
1
2
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
1
3
0
0
0
0
0
0
1
0
2
1
2
0
2
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
4
0
0
1
0
0
2
2
0
1
0
0
0
0
0
0
0
3
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
4
0
0
2
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
3
0
1
2
0
0
0
0
2
2
9
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
1
2
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
2
0
1
0
0
0
0
1
0
2
0
0
2
1
0
1
1
0
0
0
0
0
1
0
0
0
0
4
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
1
1
2
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
2
0
2
0
0
2
0
0
0
2
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
2
1
1
0
0
0
0
0
2
0
0
0
1
2
0
0
0
4
3
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
1
2
0
0
0
2
0
2
0
0
1
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
2
0
0
1
1
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
1
3
1
0
2
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
4
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
2
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
1
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
3
2
0
0
0
2
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
5
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
3
0
0
0
0
1
2
1
0
1
0
0
0
0
1
3
0
0
0
0
0
2
3
0
0
0
0
0
0
2
0
7
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
4
2
0
0
0
0
0
0
1
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
4
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
1
0
0
0
0
0
0
1
0
2
0
0
0
2
2
1
1
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
2
1
2
0
3
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
4
3
2
0
1
0
1
2
0
0
0
0
1
1
0
0
0
2
1
0
0
2
0
0
2
0
2
0
0
0
0
0
0
2
2
0
0
4
2
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
5
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
1
2
1
0
0
0
0
1
0
2
0
1
0
0
0
0
1
0
2
0
0
1
0
0
0
1
0
0
1
2
0
0
0
0
2
0
0
2
2
0
2
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
1
0
2
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
5
2
0
1
0
0
0
1
0
1
0
0
0
1
0
2
0
0
2
0
0
0
2
1
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
8
0
1
0
0
2
1
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
2
0
1
0
0
0
2
2
2
0
0
0
0
0
0
1
0
0
0
3
0
1
0
3
0
6
0
2
3
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
2
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
2
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
6
0
0
0
1
0
0
0
1
2
0
0
0
1
0
2
0
0
0
4
0
0
2
2
0
0
2
0
0
0
1
1
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
2
2
0
0
1
0
1
0
0
1
0
1
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
3
0
0
2
0
0
4
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
1
1
3
2
0
2
1
2
0
1
0
3
0
1
0
0
0
2
0
2
0
0
0
0
0
0
4
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
1
2
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
1
2
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
1
1
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
4
0
0
0
0
2
0
0
1
1
0
0
0
0
0
4
2
1
1
0
0
2
0
1
0
3
0
0
0
0
0
0
1
0
0
0
1
2
1
1
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
2
1
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
5
1
0
0
1
0
2
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
1
1
3
0
0
0
0
1
0
1
1
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
3
0
2
0
1
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
1
2
2
0
0
2
0
0
0
0
0
0
0
1
1
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
2
0
0
1
0
0
1
0
0
1
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
1
4
2
0
0
0
0
0
1
0
0
0
0
2
1
4
3
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
2
0
2
1
0
0
0
1
0
0
0
4
1
0
0
0
0
0
2
0
2
0
0
1
0
0
0
3
0
0
0
0
1
1
0
0
1
0
0
1
2
0
0
1
2
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
3
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
5
0
1
0
2
0
0
0
0
5
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
2
3
0
0
3
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
2
3
0
2
0
0
1
0
0
1
0
0
1
0
2
0
0
0
0
0
0
3
0
2
1
0
0
0
0
2
1
2
0
0
0
0
0
3
1
0
0
1
0
0
0
0
0
1
2
0
1
1
0
0
7
0
0
0
0
2
0
0
0
0
2
1
0
0
2
0
0
2
0
2
0
0
2
0
0
0
0
0
2
0
4
0
0
0
2
0
1
0
2
1
0
0
0
0
0
0
1
1
0
0
1
1
0
5
0
0
0
0
0
2
0
1
0
2
0
0
3
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
1
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
2
0
0
2
0
0
0
0
2
0
1
2
2
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
1
1
2
0
0
2
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
1
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
6
0
0
2
0
0
0
0
2
0
0
1
0
2
0
0
0
0
1
0
0
0
2
1
2
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
3
0
2
0
0
0
1
2
0
0
0
1
0
0
2
0
0
0
0
2
1
1
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
3
0
0
4
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
3
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
2
1
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
2
1
1
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
1
1
2
0
0
1
0
0
2
1
0
0
0
0
0
2
0
0
1
0
0
0
2
1
0
4
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
1
0
2
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
1
0
0
0
1
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
2
2
0
0
0
0
1
0
1
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
5
0
0
3
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
2
3
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
1
1
3
0
0
2
0
1
0
2
0
1
0
2
4
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
1
0
0
3
0
0
0
2
0
0
0
2
0
0
3
0
1
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
1
0
0
0
0
0
2
0
1
2
0
0
0
0
2
0
0
0
2
2
1
0
0
0
0
0
0
0
2
0
1
2
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
2
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
1
0
1
2
0
1
1
2
0
1
2
0
0
0
0
0
0
0
0
1
2
1
2
2
0
0
2
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
3
2
0
0
3
1
0
0
0
1
0
0
0
0
0
0
2
1
0
2
0
0
1
0
0
0
1
0
7
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
2
2
0
1
0
1
0
0
2
0
0
0
2
0
1
3
0
0
1
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
1
0
0
1
1
3
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
1
0
0
0
0
0
0
1
0
0
0
1
11
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
2
1
0
2
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
2
0
1
1
0
3
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
3
0
0
2
4
0
7
0
0
2
1
1
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
1
0
2
0
0
0
0
0
0
3
0
2
0
5
0
0
4
0
0
0
2
0
0
1
0
1
0
0
0
1
0
0
1
0
1
1
0
0
0
0
2
0
0
0
3
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
3
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
1
0
2
0
0
0
0
2
0
1
0
0
0
1
2
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
2
1
1
0
1
0
1
0
0
0
0
1
0
2
1
2
0
0
0
0
1
0
0
1
2
0
0
0
1
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
1
2
0
0
0
0
0
0
0
0
1
1
0
0
0
4
0
0
0
0
0
1
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
2
0
0
2
2
0
2
0
0
1
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
6
0
0
4
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
2
2
2
0
0
0
1
2
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
3
0
0
0
0
0
0
2
1
2
0
1
2
2
0
2
0
1
0
0
0
1
4
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
2
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
3
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
1
2
0
1
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
3
0
0
0
1
0
0
3
0
2
1
0
0
2
1
0
1
0
1
0
1
0
1
0
2
0
1
2
0
0
0
0
0
0
1
0
2
0
0
1
2
0
0
0
2
1
0
0
2
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
3
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
2
0
0
0
0
0
1
0
0
1
1
2
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
1
2
4
0
0
0
1
0
0
0
0
0
2
0
0
1
1
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
1
1
2
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
2
0
0
0
0
0
0
2
1
0
0
0
2
0
1
0
3
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
3
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
2
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
3
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
2
0
4
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
2
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
1
0
2
1
1
0
0
0
0
0
0
0
1
2
0
2
4
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
1
2
0
3
2
1
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
1
0
1
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
2
0
0
2
0
1
2
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
4
0
0
0
0
0
2
0
0
2
0
0
2
0
0
2
0
0
0
0
5
0
0
0
0
0
0
0
0
0
1
1
0
3
0
4
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
2
1
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
5
0
0
1
0
4
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
2
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
2
0
0
0
2
0
1
0
0
7
3
3
0
1
0
2
0
0
0
0
0
3
0
0
0
0
0
5
0
1
0
0
0
0
0
0
1
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
2
2
0
0
0
1
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
4
2
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
2
0
2
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
1
1
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
2
0
0
1
0
6
0
0
3
0
0
1
1
0
0
0
2
0
0
0
2
0
3
0
0
1
2
0
0
0
0
1
0
0
0
4
0
1
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
1
0
1
2
0
0
0
0
1
0
0
2
0
0
1
0
8
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
3
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
1
2
0
2
0
0
0
2
0
0
1
1
2
0
0
1
2
0
0
0
0
0
1
2
0
0
0
0
0
6
0
0
0
2
0
0
1
0
0
0
0
0
1
2
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
2
1
2
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
2
2
0
2
2
1
1
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
1
0
0
0
0
1
1
0
1
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
1
0
1
0
0
1
0
0
2
0
4
0
0
0
0
0
0
3
1
0
0
2
2
0
0
0
1
2
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
2
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
1
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
2
0
0
0
0
4
0
1
0
0
0
0
2
0
0
0
0
2
2
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
1
1
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
2
2
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
2
1
0
1
0
0
0
1
0
1
0
2
0
0
0
2
0
0
0
2
0
3
1
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
3
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
6
0
1
0
0
0
0
1
0
3
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
2
1
3
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
4
0
2
0
0
0
0
2
0
0
0
0
0
3
1
0
1
0
0
0
3
0
2
0
0
0
0
0
2
2
0
0
0
2
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
2
0
1
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
3
0
1
0
0
0
1
5
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
2
1
0
0
2
0
0
1
0
0
0
1
0
0
4
0
0
0
0
0
0
0
2
0
2
0
0
3
0
0
2
2
1
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
1
0
1
0
0
2
2
0
0
2
0
0
0
0
0
2
0
0
0
0
1
1
1
2
0
2
2
0
1
0
0
0
1
0
0
0
1
0
0
3
1
0
1
0
2
0
0
0
0
1
1
2
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
1
0
2
0
0
0
0
0
6
0
2
0
0
0
0
0
0
0
0
0
1
2
2
0
1
1
0
2
0
1
0
0
2
2
2
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
2
0
0
0
0
0
1
2
3
2
0
0
0
0
0
1
1
0
2
0
0
0
2
2
0
0
0
0
1
0
2
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
1
0
0
0
2
0
0
1
0
0
1
2
0
2
0
2
1
0
7
0
0
1
0
0
0
0
0
3
0
0
2
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
1
0
2
0
1
0
2
0
1
1
1
1
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
1
0
0
2
0
0
2
0
0
1
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
2
1
0
1
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
2
0
1
2
0
1
0
0
2
0
0
0
0
4
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
2
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
1
2
2
0
2
0
1
1
0
0
0
2
1
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
2
0
0
0
2
1
0
0
1
1
5
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
4
0
0
0
3
2
1
3
2
0
0
0
0
5
0
3
1
2
0
2
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
2
4
0
0
0
1
0
0
0
0
1
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
3
0
1
0
2
1
0
0
3
1
1
0
0
1
0
0
2
1
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
6
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
1
0
0
3
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
3
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
3
0
2
0
0
0
0
0
0
0
2
0
4
0
6
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
3
0
0
1
0
1
1
0
0
0
3
1
2
0
0
0
0
1
2
0
0
0
1
3
0
0
0
0
0
1
2
3
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
1
1
0
0
0
1
2
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
5
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
2
2
0
0
3
2
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
3
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
2
7
0
0
2
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
2
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
3
0
1
0
0
0
2
0
0
0
2
1
1
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
1
1
2
1
0
0
1
0
0
0
0
1
0
2
2
0
0
0
0
2
0
1
0
0
2
0
0
0
0
2
2
0
2
0
0
0
0
0
1
0
0
0
0
1
3
0
0
2
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
1
0
1
2
0
0
0
0
2
2
0
0
0
0
2
0
2
0
0
0
0
2
1
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
1
0
6
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
3
2
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
3
0
0
0
0
2
0
1
0
0
0
0
2
0
0
2
0
0
1
0
0
2
1
2
1
2
2
0
1
0
1
0
0
0
0
2
0
1
1
0
0
0
2
0
0
0
1
0
1
2
3
0
2
0
0
1
0
1
0
1
0
0
0
0
0
9
2
1
0
1
0
2
1
0
0
0
0
0
4
0
2
0
0
0
0
3
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
2
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
8
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
2
1
2
0
0
0
0
0
4
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
2
0
0
0
0
1
0
1
3
0
0
0
0
0
0
1
0
1
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
2
2
0
7
0
0
0
2
0
0
0
0
2
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
1
0
0
1
1
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
8
1
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
9
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
4
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
2
1
0
2
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
1
2
0
0
0
1
0
0
1
0
0
0
0
2
1
0
2
0
2
0
0
0
0
2
1
0
2
1
1
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
2
2
0
2
1
2
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
2
0
0
0
2
1
1
0
1
0
0
2
1
0
0
0
3
0
2
2
2
0
0
2
0
0
0
0
0
0
3
4
0
0
2
0
2
1
0
0
0
0
2
0
0
0
0
0
0
2
3
1
2
0
0
0
3
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
1
2
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
8
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
2
0
2
1
0
0
0
4
1
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
2
2
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
1
0
0
2
1
2
0
5
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
1
0
0
0
1
1
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
3
0
2
2
1
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
1
1
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
1
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
1
0
3
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
1
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
2
1
1
0
0
1
0
0
0
0
2
0
0
1
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
1
0
0
0
2
1
0
0
0
0
0
4
0
0
0
0
0
0
4
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
3
1
0
0
0
2
0
0
1
0
0
1
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
2
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
1
0
0
0
0
0
2
8
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
2
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
5
0
4
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
1
0
0
0
1
5
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
9
0
0
0
0
0
0
0
1
0
1
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
3
0
0
1
1
0
2
2
0
0
4
0
3
0
0
1
2
0
0
0
1
0
2
0
3
0
0
0
2
0
0
0
0
0
2
0
3
0
2
0
1
1
0
7
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
2
1
2
0
1
0
0
0
2
0
1
0
0
0
0
0
0
1
0
2
0
1
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
2
0
0
0
2
1
0
1
1
0
1
0
0
3
0
0
0
0
0
2
1
1
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
4
2
1
0
0
0
0
0
0
0
0
0
1
0
0
3
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
1
1
2
2
3
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
4
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
3
0
3
2
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
2
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
2
2
0
4
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
1
1
0
0
0
3
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
2
0
0
1
0
1
0
1
1
0
0
0
0
2
2
0
0
0
0
2
2
0
2
0
0
1
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
3
0
1
0
0
0
0
0
0
0
0
0
1
0
0
3
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
1
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
3
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
1
0
0
0
0
1
1
2
0
1
0
0
0
3
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
5
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
2
0
0
2
2
0
0
0
1
2
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
2
1
0
0
2
2
0
0
0
0
0
0
4
0
0
0
2
0
1
2
1
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
9
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
2
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
2
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
3
2
0
1
0
0
1
0
0
1
0
2
2
0
0
0
0
1
2
0
0
2
0
0
1
0
0
3
0
0
0
1
0
0
0
0
0
0
4
0
1
0
2
0
0
0
1
1
0
1
2
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
3
1
3
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
1
3
1
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
3
0
0
0
1
0
0
0
2
0
0
1
1
0
1
2
7
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
1
1
0
0
0
2
1
2
0
0
2
3
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
3
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
3
1
2
0
1
1
0
0
0
1
2
0
0
0
0
0
0
0
2
0
2
0
2
0
1
0
0
1
1
0
1
0
0
0
0
0
4
0
0
2
0
0
0
0
0
2
0
0
1
0
1
1
0
0
0
0
0
0
1
0
6
0
1
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
3
0
1
0
3
0
0
0
0
0
0
0
0
2
0
2
0
1
2
0
0
0
0
0
0
0
0
1
4
3
0
2
0
2
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
4
0
1
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
2
0
2
1
0
0
1
2
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
3
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
4
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
2
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
2
2
0
0
0
0
2
0
2
1
1
2
0
0
1
1
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
2
2
0
1
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
2
2
0
0
2
1
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
1
0
1
0
0
1
0
1
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
6
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
1
0
2
1
0
1
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
3
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
7
1
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
1
0
0
1
1
2
0
0
0
2
0
0
2
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
4
1
0
0
0
0
0
2
1
1
1
0
0
3
0
0
2
0
2
0
0
2
0
1
0
1
0
0
2
2
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
2
1
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
1
0
0
2
0
1
0
3
0
1
2
1
0
2
1
2
0
0
0
0
0
0
0
0
1
2
2
0
0
1
0
1
0
0
0
1
0
0
0
0
2
0
0
0
1
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
1
2
1
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
2
2
1
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
2
2
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
2
0
1
0
1
0
0
0
0
2
0
0
0
2
2
0
0
1
1
0
0
0
2
0
0
1
0
0
0
0
1
2
0
2
0
0
2
0
1
0
1
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
1
2
0
1
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
2
1
0
0
4
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
1
0
0
0
0
0
1
0
0
1
0
0
0
2
1
0
2
0
0
0
0
0
0
2
0
0
0
0
3
0
1
5
0
0
0
1
3
0
0
0
1
1
2
1
0
2
0
2
0
0
1
0
1
2
0
0
2
2
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
2
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
1
0
6
0
0
1
0
0
2
0
2
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
2
0
0
1
0
0
2
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
2
0
1
0
0
1
0
6
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
1
1
0
0
0
0
3
3
0
0
0
0
0
0
1
1
1
5
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
2
1
0
0
2
0
0
0
0
2
3
0
3
2
0
0
0
0
1
1
0
0
2
0
0
0
2
1
0
1
0
2
0
1
0
0
1
0
0
0
3
3
1
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
2
2
1
0
0
0
0
0
0
0
0
3
1
0
3
0
0
0
0
0
1
0
0
1
1
0
0
0
4
2
1
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
3
0
0
0
2
1
2
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
1
0
2
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
3
0
0
1
0
3
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
2
0
1
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
1
0
2
1
0
0
0
5
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
2
1
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
2
4
0
0
0
0
1
0
0
0
0
2
0
1
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
1
2
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
1
0
0
1
0
0
0
1
1
1
3
0
0
0
0
0
0
0
0
1
0
0
0
3
0
1
0
1
0
0
0
0
1
0
1
2
0
3
0
0
2
1
0
0
1
0
0
0
0
1
0
1
0
2
0
1
0
0
0
0
2
0
2
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
8
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
2
1
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
2
0
2
2
0
1
0
0
0
3
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
1
5
1
0
2
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
1
2
2
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
2
0
0
1
0
0
2
4
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
2
2
0
0
0
1
0
1
0
1
3
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
3
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
1
1
0
0
1
0
0
0
2
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
2
1
1
1
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
1
0
0
2
0
1
2
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
3
0
0
0
0
2
0
0
1
0
0
0
0
0
2
8
2
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
2
0
2
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
3
0
1
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
1
0
1
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
2
0
0
2
0
0
0
0
1
2
3
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
1
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
2
0
2
0
0
1
0
2
1
0
0
0
0
0
0
2
1
2
0
2
0
0
0
0
0
1
0
2
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
2
0
0
0
2
3
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
1
0
0
0
0
3
0
0
0
0
1
0
2
0
0
0
0
2
2
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
2
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
3
0
0
2
0
0
2
0
0
0
2
0
1
2
1
1
2
0
0
2
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
3
0
2
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
2
0
0
0
4
0
0
2
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
1
0
0
1
0
2
0
0
2
1
1
0
0
0
3
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
3
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
2
0
0
1
0
0
0
0
2
2
0
0
5
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
3
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
2
2
0
0
0
0
0
1
1
0
0
1
0
1
1
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
1
3
3
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
3
0
0
0
0
0
0
0
2
2
3
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
1
0
0
2
0
0
0
1
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
2
1
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
2
1
0
0
2
2
0
0
0
0
1
0
0
2
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
5
0
0
0
2
0
0
0
0
0
1
0
0
2
4
0
2
0
0
3
0
0
0
0
0
0
0
0
0
3
2
0
2
0
0
1
0
0
2
0
0
2
0
0
0
2
0
1
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
1
0
2
2
0
0
1
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
1
1
0
2
2
0
2
0
0
2
3
0
1
1
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
1
2
0
0
2
0
1
1
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
2
0
2
0
0
1
2
0
0
7
0
0
1
0
2
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
4
3
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
3
0
0
1
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
3
2
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
1
1
0
2
0
0
0
0
0
2
0
0
0
0
2
2
0
0
2
0
2
0
0
0
0
0
1
0
0
1
0
1
0
0
3
0
2
0
1
1
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
2
2
2
2
0
0
0
0
0
0
0
0
3
4
1
0
1
2
3
0
0
5
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
3
0
0
2
0
0
0
0
2
0
0
1
0
0
1
0
1
2
0
0
0
0
0
0
2
1
1
0
0
0
2
3
0
8
0
0
0
0
2
0
0
0
2
0
0
0
6
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
1
1
2
2
1
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
2
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
2
0
0
0
5
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
1
0
1
0
1
2
2
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
3
0
1
2
0
1
0
1
4
0
0
2
2
1
2
2
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
1
1
0
2
0
0
0
6
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
2
0
0
0
2
0
3
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
2
2
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
2
0
2
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
2
2
0
0
0
0
0
0
1
1
3
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
2
2
0
0
2
0
0
2
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
3
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
2
2
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
2
0
0
0
0
0
1
5
0
0
0
0
1
1
0
2
1
0
2
0
2
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
1
0
0
1
0
0
0
0
2
0
3
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
1
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
3
4
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
1
0
1
0
2
0
0
2
0
0
0
0
0
0
0
3
2
2
0
0
0
4
0
2
0
0
0
4
1
3
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
4
0
0
0
2
0
1
0
0
1
0
0
1
0
3
1
1
0
0
0
1
0
0
0
0
0
1
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
7
2
0
0
0
0
2
0
0
0
0
0
0
2
2
2
0
0
0
0
2
3
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
1
2
0
0
0
2
0
1
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
3
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
9
1
0
6
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
3
0
0
0
2
0
0
0
0
0
0
2
1
0
0
4
0
0
0
0
2
0
0
1
2
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
2
0
0
1
0
1
0
0
0
0
0
0
2
0
7
1
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
2
0
0
0
0
7
2
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
1
0
0
0
0
0
1
0
2
1
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
1
0
2
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
2
0
0
0
0
3
0
0
2
2
0
0
0
0
1
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
1
0
0
0
0
1
0
0
0
3
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
1
1
2
0
0
0
6
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
2
0
0
1
0
2
0
0
1
0
2
0
2
0
0
0
0
1
0
2
0
0
1
0
6
0
1
0
0
0
2
0
0
0
0
1
0
0
2
0
0
4
0
0
0
0
0
0
2
0
2
0
1
0
2
0
0
1
1
0
1
1
1
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
1
2
0
2
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
5
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
2
0
1
3
2
0
1
0
0
2
0
0
3
0
0
0
0
2
0
0
3
0
0
2
0
1
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
4
0
2
0
0
4
0
0
9
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
1
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
8
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
2
0
2
0
2
5
0
2
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
4
3
0
0
3
2
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
2
1
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
1
1
2
0
0
2
1
0
0
0
0
0
0
0
0
0
2
2
0
0
5
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
1
1
0
0
1
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
1
5
1
0
0
0
4
0
4
0
1
0
3
1
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
2
2
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
3
0
0
0
0
0
2
2
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
5
2
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
3
0
1
0
1
2
0
0
0
3
0
2
0
0
2
0
0
0
0
2
0
1
3
1
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
3
4
0
0
0
0
1
0
0
0
0
0
2
1
0
1
2
0
0
0
1
0
0
0
0
2
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
1
0
0
0
0
0
0
1
4
0
0
0
0
0
0
1
0
0
0
1
2
0
0
1
0
2
2
3
0
0
0
0
0
2
0
2
1
0
2
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
1
0
1
2
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
3
0
1
0
1
0
0
0
1
1
2
0
2
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
2
1
0
0
0
0
2
0
1
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
3
0
0
1
2
0
2
0
1
0
0
1
0
1
0
2
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
2
0
0
2
1
5
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
3
2
1
3
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
1
2
0
0
0
0
1
0
0
0
0
0
2
4
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
6
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
1
2
2
0
3
0
1
0
0
0
1
0
2
0
1
0
2
2
0
0
0
0
0
0
0
2
2
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
1
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
1
5
0
1
1
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
3
0
0
0
1
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
1
1
2
0
1
0
2
0
0
0
0
1
2
0
0
0
2
0
1
0
2
0
1
0
0
1
1
0
0
0
0
0
2
2
0
0
0
0
0
2
0
2
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
3
0
2
0
0
2
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
4
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
3
0
1
0
2
0
0
1
2
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
2
2
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
1
2
0
2
0
1
0
1
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
2
1
2
2
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
1
0
0
1
2
1
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
6
2
0
1
0
0
0
0
0
2
0
1
1
0
0
0
2
1
3
0
0
0
0
0
0
0
2
2
0
0
0
0
2
1
1
2
0
0
0
0
0
1
1
4
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
1
0
0
2
0
0
3
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
2
1
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
3
0
2
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
3
2
0
0
2
2
0
2
0
0
0
0
0
0
2
2
0
2
1
0
2
0
1
1
0
0
2
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
2
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
1
0
0
1
1
0
0
0
1
3
0
0
0
0
2
0
0
1
0
2
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
2
1
0
0
0
1
0
0
0
0
0
0
2
1
0
0
2
0
2
1
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
5
0
0
0
0
0
0
0
0
1
1
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
2
1
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
3
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
1
0
0
1
1
0
0
2
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
2
4
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
2
0
2
2
2
0
0
0
0
1
2
0
0
0
0
0
5
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
4
0
4
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
2
2
0
0
2
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
2
0
0
2
2
1
0
0
2
0
0
2
0
0
0
1
0
0
0
1
4
2
0
0
0
0
0
0
0
0
0
6
2
0
0
0
1
0
1
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
3
0
1
0
2
3
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
5
3
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
9
0
0
2
0
2
1
0
1
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
3
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
2
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
2
0
0
0
0
1
0
0
3
0
0
0
3
0
0
0
2
2
0
0
0
3
2
0
0
1
0
1
1
0
2
0
0
0
1
0
2
0
0
2
0
2
0
2
0
0
0
0
0
0
0
2
0
2
3
0
0
0
1
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
2
2
2
0
2
3
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
4
2
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
8
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
3
0
0
3
3
0
0
0
1
0
1
2
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
11
1
2
1
2
2
1
0
0
0
0
2
0
0
0
3
0
1
1
1
0
0
0
0
0
2
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
7
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
1
2
0
0
1
0
0
0
2
0
0
2
2
0
0
0
1
0
1
0
0
0
0
1
0
2
0
0
1
0
2
3
0
0
0
0
1
0
0
2
0
0
1
1
2
0
2
2
0
0
0
0
0
3
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
5
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
2
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
2
1
0
0
0
2
0
3
1
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
1
2
0
0
2
1
3
0
0
0
4
4
0
0
0
0
1
0
0
0
2
0
0
0
2
1
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
3
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
2
1
0
0
0
0
0
7
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
1
2
0
0
1
1
6
0
0
0
1
0
0
0
1
1
2
0
1
0
0
0
0
0
0
0
0
0
2
0
2
2
3
0
0
0
0
0
0
3
0
1
0
1
2
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
6
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
1
0
5
0
0
2
0
0
2
1
0
0
2
0
0
0
0
6
0
0
0
1
2
0
0
0
0
1
0
1
2
0
1
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
2
0
4
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
2
5
0
0
0
1
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
1
0
0
0
1
2
0
0
0
0
0
0
2
1
1
0
0
0
0
6
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
2
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
2
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
2
0
0
0
1
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
1
0
2
0
0
0
1
0
0
0
0
2
2
1
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
3
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
2
0
1
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
1
0
2
0
1
0
0
0
0
0
0
1
0
1
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
1
0
0
0
0
4
0
0
0
0
0
1
0
0
2
0
0
3
0
0
2
2
0
0
0
0
0
1
0
0
0
1
1
0
0
0
2
0
1
1
0
1
0
0
0
2
1
0
0
0
0
1
0
3
0
0
0
0
0
1
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
3
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
1
0
0
0
0
0
2
0
0
2
2
0
1
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
2
1
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
2
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
4
0
0
1
0
1
2
0
0
0
0
0
0
0
1
2
0
0
0
6
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
6
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
3
0
0
0
1
2
0
0
0
1
2
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
1
0
0
0
1
3
0
0
0
7
0
0
1
0
1
1
0
0
1
0
0
1
0
0
0
0
2
2
0
1
2
1
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
1
0
1
0
1
0
0
2
0
0
0
2
0
2
0
0
0
0
5
0
0
0
1
0
0
2
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
2
1
0
2
0
0
1
0
0
2
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
4
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
2
1
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
2
0
1
0
0
3
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
3
0
3
0
0
0
0
2
3
0
1
1
0
0
2
0
0
0
0
0
0
3
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
2
0
2
1
0
0
0
1
0
3
0
0
0
0
0
0
0
0
2
3
1
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
2
0
0
0
2
1
0
0
0
0
0
2
0
0
1
0
0
2
2
2
0
0
0
0
0
0
0
6
0
0
0
2
0
0
1
2
1
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
1
2
4
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
4
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
3
0
0
2
0
0
0
0
1
2
0
2
0
0
2
0
2
0
0
1
2
2
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
2
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
1
0
0
2
1
0
1
0
0
1
2
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
2
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
2
0
0
0
2
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
4
0
1
0
2
0
0
2
0
0
2
0
0
0
1
0
1
0
1
0
2
0
0
1
2
0
0
1
0
1
0
0
5
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
2
0
0
0
0
0
0
1
0
0
1
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
2
0
0
1
1
1
0
1
0
0
0
1
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
1
2
1
0
0
1
0
0
0
0
2
2
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
1
0
3
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
2
5
0
0
0
1
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
2
2
0
0
0
0
0
2
0
2
0
0
0
2
0
0
2
2
0
1
1
1
0
0
0
0
0
0
0
1
7
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
2
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
2
0
0
1
2
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
2
2
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
3
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
3
1
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
2
1
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
1
1
0
1
1
0
1
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
2
0
2
0
1
0
2
0
0
0
0
1
0
1
3
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
3
0
2
1
0
0
1
1
0
0
0
0
3
0
0
6
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
2
2
2
0
5
2
1
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
1
0
0
1
2
2
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
1
5
0
0
1
0
1
2
0
0
2
0
0
3
0
0
0
0
0
2
1
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
1
3
0
0
1
0
0
1
0
0
0
0
0
2
1
0
0
1
0
0
1
0
0
2
1
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
3
2
0
0
0
0
0
2
0
0
1
0
0
0
0
1
1
0
2
0
0
0
1
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
2
0
0
0
0
3
0
2
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
2
2
0
0
1
0
0
0
0
3
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
3
0
1
1
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
1
1
2
0
0
0
2
0
0
0
0
1
0
0
4
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
3
2
2
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
2
0
3
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
1
2
0
0
1
0
3
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
1
0
0
2
0
0
1
1
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
1
2
1
2
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
3
0
1
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
1
0
0
0
1
1
0
0
1
0
0
0
2
0
0
0
2
0
0
1
1
1
0
1
0
0
1
0
0
2
0
0
1
0
1
0
1
0
1
2
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
2
0
0
3
0
1
0
0
1
0
0
0
2
2
3
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
14
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
3
1
0
0
0
0
0
0
0
1
2
1
2
0
2
2
0
7
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
1
1
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
2
0
1
2
0
0
0
1
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
3
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
1
2
0
0
0
0
0
1
0
2
0
1
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
5
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
5
2
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
3
0
0
2
0
2
0
0
2
0
1
0
0
0
0
0
0
3
2
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
1
0
0
1
3
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
2
3
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
1
0
2
1
0
0
0
1
2
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
3
0
0
0
0
5
0
0
2
0
0
0
0
1
1
0
2
0
0
0
1
0
0
0
0
0
2
0
2
0
2
2
0
5
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
5
2
0
0
0
0
0
2
2
1
0
0
0
1
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
3
0
0
1
1
0
1
0
0
0
2
0
0
1
0
0
1
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
1
3
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
1
5
0
0
0
0
1
1
0
0
0
2
2
0
0
0
0
0
0
1
0
2
4
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
2
1
1
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
2
0
1
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
2
5
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
2
2
0
1
0
2
0
0
0
0
0
0
0
1
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
3
0
1
1
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
3
1
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
2
2
0
1
0
2
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
3
2
1
0
0
0
0
1
0
2
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
5
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
1
4
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
9
2
0
0
0
2
2
1
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
2
1
1
0
0
0
2
0
0
0
2
0
0
0
3
0
0
1
0
2
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
1
0
1
1
0
1
0
0
2
0
0
0
0
1
0
1
0
3
0
1
0
0
0
2
2
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
1
2
0
0
0
0
0
0
0
0
1
2
0
2
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
2
0
0
0
4
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
3
3
0
2
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
1
0
1
0
0
5
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
2
0
0
1
0
0
0
0
0
0
0
2
2
1
1
2
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
1
1
0
0
0
0
0
1
1
1
0
1
0
0
1
0
2
3
2
0
0
0
1
1
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
2
0
0
0
0
0
0
2
0
0
0
3
0
2
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
3
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
2
5
2
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
1
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
1
0
5
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
7
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
2
1
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
2
0
0
5
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
2
0
3
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
3
1
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
7
0
3
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
1
3
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
2
2
0
1
2
2
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
1
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
1
2
0
0
0
1
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
9
0
0
2
0
1
2
0
0
0
0
0
0
12
2
2
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
3
0
0
2
0
0
2
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
3
0
0
1
0
0
0
2
0
2
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
2
0
0
0
1
0
1
0
1
0
0
2
0
0
0
0
3
0
1
2
0
2
0
2
1
0
0
0
1
0
1
1
1
0
2
0
0
0
0
0
0
2
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
2
0
0
0
0
0
0
1
0
0
8
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
1
0
0
0
0
0
2
3
0
0
0
0
0
0
0
4
1
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
1
0
2
0
0
0
0
1
1
0
0
0
0
2
1
1
0
2
0
0
0
0
0
0
0
0
1
0
1
2
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
1
0
0
3
5
0
1
2
2
1
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
4
0
0
0
0
2
1
0
0
0
2
0
1
0
2
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
3
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
4
0
0
0
0
1
0
2
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
5
1
0
0
2
0
2
0
0
0
0
1
0
0
0
2
0
4
4
1
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
2
0
0
2
1
0
0
0
0
0
0
1
2
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
3
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
1
1
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
1
0
0
0
2
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
2
0
1
0
0
0
2
0
0
2
2
0
1
0
0
0
1
0
0
0
0
0
1
0
1
2
0
0
1
2
2
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
2
1
2
0
0
0
1
1
0
0
0
0
0
4
0
0
0
2
0
1
0
0
0
0
2
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
2
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
2
0
3
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
4
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
1
0
3
0
0
0
0
1
2
0
0
1
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
2
0
1
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
2
0
0
0
0
1
0
0
0
2
5
0
0
0
0
0
0
0
2
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
3
1
0
2
0
0
5
0
0
2
0
0
0
0
1
1
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
4
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
2
0
1
0
0
8
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
1
2
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
2
0
0
3
0
1
2
2
0
0
1
0
0
0
0
1
1
0
0
4
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
1
2
1
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
3
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
2
2
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
1
2
0
2
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
7
0
0
1
0
1
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
2
0
0
2
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
1
0
2
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
2
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
2
0
1
5
1
0
0
2
0
2
2
0
0
0
2
0
2
0
0
0
1
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
3
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
3
0
2
1
1
0
0
2
2
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
4
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
2
0
0
2
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
1
1
2
2
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
1
0
1
0
3
1
3
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
2
1
2
0
0
0
0
0
1
0
2
1
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
2
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
2
1
1
0
0
12
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
1
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
3
0
0
0
0
0
0
2
1
1
2
0
2
0
0
0
0
2
2
1
7
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
5
1
1
0
1
1
0
2
0
2
0
0
1
0
2
0
0
0
0
2
0
0
2
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
3
1
0
0
0
0
1
0
2
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
1
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
1
2
1
1
0
0
0
0
2
0
2
0
3
0
0
0
0
0
6
0
0
0
1
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
1
2
0
2
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
1
0
2
0
0
2
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
2
1
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
1
1
0
1
0
0
0
3
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
2
2
0
0
1
0
0
0
4
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
1
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
2
0
0
1
1
0
1
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
2
1
0
0
0
0
2
0
1
0
3
0
2
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
2
2
0
0
2
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
2
0
2
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
1
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
2
2
2
0
0
0
1
0
0
0
2
0
1
2
0
0
0
3
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
1
3
1
0
0
0
0
2
0
1
0
0
0
0
0
0
1
2
1
4
1
1
0
0
0
0
0
0
0
2
0
0
0
1
2
1
0
0
0
0
2
1
0
0
1
0
2
0
0
0
2
0
1
1
4
0
0
0
0
2
0
0
1
1
0
0
0
0
2
0
0
1
1
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
2
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
3
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
1
2
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
6
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
2
9
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
3
2
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
2
2
0
0
0
0
0
1
0
3
2
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
3
0
0
1
0
0
1
0
0
1
1
1
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
3
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
2
2
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
3
0
0
0
0
0
3
1
0
0
2
0
1
2
2
2
0
2
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
2
0
0
0
0
1
2
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
3
0
1
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
6
3
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
2
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
1
0
0
1
0
0
1
0
1
1
1
0
0
0
3
1
0
2
0
0
2
0
0
0
0
0
2
0
2
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
2
0
0
2
0
0
1
0
0
0
2
0
0
1
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
2
2
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
3
0
0
1
2
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
1
2
0
0
0
0
0
1
0
1
2
0
0
0
0
2
0
0
0
0
0
0
3
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
1
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
2
2
0
0
0
1
2
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
2
0
0
0
2
1
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
1
0
0
0
1
0
0
0
0
2
0
1
1
0
0
0
0
0
1
2
1
1
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
2
1
0
5
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
2
0
2
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
5
0
0
0
1
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
1
1
0
0
0
2
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
2
2
0
3
0
11
0
1
0
1
0
0
1
6
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
1
1
0
0
0
2
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
2
1
0
0
0
0
1
0
0
1
0
1
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
1
0
3
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
2
0
0
0
1
3
0
0
0
2
1
1
0
0
0
0
2
0
0
2
1
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
2
0
0
0
2
0
1
0
0
0
1
2
1
1
0
2
0
2
0
0
0
0
0
0
4
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
1
0
0
2
0
1
1
2
2
0
2
4
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
2
1
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
3
1
1
0
0
0
0
0
5
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
3
0
0
1
0
0
0
0
2
1
2
0
0
0
0
0
1
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
2
0
0
1
2
0
1
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
1
0
0
0
1
0
2
2
0
2
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
3
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
1
1
0
0
2
0
0
2
0
0
0
0
0
0
0
3
1
1
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
1
3
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
4
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
2
0
2
0
2
0
0
0
2
0
0
0
2
0
0
0
0
1
0
2
0
1
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
2
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
5
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
2
2
0
0
2
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
1
1
2
0
0
0
0
2
0
0
0
2
0
2
0
1
1
0
1
0
2
0
0
2
0
1
0
1
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
4
0
0
0
1
0
0
2
0
1
2
0
0
1
0
0
1
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
1
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
1
0
2
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
2
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
2
3
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
1
0
3
1
1
0
0
0
0
1
2
0
1
0
0
0
0
0
0
1
0
1
0
2
3
0
0
5
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
8
0
1
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
2
0
2
0
0
0
2
0
0
0
1
0
2
0
1
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
4
2
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
2
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
2
1
0
0
0
0
0
0
2
0
2
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
5
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
4
2
0
1
3
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
2
0
2
3
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
1
0
1
1
0
2
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
1
0
1
0
0
0
0
0
2
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
2
0
2
0
0
1
1
0
0
2
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
2
1
0
0
0
0
0
0
0
0
1
1
2
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
2
1
0
2
0
2
0
3
0
0
3
0
0
1
2
0
1
0
2
1
4
0
0
0
0
0
0
6
0
0
1
0
1
2
0
0
3
0
0
0
2
0
0
1
0
0
0
2
2
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
1
0
1
2
2
0
0
0
0
0
0
0
2
2
0
1
0
2
0
1
0
1
4
0
1
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
1
3
0
2
0
2
2
1
0
0
1
0
2
0
0
0
0
0
1
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
2
0
2
0
1
0
0
1
2
0
1
0
0
2
0
0
0
0
1
0
1
0
0
1
1
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
2
0
0
0
3
0
0
1
0
0
2
0
1
2
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
1
0
2
0
0
1
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
3
0
0
0
0
0
1
5
0
0
0
0
0
0
0
1
0
0
2
0
2
0
1
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
2
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
3
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
2
0
1
4
0
2
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
1
0
0
1
0
0
3
2
0
1
0
0
0
0
2
2
2
0
3
2
0
2
2
0
0
2
1
0
0
0
0
1
0
1
0
0
1
0
0
2
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
1
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
1
0
2
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
2
0
0
2
0
0
3
3
2
1
2
0
0
0
1
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
2
2
0
2
2
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
2
1
0
1
2
0
0
1
2
0
0
0
0
0
1
2
0
0
1
0
0
0
0
1
0
1
0
0
0
0
2
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
3
1
0
2
2
0
0
1
0
0
0
0
0
0
0
1
1
0
1
4
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
5
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
1
0
0
0
0
0
0
0
0
2
4
0
0
2
1
1
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
1
2
0
0
2
0
1
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
1
5
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
3
0
1
0
0
1
2
0
1
2
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
7
0
0
0
0
0
0
0
0
2
0
0
2
0
0
5
0
0
0
1
0
2
0
2
0
2
0
0
1
4
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
1
0
2
0
2
0
2
0
0
0
3
0
0
0
2
1
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
2
0
2
0
1
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
2
0
0
1
0
0
1
0
0
1
0
0
0
0
0
2
1
2
0
0
0
1
4
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
1
0
0
0
0
1
2
3
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
1
0
0
1
2
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
2
1
0
1
0
0
6
0
0
0
2
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
4
0
0
0
2
1
0
0
0
0
3
2
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
2
2
0
2
0
0
2
0
0
0
0
0
0
3
7
0
1
0
0
2
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
2
0
2
1
0
0
0
0
1
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
3
2
0
0
0
1
0
1
2
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
2
2
2
1
0
0
0
0
0
0
1
0
1
0
2
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
1
2
1
0
0
0
1
0
0
0
0
0
1
3
2
0
0
1
1
0
1
0
0
0
0
3
1
0
1
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
2
2
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
4
5
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
1
0
0
0
0
0
1
2
0
0
0
7
2
2
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
3
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
1
1
0
4
0
2
0
2
1
0
0
0
0
1
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
2
1
0
0
0
0
2
1
1
0
1
2
1
0
0
0
0
0
0
1
0
2
1
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
2
0
0
1
0
0
0
0
0
1
2
0
0
0
0
2
2
0
0
0
1
2
0
0
1
0
2
0
0
0
0
0
0
2
0
0
1
2
0
2
0
2
0
2
1
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
3
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
1
1
1
0
0
2
0
0
0
1
0
0
0
0
0
0
1
2
1
0
2
1
2
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
2
2
0
2
0
0
0
2
2
0
0
2
0
1
0
0
0
2
1
0
0
2
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
2
0
2
0
0
1
2
1
6
1
0
0
0
0
2
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
2
0
3
0
0
0
0
0
0
0
0
0
0
1
1
0
2
1
0
1
3
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
1
0
1
3
0
0
1
0
0
0
2
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
0
0
0
0
2
0
1
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
2
0
2
0
0
0
1
0
3
0
0
0
0
1
0
1
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
3
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
3
0
1
0
0
0
1
0
0
1
1
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
2
2
5
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
3
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
2
0
2
0
0
2
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
2
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
2
1
0
1
2
0
0
1
0
2
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
1
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
1
2
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
2
0
1
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
2
0
0
1
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
2
0
4
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
2
0
0
1
2
0
0
0
2
0
0
1
0
0
1
2
0
1
2
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
3
0
0
0
2
1
2
0
0
0
4
1
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
5
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
1
0
1
1
0
0
1
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
1
0
1
0
2
0
1
0
0
1
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
7
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
4
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
3
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
3
0
0
0
0
2
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
2
0
0
0
0
0
3
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
2
2
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
2
0
0
0
2
2
3
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
2
1
0
0
2
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
3
0
2
0
0
1
3
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
3
0
3
3
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
2
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
4
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
3
0
1
0
3
0
0
0
1
0
1
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
4
2
0
0
0
0
0
0
0
2
0
0
3
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
1
2
0
1
0
0
0
2
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
3
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
2
1
0
0
1
0
1
0
0
1
1
2
1
2
0
1
0
0
0
4
1
1
0
0
4
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
1
0
2
0
2
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
11
0
0
2
0
0
0
0
0
0
0
0
0
0
6
0
0
1
0
0
2
0
0
0
0
0
5
0
2
0
0
0
1
0
2
0
0
2
0
2
0
0
3
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
2
0
0
0
1
0
0
0
2
0
0
0
1
2
2
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
8
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
1
1
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
1
1
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
4
0
0
2
0
0
0
0
0
2
0
0
0
1
2
0
1
0
0
0
0
1
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
2
1
0
4
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
2
2
0
2
0
2
0
0
0
0
0
0
2
1
0
0
0
1
2
1
0
0
0
0
0
0
1
0
2
0
3
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
1
1
0
1
0
1
2
0
2
0
0
3
1
0
0
0
0
1
1
2
0
0
1
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
3
0
0
0
0
0
0
2
1
0
1
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
4
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
1
0
1
1
1
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
2
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
1
1
0
0
0
4
0
0
2
0
0
0
0
3
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
1
3
0
1
0
0
1
0
1
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
3
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
14
2
0
0
2
0
0
0
0
0
0
2
4
0
2
0
1
0
0
2
0
0
0
1
0
0
0
0
0
1
1
1
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
1
0
2
0
1
2
0
0
2
0
0
0
4
0
1
0
0
0
1
0
2
4
0
0
0
0
0
0
0
0
1
1
0
0
0
0
3
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
5
0
0
0
1
1
0
0
2
0
2
0
0
0
0
2
2
0
1
0
1
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
3
0
2
0
0
0
4
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
1
0
1
0
0
0
1
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
1
1
1
0
0
1
0
1
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
3
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
3
2
0
0
0
0
0
0
2
0
0
0
0
0
1
1
2
0
0
0
0
1
2
0
3
1
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
2
0
2
0
0
4
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
3
1
0
1
0
0
2
0
0
4
0
0
10
0
0
0
1
3
0
0
1
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
5
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
2
0
0
0
1
0
0
0
2
0
2
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
3
0
0
1
0
1
1
2
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
2
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
3
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
2
3
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
3
0
1
2
2
0
1
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
1
0
0
0
0
3
0
0
1
0
0
2
0
0
0
0
4
1
0
0
1
2
0
0
2
0
0
0
0
0
3
0
0
1
2
2
0
1
0
1
1
0
0
0
4
0
0
7
0
1
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
4
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
2
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
2
2
2
0
0
0
0
2
0
4
0
0
4
0
0
2
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
3
0
0
0
2
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
5
0
0
1
0
1
0
0
0
3
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
1
0
2
2
1
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
3
1
0
0
2
0
1
0
1
1
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
1
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
1
0
1
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
3
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
3
0
1
1
0
0
1
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
1
0
4
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
2
0
0
0
0
16
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
2
1
0
5
0
0
0
2
2
2
3
2
0
1
1
0
0
0
0
2
0
0
0
1
0
0
0
1
1
0
1
0
2
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
9
1
2
2
2
0
0
3
0
2
0
0
2
5
0
0
2
0
2
0
0
2
0
0
2
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
1
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
1
1
0
2
0
1
0
0
1
2
2
4
0
0
0
0
0
0
0
1
0
0
3
0
0
1
2
1
0
0
0
0
0
0
2
4
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
2
0
1
0
1
1
0
1
0
0
0
0
2
0
0
0
0
0
2
1
1
0
0
2
5
1
0
1
2
0
0
2
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
2
4
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
2
2
0
0
0
2
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
1
0
3
0
0
1
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
3
0
0
0
0
0
2
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
1
2
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
2
0
0
2
0
2
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
2
1
0
0
1
2
1
0
3
2
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
1
0
0
2
0
4
0
1
1
2
0
0
0
0
1
2
0
2
0
0
0
2
0
0
0
3
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
1
1
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
1
0
2
0
2
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
3
0
0
0
0
0
1
0
0
0
0
0
0
1
0
3
0
1
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
4
0
0
1
0
0
0
0
2
2
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
1
0
0
2
2
0
0
2
0
0
0
0
1
0
0
2
0
1
0
1
1
0
0
0
3
0
0
0
2
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
3
0
0
0
1
3
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
3
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
2
0
0
0
2
0
0
0
0
2
0
1
0
0
2
0
0
2
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
2
0
2
0
1
1
0
0
2
1
0
0
0
0
2
1
2
0
0
1
3
0
0
2
0
0
0
0
1
1
0
0
0
2
2
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
2
2
5
2
2
0
0
0
0
2
0
0
3
0
0
0
2
0
2
2
0
0
1
1
0
0
0
0
0
1
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
2
0
2
0
0
0
4
0
3
0
0
0
0
1
1
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
1
0
0
0
0
0
1
1
0
0
0
3
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
1
0
3
3
0
0
2
2
0
0
1
2
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
2
0
0
0
0
0
0
12
1
0
0
0
0
0
2
2
1
0
0
0
0
0
0
1
1
0
0
2
1
0
0
0
0
1
0
0
2
1
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
6
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
1
2
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
5
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
2
2
0
1
0
0
0
0
2
1
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
3
0
3
1
0
2
0
0
2
0
0
2
1
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
1
0
0
3
1
10
0
0
1
0
0
0
0
0
0
0
2
0
2
0
1
1
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
2
0
0
5
1
2
0
0
0
0
7
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
1
1
1
1
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
2
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
2
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
2
1
0
0
0
0
0
2
0
2
2
2
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
2
0
2
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
1
1
0
0
1
0
4
1
0
0
0
0
0
2
1
2
1
0
0
2
2
0
0
1
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
2
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
4
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
1
1
0
0
0
0
0
0
0
2
0
1
0
1
2
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
2
0
0
0
0
1
0
1
2
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
1
0
0
2
0
1
0
2
0
0
1
0
0
0
0
2
0
0
5
0
0
2
1
0
0
2
0
0
0
0
0
0
3
2
0
1
5
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
2
0
2
0
0
2
0
0
2
0
0
2
1
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
1
0
2
0
2
0
0
2
2
2
0
1
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
21
2
1
0
0
3
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
11
0
0
0
2
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
3
0
1
0
0
0
0
2
0
0
0
0
1
0
0
2
0
2
0
0
0
1
1
2
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
2
3
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
1
0
0
0
4
1
1
2
0
0
0
0
1
2
0
0
0
2
2
0
0
2
0
1
2
2
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
5
0
2
0
0
0
0
0
0
0
1
0
0
0
3
1
2
0
0
3
1
0
0
9
1
2
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
2
1
0
0
1
1
0
0
0
0
1
0
3
1
1
0
0
1
3
1
0
0
1
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
2
0
0
1
2
0
0
1
0
1
0
0
0
0
0
3
2
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
1
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
2
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
2
0
1
2
1
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
1
1
2
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
5
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
1
1
1
1
0
0
0
0
2
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
2
0
0
1
1
1
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
1
2
1
1
0
2
0
0
10
3
1
1
0
0
2
1
2
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
2
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
2
2
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
2
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
5
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
2
2
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
3
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
1
0
0
0
0
0
4
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
1
2
0
0
0
1
1
2
0
0
0
1
2
0
1
0
0
3
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
1
0
1
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
2
0
2
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
3
0
0
1
0
0
3
2
0
0
1
2
0
2
0
0
1
1
0
1
0
0
0
0
1
1
3
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
3
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
1
3
0
0
0
0
1
1
3
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
1
0
0
1
0
0
0
4
1
0
3
2
0
0
2
1
0
0
2
0
0
1
0
2
0
1
6
0
0
0
4
0
0
0
1
2
3
1
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
1
1
0
0
0
0
0
2
0
1
2
0
5
0
0
0
0
0
2
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
2
0
1
1
0
0
0
0
0
1
0
0
0
2
1
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
1
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
2
2
0
3
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
1
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
1
0
0
2
0
0
1
0
1
0
0
0
0
0
1
3
2
0
0
1
3
2
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
2
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
3
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
3
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
3
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
1
7
0
0
0
0
0
2
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
2
0
2
0
0
1
0
1
2
0
0
0
0
1
1
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
2
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
3
0
5
2
1
0
0
1
3
1
0
2
0
0
1
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
1
0
3
2
2
0
0
0
2
1
5
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
3
1
0
0
2
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
5
5
2
0
0
0
1
3
0
0
2
0
0
2
1
0
0
0
2
0
1
0
0
0
0
0
0
0
5
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
1
2
5
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
2
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
1
2
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
2
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
2
0
2
0
0
2
0
1
1
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
1
0
0
2
0
2
2
0
0
1
0
0
2
2
0
0
0
0
0
1
2
0
0
2
0
4
0
0
4
0
0
3
1
1
0
2
0
3
0
0
0
0
2
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
2
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
2
0
1
0
0
1
0
1
4
0
0
0
0
1
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
1
1
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
1
2
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
6
0
0
0
2
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
2
0
0
0
2
2
1
0
1
0
0
0
0
0
2
0
1
1
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
1
0
0
0
2
1
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
2
4
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
2
0
2
0
0
0
1
2
0
0
0
1
0
0
2
0
0
0
0
0
1
2
2
1
0
0
0
0
1
1
0
1
0
0
2
0
2
0
0
3
1
0
0
0
1
0
0
1
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
3
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
3
0
2
1
0
0
0
0
1
0
0
0
0
2
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
4
0
1
0
0
0
0
2
0
0
1
0
1
1
1
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
2
0
0
0
4
2
1
0
0
2
0
2
0
0
0
0
2
0
0
0
1
0
1
1
3
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
3
0
2
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
2
1
0
1
0
1
2
2
0
0
0
2
0
0
0
0
1
0
0
2
0
3
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
3
0
0
0
1
0
2
0
0
2
0
2
0
2
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
1
0
0
0
5
2
2
0
0
2
0
2
2
0
1
0
0
0
0
0
0
0
1
3
2
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
3
0
6
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
3
2
0
0
0
1
2
0
0
1
0
0
0
0
2
0
2
0
0
6
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
3
0
0
0
0
4
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
3
1
0
1
0
0
1
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
2
1
0
2
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
1
1
2
0
0
0
0
1
1
0
1
0
1
0
1
2
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
2
3
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
5
0
0
0
0
0
0
2
2
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
1
1
1
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
1
2
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
2
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
5
0
1
0
2
0
2
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
4
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
1
0
0
0
0
0
2
0
0
2
0
1
2
0
0
2
0
1
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
2
0
0
0
2
0
2
0
0
3
1
0
3
0
0
0
0
2
2
0
0
0
2
0
0
0
1
0
2
0
1
0
0
1
0
0
2
0
0
2
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
2
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
3
6
0
0
0
0
0
2
0
0
0
0
0
2
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
2
1
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
6
2
0
1
2
0
1
0
0
0
2
0
0
0
2
2
0
1
0
0
0
0
0
0
4
1
1
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
3
0
1
0
0
2
0
3
0
0
0
0
0
0
1
2
1
0
0
0
0
0
1
1
1
0
0
0
0
0
4
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
2
1
0
2
0
0
1
0
0
0
0
0
0
0
2
1
1
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
1
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
5
0
3
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
4
0
0
0
0
0
0
2
0
2
0
0
2
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
3
0
0
0
0
2
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
1
0
2
1
0
0
2
0
0
0
0
1
0
0
2
0
0
0
2
1
1
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
1
0
0
0
0
1
0
2
0
3
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
1
0
2
0
1
0
1
0
0
0
2
0
0
0
1
2
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
7
0
0
0
0
2
2
0
0
2
0
1
0
0
1
0
0
0
0
0
0
1
3
2
0
0
0
1
0
0
1
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
5
0
0
1
0
0
3
0
1
3
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
3
0
4
0
0
0
2
0
0
2
1
0
0
0
0
0
1
0
0
2
4
0
2
0
0
1
0
2
2
0
1
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
5
4
0
2
0
0
0
2
0
0
0
0
0
0
0
3
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
2
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
2
0
0
0
2
1
0
2
0
0
0
0
0
2
0
0
0
0
0
2
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
2
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
1
0
2
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
6
0
0
1
2
0
0
1
0
0
3
2
0
0
1
0
0
1
0
0
0
0
2
0
2
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
2
0
0
0
0
0
0
0
1
2
3
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
1
0
1
0
0
0
1
1
3
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
1
1
1
0
2
0
0
1
2
0
0
0
0
1
0
0
0
0
0
1
2
0
1
1
0
0
1
0
0
0
1
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
13
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
2
2
0
2
0
0
0
3
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
2
0
0
1
0
1
0
0
0
0
3
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
4
0
2
0
0
2
1
0
1
0
2
0
0
2
2
1
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
1
2
0
0
1
2
0
0
1
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
2
0
1
2
2
0
0
0
0
1
0
0
1
0
3
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
2
3
0
0
0
1
0
0
0
2
0
0
0
0
0
0
4
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
3
0
1
0
0
0
0
0
0
1
0
1
0
2
1
2
0
0
0
2
0
2
0
3
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
1
0
1
2
1
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
3
2
0
0
0
2
0
0
1
0
0
1
0
0
0
0
2
0
0
0
1
0
4
0
2
2
0
0
0
0
0
7
0
0
0
0
2
0
2
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
1
0
0
1
0
2
0
7
0
0
1
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
2
0
1
0
0
2
0
0
2
1
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
2
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
3
0
1
2
0
1
0
2
1
2
0
0
0
0
0
0
0
0
1
2
0
0
1
0
1
0
0
0
0
0
3
0
0
0
0
2
0
0
0
2
0
2
0
0
1
0
1
0
0
0
1
1
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
3
0
0
0
2
0
0
0
1
2
0
0
0
0
2
0
2
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
1
2
2
0
1
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
3
0
1
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
1
2
0
3
0
0
1
2
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
2
0
1
0
1
2
0
0
1
0
4
1
0
2
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
2
0
0
0
1
0
0
0
1
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
1
6
0
2
1
0
0
0
0
0
3
2
0
0
0
1
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
1
3
1
0
0
0
0
0
0
0
0
0
0
0
0
6
1
0
2
0
0
0
0
0
1
0
2
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
2
1
0
0
1
1
0
0
2
1
2
3
0
0
2
0
0
0
1
1
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
1
0
2
0
0
1
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
3
2
0
3
0
0
0
2
0
0
0
0
1
2
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
1
1
1
4
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
2
1
0
0
0
2
0
2
1
2
0
3
3
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
3
1
2
0
0
1
0
0
0
0
0
0
0
2
2
3
0
0
0
2
0
2
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
3
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
1
1
1
0
3
0
0
0
0
1
0
2
0
1
0
0
3
0
0
0
0
0
1
0
9
2
0
0
0
0
0
2
0
0
0
1
2
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
4
0
0
0
2
2
1
1
0
1
0
2
0
0
0
2
0
0
0
0
1
2
1
0
2
0
0
0
0
1
2
5
0
1
1
0
0
0
3
1
0
0
0
0
0
0
1
1
0
2
0
9
0
0
2
2
0
0
0
0
1
2
0
0
0
0
0
1
1
0
0
2
0
1
8
1
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
2
0
2
1
0
0
2
0
0
2
0
3
2
0
2
2
2
0
0
0
0
0
2
0
0
5
0
0
0
0
1
0
0
0
1
0
1
0
2
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
2
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
3
0
0
0
3
1
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
2
3
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
2
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
1
1
1
0
0
2
0
0
0
0
3
0
0
0
0
1
0
0
2
0
0
0
1
0
2
0
2
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
1
2
2
0
1
3
1
0
0
2
0
0
2
0
0
1
2
0
0
0
0
2
0
0
2
0
0
2
0
0
2
0
0
0
0
0
1
1
2
2
1
2
0
2
0
0
0
0
0
0
0
0
1
3
0
0
1
0
0
2
0
0
0
0
0
0
2
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
4
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
2
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
2
1
1
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
2
1
1
1
0
2
2
0
0
3
0
0
0
1
0
3
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
2
0
0
0
2
0
2
0
0
0
1
0
0
0
1
0
1
0
2
0
2
0
0
2
0
0
0
0
0
0
0
4
1
0
3
0
1
0
1
0
0
0
0
2
0
2
0
1
0
0
1
2
0
0
2
1
1
0
0
0
0
2
1
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
5
2
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
1
3
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
4
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
4
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
1
0
0
0
1
0
0
1
1
0
2
1
3
0
0
0
0
0
0
2
0
0
0
2
1
0
3
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
1
1
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
2
0
0
0
2
0
1
2
0
3
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
4
1
0
0
0
0
0
0
1
0
0
1
0
7
0
0
0
0
0
0
0
0
0
0
0
0
2
8
1
0
0
0
0
0
0
1
1
1
0
0
2
0
0
0
1
0
1
0
1
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
1
2
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
1
0
0
1
0
2
0
0
0
0
2
4
0
2
1
0
0
0
0
0
0
0
0
0
2
2
0
1
2
0
0
0
0
2
0
2
0
0
0
0
6
0
0
0
1
1
0
0
0
0
0
0
2
0
1
0
0
0
2
2
1
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
1
2
0
0
2
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
5
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
3
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
3
1
0
3
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
1
1
1
0
0
0
3
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
2
0
0
2
0
0
1
0
2
1
0
0
0
0
0
1
1
3
1
1
1
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
2
0
3
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
3
0
1
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
2
3
2
0
0
0
1
2
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
5
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
2
0
0
0
2
1
0
0
1
7
1
0
2
0
2
0
2
2
0
0
1
2
3
2
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
2
2
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
4
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
1
4
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
2
0
0
0
1
0
0
1
0
2
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
2
1
2
0
0
0
2
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
2
4
0
0
1
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
1
3
1
0
0
0
0
2
0
0
2
0
0
0
0
0
2
2
1
0
0
1
0
0
0
6
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
4
0
1
0
0
3
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
3
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
1
3
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
1
3
0
0
0
0
2
0
0
1
0
2
0
2
0
2
0
0
0
0
3
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
2
0
2
0
0
0
0
3
1
1
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
2
0
0
0
1
2
0
1
0
0
0
0
0
0
2
1
0
0
3
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
2
4
4
0
0
2
0
0
2
0
3
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
2
0
1
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
1
0
0
0
0
3
0
2
0
0
1
0
1
0
3
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
5
0
0
0
0
0
0
1
0
1
2
3
0
0
2
4
0
0
1
3
0
3
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
1
2
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
1
1
0
0
0
0
2
0
0
3
0
0
2
0
0
1
0
0
1
0
0
2
0
0
1
0
1
0
0
0
2
0
2
0
0
0
2
0
0
1
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
2
1
0
2
2
0
0
0
1
0
0
0
0
0
1
0
0
0
2
2
1
0
1
1
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
3
0
1
0
2
1
0
0
0
2
0
2
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
2
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
1
0
0
1
0
0
0
2
0
1
0
2
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
2
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
2
0
1
1
2
0
1
0
1
0
0
2
0
0
2
0
0
0
2
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
2
1
0
1
2
2
0
0
1
2
2
2
0
1
0
2
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
1
0
2
0
0
1
1
0
0
0
0
2
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
2
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
1
0
1
0
2
0
0
0
1
0
0
1
0
0
2
1
3
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
2
1
0
0
0
0
2
2
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
1
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
2
0
0
0
0
0
2
2
2
0
0
1
3
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
1
0
0
2
2
2
0
0
0
0
2
0
0
2
0
2
0
0
1
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
3
0
0
2
0
0
0
1
0
0
0
2
3
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
2
0
2
0
0
0
1
0
0
0
0
1
2
0
0
2
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
1
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
2
0
0
0
2
0
2
1
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
5
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
3
0
0
0
2
0
2
0
2
0
2
1
0
0
0
3
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
6
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
3
1
0
1
1
0
0
0
0
0
3
0
0
0
0
0
2
0
2
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
1
2
2
0
3
0
0
0
0
1
0
0
0
0
0
0
4
1
0
0
0
0
0
4
0
2
2
0
2
2
2
0
1
2
2
3
2
1
0
0
1
2
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
2
0
0
2
2
2
3
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
1
1
0
2
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
3
4
3
0
2
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
2
0
2
3
0
0
1
3
0
0
0
0
1
0
1
1
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
1
0
1
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
2
4
0
2
2
0
0
0
0
0
0
0
1
1
1
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
5
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
2
2
0
0
0
0
0
0
2
3
0
1
2
2
0
2
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
2
1
0
2
0
0
0
0
2
3
0
0
0
0
1
0
0
1
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
1
2
0
2
1
0
1
2
0
0
1
0
0
0
0
1
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
1
2
1
0
1
0
0
0
0
1
0
0
0
0
2
2
0
0
3
0
0
0
0
0
0
1
0
0
1
0
0
2
0
1
0
1
0
2
0
2
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
2
1
0
0
0
0
0
1
0
1
2
0
0
0
2
0
1
1
2
0
0
0
2
0
0
0
0
0
1
3
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
2
2
0
0
0
3
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
3
0
1
2
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
3
0
0
0
1
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
5
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
2
1
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
1
0
1
2
0
1
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
2
3
0
0
1
2
0
1
0
1
0
0
1
1
0
1
1
0
0
2
2
0
3
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
3
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
3
2
0
0
3
0
0
0
2
0
1
1
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
3
7
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
2
2
0
0
0
0
1
0
0
0
3
0
0
0
2
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
2
0
0
1
0
0
1
0
0
1
0
0
0
1
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
3
0
0
1
2
0
2
2
0
0
1
0
0
2
0
0
2
2
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
3
0
0
0
0
0
0
0
0
4
0
0
1
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
8
2
0
1
0
0
2
0
1
0
0
0
4
1
0
0
0
1
3
0
2
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
2
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
1
2
2
0
0
2
0
0
0
2
2
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
3
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
1
0
1
0
0
2
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
3
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
2
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
1
0
2
0
0
0
2
0
2
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
1
0
2
0
0
0
0
0
4
0
0
1
2
0
1
0
0
2
0
3
0
2
1
0
1
0
0
0
0
0
2
0
3
0
0
0
1
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
2
0
0
2
0
0
0
0
0
2
1
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
1
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
2
0
2
0
1
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
1
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
7
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
3
0
4
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
1
0
0
0
0
0
0
1
2
0
0
3
0
0
1
1
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
5
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
3
2
0
0
3
1
0
0
0
4
0
0
0
2
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
4
3
7
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
2
0
1
0
0
2
0
0
0
2
2
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
3
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
2
0
0
0
2
0
0
0
5
0
0
0
1
0
0
0
0
2
0
0
4
2
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
2
2
0
2
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
1
0
0
2
0
0
0
0
0
2
1
0
1
0
1
0
2
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
3
0
1
0
0
0
1
0
0
1
1
4
2
2
0
0
1
0
0
1
1
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
2
0
0
0
0
1
1
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
2
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
1
7
1
0
3
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
3
2
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
3
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
2
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
2
0
0
2
2
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
5
1
0
0
0
1
0
0
0
0
0
0
4
1
0
0
0
0
0
0
1
0
0
2
0
3
0
0
0
0
0
0
0
2
1
4
1
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
2
0
0
0
0
4
2
2
0
0
0
1
1
0
0
2
0
0
1
0
0
0
0
0
0
0
3
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
1
2
0
0
3
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
1
2
0
0
0
2
0
0
0
1
0
1
2
1
0
0
0
2
0
2
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
3
0
0
0
0
1
0
1
0
1
0
0
0
2
1
0
0
1
0
0
0
2
0
1
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
1
0
0
2
0
0
0
0
0
1
4
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
1
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
2
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
2
0
0
0
0
0
2
0
1
0
0
0
1
0
2
0
0
0
2
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
1
0
0
1
0
2
2
2
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
1
0
6
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
5
0
2
0
0
2
2
0
1
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
1
2
0
0
0
2
3
2
4
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
2
0
4
0
0
0
0
0
2
0
0
2
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
1
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
2
0
0
0
0
2
3
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
2
1
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
2
2
0
0
0
0
2
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
3
0
0
0
0
0
1
1
0
0
0
0
0
4
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
2
2
0
0
0
3
0
2
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
2
2
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
3
0
1
4
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
1
0
0
0
2
2
2
3
0
0
0
1
0
1
2
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
1
0
0
3
0
0
0
0
1
0
0
1
0
0
0
2
0
3
0
2
0
0
1
1
0
2
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
2
2
2
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
1
0
0
0
0
0
1
0
0
2
0
2
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
2
1
0
0
0
0
0
1
0
1
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
3
1
0
0
1
0
0
0
2
0
0
1
3
0
3
3
1
0
0
0
0
0
0
0
0
1
2
2
0
0
3
0
2
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
1
0
0
2
2
1
2
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
1
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
1
0
0
3
1
0
0
2
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
3
2
0
1
2
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
2
0
1
2
0
0
0
1
1
0
0
0
2
1
0
0
1
0
2
0
0
2
1
2
0
2
0
0
0
0
0
0
4
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
3
0
0
1
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
1
0
0
0
1
2
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
2
1
0
0
2
0
0
0
0
0
0
1
0
1
1
3
2
0
1
1
0
3
2
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
3
0
0
0
0
0
0
0
0
4
2
0
0
1
0
0
0
0
0
2
1
0
2
0
0
1
0
0
0
2
0
2
0
0
0
0
0
1
0
2
0
0
3
2
0
0
0
2
0
0
0
0
1
0
0
2
2
1
1
0
0
0
2
0
0
0
0
0
5
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
2
0
1
2
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
4
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
1
1
9
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
2
0
1
1
0
0
0
0
0
0
2
0
0
2
0
1
2
0
1
0
0
0
2
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
2
1
0
2
0
0
0
1
2
1
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
1
2
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
1
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
5
3
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
1
0
0
0
0
0
0
4
2
0
0
0
1
0
0
0
2
0
6
0
0
1
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
3
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
5
0
0
0
0
0
1
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
3
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
2
2
0
0
2
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
1
1
2
0
0
0
0
0
3
0
0
0
0
2
0
2
0
2
0
2
1
0
0
0
0
0
2
3
0
0
0
0
0
0
0
2
3
2
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
2
0
1
0
1
0
5
0
2
0
0
0
5
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
2
2
1
0
3
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
1
0
2
3
0
1
0
0
0
0
2
1
0
0
1
0
0
0
0
0
3
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
2
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
1
5
0
0
3
1
0
3
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
7
0
2
0
3
0
0
0
0
0
1
0
0
0
0
2
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
2
1
0
10
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
2
4
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
3
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
1
0
1
0
0
0
2
1
0
0
1
0
1
0
1
2
0
0
1
0
0
2
1
0
2
2
0
0
1
0
1
2
0
0
3
0
1
3
0
0
0
1
0
3
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
2
0
1
0
1
0
1
1
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
3
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
2
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
5
1
1
0
0
0
0
0
0
0
1
2
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
1
0
0
4
2
0
1
0
0
0
2
0
0
2
0
0
0
0
3
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
1
2
0
0
0
0
1
0
0
1
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
1
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
1
0
1
0
0
0
0
2
2
0
0
0
0
0
0
2
2
1
4
0
0
0
1
1
0
0
0
0
0
0
3
2
0
0
0
0
2
0
0
4
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
2
0
1
0
3
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
1
2
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
3
2
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
1
0
4
0
0
0
3
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
2
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
2
0
1
0
0
2
0
0
0
2
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
2
0
3
1
1
1
0
0
1
1
2
1
0
1
0
0
0
7
0
0
0
1
1
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
2
0
0
1
0
0
0
2
0
0
1
2
0
0
0
0
1
0
0
2
0
0
3
0
0
0
0
3
0
1
0
0
1
0
0
0
0
0
1
2
1
2
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
1
0
1
0
0
1
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7
1
0
0
2
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
7
0
0
0
1
0
1
1
0
0
2
2
0
0
0
0
0
0
2
0
2
1
0
0
0
5
0
0
3
1
0
1
0
0
2
0
0
0
2
0
0
0
2
2
0
0
2
2
2
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
2
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
2
1
0
2
0
0
2
2
0
0
2
2
0
0
0
1
1
0
0
1
0
1
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
5
0
0
0
1
2
0
0
0
0
0
3
1
0
0
0
0
1
0
0
3
0
2
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
1
3
0
0
0
0
0
0
0
0
0
2
0
2
0
2
2
0
0
0
1
0
1
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
1
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
2
0
2
0
0
0
2
3
0
3
1
0
0
0
0
1
0
0
0
0
0
1
3
0
1
0
0
0
0
1
0
3
1
2
0
0
0
1
1
0
0
0
0
9
0
2
0
0
0
0
0
1
2
0
1
0
0
0
3
5
0
2
0
0
0
0
0
0
0
0
0
0
2
0
4
0
0
1
3
1
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
10
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
1
0
0
0
0
0
0
3
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
1
0
0
0
1
0
0
3
0
0
0
1
0
2
0
4
0
0
1
0
0
0
1
0
2
0
2
0
0
0
0
0
0
1
0
1
0
0
0
5
0
2
0
1
0
2
0
0
0
0
2
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
2
0
0
2
2
0
2
0
0
0
0
0
0
0
0
2
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
1
2
4
1
0
1
0
0
0
0
0
2
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
1
0
0
2
2
0
0
2
0
0
0
2
0
0
0
4
0
1
0
1
0
0
2
0
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
6
0
0
0
0
0
3
0
0
2
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
1
2
0
0
0
1
0
1
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
4
1
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
4
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
4
1
1
0
0
1
1
3
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
2
2
0
0
1
0
1
3
3
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
2
0
2
0
0
1
0
2
0
0
0
1
0
0
0
2
1
0
0
0
0
3
1
0
0
3
1
0
1
2
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
3
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
3
0
0
0
2
0
2
2
0
0
0
3
1
0
1
2
0
2
1
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
2
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
4
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
3
0
0
0
0
0
0
3
1
0
0
0
0
0
0
2
0
2
0
0
0
2
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
1
0
2
0
2
0
1
2
0
0
2
0
0
1
0
0
2
0
2
0
0
0
0
2
1
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
2
0
0
0
3
0
1
1
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
2
1
1
0
0
0
0
0
5
0
2
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
4
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
2
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
3
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
2
0
0
2
0
0
1
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
1
0
1
0
0
0
1
0
0
0
3
2
0
0
0
3
2
0
0
2
1
2
0
0
0
1
0
1
0
0
1
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
2
3
0
0
0
0
0
3
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
2
2
0
2
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
3
0
0
1
1
2
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
2
0
1
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
2
0
0
1
2
2
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
7
0
0
2
0
1
1
3
1
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
1
1
2
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
6
1
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
3
5
1
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
2
1
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
1
0
1
0
0
0
0
2
0
0
2
0
0
0
0
1
0
3
0
3
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
5
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
1
2
0
0
0
0
2
7
0
3
0
1
0
2
0
0
2
0
0
2
1
0
0
0
2
0
2
2
1
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
4
1
0
1
0
0
0
0
3
2
0
2
1
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
2
1
0
0
3
0
0
0
1
0
1
0
0
2
0
0
0
2
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
2
0
0
1
0
0
1
2
0
2
1
0
2
1
0
0
0
1
0
0
4
2
0
0
0
1
0
0
0
1
2
1
1
0
2
0
0
0
3
0
0
0
0
0
0
1
0
1
1
0
2
0
2
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
2
1
2
3
0
0
0
5
2
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
1
2
0
1
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
1
0
0
0
0
1
0
0
1
2
1
0
0
0
0
0
4
1
0
2
0
0
1
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
2
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
3
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
1
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
8
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
1
0
1
0
0
2
1
0
0
0
0
2
3
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
3
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
7
0
0
4
0
0
0
0
2
2
0
1
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
6
0
0
1
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
4
2
0
0
0
0
0
1
0
0
0
2
0
2
1
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
2
0
5
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
3
0
0
0
2
0
1
0
0
0
2
0
2
1
2
4
0
0
1
0
1
0
0
0
2
0
0
2
2
1
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
1
0
1
2
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
2
0
0
2
0
0
1
1
1
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
10
2
0
0
0
0
2
0
0
3
0
0
0
2
1
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
4
0
0
2
1
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
3
0
0
0
1
1
2
2
2
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
1
0
1
0
2
0
0
0
2
0
2
2
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
1
0
0
2
0
1
0
0
0
2
3
0
0
2
0
0
0
0
2
2
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
3
0
0
0
0
0
0
2
1
0
5
0
2
0
2
0
2
0
0
1
3
0
0
2
0
0
0
0
2
0
0
0
3
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
2
0
0
1
0
0
4
0
0
5
0
5
0
0
2
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
4
3
0
2
2
2
1
0
0
1
0
0
0
2
1
1
0
0
2
0
2
2
0
0
2
0
0
0
0
2
0
1
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
1
0
4
0
0
0
0
0
0
2
0
0
2
0
0
0
1
2
1
1
0
0
0
2
0
2
0
1
2
0
1
2
0
1
0
2
1
0
0
0
0
0
2
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
1
0
3
1
0
1
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
2
1
1
0
0
0
0
1
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
3
0
0
2
0
0
1
0
0
0
0
0
0
1
0
2
0
0
2
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
2
2
0
0
2
0
1
1
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
2
0
3
0
0
0
0
2
0
0
1
0
0
2
1
2
0
0
2
0
0
3
0
0
0
2
2
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
4
2
1
0
1
0
0
0
2
0
0
1
0
0
0
0
0
1
2
2
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
1
0
0
0
2
0
0
1
2
0
1
0
1
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
2
0
1
1
0
1
1
0
0
0
0
0
1
1
0
1
0
2
0
1
0
0
0
0
0
1
0
2
2
0
0
1
1
0
1
0
0
3
0
0
0
2
2
2
0
0
1
1
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
2
0
2
1
0
1
0
0
3
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
3
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
2
0
0
1
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
1
2
0
0
1
0
2
0
1
1
1
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
4
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
4
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
3
0
0
2
0
0
0
1
0
0
3
0
0
0
1
0
0
1
1
0
2
0
0
2
0
0
0
2
0
0
3
1
0
0
0
0
0
0
2
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
2
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
1
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
1
0
0
1
0
0
0
0
0
0
1
3
2
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
2
0
2
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
2
0
1
0
2
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
1
2
0
0
0
0
0
0
3
0
0
1
2
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7
0
5
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
2
2
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
1
2
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
1
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
2
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
2
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
2
0
1
1
1
0
2
2
2
2
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
1
0
0
0
0
7
0
2
2
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
7
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
8
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
2
0
0
0
3
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
1
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
1
0
3
1
2
0
0
0
5
0
0
0
0
2
2
0
0
3
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
1
0
2
0
0
1
0
0
1
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
2
0
0
3
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
3
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
2
2
0
0
2
0
0
1
2
0
1
0
0
0
0
0
1
0
0
0
0
2
0
2
2
0
0
1
0
0
0
2
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
1
8
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
3
0
1
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
1
0
3
0
0
1
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
3
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
2
0
2
0
1
0
2
0
0
0
0
0
0
0
1
0
2
3
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
1
0
0
1
0
2
1
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
1
1
2
0
0
2
0
0
1
8
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
2
2
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
1
0
1
0
0
0
0
0
0
2
1
0
1
0
1
1
0
0
0
1
0
0
0
2
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
2
1
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
1
1
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
1
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
1
1
0
0
0
0
0
1
2
0
4
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
5
0
0
1
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
9
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
2
1
0
0
0
2
1
0
0
0
1
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
2
0
0
0
0
0
2
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
2
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
2
1
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
5
3
1
2
0
2
0
0
0
0
0
1
0
0
0
0
2
1
1
1
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
3
0
3
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
6
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
1
1
0
0
0
0
0
2
1
0
2
1
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
2
0
0
1
0
0
0
0
3
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
3
0
0
0
2
1
0
0
0
0
0
0
0
0
6
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
3
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
5
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
2
0
0
0
0
0
3
0
0
0
0
0
0
1
1
0
0
0
0
6
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
2
2
2
1
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
1
0
0
2
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
1
1
0
0
0
0
1
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
4
4
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
2
0
0
1
0
2
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
2
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
1
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
2
0
0
1
0
0
3
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
1
0
0
2
2
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
4
0
0
1
0
2
6
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
4
1
0
0
0
0
0
0
1
0
3
0
0
1
1
0
2
0
0
0
0
1
0
0
0
5
0
0
0
3
0
0
1
0
0
0
0
0
1
1
2
0
2
1
0
0
0
0
0
0
0
4
0
0
0
2
1
0
0
0
0
0
1
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
3
4
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
1
1
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
3
1
1
0
2
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
1
0
2
0
0
0
1
3
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
3
0
1
3
1
0
0
0
0
0
0
3
0
0
0
2
0
2
0
0
0
2
2
0
5
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
1
0
0
1
0
1
0
1
1
0
0
2
0
0
1
0
0
0
0
1
2
0
1
1
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
2
0
3
3
0
0
0
5
0
5
0
0
0
4
0
2
2
0
2
0
0
0
0
0
2
0
0
0
0
4
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
1
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
2
0
0
1
2
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
4
0
0
1
0
0
2
1
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
1
2
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
3
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
3
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
2
0
1
0
0
0
1
0
1
0
0
0
2
0
4
0
1
2
0
2
0
0
0
0
0
0
0
0
2
1
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
1
3
0
0
0
0
0
0
2
1
0
0
2
2
0
1
0
0
2
0
2
2
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
4
0
0
2
0
0
0
0
0
1
0
0
2
1
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
1
1
1
0
2
1
0
2
0
0
1
0
1
0
0
0
4
2
0
0
1
0
3
0
3
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
2
2
1
0
2
5
0
0
6
0
0
0
2
1
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
1
0
2
0
0
0
1
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
2
2
2
0
2
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
2
0
2
2
0
2
1
2
2
2
2
0
1
0
1
0
2
0
0
4
0
1
0
0
0
0
0
0
3
0
3
0
1
0
0
0
0
1
0
1
2
1
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
1
2
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
1
0
3
0
0
0
1
1
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
3
0
2
0
0
2
0
0
0
1
0
2
0
0
0
1
3
1
0
2
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
5
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
2
2
0
0
0
1
0
0
2
0
2
0
0
0
1
2
2
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
3
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
3
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
1
1
4
0
0
0
1
0
1
2
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
1
0
2
1
0
0
0
1
0
0
0
0
0
0
0
2
2
2
1
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
2
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
1
0
0
0
0
3
0
0
1
0
2
2
2
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
4
0
1
0
2
0
0
1
1
2
0
0
0
0
0
1
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
4
0
0
0
0
0
0
0
2
0
0
2
1
0
4
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
2
2
2
0
2
2
0
0
0
0
0
0
2
0
0
0
1
2
0
1
1
2
1
0
0
0
0
0
0
0
1
0
1
1
1
1
2
0
2
2
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
1
2
0
2
0
0
0
2
2
0
0
0
2
0
0
0
0
1
0
1
1
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
2
1
0
0
0
1
1
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
2
0
3
0
0
0
0
6
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
2
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
4
0
0
0
0
0
0
2
2
1
0
2
1
0
2
2
1
0
0
0
2
0
1
0
0
0
0
0
2
0
1
1
5
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
1
1
0
3
0
0
0
0
2
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
1
0
0
2
0
1
0
0
9
2
0
2
0
2
0
4
3
0
2
0
0
0
1
0
1
0
2
0
0
1
0
0
0
0
2
0
1
0
3
0
2
0
1
0
0
0
0
1
0
2
2
0
0
1
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
4
1
0
2
2
0
1
2
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
3
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
2
0
2
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
2
0
6
0
0
0
0
1
2
0
0
2
0
1
2
0
1
2
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
2
0
0
1
0
0
0
1
2
0
2
0
3
1
2
0
0
2
0
0
1
2
3
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
2
0
0
0
0
3
2
0
2
1
0
0
0
0
0
0
1
1
0
0
0
0
2
1
1
0
2
0
0
0
1
1
0
0
0
0
0
1
1
1
0
2
0
1
4
1
0
0
0
2
0
1
0
1
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
1
0
0
0
0
2
1
0
0
0
3
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
5
1
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
1
2
2
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
1
2
0
1
2
2
0
0
0
1
2
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
1
0
1
3
0
0
1
1
0
0
0
0
0
0
1
0
1
0
2
0
2
0
1
4
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
2
0
0
0
0
3
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
5
0
0
0
0
1
0
0
0
1
0
0
1
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
2
2
0
0
0
1
2
0
0
1
2
0
2
0
0
0
3
0
0
0
2
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
1
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
2
2
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
2
1
0
2
2
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
4
1
0
0
1
0
3
0
1
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
1
1
0
0
1
0
1
1
0
0
4
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
2
1
0
0
3
0
0
0
0
0
0
1
0
1
0
2
2
1
0
0
1
0
1
0
2
0
0
2
0
0
0
0
0
0
2
1
0
0
2
2
1
0
2
3
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
1
0
1
1
0
1
1
0
1
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
1
3
0
4
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
1
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
1
0
0
1
0
1
0
1
0
0
2
0
0
0
0
2
1
0
2
1
0
1
0
0
0
0
1
0
2
0
0
0
0
2
0
2
0
0
0
0
3
0
0
0
0
2
0
0
1
0
0
2
1
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
2
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
1
0
1
2
2
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
3
0
0
1
0
1
0
0
0
0
0
0
0
2
4
2
5
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
2
0
0
2
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
1
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
2
3
0
0
1
0
0
0
0
1
2
0
1
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
3
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
3
0
0
0
0
0
0
0
2
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
2
0
1
0
0
0
0
1
0
1
1
1
0
2
1
0
0
0
0
0
0
3
0
0
2
0
1
0
0
2
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
2
2
2
2
0
0
0
1
0
0
1
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
3
2
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
2
1
0
1
0
0
0
0
2
0
0
2
4
1
0
0
0
0
0
0
0
1
0
0
1
2
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
3
1
0
0
0
5
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
3
1
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
4
0
1
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
4
0
0
0
1
0
0
1
0
0
0
0
1
2
0
0
1
0
0
2
0
0
3
0
0
2
2
0
2
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
2
1
0
0
0
1
0
0
1
1
0
0
0
2
2
0
1
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
1
1
0
0
1
1
0
0
0
1
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
3
2
0
2
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
2
0
0
0
0
0
2
0
0
0
2
1
0
0
0
3
0
0
0
0
5
2
0
0
2
1
0
2
1
0
0
0
0
0
0
0
2
1
0
2
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
4
0
1
3
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
1
0
0
1
1
0
0
1
0
0
3
1
0
1
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
2
1
0
1
0
0
0
1
0
1
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
4
1
2
0
0
0
2
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
2
0
0
0
0
0
1
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
2
0
0
0
0
1
0
2
0
2
0
2
1
2
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
1
1
0
0
2
4
0
0
0
0
0
0
0
0
1
0
1
0
2
2
0
0
1
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
2
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
12
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
5
1
0
0
2
0
1
2
0
0
2
0
0
0
0
2
0
5
0
1
0
0
0
0
0
0
1
0
0
1
3
0
0
0
1
0
4
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
6
0
1
0
2
2
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
7
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
5
2
2
2
0
1
2
0
0
0
2
0
0
0
0
0
0
8
0
2
0
0
0
1
0
5
0
0
2
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
3
0
0
0
0
0
0
1
1
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
1
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
1
0
0
1
1
0
0
4
0
0
3
0
2
3
0
0
4
0
0
2
2
0
1
2
0
0
4
0
2
1
0
2
0
0
0
0
1
0
4
0
1
0
0
0
0
0
0
2
0
0
0
5
0
0
0
1
0
0
2
0
0
1
0
0
1
0
0
0
0
2
2
1
0
0
0
0
2
0
1
1
0
0
1
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
1
0
2
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
2
0
3
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
0
0
0
2
3
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
2
0
0
0
1
2
1
0
0
0
0
2
0
0
0
0
0
2
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
2
0
1
0
0
1
5
0
0
0
1
0
2
0
2
0
0
0
0
0
2
1
0
0
0
0
2
1
0
0
0
2
2
2
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
1
0
0
0
0
1
0
2
1
0
1
2
2
0
0
0
2
1
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
1
0
3
0
0
2
2
0
0
1
0
1
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
2
0
2
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
1
0
0
0
0
2
1
1
0
0
0
1
0
0
0
0
0
5
0
0
0
5
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
1
0
0
0
2
2
2
2
0
0
0
2
0
0
0
0
1
0
0
0
3
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
2
1
2
1
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
1
2
0
1
0
0
0
0
2
2
0
0
0
0
1
0
1
0
0
1
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
5
1
0
3
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
6
0
0
2
0
0
2
0
0
2
0
0
0
3
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
9
0
0
0
1
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
4
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
1
0
0
0
3
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
2
0
0
0
0
2
0
0
1
2
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
2
1
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
3
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
2
0
0
2
0
1
0
0
1
0
1
0
1
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
1
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
3
0
2
1
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
4
1
1
0
0
0
4
2
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
1
2
0
0
0
0
0
0
0
3
2
0
0
0
2
1
0
0
2
1
1
0
0
1
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
1
0
4
0
0
0
0
0
1
0
1
0
2
0
0
1
0
0
0
1
0
1
0
0
0
1
1
0
0
0
1
0
0
1
1
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
3
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
2
1
0
0
0
0
0
0
0
8
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
1
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
3
0
0
0
0
1
0
2
0
1
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
1
0
2
1
0
0
0
5
0
2
0
0
0
1
0
0
0
0
0
0
0
1
4
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
1
2
0
0
1
2
0
0
1
0
2
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
3
1
0
1
2
0
0
1
2
2
0
0
1
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
5
0
0
0
2
1
0
1
0
1
1
2
1
1
1
2
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
1
0
0
1
1
2
0
2
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
1
3
2
0
0
0
1
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
5
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
2
0
2
0
0
1
0
0
0
1
1
0
2
0
2
1
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
2
0
0
0
0
0
0
2
0
0
2
2
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
3
0
1
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
1
0
0
1
2
0
2
0
0
0
0
0
2
1
0
0
1
0
0
0
0
1
1
1
0
0
0
2
2
0
0
0
0
2
1
0
0
2
0
0
0
2
0
0
0
0
0
0
2
2
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
1
3
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
1
2
0
1
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
1
1
1
2
1
0
0
0
1
0
2
0
4
0
0
0
1
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
1
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
1
1
0
0
0
1
0
2
0
2
0
0
0
0
0
1
0
1
4
0
0
1
0
0
0
0
0
0
3
2
2
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
2
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
4
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
2
0
1
0
1
2
0
0
0
1
0
1
0
1
2
0
2
0
0
0
0
0
1
1
0
1
0
0
1
0
1
2
0
0
0
0
2
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
2
2
1
2
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
2
0
1
0
0
1
2
0
0
1
3
0
0
1
0
2
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
8
0
1
2
0
0
0
0
3
0
0
0
0
2
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
2
2
2
0
0
0
1
3
0
0
2
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
2
0
2
2
2
0
1
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
2
0
0
0
0
1
0
1
2
1
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
1
2
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
4
0
1
0
0
0
0
1
7
0
0
2
2
0
0
0
0
0
0
0
0
2
1
1
2
0
1
0
5
0
0
1
2
0
0
1
2
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
2
1
0
0
0
0
0
0
1
1
0
0
2
1
1
1
0
1
0
0
0
4
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
1
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
1
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
2
0
0
0
0
7
0
0
1
0
0
3
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
2
0
0
0
2
0
0
0
0
0
0
1
2
3
0
0
0
3
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
1
2
1
0
0
1
0
0
2
2
0
2
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
3
0
0
0
0
0
0
1
0
2
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
1
2
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
2
3
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
1
2
0
1
0
0
2
0
2
0
0
0
0
1
0
4
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
5
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
1
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
1
1
0
1
1
0
2
0
0
2
0
0
0
5
3
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
2
0
0
0
4
0
0
1
0
0
2
0
0
2
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
3
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
5
0
0
4
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
5
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
2
2
0
2
0
2
0
1
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
2
0
4
2
0
0
0
0
1
0
0
1
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
3
1
0
0
0
3
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
2
0
0
2
0
0
1
2
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
2
3
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
8
0
2
0
0
0
44
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
1
1
0
0
2
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
1
0
0
1
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
1
1
1
0
1
1
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
2
1
0
0
2
0
0
0
0
10
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
2
0
2
0
0
0
1
0
2
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
2
1
1
0
0
0
0
2
5
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
3
0
0
1
1
0
0
0
0
0
0
0
2
2
0
1
0
5
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
2
1
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
1
0
0
1
1
0
1
0
0
0
0
0
2
0
0
2
1
3
0
0
0
0
0
0
2
0
0
2
0
2
0
2
0
0
0
1
0
0
0
0
0
3
1
0
0
0
2
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
3
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
2
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
4
2
1
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
2
0
1
1
0
1
0
0
0
3
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
1
2
0
0
0
2
0
1
0
0
0
1
1
1
0
0
2
0
0
3
0
0
1
2
0
1
0
2
1
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
2
0
4
0
0
1
0
0
2
0
2
0
1
0
0
0
0
3
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
1
0
0
0
0
0
1
0
0
0
2
1
0
1
0
0
0
0
2
0
0
1
2
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
1
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
2
0
1
0
3
0
0
2
0
0
0
0
1
0
0
6
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
3
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
2
0
0
2
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
1
3
0
6
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
2
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
1
1
1
0
1
0
0
1
0
2
2
0
0
0
0
0
2
1
0
1
0
3
0
0
0
0
2
0
2
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
3
0
3
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
1
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
2
0
0
3
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
1
0
0
0
0
2
0
0
0
0
3
1
2
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
3
2
0
0
0
1
1
0
2
1
2
0
0
0
0
0
0
0
0
1
2
1
2
2
0
0
0
0
1
1
2
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
2
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
1
3
0
1
0
0
0
2
1
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
2
0
1
1
0
1
0
1
0
0
0
1
0
0
0
0
2
0
0
1
0
0
1
0
0
0
1
0
0
0
1
1
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
2
0
1
2
2
0
0
0
0
0
0
0
1
0
2
2
2
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
3
0
2
0
2
0
0
0
1
0
1
0
0
0
0
2
0
0
1
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
2
0
1
2
0
0
0
2
0
1
0
5
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
2
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
1
0
1
0
0
1
0
0
0
2
2
2
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
1
1
1
1
0
0
0
2
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
10
2
2
0
0
0
0
0
0
0
2
0
1
0
1
0
0
1
1
0
0
1
0
1
0
0
1
3
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
2
0
2
1
0
0
0
0
1
0
1
2
0
0
0
1
0
0
1
2
0
0
2
0
0
0
2
0
2
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
1
1
2
2
1
0
0
0
0
1
1
3
0
0
0
0
2
0
1
0
1
0
0
2
0
0
0
2
0
2
0
0
0
1
0
1
0
0
0
2
0
0
0
1
0
2
0
0
0
1
0
0
0
0
2
0
2
2
0
2
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
1
2
0
0
0
2
2
0
0
0
0
0
0
0
0
4
0
0
1
1
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
1
0
0
0
2
0
0
0
0
1
4
0
0
1
1
0
0
0
0
0
1
4
0
0
0
0
0
1
0
2
4
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
3
0
2
0
1
0
0
2
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
1
0
0
2
1
2
2
0
1
0
0
0
0
0
1
0
0
0
1
2
0
0
0
1
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
2
2
0
1
0
2
1
0
0
0
0
0
4
0
0
0
0
0
0
0
3
0
0
0
2
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
2
0
0
0
1
0
2
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
2
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
1
2
0
0
1
0
0
0
6
0
3
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
2
0
0
0
1
1
2
0
0
1
0
2
3
1
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
7
0
0
0
0
0
1
0
0
2
0
2
0
1
2
0
1
0
0
0
0
2
0
0
0
0
2
0
3
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
3
0
0
0
2
0
1
1
1
0
0
0
0
0
0
1
0
0
3
0
0
1
0
0
0
0
0
2
0
0
0
0
0
3
2
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
2
0
2
2
0
2
4
0
1
0
0
0
0
1
1
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
2
0
3
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
3
0
0
0
0
2
0
3
1
1
0
0
5
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
3
0
2
0
2
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
4
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
2
0
0
0
1
1
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
1
1
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
4
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
1
0
0
1
2
0
0
0
1
2
0
0
0
0
0
0
0
1
1
0
0
2
0
1
0
1
0
0
2
0
1
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
1
2
1
0
1
0
0
0
0
0
0
0
3
0
2
2
2
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
2
1
2
3
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
4
0
0
3
0
0
0
0
0
2
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
1
2
2
2
3
3
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
3
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
3
0
1
0
0
0
1
0
0
2
0
0
0
0
0
3
0
2
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
1
3
0
1
0
2
0
0
0
1
0
0
2
2
2
1
0
2
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
1
2
0
0
1
0
0
6
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
6
0
0
1
0
0
0
0
0
0
1
0
1
1
0
1
1
1
0
2
0
0
0
1
0
0
0
1
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
1
0
1
0
0
2
0
0
2
0
1
0
0
1
2
0
1
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
1
2
0
0
1
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
2
3
1
1
0
0
1
0
0
0
2
2
0
0
5
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
2
0
2
0
0
0
0
1
0
0
2
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
2
1
0
2
0
2
2
0
1
0
1
1
0
0
0
0
2
2
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
6
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
1
0
2
1
0
0
0
0
0
3
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
1
1
0
1
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
6
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
2
2
0
1
2
1
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
4
0
0
0
0
0
2
0
0
1
0
0
3
0
0
1
0
2
0
0
1
1
3
1
1
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
2
0
0
1
4
0
1
0
0
0
0
0
1
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
2
1
0
2
1
2
0
0
2
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
4
2
0
0
0
2
0
1
0
1
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
6
2
0
0
3
0
0
0
0
0
0
0
0
0
3
2
0
2
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
1
1
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
1
2
2
1
0
0
0
0
0
0
0
0
4
3
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
1
0
1
0
0
0
2
0
1
0
0
0
0
0
0
1
1
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
2
0
0
0
0
1
1
0
1
0
1
0
0
0
0
1
0
1
0
0
0
2
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
4
2
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
3
0
0
2
0
0
0
2
0
1
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
1
1
0
0
1
0
0
1
0
0
0
1
0
1
1
0
1
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
3
3
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
1
0
2
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
2
1
2
4
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
2
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
3
0
1
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
1
1
0
0
2
0
0
0
0
1
0
0
1
2
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
2
0
0
0
0
0
4
1
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
5
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
1
1
0
0
1
0
0
0
2
0
0
0
2
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
5
0
0
1
0
2
0
1
1
0
0
1
2
1
0
0
0
0
1
0
0
3
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
2
1
0
0
1
0
0
0
1
0
6
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
2
2
0
0
0
0
0
2
0
1
0
1
0
0
3
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
2
1
0
2
2
0
1
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
2
1
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
4
1
0
2
2
1
0
0
1
0
2
1
0
2
0
0
2
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
4
0
0
0
0
0
1
0
0
0
0
2
2
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
3
0
0
2
0
0
0
2
1
0
0
0
1
0
0
2
1
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
3
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
4
1
2
0
0
0
2
0
0
0
2
3
0
0
0
1
0
0
1
0
1
0
0
0
1
2
2
0
0
1
0
0
3
0
2
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
2
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
2
1
0
0
0
0
2
2
1
2
0
0
0
3
1
0
1
2
1
0
0
1
0
3
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
4
0
0
2
0
0
1
0
0
1
0
0
3
0
0
0
2
0
1
0
0
0
0
0
2
0
0
1
0
0
0
2
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
1
2
0
0
0
1
2
1
0
0
1
0
0
1
0
0
0
2
0
1
2
1
0
2
0
0
0
0
2
0
0
0
2
0
0
0
1
2
0
0
0
1
2
1
3
2
0
0
0
0
0
0
1
2
0
1
0
0
0
2
2
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
3
0
0
3
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
3
2
0
0
0
0
0
2
0
0
0
0
0
0
0
4
0
0
2
0
1
0
0
0
2
0
5
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
2
0
0
1
0
0
0
0
2
0
0
0
2
0
1
0
1
0
0
0
3
0
2
0
0
0
1
0
0
0
0
0
2
1
0
0
1
0
1
0
1
0
1
2
0
1
3
0
1
0
0
1
0
1
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
2
1
2
1
2
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
2
1
3
1
3
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
1
2
1
0
0
0
0
0
4
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
1
0
0
1
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
2
0
0
1
0
0
1
2
0
0
0
0
0
1
1
1
1
2
0
2
6
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
2
1
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
2
2
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
2
1
0
0
0
0
0
1
3
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
2
2
0
0
2
1
0
0
0
2
0
2
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
1
2
0
0
0
1
1
2
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
2
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
3
0
1
0
2
1
2
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
3
1
2
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
2
2
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
3
0
0
0
2
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
2
0
0
1
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
1
2
0
0
0
1
0
0
0
0
2
0
12
0
1
2
1
0
0
2
1
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
1
2
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
3
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
2
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
3
0
2
0
0
1
1
1
2
3
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
1
0
0
2
2
0
0
0
0
1
0
0
0
2
0
0
2
0
1
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
2
0
0
0
0
2
4
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
3
2
2
3
0
2
0
0
0
0
0
0
0
2
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
1
0
1
0
2
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
2
4
0
1
2
1
0
1
0
2
0
0
2
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
2
0
0
0
0
0
3
1
0
0
0
0
0
0
2
0
0
0
0
2
2
0
2
0
3
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
2
0
3
0
3
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
2
0
1
2
2
1
2
1
1
1
0
1
1
2
0
0
0
1
0
0
8
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
7
0
0
0
2
3
2
0
0
0
0
2
0
0
0
3
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
5
0
0
2
7
0
0
0
2
1
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
1
3
0
1
0
2
1
0
1
2
0
0
1
0
0
2
0
0
0
0
2
6
0
0
1
1
0
0
3
0
0
1
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
2
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
5
2
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
3
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
4
0
2
0
0
0
2
2
0
0
2
0
0
2
0
1
4
0
0
0
0
0
0
1
1
0
2
0
0
2
0
0
0
0
0
2
0
0
1
1
0
0
2
0
0
0
0
1
0
0
0
1
0
2
0
1
0
8
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
2
1
1
0
3
0
1
0
0
0
2
0
2
1
0
0
0
14
1
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
3
0
2
0
1
0
1
0
0
0
2
2
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
1
1
0
0
0
3
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
8
0
0
0
0
0
0
1
1
0
0
0
2
1
0
2
0
2
0
0
0
0
0
1
2
4
0
1
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
3
0
0
1
2
0
0
1
0
0
0
2
2
0
2
0
3
0
2
2
0
2
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
2
0
0
1
0
2
0
1
1
0
1
2
0
0
0
0
1
0
0
2
0
0
0
2
2
0
2
2
0
0
1
0
0
0
0
0
3
1
0
0
3
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
1
0
0
2
0
2
1
0
0
4
0
0
0
3
0
0
0
0
1
5
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
4
0
0
1
0
0
0
0
0
0
2
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
5
0
0
1
0
0
0
0
0
0
0
2
0
1
0
1
0
2
0
1
2
0
1
0
0
9
2
0
0
1
1
0
0
0
3
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
1
2
2
0
0
0
0
2
0
0
0
2
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
4
0
1
0
0
1
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
2
2
0
1
0
2
0
0
0
0
0
0
0
1
3
0
0
0
0
3
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
3
0
0
0
0
3
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
2
0
0
0
1
2
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
13
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
1
0
0
1
1
5
2
0
1
1
1
0
1
0
0
6
1
0
0
0
2
0
0
0
2
0
2
0
1
0
3
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
1
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
4
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
2
1
0
2
3
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
1
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
3
1
0
0
1
0
0
0
0
0
1
2
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
2
0
2
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
1
0
0
1
0
0
0
2
3
0
0
0
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
1
2
3
0
1
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
3
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
2
0
0
0
0
0
0
0
0
3
0
2
2
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
3
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
2
0
0
1
0
0
3
1
1
0
0
0
0
0
0
2
0
0
0
0
0
1
2
3
0
0
3
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
2
0
0
2
0
0
0
3
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
1
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
5
0
4
0
0
0
2
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
4
0
0
1
4
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
1
2
1
0
0
2
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
2
0
1
0
0
0
4
0
0
4
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
2
0
2
1
0
0
0
1
2
2
0
0
0
2
2
1
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
1
0
0
0
2
1
0
4
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
2
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
1
0
0
3
3
0
0
0
1
0
0
2
3
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
1
2
0
0
0
0
1
1
1
0
0
0
0
0
2
0
0
5
1
0
0
0
3
2
0
0
1
2
3
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
5
2
0
2
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
2
4
0
0
2
0
0
0
2
0
1
3
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
2
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
1
0
3
0
3
0
0
0
0
2
0
0
0
0
0
0
0
1
3
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
3
0
0
2
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
1
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
5
0
0
2
0
2
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
1
0
0
0
3
2
2
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
2
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
5
0
4
0
6
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
3
0
0
2
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
1
1
0
10
0
0
0
0
0
0
2
2
2
0
1
0
0
0
0
2
0
2
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
2
0
2
0
0
0
0
1
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
2
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
3
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
1
0
0
3
0
0
0
0
3
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
1
0
0
1
0
1
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
2
0
1
3
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
3
1
2
1
0
0
0
0
1
0
0
1
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
2
1
1
0
2
2
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
2
0
1
0
1
2
0
0
1
2
0
0
0
2
1
0
1
0
0
0
0
2
2
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
3
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
1
0
0
1
1
0
1
3
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
1
0
0
1
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
1
1
0
1
0
4
1
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
2
0
0
3
0
0
0
2
0
0
0
0
0
1
1
2
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
2
0
1
0
0
2
0
1
0
1
0
2
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
1
1
2
0
0
2
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
2
0
2
0
0
2
2
0
0
0
0
2
0
0
0
1
3
0
0
0
3
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
8
1
0
0
0
2
0
0
2
2
0
0
1
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
1
3
8
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
5
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
1
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
1
0
0
0
0
3
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
5
0
1
1
0
1
0
0
2
0
0
0
1
1
0
2
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
1
0
1
1
1
2
0
2
1
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
2
1
0
0
0
0
1
0
0
1
0
2
2
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
1
1
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
1
3
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
3
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
2
0
2
2
1
1
1
0
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
1
0
0
3
0
1
3
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
5
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
3
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
2
0
0
0
0
0
3
1
1
1
0
0
0
0
3
1
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
1
0
0
0
0
0
1
2
0
2
6
0
0
0
1
1
1
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
1
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
4
0
2
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
5
0
2
1
0
2
0
0
2
0
0
0
1
0
0
0
2
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
3
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
1
0
2
0
0
0
0
1
0
2
0
10
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
3
1
0
0
1
0
0
0
0
1
0
2
0
0
1
1
0
0
3
0
0
2
0
2
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
1
0
0
1
1
0
0
0
1
0
0
0
0
2
1
0
0
0
1
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
1
3
0
0
2
0
0
0
2
2
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
6
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
2
0
0
0
0
2
0
1
0
1
2
0
0
0
0
0
1
1
0
0
3
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
5
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
3
3
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
1
0
0
0
3
0
2
0
0
3
0
0
0
0
0
1
2
0
0
1
0
2
0
0
0
1
0
0
1
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
1
2
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
1
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
12
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
4
1
0
1
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
1
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
2
0
2
2
1
1
3
0
0
2
0
0
0
0
2
0
3
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
2
3
0
1
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
6
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
2
0
0
2
0
0
0
0
4
1
0
1
0
0
0
1
0
0
1
0
0
0
0
3
0
2
0
1
0
0
0
2
0
0
0
0
2
2
0
0
0
2
2
0
2
1
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
4
0
1
0
0
2
1
0
0
1
0
18
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
2
0
2
0
1
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
1
0
0
0
0
0
0
1
0
0
0
2
3
2
0
1
0
0
0
0
2
2
0
1
0
1
0
2
0
3
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
2
2
5
0
1
0
3
0
1
0
0
2
0
1
0
0
0
0
2
2
1
0
0
0
0
0
3
2
0
0
3
0
0
2
0
1
2
0
0
0
0
2
1
1
0
6
2
0
0
2
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
3
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
6
2
1
5
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
1
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
3
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
1
0
2
0
0
2
1
0
4
1
0
0
1
2
0
1
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
2
0
0
1
0
1
0
0
0
0
0
0
0
2
0
2
0
2
1
0
0
1
1
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
1
0
1
0
3
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
2
1
0
0
2
0
0
1
0
1
2
0
0
3
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
2
0
1
3
1
0
0
0
1
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
2
0
0
7
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
2
0
2
0
2
0
0
0
0
0
0
3
0
0
3
1
0
1
0
1
0
0
0
3
3
0
0
0
0
0
0
0
0
0
2
0
1
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
2
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
1
0
1
1
0
2
0
0
4
3
0
0
0
0
0
0
4
1
2
2
1
1
0
1
1
0
1
0
0
1
0
0
1
0
0
0
2
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
2
0
1
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
5
0
2
2
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
1
0
0
0
2
0
0
2
4
1
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
3
0
0
0
3
0
2
0
0
0
3
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
3
1
0
0
3
2
0
0
2
0
1
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
1
1
0
0
0
0
0
2
0
1
0
1
0
2
0
2
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
4
2
0
0
1
0
1
0
0
0
1
0
1
2
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
2
1
3
2
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
1
1
0
0
1
0
2
0
0
1
0
1
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
3
2
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
1
2
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
1
0
0
1
1
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
4
0
1
0
0
0
0
0
4
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
7
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
2
0
2
1
0
0
1
0
0
0
0
0
0
4
1
0
0
0
0
2
1
1
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
2
0
3
0
0
1
2
1
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
5
2
0
0
0
0
0
0
2
1
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
3
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
5
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
3
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
2
0
1
1
0
1
0
0
0
0
0
1
0
3
0
0
0
0
0
3
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
1
2
1
0
0
0
0
1
0
1
0
0
0
2
3
2
0
2
0
0
1
0
0
2
0
0
2
3
0
0
2
3
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
4
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
2
0
1
2
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
4
0
0
0
0
3
0
0
0
5
0
0
0
1
2
0
2
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
1
2
0
0
2
0
2
0
0
0
0
1
0
0
2
0
0
1
0
1
0
1
0
0
1
1
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
2
0
0
2
0
3
0
0
0
2
2
0
2
0
0
0
1
2
0
0
0
0
2
0
5
2
2
0
0
0
0
0
12
1
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
4
0
0
0
3
0
0
0
2
0
0
0
0
0
0
2
0
4
0
2
1
0
1
0
2
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
5
0
0
0
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
3
0
0
0
0
2
0
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
3
0
2
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
1
0
0
0
0
2
1
4
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
1
3
0
0
0
0
0
2
0
0
0
4
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
5
0
0
1
0
3
0
0
0
0
0
1
1
0
1
0
0
1
2
6
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
2
0
0
2
0
2
2
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
4
0
0
1
1
0
0
0
0
0
0
1
0
0
0
2
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
2
1
0
0
1
2
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
4
0
0
1
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
1
2
0
0
0
2
0
0
0
0
0
2
0
3
0
0
0
2
0
1
1
0
2
0
5
1
0
0
3
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
1
2
0
1
2
0
0
2
0
2
0
1
2
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
2
2
0
2
2
0
0
0
3
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
1
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
1
3
0
1
1
0
1
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
3
0
1
1
0
0
0
2
0
0
0
1
0
0
1
0
3
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
3
0
2
0
0
0
0
0
2
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
1
0
0
1
0
2
1
0
0
6
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
1
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
1
0
0
3
0
0
0
0
0
0
2
1
0
0
1
0
0
0
3
0
1
0
2
0
0
2
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
2
1
0
0
0
0
8
0
0
0
2
0
4
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
1
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
5
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
5
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
12
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
1
4
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
4
0
4
0
0
2
1
0
1
1
0
0
0
1
2
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
3
1
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
2
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
2
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
2
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
1
0
0
2
1
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
6
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
2
0
1
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
3
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
2
0
0
0
0
0
2
5
0
0
0
1
2
0
0
0
1
0
0
1
0
2
1
0
0
1
2
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
3
0
0
2
1
0
0
1
0
0
0
1
0
0
1
2
3
0
0
2
0
0
4
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
1
2
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
1
2
1
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
1
0
2
0
0
0
1
5
0
0
0
0
0
3
0
0
1
0
2
0
4
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
1
0
0
2
3
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
2
0
0
0
0
2
1
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
2
1
0
0
0
0
0
0
1
2
0
0
3
0
0
0
0
0
2
1
0
0
0
0
2
0
0
2
0
0
0
4
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
1
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
3
0
0
1
0
0
1
2
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
3
1
2
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
1
2
0
2
2
0
2
0
0
2
0
0
3
0
0
0
0
0
1
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
3
0
0
2
0
0
0
1
1
0
0
2
0
0
2
2
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
2
8
0
0
0
0
0
0
1
2
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
1
0
1
2
0
0
0
0
0
1
2
0
1
0
2
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
2
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
1
0
0
0
0
0
0
0
2
0
0
3
0
1
0
0
0
2
0
0
1
0
0
0
1
1
2
0
0
0
1
0
0
0
0
0
2
0
1
0
2
0
0
0
1
0
6
0
0
0
0
0
0
0
2
0
0
0
0
6
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
1
0
0
2
0
0
0
3
0
0
2
1
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
1
1
1
2
1
0
6
0
0
2
2
0
0
0
0
0
0
0
0
0
4
0
1
1
2
0
2
0
0
0
0
0
3
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
5
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
3
1
0
2
0
0
0
0
2
1
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
1
0
0
0
0
0
1
0
2
0
0
0
3
0
1
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
1
0
0
2
2
0
1
0
0
0
0
2
2
0
0
2
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
1
1
0
0
1
0
0
0
0
1
4
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
2
0
0
1
0
1
1
0
0
0
0
0
1
0
0
1
0
3
0
0
2
1
0
2
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
2
2
1
2
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
1
2
0
2
2
0
0
0
2
1
0
2
0
0
0
0
0
1
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
1
0
0
2
0
1
0
0
0
2
0
0
0
2
2
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
3
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
5
0
0
0
0
2
2
0
0
0
0
4
0
1
1
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
1
0
2
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
3
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
2
1
1
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
1
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
1
0
2
0
0
2
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
4
0
0
2
1
0
0
1
2
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
1
1
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
2
2
2
0
1
0
6
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
1
0
2
2
2
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
2
2
1
0
0
3
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
3
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
1
0
0
2
1
0
0
0
1
0
0
1
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
1
0
0
0
2
0
0
1
1
0
0
2
0
1
0
0
2
1
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
2
0
2
4
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
3
0
0
2
0
2
1
0
0
1
0
0
0
0
0
2
2
2
2
0
0
0
0
2
0
0
0
0
1
4
1
0
0
0
0
0
3
1
0
2
0
1
0
3
0
0
0
0
2
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
1
1
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
2
0
2
1
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
1
0
0
0
0
0
1
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
3
2
2
0
2
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
2
0
4
0
2
0
0
0
0
4
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
4
1
0
0
0
0
0
0
2
0
0
4
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
3
6
0
2
2
0
0
0
0
2
0
0
2
0
0
0
1
1
0
0
1
0
0
2
0
2
0
3
0
1
2
0
0
0
0
0
1
3
1
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
1
0
2
0
3
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
2
1
4
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
1
2
0
0
0
2
2
0
2
2
0
0
0
0
0
0
1
2
7
2
0
0
0
0
1
0
1
1
0
1
0
1
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
1
3
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
2
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
2
3
4
0
1
0
0
0
0
2
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
2
1
0
1
0
1
0
2
1
2
1
0
0
0
3
2
0
1
2
2
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
3
0
2
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
2
1
0
0
0
0
0
1
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
2
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
4
0
0
2
1
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
2
2
1
2
0
0
0
0
0
0
1
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
3
2
0
0
0
2
0
0
0
3
0
0
2
0
1
1
0
0
0
1
0
2
0
2
2
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
4
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
3
3
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
3
0
2
0
0
2
2
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
1
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
2
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
1
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
3
0
0
2
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
1
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
2
1
0
0
0
0
0
1
2
0
0
0
0
0
3
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
2
2
1
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
5
0
0
2
0
0
3
2
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
2
0
1
0
0
0
2
0
0
0
0
2
1
0
0
2
0
2
0
0
0
2
0
0
2
0
0
2
1
0
0
1
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
1
0
2
0
2
0
0
0
0
1
2
0
0
0
0
0
0
2
0
6
0
0
1
3
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
5
0
3
2
0
0
1
0
7
0
0
0
2
0
0
0
6
0
2
0
0
7
0
0
0
0
4
0
1
0
1
3
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
10
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
2
2
0
2
1
0
0
0
0
0
2
0
2
0
1
1
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
4
0
0
1
0
5
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
2
0
3
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
4
2
0
0
0
0
1
0
0
6
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
2
0
1
0
0
0
0
0
0
2
2
0
3
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
1
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
3
1
2
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
1
0
0
0
0
0
1
0
3
2
2
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
2
0
1
6
0
2
0
0
2
0
0
0
0
0
2
1
0
2
1
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
3
2
0
0
1
0
0
0
2
1
7
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
2
0
0
2
0
0
0
1
1
0
1
2
2
1
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
1
0
0
1
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
2
2
1
2
0
3
0
0
2
0
1
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
2
2
1
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
2
1
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
1
0
2
0
0
1
0
0
4
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
2
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
2
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
3
0
1
2
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
2
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
2
0
1
0
0
0
0
2
0
2
2
2
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
1
0
0
1
1
0
1
1
0
1
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
2
0
3
0
0
0
0
0
3
0
0
0
0
1
0
0
2
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
2
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
1
1
0
1
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
2
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
2
1
0
0
2
0
0
1
0
1
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
1
3
3
0
0
1
0
0
0
0
1
0
0
0
0
0
2
1
0
0
1
0
2
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
1
2
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
4
2
0
1
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
4
0
1
1
2
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
1
0
0
0
3
0
3
0
0
0
0
0
0
0
1
0
2
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
1
0
0
1
0
0
0
2
1
0
0
2
0
1
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
3
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
4
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
2
0
3
0
0
2
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
3
0
1
1
0
1
0
1
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
6
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
2
2
0
2
0
0
0
0
0
1
0
2
1
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
1
1
1
1
2
0
0
0
2
3
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
1
0
1
0
2
0
0
0
0
1
2
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
2
0
0
1
1
0
0
0
0
2
0
1
1
0
0
0
0
0
1
0
2
0
2
0
0
2
0
2
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
0
3
0
0
0
1
1
0
7
0
0
2
0
0
2
1
2
0
0
0
0
0
0
2
0
0
1
3
0
0
0
0
1
0
0
0
1
2
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
4
0
1
3
0
1
0
0
0
0
0
2
0
0
1
0
1
0
2
0
1
1
0
0
1
0
5
0
0
0
0
4
4
0
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
3
3
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
1
0
0
0
0
0
1
0
0
2
0
1
0
2
0
0
1
0
0
0
1
2
0
2
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
2
0
0
0
2
0
6
0
1
0
1
0
0
0
3
0
2
0
0
2
0
0
0
0
3
0
1
0
0
0
1
0
0
2
0
0
0
0
1
2
0
0
1
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
2
0
0
0
2
2
0
2
1
0
0
1
0
2
1
0
0
0
0
0
1
0
0
3
0
2
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
1
0
0
0
0
1
0
1
0
0
2
0
0
0
1
0
1
0
0
2
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
3
1
0
0
4
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
1
0
0
0
1
0
4
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
5
2
0
2
2
0
0
0
1
1
0
1
2
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
2
0
2
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
7
2
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
3
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
4
0
2
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
3
0
2
2
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
1
0
1
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
3
0
2
2
0
0
2
1
1
0
0
0
1
0
0
2
0
0
6
0
0
0
0
0
0
2
2
0
3
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
3
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
2
0
2
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
1
0
2
0
0
0
0
0
0
1
0
0
2
0
0
3
2
0
0
0
3
2
0
2
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
1
0
0
0
0
1
0
0
0
0
2
0
0
4
0
1
0
0
0
0
0
0
1
1
1
0
1
0
2
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
1
2
2
0
1
0
1
0
1
0
4
1
0
1
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
3
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
1
0
1
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
1
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
1
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
1
2
0
2
0
0
2
0
0
2
0
0
0
2
0
0
3
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
1
0
1
2
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
2
1
2
0
0
0
1
0
0
1
0
2
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
1
0
0
2
0
0
2
0
0
1
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
1
0
0
1
0
2
1
0
2
0
0
0
9
0
2
3
0
0
2
0
0
1
0
2
2
1
1
3
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
2
0
1
1
0
1
1
2
2
0
2
0
0
2
0
1
1
0
0
0
0
0
0
0
1
0
3
0
0
1
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
3
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
2
0
0
0
1
1
1
1
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
12
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
1
0
1
0
0
2
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
3
0
1
1
1
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
1
0
0
2
0
0
2
0
0
2
0
1
0
0
1
3
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
2
0
0
0
0
2
1
0
1
3
0
0
0
0
2
0
0
1
1
1
0
2
0
0
0
1
0
0
0
0
0
2
0
0
2
3
0
0
0
0
0
0
1
0
3
1
2
0
0
0
2
0
0
0
0
1
0
1
0
2
0
1
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
3
0
0
1
0
0
1
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
2
1
1
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
1
0
0
0
2
2
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
1
1
0
0
0
0
4
0
0
0
1
1
0
0
1
0
2
1
0
0
3
3
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
1
2
1
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
11
2
1
0
0
0
0
0
4
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
1
0
1
0
0
1
0
0
0
2
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
1
3
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
1
1
0
0
0
1
0
0
1
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
1
0
0
1
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
2
1
2
0
0
1
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
3
3
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
1
2
0
1
0
0
0
0
0
0
1
2
0
0
1
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
3
2
2
0
2
0
1
0
0
0
0
0
2
1
1
0
0
0
0
2
1
1
2
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
1
1
1
0
1
2
0
0
0
0
0
7
1
0
0
3
2
2
0
0
0
0
3
2
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
2
0
2
0
0
0
2
0
6
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
3
0
1
0
0
0
0
1
1
0
0
3
1
0
0
0
0
0
0
1
0
2
1
1
2
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
2
0
3
0
1
3
2
0
0
0
0
2
0
0
3
3
0
0
0
0
3
0
0
0
0
1
0
1
0
0
0
0
2
0
0
1
2
0
1
0
1
0
0
0
0
0
0
0
0
3
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
3
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
2
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
2
0
0
0
2
1
0
0
3
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
3
1
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
5
0
0
0
3
0
2
0
0
0
0
0
0
0
4
0
0
1
1
0
0
1
0
0
6
1
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
2
2
1
2
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
1
0
0
1
3
0
0
0
2
0
0
1
0
0
0
0
0
0
1
1
2
1
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
3
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
2
0
0
1
0
0
3
0
0
0
0
1
3
0
0
2
0
0
0
3
2
2
1
0
0
2
0
0
0
1
0
0
2
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
4
0
0
1
2
0
0
1
0
0
0
0
0
0
1
0
2
0
0
2
2
0
0
1
0
3
1
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
3
1
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
2
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
6
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
2
0
0
0
0
2
0
2
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
1
1
0
0
2
1
0
0
2
3
0
0
0
0
1
0
2
0
4
0
2
0
3
1
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
2
1
0
0
0
2
0
0
6
0
0
0
0
2
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
1
2
3
2
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
1
1
0
0
2
1
0
0
0
0
5
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
1
5
1
1
1
0
3
0
0
0
0
0
0
2
2
0
0
0
0
0
3
0
1
0
0
5
0
0
0
0
1
0
1
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
13
0
0
2
2
0
0
0
1
0
0
1
0
0
0
1
0
0
0
2
0
0
2
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
1
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
2
1
0
1
1
3
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
4
1
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
3
1
0
1
2
2
0
0
2
0
0
0
2
0
0
0
1
0
3
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
5
2
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
3
0
0
0
0
0
0
0
0
1
0
2
1
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
10
0
1
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
3
1
0
0
0
0
2
2
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
1
0
0
2
0
2
0
0
0
1
0
1
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
3
0
0
0
4
2
0
1
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
2
1
0
1
1
0
1
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
2
0
0
2
0
0
1
0
0
0
2
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
2
0
3
1
0
1
0
0
0
0
1
1
1
0
1
1
0
1
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
2
2
1
0
0
0
0
0
2
0
0
0
0
1
0
0
2
1
0
2
0
1
0
0
0
4
0
0
0
3
0
0
1
2
0
0
0
2
1
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
1
2
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
1
0
1
0
0
0
1
0
0
3
0
0
0
0
2
0
1
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
2
0
0
2
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
3
0
2
0
0
0
0
2
0
0
0
2
2
1
0
0
1
0
0
1
0
0
0
1
0
4
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
8
0
0
0
0
0
0
0
1
0
0
3
0
0
1
0
0
0
0
0
0
0
2
0
2
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
4
0
1
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
2
2
4
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
1
0
0
2
4
0
0
0
0
0
0
0
2
0
4
0
0
3
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
2
6
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
2
1
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
1
0
0
0
0
2
0
4
0
1
0
0
0
0
2
1
0
0
0
0
0
0
4
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
2
0
0
0
1
2
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
2
0
3
1
2
0
0
0
0
1
0
0
0
0
1
2
0
1
0
0
1
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
1
4
2
1
0
0
0
0
1
1
0
0
0
2
0
0
2
0
1
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
2
0
3
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
2
0
1
1
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
1
1
0
0
3
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
4
1
0
6
0
0
0
2
2
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
1
0
1
2
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
2
0
2
3
0
0
0
0
0
2
0
2
1
1
0
0
0
0
3
0
0
1
0
0
0
3
1
0
1
0
0
0
0
0
2
0
2
0
2
0
0
1
0
1
0
0
0
0
2
0
0
0
4
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
1
0
1
0
2
3
0
0
1
0
0
2
0
0
0
0
0
3
0
0
0
0
0
2
0
1
1
0
0
0
1
1
0
0
0
1
2
0
0
0
0
4
2
1
0
0
2
0
2
1
0
0
0
4
2
0
0
0
2
0
2
2
1
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
1
0
0
2
1
0
0
0
0
4
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
1
2
0
0
0
0
0
0
0
2
0
0
2
2
0
0
2
0
2
0
0
0
1
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
2
0
0
0
0
0
0
1
1
2
0
0
0
1
0
0
1
0
0
2
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
1
0
0
2
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
2
2
1
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
2
0
0
1
0
1
2
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
3
0
0
1
0
0
3
1
0
1
0
0
0
0
0
0
0
0
4
0
0
1
0
1
1
0
0
2
0
0
3
0
0
1
0
0
2
1
0
2
0
0
1
0
1
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
7
0
1
6
0
0
2
0
0
1
0
0
0
1
0
3
1
1
0
0
2
0
1
0
0
0
0
2
1
0
0
0
5
0
0
0
0
0
0
0
2
0
1
3
1
0
2
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
4
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
11
0
0
0
0
2
0
0
0
0
1
0
0
2
1
2
0
0
2
0
2
2
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
3
0
0
1
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
3
0
0
1
0
0
1
2
3
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
5
3
0
0
0
0
0
0
0
1
2
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
2
0
2
1
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
2
3
0
2
0
0
0
2
2
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
2
0
2
0
0
1
0
0
3
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
2
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
2
2
0
1
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
3
7
0
3
0
0
0
1
0
1
0
0
0
2
2
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
5
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
13
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
3
3
0
0
2
2
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
1
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
1
1
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
2
1
2
2
0
1
0
0
0
2
0
0
0
0
2
1
0
1
1
1
0
0
0
0
1
2
2
3
0
1
2
2
2
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
2
0
1
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
1
2
2
0
0
2
0
0
0
1
2
0
0
2
0
0
0
0
1
0
0
1
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
4
0
0
2
3
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
6
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
3
0
0
0
0
0
0
0
0
1
0
9
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
3
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
8
0
0
0
0
1
1
0
0
2
2
0
3
0
2
2
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
3
0
0
2
0
0
1
0
1
2
0
0
0
2
0
0
0
1
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
4
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
2
0
0
2
0
5
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
2
0
1
2
2
0
2
1
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
1
0
0
3
0
0
0
1
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
1
2
2
0
2
0
3
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
1
0
0
4
0
1
0
0
0
0
0
0
0
3
1
2
0
2
0
0
0
0
0
4
0
1
4
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
4
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
2
0
0
0
0
1
0
0
1
0
1
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
2
3
0
0
1
0
4
0
0
0
0
0
0
2
0
1
0
1
4
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
1
0
0
2
0
2
1
2
0
0
1
2
4
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
1
5
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
2
2
1
0
0
0
0
0
0
1
0
0
0
2
3
0
0
0
0
0
0
0
0
1
0
1
0
1
3
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
2
1
0
0
0
0
2
2
1
0
0
1
0
0
0
0
0
1
0
0
1
2
2
0
2
3
2
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
4
0
0
0
0
0
2
2
0
1
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
2
2
0
0
0
0
2
3
2
1
0
0
0
0
1
0
0
0
0
2
0
0
1
0
1
0
0
0
0
1
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
3
0
0
0
0
2
2
2
2
0
0
0
0
1
1
0
2
1
0
0
0
0
0
1
0
0
1
10
0
0
0
0
0
1
0
0
0
0
0
3
3
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
2
0
0
2
0
2
2
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
2
0
0
0
2
0
0
1
0
3
0
0
0
2
0
0
0
2
2
0
2
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
2
0
0
1
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
1
0
0
3
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
1
0
0
2
2
0
2
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
5
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
5
2
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
4
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
2
0
1
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
1
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
1
0
0
0
3
0
0
0
0
8
0
0
0
0
0
0
0
0
0
1
0
0
3
2
0
0
2
0
1
1
0
2
0
0
0
0
1
4
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
5
0
0
0
2
0
1
0
1
0
0
2
0
2
0
0
0
2
0
2
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
1
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
3
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
2
0
1
2
0
0
0
0
2
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
3
0
0
0
0
2
0
0
0
2
1
1
0
0
1
0
0
0
0
0
0
0
1
0
3
0
2
0
2
0
0
3
2
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
1
2
0
0
0
1
0
0
0
2
0
0
0
2
0
2
2
5
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
1
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
3
0
0
3
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
3
1
2
0
2
0
2
1
1
0
2
0
1
0
0
2
0
1
0
2
0
2
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
3
1
1
2
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
1
2
0
0
1
1
1
0
2
1
0
1
7
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
2
0
0
0
0
0
2
2
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
1
0
3
0
1
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
3
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
3
1
0
0
0
1
1
0
1
3
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
2
0
2
1
0
2
0
0
1
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
1
0
0
0
3
0
6
0
0
0
0
0
1
2
9
1
0
0
0
0
0
0
0
0
2
1
1
0
0
0
2
0
0
0
2
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
2
0
0
0
2
0
2
2
2
0
1
0
0
1
0
0
0
0
1
1
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
3
0
0
0
2
0
1
0
0
1
0
2
0
2
1
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
1
0
0
0
4
0
1
2
1
0
0
0
0
1
0
0
0
1
0
3
0
1
0
0
0
0
0
1
1
0
0
0
0
0
2
1
0
0
0
0
2
0
0
3
1
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
2
0
2
0
0
0
0
2
2
1
0
0
0
0
0
1
2
0
2
1
3
0
0
2
0
3
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
2
0
1
0
0
0
1
0
0
2
2
0
0
0
2
0
0
0
2
0
0
1
3
1
0
0
0
1
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
3
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
1
0
3
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
9
1
2
0
0
0
0
0
0
0
0
0
0
3
2
0
5
0
0
2
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
2
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
2
0
0
0
2
0
0
1
1
0
0
2
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
1
1
0
1
0
10
0
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
2
0
2
0
0
0
0
1
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
5
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
1
2
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
1
0
2
0
0
0
0
0
2
0
0
2
1
0
1
0
0
0
0
3
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
3
0
0
2
1
0
2
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
2
0
1
0
0
2
2
1
1
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
1
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
2
0
2
2
0
0
1
0
0
1
0
4
0
3
0
1
0
1
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
1
0
0
0
0
0
2
0
0
2
0
1
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
3
3
1
2
0
2
2
0
1
4
1
0
0
2
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
1
1
0
2
1
0
1
0
1
1
0
4
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
1
0
0
1
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
2
0
2
0
0
0
1
0
2
1
2
0
1
0
0
0
2
0
0
0
2
0
2
2
1
0
0
2
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
1
0
2
0
2
0
2
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
1
0
0
0
2
0
2
0
0
1
0
2
0
0
4
3
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
1
1
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
6
4
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
3
1
0
0
5
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
2
0
0
0
0
1
1
1
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
1
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
3
5
2
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
0
1
0
2
2
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
5
1
0
3
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
3
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
2
2
0
1
2
0
0
0
0
0
3
0
2
0
0
1
0
0
0
0
5
0
0
1
2
0
1
0
5
0
1
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
2
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
2
1
2
0
0
2
0
0
0
2
2
2
0
2
0
2
0
0
0
3
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
2
2
0
0
0
0
1
1
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
4
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
1
0
0
0
0
1
0
1
2
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
2
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
2
1
0
0
0
0
1
1
0
0
0
0
1
2
0
1
0
0
2
0
0
0
0
2
0
0
0
0
6
1
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
4
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
3
0
2
0
1
0
0
1
2
1
3
0
0
1
0
0
2
0
0
2
1
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
1
0
2
1
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
2
2
1
0
0
0
3
0
1
0
0
0
2
0
2
2
0
0
0
3
0
0
0
2
0
0
2
1
0
1
4
0
1
2
0
0
1
0
2
1
0
0
0
0
2
0
0
0
3
0
0
0
0
0
2
0
0
0
4
1
0
0
0
0
2
10
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
2
0
4
0
2
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
3
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
3
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
1
3
0
0
0
0
0
2
0
0
9
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
1
2
0
2
2
0
0
0
1
0
0
0
0
0
2
0
0
7
1
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
3
0
0
1
0
0
1
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
3
0
1
0
1
1
0
0
2
0
0
0
2
2
0
0
0
2
0
2
0
0
3
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
6
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
2
2
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
2
3
1
2
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
1
0
2
0
0
0
0
1
1
0
0
0
1
0
0
2
0
1
0
2
2
0
0
1
0
0
1
0
0
3
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
1
4
3
1
0
0
0
2
0
1
2
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
4
0
0
0
0
0
0
0
2
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
1
0
0
0
2
1
0
2
0
1
0
1
1
1
0
0
0
1
0
2
0
2
0
0
0
0
0
0
2
3
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
6
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
2
2
0
4
0
0
2
0
0
0
0
0
2
0
1
0
3
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
2
0
1
0
0
2
1
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
3
0
2
2
0
3
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
2
2
0
0
1
0
2
2
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
4
2
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
1
4
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
3
0
0
2
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
2
0
0
2
0
2
0
0
0
0
2
0
3
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
3
0
2
1
0
0
0
2
2
0
0
0
0
2
0
0
0
2
0
1
0
0
2
0
1
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
2
0
0
4
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
1
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
3
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
1
1
2
0
0
2
1
0
2
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
2
2
0
1
1
0
0
0
1
0
0
1
2
0
0
0
1
0
1
0
0
0
0
1
0
0
2
1
0
2
2
1
0
0
0
2
0
2
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
1
0
0
2
0
0
2
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
2
0
2
0
0
0
1
2
2
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
2
3
0
0
1
0
1
0
0
0
0
0
0
1
2
0
0
1
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
3
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
3
1
0
0
0
3
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
5
1
0
0
1
0
0
0
1
2
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
2
0
0
5
0
1
0
0
0
0
2
1
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
2
4
2
0
0
0
3
3
0
0
1
0
0
3
0
0
0
0
0
2
0
2
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
2
1
0
2
2
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
2
0
0
0
0
5
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
7
0
3
0
0
1
0
2
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
2
0
0
0
1
3
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
2
2
0
2
0
2
0
0
0
1
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
2
3
1
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
2
2
0
0
0
0
0
0
0
0
0
2
0
1
1
2
0
0
0
0
1
9
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
2
0
0
1
2
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
3
0
0
0
1
1
0
0
3
0
2
0
1
0
0
2
0
2
1
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
2
2
0
0
3
0
0
1
0
0
0
0
0
5
2
0
1
0
0
0
5
2
1
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
1
2
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
2
1
1
0
0
2
0
0
1
0
0
1
2
2
0
0
0
0
0
0
0
1
16
1
1
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
2
1
0
0
0
1
0
0
2
0
1
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
2
0
2
2
2
0
0
0
2
0
0
1
0
0
0
1
2
0
0
0
2
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
2
0
0
1
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
3
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
1
0
0
1
0
1
0
2
0
1
0
2
2
0
0
0
2
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
1
1
1
0
0
0
0
0
1
0
1
2
0
0
3
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
3
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
2
1
0
1
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
1
0
3
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
3
0
1
0
0
2
0
0
1
4
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
2
0
1
0
3
0
0
3
0
0
0
1
0
0
3
2
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
2
2
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
1
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
1
0
1
2
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
1
1
1
0
0
1
0
3
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
2
0
0
2
0
0
0
0
0
2
0
0
0
0
1
3
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
4
0
0
0
0
0
0
0
4
2
2
0
2
1
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
5
0
0
2
2
0
0
1
0
0
0
0
0
0
1
0
2
0
0
2
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
1
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
1
0
0
4
0
0
0
0
0
2
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
2
1
1
2
0
2
0
0
0
2
0
0
0
0
2
1
0
0
0
1
0
0
1
3
0
0
0
2
0
2
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
2
1
0
0
0
0
0
0
0
0
1
0
0
1
3
0
0
0
2
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
2
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
1
2
4
0
0
1
0
0
4
0
0
0
0
0
0
1
2
0
1
0
0
1
0
0
0
1
0
1
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
1
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
6
0
0
1
0
0
0
0
1
0
0
1
0
2
0
1
0
3
2
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
2
0
0
0
0
2
2
0
1
0
3
2
0
0
0
0
0
2
0
0
2
0
2
0
3
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
2
0
0
1
0
2
0
0
2
0
0
0
0
4
1
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
1
0
3
0
2
0
0
0
4
0
0
3
1
0
0
0
0
0
2
0
0
0
5
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
3
1
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
4
0
1
0
0
0
0
1
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
7
0
0
0
0
1
0
0
0
0
1
0
3
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
2
0
1
0
2
1
2
0
0
0
1
0
1
2
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
2
2
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
2
0
0
0
1
0
0
1
0
0
1
0
1
1
0
0
1
0
1
0
0
0
1
0
0
1
0
0
2
0
1
2
2
0
1
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
3
0
2
2
0
2
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
2
1
2
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
1
1
0
1
0
0
0
0
0
1
0
0
1
0
1
1
2
0
0
1
2
0
0
0
2
3
0
0
0
0
0
0
2
2
0
0
2
0
4
0
0
0
2
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
1
0
1
0
0
0
0
3
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
2
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
2
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
1
2
0
0
0
0
1
0
3
0
0
0
0
2
0
0
0
0
0
1
0
0
0
20
0
0
1
1
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
3
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
1
1
2
0
1
0
0
3
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
2
0
1
0
0
2
0
0
0
1
0
0
1
0
0
2
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
1
0
2
0
0
3
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
2
0
1
0
0
1
0
0
0
0
0
2
0
0
2
2
0
0
1
0
1
3
5
0
1
0
0
0
0
1
0
0
0
3
0
0
2
0
0
0
1
0
0
1
0
1
0
0
0
2
0
1
0
1
0
0
0
0
2
1
0
1
1
1
2
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
3
0
0
3
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
5
2
0
3
0
0
0
0
2
3
0
0
5
1
1
1
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
1
0
0
0
0
0
0
2
0
0
0
2
3
0
0
0
0
0
1
0
3
2
0
0
2
4
2
0
0
0
0
1
1
2
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
1
0
0
1
1
3
0
2
0
0
0
0
0
0
0
1
1
0
0
0
1
0
3
0
2
0
0
0
1
0
0
0
0
0
2
1
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
4
0
0
1
2
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
3
1
0
0
2
0
0
0
1
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
1
0
0
2
1
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
3
1
0
1
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
2
0
0
1
2
1
1
1
0
0
0
2
0
0
0
0
2
0
0
0
4
0
0
0
2
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
3
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
2
2
2
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
2
2
0
0
1
0
0
0
1
0
1
0
0
0
1
0
3
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
2
1
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
6
0
2
0
0
0
0
3
0
0
0
0
0
0
0
2
4
0
0
0
1
1
1
0
2
0
0
2
0
0
0
2
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
4
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
2
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
3
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
1
0
0
0
0
2
0
1
0
0
0
0
1
0
0
4
0
0
3
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
2
1
0
1
0
0
1
1
1
0
1
0
0
0
0
0
0
1
0
0
0
2
0
1
2
0
3
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
5
0
0
0
1
0
2
0
0
0
0
1
3
0
0
1
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
2
2
1
2
1
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
1
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
1
0
0
1
0
0
0
0
0
1
2
1
2
5
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
1
0
1
0
2
0
1
0
0
0
0
0
0
0
2
1
0
2
0
1
1
0
0
0
0
0
0
1
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
3
0
0
0
1
1
3
0
4
0
0
0
0
2
0
0
0
0
2
3
3
0
0
0
0
2
0
0
1
0
1
1
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
1
1
1
0
0
0
2
0
0
1
0
2
5
0
0
0
0
0
2
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
1
5
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
2
2
0
2
4
0
2
0
1
0
0
0
0
0
2
1
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
1
0
0
1
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
2
3
0
0
0
0
0
0
0
1
0
1
0
0
0
4
0
1
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
3
0
1
0
0
2
2
0
0
0
1
0
0
7
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
7
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
2
3
0
0
0
0
0
0
0
2
0
2
0
0
2
0
1
1
0
0
0
0
0
0
0
0
4
0
2
0
0
0
0
2
2
2
1
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
2
1
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
2
2
0
0
0
0
2
2
0
2
2
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
2
0
2
1
0
2
1
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
6
1
0
1
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
1
1
2
0
0
5
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
1
2
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
7
5
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
2
2
0
1
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
2
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
1
1
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
1
1
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
1
0
0
0
2
2
0
0
0
1
0
2
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
2
0
0
0
0
0
2
0
1
0
1
2
0
2
0
1
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
2
1
0
0
0
0
3
0
2
0
2
1
0
0
0
0
0
0
0
1
2
0
0
0
0
2
2
0
0
0
2
2
0
2
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
4
0
0
0
1
0
0
0
0
0
2
3
0
0
0
1
0
1
0
0
0
0
3
0
0
1
4
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
2
1
0
0
0
0
4
0
0
2
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
6
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
1
0
0
1
0
1
0
0
0
0
3
0
2
0
0
0
0
0
1
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
3
1
0
2
0
0
1
0
1
0
1
0
1
0
0
2
0
0
1
0
0
1
0
2
0
0
0
0
0
0
7
0
0
1
0
0
1
0
2
2
0
0
0
0
1
0
0
2
2
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
1
0
0
2
0
0
0
0
5
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
2
2
0
1
0
1
0
0
2
0
0
0
2
0
0
0
3
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
2
0
1
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
4
2
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
1
0
2
0
0
2
0
2
0
1
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
3
2
0
0
0
0
1
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
2
0
4
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
1
1
4
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
3
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
1
2
1
0
0
0
1
1
0
4
1
1
0
0
0
0
3
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
3
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
4
0
0
2
3
0
0
0
2
0
0
1
0
2
1
2
2
2
0
0
0
2
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
2
5
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
4
2
0
1
0
0
0
1
0
0
1
2
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
2
4
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
7
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
3
0
2
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
1
0
0
3
0
0
0
5
0
0
1
0
0
0
4
0
1
0
2
0
0
1
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
2
7
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
1
1
1
0
1
0
0
2
0
1
0
0
0
0
0
2
0
1
0
0
0
1
0
1
0
0
3
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
2
1
0
0
0
2
0
0
0
0
0
0
2
0
2
0
1
0
1
1
0
1
2
2
0
0
0
0
0
1
0
0
2
0
2
0
0
0
2
0
3
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
2
0
2
0
3
2
1
0
2
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
12
0
0
0
0
1
0
0
0
2
0
0
1
0
1
0
0
2
0
0
0
1
0
1
0
0
0
0
0
3
0
0
0
0
0
1
0
1
1
1
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
3
0
0
2
0
0
2
1
0
0
2
0
1
0
0
0
0
0
0
2
0
1
0
0
0
3
3
0
1
0
0
0
0
0
2
0
0
1
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
2
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
2
0
1
3
0
0
0
0
0
1
1
0
2
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
1
2
1
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
4
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
2
0
4
0
1
1
0
0
1
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
2
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
1
0
0
0
7
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
2
0
3
2
2
0
0
0
0
0
3
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
2
0
1
9
0
0
0
2
1
0
1
1
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
1
2
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
2
0
3
0
0
2
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
3
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
10
0
0
0
0
0
0
0
0
2
1
0
0
0
4
0
0
0
2
0
0
2
0
0
0
1
2
0
0
2
0
0
0
1
0
0
0
1
0
0
0
1
2
0
0
1
0
2
0
0
0
0
1
2
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
2
2
0
0
0
0
0
0
3
3
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
2
0
0
0
3
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
1
1
1
0
0
0
1
0
0
1
2
0
0
0
0
0
1
0
1
0
7
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
1
0
1
0
2
0
1
0
0
0
0
3
1
0
0
0
0
0
0
0
1
0
1
1
0
2
2
0
0
1
0
0
0
1
0
1
0
0
0
0
2
1
0
0
0
0
2
2
0
0
0
0
0
2
0
0
4
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
3
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
4
2
0
0
6
2
0
2
0
0
0
0
0
0
2
1
0
2
0
0
0
0
1
0
1
3
0
2
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
1
3
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
6
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
2
0
9
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
2
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
2
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
2
0
0
0
6
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
3
0
0
1
1
0
0
0
1
0
0
3
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
1
2
0
0
0
2
0
2
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
1
0
0
0
2
0
2
0
0
3
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
2
0
1
0
0
2
0
2
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
2
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
1
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
2
0
0
0
0
2
1
0
2
2
2
1
0
3
0
2
0
1
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
2
0
0
0
0
1
2
2
0
2
1
0
4
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
2
3
1
0
1
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
1
2
0
3
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
3
1
0
2
0
0
0
0
0
1
2
0
0
2
0
1
0
0
4
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
6
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
1
2
0
0
0
2
0
0
1
1
0
0
1
1
1
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
4
3
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
1
0
0
2
0
1
2
3
0
0
0
0
1
0
0
0
0
0
0
2
1
1
0
2
0
0
1
0
0
0
0
1
3
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
7
0
0
0
1
1
0
1
1
0
0
0
2
0
0
1
0
0
0
2
0
2
0
0
2
1
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
2
0
0
2
2
1
0
0
0
0
0
0
0
3
1
0
0
0
1
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
1
0
2
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
1
0
0
0
1
1
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
3
3
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
6
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
2
0
5
1
0
2
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
2
2
0
0
0
0
0
1
1
2
0
0
0
0
2
0
0
0
2
1
0
0
1
0
2
0
0
2
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
2
0
2
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
2
2
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
4
1
0
1
0
0
0
0
0
7
0
2
0
0
0
0
0
2
0
1
0
0
1
0
1
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
2
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
10
0
0
0
1
0
0
2
2
2
0
0
1
0
0
0
0
2
0
0
0
2
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
4
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
3
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
4
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
1
1
0
0
2
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
1
1
0
0
0
0
0
4
1
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
6
0
1
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
1
1
1
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
1
2
0
0
0
2
2
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
2
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
3
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
2
1
0
3
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
1
3
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
2
0
2
0
2
0
0
2
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
2
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
1
0
1
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
5
1
0
0
2
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
4
3
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
3
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
1
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
2
0
0
0
0
2
0
0
0
0
0
3
0
4
0
1
1
0
2
2
2
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
1
4
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
1
1
2
3
2
0
1
0
0
1
1
0
0
0
1
0
0
0
2
2
0
2
0
2
0
1
0
0
1
0
0
1
0
2
0
0
0
0
1
0
2
0
0
0
0
3
0
0
1
0
0
0
0
0
3
0
0
3
3
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
1
1
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
1
2
2
2
3
0
2
0
0
0
1
0
0
1
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
3
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
2
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
3
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
4
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
2
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
2
3
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
3
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
2
0
0
0
1
1
0
0
1
0
8
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
1
2
0
0
1
1
0
0
2
0
1
1
0
1
0
2
0
1
2
0
0
0
0
0
0
0
1
0
0
0
1
0
2
2
0
0
0
0
0
1
1
1
0
1
0
1
1
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
1
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
1
0
1
0
2
0
2
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
2
0
0
0
1
4
1
1
2
0
0
0
1
0
3
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
4
2
0
3
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
2
0
1
0
1
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
1
2
0
0
1
0
2
0
0
0
0
1
0
2
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
2
2
0
1
0
1
0
0
1
0
0
2
0
0
0
0
2
0
0
0
1
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
1
0
2
0
2
0
0
0
0
0
2
0
0
1
0
0
1
0
2
0
0
2
0
1
0
0
0
0
0
2
0
1
0
0
1
1
2
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
2
0
0
0
3
1
0
0
0
0
1
0
2
2
4
0
2
0
0
2
2
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
2
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
2
0
3
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
2
1
0
0
1
0
0
0
0
0
2
0
0
0
0
1
1
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
5
0
0
0
1
2
0
0
0
0
1
1
2
0
0
0
1
0
0
0
2
3
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
8
0
0
2
0
0
0
0
0
1
2
1
1
0
0
0
0
0
0
0
0
0
4
1
0
0
0
6
0
0
0
0
0
2
0
2
0
1
1
0
0
0
0
0
2
0
0
0
0
1
0
2
0
2
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
1
0
1
0
0
0
1
0
2
2
0
0
1
0
0
0
2
0
0
0
0
1
0
3
0
1
0
0
2
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
2
1
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
1
0
0
0
2
0
1
2
0
3
0
0
0
1
2
0
0
0
0
2
0
2
1
0
0
2
0
2
0
2
2
1
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
2
1
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
1
0
2
0
2
0
0
2
0
1
1
0
0
1
0
0
2
7
3
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
2
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
2
0
1
0
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
1
0
3
0
0
0
0
0
0
0
2
1
0
0
0
1
1
1
0
0
0
0
0
2
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
1
1
3
0
0
1
2
0
0
0
1
0
0
0
0
1
0
0
0
0
1
3
2
1
0
0
0
0
0
0
2
1
1
1
0
0
2
0
0
0
0
4
1
0
0
0
0
0
1
0
0
2
3
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
3
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
1
3
1
2
1
0
0
0
0
0
1
0
2
0
4
0
0
0
0
2
0
0
0
0
0
0
0
3
2
0
0
0
4
0
1
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
2
1
0
0
4
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
2
2
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
2
0
0
0
2
0
2
0
2
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
1
0
2
0
3
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
4
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
3
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
1
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
3
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
3
0
0
0
2
1
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
2
0
2
2
4
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
3
1
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
1
0
0
2
0
0
2
2
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
1
0
1
0
0
0
1
0
0
0
3
0
0
0
2
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
2
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
2
2
1
1
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
2
0
0
0
2
0
1
2
2
0
2
0
1
0
0
0
0
2
3
0
0
0
0
0
0
0
4
0
1
0
2
2
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
3
0
0
0
2
0
0
0
0
0
0
0
0
0
3
1
1
0
0
1
0
0
0
1
3
0
2
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
1
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
2
2
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
1
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
1
1
0
0
1
0
1
0
0
1
0
1
0
4
2
0
0
1
0
0
0
0
2
0
2
0
2
0
0
0
2
0
2
0
0
1
0
0
2
0
1
0
0
2
1
0
0
1
0
0
3
1
0
0
0
0
0
0
0
2
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
2
0
1
0
4
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
1
1
0
0
0
2
0
1
0
1
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
2
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
2
0
0
0
2
2
0
0
0
2
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
1
1
1
0
1
0
0
9
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
3
2
2
0
3
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
1
3
1
0
0
0
0
0
1
0
2
0
0
0
1
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
1
9
0
0
0
0
0
0
2
0
1
0
2
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
4
1
0
2
2
0
0
0
2
0
0
2
1
2
0
1
0
0
0
1
0
0
0
0
0
2
2
0
0
0
3
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
5
0
0
0
2
2
2
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
3
0
0
0
3
1
1
1
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
3
0
0
1
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
3
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
1
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
3
2
0
1
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
5
0
2
2
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
3
0
0
2
0
0
0
1
2
0
0
0
0
0
2
2
0
0
0
0
0
0
3
0
0
0
1
0
1
0
0
2
1
0
0
3
0
0
6
0
0
1
0
0
0
0
0
0
1
0
0
0
2
1
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
2
0
1
0
0
0
1
0
0
0
2
1
0
1
0
0
0
0
2
0
1
0
0
2
0
2
0
0
0
0
2
0
3
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
2
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
1
0
0
3
0
0
0
0
0
0
2
0
0
0
0
1
0
0
3
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
2
1
0
0
1
0
0
1
2
0
0
2
0
1
2
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
1
0
1
2
1
0
1
0
0
1
1
2
0
0
7
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
2
2
2
0
2
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
4
0
0
0
1
3
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
3
0
1
0
0
0
1
0
1
0
0
1
0
2
0
0
0
1
0
0
0
0
4
0
1
2
0
0
0
2
2
1
0
1
0
0
1
0
1
0
0
2
0
0
0
0
0
1
2
1
0
0
2
0
0
0
1
0
0
1
0
1
0
6
0
0
0
2
3
0
0
2
4
0
0
2
0
0
0
0
0
1
0
1
2
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
4
0
1
0
0
0
0
0
0
1
2
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
2
0
2
2
0
1
0
1
3
0
1
0
0
0
2
0
0
0
0
0
0
0
2
1
1
0
1
1
0
0
0
0
2
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
3
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
6
2
0
1
1
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
1
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
1
0
0
1
1
0
1
1
0
1
0
1
1
1
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
8
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
2
0
0
0
0
2
0
0
0
0
0
0
3
0
0
1
0
0
0
1
0
2
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
2
0
2
0
2
0
0
1
0
0
0
1
0
0
3
4
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
2
1
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
2
3
1
5
1
0
0
0
0
2
1
0
0
1
0
0
2
2
0
0
2
0
2
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
6
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
1
0
0
0
2
0
0
1
1
0
0
2
0
0
0
2
4
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
4
2
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
1
0
0
5
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
1
0
0
1
2
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
1
0
2
0
3
0
0
0
0
1
0
0
0
1
0
0
1
0
3
1
0
1
0
0
2
1
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
2
1
2
0
0
0
0
8
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
1
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
2
1
2
0
0
0
2
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
2
1
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
2
2
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
3
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
3
2
0
0
0
0
2
1
3
0
2
0
1
0
1
0
0
0
1
0
1
0
0
0
2
1
0
0
0
0
2
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
2
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
1
0
1
0
0
0
0
0
3
0
1
0
0
0
0
0
5
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
4
1
0
0
1
0
0
2
9
0
0
0
1
2
3
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
3
0
1
0
0
2
0
0
0
0
0
2
1
1
0
0
0
2
0
1
1
0
2
0
0
0
1
0
0
0
1
2
0
0
2
2
2
1
2
0
0
0
0
0
0
0
1
0
0
0
3
0
0
2
0
2
0
0
3
0
0
0
2
0
0
0
0
0
5
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
2
1
1
0
0
0
0
1
2
0
0
3
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
1
2
0
2
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
1
2
3
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
2
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
1
3
0
0
0
0
1
0
9
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
3
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
2
1
1
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
2
0
0
2
0
0
2
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
1
1
2
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
2
5
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
1
0
2
0
0
1
0
1
1
2
0
2
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
3
0
0
0
0
2
0
1
0
0
0
0
2
1
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
2
2
0
0
0
1
1
0
2
0
0
3
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
2
0
0
0
2
0
0
1
0
2
1
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
2
2
0
0
0
0
0
1
0
1
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
2
2
0
2
0
2
1
0
0
0
0
0
1
0
2
0
0
3
0
0
0
0
0
1
0
0
2
0
0
0
0
2
1
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
4
0
0
2
0
0
2
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
1
1
0
1
0
1
3
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
3
0
1
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
1
2
1
0
1
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
2
0
1
1
0
0
0
2
0
2
0
0
0
1
2
0
0
0
1
0
0
4
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
1
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
1
2
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
3
1
0
0
4
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
3
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
1
0
1
2
0
0
5
0
2
2
0
1
0
0
2
0
0
0
0
0
1
0
1
0
2
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
2
0
3
1
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
2
0
0
0
0
3
1
2
1
0
2
0
0
3
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
1
2
0
0
2
0
2
0
0
0
0
2
1
0
0
0
2
0
0
1
1
0
0
0
1
0
0
0
0
1
4
0
0
0
2
0
5
0
0
0
3
0
2
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
3
0
0
1
0
0
3
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
3
0
3
1
5
0
1
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
2
0
0
0
0
0
1
0
4
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
4
0
2
0
0
2
0
2
0
0
2
0
0
1
0
0
1
0
2
0
0
0
0
0
0
1
2
1
1
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
1
0
2
0
0
0
0
0
1
2
0
0
2
0
0
2
0
0
0
0
2
0
0
1
0
0
1
4
0
2
0
0
0
2
2
0
0
2
2
0
0
0
1
1
2
0
0
0
0
0
0
1
1
0
2
2
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
1
0
0
2
1
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
2
2
0
2
0
2
0
0
0
0
0
2
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
3
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
7
0
0
2
1
0
0
2
2
0
0
1
3
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
2
0
2
0
1
2
0
1
0
2
0
1
0
1
2
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
1
0
2
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
1
0
0
0
0
2
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
2
0
2
0
2
0
1
1
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
1
0
0
1
0
12
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
1
0
1
0
6
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
2
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
1
0
0
0
1
0
1
0
0
2
0
0
0
1
0
2
0
1
1
0
0
0
1
0
0
0
2
0
1
0
0
0
1
0
0
0
2
1
0
2
0
0
1
2
0
0
1
0
1
0
1
0
0
0
0
2
0
0
2
0
0
1
0
0
0
1
1
0
0
0
2
2
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
3
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
2
1
0
0
0
0
1
2
0
0
0
0
2
0
0
0
1
2
1
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
1
2
2
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
2
0
0
0
0
2
0
1
1
0
0
0
0
4
2
0
0
0
0
0
2
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
1
0
5
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
3
2
0
0
0
2
1
0
0
0
0
0
0
1
0
0
2
1
1
0
0
1
0
0
0
0
2
0
0
0
2
2
0
0
0
0
1
0
2
0
2
0
1
1
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
5
2
0
0
1
0
2
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
1
2
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
2
1
0
0
2
0
0
2
0
3
0
0
0
0
0
3
0
0
0
1
0
1
0
0
0
3
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
2
0
2
0
0
0
2
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
2
0
2
2
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
1
2
0
0
1
1
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
4
0
0
0
0
2
0
0
0
2
0
3
0
0
2
2
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
2
1
2
0
0
2
0
2
0
0
0
0
0
0
2
0
1
3
0
1
2
0
0
0
0
0
0
0
0
0
2
1
2
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
3
2
0
0
0
4
0
0
1
0
0
0
0
0
0
0
1
2
2
0
0
0
0
1
0
0
0
1
2
0
0
1
2
0
2
2
1
0
1
0
0
1
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
3
0
2
0
0
0
0
0
0
0
2
1
0
1
0
2
3
0
1
0
2
2
2
0
2
2
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
2
3
0
1
0
0
0
0
1
1
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
1
1
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
2
2
0
0
0
0
0
1
0
2
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
1
0
0
3
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
3
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
3
0
0
0
0
2
0
1
2
0
0
0
0
0
0
1
0
0
0
3
0
0
1
1
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
1
0
2
5
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
7
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
2
1
2
3
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
3
0
1
0
1
0
0
0
0
2
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
2
1
0
4
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
2
0
2
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
2
0
2
0
0
1
0
1
0
0
0
2
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
1
0
1
0
0
0
1
2
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
3
0
1
0
0
2
0
2
0
0
1
0
5
1
2
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
1
0
7
0
0
2
0
0
0
0
0
2
0
0
2
1
2
0
0
0
1
5
0
1
0
0
1
0
0
2
0
1
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
1
2
2
0
0
1
0
0
0
1
0
0
2
0
0
3
0
1
1
3
1
1
0
0
0
0
0
0
0
1
15
1
0
0
2
0
1
0
0
1
0
0
0
2
1
2
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
2
2
2
0
2
0
0
2
2
0
2
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
3
0
3
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
3
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
4
0
1
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
1
0
2
2
1
0
0
0
0
1
0
0
0
5
2
1
0
0
0
0
2
0
0
1
0
2
1
10
0
0
0
1
1
1
2
0
2
0
2
0
0
1
1
0
0
0
2
0
1
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
1
3
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
3
0
1
0
0
0
1
1
2
0
0
2
0
1
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
2
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
1
1
0
1
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
4
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
2
0
0
0
1
1
0
1
0
2
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
3
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
2
0
0
0
0
2
0
0
0
2
0
3
2
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
1
0
0
2
0
1
6
0
0
0
0
0
1
0
0
1
2
0
0
1
2
0
1
0
0
0
2
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
2
2
0
2
0
0
0
0
0
1
0
0
2
0
1
1
0
2
0
0
2
2
2
0
1
0
2
0
6
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
1
2
0
0
0
1
0
0
0
2
0
1
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
1
1
0
0
0
0
0
1
2
1
0
1
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
2
1
0
0
9
0
0
0
2
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
2
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
1
1
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
2
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
2
0
1
2
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
1
3
0
0
1
0
2
0
0
0
0
0
0
1
0
0
1
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
1
0
1
1
0
0
2
1
0
0
0
2
0
0
0
0
2
0
0
1
1
0
0
0
2
0
0
0
0
0
1
0
1
1
4
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
2
0
0
0
2
2
0
0
1
0
0
0
2
0
0
1
0
1
1
0
0
1
0
0
0
4
0
0
2
0
0
1
0
0
1
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
3
0
0
0
0
0
0
1
0
2
1
2
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
2
0
3
0
2
0
0
2
0
0
0
0
0
1
0
4
0
2
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
1
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
2
1
1
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
3
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
1
2
0
0
2
0
0
0
0
0
0
2
2
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
2
2
1
0
0
0
1
0
2
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
1
0
0
2
0
0
3
1
0
2
0
0
0
0
0
2
0
0
0
0
1
0
6
0
0
0
2
4
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
2
1
0
0
2
0
0
0
0
0
1
0
0
3
0
2
0
0
3
0
0
0
2
0
2
2
2
2
0
3
0
0
5
2
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
1
0
1
0
1
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
2
0
3
0
0
0
0
1
2
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
1
0
2
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
2
0
1
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
2
0
0
0
6
0
2
0
0
1
2
0
1
0
0
0
0
0
0
2
1
2
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
3
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
2
0
1
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
1
0
0
0
7
0
1
2
0
0
3
0
0
0
0
0
0
8
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
3
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
3
0
1
1
0
1
0
0
0
0
0
2
2
2
0
0
1
0
0
1
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
4
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
5
0
1
0
0
1
0
1
0
2
0
0
0
0
0
1
0
0
0
3
4
1
0
0
0
0
0
0
0
0
0
1
4
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
2
0
1
0
2
0
0
0
0
0
2
0
0
2
1
0
0
0
1
2
0
0
0
0
0
2
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
1
0
2
0
0
2
2
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
2
1
0
2
0
2
0
0
0
1
0
0
5
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
5
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
2
1
0
0
2
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
1
0
0
1
0
1
0
0
0
2
0
0
0
1
0
2
0
1
0
0
0
0
3
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
2
0
1
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
2
0
0
0
0
2
3
0
0
1
0
2
2
0
2
0
0
0
0
1
1
0
0
0
0
0
0
1
0
6
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
1
0
1
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
4
0
1
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
1
2
0
2
0
0
2
0
0
0
2
0
0
1
3
1
1
1
1
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
2
0
1
0
0
1
1
0
0
0
0
1
0
0
2
0
1
1
0
0
0
0
0
0
0
0
3
1
6
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
2
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
3
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
1
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
1
2
0
2
2
0
0
1
0
0
2
0
3
1
0
0
0
1
0
2
0
0
2
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
2
0
2
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
2
0
0
3
0
0
0
0
0
1
0
2
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
2
2
1
0
0
0
0
0
2
0
2
0
2
3
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
2
2
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
3
0
2
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
3
1
0
0
0
0
1
2
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
2
3
0
0
0
0
0
1
0
1
0
0
3
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
2
1
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
1
0
0
2
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
1
0
3
0
0
0
2
0
2
0
2
1
1
1
0
0
0
0
0
2
0
1
0
0
2
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
2
0
1
1
0
2
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
3
0
0
0
1
2
0
0
0
0
0
0
0
0
3
0
1
0
0
0
1
0
0
1
0
2
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
1
0
0
0
0
0
4
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
11
0
0
3
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
1
0
0
0
0
2
3
0
0
0
1
1
0
1
0
0
1
0
0
0
0
1
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
1
0
1
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
3
0
0
0
1
0
2
0
0
0
2
0
2
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
2
0
0
0
2
0
0
0
0
1
1
1
0
0
0
2
0
0
3
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
3
2
0
0
0
0
0
0
3
0
1
3
0
0
0
0
0
0
0
0
3
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
4
0
1
2
2
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
1
0
0
2
0
3
0
1
1
0
2
2
1
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
2
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
1
0
1
2
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
5
1
0
0
0
0
0
0
0
0
0
0
2
2
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
3
0
0
0
4
0
0
1
0
4
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
2
0
0
3
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
6
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
2
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
2
0
1
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
4
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
2
2
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
3
0
0
0
0
5
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
2
0
0
1
0
0
3
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
1
1
2
1
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
1
1
1
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
2
2
0
0
3
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
3
2
0
1
1
0
0
0
0
0
0
3
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
5
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
3
1
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
2
0
1
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
1
0
1
0
0
0
1
2
2
0
0
1
0
0
2
2
0
0
1
0
1
3
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
2
1
0
0
1
1
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
1
0
2
0
2
0
0
1
1
3
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
1
2
5
0
0
0
2
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
4
0
0
0
0
0
0
2
0
0
0
0
1
0
2
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
2
0
0
0
0
27
1
1
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
1
1
0
0
0
0
2
2
0
0
0
0
0
2
0
0
1
1
0
0
1
0
0
0
6
0
1
3
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
1
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
4
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
2
0
0
0
1
7
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
1
6
0
0
0
1
0
2
0
2
2
0
1
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
2
1
0
17
0
2
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
2
2
0
0
0
0
0
1
0
3
2
0
1
1
0
0
0
3
0
0
2
0
0
1
0
0
2
0
0
0
2
0
0
2
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
3
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
2
0
0
0
0
0
0
2
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
1
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
7
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
2
0
0
2
0
0
1
1
0
4
0
0
2
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
4
1
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
1
2
1
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
2
0
0
0
2
0
1
0
4
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
1
0
1
0
1
0
0
2
0
0
0
3
1
3
2
0
0
0
1
0
0
0
1
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
1
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
3
0
0
2
0
0
0
0
2
0
0
2
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
1
0
6
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
2
2
0
4
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
3
0
0
0
0
2
0
3
0
0
0
4
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
1
2
0
1
0
0
0
0
2
3
0
0
0
1
0
0
0
1
0
0
2
2
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
3
0
0
0
0
1
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
2
2
2
0
2
0
5
0
0
0
0
0
0
0
0
2
0
0
0
6
0
0
0
0
0
1
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
1
1
0
2
0
2
0
0
0
0
0
1
0
6
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
1
0
1
0
14
2
2
1
0
0
0
2
0
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
3
0
0
0
0
3
0
0
0
0
5
0
1
0
1
2
0
1
0
0
0
2
2
1
0
1
0
0
2
0
2
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
6
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
2
1
0
0
3
0
0
0
0
2
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
1
0
0
0
2
2
0
0
0
0
2
0
0
2
0
0
0
3
1
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
2
2
0
0
0
2
0
0
1
0
1
0
0
0
0
1
0
0
3
0
2
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
5
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
4
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
1
0
2
0
0
0
2
0
0
1
1
0
0
0
0
1
0
0
2
2
0
0
0
0
2
2
2
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
2
0
2
0
0
0
1
2
0
2
0
0
0
0
0
0
2
0
1
0
1
1
0
0
0
1
0
0
0
1
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
2
0
0
0
1
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
2
2
0
1
0
0
1
2
1
0
0
0
0
0
0
2
0
3
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
3
0
1
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
2
1
0
3
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
1
0
0
0
2
1
0
0
0
2
0
1
0
0
0
1
0
0
1
1
0
1
0
0
0
0
2
0
0
0
2
0
0
0
2
0
1
1
2
0
4
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
1
2
0
0
0
0
0
2
0
2
0
3
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
3
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
2
1
0
0
0
2
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
3
0
2
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
2
1
2
2
0
4
2
0
1
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
2
0
2
1
0
1
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
2
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
3
2
0
0
0
1
0
0
0
1
3
1
1
2
2
0
1
2
2
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
3
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
2
0
2
2
0
0
1
0
2
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
2
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
4
2
0
0
0
1
2
0
1
0
0
0
0
0
1
1
1
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
1
1
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
4
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
2
1
0
0
1
0
0
0
0
0
2
0
3
2
0
0
0
1
0
0
0
0
2
0
2
1
0
0
0
2
0
1
2
0
0
0
1
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
3
1
1
0
1
0
0
1
0
0
0
3
0
0
0
0
0
2
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
1
0
0
2
0
0
0
1
1
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
4
1
0
1
0
0
0
0
0
0
3
2
0
0
0
2
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
3
4
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
3
0
1
0
0
0
1
1
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
4
0
1
1
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
2
1
0
0
0
0
3
0
0
1
2
1
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
2
1
0
0
0
1
0
1
0
2
1
1
0
0
1
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
2
0
0
0
1
1
0
1
0
0
0
1
0
0
0
1
1
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
3
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
2
0
0
0
0
0
0
0
1
0
0
0
0
3
0
2
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
3
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
2
0
0
1
1
1
0
0
2
2
0
0
2
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
4
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
1
0
0
1
0
1
2
1
0
0
0
0
0
3
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
1
0
0
0
0
1
2
0
0
0
1
3
0
0
0
0
0
0
0
0
2
0
0
0
3
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
2
1
0
0
3
1
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
3
1
2
3
0
0
0
2
0
0
0
1
0
0
1
2
0
1
0
1
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
2
0
1
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
1
2
0
0
0
1
0
0
0
0
0
2
0
1
0
0
3
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
2
9
0
0
2
3
2
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
1
1
0
4
1
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
3
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
1
0
2
0
1
0
0
0
3
0
0
6
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
4
1
0
4
0
0
0
0
1
0
0
0
2
0
1
0
0
3
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
1
2
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
1
3
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
1
2
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
1
0
0
0
0
0
4
3
0
1
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
9
0
0
2
0
0
1
1
2
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
1
0
1
2
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
2
0
0
0
0
3
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
2
0
0
0
2
2
0
0
0
0
6
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
2
2
0
0
2
0
0
0
3
0
1
1
0
1
0
1
2
2
0
0
0
0
0
1
0
0
2
4
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
2
0
0
2
1
0
0
2
0
2
0
0
0
1
0
1
0
0
2
0
0
0
1
2
1
2
2
0
3
0
0
0
1
0
0
0
0
0
0
1
0
2
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
2
2
0
0
2
0
0
1
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
2
0
1
0
0
2
0
1
0
2
2
0
0
0
0
1
0
0
0
1
3
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
3
2
0
0
0
0
1
0
0
0
2
1
0
2
0
0
0
0
0
0
1
0
1
0
3
0
0
0
3
1
0
0
0
3
0
1
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
1
7
2
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
2
0
0
0
0
0
0
1
0
1
2
0
0
0
2
0
0
0
0
0
1
0
2
0
0
3
0
3
1
0
0
0
2
0
4
0
0
0
0
0
2
0
2
0
0
3
1
0
2
1
0
0
2
0
0
3
0
0
0
2
1
1
0
0
0
2
0
0
2
2
1
3
0
1
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
1
0
2
1
2
0
0
1
0
0
1
0
1
0
0
1
0
0
0
1
0
0
2
0
0
1
1
0
0
0
1
0
1
0
1
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
1
1
0
7
0
2
0
0
1
2
1
0
2
0
0
0
0
2
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
1
3
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
2
2
0
0
0
0
1
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
1
0
3
0
0
2
0
0
0
2
2
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
1
2
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
3
2
0
3
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
3
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
3
0
2
2
0
1
0
0
1
1
1
1
0
0
0
0
1
0
5
2
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
3
2
0
0
2
1
5
1
2
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
3
0
0
1
0
0
2
0
0
0
4
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
2
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
4
1
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
8
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
7
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
2
0
0
1
0
0
0
0
1
0
2
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
14
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
2
3
0
0
0
0
0
0
0
0
0
4
0
1
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
1
0
2
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
1
2
0
0
0
0
0
0
1
2
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
2
1
2
0
0
1
0
1
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
2
2
1
0
2
0
2
0
0
2
2
0
1
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
4
0
0
0
2
3
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
2
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
2
0
2
0
0
0
2
0
0
0
1
0
1
0
1
1
0
2
0
4
0
2
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
2
4
2
1
0
0
0
0
0
3
2
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
1
1
0
0
0
0
0
0
3
0
0
0
2
0
1
2
1
0
0
1
0
3
1
0
0
1
0
0
4
2
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
2
0
1
1
0
0
1
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
1
0
1
2
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
2
0
0
3
0
0
0
0
0
0
1
0
1
0
4
1
0
2
0
0
0
0
0
0
2
1
0
2
0
0
2
2
1
0
2
0
0
3
0
0
0
0
0
0
2
0
3
0
0
0
0
0
2
0
1
2
0
0
0
0
1
0
1
2
0
2
5
0
2
0
0
0
3
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
3
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
8
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
5
1
1
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
3
1
0
2
1
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
3
0
2
0
0
0
0
3
0
2
0
0
0
0
0
1
2
1
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
3
2
6
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
3
0
0
0
4
0
1
0
0
0
0
0
1
2
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
1
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
1
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
4
1
0
0
0
0
0
2
0
0
1
1
0
0
0
1
0
1
1
2
1
0
2
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
3
2
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
2
1
2
0
0
2
0
0
0
0
0
0
2
5
0
0
0
0
0
0
0
0
2
0
2
2
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
1
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
2
0
3
3
0
0
0
2
0
0
0
0
3
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
3
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
2
2
1
0
0
0
3
2
1
1
0
1
0
0
1
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
3
1
3
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
2
2
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
2
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
2
0
1
2
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
2
3
0
0
0
0
0
0
2
0
2
0
0
1
0
0
2
0
0
2
0
0
1
0
0
2
0
0
3
1
1
3
0
0
0
0
0
2
2
0
1
0
0
0
0
0
5
0
0
0
2
1
2
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
1
1
0
0
0
2
2
0
0
1
0
0
2
0
1
2
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
9
0
4
0
0
1
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
2
1
1
0
0
0
0
0
0
1
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
3
6
0
2
0
0
0
0
0
2
0
2
0
0
0
1
0
0
1
0
0
1
0
3
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
4
2
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
4
1
1
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
2
7
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
3
7
0
0
1
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
2
1
0
1
1
0
1
2
3
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
3
0
0
1
0
0
1
0
0
0
0
0
2
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
3
0
0
1
2
0
0
1
0
0
1
0
0
0
0
0
0
0
5
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
2
0
0
0
0
2
2
2
0
0
0
0
2
0
0
0
0
0
1
0
1
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
2
1
0
0
0
0
0
0
1
2
0
0
2
0
2
0
0
0
2
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
1
1
0
0
0
0
0
2
1
0
0
3
0
2
0
0
0
1
0
0
0
1
2
6
0
3
0
0
0
0
0
1
0
1
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
2
2
1
2
2
2
0
0
0
1
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
2
0
2
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
2
0
0
0
0
1
0
0
1
2
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
1
0
1
0
3
0
0
0
1
0
0
0
1
0
2
0
0
0
1
0
0
0
2
1
1
0
1
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
1
0
0
2
0
0
0
0
2
3
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
6
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
3
0
0
0
1
1
0
2
2
3
0
0
0
2
2
2
0
2
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
2
0
0
0
1
3
3
0
0
0
0
3
1
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
1
0
0
2
1
1
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
1
0
2
8
3
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
12
2
2
0
0
0
0
0
0
0
0
0
0
0
0
3
4
0
0
2
0
2
0
2
0
0
0
1
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
2
1
0
0
1
0
2
0
2
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
1
2
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
1
0
2
3
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
2
0
0
0
0
0
2
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
1
0
0
1
3
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
2
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
1
0
0
0
6
0
0
1
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
2
3
2
0
0
1
0
0
0
0
0
1
1
1
1
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
4
2
3
0
3
0
0
0
0
0
0
8
1
0
0
0
0
4
0
0
2
0
1
0
0
1
3
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
2
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
2
1
1
2
0
0
0
1
0
0
2
1
0
0
2
1
0
0
0
2
1
0
0
0
1
2
1
0
3
0
0
1
0
0
2
1
2
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
2
3
1
2
0
1
0
0
0
0
0
2
2
0
0
0
1
0
0
0
1
2
0
0
0
0
2
2
2
2
0
0
2
0
0
0
0
2
1
0
0
2
0
0
0
0
1
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
1
2
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
3
0
0
2
0
0
1
1
0
2
0
1
2
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
1
0
0
0
0
2
0
3
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
2
0
3
1
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
1
0
1
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
1
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
3
0
0
2
0
0
1
0
0
0
3
2
0
0
0
1
2
1
0
0
0
0
1
0
3
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
1
0
0
2
0
1
1
0
0
1
0
2
0
0
0
1
1
2
0
1
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
1
4
0
0
2
0
1
0
0
1
2
0
0
0
0
0
1
2
2
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
7
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
5
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
1
2
0
0
0
2
0
0
0
0
3
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
2
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
3
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
1
0
0
1
1
0
0
0
5
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
2
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
2
2
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
2
0
0
1
1
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
1
0
3
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
4
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
1
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
2
0
0
0
0
0
2
0
9
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
3
0
2
2
2
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
4
0
1
0
0
1
0
0
1
4
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
1
1
0
0
2
1
0
2
0
2
1
0
0
0
0
2
0
0
2
1
0
0
3
0
1
0
0
0
1
0
0
0
1
0
0
1
1
3
2
0
0
0
2
2
0
0
0
0
0
3
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
2
0
0
1
0
1
1
0
0
0
0
0
1
4
0
1
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
2
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
1
1
2
1
0
0
3
2
0
0
0
0
0
0
2
0
2
2
1
2
2
0
0
2
0
0
0
0
0
0
1
0
0
0
2
1
0
2
0
0
2
0
1
0
0
0
1
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
2
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
1
0
0
0
1
0
0
0
0
0
2
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
1
0
0
0
0
0
0
2
0
0
2
0
2
0
2
0
0
0
2
0
1
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
1
0
0
0
0
0
1
0
0
1
2
0
0
0
2
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
2
2
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
1
0
0
0
0
0
0
0
2
1
2
0
0
2
0
2
0
7
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
5
0
2
0
0
0
2
0
1
0
2
2
0
0
0
0
2
0
1
2
1
0
2
0
1
2
0
2
0
0
4
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
1
4
0
2
1
2
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
2
1
1
0
0
0
1
0
0
0
0
0
0
1
1
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
3
0
0
0
0
1
0
0
0
0
0
3
0
1
0
0
0
0
3
1
0
0
0
0
0
0
0
1
0
0
3
1
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
2
0
0
2
0
0
3
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
2
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
1
1
2
2
0
0
1
2
0
1
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
7
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
1
0
1
1
2
2
1
0
7
0
1
0
0
0
0
2
2
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
1
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
5
0
0
0
0
2
0
0
0
1
1
1
0
0
0
1
0
0
1
0
0
1
0
2
0
1
2
2
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
2
0
1
0
2
0
0
7
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
1
2
0
0
2
0
0
3
1
0
0
1
0
1
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
1
0
0
1
0
2
1
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
1
0
0
0
1
0
0
1
2
0
0
1
0
0
1
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
1
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
2
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
1
1
0
3
0
1
0
0
0
2
0
1
1
0
1
0
0
0
2
0
0
0
1
2
2
2
0
0
1
0
0
0
0
0
3
0
0
1
0
1
0
0
0
0
0
2
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
3
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
2
0
0
0
0
2
3
0
1
0
0
0
2
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
3
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
3
0
0
0
0
0
0
0
2
0
0
0
1
2
2
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
3
0
0
2
0
1
0
0
0
0
0
0
0
3
3
2
0
1
0
2
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
4
0
2
0
0
0
2
2
2
0
0
0
1
0
0
1
2
0
0
0
2
0
0
2
0
1
0
0
2
0
1
0
0
0
2
0
0
2
0
0
1
1
0
3
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
2
0
1
0
3
1
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
1
0
0
0
2
0
2
0
0
2
0
0
1
0
0
0
0
1
0
1
1
2
0
2
2
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
1
0
2
0
2
0
2
1
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
1
0
2
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
11
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
3
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
4
0
1
0
0
0
1
0
0
3
0
0
0
1
0
2
2
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
5
0
2
0
0
0
0
2
0
0
2
0
0
1
0
0
2
0
0
0
2
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
1
2
0
1
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
1
0
0
1
0
0
0
1
2
2
0
1
0
0
2
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
1
2
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
2
0
1
0
0
0
0
0
0
1
0
6
0
0
0
0
0
0
0
0
0
3
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
2
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
5
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
2
0
5
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
3
5
0
0
1
0
0
2
0
0
1
0
2
9
0
0
0
3
0
0
3
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
4
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
2
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
1
2
1
1
0
2
0
0
0
0
0
1
0
0
0
0
0
1
2
0
2
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
6
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
3
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
11
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
2
2
0
2
0
0
1
1
0
1
0
2
0
2
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
2
3
2
0
0
0
0
0
0
0
3
5
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
1
1
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
1
1
2
0
0
2
1
1
2
0
1
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
4
0
0
0
8
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
2
0
3
0
0
1
0
2
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
2
0
0
0
0
0
3
0
0
1
2
0
1
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
2
0
2
1
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
1
3
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
2
0
3
0
0
0
0
0
1
0
0
0
0
0
0
2
1
2
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
2
0
0
0
0
2
0
1
2
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
1
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
2
0
0
1
0
0
2
4
0
0
2
0
0
1
0
0
0
0
0
2
1
0
2
1
1
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
1
0
1
0
0
1
0
1
0
0
0
2
2
2
2
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
2
0
0
2
0
1
0
1
0
1
0
2
0
0
0
1
0
1
0
1
0
1
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
2
0
4
0
2
2
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
1
2
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
3
0
0
0
1
0
0
0
0
1
0
0
2
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
6
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
2
2
0
0
0
2
0
1
0
0
1
1
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
2
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
1
0
2
2
0
5
0
0
2
0
1
2
0
0
2
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
2
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
3
0
0
3
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
1
2
0
0
0
0
0
0
0
0
4
0
0
0
4
0
0
0
2
1
3
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
2
0
0
0
3
1
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
1
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
2
1
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
3
0
0
0
1
2
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
3
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
2
0
0
0
2
1
0
0
2
0
2
0
0
1
1
0
0
0
2
0
0
1
2
0
0
2
0
2
0
3
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
2
2
0
1
0
0
0
1
1
0
0
2
1
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
1
0
1
0
2
1
0
1
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
7
0
1
2
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
1
0
0
0
2
0
0
0
0
0
1
0
1
2
0
1
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
2
0
0
0
0
2
2
0
0
0
2
0
0
1
2
1
0
0
0
0
1
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
11
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
2
3
0
2
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
6
0
0
0
0
1
2
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
1
2
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
3
0
1
0
0
0
0
0
0
0
0
0
0
1
2
1
0
2
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
1
1
0
2
0
1
0
2
0
0
0
1
0
2
2
2
0
0
0
0
0
2
0
1
0
2
0
2
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
2
2
2
0
2
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
1
0
1
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
2
3
2
0
1
0
2
2
0
0
0
1
0
0
0
0
2
1
0
0
0
1
1
0
0
1
1
2
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
2
2
1
0
4
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
5
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
1
0
1
0
2
1
0
4
0
5
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
1
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
4
2
0
0
6
0
1
0
2
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
2
2
0
0
3
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
1
0
0
0
1
2
0
0
0
1
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
2
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
2
2
0
0
0
2
1
0
2
0
0
0
0
3
0
2
0
0
0
1
0
0
4
0
0
0
1
0
1
3
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
3
0
1
0
0
0
0
0
0
0
0
1
1
0
2
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
2
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
4
1
0
0
0
0
1
0
1
2
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
3
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
1
2
2
0
0
0
2
0
1
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
4
1
0
0
0
1
2
0
2
0
4
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
2
0
2
0
2
1
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
1
0
0
2
2
0
0
0
1
0
0
1
1
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
2
3
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
5
0
0
0
0
0
0
2
1
0
0
5
0
0
2
2
0
2
2
0
0
0
0
1
0
2
0
0
0
0
2
3
0
2
0
0
0
1
1
0
1
0
1
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
3
0
0
0
0
0
3
1
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
2
1
0
1
0
0
1
8
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
1
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
1
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
1
0
0
0
0
2
1
1
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
1
2
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
2
1
0
1
0
0
0
1
0
2
2
2
1
0
2
0
0
0
0
0
0
0
1
2
1
0
0
0
0
3
1
0
0
0
2
0
0
2
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
1
0
0
0
0
3
2
2
0
2
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
2
1
0
0
0
2
0
1
2
2
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
8
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
2
0
0
0
0
0
0
1
1
0
0
0
0
1
5
0
0
0
0
0
0
3
0
0
2
1
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
3
1
2
2
0
2
0
0
0
0
0
1
1
2
0
0
0
1
1
0
1
10
0
2
3
0
0
2
0
2
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
1
0
1
2
0
1
4
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
4
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
1
0
3
2
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
1
1
0
3
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
2
2
3
0
2
2
0
0
0
2
0
1
0
0
2
0
0
2
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
8
0
0
2
0
1
1
0
0
1
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
1
0
1
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
4
0
4
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
7
0
0
0
1
0
0
1
0
0
0
0
0
1
0
2
2
0
2
1
0
0
1
0
0
2
0
5
0
3
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
2
0
2
2
1
3
0
0
1
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
2
2
0
7
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
2
1
0
0
0
0
0
1
0
2
1
2
1
0
1
0
0
1
1
2
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
1
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
1
0
1
1
0
1
0
1
6
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
3
0
0
0
1
1
0
0
0
0
0
0
3
2
3
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
3
0
1
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
3
0
0
1
0
1
0
0
0
2
0
0
3
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
1
0
0
0
0
1
3
0
0
1
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
3
0
1
0
0
2
0
0
0
0
3
0
1
0
2
0
0
0
0
4
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
3
0
0
1
0
0
0
0
0
0
0
2
2
0
1
0
1
0
0
0
0
0
0
0
1
0
3
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
9
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
1
1
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
2
0
2
0
0
0
0
0
0
1
2
1
3
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
2
1
0
0
0
0
0
1
0
1
0
0
0
0
2
2
0
0
1
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
3
0
3
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
2
0
2
1
1
1
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
3
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
1
2
2
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
1
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
2
2
1
2
2
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
3
0
0
1
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
3
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
2
0
0
1
0
1
1
0
0
0
0
0
2
0
2
0
6
1
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
1
2
0
0
0
0
1
1
0
0
0
0
4
0
0
3
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
1
0
0
0
0
7
0
0
0
0
0
0
1
0
2
1
0
1
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
2
0
0
0
1
0
0
0
0
5
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
1
2
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
2
2
2
0
1
0
1
0
1
0
0
0
0
0
0
1
0
2
0
4
2
0
0
0
0
0
0
0
0
2
0
2
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
3
1
2
1
0
0
0
2
0
0
0
0
0
3
0
3
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
2
1
2
0
2
0
3
2
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
1
2
0
0
0
2
0
2
2
0
0
0
0
0
2
0
0
2
0
1
0
0
1
0
2
0
0
1
1
3
0
0
0
0
0
0
1
2
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
1
0
1
0
0
0
0
1
0
0
1
2
1
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
3
0
0
0
2
0
0
0
0
0
0
0
0
1
4
0
0
2
0
0
0
2
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
1
0
1
2
0
0
3
0
4
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
3
0
0
0
0
0
1
1
0
0
0
0
0
4
1
0
0
0
1
0
2
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
1
0
1
2
0
0
2
0
0
2
0
0
0
0
4
0
0
1
0
2
0
0
0
1
0
4
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
2
0
1
1
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
2
0
0
0
2
2
0
7
1
0
2
0
5
2
0
0
1
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
5
0
1
0
0
0
1
2
1
0
0
0
3
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
2
0
2
0
2
0
2
0
0
0
0
0
1
0
0
2
2
0
0
0
1
0
0
0
2
1
2
1
0
1
1
0
0
0
0
0
0
2
2
0
0
2
1
0
0
1
1
0
1
0
7
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
5
0
2
0
1
0
0
0
2
1
0
0
2
1
0
0
0
0
0
0
5
0
0
0
0
0
2
0
0
2
0
1
0
1
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
2
1
0
0
0
0
1
0
0
2
2
0
1
0
0
0
0
0
1
2
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
1
0
2
0
0
0
0
2
0
0
1
0
1
0
0
1
0
1
1
2
0
0
1
0
0
0
2
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
1
4
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
2
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
1
0
5
1
2
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
1
0
0
0
1
2
0
0
0
0
0
1
0
0
1
0
1
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
2
1
0
0
0
0
1
0
0
0
3
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
1
2
0
0
2
3
2
1
2
0
0
0
0
0
0
9
0
0
0
0
0
1
1
2
0
1
0
0
0
0
0
0
0
11
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
1
0
3
0
0
0
2
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
4
3
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
1
2
5
1
2
1
0
1
0
2
0
0
0
0
2
0
1
0
1
3
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
5
0
2
0
0
0
0
0
0
0
2
0
0
1
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
2
2
1
0
1
0
0
0
0
1
0
1
2
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
2
0
0
1
2
1
0
0
0
0
0
2
0
0
0
0
1
1
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
1
1
0
0
1
1
0
0
0
2
0
1
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
1
1
1
0
0
0
0
0
9
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
2
1
0
3
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
2
0
0
0
0
1
1
0
1
2
0
0
0
1
1
0
3
0
0
3
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
2
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
1
0
2
0
1
2
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
3
2
0
0
0
0
0
1
1
1
0
2
0
0
3
2
1
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
9
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
2
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
2
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
2
0
1
0
0
2
0
1
0
0
0
0
0
3
0
1
0
2
2
0
0
0
0
0
0
0
0
2
1
0
0
1
1
1
1
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
2
0
0
0
0
2
0
0
2
0
1
2
0
2
0
0
1
0
0
0
1
1
0
1
2
2
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
2
2
0
0
0
0
1
2
0
0
1
0
0
0
0
0
1
2
0
0
2
0
1
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
3
2
0
0
0
0
0
0
2
1
0
0
1
1
0
2
4
1
0
0
0
0
0
0
0
0
2
0
0
4
0
0
2
0
0
2
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
1
0
2
0
2
0
0
0
0
1
0
1
2
0
0
0
0
0
0
2
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
7
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
1
0
0
0
0
1
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
2
6
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
3
0
2
0
1
3
0
0
1
2
0
0
0
0
2
0
0
0
2
2
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
1
0
2
0
0
0
0
0
0
4
0
0
4
0
1
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
3
0
1
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
4
0
2
0
0
0
0
0
0
0
0
1
2
2
0
2
0
3
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
5
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
3
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
1
0
2
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
2
0
0
0
0
0
1
0
2
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
1
0
1
0
8
0
0
0
1
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
2
0
0
1
0
1
0
0
2
0
1
0
5
0
0
2
1
0
1
2
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
2
0
0
0
2
1
0
2
0
2
1
0
0
2
0
0
0
0
0
1
0
0
0
2
2
1
0
3
0
0
2
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
2
0
0
0
0
0
2
0
0
0
0
1
2
0
0
1
0
1
0
0
1
2
0
0
0
0
0
1
0
0
0
2
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
2
2
0
0
3
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
0
2
1
0
0
2
0
2
0
0
0
1
1
1
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
1
0
0
2
1
0
0
1
0
1
1
2
0
0
2
0
0
2
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
2
2
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
2
0
1
0
0
1
0
0
0
0
0
1
0
0
2
0
1
5
0
0
0
0
0
1
0
0
0
0
0
2
0
3
1
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
3
1
0
0
0
0
0
0
0
0
2
2
0
1
0
1
2
0
1
2
1
0
0
0
1
0
0
0
0
0
0
4
0
1
0
0
1
0
0
0
2
0
2
2
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
3
1
0
0
1
0
2
0
1
0
0
0
0
2
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
2
3
0
0
1
0
0
3
0
0
1
2
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
2
4
1
2
0
0
1
0
2
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
1
0
0
2
0
0
3
2
2
0
0
1
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
7
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
2
1
0
0
2
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
3
0
1
2
0
0
0
1
0
0
0
1
1
0
2
2
0
0
2
0
0
1
0
3
0
0
2
0
0
1
1
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
2
2
4
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
1
1
0
0
0
0
0
3
0
0
0
0
0
7
1
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
2
2
0
0
0
1
0
0
0
0
3
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
2
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
2
0
0
0
1
0
3
2
1
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
4
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
3
0
0
2
1
3
0
1
1
0
1
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
2
0
1
2
0
1
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
3
0
1
0
1
0
0
0
2
0
2
0
0
1
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
1
2
0
0
0
2
0
0
2
0
3
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
1
3
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
1
0
0
1
2
1
0
0
0
0
2
0
0
0
2
0
4
2
0
1
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
8
0
0
2
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
5
0
0
2
2
0
0
0
0
1
3
0
0
0
0
0
2
0
1
0
0
5
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
2
0
2
0
2
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
1
2
0
0
1
3
0
0
1
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
1
1
0
0
0
0
6
1
0
0
0
0
0
1
1
0
0
0
3
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
3
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
1
4
1
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
3
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
3
0
4
1
0
0
0
0
0
0
0
0
2
2
0
0
4
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
2
1
2
0
0
0
1
1
0
1
0
2
0
1
0
0
0
1
0
0
0
1
0
2
0
0
0
0
1
0
0
1
1
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
2
1
2
0
1
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
2
0
1
1
0
2
1
0
0
0
0
2
1
0
2
1
2
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
1
0
2
0
3
0
0
1
0
4
0
0
0
1
0
1
0
0
0
2
2
0
4
0
0
1
9
0
0
0
0
0
0
0
1
0
0
0
1
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
2
0
1
1
1
0
0
0
0
3
2
0
1
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
1
0
0
2
1
0
0
1
0
0
2
0
2
0
4
0
2
0
0
0
0
0
0
0
1
0
0
7
0
2
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
2
0
0
0
2
1
2
0
0
0
0
0
0
2
0
1
0
1
0
2
0
0
0
0
1
0
1
0
1
0
6
0
0
0
1
0
0
0
1
0
3
1
0
0
2
1
0
0
1
0
1
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
1
1
0
3
0
0
0
1
0
0
2
0
3
0
0
0
0
0
2
0
0
1
1
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
1
0
0
2
2
0
0
1
0
0
0
0
0
0
7
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
1
0
1
1
1
0
0
0
0
2
2
2
2
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
2
1
2
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
4
0
2
0
0
0
0
0
0
2
1
0
0
2
1
0
0
0
0
0
0
2
0
3
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
7
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
2
0
0
0
1
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
5
2
2
0
0
3
2
0
0
0
0
0
0
1
0
3
0
1
0
1
0
0
0
1
2
0
0
0
0
1
2
0
0
0
0
0
0
4
0
2
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
2
2
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
2
0
0
0
0
0
2
0
2
0
2
2
0
0
0
0
0
3
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
1
0
1
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
2
0
3
1
1
0
0
0
1
1
0
2
2
0
0
0
0
0
0
1
0
0
4
4
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
2
3
0
0
0
0
0
1
0
1
0
1
0
1
1
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
1
2
2
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
3
0
0
1
0
1
0
0
0
1
1
2
0
0
2
0
3
5
0
1
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
1
0
0
5
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
3
2
1
0
0
2
0
0
0
0
0
0
0
0
0
2
3
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
1
0
2
0
1
2
1
0
0
0
0
0
0
1
1
1
0
0
0
0
2
0
1
0
1
2
0
3
2
0
0
0
2
0
0
1
2
0
0
0
2
0
5
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
3
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
1
0
2
0
0
2
1
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
2
1
0
2
0
1
0
0
0
0
2
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
2
0
2
2
0
0
0
0
1
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
5
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
2
2
2
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
2
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
3
0
0
1
0
0
0
1
1
2
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
1
2
0
0
0
0
0
0
2
1
1
2
1
0
0
2
0
0
0
0
0
2
2
2
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
1
1
2
3
0
0
2
2
0
0
2
0
0
1
1
2
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
2
2
0
0
0
0
0
0
1
2
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
2
0
0
0
2
1
0
0
0
0
2
0
0
2
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
1
0
2
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
1
0
0
2
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
4
0
1
2
0
1
0
3
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
1
2
1
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
2
0
0
0
1
0
1
2
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
4
0
4
0
0
0
0
0
0
0
3
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
1
1
1
0
0
2
1
2
0
0
0
0
1
0
1
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
2
0
6
0
2
1
0
0
1
2
0
0
0
1
0
0
0
0
2
0
0
2
0
1
1
1
1
2
0
0
0
0
2
0
0
0
0
1
0
1
2
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
2
0
0
4
0
5
0
1
0
2
0
1
0
0
0
0
2
2
0
0
0
1
0
0
0
1
0
0
1
2
1
0
1
0
0
0
1
0
2
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
2
2
1
0
1
3
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
2
3
0
0
0
0
0
0
0
2
0
2
0
0
1
2
0
0
0
1
0
1
2
2
0
2
2
2
0
0
2
0
0
1
0
0
0
0
2
0
0
0
3
0
1
2
0
0
0
0
0
1
0
0
2
0
1
0
2
0
0
0
0
0
0
2
0
0
1
0
0
2
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
2
1
0
0
0
2
2
0
0
0
2
0
1
0
1
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
2
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
1
1
0
1
0
1
0
2
0
0
1
2
2
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
2
2
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
2
0
1
0
3
2
0
0
0
0
0
0
2
0
1
0
1
0
0
0
3
0
0
3
2
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
2
0
0
0
1
2
0
4
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
3
0
0
0
0
0
1
0
3
0
0
1
2
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
2
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
10
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
1
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
1
0
3
0
0
0
0
1
0
0
0
0
0
0
1
0
1
3
0
0
0
2
0
1
0
0
1
0
2
3
0
2
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
2
0
1
1
0
0
2
2
0
0
0
2
5
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
2
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
2
0
1
3
2
0
0
0
0
1
0
0
6
2
0
0
0
1
2
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
2
0
2
0
0
1
2
0
2
0
0
0
1
0
0
0
2
0
1
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
3
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
2
2
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
2
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
1
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
1
0
0
0
0
0
2
2
0
0
0
3
0
0
0
0
3
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
2
0
0
2
2
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
2
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
4
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
1
0
0
2
2
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
2
2
0
2
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
3
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
1
3
1
0
0
0
0
0
2
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
1
3
0
0
0
0
3
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
1
2
0
0
2
0
0
0
0
2
1
0
0
1
0
2
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
6
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
3
0
0
0
0
0
2
0
0
3
1
0
2
0
0
0
0
0
2
1
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
2
2
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
5
0
0
0
1
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
5
2
1
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
1
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
2
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
4
0
0
0
0
0
0
0
0
0
0
7
2
1
0
2
0
2
2
0
0
1
0
0
0
0
0
0
1
1
0
0
0
2
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
5
7
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
4
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
1
1
0
0
0
0
0
3
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
2
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
1
0
0
0
2
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
3
0
2
1
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
2
1
0
1
0
2
0
0
6
0
0
0
0
0
8
2
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
5
0
0
1
2
0
1
0
1
0
0
0
1
0
2
0
0
0
2
2
0
0
1
0
0
0
0
2
0
3
0
0
0
2
1
0
0
0
1
0
2
1
1
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
2
0
0
2
0
2
0
0
2
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
4
1
0
0
0
0
0
1
3
0
2
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
1
0
0
0
0
1
1
0
0
5
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
2
0
1
0
2
0
0
0
4
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
3
0
0
0
2
0
1
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
3
1
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
1
0
0
1
2
0
1
0
0
1
1
0
0
0
0
1
0
1
2
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
3
0
0
0
0
1
0
0
0
1
1
0
0
0
0
2
1
0
0
0
7
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
3
0
0
1
0
0
2
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
3
1
0
1
2
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
8
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
2
1
1
0
2
0
0
3
0
0
1
0
0
2
0
1
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
2
0
2
0
0
0
0
0
0
1
2
2
2
0
0
0
1
1
1
0
0
0
0
0
0
2
0
0
0
2
0
2
0
1
0
2
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
1
0
0
2
1
0
0
1
0
1
0
2
0
0
1
0
3
1
0
0
0
0
0
0
3
2
0
2
0
1
0
2
0
1
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
2
0
0
0
1
2
0
1
1
0
2
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
6
0
0
1
0
0
0
0
0
1
2
0
1
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
4
0
0
1
0
2
2
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
2
2
0
2
0
2
0
0
0
0
0
0
0
0
1
1
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
2
0
1
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
3
0
1
2
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
6
1
0
1
0
0
0
1
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
2
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
3
2
1
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
5
2
0
1
0
0
2
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
2
0
0
0
0
1
0
2
0
0
0
3
0
1
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
2
0
1
0
1
1
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
2
0
4
0
0
3
0
0
0
0
1
0
0
2
0
2
1
0
0
1
1
0
1
0
2
0
0
0
0
0
1
0
0
1
3
0
2
0
0
1
0
0
1
2
2
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
3
0
0
0
0
2
0
0
0
3
0
0
0
0
0
1
0
2
1
0
0
0
1
0
1
0
0
2
1
0
0
0
0
0
1
2
0
0
0
0
1
2
2
0
0
0
2
2
2
0
0
0
0
0
0
1
0
0
0
1
2
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
4
0
0
2
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
1
2
2
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
4
0
0
0
0
0
0
2
0
0
0
0
2
0
2
5
0
0
1
0
1
0
0
2
0
0
0
2
1
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
2
2
0
1
0
0
0
2
0
0
0
0
0
1
0
0
1
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
1
0
1
0
3
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
1
0
0
1
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
1
0
0
2
0
1
0
1
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
2
0
0
0
0
1
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
2
1
0
1
0
0
0
1
0
2
3
2
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
7
0
0
2
2
0
0
0
0
2
0
1
1
1
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
1
0
0
2
0
2
0
0
0
0
3
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
2
1
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
3
0
0
2
2
0
0
0
0
0
0
2
0
0
2
2
0
0
1
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
2
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
1
1
0
0
0
0
0
1
1
1
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
2
2
3
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
1
2
0
2
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
2
1
2
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
2
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
1
1
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
2
0
1
2
0
0
0
0
1
0
0
0
1
1
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
2
0
2
2
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
2
1
0
0
2
2
0
1
1
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
1
1
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
3
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
1
1
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
3
0
0
1
0
1
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
8
3
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
1
2
0
0
2
0
0
1
0
0
0
0
2
1
2
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
2
0
1
0
2
0
3
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
1
2
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
2
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
2
0
0
1
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
2
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
2
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
2
0
4
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
1
1
4
1
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
4
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
3
1
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
1
2
1
0
1
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
1
0
2
2
2
0
0
0
3
0
0
1
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
3
2
0
0
0
1
0
0
0
0
2
3
0
1
0
3
0
1
0
0
0
0
0
1
0
0
0
3
3
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
1
2
3
0
0
2
0
0
0
0
0
0
2
0
1
1
1
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
2
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
1
0
0
0
2
0
0
0
0
3
0
0
3
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
1
0
0
0
1
8
1
1
0
0
0
2
1
1
0
4
0
1
0
0
0
1
0
2
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
7
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
4
0
0
1
0
0
2
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
3
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
4
0
0
1
0
0
0
7
0
1
0
4
0
0
0
0
1
0
0
2
0
0
1
1
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
5
0
2
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
1
2
1
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
4
0
1
0
3
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
1
0
0
2
2
0
2
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
4
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
2
2
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
1
2
1
0
0
2
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
2
0
1
0
0
0
0
2
0
0
0
6
0
1
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
2
2
0
1
1
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
14
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
8
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
3
0
0
0
0
3
0
4
2
0
1
0
2
0
2
0
0
0
0
1
3
0
1
0
1
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
1
1
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
1
0
0
1
0
0
1
5
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
2
2
0
2
0
0
1
0
0
2
0
0
0
0
3
2
1
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
2
2
0
2
2
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
4
2
0
1
2
0
0
0
11
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
4
0
2
0
1
1
1
0
0
0
0
0
0
0
0
2
0
0
5
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
2
0
2
1
0
1
0
0
0
0
0
2
0
2
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
2
3
0
0
1
0
1
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
6
0
0
1
0
0
2
0
3
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
2
3
2
0
0
0
0
0
0
2
2
0
0
3
0
5
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
4
4
0
0
0
1
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
1
2
1
2
0
0
2
1
2
2
1
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
5
0
2
1
1
0
0
2
0
2
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
1
0
2
1
0
0
2
0
0
0
1
2
0
0
1
0
3
0
0
0
0
0
0
3
0
2
0
0
0
0
1
0
2
0
0
0
1
0
0
0
7
0
0
0
2
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
1
1
3
0
0
0
0
2
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
2
1
2
2
0
1
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
3
0
0
0
3
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
1
0
0
1
1
1
1
0
0
0
1
0
0
1
0
0
0
0
2
3
0
0
0
3
2
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
3
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
3
0
1
1
0
2
0
0
2
2
0
0
2
0
0
4
2
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
1
1
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
1
1
1
0
0
0
0
1
0
2
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
2
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
10
1
0
2
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
3
0
1
1
1
1
2
2
0
1
2
0
0
0
1
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
1
0
0
2
1
2
0
3
0
0
0
1
0
0
0
3
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
2
0
0
0
0
0
0
0
0
0
2
2
2
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
1
1
0
2
0
0
0
4
0
0
0
0
0
1
0
2
1
0
1
0
0
0
0
0
0
0
2
0
0
3
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
1
0
0
0
2
2
0
2
0
1
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
1
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
1
1
0
0
0
3
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
2
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
1
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
2
0
0
2
0
0
0
1
0
1
2
1
0
2
0
2
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
1
0
0
0
0
0
0
1
0
0
2
0
1
4
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
3
4
2
0
0
0
0
0
0
0
1
1
2
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
2
0
1
0
0
0
1
2
0
0
1
2
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
6
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
2
2
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
1
2
1
0
0
0
0
0
0
0
0
0
5
0
0
0
1
0
2
0
4
1
2
0
1
1
0
0
0
0
0
0
0
2
0
1
1
0
2
2
0
2
0
0
0
2
0
0
0
5
2
0
0
1
1
0
0
0
1
0
0
2
2
0
0
0
1
5
0
2
0
0
2
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
18
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
4
2
0
0
0
1
0
1
0
0
0
0
0
2
1
0
1
1
0
0
0
0
3
2
0
1
3
0
0
0
0
3
2
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
1
2
0
0
0
1
2
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
2
2
1
0
2
0
0
0
2
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
2
1
2
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
8
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
2
1
0
0
0
1
0
1
0
8
1
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
1
1
0
0
0
1
1
0
1
0
0
5
0
3
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
2
0
1
0
1
1
0
2
0
1
2
0
1
3
0
0
0
0
0
2
1
1
0
0
0
0
0
2
0
0
1
2
1
1
0
0
0
3
0
2
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
2
0
3
2
0
2
0
0
0
1
0
1
0
0
4
2
0
0
1
0
1
1
1
0
0
0
0
2
0
0
0
0
0
0
3
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
4
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
2
0
1
1
0
0
1
2
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
15
0
0
0
2
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
2
2
2
0
1
0
0
2
1
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
1
4
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
3
1
0
0
1
0
1
0
0
0
2
2
0
0
0
0
1
0
0
2
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
5
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
1
0
0
2
1
0
0
1
2
1
0
0
2
0
2
2
0
1
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
1
1
0
0
0
0
2
0
0
0
0
0
2
1
0
0
2
2
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
5
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
4
1
2
0
0
0
2
1
0
0
0
0
0
2
2
0
0
0
1
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
2
0
0
1
0
0
16
0
0
0
1
0
2
2
1
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
2
1
0
0
2
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
12
0
0
0
0
1
0
1
0
0
2
1
1
0
1
3
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
3
2
1
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
2
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
1
0
0
0
1
0
1
0
2
0
0
1
0
0
0
2
0
0
3
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
2
1
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
5
0
0
1
2
3
3
0
0
0
0
2
6
0
1
2
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
2
0
0
0
0
0
0
0
2
0
2
3
0
2
0
0
1
0
0
0
1
2
0
3
0
0
0
0
1
2
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
1
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
3
0
2
3
0
0
0
0
0
1
2
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
2
0
1
0
1
0
2
2
0
0
1
1
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
4
0
0
0
2
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
4
0
0
1
0
3
0
0
2
0
0
1
0
0
2
5
0
0
0
0
0
0
0
2
0
0
0
0
0
3
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
2
3
0
2
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
3
3
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
2
0
3
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
1
2
2
0
2
0
0
0
1
0
0
1
0
1
0
0
0
0
0
3
2
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
2
0
1
0
0
0
1
1
2
0
0
0
1
0
0
0
0
2
1
2
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
1
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
2
0
0
3
0
0
0
0
0
1
0
2
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
4
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
3
1
0
2
1
4
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
2
0
5
0
0
2
0
2
1
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
4
0
0
0
0
0
2
0
0
1
0
0
0
2
1
0
0
0
2
1
2
0
2
0
0
1
2
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
2
0
0
0
5
0
0
0
0
2
0
0
0
0
3
0
0
0
2
2
0
1
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
1
0
3
0
0
2
0
0
1
0
4
0
0
0
1
2
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
2
0
0
0
1
0
0
1
2
2
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
3
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
1
0
0
0
0
0
0
1
2
0
1
1
0
0
2
0
3
0
0
1
2
2
1
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
3
0
0
0
2
0
0
1
4
1
0
1
1
0
0
0
0
2
0
0
2
0
2
1
1
0
0
0
0
0
0
2
0
0
2
3
0
1
0
1
0
0
1
1
0
0
0
1
1
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
3
2
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
3
0
1
0
0
0
0
0
0
1
0
0
0
0
0
3
5
0
0
1
0
4
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
5
0
0
1
0
0
0
0
0
0
6
2
1
0
0
2
0
0
2
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
3
0
1
2
0
2
1
0
0
2
0
8
0
0
0
0
0
0
3
0
0
0
0
2
0
3
1
0
0
2
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
2
0
0
0
0
1
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
2
6
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
3
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
3
0
1
0
2
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
4
0
0
0
0
2
0
0
3
0
0
0
1
0
0
1
2
1
0
0
2
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
2
0
1
0
0
0
0
0
8
0
2
0
0
0
0
4
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
1
0
0
3
1
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
2
0
2
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
2
0
0
1
0
2
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
6
0
1
0
0
1
1
0
0
0
0
2
2
0
0
0
0
0
1
0
5
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
1
0
1
1
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
1
0
2
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
2
1
2
3
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
1
0
0
2
0
0
0
2
0
2
0
2
2
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
2
1
0
1
2
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
1
0
0
2
0
1
1
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
2
3
0
0
0
0
0
1
0
1
1
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
1
1
0
1
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
2
0
4
0
2
2
0
0
1
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
3
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
2
1
0
2
0
1
1
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
6
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
1
0
1
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
2
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
2
0
0
0
2
2
1
0
0
0
0
0
0
2
1
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
2
2
0
0
2
2
1
1
1
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
2
2
0
0
1
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
1
0
1
0
0
1
0
1
1
0
0
2
0
0
0
0
2
0
3
0
0
0
0
1
0
0
1
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
3
0
0
0
2
0
0
1
0
1
0
0
0
2
2
0
0
0
0
0
2
2
0
0
2
2
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
1
0
2
0
0
2
1
3
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
3
0
0
0
0
0
0
0
1
1
0
3
0
0
0
0
0
4
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
2
1
3
0
0
1
0
1
0
2
0
0
0
0
2
0
2
2
0
0
1
0
0
0
0
0
3
0
3
0
1
0
0
0
0
0
0
2
0
0
1
2
2
0
0
2
0
0
1
0
0
0
1
1
0
2
0
0
0
1
1
0
0
0
0
0
2
0
0
2
0
0
0
0
3
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
1
0
0
2
0
0
0
0
2
2
0
0
0
1
1
1
0
3
2
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
1
0
0
2
2
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
2
0
1
2
0
0
2
0
0
0
0
0
0
0
0
1
0
1
3
0
0
0
0
2
0
0
2
0
1
2
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
5
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
2
1
0
0
0
0
0
0
2
0
0
1
1
2
0
0
0
0
2
2
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
1
0
1
0
2
1
0
0
0
2
0
3
1
0
2
1
2
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
4
0
1
0
0
3
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
2
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
4
0
0
0
0
1
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
1
10
1
0
0
1
0
2
2
0
0
3
0
0
1
0
15
1
4
0
1
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
1
0
1
2
2
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
2
0
1
2
1
0
0
1
0
2
0
2
0
1
4
0
0
0
0
0
0
0
0
0
0
2
4
0
0
2
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
1
0
0
0
0
3
2
1
0
0
1
1
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
2
1
0
0
0
2
1
2
1
2
0
4
2
0
0
0
0
0
0
0
0
0
2
2
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
4
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
1
0
2
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
2
4
1
0
2
1
0
2
1
0
0
1
0
1
0
0
0
0
1
1
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
6
0
0
0
0
0
0
6
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
1
1
3
3
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
2
0
1
2
0
0
2
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
3
4
2
1
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
1
0
1
1
0
1
2
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
1
1
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
2
2
1
0
1
0
2
0
0
2
2
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
2
0
0
0
0
1
2
0
0
0
0
7
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
1
0
0
0
0
3
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
3
2
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
4
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
1
1
1
0
0
0
0
0
0
0
0
1
0
2
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
3
0
0
2
0
2
0
0
0
2
0
0
2
0
0
0
3
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
1
3
0
1
2
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
5
0
0
0
2
0
2
0
0
1
0
1
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
2
0
2
1
0
2
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
2
0
0
0
0
2
0
3
0
4
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
2
0
0
2
0
4
0
0
0
0
0
0
1
0
2
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
1
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
1
1
0
0
1
3
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
3
0
2
0
0
0
0
2
2
1
0
1
2
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
1
2
0
0
6
0
0
0
1
3
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
3
0
0
0
1
0
1
0
0
0
2
1
1
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
1
1
2
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
2
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
2
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
1
2
0
2
0
4
0
0
2
0
1
0
0
0
0
3
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
4
0
0
4
0
1
0
0
1
5
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
5
0
0
0
1
0
1
1
0
0
0
0
0
0
1
2
1
0
1
0
0
0
2
0
1
0
0
0
0
2
0
0
2
0
1
0
0
0
1
0
0
0
2
0
1
0
0
1
1
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
2
0
0
0
0
1
0
1
0
0
0
0
0
1
2
0
1
1
1
0
1
1
0
0
3
3
0
0
0
2
0
0
1
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
1
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
2
0
1
1
2
0
0
2
0
3
0
0
2
0
4
0
0
3
0
0
0
0
3
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
2
0
0
0
0
0
0
2
1
4
3
0
0
0
2
0
1
2
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
3
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
1
2
0
2
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
4
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
2
1
0
0
2
0
0
1
0
0
0
0
3
0
0
1
1
0
2
0
0
0
0
0
0
0
2
0
2
7
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
2
2
2
0
0
0
0
0
0
0
4
0
2
1
0
1
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
3
1
0
1
0
1
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
3
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
2
2
0
0
0
0
2
0
1
2
0
0
1
0
0
0
1
0
1
0
2
2
0
0
0
0
1
2
0
2
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
3
0
0
0
0
0
0
2
0
0
1
0
2
1
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
3
0
1
1
0
0
0
1
0
2
0
0
1
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
3
0
1
0
0
0
1
3
0
0
0
2
0
2
0
2
0
0
0
0
1
2
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
3
2
0
2
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
5
0
0
0
0
0
1
0
1
2
2
0
0
4
0
0
2
0
0
0
0
1
0
0
1
0
0
0
1
1
2
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
2
2
0
0
1
0
0
0
1
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
4
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
2
1
0
0
1
0
0
2
1
0
0
0
0
2
0
1
0
0
0
0
2
1
2
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
1
0
0
6
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
2
0
0
0
0
0
1
3
1
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
2
2
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
1
0
0
0
0
0
2
0
0
2
1
2
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
4
0
0
0
1
0
0
2
2
1
0
2
0
0
0
0
0
0
3
2
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
4
2
0
0
0
0
0
2
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
2
0
0
2
0
2
2
1
1
0
0
2
1
0
0
0
0
0
0
0
1
0
1
2
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
2
0
0
1
0
2
2
2
2
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
3
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
2
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
1
2
1
0
2
4
8
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
1
1
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
2
0
0
1
2
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
3
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
2
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
2
0
0
0
1
0
2
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
2
0
0
2
2
0
0
1
0
0
2
0
0
2
0
3
0
0
0
0
0
0
1
2
0
2
2
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
2
0
2
0
0
0
2
2
1
0
1
6
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
3
1
0
2
0
0
0
0
1
1
0
0
2
2
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
2
1
1
2
0
0
0
1
0
1
0
0
0
2
0
0
0
2
0
0
2
1
0
0
0
0
0
1
0
2
2
0
0
2
1
3
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
4
0
0
2
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
2
1
0
0
1
1
2
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
1
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
1
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
4
3
2
0
0
2
0
1
0
0
1
1
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
1
0
0
1
0
0
0
2
2
0
1
0
0
1
0
2
0
0
1
0
0
2
0
0
1
0
0
3
0
2
0
0
0
1
0
3
0
0
0
1
0
0
0
1
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
1
0
0
2
2
1
2
3
2
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
2
0
1
2
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
4
0
0
2
3
0
0
3
3
0
1
0
2
0
2
0
0
0
3
0
0
1
0
0
1
0
0
0
1
0
0
0
5
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
3
2
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
1
2
0
0
0
0
0
1
1
2
2
0
0
0
2
0
0
2
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
2
0
0
1
0
0
0
2
0
0
0
1
0
2
0
0
0
1
0
0
1
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
2
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
1
2
2
8
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
1
3
0
0
2
2
0
2
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
1
0
0
0
1
1
2
0
1
0
0
0
0
2
0
0
0
3
0
2
0
0
1
0
0
2
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
2
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
2
0
0
0
0
1
0
0
0
0
2
0
0
2
0
1
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
2
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
2
1
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
1
0
0
0
2
0
1
2
0
0
1
0
2
0
0
0
3
2
2
0
0
3
3
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
1
2
1
0
1
0
0
2
2
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
2
2
0
0
0
1
0
0
0
0
3
0
0
1
2
1
1
0
1
2
0
0
0
0
0
0
0
5
2
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
3
1
0
0
0
2
0
0
1
0
3
0
0
2
0
0
0
0
0
0
2
0
2
0
0
1
1
0
0
0
0
0
0
0
0
5
0
1
1
0
1
2
2
0
1
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
4
1
0
0
4
0
1
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
1
5
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
1
3
0
2
2
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
1
0
5
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
2
2
0
2
0
0
2
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
3
1
2
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
2
0
0
0
0
2
0
0
1
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
1
1
1
0
0
2
0
0
0
2
2
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
2
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
1
0
1
2
0
0
0
0
1
2
0
0
0
1
0
0
0
0
2
0
0
1
0
1
0
0
2
0
0
0
0
0
1
3
0
0
0
2
0
0
0
0
2
2
0
2
2
0
0
0
1
2
0
0
1
1
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
1
0
1
0
0
0
0
0
8
0
0
0
1
0
0
2
2
0
0
0
5
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
1
0
0
1
0
1
0
0
4
0
0
2
2
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
1
4
0
2
1
0
1
1
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
2
1
0
0
1
0
0
1
0
4
0
0
3
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
2
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
4
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
2
10
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
3
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
2
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
2
0
0
0
0
1
2
1
0
5
0
1
1
0
0
0
0
0
2
0
0
2
0
2
0
0
2
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
2
0
2
0
1
1
0
0
0
0
3
0
0
2
2
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
2
3
0
0
4
3
0
4
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
1
0
0
1
5
2
2
1
0
0
1
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
3
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
3
0
2
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
1
0
0
0
0
2
2
0
0
0
1
0
0
0
2
0
3
2
2
0
0
0
1
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
3
1
1
0
2
0
1
0
2
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
1
0
0
0
1
0
0
1
0
1
0
0
1
1
2
0
0
0
0
0
0
0
2
2
0
0
0
1
0
2
0
0
1
1
0
0
0
6
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
1
0
0
1
1
0
1
0
0
2
0
0
0
1
0
0
2
2
0
0
0
0
2
1
0
0
1
1
0
0
0
0
0
1
0
2
0
1
0
0
2
0
2
0
2
0
1
0
0
2
2
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
1
4
0
0
0
0
1
0
0
2
0
0
1
0
1
1
0
0
1
0
0
2
0
0
0
0
0
7
0
2
1
2
1
0
0
0
2
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
2
2
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
2
1
0
0
0
1
1
0
0
0
3
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
2
0
1
0
1
0
1
0
0
0
0
0
3
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
3
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
2
2
0
0
0
0
0
0
4
1
0
0
2
2
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
2
0
1
1
0
0
1
0
0
2
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
2
0
1
1
0
0
2
0
0
0
0
0
1
0
2
0
5
0
16
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
1
1
0
0
0
4
2
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
2
0
0
1
3
2
2
0
0
0
2
2
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
1
0
1
2
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
2
0
3
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
2
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7
0
0
2
0
0
1
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
2
1
0
0
0
1
2
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
3
2
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
3
2
0
2
0
0
0
0
1
0
1
0
3
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
2
0
1
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
4
0
0
0
0
3
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
9
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
2
0
2
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
1
0
1
2
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
2
2
0
1
2
2
0
2
0
0
0
0
1
1
0
2
0
0
2
0
0
0
2
0
0
0
2
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
64
0
1
0
1
1
4
3
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
1
2
0
1
0
0
2
0
0
0
1
0
1
1
0
0
0
2
1
0
0
2
0
0
0
3
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
2
1
1
0
0
1
0
0
0
1
0
1
0
1
2
0
0
0
0
0
2
0
0
0
2
0
0
1
1
0
2
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
2
1
0
0
0
0
0
0
0
2
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
1
0
1
0
0
1
1
1
1
0
0
0
1
1
3
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
2
0
0
1
1
2
0
0
0
1
1
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
1
0
0
2
1
0
0
0
1
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
2
2
0
0
1
0
0
2
1
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
4
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
2
0
0
2
1
2
0
2
0
1
0
1
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
1
0
0
2
0
0
0
2
0
2
0
2
1
1
1
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
1
0
0
0
1
2
0
0
2
0
0
0
0
0
2
0
0
0
0
4
0
0
0
9
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
2
0
0
1
1
0
0
0
0
2
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
2
1
0
0
0
0
1
0
0
1
0
1
0
0
2
0
0
0
0
0
1
1
0
0
0
3
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
2
0
0
0
4
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
3
0
0
0
0
0
2
5
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
2
2
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
1
0
0
2
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
1
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
2
0
1
2
0
0
2
0
0
16
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
1
0
2
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
1
0
0
1
1
1
0
1
2
2
0
1
0
0
0
0
0
1
0
0
0
0
3
0
1
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
1
0
0
0
2
0
2
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
2
0
0
2
0
1
2
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
5
0
0
0
0
0
0
1
2
0
0
1
1
1
0
3
0
0
0
0
2
3
0
0
0
0
0
0
2
0
1
1
0
0
1
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
2
1
2
0
0
0
0
0
1
0
2
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
2
2
0
0
1
0
0
0
1
0
0
0
1
3
1
2
0
0
2
0
0
2
0
1
0
0
0
1
0
1
0
2
0
1
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
1
1
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
1
2
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
2
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
4
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
2
0
0
0
0
5
0
0
0
0
2
0
0
1
4
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
1
1
1
0
6
0
0
0
1
0
0
0
1
0
0
1
1
1
0
1
0
0
0
0
0
0
0
2
2
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
4
0
0
0
0
0
0
1
0
1
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
4
3
3
0
2
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
3
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
1
2
2
2
0
0
0
0
2
0
0
2
0
0
2
0
1
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
4
0
0
0
0
0
1
0
2
4
3
1
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
3
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
2
0
1
0
3
0
0
0
0
0
2
0
0
0
0
1
1
0
1
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
1
0
4
0
1
0
0
0
1
0
0
0
0
3
0
1
0
0
0
0
3
2
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
2
1
8
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
2
1
0
0
1
1
2
0
0
0
4
1
0
2
0
0
0
0
0
2
2
5
3
0
1
1
2
0
0
2
0
0
2
0
0
0
0
0
2
2
0
2
0
3
0
2
0
0
1
1
0
3
1
1
1
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
1
0
6
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
2
0
0
2
0
1
1
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
2
1
2
1
0
0
0
0
1
0
0
0
0
1
2
1
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
3
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
3
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
5
0
2
3
0
0
1
0
1
0
0
15
2
0
0
1
0
0
2
0
1
0
1
0
0
2
0
1
1
0
0
0
1
0
2
3
0
2
0
0
0
0
0
2
2
0
0
0
10
0
0
0
0
0
1
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
4
5
0
0
0
0
0
3
0
2
0
0
1
0
0
2
0
1
1
0
2
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
4
0
3
0
0
0
0
0
0
0
0
0
1
0
0
1
2
2
0
0
0
2
1
0
0
1
0
0
1
1
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
4
0
2
0
0
2
1
0
0
1
2
1
3
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
1
2
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
1
0
2
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
2
1
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
2
0
1
0
1
0
0
2
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
2
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
2
0
1
0
0
3
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
1
0
0
2
0
0
0
0
0
1
0
0
4
0
1
0
0
5
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
4
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
2
0
2
1
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
4
0
0
2
1
0
0
0
1
0
0
0
0
1
0
0
0
0
2
3
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
3
0
0
0
0
1
0
1
2
1
0
0
0
0
0
0
0
1
0
0
0
0
2
2
1
0
2
0
0
0
2
0
2
0
0
0
1
1
0
0
0
0
1
2
0
1
0
0
0
1
0
0
1
2
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
2
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
1
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
2
0
6
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
1
0
0
1
2
0
0
1
0
0
0
1
0
0
0
0
2
0
0
2
2
0
0
2
2
2
0
0
1
0
0
0
1
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
1
2
2
3
0
0
0
3
2
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
3
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
2
0
0
0
0
2
0
0
0
2
2
0
0
3
3
1
0
2
0
0
2
0
0
0
0
0
1
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
5
0
0
0
1
1
1
1
0
1
2
0
0
2
1
0
1
0
0
2
1
1
0
0
1
0
0
0
0
1
0
1
0
0
0
2
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
3
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
4
1
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
3
1
0
3
0
0
0
0
0
0
1
3
1
0
3
0
0
0
0
0
0
0
2
0
1
0
1
2
2
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
6
0
1
0
0
0
0
0
1
0
0
0
0
0
2
1
0
1
2
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
1
0
0
0
0
1
1
0
4
0
2
1
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
1
0
1
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
2
1
0
4
1
0
1
0
1
2
0
2
4
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
3
0
3
0
0
0
0
0
0
1
2
0
0
0
1
0
2
0
0
0
2
1
0
0
0
0
0
1
0
0
6
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
1
0
0
2
0
0
2
2
2
5
0
2
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
3
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
1
3
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
3
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
4
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
4
2
1
0
4
0
0
0
0
1
0
3
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
1
0
1
0
1
0
0
0
1
0
0
3
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
1
0
2
3
0
2
1
1
1
0
0
0
0
0
9
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
3
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
2
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
2
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
4
0
0
0
1
0
0
0
0
0
2
0
2
2
0
0
0
0
2
0
0
4
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
3
0
2
0
0
0
0
2
0
1
0
1
4
0
0
0
3
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
1
0
0
4
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
1
0
1
0
3
0
0
0
0
0
0
3
0
1
0
0
0
0
0
1
3
0
2
0
2
0
0
0
0
1
1
1
0
0
4
1
0
0
0
0
1
0
0
0
0
0
3
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
3
3
3
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
1
2
3
0
0
0
0
0
1
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
6
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
1
0
0
0
1
2
2
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
1
2
1
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
2
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
1
0
2
0
0
0
8
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
1
0
0
0
2
0
3
1
1
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
1
4
0
0
4
1
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
1
0
0
0
0
0
2
0
0
1
0
1
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
1
1
0
2
1
0
0
2
0
1
0
0
1
0
0
0
5
0
2
0
0
0
0
0
3
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
2
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
3
1
1
0
0
1
1
0
0
2
0
0
0
0
0
0
1
2
1
0
0
2
0
0
0
2
0
0
2
1
0
0
0
0
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
4
0
0
0
0
0
4
2
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
4
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
1
0
0
2
2
0
0
1
0
0
1
0
3
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
1
0
0
0
2
0
0
2
0
0
0
1
0
1
0
2
0
0
0
0
2
1
0
0
0
0
3
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
4
0
1
0
2
1
0
0
0
0
0
2
1
2
0
0
0
6
0
0
0
1
0
2
2
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
6
0
0
0
2
0
4
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
3
0
2
1
2
0
0
0
0
1
0
3
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
1
0
2
0
0
0
1
1
0
0
0
0
2
0
3
0
2
2
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
4
0
2
0
5
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
4
1
0
0
0
0
0
2
0
1
2
2
1
0
0
0
0
8
0
2
0
0
2
0
0
0
0
1
1
0
0
3
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
1
0
1
0
2
0
0
1
1
0
0
0
2
0
2
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
4
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
1
2
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
2
2
0
2
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
2
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
3
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
2
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
1
2
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
3
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
1
2
2
0
0
1
0
0
0
0
0
2
0
0
3
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
3
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
2
0
1
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
2
4
1
0
0
1
0
0
2
0
0
1
2
0
9
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
3
0
6
0
1
1
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
1
0
0
0
2
1
0
0
0
0
1
1
0
0
1
0
0
0
2
0
2
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
2
0
1
2
0
2
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
2
1
0
0
2
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
2
3
0
0
0
0
2
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
7
0
0
0
0
1
1
0
0
0
0
0
0
0
3
0
0
2
0
0
0
1
2
2
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
2
0
0
2
0
2
0
2
0
1
0
1
0
0
0
0
0
0
1
0
1
2
2
0
2
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
2
1
0
0
0
1
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
2
1
0
0
0
3
0
1
2
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
2
0
1
0
0
2
0
0
0
6
0
1
0
0
1
0
2
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
3
0
0
0
1
0
0
2
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
2
0
0
2
0
3
0
0
2
0
4
2
0
0
2
0
0
1
2
0
0
0
0
0
0
3
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
1
0
0
0
2
0
0
2
2
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
7
0
0
0
0
2
0
0
0
2
1
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
1
0
4
0
0
0
0
1
2
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
5
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
2
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
3
2
0
0
0
1
0
0
4
0
1
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
5
0
0
0
1
2
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
3
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
1
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
2
0
0
2
1
0
0
2
1
2
0
1
0
0
4
0
2
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
4
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
1
0
0
0
2
1
0
0
0
3
1
0
2
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
2
1
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
2
0
4
0
2
0
1
0
0
0
0
0
0
2
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
10
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
6
0
0
0
0
0
0
2
0
1
1
1
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
2
2
0
1
0
2
0
0
0
0
0
0
1
0
0
2
0
1
2
3
0
0
0
2
0
2
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
2
1
2
0
0
1
0
0
0
0
5
0
1
0
0
1
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
2
3
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
3
0
0
2
1
2
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
1
0
0
2
0
0
5
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
3
0
0
0
1
0
0
2
0
2
0
1
2
2
2
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
3
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
2
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
2
0
1
0
0
0
0
2
1
0
1
0
0
3
0
0
0
0
2
0
0
0
2
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
1
1
0
0
1
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
2
1
2
2
1
0
0
0
0
0
0
0
0
1
2
1
0
0
2
0
0
0
0
0
0
0
4
0
1
0
0
0
2
0
0
0
2
2
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
2
3
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
3
0
0
0
2
2
2
0
0
0
0
0
1
1
1
0
0
0
2
1
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
4
1
0
1
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
2
1
0
0
0
4
0
1
2
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
4
2
0
0
0
2
0
0
0
0
0
1
1
1
0
0
0
0
0
2
2
0
0
0
2
2
0
0
1
0
0
0
0
4
0
2
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
2
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
3
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
2
0
2
0
1
3
0
0
1
8
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
4
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
2
0
0
0
1
0
0
1
2
1
1
0
0
0
0
2
0
0
2
0
1
2
0
0
0
0
0
2
2
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
4
0
0
2
0
0
0
2
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
1
0
0
0
0
2
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
1
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
1
0
0
2
2
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
0
0
2
3
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
1
1
0
1
6
0
0
1
0
1
0
0
0
0
1
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
1
0
0
0
1
0
0
0
0
10
0
0
0
0
0
0
0
2
2
3
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
2
4
0
0
0
0
1
2
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
1
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
2
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
4
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
1
0
0
0
2
0
2
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
3
0
0
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
6
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
3
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
4
0
0
0
3
1
2
0
0
0
0
1
2
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
2
2
0
0
0
0
1
0
0
0
0
0
4
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
11
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
1
1
1
0
1
0
1
1
0
2
0
2
1
0
0
2
0
0
0
1
2
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
3
1
0
0
0
2
0
0
0
1
1
0
1
0
0
1
0
2
1
0
0
0
1
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
4
1
0
0
0
0
0
0
0
0
0
0
2
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
3
0
2
1
0
2
0
0
0
0
0
0
1
0
0
2
0
0
2
1
2
0
0
2
0
1
1
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
1
2
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
2
2
1
0
0
0
0
0
0
0
0
1
2
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
4
3
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
8
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
2
2
0
1
0
1
0
1
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
2
0
2
0
1
0
2
0
2
0
1
0
0
0
0
0
0
2
2
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
1
0
0
0
0
2
0
0
3
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
2
0
2
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
2
2
2
0
0
4
0
0
0
0
2
1
0
1
0
0
0
1
2
0
0
2
0
0
1
2
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
2
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
2
2
2
1
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
1
0
0
0
1
0
1
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
2
0
2
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
1
0
2
0
0
0
0
0
0
2
0
2
0
1
2
1
0
0
0
1
0
4
0
0
0
0
1
0
4
0
2
3
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
1
0
0
1
0
3
1
1
0
0
0
2
0
2
0
0
1
0
3
2
0
2
0
0
0
0
0
0
0
2
0
3
0
0
1
1
1
0
0
0
0
0
1
0
0
0
1
0
1
1
5
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
3
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
1
0
1
0
1
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
3
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
3
0
0
2
1
0
2
1
1
0
2
0
1
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
3
1
2
0
0
0
0
2
0
3
0
2
0
0
0
0
0
0
1
0
0
0
4
1
0
0
1
0
0
0
2
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
2
0
2
3
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
2
2
0
2
0
1
2
0
0
1
2
1
0
0
2
0
1
1
2
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
2
0
2
0
0
1
0
0
0
0
1
0
0
0
3
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
1
0
0
2
0
3
0
0
0
0
2
0
0
0
1
0
1
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
3
5
0
0
0
2
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
1
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
0
3
0
1
0
0
0
3
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
1
0
2
1
0
0
2
1
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
3
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
4
0
0
1
0
1
1
9
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
1
0
1
0
5
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
1
1
0
1
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
3
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
2
0
0
2
1
0
0
0
2
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
4
0
2
0
0
1
1
0
0
0
0
2
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
1
0
1
0
0
0
4
0
0
0
2
0
0
0
2
0
0
0
5
0
0
0
2
0
0
0
0
0
6
0
0
0
0
0
0
2
0
0
0
1
1
0
0
2
2
0
0
0
0
0
2
0
2
1
0
0
0
3
2
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
2
0
2
0
0
0
0
0
1
0
2
0
5
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
1
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
2
2
2
1
0
0
0
2
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
2
0
1
2
0
0
0
0
2
1
0
0
0
0
0
0
3
1
0
0
1
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
1
0
2
2
0
0
0
1
0
0
0
0
1
1
1
0
0
0
1
2
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
5
2
0
2
0
0
0
3
2
0
0
0
1
0
0
3
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
2
0
2
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
1
1
1
0
1
0
0
0
3
0
0
0
0
2
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
3
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
3
6
1
2
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
2
1
2
0
2
0
0
0
0
4
2
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
4
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
1
1
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
2
0
0
6
0
0
0
1
1
0
3
0
0
0
0
0
0
0
2
0
4
4
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
1
0
2
0
1
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
1
0
4
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
1
1
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
2
0
0
2
0
0
1
0
2
1
0
0
0
0
0
0
2
0
0
0
1
0
0
1
1
0
0
0
1
0
0
1
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
1
3
0
0
0
0
0
2
1
0
3
0
0
0
0
0
1
0
0
2
0
3
2
1
0
1
1
0
0
0
1
0
0
1
0
0
0
0
1
0
3
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
2
2
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
2
0
0
3
0
0
2
0
0
0
0
0
1
0
1
0
0
0
2
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
1
2
0
0
1
2
0
0
0
0
2
0
2
2
0
0
0
3
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
3
0
2
1
0
1
2
3
0
0
0
0
0
0
6
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
2
0
1
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
3
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
3
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
1
0
1
0
0
0
0
2
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
1
2
1
2
0
1
0
0
0
0
3
0
0
0
0
0
4
4
0
0
1
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
2
0
3
0
0
1
3
0
1
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
1
0
2
0
0
0
2
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
4
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
3
3
2
0
0
2
0
0
0
2
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
3
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
1
1
0
2
0
0
0
0
0
0
0
1
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
3
0
2
0
0
0
0
0
0
2
0
0
5
1
0
1
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
3
0
0
0
0
0
4
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
2
1
0
0
1
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
1
0
0
0
4
0
0
0
0
2
0
0
0
0
1
2
0
0
0
4
0
0
2
0
0
0
1
0
0
2
2
0
0
0
0
2
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
2
0
2
2
0
2
2
0
0
0
0
3
0
0
0
4
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
2
0
1
0
2
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
2
2
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
1
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
1
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
1
1
0
1
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
2
0
0
1
0
0
0
0
0
2
2
1
0
0
0
1
0
0
1
0
0
0
0
0
2
0
1
2
4
0
0
1
0
1
0
0
1
0
0
1
1
0
0
0
2
1
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
3
3
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
2
0
0
0
1
2
2
0
0
1
0
0
0
0
0
2
0
3
0
0
1
0
3
2
0
0
0
0
0
0
2
0
0
1
1
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
2
1
0
0
1
2
1
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
2
1
2
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
3
1
0
0
2
0
0
0
2
0
2
2
0
0
0
1
0
0
0
1
1
0
1
0
0
2
0
0
0
2
0
0
0
0
2
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
3
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
2
0
2
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
6
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
4
2
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
2
2
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
1
0
2
3
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
1
0
0
1
0
0
0
4
0
2
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
3
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
2
0
0
0
0
0
0
2
2
0
1
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
1
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
2
0
0
0
0
2
0
1
2
2
0
0
1
0
2
1
3
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
5
0
0
1
0
2
0
0
0
0
0
1
0
1
0
0
0
2
1
0
0
0
2
2
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
2
0
1
0
1
0
0
1
2
0
0
0
0
0
2
0
0
0
0
2
0
1
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
2
0
1
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
2
1
0
0
4
1
2
0
0
1
0
0
0
1
0
0
1
0
2
0
0
0
2
0
1
0
0
0
0
1
1
0
0
0
1
1
0
0
2
0
0
0
0
1
0
2
0
2
0
0
0
0
0
1
0
0
2
0
0
2
2
2
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
1
0
2
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
3
0
0
0
0
1
0
0
0
2
2
0
1
0
1
1
2
1
0
2
0
0
0
1
0
0
2
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
1
1
0
0
0
2
0
1
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
11
0
3
0
0
0
2
0
0
0
5
0
0
2
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
3
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
3
0
0
0
1
0
1
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
2
1
0
0
3
0
0
2
0
0
0
2
0
0
0
1
4
0
0
2
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
2
0
2
0
0
5
1
2
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
2
3
1
0
0
1
0
0
0
0
0
1
0
4
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
1
1
2
0
0
3
0
2
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
1
2
0
1
0
3
0
1
0
0
7
0
2
0
3
1
2
0
1
0
0
0
0
0
2
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
3
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
1
2
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
2
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
1
0
0
2
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
2
4
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
2
0
2
0
0
0
4
0
0
0
1
1
0
0
0
2
2
0
0
0
0
2
1
0
0
0
2
0
0
2
0
2
0
3
2
0
0
0
0
0
3
0
0
0
2
3
0
0
0
1
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
3
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
4
6
0
0
0
1
1
1
2
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
2
0
2
0
2
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
1
0
4
1
0
0
2
0
2
1
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
2
0
2
0
0
0
2
0
1
0
2
0
0
3
0
0
1
5
0
0
2
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
1
1
0
0
1
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
1
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
1
0
0
2
2
2
0
0
0
0
0
2
0
1
0
0
0
0
1
1
1
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
2
0
0
0
2
0
2
0
0
0
0
0
2
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
1
1
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
2
0
2
0
0
1
0
0
0
0
1
0
1
2
0
0
1
0
0
0
0
2
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
3
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
1
0
0
1
0
0
1
0
0
1
0
2
0
2
0
0
1
0
2
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
1
2
1
0
0
0
2
0
0
0
2
2
0
0
1
0
0
0
0
0
3
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
1
0
0
0
0
0
0
1
0
1
0
2
3
0
6
0
1
0
0
0
1
0
2
4
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
1
0
1
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
1
0
0
2
0
0
0
2
0
2
1
0
0
0
0
0
0
1
0
2
2
0
1
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
4
0
0
0
1
3
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
3
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
2
0
0
2
0
0
1
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
1
0
3
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
2
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
3
1
1
0
0
0
0
2
2
0
0
2
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
1
0
0
0
2
2
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
1
0
1
0
0
2
0
0
0
1
1
0
0
2
2
0
0
0
0
2
1
0
0
0
0
1
0
0
0
2
2
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
3
0
0
0
3
0
0
0
2
2
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
2
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
2
1
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
3
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
3
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
2
1
2
0
0
0
2
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
3
0
0
0
0
0
2
0
1
0
0
7
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
2
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
1
1
0
0
0
0
2
0
2
0
1
1
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
1
4
2
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
2
0
0
2
0
0
0
0
1
2
0
0
2
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
3
1
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
1
3
0
0
0
1
2
0
0
0
1
0
0
2
0
0
0
0
1
0
11
0
2
3
0
0
2
0
0
0
0
0
0
0
0
1
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
1
1
0
2
0
1
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
2
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
3
1
0
3
1
0
1
1
1
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
1
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
1
2
0
1
1
0
0
0
0
0
0
1
0
0
2
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
1
0
3
0
2
0
1
0
1
0
0
0
0
2
4
0
0
1
0
0
0
1
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
1
2
2
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
2
1
0
1
0
0
1
0
1
0
2
0
0
0
0
3
0
1
1
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
2
1
1
0
2
0
0
1
0
2
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
2
1
3
0
0
0
0
0
0
0
2
1
2
0
2
0
5
2
2
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
4
2
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
2
0
0
0
1
2
0
0
0
0
1
0
0
0
5
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
2
0
1
2
0
11
0
0
2
0
0
0
0
0
0
4
0
1
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
1
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
3
0
1
1
1
0
1
2
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
2
0
2
0
3
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
4
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
1
0
0
1
1
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
3
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
3
2
0
0
2
0
0
2
0
0
1
2
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
1
2
0
2
0
0
0
2
0
0
1
0
0
2
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
1
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
11
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
1
2
0
1
0
0
0
0
4
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
2
1
0
1
1
1
0
0
0
0
0
0
5
0
0
0
2
0
1
0
0
0
0
3
0
0
0
2
2
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
1
0
0
0
0
1
1
0
1
1
1
0
0
2
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
3
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
2
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
5
0
2
3
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
1
0
0
0
0
0
0
2
1
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
3
0
0
1
0
0
0
1
1
0
2
0
0
0
0
19
0
0
0
0
0
2
2
2
0
0
1
0
0
3
1
0
0
0
1
0
0
3
0
0
0
0
0
0
1
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
1
0
0
3
2
1
0
0
1
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
2
0
0
2
1
0
0
1
0
0
1
1
0
0
0
0
3
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
1
0
0
0
2
1
0
0
7
0
0
0
1
0
1
0
1
0
0
2
2
0
0
0
0
2
1
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
3
0
0
2
3
2
0
1
2
0
0
2
1
0
0
0
0
0
0
0
2
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
1
1
0
3
0
2
6
0
0
2
0
2
2
0
2
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
1
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
4
0
0
0
1
0
0
2
2
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
2
0
1
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
3
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
2
0
0
0
0
0
0
1
8
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
1
1
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
3
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
2
0
1
1
0
0
0
0
0
0
1
3
1
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
2
1
0
0
1
0
0
0
2
0
2
1
3
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
2
4
0
3
2
0
2
0
0
0
1
9
0
0
1
2
1
0
2
0
1
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
2
2
1
0
1
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
3
1
0
0
2
2
0
0
0
0
1
1
2
2
0
0
2
1
0
16
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
2
0
0
0
2
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
1
0
2
2
0
0
1
0
1
1
1
0
0
2
1
4
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
1
0
1
0
0
0
2
2
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
4
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
1
0
2
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
2
0
0
0
1
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
1
0
2
0
2
0
1
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
3
2
0
2
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
5
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
3
1
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
3
1
1
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
2
1
1
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
3
0
0
0
0
0
1
0
2
0
0
0
2
0
1
0
2
0
1
0
0
1
0
0
1
2
0
0
0
0
0
1
0
2
2
0
0
1
0
0
2
0
0
0
0
0
2
3
0
1
1
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
2
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
2
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
1
2
0
0
2
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
2
2
0
0
0
0
1
1
1
0
1
0
0
3
2
0
0
0
0
1
0
0
0
0
0
0
1
1
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
3
0
0
2
0
0
0
2
0
0
0
0
2
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
2
0
0
2
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
3
0
0
0
0
0
0
0
2
1
2
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
6
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
3
0
0
2
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
2
0
1
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
5
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
3
0
2
0
0
3
0
0
0
1
2
0
0
0
0
1
0
0
0
0
2
0
4
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
2
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
2
0
2
2
0
0
0
0
1
2
0
2
0
2
0
0
0
0
0
4
0
0
0
0
0
1
0
1
0
2
2
0
2
0
0
0
2
2
3
0
0
2
2
0
0
3
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
2
1
0
0
0
0
3
0
2
0
0
0
3
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
5
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
2
1
0
0
0
0
4
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
1
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
1
0
0
3
0
0
0
0
0
1
2
0
1
0
0
0
1
3
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
4
1
2
1
4
0
0
0
0
2
1
1
1
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
1
1
0
0
1
0
3
0
0
0
2
0
0
1
2
0
2
0
1
0
0
0
0
1
0
0
0
4
1
1
0
1
1
0
0
2
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
1
1
0
1
0
0
0
0
1
1
2
0
0
0
1
0
1
0
0
1
0
0
4
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
3
2
0
0
0
0
0
7
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
2
1
0
1
0
0
0
2
0
0
0
0
1
2
0
0
2
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
2
0
2
6
0
0
0
0
0
0
0
2
1
0
2
0
0
2
1
0
0
1
1
0
0
0
0
0
0
1
2
1
0
0
0
2
0
0
0
3
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
2
0
0
1
1
2
2
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
1
0
0
1
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
2
2
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
3
0
0
0
2
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
1
2
1
1
0
0
2
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
2
1
1
0
0
0
0
0
2
0
0
4
1
0
0
0
0
1
7
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
2
0
0
0
0
0
2
0
0
2
0
1
0
1
2
0
2
2
1
0
0
0
2
0
2
0
3
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
2
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
5
0
0
0
0
1
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
2
0
0
2
0
0
0
0
1
0
2
0
0
0
2
2
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
2
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
1
0
0
2
0
2
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
1
0
0
1
1
2
0
0
0
0
0
0
2
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
4
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
3
0
0
2
2
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
2
1
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
2
1
0
2
2
1
2
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
1
0
0
0
0
0
0
1
1
0
0
3
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
1
3
2
0
0
0
4
0
2
0
0
0
1
0
0
0
0
1
0
0
0
1
2
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
2
0
0
0
1
0
1
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
4
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
7
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
2
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
1
1
0
0
0
2
1
0
1
0
0
0
1
0
2
0
3
0
0
1
2
1
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
5
0
0
4
0
2
0
0
0
0
1
0
1
0
2
1
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
2
1
1
0
2
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
4
2
0
0
2
0
2
0
0
0
1
0
1
1
0
0
0
0
0
0
0
2
0
0
0
2
4
0
0
3
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
2
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
1
0
0
0
3
0
0
0
0
0
2
3
0
0
0
0
1
0
3
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
7
1
0
0
2
1
2
0
0
1
2
0
0
2
1
1
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
3
0
2
0
1
0
0
0
0
0
0
0
1
0
1
2
0
0
1
2
2
1
0
1
1
0
0
0
0
2
2
0
0
0
1
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
3
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
1
1
0
0
1
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
2
1
0
1
0
2
1
0
0
0
1
10
0
0
0
8
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
2
2
0
2
0
0
0
0
1
1
3
0
0
1
0
2
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
5
0
2
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
2
0
0
0
2
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
2
0
1
2
0
0
0
3
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
2
0
0
1
1
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
1
1
1
0
0
0
5
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
2
0
0
0
0
1
0
1
0
0
2
0
0
2
0
2
0
2
2
1
0
0
0
1
2
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
1
0
0
0
0
0
0
3
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
3
0
0
0
0
3
2
0
0
0
0
0
0
0
1
1
0
5
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
3
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
3
3
0
2
4
0
0
2
0
0
2
0
2
2
0
0
0
0
0
0
0
4
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
2
0
0
4
0
0
1
2
2
0
0
0
2
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
2
0
0
0
0
0
1
0
2
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
2
0
0
0
3
0
0
0
0
1
0
2
2
0
0
0
0
2
0
2
0
0
1
0
0
0
0
2
0
5
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
3
1
2
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
1
1
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
2
0
1
0
1
2
1
0
1
2
0
0
0
1
0
2
0
0
1
1
1
0
0
2
0
1
0
1
2
2
2
0
0
0
2
0
0
0
0
1
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
2
0
2
1
0
0
0
0
0
0
10
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
3
0
0
0
0
2
0
0
0
0
3
2
1
1
0
0
0
2
0
0
2
0
0
1
3
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
3
0
0
2
2
2
0
0
0
2
0
0
1
2
1
0
0
0
0
0
0
1
0
0
1
1
2
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
1
0
0
0
2
0
0
0
0
7
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
1
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
2
0
0
0
1
2
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
2
2
0
0
0
1
2
0
0
0
0
2
0
0
0
4
0
2
2
1
0
0
0
0
1
0
2
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
1
0
2
1
0
2
0
0
0
0
2
0
0
0
0
1
0
0
1
0
1
0
0
0
2
2
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
1
2
0
0
2
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
1
0
2
2
0
0
0
0
0
0
2
0
3
0
0
2
0
1
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
3
2
1
0
0
1
1
0
0
0
0
0
4
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
2
2
0
0
2
2
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
2
11
0
1
2
1
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
2
1
0
0
0
2
0
0
1
0
0
1
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
5
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
3
0
2
0
0
2
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
3
0
0
2
1
2
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
1
0
0
2
0
0
1
6
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
4
0
0
2
0
2
0
0
0
2
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
2
1
1
0
2
0
0
0
0
2
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
5
0
0
0
2
0
0
1
2
0
2
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
2
1
2
0
0
1
0
0
2
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
2
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
1
0
2
1
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
6
0
0
0
2
1
0
0
0
0
7
2
2
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
1
0
0
0
2
1
0
0
0
0
3
2
0
0
0
0
0
1
0
3
0
0
0
2
0
0
0
2
0
1
0
0
2
1
0
1
0
0
0
2
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
1
1
0
1
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
3
0
0
0
0
0
0
0
0
3
1
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
2
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
2
0
0
0
2
1
0
0
0
0
2
0
1
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
3
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
1
1
0
2
0
3
1
2
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
1
1
0
0
2
2
0
2
0
1
0
0
2
0
1
0
0
0
2
0
3
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
2
0
0
0
0
0
3
0
0
0
0
2
0
0
0
2
1
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
5
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
2
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
1
0
0
0
2
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
3
0
1
4
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
1
0
1
2
0
0
3
0
0
1
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
1
1
0
1
1
2
2
0
0
0
2
0
2
0
0
0
2
0
1
0
2
0
0
0
0
0
1
0
0
1
7
0
0
1
1
0
0
0
0
0
1
0
2
0
0
0
2
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
3
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
1
0
0
2
0
2
1
0
3
2
1
0
0
1
0
0
2
2
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
3
0
3
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
2
0
0
1
0
0
0
1
0
1
0
0
2
2
2
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
6
0
0
2
1
0
0
0
0
0
1
0
0
0
6
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
2
0
1
0
0
2
0
2
3
0
0
0
0
4
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
1
2
0
0
0
0
2
0
0
0
0
0
0
0
2
2
1
0
0
1
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
1
0
0
0
1
0
0
0
1
0
0
5
0
0
0
3
0
0
0
0
0
0
0
1
0
2
0
2
0
1
0
2
1
1
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
1
0
0
2
1
3
0
0
0
0
2
0
0
0
2
0
1
2
0
0
2
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
3
0
1
0
2
0
0
3
2
0
0
0
0
3
0
0
1
1
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
3
0
0
2
0
4
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
3
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
1
4
0
0
0
0
0
2
0
2
0
1
4
0
0
0
0
0
0
0
2
0
2
0
0
1
0
1
2
0
0
0
0
2
0
0
7
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
1
0
0
0
0
1
0
2
1
0
0
3
1
0
0
2
0
0
0
3
0
2
1
0
1
0
0
1
0
0
1
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
2
2
1
3
0
0
0
2
0
0
0
0
0
1
0
0
0
2
5
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
3
0
0
3
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
2
0
1
2
0
0
2
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
3
1
0
1
0
0
2
1
0
2
0
0
0
2
0
0
2
0
2
0
0
0
0
2
0
1
0
0
3
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
2
0
2
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
5
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
1
2
0
0
0
3
1
0
0
2
0
2
0
0
0
2
1
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
2
0
0
0
0
1
0
1
0
0
2
1
2
1
0
0
0
0
0
1
2
0
0
0
0
1
0
2
0
1
0
0
0
1
0
1
0
0
1
1
0
0
0
1
2
2
0
2
2
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
1
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
1
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
1
1
0
0
1
2
1
0
0
0
5
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
2
8
0
0
0
2
0
0
0
2
0
1
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
1
2
0
0
0
0
1
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
4
0
0
1
0
0
3
0
0
0
2
0
0
0
2
2
0
0
0
1
0
0
0
1
0
0
0
2
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
2
2
0
0
0
0
2
0
1
0
2
0
1
0
0
3
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
2
0
0
0
7
0
4
0
1
0
0
1
0
0
2
0
0
0
4
0
2
0
0
1
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
12
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
1
0
0
0
1
3
2
2
0
1
1
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
3
0
2
0
0
0
0
0
3
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
4
0
0
0
1
0
0
0
1
1
2
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
1
0
1
1
0
0
2
0
1
0
1
0
0
0
0
2
0
0
2
0
0
0
0
1
1
0
2
0
0
1
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
4
1
0
2
0
1
1
0
1
0
0
2
0
2
1
4
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
4
2
0
1
0
1
2
1
0
0
0
0
2
0
1
0
0
2
1
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
6
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
4
0
2
0
0
0
1
0
0
1
1
0
1
0
0
0
2
0
0
1
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
2
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
2
1
0
0
2
0
2
0
0
0
0
0
0
0
5
0
0
0
1
2
1
0
0
4
2
0
0
2
0
2
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
4
0
0
0
2
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
1
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
1
0
2
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
1
2
0
2
2
2
1
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
15
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
9
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
2
0
0
3
2
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
1
0
0
1
0
1
0
3
0
1
1
0
1
0
1
0
0
2
0
0
0
0
0
13
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
3
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
1
2
0
0
0
0
9
0
0
0
2
0
0
2
0
2
2
0
1
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
2
0
3
0
0
0
0
0
0
0
0
0
0
5
1
0
0
1
0
2
0
3
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
3
1
3
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
2
0
1
0
0
0
0
0
2
3
0
0
0
0
0
0
1
2
0
0
1
0
0
2
0
0
0
0
3
0
0
2
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
1
1
0
7
0
0
1
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
1
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
1
2
0
0
0
2
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
1
0
1
0
0
0
2
0
0
0
1
0
0
0
0
1
2
0
0
2
1
0
0
1
0
0
0
1
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
2
0
0
2
0
2
0
3
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
6
2
0
0
2
2
0
0
0
0
2
0
0
0
3
0
1
0
0
2
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
3
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
2
0
2
0
0
0
0
0
0
3
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
1
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
5
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
1
0
0
3
0
0
1
0
0
2
0
2
1
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
6
0
0
0
0
0
0
0
0
2
3
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
2
1
1
0
0
0
0
0
2
0
0
2
0
0
0
0
3
0
0
0
0
2
0
2
0
1
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
1
1
3
0
0
0
2
0
0
1
0
0
1
0
0
1
0
2
0
2
0
3
1
0
2
0
0
1
0
0
0
0
1
0
0
2
0
1
0
2
0
0
0
0
1
0
0
1
0
0
0
2
0
2
1
0
2
0
0
0
5
3
0
0
2
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
1
0
1
0
0
0
0
0
2
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
1
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
1
0
0
0
0
0
0
3
0
0
0
0
0
2
1
0
2
0
1
0
0
5
0
0
0
0
2
0
0
0
1
2
0
0
0
2
0
0
0
2
0
0
2
0
0
0
1
2
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
2
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
3
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
2
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
1
0
4
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
4
0
0
0
0
0
0
2
2
0
0
1
0
0
0
1
0
0
1
0
0
3
1
0
0
1
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
1
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
3
0
1
3
0
0
0
1
1
0
1
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
2
0
3
2
2
0
1
2
2
1
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
3
0
0
0
0
4
3
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
4
0
0
0
0
0
2
0
0
0
2
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
1
2
0
0
0
1
0
0
0
0
0
1
0
1
1
1
0
2
0
0
0
1
0
1
1
1
1
0
0
0
0
3
0
0
3
0
0
1
2
2
0
0
0
1
0
0
2
0
0
0
0
2
1
3
0
0
5
0
0
2
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
1
2
0
0
0
0
0
2
0
1
2
0
2
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
3
0
2
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
2
0
2
2
3
0
1
0
1
1
3
1
0
0
0
1
0
0
4
0
0
0
2
2
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
3
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
3
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
2
2
1
0
2
0
2
0
0
0
1
0
0
3
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
3
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
2
0
0
2
0
0
5
0
0
2
0
1
0
0
2
0
0
0
0
1
0
0
0
0
5
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
3
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
2
0
0
2
0
1
1
2
1
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
1
0
0
2
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
2
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
1
1
2
1
2
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
1
0
0
2
0
0
0
2
0
0
1
0
0
0
0
2
1
2
0
2
1
0
2
0
0
1
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
3
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
1
2
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
1
2
2
0
0
3
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
3
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
2
2
1
0
0
0
2
0
2
0
2
2
1
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
2
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
1
0
0
2
3
1
2
0
0
2
2
0
0
1
1
0
0
3
0
0
0
0
0
0
1
3
1
2
0
0
0
2
2
2
0
1
1
2
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
1
0
2
4
0
1
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
2
1
4
0
0
0
0
1
2
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
2
2
3
0
0
0
0
1
0
0
4
0
2
0
0
0
0
0
0
2
3
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
1
4
1
0
0
0
0
2
2
0
0
1
1
0
2
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
3
0
2
0
0
0
0
1
2
2
0
0
3
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
3
0
0
5
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
3
0
1
2
0
2
9
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
2
3
0
1
0
0
0
0
0
0
2
3
0
0
0
0
4
2
1
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
1
0
0
2
0
0
0
0
0
0
0
1
0
2
2
0
1
0
0
2
0
0
0
0
0
0
1
0
1
1
0
2
1
0
0
0
2
0
0
0
0
2
0
0
0
3
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
3
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
2
0
2
2
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
8
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
1
0
0
0
0
0
3
2
0
0
0
0
10
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
1
1
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
2
0
0
2
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
2
1
3
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
1
1
2
0
0
0
2
4
0
0
0
0
0
1
0
0
0
1
0
0
1
2
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
3
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
1
2
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
2
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
1
0
1
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
3
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
1
0
0
2
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
1
1
2
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
1
1
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
1
1
0
1
0
0
0
0
2
0
0
0
3
0
0
0
0
2
0
0
0
0
1
0
0
0
0
4
0
0
2
3
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
2
0
0
0
0
0
0
1
0
1
0
0
1
0
0
3
0
0
1
0
0
2
0
0
0
2
0
1
0
0
2
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
2
2
0
0
0
2
0
0
4
0
0
1
2
0
0
0
0
0
1
0
0
1
0
0
0
6
4
0
0
0
0
0
1
1
0
0
1
0
3
0
6
1
2
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
1
0
0
1
0
5
0
0
0
0
1
0
0
0
0
1
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
2
0
1
0
1
0
0
0
0
0
1
0
0
1
0
4
0
3
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
1
1
0
2
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
4
2
0
0
0
0
3
2
0
0
0
0
0
1
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
4
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
3
0
2
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
2
0
1
1
2
1
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
1
1
2
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
2
1
0
0
0
0
0
3
0
0
2
0
0
1
0
0
1
2
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
2
0
0
1
0
0
0
0
4
0
0
0
0
0
0
1
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
2
0
0
0
2
0
2
0
1
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
3
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
2
1
1
1
0
0
0
0
0
0
0
1
0
0
0
2
1
0
2
0
0
0
4
0
1
0
1
0
1
2
0
0
0
1
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
2
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
5
0
3
0
0
2
0
0
4
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
2
1
0
2
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
1
0
1
0
0
0
0
0
0
1
0
0
1
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
1
2
1
0
2
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
9
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
4
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
1
0
0
2
0
0
1
1
0
0
0
1
3
0
0
1
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
9
2
0
0
0
0
0
2
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
3
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
3
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
2
2
0
0
0
0
0
2
0
3
2
0
2
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
3
0
2
0
3
1
0
0
0
0
0
0
0
0
3
0
0
1
3
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
2
0
0
0
0
0
0
5
0
0
0
2
0
2
3
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
3
0
2
0
0
1
0
0
0
0
2
2
0
0
1
0
1
0
9
2
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
2
0
1
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
1
1
0
2
1
2
0
0
0
0
1
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
2
0
0
3
0
0
0
0
0
1
0
1
1
0
0
0
3
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
5
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
2
0
0
0
0
1
0
1
0
2
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
1
0
2
0
0
2
2
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
2
0
2
0
2
0
0
2
0
0
0
1
0
2
0
0
1
0
0
1
0
1
2
1
0
0
0
1
0
0
0
1
6
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
3
0
0
0
0
0
0
0
1
0
1
0
1
0
0
2
0
1
0
0
1
0
0
0
4
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
2
0
0
1
0
0
1
0
2
0
0
0
1
0
1
1
0
2
1
2
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
2
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
6
0
0
0
0
1
3
0
0
1
0
2
0
2
0
1
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
2
1
0
0
0
2
2
0
0
0
0
3
0
1
0
1
2
1
0
1
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
1
2
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
1
1
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
2
0
0
0
2
2
0
2
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
3
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
3
1
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
2
0
1
0
0
0
1
0
0
1
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
1
2
0
2
0
2
1
0
2
2
0
0
0
0
0
2
0
0
0
1
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
4
0
1
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
3
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
1
1
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
1
1
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
1
3
2
0
0
0
0
0
2
3
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
1
0
0
0
0
0
1
1
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
2
2
1
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
2
1
0
0
0
2
1
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
3
1
0
0
0
0
0
0
0
0
0
1
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
1
0
2
0
0
0
0
0
0
0
3
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
2
1
0
0
0
2
0
0
1
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
2
2
0
0
0
3
1
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
3
0
0
0
1
2
0
0
1
2
0
0
2
1
0
0
0
0
2
0
0
2
0
0
3
2
0
1
1
0
3
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
2
0
0
2
0
0
1
0
0
0
2
0
2
0
0
0
1
0
2
0
1
0
0
1
0
0
2
0
0
0
3
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
1
0
0
2
0
0
0
2
0
1
0
1
0
0
0
0
0
0
1
1
2
0
0
0
0
0
1
0
0
1
0
0
1
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
2
0
0
1
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
5
2
3
0
0
0
0
1
1
1
2
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
12
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
2
0
2
1
0
0
2
0
2
0
0
0
3
0
0
0
0
0
0
2
3
0
0
1
2
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
2
1
0
0
1
0
0
0
0
0
0
0
2
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
1
2
0
0
0
2
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
8
0
0
2
0
0
0
0
0
0
0
0
2
1
1
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
6
0
0
2
0
0
0
1
1
0
0
1
2
2
1
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
2
1
0
0
0
1
0
1
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
1
0
0
1
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
1
0
1
0
0
2
0
0
1
0
1
0
0
1
0
2
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
2
0
0
2
3
0
0
0
2
0
0
0
2
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
2
0
0
0
2
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
1
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
3
2
0
3
0
0
0
2
0
0
1
0
1
0
0
0
0
2
0
0
1
0
0
7
0
0
0
0
0
2
0
1
0
2
1
1
0
0
0
0
2
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
1
2
0
2
2
0
0
0
2
0
0
0
0
1
2
0
0
1
1
0
0
0
1
2
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
2
0
0
0
1
0
0
0
0
3
0
1
1
0
2
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
3
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
1
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
1
0
2
0
0
0
0
0
2
0
2
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
4
0
2
0
0
0
0
0
0
0
1
0
5
0
0
0
0
2
2
0
0
1
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
2
5
0
1
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
1
1
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
1
1
0
0
1
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
2
1
0
0
1
0
1
1
0
0
0
2
0
0
0
2
1
0
0
0
0
0
1
4
1
0
0
0
0
2
2
0
0
0
0
1
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
3
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
9
0
2
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
2
2
2
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
2
2
0
0
1
0
0
0
0
5
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
3
0
0
0
2
0
0
5
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
2
0
1
2
0
0
1
1
1
0
1
0
0
2
0
1
0
0
1
0
2
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
3
0
0
2
0
0
0
0
0
0
0
0
0
0
7
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
3
0
0
0
0
0
0
2
1
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
1
2
0
0
0
0
3
0
1
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
3
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
2
0
2
0
0
0
0
0
0
2
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
3
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
1
0
1
2
0
0
3
1
0
2
0
0
0
0
0
0
2
1
0
0
0
0
1
1
0
1
0
1
0
0
2
0
2
0
0
0
2
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
2
0
0
2
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
2
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
4
1
0
0
0
2
2
0
3
1
0
0
0
0
0
0
1
0
1
0
2
1
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
2
0
0
2
2
0
2
0
0
1
2
0
3
2
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
3
0
0
2
0
2
0
1
0
2
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
1
0
1
2
0
1
0
0
1
0
0
0
0
2
0
0
0
0
3
0
2
2
1
2
1
1
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
2
0
2
2
0
1
0
0
0
0
0
0
0
0
1
2
1
0
1
2
0
0
0
0
2
1
0
0
0
1
4
0
0
0
0
0
2
0
2
3
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
1
2
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
2
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
1
0
3
0
0
0
0
6
1
0
0
4
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
1
0
0
1
0
1
2
0
0
0
0
0
0
0
2
0
2
0
0
1
2
2
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
3
0
0
1
0
0
0
0
0
3
1
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
3
1
0
0
3
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
2
0
2
0
0
2
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
1
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
3
0
0
0
2
1
0
0
0
0
1
0
0
0
1
1
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
1
0
0
0
4
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
2
0
0
0
1
0
2
0
0
2
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
3
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
9
0
0
0
0
0
2
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
4
0
0
3
2
0
2
0
2
3
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
2
0
2
0
2
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
1
0
1
0
0
2
0
0
0
1
2
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
2
3
0
1
0
0
0
0
1
0
0
0
0
15
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
3
0
1
0
2
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
3
2
4
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
1
2
0
1
0
0
2
1
1
1
6
0
2
2
1
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
1
0
0
1
1
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
2
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
34
3
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
2
2
0
0
1
0
0
0
2
1
1
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
3
0
2
0
3
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
5
1
1
0
0
0
0
1
0
4
0
0
1
1
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
2
1
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
2
0
4
0
0
0
0
2
2
0
0
0
0
1
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
1
2
3
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
1
4
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
3
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
2
2
0
3
0
0
0
0
3
0
0
3
1
0
0
6
2
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
2
0
1
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
6
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
3
0
0
2
0
0
0
1
5
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
2
0
0
1
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
2
1
0
6
1
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
3
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
3
1
0
1
0
0
0
0
0
0
0
0
1
0
1
3
1
1
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
1
3
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
3
0
0
2
0
0
2
0
0
0
1
0
0
0
6
2
0
0
1
2
2
0
0
1
0
0
0
0
1
2
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
2
2
0
4
0
0
0
0
0
0
0
0
2
3
0
0
2
2
0
0
0
2
0
2
2
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
2
4
0
0
0
0
1
0
0
0
2
2
0
3
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
3
0
3
2
0
0
0
0
0
2
0
2
0
0
0
0
0
2
1
2
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
2
3
0
0
0
1
0
0
0
0
0
0
0
1
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
3
0
0
4
0
0
2
0
1
2
0
2
0
2
0
0
0
0
0
1
0
0
0
2
0
1
0
0
2
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
2
1
0
0
0
2
0
3
2
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
1
1
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
1
1
0
0
2
1
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
3
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
2
0
0
1
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
9
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
2
0
2
1
0
0
2
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
2
0
0
0
0
1
1
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
3
2
0
0
0
0
0
0
0
1
0
0
2
0
0
2
2
0
0
0
1
0
0
2
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
2
0
0
1
2
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
3
0
0
0
5
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
2
0
0
1
0
0
0
0
1
0
4
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
6
0
0
0
0
1
0
1
0
0
0
0
0
0
0
3
0
0
2
2
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
3
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
1
0
0
1
0
0
0
0
2
0
0
3
2
1
1
11
0
0
2
0
2
0
0
1
0
0
0
0
2
1
0
0
0
1
2
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
1
0
2
0
0
2
0
0
0
0
2
0
1
0
0
2
0
0
0
1
0
0
8
3
1
0
0
0
0
2
1
0
2
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
3
3
0
0
2
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
3
0
2
0
0
0
0
0
0
0
0
1
1
0
1
1
0
1
0
1
2
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
5
1
0
0
2
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
1
0
0
2
1
3
0
4
2
1
0
3
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
5
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
3
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
2
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
2
0
2
3
0
0
0
0
2
0
0
0
0
1
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
5
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
1
2
2
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
4
1
2
1
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
2
0
3
0
0
0
0
1
0
2
0
0
1
0
0
5
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
4
1
0
0
0
1
2
2
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
3
0
0
0
2
0
0
0
2
0
2
1
0
1
0
0
0
4
0
0
0
2
3
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
1
1
0
2
7
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
7
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
1
0
2
0
0
1
0
2
0
0
2
0
1
0
0
1
0
1
2
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
1
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
1
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
1
0
1
1
1
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
1
3
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
1
2
0
0
0
0
1
0
0
0
0
2
2
1
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
2
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
1
0
0
5
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
3
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
2
0
1
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
2
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
1
0
1
1
1
4
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
1
2
0
0
0
0
1
2
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
1
1
3
0
0
3
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
5
0
0
2
0
0
2
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
2
2
0
0
0
2
0
0
1
0
0
0
0
1
0
1
0
0
0
3
1
2
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
1
0
2
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
3
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
1
1
2
0
0
0
0
2
0
1
3
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
2
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
4
0
1
0
1
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
2
0
0
0
0
1
0
2
0
0
0
1
0
1
1
1
2
0
0
0
0
0
0
0
0
2
0
2
3
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
2
0
1
0
0
0
4
0
0
0
1
0
0
0
2
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
7
1
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
2
0
2
0
0
1
0
0
2
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
3
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
2
3
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
5
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
1
1
0
2
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
3
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
2
2
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
2
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
3
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
2
2
0
0
0
2
1
3
0
2
0
3
1
0
0
2
1
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
2
0
0
0
0
5
3
2
0
0
0
1
0
0
0
1
0
0
0
0
5
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
2
0
3
0
0
0
0
2
0
0
0
2
1
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
1
0
2
2
4
2
0
0
0
2
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
3
0
0
2
0
0
0
2
0
2
2
1
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
2
1
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
3
2
0
0
0
0
0
0
0
3
0
0
0
1
0
0
1
0
0
1
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
1
0
3
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
1
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
3
1
0
0
0
0
2
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
2
2
0
0
0
2
0
2
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
3
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
1
2
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
1
4
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
1
2
0
0
0
0
0
5
0
0
1
0
2
0
0
0
0
0
0
2
2
3
0
1
0
0
2
0
0
0
2
1
1
0
0
0
0
0
0
3
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
2
0
0
0
0
0
0
2
3
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
1
0
0
0
1
2
0
2
0
0
0
2
2
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
4
2
0
2
0
0
0
1
0
1
0
0
0
0
0
0
2
0
3
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
1
2
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
3
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
2
0
1
0
0
1
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
5
2
0
0
0
2
0
0
0
0
1
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
3
0
2
1
0
0
1
0
0
0
0
1
0
1
0
0
0
2
2
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
1
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
1
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
4
2
0
2
0
2
1
0
0
0
2
0
2
3
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
3
0
4
0
2
0
0
3
4
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
2
0
0
0
4
0
0
0
0
0
1
0
0
1
1
2
0
0
0
2
0
0
0
0
0
0
0
1
1
1
1
0
0
1
0
1
0
1
0
0
0
0
0
0
7
4
2
0
0
1
0
11
0
0
2
0
0
2
0
0
0
1
0
0
0
0
2
0
5
0
0
0
2
0
0
0
0
0
0
1
2
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
2
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
3
0
0
2
0
0
0
0
3
0
2
0
1
1
0
1
0
0
2
3
0
1
0
0
2
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
1
1
2
0
1
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
3
1
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
1
0
2
2
0
0
0
1
2
1
0
0
1
0
0
0
0
0
0
2
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
1
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
1
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
5
2
0
0
2
0
0
0
2
0
2
0
0
0
0
5
2
0
0
0
0
0
0
1
0
3
2
0
0
0
0
0
1
0
1
2
0
1
2
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
3
0
1
0
0
0
2
0
3
0
2
0
0
0
4
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
1
0
2
0
0
0
1
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
1
2
0
0
1
0
1
0
0
2
2
3
0
0
0
0
0
0
3
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
2
0
0
1
2
0
0
0
0
1
0
1
1
0
2
1
0
0
1
0
0
2
3
3
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
2
0
1
0
0
2
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
4
0
1
1
2
0
0
0
0
2
0
1
1
0
0
0
2
3
0
0
2
1
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
2
0
2
1
2
0
0
0
0
0
3
0
0
0
0
1
0
1
0
2
0
1
0
0
2
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
4
0
0
1
1
0
0
0
2
1
0
0
0
2
0
0
1
0
1
0
2
0
0
0
2
0
0
0
0
1
1
2
0
0
1
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
2
3
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
2
2
1
2
0
0
0
0
2
2
1
0
0
1
0
0
3
0
0
3
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
2
0
0
1
0
0
0
1
0
0
0
0
0
0
4
0
1
0
0
0
0
0
3
0
0
0
5
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
2
0
0
0
1
1
2
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
1
0
3
0
0
0
0
0
2
0
0
0
0
1
5
0
1
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
3
3
0
2
0
2
0
1
0
1
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
5
0
1
2
0
0
0
0
0
0
1
2
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
2
1
4
1
0
2
0
0
1
0
0
0
0
0
1
2
1
3
0
0
0
0
1
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
1
2
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
3
0
2
0
3
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
2
1
2
0
1
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
3
0
1
0
2
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
3
2
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
4
0
0
1
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
1
0
3
0
0
0
0
2
4
0
0
0
2
0
1
0
0
2
0
1
0
1
0
2
2
2
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
2
0
1
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
5
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
3
0
0
0
0
0
0
2
0
2
0
2
0
0
0
2
1
2
1
0
0
0
0
0
1
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
3
1
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
2
1
0
0
1
2
0
0
0
0
3
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
2
2
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
3
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
1
1
0
2
0
2
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
4
1
0
0
0
0
3
0
0
0
2
0
1
0
0
2
2
1
2
0
1
0
0
0
0
0
0
3
0
2
0
2
1
0
0
0
0
2
2
1
2
2
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
2
0
1
0
1
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
2
0
2
0
2
0
0
0
2
0
0
0
0
1
0
0
2
2
0
0
0
2
1
0
1
0
2
0
0
0
0
0
0
1
0
3
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
4
0
3
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
4
0
0
0
0
0
0
4
3
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
1
2
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
2
0
3
0
0
0
0
0
0
2
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
5
1
0
2
0
0
0
0
0
2
0
0
2
0
0
1
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
2
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
1
2
0
1
2
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
1
0
1
1
0
3
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
1
0
1
0
0
1
3
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
3
0
0
0
1
2
0
1
1
0
0
0
0
1
2
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
2
0
0
2
0
2
0
0
2
0
0
2
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
2
1
4
0
0
2
0
0
0
0
0
0
0
0
0
2
2
1
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
3
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
1
1
0
0
1
1
1
0
1
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
1
2
1
0
0
0
1
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
4
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
2
0
0
1
2
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
1
0
1
2
0
1
0
0
0
0
2
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
2
0
3
0
1
1
0
1
1
2
0
0
0
0
0
2
1
0
0
0
1
1
0
1
0
0
1
0
0
1
0
2
0
0
1
0
2
0
2
0
0
2
0
0
2
0
0
0
0
3
0
0
0
2
1
2
2
0
0
0
0
0
1
0
0
0
2
1
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
1
0
0
0
1
1
0
2
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
9
0
2
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
1
1
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
2
2
2
1
1
2
0
0
2
3
0
0
0
0
2
0
0
0
0
0
0
0
0
5
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
2
0
2
0
0
2
1
0
2
0
0
3
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
3
1
1
0
0
0
0
0
0
2
2
0
0
3
0
2
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
4
0
0
1
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
2
2
2
0
0
0
0
0
0
2
3
0
1
0
0
0
0
0
0
2
2
0
1
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
3
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
4
0
0
1
2
1
0
2
0
0
0
0
2
1
0
0
2
2
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
3
0
0
3
0
1
0
2
2
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
5
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
1
0
1
0
0
0
0
0
2
0
4
1
0
1
0
0
2
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
2
0
2
1
0
0
0
6
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
2
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
2
0
2
3
0
0
0
0
3
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
2
0
0
1
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
2
1
0
1
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
2
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
3
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
3
0
0
1
0
0
0
0
0
1
2
0
0
0
0
2
0
2
1
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
3
0
1
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
2
0
0
1
0
1
0
0
0
0
1
0
0
2
0
0
0
0
1
0
1
0
2
0
1
0
0
0
0
0
0
2
1
2
1
0
1
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
3
0
1
0
0
0
0
0
2
0
0
2
1
0
2
0
1
0
1
0
0
0
2
0
0
0
1
3
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
2
0
0
1
0
2
0
0
0
0
0
1
0
2
2
0
1
0
0
0
2
0
2
0
0
0
0
2
0
2
1
2
0
0
0
0
0
0
0
0
1
0
2
3
0
4
0
0
0
1
0
0
0
0
0
0
3
0
0
0
1
1
1
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
3
0
1
2
0
1
0
0
0
2
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
2
0
0
1
1
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
3
1
2
2
2
2
2
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
2
0
0
3
0
0
1
0
0
1
0
0
0
0
0
2
1
0
0
2
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
2
2
1
0
0
0
0
0
0
0
1
0
0
0
3
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
3
2
0
2
0
0
1
0
0
0
0
0
0
0
0
3
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
1
6
0
0
1
3
0
0
2
2
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
3
1
0
0
2
0
1
0
0
2
0
0
0
0
1
2
2
1
0
0
0
2
2
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
2
0
0
0
1
0
1
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
2
0
0
0
1
0
0
0
0
1
0
3
0
1
0
1
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
1
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
2
0
2
0
0
2
0
1
4
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
2
0
1
0
0
3
0
0
1
1
0
1
0
0
2
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
1
1
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
4
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
1
0
0
2
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
4
4
0
1
0
3
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
2
0
0
0
0
2
0
0
1
6
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
2
0
2
0
0
2
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
1
4
3
0
1
3
0
1
0
0
0
0
3
0
0
0
1
2
0
6
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
1
1
2
0
0
0
0
2
2
0
0
0
0
1
0
0
2
0
1
0
0
0
1
0
0
0
0
0
3
2
1
0
1
0
0
0
0
0
2
0
0
2
2
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
1
2
2
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
2
0
0
1
2
0
1
0
0
2
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
2
1
0
1
1
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
2
1
3
0
0
0
0
0
0
0
0
0
0
0
1
0
5
1
4
3
0
3
0
0
0
1
0
0
0
1
1
1
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
2
1
2
0
2
0
0
0
0
0
0
2
2
2
1
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
1
0
0
0
0
0
0
1
2
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
2
0
0
0
1
0
2
2
0
0
0
0
0
1
0
0
0
1
0
0
2
0
2
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
4
2
0
0
0
1
0
0
1
0
0
0
2
0
1
0
0
0
0
1
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
2
1
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
3
0
0
0
2
0
0
2
0
0
0
2
0
0
2
2
0
0
0
0
0
1
0
0
0
0
2
1
0
0
1
0
1
0
0
2
0
2
2
0
1
3
4
0
0
0
2
1
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
1
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
2
2
0
2
0
0
0
1
0
2
2
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
4
0
2
1
1
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
1
0
2
0
1
0
0
0
0
1
0
0
0
0
1
0
2
0
2
0
0
2
0
0
0
1
0
1
0
1
0
0
5
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
4
0
2
0
0
2
0
0
2
0
0
0
2
3
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
5
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
1
0
0
0
0
0
1
0
0
2
2
0
1
0
0
0
0
0
2
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
2
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
2
0
2
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
4
2
1
0
2
0
0
0
3
0
3
1
0
3
0
1
0
0
0
0
0
0
0
0
2
0
5
1
0
0
0
0
0
1
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
1
2
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
2
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
2
0
2
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
3
2
1
0
1
3
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
2
4
3
0
2
1
0
0
0
0
0
0
0
2
0
0
1
1
1
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
3
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
2
2
1
0
0
1
0
0
2
2
0
1
2
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
2
0
2
1
0
1
0
0
1
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
3
0
1
2
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
5
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
2
0
0
1
1
0
4
0
1
0
0
0
0
1
0
0
0
1
0
3
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
1
0
2
0
1
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
2
0
0
0
2
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
2
3
0
0
0
0
0
2
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
1
2
0
0
0
0
0
2
1
0
0
2
0
0
0
2
0
1
1
0
0
0
0
2
0
0
0
0
2
4
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
1
0
1
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
6
0
1
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
1
0
0
0
3
1
1
1
2
0
0
0
0
0
1
1
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
3
0
2
1
0
0
3
1
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
2
0
1
0
0
0
1
0
0
1
0
1
4
2
2
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
3
0
0
0
1
1
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
2
1
2
0
0
0
3
1
8
1
1
1
0
0
0
0
0
0
7
3
0
0
0
0
2
3
0
0
3
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
2
2
1
2
1
0
0
2
3
0
0
0
1
1
0
1
5
0
0
1
0
1
0
0
0
1
2
0
2
1
0
0
0
0
0
0
2
0
1
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
3
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
1
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
2
1
0
2
0
0
0
1
1
0
1
1
0
0
0
0
1
0
1
0
0
1
2
0
0
0
0
1
0
0
2
2
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
1
3
0
0
0
0
0
5
0
2
0
0
2
0
0
5
0
2
0
1
0
3
0
1
2
0
0
0
0
1
2
0
1
0
0
3
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
6
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
1
2
0
0
1
2
2
1
0
2
1
0
1
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
2
0
1
2
0
0
0
0
2
2
2
2
0
0
0
0
1
0
0
0
8
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
5
3
0
0
2
0
0
2
2
2
0
4
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
2
0
0
1
0
0
0
1
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
2
0
0
2
0
0
0
0
0
0
3
0
0
2
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
3
0
0
0
0
0
2
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
1
1
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
2
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
1
3
0
0
0
0
0
2
3
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
1
0
1
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
1
0
2
0
2
0
0
0
1
3
0
1
1
0
2
0
0
0
0
2
0
0
1
0
0
0
1
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
3
0
1
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
2
1
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
5
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
3
0
1
0
0
0
0
0
0
1
2
1
2
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
1
3
0
0
0
0
0
1
0
0
2
0
5
2
1
0
1
0
0
1
2
0
2
1
0
0
0
0
2
0
0
4
2
0
0
0
0
2
0
0
0
0
0
0
0
4
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
1
0
2
2
0
0
1
0
3
2
0
0
0
0
0
0
1
0
0
2
0
1
0
1
3
0
0
4
1
2
0
0
0
0
1
0
0
0
0
0
1
0
2
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
3
0
2
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
2
1
0
0
0
0
3
0
0
2
0
0
0
0
0
0
1
0
2
1
0
0
0
1
1
1
1
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
1
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
1
0
0
0
1
0
2
0
1
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
3
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
2
2
0
0
0
2
0
0
0
1
0
0
0
3
0
2
0
0
1
0
0
0
0
2
0
0
1
2
0
1
0
0
3
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
2
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
1
0
4
0
2
0
0
0
0
1
2
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
3
1
0
0
0
0
0
2
1
0
0
0
1
2
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
2
0
2
0
0
0
2
0
0
0
0
0
1
3
0
0
0
0
1
0
2
2
0
0
0
0
0
0
1
1
0
0
0
0
0
4
0
0
0
0
2
1
2
2
1
0
0
0
0
3
1
0
0
2
2
0
0
0
0
0
2
0
2
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
1
0
0
1
0
1
0
0
0
3
1
1
0
0
2
0
0
0
0
2
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
1
2
1
0
0
0
0
0
0
0
1
2
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
3
1
0
0
1
0
0
3
0
0
0
0
0
2
2
0
1
0
0
0
1
0
1
0
0
1
0
2
0
1
0
1
0
1
0
0
0
0
2
0
4
0
1
0
7
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
2
7
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
2
1
0
1
1
2
0
0
0
0
0
1
0
1
0
1
2
0
0
3
1
1
0
0
0
1
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
1
2
0
0
1
2
0
3
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
13
0
0
1
1
1
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
2
1
0
2
0
0
0
1
0
2
2
5
0
0
2
1
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
1
0
4
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
2
1
0
0
0
0
3
1
0
0
0
2
0
0
1
1
1
2
0
0
0
2
1
0
0
0
2
0
1
0
1
2
1
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
1
0
2
0
0
3
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
4
0
0
0
0
0
1
0
0
0
1
3
0
1
0
2
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
2
2
1
3
0
0
3
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
4
3
0
0
0
1
0
0
0
0
0
1
0
0
0
2
1
1
0
2
0
0
0
0
1
1
2
0
0
0
1
0
3
0
2
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
4
1
2
0
0
0
2
1
0
0
0
0
0
0
1
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
2
1
0
0
1
0
0
0
0
0
0
4
0
1
1
0
1
3
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
1
2
0
2
1
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
2
0
0
0
1
2
0
2
0
0
1
0
0
0
0
0
1
5
0
1
2
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
2
0
1
1
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
2
1
0
1
0
0
2
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
3
0
2
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
2
2
2
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
2
0
2
0
0
1
0
0
2
0
1
0
0
0
10
1
2
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
2
0
0
2
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
6
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
2
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
3
1
0
2
2
0
0
0
0
0
1
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
2
0
0
2
0
0
1
0
2
2
0
0
0
0
0
3
1
0
3
0
0
0
1
1
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
2
1
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
2
0
0
2
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
2
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
1
1
0
2
2
0
0
0
2
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
2
2
0
0
0
0
0
1
0
2
0
1
3
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
1
0
1
0
1
1
2
1
1
0
1
1
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
2
2
2
0
0
1
0
0
1
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
2
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
1
1
2
1
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
5
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
3
2
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
1
0
2
0
0
0
1
2
1
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
2
2
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
1
2
2
0
0
0
0
0
7
0
3
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
3
0
0
4
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
2
1
1
0
0
0
0
0
0
0
0
0
2
1
5
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
2
0
0
1
1
0
0
1
0
3
0
0
0
0
0
0
2
0
1
0
0
2
0
1
0
1
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
2
0
2
0
0
0
2
3
3
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
3
0
1
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
3
0
0
1
0
0
0
0
0
0
0
1
5
4
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
3
0
0
0
0
3
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
2
0
2
2
0
2
0
0
0
0
1
4
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
1
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
3
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
2
1
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
1
0
0
2
0
0
0
0
1
2
3
0
0
0
0
0
2
0
0
1
0
1
0
1
0
1
0
0
1
0
2
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
2
1
0
0
0
2
1
0
3
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
2
0
1
0
0
6
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
4
0
0
0
2
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
2
0
0
0
1
0
1
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
5
1
0
0
0
0
2
0
1
0
0
0
2
2
0
0
2
7
1
1
0
3
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
2
0
0
0
2
2
2
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
2
1
0
0
0
1
0
0
0
2
2
0
0
0
0
0
1
2
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
2
0
2
1
0
0
0
0
0
0
0
4
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
1
8
0
0
0
1
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
1
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
2
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
1
0
0
1
1
0
1
0
2
0
1
3
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
4
0
0
2
0
0
0
2
0
2
3
2
2
0
0
2
0
0
0
0
0
3
0
0
0
2
4
0
0
1
0
0
2
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
2
0
0
0
0
0
2
0
0
0
1
0
3
0
0
1
2
2
0
0
0
1
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
2
0
0
3
0
0
1
0
0
0
1
1
2
0
0
0
1
0
0
0
0
2
0
0
0
1
1
1
0
0
0
0
0
2
2
0
1
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
3
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
1
1
2
0
0
2
0
0
0
0
2
2
1
1
0
0
2
0
0
0
1
2
0
1
0
1
0
0
3
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
2
2
0
1
0
0
0
3
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
2
2
0
1
1
0
2
1
0
0
0
1
0
0
2
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
4
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
2
2
0
0
1
0
0
0
0
2
0
0
1
0
0
2
2
0
2
1
0
0
0
1
1
0
0
1
3
0
0
4
1
0
0
0
0
0
1
0
0
0
1
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
1
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
1
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
3
0
0
1
2
0
1
0
4
0
1
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
3
0
0
0
2
0
2
0
1
0
0
0
0
2
0
2
4
0
0
0
0
2
0
0
0
0
0
1
0
1
2
0
0
0
3
0
0
1
2
0
0
0
0
0
1
0
0
4
0
0
0
0
2
0
1
1
0
0
0
0
0
0
2
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
1
2
0
1
2
1
1
0
0
2
1
1
0
0
0
0
0
0
0
0
3
3
0
2
0
0
2
0
0
8
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
1
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
1
0
3
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
10
0
1
0
0
0
0
0
0
0
2
0
1
3
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
3
0
0
0
0
0
2
0
0
1
0
3
0
0
1
0
0
1
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
6
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
2
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
1
2
0
0
1
0
0
0
1
0
3
0
0
1
2
0
1
0
0
0
0
0
2
2
12
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
2
0
3
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
3
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
1
1
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
1
0
1
0
0
0
0
3
0
0
1
0
1
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
2
0
1
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
3
0
2
4
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
2
1
0
0
1
0
3
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
1
2
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
2
0
2
0
1
2
0
0
0
2
0
0
4
0
0
1
0
0
2
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
2
1
2
0
0
0
0
0
0
1
0
0
7
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
2
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
2
3
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
2
1
1
0
0
0
0
0
1
0
0
1
0
1
0
2
2
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
5
1
1
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
2
0
1
0
2
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
1
0
0
0
3
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
1
0
8
2
0
0
0
2
3
0
0
1
0
0
1
0
0
0
0
6
0
0
0
2
0
2
0
1
0
0
2
0
3
1
0
0
1
0
0
0
0
0
0
2
1
1
1
0
0
2
0
3
0
0
3
0
0
0
2
0
0
0
0
0
2
1
2
0
0
0
0
1
0
0
0
0
0
7
2
0
0
0
1
0
0
0
0
0
1
2
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
1
0
0
2
0
0
1
0
1
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
2
0
1
3
0
0
0
0
1
0
2
0
1
0
0
0
0
3
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
5
1
1
0
2
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
2
0
2
0
0
1
0
1
1
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
4
2
0
2
0
0
0
0
0
2
2
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
3
0
0
3
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
3
2
0
1
0
0
2
0
0
0
0
1
0
0
0
1
0
2
0
0
2
2
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
5
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
4
1
0
0
0
2
2
0
2
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
2
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
1
0
1
2
0
0
0
1
1
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
1
0
0
0
0
2
0
2
1
2
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
3
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
1
1
0
1
0
0
1
0
1
0
0
0
2
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
2
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
3
0
0
0
0
0
2
0
0
0
0
1
2
1
0
0
2
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
1
1
0
2
0
0
2
0
0
0
0
2
2
0
0
0
0
3
0
2
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
5
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
2
0
0
1
0
0
4
0
0
0
2
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
2
0
0
0
2
0
1
1
1
0
0
0
1
0
0
2
0
2
2
0
3
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
2
0
1
2
0
0
0
0
0
1
0
0
2
2
0
0
0
0
3
1
3
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
1
0
2
0
1
3
0
0
0
1
1
0
0
0
0
1
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
1
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
2
2
0
0
0
2
0
0
0
1
0
3
0
0
1
0
0
2
1
0
3
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
1
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
2
0
1
0
2
2
0
0
1
0
0
2
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
2
2
0
0
2
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
2
0
1
1
2
4
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
1
1
1
0
2
0
0
0
0
4
0
0
0
2
1
0
1
2
0
0
0
1
0
0
0
1
1
0
2
0
0
5
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
2
0
2
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
1
1
0
0
3
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
4
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
3
0
2
0
1
3
0
1
1
0
0
0
3
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
5
2
0
1
2
0
0
1
0
1
0
0
2
0
0
0
1
0
1
1
0
0
0
1
0
0
1
0
0
0
0
2
1
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
3
2
2
1
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
2
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
2
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
2
0
0
3
1
3
0
1
2
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
3
9
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
1
0
0
0
0
1
1
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
2
1
0
0
0
0
2
2
0
0
0
0
0
2
0
3
0
2
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
1
1
2
0
0
0
0
0
0
2
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
1
0
0
0
1
3
0
1
0
0
0
0
2
0
2
1
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
1
5
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
3
0
0
0
8
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
3
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
3
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
3
0
0
2
0
3
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
2
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
1
0
0
2
0
1
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
2
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
1
0
0
2
1
2
1
0
1
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
2
0
6
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
2
0
2
0
3
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
5
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
3
0
0
0
0
0
3
0
0
0
0
1
0
2
0
0
0
0
1
2
2
0
0
0
2
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
3
0
0
2
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
1
1
0
0
3
0
0
0
0
0
0
0
0
2
0
0
2
0
0
4
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
2
2
1
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
1
0
0
0
2
0
0
0
0
1
1
1
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
3
0
2
1
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
2
0
1
0
1
0
0
1
1
0
1
2
0
0
0
0
0
2
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
1
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
4
0
0
0
0
2
0
0
0
0
1
0
0
0
1
1
2
0
2
0
2
2
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
1
3
1
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
3
2
1
1
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
1
0
0
2
1
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
3
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
3
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
2
0
0
0
2
1
1
0
1
2
1
1
0
0
1
0
0
2
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
1
4
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
3
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
2
0
1
0
0
0
0
4
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
3
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
3
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
2
0
1
0
0
0
0
1
1
0
0
1
2
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
12
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
1
1
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
1
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
2
0
0
0
1
1
0
0
3
0
0
1
0
0
2
2
0
0
0
0
0
0
1
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
1
1
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
3
2
0
0
3
0
0
2
0
2
4
0
1
0
0
0
0
0
1
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
2
0
0
0
2
0
0
0
0
1
2
0
2
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
7
2
0
0
3
0
0
0
0
0
2
0
1
2
0
2
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
2
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
3
0
0
0
1
1
0
2
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
3
0
0
2
0
0
0
1
0
0
0
2
2
0
2
0
0
0
0
7
0
0
2
1
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
3
0
2
0
0
0
0
0
0
1
0
0
2
0
1
2
2
2
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
4
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
3
0
2
0
0
0
0
0
1
2
0
1
0
0
0
0
2
1
0
0
0
6
2
0
0
0
0
1
0
1
0
0
0
0
0
0
2
2
0
0
0
2
0
1
0
0
0
0
0
2
2
0
0
0
0
1
1
2
0
2
0
1
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
2
0
0
1
1
2
0
0
0
0
0
0
1
0
3
0
0
0
2
0
0
0
0
1
0
1
0
0
7
0
0
0
0
0
1
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
2
0
0
2
0
0
3
0
0
0
1
2
0
0
0
0
3
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
2
2
1
0
0
0
0
0
5
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
2
0
0
0
0
0
1
4
1
0
0
0
1
0
0
0
0
0
1
3
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
3
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
3
0
0
0
4
0
1
0
1
2
2
0
3
2
1
2
0
0
2
0
0
1
0
2
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
2
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
3
1
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
1
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
1
1
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
1
0
1
0
0
0
0
1
0
0
0
0
2
2
0
1
1
0
0
3
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
1
0
4
2
0
0
0
0
0
0
0
2
0
0
0
3
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
3
0
4
2
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
1
1
0
0
0
1
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
1
0
2
0
0
0
0
0
2
1
1
2
0
0
0
0
1
0
1
0
0
2
0
0
0
0
2
0
0
0
6
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
4
0
1
0
0
0
1
0
2
0
2
2
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
3
0
0
0
0
0
0
0
6
0
0
1
0
0
1
6
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
3
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
3
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
1
0
0
1
0
0
4
2
0
2
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
2
0
4
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
9
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
1
0
0
1
1
2
0
0
0
0
1
2
1
1
1
3
2
1
0
0
0
0
0
0
0
1
0
1
0
0
0
3
0
0
0
3
0
0
0
2
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
2
0
0
0
2
1
0
0
0
0
2
1
0
0
1
2
0
0
7
0
0
0
0
0
0
0
2
0
1
3
2
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
1
0
2
1
1
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
2
2
0
0
2
2
0
0
0
0
0
1
0
0
1
1
0
0
1
2
0
0
0
0
0
2
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
2
1
0
1
1
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
2
0
0
1
0
2
1
1
2
0
1
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
1
4
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
2
0
2
0
0
0
1
0
0
0
0
1
0
0
1
2
1
0
0
0
0
0
4
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
1
0
2
0
0
2
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
3
0
1
0
1
0
0
1
0
1
0
0
0
0
0
3
0
0
0
0
0
1
2
0
0
1
0
0
0
0
3
0
2
2
0
0
2
0
0
2
2
3
0
2
0
1
2
0
0
0
2
0
1
0
2
0
1
1
0
0
0
2
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
3
0
0
1
2
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
2
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
1
0
0
0
0
2
0
0
0
0
1
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
1
2
0
1
2
0
0
2
0
1
1
0
2
0
2
1
0
1
0
1
0
2
1
0
0
0
2
0
0
1
7
0
0
0
0
0
0
1
2
0
0
1
0
0
1
0
0
1
1
0
0
1
0
0
2
2
2
0
2
2
0
0
0
0
0
0
1
2
0
1
2
0
0
1
0
0
1
0
2
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
2
0
0
0
1
0
0
2
2
1
1
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
2
1
0
1
2
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
1
0
0
1
2
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
3
2
0
0
0
0
2
0
0
1
5
0
0
0
2
1
1
0
0
2
1
1
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
2
1
2
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
8
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
4
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
5
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
1
0
1
2
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
2
1
4
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
2
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
2
0
2
0
2
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
3
2
2
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
2
0
1
3
0
1
1
0
0
1
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
1
1
0
1
3
2
0
1
0
0
2
0
0
1
0
0
0
0
1
0
0
1
0
0
2
0
0
0
1
0
0
0
2
0
0
4
1
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
1
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
19
0
0
0
0
6
1
0
0
0
0
0
1
0
0
2
1
1
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
2
0
0
0
2
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
1
0
0
0
0
1
2
0
1
1
1
0
3
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
1
0
1
1
1
0
0
0
0
3
1
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
3
2
0
0
3
0
0
0
0
3
2
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
2
0
0
1
2
2
0
1
0
6
2
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
5
0
0
2
1
3
0
0
0
1
0
0
0
0
0
0
0
1
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
4
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
2
2
2
0
2
1
1
0
0
1
1
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
1
1
0
2
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
4
2
0
0
0
0
0
0
1
0
1
0
3
0
0
0
3
2
0
0
2
2
0
0
0
1
0
0
0
0
0
1
2
5
2
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
2
2
0
0
0
1
1
1
0
0
0
2
0
1
4
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
1
0
0
1
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
1
0
2
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
3
0
2
0
0
3
2
0
2
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
3
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
3
0
2
0
1
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
1
2
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
3
2
0
0
2
0
0
2
0
1
1
1
0
0
0
0
2
2
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
3
0
2
0
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
8
0
0
1
0
1
1
0
0
0
0
1
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
3
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
5
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
2
0
2
0
0
2
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
1
0
0
5
0
1
3
0
0
0
0
2
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
1
0
2
0
0
0
1
0
2
0
0
0
0
0
1
0
2
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
1
0
0
0
1
2
0
2
0
0
0
1
0
2
0
0
0
2
0
2
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
3
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
5
0
2
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
2
0
0
3
0
0
0
0
2
3
0
1
0
5
0
0
0
2
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
1
1
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
1
1
3
0
0
0
0
1
0
1
0
2
0
0
3
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
2
0
0
4
1
0
3
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
1
0
1
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
1
1
0
2
0
0
0
0
3
1
1
1
0
0
0
1
0
2
0
1
2
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
2
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
2
0
0
2
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
2
1
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
2
0
2
2
0
0
1
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
1
1
0
1
0
2
2
0
0
0
1
1
0
0
0
1
0
1
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
2
0
0
2
4
0
2
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
7
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
2
1
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
2
0
0
0
2
0
0
2
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
7
1
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
2
0
0
0
0
1
1
1
1
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
1
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
4
1
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
2
6
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
1
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
1
2
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
3
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
2
3
0
0
2
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
3
0
0
0
0
1
2
2
0
0
1
2
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
1
0
1
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
3
2
0
0
0
0
0
0
1
0
3
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
2
0
0
1
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
4
1
3
1
0
0
2
0
0
0
1
0
0
0
2
0
0
3
2
1
2
0
2
0
0
0
0
0
0
0
5
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
2
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
3
1
0
2
0
2
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
3
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
4
1
0
0
2
0
1
0
0
2
0
2
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
2
0
2
0
1
0
0
4
0
0
0
3
2
0
0
2
2
1
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
2
0
1
0
1
0
1
0
0
0
1
2
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
2
0
0
1
3
0
0
1
0
1
0
0
0
0
1
0
1
0
0
1
0
2
0
0
0
0
1
0
1
0
3
0
1
0
1
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
3
1
0
2
0
0
0
0
2
1
2
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
2
1
0
1
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
2
0
0
0
1
0
0
0
3
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
1
0
0
0
2
2
0
0
6
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
2
1
3
0
0
1
0
1
3
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
2
2
0
0
0
0
1
0
2
2
3
0
0
0
2
1
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
1
1
1
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
1
0
0
1
0
3
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
14
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
5
1
0
0
2
0
0
1
0
1
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
1
0
3
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
1
0
2
0
0
0
2
0
0
1
0
1
2
0
0
1
0
1
0
1
0
1
1
0
2
0
0
1
0
0
2
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
2
2
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
2
0
0
0
0
3
0
2
2
0
0
0
0
2
0
2
0
0
0
2
0
2
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
1
0
0
0
0
2
1
0
0
2
3
2
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
1
0
2
2
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
2
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
6
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
2
0
0
1
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
2
0
0
0
0
3
0
0
0
1
1
0
2
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
1
1
0
0
0
0
0
0
2
1
0
0
0
0
0
2
2
0
0
0
2
0
1
4
0
0
0
0
0
1
0
1
0
0
2
1
3
0
0
0
2
2
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
2
1
0
1
0
0
2
0
0
0
0
0
0
0
0
1
2
1
2
0
0
0
0
3
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
4
1
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
2
1
1
1
0
0
1
0
0
0
0
1
1
0
0
3
0
0
0
0
2
0
0
1
0
0
3
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
2
0
0
0
0
1
0
1
0
1
0
1
0
0
2
0
2
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
1
1
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
3
0
0
0
0
0
0
0
0
1
0
3
1
0
0
0
2
0
0
0
0
1
0
1
0
2
0
0
2
1
1
0
0
0
2
2
0
0
0
0
0
0
1
0
0
1
0
7
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
1
0
3
0
0
2
0
0
1
0
0
1
1
2
0
1
2
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
1
2
0
0
0
0
2
0
0
0
1
2
1
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
7
0
2
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
1
0
1
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
4
0
1
0
0
0
1
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
2
6
2
2
0
0
0
2
4
0
0
0
0
0
0
0
1
4
0
4
0
2
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
3
1
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
2
2
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
4
2
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
1
1
0
0
6
0
0
0
0
0
3
2
0
1
0
3
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
3
0
2
0
0
0
0
0
1
2
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
3
2
0
0
1
0
0
2
1
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
3
0
0
0
0
9
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
2
2
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
2
1
0
0
0
0
1
2
2
0
0
0
1
0
0
3
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
2
5
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
1
1
0
2
0
2
2
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
3
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
5
0
0
0
0
1
0
0
0
0
0
3
2
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
2
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
1
0
0
1
2
0
2
0
0
1
0
0
1
0
0
2
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
1
0
0
2
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
3
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
2
0
0
1
0
0
0
0
1
1
2
1
2
6
0
0
0
0
0
0
0
0
2
0
0
0
2
2
1
0
0
0
1
0
0
0
0
0
2
0
2
1
2
0
0
0
0
0
2
0
7
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
1
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
2
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
3
2
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
2
1
0
1
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
3
0
0
0
2
0
3
2
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
3
0
0
0
2
0
0
0
0
1
1
2
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
2
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
1
0
3
0
0
2
0
0
0
1
2
0
1
1
1
0
0
0
1
0
0
0
0
2
1
2
0
0
0
2
0
0
1
1
0
0
0
1
0
0
2
0
0
0
1
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
2
1
1
2
1
2
0
0
0
0
0
0
0
0
0
2
2
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
1
0
1
0
1
1
0
0
0
0
2
0
1
1
0
0
0
0
2
0
1
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
2
2
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
3
2
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
2
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
2
0
2
0
0
2
0
2
0
0
0
3
0
1
0
0
1
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
2
0
0
0
0
1
1
1
2
0
0
0
0
0
2
0
0
1
2
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
4
1
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
3
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
2
2
1
0
0
0
0
2
0
0
0
2
1
0
1
4
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
2
0
2
0
0
8
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
1
1
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
3
2
1
0
0
0
2
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
2
2
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
1
0
0
1
3
0
1
0
1
3
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
2
0
1
0
0
0
1
0
0
1
0
2
0
2
2
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
2
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
2
0
0
2
0
0
0
1
0
0
2
3
0
0
0
0
0
1
0
0
3
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
2
0
0
0
0
0
0
2
0
0
0
1
0
1
0
2
0
0
3
0
0
0
1
2
1
0
0
0
1
0
1
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
1
3
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
6
0
0
0
0
2
0
2
0
0
1
0
0
0
1
0
1
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
2
0
0
1
0
2
1
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
2
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
4
1
1
0
0
0
0
0
0
0
2
0
0
0
5
1
2
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
3
0
0
0
2
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
1
2
0
0
0
2
0
0
0
2
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
1
0
3
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
2
2
0
0
1
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
2
0
0
2
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
3
4
0
2
0
0
2
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
1
0
4
0
0
1
0
0
0
0
1
2
4
2
2
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
1
0
0
5
1
0
0
0
0
2
0
2
2
0
2
3
0
0
0
2
0
0
0
0
0
3
1
1
0
0
0
2
0
0
2
0
1
0
1
0
0
0
0
0
0
0
1
0
3
2
1
0
0
0
3
0
0
0
0
0
0
1
2
1
0
0
0
2
0
0
0
1
0
1
0
0
0
2
1
0
2
0
1
0
0
0
0
0
1
0
0
0
0
1
0
2
1
2
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
3
1
0
1
0
1
0
3
0
1
0
0
0
0
0
2
0
0
0
6
0
0
0
2
2
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
1
1
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
2
2
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
2
2
0
1
0
1
0
0
2
0
0
0
3
0
0
0
0
0
0
1
0
3
0
0
0
1
0
4
0
1
0
0
0
0
2
0
0
0
0
0
0
3
0
0
2
0
0
1
0
2
0
1
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
1
1
0
0
0
0
1
2
0
0
0
0
0
0
1
1
1
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
2
0
0
2
0
1
2
0
4
0
0
0
0
2
0
2
2
0
0
0
0
0
3
0
0
0
0
0
0
0
2
2
0
1
2
0
2
2
0
1
2
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
1
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
3
0
0
0
2
0
1
0
0
0
0
4
4
0
0
0
0
0
2
0
2
2
0
2
0
2
0
2
2
0
0
0
0
0
0
1
0
2
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
2
0
0
2
2
0
0
0
2
0
1
0
0
3
1
0
0
0
0
0
0
1
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
3
0
1
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
2
0
4
0
2
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
3
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
3
2
0
1
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
3
0
1
0
0
1
0
0
0
0
0
0
0
2
1
0
1
0
2
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
1
2
3
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
2
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
1
0
1
2
2
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
5
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
9
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
1
1
2
0
2
1
2
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
1
2
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
1
0
1
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
2
0
0
0
1
2
0
2
1
2
2
0
2
1
1
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
2
0
2
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
1
3
4
0
0
1
0
0
1
2
0
0
0
5
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
3
0
2
0
0
0
1
3
2
0
0
0
0
0
0
2
0
1
2
2
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
3
0
0
0
0
1
0
0
3
0
2
0
0
3
0
0
2
0
3
1
0
0
1
2
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
2
0
1
0
2
0
0
0
2
2
0
1
2
0
0
1
0
0
0
0
1
1
2
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
1
0
0
0
0
3
1
2
0
1
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
4
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
3
0
0
0
3
0
2
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
13
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
3
0
1
0
2
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
5
0
0
0
6
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
1
2
2
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
1
1
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
1
0
2
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
2
0
0
7
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
1
0
0
0
1
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
2
0
0
0
0
0
0
1
0
1
2
2
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
2
0
1
0
0
2
2
2
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
1
3
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
4
0
4
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
2
1
2
0
2
0
1
0
0
0
0
2
2
0
2
0
2
0
0
0
0
0
0
0
0
1
2
2
0
1
2
0
3
0
0
0
3
0
2
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
1
0
1
1
2
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
1
0
1
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
1
2
0
1
0
1
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
1
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
2
0
1
1
0
0
2
0
0
1
2
0
1
0
1
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
1
0
0
0
2
1
0
3
0
0
0
0
0
0
0
2
2
1
0
0
0
1
2
0
0
0
0
0
3
0
1
0
0
1
1
2
0
1
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
2
2
0
0
0
0
2
0
0
2
2
2
0
0
1
1
0
0
2
5
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
3
0
0
0
3
0
0
0
2
0
0
2
0
1
0
0
0
0
1
3
0
0
0
2
0
2
0
0
0
2
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
2
0
0
1
3
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
5
0
1
0
0
2
0
0
2
1
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
1
0
3
2
0
0
2
0
0
2
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
2
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
4
4
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
2
1
11
0
0
1
0
0
0
0
0
1
1
2
1
2
3
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
2
0
2
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
1
2
2
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
3
0
0
0
0
0
1
1
1
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
2
0
0
1
0
0
0
0
0
1
1
0
0
0
0
2
0
1
0
0
0
0
0
0
1
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
1
0
0
4
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
4
0
3
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
1
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
2
0
1
1
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
4
0
0
0
0
5
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
2
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
7
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
9
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
1
0
0
2
1
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
2
2
0
1
0
0
0
1
0
2
7
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
2
3
0
0
0
0
0
2
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
1
0
0
2
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
6
0
0
0
0
0
1
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
3
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
2
0
1
0
0
0
0
1
2
0
2
0
2
2
2
0
1
2
0
1
0
0
2
1
0
0
0
2
2
0
1
2
0
1
2
1
0
3
0
0
0
0
1
0
4
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
2
0
0
0
0
0
1
0
0
0
0
1
1
0
0
4
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
1
0
1
4
1
0
1
0
0
0
2
0
1
1
0
2
0
0
1
0
0
0
1
0
6
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
2
2
1
2
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
1
0
0
2
2
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
1
0
2
2
0
0
0
0
0
0
0
0
3
0
0
2
0
0
2
1
0
2
2
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
1
2
1
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
1
0
0
0
2
0
0
0
2
0
1
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
1
0
1
0
0
0
0
1
3
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
2
2
0
0
0
0
0
0
0
1
0
2
1
0
1
0
0
1
2
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
1
0
0
0
2
2
0
0
1
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
1
1
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
2
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
2
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
2
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
1
2
0
1
0
0
1
0
0
0
0
0
0
4
1
2
0
0
1
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
1
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
5
0
1
0
2
2
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
2
0
1
0
2
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
2
0
0
2
0
0
2
0
0
0
0
1
0
1
0
0
0
2
0
0
1
0
0
0
0
1
3
0
0
0
1
0
0
0
0
1
0
1
2
0
0
0
1
0
1
1
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
2
0
2
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
1
3
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
2
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
1
2
0
2
1
0
0
0
4
1
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
1
1
7
0
2
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
6
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
3
0
0
0
0
1
0
0
0
0
0
0
0
3
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
2
1
0
1
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
2
3
0
0
0
0
2
0
1
1
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
2
1
0
1
2
0
0
0
2
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
2
0
1
0
0
0
1
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
1
2
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
5
0
0
3
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
3
0
0
0
0
3
0
0
0
2
2
1
3
1
0
0
0
1
0
0
0
2
0
0
2
0
1
0
1
0
0
0
0
0
1
0
1
0
2
1
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
3
1
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
2
0
0
2
0
2
2
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
4
0
0
1
2
0
0
0
0
2
2
0
2
0
2
0
2
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
3
0
1
0
0
1
2
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
4
0
0
1
0
1
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
3
0
1
0
2
3
0
0
0
0
1
4
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
4
1
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
3
0
0
0
0
0
2
3
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
2
0
3
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
2
1
0
0
0
0
0
1
0
1
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
1
8
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
2
0
0
3
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
1
0
0
1
0
0
1
0
0
2
0
0
0
0
0
6
0
0
0
0
0
2
2
0
0
0
2
0
1
0
0
0
0
1
0
0
0
2
0
2
1
3
0
0
0
0
0
1
3
0
0
0
1
0
1
0
0
6
0
1
0
0
1
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
1
0
0
2
0
0
0
3
0
1
8
2
1
0
5
2
0
2
0
2
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
2
0
1
0
1
1
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
3
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
3
1
0
2
1
1
0
0
1
0
0
0
3
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
5
8
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
1
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
2
0
1
0
0
0
7
0
0
1
0
0
1
1
0
0
0
1
0
2
0
1
0
0
0
0
0
2
1
0
0
1
0
1
0
0
0
2
1
0
0
0
2
0
1
0
0
0
0
0
0
2
1
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
3
0
2
0
0
0
2
1
0
0
0
2
0
0
2
0
2
2
0
0
0
0
0
1
3
0
0
2
0
0
0
0
0
0
1
0
0
0
2
2
0
1
0
3
0
2
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
1
0
0
1
2
0
0
1
0
2
0
0
0
1
2
0
0
2
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
4
0
0
1
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
2
1
3
2
0
0
0
0
0
2
1
0
0
0
3
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
2
0
0
2
1
0
3
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
2
2
4
0
1
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
6
0
0
0
1
0
0
2
0
0
0
1
0
0
2
0
0
1
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
2
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
2
0
0
2
1
2
0
1
0
0
0
0
0
0
0
1
3
0
1
0
1
0
0
0
2
0
0
0
0
3
2
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
3
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
3
0
1
2
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
1
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
5
1
0
0
0
0
0
0
0
0
2
8
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
3
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
2
1
0
2
4
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
1
1
0
2
0
1
0
0
0
2
0
0
1
0
0
0
0
2
0
0
1
0
0
1
0
1
0
2
3
0
0
0
2
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
4
2
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
6
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
3
2
2
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
3
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
3
0
2
0
0
0
0
2
2
1
2
0
0
0
0
2
0
0
1
2
0
0
2
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
3
2
3
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
3
3
0
0
2
0
2
2
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
2
2
0
1
0
0
0
0
1
2
1
0
0
0
2
2
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
4
3
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
1
1
0
3
0
0
0
0
0
2
10
2
0
0
1
0
0
0
0
0
0
0
0
2
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
2
2
1
6
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
3
4
1
0
0
0
5
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
2
0
0
0
0
1
0
1
1
0
2
0
0
0
2
1
0
1
0
0
0
0
0
1
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
1
0
3
0
0
0
0
0
2
0
1
1
2
0
2
2
0
0
0
0
2
1
0
0
7
0
0
0
0
1
2
2
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
1
0
1
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
2
0
2
0
0
1
2
0
0
2
0
2
0
2
0
0
0
2
0
0
1
0
0
0
2
0
1
0
0
1
0
0
3
0
0
0
2
0
0
0
0
1
0
0
0
1
2
2
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
1
0
2
0
0
2
3
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
1
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
1
0
1
3
1
0
2
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
1
3
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
5
0
0
0
0
1
1
0
0
2
0
0
3
0
0
0
1
0
0
0
0
0
3
1
0
0
3
0
0
0
0
0
1
1
0
0
0
0
0
2
2
0
0
1
0
1
0
2
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
1
0
1
1
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
6
2
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
3
0
0
0
0
2
2
0
0
0
1
0
0
0
0
1
0
0
2
0
0
2
0
1
4
0
0
0
2
2
0
0
2
0
0
0
0
0
0
1
0
0
0
2
1
5
0
1
0
1
1
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
7
0
0
0
0
2
0
3
0
2
2
0
0
0
2
0
0
1
1
2
0
0
1
1
0
0
0
3
0
0
1
0
0
0
2
2
0
0
0
0
0
0
1
1
0
0
0
0
0
2
2
1
0
1
0
0
0
2
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
1
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
2
0
2
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
3
0
0
1
0
0
1
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
1
0
1
0
0
0
1
2
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
1
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
1
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
1
0
0
2
0
3
0
1
1
0
0
1
0
0
1
0
0
0
2
3
0
0
0
2
1
0
0
0
0
0
1
3
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
1
0
0
0
1
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
2
1
0
2
4
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
2
0
2
2
0
0
1
1
0
0
2
0
2
1
2
0
1
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
3
3
0
0
0
2
0
3
0
0
0
0
1
0
0
1
2
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
4
0
1
3
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
3
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
2
0
0
0
0
0
1
0
0
1
2
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
2
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
2
2
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
1
2
2
1
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
2
0
0
1
0
4
0
0
2
1
1
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
3
0
0
0
2
0
1
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
3
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
6
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
2
1
0
2
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
3
3
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
2
1
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
1
0
3
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
2
2
2
0
0
0
1
0
0
0
1
0
1
2
1
0
0
0
0
2
1
2
0
1
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
4
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
3
1
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
4
0
0
0
0
0
0
0
0
3
0
0
0
1
3
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
4
0
0
1
2
2
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
3
0
2
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
4
1
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
3
1
0
2
0
1
1
0
0
0
4
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
3
0
0
1
2
1
0
0
2
1
2
2
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
2
0
0
0
1
2
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
2
1
1
0
1
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
6
0
2
0
0
0
1
0
0
0
2
0
1
0
0
3
0
1
0
1
0
0
1
0
2
0
0
0
0
0
0
0
2
0
1
3
0
0
2
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
3
0
0
1
0
0
0
0
0
0
2
5
0
0
4
2
0
0
0
0
2
1
0
0
0
0
0
0
3
2
0
2
0
3
2
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
2
1
0
0
0
0
1
2
2
0
0
0
2
2
0
0
0
0
0
2
0
1
0
0
0
1
2
0
0
0
1
0
0
0
0
2
0
1
1
1
2
0
0
3
0
0
0
0
0
0
1
2
0
2
2
1
0
2
0
0
0
0
1
1
1
0
0
0
0
0
0
2
2
1
0
0
0
3
0
0
0
2
0
0
0
2
2
0
2
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
2
0
1
1
0
1
2
0
0
2
2
1
2
0
0
0
0
0
1
1
3
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
2
3
0
0
0
0
2
0
0
2
1
0
2
0
3
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
2
0
2
0
1
2
0
0
2
0
2
1
0
0
0
0
0
0
1
0
0
0
2
4
0
1
1
1
0
0
0
0
2
0
0
2
0
1
1
0
0
1
0
0
2
2
0
0
3
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
6
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
1
2
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
1
0
2
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
1
0
0
0
1
0
0
1
5
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
2
0
0
0
1
0
0
1
0
0
1
0
0
0
2
0
0
1
1
0
0
0
0
1
0
2
2
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
3
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
3
0
0
6
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
2
0
0
0
0
8
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
2
2
0
2
0
0
1
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
2
0
2
2
0
0
0
3
1
1
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
2
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
1
1
3
0
0
0
2
2
0
0
0
2
0
0
0
0
0
1
2
2
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
2
0
2
0
0
0
1
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
2
0
0
2
0
0
0
0
1
1
0
0
0
0
2
2
1
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
1
0
2
0
1
0
0
0
0
0
0
0
4
0
1
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
4
0
0
8
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
3
0
0
0
1
1
0
0
1
14
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
2
2
0
0
0
0
0
3
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
3
0
2
0
1
0
0
0
0
0
5
0
1
1
0
0
0
0
1
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
3
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
3
0
0
2
0
0
1
0
0
0
0
2
0
9
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
1
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
2
0
0
3
0
1
0
0
1
0
0
2
0
0
0
0
1
2
0
0
0
0
0
2
3
0
0
2
0
1
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
1
0
0
0
0
2
1
0
0
0
2
0
2
0
1
0
1
1
0
1
2
2
0
0
0
2
0
0
2
0
0
1
0
1
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
2
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
9
2
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
1
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
1
0
0
2
2
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
2
2
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
2
1
0
3
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
1
0
1
0
0
2
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
2
1
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
2
0
0
1
2
1
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
3
0
0
0
0
0
0
1
2
0
0
0
5
2
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
3
0
1
0
0
0
0
1
1
0
0
0
0
1
1
2
0
0
0
0
0
2
1
0
2
1
0
0
0
0
1
3
1
0
1
0
0
0
0
1
2
0
0
0
1
1
0
2
0
2
0
0
0
0
2
1
0
1
0
0
0
1
2
0
0
1
0
0
2
0
2
0
1
0
0
4
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
2
0
0
2
0
0
0
2
2
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
2
3
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
1
0
0
0
0
0
0
1
2
0
0
1
0
2
0
0
0
0
1
0
0
0
0
2
0
0
2
2
0
0
0
3
0
0
0
0
3
0
2
0
6
0
0
2
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
1
2
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
8
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
2
0
1
1
0
3
0
2
1
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
2
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
2
2
0
0
0
1
0
3
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
2
0
0
2
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
2
1
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
1
2
4
0
2
0
0
1
0
0
0
1
0
1
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
4
0
0
0
3
1
0
0
2
0
2
0
1
0
0
0
1
0
0
3
2
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
4
0
2
1
0
0
0
0
1
0
0
0
0
3
0
3
0
0
2
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
4
1
0
0
0
0
1
2
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
2
0
2
3
0
0
0
1
0
0
2
0
0
0
2
1
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
1
1
0
2
1
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
1
1
0
0
0
0
1
2
2
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
3
0
1
1
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
5
1
0
0
0
0
0
1
0
0
2
0
1
0
2
0
2
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
2
0
1
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
1
0
6
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
1
0
0
0
0
1
0
2
1
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
2
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
4
2
0
0
1
0
2
0
0
0
0
3
0
0
0
0
2
0
2
0
2
0
0
0
0
2
0
2
2
0
0
0
0
0
3
0
0
2
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
1
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
1
1
1
2
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
3
0
1
0
0
0
0
0
1
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
3
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
2
1
3
1
0
2
1
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
1
0
3
0
0
0
0
2
1
2
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
1
0
0
0
2
1
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
9
0
1
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
2
2
0
0
1
0
1
0
0
4
0
0
0
1
2
0
1
0
0
1
0
1
0
0
0
0
4
0
3
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
4
1
0
0
3
0
0
3
2
2
0
3
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
1
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
6
2
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
3
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
2
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
1
1
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
3
1
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
2
0
2
0
0
2
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
3
2
0
0
2
2
0
0
0
0
1
1
0
0
0
5
0
0
1
0
1
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
2
1
1
1
0
0
2
1
2
14
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
2
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
2
1
0
0
2
0
0
0
0
1
0
0
1
1
0
3
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
2
1
0
0
0
1
0
1
0
0
0
0
1
0
0
3
0
0
2
2
0
0
0
1
2
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
1
2
0
0
1
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
1
1
1
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
2
1
0
3
3
2
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
1
0
0
0
0
2
0
0
0
3
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
4
2
0
1
2
2
1
0
3
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
3
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
1
1
2
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
4
0
0
0
0
0
1
0
2
0
0
1
3
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
7
2
0
0
2
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
2
2
0
0
1
0
0
0
0
0
3
0
0
0
2
0
1
0
0
0
2
0
0
0
2
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
6
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
1
2
1
0
0
0
4
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
3
1
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
1
0
2
1
4
2
0
0
0
1
0
0
1
0
0
0
0
0
0
2
2
0
1
3
0
2
0
1
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
2
0
0
2
5
1
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
2
0
1
1
0
0
0
2
0
0
0
2
0
0
2
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
2
1
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
4
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
1
0
1
1
0
0
0
1
0
1
0
0
0
0
0
5
0
0
0
2
2
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
3
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
5
0
1
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
2
2
0
1
0
0
4
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
1
1
2
0
0
0
0
2
0
0
0
1
0
0
0
0
2
1
2
1
0
1
0
0
2
1
0
0
0
2
1
0
0
0
0
0
0
2
1
0
2
2
0
0
0
0
0
0
1
0
2
3
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
2
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
1
0
0
0
2
0
0
2
3
0
2
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
1
3
0
1
0
0
0
0
0
1
1
0
0
2
1
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
1
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
2
2
0
0
0
0
0
1
0
2
0
0
1
0
1
0
0
0
0
0
3
2
0
2
1
0
2
0
0
0
0
0
1
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
7
0
0
2
0
0
1
0
0
1
1
0
2
0
0
1
1
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
2
0
0
2
0
1
2
0
0
0
0
0
4
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
1
1
0
0
0
0
2
0
0
1
5
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
3
1
0
2
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
1
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
4
0
0
0
0
0
0
3
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
2
0
0
0
1
0
2
1
0
0
0
0
2
0
0
2
0
0
0
3
0
0
1
0
0
0
0
0
2
0
3
1
1
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
2
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
3
0
2
0
0
1
0
0
0
0
1
1
1
0
3
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
4
0
0
1
0
2
1
0
0
0
2
0
0
0
0
3
0
2
2
0
0
0
0
0
2
0
0
0
3
1
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
3
0
0
2
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
1
2
0
1
1
0
0
0
0
3
2
1
1
0
2
0
0
0
0
2
0
0
2
2
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
4
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
2
1
0
2
0
2
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
3
0
0
0
0
1
1
0
2
0
1
2
0
3
0
2
0
2
0
0
1
0
0
0
1
1
0
1
0
2
0
0
1
0
2
0
1
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
3
2
0
0
0
0
0
0
0
2
0
2
0
0
0
2
2
0
0
0
1
1
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
2
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
2
4
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
3
0
0
0
2
1
0
0
1
0
0
2
2
0
2
0
0
0
2
0
2
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
3
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
1
0
2
0
0
1
0
0
0
0
0
2
1
0
0
0
2
1
0
1
0
0
0
1
2
0
0
0
1
0
0
0
0
1
2
1
2
0
0
1
0
2
1
0
0
0
0
0
0
0
2
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
2
1
0
0
0
0
0
0
2
0
0
0
0
1
2
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
2
2
0
0
1
0
0
0
0
0
0
1
3
3
0
0
0
0
0
0
0
5
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
1
0
0
0
3
1
0
2
0
0
0
0
0
0
1
2
0
0
1
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
5
1
1
0
0
0
2
0
0
0
0
0
2
0
0
2
1
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
2
2
1
0
0
0
0
2
0
0
0
1
1
0
2
1
3
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
5
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
2
0
1
0
1
0
0
0
0
1
0
1
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
3
0
2
0
2
0
0
0
0
0
2
0
0
1
0
2
1
0
5
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
2
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
3
0
0
0
2
1
1
0
0
0
1
0
0
4
4
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
1
0
2
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
1
0
1
2
1
0
0
0
0
0
2
0
4
1
0
0
1
1
0
0
0
3
1
1
0
2
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
1
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
2
0
1
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
3
1
0
1
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
2
0
3
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
5
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
2
0
0
0
2
0
0
0
2
2
0
0
2
1
1
0
0
1
0
0
2
0
3
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
2
2
0
0
3
0
1
0
0
0
1
0
1
20
0
2
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
3
0
0
0
0
8
0
4
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
2
0
1
0
0
2
0
0
2
0
1
0
4
0
0
0
1
0
0
0
0
0
0
0
3
0
1
0
2
0
0
0
0
0
5
0
0
0
0
0
1
2
0
0
0
1
0
2
0
0
2
0
4
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
4
0
0
0
2
0
4
0
1
1
0
0
0
0
0
0
0
0
1
2
16
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
4
1
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
2
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
1
0
0
2
0
2
0
0
0
6
2
2
1
0
0
0
0
2
0
0
2
1
0
0
0
2
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
2
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
1
0
0
2
2
4
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
4
0
3
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
2
2
3
0
0
0
0
0
0
0
0
0
1
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
1
0
1
0
0
0
0
6
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
2
0
1
2
0
2
1
0
0
0
2
0
1
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
3
0
0
0
2
0
0
0
1
0
2
0
0
2
0
0
0
1
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
2
5
0
0
0
0
0
1
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
1
0
3
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
3
1
0
0
2
0
3
1
2
2
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
2
0
0
0
0
0
0
1
2
0
0
2
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
3
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
2
1
0
1
1
0
2
2
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
1
0
0
0
2
2
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
2
2
1
0
1
0
0
0
1
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
1
0
0
0
1
2
2
3
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
1
0
0
0
1
0
1
0
0
0
2
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
2
1
4
0
1
3
0
2
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
3
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
5
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
2
0
2
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
2
1
0
0
2
0
0
2
0
0
2
3
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
3
2
0
0
1
4
0
2
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
7
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
3
1
0
0
2
0
2
0
0
2
5
0
0
0
2
2
0
1
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
2
0
2
0
2
0
1
1
0
1
0
0
0
0
2
2
0
0
2
0
0
0
2
1
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
3
2
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
2
0
1
0
0
1
0
0
2
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
1
2
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
2
0
0
0
1
1
0
0
0
0
2
0
0
0
3
0
0
0
1
0
0
1
2
5
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
3
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
12
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
5
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
1
2
0
2
0
0
4
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
1
0
0
3
0
0
1
0
2
0
0
1
1
0
1
3
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
2
1
2
1
0
1
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
6
1
0
0
0
0
0
0
0
0
0
5
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
3
0
0
0
7
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
2
1
0
2
2
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
5
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
3
0
0
3
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
1
0
0
3
0
0
0
2
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
2
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
2
1
0
5
1
0
0
1
0
2
2
0
0
0
0
0
1
0
0
1
0
0
1
0
1
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
4
2
2
0
1
0
0
1
1
0
2
1
2
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
2
1
1
0
2
0
0
2
0
0
0
0
4
0
1
1
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
2
1
16
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
2
0
1
0
0
1
0
0
2
1
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
1
1
5
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
2
1
0
0
2
2
3
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
1
0
0
1
3
0
6
0
0
2
0
0
0
1
0
2
0
0
1
1
0
1
0
0
0
0
0
2
0
1
0
0
1
1
0
0
0
0
1
0
1
0
2
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
6
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
2
0
2
2
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
1
2
1
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
2
0
0
0
0
1
0
2
2
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
2
0
1
0
0
2
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
3
0
0
2
1
0
3
0
4
2
0
0
1
0
2
0
1
0
0
3
0
2
0
2
0
2
0
0
0
1
0
0
0
3
1
2
0
2
1
1
1
0
0
1
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
3
0
0
0
0
0
1
0
0
1
1
0
2
0
0
0
0
0
0
0
5
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
2
0
1
2
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
4
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
5
1
0
1
0
0
0
0
0
0
0
0
2
2
4
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
3
1
2
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
3
0
3
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
2
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
2
0
0
0
2
0
1
0
2
0
0
2
0
0
0
0
0
0
1
0
0
4
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
2
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
2
0
2
0
0
1
0
0
0
0
1
0
0
0
0
9
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
5
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
5
0
0
0
0
0
0
0
0
0
3
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
4
2
6
0
0
2
0
0
0
1
1
0
2
0
2
1
0
0
2
0
1
0
0
1
1
0
0
0
0
1
5
1
0
0
0
0
0
0
0
0
0
0
0
5
0
1
1
0
1
1
0
0
2
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
1
0
0
0
2
0
6
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
1
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
2
0
1
2
1
0
0
0
0
0
0
0
1
1
0
0
1
0
1
1
0
0
2
1
0
2
0
0
0
2
0
7
0
0
0
2
2
1
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
2
1
0
1
0
1
0
0
0
0
0
2
0
2
0
0
0
0
1
4
1
0
0
0
0
0
1
2
0
2
0
0
1
0
0
0
0
3
0
0
0
0
1
0
0
1
0
1
2
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
3
3
2
0
1
0
0
0
1
1
1
2
0
0
0
0
0
0
0
0
2
0
1
0
3
3
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
3
0
2
1
0
0
1
0
0
2
0
0
0
2
0
2
1
0
0
1
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
2
1
0
0
0
4
1
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
2
0
1
0
5
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
2
0
3
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
3
0
1
2
1
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
2
4
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
2
2
3
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
1
2
2
0
0
0
1
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
1
2
0
0
2
0
0
0
1
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
1
0
0
0
0
3
1
1
3
0
0
1
0
0
0
0
1
1
0
0
1
0
5
2
0
0
0
0
0
0
1
2
1
0
2
3
0
0
2
0
0
0
0
2
0
1
0
0
0
2
1
0
0
1
0
0
0
0
0
2
0
1
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
1
2
0
0
3
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
1
2
0
0
0
1
0
0
0
0
0
3
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
3
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
1
4
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
2
0
0
0
1
0
2
0
2
0
0
0
0
0
3
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
1
3
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
1
2
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
1
0
0
0
1
0
0
2
0
0
1
1
0
0
2
0
0
0
1
0
0
2
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
8
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
3
0
0
1
1
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
2
0
2
0
1
2
0
1
0
0
0
0
0
2
2
0
0
0
0
0
1
0
1
2
0
1
0
1
1
0
1
3
0
0
0
0
1
0
2
0
0
1
0
2
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
5
0
0
0
0
1
0
0
0
2
1
0
0
1
0
1
0
0
0
2
0
0
1
0
1
1
0
2
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
5
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
2
1
7
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
1
0
2
0
1
0
0
1
1
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
3
1
0
1
0
0
2
3
0
0
0
0
0
2
0
0
0
0
1
0
0
2
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
3
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
2
2
0
2
0
0
1
0
0
0
2
0
2
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
2
2
3
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
3
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
1
0
1
1
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
2
0
2
0
1
0
0
2
1
0
0
0
0
1
0
2
2
0
0
1
1
2
0
0
0
0
1
1
0
2
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
2
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
5
0
0
1
0
2
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
2
3
3
0
0
0
2
3
1
0
0
0
2
7
2
0
0
0
2
0
0
2
3
1
0
0
1
0
0
0
0
0
4
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
2
0
0
2
0
0
0
0
2
0
1
1
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
2
1
1
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
2
0
0
3
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
1
5
0
2
0
0
2
0
0
5
1
0
0
3
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
6
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
1
1
2
1
0
0
2
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
1
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
2
2
0
0
0
3
0
0
0
0
0
2
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
3
0
0
1
0
0
1
0
0
0
1
0
0
1
2
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
3
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
1
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
5
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
1
1
0
1
0
1
0
1
0
2
0
1
2
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
4
0
0
0
1
2
2
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
2
0
2
2
0
2
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
2
0
2
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
4
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
1
3
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
4
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
3
2
0
0
0
2
0
0
2
1
1
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
3
1
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
1
4
1
2
0
0
0
0
0
0
2
0
0
0
1
0
1
0
1
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
2
0
0
0
2
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
1
2
1
0
3
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
1
2
0
0
2
0
1
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
4
0
0
0
0
1
0
0
1
0
2
3
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
2
0
0
2
0
0
2
4
1
0
1
0
0
1
0
0
0
0
1
4
0
0
0
0
4
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
2
2
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
1
0
0
5
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
2
1
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
1
2
0
1
1
0
0
0
0
2
0
2
0
0
2
0
0
0
2
0
1
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
4
0
0
2
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
0
0
0
0
1
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
1
0
0
0
2
1
1
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
3
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
3
0
1
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
2
1
0
0
0
1
0
2
2
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
2
3
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
1
1
0
3
1
1
0
2
2
0
0
0
1
0
0
0
1
0
0
0
4
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
3
0
2
0
2
0
2
3
0
0
0
2
0
3
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
1
2
0
1
1
0
0
0
1
0
0
0
2
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
2
2
0
0
0
3
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
2
0
1
0
0
1
0
0
0
1
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
2
3
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
2
2
2
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
1
0
1
0
0
0
1
2
1
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
2
1
0
0
0
0
2
0
0
0
2
0
0
1
0
0
2
0
0
0
0
1
1
1
0
0
2
0
1
1
0
0
1
0
0
0
0
0
0
0
3
1
2
0
4
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
2
0
0
0
1
0
1
2
0
0
0
0
1
0
0
0
1
2
2
0
0
0
0
1
0
2
0
0
1
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
1
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
1
3
1
0
0
0
5
0
0
2
0
0
2
0
0
0
0
0
0
0
9
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
1
1
0
0
0
1
0
0
2
0
1
1
0
0
0
1
1
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
2
2
0
0
0
0
0
1
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
3
0
2
2
0
2
0
2
0
0
0
0
2
1
1
2
1
0
0
0
1
1
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
1
2
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
4
0
1
0
0
1
0
1
0
0
1
0
0
2
1
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
2
0
2
0
0
0
1
2
1
0
0
0
0
1
0
0
1
0
0
1
0
1
0
1
0
1
2
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
1
0
0
0
0
3
0
0
0
0
0
2
1
1
1
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
2
4
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
1
3
0
0
0
0
0
3
1
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
2
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
11
0
0
0
1
2
1
0
0
2
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
2
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
2
2
0
0
0
0
2
0
0
0
0
0
0
3
0
4
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
2
0
2
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
2
3
0
0
2
0
0
1
0
0
0
0
1
0
0
2
1
2
4
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
1
2
1
2
0
0
0
3
1
2
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
4
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
6
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
2
1
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
3
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
2
0
2
1
0
0
2
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
1
2
0
0
1
0
1
0
0
1
0
1
0
0
2
0
2
0
2
0
1
0
1
3
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
2
0
4
2
2
0
0
0
2
0
0
0
1
0
1
0
2
0
0
0
0
2
0
1
0
0
0
0
0
1
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
2
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
5
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
2
0
3
0
0
1
0
0
0
2
0
2
0
0
0
4
0
0
0
1
0
0
2
0
1
1
2
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
3
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
1
2
0
0
10
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
2
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
2
0
4
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
2
2
0
0
6
1
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
2
3
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
2
0
1
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
3
0
1
0
0
1
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
1
0
0
0
2
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
2
2
2
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
1
0
0
1
2
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
1
0
0
0
0
1
0
2
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
5
0
0
2
0
1
0
0
0
0
0
1
0
3
0
0
0
2
0
1
0
0
0
0
0
0
1
2
0
0
0
3
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
1
0
2
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
1
2
0
0
0
0
2
1
2
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
2
1
2
0
0
0
0
0
0
0
0
0
2
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
3
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
1
0
2
2
0
0
0
6
0
0
0
0
1
1
0
0
0
2
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
3
1
2
0
0
0
3
0
0
2
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7
2
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
2
1
0
0
1
3
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
3
0
0
4
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
6
0
0
2
0
0
0
1
0
0
0
0
1
0
0
3
0
0
0
0
0
1
1
2
3
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
2
1
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
5
0
0
0
3
0
0
0
0
0
1
1
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
1
0
0
0
1
0
1
0
0
3
1
0
0
0
0
0
1
1
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
2
0
0
2
0
0
0
0
0
1
0
0
1
3
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
2
0
1
0
3
1
0
0
1
0
0
0
2
0
0
0
0
1
0
2
1
2
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
3
1
1
0
3
1
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
1
0
0
4
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
3
0
0
0
2
1
0
0
0
2
0
3
1
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
1
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
1
1
0
0
0
0
0
1
0
0
3
0
0
1
0
0
0
0
1
0
2
0
0
0
2
0
0
1
1
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
2
0
0
0
0
2
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
1
1
0
0
0
1
0
0
0
2
0
0
0
1
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
3
0
0
0
0
0
0
2
2
2
2
0
0
1
1
0
0
0
0
2
0
0
1
1
2
2
0
0
3
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
2
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
1
2
1
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
6
0
0
0
0
0
1
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
1
0
0
0
7
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
1
0
0
0
3
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
3
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
1
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
1
0
1
0
1
0
0
0
2
0
0
0
3
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
2
1
0
0
0
3
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
2
2
0
1
0
0
0
0
1
0
0
1
1
0
0
1
2
0
0
4
2
0
0
1
3
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
2
0
0
0
0
1
0
1
0
3
2
1
0
0
0
0
0
1
2
0
1
0
1
0
1
0
0
0
2
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
1
0
2
1
0
2
0
0
0
2
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
2
0
0
2
2
0
0
1
0
2
0
0
0
0
1
0
2
1
1
0
0
0
0
1
0
2
0
1
0
0
0
1
2
0
2
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
2
0
2
0
2
0
2
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
3
0
0
0
2
0
1
0
0
1
3
0
0
1
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
1
2
0
0
0
0
1
2
0
0
0
0
0
4
0
0
0
2
2
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
1
0
0
1
1
2
0
0
2
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
1
0
0
1
2
0
2
2
8
0
0
2
1
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
8
0
0
3
0
0
0
2
2
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
3
1
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
1
1
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
1
0
1
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
4
2
0
1
0
0
3
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
2
2
2
2
0
2
2
0
0
0
0
0
0
1
0
0
0
1
0
0
6
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
3
2
2
2
0
0
0
0
2
2
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
2
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
2
0
0
2
1
0
2
0
3
0
0
0
3
2
0
0
0
1
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
2
0
0
0
1
0
0
2
0
1
0
0
0
2
0
1
2
0
0
2
0
2
0
2
0
3
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
1
2
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
3
1
0
0
0
3
0
0
2
0
0
2
0
0
0
0
0
0
0
2
5
2
0
2
0
0
0
1
0
1
2
1
1
0
0
0
0
0
0
2
0
0
0
0
0
2
3
0
1
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
2
6
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
1
2
0
2
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
3
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
2
0
0
2
3
2
0
2
0
0
0
0
0
1
3
0
1
2
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
1
1
0
0
1
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
1
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
2
1
2
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
2
2
0
1
1
0
0
0
2
0
3
0
0
0
0
0
1
0
0
0
3
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
3
1
0
0
0
0
2
2
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
1
0
1
0
0
2
0
0
0
1
0
1
0
0
0
2
2
2
0
0
0
3
0
2
0
0
0
0
1
0
2
2
0
0
0
0
0
1
0
1
0
2
2
0
0
0
0
1
0
0
0
0
4
0
2
0
0
0
0
0
2
0
0
2
2
2
0
0
0
0
1
0
0
0
2
0
1
3
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
3
0
0
10
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
4
2
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
2
2
2
0
0
1
0
0
2
2
0
2
0
2
4
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
1
1
0
1
0
0
7
1
1
0
0
0
0
2
1
1
0
1
0
1
0
0
0
0
0
0
2
2
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
3
2
0
0
0
1
3
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
1
1
1
2
2
0
1
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
3
0
0
1
2
0
0
1
0
0
0
0
7
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
3
1
0
0
0
1
0
2
0
0
0
0
0
1
2
1
0
0
0
2
1
0
0
1
0
0
0
1
0
1
0
3
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
1
0
6
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
1
1
0
0
0
1
1
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
8
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
6
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
3
1
1
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
3
0
0
1
4
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
1
1
0
0
1
0
0
0
0
2
2
0
2
0
1
2
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
10
1
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
2
3
2
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
1
0
1
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
1
2
0
0
0
1
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
2
2
0
2
0
0
0
0
0
1
2
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
1
1
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
2
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
5
0
1
2
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
1
0
0
2
1
0
2
1
0
0
0
1
1
2
2
0
2
0
0
0
0
0
0
2
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
1
4
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
2
0
0
5
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
4
2
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
1
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
3
2
1
0
0
0
0
1
0
0
1
0
1
2
0
4
0
0
0
0
0
0
2
0
2
0
1
2
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
2
0
0
4
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
5
0
0
0
0
0
2
2
0
0
0
0
0
0
3
0
0
2
1
0
0
0
0
0
0
0
3
0
0
1
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
3
3
1
1
0
0
0
0
3
0
0
0
0
0
0
1
2
0
0
0
0
2
2
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
1
0
0
2
0
0
1
0
0
1
0
0
3
0
0
0
0
1
1
1
0
1
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
2
2
0
1
0
0
0
0
1
0
0
2
2
0
1
1
0
2
0
0
0
2
1
0
0
0
1
0
1
0
0
1
0
2
1
0
0
0
0
0
1
0
1
0
0
0
0
5
0
0
1
3
0
0
3
0
1
2
0
0
1
3
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
2
1
0
1
0
2
1
0
0
0
0
0
0
2
1
0
1
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
3
0
0
2
0
0
1
0
1
0
0
0
0
0
2
1
2
0
0
0
0
0
1
0
4
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
3
0
3
1
0
0
1
0
0
1
0
0
1
0
0
0
2
0
0
0
3
0
0
0
0
1
0
0
0
0
3
2
0
1
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
6
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
1
0
2
5
1
0
1
0
0
1
0
2
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
2
0
1
0
0
1
1
0
2
2
0
0
0
0
1
0
1
0
0
1
2
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
1
0
2
0
0
0
2
1
0
0
2
0
0
0
0
3
0
1
0
1
2
0
0
0
0
0
0
1
0
0
0
0
2
2
0
2
0
0
2
6
0
0
0
0
0
0
0
1
1
2
1
2
2
0
0
1
1
0
2
0
0
0
0
0
0
2
0
0
0
2
0
3
0
0
1
2
2
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
3
1
2
1
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
2
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
2
0
2
1
0
0
2
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
1
0
0
0
1
0
1
0
2
0
0
0
2
4
0
0
0
2
2
2
0
2
1
0
0
1
0
2
2
0
0
0
0
1
0
0
0
2
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
2
1
2
0
0
0
2
0
2
0
3
0
0
1
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
2
0
1
1
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
2
0
1
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
3
1
0
0
2
0
0
0
0
2
0
0
2
0
0
7
0
0
1
2
0
2
1
0
0
1
0
0
0
0
1
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
2
0
0
0
0
2
0
0
0
0
6
0
3
0
1
2
0
2
0
0
0
0
0
2
2
1
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
2
0
5
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
2
0
0
2
1
0
0
2
0
0
0
0
2
0
0
3
0
1
3
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
5
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
2
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
2
2
1
0
0
1
3
0
0
1
0
0
0
0
0
2
0
0
2
1
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
8
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
2
2
0
2
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
1
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
3
0
1
0
2
0
0
2
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
1
0
1
0
1
0
1
0
0
1
0
1
0
0
2
1
0
0
0
0
0
4
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
1
0
4
0
1
0
0
0
0
0
0
0
0
1
7
0
2
2
0
0
0
0
0
0
1
0
0
0
1
1
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
2
2
1
4
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
1
4
2
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
2
0
0
1
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
1
0
0
0
0
0
0
2
2
0
2
1
0
0
0
0
1
1
0
1
0
0
0
2
1
1
0
0
0
0
0
2
2
0
1
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
1
1
0
0
3
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
1
0
2
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
4
0
0
0
0
0
1
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
2
0
0
3
0
0
0
0
1
0
2
0
0
1
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
15
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
1
1
1
2
0
0
0
0
1
2
2
0
2
0
0
1
1
0
0
1
0
2
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
2
0
1
0
0
0
0
3
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
2
0
1
0
0
1
0
0
0
1
1
0
0
0
1
2
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
2
1
3
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
2
2
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
2
0
0
2
1
0
0
0
1
0
1
0
0
1
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
2
0
0
0
1
1
0
1
0
0
4
0
0
3
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
2
0
0
1
0
0
0
0
0
0
3
4
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
6
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
1
2
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
3
0
1
0
0
0
0
0
2
0
0
1
2
0
0
4
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
2
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
2
0
2
0
2
2
0
0
1
2
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
2
0
0
6
0
0
0
0
0
0
0
0
2
1
0
1
2
2
0
1
0
2
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
5
3
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
5
1
0
0
0
0
0
0
1
2
0
0
0
0
0
1
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
2
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
1
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
1
0
0
6
0
1
0
0
0
0
3
0
0
0
0
2
1
1
0
2
0
0
0
0
1
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
1
0
2
0
0
2
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
1
0
2
0
2
0
1
0
0
0
0
0
0
4
0
1
0
0
2
2
0
4
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
1
1
0
2
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
2
0
2
2
2
1
0
1
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
1
1
3
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
3
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
2
2
1
2
0
1
0
2
2
2
0
1
0
2
2
0
0
0
0
0
2
0
2
0
0
2
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
2
1
1
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
10
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
4
1
3
0
1
0
1
0
0
0
0
0
1
0
1
0
2
1
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
3
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
3
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
2
0
0
0
0
7
0
4
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
1
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
1
0
2
1
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
8
0
2
0
0
0
2
0
0
2
0
0
9
0
2
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
2
0
2
9
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
1
1
0
1
0
0
6
0
1
4
0
0
0
0
0
0
0
1
2
0
2
0
3
0
2
0
1
0
1
0
4
0
0
1
1
2
2
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
3
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
3
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
2
1
2
1
1
0
0
2
2
0
0
0
2
0
2
0
0
2
2
0
0
2
1
0
1
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
2
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
3
1
0
2
0
3
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
3
1
3
0
0
0
0
0
2
0
2
0
0
0
2
1
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
2
0
0
0
1
0
2
0
0
0
0
1
0
2
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
2
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
8
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
8
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
3
0
3
0
0
2
0
2
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
3
0
1
0
0
0
0
0
0
0
1
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
5
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
1
2
1
0
0
0
0
2
0
0
1
1
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
2
0
1
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
2
0
1
0
0
0
3
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
2
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
3
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
3
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
5
1
5
4
0
0
1
0
0
0
0
0
0
0
0
0
2
2
3
0
0
0
0
1
3
0
1
0
0
0
2
0
0
0
0
0
0
0
2
1
2
2
1
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
1
0
4
0
5
0
0
0
1
0
0
0
0
2
2
2
0
0
0
2
3
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
6
0
0
3
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
1
0
1
0
0
2
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
2
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
1
0
0
0
2
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
1
0
1
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
2
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
1
0
11
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
3
1
0
0
0
2
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
2
1
3
0
3
0
1
0
1
0
1
0
0
0
0
0
0
2
0
0
2
2
2
0
2
0
1
0
0
0
0
0
0
1
2
2
2
2
0
0
0
0
0
2
0
2
0
0
0
0
1
2
0
0
2
0
0
0
2
0
1
2
0
0
0
0
9
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
2
0
2
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
2
2
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
8
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
1
1
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
2
2
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
2
0
0
2
1
0
0
1
2
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
1
0
0
0
2
1
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
1
2
2
0
0
0
0
1
0
0
0
0
1
1
1
0
0
1
0
3
0
0
2
0
0
2
2
0
0
0
1
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
2
6
2
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
1
0
0
2
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
2
0
0
0
0
1
0
2
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
1
3
0
0
1
0
0
1
0
2
0
1
0
1
0
0
2
2
0
1
2
0
0
0
0
0
1
0
1
0
0
0
0
2
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
2
2
2
1
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
2
0
2
2
0
0
0
0
1
0
1
2
1
0
2
2
2
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
2
0
0
0
1
8
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
1
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
3
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
3
0
0
0
0
2
0
1
0
2
0
0
2
0
0
0
0
2
1
1
1
0
0
0
0
1
0
0
1
0
2
0
0
2
2
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
2
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
1
1
0
0
1
0
0
0
1
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
1
0
1
0
1
1
2
1
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
5
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
1
2
0
0
5
0
0
1
1
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
3
1
0
0
0
0
0
2
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
4
0
1
1
0
0
3
0
0
0
0
0
0
0
0
1
2
1
0
0
2
2
1
2
0
0
0
0
0
2
2
0
0
2
2
0
0
2
0
0
0
0
2
0
2
2
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
3
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
2
0
0
0
0
1
0
1
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
3
0
0
0
2
0
6
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
3
1
1
2
0
1
1
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
1
1
2
0
2
0
0
0
1
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
1
0
0
0
2
0
0
6
0
1
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
1
1
0
2
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
9
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
2
7
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
3
0
0
2
0
0
2
1
0
0
0
0
0
0
2
1
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
3
0
0
4
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
3
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
3
1
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
2
0
0
2
0
0
0
2
3
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
2
0
6
0
0
2
1
2
0
2
0
0
1
0
0
0
0
1
1
2
0
0
1
0
3
0
0
0
1
0
0
1
1
0
0
0
2
0
0
0
0
1
0
0
0
2
3
0
2
0
2
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
3
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
5
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
2
0
0
2
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
4
0
5
0
0
0
3
0
0
1
0
0
2
1
0
2
0
1
2
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
2
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
1
0
0
2
3
1
1
0
0
0
0
1
1
1
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
1
1
1
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
4
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
1
0
1
0
0
2
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
1
0
0
0
2
0
0
0
0
3
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
2
3
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
2
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
4
1
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
3
6
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
1
0
3
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
5
1
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
1
1
3
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
2
2
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
5
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
3
1
0
0
1
0
2
1
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
3
2
0
2
0
2
0
0
4
0
0
0
1
2
1
0
0
0
0
2
0
2
0
1
2
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
2
1
5
0
0
0
2
3
0
1
0
0
2
0
0
1
0
5
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
1
0
2
0
0
2
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
2
0
3
2
0
0
0
1
0
0
0
1
0
0
0
1
1
2
0
2
0
0
0
2
2
2
0
0
0
3
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
2
2
0
2
0
1
1
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
2
0
0
0
2
0
0
2
0
0
1
0
2
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
1
0
1
0
0
0
0
1
2
0
2
2
0
2
0
1
3
0
0
0
0
0
3
0
1
0
0
0
0
1
0
1
0
0
0
0
1
1
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
3
2
0
0
0
2
0
0
0
0
0
1
0
1
1
2
0
2
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
1
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
2
2
0
0
0
1
1
2
1
4
0
0
3
1
0
1
0
3
1
1
0
0
2
0
0
3
0
0
1
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
2
1
1
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
2
1
0
0
2
0
2
0
0
0
1
0
2
0
1
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
9
0
0
0
2
1
1
0
0
2
0
0
0
0
1
0
0
0
0
1
4
13
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
2
2
0
3
1
0
2
0
2
0
1
2
2
1
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
4
2
1
0
0
2
0
0
0
4
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
1
0
2
0
0
0
1
0
0
3
0
0
0
0
0
5
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
2
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
1
2
1
2
0
1
0
0
0
0
0
3
0
0
1
2
0
0
0
0
0
0
2
1
1
0
0
0
1
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
4
1
1
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
2
2
0
2
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
5
0
0
0
0
0
2
0
0
0
3
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
1
0
2
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
1
2
1
0
0
1
2
0
1
0
0
0
0
0
0
1
0
0
1
0
2
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
1
0
0
0
0
0
0
2
2
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
2
0
0
0
1
2
0
0
2
0
2
2
0
1
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
3
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
1
2
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
3
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
2
1
0
0
1
2
1
1
0
0
0
1
1
0
2
0
0
0
2
1
0
2
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
7
0
0
0
0
0
1
0
0
2
0
0
0
0
3
3
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
1
3
0
0
0
0
6
2
0
0
1
0
0
0
0
1
1
0
5
0
0
0
0
1
2
0
0
0
1
2
0
0
3
0
0
0
0
2
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
2
0
0
1
0
0
3
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
2
0
3
1
0
1
2
0
0
2
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
2
1
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
3
0
2
1
0
0
1
0
4
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
1
0
1
0
1
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
4
2
0
0
0
3
1
2
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
5
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
2
0
2
1
0
1
0
0
0
0
0
1
0
0
1
0
2
0
0
2
3
0
7
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
1
1
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
2
2
0
1
1
0
0
1
0
1
1
0
2
0
0
0
2
4
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
2
2
2
0
0
0
0
2
0
0
0
5
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
1
1
0
0
0
0
0
2
0
2
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
2
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
3
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
1
0
0
0
0
0
3
1
1
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
2
3
2
0
2
0
0
0
2
0
0
1
1
0
0
0
1
0
0
0
0
0
0
8
0
0
0
1
0
0
0
3
0
0
0
0
2
2
0
0
0
0
1
0
1
0
0
0
1
0
2
1
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
4
2
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
2
0
0
0
1
0
0
2
0
1
0
0
1
1
0
0
0
0
2
0
1
0
0
0
0
0
1
0
3
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
2
0
0
1
2
1
0
1
0
0
0
0
0
2
1
0
0
0
0
0
3
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
1
2
1
0
0
0
0
2
0
0
0
1
0
0
0
1
1
0
0
2
0
0
1
1
2
0
2
0
3
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
3
0
0
0
0
2
0
2
2
0
0
1
1
5
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
1
0
3
1
0
0
1
0
1
0
0
2
1
0
3
0
0
0
0
0
1
0
0
0
2
0
0
0
1
3
0
0
0
2
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
2
0
3
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
1
0
0
0
2
0
2
0
0
0
1
0
4
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
1
2
0
0
0
0
1
0
0
0
0
0
1
2
2
0
0
1
0
0
0
1
0
0
0
0
3
0
1
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
3
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
4
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
2
1
2
2
0
0
0
0
0
2
0
2
0
0
3
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
2
0
0
0
2
0
0
1
0
1
0
2
2
0
0
3
0
0
1
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
2
0
0
0
0
0
0
2
0
0
2
0
2
0
1
0
0
0
1
0
1
0
0
1
0
1
1
0
2
0
0
0
0
0
0
1
0
0
0
2
2
2
0
0
0
0
0
4
0
2
0
3
2
1
2
0
0
1
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
3
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
2
0
0
4
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
2
3
0
0
0
0
0
0
0
0
0
2
0
1
0
0
3
1
1
0
0
0
0
1
3
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
1
0
0
2
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
2
0
2
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
2
2
0
2
1
2
1
1
0
2
0
0
0
0
1
0
1
0
0
0
2
0
0
0
1
0
1
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
1
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
3
0
2
0
0
0
4
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
2
0
1
2
0
0
1
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
1
0
0
0
1
0
0
0
0
0
0
2
1
1
0
0
0
1
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
1
0
0
0
0
1
3
1
0
2
0
0
0
0
0
3
1
0
0
0
2
0
0
0
1
4
1
1
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
5
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
2
0
1
0
0
0
0
1
1
0
2
2
0
1
1
0
2
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
2
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
1
0
0
0
4
0
0
0
1
0
1
2
0
1
0
0
0
2
0
0
0
0
0
0
2
2
3
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
4
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
1
1
0
2
0
2
3
0
0
0
0
1
0
0
0
0
5
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
3
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
6
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
2
1
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
3
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
1
2
0
2
1
1
0
0
0
0
0
0
2
0
2
2
2
0
2
0
0
0
0
0
1
0
0
1
0
0
0
3
3
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
3
1
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
1
1
2
1
0
0
1
0
0
0
0
0
2
0
1
2
0
0
0
4
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
3
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
2
0
0
0
1
1
2
0
2
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
2
2
1
2
0
0
0
0
3
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
3
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
1
3
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
4
0
0
1
8
2
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
3
1
0
0
2
1
0
0
0
0
2
0
0
0
2
0
0
0
3
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
2
0
0
3
0
0
1
1
0
1
0
0
1
1
0
2
0
0
0
0
0
0
0
1
1
1
0
0
1
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
3
0
1
0
0
0
0
0
0
0
0
0
3
0
1
1
3
0
2
0
0
0
0
0
0
0
0
1
1
0
3
2
2
0
0
0
0
0
3
1
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
1
1
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
5
0
0
2
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
1
1
2
1
0
0
2
0
1
0
0
6
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
1
0
1
0
0
0
0
1
0
1
1
0
0
2
1
0
0
0
0
1
2
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
1
1
1
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
3
0
0
0
0
1
0
0
2
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
4
0
2
0
0
0
0
0
3
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
4
0
0
0
0
0
1
0
2
0
0
2
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
1
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
5
0
0
0
0
0
0
0
0
0
3
2
0
0
0
1
2
1
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
2
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
2
0
1
0
0
1
2
0
1
0
0
0
0
2
0
0
1
0
2
0
5
2
0
0
0
0
0
0
3
0
0
0
3
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
1
2
0
0
2
2
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
1
0
1
0
0
0
2
0
2
0
0
3
0
0
0
0
0
1
2
0
0
2
0
2
0
0
0
1
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
8
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
1
0
0
0
0
0
3
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
6
0
0
0
0
0
1
0
0
0
2
3
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
1
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
2
0
0
2
2
2
2
5
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
5
0
0
0
2
0
0
0
0
2
1
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
2
0
0
0
0
1
0
1
0
0
0
3
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
2
2
0
2
0
1
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
2
2
2
0
0
2
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
3
0
4
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
2
0
0
0
0
1
1
0
0
0
3
3
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
2
3
0
0
0
0
2
0
0
1
0
3
1
0
1
1
0
0
1
0
0
2
1
0
0
5
0
2
0
0
1
1
0
2
0
0
2
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
2
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
1
0
2
0
0
0
4
2
0
0
0
1
0
2
0
0
2
0
1
0
0
0
0
0
0
0
2
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
2
2
0
0
2
0
1
0
0
0
0
0
2
1
0
0
1
2
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
3
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
3
0
0
1
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
8
2
2
0
2
0
0
1
0
0
0
2
0
0
0
0
0
1
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
3
3
0
0
1
2
0
0
1
0
0
1
0
0
0
0
1
0
0
2
0
2
0
0
2
1
1
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
4
1
0
0
1
0
0
2
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
7
0
1
0
0
2
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
3
0
0
0
1
0
2
2
0
0
0
0
1
3
0
0
0
0
0
1
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
1
0
0
0
0
0
0
2
0
2
0
2
0
3
0
1
1
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
3
2
0
2
0
0
1
0
2
3
0
0
0
1
0
0
0
0
0
3
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
2
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
1
0
0
2
0
1
0
4
1
1
0
0
0
2
0
2
0
1
0
2
1
0
0
0
0
0
0
0
0
1
0
0
2
0
1
2
1
0
0
0
0
0
0
0
1
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
2
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
3
0
0
0
0
0
0
2
0
1
0
0
0
1
1
2
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
1
0
0
1
0
6
0
2
0
0
2
1
0
0
7
2
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
1
0
0
5
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
4
0
1
0
1
2
3
0
1
0
0
0
0
3
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
8
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
2
0
2
0
0
0
0
0
1
0
1
1
1
0
0
2
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
1
0
0
2
0
1
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
2
0
2
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
1
0
0
2
1
2
0
0
0
1
0
1
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
1
0
1
0
0
2
0
0
0
1
0
0
1
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
1
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
7
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
5
1
0
0
0
1
2
0
1
0
0
1
0
0
0
0
1
1
0
2
0
6
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
1
0
0
0
3
0
0
0
5
0
1
1
1
1
0
2
1
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
3
1
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
10
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
2
0
0
1
0
0
1
0
0
0
0
4
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
1
3
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
3
0
1
0
0
2
0
0
2
1
0
0
2
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
1
0
0
2
0
0
2
2
0
0
2
2
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
3
0
0
0
0
0
3
0
2
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
2
1
0
0
1
0
1
0
0
0
4
0
1
0
0
0
0
0
0
0
0
2
3
1
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
5
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
2
2
0
2
2
0
1
1
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
2
2
1
0
1
0
0
0
2
2
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
1
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
3
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
2
0
2
0
0
0
0
0
0
2
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
9
0
0
2
0
5
0
0
2
0
0
1
0
0
0
1
0
0
0
1
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
3
0
2
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
2
0
0
1
0
0
0
1
1
2
0
0
0
1
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
1
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
2
0
7
0
0
0
0
0
0
0
2
1
0
0
0
0
1
1
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
2
2
3
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
2
0
1
2
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
2
0
2
0
0
0
0
4
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
2
0
0
0
2
0
0
0
0
2
0
0
3
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
3
2
0
0
0
1
1
0
0
0
0
3
0
0
2
2
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
3
3
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
4
0
1
0
0
1
0
3
2
1
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
2
0
0
0
2
0
1
1
0
1
0
2
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
1
0
1
0
0
0
2
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
4
1
1
0
0
1
3
0
1
0
0
0
0
0
0
3
0
1
1
0
1
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
6
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
2
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
2
0
1
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
2
1
0
0
1
0
1
0
0
2
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
3
0
4
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
2
0
0
0
0
0
0
5
0
3
0
2
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
1
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
2
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
1
1
0
0
0
0
2
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
2
0
2
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
2
1
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
2
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
2
0
0
0
2
1
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
3
0
1
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
2
0
1
0
0
0
1
4
0
0
0
0
2
0
0
0
1
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
2
1
4
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
1
0
0
0
0
3
2
1
0
0
4
0
0
1
1
1
0
0
0
0
0
0
0
2
0
4
0
2
0
1
0
0
0
0
0
0
1
0
1
0
1
1
0
0
2
1
0
0
2
2
0
0
0
0
0
0
0
2
0
3
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
2
2
0
0
2
0
1
0
2
0
2
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
4
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
4
0
2
0
0
0
2
0
0
1
3
0
0
0
0
0
0
0
7
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
3
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
2
1
0
0
0
0
3
0
1
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
2
0
3
0
0
0
0
0
0
0
0
1
0
1
0
0
3
0
2
0
0
0
0
3
2
0
0
0
0
2
0
3
0
0
0
0
1
0
0
2
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
4
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
1
1
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
1
0
0
0
0
2
0
2
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
3
0
0
1
0
1
0
0
0
1
0
0
1
0
0
1
1
0
2
0
2
2
0
1
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
2
0
0
2
0
0
0
2
0
1
1
2
0
0
0
0
2
0
2
1
1
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
1
0
0
1
0
0
1
1
0
0
2
0
0
2
0
0
0
0
3
0
0
2
0
0
0
0
0
0
3
0
2
0
0
0
0
0
2
0
0
3
0
0
0
2
0
0
0
0
0
0
1
0
0
2
1
1
2
2
0
0
0
0
1
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
2
2
0
0
0
0
0
0
6
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
1
1
1
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
3
0
0
0
0
2
2
2
0
1
2
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
10
0
0
0
0
0
0
0
0
0
0
0
0
9
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
4
1
0
1
0
2
0
1
0
0
0
0
2
0
0
1
2
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
3
0
0
2
0
0
7
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
1
0
0
1
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
2
0
1
0
1
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
3
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
2
0
2
2
1
0
0
2
1
1
0
0
1
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
2
0
0
0
1
2
0
0
0
0
0
5
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
2
2
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
1
0
0
0
0
1
0
2
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
6
2
0
0
0
0
0
0
1
0
0
1
0
1
0
0
5
0
2
0
0
1
0
1
1
0
1
2
0
0
2
0
0
1
2
2
0
0
0
0
0
1
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
2
2
0
0
3
0
0
0
2
0
0
0
0
3
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
2
2
1
0
2
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
1
0
2
0
1
0
0
0
2
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
1
0
2
0
0
0
0
0
0
0
2
0
3
2
0
0
0
0
1
1
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
1
4
0
2
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
6
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
1
0
4
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
1
1
0
2
0
0
0
0
3
0
3
2
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
3
1
6
0
0
0
0
0
0
0
2
1
6
0
0
0
0
0
2
0
0
1
2
0
0
2
0
0
1
0
2
2
0
1
0
0
0
0
0
0
2
1
0
0
1
1
2
0
2
3
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
1
2
0
0
2
2
0
0
0
0
0
3
0
0
0
0
5
0
1
0
0
2
0
0
0
0
0
0
3
0
0
0
2
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
5
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
1
4
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
6
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
1
1
0
1
0
0
0
1
0
0
2
1
1
1
0
0
0
0
0
0
0
0
0
2
0
0
1
3
0
0
0
0
0
2
0
0
0
0
2
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
1
0
0
2
0
0
0
0
2
0
3
0
0
1
0
2
0
0
0
2
0
2
0
2
0
3
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
3
2
0
0
1
0
0
0
0
0
2
1
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
8
0
0
0
0
0
0
0
2
1
0
0
2
0
1
1
1
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
2
0
0
1
0
0
2
0
0
0
2
2
1
2
0
0
2
0
1
0
0
0
0
0
0
2
1
0
0
0
1
1
1
2
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
2
1
0
2
0
2
0
0
0
0
3
4
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
3
0
1
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
2
0
0
0
2
3
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
2
0
0
4
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
5
2
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
2
0
2
0
0
1
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
3
0
0
1
0
2
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
1
2
2
0
0
0
0
0
0
2
1
0
2
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
1
2
0
0
1
0
0
2
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
2
0
1
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
2
1
0
1
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
5
0
0
0
0
5
0
2
0
0
0
0
0
0
2
0
0
0
1
0
3
0
1
0
1
0
0
2
0
0
0
0
0
0
2
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
4
0
0
0
0
0
1
2
1
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
1
1
0
0
0
0
0
0
0
0
1
3
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
2
0
0
1
1
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
1
2
0
2
0
0
0
1
0
0
0
0
1
0
0
0
2
1
1
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
2
0
0
0
3
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
3
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
2
0
0
2
0
0
1
0
0
1
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
1
2
0
0
0
0
1
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
3
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
3
0
2
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
1
7
0
0
2
0
2
0
0
0
0
2
0
3
0
0
0
0
2
0
0
1
0
0
3
0
2
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
2
0
1
0
0
0
0
6
1
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
1
1
2
0
0
0
1
0
0
0
0
0
0
0
0
3
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
1
0
2
1
0
0
1
0
2
0
0
0
2
0
0
1
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
1
0
0
2
0
2
1
0
2
0
2
0
0
0
2
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
1
0
0
2
0
0
0
0
2
3
0
2
0
1
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
2
0
9
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
1
1
0
2
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
2
0
1
2
0
0
0
0
0
0
1
2
3
0
0
2
0
0
0
1
1
0
0
1
1
0
0
1
7
0
0
0
0
0
0
0
0
1
1
1
0
0
0
2
1
0
0
0
0
0
0
0
1
0
1
1
0
2
0
0
0
2
1
0
3
1
0
0
2
0
0
0
1
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
3
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
4
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
5
2
1
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
3
0
0
2
2
0
0
2
0
2
0
2
0
0
0
2
1
0
2
0
2
1
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
1
2
0
0
0
0
0
1
3
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
2
4
0
0
0
0
0
0
1
4
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
2
0
3
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
2
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
2
1
0
0
2
0
7
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
1
4
0
0
0
0
0
0
0
0
2
2
0
0
3
1
0
0
0
1
3
0
0
0
1
1
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
3
0
0
0
3
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
5
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
1
1
0
0
3
0
0
2
0
0
5
0
0
0
2
0
4
0
0
0
6
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
3
0
2
2
0
0
1
0
0
1
0
0
0
2
0
2
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
1
4
3
0
1
0
0
0
1
0
0
1
0
2
0
0
1
0
2
0
0
0
0
2
3
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
2
0
0
2
1
1
0
1
0
2
0
1
0
1
0
2
0
1
1
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
8
1
0
0
0
0
0
2
0
0
2
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
5
0
1
0
0
2
2
2
0
1
2
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
1
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
3
0
0
0
1
0
0
3
2
0
1
0
1
0
0
1
0
0
0
1
0
1
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
2
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
5
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
2
1
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
1
0
2
2
0
2
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
5
1
2
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
2
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
2
0
0
0
3
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
1
0
3
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
2
0
1
2
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
2
0
0
2
0
0
0
0
1
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
3
0
0
0
2
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
3
2
1
2
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
2
0
0
0
2
2
1
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
8
0
0
0
0
0
1
2
1
1
0
0
1
0
0
0
0
2
0
1
1
0
0
3
0
0
0
0
12
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
3
1
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
3
0
1
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
2
2
2
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
1
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
2
2
0
0
2
2
0
0
0
0
2
0
2
0
0
0
2
0
0
1
0
1
2
1
0
2
0
0
0
3
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
2
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
2
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
3
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
1
3
0
0
2
2
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
1
1
0
0
1
0
0
0
2
1
1
0
1
1
0
0
0
0
0
1
0
1
0
0
0
2
2
2
0
2
0
0
5
0
1
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
2
1
0
2
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
3
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
4
4
0
0
2
0
0
0
0
0
0
0
1
0
0
0
3
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
3
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
3
0
0
1
2
5
1
2
0
3
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
2
1
0
0
0
1
0
0
0
0
0
2
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
3
1
0
1
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
2
0
0
1
1
0
2
2
2
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
2
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
2
0
1
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
2
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
3
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
3
0
0
0
0
3
0
0
0
4
3
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
3
1
0
0
0
2
1
0
0
1
0
1
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
7
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
2
2
0
2
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
4
1
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
2
0
1
0
0
0
2
0
0
0
2
0
0
2
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
1
0
0
5
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
1
0
0
1
2
0
0
1
0
0
0
2
0
0
0
0
1
2
0
0
0
3
4
0
1
0
0
2
0
0
0
1
2
1
0
0
0
4
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
3
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
2
0
2
2
0
0
0
0
0
2
0
0
0
0
2
2
0
0
1
0
0
0
1
1
0
0
0
2
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
1
0
1
1
0
0
0
0
0
3
0
1
0
0
0
0
0
0
2
2
4
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
3
0
0
2
0
0
0
3
0
1
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
2
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
5
1
0
0
0
0
2
2
0
0
1
2
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
2
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
11
0
0
2
0
0
0
0
0
3
0
2
2
0
0
2
2
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
2
2
4
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
2
0
0
1
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
3
0
0
0
2
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
1
0
0
7
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
1
3
0
1
1
0
1
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
2
1
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
3
1
0
2
0
0
0
0
0
0
3
0
0
0
0
1
0
0
2
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
1
0
0
0
0
2
1
0
2
0
4
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
1
2
0
3
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
3
0
0
0
0
1
0
1
0
0
0
0
3
1
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
2
0
0
0
0
1
0
2
0
1
0
2
0
0
1
2
0
0
1
0
2
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
3
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
2
0
2
0
2
0
0
0
0
2
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
1
0
0
0
2
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
3
0
1
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
3
1
1
2
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
2
0
0
2
0
1
0
2
0
2
0
0
2
2
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
2
0
2
2
0
0
2
0
0
4
0
0
0
0
2
1
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
3
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
5
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
3
2
0
1
0
0
0
0
1
2
0
0
0
0
3
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
2
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
2
3
0
0
1
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
3
0
2
0
0
1
1
0
1
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
2
3
3
0
0
0
0
3
2
0
0
0
0
0
0
2
0
2
0
0
1
0
0
1
0
0
0
2
2
1
0
2
0
2
1
2
0
0
0
1
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
4
0
0
5
0
0
0
0
4
0
0
1
0
1
1
0
1
0
0
0
0
1
0
0
0
0
2
1
0
0
0
1
1
3
2
0
1
0
0
0
3
2
0
0
0
1
0
0
0
0
0
0
1
0
4
0
0
0
0
0
2
1
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
1
2
1
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
5
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
1
2
0
0
2
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
5
1
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
2
0
1
0
0
0
1
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
2
2
0
0
1
2
1
1
0
0
1
0
0
1
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
1
0
2
3
2
1
0
0
1
0
2
0
1
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
1
2
0
0
2
0
0
0
2
0
0
0
0
1
0
2
0
0
2
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
6
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
1
1
0
2
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
1
1
0
1
4
0
0
1
2
1
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
3
2
3
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
1
0
1
0
2
2
0
3
0
0
0
1
0
0
0
4
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
2
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
1
0
0
0
0
0
0
1
0
2
1
2
0
0
0
2
1
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
2
0
0
2
0
2
0
0
0
1
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
4
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
1
2
0
0
0
1
0
1
0
0
3
0
0
0
0
2
1
2
2
0
1
0
0
0
1
0
1
0
0
2
0
0
1
2
0
0
2
1
0
1
2
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
5
2
0
2
0
0
0
1
1
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
4
1
0
0
0
0
2
1
0
0
0
0
0
0
0
1
1
0
0
11
1
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
2
0
0
1
2
3
0
0
0
0
0
1
1
6
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
1
0
0
2
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
2
0
0
0
1
1
1
4
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
2
0
0
0
0
1
0
1
0
1
0
0
0
0
2
0
2
0
0
2
1
0
0
0
0
2
1
0
0
1
0
0
0
2
2
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
2
0
0
2
0
1
1
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
1
0
0
0
0
6
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
2
0
2
0
0
0
0
1
0
1
2
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
3
0
0
2
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
2
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
1
0
1
0
0
2
0
0
1
3
0
0
1
0
1
0
0
0
0
1
0
3
0
0
2
2
0
2
0
1
1
2
0
3
0
0
1
1
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
1
1
2
1
2
2
0
2
2
0
2
0
4
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
1
0
0
0
0
2
3
0
1
0
0
1
2
1
0
0
0
0
1
0
0
2
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
2
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
1
2
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
3
0
1
2
0
0
2
0
0
0
1
0
1
0
0
1
0
1
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
5
0
4
0
0
0
2
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
2
0
2
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
2
0
2
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
2
2
2
0
0
0
1
0
0
2
0
3
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
3
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
2
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
3
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
3
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
2
1
2
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
2
0
0
0
3
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
3
2
0
0
0
0
0
0
0
0
2
1
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
4
2
0
0
0
0
0
0
2
1
0
0
0
0
3
0
1
0
0
0
2
1
0
0
0
1
0
0
1
0
0
2
0
4
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
1
0
0
1
2
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
24
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
1
2
0
0
2
0
0
0
0
3
0
1
0
0
0
0
2
1
0
0
0
0
1
2
0
0
0
0
2
0
9
0
2
1
0
0
0
0
0
0
1
1
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
2
1
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
2
2
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
1
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
2
1
0
3
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
3
0
0
0
3
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
2
2
0
1
0
0
0
0
0
0
0
2
0
0
0
1
3
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
1
1
2
0
2
0
0
0
2
0
1
0
0
2
1
0
1
0
2
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
2
2
0
0
0
0
0
0
0
1
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
4
0
0
0
0
0
1
1
0
0
0
2
1
0
1
0
0
1
2
1
0
2
0
2
0
0
1
2
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
1
2
0
1
0
0
0
1
1
2
0
0
0
2
0
1
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
2
0
0
2
0
2
1
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
8
0
0
2
0
1
2
0
0
1
1
2
0
0
0
0
0
0
0
0
0
2
2
1
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
1
0
0
0
0
4
0
0
0
0
2
0
2
0
0
2
0
0
1
0
0
0
1
0
8
0
0
0
0
2
0
2
0
0
0
0
6
1
0
1
3
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
1
0
1
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
1
0
0
0
0
0
1
2
2
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
2
2
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
1
0
0
0
0
0
2
0
0
5
0
1
2
0
0
0
0
0
0
0
0
0
0
2
2
1
1
0
0
1
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
2
0
3
0
3
0
0
1
0
0
3
0
0
0
0
2
1
1
0
0
0
2
0
0
0
2
0
0
2
0
1
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
3
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
3
0
1
0
0
0
0
1
0
1
1
2
0
0
0
1
1
0
0
0
1
1
1
0
0
0
1
0
1
0
0
0
0
0
0
2
3
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
3
1
2
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
2
0
1
0
1
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
2
1
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
4
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
4
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
1
2
0
0
0
1
0
0
0
0
1
1
2
4
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
1
0
3
4
0
0
0
0
0
2
1
1
2
0
4
0
2
2
0
1
1
2
2
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
1
3
8
0
0
0
0
0
0
1
0
0
0
1
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
1
0
3
0
1
3
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
3
0
2
0
0
1
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
2
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
2
0
0
2
0
0
0
0
1
0
1
2
0
0
0
1
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
1
1
0
0
1
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
3
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
3
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
1
2
1
0
3
0
1
0
0
0
0
1
0
3
0
2
0
1
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
5
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
3
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
2
0
1
1
0
0
0
0
0
0
0
0
4
2
0
0
2
8
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
2
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
3
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
1
1
0
0
0
3
0
1
0
0
0
2
0
0
2
2
0
0
0
0
0
1
3
0
0
0
1
0
0
0
0
1
0
0
0
3
5
0
0
2
0
2
0
1
2
1
2
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
2
1
0
0
2
0
0
0
2
1
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
1
0
0
0
0
2
0
0
2
0
1
1
0
1
0
1
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
2
1
0
1
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
1
1
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
1
2
0
2
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
1
0
2
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
2
1
0
1
0
3
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
2
0
0
0
1
1
0
1
0
0
0
0
0
0
2
0
0
0
0
3
0
1
2
0
3
2
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
2
0
0
2
1
1
2
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
1
2
2
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
2
0
0
10
2
2
0
0
0
0
0
0
0
0
0
0
0
2
1
3
1
0
2
0
2
1
0
0
0
1
0
1
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
2
2
0
2
0
4
0
0
0
2
0
5
1
0
0
1
0
0
1
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
2
0
0
0
2
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
2
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
2
1
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
1
1
1
2
2
0
0
1
0
0
1
0
0
2
0
1
0
0
0
0
1
0
0
0
0
3
2
2
0
0
0
2
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
2
0
0
2
2
0
0
0
2
0
0
0
1
1
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
1
0
0
0
0
1
1
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
3
0
0
3
1
0
0
0
2
0
0
2
2
0
0
0
2
1
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
5
0
0
0
2
1
0
0
1
0
0
0
2
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
1
0
3
0
2
0
0
0
3
0
1
0
3
0
0
0
0
0
0
2
0
2
0
0
5
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
2
2
1
0
0
0
0
0
0
0
0
7
0
0
0
0
1
0
0
0
1
0
0
3
2
2
0
1
0
0
0
0
0
0
0
0
0
0
4
0
1
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
4
1
0
2
1
8
1
2
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
2
2
0
0
0
0
0
1
0
0
0
1
2
2
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
4
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
2
2
1
1
0
0
0
0
3
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
1
2
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
3
2
1
1
0
1
2
0
2
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
0
0
2
0
1
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
3
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
2
0
4
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
1
1
1
0
0
4
0
0
0
0
0
2
0
0
2
0
0
1
0
0
5
3
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
3
1
1
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
3
2
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
2
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
1
0
2
0
0
0
2
0
0
0
0
0
0
2
2
0
2
1
1
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
3
0
0
0
0
0
0
0
0
1
0
3
0
0
1
0
1
0
0
0
0
2
0
0
0
1
2
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
3
1
1
0
0
0
0
3
1
0
0
2
2
2
1
1
0
1
0
0
1
1
0
0
0
0
2
1
0
1
4
2
2
0
0
0
1
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
3
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
3
0
0
2
0
1
0
0
0
0
0
1
1
0
2
2
2
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
3
0
0
0
1
0
0
0
0
0
0
1
1
1
2
2
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
2
0
2
0
0
1
2
0
2
1
0
1
2
1
0
2
2
0
0
0
1
0
0
1
0
0
2
0
0
0
3
0
2
1
0
0
0
0
1
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
2
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
3
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
1
0
2
0
0
1
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
5
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
4
2
1
1
0
0
0
1
1
0
0
0
0
1
0
0
3
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
3
0
0
1
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
2
0
0
3
5
0
0
1
1
0
0
1
2
1
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
2
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
3
0
2
1
1
0
0
1
0
0
0
0
1
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
2
1
1
0
0
0
0
0
2
1
0
1
0
0
1
2
0
0
0
1
0
1
0
0
2
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
2
0
0
0
2
2
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
2
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
3
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
2
0
3
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
2
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
5
1
0
1
0
0
0
2
3
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
1
2
1
0
0
0
0
0
0
2
0
0
2
0
0
2
1
0
0
0
0
0
1
1
2
0
2
0
1
0
0
0
3
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
1
0
2
0
0
0
4
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
1
0
2
0
2
0
0
0
1
0
0
2
0
0
0
3
1
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
1
1
0
0
0
6
2
0
2
0
0
0
0
2
0
0
0
2
0
1
3
0
0
0
0
3
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
2
3
0
0
0
1
0
0
0
2
2
0
3
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
4
2
0
2
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
2
0
0
0
0
0
1
1
0
0
1
0
0
1
0
2
1
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
2
2
2
0
1
1
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
1
4
0
0
2
0
2
2
0
1
0
0
1
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
2
1
0
0
0
0
0
0
4
1
0
0
2
0
0
0
1
3
2
2
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
2
0
5
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
3
0
0
0
0
0
1
0
3
1
0
0
0
6
0
0
0
1
1
0
0
0
0
1
0
2
2
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
2
2
0
0
1
2
2
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
2
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
2
0
0
0
0
2
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
2
1
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
2
1
0
0
0
0
3
0
0
2
1
0
0
2
3
0
0
0
1
0
1
0
4
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
1
0
2
1
0
0
0
0
0
1
0
0
2
0
3
0
2
0
0
1
0
0
1
0
0
2
1
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
3
0
2
2
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
2
1
0
0
0
1
1
3
0
0
0
0
0
2
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
3
0
0
0
0
0
0
0
0
3
0
0
1
2
0
0
1
1
0
2
0
0
0
1
0
0
4
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
2
0
2
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
1
0
2
2
0
0
0
2
0
0
1
3
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
1
2
0
2
4
0
0
0
3
0
0
0
4
0
2
1
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
2
0
0
0
0
0
0
6
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
1
0
2
0
0
2
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
3
2
3
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
2
1
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
1
0
1
0
0
0
0
2
0
0
2
0
0
0
3
0
2
0
0
0
3
0
0
3
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
2
0
1
0
0
1
2
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
4
0
0
0
1
2
0
0
5
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
2
2
1
0
0
2
0
1
0
0
0
0
2
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
1
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
1
1
0
0
0
0
2
0
0
0
2
0
0
3
0
0
1
0
0
0
2
1
0
2
2
10
0
2
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
1
0
0
0
1
2
0
0
2
1
1
0
1
1
0
1
0
0
3
0
1
0
1
1
0
0
1
0
0
2
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
1
6
0
0
0
0
0
0
0
1
0
0
0
0
5
2
0
0
0
0
2
0
2
0
1
0
0
2
0
2
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
1
1
2
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
1
2
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
2
0
0
0
2
3
0
4
0
0
0
0
0
0
2
0
0
0
2
1
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
1
2
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
2
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
13
0
1
0
0
0
1
0
1
0
2
0
2
0
1
0
0
2
0
0
0
0
0
0
0
1
1
0
0
4
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
2
2
0
0
0
0
0
0
2
3
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
3
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
3
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
4
0
1
0
0
0
0
0
1
0
2
0
0
3
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
5
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
2
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
4
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
4
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
1
1
0
0
0
2
0
0
0
2
0
0
0
0
0
4
0
2
0
0
3
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
1
0
0
0
2
1
0
3
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
1
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
2
0
3
2
0
0
0
0
0
0
3
0
0
0
0
0
0
3
1
0
1
2
0
0
0
0
0
2
2
0
0
3
0
0
1
1
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
4
4
0
2
0
0
0
1
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
5
0
0
0
1
0
0
0
0
2
0
0
2
0
1
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
10
1
1
2
0
1
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
2
3
0
0
0
3
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
1
0
2
2
1
0
1
0
0
1
2
0
0
0
1
0
2
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
1
0
0
3
0
1
0
0
0
0
0
0
0
0
0
2
2
2
2
4
0
0
3
1
1
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
2
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
1
0
0
1
0
0
0
2
0
1
0
2
0
0
1
1
0
0
1
0
0
1
0
0
0
4
0
1
0
0
0
0
1
0
3
3
0
0
1
3
1
1
1
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
6
2
0
0
0
0
2
0
4
0
2
0
0
1
0
0
2
1
0
1
0
1
0
0
1
0
0
0
0
0
0
1
1
0
2
2
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
1
1
0
0
0
1
0
3
1
0
0
0
0
2
0
0
0
0
0
2
1
0
3
1
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
1
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
5
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
3
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
4
0
2
2
0
0
0
3
0
0
0
1
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
3
0
1
0
1
2
0
0
0
2
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
2
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
3
0
0
0
3
0
0
0
2
1
0
2
0
4
0
0
0
0
0
0
0
2
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
2
1
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
2
0
0
0
1
0
1
0
0
1
0
0
1
0
0
2
0
0
0
0
1
0
2
0
1
2
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
1
2
0
0
2
0
2
2
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
1
0
1
1
0
2
1
1
5
0
0
0
0
2
1
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
3
0
2
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
1
1
0
1
0
0
1
1
1
1
0
1
1
0
0
2
0
1
2
4
0
0
1
1
0
1
0
1
2
0
1
1
0
1
0
0
0
6
0
0
0
0
2
0
3
0
0
0
0
0
2
0
0
8
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
1
0
3
0
0
0
0
0
1
0
0
0
0
0
1
4
0
2
0
0
1
0
0
0
0
0
1
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
2
0
2
0
1
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
2
0
0
0
1
1
0
0
0
2
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
3
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
5
0
0
0
1
0
0
0
9
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
2
2
0
0
4
0
0
0
0
0
0
2
1
2
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
2
0
0
1
1
0
0
2
0
0
2
2
0
0
1
1
0
0
0
0
0
0
0
0
1
2
1
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
5
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
2
0
0
1
0
2
0
0
0
1
0
0
1
0
0
0
0
0
2
0
1
2
0
2
0
0
0
0
0
0
2
0
0
1
0
1
2
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
3
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
3
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
2
3
0
0
2
0
2
0
0
0
3
0
2
0
0
2
0
2
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
2
1
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
2
0
23
1
0
0
1
2
2
0
0
0
0
0
0
0
2
1
1
2
0
0
0
1
0
2
0
2
2
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
1
1
0
0
0
1
2
0
2
0
0
0
0
0
0
2
2
1
0
0
0
5
0
0
0
0
0
0
2
0
3
0
0
0
0
0
2
0
0
1
0
0
0
1
1
0
0
2
0
0
3
0
0
0
3
1
0
0
0
0
0
2
0
0
1
0
0
3
0
0
0
0
0
0
0
0
2
1
0
3
0
2
1
2
0
2
1
0
2
0
0
0
0
0
0
2
1
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
1
0
1
0
0
2
2
1
1
0
0
1
0
0
0
0
0
0
0
1
2
0
0
2
0
4
0
1
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
5
0
0
0
0
0
2
0
0
2
1
2
2
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
1
2
0
0
3
0
0
0
0
2
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
1
2
0
1
1
0
2
0
0
0
0
0
1
0
2
0
0
1
1
1
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
1
0
0
2
0
0
0
0
0
0
1
0
1
0
1
2
1
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
1
2
0
5
0
0
0
0
0
0
2
0
1
0
0
2
0
0
3
0
0
1
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
2
2
0
1
0
0
2
2
0
7
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
3
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
3
0
0
0
1
0
1
0
0
1
0
2
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
3
2
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
3
0
0
0
1
0
13
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
2
1
0
1
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
3
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
6
0
0
0
0
0
0
0
2
0
3
0
1
0
0
0
2
0
0
1
0
1
1
0
2
0
0
0
1
0
0
3
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
1
2
0
1
0
1
0
0
2
0
2
1
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
5
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
1
0
2
0
1
1
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
1
0
1
0
2
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
3
0
0
0
2
0
0
2
0
0
0
2
1
0
0
1
0
0
0
0
1
0
0
0
0
0
3
0
0
1
0
0
1
0
0
3
0
0
0
1
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
1
0
2
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
1
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
1
2
1
0
0
2
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
4
0
0
0
2
0
0
0
1
1
1
1
0
0
1
0
0
0
3
2
0
0
0
1
6
2
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
1
0
1
0
1
3
2
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
1
1
1
0
0
4
0
0
0
0
3
0
0
1
0
4
0
0
0
0
1
0
0
0
0
0
0
1
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
2
0
8
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
1
0
2
2
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
5
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
1
0
2
2
1
0
0
0
0
3
0
0
0
2
0
6
1
3
0
0
2
0
0
2
3
1
1
0
0
0
0
2
1
0
2
0
0
1
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
3
0
1
3
0
3
0
2
0
0
0
0
0
3
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
1
0
2
1
3
0
2
0
0
0
2
2
0
0
1
0
0
2
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
3
0
2
2
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
4
1
0
2
0
0
2
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
1
0
0
2
1
1
0
0
1
0
0
0
0
0
0
1
0
0
7
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
2
0
4
0
1
0
0
0
0
0
1
0
1
0
1
0
2
0
0
2
0
0
0
0
1
0
1
0
0
2
1
1
0
0
2
1
0
2
1
0
0
6
0
0
0
2
0
2
0
0
0
0
0
0
0
3
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
5
1
8
0
0
0
1
3
2
0
0
0
0
0
0
2
0
5
0
0
0
1
2
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
2
0
0
1
1
0
2
1
1
0
0
0
0
0
0
2
1
0
2
0
0
0
1
0
0
1
0
0
0
0
0
1
3
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
1
0
2
0
0
0
2
0
1
1
0
2
1
0
1
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
1
0
0
2
0
1
2
0
1
2
0
0
0
1
2
0
1
0
1
0
0
2
0
1
0
2
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
1
0
2
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
1
0
0
2
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
2
0
0
0
0
3
2
0
0
1
3
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
1
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
1
2
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
1
0
0
0
0
0
0
2
0
4
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
1
3
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
1
2
0
0
0
0
0
1
1
3
0
1
0
2
2
1
2
0
1
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
1
0
0
1
0
2
0
1
2
0
1
0
0
0
1
0
0
0
0
1
1
0
1
2
0
0
0
0
0
0
3
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
2
1
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
2
3
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
2
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
2
2
0
0
1
0
1
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
3
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
2
3
0
2
0
0
0
0
0
2
2
2
0
0
0
0
1
0
1
5
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
1
1
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
5
1
0
0
0
2
0
0
2
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
1
2
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
1
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
1
4
0
2
0
1
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
12
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
2
1
8
0
0
0
1
0
0
0
0
0
2
2
0
1
0
0
0
0
0
1
2
0
1
1
0
0
0
1
0
0
2
0
0
4
0
2
0
0
0
2
0
1
5
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
3
0
2
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
1
2
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
3
0
0
0
1
0
0
0
2
0
0
2
0
2
2
0
0
0
1
0
1
0
0
2
0
0
0
1
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
2
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
2
0
2
0
0
0
2
1
0
0
0
0
2
0
0
0
0
2
1
0
0
0
2
0
0
2
1
0
1
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
2
0
0
1
3
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
2
0
0
5
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
1
0
4
0
2
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
2
1
1
3
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
4
3
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
2
0
0
1
12
0
0
0
0
0
0
1
0
0
0
2
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
1
0
0
1
0
0
0
0
1
1
3
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
1
0
2
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
3
0
0
0
2
0
0
2
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
4
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
2
0
0
0
1
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
4
0
0
1
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
1
3
1
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
6
0
1
0
2
0
0
0
2
0
3
1
0
1
0
0
0
1
0
0
0
0
1
0
2
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
2
2
0
0
0
1
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
2
1
0
0
0
0
0
0
0
0
2
4
0
2
0
0
0
0
2
0
0
0
0
0
1
2
2
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
1
2
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
3
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
2
0
2
1
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
1
0
3
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
1
1
0
2
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
1
2
0
0
0
0
0
1
2
0
0
0
0
1
0
1
0
0
2
0
0
0
3
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
1
0
2
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
3
0
0
0
2
0
1
1
0
0
0
0
0
2
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
5
0
1
0
0
0
0
0
2
0
1
1
0
1
0
0
2
0
0
1
0
2
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
3
0
0
0
1
0
0
2
0
2
0
0
0
0
2
2
1
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
2
2
0
0
0
0
1
0
0
2
2
0
0
1
2
0
0
0
0
0
0
0
1
0
0
3
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
1
0
2
0
2
1
0
0
2
2
0
0
0
0
0
0
2
1
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
2
1
0
2
0
0
0
0
0
1
0
0
0
0
3
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
3
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
5
0
2
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
2
0
2
2
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
2
0
1
0
2
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
1
2
0
3
0
1
0
0
0
0
1
0
2
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
3
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
2
2
0
0
2
0
2
0
0
0
4
0
0
1
0
0
0
0
0
0
1
0
3
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
9
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
2
0
0
0
1
2
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
1
0
1
1
0
0
0
2
0
0
1
0
0
1
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
1
1
0
0
0
7
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
4
0
1
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
2
3
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
3
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
2
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
4
8
0
0
0
0
0
0
0
0
1
3
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
2
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
3
2
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
2
3
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
1
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
1
1
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
2
1
0
0
2
1
4
0
0
0
1
0
0
0
0
0
0
1
2
1
0
5
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
1
2
0
2
0
0
1
2
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
3
0
0
1
1
0
0
0
0
1
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
1
2
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
1
0
0
1
2
0
1
2
0
0
0
0
2
0
0
0
2
1
0
1
0
0
2
0
1
0
2
3
0
3
0
1
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
4
4
0
2
0
0
0
2
0
2
1
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
1
1
2
0
3
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
3
0
0
2
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
7
1
1
0
0
2
1
0
0
0
0
2
2
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
3
4
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
3
0
2
0
0
0
0
0
0
7
2
0
2
0
0
1
0
0
0
0
0
0
0
2
0
1
4
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
2
1
3
0
2
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
3
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
3
2
0
0
0
2
0
0
0
0
0
1
0
1
0
2
0
0
2
2
0
0
2
0
2
0
1
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
1
1
0
0
2
2
0
0
0
0
0
0
0
1
0
0
2
0
0
4
2
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
5
0
1
0
0
2
0
0
0
0
0
4
0
1
0
1
0
0
2
1
0
0
0
0
0
2
0
0
0
0
1
0
2
2
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
3
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
2
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
3
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
1
0
0
0
0
0
2
1
0
0
1
0
0
2
0
0
1
0
0
0
4
0
0
0
0
0
0
1
0
0
1
0
0
0
3
0
0
1
0
0
0
2
3
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
1
0
0
0
3
0
0
0
0
1
0
1
0
0
2
1
0
0
0
0
0
1
0
0
0
3
0
1
0
1
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
2
1
2
0
0
0
0
3
1
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
3
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
6
2
0
0
1
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
2
0
0
1
0
0
0
0
2
1
2
0
0
1
0
0
0
0
0
2
0
0
1
0
2
0
1
0
0
0
0
0
3
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
2
2
0
0
0
0
2
2
0
1
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
1
0
0
0
0
0
2
2
2
2
2
2
1
0
1
0
2
0
0
0
1
0
0
0
0
0
0
2
3
0
0
0
0
0
1
0
2
0
2
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
1
1
2
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
3
0
0
2
2
0
0
2
0
0
0
0
2
2
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
1
1
0
1
0
2
0
0
0
2
0
1
3
3
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
2
0
0
1
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
3
1
1
1
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
2
0
0
2
1
4
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
1
0
0
0
1
5
0
0
0
1
2
1
0
0
0
1
0
3
1
2
0
0
0
0
1
0
0
0
0
0
0
1
0
3
2
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
2
2
0
0
1
2
0
1
3
0
0
1
0
0
1
1
2
3
0
7
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
1
0
3
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
2
0
1
2
0
0
0
0
0
2
2
0
0
0
2
1
0
0
0
0
0
0
0
0
1
2
0
0
4
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
3
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
3
0
0
0
0
1
0
1
2
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
2
4
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
1
0
0
1
2
2
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
1
0
0
0
2
0
0
0
1
0
0
3
0
0
0
0
0
2
0
2
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
3
2
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
1
4
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
5
0
1
1
0
0
0
2
0
0
2
1
0
0
0
0
2
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
2
0
2
2
0
0
0
0
0
2
0
0
1
0
0
2
2
0
4
0
0
2
0
0
0
0
0
0
4
1
0
2
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
1
0
2
1
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
2
1
2
0
2
0
0
0
5
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
6
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
2
0
1
1
0
0
0
1
0
0
1
0
0
0
2
1
0
0
2
0
0
0
0
1
0
0
4
0
0
0
0
2
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
2
2
0
0
1
2
0
2
0
0
2
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
1
0
1
0
3
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
1
0
0
2
0
2
0
0
0
2
0
1
2
0
0
0
0
0
2
0
0
0
1
0
1
1
2
0
2
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
2
0
0
0
1
1
0
0
0
0
3
0
0
2
0
5
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
1
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
1
0
2
0
0
0
0
1
1
2
5
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
2
0
2
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
2
0
0
3
3
0
0
2
0
0
2
2
2
0
0
0
0
2
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
2
2
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
2
0
2
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
3
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
2
1
0
1
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
2
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
4
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
2
1
0
0
0
0
5
2
1
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
1
0
0
1
0
0
1
0
0
2
0
0
1
2
0
0
0
0
2
0
0
1
1
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
3
1
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
5
0
0
0
2
2
2
0
0
1
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
1
0
0
0
3
0
2
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
3
0
2
0
0
0
1
2
0
0
0
0
1
0
0
2
0
2
0
0
0
2
0
1
0
0
0
1
0
2
2
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
1
0
0
0
7
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
2
0
0
0
2
0
0
0
0
2
0
3
0
0
0
0
2
1
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
1
2
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
2
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
5
2
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
1
2
0
0
0
2
0
0
1
2
0
0
0
0
0
0
1
0
2
0
1
0
0
2
2
0
0
4
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
1
1
0
2
0
0
0
0
2
2
1
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
3
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
2
1
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
1
2
0
0
1
0
1
0
0
0
1
0
0
0
1
0
1
1
0
2
0
0
0
1
0
0
0
1
0
1
0
0
0
3
0
0
0
0
4
0
3
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
1
5
2
0
0
2
2
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
1
2
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
3
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
8
0
0
1
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
2
0
0
1
0
1
2
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
1
0
0
0
0
0
0
1
1
2
0
1
0
0
0
1
0
0
0
0
2
0
0
2
0
1
1
2
0
0
0
0
1
0
1
0
0
1
0
2
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
2
1
0
2
1
0
1
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
2
0
2
0
1
2
0
0
1
1
0
0
0
0
0
1
3
0
0
0
0
1
0
3
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
4
0
0
0
0
0
0
1
0
1
0
0
1
1
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
1
0
1
2
0
0
0
2
0
1
0
0
0
0
0
0
0
1
2
2
0
0
0
3
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
2
0
2
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
2
2
0
0
3
0
0
0
1
0
0
0
1
0
1
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
2
1
2
0
1
2
0
0
2
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
1
2
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
1
3
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
4
3
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
1
0
2
0
0
5
0
0
0
0
0
0
1
0
3
0
0
1
0
0
0
0
0
0
0
0
1
0
3
0
0
2
0
0
0
1
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
3
0
0
1
0
0
0
0
0
1
0
0
2
3
0
0
0
0
0
1
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
1
0
0
3
1
0
0
2
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
1
0
1
0
1
2
2
0
0
0
0
2
1
0
0
3
1
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
1
0
0
1
0
0
1
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
7
2
0
1
0
0
0
0
0
0
0
0
2
1
1
2
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
1
0
2
0
0
0
0
0
0
0
3
0
3
0
0
1
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
4
1
2
0
2
1
0
0
11
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
4
0
1
2
0
0
1
0
0
1
0
0
0
0
2
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
3
0
2
0
0
2
0
1
0
2
0
0
7
0
2
1
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
2
2
0
2
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
1
1
0
0
0
0
1
1
0
0
0
2
1
0
0
0
0
0
0
1
0
1
1
2
0
0
0
0
0
0
0
0
3
2
1
1
1
0
0
0
0
0
1
3
0
0
0
2
1
0
0
3
0
0
0
2
2
0
0
0
2
0
0
1
0
0
0
2
0
1
0
0
2
1
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
6
1
2
0
0
0
0
0
1
0
1
2
0
0
2
0
1
0
0
0
0
0
0
1
2
0
0
0
2
2
0
0
1
0
2
1
0
0
0
0
0
1
1
0
0
0
0
0
0
3
3
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
2
2
2
0
1
2
0
0
0
0
2
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
3
0
0
1
0
0
0
0
3
0
0
2
2
2
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
2
2
0
1
2
0
1
0
0
1
2
2
0
0
1
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
1
0
0
0
0
2
0
1
0
1
0
2
0
0
4
2
0
1
1
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
3
0
3
2
1
1
0
1
0
2
0
0
2
2
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
4
0
0
0
0
0
3
0
1
0
1
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
2
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
3
0
2
0
2
0
0
1
0
2
2
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
2
3
1
0
0
0
0
0
0
2
1
2
1
1
2
0
0
0
0
0
1
1
0
2
0
2
0
0
2
0
0
0
1
0
0
0
0
2
0
1
0
1
3
0
2
0
3
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
1
2
1
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
2
0
0
1
5
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
2
0
1
1
0
0
3
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
2
1
0
0
0
0
0
1
3
1
0
0
0
0
0
2
3
0
0
0
0
0
1
0
1
0
0
2
1
0
0
1
3
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
3
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
3
0
1
0
0
0
0
2
2
0
2
1
0
0
2
0
0
1
1
0
0
2
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
1
0
0
0
3
1
0
2
0
0
1
0
2
0
3
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
2
0
0
0
0
0
2
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
6
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
1
2
2
0
0
0
1
0
2
0
2
0
0
0
0
0
1
2
0
0
2
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
3
0
0
0
1
1
0
0
0
0
3
0
0
0
0
0
0
0
0
2
1
0
0
1
1
0
2
0
0
2
0
0
0
0
1
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
2
1
0
1
0
4
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
1
0
1
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
4
2
2
0
1
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
4
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
2
0
0
0
1
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
7
0
0
1
0
1
1
0
3
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
1
0
0
0
0
0
2
0
0
1
1
0
0
0
0
3
0
0
1
0
0
0
1
1
0
0
0
0
0
2
0
0
2
0
2
0
0
0
2
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
1
2
0
0
1
0
0
0
1
0
0
0
0
1
0
4
0
0
1
0
0
1
0
3
0
1
0
0
2
0
8
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
2
2
0
0
2
0
0
2
0
0
4
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
1
0
2
0
1
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
5
0
0
2
0
0
0
0
0
0
2
0
0
2
0
1
0
2
0
0
2
2
0
2
0
0
0
4
0
1
2
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
2
0
0
0
0
1
0
0
2
0
4
1
0
0
2
0
0
2
0
0
0
1
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
2
1
1
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
2
1
1
0
0
2
2
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
1
1
0
0
0
0
0
0
1
2
1
0
0
1
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
1
0
0
0
1
2
0
1
0
0
0
0
0
0
3
1
2
1
3
1
0
0
1
0
2
2
0
0
2
0
1
1
0
0
0
0
0
1
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
8
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
7
0
0
0
0
2
2
0
2
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
3
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
1
2
1
1
1
0
0
3
0
1
0
0
1
0
6
0
1
0
0
0
0
2
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
2
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
1
2
0
0
2
2
0
0
2
0
0
0
1
0
1
0
0
0
2
0
1
0
0
0
2
0
0
2
1
1
0
4
0
0
0
2
4
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
1
2
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
2
0
1
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
2
2
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
1
1
0
4
0
2
0
2
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
2
3
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
3
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
2
2
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
1
0
1
2
0
2
0
0
0
2
0
0
0
2
0
1
1
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
4
0
1
1
1
0
0
1
0
0
1
2
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
1
1
0
1
0
1
0
0
3
3
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
2
0
0
0
0
1
0
0
1
3
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
2
1
0
0
0
0
2
0
0
0
1
0
3
1
0
0
0
0
0
0
0
0
3
0
0
1
0
1
0
0
2
0
1
0
5
2
0
3
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
1
2
0
1
0
2
1
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
1
0
3
0
0
0
0
0
1
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
4
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
1
0
2
0
0
1
0
0
0
0
0
1
0
1
0
0
0
2
1
3
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
1
1
1
0
2
0
0
2
2
1
0
0
0
0
0
0
0
0
2
0
0
4
1
1
1
2
0
0
0
2
3
2
0
5
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
3
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
1
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
1
0
0
1
0
0
0
0
2
0
2
0
1
0
0
3
1
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
1
2
0
0
1
1
0
1
0
0
3
0
0
0
0
1
2
0
0
0
1
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
4
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
2
0
2
3
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
4
0
0
0
1
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
1
2
3
0
0
0
0
1
0
0
5
0
0
0
1
0
0
0
0
0
2
0
0
2
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
4
1
1
0
0
0
0
3
0
0
0
2
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
2
0
3
2
0
0
0
1
3
1
2
0
0
0
2
1
0
4
0
0
0
2
0
0
0
2
0
0
0
0
0
2
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
6
0
3
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
2
0
1
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
2
0
1
0
0
3
0
0
0
1
1
0
4
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
1
2
1
1
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
1
0
0
1
0
3
0
0
0
2
0
0
1
1
2
0
0
0
1
0
0
0
2
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
1
0
0
3
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
3
0
0
0
0
0
2
0
0
1
2
2
0
0
0
0
0
0
0
0
1
0
2
1
1
0
0
0
3
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
2
0
2
0
1
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
1
2
0
0
2
1
2
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
1
0
1
0
0
0
2
0
0
0
0
0
2
0
0
3
0
0
0
0
0
1
1
2
0
1
2
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
7
0
0
0
0
0
0
5
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
2
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
2
0
0
0
0
0
1
2
0
1
3
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
2
1
1
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
1
0
1
0
0
0
0
1
2
0
1
0
0
0
0
0
1
0
0
0
0
0
1
4
0
0
1
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
1
9
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
3
1
0
0
3
1
0
0
0
0
0
1
2
0
1
0
0
0
0
2
2
1
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
2
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
2
1
2
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
2
0
1
0
0
3
1
0
0
0
0
0
1
0
1
2
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
1
0
1
2
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
2
0
0
1
2
0
2
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
2
0
1
1
3
0
0
0
0
0
0
2
2
5
0
2
0
0
0
2
1
1
2
0
0
1
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
3
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
1
0
0
0
0
1
0
2
1
0
2
0
1
0
0
0
2
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
2
0
2
2
0
0
1
0
0
0
0
0
2
1
0
0
0
1
0
0
0
2
0
0
0
0
1
1
0
5
0
0
0
0
0
0
2
0
0
3
0
0
2
0
0
0
0
0
1
1
0
2
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
2
0
0
0
1
5
0
1
1
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
2
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
3
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
3
0
0
1
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
6
1
0
1
2
0
0
0
0
1
1
2
0
3
0
0
0
1
1
1
0
0
0
0
1
0
0
3
0
2
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
1
0
2
3
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
1
2
0
0
4
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
1
1
0
1
0
0
1
1
1
2
1
3
0
0
2
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
3
0
0
0
0
0
0
2
0
0
0
2
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
2
1
0
2
0
1
3
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
2
7
2
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
3
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
3
4
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
2
0
0
0
2
0
2
0
0
2
0
2
2
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
1
2
4
0
0
0
0
0
0
2
1
3
0
0
0
0
0
0
0
0
0
0
2
0
4
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
2
0
3
0
0
0
0
1
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
3
0
0
3
1
1
0
1
0
3
0
0
1
0
0
1
2
0
0
1
0
0
0
4
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
1
1
2
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
2
1
0
2
0
0
0
0
0
1
0
2
0
3
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
1
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
1
0
0
2
7
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
2
1
0
1
0
1
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
1
0
0
0
2
0
0
0
0
1
0
3
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
2
0
0
2
0
0
0
7
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
2
0
0
2
1
0
0
1
0
0
2
2
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
2
3
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
1
0
2
0
2
0
1
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
4
0
0
0
0
1
1
2
1
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
2
1
2
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
2
1
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
2
0
0
1
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
1
0
0
0
0
1
0
0
3
0
0
0
2
2
1
0
0
0
0
0
0
2
0
0
0
0
1
1
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
2
2
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
1
0
5
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
5
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
2
0
0
0
0
2
0
2
0
0
0
4
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
4
3
0
1
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
1
0
1
0
2
1
0
0
0
0
3
0
2
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
2
0
0
0
0
0
0
0
1
2
0
1
0
0
0
1
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
2
1
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
1
0
1
0
0
1
0
0
0
2
0
2
1
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
2
0
5
0
0
0
3
0
0
1
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
2
2
0
0
0
0
1
0
0
0
1
3
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
2
0
0
1
0
2
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
1
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
2
2
0
0
2
0
2
0
0
0
0
0
0
4
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
2
2
0
0
1
0
0
1
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
1
2
0
1
0
2
0
0
0
0
1
1
0
0
2
0
0
2
0
5
0
0
0
0
0
0
0
2
0
0
0
0
0
2
3
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
13
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
1
2
1
2
0
0
0
0
0
0
0
0
0
1
3
0
0
0
1
0
0
2
1
0
0
0
0
0
2
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
1
2
0
0
0
2
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
3
0
2
0
1
0
2
0
15
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
1
1
2
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
2
0
5
1
3
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
2
0
3
0
1
0
0
1
0
0
0
0
0
2
0
2
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
4
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
2
2
0
1
2
2
1
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
2
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
3
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
4
0
3
0
2
1
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
3
1
0
6
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
1
1
2
0
1
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
2
0
0
1
0
2
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
7
0
0
0
1
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
1
2
0
0
0
0
1
0
1
2
1
2
1
1
0
1
0
0
0
2
0
0
1
0
0
3
0
0
0
0
0
2
2
0
0
2
0
0
0
5
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
5
0
0
1
0
1
0
3
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
1
0
2
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
2
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
8
1
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
2
0
1
0
2
0
2
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
1
0
0
0
0
0
2
1
1
3
2
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
3
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
2
0
0
1
1
0
1
0
1
3
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
3
0
0
2
1
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
2
2
1
1
0
1
0
0
2
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
2
0
2
0
2
1
1
0
0
2
2
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
1
1
0
2
0
0
0
0
0
0
2
2
0
2
0
1
0
0
0
1
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
5
0
0
0
0
0
0
1
0
2
0
0
0
1
1
0
0
0
1
0
0
0
2
3
2
2
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
3
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
1
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
6
1
1
0
0
3
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
1
2
0
2
1
0
1
0
0
2
0
0
4
0
1
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
2
0
2
4
0
0
0
1
0
0
0
0
0
0
0
1
2
2
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
2
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
1
1
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
2
3
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
4
0
0
0
1
2
0
0
0
0
0
0
3
0
0
3
0
0
1
3
6
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
2
3
0
1
1
0
2
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
2
2
1
0
0
3
4
0
2
0
0
0
0
0
0
0
0
0
0
0
0
5
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
3
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
1
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
4
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
4
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
1
0
2
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
5
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
2
1
0
0
1
0
2
1
2
0
1
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
1
0
2
2
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
1
2
0
2
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
1
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
1
0
0
1
0
0
0
1
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
1
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
1
0
4
0
0
0
0
0
0
0
2
0
0
1
0
1
1
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
1
2
0
0
1
0
0
0
0
0
1
2
2
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
2
0
0
0
0
0
0
0
1
6
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
2
3
0
0
2
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
2
0
0
0
2
0
1
2
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
2
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
5
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
7
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
3
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
1
6
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
3
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
2
0
1
2
0
0
0
0
2
0
0
1
2
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
4
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
1
1
0
1
2
0
6
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
1
0
0
0
0
0
0
2
1
0
2
0
0
1
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
4
1
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
1
0
2
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
1
1
0
0
0
2
0
1
2
2
2
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
1
0
2
5
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
2
0
4
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
2
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
1
0
0
2
1
0
0
0
0
2
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
4
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
1
0
1
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
2
0
0
0
0
0
1
2
0
1
0
1
0
0
0
0
0
0
1
0
2
0
1
0
0
1
2
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
2
0
0
1
2
1
0
0
0
0
1
0
0
0
2
0
0
1
0
0
4
0
1
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
3
1
0
0
0
1
1
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
2
2
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
3
2
1
3
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
2
0
0
0
4
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
1
0
3
1
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
1
3
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
1
0
1
0
0
2
0
0
5
2
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
2
0
0
2
1
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
2
0
2
0
0
2
2
3
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
2
0
0
3
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
2
0
2
0
0
0
2
0
0
0
2
3
0
0
0
1
0
0
6
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
2
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
1
0
0
0
2
0
0
0
1
3
0
0
1
0
0
0
0
2
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
1
0
1
0
0
1
3
1
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
1
0
2
1
0
1
0
0
0
0
0
0
2
0
2
2
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
2
0
1
2
2
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
2
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
1
4
0
0
2
0
1
0
1
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
3
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
2
0
2
1
2
0
2
0
0
2
2
2
0
0
0
0
3
2
0
0
2
2
0
4
2
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
2
0
1
0
0
0
2
0
0
1
2
2
0
0
0
0
0
0
0
0
0
3
1
0
2
0
2
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
1
1
0
0
0
3
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
1
0
3
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
5
0
0
3
1
0
0
3
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
1
2
0
2
2
1
1
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
1
0
3
0
0
0
0
2
0
0
3
0
0
0
0
1
2
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
3
0
2
3
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
2
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
3
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
2
2
1
2
0
1
0
0
1
0
0
1
0
0
0
0
1
0
5
0
0
0
2
1
0
0
0
0
3
0
0
0
0
0
0
0
0
1
1
1
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
3
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
1
0
3
1
2
0
0
0
2
2
0
0
0
0
1
2
0
1
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
6
0
0
0
0
0
0
2
0
0
2
1
2
1
0
0
0
1
2
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
1
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
3
2
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
2
4
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
3
0
0
0
0
0
0
0
1
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
2
6
0
0
0
0
0
2
0
0
0
3
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
3
0
1
0
2
0
0
0
0
1
0
0
2
0
0
2
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
1
0
0
0
0
1
2
0
0
0
1
0
0
0
3
0
0
2
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
2
0
1
3
0
1
0
0
0
1
0
2
1
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
2
0
0
0
1
2
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
1
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
2
0
3
0
3
0
0
0
0
0
0
1
0
2
0
2
0
0
2
0
2
2
0
0
2
0
1
0
2
0
0
0
0
2
0
0
9
0
2
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
4
1
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
1
0
1
5
1
0
0
0
0
1
1
0
0
1
0
1
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
2
0
2
2
0
0
2
0
0
0
0
0
0
0
0
2
3
2
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
1
2
0
1
0
1
0
0
1
0
0
0
0
0
0
1
1
2
2
2
1
0
7
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
3
0
1
0
1
0
0
3
2
0
0
0
0
2
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
2
0
0
0
0
2
0
3
0
0
0
0
0
3
0
0
2
0
0
0
0
1
0
0
3
4
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
6
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
2
0
0
0
2
0
0
0
2
2
2
3
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
2
0
1
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
5
0
0
0
0
1
1
0
2
2
0
2
0
4
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
2
2
3
2
0
2
0
2
0
0
0
0
0
0
0
2
0
0
2
1
2
1
2
0
0
1
0
1
1
2
0
2
2
0
0
0
2
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
1
1
0
0
0
0
1
0
2
1
1
0
2
0
0
0
3
0
0
0
0
0
0
0
0
4
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
1
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
2
0
5
0
1
2
0
0
2
3
0
0
2
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
1
2
2
0
0
0
2
2
1
0
0
0
0
0
2
2
2
0
0
5
0
0
0
0
0
0
1
1
0
1
0
2
1
2
0
2
0
3
1
0
0
0
1
2
0
0
1
0
0
0
4
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
1
0
2
1
2
1
0
0
0
0
0
1
1
0
2
0
0
0
0
0
1
0
2
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
1
1
0
0
0
1
0
1
0
2
0
0
1
0
2
0
0
0
0
0
0
0
2
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
5
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
1
0
0
1
0
0
0
2
0
0
2
0
1
2
0
0
1
0
0
0
0
0
3
1
0
1
0
0
0
1
0
0
2
4
0
0
0
1
2
0
0
2
0
1
2
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
2
4
0
0
0
2
0
1
0
3
0
3
0
1
0
3
0
0
0
2
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
2
0
0
2
0
0
2
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
1
0
0
0
4
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
1
3
0
0
0
0
1
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
2
0
0
2
0
0
0
1
0
0
0
3
0
0
1
1
0
0
0
0
1
0
0
3
0
0
0
1
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
1
1
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
1
1
0
1
0
0
1
1
0
1
0
0
0
2
1
0
1
0
2
0
0
0
2
0
0
3
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
2
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
2
2
2
0
0
0
3
0
0
0
0
1
0
1
1
0
2
0
0
0
0
0
0
0
1
1
3
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
1
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
1
0
2
1
0
0
1
1
0
0
2
0
0
0
0
2
2
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
2
3
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
2
0
2
2
2
2
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
2
1
0
0
1
2
0
0
0
0
0
1
0
3
0
2
0
0
0
0
0
1
1
2
1
0
0
0
0
2
0
0
0
0
1
1
2
2
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
2
0
2
1
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
2
0
2
0
3
2
0
0
0
1
0
0
0
3
0
0
0
1
2
1
2
2
1
0
0
0
0
4
0
0
2
1
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
4
0
1
0
0
0
0
0
2
0
0
0
0
0
0
3
2
0
0
0
0
1
0
0
0
1
1
2
0
2
3
0
0
0
0
0
2
0
0
0
0
0
0
0
4
0
0
0
2
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
3
0
0
0
1
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
4
2
0
0
0
0
0
0
0
2
0
1
2
1
0
2
2
0
1
0
2
0
2
1
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
2
0
0
3
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
1
0
0
1
2
3
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
2
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
3
0
0
0
0
0
2
0
0
1
2
0
0
2
2
1
0
0
0
0
0
0
1
1
2
0
0
0
2
7
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
1
3
1
1
0
9
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
3
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
1
1
2
2
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
2
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
3
0
0
1
0
0
5
0
0
0
1
2
2
0
1
0
0
0
1
3
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7
0
1
1
1
0
1
0
1
0
5
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
1
0
0
1
2
2
3
4
2
0
1
0
0
2
1
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
5
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
1
0
0
0
2
0
1
0
0
0
2
1
0
0
0
1
1
0
0
0
1
0
2
0
2
0
0
1
0
0
0
2
0
2
0
2
0
0
0
0
0
1
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
1
0
0
0
0
0
0
0
1
3
0
0
0
2
1
0
2
0
3
2
1
0
0
3
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
1
0
5
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
1
4
0
3
0
2
0
0
0
1
0
0
1
0
0
2
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
3
0
0
0
2
0
2
0
1
0
0
2
2
0
0
1
0
0
0
1
1
0
0
0
2
0
0
0
1
0
0
0
3
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
2
2
0
2
0
0
0
2
0
0
0
1
1
2
0
2
0
2
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
2
0
6
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
2
1
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
1
2
0
0
1
0
0
3
0
0
0
2
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
2
2
2
0
0
0
0
0
1
2
3
0
0
0
0
1
0
1
0
0
2
1
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
1
0
2
2
0
0
0
2
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
1
0
0
0
2
3
1
0
0
0
1
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
1
0
0
2
0
2
0
1
0
0
0
0
0
2
2
0
0
3
0
2
0
1
2
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
1
3
0
0
1
0
0
1
0
0
0
0
1
2
0
0
0
0
1
0
1
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
2
0
1
1
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
1
1
0
2
0
1
0
1
1
2
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
3
0
0
1
0
0
1
0
1
0
1
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
3
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
2
1
0
0
2
0
0
0
0
2
2
1
0
0
1
0
0
1
0
0
0
0
0
3
1
0
0
2
0
0
0
2
0
2
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
2
0
0
1
1
0
3
0
2
0
1
0
0
0
0
1
0
1
0
0
0
2
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
4
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
3
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
2
1
2
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
5
0
0
1
1
0
2
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
2
0
0
0
0
0
1
2
0
0
0
2
1
1
0
0
2
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
4
0
0
0
1
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
1
0
0
0
0
1
0
0
0
1
0
4
1
1
0
0
0
0
0
1
0
0
2
1
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
3
0
2
0
3
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
1
0
0
5
1
0
1
0
2
1
3
0
0
2
0
0
0
0
3
0
0
0
0
0
0
1
2
1
0
0
2
0
1
0
2
0
0
0
0
2
0
1
1
2
0
0
0
0
0
2
0
3
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
1
1
0
1
0
2
1
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
3
0
2
0
1
0
0
0
0
2
6
0
0
0
0
0
1
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
6
0
1
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
5
4
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
3
0
1
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
3
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
3
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
3
0
0
1
1
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
7
2
0
0
1
5
0
0
0
2
2
0
0
0
2
0
0
2
0
0
0
0
0
2
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
1
0
0
0
0
2
0
2
2
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
4
0
0
0
1
0
0
3
0
1
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
4
0
1
0
0
0
0
1
2
0
1
1
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
2
2
0
0
1
0
0
1
0
0
0
3
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
1
0
1
0
0
0
0
0
0
4
0
0
4
0
1
0
0
0
0
0
0
0
1
0
1
0
1
2
1
0
0
0
0
0
0
0
1
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
2
1
1
0
2
0
0
0
0
0
0
0
0
0
7
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
2
1
2
2
2
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
3
1
0
1
0
0
2
0
0
0
0
0
0
0
3
0
0
0
2
0
1
0
2
1
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
9
0
0
0
2
0
4
0
1
0
0
0
0
0
2
1
0
1
0
2
0
0
0
4
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
6
0
0
0
0
0
0
0
1
0
3
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
1
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
2
0
2
0
0
0
0
0
0
2
0
0
0
3
0
1
2
0
0
2
0
3
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
2
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
2
0
0
0
0
2
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
4
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
2
0
0
0
0
2
2
2
0
1
0
2
0
0
1
0
0
2
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
1
0
0
1
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
1
0
1
2
0
1
0
0
0
1
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
3
0
0
0
0
1
0
1
0
0
0
1
2
1
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
1
0
0
1
0
0
0
0
2
1
0
1
0
1
0
1
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
4
1
0
2
1
0
0
1
0
0
1
2
0
0
0
0
0
0
2
2
0
0
2
0
2
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
3
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
2
2
0
0
0
1
0
0
0
1
0
2
0
0
2
2
0
2
0
0
0
1
0
0
0
2
5
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
5
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
4
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
1
1
0
1
0
1
1
2
0
2
0
0
3
2
1
0
2
0
0
0
4
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
1
3
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
2
1
0
3
0
1
0
0
2
0
0
1
0
2
0
0
0
0
1
0
2
0
0
1
1
0
0
0
2
1
1
0
0
0
1
0
0
0
1
0
1
0
0
2
0
0
1
0
0
0
0
0
1
2
0
0
0
2
1
2
0
1
1
0
0
0
1
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
1
0
1
0
0
1
0
0
0
2
0
1
1
0
0
2
0
0
2
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
5
0
0
0
2
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
3
1
2
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
1
0
0
0
2
1
0
0
0
0
0
2
2
0
0
0
0
0
0
1
1
1
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
1
1
2
0
0
0
0
3
0
0
0
0
1
0
0
0
2
1
1
0
1
0
1
0
0
0
4
1
0
0
0
0
0
2
1
1
0
3
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
6
0
2
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
3
1
0
0
0
0
0
0
1
0
0
0
0
2
1
0
2
0
2
2
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
2
2
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
1
1
0
0
0
0
0
1
2
2
0
0
0
1
1
0
0
0
1
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
2
0
0
0
3
1
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
4
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
2
0
0
0
2
0
0
0
0
0
1
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
5
0
0
0
0
0
2
0
0
0
1
0
0
1
0
1
0
1
0
1
0
0
0
2
1
0
0
2
0
3
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
1
1
0
2
0
2
0
0
0
0
0
0
0
0
1
2
1
0
0
0
4
0
0
0
0
0
3
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
2
0
5
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
3
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
4
1
0
0
0
0
2
2
0
0
0
0
1
0
3
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
4
0
0
2
0
0
0
0
0
1
1
0
0
1
1
0
3
0
0
1
0
0
0
1
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
4
2
0
2
0
0
0
2
2
0
0
0
0
0
2
0
0
0
1
0
2
1
0
1
0
0
0
2
0
0
0
2
0
0
0
1
2
0
1
0
0
0
1
0
2
0
0
0
0
1
1
0
2
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
3
0
0
0
2
1
0
0
1
0
0
0
1
0
0
2
3
2
0
0
0
0
1
0
0
0
5
0
0
0
1
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
8
0
0
0
0
1
0
2
0
1
2
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
2
1
0
0
0
0
2
0
0
0
1
2
0
0
0
0
3
2
0
0
0
0
0
0
0
2
0
2
0
0
2
2
0
0
0
1
0
0
1
0
2
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
3
0
3
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
2
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
4
2
11
0
0
3
1
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
3
0
0
0
0
0
1
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
5
0
0
2
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
5
0
0
0
0
1
0
0
0
4
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
3
0
0
2
0
0
0
0
0
0
3
1
2
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
2
1
0
1
2
0
1
0
0
1
0
0
1
0
0
0
3
0
0
1
0
0
0
0
2
10
0
2
0
0
0
0
0
0
0
2
0
2
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
1
1
1
3
0
0
0
2
1
0
0
0
0
1
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
2
6
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
3
0
0
0
1
0
0
0
0
0
1
2
0
1
0
8
0
0
0
0
0
1
1
0
1
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
2
1
0
2
0
0
0
3
0
0
0
2
1
0
0
2
0
0
0
0
1
0
1
0
2
0
0
0
0
0
4
1
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
2
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
3
0
0
0
0
1
0
0
0
1
0
0
0
2
0
2
2
1
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
1
2
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
2
0
0
1
2
0
0
0
0
0
1
0
0
3
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
2
0
1
0
0
0
0
0
1
1
2
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
2
0
0
2
7
0
0
0
0
0
2
0
1
0
1
0
1
0
0
0
0
0
1
1
1
3
3
1
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
1
1
2
0
4
3
0
0
0
0
0
1
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
1
1
0
0
1
2
0
0
0
0
0
1
0
0
1
0
0
3
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
3
1
0
0
1
0
0
0
1
0
0
0
0
2
3
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
4
0
0
2
1
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
2
0
2
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
3
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
1
2
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
1
0
0
0
2
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
1
0
2
0
0
2
1
0
0
0
2
0
0
0
3
0
0
1
0
0
0
0
2
1
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
3
1
0
2
0
1
0
0
0
0
0
2
0
0
0
3
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
3
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
2
2
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
1
2
3
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
3
0
1
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
2
1
2
0
0
0
0
0
0
2
2
0
0
0
1
1
0
0
0
0
0
1
1
0
1
0
0
0
1
2
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
2
0
1
0
0
2
0
2
0
1
2
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
2
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
2
3
0
0
3
1
2
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
1
1
1
2
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
5
1
0
0
1
0
0
0
0
0
0
0
0
0
3
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
2
0
0
3
0
1
0
0
0
1
0
2
0
0
1
1
1
2
5
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
1
0
0
2
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
2
0
1
0
1
0
0
0
0
1
0
0
0
1
3
1
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
1
0
2
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
1
0
0
0
1
0
2
0
0
0
1
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
3
0
2
0
0
0
0
3
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
1
5
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
3
0
1
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
1
3
0
0
0
0
0
0
2
1
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
1
1
0
0
1
0
0
0
0
2
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
2
1
2
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
2
0
0
0
1
0
0
0
2
0
2
2
1
0
4
0
0
0
2
0
1
0
0
0
0
1
1
0
0
0
0
0
2
0
0
1
0
1
0
2
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
3
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
1
2
2
0
1
1
0
0
0
0
0
0
1
0
6
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
2
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
1
0
2
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
2
1
2
0
0
0
0
2
2
0
0
0
1
0
0
0
2
0
2
0
0
1
0
0
1
0
2
0
1
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
2
0
0
2
2
0
1
0
2
0
2
1
0
4
1
1
0
1
1
0
2
2
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
1
0
0
0
0
0
0
0
0
3
0
1
0
2
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
2
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
2
0
0
0
1
2
0
3
0
1
2
3
0
0
2
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
1
1
0
0
0
2
0
0
0
0
1
2
0
2
2
0
0
1
0
0
0
1
0
3
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
3
0
0
0
0
0
1
0
2
0
1
2
0
0
1
0
1
0
0
2
0
0
0
0
1
1
2
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
2
1
0
0
0
0
0
1
1
0
0
1
2
0
1
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
4
0
0
0
0
2
0
1
2
0
2
1
0
0
0
0
0
0
0
2
1
0
0
0
4
0
0
0
0
1
0
0
2
0
0
0
0
0
5
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
5
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
1
0
1
0
1
1
2
0
2
1
2
0
1
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
2
0
0
0
0
2
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
3
1
0
0
0
0
2
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
2
1
2
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
7
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
3
0
0
0
0
0
2
0
1
0
0
0
1
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
1
0
0
1
2
0
0
0
0
0
2
0
2
0
1
1
0
0
0
4
0
0
0
0
2
0
0
1
0
0
1
0
2
0
3
0
0
2
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
3
1
0
0
1
0
1
0
0
1
2
0
0
2
2
0
2
0
0
2
0
0
0
0
1
0
3
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
1
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
2
0
0
1
0
0
1
1
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
5
0
0
2
0
0
0
1
1
2
0
3
0
0
0
1
0
0
0
1
0
0
2
1
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
1
2
0
0
0
0
1
0
0
0
2
0
0
2
2
1
0
0
2
0
2
0
0
0
2
0
0
1
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
3
1
3
0
0
0
0
0
0
0
0
1
0
0
2
2
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
1
0
2
0
2
0
1
0
1
0
0
0
1
0
0
1
2
0
0
0
2
2
2
0
0
0
0
0
5
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
2
2
0
0
0
0
1
2
1
2
3
0
1
0
0
3
0
1
0
0
2
0
0
2
4
0
0
0
0
0
0
2
0
1
0
0
0
2
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
1
0
1
2
2
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
2
0
1
2
0
0
0
0
2
1
0
0
2
0
0
1
5
0
0
0
0
0
1
0
0
0
2
1
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
1
0
0
0
0
3
1
0
2
2
0
0
0
0
2
0
0
0
0
1
0
2
0
2
0
0
0
1
0
2
1
0
0
0
0
1
0
0
1
1
2
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
2
2
2
0
0
2
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
2
1
1
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
3
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
2
3
1
0
0
0
1
1
0
0
1
0
3
3
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
2
0
0
1
0
0
2
0
0
0
1
0
0
2
0
2
1
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
2
2
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
1
0
2
5
0
1
1
1
1
0
2
0
0
0
0
0
1
0
0
1
0
0
2
2
0
1
0
0
0
0
0
0
0
1
1
3
0
0
0
1
0
0
2
0
0
1
0
0
0
0
2
0
0
2
0
0
0
2
2
2
2
2
0
0
2
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
4
1
0
1
0
0
0
0
0
0
0
5
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
1
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
1
2
0
0
0
2
0
0
0
0
0
0
1
0
3
2
3
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
2
0
6
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
4
0
0
0
0
0
0
1
1
3
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
2
2
1
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
2
1
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
2
0
4
0
0
0
0
0
0
0
0
2
0
1
0
1
0
4
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
2
0
0
1
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
1
0
0
0
0
3
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
2
1
0
0
0
0
2
0
2
2
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
2
1
0
0
2
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
2
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
1
0
1
0
2
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
5
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
1
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
3
0
1
0
2
1
0
2
0
2
1
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
4
0
2
0
0
0
2
2
0
0
0
0
1
5
1
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
1
0
0
0
1
4
1
2
0
0
2
0
6
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
1
0
0
0
1
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
9
2
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
1
1
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
2
0
0
0
6
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
3
0
1
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
1
1
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
2
2
0
1
0
0
0
1
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
2
0
2
0
0
0
0
0
0
0
4
2
0
1
0
0
0
1
0
1
1
0
1
0
1
0
0
2
0
0
0
0
0
0
2
3
1
0
0
0
0
2
0
1
1
1
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
2
1
0
0
0
0
0
0
9
1
0
0
0
0
0
1
0
0
1
0
0
2
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
3
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
3
1
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
3
0
1
0
0
0
0
2
0
1
0
0
1
2
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
4
1
0
0
0
0
0
0
2
1
2
1
2
2
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
1
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
2
2
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
3
0
2
0
1
2
2
0
3
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
3
0
2
3
0
0
0
1
0
1
0
0
0
2
0
2
0
0
0
0
0
0
2
0
1
1
0
0
1
0
3
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
3
0
0
0
2
2
0
0
4
1
0
0
0
2
0
0
1
0
0
0
2
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
4
0
0
2
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
2
0
1
0
2
3
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
2
0
2
0
0
0
0
0
0
2
0
0
1
2
0
2
0
0
0
0
1
0
1
0
0
0
0
0
4
0
1
2
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
2
2
0
0
2
0
0
2
0
0
0
0
0
0
2
1
1
0
0
0
0
0
1
0
2
2
0
0
1
0
0
0
0
0
0
1
2
1
0
0
0
0
3
0
0
0
0
0
2
0
1
1
0
0
0
0
1
2
0
0
0
1
0
0
2
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
1
0
2
1
1
3
1
0
0
0
0
2
1
2
1
0
0
1
2
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
3
0
0
2
2
0
0
0
1
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
7
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
3
0
0
0
1
2
1
1
0
1
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
2
2
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
2
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
2
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
1
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
4
8
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
3
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
1
0
0
0
2
0
0
2
0
2
0
1
2
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
1
0
0
0
2
0
2
2
0
0
0
2
0
1
0
0
1
0
2
0
2
0
3
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
1
2
0
3
0
2
1
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
2
0
0
0
0
0
4
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
2
0
3
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
2
0
2
0
1
1
0
1
0
0
2
0
0
0
0
0
0
2
5
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
2
0
1
0
1
0
0
0
1
1
0
2
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
1
0
1
1
0
0
0
0
0
0
3
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
1
1
0
0
0
7
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
1
1
1
0
0
2
5
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
2
0
2
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
2
0
2
0
0
4
0
1
4
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
1
3
0
0
0
0
0
1
0
0
0
0
0
0
0
1
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
7
1
0
2
0
0
0
0
0
1
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
1
0
0
2
0
0
0
0
2
2
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
2
0
0
0
0
2
0
1
0
0
0
2
0
0
0
1
0
0
1
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
2
1
2
2
0
1
0
0
2
0
0
0
0
0
0
1
1
1
0
1
0
0
0
2
2
2
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
2
0
0
0
0
0
0
2
2
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
2
0
2
0
0
1
0
0
2
0
0
1
0
0
2
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
4
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
3
0
1
0
0
0
3
1
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
1
2
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
4
0
0
0
0
0
3
1
0
1
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
2
4
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
1
1
1
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
3
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
2
1
2
0
0
0
0
2
1
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
2
2
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
1
0
1
0
0
1
0
3
0
0
0
0
0
0
0
1
2
2
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
3
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
3
1
1
0
0
3
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
3
0
0
0
0
0
3
0
0
0
2
1
0
0
0
2
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
1
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
1
2
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
10
2
0
0
0
2
0
0
1
0
2
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
2
0
1
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
1
2
0
0
0
0
1
0
2
0
0
0
1
0
3
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
1
2
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
2
2
0
1
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
2
0
1
0
0
0
0
1
0
0
2
2
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
2
0
1
0
3
0
3
0
0
0
0
0
1
1
0
0
2
2
0
0
0
1
0
2
0
1
4
1
0
0
0
0
0
0
1
0
5
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
4
1
1
0
3
2
0
0
0
2
0
0
0
0
3
3
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
2
1
1
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
3
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
2
0
0
4
0
0
0
0
0
2
1
0
0
0
0
0
2
0
1
1
3
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
3
0
2
1
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
3
0
1
0
0
0
0
1
0
6
1
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
15
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
1
2
0
0
7
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
12
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
3
0
1
0
0
0
0
0
0
0
0
4
0
2
0
2
0
0
0
0
0
0
0
2
0
0
1
1
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
1
3
0
2
0
2
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
3
0
1
0
2
0
0
1
0
0
1
0
0
1
2
0
0
11
0
0
0
0
0
0
0
0
1
2
0
2
0
1
2
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
2
0
1
0
5
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
3
0
1
5
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
4
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
3
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
4
1
1
1
0
1
1
2
0
1
0
0
1
2
0
0
1
0
0
0
2
1
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
1
1
5
2
0
0
0
0
0
0
0
0
1
0
0
0
0
3
1
1
0
0
1
1
0
0
1
0
0
0
0
0
1
0
4
0
0
0
2
1
0
0
1
0
0
2
0
0
0
1
0
2
0
0
0
0
0
1
0
4
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
1
0
0
0
0
2
2
1
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
1
2
5
2
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
2
1
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
1
0
1
0
0
1
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
2
0
3
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
1
0
0
0
1
0
0
0
0
2
0
0
2
1
0
0
0
0
2
0
2
1
0
0
0
0
0
1
0
1
1
0
0
1
0
3
3
3
0
0
0
0
0
0
4
0
0
0
1
0
2
2
1
0
0
0
3
0
1
0
0
0
0
0
0
3
0
0
0
2
2
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
1
1
2
0
0
1
0
0
0
0
1
0
2
0
0
0
2
0
0
0
2
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
2
0
3
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
2
2
1
0
0
0
0
0
2
0
0
1
0
0
3
0
0
0
0
2
3
1
0
1
0
2
0
0
3
0
0
0
5
0
3
0
0
2
0
1
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
3
0
2
0
2
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
3
0
1
0
0
3
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
2
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
1
0
1
2
1
0
0
6
0
0
0
0
2
0
0
0
0
1
1
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
3
2
0
0
0
2
0
0
0
0
0
1
0
1
0
0
2
0
0
1
2
0
0
0
0
0
1
2
0
0
2
0
3
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
3
1
2
2
0
0
0
2
0
0
0
1
0
1
0
0
0
0
1
0
0
0
2
2
0
2
2
2
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
3
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
1
2
2
0
0
0
0
0
0
1
1
0
3
0
0
0
0
1
1
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
5
0
2
0
1
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
1
0
1
0
0
0
0
2
0
4
0
0
2
0
0
0
4
2
0
1
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
2
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
4
0
2
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
1
1
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
1
1
4
0
2
0
0
0
0
2
2
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
1
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
1
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
13
0
0
0
0
2
0
2
0
2
0
0
4
0
0
2
2
0
0
1
1
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
2
0
0
2
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
5
3
2
0
1
1
0
0
0
1
0
3
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
5
2
0
2
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
2
0
1
2
0
0
2
0
0
1
0
1
0
0
0
0
0
0
2
1
0
0
2
1
0
0
0
0
0
0
1
0
0
2
0
0
1
1
0
1
2
1
2
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
1
1
2
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
1
1
1
1
1
0
0
0
0
0
0
0
0
2
0
0
0
2
1
1
0
0
0
2
1
0
0
0
0
0
4
2
6
2
0
1
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
1
1
0
2
2
0
1
0
2
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
2
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
8
0
0
0
0
0
0
0
2
0
0
2
3
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
2
0
2
0
1
0
1
0
2
0
3
1
0
0
1
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
3
0
0
0
2
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
3
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
1
0
0
0
0
0
2
0
2
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
2
2
0
0
0
2
1
0
1
0
1
0
0
0
1
2
0
0
0
0
0
1
0
0
1
0
0
2
1
0
0
0
1
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
4
0
0
0
1
0
2
0
0
1
1
0
0
1
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
2
0
0
2
0
2
0
0
0
0
1
0
0
0
2
0
1
0
0
0
2
0
0
2
1
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
1
2
0
4
0
1
0
0
1
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
1
2
3
1
0
2
2
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
2
2
0
3
0
0
0
0
0
7
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
2
0
0
1
0
0
0
2
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
2
4
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
1
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
3
0
0
0
1
0
0
0
2
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
3
2
0
0
1
2
0
2
0
0
2
0
0
0
0
0
0
0
1
0
1
0
2
0
1
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
2
0
2
0
0
1
1
0
0
0
0
0
3
0
0
4
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
6
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
2
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
2
1
1
2
0
0
0
0
2
1
0
0
0
0
0
0
0
5
0
0
0
0
0
0
1
0
0
2
0
1
0
2
3
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
1
0
6
0
0
0
2
3
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
6
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
2
2
2
0
0
0
2
0
3
0
1
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
3
0
0
0
0
0
2
0
1
0
0
0
2
0
1
1
0
0
3
0
0
0
4
0
0
0
0
2
2
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
2
3
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
4
4
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
3
0
0
0
4
0
0
1
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
1
3
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
3
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
2
1
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
3
0
3
0
1
3
0
0
2
2
1
0
0
0
0
2
0
0
0
0
2
2
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
2
2
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
3
1
0
0
0
0
2
0
0
0
1
0
2
0
0
0
2
2
0
2
1
0
2
2
0
0
0
0
2
1
0
0
0
0
1
4
0
0
0
0
0
0
0
9
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
2
2
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
1
0
0
3
0
0
0
0
0
2
0
0
2
0
1
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
3
2
0
0
0
0
1
0
0
0
2
0
1
0
2
0
2
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
1
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
2
2
0
1
1
0
0
0
0
0
0
2
0
0
3
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
4
2
1
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
1
0
1
0
1
0
0
2
3
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
6
0
1
3
0
0
2
2
2
1
0
0
0
1
0
1
1
0
1
0
0
2
1
3
0
1
2
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
2
1
3
0
0
1
0
2
2
0
2
1
0
1
0
2
0
0
0
0
1
0
0
1
0
0
2
3
0
0
0
0
0
1
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
4
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
1
0
8
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
2
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
1
4
1
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
2
2
1
0
0
2
0
0
1
2
0
0
0
1
0
2
0
2
1
0
0
0
0
0
1
1
1
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
3
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
3
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
2
1
0
0
1
0
0
0
0
2
0
0
0
1
0
0
2
0
0
2
0
0
2
0
0
0
1
0
0
0
0
3
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
4
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
4
0
0
0
0
0
0
0
2
0
2
0
0
0
0
3
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
2
1
9
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
8
1
0
1
0
0
0
2
0
2
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
3
0
0
0
0
11
0
1
0
0
0
0
0
0
0
0
1
0
1
0
2
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
3
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
2
0
0
0
1
3
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
2
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
4
2
0
2
0
0
0
1
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
1
0
1
0
0
2
4
0
0
0
0
0
1
0
1
3
0
0
1
8
1
0
2
0
0
2
2
2
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
3
0
0
3
0
1
0
2
0
0
1
0
1
0
0
0
2
0
0
0
0
1
0
2
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
4
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
2
0
0
0
0
1
0
0
0
1
2
0
1
0
0
0
2
0
0
2
0
0
0
0
3
1
0
1
0
2
0
0
1
0
0
0
2
0
2
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
1
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
1
7
0
0
0
0
0
0
0
0
0
5
0
0
1
0
0
2
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
5
0
0
0
0
0
0
0
2
0
1
1
1
0
2
3
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
3
0
0
0
2
3
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
2
1
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
5
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
1
1
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
2
0
0
3
1
0
2
1
0
0
1
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
1
0
2
4
0
0
5
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
2
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
2
2
2
2
0
1
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
3
1
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
1
2
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
1
1
0
0
0
2
2
0
1
0
0
0
0
0
0
0
2
0
0
5
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
3
0
1
0
0
0
2
0
1
0
0
0
0
1
0
0
0
1
0
2
2
0
1
0
0
0
2
0
1
0
2
0
0
0
1
1
0
0
0
0
0
1
0
2
1
1
0
0
0
2
0
0
2
0
0
0
4
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
2
3
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
2
0
0
2
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
3
0
1
0
2
0
1
0
1
1
0
0
1
1
0
0
0
2
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
1
5
0
2
0
0
1
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
1
1
0
1
1
0
3
0
0
1
2
1
2
1
1
0
4
0
1
2
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
2
0
0
1
0
2
2
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
2
1
2
0
2
0
0
0
0
0
1
2
0
0
1
0
0
0
0
1
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
2
1
1
2
1
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
1
2
2
0
6
0
0
0
0
0
0
0
2
2
0
0
0
0
0
5
0
0
1
0
0
0
2
2
0
1
0
1
0
1
0
0
5
0
0
0
2
1
0
0
1
2
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
1
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
3
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
1
0
6
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
3
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
8
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
5
2
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
2
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
2
0
1
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
1
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
2
3
0
0
1
1
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
1
0
2
0
2
0
2
0
0
0
2
0
1
0
0
0
0
0
4
0
2
0
0
0
2
0
0
1
0
0
1
0
1
1
0
1
0
0
1
0
0
2
0
0
0
1
0
0
0
1
0
0
0
2
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
3
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
1
0
3
0
0
0
1
0
0
0
0
0
0
0
0
1
1
3
0
2
0
2
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
2
1
1
0
1
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
3
0
0
2
0
0
0
0
3
0
0
0
0
2
2
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
1
0
0
0
2
0
5
0
0
2
0
2
2
0
3
0
1
2
0
0
0
0
2
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
4
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
1
0
0
0
2
0
2
2
2
0
0
0
0
0
1
0
0
1
0
0
0
0
3
0
1
0
2
2
0
3
1
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
3
3
2
0
0
3
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
1
0
0
1
1
0
0
0
1
1
1
2
0
0
1
0
0
3
0
0
2
0
0
0
0
0
2
0
0
3
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
1
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
1
0
0
0
1
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
2
0
0
0
0
2
0
3
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
5
0
1
0
0
1
2
0
0
0
0
2
0
1
2
0
0
1
2
2
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
5
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
1
0
0
2
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
2
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
4
2
0
0
0
0
1
3
2
1
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
1
0
0
1
4
0
0
0
0
2
0
0
0
2
2
2
0
0
2
0
0
2
1
0
1
0
0
0
2
0
0
0
0
0
0
2
0
1
2
2
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
3
1
0
0
0
0
1
5
0
0
0
2
0
0
0
0
2
1
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
0
0
0
9
2
0
0
0
0
2
0
0
0
0
4
0
0
0
0
2
0
1
0
2
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
2
0
0
1
0
0
1
0
0
0
1
0
1
0
0
1
2
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
3
9
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
1
0
1
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
12
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
4
0
0
0
1
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
1
0
1
1
2
0
0
0
0
2
0
12
0
0
0
0
1
0
2
0
4
0
0
0
1
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
5
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
2
0
0
3
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
3
0
6
0
0
0
1
0
1
0
0
2
3
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
3
0
0
0
0
2
2
1
0
0
0
0
0
1
3
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
2
0
0
0
0
0
0
1
6
2
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
1
0
2
0
0
2
0
0
0
1
0
0
2
6
0
0
2
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
3
4
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
1
0
0
2
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
1
1
0
1
0
0
2
0
0
0
0
0
2
0
0
3
0
3
0
2
0
2
0
0
2
0
0
4
2
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
1
2
0
0
0
0
1
0
2
2
2
0
0
1
0
2
1
0
0
0
1
0
0
2
0
0
0
2
0
0
1
0
2
1
3
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
2
3
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
4
2
1
0
0
0
2
2
1
0
0
0
2
0
0
1
0
0
0
0
2
1
0
0
2
1
0
0
0
0
0
1
0
2
1
0
0
1
0
5
1
0
0
0
0
0
2
0
0
0
0
1
2
1
1
0
0
3
0
0
0
0
1
0
0
0
0
2
0
0
2
0
1
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
2
2
0
2
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
2
0
2
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
2
3
1
2
1
0
0
2
2
0
1
0
5
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
1
0
2
4
1
0
1
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
1
0
1
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
1
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
3
0
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
2
2
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
1
0
2
0
0
1
0
1
0
0
2
2
0
0
2
0
0
1
0
2
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
5
0
1
2
0
0
2
0
1
3
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
3
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
2
1
1
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
2
0
0
0
2
0
0
0
0
2
0
0
1
0
0
2
0
0
4
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
2
0
0
0
2
0
0
2
0
0
2
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
1
1
0
1
0
0
2
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
6
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
1
0
0
2
0
0
6
0
0
0
0
0
0
1
1
1
0
0
2
0
3
2
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
2
1
0
0
2
2
0
3
0
0
1
0
2
0
1
0
0
1
0
1
1
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
3
0
2
0
3
0
0
0
0
1
0
0
2
1
0
0
0
0
2
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
7
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
4
0
2
2
0
0
0
0
2
0
0
0
2
0
0
2
2
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
1
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
2
2
0
0
2
2
0
0
0
0
5
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
2
1
0
0
0
0
2
0
4
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
4
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
3
0
0
2
2
2
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
1
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
1
0
2
0
0
1
0
2
0
0
0
0
0
1
0
0
1
3
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
1
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
2
2
0
1
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
3
0
0
0
0
1
2
0
1
0
2
0
0
0
0
0
0
3
0
2
1
2
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
3
0
2
0
0
0
0
2
0
0
1
0
1
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
3
0
0
2
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
1
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
2
0
0
0
1
0
2
0
4
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
3
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
2
0
0
0
2
1
0
0
1
0
0
2
0
0
0
1
1
0
0
0
2
0
0
0
3
0
0
0
0
0
0
2
0
0
2
9
0
0
2
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
1
0
0
0
0
2
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
1
0
0
0
2
0
1
2
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
3
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
2
0
0
0
2
1
6
3
0
0
1
0
0
0
0
2
0
0
0
2
0
0
2
2
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
2
0
0
0
2
1
1
0
0
0
0
1
2
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
1
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
1
1
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
4
1
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
3
0
0
0
2
0
2
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
2
2
0
1
0
0
0
0
0
0
2
0
3
0
0
0
0
2
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
2
2
0
2
0
3
0
0
4
0
0
1
0
1
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
2
0
0
0
0
0
2
0
0
0
0
1
0
2
3
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
3
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
2
0
0
1
0
0
3
0
0
2
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
2
0
0
3
3
0
0
0
1
1
0
0
2
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
2
0
1
0
0
0
1
0
1
1
0
0
2
1
2
0
0
1
0
1
0
0
0
2
3
0
0
0
0
2
4
1
2
2
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
2
0
0
2
0
1
2
0
0
1
2
0
2
0
1
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
6
2
2
0
0
0
2
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
10
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
4
2
1
0
0
1
0
0
0
0
0
0
1
0
0
2
0
2
0
0
1
0
0
0
0
1
0
0
2
1
0
1
1
0
2
0
0
0
0
0
2
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
1
3
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
6
0
0
0
2
0
0
0
2
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
1
0
0
1
3
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
1
0
0
1
0
2
1
3
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
3
2
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
1
1
2
0
2
5
0
2
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
2
0
0
1
0
0
1
0
2
0
1
0
0
0
0
0
1
1
0
0
2
2
0
0
0
2
3
0
2
2
0
0
0
0
0
3
0
0
0
4
1
0
0
0
0
2
0
0
0
0
0
1
2
2
0
0
0
0
1
1
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
4
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
1
0
1
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
2
2
2
0
0
1
0
2
0
1
1
0
2
0
1
0
0
2
0
2
1
0
0
2
0
0
0
2
0
0
0
0
0
1
2
0
0
2
2
0
0
3
0
3
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
4
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
1
0
0
0
2
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
2
2
0
2
0
0
0
3
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
2
0
0
2
2
1
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
2
0
0
2
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
8
1
0
2
0
2
0
0
5
0
2
0
1
2
0
0
2
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
1
1
1
0
0
1
0
0
1
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
2
1
0
0
2
0
2
0
0
2
0
1
3
1
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
2
1
0
0
2
0
0
0
2
2
0
2
0
1
0
0
1
0
1
0
0
0
0
0
1
2
0
0
13
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
6
0
0
2
1
0
2
1
0
0
0
0
1
1
0
0
3
0
0
0
0
0
0
0
0
0
0
2
2
2
0
3
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
2
0
0
0
0
2
3
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
2
0
0
0
0
2
3
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
7
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
2
1
0
0
0
2
0
2
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
3
0
0
0
1
1
0
2
0
3
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
2
8
0
0
0
0
8
3
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
3
3
0
0
0
0
0
0
2
0
6
2
0
2
0
2
1
0
0
0
0
0
0
0
1
0
2
0
2
3
2
1
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
1
0
0
1
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
2
0
0
0
1
0
0
0
1
0
0
0
0
0
2
1
0
0
2
0
0
2
0
0
2
1
0
2
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
2
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
3
1
0
0
0
0
2
0
1
0
0
0
0
2
0
2
0
0
3
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
1
1
0
1
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
7
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
1
0
1
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
3
0
1
0
0
0
0
0
0
0
0
2
0
0
2
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
4
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
1
1
3
0
0
3
0
0
0
0
2
0
0
0
3
0
2
0
0
0
1
0
0
0
0
2
0
0
0
3
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
2
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
3
2
0
2
0
2
1
2
0
2
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
1
4
0
1
5
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
1
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
1
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
1
1
0
0
4
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
1
0
1
0
1
0
0
4
0
1
0
2
1
1
1
1
1
0
0
1
0
0
1
0
0
0
2
1
2
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
1
0
3
1
3
0
0
0
0
1
0
2
1
1
0
0
2
0
0
0
1
2
0
0
0
0
1
0
0
3
0
0
2
2
0
0
2
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
2
0
0
1
0
0
2
0
0
1
0
0
0
1
1
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
3
1
0
1
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
1
1
2
1
0
0
0
0
2
0
0
0
4
0
1
0
2
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
2
0
1
0
2
0
2
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
4
0
0
0
0
1
0
0
0
2
0
0
3
0
2
0
0
0
3
3
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
2
0
2
0
1
0
3
1
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
1
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
2
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
3
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
8
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
1
0
2
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
2
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
1
0
2
0
1
0
0
1
0
0
2
0
0
0
3
2
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
2
2
0
0
0
2
0
2
0
2
0
0
2
0
0
0
0
4
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
3
0
0
0
0
1
0
1
0
0
0
2
1
0
0
0
0
0
0
2
1
0
0
1
2
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
2
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
1
2
0
2
0
0
0
0
1
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
2
3
0
0
0
1
0
0
0
0
1
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
6
0
0
2
0
0
0
0
0
0
0
0
3
0
2
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
4
2
0
0
0
0
0
2
0
2
0
1
1
0
0
0
2
0
0
0
2
0
0
2
1
0
1
1
2
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
3
1
2
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
3
1
0
0
1
0
0
0
0
0
3
0
1
0
0
3
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
1
1
0
1
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
1
0
0
0
0
1
2
0
0
6
0
1
1
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
2
1
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
2
2
1
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
2
1
0
0
2
1
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
1
4
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
2
0
0
0
4
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
2
2
0
0
0
2
0
0
1
0
0
0
0
0
2
1
0
0
0
2
0
0
0
2
0
3
0
0
0
0
0
2
2
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
1
2
1
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
2
0
0
2
0
0
2
1
0
0
1
0
1
1
2
0
0
0
0
2
0
0
2
0
2
0
0
0
0
2
0
0
2
1
0
0
0
1
0
2
5
0
0
2
0
0
0
0
0
1
3
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
1
0
0
2
0
0
1
0
2
0
0
0
1
0
0
1
2
0
1
0
1
1
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
1
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
6
0
2
0
0
1
2
1
2
0
0
1
0
4
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
2
0
1
0
0
0
0
0
0
2
2
1
1
1
1
0
1
0
0
0
0
0
2
0
0
2
2
0
3
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
5
1
0
0
0
1
2
1
0
0
2
0
0
2
0
0
0
0
3
0
0
0
1
2
0
2
1
0
2
0
2
0
5
0
0
2
0
0
0
0
0
0
0
5
1
0
0
0
1
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
1
0
0
1
0
0
0
3
0
0
0
0
0
8
0
2
0
0
0
1
1
0
0
2
0
0
0
2
1
0
0
0
0
0
2
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
1
0
0
0
2
0
0
1
0
0
0
0
0
1
2
0
0
0
0
2
0
2
0
0
0
0
0
3
0
0
2
0
0
0
0
0
1
0
1
0
0
2
0
1
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
1
1
2
0
0
0
0
0
0
0
1
0
1
0
2
0
2
0
1
1
1
0
4
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
1
2
0
1
0
2
1
0
2
0
1
1
1
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
2
0
0
0
2
2
2
0
0
2
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
2
0
0
3
1
0
0
1
1
3
2
0
0
0
1
0
3
1
0
0
4
0
0
0
0
0
0
0
1
0
2
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
2
0
0
0
5
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
1
3
0
1
0
0
0
0
0
0
1
2
2
0
0
2
1
0
0
0
0
0
0
0
2
1
0
1
0
0
2
0
5
1
0
0
0
0
0
2
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
1
0
0
2
0
0
1
0
0
0
0
0
4
0
0
2
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
2
0
1
1
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
1
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
1
0
0
1
1
0
0
3
3
2
0
0
2
0
1
0
0
1
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
1
0
1
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
5
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
1
2
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
1
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
1
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
6
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
2
3
1
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
3
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
2
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
1
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
2
1
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
3
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
3
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
1
1
0
3
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
5
0
0
2
2
2
0
0
0
0
1
1
0
0
1
3
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
2
3
0
1
0
0
1
0
0
0
0
0
1
0
1
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
3
1
0
0
0
0
3
0
0
0
1
0
1
0
1
0
0
2
0
0
1
1
1
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
1
0
0
1
2
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
3
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
1
3
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
5
0
2
3
2
0
2
1
0
0
0
0
0
0
0
5
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
2
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
2
1
0
0
2
0
1
0
0
0
0
0
0
0
0
3
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
3
0
0
0
0
0
1
2
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
2
1
2
0
0
0
0
2
0
0
0
0
0
3
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
2
3
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
2
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
3
0
0
0
1
0
2
0
2
0
0
0
1
0
1
0
2
0
0
0
2
2
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
4
0
0
0
1
2
0
0
0
0
0
0
2
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
4
1
0
0
0
0
0
0
2
0
0
0
1
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
5
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
2
0
0
1
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
3
1
4
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
3
5
0
0
0
0
1
0
0
1
0
2
1
0
0
0
0
0
0
1
2
0
2
0
0
1
1
1
2
0
0
0
0
0
2
0
1
3
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
3
0
0
0
1
0
1
0
0
4
0
3
0
1
0
3
0
2
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
2
0
3
0
1
0
0
0
2
0
0
2
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
5
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
4
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
3
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
2
1
1
0
2
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
1
0
0
0
0
2
1
0
2
0
0
0
0
1
0
1
0
0
1
0
0
0
0
2
0
1
1
0
0
0
0
0
0
3
0
2
0
0
1
0
0
0
0
1
0
3
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
2
0
0
2
0
0
0
3
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
4
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
1
0
1
2
0
0
0
2
2
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
3
0
0
0
0
0
0
2
0
1
0
0
0
0
0
3
0
0
0
2
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
3
1
0
0
0
0
0
3
0
1
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
1
7
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
2
0
0
0
1
0
2
0
0
2
0
0
0
4
1
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
9
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
1
0
2
0
0
0
4
0
2
0
1
2
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
3
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
14
2
0
3
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
3
2
2
2
1
0
2
0
0
0
0
0
1
0
0
0
1
0
0
1
0
2
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
19
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
2
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
2
2
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
2
1
0
2
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
1
0
0
0
1
0
0
15
1
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
1
0
3
1
2
0
0
1
0
0
1
0
0
0
0
2
0
2
0
0
1
0
0
0
1
0
0
1
0
2
0
0
0
1
2
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
2
0
0
1
0
2
1
1
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
3
0
0
0
0
0
1
0
1
0
0
0
1
0
1
2
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
1
2
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
2
2
0
1
0
0
0
2
0
1
3
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
3
1
0
0
1
0
1
1
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
2
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
2
2
0
2
0
0
0
2
0
3
0
2
0
2
0
1
1
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
2
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
3
0
0
1
0
1
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
9
1
0
1
0
0
3
0
0
0
2
0
0
1
5
0
0
0
0
0
0
1
0
0
0
0
1
3
0
1
0
0
1
1
1
1
2
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
3
0
0
1
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
3
0
2
0
0
0
0
0
2
0
0
0
0
2
0
1
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
3
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
3
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
3
1
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
3
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
1
0
0
2
1
2
0
0
2
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
1
0
0
1
1
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
3
0
0
2
0
0
0
1
0
0
0
1
2
1
1
2
0
0
2
2
0
0
0
0
2
0
0
1
0
0
0
0
3
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
3
0
0
0
2
0
2
1
1
7
2
1
0
0
1
1
0
0
2
0
0
0
1
0
0
0
2
0
2
0
0
0
0
2
0
1
0
0
1
0
0
0
2
3
0
0
2
0
4
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
1
1
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
1
0
2
2
0
0
0
0
3
1
1
0
0
0
0
0
0
0
0
0
0
3
2
2
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
1
0
2
0
0
2
1
0
1
1
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
3
1
1
0
0
0
0
1
0
0
0
0
1
0
2
0
0
2
0
0
1
0
0
0
0
0
1
2
0
2
0
3
1
0
0
1
2
2
1
2
2
0
0
0
0
0
2
0
0
0
0
0
3
0
0
2
0
5
2
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
2
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
3
0
0
3
0
0
0
3
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
4
0
0
2
0
0
0
1
1
1
0
2
0
0
0
2
0
0
2
2
2
0
0
2
1
0
0
0
0
2
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
2
2
2
2
0
0
2
0
0
2
0
0
0
1
0
2
0
0
0
2
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
9
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
3
1
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
2
2
0
0
0
0
0
3
0
1
1
0
0
0
0
0
0
0
2
3
2
3
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
2
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
1
2
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
1
4
0
2
1
0
1
0
0
1
0
0
0
2
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
4
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
8
0
0
0
2
2
0
0
2
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
10
0
0
0
0
4
2
1
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
3
1
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
1
4
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
2
0
2
3
0
0
0
1
0
0
0
0
0
2
0
3
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
4
0
0
0
0
0
2
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
1
0
1
0
1
0
0
0
0
0
3
0
2
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
1
0
0
0
0
0
0
0
0
3
0
1
1
0
0
0
2
0
1
0
0
0
1
0
0
1
0
6
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
1
1
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
2
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
2
0
1
0
0
0
0
3
0
0
2
4
0
0
1
0
0
2
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
8
0
1
1
3
0
0
1
0
0
0
3
3
0
1
1
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
1
1
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
3
0
0
0
0
0
2
0
0
2
6
0
0
2
0
0
0
0
8
0
0
0
0
0
0
3
0
0
1
0
0
1
0
0
3
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
4
2
2
2
1
1
0
1
0
0
0
2
0
0
0
3
0
0
0
0
1
0
0
0
3
0
0
0
2
1
0
0
2
2
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
4
1
0
0
0
0
3
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
2
0
1
0
0
1
2
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
2
1
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
2
2
0
0
0
0
0
0
0
0
2
0
2
2
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
3
0
0
0
2
0
0
0
0
0
0
1
0
0
0
8
0
0
0
0
1
0
0
3
0
4
0
0
1
1
0
0
0
2
0
0
0
1
2
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
1
0
0
0
2
2
0
2
0
0
0
2
0
0
0
2
0
2
0
0
0
2
0
0
2
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
5
0
2
0
0
2
0
2
0
0
0
0
0
1
2
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
2
0
0
0
3
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
3
0
1
1
2
3
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
3
0
1
0
1
2
0
2
0
0
0
0
1
0
1
3
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
3
0
0
0
0
0
2
0
0
0
0
5
0
0
2
0
2
0
2
2
0
0
0
0
2
0
0
1
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
1
1
0
0
5
0
1
2
0
2
2
0
0
3
1
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
5
0
0
0
1
0
0
0
0
5
7
0
0
0
1
0
0
1
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
7
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
3
0
0
0
0
1
0
0
2
0
0
1
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
7
0
2
0
0
1
0
0
2
0
1
0
0
3
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
2
0
0
2
0
0
2
0
1
0
0
0
1
2
1
1
0
1
0
0
0
0
1
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
2
1
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
3
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
1
0
5
3
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
1
0
2
0
0
2
0
0
0
1
0
4
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
2
0
0
0
2
0
0
2
0
0
0
1
1
0
1
0
0
1
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
4
0
0
0
0
0
0
1
2
0
0
0
2
1
0
1
1
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
3
0
3
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
2
3
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
1
3
0
2
1
0
0
0
0
3
2
0
0
0
0
0
1
0
1
0
0
0
0
2
0
1
1
1
1
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
2
2
0
3
0
2
0
2
0
0
0
0
0
0
2
0
0
3
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
3
0
0
1
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
2
1
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
3
0
0
0
0
1
2
1
0
0
0
2
1
0
0
0
0
2
0
0
0
2
2
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
10
1
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
2
1
1
0
1
0
2
0
1
0
0
0
0
0
0
0
0
11
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
1
0
0
1
0
1
0
2
0
1
2
0
2
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
1
2
1
0
0
1
0
0
0
1
0
0
0
0
3
2
0
0
0
0
2
0
0
0
0
1
1
0
0
0
3
0
0
1
0
0
1
0
0
0
0
0
0
0
1
2
0
1
1
0
0
0
0
0
0
1
2
0
0
3
0
0
0
0
0
0
1
0
0
2
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
2
0
0
1
2
0
2
1
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
1
0
0
0
0
0
6
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
10
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
1
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
1
0
2
2
1
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
8
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
2
0
0
5
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
1
1
1
0
0
1
1
0
0
1
0
1
0
10
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
2
0
1
0
3
3
0
0
0
0
0
2
0
0
0
0
4
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
1
0
1
0
0
0
3
0
0
0
0
0
0
2
0
1
0
1
2
0
0
1
1
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
2
0
1
0
0
2
0
0
1
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
1
1
0
1
0
0
0
2
0
0
0
1
0
3
3
0
0
10
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
2
0
0
0
0
2
3
2
0
1
0
0
0
1
0
0
2
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
3
0
0
0
0
2
1
2
0
0
1
1
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
1
2
1
1
0
0
0
0
0
0
2
0
0
2
1
2
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
1
0
0
0
1
6
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
6
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
2
0
0
1
1
0
0
0
0
0
0
0
1
0
2
0
1
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
3
0
0
1
0
0
0
0
2
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
2
1
0
1
0
0
2
0
3
0
0
1
0
0
0
0
0
0
0
1
0
0
0
3
0
1
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
1
5
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
1
1
0
0
1
0
1
0
0
1
2
0
0
1
3
0
3
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
1
0
0
5
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
1
0
2
0
0
2
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
2
0
0
0
2
2
3
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
1
0
2
0
0
3
2
0
1
0
0
0
0
0
1
0
2
2
0
1
2
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
3
1
0
0
0
0
2
2
0
0
0
0
0
2
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
2
1
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
4
0
3
0
0
0
0
0
0
5
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
3
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
1
0
1
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
2
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
2
5
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
1
0
0
1
0
1
0
0
1
2
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
3
7
3
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
0
1
1
2
0
0
0
1
0
0
0
0
0
0
0
1
1
2
2
4
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
4
0
0
4
2
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
1
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
2
0
1
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
2
0
1
0
1
0
0
1
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
3
0
0
1
0
0
0
0
1
0
0
0
2
1
0
0
0
0
3
1
0
0
0
0
2
1
0
1
0
0
0
0
0
3
0
3
0
0
0
0
0
0
0
1
0
0
0
3
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
6
0
2
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
3
2
1
2
0
0
0
0
0
0
0
0
1
1
3
0
2
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
2
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
3
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
2
2
0
0
2
0
0
0
1
0
0
1
1
0
1
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
1
0
1
0
1
0
2
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
3
0
2
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
2
4
0
0
1
0
2
0
0
0
0
0
1
1
3
0
1
0
3
0
4
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
1
0
2
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
2
0
2
0
1
0
0
0
0
3
1
2
0
0
2
0
0
0
0
0
2
1
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
1
3
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
2
0
2
2
0
0
0
1
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
2
2
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
2
0
0
0
0
1
0
0
1
0
0
0
0
2
1
2
0
0
0
0
0
0
2
1
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
4
4
0
2
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
2
0
0
0
0
5
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
2
0
3
1
0
0
0
2
1
0
0
2
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
3
0
1
4
0
2
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
1
2
0
0
0
0
2
0
2
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
1
2
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
2
0
0
0
0
2
2
0
0
0
0
0
4
0
0
0
0
0
1
3
2
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
1
2
0
2
0
3
0
0
0
0
4
1
0
1
0
2
0
0
2
0
0
2
0
1
0
0
1
0
3
0
0
0
1
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
6
0
0
0
0
0
2
0
1
0
0
2
1
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
1
2
0
1
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
1
2
0
0
0
0
0
0
0
2
5
0
0
0
2
0
1
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
3
0
0
0
2
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
2
0
2
0
0
1
2
2
0
0
0
0
0
0
0
5
1
0
0
0
1
2
0
0
3
0
0
3
2
1
0
0
0
0
0
0
1
1
0
0
0
1
0
2
0
3
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
2
0
0
0
0
3
0
4
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
3
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
2
3
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
5
0
1
0
1
0
3
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
2
3
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
2
0
1
0
0
0
2
0
0
1
0
2
1
0
0
2
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
2
0
0
1
0
0
2
8
0
0
1
2
0
0
2
1
1
0
0
1
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
6
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
1
2
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
4
1
1
1
0
0
2
0
0
2
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
2
0
2
0
1
0
0
0
1
0
2
1
0
0
0
2
0
1
0
2
2
0
2
0
1
0
2
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
1
0
2
0
0
1
0
0
1
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
4
0
0
0
0
0
0
1
0
0
1
0
0
0
1
2
0
0
0
1
0
2
0
0
0
1
1
0
1
0
1
2
0
2
1
0
2
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
1
2
0
1
1
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
1
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
1
0
0
6
0
0
0
0
1
0
0
1
0
0
0
2
1
0
1
0
0
0
0
0
0
0
1
0
2
2
0
2
0
0
2
0
0
2
0
0
1
1
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
2
0
0
0
0
0
0
2
0
0
0
0
3
1
0
0
0
0
2
0
0
0
3
1
0
0
0
1
0
0
0
0
2
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
2
1
4
2
2
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
1
0
1
0
0
0
0
0
0
2
0
0
2
3
0
0
0
0
2
0
0
0
2
0
3
0
0
0
0
0
1
0
0
1
2
1
0
0
1
4
0
0
0
0
1
0
0
0
0
0
0
1
1
2
0
0
1
1
1
2
2
0
0
0
6
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
1
1
1
0
0
0
1
0
0
0
0
1
0
6
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
4
0
7
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
2
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
2
1
0
1
1
0
1
0
0
1
0
1
0
2
1
1
1
0
0
0
0
0
1
2
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
1
1
0
2
1
0
0
0
0
0
1
2
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
1
0
2
0
0
3
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
2
2
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
13
1
0
0
0
2
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
1
0
4
0
0
1
3
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
1
0
0
0
0
0
5
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
2
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
2
0
0
0
2
1
0
0
0
1
0
0
0
1
0
0
0
2
0
1
0
0
1
1
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
2
0
0
2
0
0
0
0
0
0
0
2
0
1
3
0
1
0
0
0
3
0
0
1
1
0
0
2
0
0
2
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
5
0
0
2
0
1
1
1
3
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
1
0
2
1
0
0
0
0
0
0
0
2
0
1
2
0
0
1
1
0
2
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
1
0
1
2
2
0
0
0
4
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
2
2
0
1
0
3
0
0
0
5
0
0
0
1
2
0
1
0
0
0
1
0
1
0
0
0
0
0
0
2
0
1
2
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
2
2
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
1
0
8
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
5
1
0
0
0
0
2
1
0
2
0
1
0
0
0
0
0
0
0
1
0
1
0
3
1
0
1
0
0
0
1
0
0
2
1
2
0
1
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
1
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
1
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
2
0
0
5
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
1
3
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
5
0
0
1
1
0
0
0
0
1
1
0
2
1
0
0
1
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
2
0
0
0
0
0
3
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
1
0
1
0
2
1
4
0
0
1
0
0
0
0
0
0
0
0
1
1
1
2
0
0
0
0
0
0
0
2
0
0
0
2
2
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
1
2
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
8
1
1
2
0
0
0
1
0
0
0
0
0
3
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
1
0
1
2
0
0
0
0
1
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
1
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
1
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
1
0
2
0
0
0
0
2
0
0
0
0
0
3
0
0
1
0
0
0
2
1
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
2
0
0
0
0
0
0
3
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
2
1
0
0
0
0
0
2
0
0
1
3
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
5
0
0
1
0
2
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
3
0
0
0
2
1
2
0
0
3
2
0
2
0
0
0
1
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
2
0
0
0
0
0
0
2
1
0
2
0
0
2
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
2
0
0
0
2
1
0
0
0
0
1
3
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
2
0
2
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
1
3
0
0
1
0
0
0
1
0
1
0
1
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
2
0
2
0
0
1
2
3
0
0
0
0
0
2
0
2
3
0
0
0
1
2
0
1
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
1
2
1
0
1
2
2
0
0
1
0
1
0
2
1
0
0
1
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
2
3
0
0
2
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
1
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
2
5
0
1
0
0
0
1
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
2
2
2
0
0
0
0
6
0
0
1
0
0
0
1
0
1
0
2
0
1
0
0
0
0
0
0
2
0
0
0
3
0
3
0
0
1
0
0
2
0
1
1
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
2
0
3
0
0
0
0
0
2
4
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
3
0
0
0
1
0
0
0
0
1
3
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
2
0
1
2
1
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
2
1
0
0
0
1
0
0
0
0
2
0
2
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
5
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
3
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
5
1
0
0
0
0
0
0
2
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
1
0
0
3
0
2
0
0
0
2
0
0
0
2
0
0
2
1
0
5
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
1
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
2
2
0
1
0
0
0
1
0
1
0
1
3
2
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
1
0
1
0
1
0
3
0
2
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
2
0
0
2
1
13
0
0
0
0
3
0
1
2
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
1
0
0
0
0
0
0
0
0
1
3
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
3
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
4
2
0
0
0
0
1
0
0
0
4
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
2
2
0
0
1
1
0
0
2
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
1
2
0
2
0
1
0
0
0
1
0
0
2
0
2
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
1
3
0
2
0
1
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
2
1
0
0
0
0
0
0
3
0
0
1
0
1
0
2
1
0
0
0
0
1
2
0
1
0
2
0
0
1
2
1
0
0
2
1
0
0
1
0
3
1
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
2
0
2
1
0
0
0
0
1
2
0
0
2
2
6
0
0
0
0
0
2
2
0
0
2
1
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
1
0
2
0
0
0
3
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
2
0
0
1
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
2
0
4
0
1
0
0
0
0
0
0
1
2
2
1
0
0
0
2
0
0
0
2
1
0
1
2
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
3
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
3
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
2
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
2
0
2
1
0
1
1
0
3
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
5
1
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
3
5
1
0
1
0
0
1
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
2
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
4
0
0
1
0
1
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
2
0
1
0
2
0
2
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
5
0
0
0
0
0
0
0
0
2
0
0
2
2
0
1
2
1
0
0
0
1
2
1
0
0
1
1
0
0
0
1
1
4
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
1
0
0
1
0
2
0
0
0
0
0
1
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
2
2
0
0
0
0
0
0
2
1
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
5
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
2
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
1
0
2
1
1
0
0
0
1
0
1
0
0
3
0
0
2
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
2
1
0
0
2
0
0
0
0
5
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
1
0
0
5
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
2
1
1
0
0
1
0
0
0
1
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
3
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
1
5
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
1
0
1
2
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
3
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
3
0
0
1
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
1
1
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
2
0
2
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
2
2
0
0
0
0
0
1
0
0
2
2
0
0
2
2
0
0
3
0
1
0
1
2
1
0
0
1
0
1
0
0
2
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
2
0
0
3
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
2
3
0
0
1
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
2
0
0
0
0
1
2
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
4
2
0
0
1
0
0
0
0
0
1
0
0
0
0
2
1
0
0
2
1
2
1
0
0
0
0
0
2
1
0
0
1
0
4
2
0
0
0
2
3
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
3
0
0
0
0
2
0
2
0
0
2
0
0
1
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
2
0
1
1
0
0
0
2
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
6
0
2
1
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
1
1
0
0
1
1
0
0
0
2
0
0
1
0
2
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
2
2
0
4
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
2
0
0
1
0
2
1
0
0
0
1
1
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
3
2
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
1
2
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
1
1
0
1
0
1
0
0
1
0
0
2
0
0
0
2
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
3
0
1
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
4
0
0
0
2
0
1
0
0
0
0
0
0
2
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
1
0
0
2
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
2
0
0
0
0
2
0
1
1
0
0
2
0
2
3
1
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
2
0
2
0
0
0
0
0
3
0
0
1
0
0
2
0
0
0
1
0
1
0
0
0
0
0
3
1
0
0
0
2
0
0
0
0
2
1
1
2
0
0
2
0
0
1
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
2
3
0
0
0
2
3
3
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
4
0
0
2
0
0
1
3
0
1
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
1
1
3
1
0
0
2
1
1
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
3
0
0
2
0
0
0
0
0
0
1
0
2
0
0
1
2
0
2
0
0
0
0
1
2
2
0
0
0
0
2
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
2
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
2
0
3
0
0
2
0
0
0
0
1
1
0
2
0
1
1
0
2
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
1
0
0
3
0
0
0
2
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
3
0
1
2
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
1
2
1
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
2
4
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
1
1
0
0
3
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
3
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
2
1
1
0
0
1
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
8
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
2
2
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
1
0
0
2
0
2
0
1
0
3
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
1
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
3
5
0
0
0
0
0
0
0
0
0
1
1
2
0
1
0
0
0
0
1
0
0
3
1
2
0
0
0
0
2
0
0
0
0
3
0
0
0
0
3
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
2
0
2
0
0
0
0
0
1
0
0
1
0
0
2
2
0
0
0
2
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
1
0
0
0
0
0
2
0
0
1
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
1
0
2
0
2
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
2
2
1
0
0
0
0
1
2
0
0
0
1
0
2
1
1
0
2
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
2
2
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
1
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
2
1
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
10
0
0
0
8
0
0
0
0
0
2
0
0
0
1
1
0
0
0
1
2
1
1
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
1
1
0
0
1
0
0
2
0
0
0
0
1
2
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
2
1
0
0
0
1
0
1
1
0
0
0
0
1
0
1
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
3
2
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
1
1
2
0
1
0
0
0
2
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
1
0
2
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
2
0
0
0
0
1
0
2
2
1
2
1
0
2
1
0
0
0
0
0
2
1
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
2
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
7
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
3
0
0
1
0
0
2
0
7
0
0
0
0
2
0
0
0
2
2
3
2
1
1
2
2
1
0
0
1
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
1
0
1
1
0
2
2
0
0
0
0
0
1
0
1
2
1
0
0
2
0
0
0
0
0
0
0
1
0
2
0
1
0
1
0
0
0
1
2
2
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
1
2
0
0
2
0
1
0
0
0
0
2
0
0
2
0
2
1
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
1
1
0
0
0
0
2
0
0
0
1
0
2
3
2
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
1
0
2
0
0
0
0
0
0
2
1
0
1
2
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
5
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
2
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
2
0
0
1
2
0
2
0
0
0
0
2
1
1
0
0
0
1
0
1
0
0
1
13
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
3
0
0
0
1
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
1
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
5
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
2
0
1
0
0
0
0
0
0
1
0
1
2
1
0
2
2
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
1
1
0
1
0
0
0
2
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
3
0
0
1
0
0
0
0
1
0
1
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
2
0
3
2
2
1
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
3
0
0
0
2
2
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
2
0
0
1
1
0
0
4
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
2
0
3
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
1
2
1
0
1
2
0
0
0
0
0
1
0
0
0
3
0
1
0
1
0
0
0
0
0
1
0
2
2
0
1
0
0
0
0
0
0
0
2
0
1
2
0
1
1
0
0
0
2
0
0
4
0
0
2
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
2
1
0
2
0
0
1
0
0
0
1
2
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
3
0
0
0
1
0
2
0
0
2
0
0
2
0
0
1
0
0
0
1
0
1
0
1
2
1
2
3
0
0
0
2
1
1
0
2
0
0
2
0
2
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
1
1
0
0
0
0
0
3
0
0
1
2
0
0
1
0
0
0
2
2
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
2
0
0
2
0
1
0
0
1
0
2
0
0
0
1
0
0
2
2
2
1
0
0
0
2
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
2
2
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
3
1
0
1
0
2
0
0
1
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
1
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
1
0
4
2
0
0
0
0
1
0
0
0
2
0
0
1
0
0
2
0
0
1
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
3
0
0
0
1
0
1
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
3
0
1
0
0
1
3
2
6
1
0
1
0
0
0
0
1
0
0
2
0
2
0
1
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
3
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
3
2
1
0
0
0
2
0
0
1
0
0
0
1
1
0
0
0
2
0
2
2
0
0
0
2
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
2
0
0
1
0
0
0
2
0
0
1
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
1
1
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
3
0
0
4
0
1
11
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
3
2
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
3
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
1
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
1
0
0
0
1
0
0
0
1
0
1
0
0
3
0
0
0
0
1
2
0
0
0
2
1
0
0
1
0
0
0
2
0
0
0
0
2
0
2
0
2
0
0
0
0
0
1
0
0
2
0
0
0
2
0
1
0
1
2
0
0
0
0
2
0
0
1
0
2
0
2
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
2
1
0
1
1
0
2
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
1
3
2
0
0
0
3
0
0
0
0
0
0
0
2
0
0
2
2
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
4
0
0
0
0
0
1
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
5
0
0
0
0
0
0
0
0
0
0
2
1
3
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
3
2
0
1
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
6
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
2
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
4
2
0
0
0
0
0
0
0
0
4
2
4
2
0
0
0
1
2
0
0
2
0
0
0
0
1
0
1
0
1
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
2
1
1
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
1
2
0
0
0
0
2
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
1
1
0
1
0
0
1
0
0
0
1
0
0
1
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
2
1
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
4
0
0
2
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
1
2
0
0
4
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
1
0
0
1
0
0
0
3
0
0
0
2
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
3
0
1
0
1
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
2
0
2
0
0
0
2
0
0
1
2
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
5
0
1
0
0
2
1
0
0
0
0
2
0
0
0
0
3
1
2
2
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
2
0
2
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
2
2
2
1
0
2
0
1
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
3
1
0
1
0
2
0
1
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
2
0
0
0
4
0
2
0
0
0
4
0
0
1
6
2
1
0
0
0
0
0
1
1
2
1
0
2
0
0
0
2
2
0
0
2
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
5
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
3
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
4
0
0
0
0
0
0
1
3
0
0
1
0
0
0
4
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
3
1
0
4
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
1
2
1
0
0
4
0
0
0
1
0
2
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
2
0
2
1
1
1
0
0
0
1
0
0
0
1
2
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
2
5
0
2
0
0
0
1
1
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
2
0
1
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
6
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
3
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
1
4
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
2
2
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
1
1
0
2
0
0
1
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
3
0
0
9
1
0
0
0
2
0
1
0
0
0
1
2
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
4
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
1
6
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
2
1
0
1
0
2
0
0
0
0
1
0
2
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
9
0
1
0
0
2
0
3
0
2
0
0
0
0
4
0
2
0
0
0
0
6
0
0
2
0
0
1
1
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
1
0
0
1
0
3
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
2
0
0
2
1
0
0
0
0
1
0
1
0
0
0
1
0
0
2
0
0
1
0
3
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
2
0
0
1
2
0
2
0
0
1
0
0
4
0
2
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
9
1
0
2
0
0
0
0
0
0
1
2
0
2
2
0
1
1
0
1
0
0
0
2
0
0
0
0
2
2
0
0
0
2
0
0
0
0
1
2
1
0
0
0
1
0
0
0
1
0
2
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
2
3
0
0
0
2
1
0
0
0
3
0
0
2
0
0
8
0
0
2
0
0
2
0
2
0
0
0
2
0
0
0
0
0
2
0
1
2
0
0
0
1
0
0
0
0
2
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
1
0
0
0
0
0
1
4
0
1
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
2
2
0
0
0
0
1
1
0
0
0
0
2
2
0
0
0
0
0
1
0
1
0
0
1
3
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
1
2
0
0
0
2
0
0
1
0
0
0
1
2
0
2
0
0
0
0
0
1
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
3
0
0
1
0
0
0
1
2
0
0
1
1
0
0
0
1
0
0
1
0
1
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
1
0
2
0
0
0
0
2
0
0
0
0
2
4
0
0
0
1
1
2
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
4
0
0
0
0
0
1
1
1
8
2
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
8
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
3
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
1
0
0
1
0
2
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
2
0
4
0
1
1
0
0
1
0
0
0
3
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
1
1
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
2
0
0
1
6
1
0
6
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
1
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
1
0
0
0
2
0
1
0
0
2
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
1
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
2
0
2
0
2
2
0
0
0
2
0
3
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
3
0
1
0
2
2
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
1
0
2
0
0
0
0
2
0
2
2
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
4
0
0
0
0
0
2
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
2
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
1
0
0
1
0
0
2
0
2
0
0
0
1
2
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
1
2
2
3
0
0
2
0
0
0
0
0
0
0
1
1
3
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
3
0
2
0
1
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
1
2
0
0
0
0
0
0
0
0
1
2
0
3
0
0
0
0
1
0
0
0
0
1
0
0
0
2
2
3
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
2
2
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
2
0
0
1
0
0
0
0
0
0
1
0
2
5
2
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
1
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
3
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
1
1
1
0
0
0
1
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
6
0
0
1
0
0
1
0
2
0
0
1
1
0
5
0
1
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
1
0
1
2
1
0
1
1
0
0
0
2
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
5
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
1
0
1
0
0
0
0
1
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
1
0
2
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
1
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
9
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
2
0
2
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
5
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
1
0
1
0
1
0
0
2
0
0
0
0
0
1
0
1
0
0
1
4
2
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
3
1
1
1
1
0
4
0
1
3
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
2
0
3
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
3
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
6
0
2
0
0
1
0
1
1
2
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
1
4
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
2
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
2
3
2
1
1
0
0
0
0
0
0
0
1
0
0
0
6
1
2
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
1
2
1
0
1
0
0
0
1
6
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
3
0
2
0
0
0
2
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
3
2
0
1
0
0
0
0
0
2
0
1
0
0
0
2
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
4
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
2
0
2
0
0
0
0
0
2
0
0
1
0
1
0
2
0
1
1
2
0
0
0
0
2
0
3
1
1
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
7
0
0
2
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
2
1
2
0
2
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
2
2
0
0
2
0
0
0
3
0
0
2
0
0
0
0
1
0
1
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
1
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
3
1
0
1
0
0
0
2
0
0
0
0
0
2
0
0
2
1
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
2
2
0
0
0
2
0
0
0
0
0
2
2
0
0
4
0
0
0
1
0
2
0
0
2
0
1
0
0
2
0
13
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
2
0
2
0
0
1
0
0
0
0
0
0
2
1
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
2
1
5
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
3
0
1
0
0
0
3
0
1
2
0
0
0
0
2
0
0
1
0
1
2
0
0
0
0
2
1
2
1
0
0
0
3
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
4
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
1
1
0
2
0
0
1
2
2
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
4
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
3
0
0
1
1
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
5
0
0
0
0
0
3
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
2
1
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
1
0
2
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
11
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
2
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
1
2
4
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
1
2
1
0
0
3
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
1
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
1
0
1
0
2
0
0
0
0
0
1
0
1
3
2
0
0
2
0
0
0
0
1
0
1
0
3
0
2
0
0
0
0
0
2
0
1
0
0
1
0
1
0
0
0
0
0
0
3
2
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
2
3
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
5
0
0
2
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
3
0
0
1
0
2
0
2
0
1
0
0
0
3
0
0
0
2
2
1
0
0
4
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
1
0
2
0
1
2
0
0
0
0
1
1
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
2
0
0
5
1
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
4
2
0
0
0
0
2
0
0
0
0
0
3
0
2
2
0
0
0
0
1
0
0
0
1
0
1
1
1
1
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
2
0
0
1
1
0
2
0
0
0
0
2
2
6
0
2
0
0
1
0
0
1
0
2
0
1
0
2
0
1
1
2
1
0
0
0
0
2
0
0
1
2
0
0
2
1
0
3
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
2
1
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
0
3
2
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
2
0
1
0
0
1
0
1
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
2
0
5
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
1
0
2
2
0
0
0
2
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
5
1
0
2
0
0
2
0
0
0
0
5
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
3
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
1
0
0
0
0
0
2
2
2
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
1
2
0
0
0
0
2
0
2
0
1
0
0
0
0
0
1
1
0
2
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
1
0
1
0
1
3
3
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
3
0
0
0
2
9
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
2
2
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
2
1
0
2
1
0
2
0
3
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
3
0
0
0
0
0
1
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
2
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
1
1
0
1
0
0
0
0
0
0
0
2
1
0
1
0
0
0
1
0
0
0
2
0
2
2
0
1
0
0
0
0
0
0
0
3
0
1
0
0
0
0
2
0
0
1
0
0
3
0
0
0
2
1
0
0
0
0
1
0
0
1
0
1
0
0
2
2
0
0
0
0
0
1
2
1
0
0
1
0
0
0
1
0
0
6
0
0
0
0
2
0
2
0
0
0
1
1
0
1
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
2
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
2
0
0
6
0
1
0
0
0
0
0
1
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
1
0
2
1
0
0
0
3
2
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
1
4
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
3
0
0
6
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
1
0
0
0
0
1
0
2
0
0
1
2
0
0
0
2
0
5
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
1
2
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
2
0
1
0
3
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
1
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
2
0
0
0
3
0
0
0
0
0
2
2
0
1
0
1
0
2
0
0
2
0
0
0
0
0
0
0
1
0
2
2
2
1
0
0
0
0
2
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
2
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
8
0
0
0
0
0
3
0
0
2
1
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
1
0
3
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
3
1
0
1
0
0
0
0
0
0
2
2
0
1
0
0
0
1
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
2
0
2
2
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
3
1
1
0
2
0
2
0
1
0
0
3
1
0
3
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
3
2
0
1
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
3
0
8
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
3
0
0
0
1
5
0
3
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
1
5
0
1
1
1
0
1
2
1
0
0
0
0
0
0
1
4
0
0
1
0
1
0
0
0
0
0
0
3
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
2
2
0
0
0
1
0
0
1
0
1
0
0
0
0
0
2
0
0
2
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
2
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
1
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
3
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
1
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
2
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
5
0
0
1
7
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
1
2
2
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
1
0
2
1
0
0
0
0
0
1
0
0
0
0
0
2
0
3
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
3
1
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
1
2
0
1
0
0
2
1
0
0
0
0
1
0
2
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
2
2
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
8
0
2
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
1
0
0
0
7
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
1
0
0
1
2
1
2
0
0
0
1
0
3
0
2
0
0
0
3
0
0
2
0
0
1
0
0
0
2
0
1
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
1
0
2
0
1
0
0
1
0
0
0
0
2
1
0
1
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
3
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
2
0
1
0
2
2
0
0
0
3
2
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
2
0
2
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
2
2
0
1
0
0
2
2
2
0
2
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
1
1
0
0
1
0
0
0
0
2
0
2
0
0
1
0
2
0
0
2
2
2
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
1
0
0
0
0
0
0
0
0
0
0
2
0
6
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
2
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
2
0
0
0
0
0
0
0
9
1
1
0
0
0
1
0
2
0
7
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
2
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
2
1
0
1
2
2
1
0
2
1
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
2
2
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
2
0
0
2
0
0
0
1
0
0
0
2
0
0
0
2
3
1
1
0
0
1
0
0
1
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
3
2
2
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
1
0
2
0
0
0
0
0
3
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
2
2
0
0
0
1
3
0
1
0
0
0
0
0
0
1
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
2
1
0
0
0
2
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
2
1
0
0
2
1
0
2
2
0
0
0
2
0
0
0
0
0
0
2
2
0
12
0
0
0
1
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
1
2
2
0
0
0
1
0
2
0
1
0
0
1
2
0
0
0
1
0
0
0
0
1
1
0
0
1
2
0
0
0
1
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
2
0
2
0
3
0
1
1
0
0
1
3
1
0
0
0
0
0
0
0
2
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
1
0
0
0
1
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
2
3
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
4
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
1
0
2
0
1
0
2
2
1
0
0
0
0
0
0
2
2
1
2
0
1
0
1
2
3
0
0
1
0
0
0
1
1
2
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
3
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
1
0
0
1
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
1
0
5
0
0
1
0
2
0
1
2
1
0
0
1
0
0
0
1
2
0
0
0
2
3
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
2
0
0
0
0
1
0
0
0
1
1
0
1
0
1
5
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
1
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
1
0
2
0
1
0
0
2
2
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
1
1
0
0
2
0
1
3
2
0
0
0
0
0
1
0
0
0
1
0
1
0
0
2
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
1
3
0
0
0
2
2
0
0
2
2
0
1
0
0
0
0
2
1
0
0
1
0
0
0
2
1
0
2
1
0
0
0
0
1
1
0
4
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
3
2
0
0
0
0
2
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
2
0
2
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
2
0
0
2
0
0
0
1
0
0
0
2
2
0
1
0
0
2
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
1
0
2
2
0
2
0
0
1
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
3
0
0
0
2
1
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
2
1
1
0
2
0
2
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
1
1
0
2
0
2
1
1
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
4
0
0
1
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
1
2
0
0
0
1
1
0
0
0
1
0
1
0
0
2
0
3
0
0
0
0
0
0
1
0
0
3
0
0
1
2
1
0
0
2
0
0
3
1
2
0
2
0
0
0
0
2
0
0
2
0
0
1
0
2
0
0
0
1
0
2
1
0
5
0
0
2
0
0
0
0
1
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
2
2
0
0
0
1
0
0
0
1
0
0
2
0
1
0
0
2
0
2
0
0
0
0
1
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
2
0
0
0
0
2
2
1
0
0
2
0
0
0
0
2
2
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
3
1
2
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
2
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
1
1
1
2
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
2
1
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
3
2
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
3
0
2
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
3
2
1
1
2
0
0
2
1
1
0
0
0
0
0
0
0
0
9
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
1
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
7
2
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
5
0
0
0
1
0
0
0
0
0
5
0
0
0
0
3
0
0
0
2
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
2
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
2
2
0
2
0
2
2
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
1
1
0
0
4
0
1
0
0
1
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
3
0
2
2
1
0
1
0
0
0
2
3
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
1
1
0
0
0
0
0
0
0
1
0
0
0
2
1
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
9
2
0
0
0
0
2
0
2
0
0
1
0
2
1
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
6
1
2
0
1
0
0
0
0
0
1
0
2
0
0
0
2
0
0
1
0
2
2
1
0
2
1
0
0
1
2
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
1
3
0
1
0
0
1
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
1
0
0
1
0
0
0
1
0
0
0
2
0
0
1
0
0
4
0
0
1
0
0
0
1
1
0
0
1
0
2
1
0
0
3
0
0
0
0
0
0
2
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
1
3
1
2
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
2
1
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
4
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
5
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
3
0
0
0
0
2
0
0
1
0
1
0
2
0
0
0
0
0
3
1
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
9
2
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
2
0
2
1
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
3
0
2
0
0
0
0
2
0
0
1
0
0
1
0
0
1
0
2
0
1
0
0
1
1
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
3
0
2
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
2
1
0
2
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
3
2
0
0
0
0
0
0
0
2
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
1
3
0
3
0
0
0
0
6
0
0
0
0
0
0
0
0
2
1
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
2
0
1
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
3
2
1
6
0
2
1
0
0
0
0
0
0
0
1
2
2
0
0
0
1
1
3
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
5
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
1
0
2
2
0
1
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
3
1
3
0
0
2
2
0
1
0
1
2
0
2
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
5
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
1
0
2
0
0
3
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
4
0
4
0
1
0
1
0
0
0
0
1
1
2
2
0
0
0
3
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
2
0
0
1
2
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
1
0
2
0
0
0
0
0
1
0
2
1
2
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
8
0
0
0
0
2
3
2
0
1
0
0
1
2
0
2
0
2
0
0
2
0
0
0
2
0
0
2
1
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
3
2
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
4
0
0
1
0
0
1
1
0
0
0
2
0
0
0
2
1
0
0
0
0
1
1
0
0
0
0
0
0
5
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
6
0
1
0
0
1
2
0
0
0
3
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
5
0
3
0
1
2
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
2
1
2
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
1
5
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
1
2
0
0
0
0
0
0
0
1
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
4
0
2
1
0
1
0
3
1
0
3
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
1
1
0
0
2
0
2
0
0
1
0
0
0
4
2
0
0
0
0
0
0
0
0
0
4
0
0
0
1
1
0
0
0
7
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
4
0
0
1
0
0
0
1
0
3
0
0
1
0
0
2
1
0
0
1
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
1
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
1
0
3
0
0
4
2
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
1
0
0
0
0
0
1
0
2
0
0
1
1
0
0
0
0
1
0
1
2
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
3
0
0
1
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
1
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
3
0
0
0
0
0
2
0
0
0
0
3
0
0
1
1
2
0
5
2
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
1
1
1
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
2
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
1
0
0
1
0
1
0
0
1
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
3
1
1
0
0
1
0
0
0
1
0
0
1
1
0
0
2
0
1
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
3
1
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
1
0
3
2
0
0
0
0
2
0
1
2
7
0
0
0
2
0
0
1
0
0
0
1
0
0
0
1
0
0
0
2
1
1
0
0
0
1
1
0
1
0
0
0
0
2
2
3
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
1
0
2
0
0
0
1
0
1
1
0
0
0
1
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
2
0
0
1
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
3
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
2
2
0
1
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
2
0
0
1
0
1
2
2
2
0
0
0
0
0
0
0
0
3
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
3
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
2
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
4
0
1
0
0
3
0
0
3
0
0
1
0
2
0
2
2
1
2
0
0
0
0
1
1
0
0
0
0
0
1
2
0
1
0
0
0
2
3
0
1
2
1
0
2
1
2
0
2
2
0
0
3
0
0
0
0
0
0
1
0
0
1
0
1
0
2
0
0
0
2
0
1
0
0
1
0
0
0
1
0
0
1
0
0
2
2
0
2
2
0
2
3
0
0
1
2
2
2
3
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
2
0
0
2
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
3
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
2
0
3
1
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
2
0
0
0
2
0
0
0
4
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
2
2
0
0
0
0
0
0
2
0
5
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
2
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
5
2
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
1
0
2
2
0
0
0
1
7
0
1
0
0
0
0
0
0
0
0
6
5
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
3
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
1
1
0
2
2
0
0
0
0
0
0
1
1
2
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
2
0
3
0
0
0
0
2
0
0
0
0
0
0
0
1
1
2
0
0
2
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
1
0
2
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
5
0
2
0
0
0
5
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
2
1
0
0
1
0
1
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
1
0
3
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
9
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
6
0
0
0
0
0
2
0
0
0
0
4
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
3
2
1
0
0
0
0
1
2
1
0
0
0
1
0
2
0
0
1
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
2
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
5
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
3
0
0
0
2
2
0
0
0
0
0
1
0
0
3
1
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
4
0
1
0
0
2
0
3
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
2
1
0
0
0
0
0
2
0
0
0
2
1
0
3
2
0
0
2
0
0
0
1
0
0
0
1
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
5
1
2
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
3
0
0
0
0
0
0
0
1
0
2
0
5
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
2
0
2
0
0
1
0
0
0
2
0
0
0
5
0
0
0
0
0
0
1
0
0
0
3
0
0
2
0
2
2
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
2
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
3
0
1
0
0
2
1
0
0
3
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
2
6
1
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
1
2
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
1
4
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
1
0
2
0
2
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
16
0
1
0
0
1
1
0
0
0
5
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
4
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
2
1
0
0
0
2
0
3
2
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
1
0
0
0
0
2
0
0
2
0
1
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
3
3
1
0
0
0
0
0
0
2
0
0
1
2
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
3
0
2
0
0
0
7
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
1
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
1
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
3
2
0
0
2
2
0
0
0
0
0
1
0
0
0
0
1
0
0
3
3
1
2
0
0
2
0
0
0
0
0
2
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
1
0
1
0
0
0
4
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
9
0
0
1
1
0
0
2
0
0
1
0
0
0
5
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
2
1
0
29
0
0
1
2
1
2
1
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
1
1
3
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
2
2
0
0
0
2
0
0
2
0
0
0
3
0
0
0
2
0
0
0
1
0
0
0
0
0
2
1
1
0
2
4
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
2
5
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
3
0
0
0
0
1
7
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
3
0
1
0
3
0
0
0
5
0
0
1
0
0
0
0
0
0
1
0
4
0
0
0
0
0
4
0
1
2
2
2
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
4
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
2
0
0
0
2
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
2
2
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
2
0
0
0
3
1
0
0
0
0
0
0
0
6
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
1
5
0
0
0
6
1
0
1
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
1
0
2
0
0
0
2
2
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
2
1
0
1
1
0
2
3
2
0
0
2
0
0
0
0
0
0
4
0
0
0
0
2
0
4
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
5
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
2
2
2
2
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
2
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
2
0
1
0
0
0
1
2
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
2
0
2
0
2
2
0
2
0
0
0
0
1
0
0
0
0
2
1
1
0
2
0
2
0
2
1
0
1
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
2
1
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
2
3
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
3
0
0
2
2
1
3
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
1
2
0
0
1
0
0
0
2
0
0
0
1
1
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
2
5
2
1
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
3
1
0
1
1
0
0
0
4
0
0
0
0
1
0
0
0
2
0
0
0
1
0
1
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
1
1
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
1
0
1
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
1
0
0
0
0
1
1
0
0
2
0
2
0
0
0
1
0
0
1
0
0
0
2
2
5
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
3
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
5
2
0
2
1
1
0
0
2
2
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
4
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
3
0
0
0
0
0
1
1
0
1
0
0
1
0
1
0
0
0
2
0
0
0
2
0
0
0
2
2
1
1
2
0
0
0
0
2
2
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
5
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
9
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
3
3
3
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
1
0
2
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
4
0
0
0
0
0
2
2
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
1
3
0
0
2
0
0
2
0
0
1
0
0
3
0
0
1
0
1
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
1
2
0
0
0
2
0
3
0
0
0
0
0
1
3
0
0
0
3
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
3
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
4
0
0
3
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
1
2
1
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
4
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
8
0
0
1
2
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
3
4
1
2
0
0
1
0
0
2
0
0
2
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
5
0
0
0
0
0
1
0
1
0
0
1
3
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
1
2
0
0
2
0
0
0
3
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
2
1
0
4
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
2
0
2
1
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
7
0
0
0
0
0
0
1
0
4
2
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
2
2
0
0
0
1
0
0
0
1
0
2
0
0
0
2
2
0
0
0
0
0
0
2
0
0
1
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
1
2
0
0
0
2
0
0
1
0
0
6
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
3
0
0
0
0
0
0
1
0
0
2
0
0
2
1
2
0
2
1
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
2
0
0
2
2
0
1
1
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
2
0
0
0
0
2
2
0
0
0
0
0
7
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
2
1
0
0
0
2
2
1
0
3
0
0
0
0
1
0
2
0
0
0
2
2
0
0
0
1
3
0
0
0
1
0
0
0
0
1
0
0
1
0
0
5
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
3
0
0
3
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
2
0
1
0
0
0
0
1
2
0
2
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
2
2
0
3
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
3
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
2
0
0
0
6
1
5
1
0
1
2
0
1
0
1
0
0
0
4
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
2
0
0
1
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
2
0
2
0
1
0
0
0
1
0
0
3
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
1
0
2
0
0
2
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
1
0
2
0
0
0
1
0
0
0
2
0
0
6
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
2
0
2
0
0
0
0
1
0
4
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
5
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
4
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
1
1
1
0
0
1
0
2
0
0
0
0
1
0
0
0
1
0
0
0
2
1
1
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
2
0
0
0
2
2
2
2
0
0
0
0
0
0
0
0
3
0
3
1
0
0
0
0
0
2
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
1
0
2
0
1
0
0
0
0
2
0
0
0
1
0
2
0
0
0
1
0
0
0
2
0
0
1
0
1
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
3
0
0
1
0
0
2
2
0
2
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
2
1
0
2
2
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
7
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
8
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
2
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
1
0
0
2
0
0
1
1
1
2
0
0
1
0
0
0
0
2
0
2
0
0
3
0
0
0
2
0
3
2
2
0
3
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
1
0
3
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
1
0
1
0
0
2
0
3
2
0
0
0
0
0
2
2
0
0
0
0
0
0
2
1
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
3
4
0
0
0
0
0
0
0
3
1
0
1
1
2
0
0
0
1
2
0
4
2
0
0
2
1
0
0
0
1
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
1
0
0
0
1
2
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
1
2
0
2
1
1
0
0
1
1
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
3
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
3
2
0
0
0
2
0
1
3
0
2
0
0
0
0
0
3
0
2
0
2
2
1
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
2
0
0
0
2
2
0
1
0
0
0
2
0
2
0
0
1
1
0
0
0
0
2
2
0
0
0
0
0
1
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
2
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
3
0
0
1
2
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
1
0
2
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
3
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
1
0
1
1
2
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
1
0
2
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
1
0
0
2
3
0
1
2
2
2
1
1
0
0
0
2
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
5
1
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
2
0
2
2
0
3
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
2
0
3
0
1
0
0
0
0
2
2
0
0
0
1
0
3
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
3
1
0
1
0
0
1
0
2
1
2
0
0
0
4
0
0
0
0
0
0
0
1
0
3
0
4
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
1
3
0
2
2
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
6
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
3
3
0
0
0
0
2
0
0
0
3
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
1
2
0
1
0
0
0
0
0
3
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
2
0
0
2
0
0
0
1
4
0
2
1
2
0
0
0
0
0
0
0
0
1
3
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
2
0
0
1
1
2
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
1
1
0
0
2
0
0
3
0
0
0
1
0
0
0
0
1
0
0
2
0
2
0
0
0
1
0
0
2
0
0
0
0
1
0
1
0
0
2
0
0
0
0
1
0
0
2
0
0
0
2
5
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
5
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
2
2
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
2
2
0
0
0
0
2
1
1
2
1
3
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
3
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
1
1
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
4
1
1
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
1
1
1
0
0
1
2
0
0
0
0
0
0
1
0
1
2
2
0
0
2
0
0
0
1
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
6
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
3
0
0
1
1
2
2
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
1
1
2
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
1
0
0
0
0
0
0
0
2
1
2
0
0
2
1
0
0
0
0
0
1
0
0
1
0
1
0
3
0
0
0
0
0
0
0
0
0
1
0
1
0
1
2
1
0
0
0
0
0
1
3
1
1
0
0
2
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
2
2
0
2
1
2
1
0
0
0
0
0
0
0
2
0
0
2
2
3
0
2
1
0
0
0
3
0
0
0
0
1
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
2
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
3
0
0
0
0
0
1
2
0
0
2
0
0
3
0
0
0
1
1
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
1
0
0
0
2
2
0
0
0
0
2
2
2
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
2
0
0
2
3
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
3
0
0
0
0
0
2
0
2
1
0
0
1
0
0
1
0
0
0
0
0
0
3
2
0
0
0
0
1
0
1
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
2
0
0
2
2
0
2
0
1
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
3
0
0
0
2
2
0
0
0
0
2
1
0
0
0
4
2
0
2
0
2
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
1
0
0
0
2
2
0
0
0
2
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
3
0
5
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
1
2
0
0
0
0
1
0
1
0
0
0
0
6
0
2
0
2
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
1
1
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
1
0
0
0
1
2
0
1
0
0
0
2
1
1
0
1
0
0
0
2
0
0
2
0
3
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
1
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
2
2
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
1
0
0
3
0
2
0
1
0
0
0
0
2
2
0
3
2
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
1
0
1
2
2
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
3
1
0
1
0
0
2
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
1
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
4
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
1
2
0
0
1
0
0
0
1
0
2
1
0
0
1
0
4
0
0
1
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
3
0
0
2
0
0
2
2
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
2
0
6
0
0
0
2
1
0
3
1
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
3
1
1
0
0
0
3
0
0
0
1
0
2
0
0
1
0
0
1
0
0
0
1
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
3
0
0
0
1
0
1
0
0
2
0
3
2
2
0
1
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
1
0
2
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
2
0
2
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
1
0
0
0
1
2
1
0
0
0
2
0
0
0
0
0
1
1
2
0
0
0
0
0
0
1
0
2
3
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
4
2
1
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
2
4
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
3
2
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
11
2
0
0
0
0
0
0
4
7
2
0
0
0
1
0
0
0
0
0
0
5
1
1
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
4
0
0
0
0
0
1
0
0
0
0
2
2
0
2
0
0
0
0
2
2
0
0
0
0
2
3
1
1
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
3
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
3
0
0
2
1
5
0
2
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
3
0
1
1
0
2
0
2
0
1
0
1
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
2
3
2
0
0
4
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
3
1
2
0
0
0
0
0
1
1
2
0
2
0
0
1
1
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
4
1
0
0
2
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
1
0
2
1
2
0
0
2
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
1
3
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
2
0
0
2
0
1
0
6
1
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
5
0
0
0
1
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
1
2
1
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
2
4
2
0
0
0
3
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
2
0
0
2
0
0
0
2
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
1
1
0
0
0
2
1
0
1
0
0
0
0
1
1
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
2
1
0
2
0
0
1
0
0
3
1
1
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
2
2
0
0
0
2
1
0
0
0
0
0
0
3
0
1
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
3
1
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
1
0
0
0
1
0
0
2
0
7
0
1
2
0
1
0
0
0
0
2
0
1
0
1
0
0
0
0
0
2
0
0
1
0
0
1
0
0
1
0
0
2
0
0
0
0
0
5
0
0
0
1
1
0
0
0
0
1
1
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
2
0
0
0
0
1
0
3
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
2
0
3
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
2
0
0
0
0
0
0
1
0
2
0
2
0
0
0
1
0
0
0
0
1
2
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
3
5
0
2
2
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
3
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
3
0
0
2
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
2
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
2
0
2
0
2
1
0
0
0
1
1
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
3
0
2
2
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
2
0
1
1
1
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
6
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
2
0
2
2
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
2
2
1
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
2
1
0
2
0
0
0
0
0
2
3
0
1
0
0
0
2
1
2
0
1
0
0
0
1
1
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
4
0
0
1
0
0
0
0
1
1
1
1
1
1
0
0
2
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
2
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
1
1
2
0
0
0
0
0
0
2
0
2
0
1
1
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
2
0
1
0
0
0
0
4
0
0
0
1
0
0
1
2
0
0
1
0
0
1
0
0
0
2
2
2
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
3
0
0
2
3
1
0
0
0
1
0
2
1
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
3
0
0
2
1
2
1
1
1
2
0
0
0
0
2
0
2
0
0
0
0
3
2
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
2
0
0
2
1
2
2
0
0
0
1
0
2
0
0
1
2
0
0
0
0
0
2
0
0
2
1
1
0
0
0
0
1
0
3
0
0
0
1
0
0
1
0
1
0
1
0
0
0
1
1
0
0
1
0
0
2
0
0
0
0
1
0
0
0
3
0
0
0
2
0
1
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
2
1
0
0
0
1
0
0
0
0
0
1
2
0
0
0
2
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
3
0
1
0
0
0
1
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
1
3
0
0
2
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
3
0
0
0
0
1
0
3
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
1
0
1
2
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
2
2
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
3
0
0
2
1
0
1
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
2
0
1
0
6
0
2
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
1
0
0
1
1
2
1
0
0
2
0
3
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
3
0
2
0
0
0
0
0
4
2
0
0
1
0
0
1
1
0
0
0
1
2
2
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
8
0
2
0
2
0
1
0
0
1
2
0
1
0
2
2
0
0
2
0
0
0
0
4
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
1
1
1
0
2
2
0
0
2
0
0
2
0
1
0
0
1
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
2
0
0
0
3
0
2
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
1
2
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
1
0
2
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
2
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
2
2
0
0
2
2
1
0
0
0
0
1
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
2
0
1
0
4
0
0
0
0
0
0
1
2
0
1
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
3
1
3
0
2
0
0
0
2
0
0
1
0
4
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
1
3
0
1
2
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
1
0
2
0
0
0
3
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
5
3
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
1
4
0
1
0
2
0
0
2
0
2
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
1
0
0
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
2
0
0
0
3
0
0
2
0
0
0
0
0
0
2
0
3
0
2
0
3
0
0
0
1
0
0
0
0
1
1
0
0
0
3
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
1
0
2
0
2
10
0
0
2
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
1
0
1
0
2
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
2
2
2
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
1
2
0
1
0
0
1
0
1
0
0
1
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
2
0
0
0
0
2
0
0
1
0
0
2
1
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
3
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
2
1
0
2
0
1
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
2
1
0
2
2
0
0
0
2
1
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
2
0
1
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
2
0
0
1
0
0
1
0
0
1
0
0
0
0
2
1
1
0
1
2
0
1
0
0
0
0
0
2
1
0
0
1
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
2
0
0
1
0
0
2
0
2
2
0
2
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
2
0
1
2
0
0
0
0
0
0
1
1
0
0
0
0
1
1
2
0
0
1
0
0
1
1
0
0
2
0
0
1
0
1
0
0
1
0
0
2
0
3
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
2
0
1
6
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
3
0
0
1
0
0
0
0
0
1
0
0
0
3
0
2
0
3
0
0
2
0
0
2
0
0
2
0
0
0
0
2
2
0
1
0
0
1
0
1
2
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
3
0
0
0
0
2
0
0
0
5
0
9
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
2
0
1
1
1
0
0
0
0
3
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
3
0
1
0
1
1
2
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
2
0
1
2
0
2
0
0
0
2
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
4
1
0
0
0
0
2
1
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
2
1
3
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
2
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
1
0
0
0
2
0
1
5
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
1
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
2
2
0
0
0
0
0
0
2
2
1
0
2
2
0
0
1
0
0
0
1
0
2
0
2
0
0
2
1
0
0
1
0
1
1
0
1
0
0
0
2
0
2
2
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
4
0
1
0
0
0
0
4
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
1
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
1
1
2
0
0
0
0
1
0
2
2
1
0
0
3
0
0
0
0
0
4
1
0
0
0
0
0
2
0
2
1
2
0
0
0
0
0
0
2
0
2
3
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
2
1
1
0
0
1
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
2
0
0
0
1
2
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
1
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
2
0
0
1
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
3
1
0
0
1
2
0
0
0
1
2
0
0
2
0
1
0
2
0
1
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
1
4
0
0
0
3
0
0
0
1
0
0
0
2
1
0
2
0
0
1
0
1
9
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
2
2
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
1
1
1
0
2
0
0
0
0
0
1
0
3
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
2
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
7
0
2
4
2
0
1
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
2
0
0
1
3
3
0
0
0
2
0
0
0
0
3
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
1
0
3
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
2
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
3
0
0
0
0
2
0
1
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
2
0
2
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
1
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
3
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
4
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
1
2
0
0
0
0
1
0
0
0
4
0
0
2
0
0
1
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
2
0
0
0
0
0
5
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
3
0
1
0
0
0
0
0
2
0
0
0
2
0
0
2
0
1
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
1
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
3
2
2
0
0
0
1
0
0
0
0
3
0
2
0
0
1
0
0
2
0
0
1
0
2
0
0
1
0
0
0
0
0
0
9
3
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
7
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
1
0
0
0
2
3
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
3
1
0
1
0
0
1
0
1
0
0
2
0
0
0
0
0
6
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
7
2
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
1
2
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
1
0
0
0
2
0
0
1
1
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
3
2
0
0
0
0
0
2
12
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
5
0
0
2
2
1
1
0
2
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
2
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
5
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
2
0
1
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
3
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
4
0
0
0
0
2
1
0
0
0
0
4
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
3
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
3
0
0
3
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
2
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
3
5
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
2
3
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
5
0
0
2
1
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
2
2
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
3
0
0
0
0
4
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
3
0
0
0
2
0
2
0
1
1
2
0
0
1
1
0
0
0
0
0
0
0
2
3
0
0
0
3
0
0
0
2
1
0
0
0
1
0
2
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
2
5
0
0
0
0
1
0
3
0
0
1
0
0
4
1
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
2
1
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
1
2
0
1
0
0
0
0
0
0
2
0
0
0
1
0
3
0
0
0
1
0
0
0
0
2
1
2
1
0
0
0
0
0
0
0
3
0
0
4
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
1
0
0
3
0
1
0
1
2
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
3
0
0
0
0
3
1
0
2
0
2
1
0
1
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
3
0
2
3
2
0
1
0
3
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
1
0
2
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
1
0
2
2
0
0
0
2
0
0
0
0
0
0
2
0
5
0
1
1
0
2
2
0
0
0
3
0
2
0
2
0
0
2
0
1
1
1
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
4
2
0
0
1
0
0
0
0
0
0
0
1
0
2
2
0
2
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
2
2
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
4
0
1
0
0
0
0
1
3
1
0
0
1
1
1
0
1
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
3
1
0
2
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
2
0
1
0
0
2
0
2
0
0
1
0
3
2
1
0
0
0
0
0
0
1
0
2
1
0
0
1
0
3
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
1
8
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
2
1
0
2
2
0
0
0
0
0
0
0
0
0
3
0
0
2
2
0
0
2
2
0
6
1
0
0
0
1
0
1
0
0
0
0
0
3
0
1
3
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
3
2
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
1
2
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
4
0
0
0
0
0
0
2
0
0
2
0
1
0
2
3
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
4
0
0
0
0
0
2
1
3
0
0
1
3
0
0
0
2
0
1
1
0
0
0
0
0
0
0
1
1
1
0
0
1
4
1
0
0
2
0
0
0
0
0
0
0
2
0
0
2
2
0
0
2
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
1
0
1
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
2
0
2
0
0
0
2
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
9
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
2
1
0
2
0
0
0
0
0
0
3
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
4
1
0
1
0
0
0
0
0
2
0
0
2
0
2
0
0
0
1
1
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
1
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
1
2
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
3
0
0
1
0
1
0
2
4
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
7
0
0
0
3
2
0
0
0
0
5
1
0
0
0
0
2
1
1
0
0
0
3
0
1
2
0
0
2
0
0
0
2
0
0
0
1
0
0
0
2
0
0
2
0
1
1
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
4
0
4
0
1
1
2
2
0
1
2
0
0
0
1
0
0
0
0
0
2
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
1
1
0
0
2
2
1
0
0
2
0
0
0
2
0
0
1
0
1
2
0
1
0
2
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
11
1
0
2
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
12
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
1
2
0
4
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
2
0
0
2
0
0
0
0
0
1
0
0
0
3
0
3
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
1
1
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
1
0
2
0
0
2
1
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
5
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
2
2
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
2
0
0
0
0
1
0
0
1
0
0
1
0
2
0
2
0
2
0
0
1
1
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
1
2
0
1
0
0
0
1
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
2
2
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
2
2
7
0
0
0
0
0
0
5
0
0
0
0
1
0
0
0
0
0
7
0
0
0
0
0
1
1
0
0
0
0
0
1
2
0
2
1
0
0
0
0
0
0
0
1
0
1
0
1
1
2
0
0
1
0
0
1
0
3
2
0
0
0
0
0
0
2
0
1
2
0
1
1
0
2
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
2
2
2
0
1
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
2
1
0
2
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
1
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
2
2
1
0
0
0
0
0
0
0
0
2
0
0
0
2
1
1
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
2
1
2
1
2
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
2
0
0
3
0
0
2
1
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
5
2
0
0
0
1
0
0
0
1
0
2
0
0
1
1
0
3
0
1
0
0
0
2
0
0
0
0
0
2
1
0
1
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
5
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
2
3
0
0
1
0
0
0
0
2
0
2
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
2
0
0
1
1
1
0
0
0
2
0
1
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
2
0
0
0
0
0
3
0
1
0
0
0
1
0
0
0
1
1
1
0
0
0
1
1
0
0
0
0
0
0
6
2
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
3
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
4
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
2
2
0
0
0
0
0
6
0
1
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
1
1
0
1
2
1
0
0
0
0
0
0
2
3
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
2
1
1
0
1
0
0
1
2
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
1
2
1
0
0
2
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
2
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
2
1
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
1
0
2
0
0
0
0
0
0
0
4
1
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
3
0
2
1
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
3
0
2
0
0
0
1
0
0
0
0
0
0
2
1
1
0
0
2
0
0
0
1
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
3
2
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
5
0
0
5
0
2
0
2
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
1
0
0
0
2
0
1
2
2
0
0
0
0
0
1
2
0
2
4
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
2
0
1
2
2
0
0
0
0
0
0
3
0
1
0
0
1
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
1
0
2
4
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
3
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
2
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
6
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
1
0
2
2
2
1
0
1
0
0
0
0
0
2
0
0
0
0
3
0
2
0
0
0
2
0
0
0
0
0
0
0
2
1
0
1
0
0
0
1
0
2
0
0
3
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
6
0
0
0
0
0
0
0
3
0
3
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
1
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
7
1
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
4
0
0
1
2
0
2
1
0
0
0
5
1
0
1
2
0
0
3
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
5
1
0
0
3
0
2
0
0
2
0
0
0
1
1
0
0
2
0
2
1
2
0
0
4
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
5
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
2
1
2
0
1
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
2
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
8
1
0
2
0
2
0
0
0
0
2
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
2
0
2
2
1
2
0
0
2
0
2
2
0
0
0
1
0
0
0
2
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
2
2
0
1
2
2
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
2
1
2
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
1
0
0
1
0
0
2
0
0
2
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
1
1
1
0
0
0
1
0
2
0
1
2
2
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
2
3
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
4
0
0
0
0
1
0
0
0
0
0
0
1
0
2
1
0
0
0
0
2
2
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
1
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
3
0
1
1
0
0
0
0
2
1
0
0
0
0
0
6
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
1
1
2
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
11
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
3
0
2
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
1
1
0
0
2
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
2
0
2
1
0
0
2
0
0
0
2
0
1
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
1
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
2
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
8
0
4
0
0
1
0
0
2
1
0
2
0
0
1
0
0
0
0
2
0
3
0
0
0
0
1
0
0
3
0
1
1
1
2
0
0
0
2
0
0
1
0
0
0
2
2
0
1
0
0
0
0
1
2
2
1
0
0
0
2
2
0
0
2
0
0
0
0
0
2
0
0
1
0
3
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
2
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
2
1
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
0
2
1
2
0
0
1
2
0
0
0
1
0
2
0
2
0
0
0
4
3
2
3
0
3
0
0
0
2
0
1
1
0
2
2
0
0
0
0
0
2
0
0
1
1
2
0
0
0
0
2
0
0
0
0
1
0
1
1
0
0
2
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
2
0
0
2
0
1
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
1
2
0
0
1
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
3
0
1
0
0
2
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
5
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
1
0
0
1
4
0
0
0
1
2
0
2
1
2
2
0
0
1
0
1
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
2
0
2
0
1
0
0
2
2
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
1
0
0
2
2
0
1
0
0
0
0
1
0
0
0
0
0
2
0
2
0
1
0
3
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
2
0
3
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
2
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
1
0
0
2
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
1
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
2
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
10
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
3
0
1
2
2
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
5
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
1
0
0
1
0
0
2
5
2
1
0
0
2
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
3
3
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
1
2
2
0
0
0
0
1
0
0
0
3
0
0
1
0
0
0
0
2
0
1
0
0
0
0
2
5
0
1
2
0
0
2
2
0
2
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
1
0
0
1
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
3
0
1
0
2
0
0
0
0
0
0
2
0
2
0
1
2
0
1
0
0
0
0
0
1
0
3
1
0
0
0
3
0
0
0
0
0
0
1
0
1
1
2
0
0
2
2
1
4
0
0
3
0
1
0
0
0
2
0
1
0
0
2
0
2
0
2
1
0
3
0
0
0
0
0
4
0
0
0
1
0
0
1
0
0
0
1
0
0
0
2
3
1
0
0
0
0
0
0
1
0
0
1
0
0
1
2
0
0
2
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
1
1
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
6
0
0
0
5
2
1
0
0
3
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
5
0
4
0
0
0
0
0
2
0
2
1
1
1
0
0
0
0
0
0
0
0
0
0
3
0
2
0
2
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
1
2
1
6
0
2
0
0
1
0
0
0
2
0
7
0
0
3
0
0
0
1
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
1
0
0
0
0
2
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
6
0
2
0
0
0
0
1
0
0
0
0
0
2
2
2
0
0
0
0
4
0
0
2
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
3
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
2
2
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
2
1
1
1
1
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
4
1
1
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
2
1
1
0
0
2
2
3
0
2
2
0
2
2
0
0
0
4
1
0
0
0
0
3
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
2
0
2
1
0
0
0
2
0
0
1
2
0
0
1
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
1
0
0
0
1
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
1
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
2
1
2
1
1
1
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
2
2
0
0
1
2
0
2
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
1
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
1
0
0
0
0
1
1
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
1
1
0
0
0
0
0
3
0
0
0
0
0
0
2
1
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
1
0
0
3
0
0
0
2
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
3
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
5
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
2
2
0
0
2
0
0
0
0
4
0
0
2
0
0
0
3
0
0
0
1
0
1
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
1
0
2
0
2
0
0
0
0
8
0
0
2
0
1
0
2
3
0
0
0
2
1
0
1
1
2
0
3
0
0
2
0
2
0
0
0
0
0
3
0
0
2
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
1
2
1
1
2
0
0
2
0
1
0
0
0
0
0
0
1
2
0
0
0
3
0
0
0
0
1
0
1
0
2
0
1
3
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
3
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
1
0
0
0
0
2
0
0
0
1
1
0
0
1
0
1
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
9
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
2
1
2
1
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
6
2
0
0
0
2
1
2
0
0
0
1
1
0
0
3
0
2
0
0
0
0
0
0
4
0
2
1
0
3
0
2
0
0
0
0
2
0
0
0
3
0
0
0
1
0
0
0
0
0
1
6
1
0
1
0
0
0
0
0
0
2
0
0
0
2
0
1
0
1
0
2
5
1
0
0
0
0
0
0
0
4
0
0
0
0
3
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
3
1
0
0
7
0
0
0
0
0
0
1
5
0
0
1
1
0
0
0
0
0
0
0
1
5
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
1
2
1
0
0
2
0
1
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
5
0
0
1
2
0
1
2
0
0
0
1
0
0
0
1
0
0
1
0
3
0
0
2
0
0
0
0
1
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
1
0
0
0
2
0
2
2
0
0
1
1
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
2
0
0
0
1
0
2
0
0
0
0
0
1
6
0
1
0
0
0
2
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
1
2
18
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
1
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
2
1
2
0
0
0
0
0
2
0
1
2
1
0
0
0
8
0
0
4
2
1
0
0
1
2
0
0
0
0
3
1
0
0
3
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
1
1
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
1
2
1
0
0
0
1
0
0
0
2
0
0
1
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
1
1
0
2
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
1
1
2
0
1
1
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
4
0
0
1
2
0
0
2
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
3
3
0
0
2
1
0
0
0
2
1
1
0
0
0
1
0
3
0
0
2
1
0
0
0
0
0
0
2
0
2
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
3
1
0
1
1
0
5
0
0
0
0
1
2
0
0
0
0
2
0
2
0
3
1
0
0
0
2
0
0
1
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
2
0
0
1
0
0
0
0
1
0
0
0
0
2
1
0
1
0
1
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
1
0
0
1
0
2
2
0
3
1
0
1
1
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
2
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
2
0
1
2
0
0
0
2
0
4
2
0
3
0
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
5
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
2
0
5
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
5
2
0
1
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
2
1
0
0
1
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
1
2
0
0
1
0
2
1
1
0
1
0
2
1
0
0
0
0
0
0
0
3
0
1
1
0
0
0
0
0
0
0
3
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
4
1
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
1
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
2
0
2
0
0
0
1
3
0
0
0
0
0
0
0
2
0
0
0
0
1
3
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
4
0
0
2
0
0
0
0
1
0
3
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
2
0
0
0
1
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
1
1
4
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
2
0
0
1
2
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
1
0
0
1
0
0
0
0
0
1
0
3
1
0
1
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
2
2
2
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
2
0
0
0
0
0
1
0
0
1
1
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
2
0
0
0
2
0
2
2
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
2
2
1
1
1
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
7
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
2
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
1
1
2
2
0
5
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
2
0
0
0
2
0
0
0
1
1
0
0
0
1
0
1
0
2
0
0
0
1
0
0
0
0
2
1
0
1
1
0
3
0
1
2
0
2
1
2
2
0
0
0
0
0
2
2
0
0
0
2
1
0
0
0
0
0
0
1
3
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
1
0
2
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
4
2
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
3
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
2
0
0
4
0
0
0
1
2
0
0
0
0
2
4
2
2
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
3
0
2
0
0
0
0
0
2
0
2
1
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
1
2
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
4
4
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
1
0
2
0
0
0
0
6
0
0
0
3
0
4
0
0
0
0
0
2
0
0
2
0
0
0
0
3
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
2
3
0
0
0
0
0
2
0
0
3
9
2
0
0
1
1
2
2
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
3
1
2
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
3
0
0
0
1
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
2
1
0
2
0
0
0
0
0
2
3
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
1
0
0
2
2
0
0
1
0
0
2
0
0
1
2
0
2
0
0
0
0
2
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
1
1
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
7
2
0
0
3
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
2
0
0
0
0
1
0
0
0
2
0
2
1
0
4
1
0
0
0
0
2
1
0
0
0
0
1
1
0
0
2
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
1
0
1
1
2
2
1
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
4
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
1
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
3
0
0
0
0
0
1
0
0
2
0
1
4
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
2
1
0
2
1
0
0
0
0
1
0
0
0
7
0
0
0
1
3
0
0
0
1
0
0
1
0
0
0
1
0
1
2
0
0
0
0
3
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
1
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
3
2
1
1
0
4
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
1
0
1
0
2
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
5
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
1
1
2
0
1
2
0
3
0
0
0
0
0
2
0
2
3
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
3
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
1
1
0
11
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
2
1
0
0
0
0
0
0
2
2
0
0
2
0
1
1
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
3
1
0
0
0
2
0
0
8
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
2
1
0
2
0
0
0
2
0
1
0
0
1
0
0
0
2
0
2
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
1
1
2
0
0
0
2
0
0
0
0
0
2
0
1
0
0
1
1
1
0
0
0
0
0
0
1
3
1
0
0
0
1
0
3
0
0
2
2
1
0
2
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
2
2
5
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
2
2
0
3
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
2
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
2
0
0
0
0
1
2
0
0
2
0
0
0
16
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
1
2
2
0
0
1
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
3
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
4
0
0
0
0
0
0
0
0
1
1
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
1
0
0
2
0
2
2
0
1
0
0
2
0
2
0
0
1
1
0
0
0
2
0
2
2
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
1
0
0
0
0
2
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
2
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
7
1
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
1
2
0
0
1
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
1
0
0
1
0
2
0
0
5
0
0
0
0
0
0
0
1
1
2
0
0
1
1
0
1
0
0
0
0
0
0
2
0
3
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
2
2
0
0
0
0
0
1
0
1
0
3
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
3
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
3
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
2
0
2
1
0
2
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
2
0
1
0
0
2
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
2
0
1
2
2
0
0
0
0
1
0
1
0
0
0
0
1
0
5
2
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
3
0
0
1
1
0
0
3
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
2
1
1
0
0
0
0
0
0
2
1
0
0
1
1
0
0
1
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
2
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
1
3
0
2
0
2
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
1
2
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
3
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
2
0
1
1
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
2
0
0
0
0
0
3
1
0
0
1
1
0
0
0
1
2
2
3
3
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
1
0
0
0
3
2
0
0
0
8
0
2
2
2
0
0
0
0
0
0
0
3
1
1
0
4
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
4
2
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
1
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
1
0
1
2
1
5
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
1
0
0
0
0
0
0
1
0
0
2
0
0
3
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
6
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
2
2
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
1
2
1
0
2
7
1
2
0
1
3
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
2
2
3
0
0
0
0
1
0
0
0
3
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
1
0
0
1
0
0
0
0
0
2
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
2
0
0
0
0
1
0
1
0
0
2
0
0
2
1
0
0
0
0
4
6
4
0
0
0
0
0
0
0
1
0
0
0
0
4
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
4
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
2
0
2
1
2
0
0
0
0
0
0
0
0
2
0
0
2
3
0
0
0
0
0
2
0
5
0
0
0
0
0
0
0
0
0
3
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
1
0
0
1
3
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
3
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
2
0
1
0
0
0
0
3
0
4
2
0
0
0
1
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
2
1
2
1
0
0
0
0
0
0
2
1
0
0
0
0
1
2
0
0
0
0
0
0
2
2
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
2
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
3
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
5
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
1
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
1
4
6
0
1
2
0
1
3
2
0
0
1
0
2
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
1
0
2
0
0
1
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
2
2
0
1
2
2
2
3
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
2
0
0
2
2
0
0
2
0
2
0
0
3
1
2
1
0
0
0
1
0
1
0
0
0
2
1
0
0
3
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
2
0
1
1
0
0
0
2
0
0
2
0
2
0
2
1
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
3
0
0
2
0
0
0
0
1
3
3
0
0
0
0
0
0
0
0
0
0
10
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
1
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
6
0
0
0
0
2
0
0
2
2
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
2
3
0
0
2
0
0
0
0
1
0
1
2
0
0
0
0
2
0
1
0
0
0
0
0
1
0
3
0
0
0
0
1
3
0
0
3
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
5
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
1
0
2
0
1
0
2
3
1
0
0
0
0
2
2
0
1
0
0
0
1
0
3
0
0
2
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
1
0
0
0
3
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
1
1
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
1
0
0
0
0
0
4
0
0
0
1
0
0
1
0
0
6
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
3
0
0
2
0
0
0
0
1
0
3
0
0
2
2
0
0
2
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
7
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
7
0
1
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
2
2
0
1
3
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
1
0
0
2
2
1
2
0
1
0
0
2
0
0
1
1
1
0
0
5
2
1
0
0
1
0
0
2
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
2
0
0
0
0
0
1
0
0
1
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
4
2
0
0
0
0
0
0
2
2
1
0
0
2
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
3
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
7
0
0
0
1
1
2
4
0
0
0
0
2
0
1
0
2
0
0
0
0
1
0
0
0
0
1
1
0
0
0
2
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
1
1
2
0
2
3
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
2
1
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
3
1
3
1
0
0
2
0
0
2
0
0
0
0
2
0
1
0
1
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
1
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
1
0
2
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
2
1
2
0
2
0
0
1
0
0
0
0
3
1
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
1
0
0
2
0
1
0
0
0
2
1
1
0
0
1
0
0
0
5
2
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
2
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
2
0
0
0
2
0
0
5
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
6
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
3
0
1
1
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
3
0
0
0
8
3
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
1
2
2
2
0
2
1
0
0
2
2
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
2
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
2
2
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
1
0
0
2
0
0
3
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
3
0
1
0
0
1
0
3
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
3
1
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
2
2
0
0
0
2
2
0
0
2
0
2
2
0
0
0
0
1
4
0
3
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
1
0
0
3
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
2
1
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
2
0
0
1
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
2
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
1
0
0
3
4
3
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
1
0
2
1
1
0
1
2
2
2
1
0
0
2
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
2
0
0
2
0
0
0
5
2
0
0
2
0
0
1
1
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
1
2
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
3
2
0
4
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
2
1
0
2
0
2
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
2
1
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
1
0
0
0
1
1
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
3
2
0
2
1
1
0
0
1
0
2
0
0
1
0
2
0
1
0
0
0
7
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
1
0
2
0
1
2
0
0
0
0
0
0
2
0
1
0
4
0
0
2
0
0
0
0
0
0
1
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
1
0
0
2
0
0
0
1
0
0
1
2
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
4
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
1
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
1
0
0
1
1
2
1
2
3
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
2
1
2
0
0
0
5
0
0
0
1
1
0
0
2
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
2
2
0
2
0
3
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
4
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
2
0
0
1
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
2
1
1
0
0
0
1
1
0
0
1
2
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
9
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
2
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
1
1
0
0
2
0
0
0
0
0
2
0
1
2
0
0
2
0
3
0
0
0
0
0
1
2
3
0
0
0
0
0
0
0
7
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
2
0
2
0
2
0
0
0
0
3
0
1
0
0
0
2
0
0
1
0
2
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
2
1
0
0
0
2
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
1
1
4
2
0
0
2
2
1
0
2
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
1
3
0
1
0
2
0
0
0
2
0
5
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
3
0
2
5
0
1
0
0
0
2
0
0
0
0
0
2
2
0
0
1
0
0
3
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
1
1
2
2
0
2
0
2
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
2
0
0
0
0
2
4
0
1
1
0
0
0
0
0
0
1
0
4
0
2
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
3
0
0
1
0
0
0
0
0
0
0
1
0
0
2
2
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
1
1
0
0
0
1
4
0
0
2
0
0
0
1
0
2
0
2
6
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
4
2
1
1
0
0
3
0
1
0
1
0
0
0
0
1
3
0
0
0
0
0
1
0
3
0
0
1
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
1
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
2
0
1
1
1
0
0
1
0
2
0
0
0
1
0
1
2
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
4
0
1
0
0
3
0
0
0
0
3
0
0
0
1
0
2
1
3
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
3
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
3
1
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
2
1
3
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
1
8
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
1
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
1
2
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
3
0
1
0
2
0
0
0
0
0
0
0
1
0
1
0
3
2
0
0
0
0
0
1
2
2
0
0
2
0
0
0
1
0
1
0
0
0
0
0
1
0
0
2
0
0
2
0
4
0
0
0
0
3
0
1
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
2
0
2
2
2
0
1
1
0
2
2
1
0
2
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
1
0
0
1
2
0
0
0
0
1
0
0
0
3
1
0
2
1
0
0
0
0
1
3
1
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
2
4
0
0
0
1
0
2
1
0
0
0
1
0
0
2
2
0
0
0
0
1
0
1
1
1
2
0
0
1
0
1
2
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
3
0
2
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
1
2
0
0
0
0
0
1
1
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
1
0
0
2
1
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
1
1
0
0
2
0
0
2
0
0
0
2
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
1
1
0
3
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
1
0
0
1
1
2
0
3
0
0
0
0
0
2
0
2
0
0
0
0
0
2
2
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
3
4
0
1
1
0
0
0
3
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
1
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
2
0
1
0
0
1
0
2
1
0
0
0
0
0
0
0
1
0
3
0
2
3
3
0
1
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
2
3
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
2
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
2
2
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
1
5
0
0
4
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
2
1
0
0
1
1
0
0
0
2
0
0
1
0
0
1
0
0
3
4
0
2
0
0
1
0
2
1
0
1
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
3
0
2
2
0
1
0
0
0
0
0
2
0
2
0
2
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
10
0
3
0
0
0
2
1
0
1
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
6
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
7
0
2
0
0
0
3
0
2
1
0
0
0
0
0
0
0
3
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
7
0
0
0
3
4
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
2
0
0
0
4
1
0
0
0
0
0
1
3
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
1
1
0
0
2
0
0
3
0
0
0
1
2
2
0
0
0
0
2
1
1
2
0
0
2
1
5
1
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
3
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
3
1
2
0
2
0
1
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
3
0
0
0
0
1
0
0
0
0
2
0
2
0
0
2
0
2
2
0
0
0
0
0
0
1
2
0
0
0
0
2
1
1
0
0
0
0
1
2
0
4
0
0
0
0
1
0
0
1
0
0
2
0
0
3
0
0
0
1
0
1
0
3
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
1
0
0
1
2
0
1
0
0
0
2
0
0
0
0
2
3
0
0
1
4
0
0
0
0
0
0
1
2
1
0
2
0
0
0
0
0
0
0
0
2
0
0
4
12
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
1
0
0
2
2
0
0
0
2
0
0
0
0
0
2
0
0
2
2
0
2
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
6
1
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
4
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
2
2
0
0
1
0
0
0
2
0
1
0
2
1
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
2
2
1
0
1
0
2
1
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
3
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
1
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
3
5
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
3
0
0
0
4
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
1
0
2
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
1
2
0
0
0
2
1
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
1
0
0
0
0
0
0
0
4
3
0
0
0
0
1
1
0
0
0
0
1
0
1
3
1
0
0
1
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
4
0
0
0
0
2
2
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
5
0
1
4
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
2
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
1
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
3
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
1
0
0
2
0
0
0
0
2
2
0
0
2
0
0
0
4
0
4
0
2
1
2
0
0
0
1
4
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
1
3
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
2
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
3
0
0
0
0
0
2
0
1
0
0
2
2
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
2
0
0
5
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
5
1
0
0
0
0
0
0
0
1
0
1
2
0
2
0
0
0
1
1
2
2
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
18
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
1
2
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
2
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
3
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
2
1
0
0
0
0
3
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
2
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
2
1
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
3
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
1
1
4
0
0
1
0
0
0
0
1
2
0
1
0
0
0
0
4
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
3
0
0
1
0
0
4
0
0
1
0
0
0
1
0
1
0
1
0
2
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
3
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
2
0
0
1
1
1
1
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
2
0
0
1
2
0
0
2
0
0
0
2
0
0
2
0
0
0
2
2
0
1
0
0
0
0
0
0
0
2
0
0
0
1
1
0
2
0
0
0
1
2
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
2
2
0
0
0
3
0
0
0
0
1
0
0
0
0
4
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
1
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
3
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
2
0
0
4
0
0
0
0
0
0
0
0
0
2
1
1
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
4
0
0
2
0
0
4
1
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
2
0
0
2
2
1
0
0
0
0
0
0
0
2
0
0
0
1
1
0
1
0
0
0
1
0
0
0
2
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
1
0
0
3
1
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
4
0
2
2
0
0
1
0
0
0
0
1
0
3
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
3
1
1
1
0
0
1
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
3
0
0
2
0
0
1
0
0
0
1
0
0
0
7
0
0
2
0
2
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
6
0
1
1
0
1
2
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
5
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
3
1
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
2
0
2
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
3
2
0
2
0
0
1
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
2
2
1
0
0
5
0
2
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
1
0
1
1
2
2
0
0
0
0
0
2
0
0
2
0
0
2
0
3
2
1
0
0
0
0
0
0
2
1
1
4
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
8
0
2
0
0
2
0
0
0
0
0
0
1
1
0
0
2
0
2
0
1
0
0
1
0
0
0
4
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
1
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
1
0
1
1
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
2
0
0
0
0
0
0
2
1
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
2
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
1
1
1
0
1
4
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
3
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
1
0
2
0
0
1
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
2
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
2
0
0
2
0
6
0
0
3
0
0
2
1
0
0
0
0
0
0
0
0
1
0
1
0
2
0
1
2
1
0
2
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
2
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
3
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
3
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
2
0
2
2
2
2
0
1
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
2
0
2
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
6
0
0
0
2
2
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
1
0
1
0
2
0
0
0
0
2
0
0
1
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
2
0
0
1
1
0
0
1
0
2
0
0
0
1
3
0
2
0
0
1
0
0
0
0
0
0
0
1
1
2
2
0
0
1
2
0
1
0
2
1
2
0
0
2
0
0
3
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
7
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
1
2
0
0
0
3
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
1
1
2
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
1
2
0
0
3
0
0
0
0
4
0
0
0
1
0
2
0
0
0
1
2
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
1
0
0
2
1
0
1
1
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
2
0
0
1
0
0
0
0
1
0
0
1
1
1
0
0
0
0
2
0
2
0
0
0
2
2
0
0
0
0
0
2
2
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
1
2
1
0
0
0
0
1
0
3
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
1
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
2
2
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
1
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
1
0
0
2
2
0
0
1
1
0
0
1
0
2
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
3
1
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
3
0
2
0
2
0
2
1
1
0
0
1
0
2
0
2
1
0
0
2
3
0
0
0
0
1
3
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
3
2
0
4
0
0
0
1
0
0
1
1
3
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
1
0
0
2
2
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
1
1
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
2
1
0
1
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
2
2
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
4
0
0
0
2
1
2
0
0
1
0
2
0
8
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
2
3
0
0
2
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
2
0
2
0
0
1
1
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
2
0
1
0
0
2
2
0
0
0
0
0
0
0
2
2
0
1
0
0
0
1
0
0
0
0
0
0
4
1
2
1
0
0
2
0
4
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
3
0
2
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
1
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
1
1
0
0
1
0
0
0
1
0
2
1
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
2
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
3
3
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
3
0
0
0
2
0
1
0
2
1
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
1
0
0
1
2
0
0
0
1
1
2
0
1
0
4
0
1
0
0
2
3
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
8
0
0
0
2
0
0
0
0
0
1
2
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
1
0
2
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
1
2
0
0
0
0
0
1
0
4
0
1
2
0
0
0
0
0
1
1
0
3
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
3
3
2
0
0
0
0
0
3
0
0
0
3
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
1
2
0
0
1
1
3
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
3
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
2
2
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
3
0
0
2
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
4
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
1
0
1
1
0
0
0
0
1
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
2
0
0
3
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
2
0
8
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
2
0
1
2
0
0
0
2
0
0
1
0
1
0
0
0
0
2
0
1
0
0
2
0
0
0
2
0
0
2
0
1
0
1
1
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
3
2
0
2
0
1
0
0
0
0
0
0
1
0
2
0
0
1
0
0
1
1
0
10
0
0
0
0
2
2
3
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
1
0
0
2
4
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
1
2
0
0
0
0
1
0
1
0
0
0
1
0
0
0
2
1
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
2
0
3
1
1
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
1
1
0
0
2
3
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
1
4
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
1
0
0
1
3
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
2
2
0
2
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
1
0
0
0
0
3
0
2
0
2
0
0
2
1
0
0
0
1
3
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
2
0
1
0
2
0
0
0
0
0
2
2
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
1
0
1
2
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
2
0
2
0
0
1
0
0
0
0
2
2
0
0
0
0
3
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
2
0
2
0
0
2
2
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
1
2
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
3
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
3
1
0
0
1
1
0
0
0
4
0
0
0
2
0
1
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
2
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
1
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
5
1
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
1
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
1
0
0
0
0
4
0
0
0
0
2
0
0
1
2
0
0
1
0
0
0
0
2
0
1
0
0
0
1
0
2
0
0
2
0
1
2
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
9
0
0
0
8
2
0
2
0
1
1
0
1
3
0
2
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
2
0
0
2
2
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
1
2
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
3
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
1
0
1
0
1
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
2
0
1
0
0
0
2
0
0
2
1
0
0
0
0
2
1
1
0
0
0
2
0
0
0
0
0
3
0
0
0
0
2
0
0
2
0
0
0
1
1
1
0
0
0
0
0
0
0
1
1
0
0
0
3
0
0
0
0
0
2
2
0
0
0
2
0
0
1
0
1
0
2
0
0
0
2
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
14
0
0
0
0
0
0
1
0
1
1
0
4
0
1
0
0
0
0
0
1
2
0
0
0
3
0
0
0
0
1
0
1
0
1
0
3
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
3
1
1
2
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
2
1
0
1
0
0
0
1
0
3
0
2
2
0
0
2
0
0
0
0
2
0
1
0
2
0
0
0
0
2
0
2
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
2
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
1
2
2
0
1
0
0
1
0
0
0
0
0
0
1
0
0
2
0
4
2
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
4
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
2
0
1
0
2
0
0
0
1
0
0
0
0
2
5
1
1
0
8
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
2
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
2
0
1
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
1
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
1
1
2
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
2
1
0
0
5
0
0
1
0
1
0
0
1
0
0
3
0
2
0
0
0
0
1
0
0
7
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
2
0
1
0
0
0
2
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
7
0
0
1
1
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
0
3
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
2
4
0
1
0
0
1
2
0
1
0
0
0
0
0
0
1
0
0
0
1
0
4
2
0
0
0
2
2
1
0
1
1
0
0
0
0
0
0
0
0
1
7
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
1
0
1
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
2
2
0
0
1
0
0
0
2
0
0
0
2
2
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
2
1
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
2
0
0
1
0
0
1
11
2
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
1
0
0
0
0
0
0
0
2
1
0
1
0
1
2
4
0
0
2
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
2
0
3
0
0
0
2
0
0
2
0
0
0
0
1
1
0
2
0
0
0
0
0
0
2
2
0
4
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
1
2
0
0
0
1
0
4
0
0
2
0
1
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
2
2
0
0
1
0
1
3
2
0
0
0
2
6
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
1
0
4
0
1
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
4
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
9
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
2
4
0
0
1
2
2
0
2
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
2
3
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
4
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
2
0
0
0
0
0
1
3
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
1
1
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
1
0
2
2
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
1
1
0
0
0
0
1
3
3
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
1
0
1
0
0
0
0
2
0
0
0
0
2
1
1
1
0
1
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
6
0
0
0
1
0
0
0
0
5
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
5
2
0
0
2
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
2
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
3
0
0
0
1
1
0
0
1
1
0
2
0
0
0
0
0
0
0
0
1
0
2
2
2
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
1
1
3
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
5
0
0
2
1
0
1
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
1
0
1
2
0
0
2
0
1
0
0
0
0
0
0
0
1
0
3
0
0
0
0
1
0
0
0
0
0
2
1
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
1
3
2
4
0
0
0
0
0
0
0
0
2
0
1
0
0
3
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
1
6
0
0
0
2
0
0
1
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
2
2
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
3
0
0
0
0
2
2
0
0
0
0
2
0
1
0
2
0
0
0
0
0
2
0
1
1
1
0
2
3
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
3
0
9
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
3
1
0
1
0
0
0
2
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
3
1
0
0
0
0
2
0
0
0
0
2
1
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
2
0
0
8
0
1
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
1
3
0
0
0
1
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
2
1
0
0
0
0
0
0
0
3
4
0
1
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
2
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
2
0
2
1
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
1
2
0
0
1
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
2
0
0
2
2
0
0
0
0
0
1
0
0
3
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
1
2
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
2
0
0
0
0
2
1
1
1
0
0
2
2
2
0
0
0
1
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
7
0
2
0
0
0
0
0
0
2
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
3
0
0
1
1
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
1
0
0
3
0
2
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
1
0
0
0
0
0
0
1
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
4
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
3
0
2
1
0
1
0
3
0
0
0
0
0
0
0
0
0
3
1
0
0
2
0
0
1
0
0
0
0
0
0
0
4
2
3
2
1
0
0
3
0
0
0
0
2
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
1
0
0
0
2
1
6
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
2
0
0
1
2
0
0
1
0
0
0
1
0
2
0
0
3
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
1
0
3
2
1
0
11
0
8
0
0
0
1
1
0
0
0
0
0
1
0
0
0
2
1
2
0
2
0
0
2
1
0
2
0
0
0
0
0
0
0
0
3
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
1
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
1
0
1
0
5
0
0
2
0
1
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
1
1
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
3
1
1
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
3
2
1
1
2
0
1
0
0
0
0
0
0
2
2
0
1
0
0
1
0
0
0
0
0
1
0
0
2
0
0
1
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
3
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
2
2
1
0
1
2
0
0
0
0
0
3
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
2
0
0
0
1
0
2
0
0
0
3
1
0
0
0
3
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
1
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
4
0
0
1
2
0
0
0
6
0
0
1
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
3
1
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
2
1
1
0
2
2
0
1
1
0
2
3
0
0
1
0
0
0
2
2
1
0
2
0
0
3
0
2
0
2
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
2
0
0
4
0
0
0
0
1
1
0
1
2
0
0
0
3
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
3
0
0
0
0
1
0
0
0
0
1
2
1
2
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
1
1
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
2
0
1
0
1
0
0
0
1
3
0
0
1
2
0
0
4
0
0
0
0
0
0
1
0
1
0
2
2
0
0
0
0
0
2
1
2
1
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
1
0
0
0
3
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
4
0
0
0
0
2
1
0
0
1
2
0
0
0
1
0
0
0
1
1
0
3
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
2
0
0
2
2
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
1
0
0
1
0
1
1
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
1
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
2
0
0
0
3
0
0
0
0
1
0
0
1
0
0
0
0
2
2
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
1
2
0
0
0
0
1
0
0
0
0
2
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
2
1
0
0
0
1
0
0
0
2
0
0
1
0
0
0
3
0
0
0
0
0
0
0
1
2
2
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
3
0
0
2
0
0
0
0
1
0
1
0
0
2
0
0
1
0
3
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
1
0
1
1
0
1
1
1
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
2
0
0
0
0
0
1
1
0
10
0
2
0
2
0
0
0
0
3
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
2
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
2
1
0
0
0
2
1
0
0
3
0
0
1
0
0
1
0
0
4
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
3
0
2
0
0
0
0
0
2
0
0
1
2
3
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
2
0
0
1
5
0
0
0
0
0
0
0
0
0
2
2
0
1
1
0
0
0
2
1
0
1
2
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
7
0
0
0
0
0
0
1
2
0
0
0
1
2
0
1
0
0
0
0
2
0
0
0
1
1
0
0
1
2
0
0
0
0
0
1
0
0
1
0
0
1
2
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
3
1
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
1
0
0
1
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
1
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
2
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
1
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
5
2
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
6
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
2
0
1
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
4
0
1
0
0
0
0
1
1
0
3
0
0
0
2
1
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
1
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
1
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
1
0
0
1
1
0
2
0
0
0
3
3
0
2
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
2
1
0
0
0
2
0
0
1
0
0
1
0
1
0
2
2
7
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
2
4
2
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
1
0
1
2
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
2
0
1
0
0
11
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
1
0
0
0
0
6
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
4
0
0
2
3
0
0
0
3
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
1
2
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
3
0
0
0
2
0
0
0
0
3
0
2
0
2
0
2
0
3
0
0
0
0
0
1
1
0
0
1
0
3
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
2
0
2
2
2
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
1
0
0
3
2
0
0
0
1
0
0
0
2
0
0
0
0
2
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
4
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
1
1
0
0
0
1
0
0
0
0
0
1
4
2
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
2
0
3
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
3
0
2
0
2
0
0
0
11
0
0
0
0
0
0
0
4
0
1
0
0
0
0
2
0
0
2
1
1
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
3
0
0
0
0
2
0
0
1
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
3
2
0
2
0
0
0
0
0
0
0
1
1
0
2
2
0
3
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
1
2
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
2
3
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
1
0
0
0
2
0
0
1
1
0
0
1
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
1
2
0
0
1
2
1
1
0
2
0
0
0
1
2
0
0
2
0
0
2
2
0
2
2
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
1
0
4
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
4
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
3
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
2
0
2
1
0
0
0
0
0
2
0
1
0
0
2
0
1
0
0
1
2
0
4
1
0
0
0
0
0
2
0
1
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
9
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
2
1
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
3
0
2
1
0
0
0
0
2
0
2
2
2
1
0
0
0
0
1
2
0
0
2
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
1
2
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
3
0
0
0
0
0
0
0
0
0
3
0
1
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
2
0
5
0
0
2
0
0
0
0
0
0
0
0
3
2
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
3
2
0
2
4
0
0
2
0
0
0
1
2
2
0
0
0
0
4
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
3
0
0
2
0
0
3
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
1
2
0
3
0
0
0
1
1
3
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
1
0
0
0
0
0
1
7
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
1
6
2
0
0
0
0
0
0
0
2
2
0
1
1
0
2
0
3
0
0
0
0
1
0
1
6
2
0
0
0
2
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
1
0
1
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
1
1
2
0
1
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
3
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
3
0
0
0
1
0
1
2
0
0
0
0
2
2
1
1
0
1
0
8
0
0
1
0
0
0
2
0
1
0
0
0
0
2
0
0
0
1
0
0
2
0
0
2
0
0
0
2
2
0
0
0
2
1
0
0
0
2
0
4
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
2
0
2
1
0
0
2
1
0
0
2
2
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
2
0
0
0
0
0
2
1
2
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
2
2
2
0
0
3
0
0
1
1
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
3
0
4
0
0
0
0
0
0
0
5
0
0
1
0
0
0
0
1
0
0
0
2
0
3
1
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
2
2
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
2
1
0
1
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
5
0
0
2
0
0
0
1
0
2
0
0
0
1
0
2
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
3
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
1
0
0
2
1
0
0
1
0
0
1
0
0
2
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
3
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
1
1
0
1
0
0
2
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
1
0
1
1
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
3
7
2
0
0
2
1
0
0
0
1
0
2
0
0
0
3
0
0
0
1
2
0
0
1
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
1
9
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
2
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
1
1
2
0
0
1
0
3
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
2
0
1
2
2
2
2
0
0
0
0
0
0
0
0
2
1
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
5
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
2
1
0
0
0
0
0
1
0
2
0
0
0
1
0
2
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
7
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
3
0
2
0
1
1
0
0
0
0
0
0
3
2
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
1
0
0
2
2
2
0
0
2
2
0
0
0
2
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
1
0
0
0
4
2
1
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
4
0
0
0
2
0
1
0
0
0
0
2
1
2
0
2
2
0
0
0
0
1
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
4
2
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
2
2
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
1
0
2
0
0
1
2
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
3
0
0
0
2
0
1
2
0
0
2
2
0
0
2
7
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
2
1
0
0
0
1
0
0
0
3
0
0
0
0
0
0
2
2
0
2
0
0
1
0
0
1
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
2
0
0
0
1
0
0
2
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
4
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
1
4
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
1
0
0
3
1
0
0
0
0
0
1
0
0
1
0
0
0
1
7
0
0
0
3
0
1
0
0
1
1
1
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
3
3
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
2
1
1
0
0
0
1
0
0
1
0
0
1
0
2
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
1
0
0
2
0
1
0
1
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
1
0
0
1
7
1
0
2
0
2
0
0
2
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
5
2
0
0
0
0
0
0
2
0
1
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
8
0
0
0
0
4
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
3
1
0
0
0
0
2
0
0
2
2
2
0
0
1
0
0
0
0
0
0
1
1
2
4
4
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
5
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
2
1
0
0
0
0
1
0
6
0
1
0
0
1
0
0
1
0
0
0
2
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
2
0
1
0
2
0
0
1
1
2
0
1
1
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
4
0
1
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
2
2
0
1
1
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
1
0
2
0
1
0
0
0
0
2
0
0
1
3
1
0
0
2
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
1
3
1
2
0
0
2
2
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
1
0
0
3
0
0
2
0
0
0
0
0
0
0
1
0
0
0
5
0
0
0
1
0
0
0
0
2
0
0
0
2
2
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
2
1
0
0
0
0
1
1
1
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
2
0
0
1
2
2
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
1
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
4
2
0
0
6
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
1
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
2
0
0
0
0
5
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
1
2
3
0
2
0
0
0
0
0
0
2
0
1
1
0
0
0
0
1
0
0
0
1
2
0
1
0
3
0
0
0
1
0
0
0
1
0
1
2
0
0
5
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
2
2
1
0
0
0
0
0
0
0
0
8
0
0
0
0
0
1
0
0
2
0
0
6
0
0
0
0
0
0
1
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
2
0
0
1
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
2
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
1
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
3
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
1
1
0
0
1
2
1
0
0
0
1
0
3
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
1
0
1
1
0
0
2
0
0
0
0
2
0
3
0
0
2
0
0
5
0
0
2
0
0
0
0
0
0
0
0
0
3
0
1
0
0
2
1
0
0
0
0
1
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
3
1
0
1
0
0
2
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
2
2
0
2
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
2
0
2
2
2
1
4
0
0
0
0
0
0
2
0
0
0
1
5
2
0
0
0
0
0
0
2
0
1
1
0
0
0
0
4
1
0
3
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
2
2
0
0
2
0
0
0
2
0
0
1
0
0
0
0
2
2
0
0
0
2
1
0
2
0
0
0
1
2
0
0
0
0
0
0
0
2
1
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
1
0
4
0
0
2
0
0
0
0
1
0
1
1
1
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
2
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
2
0
0
1
0
0
0
4
0
0
0
1
0
0
1
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
9
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
2
0
0
2
1
0
0
2
0
0
0
1
0
0
6
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
1
2
0
5
2
0
0
0
1
0
0
0
3
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
1
1
2
1
0
2
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
3
0
0
0
2
1
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
1
2
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
2
1
1
0
2
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
4
0
4
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
1
2
3
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
1
0
0
0
2
1
1
0
0
0
0
2
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
1
1
0
2
0
2
1
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
2
3
2
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
3
0
2
0
0
0
0
0
1
0
0
0
1
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
1
2
0
0
1
0
1
0
0
0
0
0
0
0
0
1
2
1
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
2
0
0
1
0
2
0
1
0
0
2
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
3
2
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
1
2
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
5
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
1
2
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
3
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
1
3
0
1
0
1
1
0
2
0
0
0
2
2
0
0
1
2
0
1
0
0
0
0
0
1
3
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
2
0
0
2
2
0
0
2
1
0
4
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
2
0
0
1
0
1
0
1
0
0
0
0
1
3
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
2
0
0
1
0
0
0
0
7
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
5
0
0
1
0
1
1
0
0
1
0
0
1
1
0
1
0
0
2
0
0
0
0
0
0
2
1
0
2
2
0
12
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
2
1
0
0
0
0
0
0
4
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
2
0
1
0
2
3
0
0
0
4
0
1
1
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
1
0
0
0
3
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
10
0
1
0
0
0
0
0
0
0
0
1
0
11
0
1
1
0
0
0
3
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
2
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
1
0
0
0
1
0
0
0
0
2
1
0
2
0
2
2
0
0
0
0
1
0
0
0
1
0
1
0
0
0
2
0
0
0
0
1
2
2
0
0
0
0
1
2
2
0
0
0
1
0
0
0
0
0
2
6
0
0
0
3
0
3
0
1
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
2
0
1
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
1
0
3
0
0
2
0
0
0
2
0
0
0
0
0
2
1
1
1
0
0
0
0
0
0
0
0
0
1
1
1
3
2
3
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
3
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
1
0
0
2
1
0
1
0
2
0
0
0
0
0
0
2
0
1
0
0
0
2
0
1
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
2
0
0
0
0
1
1
0
1
2
0
0
2
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
1
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
3
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
2
0
2
0
1
2
2
0
0
2
0
3
0
0
0
0
0
0
1
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
3
0
1
0
0
0
0
0
1
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
2
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
1
1
0
1
2
0
0
0
2
0
0
3
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
2
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
1
0
0
0
0
0
0
1
2
0
0
1
0
2
0
6
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
2
0
1
0
0
0
0
1
3
2
1
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
3
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
4
0
0
0
0
0
8
0
0
3
2
0
0
0
0
0
0
1
0
0
0
0
0
2
1
1
0
0
0
0
0
0
3
0
1
2
0
0
0
0
0
2
0
0
0
0
0
1
2
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
1
0
0
0
0
6
0
1
0
0
0
8
1
0
2
0
1
0
2
0
0
1
0
0
0
0
0
0
0
5
0
0
0
1
0
0
0
1
1
0
0
0
1
0
3
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
1
0
1
0
0
0
0
2
0
0
0
1
0
3
0
0
1
0
0
0
0
0
1
0
2
1
1
0
0
0
0
0
0
0
0
0
0
3
2
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
3
1
0
1
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
3
3
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
2
5
0
0
0
0
0
2
3
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
9
4
1
0
0
2
0
1
0
0
2
0
0
2
0
0
0
0
3
2
2
0
0
0
0
1
1
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
3
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
2
0
0
0
0
0
2
0
2
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
1
2
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
2
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
1
0
0
0
0
2
1
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
1
0
2
0
0
0
0
1
0
1
2
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
4
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
2
0
2
0
2
0
0
1
2
0
1
0
0
0
0
2
0
0
0
0
2
0
1
2
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
1
1
1
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
1
1
0
2
2
0
0
0
0
9
0
0
0
2
0
0
2
0
0
0
1
2
0
2
1
0
0
0
0
1
0
0
2
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
1
0
1
2
1
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
4
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
3
0
2
0
0
1
0
2
1
0
0
0
0
0
2
0
0
0
1
0
3
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
1
0
0
0
1
0
0
2
0
0
0
2
0
0
1
2
2
1
0
0
0
1
0
0
2
0
0
3
3
0
1
0
0
0
0
1
1
0
0
0
2
2
1
0
1
4
0
0
1
0
2
1
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
3
1
1
0
0
1
2
2
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
1
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
1
0
2
0
0
3
1
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
2
0
1
0
0
1
0
0
1
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
2
0
0
0
1
0
2
0
4
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
1
1
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
1
1
0
2
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
2
2
4
1
0
1
2
0
0
0
1
0
2
1
0
2
0
0
0
0
0
1
0
0
0
0
1
0
1
2
1
0
0
0
1
2
0
1
0
0
0
2
0
0
1
0
0
0
1
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
5
0
0
0
0
0
1
0
2
0
0
0
0
2
0
2
0
2
0
0
0
5
2
0
2
0
0
0
0
1
0
0
1
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
1
0
1
0
0
3
0
0
0
0
0
2
0
1
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
2
1
0
0
0
0
1
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
5
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
6
0
0
1
2
2
2
0
1
0
0
0
0
0
0
2
2
0
0
0
3
2
0
0
0
2
0
1
2
0
2
2
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
1
0
2
0
0
0
0
0
2
0
0
0
0
2
3
0
0
0
0
0
1
0
0
0
0
0
3
0
0
2
1
0
2
0
0
1
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
7
0
0
0
0
0
4
3
0
0
1
0
2
0
3
0
0
0
0
2
2
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
2
1
0
3
0
1
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
2
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
1
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
3
0
0
3
0
1
0
0
0
0
3
0
1
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
5
2
1
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
5
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
2
0
0
0
2
0
3
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
2
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
2
0
0
0
0
0
2
0
1
0
0
6
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
2
0
0
0
0
0
1
3
0
0
2
0
0
0
0
0
0
0
0
0
0
5
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
1
0
0
0
2
2
0
0
3
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
8
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
2
1
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
2
2
0
2
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
2
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
4
1
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
6
0
0
0
0
0
0
1
4
0
0
2
0
0
0
0
0
0
2
0
1
0
1
0
0
1
2
0
0
1
0
0
1
2
0
1
0
0
2
0
0
0
0
0
2
1
0
0
0
1
0
0
1
0
0
0
0
9
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
2
1
0
1
2
2
2
0
0
0
2
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
2
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
1
0
0
0
0
0
0
2
0
3
3
0
0
0
0
0
0
1
0
0
2
0
0
1
0
2
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
3
0
0
0
0
1
0
1
0
2
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
1
0
0
0
0
3
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
2
0
0
0
0
0
2
3
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
1
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
4
0
1
1
0
1
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
1
2
0
0
0
0
0
0
6
2
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
3
0
0
0
0
0
0
1
0
0
1
1
0
0
2
0
0
1
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
3
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
3
0
2
0
0
0
0
2
0
0
3
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
3
2
0
0
0
0
2
2
0
0
0
0
1
0
0
2
0
1
2
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
2
0
0
0
0
0
4
0
3
0
2
0
0
2
0
1
1
0
0
0
0
1
0
1
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
2
0
0
0
1
0
0
1
0
2
0
0
0
0
2
0
3
0
0
0
1
0
2
0
0
0
4
3
0
0
0
1
0
0
0
0
1
0
0
0
0
1
3
0
0
0
0
0
0
2
2
1
0
2
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
3
1
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
2
0
1
1
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
5
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
3
2
0
2
2
0
0
2
0
0
0
0
2
2
0
0
0
0
2
0
0
0
2
0
4
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
3
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
5
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
1
0
0
0
0
0
5
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
2
0
0
0
0
0
2
1
2
0
0
0
0
1
3
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
1
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
5
0
2
0
0
0
0
0
0
0
0
0
0
3
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
2
0
0
0
0
0
2
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
2
0
0
0
2
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
2
1
0
2
0
1
0
0
0
1
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
5
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
4
3
1
1
0
0
0
0
0
0
2
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
3
0
0
0
3
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
1
1
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
2
2
0
0
0
1
1
1
4
0
0
2
1
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
3
0
2
0
0
0
2
1
0
0
0
0
0
0
3
0
0
0
0
0
1
1
0
1
0
0
0
0
0
2
0
1
0
3
0
0
5
0
0
0
0
0
0
0
0
1
1
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
3
0
1
0
0
2
0
0
1
0
0
0
2
0
2
1
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
2
0
2
1
5
0
0
0
0
0
0
0
0
0
2
2
2
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
2
1
0
0
0
2
0
1
0
0
0
2
0
0
0
5
0
0
0
0
0
1
0
0
1
0
4
0
1
0
0
0
2
0
0
4
0
0
0
0
0
0
1
1
2
1
0
2
0
2
2
0
1
0
0
2
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
2
1
0
0
0
2
0
1
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
1
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
2
0
0
12
0
0
0
0
0
0
1
2
1
1
0
0
0
0
0
0
0
0
2
0
0
0
4
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
1
2
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
3
2
0
0
2
0
0
0
0
0
0
0
1
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
4
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
2
2
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
2
0
1
1
0
2
1
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
3
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
1
0
0
11
0
0
0
2
2
0
3
2
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
1
0
0
2
0
0
0
0
0
0
0
2
3
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
1
3
0
0
2
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
3
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
2
2
0
1
0
2
1
1
0
2
0
0
0
0
0
1
0
1
1
0
0
0
0
2
0
0
0
0
2
1
0
2
3
2
1
0
0
0
6
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
1
1
1
0
2
2
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
2
0
0
1
0
0
2
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
2
1
0
0
0
2
0
0
0
0
0
2
0
0
2
0
1
0
0
3
0
1
0
2
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
3
0
2
0
0
0
0
1
1
2
0
3
0
2
0
0
2
1
0
0
0
4
0
1
0
0
4
0
0
0
0
0
1
2
1
1
0
1
0
0
2
3
0
3
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
5
0
2
0
0
0
0
0
1
2
2
0
0
0
1
0
0
0
1
0
2
1
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
2
4
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
2
0
0
2
0
0
2
0
1
0
0
0
0
1
0
2
1
2
0
0
2
0
0
2
2
0
2
1
0
0
2
0
0
1
3
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
1
0
0
2
0
0
0
1
0
2
1
0
0
0
3
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
2
0
0
0
2
0
0
1
0
0
2
1
0
0
0
1
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
1
0
0
2
1
0
0
0
4
0
0
0
3
0
0
0
2
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
2
0
1
0
1
1
0
2
1
0
1
1
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
1
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
3
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
1
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
5
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
2
1
0
2
0
0
2
1
0
2
0
0
0
3
0
0
0
0
2
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
3
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
1
0
3
0
0
0
0
0
0
0
2
0
1
2
1
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
5
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
3
0
2
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
3
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
1
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
1
0
0
0
0
0
0
0
1
2
2
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
2
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
1
2
0
2
1
2
0
0
0
1
0
0
1
2
0
0
0
1
0
0
0
0
1
2
0
1
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
1
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
1
0
0
0
0
2
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
3
0
0
0
0
1
0
2
0
1
0
1
1
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
2
0
1
0
1
0
0
0
2
0
2
0
0
0
2
0
0
0
3
0
3
0
2
0
2
0
2
0
0
1
0
2
0
2
0
0
0
0
3
2
0
0
0
0
0
0
0
3
0
0
1
0
0
0
2
0
0
3
0
2
0
0
0
2
1
0
0
0
3
0
0
0
0
0
1
2
0
1
0
0
0
2
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
3
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
4
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
2
0
0
3
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
2
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
5
2
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
2
0
1
0
2
2
0
0
1
0
1
0
0
3
0
0
4
0
1
2
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
1
0
1
0
0
1
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
3
0
0
1
0
2
0
0
0
0
11
1
2
2
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
1
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
1
2
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
2
2
1
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
3
0
0
0
0
1
1
0
2
2
0
0
1
0
1
0
1
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
1
0
2
0
0
3
0
1
0
0
2
2
1
0
1
0
0
0
0
2
2
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
1
1
3
1
2
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
2
1
0
1
0
0
2
0
2
1
0
0
0
1
2
0
0
0
0
4
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
3
2
1
0
0
1
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
1
3
0
0
1
1
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
3
2
0
0
1
2
0
2
0
0
1
0
2
0
0
0
3
3
0
0
3
0
0
0
1
0
0
2
3
0
1
0
3
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
2
0
3
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
5
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
2
0
0
2
0
0
0
0
3
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
2
0
1
0
0
8
0
0
0
0
2
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
1
0
1
0
1
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
4
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
2
0
1
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
3
1
2
1
0
2
0
0
0
2
6
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
29
0
0
2
0
0
0
1
0
2
1
1
0
0
0
0
0
1
0
2
2
0
0
0
0
0
2
2
0
0
0
1
0
0
1
0
0
0
0
2
0
2
2
0
0
0
0
1
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
2
1
0
0
0
1
1
2
0
0
0
0
0
1
0
2
0
1
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
3
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
1
0
1
0
0
0
0
1
0
0
2
0
2
0
1
0
0
0
2
0
1
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
2
3
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
3
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
2
0
1
0
0
0
0
0
1
0
2
0
2
1
0
0
2
0
0
0
2
0
0
0
1
1
0
0
2
0
0
2
0
0
1
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
2
0
2
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
2
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
2
0
0
2
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
3
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
6
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
2
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
5
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
4
0
1
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
1
2
0
2
0
0
2
2
0
1
0
0
0
0
0
0
0
2
0
2
2
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
2
0
1
0
0
1
0
0
1
0
3
4
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
4
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
2
1
4
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
2
3
0
2
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
2
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
1
0
0
0
1
0
1
2
0
0
0
1
0
2
0
0
0
2
0
0
3
2
0
0
1
2
2
2
0
1
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
1
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
1
0
2
0
0
0
6
0
0
0
2
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
1
0
2
0
0
2
0
0
0
0
1
2
0
1
0
0
0
6
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
2
0
0
0
2
0
0
1
0
1
3
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
3
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
3
0
0
0
0
0
0
0
0
1
0
0
1
1
0
5
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
4
0
2
0
2
0
2
1
0
0
0
0
0
0
1
0
0
0
1
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
1
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
5
0
0
1
0
1
0
0
0
0
1
0
2
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
1
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
2
0
0
2
0
1
0
1
1
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
1
3
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
1
0
2
0
0
0
0
4
0
3
3
0
0
0
2
5
0
0
0
2
0
1
0
3
0
2
1
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
2
1
2
2
0
1
1
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
1
0
0
1
1
1
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
2
2
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
2
2
0
0
0
0
0
2
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
1
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
2
9
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
2
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
1
1
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
1
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
3
0
0
5
0
1
1
0
1
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
1
0
2
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
2
0
2
0
5
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
2
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
3
0
0
2
0
5
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
16
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
3
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
3
0
0
0
0
4
1
0
0
2
0
0
0
2
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
1
2
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
5
1
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
1
0
0
1
0
0
0
0
0
0
2
2
0
0
1
1
0
0
1
0
0
1
2
0
1
1
0
0
0
0
2
1
0
0
2
0
1
3
0
2
1
0
0
0
2
1
0
0
0
2
1
0
0
2
0
0
0
6
0
0
2
0
0
0
3
0
0
1
0
3
0
0
0
0
0
0
2
1
2
0
0
1
0
2
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
3
3
0
2
0
0
0
0
2
0
0
0
2
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
2
0
2
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
1
1
0
0
1
2
2
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
1
0
0
2
0
6
0
0
1
0
2
0
0
0
0
0
0
0
1
7
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
2
2
2
0
1
0
0
1
0
0
0
1
0
0
1
2
0
0
0
1
1
0
0
0
0
2
0
0
0
2
1
0
0
0
0
1
1
0
0
0
0
2
0
0
0
5
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
1
0
2
0
2
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
1
0
3
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
3
0
0
2
1
0
0
0
0
2
0
0
1
0
0
0
0
3
0
0
5
0
0
0
0
0
0
2
2
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
1
0
0
5
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
4
2
1
0
2
0
0
0
0
0
0
1
1
2
0
0
0
0
0
2
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
3
1
2
2
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
3
0
0
0
3
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
1
0
0
2
2
2
2
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
3
5
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
3
2
0
2
1
0
0
0
2
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
2
2
0
0
0
7
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
1
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
3
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
3
0
0
2
0
1
0
1
0
0
0
0
0
1
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
3
0
1
0
0
0
1
0
0
0
0
2
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
10
0
0
0
0
0
0
1
0
2
0
2
3
0
0
1
0
0
0
4
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
2
1
0
0
1
0
0
3
0
0
0
0
0
2
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
1
2
0
0
2
2
1
0
2
0
0
0
0
0
0
0
0
2
3
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
1
0
2
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
2
1
0
0
1
0
0
0
3
2
0
0
0
0
0
1
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
2
3
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
1
1
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
4
1
2
0
1
0
0
0
3
0
0
0
0
3
0
1
0
0
0
0
0
4
0
3
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
1
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
4
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
1
2
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
1
0
2
2
0
0
0
0
1
0
4
0
1
0
0
0
0
0
0
0
1
0
1
0
0
2
1
0
0
2
0
0
0
3
0
0
1
0
0
1
0
0
0
0
2
1
3
0
0
0
0
0
3
1
2
0
0
1
2
0
2
0
0
0
0
0
1
0
0
0
1
1
0
1
1
0
0
0
0
0
1
1
0
0
0
2
0
1
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
2
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
1
1
0
4
0
0
1
0
0
0
0
0
0
3
2
2
0
0
0
0
0
0
0
0
4
1
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
2
2
0
1
0
0
2
6
0
0
1
3
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
4
1
1
1
0
1
1
0
2
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
1
0
1
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
3
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
1
0
0
0
4
0
1
0
0
2
0
0
0
0
2
1
0
1
0
2
0
0
0
1
0
0
0
0
0
2
2
2
2
0
1
0
0
0
0
2
0
0
2
0
0
0
5
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
3
1
0
0
0
7
1
0
0
0
0
0
1
1
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
2
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
2
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
3
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
6
2
1
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
3
0
0
1
0
0
0
3
0
0
0
0
0
0
2
0
0
0
2
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
2
1
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
2
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
2
1
0
1
2
0
0
0
1
0
2
0
0
0
6
0
0
0
0
2
1
0
0
0
0
0
0
3
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
2
0
0
2
0
1
0
4
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
3
0
3
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
1
1
0
0
0
2
0
1
1
0
0
0
0
2
0
2
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
2
0
1
0
1
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
2
4
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
3
1
4
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
2
1
2
2
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
1
1
1
2
2
0
0
0
0
0
0
1
0
0
2
0
0
3
4
2
0
2
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
1
0
0
0
2
1
0
0
1
0
2
2
0
1
0
0
0
0
1
0
0
2
2
0
0
1
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
2
0
1
0
1
2
0
0
4
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
1
1
0
0
0
1
2
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
2
0
1
0
1
0
0
0
2
0
0
0
1
2
0
0
0
2
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
2
0
0
0
2
0
0
0
2
0
0
0
0
1
1
0
0
1
0
1
0
0
0
2
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
2
0
2
2
4
0
3
1
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
2
1
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
1
0
1
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
3
0
0
0
2
0
1
0
0
2
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
3
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
3
2
0
0
0
2
0
0
2
0
1
0
1
1
0
0
0
0
0
2
0
0
0
1
0
0
0
1
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
2
0
0
2
0
0
2
1
0
2
0
2
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
1
0
0
0
0
3
2
0
1
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
3
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
5
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
3
0
0
1
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
3
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
1
0
0
0
1
0
0
3
0
1
1
0
0
0
0
0
3
0
0
3
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
1
1
0
0
3
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
2
1
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
2
2
0
0
2
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
1
3
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
2
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
1
0
3
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
3
0
2
0
0
0
0
2
3
0
0
1
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
1
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
2
0
1
2
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
1
0
0
4
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
2
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
5
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
3
0
1
1
0
0
0
0
1
1
1
1
0
0
0
0
2
0
0
1
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
2
1
0
0
1
0
0
0
0
0
0
1
1
1
0
2
0
0
2
0
1
2
0
0
0
1
0
2
1
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
3
0
0
0
0
1
0
1
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
2
0
1
0
2
0
0
3
0
0
0
0
0
15
1
1
0
0
0
0
1
0
2
0
0
1
0
0
3
2
0
0
1
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
1
2
2
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
2
1
1
2
0
0
0
2
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
2
2
2
3
0
0
2
0
0
0
0
1
0
0
2
1
3
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
2
0
0
1
3
1
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
5
2
0
0
0
0
0
0
0
1
2
0
1
0
0
3
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
2
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
3
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
3
2
0
2
0
0
1
1
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
1
0
0
2
0
0
0
2
0
0
2
2
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
3
0
0
1
0
1
0
0
3
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
5
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
2
0
3
0
0
1
1
0
0
0
0
0
2
0
0
0
0
5
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
1
0
0
2
0
0
0
0
2
0
0
0
2
0
0
1
0
0
2
1
0
0
1
0
0
0
0
2
0
0
2
0
2
0
2
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
1
2
2
0
2
2
1
0
1
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
2
0
0
1
0
0
2
4
0
0
3
0
4
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
2
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
2
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
4
1
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
2
2
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
3
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
1
0
0
0
0
2
0
1
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
1
0
0
0
2
0
0
3
0
3
0
0
0
1
0
2
0
0
2
2
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
6
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
3
2
7
2
0
2
1
0
2
0
4
2
0
1
1
0
2
3
0
2
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
1
2
1
0
0
0
2
0
0
1
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
5
0
2
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
1
0
1
0
2
0
2
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
3
0
0
0
2
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
2
4
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
4
0
0
0
0
2
2
0
0
0
0
1
0
2
0
0
0
2
2
0
0
0
0
1
0
0
2
0
0
4
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
3
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
2
1
0
0
2
0
2
0
1
0
2
3
0
2
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
1
0
2
0
0
0
7
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
1
1
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
5
0
0
0
0
0
0
5
4
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
1
0
2
1
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
1
0
1
1
2
0
0
0
0
1
0
1
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
1
0
0
0
0
2
0
1
0
2
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
3
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
2
0
0
2
0
3
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
1
4
0
0
0
0
1
0
2
0
0
2
2
0
0
1
0
1
0
0
2
1
2
0
0
1
0
1
0
0
3
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
5
1
0
1
0
2
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
3
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
4
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
2
2
0
0
0
2
0
0
1
1
0
0
0
0
0
1
11
0
0
0
0
0
0
0
0
0
2
3
0
0
1
1
0
0
0
0
1
0
2
0
0
1
0
0
0
0
5
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
1
2
0
0
0
0
0
1
1
0
1
2
0
0
0
0
0
0
0
0
2
0
3
1
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
2
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
5
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
1
0
0
0
0
1
2
2
0
0
0
2
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
2
1
0
0
2
2
2
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
5
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
2
0
0
0
1
0
0
3
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
3
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
2
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
1
1
0
1
0
2
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
2
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
4
0
1
4
1
0
0
0
0
0
0
2
0
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
2
1
0
1
2
0
2
0
0
0
2
0
0
0
2
0
0
0
0
5
0
2
1
0
4
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
2
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
3
1
0
2
1
0
0
0
4
0
0
2
0
0
1
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
3
3
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
1
0
1
0
0
1
0
2
1
0
2
0
1
0
0
0
2
0
0
0
0
1
0
0
0
3
0
0
1
0
0
2
2
3
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
2
1
1
0
0
0
0
0
10
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
3
0
2
1
0
1
0
0
0
0
0
2
2
0
1
0
2
1
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
2
0
0
4
0
0
0
0
0
0
2
0
0
0
2
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
2
0
0
1
0
0
2
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
5
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
2
0
0
1
0
0
2
0
0
0
0
0
0
1
0
2
2
0
2
8
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
2
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
1
0
2
0
0
0
3
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
2
0
0
0
0
1
2
0
1
0
2
0
2
0
1
0
0
0
0
3
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
3
0
1
0
1
0
0
2
0
0
0
1
0
2
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
1
3
0
0
0
0
0
0
0
2
0
1
0
0
3
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
2
1
0
0
0
0
2
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
1
1
2
1
2
2
0
0
1
0
2
0
0
0
2
2
0
0
1
0
0
1
2
0
0
0
0
3
0
0
0
2
0
0
1
0
0
0
0
0
1
2
0
1
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
1
4
0
2
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
1
0
0
2
0
0
2
0
2
0
0
0
2
0
0
0
2
0
3
2
0
2
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
1
1
2
0
0
1
0
4
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
1
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
1
0
3
0
3
0
1
0
2
0
0
2
0
0
0
2
0
0
1
3
0
2
1
1
0
0
3
0
0
0
0
2
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
1
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
4
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
2
0
1
0
1
2
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
1
0
0
1
0
4
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
8
0
1
0
0
1
0
4
0
0
0
2
0
1
0
0
0
0
4
1
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
2
2
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
1
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
3
0
0
0
0
0
2
1
1
2
0
0
0
0
0
0
1
0
2
1
0
0
0
1
0
1
0
1
0
1
0
1
2
0
0
2
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
1
0
0
1
1
0
0
1
0
0
0
1
1
0
0
0
0
0
2
0
4
0
0
0
1
2
0
0
0
0
0
0
1
0
1
2
0
0
0
0
1
1
0
1
1
2
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
1
0
8
0
0
1
0
3
0
0
2
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
1
2
0
3
0
7
2
2
0
1
0
1
1
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
1
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
1
0
0
1
0
2
2
0
2
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
8
0
0
8
0
0
0
0
6
0
0
0
2
0
0
0
0
0
3
0
2
1
0
0
1
0
1
0
0
2
0
1
0
1
2
0
0
2
2
0
1
0
1
0
0
0
0
0
0
1
0
1
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
7
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
1
0
1
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
1
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
3
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
1
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
1
0
1
1
0
0
0
0
2
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
3
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
1
0
4
0
0
1
1
0
0
0
2
5
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
4
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
2
1
0
0
0
0
0
1
0
0
0
1
0
0
0
3
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
2
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
3
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
3
0
0
6
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
1
0
1
0
2
0
2
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
2
0
0
3
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
1
1
0
2
0
6
0
0
2
0
0
1
0
0
0
2
0
2
0
2
1
1
1
0
1
0
0
0
0
0
0
2
0
0
3
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
4
4
1
0
2
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
6
0
0
2
0
0
0
1
0
0
0
0
1
2
2
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
2
0
1
0
1
0
0
0
0
0
1
1
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
2
2
4
2
0
2
0
1
2
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
2
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
1
2
0
0
0
1
2
0
6
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
3
0
2
0
0
2
0
1
0
0
1
0
0
2
2
0
2
0
2
1
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
3
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
2
1
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
1
1
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
1
0
2
0
0
2
1
0
5
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
3
3
0
1
0
1
2
0
0
0
2
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
1
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
1
0
0
2
0
1
0
0
2
0
0
2
0
0
0
3
0
2
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
1
0
0
2
2
0
3
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
4
0
2
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
2
2
3
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
2
0
4
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
2
2
0
0
0
0
1
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
3
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
3
0
0
1
2
0
0
0
0
0
2
2
0
4
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
1
0
0
0
1
0
0
0
0
2
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
4
1
1
0
2
1
0
1
0
0
2
0
0
0
0
0
0
0
0
2
2
0
2
2
2
0
1
0
2
1
1
1
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
2
0
0
0
2
0
0
2
0
2
0
1
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
2
1
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
2
0
2
0
0
0
0
1
0
2
3
0
0
0
0
0
0
0
0
1
2
0
4
0
0
2
0
0
0
2
0
1
0
1
0
0
0
1
1
1
0
0
2
1
0
0
0
0
2
0
0
0
0
0
2
0
1
1
1
0
2
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
2
3
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
1
0
2
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
3
0
0
1
0
1
1
0
0
1
0
0
3
3
0
0
3
0
0
1
0
0
2
1
0
0
1
0
0
0
0
2
2
0
0
0
0
0
3
1
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
10
0
0
0
1
5
0
1
0
0
5
3
2
1
0
0
2
0
2
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
1
2
0
0
0
0
0
1
0
3
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
2
2
0
1
1
0
1
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
1
0
0
0
0
2
0
1
2
0
0
0
1
0
1
0
0
0
0
1
0
1
0
1
0
1
2
0
0
3
0
0
1
0
0
0
0
1
0
0
0
1
0
1
1
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
2
0
1
0
1
1
0
0
0
0
0
1
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
3
1
0
2
0
0
0
0
1
0
0
0
0
1
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
2
0
0
0
0
2
3
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
2
1
0
0
0
0
0
0
0
2
2
0
4
0
0
0
1
0
0
2
0
5
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
3
1
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
3
0
2
0
0
0
0
0
0
2
0
1
7
0
2
0
1
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
1
2
0
0
1
0
0
0
0
0
0
0
1
1
0
2
0
3
0
0
0
0
0
0
0
0
0
2
0
0
9
0
1
0
0
2
0
0
0
0
1
2
0
0
1
0
2
0
0
0
1
0
0
2
0
7
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
1
2
0
2
1
1
0
0
0
2
2
0
0
1
0
2
0
0
0
0
1
0
0
2
0
0
1
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
2
0
0
2
1
2
2
0
3
0
2
2
0
0
2
0
0
0
0
2
0
1
0
0
2
3
0
0
0
0
0
0
0
1
0
0
2
0
2
0
1
1
3
0
0
1
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
3
2
0
0
0
0
0
0
0
0
4
0
0
0
1
2
2
1
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
2
4
0
2
0
1
0
3
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
2
0
2
0
0
0
0
0
0
0
2
3
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
3
0
0
0
0
1
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
1
0
3
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
2
0
0
3
0
0
0
0
0
2
0
0
1
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
2
4
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
1
3
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
3
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
5
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
1
5
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
12
0
0
0
0
0
0
0
0
0
0
1
1
0
0
7
2
2
0
0
0
0
2
2
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
3
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
6
0
4
0
0
0
0
0
1
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
2
0
1
0
0
1
0
0
1
1
2
1
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
4
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
3
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
2
0
1
0
5
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
2
2
3
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
2
0
1
2
2
3
0
2
2
0
0
1
0
2
0
0
0
2
0
1
1
0
0
0
3
0
0
0
2
0
0
0
3
1
1
1
0
0
0
0
1
0
0
0
0
0
2
2
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
4
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
2
0
3
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
3
0
2
2
0
0
0
0
0
2
2
1
0
0
2
0
0
0
0
0
0
0
1
3
0
1
1
1
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
3
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
1
2
2
0
1
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
6
1
0
0
0
0
0
1
0
0
0
0
0
0
1
2
1
0
2
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
1
0
2
0
0
0
0
1
3
1
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
3
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
3
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
2
0
0
0
2
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
3
1
2
0
0
0
2
1
0
0
0
0
0
0
0
3
0
0
0
0
2
2
0
0
0
0
0
3
2
0
0
3
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
1
0
0
0
0
0
0
3
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
3
0
0
2
0
0
0
0
0
0
1
8
0
0
0
2
1
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
2
1
2
2
0
0
0
0
0
0
0
0
1
2
0
4
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
5
0
0
0
0
0
0
1
0
1
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
3
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
2
0
0
0
2
2
1
0
0
0
0
0
1
0
0
2
3
0
0
2
0
1
2
0
0
0
1
0
0
0
1
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
2
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
3
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
2
0
0
0
2
0
2
0
0
1
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
1
0
2
0
1
0
0
2
0
0
1
2
2
0
1
0
0
0
0
0
0
0
0
1
0
6
0
0
1
2
0
2
0
2
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
1
0
0
2
0
0
1
1
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
3
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
5
0
0
0
0
0
0
0
1
0
1
0
0
0
5
0
1
2
0
0
0
0
0
0
0
2
0
0
0
2
3
1
0
0
1
0
0
2
0
1
0
1
0
2
0
0
0
2
1
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
3
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
4
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
4
2
0
0
0
0
4
1
0
0
0
0
0
0
0
0
2
1
0
0
0
2
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
2
0
2
0
0
1
0
0
1
0
0
0
0
0
1
0
0
2
2
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
4
0
0
2
2
0
0
0
0
0
1
0
2
1
0
0
0
0
2
3
0
1
1
2
0
3
1
0
0
0
0
3
0
0
2
1
2
1
3
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
2
0
0
1
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
4
0
0
1
0
2
0
2
1
0
2
0
0
0
3
0
3
1
0
2
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
1
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
10
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
2
0
0
2
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
5
0
2
0
0
0
0
0
0
2
0
0
1
2
1
0
0
0
0
1
1
0
0
2
0
1
0
1
0
0
2
0
0
0
0
1
2
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
3
1
0
0
2
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
1
0
1
0
0
1
0
2
0
2
0
1
0
0
2
0
0
2
1
0
3
0
1
0
0
0
0
3
1
2
0
0
1
0
0
1
0
0
0
0
0
0
2
3
0
0
0
0
0
0
3
0
1
0
0
0
2
0
0
0
0
0
0
3
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
2
4
1
0
2
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
3
1
0
3
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
1
1
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
2
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
3
0
0
0
2
0
0
0
0
1
0
0
3
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
2
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
4
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
1
4
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
1
3
0
0
2
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
2
1
2
0
0
0
1
0
1
1
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
3
0
0
2
0
0
0
0
1
2
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
2
1
0
2
0
0
0
0
2
0
0
2
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
3
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
1
0
0
2
1
0
2
0
0
0
0
0
0
3
1
1
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
1
1
0
0
1
0
0
1
0
1
0
0
3
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
3
2
0
0
0
0
5
0
1
0
1
0
2
2
2
4
0
0
1
1
1
0
0
2
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
2
0
2
1
0
0
0
1
2
2
0
0
0
1
2
0
0
0
1
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
3
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
2
2
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
2
2
0
0
1
2
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
4
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
2
2
0
0
0
0
0
3
0
3
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
2
0
0
1
0
0
0
1
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
3
3
0
0
0
0
0
0
0
0
0
1
3
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
4
0
0
1
2
0
0
2
0
0
1
4
1
3
0
3
2
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
2
0
1
1
0
0
9
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
2
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
3
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
2
1
2
1
0
0
1
0
0
1
0
1
1
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
3
0
0
0
1
0
1
0
0
1
0
1
0
0
0
1
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
3
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
1
1
0
0
2
0
3
1
0
0
0
0
0
0
1
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
7
0
1
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
1
2
0
1
0
0
3
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
2
0
2
1
4
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
3
0
0
2
0
0
2
1
0
0
2
2
0
0
0
0
2
0
0
2
0
2
0
0
1
0
0
0
2
1
1
0
0
1
1
1
0
1
1
0
0
0
2
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
2
1
0
0
0
0
0
1
2
0
0
0
0
0
1
0
2
1
1
0
1
0
0
0
0
1
3
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
3
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
2
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
1
0
2
0
2
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
2
1
2
0
0
0
2
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
3
0
3
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
3
2
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
2
2
0
0
0
0
0
0
0
2
0
0
0
3
0
0
3
0
0
1
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
7
0
0
0
0
0
0
3
2
0
2
0
0
0
2
0
0
1
0
2
0
0
0
2
0
0
1
1
2
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
2
2
0
0
0
0
2
0
2
0
0
0
2
2
0
0
0
0
0
0
0
3
1
0
0
0
2
0
0
1
2
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
1
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
2
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
2
2
4
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
1
0
0
2
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
1
0
0
0
0
5
0
0
0
0
3
0
1
2
2
1
0
0
0
2
0
0
0
2
1
0
0
2
0
0
0
0
2
1
0
0
0
2
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
2
2
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
2
1
2
0
0
0
1
2
2
0
1
0
0
0
3
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
3
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
3
0
1
0
0
2
0
0
2
1
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
2
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
1
1
0
2
0
2
0
0
0
0
0
2
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
2
0
3
0
2
0
2
2
0
0
0
1
0
0
2
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
2
2
0
0
1
1
3
2
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
2
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
2
0
0
3
1
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
2
0
0
0
0
2
2
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
3
0
0
1
3
0
0
0
2
1
1
0
2
1
0
0
1
0
1
0
1
0
0
2
2
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
3
1
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
4
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
2
1
1
1
0
0
0
1
0
1
0
0
5
0
1
1
0
0
0
1
0
1
0
0
2
0
0
0
0
1
0
1
0
0
2
0
0
0
0
1
2
0
0
2
2
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
4
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
3
0
1
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
1
0
0
0
0
2
0
2
0
2
2
1
0
0
0
2
0
0
2
0
2
2
0
0
1
0
0
2
2
0
1
1
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
5
0
0
2
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
1
0
0
0
3
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
1
1
4
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
5
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
5
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
2
0
2
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
2
1
0
0
2
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
2
0
0
1
0
1
0
3
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
2
0
2
0
0
0
1
1
0
2
0
0
5
0
0
3
0
0
3
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
10
0
0
2
0
0
0
0
0
0
0
0
2
1
3
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
1
0
0
2
0
0
1
1
1
0
1
0
0
2
0
0
1
0
2
1
0
2
0
0
0
1
0
1
0
2
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
1
0
0
0
3
0
1
0
0
0
2
0
0
0
5
2
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
3
0
0
3
0
0
0
0
0
0
0
2
0
0
1
0
0
0
4
1
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
2
0
1
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
1
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
2
0
1
0
2
1
0
0
0
1
0
0
3
2
0
0
0
0
0
2
2
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
3
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
1
2
2
0
1
2
0
0
0
0
0
2
0
0
0
0
0
2
1
0
1
0
2
0
0
0
2
0
0
1
1
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
1
3
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
5
1
0
0
1
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
1
2
0
2
2
0
0
0
0
1
0
4
1
0
0
0
0
0
0
2
3
2
1
2
0
1
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
1
6
3
0
0
0
0
0
2
0
1
0
0
0
2
0
1
0
0
1
0
0
0
0
0
1
0
6
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
1
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
2
1
1
0
0
2
0
1
1
1
0
0
0
2
0
0
0
1
0
0
1
0
3
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
2
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
3
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
2
1
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
2
1
0
0
2
2
1
0
0
0
1
0
1
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
2
0
0
1
1
0
0
0
0
0
0
1
0
0
0
2
0
2
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
5
0
0
1
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
3
0
0
1
0
0
0
0
0
0
2
1
0
0
1
1
0
0
0
2
0
0
0
1
0
0
0
0
5
2
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
5
0
2
0
0
2
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
3
0
0
1
1
0
0
1
0
0
0
0
1
2
3
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
1
0
0
5
0
0
0
1
2
0
0
2
0
0
1
0
2
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
3
1
3
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
2
2
0
2
0
0
1
0
0
1
0
0
2
0
1
0
1
0
0
0
0
2
0
1
2
0
0
2
0
2
1
0
0
0
0
0
0
1
0
2
0
0
0
0
1
2
3
0
0
0
1
0
0
0
3
0
0
0
1
0
2
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
1
1
0
2
0
0
0
1
0
0
2
0
0
0
1
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
7
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
3
2
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
1
2
1
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
1
2
0
0
3
0
0
0
0
0
0
2
0
0
1
0
1
0
1
2
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
5
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
2
0
0
1
1
1
2
0
1
1
2
1
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
10
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
2
0
2
1
0
2
2
0
0
0
2
2
0
0
1
1
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
1
2
0
0
0
1
2
1
0
0
0
1
2
0
1
0
0
0
0
0
0
2
5
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
1
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
2
0
0
2
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
1
2
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
7
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
2
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
2
0
0
0
4
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
1
1
3
0
2
1
0
0
0
0
2
0
2
2
0
0
1
0
0
0
1
2
1
0
0
0
0
0
0
1
0
0
1
1
2
2
0
1
1
0
0
0
0
0
0
0
2
2
1
0
0
2
2
0
1
0
0
0
4
0
0
1
2
1
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
3
2
0
2
0
0
0
0
2
0
1
0
0
1
1
0
0
0
0
2
0
0
2
0
1
2
1
1
1
0
0
0
0
0
0
0
0
0
1
2
0
1
2
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
3
1
1
0
0
0
1
1
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
1
0
0
3
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
1
1
1
0
0
0
0
0
2
0
0
4
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
2
1
0
3
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
2
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
1
0
0
2
0
0
0
0
0
0
2
3
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
3
0
0
0
1
2
2
0
0
0
0
2
0
2
1
2
1
1
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
2
0
0
2
1
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
3
1
0
0
0
1
2
0
0
1
0
1
0
2
0
0
0
1
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
2
0
0
0
0
0
0
2
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
1
0
2
0
0
2
0
1
0
1
1
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
1
2
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
2
2
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
4
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
2
0
1
0
1
0
0
1
0
0
1
0
2
0
1
0
2
0
1
1
0
0
2
2
1
0
0
1
0
0
0
1
0
0
1
0
0
5
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
2
0
0
0
1
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
3
0
0
0
1
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
3
2
0
2
0
0
0
1
0
0
0
5
1
0
0
0
2
2
0
0
0
2
2
0
0
2
0
0
0
2
1
0
0
1
0
0
2
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
1
1
0
0
0
1
2
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
4
0
4
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
5
0
0
2
2
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
3
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
1
2
2
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
1
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
3
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
2
0
0
1
1
0
1
2
0
0
0
0
0
2
0
0
0
0
0
2
0
3
0
1
0
0
0
1
0
0
0
0
0
0
2
1
1
0
4
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
2
0
1
0
0
0
0
1
2
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
1
1
2
0
1
0
1
3
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
2
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
2
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
3
0
2
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
1
0
0
1
0
0
0
0
6
0
1
0
2
0
0
0
5
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
5
1
0
0
0
0
0
1
0
1
2
0
0
0
2
0
1
0
0
0
1
0
2
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
1
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
2
1
0
0
0
3
0
2
0
0
3
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
3
0
0
2
0
0
0
0
4
0
0
0
0
0
1
1
1
0
0
0
2
0
1
0
4
0
0
0
0
0
0
0
0
0
2
4
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
2
0
2
1
0
0
1
2
2
0
0
0
0
2
0
0
0
0
0
0
5
0
4
0
1
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
1
0
2
0
4
0
2
0
0
2
0
0
0
2
1
0
0
0
1
0
0
2
0
4
0
2
3
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
2
0
2
0
1
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
2
0
0
0
0
2
5
2
0
1
0
0
0
0
0
0
0
0
1
1
2
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
2
0
2
0
0
2
0
0
0
2
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
3
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
1
0
0
0
1
5
0
0
0
0
1
0
2
0
0
3
0
6
0
1
0
0
0
0
0
0
0
0
2
1
0
1
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
1
0
3
1
1
0
0
0
0
2
1
0
10
0
0
0
0
5
0
0
1
0
1
0
2
2
0
1
0
1
0
2
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
1
0
0
1
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
2
0
2
0
2
0
0
2
0
1
1
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
1
1
2
0
7
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
4
0
1
1
0
0
0
0
5
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
1
0
0
0
0
1
4
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
8
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
5
1
0
1
0
0
2
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
1
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
5
0
0
0
0
0
0
0
4
1
0
4
1
0
2
0
0
0
0
0
0
0
3
1
0
0
2
0
2
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
5
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
2
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
1
0
2
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
3
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
2
2
2
0
1
0
0
0
0
0
0
1
0
0
3
0
0
0
0
1
0
2
0
0
0
0
1
0
0
5
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
2
2
0
1
0
0
2
2
0
0
0
2
0
0
0
2
1
6
0
0
0
0
1
1
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
3
0
0
1
0
0
0
0
0
2
0
1
0
1
0
1
2
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
2
0
0
0
0
2
1
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
1
0
1
0
1
2
0
1
0
1
0
0
2
2
2
2
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
1
0
0
1
0
2
0
2
0
0
0
0
2
0
0
0
8
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
2
1
1
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
6
0
0
0
0
1
0
0
0
1
1
0
2
2
0
0
0
1
0
0
0
0
0
0
1
2
0
1
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
3
0
0
0
0
2
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
1
0
0
3
0
0
0
1
0
0
0
2
0
0
0
0
1
3
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
4
0
2
0
0
0
1
0
0
3
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
4
2
0
0
1
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
2
2
1
0
0
0
0
2
0
0
0
0
0
3
2
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
2
1
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
1
0
0
0
0
9
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
1
2
0
0
0
0
1
0
0
2
1
0
2
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
1
2
0
2
0
0
1
0
0
0
1
0
2
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
5
3
0
1
0
0
0
2
1
0
0
0
0
0
3
0
0
1
2
0
1
0
0
0
1
0
0
0
0
0
0
1
4
0
2
0
0
0
0
0
0
0
0
4
1
0
5
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
1
1
0
0
5
2
0
0
1
0
0
0
0
0
2
2
2
0
0
0
0
7
0
0
0
1
2
2
0
0
0
0
0
0
1
1
0
0
0
0
2
3
0
0
0
0
0
0
0
2
0
1
0
0
1
0
4
0
0
0
0
0
0
0
0
0
1
2
1
2
0
2
0
0
0
0
0
0
2
0
2
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
1
2
0
0
0
1
0
1
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
5
0
0
0
0
1
0
1
1
0
0
1
1
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
3
0
1
0
2
0
2
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
2
2
0
0
0
1
0
0
2
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
1
0
0
0
3
3
8
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
4
0
2
4
0
2
1
0
1
1
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
4
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
3
2
0
1
0
0
0
0
1
1
2
0
0
0
0
1
0
3
0
0
0
0
1
0
0
1
0
0
2
0
1
0
0
0
0
1
2
0
2
0
0
0
0
0
2
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
4
0
0
1
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
4
0
3
0
0
1
0
2
0
1
0
0
0
2
0
0
4
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
2
2
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
1
2
0
0
0
0
1
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
2
1
0
0
1
0
0
0
0
0
2
2
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
3
2
1
0
0
0
0
0
2
3
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
6
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
1
0
0
0
0
3
0
0
1
1
0
0
4
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
1
0
1
1
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
1
0
1
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
1
5
0
2
0
0
0
2
0
0
1
1
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
1
2
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
1
2
2
0
0
2
0
0
0
0
0
1
3
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
3
1
2
1
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
2
0
0
1
0
0
0
0
2
1
0
1
1
2
0
0
0
0
4
0
0
0
0
0
2
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
3
0
0
2
0
2
0
0
0
3
0
0
0
2
0
1
0
0
0
3
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
2
2
0
0
0
0
0
0
3
0
0
0
1
0
2
0
0
1
1
1
0
0
1
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
3
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
6
0
0
0
0
0
2
0
0
1
0
0
2
1
2
1
0
0
1
1
0
0
0
1
0
3
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
1
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
2
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
1
1
1
0
2
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
3
0
0
0
0
0
2
2
0
0
0
1
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
5
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
3
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
2
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
1
0
2
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
3
0
0
3
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
1
0
0
0
2
0
0
0
1
0
1
0
0
1
0
0
0
0
2
1
0
0
1
0
0
1
0
0
0
1
2
0
0
0
0
1
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
2
2
0
2
4
0
0
1
0
0
1
2
0
0
2
0
0
0
0
0
1
1
1
0
0
0
0
1
0
2
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
4
0
2
1
3
3
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
3
0
0
0
0
0
2
3
0
0
2
2
0
0
0
2
0
0
0
5
2
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
1
1
0
0
0
0
2
0
1
0
0
0
0
2
4
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
3
1
0
0
0
0
2
2
1
0
0
0
0
2
2
0
0
0
2
1
2
1
2
0
0
0
2
0
1
0
0
0
2
0
2
0
3
1
1
0
0
2
0
2
1
0
1
2
0
0
0
2
0
0
2
0
1
2
1
0
0
0
0
0
0
0
3
0
1
2
2
0
1
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
2
0
2
0
1
0
0
0
0
1
2
1
0
0
0
0
1
0
0
0
0
0
2
1
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
2
0
0
1
3
1
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
3
0
1
3
0
2
1
1
0
0
2
1
0
0
0
0
1
5
0
1
2
0
0
2
1
0
0
0
1
0
3
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
7
0
2
1
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
1
0
1
0
1
1
2
0
0
0
2
2
0
0
3
0
0
2
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
5
0
0
0
1
0
0
2
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
3
2
0
0
0
0
0
2
1
2
0
2
0
7
0
0
0
3
2
0
0
2
0
0
2
3
0
0
0
1
0
0
1
2
0
0
0
2
2
0
0
0
0
1
2
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
4
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
2
0
2
0
0
0
1
1
1
0
2
2
2
0
0
1
0
0
0
2
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
3
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
1
2
0
1
0
1
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
4
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
1
2
0
0
0
0
2
1
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
4
5
0
0
0
0
1
0
0
0
2
0
0
2
0
1
0
0
0
1
0
10
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
6
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
4
0
7
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
6
0
0
0
0
2
0
0
2
2
2
1
0
0
0
0
0
2
0
0
8
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
3
0
0
0
0
1
0
0
0
2
0
1
0
1
0
0
0
0
0
1
2
0
1
0
1
0
0
0
0
0
0
3
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
2
0
0
0
0
2
0
1
1
1
2
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
1
0
1
0
2
0
0
1
0
0
2
0
2
0
2
0
1
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
2
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
3
0
0
3
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
2
2
0
0
0
0
2
0
0
0
1
1
0
0
0
1
0
2
0
0
2
0
2
0
2
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
4
0
0
0
0
0
0
0
0
0
0
0
0
2
2
4
0
0
0
0
1
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
2
0
1
0
3
0
0
0
2
0
1
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
2
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
1
0
0
0
1
0
0
0
0
1
0
2
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
5
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
2
2
0
0
0
2
2
0
0
0
0
0
0
1
2
0
0
0
2
2
0
0
0
2
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
3
2
0
0
1
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
3
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
2
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
2
1
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
1
0
0
3
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
3
0
0
2
1
2
0
0
0
1
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
1
1
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
3
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
1
0
1
0
0
2
2
1
1
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
3
1
0
0
0
1
1
0
1
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
2
2
0
0
2
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
2
1
0
0
1
0
0
0
1
0
2
0
0
1
0
0
3
0
0
0
3
0
0
0
0
1
1
1
1
0
2
2
2
0
0
0
0
0
4
0
0
2
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
2
2
1
0
2
0
0
0
1
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
1
5
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
1
1
2
0
0
0
0
4
0
3
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
1
1
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
3
1
0
0
0
0
0
0
0
2
0
1
0
1
0
0
4
1
0
0
0
0
0
3
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
2
0
0
0
0
1
0
2
0
0
0
0
2
0
0
2
0
0
0
0
2
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
3
2
0
6
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
1
1
0
0
1
0
2
0
0
0
0
1
0
1
2
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
3
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
2
0
0
1
0
2
2
0
0
1
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
7
0
0
0
1
0
4
0
0
1
0
2
0
0
2
2
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
2
1
0
3
0
0
0
2
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7
1
2
0
3
0
3
2
0
0
0
0
0
0
0
0
0
2
1
0
0
1
1
0
0
0
0
2
0
4
0
0
0
6
0
0
4
2
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
1
7
1
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
2
0
0
2
0
0
0
0
1
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
3
0
2
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
3
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
3
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
3
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
3
0
0
1
0
3
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
4
0
0
0
0
0
0
0
1
2
0
1
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
2
8
0
0
0
0
0
0
2
12
0
0
0
0
1
0
0
1
0
2
0
0
0
2
0
1
0
0
0
0
1
4
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
2
0
0
0
0
1
2
0
0
0
0
0
0
2
2
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
1
1
0
3
0
0
1
0
0
2
0
0
0
1
2
1
0
0
1
0
0
2
0
0
0
0
2
4
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
3
0
0
0
0
0
0
2
0
0
0
1
1
1
2
0
0
0
1
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
2
0
0
0
0
1
1
1
2
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
2
0
5
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
4
0
0
0
0
2
0
1
2
0
2
2
4
1
2
0
0
0
1
1
1
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
1
0
0
0
2
0
0
1
0
1
1
0
2
0
0
0
0
0
3
2
0
2
1
2
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
15
2
0
0
0
2
0
2
0
0
2
0
2
0
0
0
0
0
1
0
0
2
0
0
0
1
2
0
0
0
0
0
3
0
4
2
0
1
0
0
0
0
0
0
1
3
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
4
0
0
0
1
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
3
0
2
0
1
2
0
0
0
0
0
1
0
2
0
2
2
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
4
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
3
2
0
0
0
0
0
1
2
2
2
0
0
0
0
0
1
0
0
1
1
0
1
0
1
0
2
2
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
1
0
0
0
0
0
0
2
1
0
0
1
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
6
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
2
1
0
0
0
2
0
0
0
2
1
1
3
1
0
1
0
0
2
2
0
0
1
0
0
0
0
0
1
3
1
0
1
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
9
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
1
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
2
0
0
0
0
0
2
1
0
0
1
0
2
0
0
0
1
0
0
2
2
0
2
2
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
1
2
0
0
1
0
2
1
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
2
0
0
0
0
0
0
4
0
0
3
0
1
0
0
0
2
2
0
2
0
0
1
0
0
0
0
0
3
0
0
2
2
1
0
2
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
4
0
0
0
2
0
0
2
1
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
2
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
1
5
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
6
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
7
0
0
2
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
8
0
1
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
1
0
0
1
2
1
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
3
0
0
0
0
0
2
1
0
0
2
0
0
0
1
0
0
1
1
0
1
0
2
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
3
3
1
7
0
0
0
0
0
0
4
0
0
0
2
0
0
0
2
1
2
3
1
0
1
1
2
1
0
1
0
0
0
0
2
3
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
2
0
0
3
0
2
1
1
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
1
0
0
0
4
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
1
1
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
4
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
3
0
0
0
2
1
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
1
1
3
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
3
1
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
1
0
0
1
2
2
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
8
0
0
0
2
2
2
1
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
5
0
0
0
0
2
0
0
3
0
2
2
2
4
0
0
0
0
0
0
0
1
0
0
0
0
3
0
2
0
0
0
1
0
0
2
0
0
0
0
1
4
0
0
4
0
0
1
0
0
0
0
0
0
0
1
0
2
2
1
1
0
2
0
0
1
0
0
0
0
0
0
0
0
2
2
7
1
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
2
1
0
0
0
1
0
0
1
0
0
2
0
1
0
0
1
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
2
2
0
1
1
0
2
1
1
0
1
0
5
0
0
0
0
0
0
0
2
2
0
0
0
0
0
3
2
1
0
0
0
0
2
2
0
0
0
1
0
0
2
2
0
0
5
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
2
0
2
0
1
0
0
0
0
0
0
5
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
1
0
0
2
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
4
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
1
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
1
0
16
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
2
0
1
3
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
2
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
2
2
0
0
1
0
3
2
0
0
0
0
2
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
2
0
0
0
2
0
4
2
0
4
0
0
0
0
0
0
2
2
0
1
1
2
0
1
0
1
0
0
2
2
1
0
0
1
0
0
5
1
0
0
0
0
0
0
0
3
0
1
0
2
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
1
0
1
0
1
2
0
0
0
1
0
0
0
0
0
0
1
3
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
1
2
0
2
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
2
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
2
0
0
0
1
0
0
0
0
3
0
3
0
0
2
3
0
0
0
0
0
0
0
0
2
0
1
0
0
7
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
1
3
0
1
0
0
0
2
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
1
0
0
0
0
2
3
0
0
0
0
0
2
0
0
2
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
3
0
2
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
2
0
0
2
1
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
2
2
0
0
0
0
2
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
1
0
0
0
0
2
0
0
1
0
0
2
0
1
0
2
0
0
0
1
2
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
2
0
0
1
0
2
2
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
9
0
0
1
0
0
1
0
0
2
1
0
0
0
4
0
0
1
0
2
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
3
0
0
2
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
7
0
0
2
5
0
2
0
0
0
0
0
2
0
0
1
2
1
5
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
4
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
2
1
0
0
0
0
2
0
0
1
0
0
0
2
3
0
0
2
2
0
2
0
0
0
2
1
0
0
1
1
0
0
1
0
2
0
1
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
5
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
4
1
0
0
0
0
2
0
0
1
0
1
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
1
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
3
0
1
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
2
1
1
0
0
2
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
1
2
1
0
4
1
0
0
2
1
1
0
0
0
0
0
0
0
0
1
3
2
0
1
0
0
0
5
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
2
1
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
1
1
2
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
1
0
5
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
0
1
3
0
0
1
0
0
0
0
0
2
2
0
0
0
2
1
1
0
0
2
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
2
0
0
0
0
1
0
1
0
0
0
0
0
2
3
0
0
0
0
2
2
0
0
0
0
0
8
2
0
0
0
3
2
0
3
0
0
1
0
1
0
0
0
0
0
0
0
0
0
6
1
2
0
0
0
0
3
1
0
0
0
0
1
0
0
2
2
3
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
3
0
0
2
1
0
0
0
1
2
0
2
0
0
2
0
2
0
0
0
0
0
0
2
2
0
2
0
1
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
1
5
0
1
0
0
0
0
0
2
0
0
0
1
0
0
1
0
1
0
0
0
0
3
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
2
0
0
1
0
1
0
0
0
0
0
1
0
0
0
2
0
1
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
2
2
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
3
2
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
2
0
0
1
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
2
0
2
2
0
0
0
0
0
0
0
1
1
0
5
6
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
2
0
0
3
0
2
0
2
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
1
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
3
0
0
0
0
0
0
1
0
0
1
0
0
1
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
1
2
0
0
3
1
2
0
2
0
0
0
0
2
1
1
0
0
0
0
3
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
5
0
2
0
1
0
2
0
0
0
2
2
0
4
2
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
7
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
3
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
4
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
2
2
0
1
0
2
4
0
2
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
9
0
0
0
0
0
2
0
0
9
0
0
0
1
0
0
0
1
2
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
3
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
1
2
0
1
0
0
1
0
3
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
2
0
0
0
1
0
2
0
0
0
1
0
0
0
0
1
2
0
0
0
0
3
1
2
1
0
0
0
0
1
2
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
2
0
1
0
0
2
2
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
1
0
0
2
0
2
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
3
2
0
0
0
2
0
0
1
0
0
0
0
0
2
1
0
2
0
1
0
2
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
3
1
0
1
0
0
0
1
0
2
2
0
0
1
2
1
1
0
2
0
1
2
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
2
0
0
2
0
0
2
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
3
0
0
2
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
4
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
2
2
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
5
0
0
0
0
1
0
3
0
1
0
5
0
0
1
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
2
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
1
0
0
0
0
0
3
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
2
2
4
2
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
4
0
1
0
0
0
0
0
0
0
0
1
2
2
1
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
4
2
0
0
0
2
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
10
1
2
0
0
0
1
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
1
12
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
2
0
0
2
0
2
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
3
2
2
0
0
1
1
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
2
0
0
1
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
1
2
1
5
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
2
0
0
0
0
1
1
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
3
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
2
3
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
2
0
0
0
1
2
0
1
0
0
0
0
4
0
0
0
0
0
0
1
1
0
1
2
0
0
0
0
0
0
0
0
1
2
2
2
0
0
2
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
4
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
2
0
2
0
2
1
0
2
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
3
0
0
2
1
0
0
2
0
3
0
1
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
5
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
1
0
4
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
2
5
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
1
0
2
0
0
0
1
5
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
1
3
0
2
1
0
2
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
3
0
1
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
12
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
4
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
3
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
4
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
2
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
2
0
0
0
1
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
11
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
2
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
1
0
0
1
2
1
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
2
0
0
2
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
3
0
0
0
1
1
0
0
0
0
1
0
2
0
0
0
0
0
0
2
2
0
0
0
0
3
0
0
0
0
2
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
4
0
0
1
0
0
0
0
2
0
0
0
0
0
1
1
2
0
2
0
0
0
0
1
0
1
0
0
0
2
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
3
0
0
0
2
0
0
0
1
0
0
2
1
0
0
1
0
0
3
1
1
0
0
0
5
0
1
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
1
0
0
2
0
0
0
3
1
0
2
0
1
0
0
0
0
0
1
0
0
0
1
0
6
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
1
1
1
0
1
1
0
0
0
0
0
1
0
1
0
0
0
1
0
2
2
0
0
0
1
0
0
3
0
0
0
0
0
0
4
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
2
0
1
0
0
0
0
0
0
1
2
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
2
1
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
2
0
0
1
0
0
0
0
1
0
1
0
0
0
2
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
1
0
0
0
0
0
0
0
11
0
0
0
3
1
0
0
0
0
0
2
1
1
2
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
4
1
0
0
0
0
0
0
1
0
0
2
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
2
0
2
1
0
0
2
0
0
0
0
0
0
0
1
3
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
3
2
1
0
0
0
0
0
2
0
0
1
0
0
2
0
0
1
0
0
0
1
0
0
2
0
0
0
1
1
0
0
4
0
0
2
2
0
0
1
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
1
1
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
3
0
1
0
2
1
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
3
1
1
1
3
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
8
0
0
0
0
1
0
0
1
2
0
1
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
2
1
3
1
0
2
0
1
0
0
0
0
2
0
0
0
2
0
0
0
2
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
1
0
0
1
3
2
0
0
0
1
0
0
1
1
0
2
1
2
0
2
1
1
1
1
0
2
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
2
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
3
0
0
0
0
0
1
0
0
2
0
2
0
2
0
0
2
0
2
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
1
2
0
0
0
0
1
0
1
1
0
1
0
1
0
0
0
0
1
2
0
1
0
3
0
0
0
2
0
0
0
0
1
2
6
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
1
1
0
0
2
0
0
0
0
0
1
2
0
0
2
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
4
0
0
0
9
0
0
0
2
0
0
0
0
2
0
0
2
1
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
1
1
2
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
3
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
5
0
1
0
0
0
0
0
0
1
0
0
0
2
0
2
0
2
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
2
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
2
0
1
1
1
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
3
0
2
2
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
1
2
1
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
1
0
0
2
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
5
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
2
0
3
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
3
0
0
0
0
1
0
2
0
0
2
1
2
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
3
0
0
1
0
0
1
0
1
0
1
0
0
2
0
0
2
1
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
2
3
1
0
0
0
1
0
1
0
0
0
0
0
1
1
2
0
0
2
0
0
0
0
1
0
3
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
2
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
2
2
0
1
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
1
2
3
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
3
0
0
2
1
2
1
0
0
0
1
0
0
0
6
0
0
0
0
2
0
0
1
0
0
0
1
0
2
0
2
1
0
0
0
1
2
0
3
1
2
0
0
0
0
1
0
0
1
0
4
0
0
1
0
1
2
0
0
0
0
2
0
0
0
0
3
1
0
0
2
0
0
2
1
0
0
1
0
2
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
2
0
4
0
1
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
5
0
2
1
0
0
0
0
1
0
1
0
4
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
1
0
2
0
0
1
0
0
0
0
0
2
0
1
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
1
0
0
0
0
0
1
0
3
0
0
0
2
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
4
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
1
1
0
0
6
0
0
0
0
2
0
2
0
0
0
2
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
2
1
1
0
0
0
0
0
0
0
0
1
0
2
0
1
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
1
2
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
3
2
0
2
1
0
0
0
0
1
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
6
0
1
0
0
0
1
1
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
4
0
0
1
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
3
2
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
2
2
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
2
1
5
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
1
0
2
0
0
0
0
2
0
0
2
1
0
0
2
0
0
0
0
0
1
0
0
2
0
0
2
0
2
1
1
1
1
1
0
1
0
0
1
0
0
0
2
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
2
1
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
1
1
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
2
0
1
0
1
1
0
0
1
2
0
0
0
1
2
2
0
1
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
1
2
0
2
3
1
0
1
0
0
0
0
0
1
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
2
0
0
0
0
0
3
0
1
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
1
2
0
0
0
0
1
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
3
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
2
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
4
0
0
3
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
1
0
1
0
2
0
0
0
2
1
1
1
1
1
0
4
0
0
0
0
2
1
0
2
0
2
0
0
1
0
0
1
0
1
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
1
1
1
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
2
0
1
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
1
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
2
1
2
4
0
0
0
0
1
0
0
1
0
0
0
0
2
0
1
2
0
0
0
2
0
1
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
2
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
1
0
2
0
0
2
0
1
0
1
3
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
1
1
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
2
1
1
0
0
0
0
2
2
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
2
0
1
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
2
0
0
1
0
0
1
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
1
7
1
2
1
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
8
3
0
0
0
0
0
0
1
1
1
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
1
1
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
1
1
0
0
0
1
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
1
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
4
0
0
0
1
0
1
0
0
1
0
0
6
0
0
0
0
0
2
0
0
0
2
1
2
2
0
0
0
8
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
2
2
0
3
0
0
0
0
0
0
0
1
2
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
1
0
0
0
0
3
0
0
1
2
7
0
0
0
0
0
3
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
2
1
2
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
2
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
4
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
2
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
2
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
1
0
0
0
2
0
2
0
1
1
0
0
0
0
0
1
7
0
1
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
2
2
0
0
0
0
0
2
6
0
0
0
1
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
3
0
2
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
1
0
2
2
1
2
0
1
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
2
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
3
0
0
0
1
0
0
2
0
0
0
2
0
2
2
0
0
0
0
1
0
0
0
0
1
3
0
1
0
0
2
0
1
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
2
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
1
0
0
0
0
0
1
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
1
0
0
0
0
0
1
2
0
1
2
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
2
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
2
2
0
0
0
0
0
5
1
0
0
1
5
1
0
0
3
2
1
0
1
2
0
0
1
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
2
2
0
0
1
0
2
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
2
2
0
0
0
0
0
2
1
5
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
0
2
0
0
2
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
2
0
0
0
1
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
3
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
3
0
0
2
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
2
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
1
1
0
0
0
1
3
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
5
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
3
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
1
1
0
0
0
0
2
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
1
0
3
1
1
0
3
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
7
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
1
0
0
0
1
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
9
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
1
0
1
0
0
0
0
2
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
2
0
0
3
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
2
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
1
2
0
0
1
2
2
0
0
2
3
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
2
0
1
0
0
1
0
1
0
0
4
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
3
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
2
3
1
1
0
2
0
6
0
2
0
1
1
1
1
3
0
0
2
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
3
0
0
0
0
2
0
1
0
2
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
2
0
4
0
0
0
0
0
2
0
2
0
0
0
2
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
3
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
3
0
0
2
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
2
1
0
0
1
0
1
0
1
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
6
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
2
2
0
1
0
0
2
0
0
0
2
0
2
0
2
0
0
0
0
0
0
1
0
1
0
2
0
1
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
1
1
0
0
2
0
1
0
1
2
0
1
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
3
2
0
1
0
1
1
0
0
0
0
0
0
0
0
0
12
0
3
0
1
0
0
1
0
0
0
0
0
1
2
0
0
1
0
0
1
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
4
0
2
0
0
0
0
0
1
0
2
0
1
0
3
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
2
1
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
10
0
0
0
1
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
1
0
0
0
0
5
1
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
1
2
2
0
0
0
0
2
0
1
0
0
0
0
2
0
1
0
1
0
0
0
1
1
0
0
0
0
1
0
0
1
0
2
2
2
0
1
3
1
3
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
3
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
2
0
0
3
0
1
1
0
1
0
0
2
2
0
0
2
0
0
1
2
0
0
1
0
0
1
1
2
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
2
0
0
1
1
2
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
2
1
0
0
0
1
1
0
0
0
0
0
3
0
0
0
0
0
0
1
0
2
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
1
3
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
1
2
0
0
1
0
0
0
2
0
2
0
0
0
0
2
0
1
1
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
2
0
0
0
0
0
0
0
2
0
2
1
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
1
0
0
0
2
0
3
0
3
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
3
0
0
9
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
4
0
0
0
0
2
0
1
1
0
0
2
1
0
2
2
0
0
5
0
1
4
0
1
0
0
0
1
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
4
3
0
1
0
0
0
0
0
1
0
1
5
0
0
0
1
0
2
0
2
0
0
0
0
0
2
1
1
0
2
3
0
1
2
0
0
1
0
0
0
3
1
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
1
0
4
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
2
0
0
1
0
0
0
2
0
0
2
1
0
0
0
0
0
0
5
0
1
0
2
0
0
2
0
0
0
1
3
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
3
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
1
0
1
1
2
2
5
0
0
2
2
0
0
0
0
0
3
0
1
0
0
2
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
2
1
1
2
0
0
0
2
0
0
0
2
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
3
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
2
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
4
1
3
0
0
0
0
0
1
0
3
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
1
1
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
2
2
0
0
0
0
1
0
0
0
1
4
2
1
8
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
2
0
0
1
1
1
1
1
3
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
5
0
1
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
1
1
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
1
2
0
0
1
1
0
1
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
3
2
2
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
1
2
1
0
2
0
0
0
1
0
0
0
1
0
0
2
1
2
1
0
2
2
1
3
1
2
0
0
0
0
2
2
4
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
2
0
1
0
0
0
0
1
1
0
0
1
0
0
0
2
0
1
0
1
0
2
1
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
2
1
0
1
1
0
0
0
0
0
0
1
0
2
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
3
0
1
0
1
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
1
1
0
0
2
0
0
2
0
0
0
0
2
0
1
0
0
0
1
0
1
0
1
0
1
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
3
0
0
0
0
1
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
3
0
2
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
1
1
1
0
0
1
2
0
0
1
0
2
0
3
0
1
0
0
0
0
1
2
0
0
0
0
8
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
5
2
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
3
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
4
2
0
0
0
0
1
0
2
0
2
0
0
0
4
0
1
0
0
0
0
0
0
0
0
1
0
2
0
4
1
0
0
2
0
1
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
2
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
1
1
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
1
0
0
0
0
1
0
2
0
0
0
1
0
2
0
0
0
0
0
2
4
2
0
0
1
1
0
0
0
1
0
0
3
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
6
0
0
0
0
0
1
0
0
0
2
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
2
0
0
2
0
2
0
1
2
2
0
0
0
0
0
0
2
4
0
0
1
0
3
0
0
0
0
1
0
1
0
0
0
0
2
1
0
0
0
0
1
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
3
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
3
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
1
1
0
0
1
5
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
1
0
0
0
0
5
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
2
0
0
0
0
2
0
1
2
1
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
2
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
1
0
2
0
1
2
2
0
0
0
3
0
0
0
1
0
3
0
0
2
1
6
2
0
0
0
2
0
2
0
2
1
0
2
0
0
0
1
0
1
1
0
0
0
0
1
0
0
3
0
0
0
1
0
0
3
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
2
1
0
0
0
0
5
0
0
0
0
0
2
0
0
0
3
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
5
0
0
0
2
0
0
2
0
2
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
1
2
0
2
0
0
1
0
0
0
0
1
1
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
10
1
0
0
0
2
0
0
1
2
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
1
1
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
4
0
0
0
0
2
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
3
1
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
2
0
2
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
5
0
2
0
2
0
0
0
0
0
0
1
0
1
1
2
0
0
1
2
0
3
0
0
1
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
2
2
0
0
0
0
0
2
0
0
1
0
1
0
2
1
1
0
0
0
3
0
2
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
2
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
1
0
0
2
0
1
0
0
0
0
0
0
1
4
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
1
0
2
1
0
4
0
1
0
0
1
2
2
1
0
0
0
1
0
1
0
0
2
2
0
0
2
0
2
0
0
0
0
0
0
1
1
0
0
1
2
1
0
0
2
0
2
0
0
3
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
1
0
0
3
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
3
0
0
0
2
0
0
0
0
1
2
0
2
0
1
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
4
1
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
2
0
0
0
1
0
2
2
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
1
0
0
2
1
0
0
1
1
0
1
0
0
0
0
0
1
1
2
0
2
2
0
1
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
1
0
1
0
0
0
0
0
0
1
0
0
2
0
3
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
5
0
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
1
0
1
2
0
0
0
0
0
0
0
0
1
0
0
2
1
2
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
3
0
0
0
0
1
0
3
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
1
0
0
0
0
0
1
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
3
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
2
0
3
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
4
2
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
3
1
0
0
2
2
0
0
0
0
2
0
4
0
0
0
0
0
0
0
1
0
0
1
2
0
3
0
0
0
0
1
0
0
0
2
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
2
4
0
0
3
0
2
0
2
0
0
0
2
0
1
0
0
0
0
2
0
0
0
2
0
2
2
1
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
1
0
0
3
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
3
0
3
0
0
0
2
0
0
0
1
0
0
1
1
0
0
13
2
0
1
0
2
0
1
0
1
0
1
0
2
0
0
1
0
0
6
0
0
2
2
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
4
0
1
3
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
2
0
2
0
0
2
2
0
0
0
0
0
2
1
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
4
2
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
7
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
2
0
3
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
2
2
0
0
0
3
0
2
0
0
0
0
0
1
0
1
0
0
2
2
0
0
2
0
2
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
1
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
2
0
1
2
1
2
2
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
3
10
1
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
4
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
2
1
0
1
1
2
0
0
0
0
0
0
2
0
0
0
0
3
2
0
0
2
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
1
6
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
1
0
0
2
1
1
2
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
2
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
5
1
3
0
0
1
0
0
1
0
2
1
0
5
0
2
0
2
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
2
0
0
0
4
0
1
0
2
0
0
0
1
0
1
2
0
0
2
0
1
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
1
2
1
2
0
1
2
0
0
1
0
0
0
0
0
0
0
0
1
2
0
2
1
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
3
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
2
0
1
0
1
0
0
1
3
2
0
0
0
2
0
0
2
0
0
0
0
2
2
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
2
0
1
0
2
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
1
0
1
1
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
1
1
1
0
0
0
2
1
2
1
1
1
2
0
0
0
0
2
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
2
0
0
1
1
0
0
1
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
2
0
0
0
2
0
0
2
0
0
0
0
0
2
0
2
0
0
0
1
0
1
0
1
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
2
0
0
2
0
0
2
0
1
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
1
4
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
5
0
0
0
0
0
2
0
0
2
1
1
0
0
0
0
0
1
1
1
1
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
2
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
2
1
1
0
0
0
0
1
1
0
0
0
0
0
0
2
1
0
1
0
0
1
0
0
0
1
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
3
0
0
1
1
7
0
1
2
0
0
1
2
0
2
0
2
0
0
1
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
1
2
0
1
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
4
0
0
0
0
2
1
2
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
2
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
2
1
0
0
0
0
0
1
2
0
1
0
0
0
0
3
1
0
0
0
3
1
0
0
2
0
0
0
1
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
2
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
4
2
0
0
0
0
0
0
0
1
4
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
5
1
0
0
0
0
0
1
0
0
1
3
0
0
0
0
0
0
2
0
2
1
0
0
0
1
0
0
2
0
0
0
0
2
0
1
1
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
5
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
7
0
2
1
1
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
2
0
1
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
4
0
1
0
1
1
0
0
1
0
0
0
0
0
0
1
0
1
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
3
1
1
0
0
2
0
2
0
2
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
1
0
3
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
2
0
2
0
0
2
0
2
0
0
0
0
1
0
2
0
0
0
1
0
1
1
0
2
1
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
6
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
1
0
0
1
2
1
3
1
0
1
0
0
0
0
1
0
1
3
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
1
1
0
0
2
0
0
1
2
1
0
0
0
0
1
0
2
1
0
0
0
0
0
0
2
2
0
0
0
0
0
4
0
0
0
0
1
2
0
0
0
1
0
2
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
3
0
2
1
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
3
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
1
1
0
0
2
1
2
0
0
0
0
1
1
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
1
0
0
0
1
0
1
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
1
1
0
0
0
0
1
0
2
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
1
0
1
0
3
0
0
2
2
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
2
2
0
2
0
1
2
0
1
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
1
2
2
1
0
2
0
0
2
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
1
3
3
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
1
0
1
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
3
0
2
0
1
0
1
0
2
2
0
2
0
0
4
2
0
0
0
2
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
1
1
0
0
0
1
2
7
0
2
2
0
0
0
0
0
0
2
2
0
3
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
1
0
2
1
0
0
0
1
0
0
2
0
0
0
0
3
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
3
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
2
0
0
0
0
0
1
0
0
0
2
1
0
0
1
5
2
0
0
0
1
0
0
7
0
0
0
0
2
0
0
0
1
0
1
4
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
4
0
0
1
0
0
0
3
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
2
0
3
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
2
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
4
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
2
0
2
0
1
1
0
0
0
2
0
0
0
1
0
0
2
0
0
1
0
2
2
0
0
0
0
0
0
1
0
0
2
3
0
0
0
1
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
3
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
1
0
0
0
4
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
4
2
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
1
0
0
0
0
0
2
0
0
1
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
2
0
1
2
0
0
0
0
0
0
0
0
3
0
2
1
0
1
1
0
0
0
0
2
2
0
0
0
2
0
1
1
1
2
1
0
0
2
0
0
0
2
0
1
0
0
0
0
1
2
0
2
0
1
0
2
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
1
2
0
0
0
2
0
0
0
1
1
2
0
0
0
0
1
1
1
1
1
0
1
0
0
4
1
0
1
1
0
0
0
2
2
0
2
0
0
0
2
0
1
1
0
7
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
4
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
2
0
1
0
0
2
0
0
1
2
1
2
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
4
2
2
4
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
3
0
0
1
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
3
0
0
2
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
1
0
3
0
0
0
1
0
0
0
2
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
2
0
1
4
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
1
0
4
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
1
0
0
6
5
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
1
0
1
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
1
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
1
3
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
3
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
3
0
2
0
2
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
3
1
0
1
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
2
2
0
5
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
3
0
0
3
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
1
2
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
4
0
2
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
1
0
2
1
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
1
2
0
0
0
2
0
2
0
0
1
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
2
0
2
0
2
0
0
2
0
2
0
0
0
0
0
0
1
0
0
1
0
2
2
2
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
1
2
0
0
0
1
2
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
3
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
1
0
0
0
0
0
0
1
0
0
2
1
0
0
1
1
2
0
0
0
0
2
0
2
1
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
3
2
0
0
1
1
0
2
0
2
0
0
1
0
0
1
0
0
3
0
1
0
0
2
0
1
0
0
2
0
2
0
1
0
2
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
2
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
1
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
3
0
1
0
2
0
1
0
0
0
0
0
0
1
2
0
2
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
1
1
2
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
2
1
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
2
0
3
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
2
1
0
0
0
0
3
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
2
1
0
0
0
0
1
0
0
0
0
2
0
2
0
3
0
0
0
0
1
2
0
2
0
2
1
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
2
0
0
1
0
3
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
3
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
2
1
1
0
0
0
2
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
1
1
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
1
2
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
2
0
0
0
0
0
1
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
3
0
2
0
1
0
0
0
0
0
2
2
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
1
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
1
2
0
0
0
0
2
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
1
0
2
0
0
0
0
0
2
1
1
0
0
0
0
2
0
3
2
1
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
2
0
0
0
3
0
0
2
2
2
0
1
0
0
1
0
1
0
1
0
0
0
1
0
2
1
0
2
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
2
1
0
0
1
0
1
0
1
0
0
0
0
0
0
1
1
3
0
0
0
0
0
2
1
0
0
0
0
1
0
0
1
7
0
0
0
1
0
2
0
1
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
7
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
2
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
1
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
3
0
0
0
2
1
0
1
0
0
1
1
2
0
2
0
0
1
2
1
1
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
1
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
2
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
6
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
2
1
2
3
0
0
1
0
3
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
3
1
0
2
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
2
0
2
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
2
0
0
0
3
0
0
2
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
3
0
0
0
0
0
2
2
0
1
0
0
0
2
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
2
1
2
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
1
3
0
0
2
5
1
0
1
2
0
0
0
0
0
1
0
0
2
3
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
5
0
0
0
2
2
0
0
0
2
2
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
4
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
3
0
0
0
6
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
3
0
0
0
0
0
0
0
2
0
2
1
1
0
0
0
0
1
3
1
0
0
0
0
0
0
0
0
1
1
0
3
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
2
0
3
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
1
0
0
3
0
0
0
0
0
2
1
2
1
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
3
0
1
0
0
2
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
2
2
1
1
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
3
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
6
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
6
0
0
0
2
2
0
1
0
2
0
5
0
0
1
0
0
1
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
3
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
1
1
1
0
0
0
0
2
0
1
1
0
0
0
1
0
0
0
4
0
0
2
0
0
0
0
0
0
1
0
4
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
2
0
2
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
1
0
3
0
0
2
2
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
1
0
2
0
2
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
2
1
4
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
5
0
0
2
0
0
1
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
2
0
0
1
1
0
0
0
1
4
0
0
2
2
0
2
2
0
0
0
0
0
0
1
1
0
0
1
2
2
0
0
0
0
1
0
0
0
0
1
0
0
3
0
0
0
0
1
0
0
0
2
0
0
1
1
0
0
0
1
2
0
1
2
0
2
2
0
0
1
0
0
2
0
0
0
0
2
0
0
6
0
0
3
0
2
1
0
0
0
0
0
0
0
0
0
3
1
0
0
0
2
0
0
0
0
0
0
1
2
0
1
0
0
3
0
0
0
0
1
0
0
1
1
2
2
4
0
0
0
1
0
1
0
0
1
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
3
0
0
0
0
0
1
2
0
0
0
0
0
1
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
1
1
0
0
0
0
1
0
0
2
0
0
3
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
3
0
0
2
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
2
0
2
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
2
1
1
0
0
2
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
1
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
2
2
2
0
0
0
2
0
0
2
2
2
0
1
0
0
0
0
4
0
0
1
0
0
1
0
0
2
0
0
0
0
2
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
2
0
0
0
6
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
1
0
0
1
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
8
1
0
1
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
2
0
0
0
1
0
2
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
2
0
1
0
0
0
1
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
2
0
0
0
0
0
1
1
0
0
0
2
2
0
3
0
0
0
2
0
0
1
0
0
0
0
1
4
1
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
1
2
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
3
0
0
0
0
1
2
1
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
1
1
0
2
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
2
0
2
1
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
2
0
3
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
2
0
0
0
0
2
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
1
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
1
0
0
0
0
0
0
0
2
0
2
0
1
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
1
2
0
0
0
0
0
1
1
0
0
2
0
0
1
0
0
5
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
6
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
1
1
1
1
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
1
0
2
0
0
0
2
2
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
4
0
0
1
0
3
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
4
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
1
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
2
0
1
0
0
0
1
0
0
1
0
0
0
0
2
2
0
2
2
0
0
0
0
0
0
0
2
1
0
0
0
2
5
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
1
2
0
2
1
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
2
0
1
0
0
2
1
0
1
0
0
1
0
0
0
0
0
0
2
2
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
1
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
11
0
0
2
1
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
4
4
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
1
0
1
2
3
1
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
1
0
1
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
3
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
4
0
0
0
2
2
0
1
0
1
0
0
0
4
0
0
0
3
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
1
2
0
0
0
0
0
1
0
0
0
0
0
1
3
2
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
1
1
0
0
5
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
2
0
2
3
1
4
0
1
0
0
0
2
0
2
2
1
5
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
2
0
4
0
0
0
3
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
2
2
0
0
1
3
1
0
1
0
0
1
0
0
0
2
0
0
3
1
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
1
0
0
2
0
0
2
0
2
0
0
0
0
0
2
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
1
2
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
2
1
2
0
0
2
0
1
1
0
1
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
2
1
1
0
0
2
0
1
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
6
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
2
0
2
3
0
0
0
1
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
1
5
0
0
0
2
0
0
5
0
2
0
0
0
0
0
0
1
0
0
2
2
1
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
1
1
0
0
0
3
0
0
0
2
0
0
3
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
3
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
7
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
8
0
0
0
0
2
0
0
0
2
1
2
0
0
1
0
0
1
2
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
3
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
1
0
0
0
0
0
1
0
0
0
2
1
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
2
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
2
0
1
1
0
0
1
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
2
0
3
0
0
1
0
2
0
0
0
0
1
1
0
0
0
0
1
2
9
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
1
2
3
4
0
1
0
0
2
2
0
0
0
2
0
0
1
1
2
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
4
0
1
3
0
0
0
0
0
0
0
0
1
5
0
2
0
1
2
0
1
3
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
3
0
0
0
0
1
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
2
0
0
0
2
1
0
0
3
0
0
0
1
2
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
2
0
0
1
0
0
2
2
0
0
0
0
1
0
0
1
0
0
1
1
1
0
0
1
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
1
4
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
3
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
1
2
0
0
0
0
1
2
0
0
0
0
0
0
4
0
2
0
1
0
2
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
5
0
0
1
0
0
0
1
1
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
5
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
1
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
2
0
2
0
1
0
1
0
2
0
0
0
0
0
2
0
0
2
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
1
0
0
1
0
1
0
2
0
0
2
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
1
1
0
3
1
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
2
1
1
2
0
0
0
1
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
1
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
3
2
0
0
0
2
0
0
0
0
0
5
0
0
0
1
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
18
0
0
0
2
1
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
3
0
2
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
3
0
0
0
2
0
0
2
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
2
0
0
0
0
0
0
0
1
0
2
2
0
4
0
2
0
1
0
0
1
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
2
0
0
0
0
2
0
1
0
0
3
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
1
0
2
0
0
0
1
0
2
3
0
1
3
0
2
1
1
1
0
1
3
1
5
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
2
0
3
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
1
1
2
0
0
0
9
0
0
0
0
2
0
0
0
4
0
4
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
3
0
1
0
0
0
0
0
0
0
0
2
0
3
1
0
0
1
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
2
3
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
2
0
1
0
0
0
0
1
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
1
0
0
2
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
2
2
1
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
2
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
3
0
0
0
2
0
0
1
0
2
0
0
0
2
2
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
4
0
2
0
0
1
1
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
1
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
5
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
2
0
0
1
0
0
0
1
0
0
0
2
0
0
3
0
0
0
0
1
0
1
2
0
0
0
0
1
0
1
0
0
0
0
0
0
1
2
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
3
2
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
1
2
0
0
0
2
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
2
2
0
0
4
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
2
0
1
0
0
0
0
1
0
0
0
2
1
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
6
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
2
0
0
2
2
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
2
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
3
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
5
1
2
0
0
0
0
0
0
0
0
1
0
1
5
0
1
0
4
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
2
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
3
0
1
0
0
0
0
0
1
0
0
1
3
1
2
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
2
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
1
0
1
2
2
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
2
0
0
1
0
0
0
0
2
2
0
1
2
0
1
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
3
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
3
0
2
0
0
0
0
0
0
0
0
1
0
0
1
9
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
1
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
1
0
0
0
1
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
2
2
2
0
0
0
1
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
1
0
0
1
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
6
0
2
0
0
1
0
0
2
0
2
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
10
0
0
0
1
0
1
2
0
0
2
0
3
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
2
0
2
0
0
1
0
2
0
0
1
0
0
0
0
0
7
3
0
1
0
0
0
0
0
0
0
2
3
0
0
1
2
0
0
3
0
0
1
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
3
0
2
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
3
1
1
0
1
0
0
1
0
0
0
3
0
0
0
0
0
0
0
3
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
2
2
1
0
0
0
2
2
0
0
2
0
1
0
0
0
0
5
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
1
0
0
2
0
0
0
0
0
3
0
0
0
0
0
3
0
2
0
0
0
0
0
0
3
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
1
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
2
2
2
0
1
1
2
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
1
2
1
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
1
1
0
1
1
2
0
0
1
0
2
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
1
0
0
0
1
2
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
4
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
7
2
0
0
1
5
0
0
2
1
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
5
0
0
1
0
0
0
0
0
0
2
0
0
1
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
4
0
0
0
1
0
0
0
3
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
3
1
1
0
0
0
1
0
1
2
1
0
0
0
0
0
0
0
1
0
1
2
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
2
1
1
0
0
0
2
0
1
0
0
2
0
0
0
0
1
2
1
0
1
0
2
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
2
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
1
1
0
1
1
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
1
0
0
3
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
3
0
1
0
0
1
1
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
1
1
1
0
2
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
2
0
0
3
0
0
0
3
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
3
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
1
0
4
0
0
0
0
0
1
1
0
1
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
2
0
0
0
1
0
0
0
3
2
0
0
0
0
2
0
2
0
0
0
2
0
0
0
2
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
3
0
0
0
2
6
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
1
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
4
2
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
1
0
0
1
0
3
0
0
1
0
2
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
1
3
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
2
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
2
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
3
0
0
1
1
0
1
1
0
0
1
0
0
0
2
0
0
2
1
0
1
0
0
0
2
0
0
2
1
0
2
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
3
0
0
0
0
2
0
0
2
0
0
2
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
3
0
1
0
0
0
1
2
1
0
0
1
0
1
0
0
1
0
2
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
2
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
1
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
1
0
1
0
1
1
0
0
0
0
1
0
0
0
2
0
1
0
0
0
2
0
0
0
0
2
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
1
0
0
0
14
2
0
1
0
0
0
1
0
0
0
1
0
2
0
1
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
1
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
1
0
0
3
1
0
3
0
1
0
0
0
0
0
3
2
2
0
0
0
0
1
0
0
0
0
0
2
2
2
0
0
0
0
0
0
3
0
1
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
9
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
2
1
0
0
0
2
1
1
1
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
2
0
0
0
0
1
1
0
1
2
0
0
1
0
2
0
0
0
0
1
0
0
0
0
2
0
0
4
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
6
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
3
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
1
0
1
3
0
1
0
0
0
0
0
0
2
0
2
1
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
3
0
0
2
0
0
0
0
1
0
2
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
5
0
1
2
0
0
0
1
0
0
2
0
0
0
0
2
2
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
3
0
0
2
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
1
0
1
2
2
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
1
2
0
0
0
2
1
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
2
0
0
0
1
3
0
2
2
0
0
4
0
0
1
0
0
2
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
3
0
0
1
0
0
1
0
0
2
0
0
0
1
1
0
0
0
0
2
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
2
2
0
2
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
8
0
0
0
1
0
1
0
0
2
1
0
0
0
1
0
0
4
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
2
3
0
0
0
0
2
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
3
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7
0
0
0
1
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
2
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
4
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
3
0
2
0
0
0
0
0
1
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
2
0
2
0
1
0
1
1
0
0
0
1
2
0
3
0
0
0
1
2
1
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
3
0
0
2
0
1
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
1
3
0
0
1
0
0
0
2
2
1
3
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
2
0
0
3
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
1
0
1
0
0
1
1
0
0
1
0
0
0
0
0
3
0
3
0
0
1
0
2
0
0
0
3
2
0
0
0
0
2
0
0
0
2
0
1
2
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
2
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
2
0
1
0
2
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
1
1
0
2
0
1
0
0
2
0
1
1
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
3
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
2
1
0
0
1
0
1
0
1
1
0
0
0
0
1
0
2
0
0
0
0
1
2
1
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
3
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
1
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
1
0
2
0
0
0
0
1
0
0
2
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
3
1
0
0
0
1
2
0
0
0
0
0
0
0
2
1
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
2
2
0
0
2
0
0
2
1
0
0
2
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
3
1
1
0
1
1
1
2
0
0
0
0
0
2
0
0
0
0
0
2
2
2
0
3
0
0
0
0
2
0
1
0
1
2
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
2
1
0
3
0
0
1
0
0
1
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
2
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
4
0
2
0
0
0
2
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
2
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
1
0
0
0
2
1
0
0
0
0
0
0
1
3
0
2
1
2
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
1
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
2
1
5
0
1
2
0
0
2
0
2
2
1
0
0
0
1
0
2
0
0
0
2
2
1
0
0
2
0
2
0
0
0
0
2
0
0
1
1
0
1
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
3
1
0
1
0
1
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
2
2
0
0
3
1
0
0
1
0
0
0
2
0
0
2
1
0
1
2
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
2
0
0
2
0
1
0
0
0
0
0
0
1
2
0
0
0
1
2
0
0
0
0
3
0
0
1
0
0
2
0
0
2
0
2
0
2
0
4
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
2
2
0
0
0
0
0
0
0
0
0
1
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
2
2
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
1
3
0
1
0
1
0
0
2
0
0
1
0
2
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
2
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
2
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
2
0
1
0
1
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
9
0
0
2
2
0
0
2
0
0
2
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
1
0
0
0
1
0
1
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
4
0
0
4
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
1
1
1
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
3
2
0
0
0
0
0
0
1
0
0
2
0
0
0
1
1
1
1
2
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
3
0
0
2
0
0
0
1
0
0
2
2
0
1
0
3
0
0
0
0
2
0
1
0
0
1
0
0
0
0
2
1
0
1
0
2
2
0
2
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
12
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
2
0
1
1
1
1
0
0
0
2
0
0
2
0
2
1
0
0
0
1
0
2
0
0
1
2
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
2
0
0
0
2
1
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
4
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
1
2
2
0
0
2
0
0
1
0
0
0
0
1
2
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
1
0
1
0
0
0
0
0
2
0
3
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
5
0
0
1
0
0
3
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
3
0
0
0
3
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
2
0
0
0
0
0
0
1
0
0
0
1
0
3
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
1
1
1
0
0
0
0
0
0
2
0
0
3
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
3
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
3
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
3
0
0
1
2
0
2
0
0
1
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
1
3
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
1
1
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
1
1
0
1
0
0
0
0
0
1
0
0
0
0
2
0
1
1
0
0
0
0
2
0
4
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
5
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
1
2
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
1
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
4
0
2
0
2
0
2
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
7
2
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
1
0
0
0
2
0
1
0
0
0
1
0
5
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
1
2
2
0
0
0
0
0
1
0
0
2
0
0
1
0
0
2
1
0
0
0
0
1
0
0
0
3
0
0
0
2
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
2
1
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
4
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
6
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
5
0
0
0
0
1
0
2
0
2
0
6
0
2
2
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
2
1
0
1
0
1
0
0
0
0
2
2
0
0
0
1
2
1
1
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
1
0
0
1
2
0
0
0
2
1
0
0
0
2
0
0
0
4
0
5
0
0
0
0
0
0
0
0
2
1
1
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
1
0
0
1
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
1
2
0
2
0
0
1
0
0
2
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
3
0
0
0
0
0
2
0
2
2
2
2
0
0
0
0
0
0
1
0
0
1
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
3
2
0
0
0
2
0
1
2
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
4
1
0
1
0
0
1
0
0
2
0
1
0
3
2
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
1
0
0
4
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
1
0
0
1
0
1
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
2
0
0
2
2
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
2
0
1
2
0
0
1
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
2
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
1
2
0
0
2
0
0
0
1
2
0
0
0
0
0
3
0
0
0
0
0
0
0
3
0
1
0
0
0
0
2
2
2
0
1
3
0
0
2
0
0
3
1
0
0
0
0
1
0
0
2
1
1
0
0
1
0
1
0
0
0
2
0
1
0
0
0
1
0
3
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
3
0
1
0
0
0
2
0
1
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
6
0
0
0
1
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
1
2
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
1
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
1
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
2
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
4
0
1
1
2
0
0
0
5
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
2
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
1
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
1
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
3
2
0
0
2
0
2
0
2
0
2
0
0
2
0
1
0
1
0
0
0
0
0
1
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
2
1
0
1
2
1
2
0
0
0
0
2
0
1
0
0
1
2
3
2
0
0
0
2
0
2
2
0
2
0
2
0
1
0
0
2
0
3
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
1
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
1
1
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
4
0
0
0
0
0
3
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
2
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
1
0
0
0
3
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
4
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
3
0
0
2
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
2
0
2
1
3
0
0
0
0
0
0
0
0
0
0
6
2
0
0
0
0
0
0
0
1
6
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
2
2
2
0
0
0
1
0
0
0
0
0
0
0
2
0
2
1
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
3
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
4
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
1
0
1
4
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
1
0
3
0
0
0
0
1
0
0
0
1
0
0
2
2
0
0
0
0
2
2
0
1
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
2
6
0
0
1
0
2
1
0
0
0
0
3
1
0
1
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
1
0
0
0
0
1
2
2
0
2
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
1
0
0
0
0
4
1
2
2
0
0
1
0
0
0
0
1
0
0
3
0
0
0
0
2
2
2
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
5
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
3
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
1
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
1
2
0
4
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
1
1
0
3
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
5
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
3
0
0
1
0
1
1
1
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
3
0
0
1
1
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
2
0
2
0
0
2
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
1
0
0
1
0
0
0
0
1
0
0
2
1
0
0
0
0
0
3
1
2
0
1
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
2
0
0
1
1
0
0
0
1
3
1
0
4
0
0
0
0
1
1
0
0
2
3
0
7
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
1
2
0
1
0
0
0
3
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
2
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
2
2
0
0
0
0
0
4
0
0
0
0
0
0
2
0
4
0
4
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
1
0
0
0
0
2
3
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
1
0
0
0
1
2
0
2
0
0
0
0
0
0
0
5
0
2
0
2
1
0
1
0
2
0
0
0
0
1
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
8
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
2
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
2
0
1
1
0
2
0
2
0
0
0
0
6
1
2
0
2
1
0
2
0
1
0
0
1
0
4
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
3
0
1
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
2
0
1
0
4
1
1
0
0
2
0
0
1
2
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
2
0
0
0
0
2
0
3
0
0
0
1
2
1
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
1
0
0
1
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
2
3
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
1
0
1
2
0
0
0
0
1
2
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
2
2
0
0
0
1
0
2
2
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
2
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
2
2
1
1
0
2
0
0
0
0
1
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
1
1
0
0
0
2
0
0
0
3
0
0
0
0
1
0
0
2
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
3
0
2
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
2
2
1
0
2
0
2
0
0
1
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
6
0
2
0
0
0
1
1
0
0
2
0
2
0
1
0
0
0
0
0
0
1
0
0
1
0
2
12
1
2
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
1
0
0
0
1
3
1
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
3
0
0
0
1
1
0
2
0
4
0
0
0
0
1
0
2
0
0
0
0
0
2
0
1
0
0
0
2
1
1
0
1
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
3
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
2
0
1
0
0
1
0
0
0
0
4
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
3
0
0
0
0
1
0
0
2
0
2
1
0
0
0
1
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
3
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
3
4
0
0
0
2
0
1
2
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
2
0
0
1
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
2
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
4
0
0
0
2
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
4
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
2
2
0
2
0
2
0
0
0
0
1
3
0
0
1
1
2
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
2
2
0
1
2
0
0
0
2
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
1
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
1
0
0
0
0
2
0
0
1
0
0
0
2
0
1
0
3
2
0
0
0
0
2
0
0
1
0
1
0
12
0
0
0
0
1
1
2
0
0
0
0
2
0
0
1
3
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
1
1
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
2
1
1
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
2
1
0
0
0
1
0
0
1
0
1
0
0
0
2
0
0
0
2
0
0
1
0
2
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
2
0
0
2
2
4
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
2
0
0
0
0
0
1
0
0
3
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
1
0
0
0
7
1
1
0
2
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
3
0
0
0
1
2
0
1
0
0
0
0
0
0
1
2
2
1
1
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
1
0
0
3
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
1
0
2
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
3
1
1
1
0
0
0
0
2
0
0
0
0
0
2
0
0
2
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
2
0
1
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
3
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
3
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
3
2
0
0
0
2
2
1
2
0
0
0
2
2
2
0
0
0
2
0
0
0
0
0
2
0
0
0
1
2
0
0
2
0
0
0
2
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
2
0
2
0
1
0
1
0
0
2
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
3
0
0
4
0
1
0
0
1
0
0
3
2
0
0
1
2
1
3
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
1
0
3
0
3
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
1
0
2
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
8
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
2
0
0
0
1
0
0
1
0
1
0
0
0
0
2
3
2
0
0
0
0
1
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
2
0
1
2
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
1
3
0
0
0
0
1
0
0
0
0
0
1
2
0
0
2
0
3
0
2
0
0
1
0
0
2
0
0
0
0
0
0
2
1
2
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
2
0
0
0
0
0
1
2
1
0
2
0
0
1
0
1
1
0
0
0
1
1
0
0
0
0
3
0
0
2
0
0
0
0
0
0
1
0
1
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
2
0
2
0
0
0
0
0
1
0
0
0
0
3
2
0
2
0
0
0
0
0
0
0
1
0
3
2
0
0
0
1
0
0
2
0
0
1
0
3
0
1
0
0
0
0
0
1
0
0
1
2
0
0
0
1
2
1
1
0
3
1
1
1
0
3
0
3
1
1
0
0
2
1
0
0
0
0
1
1
2
0
2
0
0
1
1
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
7
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
1
0
2
2
0
0
0
0
0
0
0
6
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
2
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
2
1
2
0
0
3
0
2
0
2
1
2
0
2
0
0
1
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
2
2
0
0
1
0
0
3
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
2
0
2
0
1
4
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
2
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
1
1
0
2
0
0
0
2
1
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
1
0
1
2
1
0
1
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
3
0
2
3
0
0
1
4
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
2
2
0
0
0
2
3
0
0
0
2
0
2
1
1
0
0
0
0
0
0
1
0
0
0
2
0
2
0
1
0
0
1
0
3
0
0
2
0
0
0
0
0
0
1
1
5
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
2
2
0
0
2
1
0
4
0
2
0
1
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
1
2
0
1
0
0
1
2
0
1
0
0
0
0
0
4
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
15
0
0
0
2
0
0
0
0
2
0
6
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
1
2
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
7
1
2
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
3
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
2
0
1
2
0
3
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
3
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
2
0
0
1
0
0
0
0
10
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
2
1
2
0
2
1
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
3
0
3
1
0
0
0
0
3
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
2
0
0
0
0
0
4
0
0
0
0
0
0
0
4
2
1
0
0
1
0
1
0
0
1
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
5
0
3
0
2
0
0
1
0
0
0
0
1
0
0
1
1
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
4
0
0
1
0
0
0
1
0
2
2
0
0
0
1
0
0
0
2
0
0
0
2
1
0
2
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
3
0
2
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
3
0
1
0
1
0
2
0
0
0
0
2
0
0
1
1
1
2
0
1
2
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
4
2
0
0
1
0
0
0
2
1
0
1
0
0
1
0
2
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
1
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
2
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
2
0
0
0
0
2
2
0
0
0
2
0
0
0
1
0
0
0
0
0
1
1
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
2
0
0
0
4
0
0
0
0
0
1
0
1
0
1
2
2
1
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
3
0
0
1
0
0
0
0
1
1
0
0
0
0
0
2
1
3
2
0
0
1
2
2
1
0
0
0
0
0
0
1
2
1
1
2
2
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
2
2
1
0
0
0
0
2
0
0
0
0
2
0
2
0
0
3
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
2
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
2
0
2
0
2
3
0
0
0
3
0
1
2
0
0
0
1
0
0
0
2
0
0
0
3
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
6
7
2
1
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
1
2
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
1
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
1
0
2
1
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
4
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
3
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
2
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
1
0
0
2
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
2
1
0
2
0
0
0
2
1
1
0
0
0
4
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
2
1
0
0
1
1
0
0
0
0
0
3
2
0
3
1
1
0
0
3
2
0
2
3
0
1
0
2
0
1
0
1
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
2
0
0
0
0
3
2
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
1
0
0
0
0
3
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
7
0
0
3
2
0
0
0
4
0
0
0
2
0
0
4
0
0
0
0
0
1
0
2
3
1
0
0
2
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
2
0
1
1
0
0
2
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
2
0
1
2
0
1
0
0
1
0
2
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
1
2
0
1
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
2
0
2
2
0
5
3
0
2
2
0
0
0
0
0
2
0
2
1
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
2
0
2
1
1
0
0
2
0
2
2
0
0
0
0
0
0
2
0
1
0
0
0
1
0
1
3
0
0
0
1
0
2
1
0
0
2
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
2
0
1
1
0
0
2
0
2
0
0
0
0
0
0
0
1
0
1
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
1
3
0
0
0
0
1
1
0
0
1
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
4
0
2
0
0
0
0
2
0
2
0
0
1
0
1
0
0
2
0
2
0
0
0
2
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
2
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
2
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
2
0
0
0
4
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
1
0
0
2
0
0
0
0
0
0
1
0
2
0
2
0
0
1
0
1
1
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
2
2
0
0
0
0
0
7
0
0
0
1
0
1
0
0
0
1
0
2
3
0
1
0
0
2
0
0
0
0
0
3
0
0
0
0
1
3
0
1
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
3
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
2
1
0
0
0
0
2
1
0
2
1
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
5
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
2
0
2
2
0
0
2
2
2
0
0
0
2
2
0
0
2
1
0
2
0
0
0
0
0
0
0
2
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
3
0
2
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
2
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
2
2
2
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
2
0
2
0
1
0
0
0
2
0
1
0
2
0
0
1
0
0
0
0
1
0
0
4
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
1
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
3
0
0
3
0
2
0
5
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
2
1
1
0
2
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
3
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
2
0
0
2
1
0
0
1
0
0
0
0
0
1
1
1
0
0
1
4
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
2
5
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
2
0
3
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
3
1
1
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
1
2
1
2
0
0
1
2
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
1
1
0
0
2
1
1
2
1
0
0
0
3
0
0
0
0
0
1
0
2
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
2
0
1
2
0
0
0
1
0
1
0
0
2
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
2
0
2
4
0
2
2
1
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
5
0
2
0
0
1
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
2
0
0
0
0
1
1
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
3
0
2
0
0
0
0
0
0
2
2
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
1
0
2
0
0
2
3
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
2
0
1
0
3
1
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
2
0
2
1
0
0
0
1
0
1
0
0
1
2
0
0
2
1
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
4
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
1
0
1
2
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
1
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
2
0
0
4
0
1
2
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
7
2
0
0
2
0
0
1
0
0
0
1
0
2
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
1
3
0
0
0
2
0
1
2
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
3
2
0
0
1
0
0
1
0
1
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
3
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
2
0
0
0
0
0
2
0
2
2
3
0
0
0
0
0
1
3
1
2
1
1
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
5
1
0
0
0
0
1
4
0
2
1
0
0
1
0
0
3
0
0
0
1
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
1
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
2
0
1
0
1
0
0
1
1
1
1
2
0
2
0
0
0
0
0
1
0
0
0
4
0
0
1
0
0
3
1
1
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
2
0
0
2
0
0
2
0
2
0
0
0
2
1
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
3
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
2
0
2
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
2
1
0
0
2
1
0
0
0
0
0
0
0
4
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
2
0
3
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
2
5
0
1
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
4
0
0
6
0
0
0
0
1
2
0
0
0
0
0
2
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7
2
0
2
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
1
4
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
2
1
0
0
1
1
2
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
2
2
0
0
0
1
2
0
1
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
2
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
3
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
8
0
0
0
0
0
1
0
0
0
0
0
1
0
3
1
2
1
1
0
4
2
1
1
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
3
0
1
2
1
3
0
0
1
2
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
3
0
0
0
0
2
3
3
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
2
0
0
0
0
3
1
0
1
0
0
0
0
1
2
0
2
0
0
0
1
1
0
0
2
0
1
0
0
0
0
1
0
1
0
3
0
0
3
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
2
0
3
0
0
2
0
0
3
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
2
0
0
2
3
1
0
2
0
2
0
1
2
0
0
1
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
4
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
2
6
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
3
0
2
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
2
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
2
0
1
2
5
0
0
0
0
1
0
0
0
0
0
1
0
0
2
1
0
1
0
0
0
2
2
1
0
0
0
2
0
0
0
2
0
1
0
0
0
3
0
2
0
0
0
0
0
0
1
2
2
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
10
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
5
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
3
0
0
0
4
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
3
0
0
0
2
0
0
1
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
4
0
2
2
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
2
2
2
5
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
4
2
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
3
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
4
0
1
0
2
2
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
1
1
0
5
0
3
0
1
2
0
0
2
0
1
0
2
0
1
0
0
0
0
0
0
2
0
0
0
2
2
0
0
1
0
2
0
0
1
0
0
0
0
0
2
0
2
2
1
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
3
2
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
3
0
0
0
0
0
0
0
2
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
2
2
1
0
0
0
3
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
2
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
3
0
2
1
0
0
0
0
0
2
0
2
0
0
0
1
0
1
1
0
0
2
0
0
2
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
8
0
0
0
0
4
1
0
0
1
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
2
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
2
5
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
4
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
3
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
3
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
4
2
0
0
2
0
0
0
0
3
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
2
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
3
2
1
0
0
1
2
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
2
1
0
7
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
2
0
2
0
0
0
1
0
2
2
1
2
2
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
1
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
11
0
0
2
2
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
1
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
2
0
1
2
1
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
1
0
0
2
4
1
0
0
0
0
0
0
1
0
2
0
0
2
0
1
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
4
2
0
2
0
0
2
4
0
2
0
2
0
0
1
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
3
2
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
5
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
2
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
2
0
2
3
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
2
0
1
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
1
1
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
1
0
1
0
0
4
0
0
0
0
0
0
0
1
2
0
0
1
3
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
2
0
2
0
0
0
0
1
2
0
1
1
0
0
0
2
0
0
0
1
0
2
0
0
0
1
0
0
0
0
2
2
0
2
0
1
0
2
0
0
0
0
0
1
0
6
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
2
0
1
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
3
1
0
1
0
0
0
1
0
0
2
0
0
0
0
1
2
0
0
0
1
0
1
0
0
2
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
3
0
2
1
0
0
0
0
0
13
0
1
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
1
2
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
3
1
0
0
2
0
2
0
1
2
0
2
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
2
0
1
0
3
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
2
0
3
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
3
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
2
0
0
1
0
1
0
1
0
0
1
0
0
0
0
3
1
0
0
1
0
1
0
0
4
1
2
0
1
0
2
0
0
1
0
0
0
1
0
1
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
1
2
3
1
1
1
0
0
0
2
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
1
1
0
0
2
1
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
4
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
1
0
0
4
0
0
0
0
0
0
2
0
0
1
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
1
2
0
0
2
1
3
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
3
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
3
2
0
1
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
2
0
0
2
0
1
0
2
4
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
2
2
1
1
0
0
0
0
0
0
0
0
2
0
3
2
0
0
1
0
3
0
0
0
1
4
0
0
0
0
0
0
3
0
1
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
1
0
0
0
3
2
1
0
2
0
0
0
2
0
0
0
0
0
0
2
0
2
2
0
0
4
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
2
0
2
0
0
0
0
0
2
0
1
0
0
2
0
0
1
2
0
0
10
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
2
0
0
2
0
0
0
0
2
0
0
2
0
1
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
1
2
0
1
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
1
0
0
5
0
0
0
0
0
0
1
0
2
1
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
2
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
2
2
0
0
0
0
0
0
2
0
1
0
1
1
0
0
0
1
0
0
0
3
0
0
2
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
2
0
2
0
0
1
0
3
0
0
0
0
3
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
2
3
2
0
0
0
0
0
1
3
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
2
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
3
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
2
1
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
3
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
1
2
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
1
1
0
1
1
0
0
0
1
2
0
9
0
0
0
0
0
1
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
1
2
0
0
0
0
2
0
2
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
2
2
2
0
0
0
0
0
0
0
0
0
0
1
1
2
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
7
2
3
2
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
2
0
0
1
0
0
0
0
0
3
0
1
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
2
4
0
1
0
0
0
0
3
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
1
1
2
2
1
2
0
0
0
2
0
0
0
0
0
1
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
2
0
0
0
2
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
3
0
3
1
0
2
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
8
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
3
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
1
0
1
0
0
0
0
1
1
0
2
0
0
0
0
2
0
3
0
0
0
0
2
0
3
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
1
0
2
0
0
0
2
0
2
0
0
3
2
0
3
0
0
0
2
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
1
0
0
0
0
2
0
2
0
0
0
1
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
2
0
0
0
0
0
4
0
0
2
0
0
0
0
0
1
0
0
1
2
0
1
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
6
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
2
0
0
0
0
2
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
7
2
0
3
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
3
0
3
0
0
0
2
0
0
1
1
0
0
2
0
1
0
1
1
1
0
2
0
0
0
0
0
0
0
0
0
3
3
0
0
2
0
0
0
1
1
0
0
0
0
0
0
1
2
1
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
1
3
0
0
0
4
2
0
0
0
0
0
0
1
2
1
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
2
0
1
0
0
0
0
2
0
1
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
2
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
2
0
0
2
0
0
0
6
0
0
0
0
0
2
1
1
2
0
0
2
0
1
0
1
0
2
1
2
0
1
0
2
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
2
0
0
0
0
2
0
0
2
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
3
0
1
0
1
1
0
0
0
0
1
3
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
2
0
0
2
0
0
1
0
2
0
0
2
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
3
1
0
2
0
2
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
1
5
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
2
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
1
0
2
0
0
0
0
1
0
2
4
1
0
0
0
1
2
0
1
0
0
2
0
0
2
3
2
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
3
0
1
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
2
0
0
1
0
0
0
0
2
1
0
0
0
2
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
2
0
4
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
7
0
0
0
0
0
0
2
0
0
0
0
1
1
0
2
1
0
1
0
0
0
0
1
0
1
0
0
0
4
1
2
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
6
0
2
0
1
1
2
1
0
2
0
0
0
0
0
2
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
2
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
1
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
2
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
5
0
0
0
0
1
0
1
0
0
0
2
0
0
1
0
2
1
0
0
0
0
0
0
2
3
0
1
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
2
1
1
2
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
4
0
0
2
0
0
0
0
2
0
2
0
0
1
0
0
2
0
0
0
1
0
0
0
0
2
1
2
0
0
0
1
0
0
0
0
1
0
0
3
0
0
0
2
0
0
0
0
2
0
0
1
2
0
2
0
2
0
0
0
1
2
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
2
2
3
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
1
0
0
0
2
1
0
0
0
0
0
0
0
0
3
0
3
0
0
0
0
0
2
0
1
1
0
2
1
0
2
0
0
1
1
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
5
0
0
0
2
0
0
2
0
0
0
0
0
0
2
1
0
2
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
3
0
2
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
3
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
2
0
0
2
0
0
1
0
0
0
0
0
2
0
0
2
2
1
1
0
1
0
0
1
0
1
2
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
2
0
0
1
0
2
0
0
1
0
1
0
0
0
1
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
1
0
0
0
2
5
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
1
0
3
2
0
0
1
0
0
0
2
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
3
0
1
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
1
1
0
0
1
0
1
1
3
0
0
0
0
2
2
0
0
1
0
0
0
0
0
1
0
3
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
4
0
0
0
2
1
0
0
0
1
0
0
0
0
1
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
2
0
0
0
0
2
3
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
2
0
1
0
0
0
0
0
1
0
0
0
0
1
2
2
0
2
0
0
2
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
1
3
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
3
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
1
0
0
8
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
1
0
0
2
0
0
0
1
2
0
3
1
2
2
1
0
0
1
0
1
1
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
2
1
0
0
1
0
0
0
0
2
0
1
0
0
0
3
0
0
1
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
1
2
0
0
0
0
4
0
0
0
0
1
0
0
1
0
2
0
0
2
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
1
0
3
0
0
0
2
0
1
0
0
0
0
0
1
2
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
4
1
0
0
0
0
1
0
2
0
0
0
0
4
0
0
0
2
0
1
1
0
0
0
4
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
1
0
5
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
3
0
1
2
0
1
0
0
0
2
1
0
2
0
0
0
0
0
0
6
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
2
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
2
0
0
4
1
0
0
2
5
0
2
1
0
1
0
0
0
0
0
0
2
2
0
0
1
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
2
0
1
0
0
2
0
0
0
0
0
0
0
2
2
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
2
2
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
1
7
0
3
0
1
0
1
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
1
2
1
2
0
0
1
1
0
1
2
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
2
2
0
0
0
0
0
2
0
2
1
1
0
0
0
1
0
2
0
8
0
0
0
0
0
0
3
2
2
0
0
0
0
0
0
1
0
0
2
0
3
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
2
0
0
0
1
2
0
1
2
0
0
2
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
1
0
0
8
0
1
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
2
2
0
1
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
3
0
1
0
0
0
0
1
0
1
2
1
0
0
1
0
1
0
0
0
2
1
2
2
0
0
0
1
0
0
1
0
0
0
2
0
0
2
0
0
2
2
0
0
2
0
1
0
0
0
0
0
0
0
0
3
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
3
1
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
1
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
7
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
4
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
4
1
0
0
0
2
2
0
1
0
0
0
2
1
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
1
2
1
0
0
0
0
0
1
0
0
0
0
3
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
1
2
0
2
0
3
1
0
0
13
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
1
0
0
0
0
0
4
0
2
0
1
2
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
1
3
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
1
0
2
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
3
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
1
0
1
4
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
2
0
1
4
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
4
1
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
2
0
0
0
1
1
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
1
2
1
0
0
2
2
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
3
0
2
0
2
0
0
0
2
0
2
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
3
0
1
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
1
3
0
1
0
4
0
0
0
0
3
3
0
0
0
0
0
0
0
1
2
0
0
1
2
0
0
0
0
0
2
2
2
0
0
0
1
0
0
0
1
0
3
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
2
0
3
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
10
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
2
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
1
0
0
0
1
0
2
2
2
1
0
0
0
1
0
0
0
1
0
2
4
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
1
0
3
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
1
1
0
2
0
2
0
0
1
0
1
0
1
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
2
0
0
2
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
2
0
1
0
2
0
0
0
2
0
1
0
0
0
1
0
1
0
1
0
1
0
1
0
0
0
1
1
2
0
0
2
0
0
0
1
0
0
1
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
4
1
0
2
1
0
1
1
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
1
0
2
1
0
0
1
0
0
0
0
1
0
2
1
1
1
0
1
2
0
0
1
0
0
0
1
0
0
0
0
1
0
2
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
2
0
0
2
0
0
2
0
0
0
0
1
1
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
2
1
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
4
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
1
0
0
0
1
0
0
3
0
2
0
1
0
0
0
0
1
3
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
3
1
0
2
3
2
0
1
0
2
0
0
0
0
2
2
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
2
0
2
0
3
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
1
2
1
2
0
0
0
2
0
0
0
1
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
8
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
1
0
2
3
2
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
7
2
0
1
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
3
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
2
2
2
1
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
2
0
3
0
2
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
1
0
0
4
0
2
0
2
0
1
2
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
1
2
0
0
0
2
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
3
0
0
0
0
0
0
0
4
0
0
1
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
3
0
1
0
0
0
1
0
0
1
0
0
1
0
0
1
2
2
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
3
0
0
0
0
0
2
0
0
0
0
0
0
4
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
3
1
0
0
0
0
0
5
0
0
0
2
0
0
1
1
0
0
2
0
0
0
0
0
0
7
1
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
2
0
0
0
1
0
0
2
0
0
0
2
1
2
0
0
0
0
1
2
0
0
0
0
0
1
5
0
1
7
1
0
1
0
1
0
0
0
0
0
1
1
3
1
1
0
0
0
1
0
0
0
2
0
3
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
2
2
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
4
1
4
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
2
0
0
8
0
0
0
1
1
0
0
0
2
0
2
0
0
0
1
4
0
1
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
2
0
1
0
1
2
0
0
0
0
0
0
1
2
0
0
2
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
3
4
0
0
0
2
1
4
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
1
1
1
0
2
0
10
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
2
0
0
1
0
1
2
0
1
0
0
2
2
0
2
1
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
2
2
0
2
1
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
3
2
0
0
0
2
0
2
0
0
0
2
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
3
1
0
1
0
0
1
1
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
3
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
26
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
3
2
0
2
0
2
0
0
1
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
4
2
0
0
0
0
0
0
1
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
1
1
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
3
0
2
0
2
1
0
1
0
0
2
0
0
0
3
0
0
1
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
1
0
3
0
2
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
1
2
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
2
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
2
0
0
0
2
0
1
0
0
0
0
0
0
0
1
4
0
0
1
0
0
0
0
0
0
1
8
3
0
0
0
2
0
2
0
0
1
0
0
0
1
2
0
0
0
0
0
0
1
3
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
3
1
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
2
0
0
0
3
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
2
1
0
9
1
0
0
0
0
0
2
1
3
2
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
2
1
0
0
0
0
0
1
2
0
0
0
0
0
1
0
1
1
0
1
1
1
0
2
0
0
0
4
0
0
0
2
2
0
0
3
0
0
2
1
0
0
1
2
0
0
2
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
2
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
1
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
1
0
1
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
2
0
3
0
0
1
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
2
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
2
6
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
3
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
2
0
0
0
4
2
1
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
2
2
0
1
1
0
0
0
0
0
0
1
0
4
0
1
0
0
1
1
0
1
0
0
1
0
2
1
1
0
0
2
0
0
1
0
2
1
1
1
1
0
0
1
2
0
0
1
0
0
0
0
2
0
2
0
1
0
2
0
0
0
2
1
0
0
0
0
0
0
3
2
0
0
1
0
3
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
1
3
0
2
0
0
0
0
0
2
1
0
0
0
0
2
0
2
0
1
0
0
6
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
1
0
2
2
2
0
0
2
1
0
0
0
0
0
1
0
0
0
2
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
3
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
1
0
2
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
2
1
0
0
0
0
0
0
0
1
0
1
2
3
1
2
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
2
0
0
0
0
0
2
2
0
0
0
5
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
3
0
2
0
1
0
2
1
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
1
0
10
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
2
0
1
1
4
0
0
0
0
0
0
1
0
1
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
4
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
4
1
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
7
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
3
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
1
0
2
0
0
1
0
0
0
0
5
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
3
0
1
2
2
0
0
0
0
1
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
1
0
4
1
0
2
0
0
0
0
0
1
2
0
5
1
0
0
0
1
1
0
1
1
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
1
2
1
1
0
0
0
0
6
0
2
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
1
1
1
2
0
1
0
0
0
2
0
0
2
0
1
0
0
1
1
3
2
2
0
0
0
0
0
0
0
0
3
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
1
3
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
2
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
2
4
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
2
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
1
2
1
0
4
0
0
0
0
1
0
1
0
0
0
0
3
0
0
0
1
0
0
0
0
1
0
0
2
2
4
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
1
0
0
1
0
0
1
0
0
2
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
2
0
2
0
0
3
0
0
1
1
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
3
0
1
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
1
1
1
0
0
0
1
0
0
1
0
1
0
1
1
1
1
0
2
0
0
0
0
0
0
2
0
1
1
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
4
0
0
1
0
0
0
0
0
4
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
1
0
4
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
3
0
1
1
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
4
0
0
2
5
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
4
0
0
2
0
2
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
2
0
2
0
1
0
0
0
0
2
4
0
0
0
0
0
4
0
1
0
0
0
0
0
1
3
0
0
0
0
0
0
1
0
2
1
0
0
0
2
0
0
0
1
0
2
1
2
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
8
0
3
0
0
1
5
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
2
1
2
0
0
3
0
0
2
0
0
2
1
0
1
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
1
0
0
2
0
1
2
0
2
1
0
0
0
0
0
0
2
0
0
0
2
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
2
0
0
0
1
4
0
0
0
1
0
0
0
2
0
1
0
1
0
0
0
0
2
1
1
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
1
2
0
0
3
1
1
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
1
0
0
0
3
0
0
0
0
3
2
2
0
1
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
1
2
4
0
1
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
2
2
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
1
0
0
2
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
5
0
0
1
2
0
2
2
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
3
0
0
0
0
1
1
1
0
0
2
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
2
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
3
0
5
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
2
0
2
1
1
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
1
0
0
1
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
1
0
2
0
0
0
0
1
0
1
0
0
0
0
1
2
0
0
0
2
1
1
0
0
0
0
0
0
2
0
1
0
0
2
1
0
2
0
0
0
0
0
0
1
10
0
0
2
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
3
2
0
0
0
0
0
2
0
0
1
0
0
1
0
0
2
1
0
1
1
1
0
0
1
0
0
0
1
0
1
2
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
1
4
0
1
0
1
0
0
0
1
0
2
1
0
0
0
1
0
1
0
0
1
2
8
0
0
3
0
0
3
0
2
0
0
0
0
7
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
1
0
1
3
0
0
0
0
2
1
3
0
2
0
1
0
0
0
0
0
0
0
0
0
7
2
1
2
0
0
0
0
3
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
1
2
0
2
0
2
0
0
2
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
1
0
2
2
0
2
1
1
4
0
0
0
2
0
0
2
3
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
1
0
0
0
0
1
0
0
0
2
2
2
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
2
2
2
0
0
0
0
2
2
0
0
0
3
1
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
2
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
2
0
0
2
0
0
2
1
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
1
0
0
1
1
0
0
0
0
2
3
0
0
0
0
1
1
0
2
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
1
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
2
0
0
0
0
0
2
0
1
2
1
0
3
0
0
2
0
0
0
0
2
0
3
1
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
1
0
0
5
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
1
2
0
0
0
2
0
0
0
1
0
0
1
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
3
0
0
0
0
0
1
0
6
0
0
0
0
1
2
0
0
0
0
2
0
0
0
1
1
0
0
0
1
2
1
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
4
3
0
0
4
1
1
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
3
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
3
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
1
1
0
2
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
1
0
1
2
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
2
0
2
0
0
1
0
0
0
1
3
0
2
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
1
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
2
0
0
6
0
2
2
0
0
1
2
1
0
0
0
0
1
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
4
1
0
0
3
2
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
2
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
2
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
3
0
0
0
4
3
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
1
2
0
0
0
0
2
2
2
1
2
1
0
0
0
2
5
1
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
1
0
0
0
0
0
2
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
1
0
2
0
0
0
3
0
0
0
2
2
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
2
1
1
0
0
0
1
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
1
0
1
0
0
3
0
0
2
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
8
0
0
0
0
0
3
2
2
1
0
2
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
1
0
0
0
0
0
1
0
5
0
0
0
0
0
0
2
0
0
0
6
1
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
1
0
0
0
12
9
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
4
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
1
0
0
1
0
1
0
1
0
2
0
0
1
0
2
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
1
0
1
1
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
5
0
0
2
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
1
0
2
0
0
0
0
0
2
0
0
0
1
2
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
1
2
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
1
0
2
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
3
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
4
0
2
2
0
0
2
2
0
0
1
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
1
0
0
0
7
0
2
0
0
2
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
1
6
0
2
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
1
1
2
8
0
0
0
1
3
0
2
0
0
0
0
2
2
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
2
0
0
4
0
0
2
0
0
0
1
0
2
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
1
3
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
1
0
3
0
0
0
0
2
0
0
0
0
3
1
0
0
0
0
0
0
5
0
0
0
3
2
6
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
2
2
2
0
0
0
1
1
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
2
0
0
1
1
0
0
0
1
0
1
0
6
0
0
1
8
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
2
0
0
0
2
0
0
1
0
0
0
0
0
0
3
0
0
2
0
1
0
0
1
2
0
1
0
0
1
1
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
1
3
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
2
0
0
1
0
1
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
3
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
2
0
0
1
3
0
2
1
0
2
0
2
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
2
1
16
0
0
0
0
1
0
0
2
0
2
0
0
0
2
0
0
3
0
0
1
0
1
3
0
2
0
2
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
1
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
7
0
0
0
5
0
0
0
0
1
0
1
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
3
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
5
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
2
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
1
0
5
0
0
2
0
0
0
1
2
2
0
0
0
0
4
0
2
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
6
0
1
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
2
0
4
0
0
0
2
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
2
3
0
4
0
1
0
0
3
0
0
1
0
0
0
0
1
1
0
1
0
2
0
2
2
1
2
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
2
8
0
0
1
0
0
0
2
0
1
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
1
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
3
1
0
0
2
0
0
0
0
0
0
1
0
0
0
1
2
0
2
1
0
1
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
2
0
0
1
1
0
0
0
0
1
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
5
1
1
0
0
2
0
2
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
2
2
2
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
2
0
1
5
0
1
0
0
0
0
2
3
0
0
0
1
0
0
0
0
0
0
2
0
0
3
0
0
0
7
0
0
0
0
0
1
0
0
0
3
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
1
0
0
2
2
0
2
1
1
1
0
0
0
0
0
4
0
0
0
0
1
2
0
1
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
2
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
1
2
0
0
0
0
2
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
2
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
1
0
0
0
0
2
0
0
0
2
1
0
1
2
0
2
0
0
0
0
0
0
1
2
0
3
0
2
0
0
0
0
0
0
0
0
5
0
0
0
0
3
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
3
0
0
0
0
1
0
0
0
2
0
0
2
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
3
0
0
0
2
0
0
0
0
0
0
2
0
2
0
2
0
0
0
2
0
2
0
2
1
2
0
1
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
1
0
0
3
0
0
1
0
2
1
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
2
0
2
0
3
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
1
2
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
1
0
0
2
0
12
0
0
2
0
0
0
0
2
3
1
0
0
1
2
0
0
0
1
1
1
0
1
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
2
0
0
1
0
1
2
0
0
0
0
2
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
2
1
0
1
0
2
1
2
3
0
0
3
2
0
0
3
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
1
0
2
1
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
2
2
4
1
0
0
0
1
0
1
0
0
0
1
0
0
1
3
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
2
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
1
1
0
1
0
0
0
2
2
0
1
3
1
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
2
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
2
0
0
0
1
1
1
4
0
0
0
1
0
4
2
2
1
3
0
0
0
3
0
0
0
0
0
0
0
1
1
0
0
0
0
3
0
0
1
2
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
2
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
4
0
2
0
2
0
0
1
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
2
1
0
2
0
0
0
0
0
1
2
0
2
1
1
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
1
0
1
0
2
2
0
4
0
2
0
1
0
0
0
1
2
0
0
0
0
2
0
0
2
1
0
1
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
2
0
0
0
0
0
0
1
0
2
0
0
2
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
1
0
0
0
0
0
2
0
0
0
0
2
0
1
1
0
3
0
0
2
1
0
0
0
0
0
0
1
0
3
0
0
2
0
0
1
0
0
0
0
1
0
0
0
2
0
0
2
2
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
4
0
2
0
1
3
1
0
0
0
0
0
0
0
0
1
4
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
1
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
1
0
2
0
0
1
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
1
0
0
0
0
0
3
0
0
2
0
0
0
2
0
0
2
0
0
0
0
2
1
3
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
2
0
0
0
1
1
2
0
0
0
0
0
1
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
2
0
0
4
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
1
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
7
0
0
0
0
0
1
0
1
2
7
0
0
2
3
2
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
2
0
0
2
2
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
2
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
1
1
2
1
0
0
3
2
3
0
0
0
0
1
2
0
0
2
0
0
3
0
0
1
2
0
1
0
0
0
0
0
1
1
0
0
1
2
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
1
0
0
0
2
0
0
0
5
2
1
5
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
4
2
3
0
2
1
0
0
2
0
0
3
0
0
0
2
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
2
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
5
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
1
0
0
1
2
1
0
1
0
0
0
2
0
0
2
0
1
0
0
2
0
2
0
0
0
0
2
0
0
1
3
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
6
2
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
3
0
0
0
2
1
0
0
0
0
1
0
0
3
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
1
1
0
1
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
1
1
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
4
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
5
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
1
3
0
1
0
0
0
0
0
1
2
2
0
2
0
0
1
1
0
0
0
2
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
9
0
0
0
0
2
0
0
1
0
0
0
1
3
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
3
0
0
0
7
0
0
2
0
0
2
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
1
3
1
0
2
0
2
0
2
0
0
0
0
2
4
0
3
0
1
0
1
0
2
0
0
1
0
0
0
1
1
0
2
2
2
1
2
1
1
0
7
2
0
0
0
3
0
5
0
0
2
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
4
0
1
0
1
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
2
0
3
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
1
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
3
0
0
2
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
2
0
0
0
0
0
2
0
2
2
2
0
1
0
0
2
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
2
2
1
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
5
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
3
1
0
0
0
1
2
0
2
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
3
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
2
2
2
0
2
0
0
1
1
0
0
0
0
3
3
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
1
2
1
0
0
0
1
3
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
2
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
1
0
0
0
0
1
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
3
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
5
1
2
1
0
0
0
0
2
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
2
0
0
0
1
2
1
0
0
0
0
0
0
0
2
3
0
0
1
2
1
0
2
2
0
1
1
0
0
0
0
1
2
0
0
0
1
3
0
0
2
2
0
0
1
0
2
0
0
0
0
0
1
2
0
0
0
0
0
1
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
1
0
2
1
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
6
0
0
0
0
0
0
4
1
1
2
0
0
1
1
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
2
1
0
3
0
0
0
0
1
0
0
0
0
0
0
0
2
1
1
2
0
1
0
0
1
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
2
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
3
3
0
0
0
0
0
3
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
6
2
0
1
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
3
0
0
0
1
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
3
0
0
1
2
0
0
0
2
1
0
0
2
0
1
1
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
1
1
0
1
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
2
0
1
0
1
1
0
1
1
0
1
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
2
0
3
1
1
0
2
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
1
0
0
2
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
2
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
2
2
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
3
5
3
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
1
3
0
0
0
2
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
2
2
1
2
3
1
1
0
0
1
0
2
0
0
0
2
0
1
0
0
0
0
0
1
1
2
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
5
0
6
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
2
0
2
0
0
1
2
0
0
1
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
1
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
1
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
5
1
0
0
3
2
0
0
0
0
1
0
0
0
0
3
0
0
1
0
0
0
0
1
0
0
0
2
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
2
0
3
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
3
1
1
0
0
0
0
0
1
0
0
1
0
2
1
2
2
2
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
1
0
4
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
2
1
0
0
1
0
6
0
1
1
1
0
0
0
2
0
1
1
0
2
0
0
0
2
0
1
0
3
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
10
0
1
0
0
0
0
0
1
0
3
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
3
2
0
1
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
3
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
3
0
0
1
0
2
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
1
1
2
1
1
0
1
0
0
0
0
0
1
0
0
0
0
2
1
1
1
1
0
0
2
0
0
0
0
0
0
0
1
1
1
1
0
0
1
1
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
2
2
0
0
0
0
0
0
0
1
0
0
2
2
0
1
0
1
3
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
3
0
0
0
1
0
0
2
1
0
1
1
0
0
1
0
0
0
2
0
0
4
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
1
1
0
0
0
3
2
1
1
0
2
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
1
1
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
1
0
0
1
0
0
2
0
0
0
1
1
0
0
2
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
3
0
0
0
0
2
0
0
0
0
1
1
1
0
2
7
1
0
0
0
1
2
3
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
2
1
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
1
1
0
3
0
0
0
0
0
2
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
2
0
0
3
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
3
0
0
0
4
2
1
0
0
0
0
0
1
3
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
4
2
2
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
1
2
1
0
2
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
1
1
2
0
4
0
0
0
1
0
0
1
0
0
0
0
0
1
0
2
0
0
2
0
2
0
0
2
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
2
1
0
0
0
5
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
3
0
2
0
0
1
0
1
2
2
0
0
0
0
0
0
2
0
0
0
2
1
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
3
0
1
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
2
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
2
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
5
1
2
1
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
2
2
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
3
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
5
0
0
0
1
2
0
0
4
0
1
1
0
2
0
0
0
0
1
1
2
1
0
0
0
2
1
0
0
0
0
0
0
3
1
0
0
0
0
0
2
0
0
0
0
2
0
2
1
0
1
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
3
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
1
0
0
1
0
0
4
0
0
0
2
1
1
0
0
0
2
0
2
0
0
0
0
1
0
0
3
2
0
0
1
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
1
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
1
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
1
0
1
0
2
0
0
0
0
0
0
2
1
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
1
0
0
1
0
0
6
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
1
0
0
1
0
1
1
0
0
13
0
0
0
0
0
0
0
0
0
0
0
3
1
1
0
1
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
1
2
0
0
0
1
1
0
0
2
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
3
0
0
0
7
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
1
0
2
0
0
0
0
0
2
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
3
1
0
0
0
1
0
0
2
0
2
0
0
0
1
0
3
2
2
2
0
0
0
0
2
0
0
0
0
0
0
0
1
3
0
0
0
2
0
2
0
0
0
0
2
0
2
2
0
2
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
2
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
4
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
4
2
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
1
1
0
0
0
0
1
2
2
0
0
0
1
0
0
0
0
0
1
4
0
0
0
0
2
0
0
0
5
0
0
2
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
2
1
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
3
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
4
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
2
3
0
0
0
0
1
0
4
2
0
0
0
0
0
2
0
1
2
1
0
0
0
0
1
1
0
2
0
3
0
0
0
0
0
0
0
0
0
1
0
1
2
0
3
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
2
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
2
1
0
0
2
0
0
0
4
2
2
0
0
0
2
0
3
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
2
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
1
0
1
2
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
5
0
0
0
0
0
3
2
0
0
0
2
0
0
2
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
1
0
0
0
2
0
2
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
3
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
2
2
0
1
0
1
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
4
1
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
3
0
0
2
0
2
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
4
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
1
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
4
0
0
0
2
1
0
1
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
2
0
1
0
0
0
0
0
1
1
0
0
0
0
4
1
0
1
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
3
1
0
0
2
2
2
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
2
1
0
1
0
3
0
0
6
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
2
1
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
2
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
3
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
3
0
0
4
0
0
0
0
2
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
3
0
0
0
0
0
0
1
0
4
0
0
2
0
0
0
2
0
0
1
1
0
0
1
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
1
3
0
1
0
1
0
0
2
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
1
1
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
3
0
0
0
2
1
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
1
1
0
0
2
0
2
1
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
1
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
7
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
9
0
0
1
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
1
0
0
1
0
1
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
2
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
1
0
0
0
0
0
3
0
0
0
1
0
1
0
0
2
0
0
0
2
2
0
0
0
0
0
0
1
0
2
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
1
3
0
2
2
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
2
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
1
0
6
1
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
2
0
1
0
1
0
1
0
2
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
1
0
5
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
1
1
0
2
0
2
0
0
5
0
0
1
2
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
2
1
0
0
0
1
0
3
2
0
1
0
4
0
0
0
0
0
0
0
0
1
5
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
2
1
0
2
0
0
0
0
2
0
0
0
4
4
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
2
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
16
0
1
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
1
0
3
1
0
0
1
1
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
1
0
0
0
0
2
2
0
0
0
3
0
0
0
0
0
2
2
0
0
1
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
2
1
1
0
0
2
1
0
0
2
0
1
0
0
0
2
1
1
0
0
0
0
0
0
3
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
1
0
5
0
0
0
1
0
0
0
0
2
0
1
0
1
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
3
0
0
0
2
0
2
1
0
0
0
0
3
0
0
0
0
0
0
2
1
0
0
2
2
0
1
0
2
2
1
2
0
1
0
0
0
0
2
0
2
1
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
3
7
2
0
0
0
2
0
0
0
1
0
0
0
0
0
3
0
2
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
1
1
3
0
0
1
0
0
0
6
0
0
0
0
0
2
0
2
3
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
1
0
0
0
0
0
0
1
0
0
0
0
5
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
1
1
0
2
0
0
2
0
0
0
0
0
0
2
0
1
2
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
3
0
0
0
0
1
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
3
0
1
0
5
2
0
0
0
0
0
0
0
1
1
0
1
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
1
0
0
2
0
1
0
0
2
0
1
0
0
3
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
9
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
3
0
0
3
2
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
1
2
0
0
0
0
0
2
0
1
1
2
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
3
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
2
0
0
0
0
0
2
1
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
3
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
5
0
0
0
0
1
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
2
1
0
2
0
0
0
0
3
2
0
0
2
0
0
0
0
0
1
0
0
2
0
0
1
0
2
0
0
0
0
2
0
2
1
0
0
0
0
0
2
0
0
0
0
6
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
2
0
2
0
1
1
0
0
0
0
0
0
0
2
1
0
0
0
1
3
0
0
0
2
1
0
0
0
0
0
0
5
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
2
2
0
0
0
0
0
0
2
1
0
0
1
2
0
0
0
1
0
0
0
0
0
2
2
0
1
0
0
0
0
2
0
0
0
1
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
3
2
1
0
0
2
0
0
1
1
1
0
1
2
0
0
1
0
2
0
1
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
1
0
3
0
0
0
0
0
1
0
0
0
1
0
0
3
0
0
0
2
1
1
5
0
0
1
0
0
0
1
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
2
0
0
1
0
0
1
0
1
0
1
2
1
0
0
2
0
0
0
1
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
2
1
0
0
0
0
2
0
0
0
0
2
0
0
0
2
2
1
2
0
0
0
3
1
0
1
0
0
0
1
1
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
6
0
2
2
0
0
2
2
0
0
0
0
1
0
2
2
0
0
0
0
0
1
0
0
0
0
0
2
0
1
1
3
0
0
0
0
0
3
1
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
2
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
2
2
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
1
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
1
0
2
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
5
1
1
0
0
0
0
0
0
1
0
3
0
1
1
2
0
0
0
1
0
0
2
0
1
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
3
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
6
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
1
2
1
0
0
0
4
0
2
0
0
0
1
0
0
0
0
0
6
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
3
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
1
0
3
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
3
2
0
0
0
0
2
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
2
1
0
1
0
0
0
0
0
1
0
0
3
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
1
0
0
0
2
0
2
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
1
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
1
0
0
2
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
2
2
0
2
0
0
0
1
0
0
0
0
0
2
3
1
0
0
0
1
1
0
0
1
0
0
0
2
0
2
2
2
0
0
1
0
0
0
0
0
1
0
0
5
0
4
0
0
1
0
0
8
0
0
5
0
1
2
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
2
0
0
0
0
2
0
0
0
0
3
1
1
0
0
2
0
0
0
0
2
0
2
0
2
0
2
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
2
0
1
6
0
2
0
0
0
2
0
0
0
0
0
3
0
1
0
0
0
2
1
0
0
0
0
0
0
2
1
0
0
0
2
1
1
1
0
3
2
1
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
6
0
0
2
2
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
1
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
2
1
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
1
0
1
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
1
2
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
4
2
0
0
3
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
5
1
0
0
0
2
0
0
2
1
2
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
6
0
0
0
0
0
0
2
0
0
0
0
0
1
2
2
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
2
0
2
2
1
0
0
2
0
0
1
1
2
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
2
0
0
1
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
2
1
2
0
3
0
0
2
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
2
1
0
0
4
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
3
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
2
0
0
0
0
0
0
2
1
0
0
0
3
0
0
0
2
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
1
3
1
3
0
0
0
0
0
0
0
0
0
2
0
1
6
0
0
0
0
0
0
0
0
1
0
0
1
0
5
0
0
0
0
0
2
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
4
0
0
1
0
2
0
3
0
0
2
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
1
1
1
0
2
2
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
1
1
2
0
0
0
0
0
3
1
0
2
0
0
0
0
1
2
0
1
1
0
0
0
0
2
0
1
2
0
4
0
2
1
2
1
2
1
2
0
1
0
0
0
2
0
0
0
2
3
2
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
1
3
0
0
0
0
0
2
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
3
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
1
0
0
2
0
0
0
1
1
1
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
2
3
0
0
0
2
1
0
0
0
0
2
0
2
1
0
0
1
0
0
0
2
0
0
0
1
0
0
0
1
1
3
0
0
0
1
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
2
2
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
2
0
0
1
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
1
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
1
1
0
2
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
2
0
2
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
2
0
1
1
3
4
0
0
0
0
2
2
1
1
1
0
0
0
0
2
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
3
2
0
0
1
6
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
2
0
2
0
0
3
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
3
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
3
1
1
0
0
0
0
0
1
0
1
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
6
0
1
0
1
0
0
0
0
0
0
0
2
0
1
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
1
0
1
1
0
2
2
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
2
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
1
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
1
2
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
5
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
1
0
0
0
0
0
0
0
1
3
4
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
1
3
0
0
3
1
0
2
2
0
0
1
0
0
2
0
0
0
0
2
0
2
2
0
2
0
0
0
0
0
0
1
8
2
2
1
0
0
2
0
2
0
1
0
0
0
0
2
1
1
0
0
0
1
1
0
0
0
0
0
1
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
2
1
0
1
0
2
1
0
0
2
1
1
0
2
0
3
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
5
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
2
0
0
3
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
3
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
1
0
0
0
1
0
0
0
2
3
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
2
0
2
2
6
1
1
0
0
1
0
0
5
0
0
0
2
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
1
0
1
1
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
1
1
2
2
0
0
0
1
0
0
2
1
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
3
0
2
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
2
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
3
0
0
1
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
2
1
0
0
1
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
4
0
2
0
0
0
3
0
0
0
0
0
0
0
0
1
2
0
0
1
3
1
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
3
0
2
1
0
0
3
0
2
0
0
0
0
2
0
2
0
0
0
1
0
1
3
0
0
2
0
2
1
0
0
0
0
0
0
0
1
0
0
1
3
0
0
0
0
0
0
0
0
0
6
0
0
2
0
0
0
1
1
0
4
0
1
0
0
2
0
2
1
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
1
2
0
2
2
1
0
0
0
0
0
2
2
0
1
2
0
0
0
0
1
0
0
0
0
0
0
1
0
1
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
2
1
0
0
0
0
1
2
0
0
2
0
0
0
1
0
0
0
0
5
1
0
0
0
1
0
0
4
0
0
0
0
0
0
0
4
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
19
0
1
0
2
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
1
0
1
0
0
1
1
2
0
2
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
1
1
4
0
0
0
0
1
0
2
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
2
0
2
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
3
1
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
2
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
6
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
3
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
2
0
2
3
0
0
0
0
3
0
1
0
0
0
0
0
0
2
0
1
2
0
2
0
0
2
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
2
1
4
0
0
0
1
0
0
0
1
0
0
1
2
2
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
3
1
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
3
1
0
0
0
1
0
0
2
2
1
2
1
0
0
0
0
0
1
0
7
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
2
0
0
0
2
0
2
0
4
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
1
0
0
1
0
4
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
2
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
3
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
1
0
2
0
0
2
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
1
1
0
2
0
0
0
0
1
1
1
0
0
1
0
0
2
1
0
2
0
1
0
0
0
0
0
1
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
2
2
0
0
0
0
4
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
2
1
1
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
3
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
2
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
4
0
0
0
0
0
1
1
0
1
0
0
2
0
0
3
2
0
1
0
0
1
1
0
0
0
0
3
0
2
3
0
0
0
1
0
1
0
3
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
2
0
6
1
0
0
0
0
1
0
0
0
0
1
0
0
4
1
0
0
0
0
3
0
2
1
2
0
0
1
0
0
0
2
0
4
2
0
0
0
0
0
2
0
0
1
0
0
3
0
0
1
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
1
0
0
2
1
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
1
1
1
1
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
2
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
1
0
2
2
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
3
0
2
0
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
1
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
1
0
2
0
3
0
0
2
0
0
0
0
1
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
1
0
2
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
3
0
3
2
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
2
4
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
1
1
0
0
0
2
0
0
0
2
1
1
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
4
0
1
0
0
0
3
0
0
0
0
0
0
0
4
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
3
0
0
2
0
0
1
0
3
0
0
0
0
0
0
0
1
0
0
2
0
2
1
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
3
2
0
2
2
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
2
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
3
0
0
0
3
0
1
0
1
0
1
3
3
0
1
1
2
0
0
0
0
1
2
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
4
0
0
5
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
3
0
1
0
0
0
1
1
0
1
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
2
1
2
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
1
3
2
0
1
1
0
0
0
0
1
0
1
2
2
2
0
3
0
0
0
0
0
0
0
0
2
0
0
3
0
1
1
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
1
0
1
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
3
0
0
3
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
2
2
0
3
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
1
0
1
0
0
1
2
0
0
0
0
2
0
0
0
0
0
1
7
1
3
1
0
2
0
2
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
4
0
0
1
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
1
0
1
1
0
2
2
0
0
0
0
4
0
1
0
0
0
1
3
2
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
2
0
0
0
0
2
2
0
0
3
1
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
2
0
0
1
0
2
0
2
1
0
8
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
4
2
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
3
0
0
2
0
2
2
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
3
2
0
0
2
1
4
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
3
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
1
1
1
0
0
0
0
2
1
1
1
0
0
2
0
0
0
2
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
1
2
0
0
0
0
2
0
0
1
0
0
2
1
0
1
1
2
2
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
4
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
1
0
2
0
0
0
0
7
2
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
2
1
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
3
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
3
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
3
3
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
1
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
2
0
1
1
0
2
0
0
2
0
2
2
0
1
2
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
1
2
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
5
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
3
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
6
2
0
0
2
0
0
0
0
2
0
0
1
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
2
0
1
0
0
1
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
3
0
0
0
2
0
2
0
1
1
0
0
0
2
0
0
0
0
1
0
0
0
7
0
2
0
2
0
2
1
0
0
0
0
2
0
1
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
2
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
3
1
0
0
0
2
0
1
2
0
0
0
2
0
0
0
2
1
0
3
0
0
1
0
0
0
0
0
4
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
1
0
2
1
0
2
0
0
0
0
0
3
0
0
1
0
1
2
2
0
0
0
0
0
1
1
3
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
2
1
0
0
2
1
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
1
2
3
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
7
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
4
0
0
0
0
0
1
2
0
0
0
0
3
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
4
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
6
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
5
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
1
2
1
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
1
0
0
1
0
2
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
2
2
3
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
2
0
0
0
0
0
0
1
1
0
0
0
3
0
0
1
0
2
0
0
0
0
3
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
2
2
2
0
1
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
2
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
1
2
0
1
1
0
0
0
0
0
2
0
0
0
2
0
0
1
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
7
2
0
0
0
0
0
2
2
1
0
1
0
0
0
0
1
0
0
4
2
1
0
0
3
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
1
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
2
0
1
0
0
0
0
1
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
3
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
1
2
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
1
2
2
0
0
0
0
2
0
0
1
2
2
0
1
1
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
8
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
1
0
0
0
0
1
0
1
1
0
3
3
0
4
0
0
0
0
0
1
0
0
0
0
0
1
0
2
1
0
2
0
2
0
0
6
0
1
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
2
2
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
1
0
2
2
0
2
0
5
1
0
0
0
0
0
0
0
0
0
0
1
1
0
3
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
3
2
2
0
0
0
0
0
0
0
0
0
0
0
2
1
2
2
0
0
0
0
0
0
1
1
0
1
1
0
0
0
2
0
0
0
0
0
1
0
3
1
0
1
0
0
0
0
0
1
0
0
2
1
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
2
0
2
6
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
1
0
1
0
1
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
4
0
3
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
1
0
2
1
0
0
0
0
3
1
0
0
1
0
0
0
2
1
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
2
0
0
0
0
0
1
0
1
4
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
2
0
0
0
0
0
1
0
2
0
1
1
2
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
13
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
1
0
0
2
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
2
2
2
0
0
0
0
0
0
4
0
0
2
0
0
1
0
0
0
1
0
1
2
0
0
0
0
0
3
0
0
0
0
0
2
2
0
1
0
2
0
0
2
4
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
1
0
0
2
2
0
0
0
2
0
1
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
1
0
2
0
1
0
1
0
1
1
0
0
0
3
0
2
2
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
2
0
0
0
0
0
0
1
2
0
1
0
1
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
4
0
2
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
2
5
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
2
0
2
0
1
0
2
0
0
0
2
0
2
0
1
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
1
0
1
0
0
0
2
1
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
1
0
0
1
0
0
2
0
0
3
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
2
1
0
5
0
1
0
0
0
0
0
2
1
0
0
0
0
2
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
2
1
0
0
1
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
3
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
1
1
0
0
0
0
0
2
0
0
2
2
0
0
0
0
1
2
1
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
1
3
2
0
0
1
0
0
2
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
2
0
0
0
0
0
1
0
2
0
1
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
1
3
1
1
0
0
0
0
1
2
2
0
0
0
1
0
2
1
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
1
0
0
0
2
0
0
1
0
2
0
0
0
0
2
0
0
0
2
0
0
2
1
0
2
0
0
0
0
0
0
2
2
0
0
0
0
2
1
0
0
0
2
50
0
0
0
1
0
0
3
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
2
0
0
0
0
1
0
1
0
2
1
0
0
0
0
1
0
0
0
1
2
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
1
0
2
0
0
1
0
0
0
3
0
3
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
3
0
0
1
0
0
1
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
7
0
0
2
0
0
0
2
0
0
2
1
0
0
1
1
2
0
0
2
12
0
1
0
1
1
0
1
0
1
0
2
2
0
0
0
0
0
7
0
0
2
0
0
0
0
0
0
2
0
1
2
0
1
2
2
2
1
0
0
0
0
0
0
1
0
0
2
1
0
2
0
0
0
0
0
1
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
2
4
0
0
2
0
0
0
0
0
2
0
0
3
2
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
3
0
0
0
2
0
0
1
0
0
0
0
0
0
0
3
0
0
2
2
2
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
1
0
1
1
0
0
3
0
0
1
2
2
0
1
1
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
3
0
0
0
1
0
0
0
0
0
0
1
0
6
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
6
0
2
0
0
0
0
3
0
0
0
0
1
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
4
0
3
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
3
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
3
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
2
0
4
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
6
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
3
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
4
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
2
0
0
1
0
1
1
0
0
0
4
0
0
0
0
2
0
0
4
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
6
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
3
0
1
0
2
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
3
2
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
1
0
1
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
2
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
1
0
0
3
0
2
0
1
0
0
0
0
2
2
0
0
3
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
3
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
1
0
1
2
0
1
1
1
2
1
2
0
0
0
0
1
0
0
0
1
0
0
0
1
0
3
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
3
0
0
0
1
0
1
2
1
0
0
2
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
2
0
2
0
1
0
0
0
0
0
0
0
0
0
6
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
2
1
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
2
0
0
0
3
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
4
0
1
0
0
0
0
0
1
0
0
1
0
0
2
2
0
0
0
0
0
1
0
0
2
0
2
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
1
3
0
1
0
1
0
0
0
3
0
0
8
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
2
0
0
2
0
0
1
0
0
0
0
2
1
0
0
0
0
2
1
0
2
0
0
0
2
0
1
0
0
0
6
3
0
0
0
1
0
2
0
0
0
1
0
0
0
1
0
1
2
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
3
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
1
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
3
0
1
1
0
1
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
5
0
0
1
0
0
0
0
0
2
0
2
2
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
2
1
0
0
0
1
0
0
3
0
0
0
1
0
0
0
0
1
2
0
1
0
1
2
2
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
2
1
0
2
0
0
0
1
0
0
3
0
0
3
0
1
1
0
0
0
2
0
0
0
0
0
2
0
1
2
0
1
0
0
3
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
1
0
0
1
2
0
0
2
0
0
0
0
1
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
3
0
0
0
0
0
1
0
2
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
3
0
2
0
0
0
1
0
0
4
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
2
0
1
0
0
2
0
2
0
2
3
0
1
0
0
0
0
2
0
0
0
0
1
0
3
4
0
0
1
2
2
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
2
1
0
0
0
0
0
2
2
0
2
0
0
10
0
0
0
0
0
0
2
1
0
0
2
6
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
3
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
2
0
2
0
2
0
0
0
0
0
3
0
0
0
0
0
0
1
0
2
2
7
0
0
0
0
1
0
2
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
1
1
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
3
5
0
0
0
0
4
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
1
0
0
0
2
0
0
3
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
2
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
1
0
1
3
2
0
0
0
0
3
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
1
0
0
6
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
1
2
0
0
0
0
1
1
0
2
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
1
0
0
1
2
1
2
1
1
0
6
0
0
0
0
1
0
0
0
0
0
1
0
0
2
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
2
1
0
0
0
0
2
0
0
3
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
2
0
0
1
0
1
0
0
0
0
0
1
1
3
1
0
0
1
0
0
0
0
0
2
1
0
1
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
1
0
0
0
0
2
0
2
0
1
0
0
0
1
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
3
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
2
0
0
1
0
0
3
2
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
3
0
0
2
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
2
0
0
1
0
0
0
0
0
0
0
2
1
2
1
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
1
2
0
0
0
0
0
0
1
2
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
1
0
2
2
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
2
0
0
0
0
0
0
2
0
0
1
1
0
0
8
1
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
4
0
0
0
1
2
0
0
0
2
0
0
2
2
1
0
0
0
0
0
0
1
0
0
0
0
2
0
3
0
0
2
0
0
0
0
0
0
3
0
1
0
2
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
1
0
2
0
0
0
1
2
0
1
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
2
1
1
0
0
1
1
2
0
0
0
0
2
1
1
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
5
0
0
0
0
1
0
1
1
0
1
0
0
0
0
2
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
3
3
0
0
2
0
0
0
0
1
2
0
0
0
0
1
1
0
1
2
1
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
2
1
2
0
0
1
0
0
2
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
4
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
2
0
1
1
0
0
0
1
0
0
0
0
0
0
2
0
2
0
2
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
1
0
1
0
0
2
1
0
1
1
0
2
0
1
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
2
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
2
0
0
2
1
0
0
1
0
2
0
3
2
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
1
1
0
2
0
1
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
2
2
2
0
1
1
0
1
0
0
0
0
0
0
2
0
0
1
1
0
0
2
1
0
0
0
1
0
0
0
0
1
2
0
0
2
0
0
6
0
0
0
0
1
0
0
0
0
0
0
2
2
4
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
1
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
1
2
0
0
1
3
0
2
0
0
2
2
2
0
0
2
0
0
0
2
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
8
0
0
1
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
1
0
0
0
0
1
0
0
0
1
2
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
8
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
2
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
3
0
2
2
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
3
1
0
1
1
4
1
0
2
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
3
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
1
1
1
0
1
1
0
1
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
8
2
2
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
2
1
0
0
0
2
0
0
0
0
2
3
0
1
0
0
0
0
0
1
0
0
0
0
2
1
1
0
0
0
2
1
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
3
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
2
2
0
2
0
1
0
0
2
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
2
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
2
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
2
0
0
1
0
0
2
0
3
2
0
0
3
1
0
0
0
2
2
2
0
0
3
3
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
2
0
0
0
1
0
0
2
0
0
2
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
3
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
1
0
0
0
0
0
2
1
2
0
0
0
0
0
0
2
0
1
0
0
0
2
1
2
0
0
0
0
0
0
0
1
1
2
0
0
1
1
0
0
0
0
2
1
1
0
0
0
7
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
4
3
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
2
0
0
0
3
0
3
0
0
1
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
1
1
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
2
0
0
1
2
0
0
0
1
0
0
0
0
0
2
0
2
1
0
0
0
2
2
0
2
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
2
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
2
1
0
0
11
0
0
0
1
2
1
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
1
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
1
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
1
0
5
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
2
3
2
2
0
1
2
1
2
0
0
0
0
0
0
0
0
2
1
0
1
0
3
0
0
1
0
0
0
0
0
0
1
1
0
1
1
0
0
1
1
0
0
0
0
0
6
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
2
2
1
0
0
2
2
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
3
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
1
0
0
0
1
0
2
0
0
0
0
0
2
0
1
1
0
0
1
0
0
0
3
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
2
0
1
0
0
0
0
0
0
0
0
4
1
0
2
0
0
0
1
3
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
4
0
0
0
1
0
1
0
0
2
3
0
0
0
0
1
2
1
0
0
2
0
0
0
0
2
0
0
1
1
2
0
0
0
1
0
0
2
0
1
1
0
6
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
1
0
2
1
0
0
0
2
1
1
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
3
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
3
0
2
1
1
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
2
0
0
0
9
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
1
0
1
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
2
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
2
0
0
1
0
0
0
0
2
3
3
0
1
0
1
0
2
4
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
3
1
0
0
2
1
1
1
0
0
0
0
2
1
1
0
0
0
0
0
2
0
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
4
1
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
1
0
2
0
1
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
1
1
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
6
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
2
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
2
1
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
1
0
1
2
2
0
0
0
1
1
2
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
2
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
1
0
0
2
1
0
0
1
0
0
1
0
0
0
2
0
1
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
4
0
0
1
0
1
1
0
0
0
0
2
6
0
0
0
0
0
0
0
6
0
0
0
2
0
0
0
0
1
0
0
2
4
1
0
0
0
2
1
2
1
0
0
0
0
0
1
2
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
2
1
0
0
0
3
0
0
0
2
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
1
2
3
2
2
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
2
1
0
0
0
2
0
0
1
0
0
1
3
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
2
0
1
0
0
2
0
2
0
0
2
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
1
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
8
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
4
0
2
0
0
2
0
0
0
1
0
0
3
0
2
0
2
0
0
1
2
1
0
2
0
1
2
2
2
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
3
0
0
0
0
2
0
0
1
0
0
3
2
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
1
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
1
0
0
2
0
1
0
0
0
0
0
1
1
0
0
0
0
0
2
0
1
0
0
3
0
0
0
0
2
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
2
2
1
0
1
0
0
1
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
3
0
1
0
0
0
0
4
0
1
0
0
0
0
2
0
0
0
0
0
3
3
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
1
0
0
0
1
0
1
1
5
0
2
0
0
1
2
1
1
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
1
1
2
0
2
0
0
1
0
1
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
4
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
3
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
1
2
2
0
0
0
2
2
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
2
2
1
0
0
3
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
1
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
2
1
0
2
1
0
0
0
0
0
3
0
0
1
0
1
1
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
2
0
0
2
0
2
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
2
0
0
1
0
2
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
3
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
2
1
0
0
0
1
1
0
0
0
0
0
0
2
0
1
2
0
1
0
0
0
0
2
0
3
0
1
0
0
0
4
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
3
0
1
0
0
0
2
0
1
0
0
0
0
2
1
0
0
2
2
0
1
2
1
1
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
1
0
5
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
2
2
1
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
6
0
0
1
2
1
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
2
2
0
0
0
0
0
1
1
0
2
2
2
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
1
0
0
0
0
0
1
1
0
0
17
1
1
1
0
0
0
0
4
1
2
0
0
2
2
0
0
0
0
0
0
1
3
1
0
0
0
0
0
0
3
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
2
0
0
2
0
0
0
1
3
0
2
0
0
1
0
0
1
0
1
0
0
0
1
0
0
2
0
0
0
1
1
0
0
0
1
0
0
0
3
2
1
0
2
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
1
1
1
1
0
0
0
0
0
3
1
0
2
0
0
0
0
0
1
3
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
10
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
1
1
1
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
3
0
1
4
0
1
0
0
0
1
0
0
1
0
0
2
0
0
0
2
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
2
2
0
1
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
4
0
1
2
0
0
2
0
2
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
1
1
0
0
0
9
0
0
1
0
0
0
0
1
3
2
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
2
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
3
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
3
0
0
2
2
2
0
0
2
0
1
2
0
0
0
1
0
0
0
0
2
0
2
0
2
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
2
0
0
2
0
0
0
0
1
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
2
1
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
3
1
3
0
0
0
2
0
0
0
0
1
0
0
0
1
0
1
0
2
3
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
2
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
1
1
0
1
0
2
1
0
2
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
2
0
0
2
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
6
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
2
0
2
0
0
0
0
2
0
0
0
0
0
4
1
0
0
1
3
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
3
1
2
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
7
0
0
0
2
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
4
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
2
0
0
0
3
1
1
0
1
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
7
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
1
2
1
0
2
0
0
0
1
0
0
0
0
0
4
1
1
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
1
0
1
0
3
0
0
1
0
0
0
0
0
1
0
3
0
1
0
1
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
1
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
1
1
2
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
3
0
2
0
2
0
1
2
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
1
0
0
0
6
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
2
0
8
0
0
2
2
0
1
0
1
0
2
0
0
0
0
2
0
0
0
0
2
0
1
1
2
0
0
2
0
1
3
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
6
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
1
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
1
0
2
0
0
2
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
1
0
3
2
0
0
2
0
0
0
0
3
0
0
1
0
0
0
1
0
0
0
0
2
2
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
2
1
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
2
0
0
3
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
1
0
0
2
3
0
0
0
0
0
0
2
0
0
1
0
0
0
4
0
0
1
0
1
2
2
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
2
4
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
2
1
2
0
0
2
0
0
0
0
2
0
0
1
0
0
0
1
0
1
0
0
1
1
0
1
0
0
0
0
0
2
1
1
0
0
0
0
6
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
6
0
0
4
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
1
0
2
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
3
2
0
0
2
0
2
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
1
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
5
1
0
4
0
0
0
0
0
2
0
0
2
0
0
1
2
2
0
0
2
0
4
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
1
0
0
2
0
0
1
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
5
2
0
0
0
0
0
0
1
1
2
0
0
0
3
0
0
0
0
0
1
0
1
0
2
0
0
3
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
2
0
1
0
0
0
2
0
2
2
0
0
0
0
0
1
3
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
3
0
0
5
0
0
1
0
1
0
0
1
0
0
0
0
2
1
0
0
0
3
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
3
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
1
0
2
1
0
2
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
1
0
1
0
2
0
0
4
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
2
0
4
0
0
3
0
0
0
1
2
0
2
1
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
1
2
0
0
2
2
0
0
0
0
0
2
0
3
8
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
1
1
0
2
0
0
0
1
0
1
0
2
0
2
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
2
0
0
1
0
0
0
0
0
1
2
0
0
3
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
1
1
0
0
0
0
0
1
0
3
1
0
0
2
0
0
0
0
0
2
0
0
4
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
3
0
0
1
0
0
3
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
1
0
0
0
0
1
2
2
0
1
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
1
2
0
1
0
0
0
1
0
0
0
2
2
0
0
1
0
2
0
0
0
0
5
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
3
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
3
0
0
0
2
0
0
0
0
0
1
2
2
2
0
9
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
1
2
2
6
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
1
0
1
0
0
0
0
0
0
1
2
0
1
0
0
2
1
0
2
0
0
0
2
0
1
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
1
0
3
0
0
1
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
1
1
0
0
0
0
2
0
1
3
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
2
3
0
1
0
2
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
1
0
2
0
2
0
0
13
0
0
1
0
0
0
0
0
0
1
2
0
0
2
0
0
4
0
0
0
1
0
2
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
1
0
2
2
0
0
0
2
0
1
1
2
0
1
0
1
0
0
0
0
0
1
0
0
2
0
2
0
3
0
0
0
3
0
2
0
0
0
1
0
0
0
0
3
1
1
0
2
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
2
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
2
0
0
2
2
2
0
0
0
0
1
0
0
0
1
2
0
0
0
4
0
0
0
0
0
0
2
1
1
0
1
0
0
0
0
0
0
3
0
2
0
0
0
2
0
0
0
0
0
3
2
0
3
0
0
0
0
2
2
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
3
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
2
1
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
7
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
2
0
1
0
0
1
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
3
1
0
0
4
0
0
2
0
2
0
1
1
0
0
0
0
0
5
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
2
2
2
0
7
1
0
0
0
0
1
0
0
0
1
0
4
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
1
0
0
1
2
0
0
1
0
2
1
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
2
2
2
0
0
2
0
0
0
0
3
0
0
1
0
0
3
1
0
0
1
0
0
2
1
1
1
1
0
0
1
0
0
0
3
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
3
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
2
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
2
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
2
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
1
0
1
0
1
0
0
2
2
0
0
0
0
0
0
2
0
2
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
2
2
0
0
2
3
1
0
0
0
0
0
0
0
0
4
0
0
0
0
3
0
2
0
0
0
0
1
0
0
0
2
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
3
1
0
0
0
2
1
0
0
0
0
0
1
1
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
3
2
3
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
2
2
0
0
9
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
5
0
1
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
2
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
1
2
0
1
0
0
0
0
0
3
0
0
4
0
2
0
1
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
2
0
0
1
0
2
0
0
0
0
0
1
0
0
0
3
0
0
0
2
0
1
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
2
0
1
0
2
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
2
0
0
1
0
4
0
0
0
0
6
0
0
0
1
2
0
0
0
0
2
1
0
0
0
0
0
4
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
3
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
1
3
1
0
0
0
3
0
0
0
0
0
0
1
0
0
0
1
0
0
0
3
0
0
2
0
4
0
0
0
3
1
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
2
2
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
2
0
0
0
0
0
0
0
1
2
1
0
0
0
1
0
0
0
0
1
2
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
2
1
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
2
1
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
1
0
0
2
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
2
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
1
0
0
0
2
0
0
1
2
0
0
1
0
2
0
1
0
2
1
0
0
0
0
2
0
2
1
0
0
2
2
0
0
2
2
0
0
2
0
0
0
2
0
0
0
0
1
2
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
2
0
0
0
0
0
2
2
0
0
3
0
0
1
0
2
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
3
0
0
0
3
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
2
0
1
0
3
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
2
4
0
0
0
0
0
2
1
0
0
2
0
2
1
0
2
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
2
0
1
0
0
0
2
2
0
0
0
2
0
0
2
1
0
0
1
1
1
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
1
0
1
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
2
2
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
2
0
0
1
2
0
1
0
0
0
0
1
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
6
2
0
1
1
1
0
0
0
0
0
2
0
4
1
2
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
1
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
3
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
1
0
3
1
0
2
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
2
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
1
0
0
4
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
3
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
1
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
2
0
1
0
0
2
0
0
0
0
3
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
2
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
1
0
0
0
0
0
0
1
0
0
1
0
2
0
2
0
0
0
6
0
2
0
4
2
0
0
0
5
6
0
0
2
0
0
0
0
0
0
0
1
0
0
1
2
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
3
0
0
0
0
2
0
0
1
0
2
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
1
0
2
0
1
2
0
0
1
0
1
0
0
0
2
1
0
2
1
0
0
0
2
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
2
0
3
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
3
2
0
0
0
0
2
0
0
0
0
1
0
1
2
0
0
0
2
0
1
0
1
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
2
2
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
2
0
3
0
0
0
1
0
0
0
0
1
1
0
2
1
3
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
2
2
2
0
0
0
0
1
0
0
0
0
1
2
1
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
2
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
1
2
0
0
0
0
2
0
1
0
0
1
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
2
0
0
2
0
0
0
0
0
1
1
0
0
1
3
2
0
0
0
0
0
0
1
1
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
2
2
0
0
0
0
0
0
0
0
1
1
1
0
1
3
1
0
2
2
0
1
0
1
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
2
0
2
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
2
0
5
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
1
6
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
2
2
0
2
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
1
4
0
0
0
1
1
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
5
0
0
0
0
0
2
0
2
0
1
0
2
0
0
0
0
0
0
2
0
1
0
1
0
0
1
0
0
0
2
0
2
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
1
0
1
0
0
0
0
0
1
0
0
2
3
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
2
0
2
1
0
4
1
0
0
2
0
0
3
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
1
0
1
2
1
2
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
4
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
1
2
0
4
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
3
0
0
5
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
2
0
0
2
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
2
1
0
2
3
0
1
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
10
4
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
7
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
1
0
0
1
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
6
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
2
0
0
1
1
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
1
2
0
3
1
0
0
2
0
2
0
1
2
0
1
2
2
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
1
2
0
0
0
0
1
2
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
1
1
0
0
1
0
0
0
0
1
0
0
2
0
0
0
3
2
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
2
0
1
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
3
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
2
0
0
0
0
1
1
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
3
0
0
2
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
2
1
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
2
0
1
0
0
1
1
1
4
0
0
0
1
4
0
0
2
0
0
1
0
0
1
0
0
0
1
1
3
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
2
2
0
0
0
0
2
0
0
3
0
0
0
0
0
1
0
0
0
2
0
0
2
2
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
1
0
0
0
0
0
0
1
0
0
2
4
2
0
0
0
0
0
0
0
2
0
2
1
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
3
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
2
0
0
0
0
1
0
1
1
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
3
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
1
2
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
3
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
3
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
2
2
0
2
4
0
3
1
1
1
0
0
0
0
3
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
4
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
2
2
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
4
0
0
1
1
0
0
0
1
0
0
2
0
0
2
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
3
0
0
0
0
1
0
0
3
1
0
0
0
0
0
3
0
0
0
0
3
0
0
1
1
0
0
0
2
3
0
0
1
1
2
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
4
0
1
1
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
1
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
1
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
2
0
2
0
0
4
0
5
0
0
0
0
0
0
0
0
3
2
0
2
0
2
2
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
2
3
0
0
2
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
3
2
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
2
2
0
0
0
1
1
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
2
2
2
0
0
1
0
1
2
0
0
0
2
1
1
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
2
1
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
6
0
0
0
1
0
0
0
1
0
0
3
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
1
2
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
1
2
0
0
2
1
2
0
0
0
1
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
1
2
0
0
0
1
1
0
0
0
2
0
2
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
3
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
5
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
3
0
2
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
6
0
1
0
3
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
1
2
0
0
2
0
0
2
2
0
0
0
1
1
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
1
1
2
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
2
2
1
2
2
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
1
1
0
1
0
0
0
0
0
0
1
2
0
0
0
0
6
0
2
0
1
0
0
0
0
1
0
0
2
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
2
0
1
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
3
1
2
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
1
1
0
0
3
1
2
0
0
0
0
0
0
3
0
0
3
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
1
2
0
2
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
1
0
1
0
2
0
0
2
1
1
2
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
2
0
0
0
0
0
0
1
0
10
0
0
0
0
0
1
0
1
2
0
0
1
0
0
1
2
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
1
0
2
2
0
0
2
0
0
2
2
0
0
1
1
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
3
1
1
0
0
0
1
0
1
2
0
0
0
0
1
2
0
2
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
0
2
1
1
1
1
0
0
0
2
0
0
1
2
0
0
1
0
1
2
0
1
0
0
0
0
0
0
1
3
0
0
1
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
1
0
2
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
2
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
1
0
2
0
2
0
1
0
0
0
0
2
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
3
0
0
0
2
0
0
1
5
0
0
0
0
0
2
0
2
0
1
0
1
0
2
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
1
0
0
0
0
2
5
3
2
2
0
0
0
1
0
0
0
0
0
0
0
3
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
3
2
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
3
0
0
0
0
1
0
0
0
1
1
0
0
0
0
2
0
2
2
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
2
2
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
2
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
2
1
0
3
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
2
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
3
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
3
2
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
2
0
2
1
0
0
0
1
0
2
0
1
0
0
0
2
1
0
0
0
0
0
4
1
2
2
1
0
0
0
2
0
0
0
2
0
0
0
0
0
2
1
0
0
0
1
0
1
0
0
2
0
0
2
0
0
0
0
0
0
2
2
0
2
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
1
0
2
0
0
1
2
0
0
1
0
0
0
2
1
0
0
0
0
0
5
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
2
1
1
0
2
0
0
0
2
0
1
1
2
0
0
0
4
0
0
0
0
0
0
0
1
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
2
2
0
0
0
0
2
1
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
4
3
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
3
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
4
1
0
0
0
4
0
0
0
0
0
0
0
0
1
1
0
7
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
3
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
2
1
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
1
0
1
0
2
0
1
1
0
2
1
1
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
3
0
2
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
2
3
0
1
0
0
1
1
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
3
1
0
0
3
0
3
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
5
0
0
2
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
1
1
2
0
2
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
4
0
0
1
0
2
0
2
0
0
0
0
0
0
2
0
0
0
2
1
1
0
0
0
1
0
0
2
0
1
0
0
0
0
1
0
0
0
1
0
0
2
2
2
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
4
0
0
2
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
1
0
0
0
1
0
0
0
2
0
2
2
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
6
0
0
0
2
2
0
0
0
0
1
0
0
1
0
1
0
0
0
3
0
0
1
0
0
1
2
0
0
1
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
1
1
0
0
2
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
3
2
0
0
1
0
0
1
0
0
2
0
1
2
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
2
0
1
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
4
0
0
3
2
0
0
0
0
0
0
0
0
0
1
5
0
3
0
0
0
0
0
0
3
0
2
1
0
0
0
0
0
0
0
0
2
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
1
0
0
0
0
0
0
0
2
2
0
1
0
0
0
2
0
0
0
0
2
0
2
1
0
2
2
2
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
3
0
4
0
1
1
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
2
2
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
1
1
2
0
1
0
2
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
1
0
2
1
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
4
0
0
0
1
1
0
0
1
2
0
0
0
1
1
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
2
2
0
0
0
0
1
1
0
0
0
0
0
1
2
1
0
0
0
0
1
0
3
0
0
1
1
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
1
1
0
0
1
0
2
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
1
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
1
0
1
0
3
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
1
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
6
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
3
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
1
0
1
0
1
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
7
2
2
0
0
0
0
2
2
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
1
0
0
0
0
3
0
3
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
2
0
2
1
0
0
2
2
2
0
0
0
0
0
2
1
3
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
1
0
1
0
0
0
0
2
2
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
3
0
3
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
2
1
0
2
0
0
0
0
0
2
0
2
1
1
0
0
0
0
1
0
2
2
2
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
3
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
3
0
0
0
0
1
0
0
0
0
2
0
1
0
0
2
0
0
2
4
0
1
0
0
0
0
0
1
0
0
0
2
1
2
1
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
3
0
0
2
0
0
0
0
0
2
0
1
0
0
1
0
0
1
2
0
0
0
0
1
0
0
0
0
2
0
1
0
2
0
0
0
0
4
2
0
0
2
1
4
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
3
0
0
3
0
0
0
0
2
0
0
0
0
1
0
1
0
0
1
2
2
1
0
0
1
3
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
3
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
1
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
2
2
0
0
0
2
1
0
1
2
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
4
2
0
0
0
0
0
0
0
6
1
1
1
0
0
2
1
2
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
1
0
1
0
0
3
0
0
0
1
0
1
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
4
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
3
0
0
0
2
3
0
0
6
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
2
0
0
0
1
0
0
1
0
1
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
1
0
1
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
3
0
2
1
0
0
2
0
0
0
0
0
1
2
0
0
0
0
1
2
0
0
0
0
3
2
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
4
0
1
2
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
4
1
2
0
0
0
1
1
0
3
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
2
0
0
1
0
1
0
0
1
0
0
0
0
0
6
0
0
0
0
0
0
2
0
0
0
1
2
0
1
0
0
0
0
0
0
2
0
0
1
1
1
2
0
3
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
2
2
1
0
0
2
0
0
0
2
0
0
1
0
0
0
2
7
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
9
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
3
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
2
0
1
0
2
0
0
3
1
0
2
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
3
0
2
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
1
1
0
0
0
0
0
1
0
1
0
0
3
0
0
0
0
1
0
0
0
2
0
1
1
0
0
2
0
0
2
0
0
0
0
0
1
0
2
0
1
2
0
0
0
1
1
1
0
0
0
0
0
2
0
6
0
0
0
0
0
0
0
0
0
0
1
2
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
1
0
0
0
3
0
2
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
1
0
2
2
0
0
0
0
1
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
1
2
0
2
0
0
0
0
0
1
0
0
3
2
0
0
0
0
1
0
0
1
1
0
2
1
0
1
0
0
2
0
0
0
1
0
0
0
0
2
0
1
0
1
13
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
1
1
0
1
0
1
3
0
0
0
2
0
0
0
1
3
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
3
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
6
0
0
0
0
0
0
1
0
2
2
0
0
0
1
2
0
0
0
2
0
2
0
0
1
0
0
2
2
1
4
0
0
2
0
0
0
3
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
1
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
2
0
1
0
0
2
1
2
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
3
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
2
1
0
3
0
1
0
0
4
1
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
4
0
0
0
0
2
0
0
1
4
0
0
0
1
0
0
2
0
0
0
1
0
1
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
2
0
0
2
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
2
0
1
0
3
0
0
0
2
1
1
0
0
3
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
2
1
2
0
0
0
0
0
1
2
1
2
4
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
1
1
0
2
0
1
0
0
2
0
1
0
0
1
0
0
0
3
0
0
1
0
0
0
1
1
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
3
0
2
0
0
0
0
0
2
0
0
1
2
0
0
0
1
3
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
1
0
0
0
0
7
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
2
2
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
1
0
0
0
2
0
1
0
4
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
1
0
1
0
0
1
0
1
0
0
0
1
0
1
0
0
0
2
1
3
0
0
2
0
0
2
2
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
1
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
4
0
1
0
0
0
2
1
0
0
0
0
0
1
2
0
2
0
0
0
1
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
1
0
0
3
0
2
3
0
2
0
0
0
3
0
0
2
0
3
1
0
0
1
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
5
2
0
0
0
2
5
0
1
1
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
5
1
0
0
0
0
0
0
0
3
0
1
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
1
2
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
1
1
0
2
2
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
3
2
1
2
0
0
0
0
1
0
1
0
2
0
0
0
0
0
2
0
2
0
0
0
0
1
0
4
0
0
0
0
0
0
0
1
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
6
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
3
2
0
1
1
0
0
2
2
0
2
0
0
0
0
0
1
0
0
0
2
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
1
1
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
5
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
5
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
5
0
6
0
2
0
0
0
1
0
0
1
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
2
0
0
1
0
0
0
1
0
0
2
0
0
1
0
1
1
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
1
1
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
2
0
1
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
2
6
0
1
0
0
0
0
0
0
0
0
1
2
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
4
1
1
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
2
0
0
0
2
1
0
2
2
1
1
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
2
8
0
0
0
1
5
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
4
2
0
0
2
0
0
0
2
3
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
2
0
0
0
0
2
2
0
0
0
1
0
2
0
1
0
0
0
2
0
0
0
1
2
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
3
0
0
2
0
3
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
1
2
0
0
0
2
2
1
4
0
0
0
0
0
2
0
0
0
0
0
0
0
0
5
5
0
0
0
0
0
0
0
0
0
0
9
0
0
0
3
2
0
0
1
0
0
0
1
0
1
0
0
0
0
0
3
1
2
0
1
0
0
2
1
0
0
0
2
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
2
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
2
4
2
0
0
0
1
0
3
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
4
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
1
2
0
0
3
1
2
0
1
0
0
0
2
0
2
2
2
0
0
0
1
0
0
0
0
2
0
0
3
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
1
0
0
3
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
4
0
2
1
0
0
0
0
0
0
1
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
1
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
2
2
0
3
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
1
2
0
0
0
2
1
0
2
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
1
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
2
1
0
0
0
0
0
0
0
0
2
0
2
0
3
2
0
2
0
1
0
1
0
0
0
2
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
2
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
4
4
0
0
0
0
1
2
4
2
2
0
1
6
1
3
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
3
0
2
1
0
0
0
0
2
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
2
1
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
1
0
1
0
0
0
0
1
0
0
0
3
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
3
3
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
3
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
1
2
0
0
0
0
0
0
0
2
1
1
1
2
0
2
0
1
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
3
1
0
0
0
1
1
1
0
1
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
2
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
3
0
0
0
1
0
1
0
1
1
1
2
0
1
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
3
0
0
0
0
3
0
2
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
4
0
2
0
0
0
0
0
1
2
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
4
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
3
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
2
2
0
1
0
0
3
3
0
0
0
0
2
0
0
0
1
0
1
2
2
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
4
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
2
0
0
0
1
1
1
0
0
2
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
14
0
0
2
1
1
0
0
1
0
1
0
0
0
0
0
0
0
4
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
1
3
1
0
0
2
2
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
2
0
0
0
1
0
0
0
0
0
0
0
3
1
0
0
0
2
0
0
1
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
1
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
2
0
1
0
1
1
0
0
1
0
0
0
0
1
1
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
1
0
2
1
2
2
2
0
2
2
1
2
0
0
1
0
0
0
0
0
2
0
0
1
1
0
0
0
1
2
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
3
1
0
0
2
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
2
0
0
1
1
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
9
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
3
0
2
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
5
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
8
0
3
0
1
0
1
1
0
0
0
0
0
0
2
1
0
0
2
0
2
0
2
0
1
1
0
0
1
0
0
0
0
0
1
0
2
2
2
4
0
0
0
2
1
0
0
1
0
0
4
0
2
1
0
3
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
1
3
1
1
0
6
1
0
0
0
1
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
2
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
2
2
0
2
0
1
0
0
1
0
2
0
0
0
0
0
1
0
0
1
2
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
1
0
0
0
0
2
1
1
0
1
0
0
1
2
0
0
2
3
1
0
0
0
1
1
0
4
2
0
0
0
0
1
0
0
0
0
1
0
4
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
1
2
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
3
1
0
1
0
2
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
2
2
0
3
0
1
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
3
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
3
2
0
0
0
2
0
2
1
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
3
2
0
0
0
0
1
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
2
0
1
0
2
0
2
0
0
1
0
2
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
3
0
0
2
0
2
1
0
0
0
0
0
2
1
0
0
1
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
1
3
0
0
0
0
2
0
0
0
0
0
1
0
1
2
1
0
0
0
0
0
2
3
2
2
0
0
0
0
0
0
1
0
3
1
0
0
3
0
1
0
0
0
2
0
2
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
5
0
0
2
1
0
0
0
0
0
2
1
0
0
0
0
0
1
0
4
1
0
0
0
1
0
0
0
0
0
2
2
0
0
0
2
0
2
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
1
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
5
0
2
0
0
1
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
2
0
0
1
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
4
0
1
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
1
0
1
2
4
2
0
0
0
0
0
0
0
1
1
0
1
2
0
2
0
0
2
0
2
0
0
2
0
2
0
1
0
0
0
0
0
0
0
3
0
4
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
2
0
0
0
1
0
2
0
0
0
1
0
1
1
0
2
0
2
0
0
0
1
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
1
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
1
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
3
0
1
2
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
2
0
0
1
0
0
0
1
0
1
0
0
0
2
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
1
0
0
0
0
0
0
2
0
1
0
3
0
0
0
2
0
0
0
0
0
1
2
3
0
2
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
1
0
6
1
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
2
2
0
0
4
2
0
2
0
1
1
0
0
0
1
0
0
0
3
0
0
1
0
0
0
1
0
1
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
1
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
3
2
0
1
0
0
2
0
0
1
1
2
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
4
0
0
0
0
5
3
0
0
1
0
1
2
0
2
0
1
0
2
0
1
0
1
1
1
0
0
0
1
0
0
0
0
0
0
2
1
0
0
2
0
0
1
0
0
2
0
1
1
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
1
0
0
3
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
6
5
0
2
0
0
0
0
0
1
0
0
1
1
2
0
1
0
0
1
1
0
0
0
2
1
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
2
0
5
0
0
2
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
1
0
3
0
0
0
0
0
2
0
0
1
0
2
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
1
2
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
1
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
3
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
1
2
0
0
0
0
1
0
3
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
6
0
0
0
0
0
0
3
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
4
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
2
1
0
0
0
0
0
0
1
3
0
1
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
4
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
1
1
0
0
0
0
2
0
1
0
5
0
0
1
0
1
0
1
0
0
0
1
0
0
1
2
0
0
0
0
0
0
8
1
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
3
0
2
2
0
1
2
1
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
1
2
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
4
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
1
0
1
2
0
1
2
0
0
0
3
2
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
2
0
0
1
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
2
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
3
0
0
0
1
0
0
0
0
0
1
0
0
0
2
1
5
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
1
2
1
0
1
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
2
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
2
0
0
1
0
0
1
0
0
1
0
1
1
0
0
0
2
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
2
1
0
0
0
8
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
1
0
0
0
0
2
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
3
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
2
0
0
2
0
1
0
0
0
2
0
2
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
2
0
2
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
2
0
1
0
0
3
0
0
2
0
0
0
0
1
0
0
0
0
3
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
2
0
0
0
1
2
0
1
0
1
1
0
1
0
0
0
0
0
0
1
0
2
1
1
0
0
0
0
0
0
1
0
0
2
0
0
0
4
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
1
2
0
4
0
0
3
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
2
1
0
2
0
1
0
0
1
1
1
2
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
1
0
1
0
3
0
0
1
0
1
1
0
0
1
0
0
1
1
1
7
2
1
0
1
1
0
3
0
3
0
0
0
1
0
0
0
0
0
0
3
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
1
1
1
0
0
0
1
0
0
2
0
2
0
0
1
0
0
2
0
2
1
0
0
0
1
1
2
0
0
2
0
0
0
0
3
0
1
0
2
0
0
2
0
0
0
1
2
1
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
1
6
6
0
0
0
0
0
0
0
0
1
0
0
3
2
0
0
0
0
1
1
3
0
0
0
0
0
0
1
0
1
0
0
0
1
0
2
0
2
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
2
0
2
0
0
1
2
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
2
0
1
3
0
0
2
0
0
0
0
0
0
0
2
2
0
1
0
0
3
0
0
2
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
3
0
3
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
1
0
1
0
1
0
0
0
3
0
0
0
0
1
0
0
0
0
0
1
2
1
0
1
0
1
0
0
0
2
0
1
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
2
3
4
2
1
1
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
1
2
1
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
3
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
3
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
2
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
1
1
0
1
2
0
0
1
2
0
3
0
2
0
0
0
1
0
0
0
0
0
0
0
1
2
0
2
0
0
0
3
2
0
0
0
1
2
2
0
0
3
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
1
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
4
0
1
0
0
2
1
0
0
0
0
0
0
0
0
3
0
0
0
1
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
3
1
0
3
0
0
0
0
0
2
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
2
3
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
6
0
2
2
3
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
2
0
0
0
1
0
0
4
4
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
1
0
0
2
1
0
0
0
2
1
1
1
0
0
0
0
0
2
2
0
0
0
0
0
0
3
0
0
0
2
0
0
1
0
0
1
0
2
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
2
2
0
0
1
0
1
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
1
2
0
2
1
0
0
0
0
0
0
2
5
0
1
0
0
1
2
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
1
0
2
0
2
0
2
0
0
0
0
0
4
0
0
0
2
0
4
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
3
0
0
0
6
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
1
2
0
1
0
2
0
0
1
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
2
0
0
1
0
2
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
1
0
2
0
0
5
0
1
0
1
0
2
1
0
0
0
0
0
0
0
0
1
2
0
1
2
1
0
0
0
0
2
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
3
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
3
0
1
0
3
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
2
0
0
0
3
0
0
2
0
0
0
2
2
4
0
0
0
0
1
0
0
0
0
0
1
0
0
4
1
0
1
0
2
0
0
0
2
0
0
1
0
0
2
0
0
2
0
0
0
0
0
1
2
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
2
0
0
0
0
2
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
2
0
2
4
0
0
0
0
2
0
3
0
0
0
0
0
0
0
2
2
1
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
4
0
3
0
3
1
0
0
3
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
2
1
0
1
1
0
0
0
0
2
1
0
0
0
1
1
1
0
2
0
0
1
0
0
0
0
2
0
0
2
0
1
0
0
1
0
0
0
0
0
2
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
3
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
1
0
0
0
1
0
2
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
2
1
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
2
0
0
1
0
0
2
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
3
0
1
0
0
2
0
0
0
0
1
1
0
2
2
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
5
0
2
4
0
1
0
0
0
1
0
1
0
0
0
2
0
0
0
2
2
0
1
0
1
1
2
0
1
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
2
0
1
0
0
0
0
0
1
0
4
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
1
1
0
0
0
0
0
0
1
0
2
2
0
0
2
1
2
0
1
0
0
2
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
1
0
0
2
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
1
0
2
1
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
8
1
0
0
1
0
0
0
0
0
0
0
5
0
2
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
2
0
0
0
2
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
1
0
0
2
1
0
0
2
1
2
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
4
0
2
1
0
0
0
0
0
1
0
1
0
0
4
0
0
1
0
0
0
0
2
1
2
0
2
1
1
2
0
0
2
0
0
0
0
0
1
0
2
1
0
1
0
0
0
0
0
0
0
4
0
2
0
1
1
1
0
0
0
0
2
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
1
0
0
2
0
0
0
1
0
10
0
2
0
0
0
0
1
0
0
0
0
2
0
1
0
0
2
0
1
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
1
0
2
2
1
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
3
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
3
0
2
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
2
0
0
4
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
2
0
2
0
1
0
0
0
0
2
0
3
3
0
2
2
0
0
0
0
1
2
1
0
0
0
0
0
2
0
0
2
2
1
0
0
0
0
1
2
1
0
0
9
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
1
2
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
1
0
0
2
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
1
2
0
0
0
0
3
2
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
1
0
2
1
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
2
1
1
0
1
0
1
0
0
0
0
1
0
2
1
0
0
0
3
1
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
2
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
3
0
2
1
0
0
2
0
0
0
0
0
0
0
0
3
0
0
2
0
2
2
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
2
0
1
0
2
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
1
0
0
1
2
0
2
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
2
2
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
4
0
0
0
2
2
0
0
0
0
0
2
0
0
1
0
0
0
0
3
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
3
3
0
0
2
0
0
1
1
0
0
2
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
24
0
0
0
0
0
2
0
3
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
1
0
2
0
0
0
1
0
1
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
1
0
0
1
1
0
1
0
0
0
2
0
0
2
0
0
0
1
0
2
0
2
2
0
0
2
0
0
1
0
1
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
1
3
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
2
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
1
2
2
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
3
0
0
1
0
0
0
0
0
2
0
2
0
0
2
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
3
0
1
1
1
1
0
0
1
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
1
0
0
3
1
1
3
0
0
2
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
2
0
0
1
0
1
0
4
2
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
1
1
0
0
0
2
0
1
0
0
0
1
2
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
1
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
1
0
3
1
0
4
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
1
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
2
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
8
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
3
0
2
0
0
0
1
0
0
0
3
0
0
1
0
0
0
0
0
0
0
2
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
2
0
1
0
2
0
0
0
0
1
0
1
1
1
0
0
6
0
0
0
1
1
9
0
1
0
0
0
0
2
0
0
0
0
0
0
0
6
2
0
0
0
0
0
0
0
1
1
0
1
0
1
1
0
0
2
0
1
0
0
0
0
0
1
0
0
0
1
0
0
2
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
2
0
0
0
2
0
0
0
0
0
1
0
1
0
1
3
0
0
2
0
4
0
0
0
0
0
0
0
1
1
0
0
0
2
0
1
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
1
0
2
1
2
0
0
1
0
0
2
0
0
0
0
2
0
0
0
2
0
1
0
2
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
5
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
6
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
2
0
2
0
0
0
0
0
2
0
1
0
1
3
1
0
0
0
0
0
0
1
0
0
3
0
1
0
1
0
0
0
0
0
0
0
2
2
3
2
0
1
1
0
1
2
0
1
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
2
2
0
0
2
0
0
0
2
0
0
0
0
1
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
2
1
0
2
0
0
0
0
2
2
0
1
0
0
0
4
0
0
0
2
0
3
1
2
1
1
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
1
0
1
1
0
2
2
0
0
0
0
0
0
3
0
1
0
0
0
2
0
1
0
1
1
0
0
0
0
1
0
1
0
3
0
0
0
1
1
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
4
0
0
0
2
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
1
0
3
0
0
0
0
2
1
0
2
2
0
1
1
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
3
0
2
2
1
0
0
0
2
0
0
3
1
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
1
0
0
0
0
0
0
0
6
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
2
2
4
2
1
1
1
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
3
3
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
1
0
2
0
1
1
0
1
0
0
0
0
2
0
0
2
0
0
0
2
0
1
0
1
0
0
1
2
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
1
0
0
0
0
3
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
6
0
0
1
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
4
0
0
0
0
3
0
1
1
0
2
0
4
0
1
1
5
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
1
0
2
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
2
5
0
0
0
1
0
0
2
0
2
1
0
0
0
0
2
1
0
0
0
0
4
0
4
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
1
0
2
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
1
0
0
0
2
0
0
2
0
2
3
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
2
0
0
0
0
0
1
0
2
0
0
0
2
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
1
0
1
0
0
1
1
1
2
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
4
2
1
0
1
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
9
0
0
0
0
0
0
4
0
0
0
3
0
0
0
0
0
1
0
0
0
2
3
0
0
0
0
0
0
2
0
1
1
0
0
0
0
3
0
0
0
0
0
1
0
0
6
0
0
3
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
2
0
0
0
2
0
0
0
0
0
0
1
0
0
1
3
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
3
0
1
1
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
1
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
2
2
0
0
0
1
2
3
0
0
2
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
2
2
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
3
1
1
1
0
2
3
0
1
0
0
0
0
2
0
0
0
1
1
1
2
1
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
2
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
2
0
1
0
5
2
1
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
7
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
1
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
2
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
2
0
0
0
0
0
0
2
0
2
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
1
0
0
0
3
0
0
0
0
1
2
0
0
0
0
3
0
0
0
1
1
0
0
0
0
0
0
0
2
0
1
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
3
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
4
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
3
0
1
0
0
0
0
0
0
2
0
0
3
1
0
0
0
0
0
0
2
0
0
3
0
0
0
1
0
4
1
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
4
1
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
3
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
2
2
0
1
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
4
0
1
0
0
0
0
2
0
0
0
1
0
0
0
6
0
0
0
0
0
0
0
0
2
1
0
1
0
1
0
0
1
0
0
0
0
2
0
0
2
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
2
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
2
2
4
0
0
2
2
0
0
0
1
0
0
0
3
0
1
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
2
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
2
0
1
0
1
0
0
0
0
0
1
0
2
0
0
2
1
0
0
0
1
0
1
0
1
2
0
2
2
1
1
1
0
0
1
0
0
0
0
0
0
0
0
1
2
1
2
0
0
0
0
0
0
0
0
2
0
0
0
4
1
1
0
0
0
0
0
1
0
1
1
0
0
2
0
0
1
2
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
4
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
1
0
0
3
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
2
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
2
1
2
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
3
0
1
0
0
1
4
0
0
0
0
0
0
1
2
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
2
1
0
2
2
0
2
0
2
3
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
2
0
0
0
2
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
2
0
1
0
1
2
0
0
0
1
5
0
0
0
0
0
0
0
0
0
1
2
1
0
0
1
0
1
1
0
0
0
2
1
0
0
4
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
1
1
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
1
0
3
0
3
0
0
2
1
0
0
0
0
0
1
0
0
0
2
0
0
2
0
1
1
0
0
1
0
1
2
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
1
1
2
1
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
2
1
1
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
2
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
3
0
0
2
2
0
0
0
0
1
0
3
0
2
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
1
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
5
5
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
3
0
0
2
0
1
1
1
0
1
2
0
0
0
0
1
0
1
0
0
0
0
0
0
2
2
1
2
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
1
0
0
7
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
10
0
1
0
2
0
2
1
1
0
0
0
0
2
0
2
3
0
0
1
0
2
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
2
3
0
0
0
2
0
0
0
4
0
0
1
0
0
0
0
0
1
2
0
0
1
0
3
0
0
0
0
0
0
0
0
0
3
1
0
0
0
1
1
2
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
1
0
2
0
2
2
0
1
0
0
1
0
1
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
1
2
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
2
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
1
0
0
1
0
1
0
0
1
1
0
1
0
0
2
0
0
1
0
0
3
0
0
1
0
0
0
0
0
0
1
0
2
2
1
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
2
0
5
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
5
1
0
0
0
0
0
0
0
0
2
0
0
0
0
3
1
0
3
0
0
0
4
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
2
1
0
2
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
3
2
0
0
0
1
3
1
0
0
2
0
0
0
0
3
0
0
0
0
1
1
1
0
1
0
1
0
0
1
2
0
0
0
3
0
3
0
1
1
0
0
0
1
1
1
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
2
3
2
0
0
2
0
0
0
0
0
0
0
2
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
9
2
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
2
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
4
2
3
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
3
0
2
0
0
0
1
2
0
0
0
2
3
0
0
1
0
2
2
0
2
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
2
0
3
0
2
0
2
0
3
0
3
0
0
1
1
0
0
0
1
0
0
1
2
0
0
2
0
0
0
4
0
2
1
0
0
0
1
0
0
2
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
5
0
0
0
0
0
2
0
2
0
1
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
2
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
2
1
2
1
0
2
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
5
0
0
0
0
1
7
0
2
0
0
0
0
0
0
2
0
1
0
2
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
1
0
1
1
2
0
0
0
0
2
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
6
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
1
0
2
1
0
0
0
0
1
0
0
0
2
0
0
2
0
1
0
2
0
0
1
0
1
1
2
0
0
0
0
0
0
1
2
0
1
3
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
1
0
1
0
0
0
2
2
0
1
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
2
0
1
0
0
0
7
0
1
2
0
0
0
0
0
1
0
0
1
0
2
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
1
0
0
1
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
3
1
0
0
1
2
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
2
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
4
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
1
0
2
1
2
1
0
3
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
1
2
0
0
1
1
0
0
0
2
0
0
0
5
0
0
0
0
1
0
0
1
0
0
0
0
5
0
2
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
3
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
1
0
0
0
0
1
2
0
0
0
1
0
0
0
0
1
0
0
1
0
0
2
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
3
0
2
1
0
2
2
0
0
0
0
0
1
0
0
0
0
2
0
0
1
1
0
0
0
0
0
3
0
0
0
0
2
1
0
0
1
0
0
0
2
2
0
2
0
0
1
0
3
0
0
2
1
0
2
0
0
0
1
0
0
1
0
0
0
1
0
0
0
2
0
2
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
4
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
1
2
1
0
0
0
0
2
0
0
1
2
0
0
0
3
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
3
1
0
0
0
0
0
0
1
0
0
0
2
1
0
0
3
0
0
0
1
1
0
0
0
4
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
1
1
1
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
1
0
0
1
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
2
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
1
1
0
0
1
2
2
2
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
1
0
1
0
3
0
0
0
3
0
0
0
0
1
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
3
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
4
0
0
0
2
0
0
2
1
0
0
0
0
0
0
2
1
1
0
0
0
0
1
0
1
0
2
0
0
0
1
0
0
0
0
0
1
0
1
2
0
0
0
1
0
0
0
4
0
1
2
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
1
0
1
3
0
2
0
0
0
0
1
0
2
0
0
0
1
1
0
1
0
0
0
0
2
1
2
0
1
0
0
0
1
2
0
0
2
2
0
0
0
0
2
0
0
0
2
3
1
0
0
0
2
4
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
3
0
0
0
0
0
0
0
1
0
2
2
2
0
2
0
2
0
0
0
4
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
4
0
2
0
0
1
1
0
0
0
4
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
1
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
1
0
0
1
0
2
2
0
0
0
0
0
0
0
2
0
0
1
0
3
4
0
2
2
0
0
2
0
0
0
0
0
0
0
1
0
2
2
0
0
1
1
0
0
0
0
0
0
2
0
0
5
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
1
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
2
0
0
2
0
2
0
2
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
2
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
1
0
0
2
0
2
0
1
1
0
2
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
1
2
0
0
0
1
1
2
0
0
0
0
0
0
0
3
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
6
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
2
0
2
2
0
0
0
0
0
0
0
8
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
1
2
0
0
0
0
2
0
0
1
0
0
1
1
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
2
0
0
1
1
0
0
0
0
6
2
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
6
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
2
2
1
0
0
0
0
1
0
5
1
0
2
1
0
0
0
0
0
2
0
0
1
0
0
2
0
2
0
0
3
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
1
0
2
2
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
1
0
0
1
0
0
0
1
0
1
1
0
2
2
0
0
0
0
0
0
0
0
3
0
0
0
2
0
1
1
0
0
0
1
1
0
0
1
0
0
0
1
1
0
0
0
2
0
2
0
0
0
1
0
0
1
0
0
2
2
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
3
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
1
0
1
1
1
0
0
0
0
0
2
2
0
0
4
0
0
2
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
3
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
1
1
0
1
0
2
0
1
0
0
5
1
0
4
0
0
0
0
0
0
0
3
1
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
1
2
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
1
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
3
0
1
0
0
3
3
0
1
3
0
0
0
0
0
1
1
2
2
0
0
0
1
2
2
0
0
2
2
0
1
0
6
0
0
1
1
1
2
0
1
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
1
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
3
2
2
1
1
0
1
0
0
1
0
0
1
0
0
1
0
0
0
2
2
2
0
2
2
1
0
1
0
0
2
0
0
1
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
1
0
0
1
2
0
2
1
0
2
0
0
3
0
1
0
1
1
0
2
0
0
0
0
0
6
0
2
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
1
2
0
1
0
0
1
1
0
0
0
1
0
1
0
1
2
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
4
0
0
0
0
2
0
0
2
2
0
0
0
1
2
1
0
0
1
1
0
0
0
0
0
4
1
0
0
1
0
2
0
0
1
0
0
0
2
0
2
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
2
2
2
0
0
2
1
0
0
0
4
2
0
0
1
0
0
0
1
0
2
0
2
1
0
0
0
0
2
0
0
1
0
2
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
2
2
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
2
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
1
0
0
1
0
0
1
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
1
1
0
0
0
3
2
1
0
0
0
0
1
3
0
0
2
0
2
0
3
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
2
0
0
0
0
2
0
0
5
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
3
0
0
0
2
0
1
0
0
0
0
0
0
1
0
1
0
0
0
2
1
0
2
1
1
0
0
0
0
0
1
0
0
0
3
0
2
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
3
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
2
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
9
0
0
0
1
0
1
0
0
4
0
2
6
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
4
0
2
0
2
0
1
0
0
0
0
1
2
1
0
1
2
3
1
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
2
1
0
0
3
0
0
0
0
0
0
0
0
0
1
0
4
0
1
0
0
0
2
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
4
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
2
2
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
2
1
0
2
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
3
0
2
0
0
0
0
0
0
1
0
4
2
2
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
2
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
13
0
0
0
0
1
1
1
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
1
0
0
0
1
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
2
0
3
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
6
0
1
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
6
0
1
0
2
0
0
1
0
0
0
0
1
1
0
2
1
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
1
0
0
0
2
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
6
0
0
0
2
2
1
0
0
0
2
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
2
2
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
1
2
1
0
2
2
2
2
0
0
0
1
2
0
0
2
0
3
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
2
0
0
0
1
2
0
1
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
3
1
0
0
0
0
0
0
0
1
1
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
2
0
0
1
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
2
1
2
0
1
0
0
0
1
1
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
2
0
0
7
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
3
0
0
0
2
0
0
2
2
0
2
0
2
1
0
1
0
2
1
0
0
2
0
0
0
0
2
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
1
2
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
2
2
0
0
0
0
0
3
0
1
0
0
0
2
0
0
0
1
0
2
1
0
0
1
0
2
0
0
0
0
0
0
0
9
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
1
0
0
2
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
3
0
1
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
1
0
0
2
0
0
2
0
0
0
0
0
0
2
2
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
1
0
1
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
1
0
0
0
0
0
1
0
0
2
0
0
3
0
0
0
2
0
0
1
1
1
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
1
1
1
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
5
2
2
0
0
0
0
2
0
0
2
0
2
0
0
0
1
0
0
1
2
2
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
1
1
0
0
0
0
0
0
2
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
8
2
2
1
0
2
0
0
3
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
3
0
0
0
1
2
1
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
1
5
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
1
0
0
0
0
0
1
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
3
3
2
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
2
1
0
0
1
0
0
0
1
3
0
0
0
0
0
1
0
0
4
0
0
0
1
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
1
1
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
2
0
0
0
2
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
3
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
2
1
2
0
3
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
1
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
3
0
0
0
0
0
0
0
1
0
1
1
1
1
0
1
0
2
0
0
0
1
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
1
0
0
2
0
1
5
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
1
0
0
0
3
0
1
3
1
2
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
2
0
1
0
4
0
1
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
2
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
1
2
1
0
0
0
1
2
0
1
0
0
2
0
2
2
2
2
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
3
1
0
0
2
0
0
0
0
0
0
3
0
0
0
1
0
0
1
0
0
2
0
0
5
0
0
0
0
0
0
0
1
0
1
0
2
1
0
0
0
0
0
2
0
0
0
1
1
0
3
1
0
0
4
0
0
0
2
2
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
9
0
0
1
3
0
2
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
3
0
4
0
0
1
2
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
1
0
1
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
1
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
3
0
4
2
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
3
0
2
0
0
2
0
0
1
2
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
3
0
0
0
0
2
0
6
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
1
1
0
0
0
2
0
0
2
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
1
1
0
3
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
2
0
0
2
0
0
0
0
0
3
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
2
1
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
1
2
0
0
0
3
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
2
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
1
2
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
6
0
0
1
1
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
1
0
2
0
0
3
0
1
0
1
0
0
0
6
0
0
0
0
2
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
2
0
0
1
0
5
0
1
1
0
0
2
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
2
0
0
0
2
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
2
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
3
0
1
0
0
0
1
2
0
1
2
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
3
0
0
1
2
2
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
3
0
0
0
1
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
3
0
0
0
1
0
1
0
0
2
0
0
0
1
2
2
0
0
0
2
1
0
1
0
0
0
0
3
1
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
1
4
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
4
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
1
0
0
0
2
0
0
0
0
2
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
1
1
0
4
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
3
0
1
1
1
0
0
0
0
0
1
0
0
4
0
0
0
2
2
0
2
1
0
0
3
0
0
3
2
0
1
0
2
0
0
0
1
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
1
1
1
0
1
0
0
0
5
0
0
0
2
0
2
0
3
0
3
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
1
3
0
0
0
1
0
0
1
0
0
0
0
2
0
0
4
0
1
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
2
1
0
0
0
1
2
0
0
2
0
0
1
1
0
11
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
2
1
1
0
6
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
1
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
5
2
0
0
0
0
0
0
0
0
0
2
0
1
2
0
1
0
3
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
2
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
3
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
1
0
2
2
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
1
2
2
1
0
0
0
2
0
0
0
0
1
1
3
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
1
0
2
1
0
0
0
0
1
2
0
0
0
0
0
0
1
3
0
0
2
0
0
0
0
4
2
0
1
6
0
1
2
5
0
1
0
1
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
2
2
0
0
0
2
2
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
1
0
2
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
3
0
0
0
0
0
0
0
1
0
0
0
7
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
2
0
0
2
0
3
0
0
0
1
2
1
1
2
3
0
2
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
3
0
0
0
0
0
1
2
0
2
0
0
0
0
1
0
1
1
0
1
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
2
0
0
0
1
1
0
0
0
1
0
2
0
0
3
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
3
0
1
1
2
0
0
2
0
0
0
0
2
0
0
0
0
2
2
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
1
2
2
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
1
1
2
3
0
0
2
0
0
0
2
1
0
0
2
1
0
0
0
2
1
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
1
0
2
0
1
1
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
3
16
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
2
2
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
1
2
1
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
2
0
0
0
0
0
1
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
1
0
0
0
1
3
0
0
0
0
2
0
0
0
0
0
1
2
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
2
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
3
0
2
0
0
0
0
0
2
2
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
2
0
1
0
3
4
0
0
0
3
2
0
2
2
2
2
1
0
0
0
0
0
1
0
1
0
0
0
0
4
0
0
0
0
0
0
1
0
0
2
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
3
2
0
0
2
5
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
1
2
0
2
0
0
0
2
0
0
0
0
1
0
0
1
2
0
0
0
3
0
0
0
0
0
1
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
4
0
1
0
0
0
0
0
0
1
0
2
0
4
0
2
0
2
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
1
2
0
0
1
0
0
7
0
2
1
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
1
1
1
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
2
5
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
2
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
3
1
0
0
0
0
0
0
0
0
2
0
3
4
6
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
2
0
2
0
0
1
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
1
2
0
0
0
0
2
0
1
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
2
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
2
1
0
1
0
0
0
0
0
0
0
0
0
1
3
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
1
0
1
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
2
1
1
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
3
1
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
2
0
0
3
0
2
0
0
2
1
0
1
0
0
2
2
0
0
2
2
0
0
1
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
2
1
0
0
0
1
1
0
0
0
1
0
2
2
0
2
0
0
5
0
0
0
2
0
0
0
1
0
0
0
5
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
3
1
0
1
0
0
0
1
0
0
0
2
0
0
1
0
5
0
2
1
2
0
0
1
1
0
2
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
4
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
4
0
1
3
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
2
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
9
0
0
1
0
0
1
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
1
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
1
0
1
0
0
0
1
0
0
0
3
0
0
1
0
2
0
0
1
1
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
3
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
1
0
1
3
0
0
1
0
0
1
3
0
0
5
0
0
0
0
1
0
0
7
0
1
3
0
0
0
3
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
1
0
0
6
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
2
2
0
2
0
2
1
0
1
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
2
0
3
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
3
0
2
0
0
0
0
1
0
0
2
2
0
1
0
1
0
2
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
3
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
2
0
0
2
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
2
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
2
1
0
0
0
2
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
3
0
0
0
1
2
0
0
0
0
0
0
1
2
1
0
0
0
1
0
0
1
2
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
2
1
0
0
2
0
0
1
2
0
0
0
1
0
0
7
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
4
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
2
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
3
0
0
0
1
0
0
0
2
0
0
0
0
3
0
0
2
0
2
3
0
1
1
0
0
0
0
0
0
0
0
0
2
0
2
3
3
0
0
0
0
0
2
0
0
0
0
0
5
3
0
1
2
0
0
1
0
0
0
1
0
3
2
0
0
1
0
0
0
0
0
0
2
0
0
2
1
0
2
1
0
2
2
1
0
0
0
0
0
1
1
2
0
0
1
8
0
2
1
0
0
0
0
0
0
1
0
0
0
0
3
2
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
2
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
6
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
2
0
2
2
0
0
1
0
0
0
0
2
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
5
0
1
0
3
0
0
0
0
0
2
0
1
0
0
0
3
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
2
0
0
3
0
0
0
2
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
3
1
2
0
0
0
0
0
0
1
0
2
0
2
0
1
2
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
3
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
3
0
0
1
2
0
0
0
1
0
6
3
3
0
0
1
1
0
0
2
0
0
0
0
0
2
2
2
0
0
1
2
1
0
0
2
0
2
1
0
0
0
1
0
0
0
4
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
1
1
1
0
0
2
0
0
0
0
1
1
1
0
0
3
0
2
0
0
0
1
0
0
0
0
0
2
0
4
1
0
2
0
0
2
2
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
4
1
1
1
0
0
0
0
0
2
0
0
0
0
0
2
1
1
2
0
0
1
1
0
0
0
0
0
0
2
3
0
0
0
0
2
0
0
1
1
0
0
0
0
0
2
0
1
1
0
2
0
0
1
0
2
3
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
1
0
2
0
2
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
2
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
3
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
3
0
0
0
0
4
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
2
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
1
3
0
0
1
0
0
0
0
0
0
1
0
3
0
0
0
0
0
2
0
0
3
0
1
0
0
0
1
2
0
0
0
0
1
2
1
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
2
2
1
0
0
0
2
2
0
2
0
0
0
1
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
8
0
0
0
2
0
0
0
1
0
0
0
1
0
2
0
0
1
2
0
0
5
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
1
1
6
0
1
0
0
0
0
0
2
1
0
4
3
0
2
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
3
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
3
0
6
0
0
0
1
0
1
0
0
2
2
0
1
0
0
2
0
0
1
0
1
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
1
3
0
0
0
0
0
0
0
1
1
1
2
2
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
2
5
0
1
0
1
3
0
0
0
0
2
2
2
0
1
0
1
0
3
0
0
5
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
1
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
1
0
0
0
0
3
0
0
0
0
3
0
0
1
1
0
2
0
0
0
1
0
0
0
0
0
0
1
0
1
1
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
3
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
1
0
0
0
4
2
0
1
1
0
0
2
2
6
0
0
0
0
2
1
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
2
0
0
0
5
1
0
0
0
0
0
0
0
1
2
0
0
0
9
2
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
1
0
2
1
0
0
0
0
1
0
0
3
0
0
2
0
0
0
0
0
2
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
1
0
1
2
0
0
0
0
1
0
2
1
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
4
0
2
0
0
2
2
2
0
1
2
1
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
1
0
0
0
2
2
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
4
0
2
1
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
3
1
0
0
0
0
0
2
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
2
1
0
0
0
0
2
1
0
0
0
0
1
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
1
2
0
2
0
1
2
0
0
1
2
0
1
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
3
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
3
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
4
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
2
0
0
1
0
0
0
1
0
0
0
4
0
0
0
1
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
1
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
3
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
7
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
3
2
0
0
0
1
0
0
0
0
2
1
3
0
2
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
2
0
0
2
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
4
0
2
0
1
0
0
0
2
0
1
0
0
0
0
0
0
2
1
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
1
0
0
0
1
0
1
0
1
0
0
0
0
2
1
2
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
11
1
0
0
2
0
0
0
0
1
2
0
1
0
0
1
2
0
0
0
0
1
0
1
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
1
2
0
1
2
0
1
1
0
1
0
0
0
2
0
0
0
1
2
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
3
0
0
0
1
0
2
2
0
0
1
0
0
2
2
2
0
0
0
1
0
2
0
0
0
0
0
4
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
5
0
2
1
0
0
0
1
0
2
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
2
1
1
1
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
4
0
1
0
0
0
0
0
0
1
0
1
0
1
2
0
0
0
0
1
0
2
0
0
2
0
0
1
0
0
2
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
5
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
1
0
0
3
0
0
2
0
0
0
0
1
6
0
0
1
0
0
0
0
0
0
0
4
2
0
0
0
0
0
2
4
0
2
0
0
0
0
0
1
0
0
1
0
0
2
2
0
0
0
3
0
0
1
0
0
2
2
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
2
0
2
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
2
2
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
2
1
0
1
0
0
1
0
0
1
0
1
0
0
0
0
4
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
3
0
3
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
2
0
1
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
3
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
2
0
3
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
1
2
0
1
0
0
0
3
0
0
1
0
2
1
0
1
0
2
0
1
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
1
9
0
0
0
0
0
1
2
2
3
2
0
0
0
2
0
1
0
0
2
0
0
0
0
0
2
0
0
0
2
0
1
0
0
1
0
1
0
0
2
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
3
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
2
0
2
1
0
1
1
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
2
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
3
2
2
0
0
1
0
2
0
0
0
0
0
1
0
0
3
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
2
2
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
2
0
2
0
4
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
5
0
0
0
1
0
1
0
2
0
0
0
5
2
0
0
0
0
0
1
1
1
1
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
1
0
0
2
2
3
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
2
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
3
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
1
1
0
0
2
0
2
0
0
0
0
6
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
6
0
0
0
0
0
0
0
2
0
0
0
2
2
2
0
1
2
1
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
2
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
5
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
2
0
0
1
0
2
0
1
2
0
0
2
0
0
0
0
1
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
3
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
4
0
0
6
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
2
0
7
1
2
0
0
1
0
0
0
0
0
0
0
2
0
2
0
1
0
2
2
2
0
2
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
5
0
0
0
0
1
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
1
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
2
2
0
2
2
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
2
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
1
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
3
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
1
1
1
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
3
1
0
0
0
0
0
1
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
1
1
0
0
1
0
0
2
0
0
0
4
0
5
0
0
2
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
2
0
1
0
0
0
0
0
0
4
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
1
0
2
2
2
1
0
0
0
2
2
0
1
0
2
1
1
2
6
0
0
3
0
0
0
1
0
0
2
0
0
0
1
1
0
0
0
0
0
0
3
0
0
0
0
1
0
1
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
2
1
0
0
0
0
2
0
0
1
0
1
0
2
2
0
3
1
0
0
0
1
0
2
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
3
2
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
1
1
1
0
0
0
2
0
0
4
0
0
0
0
1
1
0
4
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
6
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
2
2
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
3
1
0
2
2
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
3
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
4
1
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
2
1
2
0
2
0
0
0
0
0
0
0
1
1
0
2
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
1
0
2
0
0
0
0
0
3
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
1
0
0
3
0
0
2
2
0
0
2
1
0
0
0
0
0
1
0
1
0
0
3
0
0
0
0
1
0
0
2
0
0
1
0
1
0
0
0
0
0
0
2
0
0
2
4
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
2
0
0
1
0
0
0
0
0
0
0
1
1
0
1
2
0
1
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
9
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
1
1
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
3
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
1
1
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
6
0
0
1
0
1
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
3
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
1
0
0
2
0
3
0
1
0
0
1
0
0
0
0
0
0
0
3
1
1
0
4
1
2
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
4
0
0
1
0
1
2
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
2
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
5
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
2
0
1
0
0
0
1
0
0
0
2
4
0
0
2
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
5
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
3
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
1
2
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
2
1
0
0
0
0
0
0
2
0
4
0
1
1
0
0
0
0
0
1
0
0
0
0
2
0
1
2
0
2
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
1
1
0
0
0
1
2
0
0
2
0
0
2
2
0
0
1
0
1
2
2
0
0
4
0
0
0
0
1
0
0
0
2
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
3
0
1
1
0
1
1
0
0
1
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
2
5
0
0
2
0
1
0
2
0
2
1
4
0
1
2
0
0
2
0
3
1
0
0
1
0
0
3
0
3
0
1
0
1
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
3
2
0
0
1
3
0
2
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
4
0
0
1
0
0
0
0
0
3
0
2
1
0
1
1
0
0
0
0
4
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
2
1
3
0
2
0
0
2
0
0
0
0
0
0
1
2
0
0
1
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
9
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
1
0
0
1
2
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
6
1
2
1
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
9
0
2
0
0
2
2
5
0
0
0
0
0
0
0
2
2
1
0
0
1
0
0
0
0
0
2
0
0
4
1
1
2
5
0
2
0
0
2
0
1
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
2
0
1
0
0
0
1
0
2
0
2
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
2
0
1
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
5
0
2
0
0
1
0
0
3
0
0
0
0
0
0
1
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
1
0
0
0
0
0
0
3
0
0
2
0
1
0
2
0
1
3
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
3
0
0
1
0
1
0
0
0
0
1
2
0
0
0
0
0
2
0
2
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
1
0
2
1
0
0
0
0
0
8
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
2
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
3
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
1
1
0
2
1
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
5
1
0
0
0
0
3
0
0
0
0
1
3
1
0
0
0
0
0
0
1
2
0
0
2
0
1
1
2
0
0
0
0
0
0
1
2
3
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
2
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
4
0
1
0
0
0
0
0
2
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
2
1
1
0
0
0
0
1
2
4
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
4
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
3
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
2
1
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
1
0
0
0
0
0
2
0
4
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
4
7
3
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
2
17
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
2
0
3
2
0
1
0
0
3
2
0
1
0
1
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
2
0
0
1
0
2
0
1
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
6
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
2
0
0
0
1
2
0
0
1
0
0
0
2
2
0
0
0
0
0
0
1
1
2
0
0
0
2
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
2
0
1
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
5
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
3
0
0
0
0
0
0
0
0
2
0
2
0
2
0
1
0
1
0
0
0
0
0
0
2
1
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
2
1
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
2
0
3
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
3
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
2
0
0
0
2
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
2
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
2
0
7
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
1
0
0
0
0
0
2
0
3
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
3
0
2
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
3
0
0
1
2
0
0
0
0
0
2
2
3
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
2
1
1
0
0
0
0
0
2
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
3
2
1
0
0
0
0
0
0
3
1
3
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
3
0
1
0
2
0
2
0
0
0
3
1
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
3
0
2
1
2
2
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
3
0
2
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
1
5
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
2
2
2
4
0
0
0
1
0
0
1
3
9
2
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
2
0
1
0
0
0
0
2
0
2
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
4
0
0
0
0
1
0
4
0
0
1
1
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
1
0
0
2
0
0
0
2
2
2
0
0
0
1
0
3
0
0
1
2
2
0
1
0
1
0
1
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
2
0
0
1
1
6
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
2
0
0
0
0
0
2
0
0
1
0
0
0
3
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
1
4
2
1
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
1
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
3
0
1
0
0
0
2
3
2
0
1
0
0
0
0
1
1
0
0
0
1
1
0
0
0
2
0
1
2
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
6
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
1
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
3
0
0
0
2
0
0
0
1
0
0
0
0
0
2
2
0
1
0
0
0
1
0
1
0
2
2
1
1
0
1
2
0
0
0
5
0
1
0
0
0
2
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
3
1
0
0
1
0
0
0
0
2
0
2
3
2
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
1
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
1
0
2
0
0
0
0
1
0
2
0
0
3
0
0
2
0
2
2
0
0
0
2
4
1
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
2
1
0
2
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
1
2
0
0
8
0
0
2
2
0
0
0
0
1
0
0
0
4
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
4
0
3
0
0
1
2
0
0
0
1
0
0
0
0
1
0
0
3
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
1
2
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
1
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
2
0
2
0
0
0
0
0
0
2
0
0
3
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
2
0
3
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
2
2
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
1
0
0
0
0
1
0
1
0
3
2
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
1
0
0
0
0
3
0
0
1
0
0
1
0
1
0
3
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
2
0
0
0
0
1
1
2
2
0
0
2
0
0
0
3
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
1
0
0
0
2
0
1
0
0
2
1
2
0
0
4
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
1
2
0
2
2
0
0
0
0
7
0
0
1
2
0
0
0
0
0
2
2
0
0
0
1
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
1
0
2
0
0
0
0
0
0
1
2
2
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
2
0
0
2
3
0
0
0
0
2
0
0
0
2
1
0
0
0
0
2
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
5
0
2
1
0
1
0
3
1
2
0
2
0
0
0
0
0
3
2
0
3
2
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
1
2
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
2
0
1
1
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
1
0
2
0
1
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
1
0
2
1
0
0
2
2
0
3
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
2
1
3
0
0
0
0
0
0
0
2
0
0
1
2
0
1
1
0
0
0
0
2
1
0
0
0
1
2
1
0
0
0
0
0
1
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
1
2
0
0
0
0
0
1
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
6
0
2
0
2
0
1
0
2
2
0
1
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
2
0
1
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
1
1
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
1
2
1
0
0
0
0
0
2
0
0
0
2
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
2
2
1
0
1
0
0
1
0
1
0
6
0
1
0
0
0
3
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
1
2
0
0
1
1
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
1
0
0
0
0
0
0
2
0
0
1
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
1
0
0
0
2
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
2
1
0
0
2
1
3
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
7
0
0
0
2
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
2
1
0
0
0
0
0
0
0
1
0
2
0
1
0
0
1
0
0
0
2
0
1
0
0
2
1
1
2
0
0
0
0
0
0
1
0
2
0
0
5
2
0
1
0
0
0
0
2
2
0
0
1
0
0
0
2
0
3
0
1
1
0
0
0
2
0
0
0
0
2
0
3
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
1
1
1
0
0
0
2
0
0
2
0
1
0
1
1
0
0
0
2
0
0
0
2
0
0
1
0
2
0
2
0
0
0
0
0
0
2
1
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
7
1
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
3
0
0
0
0
0
1
1
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
1
0
2
2
0
1
2
0
0
0
1
2
0
1
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
8
0
0
0
3
3
0
3
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
1
0
0
3
0
0
3
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
5
1
1
0
0
2
0
0
1
0
0
0
1
1
0
1
0
1
0
1
0
0
1
0
2
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
2
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
2
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
3
2
1
0
2
0
1
0
0
0
0
0
1
0
0
0
1
4
0
0
4
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
2
0
0
0
3
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
5
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
2
0
4
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
2
3
1
2
0
0
0
1
1
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
2
1
0
0
2
0
2
1
0
0
0
4
0
0
0
0
0
0
1
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
1
1
0
1
0
2
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
2
4
2
0
0
0
0
0
2
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
2
0
1
5
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
1
0
0
0
3
0
3
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
2
2
0
0
2
0
0
0
0
0
0
0
2
2
0
1
2
0
1
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
1
0
0
1
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
3
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
1
5
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
1
0
2
0
0
5
0
0
1
0
1
0
0
0
0
2
0
1
0
2
0
0
2
0
0
2
0
0
5
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
2
0
2
0
0
0
0
0
3
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
6
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
2
3
0
0
1
0
3
1
6
0
0
1
0
0
0
2
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
2
0
0
0
2
0
2
3
1
0
0
0
0
2
2
0
0
2
2
0
0
2
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
2
0
1
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
3
0
0
0
0
0
3
3
0
1
0
0
0
1
0
0
1
0
0
1
1
0
1
0
1
0
2
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
3
1
0
0
0
2
0
2
1
0
0
0
1
0
0
2
0
0
0
0
4
0
0
0
0
1
1
0
0
0
0
0
1
0
2
0
6
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
2
0
0
1
3
0
0
0
3
0
0
0
0
0
4
0
0
0
0
0
0
2
0
1
0
0
0
3
0
0
2
0
1
0
0
1
0
0
2
0
3
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
1
0
0
1
1
0
0
2
1
1
0
0
2
2
0
0
1
1
0
0
2
0
0
0
2
1
0
0
0
0
0
0
1
2
0
1
1
1
2
0
0
3
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
1
0
0
4
0
2
0
0
1
1
0
2
0
0
0
0
0
0
1
1
2
0
0
0
2
0
2
0
0
0
0
0
0
0
2
1
3
2
0
2
2
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
1
2
2
0
1
0
1
2
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
2
0
1
1
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
4
0
1
0
0
0
0
0
0
2
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
3
0
2
2
1
0
0
0
2
0
0
1
1
3
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
1
0
2
1
0
1
0
0
0
0
1
0
0
0
1
2
1
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
1
1
1
0
1
0
1
0
1
0
0
0
0
2
1
0
0
0
2
2
0
0
1
0
2
1
0
0
0
0
0
2
1
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
2
0
0
2
0
0
0
0
2
0
2
0
1
0
2
0
0
1
0
0
0
0
0
0
0
2
2
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
1
2
2
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
2
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
2
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
2
1
0
0
0
11
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
2
1
0
0
2
0
1
1
2
0
2
2
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
3
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
1
1
0
0
0
1
2
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
1
2
0
0
2
2
2
0
2
3
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
8
0
0
0
0
0
7
0
2
0
2
0
1
0
1
0
5
3
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
3
0
0
0
3
1
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
2
0
1
0
0
2
0
0
2
0
1
0
0
0
0
0
2
0
1
2
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
1
2
0
0
1
0
0
0
0
0
1
2
0
0
0
1
2
0
0
0
0
0
2
0
2
1
1
0
1
1
2
0
0
0
0
0
4
0
1
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
1
2
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
2
3
2
0
2
0
3
1
0
2
0
0
2
0
0
0
1
0
2
0
0
0
0
0
2
2
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
3
0
0
1
0
3
0
0
0
0
0
0
0
2
0
1
1
0
1
0
0
0
0
0
1
0
0
2
1
1
4
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
1
1
0
0
0
0
3
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
2
2
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
4
0
0
2
0
0
1
0
3
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
2
1
0
0
0
0
2
3
1
0
2
2
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
2
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
2
0
0
2
0
0
2
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
1
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
2
2
0
1
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
12
0
0
1
1
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
2
2
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
4
2
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
1
0
0
0
2
0
1
0
0
0
0
1
2
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
7
0
3
0
2
0
1
2
1
0
0
3
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
2
2
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
1
2
0
0
1
3
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
3
0
0
0
2
0
0
0
1
3
3
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
1
2
0
0
0
7
0
0
2
0
0
0
0
3
1
0
0
0
0
2
0
0
1
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
2
2
1
1
0
0
1
0
2
0
0
0
0
1
2
2
1
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
2
0
2
0
0
2
0
0
3
1
0
0
2
0
1
0
0
1
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
2
0
0
0
1
0
1
2
0
0
0
1
1
0
0
0
0
0
0
2
0
0
1
0
0
1
1
0
0
0
1
0
2
2
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
2
0
3
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
8
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
5
0
1
1
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
1
0
1
0
1
0
1
0
1
0
2
2
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
2
1
0
0
0
0
0
1
1
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
2
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
1
0
6
2
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
3
2
0
1
2
0
1
0
0
0
2
0
4
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
3
2
0
0
1
3
0
0
0
0
3
1
0
1
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
1
2
0
1
0
0
1
2
1
0
0
0
0
2
1
0
0
0
0
0
1
4
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
1
0
3
0
0
2
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
1
2
1
0
2
0
0
1
0
0
0
0
0
3
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
2
2
1
0
0
1
1
1
0
2
0
0
0
2
0
1
0
1
2
3
0
0
0
0
0
0
2
1
0
0
0
0
3
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
1
2
0
0
1
0
2
0
0
0
0
1
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
1
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
4
4
2
2
2
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
1
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
2
0
1
1
0
2
0
1
0
0
1
1
0
0
0
0
4
0
0
0
0
0
0
0
0
1
4
2
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
1
0
0
0
0
1
1
2
0
2
0
0
1
1
0
0
0
0
0
2
0
0
0
0
1
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
2
3
0
0
0
0
0
0
1
0
0
1
0
0
4
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
2
2
0
0
0
2
1
0
0
0
0
0
0
0
1
1
0
0
0
2
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
2
2
0
0
2
2
0
2
0
0
2
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
3
0
2
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
5
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
2
0
0
0
2
0
0
0
1
0
2
0
0
1
2
2
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
2
0
0
0
1
0
0
0
0
0
8
0
0
0
2
0
0
1
2
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
3
3
2
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
3
0
2
2
0
0
0
0
0
0
0
0
2
0
5
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
1
0
0
0
1
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
2
3
0
1
0
1
0
1
0
2
0
0
0
1
0
0
0
0
4
0
0
0
0
0
2
1
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
2
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
2
0
0
1
1
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
3
0
0
2
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
4
0
0
2
1
0
0
8
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
1
1
0
0
0
0
0
0
1
0
2
0
0
0
0
5
0
0
0
2
0
0
1
0
0
0
2
0
2
0
0
2
0
0
3
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
1
0
0
0
2
0
0
2
0
0
0
2
4
1
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
1
3
2
0
0
0
0
1
0
1
1
2
0
0
2
1
0
1
0
0
0
0
2
2
0
2
0
0
0
1
4
0
0
0
0
0
0
0
2
1
0
1
0
0
1
1
7
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
2
0
0
1
1
1
2
2
0
3
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
1
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
1
0
0
1
0
1
0
0
0
0
2
0
0
0
0
1
1
2
1
0
2
0
0
0
0
0
3
1
0
0
0
0
2
0
2
1
1
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
6
0
0
0
0
0
1
0
2
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
2
0
2
6
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
5
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
3
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
5
1
0
0
2
2
1
5
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
1
0
0
1
1
0
0
1
0
1
1
0
0
0
0
1
0
0
0
2
1
2
0
0
0
0
2
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
1
0
2
0
0
2
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
2
1
0
0
1
3
2
0
0
0
0
3
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
3
0
1
0
2
0
1
0
0
0
0
1
0
4
0
2
1
1
0
0
0
2
0
0
0
1
0
0
9
0
0
0
1
0
2
0
0
2
2
0
0
0
3
0
1
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
2
0
0
2
0
0
0
2
0
0
0
2
8
0
0
0
2
0
0
0
2
0
3
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
3
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
4
0
0
0
0
0
0
3
1
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
2
3
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
2
0
2
0
0
3
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
1
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
2
3
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
1
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
3
0
0
3
0
2
0
0
0
0
0
1
1
1
2
0
0
0
0
0
0
0
0
0
1
3
0
2
0
2
4
0
0
0
0
2
2
39
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
2
0
0
0
2
1
0
0
4
0
0
0
0
2
0
0
2
1
0
1
0
3
2
0
0
0
0
0
1
0
0
0
0
1
0
3
1
0
1
1
0
0
0
0
2
0
1
1
0
1
1
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
5
0
1
0
2
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
4
0
0
2
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
2
0
1
0
0
0
0
1
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
4
0
0
0
2
1
0
0
0
1
0
0
0
4
0
0
0
1
0
2
4
0
0
1
1
0
1
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
1
0
2
0
0
0
3
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
9
5
1
0
0
1
0
0
2
0
0
0
2
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
3
0
1
0
0
0
0
0
0
0
2
2
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
2
0
0
0
1
1
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
1
2
1
0
0
0
2
7
0
2
0
4
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
2
0
2
1
2
0
0
0
0
2
0
1
2
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
4
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
1
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
2
0
0
0
0
1
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
2
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
3
0
1
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
9
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
5
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
1
0
0
11
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
2
0
1
2
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
1
1
1
0
2
2
0
0
0
0
0
2
0
0
0
1
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
1
1
3
0
0
0
0
0
0
0
0
0
0
1
0
1
2
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
1
3
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
2
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
2
1
0
0
1
1
0
2
0
0
0
1
0
0
0
0
1
0
0
1
2
2
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
1
0
1
0
3
0
0
0
0
0
0
1
0
0
3
0
1
0
1
1
0
0
3
0
0
0
0
2
1
0
2
0
0
0
2
0
4
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
4
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
5
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
2
3
2
0
0
0
1
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
3
2
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
4
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
3
0
2
2
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
3
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
3
0
0
2
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7
1
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
1
1
2
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
2
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
2
1
1
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
1
0
2
0
0
0
0
0
0
1
0
2
1
0
2
0
0
0
0
0
3
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
1
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
3
0
7
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
1
1
2
0
0
0
2
0
0
0
0
2
0
0
1
0
1
0
0
0
0
2
2
0
0
2
0
0
0
2
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
4
1
2
0
0
0
2
0
0
0
0
0
2
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
2
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
3
1
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
3
0
0
0
0
1
0
1
0
1
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
2
1
2
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
1
0
2
0
0
0
2
0
1
2
0
0
0
2
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
5
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
2
0
0
0
16
0
2
0
2
1
2
0
0
0
0
0
0
0
2
0
0
0
0
10
0
2
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
1
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
1
0
2
0
0
1
0
0
0
1
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
2
5
0
2
0
0
0
2
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
1
0
0
0
1
0
0
4
1
0
0
0
1
0
0
1
0
0
4
0
1
3
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
1
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
2
0
0
6
0
0
0
0
0
4
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
6
0
0
0
0
1
1
0
2
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
4
2
2
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
1
0
4
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
4
1
0
0
0
0
0
0
0
2
0
2
3
0
2
0
2
1
0
0
0
0
0
1
2
1
0
0
0
0
2
0
0
2
0
0
0
1
0
0
3
0
0
1
2
0
0
1
1
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
2
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
1
0
2
0
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
3
0
0
0
0
0
0
0
2
1
0
2
0
2
0
0
0
2
1
0
0
0
1
0
2
0
0
0
0
6
2
0
0
2
0
0
0
0
0
2
0
0
0
2
2
2
1
0
1
0
2
1
0
0
0
0
0
1
0
2
0
0
0
2
1
0
1
1
0
2
1
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
1
0
0
0
0
1
1
2
0
1
1
2
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
1
1
4
1
0
0
0
0
0
2
2
2
1
0
0
0
0
2
0
0
0
0
0
0
3
0
1
1
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
1
12
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
1
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
1
0
2
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
3
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
1
1
2
0
0
0
2
0
2
0
0
1
0
0
1
0
0
3
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
4
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
1
0
0
1
0
0
0
0
0
1
0
0
2
1
0
0
0
1
2
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
12
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
3
0
1
0
2
0
2
0
0
2
0
1
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
1
0
2
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
1
3
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
1
3
0
0
0
0
0
1
6
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
5
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
1
0
0
0
1
0
1
0
0
0
1
1
1
1
0
0
1
0
0
2
0
0
0
1
0
2
0
2
0
0
0
1
0
0
0
2
0
1
0
0
0
2
0
0
2
2
0
0
0
0
0
0
1
1
0
0
2
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
5
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
2
0
0
1
0
1
0
0
1
8
0
0
0
0
2
0
0
0
1
0
0
4
0
2
0
2
0
2
2
0
1
0
2
1
0
0
1
1
0
0
2
1
0
1
0
0
0
0
2
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
2
2
1
1
0
0
1
0
1
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
2
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
2
0
1
1
0
0
0
0
1
2
0
0
0
0
1
1
2
0
2
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
2
2
0
1
0
2
0
0
2
0
0
0
0
2
0
2
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
2
3
0
3
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
1
0
0
0
0
0
0
2
1
0
0
2
0
0
0
1
2
0
1
1
0
0
2
0
0
0
0
0
3
0
2
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
2
1
0
1
2
0
0
0
0
0
0
0
0
0
0
1
3
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
3
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
1
0
1
0
2
0
0
0
1
1
0
0
2
3
0
0
2
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
1
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
1
0
1
0
1
0
0
3
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
2
0
0
3
0
0
0
2
1
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
2
0
0
3
0
0
1
1
1
3
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
1
0
0
0
1
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
3
1
0
1
0
0
0
0
1
0
3
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
1
0
3
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
3
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
2
0
0
0
2
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
1
0
0
0
2
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
10
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
8
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
1
1
0
1
0
8
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
2
1
8
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
4
2
0
0
0
0
0
0
1
1
0
1
0
2
1
2
0
0
2
0
2
1
0
2
0
2
0
0
0
2
0
0
0
0
2
0
1
2
0
0
0
0
0
3
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
1
0
0
0
0
0
0
3
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
1
2
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
3
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
2
0
0
2
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
1
1
0
0
2
0
2
0
0
1
2
1
0
0
0
0
0
0
3
1
2
1
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
2
0
1
0
1
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
6
0
1
0
1
1
0
0
1
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
2
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
1
0
0
2
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
1
1
0
0
1
0
1
0
2
1
0
0
1
7
0
0
0
0
3
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
3
0
4
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
1
0
0
0
1
2
2
0
0
0
1
1
2
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
2
0
0
3
1
1
0
0
0
1
0
0
0
0
0
0
0
2
4
1
0
1
2
2
1
2
2
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
2
1
0
0
0
6
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
1
0
0
0
2
3
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
1
4
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
1
0
0
0
0
0
0
2
1
0
0
2
0
0
3
0
3
1
0
0
1
0
0
0
7
0
0
0
0
0
0
2
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
1
1
1
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
2
0
2
2
0
1
1
0
0
0
0
0
0
0
1
0
0
0
2
4
0
0
0
0
0
0
0
0
0
3
2
0
0
0
1
0
0
2
0
0
0
1
2
0
0
0
0
0
0
7
0
0
1
0
0
1
0
0
2
0
0
1
0
1
0
4
1
0
0
0
0
0
0
2
0
1
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
1
1
0
1
0
2
0
1
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
2
0
1
2
0
0
2
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
1
5
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
1
0
1
3
1
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
1
3
1
1
0
0
0
2
0
2
0
0
0
0
0
0
4
0
2
2
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
1
2
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
2
0
4
0
2
0
0
0
0
0
0
1
1
3
0
1
0
2
0
0
0
0
0
0
0
0
1
1
2
0
2
0
0
0
0
0
0
2
1
0
0
0
1
0
0
1
0
2
0
0
2
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
1
2
0
0
1
0
1
1
0
2
0
0
0
0
0
1
0
2
1
0
2
0
0
0
0
1
0
2
0
0
0
0
0
2
2
1
0
1
1
1
0
2
1
0
2
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
2
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
1
0
2
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
3
0
0
1
0
0
0
2
0
1
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
1
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
5
1
0
0
0
0
0
0
0
2
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
1
0
0
2
1
0
1
0
0
0
2
0
0
0
0
1
0
0
1
0
0
2
2
0
0
0
0
0
1
0
0
1
0
1
0
0
2
0
0
1
0
2
1
0
2
0
0
1
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
3
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
1
2
1
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
2
0
1
0
0
0
0
1
1
1
0
0
0
0
2
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
3
3
1
0
0
2
0
0
0
2
0
3
0
0
0
0
2
1
0
1
1
0
0
0
0
0
1
0
1
0
2
1
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
3
0
0
1
0
1
1
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
1
2
2
0
0
0
0
9
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
1
0
0
0
0
1
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
2
0
0
1
0
2
0
0
1
0
0
1
0
0
0
2
1
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
4
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
4
0
0
2
1
0
2
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
2
0
0
0
0
2
0
0
0
0
1
0
2
0
0
3
1
0
0
1
2
0
0
0
1
2
3
0
0
0
1
0
1
0
0
2
0
1
0
0
2
0
0
0
0
1
0
0
2
1
2
1
1
2
0
0
2
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
1
1
0
0
1
0
2
1
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
2
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
8
0
0
0
0
0
0
2
0
2
0
0
0
2
0
2
0
0
2
0
2
0
1
2
2
1
2
3
0
0
0
0
0
0
0
0
0
1
1
0
0
3
0
0
0
1
0
0
2
0
2
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
1
0
0
0
0
3
0
0
0
2
0
0
0
2
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
5
0
0
0
1
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
3
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
2
0
3
1
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
2
1
0
1
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
3
2
0
0
2
0
0
0
0
1
0
0
0
3
0
0
0
1
1
0
0
0
0
1
2
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
2
0
0
0
0
3
0
1
7
0
0
1
1
0
0
0
0
0
2
1
1
0
3
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
2
0
2
0
0
0
0
1
1
0
0
0
0
4
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
3
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
7
0
0
0
1
0
0
0
0
0
0
0
1
0
3
2
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
2
1
0
1
0
0
0
0
1
0
0
0
0
0
2
1
0
2
1
0
0
0
0
2
1
0
6
0
0
0
0
6
0
0
0
0
3
2
0
3
0
0
2
0
3
1
0
0
0
0
0
0
2
0
3
0
0
2
0
0
2
0
0
1
1
0
0
0
2
0
4
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
1
0
2
0
0
0
0
0
0
2
0
1
1
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
6
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
2
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
3
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
1
1
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
1
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
9
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
1
2
0
1
2
1
0
0
1
0
0
0
0
0
2
0
3
0
2
2
0
0
1
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
7
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
1
0
0
0
7
0
0
0
0
0
0
3
0
9
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
1
2
0
1
2
0
0
0
0
0
1
0
1
0
1
2
0
0
0
0
1
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
3
0
0
1
1
0
1
1
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
5
0
0
1
0
0
0
2
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
2
0
0
0
3
0
2
0
0
0
0
0
2
0
2
3
2
3
2
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
2
0
1
0
0
0
2
1
0
0
0
1
0
0
0
0
2
0
4
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
3
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
3
2
1
2
2
0
1
0
0
2
0
0
1
2
2
0
0
1
0
0
0
4
3
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
3
0
0
0
0
3
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
1
0
1
1
0
1
0
0
0
2
0
0
1
0
0
0
2
0
1
0
0
2
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
6
0
2
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
4
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
6
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
1
2
0
2
0
0
0
2
2
2
1
0
0
2
0
1
1
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
2
1
0
1
0
0
1
0
0
0
1
0
0
2
0
0
1
0
0
2
1
1
1
0
0
0
2
0
2
1
0
0
0
1
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
3
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
2
0
0
0
2
1
2
2
0
0
1
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
1
0
2
2
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
2
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
1
3
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
2
2
3
0
0
0
2
2
0
0
0
0
0
0
0
4
2
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
4
0
0
0
2
0
2
1
0
0
0
1
1
1
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
2
0
0
4
2
0
1
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
2
1
2
0
1
1
0
10
2
1
0
0
0
0
0
1
0
8
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
1
0
0
2
2
0
0
0
2
0
0
0
0
2
0
0
0
0
2
2
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
5
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
1
0
1
0
0
0
0
2
0
2
0
0
0
0
0
3
1
1
0
0
2
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
1
2
0
0
0
0
0
1
0
0
0
1
2
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
1
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
1
2
0
2
4
0
2
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
1
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
2
0
0
0
0
0
6
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
3
0
1
0
0
1
0
0
0
3
0
1
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
2
0
1
2
0
0
2
2
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
1
0
3
0
2
0
0
2
1
1
0
1
2
0
0
0
0
0
0
0
3
1
1
0
0
1
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
3
0
3
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
1
0
0
0
0
0
0
0
0
0
1
2
2
2
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
4
0
0
0
0
0
0
0
2
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
2
2
0
0
0
1
0
1
0
3
0
0
0
0
0
0
2
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
2
2
2
0
0
2
0
0
0
2
0
0
2
0
0
0
1
0
1
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
1
2
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
1
0
1
0
0
0
1
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
1
1
0
1
3
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
4
0
0
0
1
0
2
0
0
0
0
2
2
0
1
6
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
2
1
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
1
2
0
0
0
2
4
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
1
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
3
0
1
2
0
0
0
0
0
0
1
0
2
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
2
1
2
4
0
0
0
2
0
0
0
1
0
0
2
1
0
4
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
3
2
0
0
0
0
2
0
2
0
0
1
0
1
2
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
2
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
1
2
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
1
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
1
1
1
2
0
0
0
0
0
0
0
0
0
5
1
0
0
0
0
0
0
0
0
0
1
3
1
0
0
0
2
0
0
0
3
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
4
0
2
0
3
0
0
2
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
1
0
2
0
0
0
1
0
2
2
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
2
2
0
1
2
1
0
0
2
0
0
0
4
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
2
2
1
2
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
1
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
1
0
1
2
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
7
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
7
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
2
0
3
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
1
0
0
1
1
0
0
0
2
0
0
0
0
0
1
0
2
3
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
7
0
0
1
1
1
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
2
0
2
0
0
0
2
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
2
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
1
0
2
1
0
7
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
1
1
2
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
1
5
0
0
1
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
1
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
3
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
3
0
0
0
2
0
0
1
1
0
1
1
0
0
0
0
0
0
2
4
0
0
2
3
0
0
0
4
0
0
2
0
0
0
0
0
0
0
0
6
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
1
0
3
0
1
0
0
0
0
0
0
1
0
2
0
0
0
1
0
1
0
0
0
0
7
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
1
1
0
2
0
1
0
0
0
1
1
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
3
0
0
2
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
3
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
2
0
1
2
0
0
0
0
1
0
7
0
0
0
0
0
0
0
1
0
0
0
3
0
6
0
2
0
0
1
1
0
0
2
1
0
0
2
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
2
1
0
2
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
2
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
3
0
2
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
3
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
2
1
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
5
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
3
0
1
0
0
2
1
0
2
0
0
0
0
0
0
0
0
2
0
1
0
2
0
2
0
1
2
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
3
0
0
2
2
0
0
0
4
1
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
1
0
0
0
0
2
0
0
2
2
0
0
0
0
2
0
0
1
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
3
3
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
1
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
5
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
2
0
2
0
0
1
0
0
1
0
0
1
0
0
0
2
0
0
2
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
4
2
1
0
0
1
0
0
0
0
2
0
1
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
3
0
0
1
4
0
1
5
0
0
3
0
0
1
0
1
0
1
0
0
0
0
2
3
0
2
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
2
2
0
0
0
0
1
1
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
2
0
3
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
1
0
0
0
0
1
1
0
0
2
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
2
1
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
2
2
1
1
2
0
1
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
2
0
0
0
0
2
0
0
1
0
0
0
2
0
0
2
0
2
0
0
0
0
0
1
0
2
1
1
0
0
2
0
0
0
2
0
0
1
2
0
0
3
0
0
0
1
0
0
0
4
0
0
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
5
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
2
2
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
1
0
0
2
0
0
0
0
0
0
1
4
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
3
0
1
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
6
2
0
2
1
1
3
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
3
0
0
1
0
0
0
3
0
0
0
0
1
0
0
1
3
0
0
2
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
3
0
0
2
0
0
0
1
1
0
0
0
0
1
2
1
2
0
0
0
1
0
0
0
2
0
0
1
1
6
0
1
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
2
2
0
2
0
5
1
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
1
0
0
0
2
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
4
0
2
1
0
0
1
0
0
0
2
2
0
0
0
0
0
0
2
2
0
1
1
0
0
2
1
0
3
2
2
2
0
3
0
4
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
5
0
0
2
1
0
0
1
0
0
2
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
4
0
4
0
0
0
0
0
1
1
0
0
2
0
1
0
2
2
0
0
0
2
0
0
0
1
1
0
0
0
0
2
1
1
0
0
0
0
0
0
1
1
0
1
0
0
2
0
1
0
1
0
1
2
2
0
1
0
0
0
0
1
0
0
5
0
0
1
0
0
0
0
1
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
2
0
3
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
1
1
2
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
1
2
0
1
2
0
3
0
2
0
2
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
1
0
0
0
2
2
0
0
0
1
0
0
0
3
0
0
0
1
0
1
0
1
2
0
0
1
0
0
2
0
0
1
0
0
0
5
0
0
0
0
0
0
0
2
0
1
0
0
2
2
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
2
1
3
2
0
2
0
0
0
1
0
3
1
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
2
2
1
0
0
1
0
2
0
0
0
1
4
3
1
0
0
1
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
3
3
0
0
0
0
1
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
2
0
2
0
3
2
0
2
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
4
0
0
1
1
0
1
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
6
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
1
0
4
0
0
0
0
2
3
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
1
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
1
1
0
2
4
3
2
2
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
1
2
1
2
1
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
9
0
0
0
0
2
0
0
1
0
0
7
1
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
1
0
1
0
0
0
0
2
0
0
1
0
0
1
0
0
3
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
2
0
1
1
1
3
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
1
0
1
1
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
2
6
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
1
1
0
0
1
0
0
1
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
1
4
2
1
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
1
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
2
0
0
0
4
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
1
2
0
0
0
1
0
0
0
1
0
2
0
0
1
0
0
2
0
0
2
0
0
2
0
0
0
0
0
3
1
1
0
2
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
2
0
2
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
5
0
0
2
0
0
0
0
0
0
0
3
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
1
4
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
3
1
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
1
0
1
2
0
0
0
0
0
0
0
0
5
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
2
0
0
2
1
0
0
0
0
0
2
0
0
5
0
0
0
0
2
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
1
0
0
2
0
0
2
0
0
0
1
0
1
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
2
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
1
0
2
0
0
8
0
0
0
0
0
1
0
0
1
0
2
0
0
0
2
3
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
2
0
0
0
0
0
5
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
3
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
2
2
0
0
0
0
0
2
0
1
0
2
1
0
1
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
3
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
3
4
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
2
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
1
3
0
0
1
0
0
0
0
0
0
2
4
0
0
2
2
0
3
1
1
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
2
2
0
0
2
2
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
1
1
0
0
0
2
0
0
1
5
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
3
2
0
0
0
2
2
0
0
6
1
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
3
0
0
1
0
1
0
0
1
0
0
2
0
0
2
0
0
2
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
4
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
2
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
2
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
2
0
0
0
0
0
0
6
2
0
0
0
0
0
1
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
1
1
0
2
2
0
1
0
0
4
0
0
0
0
2
0
0
1
1
0
1
3
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
1
2
1
0
1
0
0
0
0
2
2
0
2
0
0
0
1
0
0
2
1
3
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
5
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
2
0
0
2
0
0
0
1
1
0
0
1
1
2
1
0
0
2
0
0
0
0
0
3
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
1
0
5
0
2
0
0
0
0
0
0
0
1
0
0
0
2
3
2
1
0
0
1
0
0
1
2
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
2
2
0
0
2
0
2
0
0
0
0
0
0
0
1
3
0
1
0
0
0
1
0
2
0
0
3
0
0
0
0
1
1
4
1
0
1
0
4
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
2
0
2
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
1
2
2
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
1
0
0
2
1
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
2
0
2
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
2
1
0
0
1
0
0
0
2
0
0
2
3
0
0
1
2
1
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
1
0
0
1
0
0
2
0
0
1
2
0
2
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
2
0
1
0
1
0
1
0
0
0
5
0
1
2
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
1
0
2
0
0
2
0
0
1
2
0
0
0
0
2
0
0
0
1
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
3
1
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
4
1
0
0
2
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
1
2
2
2
0
0
0
0
2
0
0
2
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
2
2
0
0
0
0
0
0
1
0
1
2
2
2
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
1
1
0
1
0
1
0
0
0
0
0
2
4
0
0
0
0
0
1
2
0
0
0
0
0
4
0
1
0
0
0
0
1
2
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
3
1
0
0
0
0
0
0
1
2
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
4
0
1
0
1
0
0
2
2
2
0
5
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
2
1
0
0
0
0
2
0
0
2
2
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
1
0
1
2
0
1
0
2
1
0
2
1
0
0
0
3
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
1
0
0
0
0
0
1
0
0
5
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
2
0
1
1
1
0
0
0
0
0
2
0
0
2
5
0
1
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
1
1
0
2
0
0
0
0
0
1
0
0
2
0
0
0
1
1
0
0
2
0
0
0
0
2
0
0
0
0
2
2
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
5
1
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
1
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
2
0
2
0
0
0
0
0
2
1
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
2
0
1
0
0
0
1
1
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
2
2
2
1
0
0
0
0
0
0
2
0
0
0
0
2
2
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
2
0
1
0
2
0
0
0
2
0
1
2
0
0
0
8
0
0
1
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
1
0
0
0
2
0
0
1
0
1
2
0
0
0
2
1
4
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
4
0
0
0
0
0
0
0
0
3
0
4
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
2
0
2
0
0
0
1
1
0
1
0
2
1
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
2
0
2
0
1
3
0
1
0
0
0
3
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
2
0
0
0
0
0
0
0
2
0
2
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
1
0
2
2
0
0
1
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
2
0
0
0
0
0
2
0
0
0
1
2
0
1
2
1
0
0
0
4
2
0
3
0
0
1
2
0
2
4
1
1
2
0
2
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
2
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
1
0
1
4
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
2
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
2
1
0
1
0
0
0
0
2
3
0
0
0
2
0
0
0
0
0
0
4
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
2
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
2
0
0
0
1
0
1
1
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
1
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
2
0
0
0
0
1
0
2
1
1
0
0
0
2
0
2
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
2
0
2
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
3
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
3
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
2
2
0
0
2
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
1
7
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
3
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
1
0
1
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
3
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
3
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
1
1
0
0
2
0
0
0
0
2
0
0
2
0
0
2
1
0
2
2
0
0
0
0
0
0
0
5
0
0
0
1
0
0
0
0
0
2
2
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
2
0
0
2
0
2
0
1
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
1
1
1
0
0
0
2
0
0
3
0
0
0
0
2
0
0
1
0
1
0
2
0
0
4
1
2
1
0
0
2
0
0
1
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
1
0
2
0
0
0
3
3
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
2
1
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
4
0
4
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
3
0
0
2
0
1
2
2
0
0
0
0
1
2
0
0
1
0
0
0
2
0
4
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
1
2
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
2
0
2
0
2
0
0
0
0
0
0
1
0
1
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
1
2
4
0
0
0
0
4
0
0
0
0
0
2
0
0
0
2
0
0
0
2
2
0
2
0
1
2
0
1
1
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
5
1
0
0
0
0
0
1
0
1
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
3
0
2
2
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
5
0
0
2
0
0
0
0
1
0
0
2
1
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
1
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
1
0
1
0
0
2
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
2
0
0
2
2
0
0
1
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
3
0
0
0
0
2
1
0
0
0
4
0
0
2
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
3
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
2
3
1
0
0
0
0
0
0
0
0
0
0
1
0
2
1
1
1
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
2
0
0
0
1
2
0
0
2
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
1
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
1
1
0
3
1
0
2
1
4
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
5
2
0
2
2
2
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
2
0
1
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
1
0
0
2
1
0
4
0
0
0
1
0
0
0
2
0
0
0
1
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
2
0
0
1
2
3
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
2
2
0
0
0
2
1
0
2
0
0
2
0
0
0
1
0
0
0
0
3
0
0
1
1
6
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
2
1
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
2
2
0
0
0
0
0
2
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
1
0
0
1
0
1
0
0
0
0
1
0
2
2
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
2
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
2
0
2
0
0
0
0
0
1
3
0
1
0
0
2
0
0
3
0
0
4
0
0
2
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
2
0
1
0
0
0
0
6
1
0
0
1
0
0
0
0
2
0
1
0
4
0
0
2
1
0
4
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
9
0
2
0
0
0
2
1
0
0
2
0
2
1
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
1
1
1
0
0
2
0
0
0
8
0
0
1
0
2
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
2
0
0
0
0
2
2
2
0
0
0
1
2
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
4
0
0
1
0
2
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
1
0
1
0
0
1
0
0
0
2
0
0
0
0
0
4
1
1
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
9
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
2
0
0
5
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
4
0
0
0
1
0
1
0
0
2
0
2
0
2
0
0
1
1
2
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
2
2
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
3
0
0
3
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
2
0
0
1
0
3
1
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
4
0
0
0
0
0
0
1
0
0
3
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
2
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
1
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
3
2
0
0
0
0
1
0
2
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
1
0
2
2
0
0
3
1
0
0
0
0
2
2
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
1
4
0
2
2
0
0
0
0
1
0
0
2
1
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
2
0
1
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
1
0
0
1
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
2
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
3
0
0
0
2
0
0
3
0
2
0
0
0
2
0
0
2
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
4
0
0
0
8
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
1
0
0
2
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
1
1
1
0
0
2
0
0
0
0
0
0
2
0
1
0
0
1
2
0
0
0
0
0
0
0
2
2
0
0
1
1
0
0
1
2
0
1
0
0
0
0
2
0
1
1
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
2
0
2
1
1
3
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
1
2
1
0
1
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
2
0
2
0
0
1
1
0
0
0
0
0
1
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
1
2
0
3
6
1
0
0
0
0
2
0
5
1
0
2
0
0
0
1
0
0
2
2
0
0
0
1
1
4
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
1
0
0
2
2
1
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
1
0
1
0
0
2
0
1
0
0
1
0
0
0
0
1
0
5
0
0
2
1
0
0
0
0
0
0
2
0
0
2
0
0
0
1
2
0
0
1
1
4
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
1
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
1
2
0
2
0
0
0
2
2
0
0
0
4
1
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
4
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
1
0
0
0
0
4
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
1
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
2
0
2
0
0
6
0
0
2
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
2
2
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
3
0
2
0
0
0
0
1
0
1
2
0
0
0
0
0
2
0
0
0
0
1
2
0
2
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
2
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
1
0
0
0
1
0
2
1
0
0
2
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
5
2
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
1
2
0
0
0
0
1
0
0
0
0
2
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
2
2
0
0
2
0
0
0
0
0
1
2
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
1
0
0
0
2
0
0
2
0
10
2
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
3
0
0
1
2
0
2
0
0
0
2
0
0
0
0
3
2
1
1
0
0
0
0
1
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
2
2
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
2
1
0
2
0
1
0
1
2
0
0
0
1
0
2
0
0
0
0
0
0
3
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
1
0
0
1
0
0
1
0
0
0
1
1
0
2
1
2
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
1
1
5
1
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
8
0
1
0
0
2
0
0
0
0
0
1
0
2
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
4
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
2
1
0
2
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
8
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
1
0
2
0
0
0
0
0
0
2
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
4
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
2
1
2
0
0
0
0
1
0
0
1
0
1
2
0
2
0
0
2
0
3
0
1
0
0
0
1
0
0
0
0
1
1
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
1
0
0
0
0
0
0
0
3
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
3
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
2
1
0
2
0
2
2
0
0
0
0
1
0
2
2
1
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
3
3
0
0
0
2
3
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
2
2
0
0
0
1
0
0
2
0
0
0
0
1
2
0
2
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
1
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
2
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
3
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
6
2
1
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
1
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
1
2
0
0
2
1
2
0
2
0
1
0
0
2
0
0
1
0
0
2
0
0
1
0
0
0
4
0
0
0
1
2
0
0
2
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
2
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
6
0
2
0
0
1
0
2
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
2
3
0
0
0
1
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
3
0
0
5
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
3
0
0
0
1
0
0
2
1
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
3
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
2
1
0
0
0
0
9
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
2
0
4
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
2
1
0
0
0
1
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
1
2
0
0
0
0
1
1
0
0
0
0
0
6
3
0
2
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
1
3
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
7
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
3
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
4
0
2
0
0
0
2
0
2
0
2
0
0
2
0
0
0
0
2
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
2
0
0
1
1
3
0
0
0
0
1
0
0
2
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
7
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
1
0
1
0
0
2
0
0
0
0
2
0
0
0
2
1
2
1
0
0
10
0
0
0
1
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
2
0
3
0
1
2
1
0
0
0
5
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
2
1
0
0
2
1
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
1
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
5
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
3
3
2
0
0
3
1
1
0
1
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
2
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
13
0
0
0
0
0
2
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
1
0
0
0
1
0
0
0
0
2
0
0
1
0
1
2
0
0
0
0
0
0
2
0
0
2
0
0
1
2
0
0
0
1
2
0
1
1
0
0
0
0
1
2
0
1
0
0
0
0
1
2
2
0
1
0
0
2
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
2
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
2
2
0
0
0
0
0
0
1
0
0
2
0
2
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
3
0
1
1
0
0
1
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
2
0
2
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
3
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
3
0
0
3
1
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
2
2
1
0
9
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
2
2
2
0
0
1
0
2
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
1
0
0
2
0
0
4
0
2
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
1
2
0
1
2
0
0
1
0
2
5
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
2
0
0
1
0
0
0
1
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
1
0
1
2
1
0
1
0
2
0
0
0
0
2
2
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
2
1
0
2
0
2
0
1
0
8
0
0
0
1
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
4
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
9
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
1
0
0
3
1
1
0
0
1
0
0
0
0
0
1
0
3
0
0
0
2
0
1
0
0
0
0
1
0
0
2
0
0
2
2
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
3
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
4
0
0
2
0
0
0
1
0
0
3
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
3
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
1
1
0
0
0
1
0
0
2
2
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
3
0
0
0
0
0
1
1
0
0
0
1
0
0
0
2
0
1
0
1
2
0
1
3
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
2
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
5
3
0
2
0
0
0
2
2
0
2
2
1
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
3
0
1
0
0
4
0
1
0
0
1
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
1
0
0
0
0
5
0
1
0
0
0
0
0
2
2
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
3
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
5
0
1
2
0
0
0
0
0
3
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
2
2
0
2
0
2
0
0
1
1
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
4
9
2
2
0
0
0
0
0
0
0
1
5
0
0
0
0
0
0
1
1
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
2
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
2
0
0
0
1
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
1
2
1
0
0
0
0
0
0
1
0
2
0
1
2
0
0
0
0
2
0
0
1
0
2
0
3
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
1
1
2
0
2
0
0
0
0
1
2
0
1
0
2
2
5
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
4
2
0
0
0
0
0
0
0
2
2
0
0
0
2
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
3
2
2
2
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
4
0
1
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
2
0
0
0
1
3
0
1
0
0
0
2
0
1
0
0
0
0
0
0
1
3
2
1
0
0
0
0
0
0
2
0
0
1
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
5
0
0
0
1
0
2
0
2
0
0
1
0
1
0
2
1
2
0
2
0
1
0
0
0
2
0
2
0
0
0
0
1
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
11
0
0
0
1
0
1
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
2
0
0
0
0
0
1
0
2
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
1
1
0
1
0
0
0
1
0
3
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
2
0
1
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
1
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
2
0
0
0
1
0
2
2
0
0
0
3
0
0
0
0
2
0
0
1
1
2
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
2
0
2
0
0
0
1
0
0
1
0
0
0
0
2
0
0
1
2
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
3
0
2
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
1
2
0
0
2
0
0
0
1
0
0
4
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
1
1
2
2
0
0
0
0
2
0
0
0
1
0
1
1
0
2
0
0
0
2
0
0
1
0
2
0
0
0
2
1
0
0
0
1
0
0
2
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
3
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
1
0
1
1
0
0
0
1
0
0
1
3
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
1
0
1
0
0
0
1
0
0
2
0
0
2
0
0
0
0
1
0
2
0
0
0
0
1
7
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
2
1
0
0
3
2
2
0
0
0
0
2
0
0
3
0
1
0
0
0
0
0
0
1
0
0
4
2
0
0
0
4
0
0
1
2
1
0
0
0
2
0
0
0
2
0
0
0
2
0
0
1
2
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
5
0
0
0
0
0
2
1
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
2
2
2
0
0
0
0
3
1
0
0
0
0
0
3
0
0
0
3
2
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
1
0
0
0
0
1
1
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
8
2
0
1
0
0
2
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
13
0
1
0
1
0
2
0
0
0
0
0
3
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
4
0
1
0
1
0
0
0
0
1
0
0
0
2
0
0
0
2
1
2
0
2
0
2
0
0
0
0
0
2
1
2
0
3
0
1
0
0
0
2
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
1
0
1
2
0
0
0
1
0
0
8
0
0
0
0
2
0
2
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
2
0
0
0
0
1
0
3
0
2
2
0
0
0
0
0
0
0
2
0
0
2
0
0
1
2
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
2
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
5
0
0
2
2
0
0
1
1
0
1
0
2
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
4
0
0
0
0
0
0
2
0
0
1
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
1
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
2
0
0
0
0
1
1
0
0
2
0
1
0
0
0
0
2
1
0
0
0
1
2
2
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
2
1
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
1
0
0
0
1
0
0
0
0
7
0
0
0
0
0
1
0
0
0
0
0
0
1
3
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
4
0
0
0
2
1
0
0
0
0
1
0
0
1
0
0
1
0
4
0
1
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
2
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
2
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
4
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
6
0
0
0
2
2
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
1
0
1
0
0
0
2
1
1
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
2
2
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
2
0
0
0
0
0
2
0
0
0
0
0
0
1
1
2
1
0
0
0
0
0
0
0
0
0
0
2
0
6
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
4
2
0
1
1
0
0
1
0
0
2
0
2
0
7
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
2
0
1
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
5
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
6
1
0
3
0
0
2
1
0
1
0
0
0
0
0
1
0
1
2
0
0
0
0
2
0
0
0
0
2
0
1
1
2
0
0
0
0
0
0
1
0
0
0
1
0
1
0
2
2
0
0
3
0
3
0
0
0
2
0
0
0
3
1
0
0
0
0
4
0
0
2
0
0
1
3
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
2
0
2
1
0
0
0
2
0
0
0
0
0
0
1
2
1
0
5
0
0
0
0
8
1
0
0
0
0
14
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
2
2
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
3
2
0
0
0
0
1
0
2
2
0
2
1
0
0
2
1
0
3
0
0
2
0
1
2
1
1
2
0
0
0
0
0
0
1
2
0
1
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
3
0
0
0
1
2
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
2
0
2
2
0
0
0
2
0
0
5
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
3
0
4
1
0
0
0
0
0
0
2
0
0
3
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
4
0
0
0
0
0
2
1
1
0
1
1
0
0
1
0
2
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
3
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
2
1
6
2
0
0
0
1
0
0
2
3
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
2
0
0
0
0
2
1
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
3
0
0
0
0
2
0
0
0
0
3
0
2
0
1
0
2
1
3
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
3
1
0
0
0
0
0
0
1
3
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
4
2
0
1
0
2
3
1
1
0
1
2
1
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
3
2
0
3
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
3
1
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
1
1
0
0
0
2
3
2
0
0
1
0
2
0
0
3
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
1
0
0
1
1
0
0
0
1
3
0
1
0
2
0
1
1
0
0
0
0
0
0
0
0
3
1
2
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
2
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
2
3
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
3
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
3
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
1
1
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
2
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
3
0
3
0
0
0
2
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
1
0
1
2
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
2
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
1
0
0
0
0
1
1
0
2
3
0
0
0
0
0
2
0
1
1
0
0
0
0
0
1
3
0
0
0
1
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
1
0
1
1
0
2
0
0
0
0
2
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
1
0
0
0
2
0
1
0
1
2
1
0
0
0
1
0
0
0
0
3
0
0
1
0
3
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
3
0
1
5
0
0
0
0
0
0
0
0
0
1
2
1
0
1
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
2
2
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
1
2
0
0
0
0
1
0
0
0
2
0
0
6
0
3
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
1
0
0
3
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
3
0
0
1
0
2
0
0
0
1
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
11
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
4
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
2
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
3
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
1
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
2
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
4
0
1
0
1
0
0
0
0
0
1
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
1
2
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
2
1
1
1
2
0
0
0
1
0
0
0
0
0
0
1
2
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
2
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
3
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
2
1
0
0
3
0
0
0
1
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
1
2
3
0
0
3
1
0
1
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
2
0
0
3
0
4
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
1
0
3
0
0
2
0
0
0
1
0
0
0
0
0
3
0
0
0
2
0
0
0
1
1
0
0
0
0
0
1
0
0
0
3
0
0
0
1
2
2
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
2
0
4
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
2
0
3
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
1
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
1
0
0
0
0
0
0
0
1
0
0
0
0
0
3
1
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
1
0
0
2
2
2
3
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
2
0
0
0
0
0
0
1
0
3
0
0
0
0
0
2
2
0
1
3
3
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
2
0
2
1
0
1
0
0
2
3
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
1
0
1
0
1
0
0
1
1
0
1
0
0
0
0
1
0
0
2
0
0
1
0
2
9
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
4
0
1
0
0
1
2
0
2
2
2
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
1
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
2
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
3
2
0
0
2
1
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
1
3
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
1
2
0
0
0
1
1
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
2
0
0
0
3
0
0
0
1
2
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
2
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
2
0
0
1
3
0
0
0
0
0
2
0
0
1
1
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
2
1
0
0
0
0
1
1
0
6
1
0
0
2
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
3
2
0
1
2
1
1
0
0
1
0
0
0
0
2
1
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
1
2
0
0
0
1
1
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
2
0
1
0
2
0
3
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
2
0
2
1
0
0
0
1
2
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
3
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
2
2
3
0
4
0
0
1
0
0
3
1
0
0
0
1
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
2
0
1
1
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
2
2
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
3
0
1
0
1
0
1
0
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
3
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
3
0
0
0
0
0
2
1
3
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
2
0
2
1
0
0
1
1
0
0
0
4
0
1
0
0
0
0
0
1
2
3
0
0
0
0
0
1
1
0
2
0
2
0
0
1
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
1
0
1
0
0
4
3
1
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
2
3
0
0
0
2
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
3
2
0
0
0
0
0
0
1
0
0
4
1
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
1
2
0
1
0
0
0
1
0
0
0
2
1
3
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
1
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
2
1
2
0
0
4
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
2
0
0
0
0
1
2
0
0
0
2
3
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
1
1
0
1
0
0
0
0
1
0
0
1
2
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
2
1
2
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
2
0
3
0
0
0
0
0
0
1
1
2
1
0
0
0
0
1
0
0
0
2
0
0
8
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
1
0
1
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
2
0
0
2
0
0
3
0
2
0
0
13
0
2
1
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
2
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
4
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
3
0
2
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
1
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
4
0
0
0
0
0
0
0
2
0
3
1
0
0
1
0
1
0
0
1
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
4
0
1
0
1
0
0
0
1
0
0
0
1
1
0
0
2
0
0
0
0
0
2
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
1
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
3
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
2
0
2
0
0
0
2
1
2
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
1
1
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
2
0
3
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
1
3
0
0
0
0
1
2
0
0
0
1
0
0
0
1
0
0
2
0
0
2
0
0
1
0
0
0
2
0
0
0
2
0
1
0
0
0
2
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
2
0
2
0
0
1
0
0
1
0
0
0
0
0
1
3
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
4
2
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
1
0
0
0
2
4
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
1
0
0
0
0
0
1
0
2
2
1
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
1
0
0
2
0
1
2
0
0
0
0
0
0
0
0
1
0
1
0
0
1
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
2
0
0
1
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
2
0
0
3
0
2
0
2
0
0
0
2
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
2
2
1
0
1
0
0
0
2
0
0
0
2
2
2
2
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
2
3
1
0
0
0
0
0
0
1
2
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
2
1
0
1
1
0
1
1
0
0
0
0
1
0
1
2
0
1
0
1
1
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
1
0
1
0
2
0
1
2
0
2
0
0
0
0
1
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
3
0
0
2
0
2
0
0
1
2
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
3
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
2
2
2
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
3
1
0
0
3
1
2
0
0
0
1
0
0
0
2
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
2
1
0
0
0
0
0
0
1
0
0
1
0
0
2
1
0
0
1
3
1
0
0
0
0
0
0
2
2
0
2
0
1
0
1
0
2
1
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
2
0
0
2
0
0
2
0
0
12
2
1
0
0
3
0
2
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
1
2
3
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
2
2
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
3
2
0
0
1
1
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
2
0
1
0
0
1
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
4
0
0
0
2
0
1
1
0
0
0
2
0
0
0
0
2
0
0
1
0
2
0
2
0
1
5
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
1
0
0
2
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
1
0
0
0
1
0
1
1
1
0
0
0
2
0
0
1
0
2
5
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
2
0
0
0
3
0
2
0
0
0
4
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
3
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
9
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
3
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
2
6
0
0
1
0
0
0
1
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
2
0
2
0
2
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
3
0
0
0
3
3
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
3
0
1
0
0
0
2
0
1
2
0
0
0
0
0
1
0
0
1
2
3
0
2
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
1
0
1
1
2
0
1
2
0
0
0
0
0
2
1
0
0
2
1
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
5
0
0
0
2
0
0
0
2
1
0
0
0
0
1
3
8
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
2
2
0
0
0
0
2
2
0
0
0
0
0
7
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
4
0
0
2
1
0
0
0
0
0
0
1
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
5
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
1
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
1
0
2
0
3
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
1
0
2
0
3
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
1
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
4
0
0
0
0
1
2
0
1
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
2
0
0
3
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
2
0
3
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
2
5
0
0
1
2
0
0
0
2
0
0
2
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
1
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
1
0
1
2
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
2
1
1
0
0
1
0
0
1
0
0
0
2
1
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
2
0
0
0
3
0
1
0
0
1
0
1
0
2
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
3
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
2
0
1
0
0
2
0
0
3
0
3
0
0
2
0
1
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
6
1
0
0
0
0
0
0
3
0
0
0
4
2
1
0
0
0
0
2
0
2
0
2
0
3
2
1
0
0
0
0
0
0
2
2
0
0
4
1
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
1
0
0
2
0
0
0
0
1
4
0
1
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
2
1
2
2
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
1
2
0
0
1
1
0
2
2
0
0
2
2
0
3
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
3
0
1
2
0
4
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
1
0
2
0
2
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
3
2
0
3
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
2
2
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
1
1
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
2
0
1
0
0
0
1
0
1
1
0
0
0
2
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
3
0
2
0
0
2
1
0
0
4
0
4
0
2
1
0
0
0
0
0
0
0
0
0
3
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
2
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
2
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
1
0
2
0
0
0
0
1
0
3
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
1
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
2
1
0
0
0
0
1
0
0
0
2
1
0
0
2
0
0
0
1
1
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
1
1
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
3
0
0
0
1
2
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
2
0
0
1
2
1
0
1
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
2
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
4
0
2
0
0
0
0
1
0
0
0
2
0
0
0
1
0
1
1
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
2
0
2
5
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
2
0
2
0
2
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
2
3
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
6
0
0
2
0
3
0
0
1
1
0
0
0
0
0
0
1
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
2
1
0
0
0
0
0
0
0
3
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
3
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
3
1
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
1
2
2
0
0
0
0
0
0
0
1
0
2
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
2
0
1
0
0
0
2
0
0
0
4
0
0
0
0
0
0
2
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
2
0
0
0
2
0
2
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
2
0
1
1
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
1
2
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
5
0
0
0
0
1
2
0
2
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
2
1
2
0
1
2
0
1
0
0
1
0
0
0
2
0
1
0
0
2
1
0
0
0
0
0
2
2
1
0
0
3
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
4
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
2
2
0
2
0
0
0
0
0
0
3
0
0
2
0
0
2
0
0
0
3
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
3
0
1
0
0
0
1
0
0
0
0
1
2
0
0
0
2
0
0
1
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
7
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
4
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
2
0
0
0
1
0
0
1
0
0
0
0
2
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
2
0
1
0
0
0
2
0
2
0
0
4
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
4
0
0
2
0
0
2
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
2
0
1
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
2
0
0
0
0
0
1
6
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
2
1
0
0
0
0
1
0
0
0
0
1
2
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
2
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7
1
0
0
0
1
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
3
2
0
2
1
0
0
2
2
1
0
0
1
0
0
0
1
4
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
2
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
1
2
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
4
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
1
0
1
0
3
0
0
1
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
3
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
1
0
0
3
0
0
3
0
0
1
2
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
3
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
8
1
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
1
2
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
4
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
1
0
0
0
1
2
0
1
0
0
1
0
0
0
0
1
0
0
1
2
0
0
0
1
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
2
2
0
0
0
0
1
2
1
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
8
0
0
0
0
2
1
0
1
0
0
0
0
1
0
0
2
0
0
2
0
0
1
2
0
0
0
0
0
2
1
1
0
2
2
0
2
0
2
1
0
0
0
3
2
1
0
3
0
0
0
0
0
0
3
0
0
0
0
0
0
4
0
0
1
0
0
1
0
0
3
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
1
0
2
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
2
0
0
2
2
0
0
0
0
1
0
2
0
0
0
0
2
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
5
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
2
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
4
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
2
0
3
0
3
0
2
0
1
0
0
0
0
0
0
0
0
0
0
10
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
1
2
0
1
0
0
0
2
0
0
0
0
2
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
1
0
0
1
2
1
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
2
1
0
2
2
0
0
0
1
0
0
0
0
0
0
0
1
1
0
2
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
1
0
1
0
2
0
2
2
0
2
3
0
0
0
0
2
2
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
1
0
0
2
0
0
0
0
2
2
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
1
3
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
2
0
2
1
0
0
0
3
0
0
0
0
0
2
0
0
2
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
2
1
1
0
0
0
3
0
2
0
0
0
0
0
0
0
2
0
2
2
0
1
0
0
1
1
2
0
0
0
0
2
2
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
1
3
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
1
0
2
0
1
0
0
0
0
2
0
0
1
1
0
0
0
0
1
0
0
0
1
3
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
1
1
0
0
1
2
2
2
0
0
2
1
0
0
0
0
0
6
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
2
0
1
0
1
3
1
0
0
0
0
1
0
1
0
0
1
0
0
3
2
0
0
0
3
1
0
0
0
0
0
2
0
1
1
1
0
1
0
0
0
0
0
0
1
0
1
0
2
0
0
2
2
0
0
0
0
0
0
2
6
0
1
0
0
0
0
2
2
0
0
0
2
0
0
0
0
3
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
13
0
1
1
0
3
0
0
0
2
0
1
2
0
0
3
1
0
0
1
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
2
1
0
1
1
0
0
3
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
2
2
2
0
1
0
0
2
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
1
0
0
1
2
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
2
0
0
0
1
0
1
1
0
2
2
1
0
1
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
2
2
1
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
2
0
0
0
1
1
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
2
0
0
4
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
3
0
1
2
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
4
0
0
2
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
2
1
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
2
0
0
0
0
1
1
2
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
2
0
0
1
0
0
0
0
2
0
0
1
1
2
0
0
0
5
18
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
2
2
0
2
0
1
0
0
0
1
0
1
0
0
0
0
0
0
3
0
0
0
0
3
2
0
0
1
0
0
0
1
0
0
0
0
0
1
0
2
3
0
2
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
2
0
1
2
0
0
2
0
0
0
0
2
1
0
0
3
2
0
1
0
0
0
0
3
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
1
0
1
2
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
1
0
0
0
0
3
0
1
0
0
0
1
2
1
1
0
0
0
0
0
0
1
3
1
0
0
1
0
0
0
1
0
0
0
1
1
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
3
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
2
0
0
0
2
0
0
0
1
0
2
0
1
1
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
2
1
0
3
5
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
2
1
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
1
0
0
0
3
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
1
0
1
0
0
0
0
4
0
0
1
3
0
0
0
0
5
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
3
1
2
1
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
1
0
0
0
0
0
0
0
2
2
0
0
1
0
1
1
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
2
0
1
3
2
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
1
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
2
1
0
0
1
0
2
1
0
1
0
0
4
3
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
1
8
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
2
1
2
0
0
2
2
1
0
0
0
0
2
1
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
1
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
3
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
4
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
1
0
2
0
0
0
0
2
0
0
0
3
1
0
0
2
0
0
0
0
0
2
1
1
1
0
0
0
0
3
0
0
0
2
0
0
0
1
0
0
0
0
2
0
1
0
3
4
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
1
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
1
0
0
0
2
2
0
0
0
7
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
2
0
1
1
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
4
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
3
0
0
0
1
0
2
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
3
4
2
0
0
0
0
0
1
3
0
0
0
1
0
0
0
0
2
3
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
3
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
2
0
1
0
4
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
2
0
2
0
0
2
2
1
0
0
0
0
3
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
2
1
0
0
6
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
3
1
0
0
2
2
0
2
2
0
0
0
1
0
1
0
0
0
2
0
2
1
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
2
0
2
0
0
0
2
1
0
3
0
0
1
2
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
2
0
3
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
1
1
2
0
1
0
0
0
0
0
0
0
0
7
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
3
0
0
0
0
0
0
3
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
1
0
0
0
1
0
1
0
1
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
1
1
0
2
0
0
1
0
0
3
0
2
0
0
2
0
1
0
1
0
0
0
5
0
0
2
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
3
2
0
1
1
0
0
0
2
0
0
1
2
0
1
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
1
2
1
0
0
0
2
0
3
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
1
0
0
0
2
2
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
3
2
2
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
2
1
0
0
0
1
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
6
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
1
2
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
1
0
1
3
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
2
0
0
0
2
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
2
0
2
0
1
0
0
0
0
1
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
2
2
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
1
0
0
1
0
1
3
1
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
1
1
1
2
0
1
0
0
2
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
1
0
2
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
1
0
1
2
0
3
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
1
0
2
0
0
0
2
0
0
2
0
0
0
3
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
2
2
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
4
0
0
0
0
2
1
1
0
2
0
1
0
0
1
4
0
0
2
2
1
0
1
0
0
0
0
1
2
0
2
0
0
2
0
0
2
0
0
1
0
0
4
0
2
0
1
0
2
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
2
0
0
1
0
4
0
1
0
0
0
1
0
1
1
2
2
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
2
0
1
0
0
0
2
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
5
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
2
2
0
1
0
0
0
0
0
0
1
0
0
0
3
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
5
3
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
5
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
3
1
0
2
0
0
0
0
0
1
0
0
0
2
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
4
2
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
1
2
0
0
0
2
0
0
2
4
1
0
2
0
1
0
2
0
0
1
0
0
1
2
0
0
0
2
0
0
0
0
4
1
0
0
0
3
0
0
0
1
0
0
1
2
0
0
0
2
0
0
0
3
0
0
0
2
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
1
2
0
0
1
0
0
1
0
0
0
2
0
0
1
0
8
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
2
0
0
0
2
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
3
0
2
0
0
3
0
0
0
0
0
1
0
0
0
2
0
0
1
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
2
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
2
0
1
0
0
0
2
3
1
1
0
0
0
0
0
1
0
0
2
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
2
0
0
0
1
0
0
0
0
0
0
1
0
0
2
3
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
3
2
2
2
1
2
2
0
0
0
0
3
3
0
0
0
0
0
0
2
2
0
0
1
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
1
3
0
0
5
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
1
1
2
0
0
0
0
1
0
0
0
0
0
0
2
1
10
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
2
1
0
1
0
0
0
0
0
0
2
1
0
4
2
0
0
0
0
0
0
2
0
3
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
2
0
0
7
0
0
0
0
1
1
2
0
0
0
0
0
0
2
3
1
0
2
0
0
0
1
1
0
0
0
0
0
3
0
2
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
1
0
2
0
1
0
2
2
1
0
1
0
1
0
0
2
0
0
0
0
0
0
2
2
0
3
0
0
0
0
1
2
0
0
1
0
0
2
1
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
1
0
4
0
0
0
0
0
0
0
3
2
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
2
0
1
2
0
3
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
1
0
1
0
3
2
0
3
0
0
0
0
0
0
0
0
0
1
2
0
1
0
2
3
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
4
2
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
1
0
1
0
0
0
4
0
1
0
3
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
2
0
0
0
0
1
0
2
1
2
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
4
0
0
0
0
0
0
0
3
0
1
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
2
5
0
2
0
4
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
1
2
0
1
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
2
0
0
2
0
0
0
0
1
1
5
1
0
0
0
2
1
0
0
0
1
4
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
2
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
4
0
0
4
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
2
2
0
0
0
0
0
2
0
1
0
0
0
0
0
5
2
0
5
0
0
3
0
0
0
3
2
0
2
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
6
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
2
1
0
2
0
0
0
7
0
1
3
0
0
0
2
0
0
0
2
0
2
0
0
0
0
3
1
0
2
0
0
2
0
0
2
2
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
3
2
0
3
0
0
0
0
2
0
2
2
0
0
1
0
1
0
2
2
0
0
0
0
0
1
0
1
0
1
1
1
0
1
6
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
3
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
3
0
0
0
0
1
0
2
0
0
0
2
2
0
0
0
0
1
0
0
1
0
2
0
2
0
1
0
2
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
6
1
0
0
0
1
0
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
1
0
0
0
1
0
0
4
0
0
0
0
1
0
2
0
1
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
1
1
1
1
1
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
2
2
0
5
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
2
0
1
0
1
0
1
0
0
0
0
0
5
0
0
0
0
0
5
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
3
2
0
0
0
1
1
2
0
0
0
0
0
0
0
2
1
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
2
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
2
0
0
0
2
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
1
1
3
1
2
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
11
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
2
2
2
0
0
1
0
0
3
2
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
6
0
0
0
0
0
0
2
0
0
0
3
1
0
1
1
1
0
0
1
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
2
0
3
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
3
1
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
3
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
1
1
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
1
1
0
1
1
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
1
2
0
0
0
1
1
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
7
2
0
0
0
1
0
0
0
2
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
2
0
0
3
0
0
0
1
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
2
1
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
1
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
1
2
1
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
1
4
0
0
1
0
0
0
3
0
0
0
0
0
1
0
0
1
1
0
0
0
0
2
2
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
2
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
1
3
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
9
0
2
0
0
0
0
0
2
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
3
2
0
0
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
4
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
3
1
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
3
0
0
0
0
2
0
2
0
1
0
1
0
3
0
0
1
0
0
0
0
1
1
1
0
0
2
1
0
0
2
0
7
0
1
0
0
1
0
0
0
1
2
2
1
0
0
0
0
1
0
0
0
0
0
2
0
7
0
0
0
0
2
0
3
0
0
0
0
1
0
4
1
0
0
0
3
0
0
0
0
1
0
1
2
0
0
0
3
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
4
0
2
0
0
1
0
0
0
0
0
0
1
0
0
2
2
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
1
0
1
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
3
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
8
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
4
0
0
2
1
0
1
0
1
0
2
0
1
0
2
0
0
0
0
1
0
0
2
0
2
0
0
0
2
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
2
1
0
0
2
0
0
1
0
0
0
0
0
0
1
1
1
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
1
4
5
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
2
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
1
0
0
2
2
0
0
2
2
2
0
1
0
0
0
0
0
0
1
0
1
2
0
1
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
1
0
0
2
0
0
2
2
0
0
5
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
1
1
1
0
0
0
0
2
2
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
3
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
1
1
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
2
2
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
2
2
0
2
2
0
0
0
1
0
3
0
0
2
1
0
0
0
0
0
0
2
0
0
0
3
0
1
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
2
0
2
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
2
0
2
4
0
0
3
0
0
1
0
0
0
2
0
0
0
0
0
1
0
2
1
0
2
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
1
0
2
0
1
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
5
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
2
1
0
0
0
0
2
1
0
0
1
0
0
1
0
0
1
1
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
1
0
0
3
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
1
2
0
0
0
1
0
0
0
1
0
0
2
0
0
0
1
0
2
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
1
0
0
0
2
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
2
0
0
0
0
1
2
1
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
3
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
1
1
0
1
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
1
0
1
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
2
0
0
0
4
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
2
1
0
0
1
0
0
0
0
1
0
1
0
0
0
3
0
2
0
1
0
1
0
0
1
0
0
0
0
0
1
1
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
3
0
0
0
0
1
0
0
2
1
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
2
0
2
0
0
1
1
2
0
0
0
0
0
2
1
1
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
1
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
6
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
3
0
4
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
3
0
0
0
0
0
0
1
2
0
0
2
0
0
0
1
4
0
0
1
2
0
0
0
2
0
0
0
0
0
0
1
2
0
0
2
0
1
0
0
0
0
3
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
1
0
1
0
3
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
1
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
2
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
2
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
4
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
2
1
1
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
2
1
0
2
2
0
0
0
2
4
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
1
0
0
4
2
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
4
2
0
0
0
1
0
0
0
0
1
0
1
2
0
0
3
0
0
1
2
0
4
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
1
2
1
0
2
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
4
0
0
0
0
0
0
0
0
2
0
0
2
1
1
0
0
0
1
0
0
1
1
2
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
2
1
0
0
0
0
0
1
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
2
0
0
1
0
2
4
0
0
0
0
2
0
0
0
2
1
0
0
0
0
1
0
0
2
1
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
1
1
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
3
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
7
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
2
0
0
0
4
0
0
2
0
0
0
0
2
0
2
0
0
2
0
0
1
0
0
2
0
0
0
0
0
2
1
0
0
2
0
1
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
1
0
0
0
1
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
6
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
3
2
1
0
0
4
0
3
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
2
0
0
2
0
0
0
1
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
2
0
0
4
0
0
1
0
0
0
2
2
0
0
1
1
2
0
0
0
2
11
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
1
0
0
0
0
2
0
1
2
0
0
0
0
0
2
0
1
0
1
0
2
0
3
0
0
1
0
0
0
0
0
0
0
3
2
3
0
1
1
0
2
1
4
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
3
1
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
2
0
0
1
0
1
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
2
0
2
2
0
0
2
0
0
1
2
3
0
2
0
0
0
2
0
0
2
2
0
2
0
3
0
0
0
0
2
0
0
0
0
2
0
0
0
1
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
2
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
2
3
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
1
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
2
0
2
1
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
1
0
0
2
2
0
1
0
0
1
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
3
0
0
0
0
3
1
0
0
0
1
2
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
2
2
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
2
2
0
0
0
1
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
1
2
2
0
3
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
1
1
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
2
0
0
1
0
0
0
0
0
2
2
0
0
0
0
2
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
3
2
3
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
1
2
0
0
1
0
0
2
1
0
2
0
1
0
2
2
0
0
0
0
2
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
2
0
3
1
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
2
1
0
0
0
4
3
0
0
0
1
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
1
0
0
0
1
0
0
0
3
1
2
0
0
0
0
4
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
1
1
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
1
4
0
1
0
0
2
0
0
0
0
2
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
5
1
1
1
2
3
0
0
0
0
0
1
0
0
0
0
0
3
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
1
5
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
2
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
2
2
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
3
3
0
2
0
1
0
0
0
0
0
1
0
0
2
1
0
0
1
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
1
0
0
0
0
1
0
0
5
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
1
3
0
0
2
1
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
2
0
2
0
0
0
2
0
0
3
0
1
0
0
0
0
0
0
2
0
0
0
6
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
3
2
0
0
2
0
1
0
0
1
2
0
0
0
4
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
2
1
1
0
0
1
0
2
0
3
0
0
2
0
0
0
0
2
0
2
0
0
2
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
1
7
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
2
0
1
1
0
0
0
0
0
0
0
0
0
1
2
0
1
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
2
0
5
0
0
0
1
1
0
0
0
0
0
1
2
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
3
0
0
1
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
2
2
3
1
1
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
1
0
2
3
0
1
2
0
0
0
0
0
2
0
0
0
0
2
2
2
1
1
2
2
0
0
0
0
0
0
0
4
1
0
2
2
1
0
0
2
0
0
0
0
0
0
3
2
2
1
3
0
1
0
0
2
0
0
0
0
0
0
1
0
0
4
2
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
3
0
1
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
3
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
2
0
1
0
0
0
1
1
2
1
0
1
1
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
9
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
3
0
1
2
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
5
2
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
2
0
0
3
0
1
2
0
0
2
0
0
0
0
0
1
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
1
0
1
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
4
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
2
5
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
3
0
1
2
2
2
0
0
2
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
3
2
0
2
2
0
0
2
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
3
0
1
0
0
0
4
3
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
3
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
2
0
0
0
2
2
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
2
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
3
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
2
0
1
0
2
0
2
0
0
0
2
0
0
3
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
14
1
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
1
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
4
0
2
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
3
2
1
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
2
3
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
2
0
0
0
0
4
0
2
2
0
0
0
0
0
0
2
0
0
4
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
7
0
2
1
0
1
1
0
0
0
1
13
0
1
0
2
0
0
0
1
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
2
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
1
0
4
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
1
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
2
2
4
1
2
0
0
0
0
0
0
2
0
0
7
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
2
1
2
0
2
0
0
1
0
1
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
7
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
2
1
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
4
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
1
0
0
0
0
2
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
3
0
0
2
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
1
1
0
0
2
2
0
1
0
0
0
0
0
0
0
0
1
1
2
0
1
0
0
0
0
0
2
2
0
0
2
2
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
1
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
4
1
0
0
2
0
2
1
1
0
2
1
0
0
1
0
0
2
2
0
0
0
0
0
0
1
0
2
0
1
0
5
2
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
2
0
2
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
1
3
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
1
0
0
0
0
1
0
0
2
1
0
0
1
2
0
2
0
0
1
0
0
1
0
0
0
2
0
1
1
1
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
3
1
2
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
4
1
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
4
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
3
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
4
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
1
0
0
1
0
0
2
2
0
0
1
1
0
1
1
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
6
0
2
1
0
2
0
0
1
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
3
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
4
0
2
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
2
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
2
0
0
0
0
1
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
2
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
2
1
0
0
1
0
0
0
0
0
0
1
0
1
0
2
5
0
0
0
0
4
0
0
0
0
2
0
0
2
0
0
1
1
0
0
1
0
0
2
1
0
0
0
2
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
1
0
0
0
1
0
2
1
1
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
1
0
2
0
3
0
0
0
2
0
1
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
1
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
1
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
1
0
2
0
1
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
3
0
0
0
0
0
2
0
0
2
0
2
0
4
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
2
0
0
0
0
0
0
4
0
2
2
1
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
3
0
0
0
1
2
4
3
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
2
0
0
0
2
0
0
0
0
0
1
0
0
2
1
1
0
3
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
2
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
2
1
1
6
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
1
2
0
0
0
1
2
0
0
1
2
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
3
0
0
0
0
0
2
4
2
1
0
0
2
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
1
0
2
4
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
4
0
2
0
0
1
0
1
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
4
0
1
3
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
1
0
2
1
0
1
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
1
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
2
0
1
0
0
2
1
0
1
0
1
0
1
0
0
1
0
0
0
0
0
4
0
0
0
0
2
1
0
0
2
3
0
1
0
0
3
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
3
0
0
2
1
2
0
0
0
0
0
0
3
0
0
1
1
1
0
1
1
0
0
4
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
2
3
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
1
1
2
0
0
1
3
0
1
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
8
2
1
0
1
0
0
0
0
0
0
0
3
3
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
1
0
0
1
0
0
1
0
1
0
0
0
2
0
0
0
0
1
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
2
2
2
0
0
0
0
1
0
0
1
0
0
2
0
1
1
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
2
0
0
2
2
0
0
8
1
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
2
2
0
1
0
1
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
3
0
1
0
0
0
0
2
0
0
2
0
1
0
0
1
0
0
0
2
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
2
0
1
3
0
3
0
2
2
0
2
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
2
1
0
0
1
1
0
0
0
0
0
2
2
0
1
1
0
3
0
0
1
0
0
1
0
0
0
3
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
1
0
1
0
2
0
0
1
0
0
0
0
1
0
0
2
0
0
0
3
0
0
0
5
0
0
0
2
0
3
2
2
0
0
0
0
0
0
0
0
1
0
1
0
0
1
2
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
1
0
2
2
0
0
2
0
2
0
3
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
1
0
0
0
1
1
2
0
0
1
2
0
0
0
0
0
2
2
0
0
2
0
0
1
2
0
0
0
2
0
0
0
3
0
0
0
1
2
0
0
3
0
2
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
4
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
1
2
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
2
0
0
0
1
1
0
0
0
3
0
0
2
0
0
1
0
0
0
0
0
0
0
0
3
1
1
2
2
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
2
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
1
1
0
0
0
0
0
11
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
1
3
2
2
0
0
5
2
0
0
0
0
2
2
3
1
0
0
0
1
0
3
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
1
0
0
0
0
0
2
0
2
0
1
1
0
2
2
2
1
0
1
2
0
0
0
0
0
3
0
0
0
0
2
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
2
1
1
0
0
2
0
0
0
0
0
0
8
0
2
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
1
0
2
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
2
0
0
0
0
0
3
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
6
2
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
2
1
0
1
0
0
2
1
0
3
2
0
0
2
1
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
6
2
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
1
0
2
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
2
1
3
0
0
2
0
0
2
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
2
4
0
0
2
0
9
1
0
0
0
0
1
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
2
2
1
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
1
0
0
0
0
8
0
0
0
2
0
2
2
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
5
0
0
5
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
2
1
3
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
1
0
0
2
0
1
0
0
1
2
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
1
0
2
4
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
2
3
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
2
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
2
2
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
1
1
0
1
0
0
0
0
0
0
3
1
0
0
0
1
0
2
0
0
0
1
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
5
0
4
0
0
2
0
0
1
2
0
0
0
0
2
0
0
0
1
1
0
0
1
0
0
0
0
1
0
4
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
1
0
0
2
3
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
2
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
1
2
0
0
0
2
0
0
0
0
2
3
1
0
3
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
3
0
2
0
0
0
1
0
0
1
0
0
0
0
2
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
7
0
0
0
0
2
2
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
1
2
0
0
2
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
1
1
0
0
1
0
0
1
0
0
0
2
4
0
0
0
1
0
0
2
0
2
0
1
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
1
3
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
2
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
4
1
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
3
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
8
0
0
0
0
0
0
2
1
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
3
1
0
0
0
0
2
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
5
0
0
0
2
0
0
0
0
0
1
0
2
0
1
2
0
0
0
1
0
0
0
0
0
1
0
0
2
1
0
0
0
1
0
2
0
0
2
4
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
1
1
0
0
0
0
0
6
0
0
2
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
3
0
0
0
0
1
0
2
1
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
1
0
0
1
0
0
11
0
1
0
0
2
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
1
2
0
0
2
0
0
0
0
2
1
0
0
2
0
1
0
0
2
0
1
1
0
0
2
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
5
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
1
3
0
0
2
0
0
0
1
0
2
0
0
1
0
0
1
0
0
4
0
0
2
0
0
2
0
1
2
0
2
0
0
0
2
0
0
1
2
3
0
0
1
0
2
0
2
1
0
1
0
0
0
0
0
0
2
0
0
1
0
0
2
0
3
0
0
2
0
0
0
2
1
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
3
0
1
0
0
2
0
2
0
0
0
0
0
1
5
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
1
1
0
2
0
0
1
0
2
0
2
0
0
0
0
0
3
0
1
0
0
2
0
0
1
0
0
0
0
0
1
0
0
5
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
2
0
2
0
0
0
0
0
2
0
1
2
0
2
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
2
0
1
0
1
0
0
2
0
0
0
2
0
1
0
0
1
0
0
0
0
0
2
0
3
3
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
6
2
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
1
0
1
3
0
5
1
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
0
2
2
4
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
3
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
1
0
1
0
0
0
0
1
0
1
6
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
2
1
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
9
0
0
0
0
2
0
1
0
0
0
0
0
0
2
1
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
5
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
1
1
0
0
0
0
1
0
3
2
1
0
0
0
2
0
0
0
0
0
1
0
0
0
2
2
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
1
0
5
0
0
0
0
1
0
0
0
5
0
0
0
1
1
0
4
0
0
0
0
0
2
0
0
1
0
0
0
0
1
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
11
0
0
0
0
0
2
0
0
0
1
0
0
4
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
1
0
0
0
0
1
0
0
0
2
0
2
0
0
3
0
0
0
1
1
0
0
0
0
0
3
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
6
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
5
0
0
0
1
0
0
0
0
2
0
0
1
0
4
0
1
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
2
0
0
0
0
1
0
2
1
2
0
0
0
0
0
0
0
0
0
2
1
0
2
2
1
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
1
0
1
0
3
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
2
0
0
2
0
0
0
2
3
0
2
0
0
0
0
0
0
1
0
3
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
1
0
0
0
0
0
10
0
0
1
0
0
0
0
0
3
0
0
0
1
0
0
0
0
1
0
0
1
0
3
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
2
1
0
0
0
1
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
2
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
2
1
0
0
0
0
0
2
2
0
0
0
1
0
2
0
0
0
0
1
1
0
0
0
1
1
0
0
0
2
0
0
0
0
0
1
2
1
0
0
2
2
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
2
4
2
0
1
0
2
2
2
1
0
0
0
0
0
0
0
0
1
2
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
2
1
3
1
0
0
0
0
0
2
0
0
2
0
1
0
1
1
0
0
0
0
0
0
0
1
0
3
0
1
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
2
0
3
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
8
0
2
2
0
1
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
2
0
0
0
0
2
0
0
0
1
0
1
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
2
1
2
0
0
1
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
1
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
2
3
1
3
0
5
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
5
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
7
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
4
2
0
0
0
2
0
0
1
1
1
2
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
1
2
0
0
0
0
1
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
2
0
0
0
0
2
0
0
1
0
2
1
1
3
1
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
1
0
0
0
2
3
0
0
0
1
0
0
0
0
0
1
0
3
0
0
1
1
0
0
0
0
0
0
1
0
2
2
0
0
2
0
0
0
0
0
2
0
0
0
0
4
0
1
0
1
0
0
0
2
2
0
1
0
0
0
0
0
2
0
0
4
0
0
0
0
0
0
1
0
0
0
0
2
1
0
1
1
0
0
0
0
0
0
4
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
3
0
0
2
0
0
0
0
1
3
0
0
0
1
2
1
2
0
0
0
1
4
0
0
0
0
0
0
4
2
2
0
1
0
0
0
0
0
0
8
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
5
0
0
1
0
0
0
1
0
2
0
0
0
3
0
2
0
0
0
1
0
0
0
0
0
0
1
2
0
0
15
0
0
1
0
0
0
0
2
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
1
0
3
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
2
2
1
0
2
0
0
0
0
4
0
2
0
2
0
0
0
1
1
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
3
0
0
4
0
2
1
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
1
2
2
1
0
0
1
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
2
0
0
2
1
2
0
0
0
0
2
0
4
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
3
1
4
1
0
2
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
5
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
3
0
0
2
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
1
3
0
0
2
2
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
1
0
2
4
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
2
1
2
1
1
0
0
0
3
0
0
0
0
0
2
0
0
0
0
1
0
4
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
1
2
1
0
0
0
1
2
0
2
0
0
0
0
3
0
2
0
2
0
0
0
0
2
0
0
0
1
1
1
0
6
0
0
1
2
2
0
0
1
0
0
0
2
0
0
0
1
0
2
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
2
0
1
0
0
0
1
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
3
0
2
0
0
2
0
0
0
2
0
0
0
0
1
2
0
0
0
1
0
2
0
0
0
3
0
1
2
1
2
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
1
2
0
0
0
1
2
0
0
1
1
4
1
0
0
0
0
0
0
0
1
0
0
3
0
0
0
2
2
2
0
2
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
1
2
0
3
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
1
0
0
2
1
0
0
0
0
2
0
0
0
3
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
6
0
2
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
2
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
5
1
0
0
2
0
0
0
0
0
1
0
0
0
3
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
1
2
0
0
2
0
2
1
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
1
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
2
1
1
0
0
0
1
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
1
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
1
0
0
3
0
0
2
0
0
0
3
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
2
2
0
1
1
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
3
2
0
1
0
0
2
0
0
2
0
0
2
0
4
0
0
0
2
0
0
3
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
3
0
0
1
0
0
0
0
0
0
0
0
0
1
0
4
0
2
0
0
0
0
0
0
0
1
1
3
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
2
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
2
2
1
0
0
0
0
0
0
2
3
0
0
1
0
0
2
0
0
2
0
2
0
2
1
0
0
1
1
0
0
0
2
3
0
2
0
0
2
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
4
0
0
0
0
2
1
0
2
1
0
2
0
2
0
2
0
1
0
0
0
0
0
2
0
0
0
1
0
3
0
0
0
0
0
1
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
2
0
2
0
2
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
3
0
0
0
1
1
0
2
3
0
0
0
2
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
1
0
0
1
1
1
2
0
0
0
0
0
0
3
2
0
0
0
2
1
0
0
0
0
0
0
2
2
4
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
3
1
1
3
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
3
1
0
0
0
4
0
0
0
1
0
0
0
0
1
2
2
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
2
0
0
1
0
2
0
0
0
0
3
0
0
0
2
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
2
2
0
0
2
0
2
2
0
2
0
1
2
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
1
0
2
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
2
1
2
0
0
2
0
0
0
0
0
0
3
2
0
1
0
0
0
0
0
1
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
1
0
4
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
3
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
2
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
3
3
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
2
0
0
2
0
0
0
2
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
1
2
2
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
5
0
0
1
0
0
2
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
1
0
1
0
0
4
0
2
2
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
3
0
1
0
1
7
1
0
0
0
0
0
2
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
4
1
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
2
0
3
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
2
2
0
0
0
0
1
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
2
3
0
0
0
0
1
0
2
1
1
1
2
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
2
0
7
0
0
0
0
2
0
0
0
0
3
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
2
2
0
2
0
0
0
2
0
0
0
1
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
3
0
0
0
2
0
3
1
0
0
2
0
0
0
3
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
7
0
0
0
0
0
3
2
1
0
0
2
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
2
0
0
0
0
1
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
5
0
0
0
0
4
2
0
0
2
0
1
1
2
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
1
0
1
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
1
2
4
0
2
0
0
1
1
1
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
4
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
3
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
1
1
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
9
0
1
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
3
1
0
0
0
1
0
2
0
0
2
0
1
0
0
1
0
2
1
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
1
2
1
0
0
1
0
0
0
1
0
0
0
0
2
2
0
0
0
0
4
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
1
0
0
0
1
0
2
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
1
2
1
0
2
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
3
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
3
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
1
2
0
0
0
0
3
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
3
0
0
5
0
0
0
0
0
0
1
0
1
1
2
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
2
1
0
0
2
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
2
0
2
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
2
0
0
0
0
2
1
0
2
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
2
2
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
1
2
0
0
0
1
0
0
2
2
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
3
0
0
0
1
2
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
2
3
0
0
0
0
1
0
1
3
0
0
0
1
0
2
2
0
0
0
0
0
1
0
0
3
1
0
0
0
0
2
2
0
8
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
3
0
0
3
0
1
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
8
0
0
0
0
0
0
0
1
2
1
1
0
1
0
0
1
0
0
0
3
2
0
0
0
1
0
0
1
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
3
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
2
0
1
0
1
0
3
0
0
1
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
3
0
0
0
0
0
0
0
1
0
1
1
1
0
2
0
0
0
1
0
0
1
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
2
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
6
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
3
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
1
0
0
3
0
0
0
0
0
2
2
0
1
0
0
0
0
3
0
0
0
4
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
2
0
2
0
1
0
0
0
0
1
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
4
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
4
1
0
2
0
0
0
0
0
1
0
0
0
0
1
2
0
2
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
1
0
0
2
0
0
0
0
0
3
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
5
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
2
0
2
0
0
2
5
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
1
0
0
2
0
0
0
2
2
0
1
2
3
0
0
1
0
0
0
0
0
2
2
0
1
1
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
3
0
0
0
0
2
0
3
0
0
0
0
2
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
1
0
1
2
0
2
2
3
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
1
0
0
0
0
0
2
1
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
2
0
2
0
0
2
0
0
2
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
1
1
0
0
0
3
0
0
0
0
0
1
2
3
0
0
1
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
2
2
1
2
1
1
0
0
0
1
0
0
1
1
1
4
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
5
0
0
0
2
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
1
0
0
0
1
0
0
0
3
0
0
0
2
0
1
0
0
0
0
0
2
6
0
0
1
0
0
0
0
0
0
2
0
2
2
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
1
0
0
0
0
3
1
0
1
0
0
0
1
2
0
1
2
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
1
0
0
3
0
0
2
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
1
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
2
1
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
1
0
0
0
2
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
6
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
8
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
1
1
2
1
1
0
0
0
0
0
2
0
0
3
0
0
1
0
2
2
1
0
0
1
0
0
3
0
0
0
0
0
0
1
1
2
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
1
0
2
2
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
4
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
2
2
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
3
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
1
0
2
1
1
0
0
1
0
0
0
2
3
0
0
0
2
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
2
2
0
0
2
2
2
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
5
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
7
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
8
2
0
0
2
0
0
0
0
0
0
0
3
0
0
0
2
2
3
0
0
0
0
2
0
0
2
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
7
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
1
0
0
0
13
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
2
0
2
1
0
0
1
1
0
1
2
0
0
1
0
0
0
0
1
2
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
1
2
0
0
0
0
0
0
5
0
3
0
0
2
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
1
1
0
0
0
0
1
0
0
0
1
0
2
0
2
0
0
0
2
0
0
0
2
0
0
0
2
0
0
1
0
1
2
2
0
0
2
0
0
0
0
2
2
0
1
0
0
1
1
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
2
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
9
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
2
1
0
2
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
5
1
0
0
0
0
0
0
3
0
1
0
2
1
0
0
2
0
1
0
0
0
0
1
0
0
1
2
0
0
3
1
0
0
0
2
0
0
0
0
0
0
0
2
1
1
5
0
0
0
0
0
0
0
0
0
3
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
1
0
0
1
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
2
2
0
2
0
0
1
1
1
0
0
2
0
0
0
2
0
2
0
0
1
2
4
0
0
1
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
1
0
1
0
2
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
2
0
2
9
0
3
0
0
0
2
0
2
0
0
0
1
0
0
1
0
1
2
2
0
0
1
0
0
0
1
0
1
0
2
0
0
0
2
0
0
0
0
1
0
2
1
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
1
0
0
0
0
3
0
0
0
0
0
0
12
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
3
0
2
0
0
0
0
1
2
2
0
1
0
0
0
2
2
0
0
0
0
2
0
0
0
1
0
1
2
0
0
2
2
0
0
0
2
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
2
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
1
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
1
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
3
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
6
0
3
0
1
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
1
0
0
2
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
3
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
1
0
0
1
0
0
0
1
0
0
0
0
1
2
2
0
0
2
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
3
0
0
1
1
0
2
0
2
0
0
4
0
0
0
2
0
0
2
0
0
0
2
0
0
2
0
0
0
1
2
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
2
1
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
2
1
0
0
2
0
0
0
0
1
5
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
3
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
1
0
0
0
2
0
1
0
0
1
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
2
0
0
0
0
0
1
0
2
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
3
0
2
0
2
0
1
0
0
1
0
2
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
1
4
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
2
1
1
0
2
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
1
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
2
1
2
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
1
0
1
2
0
0
0
0
0
0
0
1
0
0
1
2
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
3
0
1
0
0
0
2
0
0
0
0
0
2
2
2
1
0
0
0
2
1
0
2
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
2
0
1
0
0
2
0
0
0
2
2
2
0
0
2
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
3
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
2
2
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
4
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
5
0
0
1
2
0
0
0
0
1
0
1
0
0
1
0
1
1
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
3
2
2
0
0
0
0
1
1
0
0
0
0
1
2
2
0
0
0
3
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
4
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
1
0
0
0
2
1
2
0
2
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
3
0
0
0
0
0
3
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
2
1
0
0
2
0
0
0
2
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
1
0
0
0
1
0
3
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
2
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
3
0
0
0
0
1
0
4
0
0
2
2
4
0
0
1
1
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
1
0
2
2
9
0
0
0
0
0
14
1
0
0
2
0
3
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
2
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
2
0
1
0
2
0
0
0
0
3
0
2
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
3
2
0
0
1
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
1
2
6
2
0
2
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
1
1
0
0
2
0
0
0
0
0
0
3
2
1
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
2
4
0
0
0
0
1
0
0
0
2
0
0
0
2
0
1
0
0
0
2
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
2
0
0
0
2
1
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
1
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
1
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
2
1
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
1
4
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
3
0
0
2
0
0
2
3
1
0
1
0
0
0
2
0
0
1
2
1
0
2
0
1
0
0
0
2
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
2
2
0
2
1
0
0
2
0
0
0
4
0
1
5
2
0
0
0
0
2
1
0
0
0
2
0
0
2
0
0
0
0
0
0
2
2
1
0
1
0
0
0
0
2
0
0
0
1
2
0
1
0
0
0
0
1
1
0
0
0
0
1
2
1
0
0
0
0
0
1
2
0
1
2
1
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
2
2
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
2
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
2
0
2
1
0
0
0
1
2
0
0
1
0
2
2
0
2
1
2
1
0
0
0
0
0
2
0
0
1
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
3
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
2
0
2
0
1
1
0
1
1
0
0
0
0
0
0
0
2
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
5
0
0
0
0
0
0
1
0
1
2
1
2
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
3
2
2
2
0
0
2
0
0
1
0
0
0
5
0
0
0
0
1
1
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
3
0
1
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
4
0
0
1
0
0
0
0
0
1
0
0
0
4
0
3
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
2
0
1
0
2
1
0
0
1
0
0
2
0
1
1
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
2
1
0
2
0
0
0
0
0
0
0
2
0
1
0
0
1
1
0
0
0
0
3
0
0
0
1
1
0
0
3
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
2
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
2
0
1
0
0
3
0
0
1
0
0
0
0
2
0
0
0
0
2
2
1
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
1
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
4
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
4
0
0
0
0
0
2
0
0
0
1
2
1
0
0
2
6
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
4
4
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
1
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
1
2
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
3
0
0
0
0
3
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
3
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
3
1
2
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
1
0
1
1
0
2
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
2
0
2
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
2
1
0
0
2
0
0
3
0
1
0
0
0
0
0
2
0
2
0
0
0
0
2
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
3
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
3
1
1
0
0
2
1
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
1
2
1
2
0
0
1
1
0
0
0
0
0
2
0
0
0
0
1
2
2
0
1
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
2
4
0
2
0
0
0
0
0
0
1
0
0
0
2
3
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
4
0
0
1
0
1
1
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
1
1
0
1
0
1
1
0
1
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
2
0
0
0
0
2
0
2
2
0
0
1
0
3
0
0
0
0
0
0
4
0
1
0
0
0
2
0
0
1
0
0
0
0
0
3
0
0
1
0
2
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
1
2
0
0
0
0
0
2
0
2
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
2
0
0
2
0
0
0
1
1
0
3
2
0
0
2
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
6
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
1
0
0
0
4
0
0
1
0
0
0
0
0
1
0
1
0
1
2
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
4
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
3
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
2
0
0
0
1
0
2
0
0
2
0
0
2
0
0
0
0
0
1
0
1
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
2
0
0
0
4
2
1
0
1
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
1
0
1
0
1
0
0
0
2
0
2
2
0
0
2
0
0
1
2
0
1
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
1
1
0
2
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
2
2
0
0
2
0
0
2
0
0
0
1
2
0
0
0
1
1
0
0
0
0
2
0
1
1
0
2
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
2
4
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
1
1
0
0
0
2
1
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
1
0
5
0
0
0
0
0
0
0
1
0
2
2
0
1
1
1
2
0
2
0
0
0
0
0
0
0
1
0
0
2
0
1
1
3
0
0
0
0
0
0
0
3
0
0
2
3
0
0
0
0
0
0
0
0
0
0
2
0
0
2
4
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
2
0
1
0
2
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
2
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
1
0
0
0
0
1
0
5
0
0
0
0
0
3
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
2
1
0
0
0
0
0
0
0
1
0
0
1
0
0
2
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
4
0
0
0
2
0
0
4
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
2
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
1
2
0
0
1
1
2
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
5
0
0
0
1
0
1
0
0
2
0
0
2
0
1
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
2
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
1
2
1
2
0
1
0
0
0
0
0
0
1
2
0
1
2
1
1
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
1
2
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
1
2
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
1
0
0
0
0
4
0
0
2
0
2
1
0
0
1
0
0
0
0
0
1
0
0
3
0
1
1
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
1
2
0
0
1
2
2
0
2
0
2
0
0
0
1
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
1
0
0
2
0
1
1
0
0
0
2
1
0
0
1
0
0
0
0
0
0
2
1
1
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
2
0
1
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
2
2
0
0
1
0
0
0
0
0
0
0
2
1
0
1
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
3
0
0
0
0
2
2
0
0
2
2
2
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
2
0
0
0
0
0
0
0
2
2
0
2
1
0
0
0
2
3
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
3
0
0
0
0
0
2
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
1
0
0
0
0
4
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
1
2
0
0
1
2
0
0
0
0
0
0
10
0
1
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
1
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
3
0
0
0
0
0
0
3
0
0
0
1
0
1
0
0
1
1
0
1
2
0
0
0
0
1
4
1
0
0
1
4
0
1
0
0
0
2
2
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
1
0
2
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
2
0
6
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
2
3
0
0
0
0
0
0
0
1
0
0
2
1
0
1
0
0
0
0
0
0
2
1
0
0
1
0
1
3
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
4
2
0
0
0
1
0
0
0
1
1
6
2
0
0
1
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
2
3
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
1
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
3
0
0
1
0
0
0
1
0
2
0
2
0
0
0
1
0
0
0
0
0
1
0
0
6
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
2
0
0
3
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
2
0
3
1
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
1
2
0
0
0
0
6
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
3
2
0
0
0
0
0
1
0
1
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
2
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
1
0
0
2
2
0
1
0
2
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
8
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
3
2
0
2
0
0
0
0
0
3
0
1
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
3
0
1
1
0
2
0
0
0
0
2
0
0
0
2
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
1
0
0
0
0
0
3
1
1
0
1
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
1
0
0
2
0
0
2
0
0
0
4
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
1
0
1
0
0
0
0
0
2
0
2
0
0
1
2
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
4
0
0
0
1
2
0
0
3
0
0
0
0
0
2
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
0
2
0
2
1
0
2
0
0
0
0
1
0
0
0
2
1
0
2
0
5
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
2
0
0
0
2
0
1
0
0
0
1
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
2
1
1
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
4
1
0
0
2
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
3
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
1
0
1
0
2
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
2
0
0
0
0
0
0
2
2
0
0
0
0
0
1
2
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
2
1
1
0
2
0
0
2
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
3
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
2
1
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
2
0
0
1
0
0
4
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
2
0
0
0
0
1
0
0
4
0
2
0
0
2
2
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
2
0
0
1
3
0
0
2
0
0
0
2
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
6
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
1
1
3
1
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
2
1
0
1
0
2
0
1
0
0
0
3
0
0
1
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
3
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
3
0
0
0
0
0
5
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
1
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
3
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
3
2
0
0
1
0
0
2
0
0
1
0
0
0
0
2
1
0
0
3
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
3
0
0
0
1
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
3
1
1
0
0
0
2
0
3
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
1
2
1
3
0
2
0
0
0
0
3
0
0
0
1
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
2
0
1
0
1
0
0
0
0
0
0
0
1
2
0
0
2
2
0
0
0
0
2
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
2
0
0
0
2
1
0
0
2
2
2
0
5
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
4
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
1
0
0
0
0
0
0
4
2
2
0
3
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
2
0
1
0
2
0
0
0
0
0
0
1
0
0
0
2
1
1
0
0
0
0
1
0
0
2
0
3
0
0
0
0
3
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
4
0
0
0
0
0
0
0
0
0
2
0
3
0
2
0
1
0
1
0
1
0
0
2
0
0
1
1
0
3
2
0
2
1
0
4
1
0
2
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
1
0
0
0
0
0
0
0
1
0
0
0
1
2
1
0
2
0
2
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
1
1
0
0
0
1
1
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
3
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
2
0
0
1
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
8
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
2
2
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
3
1
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
5
0
2
0
2
0
0
2
0
2
2
0
0
0
0
0
1
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
1
0
1
2
2
0
1
0
0
0
0
2
0
3
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
3
1
1
0
0
0
1
0
2
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
7
0
3
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
2
2
0
0
1
0
0
0
0
2
3
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
2
0
0
6
0
1
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
2
0
2
1
0
0
1
0
0
0
0
0
0
0
2
0
3
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
1
0
0
1
0
0
0
0
1
0
0
1
1
0
0
2
1
0
0
0
2
0
0
1
2
0
0
0
1
0
0
2
0
0
0
1
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
5
0
0
1
0
3
0
0
0
1
2
2
0
0
2
2
1
0
0
2
2
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
2
0
2
0
0
1
0
0
2
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
1
2
0
0
0
0
3
2
0
0
2
0
0
3
0
0
0
0
0
0
0
2
0
3
3
1
3
0
0
1
0
0
0
1
0
0
1
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
1
5
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
1
1
0
0
0
2
0
1
0
1
0
0
0
2
0
2
0
0
0
1
2
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
2
0
0
1
2
2
0
0
0
0
0
0
1
0
1
2
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
2
0
0
0
0
1
0
1
2
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
2
0
0
0
0
0
1
0
4
0
0
0
0
1
0
0
0
0
3
0
0
0
1
0
3
0
0
0
0
0
0
1
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
6
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
2
2
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
1
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
2
0
1
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
1
1
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
2
1
0
0
0
1
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
1
0
0
0
0
1
0
0
2
2
0
2
2
0
1
0
0
4
0
0
0
1
0
0
2
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
7
1
1
1
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
2
0
0
0
0
0
2
1
0
1
0
2
1
0
0
0
2
1
0
1
0
0
2
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
3
0
2
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
2
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
2
1
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
5
0
0
0
3
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
1
1
0
1
4
0
2
0
0
0
3
0
0
0
1
0
0
0
1
0
0
2
0
0
2
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
1
1
0
0
1
0
0
2
0
2
0
0
0
0
3
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
2
1
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
1
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
4
0
1
0
2
0
0
2
1
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
1
1
0
0
0
2
0
0
0
0
0
2
0
0
0
2
2
0
0
0
1
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
2
1
0
1
0
0
0
0
1
1
0
0
2
0
0
0
0
0
2
1
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
3
3
0
2
2
0
1
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
1
0
1
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
2
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
3
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
2
4
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
2
0
1
0
2
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
3
2
2
0
0
1
0
0
1
3
3
0
0
0
2
2
0
0
7
0
2
0
8
2
0
1
0
0
1
0
1
0
0
0
2
0
0
0
1
0
0
1
0
2
0
0
0
0
2
0
4
1
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
3
1
0
4
0
0
0
0
10
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
1
0
2
0
0
0
2
0
0
0
0
1
0
0
1
0
2
2
0
2
1
0
0
1
0
5
0
0
0
0
2
1
0
2
0
2
0
0
0
0
0
1
0
0
1
0
2
0
0
1
0
0
1
0
0
0
1
0
2
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
2
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
2
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
1
0
0
0
1
2
2
0
0
1
2
2
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
1
3
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
3
1
2
0
4
1
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
3
0
1
0
1
0
0
4
0
0
0
0
2
0
1
0
6
0
0
0
2
4
0
2
2
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
1
1
0
1
0
0
0
0
1
2
0
0
1
1
4
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
3
0
0
0
1
0
2
0
0
1
0
1
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
2
0
3
1
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
4
1
0
0
2
2
2
0
2
0
0
2
0
1
0
0
0
4
0
0
0
2
2
4
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
2
3
0
1
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
3
2
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
4
0
0
2
0
4
2
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
1
0
0
0
0
0
0
0
1
0
0
2
2
0
1
0
0
1
0
0
0
0
0
1
0
2
0
0
0
2
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
1
2
1
0
0
0
1
1
0
0
0
0
0
1
0
0
2
2
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
5
2
0
0
1
0
0
0
0
0
0
0
0
2
1
2
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
1
1
0
0
0
0
2
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
3
1
1
0
1
0
0
0
2
2
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
1
0
0
2
0
0
0
3
0
0
0
3
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
2
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
3
1
2
0
0
0
0
0
0
0
2
0
1
0
0
1
1
0
0
1
0
1
1
0
0
0
0
1
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
3
0
0
1
1
1
1
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
2
0
0
2
0
1
0
2
0
0
0
0
0
1
0
0
6
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
3
0
2
0
1
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
2
1
0
1
0
0
0
0
0
0
0
3
0
1
0
2
0
0
2
0
0
1
0
1
0
0
0
0
1
0
1
2
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
3
0
0
0
2
0
0
0
0
1
0
1
0
2
2
0
0
0
2
0
0
0
0
3
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
2
0
0
0
0
0
0
0
0
1
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
2
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
3
2
0
0
0
2
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
2
0
0
0
0
2
0
0
2
1
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
3
2
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
3
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
2
1
0
0
0
0
0
0
5
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
3
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
2
1
1
0
0
0
2
0
0
0
0
4
0
0
0
1
1
0
0
0
0
0
0
2
2
0
0
0
0
0
3
0
0
0
4
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
2
2
1
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
2
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
1
1
0
2
0
0
2
0
0
2
2
0
0
0
0
2
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
1
2
0
2
2
3
1
0
3
0
1
3
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
4
0
0
1
0
0
0
0
0
1
0
1
1
0
2
1
0
0
0
0
2
0
1
0
0
0
2
0
0
0
2
2
0
0
0
0
0
1
0
1
0
2
2
0
0
0
0
0
2
2
0
0
1
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
2
0
0
2
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
16
0
0
2
0
2
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
2
0
3
0
0
0
0
0
0
0
0
0
0
2
0
3
0
2
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
1
3
0
0
1
0
0
0
2
0
0
3
0
0
2
1
0
0
0
0
1
2
2
2
1
1
2
0
0
0
0
0
7
3
0
0
0
0
0
1
0
1
0
0
7
1
0
0
0
0
1
0
0
0
2
0
0
2
0
10
0
1
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
2
1
0
0
5
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
1
2
1
0
0
2
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
23
2
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
4
0
0
4
0
0
0
0
0
0
0
2
0
5
1
0
0
0
1
0
0
0
2
0
0
0
0
3
0
0
0
0
0
1
1
0
0
1
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
1
0
1
0
3
3
0
0
0
0
2
0
0
0
3
1
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
2
1
0
0
0
0
2
2
0
0
2
3
1
0
0
0
0
0
0
2
3
0
2
0
0
0
1
1
0
0
1
2
0
0
1
0
0
2
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
2
0
0
0
1
1
1
1
0
0
0
0
0
2
0
3
0
1
0
0
3
2
0
0
0
0
0
1
1
0
1
2
0
2
0
0
3
0
1
0
2
0
1
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
4
0
0
0
0
1
0
0
3
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
2
0
0
0
0
0
0
2
3
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
4
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
1
0
0
0
5
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
2
1
2
0
0
0
0
0
2
0
2
0
1
1
0
0
0
1
0
1
2
0
0
0
0
0
1
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
4
0
0
1
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
3
1
0
2
3
2
0
0
0
1
2
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
3
0
1
0
6
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
1
0
0
0
0
0
0
0
3
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
5
0
1
0
1
0
0
3
0
0
0
0
0
2
1
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
1
1
0
2
2
0
1
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
3
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
2
2
0
0
1
2
0
3
0
0
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
3
0
1
2
1
0
0
0
0
4
1
0
0
0
0
0
0
0
2
1
2
1
1
3
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
3
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
6
0
0
1
1
0
0
0
0
0
0
2
0
1
1
0
2
1
2
2
0
1
0
0
3
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
31
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
2
0
0
0
2
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
2
0
0
0
1
0
0
1
2
0
0
0
0
1
0
0
1
0
0
1
0
0
3
0
1
0
0
2
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
2
2
0
2
0
0
0
1
1
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
3
0
0
0
4
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
1
0
2
0
0
2
1
0
1
1
0
0
0
2
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
3
1
0
0
0
0
2
2
1
0
0
0
0
0
1
1
0
0
0
2
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
3
0
0
0
3
0
0
2
1
0
0
0
0
0
0
2
1
0
0
2
0
0
3
3
0
0
0
0
1
0
0
0
2
0
1
0
0
2
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
1
0
2
3
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
3
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
1
0
2
1
0
0
2
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
4
2
0
0
0
2
0
0
5
0
0
0
0
0
1
0
0
0
0
4
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
1
0
0
0
0
0
1
0
6
3
0
0
1
2
1
3
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
1
0
1
0
0
0
0
1
0
0
0
2
0
3
0
1
1
0
0
1
0
2
0
1
0
0
0
1
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
2
2
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
4
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
1
0
2
1
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
1
0
0
0
0
0
3
0
0
2
2
2
0
0
0
1
1
1
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
1
0
0
0
0
0
0
0
2
1
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
1
1
1
5
1
0
0
0
0
0
0
1
0
2
2
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
1
2
0
0
0
0
0
1
1
0
0
0
0
2
0
0
4
0
2
0
0
0
0
0
0
0
2
0
0
1
0
2
0
1
0
0
2
0
0
1
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
3
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
1
4
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
2
0
2
0
0
2
0
0
1
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
1
0
1
6
1
2
0
3
0
0
2
0
0
0
0
0
1
0
2
0
0
0
1
0
0
2
1
1
0
0
0
2
0
0
1
3
0
0
0
0
2
2
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
2
2
1
0
0
0
2
0
2
0
1
0
0
1
0
0
0
1
0
0
0
2
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
2
3
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
2
1
2
0
5
0
2
0
0
0
0
0
0
0
2
1
2
4
0
0
3
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
3
0
1
1
0
0
1
2
0
0
1
3
0
0
0
0
0
1
0
3
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
2
2
2
1
0
1
0
2
0
0
0
0
0
0
1
0
2
0
2
0
9
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
2
1
0
0
2
0
1
0
0
0
0
1
1
0
0
2
0
1
0
0
1
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
2
0
0
2
0
0
0
1
0
0
2
5
0
1
0
0
0
2
1
0
0
0
1
0
0
1
0
2
2
0
2
1
2
0
0
0
0
1
0
0
1
0
1
2
1
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
4
2
0
1
2
3
0
2
1
0
0
0
0
1
0
0
0
2
2
0
1
0
2
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
3
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
1
0
0
2
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
1
1
1
0
0
0
1
1
0
0
1
0
0
0
2
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
4
0
0
1
4
0
0
0
1
0
0
0
1
0
0
3
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
3
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
1
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
1
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
2
0
1
0
0
4
1
0
0
2
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
2
0
5
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
5
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
1
0
0
0
2
0
0
1
2
0
0
0
0
1
0
1
1
1
0
1
0
2
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
2
0
1
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
2
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
1
0
1
0
1
0
0
0
1
2
0
1
0
0
0
1
0
0
0
1
0
0
0
0
6
0
2
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
1
0
3
0
1
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
1
2
0
0
0
0
2
0
0
0
0
0
0
1
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
1
2
1
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
2
0
0
0
0
0
0
0
2
2
1
0
3
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
2
2
1
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
1
2
1
0
1
1
0
2
0
0
2
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
2
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
6
0
2
0
0
1
1
0
0
0
0
2
0
0
0
1
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
1
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
1
0
0
0
0
2
5
0
0
2
0
2
0
0
0
0
0
0
1
3
0
1
1
0
2
0
0
0
0
1
2
0
2
2
0
0
0
1
2
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
2
0
2
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
1
0
0
0
0
1
1
0
0
0
0
1
2
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
2
2
2
2
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
2
1
2
2
0
0
11
0
0
0
0
2
0
0
1
3
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
1
1
0
0
2
0
0
0
3
0
2
0
0
2
0
0
3
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
3
0
1
2
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
3
0
0
3
0
1
0
0
0
0
1
0
1
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
1
1
2
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
1
1
0
2
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
2
0
1
1
1
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
1
0
0
3
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
2
2
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
3
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
2
1
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
1
0
1
0
0
0
2
0
2
2
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
3
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
3
0
1
2
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
3
0
0
1
0
2
0
0
0
0
0
2
0
0
1
2
0
0
5
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
5
0
0
0
0
2
1
0
0
0
0
1
0
1
0
0
0
1
0
2
0
0
0
0
1
0
0
3
0
0
1
1
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
1
0
0
2
0
0
1
0
0
1
0
0
2
0
0
0
1
0
2
0
1
0
0
0
0
2
0
0
0
2
0
0
1
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
1
1
0
0
1
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
1
1
2
0
1
0
0
0
2
2
0
0
0
1
1
0
2
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
1
0
0
1
0
0
0
2
3
1
1
1
2
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
4
0
0
1
2
0
0
2
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
3
0
2
1
1
0
0
0
0
1
0
2
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
2
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
3
0
0
0
2
0
0
0
0
2
1
0
3
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
2
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
6
0
0
3
1
0
2
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
4
0
1
0
0
0
0
0
0
1
0
2
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
1
0
0
1
0
0
0
2
0
1
2
0
1
1
2
0
0
0
0
5
0
0
0
0
1
2
0
2
1
0
2
0
1
5
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
3
2
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
1
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
1
1
2
1
0
1
2
1
0
0
0
2
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
3
0
0
2
0
1
0
1
1
0
2
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
2
2
0
0
0
0
0
2
3
0
2
0
0
0
0
0
1
1
0
0
0
0
0
1
2
0
0
0
0
0
2
1
2
0
0
2
0
2
2
0
0
0
0
0
0
0
2
6
0
1
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
1
2
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
2
2
1
0
0
0
2
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
2
0
0
2
0
0
0
4
0
0
0
1
0
0
0
1
0
0
0
4
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
2
0
1
2
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
2
2
0
0
0
1
0
2
0
1
2
0
0
0
0
0
0
2
0
2
2
0
2
2
1
0
0
1
2
1
2
0
0
1
2
2
2
0
0
0
1
0
0
0
1
2
0
1
0
0
1
0
0
2
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
2
0
1
1
0
0
2
1
0
0
0
0
3
3
0
0
1
0
2
0
1
0
0
0
2
0
0
0
0
4
0
0
2
0
0
0
2
0
0
0
0
2
0
0
1
1
0
0
0
3
0
0
0
1
0
0
0
3
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
5
0
0
0
6
0
0
2
0
1
0
0
3
1
1
0
0
0
1
0
1
1
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
2
0
0
2
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
1
2
2
2
0
0
0
0
0
2
0
1
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
2
0
0
0
0
0
0
1
1
0
1
0
1
1
0
2
1
0
2
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
1
0
1
0
2
2
0
0
0
2
2
0
0
0
2
2
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
4
1
0
1
0
0
0
1
0
2
0
0
0
2
0
1
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
3
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
3
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
1
2
0
3
0
1
0
0
0
1
0
0
0
0
0
0
3
2
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
2
0
1
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
3
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
2
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
1
2
0
0
0
2
2
0
0
2
0
2
2
2
0
0
5
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
1
2
0
1
0
0
3
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
3
0
2
0
0
2
0
0
0
0
0
0
1
0
0
2
2
2
1
0
1
1
1
0
0
2
1
2
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
3
0
0
2
0
0
0
0
2
4
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
1
0
2
2
3
0
0
6
4
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
1
0
0
0
1
2
2
0
1
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
4
0
0
0
0
1
0
5
0
1
0
1
2
0
0
0
2
0
0
0
1
1
0
0
1
0
0
0
3
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
1
0
0
0
0
1
2
0
1
3
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
1
0
0
2
3
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
2
0
0
3
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
3
2
0
0
0
0
1
1
2
0
0
0
0
0
0
3
1
2
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
2
1
2
0
2
0
2
0
0
0
0
0
2
0
3
1
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
3
0
2
0
2
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
5
0
0
2
0
0
3
0
1
0
0
0
3
0
0
0
0
0
2
0
1
5
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
2
1
0
2
0
0
1
1
0
1
0
0
0
0
0
0
0
2
0
1
0
0
2
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
2
1
2
0
0
0
3
0
0
2
0
2
0
0
0
0
3
0
0
2
1
1
2
0
0
1
0
0
1
3
1
0
1
0
0
2
1
0
1
4
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
3
0
0
2
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
3
0
2
0
2
4
0
0
0
0
0
1
1
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
3
5
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
1
2
1
0
1
1
0
0
2
0
2
1
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
5
0
0
0
0
0
0
1
0
0
0
0
0
1
1
2
1
2
0
1
0
0
0
0
0
2
0
0
0
0
0
3
3
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
2
1
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
3
0
0
1
1
0
1
0
1
0
1
0
0
0
0
1
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
3
4
1
0
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
2
0
0
0
0
0
2
0
0
0
2
0
5
0
2
0
0
0
1
0
0
1
2
0
0
0
0
5
0
0
2
0
0
1
0
0
0
1
0
0
2
0
2
0
0
0
1
0
3
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
2
0
0
2
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
1
0
1
0
0
5
0
0
0
0
1
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
5
0
1
0
0
2
1
2
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
5
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
1
0
2
1
2
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
2
1
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
3
0
2
0
0
3
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
2
2
0
0
0
0
0
0
0
2
1
1
4
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
11
0
0
0
0
1
0
0
0
0
1
0
0
7
2
0
0
0
0
1
0
0
1
2
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
7
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
3
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
3
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
5
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
1
0
0
0
2
0
0
4
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
1
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
4
0
0
0
2
2
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
1
0
0
1
2
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
4
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
2
0
2
1
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
1
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
4
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
3
0
0
0
0
4
2
0
0
1
3
0
0
3
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
2
0
2
0
1
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
1
0
9
2
0
0
6
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
1
2
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
2
3
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
1
0
1
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
1
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
1
0
1
0
0
0
0
0
1
3
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
2
0
0
0
0
0
0
2
2
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
6
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
2
0
2
2
0
0
0
2
0
0
1
0
0
0
0
1
0
2
0
0
2
1
0
0
1
0
2
0
0
0
0
0
0
2
0
0
1
1
0
0
1
0
0
0
0
2
0
1
1
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
2
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
3
0
0
2
1
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
1
1
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
2
0
0
1
0
0
2
0
0
0
2
0
2
0
2
0
0
0
0
1
0
3
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
4
0
0
0
2
0
2
0
2
1
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
1
0
0
0
0
0
2
0
0
0
0
0
1
1
0
6
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
4
0
0
1
0
0
0
1
0
1
0
1
0
0
2
0
0
0
0
0
0
0
3
0
0
0
2
0
2
0
0
9
0
1
0
1
0
1
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
2
2
2
0
2
0
1
2
0
0
0
0
0
1
0
0
0
2
0
1
0
0
4
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
3
2
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
3
0
0
1
0
0
0
0
2
0
1
0
0
3
0
0
0
0
2
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
2
1
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
5
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
2
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
1
1
0
0
2
2
0
0
4
0
0
2
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
1
0
2
0
2
0
2
0
2
2
0
0
2
0
0
1
0
0
3
0
0
0
0
2
0
0
3
0
0
0
2
0
1
1
0
0
2
0
0
0
0
0
2
1
1
2
0
0
0
0
2
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
1
0
0
1
0
0
0
0
4
0
0
1
1
0
0
0
0
1
0
0
1
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
6
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
2
4
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
1
1
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
2
2
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
2
0
0
0
1
2
0
0
0
0
1
1
1
1
0
2
0
1
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
2
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
5
0
0
0
0
0
0
0
6
0
0
0
2
0
0
0
0
1
0
1
0
0
2
5
4
2
0
2
0
0
0
2
0
0
2
1
4
0
0
0
0
0
1
0
2
2
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
1
1
0
0
0
0
11
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
1
1
0
2
1
0
0
0
1
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
1
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
3
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
4
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
2
1
0
0
0
2
0
2
0
1
0
0
1
2
0
0
0
0
0
2
3
0
0
2
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
1
3
0
1
0
3
0
1
0
0
1
2
0
1
0
1
1
2
0
0
0
0
2
6
0
0
0
0
0
4
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
2
0
1
1
2
2
0
0
0
1
0
0
2
2
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
2
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
5
0
1
0
6
0
2
0
0
2
2
0
0
1
0
1
0
2
0
2
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
2
1
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
2
0
2
0
0
1
0
0
2
2
0
0
3
1
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
1
2
0
0
0
0
0
0
1
0
2
0
0
1
0
4
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
2
1
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
3
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
3
0
0
0
1
0
0
0
2
0
1
0
2
0
0
2
0
1
2
0
3
0
0
0
3
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
3
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
6
0
0
1
0
0
0
0
0
0
0
1
0
2
3
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
3
0
0
0
2
3
0
2
0
0
3
2
0
0
0
0
0
0
0
0
2
1
0
0
2
0
1
0
0
0
1
0
0
0
1
0
2
2
0
0
5
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
3
2
0
0
0
0
0
2
0
2
0
0
3
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
2
0
0
2
0
1
11
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
2
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
1
2
1
0
0
0
1
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
2
3
0
0
0
2
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
7
0
0
1
0
0
1
1
0
0
0
0
1
4
0
3
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
2
0
2
2
2
0
0
2
0
1
2
3
0
1
0
1
0
0
1
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
1
0
3
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
3
0
0
2
0
1
0
0
0
0
0
0
5
1
0
0
1
0
2
1
1
1
0
0
0
0
0
0
2
0
1
1
1
0
0
3
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
1
1
0
0
3
1
0
2
0
1
5
0
0
0
0
0
3
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
3
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
3
0
1
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
10
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
7
0
3
0
2
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
2
0
0
4
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
2
2
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
4
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
2
1
0
0
0
0
2
1
0
0
0
0
0
2
0
0
3
0
0
0
3
1
0
1
0
0
2
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
2
2
0
0
0
1
2
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
2
0
3
0
0
0
0
2
0
1
0
0
0
1
1
0
2
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
2
2
0
0
0
0
2
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
6
1
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
1
2
0
2
2
0
2
0
0
2
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
2
0
0
0
2
0
6
0
0
0
0
0
0
0
2
4
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
3
0
1
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
1
9
0
2
0
0
0
1
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
2
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
2
2
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
2
0
1
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
5
0
0
0
0
0
0
0
0
2
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
2
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
3
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
2
0
0
0
4
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
10
0
0
2
0
0
2
3
2
1
1
0
0
1
0
0
0
0
0
1
2
0
0
2
0
0
0
0
1
0
0
3
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
2
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
3
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
1
0
3
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
1
2
0
0
0
0
0
2
3
0
0
0
0
0
0
0
3
0
0
2
2
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
2
0
0
2
1
0
2
0
0
2
1
1
0
0
0
1
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
2
1
0
0
0
0
0
0
2
2
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
1
0
0
2
3
0
0
0
2
0
0
1
1
0
0
0
0
1
1
0
0
0
0
1
3
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
1
0
3
0
1
2
5
0
0
0
0
2
0
1
0
1
0
1
0
2
1
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
3
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
4
1
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
2
1
2
0
1
0
2
0
0
1
2
0
2
1
0
1
0
0
0
3
0
0
1
0
0
1
1
1
0
0
1
0
0
3
2
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
1
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
4
2
2
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
2
5
0
0
0
0
1
0
1
0
0
0
0
0
0
4
0
0
0
0
1
0
2
0
1
0
0
1
1
0
0
0
3
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
3
0
1
0
0
0
1
0
0
0
0
8
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
1
0
0
0
2
1
0
0
0
1
0
1
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
2
1
0
0
0
0
3
0
0
0
0
0
1
1
2
2
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
2
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
6
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
2
0
1
1
0
1
0
0
2
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
2
0
0
4
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
1
0
0
0
2
0
0
0
1
0
1
0
0
0
2
0
0
2
0
0
1
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
2
0
0
0
0
0
2
3
0
0
0
1
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
4
0
2
0
2
0
0
2
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
2
0
0
2
0
2
0
0
0
1
0
0
0
0
1
2
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
1
0
0
2
1
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
2
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
2
0
0
0
2
2
2
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
1
0
0
2
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
4
3
0
1
0
0
2
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
4
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
2
0
2
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
1
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
1
0
2
0
1
2
0
3
0
0
0
0
4
0
0
2
4
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
2
0
1
0
0
1
1
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
1
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
1
0
6
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
3
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
3
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
3
3
0
0
1
0
0
0
3
1
0
0
0
4
1
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
3
0
0
0
0
1
0
2
0
0
0
1
0
1
1
0
0
1
0
1
0
0
0
0
0
2
1
0
0
1
0
2
0
1
0
0
1
0
0
0
1
1
0
0
2
0
1
0
1
2
2
0
3
1
0
2
0
1
0
0
0
2
0
0
0
3
0
0
3
0
0
0
0
0
2
0
0
5
0
0
0
1
0
3
0
0
0
0
0
0
0
0
2
1
0
1
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
2
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
3
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
1
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
4
0
0
2
2
1
0
2
0
0
5
0
0
1
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
3
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
1
2
0
2
1
0
0
0
0
0
0
0
0
0
2
2
2
0
1
0
1
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
1
0
1
2
0
0
2
0
2
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
2
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
1
1
0
0
0
0
0
0
0
5
0
2
0
2
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
1
3
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
4
3
1
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
4
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
2
0
0
1
2
0
0
0
0
2
1
1
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
1
0
1
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
1
2
0
2
0
0
1
0
0
0
2
3
0
0
2
0
0
1
0
0
1
0
0
0
0
2
0
1
4
0
0
1
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
2
2
0
2
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
1
0
1
1
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
1
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
2
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
3
2
0
0
1
0
0
2
3
2
2
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
1
0
1
0
1
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
1
2
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
2
2
2
0
2
1
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
3
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
1
0
1
0
0
0
1
0
0
2
0
0
0
0
3
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
4
1
0
2
0
0
3
1
2
0
0
0
0
0
0
0
2
0
5
0
0
0
2
0
0
0
0
2
0
0
2
0
1
0
2
0
1
1
0
3
0
0
1
0
2
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
2
0
0
0
2
0
0
1
1
0
1
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
2
0
0
0
2
2
0
1
0
2
3
2
1
0
0
0
0
2
0
0
0
2
0
0
3
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
2
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
4
1
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
2
2
0
0
0
0
1
0
2
2
0
0
0
0
0
0
1
0
2
0
2
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
2
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
3
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
2
1
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
2
2
2
0
0
1
2
0
0
0
0
0
0
0
0
0
3
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
6
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
1
0
0
2
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
2
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
1
2
2
0
1
0
0
0
0
1
0
1
0
0
1
0
1
0
1
2
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
2
1
0
0
0
1
3
1
2
2
0
0
0
2
0
0
0
1
0
0
0
0
0
1
1
1
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
4
0
0
10
0
0
2
0
1
0
0
0
2
0
2
0
3
0
0
2
1
0
0
0
0
1
1
2
2
2
0
0
0
0
0
0
0
3
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
1
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
3
2
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
2
4
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
2
0
2
1
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
3
2
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
5
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
1
1
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
2
0
1
2
0
0
0
0
0
0
0
7
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
2
0
0
0
4
0
0
4
0
0
0
0
0
0
0
0
1
1
0
1
2
0
1
0
2
0
0
3
0
1
0
0
0
0
2
0
0
0
1
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
1
2
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
1
0
0
2
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
2
0
1
0
0
1
0
0
1
0
1
0
1
2
0
2
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
3
0
0
0
0
1
0
2
3
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
2
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
1
1
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
4
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
2
0
4
0
0
0
0
0
0
1
0
0
0
2
0
0
4
1
0
1
0
0
2
0
1
1
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
2
2
0
0
0
0
1
0
1
0
0
0
1
0
2
0
0
1
0
0
0
2
0
0
0
0
2
2
0
0
1
0
0
1
3
1
0
0
0
2
0
2
0
0
1
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
1
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
4
0
0
2
1
0
1
0
0
1
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
5
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
3
0
0
1
0
4
0
0
0
0
0
0
0
0
0
2
0
3
2
2
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
1
5
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
1
0
2
3
0
0
0
0
0
0
2
0
0
2
0
1
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
3
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
3
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
2
0
0
0
1
0
0
1
0
1
2
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
4
2
0
2
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
6
0
2
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
2
0
0
1
1
1
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
1
0
0
2
1
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
5
1
0
1
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
1
0
0
0
0
0
1
2
0
0
3
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
2
0
2
0
1
0
0
3
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
2
2
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
3
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
3
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
3
0
0
1
0
3
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
5
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
1
0
2
0
0
1
2
3
0
0
1
0
0
0
1
0
0
0
0
0
0
3
0
1
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
1
2
1
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
5
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
2
2
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
3
3
0
0
0
0
0
0
6
0
0
0
1
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
1
0
0
3
0
0
1
0
0
0
0
2
2
0
1
0
2
0
0
0
0
0
0
0
3
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
1
0
2
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
2
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
1
1
0
0
2
0
2
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
1
2
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
1
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
1
0
5
0
0
0
0
0
0
0
1
0
0
1
1
0
0
2
0
0
1
0
3
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
4
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
1
0
2
0
0
1
0
1
0
2
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
2
0
0
2
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
5
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
2
0
0
8
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
2
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
2
2
0
0
2
2
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
3
0
0
0
0
0
0
0
2
1
0
0
3
0
2
0
0
1
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
2
0
1
0
2
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
1
1
0
0
3
0
1
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
1
0
0
4
2
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
9
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
3
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
1
0
0
0
1
0
0
2
0
0
0
1
1
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
4
1
0
1
0
3
0
0
0
0
0
1
2
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
1
0
0
3
1
0
0
0
2
0
0
0
4
0
0
0
0
0
2
0
0
2
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
1
2
1
0
0
0
0
0
0
1
0
3
0
0
1
1
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
2
2
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
1
0
3
3
4
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
2
2
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
3
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
2
0
0
0
0
4
2
0
0
1
0
1
1
0
0
2
0
2
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
1
0
0
0
0
2
0
0
1
0
0
0
0
2
2
0
1
2
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
2
1
0
0
0
0
0
3
1
0
2
2
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
1
2
1
1
0
0
2
0
0
0
0
0
0
1
3
0
0
1
2
1
0
0
0
2
2
3
0
1
0
0
2
3
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
2
1
0
0
1
0
0
0
0
0
1
0
1
0
2
0
0
1
0
1
0
2
0
1
0
0
0
1
0
0
1
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
1
0
2
2
0
0
0
2
0
0
0
0
1
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
2
2
0
1
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
1
1
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
7
0
0
2
1
1
0
6
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
2
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
3
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
6
0
0
0
0
3
0
0
1
0
0
1
1
1
0
0
0
0
0
2
0
1
0
2
1
1
0
0
0
1
2
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
3
0
1
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
2
0
0
1
1
0
1
2
1
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
8
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
2
0
0
0
0
0
0
2
0
0
2
0
1
0
1
6
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
1
0
0
0
1
1
0
2
0
0
2
9
2
0
0
0
0
0
0
2
1
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
3
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
2
0
1
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
2
2
2
1
2
2
0
1
2
0
0
0
1
0
1
0
0
3
0
0
0
2
2
1
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
4
2
0
0
2
0
1
0
2
0
2
1
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
2
1
0
1
0
0
0
1
0
0
2
0
1
0
0
0
0
0
1
0
0
0
2
2
0
0
0
2
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
3
0
0
1
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
2
0
1
0
2
0
0
2
0
0
0
2
1
0
0
0
0
2
0
0
0
1
1
0
4
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
2
2
3
0
0
0
0
2
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
1
1
0
0
2
1
0
0
2
0
0
2
1
1
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
2
0
0
0
0
3
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
1
2
0
0
1
0
1
0
0
0
2
0
0
0
0
3
3
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
8
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
7
0
0
0
0
0
0
0
1
0
0
1
2
0
4
2
3
0
0
1
0
0
2
0
0
2
0
0
0
1
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
2
2
0
0
1
2
5
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
2
0
11
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
3
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
3
0
0
0
1
0
0
0
0
1
0
2
2
0
1
0
1
0
2
0
0
0
0
0
0
0
4
2
0
0
0
0
1
0
0
0
1
0
1
0
0
4
0
0
0
1
0
0
0
3
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
2
0
0
0
0
0
0
2
2
1
2
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
3
0
0
1
0
0
0
2
0
0
0
0
1
0
1
0
2
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
1
0
2
0
0
2
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
2
2
2
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
2
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
2
2
4
0
0
1
0
2
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
3
1
0
1
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
1
0
0
0
1
0
0
0
0
0
1
0
0
3
0
0
0
0
1
0
0
1
0
0
0
1
0
2
0
0
1
0
2
0
0
2
0
1
0
3
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
4
2
0
0
0
2
0
2
0
0
1
0
0
0
1
0
0
0
0
2
2
2
0
3
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
2
1
0
0
2
0
2
0
1
0
1
2
0
0
2
0
0
0
0
1
10
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
10
2
0
1
0
3
0
0
0
0
0
0
0
0
0
2
0
0
1
0
3
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
1
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
2
1
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
4
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
2
1
1
0
0
1
0
1
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
2
0
1
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
3
0
2
0
0
1
0
2
0
3
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
2
0
0
0
0
0
6
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
2
1
0
2
0
0
0
0
0
0
1
0
0
2
0
2
1
0
0
3
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
1
2
1
0
0
7
0
3
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
2
2
0
0
1
0
2
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
2
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
2
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
3
2
0
0
0
2
0
1
1
1
0
0
0
0
0
0
1
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
3
0
0
0
0
1
0
2
0
0
1
1
0
0
1
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
6
1
1
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
2
0
1
1
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
3
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
2
0
1
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
1
0
3
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
2
0
2
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
2
2
2
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
2
0
0
1
0
2
0
2
1
0
1
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
4
1
0
0
1
0
1
0
0
1
0
2
0
3
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
1
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
1
2
0
2
0
0
0
2
1
0
2
2
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
2
3
0
1
0
1
0
0
2
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
1
2
0
0
0
4
0
0
0
0
0
0
1
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
1
0
1
0
3
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
2
0
3
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
3
0
1
0
2
0
0
0
0
0
2
0
1
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
2
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
5
2
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
3
2
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
2
2
1
0
0
0
4
0
0
0
0
2
0
0
0
0
1
0
1
0
0
3
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
2
2
5
2
0
2
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
3
0
0
0
1
0
1
0
0
0
0
2
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
2
0
3
1
0
0
1
0
0
3
0
0
0
2
0
0
0
1
0
0
0
0
2
2
0
0
1
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
4
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
2
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
5
2
0
3
0
0
0
0
0
1
0
0
0
1
6
0
1
0
0
0
0
0
0
0
0
0
2
3
0
0
0
1
0
0
0
0
0
1
0
2
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
2
0
0
2
0
0
1
3
0
0
0
0
0
1
0
0
0
0
2
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
1
3
0
0
1
1
0
3
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
3
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
2
0
0
1
0
1
2
0
0
14
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
1
0
0
0
0
3
1
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
3
0
0
1
0
2
0
3
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
1
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
1
0
0
0
1
0
2
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
5
0
0
3
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
1
3
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
1
2
0
1
2
0
1
2
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
3
0
0
2
0
0
1
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
1
1
0
2
0
0
1
0
2
0
0
0
1
0
0
0
0
0
1
2
0
1
2
2
0
1
0
0
0
1
0
0
0
0
0
0
1
0
2
0
1
0
0
2
0
0
0
0
0
0
2
0
1
2
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
3
1
1
0
0
1
2
0
0
0
0
2
1
1
0
0
1
1
2
1
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
1
1
0
0
0
2
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
2
0
3
2
0
3
0
0
2
0
0
2
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
3
0
0
0
1
0
0
1
1
0
0
0
0
1
1
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
2
4
0
0
0
0
0
0
1
1
0
2
4
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
1
2
0
0
1
2
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
2
0
0
0
3
0
0
0
1
0
0
0
1
1
0
0
1
0
1
0
0
0
0
2
1
1
0
0
0
0
0
1
2
1
2
2
1
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
2
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
1
2
0
0
0
0
0
0
2
0
0
0
0
1
2
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
2
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
2
0
0
0
0
0
1
3
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
2
0
2
1
0
0
0
4
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
6
2
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
3
0
0
0
0
0
0
0
0
0
0
0
1
1
5
0
0
1
0
4
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
3
2
0
0
1
0
0
0
0
3
1
0
0
2
0
0
0
0
10
0
0
2
0
0
1
1
0
0
2
1
1
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
4
0
0
3
2
1
0
2
2
0
0
0
1
1
0
0
0
0
2
0
3
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
3
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
2
0
0
2
2
1
1
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
3
2
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
1
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
2
0
0
0
0
0
0
1
0
2
1
0
0
0
0
1
5
0
0
1
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
2
0
2
0
2
0
0
1
0
0
5
1
2
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
2
2
0
1
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
2
0
1
0
0
0
3
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
1
0
0
2
1
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
2
0
1
1
0
0
0
0
0
0
2
0
0
0
0
1
1
2
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
3
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
6
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
1
0
0
0
0
0
0
0
1
0
2
4
0
0
2
0
0
2
2
0
0
2
0
0
0
0
0
0
0
2
0
2
0
1
0
0
2
0
2
0
2
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
1
2
0
2
0
0
1
0
0
0
1
2
0
0
0
2
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
2
2
2
0
0
0
0
0
0
0
0
0
3
0
0
1
0
1
2
0
1
0
8
0
0
0
0
0
1
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
1
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
2
0
1
2
0
0
4
1
0
0
0
0
0
1
0
2
1
0
0
1
1
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
1
0
2
0
1
1
0
0
0
0
0
2
0
0
3
0
1
2
0
0
3
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
3
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
1
2
0
0
1
2
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
2
0
0
2
1
0
0
0
1
0
2
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
4
1
1
2
0
1
4
1
0
0
0
0
0
2
0
0
0
2
1
0
2
2
1
0
2
0
0
0
1
1
0
1
1
0
2
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
3
0
2
0
0
1
0
0
0
1
2
0
0
0
0
2
0
0
0
2
0
0
0
2
1
0
1
5
2
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
2
1
2
0
0
0
0
0
0
1
0
0
6
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
3
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
1
1
1
0
1
0
0
0
0
1
0
1
2
0
0
0
0
0
6
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
2
4
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
2
0
0
0
2
2
0
0
0
0
2
0
0
1
1
0
1
2
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
5
0
1
3
0
3
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
1
3
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
1
2
0
0
0
1
4
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
3
0
2
0
0
2
0
0
0
0
0
0
3
1
0
0
0
1
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
1
0
0
0
0
2
1
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
2
4
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
2
2
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
4
1
2
0
1
0
0
0
0
1
0
3
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
1
0
0
2
0
0
0
0
2
0
2
0
0
0
0
1
2
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
1
3
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
7
1
0
1
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
3
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
3
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
2
0
2
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
4
1
0
6
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
4
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
7
0
0
1
0
0
1
0
0
0
0
0
2
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
3
0
0
0
1
0
1
1
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
4
3
0
0
0
3
0
0
1
0
0
0
2
2
0
0
0
0
2
0
1
0
1
0
1
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
3
0
0
0
2
1
4
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
4
0
1
0
1
0
2
0
0
4
2
0
6
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
1
2
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
2
2
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
2
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
2
2
0
1
2
0
0
0
1
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
2
0
2
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
3
0
0
0
1
2
0
5
0
0
1
0
0
2
2
2
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
2
0
1
1
0
1
0
0
0
1
2
2
0
0
0
2
0
0
1
0
3
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
1
1
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
2
1
0
0
8
0
0
3
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
1
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
5
0
0
2
0
0
5
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
5
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
3
2
2
0
2
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
1
2
0
0
3
0
0
0
0
0
0
1
1
3
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
3
5
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
1
4
0
0
1
2
1
0
0
0
0
0
0
2
0
1
2
5
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
1
2
2
0
0
0
0
0
1
1
0
0
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
1
0
1
0
0
0
1
0
2
0
0
12
0
2
0
0
0
0
1
5
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
1
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
3
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
2
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
2
3
0
0
0
2
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
3
0
1
1
1
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
4
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
1
2
0
2
1
2
0
0
0
0
0
0
1
2
1
0
0
1
1
1
0
4
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
3
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
1
2
0
1
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
4
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
1
3
1
0
0
0
0
5
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
5
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
7
0
2
0
2
0
0
0
1
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
1
0
1
0
3
1
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
2
0
0
2
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
2
0
2
1
0
0
0
0
4
2
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
5
0
0
0
0
0
2
1
0
2
0
0
0
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
1
2
0
1
3
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
2
0
0
0
1
0
1
2
1
0
1
2
0
0
0
0
4
1
1
0
1
0
0
0
0
2
3
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
3
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
1
0
2
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
1
0
0
0
0
1
0
0
1
0
1
0
0
7
0
0
2
0
0
1
0
0
0
0
0
0
1
3
1
2
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
3
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
3
0
0
0
0
1
0
0
2
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
1
1
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
1
0
0
2
2
1
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
1
0
1
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
2
0
0
0
0
1
0
1
3
1
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
1
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
9
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
1
0
3
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
3
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
1
3
0
0
0
0
0
0
1
0
0
0
0
1
2
0
2
2
0
0
1
2
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
2
2
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
1
0
0
0
0
2
2
2
0
0
0
0
0
0
3
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
2
0
0
0
0
0
0
1
1
2
2
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
3
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
1
2
0
1
0
1
2
0
0
0
1
0
0
1
0
0
0
3
1
0
0
0
0
0
0
0
1
2
3
0
0
0
2
2
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
5
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
2
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
2
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
1
2
0
0
0
0
1
0
4
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
1
0
0
0
0
2
1
0
0
2
0
0
0
1
0
0
0
0
0
2
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
2
0
2
2
0
2
0
0
2
0
1
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
2
0
0
0
2
0
0
0
1
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
2
1
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
2
2
0
4
0
1
0
2
0
0
0
0
0
0
2
0
2
0
0
0
1
0
2
0
0
0
1
1
1
0
0
0
0
2
0
0
1
0
3
0
0
0
0
0
8
0
2
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
6
0
1
0
1
0
0
0
0
0
0
8
0
1
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
2
1
0
0
0
0
0
3
0
0
0
1
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
5
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
8
0
0
1
0
0
0
0
2
0
0
1
0
0
0
2
2
1
0
0
0
0
0
0
2
0
0
0
2
0
1
0
2
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
1
2
0
0
0
1
0
0
1
2
0
0
0
0
2
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
1
2
0
2
2
0
0
4
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
2
0
0
0
1
1
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
3
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
6
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
2
1
0
1
0
0
1
0
0
0
0
0
1
0
2
0
2
0
0
2
1
0
1
2
2
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
8
1
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
1
2
0
1
0
0
1
1
1
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
1
1
1
0
1
0
0
0
0
0
0
2
0
0
1
3
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
3
0
0
0
0
2
0
0
0
0
1
0
2
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
2
1
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
2
0
1
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
2
1
0
0
1
0
1
0
0
0
0
0
0
1
0
1
4
0
0
0
2
0
0
0
2
0
2
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
2
0
2
0
0
0
0
1
0
1
3
0
0
2
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
5
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
6
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
1
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
3
0
4
0
0
0
6
1
1
0
2
3
1
3
1
0
1
0
0
0
1
1
0
0
0
0
0
2
0
1
0
0
2
0
0
2
0
0
0
0
0
1
2
1
1
0
0
0
7
0
0
2
0
0
0
0
0
4
0
0
0
0
0
2
1
0
2
2
0
1
1
0
0
2
0
0
0
0
0
0
1
0
0
0
1
1
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
3
1
0
1
0
0
2
0
1
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
1
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
1
2
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
1
0
0
0
2
2
5
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
1
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
4
0
2
0
0
1
0
0
7
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
1
0
2
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
2
2
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
3
0
2
0
1
0
0
2
2
1
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
2
4
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
1
0
0
1
0
1
0
0
0
1
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
1
0
1
2
3
0
1
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
2
2
0
0
0
0
0
2
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
2
0
0
0
1
3
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
1
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
2
0
0
0
3
0
1
0
0
2
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
3
0
0
1
0
0
0
0
0
2
3
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
5
1
3
0
0
0
2
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
2
2
0
0
0
4
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
1
0
2
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
1
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
12
2
0
0
0
0
1
0
0
1
1
2
0
0
0
0
1
1
0
0
0
0
0
0
2
1
0
1
0
0
0
0
1
2
1
0
0
1
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
2
1
0
0
0
2
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
1
0
0
0
0
0
2
0
1
0
0
2
1
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
3
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
1
1
0
0
0
0
0
0
2
1
0
0
2
1
0
0
0
0
1
0
0
0
3
2
2
0
0
3
0
1
0
1
0
0
1
0
0
0
2
0
0
0
1
0
2
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
2
0
5
1
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
5
1
3
0
8
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
1
0
0
3
0
2
2
0
0
0
2
0
0
0
0
1
2
0
0
0
0
2
0
0
2
1
0
3
0
1
1
3
0
1
0
0
0
0
0
0
3
3
0
0
0
2
1
3
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
2
2
2
1
0
0
0
1
1
0
2
0
0
0
0
0
0
3
0
0
1
2
0
0
2
0
0
0
0
3
2
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
5
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
5
0
0
2
2
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
3
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
3
0
2
1
0
0
3
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
1
0
0
0
0
0
3
0
0
1
0
0
1
0
2
0
0
0
0
2
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
4
1
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
1
2
0
2
0
3
0
0
0
0
0
0
0
3
0
2
0
2
1
0
0
0
0
1
3
0
2
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
7
0
0
2
2
0
0
0
1
1
0
0
0
2
4
0
2
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
7
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
2
0
0
2
0
3
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
1
0
1
2
1
0
0
0
0
1
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
1
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
1
0
2
0
2
0
5
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
4
0
1
3
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
3
1
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
1
0
2
2
0
0
0
3
0
0
0
1
0
1
0
0
0
1
0
0
1
3
4
0
1
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
2
1
0
0
1
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
2
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
1
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
2
1
2
5
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
4
0
2
0
0
0
0
2
2
0
4
2
0
0
0
0
0
0
0
0
0
0
0
0
1
7
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
1
0
1
2
0
0
2
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
3
1
0
1
0
0
2
0
2
1
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
2
0
1
1
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
3
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
1
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
4
0
0
2
0
0
2
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
1
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
1
3
14
0
0
1
1
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
2
0
2
0
0
0
0
0
0
1
2
0
0
0
2
1
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
3
0
0
2
2
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
2
0
0
1
1
0
0
0
0
0
0
1
0
0
1
2
0
0
0
1
1
1
0
2
0
0
0
0
2
0
1
0
2
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
2
1
4
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
1
2
0
2
2
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
1
0
1
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
1
0
0
1
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
2
2
0
0
0
0
1
0
0
0
0
0
2
2
2
0
0
1
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
2
0
0
1
0
1
1
2
0
0
0
0
0
2
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
1
1
0
2
0
2
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
1
2
3
0
1
0
0
0
0
2
2
2
2
2
1
2
0
1
1
0
0
7
2
0
1
2
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
3
1
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
1
0
2
0
2
0
2
0
0
0
0
2
2
2
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
1
0
0
0
2
2
0
0
2
0
0
0
0
0
3
0
0
0
0
0
2
0
0
1
0
0
0
0
0
4
0
2
2
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
3
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
3
0
0
0
0
2
0
1
5
1
1
1
0
2
0
0
1
2
2
0
0
0
2
2
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
4
3
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
1
3
0
0
0
0
0
1
0
1
0
3
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
2
0
0
2
0
0
0
1
0
0
0
3
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
4
2
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
2
0
0
2
0
0
0
0
0
0
2
0
0
0
1
2
0
2
1
0
0
0
2
2
2
0
0
2
0
0
2
0
3
0
1
0
1
0
0
1
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
1
0
2
0
1
0
2
0
0
0
2
0
2
0
0
0
0
0
1
0
2
2
0
1
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
1
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
3
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
3
2
0
0
0
0
0
1
3
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
3
0
0
0
2
1
0
2
2
0
0
0
0
0
1
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
3
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
2
1
0
1
0
2
0
0
0
0
0
0
0
3
0
2
1
2
2
1
1
2
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
1
2
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
6
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
1
2
2
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
1
1
1
0
1
0
0
0
1
1
2
0
0
0
0
0
0
2
0
0
1
0
1
0
2
0
0
0
2
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
3
0
2
0
0
0
0
0
2
0
0
2
0
0
0
1
0
1
0
2
0
0
0
2
0
0
2
2
0
3
0
0
3
0
0
1
0
1
0
1
0
2
0
1
4
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
3
0
0
0
0
0
0
2
0
0
1
1
1
0
0
1
0
0
0
0
3
0
0
0
1
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
4
0
0
2
0
2
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
1
1
2
4
0
1
2
1
0
0
0
1
1
0
0
0
0
0
1
1
0
2
2
2
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
4
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
2
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
2
0
1
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
5
0
0
0
0
2
3
0
0
0
0
4
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
5
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
1
0
1
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
1
0
0
1
0
2
0
2
1
3
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
1
1
0
0
2
0
0
0
1
2
0
0
0
0
0
0
1
0
1
0
13
1
1
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
4
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
4
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
1
1
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
1
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
3
0
0
0
0
0
0
1
0
2
0
0
0
1
1
0
0
0
0
3
0
0
0
0
2
0
1
0
0
1
0
2
1
0
0
0
2
2
0
0
0
0
0
1
0
0
0
2
0
2
1
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
2
0
2
0
3
0
0
0
1
0
0
2
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
1
0
1
0
1
1
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
1
1
0
0
0
2
0
1
0
1
1
0
2
0
0
0
0
0
2
0
1
0
0
2
2
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
1
0
0
2
0
2
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
6
0
1
1
1
0
0
0
0
0
2
0
0
0
0
1
2
0
0
2
2
0
0
0
0
0
0
1
0
0
1
0
0
0
4
0
0
1
1
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
4
3
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
5
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
3
0
0
2
5
0
2
0
0
0
1
0
0
0
0
0
3
2
0
2
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
2
0
2
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
2
0
0
0
3
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
4
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
6
0
0
0
1
0
0
1
0
1
0
0
0
0
0
3
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
2
2
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
2
0
2
0
0
3
0
0
0
0
1
2
0
4
0
1
0
2
0
0
0
1
2
1
0
0
0
0
0
0
1
2
1
1
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
2
0
0
1
1
2
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
2
1
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
2
1
0
0
0
1
0
2
1
0
0
0
0
1
0
0
1
0
0
0
0
1
2
0
1
0
0
2
0
0
4
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
5
0
2
0
0
2
2
2
0
0
0
0
1
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
2
0
1
3
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
2
2
0
1
2
0
0
0
2
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
1
1
0
2
0
1
0
0
1
1
0
0
0
2
0
0
1
1
0
0
0
0
2
0
0
0
2
0
0
0
0
5
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
2
1
1
1
0
0
0
0
0
1
1
2
3
0
0
0
0
2
1
0
0
0
2
0
2
0
0
3
0
0
0
1
0
0
0
2
0
1
3
0
0
0
2
0
1
0
0
0
0
2
0
0
0
2
2
0
0
0
0
1
1
0
0
2
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
4
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
2
0
1
0
0
2
0
0
0
0
2
1
2
1
0
0
0
2
0
0
1
3
1
2
0
0
2
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
2
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
1
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
2
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
2
0
0
1
0
0
1
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
1
1
0
0
2
0
2
3
0
0
1
0
0
1
0
2
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
2
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
1
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
9
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
1
1
1
0
0
1
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
2
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
2
2
4
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
3
5
0
0
8
0
0
0
0
0
0
0
0
0
0
0
9
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
3
0
1
0
2
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
1
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
6
0
0
0
3
0
0
0
0
2
0
0
0
2
0
0
2
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
1
0
0
2
2
0
0
0
0
0
2
0
0
1
0
2
0
0
0
1
0
0
2
0
0
0
2
0
1
0
0
0
0
2
5
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
8
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
2
0
4
0
2
0
2
0
1
2
0
0
0
1
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
4
2
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
1
1
1
0
3
0
0
0
1
2
1
2
4
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
3
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
2
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
2
0
1
0
2
1
1
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
2
1
0
0
1
0
2
0
0
1
1
2
2
1
2
0
0
0
3
2
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
2
2
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
6
1
0
0
0
4
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
3
1
2
1
0
0
1
2
0
1
1
1
0
0
2
0
1
0
1
2
0
0
0
0
2
0
5
0
0
4
0
1
0
0
1
0
0
1
0
1
0
0
0
0
3
0
9
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
2
3
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
2
0
2
1
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
9
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
2
1
1
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
2
0
2
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
1
1
0
1
0
3
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
2
0
1
0
0
0
0
2
0
1
1
2
0
0
1
0
2
0
0
0
0
0
0
2
7
0
0
0
0
0
1
2
1
1
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
1
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
1
2
0
1
0
1
0
2
0
0
0
2
2
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
2
0
0
0
6
0
7
0
0
0
0
1
0
0
2
3
0
0
0
2
0
0
2
0
0
0
2
1
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
3
1
0
0
2
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
3
0
0
0
0
0
1
0
0
0
2
0
0
0
1
2
0
0
0
0
2
0
0
0
2
0
0
2
0
0
1
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
3
0
0
4
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
3
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
2
2
0
2
0
0
0
0
2
2
0
0
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
4
0
0
0
0
0
2
0
1
3
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
2
5
0
7
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
2
2
0
2
0
2
0
2
0
1
0
0
1
0
0
1
0
0
0
2
0
0
0
2
1
0
1
0
3
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
3
0
0
2
0
0
5
0
1
0
0
0
1
1
3
0
0
0
1
5
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
1
0
2
2
1
0
0
0
0
0
0
0
2
2
2
4
0
0
0
0
0
0
0
0
0
1
0
0
0
5
0
3
1
1
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
1
0
0
0
0
4
0
2
0
0
0
0
2
3
0
0
0
0
1
0
2
1
0
0
2
0
0
0
3
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
1
1
1
0
1
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
4
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
2
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
4
1
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
1
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
1
0
0
0
1
2
1
0
0
1
0
0
0
0
0
5
0
1
2
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
2
2
3
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
5
0
0
0
0
0
0
0
0
1
0
0
1
2
2
0
0
2
0
1
1
0
0
2
2
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
1
1
0
2
1
1
0
0
0
1
0
0
0
0
1
2
1
0
0
0
0
1
0
0
3
0
0
2
0
1
2
0
0
2
0
0
2
0
0
0
3
0
0
0
0
1
0
1
1
4
0
0
0
4
0
0
1
0
0
0
4
0
0
1
0
0
0
0
0
0
2
0
0
0
1
2
0
0
1
0
1
0
2
0
0
1
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
2
1
0
0
0
0
0
0
0
1
2
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
1
2
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
2
0
1
0
0
2
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
1
0
1
0
0
0
0
2
2
1
2
0
2
0
0
0
1
2
0
0
0
2
1
0
0
1
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
2
1
1
0
0
0
0
0
0
0
2
1
1
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
1
0
0
1
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
1
0
0
0
1
2
2
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
2
0
2
0
3
1
0
1
0
0
0
3
0
1
2
2
0
1
0
0
0
0
0
0
0
3
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
1
1
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
2
2
0
0
0
0
1
0
0
3
2
0
0
1
0
1
0
0
0
0
1
0
0
1
2
0
1
0
0
1
0
2
0
0
0
0
1
4
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
3
0
0
1
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
3
1
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
2
0
0
6
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
2
1
0
0
2
2
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
1
0
0
3
0
0
1
0
1
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
1
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
1
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
5
2
0
0
0
2
0
0
0
1
1
0
1
0
2
0
0
2
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
2
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
4
4
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
2
2
0
1
0
0
1
1
0
0
1
1
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
1
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
2
0
0
0
2
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
2
0
0
0
0
0
2
2
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
2
0
2
0
2
0
0
1
0
0
0
0
0
1
12
1
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
2
0
0
0
3
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
3
0
2
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
6
2
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
2
0
0
0
0
0
2
1
0
0
0
0
2
2
2
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
1
2
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
1
2
0
1
2
0
3
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
6
1
0
1
0
0
1
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
2
0
1
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
2
0
0
2
0
1
1
2
0
0
0
3
0
0
0
0
0
0
2
0
0
1
0
0
0
4
0
0
0
0
1
2
0
0
0
0
2
0
0
0
1
1
1
0
0
2
0
0
0
4
2
1
0
0
2
1
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
2
0
1
2
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
3
0
0
0
0
0
0
7
2
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
1
0
1
6
1
0
0
0
0
0
3
0
1
0
2
1
0
0
2
0
1
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
1
2
2
0
0
2
0
0
0
0
0
1
0
1
0
0
0
2
0
2
0
3
0
0
0
0
0
0
0
1
3
0
0
0
0
0
1
0
3
0
0
0
0
0
1
2
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
2
1
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
2
2
0
0
0
0
1
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
3
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
8
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
2
1
2
0
3
1
3
0
0
0
1
0
2
0
4
0
0
2
4
3
0
0
1
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
2
4
0
0
0
0
0
1
1
0
0
0
0
1
2
2
4
0
0
1
0
0
4
2
2
1
2
0
0
0
2
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
5
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
5
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
4
1
2
0
0
0
0
0
0
0
0
1
0
0
1
0
1
2
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
1
0
0
2
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
3
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
1
0
0
0
0
0
0
2
2
2
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
2
2
5
1
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
2
0
0
0
0
0
0
0
0
1
0
6
2
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
2
0
2
1
1
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
3
1
0
1
0
0
0
0
2
0
0
2
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
2
3
0
2
0
0
2
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
3
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
3
0
0
1
0
0
1
0
0
0
2
0
2
0
2
0
0
0
0
1
0
2
2
0
0
0
0
1
0
0
0
1
1
2
0
1
0
1
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
5
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
1
2
0
0
1
0
0
0
7
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
2
2
0
0
0
0
1
0
0
0
2
0
2
0
0
2
1
1
2
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
2
0
0
1
0
0
2
0
1
0
0
0
9
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
2
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
4
1
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
3
0
2
1
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
1
1
0
0
1
0
0
2
0
2
1
0
0
1
0
0
1
0
5
0
0
0
0
0
1
0
2
0
0
1
1
1
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
2
1
0
2
0
0
1
2
0
2
0
0
0
0
1
0
0
2
2
0
0
0
3
2
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
1
0
2
3
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
4
0
0
1
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
3
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
2
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
1
0
3
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
4
2
1
1
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
1
2
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
1
0
0
1
0
0
0
2
2
0
0
2
0
3
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
2
0
0
0
0
0
1
2
0
1
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
1
2
0
2
2
3
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
2
2
0
0
1
0
0
0
0
0
3
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
1
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
1
2
0
1
1
0
1
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
1
0
2
2
1
0
0
1
0
0
0
4
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
1
2
2
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
11
0
3
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
1
9
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
2
2
1
0
1
0
0
0
0
0
2
0
5
0
0
2
1
0
0
1
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
3
0
0
0
1
0
0
2
0
1
0
0
0
3
1
0
0
2
2
1
0
2
1
0
1
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
1
0
0
0
0
1
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
2
3
0
1
0
2
0
2
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
3
0
2
4
0
0
0
0
0
0
3
2
1
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
2
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
1
0
5
0
0
0
2
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
1
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
1
2
0
0
0
1
1
0
0
0
2
11
0
0
0
1
0
5
0
0
1
0
2
0
0
0
0
5
0
2
0
2
0
0
3
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
2
0
0
0
0
0
2
0
0
2
0
2
1
8
0
1
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
1
0
2
0
0
0
6
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
3
0
1
1
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
1
0
1
2
0
0
0
2
0
1
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
2
0
0
2
0
2
0
2
0
0
0
2
0
2
0
1
0
0
2
0
0
0
1
2
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
4
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
3
0
0
0
1
0
2
0
0
2
2
0
0
2
2
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
1
0
2
0
0
3
2
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
2
0
0
0
1
1
0
1
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
5
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
2
0
2
0
0
0
0
1
1
2
0
0
0
0
0
1
1
1
0
2
0
1
2
1
0
0
0
0
3
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
1
0
3
2
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
7
0
0
2
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
2
0
0
2
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
2
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
2
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
8
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
4
1
0
0
3
0
0
0
2
0
1
0
0
0
2
8
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
3
2
0
0
1
0
1
2
1
0
0
0
2
0
1
0
0
1
1
1
0
0
2
0
0
2
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
2
0
0
2
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
1
3
3
0
0
2
2
0
0
2
0
2
0
0
0
0
2
1
0
0
0
1
0
0
1
1
0
0
0
0
2
0
2
0
0
2
0
0
2
0
0
0
1
1
0
2
2
1
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
3
0
2
0
1
2
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
5
0
1
1
0
0
2
0
0
0
0
0
0
0
2
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
3
0
0
0
0
2
0
1
1
1
0
1
2
1
0
2
1
0
1
0
0
0
1
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
4
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
1
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
1
0
0
0
2
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
2
1
0
0
0
0
0
0
0
2
2
1
0
4
0
0
0
0
0
0
0
3
0
1
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
1
0
1
1
0
0
5
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
3
0
2
2
0
0
4
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
1
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
3
2
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
3
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
2
2
4
0
0
0
2
2
5
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
2
1
0
0
2
1
0
1
0
0
0
0
0
0
1
0
1
1
1
0
0
0
2
3
0
1
0
0
0
1
0
0
0
1
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
1
0
0
0
2
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
1
2
0
0
0
0
0
0
0
1
0
3
1
1
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
2
1
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
1
0
0
2
0
1
1
0
0
2
0
1
0
0
0
1
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
2
1
0
0
1
0
1
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
1
0
0
0
0
1
0
0
3
0
0
0
1
0
2
2
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
1
0
1
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
1
0
0
0
1
0
0
1
0
0
0
0
2
0
1
0
1
1
0
0
0
0
2
1
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
1
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
1
3
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
1
2
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
1
1
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
2
0
1
2
0
0
0
1
0
0
1
0
0
2
0
2
0
0
0
1
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
3
2
0
0
0
1
0
3
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
3
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
2
0
0
0
0
7
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
2
1
0
2
2
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
2
0
0
4
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
2
0
0
0
3
0
2
0
0
2
0
2
0
2
0
0
2
0
1
0
0
0
3
0
0
2
2
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
4
0
0
2
2
0
2
1
0
0
0
2
0
0
0
0
0
0
0
1
4
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
2
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
2
1
2
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
4
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
1
2
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
2
0
0
3
0
0
1
0
3
0
2
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
3
0
0
0
2
0
0
0
1
0
7
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
1
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
5
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
9
0
0
0
0
2
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
1
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
2
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
1
0
0
0
1
0
0
1
2
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
1
0
0
2
0
1
0
1
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
2
1
1
1
0
0
0
0
0
2
0
1
0
0
1
0
1
4
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
5
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
1
0
0
0
1
2
0
0
0
2
2
2
0
0
0
1
0
0
0
0
0
1
1
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
1
3
0
0
0
0
1
0
2
0
4
0
0
1
0
0
0
0
0
0
0
2
0
0
1
1
2
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
2
1
2
1
0
1
0
0
0
8
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
10
0
0
1
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
1
2
1
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
2
2
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
2
0
0
2
0
0
0
1
1
0
2
0
1
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
1
1
0
2
0
0
3
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
2
1
0
0
0
0
2
0
2
1
2
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
2
0
0
0
2
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
5
0
0
0
0
2
1
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
1
2
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
2
0
3
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
6
0
0
2
0
0
4
2
0
1
2
0
0
0
0
0
0
1
0
4
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
3
2
0
1
1
0
0
0
2
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
2
0
1
3
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
1
2
0
0
0
0
1
0
1
2
2
2
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
2
0
2
0
1
2
0
0
4
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
1
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
2
3
0
0
0
0
0
1
0
2
0
3
1
0
0
0
0
1
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
2
0
0
0
0
2
0
0
0
2
0
2
2
0
0
0
0
3
1
0
0
3
0
0
0
4
0
0
0
0
0
2
1
2
1
1
1
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
2
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
5
2
0
0
0
1
0
0
0
2
2
0
1
0
1
0
0
0
0
0
0
0
0
0
1
4
1
1
1
0
0
0
0
1
2
0
0
0
1
1
0
0
2
0
2
0
0
0
0
3
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
2
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
1
0
2
1
2
1
0
2
1
1
0
0
0
2
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
1
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
4
0
2
0
0
0
0
1
2
2
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
6
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
1
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
3
0
0
0
1
2
0
2
0
0
1
0
0
0
0
2
4
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
1
0
0
0
2
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
1
0
0
1
1
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
2
0
0
2
0
2
0
0
1
0
1
0
2
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
2
0
2
0
0
3
0
1
0
1
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
3
0
1
0
1
0
0
0
0
0
1
0
0
2
1
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
6
0
0
1
0
1
1
0
0
0
1
3
0
0
0
2
2
3
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
1
2
0
0
1
0
0
0
1
0
2
2
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
1
7
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
2
0
0
4
0
0
2
2
2
0
0
0
7
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
3
1
0
0
1
0
1
0
3
0
0
1
0
0
0
0
0
1
1
0
0
1
0
2
1
3
0
0
0
1
0
1
1
0
1
0
0
0
0
0
2
0
2
1
1
0
2
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
2
1
0
0
0
0
1
3
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
4
1
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
2
0
0
2
0
0
0
1
7
0
0
2
0
0
0
0
0
1
1
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
1
1
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
4
2
0
1
2
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
4
0
2
0
0
1
0
0
0
1
0
3
0
1
3
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
6
0
2
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
7
2
0
2
1
1
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
4
0
2
0
0
1
1
0
0
0
0
0
2
0
0
0
2
2
2
0
0
0
0
2
0
2
1
1
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
2
1
2
0
1
0
1
0
1
0
1
0
0
4
0
0
0
0
0
0
1
1
0
0
0
1
0
2
2
0
0
0
0
2
2
0
0
2
3
0
0
3
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
3
1
0
0
0
3
0
1
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
2
1
0
0
1
1
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
2
0
2
0
0
2
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
1
0
0
2
1
0
0
0
0
0
0
3
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
1
0
3
0
1
2
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
2
2
0
1
0
2
0
0
0
0
2
0
0
0
0
2
0
0
1
2
0
2
2
2
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
1
0
1
0
0
2
0
2
0
1
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
3
0
2
0
0
0
0
0
1
0
5
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
1
2
2
2
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
2
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
1
0
0
1
0
0
0
0
0
1
2
1
3
0
0
0
0
0
1
0
1
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
3
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
3
0
0
2
2
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
2
1
1
0
1
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
2
0
4
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
2
0
1
0
0
3
0
1
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
2
2
0
2
0
0
2
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
2
1
0
2
0
2
2
2
2
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
1
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
2
0
0
0
2
0
0
1
0
0
1
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
3
1
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
1
0
0
3
0
1
0
0
2
0
0
0
1
0
1
0
0
0
0
1
0
0
1
2
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
1
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
1
0
0
1
0
1
2
0
0
1
0
2
0
0
0
0
2
1
0
1
0
1
0
1
1
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
1
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
2
1
0
0
0
0
1
0
0
1
0
0
0
0
2
0
9
0
1
0
1
2
2
0
0
0
0
0
0
0
0
0
2
1
1
0
1
1
2
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
3
0
0
1
0
0
3
2
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
2
2
2
3
0
1
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
2
2
2
0
2
0
4
2
0
0
0
0
0
0
4
0
2
0
3
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
1
0
0
0
3
0
3
0
0
0
0
0
1
0
3
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
3
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
1
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
2
1
4
2
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
3
1
1
1
2
0
2
0
0
1
0
1
2
0
0
0
0
0
2
0
2
0
3
0
0
1
1
0
0
0
0
3
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
1
0
0
2
1
0
0
0
2
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
3
1
0
0
2
1
0
0
2
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
9
1
0
1
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
1
2
0
0
2
1
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
2
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
1
4
0
1
0
0
5
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
2
0
0
2
0
0
2
0
2
0
0
1
0
1
0
1
3
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
2
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
3
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
1
1
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
1
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
5
0
1
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
1
0
0
1
2
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
1
1
0
0
0
0
0
3
2
1
0
0
1
0
0
2
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
2
0
2
1
0
1
2
1
0
1
2
2
0
2
0
2
0
0
0
5
0
0
2
0
0
0
0
2
0
0
1
1
3
0
0
9
0
7
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
2
1
0
0
0
2
1
0
0
1
0
1
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
2
3
0
2
0
0
0
0
0
0
3
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
3
0
1
0
0
0
0
0
0
0
3
0
0
0
1
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
4
0
4
0
1
0
0
0
4
1
0
0
3
0
0
2
0
0
0
3
0
2
1
0
1
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
6
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
5
0
0
2
0
0
0
0
0
0
2
0
1
1
0
0
2
0
1
0
2
0
1
1
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
1
0
2
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
2
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
5
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
6
2
0
0
0
0
0
0
1
2
0
0
0
6
1
0
0
0
3
0
0
0
0
0
1
0
2
1
0
3
0
0
0
0
0
0
0
0
2
1
1
2
1
0
0
1
0
2
1
0
0
0
0
2
0
2
5
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
1
0
0
0
0
2
0
2
2
2
0
0
1
1
3
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
7
2
0
0
0
0
1
0
2
0
0
0
0
4
3
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
3
0
0
0
0
2
2
0
0
1
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
4
1
0
0
0
1
2
0
2
0
0
0
0
2
0
1
0
0
0
2
1
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
1
2
0
2
0
0
0
0
3
0
0
2
5
1
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
1
1
2
0
0
0
2
0
0
2
0
2
0
0
0
1
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
1
2
0
0
0
0
9
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
3
0
0
1
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
2
2
0
0
0
0
3
0
1
2
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
2
2
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
2
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
1
0
0
0
0
1
0
0
2
0
1
0
0
0
2
2
0
0
0
2
0
2
1
0
0
0
0
3
0
2
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
2
0
1
0
0
0
0
2
2
3
0
0
0
0
0
2
0
2
0
2
2
0
3
0
0
1
0
2
0
0
4
2
0
2
2
1
0
2
2
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
1
0
4
0
1
1
0
0
0
2
2
0
0
0
0
1
0
0
2
2
0
0
0
6
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
2
0
0
1
2
1
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
3
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
1
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
2
0
0
0
1
0
2
0
0
2
1
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
3
0
0
0
1
0
2
0
0
4
0
0
0
0
1
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
2
2
0
0
0
0
0
0
2
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
2
3
3
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
1
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
1
2
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
4
0
0
0
2
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
1
0
2
0
0
1
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
1
0
2
0
2
1
1
0
2
1
2
1
0
0
2
0
1
0
0
0
2
0
1
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
9
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
3
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
2
3
2
0
0
0
1
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
3
0
0
1
1
0
0
0
0
0
0
0
1
2
0
0
0
0
1
7
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
2
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
3
0
0
2
1
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
1
0
0
1
3
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
2
0
2
1
0
2
1
0
0
0
0
1
0
0
3
0
0
1
1
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
6
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
3
0
0
0
1
0
0
0
0
0
1
2
0
2
0
0
0
2
0
2
0
2
0
0
1
3
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
3
0
3
0
0
0
2
0
0
2
0
2
2
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
1
2
0
0
0
2
1
0
0
0
0
2
0
0
0
0
2
2
0
0
0
1
2
2
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
5
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
3
1
2
0
0
0
2
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
4
2
0
0
1
1
0
0
0
0
2
0
0
0
2
0
0
0
0
1
2
2
0
0
0
0
2
0
0
0
0
0
0
2
1
0
1
0
1
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
3
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
1
3
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
1
1
2
0
1
1
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
1
0
0
0
1
1
0
0
2
2
2
0
0
0
0
0
1
2
0
0
0
1
0
2
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
2
0
3
0
0
2
0
0
1
0
2
1
0
0
0
2
0
0
1
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
9
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
3
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
3
0
2
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
3
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
6
2
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
2
1
1
0
0
0
2
0
0
0
0
1
0
3
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
2
3
0
1
0
6
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
1
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
3
1
0
1
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
3
0
2
1
0
0
0
0
1
0
0
0
2
0
0
0
0
3
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
4
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
6
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
1
0
2
1
2
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
2
1
0
2
0
1
0
0
0
0
0
0
1
0
0
0
2
0
2
0
1
0
0
0
0
0
0
2
2
0
2
4
0
0
3
0
0
0
0
1
1
0
0
0
1
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
1
0
2
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
1
0
0
0
1
2
2
0
0
1
0
0
0
0
2
0
0
0
3
0
0
1
2
3
0
4
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
3
0
2
2
6
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
1
0
0
0
2
0
0
1
0
1
0
0
0
1
1
0
2
1
1
1
0
1
0
0
0
0
0
2
1
0
0
0
0
0
1
2
0
0
1
0
1
0
2
2
2
1
0
1
0
1
0
1
0
1
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
1
0
2
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
3
0
1
0
0
0
0
2
0
0
0
0
1
2
2
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
4
1
0
0
0
1
0
0
0
0
0
3
2
0
0
0
1
1
0
0
4
0
0
0
0
0
0
0
0
0
2
1
0
0
2
1
2
0
0
0
0
1
0
0
2
0
0
0
0
1
0
3
0
0
0
0
0
0
1
1
0
0
3
1
0
0
0
0
1
0
0
1
0
2
0
1
0
0
1
0
0
2
0
0
1
1
2
0
2
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
3
0
0
0
0
0
0
0
1
8
3
0
0
0
0
0
2
0
0
1
2
2
0
2
1
0
1
2
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
6
0
0
0
0
0
2
1
0
0
2
0
0
4
0
0
4
1
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
1
1
0
1
0
0
0
0
0
2
3
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
1
0
2
1
1
1
0
0
0
0
0
2
0
0
1
0
0
0
2
0
2
0
0
0
0
2
2
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
1
2
0
0
0
1
10
0
2
8
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
4
0
0
0
0
0
0
2
1
0
2
4
2
2
0
0
2
0
0
0
0
0
0
0
0
6
0
0
0
0
0
4
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
1
0
1
0
2
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
1
1
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
2
2
2
0
1
2
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
1
2
1
0
0
1
0
0
2
0
2
0
1
0
3
2
0
4
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
2
0
0
0
4
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
1
0
0
0
1
2
0
0
0
2
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
3
0
0
1
0
3
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
1
1
2
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
2
2
0
0
2
0
0
0
3
2
0
1
0
0
0
0
3
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
3
1
0
1
0
0
0
2
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
2
0
0
0
1
0
2
0
1
0
0
2
0
0
0
1
0
0
1
0
2
1
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
5
2
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
2
2
0
0
0
0
0
0
3
0
0
0
0
0
0
2
1
0
0
0
0
0
1
2
0
0
0
0
0
1
1
4
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
3
0
0
1
0
1
0
1
0
0
1
3
0
2
0
0
0
0
0
1
1
0
0
0
2
0
0
0
1
0
0
0
0
1
1
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
2
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
1
2
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
1
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
1
0
0
0
0
0
0
0
0
1
0
0
5
0
8
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
3
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
1
0
2
0
2
0
0
0
0
2
2
1
0
1
3
0
0
2
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
1
0
0
5
1
4
0
1
0
0
0
0
0
2
1
0
0
2
1
0
0
1
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
2
0
0
2
0
4
1
2
0
0
2
0
2
0
0
0
0
0
0
2
3
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
2
0
0
0
0
6
0
2
0
0
2
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
1
0
0
0
1
0
0
2
0
1
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
2
0
0
0
1
2
4
3
2
1
2
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
2
0
1
0
0
2
1
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
2
0
3
0
0
0
0
0
0
2
2
0
0
1
0
0
0
2
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
4
1
0
1
0
0
0
1
3
0
0
0
1
1
0
1
0
0
0
0
2
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
2
0
1
0
2
0
0
0
0
0
2
0
1
1
2
0
0
0
0
0
1
7
0
0
0
0
0
3
0
0
1
0
0
2
1
0
0
0
1
0
0
0
0
0
1
0
2
0
1
0
0
0
0
1
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
4
1
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
5
0
0
0
2
0
0
0
0
2
0
1
0
0
2
0
2
0
0
0
0
1
3
0
0
1
3
2
0
0
1
0
1
1
0
1
0
0
2
0
1
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
4
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
1
1
2
0
0
1
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
1
0
1
0
0
0
2
0
0
3
0
2
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
2
0
0
0
0
0
0
7
0
1
0
0
0
0
0
0
2
2
2
1
0
1
0
0
2
5
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
1
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
2
0
1
1
3
0
1
0
0
0
1
0
0
2
0
0
0
1
4
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
1
0
2
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
2
0
2
1
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
3
0
3
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
2
0
3
1
3
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
5
1
0
0
0
0
0
2
3
0
0
0
0
0
1
0
0
1
0
2
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
2
5
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
2
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
2
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
6
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
2
0
2
2
0
1
0
1
3
0
0
1
3
0
0
0
0
0
2
0
0
0
0
2
0
1
0
1
0
0
0
2
0
0
1
0
0
1
0
0
1
0
0
0
0
1
1
0
0
2
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
2
1
0
0
1
0
1
2
0
0
1
0
0
0
1
0
0
0
2
0
0
0
1
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
3
0
1
2
0
0
0
0
1
3
0
0
4
0
1
1
2
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
1
3
0
0
0
2
0
1
2
0
0
0
0
11
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
1
0
0
0
1
1
0
0
0
0
1
2
0
0
0
0
1
0
0
0
1
2
0
0
0
0
1
0
0
2
1
0
0
1
0
0
2
0
0
3
0
0
0
0
10
1
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
2
2
2
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
3
2
0
0
0
0
0
3
0
1
2
0
2
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
2
0
0
0
1
1
2
0
0
1
0
0
2
0
0
0
0
0
0
5
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
1
1
0
0
0
2
2
0
2
0
0
0
0
0
1
0
1
0
0
2
0
0
0
1
2
6
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
4
1
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
3
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
3
1
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
2
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
1
3
0
0
0
2
1
1
0
1
2
1
0
0
0
2
0
0
0
0
0
2
0
0
3
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
4
2
3
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
2
0
1
2
0
0
0
0
0
0
0
2
0
0
0
3
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
2
2
1
0
2
0
0
5
0
1
0
1
0
0
0
0
0
0
0
3
0
1
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
3
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
3
2
0
4
2
0
0
0
2
2
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
2
1
2
0
0
1
0
0
0
0
0
0
0
1
1
2
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
2
0
1
0
0
1
1
1
0
3
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
3
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
2
0
2
0
0
0
2
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
4
0
2
3
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
1
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
1
1
0
2
0
0
2
0
0
0
0
3
0
0
0
0
0
2
1
1
0
2
0
0
0
1
1
0
0
0
2
0
0
0
0
0
1
0
1
0
0
2
0
0
8
0
0
1
0
0
0
1
0
0
3
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
1
0
0
0
1
3
0
8
3
0
1
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
1
0
1
0
1
0
1
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
7
0
2
0
2
0
0
2
0
0
0
2
0
4
1
0
2
0
0
0
0
0
2
0
0
3
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
5
0
1
0
0
0
0
0
0
0
2
0
3
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
1
0
1
0
0
1
2
1
2
1
2
0
0
0
0
2
0
0
2
0
0
2
5
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
1
0
0
0
1
0
0
2
0
1
0
1
1
0
0
0
0
0
1
0
0
0
2
0
5
1
0
0
0
0
0
0
0
0
0
4
2
2
0
0
0
1
0
0
0
0
2
0
0
0
1
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
5
0
0
2
1
0
0
0
0
0
2
3
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
2
0
3
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
2
6
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
3
0
2
1
0
1
0
0
1
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
1
0
1
0
2
0
2
0
0
1
0
0
2
0
0
0
2
0
0
0
3
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
2
0
2
0
0
1
2
0
1
0
0
2
0
0
0
2
1
0
2
1
2
0
0
0
2
0
1
1
2
0
0
1
0
0
0
0
0
0
0
2
0
2
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
2
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
3
2
0
0
0
0
0
1
0
1
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
5
2
0
1
1
0
0
2
0
0
0
0
0
0
2
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
4
0
0
0
0
0
2
0
2
0
0
1
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
1
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
2
1
0
0
0
0
0
0
4
0
0
0
2
0
0
4
0
0
3
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
2
0
1
0
0
1
2
2
0
0
1
2
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
2
1
0
3
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
2
2
0
7
0
2
1
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
5
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
3
0
0
0
1
0
2
1
1
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
3
0
0
0
0
0
0
1
1
1
0
1
0
1
1
0
0
0
0
0
2
0
0
1
1
2
0
0
1
1
2
0
3
0
2
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
6
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
3
0
1
0
0
2
0
0
2
1
0
1
0
0
0
0
0
0
1
11
0
0
0
0
0
0
1
0
0
0
1
0
4
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
1
0
0
2
0
0
0
4
0
4
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
2
2
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
2
0
1
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
2
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
2
2
1
2
0
0
2
2
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
3
0
1
0
1
1
0
0
2
2
1
0
0
0
0
1
0
0
0
0
2
2
0
2
1
0
0
1
2
0
0
2
0
0
0
0
1
0
0
0
5
0
1
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
1
2
0
3
1
2
4
2
0
0
0
2
0
0
0
0
0
2
2
2
2
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
3
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
1
1
0
1
0
1
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
4
0
1
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
2
0
2
1
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
1
1
0
0
0
0
2
0
3
0
2
0
1
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
3
0
1
0
0
0
0
2
0
1
1
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
6
1
0
0
0
0
1
1
0
2
0
0
0
7
2
0
0
1
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
2
0
3
0
0
0
0
1
0
0
1
0
2
0
0
0
3
2
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
2
0
0
1
1
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
2
0
0
1
0
3
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
1
0
1
0
1
0
0
0
2
0
2
2
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
1
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
3
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
3
0
0
0
0
2
0
1
0
2
0
1
11
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
2
0
1
0
0
0
0
0
0
0
0
9
2
0
0
0
1
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
2
0
1
0
1
1
0
1
2
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
2
1
0
0
0
0
0
0
0
4
0
0
3
2
0
0
0
0
2
4
0
0
2
2
0
0
0
0
1
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
7
0
2
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
2
1
0
0
2
0
1
0
1
1
0
0
2
2
0
1
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
4
0
0
0
0
2
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
3
2
0
0
1
2
2
0
0
0
0
0
0
0
0
0
3
0
0
2
2
0
0
0
0
2
0
0
0
0
0
5
0
1
0
1
2
2
1
1
1
1
0
0
3
0
0
0
0
3
0
0
2
2
2
0
0
0
0
0
1
0
2
0
0
0
3
1
0
0
0
0
1
0
1
0
1
0
0
1
2
0
3
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
2
0
0
1
0
0
0
1
1
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
2
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
1
0
2
0
3
0
0
0
0
0
0
0
2
2
1
0
2
0
2
0
0
0
1
0
0
0
0
0
2
0
2
1
0
0
0
0
0
2
0
2
2
0
2
0
0
0
2
0
1
0
0
1
0
0
1
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
2
5
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
1
2
0
2
0
3
1
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
2
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
2
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
4
2
0
1
0
1
0
1
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
5
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
7
0
0
0
0
0
0
0
3
3
1
0
0
0
0
0
0
2
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
1
0
1
1
1
0
0
0
1
0
0
2
1
0
0
0
1
0
0
2
3
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
1
0
1
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
5
0
10
0
1
0
0
1
0
2
3
0
0
0
0
2
0
0
0
0
0
0
0
2
1
1
0
0
0
1
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
9
2
0
4
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
2
1
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
2
0
0
2
0
1
1
0
0
0
0
0
0
2
2
0
1
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
1
0
1
0
2
0
0
0
0
0
0
1
0
0
4
0
3
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
6
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
1
2
0
0
0
0
3
0
1
0
4
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
1
0
0
0
0
0
5
0
0
2
0
0
0
0
0
12
0
1
1
0
2
2
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
2
0
0
0
1
0
0
1
1
2
0
0
1
2
1
0
0
0
0
0
0
0
3
0
0
0
0
0
2
3
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
1
2
0
4
0
0
0
0
2
1
0
0
0
2
1
0
2
2
3
2
0
0
0
0
0
0
1
0
1
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
1
0
0
0
3
0
1
0
0
1
0
0
0
0
0
0
0
5
0
0
0
0
0
1
2
0
0
0
0
0
2
2
0
0
0
4
0
0
1
0
0
2
2
0
2
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
2
0
1
0
0
0
0
1
2
0
0
2
0
0
0
0
0
1
0
1
3
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
2
0
3
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
3
0
0
0
0
2
2
0
1
2
0
0
0
0
1
0
2
0
0
0
0
0
0
2
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
2
0
1
1
0
0
0
0
1
0
1
0
0
0
0
3
0
2
0
0
1
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
3
0
5
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
1
0
1
0
3
1
0
0
3
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
2
0
0
0
0
0
0
2
2
0
0
2
1
2
0
1
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
3
0
2
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
2
2
0
0
0
2
0
0
1
8
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
1
0
0
0
2
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
1
11
1
0
1
2
0
0
3
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
2
0
2
0
2
0
1
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
1
0
0
2
0
0
2
0
0
0
0
3
0
2
0
0
1
0
2
5
2
3
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
4
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
1
7
0
1
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
4
0
0
1
2
0
0
0
2
0
2
0
1
3
1
0
1
0
0
0
0
2
2
0
1
2
0
2
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
1
2
0
0
2
1
0
0
0
0
0
0
0
0
0
2
1
0
1
0
1
2
0
4
0
0
0
0
2
0
0
4
1
0
0
2
0
0
1
0
2
0
0
2
0
0
2
0
0
0
0
0
3
2
0
1
0
0
2
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
1
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
3
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
2
1
0
0
0
0
0
2
0
0
0
2
0
2
0
3
0
0
0
0
0
0
0
1
0
2
0
2
2
0
1
2
0
0
2
0
0
1
2
0
0
0
0
0
0
3
0
0
0
1
2
0
0
0
0
1
0
0
0
0
2
0
2
1
1
1
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
1
6
0
0
1
0
0
0
0
3
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
2
0
2
1
0
0
1
0
0
3
0
0
0
2
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
4
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
2
1
0
2
0
1
0
0
1
0
0
0
1
0
1
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
2
1
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
1
1
0
2
0
0
1
3
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
1
0
0
0
0
0
2
0
0
0
3
0
0
0
2
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
7
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
3
0
0
0
2
1
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
1
1
0
4
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
1
0
2
1
0
0
0
1
1
0
0
0
2
2
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
2
2
0
1
0
0
0
0
3
0
0
2
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
1
2
1
0
0
3
0
1
0
0
2
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
7
0
0
2
2
2
1
0
0
0
0
7
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
1
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
2
2
2
0
2
0
1
0
0
0
0
0
0
0
2
2
0
1
0
2
1
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
2
0
2
0
2
0
0
0
1
2
0
0
0
0
2
2
0
2
0
2
0
0
2
0
0
3
0
0
0
0
0
0
0
0
1
2
1
0
0
1
0
2
0
0
2
3
0
2
0
0
1
0
0
0
0
0
0
2
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
2
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
3
0
0
2
0
2
2
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
1
1
5
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
1
1
0
0
0
0
2
1
0
0
0
0
0
2
2
0
0
1
0
2
0
0
0
2
0
0
0
1
0
2
1
0
2
0
0
0
0
0
0
2
1
0
0
1
2
0
0
0
0
0
1
2
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
1
0
0
2
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
3
0
0
0
0
0
0
1
1
1
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
4
0
0
0
1
1
2
0
2
0
2
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
2
0
0
0
3
0
0
1
2
0
0
0
0
0
1
0
0
0
0
1
0
0
2
1
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
1
7
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
4
0
0
2
1
2
0
0
0
1
0
0
1
0
1
2
0
0
0
1
0
0
0
0
0
0
1
0
3
0
0
3
2
1
0
3
1
0
0
0
0
0
0
2
2
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
1
2
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
2
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
2
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
1
0
2
1
0
0
0
2
0
2
0
2
2
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
2
3
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
2
0
0
0
2
2
0
0
0
2
0
0
2
0
0
0
1
2
1
2
0
0
1
0
0
2
1
0
2
0
0
0
0
0
0
1
0
1
2
0
2
0
3
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
2
2
0
0
2
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
3
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
4
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
2
1
0
0
0
0
0
0
2
0
0
0
2
2
0
0
1
0
0
1
1
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
1
0
1
3
2
0
0
0
1
0
0
2
0
0
1
2
0
0
0
0
0
2
1
2
0
1
0
3
1
0
0
0
0
2
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
2
0
1
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
2
0
2
0
0
0
0
2
0
0
2
1
0
0
0
0
2
2
0
1
0
0
0
2
0
0
0
0
2
0
0
2
2
2
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
2
2
1
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
2
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
2
0
0
0
0
2
1
3
4
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
2
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
2
0
2
0
0
1
0
0
0
1
0
1
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
3
0
0
0
0
4
2
1
1
1
1
1
2
0
6
0
2
0
0
0
3
0
0
0
2
0
0
2
1
0
0
1
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
1
1
1
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
2
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
2
2
0
11
2
0
0
1
0
8
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
2
1
0
0
0
0
0
0
0
1
0
0
1
2
0
1
0
0
0
0
0
0
2
0
1
1
0
0
2
0
0
0
2
0
0
0
0
0
1
1
1
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
1
2
0
2
0
1
0
0
0
2
0
0
0
0
0
2
0
2
0
2
6
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
3
0
0
0
1
0
1
0
1
2
0
0
0
0
2
0
1
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
4
0
0
1
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
2
0
1
0
1
2
1
0
0
2
0
2
0
2
0
0
2
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
1
0
4
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
3
0
0
0
1
0
0
0
1
2
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
3
0
0
4
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
3
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
3
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
3
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
1
1
1
0
2
0
0
1
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
3
0
0
2
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
1
2
2
1
1
0
0
2
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
1
0
4
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
1
1
1
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
4
0
0
0
1
0
0
0
0
4
0
1
2
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
3
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
2
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
6
2
0
0
0
2
2
1
0
1
2
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
1
0
2
0
2
0
1
1
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
2
0
0
2
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
3
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
3
1
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
1
2
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
2
0
2
0
0
0
0
3
0
0
0
0
0
1
4
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
3
0
0
0
2
0
1
0
0
0
1
0
0
0
3
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
6
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
3
0
0
1
0
2
0
1
0
0
1
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
2
2
0
0
1
0
2
0
2
0
0
2
2
0
1
0
0
0
1
2
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
4
0
0
1
0
1
2
0
0
1
1
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
9
0
0
0
0
0
0
0
0
1
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
2
0
0
1
2
0
0
0
1
0
0
0
1
1
0
0
0
2
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
5
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
11
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
2
2
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
3
2
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
2
0
2
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
2
2
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
2
4
0
0
2
0
0
0
1
1
0
0
2
0
0
0
0
0
2
0
1
0
0
0
2
2
0
0
1
2
0
0
1
2
0
1
0
0
3
0
0
2
1
2
0
2
0
0
1
0
3
0
0
0
0
0
1
0
0
2
0
0
0
2
0
2
3
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
3
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
2
0
0
1
3
0
2
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
3
1
0
0
0
0
0
0
0
3
0
2
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
3
1
0
2
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
3
1
0
0
0
0
0
0
0
1
0
1
0
2
2
2
0
0
0
2
2
0
1
0
0
1
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
2
0
2
1
0
0
0
2
0
0
0
0
0
0
2
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
1
2
0
0
0
0
0
0
0
5
0
0
0
0
0
1
1
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
1
2
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
5
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
5
0
0
1
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
1
1
0
1
0
0
0
0
0
2
1
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
2
0
3
1
0
0
0
0
0
0
0
2
0
0
0
3
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
1
0
1
0
0
0
3
0
0
0
2
0
0
0
2
0
2
0
0
2
0
0
0
0
1
5
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
1
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
3
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
1
0
0
2
0
2
2
1
0
1
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
1
2
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
1
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
5
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
2
3
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
2
2
2
0
2
0
2
0
2
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
2
0
3
2
0
0
0
2
1
2
0
0
0
0
0
0
0
3
0
4
2
0
0
0
2
1
0
0
0
0
0
2
0
2
0
0
0
1
0
1
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
1
0
0
1
3
0
3
0
2
0
0
1
0
1
0
2
0
0
0
0
0
2
1
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
2
2
0
0
0
0
0
0
0
2
0
0
0
2
3
0
0
0
0
1
0
2
1
0
0
0
2
0
2
0
0
2
2
0
1
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
3
0
0
0
0
3
0
0
0
0
0
2
0
0
2
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
3
0
3
3
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
5
0
0
2
2
0
1
0
0
1
0
0
2
0
0
1
1
1
0
1
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
4
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
4
1
0
1
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
3
0
0
0
2
0
0
0
0
2
0
0
1
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
3
0
0
0
0
0
0
3
0
1
0
1
1
0
1
2
0
0
1
0
2
0
2
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
1
3
0
0
0
0
2
0
1
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
1
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
3
22
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
4
0
0
5
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
3
2
0
2
0
0
0
0
0
2
2
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
3
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
1
0
0
4
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
1
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
3
2
0
1
0
0
0
0
0
1
0
2
0
0
0
0
2
1
0
0
0
1
0
0
1
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
1
2
4
0
0
1
0
0
0
0
4
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
1
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
3
2
0
0
0
0
0
0
3
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
1
0
1
0
1
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
3
0
0
0
5
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
3
0
2
7
1
0
0
0
0
0
0
0
0
2
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
2
0
0
0
2
0
0
0
1
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
3
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
3
0
0
0
0
1
0
1
0
0
0
0
0
2
1
0
0
3
8
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
1
1
0
1
0
1
1
1
4
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
1
2
0
1
0
1
1
3
1
0
0
0
3
0
0
0
0
0
0
0
0
1
1
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
6
0
0
0
0
2
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
2
0
3
0
0
0
2
0
7
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
1
2
0
0
0
2
3
0
0
0
0
0
0
1
3
1
0
1
0
0
0
0
0
0
2
3
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
5
2
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
1
2
0
0
1
0
0
0
0
1
0
0
2
0
0
0
1
1
0
0
0
0
4
1
0
0
0
3
0
0
0
1
2
0
0
0
0
2
0
2
0
3
0
0
0
0
2
0
0
0
3
0
1
0
1
0
3
2
1
0
0
1
1
2
0
0
0
2
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
1
5
8
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
1
0
1
1
0
1
2
0
0
3
0
0
2
0
0
0
0
0
2
0
0
2
0
4
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
3
0
2
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
2
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
2
2
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
2
0
2
0
0
0
2
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
1
2
0
0
2
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
3
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
4
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
2
1
0
0
0
0
0
1
0
0
2
0
0
2
0
0
1
0
0
0
0
1
0
4
0
0
0
2
1
0
0
1
0
3
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
1
0
0
2
0
0
1
1
0
0
2
0
0
4
0
2
0
0
0
1
2
0
0
0
2
0
0
0
1
0
1
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
3
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
3
1
0
0
0
0
0
0
2
3
0
0
0
0
1
0
0
0
0
2
0
0
0
0
4
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
1
0
0
0
4
0
0
0
0
2
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
2
3
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
3
0
4
0
0
6
0
0
2
0
1
0
0
0
0
0
2
0
2
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
2
2
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
2
1
0
0
0
0
0
1
2
5
0
1
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
1
2
0
0
0
2
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
2
1
0
3
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
3
0
2
0
0
0
0
1
0
3
0
0
0
0
1
3
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
2
0
0
0
0
0
2
0
0
0
0
2
2
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
4
0
1
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
1
1
0
2
0
2
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
5
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
2
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
2
0
2
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
4
0
2
0
0
2
2
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
2
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
2
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
5
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
1
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
2
2
0
3
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
4
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
2
0
3
0
0
3
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
2
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
5
2
0
1
0
0
0
2
2
0
1
0
0
0
2
1
3
0
0
2
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
1
0
0
0
0
1
0
1
1
0
0
0
0
1
0
2
1
0
2
0
0
0
0
4
0
0
1
0
0
2
1
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
2
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
1
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
1
0
0
2
0
1
1
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
5
0
0
0
0
2
0
0
0
0
0
0
3
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
1
0
1
0
0
2
2
0
0
0
0
0
2
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
2
0
0
2
2
0
0
0
0
0
2
1
1
0
1
0
2
0
0
1
0
1
0
2
0
0
0
0
0
1
1
0
0
0
0
0
3
2
0
2
1
0
0
0
0
0
2
0
0
0
1
1
1
0
2
0
0
1
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
1
0
1
2
0
0
1
4
3
0
0
0
0
0
0
0
0
0
0
5
0
0
3
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
2
1
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
3
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
1
0
0
0
0
2
2
1
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
3
0
0
2
0
0
0
0
0
0
0
0
0
0
2
3
0
1
1
3
0
0
2
0
1
0
0
0
2
0
0
1
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
1
2
0
0
1
1
0
0
0
0
0
1
1
0
1
0
0
2
0
0
1
1
0
0
2
1
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
5
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
6
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
2
0
0
2
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
4
0
0
2
0
0
0
0
0
0
0
0
8
0
0
0
0
0
0
0
0
0
0
0
5
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
3
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
2
0
0
2
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
4
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
5
6
0
3
0
2
3
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
2
0
0
0
8
0
3
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
2
1
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
1
0
0
0
0
0
1
2
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
9
3
0
2
1
0
0
0
0
0
0
2
1
0
0
0
2
0
0
1
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
2
1
0
1
1
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
1
2
2
0
0
0
0
2
1
2
1
0
1
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
4
1
0
2
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
1
1
1
2
2
0
2
0
0
1
1
0
0
0
1
0
0
0
0
1
1
1
3
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
2
0
9
0
1
2
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
3
0
0
2
0
0
2
0
0
0
1
1
0
1
0
0
0
2
0
1
0
0
2
0
2
0
2
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
1
3
0
0
0
0
0
0
2
1
0
0
0
0
1
0
2
0
1
0
3
0
0
2
0
3
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
3
1
1
2
0
1
1
2
1
0
1
0
0
0
0
0
3
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
1
5
0
0
0
0
0
2
1
0
0
2
0
0
0
1
0
4
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
6
2
2
1
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
2
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
2
1
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
2
0
0
1
2
0
1
0
3
0
0
0
0
0
0
2
0
2
0
0
0
1
1
2
2
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
2
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
2
0
1
1
0
4
0
0
4
0
0
0
0
0
0
1
0
0
0
3
1
0
0
1
0
0
0
0
1
2
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
3
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
1
0
2
0
0
0
2
1
0
0
0
0
0
2
2
1
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
2
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
1
2
1
0
2
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
1
0
1
0
2
0
4
0
0
0
1
1
2
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
3
0
0
1
0
0
0
0
4
1
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
2
0
3
0
0
1
0
0
3
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
2
1
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
6
1
2
1
0
0
0
0
1
0
0
0
0
3
2
0
1
0
0
0
0
0
0
0
3
0
3
0
0
0
0
1
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
3
2
0
1
0
2
0
1
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
2
0
0
0
0
3
0
0
1
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
2
2
0
2
0
0
1
0
0
0
1
0
0
1
0
2
2
5
0
1
0
0
0
0
3
0
0
1
1
0
0
1
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
2
0
1
1
2
0
0
0
1
1
0
0
2
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
1
2
0
0
0
0
2
0
0
5
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
4
2
0
0
0
0
0
0
0
2
2
0
2
3
0
0
2
1
1
0
0
2
0
0
4
0
0
0
3
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
2
0
2
0
2
0
1
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
1
1
2
6
0
1
0
1
4
0
2
3
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
1
0
0
0
0
0
2
2
0
0
0
0
0
0
2
2
0
2
2
0
0
0
3
0
0
3
0
4
0
0
0
0
1
1
0
0
1
0
2
55
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
3
2
0
0
0
0
0
0
2
0
0
2
1
0
0
1
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
2
0
0
3
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
1
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
9
0
2
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
1
0
1
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
1
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
1
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
2
0
2
0
0
0
2
0
0
0
2
0
0
1
0
0
0
1
2
0
0
2
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
1
0
1
0
0
0
1
2
0
0
0
3
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
2
2
2
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
2
1
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
1
1
1
2
0
0
2
2
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
1
2
0
1
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
2
0
1
0
2
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
2
2
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
10
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
2
2
0
0
0
0
3
1
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
1
0
0
0
2
1
0
2
1
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
1
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
2
0
2
0
0
0
0
0
0
3
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
3
0
0
0
0
1
0
0
0
0
9
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
1
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
1
2
0
2
0
0
0
0
1
0
0
0
0
0
2
1
0
2
2
0
1
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
10
0
0
0
0
0
0
0
0
0
0
2
0
4
0
2
3
0
0
6
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
1
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
1
2
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
2
0
1
2
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
1
1
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
3
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
3
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
1
0
0
0
0
0
0
0
2
1
1
1
0
6
0
0
0
1
0
0
0
3
1
0
0
0
0
1
0
0
0
0
0
2
2
2
1
0
2
2
0
2
0
0
1
0
0
1
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
1
0
2
1
1
2
0
0
1
0
0
1
2
0
1
2
0
2
0
0
0
1
1
0
0
5
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
4
0
1
1
0
1
0
2
0
2
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
1
4
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
3
0
0
0
0
2
0
0
0
1
0
1
0
0
1
2
1
0
1
0
1
0
0
0
0
5
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
2
0
3
0
0
0
0
0
1
2
1
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
4
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
1
0
1
0
0
0
0
1
0
2
2
1
0
0
2
0
0
0
0
0
4
0
1
0
3
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
2
1
2
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
2
1
0
2
1
1
0
0
2
0
0
0
0
1
0
0
0
0
3
0
1
1
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
1
0
2
2
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
2
0
2
0
0
0
1
2
0
3
0
0
1
0
0
0
0
0
0
0
4
0
0
0
1
1
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
4
0
0
2
0
1
0
2
1
1
0
0
0
0
0
1
2
0
0
0
0
2
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
2
1
2
0
0
0
2
0
1
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
3
2
0
0
0
0
2
0
2
0
0
0
0
0
2
0
2
0
2
0
0
0
2
0
0
0
0
0
0
1
1
0
2
0
1
1
0
1
0
0
0
2
3
0
0
0
0
0
1
0
1
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
2
6
0
1
2
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
2
0
4
0
1
0
0
0
0
0
1
0
2
2
0
0
0
1
2
0
1
0
0
1
0
2
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
4
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
6
0
0
0
0
0
0
0
2
0
2
0
0
1
0
2
0
2
0
0
0
2
0
3
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
2
0
0
0
0
1
1
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
4
0
2
0
1
0
0
0
2
0
0
0
0
2
3
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
3
0
0
0
0
0
0
2
0
0
4
2
0
1
0
0
2
0
0
0
1
0
0
1
2
2
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
3
0
0
0
1
5
0
0
2
0
0
0
0
0
1
0
1
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
1
0
0
2
0
0
0
1
0
1
0
3
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
2
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
1
0
0
0
4
0
0
1
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
2
5
2
1
0
0
1
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
1
0
0
2
0
0
0
0
0
0
0
0
0
2
1
1
1
0
1
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
1
0
0
2
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
4
0
0
0
2
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
2
2
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
1
0
0
3
0
1
0
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
0
0
2
2
0
1
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
1
0
2
2
0
1
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
3
0
0
0
0
1
0
0
2
2
2
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
2
0
1
5
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
2
0
0
1
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
1
0
3
0
0
2
0
0
2
0
0
0
2
0
0
0
1
2
2
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
2
0
0
2
0
1
1
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
1
0
0
2
0
1
3
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
2
1
1
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
1
0
0
2
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
1
1
0
1
2
0
0
0
0
2
0
0
0
0
1
1
2
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
1
4
1
0
0
1
0
0
1
2
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
1
0
2
0
0
0
2
0
2
1
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
2
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
4
2
0
2
1
0
0
0
0
0
0
0
3
2
0
0
0
1
0
0
1
0
0
3
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
1
1
1
0
1
2
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
1
0
0
0
0
3
0
0
0
2
2
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
3
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
3
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
4
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
1
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
5
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
5
0
2
0
1
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
1
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
3
0
0
1
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
3
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
2
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
1
0
4
0
2
0
0
0
1
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
2
1
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
1
0
0
2
3
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
14
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
5
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
5
0
1
0
0
0
0
2
0
0
2
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
3
1
0
0
0
3
0
0
0
0
0
3
1
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
1
3
0
3
1
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
1
1
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
1
10
1
0
3
0
1
0
0
0
2
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
1
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
3
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
3
2
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
4
0
1
0
0
0
0
0
0
0
0
2
0
4
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
3
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
1
0
0
0
0
2
1
0
0
3
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
3
0
0
0
0
0
0
2
0
0
2
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
2
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
2
0
0
0
1
2
2
2
0
0
2
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
2
0
1
1
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
1
2
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
1
1
0
0
0
0
2
0
1
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
3
1
0
0
0
1
0
0
0
2
0
0
3
0
0
0
2
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
6
3
1
1
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
1
0
0
3
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
2
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
8
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
4
0
2
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
1
3
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
2
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
2
1
2
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
3
2
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
1
1
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
4
1
2
0
2
3
2
1
0
0
1
0
0
2
0
0
1
0
0
0
3
0
0
4
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
1
0
0
2
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
9
0
1
2
1
1
2
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
7
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
2
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
2
2
2
1
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
1
1
1
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
1
0
2
0
0
0
2
0
0
1
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
3
0
0
0
1
0
1
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
2
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
3
2
1
0
2
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
2
1
1
1
0
0
0
0
2
2
0
0
1
3
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
5
0
0
2
0
0
0
0
2
1
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
1
3
0
0
0
1
0
1
0
1
2
1
0
0
1
0
0
0
6
0
3
1
0
1
0
0
2
0
0
1
1
0
0
1
0
2
0
0
0
2
0
0
1
1
2
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
1
0
0
2
0
0
0
0
0
0
4
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
2
0
2
3
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
2
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
1
4
0
0
2
0
1
0
2
0
0
0
0
4
0
0
0
0
0
1
0
0
6
0
1
0
0
0
0
0
0
0
0
2
2
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
3
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
2
0
1
0
1
0
2
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
2
0
0
1
0
0
0
1
2
0
2
1
0
0
0
0
0
2
0
0
1
0
2
0
0
2
1
2
3
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
2
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
1
2
0
1
0
0
0
0
0
1
2
0
2
0
0
0
8
0
2
0
0
1
0
0
2
0
0
0
1
1
0
0
2
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
1
0
0
2
4
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
5
1
0
0
1
0
3
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
1
2
0
0
0
4
0
0
0
0
2
0
0
0
0
3
0
0
0
2
0
2
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
1
2
1
0
0
1
1
2
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
8
0
0
0
0
3
0
1
0
1
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
3
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
2
2
0
0
0
2
1
0
0
1
0
0
2
1
0
2
0
0
0
0
1
0
0
2
1
0
0
0
5
1
2
1
0
2
2
0
1
1
0
3
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
3
1
1
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
1
0
2
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
1
1
0
1
0
3
0
0
0
1
0
0
2
2
0
3
1
1
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
1
3
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
1
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
3
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
5
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
1
0
2
0
0
0
0
0
1
0
0
3
0
2
0
0
0
0
1
0
0
1
2
0
0
0
1
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
8
0
0
0
1
2
0
0
0
1
1
0
0
1
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
1
1
0
4
1
0
3
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
1
0
0
2
0
0
0
2
0
0
1
1
0
1
0
0
0
2
0
0
2
0
2
0
1
0
0
0
0
0
0
0
2
2
2
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
7
0
0
0
0
0
1
2
0
0
3
0
0
1
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
2
0
0
2
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
9
2
1
0
1
0
0
0
2
1
0
0
7
2
0
0
1
0
0
0
0
4
0
1
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
1
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
1
0
2
0
0
2
1
0
0
1
0
6
0
0
2
0
0
0
1
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
1
1
0
2
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
1
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
1
2
0
2
0
0
1
0
0
0
2
0
2
0
0
0
0
0
6
2
0
0
0
0
1
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
1
1
2
1
0
0
0
8
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
1
1
0
0
0
0
0
2
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
3
0
0
0
0
1
1
0
2
1
1
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
1
1
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
1
2
0
2
0
0
0
0
0
6
0
2
0
1
0
2
0
0
0
0
1
0
3
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
5
0
0
1
0
1
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
1
0
0
3
0
0
0
0
0
5
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
2
1
0
0
2
0
0
1
0
0
1
1
0
1
2
1
0
0
0
0
1
0
2
0
0
0
3
0
0
0
0
0
0
0
2
0
0
2
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
2
0
0
0
0
2
0
0
0
0
2
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
3
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
5
2
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
2
2
0
1
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
3
1
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
7
0
0
0
2
0
0
1
0
0
1
0
1
0
0
0
0
0
0
2
2
3
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
2
0
1
3
0
0
0
0
3
0
0
0
0
0
0
2
2
0
0
2
0
0
2
0
0
0
0
0
2
0
3
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
2
2
1
0
0
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
4
0
1
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
2
0
1
1
1
0
0
0
0
1
3
0
2
1
0
1
0
0
1
0
2
0
0
1
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
6
2
0
0
0
0
0
0
1
0
0
0
0
0
2
4
0
1
0
0
0
0
4
0
2
0
0
0
0
0
0
0
2
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
4
0
0
0
0
1
1
2
2
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
2
0
0
2
2
0
1
2
0
1
0
0
0
0
0
0
0
0
0
4
3
0
0
0
0
0
0
1
0
0
2
1
0
0
8
0
0
1
0
0
0
1
1
1
0
1
0
0
0
0
0
2
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
1
1
0
3
0
2
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
1
1
0
2
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
3
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
1
1
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
1
0
0
1
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
2
3
0
0
0
0
2
2
0
0
0
0
1
0
0
0
1
0
3
0
0
0
2
1
0
0
0
0
1
0
0
0
2
2
0
2
0
0
1
0
0
0
2
2
2
0
0
0
0
2
0
2
0
2
1
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
1
0
1
0
1
0
2
0
1
2
0
1
0
2
0
0
0
0
3
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
5
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
2
0
2
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
2
2
0
2
2
0
0
0
0
0
3
0
2
0
2
0
1
1
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
3
1
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
2
1
1
0
0
0
0
1
0
0
0
0
0
0
4
0
2
0
2
0
0
0
2
1
0
2
0
2
0
2
0
0
1
0
1
0
0
0
2
0
0
0
0
1
1
0
3
1
0
1
0
3
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
5
1
2
0
8
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
5
1
0
1
0
1
0
0
2
2
1
0
2
0
0
0
1
2
0
0
0
0
0
0
1
0
0
2
0
0
1
0
2
1
0
3
0
1
0
1
0
0
0
0
0
3
0
2
0
2
0
0
2
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
2
0
4
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
3
0
0
1
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
1
0
0
0
0
2
1
3
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
3
0
1
0
0
0
0
0
2
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
2
0
0
2
1
1
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
8
1
1
0
0
0
0
0
0
0
0
0
0
0
3
1
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
2
2
0
0
0
0
1
0
0
0
1
1
0
0
3
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
2
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
1
1
8
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
3
0
2
0
0
0
0
0
3
1
1
1
0
0
2
0
1
0
0
0
0
0
0
2
0
2
0
1
2
0
0
2
0
0
0
0
0
0
1
0
2
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
2
2
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
4
2
0
2
0
0
0
0
1
0
0
0
0
2
0
1
1
1
0
0
0
2
0
1
2
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
6
2
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
1
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
3
4
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
2
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
3
3
0
0
0
1
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
3
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
1
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
2
0
4
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
1
1
1
0
0
1
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
1
0
0
1
0
0
2
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
2
1
2
0
1
0
0
2
0
2
0
1
0
1
0
2
0
0
0
2
2
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
1
2
0
2
0
0
2
0
1
0
0
0
1
2
0
2
1
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
2
0
1
0
2
2
0
0
0
0
0
2
0
0
0
2
0
2
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
1
1
0
0
2
0
0
0
0
0
2
1
2
0
0
2
0
2
0
2
0
0
0
0
0
0
1
0
0
0
1
3
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
1
0
1
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
3
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
1
2
0
0
0
3
0
0
0
0
0
0
0
0
0
1
2
1
0
0
2
0
0
2
0
0
2
0
0
0
0
1
0
0
0
1
0
1
2
2
0
0
0
0
7
0
1
5
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
2
0
0
0
0
0
0
2
0
1
3
0
1
0
0
0
0
0
0
0
0
0
7
0
0
1
0
3
1
0
0
0
0
2
2
1
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
1
2
1
0
0
0
2
0
1
0
0
0
0
0
3
0
1
1
0
0
0
0
0
0
3
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
7
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
1
0
0
2
3
0
1
0
0
0
0
1
0
0
0
0
2
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
5
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
1
3
0
0
0
0
3
0
2
0
0
1
3
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
3
0
0
0
0
2
0
0
0
0
0
0
3
0
2
0
1
0
0
1
1
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
5
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
4
0
2
1
0
0
0
2
2
0
0
0
0
0
0
1
1
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
1
0
2
0
0
2
1
0
2
0
0
2
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
2
0
0
1
1
2
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
3
0
1
1
0
1
4
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
2
0
0
3
0
0
1
0
0
0
0
2
0
1
0
1
0
2
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
2
2
0
0
0
1
2
2
0
0
0
0
0
0
2
0
0
0
2
1
0
2
2
0
1
0
0
0
2
1
0
1
0
0
1
0
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
2
1
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
3
2
0
0
0
0
1
0
0
0
0
1
0
0
1
1
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
1
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
4
0
0
0
1
1
19
2
0
0
2
2
0
1
0
0
2
0
1
17
0
0
1
1
0
0
0
0
2
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
2
1
1
0
1
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
2
1
0
1
0
3
0
1
1
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
2
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
3
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
5
1
0
1
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
1
2
2
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
1
1
0
0
0
2
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
3
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
4
0
0
1
1
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
2
1
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
5
0
0
1
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
5
0
0
2
0
0
0
0
2
0
0
0
0
2
2
0
3
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
1
0
0
0
0
3
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
3
0
0
1
0
0
1
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
1
2
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
2
0
0
1
0
0
2
0
0
2
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
3
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
2
0
0
0
3
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
1
0
0
0
1
0
2
0
0
0
0
0
0
2
4
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
2
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
2
0
1
0
1
2
2
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
3
0
0
1
1
1
0
0
1
0
0
2
3
0
0
2
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
1
1
0
1
0
1
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
1
0
2
0
0
1
0
2
0
0
2
0
2
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
2
0
0
0
0
2
0
0
0
2
2
2
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
1
0
0
0
0
2
2
1
0
0
0
0
2
1
0
1
0
2
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
1
3
0
0
0
0
0
1
0
0
2
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
3
0
2
0
2
2
2
0
1
0
0
0
0
1
1
0
0
1
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
1
1
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
2
1
0
4
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
1
0
0
1
3
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
3
0
0
0
0
2
0
0
0
2
0
0
0
0
0
4
0
0
2
0
0
0
0
0
2
0
0
3
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
1
0
0
0
2
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
4
2
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
1
0
0
0
1
2
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
2
0
2
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
4
0
0
0
0
1
2
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
1
3
1
1
0
0
2
0
2
0
0
2
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
1
0
0
1
1
0
0
2
0
0
0
0
0
0
1
0
3
0
1
0
0
0
0
0
0
1
7
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
3
0
1
0
0
2
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
2
0
0
0
1
0
3
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
2
3
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
1
0
0
0
0
0
1
0
2
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
3
0
1
0
2
0
0
0
0
2
0
0
1
0
3
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
1
0
1
0
0
4
0
0
1
0
0
0
2
0
1
2
0
0
2
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
3
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
7
0
0
0
0
0
1
0
0
0
1
0
1
0
2
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
6
0
2
1
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
3
0
2
1
0
1
0
1
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
1
2
0
0
1
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
3
0
0
1
0
0
0
2
0
0
3
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
3
0
0
2
1
0
0
0
0
0
0
0
8
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
3
1
3
0
0
2
0
0
5
0
1
0
0
1
0
0
0
2
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
1
0
1
0
1
0
0
2
0
0
0
0
0
2
2
1
1
11
0
0
5
0
0
2
0
0
0
0
1
0
1
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
1
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
2
0
0
1
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
1
1
0
3
0
0
0
2
0
1
0
0
0
2
1
1
0
0
0
0
3
0
2
0
0
0
0
2
0
0
0
2
0
3
0
0
0
0
0
0
3
0
0
0
0
0
2
1
0
0
2
1
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
3
1
0
0
0
2
0
3
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
1
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
3
0
1
0
4
0
0
0
1
1
0
0
1
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
8
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
1
0
2
0
0
1
0
0
0
0
0
1
4
0
0
0
0
1
0
0
0
1
2
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
2
2
1
0
2
0
0
4
0
0
0
0
0
3
2
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
2
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
2
0
0
2
0
1
0
0
1
0
0
2
0
3
0
0
2
0
0
0
3
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
1
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
2
0
0
0
0
1
0
0
3
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
2
1
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
3
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
2
0
0
0
2
1
0
0
0
0
1
0
0
2
0
0
0
0
1
2
2
1
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
2
1
2
2
0
0
1
0
1
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
1
4
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
2
2
2
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
1
2
0
0
0
1
1
0
2
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
1
2
1
0
3
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
1
1
0
0
0
3
0
0
0
0
2
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
1
1
0
0
2
2
0
0
2
0
0
0
0
3
0
0
0
0
1
2
0
0
1
0
0
0
2
2
0
0
0
2
0
1
0
0
0
0
0
1
0
1
0
2
0
2
0
0
1
1
3
0
0
0
0
0
2
0
0
1
2
0
0
0
0
2
1
0
2
1
0
0
0
0
0
0
0
2
0
0
2
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
3
1
0
1
1
0
2
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
3
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
2
0
0
3
2
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
1
0
0
2
0
0
3
0
2
0
1
1
1
0
2
0
0
0
3
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
1
3
0
0
1
1
0
0
0
0
0
2
2
0
3
0
0
0
0
0
0
2
0
0
1
1
2
0
0
0
1
0
0
2
1
3
0
0
0
3
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
2
0
0
0
1
0
0
0
3
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
5
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
3
3
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
1
2
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
3
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
5
3
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
5
0
2
1
0
0
1
1
0
0
0
4
1
0
0
1
0
2
0
1
1
2
0
0
0
0
1
1
0
0
1
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
7
2
0
0
3
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
2
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
2
3
0
0
0
2
1
2
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
3
1
0
1
1
0
0
0
2
1
0
0
0
2
2
0
1
0
0
2
0
0
0
3
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
2
0
2
2
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
2
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
2
0
0
0
2
2
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
5
0
0
0
0
0
0
2
0
1
0
5
0
2
0
0
0
0
1
1
2
0
0
0
0
0
2
0
0
0
0
0
2
0
2
2
0
0
0
0
0
1
0
1
0
0
2
0
0
0
2
0
5
0
0
0
0
0
0
1
0
0
0
0
1
3
0
0
4
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
1
0
1
0
0
2
2
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
2
0
1
2
3
0
1
0
0
0
0
0
0
1
2
0
0
0
0
1
0
1
0
0
1
5
0
0
0
0
0
0
2
1
0
0
0
2
1
0
0
0
0
0
0
0
2
2
0
0
0
1
0
2
0
0
4
0
0
0
0
6
0
0
2
0
2
0
0
0
0
3
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
2
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
2
0
0
0
0
2
0
2
2
6
0
1
0
0
1
0
0
0
1
0
3
0
0
2
0
0
2
0
0
1
0
0
0
2
2
0
4
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
2
1
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
3
0
0
1
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
1
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
2
2
1
2
0
1
2
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
4
2
0
2
2
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
3
0
1
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
2
0
0
0
1
0
0
0
0
0
1
2
0
1
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
1
0
1
1
1
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
3
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
2
0
0
7
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
1
0
2
0
0
1
0
3
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
3
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
1
0
0
0
0
1
0
0
2
0
0
0
2
0
1
3
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
1
6
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
2
0
1
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
6
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
2
1
3
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
1
0
0
0
0
2
2
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
1
3
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
5
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
1
2
1
0
0
0
0
1
1
2
4
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
7
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
2
0
1
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
1
0
1
0
2
0
1
0
2
2
0
0
2
0
1
2
0
0
0
0
0
2
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
3
2
0
0
1
1
0
0
0
2
2
0
1
0
0
0
0
3
0
0
3
0
0
0
0
0
0
2
1
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
4
0
1
0
0
1
1
1
0
0
0
1
2
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
2
0
4
0
2
0
1
0
2
0
0
0
0
0
0
1
5
0
0
0
0
2
2
0
4
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
2
2
0
0
1
2
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
3
1
0
0
1
0
0
0
3
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
2
0
3
0
0
0
0
0
0
0
1
0
0
1
2
0
2
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
2
0
0
0
1
2
1
1
0
2
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
2
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
2
0
0
1
0
0
0
0
3
0
0
0
1
2
0
0
2
0
0
0
1
0
0
1
2
0
0
0
1
0
1
0
1
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
2
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
3
1
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
2
0
0
7
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
3
2
0
0
2
2
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
2
0
1
6
0
0
1
1
0
0
1
0
0
2
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
2
1
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
2
0
0
2
0
0
0
0
2
0
0
2
5
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
2
1
0
0
0
3
1
1
0
0
1
5
0
0
0
0
1
1
1
3
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
3
1
0
0
0
0
2
0
0
2
0
1
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
1
2
0
1
0
18
3
4
0
0
0
0
2
1
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
1
0
2
0
0
1
0
0
1
0
0
0
3
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
1
0
1
0
0
1
3
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
3
0
1
0
0
0
0
0
0
2
0
1
0
0
1
0
2
0
0
0
1
0
0
0
6
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
2
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
1
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
2
0
0
0
0
2
2
2
0
2
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
8
0
2
2
0
2
0
0
0
0
0
0
0
6
1
0
0
0
2
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
2
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
8
0
0
0
0
0
0
1
1
3
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
3
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
2
1
0
1
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
1
1
0
0
2
0
0
1
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
1
2
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
4
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
3
3
0
0
0
0
0
0
0
0
1
1
0
0
5
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
3
2
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
2
0
0
0
0
2
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
4
0
0
3
0
0
0
0
0
0
1
0
0
1
1
0
1
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
3
2
0
2
2
0
0
0
0
2
0
0
1
0
1
0
0
0
0
1
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
1
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
2
0
0
0
2
0
0
0
0
3
0
2
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
8
0
3
0
2
0
5
0
0
0
0
1
0
0
0
0
0
0
2
0
0
10
0
0
3
0
2
2
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
1
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
2
2
0
0
0
1
0
0
1
0
0
1
0
2
1
2
0
2
0
1
0
0
2
3
0
0
1
0
0
2
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
2
0
1
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
2
1
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
2
0
3
2
0
0
0
2
0
0
0
0
0
0
2
0
2
0
3
0
0
0
1
0
0
0
1
2
0
0
6
0
4
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
2
0
4
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
2
0
0
0
2
0
0
1
0
0
0
0
1
0
1
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
4
2
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
2
0
0
0
7
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
2
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
2
0
1
1
0
0
2
2
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
1
2
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
1
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
2
1
0
0
5
1
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
2
0
0
0
0
2
1
0
0
0
0
3
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
1
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
4
0
0
2
0
0
1
0
0
3
0
0
0
0
0
0
2
0
2
0
2
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
2
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
4
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
4
0
2
2
0
0
0
1
2
2
0
0
0
3
0
2
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
3
0
2
0
0
0
0
0
0
0
3
0
0
0
2
1
0
0
0
0
2
2
0
0
3
0
0
0
0
0
1
2
2
2
0
0
1
0
0
1
0
2
0
0
2
0
0
0
2
0
0
0
0
1
0
2
1
2
0
3
0
0
0
1
1
2
0
3
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
1
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
5
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
1
0
0
1
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
6
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
1
0
0
0
0
0
0
2
1
1
0
0
0
0
0
3
0
0
2
0
0
0
1
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
3
0
0
1
0
0
0
1
0
1
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
2
0
0
1
0
0
1
0
0
0
0
0
2
0
2
1
0
2
1
0
0
0
0
2
2
2
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
3
0
1
1
0
0
1
1
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
2
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
2
2
0
0
0
0
0
1
0
0
0
0
0
2
0
1
1
1
0
0
0
0
2
0
0
0
5
0
0
0
0
1
0
0
2
0
0
0
0
1
2
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
3
0
2
0
1
0
0
2
1
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
1
2
0
0
3
1
0
0
0
0
0
1
0
5
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
1
1
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
1
2
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
2
0
0
1
2
0
0
0
0
0
0
2
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
4
0
0
2
1
0
2
0
2
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
2
1
0
0
0
0
0
0
2
0
2
0
0
0
2
1
0
0
0
0
0
1
0
0
0
1
2
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
2
0
2
1
0
2
0
1
1
0
0
1
0
1
2
0
0
0
2
2
0
0
3
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
8
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
4
2
2
0
1
2
0
0
3
0
0
1
0
0
0
0
2
0
2
0
1
0
3
0
1
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
3
1
2
1
0
0
0
1
2
1
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
1
1
1
1
0
0
2
0
0
2
0
0
2
0
0
0
0
0
2
0
3
0
0
0
0
0
1
0
2
2
0
0
2
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
2
0
0
0
0
1
2
0
1
0
2
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
2
0
2
0
1
0
0
2
0
0
1
0
0
4
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
3
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
1
0
0
0
2
0
0
0
0
2
0
0
0
0
2
5
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
4
0
0
1
0
0
2
1
0
2
0
0
0
3
1
0
1
0
0
2
0
0
2
1
1
2
2
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
2
0
0
0
0
1
0
0
1
1
0
0
0
0
0
2
0
0
0
0
1
0
2
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
6
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
3
6
0
0
0
0
0
2
0
0
2
1
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
6
0
0
2
0
0
0
0
1
0
0
0
1
2
0
2
0
0
0
0
0
1
0
0
0
5
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
0
2
1
0
1
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
1
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
1
1
0
2
0
3
1
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
2
1
0
0
6
0
0
0
5
0
0
0
1
0
0
6
0
2
0
2
1
0
1
0
0
0
0
3
2
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
4
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
2
2
0
2
0
0
0
2
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
1
1
2
0
1
2
3
0
2
1
0
0
0
0
0
1
2
0
0
2
0
1
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
1
0
1
2
1
2
0
0
0
2
0
1
0
0
0
0
0
0
0
7
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
3
0
1
0
0
1
0
0
0
1
1
3
2
0
2
0
0
0
1
4
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
2
1
1
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
7
2
0
0
0
0
0
0
2
1
0
0
0
0
0
1
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
1
0
5
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
3
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
1
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
5
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
5
1
0
1
0
2
0
0
2
0
0
0
3
2
0
0
0
0
2
0
1
0
2
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
1
0
0
4
2
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
1
2
1
1
0
0
2
0
1
0
1
1
0
0
0
0
3
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
1
1
0
2
3
2
0
0
0
1
1
0
0
0
0
0
0
0
4
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
2
1
0
1
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
4
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
2
1
0
3
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
1
1
0
1
1
0
2
2
1
3
0
3
1
0
0
0
2
0
0
0
1
1
1
0
2
2
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
3
0
1
0
0
1
1
2
1
0
0
0
4
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
1
0
0
3
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
3
2
1
0
0
1
0
0
0
0
1
0
0
0
0
2
0
1
0
1
2
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
1
0
0
1
0
0
2
0
0
2
0
1
0
0
0
0
2
2
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
1
1
0
1
0
0
0
0
0
2
0
2
0
0
0
0
1
3
0
2
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
2
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
3
0
0
0
1
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
3
0
1
0
2
2
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
3
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
2
1
1
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
1
0
2
2
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
5
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
1
2
0
0
2
2
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
1
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
4
0
0
0
0
0
0
0
0
0
0
3
2
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
2
0
0
1
2
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
2
0
1
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
1
1
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
2
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
2
0
0
0
1
0
1
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
2
1
0
0
0
2
0
0
0
0
0
1
0
3
0
0
0
3
2
0
0
0
1
0
1
0
0
3
0
0
1
0
0
1
0
0
1
0
0
0
0
1
3
0
2
0
0
2
0
2
2
0
0
0
3
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
3
0
0
1
3
0
0
0
0
0
0
2
1
0
0
0
0
1
0
1
1
0
0
0
0
0
1
2
1
3
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
2
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
1
2
0
2
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
4
0
0
1
2
0
0
1
1
0
0
0
2
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
1
0
0
0
2
0
0
2
2
1
2
0
2
0
0
1
0
2
1
0
0
3
0
0
1
0
1
0
0
0
2
0
1
0
0
0
2
0
3
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
2
0
0
0
2
0
0
0
2
1
0
0
0
0
0
1
2
2
0
0
2
0
0
0
1
0
0
1
0
0
0
0
3
0
9
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
15
0
0
0
5
0
0
1
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
1
1
1
2
1
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
1
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
2
0
2
0
1
0
2
0
0
0
1
1
2
0
0
0
0
2
2
0
0
0
1
0
1
2
0
2
0
3
0
0
1
0
2
0
3
8
0
0
0
0
4
4
0
0
0
0
4
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
3
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
2
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
3
1
0
0
0
0
0
0
0
0
2
1
4
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
2
1
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
3
1
0
2
0
1
2
0
0
0
1
0
1
0
0
0
0
0
0
1
2
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
1
2
0
1
0
0
0
0
0
0
0
0
5
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
2
0
0
0
0
0
3
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
2
0
2
3
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
5
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
2
0
0
0
0
1
0
4
0
2
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
2
3
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
1
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
3
0
0
0
3
0
2
0
0
0
2
2
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
1
1
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
5
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
3
1
4
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
1
1
2
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
1
3
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
1
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
3
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
2
0
2
0
1
0
0
0
1
1
0
0
0
0
2
0
0
0
0
1
0
3
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
1
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
3
2
0
0
0
0
0
0
5
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
1
0
1
0
0
1
0
2
0
2
0
0
0
0
0
2
0
1
5
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
3
0
0
0
1
1
0
0
0
0
0
7
0
1
0
0
0
0
2
0
0
0
0
4
4
0
1
0
0
0
9
1
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
2
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
1
8
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
3
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
3
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
1
0
0
0
3
0
2
0
2
2
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
1
2
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
1
2
0
2
0
0
0
0
2
0
0
1
0
3
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
2
1
0
0
4
2
0
0
0
0
0
0
1
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
3
2
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
3
0
0
0
0
0
3
0
0
0
2
0
0
2
0
2
2
0
1
0
0
1
0
0
0
2
0
1
1
1
0
1
1
0
0
1
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
2
0
3
2
0
2
1
0
0
0
0
2
0
1
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
2
2
0
1
0
0
0
3
0
1
0
5
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
2
1
1
0
5
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
1
0
2
0
2
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
2
0
1
0
0
0
0
0
1
0
0
4
0
0
0
1
0
0
0
0
0
1
0
6
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
3
1
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
5
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
2
0
0
1
4
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
3
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
1
0
1
2
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
1
1
1
0
1
2
0
1
0
0
0
0
2
2
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
1
0
1
0
0
0
0
0
1
0
0
0
1
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
2
1
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
2
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
2
1
0
0
1
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
5
0
2
0
0
1
0
0
0
1
0
2
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
1
1
2
0
0
0
2
3
0
0
2
0
1
0
0
0
2
0
0
1
0
0
2
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
1
1
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
7
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
3
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
13
0
0
2
0
2
1
1
0
2
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
3
1
0
0
0
3
3
0
1
0
1
0
0
1
0
1
0
1
0
0
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
2
0
2
0
2
2
1
0
0
0
1
0
0
0
2
0
0
0
2
1
0
0
0
1
0
0
0
0
1
3
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
2
0
1
0
1
3
0
1
0
0
2
0
2
2
0
1
0
0
0
2
0
1
1
0
2
0
0
0
0
0
3
0
0
0
0
0
0
2
2
1
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
3
0
1
0
0
0
2
2
2
0
0
0
2
0
0
2
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
7
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
2
0
1
0
2
0
3
0
1
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
1
3
0
0
2
0
1
0
1
1
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
3
2
0
0
0
0
0
1
2
0
0
2
0
0
1
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
2
0
2
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
2
0
0
1
1
0
2
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
2
0
1
0
0
0
0
1
0
1
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
3
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
1
0
0
0
1
0
0
0
1
0
1
7
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
3
0
0
0
5
0
0
2
1
0
0
0
0
2
0
2
0
0
0
0
2
1
0
0
1
0
0
0
1
2
0
0
0
2
2
0
0
1
0
0
1
2
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
2
1
0
0
1
2
0
0
0
1
0
1
0
3
0
0
0
0
0
0
2
0
0
0
5
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
1
1
0
0
2
0
0
0
1
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
3
0
2
0
2
0
2
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
5
4
0
0
1
0
0
0
1
2
0
0
0
1
0
0
0
5
0
1
3
0
0
0
2
2
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
2
2
2
0
1
0
0
0
0
0
0
2
0
0
2
0
0
2
2
2
1
0
0
1
0
0
0
0
0
8
0
0
2
0
2
1
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
2
0
0
0
0
0
0
3
1
0
4
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
2
2
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
1
0
1
0
0
2
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
1
0
0
0
1
0
0
1
1
0
2
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
1
0
3
0
2
0
0
0
1
1
2
2
2
0
0
1
0
0
2
3
2
2
1
0
0
3
0
1
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
2
0
0
0
0
0
0
0
0
0
2
2
1
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
2
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
4
0
0
0
0
1
1
2
1
0
1
1
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
2
0
0
1
1
0
0
0
2
2
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
2
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
5
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
3
0
0
0
5
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
2
2
0
4
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
1
0
1
0
1
1
0
2
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
5
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
2
0
1
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
2
0
5
0
0
0
1
0
0
0
4
2
0
0
0
0
2
0
0
0
1
1
0
1
0
0
2
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
1
0
1
0
2
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
5
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
2
0
0
0
0
2
1
0
0
0
2
2
2
1
0
0
0
0
0
0
0
1
0
0
1
3
0
1
0
0
1
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
2
0
1
0
0
1
0
0
0
1
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
3
0
2
8
0
0
0
0
1
1
1
0
3
0
0
0
1
0
0
0
0
0
0
2
0
3
0
0
0
1
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
3
2
0
2
0
0
0
2
0
0
1
0
1
0
2
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
6
0
1
0
0
1
0
1
0
0
1
0
0
1
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
2
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
2
0
6
0
2
2
0
2
1
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
3
0
0
1
0
0
2
0
3
0
0
0
2
0
0
0
4
0
2
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
1
4
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
2
0
2
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
3
1
0
0
0
0
0
0
2
0
0
1
0
0
0
2
2
0
1
0
0
0
0
1
0
0
0
5
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
1
4
1
0
0
0
2
0
2
0
0
0
1
0
0
2
0
0
1
0
0
1
0
1
0
0
0
0
5
3
0
0
0
0
0
0
0
0
0
2
0
0
4
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
1
2
1
1
0
0
0
0
0
0
0
0
1
0
8
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
1
0
3
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
1
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
4
1
0
2
0
0
2
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
2
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
2
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
1
1
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
2
0
0
0
1
0
4
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
1
1
0
0
2
0
9
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
1
0
0
1
0
1
1
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
3
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
7
0
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
2
2
2
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
1
1
2
0
2
0
2
2
1
0
1
0
0
1
0
2
0
0
1
1
0
0
0
0
2
0
0
0
0
2
0
0
0
2
2
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
1
0
0
4
0
0
0
2
2
1
2
0
5
1
0
2
2
0
0
1
2
0
0
0
2
0
1
1
0
0
0
2
2
0
2
3
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
3
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
1
1
4
3
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
7
0
0
0
0
1
0
0
3
0
1
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
1
12
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
10
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
1
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
1
0
2
3
0
0
0
0
0
0
2
0
2
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
2
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
2
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
1
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
1
2
3
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
4
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
7
1
2
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
2
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
9
0
1
0
0
0
6
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
3
0
0
0
1
2
2
0
3
0
0
0
0
0
0
1
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
4
0
0
1
0
2
0
3
0
1
0
0
0
1
1
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
0
2
1
0
1
3
0
3
0
0
0
0
0
0
0
0
1
1
2
0
0
1
2
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
1
4
0
0
3
0
0
0
0
1
1
0
0
2
5
0
0
0
4
3
0
0
0
0
1
0
2
2
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
1
1
0
0
0
0
0
0
3
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
1
0
4
1
0
0
0
0
2
1
0
2
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
1
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
2
0
0
1
0
0
0
2
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
1
1
0
0
2
0
0
0
1
0
2
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
1
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
3
0
0
0
3
0
0
0
0
0
0
0
0
1
2
0
0
2
1
0
0
0
1
0
0
0
0
2
8
2
1
3
1
0
0
0
0
0
2
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
1
2
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
5
2
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
1
0
0
2
2
0
2
0
0
0
2
2
1
0
0
0
0
2
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
3
0
2
2
0
0
0
1
0
0
0
0
0
2
0
2
2
0
0
2
0
0
2
0
0
0
1
1
2
0
0
0
6
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
1
1
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
4
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
1
0
1
0
1
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
2
0
2
2
0
0
0
2
0
0
1
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
6
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
2
6
1
1
0
0
4
0
0
2
0
0
0
1
1
2
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
3
0
1
0
0
0
1
0
0
2
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
2
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
2
1
0
0
0
1
0
0
2
0
1
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
1
0
2
0
0
3
0
1
0
0
0
1
0
0
1
0
1
2
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
3
0
2
0
0
1
0
0
0
0
2
0
0
1
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
1
0
2
1
1
0
1
0
1
2
0
0
0
0
0
0
1
1
0
0
0
2
0
2
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
2
0
1
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
1
1
1
0
0
0
0
0
1
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
3
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
2
0
0
0
0
0
2
2
0
3
0
1
0
0
0
1
2
0
0
0
0
2
0
0
0
2
0
0
2
2
0
1
2
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
1
0
1
0
0
0
0
0
1
0
1
0
0
0
1
1
0
1
1
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
2
0
3
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
2
1
0
0
3
0
0
2
1
0
0
0
2
0
0
0
4
0
0
0
0
0
2
0
0
0
1
0
2
0
4
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
1
0
0
1
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
4
0
0
0
0
0
2
2
2
0
2
0
0
0
2
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
1
0
0
0
2
0
0
2
1
1
0
0
0
0
2
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
2
0
0
3
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
2
0
1
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
5
0
0
0
0
2
0
0
0
1
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
2
1
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
1
0
0
1
0
1
0
0
3
0
2
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
1
0
1
1
0
0
0
0
3
0
2
0
0
0
0
1
2
0
2
0
2
0
1
2
0
2
1
0
0
0
0
1
0
0
2
1
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
2
1
0
0
7
0
0
0
2
0
0
0
0
0
2
0
2
1
2
0
0
0
0
1
2
5
0
0
0
3
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
2
0
0
0
4
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
2
0
0
1
1
0
0
1
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
2
2
2
1
0
0
4
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
3
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
4
2
0
1
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
5
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
2
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
6
0
0
2
0
0
2
0
3
0
2
0
0
0
3
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
1
1
0
0
0
0
0
0
0
3
1
0
2
1
0
0
0
0
0
3
0
2
0
0
0
1
0
0
1
0
0
2
0
0
1
0
0
2
0
2
0
0
0
7
2
0
5
0
0
0
0
3
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
2
2
1
0
1
0
1
3
2
0
0
1
0
0
1
1
0
5
0
0
1
2
0
0
0
0
3
0
2
3
0
1
2
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
2
0
0
0
2
0
0
0
2
2
0
0
0
2
2
0
0
0
0
0
0
2
0
1
2
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
2
5
0
0
2
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
3
0
0
0
0
1
1
0
0
4
0
0
0
0
0
0
0
0
7
0
0
2
2
0
0
1
0
2
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
2
1
2
0
0
0
0
0
0
0
0
0
0
4
1
1
0
2
3
2
0
0
0
2
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
3
2
2
2
0
0
0
2
1
2
1
0
0
0
0
0
3
0
0
2
0
0
2
0
0
0
0
3
0
0
0
0
0
0
4
0
4
2
0
1
4
0
0
0
0
0
0
0
0
2
0
19
0
0
0
0
0
0
1
1
0
1
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
1
0
2
0
2
3
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
3
0
0
2
1
2
0
0
0
0
2
0
0
0
0
0
2
0
1
0
3
0
0
2
0
3
0
2
0
2
0
0
0
3
1
1
0
0
0
0
0
2
0
3
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
3
0
0
2
0
0
1
2
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
6
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
1
0
0
0
0
1
0
2
0
0
1
0
1
2
2
0
0
0
3
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
1
0
2
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
3
0
0
0
0
1
0
0
0
3
1
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
2
0
0
1
0
2
0
0
0
0
0
0
1
0
3
0
0
0
0
0
5
0
0
2
1
0
1
2
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
2
0
1
0
1
0
1
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
8
0
0
1
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
3
0
0
0
0
2
0
2
0
0
0
0
3
2
0
5
0
3
0
0
0
1
1
0
1
0
2
0
0
0
0
2
0
0
2
0
1
0
2
2
0
1
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
1
0
1
0
0
0
3
0
0
1
0
2
2
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
3
0
1
2
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
1
1
0
0
0
2
7
0
0
3
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
0
3
1
0
2
0
1
0
0
1
1
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
1
1
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
4
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
3
1
0
2
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
5
2
0
1
0
1
0
1
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
1
0
2
3
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
1
1
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
1
0
2
0
2
0
2
2
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
3
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
2
0
0
0
1
0
2
0
1
1
1
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
2
0
1
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
2
0
0
0
0
0
0
0
2
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
1
3
1
2
3
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
2
1
0
0
0
0
0
2
2
0
0
4
2
0
0
0
0
2
2
0
0
2
0
0
1
0
0
2
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
4
0
0
0
1
0
1
0
0
0
3
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
2
0
0
2
1
0
2
2
1
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
3
0
2
0
0
2
0
0
0
0
0
1
0
0
0
2
2
0
0
2
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
2
2
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
2
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
1
0
2
0
2
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
3
0
1
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
2
0
0
2
0
0
0
0
1
2
0
0
0
3
0
0
0
0
3
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
5
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
6
0
0
0
0
2
0
0
0
2
0
1
2
1
0
0
0
0
5
1
0
1
2
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
5
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
2
0
1
0
1
2
0
0
0
0
0
0
0
0
0
3
0
0
0
3
0
0
0
0
4
1
2
0
0
2
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
5
0
2
0
2
2
0
0
0
1
0
0
1
0
2
0
2
0
0
1
0
2
0
0
3
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
4
0
0
0
1
0
1
0
0
0
2
0
0
1
3
0
0
0
0
0
2
2
2
0
2
0
0
0
2
0
0
0
0
0
0
1
0
4
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
1
0
0
2
1
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
6
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
2
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
3
0
0
0
0
0
2
0
1
0
2
0
0
3
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
1
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
2
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
2
1
3
0
0
0
1
1
0
0
2
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
8
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
3
1
0
0
0
0
0
14
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
1
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
1
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
4
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
2
0
3
0
2
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
3
0
0
0
1
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
1
0
0
0
2
2
1
0
0
0
1
0
0
1
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
1
3
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
1
0
0
1
0
0
0
1
2
2
0
2
0
0
0
1
0
0
0
3
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
1
2
0
1
1
2
0
0
0
0
0
0
0
3
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
1
0
0
2
0
1
0
1
0
2
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
1
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
4
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
3
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
2
2
3
0
1
0
2
0
0
3
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
2
0
0
2
1
4
3
1
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
1
2
0
3
2
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
3
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
1
2
2
0
0
0
1
3
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
1
0
3
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
3
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
2
0
2
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
2
1
1
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
1
0
3
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
2
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
1
0
2
0
0
0
1
0
2
0
1
0
0
0
0
0
0
1
0
0
2
0
0
3
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
1
1
0
1
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
1
2
4
2
0
0
1
1
0
0
0
0
0
0
4
1
0
0
2
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
2
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
3
1
3
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
1
1
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
3
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
2
0
0
1
2
0
0
0
0
2
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
1
1
0
0
0
0
2
0
0
1
0
0
0
1
3
0
0
1
0
0
2
2
1
0
0
0
1
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
2
1
1
0
1
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
2
1
1
0
0
0
1
2
0
0
0
0
0
1
1
0
1
2
1
0
0
7
0
1
4
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
3
0
0
0
0
2
2
5
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
2
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
2
1
2
0
0
0
4
0
0
0
1
0
0
1
2
0
1
2
1
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
1
1
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
3
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
1
2
1
0
1
0
1
2
0
0
0
2
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
2
2
0
0
1
0
2
2
0
0
2
0
0
0
0
0
0
2
0
1
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
2
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
2
0
0
4
0
0
0
1
0
1
1
1
2
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
2
1
0
0
1
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
3
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
2
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
2
1
1
0
0
2
0
0
0
0
1
4
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
2
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
1
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
2
0
0
7
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
1
2
0
0
0
0
1
0
0
0
1
0
0
1
0
0
2
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
1
0
3
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
10
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
3
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
6
0
0
0
0
0
1
0
1
2
0
0
0
2
0
0
1
1
0
0
3
0
0
0
2
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
2
3
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
2
0
0
0
2
0
0
2
0
3
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
2
1
2
0
0
0
2
2
3
0
0
0
1
0
2
0
0
0
0
1
1
0
1
0
2
0
0
0
0
0
0
0
0
3
2
0
2
1
0
0
0
2
0
0
0
3
0
0
0
2
0
8
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
1
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
2
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
1
1
0
0
0
2
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
1
1
0
0
0
0
0
1
9
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
1
1
0
0
0
0
1
2
1
0
0
0
2
0
3
0
0
0
0
0
3
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
2
2
2
0
2
0
3
0
0
0
0
0
0
0
1
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
0
5
2
0
0
0
0
0
3
0
1
0
1
0
0
0
0
0
0
0
5
1
2
2
2
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
1
0
0
1
2
0
3
1
4
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
1
2
1
1
1
0
0
0
0
2
0
0
4
0
0
2
1
0
0
0
0
1
1
1
0
0
0
0
0
2
0
2
0
0
0
1
0
2
0
0
0
0
0
0
3
3
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
2
0
0
0
0
0
2
1
2
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
3
0
2
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
2
0
0
1
0
1
4
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
1
2
1
0
0
0
2
0
0
0
0
0
0
2
2
0
1
0
0
0
0
4
0
0
2
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
2
0
0
4
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
3
0
0
1
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
2
2
0
1
0
0
0
2
2
0
2
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
3
2
0
0
0
2
0
2
2
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
3
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
6
0
0
0
0
0
1
2
0
1
0
4
0
0
0
0
0
0
0
4
0
4
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
2
0
1
1
0
0
0
0
0
2
2
0
0
2
1
2
0
0
0
1
0
0
0
2
0
3
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
7
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
3
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
1
0
0
0
1
0
1
0
0
1
0
0
1
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
4
0
1
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
2
4
1
0
4
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
2
0
2
1
0
0
0
1
0
0
0
1
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
2
1
1
0
0
2
2
1
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
2
0
2
0
0
0
0
0
2
0
0
0
2
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
1
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
2
0
0
3
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
4
1
0
0
0
3
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
2
0
0
0
0
2
0
0
0
3
0
0
2
1
1
1
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
3
0
0
1
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
4
0
0
0
0
0
0
2
1
2
0
0
1
0
0
3
0
0
0
0
0
0
1
0
1
1
0
2
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
1
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
1
2
0
2
0
0
0
0
2
0
0
2
0
0
0
2
0
1
0
0
0
0
1
1
0
0
1
1
2
0
0
1
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
3
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
1
1
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
2
3
0
0
0
1
0
0
1
1
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
3
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
3
0
0
2
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
5
1
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
3
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
1
0
1
4
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
5
0
2
0
1
1
0
3
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
4
0
0
0
0
1
0
1
0
0
2
0
3
1
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
1
0
0
0
0
0
0
0
0
11
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
1
0
0
2
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
2
0
2
2
0
0
2
0
0
0
1
1
4
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
2
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
1
2
1
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
2
0
2
0
0
2
0
0
0
0
1
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
4
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
1
0
0
0
0
0
1
1
0
3
0
0
2
0
0
0
2
0
1
0
0
0
0
1
0
0
0
6
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
5
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
5
0
3
3
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
1
0
0
0
0
1
1
0
0
3
0
0
0
0
0
2
0
1
0
0
2
0
0
0
2
0
0
0
0
2
1
0
1
3
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
1
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
3
0
1
0
0
2
0
0
0
0
0
0
2
0
1
2
0
0
0
2
1
0
1
0
1
0
1
0
2
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
1
0
3
1
0
0
0
0
0
2
0
0
0
0
2
1
0
0
1
1
0
0
2
0
1
0
1
0
0
0
3
2
2
0
0
0
0
0
0
2
3
1
0
0
0
0
1
0
0
1
0
4
2
1
1
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
6
1
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
1
0
0
1
0
1
0
1
2
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
2
0
2
0
1
0
1
2
0
1
0
2
2
0
1
2
0
0
2
0
0
2
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
2
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
1
0
0
2
0
0
1
1
1
1
2
0
2
1
0
0
0
0
1
0
0
0
0
1
1
0
2
0
0
0
1
0
0
2
0
0
3
2
0
0
2
0
0
0
0
1
1
0
0
0
1
2
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
2
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
2
0
2
0
1
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
1
2
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
1
0
0
0
2
0
1
0
3
0
0
0
0
0
0
3
0
0
1
1
2
1
0
0
0
2
1
0
2
0
0
0
0
0
0
1
2
1
2
0
0
1
0
0
0
3
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
2
0
0
2
1
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
6
1
0
0
0
2
0
0
2
1
0
0
3
0
2
0
0
0
0
2
0
2
0
0
3
0
4
2
0
3
1
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
5
1
2
2
2
0
2
1
0
2
1
1
0
3
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
2
2
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
2
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
3
0
2
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
2
2
0
0
2
0
0
0
2
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
1
1
0
3
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
4
0
0
0
0
3
0
0
1
1
0
1
0
0
0
3
0
0
1
0
4
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
2
1
2
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
2
2
0
0
0
4
2
0
0
2
0
0
0
0
0
0
0
0
0
5
1
0
2
1
0
0
2
3
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
2
0
0
2
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
2
1
0
0
0
0
0
1
2
0
1
0
0
0
0
1
3
0
0
2
0
0
0
0
0
1
2
0
0
0
2
0
0
0
1
0
0
1
2
1
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
5
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
3
0
0
0
0
0
2
0
1
0
0
2
0
1
0
0
1
0
0
0
3
2
1
0
0
0
2
0
0
0
0
2
1
0
1
2
0
0
0
0
1
1
0
0
0
2
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
2
2
0
0
0
0
0
2
0
2
2
0
2
1
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
5
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
2
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
2
0
0
0
1
0
0
1
0
0
0
3
0
0
0
2
0
0
0
0
0
3
2
0
0
1
0
0
0
0
4
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
3
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
2
2
4
1
0
6
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
1
2
1
3
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
1
0
0
2
0
0
0
1
0
0
3
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
2
0
1
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
4
0
0
0
0
6
1
2
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
1
2
2
1
0
0
1
3
1
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
4
0
0
4
0
0
0
0
0
1
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
6
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
2
0
0
4
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
1
0
0
3
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
4
1
0
0
1
2
2
2
1
0
1
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
2
0
1
0
0
0
2
1
3
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
2
1
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
2
0
3
0
0
0
0
1
1
0
2
0
2
0
0
1
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
2
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
5
0
0
0
0
0
2
0
0
1
0
0
0
0
3
0
2
0
2
0
0
2
0
2
1
0
1
2
0
1
0
1
0
1
1
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
1
0
0
2
0
0
1
1
2
2
0
0
1
0
0
0
0
0
2
2
1
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
1
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
3
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
2
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
3
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
3
1
0
0
0
0
2
1
6
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
1
0
2
0
0
2
0
0
0
0
0
0
0
1
0
3
0
2
0
2
0
2
0
0
3
2
0
0
0
1
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
2
0
1
0
2
0
0
3
1
0
0
0
0
0
2
0
1
2
0
3
0
0
1
0
1
0
0
1
2
3
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
1
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
2
5
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
5
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
4
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
5
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
1
0
2
1
0
2
0
0
3
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
5
1
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
1
0
0
3
7
1
0
1
1
0
3
0
4
0
0
0
0
0
1
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
1
0
0
1
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
2
1
0
0
0
2
0
3
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
2
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
2
0
0
2
1
0
0
2
0
0
0
0
1
0
1
1
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
15
0
0
0
0
0
0
2
0
2
0
1
2
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
2
2
2
0
2
0
0
0
1
0
1
0
0
0
0
1
2
0
0
0
2
0
4
0
1
1
0
0
0
0
0
0
0
0
2
4
0
0
1
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
1
0
9
0
1
0
0
1
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
2
2
0
0
0
0
2
0
13
0
0
0
3
0
2
0
0
2
0
1
1
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
3
2
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
5
1
0
1
0
0
0
1
0
1
0
0
0
3
0
0
2
1
0
2
0
0
0
2
0
0
0
0
0
3
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
2
0
2
0
2
1
1
0
1
0
0
0
0
1
0
0
0
0
2
0
1
1
0
1
2
0
0
1
2
0
1
0
0
1
0
0
14
0
0
0
1
1
2
0
0
0
0
0
0
0
0
2
2
1
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
1
2
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
7
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
1
2
0
1
2
3
0
0
0
1
2
0
0
0
0
0
2
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
2
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
4
3
0
0
0
1
0
0
0
0
0
2
0
4
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
4
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
1
0
1
1
0
4
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
2
0
0
0
0
0
2
0
2
6
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
3
0
0
0
2
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
1
0
11
0
3
0
0
0
0
1
2
0
0
2
2
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
1
0
2
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
2
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
4
0
1
0
0
1
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
3
2
0
0
0
2
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
0
2
0
0
0
4
0
2
0
3
0
2
0
0
1
1
0
0
0
1
1
1
2
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
2
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
1
1
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
3
0
2
0
0
0
1
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
1
0
0
1
0
0
0
2
2
0
0
0
1
0
0
3
2
3
4
0
0
0
2
2
0
2
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
1
0
0
1
1
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
4
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
20
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
5
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
1
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
3
0
0
0
0
0
0
1
2
3
2
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
5
1
0
0
0
2
0
1
0
1
0
2
0
1
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
1
3
0
0
0
0
0
4
1
3
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
1
1
1
1
0
0
0
0
0
0
2
1
1
3
1
1
0
0
0
2
5
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
2
0
2
0
0
1
0
0
0
1
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
1
0
2
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
3
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
2
0
2
1
1
0
0
0
0
1
0
0
0
1
2
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
1
0
3
0
3
0
3
0
1
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
1
1
0
3
0
0
0
2
0
1
0
2
0
0
0
3
1
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
3
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
1
1
1
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
4
0
0
0
2
0
3
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
3
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
2
1
0
0
0
0
0
2
0
1
0
0
0
3
0
0
2
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
2
0
2
0
0
0
3
0
0
0
0
0
2
1
1
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
3
0
2
1
0
0
0
1
0
0
0
0
3
0
1
0
1
2
1
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
3
0
1
0
2
0
1
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
2
2
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
1
0
1
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
3
0
0
0
0
2
3
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
2
2
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
4
1
2
3
0
0
0
2
0
4
1
1
0
0
5
0
0
0
0
2
1
4
2
2
2
2
0
1
0
0
0
0
1
0
0
0
1
2
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
2
3
1
0
0
0
0
4
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
1
2
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
2
2
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
1
2
0
1
0
0
0
0
0
0
1
0
0
0
3
0
0
2
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
1
0
0
0
1
0
0
2
1
0
0
1
0
0
2
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
2
0
2
3
0
2
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
2
0
0
2
0
0
2
0
2
1
0
0
1
0
0
0
1
1
0
2
0
1
0
3
1
0
1
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
3
2
0
0
3
2
0
0
2
0
4
0
0
0
0
1
2
0
0
0
0
1
1
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
3
0
2
0
1
0
0
2
0
1
2
0
2
0
0
0
2
1
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
2
0
1
1
2
0
1
1
1
0
0
0
0
2
0
0
1
0
7
1
0
0
0
1
0
0
0
0
0
0
0
2
0
1
2
0
0
0
2
3
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
1
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
1
2
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
7
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
1
2
2
1
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
8
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
7
0
0
4
0
0
0
2
2
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
4
0
2
1
2
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
2
1
2
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
3
0
4
0
2
0
2
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
2
0
1
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
1
1
0
0
0
2
1
0
0
0
0
0
2
0
2
0
0
2
0
2
0
2
0
0
0
0
0
2
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
1
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
6
0
0
0
0
0
3
0
0
0
0
1
1
1
0
2
0
0
0
0
3
3
0
1
0
0
0
0
0
0
0
1
1
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
3
0
1
3
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
1
0
2
0
0
5
0
0
3
0
2
0
0
1
0
0
0
2
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
5
0
0
0
0
0
0
2
1
2
1
0
0
1
0
0
0
0
0
2
2
0
0
2
2
0
0
0
2
1
0
0
0
0
1
0
0
1
0
2
0
1
0
1
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
1
2
0
0
3
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
4
0
0
0
2
1
2
0
2
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
3
0
2
0
0
1
1
2
0
0
0
0
0
2
0
0
1
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
2
0
0
1
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
1
0
0
1
1
1
2
1
0
1
0
0
2
0
0
0
0
0
2
0
1
0
1
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
2
0
2
0
2
0
3
2
2
1
0
0
0
0
0
2
1
0
3
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
2
1
1
0
1
0
0
1
1
1
2
3
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
3
0
0
0
0
3
0
0
0
1
0
0
0
2
0
2
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
2
0
2
1
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
2
2
0
0
2
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
2
2
0
0
0
1
0
2
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
4
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
1
0
2
2
0
0
0
0
0
3
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
1
0
0
0
0
0
1
2
0
1
0
0
0
0
0
2
2
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
1
1
0
1
2
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
1
2
1
2
3
2
0
2
0
0
4
0
0
0
0
2
1
0
0
0
1
1
2
0
2
0
0
2
1
0
0
1
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
4
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
2
0
1
0
0
0
2
0
2
0
1
0
2
1
0
0
0
2
0
1
0
0
1
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7
0
0
0
3
2
2
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
5
0
2
0
1
0
1
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
3
0
0
0
0
2
0
2
0
0
0
1
0
0
0
1
0
3
0
0
2
2
0
1
0
0
0
0
2
2
0
2
1
2
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
1
0
0
0
1
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
3
0
0
2
0
0
2
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
1
2
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
2
2
0
0
1
0
0
2
2
0
0
0
0
0
0
0
2
1
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
4
0
3
0
0
2
0
0
1
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
1
2
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
1
0
0
3
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
1
1
2
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
3
1
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
3
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
2
2
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
1
0
0
2
1
0
2
0
0
5
0
0
0
2
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
2
2
0
0
0
1
1
0
1
0
0
2
0
0
0
0
0
0
0
0
3
0
0
1
0
1
0
2
2
1
3
1
0
0
0
0
3
0
0
3
0
0
0
0
0
0
1
0
0
1
2
0
2
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
5
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
2
0
0
1
0
1
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
2
0
0
1
3
0
0
4
2
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
2
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
2
0
1
0
0
0
0
0
0
2
3
0
2
3
0
0
2
0
0
2
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
3
0
0
2
2
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
3
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
1
0
0
1
0
2
0
1
0
0
1
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
2
0
0
0
0
1
0
2
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
5
0
1
1
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
4
0
1
0
2
1
0
0
1
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
1
2
0
0
2
1
0
0
0
0
1
1
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
2
0
1
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
1
1
0
1
0
4
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
1
0
0
4
3
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
4
0
1
0
1
0
0
0
1
1
0
0
0
0
3
2
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
2
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
1
0
1
1
0
0
0
2
0
1
2
0
0
0
4
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
2
1
0
1
0
2
1
0
0
0
0
2
2
2
1
0
1
0
0
1
2
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
2
0
1
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
5
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
5
1
3
0
0
0
1
0
1
0
0
0
0
0
0
1
2
0
3
0
0
2
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
5
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
3
0
0
0
2
0
2
1
0
0
2
0
0
2
0
0
1
2
0
1
2
3
0
2
0
3
0
11
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
1
1
1
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
2
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
1
1
0
1
0
0
0
0
2
0
0
2
1
0
0
0
2
0
1
0
0
2
0
3
2
0
0
0
0
1
0
0
0
2
2
0
2
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
1
0
0
2
0
0
0
0
2
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
2
0
1
0
0
0
0
1
0
0
0
3
0
0
0
2
0
1
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
3
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
2
0
0
2
0
0
0
3
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
4
2
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
3
0
2
0
0
1
0
2
2
2
0
1
2
0
2
0
0
1
0
0
0
0
0
1
0
3
0
0
0
0
0
2
3
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
1
1
0
0
1
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
2
0
3
0
1
0
2
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
2
0
0
0
1
0
2
1
0
0
2
1
0
0
1
0
2
0
2
1
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
2
0
0
2
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
2
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
4
0
2
0
0
2
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
1
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
1
0
1
0
4
0
0
0
0
0
1
0
0
0
0
2
0
0
1
1
0
1
1
1
0
0
0
3
0
0
0
1
2
0
0
2
1
4
0
2
2
0
0
1
0
1
0
0
1
0
0
0
2
0
3
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
5
0
0
2
0
0
0
3
0
0
3
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
2
1
2
0
0
0
0
0
0
2
0
2
0
0
3
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
1
0
0
0
2
1
0
0
0
1
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
3
0
0
2
0
1
2
1
0
0
0
0
0
0
0
2
2
1
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
1
2
0
1
0
0
0
0
0
0
3
2
1
0
0
2
0
2
0
0
2
0
0
1
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
1
0
2
0
0
1
0
2
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
1
0
0
0
2
0
0
1
1
0
0
1
3
0
1
0
0
0
1
0
0
0
0
0
0
6
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
4
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
2
2
2
1
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
3
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
3
0
0
0
0
1
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
5
2
0
0
0
0
3
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
3
7
0
0
0
0
0
0
0
0
0
1
1
2
1
2
0
5
2
6
0
5
0
2
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
3
1
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
2
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
2
1
0
1
2
2
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
4
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
1
1
1
2
0
1
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
2
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
2
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
2
0
0
2
0
0
2
0
0
0
0
0
2
5
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
3
0
2
0
1
0
0
0
0
1
0
0
0
1
2
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
2
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
1
1
0
1
0
0
8
1
0
1
0
0
2
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
2
0
0
0
0
1
1
0
0
0
0
2
0
1
0
1
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
3
2
2
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
5
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
3
0
0
1
0
0
0
0
0
0
0
3
0
0
2
0
1
0
0
0
0
2
0
0
1
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
1
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
2
0
2
0
0
0
2
0
0
0
0
2
0
1
0
1
1
0
0
1
1
0
0
0
0
0
1
0
0
1
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
2
0
3
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
1
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
2
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
6
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
2
0
0
2
0
0
0
1
0
0
4
0
1
0
0
2
2
0
0
0
0
2
0
0
0
3
0
0
3
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
2
0
0
0
2
0
0
0
1
0
3
0
0
0
0
1
0
1
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
1
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
1
3
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
6
0
0
0
1
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
2
0
0
1
0
1
0
0
1
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
4
0
5
1
0
0
2
0
0
0
0
0
0
0
0
0
2
1
1
0
2
0
0
2
1
1
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
2
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
3
1
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
2
1
0
2
0
0
2
0
0
0
1
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
5
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
3
0
0
0
0
0
2
1
0
0
0
0
1
0
0
1
0
0
0
0
2
0
2
0
1
0
0
0
2
0
0
1
0
0
2
0
0
0
0
2
0
1
0
2
0
1
0
1
2
1
0
0
0
0
0
0
1
0
0
0
1
3
0
0
1
0
2
2
0
0
0
0
0
1
4
1
0
1
0
0
0
1
0
0
0
0
0
0
0
20
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
4
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
2
0
0
0
0
0
1
2
0
1
0
0
0
1
0
1
0
2
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
1
1
0
0
2
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
1
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
7
0
0
0
1
2
0
0
2
1
1
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
2
2
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
2
6
1
2
1
0
0
0
2
1
1
2
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
1
2
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
2
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
3
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
1
0
0
0
2
2
0
0
4
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
3
0
0
0
0
0
0
1
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
2
0
0
0
2
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
4
1
3
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
2
0
1
2
1
7
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
3
0
2
2
0
0
0
0
1
0
2
0
0
0
2
1
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
1
0
0
2
0
0
0
0
5
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
3
0
0
0
0
0
0
0
0
2
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
6
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
4
0
1
1
0
2
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
2
0
0
1
0
0
2
5
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
1
0
1
0
0
1
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
1
0
0
0
2
1
0
0
1
0
0
0
2
1
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
1
1
0
1
0
0
2
0
1
0
1
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
2
0
4
0
0
0
0
0
0
1
0
2
0
3
0
0
0
0
0
0
2
0
0
0
2
0
4
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
3
0
0
3
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
1
0
0
0
0
0
0
2
1
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
2
1
2
0
1
0
1
2
0
2
0
2
0
0
1
1
4
0
0
0
1
0
1
5
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
1
1
0
0
0
0
0
2
0
0
2
1
0
1
0
0
2
0
0
0
0
2
0
0
0
4
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
3
0
2
4
0
0
0
0
1
0
2
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
2
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
1
0
0
7
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
2
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
3
1
0
0
0
2
2
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
8
0
0
0
2
3
0
0
0
2
1
0
0
1
3
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
2
0
0
1
0
0
0
0
3
0
0
0
0
3
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
2
1
1
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
1
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
1
1
1
0
0
2
0
0
0
3
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
3
0
2
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
3
0
2
2
2
0
2
0
0
0
0
0
0
0
0
0
0
4
0
3
0
0
0
1
1
0
0
2
1
0
1
1
0
0
0
2
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
2
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
3
3
0
0
1
0
0
0
4
0
2
1
3
0
0
0
0
1
0
0
0
0
0
2
0
2
0
2
0
0
2
0
0
2
0
0
1
0
0
1
0
0
0
0
1
0
0
2
0
2
0
0
1
0
0
0
2
0
0
0
0
2
0
2
2
2
0
2
0
2
0
0
0
0
0
0
0
2
0
3
0
1
0
0
0
2
1
0
0
2
0
0
2
0
2
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
2
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
1
0
0
0
2
0
0
0
2
0
0
3
1
1
0
3
1
0
3
0
0
2
1
0
0
0
1
0
0
1
0
0
3
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
1
2
0
2
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
4
2
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
2
0
1
0
0
2
3
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
1
2
0
0
1
0
0
1
0
0
0
2
0
0
0
0
2
0
2
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
1
2
0
2
0
0
0
0
0
1
0
2
0
0
1
0
0
1
0
1
1
2
1
0
0
0
0
0
1
0
1
5
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
2
2
0
0
0
0
0
3
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
1
0
0
1
2
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
1
0
0
1
1
0
0
0
2
1
0
0
1
0
2
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
3
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
3
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
3
2
1
0
1
0
3
0
4
1
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
5
0
0
0
3
0
1
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
3
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
1
2
0
0
2
0
0
0
3
0
0
1
1
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
7
0
0
0
2
1
0
0
0
2
1
0
2
0
0
0
0
1
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
4
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
1
0
2
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
2
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
1
3
0
0
0
2
1
0
0
1
2
0
0
0
3
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
4
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
2
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
1
3
1
0
0
0
2
0
0
2
0
0
1
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
2
1
0
0
0
0
1
3
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
2
0
1
0
0
1
0
0
0
1
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
3
1
2
0
0
4
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
1
0
7
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
2
0
0
1
0
2
0
1
0
0
0
0
2
0
0
3
0
1
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
1
0
2
0
1
0
2
0
3
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
3
0
2
0
0
2
0
0
4
2
1
0
0
0
1
0
0
0
0
0
0
6
0
2
0
0
0
0
0
2
0
2
2
0
3
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
1
0
0
2
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
4
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
4
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
1
1
2
0
0
2
0
0
0
2
0
0
0
0
1
1
0
0
1
1
0
2
2
2
1
0
0
0
2
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
1
0
0
7
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
2
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
1
0
5
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
2
0
2
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
5
0
0
2
3
0
0
0
0
0
2
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
2
2
3
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
1
1
0
0
0
1
1
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
2
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
8
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
2
1
0
3
0
0
0
1
0
0
0
0
0
0
2
2
2
0
0
0
1
0
0
0
0
1
0
0
1
1
0
2
0
0
0
0
1
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
3
0
1
1
0
1
0
0
2
0
0
1
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
3
2
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
2
0
0
1
0
0
1
0
0
0
1
2
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
2
0
1
0
0
2
0
2
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
1
0
1
1
0
1
0
0
1
2
0
2
2
0
0
0
0
0
0
0
1
0
1
0
2
0
1
3
0
0
1
0
0
1
1
0
1
2
0
1
1
0
1
1
0
0
0
2
0
1
0
2
1
0
2
2
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
7
3
0
0
0
0
0
0
0
2
1
2
0
1
0
0
0
0
1
3
2
0
3
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
1
1
6
0
0
0
0
2
1
0
2
1
1
0
0
0
0
0
0
0
0
5
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
4
0
1
0
3
0
0
0
2
2
1
0
0
1
0
0
4
0
0
3
1
0
0
2
0
0
0
1
1
1
0
2
1
0
0
3
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
2
0
0
1
2
2
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
3
3
0
0
0
5
0
3
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
3
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
2
2
0
0
0
0
0
0
0
2
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
2
0
5
2
0
0
1
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
2
2
0
0
0
0
2
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
3
0
0
1
2
0
0
0
0
1
0
0
0
0
0
2
0
1
4
0
0
0
2
0
0
0
0
1
1
2
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
2
0
3
1
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
3
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
4
1
0
0
0
0
0
1
2
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
4
5
1
3
0
1
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
1
4
1
2
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
1
0
0
0
0
2
0
0
4
0
0
0
0
0
0
2
2
1
2
0
0
0
2
2
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
2
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
3
0
0
0
2
0
0
0
2
0
2
0
0
1
1
1
0
0
2
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
7
0
0
0
0
0
1
0
0
0
1
0
1
0
0
2
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
5
0
0
0
0
1
0
2
3
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
1
0
0
2
1
0
2
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
1
0
3
0
0
0
0
0
0
0
0
0
1
0
0
3
0
2
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
2
0
1
1
0
2
2
0
0
3
0
0
1
1
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
3
0
0
0
1
2
0
2
0
0
0
2
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
3
0
1
5
0
0
0
0
1
0
0
3
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
1
1
1
2
3
0
0
0
1
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
3
1
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
2
3
0
0
2
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
3
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
3
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
2
2
0
1
0
0
0
0
1
2
0
1
0
1
3
0
0
0
5
0
0
0
0
1
0
1
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
2
3
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
13
0
2
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
3
1
0
0
0
0
0
2
0
1
0
0
0
1
1
1
2
0
0
0
1
0
0
1
1
1
0
2
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
2
0
0
3
0
0
2
1
0
0
0
1
0
0
0
0
0
1
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
6
1
0
0
0
1
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
3
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
2
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
3
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
2
0
0
0
1
0
1
1
0
0
0
0
2
0
0
0
0
0
1
2
2
0
0
0
2
0
0
1
6
8
0
4
2
0
2
0
0
0
0
0
0
1
2
2
0
0
3
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
1
0
2
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
1
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
8
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
2
0
0
0
0
0
0
3
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
2
0
1
0
1
0
0
2
0
0
0
2
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
3
2
0
0
0
0
0
0
1
0
0
3
0
1
3
4
0
0
0
0
0
1
0
0
2
0
0
0
1
2
0
0
2
0
1
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
2
0
2
7
0
0
2
0
0
3
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
1
1
0
2
3
0
0
0
0
0
0
0
2
1
0
1
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
2
6
0
0
0
0
2
0
0
0
0
0
2
3
0
0
0
1
0
0
0
0
1
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
1
1
2
0
0
2
1
0
0
0
0
1
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
1
1
0
1
0
0
2
1
0
0
1
0
0
5
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
10
0
0
0
2
1
1
0
0
0
0
0
0
1
3
0
0
0
0
0
1
0
0
1
0
3
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
2
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
3
1
2
0
2
0
2
0
1
0
0
5
0
0
0
2
0
3
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
3
0
1
0
1
2
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
3
1
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
2
1
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
1
1
0
0
0
0
1
5
0
2
0
1
2
0
2
1
0
0
2
0
0
3
0
0
2
0
2
0
0
2
1
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
3
1
0
0
0
0
1
0
0
0
0
0
0
2
0
1
1
0
1
2
0
1
0
0
2
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
8
0
0
0
0
1
1
0
0
0
0
0
1
2
0
0
1
3
0
0
1
1
0
0
0
1
0
0
0
1
2
0
0
0
0
0
1
0
0
3
0
0
1
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
1
2
1
0
1
0
0
1
2
0
0
0
2
0
1
0
2
1
2
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
1
0
2
1
4
1
0
0
2
2
0
0
0
0
2
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
3
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
7
0
2
1
0
0
0
0
2
0
2
0
1
0
2
1
0
0
0
2
0
0
0
0
0
2
0
2
2
0
1
2
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
1
0
0
0
0
1
1
2
0
1
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
3
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
1
2
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
1
1
2
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
1
0
2
0
2
0
2
0
0
0
0
0
2
0
0
0
2
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
1
1
2
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
3
0
1
0
0
0
2
2
0
0
2
0
0
0
2
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
4
2
2
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
2
0
0
0
0
0
0
0
2
3
0
0
2
0
0
0
1
0
1
0
1
0
0
2
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
2
6
0
1
0
0
0
4
0
0
1
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
1
0
1
0
2
2
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
2
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
3
1
1
0
0
0
2
0
1
2
1
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
3
1
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
3
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
2
3
0
0
0
0
2
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
3
0
4
0
0
0
0
3
0
4
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
4
1
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
2
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
3
0
1
1
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
1
0
0
0
0
5
2
0
0
2
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
3
0
1
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
3
0
0
2
1
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
2
0
3
1
1
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
1
0
2
0
0
3
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
2
0
0
0
1
2
0
0
4
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
1
0
2
0
3
0
0
0
0
0
2
1
2
0
0
0
1
0
1
0
0
0
2
0
0
2
0
0
0
0
1
1
1
0
0
0
0
1
2
1
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
2
2
2
0
2
0
1
0
0
0
0
1
0
1
0
1
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
2
1
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
3
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
2
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
1
2
2
1
0
0
0
0
0
1
0
0
0
1
0
6
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
1
1
2
2
0
0
3
2
0
0
8
0
0
2
3
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
4
0
0
2
0
0
0
1
0
0
2
2
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
2
2
0
1
0
0
2
0
0
1
0
0
0
3
0
2
0
0
0
0
0
0
1
2
2
0
2
1
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
2
2
0
0
3
0
0
2
3
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
2
0
0
0
2
1
2
0
0
0
0
0
0
4
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
2
0
2
0
3
0
0
0
0
0
2
0
2
0
0
1
1
0
0
1
0
0
0
2
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
4
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
7
0
2
0
0
0
2
2
0
0
0
4
0
2
0
0
2
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
13
0
0
0
0
0
0
0
0
7
0
1
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
6
0
2
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
2
0
0
0
1
1
0
3
2
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
1
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
2
0
3
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
1
0
3
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
3
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
3
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
2
0
2
0
0
0
2
0
2
3
0
2
0
0
2
0
1
0
0
0
0
2
0
2
0
1
3
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
1
0
0
0
4
1
0
0
0
0
0
0
0
0
1
0
0
3
0
2
0
1
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
2
1
0
6
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
3
0
0
1
0
0
3
4
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
2
2
2
0
0
0
2
0
0
0
1
2
0
4
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
2
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
1
2
0
0
0
2
4
2
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
1
0
0
1
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
1
0
0
1
0
2
0
0
1
0
0
0
1
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
2
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
1
0
2
1
0
0
2
0
2
0
0
0
0
1
0
1
0
0
1
2
0
0
1
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
2
0
3
2
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
1
1
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
1
1
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
3
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
1
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
7
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
1
0
0
1
0
0
0
0
0
0
1
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
1
2
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
1
3
0
0
0
3
0
0
2
0
1
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
2
0
0
0
0
2
1
0
2
0
0
0
1
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
4
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
2
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
3
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
1
0
2
4
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
4
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
3
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
11
0
2
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
1
1
2
1
0
2
1
0
0
1
0
1
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
2
8
0
0
0
0
0
1
4
0
0
0
3
0
0
0
0
0
0
6
0
0
0
0
0
1
0
4
1
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
2
2
0
0
0
0
1
2
1
0
0
0
2
2
0
0
0
0
0
1
1
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
2
1
0
1
3
0
2
0
0
0
2
1
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
2
0
0
0
2
0
2
3
2
0
1
0
0
2
0
0
0
1
1
2
0
0
0
2
2
2
0
0
2
1
0
0
0
1
2
0
1
3
2
0
0
0
1
0
0
1
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
3
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
4
2
0
0
0
0
0
0
0
0
1
1
1
3
0
0
1
3
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
3
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
6
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
1
0
0
3
0
2
2
0
0
0
0
1
1
3
0
0
0
1
1
0
0
1
1
0
0
0
0
0
2
0
0
1
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
9
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
1
3
0
3
0
0
0
0
0
0
1
1
0
1
0
2
0
1
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
2
0
6
0
2
0
0
0
0
2
0
0
1
0
0
0
3
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
1
2
0
1
0
0
0
4
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
3
0
2
0
0
0
1
0
2
0
2
2
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
2
0
2
0
0
3
1
0
0
4
0
1
0
0
0
0
2
0
3
0
0
0
0
0
0
2
0
0
2
0
2
1
1
0
2
0
0
1
0
0
0
0
0
0
2
0
0
1
1
2
0
1
0
2
2
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
3
0
0
0
2
1
0
0
0
2
1
0
2
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
9
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
2
5
2
0
0
1
0
0
0
2
0
1
0
2
2
0
0
0
0
0
0
3
2
24
0
0
1
0
2
0
0
0
0
2
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
1
0
0
0
2
0
0
1
0
0
0
0
1
2
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
9
0
0
0
0
0
2
0
2
0
0
3
0
1
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
1
1
0
1
2
0
1
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
3
0
0
0
0
4
0
0
4
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
2
2
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
1
0
0
3
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
1
0
0
0
0
2
1
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
3
1
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
4
0
0
1
1
2
0
2
0
2
0
0
1
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
2
1
2
2
0
0
1
1
0
2
0
0
1
0
0
0
2
0
2
1
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
1
0
0
1
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
1
2
2
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
2
2
1
0
1
1
0
0
0
0
2
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
2
0
2
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
2
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
4
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
1
2
0
0
0
0
0
3
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
1
1
0
0
0
1
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
1
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
1
0
0
0
2
1
2
1
0
0
1
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
2
0
1
0
0
1
0
2
0
0
2
0
2
0
1
0
1
0
0
0
0
1
0
1
0
0
2
0
0
0
0
1
2
1
0
0
0
0
0
0
0
2
3
0
1
0
0
0
0
1
0
0
0
1
0
0
2
0
0
1
1
0
0
0
1
0
0
0
1
2
2
0
0
0
0
0
2
0
0
1
3
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
4
0
0
0
0
0
0
2
2
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
2
0
0
0
1
1
1
0
1
0
2
0
0
6
0
0
0
0
0
2
0
1
0
0
1
0
1
0
1
0
0
0
0
2
1
0
0
2
0
0
0
1
0
2
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
4
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
1
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
6
0
0
1
0
6
0
4
2
0
0
0
0
0
2
0
0
0
1
0
0
0
1
2
0
1
0
2
3
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
2
2
1
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
6
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
3
2
2
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
1
0
0
2
0
0
1
0
0
0
0
1
1
0
1
0
0
2
1
0
0
0
1
0
2
0
2
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
2
1
0
0
3
0
1
2
0
1
1
0
0
2
2
0
2
0
0
0
0
0
0
2
3
1
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
1
2
0
1
3
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
3
0
0
0
0
0
2
0
3
0
0
0
0
0
0
3
2
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
2
0
2
0
0
1
2
2
0
0
0
0
3
1
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
2
0
0
0
2
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
3
1
0
0
0
0
0
0
0
0
1
0
0
1
0
2
2
0
1
2
0
0
2
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
9
2
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
2
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
1
1
0
1
0
0
6
0
4
0
0
0
1
0
0
0
2
0
0
4
0
0
0
2
0
0
3
0
0
0
2
2
0
0
0
2
1
0
0
0
0
1
0
2
2
0
1
8
0
0
0
0
1
2
0
0
0
0
2
0
2
0
2
1
0
0
2
0
0
0
2
0
2
0
2
0
0
1
2
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
2
3
2
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
2
2
1
2
0
1
0
0
0
0
2
1
0
0
0
0
2
0
0
0
4
0
0
0
0
0
1
0
0
0
0
2
0
1
2
2
0
1
0
0
2
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
4
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
2
1
0
0
0
2
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
1
0
2
0
0
0
0
0
0
0
1
3
4
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
1
2
0
1
0
0
0
0
1
1
1
0
0
2
2
2
3
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
3
3
2
2
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
1
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
4
2
0
0
0
3
3
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
2
0
0
2
0
0
3
1
0
0
0
0
1
0
3
1
0
0
1
0
0
0
1
0
1
1
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
1
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
2
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
4
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
1
0
0
2
2
1
0
0
0
3
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
1
2
1
0
2
0
0
3
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
3
1
0
2
0
2
4
0
1
0
2
0
2
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
2
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
1
2
0
0
0
0
0
0
1
1
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
3
0
0
1
0
0
0
2
2
0
0
8
0
2
1
0
0
2
0
0
0
1
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
3
0
0
0
0
0
0
2
2
0
0
0
1
1
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
6
0
0
2
0
2
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
1
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
2
0
1
0
0
0
1
1
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
3
0
5
0
0
0
0
0
0
0
0
3
0
1
0
2
3
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
2
0
1
0
0
0
0
0
3
0
0
0
2
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
2
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
3
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
2
1
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
2
1
1
0
1
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
3
0
1
2
0
0
2
0
0
0
0
0
8
2
0
0
0
0
2
0
0
0
2
1
0
1
0
0
0
0
2
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
1
0
0
0
0
0
2
1
1
1
0
4
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
3
0
2
3
2
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
2
0
1
1
1
0
3
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
2
0
0
0
2
0
1
1
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
1
2
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
1
0
1
1
0
0
0
0
0
0
0
2
1
1
0
2
0
1
2
0
1
0
0
0
2
0
0
0
0
0
2
0
0
3
1
0
0
0
1
2
0
0
0
0
2
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
1
1
0
0
0
0
0
0
2
0
3
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
3
3
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
1
1
1
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
1
0
0
1
4
1
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
1
0
0
2
0
1
0
0
0
4
0
0
4
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
2
1
0
0
0
0
0
0
2
0
0
0
1
1
1
1
2
0
2
2
0
0
0
0
0
3
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
1
2
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
1
0
0
0
0
0
0
0
2
2
1
2
0
0
2
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
1
0
0
2
0
2
0
2
0
1
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
3
2
0
2
1
0
0
0
0
2
0
0
2
2
0
1
0
2
0
0
0
0
0
0
0
1
0
3
1
0
2
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
2
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
2
0
1
0
3
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
5
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
1
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
1
1
0
0
1
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
2
2
1
1
3
0
0
4
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
3
2
2
0
0
3
0
0
0
0
0
0
0
0
5
0
0
0
2
0
2
0
0
0
0
0
0
1
0
1
0
0
2
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
6
3
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
2
1
0
0
3
1
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
1
3
0
2
0
0
0
6
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
2
0
0
3
0
0
0
0
0
0
0
1
1
1
1
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
2
1
2
2
2
3
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
4
2
0
0
0
0
0
0
0
0
2
3
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
3
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
2
0
1
0
0
0
0
0
1
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
4
1
0
2
0
2
0
0
3
5
0
1
0
2
0
0
0
0
0
0
0
3
0
2
3
3
0
0
0
0
0
0
2
0
0
0
3
1
0
0
5
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
1
1
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
1
0
0
0
0
1
0
1
0
0
0
0
2
0
1
2
2
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
1
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
2
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
3
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
2
0
0
0
1
0
2
0
0
0
1
0
1
1
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
2
0
2
0
0
2
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
4
0
1
0
2
0
0
2
1
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
1
1
0
2
2
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
2
0
0
3
0
0
0
1
0
2
0
1
0
0
0
2
0
0
7
0
1
1
2
0
0
0
0
0
0
0
0
1
1
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
4
1
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
2
0
0
3
5
0
1
0
1
2
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
7
0
0
0
1
0
0
1
0
0
0
2
2
2
1
0
0
1
2
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
1
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
3
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
2
2
0
0
0
0
2
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
2
0
0
0
4
0
0
2
0
1
0
1
2
0
0
1
1
0
2
1
1
0
0
1
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
3
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
2
0
0
0
0
3
0
1
0
0
0
2
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
2
0
0
2
0
0
0
0
2
1
1
0
0
0
1
0
2
1
0
0
2
2
0
0
4
1
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
5
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
2
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
3
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
2
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
1
6
0
0
0
0
0
0
0
0
2
1
2
0
0
1
3
0
0
0
0
0
2
2
0
1
0
0
0
2
0
0
1
0
0
5
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
2
2
7
0
2
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
3
0
2
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
1
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
2
0
0
3
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
4
1
0
0
0
2
0
0
0
0
0
0
0
2
3
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
1
0
1
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
10
0
0
1
1
0
1
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
1
2
0
0
0
0
0
2
1
1
0
0
1
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
4
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
2
1
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
2
0
2
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
3
0
1
2
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
2
3
3
0
1
0
2
0
0
0
0
2
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
1
0
0
0
0
2
3
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
1
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
1
2
0
0
0
0
1
0
2
2
0
0
2
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
1
0
0
0
2
1
2
2
2
2
1
1
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
3
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
1
0
0
0
2
1
2
0
0
0
0
2
0
0
0
0
4
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
2
1
1
0
0
2
0
1
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
3
1
0
2
0
2
2
0
0
0
0
1
0
0
0
1
1
1
0
0
0
2
0
2
2
1
1
0
1
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
3
0
0
1
0
1
0
2
1
2
0
0
0
0
0
0
1
2
2
0
0
0
0
3
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
2
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
3
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
2
2
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
1
1
0
2
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
2
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
2
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
6
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
4
0
4
2
0
3
2
0
0
0
0
0
0
2
5
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
1
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
3
2
2
0
2
2
0
0
0
2
1
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
1
0
1
0
2
0
0
0
0
0
2
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
1
3
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
6
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
8
0
0
1
0
0
0
0
0
0
0
2
1
0
8
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
2
0
0
2
0
1
0
0
1
1
0
0
0
0
1
0
6
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
2
0
0
0
0
0
1
2
0
2
0
0
0
0
1
0
0
4
0
2
0
0
1
2
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
8
0
0
0
0
1
0
0
1
0
1
1
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
2
1
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
2
1
0
3
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
4
0
2
0
2
0
0
0
0
0
3
0
2
2
0
1
0
0
2
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
4
2
0
0
3
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
1
1
0
0
0
0
1
1
0
0
1
2
0
0
0
0
2
0
0
2
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
2
2
0
0
0
0
0
0
3
0
0
0
0
2
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
1
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
3
0
1
3
1
0
0
0
0
2
2
0
0
2
0
2
3
2
0
2
0
0
2
0
0
2
0
0
0
0
0
1
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
3
0
4
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
3
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
3
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
1
0
2
0
0
2
0
6
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
1
2
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
1
1
4
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
3
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
1
0
0
1
1
0
0
0
0
0
1
0
4
1
0
0
1
0
0
2
0
0
0
2
0
1
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
6
1
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
3
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
2
0
2
0
0
0
2
0
0
0
0
3
0
0
0
0
1
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
2
0
1
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
1
0
1
1
0
2
0
0
0
0
0
0
0
6
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
2
0
0
0
0
2
0
0
1
2
0
0
2
0
1
0
1
1
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
2
2
0
0
2
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
4
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
2
0
0
0
1
0
0
0
2
0
2
0
0
3
0
1
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
3
0
0
2
2
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
3
0
7
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
3
0
0
0
1
0
0
2
1
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
2
1
0
0
0
0
0
0
4
0
0
0
0
1
0
0
1
0
0
0
3
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
2
0
0
3
0
0
1
0
0
0
1
0
0
0
0
0
0
6
2
2
0
0
2
2
1
1
0
0
0
0
0
2
0
0
3
0
0
0
2
2
2
0
0
3
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
2
2
3
1
0
0
0
0
0
0
0
0
0
0
0
6
0
0
2
0
0
2
0
2
0
0
0
0
2
2
0
0
0
0
1
2
0
0
0
1
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
2
2
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
3
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
3
2
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
4
1
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
4
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
1
0
0
2
0
2
0
0
1
0
0
5
0
0
2
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
1
2
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
4
0
2
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
1
0
2
4
1
0
0
0
0
0
0
0
0
0
0
0
2
2
1
1
1
0
2
1
0
2
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
3
0
0
0
0
0
3
0
0
0
0
0
0
2
2
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
8
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
2
2
2
1
0
1
6
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
2
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
2
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
2
1
1
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
1
1
0
3
0
1
0
0
0
0
0
0
0
1
3
0
0
1
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
5
0
0
0
0
0
2
1
2
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
2
3
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
1
2
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
5
0
2
0
0
0
0
0
2
0
1
1
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
3
0
0
3
0
2
0
1
1
0
2
1
0
3
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
3
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
3
1
0
0
0
1
0
0
1
0
0
0
1
0
0
2
2
2
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
3
2
0
0
0
0
0
0
1
1
2
1
0
1
2
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
3
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
4
2
0
0
0
1
1
0
0
0
2
0
0
2
0
0
4
0
2
2
0
1
0
1
0
0
0
1
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
4
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
1
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
2
2
2
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
1
0
0
3
0
0
3
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
1
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
4
0
0
0
0
0
1
0
0
1
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
3
0
1
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
1
1
0
0
0
2
0
2
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
2
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
1
0
0
2
2
0
0
0
0
0
0
1
1
1
0
0
1
0
2
0
0
0
2
0
0
2
7
0
2
0
0
1
0
0
0
0
0
0
1
2
0
0
2
2
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
1
6
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
2
0
3
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
1
0
2
1
0
0
0
1
0
0
10
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
1
1
2
0
0
0
0
0
2
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
2
0
1
1
1
4
0
0
0
0
0
0
2
0
1
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
2
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
1
2
1
1
0
2
0
0
1
0
1
1
0
0
1
0
2
1
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
1
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
1
0
1
1
0
0
2
0
0
0
0
0
2
0
0
2
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
1
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
1
2
1
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
2
0
2
0
5
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
5
0
0
1
1
0
0
0
0
4
0
0
0
0
0
1
2
0
0
0
0
1
0
1
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
2
1
0
2
0
0
2
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
7
0
0
2
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
4
0
0
0
0
0
2
0
0
6
0
0
0
1
6
0
0
0
0
0
1
0
0
0
0
3
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
1
0
0
0
2
2
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
3
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
3
2
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
10
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
5
0
0
2
0
4
0
2
0
2
2
0
1
1
0
0
1
0
0
0
0
1
0
0
1
2
1
0
0
1
0
0
0
0
0
0
0
0
2
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
1
0
0
2
2
0
0
4
3
0
0
2
0
0
0
0
6
1
1
1
0
1
1
0
0
0
0
0
0
0
4
0
0
0
0
0
2
0
2
0
0
0
2
1
0
0
0
0
3
0
0
0
0
0
0
1
0
2
2
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
7
0
1
0
0
5
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
7
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
1
0
2
1
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
4
0
0
2
2
0
2
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
1
1
3
0
2
0
0
1
0
0
0
0
0
1
0
0
3
0
0
0
0
0
1
1
2
1
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
5
2
1
0
3
1
0
0
0
0
1
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
3
0
0
0
0
0
2
1
0
2
0
2
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
9
0
1
0
0
2
0
0
0
3
0
2
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
5
1
0
2
2
0
1
0
2
0
1
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
3
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
2
2
1
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
4
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
3
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
5
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
2
0
1
0
0
0
0
0
0
1
7
0
1
0
0
0
0
0
0
1
0
0
5
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
1
3
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
1
0
2
1
2
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
2
0
2
1
2
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
3
0
3
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
2
0
0
0
2
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
4
0
0
0
0
0
1
0
3
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
9
0
0
0
0
0
0
0
0
0
1
0
0
0
5
1
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
2
0
2
0
1
2
0
1
1
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
1
1
0
0
0
2
0
0
2
0
0
0
0
1
2
0
1
0
1
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
2
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
1
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
2
0
0
0
0
0
2
0
1
1
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
1
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
2
2
1
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
6
0
0
0
0
0
0
0
0
0
0
13
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
3
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
5
0
0
0
0
2
3
0
0
0
0
0
1
1
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
4
2
0
0
0
0
1
0
0
0
0
0
0
1
4
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
2
2
0
0
0
2
2
0
2
2
2
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
2
3
0
0
0
0
0
3
1
2
2
0
0
1
0
0
3
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
1
0
2
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
1
0
0
2
1
0
2
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
2
1
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
3
0
0
0
0
0
0
0
3
0
2
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
2
0
0
0
0
2
0
4
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
1
2
0
1
0
0
2
0
0
0
0
2
2
4
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
2
2
0
0
0
0
0
1
1
1
0
0
0
0
0
1
2
2
0
0
0
0
0
1
0
0
0
1
2
1
0
3
1
0
3
0
1
0
0
0
0
0
0
0
1
0
0
0
0
3
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
1
1
0
1
2
0
0
2
0
2
2
0
1
2
1
0
0
2
0
0
0
0
2
0
0
2
1
2
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
6
2
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
2
0
6
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
2
0
0
1
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
3
2
0
0
0
0
0
1
0
0
0
1
2
1
0
0
0
0
1
0
0
0
0
0
1
0
2
0
1
0
1
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
2
1
0
0
1
1
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
1
0
0
0
0
1
0
0
0
3
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
2
0
0
1
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
1
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
4
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
2
0
2
2
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
2
1
0
0
0
0
0
0
3
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
2
1
2
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
6
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
3
0
0
3
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
2
2
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
2
0
0
2
0
0
0
2
2
0
0
0
2
0
1
2
0
2
0
2
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
3
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
2
1
1
0
0
0
0
0
2
0
0
1
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
3
0
1
1
0
0
0
0
0
5
0
0
0
0
0
2
1
2
0
0
0
2
2
2
0
0
0
0
0
0
1
1
2
0
0
0
0
1
2
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
3
0
1
1
0
0
2
1
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
2
0
1
0
0
1
0
0
0
0
4
0
0
0
0
3
0
1
0
1
0
2
0
0
0
1
0
2
0
0
0
0
0
0
3
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
3
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
2
0
0
2
0
1
2
0
4
0
0
0
2
1
3
1
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
1
0
0
0
0
2
2
0
0
0
1
0
1
2
0
0
1
2
1
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
2
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
3
0
0
2
1
0
0
0
2
0
1
1
3
2
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
1
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
1
0
1
0
0
0
0
0
0
1
0
3
0
2
2
2
2
2
3
0
1
0
0
0
1
0
0
0
0
2
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
6
0
1
0
2
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
2
2
0
0
1
2
0
0
2
0
0
3
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
2
0
0
3
1
0
0
1
1
0
1
0
0
0
2
3
0
0
2
0
0
0
0
0
0
0
0
2
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
4
2
0
0
0
0
2
0
0
0
0
3
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
1
0
0
1
0
2
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
2
2
1
0
0
0
3
2
0
2
0
0
0
1
3
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
3
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
2
6
0
2
0
0
0
0
0
1
6
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
2
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
1
2
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
1
0
0
0
0
3
0
1
0
1
0
0
0
1
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
1
0
1
0
0
0
0
2
2
0
0
1
1
0
1
1
0
1
1
3
2
2
1
0
0
0
1
1
0
1
0
0
0
0
0
2
0
0
1
2
0
0
2
0
0
1
2
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
4
4
0
1
0
0
0
0
0
2
3
2
0
2
0
1
0
0
0
4
0
0
0
0
4
2
2
0
0
2
0
1
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
1
0
0
0
0
1
0
0
3
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
1
0
2
0
0
0
0
0
0
0
0
2
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
1
1
0
2
1
0
0
0
2
0
0
0
0
0
8
0
2
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
1
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
2
0
1
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
2
0
0
3
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
2
0
0
0
0
2
0
0
0
1
2
2
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
4
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
2
0
0
2
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
2
0
1
0
0
1
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
3
0
2
1
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
1
0
0
0
3
0
0
0
2
1
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
1
2
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
1
3
1
0
0
4
0
2
1
0
0
0
0
0
2
11
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
1
2
0
0
2
0
1
1
0
0
2
0
0
0
2
2
0
2
0
1
0
0
0
1
0
0
0
0
3
1
0
1
3
3
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
4
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
3
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
2
2
1
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
3
0
1
0
0
0
2
0
4
0
0
0
0
1
11
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
2
1
0
1
0
1
0
0
0
1
0
0
2
0
0
0
0
10
0
0
0
0
0
0
0
0
0
0
0
1
0
3
2
0
0
2
2
0
0
1
0
0
0
1
0
0
0
0
2
2
0
0
0
2
4
0
0
6
0
0
0
0
5
0
0
2
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
2
4
0
0
0
2
4
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
2
0
2
0
1
2
3
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
3
0
0
0
3
0
0
0
0
3
0
1
0
3
2
1
2
0
0
0
1
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
2
8
2
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
1
0
2
0
0
0
5
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
1
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
5
2
0
0
0
0
0
0
3
2
0
0
0
4
0
0
0
0
0
4
0
0
5
0
0
0
2
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
1
0
0
0
1
6
0
0
5
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
1
2
0
1
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
2
0
0
0
1
2
0
1
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
4
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
2
0
3
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
1
1
0
0
0
2
0
2
5
1
0
0
0
0
2
0
0
4
2
1
0
0
0
0
0
0
2
0
0
2
0
0
0
3
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
2
1
0
2
0
4
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
4
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
10
0
0
6
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
4
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
1
0
1
0
0
1
0
1
0
2
0
1
0
1
0
6
0
1
0
0
0
1
2
0
0
1
1
1
0
0
0
1
1
0
0
6
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
2
2
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
2
2
0
1
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
2
0
2
1
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
1
0
0
0
0
0
0
1
0
0
9
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
2
0
3
0
2
0
0
4
0
1
0
1
1
2
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
11
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
2
0
2
0
1
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
5
0
0
2
0
0
1
0
1
3
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
8
1
0
2
2
0
1
0
0
0
1
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
3
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
1
1
0
1
1
0
1
0
2
0
0
0
0
2
0
1
1
0
0
0
3
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
1
0
0
2
0
1
0
0
0
0
1
0
3
0
0
0
2
0
0
0
0
0
0
5
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
3
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
1
0
0
0
0
1
0
1
0
0
0
2
1
0
2
0
1
1
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
3
0
0
0
0
0
0
3
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
3
0
0
0
0
0
0
2
0
1
0
1
0
0
1
2
0
1
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
1
0
2
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
2
0
0
0
3
1
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
1
0
0
2
0
0
2
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
3
1
0
2
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
2
0
0
2
0
0
0
0
2
2
1
0
0
0
0
0
0
0
2
0
2
0
4
0
0
0
0
0
0
0
2
0
2
2
1
0
1
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
4
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
3
0
5
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
3
0
0
0
0
0
4
0
0
0
0
0
2
0
0
3
0
2
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
2
0
2
1
0
3
0
0
1
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
2
0
0
1
0
2
0
0
0
1
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
3
0
0
0
0
0
0
1
0
0
1
0
0
0
1
2
0
2
0
0
0
0
0
0
2
0
1
2
0
1
0
0
0
0
1
0
0
2
1
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
3
0
0
1
2
0
0
1
0
0
0
2
1
1
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
2
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
3
6
2
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
2
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
2
0
4
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
2
0
0
0
1
0
0
5
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
3
0
0
0
2
2
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
4
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
3
0
0
2
0
0
0
0
0
1
1
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
3
0
0
0
0
1
3
0
2
0
0
2
1
4
4
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
2
0
2
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
2
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
1
1
3
0
0
2
0
0
0
3
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
3
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
2
1
0
0
0
0
2
1
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
4
0
0
0
0
0
1
0
0
3
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
2
0
0
3
0
1
1
0
0
0
0
0
0
0
0
1
0
5
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
3
0
3
0
0
1
1
2
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
2
0
0
2
0
1
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
2
2
0
2
0
0
0
2
0
2
0
4
1
0
1
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
2
0
2
0
0
0
0
2
0
0
0
0
0
5
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
4
2
0
2
0
0
2
0
1
1
2
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
2
0
0
0
3
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
3
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
1
1
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
3
0
0
0
0
0
1
0
0
2
2
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
1
1
0
1
2
1
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
5
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
1
2
0
2
2
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
3
0
0
0
0
0
3
0
0
0
0
1
0
0
1
0
0
1
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
3
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
4
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
7
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
5
0
0
0
2
1
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
4
2
0
2
0
0
0
1
0
0
0
2
0
0
2
2
0
2
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
1
3
1
0
6
0
0
0
0
0
0
0
0
0
0
0
0
1
0
5
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
1
0
1
0
0
0
0
0
0
0
1
0
1
4
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
1
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
2
2
0
1
1
0
1
0
0
0
0
4
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
2
0
0
4
0
0
0
0
0
1
0
0
0
0
1
0
1
2
0
0
0
1
0
0
0
2
0
0
2
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
3
0
0
0
0
1
0
0
0
0
1
2
3
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
2
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
3
1
0
0
0
0
1
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
3
2
0
0
0
2
0
1
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
2
1
2
0
1
1
0
0
1
0
4
0
0
0
0
0
1
1
1
2
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
2
1
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
4
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
1
4
0
1
0
2
1
0
2
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
1
2
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
1
4
0
1
0
0
0
1
1
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
2
0
0
0
0
2
1
2
0
0
0
2
1
0
0
0
2
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
3
3
0
1
2
2
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
3
0
0
0
1
0
0
3
1
0
0
1
0
0
0
0
0
2
0
0
0
2
0
7
0
2
0
0
3
0
14
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
2
0
0
2
0
1
3
0
0
0
3
0
1
0
2
2
0
0
0
0
1
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
4
0
0
0
1
0
2
0
0
0
0
0
0
2
0
1
0
0
0
5
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
7
0
3
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
2
2
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
4
0
1
1
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
1
2
0
2
0
2
0
0
0
0
0
2
0
2
1
1
4
0
2
0
0
0
0
1
0
0
2
2
0
0
1
0
0
0
1
0
1
0
0
0
0
2
0
0
0
1
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
15
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
3
0
0
0
0
0
0
1
0
1
0
0
0
0
1
2
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
1
0
4
0
0
0
2
0
0
0
1
0
2
1
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
7
1
0
0
0
0
0
0
0
2
1
1
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
1
2
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
2
0
1
0
1
0
0
0
0
0
0
1
1
0
0
3
0
0
0
0
0
6
0
0
1
0
2
0
1
2
2
0
1
0
0
0
1
0
2
2
1
1
0
0
0
0
0
1
0
2
2
1
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
2
0
2
0
0
0
0
1
0
1
1
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
7
0
0
3
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
2
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
3
0
2
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
2
0
0
9
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
3
3
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
1
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
2
3
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
2
2
0
1
0
0
0
0
0
0
0
0
1
4
0
2
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
1
0
1
0
1
0
0
0
0
2
0
0
2
0
0
0
1
2
2
0
0
1
0
2
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
1
1
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
2
0
1
0
0
0
0
1
2
0
0
0
2
2
0
0
0
0
0
0
1
0
0
2
1
2
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
2
4
1
0
0
1
0
0
0
1
0
3
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
2
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
3
2
0
1
0
2
0
1
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
3
2
0
1
0
0
0
0
0
0
2
0
0
3
0
0
0
0
2
2
0
1
0
1
1
1
0
2
0
0
2
0
0
2
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
3
3
0
0
3
1
0
1
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
1
2
3
1
1
0
0
4
0
0
2
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
9
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
1
1
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
2
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
2
0
0
2
0
0
0
0
0
7
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
1
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
2
2
2
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
1
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
2
1
4
0
2
0
0
1
0
1
0
0
2
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
1
0
0
0
0
1
0
2
1
0
0
2
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
9
3
0
1
2
0
0
1
1
0
1
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
5
0
2
0
0
1
0
2
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
6
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
1
1
0
0
3
0
2
0
1
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
1
2
0
2
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
2
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
6
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
3
0
1
0
0
2
0
0
0
0
3
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
2
1
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
1
0
2
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
1
0
2
0
0
2
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
2
0
0
1
0
0
2
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
1
1
0
0
0
1
0
0
1
0
3
0
0
0
1
1
2
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
3
0
0
0
0
0
2
0
0
2
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
1
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
2
0
0
0
0
2
1
0
2
0
1
0
0
0
0
1
6
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
2
0
2
0
0
0
0
0
0
2
0
2
0
1
1
2
2
1
0
0
0
0
0
1
1
0
1
0
0
2
1
2
0
2
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
3
0
0
0
0
0
1
2
0
0
2
1
1
0
0
1
0
0
0
0
0
4
2
1
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
1
2
0
2
0
2
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
3
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
3
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
2
0
0
0
0
1
0
2
1
0
0
0
0
0
0
4
0
0
0
2
1
0
0
0
0
0
4
0
3
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
1
0
2
0
3
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
2
0
0
2
0
1
0
2
1
0
0
1
0
0
0
0
0
0
0
0
2
0
1
2
1
1
0
2
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
1
0
0
2
0
0
0
2
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
2
0
3
0
0
0
2
1
0
0
2
1
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
1
0
0
1
0
1
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
2
0
5
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
2
1
0
0
1
3
0
1
1
0
0
0
0
2
1
0
0
0
0
2
0
0
0
2
0
0
0
5
0
0
0
1
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
1
3
0
2
0
0
2
0
0
2
2
0
0
1
1
2
1
0
0
0
0
1
0
0
0
3
2
0
1
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
2
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
1
0
2
1
0
0
0
0
1
0
1
3
0
0
0
0
0
2
0
0
0
1
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
1
0
2
0
0
2
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
1
0
0
2
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
1
0
1
1
0
1
1
0
2
0
2
0
0
0
1
2
0
1
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
5
1
0
0
1
1
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
5
0
0
0
0
1
0
1
0
0
0
1
0
0
1
1
0
0
1
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
1
1
1
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
1
2
0
0
0
0
1
0
0
0
0
1
3
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
1
0
1
0
0
0
1
0
0
1
0
2
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
3
0
0
0
0
2
0
0
0
0
1
1
0
1
0
1
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
2
2
0
0
0
0
2
1
0
0
2
0
0
1
0
2
0
1
0
0
2
0
1
1
0
0
2
0
1
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
2
0
0
2
0
1
0
1
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
1
1
0
3
4
0
0
0
0
1
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
3
2
0
0
0
0
0
0
0
1
0
2
1
0
5
0
2
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
2
0
1
2
1
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
1
0
0
0
0
0
1
2
0
0
1
2
3
0
0
2
2
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
1
0
0
1
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
1
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
2
0
0
1
0
1
0
0
0
0
0
2
0
0
2
0
4
10
0
0
3
0
2
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
3
0
0
0
1
2
0
2
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
2
1
0
2
0
0
3
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
2
1
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
2
0
0
4
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
2
1
0
1
1
2
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
4
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
3
0
2
0
0
0
2
0
2
2
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
6
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
2
0
2
0
0
0
2
1
0
0
2
0
0
0
1
2
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
1
2
1
0
0
0
1
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
5
0
0
0
1
1
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
5
0
0
2
2
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
1
0
0
1
0
3
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
3
0
2
2
2
0
0
0
0
1
0
0
0
1
2
2
0
5
3
0
0
1
0
2
0
0
8
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
2
1
4
0
2
0
1
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
5
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
1
0
0
0
0
0
0
1
3
2
0
0
1
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
2
0
0
0
0
0
2
1
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
1
0
0
1
1
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
1
0
1
0
0
0
0
0
0
2
0
1
3
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
1
0
1
0
2
2
2
3
6
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
1
0
1
0
1
0
0
0
0
3
0
3
0
1
0
2
0
1
2
0
0
0
0
1
1
0
2
1
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
4
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
1
2
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
3
0
1
0
0
0
0
1
0
0
2
0
1
1
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
1
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
3
0
0
0
2
0
1
0
1
0
0
0
0
1
1
3
0
0
1
0
0
2
2
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
1
0
1
0
0
0
1
0
3
7
0
3
0
0
0
2
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
1
0
1
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
2
2
1
0
0
1
0
1
0
0
0
1
0
0
1
2
0
0
2
1
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
2
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
2
0
2
0
0
1
2
3
2
1
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
2
2
1
0
0
3
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
2
0
3
0
0
0
0
0
1
0
4
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
2
0
0
2
0
0
0
2
0
0
1
0
2
0
3
0
0
1
0
0
0
0
0
1
2
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
4
1
0
0
1
0
0
2
0
0
2
2
0
0
0
0
2
0
0
0
3
0
0
0
2
0
1
3
0
0
0
1
0
2
0
0
0
0
0
0
0
0
3
1
0
0
0
0
1
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
2
2
3
0
0
0
1
0
0
1
0
2
1
0
0
2
2
0
0
5
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
1
0
0
0
12
2
0
0
3
0
0
1
0
1
0
0
0
0
2
1
0
0
0
2
0
2
1
0
2
0
0
3
0
2
0
3
0
0
0
0
0
0
0
1
2
0
0
2
1
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
2
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
2
1
2
0
0
1
0
3
0
0
2
0
0
0
0
2
2
0
0
2
0
0
0
1
0
0
0
0
2
0
2
0
0
1
0
1
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
2
2
0
0
0
2
0
0
0
0
0
0
2
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
3
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
4
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
1
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
1
12
0
1
1
0
3
0
0
0
0
1
0
1
0
0
0
0
0
0
6
0
3
0
0
0
0
3
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
1
3
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
2
4
0
0
0
0
0
0
0
2
0
2
1
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
6
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
2
1
0
1
0
1
0
0
2
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
2
2
0
0
0
0
0
0
2
0
1
0
1
1
0
0
0
2
0
0
0
0
0
0
0
5
0
1
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
1
1
2
2
1
0
0
0
0
1
1
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
3
1
3
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
1
0
0
2
0
2
0
1
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
1
0
1
2
0
0
0
1
1
0
0
3
0
0
1
0
2
1
0
0
2
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
2
0
0
5
1
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
2
2
0
2
1
2
0
0
0
0
0
0
1
0
0
0
1
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
2
0
1
0
0
0
4
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
6
0
3
0
0
0
0
3
0
0
0
1
2
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
2
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
5
0
1
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
3
0
2
0
0
0
2
0
1
1
0
3
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
2
0
1
0
1
0
0
0
0
2
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
1
0
0
2
1
0
1
0
0
0
2
0
0
0
2
0
0
0
1
1
1
0
3
2
2
1
0
0
1
0
0
0
2
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
2
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
7
0
1
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
7
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
2
0
0
0
1
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
4
1
2
0
0
0
0
0
1
0
0
0
4
0
0
0
0
2
0
0
2
0
1
0
1
0
2
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
6
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
1
0
0
1
0
2
0
0
0
0
2
0
0
0
0
2
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
1
1
0
0
3
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
1
3
1
0
0
0
1
0
0
1
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
1
0
0
2
0
0
1
0
0
0
0
1
0
0
8
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
2
0
0
0
0
2
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
1
0
0
2
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
2
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
4
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
1
3
2
2
0
0
2
1
0
0
0
2
0
0
0
0
0
0
1
0
2
3
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
1
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
1
0
0
0
5
0
0
0
0
2
0
0
0
0
2
0
1
0
2
0
0
1
0
0
3
0
1
2
1
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
1
3
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
3
0
1
1
0
0
0
0
1
0
0
1
0
0
3
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
5
1
2
1
0
0
0
0
1
2
2
3
0
1
1
2
0
2
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
1
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
2
2
0
0
0
2
0
1
2
0
0
0
0
1
1
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
1
1
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
1
0
0
2
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
7
0
0
0
4
0
1
0
1
0
1
0
0
0
3
1
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
3
0
0
0
2
1
1
1
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
3
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
6
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
1
0
0
1
0
0
0
2
0
2
0
2
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
1
1
0
0
0
2
2
0
0
2
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
1
0
0
1
1
0
0
1
1
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
1
0
2
2
2
0
2
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
1
1
1
0
2
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
1
0
0
1
0
0
1
1
1
1
2
0
2
3
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
3
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
2
1
0
1
2
0
0
0
1
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
1
0
2
2
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
2
0
2
1
2
0
0
0
0
0
0
1
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
2
1
2
2
2
1
0
2
0
0
0
0
0
0
1
1
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
1
1
2
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
1
0
0
2
1
0
2
0
0
0
1
0
0
0
0
0
1
2
2
0
0
0
0
0
1
0
2
2
0
0
0
0
0
1
0
0
0
2
0
1
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
1
3
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
1
1
0
0
0
2
0
0
0
3
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
2
0
0
1
0
1
2
0
1
1
0
2
0
0
1
0
0
0
0
0
0
0
0
3
1
0
1
3
0
0
0
0
2
1
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
2
1
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
2
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
4
0
0
0
0
0
2
0
8
0
0
0
2
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
7
0
0
2
0
0
0
0
0
0
1
2
1
2
0
0
0
0
0
3
1
0
0
0
0
0
2
2
4
1
0
0
0
2
1
3
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
2
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
2
0
0
0
2
1
0
0
1
0
0
2
0
0
0
1
0
0
1
0
0
3
0
2
2
0
1
1
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
1
0
2
2
0
0
0
2
0
0
0
1
2
0
1
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
2
1
2
0
0
2
0
0
1
0
1
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
2
1
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
4
0
0
5
0
1
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
2
0
1
1
3
0
0
1
1
1
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
1
3
0
0
2
3
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
6
1
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
3
2
0
0
1
2
0
3
1
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
1
2
0
1
0
0
0
1
1
0
0
0
2
0
0
2
0
0
0
0
1
0
0
2
4
2
0
2
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
1
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
2
1
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
15
0
0
1
0
0
1
2
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
1
0
0
1
0
0
2
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
1
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
3
1
1
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
1
1
2
0
3
0
1
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
1
2
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
4
2
2
1
0
0
0
0
0
2
0
0
0
0
1
2
0
1
1
0
1
0
1
3
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
1
1
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
5
0
0
3
0
1
1
0
0
0
2
0
0
0
0
2
3
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
2
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
2
0
2
1
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
5
0
0
0
0
2
0
0
0
3
0
1
0
0
3
0
6
0
1
0
0
0
0
2
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
2
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
2
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
1
1
0
0
1
0
0
0
1
0
0
1
0
0
3
0
2
0
0
0
0
0
0
0
0
0
2
2
0
1
1
1
0
0
0
2
0
0
0
0
3
0
1
3
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
2
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
2
0
3
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
2
0
0
4
0
1
0
2
1
0
0
0
1
0
2
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
8
0
0
0
0
2
1
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
1
1
0
1
0
0
1
0
0
3
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
1
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
4
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
3
1
0
2
0
0
2
0
0
1
0
0
0
0
4
6
2
0
0
0
2
0
0
0
0
0
0
0
9
0
1
0
0
0
0
1
0
0
0
0
0
2
0
2
0
1
0
0
3
0
1
0
1
0
0
1
0
0
0
1
3
0
0
1
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
3
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
1
1
0
0
0
0
0
0
0
0
0
2
4
2
2
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
1
0
4
0
2
0
0
0
1
0
1
0
4
0
0
0
0
0
2
0
0
0
1
3
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
3
0
2
0
1
0
1
0
0
0
0
3
0
0
1
0
2
0
0
0
2
1
0
0
0
0
0
7
0
0
2
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
2
2
0
0
2
2
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
5
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
2
0
2
0
2
4
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
1
0
1
0
3
0
0
0
0
0
0
0
1
0
2
0
0
2
2
1
0
0
2
0
0
2
0
0
1
0
0
1
0
2
0
0
0
0
0
2
0
1
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
2
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
2
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
2
0
2
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
2
2
0
1
0
1
1
0
0
0
0
0
0
0
0
0
2
3
0
0
1
1
1
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
2
0
0
5
0
4
1
0
0
0
0
0
0
1
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
4
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
1
1
0
3
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
2
1
1
0
0
0
0
0
0
1
0
2
2
0
1
0
0
1
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
2
0
0
1
0
1
2
0
3
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
2
0
2
0
0
0
2
0
0
2
0
2
0
2
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
3
1
2
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
2
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
2
2
0
0
0
0
1
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
2
0
1
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
1
0
0
2
2
0
0
2
0
0
0
0
2
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
2
1
0
0
2
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
1
1
1
2
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
1
2
1
0
0
0
0
0
0
0
3
0
0
1
0
3
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
2
0
0
0
2
0
0
0
0
2
0
0
2
1
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
4
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
2
1
0
2
4
1
0
0
0
1
0
0
0
0
1
0
0
0
2
0
2
0
0
0
3
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
5
1
0
2
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
1
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
1
0
0
1
2
0
0
2
0
0
0
1
0
0
0
0
0
3
3
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
1
3
0
0
0
1
0
2
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
1
2
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
4
0
0
1
0
0
2
0
1
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
3
2
0
0
0
0
2
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
5
2
2
0
2
2
2
2
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
4
2
1
1
1
0
1
0
1
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
4
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
2
0
3
0
0
0
0
0
0
0
1
2
0
0
1
0
3
0
0
0
1
2
0
2
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
6
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
3
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
2
0
0
0
1
0
2
0
0
1
2
0
0
1
0
0
0
1
0
0
0
1
0
2
0
0
0
2
3
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
1
1
0
0
0
0
0
3
1
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
4
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
3
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
1
1
0
1
1
0
0
0
0
2
1
0
0
2
0
0
0
0
0
2
0
0
0
2
0
2
3
0
1
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
2
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
5
0
1
1
1
0
0
0
2
0
0
0
2
0
1
1
0
2
0
0
0
2
0
0
1
0
2
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
3
0
1
0
0
0
2
0
2
2
0
0
0
0
3
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
2
3
0
0
2
0
0
1
2
0
0
0
0
0
2
0
1
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
8
2
0
0
1
3
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
15
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
1
0
2
2
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
2
3
0
0
2
0
0
3
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
1
0
0
1
0
0
0
3
2
1
4
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
2
0
2
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
4
0
0
1
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
3
0
0
2
0
3
0
0
0
0
0
1
1
0
0
0
0
2
2
0
0
2
0
0
0
1
0
1
0
0
2
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
2
2
0
0
0
0
4
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
2
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
2
0
1
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
1
0
1
0
1
0
2
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
24
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
2
1
0
0
0
0
1
2
0
0
0
4
2
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
4
1
1
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
1
3
0
0
0
0
0
0
6
0
0
1
0
2
0
0
0
0
4
2
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
1
3
0
0
0
4
0
0
0
0
2
1
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
2
2
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
3
1
1
0
0
0
1
3
0
0
2
0
0
0
0
0
2
1
1
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
2
13
0
0
1
0
0
2
0
0
0
3
0
0
3
0
2
0
0
0
0
0
0
2
0
1
0
0
0
3
0
1
0
1
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
1
2
2
0
1
0
2
1
0
0
2
0
0
0
0
0
0
0
2
0
0
1
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
1
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
2
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
1
2
2
0
0
0
0
2
0
0
2
0
0
0
1
0
0
1
0
2
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
4
2
1
1
0
2
0
2
1
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
2
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
3
0
0
0
0
0
0
1
2
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
1
0
0
1
3
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
2
1
1
2
0
0
0
0
0
0
1
0
0
0
4
0
2
0
0
0
1
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
1
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
2
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
2
1
0
2
0
1
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
3
0
1
1
0
0
0
0
0
2
0
0
1
0
0
1
0
2
0
0
2
3
0
0
0
1
1
0
0
0
1
2
0
3
0
0
4
0
1
2
1
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
3
2
2
6
2
1
1
0
0
0
0
0
0
2
3
0
0
5
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
3
0
1
0
0
2
1
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
5
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
2
1
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
2
0
0
0
0
2
2
0
0
1
2
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
8
0
0
0
4
0
0
0
0
0
0
0
0
5
0
2
0
0
0
2
0
0
1
0
3
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
3
1
0
0
0
1
0
0
2
1
0
0
3
0
1
1
0
2
2
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
2
1
0
0
0
0
0
1
1
4
0
1
1
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
2
0
1
1
0
2
0
0
1
1
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
2
0
0
1
2
0
2
2
0
1
0
1
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
2
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
1
2
0
0
9
0
2
0
0
1
0
0
3
1
1
1
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
2
1
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
2
1
0
0
0
0
0
0
0
0
0
0
2
1
1
2
0
0
3
1
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
3
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
3
0
1
0
1
0
0
0
2
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
6
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
2
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
3
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
3
0
1
0
0
0
1
0
0
0
5
0
0
0
0
0
0
0
1
2
1
2
0
0
0
0
0
0
0
1
1
2
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
4
0
2
1
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
3
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
7
0
0
0
2
0
0
0
0
1
0
0
1
2
2
0
1
0
0
0
0
0
0
3
0
0
0
0
3
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
3
0
0
0
4
0
0
0
3
2
0
0
2
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
2
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
1
1
0
0
0
0
0
0
2
1
0
1
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
1
1
0
1
2
0
0
0
0
0
1
0
0
0
0
6
0
0
0
0
0
0
0
0
0
1
7
0
2
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
3
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
5
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
2
2
0
0
0
2
0
0
1
0
0
1
0
0
0
0
2
0
4
2
1
0
0
0
0
0
2
2
0
1
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
3
0
0
0
2
0
0
1
1
0
0
1
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
2
3
0
1
0
2
0
0
3
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
3
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
2
0
1
0
2
0
1
2
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
1
0
1
0
1
0
0
5
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
1
0
4
0
2
1
0
0
2
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
2
4
0
2
0
0
3
0
1
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
3
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
1
0
7
0
0
0
0
0
3
1
0
0
0
0
0
2
0
2
0
0
0
0
0
1
4
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
2
0
1
1
0
0
0
0
2
0
0
1
0
1
0
1
1
2
0
0
0
0
0
4
3
0
0
1
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
1
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
3
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
1
0
1
0
0
1
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
1
2
0
0
1
0
2
2
2
0
15
0
0
0
0
0
1
0
4
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
1
0
0
0
2
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
1
6
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
3
1
0
0
1
0
0
0
0
0
6
0
3
0
1
0
1
0
0
0
1
2
0
0
0
1
0
1
0
2
1
0
1
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
3
0
2
0
0
0
0
1
2
2
2
1
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
7
1
0
0
0
0
0
2
1
1
1
2
2
2
2
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
2
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
5
0
0
0
0
1
0
0
1
0
2
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
2
1
1
0
0
1
0
0
0
0
0
2
1
2
0
0
0
0
0
0
3
0
1
0
3
0
0
0
0
0
0
0
2
1
0
0
2
3
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
1
0
0
0
2
1
2
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
3
2
0
0
0
0
1
0
0
0
2
1
0
4
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
3
2
1
0
0
0
0
1
0
0
2
1
0
0
5
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
8
0
0
3
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
1
1
0
0
2
0
0
0
0
0
1
0
0
1
2
0
0
4
3
0
0
0
0
1
0
0
0
0
1
0
2
1
0
1
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
2
1
0
0
2
2
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
2
0
1
0
1
0
1
0
0
0
1
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
1
0
1
0
2
0
3
1
0
1
2
1
0
0
2
0
1
0
0
2
0
0
4
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
1
0
0
2
0
3
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
1
4
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
7
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
2
0
0
0
1
3
0
0
0
0
0
1
0
2
0
2
0
2
0
2
0
0
2
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
2
0
3
2
2
0
0
0
1
0
0
1
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
2
0
0
0
1
0
0
0
0
2
1
0
0
3
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
3
1
0
0
2
1
1
3
0
0
0
0
0
0
2
0
0
0
0
2
0
0
4
0
0
2
0
1
0
0
0
0
3
0
0
1
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
2
4
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
2
1
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
2
2
0
0
0
2
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
2
0
0
9
0
0
0
0
0
0
5
1
0
0
0
0
0
0
0
0
0
2
2
2
1
4
0
0
4
0
0
6
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
1
0
0
0
0
0
3
1
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
4
0
1
0
0
0
0
1
0
1
0
0
1
0
0
2
1
3
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
3
0
1
1
2
0
0
0
0
0
0
0
1
0
0
0
0
4
0
1
0
0
1
0
2
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
1
0
0
1
1
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
2
0
0
0
1
0
0
3
0
0
0
2
3
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
2
2
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
2
0
2
2
1
0
0
0
0
0
0
0
0
2
0
3
1
3
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
1
3
0
0
0
0
0
2
0
0
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
1
0
0
3
1
3
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
1
3
0
3
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
1
0
0
2
0
0
1
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
2
0
1
0
0
0
0
0
4
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
2
2
0
0
0
1
1
0
0
0
0
0
3
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
4
6
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
4
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
6
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
1
0
2
1
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
3
1
0
1
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
1
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
9
2
0
2
2
0
0
0
1
0
0
3
2
2
2
0
0
0
2
0
1
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
3
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
1
0
1
0
0
0
2
0
1
1
0
0
0
0
1
0
0
1
1
0
2
0
0
0
2
0
0
0
0
0
0
0
2
2
0
1
0
0
0
2
0
0
1
2
1
0
0
0
0
0
0
1
2
0
0
1
0
3
0
0
2
0
0
1
2
0
2
0
0
2
1
0
0
0
2
1
0
0
3
0
0
0
0
0
1
0
1
0
0
0
3
2
0
0
0
0
0
0
2
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
3
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
1
0
0
1
0
0
2
7
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
3
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
5
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
1
2
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
3
0
0
1
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
2
0
2
0
0
0
0
1
1
1
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
2
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
2
1
1
0
0
0
1
2
0
0
0
0
1
0
0
1
0
1
2
0
0
2
2
0
0
0
1
0
3
0
0
0
1
0
1
1
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
2
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
1
0
3
0
3
3
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
9
0
0
0
0
0
1
0
0
0
2
0
0
0
2
3
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
2
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
3
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
1
0
3
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
5
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
1
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
2
0
1
0
0
0
0
0
0
1
2
0
1
0
0
1
2
2
3
1
3
0
0
1
0
0
0
0
0
0
2
1
1
2
0
0
1
0
0
0
0
2
0
1
2
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
3
0
0
0
0
0
0
0
1
0
0
1
3
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
3
0
0
1
1
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
3
0
0
0
0
0
0
1
0
2
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
2
0
0
0
0
2
0
2
0
1
0
0
1
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
3
5
2
3
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
1
0
2
0
2
1
1
1
0
0
0
0
0
2
0
0
0
1
0
1
0
0
3
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
4
0
2
0
1
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
1
0
2
0
0
0
2
0
0
1
1
0
0
3
0
0
0
1
1
0
0
0
0
2
1
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
1
1
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
1
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
1
0
1
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
1
0
1
0
2
0
2
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
2
1
2
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
2
3
0
1
2
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
2
2
0
1
1
0
0
0
2
0
2
0
2
0
0
4
0
2
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
2
0
2
0
0
0
0
0
0
2
0
1
0
2
2
2
0
0
0
1
1
0
0
1
1
0
0
0
2
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
1
0
1
3
0
0
0
0
0
0
0
0
1
0
2
0
0
1
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
2
0
0
0
0
0
2
0
2
1
0
0
0
0
5
0
0
3
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
2
2
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
3
0
2
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
2
2
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
2
2
1
2
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
2
1
2
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
3
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
2
0
0
4
0
0
0
0
0
0
1
3
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
2
0
2
2
0
0
1
1
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
3
0
2
0
0
0
0
0
0
0
0
1
3
0
1
0
0
0
0
2
1
0
2
1
0
1
0
2
0
0
5
0
0
2
0
2
0
1
0
0
0
0
0
3
0
0
1
0
4
1
1
0
1
0
1
1
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
2
0
0
1
0
2
0
0
0
2
0
0
0
0
0
1
0
0
3
0
2
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
2
0
0
0
1
0
1
0
0
0
0
2
2
1
0
0
3
0
0
0
0
1
0
0
0
0
1
0
2
0
1
3
1
0
0
0
2
1
0
2
0
0
0
2
0
0
0
2
4
0
0
0
0
0
2
0
0
0
0
2
0
0
3
0
0
0
0
0
0
3
0
1
0
0
0
0
2
0
0
1
2
4
1
0
3
0
0
0
2
1
0
0
0
1
0
0
0
0
3
1
1
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
3
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
2
0
0
1
2
0
0
1
1
4
0
0
0
0
0
0
0
0
0
1
0
2
2
0
2
0
0
4
0
0
0
0
1
1
0
1
1
0
0
0
1
2
0
0
0
0
5
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
7
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
2
0
1
0
0
3
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
2
1
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
1
3
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
2
0
0
0
1
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
1
2
1
0
1
0
0
0
0
0
0
0
0
0
0
3
0
2
0
2
0
1
0
2
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
1
0
0
0
0
1
0
0
2
3
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
2
0
0
2
0
1
0
0
0
3
0
0
0
0
0
0
1
2
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
2
0
2
0
0
0
0
0
1
0
2
0
2
0
0
2
1
0
0
1
0
0
0
0
0
0
0
3
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
1
2
2
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
2
0
0
1
1
1
2
0
0
3
0
0
1
0
0
1
0
0
0
1
2
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
5
0
0
0
0
0
0
1
0
0
1
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
1
0
2
0
0
0
0
2
0
2
0
0
0
0
3
0
0
0
2
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
2
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
1
3
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
2
2
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
1
1
0
0
1
2
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
1
1
1
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
2
1
0
2
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
2
0
0
1
1
0
2
0
0
1
0
0
0
2
2
3
4
0
1
2
0
4
0
2
0
0
0
2
1
2
0
0
0
0
0
0
0
0
2
0
1
1
0
4
1
0
0
0
3
0
0
0
0
0
3
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
3
9
9
0
3
9
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
3
1
1
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
1
0
1
0
0
0
2
0
0
0
2
1
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
5
0
0
0
2
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
4
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
1
0
0
0
0
2
2
2
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
3
0
0
0
0
3
0
0
0
0
0
0
1
0
3
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
1
3
0
0
0
2
0
0
1
1
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
3
1
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
3
0
0
0
3
1
0
1
1
0
0
0
0
0
0
0
0
0
0
5
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
1
0
0
0
2
3
0
0
0
0
1
1
0
2
1
0
0
2
0
0
0
0
3
1
0
0
0
0
0
2
0
1
0
0
5
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
1
2
2
0
2
0
0
0
0
2
0
2
0
0
0
0
1
0
1
0
0
3
3
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
1
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
4
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
2
0
2
4
1
0
0
1
1
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
2
0
0
0
0
0
2
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
1
4
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
2
1
0
2
0
1
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
2
2
0
0
2
1
1
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
2
0
0
2
0
0
0
0
2
0
0
0
0
0
2
1
1
1
0
1
0
1
3
6
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
1
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
5
0
2
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
1
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
1
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
2
0
0
0
0
0
0
1
2
1
2
0
0
0
3
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
11
0
0
0
0
2
0
0
2
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
2
0
2
2
0
0
1
0
0
1
0
1
2
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
4
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
1
1
0
2
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
3
0
0
0
1
0
1
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
3
1
0
2
0
0
0
1
2
0
0
3
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
1
2
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
1
1
2
0
0
1
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
5
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
2
1
1
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
2
2
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
2
0
1
0
0
1
2
1
0
0
0
2
0
0
0
1
1
0
0
4
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
2
1
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
1
1
0
0
1
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
3
1
0
0
0
0
1
0
0
0
2
2
0
2
0
1
0
0
0
0
0
0
3
0
0
3
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
2
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
3
0
2
0
2
0
0
0
0
0
1
0
0
0
0
4
3
0
0
0
3
0
0
0
0
0
1
0
0
1
0
0
0
2
0
1
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
3
0
0
1
0
0
0
0
2
0
0
2
0
0
0
3
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
2
0
0
0
0
2
2
0
0
0
0
1
2
0
2
0
0
2
1
0
1
0
0
0
0
0
0
0
0
3
4
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
1
0
4
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
1
1
1
1
2
0
1
1
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
3
0
1
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
2
10
0
0
2
0
0
0
0
0
0
2
0
0
2
0
1
0
1
0
2
0
0
5
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
7
0
0
0
0
0
1
4
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
1
0
0
1
0
0
2
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
2
0
2
0
0
2
0
1
1
0
1
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
6
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
1
0
2
0
0
0
0
2
0
0
2
0
0
0
3
0
0
1
0
0
2
0
2
0
0
2
0
0
0
1
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
5
0
0
3
0
0
0
5
0
0
0
0
2
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
1
0
4
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
3
0
0
0
3
0
0
1
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
2
0
0
0
0
3
1
2
0
1
2
0
0
0
0
0
0
5
0
1
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
2
0
1
0
0
4
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
1
0
0
2
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
2
0
0
1
0
2
2
0
0
0
1
0
2
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
3
0
3
1
0
0
2
0
1
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
2
0
2
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
1
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
7
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
1
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
1
0
1
0
0
3
2
0
0
2
0
2
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
8
0
0
0
2
1
0
2
0
2
2
1
2
2
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
1
0
0
3
0
0
3
0
0
0
0
1
0
2
0
0
0
0
1
3
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
2
1
0
1
0
0
2
0
0
0
0
0
2
2
0
1
0
0
0
0
2
0
0
2
0
1
0
1
1
0
0
2
1
2
0
0
0
1
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
8
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
2
1
0
1
0
0
0
2
0
0
0
1
1
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
4
0
0
1
0
0
0
1
0
0
0
3
2
0
0
1
2
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
1
0
0
5
0
0
2
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
1
0
1
2
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
0
0
0
0
0
1
0
3
0
2
0
1
1
0
3
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
4
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
2
2
0
4
0
0
0
0
0
0
0
0
0
1
4
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
2
0
0
0
2
0
1
0
0
2
2
0
2
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
11
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
1
2
1
0
1
0
0
0
0
0
0
0
0
0
4
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
2
0
1
3
1
1
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
1
0
0
2
0
0
1
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
5
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
4
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
1
0
1
0
1
2
0
0
2
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
2
0
0
0
1
1
0
0
1
0
2
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
2
0
0
3
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
4
1
4
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
2
2
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
1
0
0
0
0
1
1
0
1
1
0
0
0
2
0
0
2
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
1
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
2
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
3
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
3
0
1
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
3
0
0
0
0
0
1
2
0
0
0
0
0
0
3
0
2
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
2
0
2
0
0
1
0
0
2
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
3
1
0
0
0
2
1
0
0
2
0
0
0
0
0
7
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
1
1
2
0
1
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
2
2
3
0
0
0
2
1
2
1
0
0
1
0
0
2
0
2
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
1
0
0
0
2
1
1
4
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
3
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
1
0
6
1
0
0
0
0
0
0
7
2
2
0
0
1
2
0
1
0
1
0
2
0
0
0
3
0
0
0
0
0
2
0
0
2
0
2
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
3
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
1
2
0
0
0
0
2
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
1
0
2
1
1
1
0
0
0
0
1
2
0
1
0
0
1
1
0
0
0
0
2
0
0
1
0
1
0
0
2
0
1
0
0
0
0
2
0
0
0
0
3
0
0
0
1
0
1
0
0
2
1
0
0
0
0
0
0
0
0
2
0
4
0
0
1
0
0
0
0
0
0
0
5
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
2
0
0
0
0
0
0
1
1
1
0
0
2
0
0
2
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
3
0
0
1
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
1
3
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
2
0
1
0
1
0
0
0
0
1
0
0
0
2
0
0
0
1
2
0
2
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
2
0
0
1
0
2
2
0
0
0
1
0
0
6
1
0
0
1
0
0
2
2
0
0
2
0
0
1
0
0
1
0
0
0
1
0
0
0
0
3
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
1
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
1
1
0
0
0
3
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
2
0
1
0
0
1
0
0
0
3
0
2
1
0
4
0
1
1
1
0
0
0
0
4
2
1
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
1
1
3
0
0
0
0
0
2
0
0
0
1
0
1
0
0
3
0
0
1
0
0
3
0
0
0
1
0
0
0
0
0
4
0
2
0
0
6
1
0
2
0
1
0
0
0
0
0
4
0
1
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
2
0
0
10
2
0
1
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
1
1
2
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
1
0
1
0
0
2
0
0
1
0
0
0
0
3
0
0
2
0
0
0
0
2
0
0
0
1
0
2
0
0
1
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
3
0
2
0
0
0
0
1
3
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
1
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
3
1
0
0
0
1
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
2
0
1
0
0
1
0
1
2
2
0
0
0
0
1
2
2
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
2
0
0
0
0
2
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
1
0
1
0
0
0
0
1
1
1
2
0
0
0
1
0
2
0
0
1
1
0
0
0
0
0
0
3
0
0
1
0
0
2
0
1
0
0
0
0
0
2
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
5
0
1
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
2
2
0
1
1
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
3
1
0
0
1
2
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
1
0
0
0
1
0
0
0
0
0
2
0
3
0
0
0
0
1
2
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
1
2
2
2
2
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
2
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
1
0
2
0
1
3
0
0
2
0
0
0
0
1
0
0
0
0
0
2
1
0
0
3
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
4
0
0
2
0
0
2
0
2
0
0
0
0
0
2
1
0
0
0
2
0
0
6
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
4
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
3
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
1
0
0
0
0
6
0
0
2
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
1
0
2
1
0
0
0
1
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
1
0
0
1
1
0
1
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
1
0
3
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
4
2
0
1
2
0
1
2
0
0
2
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
2
3
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
6
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
4
1
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
5
0
1
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
8
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
2
3
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
2
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
3
3
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
3
2
3
0
0
0
2
1
1
0
0
0
0
0
0
1
0
4
0
2
0
0
1
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
2
2
0
0
2
0
0
2
0
0
1
0
0
1
0
2
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
4
0
0
0
0
0
1
1
1
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
1
0
1
0
1
0
2
1
0
0
0
0
0
2
0
0
4
1
0
0
0
0
0
0
0
0
2
1
1
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
2
3
2
0
2
0
1
2
0
0
2
0
1
0
0
0
0
0
0
0
0
1
3
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
1
2
0
0
0
0
1
4
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
2
1
0
0
0
1
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
4
0
0
1
1
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
3
4
0
0
0
0
1
1
0
2
0
1
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
5
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
3
0
0
2
0
0
0
0
2
0
0
2
1
2
0
0
0
0
0
0
0
0
2
0
0
1
1
1
2
0
0
1
0
0
0
1
4
0
0
0
0
4
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
1
2
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
2
0
0
0
2
0
2
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
4
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
3
2
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
5
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
3
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
2
1
2
0
0
1
2
2
3
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
2
0
0
0
1
0
0
4
0
1
2
1
1
2
0
0
1
0
0
0
0
0
0
0
0
11
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
2
0
1
3
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
1
0
0
0
1
1
0
0
0
0
3
0
1
0
1
0
0
0
1
0
0
2
2
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
1
2
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
3
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
3
0
0
1
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
1
2
1
3
1
2
1
2
0
0
0
0
0
0
2
0
0
2
2
0
2
0
0
0
0
0
0
2
1
0
1
0
0
0
1
0
0
0
1
0
0
0
2
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
1
2
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
2
0
4
2
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
2
0
2
0
0
2
0
2
0
0
2
0
2
0
0
0
0
2
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
1
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
1
0
0
3
0
0
2
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
1
0
2
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
1
0
1
0
0
0
3
0
2
0
0
0
3
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
1
0
0
0
1
2
0
0
0
4
1
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
1
2
2
0
0
0
0
0
1
0
0
0
0
0
3
2
0
0
2
0
0
0
1
0
2
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
2
0
1
0
3
2
2
0
2
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
3
2
0
0
0
0
0
2
0
0
0
0
3
0
0
0
1
2
0
2
0
0
2
0
3
0
0
0
0
0
2
0
0
0
0
5
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
3
0
0
0
1
2
0
0
0
0
0
0
0
2
0
2
2
1
0
0
1
0
0
0
1
0
0
0
0
0
0
2
2
1
3
0
0
0
0
0
2
0
0
2
2
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
6
0
0
3
0
0
0
0
1
0
0
0
1
0
0
0
1
0
2
3
0
0
2
1
0
0
0
0
2
2
0
0
2
0
1
0
0
0
2
0
3
2
1
0
0
0
1
0
0
1
0
0
3
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
1
1
2
2
2
0
0
0
0
2
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
3
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
2
0
2
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
2
1
0
0
0
1
2
1
0
0
0
0
0
0
0
1
0
3
0
2
0
0
0
2
1
0
0
1
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
3
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
1
1
0
2
0
0
1
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
7
0
0
0
0
0
1
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
4
0
0
1
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
6
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
4
0
2
0
0
1
0
0
0
0
1
0
0
0
2
2
0
0
0
0
1
0
1
0
0
1
0
0
0
2
2
3
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
5
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
1
0
2
0
0
0
2
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
1
2
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
2
0
0
2
2
0
0
4
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
4
0
0
0
2
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
1
2
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
1
2
0
0
3
0
0
1
0
0
0
0
1
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
2
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
1
1
0
0
5
0
0
0
0
1
0
3
1
2
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
1
0
0
0
0
0
0
0
0
6
0
1
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
4
0
1
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
3
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
1
2
2
0
0
0
0
1
0
0
0
0
0
0
0
3
2
0
0
1
0
2
3
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
1
0
2
0
2
0
1
0
0
0
0
0
1
1
1
0
0
0
1
1
1
0
0
0
0
6
0
0
0
1
0
2
1
0
2
0
0
1
0
0
1
0
0
0
0
1
3
0
0
3
1
0
2
0
1
0
0
1
0
1
0
0
0
0
1
2
0
0
2
0
0
1
0
0
0
0
0
0
0
3
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
1
1
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
2
2
1
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
1
0
0
1
8
0
2
0
1
0
0
0
0
0
2
2
0
2
1
2
0
1
0
0
2
0
0
2
1
0
2
3
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
4
1
2
0
1
0
0
2
0
0
0
1
0
0
0
1
2
1
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
7
0
0
0
0
0
0
0
1
0
2
0
1
0
0
1
1
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
2
2
0
0
1
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
2
0
0
2
0
0
2
0
0
0
0
2
1
0
0
2
2
0
2
0
0
0
0
0
0
1
2
1
0
0
2
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
2
1
2
1
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
3
2
0
0
0
0
0
2
1
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
3
1
1
0
0
2
4
0
0
3
0
0
0
0
0
0
0
1
2
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
1
1
0
0
0
5
0
0
0
2
0
0
2
0
2
2
0
0
1
0
2
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
3
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
2
1
0
0
1
0
4
4
2
0
5
1
1
0
1
1
0
2
0
0
0
0
0
0
0
5
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
3
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
5
0
0
0
0
0
0
2
0
0
3
0
0
0
0
1
0
0
0
0
2
1
0
0
3
0
1
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
1
1
1
0
1
0
0
2
0
0
0
0
2
1
0
1
0
1
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
2
1
0
0
0
2
1
0
0
0
2
0
0
0
1
2
0
2
1
0
0
0
2
1
2
0
1
0
1
0
0
0
0
0
0
0
0
3
0
1
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
3
0
1
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
2
2
0
0
0
0
1
0
3
1
2
1
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
2
2
0
0
2
1
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
2
1
0
1
0
0
0
1
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
4
1
0
0
0
0
0
0
1
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
1
2
0
2
0
0
0
0
0
2
0
0
2
0
1
2
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
1
2
0
0
1
0
1
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
3
0
0
0
2
2
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
1
0
0
3
0
0
1
0
0
0
1
0
1
0
0
2
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
1
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
2
0
0
1
2
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
1
0
2
2
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
1
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
2
0
1
0
1
2
0
0
3
0
0
3
0
4
1
0
0
1
0
1
0
0
1
2
0
4
0
1
0
1
2
0
0
2
0
2
0
2
3
0
0
0
0
0
0
0
2
3
0
0
0
0
2
0
0
1
0
1
2
1
0
0
0
0
0
0
0
0
1
0
2
0
0
2
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
3
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
1
2
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
2
0
1
0
2
0
0
2
0
0
0
0
1
3
0
2
0
0
0
2
0
0
0
3
0
1
1
0
0
0
0
1
1
0
1
0
0
0
2
0
1
2
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
5
2
0
0
0
0
0
0
0
2
2
2
0
0
2
0
0
3
0
0
0
0
0
0
1
0
0
0
1
2
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
7
0
1
0
0
0
0
0
1
0
0
0
0
1
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
2
0
0
0
0
0
0
0
2
0
0
5
2
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
1
2
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
1
0
1
0
0
1
2
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
4
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
2
0
0
0
2
0
0
0
1
0
0
1
0
2
0
0
0
0
1
1
0
1
1
0
0
0
1
0
1
0
2
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
1
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
2
0
1
0
2
0
0
0
0
1
0
0
0
0
0
10
0
0
0
3
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
1
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
3
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
2
2
0
1
0
0
0
0
0
0
0
2
2
0
5
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
2
2
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
1
0
1
0
1
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
3
0
0
0
0
2
0
3
0
2
1
0
0
0
1
0
0
0
0
1
0
0
1
0
2
0
0
0
2
0
0
2
0
0
2
0
0
1
0
0
0
0
0
1
1
0
1
2
0
3
0
0
1
1
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
6
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
1
0
0
0
1
2
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
5
0
8
0
0
0
1
0
3
0
1
2
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
2
0
2
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
1
0
0
0
0
0
2
0
0
3
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
2
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
2
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
3
0
0
0
0
0
0
2
2
0
5
1
1
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
1
0
1
0
1
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
2
0
0
0
2
0
0
2
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
1
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
1
0
1
0
0
2
3
2
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
1
0
9
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
2
0
2
2
2
0
2
2
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
8
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
1
2
0
0
2
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
1
1
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
2
2
0
0
0
0
1
0
0
0
0
0
1
0
2
0
1
0
0
2
1
0
2
0
0
0
1
0
0
0
0
0
0
6
0
1
0
1
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
2
1
0
0
0
1
0
0
2
1
0
0
0
0
0
0
2
0
0
0
1
1
1
0
0
5
1
0
0
2
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
2
3
0
0
1
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
2
0
0
1
0
1
0
0
0
1
0
2
0
3
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
1
0
0
0
0
0
0
2
0
0
3
0
10
0
0
2
2
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
2
2
0
0
0
0
2
0
0
3
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
5
2
2
0
0
0
3
0
0
0
0
2
0
0
0
0
0
1
2
0
0
2
0
2
0
0
1
0
0
0
0
0
3
1
0
0
2
3
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
4
0
1
1
0
0
0
0
2
0
0
0
1
2
0
0
0
1
0
0
0
0
2
3
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
2
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
2
0
0
0
6
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
3
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
1
0
2
2
0
0
2
2
0
0
2
2
0
2
0
1
0
0
0
2
2
0
0
0
0
2
2
0
0
1
1
0
2
0
0
0
0
2
0
2
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
2
0
0
0
0
0
3
0
0
2
0
0
1
0
2
1
0
0
2
0
0
0
0
1
3
7
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
2
4
0
0
0
1
0
2
2
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
6
0
0
0
0
2
1
0
1
0
0
2
0
0
2
0
0
0
0
0
3
0
2
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
3
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
1
2
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
4
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
5
0
0
0
0
1
1
0
0
0
3
1
0
1
0
0
2
1
0
0
0
1
2
0
0
1
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
2
2
0
0
3
0
5
0
1
0
0
0
1
0
0
2
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
2
0
0
2
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
3
2
0
0
0
0
1
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
1
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
1
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
2
0
2
2
0
0
0
2
3
2
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
1
2
0
0
0
1
0
1
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
3
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
4
1
2
0
0
2
0
0
1
0
6
0
0
2
0
0
0
0
0
1
0
2
0
0
2
1
0
1
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
1
1
0
3
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
1
1
0
1
0
0
0
0
2
3
0
0
0
0
0
0
1
0
0
0
4
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
1
0
0
0
1
0
5
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
5
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
1
1
0
0
1
0
0
0
0
0
0
3
2
2
0
0
1
0
0
0
0
0
0
3
1
0
0
1
0
0
0
0
2
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
4
1
0
0
0
0
0
1
2
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
2
2
0
0
0
0
0
2
0
0
2
0
0
1
0
2
2
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
3
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
6
1
0
3
0
1
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
3
3
0
0
0
0
0
0
0
0
3
0
0
3
0
0
0
0
1
2
0
6
0
0
1
0
3
0
0
0
0
0
2
0
0
0
7
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
4
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
4
0
1
0
0
0
1
5
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
3
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
3
0
0
2
0
0
0
0
2
0
1
0
0
2
2
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
5
2
1
0
0
0
1
4
2
3
0
0
0
0
0
0
0
3
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
2
0
3
0
1
0
2
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
2
0
0
0
0
2
4
1
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
1
2
1
1
2
0
0
3
2
0
0
0
0
11
0
0
0
0
0
2
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
1
1
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
2
0
1
0
2
0
0
0
1
0
0
0
0
0
0
1
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
2
0
0
0
0
2
0
0
0
0
1
0
1
2
3
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
3
0
0
0
0
0
0
0
1
0
0
1
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
1
1
0
3
2
0
0
1
0
0
0
0
0
0
4
0
1
0
1
0
0
1
2
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
1
1
0
0
7
1
2
0
2
2
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
1
0
3
0
0
0
0
1
0
0
0
0
4
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
1
0
0
2
0
2
2
5
0
0
0
0
5
2
0
0
1
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
5
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
5
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
2
0
1
2
0
1
0
2
0
0
0
0
0
5
0
0
1
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
2
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
2
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
1
1
1
0
0
0
1
1
0
0
0
2
1
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
1
2
2
0
8
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
2
0
0
0
2
1
0
1
2
1
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
2
0
0
0
0
0
0
1
2
0
1
0
2
0
1
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
4
0
0
0
3
3
0
1
0
1
0
1
2
0
2
0
1
0
0
0
0
0
3
2
0
0
6
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
3
2
0
0
0
0
0
0
0
1
0
0
0
2
1
1
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
3
0
1
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
5
0
4
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
3
1
0
0
2
0
0
0
0
0
1
3
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
1
0
0
0
2
2
0
0
1
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
3
1
0
0
2
0
0
1
0
0
0
2
0
0
1
2
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
1
2
0
0
0
1
0
0
0
1
2
2
0
1
0
0
0
0
3
1
0
3
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
2
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
2
0
0
2
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
1
2
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
2
0
2
0
2
0
1
0
1
3
0
0
0
3
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
2
1
0
0
0
0
0
1
0
0
2
0
0
1
0
6
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
2
0
0
0
0
1
0
2
1
0
1
0
0
1
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
2
1
0
0
1
0
0
2
2
0
0
1
5
1
2
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
4
0
0
0
0
1
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
11
3
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
1
0
0
3
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
3
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
2
0
1
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
3
0
0
0
1
0
0
0
0
0
0
3
0
2
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
9
0
0
6
0
0
1
0
2
0
0
0
1
0
1
0
1
1
0
2
3
0
1
0
2
2
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
1
2
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
2
2
0
0
1
0
1
0
0
2
0
1
0
0
0
1
1
1
0
1
3
0
0
0
0
0
0
1
2
0
2
0
0
0
0
2
0
0
3
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
5
5
0
3
0
2
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
2
0
1
0
1
2
0
2
0
3
0
1
0
0
2
1
0
0
2
0
0
0
0
1
1
0
3
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
3
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
5
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
2
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
1
0
1
0
0
0
0
1
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
3
2
0
0
0
1
4
0
0
0
0
0
0
0
1
1
1
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
3
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
1
1
0
0
0
0
2
0
0
1
0
1
2
1
2
1
0
2
0
1
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
18
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
3
0
0
2
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
1
2
0
0
0
1
0
0
0
0
0
1
1
0
2
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
1
0
0
2
12
0
0
2
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
2
0
0
2
1
0
0
0
0
1
0
0
0
1
6
0
2
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
2
0
0
1
1
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
1
0
0
2
0
0
0
0
2
0
3
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
5
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
1
0
0
1
0
0
1
0
0
1
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
2
0
0
5
0
0
3
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
4
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
1
0
1
0
1
2
0
0
2
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
2
0
0
0
4
0
2
0
0
0
0
0
0
0
2
0
0
0
1
2
0
1
0
0
1
0
0
0
3
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
3
0
2
1
0
0
0
0
2
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
3
1
0
0
0
0
1
0
0
0
1
2
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
9
0
0
0
0
1
0
0
0
1
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
1
0
0
2
0
1
3
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
9
0
1
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
7
0
0
0
1
0
0
2
0
1
2
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
4
3
0
0
0
0
2
0
0
0
1
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
13
1
0
0
0
2
1
0
1
1
2
0
0
0
0
0
2
0
0
1
1
0
1
0
0
0
0
0
3
0
0
0
0
0
1
0
1
2
0
0
2
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
4
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
1
1
1
0
0
0
0
4
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
3
0
3
0
0
0
0
0
0
0
0
0
0
0
2
1
1
1
0
0
1
0
1
0
2
1
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
1
2
0
1
0
2
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
2
1
0
0
0
0
0
0
3
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
1
1
6
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
2
0
0
0
0
2
0
3
0
0
0
0
0
0
2
1
1
0
2
0
1
0
0
1
0
0
2
2
0
0
1
1
0
0
2
0
1
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
1
1
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
3
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
1
0
0
0
0
2
0
2
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
2
0
1
2
1
0
0
0
0
2
0
0
0
1
0
0
0
1
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
3
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
1
4
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
1
0
2
0
0
1
0
2
3
0
0
0
1
0
2
0
0
0
0
0
0
1
4
0
0
2
3
2
0
0
1
0
0
0
0
1
0
0
3
0
2
0
3
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
3
0
0
1
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
1
0
0
0
0
1
0
0
0
0
1
3
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
2
0
0
1
0
1
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
4
0
0
1
0
0
0
2
2
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
1
3
0
0
1
0
2
1
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
3
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
2
0
4
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
1
0
4
1
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
1
0
2
0
2
0
0
0
2
1
0
0
1
0
2
0
0
0
0
2
0
0
0
1
0
0
1
0
0
2
2
0
2
1
3
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
2
0
0
0
0
0
0
0
1
0
0
3
0
2
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
1
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
5
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
1
0
1
2
1
0
2
0
2
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
3
0
0
0
0
3
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
1
0
0
0
2
0
0
0
0
1
0
1
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
2
1
0
0
2
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
11
0
0
2
0
0
0
0
1
0
0
0
2
0
1
0
3
1
0
0
0
0
0
0
3
0
2
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
1
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
5
2
1
0
0
1
0
2
1
0
2
0
0
2
0
0
0
2
2
0
0
0
1
1
0
1
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
2
0
1
0
1
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
8
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
4
1
0
3
0
0
2
0
0
0
0
2
2
0
0
0
0
3
0
0
0
1
1
0
0
4
2
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
9
0
5
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
1
0
0
8
0
1
1
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
2
3
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
2
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
1
0
0
1
2
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
3
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
6
0
1
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
2
11
0
3
0
0
0
0
0
4
1
0
0
3
0
0
0
0
0
1
2
0
0
0
1
2
3
0
0
0
1
0
0
0
0
0
2
0
2
0
2
0
0
3
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
1
0
1
2
0
0
2
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
2
1
1
0
0
0
1
0
2
0
0
0
0
2
0
0
0
3
0
0
2
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
1
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
1
1
0
0
0
0
0
2
0
3
0
0
0
3
0
2
0
1
2
0
2
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
3
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
1
0
1
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
1
2
0
1
0
0
0
0
0
2
1
0
0
1
0
0
1
0
0
0
0
1
0
1
0
2
2
0
0
2
1
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
2
0
1
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
2
0
1
0
2
2
4
2
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
4
0
1
0
0
4
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
2
0
1
0
0
2
0
0
0
0
2
0
0
3
0
0
0
2
2
1
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
1
1
1
1
0
2
0
0
0
0
0
0
2
2
2
0
0
1
0
0
0
1
1
2
0
1
4
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
2
1
0
0
7
3
3
0
0
0
0
2
0
0
2
0
0
0
2
2
2
0
2
1
0
2
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
3
0
0
2
0
0
0
0
2
0
2
0
0
1
2
2
0
0
0
1
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
2
0
0
2
0
2
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
4
0
0
0
0
0
1
0
0
2
0
0
0
2
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
4
0
0
0
0
0
3
0
0
0
0
2
0
0
1
0
0
0
2
0
2
2
0
0
0
2
1
0
0
2
1
1
1
0
0
2
0
0
1
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
2
3
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
3
1
0
0
0
0
0
2
3
0
4
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
3
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
2
1
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
3
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
3
0
0
3
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
1
0
0
0
0
3
0
1
0
0
0
0
2
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
5
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
2
0
0
2
0
0
0
2
0
0
1
0
1
0
0
0
0
1
2
0
0
0
2
1
0
0
1
2
0
0
1
0
0
2
0
0
2
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
3
2
2
0
0
7
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
3
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
8
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
2
1
2
3
0
1
1
0
1
1
1
0
1
0
2
0
0
0
2
0
2
0
1
0
0
1
0
2
1
0
2
0
4
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
2
1
0
0
2
1
0
0
0
0
0
1
0
1
0
3
1
2
1
2
0
0
0
0
2
0
2
0
1
1
0
0
0
0
2
2
1
2
0
1
0
2
0
0
2
2
2
0
0
0
0
0
2
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
2
2
0
0
6
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
3
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
4
1
0
1
0
1
0
0
2
0
0
0
0
2
1
2
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
1
0
0
0
1
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
2
0
1
2
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
1
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
1
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
5
0
0
0
0
0
0
0
1
0
0
2
1
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
3
1
1
0
1
1
0
0
0
0
2
1
0
2
1
0
6
0
1
0
3
0
0
0
2
0
3
0
0
0
2
0
0
0
2
3
0
1
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
4
0
2
0
2
0
0
2
0
0
2
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
2
2
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
1
1
2
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
3
0
0
0
0
2
0
0
1
0
0
1
0
2
0
0
0
0
4
2
0
0
0
0
0
1
0
0
1
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
3
2
0
0
0
1
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
2
1
0
0
0
1
0
0
0
3
0
1
1
0
0
0
0
2
2
1
0
0
0
0
0
0
2
0
0
0
2
1
0
1
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
1
0
0
0
1
0
0
2
0
2
4
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
2
1
0
0
0
2
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
1
0
2
0
0
0
0
1
0
0
2
0
0
2
1
3
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
3
0
9
0
0
0
0
0
0
0
2
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
1
2
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
11
1
0
2
1
0
2
0
0
0
1
0
0
0
0
2
0
2
0
0
2
2
0
1
0
0
0
1
0
0
0
0
0
0
5
0
0
0
1
0
0
0
0
0
0
2
3
0
5
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
4
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
1
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
3
1
2
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
2
1
0
0
2
0
0
1
1
0
0
2
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
2
0
0
2
0
0
2
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
1
5
0
1
0
1
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
2
0
1
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
3
0
0
1
0
0
2
0
3
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7
0
1
1
0
0
0
3
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
1
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
2
0
0
0
1
2
0
1
1
0
0
2
0
2
3
2
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
2
0
0
1
5
2
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
1
1
0
0
0
1
0
0
2
0
0
0
0
4
2
0
1
0
0
0
0
0
0
2
1
2
0
0
0
0
2
2
0
0
0
3
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
4
1
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
4
0
0
0
4
0
2
0
1
0
0
0
0
0
0
0
2
3
0
0
0
0
2
0
0
0
0
2
0
2
3
0
0
0
0
0
0
0
5
0
0
0
0
2
0
3
0
2
0
0
0
0
0
0
0
2
2
2
3
0
2
0
0
0
2
0
0
1
1
0
0
0
1
0
0
1
2
0
0
0
0
0
0
2
0
0
0
2
0
2
0
2
0
0
0
0
2
0
1
2
0
0
2
0
0
0
4
0
0
1
0
2
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
3
0
0
0
2
0
0
0
1
0
0
2
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
2
2
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
1
3
1
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
1
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
2
0
1
0
1
0
0
2
3
0
0
0
1
0
0
1
0
3
2
0
0
3
0
0
0
1
0
0
0
7
2
2
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
1
2
0
0
1
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
1
0
1
0
2
0
1
1
0
0
0
1
2
1
0
0
0
2
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
1
2
0
0
0
0
2
0
0
1
1
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
1
0
0
0
1
0
2
0
1
0
0
2
1
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
2
1
2
0
0
2
0
0
0
0
0
3
0
0
0
0
2
2
0
0
0
0
2
0
4
0
1
0
2
1
0
4
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
6
0
0
1
0
0
0
0
2
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
1
0
0
0
2
2
1
0
0
1
0
0
2
0
2
0
3
0
2
0
0
0
3
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
1
3
0
0
2
0
0
0
0
0
2
3
0
2
0
2
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
2
0
1
1
0
0
1
0
0
1
0
1
2
0
2
0
1
0
0
0
0
3
0
0
1
0
2
0
0
0
3
2
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
3
0
2
0
1
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
1
0
1
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
2
3
0
0
2
0
2
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
2
4
0
2
0
0
0
0
0
2
0
0
2
0
1
0
1
0
0
0
0
2
0
3
0
0
0
0
1
0
0
2
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
6
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
2
0
2
0
0
0
1
0
1
0
0
0
0
0
0
2
0
2
1
1
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
1
0
1
1
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
6
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
2
0
0
2
0
0
0
1
4
0
0
0
0
0
1
1
0
0
0
3
0
0
2
0
0
0
0
0
1
0
0
2
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
4
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
3
1
0
0
0
0
2
0
0
1
0
2
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
1
0
5
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
4
0
2
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
3
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
2
1
0
0
0
1
5
2
1
2
2
0
0
0
0
0
0
5
0
0
0
0
0
1
1
4
2
1
3
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
3
1
0
0
0
0
0
2
0
6
0
0
2
1
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
2
0
0
1
1
0
1
0
0
3
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
1
2
1
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
1
3
0
0
0
1
0
0
0
2
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
1
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
1
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
2
2
0
0
3
0
0
0
1
0
0
0
0
0
2
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
1
0
2
0
0
0
1
2
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
1
0
2
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
7
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
4
0
0
0
5
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
2
6
1
0
0
1
0
1
0
0
0
3
0
1
1
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
3
1
0
0
0
0
0
0
1
0
2
0
0
3
0
0
0
0
0
0
0
0
2
0
1
1
2
3
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
5
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
2
0
0
2
0
0
0
2
0
1
3
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
1
1
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
5
0
0
0
0
2
3
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
2
1
0
0
0
3
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
1
1
0
0
0
0
0
1
1
0
2
0
0
3
0
0
0
0
3
0
0
1
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
2
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
2
1
0
0
2
1
0
0
3
2
0
0
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
2
0
1
0
0
0
1
0
0
1
0
0
0
2
0
0
2
0
0
0
0
2
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
2
3
0
2
0
0
0
0
1
0
0
0
1
3
1
0
1
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
2
0
1
0
0
3
0
0
1
3
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
1
0
0
0
2
0
4
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
6
0
0
1
0
1
0
0
2
0
1
0
0
0
3
0
0
0
0
1
3
0
2
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
2
0
1
1
2
0
0
0
0
0
4
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
2
0
0
0
2
0
4
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
2
2
0
0
0
1
3
0
0
0
3
2
0
2
1
2
0
3
2
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
1
4
0
0
0
1
0
0
1
2
0
1
2
0
0
0
0
1
2
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
2
4
0
0
2
2
2
0
2
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
1
0
0
0
1
0
0
2
2
1
0
0
0
0
0
1
0
1
0
0
0
0
0
8
2
0
2
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
3
0
1
0
0
2
0
2
0
0
0
0
6
2
0
0
1
0
0
2
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
1
1
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
1
0
2
1
1
0
0
0
1
0
2
1
0
0
4
1
0
0
0
0
0
0
1
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
1
0
0
1
0
2
0
0
1
0
2
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
1
0
0
2
0
0
0
1
2
0
1
0
0
0
2
2
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
2
1
3
0
0
0
0
0
2
0
0
0
0
0
0
0
4
0
0
2
0
0
2
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
3
0
3
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
1
3
1
1
0
0
2
0
0
0
0
1
1
0
0
0
0
0
1
0
5
0
1
0
0
0
1
0
1
0
0
0
1
2
0
2
1
0
1
2
0
0
0
0
0
0
0
3
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
2
0
0
0
0
1
1
0
0
0
0
0
2
1
0
1
0
2
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
2
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
4
0
2
0
0
0
0
0
0
0
1
2
0
0
0
1
0
2
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
3
0
2
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
1
0
1
0
0
1
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
1
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
3
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
1
0
0
3
0
0
1
0
2
1
0
3
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
2
0
1
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
7
0
0
0
2
0
0
0
2
1
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
2
0
5
0
0
0
0
0
0
1
0
0
2
1
0
2
5
0
3
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
3
0
0
0
0
8
0
1
1
0
0
0
0
0
4
0
0
0
1
0
0
2
2
0
1
0
1
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
3
1
1
0
0
3
0
0
3
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
1
0
0
2
0
0
1
0
6
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
3
2
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
4
0
0
0
2
1
0
0
4
0
1
0
0
0
0
0
0
0
1
3
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
1
2
0
0
2
0
0
0
0
0
1
0
0
6
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
2
2
0
0
1
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
1
0
1
0
0
10
0
1
0
0
2
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
2
0
2
0
0
2
0
0
0
0
2
3
1
3
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
3
0
0
3
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
8
0
1
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
1
1
1
4
0
0
0
2
0
0
2
0
0
2
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
5
0
2
0
0
0
0
1
0
1
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
1
1
2
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
2
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
3
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
3
0
0
0
0
3
0
0
0
0
1
0
0
0
0
1
2
0
0
3
0
2
0
2
1
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
2
0
2
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
1
0
0
2
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
2
0
1
3
1
0
0
0
2
2
0
0
0
0
0
0
2
2
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
11
0
0
2
0
0
1
0
12
2
0
0
0
0
0
4
0
1
2
0
0
2
0
1
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
2
2
0
2
1
2
2
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
1
0
2
0
2
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
4
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
2
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
1
1
2
0
0
0
1
1
0
3
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
2
3
0
0
0
2
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
1
0
2
0
0
0
2
1
0
0
0
0
1
0
0
2
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
3
0
2
0
0
0
0
2
0
3
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
3
2
0
1
0
2
0
3
0
0
0
0
1
3
1
0
0
2
2
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
2
0
0
0
0
0
0
0
1
3
0
1
0
0
0
0
2
2
0
0
0
0
1
0
0
1
0
2
3
1
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
6
2
0
0
1
0
0
0
0
6
0
0
2
0
1
0
2
0
1
0
0
1
0
2
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
2
0
3
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
1
1
1
2
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
2
1
0
0
3
2
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
1
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
2
1
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
2
0
1
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
2
2
2
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
4
0
0
0
2
0
1
0
1
0
0
0
0
1
1
0
0
0
5
0
0
0
2
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
2
0
0
1
0
0
1
0
3
0
0
0
1
2
0
3
0
0
0
0
0
1
0
0
0
1
2
1
0
2
0
0
3
0
1
0
0
0
0
2
1
0
0
0
0
2
0
2
2
1
0
0
0
0
0
0
0
3
1
0
0
0
0
2
1
2
0
0
0
0
0
1
0
2
0
0
2
0
2
1
2
0
0
0
0
1
0
1
0
0
0
2
0
0
2
0
0
1
0
1
0
0
2
1
0
2
1
0
1
0
0
0
1
0
2
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
1
1
1
1
9
0
1
2
0
0
2
2
0
0
2
2
0
0
1
1
0
0
0
0
0
0
1
1
2
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
1
0
0
0
0
2
3
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
2
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
2
0
2
0
1
1
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
3
0
0
0
2
1
0
3
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
2
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
2
0
0
3
0
0
0
1
1
0
1
1
0
0
2
1
2
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
2
2
1
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
1
0
4
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
3
1
0
0
0
0
1
1
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
1
0
2
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
1
0
2
0
2
2
0
3
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
6
0
2
2
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
1
1
0
0
0
2
1
0
0
0
1
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
9
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
2
3
2
0
0
0
0
0
1
0
0
0
2
0
0
1
2
0
2
0
0
0
1
0
1
0
11
0
1
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
1
0
3
0
0
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
2
0
0
0
0
0
2
0
0
1
2
0
2
2
1
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
2
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
2
0
2
0
0
0
1
3
2
0
3
0
0
0
5
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
4
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
2
2
1
0
0
0
0
2
0
0
0
0
1
11
0
0
1
0
0
1
0
0
2
0
0
1
7
0
0
0
0
0
0
0
0
3
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
3
0
0
0
2
0
0
0
0
0
2
2
0
2
0
1
2
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
3
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
2
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
3
4
0
3
0
0
0
0
0
0
2
1
0
0
0
0
3
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
4
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
2
1
0
0
1
1
2
0
0
2
0
0
5
0
7
0
2
0
1
0
0
2
0
0
0
0
0
2
0
0
0
2
0
1
2
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
1
0
0
0
3
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
2
3
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
1
0
0
4
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
1
1
0
0
1
0
5
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
2
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
2
0
0
3
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
2
0
2
0
1
0
0
0
2
4
0
0
2
0
1
0
0
5
2
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
1
1
0
0
1
2
3
0
0
0
0
1
0
0
1
0
1
0
0
3
0
0
0
0
0
1
1
0
0
0
0
3
0
0
0
0
0
1
0
2
0
0
2
2
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
2
1
0
2
0
0
1
3
0
0
0
0
0
0
3
3
1
0
2
0
0
0
0
2
0
0
0
0
0
4
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
2
0
2
2
0
1
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
2
0
2
0
0
0
0
7
1
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
4
2
1
2
0
0
0
0
0
0
0
0
0
0
1
0
4
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
1
0
0
0
2
0
0
1
2
0
2
0
0
2
0
2
2
0
0
5
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
7
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
1
3
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
2
2
0
1
0
1
0
0
0
0
0
2
0
2
0
2
0
0
2
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
1
0
0
1
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
3
0
0
0
2
0
3
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
1
0
1
2
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
8
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
3
2
0
0
0
4
0
0
0
0
0
0
5
0
0
1
0
2
0
0
1
0
0
0
0
3
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
3
4
2
1
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
2
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
2
2
0
0
2
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
3
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
2
0
0
1
0
0
0
0
0
2
3
23
0
3
0
0
2
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
5
2
1
0
0
2
2
1
0
3
0
2
0
0
5
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
2
0
2
1
1
0
1
0
2
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
2
0
8
0
0
1
0
2
0
0
2
1
1
0
0
0
0
5
0
0
0
0
0
2
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
2
1
2
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
3
0
1
2
1
1
0
0
0
3
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
1
1
0
1
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
2
0
1
0
1
0
0
2
0
0
0
0
0
2
0
2
2
0
1
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
2
1
1
1
0
0
0
0
0
0
0
0
2
0
4
5
0
0
0
0
0
1
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
1
1
1
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
2
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
2
0
0
2
0
1
1
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
1
0
1
0
0
2
1
0
0
0
0
0
1
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
2
0
1
2
2
0
0
0
1
0
0
2
0
2
0
3
1
0
0
0
2
2
0
0
0
0
0
0
0
4
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
1
2
2
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
4
0
0
0
0
0
0
9
2
0
0
0
3
1
0
0
1
0
2
0
2
0
0
0
0
0
2
1
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
2
1
2
1
2
2
0
1
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
1
2
0
2
0
0
0
0
0
0
1
4
0
0
3
0
2
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
1
2
0
0
1
0
0
5
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
2
0
0
0
0
1
1
0
0
1
0
1
0
1
1
0
0
0
1
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
3
0
2
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
4
2
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
1
0
4
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
1
0
2
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
1
1
2
1
0
0
1
0
2
2
0
0
0
1
0
8
0
0
0
0
0
0
1
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
1
0
0
0
2
0
1
0
0
0
3
0
0
1
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
19
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
1
2
0
0
0
0
2
4
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
2
3
0
2
0
0
0
0
0
0
1
0
0
1
0
1
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
2
2
0
0
0
0
3
0
1
2
2
0
3
0
0
1
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
1
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
5
0
0
2
0
1
0
0
0
4
0
1
1
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
2
2
3
0
0
0
1
0
0
1
0
0
2
0
0
0
1
0
0
0
2
0
1
0
0
1
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
1
2
0
0
1
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
1
0
1
2
2
2
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
4
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
1
0
1
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
3
2
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
6
0
0
2
0
0
2
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
2
0
0
0
0
2
2
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
2
1
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
1
4
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
2
0
6
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
2
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
6
0
1
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
3
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
1
2
3
0
0
0
0
0
0
3
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
3
2
0
0
0
0
0
1
4
0
0
0
0
0
0
2
0
0
2
2
1
0
0
1
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
7
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
2
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
3
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
1
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
3
0
0
2
2
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
2
0
2
0
0
1
2
0
0
1
3
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
1
0
0
0
0
1
2
0
0
0
2
1
0
3
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
3
0
1
1
2
2
0
2
1
1
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
2
1
0
0
1
0
0
0
2
0
2
0
0
0
1
0
0
0
0
1
0
1
3
2
0
2
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
2
0
0
0
0
1
4
2
0
0
0
1
3
0
0
1
0
0
0
0
0
4
0
2
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
2
0
0
1
2
1
0
0
2
0
2
0
0
3
0
0
0
1
0
0
0
3
2
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
1
3
0
0
2
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
3
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
3
0
3
0
2
0
0
1
0
0
0
2
5
0
0
3
0
1
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
2
0
0
0
0
0
0
2
0
1
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
3
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
5
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
1
0
1
0
2
0
6
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
2
0
0
0
0
2
0
1
0
0
0
1
0
2
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
2
0
1
2
0
2
0
0
0
0
0
0
0
0
0
1
1
0
3
0
1
2
0
0
0
0
2
0
0
0
0
1
1
0
1
0
1
0
0
4
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
2
1
0
2
0
0
0
1
0
4
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
1
1
3
2
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
2
0
1
3
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
4
0
2
1
1
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
5
0
3
0
0
2
0
0
0
0
0
0
0
3
0
1
0
0
1
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
2
1
0
0
2
0
0
0
1
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
1
0
0
0
2
0
0
2
1
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
2
0
1
2
1
2
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
5
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
3
4
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
3
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
3
0
2
0
3
4
0
0
1
0
0
0
1
0
0
0
2
1
0
0
2
0
2
0
1
0
0
1
2
0
0
0
2
1
2
0
0
1
2
0
3
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
8
0
0
0
5
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
1
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
3
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
2
0
0
3
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
1
0
1
0
2
1
0
1
0
0
0
0
1
0
0
0
0
2
0
0
2
1
0
0
2
0
1
0
1
1
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
2
0
0
0
0
0
0
0
1
0
0
0
3
0
1
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
1
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
6
0
2
0
0
0
0
2
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
12
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
3
1
0
0
0
0
0
0
1
0
0
0
1
5
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
4
2
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
3
2
0
0
0
2
0
2
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
3
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
2
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
3
1
0
1
0
0
1
1
0
1
0
1
0
3
4
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
1
2
0
3
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
3
1
0
3
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
1
0
1
2
2
0
0
0
0
0
2
2
0
0
1
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
6
8
0
2
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
2
1
1
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
5
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
1
0
0
0
0
2
0
2
0
0
2
0
0
0
0
2
1
1
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
2
0
0
0
0
0
2
2
0
0
2
4
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
1
0
2
0
1
0
2
2
0
0
0
0
0
0
0
3
0
0
0
0
0
2
1
0
2
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
2
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
1
3
4
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
1
0
1
0
0
0
0
0
2
0
0
4
1
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
3
2
0
0
0
0
1
2
2
0
0
1
1
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
1
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
1
0
3
2
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
2
0
3
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
2
0
1
0
0
3
1
1
3
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
3
0
0
0
0
0
0
4
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
2
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
3
0
0
0
2
2
1
0
0
0
0
0
0
0
4
0
2
2
0
1
0
0
0
0
0
0
0
1
0
0
1
2
2
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
1
2
1
0
0
4
4
0
0
2
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
5
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
1
0
2
0
0
0
1
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
3
1
0
0
0
0
1
2
2
0
0
0
1
8
0
2
2
0
0
1
0
0
0
0
2
0
0
0
5
0
2
0
2
0
2
0
2
0
0
2
0
1
0
0
0
0
0
0
6
0
0
1
1
0
0
0
1
1
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
9
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
2
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
2
1
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
3
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
2
0
2
0
0
2
0
2
0
0
0
0
0
0
2
0
0
4
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
6
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
3
2
0
2
0
0
0
0
0
1
0
0
2
1
0
2
5
0
3
0
1
2
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
1
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
1
2
0
2
0
0
2
2
0
2
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
2
0
0
1
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
2
3
12
2
1
8
1
0
0
0
0
1
0
0
2
2
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
1
2
1
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
2
0
0
1
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
4
1
0
1
0
0
0
2
2
1
0
1
0
0
2
0
0
0
3
0
0
1
0
1
1
0
5
2
0
2
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
1
1
0
0
0
0
2
0
0
0
1
0
2
5
0
1
0
0
0
1
0
0
1
4
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
6
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
2
0
2
0
0
1
0
2
0
0
0
0
0
0
0
1
0
2
0
0
1
1
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
2
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
2
2
0
0
1
0
1
0
1
0
2
0
0
1
1
0
0
0
0
0
0
2
1
1
1
0
0
0
0
0
0
2
3
2
1
0
3
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
1
0
0
1
0
2
0
0
0
0
0
0
2
0
0
1
2
2
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
4
0
0
0
0
0
1
0
0
2
0
0
0
1
0
2
3
0
0
0
2
1
0
1
2
6
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
1
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
10
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
4
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
1
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
2
1
0
0
0
1
2
2
1
0
0
0
0
0
1
0
2
1
0
0
2
0
1
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
4
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
1
2
4
2
1
1
0
0
0
0
1
0
0
0
1
0
1
2
2
0
1
0
1
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
4
3
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
3
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
3
0
0
1
0
0
2
0
0
0
1
4
0
0
2
0
0
1
0
0
0
0
0
1
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
1
0
0
0
2
0
0
1
0
0
0
1
2
0
0
0
2
2
2
0
2
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
1
1
0
0
0
0
2
1
0
1
0
0
2
0
1
1
0
3
0
1
2
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
8
1
0
1
1
1
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
1
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
7
0
2
0
0
3
2
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
3
0
3
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
1
0
2
2
1
3
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
9
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
2
0
0
0
11
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
2
0
3
1
0
1
0
0
2
0
0
0
0
2
2
0
1
0
0
0
1
0
2
0
0
0
0
1
1
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
2
3
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
1
5
2
2
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
1
1
0
0
1
0
0
1
0
0
0
3
0
0
1
0
0
2
0
0
0
1
1
0
0
2
0
0
0
3
2
0
1
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
1
2
0
0
0
1
1
0
0
0
0
3
3
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
3
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
3
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
3
2
0
0
0
0
1
0
0
0
3
0
1
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
2
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
1
3
0
0
0
0
0
0
0
0
1
2
0
3
1
0
0
2
0
1
0
0
0
1
0
1
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
1
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
4
0
0
2
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
3
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
1
0
4
0
0
0
0
0
0
2
0
0
0
4
0
0
0
1
0
0
1
2
0
2
0
0
0
2
0
1
0
0
1
0
0
0
8
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
1
0
1
0
0
2
0
0
2
0
0
1
0
0
1
0
2
0
0
0
1
0
0
1
0
1
0
1
0
0
0
4
0
0
1
0
0
0
0
0
1
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
1
0
0
3
0
0
2
0
0
0
1
0
0
0
1
2
0
0
1
0
0
1
0
0
0
6
2
0
0
0
5
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
2
0
0
1
0
2
1
0
0
0
0
2
1
0
5
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
2
0
2
0
0
0
0
0
0
1
0
0
0
2
2
1
2
2
3
0
1
0
0
0
0
1
0
4
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
3
1
0
0
1
2
0
0
0
0
0
1
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
2
2
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
1
1
0
4
0
0
0
1
0
0
1
2
0
3
0
1
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
10
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
2
0
0
2
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
3
0
0
0
0
3
0
1
0
0
1
0
1
2
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
10
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
2
0
0
0
0
0
2
0
0
0
1
0
3
1
0
0
4
1
3
1
0
0
2
0
0
0
0
0
2
0
1
0
0
1
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
2
1
0
0
0
0
2
1
0
0
1
0
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
2
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
2
2
0
1
1
0
0
0
0
1
0
0
0
0
1
2
0
2
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
3
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
1
2
0
0
0
2
0
0
1
0
0
1
0
0
4
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
1
0
1
0
0
3
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
1
2
0
1
1
0
0
2
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
4
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
1
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
2
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
2
2
0
0
0
0
1
2
0
0
0
2
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
1
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
1
1
1
0
0
0
0
0
3
0
0
0
0
0
0
1
2
2
0
0
1
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
4
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
1
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
8
0
0
0
0
2
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
5
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
1
0
0
2
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
2
0
0
1
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
1
1
2
2
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
13
2
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
3
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
1
0
2
0
1
0
0
0
1
1
0
1
1
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
2
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
4
1
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
1
2
1
0
2
0
0
0
0
0
1
2
0
0
2
0
0
0
2
2
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
2
0
1
0
1
2
2
0
0
0
0
0
2
0
1
0
0
1
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
2
0
2
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
1
2
0
1
0
1
0
0
0
2
1
0
1
0
0
1
0
2
2
1
0
2
3
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
1
2
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
2
0
1
0
0
3
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
3
0
2
1
2
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
2
0
0
1
2
0
0
1
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
1
0
0
1
1
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
2
0
0
0
0
0
0
1
0
0
1
2
1
3
0
0
0
1
0
0
0
0
1
2
2
1
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
1
1
0
0
2
0
0
0
4
0
0
0
0
0
1
0
0
0
3
1
0
0
1
0
0
0
0
2
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
1
1
2
0
0
0
0
0
0
0
1
0
3
0
0
0
2
2
2
0
0
6
1
0
0
0
2
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
8
0
0
1
0
1
1
0
1
0
2
0
0
0
0
2
0
1
0
0
0
4
0
2
0
0
1
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
1
2
0
1
0
1
1
0
0
2
2
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
2
1
0
0
0
2
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
1
1
0
1
2
3
0
0
1
0
0
3
0
0
0
2
0
0
0
2
0
2
2
0
5
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
3
2
2
1
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
2
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
4
1
2
0
1
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
2
0
0
2
2
0
1
0
2
1
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
3
0
1
2
2
1
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
2
0
8
0
1
0
0
0
0
0
2
0
1
0
1
0
0
0
1
0
4
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
1
1
2
0
0
0
1
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
6
2
1
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
2
0
0
0
1
0
2
0
0
0
2
1
1
1
0
0
0
1
1
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
1
0
0
1
0
0
2
0
3
1
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
2
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
2
0
5
0
0
1
0
1
3
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
1
0
0
2
2
0
2
0
1
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
3
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
6
0
0
0
0
1
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
1
0
1
1
0
1
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
1
0
0
0
2
0
2
0
0
0
1
0
0
5
0
1
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
2
0
1
0
0
1
1
1
0
0
3
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
2
0
1
0
0
1
0
0
0
2
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
1
0
0
0
2
0
0
0
2
0
0
0
2
0
5
0
0
0
0
0
1
1
0
2
0
1
3
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
2
0
1
0
0
1
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
3
2
0
2
1
0
0
0
1
0
2
1
1
2
2
0
0
0
0
0
0
1
1
0
0
0
7
0
0
0
0
0
2
0
1
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
2
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
6
0
0
0
1
0
0
0
1
2
0
0
0
1
0
0
0
0
8
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
3
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
2
2
0
10
0
2
0
1
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
2
2
0
1
0
1
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
4
0
0
0
0
0
0
0
3
2
0
0
0
2
0
2
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
2
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
1
0
4
0
0
3
1
2
0
1
0
0
0
0
1
0
0
2
1
0
0
0
0
0
2
0
1
0
1
0
1
0
1
0
0
0
0
1
0
0
0
3
2
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
1
0
0
2
0
2
0
0
1
1
2
2
0
0
1
0
0
0
0
0
1
0
2
0
0
0
1
3
1
0
0
1
0
0
2
2
4
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
2
1
0
0
0
1
0
0
2
2
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
1
1
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
1
0
1
0
0
0
1
0
0
2
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
2
0
2
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
2
0
1
2
0
4
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
2
1
0
1
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
1
2
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
5
0
0
0
0
1
0
2
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
5
0
0
3
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
3
1
1
2
0
0
0
0
0
1
0
0
0
3
1
0
0
1
0
1
0
2
2
2
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
3
0
2
0
0
0
0
0
0
1
0
0
1
0
0
1
0
4
0
0
0
2
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
2
2
1
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
2
0
1
0
0
0
0
2
0
0
2
0
0
0
8
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
3
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
3
0
1
4
0
0
3
0
0
2
0
1
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
1
1
0
0
0
0
0
0
0
0
4
1
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
3
0
0
0
1
0
0
0
0
0
1
0
1
0
0
2
2
0
1
0
3
0
0
3
2
0
0
1
0
2
0
0
2
0
0
0
2
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
1
0
2
0
0
0
0
0
0
0
2
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
2
0
0
1
0
1
0
0
0
1
1
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
1
0
0
0
1
1
0
0
1
0
2
0
1
4
0
0
0
0
0
0
1
1
0
2
0
2
0
1
0
0
3
0
0
0
0
0
0
0
0
1
0
2
1
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
1
0
0
2
4
0
0
0
0
0
0
0
0
1
0
0
1
0
3
0
0
1
1
0
0
0
0
2
0
0
0
1
0
0
0
0
1
2
1
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
3
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
1
1
0
0
0
0
2
0
0
0
2
0
0
0
1
3
0
0
1
0
0
0
0
0
0
0
0
2
1
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
3
0
0
0
2
1
0
0
0
0
0
0
0
3
0
3
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
3
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
4
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
2
3
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
1
2
2
0
2
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
2
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
3
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
2
0
1
0
1
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
2
0
0
0
1
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
1
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
2
0
0
1
2
1
0
1
0
0
0
0
2
3
0
1
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
3
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
6
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
2
1
1
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
2
0
0
1
0
1
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
1
2
1
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
2
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
2
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
4
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
2
0
2
0
0
0
4
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
2
2
0
4
1
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
2
0
0
0
0
0
0
1
0
1
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
3
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
3
0
0
1
1
0
1
2
2
0
1
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
3
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
1
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
2
0
1
0
0
0
0
0
1
0
1
0
0
0
1
2
0
0
0
1
0
1
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
12
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
1
2
1
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
1
2
0
0
0
1
1
0
0
0
1
0
0
1
0
1
0
2
0
2
0
0
0
0
1
0
0
0
0
1
0
2
0
1
0
0
0
0
2
0
1
0
0
2
1
0
0
2
0
1
0
0
0
5
0
0
1
1
0
0
0
0
2
0
2
0
2
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
1
2
0
2
0
0
2
0
2
0
2
0
0
2
0
0
1
0
1
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
7
0
0
0
0
0
0
2
0
1
0
1
2
0
0
0
0
0
0
0
0
2
0
3
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
1
0
2
2
1
3
0
0
0
0
1
1
0
0
0
0
0
0
2
0
2
0
0
0
2
1
0
0
0
2
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
3
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
1
1
2
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
2
1
1
0
0
1
0
2
2
0
0
0
0
0
0
0
2
0
0
2
0
0
5
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
1
1
0
0
0
0
1
3
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
1
0
3
0
0
0
0
2
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
2
2
0
2
0
0
2
0
0
0
0
0
0
1
1
0
0
0
2
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
3
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
2
0
1
2
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
4
0
1
0
0
0
0
2
0
1
2
0
4
1
0
0
0
0
0
2
0
0
0
0
2
0
0
1
5
1
0
0
1
0
1
0
1
2
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
5
2
0
0
0
0
0
0
1
0
0
4
0
0
2
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
2
0
0
2
0
0
0
0
2
0
1
0
2
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
1
0
0
0
2
0
0
1
2
0
0
0
0
2
0
2
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
1
0
1
0
0
1
0
2
1
0
5
0
0
0
1
0
0
1
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
2
0
1
0
0
0
0
1
2
2
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
7
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
3
0
2
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
1
0
3
0
0
0
2
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
2
1
1
0
2
0
0
0
0
2
0
0
0
0
2
2
0
0
0
2
0
0
1
0
0
0
0
2
0
1
0
0
3
2
0
1
0
2
0
1
0
0
2
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
4
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
3
0
0
2
0
0
0
1
0
0
0
4
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
1
0
0
0
3
0
1
0
0
0
1
1
0
0
0
0
0
2
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
2
0
0
2
2
0
2
0
0
1
2
0
11
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
2
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
3
0
0
0
0
0
4
0
0
1
0
0
0
1
0
0
2
0
0
3
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
1
0
0
0
2
0
1
0
0
1
2
0
2
1
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
2
2
3
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
1
3
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
4
0
0
0
0
1
0
0
0
0
1
2
0
1
2
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
6
0
0
0
0
0
6
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
2
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
1
0
0
1
1
0
0
2
0
0
0
1
0
1
2
2
0
0
0
0
0
0
2
0
0
3
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
1
0
1
0
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
3
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
1
2
0
0
0
2
0
0
1
0
1
0
0
2
1
0
0
0
2
1
0
0
0
0
0
4
0
2
1
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
1
2
0
0
0
0
3
0
0
0
2
0
1
0
0
0
1
1
0
0
0
8
0
2
2
2
0
0
0
0
0
1
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
1
0
2
3
2
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
1
0
0
3
0
2
0
1
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
1
0
2
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
1
0
0
1
1
0
0
2
2
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
2
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
6
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
5
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
3
1
0
0
1
2
0
0
0
0
0
2
1
0
0
1
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
1
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
1
1
0
0
0
1
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
1
2
0
0
2
0
0
0
2
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
2
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
4
0
0
1
0
0
0
0
2
2
1
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
2
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
2
5
0
0
0
0
0
1
0
1
0
7
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
5
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
4
0
0
2
0
4
0
0
0
8
0
1
0
2
0
0
0
4
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
2
0
0
2
0
0
0
0
2
0
0
1
0
0
0
1
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
1
3
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
1
1
2
2
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
4
0
2
2
0
1
0
2
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
2
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
4
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
3
0
0
2
2
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
2
0
0
2
1
1
0
0
2
1
0
0
1
0
0
0
4
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
3
0
0
0
2
2
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
3
0
0
0
0
0
2
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
2
0
0
2
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
2
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
3
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
2
2
1
0
0
0
0
0
0
0
1
2
0
0
3
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
5
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
1
4
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
1
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
2
3
0
2
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
2
1
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
1
2
0
0
1
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
4
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
2
0
0
0
2
1
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
2
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
3
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
2
1
0
0
0
4
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
5
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
1
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
5
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
1
2
0
0
0
0
0
1
0
0
0
2
0
2
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
2
0
3
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
2
0
1
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
3
0
0
0
1
0
0
0
0
1
2
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
3
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
5
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
2
0
1
2
0
0
3
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
3
1
1
0
2
2
0
1
0
0
0
0
0
0
1
2
1
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
1
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
2
3
5
0
0
2
1
0
2
0
1
0
0
0
2
0
0
0
0
2
0
0
1
1
0
0
1
0
0
0
0
0
0
2
1
0
1
0
0
1
2
1
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
3
0
2
0
0
1
0
0
0
0
2
2
0
0
2
0
3
0
1
0
0
0
0
0
0
0
0
1
0
4
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
3
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
3
0
0
0
0
0
6
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
1
2
0
0
0
1
0
2
3
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
1
0
0
0
0
2
2
0
0
0
0
7
0
0
0
0
0
3
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
6
0
1
0
0
3
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
4
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
2
4
1
0
0
0
0
5
0
0
0
1
0
0
0
0
0
1
0
0
2
1
1
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
1
0
0
3
2
0
0
1
0
2
0
1
0
1
0
0
0
0
3
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
2
0
0
2
0
2
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
1
0
0
0
0
2
2
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
5
0
0
1
0
0
2
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
1
0
6
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
3
0
0
0
1
0
1
0
0
1
0
2
1
2
0
0
0
0
1
0
1
0
2
1
1
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
1
2
3
0
3
0
0
0
1
0
0
0
0
1
3
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
2
1
2
0
1
0
1
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
4
3
0
0
1
0
0
4
1
2
1
0
0
2
1
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
2
0
3
0
0
1
0
0
0
0
0
2
0
1
0
1
0
0
0
3
0
0
1
3
0
0
1
3
0
0
2
0
2
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
3
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
2
0
2
0
0
0
1
7
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
2
0
0
1
0
0
3
0
1
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
3
4
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
2
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
3
1
3
0
0
1
2
3
0
0
0
0
1
1
0
0
0
2
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
2
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
2
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
1
0
0
0
2
0
0
2
0
0
0
2
0
1
6
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
1
1
1
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
5
0
0
2
2
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
1
0
0
2
0
3
1
0
0
0
0
0
0
2
2
1
0
0
2
0
1
0
1
0
0
0
0
2
0
2
0
0
0
0
0
1
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
7
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
3
0
0
0
2
0
0
1
0
0
0
0
6
0
0
0
0
0
3
1
0
0
0
1
2
4
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
4
3
4
0
0
0
0
0
3
3
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
2
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
3
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
2
0
0
3
0
0
5
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
1
0
0
0
1
0
2
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
4
1
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
5
1
0
0
0
0
0
0
0
0
0
0
2
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
1
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
2
0
0
0
2
0
2
0
7
0
0
1
0
0
0
0
1
1
0
2
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
3
2
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
5
0
0
0
0
0
2
0
0
2
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
2
0
0
0
0
6
1
0
0
0
1
2
0
0
1
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
2
1
0
5
0
0
0
0
0
0
1
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
2
1
0
0
0
0
0
0
0
1
0
3
0
1
1
0
0
2
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
1
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
2
1
1
1
0
0
0
0
0
0
1
1
0
3
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
7
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
2
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
1
0
0
4
0
0
1
0
1
2
2
0
0
0
2
0
0
1
0
2
0
0
0
0
0
2
0
1
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
1
2
0
3
0
0
0
0
1
0
0
0
0
0
0
0
1
0
3
0
0
0
2
0
2
1
0
2
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
5
0
0
0
1
0
0
2
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
3
0
0
2
2
0
1
0
0
0
1
2
2
2
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
1
1
1
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
3
0
0
2
0
0
0
2
2
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
1
0
0
2
0
0
2
0
1
3
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
7
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
1
0
5
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
2
0
2
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
3
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
2
0
0
0
2
0
0
3
0
0
2
0
0
0
2
0
1
0
0
0
2
0
0
0
0
2
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
1
1
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
8
0
0
6
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
1
8
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
2
0
0
3
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
1
0
1
0
2
0
0
0
0
2
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
1
2
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
4
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
2
0
1
2
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
2
0
0
1
0
0
2
3
0
1
0
1
0
0
1
0
0
0
0
2
2
0
0
0
0
0
1
1
2
1
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
2
0
0
0
0
0
0
1
1
2
0
1
1
0
0
0
0
0
1
0
0
0
2
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
2
2
0
2
2
0
0
1
2
2
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
1
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
3
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
5
0
2
0
0
0
4
0
2
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
1
0
2
0
1
0
0
0
0
1
2
2
3
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
1
2
1
0
0
0
6
0
0
0
0
2
0
0
0
1
2
0
0
1
0
2
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
2
0
1
1
0
0
3
0
0
0
1
1
0
2
1
2
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
1
0
4
0
0
0
1
0
0
0
2
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
3
1
0
0
0
0
2
0
0
0
0
2
0
3
2
0
1
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
4
0
0
0
1
0
0
1
0
1
2
0
0
2
2
0
0
0
3
0
0
0
0
1
0
2
3
0
0
2
0
1
0
0
0
2
0
0
4
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
2
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
4
2
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
1
1
2
1
0
0
2
0
0
0
0
0
0
1
1
1
2
0
0
0
0
0
1
0
0
0
1
0
0
2
0
1
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
3
0
0
2
0
0
0
0
0
1
0
0
6
0
2
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
2
2
1
0
0
1
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
1
2
2
0
0
0
2
0
0
3
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
2
2
0
2
0
2
0
0
0
1
0
0
2
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
1
0
5
0
0
0
0
0
0
0
0
2
0
0
0
0
2
4
0
0
0
1
0
0
0
0
0
0
0
0
0
2
3
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
3
0
1
1
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
1
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
5
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
1
0
0
0
2
4
0
2
0
0
0
2
0
1
2
1
0
2
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
6
2
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
3
1
0
0
0
1
0
1
0
1
1
0
0
2
0
1
1
0
0
0
0
0
2
0
11
0
0
0
0
1
0
0
3
0
2
0
3
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
1
2
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
1
2
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
8
0
0
0
2
0
0
0
2
0
0
0
0
0
9
0
0
0
2
0
1
1
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
3
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
2
0
1
0
0
2
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
4
0
1
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
0
2
0
1
0
2
0
0
0
0
0
2
0
1
2
1
1
0
0
0
0
0
1
0
2
1
0
5
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
2
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
2
0
0
0
3
1
0
0
0
0
0
0
0
0
0
2
1
1
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
1
3
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
1
0
0
2
2
2
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
1
2
0
0
0
0
2
0
2
2
0
2
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
1
1
1
1
0
0
0
0
1
0
0
2
3
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
6
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
1
0
3
1
0
1
0
0
0
1
0
0
0
0
1
1
3
0
0
0
1
2
0
3
0
0
0
2
0
0
0
0
0
0
3
0
2
0
0
7
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
2
1
1
2
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
2
2
2
1
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
2
0
2
1
2
3
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
3
0
2
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
2
2
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
2
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
2
0
0
3
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
1
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
2
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
2
0
1
0
0
1
2
0
0
0
3
0
0
0
1
0
0
1
0
2
0
0
0
1
0
0
0
1
0
0
1
0
1
0
1
0
0
2
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
2
0
1
0
0
0
0
0
0
0
0
0
5
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
3
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
1
1
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
4
0
0
0
1
0
2
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
1
0
0
1
3
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
5
0
0
0
2
1
0
0
2
0
0
0
2
0
1
0
0
0
2
0
2
1
1
3
0
0
0
2
2
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
2
0
0
0
1
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
1
3
1
0
0
0
8
0
0
0
1
0
0
0
0
0
0
2
0
1
2
0
0
1
0
0
0
0
1
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
1
10
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
1
0
0
0
1
0
2
0
0
0
3
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
1
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
4
1
0
0
1
0
0
0
1
1
0
0
0
0
2
3
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
2
0
1
0
0
0
0
0
0
4
0
0
0
3
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
4
0
0
0
2
0
0
0
2
0
0
0
1
0
2
0
0
1
2
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
2
0
1
2
0
3
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
1
0
1
1
2
0
0
1
0
2
0
1
0
0
0
2
0
2
2
0
0
0
0
5
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
0
1
0
0
0
0
2
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
3
0
0
0
0
0
0
2
0
0
0
0
0
0
5
0
0
0
0
0
0
1
0
1
1
0
4
1
1
0
0
0
1
0
0
2
0
0
2
3
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
2
1
0
1
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
1
3
0
1
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
2
0
1
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
7
0
0
4
0
2
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
3
0
2
0
0
0
0
0
2
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
5
0
0
1
1
0
0
0
0
0
0
3
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
2
2
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
2
0
0
3
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
2
0
2
0
4
2
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
6
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
2
2
7
0
1
1
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
4
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
2
0
0
2
0
0
2
1
0
0
0
0
0
0
1
1
2
0
0
0
0
1
0
1
0
0
0
0
2
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
10
0
0
1
2
0
0
5
0
0
1
0
0
0
2
2
2
2
1
0
0
1
0
0
0
0
2
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
2
3
1
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
3
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
2
1
0
2
1
0
1
0
1
1
0
0
0
2
0
0
0
2
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
1
0
3
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
2
0
0
1
0
0
1
0
1
0
1
2
3
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
8
1
0
0
1
0
0
0
0
0
0
2
2
0
0
5
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
2
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
4
1
3
0
1
0
2
0
0
1
0
0
0
0
0
1
3
0
2
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
3
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
1
0
2
0
0
2
0
0
0
0
4
0
0
0
0
0
9
0
0
0
0
6
2
0
0
0
0
0
0
0
0
2
0
2
0
4
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
2
3
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
7
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
2
0
0
0
1
1
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
2
0
1
0
1
0
0
0
0
0
0
1
2
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
1
0
0
0
0
0
1
0
2
0
0
0
0
2
2
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
4
0
0
0
0
1
0
0
4
1
0
2
0
0
2
0
0
0
0
0
2
2
2
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
3
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
2
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
1
2
0
0
0
0
2
3
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
2
0
0
2
0
1
1
0
1
0
2
0
0
0
0
0
0
2
0
0
1
2
2
4
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
2
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
4
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
3
1
0
0
0
0
0
2
0
0
0
2
0
0
0
3
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
2
2
0
0
0
0
2
0
1
0
2
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
2
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
2
0
1
0
1
0
1
0
0
0
1
0
0
0
2
0
0
7
2
0
0
1
2
0
0
0
2
1
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
1
0
0
0
4
0
0
0
0
0
0
0
0
4
0
1
0
0
0
2
0
0
3
0
0
0
1
0
2
0
0
0
0
0
0
0
3
0
2
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
2
1
0
0
1
2
0
0
0
0
2
2
0
1
0
4
0
0
0
0
0
3
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
2
1
0
2
0
1
1
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
2
0
0
1
0
1
3
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
5
0
2
4
0
1
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
1
0
1
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
1
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
3
2
0
0
0
0
2
0
0
0
1
0
2
0
0
0
2
0
0
2
0
0
0
2
0
0
2
4
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
2
0
0
1
2
0
1
4
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
2
1
2
0
0
3
0
0
2
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
3
0
2
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
2
0
2
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
1
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
1
1
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
1
1
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
2
0
0
2
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
4
0
1
2
0
0
0
0
2
3
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
5
0
1
0
2
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
3
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
2
0
0
1
0
1
0
0
0
1
2
2
0
1
0
0
0
0
2
0
1
0
0
0
0
2
3
3
0
0
0
0
1
0
4
2
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
2
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
1
2
2
0
0
0
1
5
0
0
0
0
5
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
1
0
0
0
2
0
0
1
0
2
0
0
0
1
1
2
0
0
0
0
0
0
0
1
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
3
0
0
1
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
2
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
2
1
0
0
1
0
0
2
1
1
0
2
0
1
2
1
0
2
1
1
1
1
0
0
0
0
0
1
1
0
0
1
0
2
0
5
0
2
0
0
0
2
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
1
0
0
1
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
5
3
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
1
1
0
0
0
0
0
3
0
0
1
0
4
2
2
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
2
0
0
0
0
3
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
2
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
2
0
0
0
0
1
0
0
0
3
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
2
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
2
2
1
1
2
0
0
2
1
2
0
2
0
0
1
6
2
0
1
4
0
1
1
0
0
9
1
0
2
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
3
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
6
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
3
0
0
0
0
0
0
2
0
0
2
1
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
4
0
0
1
0
0
0
0
0
2
1
1
3
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
5
0
2
0
0
0
0
0
0
1
1
0
0
1
8
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
4
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
2
0
0
1
1
0
0
0
3
4
2
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
7
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
3
0
0
1
0
1
0
0
2
0
0
0
0
2
0
0
0
4
0
0
1
2
0
0
0
0
0
0
0
0
2
0
1
0
0
3
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
2
2
0
0
1
3
0
0
0
0
1
0
0
0
0
1
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
2
1
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
3
5
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
1
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
5
0
1
1
0
0
0
0
0
0
0
0
3
2
1
0
1
0
0
0
1
0
0
0
0
1
2
0
2
2
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
1
0
0
0
0
0
2
1
0
1
2
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
5
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
3
0
0
1
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
1
1
0
0
0
0
0
1
0
0
0
2
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
2
0
2
0
0
0
1
0
0
0
0
2
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
4
0
3
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
1
1
3
0
2
0
11
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
1
1
2
2
0
1
0
0
0
0
0
2
1
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
2
1
0
0
0
0
8
1
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
2
2
0
1
0
0
0
0
0
1
2
0
0
0
0
0
2
1
2
0
0
1
0
0
0
0
0
2
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
1
1
4
1
0
2
2
1
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
2
5
0
0
0
1
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
1
0
0
0
2
0
0
0
0
0
2
2
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
1
0
1
0
1
0
0
2
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
5
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
1
1
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
1
0
0
0
0
2
0
0
2
1
2
0
0
0
0
0
0
0
0
6
0
0
0
1
3
1
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
1
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
3
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
2
4
0
0
0
0
1
0
0
2
0
2
1
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
4
0
2
2
0
0
0
0
1
1
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
5
0
0
0
2
2
0
1
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
2
1
2
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
3
0
0
1
0
0
0
1
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
4
3
0
1
0
0
1
0
0
1
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
1
0
0
0
0
2
0
0
0
2
2
0
0
0
2
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
2
2
0
0
0
2
1
0
0
0
1
2
0
0
0
1
0
2
0
2
0
1
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
4
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
2
0
2
0
1
2
0
2
3
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
3
1
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
2
0
0
4
0
0
0
1
2
0
1
0
0
2
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
3
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
2
1
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
1
0
0
0
0
2
1
0
3
1
0
0
0
0
0
1
0
0
2
0
1
2
1
0
0
1
0
0
1
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
1
0
0
0
1
1
2
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
5
1
0
0
2
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
2
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
4
0
2
2
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
2
2
0
0
0
4
2
0
2
0
0
0
0
0
3
0
0
1
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
2
1
1
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
2
0
2
0
0
0
0
0
1
0
0
0
1
0
4
0
1
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
2
0
0
0
2
2
2
0
2
0
1
0
0
0
0
1
1
0
0
0
2
1
0
0
3
0
1
0
0
0
0
0
0
0
0
0
2
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
2
1
0
0
2
0
1
0
0
0
0
1
0
2
0
0
0
2
1
0
0
0
0
0
1
0
0
1
2
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
2
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
2
0
6
0
0
0
1
0
0
1
4
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
2
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
2
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
4
0
0
0
0
2
0
1
0
0
0
0
0
1
1
0
5
0
0
0
0
1
0
0
2
2
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
4
0
0
2
0
0
0
1
0
1
2
2
0
3
1
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
1
2
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
1
1
1
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
3
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
1
1
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
4
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
3
0
1
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
1
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
1
0
0
0
1
0
0
3
0
0
2
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
3
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
0
1
2
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
1
1
0
2
2
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
2
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
2
5
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
1
0
3
0
0
0
1
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
2
1
1
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
2
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
3
0
0
0
0
0
5
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
3
1
4
1
0
1
0
0
2
0
0
1
0
0
1
2
0
1
2
0
0
0
0
0
1
1
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
2
2
2
0
0
0
1
0
2
0
0
1
0
0
0
2
0
2
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
2
0
1
0
0
0
0
0
0
0
0
3
0
3
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
3
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
1
2
1
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
3
2
2
0
0
0
1
1
1
0
0
2
0
0
1
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
2
0
2
0
1
0
0
0
1
0
0
2
0
1
0
2
0
0
0
2
0
0
0
0
2
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
2
1
2
2
0
0
0
0
0
0
0
0
0
0
0
4
2
2
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
1
3
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
2
0
0
0
0
2
0
1
0
2
4
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
1
1
0
0
2
0
2
0
3
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
5
1
0
1
1
1
0
0
0
0
2
0
0
1
0
3
1
5
2
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
1
2
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
7
1
0
0
0
0
1
0
0
0
0
0
0
3
0
1
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
1
0
1
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
5
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
3
0
1
1
1
0
0
0
5
1
0
0
3
0
2
0
2
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
1
1
0
1
1
0
1
1
1
2
2
0
1
0
2
0
1
0
1
0
0
0
0
0
0
0
2
0
2
2
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
2
1
1
0
0
2
0
0
2
1
0
0
0
0
1
0
0
0
0
2
0
2
1
1
0
0
0
0
0
0
5
6
2
1
0
0
5
0
0
1
1
0
0
0
22
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
2
0
0
0
0
3
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
4
1
1
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
3
1
0
2
0
2
0
0
0
0
0
1
0
0
0
1
0
0
2
2
0
0
2
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
3
0
0
2
1
0
0
2
0
0
3
0
1
0
0
1
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
4
0
2
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
2
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
3
0
0
1
2
0
0
0
0
1
0
2
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
3
0
1
1
1
0
0
1
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
2
4
0
0
0
0
1
2
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
3
0
0
0
0
0
0
2
1
1
0
0
3
2
1
0
0
0
1
0
0
0
0
0
1
0
0
0
3
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
2
0
2
1
0
0
0
0
2
2
0
0
0
0
2
0
1
0
1
1
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
1
0
4
0
0
0
0
5
0
0
0
0
1
0
2
0
0
1
12
0
1
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
4
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
1
2
0
0
0
1
0
0
1
2
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
2
0
1
2
1
0
1
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
5
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
6
0
0
0
0
2
0
1
0
2
0
1
2
0
1
5
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
1
0
1
0
4
0
0
0
0
0
0
2
0
0
0
0
3
0
1
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
4
0
0
0
1
0
0
0
3
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
1
0
2
0
2
0
0
0
0
0
0
12
0
0
0
0
0
4
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
3
0
0
1
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
4
0
0
1
0
0
3
0
4
0
0
2
0
2
0
0
2
0
0
0
0
1
0
1
0
2
0
0
1
0
0
0
1
3
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
3
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
1
2
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
12
2
0
0
0
0
2
0
0
0
0
2
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
4
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
1
2
0
1
0
0
2
2
0
2
0
1
0
0
0
0
2
0
2
1
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
3
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
4
2
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
1
0
0
0
2
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
2
2
0
1
3
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
3
1
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
3
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
3
0
0
2
0
0
2
0
0
1
0
3
0
0
0
0
0
0
0
0
0
5
0
0
0
1
3
0
0
0
2
0
0
0
0
0
1
0
0
0
0
6
0
0
4
0
2
2
0
1
0
1
0
2
0
1
1
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
2
2
0
0
1
2
0
0
0
0
0
0
0
1
7
2
0
0
2
0
1
2
0
1
0
0
4
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
1
0
2
0
5
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
1
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
2
0
0
4
0
0
0
0
0
3
2
0
2
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
4
0
0
0
0
0
0
4
1
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
1
3
0
0
2
0
0
1
0
3
0
0
0
2
0
0
0
0
1
0
2
2
0
0
0
0
0
0
1
2
0
0
0
1
0
2
2
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
2
2
0
1
2
0
2
1
4
1
0
1
2
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
5
0
0
0
1
0
2
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
2
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
3
3
0
0
2
1
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
1
0
3
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
11
0
0
0
0
2
0
0
0
1
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
1
2
2
2
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
2
0
1
2
2
0
0
0
0
0
0
2
0
0
0
3
0
4
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
2
0
0
2
0
0
0
0
3
2
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
2
5
2
0
0
0
2
2
0
2
1
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
8
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
2
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
3
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
2
1
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
2
0
3
0
3
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
2
2
0
1
0
0
3
0
2
1
0
0
0
0
1
2
0
2
0
0
0
1
0
1
0
0
1
0
0
1
0
0
1
2
1
0
0
0
0
0
0
0
0
1
1
2
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
8
6
2
0
1
0
0
0
0
2
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
1
0
1
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
3
1
0
1
0
0
0
0
0
0
0
3
0
2
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
4
2
2
1
0
0
0
0
0
0
0
0
0
0
0
1
5
2
5
1
1
0
0
0
1
0
1
0
0
0
1
0
2
0
0
1
0
0
0
1
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
1
0
0
0
0
0
0
0
1
3
2
0
2
0
1
0
0
0
2
0
0
1
0
0
2
1
2
2
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
8
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
3
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
2
0
0
0
0
0
1
0
1
0
0
2
2
0
0
2
0
0
2
1
0
0
0
0
2
1
2
1
0
1
0
0
0
4
0
2
0
2
0
0
1
2
0
0
0
0
0
2
2
0
2
0
0
0
2
0
0
0
2
0
0
2
2
0
0
0
1
0
0
0
0
1
0
1
2
0
0
0
3
0
1
0
2
0
0
0
5
0
0
0
1
2
0
0
0
3
1
0
3
0
0
1
0
0
1
0
1
1
0
0
0
1
0
0
0
1
1
0
0
0
1
2
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
2
0
0
0
0
0
2
2
0
0
3
2
0
0
1
2
2
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
3
1
3
0
0
0
0
1
1
1
0
0
5
0
0
1
0
0
0
1
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
2
0
2
2
0
0
2
1
0
0
0
0
2
0
2
0
2
1
1
1
0
0
0
0
2
2
0
0
1
4
0
0
0
0
0
2
0
0
0
0
0
0
1
0
3
1
1
0
0
0
0
0
0
0
2
0
2
1
0
2
0
0
1
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
2
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
7
2
1
0
3
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
3
0
0
0
1
0
2
0
0
0
1
2
0
0
0
0
1
0
0
1
0
1
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
2
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
2
0
0
0
0
0
0
0
1
0
2
2
0
0
1
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
2
0
1
0
2
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
1
3
0
1
2
1
0
0
0
0
2
0
0
0
0
6
0
0
1
2
0
0
0
0
0
0
3
0
0
0
2
0
0
0
2
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
1
0
1
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
5
0
1
5
0
3
0
2
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
2
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
1
0
1
0
2
0
0
0
2
0
0
0
2
0
2
0
1
0
0
2
0
0
0
0
0
4
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
2
0
0
0
4
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
1
0
4
1
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
3
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
3
0
0
0
1
0
2
0
0
0
0
0
0
0
1
3
0
0
1
1
0
0
0
0
1
1
0
1
0
0
0
0
2
2
0
0
0
0
0
0
1
2
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
1
0
0
1
0
1
0
0
1
0
0
0
3
1
0
0
0
0
0
4
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
2
0
1
0
2
0
0
1
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
2
2
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
2
0
1
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
1
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
3
1
0
0
0
0
0
0
0
1
0
1
0
8
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
3
2
2
0
0
0
0
0
0
1
2
0
0
0
1
0
0
1
0
0
0
1
0
2
0
0
0
0
5
0
0
0
0
0
1
0
2
2
1
3
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
3
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
1
3
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
9
0
1
0
5
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
1
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
5
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
2
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
1
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
2
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
2
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
2
0
0
1
0
0
0
0
0
2
1
1
0
0
0
0
2
2
0
1
1
0
0
2
2
0
2
0
0
0
0
0
0
1
0
0
0
3
1
0
1
1
0
0
1
0
0
0
9
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
2
0
0
0
0
1
0
0
0
5
1
0
1
2
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
2
0
0
0
0
4
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
2
1
0
0
0
0
5
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
2
0
1
0
2
0
0
0
0
0
1
3
0
1
0
1
0
0
0
0
2
3
0
0
0
0
0
1
0
0
2
1
0
0
0
1
0
0
1
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
3
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
1
1
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
3
0
0
0
1
0
1
0
0
0
0
0
0
0
2
1
2
2
0
1
0
1
0
0
0
0
0
0
2
0
1
0
0
0
1
0
2
0
0
3
0
0
0
2
0
0
0
0
0
0
2
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
3
3
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
1
0
0
3
0
1
1
0
0
2
2
1
0
1
2
0
1
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
2
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
2
0
1
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
5
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
2
0
2
0
2
2
0
0
0
0
0
0
0
1
0
1
0
1
3
0
0
0
0
0
1
0
0
1
0
0
0
3
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
1
1
0
2
1
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
1
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
2
2
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
2
1
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
2
0
0
2
0
1
0
8
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
1
0
5
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
1
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
2
0
1
0
0
2
0
0
2
2
0
0
2
0
1
0
0
0
0
0
2
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
2
0
1
3
0
0
0
0
0
0
7
0
2
0
1
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
6
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
3
0
0
0
2
0
0
0
0
0
3
0
0
3
2
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
2
1
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
2
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
1
2
2
4
0
1
1
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
1
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
3
6
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
2
2
2
0
0
1
0
0
0
0
1
0
1
1
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
1
0
0
0
10
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
2
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
2
0
1
0
0
4
2
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
2
0
0
2
2
0
2
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
5
0
0
1
2
2
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
2
0
2
0
0
1
0
2
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
1
0
2
1
3
0
0
1
2
0
0
0
1
0
9
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
4
0
2
0
1
0
0
2
0
0
0
0
2
0
0
1
0
0
1
2
0
1
0
0
0
0
0
0
0
1
0
0
3
0
0
1
0
1
3
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
2
9
0
0
2
0
0
0
2
0
5
0
0
0
3
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
6
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
3
0
0
2
1
0
2
2
0
3
1
0
1
1
0
0
0
1
3
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
3
1
0
0
0
0
0
0
0
0
0
0
1
2
1
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
3
0
3
2
0
0
0
0
0
0
4
0
0
1
1
0
0
0
0
1
2
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
3
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
2
2
0
0
0
3
0
1
0
2
0
0
0
0
0
0
0
0
0
2
1
1
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
3
0
1
0
0
0
0
0
2
0
0
0
0
0
2
2
2
1
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
5
1
0
0
2
0
0
0
1
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
3
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
3
0
2
1
0
0
1
1
0
0
2
0
0
0
2
0
0
2
0
2
0
0
0
1
0
0
0
2
0
0
1
0
6
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
2
1
0
2
0
0
1
2
3
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
6
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
3
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
1
4
0
0
3
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
3
0
0
1
0
2
0
0
0
0
0
0
0
0
2
2
0
1
2
0
0
0
0
0
2
0
0
2
0
0
0
0
2
2
0
1
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
2
0
0
0
0
1
1
7
0
1
1
3
0
0
0
0
0
0
2
0
1
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
2
0
0
3
0
0
2
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
2
0
1
0
2
0
0
0
0
0
3
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
4
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
8
0
0
0
3
0
0
0
2
0
0
2
0
0
1
2
3
0
0
0
0
0
0
2
1
0
2
0
1
0
0
0
0
2
0
0
0
0
2
0
2
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
6
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
2
0
0
2
6
0
2
2
1
0
0
2
0
0
0
0
1
0
1
1
0
0
0
1
0
0
1
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
1
0
0
2
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
9
0
0
2
1
0
0
1
0
1
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
5
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
2
1
0
0
0
0
1
0
2
0
0
1
0
0
2
0
1
2
0
0
1
2
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
1
1
2
1
0
0
1
0
0
0
0
0
3
0
0
0
0
0
1
0
0
2
1
0
1
0
0
0
0
1
2
1
0
0
0
1
1
0
0
2
2
0
3
2
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
3
0
0
1
2
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
4
0
2
2
0
1
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
2
1
0
0
0
1
0
0
0
0
2
0
1
0
0
2
0
0
1
0
2
0
1
0
0
1
0
0
1
2
0
3
0
1
0
0
2
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
3
0
5
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
1
2
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
3
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
1
0
3
0
0
0
6
0
2
0
3
0
0
0
0
1
1
0
0
0
0
0
1
0
2
0
0
2
0
0
0
1
1
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
1
1
0
0
0
0
0
2
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
9
1
2
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
3
2
0
0
0
2
0
0
1
0
0
0
2
2
2
0
0
1
0
0
0
1
0
0
0
0
2
2
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
2
0
2
0
0
0
0
0
2
2
0
0
0
0
1
0
2
0
0
3
0
0
0
1
0
0
5
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
6
0
0
1
0
0
6
1
0
2
0
0
0
2
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
5
0
0
0
5
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
1
0
2
0
1
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
2
0
1
2
3
0
0
2
0
1
0
0
0
9
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
2
0
1
0
1
0
0
0
0
1
0
0
0
2
0
2
1
3
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
1
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
4
2
0
0
0
0
0
0
0
1
5
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
1
0
0
0
0
0
2
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
3
1
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
1
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
1
0
0
0
1
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
4
0
0
0
2
0
0
0
0
0
0
0
3
0
2
0
2
0
0
4
0
0
2
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
3
0
1
1
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
3
1
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
1
0
1
0
0
1
0
3
1
2
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
3
6
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
3
1
0
0
3
0
1
2
1
1
2
0
1
0
0
1
0
1
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
1
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
3
2
2
0
0
1
0
0
0
0
0
1
0
4
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
4
0
1
1
0
0
5
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
1
0
2
0
0
0
6
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
1
0
1
0
0
0
0
3
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
2
0
0
1
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
2
1
0
1
0
0
1
0
0
0
0
1
0
0
1
2
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
2
3
0
1
0
2
0
0
1
2
2
2
0
8
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
2
0
1
0
0
0
2
0
7
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
2
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
1
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
4
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
3
0
0
2
0
0
0
4
0
0
1
0
0
0
1
0
0
0
2
0
1
0
1
2
0
0
4
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
2
0
1
0
0
0
2
0
0
0
0
0
2
2
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
3
1
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
2
0
1
0
0
0
0
1
3
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
1
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
2
0
1
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
1
0
0
3
0
2
0
1
2
1
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
3
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
1
1
2
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
2
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
3
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
2
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
2
0
0
0
10
0
2
0
0
5
0
0
4
0
0
6
0
0
3
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
3
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
3
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
3
2
0
0
0
0
3
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
2
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
1
0
2
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
3
0
1
4
0
1
0
0
0
1
1
0
0
0
5
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
3
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
1
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
2
0
2
2
0
0
3
0
0
0
1
0
1
1
0
2
2
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
3
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
2
2
0
0
2
0
0
2
0
0
0
1
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
1
1
0
0
2
2
0
1
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
3
0
0
2
0
0
1
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
1
2
0
0
0
0
0
0
2
2
0
0
0
1
1
0
0
0
0
0
0
0
0
3
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
5
0
0
2
0
0
0
1
0
1
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
3
1
0
0
2
0
1
0
0
0
0
0
2
1
1
0
0
0
0
0
1
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
3
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
2
0
11
0
3
0
0
0
1
1
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
4
0
0
0
1
0
1
2
0
0
3
0
1
0
4
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
12
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
1
2
3
0
0
0
0
1
2
1
0
0
0
1
0
0
0
2
0
0
0
1
2
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
2
0
0
1
2
0
2
4
1
0
0
3
0
0
0
0
2
0
5
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
1
0
0
0
1
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
2
3
0
0
0
1
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
2
0
0
0
0
0
0
3
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
2
1
0
0
0
1
0
0
2
1
0
0
0
3
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
4
0
0
0
2
0
0
1
2
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
8
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
2
2
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
3
0
0
0
2
1
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
2
0
1
2
0
0
2
1
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
2
0
0
0
1
0
1
1
0
1
0
2
2
0
0
0
0
0
0
0
0
3
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
4
1
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
5
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
5
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
2
2
0
0
0
2
2
2
0
0
0
0
1
0
0
0
0
0
0
0
1
2
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
1
2
1
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
1
2
0
0
1
0
0
1
0
0
2
2
0
0
0
0
0
0
0
3
0
1
0
0
1
0
2
1
2
0
0
0
0
0
0
0
0
0
2
0
1
9
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
7
0
0
0
0
0
1
0
1
2
2
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
1
4
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
5
0
2
1
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
6
0
0
0
1
0
1
4
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
3
0
1
0
0
0
0
0
1
0
0
2
0
2
0
0
1
3
1
0
0
1
0
0
0
1
0
0
0
2
2
0
0
0
0
0
1
0
0
0
2
0
0
1
2
1
1
0
3
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
3
2
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
1
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
1
0
0
2
2
0
0
5
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
1
1
2
0
0
0
0
0
2
0
1
0
0
0
2
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
4
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
2
2
0
0
0
0
1
0
0
1
1
0
4
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
3
0
3
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
1
0
1
1
0
2
2
0
0
0
0
0
5
1
1
0
1
0
2
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
2
1
0
2
0
0
2
0
1
0
2
0
0
0
3
0
0
0
2
0
0
0
0
2
1
0
0
0
1
0
0
3
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
1
3
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
1
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
1
1
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
1
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
1
0
3
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
1
0
0
1
1
0
0
0
0
0
3
0
0
0
0
1
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
3
0
0
0
1
0
0
0
0
0
0
4
0
0
2
0
0
0
0
3
1
0
0
0
0
0
1
1
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
2
0
1
0
2
1
0
4
0
3
2
0
0
0
0
0
0
0
2
0
0
1
2
0
0
1
0
0
0
1
0
1
0
0
0
0
0
2
0
1
1
0
0
3
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
2
3
0
2
0
0
0
0
3
0
2
0
4
0
2
0
0
1
1
0
3
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
1
2
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
1
2
0
0
2
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
1
0
0
2
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
3
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
2
0
1
0
1
0
0
0
1
0
2
0
0
1
2
2
0
0
0
1
0
1
0
0
0
0
0
0
2
5
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
1
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
2
3
0
2
0
0
0
2
1
0
3
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
1
2
1
1
0
1
2
0
2
2
0
0
0
0
2
0
2
0
0
0
2
0
1
0
1
0
0
1
2
0
1
0
1
2
0
0
14
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
1
0
2
0
0
0
1
1
0
1
0
0
0
2
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
2
1
2
2
0
0
0
0
0
0
2
0
0
0
2
4
2
0
0
0
0
0
2
2
0
1
0
0
1
1
1
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
1
4
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
3
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
3
0
5
0
0
0
0
0
0
3
0
0
0
1
0
1
0
0
0
2
1
0
0
3
0
2
0
0
2
1
0
0
0
0
3
0
1
0
0
3
2
0
0
0
0
0
0
0
1
0
2
2
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
1
0
0
0
0
1
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
2
0
0
1
0
1
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
4
0
2
0
0
1
2
2
0
0
0
4
0
1
0
4
0
3
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
1
0
0
0
0
0
0
2
0
2
1
0
2
0
2
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
2
0
2
1
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
2
2
0
2
0
0
2
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
2
0
2
0
0
2
0
2
0
3
0
6
0
0
0
2
0
0
1
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
4
3
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
4
0
1
0
0
1
0
2
1
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
5
0
2
0
1
0
0
0
0
0
0
2
4
0
0
0
1
0
0
0
0
0
0
0
0
3
0
2
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
6
1
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
1
0
0
0
0
0
1
2
2
1
2
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
2
2
0
2
0
0
0
1
0
0
0
1
0
0
0
2
1
1
0
0
1
1
0
0
0
1
1
0
0
0
0
2
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
6
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
1
0
3
0
0
1
0
0
0
0
0
2
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
2
1
0
0
0
0
2
1
0
4
0
0
0
0
0
1
2
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
8
0
0
0
0
0
2
0
1
0
0
0
0
2
0
2
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
2
0
0
1
0
0
1
0
0
0
0
0
2
1
0
1
2
0
1
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
2
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
2
0
0
4
2
0
0
0
1
0
2
1
2
0
0
0
0
0
2
0
0
0
2
2
1
0
0
0
2
0
0
0
0
6
5
0
1
1
0
0
0
1
0
0
1
0
0
2
0
0
1
0
2
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
2
3
0
0
0
0
0
0
2
0
1
0
1
1
0
0
0
2
0
0
0
0
0
1
0
1
0
2
1
3
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
5
0
0
3
0
0
0
1
0
4
0
0
0
0
3
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
1
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
2
2
0
0
2
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
6
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
1
0
1
0
0
0
0
0
0
0
7
0
0
0
2
0
1
0
1
3
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
2
0
0
0
2
0
0
1
2
2
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
1
1
0
0
2
0
0
1
2
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
4
0
0
0
0
1
0
1
0
0
0
0
1
2
0
0
0
0
0
3
0
0
0
0
0
0
0
1
4
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
3
2
0
1
0
0
2
1
1
0
0
1
0
0
0
2
2
0
0
3
0
0
1
1
0
0
0
2
0
0
0
0
0
3
1
0
0
3
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
0
0
0
5
0
0
0
1
0
1
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
1
2
2
0
1
0
0
0
6
0
0
0
0
0
1
0
0
0
0
4
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
3
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
2
2
0
0
1
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
1
0
2
0
0
0
0
0
2
0
0
1
0
0
1
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
3
1
1
0
0
0
0
0
0
0
1
0
0
0
2
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
10
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
2
0
0
2
1
0
2
4
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
1
0
3
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
2
1
23
1
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
1
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
2
3
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
1
2
5
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
5
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
6
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
2
5
1
0
0
0
0
0
0
2
0
2
0
1
0
1
0
0
0
2
0
0
2
0
0
0
0
0
1
0
3
2
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
2
0
1
1
0
0
0
2
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
3
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
1
0
1
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
3
0
0
0
0
0
0
2
1
2
0
0
2
0
0
0
0
2
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
1
0
2
0
0
1
0
2
2
0
0
2
0
0
1
0
0
0
2
0
0
0
2
0
6
0
1
2
0
0
2
0
0
0
0
3
0
2
2
0
0
0
3
0
2
0
0
0
2
0
1
0
0
2
1
0
0
0
0
1
0
2
0
0
1
2
0
1
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
2
0
4
0
0
0
0
1
0
1
0
0
1
0
3
0
0
0
0
0
0
0
0
1
3
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
3
0
0
4
3
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
3
0
0
0
0
1
0
2
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
1
0
1
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
2
0
0
0
2
1
2
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
2
2
0
0
0
1
0
0
0
3
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
2
17
1
0
0
1
0
1
0
0
0
0
1
0
1
2
0
0
0
0
0
1
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
5
1
4
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
3
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
11
0
0
0
0
0
2
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
1
0
3
2
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
1
0
0
0
1
2
0
0
0
1
0
0
0
1
0
0
0
0
3
1
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
4
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
2
0
0
1
0
0
0
1
0
0
5
2
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
1
2
2
0
0
1
0
2
2
0
0
0
0
0
0
2
2
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
2
0
0
0
2
0
1
1
0
2
0
0
2
1
0
0
0
0
0
0
0
2
2
3
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
1
0
0
2
0
0
0
3
1
0
0
1
0
0
0
1
0
1
0
0
2
7
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
5
0
3
2
0
1
0
0
1
6
0
1
0
0
0
0
1
0
3
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
2
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
2
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
1
0
3
0
1
2
0
0
2
0
0
0
0
2
1
0
1
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
1
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
2
0
0
2
0
4
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
1
1
0
2
0
0
2
0
0
1
2
0
0
0
2
0
0
0
0
2
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
5
0
0
0
0
2
0
0
0
3
2
0
0
0
0
0
1
0
2
0
0
0
0
2
0
1
0
0
2
0
0
0
2
1
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
2
0
0
0
0
0
2
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
2
0
0
1
0
0
2
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
2
0
0
1
0
0
0
0
1
0
0
23
0
0
3
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
1
2
0
0
1
0
0
1
0
0
3
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
5
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
2
2
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
2
1
1
0
5
0
0
0
1
0
1
1
0
0
0
0
2
2
0
0
0
0
0
3
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
9
0
0
0
1
0
0
0
1
0
3
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
1
0
0
1
2
4
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
3
0
1
0
0
3
0
1
0
0
3
0
0
1
2
0
0
0
1
1
0
0
9
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
4
1
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
13
0
2
0
0
2
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
2
0
0
0
1
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
6
1
0
0
0
2
0
0
2
2
2
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
2
1
3
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
2
2
0
2
0
1
0
0
0
0
0
0
0
0
3
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
3
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
2
0
4
0
0
0
2
1
0
1
2
0
1
0
1
4
1
2
0
0
1
0
0
0
0
1
0
1
0
4
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
1
4
0
1
2
0
0
0
0
0
1
2
0
0
0
2
0
1
0
1
0
0
0
0
2
0
0
1
3
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
23
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
4
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
2
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
3
1
0
0
2
0
1
2
0
0
0
0
1
0
0
0
2
2
0
0
0
4
1
2
0
0
1
0
1
0
1
0
0
0
0
2
2
0
0
1
0
0
3
0
0
1
0
3
0
0
6
0
2
2
0
1
0
1
1
0
0
1
4
0
2
0
0
0
2
0
0
1
1
0
0
0
0
2
1
0
2
0
0
1
3
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
2
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
3
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
6
0
0
0
2
1
0
0
0
1
0
0
2
1
0
0
1
2
0
2
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
2
0
1
0
0
1
0
0
0
0
2
0
0
0
0
2
2
1
0
0
0
0
0
1
2
2
0
0
0
0
2
1
0
1
0
0
0
2
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
1
0
2
0
1
1
0
0
0
2
3
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
8
0
0
0
0
0
0
0
0
1
0
0
0
3
0
1
0
0
1
0
0
0
0
0
0
2
1
0
0
2
1
0
1
0
0
1
3
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
3
1
0
0
0
0
0
2
0
0
7
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
3
0
2
0
0
0
0
3
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
1
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
2
1
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
2
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
1
0
0
0
0
0
0
3
0
2
0
2
0
2
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
1
2
0
1
2
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
2
4
0
0
0
0
0
0
0
2
0
1
4
2
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
1
0
0
2
0
0
2
0
0
1
0
1
0
0
0
0
0
3
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
5
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
3
0
2
0
0
1
0
0
0
0
2
1
1
0
0
1
0
0
0
4
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
2
1
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
2
3
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
3
1
0
0
0
1
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
2
4
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
1
3
2
1
0
0
0
0
0
1
0
0
0
0
6
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
2
1
0
2
0
0
2
3
0
0
0
0
1
0
0
2
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
2
0
0
2
0
0
0
2
0
0
0
2
0
0
2
1
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
1
0
2
0
0
0
0
2
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
4
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
2
0
4
0
0
0
1
0
1
2
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
3
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
1
2
0
0
0
1
1
0
0
0
0
0
1
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
4
0
0
2
0
1
3
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
3
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
2
2
3
6
0
2
0
5
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
2
0
3
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
2
0
2
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
3
0
1
0
3
0
0
0
0
0
0
0
0
3
0
1
0
2
0
5
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
1
1
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
2
2
1
0
0
1
0
0
0
1
3
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
3
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
1
0
0
0
2
0
0
2
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
3
3
0
2
0
1
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
1
1
0
0
0
1
0
1
0
3
0
0
4
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
5
1
0
0
0
0
0
2
0
0
0
2
0
2
0
0
1
0
0
1
0
0
2
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
3
0
6
0
0
0
2
1
0
0
0
0
2
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
1
8
4
0
0
0
1
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
2
0
0
3
0
1
0
0
0
0
2
0
0
1
0
0
0
2
0
2
0
5
2
2
0
0
0
0
0
0
0
3
0
0
0
2
2
0
2
0
0
0
0
0
0
2
2
0
1
0
0
3
0
0
2
5
0
0
0
1
1
2
0
0
0
0
0
0
0
0
3
0
0
3
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
1
0
0
2
2
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
1
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
1
0
1
2
1
1
0
0
0
0
0
5
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
1
1
0
1
1
2
0
0
1
0
2
0
0
1
0
1
1
2
0
1
0
0
0
5
0
0
0
0
2
2
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
6
0
1
1
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
5
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
2
2
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
2
1
1
0
0
2
0
0
1
0
2
2
0
0
2
0
2
0
0
0
2
0
0
1
3
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
2
5
0
0
0
0
0
0
1
0
2
0
1
0
2
0
0
3
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
1
0
0
2
0
0
0
0
1
1
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
1
2
0
0
1
0
3
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
1
3
0
0
2
2
0
0
0
0
0
1
1
0
0
1
0
2
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
2
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
2
1
0
1
0
0
0
0
0
2
1
1
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
2
4
2
1
0
0
0
1
4
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
3
0
0
0
0
0
1
1
1
0
0
0
1
0
1
0
1
2
0
0
1
2
0
0
0
2
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
1
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
3
0
0
0
1
0
2
0
0
2
0
0
0
0
9
0
1
1
0
0
1
0
0
7
0
2
2
0
2
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
1
0
0
0
0
0
1
0
0
2
0
0
2
1
0
0
0
1
0
0
0
0
0
2
0
1
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
5
0
0
0
0
0
0
4
0
0
0
0
0
0
0
8
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
1
5
0
0
0
1
2
1
2
2
3
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
2
3
0
0
0
2
0
0
0
0
1
0
0
0
2
0
2
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
1
1
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
4
2
1
0
2
0
0
0
0
2
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
1
0
2
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
1
0
0
2
0
1
0
0
0
1
0
2
0
0
0
2
2
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
4
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
1
0
0
0
0
0
1
0
0
2
7
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
5
0
0
2
0
3
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
1
0
0
0
1
1
3
1
0
0
0
0
1
0
1
1
0
0
2
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
1
1
0
0
0
0
0
2
0
0
3
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
1
0
2
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
2
0
2
2
0
0
1
0
0
2
2
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
1
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
2
0
1
0
0
1
2
1
0
0
0
0
0
0
0
0
0
2
1
2
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
3
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
1
3
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
1
6
1
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
17
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
1
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
3
0
0
0
2
1
0
0
0
1
0
2
1
0
0
1
2
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
2
0
2
2
0
0
2
0
2
0
0
0
0
0
2
1
0
0
1
0
2
0
0
0
0
2
1
0
0
0
0
2
0
0
2
2
0
0
0
1
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
2
2
1
1
1
0
0
0
0
0
2
0
3
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
6
0
0
1
0
2
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
2
2
0
0
0
0
0
0
0
2
1
0
1
2
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
4
1
1
0
0
0
0
5
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
2
0
0
2
1
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
3
0
2
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
1
0
0
0
2
0
0
0
1
3
0
0
0
2
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
6
0
0
8
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
1
1
0
0
0
1
0
0
0
0
2
3
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
2
0
0
0
0
3
0
0
0
0
0
1
1
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
2
0
3
1
0
0
0
0
0
0
0
0
0
2
4
2
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
2
0
2
0
1
0
0
3
1
2
0
1
1
0
2
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
2
1
0
2
0
0
0
0
1
0
1
1
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
1
0
0
0
0
0
2
1
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
2
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
4
1
1
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
2
0
1
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
4
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
10
1
0
0
0
0
1
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
2
0
0
1
0
1
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
6
2
0
0
1
1
2
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
2
2
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
2
2
0
0
0
0
0
0
1
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
4
1
0
0
0
3
1
1
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
2
2
0
0
0
1
4
0
0
0
2
0
2
0
1
0
1
0
0
0
0
2
0
0
0
1
0
0
2
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
2
1
0
0
2
0
0
1
0
3
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
2
0
0
0
1
0
0
0
1
0
0
2
0
1
0
2
1
0
0
0
0
0
2
0
0
0
0
5
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
3
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
1
0
2
0
0
0
0
0
2
0
1
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
2
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
1
0
0
0
0
2
2
0
0
0
1
4
2
0
2
4
0
1
0
0
0
1
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
3
2
0
0
1
0
0
0
2
0
0
0
0
0
3
1
0
0
0
0
0
0
0
2
0
1
0
0
5
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
2
0
1
0
0
1
1
0
5
0
0
0
0
0
0
5
0
0
0
0
1
3
1
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
4
0
2
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
3
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
3
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
2
0
1
1
3
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
4
1
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
1
2
0
0
0
4
1
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
1
2
0
1
0
0
0
0
2
0
0
0
0
0
3
5
0
2
0
2
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
3
1
2
0
0
0
0
3
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
3
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
1
2
25
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
1
0
0
0
2
0
0
0
0
5
2
0
0
0
0
0
2
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
3
0
0
0
0
1
2
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
3
0
2
0
1
0
0
0
1
0
0
2
0
0
0
0
0
1
2
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
1
1
0
1
0
0
0
1
0
2
0
1
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
1
0
6
0
2
2
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
4
1
1
2
0
0
1
1
1
1
0
0
0
0
0
0
1
1
3
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
4
0
1
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
1
2
0
2
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
2
1
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
1
2
0
0
2
0
2
0
0
0
0
1
2
0
0
0
0
0
2
0
0
2
0
1
0
0
2
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
4
3
0
0
2
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
2
2
0
0
1
0
1
0
2
2
1
0
1
0
0
6
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
1
3
1
0
1
0
2
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
2
0
0
0
1
0
1
2
0
0
2
0
1
0
0
0
2
0
5
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
1
1
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
2
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
1
0
11
0
1
0
0
0
0
0
1
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
4
0
0
1
0
2
0
0
0
1
9
2
0
0
2
0
0
3
0
1
0
0
0
0
0
0
2
0
2
4
0
0
1
1
0
2
2
0
1
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
2
1
0
0
0
0
1
0
1
0
1
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
6
0
2
0
0
1
0
0
0
0
0
0
1
0
3
1
0
2
0
0
0
0
0
2
0
0
1
0
0
3
1
1
0
1
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
7
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
3
1
1
0
0
1
2
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
3
2
0
0
0
3
2
2
0
0
0
0
1
0
0
1
0
0
0
1
1
2
1
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
3
0
0
0
0
0
0
1
0
0
0
2
1
1
3
0
0
2
0
0
0
0
0
0
1
1
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
1
1
0
0
0
2
0
0
0
1
0
0
1
0
0
0
2
0
0
0
1
2
0
0
0
1
2
2
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
4
0
0
3
0
0
2
0
0
0
0
0
0
4
1
0
0
0
0
0
3
0
0
0
3
0
0
0
0
3
2
0
0
0
1
0
2
0
0
0
0
0
0
2
1
0
0
0
0
2
0
4
0
0
1
0
0
0
0
0
3
0
2
1
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
1
4
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
2
0
0
0
0
0
0
0
3
0
0
2
0
0
0
3
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
1
1
0
0
0
1
4
0
1
0
0
0
0
0
0
2
1
0
0
1
0
2
0
0
0
0
0
0
0
1
2
0
0
3
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
3
2
0
0
0
1
0
0
0
0
1
1
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
2
0
2
4
0
1
0
0
0
2
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
2
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
1
0
1
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
2
0
1
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
1
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
2
2
2
0
0
0
4
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
2
2
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
3
0
0
0
2
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
1
0
0
1
0
0
0
1
2
0
1
1
0
0
0
0
0
0
0
2
0
0
0
2
0
3
0
1
0
0
0
0
0
0
1
0
1
0
5
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
2
2
1
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
1
3
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
3
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
1
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
3
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
1
1
0
1
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
1
0
2
0
0
1
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
3
0
0
2
0
0
0
2
0
5
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
3
0
0
2
0
0
2
1
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
3
0
0
1
3
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
2
0
2
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
2
3
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
1
2
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
2
1
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
1
0
4
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
4
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
2
0
1
0
1
0
2
2
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
6
2
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
2
1
3
0
0
0
2
3
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
3
0
3
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
4
0
0
2
0
0
0
0
1
0
0
0
0
0
2
1
1
0
1
1
0
1
0
1
0
1
0
2
0
1
0
0
0
1
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
5
1
2
2
0
0
0
0
0
1
0
0
2
4
1
2
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
2
1
3
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
2
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
6
2
1
0
0
0
0
0
3
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
3
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
1
4
0
0
0
0
2
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
3
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
3
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
1
2
0
0
0
0
0
3
0
0
0
0
0
3
0
0
0
0
0
3
0
0
0
0
0
0
2
0
1
2
0
0
0
0
1
2
0
0
3
0
0
2
0
0
0
1
0
0
0
2
0
0
1
0
0
0
1
0
0
0
2
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
2
0
1
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
1
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
4
0
0
0
0
0
0
0
1
0
1
2
0
1
1
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
2
0
0
0
0
0
0
1
0
0
0
0
0
5
0
2
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
1
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
3
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
2
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
1
0
0
0
1
0
0
0
2
0
0
2
0
0
0
2
1
0
0
2
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
2
1
0
0
0
2
2
0
2
0
1
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
2
0
4
0
0
0
0
0
2
0
0
0
0
0
2
3
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
1
2
0
0
2
0
0
1
2
0
1
0
0
0
0
0
0
1
0
0
4
0
2
0
0
2
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
1
0
0
0
0
5
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
2
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
3
2
0
0
0
0
0
0
0
0
2
0
0
1
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
1
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
7
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
1
4
0
2
0
0
0
2
1
2
0
2
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
1
0
1
0
0
0
3
2
2
0
0
1
2
1
2
0
0
0
1
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
1
0
2
0
2
0
6
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
8
0
0
0
0
0
0
2
0
0
0
1
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
7
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
2
0
0
0
1
0
0
4
0
2
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
1
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
2
0
0
0
1
0
0
1
0
0
1
1
0
10
0
0
0
0
0
0
2
3
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
1
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
3
0
2
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
5
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
6
0
0
0
1
0
1
2
2
0
0
2
0
3
0
0
0
0
1
4
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
2
0
0
0
0
0
0
3
0
0
0
0
1
0
0
7
2
0
0
0
0
1
0
0
1
0
0
1
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
2
0
0
2
0
1
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
2
0
0
2
0
0
0
0
2
0
0
0
1
7
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
1
1
0
1
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
4
0
2
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
9
0
2
2
1
0
0
0
0
0
0
0
0
0
1
2
0
2
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
7
2
0
3
0
2
0
0
0
2
0
0
0
0
2
0
1
1
3
0
0
4
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
1
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
2
2
0
0
0
1
0
2
0
0
0
2
0
0
0
0
1
0
0
3
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
4
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
3
0
0
0
0
3
2
0
0
0
0
0
0
2
0
0
0
0
2
1
0
1
0
2
1
0
2
0
0
0
1
0
3
0
0
0
0
2
1
0
0
0
1
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
2
2
0
2
2
1
0
2
0
0
0
0
0
0
3
0
1
0
1
0
2
1
2
0
1
0
1
0
0
2
1
0
3
2
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
3
1
1
0
0
0
0
6
0
2
0
0
1
2
0
0
2
0
0
1
0
0
0
0
2
1
0
0
0
1
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
2
1
1
2
0
0
1
0
0
2
2
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
1
0
2
0
0
2
0
0
2
1
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
3
1
0
2
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
7
0
0
0
0
0
0
0
3
0
1
0
0
0
2
0
2
2
0
0
2
0
0
0
2
3
0
0
2
0
1
0
0
0
0
2
0
1
0
0
0
7
0
2
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
2
10
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
5
2
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
2
2
2
0
0
2
0
1
0
0
2
1
0
3
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
3
2
0
0
0
0
2
1
0
0
2
0
1
1
1
0
0
0
0
1
1
0
7
0
2
0
1
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
2
1
0
0
0
0
2
2
0
1
0
0
3
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
3
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
1
0
0
0
0
0
0
0
0
1
2
2
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
3
0
1
1
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
3
0
0
2
0
1
0
0
0
2
1
0
0
0
0
0
0
0
1
4
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
4
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
3
0
0
2
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
1
0
1
1
1
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
3
0
2
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
3
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
1
2
0
0
0
2
3
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
2
0
0
0
0
2
1
2
0
0
0
0
0
0
0
1
0
0
0
2
3
2
0
2
0
2
0
0
1
1
2
3
0
1
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
1
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
1
1
2
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
1
0
0
0
0
0
3
0
0
0
1
1
1
1
0
0
0
1
0
0
0
0
0
0
0
1
2
2
1
0
0
0
2
1
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
2
0
3
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
1
1
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
4
0
2
3
0
0
2
0
0
0
0
1
1
0
0
0
0
1
3
0
0
0
0
1
0
2
0
0
0
2
1
1
0
0
0
2
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
1
2
0
0
2
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
2
0
0
3
0
0
0
0
1
1
2
0
0
0
1
0
2
1
2
0
5
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
1
0
0
2
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
2
0
0
0
0
2
2
0
0
0
2
0
0
3
0
0
0
2
0
0
0
0
0
1
2
0
0
3
3
0
0
2
0
0
0
0
0
0
0
1
1
0
0
3
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
2
2
0
0
1
0
0
2
0
1
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
2
0
0
1
1
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
1
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
2
0
0
0
0
0
0
12
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
2
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
1
2
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
2
0
2
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
1
3
2
0
2
0
0
0
0
0
4
2
2
1
0
1
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
3
0
2
0
1
0
0
0
0
0
1
2
0
1
0
0
0
2
0
3
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
1
0
2
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
2
0
0
0
0
2
1
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
1
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
1
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
3
1
0
0
2
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
2
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
1
0
2
0
0
0
1
0
1
0
0
0
0
0
0
1
4
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
2
2
0
2
0
3
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
1
3
0
2
2
0
0
1
3
1
1
0
0
0
1
0
1
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
4
0
2
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
2
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
1
0
2
0
0
1
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
2
0
2
0
4
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
1
2
2
0
0
0
0
0
0
1
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
1
0
2
2
2
0
0
0
0
0
1
0
0
2
0
0
0
3
0
1
0
1
0
0
0
0
7
0
0
0
0
0
0
0
0
0
2
2
0
4
0
4
0
1
1
0
0
0
0
2
0
0
0
0
1
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
3
0
1
0
0
3
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
2
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
2
1
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
2
2
0
2
0
0
0
4
1
0
0
2
0
2
0
0
0
5
0
1
0
0
0
2
0
0
2
0
0
0
0
1
2
0
0
0
0
0
2
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
5
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
1
0
5
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
1
0
0
0
0
2
0
0
0
2
2
1
0
0
1
0
0
4
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
1
0
1
1
2
0
3
1
0
1
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
3
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
3
0
0
2
0
0
0
0
0
1
0
0
2
3
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
1
2
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
3
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
1
0
2
2
0
0
1
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
5
0
0
2
0
0
0
0
0
0
2
3
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
2
1
1
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
1
0
1
1
1
0
0
0
3
4
0
0
0
0
1
2
0
0
0
0
0
2
0
1
2
0
0
0
0
0
4
2
0
0
0
0
0
0
2
1
1
0
0
0
3
0
1
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
4
1
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
1
0
1
0
0
0
0
3
0
2
0
2
0
0
0
2
0
0
1
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
3
0
0
0
0
0
1
0
0
0
1
3
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
2
0
0
6
0
0
0
0
0
0
0
0
1
2
1
3
0
0
0
0
2
4
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
1
0
0
2
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
3
0
1
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
1
1
0
1
0
0
0
0
0
3
0
0
1
0
0
0
1
0
0
0
0
0
0
1
3
0
0
0
0
0
1
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
2
1
0
1
0
3
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
3
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
8
2
1
0
0
2
0
0
2
0
0
0
1
1
0
1
0
0
0
1
0
2
2
0
0
0
0
2
0
0
1
0
0
0
4
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
1
1
2
0
0
0
0
0
0
0
2
0
0
1
1
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
3
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
1
2
0
0
3
0
0
0
0
2
1
0
0
0
1
0
0
0
2
0
0
3
0
0
0
1
0
0
0
3
0
7
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
3
0
0
2
0
0
2
0
1
1
0
0
0
0
0
0
0
2
1
0
0
0
2
1
0
2
2
0
0
2
2
0
0
0
2
0
0
2
2
4
0
0
0
0
0
0
1
0
0
0
0
3
2
0
1
1
0
2
2
0
1
0
2
0
0
2
0
0
0
3
0
0
1
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
9
0
0
0
3
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
3
2
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
3
1
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
2
0
0
0
2
2
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
2
0
1
1
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
3
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
2
0
1
0
0
0
0
1
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
2
3
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
3
0
0
0
0
0
0
2
3
0
1
0
1
2
0
0
0
2
0
0
0
2
0
3
1
0
0
0
2
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
1
2
0
1
2
0
0
2
0
0
6
0
0
0
0
0
1
0
0
0
1
1
0
2
2
2
0
0
2
0
0
0
0
0
0
0
0
1
3
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
1
0
0
1
0
0
0
1
0
0
2
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
2
2
1
0
2
5
1
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
3
0
0
4
0
2
0
0
0
0
1
2
0
2
0
0
0
0
0
1
2
0
2
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
6
2
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
1
2
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
4
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
1
1
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
2
1
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
2
0
1
1
0
1
0
1
0
1
3
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
2
2
1
1
1
0
0
0
0
1
0
1
0
0
1
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
2
0
0
1
0
2
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
1
2
2
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
2
1
0
0
0
1
0
1
0
0
1
0
0
0
1
0
1
0
0
0
1
0
3
0
0
0
0
0
0
2
0
1
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
2
0
0
2
0
1
0
2
0
2
0
0
0
3
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
3
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
1
0
3
0
3
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
2
0
1
2
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
1
0
2
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
2
0
0
0
2
2
0
0
3
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
2
0
3
3
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
1
1
0
0
2
5
0
1
0
0
0
1
2
5
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
5
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
1
0
2
2
1
0
3
1
2
2
0
0
0
0
0
0
0
2
2
0
1
0
0
0
1
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
2
3
0
0
0
0
0
2
0
0
0
2
1
0
0
0
1
1
0
0
1
0
0
0
0
2
2
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
4
1
1
2
1
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
2
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
1
2
1
0
0
2
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
3
0
1
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
2
1
0
0
2
1
0
0
0
0
0
0
0
0
0
3
0
2
1
0
0
0
0
1
0
0
0
0
3
0
0
0
0
1
0
1
0
2
0
0
0
0
1
1
1
1
0
4
2
0
0
3
0
0
0
0
0
1
1
3
1
0
2
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
2
0
0
0
0
1
1
0
0
2
0
0
2
0
7
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
1
0
0
1
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
3
3
0
0
2
0
0
1
0
5
1
0
1
1
2
0
0
0
0
2
0
1
2
0
1
0
0
0
0
0
0
0
3
0
2
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
3
1
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
5
0
0
0
2
0
1
1
0
0
0
1
0
0
1
0
0
2
0
1
2
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
1
0
2
8
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
2
0
0
0
0
1
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
1
0
0
0
0
0
0
0
5
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
1
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
1
0
0
1
0
0
0
1
1
0
1
0
0
0
1
0
0
0
2
0
0
1
0
2
0
3
0
0
0
4
0
0
0
0
0
0
0
1
0
0
1
0
1
0
2
0
2
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
4
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
1
0
0
2
1
0
0
2
0
0
0
0
0
2
0
0
2
0
1
0
0
0
2
1
0
0
2
8
0
0
1
0
2
1
2
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
2
0
2
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
1
0
3
0
4
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
5
0
0
0
1
0
1
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
2
4
0
0
0
0
2
0
0
0
0
1
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
2
1
1
0
0
0
0
1
1
0
0
0
2
1
0
1
0
7
0
0
0
0
0
0
0
0
0
0
0
2
0
3
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
3
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
1
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
2
0
0
1
1
0
2
0
0
0
1
0
0
0
0
1
1
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
4
0
0
0
0
0
1
0
0
0
0
0
0
2
3
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
3
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
2
0
4
0
0
0
1
0
0
0
2
0
0
1
0
1
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
1
1
0
0
0
0
2
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
1
1
1
0
1
0
0
0
0
0
0
2
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
2
2
0
1
0
0
0
0
0
0
0
5
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
4
2
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
2
2
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
2
0
2
0
0
0
0
3
0
0
0
3
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
2
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
2
1
2
1
1
0
0
2
2
0
1
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
2
0
1
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
1
1
2
1
2
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
7
0
2
0
3
0
0
0
2
0
0
1
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
3
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
3
2
2
0
0
1
0
0
1
0
0
0
0
0
0
2
0
1
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
3
0
1
0
0
2
0
2
0
0
2
0
0
0
3
0
0
2
0
2
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
1
0
0
0
3
1
0
0
0
2
0
2
2
0
2
0
0
1
0
0
2
0
0
1
0
0
3
1
0
0
7
0
0
0
4
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
3
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
1
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
1
0
3
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
2
1
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
5
0
0
1
1
0
0
4
0
0
0
0
0
1
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
3
0
0
0
0
0
0
2
1
0
3
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
1
0
0
1
0
1
1
0
0
0
0
1
2
1
0
2
0
1
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
1
2
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
3
0
3
1
0
0
0
0
2
0
1
0
0
0
1
0
0
0
1
2
0
1
0
0
0
2
0
0
0
3
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
1
1
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
2
1
0
0
1
0
1
1
0
3
0
0
1
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
2
1
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
1
0
0
2
0
0
1
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
2
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
1
0
0
3
1
0
0
0
0
1
0
2
3
1
0
1
0
0
0
0
0
2
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
1
1
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
1
2
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
1
0
1
2
2
0
0
1
0
2
2
0
0
0
0
0
0
1
0
0
2
0
0
1
0
2
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
2
2
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
2
0
0
3
0
1
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
1
0
2
1
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
1
3
0
0
0
0
1
0
0
1
0
2
0
0
0
0
1
0
0
0
0
7
0
0
1
1
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
8
1
0
0
0
2
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
5
0
0
0
1
0
0
0
1
0
1
0
3
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
2
0
0
0
0
1
2
3
0
0
0
0
0
0
0
0
0
5
0
0
0
3
0
2
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
2
0
1
0
0
0
2
0
0
0
2
0
0
0
0
2
2
0
1
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
1
0
0
1
0
0
0
1
0
0
0
0
3
0
2
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
5
2
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
2
0
0
3
0
0
0
0
0
0
0
1
0
0
0
2
1
1
1
0
0
1
2
0
0
0
0
3
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
1
0
0
2
0
2
0
0
0
3
0
0
0
1
1
0
1
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
2
0
0
0
1
0
0
1
3
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
1
2
0
0
1
1
0
2
2
0
0
0
2
0
0
0
0
0
1
0
1
0
0
2
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
1
0
2
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
4
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
3
7
1
0
0
1
0
1
0
0
0
0
2
0
0
0
2
6
2
2
0
0
1
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
2
3
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
8
1
0
1
0
2
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
1
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
2
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
2
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
3
1
0
1
0
0
2
0
0
1
0
0
0
2
1
0
0
0
0
1
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
1
0
0
0
2
3
0
0
0
1
0
3
0
0
0
2
0
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
2
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
1
2
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
5
2
2
0
0
0
0
1
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
4
2
2
2
0
0
0
0
2
5
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
5
2
0
0
0
0
0
0
0
0
0
2
1
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
2
0
1
0
3
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
1
2
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
3
2
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
1
3
1
1
0
2
0
1
1
0
1
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
2
0
1
0
0
0
1
0
3
0
0
0
1
0
0
3
0
0
3
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
1
1
0
0
0
5
0
0
3
0
0
2
0
0
0
1
1
0
1
0
1
2
0
0
0
0
2
0
0
0
0
2
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
2
0
2
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
2
1
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
1
0
0
0
1
0
0
1
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
3
0
0
0
2
0
2
0
1
2
0
0
3
0
0
4
0
1
0
3
0
0
0
0
1
0
2
2
0
0
0
0
0
0
1
0
3
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
1
0
1
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
5
0
0
0
0
0
0
2
0
1
0
1
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
4
1
0
0
2
0
0
0
0
0
3
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
2
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
1
1
0
2
0
0
1
0
3
3
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
3
0
0
0
0
1
2
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
6
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
3
5
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
1
0
0
1
0
0
0
1
2
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
2
3
0
0
0
2
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
3
2
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
2
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
2
5
0
0
1
0
1
0
0
2
0
1
0
0
0
0
3
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
2
1
0
0
4
1
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
3
0
0
2
0
2
2
0
0
3
0
0
0
0
0
0
0
2
0
1
3
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
3
1
2
0
0
1
0
0
1
0
0
0
0
1
0
0
0
2
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
2
2
0
1
1
0
2
0
0
0
0
1
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
5
2
0
0
0
0
2
2
0
0
0
0
0
3
0
0
0
1
2
0
0
2
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
3
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
2
0
0
0
0
1
1
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
1
0
0
0
7
0
0
1
0
0
0
0
2
0
2
0
0
0
2
2
0
0
0
0
1
2
0
0
1
3
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
1
3
0
0
1
2
0
3
0
0
0
0
3
0
0
0
0
2
0
0
8
0
0
0
0
2
1
0
2
0
0
2
1
2
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
2
0
0
2
0
1
0
2
0
0
3
3
3
0
0
0
3
0
0
0
0
0
5
1
0
0
0
0
0
2
0
0
2
0
0
1
0
2
1
0
0
0
1
3
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
3
1
0
0
0
0
3
0
0
0
1
0
0
0
0
0
1
1
0
2
1
0
0
0
0
1
0
0
2
0
2
0
1
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
2
0
0
2
0
2
0
0
0
2
0
3
0
2
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
1
0
0
3
0
0
2
0
0
0
0
2
0
0
1
0
2
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
2
3
0
0
0
0
0
1
0
0
0
0
3
0
0
9
3
0
1
0
2
0
1
0
2
0
0
0
0
0
0
2
4
0
0
0
1
1
2
0
1
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
1
0
0
1
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
2
0
1
0
2
0
0
0
1
0
2
0
0
1
0
0
2
0
0
0
0
0
0
4
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
1
1
0
2
6
0
0
1
0
2
4
0
2
0
0
1
0
0
1
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
2
1
1
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
3
0
0
0
1
1
4
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
3
0
2
0
3
1
0
0
0
0
2
0
4
0
0
0
2
1
1
1
0
0
0
0
0
4
0
1
3
2
0
0
1
1
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
2
1
0
0
0
3
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
3
0
1
0
1
0
2
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
2
0
2
1
2
0
2
0
2
0
0
0
0
0
2
0
0
1
1
0
0
1
0
0
5
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
3
2
1
0
0
2
0
1
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
2
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
2
3
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7
2
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
1
1
0
0
1
1
0
4
0
0
1
0
0
0
1
0
0
0
4
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
3
1
0
0
0
0
0
1
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
1
0
0
2
0
0
0
0
2
0
0
1
4
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
8
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
1
3
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
1
0
0
0
3
0
2
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
2
2
0
0
0
0
0
2
1
0
0
0
0
2
1
0
0
1
2
0
0
1
0
0
0
0
1
1
0
0
0
1
0
20
0
0
0
0
0
1
2
1
0
0
0
4
0
0
0
0
0
0
0
0
0
1
3
0
2
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
3
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
2
0
0
1
0
2
0
0
0
0
1
0
1
0
1
0
2
0
0
2
0
1
0
0
2
0
0
0
0
1
0
2
2
0
0
1
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
3
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
2
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
3
0
1
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
1
0
1
2
1
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
6
0
0
0
0
0
0
0
0
1
0
1
0
1
0
2
0
2
0
3
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
5
4
0
0
2
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
1
1
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
7
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
2
2
0
1
1
0
0
2
0
1
2
0
0
0
0
3
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
3
0
0
5
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
1
0
0
0
1
7
1
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
1
2
0
0
2
0
0
0
0
2
0
2
1
3
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
1
2
0
1
1
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
2
1
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
3
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
3
1
0
2
0
1
2
0
0
0
0
0
0
0
4
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
1
1
0
2
0
0
0
0
0
0
0
2
0
1
0
0
1
3
2
1
0
0
0
0
0
2
0
12
1
0
0
2
1
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
6
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
2
1
0
0
0
2
0
0
0
0
0
1
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
2
1
0
0
0
1
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
2
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
2
1
0
0
2
0
0
0
0
0
0
2
3
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
1
0
1
0
4
0
2
0
0
0
0
2
1
2
0
0
0
0
4
0
0
0
0
0
0
4
2
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
1
1
0
2
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
2
0
0
1
0
2
0
4
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
2
0
2
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
4
0
0
0
2
2
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
5
1
0
0
0
0
0
0
1
0
1
0
1
2
0
0
1
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
1
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
2
0
0
0
0
0
0
1
2
2
0
0
2
0
1
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
3
0
0
0
0
0
1
0
0
0
2
0
2
2
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
3
0
2
0
2
0
0
0
2
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
1
0
0
0
2
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
2
2
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
3
1
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
1
0
1
0
0
1
2
0
1
1
2
0
0
0
0
0
0
0
0
0
0
1
0
5
1
1
0
1
2
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
6
1
0
0
1
0
0
1
0
0
0
1
2
4
1
2
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
1
1
1
0
0
0
0
0
0
1
1
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
3
0
0
0
2
1
0
0
0
0
0
0
1
0
2
2
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
2
0
0
1
4
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
3
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
1
0
5
0
0
2
0
0
1
0
0
2
3
1
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
1
3
0
0
0
0
0
0
2
1
0
2
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
2
0
0
0
1
0
0
2
0
0
7
0
0
1
0
1
2
0
3
0
3
0
3
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
2
1
1
0
0
0
0
2
2
0
1
0
2
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
4
0
1
3
0
0
0
0
0
0
0
0
0
7
0
0
3
0
0
0
0
1
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
2
0
0
0
0
2
0
0
0
1
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
2
2
0
2
0
0
1
2
0
0
0
2
0
1
2
2
0
1
3
0
1
2
0
1
1
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
2
2
2
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
1
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
2
0
2
3
2
0
0
3
0
0
0
0
2
2
0
2
0
0
1
0
0
0
1
0
2
2
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
4
2
0
0
0
3
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
3
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
1
0
2
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
1
0
2
0
0
0
0
0
1
1
2
0
0
0
0
0
0
1
1
1
0
2
0
0
0
2
0
0
1
0
2
0
0
0
3
0
0
3
0
2
0
1
0
2
0
0
2
0
0
1
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
2
1
0
0
1
0
0
1
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
2
0
1
2
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
2
1
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
3
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
3
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
6
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
2
0
0
5
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
2
0
0
0
0
4
0
0
1
1
0
2
0
2
0
1
2
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
1
1
2
0
0
0
0
0
0
0
0
1
2
0
0
2
1
0
0
2
1
0
0
0
0
0
0
0
0
1
0
2
1
0
5
3
0
1
0
0
2
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
3
0
1
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
1
0
1
1
1
0
1
1
1
0
2
2
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
2
0
0
0
3
0
2
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
2
0
2
0
0
0
0
2
0
2
0
0
1
1
0
1
3
0
0
0
0
1
1
1
0
0
0
0
4
0
0
0
1
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
4
0
0
1
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
10
0
0
2
1
0
2
0
4
0
0
0
0
1
4
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
2
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
3
1
0
0
0
0
3
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
2
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
5
0
2
0
2
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
2
1
1
0
0
0
1
0
0
0
4
0
0
2
1
0
3
2
3
0
0
0
0
0
0
0
2
1
0
3
1
0
0
0
0
0
4
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
1
0
0
1
2
0
0
0
2
0
0
0
1
0
0
1
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
1
7
0
0
0
0
0
0
0
0
0
1
0
0
1
1
2
0
0
0
0
1
1
0
0
0
0
0
2
0
2
0
0
0
1
0
1
0
0
1
2
0
2
2
0
0
2
1
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
1
1
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
2
0
2
0
0
3
2
0
1
3
0
0
0
3
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
3
0
1
1
0
0
0
2
0
0
0
0
2
0
0
0
2
1
0
0
2
3
0
0
0
0
0
2
0
3
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
5
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
6
0
1
0
0
0
4
1
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
2
2
1
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
2
0
1
0
2
1
0
2
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
2
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
1
0
1
0
0
1
0
1
0
2
0
0
0
2
0
0
1
0
3
0
2
0
0
2
2
0
0
0
0
0
0
1
0
0
2
0
1
0
2
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
1
0
0
0
0
0
1
2
2
2
0
0
2
0
6
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
3
0
2
0
1
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
2
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
3
0
0
2
0
0
2
0
1
1
1
0
1
0
0
0
0
1
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
3
0
0
0
0
0
2
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
3
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
3
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
8
0
0
0
0
0
0
3
2
0
1
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
1
2
0
2
0
0
0
0
0
0
1
0
0
1
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
3
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
2
3
0
0
0
2
0
2
0
1
0
0
1
0
2
0
1
0
1
2
2
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
5
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
2
0
2
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
1
0
0
0
2
1
2
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
7
0
0
2
0
0
0
1
2
0
0
0
0
2
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
3
1
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
2
0
3
0
1
0
0
1
0
1
1
0
0
0
0
3
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
2
0
3
0
7
0
0
0
2
0
0
1
4
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
2
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
2
0
0
0
0
0
1
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
1
0
1
1
0
3
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
2
0
2
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
2
2
0
0
0
0
0
0
0
0
4
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
2
0
0
0
0
0
1
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
1
0
5
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
14
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
1
0
0
2
0
0
1
0
0
0
0
0
1
0
2
0
0
2
0
0
3
0
0
0
1
0
0
0
0
1
0
0
1
0
2
1
0
0
0
0
0
2
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
4
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
3
0
1
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
1
0
0
1
0
0
3
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
6
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
1
0
2
1
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
4
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
3
0
0
0
2
2
0
0
0
0
0
1
2
0
0
0
0
0
1
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
2
1
2
1
0
0
2
3
0
1
1
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
3
0
0
2
0
0
0
2
0
0
3
0
9
1
0
0
0
2
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
2
1
0
3
0
0
0
1
0
0
0
0
0
0
2
1
0
0
2
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
3
0
2
0
0
0
1
0
2
0
1
2
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
1
2
0
0
0
0
1
0
1
2
2
0
0
0
0
0
0
0
1
0
3
2
0
2
1
0
2
0
0
0
0
2
0
0
0
1
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
2
0
0
1
0
0
0
1
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
2
0
1
1
1
1
0
0
1
1
0
0
1
0
0
0
1
0
1
0
2
1
0
1
0
0
2
0
2
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
4
0
1
4
0
0
0
1
2
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
2
1
1
0
0
1
1
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
1
0
0
2
1
0
8
0
0
1
0
1
2
0
0
0
5
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
2
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
6
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
2
1
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
1
0
2
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
1
1
0
0
1
0
2
0
1
0
2
2
0
2
0
1
0
0
0
0
0
0
3
1
0
0
2
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
2
2
0
0
1
0
0
0
0
0
1
0
2
0
0
0
1
1
1
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
2
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
2
8
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
2
0
2
1
0
0
0
0
0
0
0
0
2
0
0
2
3
0
0
0
0
0
0
0
0
2
0
3
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
1
0
2
0
0
0
0
18
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
5
0
0
0
0
0
3
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
1
0
0
0
2
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
3
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
5
2
0
2
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
7
0
0
0
0
1
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
1
0
2
0
1
0
0
0
0
2
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
2
0
0
6
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
3
0
0
0
0
0
0
0
0
1
0
1
3
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
1
0
2
0
0
2
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
3
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
2
1
2
0
0
0
0
0
0
0
0
1
0
4
0
0
1
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
1
2
1
0
4
0
0
0
0
0
0
0
2
0
0
2
1
0
4
0
0
0
5
3
0
2
0
0
1
0
0
3
2
0
0
0
0
0
2
2
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
2
0
0
0
0
0
3
1
1
0
0
0
2
0
1
0
2
0
0
2
0
1
0
1
0
0
0
0
0
0
0
1
1
0
1
3
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
2
1
0
0
0
1
0
0
1
0
2
0
0
2
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
5
0
0
1
0
0
2
0
1
0
1
0
2
0
2
0
0
2
1
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
2
3
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
6
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
1
2
0
0
0
2
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
1
0
0
0
0
1
1
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
1
2
4
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
3
0
0
0
0
0
1
0
0
0
0
2
1
0
2
1
0
2
0
2
0
2
0
0
0
0
2
0
0
1
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
2
0
0
2
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
1
0
1
2
1
3
2
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
2
2
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
2
0
2
1
0
0
1
0
0
0
3
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
3
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
6
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
1
3
3
2
0
0
2
0
0
0
0
0
0
0
0
0
2
3
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
5
0
0
0
0
1
0
1
0
0
0
0
2
2
1
1
0
0
0
0
1
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
2
0
0
0
0
0
0
0
2
2
1
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
2
2
0
1
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
2
0
0
3
0
0
0
0
1
1
1
0
0
0
0
0
3
1
1
0
0
1
0
0
2
0
3
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
1
0
0
0
0
2
2
0
0
0
2
2
3
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
1
0
0
5
0
0
0
0
0
1
0
0
0
0
1
0
0
2
3
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
3
1
0
1
0
0
0
0
1
2
0
3
0
0
2
2
1
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
1
1
0
0
0
1
1
2
0
0
0
0
0
0
0
0
2
0
2
0
5
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
2
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
1
2
0
0
0
0
2
0
0
0
2
2
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
2
0
4
0
1
2
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
2
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
1
0
0
0
0
1
0
0
2
0
1
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
3
0
0
0
0
0
1
0
2
0
1
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
8
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
1
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
1
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
1
1
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
2
1
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
1
2
0
2
3
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
1
0
0
0
3
1
0
1
2
0
0
0
0
0
1
2
2
0
2
0
1
0
0
0
0
0
1
0
2
2
0
0
1
0
0
0
2
0
0
1
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
4
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
3
0
1
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
1
2
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
5
3
0
0
0
2
0
0
2
0
0
1
3
0
0
0
1
1
0
2
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
2
2
0
0
0
2
2
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
2
1
0
3
0
0
0
0
4
0
4
0
0
0
1
0
0
0
2
0
0
0
3
2
0
0
0
0
0
2
1
1
2
0
2
0
1
0
0
0
1
2
1
0
0
0
2
0
0
2
1
0
0
0
1
0
2
0
0
1
0
0
1
0
0
0
3
0
5
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
1
2
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
2
1
2
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
2
2
0
0
0
1
0
0
2
0
0
0
2
0
1
3
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
7
0
0
0
0
1
0
0
0
3
0
0
0
0
0
2
1
3
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
1
0
1
0
2
0
2
0
2
0
1
0
2
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
1
1
0
1
0
0
0
3
0
0
1
0
0
3
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
3
1
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
3
0
1
1
1
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
2
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
1
3
0
0
0
0
1
3
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
5
3
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
1
1
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
1
0
0
0
2
0
0
0
2
0
0
0
4
0
1
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
3
1
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
4
0
0
0
2
2
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
1
1
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
2
1
0
1
0
1
0
0
2
0
0
0
5
0
0
0
0
3
1
1
1
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
3
2
0
0
0
2
0
0
0
2
0
0
0
1
2
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
2
0
0
0
2
0
0
0
0
1
0
2
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
2
1
0
1
0
0
0
1
0
0
2
0
1
0
2
0
0
0
3
0
0
0
0
0
2
1
0
0
0
0
0
4
3
0
0
1
0
0
0
0
0
1
2
2
0
0
0
1
0
0
0
1
0
0
0
2
1
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
2
1
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
2
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
1
0
0
2
2
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
2
0
0
1
1
2
0
2
1
1
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
2
0
0
0
0
0
2
0
4
1
2
2
1
0
0
0
2
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
2
0
0
2
0
0
1
1
0
2
0
1
0
2
0
0
2
1
0
0
0
0
2
0
0
0
2
0
1
2
0
0
1
3
0
0
0
0
1
0
1
0
7
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
3
0
1
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
3
0
1
0
1
0
0
0
0
1
0
1
0
1
0
0
2
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
2
0
0
4
0
1
0
0
0
0
0
2
1
2
2
2
0
1
0
0
0
1
0
1
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
3
0
2
0
0
0
2
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
2
0
0
1
3
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
3
2
0
3
0
0
0
0
1
0
0
4
0
0
3
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
4
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
4
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
3
0
0
2
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
1
0
0
1
0
0
0
9
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
3
4
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
1
0
3
0
0
0
0
0
0
0
1
1
2
4
1
1
1
1
1
0
0
0
0
0
2
1
0
1
0
0
0
0
0
2
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
3
0
1
0
0
0
0
5
0
0
0
0
0
2
0
0
2
0
1
2
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
1
4
0
0
1
0
0
0
2
0
0
0
1
1
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
3
0
0
0
0
0
1
1
0
0
2
0
0
0
2
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
4
0
1
0
0
0
0
2
0
2
0
1
1
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
1
0
1
0
0
2
0
0
0
0
0
3
4
1
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
2
0
2
0
0
2
0
0
0
2
2
0
0
0
0
1
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
1
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
2
0
6
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
2
0
0
0
0
1
0
5
1
0
0
0
0
1
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
1
1
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
2
0
0
2
0
0
0
2
2
0
0
1
0
2
1
0
0
3
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
2
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
2
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
7
0
0
2
1
1
2
0
0
0
1
0
0
2
0
0
0
1
0
0
1
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
2
1
0
1
0
2
3
2
2
0
1
0
0
1
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
4
0
2
1
1
0
0
1
0
2
0
0
0
0
0
1
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
1
2
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
4
0
0
0
2
0
1
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
2
1
0
3
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
2
2
0
2
1
1
1
0
0
0
0
1
1
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
3
3
0
1
1
1
2
1
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
2
2
0
2
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
2
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
2
0
2
0
0
3
0
3
0
2
1
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
1
3
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
1
0
2
3
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
2
2
0
2
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
2
1
2
0
0
2
0
1
0
0
1
0
3
0
0
0
2
0
0
0
3
2
0
0
0
0
0
1
0
2
2
0
0
0
1
0
0
0
1
2
0
0
1
0
0
0
6
0
0
0
3
0
0
1
0
0
0
0
0
0
1
0
0
1
2
18
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
2
0
0
1
0
0
0
1
2
0
0
0
0
1
0
0
0
1
1
2
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
4
0
0
0
0
0
0
6
0
0
0
2
0
0
0
0
0
0
0
1
0
2
1
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
2
0
1
0
0
2
0
1
0
0
0
0
1
0
0
3
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
2
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
2
2
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
1
1
2
0
0
0
0
0
0
2
0
0
1
0
2
2
0
0
0
3
0
1
0
3
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
8
0
0
0
0
2
0
0
0
0
0
3
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
2
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
1
1
2
3
0
0
0
0
0
0
0
0
1
1
1
2
0
0
0
0
1
2
3
1
2
1
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
1
0
3
0
0
0
1
0
0
1
0
0
0
0
2
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
4
0
2
0
0
0
0
0
0
0
1
0
0
0
1
2
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
2
2
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
6
0
0
0
0
0
3
0
0
0
0
0
1
1
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
6
1
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
1
0
1
1
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
2
3
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
3
2
0
0
0
0
2
1
0
3
3
1
2
2
0
0
0
2
0
0
0
0
0
1
1
1
0
1
0
0
0
4
0
0
0
0
0
2
0
2
0
1
1
0
0
0
0
0
2
0
1
0
0
1
1
0
0
0
0
0
4
2
0
2
0
3
0
0
0
0
0
2
1
0
0
1
0
0
0
1
0
0
5
5
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
3
0
0
0
1
0
1
0
2
0
0
0
0
2
1
0
0
0
1
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
3
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
1
0
0
0
3
0
0
0
0
0
0
0
1
0
2
0
0
2
0
1
1
0
0
1
0
0
0
0
0
0
2
2
0
0
0
1
0
0
2
2
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
1
0
1
0
2
0
0
1
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
3
0
0
0
2
0
0
0
0
0
1
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
1
1
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
2
0
0
0
0
1
0
0
0
3
0
0
2
0
0
2
0
0
0
0
0
0
2
2
0
0
1
0
0
0
1
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
1
0
0
1
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
2
3
6
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
2
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
2
0
2
2
0
0
0
0
0
0
1
0
1
0
0
1
2
0
2
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
3
1
3
0
0
0
0
2
0
0
1
0
2
0
0
0
0
2
0
1
0
0
2
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
5
0
2
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
1
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
3
0
0
0
0
2
0
1
0
0
2
2
0
0
0
0
0
2
0
0
1
0
0
1
2
0
0
0
0
0
0
3
2
0
0
1
0
1
0
0
2
0
2
0
5
0
0
0
2
0
0
1
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
5
1
2
1
0
0
0
0
0
0
0
0
0
0
1
0
2
2
2
1
1
0
2
0
0
1
1
1
2
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
5
1
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
1
0
0
0
0
2
0
2
0
0
1
2
0
2
0
5
0
0
0
0
0
2
0
0
0
1
0
0
0
4
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
4
1
2
0
0
0
0
1
2
0
2
0
0
0
0
0
0
1
0
1
1
0
0
0
2
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
3
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
1
2
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
2
1
0
0
0
0
0
2
1
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
4
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
1
3
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
3
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
4
2
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
2
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
2
0
2
1
3
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
3
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
2
0
3
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
3
2
0
0
0
2
0
0
0
2
0
0
0
1
0
2
0
0
0
1
0
7
2
0
0
0
0
2
0
0
2
0
1
0
0
0
0
4
0
1
1
4
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
2
2
0
0
1
0
0
1
0
0
0
1
1
1
0
0
0
2
0
1
3
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
1
0
0
0
0
0
2
1
0
1
0
0
2
2
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
4
0
2
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
5
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
2
0
0
0
0
1
0
0
2
0
0
1
0
0
0
3
0
0
1
0
1
0
0
0
1
2
0
1
0
2
0
0
1
0
0
0
0
0
0
0
1
2
0
0
2
3
0
0
2
0
1
0
0
0
0
0
0
3
0
0
7
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
5
0
0
0
0
1
0
3
4
0
0
0
2
2
0
0
0
0
0
8
1
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
2
4
0
1
2
0
0
2
0
0
2
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
1
1
3
2
0
0
0
0
4
3
0
0
0
0
0
0
3
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
0
0
3
1
3
0
0
0
0
0
1
0
1
0
0
0
0
2
1
1
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
2
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
2
0
0
0
1
13
0
0
2
0
0
0
0
0
1
0
1
0
0
0
2
2
0
2
0
0
0
2
0
0
0
1
2
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
4
0
0
0
1
0
2
0
0
0
0
1
0
0
0
1
0
0
2
0
1
0
0
2
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
2
2
0
0
3
0
0
0
0
1
0
0
0
2
0
2
0
0
0
2
0
0
2
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
1
0
6
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
3
1
0
0
2
2
1
0
0
0
0
0
0
0
0
3
0
1
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
1
0
0
2
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
1
3
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
3
0
0
0
2
0
0
0
1
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
4
0
2
0
1
0
0
0
0
1
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
4
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
2
1
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
2
1
0
0
1
2
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
2
1
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
1
3
0
1
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
9
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
3
0
0
0
0
2
0
2
0
0
3
0
0
0
0
2
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
3
1
0
2
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
1
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
5
0
3
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
1
0
2
0
1
0
3
0
0
1
0
0
0
0
0
1
1
0
2
0
3
0
0
0
0
1
0
1
0
2
0
2
1
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
1
0
1
0
0
0
2
0
1
1
0
0
0
0
2
0
2
0
1
1
0
0
0
2
0
0
0
0
3
0
0
1
0
2
0
0
0
0
0
0
1
0
5
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
5
0
1
0
0
1
0
3
2
0
0
0
3
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
7
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
1
3
0
2
0
0
2
0
0
1
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
1
2
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
1
0
2
0
0
0
0
0
1
0
2
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
3
0
0
0
1
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
1
0
1
0
0
0
0
0
0
0
2
3
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
3
3
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
2
2
0
2
1
0
0
0
0
1
0
2
2
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
3
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
1
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
1
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
2
0
3
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
1
0
2
1
2
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
6
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
5
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
5
2
0
2
0
0
3
0
0
0
0
0
0
2
0
2
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
1
0
0
0
1
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
1
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
3
0
0
0
3
0
0
0
0
13
0
0
5
0
0
1
2
0
2
0
2
0
1
0
0
0
2
0
0
0
2
3
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
1
2
0
2
1
0
8
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
4
2
0
0
0
0
0
1
0
0
0
2
0
0
4
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
1
1
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
5
0
0
0
0
1
0
0
2
0
0
0
0
0
3
0
0
0
0
0
2
0
1
1
0
2
0
0
0
0
0
0
7
2
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
4
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
2
4
2
2
0
1
0
0
0
0
0
0
1
0
1
0
2
0
0
0
1
0
0
0
0
4
1
0
0
0
0
1
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
2
1
0
3
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
2
0
0
1
0
2
1
0
1
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
2
0
0
0
1
2
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
3
1
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
8
0
0
0
0
1
3
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
2
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
2
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
1
2
0
1
2
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
1
0
2
2
0
2
0
0
0
0
1
2
2
0
0
0
2
1
0
0
0
0
0
0
1
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
4
0
0
2
1
0
0
0
0
5
0
0
0
0
4
0
0
0
0
0
0
2
0
0
3
0
4
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
1
2
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
2
0
0
0
0
2
0
0
1
0
0
0
1
0
0
3
0
0
3
0
0
0
1
0
0
0
0
2
0
0
0
0
0
7
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
4
0
0
2
0
0
2
0
2
1
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
1
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
6
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
2
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
2
0
1
2
0
1
1
0
0
0
0
1
0
0
0
0
3
1
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
3
0
0
0
1
2
1
0
0
0
0
0
0
3
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
2
1
0
0
0
0
0
2
4
0
0
0
0
3
0
0
2
2
0
0
0
2
0
0
0
3
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
3
0
0
0
0
3
0
0
0
1
2
0
2
0
2
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
3
0
0
1
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
4
1
0
0
0
0
1
0
2
2
2
5
0
0
0
2
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
2
1
0
0
3
0
0
0
1
0
2
0
0
4
0
0
0
0
0
2
2
0
0
0
0
2
1
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
2
1
0
1
0
2
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
4
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
2
0
0
0
2
1
0
0
0
1
0
0
0
0
2
0
0
0
0
6
0
0
3
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
2
2
0
0
0
3
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
1
0
0
0
0
0
2
0
0
1
0
0
0
1
0
2
0
0
0
1
0
0
2
0
2
1
0
0
0
2
1
0
2
0
0
0
0
0
2
0
0
0
0
1
2
1
0
0
0
0
0
0
1
0
0
0
2
0
1
1
2
0
0
0
0
1
3
0
2
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
3
0
0
0
0
1
2
1
0
1
0
0
2
0
2
0
1
0
0
2
0
2
0
1
0
4
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
1
1
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
3
2
0
3
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
3
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
1
0
0
0
0
0
0
0
5
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
1
0
0
2
0
0
0
3
0
0
0
4
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
1
2
0
0
0
0
0
2
1
1
1
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
11
0
0
0
0
0
2
0
5
0
0
0
0
0
0
0
0
1
2
0
2
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
6
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
1
0
2
0
0
0
2
0
0
0
7
0
3
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
3
3
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
1
1
0
0
1
0
2
0
0
0
1
0
0
0
1
2
0
1
0
1
0
0
1
3
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
1
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
2
2
0
0
0
0
1
0
2
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
4
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
2
3
1
0
1
0
0
0
4
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
1
1
3
1
0
0
0
0
2
0
0
1
0
0
1
2
0
2
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
3
0
0
0
0
2
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
1
2
0
0
2
2
0
0
0
0
0
0
1
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
2
1
0
0
1
0
2
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
2
2
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
5
0
0
0
9
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
4
0
0
0
0
2
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
3
0
1
0
0
1
0
2
1
0
2
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
1
0
0
0
0
2
2
0
0
0
0
3
0
0
1
0
2
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
5
0
1
0
3
5
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
2
2
0
2
3
1
0
0
2
1
0
0
1
0
0
1
0
1
0
0
0
2
0
0
2
0
0
2
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
2
1
0
0
1
0
0
2
0
2
1
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
4
0
1
0
0
0
0
1
0
0
0
0
0
3
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
2
0
0
1
1
0
1
1
0
0
0
0
1
2
0
0
0
0
0
3
0
1
0
1
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
1
1
0
1
1
0
2
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
1
7
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
7
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
2
2
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
4
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
2
5
0
1
0
0
4
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
6
0
1
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
1
0
1
2
0
0
0
0
3
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
3
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
3
0
1
2
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
2
2
0
0
0
1
0
0
2
0
0
1
2
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
1
1
0
1
3
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
2
0
0
1
5
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
1
0
0
2
0
1
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
4
0
0
3
0
0
0
0
0
0
0
2
0
0
0
2
1
0
2
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
2
0
1
0
0
0
0
1
3
1
1
1
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
3
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
3
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
3
0
3
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
4
0
1
0
1
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
1
0
2
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
1
2
0
1
0
5
1
3
0
1
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
5
0
1
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
3
0
0
0
2
0
0
0
1
0
0
2
0
0
2
2
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
3
1
0
1
0
0
1
0
0
1
0
0
0
2
0
0
0
0
5
0
2
2
0
2
1
2
0
2
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
3
2
0
0
4
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
5
0
0
0
0
1
0
0
0
0
0
0
6
0
0
0
0
0
1
0
0
0
3
0
0
2
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
4
2
0
0
0
0
0
0
0
2
0
0
1
1
0
1
0
0
0
0
0
0
0
2
2
0
1
0
0
0
2
0
1
0
0
0
4
0
0
1
4
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
9
2
2
0
0
2
0
0
0
0
0
3
0
0
2
1
2
0
0
0
1
0
0
0
0
0
4
1
0
1
1
1
0
0
0
0
0
0
0
0
1
0
4
0
0
0
2
0
0
0
1
5
0
0
0
0
0
0
0
0
0
0
2
0
0
4
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
3
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
1
0
1
0
1
0
0
0
0
0
1
0
1
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
1
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
3
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
5
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
1
2
0
0
1
0
0
0
0
2
1
1
0
0
0
1
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
6
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
1
0
0
0
0
2
4
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
4
0
1
2
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
3
0
2
0
2
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
5
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
5
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
4
0
0
0
1
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
2
2
3
0
0
0
0
0
1
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
2
1
4
1
0
2
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
5
4
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
2
0
0
0
1
0
2
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
2
1
1
2
6
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
1
1
0
0
2
0
0
0
2
2
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
2
1
0
0
0
0
0
1
0
1
0
1
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
1
2
1
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
2
0
2
2
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
2
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
1
0
2
0
2
0
0
0
1
0
2
0
2
5
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
4
0
0
0
0
0
2
0
1
0
2
0
0
1
0
0
0
0
0
2
0
0
0
3
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
2
2
0
0
0
1
0
0
2
0
0
0
0
0
0
3
0
0
1
0
0
0
1
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
4
2
0
0
0
0
2
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
5
1
0
1
0
0
1
2
2
0
0
1
0
0
0
5
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
1
1
0
1
0
1
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
2
2
0
0
2
1
0
1
0
0
0
0
0
0
0
2
2
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
1
0
0
2
0
1
2
0
0
0
0
0
1
0
2
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
3
0
0
2
0
0
0
0
1
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
1
1
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
6
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
2
1
0
0
0
3
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
1
0
2
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
2
0
1
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
6
2
1
0
1
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
2
1
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
2
0
0
2
0
1
2
0
2
0
0
2
2
4
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
2
0
0
2
0
1
4
1
0
0
0
0
1
0
2
0
0
0
0
3
0
0
1
0
2
0
1
0
0
0
0
0
0
0
1
2
0
0
0
1
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
2
0
0
1
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
2
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
2
0
2
5
2
1
0
0
0
1
0
0
0
0
0
0
2
1
2
0
0
1
0
0
2
2
0
0
0
2
0
1
0
4
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
4
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
3
1
0
2
0
4
0
0
0
2
0
0
0
0
2
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
2
8
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
1
1
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
2
0
0
1
1
2
0
0
0
0
0
0
0
6
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
6
0
2
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
1
1
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
2
1
2
3
0
1
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
3
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
2
0
0
1
0
0
0
1
0
0
0
0
0
0
7
1
0
0
0
2
0
2
0
0
0
0
2
1
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
1
2
2
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
3
1
2
2
1
0
0
0
1
0
0
0
0
2
3
0
0
0
4
0
2
0
2
2
2
2
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
2
1
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
4
1
0
0
0
0
1
0
2
0
0
0
1
0
2
0
0
2
0
0
1
2
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
1
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
2
1
5
2
1
2
0
1
0
0
1
3
0
0
1
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
2
0
1
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
1
1
0
0
0
0
2
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
3
3
0
0
2
4
1
2
1
2
0
0
0
1
0
2
0
0
0
3
0
0
0
0
2
2
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
2
0
2
0
3
2
0
1
0
2
0
0
1
1
0
0
0
0
0
2
0
0
0
0
2
0
1
2
0
0
3
2
0
0
0
2
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
2
0
1
2
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
2
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
1
0
3
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
4
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
1
1
2
0
2
0
0
0
2
0
0
0
0
1
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
1
0
0
3
0
0
0
0
0
0
0
1
2
0
0
1
1
2
1
1
2
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
3
0
0
3
0
1
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
1
0
4
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
2
0
0
1
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
1
4
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
1
0
2
1
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
1
1
0
2
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
1
0
2
0
1
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
3
1
0
2
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
2
1
3
0
0
0
0
0
0
0
4
0
2
0
0
2
2
0
2
2
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
1
0
0
0
0
2
0
1
0
1
0
0
0
1
0
0
0
0
0
0
5
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
1
0
0
1
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
2
1
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
2
1
5
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
2
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
4
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
2
0
0
2
1
1
0
0
0
0
0
0
0
5
1
0
1
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
2
1
0
1
1
0
2
1
2
2
0
0
0
0
0
0
0
1
2
0
2
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
2
2
0
0
1
1
1
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
2
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
3
1
0
0
1
2
0
1
1
5
0
1
0
0
0
0
0
0
0
0
0
0
3
2
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
3
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
1
1
0
3
0
2
1
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
2
3
0
0
0
0
1
0
0
0
2
0
0
0
3
0
0
0
1
0
1
2
0
0
0
0
0
5
0
0
0
0
0
1
0
1
2
2
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
1
0
0
0
2
0
0
0
0
0
0
3
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
1
0
0
1
0
0
2
1
2
0
1
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
2
0
2
2
0
0
0
0
0
0
0
3
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
4
0
1
1
0
0
0
0
1
0
2
2
1
0
0
0
0
1
2
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
1
0
0
1
0
3
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
1
3
2
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
1
0
1
2
0
0
2
1
0
2
1
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
2
2
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
2
0
0
2
0
0
2
1
0
0
0
4
0
2
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
3
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
6
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
1
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
3
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
1
2
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
10
9
2
0
0
2
0
0
0
1
1
0
1
0
0
0
1
0
0
2
2
0
0
3
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
2
2
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
6
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
2
2
0
1
1
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
1
0
0
2
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
1
0
2
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
2
0
0
2
2
0
3
1
0
0
0
0
0
1
1
2
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
2
2
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
7
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
1
0
0
0
2
0
0
0
0
1
0
0
2
2
0
1
0
0
0
0
0
1
0
0
2
0
0
0
1
0
1
0
1
0
2
0
2
0
0
0
0
0
0
2
1
0
3
0
0
0
2
0
0
0
1
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
3
0
1
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
1
0
2
0
1
0
2
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
2
0
2
0
0
2
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
3
0
2
0
0
1
0
1
0
2
0
3
0
0
0
2
0
0
0
0
0
3
1
1
0
0
2
1
0
2
1
0
1
2
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
1
0
2
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
1
3
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
2
0
0
1
1
0
0
2
2
0
0
2
0
0
2
0
0
0
4
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
2
0
0
0
1
0
0
2
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
2
0
3
1
0
0
2
0
0
0
1
0
0
0
1
0
1
0
1
0
0
1
2
0
0
0
3
0
1
3
0
1
0
1
0
0
7
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
2
0
2
1
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
2
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
3
0
0
0
1
1
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
3
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
5
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
1
0
0
1
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
3
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
2
0
0
0
0
2
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
2
1
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
1
0
1
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
1
1
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
3
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
4
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
3
0
0
0
0
0
0
2
0
0
2
2
0
1
0
0
0
3
0
0
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
2
1
0
0
0
0
4
0
2
0
1
2
0
0
0
0
3
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
3
4
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
5
1
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
2
0
0
2
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
2
0
0
0
0
4
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
7
1
2
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
3
0
0
1
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
2
0
2
0
0
3
0
2
0
0
0
0
0
0
0
3
3
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
2
0
0
0
0
0
2
0
5
0
1
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
2
0
1
1
0
0
1
0
1
0
0
0
3
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
4
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
3
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
8
1
8
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
3
1
0
0
0
0
10
2
0
0
0
2
1
3
2
0
0
1
0
0
0
0
0
0
1
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
1
0
0
2
2
1
1
0
0
1
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
2
2
0
0
0
0
0
1
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
2
1
1
2
0
0
0
0
1
1
3
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
1
0
0
0
0
0
3
0
0
0
0
2
0
2
0
2
0
0
0
0
0
1
4
0
2
3
0
0
0
0
0
1
0
2
1
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
3
0
1
0
1
0
1
0
0
0
2
0
1
1
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
2
2
0
2
2
2
1
0
2
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
1
0
0
0
0
0
1
0
2
0
2
0
1
1
0
1
0
2
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
1
0
0
2
0
0
0
2
0
2
0
0
1
1
2
1
1
0
0
0
0
0
0
1
0
1
0
1
0
1
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
1
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
2
0
0
0
0
0
0
2
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
3
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
2
0
2
0
0
0
2
2
0
0
0
0
0
0
2
3
0
0
0
1
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
2
1
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
5
0
0
0
2
0
0
2
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
3
1
0
0
0
1
0
0
0
0
2
0
3
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
2
1
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
3
0
0
0
0
0
0
0
0
2
3
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
1
2
2
3
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
1
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
4
1
0
0
0
0
2
0
0
1
0
0
1
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
5
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
1
0
0
0
0
0
2
10
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
1
1
0
0
0
2
0
0
1
0
3
0
2
0
0
0
1
2
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
1
0
3
0
3
0
0
1
0
0
1
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
3
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
1
0
5
2
0
2
1
0
1
1
0
1
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
3
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
2
2
1
3
2
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
3
1
2
0
0
1
1
2
2
0
0
2
0
1
0
0
3
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
3
2
1
0
1
0
0
0
0
0
1
0
0
0
1
2
1
1
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
1
1
1
2
0
0
2
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
2
2
1
0
0
0
1
2
0
0
0
1
0
2
0
0
0
0
0
0
2
2
2
0
0
0
0
1
0
2
0
0
3
0
0
0
0
0
0
3
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
1
0
0
1
1
1
0
0
3
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
2
2
0
2
0
2
0
0
0
1
0
0
0
1
0
0
0
0
1
4
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
2
0
1
0
0
0
2
2
0
0
0
0
1
0
1
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
1
1
1
0
2
0
1
0
2
0
0
1
1
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
2
0
0
0
0
2
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
2
0
0
0
0
2
1
2
0
0
0
0
0
0
1
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
1
0
0
1
2
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
4
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
2
0
0
0
4
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
3
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
2
1
0
0
1
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
4
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
1
3
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
7
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
1
0
2
0
0
1
1
2
0
0
0
2
0
1
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
2
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
4
0
0
1
0
0
2
0
2
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
2
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
2
0
1
0
5
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
2
0
0
0
2
0
0
0
3
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
2
0
0
0
1
1
2
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
3
0
0
0
3
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
2
0
0
0
2
0
0
0
2
0
0
2
2
0
2
1
3
0
1
0
1
0
0
1
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
3
0
1
8
2
0
1
0
0
0
1
0
0
2
0
1
0
0
0
1
2
2
1
0
0
1
0
0
0
0
0
0
2
1
1
2
1
1
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
4
2
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
1
0
0
0
6
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
2
0
0
1
0
0
0
2
0
0
0
0
3
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
2
0
4
0
0
0
0
0
1
0
2
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
4
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
1
2
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
2
0
1
0
0
0
1
0
0
0
0
0
2
3
3
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
2
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
13
0
0
0
0
4
1
0
0
0
0
1
0
0
0
2
0
0
3
0
0
0
1
0
2
0
0
0
2
0
1
0
2
0
1
0
2
1
1
0
1
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
5
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
1
1
0
0
4
0
1
0
0
0
0
0
3
2
3
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
2
4
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
1
2
2
0
2
0
0
0
0
0
0
2
1
0
0
0
0
2
2
0
0
3
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
2
0
0
2
1
0
0
0
1
0
0
0
0
3
0
0
2
2
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
2
0
2
1
0
1
0
0
1
0
1
3
0
0
0
0
0
3
0
0
4
0
0
0
0
0
0
0
3
0
0
1
2
0
0
1
1
2
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
2
0
2
0
0
0
0
0
2
1
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
1
0
0
1
0
0
0
0
2
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
2
0
1
0
2
0
2
0
0
0
0
0
1
0
0
3
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
2
1
2
2
1
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
3
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
2
1
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
3
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
3
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
1
2
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
2
1
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
3
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
2
2
0
2
0
0
3
1
2
1
0
1
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
1
1
0
0
0
1
0
0
0
0
1
0
1
1
0
2
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
4
0
2
1
0
0
3
0
0
2
0
1
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
3
0
1
0
0
2
0
1
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
2
1
0
0
0
1
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
3
1
1
0
0
0
0
1
0
0
3
2
0
0
0
0
1
1
0
0
2
2
0
0
3
0
0
0
0
1
8
0
0
0
0
2
0
0
0
1
2
2
0
0
0
0
0
0
2
0
0
4
0
0
2
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
3
0
0
2
0
2
0
0
1
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
4
1
1
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
1
0
1
0
0
0
5
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
2
0
0
1
0
0
0
2
0
1
0
0
2
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
7
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
2
0
0
1
0
1
1
3
0
8
0
0
2
3
0
0
1
0
0
1
0
1
0
1
1
1
1
0
0
0
0
1
2
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
3
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
2
0
1
0
0
2
2
0
0
0
0
2
0
0
0
0
0
1
0
0
1
5
0
1
0
0
1
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
1
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
3
1
1
0
0
0
1
0
0
0
3
0
0
0
1
1
1
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
1
1
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
1
2
0
0
0
2
1
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
4
0
2
0
1
0
0
0
0
0
1
1
1
1
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
2
0
6
0
1
0
2
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
2
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
5
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
2
1
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
6
0
0
1
0
2
0
1
0
0
0
0
0
0
1
0
2
0
2
3
0
1
1
0
3
2
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
5
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
4
0
0
0
1
0
0
0
1
0
0
2
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
1
1
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
2
2
3
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
3
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
1
0
1
2
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
1
0
0
1
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
3
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
3
1
0
2
0
0
0
0
1
0
0
2
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
1
1
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
3
0
0
0
0
0
0
1
0
1
0
0
1
2
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
1
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
5
0
0
0
1
1
0
0
0
0
0
2
1
0
0
1
0
2
0
0
2
0
0
2
1
1
0
0
0
0
0
0
2
0
0
1
2
0
0
2
2
2
0
0
2
0
0
0
1
0
0
0
8
0
0
0
0
1
0
0
0
0
2
0
2
2
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
1
0
1
0
0
0
0
0
2
0
0
2
0
0
1
1
2
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
1
0
0
2
3
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
3
0
0
2
1
0
0
2
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
2
1
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
6
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
1
2
1
0
0
2
3
0
2
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
1
2
0
0
0
0
0
1
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
1
0
0
1
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
2
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
1
1
3
2
0
2
0
0
1
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
1
2
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
3
2
2
0
0
0
1
0
3
0
1
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
1
0
0
1
0
1
1
0
0
1
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
2
0
2
3
0
0
0
0
1
0
0
0
0
2
1
0
1
0
0
2
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
1
0
0
3
2
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
1
0
0
2
0
0
1
2
0
2
2
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
1
0
2
0
0
0
2
0
2
0
0
0
2
1
0
0
4
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
2
2
0
0
0
0
2
0
0
1
0
1
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
2
1
3
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
1
0
1
0
0
1
0
1
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
3
0
0
1
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
4
0
0
0
0
3
0
0
0
0
0
3
2
2
0
1
0
1
0
0
2
0
0
0
1
0
1
0
0
4
6
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
4
2
1
0
0
0
0
7
0
1
0
0
0
0
1
0
0
0
0
13
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
3
1
1
0
0
1
0
0
0
0
0
2
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
2
3
2
0
0
0
0
2
0
1
1
2
1
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
1
0
0
3
1
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
1
0
1
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
2
1
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
2
0
0
0
1
0
0
3
0
0
1
0
0
1
1
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
2
0
0
0
3
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
2
0
0
2
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
3
1
0
0
1
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
1
2
2
0
2
0
0
1
1
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
3
1
2
1
4
0
0
0
1
0
0
1
1
2
1
1
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
2
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
1
0
2
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
5
0
3
0
2
1
7
1
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
3
2
1
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
1
4
0
7
1
0
2
3
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
5
0
0
0
0
0
1
1
2
1
2
1
1
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
2
0
3
2
0
1
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
1
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
4
1
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
3
0
0
0
1
0
2
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
3
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
1
0
3
0
0
2
2
0
0
0
0
0
0
0
0
0
1
1
2
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
2
0
0
1
2
0
2
2
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
1
1
0
2
0
1
0
0
2
0
2
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
1
0
3
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
3
0
0
3
0
1
0
2
0
0
1
2
2
0
7
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
1
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
2
0
1
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
2
0
0
3
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
2
4
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
2
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
3
0
2
0
1
7
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
3
0
0
2
0
1
0
0
0
0
0
0
3
0
0
2
0
0
1
0
0
0
0
2
0
0
4
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
3
1
2
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
1
0
3
2
1
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
2
1
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
3
0
4
1
0
0
0
0
0
0
0
0
3
1
0
1
0
0
0
0
0
0
0
1
8
0
1
0
0
1
0
2
0
0
1
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
3
0
0
0
2
0
0
0
0
3
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
1
0
0
2
0
1
2
0
0
1
0
0
0
0
0
0
0
2
0
0
1
2
1
0
0
0
0
0
0
0
1
0
1
0
2
1
1
0
1
0
0
0
0
2
0
0
0
1
0
1
2
0
1
0
0
0
1
1
0
0
0
0
2
0
0
0
2
1
1
0
0
0
0
0
0
0
0
2
0
0
3
0
0
2
0
0
0
1
3
3
1
0
0
0
1
1
1
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
2
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7
2
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
1
0
1
0
0
0
0
0
0
0
2
10
1
1
0
1
2
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
1
2
0
0
1
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
3
0
0
0
0
0
2
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
5
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
1
1
2
0
0
1
0
1
2
0
0
0
1
0
2
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
3
0
0
0
0
2
0
0
3
2
0
0
0
0
0
0
1
0
0
6
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
4
2
1
0
0
1
2
0
0
2
0
0
0
1
0
2
3
0
0
0
2
0
0
2
3
0
0
2
0
0
0
2
0
1
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
3
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
1
0
0
1
1
2
0
0
0
0
0
2
0
0
0
2
7
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
1
4
0
1
0
0
0
0
0
0
1
3
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
2
2
2
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
2
4
1
0
1
0
0
0
1
0
0
0
0
1
0
2
0
2
0
0
0
1
0
2
0
1
0
0
3
0
0
0
2
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
4
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
4
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
2
2
9
1
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
1
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
7
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
1
1
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
1
0
2
0
1
0
0
0
0
0
0
0
1
0
0
4
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
1
0
0
3
2
0
0
0
0
0
0
3
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
2
0
0
0
5
0
0
0
0
2
0
0
0
0
1
0
1
0
0
1
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
3
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
1
0
0
2
0
0
0
2
1
0
0
0
0
0
0
2
1
0
0
0
0
1
0
2
2
0
0
0
2
0
0
0
0
0
0
2
0
2
0
1
0
0
2
0
3
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
8
2
0
0
1
2
1
0
0
2
0
0
0
0
2
0
3
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
1
2
0
0
0
0
0
0
6
0
1
1
0
1
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
3
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
1
2
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
4
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
1
1
2
0
3
0
0
0
0
0
0
0
0
1
0
0
0
3
1
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
2
2
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
2
2
0
0
0
0
2
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
2
1
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
6
2
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
2
0
4
0
1
0
0
5
1
0
0
1
1
0
2
2
1
0
0
1
0
0
0
0
0
4
1
0
0
0
1
0
1
0
0
0
0
0
0
3
0
1
2
0
2
0
0
3
3
2
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
1
0
2
1
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
2
2
0
1
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
2
0
2
0
0
2
1
0
0
0
12
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
3
2
0
1
0
0
0
2
0
0
2
0
1
4
0
0
0
1
0
1
0
0
0
0
0
3
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
2
1
0
0
2
0
0
0
0
0
4
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
3
0
0
1
0
3
4
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
2
0
2
0
0
2
1
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
2
2
1
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
1
2
2
1
2
0
1
0
0
0
0
1
0
0
1
0
0
2
1
0
0
1
2
0
0
0
4
1
0
0
0
0
3
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
3
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
1
0
2
1
0
1
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
3
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
1
0
0
0
3
0
0
0
3
0
1
2
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
2
4
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
7
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
3
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
1
1
0
0
0
0
0
3
0
1
1
1
0
2
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
1
1
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
2
0
0
0
0
3
0
0
1
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
2
2
0
0
0
1
0
0
0
2
2
0
0
1
2
0
0
0
0
0
0
1
2
0
1
0
0
0
4
1
0
0
2
1
3
0
0
0
1
0
0
2
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
2
0
1
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
1
0
2
1
0
2
1
0
0
0
2
0
0
0
0
3
0
0
0
1
2
0
1
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
7
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
2
1
2
0
1
2
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
1
2
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
3
4
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
3
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
1
0
1
0
0
0
0
2
2
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
1
0
1
0
0
1
0
2
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
1
1
0
0
3
2
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
2
0
0
3
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
1
0
1
0
0
0
0
0
0
1
5
0
0
0
0
2
0
1
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
4
1
2
0
0
0
4
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
3
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
2
0
0
0
0
0
0
0
1
0
0
1
3
0
0
0
0
0
0
0
0
1
0
3
0
0
1
0
2
0
1
1
0
0
0
0
0
0
0
0
0
1
3
0
1
0
0
3
0
0
0
0
0
0
8
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
1
0
0
5
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
2
3
1
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
2
0
0
2
3
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
1
1
1
0
0
0
0
1
2
0
0
2
0
1
0
0
0
2
2
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
3
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
3
0
0
0
1
0
3
0
2
0
0
0
0
0
0
0
3
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
3
2
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
3
0
0
2
0
0
0
0
2
0
3
0
0
0
0
2
1
2
0
2
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
1
4
1
0
3
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
2
1
1
0
0
0
2
0
0
2
0
0
0
2
0
2
0
0
1
1
1
0
0
2
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
4
0
0
0
0
2
0
3
1
2
0
0
0
0
0
3
0
0
0
0
2
2
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
4
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
1
0
2
2
1
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
2
0
0
1
0
1
0
0
0
0
0
0
0
2
0
1
1
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
3
2
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
2
0
0
0
0
2
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
1
0
2
0
2
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
12
0
5
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
2
0
0
0
0
0
0
0
0
0
0
3
0
1
1
0
1
0
0
4
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
1
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
2
1
1
0
0
0
0
0
0
0
0
3
0
0
2
0
0
1
0
1
1
0
0
0
0
1
2
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
3
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
2
2
1
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
2
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
2
0
1
1
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
1
2
0
1
1
1
3
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
2
0
0
0
0
1
2
0
0
0
0
1
0
2
2
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
3
1
2
2
2
0
1
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
2
3
1
1
0
0
0
0
0
1
3
0
1
1
0
0
1
2
2
1
0
2
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
2
2
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
1
0
0
1
0
0
0
0
0
0
0
2
0
1
0
1
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
2
0
0
0
2
2
0
0
1
0
1
0
0
0
2
1
1
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
4
0
0
0
0
0
0
1
0
0
7
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
2
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
1
0
2
0
1
1
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
1
0
0
2
0
1
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
8
1
0
1
0
0
0
0
0
0
6
0
0
1
0
0
0
2
1
5
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
3
0
1
1
2
0
1
1
0
0
1
0
1
0
0
0
0
2
1
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
1
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
1
0
1
0
0
0
0
6
1
1
1
3
2
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
1
3
0
1
0
0
0
0
0
2
1
0
2
0
1
0
2
0
2
0
0
2
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
2
1
0
0
1
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
2
2
0
0
0
0
0
0
0
0
2
0
2
0
0
1
1
1
0
0
0
0
2
0
0
2
1
3
0
0
0
2
2
0
2
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
2
0
2
2
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
3
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
1
2
0
2
0
0
0
3
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
2
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
1
0
2
0
2
1
0
0
0
1
0
0
1
2
0
0
2
2
0
1
0
0
0
0
1
0
2
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
3
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
12
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
4
0
0
0
0
0
0
2
3
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
2
0
2
1
2
1
0
0
0
0
0
0
1
0
2
2
2
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
1
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
2
1
1
0
0
0
0
0
1
3
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
3
2
2
0
0
0
4
0
2
0
2
3
0
0
1
0
2
2
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
1
0
3
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
3
1
0
0
1
0
2
0
2
0
0
0
2
2
1
0
2
0
2
1
0
0
0
0
0
3
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
4
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
4
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
5
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
2
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
1
0
0
0
0
0
13
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
3
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
1
5
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
2
1
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
2
0
0
0
0
2
0
2
0
0
3
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
4
0
1
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
4
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
1
0
1
1
2
0
0
2
0
0
1
1
0
0
7
2
0
0
2
0
0
0
0
0
0
1
3
0
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
1
2
2
0
0
0
4
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
3
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
2
2
3
0
0
0
0
0
0
0
0
2
5
0
2
0
0
0
0
0
0
0
0
2
2
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
2
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
5
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
3
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
9
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
6
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
3
2
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
5
0
0
0
0
0
1
2
0
1
2
0
0
0
2
0
0
0
0
1
1
0
0
0
0
2
1
2
0
0
0
1
2
1
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
3
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
5
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
2
2
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
2
0
0
0
0
2
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
4
0
2
2
0
0
0
3
2
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
3
0
2
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
4
2
0
1
1
0
1
2
3
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
3
0
1
1
1
1
0
0
0
0
0
0
0
5
0
0
1
1
0
2
0
2
4
1
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
1
2
2
0
1
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
1
0
1
0
0
0
0
0
0
1
2
0
0
0
0
2
1
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
1
1
0
2
2
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
2
0
0
3
0
0
1
0
0
0
0
0
3
1
0
0
2
1
0
0
0
0
0
0
2
0
0
0
1
0
1
0
2
0
0
0
0
1
1
2
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
2
2
0
0
0
7
0
0
2
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
2
0
2
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
4
0
1
0
2
1
0
0
1
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
2
0
2
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
15
0
0
1
0
2
0
0
0
4
0
0
0
0
0
1
0
0
0
0
3
3
0
1
0
0
2
0
1
2
2
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
2
3
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
4
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
1
1
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
2
2
0
0
2
0
1
0
0
0
0
0
0
4
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
2
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
1
0
0
1
2
2
0
0
0
1
2
0
0
0
0
0
2
0
0
0
1
1
0
2
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
2
3
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
1
2
0
0
3
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
2
0
3
0
0
0
2
0
0
0
0
1
0
2
2
3
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
2
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
2
2
0
0
0
2
0
2
0
0
2
0
2
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
5
8
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
4
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
6
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
4
1
0
1
0
0
0
0
0
2
1
0
0
1
0
3
0
1
0
0
0
0
0
1
0
0
0
0
0
1
2
1
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
1
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
2
3
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
3
0
0
0
0
0
0
2
0
3
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
1
2
0
0
0
2
0
10
0
0
0
0
0
0
0
1
1
2
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
1
0
0
0
0
0
1
1
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
1
0
1
0
3
2
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
1
0
16
0
1
5
3
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
2
4
0
2
0
0
0
0
1
0
1
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
1
4
2
2
0
0
0
0
0
2
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
2
3
0
0
0
0
1
0
0
0
0
0
0
1
1
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
3
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
3
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
3
1
1
0
0
2
0
2
0
0
0
0
2
0
0
2
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
2
0
2
0
0
3
2
0
2
0
1
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
3
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
1
0
1
2
0
0
0
1
0
0
2
3
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
7
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
2
0
7
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
3
1
2
2
0
0
2
1
1
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
3
0
0
2
0
0
0
0
0
0
1
0
2
2
1
1
3
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
2
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
2
1
0
0
1
0
0
2
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
2
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
3
0
0
6
0
0
0
2
0
0
0
2
0
0
2
1
0
2
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
7
0
0
0
0
4
0
1
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
1
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
2
0
0
0
2
0
0
0
1
0
3
1
0
0
0
0
0
0
0
2
0
2
0
0
3
0
0
2
1
0
4
0
2
1
0
0
0
1
0
0
1
0
0
0
2
0
0
0
1
0
0
0
1
0
2
0
0
2
1
0
0
0
0
0
0
2
0
1
0
1
0
2
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
1
0
0
5
0
0
0
2
0
2
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
1
2
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
7
2
4
0
1
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
3
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
2
1
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
2
0
1
0
0
0
4
0
0
0
0
0
2
0
0
0
2
4
2
3
5
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
2
2
0
0
0
0
0
7
0
2
1
1
0
2
0
0
2
1
0
1
0
0
4
2
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
2
2
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
2
1
0
0
2
3
0
0
1
3
0
0
0
0
0
0
0
3
0
0
3
2
0
0
0
1
0
0
0
0
2
2
0
0
0
0
1
0
0
3
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
5
2
1
1
2
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
7
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
2
0
0
0
2
0
3
1
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
2
0
2
0
0
2
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
1
0
0
0
0
0
0
0
2
1
0
3
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
2
0
0
0
3
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
2
2
2
1
0
0
2
0
0
0
1
0
0
1
0
0
2
1
0
1
0
1
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
5
2
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
5
0
0
2
1
0
0
2
0
0
2
0
0
0
0
0
1
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
3
1
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
3
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
1
1
0
0
0
2
0
0
2
0
0
1
1
1
2
2
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
4
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
2
0
1
0
0
5
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
1
0
0
0
1
2
2
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
1
1
0
2
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
9
1
0
2
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
4
0
0
0
0
0
2
0
1
1
0
0
0
2
2
0
2
0
2
0
0
0
0
2
0
2
0
5
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
7
0
0
0
1
0
4
0
0
0
0
0
2
0
0
7
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
2
0
0
0
0
1
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
2
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
3
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
1
0
1
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
3
1
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
3
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
2
2
1
0
0
1
0
0
1
0
0
0
0
0
1
2
0
0
0
1
1
0
0
0
2
0
0
0
0
3
0
2
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
1
0
0
2
0
0
0
1
1
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
1
1
0
0
0
1
0
2
1
0
1
1
0
2
2
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
2
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
1
0
0
0
0
5
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
2
4
1
0
3
1
2
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
1
0
0
0
1
1
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
3
4
0
0
0
0
1
2
0
0
0
0
0
0
2
2
0
1
3
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
4
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
7
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
3
0
1
0
0
0
0
2
0
0
2
1
0
1
0
2
0
1
0
2
2
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
19
1
0
0
1
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
2
0
1
1
2
0
0
0
2
0
3
1
0
0
1
0
1
1
2
0
2
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
2
2
0
1
1
2
0
1
1
0
0
0
0
0
1
0
0
0
1
1
2
1
1
0
0
0
0
0
2
1
0
1
0
0
8
0
0
0
1
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
5
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
2
0
3
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
2
1
0
0
0
0
0
0
0
1
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
1
0
2
0
0
0
0
1
2
0
0
3
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
1
0
1
1
0
1
0
0
0
0
2
0
0
0
0
0
1
2
2
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
5
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
3
0
0
1
0
0
0
0
0
0
0
0
1
3
0
0
0
1
0
0
0
0
0
3
0
0
8
1
0
0
1
0
0
1
0
0
0
1
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
3
0
0
0
3
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
1
1
1
0
0
0
1
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
2
2
1
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
2
0
0
3
0
0
0
1
0
2
0
1
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
1
0
0
1
1
0
2
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
1
2
1
0
1
1
1
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
2
2
4
0
0
0
0
0
2
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
2
0
0
2
2
0
0
0
0
0
1
1
0
2
2
0
0
0
1
0
0
0
0
3
0
0
0
0
0
3
2
0
0
0
0
1
0
4
1
0
0
0
0
0
2
2
0
0
1
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
4
0
0
0
2
1
1
0
1
1
3
0
0
3
0
0
0
1
1
0
4
0
0
2
1
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
3
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
1
0
0
2
0
0
0
0
2
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
2
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
4
1
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
2
0
2
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
1
0
2
0
1
0
0
1
0
1
3
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
3
2
0
0
4
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
3
0
0
0
0
3
0
1
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
2
1
0
0
0
2
1
2
0
0
0
1
1
0
2
0
0
0
2
1
0
0
0
0
0
0
3
0
0
1
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
1
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
2
0
1
0
0
3
0
0
7
2
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
1
3
1
0
0
0
0
0
0
0
1
0
0
0
5
0
0
0
0
0
0
0
2
2
0
0
0
1
1
2
2
3
0
0
0
0
0
1
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
3
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
3
0
0
3
0
1
0
0
1
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
2
0
0
0
0
0
2
0
0
1
0
0
1
1
0
0
0
0
2
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
2
2
0
0
0
1
2
0
0
0
0
1
0
2
0
0
3
0
2
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
1
2
3
0
1
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
1
0
0
0
1
1
0
2
1
1
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
2
0
0
1
0
0
3
0
0
1
2
0
0
1
2
0
0
0
2
0
2
1
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
1
2
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
3
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
2
0
0
1
0
2
0
0
2
2
0
0
0
0
0
1
0
2
0
0
0
1
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
2
1
2
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
3
0
0
0
0
2
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
1
0
2
2
0
2
3
2
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
1
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
9
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
1
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
2
0
1
0
2
3
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
1
0
2
0
1
4
2
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
3
0
0
2
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
4
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
2
0
1
2
0
0
2
0
2
0
0
0
2
2
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
2
1
0
1
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
2
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
1
1
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
2
2
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
1
0
2
0
1
0
1
0
0
0
1
0
2
2
2
0
1
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
7
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
2
0
0
0
0
0
0
3
0
4
1
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
4
0
3
0
0
0
0
0
0
0
7
2
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
2
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
1
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
6
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
2
3
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
3
2
0
0
8
0
2
0
0
0
0
0
0
1
0
2
0
0
0
1
0
2
0
1
0
2
3
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
1
1
0
4
0
0
3
0
2
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
3
0
0
3
2
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
3
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
2
0
3
0
1
0
0
0
0
2
0
0
0
0
1
0
2
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
4
0
0
0
2
0
4
0
0
0
0
1
0
0
0
1
0
2
1
2
0
0
1
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
1
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
1
0
2
0
0
2
2
0
0
1
0
0
3
0
0
0
0
2
2
0
0
0
0
0
6
0
2
0
2
1
1
0
0
0
0
0
2
1
0
2
0
0
0
0
1
0
1
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
2
1
0
0
1
0
2
0
1
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
2
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
4
2
2
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
5
0
1
0
0
0
1
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
1
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
2
5
1
0
2
2
0
0
0
0
0
0
3
0
2
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
1
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
3
0
0
0
1
0
0
0
0
0
0
1
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
1
0
0
0
3
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
2
0
6
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
2
0
1
0
2
1
0
0
1
2
0
0
0
0
2
0
1
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
2
0
0
2
1
2
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
7
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
2
1
0
5
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
1
0
0
0
1
3
2
0
0
1
0
1
0
0
0
0
1
0
0
1
0
2
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
4
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
2
1
0
0
1
0
0
1
2
0
2
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
2
1
0
0
3
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
3
2
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
3
0
1
0
3
0
2
0
0
0
1
0
0
1
2
0
1
0
0
0
0
2
1
0
0
1
0
0
4
0
0
0
1
0
0
0
0
3
0
0
0
0
1
0
1
0
0
0
2
0
0
0
1
0
1
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
4
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
1
1
0
0
0
2
0
0
0
2
0
0
0
2
2
1
0
1
3
0
0
0
0
0
0
2
1
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
2
0
0
0
0
2
0
0
0
0
0
2
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
2
0
1
0
0
1
8
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
2
2
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
1
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
1
0
0
1
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
1
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
2
0
2
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
3
0
2
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
3
3
0
0
0
1
2
1
0
0
1
2
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
2
2
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
2
0
0
4
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
1
0
0
1
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
11
1
0
1
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
2
1
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
1
0
0
1
2
0
0
0
0
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
3
0
0
2
0
0
0
1
0
3
0
1
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
3
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
2
2
0
0
0
0
0
2
0
0
2
1
2
0
2
0
19
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
1
0
0
0
0
0
0
2
0
1
0
2
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
1
0
0
0
0
2
0
1
2
0
1
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
2
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
1
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
4
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
2
0
1
0
5
0
0
0
0
0
0
0
0
0
0
0
0
2
6
0
0
2
2
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
2
0
0
0
0
0
0
3
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
1
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
2
0
1
0
0
0
2
1
2
0
0
0
0
0
0
4
3
0
0
0
2
0
1
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
1
0
0
0
0
0
2
1
0
1
0
0
0
0
2
1
2
1
0
1
0
0
0
1
0
0
3
0
2
1
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
3
1
0
0
2
0
1
0
0
1
0
1
0
0
0
0
0
3
0
0
1
0
0
0
0
1
0
1
1
0
0
0
1
2
0
0
0
2
0
0
0
0
0
2
0
0
0
2
1
0
0
1
0
0
2
0
2
0
2
4
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
2
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
1
2
0
0
0
1
1
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
1
3
0
0
0
1
2
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
2
3
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
2
0
1
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
5
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
2
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
2
2
0
0
4
0
0
0
0
1
0
0
1
0
0
2
0
0
0
1
1
0
0
1
0
0
3
0
0
0
0
0
3
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
9
0
1
1
0
0
2
0
0
0
0
0
0
0
1
0
1
3
2
0
0
0
0
0
0
0
0
0
0
2
1
1
1
0
0
0
0
0
0
3
0
0
2
0
0
0
0
1
1
0
0
3
0
0
0
0
0
1
1
2
0
0
1
0
1
1
2
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
2
0
0
1
0
0
2
2
0
0
0
0
1
0
0
1
0
0
0
8
2
0
0
0
2
0
2
0
0
1
1
0
3
0
1
2
5
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
7
0
2
0
0
0
0
0
2
3
5
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
1
0
1
1
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
3
0
0
0
3
2
2
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
3
0
2
2
1
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
2
0
1
0
0
0
2
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
4
1
0
0
0
0
8
0
1
0
0
0
2
0
0
2
0
0
2
2
0
0
2
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
1
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
1
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
2
0
2
0
6
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
1
1
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
2
1
2
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
1
0
0
0
0
1
0
0
3
0
0
2
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
1
0
0
0
4
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
1
2
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
3
0
0
2
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
3
0
0
0
3
1
0
0
3
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
2
0
0
1
2
0
0
3
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
1
0
0
0
2
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
5
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
4
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
2
0
2
0
0
0
0
0
0
0
1
0
0
0
3
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
1
0
0
2
0
0
0
0
0
1
0
3
1
0
0
1
0
0
0
1
0
3
0
0
0
0
0
0
0
2
0
2
0
3
0
2
0
0
1
0
0
0
0
1
0
0
1
1
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
1
0
0
0
1
0
0
1
0
2
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
1
0
0
0
1
0
0
0
0
2
2
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
3
0
0
0
2
0
0
0
0
1
0
0
6
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
7
2
2
0
0
2
1
0
2
4
0
0
0
0
0
0
0
0
3
2
0
0
3
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
1
2
2
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
3
3
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
4
0
1
0
1
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
2
0
0
0
0
0
2
1
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
1
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
3
0
0
0
0
1
2
0
0
2
0
0
0
0
0
1
0
2
0
2
2
0
0
4
0
0
2
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
2
0
0
1
2
0
0
0
3
0
0
2
0
2
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
4
0
1
0
0
2
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
2
0
0
1
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
5
0
0
0
0
0
0
2
1
2
0
2
2
2
0
0
1
0
1
0
0
1
0
1
0
2
0
0
0
1
0
0
0
2
0
0
0
2
0
2
1
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
3
0
0
0
2
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
1
1
0
0
2
0
0
3
0
2
2
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
3
0
0
0
0
1
0
0
0
0
0
2
1
0
0
1
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
2
0
0
0
2
0
2
0
0
0
5
0
0
0
0
0
0
0
0
2
0
3
1
0
2
0
0
0
1
2
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
2
0
1
2
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
1
0
0
0
1
0
3
0
0
1
0
0
0
0
0
2
0
2
0
0
2
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
2
2
0
0
0
1
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
2
0
0
0
0
2
0
0
2
1
0
1
0
0
0
0
0
2
0
0
4
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
3
0
2
0
1
1
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
1
0
0
2
0
0
3
0
4
5
0
0
0
1
0
1
3
1
0
0
1
0
0
0
0
0
2
1
1
0
2
2
2
0
0
0
1
1
0
0
0
0
2
2
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
2
2
0
2
1
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
1
0
0
1
1
1
0
0
0
0
0
2
0
1
1
0
3
2
0
1
0
1
1
2
0
1
0
0
0
1
0
2
0
1
0
0
0
1
1
0
0
0
1
0
2
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
3
0
0
0
2
2
2
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
3
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
4
6
1
0
0
2
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
3
0
1
0
0
0
2
4
0
0
0
1
0
0
0
0
0
0
2
0
2
2
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
2
1
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
3
0
1
0
1
0
1
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
3
0
0
0
1
0
0
0
0
0
2
4
0
2
2
0
0
1
0
2
0
1
0
0
2
0
1
0
1
1
0
3
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
3
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
4
2
2
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
3
2
0
1
0
0
1
2
0
0
0
2
0
0
2
2
0
1
0
0
2
0
1
0
0
0
2
0
0
0
0
4
2
0
0
1
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
4
0
1
0
2
0
0
0
2
0
2
0
1
2
0
0
0
2
1
1
0
1
1
0
0
0
3
0
2
0
0
1
0
0
1
1
0
0
0
1
0
0
0
1
2
2
0
2
0
0
0
0
0
0
0
1
0
1
0
2
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
4
1
0
0
0
0
1
0
0
0
0
5
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
3
0
0
0
0
1
0
3
2
0
0
10
0
0
0
0
1
2
1
1
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
1
1
0
2
0
2
0
1
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
1
0
0
0
0
0
0
0
1
0
7
0
1
1
4
0
2
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
2
1
0
0
1
1
0
0
2
0
1
0
0
0
0
0
0
3
2
0
1
1
0
0
0
1
0
2
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
3
3
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
3
0
0
2
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
2
0
0
0
2
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
7
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
1
0
1
1
2
0
0
3
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
1
0
2
1
2
1
0
0
1
0
0
0
0
0
0
0
2
1
1
0
1
0
0
2
0
0
0
0
0
1
1
0
0
1
0
0
0
3
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
1
3
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
7
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
3
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
3
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
1
1
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
5
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
1
1
0
2
0
0
0
3
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
2
0
0
0
0
2
1
0
0
1
0
2
1
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
1
0
0
1
1
0
0
0
0
4
0
0
1
0
1
0
2
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
2
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
1
0
0
0
0
0
0
2
2
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
1
1
0
0
1
0
4
1
0
0
1
0
2
0
0
0
4
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
1
0
0
0
0
1
0
3
2
0
0
0
0
0
2
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
2
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
2
0
0
0
0
0
4
2
1
3
0
5
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
2
1
2
0
0
0
0
0
2
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
4
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
4
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
3
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
2
2
1
0
0
1
0
2
0
1
0
1
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
2
0
2
0
0
0
0
0
0
0
2
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
2
0
0
0
0
0
3
1
0
2
0
0
2
1
0
0
0
3
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
2
0
1
0
0
1
0
2
1
0
0
0
1
0
0
2
0
0
0
1
0
0
0
1
0
0
6
0
0
1
1
1
0
1
1
0
0
0
2
0
0
0
0
0
0
2
3
2
0
4
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
1
0
3
1
1
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
2
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
8
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
6
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
2
1
0
0
0
2
2
1
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
3
0
0
0
0
0
0
1
0
3
0
0
0
0
1
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
3
0
1
0
0
3
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
3
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
1
1
0
1
0
1
0
0
0
1
0
0
0
0
0
2
1
1
1
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
1
1
2
1
0
0
2
6
0
0
0
0
0
1
0
0
1
2
0
0
0
0
1
0
2
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
5
0
0
0
3
1
0
0
1
0
0
0
0
2
0
1
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
4
0
0
0
0
0
0
2
0
0
0
2
4
0
0
2
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
6
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
2
1
0
2
0
2
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
1
0
3
0
0
0
0
0
0
0
1
0
1
2
1
3
0
0
0
0
0
0
2
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
2
0
1
2
0
0
1
0
2
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
3
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
2
0
0
3
0
0
0
1
1
0
0
3
0
0
0
0
0
2
0
2
0
2
0
0
0
1
0
2
0
0
2
0
0
1
0
2
1
1
0
1
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
2
2
0
0
0
1
1
1
0
0
0
1
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
1
2
0
0
0
0
0
0
0
1
1
5
0
0
0
0
0
0
0
3
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
1
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
16
0
2
0
1
4
2
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
2
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
3
0
0
1
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
3
0
0
0
4
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
2
2
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
2
0
0
0
0
1
2
0
0
0
2
0
3
1
0
1
0
0
0
0
1
0
3
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
3
0
1
0
0
0
0
2
2
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
1
2
1
1
0
0
2
0
8
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
2
1
3
4
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
3
2
0
1
0
1
1
4
0
2
0
0
0
2
0
0
0
0
5
0
1
0
0
1
2
4
0
1
0
0
0
2
1
1
0
0
0
0
0
0
1
2
0
0
0
1
1
0
0
0
1
0
0
0
2
2
1
0
0
0
0
3
0
1
0
0
0
1
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
3
2
0
0
0
1
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
2
2
0
2
0
1
0
0
0
0
0
0
0
0
0
1
1
2
0
0
1
0
0
1
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
3
0
0
2
0
0
0
0
0
0
1
0
3
0
0
0
0
1
0
0
0
0
1
0
2
0
1
0
0
0
1
0
0
0
1
0
2
0
1
0
0
1
0
5
0
0
0
0
0
2
0
1
0
0
1
1
0
0
0
0
0
1
0
0
6
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
2
1
0
1
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
1
0
0
0
0
2
1
0
2
0
0
0
0
2
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
1
0
1
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
1
2
0
0
0
1
1
0
0
0
0
1
0
0
1
0
2
1
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
8
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
1
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
1
0
0
0
0
0
2
0
0
3
0
2
0
0
0
1
0
0
0
0
3
0
0
2
0
2
1
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
1
0
3
0
0
1
0
1
0
0
0
1
0
2
0
0
2
0
0
0
3
2
0
1
0
0
1
0
2
0
1
0
1
0
0
1
3
0
1
0
0
1
0
1
0
1
0
0
0
2
0
0
0
0
0
2
1
2
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
2
0
0
1
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
4
0
0
1
1
1
0
0
0
2
2
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
3
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
2
0
0
1
0
0
0
3
1
1
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
1
2
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
3
0
0
0
0
0
0
0
7
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
2
0
0
1
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
2
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
1
0
2
0
2
0
0
0
0
0
3
1
0
0
0
0
2
1
0
0
0
0
1
0
0
1
2
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
2
2
0
0
2
0
0
0
0
1
0
0
1
1
0
2
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
2
0
0
2
0
1
0
0
2
0
0
0
1
3
0
1
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
2
0
1
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
3
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
1
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
2
0
0
1
0
0
3
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
3
0
2
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
3
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
3
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
5
0
0
0
0
2
0
0
0
0
0
3
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
5
0
0
0
1
0
0
0
2
0
2
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
1
3
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
1
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
2
1
1
0
1
2
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
1
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
2
0
0
0
2
1
2
0
0
4
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
2
1
2
0
0
0
0
1
0
1
1
0
3
0
1
0
0
0
1
1
0
0
0
0
0
2
0
0
0
3
0
0
2
0
0
0
0
0
1
1
1
1
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
1
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
3
2
0
0
0
0
0
2
0
0
0
0
0
0
3
1
1
4
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
3
0
0
0
1
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
1
3
0
0
0
1
1
0
1
3
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
3
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
10
0
0
0
0
0
1
1
0
2
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
7
0
3
0
0
1
0
1
0
0
2
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
2
0
0
1
2
0
0
0
2
2
0
1
0
2
6
2
0
0
0
0
0
1
0
0
1
0
4
0
0
0
3
0
0
2
1
1
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
3
1
2
0
0
0
0
0
0
0
2
0
1
2
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
2
2
2
0
0
0
1
0
0
0
0
4
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
4
0
1
2
0
6
0
3
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
6
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
4
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
2
2
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
1
0
0
2
1
0
2
0
2
0
5
1
0
0
0
2
0
1
1
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
3
1
0
1
2
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
4
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
3
0
0
0
0
0
0
2
0
0
0
3
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
2
7
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
1
1
0
0
0
0
7
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
3
0
1
1
1
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
1
0
0
0
1
0
2
0
0
3
1
2
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
3
3
0
2
0
2
0
0
3
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
2
0
2
0
1
0
0
1
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
2
0
0
0
0
1
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
3
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
3
0
2
0
0
2
0
2
0
2
0
2
0
0
0
0
1
0
0
0
0
0
3
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
3
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
2
1
0
1
0
2
2
0
0
0
2
2
0
0
0
0
0
2
1
0
0
2
0
0
2
0
0
0
0
0
0
2
1
0
1
3
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
1
0
1
0
1
2
0
0
0
0
0
1
0
2
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
3
2
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
3
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
1
3
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
2
1
1
0
0
0
0
2
0
1
0
1
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
2
2
0
0
3
0
0
0
0
0
0
0
0
0
1
1
0
1
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
3
0
0
0
0
2
1
0
0
1
1
2
0
0
4
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
1
0
1
1
1
0
0
0
0
0
2
4
2
0
5
0
0
1
0
0
0
0
0
0
0
1
1
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
1
3
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
3
1
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
2
0
2
0
2
0
0
0
0
1
0
0
0
0
2
0
0
6
2
1
0
0
0
0
0
0
2
0
0
2
0
2
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
1
1
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
1
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
2
2
0
4
0
0
0
2
0
0
0
0
0
0
1
0
3
0
2
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
3
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
6
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
1
0
1
2
0
1
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
1
2
1
0
0
0
0
2
0
0
0
0
0
0
3
0
5
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
1
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
2
1
0
0
1
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
3
0
2
0
1
0
0
2
7
0
0
2
0
0
0
0
2
0
5
0
0
2
1
0
1
0
0
0
0
2
1
1
0
0
0
3
1
4
0
0
2
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
1
0
0
1
2
0
1
0
1
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
3
0
1
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
2
0
0
0
1
0
0
0
0
3
0
0
0
0
3
0
0
3
0
1
0
1
2
1
0
0
0
2
0
2
1
0
0
2
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
2
1
0
0
0
0
1
1
0
2
1
0
1
0
0
0
0
2
0
1
0
1
3
2
2
0
1
1
0
0
2
0
2
0
1
4
1
0
3
0
1
0
2
3
0
0
0
1
6
0
0
3
0
0
0
0
1
0
0
0
0
1
2
0
0
0
1
2
0
0
1
1
0
0
0
0
3
0
0
2
0
2
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
1
0
1
0
0
1
0
0
1
0
4
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
2
0
1
0
0
3
2
0
0
0
0
0
0
1
0
1
0
0
0
2
0
3
0
2
0
0
0
0
0
2
0
0
0
1
0
1
2
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
3
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
4
0
2
1
3
1
0
0
1
2
0
0
0
2
0
0
0
1
0
0
1
0
1
2
0
0
0
0
0
1
1
1
0
2
1
0
8
0
0
0
0
0
0
0
0
2
0
0
0
1
0
3
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
2
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
3
1
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
5
0
0
0
1
0
0
0
0
0
2
0
2
3
4
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
2
5
2
0
2
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
1
1
0
0
0
1
0
2
2
0
0
2
0
3
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
6
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
3
0
0
1
0
0
2
2
2
1
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
1
1
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
2
1
2
0
0
0
1
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
3
2
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
2
0
0
0
0
1
3
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
2
0
1
0
0
0
0
3
2
0
2
0
0
0
5
0
0
2
1
0
0
2
1
0
0
0
2
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
2
0
3
0
1
2
1
0
0
2
0
0
0
1
1
2
0
1
0
0
2
1
2
0
0
0
0
0
0
0
1
0
1
0
0
0
2
3
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
2
0
0
0
1
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
1
0
2
0
0
0
0
0
0
3
0
0
0
0
2
0
3
1
2
1
0
0
2
0
0
0
0
1
3
0
0
2
0
0
2
2
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
1
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
2
0
2
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
1
2
0
0
1
0
1
0
2
0
0
0
0
0
0
2
0
0
3
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
2
3
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
4
1
0
0
0
0
0
0
1
0
0
0
0
0
1
4
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
3
0
2
1
3
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
3
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
2
0
1
1
0
1
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
4
0
1
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
1
0
3
2
0
2
0
1
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
6
0
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
2
0
0
0
5
0
0
3
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
2
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
1
0
1
0
0
0
1
0
1
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
2
2
1
0
1
0
0
0
10
1
0
0
0
1
0
0
0
0
0
2
0
2
0
0
2
1
0
0
0
1
0
0
0
2
2
1
0
1
1
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
2
2
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
5
2
1
0
0
1
0
2
1
0
0
2
0
0
1
1
1
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
6
1
0
0
0
0
0
1
0
0
1
0
0
0
3
0
0
0
0
2
0
0
0
1
0
2
0
2
0
0
2
0
0
3
0
1
0
0
2
0
1
0
0
0
2
0
0
2
0
0
2
0
5
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
3
0
0
0
1
0
0
0
0
0
0
0
0
2
2
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
2
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
7
0
0
2
0
0
0
1
0
0
2
0
2
0
0
1
1
0
0
0
0
2
0
0
0
0
0
1
1
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
5
0
1
0
0
0
0
2
0
0
0
0
0
3
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
1
1
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
1
2
0
0
2
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
5
0
1
0
1
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
6
0
0
1
0
0
0
0
0
0
0
0
4
2
0
0
0
2
1
1
1
0
0
0
2
0
1
1
0
0
0
2
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
8
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
2
0
0
3
0
0
1
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
3
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
4
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
1
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
3
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
4
0
1
0
1
2
0
1
1
0
0
0
0
0
0
0
9
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
2
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
1
3
0
0
2
2
0
0
0
0
0
0
2
1
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
2
1
0
0
0
4
0
0
4
0
0
2
0
1
0
0
1
1
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
2
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
3
2
0
1
0
0
0
1
0
0
0
5
0
0
0
0
0
2
0
3
0
0
2
0
0
0
0
0
0
0
2
0
0
6
2
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
2
0
0
4
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
2
0
2
1
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
1
2
0
0
2
0
0
1
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
2
0
1
1
3
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
5
2
1
0
0
2
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
2
0
1
0
0
0
2
2
0
0
0
0
0
2
1
0
0
0
2
0
4
1
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
1
0
0
3
0
0
0
0
0
0
1
0
0
0
0
1
2
1
0
3
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
2
0
3
0
0
0
0
0
0
0
0
0
0
1
2
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
3
0
1
0
0
1
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
3
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
2
2
2
0
2
0
0
0
1
1
1
0
0
0
0
0
1
0
0
1
0
0
2
0
2
0
0
0
0
3
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
2
0
1
0
0
1
0
1
5
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
4
0
0
0
6
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
2
0
2
0
0
0
3
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
1
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
1
0
0
0
3
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
1
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
1
4
0
0
0
2
0
0
0
2
3
0
0
0
3
0
0
0
0
0
5
0
0
0
0
0
0
2
2
2
0
0
0
2
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
1
1
2
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
1
2
0
2
0
0
1
0
0
2
0
0
2
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
3
0
0
0
0
0
2
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
2
0
1
0
0
0
1
0
0
1
1
0
2
0
0
0
0
3
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
1
0
2
3
0
0
0
0
0
2
2
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
6
0
1
1
0
0
1
0
2
0
0
0
0
0
0
2
0
0
3
0
0
0
1
3
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
1
0
1
2
1
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
3
2
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
5
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
2
2
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
1
0
4
0
3
0
0
0
0
0
11
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
3
0
2
0
0
2
1
1
0
0
0
0
0
0
0
0
2
0
1
0
2
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
1
0
0
3
1
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
4
0
0
0
0
2
0
0
0
0
1
1
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
3
0
0
0
0
0
0
2
0
2
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
2
0
0
0
2
1
0
0
0
2
0
5
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
2
1
2
0
1
0
0
1
2
0
0
0
1
0
0
0
0
0
0
3
1
0
0
0
1
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
1
3
0
1
0
0
0
0
0
0
0
0
2
1
1
2
0
0
1
0
1
0
2
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
10
0
2
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
1
0
1
0
0
0
5
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
2
0
0
2
0
0
1
1
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
3
0
2
2
0
0
0
0
0
0
2
0
0
0
0
1
4
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
2
0
0
1
0
0
1
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
3
0
0
2
1
3
0
0
0
0
0
1
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
4
1
1
0
0
0
1
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
2
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
1
1
1
0
0
0
0
0
1
1
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
3
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
1
1
1
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
2
2
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
3
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
3
2
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
4
0
1
2
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
2
0
1
2
0
0
1
1
0
0
0
0
0
0
2
0
0
1
0
2
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
6
0
0
1
2
0
0
0
0
1
0
2
2
0
1
0
0
2
0
1
0
0
1
0
0
1
3
0
2
0
0
0
0
1
0
1
0
0
1
0
0
1
0
1
0
2
2
0
2
2
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
1
0
2
0
0
0
0
0
0
0
2
1
0
1
0
0
0
2
0
2
1
0
0
2
3
0
2
1
0
2
3
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
4
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
4
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
1
0
9
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
2
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
1
1
0
3
2
0
2
0
0
2
2
0
0
0
0
0
2
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
2
1
1
2
0
1
0
0
0
0
1
0
0
2
1
0
1
0
2
0
2
2
2
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
2
2
0
2
2
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
5
0
0
2
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
1
1
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
2
0
0
0
1
0
0
0
2
0
1
0
1
0
0
0
0
0
0
1
3
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
3
2
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
2
0
2
0
1
0
0
0
2
2
1
0
0
1
0
0
0
1
2
0
1
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
2
1
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
1
1
0
1
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
1
0
1
2
1
0
0
0
0
0
0
0
0
0
0
6
0
0
2
3
2
0
0
2
0
0
1
2
0
2
0
7
2
0
0
2
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
2
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
3
1
1
0
0
0
0
1
0
2
0
0
0
1
2
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
6
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
3
0
0
3
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
3
0
2
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
3
0
0
1
0
1
0
1
0
0
0
0
0
2
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
1
1
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
2
0
2
3
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
5
0
0
0
3
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
2
0
0
1
2
0
0
0
1
1
0
0
0
1
2
0
0
1
0
0
1
0
1
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
2
1
2
1
0
1
0
0
0
0
2
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
2
1
0
2
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
5
0
1
0
2
0
0
0
1
0
0
0
0
0
0
3
0
0
1
0
0
2
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
1
0
2
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
3
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
5
3
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
3
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
3
0
0
2
2
0
2
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
4
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
1
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
2
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
2
0
9
2
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
2
2
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
2
0
0
1
2
1
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
2
0
1
0
1
1
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
2
1
0
0
0
0
2
0
2
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
3
0
0
1
0
0
2
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
1
0
0
0
0
9
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
1
0
3
2
1
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
2
4
0
3
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
3
0
0
0
0
0
0
4
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
1
0
2
2
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
2
0
0
1
2
0
0
0
0
1
0
1
1
2
1
0
0
0
1
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
1
0
0
0
0
1
2
0
0
1
0
2
0
0
0
0
2
1
4
0
0
2
0
2
0
2
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
1
2
0
2
0
2
1
0
2
4
0
0
3
1
4
0
0
0
0
1
0
0
1
0
3
0
2
0
0
0
2
2
0
0
0
1
0
0
0
3
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
4
0
0
0
1
0
0
0
0
0
0
1
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
3
0
0
1
0
0
0
2
0
0
1
0
0
1
0
2
2
0
0
0
0
2
1
1
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
3
0
0
1
1
1
2
0
0
0
0
1
0
2
0
2
0
2
0
0
3
2
1
0
0
1
0
2
0
1
0
3
0
0
0
0
0
1
2
3
1
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
3
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
4
3
0
0
0
1
0
0
2
0
1
0
1
0
0
1
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
2
1
1
0
2
0
0
2
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
3
0
1
0
2
0
1
0
2
0
0
2
1
3
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
1
0
4
0
0
1
1
0
0
0
0
0
0
0
2
0
2
1
0
0
0
1
0
0
1
2
0
0
0
0
0
1
0
0
1
3
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
2
0
0
1
0
1
0
1
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
16
0
1
1
0
0
2
2
0
0
1
0
2
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
2
0
0
1
0
0
3
1
0
0
0
1
0
0
0
0
0
0
0
0
3
0
2
0
3
0
6
1
6
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
2
1
2
1
0
1
2
1
0
0
2
0
0
0
1
1
0
4
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
1
0
1
2
1
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
2
1
0
2
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
1
0
0
0
0
2
0
1
0
0
1
1
0
0
0
1
0
0
2
4
1
1
0
0
0
2
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
1
0
0
0
0
2
0
0
0
2
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
2
0
1
2
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
2
0
4
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
1
1
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
9
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
4
2
1
0
0
0
2
0
0
0
0
1
1
0
2
0
0
0
0
0
2
0
3
0
0
0
0
0
0
3
0
0
0
2
0
0
1
0
0
1
0
0
0
0
2
3
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
6
0
0
0
0
0
11
2
1
0
1
0
0
0
0
1
0
0
2
0
13
2
0
2
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
5
0
1
0
0
1
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
2
1
0
1
0
0
0
2
0
1
0
1
0
1
0
0
3
2
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
1
0
1
0
1
0
0
0
0
1
2
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
4
2
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
1
1
2
0
0
0
0
0
0
0
2
0
0
2
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
4
0
2
2
0
2
0
0
0
0
0
0
1
2
0
0
1
1
0
2
3
2
0
0
0
3
0
0
0
1
0
1
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
1
0
1
0
0
0
0
2
0
2
0
4
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
1
0
0
1
0
0
0
3
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
2
3
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
1
0
0
2
2
1
0
0
0
3
1
0
0
0
1
0
0
0
0
2
0
0
2
1
0
0
0
1
0
3
3
1
0
0
0
0
1
0
0
3
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
1
0
0
3
0
0
0
1
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
1
2
2
1
0
0
0
6
0
2
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
2
0
1
0
0
0
0
3
1
0
1
0
0
0
0
2
3
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
4
2
0
0
0
0
2
0
2
2
0
0
1
2
0
0
2
1
0
0
2
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
2
0
2
0
1
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
2
1
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
2
0
0
1
5
0
0
0
0
0
1
3
0
0
2
0
2
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
1
0
0
0
0
2
0
1
0
0
0
2
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
2
0
4
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
4
0
0
2
2
0
0
0
0
2
1
1
0
0
1
0
1
0
0
0
0
0
2
0
0
0
2
1
1
1
4
0
0
2
0
0
0
0
0
8
2
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
1
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
2
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
5
0
2
0
2
0
3
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
3
0
1
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
5
0
0
0
1
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
4
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
2
0
0
1
0
0
1
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
2
1
0
0
0
4
1
0
0
0
2
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
3
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
1
0
0
0
2
2
2
0
0
0
2
2
0
3
0
2
0
2
2
2
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
1
4
0
0
0
1
0
0
0
0
0
0
0
0
0
7
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
1
0
0
1
0
0
0
0
2
0
2
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
1
2
7
0
8
0
0
1
2
0
0
0
0
1
0
0
2
0
0
0
2
0
1
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
4
2
1
0
0
0
0
0
0
0
1
1
0
0
2
0
0
2
0
0
2
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
1
0
3
0
0
0
0
2
1
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
5
0
2
0
0
0
2
0
0
0
0
2
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
3
0
1
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
1
2
0
0
0
1
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
7
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
2
0
0
1
0
1
0
1
1
0
0
0
5
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
4
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
3
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
11
1
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
1
0
3
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
2
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
4
0
2
0
2
1
0
3
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
1
0
0
0
0
4
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
1
2
1
0
0
0
0
0
0
1
0
2
2
1
1
0
0
1
2
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
7
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
4
0
0
0
1
0
1
0
0
0
0
2
2
0
0
1
0
0
0
0
1
1
0
5
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
2
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
3
2
0
2
1
1
1
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
4
0
2
0
0
0
0
0
1
0
2
0
0
1
0
0
0
1
0
2
0
0
0
2
0
0
2
0
4
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
5
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
3
1
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
2
0
2
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
3
0
2
0
0
0
0
0
0
1
0
0
2
1
0
0
0
2
2
0
0
0
2
0
0
0
1
2
1
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
2
1
2
2
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
10
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
12
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
4
0
2
1
0
1
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
1
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
3
0
0
0
0
0
0
0
1
0
2
0
0
2
1
1
1
1
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
1
2
1
0
0
3
0
0
0
0
0
1
1
0
0
0
0
0
2
2
0
0
1
1
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
1
0
0
3
0
0
2
2
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
2
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
7
2
2
0
0
0
1
0
0
0
0
0
0
1
2
0
2
1
4
0
1
1
0
1
2
0
0
3
0
0
0
0
0
1
0
1
0
2
2
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
1
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
10
0
2
0
0
1
0
0
0
0
2
2
2
0
0
0
2
0
0
0
0
0
0
2
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
1
1
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
4
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
2
1
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
2
0
6
1
0
0
0
0
0
1
0
1
0
0
2
2
0
0
0
0
0
0
2
0
1
2
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
1
0
0
1
0
0
0
2
0
0
1
0
0
0
1
0
1
0
0
0
0
0
4
0
1
1
2
1
0
1
0
0
2
0
0
1
0
0
1
0
0
0
0
2
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
2
0
2
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
2
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
2
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
1
3
0
5
0
0
0
0
0
0
0
3
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
4
1
0
2
0
3
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
1
0
2
1
0
2
1
0
0
2
0
1
0
0
0
0
0
2
0
2
0
0
0
0
2
0
3
2
0
0
0
0
1
1
0
0
0
0
0
0
3
0
2
0
0
0
2
0
0
0
0
1
0
0
1
0
2
0
0
1
3
0
1
0
0
2
3
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
1
0
0
3
2
0
2
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
2
1
2
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
1
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
5
0
0
0
2
0
0
2
0
0
0
0
1
4
0
0
2
1
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
9
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
1
2
2
0
0
0
1
0
0
0
0
1
0
0
1
0
2
0
0
0
1
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
2
0
1
0
2
2
2
2
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
2
0
1
1
1
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
2
0
5
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
1
0
0
2
0
0
1
1
0
0
0
0
0
2
0
2
2
0
3
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
5
0
0
1
0
0
0
0
1
1
2
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
1
1
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
2
1
2
2
0
0
0
1
0
0
0
0
0
0
1
2
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
1
0
2
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
3
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
8
0
2
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
5
2
0
2
0
2
0
0
3
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
3
2
0
2
1
0
1
0
0
2
1
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
2
1
1
0
0
0
0
0
0
0
1
0
0
1
0
1
2
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
3
0
2
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
4
2
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
1
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
1
1
0
0
0
1
0
0
1
0
2
2
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
3
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
1
2
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
3
1
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
2
0
0
1
0
0
1
3
0
0
2
2
0
0
0
0
0
0
1
2
0
0
1
0
3
0
1
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
1
1
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
1
0
0
2
2
0
0
1
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
3
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
2
1
0
0
2
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
3
0
1
2
1
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
1
2
0
1
0
1
0
0
0
1
0
1
1
1
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
4
0
0
2
2
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
2
0
0
0
11
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
3
0
2
0
0
1
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
0
2
2
0
2
0
0
0
1
1
0
0
0
0
0
1
0
2
0
1
0
1
3
0
4
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
2
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
3
0
2
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
1
2
0
1
1
0
0
4
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
9
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
2
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
1
2
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
3
2
0
0
0
0
0
0
2
2
1
0
2
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
1
1
2
0
0
0
1
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
2
0
2
0
1
0
2
0
2
0
0
0
0
1
2
1
1
0
0
2
0
2
1
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
1
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
1
2
0
0
2
0
0
0
1
0
2
1
2
0
0
0
2
1
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
1
0
0
0
0
2
0
3
2
0
0
0
1
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
1
0
1
0
2
0
2
0
0
0
1
0
0
1
1
0
1
0
0
0
2
0
2
0
3
0
2
0
1
0
0
2
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
1
1
1
0
0
0
2
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
3
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
3
0
3
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
1
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
2
5
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
4
2
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
3
2
0
0
0
2
0
0
0
1
0
4
0
1
0
0
0
2
0
0
2
0
0
0
2
2
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
2
2
0
0
4
0
1
2
3
0
2
0
1
1
0
1
0
0
2
0
0
0
0
0
0
2
0
1
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
2
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
3
2
0
1
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
2
0
5
1
3
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
3
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
3
0
1
0
0
0
2
0
0
1
0
0
0
4
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
1
0
0
0
1
0
2
0
1
1
1
0
0
0
2
1
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
1
1
0
0
0
0
0
0
1
0
0
3
0
0
2
0
0
1
0
0
1
0
0
0
0
2
0
2
0
0
1
2
1
0
0
0
3
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
1
0
0
0
2
0
0
0
0
2
1
0
2
0
0
0
1
0
1
0
0
2
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
3
2
0
0
0
3
1
0
0
0
0
0
2
1
0
0
0
0
0
2
0
2
0
1
2
0
1
0
1
0
0
0
1
0
0
0
0
0
2
0
0
1
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
1
0
1
0
0
1
0
0
2
1
0
1
0
1
0
0
0
0
1
1
1
0
0
0
1
0
1
0
0
2
3
0
1
2
0
0
1
0
0
1
2
1
0
0
0
0
0
0
0
1
0
2
2
0
1
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
4
0
3
0
1
0
0
0
0
0
5
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
2
2
0
0
1
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
2
1
0
0
2
0
0
2
0
2
0
0
0
0
0
0
4
1
3
0
1
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
1
0
0
0
1
0
2
0
0
2
0
1
0
0
2
2
1
0
1
0
0
0
0
0
2
1
0
0
0
0
2
0
1
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
2
0
1
0
1
0
2
4
1
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
2
2
0
0
3
0
1
2
0
1
4
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
2
0
1
1
2
0
5
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
5
2
1
1
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
2
1
0
0
0
2
0
2
0
0
0
3
0
0
1
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
2
0
2
1
3
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
2
2
0
0
3
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
2
0
0
1
0
0
0
1
1
0
0
0
1
0
1
0
1
0
0
0
2
1
0
0
0
0
0
0
0
1
1
2
0
0
1
0
1
2
0
1
1
0
0
1
0
2
1
0
1
0
0
1
2
2
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
2
1
0
0
1
1
0
0
2
0
0
0
0
0
3
1
0
0
2
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
4
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
2
2
1
1
0
0
0
2
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
2
0
0
1
2
0
0
0
2
0
0
6
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
1
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
1
2
2
1
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
2
4
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
10
0
0
0
0
0
0
2
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
3
2
0
0
1
0
0
1
0
0
0
0
0
0
0
3
0
0
3
0
0
0
2
1
3
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
1
0
4
0
0
0
0
0
0
1
3
0
0
2
1
0
0
1
0
0
0
0
0
2
0
0
0
0
1
1
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
1
0
1
0
0
0
0
1
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
1
0
1
1
0
0
1
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
2
0
0
2
0
0
0
0
0
0
2
2
0
0
1
0
1
0
0
0
2
0
0
3
0
0
0
0
0
1
1
0
0
0
1
0
1
2
0
1
1
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
2
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
3
0
2
0
1
0
0
0
0
0
0
0
1
2
2
0
2
0
0
0
0
2
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
3
0
0
0
1
1
1
1
0
0
0
2
0
1
0
0
0
1
1
0
0
1
1
1
0
0
0
0
2
2
3
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
3
0
1
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
1
0
0
1
0
1
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
8
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
5
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
3
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
5
0
0
2
0
0
1
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
3
0
0
0
2
0
1
1
0
1
0
0
0
0
4
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
3
0
0
0
2
0
2
0
0
2
0
0
0
0
2
0
2
2
1
1
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
2
0
1
0
1
0
0
0
0
3
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
5
0
0
9
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
2
1
0
0
0
0
0
0
3
0
1
2
2
0
0
0
1
0
1
0
0
1
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
2
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
1
1
0
0
3
0
0
2
0
0
0
2
0
0
2
2
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
3
3
0
0
0
0
1
2
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
1
1
0
2
0
0
2
0
0
2
2
0
2
0
0
0
0
1
1
0
0
0
2
0
0
1
1
1
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
3
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
1
0
0
0
5
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
3
0
0
0
2
0
0
0
3
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
2
0
0
3
0
0
1
0
0
0
0
2
0
3
0
0
0
0
2
0
1
0
2
0
4
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
2
0
1
2
0
0
0
0
1
0
1
0
2
0
1
1
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
2
2
0
0
2
1
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
4
0
0
0
0
1
0
0
2
0
1
0
0
0
1
0
4
0
0
4
1
1
2
0
1
0
0
3
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
1
3
0
2
1
1
2
0
1
0
0
0
0
2
0
0
4
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
4
2
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
4
1
1
1
0
2
0
0
0
0
2
0
0
0
0
0
0
11
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
1
0
0
1
0
0
0
0
1
2
0
0
0
2
2
0
0
0
1
0
0
1
0
0
1
2
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
1
0
0
2
0
0
0
1
0
1
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
2
0
7
0
1
0
0
0
0
3
0
0
0
2
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
2
0
0
0
0
0
1
0
0
0
2
0
2
0
0
4
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
1
1
0
1
0
0
2
0
3
0
0
1
1
2
0
1
0
0
0
1
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
1
4
0
0
0
1
2
0
3
1
1
0
0
2
1
0
0
0
0
0
0
1
0
0
1
3
0
2
1
0
0
0
0
0
0
0
3
0
0
3
1
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
2
0
2
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
1
0
0
2
0
0
0
0
0
1
0
0
0
1
0
1
4
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
2
2
0
0
4
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
4
1
3
2
0
0
0
0
0
0
0
0
4
0
0
0
4
0
0
0
0
0
0
0
0
1
2
0
1
1
0
0
0
1
0
0
2
0
0
0
2
2
0
3
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
5
1
0
1
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
3
0
3
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
1
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
2
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
3
0
2
0
0
0
0
0
0
1
0
2
0
1
0
0
0
2
2
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
2
0
2
2
0
0
0
1
0
0
3
0
0
0
1
0
1
2
2
1
0
0
0
0
0
0
2
0
0
0
2
0
2
0
3
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
2
2
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
1
0
0
0
0
0
2
0
1
2
0
0
0
0
0
1
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
2
1
0
1
2
0
0
0
0
0
0
2
0
0
1
0
2
2
0
1
0
0
0
0
0
0
1
1
0
3
0
1
2
0
0
0
0
2
0
0
0
1
0
1
2
4
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
3
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
3
0
0
1
0
2
0
2
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
2
1
0
0
0
0
2
2
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
3
1
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
4
1
2
0
1
0
1
0
0
0
0
0
2
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
2
2
0
3
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
3
0
2
0
0
0
2
0
0
0
0
2
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
3
0
0
0
0
3
1
0
0
0
0
0
0
4
0
0
0
2
1
0
0
2
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
1
0
1
1
2
0
6
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
2
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
1
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
6
0
1
0
0
0
0
0
2
2
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
1
0
0
0
0
4
0
0
0
2
1
0
0
1
1
0
0
0
0
0
2
0
0
3
0
0
0
0
0
2
0
0
2
2
2
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
1
1
1
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
3
0
0
2
0
0
2
0
0
2
0
0
2
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
3
0
0
0
0
1
5
2
1
0
0
0
0
0
6
0
0
0
0
2
1
0
1
2
0
0
0
0
2
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
2
1
1
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
2
0
1
0
4
0
0
0
1
0
0
2
0
2
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
3
1
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
2
0
2
1
0
0
0
1
0
0
0
1
2
0
0
0
0
2
0
0
0
0
1
0
0
1
0
5
2
2
0
2
0
3
0
0
0
2
2
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
2
0
0
0
2
2
0
2
0
0
1
2
0
0
0
0
0
3
0
0
0
0
0
2
1
0
2
0
0
1
0
1
0
0
2
0
2
0
0
0
0
0
0
1
2
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
5
0
0
1
0
1
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
2
0
0
0
2
1
0
1
0
0
0
0
0
0
0
2
1
1
0
2
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
2
0
0
3
1
2
0
0
0
0
0
0
0
1
0
2
1
1
1
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
1
1
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
3
0
0
0
0
0
0
0
0
4
0
0
0
1
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
1
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
1
2
0
0
0
0
0
0
4
2
0
0
1
0
0
0
2
0
0
0
0
0
0
1
2
2
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
1
0
1
0
2
0
2
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
2
0
1
0
0
3
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
3
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
1
0
3
0
0
0
3
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
4
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
3
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
3
0
0
3
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
2
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
1
1
0
0
2
0
0
0
1
0
3
2
2
1
0
2
1
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
1
0
0
0
2
0
3
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
1
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
2
1
0
1
0
0
0
0
0
1
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
2
2
0
1
2
0
0
0
0
0
0
0
0
0
1
2
0
0
1
4
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
2
2
0
1
1
0
6
0
1
0
0
0
0
0
0
0
0
0
0
2
2
3
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
2
1
0
0
0
0
1
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
2
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
2
0
1
2
1
3
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
1
0
0
0
0
2
0
0
0
0
0
0
0
5
0
0
0
1
0
0
0
1
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
1
0
0
0
1
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
3
0
2
0
0
0
0
1
0
0
1
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
3
0
1
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
3
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
2
0
0
0
0
1
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
1
2
0
1
0
0
2
0
2
0
0
1
0
0
1
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
2
0
1
0
0
0
0
1
0
0
2
1
2
0
0
0
0
0
1
0
2
2
0
1
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
5
0
2
0
0
0
0
0
1
3
0
0
2
0
0
0
0
0
2
2
1
0
4
0
2
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
2
2
0
0
0
0
0
0
0
1
1
0
0
0
1
0
2
0
1
1
0
0
2
0
0
1
2
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
3
0
0
0
0
1
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
2
2
0
1
0
3
0
2
3
0
2
1
0
5
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
3
0
1
0
1
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
19
1
0
0
1
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
5
0
1
0
0
0
0
0
0
0
1
0
0
1
0
2
2
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
2
5
0
0
0
1
0
2
1
0
0
0
0
4
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
3
1
1
0
0
2
0
0
0
0
0
0
1
0
0
3
1
0
0
0
2
0
0
2
0
0
0
1
0
3
0
0
0
0
0
1
3
0
2
1
2
0
0
0
1
3
0
0
0
0
0
4
2
0
1
0
0
2
2
0
0
1
0
0
0
0
0
0
4
0
1
0
0
0
2
1
1
2
0
0
2
2
1
0
0
0
2
0
0
0
0
1
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
4
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
2
1
2
2
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
1
1
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
4
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
3
0
2
2
2
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
5
0
0
2
0
2
0
2
0
1
0
0
0
0
0
0
0
0
3
0
1
0
2
3
1
0
0
0
3
1
0
0
0
0
1
0
0
1
0
0
0
4
1
0
0
1
0
0
2
3
0
1
0
0
0
0
2
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
1
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
3
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
1
2
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
1
0
0
2
0
4
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
2
0
1
0
0
0
0
0
2
0
0
0
0
1
3
0
0
0
0
1
0
0
0
0
1
0
2
2
1
2
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
4
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
8
0
0
2
2
1
1
0
2
3
0
2
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
1
1
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
1
1
1
8
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
3
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
1
3
0
0
0
0
2
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
2
2
0
4
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
1
0
1
0
1
1
0
0
0
1
0
0
0
1
1
3
0
0
2
0
0
0
0
2
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
2
1
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
3
2
0
0
0
0
0
0
0
1
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
1
0
0
0
0
1
0
2
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
1
0
2
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
1
1
0
2
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
1
0
0
0
1
1
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
2
0
5
0
0
3
0
0
0
0
0
2
0
0
2
0
0
0
1
0
2
0
0
0
2
2
1
0
0
0
1
0
0
0
0
0
3
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
3
0
1
0
0
3
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
5
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
1
2
0
0
1
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
3
0
0
1
2
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
6
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
1
3
0
2
0
2
0
0
2
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
2
0
0
0
0
2
0
0
2
0
0
1
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
3
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
10
0
0
1
0
8
0
0
0
0
0
0
2
0
2
0
0
1
0
2
0
0
0
1
0
4
0
0
0
0
2
0
0
2
0
0
1
0
2
0
0
1
0
0
0
0
0
0
1
2
2
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
2
0
2
0
0
0
0
0
0
5
1
0
0
1
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
3
2
0
0
0
0
2
2
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
2
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
1
0
1
1
0
2
2
0
0
2
0
0
0
0
2
1
3
0
0
0
0
0
0
0
0
0
14
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
16
0
0
0
0
3
0
0
0
1
0
1
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
6
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
1
0
1
2
0
0
0
0
0
3
2
2
0
0
0
0
2
0
0
2
2
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
1
1
2
0
0
1
0
1
0
1
0
0
0
1
0
0
3
3
2
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
3
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
3
0
0
0
0
0
3
0
0
0
2
0
0
0
1
0
0
0
2
1
0
2
1
0
2
0
0
1
0
0
2
0
2
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
3
0
0
1
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
2
0
2
0
0
1
0
0
1
3
2
0
0
0
0
0
0
0
0
1
2
4
0
1
0
5
1
0
0
0
0
0
0
0
0
0
1
0
1
3
2
0
0
0
0
0
0
0
0
1
1
0
1
2
2
0
0
0
0
1
2
0
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
5
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
2
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
2
0
4
1
2
0
0
2
0
8
2
1
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
3
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
3
1
0
2
1
0
0
0
2
0
0
0
0
0
0
3
1
2
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
1
0
1
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
2
0
0
1
2
0
0
0
2
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
4
2
0
2
0
0
0
0
1
0
0
4
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
2
0
2
0
1
0
0
1
2
0
1
0
0
2
1
0
5
0
0
0
0
0
0
0
1
0
0
2
0
0
1
1
0
0
0
3
0
0
0
1
1
2
1
1
2
0
1
1
1
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
3
0
0
0
0
1
0
0
0
0
3
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
2
1
0
0
0
0
0
0
0
0
1
0
0
1
0
2
1
1
0
1
0
1
0
0
0
0
3
2
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
1
0
0
2
3
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
3
0
2
3
1
0
0
0
0
1
0
2
0
0
0
0
0
2
1
3
0
5
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
2
0
1
0
0
0
1
1
0
0
1
0
1
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
11
1
0
0
1
1
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
2
0
1
1
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
6
0
1
0
0
0
0
0
0
0
1
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
5
0
4
0
0
0
1
0
2
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
3
0
2
4
2
1
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
2
1
2
0
0
0
0
0
0
1
0
0
0
1
0
1
0
2
0
0
2
0
0
2
0
2
1
0
0
0
1
5
0
2
0
0
10
0
1
0
0
0
0
0
2
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
3
0
0
0
2
0
0
3
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
1
2
0
0
0
0
0
1
2
0
0
1
2
0
0
0
0
0
2
2
2
0
1
0
0
0
0
1
1
2
1
0
0
2
1
0
1
0
1
0
0
0
2
0
0
2
0
0
2
0
0
2
0
0
0
2
2
0
2
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
2
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
1
0
2
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
5
2
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
3
2
2
0
1
0
0
1
0
0
0
1
0
0
0
7
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
2
1
0
1
2
1
0
0
0
0
0
0
4
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
1
2
1
0
0
0
0
0
4
0
2
0
0
3
0
0
1
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
3
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
3
0
0
0
0
0
0
0
0
3
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
4
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
2
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
4
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
1
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
6
0
1
0
1
2
0
0
1
0
0
0
0
0
2
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
2
3
1
2
0
0
2
0
0
0
0
0
5
0
0
0
0
0
1
0
0
3
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
1
0
3
0
0
1
0
2
0
0
0
0
0
0
0
0
3
0
0
0
3
0
1
0
0
0
2
0
0
1
1
0
0
2
0
0
0
1
1
0
0
0
0
3
0
0
3
0
0
0
1
2
0
1
1
2
1
0
0
2
2
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
4
0
2
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
3
0
0
2
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
1
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
2
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
4
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
1
1
1
1
0
0
0
2
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
10
1
0
1
1
0
1
0
2
0
2
0
0
0
0
0
2
3
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
5
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
3
1
1
0
0
1
0
1
0
0
1
0
0
0
0
2
0
2
1
1
0
0
0
2
2
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
2
2
0
0
2
2
0
0
2
0
0
2
0
0
0
3
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
1
1
0
1
0
1
0
0
0
0
2
0
1
0
1
0
0
0
0
0
2
2
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
2
0
4
0
0
0
0
0
0
4
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
1
1
1
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
4
1
1
2
0
1
0
0
0
0
1
0
3
0
3
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
2
0
1
0
1
2
0
2
0
0
0
2
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
2
0
1
0
1
0
1
1
0
0
0
0
0
0
3
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
1
0
0
1
0
1
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
3
0
2
0
2
1
1
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
1
0
0
0
0
1
1
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
1
0
2
0
0
1
0
0
1
0
2
0
1
0
0
2
0
2
1
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
2
1
0
0
0
0
0
2
0
0
0
2
0
0
2
1
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
1
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
4
1
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
1
3
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
1
0
0
0
0
0
1
0
1
2
1
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
1
0
0
4
0
0
1
0
0
3
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
8
2
4
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
1
2
6
0
2
0
1
0
1
0
0
2
2
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
3
0
0
2
0
0
0
0
2
1
0
2
0
0
2
5
1
1
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
2
1
0
0
0
0
0
0
1
2
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
4
2
1
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
3
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
2
0
2
0
0
0
0
3
0
1
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
2
0
0
2
0
0
3
0
1
0
0
2
2
0
0
2
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
2
1
0
0
0
0
0
0
1
2
0
0
0
0
3
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
2
0
2
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
2
0
2
2
0
0
2
0
2
1
0
1
0
0
0
0
0
2
0
1
2
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
3
1
0
1
1
0
2
2
3
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
1
0
0
0
0
0
0
1
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
3
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
3
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
2
0
0
0
1
0
1
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
3
0
2
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
2
0
2
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
1
5
0
0
0
0
1
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
4
0
1
0
0
1
2
0
0
0
0
1
0
0
0
0
4
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
3
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
3
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
1
0
0
0
4
0
1
1
0
0
1
0
1
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
1
0
0
0
1
1
0
0
4
0
2
0
2
0
0
0
0
0
0
0
4
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
1
2
1
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
3
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
2
0
1
1
0
0
0
6
1
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
4
0
0
0
0
0
0
0
1
2
0
1
0
0
2
0
0
3
2
2
3
2
2
1
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
8
0
1
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
1
1
0
0
1
3
0
0
3
0
1
2
0
0
0
0
0
0
2
1
2
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
1
0
0
1
1
1
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
1
1
0
0
0
1
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
1
4
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
2
0
0
0
2
0
3
1
0
3
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
2
2
0
1
0
2
0
1
0
0
1
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
2
1
1
0
1
1
1
2
0
0
1
0
1
1
0
0
2
0
1
1
0
2
0
0
0
1
0
0
1
0
0
2
0
1
0
0
1
1
0
0
2
1
0
0
0
0
2
0
0
0
0
0
1
0
2
0
2
1
0
0
2
2
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
2
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
2
1
0
2
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
1
2
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
2
0
0
2
1
1
0
0
0
0
0
0
0
2
0
0
3
0
0
2
0
2
0
1
0
0
2
0
1
1
0
0
0
0
0
0
0
2
1
1
0
0
0
0
3
3
0
0
0
0
0
1
2
0
1
0
0
0
0
2
1
3
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
5
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
4
0
1
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
3
0
1
1
1
0
0
0
0
1
1
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
4
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
2
2
0
0
0
1
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
3
0
0
0
2
3
0
0
0
0
0
1
0
2
1
0
0
0
0
1
0
1
2
0
0
0
0
2
0
2
0
2
0
0
1
0
0
1
2
0
0
5
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
1
0
3
0
0
0
0
0
0
1
0
0
4
1
0
1
2
5
0
4
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
3
1
1
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
1
0
1
1
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
3
0
0
3
2
0
1
0
1
0
0
3
0
0
0
0
10
0
0
3
0
0
2
0
2
0
0
0
0
2
2
3
0
1
0
0
0
2
0
3
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
2
0
0
2
2
0
1
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
2
0
0
1
2
0
2
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
1
2
0
0
1
0
0
0
2
0
0
1
1
0
1
0
0
0
1
0
0
10
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
1
0
2
1
0
2
0
0
0
0
0
0
5
0
0
0
0
1
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
2
0
0
1
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
3
0
2
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
2
1
0
0
1
0
0
0
2
0
2
1
0
2
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
2
2
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
2
0
0
0
2
0
1
2
0
0
1
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
1
2
0
1
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
4
2
0
0
0
1
0
2
0
0
0
3
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
2
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
3
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
4
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
2
5
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
2
1
2
0
0
0
0
0
0
2
0
3
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
1
0
0
6
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
1
4
0
1
1
0
0
0
1
10
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
2
0
0
1
0
0
0
0
0
2
0
1
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
1
2
0
1
0
0
0
2
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
3
2
0
3
0
0
3
0
0
0
0
0
0
5
0
1
0
0
1
0
1
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
3
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
3
0
1
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
2
1
0
1
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
7
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
2
0
4
0
0
0
0
3
0
0
0
0
1
0
0
2
0
0
0
1
0
2
1
0
3
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
8
0
0
0
0
2
0
2
0
0
2
0
0
1
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
1
0
0
1
3
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
2
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
2
2
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
5
0
1
2
1
1
0
0
2
0
0
2
0
2
1
1
0
0
0
0
1
0
2
0
0
0
0
0
5
0
0
0
0
2
0
2
0
0
0
0
2
0
2
2
2
0
2
5
0
2
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
1
0
0
1
0
2
0
2
0
0
0
0
0
0
1
3
0
2
0
2
0
0
0
0
0
0
0
2
1
0
3
0
2
0
0
0
1
0
0
1
0
1
0
0
1
0
1
6
0
0
0
0
0
0
1
0
1
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
4
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
1
0
1
0
2
0
0
1
0
2
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
6
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
2
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
2
0
2
0
1
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
1
0
1
2
0
0
0
0
1
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
3
0
2
0
1
0
0
1
2
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
3
0
0
0
0
1
1
0
5
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
1
0
3
0
2
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
3
0
1
0
0
3
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
4
0
2
0
0
0
0
0
2
3
0
0
0
0
1
1
0
0
0
2
0
0
2
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
2
0
0
2
0
2
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
1
1
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
1
2
0
0
0
2
2
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
1
2
2
2
0
0
2
1
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
3
1
0
0
0
0
6
0
0
0
0
2
0
0
1
0
0
1
2
1
2
0
0
6
0
0
0
1
0
0
1
2
0
0
0
0
2
0
0
4
0
1
0
0
0
0
0
1
0
2
0
5
0
2
1
0
1
1
2
1
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
1
0
0
0
0
0
0
1
4
2
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
2
0
2
3
0
0
4
1
0
0
2
0
0
0
0
1
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
2
2
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
1
4
0
0
0
0
1
0
2
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
6
0
3
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
1
0
0
2
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
2
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
2
1
0
1
0
0
0
0
2
0
1
0
1
0
1
0
0
0
0
1
4
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
2
0
1
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
2
0
2
2
0
0
0
0
1
1
2
0
1
0
2
1
0
0
0
0
2
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
3
2
0
1
2
1
1
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
1
3
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
2
2
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
3
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
1
1
0
4
0
0
0
0
0
0
0
0
2
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
3
1
0
1
0
0
2
0
6
2
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
1
0
3
0
0
0
0
0
0
0
2
0
1
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
7
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
4
0
0
0
0
2
0
0
2
0
2
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
2
2
2
0
0
2
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
2
0
0
0
0
0
1
0
0
0
2
0
0
3
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
1
1
0
0
0
2
0
0
0
6
0
0
0
1
1
0
0
0
0
3
0
0
0
1
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
2
2
0
0
0
1
0
0
1
0
2
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
2
3
0
0
0
0
0
1
0
0
0
3
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
2
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
9
0
2
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
1
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
1
0
0
0
2
3
1
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
2
2
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
3
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
1
0
0
2
2
0
0
1
0
1
1
1
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
1
0
0
0
1
0
0
4
1
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
1
2
0
1
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
1
0
0
1
0
0
1
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
1
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
2
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
2
2
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
1
0
0
0
0
2
0
0
0
0
1
2
1
0
0
0
0
1
0
2
1
0
0
0
2
0
0
0
0
2
1
0
2
0
2
1
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
4
0
0
0
0
0
0
0
2
2
0
1
0
0
2
2
0
0
0
0
0
2
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
1
1
1
0
0
2
0
0
0
7
0
0
2
0
0
0
0
0
0
0
1
0
1
2
0
0
2
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
8
0
0
0
0
0
2
3
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
2
0
0
2
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
2
3
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
1
1
3
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
3
0
0
1
0
0
1
2
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
2
0
0
2
0
0
0
0
4
0
0
0
0
0
0
0
2
5
0
1
0
0
0
0
0
0
0
2
1
2
0
0
3
0
0
2
0
2
0
1
0
0
2
0
0
0
0
0
0
2
1
0
6
2
0
0
2
0
0
1
2
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
3
0
0
2
0
0
0
0
0
0
0
1
0
3
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
1
2
0
0
1
2
0
0
0
0
0
1
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
5
0
0
0
2
1
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
3
0
2
0
2
0
1
0
0
0
0
1
6
0
0
0
4
0
0
0
3
2
0
0
0
2
3
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
1
0
2
2
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
3
0
0
1
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
4
0
4
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
1
2
0
0
0
0
2
0
1
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
1
0
0
0
0
2
1
0
2
0
1
0
2
0
2
2
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
1
0
0
1
1
0
0
0
0
1
0
4
0
0
0
1
0
0
0
2
0
1
1
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
1
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
2
2
0
2
3
0
0
0
0
1
0
3
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
1
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
1
7
1
0
0
0
0
0
0
2
0
0
0
0
0
4
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
5
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
2
2
0
1
0
0
1
0
0
0
2
2
1
0
0
0
0
2
0
3
0
1
0
0
0
2
0
1
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
1
2
0
0
0
1
1
0
1
0
0
0
1
0
0
0
2
2
1
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
1
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
1
5
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
5
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
2
0
2
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
3
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
4
0
0
4
0
2
0
1
0
2
1
2
0
0
0
0
0
0
1
0
0
0
2
1
0
1
0
5
0
0
1
0
0
1
2
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
3
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
2
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
2
0
1
0
3
0
0
0
3
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
11
0
0
2
0
0
0
0
2
0
1
0
0
0
1
0
2
1
1
0
2
0
1
2
0
0
0
0
0
1
0
1
2
0
2
1
0
0
1
1
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
2
1
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
1
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
4
0
0
2
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
2
0
1
0
1
0
1
2
1
0
0
0
1
0
1
1
2
2
3
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
1
0
0
1
0
0
0
0
0
2
3
0
0
0
5
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
1
1
0
1
0
0
2
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
5
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
1
1
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
1
2
2
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
2
0
0
1
2
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
2
0
0
0
0
0
4
3
0
2
0
0
0
0
0
2
0
2
1
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
4
0
0
0
2
1
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
4
1
0
3
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
3
0
2
1
0
0
0
0
1
0
1
0
0
0
0
0
0
2
2
0
0
0
1
0
3
0
0
2
1
5
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
1
0
0
2
5
2
0
2
1
1
6
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
2
1
0
0
1
0
0
0
0
0
1
0
0
1
3
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
7
0
1
1
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
2
0
1
0
0
0
2
0
0
2
1
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
2
2
0
2
0
0
0
0
1
2
0
1
0
1
2
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
5
0
0
1
0
2
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
3
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
7
0
1
0
2
0
0
0
0
0
3
1
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
4
2
0
0
0
0
0
0
1
2
0
0
0
0
2
2
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
6
0
0
0
0
0
0
1
0
1
2
2
0
0
0
2
0
0
4
2
0
0
0
0
2
2
0
0
0
0
0
1
0
1
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
2
2
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
1
0
4
2
0
0
0
0
0
0
0
2
0
2
2
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
1
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
4
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
2
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
3
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
2
0
0
0
2
1
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
1
2
0
1
1
0
0
2
0
0
0
0
0
2
0
0
1
1
0
1
0
2
0
2
2
0
0
0
2
0
2
0
2
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
1
1
0
3
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
7
0
0
0
1
1
5
0
0
0
0
0
0
0
0
0
1
1
0
3
0
2
0
0
0
2
0
2
0
0
0
1
0
2
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
2
0
2
1
2
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
4
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
3
0
0
2
0
2
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
3
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
2
0
2
0
0
1
0
0
0
1
0
2
0
4
1
0
0
1
0
0
0
1
0
2
0
0
0
1
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
2
6
2
2
2
1
2
2
0
3
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
1
2
1
1
0
0
0
0
1
0
2
0
0
0
0
2
2
0
0
0
1
1
0
0
0
0
0
2
1
0
0
0
1
1
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
2
2
2
2
0
2
0
1
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
3
2
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
2
0
0
2
1
0
0
0
0
1
0
0
0
0
2
1
0
1
0
0
0
0
1
0
4
0
1
0
0
2
1
0
0
2
0
1
0
1
0
1
0
1
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
3
0
0
3
0
2
0
2
0
2
0
1
2
0
2
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
1
2
0
2
0
0
0
1
0
0
0
1
0
0
2
0
0
1
0
2
2
0
0
3
0
0
0
0
1
0
1
2
0
1
0
0
0
0
0
0
2
2
0
0
1
4
0
0
0
2
0
2
0
0
0
0
0
2
1
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
3
0
1
0
2
0
2
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
4
0
2
0
1
0
0
8
2
0
1
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
2
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
2
0
3
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
1
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
2
0
0
0
1
0
1
0
0
1
0
0
1
0
3
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
3
0
0
0
0
0
0
0
1
1
0
1
0
0
0
3
0
0
2
0
0
1
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
1
2
0
0
0
0
2
1
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
1
0
3
0
2
1
1
0
0
0
1
0
0
0
2
2
0
0
0
0
2
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
2
1
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
2
1
0
0
1
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
2
0
2
2
2
0
0
0
2
1
0
0
2
0
0
0
0
0
0
2
0
0
0
3
0
0
0
2
1
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
5
0
1
1
0
2
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
3
0
0
0
0
2
0
0
0
2
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
2
0
0
2
0
2
0
1
2
2
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
5
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
1
1
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
4
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
3
0
0
0
2
0
0
0
0
3
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
1
0
1
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
3
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
3
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
1
0
0
0
0
0
0
1
0
3
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
1
0
2
0
0
0
3
2
0
2
0
0
0
1
0
0
0
0
1
0
2
3
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
2
1
0
1
0
0
0
0
1
2
0
0
0
1
0
1
0
3
0
0
0
2
8
0
0
1
0
1
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
2
0
1
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
1
3
0
0
0
2
8
0
0
0
0
1
0
1
1
0
1
0
0
1
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
4
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
1
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
7
0
1
0
0
0
2
0
0
0
3
0
0
7
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
1
0
4
0
1
2
2
0
0
0
0
2
0
1
0
0
2
0
0
1
1
0
1
0
0
0
0
4
0
2
0
0
0
3
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
1
1
0
2
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
2
2
0
2
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
1
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
2
0
1
0
0
0
0
0
2
1
0
1
0
0
0
1
0
2
1
0
0
0
0
0
0
0
10
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
2
1
2
0
1
2
0
0
2
1
0
1
0
1
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
1
1
0
2
0
0
1
0
0
0
0
0
1
0
0
0
1
0
2
1
0
0
0
0
1
2
0
4
1
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
1
2
2
0
2
0
2
2
0
0
0
0
2
0
0
1
0
1
0
2
0
0
0
0
3
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
1
0
0
1
1
0
0
0
1
0
0
0
0
0
1
3
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
2
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
1
0
1
5
0
0
0
2
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
2
0
0
0
2
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
1
0
0
0
0
0
2
1
0
0
1
0
0
0
0
1
0
0
2
0
3
0
1
0
0
0
0
1
0
2
0
2
1
1
0
0
0
0
1
0
1
0
0
0
2
0
1
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
1
2
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
6
0
1
0
0
0
2
0
1
0
3
0
1
0
0
0
3
0
0
1
0
0
0
2
0
1
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
3
4
5
1
0
0
0
3
0
2
2
1
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
4
3
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
3
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
6
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
1
1
2
0
0
1
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
1
1
0
0
0
1
0
0
0
1
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
1
0
4
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
5
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
4
0
0
1
2
0
2
2
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
1
1
1
2
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
2
0
0
2
0
1
0
0
0
2
0
1
0
0
0
2
0
3
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
6
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
2
1
0
1
0
2
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
2
2
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
5
0
0
2
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
1
0
2
0
1
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
1
0
1
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
1
2
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
3
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
1
2
0
0
0
0
2
0
1
2
2
0
0
0
0
0
2
0
1
0
1
0
0
3
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
1
1
1
0
0
2
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
4
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
1
1
1
3
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
3
0
2
0
0
1
0
0
0
3
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
1
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
7
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
5
0
1
0
1
0
1
0
0
1
0
2
2
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
1
0
0
0
0
0
1
0
2
1
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
1
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
2
6
0
0
0
1
0
0
3
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
3
2
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
1
1
0
1
0
1
0
0
0
3
0
0
2
2
1
0
2
0
0
1
0
0
1
0
1
0
0
2
0
2
0
1
4
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
2
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
1
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
5
0
0
0
0
0
0
0
0
1
2
0
0
1
1
0
1
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
1
1
1
0
0
0
0
0
1
0
0
2
2
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
1
2
0
1
0
0
2
0
0
0
0
0
0
3
0
0
2
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
2
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
1
0
1
0
1
2
0
0
0
0
2
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
1
3
0
2
0
0
2
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
2
0
0
0
0
3
0
0
2
0
0
0
0
4
0
0
2
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
2
2
0
0
3
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
3
2
3
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
1
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
3
0
0
5
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
1
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
1
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
1
2
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
4
2
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
2
2
2
0
0
0
0
0
0
2
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
5
0
3
1
2
1
1
0
1
1
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
1
0
2
0
0
2
1
1
0
2
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
3
3
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
3
0
0
2
1
0
0
1
0
0
1
2
0
1
2
0
2
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
2
0
0
0
0
0
1
1
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
4
0
0
0
1
0
3
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
3
1
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
1
2
0
1
0
3
0
1
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
7
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
2
2
0
0
2
0
2
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
1
0
4
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
2
0
1
0
0
1
0
0
0
2
0
0
0
1
0
0
2
0
1
2
0
0
11
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
2
0
1
0
0
0
1
0
1
0
0
2
0
1
1
1
0
1
0
0
0
2
1
0
0
0
3
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
4
0
0
0
0
4
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
1
3
0
0
0
0
0
0
0
0
0
1
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
3
0
0
0
0
2
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
3
0
2
0
1
2
0
2
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
2
0
2
1
0
0
2
0
0
1
0
0
1
3
0
0
0
0
0
2
0
0
0
1
0
2
3
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
2
2
2
0
0
0
1
1
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
1
2
1
1
0
1
1
0
2
1
0
0
0
0
3
1
1
0
1
0
1
0
0
0
0
0
0
0
1
2
2
0
3
2
0
0
1
1
0
0
0
0
1
1
1
1
0
0
0
0
0
2
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
6
1
0
0
2
1
0
0
1
0
0
0
3
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
2
1
0
0
1
1
0
2
0
0
0
1
1
0
0
2
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
2
1
0
0
1
0
2
1
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
1
1
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
4
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
1
1
2
0
0
0
0
2
1
0
0
2
0
0
1
0
0
1
0
0
0
0
1
2
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
2
0
0
0
1
1
0
2
0
1
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
1
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
7
0
0
0
0
0
0
1
0
2
0
2
0
1
0
0
0
2
0
0
1
0
0
1
2
0
1
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
1
0
0
0
2
0
0
0
0
0
0
1
2
0
1
0
4
0
0
0
0
3
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
2
0
0
2
1
4
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
5
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
5
0
1
0
0
1
2
0
0
0
2
1
2
0
0
0
1
0
0
1
0
2
0
2
1
1
0
5
0
0
0
0
1
1
0
0
0
0
2
0
0
0
3
0
0
3
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
1
0
1
1
2
0
0
1
2
0
0
0
2
0
2
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
3
0
0
2
2
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
3
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
4
0
0
1
2
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
2
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
1
2
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
5
0
0
0
1
2
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
1
0
1
1
0
1
0
0
0
2
0
0
0
0
6
0
0
0
0
2
1
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
2
0
0
0
3
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
1
0
1
0
0
3
1
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
1
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
2
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
1
3
0
0
2
0
0
0
0
0
0
0
0
0
0
4
0
2
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
2
1
0
2
0
0
0
2
0
0
4
0
4
2
1
0
1
0
0
0
2
0
0
0
0
7
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
1
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
2
1
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
2
1
1
2
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
1
0
0
2
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
3
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
1
0
2
0
3
0
3
0
0
0
0
0
1
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
2
4
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
5
0
1
0
0
0
2
0
0
0
0
0
1
2
1
0
0
0
2
2
1
1
1
0
0
0
7
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
3
0
0
1
0
0
0
1
0
0
0
0
1
4
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
1
0
0
0
2
1
0
0
0
2
0
0
0
1
0
0
0
1
3
2
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
3
3
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
1
0
2
0
0
1
0
0
0
0
1
1
0
1
0
2
0
0
0
0
0
1
1
0
0
0
2
2
0
0
2
0
0
0
1
2
0
2
2
0
0
0
1
0
1
1
1
1
0
0
0
0
0
7
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
3
0
0
0
4
0
0
2
0
0
2
0
1
2
0
0
0
0
0
0
2
2
0
1
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
2
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
1
0
2
0
2
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
2
0
0
2
2
2
0
0
0
2
2
0
2
1
0
2
0
0
2
0
0
1
2
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
1
0
2
1
3
0
2
2
0
0
0
0
4
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
1
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
3
2
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
1
0
2
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
2
0
2
1
3
2
1
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
3
2
2
1
0
3
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
1
0
2
0
0
0
1
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
2
1
5
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
1
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
2
5
0
0
0
0
0
0
2
0
0
2
0
2
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
3
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
1
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
1
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
11
0
2
0
0
0
1
2
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
2
0
0
0
0
0
0
1
3
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
1
2
0
0
1
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
2
0
2
1
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
3
1
1
0
0
1
0
1
1
0
0
0
1
2
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
2
3
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
3
2
1
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
3
1
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
2
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
5
0
0
0
0
1
0
0
0
0
3
0
1
0
1
2
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
4
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
1
2
0
0
1
0
0
1
0
0
0
0
1
2
0
4
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
1
0
0
2
0
0
0
0
1
0
2
0
0
0
0
2
0
0
3
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
2
6
0
0
0
1
0
0
0
1
0
0
1
0
0
0
2
0
1
1
0
0
0
2
0
0
0
1
0
0
0
3
0
0
0
2
0
1
3
1
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
1
0
6
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
2
0
4
0
0
1
2
0
0
7
0
0
0
0
0
0
2
0
0
2
0
1
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
1
0
0
0
5
2
1
0
0
0
2
1
0
0
1
0
2
3
5
0
3
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
2
1
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
2
2
0
2
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
3
0
0
0
2
0
0
0
2
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
8
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
8
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
2
10
0
0
1
2
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
3
1
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
2
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
3
0
0
0
3
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
1
0
0
1
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
2
0
1
2
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
1
2
2
0
3
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
4
0
0
0
1
0
0
2
0
0
0
1
0
2
1
0
1
0
0
2
1
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
5
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
2
2
0
0
0
0
1
0
0
1
0
0
0
0
1
2
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
1
1
0
3
0
0
0
0
0
2
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
3
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
2
0
3
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
1
0
1
0
0
0
0
0
1
2
0
2
2
0
0
0
2
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
7
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
4
0
1
0
0
2
0
0
1
3
0
3
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
3
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
5
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
1
0
2
1
0
0
0
0
3
2
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
1
1
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
1
2
0
0
1
0
1
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
2
2
3
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
1
0
0
0
0
0
1
0
0
2
2
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
3
0
0
2
2
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
2
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
2
0
0
2
1
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
1
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
2
0
0
0
1
0
2
0
0
1
0
1
0
0
0
3
1
1
1
0
2
0
0
0
1
2
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
3
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
9
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
1
0
3
1
0
2
0
0
2
0
2
0
0
3
0
1
0
0
0
1
0
0
2
0
0
0
7
0
2
3
0
0
1
0
0
4
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
5
0
0
2
1
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
2
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
1
0
1
0
0
3
1
0
1
0
0
0
0
5
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
2
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
2
1
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
3
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
1
1
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
3
0
0
0
0
0
0
1
2
2
1
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
1
0
0
0
0
1
0
2
0
2
0
1
0
3
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
1
2
0
2
1
0
1
0
0
2
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
2
0
0
4
0
0
0
1
1
0
0
0
0
0
0
0
8
1
0
0
2
0
0
1
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
4
3
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
1
1
0
4
1
0
0
0
0
3
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
3
0
3
0
2
0
0
0
1
0
1
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
4
2
2
0
1
0
1
1
1
0
2
0
0
0
0
0
1
1
0
0
0
0
2
2
0
0
0
0
0
0
0
1
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
1
0
3
0
0
0
0
0
0
2
2
0
1
0
0
0
4
0
2
2
0
0
0
1
1
1
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
3
0
0
0
3
0
2
1
0
3
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
5
0
0
0
0
0
4
0
0
0
1
0
0
1
0
0
0
0
0
0
0
6
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
3
2
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
3
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
1
0
0
4
2
0
0
2
1
2
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
4
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
5
0
1
1
2
0
0
0
0
1
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
1
0
2
2
0
0
0
0
0
0
0
2
1
0
0
0
2
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
1
1
1
0
1
4
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
4
0
0
0
3
1
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
3
0
0
2
0
1
0
0
1
2
0
0
0
0
0
2
3
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
2
2
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
2
3
2
2
0
0
0
0
1
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
3
2
0
0
0
0
0
1
0
0
0
1
1
2
0
0
2
2
0
2
0
0
0
4
0
0
0
2
2
0
1
1
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
2
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
2
0
2
1
0
1
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
3
0
2
2
0
0
1
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
4
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
5
0
1
1
0
3
0
0
1
0
0
0
2
0
1
0
0
0
0
0
1
0
0
1
2
1
0
0
1
0
0
0
0
0
1
0
1
2
0
0
0
0
0
4
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
8
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
3
0
0
0
2
0
1
0
0
3
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
1
1
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
3
0
0
2
0
0
4
0
2
0
2
0
0
0
1
0
0
0
0
2
0
5
0
0
1
0
1
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
2
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
1
1
0
0
1
0
5
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
2
0
0
0
0
2
2
0
1
0
0
0
0
0
0
3
0
0
0
0
1
0
0
2
3
0
0
1
0
0
4
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
3
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
3
0
2
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
1
0
0
2
0
0
2
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
1
1
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
1
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
1
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
1
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
1
3
0
0
1
0
0
0
0
1
6
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
4
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
6
0
0
1
0
0
1
0
0
2
1
1
3
0
2
0
2
1
0
2
0
0
3
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
4
2
0
0
0
0
0
2
3
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
1
0
1
0
0
0
0
0
0
0
3
0
0
0
2
0
1
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
3
1
0
2
0
0
2
2
1
0
1
0
0
0
0
0
0
0
2
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
2
0
1
0
0
0
0
2
0
3
0
2
1
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
11
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
3
0
2
2
2
0
2
0
0
0
2
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
2
0
0
0
2
0
2
0
0
1
0
0
0
0
0
5
2
0
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
5
0
0
0
0
2
2
0
0
0
1
0
0
0
0
3
0
0
0
1
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
2
2
3
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
3
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
4
0
0
2
2
0
0
0
0
0
0
2
3
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
1
1
0
0
2
0
1
0
0
2
0
0
2
0
0
1
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
4
0
1
0
1
0
0
0
0
2
1
0
1
0
2
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
2
2
0
0
3
2
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
3
0
0
0
2
3
0
0
0
0
2
2
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
9
0
2
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
1
1
0
1
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
1
0
0
0
0
1
2
1
2
0
0
2
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
2
5
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
9
0
0
0
3
0
0
0
1
0
1
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
2
0
0
3
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
2
2
0
0
0
0
0
1
2
3
0
0
0
0
0
0
2
0
0
4
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
2
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
2
2
1
0
0
0
0
2
0
0
2
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
2
2
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
3
2
0
0
0
0
3
1
2
0
1
0
3
0
0
0
2
1
0
1
3
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
3
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
2
0
1
0
0
0
0
2
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
1
0
1
0
0
0
4
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
2
4
0
0
0
0
0
2
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
5
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
1
0
2
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
2
0
0
0
0
1
0
1
1
0
0
0
0
7
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
3
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
4
2
0
1
2
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
2
0
1
2
1
0
0
0
0
0
0
3
2
1
0
0
0
0
1
0
1
0
0
2
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
6
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
2
0
1
3
0
0
3
0
0
2
0
0
2
0
1
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
3
0
1
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
1
0
0
0
3
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
1
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
2
0
0
0
0
0
0
2
0
0
0
3
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
1
0
2
0
0
0
1
0
0
1
0
1
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
5
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
3
1
1
0
0
0
0
0
0
2
0
0
0
1
0
1
1
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
3
2
2
0
4
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
3
0
0
0
1
0
1
0
0
0
1
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
4
0
0
1
0
0
3
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
2
0
2
0
0
0
1
0
0
3
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
1
2
2
0
0
0
1
0
0
0
6
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
2
1
0
3
2
0
0
1
0
0
2
0
0
1
0
0
0
2
1
1
0
0
0
0
0
2
0
0
1
0
3
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
3
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
1
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
3
0
2
0
0
0
1
0
0
0
0
0
1
1
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
2
2
2
1
0
0
0
1
2
3
2
0
0
1
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
3
0
5
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
4
0
0
0
0
0
1
0
1
2
0
0
1
0
0
0
1
1
0
0
0
2
0
2
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
5
0
0
1
0
3
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
2
0
1
0
0
2
0
0
1
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
1
0
0
0
1
0
2
0
2
0
3
3
0
2
0
0
1
0
0
0
3
0
0
0
0
1
4
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
1
1
0
1
0
0
0
1
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
2
0
0
1
0
0
1
3
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
6
0
2
0
2
0
0
2
0
1
2
1
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
2
1
0
0
1
3
0
1
0
1
2
3
2
0
0
0
2
0
1
0
0
0
0
0
2
2
0
3
0
0
0
1
0
0
0
0
2
0
3
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
8
0
0
1
2
0
0
0
0
0
0
0
3
0
3
1
0
0
0
1
1
2
0
1
0
0
0
3
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
3
0
1
0
2
0
0
0
2
0
0
2
0
0
0
0
1
0
1
2
0
1
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
3
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
4
0
0
0
0
1
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
2
0
0
0
0
0
0
4
2
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
8
0
0
0
0
1
0
0
0
6
0
1
1
1
1
0
0
0
0
0
1
0
8
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
2
1
0
2
0
0
1
2
1
0
0
1
0
3
1
0
0
1
0
1
0
0
0
0
2
0
1
0
1
0
0
0
1
0
0
0
0
0
0
3
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
6
0
0
1
2
0
6
0
0
0
1
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
1
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
1
0
5
2
0
0
0
2
0
1
8
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
1
3
0
0
0
0
0
0
2
0
1
1
0
2
0
0
0
0
3
1
0
0
0
0
0
0
2
0
0
0
1
3
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
7
2
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
1
0
2
0
0
0
2
1
3
0
0
0
0
0
0
0
0
0
0
7
0
2
0
0
2
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
2
0
0
0
0
0
0
0
1
1
1
0
1
2
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
2
1
1
0
0
0
2
0
0
0
0
0
2
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
1
2
0
0
1
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
1
1
2
0
0
0
2
2
1
0
0
2
0
0
0
4
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
2
1
0
1
0
0
0
0
1
1
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
2
1
1
1
1
0
3
0
0
0
0
0
0
0
2
0
1
0
0
1
0
1
2
2
0
0
0
0
0
3
0
0
0
3
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
1
0
0
2
1
0
0
1
0
0
0
0
3
0
0
0
4
0
0
2
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
1
3
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
2
0
0
2
1
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
1
1
3
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
2
0
2
0
1
0
0
1
0
0
2
0
2
1
0
0
2
0
2
0
2
2
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
2
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
1
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
5
0
2
0
0
0
0
3
0
0
0
0
0
0
3
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
2
0
2
0
0
2
0
2
1
4
2
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
5
1
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
3
0
1
2
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
5
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
3
0
1
0
2
0
0
2
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
1
0
2
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
2
2
0
2
0
2
0
0
0
0
0
1
0
1
1
0
4
0
0
1
2
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
3
0
4
0
2
0
0
2
0
0
0
1
0
1
0
0
0
1
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
2
0
0
1
0
2
1
0
0
0
0
0
0
0
0
3
0
0
0
1
1
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
1
1
0
2
0
1
0
0
0
1
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
6
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
2
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
11
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
2
0
0
2
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
3
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
2
1
0
0
0
1
1
2
0
2
0
2
1
0
0
0
2
0
0
0
0
0
2
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
1
0
0
2
1
0
0
0
2
0
2
2
0
2
0
0
0
0
0
1
0
0
0
0
0
2
2
0
1
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
1
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
1
3
0
2
0
2
0
0
0
0
2
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
2
1
1
0
0
0
0
0
2
0
0
1
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
2
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
4
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
2
2
0
1
1
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
4
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
1
1
1
0
5
2
1
0
0
0
1
0
2
2
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
1
0
0
0
6
0
1
0
0
0
0
0
2
0
1
1
0
0
0
0
2
0
0
0
0
2
0
0
3
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
1
0
0
1
0
1
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
1
0
2
0
0
0
0
1
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
2
0
2
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
2
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
1
0
0
0
0
0
5
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
2
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
2
1
0
0
0
0
0
3
0
0
0
1
0
0
5
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
1
0
1
0
1
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
2
1
0
0
0
0
0
2
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
1
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
2
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
2
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
2
0
3
0
3
0
0
1
2
0
0
0
1
3
2
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
2
2
0
0
1
0
0
1
0
0
0
1
0
0
0
0
2
0
1
0
0
0
2
3
0
0
0
0
0
0
0
0
2
0
8
0
0
0
0
0
0
1
0
1
0
0
1
4
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
1
0
1
0
6
0
0
0
0
6
0
0
0
2
1
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
2
3
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
1
2
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
5
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
3
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
2
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
1
1
0
0
1
0
1
0
4
0
0
0
0
0
1
1
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
2
0
0
0
0
1
0
0
3
0
2
0
1
0
0
1
0
1
2
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
3
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
1
0
0
0
1
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
1
0
1
0
0
2
0
0
1
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
2
0
1
1
0
1
0
0
0
1
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
3
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
2
0
0
1
3
0
0
1
0
0
0
0
0
0
1
0
0
0
0
3
0
2
0
0
1
0
0
0
0
1
0
0
0
2
1
0
0
1
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
1
2
0
1
0
0
1
1
0
0
0
0
0
0
2
0
1
3
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
2
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
2
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
2
1
2
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
3
0
0
0
1
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
2
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
2
1
0
0
14
0
1
0
0
0
3
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
1
0
1
0
1
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
2
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
3
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
2
1
3
0
0
0
0
1
2
1
2
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
2
0
2
0
4
0
0
0
0
2
0
3
1
1
1
1
0
0
2
0
0
1
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
1
0
0
2
0
0
2
0
0
0
0
0
5
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
6
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
1
2
0
0
1
0
0
1
1
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
2
1
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
2
1
0
3
0
3
0
0
0
2
0
0
0
0
0
2
0
0
0
2
1
0
2
1
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
2
0
1
0
0
0
0
1
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
2
0
0
1
0
0
0
0
0
0
1
0
0
1
1
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
4
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
13
0
0
1
2
0
0
0
0
1
2
0
1
4
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
2
0
0
2
0
0
0
0
5
0
2
0
2
1
0
2
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
2
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
1
1
0
0
2
0
2
0
0
0
1
1
1
0
2
2
1
2
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
1
0
0
1
0
1
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
1
2
2
0
0
2
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
1
0
1
0
0
0
0
2
0
3
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
1
1
1
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
2
0
2
0
0
0
0
0
1
1
0
0
2
1
0
0
2
1
2
0
4
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
3
0
2
3
0
0
0
0
0
0
0
0
0
0
0
6
3
0
0
0
1
0
0
0
4
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
2
2
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
2
0
2
2
1
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
2
0
2
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
1
0
0
3
0
0
0
0
0
0
0
2
1
0
0
2
1
3
0
2
0
2
0
0
4
1
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
1
0
1
6
0
0
0
0
0
0
1
0
2
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
6
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
1
1
0
2
1
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
1
0
2
0
0
1
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
2
0
0
0
1
2
0
0
0
0
1
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
3
2
0
0
2
2
1
0
0
0
0
1
0
2
0
0
0
0
1
0
1
0
4
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
5
0
2
1
0
1
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
2
0
0
1
1
1
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
1
0
2
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
3
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
1
1
0
2
0
1
0
0
0
0
2
0
0
0
3
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
5
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
2
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
8
0
0
0
0
0
0
0
0
2
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
4
2
0
2
1
0
0
0
2
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
2
0
1
0
4
1
0
0
0
2
0
0
0
0
2
5
3
0
0
0
0
0
2
0
0
0
0
2
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
2
1
0
1
0
2
0
1
0
0
0
1
2
6
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
1
0
4
2
1
2
0
0
2
0
0
0
2
0
0
0
4
0
2
0
0
0
0
0
1
0
1
0
0
0
2
1
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
2
0
0
0
0
1
0
0
2
2
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
3
3
0
0
0
0
0
0
0
2
2
0
2
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
4
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
2
0
0
0
1
0
0
0
0
0
0
0
2
5
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
1
1
0
0
1
1
0
0
1
1
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
2
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
1
2
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
2
0
1
0
0
1
0
0
0
1
1
0
2
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
3
1
0
0
0
0
0
0
0
1
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
1
4
0
0
0
0
0
0
1
2
0
0
1
2
0
0
0
0
0
0
0
0
2
3
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
1
0
0
1
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
2
0
0
0
2
2
0
0
0
2
0
2
2
1
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
2
2
1
0
1
0
1
0
2
1
0
0
0
0
0
1
0
0
0
5
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
2
1
1
0
0
2
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
2
1
1
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
1
0
0
1
0
1
1
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
2
1
4
0
0
0
0
0
2
0
0
0
0
5
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
1
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
2
0
0
0
2
0
1
3
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
1
0
0
0
3
0
0
0
0
0
2
0
1
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
1
6
2
0
0
2
0
1
0
3
0
0
0
1
1
0
0
2
2
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
5
0
2
2
0
1
0
3
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
2
0
2
0
0
3
2
1
0
0
0
0
0
0
2
0
0
0
2
2
0
2
0
0
1
2
0
1
0
0
0
2
1
0
0
1
0
1
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
3
0
1
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
2
0
0
0
1
2
0
1
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
2
3
0
2
0
1
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
8
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
3
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
2
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
3
0
0
0
0
2
0
0
0
1
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
2
1
0
0
4
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
4
0
0
0
0
0
0
0
0
3
3
0
0
3
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
2
0
4
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
2
0
1
0
1
0
0
1
0
0
0
5
0
2
0
0
2
2
0
0
0
0
0
0
1
2
3
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
2
0
0
0
2
0
4
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
2
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
4
2
3
0
2
0
0
0
0
0
0
1
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
1
2
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
6
1
2
2
1
0
0
0
3
3
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
1
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
1
0
3
0
0
1
0
0
0
1
0
0
0
0
0
0
2
3
0
0
0
2
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
2
1
2
1
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
6
0
0
0
1
0
0
2
0
0
1
1
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
1
0
2
0
0
1
0
0
0
0
1
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
1
2
0
2
1
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
4
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
1
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
1
3
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
2
0
1
0
1
2
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
3
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
1
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
3
5
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
8
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
2
0
1
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
5
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
3
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
5
0
2
3
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
1
2
0
0
0
0
0
1
2
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
2
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
1
0
1
1
2
0
0
1
2
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
1
1
0
2
0
0
0
3
1
0
0
0
0
2
2
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
5
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
1
0
0
0
2
2
0
2
0
0
0
1
0
2
1
1
0
2
2
1
0
1
0
0
0
0
0
1
0
0
3
0
2
0
0
1
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
1
0
0
1
1
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
1
1
1
0
3
5
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
2
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
1
0
0
0
0
7
1
2
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
4
0
0
1
0
2
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
4
0
0
5
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
1
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
4
0
0
0
0
2
0
0
0
0
0
6
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
1
2
1
0
3
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
1
0
0
0
0
2
0
0
0
0
1
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
1
2
0
1
0
2
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
1
1
0
2
0
2
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
1
1
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
1
0
2
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
2
0
0
0
0
0
1
0
0
0
0
3
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
3
0
1
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
1
0
1
0
2
0
0
0
0
0
1
3
0
0
0
0
0
0
2
0
1
0
0
0
0
2
1
0
0
1
5
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
1
0
0
3
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
1
1
0
1
0
2
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
1
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
2
0
2
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
1
2
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
7
0
1
0
0
0
0
1
0
0
0
0
1
0
0
6
0
1
2
0
0
0
0
1
1
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
2
2
0
1
0
0
0
0
0
0
2
1
2
0
1
0
0
0
0
0
0
0
0
0
1
2
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
2
1
2
0
1
1
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
3
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
2
0
1
2
0
0
1
0
0
0
1
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
2
0
1
0
0
4
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
3
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
2
7
0
0
2
0
2
2
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
2
0
0
1
0
0
0
1
1
0
1
1
2
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
5
1
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
5
0
0
2
3
0
0
0
0
1
3
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
5
2
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
1
0
0
0
0
3
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
4
1
0
2
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
1
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
1
0
0
1
2
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
1
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
10
1
1
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
3
0
0
0
7
0
1
3
0
0
0
0
0
3
0
1
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
2
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
2
2
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
2
0
0
2
1
0
2
0
0
0
0
1
0
3
0
1
0
2
0
1
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
2
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
1
2
0
0
0
1
2
0
0
0
0
0
0
1
0
1
0
1
0
2
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
5
0
0
1
0
2
1
0
0
0
3
0
1
0
0
1
0
0
0
2
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
1
0
0
2
0
3
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
1
2
1
0
0
2
0
1
0
1
1
2
0
0
0
0
1
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
2
0
0
2
1
2
2
0
0
0
2
3
0
0
2
0
0
0
3
0
3
2
0
0
0
0
0
6
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
1
0
2
0
0
1
0
1
2
0
2
0
1
0
3
1
0
0
0
0
0
0
0
0
0
2
0
3
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
1
0
1
0
0
2
2
0
0
0
0
0
2
0
0
1
4
0
1
0
0
1
0
0
0
0
0
2
0
2
0
1
2
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
3
0
0
1
0
0
1
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
1
3
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
2
0
1
0
0
0
3
0
0
0
2
1
0
0
0
0
2
0
0
2
0
0
0
2
0
1
0
0
1
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
3
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
3
0
0
0
0
0
2
0
0
0
0
1
2
0
1
0
6
0
0
2
0
0
0
0
2
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
4
0
0
0
0
0
2
2
0
0
0
0
1
2
0
0
0
2
0
0
0
1
0
1
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
5
1
0
0
0
0
2
0
1
0
0
0
1
0
0
1
0
0
0
1
2
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
1
0
0
0
1
0
0
0
2
1
0
1
1
2
0
3
0
0
2
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
1
1
2
0
2
0
0
2
0
2
2
0
0
0
1
0
0
1
0
0
0
0
0
3
0
1
0
0
1
0
1
0
0
3
1
0
3
2
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
4
2
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
1
1
0
0
0
0
2
0
0
0
0
0
0
4
2
0
0
1
3
0
0
2
0
1
2
0
1
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
3
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
2
4
0
3
0
1
0
0
0
0
0
1
0
0
0
0
2
1
0
5
0
0
0
0
0
1
0
0
3
0
1
0
2
0
0
3
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
3
0
1
0
0
2
0
0
0
0
0
0
3
1
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
6
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
7
1
0
1
0
0
0
0
0
0
0
0
1
2
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
1
0
0
2
2
0
1
0
1
0
1
1
0
2
0
0
0
3
2
1
0
3
0
0
0
0
0
2
2
0
2
0
1
1
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
7
0
0
0
0
0
0
1
0
3
0
0
0
1
1
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
1
0
0
3
0
0
2
0
0
1
0
0
0
1
0
1
0
2
0
0
2
1
0
2
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
2
0
0
2
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
1
2
0
2
0
0
4
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
3
3
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
2
0
1
0
0
0
0
1
0
0
0
1
2
0
2
0
1
0
1
0
1
0
0
2
0
0
1
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
1
0
0
13
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
4
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
6
1
0
1
2
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
2
0
0
1
0
2
0
0
2
0
1
0
0
1
1
0
0
1
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
2
0
0
1
0
1
2
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
2
0
0
0
0
1
0
2
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
2
5
0
2
0
0
0
0
1
1
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
6
1
0
0
2
0
1
0
0
1
2
1
1
3
1
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
1
1
1
0
0
0
0
0
5
1
2
0
0
0
2
0
2
0
0
0
0
4
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
3
1
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
3
1
2
0
0
0
1
0
2
0
1
1
0
0
2
0
0
0
0
2
0
1
2
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
1
2
0
0
2
0
0
0
0
2
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
1
1
3
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
1
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
2
0
0
1
1
0
6
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
2
0
1
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
1
0
1
1
0
0
1
0
0
2
1
1
0
1
1
2
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
2
0
2
0
0
0
2
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
1
1
0
2
2
0
0
0
1
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
7
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
2
0
0
1
2
0
0
5
2
1
0
1
0
1
0
0
0
0
0
0
0
2
1
1
0
1
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
2
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
4
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
3
0
0
2
0
0
1
0
1
1
0
0
0
0
0
2
0
3
0
0
0
0
0
2
0
0
0
0
0
0
2
2
2
0
1
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
4
0
0
1
1
0
0
0
1
1
0
0
0
0
0
2
0
2
3
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
2
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
5
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
2
0
0
2
0
0
2
0
0
1
0
1
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
6
3
0
0
1
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
1
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
5
2
3
0
0
2
0
1
0
0
0
0
1
2
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
2
0
0
0
1
0
2
0
5
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
2
1
4
0
1
0
0
2
0
0
2
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
8
2
0
1
0
0
0
0
0
2
1
0
0
0
1
3
0
2
1
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
4
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
2
2
0
0
0
2
1
1
2
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
1
0
1
0
2
1
0
0
0
1
0
0
0
0
0
0
1
0
3
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
1
0
0
0
0
0
0
0
8
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
1
0
0
1
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
2
0
2
0
2
0
2
1
0
0
0
2
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
1
1
1
0
1
0
1
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
1
1
0
1
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
1
0
1
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
2
0
0
0
0
1
0
1
0
2
0
1
2
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
6
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
2
0
0
0
2
2
0
0
3
2
0
1
0
5
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
2
0
2
0
1
0
2
2
0
0
0
0
3
0
0
0
0
1
0
2
1
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
2
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
7
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
3
2
0
2
0
3
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
2
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
3
0
0
2
0
4
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
3
1
0
2
0
1
2
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
1
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
9
0
2
0
1
0
0
1
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
1
2
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
3
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
2
0
2
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
1
0
1
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
3
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
3
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
4
2
0
0
0
0
2
2
0
0
0
1
0
2
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
15
0
3
0
0
0
3
2
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
2
0
0
0
1
0
0
3
1
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
2
1
2
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
2
2
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
4
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
6
0
3
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
2
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
2
1
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
2
0
3
0
2
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
3
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
5
0
0
0
0
0
0
0
0
0
3
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
3
0
1
3
0
1
0
1
2
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
1
0
0
0
3
0
0
1
0
1
0
0
1
1
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
1
0
2
0
0
1
0
0
0
0
4
2
1
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
7
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
3
1
0
0
0
1
3
0
1
0
1
3
2
0
1
1
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
2
0
0
2
1
0
3
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
2
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
2
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
3
2
0
0
1
3
2
2
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
1
1
0
0
0
0
0
1
0
2
0
0
0
0
4
2
0
0
0
0
0
0
0
0
1
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
3
5
0
0
0
2
0
0
0
0
1
0
2
0
1
1
2
2
2
0
1
0
0
0
2
0
2
0
0
2
2
0
0
2
0
0
2
0
1
2
0
0
0
2
0
1
3
0
0
0
0
0
0
0
2
0
0
0
4
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
9
0
1
0
0
2
1
0
1
1
2
2
3
0
1
0
0
5
0
0
0
0
1
0
2
0
0
3
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
3
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
1
2
0
0
0
2
0
0
0
2
0
1
0
2
0
0
0
0
0
0
2
2
0
0
2
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
8
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
2
0
0
0
0
0
2
2
0
0
0
0
1
0
1
9
2
2
0
2
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
2
1
1
0
2
1
0
0
0
0
0
0
2
0
0
0
1
0
2
1
1
2
0
0
3
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
2
0
2
0
2
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
3
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
3
0
0
2
0
0
0
1
2
2
0
0
0
0
1
2
0
0
0
2
0
0
0
1
1
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
5
0
0
1
0
4
0
0
0
0
0
0
0
0
0
5
3
0
0
0
2
0
0
0
1
2
1
0
0
0
0
0
0
1
0
0
0
0
3
0
5
0
3
2
0
0
0
2
0
3
2
2
2
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
3
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
2
0
0
0
4
0
0
1
1
0
0
0
4
0
1
2
0
0
0
0
0
0
0
0
0
2
1
0
2
0
2
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
3
1
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
11
3
0
0
3
0
0
2
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
4
2
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
1
5
0
0
0
0
1
0
2
0
0
2
0
0
0
2
2
0
2
0
2
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
2
0
0
0
0
0
1
1
1
1
1
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
1
0
1
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
2
1
2
0
1
0
2
0
0
1
0
0
1
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
3
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
3
0
2
0
1
0
4
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
1
1
2
0
0
5
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
3
2
0
0
3
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
2
1
2
0
0
0
2
0
2
0
0
0
0
1
1
0
0
5
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
1
2
0
2
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
5
2
1
0
1
1
0
0
0
2
0
3
0
1
0
1
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
1
0
0
1
0
0
1
0
0
1
0
0
0
0
3
0
0
2
0
0
1
0
1
0
0
0
0
1
0
2
2
0
0
3
0
2
0
2
0
1
0
6
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
2
0
1
2
1
1
2
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
1
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
2
0
1
2
0
2
2
0
0
1
0
0
0
0
0
0
0
1
0
0
2
3
0
2
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
2
2
3
0
0
3
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
1
0
0
2
0
4
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
2
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
3
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
2
0
2
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
3
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
2
3
2
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
3
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
1
0
2
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
2
3
0
0
0
0
2
1
0
0
0
0
0
0
2
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
2
0
1
0
2
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
4
0
0
1
1
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
2
0
0
2
0
0
1
1
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
5
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
3
2
0
3
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
2
3
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
2
0
0
3
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
2
0
0
2
0
1
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
5
0
0
0
0
1
0
0
1
3
1
0
0
1
0
2
0
0
2
0
0
0
0
2
0
0
0
5
0
2
0
2
6
0
0
2
2
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
1
0
0
1
4
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
3
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
1
0
0
0
0
3
2
0
0
0
0
0
1
0
0
0
1
0
1
0
2
0
0
0
0
0
1
0
0
1
0
0
1
0
0
3
0
0
2
0
1
0
0
0
0
2
1
0
0
1
0
0
2
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
1
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
6
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
1
2
0
2
2
1
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
1
0
0
0
4
2
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
4
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
2
1
0
0
0
0
0
6
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
1
0
0
2
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
1
0
0
0
0
1
0
0
1
0
2
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
4
1
0
0
0
0
0
1
1
0
0
0
0
0
3
1
0
0
0
2
0
2
0
4
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
1
0
0
0
0
2
3
0
1
0
0
0
0
2
0
1
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
3
0
0
0
0
0
0
0
2
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
5
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
3
0
0
0
0
0
2
2
0
0
0
3
0
1
2
1
0
1
0
0
3
0
1
0
0
0
0
3
0
2
0
0
3
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
5
0
2
0
0
0
2
2
2
4
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
3
2
0
0
0
1
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
2
0
1
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
1
1
1
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
2
0
0
1
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
1
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
1
0
10
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
1
6
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
1
10
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
3
0
2
2
3
0
0
2
0
1
0
0
0
0
0
0
2
0
2
4
0
0
0
2
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
1
0
0
0
2
3
0
0
0
0
1
0
0
0
0
1
3
0
2
0
2
1
1
0
0
0
0
0
2
0
0
2
0
0
0
2
0
1
3
1
1
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
1
0
1
0
0
2
2
0
0
2
2
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
1
3
4
2
0
0
0
0
0
0
0
0
1
0
0
4
0
2
2
0
0
4
1
0
0
0
2
0
0
2
0
0
0
0
1
0
0
1
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
1
0
0
0
2
0
0
3
1
0
0
0
1
0
0
0
5
0
1
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
3
1
3
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
1
0
1
0
0
0
1
4
0
0
0
0
2
0
1
0
2
3
0
1
0
2
0
0
0
0
5
0
1
0
0
0
0
3
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
1
0
0
1
1
2
1
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
1
1
0
2
0
0
0
1
0
0
0
0
0
0
0
1
2
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
2
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
4
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
1
1
0
1
0
0
1
0
6
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
1
0
0
1
0
1
0
2
0
0
2
2
0
0
2
2
0
0
2
1
0
0
1
0
3
0
0
0
0
1
2
2
1
1
2
0
0
0
1
1
0
0
0
0
1
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
1
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
5
2
0
0
2
0
1
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
2
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
2
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
1
0
0
0
2
0
0
0
1
0
0
0
0
0
2
1
2
0
0
0
0
2
0
0
0
0
0
0
1
0
1
4
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
2
2
1
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
1
2
0
3
0
0
0
0
0
0
1
0
0
1
2
0
0
0
3
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
2
0
0
3
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
5
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
6
2
0
0
0
0
0
1
0
2
0
1
0
3
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
1
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
3
0
1
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
1
2
0
1
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
2
0
0
0
2
0
2
0
0
4
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
4
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
1
0
0
2
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
2
2
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
1
3
0
2
2
1
1
1
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
4
0
2
0
0
0
2
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
1
1
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
2
1
0
2
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
4
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
1
2
2
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
3
0
1
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
2
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
3
0
0
0
0
2
2
1
0
2
2
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
2
0
1
0
0
0
0
5
2
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
2
1
0
1
0
0
0
2
0
0
0
1
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
5
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
1
2
0
0
0
0
1
0
2
0
1
1
0
1
0
2
0
0
1
0
0
0
2
2
0
0
1
0
3
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
3
0
5
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
5
2
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
2
0
1
1
1
0
0
1
0
0
2
0
0
0
0
0
0
0
3
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
3
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
2
0
0
2
1
0
0
0
0
2
0
0
2
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
5
0
1
0
0
0
2
2
0
3
1
0
0
0
1
1
0
0
0
3
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
1
1
2
0
0
0
0
0
1
4
1
1
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
2
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
2
0
2
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
2
1
0
0
0
1
0
0
2
0
1
0
0
2
0
2
0
0
2
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
1
1
1
0
2
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
1
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
2
0
0
0
1
1
0
0
0
1
0
0
0
1
3
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
1
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
3
0
0
2
4
0
0
0
0
0
2
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
2
3
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
2
0
1
2
0
1
0
0
1
0
0
1
0
10
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
1
1
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
2
0
0
2
1
0
1
0
1
0
0
0
1
0
0
2
0
0
0
0
0
2
0
1
2
2
0
1
0
0
2
0
0
0
0
0
1
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
1
2
1
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
2
0
1
0
1
1
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
2
1
2
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
5
0
1
1
1
2
0
0
0
2
2
0
1
1
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
2
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
7
0
3
1
0
0
1
0
0
2
1
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
1
3
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
3
0
0
2
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
2
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
2
1
1
0
1
0
0
0
3
0
0
0
2
0
0
0
1
0
0
1
0
0
3
1
3
0
0
0
0
1
0
0
0
0
0
0
5
0
0
0
0
0
2
0
2
2
0
0
1
2
0
0
2
1
0
0
0
0
0
2
0
1
0
1
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
5
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
1
3
0
0
1
0
1
1
0
2
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
3
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
2
0
2
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
4
1
0
1
0
0
0
2
0
2
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
7
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
1
2
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
3
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
2
1
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
2
0
1
2
0
1
0
0
0
2
0
0
0
0
1
0
0
1
1
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
2
0
1
2
0
0
1
0
0
0
0
0
1
0
1
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
2
2
0
0
0
1
2
0
0
0
0
1
1
0
0
1
0
2
0
0
0
0
2
1
2
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
2
0
0
0
3
1
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
2
2
0
0
0
1
2
0
0
0
0
0
7
0
0
0
0
0
0
0
0
1
1
3
0
0
0
1
0
0
0
0
1
0
1
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
1
0
0
0
1
0
4
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
1
0
0
0
0
0
3
2
3
0
1
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
1
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
3
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
1
0
0
0
1
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
1
2
2
3
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
2
1
0
0
0
0
0
2
1
1
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
10
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
3
0
0
0
0
1
0
2
0
0
0
0
0
0
2
2
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
4
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
3
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
3
0
3
1
1
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
2
1
0
0
1
0
0
0
0
2
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
2
0
2
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
2
0
0
1
0
0
3
0
0
0
6
0
0
2
0
2
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
1
2
0
1
0
2
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
1
3
2
1
0
2
0
0
2
1
0
0
1
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
4
2
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
1
1
0
0
2
0
0
0
0
0
0
5
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
1
0
2
0
0
3
0
0
1
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
2
1
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
1
0
0
0
0
5
0
0
0
0
0
0
0
0
0
2
0
0
0
7
0
0
3
0
0
0
2
2
0
0
0
2
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
2
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
1
0
0
0
2
0
0
1
0
4
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
3
1
0
0
0
0
0
0
2
0
1
1
1
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
1
2
2
2
0
0
0
2
0
2
0
2
1
0
0
1
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
2
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
1
1
0
2
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
4
2
0
0
0
0
0
2
1
0
2
0
0
0
4
1
0
0
0
0
5
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
2
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
1
2
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
2
3
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
2
1
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
2
0
2
0
1
0
0
0
1
0
2
0
0
0
0
1
2
3
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
1
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
3
1
0
1
0
2
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
3
2
0
0
0
2
2
0
3
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
2
0
0
0
2
0
2
1
0
1
2
0
2
0
0
5
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
5
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
4
1
1
3
0
0
2
0
2
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
1
1
1
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
3
1
0
0
0
1
0
0
0
0
1
2
0
2
0
0
0
2
1
1
2
0
2
1
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
3
0
0
1
1
0
0
2
0
1
3
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
8
4
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
3
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
1
2
2
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
2
0
1
0
1
0
2
0
2
2
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
6
1
1
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
1
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
2
0
3
0
1
2
2
0
0
2
0
0
0
0
1
0
2
3
1
2
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
1
0
1
0
0
0
1
0
0
0
0
0
0
1
2
0
1
0
1
0
0
2
0
0
0
1
0
3
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
2
1
0
0
0
1
0
0
1
1
2
2
2
0
0
0
0
0
0
0
0
3
1
3
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
2
0
0
0
0
2
1
0
0
0
1
0
0
9
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
1
0
0
0
1
3
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
1
2
0
1
0
0
1
0
1
0
0
0
2
0
0
3
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
1
0
1
0
0
1
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
2
1
0
1
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
5
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
1
0
1
1
2
0
4
1
0
0
0
0
1
0
0
0
1
0
0
0
0
2
1
0
1
0
0
1
2
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
11
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
1
0
0
0
1
0
0
2
0
0
2
0
0
3
0
0
0
0
0
3
1
0
0
0
6
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
3
0
0
0
2
0
1
0
1
0
0
0
2
0
0
0
1
0
0
0
2
0
0
6
3
6
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
1
1
0
10
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
7
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
1
2
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
2
0
1
1
0
0
2
0
2
1
0
0
1
0
0
3
0
0
0
0
2
1
2
0
0
0
0
0
1
0
0
1
0
1
0
2
0
0
0
0
0
4
0
0
2
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
5
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
1
0
1
1
2
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
5
0
0
1
2
0
0
2
0
3
1
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
2
0
0
0
2
3
0
2
2
0
3
1
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
3
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
3
0
0
0
0
2
0
0
0
0
3
0
1
0
0
0
0
2
0
0
1
0
0
2
0
0
1
0
0
2
0
2
0
0
0
1
2
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
9
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
3
0
0
1
2
0
0
0
0
0
5
0
1
1
1
0
3
0
0
0
0
0
0
0
0
0
0
1
0
1
2
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
3
0
0
0
0
2
0
2
0
0
0
0
2
2
5
0
0
1
2
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
1
0
0
0
1
0
2
0
0
1
0
0
0
4
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
3
0
1
0
0
0
2
5
1
0
0
0
0
3
0
1
0
0
0
1
0
0
3
2
2
1
0
0
0
0
1
0
0
2
0
0
3
0
0
1
1
0
2
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
1
2
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
2
0
0
0
0
0
0
3
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
2
0
9
0
1
0
2
0
0
1
0
1
0
0
3
0
0
0
0
3
0
0
0
0
0
0
0
2
2
0
4
0
0
0
0
0
0
0
1
0
0
9
1
2
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
3
0
0
0
0
2
0
0
0
0
0
5
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
3
0
2
1
2
0
0
0
1
0
0
0
0
1
3
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
2
0
0
2
0
0
1
0
0
0
1
0
4
2
3
0
0
0
0
0
0
0
0
3
1
0
3
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
1
0
0
2
1
2
0
1
0
0
1
0
1
1
6
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
5
0
2
2
0
0
1
0
2
0
0
0
0
0
1
0
1
0
0
1
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
2
0
0
2
3
0
0
0
2
0
0
0
0
0
0
1
0
0
1
1
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
2
0
0
1
0
0
0
0
0
2
0
1
1
0
0
2
0
0
0
0
4
1
2
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
2
1
2
0
0
2
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
1
2
0
0
0
0
2
0
2
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
1
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
1
0
0
0
0
2
0
1
0
3
1
0
0
0
1
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
2
0
1
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
3
0
1
0
0
0
0
0
0
0
0
0
2
2
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
1
1
3
0
0
0
2
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
4
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
3
0
2
3
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
2
0
0
3
2
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
3
1
0
0
0
1
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
2
3
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
1
2
0
2
0
2
0
0
0
0
1
0
0
3
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
5
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
2
0
2
0
0
1
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
1
0
1
0
2
0
2
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
2
0
0
1
2
0
1
1
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
2
1
1
0
0
1
1
0
0
0
2
0
3
2
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
5
2
0
0
0
0
0
2
0
0
2
1
0
0
2
0
0
0
2
0
0
0
0
1
2
2
2
0
1
4
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
2
0
0
1
1
0
0
0
0
0
2
1
0
0
1
1
2
0
0
2
1
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
2
0
0
2
2
0
0
1
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
1
0
0
1
0
0
1
0
2
0
0
0
4
0
2
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
2
0
0
0
0
0
2
0
2
1
0
0
2
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
1
0
0
3
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
3
0
0
2
0
0
3
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
2
0
2
0
0
0
1
1
0
2
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
2
0
0
1
0
2
0
0
3
0
0
0
0
0
0
0
1
1
1
0
0
11
0
0
0
0
0
0
0
0
0
0
1
3
0
2
0
0
0
0
2
0
0
0
0
1
1
2
0
0
0
0
0
0
2
0
1
0
1
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
1
2
1
0
0
0
2
9
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
1
0
0
0
0
5
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
2
2
0
8
0
0
0
2
1
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
1
1
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
3
1
4
0
0
0
1
0
0
2
0
0
0
0
1
0
2
0
0
1
0
0
4
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
1
11
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
2
2
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
1
0
2
2
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
1
0
0
0
0
2
2
1
0
0
0
1
1
0
2
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
4
0
0
0
3
0
0
0
0
0
2
0
0
3
2
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
3
2
0
0
0
0
0
0
1
0
0
0
1
0
3
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
1
0
0
0
1
2
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
1
0
0
1
0
0
1
0
0
1
0
0
2
0
0
1
2
2
0
0
0
0
2
0
2
0
2
0
0
0
0
2
2
1
0
0
2
2
1
0
0
2
0
2
0
0
0
0
4
2
0
0
0
0
0
2
1
2
1
0
2
0
0
0
0
0
0
3
2
0
3
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
2
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
2
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
1
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
3
0
2
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
2
0
0
2
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
2
3
0
1
0
0
1
1
0
1
2
2
2
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
1
0
0
0
0
1
0
6
6
1
0
0
0
0
0
1
0
0
1
0
1
0
1
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
2
1
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
1
2
2
0
0
1
0
2
0
0
0
0
2
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
2
0
2
2
0
0
0
1
0
0
0
0
0
1
1
0
0
1
2
0
4
1
2
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
3
0
1
0
1
0
0
0
3
0
0
0
1
0
3
0
0
0
0
0
0
8
1
0
3
1
0
5
0
0
2
0
1
0
0
2
0
0
2
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
2
2
0
0
1
2
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
1
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
5
0
0
0
2
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
3
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
4
0
0
0
0
1
0
0
0
0
7
0
2
0
0
1
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
2
0
2
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
2
2
1
0
1
3
0
2
0
0
0
0
1
0
1
1
0
0
0
0
1
1
1
0
0
3
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
2
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
3
0
0
1
0
0
0
2
0
0
0
0
1
0
6
1
2
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
2
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
2
0
0
0
3
5
1
0
0
0
1
1
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
1
2
3
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
2
0
2
2
2
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
3
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
1
1
1
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
1
2
0
0
1
0
2
0
0
0
0
3
1
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
2
0
1
2
0
1
1
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
1
4
0
1
1
3
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
1
0
2
0
4
0
0
0
2
0
2
0
0
0
0
0
0
2
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
1
0
0
0
3
0
0
0
1
0
1
0
1
1
0
1
0
0
0
0
2
0
0
0
0
0
2
0
1
3
0
1
1
2
0
0
3
2
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
3
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
3
0
0
0
0
1
2
2
1
1
2
0
0
2
0
0
0
0
0
1
3
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
5
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
2
0
0
1
0
1
0
0
0
0
1
0
1
5
2
0
0
0
0
0
0
1
1
1
0
2
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
2
0
0
0
0
2
3
1
0
0
0
0
0
1
0
2
2
0
3
0
0
0
0
0
2
0
0
0
0
0
3
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
4
0
0
0
0
0
0
0
1
1
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7
0
0
3
0
4
0
0
0
0
2
0
2
1
0
2
2
0
2
1
0
0
0
0
0
1
2
0
0
0
2
2
2
2
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
2
0
0
0
0
0
0
2
0
1
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
2
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
1
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
3
0
0
1
2
0
0
0
2
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
1
1
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
2
0
0
2
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
1
1
1
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
3
2
0
2
0
0
0
0
0
4
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
1
2
1
0
1
0
2
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
2
1
0
2
0
0
5
0
3
0
0
0
0
2
0
0
1
0
1
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
2
0
2
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
2
0
0
0
3
0
0
0
0
0
0
1
2
0
6
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
3
0
2
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
3
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
3
0
0
0
0
0
0
0
0
1
2
0
2
0
0
2
0
0
0
0
0
1
0
2
0
1
0
0
0
2
1
0
0
0
1
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
4
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
1
1
0
0
0
2
0
0
0
1
0
3
0
1
0
0
3
0
0
1
0
0
0
0
1
3
0
0
1
0
1
0
2
0
2
2
0
0
1
0
0
0
0
0
3
0
0
2
1
1
4
0
0
0
2
0
0
2
1
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
1
0
0
1
0
0
0
4
0
2
0
0
1
0
0
0
0
0
0
0
1
1
3
0
0
0
0
1
0
0
0
1
0
0
2
2
1
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
3
0
0
0
0
0
0
0
0
4
1
0
0
2
0
2
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
1
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
2
0
0
0
3
2
0
0
1
0
1
0
0
2
0
0
0
2
0
0
1
0
0
2
0
1
0
0
0
0
0
0
2
0
2
0
0
1
2
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
2
0
1
2
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
2
0
3
0
0
1
1
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
1
0
3
0
0
0
0
2
0
0
0
5
0
2
2
0
0
0
4
0
2
0
2
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
1
0
1
0
0
0
2
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
2
3
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
1
0
0
3
0
2
0
0
0
6
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
3
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
1
0
0
0
0
1
0
0
0
1
0
0
0
7
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
3
0
0
0
0
0
3
2
2
1
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
1
2
0
1
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
2
1
2
2
0
0
1
1
1
0
0
0
1
1
0
2
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
1
0
0
0
1
0
0
0
4
1
0
0
0
0
2
0
2
0
0
0
0
1
2
2
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
1
4
5
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
3
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
5
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
2
0
2
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
1
2
0
0
0
0
0
1
2
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
1
0
0
0
0
2
1
1
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
6
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
1
5
1
0
0
3
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
2
1
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
5
2
3
0
0
0
0
0
1
0
23
0
0
0
0
0
3
0
0
0
0
4
0
3
0
2
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
3
0
2
0
2
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
7
0
0
0
1
2
2
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
4
2
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
2
0
2
0
0
0
3
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
5
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
2
0
1
1
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
1
2
0
2
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
1
0
2
0
0
0
0
0
1
0
2
3
0
0
2
0
0
0
0
0
0
0
0
1
3
0
2
0
0
3
0
0
0
0
0
0
2
5
0
4
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
5
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
2
0
0
1
1
0
1
0
0
2
2
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
2
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
4
0
1
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
2
2
0
0
0
0
1
1
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
1
2
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
2
2
1
0
2
0
0
0
0
1
0
3
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
2
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
2
2
0
1
1
0
0
1
0
2
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
2
0
2
0
1
2
0
0
6
1
2
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
2
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
9
2
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
1
5
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
1
1
2
0
0
2
0
0
1
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
3
0
0
3
0
2
2
0
0
2
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
1
0
1
0
1
0
0
0
0
2
0
1
0
0
0
0
1
0
1
0
0
0
2
1
0
0
0
0
5
0
0
0
1
0
1
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
2
0
2
0
3
0
0
3
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
2
0
1
0
0
0
0
1
0
0
2
0
0
0
4
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
3
0
4
0
1
0
0
0
0
0
6
2
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
1
0
0
1
0
2
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
1
0
2
0
0
2
0
2
0
1
2
0
0
0
1
0
0
2
0
0
0
0
1
0
2
0
2
1
0
2
1
0
0
0
0
0
0
0
0
2
0
1
0
2
0
2
0
2
0
0
0
0
0
0
0
0
2
3
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
4
6
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
3
0
0
0
2
1
0
0
1
0
0
0
0
0
9
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
2
0
0
1
0
0
0
0
0
1
6
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
2
3
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
1
2
1
1
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
2
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
1
0
1
7
1
3
0
0
0
0
0
3
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
8
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
4
0
1
0
0
0
0
0
0
0
1
0
7
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
3
0
0
0
1
1
0
0
2
1
0
3
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
1
0
1
0
0
0
3
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
2
1
0
2
0
1
1
0
0
0
0
2
0
2
1
2
0
0
1
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
1
1
2
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
1
0
0
2
2
0
6
0
0
0
0
0
2
0
2
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
5
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
5
0
1
0
0
2
0
0
0
0
0
0
0
3
1
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
2
0
1
0
0
1
1
1
0
0
3
2
1
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
2
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
2
0
0
0
0
2
1
0
1
0
0
2
2
0
0
0
0
0
0
1
0
0
0
1
0
1
2
0
0
0
2
1
0
0
0
1
0
0
0
0
2
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
2
4
0
0
1
0
0
1
0
0
0
1
2
0
1
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
2
0
2
0
1
0
0
2
0
0
0
1
1
0
0
0
1
0
3
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
3
1
3
0
0
0
0
0
0
0
0
1
0
1
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
2
0
0
2
2
1
1
0
0
1
0
0
0
0
0
5
0
0
1
0
0
1
0
0
0
2
1
0
0
2
0
0
0
0
0
1
0
0
1
0
1
0
0
2
1
0
2
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
4
0
0
3
0
0
1
0
2
0
0
0
1
0
1
0
0
0
1
1
0
0
1
1
1
5
0
0
2
0
0
0
0
2
3
1
0
0
0
1
2
0
0
0
0
0
0
0
0
1
1
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
3
1
0
0
1
0
1
0
0
0
2
0
0
0
0
0
1
2
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
3
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
2
0
0
1
0
2
0
2
2
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
3
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
2
0
2
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
3
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
2
1
0
0
0
0
0
1
0
0
1
0
0
2
0
1
0
3
0
0
0
1
0
0
0
1
0
0
1
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
3
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
5
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
3
0
3
0
0
0
2
0
0
1
1
0
0
0
0
2
0
0
1
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
3
0
7
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
2
2
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
5
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
2
5
1
4
0
1
0
0
0
3
3
0
3
1
0
0
0
0
1
1
3
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
6
2
0
0
1
0
2
0
0
2
2
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
10
2
2
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
2
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
3
1
2
0
0
0
1
0
2
0
1
0
0
2
0
1
1
0
1
0
0
0
0
2
1
0
0
0
0
3
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
3
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
3
2
0
0
0
4
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
2
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
1
1
1
2
0
0
1
1
0
0
0
2
3
1
0
0
0
0
1
0
0
0
3
0
3
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
2
3
0
0
0
1
0
0
0
0
0
0
0
0
3
0
1
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
4
2
2
1
0
0
1
0
0
0
3
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
1
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
1
2
0
1
0
2
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
2
1
0
5
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
2
0
0
0
1
2
0
0
0
0
0
4
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
1
3
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
2
1
1
1
3
0
0
0
0
2
0
2
0
0
0
0
4
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
1
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
4
0
3
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
1
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
4
0
0
0
1
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
14
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
2
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
3
0
1
1
0
0
0
1
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
2
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
1
0
0
0
2
2
0
0
1
0
0
0
1
0
1
1
1
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
1
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
3
1
0
0
4
0
0
1
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
6
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
2
0
0
0
0
1
2
1
1
0
0
0
0
0
0
2
0
0
0
2
2
0
1
0
0
0
2
0
0
5
2
0
0
0
0
0
1
0
0
2
0
0
0
1
1
0
1
0
0
0
0
0
8
0
0
0
0
0
0
0
0
0
3
0
2
3
0
0
0
0
6
0
0
0
0
0
5
0
0
0
0
2
1
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
1
2
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
1
0
0
0
2
0
3
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
1
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
4
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
3
0
0
0
0
0
0
0
2
2
2
0
0
2
0
0
0
2
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
1
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
2
0
2
2
0
0
2
1
0
0
0
1
5
0
1
3
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
1
0
1
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
1
0
0
2
0
0
0
0
0
0
2
2
3
0
2
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
2
0
1
0
6
1
0
0
3
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
3
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
2
2
1
2
0
0
0
0
0
0
1
0
0
1
1
0
0
2
0
0
0
0
2
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
1
0
1
0
0
0
2
1
0
0
0
0
1
0
2
0
0
4
2
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
3
2
0
0
1
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
2
0
0
0
0
2
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
2
2
0
0
0
0
3
0
2
0
0
0
1
0
0
0
2
0
0
1
0
0
0
1
0
1
0
1
2
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
1
2
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
3
0
1
3
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
2
0
1
0
0
0
0
2
3
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
2
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
2
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
3
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
2
0
0
2
0
1
0
0
0
3
2
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
2
1
0
0
0
0
3
0
0
2
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
2
0
0
2
2
0
0
0
7
0
0
0
2
0
0
0
0
0
1
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
3
0
4
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
2
1
0
4
0
0
0
0
0
0
0
1
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
3
2
2
0
1
0
0
1
0
0
0
0
2
1
0
0
0
0
2
1
3
0
0
0
1
2
0
0
2
1
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
2
0
0
2
1
0
0
2
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
3
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
5
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
1
0
0
0
0
0
0
2
0
0
1
1
1
0
0
0
0
0
0
0
0
1
2
0
0
8
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
2
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
3
1
0
0
0
0
2
1
2
0
0
0
0
3
8
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
2
2
1
2
1
0
1
1
3
0
0
0
2
1
1
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
2
0
0
0
2
2
1
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
2
2
0
3
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
3
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
1
1
0
0
0
2
0
1
0
2
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
1
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
3
2
1
2
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
1
3
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
3
2
0
0
0
1
0
0
0
0
1
1
0
0
2
1
0
1
0
0
1
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
2
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
2
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
2
2
1
0
0
0
0
0
1
0
2
0
3
0
0
2
0
1
1
0
1
0
4
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
2
0
1
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
4
0
2
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
2
2
2
0
0
0
5
0
2
0
0
0
0
0
1
1
0
0
0
0
1
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
1
0
1
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
3
1
1
0
1
2
0
0
0
0
2
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
2
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
6
0
2
0
0
1
0
0
1
0
0
1
0
0
2
2
2
1
1
1
3
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
2
1
0
0
0
0
4
0
0
0
0
0
0
1
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
2
0
2
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
2
0
0
2
2
2
0
0
0
3
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
2
3
0
0
1
0
0
1
0
0
0
0
0
2
1
0
2
1
0
0
2
0
0
0
0
5
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
3
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
5
0
0
0
0
1
0
3
0
0
0
1
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
2
0
2
0
2
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
6
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
1
1
0
0
0
0
0
1
0
2
0
1
0
0
2
0
0
0
0
2
1
0
0
2
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
2
0
0
2
0
2
0
0
2
0
0
0
1
0
1
0
0
0
0
0
3
2
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
4
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
8
0
0
2
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
2
0
0
3
1
0
0
0
0
0
0
3
0
0
0
1
0
1
0
1
0
0
0
1
2
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
2
0
2
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
4
1
0
0
0
0
1
0
0
1
0
1
0
2
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
1
0
0
0
1
2
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
1
0
0
3
0
2
2
0
1
0
2
0
0
0
1
0
0
0
0
1
1
0
2
1
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
3
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
23
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
2
0
1
2
2
0
0
0
0
0
4
0
0
0
1
0
1
0
0
0
0
1
0
0
2
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
7
0
1
0
1
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
7
0
2
2
2
0
1
0
0
0
1
0
3
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
2
1
0
1
0
0
0
0
6
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
2
0
0
0
1
0
2
0
0
2
0
0
0
1
2
4
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
1
0
0
4
0
1
2
2
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
2
2
0
0
0
1
0
0
0
0
0
2
0
0
1
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
2
0
0
2
0
0
0
1
2
0
2
0
0
0
0
0
0
0
1
0
0
0
3
2
1
0
2
0
3
0
0
2
0
0
0
3
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
2
0
0
0
0
0
0
1
0
0
0
2
2
0
0
4
0
1
0
5
0
0
0
0
0
3
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
7
2
0
0
0
1
0
2
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
3
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
5
0
0
1
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
2
2
0
0
1
0
1
2
1
1
0
1
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
3
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
2
0
0
3
0
1
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
3
0
0
0
1
0
0
2
3
2
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
2
0
0
2
0
0
0
0
3
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
2
1
1
2
0
0
0
0
0
2
0
4
0
0
2
0
0
0
0
3
2
1
0
0
0
2
0
1
2
0
2
0
2
0
1
0
1
0
2
0
0
0
2
0
0
0
3
0
0
0
2
0
0
2
1
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
2
1
0
0
0
0
3
0
0
1
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
4
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
1
0
0
1
1
0
2
0
1
0
0
9
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
2
1
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
3
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
1
1
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
1
2
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
3
0
0
1
0
0
0
6
0
0
0
0
2
5
0
1
1
0
3
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
1
2
0
3
2
0
0
0
0
2
3
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
5
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
5
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
1
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
1
0
3
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
1
0
0
0
2
0
1
0
0
0
1
0
1
2
0
5
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
1
2
0
0
0
1
0
0
0
2
2
1
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
10
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
3
0
0
0
0
0
0
0
1
1
1
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
3
0
0
0
2
4
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
1
0
0
0
0
2
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
2
0
4
1
0
1
1
0
2
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
2
2
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
11
0
0
2
2
0
0
1
0
2
0
1
0
1
0
1
0
2
0
0
0
0
0
0
1
2
1
2
1
1
1
0
1
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
3
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
4
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
2
0
2
0
1
0
0
0
0
0
3
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
5
0
0
0
0
0
0
5
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
2
0
1
3
0
0
0
0
2
1
0
0
0
0
0
0
1
2
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
2
5
0
1
0
2
1
0
1
2
0
0
6
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
1
0
0
0
2
2
0
0
0
6
1
1
0
0
4
0
4
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
1
0
0
0
0
0
0
0
3
0
0
0
0
2
0
1
0
3
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
2
1
0
0
0
2
0
0
1
0
0
0
0
1
0
4
0
1
0
0
3
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
3
1
0
0
0
0
0
2
2
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
2
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
3
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
2
0
0
0
2
0
0
0
1
0
1
2
0
0
0
0
3
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
2
2
1
1
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
1
0
0
0
1
0
1
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
1
1
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
2
1
0
3
0
0
0
0
0
0
1
0
0
0
0
1
0
0
4
0
0
2
2
0
2
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
1
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
5
0
0
0
0
1
0
0
1
1
2
0
6
0
0
0
4
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
4
0
0
1
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
1
6
0
0
3
1
1
1
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
1
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
1
1
0
0
0
4
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
1
0
2
1
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
3
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
3
0
0
0
0
1
0
0
0
2
1
0
0
0
0
1
1
2
0
2
1
0
2
0
0
0
0
0
1
0
2
0
0
0
0
1
4
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
2
0
2
1
1
0
0
2
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
2
2
0
2
0
0
0
0
2
0
2
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
3
2
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
3
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
1
0
1
0
1
0
4
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
1
1
0
0
0
2
1
0
1
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
1
0
0
1
0
5
0
0
0
1
0
1
2
0
2
0
0
0
2
1
2
0
0
0
0
2
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
1
0
1
0
2
1
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
2
1
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
1
2
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
2
0
0
0
0
0
2
0
0
2
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
1
1
0
0
0
0
0
2
1
0
5
2
0
0
1
0
2
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
1
0
0
0
0
0
4
2
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
1
0
1
0
1
0
0
0
1
1
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
3
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
2
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
1
2
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
3
0
0
1
0
0
0
1
0
7
1
0
0
0
2
0
2
0
2
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
1
0
4
2
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
6
0
1
0
1
0
2
1
0
1
2
0
0
3
0
0
0
0
2
0
1
0
0
2
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
1
2
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
3
0
0
1
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
4
1
2
0
1
0
0
0
0
1
2
0
3
0
0
0
2
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
3
0
0
2
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
1
0
0
0
0
0
0
1
0
2
2
1
1
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
1
2
1
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
1
0
2
0
0
0
0
0
0
3
2
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
9
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
4
0
0
0
0
0
0
0
3
0
1
7
0
0
0
2
1
0
0
0
2
1
0
0
0
0
0
0
0
4
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
1
0
2
0
0
1
0
0
0
3
0
0
1
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
2
1
4
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
3
1
0
0
0
0
0
0
0
2
0
0
2
0
0
4
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
1
1
1
0
2
0
0
0
0
2
1
1
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
2
1
0
2
0
1
0
0
0
0
0
3
2
0
0
5
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
2
3
2
1
2
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
2
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
3
0
1
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
1
1
0
0
1
0
0
1
3
1
0
0
1
0
0
3
0
0
1
1
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
6
0
4
0
0
2
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
2
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
5
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
2
2
1
0
0
0
0
0
0
2
2
0
1
0
0
0
1
2
0
2
1
0
0
1
1
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
2
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
5
0
0
2
2
0
0
0
2
0
1
0
0
2
0
1
1
1
0
7
0
0
0
0
0
0
0
0
1
0
0
1
3
1
0
0
0
0
4
2
0
0
0
0
0
0
0
2
0
0
0
3
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
1
0
0
0
0
0
0
1
3
0
0
1
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
1
2
1
2
1
1
1
0
0
0
0
2
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
1
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
1
0
0
3
0
2
0
2
0
0
0
0
0
0
0
2
1
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
3
0
0
0
0
1
2
0
0
0
0
0
0
0
2
20
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
2
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
3
0
0
0
1
0
0
0
1
0
0
2
1
0
0
0
2
0
0
0
0
0
0
1
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
1
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
1
0
4
0
2
0
0
0
1
0
2
1
1
2
2
0
0
0
2
2
0
0
0
1
0
0
2
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
3
3
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
5
0
0
0
0
1
0
0
0
0
0
3
0
2
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
1
0
0
0
0
1
2
0
0
0
1
0
1
2
2
0
0
0
0
0
1
2
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
2
2
1
0
0
0
0
0
3
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
2
0
0
0
0
0
2
0
0
0
1
0
2
0
0
1
2
0
2
0
0
0
0
3
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
3
1
0
0
0
2
1
0
2
0
0
2
0
0
2
2
1
0
2
0
0
0
0
1
0
0
0
0
1
0
4
0
0
0
1
0
0
1
0
0
0
0
0
2
1
1
1
1
1
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
3
2
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
2
1
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
3
0
0
2
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
1
2
2
0
2
0
0
0
0
0
4
0
2
6
0
1
1
0
0
0
2
0
3
1
1
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
2
1
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
1
1
0
0
3
0
0
1
0
0
0
0
1
4
0
2
2
0
0
0
0
0
0
2
1
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
5
0
0
1
0
0
0
0
0
0
1
1
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
2
1
0
0
0
0
0
1
1
2
0
0
0
3
0
2
0
1
0
0
5
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
3
0
0
0
2
0
0
0
1
0
0
2
0
2
0
2
2
1
0
0
1
3
2
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
1
0
1
1
4
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
2
0
2
0
0
1
0
0
0
4
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
1
3
0
0
0
0
0
0
8
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
4
1
2
0
3
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
2
2
0
0
1
0
3
0
0
0
5
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
3
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
3
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
2
2
0
0
0
0
0
2
2
1
0
1
0
1
2
0
0
2
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
5
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
1
0
0
1
1
2
2
0
2
0
2
0
0
0
0
0
1
0
1
0
1
2
2
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
3
0
0
0
0
0
0
0
1
0
2
2
3
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
1
0
0
2
0
1
0
2
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
3
0
0
0
2
0
0
1
1
4
0
0
0
2
1
0
0
0
0
1
0
1
0
2
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
2
0
0
3
2
1
1
0
0
0
0
2
1
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
3
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
1
1
1
0
2
0
2
3
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
1
0
0
0
6
1
1
0
0
0
0
0
1
0
0
0
0
2
0
1
1
2
0
0
2
1
2
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
2
0
0
0
4
1
3
0
1
0
1
0
1
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
2
0
0
0
1
0
4
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
1
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
13
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
1
0
1
0
3
2
2
0
0
0
0
3
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
3
0
1
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
2
1
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
1
0
3
1
1
0
1
0
0
1
2
0
0
0
0
1
0
0
2
0
0
0
0
1
2
0
0
0
0
0
3
0
1
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
1
2
4
0
2
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
1
4
0
2
0
0
6
0
1
1
3
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
5
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
2
3
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
1
0
2
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
2
0
0
0
0
2
0
0
0
0
0
0
0
6
0
1
0
0
0
0
0
0
0
2
1
0
0
0
1
3
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
2
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
4
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
3
0
1
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
4
0
2
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
2
0
0
0
0
1
0
0
1
0
0
0
1
2
0
2
0
0
0
0
2
3
0
0
0
0
1
0
1
3
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
36
0
2
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
2
0
2
2
5
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
1
2
0
0
0
0
0
2
1
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
4
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
2
2
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
2
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
1
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
2
4
0
3
0
0
1
0
1
2
0
1
2
1
0
0
0
0
0
0
0
0
0
2
1
0
1
0
1
0
0
0
2
2
0
0
0
0
0
2
1
1
0
1
0
1
1
0
1
0
0
1
0
0
0
0
0
4
0
0
2
1
0
0
1
2
2
0
0
0
1
6
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
1
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
2
3
3
0
0
0
0
0
1
1
0
2
0
0
3
0
0
0
1
2
0
0
0
0
1
0
0
0
0
2
0
0
2
0
2
0
0
1
0
2
0
2
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
1
2
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
2
0
2
1
0
2
0
0
0
0
0
1
0
0
8
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
3
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
1
0
0
0
2
3
0
0
0
1
0
0
1
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
3
0
0
2
2
0
0
0
0
2
0
1
1
0
2
0
0
0
2
0
2
1
1
0
0
2
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
2
1
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
2
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
2
2
0
0
2
0
1
0
0
1
0
1
1
0
2
0
0
2
0
2
0
1
0
0
3
2
0
2
0
0
2
1
0
0
0
0
2
0
0
0
6
3
0
0
2
2
0
1
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
2
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
3
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
3
0
0
0
0
0
0
2
0
3
0
0
0
0
0
1
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
1
1
2
0
0
2
0
0
0
1
2
0
0
0
0
0
0
6
0
0
0
2
0
0
0
1
2
0
0
0
0
3
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
2
0
0
1
2
0
0
4
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
2
2
1
0
0
0
0
1
0
0
0
0
0
1
2
2
0
1
2
1
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
2
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
3
0
0
0
0
0
1
0
0
0
1
2
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
4
0
2
0
1
0
0
3
2
0
5
0
1
0
2
0
0
0
0
0
2
1
0
0
0
0
0
4
0
0
0
2
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
1
0
1
2
0
0
0
1
0
1
0
0
2
2
0
0
0
5
0
4
3
0
0
0
1
0
0
1
2
0
3
0
2
0
0
0
1
2
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
8
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
1
0
0
3
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
2
0
1
1
0
0
0
3
0
0
0
1
0
0
3
0
0
0
0
0
0
2
0
1
1
0
0
0
0
1
1
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
4
0
0
1
0
0
2
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
3
2
0
2
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
2
1
0
0
1
2
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
1
2
2
3
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
1
0
0
1
0
0
0
3
0
0
0
1
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
3
1
0
0
0
0
0
1
1
0
1
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
3
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
1
0
0
1
2
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
3
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
3
0
0
3
0
0
0
0
0
1
0
0
0
2
0
4
0
0
0
0
0
1
0
3
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
3
2
0
2
0
0
0
0
2
5
0
2
0
0
2
0
0
0
0
0
0
2
3
2
0
4
0
0
0
0
0
1
0
0
3
0
0
1
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
2
0
0
0
1
1
2
0
0
1
1
0
0
2
2
0
0
3
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
2
1
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
9
0
0
5
2
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
2
0
1
0
2
0
0
0
3
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
2
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
10
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
1
2
0
0
2
0
2
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
3
0
0
2
0
0
0
0
2
0
0
1
2
0
1
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
2
0
1
2
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
2
0
2
1
2
0
0
1
2
2
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
3
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
2
0
2
0
1
0
0
0
0
0
0
1
3
1
0
0
0
0
0
0
0
0
1
2
0
2
1
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
1
1
0
2
0
1
1
0
0
2
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
2
1
2
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
2
1
0
0
4
3
0
1
2
2
1
0
2
0
0
0
0
0
0
0
0
0
2
2
0
2
0
1
0
0
2
0
1
0
0
0
0
0
0
1
0
2
2
0
0
0
0
1
1
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
1
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
2
2
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
1
0
2
0
0
0
0
0
1
0
4
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
2
0
0
0
1
0
0
0
1
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
5
1
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
3
0
1
1
0
0
2
0
3
1
0
0
2
0
0
1
0
0
0
2
0
0
0
3
0
0
2
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
3
0
0
2
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
2
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
1
2
0
2
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
3
2
0
0
2
1
0
2
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
3
1
0
2
0
0
0
0
0
0
0
3
0
0
0
0
2
2
0
0
1
0
0
0
0
0
2
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
2
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
2
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
3
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
2
3
1
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
1
0
1
0
2
0
0
0
0
0
0
6
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
3
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
1
1
0
0
1
1
0
0
1
0
0
0
0
0
1
2
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
2
1
1
2
4
0
1
0
0
2
0
0
0
1
0
1
0
2
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
4
1
0
0
2
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
5
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
2
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
2
3
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
3
0
0
2
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
2
4
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
2
0
2
0
4
0
3
0
2
0
0
2
0
0
0
2
1
0
0
0
0
0
0
5
0
2
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
2
0
0
0
2
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
2
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
3
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
6
0
0
0
1
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
2
0
2
0
1
0
1
0
1
3
1
0
0
0
2
0
0
0
2
0
1
0
1
1
1
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
1
3
1
0
0
0
4
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
1
1
0
2
0
0
0
2
0
2
1
0
0
1
0
0
0
2
0
2
0
1
0
0
0
2
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
3
0
0
2
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
2
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
1
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
1
1
2
2
0
0
1
1
3
2
0
0
0
2
3
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
1
2
0
0
0
1
0
1
0
0
0
2
2
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
1
0
0
1
0
0
1
0
0
0
1
2
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
4
3
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
3
2
0
0
2
0
2
1
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
1
0
0
0
0
2
0
0
1
1
0
0
2
2
0
0
0
1
0
0
2
1
0
0
2
0
0
2
2
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
4
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
6
1
0
2
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
2
0
1
0
0
0
0
0
0
3
0
0
1
0
1
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
2
0
0
0
4
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
4
0
1
0
2
0
0
3
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
5
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
2
0
0
2
1
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
3
0
0
1
0
0
0
0
1
0
0
3
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
3
0
0
0
2
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
3
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
32
2
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
1
1
0
0
0
3
2
2
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
3
1
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
6
0
2
0
2
0
0
0
0
5
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
1
0
1
3
0
0
0
1
2
0
0
0
0
1
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
2
0
3
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
3
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
4
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
3
0
0
0
0
0
3
0
2
0
0
0
0
0
3
0
0
1
1
3
0
2
2
1
2
0
2
0
0
0
2
0
1
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
2
2
0
2
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
1
1
0
3
0
0
0
0
0
3
0
2
2
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
3
2
1
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
4
0
2
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
1
2
0
0
1
0
0
0
0
0
0
2
0
0
2
1
2
0
0
1
0
0
0
3
0
2
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
2
1
0
2
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
1
0
2
0
0
0
0
1
1
2
0
0
2
0
0
0
1
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
2
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
4
0
0
0
1
2
3
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
2
2
1
0
1
0
0
0
0
0
2
2
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
4
2
1
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
1
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
1
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
2
1
4
0
0
0
0
0
1
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
1
2
0
0
2
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
3
0
0
0
0
1
2
0
0
1
0
3
0
0
0
0
2
0
2
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
2
1
0
2
0
0
1
1
0
2
4
0
0
0
1
5
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
2
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
1
2
2
0
1
0
0
0
1
0
0
0
0
1
1
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
1
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
13
0
0
2
0
1
0
1
0
0
4
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
4
0
2
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
4
0
0
28
0
0
0
1
0
2
0
0
0
0
0
0
3
2
1
3
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
2
0
1
1
2
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
2
0
1
0
0
1
2
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
4
0
0
2
0
0
3
2
0
0
1
0
1
0
0
0
2
0
2
0
0
0
0
0
1
2
0
3
0
0
1
5
0
1
0
0
0
2
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
1
0
0
0
0
0
2
0
1
2
0
0
0
1
0
0
0
0
1
1
0
0
14
0
0
0
0
0
2
2
1
2
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
2
0
0
2
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
2
0
0
2
2
0
0
0
0
0
1
0
0
1
1
0
1
0
2
0
0
2
1
0
2
0
0
0
0
2
3
0
0
0
0
1
0
0
0
0
0
1
2
1
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
2
0
0
0
2
0
0
1
0
2
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
13
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
4
0
1
1
3
0
0
2
1
0
0
1
1
1
0
0
0
0
0
0
0
0
3
1
1
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
1
0
0
1
1
2
1
2
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
3
0
2
0
0
4
0
2
0
0
1
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
1
2
0
0
2
2
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
3
0
0
0
2
3
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
3
3
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
2
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
1
0
0
2
0
0
0
1
0
3
0
0
0
0
2
0
0
2
2
0
7
0
0
0
0
0
1
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
1
0
0
0
0
0
0
3
0
0
0
1
0
2
0
0
0
0
0
0
2
0
4
0
0
2
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
4
0
1
3
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
1
1
2
1
0
4
0
0
0
0
0
3
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
3
2
0
0
0
0
1
0
7
0
1
3
1
0
0
0
0
0
0
0
0
2
1
0
2
1
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
4
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
1
2
0
2
0
1
0
0
2
0
0
0
0
0
0
4
0
0
0
2
0
2
0
0
2
1
0
0
0
0
0
0
0
2
1
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
2
0
0
1
0
0
2
1
0
1
0
1
0
2
0
0
1
1
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
2
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
2
0
0
0
1
0
0
5
0
1
2
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
3
2
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
2
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
7
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
1
0
2
1
0
5
2
0
0
1
0
2
0
2
0
0
0
0
4
0
0
0
0
0
1
0
3
2
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
1
2
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
2
2
1
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
2
1
0
0
2
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
2
0
2
0
0
0
1
2
0
0
0
1
1
1
0
3
0
2
3
0
0
0
1
2
2
0
2
2
0
2
0
0
1
2
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
8
0
0
0
0
2
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
1
2
1
2
0
2
0
1
2
0
0
0
2
0
1
0
0
0
1
1
0
2
0
1
0
0
0
0
0
2
0
0
1
0
0
0
1
0
5
1
0
0
0
0
1
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
3
0
2
0
0
0
2
2
1
1
0
0
0
1
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
1
0
2
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
2
0
0
0
1
0
1
0
1
0
0
0
1
0
0
2
0
0
0
0
0
3
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
2
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
4
0
0
0
2
0
0
0
2
0
2
1
0
0
0
2
0
0
2
0
0
0
1
0
0
0
3
0
2
1
0
0
1
0
0
0
2
2
10
0
0
1
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
2
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
2
0
4
0
0
0
1
0
0
0
0
1
0
0
0
1
2
0
0
3
0
0
0
0
2
0
0
3
2
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
2
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
3
0
1
0
0
1
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
11
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
1
1
2
2
0
0
0
0
0
0
0
2
0
0
1
0
2
2
0
0
0
1
2
0
0
0
0
1
0
0
0
0
3
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
3
0
0
0
2
1
0
0
2
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
1
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
1
0
2
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
2
0
0
0
0
0
2
0
2
0
8
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
3
0
0
0
3
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
3
0
0
0
0
0
1
0
0
0
0
0
3
0
0
1
0
0
0
1
0
0
0
0
1
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
2
3
0
2
2
0
3
0
0
0
0
2
0
1
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
11
0
2
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
1
0
2
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
2
0
3
0
0
0
0
0
0
0
1
2
2
2
1
0
1
2
0
0
0
2
0
4
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
1
4
0
0
0
5
0
2
0
0
0
0
0
0
0
1
0
1
0
0
2
0
1
0
0
3
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
1
1
0
0
0
0
2
0
0
0
0
1
1
1
2
2
0
2
0
0
2
1
0
1
0
2
2
2
0
0
2
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
3
0
0
2
2
0
4
0
0
0
0
0
0
4
0
0
2
1
1
0
0
0
0
0
0
2
0
0
0
0
0
9
0
0
0
0
0
2
1
0
1
2
1
1
3
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
1
0
0
1
0
2
1
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
1
1
0
0
2
0
0
0
1
2
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
1
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
6
0
0
0
0
0
0
0
0
8
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
6
2
0
0
0
2
0
0
0
2
0
0
2
1
0
2
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
2
0
0
4
0
0
1
1
3
0
1
2
0
0
0
1
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
1
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
4
0
1
1
2
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
2
1
2
0
0
0
0
0
0
0
0
0
1
1
0
1
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
1
0
0
1
0
0
0
0
2
2
0
2
0
2
0
0
0
0
1
0
0
0
0
0
1
1
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
2
0
2
0
0
1
2
3
0
7
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
2
0
1
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
2
3
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
2
2
0
0
0
0
2
0
2
0
0
0
0
0
1
2
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
5
0
0
0
1
1
2
0
0
0
0
0
1
0
0
0
0
0
2
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
1
1
0
0
0
2
0
1
0
0
1
0
6
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
2
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
4
0
1
2
0
0
2
0
0
0
0
3
0
3
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
2
2
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
3
1
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
3
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
1
2
0
1
0
0
0
0
0
0
2
0
0
2
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
1
2
0
0
0
0
2
0
2
1
0
0
0
0
1
0
1
0
3
0
0
2
0
0
0
2
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
2
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
1
0
1
1
0
1
0
0
3
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
1
0
2
0
0
0
1
1
0
1
0
0
0
0
3
0
0
0
0
0
0
0
1
2
0
2
0
0
1
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
2
2
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
4
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
3
0
0
0
0
1
0
2
0
0
1
0
3
0
0
3
0
2
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
3
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
1
0
2
0
2
0
0
0
0
1
6
0
0
3
0
2
0
0
1
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
2
0
2
1
0
0
0
0
3
0
0
0
0
0
0
1
2
0
0
0
1
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
1
1
0
2
0
0
0
0
1
0
0
0
0
0
4
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
2
0
0
0
2
1
2
3
4
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
1
1
2
0
0
0
2
0
0
0
0
0
2
2
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
2
1
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
2
1
2
0
0
0
0
2
0
1
0
3
1
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
2
0
1
1
0
2
0
0
0
0
0
0
3
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
1
4
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
2
0
0
1
0
0
4
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
1
2
2
2
2
0
0
0
0
0
1
0
5
0
0
0
0
0
1
1
0
3
1
0
1
0
0
0
0
1
2
4
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
5
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
3
1
0
0
0
0
0
1
0
0
2
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
3
0
0
0
0
2
0
0
1
0
0
0
1
0
0
2
0
5
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
1
0
0
0
1
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
1
0
0
2
0
4
0
2
0
0
2
3
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
3
1
0
0
0
0
0
0
0
0
3
0
3
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
1
1
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
3
0
0
0
0
0
6
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
1
1
1
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
8
1
0
1
0
5
0
0
1
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
4
0
0
0
1
1
3
0
0
0
2
0
0
0
2
0
1
0
0
3
0
5
0
0
0
1
1
0
2
0
0
0
4
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
2
0
0
2
0
0
1
0
0
1
1
0
0
0
1
2
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
2
0
3
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
2
2
5
2
2
0
0
0
0
0
1
2
1
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
2
0
6
1
2
2
0
0
2
0
0
5
2
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
3
0
0
2
2
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
2
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
2
0
1
0
0
0
7
0
1
1
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
4
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
2
2
4
1
0
0
0
2
2
0
0
2
1
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
2
0
0
0
0
1
0
3
0
0
0
0
4
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
1
0
1
0
0
2
0
0
0
0
1
0
0
0
0
1
2
7
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
2
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
5
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
2
0
1
1
0
2
0
0
0
1
1
0
0
1
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
2
2
1
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
1
0
0
0
2
0
0
0
3
0
0
0
2
0
0
1
1
0
1
2
0
4
2
0
0
0
3
9
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
2
2
0
0
0
0
0
2
1
0
0
1
1
0
0
2
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
3
0
0
0
1
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
3
1
1
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
2
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
1
0
9
0
1
0
0
0
0
0
0
0
0
1
0
3
0
4
1
1
2
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
2
3
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
2
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
1
3
0
2
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
1
0
0
5
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
1
2
0
0
1
0
5
0
1
0
0
0
2
0
0
0
2
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
2
0
2
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
4
0
0
0
0
2
1
2
2
2
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
3
0
0
0
2
0
0
1
1
3
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
3
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
4
0
0
2
0
0
0
1
0
0
3
0
3
0
0
1
1
0
1
0
1
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
2
0
0
0
2
0
1
0
0
1
0
0
2
0
2
2
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
5
0
0
0
0
0
0
0
0
2
2
0
0
0
2
1
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
1
0
0
0
1
0
0
0
2
0
0
2
0
1
6
2
0
0
0
0
0
0
1
0
2
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
3
3
0
0
0
1
0
0
0
0
1
0
0
1
0
2
0
0
1
0
0
2
0
0
0
0
0
2
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
1
0
2
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
2
0
7
0
0
0
0
1
1
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
2
0
0
3
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
1
0
2
3
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
2
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
1
1
3
0
0
0
0
0
0
0
0
5
2
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
1
1
2
1
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
2
3
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
2
2
0
0
0
2
1
0
0
0
0
1
1
1
0
0
0
0
0
0
1
1
2
0
0
0
3
0
0
0
1
1
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
2
0
0
0
4
0
0
1
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
2
0
3
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
2
2
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
1
0
2
0
1
0
0
0
0
2
0
0
0
0
3
0
1
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
1
0
2
0
0
0
2
1
2
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
2
1
1
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
1
2
2
0
0
1
2
0
0
0
2
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
1
2
0
3
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
5
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
2
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
3
0
0
1
1
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
7
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
3
0
0
0
0
0
0
0
1
2
0
0
0
1
1
0
0
0
2
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
2
2
0
2
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
1
2
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
2
1
2
0
0
2
0
0
1
0
0
3
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
2
0
1
0
0
4
0
2
2
0
0
0
0
1
0
2
2
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
3
5
0
1
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
1
0
0
0
1
2
0
0
0
1
2
6
0
0
1
0
2
0
2
0
0
0
1
1
0
0
2
0
0
1
0
0
2
2
0
2
0
1
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
3
0
0
0
0
2
0
0
15
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
3
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
1
2
0
0
0
2
0
0
2
0
0
0
0
0
1
0
1
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
1
2
0
0
2
2
2
1
2
0
0
0
0
0
4
1
0
3
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
3
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
1
0
0
2
2
0
0
0
0
0
4
0
0
2
0
0
1
0
1
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
2
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
1
1
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
3
0
0
1
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
1
0
1
0
0
2
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
3
0
2
1
2
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
3
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
2
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
2
0
0
0
0
0
2
0
3
0
1
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
2
2
1
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
2
0
0
1
0
0
0
0
0
1
0
1
0
5
0
0
0
1
1
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
5
0
1
0
0
0
0
0
0
6
0
0
0
0
0
2
0
0
1
0
1
0
0
2
0
2
0
0
0
0
0
0
2
0
1
2
0
0
2
0
0
0
0
4
0
2
0
0
0
3
2
2
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
2
3
0
0
2
2
0
0
2
0
0
0
0
1
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
2
1
0
0
0
0
2
0
0
1
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
5
2
1
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
1
1
3
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
1
0
0
2
0
0
0
2
0
1
0
0
0
0
0
1
0
0
1
0
0
0
3
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
3
0
0
2
0
0
0
3
0
0
4
0
0
0
2
0
2
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
3
4
2
0
1
2
0
0
0
0
3
0
0
0
2
2
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
1
0
3
0
0
0
1
0
0
0
0
1
7
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
3
0
2
1
0
1
1
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
8
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
2
1
0
0
0
0
0
1
1
1
2
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
3
2
2
0
0
1
0
0
0
0
0
1
2
1
3
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
3
0
0
4
1
0
0
0
0
0
1
0
2
0
0
0
0
0
3
0
0
3
0
2
0
0
2
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
1
1
0
1
2
0
2
0
0
2
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
1
0
0
5
1
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
2
2
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
2
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
5
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
5
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
4
0
0
1
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
2
0
2
1
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
4
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
1
2
0
1
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
1
1
0
0
0
0
2
1
0
0
0
0
4
0
0
1
1
2
0
0
0
1
0
0
3
1
0
0
0
0
0
7
0
0
2
2
4
0
1
0
0
0
0
0
0
2
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
2
3
0
2
0
0
1
2
0
2
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
2
1
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
3
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
4
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
1
1
0
0
0
0
1
1
0
2
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
2
3
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
5
0
0
1
0
2
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
4
1
2
0
0
0
0
0
0
2
0
1
1
0
1
0
0
0
0
0
0
2
2
1
1
1
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
1
0
0
0
1
0
0
2
2
0
0
0
3
0
2
0
0
2
1
2
0
0
0
0
3
0
0
1
1
0
0
2
0
2
0
0
1
0
0
0
0
0
2
1
0
0
0
2
0
2
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
2
0
0
0
0
2
2
0
0
0
0
1
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
1
0
0
0
0
0
0
0
3
0
0
0
3
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
6
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
1
0
1
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
5
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
2
3
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
2
0
2
0
2
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
1
0
2
0
2
0
1
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
3
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
1
0
0
0
0
0
0
0
2
0
1
0
0
3
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
1
0
1
0
0
0
0
0
2
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
7
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
2
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
2
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
1
0
0
1
1
0
0
0
1
1
1
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
1
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
2
2
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
7
0
2
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
2
0
0
1
0
0
2
1
0
0
0
2
1
1
0
1
0
1
0
2
0
0
0
0
1
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
2
1
1
2
0
0
2
2
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
1
1
1
3
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
5
0
0
2
0
0
0
0
4
1
0
0
2
0
0
1
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
1
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
2
3
1
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
2
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
3
0
0
0
0
2
0
0
0
0
0
0
0
1
5
0
0
0
0
0
0
0
0
0
1
1
1
0
0
2
1
1
0
1
0
2
0
3
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
2
1
0
0
2
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
2
0
0
2
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
1
0
3
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
2
0
0
3
2
0
4
1
1
1
0
0
0
1
0
0
0
2
1
2
0
0
5
0
1
0
0
0
0
0
1
0
2
0
0
1
4
2
0
1
0
0
2
0
3
0
0
1
0
0
0
0
0
4
2
0
0
0
0
1
0
1
2
2
0
0
1
0
3
2
2
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
2
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
1
2
0
2
0
4
0
0
0
0
3
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
2
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
2
0
2
0
1
0
0
0
0
1
0
2
0
2
1
3
3
0
0
7
0
0
0
0
0
2
1
2
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
2
0
0
2
2
0
0
0
0
2
2
0
1
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
3
4
0
1
0
0
0
1
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
2
12
0
2
0
0
0
4
2
1
2
0
0
0
1
1
0
4
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
2
2
0
2
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
1
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
1
2
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
1
0
2
2
0
0
0
2
0
0
0
0
0
1
1
2
0
0
0
0
1
0
2
0
3
0
0
0
0
0
0
0
5
0
0
0
2
0
2
2
0
2
0
0
0
0
0
4
0
0
0
2
0
2
1
0
0
0
0
0
0
2
0
1
0
0
0
1
0
3
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
2
2
0
0
0
0
0
1
2
0
0
2
9
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
1
2
0
0
0
1
0
0
0
0
0
0
0
3
0
2
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
1
1
1
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
1
1
0
2
0
1
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
2
0
2
0
0
2
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
3
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
3
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
1
2
0
1
0
3
2
0
0
0
0
2
0
1
0
3
0
0
0
1
0
0
0
1
0
0
1
2
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
5
3
1
0
0
3
0
1
0
0
1
0
1
0
0
1
0
0
0
2
0
0
1
0
0
0
0
1
1
0
0
2
0
2
0
2
1
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
1
0
0
1
0
0
2
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
1
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
2
0
2
1
0
0
0
1
0
0
0
2
0
0
0
2
1
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
2
0
2
2
0
1
0
0
6
0
2
2
0
0
2
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
2
0
0
0
3
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
2
4
2
2
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
2
0
0
4
2
2
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
1
0
1
0
1
4
0
4
0
0
0
0
1
2
2
0
0
1
0
0
0
0
2
0
2
0
0
1
0
0
0
2
1
0
0
0
0
7
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
5
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
4
0
2
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
3
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
2
0
1
0
1
2
1
2
2
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
6
1
2
0
1
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
2
1
0
1
0
0
3
0
0
0
0
0
0
0
2
0
2
0
0
0
1
2
0
0
0
0
0
0
0
1
0
2
2
0
2
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
4
1
0
0
1
0
6
0
0
0
0
0
0
2
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
2
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
2
0
0
1
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
4
0
1
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
2
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
1
1
0
2
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
3
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
1
0
0
0
0
0
3
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
5
2
0
0
0
0
2
0
0
0
0
3
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
2
0
0
0
0
1
1
0
0
0
2
0
1
1
2
0
0
0
0
0
1
0
2
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
4
1
0
0
1
0
0
0
1
0
0
1
0
2
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
2
0
0
1
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
2
0
0
0
0
1
0
0
0
0
0
1
1
1
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
2
0
0
0
0
0
2
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
3
0
2
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
1
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
2
0
0
0
0
2
2
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
1
1
3
0
0
0
0
2
0
4
0
3
0
0
0
2
3
0
2
2
0
0
0
1
0
1
0
0
2
0
0
0
1
2
0
0
0
0
0
1
0
2
0
1
0
0
0
0
6
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
2
0
0
2
0
0
0
2
1
0
0
0
0
0
1
1
2
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
2
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
2
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
2
1
0
0
0
0
2
2
0
0
0
2
0
1
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
3
2
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
8
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
1
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
2
4
0
0
0
3
0
0
0
2
0
0
0
2
0
0
2
0
0
0
1
0
0
2
0
2
0
1
0
1
0
0
0
2
3
0
0
1
0
0
1
1
0
0
0
4
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
3
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
2
2
2
0
0
0
0
0
0
2
0
0
0
3
2
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
1
0
0
1
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
3
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
1
0
2
0
0
0
1
2
0
2
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
3
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
3
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
1
1
0
1
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
4
0
0
0
1
0
0
0
0
3
0
2
0
1
0
0
0
0
5
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
1
0
4
0
0
2
0
0
0
0
2
0
0
1
1
0
0
0
2
0
2
0
0
1
2
0
1
2
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
1
0
1
4
0
0
0
0
0
2
4
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
4
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
3
0
1
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
2
2
5
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
2
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
2
1
0
0
2
0
0
0
0
2
0
2
0
0
1
1
1
0
0
0
0
6
2
0
0
0
1
0
0
0
1
0
0
3
0
1
1
0
0
0
0
0
0
0
0
2
0
1
1
0
1
0
0
0
2
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
2
3
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
2
0
4
0
0
0
0
0
2
0
1
4
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
3
1
0
0
0
0
1
0
0
5
0
0
2
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
1
0
3
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
4
0
0
3
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
2
0
0
0
2
0
2
2
1
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
3
0
0
0
3
0
0
0
2
0
0
0
0
0
3
0
0
2
1
0
0
0
0
0
1
0
7
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
2
0
0
0
2
0
2
2
2
0
2
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
2
0
1
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
1
0
0
2
2
1
0
0
0
0
2
2
1
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
2
0
1
0
1
0
2
0
0
0
0
1
1
0
2
0
1
0
0
0
1
2
0
0
2
0
1
0
0
2
0
0
1
1
0
0
0
0
2
2
3
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
1
1
0
2
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
2
0
7
0
0
2
0
0
0
0
0
1
0
1
1
0
1
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
3
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
4
0
0
2
0
0
0
0
0
0
2
5
1
0
0
0
1
0
1
0
3
0
0
0
0
1
0
1
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
1
0
0
0
1
0
0
0
0
3
0
0
1
0
1
0
0
0
2
0
2
0
0
0
0
0
4
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
1
0
0
0
0
1
1
0
0
0
1
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
1
0
1
0
0
0
1
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
4
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
2
0
0
0
2
0
0
0
0
0
0
10
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
1
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
2
2
0
0
1
2
0
0
0
0
0
0
2
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
1
1
0
2
2
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
8
0
0
0
1
2
0
0
0
1
0
2
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
2
2
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
1
0
3
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
2
4
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
1
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
2
3
0
1
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
5
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
2
1
0
0
2
0
0
4
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
1
0
3
0
0
1
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
1
0
0
0
1
2
0
0
1
0
0
0
0
4
2
2
1
1
0
1
0
0
0
0
3
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
1
2
1
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
1
0
1
0
0
2
1
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
3
0
0
0
0
0
0
0
0
1
2
0
0
0
2
1
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
2
0
0
0
2
0
0
0
0
0
3
1
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
1
0
3
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
3
2
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
1
0
1
0
1
3
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
9
2
4
0
0
0
0
0
1
0
2
0
0
0
1
0
0
1
1
0
2
0
1
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
5
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
4
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
1
2
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
4
4
0
0
0
1
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
3
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
3
0
0
1
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
1
0
2
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
2
1
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
3
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
1
0
2
1
1
1
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
3
0
2
2
2
4
1
0
0
0
2
1
0
0
0
1
1
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
1
0
1
1
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
2
0
0
2
0
0
1
2
0
1
1
0
0
5
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
2
1
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
4
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
1
1
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
2
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
2
0
2
3
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
3
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
2
1
0
0
0
0
0
1
0
0
0
0
1
3
0
0
0
0
2
1
0
0
0
1
0
1
0
0
1
0
0
2
2
0
3
2
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
1
0
0
1
0
3
2
0
0
1
3
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
3
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
1
1
0
0
0
2
1
2
2
0
0
1
0
1
0
1
0
0
0
0
2
0
0
3
0
0
0
2
0
3
3
0
0
0
2
3
0
0
0
4
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
2
2
1
0
1
0
0
0
3
2
0
0
2
1
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
2
0
0
2
0
1
0
2
0
1
0
0
0
0
0
0
2
1
2
2
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
3
1
0
2
2
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
2
0
2
1
1
0
0
0
0
0
0
1
0
0
4
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
2
2
0
0
0
0
2
0
0
3
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
3
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
11
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
2
0
0
0
1
0
0
0
0
1
1
0
0
0
2
0
0
1
0
0
0
1
1
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
3
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
3
2
0
1
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
21
2
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
1
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
3
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
3
0
0
1
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
2
1
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
3
2
0
0
0
4
0
0
0
0
0
2
0
2
0
0
0
0
1
1
1
0
0
0
0
1
2
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
2
1
1
0
0
0
0
2
1
0
0
0
0
0
1
2
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
1
2
0
2
0
0
0
0
8
0
0
0
0
0
0
1
4
0
0
0
0
0
4
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
1
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
3
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
7
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
1
0
0
0
3
0
0
3
0
0
0
0
0
1
2
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
2
0
0
1
1
0
0
0
2
0
0
2
0
1
1
0
0
0
4
0
0
1
0
0
0
0
1
0
0
2
2
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
2
1
2
0
1
4
2
2
0
0
3
0
0
2
0
0
4
0
1
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
6
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
2
0
0
0
1
1
2
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
2
0
0
0
1
2
0
0
0
1
0
0
0
2
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
2
0
1
0
0
2
2
2
0
0
2
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
2
1
1
0
0
0
0
2
0
0
2
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
1
0
0
0
2
0
3
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
2
0
1
0
0
0
0
0
2
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
2
0
0
0
2
0
0
0
0
1
2
2
0
0
0
0
1
0
2
0
2
1
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
7
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
3
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
2
4
0
0
0
2
3
0
3
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
1
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
2
1
0
2
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
1
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
6
1
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
5
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
3
4
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
2
1
2
0
0
1
2
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
1
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
3
0
1
4
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
1
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
4
4
1
0
0
0
0
0
5
2
0
0
0
2
1
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
2
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
2
4
0
0
0
0
0
0
0
0
0
2
0
1
0
3
0
0
2
0
0
2
0
0
1
3
0
0
0
1
1
2
0
0
1
1
0
0
1
2
0
0
2
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
2
0
1
2
0
2
0
0
0
0
0
2
0
0
0
1
0
0
1
2
1
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
3
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
2
4
0
0
0
0
0
2
0
0
0
2
2
3
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
1
2
0
1
0
4
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
3
4
0
0
0
0
0
0
0
1
1
0
0
1
0
2
0
2
3
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
2
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
5
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
1
2
0
3
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
1
5
0
0
2
0
0
0
1
0
0
2
0
2
0
0
0
0
3
0
0
0
2
0
0
1
0
0
2
0
0
0
2
2
0
0
0
0
1
0
0
1
0
0
0
3
2
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
2
1
1
1
1
1
2
4
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
1
0
1
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
2
0
3
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
1
4
0
0
0
0
0
0
1
0
4
0
4
1
2
6
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
2
1
2
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
1
3
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
8
1
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
2
1
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
1
0
1
2
0
0
0
0
2
0
0
0
0
2
1
3
0
0
0
1
0
2
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
2
0
1
0
3
2
0
2
0
2
1
2
0
2
1
0
1
0
0
0
1
0
2
0
0
0
0
0
0
4
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
2
1
0
2
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
3
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
2
0
0
0
1
0
0
1
0
1
2
0
1
0
1
0
0
3
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
4
0
2
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
2
0
1
0
1
0
0
0
0
1
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
3
0
0
1
0
1
0
0
0
0
2
0
0
4
0
0
0
4
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
2
1
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
2
1
0
2
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
2
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
2
0
0
0
2
0
2
0
1
0
0
1
0
2
1
0
0
0
0
1
0
0
1
1
0
0
1
8
2
2
2
0
0
0
2
1
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
1
1
0
1
0
0
0
0
4
0
0
0
0
0
0
1
0
4
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
2
0
0
1
0
0
0
1
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
2
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
4
1
4
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
1
2
0
0
0
0
2
0
1
2
3
0
1
0
0
0
0
0
2
2
1
0
0
1
2
2
2
0
0
1
0
0
1
0
0
0
2
0
0
0
1
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
2
1
0
0
0
2
0
0
0
1
0
2
1
0
0
0
0
2
0
0
0
1
7
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
4
1
1
0
0
0
1
0
5
2
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
3
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
2
0
1
0
0
0
0
3
0
0
0
0
3
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
3
0
0
0
0
0
2
0
0
1
0
0
0
0
4
0
0
0
0
2
2
0
1
0
2
0
0
0
0
0
4
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
1
0
2
1
1
0
0
0
1
0
0
0
0
0
0
3
1
1
0
2
2
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
4
0
1
1
0
0
0
5
0
0
0
1
0
0
0
0
1
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
2
0
4
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
1
0
1
2
0
0
0
0
0
0
0
2
1
2
0
4
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
1
2
1
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
2
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
9
3
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
1
0
0
0
2
1
0
0
0
1
0
2
2
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
1
1
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
2
0
4
0
1
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
2
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
1
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
1
0
3
0
2
2
0
0
2
0
0
1
1
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
1
3
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
6
1
0
1
0
0
0
2
1
0
0
1
0
0
2
0
0
3
0
0
0
1
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
4
0
0
1
2
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
3
0
1
2
2
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
1
1
0
0
1
10
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
1
0
2
0
0
1
0
1
0
0
2
0
0
2
0
2
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
2
0
1
0
0
1
0
0
2
0
0
0
0
1
0
5
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
2
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
1
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
3
0
1
3
0
0
1
2
0
2
0
1
0
0
1
2
0
0
0
0
0
0
0
4
1
0
1
1
0
0
0
1
0
0
2
1
2
0
0
0
1
0
0
1
0
1
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
1
0
0
2
1
0
0
0
0
2
0
0
0
0
0
2
0
2
0
1
0
0
0
0
1
1
0
3
0
0
0
0
2
2
1
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
6
0
1
0
2
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
1
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
2
0
0
4
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
2
0
1
0
1
1
0
0
3
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
3
2
1
1
0
0
2
1
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
3
1
0
0
1
0
0
0
1
0
0
0
2
2
2
0
1
0
1
1
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
3
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
1
0
0
0
1
0
3
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
3
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
2
0
0
0
0
3
0
1
2
0
2
0
2
2
1
0
0
0
0
0
2
0
0
0
0
3
0
1
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
2
0
1
0
0
0
2
0
0
0
2
0
1
0
0
0
1
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
2
1
0
1
3
0
0
1
0
1
0
1
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
1
0
1
2
0
0
0
1
0
2
0
0
0
0
0
0
1
1
0
0
0
2
0
0
2
0
2
0
0
0
0
2
3
0
0
3
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
2
0
0
2
0
0
0
0
2
0
0
1
2
0
2
0
0
0
0
0
0
0
2
2
2
3
0
1
2
0
0
0
0
0
0
4
1
2
0
0
1
1
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
2
0
0
0
11
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
2
2
0
0
0
1
0
0
0
0
0
1
3
0
3
1
0
0
0
1
2
0
0
0
0
2
1
0
0
0
0
4
0
0
0
0
4
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
2
0
0
3
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
2
0
2
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
1
2
0
2
3
2
2
3
0
0
0
0
0
0
2
0
0
0
2
0
4
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
1
0
0
1
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
4
3
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
2
0
0
0
0
1
0
1
0
2
0
0
0
0
0
1
0
1
0
0
0
2
0
0
1
0
1
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
6
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
3
0
2
0
0
0
2
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
1
0
1
0
4
0
0
0
0
2
0
0
0
0
1
3
0
0
1
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
2
3
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
3
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
2
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
2
0
1
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
7
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
3
0
0
0
1
2
0
2
0
1
0
0
3
3
0
0
0
0
0
0
0
0
1
0
0
2
0
0
6
0
0
3
0
0
0
0
0
0
0
0
0
3
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
2
2
0
0
0
0
0
0
0
0
1
0
0
3
0
1
0
0
2
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
1
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
2
1
0
0
0
0
1
2
0
0
2
0
1
0
2
0
0
0
0
0
2
0
4
0
0
0
1
0
3
0
0
0
0
2
0
0
0
0
1
0
2
0
0
2
0
0
0
2
0
0
0
0
3
0
0
1
2
1
0
2
0
7
2
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
7
0
1
0
0
0
0
1
0
0
0
0
1
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
1
0
0
2
0
3
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
2
2
1
2
1
0
0
0
0
1
2
0
0
2
2
0
3
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
2
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
3
0
0
2
0
0
0
1
2
0
0
0
0
0
0
3
0
0
2
0
0
0
5
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
2
1
2
2
1
1
1
0
1
0
0
0
0
2
1
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
2
0
0
0
0
0
1
0
0
1
0
1
1
0
1
1
4
2
0
1
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
1
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
2
0
2
0
1
0
0
7
0
0
0
0
2
0
0
1
3
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
5
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
2
0
0
1
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
3
2
2
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
3
2
1
0
0
2
0
0
0
1
9
0
0
0
0
5
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
1
0
0
3
0
2
0
0
2
2
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
3
0
0
0
0
2
0
2
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
3
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
1
3
0
2
0
0
0
2
0
0
0
0
4
1
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
3
0
1
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
9
0
0
0
0
0
0
0
0
0
0
0
0
1
2
3
1
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
3
2
2
0
0
2
0
0
0
2
0
0
0
0
0
1
2
0
10
1
0
0
0
2
1
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
2
1
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
3
0
2
0
1
0
0
0
0
2
0
0
0
0
2
0
1
0
1
0
5
0
0
0
0
0
0
1
1
0
0
1
2
0
0
1
0
2
0
1
2
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
2
0
0
0
9
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
1
0
1
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
1
2
0
0
2
0
0
3
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
2
1
0
0
0
0
0
4
0
2
0
0
3
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
1
0
0
0
0
0
3
1
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
2
0
2
2
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
1
0
0
3
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
1
1
0
0
4
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
4
0
0
2
0
0
0
0
0
0
0
0
3
0
1
0
0
2
0
0
0
0
4
1
0
0
2
0
3
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
1
0
0
0
1
0
3
0
0
0
1
1
0
0
0
3
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
2
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
5
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
5
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
3
0
0
2
1
0
0
0
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
1
0
0
0
0
0
2
3
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
4
0
0
0
1
1
0
0
0
2
2
2
2
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
3
0
2
0
0
0
0
0
0
3
0
0
2
0
0
3
0
0
0
0
0
0
0
2
2
2
0
1
0
7
0
1
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
1
1
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
3
0
0
0
0
1
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
1
0
0
0
3
4
0
0
0
2
0
0
0
0
0
2
0
0
2
2
2
0
0
1
0
2
0
0
0
1
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
2
0
0
2
0
1
1
0
0
0
0
0
0
1
0
1
0
2
0
2
0
0
0
1
1
2
0
0
0
4
0
0
0
0
0
2
0
4
0
0
0
1
0
0
2
1
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
3
0
3
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
19
0
1
0
1
0
2
0
0
0
0
1
1
2
0
0
0
1
0
2
1
0
0
0
6
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
1
0
0
2
1
0
0
1
0
1
0
4
0
0
0
0
2
1
0
1
0
0
1
2
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
4
0
0
2
0
0
1
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
2
1
0
2
0
0
0
0
0
2
0
1
2
0
0
0
0
1
0
0
1
2
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
1
0
3
0
2
1
1
0
0
0
0
0
0
0
0
0
3
1
0
0
0
7
0
0
2
0
0
0
0
1
0
0
1
0
0
0
1
0
2
3
0
0
0
0
1
2
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
1
2
0
0
1
0
0
0
3
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
6
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
2
0
0
0
2
0
1
0
0
2
0
2
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
2
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
2
0
0
1
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
4
1
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
3
0
1
0
0
1
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
6
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
2
0
1
0
0
0
1
0
0
0
1
0
1
1
1
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
8
1
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
3
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
2
1
1
0
0
1
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
1
1
2
1
0
0
0
0
0
0
0
2
0
0
1
0
0
1
1
0
2
1
0
0
2
0
2
1
0
0
2
0
0
2
0
0
0
1
1
2
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
4
0
0
0
0
4
1
0
0
1
5
2
0
0
0
0
0
0
0
0
1
1
1
0
1
0
1
0
1
0
0
1
0
0
3
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
2
0
4
0
2
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
2
0
2
0
0
1
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
10
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
1
0
1
0
2
0
1
0
2
1
1
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
2
0
2
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
2
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
2
0
0
0
2
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
3
2
1
0
4
0
0
1
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
1
2
0
0
0
5
0
0
2
0
0
0
1
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
2
0
0
1
0
0
1
3
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
3
2
0
0
0
0
0
2
2
0
2
0
2
1
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
1
0
2
0
1
1
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
2
0
2
1
0
0
2
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
5
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
1
3
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
3
0
0
0
1
0
2
0
2
0
0
0
1
0
2
1
0
0
0
0
0
3
0
1
0
0
3
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
4
1
1
1
0
0
0
0
1
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
1
1
0
0
0
0
0
0
0
2
0
1
1
0
3
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
2
1
0
1
1
0
1
2
0
0
0
0
2
1
0
0
0
0
0
2
0
0
2
1
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
2
0
0
0
0
0
1
0
0
0
0
0
4
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
2
0
2
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
3
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
1
5
0
0
1
1
0
0
1
1
0
1
2
0
0
2
0
3
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
3
0
2
1
1
0
0
0
0
0
0
0
0
3
0
6
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
1
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
3
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
1
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
2
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
2
6
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
2
0
2
0
0
0
1
2
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
5
0
0
0
0
0
2
0
0
0
1
2
0
0
0
1
0
0
2
1
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
2
2
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
5
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
1
1
0
1
0
1
3
0
2
0
2
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
2
2
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
3
0
0
0
1
0
2
0
0
1
2
0
0
0
1
2
0
0
0
0
0
1
0
2
3
0
0
3
0
4
3
2
0
0
0
0
0
2
0
0
0
0
7
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
6
1
0
1
0
0
0
2
0
1
2
2
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
3
2
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
1
5
0
0
0
2
0
0
0
0
2
0
0
0
0
0
3
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
1
0
4
0
0
0
2
0
1
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
3
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
2
2
0
0
0
1
1
0
0
0
2
0
0
4
1
0
2
0
3
0
2
2
0
2
0
1
0
0
0
1
0
0
0
0
4
0
0
2
0
0
0
0
3
0
1
0
0
0
0
0
3
0
2
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
2
0
2
0
2
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
2
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
5
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
3
0
1
0
1
0
2
1
3
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
7
0
0
0
0
5
0
2
0
0
0
1
0
1
0
0
1
0
2
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
3
0
0
2
0
2
1
0
0
1
0
0
1
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
1
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
1
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
1
0
0
2
0
2
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
4
1
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
1
0
2
0
4
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
3
0
0
0
1
1
1
1
2
0
0
0
0
0
0
2
0
0
0
1
0
1
0
2
0
0
2
0
3
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
5
0
0
0
0
3
3
0
0
0
2
0
0
4
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
3
0
0
0
1
0
0
2
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
2
0
3
0
0
0
1
3
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
5
0
4
6
0
0
1
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
2
0
2
0
2
1
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
2
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
4
1
0
0
0
5
3
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
3
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
1
0
0
1
4
0
0
0
1
0
1
0
3
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
3
1
0
0
0
1
3
0
0
1
0
2
0
0
0
0
0
1
0
0
1
0
1
0
2
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
1
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
2
2
0
0
2
0
0
0
0
0
0
0
0
1
0
3
0
2
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
2
0
2
3
0
0
2
0
1
2
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
2
2
2
0
1
0
2
0
2
2
0
2
0
0
0
0
0
0
3
0
0
0
0
2
1
0
2
0
0
2
0
1
0
0
1
0
0
1
0
2
1
0
0
0
0
2
2
0
0
4
0
0
0
1
0
0
0
0
0
4
0
0
1
0
0
0
2
1
0
0
0
2
1
0
0
0
1
0
1
0
0
0
0
0
0
3
1
4
0
0
2
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
2
6
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
3
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
2
1
0
1
0
0
2
0
0
1
0
0
0
0
0
0
2
0
2
2
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
3
3
0
0
0
2
0
0
0
1
2
1
0
0
1
0
0
1
0
0
0
1
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
1
1
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
2
1
0
2
1
0
0
1
0
6
2
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
1
0
1
2
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
2
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
1
2
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
6
0
0
0
3
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
2
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
1
0
0
0
4
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
2
1
0
2
0
0
0
1
0
3
2
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
2
1
0
2
2
0
0
0
1
0
0
1
0
0
0
0
0
3
2
0
0
0
4
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
1
0
0
4
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
2
1
1
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
1
0
0
0
0
6
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
2
0
3
0
2
1
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
1
0
0
0
0
2
0
0
1
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
3
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
3
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
1
0
0
0
3
0
0
0
0
2
0
0
0
2
1
0
1
0
0
0
1
1
0
0
5
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
1
0
0
2
0
0
2
0
0
0
3
0
0
0
0
0
0
2
0
0
2
2
1
0
2
0
0
2
1
1
0
0
0
0
0
2
0
2
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
9
0
0
2
0
0
0
0
3
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
3
0
1
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
2
0
0
1
0
0
5
0
1
0
0
0
1
0
1
0
1
0
1
2
0
2
0
0
0
0
0
0
3
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
2
0
2
2
2
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
5
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
1
0
2
0
0
0
1
2
0
2
0
0
2
0
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
2
1
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
1
1
2
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
1
0
0
2
0
2
0
0
1
2
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
1
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
3
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
1
0
3
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
1
0
1
0
0
0
0
1
0
0
0
2
0
1
0
1
0
0
0
2
2
0
0
0
0
0
0
0
2
4
0
0
0
0
0
1
0
1
0
0
0
1
1
0
2
0
2
0
0
2
0
0
0
0
0
1
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
3
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
4
0
2
1
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
1
0
0
0
6
0
0
0
0
2
1
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
4
0
0
0
0
0
1
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
2
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
2
2
0
2
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
1
1
2
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
1
0
2
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
5
0
0
0
0
0
0
0
1
2
0
2
1
0
0
0
0
1
0
0
2
2
0
0
0
0
1
0
0
0
2
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
3
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
2
2
0
0
0
0
1
1
3
2
0
0
0
0
0
0
0
0
0
2
0
0
3
2
0
2
0
0
0
0
0
0
1
1
0
2
1
2
0
0
0
0
0
4
0
3
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
1
0
0
2
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
1
0
0
1
1
1
0
0
0
0
0
0
0
3
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
3
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
2
0
0
2
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
1
0
0
1
0
0
0
1
0
0
0
2
0
0
1
2
0
0
0
0
0
0
3
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
3
1
1
0
0
0
0
0
2
0
2
1
0
0
1
1
0
1
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
1
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
1
0
2
3
0
1
0
0
0
1
0
0
1
1
0
0
0
0
2
1
1
0
0
1
0
0
3
2
0
0
0
0
2
0
0
0
1
0
0
1
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
2
0
0
1
0
0
0
0
3
1
1
0
0
0
2
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
3
0
2
2
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
8
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
3
9
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
2
0
0
4
0
0
1
0
3
0
1
0
3
0
1
0
0
2
0
0
1
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
3
0
2
1
0
0
0
0
2
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
3
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
3
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
2
1
1
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
2
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
1
0
0
5
0
3
3
0
0
2
1
0
0
4
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
3
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
5
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
1
2
0
0
0
0
1
1
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
3
0
0
0
0
2
1
6
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
2
2
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
3
2
0
0
0
0
2
0
1
0
1
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
2
0
0
1
0
2
0
0
2
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
3
0
0
2
0
2
0
1
1
0
0
0
0
1
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
3
0
0
0
0
2
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
3
1
0
0
4
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
2
2
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
2
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
1
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
1
0
3
0
0
0
1
0
0
0
0
3
3
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
2
0
1
0
0
1
2
1
0
0
0
0
0
2
1
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
2
0
0
0
1
0
1
0
3
2
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
2
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
5
0
0
2
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
1
2
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
2
2
2
0
1
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
2
3
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
3
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
5
0
0
1
2
0
1
0
0
0
0
1
1
1
0
2
2
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
2
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
2
4
0
0
0
0
0
2
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
1
2
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
2
1
3
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
2
2
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
2
1
1
2
2
0
0
2
0
2
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
7
2
2
0
0
0
1
0
0
0
0
0
0
0
2
2
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
2
0
0
0
2
1
0
1
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
2
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
2
1
0
0
2
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
7
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
2
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
3
0
0
0
0
2
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
2
1
0
0
0
0
0
0
1
1
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
2
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
5
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
2
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
3
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
1
1
0
0
1
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
10
2
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
4
0
0
1
0
0
3
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
2
2
2
0
2
0
0
0
2
0
0
0
2
1
0
0
6
0
1
2
0
0
0
0
0
2
0
0
0
0
2
2
0
0
1
2
0
0
2
0
2
0
0
6
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
10
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
1
1
0
0
2
2
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
1
0
2
0
0
0
0
3
0
1
0
0
0
1
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
1
0
1
0
3
2
1
0
2
0
0
0
2
0
0
0
1
0
0
0
0
2
0
1
0
2
0
0
0
0
1
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
1
0
1
0
0
0
2
1
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
2
0
0
0
0
2
0
1
3
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
2
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
3
2
0
1
1
0
1
3
0
0
0
5
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
3
1
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
2
0
0
0
1
1
0
0
0
2
0
0
0
2
0
3
0
1
2
1
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
3
1
1
0
1
0
0
0
4
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
4
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
3
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
1
0
0
0
2
0
2
3
0
0
2
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
1
2
0
2
0
0
0
0
0
0
0
0
0
5
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
1
2
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
4
0
2
0
0
1
0
2
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
1
0
4
1
0
0
1
1
2
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
1
0
1
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
2
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
2
2
0
1
0
1
2
0
0
0
0
5
0
0
1
1
2
0
0
2
0
0
2
0
0
2
0
0
2
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
2
0
2
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
3
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
2
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
3
1
0
0
1
3
0
1
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
3
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
2
8
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
5
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
3
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
5
0
0
0
0
2
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
2
0
2
3
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
3
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
1
1
0
1
0
1
1
0
0
0
1
0
0
4
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
1
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
3
0
0
0
3
1
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
4
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
2
2
2
2
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
1
1
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
1
0
0
2
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
3
1
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
2
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
2
0
1
0
0
0
1
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
2
0
2
0
0
0
0
0
2
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
1
0
0
2
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
2
1
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
1
0
0
0
2
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
2
0
2
1
1
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
1
2
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
2
0
0
0
2
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
2
0
0
0
4
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
2
1
2
0
2
0
1
0
0
0
0
2
2
0
0
0
0
0
1
0
2
0
0
1
2
1
0
0
0
0
0
0
2
0
0
2
0
2
2
0
0
0
2
0
0
3
1
0
1
0
2
2
2
0
0
1
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
1
1
3
0
0
0
1
0
0
1
0
2
0
3
0
0
0
0
0
0
0
1
0
0
1
1
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
4
0
1
0
2
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
1
1
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
4
1
0
0
1
0
0
2
0
0
1
0
0
2
0
0
0
1
1
0
0
0
1
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
1
0
0
0
0
2
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
3
0
1
2
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
1
4
3
0
0
0
4
0
0
0
2
0
0
1
0
1
0
2
2
1
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
1
0
0
0
0
0
3
0
0
0
0
0
1
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
1
0
1
0
0
1
0
0
1
0
0
0
2
0
2
3
0
0
0
0
0
2
1
0
0
3
0
1
0
2
1
2
0
0
0
0
0
0
0
1
2
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
4
0
0
0
0
0
0
15
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
2
0
1
1
0
0
0
0
2
0
0
2
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
4
0
2
0
0
0
0
0
0
0
0
1
1
1
0
0
2
0
0
0
6
0
0
1
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
6
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
3
1
0
0
0
0
0
2
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
3
0
0
1
0
3
0
0
0
3
0
0
2
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
1
3
1
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
1
1
3
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
3
3
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
2
0
0
1
0
2
3
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
3
0
0
0
0
3
0
2
0
2
2
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
4
0
0
0
0
0
3
1
0
1
0
2
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
1
6
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
1
2
0
0
0
2
0
4
0
0
5
0
0
0
2
2
2
2
0
0
0
2
0
0
0
2
0
0
0
3
4
0
0
0
3
0
0
1
0
2
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
3
0
0
0
0
1
0
0
2
0
0
1
0
0
1
0
1
0
0
0
0
1
0
1
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
3
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
3
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
3
0
0
0
0
2
0
0
0
1
0
0
0
1
2
2
0
0
0
0
0
2
1
1
0
1
2
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
3
0
0
0
0
0
0
1
0
0
1
0
0
0
3
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
1
0
0
0
1
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
3
0
0
3
0
0
0
0
0
5
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
3
0
2
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
5
0
0
0
1
0
0
2
0
0
0
0
0
1
0
1
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
2
0
2
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
1
1
0
0
0
1
1
0
3
1
0
1
0
0
2
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
5
1
2
0
2
0
3
0
0
0
0
0
0
1
22
7
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
3
0
0
2
1
2
1
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
6
0
0
1
0
0
0
0
0
0
1
0
3
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
7
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
2
0
0
0
1
1
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
2
1
0
0
0
0
0
0
1
0
0
3
0
0
2
0
5
0
1
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
2
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
4
0
0
0
0
1
0
0
0
2
0
4
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
2
8
0
2
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
1
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
2
2
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
2
1
1
2
0
0
1
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
1
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
3
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
3
0
1
1
1
0
0
1
0
0
0
2
1
0
1
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
3
0
2
3
0
0
5
0
0
0
0
0
0
0
0
3
0
0
1
1
0
1
0
1
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
2
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
2
1
0
1
0
2
0
0
0
0
0
0
0
1
1
0
0
0
2
0
2
0
1
0
0
0
2
0
2
0
0
1
0
0
1
0
1
0
3
0
0
0
0
0
0
1
0
0
0
1
3
0
1
0
0
2
0
1
0
0
0
0
2
0
1
1
0
0
2
0
0
1
0
4
0
3
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
3
1
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
1
1
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
2
0
0
0
2
2
0
3
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
2
1
2
0
0
0
0
0
6
0
2
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
1
0
0
2
3
0
0
3
0
0
0
2
0
0
0
0
0
1
2
1
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
2
0
2
0
2
0
2
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
1
2
5
0
2
3
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
6
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
3
2
0
0
0
0
3
1
0
0
2
0
0
0
0
1
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
4
1
2
0
3
0
0
1
2
0
2
0
0
0
0
0
3
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
2
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
3
1
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
4
2
0
3
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
4
0
0
0
0
0
0
0
2
0
5
0
2
0
0
0
1
2
0
2
0
0
0
2
0
1
0
0
0
0
2
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
1
3
1
0
0
0
0
0
0
2
0
3
0
1
2
2
0
0
1
0
1
0
0
0
0
0
3
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
2
0
0
0
0
0
1
0
0
0
2
0
1
2
0
0
0
0
1
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
2
2
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
3
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
2
0
0
0
1
0
3
1
0
1
0
0
2
2
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
2
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
6
0
0
0
3
0
0
1
0
0
0
0
0
1
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
3
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
3
0
1
0
2
1
3
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
5
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
3
0
0
0
0
3
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
1
2
0
0
0
0
4
2
1
0
0
0
0
0
1
0
1
0
0
0
3
0
0
1
2
4
0
0
3
0
0
1
0
0
2
0
0
0
0
0
1
0
2
0
0
2
0
0
0
2
0
1
0
0
2
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
4
0
0
0
1
1
2
0
0
0
0
0
2
0
1
0
0
0
0
3
0
0
0
2
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
2
14
0
1
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
2
0
2
1
1
0
1
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
3
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
3
0
0
0
0
1
3
0
0
0
2
2
0
0
1
0
2
2
0
0
1
0
0
0
1
0
0
1
0
0
0
0
2
0
1
1
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
2
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
2
2
0
0
2
0
0
0
0
2
2
0
1
0
0
0
1
0
0
0
0
0
2
0
2
2
2
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
2
2
0
0
0
2
0
0
0
2
0
3
0
2
0
0
2
0
1
0
0
2
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
1
0
0
1
0
2
0
1
1
0
1
0
0
4
0
0
1
4
2
0
0
0
0
2
0
2
0
0
2
2
2
0
2
0
0
0
1
1
2
0
2
0
0
0
3
0
0
0
0
0
0
0
2
0
2
2
0
0
2
0
0
0
0
2
0
1
2
0
1
0
0
0
0
0
0
0
1
0
6
0
2
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
1
0
1
1
0
0
0
2
0
0
0
2
0
2
0
0
1
0
4
0
0
0
3
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
3
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
6
0
0
3
0
0
1
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
2
0
2
1
0
1
0
1
0
1
1
0
1
2
0
0
0
2
0
0
0
0
0
1
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
3
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
2
1
0
0
0
3
0
0
0
0
0
1
0
0
0
0
1
0
2
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
2
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
1
2
0
0
0
0
2
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
0
0
3
0
0
2
2
0
1
0
0
0
0
2
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
1
2
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
1
1
2
0
0
0
0
0
1
6
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
2
3
2
2
0
0
0
0
0
0
1
1
1
0
2
0
0
2
0
0
0
0
1
0
0
1
0
1
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
3
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
1
1
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
1
0
12
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
1
0
0
0
0
4
0
0
0
0
0
0
0
2
1
0
2
2
1
1
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
1
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
1
0
1
0
2
0
1
2
0
0
1
0
0
1
0
0
0
3
0
0
12
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
2
2
0
0
3
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
3
0
0
2
0
0
0
0
0
0
0
0
1
0
2
3
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
2
0
0
1
0
0
0
0
1
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
1
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
4
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
3
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
2
0
0
1
0
1
0
1
2
2
0
0
0
2
2
5
0
0
2
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
1
1
0
0
0
2
1
2
0
0
2
0
0
0
0
3
0
0
0
2
0
0
0
0
0
2
0
2
2
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
2
2
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
3
0
0
1
3
0
0
0
0
11
0
1
1
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
1
0
3
0
2
0
1
0
1
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
4
0
0
0
2
0
0
3
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
2
0
1
3
0
0
2
0
0
0
1
0
0
0
0
0
1
1
0
1
2
0
0
0
0
0
0
1
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
2
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
3
2
0
0
0
0
0
1
2
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
4
0
0
0
0
0
1
1
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
3
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
2
0
0
0
0
0
1
0
0
0
5
1
0
0
3
5
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
2
0
0
0
2
1
0
0
1
2
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
2
0
1
0
2
2
0
0
0
0
1
0
1
0
2
2
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
3
0
0
1
2
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
2
1
1
0
2
0
0
2
1
0
2
1
0
2
0
0
0
0
0
1
2
0
0
0
0
2
0
2
0
0
0
1
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
3
0
0
2
0
2
0
0
0
0
2
0
0
0
2
3
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
1
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
1
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
2
0
0
2
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
1
1
0
0
1
0
0
1
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
1
0
1
0
0
0
2
0
0
2
0
0
1
0
1
2
0
3
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
1
1
0
1
0
0
0
0
2
0
1
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
5
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
1
2
2
5
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
3
0
0
0
2
0
1
0
1
0
0
0
3
1
0
0
0
0
0
2
0
0
0
0
4
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
3
0
1
0
0
4
0
0
0
0
0
2
2
0
1
2
0
0
1
3
0
0
0
2
1
0
1
0
0
1
0
0
0
1
2
0
0
0
0
0
0
2
0
0
1
3
0
2
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
1
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
1
1
0
1
2
0
0
0
1
0
0
1
2
0
3
0
2
1
0
0
0
0
0
0
0
2
3
0
0
0
0
0
5
0
0
1
0
0
0
1
0
0
0
0
0
3
3
0
0
0
0
0
0
2
2
1
0
0
0
0
0
2
1
0
0
2
2
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
3
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
2
2
0
1
0
0
0
0
2
0
4
0
0
0
2
2
1
0
0
0
2
0
2
1
0
1
1
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
2
0
0
0
1
2
0
0
0
2
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
1
2
0
0
0
0
6
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
2
1
0
2
0
2
0
0
0
0
2
2
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
3
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
4
1
1
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
1
0
2
1
0
0
0
2
0
1
1
0
0
0
0
0
2
1
2
0
0
3
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
3
0
0
0
1
2
0
0
2
1
0
1
3
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
3
0
0
1
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
2
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
1
0
1
0
1
0
0
1
2
0
0
0
0
1
0
0
0
1
0
3
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
2
0
0
0
0
0
0
0
1
0
0
3
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
6
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
2
1
0
0
1
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
2
0
0
2
2
1
2
1
1
0
0
0
0
1
1
0
0
0
0
2
1
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
6
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
2
0
0
0
1
1
0
0
0
2
0
0
0
1
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
2
0
1
2
0
0
0
0
0
0
2
1
0
0
0
0
1
0
1
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
3
0
1
0
0
0
0
0
1
0
2
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
2
1
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
2
0
0
0
0
0
0
0
2
1
0
2
0
2
0
0
0
0
2
1
0
0
0
2
0
0
0
2
0
0
0
0
2
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
2
0
1
0
1
0
1
0
0
0
0
2
4
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
5
1
0
0
0
0
1
0
0
0
0
1
5
1
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
4
3
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
4
0
0
2
0
2
2
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
4
0
2
0
0
0
1
0
0
0
0
2
0
0
1
0
2
2
0
6
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
7
1
2
0
0
0
0
1
0
0
0
0
3
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
2
0
0
0
1
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
1
0
0
2
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
2
0
1
0
2
0
0
0
4
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
3
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
2
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
4
0
1
0
0
0
0
2
0
0
0
0
0
1
0
3
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
2
0
1
3
0
1
0
2
0
0
1
0
0
0
2
0
1
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
3
3
0
1
0
0
1
3
2
2
0
0
0
2
3
1
0
0
0
0
0
0
1
3
0
0
2
0
0
0
1
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
2
0
0
0
1
0
2
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
2
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
1
2
0
3
0
0
0
4
0
0
0
0
2
0
0
0
0
2
1
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
1
0
4
2
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
2
1
0
1
0
0
0
0
1
0
0
0
2
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
1
0
1
0
6
2
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
7
1
0
0
2
2
1
0
0
0
0
0
2
0
0
0
0
1
1
0
3
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
3
0
0
2
0
0
1
3
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
4
4
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
2
5
0
0
0
2
1
0
0
1
0
0
0
2
1
0
0
3
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
1
2
1
0
0
2
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
3
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
1
0
1
0
2
0
1
1
0
0
2
1
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
2
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
2
0
3
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
1
0
0
0
0
2
0
3
0
0
2
3
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
6
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
2
0
0
3
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
6
0
1
0
0
0
0
2
0
0
4
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
1
4
0
0
2
0
0
1
0
1
0
0
0
2
2
2
0
0
0
0
0
2
1
0
0
1
4
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
3
0
1
1
2
0
0
0
0
0
4
0
2
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
2
0
0
2
1
0
1
1
0
1
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
2
2
0
0
0
1
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
4
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
1
5
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
4
1
0
0
2
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
3
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
2
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
1
1
0
0
1
0
1
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
4
0
0
0
4
0
0
0
1
0
1
0
0
0
0
1
1
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
1
0
0
0
2
2
0
0
3
0
0
2
0
1
0
0
3
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
1
3
0
0
3
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
2
1
0
0
2
0
2
1
0
0
0
0
0
0
2
2
0
2
0
0
0
3
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
3
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
3
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
2
0
0
4
0
0
0
1
2
17
1
0
2
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
2
0
0
0
0
1
0
2
0
0
0
2
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
7
0
0
0
0
2
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
9
0
3
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
1
1
0
0
0
1
0
0
0
3
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
1
0
0
2
0
0
0
1
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
1
0
0
0
3
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
5
2
0
1
1
0
0
0
0
0
0
2
0
2
3
0
0
1
0
0
0
2
0
1
0
0
2
2
2
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
2
0
0
0
11
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
1
1
2
0
0
3
0
0
0
0
1
0
2
1
1
0
0
0
0
0
0
0
2
2
0
1
0
0
2
2
0
0
0
1
0
0
1
0
0
0
0
0
2
0
1
9
0
1
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
1
1
0
1
0
0
3
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
1
0
0
0
0
8
1
0
0
0
2
0
0
0
0
0
2
0
1
0
0
2
0
0
0
1
3
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
2
0
2
4
1
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
3
2
0
0
1
0
0
0
3
0
2
0
1
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
1
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
1
3
0
0
1
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
2
2
0
0
0
2
1
2
0
0
0
1
0
0
0
0
3
0
0
0
1
0
0
5
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
1
5
0
1
0
0
0
2
0
1
0
0
0
3
0
0
0
1
0
1
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
1
0
3
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
1
0
1
0
1
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
3
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
1
2
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
2
1
1
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
4
2
2
0
0
0
5
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
3
0
1
0
2
2
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
3
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
6
0
0
0
0
0
0
0
0
2
0
0
2
1
0
2
2
0
3
0
1
0
1
0
0
0
1
0
0
2
0
2
0
0
0
1
0
0
1
0
0
0
0
2
0
0
2
0
0
0
1
0
1
0
0
2
1
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
1
0
1
0
0
0
0
0
0
0
2
1
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
7
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
6
0
0
0
0
0
0
0
1
0
1
0
5
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
2
0
0
2
0
0
0
0
0
0
1
0
2
2
0
0
0
0
2
0
0
3
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
13
0
0
0
0
0
0
0
2
0
0
0
0
4
0
0
1
1
0
0
2
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
1
4
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
2
0
0
2
0
4
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
1
1
0
2
2
0
0
2
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
4
0
0
1
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
2
0
0
0
2
0
0
4
2
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
1
0
0
3
1
0
0
0
0
1
0
0
2
0
2
0
0
2
0
0
1
0
2
1
2
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
2
0
0
2
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
2
0
1
0
1
1
0
0
2
0
0
0
0
1
2
0
0
0
3
0
2
0
0
2
3
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
2
1
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
2
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
1
2
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
2
0
0
1
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
1
1
0
1
0
3
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
2
0
2
0
1
0
1
6
0
2
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
2
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
3
1
0
0
0
2
0
0
3
1
2
0
2
1
0
1
1
1
0
5
0
0
0
0
0
0
0
2
1
0
2
1
0
2
0
0
0
0
2
0
0
0
1
0
0
0
2
7
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
3
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
3
1
0
0
0
1
0
6
0
0
0
0
0
0
2
2
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
1
0
1
3
3
0
1
0
0
0
2
0
1
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
1
0
0
2
0
0
0
3
2
0
5
1
0
1
0
0
3
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
1
0
0
1
1
0
0
0
1
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
1
0
0
2
0
0
0
0
1
2
0
0
1
2
1
2
0
0
3
0
2
0
0
1
0
0
0
0
2
1
0
0
2
1
1
0
0
0
0
0
0
0
3
0
0
2
0
0
3
0
1
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
1
2
0
0
0
1
0
0
2
0
2
0
0
0
2
1
4
0
0
0
0
0
0
2
0
0
2
0
1
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
2
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
8
0
0
0
0
1
0
0
0
1
1
2
0
1
0
2
0
0
0
0
0
0
2
0
0
0
7
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
1
2
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
5
0
0
1
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
2
2
0
0
1
1
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
2
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
4
2
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
2
1
0
0
0
0
0
5
0
2
2
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
1
0
3
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
3
0
0
2
1
2
1
0
2
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
5
0
1
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
5
0
0
0
0
0
3
0
0
0
0
2
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
2
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
3
0
0
0
0
0
1
1
2
0
0
0
1
0
0
1
0
0
1
1
0
1
1
0
0
0
2
1
2
0
0
0
0
2
0
0
0
0
2
2
1
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
1
0
0
2
4
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
5
2
1
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
3
0
0
1
0
0
0
0
1
2
0
0
0
1
0
0
0
0
1
0
0
1
2
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
5
1
0
0
0
0
0
0
2
0
0
0
2
5
1
1
0
0
2
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
3
0
1
0
0
0
1
0
0
0
0
3
1
0
0
0
0
2
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
1
0
0
2
0
0
5
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
3
0
0
0
2
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
2
0
0
0
1
0
0
1
1
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
1
0
0
0
0
0
2
2
2
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
4
0
0
1
2
0
1
1
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
1
1
0
0
6
0
0
0
0
0
2
2
0
0
6
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
1
1
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
1
2
0
1
1
1
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
7
1
2
0
0
0
0
2
0
2
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
1
1
2
0
0
0
0
0
0
1
0
0
0
0
0
3
0
2
0
0
0
0
0
2
1
0
1
1
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
1
0
0
0
0
0
1
2
2
2
1
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
4
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
10
1
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
2
0
1
1
2
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
4
0
0
1
0
2
0
0
2
0
0
2
0
2
2
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
3
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
3
0
0
1
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
3
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
2
0
2
0
2
0
2
1
0
0
0
0
0
1
3
1
1
0
0
0
1
0
0
0
0
5
0
0
0
0
0
0
0
0
2
1
3
0
0
3
1
0
0
0
2
0
2
2
0
0
0
0
1
0
0
0
0
0
3
0
0
1
0
3
0
2
0
0
1
1
1
0
0
0
5
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
1
1
0
0
0
0
3
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
2
1
1
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
2
0
1
0
1
0
0
0
0
0
7
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
2
0
3
0
0
0
3
0
1
0
0
0
2
0
0
0
0
2
1
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
1
0
0
0
2
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
1
0
4
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
1
3
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
2
0
0
0
2
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
9
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
2
1
0
0
1
1
0
2
0
0
2
1
0
2
0
0
2
1
0
0
3
0
1
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
2
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
0
0
1
0
2
1
3
2
0
0
1
2
0
0
3
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
2
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
2
0
1
0
2
0
0
2
1
0
0
0
0
2
0
0
1
1
1
0
1
0
2
0
0
0
0
0
6
0
0
0
0
2
1
0
1
0
0
2
0
1
0
0
0
0
3
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
2
0
0
0
4
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
4
2
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
2
3
0
0
0
0
1
1
0
0
0
0
0
0
2
2
0
0
3
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
4
0
0
0
1
0
0
0
1
2
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
1
0
2
0
0
0
3
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
1
0
0
0
4
0
0
0
0
0
1
3
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
6
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
1
2
1
0
0
0
0
0
1
0
0
0
2
1
0
0
2
0
1
0
0
0
1
2
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
2
0
7
0
0
0
3
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
4
1
0
1
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
2
0
0
0
0
0
1
0
0
0
2
0
0
1
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
2
1
3
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
4
0
1
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
2
1
2
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
2
0
0
0
0
0
3
0
0
0
2
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
1
0
0
0
0
3
0
0
0
0
2
0
0
3
0
1
1
0
0
0
1
0
0
0
0
1
0
3
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
1
5
0
1
0
0
1
0
0
0
0
2
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
2
4
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
1
0
1
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
1
1
2
2
1
2
0
0
0
0
0
0
0
1
0
2
2
1
0
0
1
0
0
0
1
3
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
6
0
0
0
0
1
0
2
0
0
0
0
4
0
1
0
0
0
0
1
0
0
8
0
0
0
0
0
0
1
0
1
2
1
0
0
0
0
0
0
5
1
0
0
0
0
0
2
0
2
1
1
0
1
0
0
0
1
1
1
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
1
0
0
0
0
1
1
1
0
2
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
3
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
1
2
0
0
0
1
1
0
2
0
5
2
0
0
1
0
0
0
2
0
0
0
3
0
1
3
0
0
3
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
2
0
0
6
0
3
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
1
0
0
6
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
2
2
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
4
0
0
0
0
0
2
0
1
0
1
0
2
0
1
0
0
0
0
0
3
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
7
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
5
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
5
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
3
1
0
0
1
1
0
0
0
1
0
0
0
18
0
0
0
0
0
1
1
0
0
1
0
0
0
3
0
1
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
1
0
1
0
2
1
0
0
0
2
0
0
2
2
0
1
0
5
1
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
2
0
0
2
2
0
2
1
0
0
4
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
8
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
1
1
0
2
0
0
3
2
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
3
0
2
1
0
1
3
0
1
0
0
0
0
0
1
0
0
3
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
3
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
3
0
1
1
0
0
2
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
2
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
3
1
1
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
5
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
1
1
2
0
13
0
0
0
0
0
2
3
0
0
0
1
0
0
3
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
1
2
0
1
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
2
1
1
0
0
2
0
0
0
0
1
3
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
1
0
0
0
2
0
0
2
1
0
0
0
1
0
0
0
3
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
1
0
0
0
2
1
2
0
1
0
1
0
0
0
0
1
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
1
1
1
1
0
0
2
2
0
1
0
0
0
0
1
1
0
0
1
1
0
0
0
0
1
0
1
0
2
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
6
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
3
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
1
1
0
0
2
0
3
0
2
0
1
0
0
0
1
0
2
0
0
0
2
0
2
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
2
1
3
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
1
1
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
1
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
4
0
0
0
0
2
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
2
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
3
0
0
2
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
3
1
0
0
0
0
0
0
1
0
3
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
1
0
3
0
0
0
1
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
1
2
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
1
0
2
2
0
0
0
2
2
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
6
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
2
0
4
0
0
0
0
3
7
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
2
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
2
1
2
1
0
1
0
1
2
0
0
0
0
0
0
13
0
0
0
0
0
0
0
0
0
1
2
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
4
2
0
0
0
0
0
1
1
3
0
0
0
0
4
0
0
0
2
0
0
0
1
0
0
2
2
0
1
0
0
7
0
1
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
1
0
0
1
1
2
1
1
0
0
0
2
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
1
0
9
2
0
0
0
0
1
1
0
1
0
2
0
0
1
0
2
2
0
0
2
0
1
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
3
0
2
0
0
0
1
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
3
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
4
0
0
1
0
0
0
0
0
0
2
0
1
0
2
0
0
0
2
0
0
1
1
0
0
0
2
0
0
0
2
0
0
4
0
0
0
0
1
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
5
2
5
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
2
2
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
1
1
0
0
3
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
3
0
0
5
0
0
2
0
0
0
6
0
0
0
1
0
2
2
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
1
0
0
1
0
0
2
2
0
0
0
0
0
0
0
2
1
0
1
0
2
1
0
0
0
0
0
1
0
1
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
1
2
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
1
0
2
0
1
1
0
2
0
0
0
1
1
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
1
1
1
0
0
0
0
0
0
0
2
0
1
0
0
3
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
2
0
0
0
0
5
0
3
0
0
0
0
1
0
0
0
3
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
2
0
2
0
1
0
0
0
1
0
4
0
0
0
0
0
2
0
2
0
0
0
0
5
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
3
0
0
0
1
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
9
0
0
0
2
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
2
0
5
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
1
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
1
0
0
0
2
0
2
0
0
4
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
1
0
0
2
0
2
0
0
2
0
0
0
0
0
1
3
0
0
0
2
2
0
0
0
0
0
0
0
1
0
3
0
2
0
2
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
2
0
0
0
2
0
0
0
1
2
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
1
1
0
0
1
0
0
0
2
0
0
0
0
0
3
0
1
1
0
1
0
3
0
0
3
2
1
0
0
0
0
0
0
0
0
3
0
0
4
0
1
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
1
0
2
1
0
2
0
0
0
0
0
0
0
0
1
1
1
0
0
2
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
1
2
0
0
4
0
0
1
0
2
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
6
0
0
0
2
0
0
1
0
2
0
0
0
0
1
1
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
4
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
2
0
0
3
0
5
1
1
1
0
2
1
2
2
0
0
0
0
0
0
1
2
2
0
0
0
0
0
2
2
2
0
1
0
1
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
2
2
2
2
1
0
0
2
1
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
2
1
0
1
0
1
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
1
0
1
0
1
0
0
3
0
3
1
0
0
4
0
0
1
3
0
2
2
0
1
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
2
2
0
0
0
2
0
3
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
2
1
0
2
0
3
0
0
0
0
0
0
0
0
0
2
1
0
3
2
0
0
0
0
3
1
0
0
0
1
0
0
0
0
1
0
2
2
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
3
0
2
2
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
2
3
0
1
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
5
0
0
2
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
2
0
0
0
2
0
0
2
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
1
2
1
1
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
4
0
1
0
0
0
0
0
1
1
0
0
0
0
2
1
0
0
0
0
2
1
0
10
0
0
0
0
0
2
0
2
2
2
0
0
0
0
2
0
0
1
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
2
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
1
0
0
0
6
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
1
3
0
0
0
0
0
1
2
0
0
3
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
2
0
0
3
0
0
0
3
3
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
1
1
2
3
1
0
1
1
2
1
0
0
0
0
0
0
1
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
2
2
1
1
2
2
0
0
0
0
0
0
0
0
3
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
1
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
3
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
3
1
0
0
0
1
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
2
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
2
1
1
0
0
2
2
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
5
0
0
0
0
1
0
1
0
6
0
0
1
2
1
0
0
0
0
0
2
0
0
0
1
0
3
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
2
0
0
1
0
2
0
1
0
4
1
2
0
2
0
0
1
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
3
0
3
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
3
3
0
0
0
0
1
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
2
2
1
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
1
13
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
3
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
3
0
2
2
0
0
3
1
1
1
0
1
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
5
0
2
1
4
0
0
4
0
1
0
0
0
3
0
0
1
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
2
1
2
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
2
0
0
1
0
2
0
0
0
0
0
1
2
0
0
0
0
1
0
0
1
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
1
1
0
2
0
0
0
0
7
0
1
2
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
2
2
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
2
0
1
0
1
0
0
0
0
0
1
2
3
0
0
2
0
0
0
0
2
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
3
0
3
0
5
0
0
2
2
1
2
3
2
0
0
0
1
0
0
0
0
0
2
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
3
0
0
2
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
3
2
0
2
0
0
0
2
0
0
1
0
0
2
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
2
0
0
0
1
3
1
0
0
0
2
0
0
0
3
2
1
0
0
4
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
2
0
1
2
0
1
1
0
0
0
0
0
1
0
2
0
0
2
1
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
5
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
1
0
0
1
0
2
4
0
1
0
3
1
2
2
0
0
2
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
9
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
1
1
1
0
1
0
4
0
3
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
1
2
0
2
2
1
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
2
1
0
0
0
2
0
0
0
0
0
1
0
2
0
0
1
1
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
3
0
0
1
0
2
0
2
0
0
0
1
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
1
0
0
0
1
1
0
3
1
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
4
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
1
0
1
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
2
0
1
0
2
1
2
0
0
0
0
0
0
2
0
2
3
0
0
0
2
0
1
1
0
1
0
0
0
0
0
2
0
0
1
0
3
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
2
0
0
1
0
0
1
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
1
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
1
2
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
1
0
2
0
2
0
0
0
4
2
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
2
0
0
0
0
3
0
2
0
0
0
0
2
0
0
2
2
0
0
0
0
0
2
3
0
0
0
0
2
0
0
0
1
0
0
1
0
2
0
2
4
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
3
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
1
0
1
0
0
0
0
0
1
2
1
0
0
2
0
0
2
0
2
0
0
0
1
1
0
0
0
2
0
0
0
1
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
1
0
0
11
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
2
3
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
1
0
1
2
2
0
0
0
0
0
1
0
3
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
1
0
2
1
0
2
1
0
0
0
1
0
0
0
0
2
0
0
1
2
4
1
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
3
0
0
0
0
1
2
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
1
1
0
4
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
2
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
1
0
0
0
0
3
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
1
0
3
1
0
0
0
0
0
0
1
1
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
3
1
1
0
0
2
0
1
0
0
0
2
1
0
0
2
0
0
0
3
0
0
1
0
6
0
2
1
0
0
0
0
1
0
1
0
0
1
8
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
7
0
1
1
1
4
2
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
1
3
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
2
1
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
1
1
1
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
5
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
1
1
0
0
0
1
0
4
0
2
0
0
0
2
0
0
0
0
0
5
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
4
0
2
2
4
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
2
1
0
2
0
1
0
0
2
0
0
2
0
0
0
1
0
2
0
0
0
0
0
3
1
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
2
1
1
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
1
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
2
2
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
4
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
3
0
0
0
0
0
1
0
2
2
4
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
3
0
0
0
1
0
0
0
0
2
1
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
3
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
2
1
2
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
1
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
2
0
0
0
0
1
0
0
1
0
0
0
1
1
0
2
0
0
4
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
9
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
1
1
0
0
0
3
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
2
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
4
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
2
0
2
0
0
1
1
0
1
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
1
0
0
0
0
2
0
0
2
2
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
7
0
6
0
0
0
0
1
3
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
1
2
0
0
0
0
0
2
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
1
0
2
0
1
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
1
3
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
2
2
4
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
2
0
1
1
0
0
0
1
0
0
0
0
0
2
1
0
1
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
2
2
0
0
0
0
0
0
3
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
2
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
3
0
2
0
1
0
0
0
0
1
1
1
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
2
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
3
0
3
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
2
0
2
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
2
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
1
0
2
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
5
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
3
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
0
1
2
0
3
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
2
0
0
3
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
4
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
2
0
0
0
2
0
3
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
1
0
1
2
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
7
0
1
0
1
0
0
1
1
0
0
1
5
0
3
1
0
0
2
0
0
0
1
9
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
4
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
2
0
0
0
0
2
1
0
3
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
1
0
0
1
1
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
9
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
2
3
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
2
0
1
0
0
1
0
0
1
0
0
0
0
3
0
0
0
0
0
2
1
0
0
0
2
1
0
1
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
6
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
3
1
0
0
0
0
0
1
1
0
0
0
4
0
0
0
0
0
0
1
1
2
3
1
0
0
0
2
0
0
1
0
1
2
0
0
1
0
2
0
0
0
1
1
0
1
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
2
0
1
1
0
0
1
1
1
0
0
0
0
1
0
0
0
4
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
4
0
0
0
0
0
5
0
2
0
0
0
0
0
0
0
2
0
0
0
1
1
4
0
0
1
0
0
0
2
0
0
0
9
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
5
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
2
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
4
3
0
0
0
0
2
1
0
0
3
0
1
0
0
0
2
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
1
0
2
1
2
1
0
2
0
1
0
0
3
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
3
0
0
2
0
0
1
1
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
2
0
0
0
4
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
9
0
0
0
0
1
2
0
0
2
0
0
0
0
0
1
2
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
1
0
2
0
0
0
2
0
1
0
0
1
2
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
5
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
1
0
3
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
1
1
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
1
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
1
2
0
0
1
2
1
1
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
4
0
0
0
0
0
1
1
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
1
0
1
0
0
0
0
2
3
0
0
0
1
2
0
0
4
0
0
1
2
0
0
0
0
0
0
1
2
0
0
0
0
1
2
0
2
0
4
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
1
0
0
0
2
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
1
2
2
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
1
0
2
5
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
1
1
0
0
0
2
0
0
0
0
0
0
4
2
1
0
0
0
0
0
0
1
0
0
4
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
1
2
0
0
0
0
0
4
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
1
0
4
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
3
0
1
0
0
0
0
2
0
0
0
6
0
1
0
1
0
2
0
2
2
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
3
0
0
8
0
2
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
3
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
5
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
1
0
3
0
0
0
2
5
0
0
0
0
3
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
15
1
0
0
0
0
3
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
1
0
0
1
0
0
2
1
1
0
0
0
0
0
2
0
0
1
0
0
1
1
0
0
1
0
0
0
1
2
0
4
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
3
0
1
0
0
2
2
0
1
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
2
0
0
3
0
0
0
2
0
1
0
0
0
1
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
1
0
2
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
1
13
0
0
3
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
2
3
3
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
3
1
0
1
0
0
2
0
1
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
2
1
2
1
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
1
2
0
2
2
0
0
0
0
7
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
1
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
1
1
0
0
5
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
3
0
0
0
0
1
0
4
0
0
0
0
0
0
0
1
0
2
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
1
0
0
2
0
0
0
1
0
3
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
1
0
2
0
0
1
2
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
2
0
0
0
0
4
0
2
0
0
2
0
0
1
0
0
0
1
0
0
0
1
2
1
0
0
2
0
1
0
0
0
4
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
1
1
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
2
0
0
0
1
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
1
0
2
0
2
1
0
0
0
0
0
3
0
2
1
1
0
0
2
0
1
1
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
1
2
2
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
15
0
0
2
0
0
0
2
0
0
0
0
1
2
0
2
0
1
2
0
0
0
0
0
2
0
2
1
0
1
0
1
0
0
0
0
1
0
2
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
3
3
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
2
0
0
2
0
0
2
0
0
2
0
0
0
0
0
3
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
3
2
0
0
0
0
3
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
0
0
1
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
2
0
0
0
0
0
0
3
1
0
2
0
0
0
0
0
0
0
0
1
2
0
2
0
3
0
1
0
2
2
0
0
0
0
1
0
0
0
3
0
1
1
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
3
0
1
0
0
0
0
0
0
2
0
4
2
0
2
1
0
0
0
0
0
1
0
0
1
1
2
0
1
0
0
0
0
1
1
0
2
1
0
0
0
0
0
1
8
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
3
1
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
2
1
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
1
0
0
2
3
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
2
0
0
3
0
2
2
1
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
1
2
0
1
0
0
2
0
0
0
2
1
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
2
0
0
1
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
1
0
0
2
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
3
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
1
2
0
0
2
0
0
0
1
0
0
3
1
0
0
0
2
0
1
0
0
2
2
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
3
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
5
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
2
0
0
0
2
2
0
0
0
2
0
0
0
1
0
1
0
0
0
2
0
1
0
2
2
0
0
0
0
0
2
0
0
0
1
0
3
1
0
3
0
1
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
2
2
0
0
0
0
0
2
2
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
2
2
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
2
2
0
0
0
4
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
1
2
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
4
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
1
2
2
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
2
1
0
0
1
1
0
1
0
2
0
2
0
0
3
0
0
0
0
0
1
2
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
1
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
11
0
0
0
4
1
3
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
4
0
0
0
3
0
0
0
2
0
0
2
0
0
0
2
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
2
0
0
2
2
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
3
5
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
8
0
2
1
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
5
0
0
2
0
0
2
0
0
6
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
3
0
2
0
0
0
2
0
0
0
2
1
0
2
1
1
0
0
2
0
0
0
0
1
0
0
0
0
3
0
0
0
3
0
0
8
0
0
2
0
3
1
0
0
0
0
0
2
1
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
1
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
6
2
2
0
1
0
0
2
0
0
0
1
0
0
0
2
2
0
1
0
0
0
1
0
0
3
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
3
0
2
2
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
3
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
1
2
0
0
0
0
0
0
1
2
3
0
0
2
1
0
0
0
0
1
0
2
2
0
1
1
0
0
0
0
0
0
0
2
2
2
1
0
0
1
0
1
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
1
1
0
0
2
2
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
7
0
0
0
1
0
0
0
0
0
1
0
0
0
3
0
0
1
0
2
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
2
2
1
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
3
5
0
0
0
0
1
0
0
1
0
0
3
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
3
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
4
1
0
1
0
0
0
0
2
1
0
0
0
2
2
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
4
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
2
1
0
0
0
0
0
1
0
1
0
2
1
0
0
0
0
0
0
5
0
0
0
0
1
0
1
2
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
2
0
2
2
2
1
0
0
0
0
0
0
2
0
6
0
0
0
0
1
0
2
0
2
0
0
0
2
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
2
0
0
3
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
3
0
0
0
0
0
2
1
0
0
0
0
5
0
1
0
0
0
1
0
0
0
3
1
0
2
0
1
0
1
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
1
1
0
0
1
0
0
4
0
0
0
0
2
3
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
8
1
0
0
0
0
0
0
3
0
1
1
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
1
0
0
1
0
2
2
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
1
1
2
0
1
0
0
0
0
0
2
0
0
0
0
2
2
0
2
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
2
2
0
0
1
0
1
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
1
0
0
2
0
1
0
2
2
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
1
3
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
1
5
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
1
2
0
2
0
2
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
2
1
0
1
1
0
2
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
4
2
0
2
0
0
1
2
0
2
0
1
0
0
2
2
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
2
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
3
0
1
1
2
0
0
0
1
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
3
0
1
0
2
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
1
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
2
0
2
0
0
3
0
1
0
0
2
0
0
1
0
0
0
1
0
0
0
0
1
0
2
0
0
1
1
0
0
0
0
0
1
0
0
2
0
0
0
1
0
2
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
1
0
0
0
2
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
1
0
0
2
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
4
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
5
0
0
2
3
0
2
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
2
0
0
0
0
2
1
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
2
1
0
0
0
2
1
0
2
3
0
0
0
0
1
0
0
0
1
0
0
0
0
1
3
0
2
1
0
0
0
2
0
2
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
2
0
0
1
0
1
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
2
4
2
0
0
0
0
0
0
1
0
0
2
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
2
3
0
2
0
2
0
0
0
0
0
0
0
1
2
4
2
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
1
2
2
1
0
0
1
2
0
0
0
0
0
2
0
2
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
3
1
1
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
1
2
1
1
0
0
2
0
0
1
0
0
1
0
0
0
2
1
2
1
1
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
5
0
1
1
0
0
0
0
1
0
2
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
3
0
4
0
0
0
0
0
9
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
2
0
2
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
1
1
0
0
0
6
3
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
1
0
4
1
0
0
0
5
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
2
0
2
0
0
0
0
1
0
2
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
4
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
3
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
2
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
2
2
2
0
0
1
2
1
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
3
1
1
0
1
0
0
0
1
2
0
0
0
0
2
0
1
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
1
2
0
2
0
0
1
0
0
0
2
2
0
0
1
0
1
1
0
0
0
0
0
0
1
0
1
0
0
2
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
2
0
0
0
3
0
0
2
0
0
0
0
3
0
0
1
2
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
4
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
1
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
1
0
1
0
2
0
0
0
0
2
0
0
1
1
0
1
0
2
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
2
0
2
1
1
0
1
0
3
2
0
5
1
0
1
0
2
0
1
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
1
1
0
0
2
0
1
1
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
2
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
3
0
2
1
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
1
0
0
0
0
0
1
0
0
1
2
0
3
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
18
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
3
0
2
0
3
2
0
0
1
0
1
1
1
0
0
0
0
0
0
2
1
0
0
2
0
0
0
1
2
2
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
3
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
2
1
0
0
1
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
1
2
0
1
0
0
4
0
0
0
1
0
2
0
0
0
0
1
3
0
0
1
0
1
0
0
3
0
0
0
0
0
1
0
0
0
0
4
1
1
0
0
0
0
0
2
1
0
0
0
1
2
0
0
0
2
3
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
1
0
2
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
2
1
0
0
0
2
0
0
1
0
0
1
0
1
3
1
0
2
0
2
1
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
2
0
0
0
0
0
0
2
0
0
16
2
0
1
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
2
1
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
1
0
2
2
0
0
0
0
0
3
0
0
0
0
1
1
2
0
0
0
0
1
0
0
0
3
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
3
0
0
0
4
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
3
0
2
0
0
4
0
0
3
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
4
2
0
0
0
3
0
0
0
2
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
4
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
2
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
3
0
2
1
2
0
0
0
0
0
0
1
0
1
0
1
0
1
0
3
0
1
0
0
4
0
1
0
0
0
0
2
1
1
0
0
1
0
2
0
0
0
0
0
0
1
1
0
2
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
2
4
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
19
0
0
0
0
0
4
0
0
3
0
2
0
0
0
0
1
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
1
2
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
1
0
2
0
0
2
2
0
0
0
0
0
0
0
0
3
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
1
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
3
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
1
0
0
2
2
0
0
1
0
0
0
2
1
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
2
0
0
1
2
0
0
1
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
4
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
3
2
0
0
0
1
0
0
1
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
4
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
2
0
1
0
1
2
0
0
0
1
0
2
1
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
2
2
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
1
1
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
3
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
2
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
0
0
1
0
2
1
0
0
1
0
8
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
1
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
2
1
1
0
4
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
3
0
2
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
2
0
0
1
0
3
0
2
1
2
1
0
0
0
0
2
0
0
0
0
0
1
4
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
1
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
1
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
2
2
0
0
0
0
0
0
2
0
1
1
0
4
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
2
1
0
0
0
0
0
0
5
2
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
1
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
2
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
2
0
4
1
0
0
1
0
0
0
0
1
0
0
0
3
0
3
0
0
0
2
1
2
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
4
1
2
2
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
3
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
4
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
2
6
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
1
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
3
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
1
2
0
0
1
0
2
0
0
0
0
1
1
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
3
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
5
0
1
0
0
0
0
0
5
0
0
2
0
0
2
0
0
0
0
0
0
0
3
1
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
2
2
0
0
0
2
0
0
1
0
0
5
2
0
0
2
0
0
3
0
2
0
0
0
1
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
3
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
3
2
0
0
1
0
0
3
0
0
0
0
1
1
0
0
0
2
0
0
2
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
2
0
0
6
1
1
1
0
1
1
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
2
0
0
0
0
1
0
0
2
1
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
1
2
0
0
2
2
0
0
3
0
0
0
0
1
0
3
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
3
2
0
0
0
0
0
0
2
0
0
0
1
3
4
0
0
0
0
0
0
0
0
0
0
2
2
0
0
3
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
2
2
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
1
0
3
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
1
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
5
0
0
0
0
0
2
0
0
0
0
1
0
2
0
1
1
0
0
0
0
0
2
0
0
0
0
0
1
5
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
2
2
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
3
0
0
2
0
0
1
0
0
0
2
0
0
0
1
0
0
2
2
1
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
2
0
0
1
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
6
0
0
0
0
4
0
0
0
2
0
0
2
0
0
0
0
0
2
2
2
2
0
0
0
1
0
0
0
0
0
0
0
2
0
11
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
4
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
7
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
7
0
1
0
1
0
6
1
0
4
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
1
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
1
0
2
0
0
0
0
2
0
0
0
1
0
0
0
5
0
0
0
1
3
0
0
0
0
0
1
0
2
0
1
0
0
0
0
2
0
2
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
1
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
1
0
0
1
0
2
0
0
2
0
1
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
2
1
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
1
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
1
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
2
0
2
2
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
1
0
0
3
0
0
1
0
1
2
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
3
0
0
2
1
1
0
2
0
0
0
3
0
0
1
0
2
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
3
0
0
2
1
2
2
0
3
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
2
1
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
3
1
0
0
1
0
0
0
2
1
0
0
0
0
0
1
0
2
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
3
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
3
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
6
0
1
0
0
0
0
0
0
0
0
9
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
2
0
0
0
1
0
1
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
6
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
2
1
1
3
0
0
1
0
0
1
0
0
0
3
1
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
2
0
0
2
0
2
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
1
1
0
0
0
0
2
0
1
0
0
2
2
0
2
0
1
2
2
1
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
2
0
1
0
0
0
0
2
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
1
0
0
3
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
7
2
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
4
0
0
0
2
0
0
1
1
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
5
0
0
2
3
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
2
0
3
0
1
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
4
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
1
0
0
0
2
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
3
3
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
11
0
0
2
0
3
0
0
1
2
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
2
0
5
0
0
1
0
0
1
0
2
2
2
2
0
0
0
1
0
2
2
0
0
0
0
1
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
1
0
0
0
0
0
1
0
0
0
2
0
1
0
0
3
3
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
2
0
0
2
2
0
4
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
3
4
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
2
0
0
1
0
0
0
1
2
0
0
0
0
0
0
2
2
0
0
3
2
0
0
0
1
0
0
0
3
3
0
0
3
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
2
1
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
4
1
0
0
2
0
2
0
0
0
0
2
0
3
0
2
0
0
0
0
0
0
2
0
0
0
2
2
0
1
0
1
1
0
0
0
1
0
0
0
1
0
0
2
0
2
0
0
0
0
2
1
0
0
0
3
2
0
0
0
2
1
1
3
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
2
2
0
1
0
2
0
5
0
1
0
0
0
11
0
0
0
0
0
0
0
0
2
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
2
0
3
0
0
1
0
3
3
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
1
0
3
0
1
0
2
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
1
0
1
0
0
0
0
1
0
1
0
1
0
0
0
2
1
0
1
8
0
2
2
0
1
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
5
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
1
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
1
0
0
0
0
1
0
2
0
0
3
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
1
2
1
0
2
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
1
0
0
2
1
1
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
2
1
0
0
1
0
0
1
1
1
2
0
0
2
0
2
0
1
3
0
3
1
0
0
0
0
0
0
1
3
1
2
0
2
0
3
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
3
0
0
5
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
2
0
2
1
1
2
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
3
0
2
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
1
1
0
0
1
2
0
2
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
4
0
0
0
0
0
0
4
2
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
1
0
1
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
1
0
2
0
2
0
0
4
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
1
2
2
3
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
1
0
2
0
0
0
2
0
0
1
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
3
3
1
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
1
2
0
0
2
0
0
1
2
0
0
0
1
1
0
0
0
1
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
3
1
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
1
0
0
2
1
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
2
0
0
0
0
0
0
1
2
0
0
4
1
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
1
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
1
0
0
2
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
4
0
0
0
3
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
1
0
2
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
2
0
0
0
0
0
1
0
0
2
0
1
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
2
4
0
0
0
0
0
2
0
0
1
0
4
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
10
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
2
1
0
2
0
0
0
2
1
2
0
0
2
2
2
0
0
2
0
0
0
2
0
0
0
2
2
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
4
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
1
2
2
0
2
0
1
0
0
0
1
0
3
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
3
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
2
2
0
2
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
4
1
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
4
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
2
7
2
0
0
0
0
2
2
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
1
0
1
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
1
0
3
0
0
0
4
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
2
0
1
0
2
2
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
2
1
0
0
0
3
0
1
3
2
0
0
0
0
0
0
2
0
0
2
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
3
0
0
0
0
0
1
0
3
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
2
1
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
5
1
0
0
1
0
0
1
0
0
1
0
0
1
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
4
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
7
0
1
0
0
1
0
2
0
0
0
0
0
0
1
0
0
1
2
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
3
0
0
0
0
0
0
1
1
2
2
0
0
2
0
2
0
0
4
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
2
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
1
2
0
0
0
3
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
3
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
1
1
1
0
0
0
0
0
0
2
0
1
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
5
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
2
0
2
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
2
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
3
2
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
2
0
1
3
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
2
0
1
0
0
0
0
0
1
1
0
0
0
1
1
1
1
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
2
0
0
2
0
0
2
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
1
0
1
0
0
0
1
2
0
2
0
0
2
0
0
0
0
0
0
0
1
2
0
1
0
0
1
0
2
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
4
0
2
1
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
2
0
0
2
0
0
1
0
0
0
0
2
0
5
0
0
0
2
0
0
0
1
0
2
2
0
0
0
1
5
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
8
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
1
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
3
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
1
0
0
3
0
4
0
4
2
0
0
0
0
1
0
0
2
1
0
1
0
0
2
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
2
0
1
1
2
0
2
3
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
2
0
0
1
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
4
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
2
0
0
1
0
0
0
1
0
0
0
4
1
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
3
0
2
0
1
2
0
0
0
0
1
2
0
0
1
1
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
1
1
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
2
0
0
1
0
0
1
1
0
0
0
3
1
0
5
0
0
1
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
2
1
0
1
1
2
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
4
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
1
0
0
0
0
0
0
0
1
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
2
0
0
8
1
0
0
0
0
4
0
0
0
0
0
2
2
0
0
3
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
2
0
0
1
0
1
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
3
2
0
0
0
2
0
2
0
0
0
0
1
3
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
4
0
0
0
0
0
0
0
5
0
0
1
0
1
0
0
1
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
1
0
4
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
2
0
0
0
1
0
0
0
0
3
0
1
2
0
0
2
5
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
2
2
0
0
3
0
0
0
0
0
0
0
2
2
0
0
0
0
2
2
0
0
6
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
1
1
0
2
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
3
1
0
4
0
0
2
0
7
0
0
2
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
2
1
1
0
0
0
2
2
0
1
2
0
3
0
0
0
0
0
0
1
0
0
0
0
3
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
3
2
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
3
3
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
2
0
0
3
0
0
0
0
2
0
0
0
1
1
0
0
2
0
0
1
1
0
2
1
0
1
0
0
0
0
2
0
1
2
0
0
3
0
1
0
0
0
0
1
1
1
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
6
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
1
1
0
1
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
3
0
0
1
0
3
0
0
0
2
0
0
0
2
0
0
1
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
2
1
0
0
0
3
0
1
0
1
0
0
1
0
0
2
0
0
0
2
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
1
0
0
0
2
0
0
1
0
0
1
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
1
0
1
0
0
1
0
0
0
0
1
1
2
2
0
0
0
1
2
0
1
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
4
0
1
0
0
0
0
1
1
0
2
0
0
0
1
0
0
0
2
1
1
0
0
0
0
1
3
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
2
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
1
0
0
1
0
0
3
0
0
0
0
1
0
0
0
0
2
0
2
0
0
2
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
1
1
0
1
1
0
0
0
0
0
0
2
0
0
0
1
0
0
1
1
1
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
3
0
3
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
4
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
1
1
1
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
2
0
1
1
0
1
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
1
1
0
0
2
0
1
0
0
0
0
3
5
3
0
1
0
0
0
1
0
1
0
0
0
0
2
2
2
0
0
0
0
0
1
0
0
0
0
1
0
2
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
2
2
2
0
0
0
0
0
0
1
0
0
1
0
0
2
2
0
1
2
0
2
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
2
0
6
0
0
1
0
1
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
1
2
3
1
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
1
2
1
0
2
0
4
0
1
2
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
3
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
1
3
2
0
3
0
0
1
0
0
3
3
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
1
0
0
2
0
0
0
1
2
0
4
0
2
0
0
0
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
1
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
3
1
0
0
0
0
0
0
0
0
1
0
1
0
3
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
1
2
1
0
2
0
0
0
3
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
1
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
5
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
6
2
0
2
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
2
0
0
2
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
5
0
0
0
0
0
0
1
0
0
0
0
1
2
1
0
1
0
0
0
0
0
0
4
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
1
1
0
0
2
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
1
0
0
2
1
0
0
0
1
0
1
0
0
0
1
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
1
0
1
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
2
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
3
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
2
0
2
0
2
1
2
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
5
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
2
0
0
1
2
0
0
2
0
0
0
2
2
0
2
0
2
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
2
0
0
2
0
0
0
2
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
2
2
0
0
2
0
0
0
0
3
0
2
0
0
0
0
0
0
0
2
0
2
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
5
0
0
0
0
2
0
0
0
2
0
0
0
2
0
1
0
0
0
10
2
0
0
0
0
1
0
0
0
0
1
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
3
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
4
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
4
2
1
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
1
1
0
1
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
2
0
0
1
2
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
1
2
0
0
0
5
1
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
2
2
0
2
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
4
0
0
0
2
0
1
0
0
2
0
0
1
0
0
0
2
0
2
2
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
1
0
1
0
3
1
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
1
0
0
2
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
1
1
0
0
2
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
6
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
1
2
0
0
4
2
0
0
0
0
1
1
2
3
1
0
0
1
0
3
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
1
3
1
0
2
0
0
0
1
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
1
3
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
4
0
0
1
0
0
0
0
2
0
0
0
0
1
0
1
0
1
1
0
0
1
1
0
1
0
1
1
0
3
0
3
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
2
0
2
0
2
0
2
0
1
0
1
12
0
0
3
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
2
0
0
1
0
1
0
0
2
0
1
2
0
1
0
0
0
2
0
0
0
0
4
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
1
0
2
1
0
0
1
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
1
3
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
2
0
0
0
0
0
0
2
1
2
1
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
3
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
7
0
2
0
1
0
0
2
0
0
1
0
0
0
1
1
1
0
3
0
0
0
0
0
0
1
0
1
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
3
0
12
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
5
1
2
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
7
0
0
0
2
0
0
0
1
8
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
1
1
2
0
0
3
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
2
1
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
1
0
5
1
0
0
0
2
1
0
0
0
2
1
3
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
2
1
0
2
0
0
0
1
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
7
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
4
4
0
0
1
0
1
0
0
0
0
0
2
1
2
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
7
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
2
0
0
2
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
1
0
0
2
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
2
0
0
0
0
1
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
17
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
3
0
0
1
0
0
0
5
0
0
3
1
0
2
0
2
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
3
1
2
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
2
0
1
0
1
0
1
0
3
0
1
2
1
0
0
2
2
0
0
0
0
2
2
2
0
2
0
1
0
0
0
0
2
0
0
0
3
0
0
0
2
0
0
0
3
1
0
0
1
0
0
0
0
3
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
3
0
0
1
2
0
1
0
0
0
0
1
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
1
0
1
0
0
0
1
2
0
0
0
2
0
1
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
3
1
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
3
0
4
0
0
0
0
1
0
0
3
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
1
2
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
5
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
1
2
0
2
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
3
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
2
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
2
0
0
2
1
0
0
0
3
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
3
0
1
0
0
0
0
0
3
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
1
0
0
0
0
0
2
1
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
1
0
0
0
2
1
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
3
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
1
2
0
5
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
1
0
2
2
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
1
1
2
1
0
0
2
0
6
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
2
0
0
0
1
0
0
1
2
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
1
1
0
2
0
2
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
5
0
0
0
0
0
1
2
0
1
0
2
1
0
0
0
2
0
0
0
1
0
1
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
1
0
1
0
2
0
0
2
1
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
2
2
0
0
1
0
3
0
0
3
0
0
0
1
1
2
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
2
1
1
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
3
0
0
1
0
0
2
0
4
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
2
1
0
2
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
1
0
4
0
1
1
0
0
2
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
1
2
0
2
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
5
3
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
6
0
2
0
1
0
0
0
2
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
2
1
0
0
3
0
0
4
0
3
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
2
1
0
1
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
2
1
0
0
2
1
1
0
0
0
0
0
2
2
0
0
0
2
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
1
0
6
1
0
0
1
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
1
0
0
2
1
0
0
0
0
1
2
3
0
0
3
0
0
0
0
1
0
2
0
0
1
0
0
1
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
1
2
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
3
2
1
1
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
4
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
2
0
0
1
1
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
2
1
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
2
0
4
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
1
0
0
2
0
2
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
1
2
1
0
0
11
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
1
1
1
3
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
2
0
0
0
4
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
2
0
0
0
0
2
0
0
0
1
1
0
1
0
2
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
1
2
0
1
3
0
0
2
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
3
0
0
0
0
0
3
1
5
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
1
0
0
2
0
0
0
2
3
0
1
0
1
0
0
1
0
0
0
0
2
0
0
0
3
0
2
0
0
0
0
1
0
0
1
0
0
1
3
0
1
2
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
1
4
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
0
0
1
0
0
3
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
1
0
0
0
0
0
1
2
0
0
0
1
0
0
0
2
0
1
1
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
5
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
2
0
2
2
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
3
0
0
2
0
0
1
2
0
0
0
0
0
4
0
4
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
1
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
1
0
3
0
1
0
0
0
0
0
1
0
1
0
0
1
2
0
0
1
0
0
0
0
0
0
5
0
0
0
0
0
2
0
0
0
2
4
0
0
0
1
0
0
3
2
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
7
0
2
0
0
0
0
1
2
0
0
0
3
0
0
0
0
0
0
0
0
0
3
3
0
1
0
0
0
1
1
0
2
0
0
0
0
2
1
0
0
0
0
2
0
0
0
2
0
2
0
2
11
1
0
0
0
0
2
0
0
1
0
1
0
0
2
0
0
0
0
0
3
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
6
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
2
0
0
0
0
0
0
1
0
0
2
3
0
0
0
1
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
3
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
2
0
1
3
0
0
0
0
0
2
0
0
3
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
1
2
2
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
1
3
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
3
0
0
0
2
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
2
2
7
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
6
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
1
0
0
0
2
0
2
1
2
0
0
0
0
2
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
1
1
0
0
2
2
0
1
1
0
0
1
2
2
0
0
2
0
0
1
1
1
1
0
1
0
0
0
1
0
0
0
2
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
1
0
1
1
2
0
0
0
2
0
4
0
0
0
1
0
1
0
0
1
0
0
0
2
2
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
2
0
0
3
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
2
2
0
0
2
2
2
0
2
0
0
0
4
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
2
1
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
3
2
0
0
0
2
1
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
4
0
1
0
0
0
2
0
3
2
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
2
0
0
5
2
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
2
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
2
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
1
0
0
3
0
0
2
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
1
0
4
2
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
3
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
8
2
0
0
0
1
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
1
1
1
2
0
2
2
0
0
0
4
0
1
0
3
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
6
0
0
0
1
0
0
2
0
0
0
0
2
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
1
0
0
1
3
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
2
1
2
0
2
0
0
2
0
0
1
0
0
0
1
0
0
0
2
0
0
5
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
5
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
2
0
0
0
1
1
1
2
0
0
0
0
0
0
0
0
0
1
0
1
1
3
0
0
0
1
0
0
2
0
2
0
2
2
0
0
1
2
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
5
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
2
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
1
0
8
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
1
0
4
2
0
2
1
0
0
0
0
0
0
0
0
3
1
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
3
0
0
2
1
2
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
2
0
4
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
1
2
0
4
0
0
2
1
0
0
1
0
6
1
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
2
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
4
0
0
0
0
0
0
1
2
0
1
2
0
0
0
2
0
1
0
0
0
0
1
0
2
1
0
0
0
2
0
0
2
1
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
1
0
0
2
2
0
0
0
0
1
0
0
0
1
2
0
2
0
0
0
0
2
0
1
2
0
0
1
2
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
3
1
0
0
0
1
4
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
2
0
0
3
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
2
2
2
2
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
5
0
0
0
1
1
2
0
2
0
0
0
0
1
1
0
0
0
0
0
0
2
2
1
0
0
0
1
0
1
0
0
3
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
2
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
1
1
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
2
0
0
1
0
0
1
0
3
0
1
0
0
0
0
0
3
0
0
0
0
0
1
1
1
0
1
0
1
1
2
2
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
3
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
2
0
0
1
0
0
0
0
5
0
1
1
0
0
11
2
3
0
0
4
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
1
0
0
2
0
0
0
1
0
0
0
0
0
0
1
3
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
2
0
4
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
1
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
3
0
0
0
0
0
2
0
0
0
1
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
3
0
0
0
0
0
1
0
0
0
3
0
1
1
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
3
0
2
2
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
2
0
0
1
1
0
0
0
1
0
0
0
3
0
1
0
0
0
2
0
0
1
0
0
1
0
0
2
3
0
0
1
2
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
2
0
3
1
1
2
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
2
0
0
0
0
0
1
2
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
2
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
2
0
0
0
1
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
2
1
2
0
0
1
2
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
2
0
2
0
0
0
0
0
1
1
0
0
0
2
0
0
0
2
2
0
1
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
2
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
2
0
0
2
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
1
0
2
0
0
0
0
1
2
0
0
2
0
2
0
0
0
0
0
1
2
0
0
2
0
2
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
3
1
0
0
0
2
0
0
2
0
1
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
2
0
0
0
0
0
4
0
0
0
1
0
1
0
0
2
0
0
0
0
0
3
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
1
0
3
0
0
3
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
3
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
3
0
0
0
2
0
2
0
0
3
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
2
0
1
1
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
2
0
0
0
3
0
2
0
0
0
0
1
0
0
1
0
2
1
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
1
0
3
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
3
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
12
0
0
0
0
0
0
2
2
0
0
1
0
0
2
0
0
2
2
0
2
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
2
1
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
1
2
2
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
2
2
0
0
2
0
0
0
0
0
2
0
3
0
1
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
2
0
0
2
1
0
0
0
0
2
1
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
1
0
1
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
4
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
2
2
0
0
2
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
2
0
0
4
1
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
1
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
1
0
0
0
3
0
0
0
0
0
9
1
1
0
0
0
1
1
0
2
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
3
0
2
0
1
3
0
0
0
0
0
1
1
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
1
2
0
2
1
1
0
0
0
4
0
2
1
0
0
0
0
0
0
3
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
3
0
0
0
1
1
0
0
0
0
0
0
2
0
2
1
11
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
2
0
0
1
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
2
0
0
0
0
1
0
2
0
0
1
1
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
1
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
2
1
0
2
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
8
0
0
0
0
0
0
1
0
4
0
1
0
1
0
8
0
0
0
5
0
0
0
0
0
0
1
2
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
2
0
0
2
3
0
0
0
0
0
1
0
0
0
0
0
0
5
0
0
1
0
0
0
0
1
2
2
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
2
1
0
0
0
2
0
0
2
0
0
0
0
2
2
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
1
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
6
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
2
1
0
1
0
1
2
0
0
1
2
1
1
0
2
1
2
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
2
0
2
0
0
0
0
1
2
0
0
1
1
0
2
4
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
2
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
7
0
2
1
0
0
0
0
1
1
0
2
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
2
0
0
0
1
1
0
2
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
1
0
0
0
0
2
1
0
0
0
1
2
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
3
0
1
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
4
0
0
0
1
2
1
0
1
1
0
1
0
0
2
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
1
1
0
0
0
1
2
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
2
2
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
1
2
2
0
0
2
0
2
0
0
0
3
0
1
0
0
0
0
0
0
0
2
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
4
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
1
0
4
2
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
4
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
1
2
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
2
0
0
0
0
0
0
3
1
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
1
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
4
0
3
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
2
2
0
0
1
2
0
0
1
0
9
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
2
0
1
4
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
10
3
0
0
0
1
0
0
0
1
2
0
0
2
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
1
2
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
4
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
1
1
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
2
0
3
0
1
0
0
0
0
0
2
0
0
2
0
1
0
1
2
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
1
1
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
2
2
2
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
1
0
0
2
2
0
1
0
0
0
2
0
0
1
1
2
0
0
0
0
0
0
1
0
0
1
0
0
0
2
3
0
3
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
5
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
1
3
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
2
6
1
0
0
0
2
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
2
1
0
1
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
3
0
0
2
2
1
0
2
1
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
3
2
0
1
2
0
0
1
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
1
0
2
1
2
0
0
0
0
1
0
2
0
0
1
0
0
0
6
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
1
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
2
0
0
2
0
0
0
2
1
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
2
2
1
0
4
0
0
0
4
0
0
1
0
0
0
0
1
1
0
0
0
3
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
2
0
0
0
2
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
7
0
0
2
0
0
1
0
0
0
0
0
2
3
2
0
0
0
0
0
3
0
0
1
0
3
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
2
0
1
1
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
2
0
0
0
1
0
2
0
0
0
2
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
1
6
2
8
0
0
2
0
2
0
0
0
0
0
0
1
2
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
2
0
0
2
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
2
1
5
0
0
0
0
0
0
0
0
0
0
2
0
0
5
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
3
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
2
0
0
1
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
3
1
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
2
1
2
0
0
1
0
0
1
6
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
4
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
3
0
2
1
0
0
0
1
3
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
3
0
0
0
1
0
1
3
2
0
1
1
0
2
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
2
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
1
1
0
0
0
1
1
0
0
2
4
0
0
0
0
0
0
3
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
7
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
5
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
3
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
2
0
2
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
3
1
0
0
1
1
3
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
2
0
0
0
1
2
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
2
0
0
1
0
0
0
1
0
10
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
3
1
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
1
0
2
0
0
0
2
0
0
2
2
1
2
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
2
0
1
0
0
1
0
0
0
0
2
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
2
0
0
0
0
2
0
1
0
1
0
0
0
0
1
3
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
4
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
1
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
2
1
0
0
2
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
4
0
0
0
0
2
0
0
0
1
0
0
3
1
0
0
0
0
0
0
0
0
1
0
1
1
3
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
3
1
1
0
0
0
0
0
0
3
1
0
0
2
0
1
0
0
0
0
0
2
0
1
2
0
0
1
0
0
0
0
0
1
2
2
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
5
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
2
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
2
2
4
0
0
1
3
0
0
0
2
0
0
1
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
1
0
0
1
1
0
0
0
0
0
3
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
3
0
0
1
1
0
0
0
0
0
3
0
1
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
1
0
0
2
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
1
0
0
2
2
0
0
0
0
0
0
0
1
0
1
2
1
1
2
0
0
0
0
2
0
0
0
0
0
2
2
2
0
2
0
0
1
0
0
1
0
0
0
0
2
0
1
0
0
2
2
0
0
2
0
0
0
2
1
0
1
2
1
1
2
7
3
2
2
0
0
0
0
0
0
2
0
2
2
0
0
0
0
2
0
2
0
2
1
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
1
2
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
3
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
2
0
1
0
1
0
0
0
2
0
1
1
0
0
0
0
1
2
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
3
0
0
0
0
0
10
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
1
0
0
0
1
1
1
1
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
5
0
1
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
2
0
0
1
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
2
2
0
0
1
0
0
0
0
0
0
1
1
0
0
0
3
0
1
0
0
0
1
0
1
0
1
0
1
2
0
1
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
3
2
4
0
0
0
0
0
0
1
0
0
0
0
1
1
3
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
1
2
0
1
0
1
0
0
2
0
0
0
0
0
0
0
1
2
0
0
1
2
0
0
2
0
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
1
1
0
0
0
0
3
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
2
0
0
1
0
1
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
1
0
2
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
2
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
1
1
1
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
2
0
0
0
2
1
1
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
2
0
1
0
0
3
0
1
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
4
1
0
1
1
0
1
0
1
0
0
1
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
6
0
0
0
0
2
0
0
0
0
0
4
1
2
1
1
0
2
0
2
0
0
0
0
0
0
0
0
2
2
2
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
1
0
0
0
0
0
4
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
1
2
0
0
6
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
1
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
2
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
2
1
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
1
1
0
0
2
2
0
0
2
0
0
0
0
1
0
0
1
1
0
0
0
0
0
2
1
1
0
0
1
0
1
0
0
0
0
2
0
2
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
4
0
0
0
0
1
2
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
1
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
5
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
2
0
1
2
0
1
2
0
0
0
0
0
2
2
0
0
1
1
1
0
0
0
0
1
1
7
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
2
0
0
0
1
1
0
0
2
0
0
0
1
2
1
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
6
1
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
2
8
0
0
0
2
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
2
0
0
0
2
0
0
2
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
1
0
0
3
2
0
0
0
3
1
1
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
2
0
1
1
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
2
1
0
0
0
0
3
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
3
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
3
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
7
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
3
0
2
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
1
2
2
2
4
0
0
0
0
0
0
0
0
0
1
0
1
0
3
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
3
1
2
0
2
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
1
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
1
0
1
2
0
2
1
0
1
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
4
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
3
3
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
2
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
2
0
1
2
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
1
1
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
3
0
0
7
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
3
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
1
0
2
0
0
2
0
0
1
1
1
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
3
0
0
0
0
0
1
0
0
0
2
0
1
0
0
1
0
2
0
2
0
1
2
0
2
0
0
0
3
0
0
0
2
2
0
0
0
2
0
0
3
0
0
0
0
0
0
6
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
2
0
0
0
0
0
0
1
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
2
2
0
2
1
4
0
0
0
0
0
0
0
0
0
1
0
0
5
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
2
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
3
2
2
3
0
0
0
2
1
0
1
0
0
2
2
2
0
0
0
0
0
0
9
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
1
0
0
1
0
2
1
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
1
0
0
1
1
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
1
0
2
0
0
0
2
0
0
0
3
0
0
1
0
0
0
0
0
1
0
3
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
1
0
0
0
0
1
0
1
1
2
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
1
1
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
1
0
0
0
3
0
0
2
2
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
2
1
1
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
3
0
0
0
2
1
0
0
0
2
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
2
1
0
0
2
0
0
0
2
0
1
10
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
2
1
0
6
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
16
0
0
0
0
4
1
0
1
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
1
2
0
2
0
0
1
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
2
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
3
0
0
0
2
0
0
1
1
0
2
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
3
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
3
2
0
1
0
0
1
0
0
0
2
0
2
0
0
3
0
1
0
0
0
0
2
0
3
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
5
0
3
5
0
0
0
1
0
0
1
0
0
0
0
3
0
0
0
1
0
0
2
0
0
3
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
3
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
1
1
2
2
1
0
0
0
0
1
0
2
2
0
1
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
1
2
0
0
2
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
2
0
0
1
2
1
2
0
0
0
0
0
0
0
2
1
1
0
0
0
1
5
1
2
2
1
0
0
0
0
0
0
2
0
0
1
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
4
2
0
0
0
0
0
1
2
0
0
0
1
0
0
0
1
1
0
3
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
2
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
2
0
0
2
2
1
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
1
0
6
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
1
0
0
2
0
0
0
0
0
0
0
5
0
0
1
0
0
0
0
0
0
0
0
0
0
1
3
2
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
3
0
1
0
0
0
0
3
1
0
0
0
0
0
0
2
0
0
0
0
0
0
4
0
0
2
3
0
0
0
0
2
0
0
0
0
1
0
1
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
1
1
0
0
0
0
3
0
2
0
0
1
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
1
3
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
4
0
0
1
0
0
3
0
0
0
0
0
0
0
2
0
3
0
0
1
2
0
0
0
0
0
0
1
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
5
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
4
0
1
0
0
0
0
0
0
2
0
0
1
5
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
5
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
3
2
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
2
0
0
1
1
0
0
0
0
1
4
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
7
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
10
2
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
1
2
0
1
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
3
0
0
0
0
2
2
0
0
0
1
2
0
0
0
0
1
0
0
2
1
0
1
0
0
0
4
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
2
0
0
0
2
1
0
0
1
0
0
0
0
1
0
0
1
4
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
2
0
1
0
0
0
0
5
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
1
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
2
0
0
0
2
0
1
1
0
2
2
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
3
0
2
3
2
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
5
0
0
0
2
0
1
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
1
0
0
4
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
1
0
0
0
0
3
0
1
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
2
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
1
4
1
0
0
0
2
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
3
2
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
6
0
0
0
1
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
4
0
0
0
1
2
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
1
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
1
2
0
0
0
2
3
0
2
0
2
0
1
1
2
1
1
0
0
0
0
1
0
0
1
0
0
1
1
0
0
1
2
2
1
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
3
2
0
0
1
1
0
1
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
1
1
0
0
0
0
4
0
0
2
1
0
0
1
0
3
0
0
0
0
3
0
0
0
5
1
1
1
1
2
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
3
4
1
1
0
0
0
0
1
4
1
3
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
1
0
7
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
1
1
1
0
0
0
0
0
2
1
0
0
0
2
3
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
3
0
1
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
3
0
2
1
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
1
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
1
1
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
2
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
2
0
0
0
2
0
1
0
0
2
0
1
0
0
0
2
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
1
1
1
0
2
0
1
0
0
4
0
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
1
2
0
0
1
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
1
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
2
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
3
7
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
3
2
0
0
2
0
0
0
1
8
0
0
1
0
0
2
0
0
0
0
0
4
2
0
2
0
1
1
0
0
1
0
0
0
2
0
3
0
0
0
0
1
1
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
1
0
0
5
0
0
1
0
1
0
1
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
2
4
2
0
3
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
2
2
0
1
0
2
0
0
0
3
0
0
2
0
0
0
0
2
4
0
2
1
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
1
2
1
0
2
0
1
3
0
2
0
0
2
0
1
1
0
0
2
0
2
0
0
0
3
0
0
0
2
0
3
0
0
1
0
1
0
0
0
0
0
0
2
2
0
0
2
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
3
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
2
0
4
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
2
0
1
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
1
2
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
1
2
1
1
0
2
0
2
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
1
0
0
0
1
3
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
3
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
1
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
1
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
14
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
1
0
5
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
6
0
0
0
2
1
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
1
0
0
0
0
2
0
0
0
0
1
0
0
0
2
1
0
0
0
0
1
0
0
0
1
0
0
1
0
2
3
0
2
2
0
0
0
0
3
0
0
7
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
1
0
2
1
3
2
0
0
0
0
0
2
2
0
1
1
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
2
0
0
2
0
2
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
1
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
1
2
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
1
0
1
0
0
0
0
0
0
1
0
1
1
0
0
2
0
0
2
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
2
0
0
0
3
0
0
0
1
0
2
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
1
0
2
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
4
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
1
0
1
2
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
1
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
1
0
0
1
0
0
0
0
2
2
2
0
1
0
1
0
0
1
0
0
0
0
2
0
0
0
1
0
0
2
0
1
0
0
0
2
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
1
2
0
2
1
0
0
0
0
0
2
0
0
2
1
1
0
0
1
0
0
0
0
2
3
0
1
0
1
1
0
0
0
2
0
0
0
0
1
0
0
3
0
1
1
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
3
3
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
1
0
0
0
3
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
3
0
2
0
3
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
1
1
1
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
2
0
1
0
0
1
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
4
4
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
9
2
1
0
1
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
2
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
2
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
1
1
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
4
2
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
3
0
1
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
1
0
0
2
1
0
0
1
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
2
0
0
0
1
0
0
0
0
0
1
2
2
2
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
2
2
0
2
1
0
0
1
1
0
3
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
2
0
0
0
0
1
0
0
3
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
2
0
0
1
2
0
2
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
1
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
2
1
1
0
2
0
0
0
1
0
0
1
0
0
0
1
0
0
2
0
2
0
2
0
0
0
0
1
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
2
0
1
0
2
0
0
0
0
0
2
0
1
0
2
2
2
0
0
0
2
0
0
0
2
0
0
2
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
1
2
0
1
0
0
1
0
0
1
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
2
0
2
0
0
0
1
0
0
0
2
3
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
2
0
0
0
0
2
2
0
0
2
2
1
0
0
0
0
0
0
0
0
2
0
1
3
0
1
0
0
0
0
0
1
3
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
1
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
1
2
2
0
0
0
6
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
2
1
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
1
1
0
0
0
0
14
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
1
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
3
0
0
2
0
0
0
3
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
2
0
2
2
1
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
2
1
0
0
1
0
0
0
1
5
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
3
0
0
0
0
4
0
1
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
3
1
0
1
2
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
3
0
0
0
0
0
0
1
1
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
1
2
0
1
2
2
2
0
0
0
0
2
1
0
2
0
0
1
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
1
0
2
0
1
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
2
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
2
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
2
0
2
0
2
2
0
1
0
0
0
1
0
0
0
0
1
4
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
1
0
0
1
0
0
2
0
0
2
0
1
3
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
3
0
2
1
1
2
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
2
0
0
3
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
2
1
4
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
1
3
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
4
0
0
0
0
1
0
6
0
0
0
0
1
0
4
2
2
0
0
1
0
0
4
0
0
0
0
1
0
1
0
0
3
3
3
0
0
0
0
1
0
2
0
0
0
0
0
2
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
5
0
0
0
0
2
2
4
0
2
0
0
0
0
2
0
0
2
2
0
2
0
2
0
0
1
0
0
0
5
0
0
0
1
0
0
0
0
2
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
2
2
1
0
0
3
0
0
2
0
0
0
0
0
1
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
2
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
2
1
0
0
0
0
3
0
0
2
0
0
0
1
0
0
1
0
1
0
0
0
2
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
1
0
0
1
0
2
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
2
1
0
1
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
1
0
4
0
2
2
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
3
0
1
0
0
6
1
4
0
1
0
0
0
2
0
2
0
7
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
1
1
0
0
3
0
0
0
0
2
0
0
2
0
0
1
1
2
0
0
1
0
3
0
3
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
2
0
0
2
0
2
0
0
0
0
0
3
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
3
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
1
1
0
2
0
1
6
1
0
1
2
0
0
0
0
0
0
4
0
0
0
2
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
1
2
0
0
0
0
0
0
1
0
1
0
0
0
0
2
3
0
2
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
1
0
0
6
0
0
0
0
0
0
2
0
0
0
0
0
1
3
1
0
0
2
0
0
1
2
0
0
1
0
0
0
0
1
0
1
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
2
0
2
2
0
1
0
0
0
0
3
1
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
5
3
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
1
1
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
2
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
2
2
0
1
0
0
0
0
1
0
0
0
1
0
0
2
0
2
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
4
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
3
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
3
0
0
0
1
0
0
2
0
0
2
0
0
2
0
2
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
2
0
2
0
0
0
0
1
7
2
0
0
1
0
0
0
0
0
2
4
0
0
0
2
0
0
3
0
0
0
0
0
1
0
0
0
0
2
3
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
6
0
0
0
0
2
0
0
2
0
1
0
0
0
0
5
0
0
0
0
0
2
1
2
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
1
1
0
0
7
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
2
0
0
0
0
2
3
0
0
0
0
0
1
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
3
2
0
1
1
0
1
2
0
0
0
0
0
0
3
1
2
0
1
2
0
2
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
2
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
3
1
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
3
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
4
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
3
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
5
0
3
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
2
0
1
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
2
3
0
2
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
2
2
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
2
0
2
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
3
0
0
0
0
7
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
9
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
1
1
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
7
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
7
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
1
0
0
1
0
1
1
0
0
2
2
0
0
0
0
0
6
0
7
4
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
1
1
0
0
0
0
3
0
0
1
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
3
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
5
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
7
0
2
0
0
2
0
2
0
3
0
0
0
0
0
2
1
0
0
0
0
1
1
0
2
0
0
0
0
2
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
3
0
0
1
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
1
0
1
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
1
2
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
4
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
7
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
2
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
2
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
1
2
0
0
2
0
0
0
1
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
7
0
1
0
0
0
1
2
1
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
2
0
1
1
1
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
1
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
1
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
6
1
1
0
0
0
0
1
2
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
4
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
1
0
0
1
2
0
1
0
1
1
0
0
1
0
0
1
0
6
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
1
0
0
2
0
2
0
2
1
0
0
0
0
0
3
0
1
0
0
2
0
0
3
2
1
1
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
3
2
2
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
2
0
0
2
0
1
0
0
0
0
0
0
0
0
1
1
2
0
0
1
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
2
1
4
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
2
2
0
0
0
1
1
2
0
0
0
0
0
1
0
2
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
1
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
4
0
0
0
3
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
2
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
4
0
0
2
1
0
0
0
0
2
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
1
0
3
0
1
0
0
2
0
0
0
0
2
1
1
1
2
1
0
0
0
1
0
0
0
0
1
0
0
1
2
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
3
0
0
0
0
0
0
0
2
2
1
0
4
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
1
0
2
0
0
0
1
2
1
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
2
0
0
3
0
0
0
0
0
0
0
2
0
1
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
2
2
0
0
3
0
0
0
1
0
0
1
2
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
1
1
0
2
1
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
1
2
0
0
0
0
1
1
1
4
0
0
2
0
2
1
2
0
0
0
1
0
0
0
6
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
1
0
0
2
1
0
0
2
16
0
0
0
0
4
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
1
0
1
3
0
0
0
0
1
0
2
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
2
0
1
2
1
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
1
2
0
0
2
2
0
2
0
0
5
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
2
1
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
1
0
0
2
3
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
3
1
1
0
0
1
0
0
0
0
1
2
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
1
0
2
1
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
2
1
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
1
2
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
2
2
0
2
0
0
1
0
0
0
2
0
1
0
2
2
0
2
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
2
2
3
0
0
0
2
0
0
2
0
2
0
0
2
0
2
1
0
0
2
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
7
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
1
0
2
0
2
0
0
1
0
0
0
0
0
2
0
1
0
5
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
3
1
0
0
1
0
0
0
0
0
1
1
0
1
1
0
0
0
1
0
2
0
0
3
0
0
0
0
0
0
1
0
1
0
3
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
2
1
0
2
0
0
0
2
1
0
1
2
7
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
4
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
4
1
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
2
2
0
0
0
0
0
2
0
1
2
2
0
4
0
0
0
0
0
1
6
2
0
0
0
1
1
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
1
0
1
0
0
1
0
0
1
0
2
0
2
0
0
0
1
0
5
0
0
0
0
2
0
0
0
2
2
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
3
2
4
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
1
4
0
1
0
0
1
0
0
0
1
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
3
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
3
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
2
0
0
7
0
0
0
0
0
0
0
1
0
1
1
0
0
2
1
1
0
0
0
0
0
5
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
1
0
0
0
0
1
1
0
1
0
0
0
0
1
0
1
3
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
2
0
0
11
3
3
0
1
0
2
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
2
0
0
1
0
0
0
2
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
3
1
0
0
0
0
1
1
0
0
2
3
0
1
1
0
0
0
3
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
1
1
1
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
3
0
0
2
0
0
1
3
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
1
1
1
0
3
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
3
0
0
0
2
0
2
2
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
3
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
2
0
0
0
0
0
2
1
1
0
1
2
0
0
0
0
0
1
0
0
0
0
0
1
0
3
0
0
0
0
0
3
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
3
0
0
0
1
0
0
2
0
0
0
1
2
0
0
0
0
0
3
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
3
0
0
0
0
0
0
2
0
2
0
0
0
3
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
2
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
2
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
2
0
0
0
1
0
4
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
2
0
4
1
0
0
0
0
0
2
0
0
1
1
0
0
2
3
0
0
0
0
1
0
0
1
2
0
1
1
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
2
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
1
0
0
2
0
1
0
0
0
0
0
1
2
1
0
2
0
1
5
0
0
0
0
0
0
1
0
0
2
0
0
5
0
0
0
1
1
0
1
0
0
0
1
0
1
0
1
2
1
0
0
2
0
0
0
1
0
2
0
1
0
0
0
0
0
1
0
2
3
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
1
1
2
2
0
2
0
0
0
0
0
0
0
0
4
0
0
0
2
2
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
1
0
1
2
0
0
0
0
1
0
0
0
0
1
2
2
0
0
4
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
4
0
0
0
0
2
0
3
0
0
0
0
1
0
0
0
1
1
2
0
0
1
1
0
0
1
0
0
1
1
0
0
0
0
7
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
2
0
0
2
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
6
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
3
0
0
1
0
0
2
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
1
4
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
4
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
1
2
0
0
0
0
0
1
0
0
2
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
3
0
0
2
0
1
0
2
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
6
1
0
4
2
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
2
2
0
0
0
1
2
2
0
0
0
0
0
0
0
0
3
3
1
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
2
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
1
0
0
2
0
0
0
0
1
0
3
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
5
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
2
0
1
0
0
3
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
1
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
1
1
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
1
0
2
1
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
1
0
2
0
0
0
1
1
0
0
2
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
3
0
0
0
1
0
0
0
0
1
6
0
2
0
0
3
1
0
0
0
0
0
0
0
0
1
2
1
0
0
0
1
2
0
0
1
4
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
2
2
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
3
0
0
0
2
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
2
0
0
0
4
0
2
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
4
0
0
0
0
2
6
0
0
0
0
0
0
1
2
2
2
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
1
0
0
0
1
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
1
3
1
3
0
0
0
1
1
1
2
0
0
2
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
1
0
5
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
7
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
1
2
0
0
0
0
2
2
0
0
3
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
4
0
1
1
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
2
0
0
0
1
0
3
0
0
0
0
3
0
0
0
0
1
0
0
0
3
0
0
0
0
0
2
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
2
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
1
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
2
0
2
0
0
0
0
0
1
2
0
0
0
2
0
1
0
0
0
0
0
0
1
0
2
0
0
2
1
0
0
0
0
2
0
3
0
1
2
0
0
2
0
0
2
0
0
1
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
6
0
0
0
0
1
0
0
0
2
0
0
0
0
1
2
0
0
0
2
0
3
0
0
1
1
0
1
2
7
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
3
0
0
0
0
0
2
0
0
0
0
0
1
0
3
0
0
0
0
0
1
2
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
2
1
0
0
2
0
2
1
0
1
1
0
0
1
0
0
0
0
0
0
3
0
0
0
0
1
0
0
1
1
0
0
2
1
2
0
0
0
0
0
2
2
2
0
0
0
1
1
0
0
0
0
0
0
1
2
0
0
0
0
0
2
2
0
0
1
2
0
0
1
0
0
0
0
1
2
0
2
0
0
0
2
0
0
3
0
0
2
0
0
0
2
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
2
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
2
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
3
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
2
1
1
2
0
0
0
2
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
2
0
3
0
3
0
1
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
2
2
2
0
0
0
2
0
0
0
0
1
0
0
0
2
0
2
1
0
0
0
0
0
1
0
0
2
3
0
0
0
0
0
0
0
2
0
0
1
1
0
0
1
2
0
2
0
0
0
0
2
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
3
0
2
0
0
0
0
0
0
2
3
0
0
0
2
0
0
2
0
0
0
0
1
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
3
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
1
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
2
0
1
2
1
0
2
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
4
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
1
0
0
1
3
0
1
0
1
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
1
2
2
0
0
1
0
0
0
0
0
1
0
2
0
1
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
2
2
0
0
0
0
0
0
0
0
0
2
1
2
0
0
3
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
2
1
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
2
0
0
0
2
1
0
0
0
2
1
0
0
1
2
0
0
0
0
0
0
0
0
3
0
1
1
0
0
0
0
0
2
0
2
0
0
0
0
1
2
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
2
1
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
2
5
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
1
6
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
2
0
0
1
1
1
0
4
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
2
0
4
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
2
1
2
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
3
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
2
0
2
0
0
0
0
0
0
6
0
0
3
0
1
0
0
0
3
0
2
0
2
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
10
0
0
2
0
0
1
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
2
1
1
0
0
0
1
0
0
1
0
0
0
0
2
0
0
1
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
1
0
0
0
3
0
2
0
0
2
1
3
0
2
1
1
0
0
0
2
0
0
0
0
3
1
0
1
1
0
0
0
0
0
1
0
6
2
0
0
3
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
2
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
4
3
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
3
4
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
1
0
0
2
0
2
0
0
0
0
0
0
0
1
2
1
0
0
1
2
2
0
0
2
0
0
0
0
2
0
2
2
1
0
3
3
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
2
0
1
0
2
1
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
3
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
2
0
0
1
2
0
0
0
1
0
1
2
2
1
0
0
0
0
6
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
1
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
1
0
0
0
2
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
4
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
2
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
1
0
2
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
2
2
0
0
0
0
1
0
3
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
2
2
2
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
4
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
1
0
1
3
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
1
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
4
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
4
0
0
2
0
1
0
0
0
0
2
1
0
0
1
0
1
0
1
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
2
1
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
1
1
2
0
0
0
0
2
2
0
1
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
4
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
1
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
2
2
0
0
0
1
1
3
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
4
0
0
0
3
0
0
2
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
2
2
1
1
1
0
4
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
3
0
0
0
2
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
1
0
0
0
0
0
2
0
2
0
2
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
1
2
2
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
1
0
1
0
2
1
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
2
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
6
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
2
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
2
0
0
0
9
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
2
0
0
0
1
0
0
2
0
0
2
0
0
0
1
1
4
0
0
0
5
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
2
3
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
6
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
1
2
0
0
2
0
0
5
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
1
1
0
0
0
0
0
3
0
0
0
0
1
2
0
2
2
1
1
0
0
0
0
0
0
2
1
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
3
0
2
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
1
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
1
0
0
1
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
2
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
3
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
5
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
2
2
1
2
0
2
1
0
0
0
0
0
1
1
0
0
0
2
2
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
3
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
2
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
3
0
0
1
0
0
1
0
0
2
0
0
0
2
0
0
2
2
0
0
1
0
0
2
2
0
2
0
0
1
2
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
2
0
0
0
0
3
0
0
0
0
1
0
3
0
0
0
0
0
3
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
1
0
0
0
0
0
0
2
0
0
0
2
2
0
0
3
0
1
0
0
2
0
0
0
0
1
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
4
0
1
0
0
4
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
1
0
2
2
1
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
2
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
2
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
3
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
1
0
1
0
0
1
1
0
1
0
0
0
0
0
3
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
1
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
4
0
0
0
2
0
1
0
0
1
1
0
0
1
3
0
0
1
0
2
0
1
1
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
4
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
2
2
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
1
1
0
0
0
1
0
2
0
0
0
1
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
1
2
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
2
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
2
0
0
2
0
2
1
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
5
0
3
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
5
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
2
0
0
0
0
1
0
1
0
0
0
2
1
0
0
0
0
1
0
2
0
1
0
0
0
2
0
0
0
3
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
1
1
1
0
8
0
0
0
2
2
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
2
1
0
0
0
0
0
0
0
5
0
1
0
1
1
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
3
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
2
2
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
1
1
2
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
1
2
0
0
2
0
0
0
2
0
1
0
0
1
0
0
1
1
1
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
2
1
0
2
1
0
4
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
5
1
0
1
0
0
0
0
1
0
0
3
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
4
0
0
0
0
3
2
0
3
0
0
2
0
0
3
1
0
2
0
0
0
2
3
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
2
2
0
0
0
1
0
0
2
0
0
1
2
1
1
0
0
0
0
1
0
0
0
2
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
5
2
0
0
0
0
2
0
0
0
0
0
2
0
0
1
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
1
0
0
0
2
2
0
0
2
0
0
0
2
0
0
1
2
2
0
0
1
0
0
0
0
0
0
0
0
2
0
4
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
1
0
1
1
0
0
2
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
2
0
0
1
0
0
0
1
0
1
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
3
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
2
4
0
3
0
1
0
0
0
1
1
2
0
0
3
0
0
0
0
0
2
0
0
2
0
0
4
0
2
2
0
1
0
0
2
0
0
1
1
0
0
0
0
0
0
0
1
0
0
5
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
2
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
2
3
1
0
0
0
5
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
4
0
2
1
0
0
1
0
0
0
0
0
2
1
2
0
0
0
3
1
0
0
0
0
2
0
2
0
2
4
0
2
0
1
3
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
3
0
0
0
0
2
0
1
0
1
0
0
0
2
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
6
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
3
0
0
1
2
2
2
0
2
0
2
0
2
0
0
0
0
0
0
2
2
0
2
2
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
1
1
2
2
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
4
2
0
1
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
1
0
2
3
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
2
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
2
1
0
1
0
0
1
0
2
2
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
3
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
1
0
1
1
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
2
0
1
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
3
2
0
1
0
0
0
1
2
0
0
0
0
0
0
2
1
0
1
0
2
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
2
1
2
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
2
0
2
1
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
1
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
1
1
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
1
4
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
3
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
2
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
1
3
1
0
0
2
0
2
0
1
0
1
0
1
0
0
0
0
2
0
0
0
1
1
3
0
0
0
0
1
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
5
0
1
0
1
0
0
2
0
0
0
0
3
0
0
0
0
0
1
2
0
0
1
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
1
1
2
2
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
2
1
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
3
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
1
3
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
3
0
0
0
2
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
4
0
2
0
0
0
0
0
0
0
2
2
3
0
0
0
0
0
0
0
0
3
0
3
2
1
0
2
0
0
0
0
0
0
2
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
1
2
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
1
1
0
0
0
1
0
2
2
0
2
0
0
0
0
3
0
1
0
0
0
2
1
0
0
0
0
2
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
5
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
3
2
0
1
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
1
0
2
3
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
5
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
2
0
0
2
0
2
2
0
2
2
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
1
7
1
0
0
2
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
4
2
0
0
2
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
4
0
0
3
0
0
1
1
0
2
1
0
15
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
4
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
2
0
0
2
0
0
0
0
3
2
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
2
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
3
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
2
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
4
2
2
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
2
2
0
1
2
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
3
2
0
0
0
2
0
1
0
0
0
0
4
0
0
1
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
2
0
0
2
1
2
0
1
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
2
0
0
2
0
2
1
0
0
1
2
1
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
3
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
3
0
1
0
0
0
0
0
0
0
0
1
4
0
3
0
0
2
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
1
0
0
1
2
5
0
0
0
0
0
0
0
0
0
0
1
2
0
0
3
0
0
0
0
0
0
3
1
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
3
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
7
0
5
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
3
1
0
0
0
2
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
2
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
1
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
2
2
0
0
0
1
0
1
0
1
0
0
1
2
0
0
0
1
0
0
0
0
2
4
0
0
2
2
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
1
0
0
3
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
2
0
0
2
0
2
0
1
2
0
2
0
1
0
0
2
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
2
3
1
0
0
2
0
0
2
1
1
0
0
1
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
3
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
2
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
2
1
0
2
0
0
0
0
2
0
2
0
0
2
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
3
0
0
0
0
0
0
0
2
0
0
1
3
0
0
0
0
0
2
2
2
0
0
1
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
8
0
0
2
0
0
0
1
0
1
1
0
0
0
2
1
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
1
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
3
0
0
1
0
0
0
3
0
0
0
1
0
0
2
0
3
0
0
0
1
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
2
0
0
0
1
0
1
1
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
2
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
2
7
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
1
0
3
2
0
0
1
1
0
0
0
0
0
0
0
1
0
2
0
1
0
3
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
2
1
0
0
1
0
0
2
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
2
0
0
4
2
0
0
0
0
0
1
0
0
0
0
1
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
1
0
2
0
4
0
0
0
0
0
0
2
0
2
0
3
2
0
0
2
0
2
1
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
3
1
1
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
1
0
4
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
2
0
0
2
2
0
0
0
0
3
0
0
0
2
1
0
0
0
0
2
0
2
1
3
1
1
0
1
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
3
0
2
0
0
0
2
4
2
0
0
0
0
0
0
0
2
2
0
0
1
1
0
2
0
0
3
4
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
3
0
0
4
1
2
2
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
10
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
1
2
0
0
0
0
4
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
3
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
2
0
1
0
2
0
1
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
1
0
1
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
3
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
2
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
2
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
1
0
0
3
0
1
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
1
7
1
0
0
2
0
0
2
0
1
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
3
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
4
0
0
2
0
0
0
0
2
1
0
0
0
0
2
0
0
1
2
2
1
0
2
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
2
0
1
2
0
0
0
0
2
0
0
0
0
2
0
0
1
0
6
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
13
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
1
2
4
0
2
1
0
0
2
0
0
0
0
1
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
1
3
2
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
3
0
4
1
2
0
0
0
4
0
0
3
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
2
2
1
0
1
0
0
0
2
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
5
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
5
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
1
0
0
0
1
1
1
0
0
2
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
1
0
0
0
2
1
0
0
2
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
2
0
0
1
2
0
1
0
0
1
0
0
0
0
1
0
0
0
2
1
0
0
0
0
2
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
3
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
5
0
3
2
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
1
1
0
0
2
0
1
0
2
0
0
0
0
0
1
4
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
8
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
2
1
2
0
0
0
0
1
0
0
3
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
2
0
1
3
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
2
0
0
0
0
0
0
0
1
0
1
0
4
1
0
0
0
0
2
0
2
1
2
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
9
2
0
0
0
3
0
2
0
0
0
0
0
0
1
0
0
0
1
0
2
0
2
0
0
0
0
0
9
0
0
0
0
0
0
1
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
3
0
2
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
1
4
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
1
0
2
0
1
2
0
0
0
0
0
1
0
0
0
3
0
3
0
0
0
0
0
2
2
0
0
0
0
1
0
3
0
1
1
1
0
2
1
2
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
1
0
1
0
0
1
1
0
0
0
0
0
1
0
0
2
2
0
0
1
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
3
0
2
0
3
1
0
0
0
0
0
0
0
0
0
0
1
1
2
2
1
2
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
5
1
0
0
0
0
2
0
2
2
0
0
1
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
5
0
0
0
0
1
0
2
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
1
1
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
3
0
0
0
1
2
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
1
0
1
0
2
0
0
0
1
0
2
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
3
0
0
0
0
2
0
1
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
2
2
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
2
0
0
1
0
0
0
0
1
2
0
2
0
0
0
2
0
3
2
0
0
0
0
1
1
0
0
1
2
2
1
1
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
3
0
0
0
0
0
0
1
6
0
2
0
0
2
0
0
0
1
2
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
0
0
1
0
0
1
3
0
0
0
0
1
1
4
0
0
1
0
0
0
0
2
1
3
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
5
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
1
0
0
2
1
0
0
0
1
2
0
0
0
0
2
0
0
0
1
1
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
3
2
0
2
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
3
1
0
1
0
2
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
1
4
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
2
0
3
0
2
0
0
0
2
0
0
0
1
2
0
0
2
0
0
0
0
0
1
0
1
1
0
0
2
0
2
4
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
1
2
0
0
0
0
2
0
1
0
0
0
0
0
0
2
1
0
2
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
1
0
0
2
0
0
13
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
4
0
2
0
0
1
0
2
0
0
1
0
1
0
0
2
0
1
0
1
0
0
0
1
2
1
1
0
0
0
7
0
0
0
1
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
2
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
4
0
0
3
0
0
1
1
4
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
2
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
2
0
3
0
4
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
7
0
0
1
0
1
2
2
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
2
4
2
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
3
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
1
2
0
0
10
0
0
2
0
1
0
1
2
0
0
0
1
1
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
3
2
0
1
2
2
0
1
0
1
1
0
0
5
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
5
0
0
0
0
2
0
0
0
0
1
2
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
1
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
15
1
1
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
2
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
3
0
0
4
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
1
0
0
1
2
1
2
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
1
0
0
13
0
0
2
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
4
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
2
1
0
0
2
0
0
4
3
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
1
0
0
0
0
2
0
0
2
0
0
0
0
3
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
3
0
2
0
0
2
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
9
0
2
0
0
2
1
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
5
0
0
1
0
1
3
0
0
0
0
1
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
1
1
0
3
0
0
1
0
0
0
0
1
0
0
0
1
0
3
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
2
0
1
1
0
0
0
0
3
0
1
0
1
0
0
0
0
0
1
1
0
1
0
1
0
0
2
2
0
2
1
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
2
3
0
0
0
1
0
0
1
0
0
1
0
0
3
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
1
0
1
0
0
1
0
0
0
0
4
2
0
0
2
0
0
0
0
1
2
2
0
0
0
0
0
2
2
0
1
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
6
1
0
0
1
2
2
0
0
1
2
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
3
0
0
0
0
0
1
0
4
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
4
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
3
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
4
3
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
5
0
0
0
0
0
0
0
3
0
2
1
0
0
0
0
0
1
0
2
0
2
0
1
0
0
2
0
0
2
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
6
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
2
0
0
0
2
1
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
1
0
0
0
0
0
2
1
1
0
0
0
0
0
0
2
2
0
0
4
0
1
0
1
1
2
0
0
3
0
1
1
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
2
1
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
1
3
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
3
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
3
0
1
0
1
2
3
0
0
1
0
4
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
1
1
0
2
1
2
0
0
0
0
1
3
2
0
0
2
0
0
0
0
2
0
0
1
0
0
0
1
0
0
1
0
0
1
0
2
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
1
2
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
2
0
0
0
1
0
0
1
0
3
0
2
0
0
0
0
0
0
0
1
0
3
1
0
0
0
0
0
1
0
0
0
2
0
1
8
0
0
1
2
2
0
1
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
3
3
0
0
0
0
3
1
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
1
0
2
0
1
2
2
2
0
0
0
1
0
3
0
2
0
2
1
1
2
1
0
0
0
0
0
0
0
0
1
0
0
3
2
0
0
0
0
0
1
0
0
2
2
0
2
1
0
1
0
0
0
0
1
2
1
0
1
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
3
0
1
0
2
0
2
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
3
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
9
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
1
0
0
1
2
0
1
0
0
0
0
0
4
6
1
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
1
0
0
0
0
0
3
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
6
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
2
1
0
1
0
2
0
3
0
1
1
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
2
0
0
1
2
0
0
0
0
1
0
0
0
2
1
2
0
1
0
2
2
1
2
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
2
0
1
0
0
4
2
2
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
11
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
9
1
0
1
0
1
1
0
0
3
1
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
2
0
0
2
0
0
1
0
1
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
3
2
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
2
0
0
1
1
1
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
2
1
0
2
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
2
2
0
0
2
2
0
0
0
0
0
2
0
2
1
0
0
2
1
0
0
0
0
1
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
5
0
2
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
2
0
0
1
2
2
0
0
0
0
3
0
1
2
2
0
0
1
2
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
2
0
0
0
1
0
0
1
1
2
0
1
0
2
1
3
1
1
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
2
0
0
0
0
0
1
2
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
2
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
6
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
2
0
2
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
2
1
0
0
2
0
0
0
0
0
2
1
0
0
2
0
2
0
2
1
2
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
3
0
1
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
5
0
0
0
2
2
0
0
0
0
2
0
0
0
3
0
0
3
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
2
0
0
0
0
1
0
2
0
0
0
1
0
0
0
2
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
4
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
7
2
0
0
0
1
0
0
0
3
2
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
2
0
0
1
0
0
0
0
1
1
0
2
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
2
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
1
0
0
2
1
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
2
3
0
0
4
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
1
0
2
3
0
4
1
0
0
0
1
2
2
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
8
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
1
0
4
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
3
0
2
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
5
0
0
6
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
1
0
0
6
0
2
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
1
1
2
0
1
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
7
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
1
0
0
0
0
1
0
2
0
0
0
0
0
2
1
0
0
2
2
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
1
0
1
0
2
0
0
0
0
0
0
1
0
2
2
0
0
0
0
1
0
0
0
0
0
0
1
2
2
0
0
0
0
1
0
0
0
1
2
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
1
1
0
0
0
1
1
0
1
0
0
2
0
1
5
2
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
4
3
0
0
0
0
1
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
3
0
0
2
0
2
0
0
2
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
3
0
0
0
1
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
2
2
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
2
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
1
3
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
1
1
2
0
0
0
2
2
2
1
2
4
0
2
0
0
0
2
4
0
0
0
0
0
0
3
0
1
0
2
1
0
1
0
2
1
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
1
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
2
0
0
1
1
1
3
0
0
1
0
1
1
1
0
0
2
0
0
0
1
1
0
1
0
0
1
1
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
1
0
0
0
0
2
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
1
0
1
0
0
0
0
3
0
0
2
0
0
0
0
0
0
3
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
1
1
0
0
3
0
2
0
0
0
0
0
0
1
1
0
0
0
0
2
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
2
1
0
2
0
0
0
1
0
0
2
1
0
0
0
2
0
3
8
0
0
0
0
0
0
0
1
0
0
1
0
0
1
2
0
2
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
4
0
0
0
2
0
1
0
1
0
0
0
1
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
1
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
4
1
2
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
4
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
3
1
1
1
0
1
2
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
2
0
3
0
0
0
2
0
0
0
0
0
1
0
0
1
2
0
0
2
0
2
0
0
0
0
0
14
2
0
0
0
0
2
2
0
1
0
0
0
0
0
2
0
0
0
2
0
0
1
0
1
0
3
2
1
1
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
3
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
4
0
0
2
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
5
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
6
1
0
0
2
0
1
0
3
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
2
0
1
0
2
2
0
1
0
1
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
3
0
2
0
2
1
0
0
0
2
2
0
1
1
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
4
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
3
0
1
1
0
0
0
0
0
3
2
0
2
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
1
2
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
2
1
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
3
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
1
4
2
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
3
0
0
0
0
0
2
0
1
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
3
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
4
1
0
1
0
1
0
3
2
1
0
1
0
0
0
0
0
1
2
1
1
0
3
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
1
3
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
2
1
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
3
0
2
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
1
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
2
0
0
0
0
1
0
2
0
0
2
0
1
0
2
0
0
0
1
0
0
0
3
0
0
1
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
3
0
2
1
0
1
0
0
0
0
0
1
0
2
0
0
2
1
2
0
2
2
1
2
0
0
1
0
0
0
2
0
1
0
1
4
1
0
3
0
0
2
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
3
2
0
1
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
1
3
6
1
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
6
0
0
0
1
0
0
0
0
2
0
2
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
3
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
3
1
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
2
3
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
2
1
6
0
0
2
0
0
0
0
0
0
1
0
2
1
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
2
0
2
0
0
0
1
0
0
0
1
0
2
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
2
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
2
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
1
0
1
2
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
2
5
0
1
0
1
0
0
18
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
2
1
0
1
0
3
1
1
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
1
0
1
0
0
0
0
0
2
0
4
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
4
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
2
1
0
0
0
0
3
0
0
1
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
8
2
0
0
0
0
0
3
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
2
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
1
2
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
1
2
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
1
0
0
2
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
3
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
2
1
0
1
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
1
2
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
2
1
4
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
2
0
3
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
3
1
0
0
1
0
0
0
0
2
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
2
0
0
0
13
1
0
0
2
0
0
0
0
2
0
5
0
0
0
0
0
0
0
2
0
0
0
2
2
2
0
2
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
3
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
1
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
4
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
2
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
1
0
0
2
4
2
2
1
0
0
0
2
0
1
0
0
3
0
2
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
1
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
3
1
0
0
0
1
0
0
1
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
1
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
3
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
1
0
1
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
1
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
5
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
2
0
0
0
0
0
2
1
0
1
2
5
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
3
1
1
3
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
3
0
0
0
0
2
0
0
0
0
0
0
2
2
0
1
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
1
0
0
0
2
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
3
0
2
4
3
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
2
0
0
0
2
0
2
0
0
0
1
0
0
0
2
0
0
1
2
1
2
1
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
2
1
0
0
0
0
1
0
0
2
0
0
0
0
2
3
1
1
0
1
0
0
0
2
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
2
1
0
0
2
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
2
0
0
1
0
0
0
2
0
0
0
1
4
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
2
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
3
1
0
0
0
2
0
1
2
0
0
2
0
0
0
0
2
0
1
2
0
1
0
0
1
0
0
3
0
1
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
2
3
0
0
0
0
0
0
3
0
3
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
2
0
0
0
0
1
2
1
0
2
0
0
0
1
0
0
0
0
1
1
0
1
1
0
1
2
0
0
0
0
2
0
1
2
0
2
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
2
2
0
0
0
0
0
1
0
0
2
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
1
1
0
0
1
4
0
0
0
0
0
1
0
2
2
2
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
1
0
0
1
2
3
0
1
0
1
3
0
0
2
5
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
3
0
0
1
0
0
0
3
0
2
2
0
0
1
2
0
0
0
0
0
0
0
0
2
0
1
0
3
0
0
0
0
2
1
1
0
0
0
0
0
0
0
1
4
0
1
0
0
0
0
0
0
0
0
0
5
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
2
0
0
2
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
1
1
0
0
0
1
0
0
0
0
0
2
0
1
0
0
1
0
1
0
0
2
3
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
2
0
0
0
0
2
2
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
2
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
2
0
0
2
0
0
7
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
2
3
0
1
0
4
0
0
0
0
0
3
2
0
0
2
0
0
1
1
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
1
0
8
0
0
2
4
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
1
0
0
0
0
2
0
0
0
2
2
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
4
0
2
0
0
2
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
2
0
0
1
0
0
1
0
0
1
0
1
2
0
0
0
0
1
0
0
2
0
1
0
0
0
2
2
0
1
0
0
0
2
0
2
2
0
0
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
10
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
9
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
2
0
2
1
1
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
2
1
2
1
2
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
3
0
0
0
1
2
4
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
2
4
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
1
1
1
1
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
1
2
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
2
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
3
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
2
0
2
0
2
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
2
1
0
1
0
2
0
0
0
1
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
1
0
0
0
1
0
2
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
4
0
0
1
0
0
1
1
0
0
3
0
0
0
1
0
0
2
0
0
0
0
1
0
2
2
0
0
0
1
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
2
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
1
4
1
0
2
2
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
3
3
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
7
0
3
0
0
0
1
2
0
0
0
5
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
1
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
3
0
0
0
0
3
2
0
0
1
0
4
0
1
3
0
0
1
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
1
0
1
2
0
2
0
1
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
1
1
0
1
1
0
0
0
0
0
1
0
0
2
0
0
0
0
1
2
0
0
1
0
0
0
0
0
4
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
3
0
0
3
3
0
0
3
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
1
2
0
1
0
2
2
3
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
1
0
1
1
0
0
2
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
2
1
2
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
1
2
0
0
0
0
0
1
3
0
2
0
2
0
0
0
0
2
0
0
3
0
0
0
1
1
0
0
2
0
0
1
1
1
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
4
0
0
3
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
2
1
1
1
0
6
3
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
3
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
3
1
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
1
0
3
0
1
1
0
0
0
0
0
0
0
1
0
2
0
0
7
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
5
1
0
2
2
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
2
0
2
1
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
1
2
0
0
0
1
0
2
0
0
0
0
0
2
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
1
0
0
2
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
2
1
0
2
0
0
1
0
0
1
1
0
0
0
2
0
1
0
0
2
1
0
1
0
2
0
0
0
2
0
0
1
0
0
0
0
2
0
1
1
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
2
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
1
0
0
0
1
0
1
0
0
0
2
0
1
0
0
2
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
5
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
1
3
1
0
0
0
0
0
0
0
0
1
1
1
0
0
2
0
2
0
0
0
0
0
0
0
0
1
2
1
1
1
0
0
0
2
0
0
1
2
2
0
0
0
0
2
1
0
1
0
0
0
0
0
0
2
0
2
1
2
0
2
0
0
1
0
4
1
2
1
0
0
0
2
2
0
2
0
1
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
4
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
2
3
0
0
0
0
4
0
0
1
1
0
1
0
0
0
0
0
1
1
0
0
0
0
2
0
2
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
1
1
0
0
2
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
2
0
0
5
1
0
0
2
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
2
2
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
3
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
3
0
2
2
0
0
3
0
2
2
0
0
1
2
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
1
0
5
2
1
3
0
0
0
0
0
0
0
0
1
0
8
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
3
0
1
0
3
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
4
2
1
1
0
0
3
2
0
0
1
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
1
2
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
1
0
0
0
5
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
3
0
0
2
1
0
1
0
0
2
2
0
0
0
0
2
1
0
2
0
0
0
2
2
0
0
2
1
0
6
0
1
1
1
0
9
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
6
0
0
0
0
0
3
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
4
0
0
0
1
1
7
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
4
0
0
0
0
3
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
1
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
3
0
1
0
0
2
1
0
0
1
2
0
0
1
0
2
2
1
1
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
5
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
1
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
4
2
0
0
0
1
1
0
0
0
0
0
2
0
0
0
1
0
3
7
0
0
2
1
0
2
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
1
3
2
3
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
2
0
0
0
0
0
1
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
1
3
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
6
0
0
0
0
0
5
0
13
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
1
2
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
1
0
2
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
1
0
0
1
0
0
0
0
2
0
2
0
1
2
1
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
1
1
0
1
1
0
3
1
1
1
0
2
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
1
2
0
0
1
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
6
1
0
0
1
0
2
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
3
0
0
0
1
0
0
2
0
0
0
1
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
2
0
1
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
2
2
0
0
0
0
0
0
1
0
2
2
0
1
0
0
5
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
3
2
0
0
2
2
1
0
1
0
2
0
3
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
1
2
0
0
2
2
0
0
2
1
2
0
0
1
0
0
2
0
2
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
2
0
0
2
1
1
2
0
0
1
1
0
0
0
1
0
0
1
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
1
2
0
0
3
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
5
0
0
1
0
0
0
2
1
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
3
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
1
0
2
0
0
0
0
0
0
3
0
2
1
0
0
0
1
0
4
1
0
1
0
0
0
0
0
0
0
0
1
2
0
2
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
6
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
2
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
2
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
6
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
6
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
2
3
0
1
0
0
0
0
0
0
0
0
2
1
0
0
2
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
2
0
1
0
1
2
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
2
2
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
2
0
0
1
1
0
0
0
0
0
5
0
1
0
0
0
2
0
0
0
0
0
1
0
0
3
0
1
0
0
0
0
0
0
0
0
1
0
2
2
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
6
0
0
0
0
0
1
0
0
0
0
0
0
3
0
3
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
2
0
2
0
0
0
0
2
0
2
5
2
0
2
0
0
0
0
1
0
0
0
0
0
0
3
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
1
0
0
0
0
1
0
0
3
0
2
0
2
1
1
1
0
1
2
1
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
1
1
1
0
0
0
0
2
0
1
2
1
0
2
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
1
3
0
1
0
0
2
1
2
1
0
7
1
0
0
3
0
0
0
2
1
0
1
3
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
2
0
1
1
0
2
2
0
2
0
0
0
0
2
1
1
0
1
0
3
0
2
0
0
0
0
0
0
2
0
1
0
1
0
1
0
0
0
0
2
0
0
0
1
0
7
0
2
0
0
0
0
0
0
0
0
2
0
0
2
1
0
3
0
0
0
0
2
0
0
0
0
1
2
0
0
2
0
1
1
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
3
2
0
2
0
0
0
0
0
0
0
1
2
0
0
1
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
5
0
2
0
3
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
2
0
2
0
0
1
0
2
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
2
0
2
0
2
0
0
0
3
0
0
0
0
1
1
0
0
0
0
4
0
0
0
2
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
3
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
2
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
2
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
2
1
0
1
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
5
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
3
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
1
1
0
0
1
1
2
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
2
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
1
3
0
0
0
0
1
0
0
0
0
0
2
0
2
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
3
0
2
0
2
0
2
0
0
0
1
1
0
0
0
1
2
2
0
0
0
0
4
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
2
0
2
1
0
2
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
2
1
0
0
0
2
0
0
1
0
1
0
0
0
2
1
0
0
0
1
2
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
1
1
1
1
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
2
1
0
0
0
1
0
0
0
0
3
3
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
4
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
1
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
2
2
0
0
2
0
0
0
2
2
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
2
0
1
0
0
0
1
0
2
0
0
1
0
0
2
1
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
4
2
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
6
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
1
0
3
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
3
0
1
0
0
1
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
2
0
0
2
1
1
0
0
0
0
1
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
2
1
2
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
2
0
2
0
1
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
5
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
4
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
1
0
0
0
0
2
0
0
0
0
2
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
3
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
2
2
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
1
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
1
1
0
0
0
0
2
0
0
0
0
0
0
4
0
0
3
4
0
0
1
0
0
0
1
0
0
0
2
0
0
0
3
2
0
1
0
0
0
0
0
2
0
0
1
0
1
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
4
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
5
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
3
0
1
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
1
0
2
0
0
0
0
2
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
3
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
7
0
0
2
2
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
1
0
2
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
1
0
0
0
2
0
1
0
1
4
1
0
0
0
0
2
2
0
0
0
0
1
1
0
0
2
0
0
0
3
0
0
0
4
1
0
0
3
0
0
1
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
7
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
2
2
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
4
0
1
1
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
1
3
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
3
3
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
2
0
3
0
6
1
2
3
0
1
0
0
1
1
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
1
0
2
0
2
1
0
0
0
0
0
1
2
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
6
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
1
0
0
0
0
0
0
0
1
0
0
0
0
0
5
0
2
0
0
1
0
1
0
0
2
0
0
0
3
0
2
0
0
0
0
0
0
0
0
1
0
2
1
0
1
0
0
0
2
0
0
3
1
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
2
0
1
0
1
0
0
2
1
0
0
0
2
0
0
0
0
0
4
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
2
1
0
0
1
3
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
2
0
0
1
1
1
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
3
1
0
1
1
0
0
0
1
0
0
0
1
0
0
0
2
0
3
0
2
0
0
0
2
0
0
0
0
0
1
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
12
0
0
0
1
1
2
0
0
0
1
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
5
0
5
0
0
2
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
2
2
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
2
0
2
0
0
1
0
0
0
2
0
0
1
1
1
2
1
0
1
0
0
2
1
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
1
0
0
0
0
0
0
0
2
3
0
0
1
1
2
2
1
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
1
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
2
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
6
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
2
0
0
0
0
0
2
0
0
0
0
2
2
1
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
2
0
1
0
0
0
1
1
2
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
2
0
2
0
0
1
0
1
2
1
1
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
1
0
6
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
2
0
2
0
2
0
0
0
0
0
2
0
0
0
2
0
0
5
0
0
1
1
0
0
1
2
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
3
0
0
0
0
0
1
0
2
1
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
1
0
0
4
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
1
2
1
0
0
4
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
1
3
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
4
0
0
1
0
0
2
0
4
0
0
0
0
1
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
2
2
0
0
0
0
0
1
2
1
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
2
1
0
0
2
0
0
0
2
0
2
0
0
2
0
1
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
1
2
0
0
2
0
0
0
2
2
0
0
0
0
2
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
2
1
0
0
0
1
2
0
18
0
0
4
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
4
0
0
0
1
2
0
1
1
0
0
0
0
0
0
1
2
2
0
0
0
1
1
0
0
0
2
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
1
2
0
0
0
0
0
1
0
0
0
1
0
1
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
6
0
0
0
0
3
0
0
2
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
1
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
1
0
0
0
0
0
1
1
0
0
0
0
1
1
2
0
0
0
3
0
0
0
1
4
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
2
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
2
0
2
0
0
0
0
1
0
0
2
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
5
0
0
2
0
1
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
1
0
2
0
2
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
2
1
0
0
2
0
1
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
3
0
0
0
0
0
0
0
1
1
1
0
1
1
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
4
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
2
0
0
1
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
1
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
1
2
0
0
0
0
2
0
1
0
0
0
1
1
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
3
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
1
0
2
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
1
0
0
1
0
3
0
0
0
0
1
2
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
5
0
0
0
0
0
0
0
0
2
0
1
0
1
0
2
0
1
0
5
0
1
0
0
0
2
1
0
0
2
0
2
0
0
0
0
0
4
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
1
2
6
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
5
2
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
2
1
0
0
0
1
0
0
1
0
0
0
2
1
0
0
2
1
0
1
2
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
2
0
0
2
0
2
1
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
21
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
2
2
2
1
0
0
0
1
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
2
0
2
0
0
4
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
1
1
1
0
2
0
0
0
0
0
0
0
4
0
0
2
1
0
2
0
0
0
0
2
0
2
0
1
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
2
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
3
0
0
4
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
6
0
1
3
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
8
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
3
2
2
0
2
0
0
0
0
0
0
0
1
2
0
0
0
5
2
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
2
0
1
0
0
2
0
1
0
0
0
0
0
3
0
0
1
0
2
0
0
1
1
0
0
0
0
0
0
1
2
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
2
0
0
2
0
0
0
1
2
0
0
0
2
1
2
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
5
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
3
2
1
2
2
0
0
0
0
0
0
0
1
0
1
2
0
2
0
1
0
0
3
2
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
2
0
0
2
2
0
4
0
1
0
0
1
0
1
1
0
0
0
2
0
0
0
0
0
0
0
1
2
0
1
0
0
1
0
0
0
1
0
2
1
0
3
0
0
0
1
2
2
0
0
0
1
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
2
1
0
0
0
0
0
2
0
0
0
1
1
0
0
0
1
0
0
0
2
0
0
0
0
0
1
2
0
1
0
1
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
6
0
1
1
1
0
0
0
1
1
2
0
0
2
0
0
1
0
0
2
2
1
1
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
1
0
0
1
2
2
0
2
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
1
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
2
1
0
1
0
0
1
0
0
1
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
2
1
2
1
0
2
0
1
0
0
0
0
0
1
1
0
0
1
0
2
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
2
0
2
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
3
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
5
0
0
0
0
0
1
2
1
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
2
2
0
0
1
2
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
1
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
3
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
1
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
3
0
0
1
2
0
0
3
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
1
2
2
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
2
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
1
3
0
0
0
0
1
0
1
1
2
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
3
0
0
1
0
0
0
1
3
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
3
2
0
0
1
0
0
1
0
1
3
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
2
0
0
0
2
2
1
0
0
2
0
0
4
0
0
0
0
0
2
3
1
0
0
0
0
1
5
0
0
0
0
0
1
0
1
2
0
1
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
2
0
2
1
0
0
0
0
0
0
0
0
1
0
0
4
0
1
0
0
0
1
2
1
5
3
0
1
1
0
1
1
0
1
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
3
3
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
2
0
0
2
0
0
0
2
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
3
0
1
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
1
2
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
1
5
0
0
2
0
0
0
2
0
0
2
0
2
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
2
0
0
0
0
0
2
2
1
0
0
2
0
0
2
0
0
0
0
0
0
1
0
1
2
0
1
1
1
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
1
0
0
0
0
0
1
1
0
1
20
0
2
0
3
1
0
0
1
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
6
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
1
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
2
0
1
0
0
0
0
2
2
1
0
2
0
1
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
1
1
4
2
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
0
2
0
1
4
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
4
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
2
2
0
0
0
1
1
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
1
0
3
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
3
0
0
0
0
1
0
0
2
2
0
0
0
0
1
0
1
3
0
0
2
0
0
2
2
0
1
0
0
0
0
0
1
0
0
1
2
0
0
0
1
0
0
3
0
1
1
0
0
4
2
0
0
0
4
2
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
1
0
0
0
5
0
0
0
0
0
0
0
2
1
0
2
0
2
1
0
0
0
0
2
0
0
1
0
0
0
2
1
0
0
0
0
1
2
0
0
1
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
3
0
0
0
0
2
0
0
1
0
3
1
1
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
1
4
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
3
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
2
0
0
2
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
3
0
1
0
0
0
0
1
0
0
0
0
0
7
3
0
0
0
0
2
0
2
0
0
0
0
0
0
3
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
2
0
0
2
1
1
0
2
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
2
1
0
1
0
0
0
0
1
0
0
2
1
0
0
8
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
2
2
0
0
1
0
1
3
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
1
0
0
3
0
0
0
0
0
0
0
0
2
5
2
0
0
1
0
3
0
3
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
2
0
0
2
1
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
1
0
2
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
1
0
0
1
2
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
5
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
2
0
0
0
0
0
0
0
2
1
2
0
2
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
1
3
0
1
0
0
2
2
0
3
0
0
2
3
0
1
0
1
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
2
0
0
2
0
1
3
1
1
2
0
0
0
2
0
1
1
2
0
0
2
0
0
1
1
1
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
1
2
0
0
0
0
4
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
2
0
0
1
2
0
2
0
0
0
2
1
0
0
0
0
0
0
4
2
1
0
2
0
2
0
2
3
0
0
0
1
0
0
0
0
2
1
1
0
1
1
0
0
7
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
2
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
1
0
0
1
0
2
2
2
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
1
3
2
0
0
0
0
1
2
0
0
0
0
2
3
2
0
0
0
0
2
1
2
0
0
0
2
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
4
1
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
2
0
0
0
0
1
0
1
0
0
1
0
1
0
2
0
0
0
0
0
0
3
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
5
0
1
0
0
0
1
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
2
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
1
0
1
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
6
0
0
0
2
2
1
0
0
2
0
1
0
0
0
0
2
1
0
0
0
0
1
0
3
2
0
2
3
1
0
0
0
0
0
0
1
0
0
2
0
1
0
2
0
0
0
2
2
0
0
6
2
0
0
1
0
2
0
0
0
0
2
0
1
0
0
0
0
0
1
0
3
0
0
0
0
0
0
1
0
0
3
2
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
2
1
0
1
1
0
2
3
1
1
0
0
0
0
0
0
0
0
0
2
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
2
2
0
1
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
6
0
0
0
0
0
0
0
0
2
0
0
0
3
1
0
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
4
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
2
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
2
0
3
0
0
1
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
3
0
1
2
0
0
1
0
2
0
4
0
0
0
0
1
0
0
2
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
2
3
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
3
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
2
7
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
1
2
2
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
3
0
3
2
0
0
0
0
0
0
2
2
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
3
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
1
0
0
0
1
1
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
2
0
0
3
0
1
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
3
0
0
0
2
0
0
0
0
7
0
1
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
2
2
0
0
1
0
1
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
2
2
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
2
1
0
0
0
1
2
0
2
0
2
0
0
0
0
0
0
2
0
0
2
0
0
2
1
1
0
2
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
1
0
0
0
3
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
2
1
0
0
0
0
0
0
1
0
2
0
0
2
1
0
0
0
0
0
2
0
2
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
1
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
16
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
1
1
2
1
0
0
1
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
2
4
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
4
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
12
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
3
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
1
0
1
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
3
0
2
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
1
0
1
1
0
0
1
0
2
0
0
0
0
0
8
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
2
0
0
1
1
0
2
0
2
0
3
1
2
0
1
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
2
1
2
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
2
0
1
1
0
0
4
0
1
0
0
2
0
1
0
0
1
1
0
2
0
0
0
0
3
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
4
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
2
2
0
0
0
0
0
3
2
0
1
0
3
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
5
1
1
0
0
1
1
0
2
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
2
0
2
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
2
1
0
0
0
0
0
1
1
0
0
2
0
0
3
0
0
0
0
0
0
0
4
2
0
0
0
0
1
0
0
0
0
5
3
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
2
2
1
0
0
2
0
0
0
0
0
0
0
1
0
1
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
1
0
1
1
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
1
1
0
2
0
0
1
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
2
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
1
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
3
0
0
0
0
0
0
0
3
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
3
0
2
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
4
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
1
0
4
2
0
1
1
0
0
0
0
2
0
0
0
0
1
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
2
0
2
0
0
0
2
0
1
0
2
3
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
3
2
0
2
2
0
1
0
0
1
2
0
0
1
0
1
2
0
0
3
0
0
0
1
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
2
1
0
0
2
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
2
1
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
2
2
0
0
0
0
2
0
0
0
1
0
1
0
1
1
1
0
3
0
0
0
1
2
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
2
1
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
2
0
2
0
0
0
0
3
1
0
2
0
0
0
2
0
1
0
0
0
0
0
2
2
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
3
0
0
0
0
1
0
0
0
1
0
0
3
3
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
1
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
2
1
0
0
0
0
0
0
0
4
1
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
16
0
0
0
2
1
0
0
0
0
0
0
1
0
1
1
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
1
0
0
1
0
2
0
1
1
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
3
1
0
0
0
0
1
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
4
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
3
2
1
0
1
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
1
0
1
0
1
0
0
0
0
0
0
2
4
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
4
0
0
0
1
2
0
0
0
0
3
0
0
1
2
0
2
0
0
0
0
0
2
1
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
2
0
0
1
3
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
3
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
2
2
0
2
2
0
0
0
0
2
0
0
7
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
4
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
1
0
0
2
5
2
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
1
0
0
2
2
0
1
3
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
2
1
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
5
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
3
0
1
2
0
1
0
0
0
0
0
1
0
0
3
0
0
0
0
2
0
0
0
0
0
0
3
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
1
0
0
1
0
1
0
2
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
1
2
1
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
1
0
0
0
0
1
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
5
1
2
0
0
0
0
2
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
2
0
0
0
2
1
2
0
0
0
0
0
2
5
0
0
3
7
0
0
2
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
3
2
0
0
1
0
0
0
0
7
0
0
3
0
0
0
0
0
1
0
0
1
0
0
0
0
2
1
1
0
0
0
0
2
0
0
0
1
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
5
0
2
2
0
0
0
1
1
0
1
0
0
0
0
0
3
1
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
1
2
2
0
0
0
0
0
0
0
1
3
0
0
0
0
1
0
2
1
2
1
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
1
0
1
1
0
1
2
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
1
0
1
0
0
0
1
1
0
1
0
0
0
2
1
1
0
2
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
9
0
0
7
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
5
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
3
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
2
0
0
0
0
0
5
0
2
2
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
2
1
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
4
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
1
1
0
1
2
0
0
0
0
2
0
1
0
0
0
0
0
2
1
1
0
0
1
0
2
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
2
2
0
0
0
0
0
1
0
0
0
2
0
1
2
0
0
0
1
0
1
1
1
0
0
3
0
0
2
0
0
0
1
2
1
0
0
0
0
1
0
1
0
0
0
1
2
0
0
2
0
0
0
0
1
1
2
2
3
2
2
0
0
0
2
0
1
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
1
0
0
2
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
5
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
4
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
7
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
3
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
2
1
2
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
1
1
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
2
2
2
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
3
1
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
7
0
0
1
1
0
2
0
0
0
0
0
0
0
0
1
0
0
1
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
1
3
2
0
0
0
2
3
0
0
1
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
2
0
0
0
0
0
4
0
0
1
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
2
1
0
0
0
0
1
0
0
6
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
3
0
0
0
0
1
1
0
2
0
0
3
2
0
0
1
0
0
0
0
1
0
0
3
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
3
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
3
0
1
2
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
1
2
0
3
0
1
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
1
1
0
3
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
4
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
3
0
0
0
0
0
0
2
1
0
4
4
0
0
0
0
0
1
0
2
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
2
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
1
2
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
4
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
5
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
1
1
0
0
1
1
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
3
1
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
4
0
0
0
2
1
2
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
1
2
2
0
0
0
2
1
0
1
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
3
2
1
0
2
0
0
0
0
2
0
0
0
0
1
1
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
1
0
3
0
1
2
0
0
0
0
0
0
1
0
1
1
2
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
1
0
2
0
5
1
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
4
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
2
1
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
1
0
0
3
0
0
2
2
2
0
0
1
1
0
2
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
3
0
0
0
0
1
0
0
0
2
3
0
0
0
0
0
0
0
3
4
0
1
0
0
0
2
0
0
1
4
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
2
0
3
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
2
1
0
2
2
1
0
2
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
8
1
0
1
0
0
0
0
0
0
0
2
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
1
0
0
0
0
0
6
0
0
0
0
0
6
0
0
0
0
0
0
1
0
0
0
1
2
0
1
0
0
0
2
0
3
0
0
0
0
0
0
2
0
4
0
1
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
3
2
0
1
0
0
2
0
0
0
1
1
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
2
2
2
0
0
0
2
0
0
0
1
0
0
0
1
2
0
0
0
3
2
0
0
0
0
1
2
0
0
0
0
0
0
0
1
2
0
2
0
2
1
0
0
0
0
1
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
1
2
2
3
0
0
0
0
0
0
3
1
0
0
3
0
0
0
0
2
1
0
1
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
1
2
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
1
0
0
0
1
0
3
0
1
0
0
0
0
1
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
2
1
0
2
0
1
0
0
0
1
0
1
1
1
0
0
0
0
0
2
0
2
3
0
2
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
1
0
2
0
0
0
0
0
0
0
1
2
0
0
0
2
1
0
6
0
0
0
0
0
1
0
0
0
0
0
0
2
4
0
0
0
2
0
0
0
2
1
0
0
4
0
0
0
2
0
0
3
1
0
0
3
0
1
0
0
0
1
0
0
1
2
0
0
0
3
2
0
0
1
0
0
0
3
0
2
1
0
0
0
2
0
0
0
1
0
2
0
0
1
0
1
5
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
3
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
3
0
0
1
0
0
1
2
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
1
0
5
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
3
1
1
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
2
0
1
0
2
0
0
0
2
2
5
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
3
0
1
0
0
0
1
0
0
2
0
0
0
0
1
1
2
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
1
2
0
3
2
0
0
0
1
0
0
1
0
1
1
0
0
4
0
1
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
2
2
0
2
0
1
0
2
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
2
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
2
2
0
2
0
1
0
0
1
1
0
0
0
1
2
0
1
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
6
0
0
1
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
5
0
0
0
7
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
3
0
0
1
0
0
1
0
0
0
2
1
0
0
1
1
0
0
1
0
0
2
0
2
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
3
1
0
1
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
2
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
11
1
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
3
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
6
1
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
2
1
2
0
0
2
0
0
0
0
0
0
0
1
0
0
3
1
0
1
0
0
0
0
1
0
1
1
3
2
1
0
0
0
3
0
0
0
3
2
0
0
0
0
0
0
0
0
1
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
3
1
2
0
0
0
0
2
0
0
0
0
0
0
0
3
2
0
2
0
5
0
0
1
0
1
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
1
1
2
2
0
0
5
0
0
0
1
0
0
1
0
0
0
0
4
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
1
0
1
0
0
3
1
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
2
0
0
2
0
0
2
6
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
2
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
4
0
1
0
0
0
2
0
0
0
1
0
4
0
0
0
3
0
0
2
2
0
0
0
5
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
1
2
0
1
0
0
1
2
1
1
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
2
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
2
1
0
0
1
0
2
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
7
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
2
1
0
0
0
1
3
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
2
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
2
0
4
0
0
1
2
0
1
3
0
3
0
5
0
1
0
2
1
0
2
1
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
2
0
0
1
0
0
1
1
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
3
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
1
1
0
0
0
0
0
1
0
2
2
2
2
0
3
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
1
0
2
0
0
0
0
1
0
0
0
3
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
3
0
0
0
1
1
0
0
2
0
0
0
0
2
1
2
0
0
1
0
0
2
0
0
0
2
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
6
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
2
0
1
0
2
0
0
1
0
0
0
0
0
4
0
1
1
0
0
0
9
6
0
1
2
0
0
0
1
0
0
0
1
0
0
0
2
0
0
2
0
2
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
6
0
0
0
0
1
3
2
1
0
0
0
1
2
2
2
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
2
0
0
2
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
5
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
1
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
2
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
1
1
0
0
2
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
3
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
8
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
3
0
0
0
0
0
2
0
2
1
0
0
0
0
2
0
0
2
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
1
0
3
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
2
0
0
0
0
1
2
0
0
0
1
0
1
0
0
0
0
0
0
1
0
3
0
2
0
0
0
1
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
2
3
0
0
1
0
0
0
0
3
0
0
0
0
0
1
1
1
0
0
0
1
0
3
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
2
0
2
1
0
0
3
0
1
0
0
0
1
0
0
0
0
0
0
9
2
0
0
0
0
0
0
0
1
0
0
0
2
0
1
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
4
0
1
0
0
0
0
0
4
2
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
3
1
0
0
0
0
0
2
0
0
2
0
0
0
2
2
2
0
0
2
0
1
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
1
1
1
2
0
1
10
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
3
0
0
0
0
1
0
0
0
0
1
1
2
0
0
0
0
0
6
0
0
0
2
0
2
0
0
0
0
2
1
3
0
3
0
2
0
0
0
0
0
0
0
1
2
0
1
0
3
0
0
0
2
0
0
0
1
0
1
0
2
1
0
0
2
0
0
0
0
0
0
0
1
0
1
1
2
0
0
0
0
0
1
2
0
2
0
2
0
0
0
2
0
1
3
3
0
0
0
0
0
0
7
0
2
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
5
0
1
0
0
0
1
0
2
0
0
0
0
0
0
2
0
2
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
1
0
0
0
2
1
0
1
0
1
0
0
1
0
2
2
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
1
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
14
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
2
0
1
0
1
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
1
4
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
1
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
2
0
5
0
0
3
0
0
0
3
0
0
0
0
0
1
1
0
0
2
0
2
0
2
0
2
0
1
0
2
0
0
0
1
0
0
3
0
0
3
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
1
1
0
0
1
0
0
2
2
0
0
0
2
1
0
0
2
0
1
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
5
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
6
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
1
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
1
3
0
0
0
2
0
0
0
4
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
3
1
0
6
0
0
0
0
0
2
0
3
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
2
1
0
2
0
0
0
2
2
0
0
0
0
0
0
0
2
2
2
0
0
0
1
2
0
0
0
1
2
0
0
3
0
0
4
0
0
1
1
0
1
1
0
1
0
0
0
0
0
0
0
0
1
2
0
0
1
0
3
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
3
0
2
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
3
0
0
2
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
3
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
5
1
0
0
2
0
0
3
2
0
3
0
2
0
2
1
0
0
2
0
2
2
0
0
0
0
0
1
2
2
0
0
0
0
0
0
2
3
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
3
2
0
1
0
1
0
0
0
1
0
0
2
0
0
0
0
1
0
0
1
0
0
1
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
3
1
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
2
0
0
0
1
0
1
2
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
2
0
0
2
0
1
0
1
0
0
1
2
1
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
3
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
1
0
0
0
0
0
1
1
0
1
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
2
2
0
0
0
8
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
4
2
0
0
2
2
0
0
0
0
0
0
1
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
7
0
0
2
0
0
0
3
0
2
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
2
0
0
0
3
0
0
0
0
2
1
0
1
0
0
3
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
10
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
3
0
0
2
0
0
0
1
0
0
1
0
0
0
2
0
1
0
0
0
0
2
0
0
1
0
5
0
0
3
1
0
0
1
0
0
0
1
0
1
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
3
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
2
3
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
2
1
6
0
1
0
1
0
0
2
0
0
2
1
0
0
0
0
1
0
15
0
0
0
0
0
1
1
0
0
2
0
0
2
0
0
0
1
3
2
0
0
2
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
1
2
0
2
0
1
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
1
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
3
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
2
1
0
0
2
1
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
1
0
2
0
0
3
1
0
0
1
2
0
0
0
0
0
1
0
0
0
2
0
1
0
2
0
0
1
0
0
0
4
0
1
1
0
1
2
0
0
0
0
0
0
0
0
2
1
1
0
2
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
4
0
1
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
1
5
0
2
0
0
0
0
1
1
0
0
2
0
0
0
0
0
1
2
0
0
0
2
0
1
2
1
0
0
0
0
4
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
6
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
2
0
1
0
0
0
0
4
0
2
0
0
3
0
0
2
0
0
0
2
0
0
0
1
1
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
2
0
0
3
0
3
0
0
0
0
0
1
0
0
0
2
2
0
0
0
3
0
0
0
1
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
3
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
4
0
0
1
0
1
3
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
2
3
0
1
0
2
0
0
0
0
2
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
1
0
0
0
1
1
0
1
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
1
1
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
3
1
0
2
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
1
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
2
1
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
3
2
1
2
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
1
2
3
0
0
0
0
1
0
0
0
1
1
0
2
0
1
0
0
1
1
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
3
1
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
1
0
1
1
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
1
0
0
0
1
0
0
2
5
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
2
0
2
1
4
1
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
1
0
0
0
5
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
5
1
0
2
0
2
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
2
0
1
0
0
0
1
0
0
0
2
2
0
2
0
0
0
2
1
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
4
0
1
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
3
1
1
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
3
0
0
5
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
1
13
2
1
0
2
0
0
2
0
0
0
0
4
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
2
0
0
0
2
0
0
0
1
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
3
3
4
1
0
0
0
0
2
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
2
1
0
0
1
4
0
1
2
1
2
3
0
0
0
1
2
1
0
0
1
5
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
3
0
1
0
0
1
0
0
2
0
0
0
3
0
0
1
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
2
4
0
0
0
1
0
1
0
2
0
2
0
0
0
2
0
3
0
1
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
2
1
0
0
0
0
3
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
3
1
0
1
0
0
0
0
3
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
4
2
0
1
0
0
0
0
0
0
0
0
0
3
0
0
3
0
1
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
3
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
1
2
0
0
0
0
7
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
2
2
0
2
0
1
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
1
2
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
1
1
0
1
0
0
2
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
3
0
3
3
4
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
3
0
0
0
2
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
2
0
1
1
1
0
0
0
0
0
1
0
0
0
1
0
0
2
2
0
0
0
1
2
0
2
0
1
0
0
0
0
0
0
3
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
2
0
0
0
1
2
2
0
0
2
1
0
2
0
0
0
2
0
0
7
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
2
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
1
0
0
2
2
2
1
0
0
1
0
0
0
0
1
0
0
2
0
2
0
3
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
3
0
0
0
0
0
2
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
1
1
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
3
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
1
2
0
1
0
0
1
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
3
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
2
2
0
0
0
4
0
0
3
0
0
0
0
0
0
1
0
2
1
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
2
2
2
0
0
0
2
0
0
2
0
0
0
5
0
2
0
2
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
5
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
4
0
0
5
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
3
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
2
0
0
0
0
2
0
2
1
0
2
0
2
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
6
3
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
1
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
2
0
0
1
0
2
0
0
0
1
0
0
0
2
3
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
2
0
1
2
4
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
1
0
0
0
3
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
1
4
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
1
0
1
0
0
9
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
3
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
1
0
0
1
0
0
0
1
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
3
0
0
0
1
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
2
3
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
2
0
1
2
2
0
0
0
0
0
0
2
0
0
1
2
0
0
0
2
0
0
0
0
0
1
1
0
1
0
0
0
0
0
2
0
0
0
0
0
2
4
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
4
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
2
0
0
2
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
1
0
0
1
0
2
1
0
0
1
1
3
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
4
0
0
2
1
0
1
0
1
2
0
1
0
0
0
2
0
2
0
0
0
0
0
1
1
1
0
1
0
1
2
0
0
1
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
5
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
3
0
2
0
0
3
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
2
1
0
0
2
0
1
0
2
0
1
0
1
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
2
0
0
2
0
1
0
0
0
0
1
2
0
1
2
0
0
0
3
1
0
0
0
0
0
0
0
0
2
1
0
1
0
3
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
5
0
0
0
0
2
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
5
0
2
0
2
0
0
0
1
0
1
1
0
2
0
1
2
2
0
0
0
0
2
0
0
0
0
0
0
0
1
2
1
0
0
0
0
3
0
0
0
0
2
2
2
0
2
0
0
2
1
0
2
0
0
2
1
0
0
1
2
0
0
0
0
1
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
1
1
0
6
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
3
0
0
1
0
0
1
1
0
0
0
0
0
2
1
0
0
0
1
0
2
0
0
0
0
2
1
0
0
4
0
0
1
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
2
0
2
0
0
1
0
1
2
0
0
2
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
1
0
0
0
2
0
0
2
0
0
0
0
2
2
3
1
0
0
0
2
1
2
1
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
1
2
0
2
0
0
1
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
2
2
0
1
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
2
0
1
2
1
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
1
0
0
2
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
1
2
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
3
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
4
0
0
0
0
2
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
1
1
0
2
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
2
0
0
0
3
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
1
0
0
2
1
0
1
0
0
1
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
4
1
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
3
0
2
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
1
2
2
1
0
0
2
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
3
0
0
5
0
0
0
1
1
1
0
0
0
3
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
1
0
0
0
2
0
0
2
1
0
2
0
0
0
0
0
1
0
5
2
0
0
1
0
2
1
0
0
0
0
0
1
0
0
1
0
2
0
2
3
0
3
0
0
2
1
0
4
0
0
0
0
0
7
0
0
0
2
0
0
0
0
1
0
0
1
2
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
3
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
2
0
0
0
0
0
0
0
0
1
3
2
0
2
2
0
2
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
1
0
1
0
0
0
0
1
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
1
0
0
0
0
2
0
0
0
1
2
0
0
2
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
7
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
5
0
2
0
0
2
0
1
1
0
0
0
0
0
1
0
0
0
3
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
2
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
2
0
0
1
0
7
0
0
0
0
2
1
1
1
0
1
0
0
0
0
0
0
2
0
3
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
1
0
0
0
2
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
1
2
3
2
1
0
1
1
0
0
0
0
0
0
1
3
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
2
0
0
0
0
0
1
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
1
0
1
0
0
0
2
0
2
3
0
0
0
0
5
2
0
0
0
0
1
2
2
0
0
0
1
0
0
0
1
1
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
1
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
2
0
5
0
0
0
0
3
0
1
0
0
0
1
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
2
0
0
0
0
0
1
0
1
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
1
0
2
3
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
1
1
3
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
2
0
0
2
0
0
0
0
0
2
0
2
1
0
0
0
0
0
1
0
2
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
2
0
1
2
4
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
3
0
2
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
3
0
2
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
1
0
0
0
0
0
0
0
4
1
0
0
0
1
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
1
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
2
0
4
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
2
2
1
2
0
0
0
0
0
0
0
1
0
3
0
0
0
2
0
1
0
0
0
2
0
0
0
3
1
2
0
1
0
0
0
0
0
0
3
0
0
1
0
0
0
0
2
0
0
0
0
3
0
2
0
0
0
2
2
2
0
0
0
0
0
0
1
2
0
0
0
0
2
0
1
2
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
5
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
1
1
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
11
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
1
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
2
0
0
0
0
0
4
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
1
0
1
1
0
2
0
0
0
1
0
0
7
0
1
0
0
0
0
0
0
2
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
3
2
0
1
0
0
0
0
0
2
2
0
1
0
1
0
1
0
1
0
0
1
2
0
2
0
0
0
0
0
4
1
0
0
2
1
1
0
0
0
0
1
1
0
0
0
1
0
1
0
2
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
6
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
4
0
0
0
0
0
0
0
2
0
2
0
0
2
1
2
1
0
3
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
2
3
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
5
1
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
3
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
2
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
5
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
2
2
0
1
1
0
3
0
0
0
1
0
0
0
0
0
0
0
0
1
2
3
0
0
0
0
0
0
2
1
3
0
0
0
2
1
0
3
0
0
2
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
3
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
2
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
1
0
1
0
0
0
0
0
1
0
2
0
0
2
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
3
0
0
0
0
2
1
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
2
0
0
0
1
0
0
0
0
1
1
0
0
0
3
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
1
0
0
0
1
1
0
6
0
0
1
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
1
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
2
0
0
0
0
0
1
0
6
3
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
3
0
0
3
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
1
0
2
0
1
0
0
0
0
0
4
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
3
0
0
0
1
0
1
0
0
0
2
0
0
0
0
1
1
0
0
1
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
1
2
0
0
1
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
2
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
1
2
0
2
0
2
1
0
0
1
2
2
0
0
0
2
0
1
0
1
0
0
0
0
0
0
3
0
0
2
0
0
2
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
1
0
0
2
0
0
0
3
0
0
0
0
0
2
1
0
2
2
0
0
1
0
1
0
2
0
0
0
0
1
0
0
0
0
3
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
2
0
4
0
2
0
0
0
0
0
0
0
0
0
2
3
3
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
2
4
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
1
3
1
0
3
0
0
0
0
0
0
2
2
0
0
0
0
3
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
1
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
2
0
1
2
0
0
1
0
2
2
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
5
1
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
1
0
2
0
1
0
0
1
0
1
2
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
3
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
1
1
2
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
2
1
1
2
0
0
0
2
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
1
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
4
0
2
0
0
0
3
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
1
0
2
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
1
5
0
0
0
3
2
0
2
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
2
0
1
0
2
0
0
0
0
0
0
2
1
2
0
1
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
1
0
0
0
1
2
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
2
0
0
0
3
2
0
0
0
0
0
3
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
1
0
2
1
3
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
1
7
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
2
3
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
3
0
2
0
0
0
2
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
1
2
0
2
1
0
0
2
0
1
0
2
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
2
1
0
0
0
2
2
1
0
0
1
0
2
0
0
0
0
0
2
0
0
2
0
1
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
5
0
0
0
0
0
0
2
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
2
2
0
1
0
0
0
1
0
4
0
0
0
0
0
0
0
1
0
0
1
0
1
2
0
0
0
0
2
0
0
0
0
0
2
1
4
0
0
0
0
0
0
3
4
0
1
3
1
0
0
0
5
0
0
0
0
2
0
0
2
1
2
1
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
5
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
1
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
3
0
0
2
0
0
0
0
1
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
7
0
1
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
2
0
0
0
0
2
0
0
0
0
0
0
2
0
2
2
0
2
0
0
0
0
1
0
0
0
1
0
2
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
2
0
0
2
7
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
1
3
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
2
0
0
0
0
0
1
1
3
0
0
0
0
0
0
1
0
2
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
4
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
1
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
2
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
3
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
5
0
0
0
4
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
1
0
0
0
0
3
0
0
4
0
3
1
0
0
2
1
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
6
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
2
2
4
0
0
0
0
0
2
1
0
0
0
2
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
3
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
2
2
0
1
0
0
0
0
0
5
1
0
2
0
0
0
0
0
0
0
0
1
0
2
4
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
1
1
1
2
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
2
0
1
0
0
0
1
1
2
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
2
0
3
0
0
1
0
1
0
2
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
2
1
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
2
0
0
2
6
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
1
2
0
0
0
1
0
0
0
0
2
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
11
0
1
1
2
0
0
2
0
0
1
1
1
0
1
1
0
0
3
2
0
1
0
2
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
2
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
1
2
3
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
1
2
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
4
0
0
0
0
1
2
0
0
2
0
0
0
0
0
2
0
0
2
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
1
0
0
0
1
0
0
0
2
1
0
2
0
0
0
0
0
2
3
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
1
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
1
0
1
0
2
0
0
2
0
0
0
0
0
3
0
1
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
1
1
0
0
0
3
2
1
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
1
2
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
2
2
1
1
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
1
0
0
0
0
0
2
0
1
0
0
3
0
0
0
0
1
0
0
0
1
0
0
0
0
0
5
2
0
0
2
7
4
0
0
1
0
0
0
1
0
0
3
0
0
0
0
0
1
0
2
0
0
0
2
1
0
0
1
0
0
1
0
0
0
2
0
0
3
0
0
0
0
0
0
2
1
1
2
0
0
2
2
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
1
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
1
2
0
0
0
0
0
4
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
2
0
1
0
0
3
0
0
1
0
1
2
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
5
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
1
0
2
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
3
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
2
2
3
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
2
0
1
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
3
0
3
0
0
0
0
0
0
0
0
1
2
0
0
2
0
2
0
2
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
1
0
0
0
2
2
1
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
3
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
4
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
2
0
7
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
4
0
2
0
1
0
1
0
0
1
0
0
1
0
2
0
0
0
0
0
2
2
0
0
0
2
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
2
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
3
0
3
0
5
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
3
1
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
2
1
0
0
1
0
0
0
0
0
2
1
0
1
0
0
0
0
0
1
0
3
0
1
0
0
0
0
14
2
0
0
1
0
0
7
0
0
0
1
0
0
2
1
0
0
2
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
3
2
0
0
0
0
0
0
0
2
2
2
0
0
1
0
0
1
0
0
0
0
0
2
0
0
2
0
2
0
0
0
5
0
0
0
1
0
0
1
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
2
0
0
0
0
0
2
1
0
0
0
2
0
1
0
0
0
0
7
0
0
0
0
3
2
4
1
0
1
0
0
2
2
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
4
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
5
0
0
1
2
0
0
1
0
0
0
1
0
0
0
1
0
2
0
0
2
0
0
0
0
0
2
3
0
0
0
1
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
1
1
0
2
0
1
2
0
0
0
0
0
3
0
5
1
5
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
9
1
0
0
0
0
1
0
0
0
0
2
0
0
2
2
0
1
1
0
2
0
0
1
2
0
0
0
0
0
0
0
3
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
2
0
1
0
0
0
2
2
0
0
0
0
0
0
1
0
2
0
0
2
1
0
0
0
0
2
0
0
2
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
1
2
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
1
1
1
0
2
1
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
2
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
2
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
1
0
1
0
0
0
2
0
4
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
2
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
1
0
1
0
0
0
0
0
1
1
0
2
1
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
1
0
1
0
1
0
0
2
0
1
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
1
3
0
1
0
0
0
2
2
1
0
0
2
0
0
0
2
0
0
2
0
1
2
0
0
0
2
1
2
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
3
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
1
3
4
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
2
2
0
0
0
0
4
2
0
0
1
0
2
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
6
0
2
0
0
0
3
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
2
2
0
0
0
0
0
0
0
0
2
2
0
3
2
0
0
1
0
0
0
0
0
4
2
0
0
0
2
0
0
0
0
1
0
2
0
0
0
2
0
1
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
2
1
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
2
1
0
0
0
0
1
1
1
0
0
1
0
1
2
0
0
0
2
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
10
2
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
6
1
0
0
1
0
0
1
0
2
0
2
0
0
0
0
0
0
2
0
2
0
0
0
1
2
0
0
0
0
0
0
2
1
7
1
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
1
2
1
1
0
0
2
0
0
0
0
0
1
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
3
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
1
0
1
1
3
0
0
2
0
0
0
0
0
2
1
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
5
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
1
0
0
1
0
1
0
0
2
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
5
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
1
2
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
2
2
0
0
0
0
0
0
0
0
2
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
2
2
0
0
0
1
0
0
0
0
0
2
0
2
2
4
0
1
0
0
0
0
0
0
1
2
1
0
0
0
0
0
1
0
0
3
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
1
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
12
2
2
0
2
0
1
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
1
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
1
2
0
3
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
2
0
0
0
2
0
0
1
2
0
0
2
0
0
0
2
4
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
3
0
3
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
3
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
3
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
1
2
0
0
1
0
3
0
2
2
0
0
0
2
2
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
2
0
1
1
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
1
0
0
3
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
3
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
1
0
1
1
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
5
1
2
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
5
0
0
1
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
1
0
0
0
2
0
0
1
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
1
2
0
0
0
3
3
0
0
0
0
2
1
0
0
2
0
0
0
0
0
2
3
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
3
2
0
0
0
1
0
1
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
1
2
0
5
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
5
0
0
0
2
0
0
1
0
0
1
1
0
2
2
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
2
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
2
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
2
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
2
0
0
1
3
1
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
5
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
2
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
1
2
0
0
0
0
1
0
0
0
1
1
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
2
0
1
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
4
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
1
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
1
2
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
3
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
1
0
1
0
2
0
0
1
0
0
6
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
5
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
2
0
0
2
0
0
0
2
0
0
2
0
2
0
0
0
0
0
4
2
0
0
2
3
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
2
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
1
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
2
1
0
2
2
4
0
0
0
2
0
0
1
1
1
2
2
0
1
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
2
2
1
1
1
0
0
0
0
1
2
0
0
2
0
0
5
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
1
1
0
0
0
0
1
0
0
0
0
2
0
1
0
0
2
0
0
0
0
2
0
1
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
4
0
0
0
3
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
1
2
0
0
0
1
0
0
0
2
0
3
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
2
2
0
0
0
0
0
1
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
7
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
2
1
2
1
0
4
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
2
0
0
0
1
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
5
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
2
0
0
0
0
0
3
0
0
1
0
0
0
2
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
5
0
0
1
1
0
0
2
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
1
0
0
0
2
0
0
2
0
1
1
0
0
0
2
0
0
0
0
0
2
2
0
2
1
0
1
0
0
0
0
0
2
2
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
2
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
2
1
2
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
2
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
1
0
0
2
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
2
1
0
0
3
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
1
0
2
0
1
0
0
0
0
2
0
0
0
2
0
2
9
0
2
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
2
0
0
0
0
2
0
0
0
0
1
0
0
0
4
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
1
1
0
0
0
0
2
0
0
0
0
2
1
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
3
1
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
1
3
0
0
1
2
1
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
2
1
2
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
1
1
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
1
0
0
1
0
0
0
2
1
0
0
1
3
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
1
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
1
0
1
1
0
2
1
0
0
1
2
0
0
0
2
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
4
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
3
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
3
1
1
0
1
0
0
0
0
2
0
1
1
0
0
2
0
1
0
0
2
2
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
2
0
0
0
2
1
1
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
2
0
0
0
0
1
2
0
1
2
1
0
0
0
1
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
2
0
2
2
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
2
1
2
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
3
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
1
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
4
2
0
0
0
0
0
1
0
0
1
0
2
0
0
0
1
1
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
5
0
1
0
0
0
1
0
0
0
0
2
1
0
1
0
0
1
0
2
0
0
0
0
0
4
3
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
1
0
1
0
0
5
1
0
0
0
0
1
2
0
0
0
0
2
0
4
0
1
2
0
0
0
3
1
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
1
0
1
0
2
0
2
0
2
0
0
0
1
0
2
0
0
0
0
1
0
2
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
5
0
1
2
5
0
2
0
0
0
1
2
0
0
0
1
1
0
0
1
0
1
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
3
1
0
0
0
3
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
2
1
0
0
0
0
0
0
1
2
1
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
1
4
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
3
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
1
2
1
0
1
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
1
2
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
1
0
2
2
0
0
2
2
0
0
2
2
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
1
1
2
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
1
0
0
0
0
0
0
0
2
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
3
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
2
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
1
0
0
0
0
0
1
2
0
3
0
0
0
0
0
1
0
0
0
2
0
1
0
2
0
0
0
0
2
0
0
0
0
0
2
0
2
2
0
0
0
0
0
2
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
1
2
0
0
1
3
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
3
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
4
0
0
0
0
0
1
0
1
2
0
0
1
1
2
0
0
0
8
0
0
2
0
0
1
2
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
3
1
0
0
0
0
2
0
0
0
0
0
2
0
0
5
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
1
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
3
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
2
1
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
1
0
0
3
2
1
1
0
0
0
2
0
0
1
0
2
0
0
1
0
0
0
1
0
0
0
0
3
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
2
0
0
0
3
0
3
1
0
0
0
0
2
0
0
0
2
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
2
1
1
0
1
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
1
0
0
0
0
0
1
0
0
2
0
0
2
2
1
0
0
0
2
1
1
1
3
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
2
0
1
0
2
0
1
0
1
2
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
2
0
0
0
0
0
2
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
2
0
1
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
3
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
1
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
8
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
1
2
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
1
0
2
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
1
0
0
1
1
0
0
2
2
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
3
0
1
2
0
0
2
0
0
0
0
0
0
0
0
2
2
0
1
0
0
3
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
1
1
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
2
0
2
0
2
2
0
0
0
0
0
2
0
1
0
2
0
0
2
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
14
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
15
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
1
1
0
1
0
1
1
0
2
0
0
0
2
2
0
0
0
2
3
0
0
1
0
0
1
2
0
0
0
0
2
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
1
0
1
0
0
0
0
0
2
1
0
0
0
0
0
6
0
2
1
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
2
0
0
1
0
2
0
0
1
0
2
0
0
0
0
0
0
2
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
3
0
0
0
1
0
0
0
0
1
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
7
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
3
0
0
2
0
2
0
0
0
4
0
0
0
4
0
0
0
0
0
0
1
0
0
2
1
0
2
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
2
1
0
0
0
0
2
0
0
2
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
3
0
0
0
0
2
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
3
0
2
0
0
2
0
0
0
0
0
2
2
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
2
0
0
1
0
0
0
1
1
0
0
0
7
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
4
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
2
0
0
2
1
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
1
0
0
0
0
0
1
0
0
2
2
0
1
0
0
0
0
0
2
0
1
0
2
0
4
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
1
0
0
0
1
0
1
0
1
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
1
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
1
2
0
3
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
2
0
0
5
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
2
3
0
1
1
2
0
0
0
0
0
0
0
1
0
0
2
2
0
2
0
1
0
0
0
1
4
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
4
0
0
0
0
1
0
0
0
0
3
0
0
1
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
2
0
1
2
1
0
0
2
2
0
3
0
0
2
1
0
0
0
2
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
2
0
2
0
3
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
2
0
2
0
1
0
0
1
0
0
0
2
0
0
2
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
5
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
4
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
2
2
0
0
2
0
0
0
0
1
0
3
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
3
5
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
2
1
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
1
0
1
0
0
0
0
5
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
5
0
0
3
0
3
0
0
0
2
2
2
2
0
0
3
0
1
1
1
0
0
3
0
2
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
5
0
1
0
0
0
0
0
2
0
0
1
2
1
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
5
2
0
2
0
2
0
0
0
0
2
1
1
0
1
0
2
0
1
1
1
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
13
0
2
2
0
0
0
0
0
1
0
0
2
1
0
0
2
0
0
1
1
0
0
0
0
0
0
0
1
0
2
0
0
1
1
0
0
0
0
1
0
2
1
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
1
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
3
0
0
0
3
0
0
2
2
0
2
0
1
1
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
2
1
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
1
0
0
1
0
0
1
0
0
2
0
0
1
2
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
2
1
0
3
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
2
1
0
0
2
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
1
1
0
6
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
3
3
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
1
0
1
0
0
0
0
0
2
0
0
0
1
0
2
0
0
1
1
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
2
0
1
3
0
0
1
0
2
0
0
1
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
2
1
0
2
2
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
3
2
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
10
0
0
0
0
0
0
0
2
2
0
1
1
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
2
0
0
0
1
2
0
1
2
0
2
0
1
1
1
0
2
0
0
2
1
2
0
2
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
1
2
2
0
0
1
2
1
0
0
0
2
2
3
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
1
0
1
0
0
1
1
2
0
0
7
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
2
0
0
5
0
0
2
0
0
0
1
0
2
0
0
0
0
1
1
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
1
2
0
0
0
1
3
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
2
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
2
2
0
0
0
0
3
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
3
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
3
0
0
0
1
0
2
0
1
3
0
1
7
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
5
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
2
1
0
1
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
3
0
0
1
0
4
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
2
0
1
2
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
1
4
0
0
0
0
2
0
0
0
2
0
0
1
0
0
1
2
0
0
0
0
1
2
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
2
2
0
1
0
0
3
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
2
3
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
1
0
1
0
0
0
0
2
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
7
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
1
1
0
2
2
0
3
0
0
3
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
6
0
0
4
0
0
0
0
0
0
1
0
1
5
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
2
1
0
0
0
0
0
2
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
4
0
4
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
2
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
2
3
0
0
2
0
0
0
0
1
0
1
2
0
4
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
2
0
1
0
0
0
0
0
2
0
0
0
1
2
1
0
0
0
2
0
2
0
3
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
2
1
0
0
0
1
1
6
0
0
0
0
0
7
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
1
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
2
2
0
1
0
1
0
0
0
0
0
3
0
0
2
0
0
0
0
2
4
0
2
0
2
0
2
0
0
0
1
0
0
0
0
0
2
1
0
0
2
0
0
0
0
1
0
0
3
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
6
2
0
2
2
0
0
0
1
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
4
0
0
0
0
0
1
0
0
0
2
2
2
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
1
0
0
2
1
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
5
2
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
1
2
0
4
0
0
0
0
1
1
4
0
0
0
4
0
1
0
1
1
2
0
0
0
0
0
2
2
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
7
0
0
2
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
2
1
1
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
3
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
1
0
2
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
3
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
1
0
0
0
0
3
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
5
0
2
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
2
1
0
0
0
0
1
0
0
0
0
3
0
1
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
6
0
0
2
3
0
0
0
0
0
0
0
1
1
3
0
0
0
2
0
0
0
1
0
0
1
0
0
1
2
0
0
0
1
0
2
0
0
0
0
7
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
1
0
0
2
2
1
0
2
0
0
2
1
0
0
1
0
1
0
0
0
2
0
0
1
0
0
0
0
0
2
0
1
1
2
0
1
0
2
0
2
0
0
0
0
0
2
0
0
0
1
0
0
5
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
5
0
0
0
0
0
0
0
3
0
1
0
1
0
0
0
0
0
0
2
0
2
0
1
0
2
2
1
0
0
0
0
1
0
0
0
2
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
5
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
1
0
1
1
2
0
0
0
3
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
1
4
2
0
0
1
1
0
0
0
0
0
0
1
1
0
2
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
1
1
0
0
0
2
2
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
1
0
0
0
0
0
1
3
0
0
0
1
0
0
0
2
1
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
2
0
0
0
4
0
2
0
2
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
3
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
1
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
1
1
3
0
0
2
0
0
0
1
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
2
2
0
2
2
0
3
1
2
0
1
1
2
0
0
0
2
1
2
0
0
0
0
1
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
2
1
0
1
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
2
0
2
1
0
0
3
1
5
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
2
0
2
0
0
2
0
0
0
0
0
2
0
2
0
3
3
0
0
0
2
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
1
0
0
1
2
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
6
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
1
1
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
2
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
2
0
4
0
0
2
0
0
0
7
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
2
2
0
0
0
1
0
2
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
1
1
0
2
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
4
1
0
0
0
0
4
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
1
2
0
0
1
0
0
1
0
0
0
2
1
0
2
0
2
3
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
4
0
0
2
2
0
0
1
0
0
0
1
2
0
0
2
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
2
0
0
1
0
0
2
0
1
0
1
0
1
0
1
2
0
0
2
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
3
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
3
1
5
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
1
0
2
0
1
0
0
2
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
5
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
3
0
2
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
1
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
1
0
1
0
8
0
0
0
0
3
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
3
2
1
0
0
3
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
1
3
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
2
0
2
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
1
2
0
0
0
0
0
2
0
0
2
2
2
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
1
0
2
2
2
0
0
0
1
0
0
0
0
0
0
1
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
2
0
2
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
2
1
0
0
1
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
2
0
0
2
1
0
0
2
1
0
0
2
0
0
2
0
1
0
0
2
0
1
0
0
0
0
0
0
3
0
0
5
0
3
0
0
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
2
3
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
4
0
0
5
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
1
1
1
0
1
2
2
2
2
2
0
0
0
0
0
0
0
2
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
5
0
0
0
1
0
0
0
0
0
0
0
1
1
2
2
2
3
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
2
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
2
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
2
0
0
0
0
0
1
0
0
3
0
0
0
0
0
1
4
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
3
0
0
0
2
1
4
0
0
0
7
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
2
2
0
2
0
1
0
2
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
1
2
0
1
0
0
0
2
0
0
1
2
6
1
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
3
0
2
0
2
1
0
0
2
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
4
3
0
2
0
0
0
0
1
0
0
1
0
0
0
1
4
0
0
2
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
6
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
2
0
0
3
0
0
2
0
1
0
2
0
0
1
1
0
0
0
0
0
0
0
0
4
4
0
2
0
0
2
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
1
2
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
2
0
0
1
0
0
0
3
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
1
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
2
0
0
1
0
0
0
0
0
2
0
0
0
1
0
2
0
2
0
0
1
2
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
3
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
1
0
0
0
1
0
0
3
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
1
1
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
1
2
0
7
1
0
2
0
0
0
0
0
1
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
2
2
1
1
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
2
0
0
0
1
0
2
2
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
4
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
2
2
1
2
0
2
0
0
2
0
0
0
0
1
2
0
0
0
1
0
0
0
1
0
2
0
0
0
0
2
1
1
2
0
0
0
0
0
0
0
2
0
0
0
0
1
1
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
1
0
0
1
3
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
1
0
0
0
1
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
3
3
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
1
0
0
0
0
3
0
3
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
3
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
1
3
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
3
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
4
0
0
2
1
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
1
0
0
5
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
3
2
0
2
0
0
0
0
0
3
0
0
2
4
0
1
0
0
1
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
3
0
0
3
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
2
0
0
2
1
0
3
0
0
0
0
2
0
0
1
0
0
0
0
0
2
3
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
3
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
1
0
2
2
0
0
0
0
0
2
0
0
1
0
0
2
1
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
3
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
3
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
2
1
1
0
0
2
0
0
0
0
0
0
0
3
2
0
0
0
0
1
0
1
0
0
0
0
2
0
3
0
5
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
1
0
3
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
2
2
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
2
2
1
0
1
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
3
0
2
0
0
7
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
3
0
0
0
1
0
0
2
1
1
0
0
0
0
0
0
2
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
2
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
2
0
1
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
2
0
0
1
0
0
2
0
1
0
0
1
0
2
1
0
0
2
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
1
1
0
0
2
4
0
0
0
2
1
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
1
1
0
2
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
2
0
1
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
1
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
5
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
7
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
2
0
0
3
0
1
0
2
0
0
2
0
2
0
0
0
0
7
0
1
0
0
0
2
2
0
2
0
0
0
0
0
2
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
1
0
0
3
0
2
1
1
2
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
1
0
1
0
1
0
0
0
0
0
0
0
2
3
0
2
1
0
0
0
3
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
2
1
0
0
2
0
0
0
0
2
1
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
1
0
2
0
4
0
0
0
0
2
1
1
0
0
4
0
2
0
2
0
2
1
0
3
1
0
0
0
0
0
0
1
0
0
0
2
2
0
1
0
2
2
2
0
0
1
0
1
0
2
2
1
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
1
0
0
0
3
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
3
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
5
0
0
1
0
1
2
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
2
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
3
6
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
5
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
1
1
0
0
1
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
2
2
0
0
0
0
0
0
2
0
0
3
0
0
0
2
0
0
2
0
1
0
0
0
2
1
1
0
0
0
0
4
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
3
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
1
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
3
0
0
1
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
1
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
2
0
1
5
0
1
0
2
0
0
1
2
1
0
1
0
0
0
0
0
0
2
0
1
0
0
1
0
2
0
0
0
0
2
0
0
0
3
2
0
1
0
0
0
0
1
0
0
0
3
2
0
0
0
1
3
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
1
3
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
3
0
5
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
2
1
0
0
1
2
0
3
0
0
2
3
1
0
0
0
1
2
0
0
0
0
0
0
0
2
0
1
0
0
0
1
1
1
0
2
0
0
0
0
0
1
2
0
2
0
0
0
2
0
0
0
0
1
2
2
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
5
0
0
0
0
2
0
0
0
2
0
1
1
3
1
0
0
1
0
3
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
1
0
3
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
3
0
0
2
0
0
0
0
1
3
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
2
0
4
0
0
0
0
2
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
8
0
0
0
0
0
2
0
0
0
6
0
0
1
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
3
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
2
3
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
2
1
1
0
0
4
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
2
1
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
1
0
0
2
0
2
1
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
3
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
1
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
1
0
0
0
0
0
1
2
3
0
5
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
2
3
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
1
0
2
3
0
0
0
0
1
0
0
2
1
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
2
0
4
0
1
3
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
1
3
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
1
1
2
0
0
4
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
3
1
1
3
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
2
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
3
1
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
3
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
7
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
3
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
4
3
0
1
0
0
0
0
0
2
0
0
1
0
1
0
3
0
0
0
2
0
0
0
2
0
0
0
0
3
0
2
1
2
0
0
0
0
0
0
3
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
2
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
2
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
6
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
1
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
6
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
3
0
1
0
0
0
0
0
0
0
1
0
0
2
0
1
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
1
0
0
5
0
0
2
2
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
3
0
0
3
4
0
0
0
4
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
2
0
1
1
0
0
0
0
2
1
0
0
0
0
1
1
0
0
0
0
0
1
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
3
1
0
0
0
0
2
0
0
0
0
0
1
0
2
0
2
1
0
0
0
0
0
0
2
0
0
0
0
3
0
1
1
0
2
2
1
2
0
0
0
0
0
3
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
3
0
0
1
2
1
0
0
1
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
2
3
1
0
2
0
2
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
1
0
0
0
2
2
2
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
2
0
0
0
0
0
0
0
0
0
2
7
1
2
3
0
0
0
0
0
1
0
1
0
0
6
0
0
0
1
2
1
0
0
1
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
2
1
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
1
2
0
0
0
1
0
0
0
2
1
0
0
0
0
1
0
0
2
0
0
1
2
0
0
1
0
0
0
0
1
0
1
4
1
1
0
0
0
1
0
1
0
0
0
0
3
0
3
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
1
1
1
0
0
0
0
1
4
1
0
1
0
0
0
0
0
0
0
2
1
0
0
5
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
1
0
0
0
0
2
1
0
0
0
3
0
0
0
0
1
0
1
0
1
0
3
4
0
1
1
3
0
0
0
2
0
0
0
0
1
1
0
0
0
1
3
0
0
1
0
0
0
0
1
0
0
0
2
0
2
2
0
0
1
0
2
0
2
0
2
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
4
1
0
2
1
1
0
2
2
0
0
0
0
1
1
0
0
6
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
5
0
4
0
1
0
0
0
0
2
0
0
0
1
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
3
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
3
0
4
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
1
0
0
0
3
0
3
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
2
1
0
0
0
0
5
0
1
0
1
0
3
3
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
1
0
4
1
0
3
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
2
1
0
0
0
0
1
3
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
2
2
0
0
0
0
3
0
9
1
2
0
3
0
0
0
4
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
2
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
1
2
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
1
0
4
0
0
0
0
3
0
0
1
2
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
3
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
1
2
0
0
0
0
2
0
0
1
0
0
0
1
3
1
0
0
0
0
3
2
1
0
0
1
3
0
0
0
3
1
0
1
2
0
0
0
2
2
0
0
0
2
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
1
0
0
5
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
2
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
2
2
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
2
0
1
0
0
0
0
1
2
1
2
0
0
0
0
0
0
0
2
1
0
3
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
2
0
0
0
0
2
1
0
0
0
0
0
3
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
2
2
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
2
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
2
0
0
1
1
0
0
0
0
2
0
0
1
0
2
2
0
1
0
0
0
2
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
1
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
3
0
0
0
1
0
0
0
0
2
2
0
0
0
3
0
0
2
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
1
0
1
3
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
3
1
0
0
0
0
0
2
2
0
0
2
1
4
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
1
0
0
2
2
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
1
2
1
1
2
0
0
5
2
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
1
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
1
1
0
2
1
2
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
3
0
0
0
1
0
1
0
0
0
0
0
1
0
0
2
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
2
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
3
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
2
0
1
2
2
0
0
0
0
1
0
0
0
0
1
0
3
0
0
1
0
0
0
0
2
2
0
0
2
1
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
2
1
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
1
0
5
1
5
0
1
2
0
0
0
0
0
0
0
1
0
0
2
3
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
2
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
2
0
1
0
1
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
1
2
0
0
2
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
1
2
1
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
3
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
1
0
0
0
0
0
2
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
2
0
0
1
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
2
1
0
1
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
3
0
1
0
2
0
0
2
1
1
0
0
1
0
0
0
2
1
0
0
2
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
3
0
0
2
2
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
8
3
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
3
2
0
1
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
3
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
2
0
0
0
1
2
0
2
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
4
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
2
2
0
0
0
2
1
2
2
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
5
2
1
1
1
0
0
0
0
0
0
5
0
0
0
0
1
0
4
0
0
0
0
1
0
0
1
1
0
2
2
2
0
0
0
0
0
1
0
0
2
0
0
0
3
0
0
1
0
0
0
0
1
0
0
0
5
0
1
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
2
1
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
1
0
2
1
2
0
2
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
1
1
0
0
0
2
0
0
0
2
0
1
0
0
1
0
1
0
0
1
0
3
1
0
1
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
2
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
5
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
7
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
1
0
0
0
3
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
1
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
3
0
0
0
1
0
1
1
0
1
0
0
1
0
0
0
0
1
2
0
2
0
0
0
0
0
2
0
0
3
0
0
2
0
0
0
0
0
3
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
2
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
2
2
0
1
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
3
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
1
2
0
2
1
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
2
0
1
1
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
3
0
0
8
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
1
2
2
0
0
2
0
0
0
0
2
0
0
0
0
3
1
0
0
2
0
2
1
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
2
0
0
0
5
1
1
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
2
0
3
0
0
1
0
0
0
0
2
0
0
3
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
5
1
0
2
0
2
0
0
0
11
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
1
2
0
0
0
1
0
0
1
0
0
1
1
0
0
2
0
0
2
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
6
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
3
1
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
1
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
3
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
2
0
0
0
0
5
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
2
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
1
0
0
0
0
0
5
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
3
0
1
0
2
0
0
0
0
0
1
0
1
0
2
0
0
0
2
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
2
0
2
0
2
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
3
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
1
1
0
0
0
2
0
2
0
1
3
0
0
1
0
0
0
0
0
2
0
1
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
1
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
4
0
3
0
2
0
0
0
0
0
5
0
2
0
0
0
0
2
0
0
0
2
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
4
0
1
0
0
0
0
0
1
0
0
0
0
2
1
1
0
0
0
2
0
0
0
0
0
1
0
0
1
2
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
1
4
2
0
0
0
0
0
0
0
0
0
1
2
0
0
2
2
0
0
0
2
0
2
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
3
1
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
1
0
1
1
3
0
2
1
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
2
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
2
2
1
0
0
0
2
0
0
2
1
0
1
0
0
0
0
3
0
0
2
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
1
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
3
0
1
4
0
0
0
1
2
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
3
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
3
0
1
1
0
0
0
0
2
0
1
0
1
1
0
0
0
0
0
0
2
0
0
0
1
1
1
0
2
0
1
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
2
0
0
2
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
4
0
0
1
2
0
0
0
0
0
0
0
0
0
0
5
0
2
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
2
1
0
2
0
1
1
0
0
3
1
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
4
0
2
0
0
5
2
0
1
0
0
0
0
0
0
0
0
2
2
2
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
1
1
0
4
3
2
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
6
2
0
0
5
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
2
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
1
0
0
0
2
1
0
1
0
1
0
0
3
1
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
11
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
3
0
0
1
2
1
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
3
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
3
2
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
1
3
1
0
0
0
0
0
2
0
0
0
0
2
2
1
0
0
2
0
0
0
0
1
0
0
2
1
0
0
2
2
0
2
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
1
0
0
0
2
0
0
0
0
2
0
3
1
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
1
0
0
8
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
3
1
1
0
0
0
1
0
5
0
0
1
0
3
1
0
0
0
0
0
1
1
5
1
0
0
0
0
0
8
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
2
0
0
0
3
0
0
6
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
1
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
3
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
2
0
1
2
2
0
2
0
0
0
0
1
2
5
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
1
4
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
2
0
0
2
0
3
0
1
0
0
2
0
0
6
0
0
0
1
0
0
2
2
0
2
0
0
2
0
0
1
2
1
0
0
0
2
0
1
0
0
0
0
1
0
2
0
0
2
0
0
0
1
0
2
0
1
0
0
0
0
1
0
0
0
0
3
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
2
0
2
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
3
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
3
0
2
2
1
0
0
2
0
0
0
2
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
3
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
2
0
0
2
0
0
0
0
0
1
4
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
1
0
1
0
1
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
2
1
0
1
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
1
0
0
2
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
2
1
0
0
0
0
1
2
0
0
0
0
1
0
0
1
2
0
0
2
1
1
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
3
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
2
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
1
1
0
1
0
0
1
0
0
7
3
0
0
0
1
0
0
1
0
1
1
0
2
0
0
0
0
1
0
0
0
2
2
1
0
0
1
1
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
2
0
0
3
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
1
0
0
0
0
3
1
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
1
9
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
2
0
0
3
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
2
2
3
0
0
1
0
0
1
0
0
0
0
0
0
3
3
0
2
0
1
0
0
2
0
0
2
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
1
5
0
2
0
0
0
0
1
0
0
0
2
0
2
0
0
3
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
5
5
0
2
0
3
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
5
0
0
1
0
0
0
0
0
0
4
2
0
1
0
1
6
1
0
0
0
0
0
1
0
0
0
0
1
3
0
1
0
0
0
0
0
2
0
0
0
0
3
0
0
1
1
0
0
0
0
1
0
0
3
0
0
0
0
2
0
0
0
3
0
0
0
0
1
0
0
1
2
2
0
0
0
0
2
0
0
2
0
0
0
0
1
0
2
2
5
0
0
0
1
2
0
0
0
0
0
0
1
0
0
2
0
3
2
1
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
3
0
2
1
1
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
3
2
0
2
0
0
0
1
0
0
1
1
1
0
2
0
0
0
1
0
2
1
0
2
0
1
0
0
0
1
0
0
1
0
0
0
0
4
0
0
0
0
1
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
1
1
0
0
0
0
0
1
0
3
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
2
1
0
0
3
0
0
0
4
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
2
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
2
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
3
2
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
1
4
0
0
0
0
0
0
1
0
3
1
0
0
0
2
0
1
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
4
1
0
0
0
0
0
1
0
0
0
0
2
0
2
2
0
0
0
3
0
0
0
0
0
0
0
0
1
0
2
2
0
0
2
2
0
2
2
0
0
0
0
2
1
0
0
2
0
1
1
0
0
1
0
1
0
1
0
1
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
3
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
3
0
0
0
0
0
1
0
0
0
0
0
3
2
2
0
0
0
4
0
2
0
0
0
0
0
0
0
2
0
3
1
2
0
1
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
2
0
0
5
2
0
0
0
0
0
1
0
2
1
0
2
0
2
2
0
0
3
0
2
0
0
2
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
2
0
0
2
0
0
0
0
0
0
0
1
0
2
0
2
1
0
2
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
2
0
1
2
0
0
0
0
0
0
6
1
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
1
1
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
1
0
1
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
7
2
0
0
0
2
1
6
0
0
1
0
0
0
0
0
0
0
3
2
0
0
0
1
0
0
0
0
0
0
1
0
2
2
0
0
1
1
0
0
0
2
0
0
0
1
0
0
0
0
8
0
0
0
0
0
0
0
0
2
0
2
3
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
3
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
2
0
0
0
2
2
1
0
0
2
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
2
3
0
0
0
1
3
1
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
2
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
2
0
1
0
0
1
0
0
2
0
0
0
0
0
0
1
2
3
0
0
0
2
0
0
0
0
2
1
0
0
2
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
3
0
0
1
2
0
0
4
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
2
0
0
0
0
0
0
0
3
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
3
0
0
0
0
1
1
0
0
0
1
0
0
0
1
1
2
2
0
0
0
0
0
0
0
1
0
0
2
0
0
1
1
3
0
0
0
0
0
0
1
2
0
4
0
1
0
0
1
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
2
3
2
2
0
0
0
0
0
0
2
0
0
2
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
5
0
0
1
1
0
0
0
1
0
0
0
0
1
0
1
2
1
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
2
0
1
2
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
1
0
0
0
0
0
0
2
2
0
0
1
0
2
2
0
2
2
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
2
0
0
0
0
0
0
0
3
3
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
2
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
1
0
1
0
0
2
0
0
0
0
0
0
1
1
0
0
3
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
3
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
3
0
4
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
5
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
3
1
0
0
0
3
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
2
0
0
0
0
0
0
0
1
1
2
0
2
0
0
0
0
0
0
0
3
0
0
1
2
0
0
1
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
3
0
0
1
0
1
1
2
2
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
1
3
0
0
3
2
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
2
0
1
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
1
1
0
0
3
0
0
0
0
0
8
0
0
0
0
1
0
0
1
0
2
0
0
0
2
0
2
1
0
0
0
0
0
0
0
1
0
1
0
0
0
4
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
2
1
0
2
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
1
0
1
0
0
2
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
1
1
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
2
2
2
0
0
1
0
0
0
1
2
0
0
0
0
1
0
0
0
3
0
0
0
0
2
2
0
0
1
1
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
1
1
0
0
1
0
2
0
0
0
4
0
0
2
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
2
1
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
1
0
2
0
1
1
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
2
0
0
1
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
1
2
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
1
0
0
2
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
2
3
1
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
1
0
2
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
4
0
1
1
8
0
2
0
0
1
0
0
0
0
1
0
0
0
5
0
1
0
0
1
1
0
2
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
2
1
4
0
0
0
1
0
0
0
0
0
2
1
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
3
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
3
1
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
1
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
2
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
1
0
2
1
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
2
2
2
1
2
0
0
0
0
2
2
0
0
1
0
2
0
1
0
0
0
3
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
2
1
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
1
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
2
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
3
1
0
0
0
2
0
0
2
1
0
0
0
0
0
0
1
1
0
0
1
2
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
2
2
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
12
1
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
1
0
1
0
0
0
1
0
0
2
1
1
1
1
0
2
0
0
2
0
1
0
1
0
1
0
0
0
3
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
1
1
0
0
0
0
0
0
1
0
0
0
2
1
0
0
2
0
0
0
0
2
0
0
0
2
1
0
0
0
3
0
1
0
0
0
0
0
0
0
2
3
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
1
0
2
1
0
2
0
0
2
0
1
2
0
0
0
0
4
0
1
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
1
0
0
0
0
0
2
0
0
0
2
1
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
2
0
2
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
3
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
2
1
0
0
2
1
0
3
0
0
0
0
0
0
0
1
0
2
0
2
1
0
2
0
0
0
0
0
0
2
0
0
0
1
2
2
0
0
0
0
0
2
0
0
1
1
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
5
3
3
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
1
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
2
2
0
0
1
0
4
0
0
1
0
0
0
4
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
1
0
1
0
0
0
0
0
1
0
0
3
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
2
2
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
3
2
0
1
0
0
0
0
1
0
1
1
0
1
0
0
0
2
3
2
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
3
0
0
1
0
0
3
2
0
0
1
0
0
1
0
2
0
0
0
3
1
2
0
2
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
1
0
1
0
0
0
3
0
0
0
3
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
2
0
0
2
2
1
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
4
0
1
0
0
2
0
0
1
2
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
2
0
0
2
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
4
0
0
0
0
2
1
0
2
0
0
0
0
1
1
0
1
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
1
1
0
0
1
0
0
1
0
1
2
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
2
3
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
4
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
2
1
1
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
1
3
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
3
0
2
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
1
2
2
0
0
1
0
0
4
2
0
0
0
1
3
0
0
0
1
2
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
2
0
1
2
0
1
3
0
0
0
0
2
0
0
0
2
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
4
0
2
0
2
2
1
0
0
0
0
1
2
0
3
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
2
0
0
0
0
2
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
4
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
2
8
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
1
1
0
0
3
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
1
0
1
0
0
0
2
1
1
0
0
4
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
3
0
0
0
0
1
0
0
3
2
2
0
0
1
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
4
0
1
0
0
1
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
2
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
2
2
1
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
2
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
3
0
2
0
0
0
0
2
0
0
0
0
0
1
0
2
0
2
2
0
1
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
1
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
1
0
0
0
1
1
0
0
3
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
2
0
1
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
2
2
0
5
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
3
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
2
0
1
0
3
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
2
0
1
0
4
0
1
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
4
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
4
0
0
0
1
0
0
0
0
0
0
1
0
0
3
0
1
0
2
0
4
0
0
2
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
4
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
1
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
3
0
2
0
1
3
0
0
0
0
0
4
0
0
0
3
1
2
0
0
0
0
0
0
0
1
0
2
1
0
0
0
3
0
0
2
1
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
3
0
2
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
1
0
0
2
6
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
1
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
3
2
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
2
1
1
0
0
0
2
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
1
0
2
2
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
1
0
2
0
0
0
1
0
0
0
2
1
0
0
0
2
2
0
0
0
1
0
0
1
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
1
0
0
0
1
0
2
4
0
0
0
0
1
0
1
0
0
0
6
0
0
2
7
0
0
2
0
1
0
0
1
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
3
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
2
0
0
0
4
0
0
0
0
0
0
2
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
2
0
2
0
0
0
1
0
0
2
0
0
0
0
9
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
1
0
4
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
2
0
0
3
1
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
1
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
3
0
0
0
2
1
1
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
4
6
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
4
0
0
0
0
2
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
1
0
1
0
0
0
2
0
0
2
0
0
0
2
0
1
0
2
0
0
0
0
0
7
0
0
1
0
0
2
0
1
0
0
0
0
3
1
0
0
1
1
2
0
0
0
0
0
0
0
2
0
0
3
2
0
1
0
0
0
3
0
0
0
0
0
0
0
3
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
2
1
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
5
1
0
0
0
0
0
0
2
1
0
1
2
0
0
1
0
0
0
0
0
0
0
2
2
0
2
0
2
0
0
0
1
1
0
1
0
0
0
1
0
0
0
2
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
3
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
2
0
0
2
2
2
0
1
0
2
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
2
0
0
0
0
4
0
0
3
0
1
2
1
0
2
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
3
2
0
0
0
0
0
2
0
2
0
0
0
0
1
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
3
2
1
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
3
2
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
2
0
0
0
1
0
0
0
0
1
0
0
4
1
3
2
4
0
0
0
2
2
0
1
2
0
1
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
1
0
3
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
1
0
1
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
3
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
4
0
0
2
0
1
0
2
0
0
1
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
2
0
0
0
1
2
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
1
0
0
0
2
0
0
0
3
0
3
0
2
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
2
1
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
1
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
2
1
0
0
0
0
1
0
1
2
0
2
0
0
0
0
0
0
3
0
0
0
0
1
1
0
0
0
0
0
1
0
4
0
0
2
0
0
1
5
0
2
0
0
0
0
1
1
0
4
1
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
1
2
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
2
1
0
1
1
0
0
0
0
2
0
0
0
0
2
2
0
2
0
2
0
1
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
2
2
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
2
1
0
6
1
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
2
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
4
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
4
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
3
0
0
0
1
0
0
0
2
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
1
0
1
1
0
0
1
0
1
0
0
0
0
0
4
0
2
0
0
0
0
0
0
2
1
1
0
0
0
3
0
1
0
1
0
1
0
0
1
0
1
0
2
1
1
0
1
1
0
0
0
1
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
3
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
8
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
3
1
0
1
0
0
1
2
0
0
2
0
0
2
0
0
2
0
0
0
1
0
0
0
0
3
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
3
0
2
1
0
0
2
1
0
0
0
0
0
0
2
1
0
0
3
0
2
0
2
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
4
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
2
0
1
0
1
0
0
0
0
0
0
10
0
0
0
0
0
1
0
0
0
0
0
2
0
1
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
2
6
0
0
0
0
0
0
0
0
0
1
0
0
2
1
2
1
0
0
0
0
0
0
0
1
6
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
2
0
4
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
7
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
1
3
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
3
0
0
0
0
0
1
2
2
0
0
0
0
3
0
0
0
1
0
0
3
0
0
1
0
2
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
3
1
0
2
0
0
1
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
1
1
2
0
0
0
0
0
1
6
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
3
0
0
0
0
0
5
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
5
0
0
0
1
6
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
2
2
0
0
2
2
1
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
1
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
5
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
4
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
1
2
2
0
0
1
0
0
2
2
4
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
2
0
1
1
0
0
0
0
0
0
4
0
0
0
0
0
0
2
0
0
0
1
0
0
0
5
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
3
2
1
1
0
0
0
0
0
2
1
0
0
2
2
0
0
0
1
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
1
0
0
3
0
1
1
0
0
0
0
1
0
0
2
2
0
1
1
0
0
0
1
0
0
0
0
2
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
2
0
4
0
0
0
0
0
0
1
0
1
0
0
0
3
1
1
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
2
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
3
1
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
3
3
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
2
1
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
1
1
1
0
0
0
0
2
3
0
2
0
0
0
0
0
2
0
0
1
0
0
9
0
1
0
0
1
1
0
0
1
0
1
1
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
4
1
0
0
3
0
0
0
1
0
0
0
4
0
0
0
1
3
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
2
0
0
1
0
1
0
2
0
0
10
0
0
0
0
4
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
2
0
0
6
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
4
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
3
1
0
0
2
1
6
0
0
0
2
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
3
0
3
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
5
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
3
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
2
0
0
2
0
0
0
0
0
2
1
0
0
0
1
1
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
1
0
0
4
0
0
3
0
1
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
1
0
0
1
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
2
0
1
0
0
2
0
0
0
1
0
0
1
0
2
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
8
0
7
0
0
1
0
0
1
0
0
0
1
1
0
0
1
2
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
5
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
4
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
1
0
1
0
0
1
0
2
0
0
0
2
0
0
2
0
0
0
1
1
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
3
0
0
0
0
0
1
4
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
1
1
0
0
0
1
1
2
2
2
2
0
2
0
0
0
0
2
0
0
0
2
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
3
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
1
0
1
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
6
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
5
0
0
0
0
0
0
5
0
0
0
1
1
0
0
2
0
2
2
0
0
1
1
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
1
0
0
0
0
1
0
0
2
1
0
2
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
5
0
0
2
0
0
1
0
0
0
0
2
3
0
0
2
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
2
0
1
1
0
2
0
0
0
0
2
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
3
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
1
0
1
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
1
0
1
2
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
1
0
4
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
4
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
1
0
2
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
6
0
0
0
0
0
0
0
4
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
4
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
2
1
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
3
0
0
2
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
3
1
0
0
2
1
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
1
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
2
0
2
1
0
0
2
0
4
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
1
0
0
3
2
0
2
0
0
0
1
3
0
0
1
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
1
2
3
0
2
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
3
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
3
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
3
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
2
2
0
0
0
0
3
0
1
0
0
0
0
2
3
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
3
0
0
2
0
2
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
2
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
5
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
1
0
1
0
2
0
1
0
2
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
1
0
1
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
3
0
1
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
1
0
0
1
3
0
0
1
0
0
0
0
1
0
1
0
0
0
1
1
0
0
1
0
0
1
0
2
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
3
4
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
2
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
1
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
5
1
0
2
0
0
0
3
0
0
0
5
0
2
1
0
0
0
0
0
0
1
0
1
2
0
0
8
0
0
1
2
0
0
0
0
5
0
2
2
3
0
0
0
0
1
0
2
0
2
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
4
4
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
3
2
2
0
0
0
0
0
1
0
1
0
0
0
0
2
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
3
0
0
0
0
2
0
2
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
3
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
1
2
1
3
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
2
0
3
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
7
0
3
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
3
0
0
0
0
0
0
1
2
0
1
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
1
1
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
2
0
0
0
3
0
0
0
0
0
1
0
0
0
0
1
0
0
3
9
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
1
2
0
0
2
0
2
0
0
3
1
2
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
5
0
0
0
0
0
0
4
2
0
0
1
0
1
0
2
0
0
0
2
0
0
0
2
0
2
0
0
1
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
4
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
1
0
2
0
0
0
0
0
2
2
2
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
2
0
0
0
0
0
2
2
1
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
13
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
3
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
3
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
2
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
1
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
3
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
3
0
0
3
0
0
0
0
0
0
0
0
2
0
1
1
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
2
1
1
2
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
5
0
0
0
0
2
1
0
0
0
3
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
2
1
0
2
0
2
0
1
0
0
0
3
1
0
0
3
0
0
0
0
0
0
1
0
2
0
1
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
2
0
0
2
0
1
1
0
0
1
0
0
0
2
0
0
1
0
2
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
1
2
0
0
0
0
0
2
1
0
2
0
1
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
2
0
0
2
0
0
4
0
0
0
0
0
0
2
1
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
1
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
3
2
0
0
0
1
0
0
0
1
0
2
0
2
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
1
0
0
0
1
2
0
1
0
0
0
2
0
0
2
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
1
0
1
1
3
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
5
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
8
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
3
5
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
3
0
0
2
0
3
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
5
0
0
0
2
1
0
0
0
1
0
0
0
1
1
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
1
0
0
3
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
2
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
2
0
1
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
5
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
1
2
0
0
0
2
2
0
0
0
0
1
0
2
1
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
2
0
0
0
0
2
2
0
2
2
2
0
0
2
1
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
1
0
0
0
0
1
0
1
0
0
1
0
5
1
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
1
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
2
0
0
1
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
2
0
0
0
0
0
0
0
2
1
1
2
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
2
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
1
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
2
0
2
0
0
0
0
0
0
6
2
2
0
1
0
0
0
0
1
0
1
0
3
1
4
0
0
2
1
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
3
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
4
2
0
0
0
0
0
0
2
2
0
2
0
1
0
0
0
1
0
0
0
0
1
1
2
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
1
0
2
0
0
0
0
2
0
0
3
0
0
2
0
0
0
4
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
2
0
0
3
0
1
1
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
2
0
1
0
2
2
2
0
0
0
0
1
0
0
1
2
0
0
0
0
0
3
0
0
1
0
0
0
1
0
0
1
1
3
0
0
0
0
1
3
1
0
0
0
0
0
1
0
0
0
1
1
2
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
3
0
2
0
0
1
1
0
0
1
4
6
0
2
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
2
0
2
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
3
0
1
0
0
3
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
2
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
5
0
0
0
1
0
0
2
0
0
1
0
0
0
2
0
0
1
0
0
1
0
0
2
0
0
3
0
0
0
0
1
0
0
3
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
2
2
1
0
0
1
1
0
2
2
2
0
1
0
1
0
0
0
0
2
2
0
1
2
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
3
0
2
2
0
0
0
0
0
0
0
0
0
2
0
1
4
0
4
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
2
1
0
5
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
3
0
0
0
0
0
1
2
0
2
0
0
1
1
0
0
0
0
0
2
1
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
2
0
2
0
0
0
0
0
3
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
4
0
0
0
0
0
1
4
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
7
0
0
1
0
0
0
0
0
1
0
0
0
2
2
2
0
0
0
0
0
0
0
1
0
4
0
4
1
1
0
0
0
0
2
0
2
5
1
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
1
0
0
2
2
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
2
0
0
0
0
0
2
0
17
0
0
0
2
0
2
0
0
1
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
7
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
3
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
5
0
0
1
0
1
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
1
3
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
1
0
0
2
2
0
0
0
0
2
3
2
0
0
0
0
0
0
0
1
0
0
0
0
3
2
2
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
1
1
0
0
2
0
0
0
3
2
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
1
0
2
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
3
1
0
0
0
0
3
0
1
0
2
1
0
2
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
2
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
2
0
0
1
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
2
0
1
2
2
0
0
6
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
2
0
1
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
2
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
2
0
1
2
1
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
1
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
1
2
1
2
0
1
0
0
2
0
2
0
0
1
1
2
0
0
0
0
1
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
2
2
0
0
0
1
2
0
0
0
0
1
1
1
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
3
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
5
0
0
0
0
0
0
5
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
7
0
0
0
0
0
1
0
0
3
2
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
2
0
1
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
2
0
3
0
0
0
3
2
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
7
0
0
2
0
0
2
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
2
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
6
1
0
1
0
0
0
0
0
0
0
1
1
1
0
2
0
1
1
0
0
0
2
0
0
5
2
2
0
2
0
0
0
2
0
0
1
0
3
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
2
2
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
18
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
3
0
1
0
0
0
1
0
0
1
0
1
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
3
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
1
0
1
6
0
0
0
0
0
0
1
0
0
2
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
2
2
1
0
0
1
0
0
0
1
1
0
0
2
0
3
0
0
2
0
1
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
1
0
3
2
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
2
0
1
0
2
0
0
1
1
0
1
0
0
0
2
2
0
1
1
1
0
0
0
0
0
1
2
0
5
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
4
1
0
1
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
4
0
0
0
0
0
2
0
2
0
0
1
0
0
0
1
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
2
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
1
0
0
0
1
2
3
0
3
1
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
1
0
1
0
1
0
0
0
0
0
0
0
1
1
0
1
2
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
1
1
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
1
0
0
1
2
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
1
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
1
1
0
1
3
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
1
1
2
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
1
2
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
1
1
0
2
0
0
0
0
0
0
0
0
2
5
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
3
1
1
1
0
0
2
0
0
2
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
1
1
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
6
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
2
2
0
0
1
0
2
2
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
3
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
2
2
0
2
0
0
2
0
0
1
0
0
3
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
2
2
0
3
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
1
0
1
0
0
0
3
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
2
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
5
0
2
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
2
0
3
0
2
1
0
0
0
0
0
1
1
4
2
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
1
0
0
0
1
1
2
0
2
0
2
0
0
0
0
0
2
0
0
0
1
6
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
3
0
1
1
0
0
0
1
0
0
0
1
0
0
0
2
0
1
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
1
0
4
0
1
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
2
0
0
0
2
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
1
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
1
0
2
1
0
1
0
0
1
0
0
2
4
0
0
0
3
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
1
0
0
0
2
1
0
0
2
1
0
2
0
3
0
0
4
0
0
0
0
0
0
0
0
4
0
0
0
0
3
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
1
1
4
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
3
0
2
0
0
0
0
0
0
0
1
2
0
0
1
0
1
0
1
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
1
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
3
0
0
0
0
2
0
2
4
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
2
2
2
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
3
0
0
2
0
5
2
0
0
0
0
2
0
0
0
0
2
0
2
0
0
2
0
0
2
1
0
0
1
3
0
1
0
0
0
0
0
0
0
2
3
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
1
1
0
1
3
1
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
1
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
7
0
0
1
2
2
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
3
0
1
1
2
1
2
0
0
0
0
0
0
0
0
0
3
2
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
2
0
0
0
0
1
0
0
2
2
0
0
0
0
1
0
2
0
2
0
0
0
1
0
0
0
1
0
0
1
0
1
3
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
5
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
1
1
0
1
2
0
0
0
0
0
0
2
0
0
0
1
5
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
4
1
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
1
0
0
8
0
0
2
4
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
6
0
2
0
0
0
1
0
0
0
5
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
2
4
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
1
0
1
0
0
0
0
4
0
1
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
1
2
0
0
0
1
0
0
0
2
0
2
0
0
0
0
2
1
2
0
2
0
1
0
0
2
1
2
1
1
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
1
0
2
6
0
0
0
0
2
0
1
8
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
3
2
0
0
0
0
1
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
2
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
3
0
1
0
0
1
0
0
0
0
4
2
0
0
0
0
0
0
1
3
0
0
0
1
0
0
1
0
1
0
0
0
2
0
0
0
0
0
1
0
1
0
1
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
1
3
0
0
2
0
0
0
0
5
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
1
1
1
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
5
2
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
4
0
2
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
3
0
0
2
0
1
0
0
2
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
3
0
0
0
2
0
2
0
0
0
2
0
0
2
3
2
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
4
0
2
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
1
1
0
0
1
0
0
0
0
0
1
1
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
6
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
5
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
1
2
3
0
0
0
0
0
0
2
2
0
1
2
0
0
0
0
4
0
0
0
1
1
0
1
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
3
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
2
0
1
1
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
2
3
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
2
1
0
0
3
0
0
0
0
2
0
0
2
1
0
0
0
0
0
1
0
0
2
0
0
1
0
0
1
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
2
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
6
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
1
2
0
0
0
2
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
1
0
0
0
0
0
1
5
0
0
0
0
2
0
0
0
1
0
3
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
2
0
2
1
2
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
3
0
0
1
0
0
1
3
1
0
1
0
0
0
0
0
2
0
1
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
2
2
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
4
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
2
0
1
0
0
5
0
1
0
0
0
2
0
0
0
0
1
1
0
0
0
0
2
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
2
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
4
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
3
0
0
0
0
1
1
0
2
1
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
6
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
2
2
0
0
0
0
0
2
0
0
0
5
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
1
2
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
2
1
0
0
0
0
2
1
0
0
0
3
1
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
1
0
0
0
2
0
0
0
0
2
0
1
2
1
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
5
2
2
1
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
5
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
1
0
1
2
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
2
1
0
0
2
0
0
0
2
0
2
0
0
3
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
3
0
0
1
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
1
0
0
1
0
0
0
0
0
2
1
0
2
5
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
1
0
1
0
0
0
2
0
0
0
0
0
1
0
2
0
0
1
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
2
0
2
1
1
0
0
0
0
0
2
0
0
1
0
0
1
0
0
2
0
2
2
4
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
5
0
0
0
1
2
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
1
1
0
0
1
4
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
1
0
2
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
1
10
0
2
0
1
2
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
2
1
0
0
1
0
2
0
0
1
1
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
1
0
0
0
0
0
4
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
2
2
2
0
0
0
1
0
0
0
0
2
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
2
0
2
1
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
1
0
6
2
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
2
2
3
1
0
2
1
0
0
0
0
1
0
1
0
2
1
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
2
0
1
2
0
0
2
2
1
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
1
0
0
1
1
0
2
0
2
0
0
0
0
0
0
3
0
0
0
0
2
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
2
0
0
2
0
1
2
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
2
0
0
0
3
0
0
0
2
0
2
2
0
0
0
0
2
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
2
2
1
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
2
1
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
3
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
1
0
1
2
1
0
3
1
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
2
0
1
0
0
2
1
0
2
0
2
3
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
1
0
0
1
0
0
2
2
2
0
2
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
2
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
3
0
0
2
1
1
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
2
2
0
0
2
0
0
1
2
0
2
0
0
0
0
0
0
1
1
3
0
0
0
0
0
0
1
1
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
1
0
0
0
2
1
1
0
0
0
0
0
0
1
0
0
0
3
3
0
0
0
2
1
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
1
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
2
0
2
0
1
4
0
0
0
0
1
0
1
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
5
4
0
0
0
0
2
0
0
0
2
0
2
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
2
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
3
0
2
0
0
0
0
2
0
3
0
0
0
0
0
1
0
0
0
2
1
0
0
0
1
0
0
2
0
0
1
0
0
0
1
1
1
0
0
0
2
0
0
1
2
0
1
0
1
0
1
0
0
0
1
0
0
2
2
0
0
0
0
0
0
3
1
0
0
0
0
2
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
3
0
2
1
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
2
2
2
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
3
2
0
4
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
3
2
0
0
0
0
0
2
1
1
0
1
0
0
2
0
0
1
1
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
3
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
1
1
0
0
0
0
2
0
0
0
0
4
2
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
9
2
0
0
1
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
4
2
0
0
0
0
0
1
2
2
0
0
0
0
0
1
0
1
2
0
0
0
7
0
0
2
2
0
0
0
0
0
0
2
1
0
0
0
0
2
2
0
1
1
0
0
2
0
0
0
2
0
0
1
1
0
3
0
0
2
0
0
0
0
2
1
0
0
2
0
0
1
0
0
0
0
1
0
3
0
0
0
0
2
2
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
3
0
0
2
0
1
0
0
0
0
0
0
0
3
0
0
0
0
2
1
0
0
0
1
0
0
0
1
0
0
3
1
0
0
0
0
2
0
2
0
0
2
0
2
0
2
0
0
0
0
1
2
1
0
0
4
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
3
2
0
0
0
0
0
0
1
3
0
1
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
1
1
0
0
0
0
0
1
2
0
0
0
2
0
2
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
3
3
0
0
0
0
1
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
1
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
1
5
0
0
1
0
0
1
0
0
2
1
0
0
0
1
1
0
0
0
0
2
1
0
0
1
0
0
0
7
2
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
2
0
2
2
0
2
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
3
0
0
0
1
0
0
0
1
1
2
0
0
0
1
3
1
1
0
0
0
2
1
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
2
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
2
0
11
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
3
2
0
0
0
1
0
0
0
0
1
2
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
2
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
2
0
0
2
0
0
0
2
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
4
0
3
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
2
4
1
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
1
2
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
1
2
0
0
1
1
0
2
0
1
2
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
6
5
0
0
0
1
1
0
0
2
0
0
0
0
0
1
2
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
7
0
1
0
2
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
1
2
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
4
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
4
0
0
2
0
2
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
4
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
1
1
3
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
4
0
0
0
0
2
0
0
2
0
0
2
1
1
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
2
1
0
0
0
1
0
0
0
1
0
0
0
1
2
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
2
2
1
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
3
0
2
5
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
2
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
1
5
0
2
0
1
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
2
1
1
0
0
0
2
1
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
3
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
2
0
0
1
2
0
1
0
0
1
0
0
2
0
2
0
0
2
0
1
1
0
1
1
0
2
0
0
0
1
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
6
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
2
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
8
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
2
2
0
0
1
0
0
0
0
2
0
0
1
0
1
0
0
3
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
2
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
1
0
0
7
0
4
0
1
0
1
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
3
0
0
0
0
2
0
0
0
0
0
0
1
1
0
3
0
2
0
0
0
0
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
1
0
0
0
1
0
1
1
0
0
2
1
0
0
0
0
4
0
0
0
0
0
3
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
4
0
0
0
0
1
2
3
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
4
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
3
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
12
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
7
5
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
2
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
1
2
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
2
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
1
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
2
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
5
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
1
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
2
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
1
0
0
0
0
3
0
2
1
0
0
9
0
2
0
0
4
0
0
0
1
0
0
1
1
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
3
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
1
0
0
6
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
2
0
1
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
1
1
0
0
1
0
2
0
0
0
2
0
0
0
2
0
2
1
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
4
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
2
0
12
2
4
0
3
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
2
0
4
0
2
0
1
2
0
0
1
2
0
2
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
3
0
1
1
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
2
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
3
1
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
1
0
0
1
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
0
0
2
1
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
2
3
4
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
1
2
0
0
0
2
2
1
1
0
0
0
3
0
0
0
0
0
0
0
0
1
0
1
1
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
2
1
0
2
2
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
1
0
6
0
0
1
1
0
1
0
0
0
0
0
2
0
0
0
0
1
0
1
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
1
2
3
0
0
0
0
0
0
0
0
0
5
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
1
1
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
3
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
2
1
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
2
0
2
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
6
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
6
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
1
0
0
0
0
0
0
3
0
0
0
2
0
0
6
2
0
2
0
0
0
3
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
7
0
0
0
0
0
1
0
3
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
3
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
1
3
2
0
1
0
0
0
0
2
0
2
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
3
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
4
1
0
0
0
0
2
1
0
0
0
1
1
0
1
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
3
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
2
0
2
2
1
0
0
0
0
0
3
0
0
0
2
0
1
0
0
0
2
1
0
0
0
0
0
0
1
0
4
0
1
0
0
1
2
0
1
0
0
0
0
1
0
3
0
0
3
0
0
1
0
1
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
1
0
1
0
0
0
1
0
2
0
0
0
2
0
2
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
2
0
1
0
2
1
0
0
0
2
0
1
0
1
1
0
0
0
1
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
3
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
2
4
1
0
3
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
2
2
0
0
2
0
2
0
2
1
2
1
1
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
1
0
4
0
2
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
2
0
0
2
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
4
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
2
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
2
0
3
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
2
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
5
0
2
2
0
0
0
2
0
2
0
2
0
0
2
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
5
0
0
2
0
2
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
5
0
0
0
0
0
0
1
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
2
0
0
1
2
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
1
2
0
4
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
1
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
1
1
0
0
2
0
0
0
2
0
9
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
1
1
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
2
2
0
1
1
0
1
0
2
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
3
0
0
1
2
0
0
0
0
1
2
0
0
0
2
0
0
1
0
0
4
0
0
0
0
1
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
2
2
0
0
0
0
0
0
0
2
0
1
0
1
0
2
0
0
0
4
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
3
0
0
0
2
0
0
2
2
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
4
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
1
1
0
1
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
4
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
2
0
2
0
0
0
0
0
0
0
2
0
0
0
1
4
7
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
1
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
4
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
1
0
2
0
2
0
0
0
0
2
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
5
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
2
2
0
2
0
0
2
0
0
0
1
3
5
0
0
1
1
0
0
0
0
2
0
0
0
0
3
2
2
0
3
0
0
0
2
2
0
0
2
1
0
2
3
0
0
0
1
0
2
1
1
1
0
0
0
0
0
2
0
0
2
0
0
0
4
0
0
2
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
1
0
0
0
0
1
0
2
2
0
2
2
1
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
1
0
2
2
1
0
2
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
2
0
2
0
1
0
2
1
0
0
2
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
1
0
1
0
1
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
2
0
2
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
4
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
1
5
0
2
1
1
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
1
2
2
0
1
0
0
0
2
0
0
1
0
0
1
0
0
0
0
2
0
0
1
0
0
0
1
1
4
1
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
1
0
0
2
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
5
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
3
0
0
2
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
1
1
0
7
0
0
0
0
0
2
0
1
0
0
2
0
0
1
0
0
0
4
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
1
0
2
0
2
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
2
1
0
0
0
0
2
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
4
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
6
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
1
1
3
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
1
1
0
0
0
0
0
0
0
5
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
5
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
2
0
4
2
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
3
0
2
0
2
1
2
4
0
0
0
0
4
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
2
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
1
0
0
0
2
2
2
1
0
0
0
0
2
0
0
1
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
3
0
2
2
0
0
2
0
0
0
6
0
0
0
0
0
0
1
0
0
0
0
1
0
1
2
0
0
0
1
0
0
0
0
0
0
0
2
3
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
1
0
0
1
0
0
1
2
0
0
1
2
1
0
0
0
2
1
0
0
2
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
1
0
0
0
4
0
0
0
2
0
0
0
0
0
1
0
0
3
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
2
1
3
1
0
2
0
0
0
0
0
0
0
2
0
0
0
1
2
0
1
0
0
2
1
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
2
0
3
3
0
0
0
0
0
0
0
0
0
1
3
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
4
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
2
2
1
0
0
0
1
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
1
0
2
0
9
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
1
0
0
0
0
0
1
0
2
2
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
2
1
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
1
0
0
0
0
2
0
1
0
2
0
1
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
2
0
0
2
3
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
2
3
0
1
1
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
1
0
0
2
5
1
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
6
0
0
1
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
3
1
1
0
0
1
0
0
0
0
0
0
2
0
1
0
0
1
2
0
0
0
0
0
1
2
0
1
0
0
0
2
0
0
0
2
1
0
1
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
3
0
2
0
0
1
0
0
0
0
0
2
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
8
0
1
0
0
1
0
0
0
0
0
1
0
0
1
2
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
2
0
1
0
0
0
0
0
0
2
1
2
0
0
0
0
2
0
1
0
0
0
0
2
0
0
1
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
1
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
1
0
0
2
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
4
0
0
0
0
2
0
0
2
0
1
2
2
1
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
1
0
2
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
2
2
0
0
2
0
0
0
1
0
0
0
0
0
2
0
2
0
2
0
3
0
0
0
0
3
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
4
0
0
0
0
1
0
1
0
0
0
0
0
1
5
0
2
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
2
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
5
2
5
0
0
0
3
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
1
3
0
1
0
0
0
0
9
1
0
0
2
4
0
0
0
1
1
0
1
3
2
0
1
0
0
0
15
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
2
1
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
2
0
0
0
1
1
3
0
0
0
0
0
1
2
6
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
1
0
0
0
0
2
0
2
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
1
0
0
0
0
0
0
3
0
0
2
0
0
0
2
0
0
0
0
0
4
0
0
0
1
0
0
1
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
5
1
4
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
3
0
2
0
0
0
0
0
0
1
0
1
0
3
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
3
1
0
0
2
2
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
5
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
2
0
0
0
2
0
0
2
0
1
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
1
1
0
0
0
0
0
2
0
3
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
1
0
0
0
1
0
2
0
0
2
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
3
1
2
0
0
0
0
0
0
0
1
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
2
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
2
2
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
2
0
0
2
1
0
1
0
1
0
0
0
1
2
1
1
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
5
1
0
0
0
0
0
0
0
0
3
2
0
0
0
2
0
0
0
0
0
1
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
2
0
0
0
2
0
0
0
1
0
1
1
1
0
2
2
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
1
0
3
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
1
0
0
1
0
1
0
0
0
1
0
0
3
0
0
2
0
2
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
2
1
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
1
0
0
0
0
3
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
1
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
4
2
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
3
1
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
9
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
3
0
0
0
0
0
0
0
0
0
2
1
1
0
1
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
1
0
4
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
5
0
0
1
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
1
0
0
2
0
0
0
0
2
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
2
1
2
0
0
1
0
0
3
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
2
1
0
0
1
1
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
2
0
0
0
1
1
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
1
0
2
0
0
0
2
0
2
0
0
0
1
0
2
0
2
0
0
0
0
1
0
0
0
1
0
1
0
0
7
0
0
1
0
1
1
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
1
3
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
1
0
0
0
1
1
0
0
3
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
4
0
2
1
0
2
0
0
2
0
3
0
0
0
0
0
4
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
4
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
2
4
0
1
0
0
2
0
0
1
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
3
0
5
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
1
1
0
0
2
0
0
0
0
4
2
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
3
0
0
0
2
0
3
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
2
0
0
2
0
0
0
0
1
3
0
0
0
1
0
0
0
0
2
0
0
1
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
1
0
0
0
1
0
0
0
0
2
0
2
0
0
0
1
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
2
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
2
2
2
0
0
0
0
2
0
0
0
4
2
1
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
5
2
0
0
1
1
0
0
0
2
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
8
0
0
0
0
2
1
1
0
3
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
4
0
2
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
2
0
0
0
0
2
0
0
0
0
2
1
2
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
6
0
1
0
0
3
0
0
0
1
0
0
0
0
0
1
0
0
0
4
0
1
0
0
2
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
4
2
0
0
0
0
0
0
0
1
4
0
0
2
1
1
0
0
0
1
0
0
1
2
0
0
1
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
1
2
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
3
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
3
0
2
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
2
0
0
2
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
1
0
2
1
0
2
2
0
0
3
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
6
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
1
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
4
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
4
1
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
2
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
2
2
1
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
2
2
2
0
0
0
0
0
1
0
0
2
0
1
0
2
2
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
1
3
0
0
0
0
0
2
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
3
1
0
0
1
0
0
0
0
1
1
0
1
0
0
0
2
0
0
3
1
0
1
1
0
0
0
0
2
2
0
2
1
2
0
1
0
1
1
0
1
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
2
0
0
0
2
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
3
1
0
0
1
1
0
0
0
2
2
0
0
0
1
0
1
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
1
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
1
1
0
0
2
0
0
5
1
0
0
0
1
2
0
0
1
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
1
0
1
0
2
0
0
0
0
0
1
0
0
0
3
1
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
4
0
0
1
0
0
0
0
4
0
2
1
0
0
1
0
1
0
1
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
4
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
1
0
0
2
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
5
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
2
2
1
0
0
0
0
0
1
0
3
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
1
0
0
2
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
2
2
1
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
1
1
0
2
0
0
0
0
0
1
3
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
3
2
0
1
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
2
4
4
0
1
1
0
1
0
5
2
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
4
0
0
0
0
0
1
1
0
0
0
1
3
0
1
0
2
0
1
0
0
0
5
0
0
0
0
2
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
3
1
0
0
0
0
0
1
2
0
1
0
1
3
0
3
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
3
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
3
1
0
0
1
0
0
0
0
0
0
2
0
3
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
3
1
0
2
0
0
0
0
0
2
0
1
0
2
0
0
0
2
1
0
0
0
2
0
1
0
2
2
2
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
2
2
0
0
0
3
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
5
0
0
1
0
0
10
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
3
1
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
1
0
2
0
0
0
2
0
5
2
0
0
0
0
0
0
0
0
0
2
2
0
1
0
1
0
0
2
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
3
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
1
1
2
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
12
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
2
0
3
2
0
0
0
2
2
0
0
1
2
0
0
0
0
0
0
3
1
1
0
0
0
0
0
2
1
2
0
1
0
0
2
0
0
1
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
9
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
5
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
0
0
6
1
0
0
1
0
1
2
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
4
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
2
2
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
9
0
0
0
0
0
0
2
0
2
1
0
0
5
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
5
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
2
1
1
0
0
0
0
3
0
2
0
8
5
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
2
2
0
0
2
2
0
0
0
1
0
3
0
1
3
0
0
0
0
0
0
0
0
3
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
3
0
2
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
6
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
1
1
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
1
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
3
0
0
1
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
2
0
0
1
1
0
2
2
0
3
0
1
0
1
2
2
1
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
3
0
2
2
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
2
0
1
2
0
0
0
0
0
0
0
0
0
1
0
4
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
1
0
0
0
1
0
0
2
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
3
1
0
0
0
0
2
1
0
3
0
0
2
0
2
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
5
0
2
2
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
15
2
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
3
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
3
0
0
0
0
2
2
0
0
0
3
0
0
0
1
0
0
0
0
0
0
2
1
1
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
3
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
1
0
0
0
4
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
2
6
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
2
0
7
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
1
0
0
0
0
0
1
0
7
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
1
3
1
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
2
2
0
1
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
3
1
0
0
0
0
1
0
0
3
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
1
11
1
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
5
0
1
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
2
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
2
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
5
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
1
1
0
0
0
1
0
0
0
0
0
0
0
4
0
0
1
0
0
0
2
2
0
0
2
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
4
0
0
1
0
2
1
1
0
0
0
0
0
0
1
0
0
0
2
1
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
1
0
0
0
2
0
1
0
0
0
2
2
0
0
1
2
1
0
0
0
0
1
0
0
0
0
1
1
0
0
2
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
3
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
2
4
3
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
3
0
0
1
1
0
0
1
0
0
2
0
0
0
0
2
0
0
3
4
0
0
0
0
1
0
2
2
0
1
0
0
0
0
0
0
2
0
4
0
0
0
0
0
1
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
1
1
0
2
0
2
7
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
2
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
1
2
0
0
1
0
0
1
0
0
0
2
0
0
1
1
3
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
3
2
0
3
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
3
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
1
0
0
0
0
0
2
0
2
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
4
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
2
0
0
0
0
0
3
0
0
1
0
0
0
2
2
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
2
0
0
1
0
2
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
1
4
0
0
2
3
1
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
2
0
0
0
1
1
0
2
2
0
0
0
0
0
0
3
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
2
0
0
2
1
0
0
0
0
0
1
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
1
3
0
2
0
11
3
0
2
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
4
0
0
1
0
0
2
0
1
0
1
0
2
2
0
1
0
1
0
1
0
0
0
2
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
2
1
0
0
1
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
2
0
0
2
0
0
0
0
2
0
0
2
0
1
3
0
0
0
1
0
0
0
0
3
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
2
0
0
1
0
1
1
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
3
1
0
0
0
2
0
0
0
2
0
0
7
0
2
0
3
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
2
1
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
3
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
2
0
0
1
0
4
1
0
0
2
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
1
2
2
0
2
3
1
2
0
5
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
3
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
2
1
2
0
1
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
3
0
0
2
0
1
0
0
0
0
0
0
0
1
3
1
0
0
0
2
3
2
0
1
0
1
0
1
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
3
0
0
0
2
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
3
2
1
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
9
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
8
0
0
0
0
0
0
0
0
2
0
0
1
1
0
2
0
3
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
3
0
2
0
0
0
0
2
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
1
1
2
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
2
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
1
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
1
1
0
0
2
0
0
0
3
0
0
0
0
0
1
3
0
0
0
0
0
0
0
1
2
2
0
0
1
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
10
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
3
7
0
0
0
1
2
0
0
3
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
3
2
2
0
5
0
0
1
0
0
2
0
0
0
4
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
1
0
1
2
0
0
1
2
0
0
0
0
0
0
0
0
1
1
0
0
0
1
7
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
1
0
0
3
1
0
0
2
0
0
0
0
0
0
2
2
0
2
0
0
0
0
1
0
1
0
0
0
0
0
2
1
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
1
0
1
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
2
1
0
0
0
0
0
2
0
1
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
1
0
0
1
1
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
2
1
2
0
0
0
0
5
2
0
0
0
0
2
0
2
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
3
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
3
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
2
0
0
0
0
0
1
0
0
0
0
0
0
5
0
2
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
1
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
5
0
0
5
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
1
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
3
0
0
0
0
0
2
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
4
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
4
0
3
0
0
3
2
1
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
1
2
0
0
2
2
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
3
0
0
0
0
1
0
7
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
1
0
0
1
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
3
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
2
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
3
0
0
2
0
0
0
1
0
0
1
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
2
0
0
0
0
0
0
4
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
2
0
1
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
3
2
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
1
0
0
1
0
1
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
1
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
4
2
1
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
4
1
1
0
0
0
0
0
0
0
0
0
0
2
5
0
0
0
0
0
0
0
0
0
2
0
0
4
5
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
3
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
1
0
1
2
3
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
6
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
3
0
1
0
2
0
0
0
0
2
0
0
2
0
2
1
2
2
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
1
0
0
0
0
2
2
0
0
1
0
0
2
0
2
0
3
0
0
0
0
2
0
0
4
0
0
0
0
1
0
0
0
2
1
2
0
0
0
1
1
2
0
0
0
2
0
0
1
1
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
1
0
1
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
1
0
0
0
1
0
0
2
2
1
0
0
0
1
0
0
0
0
0
3
0
0
0
2
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
2
2
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
3
0
0
0
3
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
2
0
0
0
2
0
0
0
2
0
0
1
2
1
0
0
0
0
0
0
0
0
10
2
0
0
4
2
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
1
1
1
0
0
0
2
0
0
0
2
0
1
1
0
0
1
0
0
1
0
0
0
2
1
1
0
0
0
0
1
0
0
0
2
0
1
2
1
0
0
1
2
0
0
0
0
2
0
0
0
0
2
0
0
2
0
2
1
0
1
0
0
2
0
0
2
0
0
0
2
0
0
0
1
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
2
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
1
0
0
1
0
0
0
4
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
2
3
0
0
0
0
2
0
0
0
2
0
6
0
0
0
0
0
1
1
0
0
3
0
0
2
0
1
0
2
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
2
2
0
0
0
0
0
1
2
0
0
0
0
1
0
1
0
0
0
3
0
1
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
4
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
2
1
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
3
1
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
2
0
0
0
1
0
0
0
0
0
3
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
3
0
0
2
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
5
0
2
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
2
0
0
0
0
0
1
1
3
3
2
0
0
0
0
0
0
1
1
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
1
0
2
2
2
0
0
0
0
0
0
0
2
0
1
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
4
0
0
0
3
0
2
0
0
0
0
1
1
0
0
4
1
1
0
3
2
0
0
0
0
0
0
0
0
0
6
0
0
1
0
0
0
0
0
1
2
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
3
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
1
0
0
1
1
0
1
0
0
2
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
3
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
3
0
1
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
1
0
0
0
1
0
0
0
0
3
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
7
0
2
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
4
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
7
0
0
1
0
0
0
1
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
10
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
2
3
0
1
0
1
7
3
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
5
3
0
0
2
1
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
1
0
0
0
1
0
1
0
0
0
0
0
2
1
2
2
0
0
0
5
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
5
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
1
0
0
0
3
1
0
1
1
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
2
2
0
0
4
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
3
0
0
6
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
2
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
1
2
0
0
0
0
2
0
3
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
1
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
1
0
0
0
0
0
2
1
0
2
0
0
1
1
0
2
4
0
1
0
0
1
0
0
0
0
0
4
2
0
1
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
2
0
0
0
0
0
1
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
3
0
0
0
0
1
0
0
0
0
0
0
0
0
1
3
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
2
1
1
0
3
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
3
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
3
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
3
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
5
0
0
0
0
1
2
0
0
0
3
0
2
0
1
2
2
0
0
2
0
0
0
2
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
13
0
0
0
0
0
0
1
0
0
2
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
2
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
2
1
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
1
2
1
1
0
0
1
0
2
0
0
0
0
0
0
2
1
0
2
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
2
0
2
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
2
2
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
7
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
2
0
0
1
2
2
2
0
0
0
0
0
0
2
3
0
0
0
0
2
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
3
0
0
2
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
3
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
4
1
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
2
2
0
0
0
1
0
0
0
0
5
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
1
0
0
0
2
4
0
3
2
0
2
0
0
2
0
0
2
2
1
0
0
1
0
0
2
0
1
0
0
0
1
0
1
0
2
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
2
2
1
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
1
0
0
3
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
2
2
2
1
0
0
4
2
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
2
0
2
0
1
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
7
0
3
0
0
0
0
2
2
0
0
1
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
3
0
0
8
0
0
0
1
0
3
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
3
1
0
2
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
7
1
0
2
0
0
0
0
0
0
1
0
2
1
0
0
0
2
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
2
0
0
0
0
1
0
0
1
2
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
1
0
1
0
3
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
6
0
0
2
0
1
1
0
0
2
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
2
0
0
0
0
3
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
1
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
3
1
1
2
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
1
1
0
0
0
0
2
2
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
1
1
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
3
3
0
0
1
0
0
0
1
0
0
0
0
0
4
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
1
1
2
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
2
0
2
0
0
1
0
0
0
0
0
0
0
1
1
0
0
2
0
0
1
0
0
3
0
0
0
0
0
1
2
0
0
0
0
0
3
0
0
1
0
0
0
2
0
2
0
4
0
1
2
0
0
0
0
1
1
0
3
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
2
1
3
0
3
0
0
0
0
2
0
1
0
0
0
0
12
2
0
0
1
0
2
0
0
0
1
1
0
0
2
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
1
2
1
0
3
0
3
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
2
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
5
0
0
0
0
0
1
1
1
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
1
0
2
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
3
0
2
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
3
1
0
0
1
0
0
1
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
1
0
0
1
0
1
0
0
0
4
0
0
0
0
0
0
1
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
2
0
1
0
2
0
2
0
2
0
0
1
4
0
0
3
1
2
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
4
0
1
1
0
0
0
0
0
2
1
0
0
0
0
1
0
3
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
3
0
0
2
0
0
3
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
3
1
2
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
1
0
1
0
1
0
1
0
1
0
1
0
0
1
0
2
0
0
0
0
0
0
2
0
1
0
1
2
1
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
5
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
4
1
2
0
0
2
1
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
2
1
1
2
0
0
1
2
0
7
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
3
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
1
0
0
0
0
5
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
1
0
0
1
2
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
4
0
0
0
1
0
0
1
0
0
0
0
0
0
0
3
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
2
1
0
0
1
0
0
1
0
2
0
1
0
0
1
1
3
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
2
0
0
0
1
1
0
0
1
0
0
0
1
0
0
1
0
2
0
6
0
0
0
2
1
0
0
0
2
0
0
0
3
4
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
5
0
0
3
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
3
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
1
2
1
0
0
3
0
2
0
1
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
3
0
1
1
2
0
2
0
0
0
0
3
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
2
1
0
0
0
0
0
0
1
0
2
2
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
2
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
2
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
2
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
8
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
2
0
2
0
4
0
0
0
3
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
1
1
0
0
0
0
0
0
0
0
1
2
2
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
1
2
1
2
0
0
0
1
0
1
0
1
0
0
0
0
0
1
1
2
1
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
2
0
0
0
1
0
2
1
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
1
0
2
2
3
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
2
0
0
0
0
2
0
2
0
0
2
2
0
1
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
1
2
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
2
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
4
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
3
0
2
0
0
0
0
0
0
0
2
4
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
1
1
0
0
0
0
0
0
4
0
0
0
0
0
1
2
0
0
0
1
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
3
1
0
0
0
0
1
0
1
1
1
2
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
4
0
0
0
2
1
0
0
1
0
3
0
1
0
0
0
1
2
1
0
0
0
0
0
0
0
1
1
2
1
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
2
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
1
0
0
1
0
0
2
0
2
0
0
0
0
2
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
1
0
1
0
0
0
2
0
0
2
1
0
0
2
0
0
4
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
2
1
4
2
0
2
0
0
0
2
1
0
0
1
1
0
0
0
2
2
0
2
0
1
1
0
1
0
2
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
3
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
3
0
0
2
2
0
2
1
0
0
0
0
1
0
0
2
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
1
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
1
0
1
1
0
2
0
1
0
0
0
0
0
2
4
0
0
0
0
0
1
0
0
1
0
0
2
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
2
0
0
0
0
4
0
0
0
1
1
0
2
0
0
1
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
2
2
0
1
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
1
0
0
0
2
3
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
1
0
1
1
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
2
0
0
0
0
1
0
0
2
1
3
2
0
0
0
0
2
1
0
0
0
0
0
0
2
3
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
2
2
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
1
2
0
0
2
2
2
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
6
1
0
0
1
0
0
0
0
0
1
0
2
3
0
0
0
0
0
0
0
3
0
0
2
0
0
0
2
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
5
1
0
0
2
0
0
1
1
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
2
0
0
0
2
0
1
0
0
1
0
1
0
1
0
0
1
2
0
0
0
2
0
0
0
0
0
1
2
1
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
2
1
1
3
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
2
0
1
0
0
0
2
1
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
2
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
2
4
0
0
0
0
2
1
0
0
2
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
2
0
1
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
3
0
2
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
2
0
0
1
0
0
0
1
0
0
0
0
2
0
2
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
1
0
1
2
0
0
0
0
2
0
0
0
0
0
1
1
0
0
1
0
0
2
0
0
1
2
0
2
4
0
2
2
0
0
1
0
2
0
1
0
0
0
0
0
2
0
0
0
2
0
0
2
1
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
1
0
0
2
0
1
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
2
1
2
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
1
0
1
1
1
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
2
0
1
0
0
0
0
3
0
0
0
1
0
1
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
1
0
0
2
0
0
1
2
0
0
1
2
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
1
0
0
0
1
0
3
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
1
0
0
0
3
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
33
0
0
1
1
0
0
1
0
1
0
0
0
0
1
1
1
0
2
0
0
0
0
0
1
0
0
2
0
1
2
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
5
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
5
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
3
0
0
0
0
2
0
0
1
1
0
0
0
0
0
2
3
0
1
0
1
0
0
2
0
3
0
0
1
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
4
0
0
0
1
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
1
0
0
0
0
0
0
1
2
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
4
0
2
4
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
7
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
2
0
2
0
0
1
3
0
0
0
0
0
0
0
0
0
0
1
2
2
1
0
0
2
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
1
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
2
2
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
3
1
0
0
0
0
3
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
1
1
1
2
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
1
3
3
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
6
0
0
3
0
0
0
0
0
0
2
0
2
0
0
2
0
1
1
1
0
2
0
0
0
0
0
0
0
0
0
3
0
0
2
0
1
1
0
2
0
0
1
0
2
1
0
0
0
1
0
1
1
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
1
3
0
0
1
0
0
0
2
0
0
1
0
1
0
0
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
3
0
0
0
1
2
1
2
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
2
1
0
0
0
0
0
1
0
2
1
0
0
0
2
0
1
1
0
0
0
0
0
0
1
0
3
0
0
2
1
0
0
0
0
1
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
2
0
1
2
0
0
1
2
2
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
5
0
0
2
0
2
1
0
1
0
0
0
0
0
3
0
0
0
2
0
0
0
0
1
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
1
0
0
0
0
0
0
1
7
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
1
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
9
0
2
0
3
0
1
0
0
1
0
0
0
0
0
0
0
0
1
2
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
1
1
1
3
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
1
2
0
0
0
2
0
0
1
0
2
0
0
1
0
2
0
7
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
1
0
0
1
0
0
1
0
2
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
3
0
1
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
2
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
5
0
0
0
1
3
0
1
0
0
2
0
0
0
0
4
1
0
0
2
2
0
0
0
1
0
2
0
0
0
2
1
0
0
0
1
0
0
2
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
1
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
3
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
2
0
1
0
0
2
0
0
0
2
2
0
0
0
1
2
1
0
1
0
0
0
0
0
0
0
0
0
0
6
0
2
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
1
0
1
0
0
0
0
2
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
1
0
2
0
0
0
0
1
2
0
0
0
0
2
1
1
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
1
0
0
1
0
0
0
2
0
0
0
1
1
0
0
1
1
0
2
0
0
2
0
0
0
0
0
1
2
0
1
2
1
0
0
0
0
0
0
0
0
0
1
0
0
3
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
1
0
0
2
2
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
2
1
1
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
3
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
2
0
0
0
0
0
3
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
10
0
0
0
0
1
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
1
2
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
1
0
0
0
1
0
0
3
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
6
0
0
0
2
0
2
0
0
0
1
3
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
2
0
0
0
0
1
0
1
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
2
0
0
0
1
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
11
0
1
4
1
0
0
0
0
0
1
0
0
0
0
4
2
1
0
0
0
0
0
0
0
0
1
0
1
0
1
1
1
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
2
0
0
0
0
3
1
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
2
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
5
0
0
2
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
1
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
4
0
3
1
0
0
1
0
1
0
0
0
2
0
4
0
1
3
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
4
1
0
0
0
0
0
1
5
0
0
0
0
0
0
0
0
0
0
1
1
2
1
0
0
0
0
0
1
0
0
0
1
2
1
1
0
0
0
2
0
0
0
0
1
0
0
2
1
0
0
6
0
2
0
0
1
1
2
0
2
0
0
0
0
0
2
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
1
0
1
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
4
0
1
0
0
0
1
0
0
0
2
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
2
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
2
1
3
1
0
2
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
1
0
0
0
0
1
4
0
1
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
1
0
0
0
1
0
0
3
0
0
7
0
0
0
0
1
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
8
0
1
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
1
2
0
1
0
0
0
0
0
2
0
0
1
0
0
2
1
0
0
0
0
0
0
0
2
2
0
4
0
0
0
0
3
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
2
0
1
0
2
1
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
2
1
0
0
0
0
0
2
0
0
0
1
1
2
1
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
2
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
2
2
0
0
0
0
0
0
0
2
0
0
2
3
0
1
0
0
2
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
1
0
1
2
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
4
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
2
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
2
0
0
0
0
0
0
0
1
3
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
2
0
2
0
2
0
2
0
0
1
0
0
1
2
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
2
2
0
0
2
0
3
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
1
1
0
0
2
0
2
0
0
0
1
1
0
0
1
2
1
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
11
0
1
1
0
0
1
0
0
0
1
0
0
4
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
2
0
1
1
0
2
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
1
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
6
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
3
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
1
4
2
1
0
0
2
0
0
1
0
3
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
1
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
1
2
0
0
3
0
0
0
1
0
0
0
0
0
0
4
0
3
1
1
0
1
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
2
0
0
0
2
0
0
0
3
0
1
1
0
0
0
1
0
0
0
2
1
0
0
0
1
0
0
0
2
0
1
4
0
0
0
2
0
0
1
2
2
0
2
1
0
1
0
0
0
0
0
1
0
1
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
5
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
4
1
0
0
0
0
3
0
0
2
0
0
0
0
0
2
1
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
3
0
1
0
0
0
0
0
2
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
3
0
0
0
0
1
1
0
0
1
0
1
2
2
1
1
0
0
0
0
2
0
0
1
0
0
0
4
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
3
1
1
0
3
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
2
1
2
0
1
0
0
0
1
1
0
0
0
0
2
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
2
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
1
2
0
0
0
2
2
2
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
2
1
2
0
1
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
1
0
0
2
0
0
1
2
0
0
1
8
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
1
0
0
2
1
0
0
0
5
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
4
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
3
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
1
1
0
0
0
0
0
1
0
0
1
3
0
3
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
2
0
0
1
0
1
0
0
0
1
0
2
0
2
0
0
2
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
2
0
2
0
0
2
0
0
0
0
1
2
3
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
1
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
1
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
3
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
2
0
0
1
0
0
0
0
3
1
0
0
2
0
2
0
0
0
0
0
0
3
0
0
0
2
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
2
1
0
1
0
0
1
0
0
3
0
0
0
0
0
0
4
0
1
0
1
1
1
0
0
2
2
1
0
0
0
0
0
0
2
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
2
0
0
1
0
0
0
0
0
0
1
0
0
4
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
2
7
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
6
0
0
0
0
0
0
1
0
0
2
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
5
0
0
0
0
2
1
1
0
0
1
0
0
0
0
2
1
0
1
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
2
2
0
1
0
0
0
0
0
1
0
0
1
0
3
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
1
1
0
2
0
0
1
0
0
0
0
0
0
0
2
1
1
0
1
0
0
1
2
0
0
0
0
0
0
0
2
0
0
3
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
2
2
0
3
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
1
0
2
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
3
0
1
0
0
2
3
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
3
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
2
1
0
0
1
0
2
0
0
0
0
0
0
0
1
2
0
0
0
6
0
0
0
2
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
2
3
2
0
0
0
0
0
0
1
2
1
0
0
0
0
1
0
0
2
0
0
0
2
0
1
0
0
0
11
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
2
0
1
0
2
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
1
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
2
3
0
0
0
3
1
2
1
0
1
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
3
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
4
0
1
0
1
7
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
3
0
0
0
2
0
1
3
0
2
0
0
0
2
2
3
0
2
0
3
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
1
3
2
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
2
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
11
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
7
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
1
1
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
1
0
0
4
0
0
0
0
0
0
0
0
1
0
4
0
3
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
1
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
2
0
2
0
0
0
0
1
2
0
0
0
0
0
0
1
1
0
0
1
0
5
1
0
0
0
1
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
1
1
2
0
2
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
4
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
1
1
2
0
2
0
0
1
0
0
0
0
1
0
2
0
0
0
1
0
0
0
4
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
3
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
2
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
1
1
0
0
0
0
0
0
2
4
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
1
1
0
0
0
1
2
0
1
0
2
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
2
1
1
4
0
0
0
1
0
0
0
1
0
1
2
0
0
0
0
0
2
2
0
0
1
0
0
0
0
1
0
0
3
1
0
2
0
0
0
2
0
3
0
1
0
1
0
0
1
0
0
1
0
2
0
2
0
0
0
0
0
2
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
1
2
0
3
0
0
0
0
2
0
0
0
0
1
2
0
6
0
0
0
0
0
1
0
9
0
0
0
0
0
0
1
0
1
0
1
1
0
0
1
0
2
0
1
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
4
0
1
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
3
0
0
2
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
1
3
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
1
2
0
0
0
0
0
1
0
0
3
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
3
1
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
5
1
0
0
1
0
0
0
0
1
0
0
0
0
0
2
5
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
1
6
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
5
0
2
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
6
0
1
0
0
2
0
0
0
2
2
1
0
0
1
0
0
1
3
2
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
3
0
2
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
2
0
2
2
0
0
0
0
1
3
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
1
0
0
1
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
3
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
3
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
4
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
1
2
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
2
8
0
0
0
0
0
2
0
1
0
2
0
2
0
0
0
2
2
0
0
2
0
0
0
0
2
0
1
6
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
3
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
2
0
2
2
2
2
0
0
0
0
0
0
0
0
0
0
2
1
2
0
2
0
0
0
0
4
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
1
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
1
0
0
1
0
0
2
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
1
0
0
0
2
0
0
1
0
0
0
1
0
2
0
0
2
3
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
4
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
2
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
1
0
1
0
0
1
0
1
0
0
0
0
0
1
1
0
2
1
0
0
0
0
0
0
3
2
0
2
2
0
0
4
2
0
0
0
0
0
0
3
1
1
2
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
2
0
0
1
0
2
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
3
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
2
2
1
0
1
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
3
2
0
2
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
2
3
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
3
0
4
1
2
0
3
0
0
0
0
0
2
0
0
0
0
0
0
1
2
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
6
3
0
2
2
2
0
0
0
0
2
0
1
0
2
3
0
0
0
1
0
0
0
2
1
2
1
0
0
0
0
0
0
1
0
1
2
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
1
1
1
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
1
1
0
0
0
0
0
1
0
0
2
2
3
0
0
0
1
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
3
0
0
0
0
0
0
0
2
1
2
0
2
0
0
0
0
0
0
2
2
0
0
0
2
0
2
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
1
2
1
0
0
0
0
1
0
0
0
0
0
0
0
3
2
0
0
0
0
0
2
0
0
1
1
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
2
0
0
1
1
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
2
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
2
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
1
2
2
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
3
1
0
0
0
4
0
0
0
0
0
3
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
1
0
0
0
1
0
2
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
4
0
0
2
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
1
1
2
2
0
0
0
0
0
0
0
0
4
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
2
0
2
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
3
0
0
0
0
0
0
12
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
2
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
4
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
2
3
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
2
0
1
0
0
0
0
0
2
0
2
0
0
0
0
2
2
0
1
0
3
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
1
0
1
2
0
0
3
0
0
0
0
0
0
0
0
3
0
0
1
0
0
3
2
2
0
0
1
0
0
1
0
2
0
1
1
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
1
0
0
0
0
2
0
0
3
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
7
1
3
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
1
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
1
0
0
2
0
0
2
0
0
1
0
0
0
2
0
0
0
4
0
1
0
2
0
0
0
0
1
1
0
1
0
1
2
1
0
2
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
1
0
0
2
0
0
1
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
3
0
3
0
0
1
0
0
0
0
0
11
1
0
0
0
0
0
0
0
0
1
2
0
2
0
1
0
2
0
0
0
0
0
1
2
0
1
2
0
1
0
0
2
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
1
1
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
3
0
2
0
1
0
3
0
0
0
0
0
3
0
0
1
4
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
2
1
0
1
1
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
1
2
2
0
0
1
0
1
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
1
8
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
2
0
0
2
0
2
1
1
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
1
0
0
0
0
0
2
0
0
1
1
1
0
1
4
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
3
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
4
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
1
0
1
0
0
0
0
1
2
0
1
2
1
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
3
0
0
0
0
1
0
0
0
1
0
1
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
2
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
1
1
2
0
2
0
1
0
0
0
0
1
2
0
0
1
1
0
1
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
2
1
0
2
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
4
0
0
2
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
2
1
1
1
0
0
1
0
0
0
0
0
0
0
0
1
1
2
0
0
1
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
2
2
0
2
1
0
0
2
0
0
2
0
0
0
0
1
0
0
2
0
2
4
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
3
1
0
0
3
0
0
0
0
0
0
2
0
6
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
6
0
4
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
2
2
1
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
2
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
1
3
0
1
2
0
1
0
0
1
0
0
0
0
0
3
4
0
1
1
1
0
0
1
2
0
0
0
2
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
2
2
0
0
0
0
0
1
2
0
0
1
0
0
1
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
2
0
4
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
1
0
1
0
2
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
3
0
2
0
0
2
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
2
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
5
2
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
2
0
2
2
0
0
0
0
1
0
0
2
2
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
3
0
0
0
1
1
0
1
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
2
0
0
1
0
1
0
0
2
0
2
0
0
0
2
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
3
2
0
0
0
1
0
1
0
0
0
2
2
1
0
0
0
1
0
0
2
0
1
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
2
1
0
0
2
0
2
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
1
1
0
1
1
0
0
0
0
0
0
2
0
0
0
7
0
0
0
0
0
2
0
0
2
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
11
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
3
1
0
1
1
1
0
2
0
0
0
0
0
2
5
0
0
0
1
2
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
1
0
0
0
0
2
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
1
0
2
2
0
0
1
0
0
2
0
0
1
2
0
0
0
1
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
1
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
1
0
0
0
0
8
0
0
0
0
0
1
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
1
0
2
0
0
1
2
0
0
0
0
0
5
0
0
1
0
1
0
0
0
0
2
0
1
2
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
3
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
2
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
3
3
5
8
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
1
0
0
0
0
1
1
0
1
0
0
2
0
0
1
0
0
0
0
0
0
2
1
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
4
2
0
1
1
2
0
0
0
1
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
1
0
1
0
1
0
2
0
0
2
0
0
0
0
5
0
0
0
0
1
0
0
0
0
1
0
0
1
3
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
1
1
0
8
1
0
0
0
3
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
2
0
2
0
0
1
3
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
5
2
0
1
0
0
0
0
0
3
0
1
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
2
2
0
0
1
0
1
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
1
1
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
1
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
2
2
0
4
0
0
0
1
0
1
0
0
0
1
0
2
0
0
0
0
0
0
2
1
0
0
0
0
2
0
1
0
0
1
1
0
0
0
3
0
0
0
0
0
0
2
0
0
1
2
1
0
2
0
0
0
0
0
1
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
3
1
0
2
0
2
0
0
0
0
2
1
0
1
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
1
1
0
1
0
0
0
0
2
0
0
1
2
0
0
0
0
0
2
2
0
0
2
0
0
0
1
2
0
0
0
0
2
0
0
0
0
2
0
0
2
2
0
0
1
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
1
0
2
1
1
0
0
0
0
0
0
1
0
2
1
0
2
0
0
1
2
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
2
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
2
4
1
0
2
1
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
1
1
2
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
3
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
3
2
2
0
0
0
0
4
0
0
2
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
3
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
2
2
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
1
0
0
2
3
0
0
0
0
1
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
1
0
0
0
2
0
0
1
0
0
2
0
4
0
1
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
3
2
0
0
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
1
1
2
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
5
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
5
0
0
1
1
0
0
1
0
0
1
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
1
0
2
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
3
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
2
0
0
1
0
2
2
0
0
0
1
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
2
0
1
0
0
0
3
1
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
3
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
1
0
0
0
0
6
0
0
0
0
2
0
0
2
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
3
0
0
0
0
0
0
2
0
0
3
1
0
0
0
1
1
0
2
0
0
1
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
3
0
0
1
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
4
1
0
0
0
0
2
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
2
2
0
1
0
0
2
0
0
0
0
0
4
1
0
0
0
0
2
0
0
0
15
0
0
0
0
0
3
0
1
3
0
0
1
0
1
0
1
0
0
0
1
0
0
0
2
0
0
6
0
0
0
0
0
2
0
0
3
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
5
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
3
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
1
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
4
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
2
1
0
0
0
0
0
2
2
1
0
0
0
2
0
0
0
0
1
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
2
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
5
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
2
0
3
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
1
0
0
2
1
0
0
0
0
0
2
0
0
0
1
2
0
0
4
0
1
0
1
0
0
0
0
0
0
1
2
0
3
0
0
0
2
1
1
0
0
0
0
1
0
0
2
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
2
1
0
0
0
0
0
0
0
2
0
0
0
0
1
3
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
2
0
0
0
0
2
0
1
0
0
0
0
3
0
2
0
0
3
2
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
3
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
2
1
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
1
9
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
1
0
1
0
7
1
0
0
0
0
2
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
2
2
0
0
0
0
0
1
0
1
0
1
2
2
0
2
0
0
2
0
0
3
0
0
0
0
0
0
0
1
1
0
2
0
1
3
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
4
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
3
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
2
0
0
1
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
2
1
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
2
0
0
0
2
0
0
1
0
0
1
2
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
1
0
0
2
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
2
4
0
1
0
2
0
2
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
2
0
1
1
0
2
0
0
0
3
0
1
1
1
1
0
1
2
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
2
1
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
3
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
5
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
4
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
1
1
0
0
1
2
0
0
0
0
0
2
2
0
0
2
1
2
0
1
0
0
2
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
1
0
4
3
0
0
0
0
0
2
1
0
0
3
0
2
0
0
0
2
1
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
7
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
1
0
0
1
0
0
0
0
2
1
0
2
1
0
3
0
0
0
1
2
0
2
0
3
2
0
0
1
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
1
1
5
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
3
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
2
0
0
1
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
8
5
0
0
1
0
1
0
0
0
1
0
0
3
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
4
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
1
7
1
0
0
0
0
2
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
4
2
1
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
3
0
0
0
3
1
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
4
0
0
2
0
0
3
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
1
0
2
2
0
1
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
3
0
0
2
0
0
1
0
1
2
0
0
0
0
0
2
2
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
4
1
0
0
0
2
0
0
3
0
0
2
0
0
2
0
0
0
1
0
0
1
1
0
0
2
2
0
0
0
0
3
0
0
1
1
0
0
0
0
1
6
0
0
2
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
0
2
0
0
3
2
0
0
0
0
0
1
0
2
2
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
3
0
0
0
0
0
3
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
3
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
2
0
2
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
1
0
0
0
0
0
2
0
2
0
0
1
0
0
0
1
0
5
0
0
0
1
0
1
0
1
0
0
2
0
4
0
0
0
0
0
0
1
1
2
0
0
0
1
0
1
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
2
0
0
2
1
1
0
0
0
0
0
0
0
0
0
1
0
2
2
2
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
3
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
3
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
3
0
0
0
0
1
0
0
0
1
0
0
3
0
0
0
0
0
0
0
1
0
1
0
2
1
0
4
0
0
0
0
0
0
2
2
0
0
0
2
0
0
2
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
6
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
1
0
0
0
0
2
2
0
1
0
1
0
0
1
2
0
2
0
0
0
0
1
0
0
2
1
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
1
1
2
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
2
2
0
0
1
1
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
3
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
1
1
0
0
1
2
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
1
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
1
0
2
4
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
2
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
4
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
2
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
1
0
0
0
0
1
1
1
0
0
2
0
0
2
0
0
2
1
0
2
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
1
0
3
0
0
0
1
3
1
0
0
0
1
0
0
0
1
1
0
0
0
0
2
2
0
0
0
1
0
1
1
2
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
1
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
2
1
1
0
0
0
1
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
3
0
3
0
0
0
0
0
0
2
0
2
0
0
0
0
2
1
0
5
0
0
2
1
0
0
0
1
0
0
1
1
2
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
13
0
0
1
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
1
2
2
4
1
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
2
3
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
8
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
2
2
1
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
1
0
1
1
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
1
2
2
0
1
0
0
0
0
0
0
3
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
1
1
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
4
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
1
0
0
1
3
0
0
0
0
0
0
0
10
0
3
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
2
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
1
1
2
0
0
7
0
1
0
3
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
2
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
6
0
2
0
1
0
0
0
1
0
0
0
0
3
2
0
0
1
0
0
0
2
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
1
0
2
1
0
0
2
0
0
0
2
0
0
0
4
0
2
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
2
3
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
1
2
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
5
1
0
0
0
1
2
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
3
0
0
0
0
0
2
0
0
6
0
2
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
2
1
2
0
0
0
0
2
1
0
1
2
0
1
0
0
1
3
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
2
2
0
0
0
0
0
2
1
2
2
1
0
2
0
1
0
0
0
4
2
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
1
0
1
0
0
3
1
0
2
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
2
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
2
0
0
0
0
9
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
1
0
1
1
1
3
0
0
0
1
1
0
2
0
1
0
1
11
0
1
0
0
0
0
2
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
2
1
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
3
0
0
0
0
1
0
0
0
0
0
3
0
0
1
0
0
0
2
0
0
0
0
0
0
1
2
0
1
6
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
1
0
0
0
0
0
2
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
3
1
0
0
1
0
0
0
2
0
0
0
0
0
1
1
1
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
4
0
2
0
0
0
0
0
2
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
4
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
3
0
1
0
0
14
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
1
0
0
2
0
0
1
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
2
2
1
3
0
1
0
2
0
0
0
0
0
2
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
1
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
3
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
5
0
3
0
2
0
0
0
0
1
0
0
1
3
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
1
2
2
1
0
0
0
7
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
1
2
0
0
2
0
0
0
0
2
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
1
1
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
4
1
0
0
0
1
1
2
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
3
2
0
0
0
0
4
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
2
0
1
2
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
4
0
0
0
2
0
0
1
7
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
1
2
0
0
0
0
2
0
1
0
0
4
0
0
1
0
0
1
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
2
0
3
0
0
1
0
0
0
0
2
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
2
0
0
0
0
0
0
5
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
1
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
2
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
1
2
1
0
2
1
2
0
0
0
0
0
0
5
2
0
2
0
0
0
0
1
0
2
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
7
1
1
0
0
0
1
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
4
2
1
0
0
0
0
1
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
1
0
1
0
1
0
0
0
0
1
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
3
0
0
0
0
0
1
1
0
1
4
0
0
0
1
1
2
0
2
0
0
1
4
0
0
0
1
0
0
0
0
0
2
0
0
2
2
0
0
0
2
0
0
2
0
1
0
0
0
0
0
1
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
1
2
0
1
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
4
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
1
0
3
1
0
0
0
0
0
0
0
0
2
0
3
6
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
2
0
2
2
0
1
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
1
4
0
0
0
0
2
0
3
0
2
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
3
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
6
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
1
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
1
1
0
0
1
2
0
0
0
0
0
2
0
2
2
1
0
0
0
0
0
0
0
0
3
0
1
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
2
2
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
3
0
0
0
0
4
1
0
0
0
2
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
1
0
0
0
0
2
4
0
0
5
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
8
2
2
0
1
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
3
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
5
0
0
0
0
1
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
2
0
0
0
2
0
3
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
1
3
0
0
0
0
0
2
1
2
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
1
0
0
0
2
0
0
2
0
0
0
0
1
0
2
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
3
2
0
1
1
0
0
0
2
2
1
0
3
0
0
0
0
0
1
1
0
0
0
2
0
0
4
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
4
1
0
0
0
0
3
2
0
0
0
0
0
0
2
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
2
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
3
1
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
2
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
2
1
1
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
4
1
0
1
0
2
0
1
2
2
0
0
2
0
0
0
0
0
0
1
2
0
0
0
1
4
0
0
0
2
0
1
2
4
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
1
1
0
0
2
0
2
0
0
1
0
0
0
0
1
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
3
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
1
0
1
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
3
0
2
1
0
3
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
2
0
0
0
0
0
0
0
0
2
0
1
3
0
0
0
0
0
0
0
0
0
2
0
0
5
0
2
2
2
0
1
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
1
0
2
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
5
0
2
0
2
0
0
0
0
2
0
0
11
0
1
1
4
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
2
2
0
2
0
0
0
0
0
0
2
0
0
1
2
0
0
0
1
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
1
1
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
5
0
0
2
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
8
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
9
1
0
0
0
1
2
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
1
2
0
2
2
0
0
0
0
0
0
1
1
0
0
1
1
0
2
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
2
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
1
2
1
2
2
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
3
0
0
0
0
3
0
0
4
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
2
3
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
5
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
3
1
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
2
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
3
1
0
0
0
2
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
4
1
3
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
3
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
2
1
0
0
0
0
1
2
0
0
2
4
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
2
0
1
1
0
0
0
3
2
0
0
1
0
0
0
0
0
0
0
0
2
1
0
2
1
0
0
1
0
0
2
0
0
1
2
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
2
0
5
0
0
0
1
2
0
0
4
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
3
0
0
1
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
2
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
2
10
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
3
0
1
2
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
3
1
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
1
0
0
0
3
0
0
2
0
0
1
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
3
0
1
1
0
0
0
0
0
0
0
0
1
0
0
5
7
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
2
1
0
0
0
0
0
0
1
0
4
2
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
2
1
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
6
0
1
2
0
0
0
0
2
0
1
0
0
2
1
0
1
2
0
0
1
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
10
3
0
1
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
2
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
1
0
0
0
0
2
1
0
0
0
2
0
2
0
0
0
0
0
0
4
0
0
0
1
1
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
2
2
2
0
2
1
0
0
0
0
0
0
0
1
0
2
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
4
0
0
0
0
0
2
4
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
1
2
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
1
0
2
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
5
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
2
0
2
2
2
3
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
2
0
0
0
0
5
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
6
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
1
0
0
1
0
0
1
0
0
0
0
0
2
1
2
0
0
1
1
0
0
1
0
0
1
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
3
0
1
0
0
0
0
0
2
0
0
0
1
0
0
2
0
7
1
0
0
0
0
0
2
0
2
1
0
0
2
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
2
0
0
0
2
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
3
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
1
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
3
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
11
0
0
0
2
1
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
2
0
0
0
0
2
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
2
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
3
1
0
0
1
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
5
0
1
1
3
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
2
4
0
0
2
0
1
0
0
5
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
1
1
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
3
0
0
3
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
2
0
2
0
2
2
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
5
0
1
2
0
0
0
0
0
2
0
0
1
0
0
0
2
2
2
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
2
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
6
2
0
0
0
2
0
0
0
0
1
2
0
0
4
1
0
0
0
0
0
0
0
1
0
0
1
0
2
0
2
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
2
7
0
1
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
1
2
0
2
0
0
0
2
0
0
0
0
8
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
5
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
1
0
6
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
2
0
0
0
1
1
2
0
0
0
0
4
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
4
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
4
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
4
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
3
0
0
1
0
2
1
2
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
3
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
2
0
0
0
0
0
2
1
0
1
2
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
1
1
0
1
0
1
0
0
0
1
0
0
2
0
2
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
2
1
3
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
3
0
2
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
2
5
3
0
5
0
0
2
2
0
1
1
1
0
0
0
0
0
0
0
0
0
3
0
1
1
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
3
0
1
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
2
0
1
0
0
0
0
0
2
0
2
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
2
0
1
0
1
1
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
1
1
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
2
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
1
3
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
2
1
0
0
0
0
1
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
3
2
0
0
0
0
0
2
0
0
1
0
0
0
1
1
0
1
1
0
1
1
4
0
3
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
2
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
3
0
0
0
0
0
3
2
2
1
1
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
3
0
0
0
0
1
3
0
0
0
3
0
0
0
1
1
0
0
0
2
0
0
1
4
0
0
0
3
2
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
8
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
2
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
1
1
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
3
0
2
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
2
1
0
0
0
0
2
0
0
1
0
0
2
0
0
2
0
0
0
2
3
0
0
0
0
2
0
0
0
0
2
2
2
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
3
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
2
0
1
0
1
0
1
0
0
0
0
0
0
1
0
3
0
0
0
1
2
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
2
1
0
1
0
0
3
0
0
0
0
0
2
1
0
0
3
2
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
1
1
1
0
0
1
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
3
0
0
2
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
1
0
1
0
0
0
0
1
0
0
2
1
0
1
1
0
2
0
0
2
3
2
1
0
0
2
2
3
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
2
0
1
0
0
2
1
0
0
2
0
1
0
0
0
1
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
1
0
0
0
0
2
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
2
1
3
0
0
1
0
0
0
0
0
1
0
0
0
2
3
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
12
0
0
2
2
0
2
0
0
0
1
0
3
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
1
2
1
1
0
0
0
1
0
0
0
0
0
0
0
2
1
0
1
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
2
0
2
0
0
0
1
0
0
2
0
2
0
0
1
0
1
0
2
0
0
0
1
0
1
0
0
0
3
0
0
1
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
5
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
2
3
0
0
0
3
0
2
0
0
0
0
0
0
0
13
3
0
0
0
0
0
0
0
0
2
0
0
4
0
2
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
23
0
0
0
0
1
2
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
2
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
2
0
2
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
1
0
2
0
2
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
1
1
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
1
0
2
1
0
2
0
0
0
1
0
0
0
0
2
4
0
0
4
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
2
0
0
1
0
2
0
1
0
2
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
1
2
2
1
0
2
1
0
1
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
3
0
0
2
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
3
2
0
0
0
0
0
0
3
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
3
0
1
0
0
0
1
0
0
2
1
1
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
1
0
2
0
1
0
0
0
1
0
2
0
6
1
2
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
2
4
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
3
3
1
0
0
0
0
0
0
4
0
0
0
0
1
2
4
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
3
0
0
0
1
1
1
1
0
0
1
2
0
0
0
2
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
2
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
3
0
0
1
0
2
0
1
0
0
0
2
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
2
2
2
0
1
0
0
3
0
0
0
2
2
7
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
3
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
2
0
0
0
0
0
2
1
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
2
1
0
2
0
1
1
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
3
0
0
1
0
2
1
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
1
1
0
0
1
0
0
1
3
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
1
2
3
0
0
1
0
0
0
2
0
0
2
0
0
0
0
1
4
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
2
1
0
1
0
0
0
0
3
0
1
2
2
1
0
1
0
0
3
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
1
0
1
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
2
1
2
0
0
0
1
0
0
0
0
1
1
0
1
1
1
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
1
0
0
0
0
1
2
0
0
2
0
0
0
0
0
5
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
1
2
0
0
0
2
0
1
0
0
3
0
2
1
0
1
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
8
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
2
0
0
1
2
0
1
0
0
0
4
0
3
0
1
0
0
0
0
2
0
0
0
3
9
0
1
2
0
0
0
1
2
0
3
0
0
0
1
0
0
0
3
0
2
0
0
0
1
0
0
2
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
6
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
5
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
2
0
2
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
3
1
0
0
0
0
0
1
0
2
5
1
0
1
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
3
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
3
0
0
0
1
0
0
0
0
1
0
3
0
0
0
2
0
6
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
6
3
1
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
4
0
0
2
5
0
0
0
0
0
3
0
0
0
0
0
0
0
0
4
0
2
0
0
1
1
0
0
2
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
1
2
3
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
3
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
2
0
1
0
0
0
0
0
1
1
0
0
0
2
1
0
2
2
0
2
0
0
0
2
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
1
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
5
0
0
0
0
0
2
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
2
2
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
2
0
1
1
0
1
0
0
0
0
0
0
0
2
2
1
0
2
0
2
0
0
2
0
0
2
0
2
0
0
0
0
0
2
0
2
1
0
1
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
2
0
2
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
1
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
2
0
1
0
0
0
0
0
2
1
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
6
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
4
0
2
0
0
0
2
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
2
0
1
1
0
2
0
1
6
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
1
0
0
0
2
1
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
4
0
2
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
1
0
4
1
0
0
0
0
3
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
2
2
2
0
0
0
0
0
1
2
0
0
0
0
2
0
0
1
0
0
2
1
0
0
0
0
1
0
0
0
2
0
0
2
0
0
2
1
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
1
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
2
0
0
1
1
1
0
4
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
2
1
4
2
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
3
4
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
5
2
5
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
1
1
2
0
0
0
0
0
1
0
0
1
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
2
2
0
0
2
1
0
0
0
2
0
1
2
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
1
2
4
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
1
2
0
0
0
3
0
0
0
0
0
0
0
2
2
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
2
0
1
0
0
0
2
0
0
0
0
2
1
0
2
1
0
1
0
0
0
0
0
2
0
0
2
0
0
2
1
0
0
0
1
2
0
1
0
1
0
0
0
2
2
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
1
1
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
1
2
0
0
1
0
0
0
0
0
2
2
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
2
0
1
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
3
0
0
0
1
0
0
0
0
0
2
1
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
3
0
2
2
0
2
2
0
0
2
0
0
1
0
2
0
0
0
0
0
6
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
5
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
2
0
2
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
2
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
2
0
0
0
1
2
2
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
2
0
6
2
0
2
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
3
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
5
2
0
0
2
1
1
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
2
0
0
0
0
0
2
1
0
0
1
0
0
0
2
0
0
1
0
0
2
0
0
2
0
1
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
1
0
0
0
1
0
2
2
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
3
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
1
0
0
0
1
0
2
0
1
0
0
0
0
5
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
1
0
2
0
0
1
1
2
0
1
2
0
1
1
0
0
0
0
1
8
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
2
1
0
0
3
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
1
1
0
2
0
2
0
0
0
0
0
1
0
0
2
0
2
1
0
1
0
2
2
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
2
1
1
2
0
0
2
0
0
0
0
1
0
1
2
0
1
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
1
3
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
1
0
0
1
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
1
1
3
0
0
0
1
0
0
0
2
0
1
0
2
0
2
0
0
2
1
1
0
0
0
2
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
2
0
1
2
2
0
0
0
0
0
0
1
0
2
0
0
0
0
1
2
0
2
0
2
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
1
1
0
0
0
0
3
0
0
1
0
0
0
1
0
0
2
2
0
0
1
2
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
6
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
2
0
0
0
2
0
0
3
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
1
0
1
1
0
0
2
0
0
3
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
1
1
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
6
0
0
0
0
1
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
4
0
0
0
0
1
0
0
0
0
0
2
0
1
0
2
0
0
3
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
4
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
6
0
1
0
0
0
0
1
0
0
0
2
0
0
2
2
0
2
2
6
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
2
0
1
6
0
1
1
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
7
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
1
0
1
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
2
0
4
0
0
0
4
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
1
0
3
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
2
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
11
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
2
0
0
4
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
3
0
0
2
1
1
0
2
0
1
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
1
6
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
2
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
1
0
0
0
2
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
1
3
0
0
2
0
0
0
0
1
0
8
0
0
1
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
3
2
0
0
0
0
0
0
3
0
2
0
0
1
2
0
0
2
0
2
2
2
0
0
1
0
0
0
4
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
0
2
1
0
0
0
4
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
2
0
0
0
2
0
2
1
0
0
0
1
1
0
0
0
0
0
2
0
0
0
1
2
1
0
0
2
0
0
3
0
2
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
2
0
2
0
0
0
0
0
0
3
0
0
0
0
1
0
0
2
0
0
0
0
3
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
7
1
0
0
0
0
0
0
2
0
0
3
0
0
0
2
2
1
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
1
0
0
0
1
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
1
0
0
0
0
0
0
1
0
1
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
3
2
1
0
2
1
0
0
0
1
0
1
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
3
0
0
0
0
2
0
0
0
0
0
2
0
1
0
2
1
0
0
0
1
0
0
2
3
0
1
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
2
0
3
0
2
3
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
6
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
2
3
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
2
0
2
0
2
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
1
0
1
2
0
2
0
1
1
0
1
3
2
1
1
0
2
0
0
0
3
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
2
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
4
0
0
0
0
0
2
2
1
0
0
0
0
2
0
0
0
0
0
1
0
1
0
1
1
0
0
2
0
0
0
1
2
0
21
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
1
0
0
0
0
0
0
0
5
0
0
0
0
1
6
2
2
0
0
2
1
0
0
0
0
0
0
0
0
3
0
0
2
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
1
2
0
1
0
0
1
0
0
1
1
0
0
0
1
0
1
0
0
2
0
0
0
0
1
0
0
1
2
0
0
0
4
1
0
1
0
0
0
1
0
0
0
2
0
0
0
0
7
0
1
0
0
0
0
0
2
0
0
0
0
0
4
0
0
0
0
1
2
0
0
0
2
3
0
0
0
0
0
1
1
3
2
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
3
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
2
0
1
1
0
4
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
1
1
1
0
0
1
0
0
0
0
3
1
0
0
1
0
0
0
0
0
5
0
0
1
2
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
2
2
2
0
0
0
0
2
0
0
0
9
3
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
1
0
0
3
0
4
2
0
0
0
0
1
3
0
0
0
0
0
0
3
0
0
0
3
2
0
0
0
0
2
0
0
0
0
0
2
0
0
3
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
3
0
2
2
1
2
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
1
0
0
2
2
0
1
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
3
1
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
2
0
3
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
2
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
2
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
2
2
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
2
0
1
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
3
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
1
1
2
0
1
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
2
0
1
0
2
2
0
0
0
0
1
1
2
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
4
0
0
1
0
1
0
0
4
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
1
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
2
0
0
1
2
0
0
4
0
0
0
0
1
2
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
3
0
0
2
0
0
1
0
0
1
1
0
1
0
2
2
2
0
0
0
0
0
2
0
0
0
0
0
0
4
0
1
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
3
0
0
1
0
4
0
0
0
2
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
2
0
2
0
1
0
1
0
2
0
0
0
0
2
2
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
2
0
2
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
2
5
2
0
1
0
0
0
0
0
1
0
1
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
3
0
0
0
1
0
0
0
2
0
0
0
2
1
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
1
1
0
0
2
0
0
0
1
3
0
0
2
0
7
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
3
3
0
0
2
2
0
2
0
0
0
2
1
0
0
1
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
3
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
1
1
4
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
3
0
0
0
0
0
2
2
0
0
2
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
1
1
0
0
2
0
0
1
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
2
0
0
0
0
1
2
0
0
1
0
3
0
0
0
0
1
5
0
0
1
0
1
3
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
3
1
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
2
0
0
0
4
0
0
1
0
0
2
0
0
0
2
1
0
1
0
2
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
3
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
2
0
0
0
0
1
0
3
0
0
1
1
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
1
4
1
0
0
1
0
2
0
1
0
0
2
0
1
0
0
0
0
3
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
1
0
0
0
1
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
3
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
5
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
2
0
2
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
3
2
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
3
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
2
0
2
0
2
0
0
0
0
2
0
1
1
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
3
2
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
3
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
4
0
0
0
2
0
0
2
0
0
0
0
0
6
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
2
3
1
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
1
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
2
0
1
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
5
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
4
1
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
2
0
1
2
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
3
0
0
0
0
1
1
0
1
0
1
0
2
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
2
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
1
2
3
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
4
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
3
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
7
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
1
2
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
6
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
3
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
5
0
0
0
0
0
0
1
1
0
0
0
0
2
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
3
2
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
2
0
2
0
0
4
0
0
0
0
0
3
2
0
0
0
1
1
2
0
2
2
0
0
0
0
1
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
2
1
1
0
0
0
0
0
0
0
0
1
1
0
1
3
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
1
0
1
1
1
0
1
2
0
0
2
1
0
0
2
0
0
1
0
0
0
1
0
0
0
0
3
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
1
1
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
2
0
1
0
0
0
0
8
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
2
1
0
0
1
0
1
0
2
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
1
0
0
0
1
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
4
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
14
0
0
0
0
1
0
1
0
0
0
2
0
1
0
0
2
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
3
0
0
1
0
0
2
1
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
3
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
1
1
0
1
0
2
0
0
0
0
1
0
0
0
0
2
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
2
1
1
0
1
0
0
1
0
0
1
2
0
2
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
1
0
3
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
2
1
0
3
1
2
2
2
0
0
0
0
1
2
1
2
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
2
0
1
2
0
0
0
2
0
0
0
4
2
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
2
0
0
2
2
2
0
0
1
0
1
1
4
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
5
0
0
0
0
1
1
2
0
2
0
0
0
0
0
1
0
4
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
1
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
7
0
0
0
0
1
1
2
2
1
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
5
1
2
2
0
2
2
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
1
0
0
2
3
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
2
4
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
2
2
0
2
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
2
2
0
2
0
0
1
2
0
0
0
1
0
0
1
0
2
0
5
0
0
0
0
0
0
0
2
3
1
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
3
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
6
0
0
0
0
0
0
3
0
5
0
0
5
0
0
0
1
0
0
0
0
0
0
0
0
4
0
1
0
0
2
0
0
0
1
0
2
2
1
0
0
2
0
1
0
2
0
3
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
3
0
1
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
1
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
2
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
3
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
2
0
1
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
1
1
0
0
2
0
0
0
0
0
1
0
2
0
0
1
0
2
0
2
0
0
4
0
0
0
0
0
0
0
2
0
1
1
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
2
0
0
2
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
6
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
1
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
3
0
0
37
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
5
2
1
0
1
0
0
3
2
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
5
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
1
0
1
0
2
1
1
2
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
5
0
0
3
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
3
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
1
2
0
0
0
0
4
0
0
1
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
1
0
0
0
0
2
1
0
0
0
0
1
0
2
1
0
2
0
0
1
1
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
5
1
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
1
0
2
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
3
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
3
2
0
0
0
0
0
0
1
2
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
2
1
0
0
0
2
0
1
1
3
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
6
0
0
1
0
1
0
0
0
0
2
3
1
0
2
0
0
2
0
2
1
2
0
0
0
0
0
0
1
1
0
0
0
3
1
0
0
0
0
0
2
0
0
0
2
0
2
2
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
2
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
3
0
0
0
0
0
1
0
0
0
1
0
0
0
0
4
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
3
2
1
0
2
0
0
0
0
1
0
0
0
0
0
2
0
1
2
1
0
0
0
1
0
0
0
0
0
0
2
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
1
2
2
0
0
2
0
0
1
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
1
0
0
0
1
0
0
1
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
2
0
0
0
2
0
2
2
1
0
0
0
1
0
2
2
0
1
0
0
0
1
0
0
16
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
1
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
1
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
1
1
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
1
3
0
0
0
0
0
0
0
0
1
1
4
0
0
0
3
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
5
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
2
0
0
3
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
3
0
1
0
0
0
1
0
3
4
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
2
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
4
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
1
1
0
2
0
0
2
0
0
1
0
3
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
2
1
0
0
0
0
0
0
0
1
0
2
2
0
0
1
3
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
1
0
3
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
2
0
3
0
0
0
2
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
1
1
3
2
1
1
0
0
0
0
0
0
1
2
2
1
0
0
1
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
2
1
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
5
0
1
0
0
1
0
0
0
0
0
0
9
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
3
4
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
3
1
1
1
2
0
0
1
0
0
0
2
0
1
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
4
0
0
3
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
2
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
2
0
0
0
2
0
0
0
0
0
2
0
1
0
0
1
0
1
3
0
0
0
0
0
2
1
0
0
1
0
2
0
0
0
0
0
0
1
0
2
1
0
0
1
0
0
0
0
0
1
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
4
1
0
0
0
0
0
0
0
1
3
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
1
0
0
0
1
2
0
2
0
0
0
1
1
0
0
0
2
0
0
0
1
0
0
3
0
0
0
0
0
0
2
1
3
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
10
0
0
2
0
1
1
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
1
0
3
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
1
0
1
0
2
0
1
0
0
0
3
0
0
1
1
0
0
0
0
0
2
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
4
1
0
0
0
2
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
1
1
1
0
0
3
0
1
0
0
0
0
1
2
0
0
0
3
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
5
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
1
0
3
0
0
0
0
13
0
2
2
2
0
1
0
0
1
1
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
1
2
4
0
0
3
6
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
3
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
1
0
1
2
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
2
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
1
1
0
0
0
1
0
0
0
1
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
1
1
0
2
0
0
0
2
0
0
3
0
0
0
0
2
0
1
0
0
2
4
0
0
0
0
2
1
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
7
0
0
2
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
1
2
1
6
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
5
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
6
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
3
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
1
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
2
1
2
0
0
0
4
0
1
0
0
0
0
0
0
1
0
0
3
0
1
2
0
0
0
0
0
0
1
0
0
0
0
1
2
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
3
0
1
0
0
4
0
8
0
0
1
0
0
0
2
0
0
0
0
1
0
1
2
0
0
0
0
0
1
0
0
1
0
2
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
2
2
2
1
2
0
2
1
0
0
0
1
0
0
1
0
3
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
3
2
0
2
0
0
0
0
2
0
0
2
0
5
1
0
0
0
0
0
0
0
0
1
2
4
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
2
2
1
0
0
4
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
3
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
3
0
2
2
1
0
0
0
2
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
1
0
2
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
1
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
3
0
2
0
0
0
1
1
2
0
0
4
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
1
1
1
0
0
0
0
4
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
1
0
2
0
1
0
0
2
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
1
0
0
1
1
0
0
0
1
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
1
0
1
2
0
0
2
2
0
2
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
3
2
0
0
0
0
0
1
0
0
0
1
1
2
0
0
0
0
0
2
0
0
2
1
3
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
7
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
2
2
1
0
0
0
0
1
3
0
0
0
0
2
0
0
0
1
5
0
1
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
2
1
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
2
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
3
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
3
0
0
0
2
0
1
0
0
2
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
1
0
1
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
1
0
0
7
0
0
0
4
0
1
2
0
0
2
0
0
2
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
8
0
2
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
0
0
1
2
1
0
1
1
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
2
1
0
2
0
2
0
0
0
0
0
1
2
0
0
0
2
0
1
0
0
2
1
2
0
0
0
0
0
0
0
0
0
4
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
2
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
3
2
0
0
0
2
1
1
0
0
0
0
1
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
5
0
0
3
0
0
0
0
0
3
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
1
0
2
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
6
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
2
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
1
2
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
1
0
0
2
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
4
0
0
0
3
0
0
0
1
0
0
0
0
2
0
1
2
2
4
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
1
1
0
1
1
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
2
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
1
0
0
2
7
1
0
0
0
2
0
0
0
0
0
0
0
2
0
4
0
0
1
1
0
0
3
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
2
0
0
2
3
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
2
0
0
1
0
0
0
0
1
2
0
0
0
0
1
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
1
0
5
0
0
1
1
3
0
0
0
0
0
0
0
0
4
0
2
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
1
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
3
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
2
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
0
0
2
0
0
0
0
1
0
1
2
0
0
0
2
0
1
1
0
0
0
0
2
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
24
1
0
4
0
2
0
0
0
1
0
0
0
2
0
0
1
2
0
0
0
0
0
1
0
2
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
2
0
2
0
2
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
2
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
2
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
2
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
2
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
3
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
1
1
2
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
3
0
0
1
0
0
0
0
2
3
0
0
2
0
2
0
1
0
0
1
0
0
0
0
2
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
1
0
0
3
0
1
0
0
0
0
1
0
0
3
2
0
0
0
0
1
0
3
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
2
0
3
0
0
0
1
0
0
0
0
2
0
0
0
2
0
3
2
0
2
1
0
0
0
0
0
1
1
0
1
0
0
1
3
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
1
1
0
0
3
3
0
0
0
0
1
3
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
5
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
1
0
2
0
0
0
1
0
0
0
4
0
0
1
2
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
1
0
0
0
0
2
0
1
0
0
0
2
1
2
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
2
0
0
0
0
0
2
0
2
0
0
0
1
0
2
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
1
0
0
2
2
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
1
0
0
1
0
1
0
1
1
0
4
0
0
0
0
2
2
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
2
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
4
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7
0
0
1
1
0
2
0
0
1
0
0
6
1
0
0
1
1
0
0
0
0
1
2
1
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
2
3
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
1
0
0
4
0
0
0
2
1
1
1
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
2
0
0
2
0
2
0
0
2
0
0
0
0
0
1
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
2
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
1
2
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
2
0
0
1
0
2
0
0
0
1
0
0
1
2
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
1
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
1
1
1
2
1
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
1
2
0
0
2
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
7
0
2
2
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
1
0
0
2
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
1
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
2
0
0
1
2
0
0
0
0
0
0
1
0
0
0
2
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
3
0
1
1
1
0
1
2
0
0
2
2
1
0
0
1
1
0
0
0
0
1
0
2
0
1
1
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
6
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
1
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
5
0
2
0
4
0
1
0
5
0
3
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
5
0
1
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
9
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
1
1
1
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
3
0
1
0
0
0
0
1
0
0
0
0
0
4
0
2
0
0
0
0
1
0
3
2
0
0
0
2
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
5
0
2
0
0
0
3
1
9
2
2
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
2
0
0
0
0
1
0
0
1
0
0
2
2
0
2
0
0
2
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
1
2
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
1
0
0
0
2
0
1
0
2
2
0
0
2
1
5
0
0
2
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
1
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
3
0
0
1
0
2
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
1
0
0
3
0
0
0
0
3
0
0
0
1
0
0
0
0
2
1
0
1
1
0
2
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
3
5
0
1
0
0
1
3
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
1
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
10
0
0
2
0
0
0
0
3
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
3
0
0
0
1
0
1
0
0
2
0
0
1
0
0
1
3
0
0
0
0
0
1
0
0
2
0
0
3
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
1
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
2
2
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
1
0
0
1
0
0
3
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
4
0
1
1
0
2
1
0
0
0
2
0
0
0
1
0
0
0
0
1
2
2
0
0
0
0
0
0
2
4
0
0
1
0
1
1
0
0
0
0
0
0
3
0
0
2
3
0
0
2
4
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
2
0
1
4
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
2
0
2
0
0
1
0
0
0
0
1
0
0
0
3
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
2
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
4
0
2
0
3
1
0
0
0
0
0
3
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
3
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
1
1
0
0
0
0
1
0
1
1
0
0
0
2
0
1
0
0
0
0
0
0
0
2
3
0
0
0
1
0
0
2
1
0
0
1
2
3
1
1
0
0
0
1
0
0
1
0
0
0
0
3
0
1
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
2
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
2
0
0
0
0
3
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
2
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
2
0
0
0
0
0
1
0
2
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
4
0
2
1
0
4
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
2
2
1
0
2
0
2
3
0
0
0
0
0
3
0
0
3
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
1
1
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
1
0
0
1
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
4
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
3
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
1
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
1
3
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
2
0
0
0
0
1
0
0
0
0
0
2
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
2
0
0
0
2
0
0
4
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
1
2
0
3
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
2
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
3
1
0
0
0
0
0
0
0
0
0
3
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
6
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
2
1
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
1
3
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
2
2
0
0
1
1
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
1
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
2
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
2
0
1
0
0
1
0
0
1
0
2
0
0
8
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
2
0
2
0
0
0
1
0
0
0
0
0
1
2
1
0
0
0
0
1
1
0
0
0
1
0
1
1
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
2
0
2
0
2
2
0
2
0
1
0
2
1
0
4
2
0
3
0
2
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
1
0
3
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
3
1
0
1
0
2
0
0
0
0
0
0
1
7
1
1
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
2
1
0
0
0
1
2
0
1
0
2
0
1
0
1
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
2
0
2
0
0
2
0
1
0
0
0
1
0
0
1
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
2
4
0
0
0
2
0
0
0
0
2
4
0
0
1
0
2
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
1
0
1
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
3
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
1
0
1
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
1
2
6
0
3
0
2
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
1
2
0
0
0
3
2
0
0
0
0
0
2
0
0
2
1
0
0
1
0
0
0
0
0
1
1
2
2
0
1
0
0
0
1
0
0
0
0
1
3
0
0
0
0
1
0
1
0
0
0
2
0
0
1
0
1
2
0
1
0
0
0
0
0
0
0
1
2
0
1
1
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
2
2
2
0
0
1
1
0
0
2
1
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
2
2
3
0
2
2
0
0
0
0
0
0
0
0
0
1
2
4
0
0
2
1
0
1
0
0
0
0
1
0
2
4
0
0
0
8
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
1
0
0
1
0
0
0
3
0
3
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
2
1
0
0
0
3
0
0
0
0
0
0
7
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
3
0
0
0
0
0
3
2
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
5
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
1
0
0
0
2
1
0
0
0
0
0
0
1
0
0
3
0
0
0
0
2
0
0
0
3
2
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
2
1
0
0
1
2
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
2
0
1
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
2
0
1
0
0
0
0
0
2
3
0
0
2
0
0
0
0
0
1
0
0
2
0
2
1
1
0
4
0
0
0
1
2
0
0
0
1
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
2
0
1
0
2
0
0
0
0
2
0
0
0
0
0
1
0
5
0
0
0
0
2
0
0
0
0
0
1
0
8
2
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
7
2
0
1
0
1
0
2
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
2
2
0
2
2
0
0
0
0
0
2
1
1
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
1
1
2
0
0
1
2
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
4
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
2
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
3
0
1
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
1
0
0
2
3
0
1
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
3
0
0
0
0
1
2
0
0
0
1
0
0
1
0
0
0
0
2
0
2
0
0
2
0
1
0
0
0
1
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
1
0
0
0
1
3
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
2
0
0
2
0
2
0
0
1
2
2
0
2
2
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
1
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
4
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
2
0
2
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
1
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
4
0
2
2
0
0
1
0
0
0
0
0
0
2
0
0
3
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
3
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
2
1
0
2
0
0
0
0
4
0
0
0
1
0
1
0
0
0
1
1
1
0
3
0
3
0
2
0
0
0
0
4
0
0
0
0
0
0
1
2
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
5
0
0
2
0
0
0
0
0
2
1
0
2
0
0
1
0
0
2
2
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
1
0
0
0
8
1
0
0
0
1
0
0
1
2
0
0
0
1
0
0
0
0
0
1
0
1
0
1
1
0
1
1
0
0
2
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
1
0
0
0
1
0
0
0
6
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
1
0
1
0
0
0
1
0
0
2
1
0
0
1
0
0
0
5
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
2
0
1
2
1
1
0
0
0
0
0
0
0
0
0
0
0
8
0
0
0
0
0
1
1
1
0
1
0
0
2
0
1
1
1
2
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
1
0
1
0
0
2
0
0
2
1
0
0
0
0
0
0
2
0
1
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
1
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
2
2
2
0
0
0
6
0
1
0
0
1
0
2
2
0
0
1
0
0
1
2
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
4
2
0
0
0
0
3
0
0
0
2
2
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
2
0
2
0
2
0
1
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
1
1
0
0
0
0
2
1
0
0
1
0
0
0
0
1
1
0
0
0
2
2
0
0
3
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
2
0
1
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
3
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
2
0
0
3
1
0
0
0
0
2
3
2
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
2
0
0
0
2
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
1
1
2
3
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
2
1
0
2
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
2
0
2
0
0
1
2
1
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
2
0
0
1
0
0
1
1
1
0
0
0
0
2
0
0
0
1
2
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
1
1
0
2
0
1
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
2
1
0
1
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
2
2
3
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
1
5
0
0
0
0
0
0
1
0
0
2
4
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
3
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
1
2
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
7
0
2
0
0
1
0
0
0
0
0
2
0
1
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
3
0
0
0
0
1
1
0
0
0
0
3
1
0
2
2
0
1
0
0
0
0
0
0
0
3
1
1
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
3
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
2
2
1
0
0
0
0
0
1
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
4
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
1
0
1
0
2
0
0
0
0
0
0
1
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
3
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
1
0
1
0
2
1
2
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
2
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
2
1
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
2
0
1
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
6
0
2
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
2
0
1
2
0
0
0
0
2
1
0
0
0
6
0
3
0
3
2
0
0
1
0
0
0
0
0
2
0
2
0
0
0
2
1
2
0
0
1
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
1
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
2
0
4
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
2
0
1
2
0
0
0
0
0
4
0
0
0
3
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
2
3
0
0
1
0
0
0
1
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
4
0
0
0
0
0
0
3
0
0
0
0
2
1
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
1
0
0
2
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
4
0
0
2
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
2
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
2
1
0
2
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
3
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
1
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
2
2
1
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
2
0
0
0
5
3
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
2
1
0
0
2
1
0
0
3
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
8
0
2
0
2
3
1
0
0
0
0
0
1
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
3
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
3
0
1
1
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
1
0
1
1
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
1
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
2
1
0
0
4
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
4
0
0
1
5
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
2
0
1
0
1
0
0
0
0
1
3
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
3
0
0
1
0
0
0
0
2
0
0
0
1
0
2
0
2
2
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
5
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
1
1
0
0
0
0
0
0
2
0
1
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
1
0
3
0
0
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
2
1
0
1
0
0
2
0
0
0
2
0
0
1
0
0
0
1
0
0
1
0
2
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
1
1
0
2
9
0
0
0
0
0
2
0
7
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
1
0
0
0
4
2
0
1
1
0
0
0
0
1
2
0
0
2
0
0
0
0
0
5
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
3
2
0
0
1
0
2
0
0
0
2
1
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
1
0
1
0
0
0
2
0
0
2
2
0
0
0
2
0
0
1
0
0
0
6
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
3
1
1
1
2
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
2
2
0
2
1
0
0
1
0
1
0
0
2
1
0
0
0
1
1
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
2
0
0
0
1
0
0
2
0
1
6
0
0
0
5
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
3
1
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
1
1
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
4
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
3
0
0
2
0
2
1
1
0
0
0
1
0
2
0
0
0
0
1
0
2
2
0
2
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
2
1
1
0
2
2
3
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
1
0
2
0
0
0
1
0
0
0
1
2
0
1
1
0
0
2
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
2
0
1
0
4
0
0
0
0
1
2
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
3
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
2
0
1
3
1
0
0
0
1
0
0
1
3
1
1
1
1
2
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
3
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
3
0
0
0
0
1
0
0
1
2
0
0
0
0
1
1
0
0
2
2
0
0
0
3
1
0
0
0
1
0
1
2
1
0
0
2
0
1
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
2
0
0
0
1
2
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
2
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
1
0
1
0
0
2
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
1
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
1
2
2
0
0
0
2
0
1
0
0
0
0
2
0
0
0
2
2
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
2
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
2
0
0
3
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
1
0
2
0
3
0
0
0
2
3
1
0
0
2
0
1
0
0
1
0
0
0
0
0
0
3
0
0
0
0
2
0
1
0
0
1
0
0
2
0
0
2
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
2
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
2
0
0
0
1
1
0
0
0
0
0
1
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
1
3
0
0
0
0
1
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
1
1
0
0
0
0
0
3
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
1
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
2
2
0
2
0
2
0
0
2
0
0
1
2
0
1
2
0
1
0
0
1
2
0
0
1
0
2
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
2
2
3
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
3
0
1
0
2
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
1
2
2
1
1
0
0
2
0
0
2
0
0
1
2
0
0
2
1
0
1
0
0
3
1
0
1
0
2
0
0
0
4
2
0
0
0
2
0
0
0
0
1
0
0
0
0
4
0
0
0
0
1
0
0
0
2
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
2
2
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
3
0
1
0
0
0
4
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
4
0
0
0
0
5
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
1
8
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
1
1
0
2
0
0
3
0
2
0
0
1
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
5
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
2
0
0
3
3
0
0
2
0
0
2
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
6
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
3
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
1
1
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
1
0
0
0
0
1
0
1
0
0
0
3
2
0
0
0
3
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
3
0
0
0
0
0
3
0
0
1
0
0
3
0
0
0
1
0
0
3
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
2
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
1
2
0
1
0
0
0
0
0
0
1
6
2
1
0
1
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
5
0
1
0
0
3
0
2
0
0
0
0
0
1
2
1
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
1
0
0
0
0
2
1
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
1
0
2
0
0
0
0
0
0
0
2
2
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
1
0
0
1
0
0
0
0
0
2
2
0
0
2
0
0
0
3
0
1
0
2
0
0
0
2
2
0
0
0
0
0
1
2
1
1
0
0
0
3
1
1
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
2
0
1
0
0
0
0
2
0
4
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
3
1
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
8
1
0
0
2
2
0
0
1
0
1
0
3
0
0
0
2
0
2
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
2
1
0
1
0
3
0
0
0
2
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
1
2
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
4
0
0
0
0
3
0
0
2
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
1
0
2
2
2
0
0
1
0
0
0
2
1
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
2
0
0
1
0
2
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
2
0
0
2
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
1
2
3
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
1
0
4
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
2
1
1
0
2
2
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
6
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
1
4
1
0
0
2
0
0
0
1
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
1
0
0
0
3
0
0
2
1
2
0
0
0
0
0
0
2
0
2
4
0
0
0
0
1
0
3
0
1
0
0
0
0
2
0
2
0
0
0
2
2
0
1
0
0
0
2
0
1
0
0
1
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
1
3
0
1
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
2
0
0
0
1
0
2
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
3
0
1
0
2
1
2
0
1
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
2
0
0
2
0
0
1
2
0
0
0
1
2
0
1
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
2
0
0
0
0
2
0
0
1
0
0
2
0
0
0
2
2
0
1
0
0
0
0
4
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
7
1
0
2
0
0
2
1
1
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
1
2
0
0
0
2
2
2
0
0
0
0
2
0
2
3
1
0
0
1
1
0
0
0
1
0
0
0
1
2
0
1
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
1
0
2
0
0
0
0
2
1
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
1
2
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
2
0
0
1
0
0
1
0
0
0
0
1
2
0
0
2
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
2
4
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
5
0
2
0
0
0
0
1
0
0
0
2
1
0
1
1
0
0
0
0
1
1
2
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
3
0
0
1
3
1
0
1
0
0
1
0
0
0
0
2
0
0
0
0
1
1
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
8
2
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
2
0
2
0
0
1
0
0
2
0
0
1
2
0
0
0
3
0
0
2
0
2
3
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
4
1
2
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
1
1
0
4
0
0
2
0
1
0
0
0
0
0
0
1
2
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
1
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
3
1
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
3
2
2
0
0
0
0
0
0
2
2
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
2
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
1
0
0
0
0
2
0
0
1
0
0
1
0
4
1
1
1
0
1
0
0
3
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
4
0
0
0
0
6
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
5
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
1
2
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
2
1
1
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
3
0
0
0
1
0
0
1
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
1
1
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
3
3
0
0
0
0
0
0
2
1
0
0
1
0
0
0
1
0
1
5
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
2
0
2
0
0
0
0
2
0
0
0
0
2
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
2
2
2
0
0
0
1
2
2
1
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
3
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
2
0
1
1
0
2
0
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
2
2
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
3
0
2
4
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
2
2
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
5
0
0
0
0
0
0
2
0
0
0
2
0
1
5
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
5
0
2
0
0
0
0
0
1
0
0
0
0
4
0
0
2
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
2
2
0
0
1
0
0
0
1
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
3
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
2
1
1
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
1
3
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
2
0
0
1
3
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
1
2
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
1
0
0
1
0
0
2
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
1
2
2
0
0
0
1
0
0
2
0
0
1
2
0
2
2
0
1
0
3
1
2
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
2
2
2
0
0
0
0
0
4
0
0
2
0
0
2
0
0
0
2
2
2
3
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
2
1
2
0
0
2
0
0
0
7
0
0
2
2
2
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
1
1
0
2
0
3
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
1
2
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
1
2
1
0
0
0
0
2
0
0
0
0
0
2
0
2
2
0
2
2
0
2
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
3
0
0
1
0
2
2
1
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
3
0
0
0
0
2
1
4
0
0
0
2
0
0
1
0
0
0
0
0
2
2
0
1
0
2
0
0
0
0
1
0
4
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
2
2
0
0
2
0
0
2
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
1
0
1
2
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
1
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
3
0
0
0
0
1
0
1
0
2
0
0
0
1
2
2
2
2
0
3
0
0
0
2
0
0
0
0
0
1
1
0
0
0
1
0
0
0
2
0
0
0
0
0
2
3
0
2
0
0
3
0
1
1
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
2
2
0
0
7
0
3
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
1
1
1
0
1
0
0
0
0
0
0
3
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
3
0
2
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
1
1
0
1
0
2
0
2
0
2
0
0
0
0
0
0
0
2
0
1
1
0
1
0
1
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
1
0
0
8
0
0
0
2
2
1
0
1
1
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
2
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
2
4
2
1
0
0
0
0
0
0
0
0
0
1
0
6
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
8
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
3
1
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
2
0
2
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
5
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
8
0
1
0
0
3
0
0
0
0
0
1
0
2
2
0
0
0
1
0
0
0
2
2
0
2
0
0
2
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
2
1
0
1
4
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
2
1
0
3
0
0
1
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
3
0
0
1
2
0
0
0
0
0
0
2
2
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
2
0
2
0
2
1
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
5
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
2
0
0
0
1
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
3
0
0
2
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
5
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
0
0
2
0
0
0
0
2
0
0
0
0
4
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
2
0
2
0
0
0
6
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
4
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
4
0
0
2
1
0
3
0
1
0
0
2
1
1
0
1
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
2
2
0
0
0
0
0
2
0
0
1
1
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
1
0
3
0
0
2
0
1
0
0
0
1
0
0
0
0
2
1
0
2
2
0
0
0
2
0
0
0
0
1
2
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
2
2
0
1
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
2
2
1
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
1
0
1
0
3
0
1
1
1
0
0
0
0
5
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
3
0
0
0
0
0
0
0
0
0
6
0
0
2
0
0
2
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
1
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
3
0
3
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
4
3
2
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
1
1
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
1
0
0
0
0
0
5
0
0
0
0
0
2
0
2
0
1
0
1
0
0
2
0
2
0
0
2
0
0
2
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
2
0
1
3
0
0
1
0
0
0
0
0
0
1
0
0
1
2
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
1
2
0
1
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
2
0
0
0
0
3
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
7
0
2
0
3
0
0
0
1
0
0
2
1
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
2
1
0
0
2
0
2
0
0
2
0
0
0
2
0
0
0
2
0
0
1
1
0
0
0
4
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
2
10
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
2
2
2
0
0
0
0
2
0
2
0
1
0
5
0
0
0
1
1
0
1
0
0
0
0
1
3
2
0
2
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
1
3
1
0
0
10
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
6
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
2
0
0
2
0
0
2
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
3
0
0
0
1
0
0
0
0
0
0
1
0
4
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
2
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
1
0
0
2
0
2
0
0
0
0
0
0
3
0
0
0
0
0
1
0
3
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
1
1
2
0
0
0
0
2
0
1
2
1
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
2
0
0
3
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
1
0
1
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
1
1
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
3
0
0
1
1
2
0
0
0
0
1
1
1
2
1
0
2
0
0
0
0
0
0
2
0
1
0
0
5
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
1
0
0
0
0
0
1
1
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
2
1
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
3
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
5
2
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
3
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
1
0
0
2
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
3
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
3
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
2
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
2
2
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
1
1
0
0
0
4
0
2
0
0
0
2
7
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
1
1
2
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
2
0
2
0
0
0
3
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
3
0
3
0
0
0
0
1
0
0
4
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
3
0
3
0
0
1
0
0
0
0
0
0
0
0
2
0
7
0
1
1
0
0
0
0
2
2
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
2
2
0
0
1
0
0
0
2
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
3
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
2
0
1
0
0
0
0
2
0
0
0
1
0
0
3
0
2
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
1
0
0
3
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
3
2
0
0
0
0
0
1
1
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
2
0
0
0
0
0
0
0
0
0
5
0
1
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
7
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
6
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
1
0
0
1
0
0
1
2
0
1
2
1
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
2
0
1
1
0
2
0
0
1
0
0
0
0
1
4
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
2
0
2
0
1
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
1
0
0
2
0
2
0
0
2
0
0
0
1
0
1
0
0
2
0
0
0
0
1
3
0
0
0
3
0
0
0
0
0
0
0
0
0
1
1
2
0
0
2
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
1
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
4
0
1
0
0
0
4
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
2
2
3
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
1
11
0
0
0
3
0
0
0
3
0
0
0
1
0
0
0
0
1
0
0
2
1
1
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
2
3
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
2
1
4
0
0
0
0
0
4
0
0
2
0
2
2
0
1
0
0
0
0
0
0
0
0
9
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
3
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
1
0
5
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
1
2
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
2
2
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
1
2
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
11
0
1
0
0
0
1
1
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
1
1
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
1
2
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
3
0
0
1
0
0
0
0
0
0
0
2
0
0
6
0
0
3
0
0
0
0
0
0
0
0
0
2
3
0
0
0
4
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
2
1
2
1
0
0
0
0
3
0
0
0
0
2
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
1
0
0
2
1
1
0
0
0
0
0
0
1
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
2
2
0
1
1
0
0
0
1
0
0
0
0
1
0
0
4
1
0
0
0
0
0
0
0
0
2
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
2
1
1
2
0
0
3
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
2
6
1
0
0
0
2
2
0
2
1
0
0
0
0
0
0
1
0
2
0
0
1
1
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
2
3
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
2
1
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
9
0
2
0
0
4
0
0
0
0
4
3
1
0
0
0
0
0
0
1
0
2
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
3
0
0
1
0
0
0
0
0
0
3
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
1
1
0
3
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
2
0
0
1
0
0
0
2
0
1
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
4
0
0
0
0
2
2
4
0
0
4
0
1
3
0
1
0
0
2
2
3
0
1
2
0
0
0
0
2
1
0
0
2
0
1
0
0
0
0
0
0
2
0
3
0
0
0
1
1
0
0
2
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
5
2
3
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
5
2
0
0
1
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
4
0
0
1
0
3
2
1
0
3
1
1
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
2
0
0
0
0
0
1
5
1
0
2
1
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
9
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
3
0
0
2
2
1
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
4
0
0
0
2
0
1
2
0
2
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
3
0
0
1
0
0
0
2
3
0
3
0
0
0
0
0
0
0
2
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
1
1
0
3
1
1
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
2
0
0
0
0
2
2
0
0
1
1
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
1
1
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
2
0
4
0
0
2
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
2
0
1
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
2
1
3
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
3
0
0
3
0
0
1
0
0
1
0
0
4
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
2
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
3
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
1
0
1
0
0
1
0
6
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
2
0
1
0
0
2
0
2
1
0
0
0
0
0
0
2
2
1
0
0
2
1
1
0
0
0
7
0
3
0
1
0
0
2
0
0
0
1
2
0
0
0
2
0
2
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
4
0
3
1
0
2
0
2
0
0
0
1
0
1
1
1
0
0
0
2
2
0
0
2
0
2
0
0
0
0
1
0
3
0
1
1
0
0
0
0
0
2
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
10
1
0
0
0
1
0
0
0
0
0
1
1
0
2
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
2
3
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
1
0
1
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
2
0
0
0
0
1
0
0
3
0
1
0
0
0
2
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
1
0
0
0
0
0
1
0
0
6
1
3
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
1
1
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
1
0
0
1
2
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
12
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
1
1
1
0
4
0
0
0
0
0
0
0
1
4
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
1
0
1
2
0
2
0
0
0
2
1
0
1
0
0
1
0
0
2
2
1
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
2
2
0
0
0
2
5
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
2
0
2
0
0
1
0
2
0
0
4
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
2
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
3
4
0
0
1
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
5
0
0
1
2
2
0
0
0
0
0
0
1
0
0
2
3
3
0
3
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
2
1
0
2
0
0
0
0
0
3
0
2
2
0
0
1
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
3
1
1
3
2
0
3
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
2
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
15
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
3
1
2
2
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
3
3
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
5
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
1
0
0
0
0
2
0
2
0
2
2
0
0
0
0
1
0
2
3
1
0
0
0
3
0
0
1
0
0
0
0
0
2
2
0
2
0
0
1
0
3
2
0
0
0
2
0
2
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
6
2
0
0
0
1
0
2
2
0
0
2
0
1
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
2
0
0
0
0
4
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
5
1
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
2
4
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
2
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
3
1
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
2
0
0
0
2
3
0
0
0
2
0
1
0
3
2
0
1
1
0
0
6
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
3
0
0
0
2
0
2
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
2
0
2
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
1
0
0
0
2
0
1
2
0
0
0
0
0
2
1
3
0
0
0
0
0
2
1
0
1
0
0
0
0
0
2
1
2
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
1
0
3
0
0
0
1
0
0
0
1
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
2
2
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
2
0
0
1
2
0
2
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
4
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
2
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
2
0
2
0
2
1
0
0
0
0
0
0
2
3
3
0
2
0
0
0
2
2
0
0
0
1
0
0
0
1
2
1
0
2
0
1
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
4
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
2
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
2
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
1
2
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
1
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
3
1
1
0
2
0
1
5
0
0
0
0
0
0
4
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
1
1
3
1
0
1
0
0
0
1
1
0
0
0
0
2
0
0
1
0
0
2
0
1
0
0
2
1
0
0
0
0
0
1
0
0
1
1
0
0
0
2
1
2
0
0
0
0
0
0
0
3
2
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
3
0
0
2
0
3
0
0
1
0
0
2
2
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
1
0
2
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
1
0
2
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
2
0
0
2
0
2
0
0
0
1
4
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
1
1
0
0
3
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
1
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
3
2
2
0
2
0
0
0
1
0
0
0
0
0
0
2
1
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
10
0
0
0
1
3
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
2
0
0
0
1
0
0
2
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
1
0
1
0
0
1
1
0
0
2
0
0
0
2
0
4
1
1
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
2
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
1
0
2
1
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
3
0
2
0
5
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
3
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
3
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
2
0
2
0
2
1
0
0
1
0
0
2
2
0
3
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
1
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
3
0
4
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
2
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
2
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
1
1
0
0
2
5
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
2
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
3
0
0
2
2
0
0
0
0
1
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
1
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
1
2
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
1
0
0
2
0
2
3
0
0
0
3
0
0
0
2
0
2
4
0
0
2
0
0
1
2
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
1
0
0
0
0
3
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
3
0
0
0
0
1
1
2
2
2
3
0
0
0
0
1
0
0
0
2
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
1
0
0
0
2
0
0
5
1
0
0
0
0
0
0
0
0
0
0
0
2
4
2
0
0
1
0
0
2
0
0
1
0
0
0
1
1
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
2
2
0
2
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
2
1
0
2
0
2
0
2
0
0
0
0
3
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
2
1
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
3
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
1
2
0
1
0
0
1
0
0
0
2
3
0
0
2
0
3
1
0
0
0
0
2
0
0
0
0
6
0
0
1
2
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
4
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
1
0
1
0
0
0
0
0
2
0
4
1
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
2
1
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
1
2
2
0
2
0
6
2
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
2
4
0
0
2
0
0
2
0
0
0
0
0
0
0
5
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
3
0
0
0
1
1
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
1
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
2
2
0
3
2
0
0
0
0
0
0
0
0
2
0
0
5
0
0
0
0
0
0
2
0
0
0
0
4
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
2
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
3
0
0
2
2
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
1
0
4
1
0
2
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
1
0
3
0
0
0
0
0
0
0
7
0
0
0
3
2
0
0
0
0
0
0
1
2
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
3
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
1
2
1
0
0
0
2
0
0
1
0
1
0
0
1
0
0
0
1
2
0
0
2
0
0
2
0
0
2
0
0
0
1
0
0
1
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
1
0
2
2
0
2
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
2
0
0
2
0
0
0
0
2
0
0
2
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
2
2
0
0
0
0
0
0
0
2
0
0
3
0
3
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
7
0
0
0
2
0
0
0
0
0
0
6
0
0
0
2
0
2
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
2
2
0
0
0
0
0
1
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
1
2
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
3
1
1
0
0
0
0
0
2
0
0
0
2
0
0
1
3
0
1
1
0
1
2
0
0
0
0
0
1
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
6
2
0
1
0
0
0
0
0
1
2
0
2
4
2
0
0
0
0
2
0
0
0
1
4
0
1
0
0
0
0
0
1
0
1
0
1
0
0
3
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
1
0
2
1
0
0
0
0
5
0
0
4
0
0
0
0
0
8
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
2
0
0
1
0
1
0
0
0
2
0
2
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
2
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
1
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
2
0
1
8
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
2
0
1
0
0
0
1
2
0
0
0
0
0
0
7
2
0
0
0
0
2
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
3
0
0
0
0
0
0
5
0
0
0
0
0
1
0
4
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
3
0
0
1
0
0
0
0
0
1
0
2
5
0
0
0
0
1
0
2
0
0
0
3
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
2
0
0
2
1
0
1
0
2
0
9
0
0
2
0
0
0
0
0
2
0
1
2
0
0
0
1
0
2
0
0
0
0
0
2
0
1
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
1
0
2
0
0
0
3
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
2
0
6
0
0
1
0
0
0
2
0
0
0
0
0
2
1
2
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
1
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
2
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
3
2
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
1
2
0
0
1
0
2
1
0
2
0
2
0
0
1
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
2
0
2
1
0
0
1
0
0
1
0
0
1
0
2
0
0
2
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
1
1
0
1
2
0
3
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
2
0
1
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
1
0
0
2
0
0
0
1
0
1
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
2
1
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
1
0
1
0
0
2
0
0
1
0
0
2
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
1
0
1
0
2
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
1
1
0
5
3
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
9
1
0
2
2
1
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
3
0
3
1
2
0
0
0
0
3
0
0
0
0
1
0
0
0
2
2
0
0
2
0
0
0
1
2
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
6
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
3
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
6
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
2
2
6
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
3
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
8
2
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
2
5
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
4
2
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
1
0
0
1
0
0
4
0
0
0
0
0
3
0
0
0
0
0
1
0
0
3
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
1
0
0
1
0
0
0
0
1
0
0
3
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
1
0
0
1
0
1
2
0
0
0
4
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
3
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
2
0
0
2
1
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
2
4
0
0
2
0
0
0
1
0
1
1
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
2
1
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
3
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
2
0
0
0
0
0
2
0
0
0
3
1
0
3
2
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
1
0
0
0
2
0
1
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
2
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
2
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
6
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
3
0
1
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
2
2
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
3
0
0
0
0
2
1
0
0
1
0
0
2
0
2
1
0
0
0
0
0
0
0
0
3
0
1
0
0
0
1
0
6
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
1
0
0
2
0
2
4
2
1
2
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
3
0
0
0
0
1
0
0
0
0
0
1
0
1
1
1
1
0
1
0
2
0
0
0
0
0
1
0
1
0
1
1
2
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
1
0
0
0
1
1
0
2
0
0
0
2
0
2
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
2
2
1
0
0
0
0
0
0
0
0
2
1
0
0
3
0
0
1
0
1
0
0
2
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
3
0
3
0
2
2
0
0
0
0
0
3
0
0
4
0
0
2
0
2
0
0
1
0
3
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
3
1
2
2
0
0
0
1
0
0
0
0
0
2
0
2
0
1
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
2
0
0
1
0
1
0
0
1
0
0
0
0
0
0
2
2
0
1
2
0
0
4
1
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
3
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
2
2
0
3
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
1
2
0
0
3
2
1
0
2
0
0
1
0
0
2
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
2
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
3
0
0
0
1
0
1
0
0
0
0
2
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
5
2
0
1
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
1
0
0
0
0
0
0
1
2
2
0
0
3
1
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
1
0
2
0
2
0
0
1
1
1
2
2
0
5
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
2
0
2
0
0
0
0
1
2
0
0
0
0
6
0
1
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
1
1
0
1
2
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
3
0
3
1
0
1
0
0
0
0
1
0
0
0
1
1
0
0
1
2
0
0
0
0
0
0
0
1
0
0
2
0
0
1
2
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
3
0
0
2
0
0
0
0
0
0
1
0
1
0
1
0
0
2
1
0
1
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
3
0
2
0
0
0
0
1
0
0
0
1
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
4
0
0
0
1
2
0
0
0
0
0
0
5
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
1
0
0
4
0
0
0
0
1
1
1
0
0
2
0
0
0
0
1
0
0
0
0
0
1
2
3
0
0
0
0
0
0
2
1
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
2
0
3
0
0
0
0
0
2
0
0
2
1
4
0
0
0
0
3
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
1
8
0
0
0
0
0
0
0
0
3
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
2
0
0
2
0
2
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
2
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
1
0
1
0
0
0
0
0
0
1
4
1
0
0
0
0
1
0
0
1
3
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
1
2
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
7
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
2
0
0
1
0
0
0
1
0
3
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
2
0
0
0
0
2
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
4
1
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
6
0
0
1
1
0
0
0
1
2
0
2
0
2
0
0
0
2
1
1
0
0
0
1
0
2
1
0
0
0
0
0
2
1
0
0
0
1
0
0
0
4
2
0
0
0
2
0
0
1
0
0
0
1
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
3
0
0
0
0
0
0
2
2
0
0
0
0
1
1
2
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
2
0
1
0
0
1
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
3
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
2
0
0
0
1
0
2
0
1
0
0
1
0
0
0
2
0
2
1
0
0
0
1
0
0
0
1
2
0
0
0
0
1
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
3
0
0
0
4
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
3
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
2
1
2
0
2
2
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
3
0
0
0
2
3
0
1
0
2
0
0
1
0
1
0
2
2
0
2
0
0
0
0
0
0
0
2
0
0
2
1
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
3
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
3
0
1
0
4
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
2
2
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
1
2
0
0
0
0
0
3
0
3
0
2
0
1
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
3
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
3
1
0
0
0
0
0
1
2
1
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
2
0
1
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
2
2
1
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
2
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
2
0
2
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
2
0
0
2
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
3
2
1
2
2
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
6
4
6
0
1
1
0
0
0
0
0
0
0
0
0
1
2
0
1
0
1
1
0
0
0
0
1
0
0
2
0
0
0
1
1
2
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
1
0
1
0
0
0
0
0
0
2
2
5
0
2
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
2
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
1
0
0
1
0
4
0
0
0
1
2
0
0
0
0
1
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
4
0
2
0
6
0
0
0
2
0
2
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
1
5
0
2
1
0
2
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
1
2
0
0
0
0
1
1
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
1
1
0
2
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
5
1
0
1
0
0
0
0
0
0
0
2
0
3
2
1
0
1
0
0
0
0
0
0
2
0
2
0
1
2
0
1
0
0
0
1
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
2
2
2
0
2
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
1
2
0
5
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
1
2
0
0
1
0
0
0
0
6
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
1
1
1
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
3
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
3
0
0
1
0
1
0
0
0
1
0
2
0
2
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
2
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
5
3
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
3
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
3
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
2
1
1
0
0
1
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
1
2
0
0
2
0
1
0
0
0
0
0
0
3
1
0
0
3
0
2
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
3
1
0
0
0
1
0
2
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
3
0
0
0
0
0
1
0
1
0
0
0
1
0
6
1
1
1
0
0
2
0
0
0
2
0
0
0
0
0
1
0
1
2
1
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
2
0
1
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
2
0
0
1
3
0
4
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
2
0
0
1
2
0
0
2
0
0
1
0
0
0
0
0
0
0
1
3
0
1
2
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
2
2
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
3
0
2
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
3
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
2
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
1
0
0
2
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
5
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
2
1
0
0
3
0
1
0
0
2
2
2
0
1
1
1
0
0
0
0
0
0
5
0
0
0
1
2
0
0
1
0
2
2
0
0
0
0
2
0
2
0
1
2
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
1
0
0
2
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
5
0
0
0
0
0
1
0
0
0
3
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
2
0
2
0
1
0
1
0
0
0
1
0
1
4
1
0
2
8
0
1
2
0
0
1
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
2
3
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
5
0
0
0
0
2
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
2
1
1
1
0
0
0
0
0
0
0
0
1
2
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
4
0
0
2
1
0
0
0
0
0
0
1
0
0
4
2
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
2
0
0
0
1
0
0
0
0
2
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
1
2
0
0
0
1
2
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
1
1
1
0
0
0
1
1
1
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
2
0
0
2
0
0
0
0
2
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
1
0
0
0
2
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
3
2
0
0
0
0
0
0
0
0
0
0
0
2
0
3
3
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
1
2
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
3
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
2
1
1
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
2
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
1
1
2
0
0
0
0
2
1
0
0
2
0
3
2
1
0
2
0
0
0
0
0
0
0
0
0
0
3
1
4
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
2
1
0
0
0
3
1
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
3
0
1
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
2
1
0
0
0
2
0
2
2
0
4
0
1
0
2
0
0
0
0
2
0
0
0
3
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
2
2
0
0
0
2
0
0
0
0
2
0
1
1
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
2
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
6
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
1
0
2
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
8
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
2
0
0
0
0
1
1
0
2
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
2
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
5
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
8
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
1
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
2
0
1
0
0
1
1
1
0
0
2
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
2
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
2
0
2
0
2
0
0
0
0
0
5
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
1
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
2
0
0
0
1
2
0
0
0
0
2
2
0
0
1
0
0
0
0
0
2
2
0
1
0
0
0
0
0
2
2
5
0
0
0
0
0
0
0
0
0
2
0
3
0
0
1
0
0
0
0
0
2
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
4
2
1
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
1
1
1
3
0
0
0
1
0
0
1
2
0
1
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
1
0
0
3
1
0
0
0
0
1
1
0
2
0
0
0
0
1
0
2
3
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
1
0
0
0
2
1
0
2
4
0
0
2
0
1
0
2
0
0
0
1
0
2
1
0
0
0
0
0
0
0
2
0
1
0
1
0
0
1
3
0
0
0
2
0
0
1
5
2
0
0
1
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
5
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
1
3
0
1
0
2
0
0
0
1
2
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
2
0
0
0
2
0
0
2
0
1
1
0
0
2
1
0
0
0
12
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
1
2
0
1
0
0
0
0
0
0
0
3
0
3
0
0
0
0
0
0
0
0
0
4
0
2
0
3
0
0
0
0
0
0
0
1
3
4
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
3
0
0
0
1
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
2
0
2
0
0
0
1
2
0
0
0
0
2
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
3
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
2
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
1
0
0
0
5
0
0
1
3
1
0
0
1
2
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
2
0
0
1
0
0
0
0
0
1
0
0
2
1
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
7
1
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
1
1
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
2
1
0
0
0
0
0
1
2
0
0
2
0
0
0
1
0
0
0
0
4
2
0
0
0
0
0
0
0
4
0
0
0
0
0
0
2
2
0
1
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
2
0
0
3
0
0
3
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
1
0
0
0
0
1
0
0
2
0
1
1
0
1
0
0
0
0
1
2
0
0
0
1
4
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
1
0
0
1
0
2
0
1
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
2
1
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
4
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
1
1
2
0
1
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
3
0
0
0
0
2
1
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
1
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
2
0
1
2
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
8
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
4
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
2
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
1
1
0
2
0
1
2
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
2
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
4
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
3
0
0
1
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
2
1
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
5
0
0
2
1
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
1
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
1
0
1
0
0
0
0
3
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
3
5
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
3
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
2
0
0
0
2
0
0
1
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
2
3
3
1
1
2
0
0
0
5
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
3
0
3
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
5
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
4
2
0
0
0
2
0
3
0
0
1
0
0
1
0
0
0
4
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
2
0
0
1
0
2
0
2
2
0
0
0
0
0
0
2
0
0
1
1
2
0
1
1
0
3
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
5
2
0
0
0
3
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
7
0
0
0
2
0
0
0
2
0
0
0
0
5
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
2
0
4
0
0
1
0
0
0
1
1
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
1
2
0
0
1
0
0
0
0
2
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
1
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
4
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
2
0
0
0
0
3
0
0
0
0
0
2
0
2
1
0
1
0
0
2
1
0
0
0
0
0
0
2
2
2
0
0
0
1
0
5
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
3
2
1
2
0
2
3
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
2
1
0
0
0
0
2
0
0
0
0
1
3
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
4
2
0
2
0
0
0
0
0
0
0
2
0
0
2
0
2
2
0
0
0
1
1
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
2
2
0
0
1
0
0
0
0
0
0
1
2
0
1
0
1
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
7
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
2
0
0
0
0
0
2
0
1
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
1
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
3
0
0
0
0
0
0
0
0
1
0
0
2
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
6
0
0
1
0
0
1
0
2
1
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
7
0
0
0
0
2
3
0
0
0
1
0
0
0
2
0
4
0
2
0
0
0
2
0
0
1
3
1
0
0
0
0
0
0
0
2
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
1
0
0
0
0
0
0
0
0
2
1
15
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
2
2
0
0
2
3
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
7
0
0
0
1
0
2
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
1
1
0
0
2
0
0
0
0
2
2
1
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
3
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
1
2
0
0
0
0
0
0
0
0
2
2
3
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
2
0
1
3
0
0
0
0
0
0
0
0
2
0
0
1
0
1
1
1
0
1
0
0
2
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
2
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
3
3
2
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
7
0
0
0
1
0
0
2
0
0
0
0
0
7
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
1
0
0
1
1
0
1
1
2
3
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
3
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
3
0
1
2
0
0
1
0
0
2
1
0
0
0
2
0
0
0
1
2
0
1
0
0
0
0
0
0
0
1
3
0
0
2
1
0
0
0
0
1
2
3
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
4
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
1
0
0
2
0
0
3
0
0
0
0
1
0
0
2
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
2
0
1
0
2
0
0
0
1
0
0
0
0
0
2
0
0
3
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
4
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
5
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
2
2
5
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
2
0
0
2
1
0
0
0
0
1
1
0
0
0
0
0
2
2
0
0
1
0
2
0
1
0
0
1
2
1
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
3
3
0
2
0
0
2
0
0
0
0
0
0
0
2
1
7
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
1
0
1
0
1
2
2
0
0
0
0
0
1
1
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
1
0
0
0
0
1
0
0
1
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
2
1
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
2
0
0
2
0
1
0
0
0
0
1
1
0
0
2
0
0
0
1
0
0
1
1
2
0
1
0
0
1
0
0
1
2
0
0
0
0
0
0
0
2
1
0
1
0
7
0
1
0
1
0
0
1
0
0
3
0
2
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
2
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
1
0
0
0
0
0
1
2
0
0
1
2
0
0
0
0
1
3
2
0
2
0
0
0
0
0
2
0
3
0
0
0
2
0
0
1
0
1
0
0
2
1
0
0
1
1
1
0
0
0
0
2
0
3
1
0
1
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
4
0
2
2
0
0
2
0
0
2
1
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
1
0
0
0
2
3
2
2
0
0
6
0
0
5
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
1
0
0
0
2
1
0
1
0
2
0
0
0
2
0
0
0
2
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
2
3
0
0
0
0
0
0
0
0
0
1
1
2
2
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
2
2
0
0
0
1
0
0
5
0
0
0
0
0
3
1
2
0
0
2
0
3
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
2
1
0
0
0
0
0
0
4
0
0
0
0
4
2
0
0
2
0
0
0
0
0
2
0
2
1
4
2
1
0
0
0
0
2
2
0
0
1
0
2
0
0
0
1
0
0
1
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
2
7
0
0
0
0
0
2
2
0
0
0
2
0
0
0
2
0
4
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
2
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
1
0
2
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
2
1
2
1
2
0
1
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
2
1
3
0
0
0
1
0
0
0
0
0
5
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
2
0
0
1
1
1
0
0
7
1
0
0
0
0
0
0
0
3
0
0
0
0
1
1
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
2
2
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
3
1
0
0
0
0
0
1
2
1
0
0
0
0
1
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
1
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
3
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
2
1
0
0
0
0
2
0
0
0
2
0
2
3
2
2
1
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
1
2
0
0
2
0
0
1
1
0
0
2
2
4
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
3
0
1
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
2
0
3
0
0
0
0
1
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
5
3
0
0
0
0
2
1
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
3
0
0
0
0
0
2
3
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
1
2
1
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
2
2
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
4
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
3
0
0
0
0
2
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
3
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
5
0
0
1
2
0
0
0
0
0
4
0
1
0
0
0
0
2
0
2
2
0
2
2
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
1
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
2
3
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
1
2
1
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
2
2
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
1
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
9
3
0
0
0
0
0
0
1
0
0
1
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
2
1
0
1
0
1
0
0
0
2
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
1
0
2
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
3
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
2
0
0
0
2
0
0
0
0
0
2
3
0
0
2
0
1
0
0
0
0
0
0
0
3
0
0
0
0
8
0
0
0
0
0
0
2
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
3
0
0
0
0
9
2
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
2
1
0
0
0
2
0
0
0
1
0
0
1
1
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
3
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
2
0
0
2
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
3
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
2
0
0
4
1
0
0
1
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
3
0
2
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
1
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
1
0
1
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
1
0
2
0
0
5
1
0
2
0
1
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
1
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
2
0
2
0
0
0
0
0
1
0
0
0
2
2
0
0
0
1
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
0
0
8
0
0
3
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
2
0
0
0
0
0
1
0
2
0
0
1
5
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
1
1
3
6
0
0
0
0
0
1
0
0
1
1
0
11
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
2
1
2
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
1
0
3
0
3
0
0
0
0
0
1
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
2
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
4
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
2
0
1
0
1
0
1
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
3
0
0
1
0
0
0
0
0
0
0
2
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
3
0
0
0
1
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
6
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
3
0
0
0
0
0
2
2
0
0
0
1
0
3
0
0
0
0
0
0
0
1
2
0
2
1
0
0
2
1
1
0
0
0
0
3
0
0
1
0
0
0
0
0
2
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
3
0
0
0
0
0
0
0
3
0
2
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
1
0
0
3
0
0
2
1
0
0
0
0
0
0
0
2
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
2
1
1
2
3
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
5
0
0
1
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
7
0
0
0
0
5
0
0
1
0
0
2
1
0
0
0
2
0
3
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
1
0
2
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
1
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
5
0
0
1
3
0
0
0
2
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
2
0
1
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
2
2
0
0
1
0
0
0
0
0
0
2
0
0
4
1
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
1
0
1
0
2
0
0
2
0
0
0
0
0
1
1
0
0
1
2
2
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
2
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
3
0
0
3
1
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
6
0
0
0
3
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
2
0
3
0
1
0
2
0
0
0
0
0
0
10
0
0
0
0
1
2
0
0
0
1
0
0
1
0
2
0
3
0
0
2
2
0
0
0
0
0
0
0
1
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
7
0
0
0
0
0
0
0
2
1
0
1
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
2
0
1
0
0
0
1
1
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
3
0
0
1
0
0
2
0
0
0
0
5
0
0
0
2
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
3
0
2
0
1
0
0
2
0
0
0
0
1
0
1
1
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
2
1
1
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
2
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
2
0
0
2
0
0
0
1
0
0
2
0
2
1
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
1
1
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
2
1
1
0
2
2
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
1
0
0
0
15
0
0
0
2
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
2
1
0
2
0
2
0
0
0
1
0
2
0
0
0
1
2
0
0
0
0
2
0
0
0
2
4
0
0
0
1
0
0
0
0
2
0
1
0
2
1
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
2
1
0
0
0
0
0
0
3
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
2
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
3
1
0
1
0
0
0
1
0
0
0
0
1
0
2
0
0
3
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
1
3
0
2
0
0
0
1
0
2
11
1
0
2
1
0
2
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
1
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
1
2
4
0
0
0
1
0
0
0
0
2
0
0
2
1
0
0
2
0
0
4
0
0
0
3
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
1
0
2
0
2
2
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
6
0
0
1
0
0
1
0
0
2
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
2
0
0
1
1
0
0
0
0
0
0
2
0
4
0
1
0
0
0
7
0
0
0
0
0
1
2
0
0
0
0
1
2
0
2
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
4
1
0
0
0
0
1
6
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
2
0
0
0
0
0
2
4
0
0
0
0
0
1
0
0
0
3
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
1
1
0
2
0
2
0
0
1
0
0
2
0
0
0
0
0
0
2
1
0
0
1
0
0
1
1
1
2
0
0
0
0
0
0
0
1
2
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
2
0
0
0
0
0
0
2
0
2
0
0
2
1
3
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
1
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
1
1
1
1
2
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
3
0
0
0
1
3
0
5
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
3
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
1
0
0
0
0
3
0
1
0
0
0
2
1
0
0
0
0
0
2
0
3
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
15
1
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
1
0
2
2
0
0
0
0
1
0
0
0
0
5
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
2
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
3
0
0
0
3
2
0
0
0
0
0
0
0
0
0
7
0
0
1
1
0
2
2
2
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
3
1
0
1
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
3
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
1
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
2
5
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
2
0
0
2
0
0
3
0
0
0
0
2
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
1
0
0
0
0
3
1
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
1
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
4
0
0
2
1
0
0
0
0
0
2
0
2
0
1
0
0
0
2
1
0
0
0
1
0
2
0
0
1
1
0
0
5
0
1
2
0
0
2
0
1
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
5
0
2
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
6
0
0
0
0
2
0
0
0
0
1
0
1
0
0
9
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
1
2
1
0
0
0
0
2
0
0
1
0
1
1
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
1
2
0
1
0
0
0
0
2
0
0
0
6
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
2
0
0
0
2
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
1
0
3
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
6
0
0
0
0
0
0
1
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
2
1
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
2
1
0
0
2
0
0
2
1
0
4
0
0
0
0
0
0
1
0
0
0
0
0
2
1
1
0
0
1
0
0
0
0
3
0
0
0
1
0
0
1
0
2
2
1
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
1
0
1
2
0
2
0
0
1
0
0
2
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
2
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
1
0
0
2
0
2
3
2
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
1
0
0
1
1
0
0
0
0
3
0
0
0
0
0
0
0
4
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
3
0
3
0
0
0
0
0
0
3
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
5
1
0
1
0
0
1
0
3
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
3
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
1
0
2
2
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
1
0
1
0
1
1
0
0
0
1
0
0
1
0
1
0
2
0
1
0
2
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
2
2
1
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
2
2
0
3
0
2
0
2
0
1
3
0
0
4
0
1
1
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
5
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
1
2
0
0
1
0
0
0
0
1
0
0
2
0
3
0
1
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
3
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
3
0
0
1
2
0
2
1
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
7
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
2
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
2
0
0
1
0
0
2
2
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
2
2
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
5
2
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
1
0
0
1
0
0
0
2
1
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
1
1
0
2
0
1
0
0
2
0
0
0
3
0
0
2
0
1
0
1
0
2
2
2
1
1
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
5
0
2
0
0
0
1
0
1
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
6
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
2
0
0
2
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
2
0
1
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
5
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
1
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
2
0
0
1
0
0
1
0
0
0
0
0
1
0
6
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
5
0
0
3
0
2
1
2
0
2
0
0
1
0
1
0
0
1
2
0
0
1
0
0
0
1
2
1
0
0
1
0
1
0
2
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
3
8
0
0
2
0
0
0
0
1
0
0
1
0
0
0
1
2
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
2
1
1
0
0
0
0
2
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
2
2
1
0
0
0
0
1
0
1
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
1
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
2
1
2
1
0
2
0
0
2
1
0
0
0
0
1
2
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
1
0
2
2
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
1
0
14
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
1
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
1
0
1
0
3
4
0
0
0
0
0
0
0
0
2
0
0
3
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
4
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
1
0
3
0
0
0
0
0
0
2
0
2
0
1
0
0
2
0
2
0
0
2
0
0
1
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
3
2
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
3
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
2
2
0
0
1
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
2
0
0
5
1
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
1
0
2
0
2
0
0
0
1
0
4
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
1
0
0
0
3
1
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
1
0
1
0
0
0
0
5
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
1
0
1
0
0
0
0
0
0
4
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
5
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
3
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
5
0
2
2
0
0
1
0
2
0
1
0
1
0
0
0
0
0
0
0
2
0
1
1
2
4
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
3
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
4
0
0
2
0
0
1
0
4
0
0
0
0
2
0
1
0
0
0
3
0
5
1
1
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
1
2
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
6
2
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
1
0
0
2
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
1
0
1
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
2
3
0
0
4
0
3
0
4
0
1
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
1
2
0
1
4
0
1
0
2
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
1
0
1
0
0
1
1
1
1
0
2
0
1
0
0
0
0
1
1
0
0
0
0
7
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
6
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
1
0
0
2
0
0
0
0
2
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
2
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
9
0
1
3
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
1
1
0
0
1
0
0
0
3
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
2
0
1
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
2
0
5
0
2
0
0
0
0
0
0
0
2
5
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
4
0
1
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
1
1
0
1
0
0
2
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
2
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
2
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
1
0
2
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
1
0
0
0
0
1
0
0
0
0
0
1
1
1
1
0
2
0
0
0
1
0
0
0
2
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
2
0
1
0
0
0
3
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
1
2
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
2
1
0
0
0
0
0
1
2
0
1
0
0
0
0
0
2
0
0
1
0
0
1
0
1
0
0
0
1
0
1
0
1
0
0
1
1
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
2
0
0
0
1
0
0
0
2
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
2
0
2
0
1
1
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
1
1
0
0
0
0
1
2
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
2
0
1
2
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
2
4
0
0
0
0
0
0
0
9
3
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
1
0
0
1
0
0
3
3
0
0
4
0
0
0
1
0
0
0
0
3
0
0
0
0
2
0
0
0
1
2
1
2
0
0
0
0
0
0
0
1
0
0
2
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
5
0
1
0
2
0
0
0
1
0
0
3
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
2
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
2
0
0
1
0
0
1
0
0
0
0
0
2
0
2
0
0
5
1
0
0
2
0
0
0
0
1
1
0
0
0
0
1
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
10
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
3
3
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
3
0
0
0
2
2
2
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
1
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
1
0
1
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
3
0
2
0
2
2
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
1
0
1
1
0
1
2
2
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
2
0
0
1
0
0
3
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
2
1
0
0
0
1
0
0
0
1
2
0
0
0
0
2
2
0
0
3
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
1
0
0
0
1
2
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
1
1
0
0
0
3
0
0
0
5
0
0
0
1
2
0
0
2
0
2
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
1
2
0
2
0
1
0
0
0
3
1
1
0
0
2
0
1
0
2
3
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
1
9
2
0
0
1
0
0
1
0
0
0
0
1
0
1
2
2
5
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
3
0
0
1
0
0
0
2
0
3
0
0
0
0
1
2
1
0
0
1
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
1
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
2
0
0
1
0
0
0
3
0
0
0
0
1
1
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
3
0
0
0
2
0
0
0
0
1
0
0
2
0
2
0
0
0
0
1
0
0
0
2
0
2
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
2
0
1
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
2
0
0
0
0
0
0
1
0
0
3
0
0
0
2
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
1
0
2
0
0
0
1
1
0
0
2
0
0
0
3
0
2
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
2
5
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
10
1
0
0
0
0
0
6
0
0
0
0
2
0
0
0
2
0
0
2
2
6
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
2
2
0
0
0
0
1
0
0
0
3
0
1
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
3
0
0
0
0
0
0
0
0
0
0
13
1
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
1
0
1
0
1
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
3
0
2
0
0
2
0
0
0
1
0
1
0
0
0
0
3
3
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
2
0
0
2
0
6
0
0
2
0
0
2
2
0
1
2
0
0
0
0
0
0
2
0
0
2
2
0
1
0
0
2
0
0
0
0
0
1
0
0
2
3
0
0
0
1
0
0
1
0
2
1
2
0
0
2
0
0
0
0
0
1
0
0
0
2
0
4
1
0
0
0
3
0
2
0
2
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
1
2
0
1
0
3
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
3
0
0
1
2
2
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
1
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
1
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
1
2
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
2
2
1
0
0
1
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
2
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
4
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
2
0
0
0
3
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
4
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
2
0
0
1
0
0
0
1
0
0
0
1
0
2
0
4
0
1
1
0
0
2
0
1
1
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
1
0
0
2
2
1
4
0
2
0
0
2
0
0
0
0
0
1
2
2
0
0
0
3
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
5
0
0
0
2
0
0
1
2
1
0
0
1
0
0
0
1
1
0
2
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
5
0
0
0
0
0
0
0
4
1
2
0
0
1
0
1
1
2
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
5
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
2
0
0
1
3
1
3
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
3
0
0
2
0
0
8
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
1
1
1
0
0
0
2
0
2
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
4
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
2
0
0
0
0
0
0
3
0
0
0
7
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
2
0
1
0
2
0
0
0
0
0
1
0
0
2
5
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
3
1
1
0
0
0
0
0
0
0
0
0
0
0
3
1
1
0
0
0
0
1
0
0
0
0
0
0
10
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
3
0
1
0
0
0
2
0
0
0
0
2
2
0
2
0
1
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
1
1
0
0
2
0
0
0
0
0
1
0
0
0
4
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
3
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
1
3
0
2
0
1
0
0
2
0
0
0
0
0
0
1
1
2
3
0
2
3
3
1
0
0
0
1
1
3
0
4
0
0
0
0
0
0
0
1
3
0
0
0
0
1
0
0
2
2
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
2
0
0
2
0
0
0
4
0
4
0
0
0
1
0
0
0
1
0
0
0
0
3
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
1
0
1
0
1
0
0
1
0
1
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
4
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
1
0
0
2
2
2
0
0
0
0
0
0
0
0
2
0
6
0
0
0
0
0
3
1
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
1
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
2
0
1
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
4
0
1
0
0
0
1
1
0
0
0
0
0
2
2
0
0
0
8
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
2
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
1
0
2
0
0
0
0
4
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
1
0
0
0
0
0
0
0
0
0
0
1
1
2
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
6
0
1
0
0
0
0
2
0
0
0
3
0
1
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
1
0
2
1
3
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
2
0
0
0
3
0
0
0
0
1
0
0
0
2
0
1
1
2
0
0
0
2
3
1
2
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
2
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
3
0
1
0
2
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
2
0
0
0
2
0
4
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
1
0
1
0
1
9
0
2
0
0
2
0
0
0
0
1
4
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
1
0
0
2
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
3
5
1
2
3
0
1
0
0
0
0
0
0
1
1
0
2
0
0
4
0
0
0
0
0
0
2
0
2
0
0
0
2
1
0
0
0
0
5
1
0
1
4
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
1
0
0
0
0
2
0
3
2
1
0
0
0
0
2
1
0
0
0
0
0
4
0
0
1
2
0
0
2
1
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
0
2
2
1
0
0
0
0
0
0
0
2
0
3
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
1
0
1
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
7
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
1
0
3
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
1
0
3
1
1
1
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
2
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
1
2
2
0
1
0
0
0
0
2
0
2
4
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
1
2
0
0
0
0
3
0
0
2
0
0
0
1
0
0
0
1
2
0
0
2
0
1
0
0
2
0
0
1
0
0
1
2
0
1
4
0
2
0
0
0
0
0
1
1
2
0
0
1
0
0
1
0
0
2
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
3
0
0
0
0
2
2
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
3
0
0
1
0
2
1
5
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
5
0
0
0
2
0
3
0
0
2
0
0
0
1
0
1
0
0
0
1
2
0
0
0
1
0
0
5
0
0
4
0
0
1
2
0
2
3
1
1
0
0
0
0
0
4
0
0
1
1
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
2
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
2
0
0
0
3
1
1
0
0
0
0
0
0
0
0
0
1
0
3
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
1
0
1
0
2
2
0
2
0
1
1
1
0
0
0
0
1
2
0
2
0
1
0
0
0
2
0
0
0
0
0
0
5
3
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
1
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
2
2
0
0
0
0
2
0
0
5
0
0
2
2
0
0
0
1
3
0
0
2
0
4
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
3
0
0
0
0
0
0
0
2
0
0
2
0
3
0
0
0
0
2
0
0
3
1
0
0
1
0
0
2
0
0
0
0
0
0
0
2
1
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
2
0
1
0
3
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
1
0
0
0
2
0
0
1
0
0
0
1
1
0
1
1
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
1
3
0
0
1
0
1
0
0
0
0
1
2
0
2
1
0
0
1
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
2
0
0
3
2
0
1
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
1
1
0
1
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
4
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
2
0
0
0
1
0
0
0
2
0
0
3
0
0
0
1
0
0
1
0
2
3
0
0
0
0
0
0
0
0
2
2
0
3
0
0
2
0
0
2
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
3
0
1
1
1
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
2
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
1
1
0
1
2
1
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
1
0
0
1
3
0
0
0
0
1
0
0
1
0
0
2
0
0
0
1
0
1
0
0
3
0
0
0
2
0
0
0
2
1
1
1
0
0
0
0
0
0
0
1
0
0
1
1
2
0
3
1
0
1
3
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
2
0
0
1
1
0
0
0
2
0
6
2
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
1
0
0
0
0
2
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
2
4
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
1
2
1
2
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
4
0
1
0
0
0
2
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
4
0
0
0
0
1
1
0
0
4
1
0
3
0
2
0
0
1
0
0
0
1
0
0
0
0
0
1
2
1
0
1
0
0
0
2
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
4
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
2
0
5
0
2
0
2
0
0
0
0
2
0
0
2
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
3
1
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
3
0
1
1
0
0
1
0
2
1
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
3
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
5
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
3
1
0
0
2
3
0
0
0
0
0
0
0
1
2
0
2
3
0
0
2
0
0
0
1
0
2
0
0
0
1
0
0
0
0
1
0
0
1
1
3
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
1
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
1
0
0
4
0
0
1
1
0
1
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
1
0
0
2
0
1
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
3
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
1
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
3
0
0
0
2
0
0
1
0
0
0
0
2
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
2
0
1
1
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
4
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
9
1
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
2
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
4
1
0
1
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
3
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
1
0
4
0
0
0
9
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
3
0
0
0
0
1
2
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
3
1
0
0
0
0
0
2
0
0
1
0
0
0
0
1
12
0
1
0
0
0
0
0
0
1
2
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
1
7
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
1
0
2
0
1
1
2
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
3
1
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
4
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
4
7
0
0
0
0
0
2
1
0
1
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
9
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
3
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
3
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
1
1
0
2
0
0
0
2
0
1
0
0
2
1
0
0
0
2
1
0
0
1
0
0
0
0
0
0
3
0
0
1
1
1
0
0
0
0
0
2
0
1
1
0
0
1
0
1
0
0
0
2
0
0
0
2
2
1
0
0
1
0
0
0
1
0
1
0
1
0
0
0
3
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
1
0
1
0
0
0
1
1
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
6
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
1
1
0
0
0
1
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
2
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
2
0
1
0
0
0
0
2
0
0
1
0
3
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
3
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
2
5
0
0
1
1
0
0
2
2
2
0
1
0
0
0
0
0
0
1
0
1
2
2
0
0
0
0
0
0
0
0
0
5
0
3
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
1
0
0
0
0
3
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
1
0
1
0
0
0
1
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
2
0
2
0
1
0
1
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
1
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
3
0
0
0
0
0
2
2
0
0
0
2
2
2
0
0
1
2
0
0
0
0
1
1
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
1
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
6
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
1
5
0
0
1
0
1
0
1
2
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
4
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
3
0
0
2
0
0
0
6
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
3
0
0
0
1
1
2
1
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
2
0
5
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
2
0
0
0
1
0
3
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
1
0
2
0
0
3
0
2
1
2
0
0
2
2
0
0
0
0
1
2
0
2
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
4
0
0
1
0
0
1
0
0
0
0
1
0
2
1
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
2
1
0
1
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
1
1
1
1
0
0
0
0
0
0
0
0
1
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
2
0
2
0
0
0
0
2
0
2
1
2
0
0
0
0
0
2
0
2
2
0
0
0
1
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
1
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
4
1
2
2
0
0
0
0
2
0
0
0
1
0
1
0
0
2
0
0
2
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
3
0
0
2
0
0
2
0
1
0
2
2
0
2
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
1
2
0
0
0
0
1
0
0
0
2
0
2
7
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
1
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
1
3
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
2
1
2
0
1
0
2
3
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
4
0
0
1
0
3
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
2
0
2
0
0
0
0
0
2
2
0
0
2
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
5
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
1
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
1
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
3
0
0
2
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
6
0
0
0
2
1
0
2
2
0
2
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
3
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
1
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
1
0
0
0
2
0
3
0
2
1
1
2
1
0
0
0
0
2
0
1
1
1
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
3
2
0
0
0
0
1
0
1
0
0
0
0
3
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
4
5
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
1
2
0
2
1
0
0
2
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
2
0
2
0
1
0
0
0
0
1
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
2
1
0
0
1
2
0
0
2
0
0
0
0
0
0
2
0
0
3
0
1
0
0
0
2
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
1
2
2
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
1
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
5
0
2
0
0
0
2
0
0
0
0
0
1
1
1
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
2
2
2
2
0
2
0
1
2
5
1
0
2
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
3
0
1
0
1
2
1
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
1
0
1
0
0
0
3
0
0
1
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
3
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
1
0
0
0
0
1
0
0
0
0
1
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
3
0
0
0
0
0
0
2
0
0
0
2
3
0
0
0
1
0
0
3
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
1
0
2
0
0
7
0
2
0
0
0
0
1
0
0
0
0
1
1
2
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
1
0
2
2
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
2
0
2
0
0
0
1
0
2
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
2
2
0
3
0
0
0
0
0
0
0
1
1
0
0
3
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
3
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
2
1
2
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
1
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
6
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
1
2
0
0
2
2
0
0
2
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
1
0
0
3
1
0
1
0
0
1
0
0
0
1
0
2
0
0
2
0
0
0
0
2
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
3
2
0
0
1
0
0
2
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
2
2
3
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
1
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
1
1
0
1
0
0
0
1
0
0
2
0
0
0
1
0
0
0
1
0
0
0
3
0
0
0
0
0
0
2
1
2
0
0
2
2
1
0
0
0
0
1
2
0
0
0
0
0
1
2
2
0
0
0
2
2
0
1
1
0
0
0
0
0
2
0
0
0
1
0
1
0
1
2
1
4
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
2
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
3
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
3
0
1
0
0
0
1
3
1
1
0
0
0
0
0
0
0
0
0
2
7
3
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
1
2
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
4
0
1
2
0
2
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
3
0
0
0
2
0
0
0
0
1
0
2
2
0
0
0
0
2
2
0
0
0
0
0
0
3
0
2
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
1
0
0
0
2
0
0
0
2
2
1
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
2
4
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
2
0
0
2
0
0
2
0
0
0
0
0
2
1
0
0
0
1
4
0
0
2
0
0
0
1
3
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
1
0
0
2
1
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
2
0
0
3
0
1
0
0
0
1
0
0
0
0
4
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
3
0
0
0
1
0
0
0
0
0
0
3
0
0
1
0
0
0
0
1
0
1
1
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
1
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
2
0
4
0
2
0
0
0
1
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
1
1
2
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
7
0
0
0
0
0
1
1
0
0
0
1
0
2
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
2
0
2
0
1
2
0
4
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
2
0
0
2
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
2
0
12
0
0
2
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
3
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
3
2
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
2
2
0
1
0
4
0
1
0
1
0
0
0
1
2
0
0
5
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
1
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
8
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
3
0
0
5
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
5
0
0
1
1
0
2
0
0
0
1
0
3
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
3
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
3
0
0
0
1
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
2
0
0
2
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
2
0
1
0
0
2
4
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
3
0
1
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
2
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
3
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
5
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
11
2
2
0
0
0
0
0
0
0
3
0
0
1
0
0
1
0
0
2
0
0
2
2
0
0
1
2
0
0
2
0
0
2
0
0
1
1
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
1
1
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
1
0
0
0
1
0
2
6
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
2
0
0
2
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
2
1
0
0
3
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
1
0
3
1
0
0
0
3
0
0
3
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
3
0
2
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
5
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
7
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
2
0
1
2
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
2
0
1
1
0
3
0
1
5
0
1
0
0
0
0
0
1
0
0
0
0
1
1
2
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
6
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
2
0
0
0
2
0
0
0
0
2
0
2
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
2
1
0
3
0
0
1
1
1
0
1
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
0
0
0
4
0
2
2
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
2
0
1
1
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
1
0
1
0
2
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
2
0
0
2
1
0
0
0
0
11
2
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
1
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
2
0
4
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
1
2
0
0
1
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
4
1
0
0
1
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
2
3
0
0
0
2
0
0
1
3
0
0
0
0
3
2
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
1
0
1
0
0
1
0
0
2
0
1
0
3
0
0
0
0
0
0
0
0
0
7
1
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
2
3
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
3
0
0
1
0
0
2
0
1
1
0
1
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
2
2
3
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
5
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
3
0
0
0
0
1
0
1
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
1
2
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
7
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
2
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
1
2
0
2
2
0
0
2
7
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
1
0
0
2
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
4
1
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
1
2
3
1
0
1
2
2
0
0
0
0
0
0
6
1
0
0
2
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
2
2
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
3
0
1
3
0
0
0
0
2
0
0
2
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
1
0
0
0
12
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
2
2
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
2
2
0
0
2
0
0
0
0
1
0
0
0
7
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
1
3
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
2
0
0
0
0
1
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
1
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
1
0
0
0
0
0
2
1
0
2
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
1
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
2
0
1
0
0
0
0
0
0
1
0
1
0
0
3
1
2
0
2
0
0
0
2
0
1
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
5
0
0
1
0
1
0
0
0
0
0
0
2
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
2
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
1
1
1
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
1
0
0
0
0
0
2
1
2
0
0
1
2
0
1
0
5
0
0
0
0
4
0
5
0
0
0
2
15
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
3
2
0
2
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
1
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
3
0
0
1
1
0
2
0
0
1
0
0
0
1
0
1
2
0
0
1
0
1
0
0
1
0
0
0
0
0
1
2
0
0
2
0
1
0
0
0
0
2
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
1
0
2
0
5
2
0
0
0
2
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
2
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
1
0
0
0
0
0
0
3
1
1
2
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
1
0
1
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
9
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
2
0
1
3
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
3
1
0
0
2
0
1
0
0
0
1
0
0
9
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
1
3
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
3
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
5
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
3
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
5
0
0
0
0
0
1
0
0
5
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
1
0
2
0
0
1
3
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
4
0
2
1
0
2
0
0
0
1
2
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
1
2
0
2
0
0
0
2
0
1
0
0
0
2
0
0
5
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
2
0
2
0
3
0
1
0
1
2
0
0
0
0
0
0
1
2
0
2
0
0
3
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
1
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
2
0
0
4
4
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
3
0
0
0
2
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
3
0
1
0
2
0
0
0
0
1
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
2
0
3
2
0
0
0
1
0
0
1
0
2
0
1
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
4
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
1
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
1
1
2
0
3
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
3
1
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
3
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
1
2
1
0
0
0
0
1
0
0
0
0
4
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
3
1
0
2
2
0
0
1
2
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
5
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
3
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
1
0
0
0
0
1
1
0
1
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
6
0
2
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
2
2
1
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
2
0
1
1
0
0
0
0
6
0
0
0
1
0
2
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
1
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
3
1
0
2
0
0
0
0
3
0
1
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
4
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
2
0
0
0
0
0
1
0
0
0
1
0
0
1
0
2
2
4
0
2
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
3
0
3
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
1
0
2
0
2
0
0
1
0
4
0
0
1
1
0
0
0
2
0
2
4
0
1
0
3
0
0
0
1
1
0
0
7
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
3
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
6
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
1
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
2
0
2
0
1
0
1
0
0
1
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
2
0
1
0
0
0
0
3
2
2
5
0
1
1
2
2
0
0
0
1
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
2
1
0
0
0
0
0
3
1
0
0
2
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
1
0
2
1
2
2
0
0
0
0
0
2
2
2
3
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
3
4
0
0
5
0
0
1
0
0
0
2
0
0
1
0
0
2
0
0
2
0
0
0
0
2
0
1
0
2
1
3
0
2
0
0
0
0
0
0
1
0
0
0
2
2
2
0
0
0
1
2
0
0
0
0
0
2
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
5
2
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
2
0
0
0
0
1
3
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
2
0
0
1
0
1
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
1
1
0
0
1
0
2
1
0
1
1
0
0
2
0
2
0
3
0
0
0
1
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
5
0
0
1
0
1
1
0
1
1
0
1
0
2
0
0
0
1
0
1
0
0
0
2
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
2
2
0
0
2
0
0
0
0
2
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
3
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
2
1
0
0
0
0
2
0
0
0
2
3
0
1
0
0
0
2
0
2
0
0
1
2
0
0
0
1
2
0
0
0
0
2
0
0
0
3
0
0
0
0
0
1
3
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
2
0
2
0
2
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
1
1
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
2
1
0
2
1
0
0
0
3
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
1
1
0
0
0
0
2
0
1
2
0
0
0
0
0
3
2
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
1
1
0
0
0
0
0
0
2
2
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
1
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
4
2
0
0
0
0
2
0
0
0
3
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
2
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
2
4
0
0
2
0
1
2
0
1
0
2
2
0
0
0
0
1
0
0
1
2
2
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
2
1
0
0
0
0
0
1
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
3
0
0
0
0
0
3
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
2
0
1
0
0
2
0
0
0
1
0
0
0
0
0
3
0
0
2
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
4
0
0
1
3
0
0
0
0
0
0
0
2
0
0
0
1
1
0
1
1
0
3
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
1
1
2
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
3
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
2
0
0
0
2
0
1
0
0
0
0
0
3
2
0
2
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
3
0
0
0
0
0
2
0
0
0
3
1
1
1
0
1
1
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
2
1
2
0
0
0
4
0
0
0
0
0
0
0
0
0
1
4
4
2
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
1
2
0
1
1
0
2
0
0
0
2
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
1
0
2
0
0
0
0
2
1
0
0
0
1
0
2
0
0
0
1
0
3
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
2
0
4
0
0
0
0
2
0
0
0
3
2
2
1
2
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
1
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
2
1
2
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
4
1
0
0
2
0
2
0
0
0
0
0
0
2
3
1
1
3
2
0
0
2
0
0
0
0
0
0
1
3
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
3
0
1
0
1
0
0
0
0
0
0
2
0
0
3
0
1
0
0
0
2
2
0
0
0
1
0
0
2
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
1
0
0
0
0
0
0
3
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
1
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
2
2
1
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
1
0
0
1
0
0
0
0
2
3
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
2
0
0
0
1
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
1
2
0
1
0
0
0
1
0
0
0
0
2
2
2
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
1
0
0
1
0
1
0
7
0
2
0
0
2
0
2
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
4
0
0
1
2
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
1
2
1
0
0
0
0
0
0
1
0
0
3
0
0
0
0
2
0
0
0
2
0
2
0
2
0
3
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
2
0
1
1
2
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
2
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
4
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
2
2
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
1
0
0
0
2
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
2
2
1
0
0
0
0
1
0
0
0
1
1
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
1
0
0
2
0
1
0
0
0
0
0
2
1
0
4
1
0
0
0
2
0
0
0
1
1
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
0
1
0
1
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
2
0
0
1
0
2
0
0
1
0
2
0
0
0
4
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
1
2
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
1
1
0
0
1
0
0
1
0
2
0
0
0
1
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
2
2
2
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
9
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
1
0
2
6
0
0
0
0
0
1
0
1
0
1
4
0
2
0
0
1
2
1
0
0
0
0
2
0
0
0
0
0
0
0
3
3
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
4
1
2
0
1
0
1
1
0
0
2
0
0
0
1
2
0
1
0
0
3
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
6
0
2
0
0
0
0
0
0
0
0
1
0
2
3
0
1
0
0
0
0
2
0
0
0
0
0
1
1
0
1
0
2
0
0
0
0
0
0
2
0
4
0
3
0
2
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
2
0
2
1
0
0
2
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
2
0
2
0
0
4
0
0
2
0
0
0
0
0
0
0
2
0
0
1
1
1
0
0
0
1
0
1
1
0
0
0
1
2
2
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
2
3
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
1
2
0
0
0
2
1
1
0
1
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
1
0
0
0
2
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
4
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
1
0
0
2
1
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
1
1
0
1
1
1
2
0
2
0
0
2
0
0
3
0
0
0
0
0
3
2
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
2
1
1
2
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
4
0
2
0
0
0
0
0
0
4
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
1
3
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
1
0
2
1
2
0
1
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
2
4
0
0
0
0
2
5
0
0
0
2
0
0
1
0
0
0
0
3
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
2
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
4
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
4
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
1
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
3
0
1
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
2
0
0
0
0
2
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
3
0
0
0
4
2
2
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
1
0
0
0
0
0
0
0
2
2
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
1
0
0
1
0
0
1
0
0
3
1
2
0
1
0
0
0
0
0
4
2
1
0
0
0
2
0
0
3
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
2
3
0
0
0
0
0
2
0
0
0
0
0
0
2
0
3
0
0
2
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
1
1
2
0
3
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
1
0
2
3
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
2
0
0
0
0
1
1
0
0
0
0
1
0
0
0
3
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
2
12
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
3
2
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
2
0
0
1
0
0
1
0
0
0
0
1
0
0
0
2
1
0
0
0
0
1
0
0
0
0
1
0
2
0
1
0
0
0
0
1
2
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
1
0
2
1
1
1
1
2
0
0
2
0
1
2
0
0
0
0
2
2
2
1
0
2
0
0
2
0
0
2
0
1
0
0
1
1
2
2
0
0
2
0
3
0
2
0
0
2
2
0
2
0
0
0
0
4
2
0
1
0
0
2
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
1
0
2
1
0
0
0
0
0
5
0
0
0
0
0
0
2
0
2
0
0
0
0
7
0
5
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
3
0
2
0
2
2
0
0
0
0
1
0
1
2
0
0
1
0
0
0
0
0
3
0
4
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
1
0
0
2
0
0
0
0
1
5
0
0
0
0
1
1
2
0
0
0
2
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
3
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
13
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
2
1
0
0
0
4
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
5
0
0
2
2
0
0
3
0
2
0
0
1
0
1
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
4
2
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
6
0
0
0
0
0
0
0
0
0
3
1
1
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
1
2
1
0
0
1
1
0
0
0
0
1
0
1
2
0
2
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
2
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
9
0
0
0
1
0
0
0
0
2
1
0
0
2
0
2
2
2
0
0
0
0
0
0
0
2
1
0
0
1
0
1
1
2
1
1
0
0
0
0
0
0
0
1
3
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
2
0
1
1
0
0
2
0
0
0
0
1
1
2
0
0
0
0
0
0
1
1
2
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
1
0
2
0
2
0
5
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
6
0
0
1
1
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
2
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
5
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
2
2
5
2
0
1
0
0
0
4
0
0
0
0
3
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
5
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
2
0
0
1
0
2
2
0
1
3
0
1
0
0
1
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
2
0
0
0
1
0
0
0
0
4
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
1
1
1
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
3
0
2
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
3
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
3
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
2
0
0
2
1
0
0
0
0
1
1
4
0
0
0
0
0
0
0
2
2
0
1
0
0
0
2
0
1
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
2
0
3
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
1
1
1
0
0
1
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
1
1
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
2
0
0
1
0
0
1
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
8
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
2
2
0
1
0
2
0
0
0
0
1
0
0
1
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
4
1
0
0
0
0
2
1
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
7
0
0
0
0
1
0
2
3
0
0
0
0
0
2
0
2
0
1
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
3
1
0
1
0
3
1
0
0
1
0
2
0
2
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
1
3
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
4
0
0
0
0
0
0
3
1
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
4
0
0
2
0
0
1
2
2
2
0
0
0
0
0
0
0
0
2
0
2
2
1
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
2
1
0
0
0
0
0
2
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
1
0
1
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
5
0
0
1
0
0
0
0
1
0
1
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
7
0
0
2
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
2
0
0
1
0
1
0
0
0
0
0
1
1
1
0
0
2
2
0
1
0
0
0
2
1
0
0
0
0
0
0
4
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
3
0
0
0
0
0
0
0
2
0
0
3
0
0
2
4
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
3
0
2
3
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
1
0
2
0
0
0
0
2
0
0
2
0
1
2
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
2
1
2
2
0
0
0
2
0
0
1
0
2
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
5
0
0
0
3
1
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
2
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
1
0
0
0
0
4
1
0
0
1
0
1
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
2
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
3
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
1
0
3
1
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
2
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
3
2
0
3
1
0
5
1
2
0
0
2
3
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
1
3
0
0
0
2
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
1
2
1
0
0
0
0
1
0
0
2
0
0
0
1
1
0
0
6
0
2
0
1
1
0
0
1
2
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
1
0
1
0
0
2
1
0
0
0
0
3
3
1
2
0
0
0
0
0
0
0
1
1
2
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
2
0
0
0
0
0
2
0
2
0
0
1
0
0
2
0
3
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
2
0
3
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
2
0
0
0
1
0
1
2
0
2
0
0
0
0
3
2
1
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
2
0
0
1
2
0
0
0
2
1
0
0
2
0
1
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
4
2
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
2
2
0
2
0
0
0
0
0
0
0
0
0
2
3
1
0
2
0
0
0
1
4
0
2
0
0
0
0
5
3
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
2
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
4
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
1
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
2
0
1
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
4
0
0
3
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
7
0
0
0
2
0
0
3
0
1
1
0
0
0
1
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
1
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
5
0
2
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
7
0
0
0
0
0
1
0
2
0
0
1
0
2
0
2
0
0
0
0
0
1
3
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
2
0
6
0
5
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
6
0
2
1
0
0
1
0
0
4
0
0
1
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
2
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
2
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
2
2
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
2
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
4
0
0
1
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
1
1
0
0
1
2
0
3
2
0
0
0
1
2
2
0
1
2
0
1
0
2
0
0
1
0
2
0
0
1
3
2
0
2
0
0
1
0
0
2
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
2
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
1
2
0
0
0
0
0
0
1
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
2
1
1
2
0
0
0
0
1
1
1
1
0
0
0
2
0
1
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
3
0
2
2
0
2
1
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
2
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
6
0
1
0
0
0
0
2
2
0
0
0
1
3
0
0
0
1
0
2
0
0
0
2
1
1
0
0
1
0
1
1
1
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
1
2
0
0
0
0
0
0
2
0
0
1
0
0
0
4
4
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
2
0
0
1
0
1
0
2
2
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
2
1
1
0
0
2
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
3
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
1
0
2
0
0
1
0
0
4
1
0
0
0
0
0
3
2
0
0
0
0
0
1
14
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
5
1
1
2
0
0
0
1
0
0
1
0
0
0
1
2
1
0
0
0
0
1
0
0
0
2
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
1
2
1
0
1
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
1
0
2
0
0
1
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
1
3
0
0
0
0
0
11
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
1
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
3
5
2
1
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
1
1
0
0
1
2
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
1
0
3
2
2
0
0
0
0
0
1
1
0
1
0
1
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
2
0
0
2
0
2
0
0
0
0
0
0
0
1
1
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
2
1
0
0
0
2
0
2
0
2
1
1
0
0
0
1
0
0
0
0
1
0
0
3
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
5
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
1
0
0
3
0
0
0
0
0
0
0
2
4
0
0
0
0
0
1
3
0
0
2
0
0
0
3
0
0
0
1
0
0
0
0
0
0
3
0
2
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
4
0
0
2
1
2
0
0
2
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
2
2
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
1
0
1
1
1
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
3
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
3
0
0
1
0
1
1
0
1
0
0
1
1
0
2
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
1
0
0
0
0
2
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
3
0
0
1
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
1
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
4
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
4
0
0
0
0
0
0
0
2
2
0
2
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
3
0
1
0
1
0
0
3
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
2
0
1
1
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
2
0
0
0
1
2
0
0
0
0
1
0
2
0
0
1
0
0
0
1
0
0
0
0
0
13
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
3
1
2
0
0
2
2
0
0
0
0
0
0
0
0
0
1
2
0
1
0
8
1
0
2
2
0
0
0
0
1
1
0
0
0
0
2
0
3
0
0
0
2
1
1
0
0
0
0
0
3
1
0
0
0
0
0
1
0
0
0
1
0
0
2
0
2
0
1
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
2
0
0
2
1
0
1
2
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
2
0
2
0
0
1
0
2
1
0
0
0
0
2
0
1
2
0
1
0
0
0
2
0
0
0
3
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
3
0
0
0
1
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
5
0
0
3
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
3
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
2
0
0
0
1
0
2
1
2
0
0
0
2
0
3
2
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
1
0
0
1
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
3
0
0
1
0
6
0
4
1
0
0
0
2
0
1
0
0
1
1
2
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
1
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
4
1
1
1
0
2
1
0
0
0
0
1
0
1
1
0
2
2
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
3
2
0
2
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
2
0
0
1
2
0
0
1
0
0
0
0
2
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
6
1
1
1
0
0
1
0
0
0
2
1
0
0
0
0
0
1
0
0
0
3
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
2
0
0
0
0
0
0
2
1
1
0
4
0
0
2
0
1
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
1
0
0
4
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
2
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
5
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
1
0
0
0
0
1
2
0
0
1
4
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
1
0
1
2
1
3
0
0
2
0
3
0
0
1
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
1
0
2
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
1
0
2
3
1
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
3
0
0
0
1
0
0
1
0
2
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
3
2
0
1
0
0
1
0
0
2
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
1
1
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
1
0
1
0
0
0
10
0
0
0
1
0
0
0
1
0
0
1
2
0
0
0
0
1
0
0
1
0
0
2
2
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
2
0
1
1
1
1
0
0
2
0
0
0
0
1
0
0
1
2
0
1
0
2
0
0
2
0
0
2
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
3
0
0
1
0
2
0
0
0
1
0
1
0
0
0
3
1
1
0
0
2
1
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
1
1
0
0
2
2
2
0
0
0
0
0
1
1
2
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
2
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
5
0
0
0
0
2
2
0
0
0
2
0
0
2
0
0
1
1
2
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
2
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
2
1
0
0
2
0
0
0
0
0
0
3
1
0
0
0
1
0
0
0
2
2
2
0
0
0
0
2
0
0
0
3
0
2
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
1
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
2
0
0
2
0
0
0
0
0
2
0
1
0
1
0
0
0
0
1
2
0
2
0
0
0
2
0
2
2
0
1
2
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
1
3
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
1
0
0
1
0
2
0
2
2
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
3
0
0
1
0
0
0
0
1
2
0
0
0
3
2
1
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
2
2
0
0
0
0
2
2
0
0
0
0
1
2
0
0
1
0
0
0
2
2
3
5
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
2
0
0
0
2
1
1
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
1
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
1
0
2
0
0
2
2
2
0
0
0
2
0
0
0
0
3
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
2
0
0
0
0
0
0
2
0
1
1
2
2
0
0
0
0
2
1
0
0
0
3
0
1
1
0
0
1
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
1
6
0
0
0
2
1
1
0
0
0
1
0
0
0
2
0
1
3
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
1
1
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
2
0
1
0
0
0
0
0
2
3
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
1
2
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
2
1
0
0
1
0
2
0
0
0
1
1
0
0
0
0
0
1
0
0
2
0
0
1
1
0
0
0
0
1
3
2
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
1
2
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
2
2
0
0
0
0
0
1
1
0
0
2
0
1
0
0
0
1
0
0
3
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
4
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
2
2
0
0
5
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
3
0
0
1
0
0
1
0
0
1
1
0
0
1
2
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
1
2
0
0
0
0
0
1
0
0
3
0
0
2
0
0
0
0
5
0
0
0
0
3
1
0
1
0
0
0
0
0
1
0
3
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
1
1
0
0
0
3
0
2
2
0
0
4
0
0
0
2
2
0
0
2
0
0
0
0
1
0
4
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
3
0
3
0
1
1
0
0
1
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
3
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
1
0
2
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
2
1
0
0
1
2
0
0
1
4
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
2
0
0
0
0
2
3
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
1
0
0
0
2
4
0
0
0
3
0
0
0
0
0
0
0
3
0
0
2
2
0
0
0
0
0
2
0
0
2
1
0
1
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
3
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
1
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
3
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
2
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
4
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
1
1
0
1
0
0
0
0
0
0
0
2
0
1
3
0
1
0
0
2
0
2
0
0
0
0
0
0
3
1
0
0
0
0
0
0
1
5
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
2
2
0
0
1
0
3
0
0
0
2
1
2
0
0
0
0
0
0
2
2
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
1
0
3
2
0
0
2
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
1
0
3
1
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
2
0
1
1
0
0
1
0
2
1
0
0
0
3
0
2
1
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
3
0
0
0
0
2
1
0
3
0
0
1
0
2
0
0
0
1
2
2
1
0
0
0
0
0
1
1
0
0
0
2
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
1
1
0
0
0
3
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
2
2
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
2
2
4
0
0
0
1
0
2
0
0
2
0
0
3
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
1
0
1
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
2
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
1
0
2
0
1
0
0
0
2
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
4
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
2
2
1
3
0
0
0
0
0
1
0
0
2
0
0
3
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
3
0
0
0
2
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
2
0
0
0
0
2
0
0
3
0
0
0
1
1
0
0
0
0
1
0
0
1
0
2
1
2
0
1
0
2
0
0
1
0
0
0
0
1
3
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
2
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
6
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
7
0
0
0
0
1
0
1
0
2
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
1
0
1
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
4
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
1
0
1
1
1
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
1
2
1
2
0
2
0
1
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
2
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
5
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
1
0
2
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
2
4
0
0
7
0
0
0
0
0
0
1
0
0
2
0
1
2
1
5
1
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
4
1
0
1
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
1
0
0
2
1
2
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
4
2
1
0
2
0
0
2
0
0
2
1
2
1
0
1
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
3
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
3
0
0
0
0
2
2
0
2
0
2
0
0
1
0
0
0
0
1
0
0
4
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
2
1
0
0
0
0
5
2
0
0
1
1
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
2
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
4
2
1
0
0
1
0
0
0
0
0
3
0
0
0
1
0
1
0
6
0
0
0
0
3
0
0
2
0
0
4
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
8
0
2
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
3
0
0
0
2
0
0
1
1
1
1
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
2
1
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
2
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
1
1
0
0
0
0
2
0
0
2
0
0
0
0
4
0
0
1
1
1
0
2
0
0
1
0
0
0
0
1
0
4
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
1
1
0
0
0
2
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
2
1
1
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
1
1
0
1
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
1
2
0
0
0
0
0
1
0
0
0
0
2
4
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
2
0
2
1
0
2
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
2
3
0
0
0
0
0
0
1
1
0
2
3
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
3
0
1
0
2
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
3
0
0
2
1
0
0
0
0
1
0
0
0
0
0
3
0
2
0
1
0
3
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
1
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
1
0
2
0
0
1
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
1
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
2
0
1
1
0
1
0
1
0
9
0
0
0
0
0
1
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
5
2
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
2
1
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
2
0
0
1
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
1
3
0
0
2
0
0
0
0
2
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
4
0
1
0
0
0
0
0
0
2
1
0
0
0
1
1
0
0
4
2
0
0
4
0
0
0
0
3
0
0
0
1
0
0
0
1
0
3
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
5
1
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
2
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
3
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
1
1
2
0
0
0
2
1
0
2
0
0
0
1
1
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
2
2
0
0
0
2
3
0
2
1
0
0
0
0
2
0
1
0
0
1
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
3
1
6
1
0
0
0
0
0
0
1
0
0
4
0
2
1
0
2
0
0
0
0
0
1
0
0
1
2
0
1
1
0
0
0
0
0
0
5
0
0
0
0
3
0
0
0
2
0
0
0
0
1
0
1
3
0
0
0
0
1
0
0
0
1
3
2
1
0
0
0
2
0
0
0
0
0
1
1
2
2
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
2
2
1
2
0
0
1
0
0
0
0
0
0
0
1
1
3
1
1
0
0
0
0
0
0
0
5
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
2
1
0
0
0
1
1
3
1
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
2
0
1
0
0
2
0
0
2
2
2
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
4
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
1
0
1
0
0
1
0
0
1
0
2
0
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
1
2
0
0
0
3
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
1
1
2
1
2
0
0
0
0
0
0
1
3
0
2
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
2
1
3
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
2
0
1
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
2
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
1
0
1
2
1
0
0
0
1
1
0
0
0
2
0
0
0
0
2
1
0
0
0
1
2
2
0
0
0
0
2
0
0
0
0
7
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
8
2
0
1
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
1
0
0
0
2
1
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
3
0
0
0
2
0
5
0
3
0
0
0
3
0
0
0
0
1
2
0
0
0
0
0
5
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
3
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
1
2
0
1
0
2
0
0
2
0
0
2
3
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
4
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
2
0
2
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
2
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
3
0
4
1
0
1
0
2
2
1
0
0
0
2
2
2
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
2
2
0
3
2
1
0
0
0
0
0
2
1
0
1
2
2
0
0
2
2
0
0
0
0
1
0
0
0
0
3
0
0
0
5
1
0
0
0
2
0
1
0
0
0
0
1
2
0
0
0
0
0
1
1
1
0
2
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
1
3
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
2
2
0
0
4
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
1
0
5
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
2
0
0
0
2
0
0
1
0
0
1
2
0
0
2
1
0
1
14
0
0
0
2
0
3
2
1
0
0
0
0
2
1
1
0
0
0
0
0
0
1
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
2
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
1
2
0
1
3
1
1
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
3
0
0
5
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
4
0
0
2
0
0
2
1
0
0
0
1
0
0
2
2
0
0
0
0
0
1
3
0
0
0
0
0
0
5
1
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
2
2
0
0
0
2
0
1
0
0
2
0
0
1
0
0
0
1
2
2
0
0
1
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
7
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
5
0
0
0
2
0
0
2
1
0
1
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
14
0
0
0
0
0
0
0
0
0
3
0
1
2
1
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
3
0
0
0
0
3
1
2
0
0
0
0
1
1
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
6
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
3
0
0
4
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
2
0
0
0
1
0
2
3
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
1
1
2
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
5
0
0
0
0
0
1
1
2
0
0
2
0
0
0
3
1
0
0
0
2
0
3
0
2
0
0
0
0
0
2
0
2
0
2
1
1
0
0
0
1
2
0
0
0
0
2
0
0
2
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
1
2
0
2
2
4
2
2
1
1
2
0
0
0
0
2
0
0
3
3
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
1
1
1
0
0
0
1
1
0
2
0
1
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
2
0
0
0
0
0
3
1
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
3
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
3
0
0
1
1
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
3
0
0
0
4
0
1
0
0
0
0
0
2
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
1
0
0
2
2
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
1
1
2
0
1
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
1
3
0
0
3
0
0
0
1
0
0
0
2
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
2
3
0
0
2
0
1
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
11
0
0
1
0
0
0
0
0
0
0
2
1
0
1
1
0
0
0
2
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
1
0
3
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
2
2
2
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
2
0
1
0
0
0
0
1
0
0
1
0
2
0
0
0
2
1
0
0
2
2
0
2
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
1
1
1
1
1
1
2
1
0
0
1
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
9
0
2
0
0
2
0
0
0
1
0
0
1
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
2
3
0
0
0
0
2
1
0
1
0
2
0
0
3
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
2
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
3
0
0
0
0
2
0
1
0
0
0
2
0
1
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
2
0
0
1
0
1
2
0
2
2
0
2
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
1
0
0
0
3
1
2
2
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
4
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
8
0
0
1
2
0
2
0
2
0
2
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
3
0
0
0
0
0
1
2
3
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
2
0
0
0
1
0
1
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
3
0
0
0
1
0
0
0
8
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
2
2
0
0
0
0
0
0
2
0
0
3
0
0
0
1
0
0
2
4
0
0
0
2
0
3
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
1
0
2
2
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
4
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
4
0
0
0
0
1
0
0
0
1
0
2
0
0
2
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
4
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
2
1
0
0
2
0
0
0
0
0
4
0
2
4
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
2
0
0
1
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
1
0
0
1
0
0
0
0
2
0
0
0
4
0
0
0
2
0
2
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
1
0
1
0
0
0
0
0
2
1
0
2
0
0
1
0
4
1
0
0
1
0
0
0
0
0
0
0
1
2
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
1
0
0
0
1
1
0
0
0
3
0
2
0
1
0
0
0
1
1
0
6
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
1
2
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
4
1
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
7
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
8
1
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
1
0
0
1
2
0
0
1
0
0
0
1
0
0
0
0
0
1
0
2
0
0
2
0
1
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
3
3
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
1
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
3
0
1
0
2
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
3
0
1
0
0
0
0
1
0
0
0
1
0
0
2
2
0
1
0
0
0
3
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
2
0
0
1
0
0
2
0
0
1
0
0
0
0
2
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
2
0
0
0
0
0
0
5
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
1
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
1
0
1
1
2
0
0
0
0
0
0
0
0
0
2
4
0
0
0
2
0
0
3
0
0
3
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
2
0
0
4
0
2
0
0
0
0
0
0
0
0
2
0
1
1
2
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
2
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
2
1
0
0
0
1
0
0
0
0
0
2
0
0
2
0
2
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
2
3
1
1
0
0
2
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
3
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
3
0
0
2
0
2
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
4
2
0
0
0
0
0
2
0
0
0
3
0
0
0
1
0
0
0
0
0
2
2
1
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
1
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
2
1
0
0
1
0
1
3
2
2
0
0
0
2
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
3
0
0
0
0
0
0
0
0
2
0
1
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
1
2
0
1
1
0
1
0
0
1
1
0
0
0
1
4
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
2
2
0
0
0
2
0
0
0
0
2
0
1
2
0
1
0
0
1
0
0
2
0
0
0
0
2
0
1
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
1
0
0
2
1
0
0
7
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
2
0
2
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
1
5
0
1
0
0
0
1
0
1
0
2
0
1
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
2
2
0
0
0
0
1
1
0
2
0
0
4
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
1
1
0
2
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
2
0
0
0
2
2
0
0
1
0
0
0
0
0
2
0
0
0
0
1
1
2
0
0
1
2
0
0
0
0
0
3
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
2
0
0
1
3
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
2
2
4
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
2
3
1
0
2
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
1
0
0
0
3
1
0
0
0
0
2
1
2
0
0
0
0
3
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
1
2
0
0
2
0
0
0
0
2
0
0
0
2
1
0
1
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
1
0
0
0
5
0
2
0
0
0
0
2
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
3
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
2
1
0
2
0
0
0
3
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
2
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
9
0
0
0
0
3
2
0
0
0
0
1
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
2
2
0
0
4
0
1
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
2
0
2
0
0
1
0
0
0
0
0
1
2
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
2
2
4
0
0
2
0
1
1
0
0
0
0
2
0
0
2
3
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
2
1
0
2
0
0
0
2
0
0
2
1
0
0
1
1
1
2
0
0
0
0
0
0
0
0
0
0
2
2
1
0
3
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
2
1
1
0
0
0
0
0
1
0
0
0
4
0
0
2
0
0
0
0
0
0
3
0
1
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
2
1
3
0
1
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
1
2
0
0
0
1
0
0
0
3
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
1
0
0
0
3
0
2
1
0
0
2
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
5
2
0
0
0
0
0
0
0
0
0
0
0
2
4
0
0
1
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
2
0
0
0
0
0
2
2
2
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
4
0
0
0
0
0
0
0
2
2
2
0
0
0
0
2
0
0
0
3
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
5
0
0
0
0
0
0
6
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
2
1
0
0
0
2
0
0
0
1
0
4
0
1
0
4
0
2
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
2
1
1
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
1
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
3
0
0
0
2
2
1
0
0
0
1
4
3
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
2
0
1
0
0
0
2
0
0
1
1
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
2
0
1
0
0
0
0
1
1
0
0
0
0
1
0
2
0
0
3
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
4
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
2
1
0
0
0
0
0
1
0
2
2
0
2
0
2
1
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
5
1
2
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
3
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
1
2
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
2
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
1
0
0
0
3
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
1
1
0
1
0
0
1
2
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
4
0
0
2
0
1
2
3
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
1
0
1
1
3
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7
0
0
1
0
0
1
0
0
0
2
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
1
0
0
0
0
1
0
0
3
0
1
0
1
0
0
0
1
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
2
1
4
0
0
0
0
1
0
1
1
1
0
0
3
1
1
0
0
0
1
2
2
0
2
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
1
0
1
0
2
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
2
0
1
2
2
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
1
0
1
0
2
1
0
0
2
1
1
0
1
0
0
2
1
2
0
1
0
4
0
1
0
0
0
0
2
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
1
0
0
2
0
0
0
0
2
0
0
1
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
1
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
1
2
0
0
1
1
0
2
0
1
2
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
2
0
2
0
0
4
2
0
0
0
0
0
2
0
0
0
0
0
2
2
0
7
1
0
0
1
0
0
1
0
0
0
0
0
0
0
4
1
0
3
0
0
0
1
2
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
1
6
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
2
0
0
0
0
0
2
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
2
0
0
1
0
2
0
0
2
1
0
2
0
0
0
3
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
12
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
1
0
1
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
1
0
0
0
2
0
0
0
2
0
0
7
0
0
0
1
0
0
0
0
2
2
1
0
0
0
1
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
3
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
3
1
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
1
0
1
0
0
0
0
1
1
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
4
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
13
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
3
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
1
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
2
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
1
0
2
1
0
0
1
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
1
1
0
0
1
2
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
2
1
0
2
0
0
0
0
0
0
0
0
2
1
0
2
5
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
2
1
2
1
0
0
0
2
0
1
0
0
0
0
2
3
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
2
0
3
1
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
2
0
1
3
0
1
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
2
0
0
3
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
6
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
1
2
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
3
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
2
0
0
1
4
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
2
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
11
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
2
0
2
0
0
5
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
1
2
0
0
2
2
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
2
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
1
0
0
0
1
0
0
0
2
0
1
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
2
0
0
2
0
2
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
1
2
0
4
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
1
1
0
0
1
2
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
1
0
0
1
0
0
5
0
1
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
2
0
2
0
0
2
0
1
0
0
2
0
2
0
0
0
0
2
0
0
0
0
1
1
2
5
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
5
0
3
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
2
0
0
2
0
0
2
0
0
0
2
2
0
2
13
0
2
0
0
0
0
1
0
0
0
1
0
0
2
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
3
0
0
0
1
0
0
3
0
1
0
1
0
0
0
2
0
0
0
0
0
1
0
4
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
1
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
3
2
0
0
3
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
1
0
1
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
1
0
0
3
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
1
0
2
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
3
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
2
1
0
0
0
2
0
1
0
1
0
0
2
0
0
1
2
3
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
8
0
0
0
2
0
0
2
0
0
0
2
1
0
0
0
0
0
10
0
0
0
3
0
1
1
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
4
0
0
0
0
0
1
1
1
0
0
0
1
0
0
5
0
0
0
0
2
2
2
0
1
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
1
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
1
0
0
0
0
0
2
0
1
1
0
2
0
0
0
0
0
1
0
1
0
1
0
0
2
1
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
1
2
0
1
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
2
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
1
0
2
0
0
1
2
2
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
1
0
0
2
0
4
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
3
0
1
2
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
2
2
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
3
2
2
7
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
3
0
1
2
1
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
2
1
0
5
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
1
1
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
4
0
0
0
0
0
0
3
0
2
0
0
1
0
0
0
2
0
1
0
0
0
3
0
0
3
0
1
2
0
0
0
0
0
0
2
0
0
0
0
5
0
0
0
3
0
0
0
0
1
0
0
0
2
0
0
2
0
8
0
0
0
0
0
2
0
0
0
0
1
0
1
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
2
0
0
0
0
9
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
1
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
2
3
0
0
0
0
0
2
3
0
0
0
0
1
2
0
0
0
0
0
1
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
1
2
0
1
1
0
0
1
0
0
0
0
1
0
2
1
0
0
2
0
2
1
1
0
0
0
2
1
0
1
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
2
0
0
0
0
3
0
0
3
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
1
0
2
0
0
0
0
0
0
0
2
2
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
2
0
0
1
0
2
0
2
0
0
0
0
0
0
1
0
2
0
0
1
0
0
1
1
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
1
2
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
3
0
0
2
0
0
0
0
2
0
0
2
0
0
4
0
0
0
0
0
0
2
1
1
1
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
1
1
0
0
0
1
0
1
0
0
1
0
0
0
0
2
0
0
1
2
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
4
3
0
0
0
0
0
0
0
0
3
0
0
0
4
0
2
0
0
0
0
2
0
2
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
3
0
0
0
0
0
2
1
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
3
0
0
0
0
2
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
1
0
0
0
0
2
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
5
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
1
0
0
0
1
2
0
0
0
0
1
0
1
0
0
0
2
0
0
0
2
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
5
0
3
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
3
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
1
0
0
0
2
0
0
0
1
2
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
2
1
2
0
1
1
1
0
0
2
0
0
1
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
1
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
2
0
3
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
2
0
0
0
0
0
2
0
2
2
0
2
0
0
0
2
1
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
1
0
0
0
4
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
1
3
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
1
0
0
1
0
2
0
1
0
0
0
0
0
0
0
2
2
0
0
3
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
3
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
2
6
2
1
0
0
2
0
0
0
3
1
0
0
0
0
5
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
2
0
2
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
1
0
0
0
3
0
2
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
3
1
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
9
0
0
0
0
0
0
0
0
0
0
3
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
1
1
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
2
1
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
1
1
1
0
2
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
1
0
0
0
0
0
0
0
1
0
0
0
1
3
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
3
0
0
0
0
1
0
0
2
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
2
2
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
1
1
0
0
0
0
0
0
0
1
0
0
2
0
0
2
3
3
0
0
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
2
0
0
2
2
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
2
1
0
3
0
0
1
2
1
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
3
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
1
0
0
0
2
0
0
1
2
0
1
0
0
2
4
0
0
2
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
11
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
9
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
1
2
0
0
2
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
1
2
0
1
2
0
0
0
1
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
2
0
0
0
1
0
0
1
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
3
2
3
0
2
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
13
0
3
0
0
0
0
0
5
3
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
1
2
0
2
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
2
0
2
2
0
2
0
0
1
0
0
1
0
0
0
0
1
0
0
0
4
0
1
0
0
0
1
1
0
0
2
0
0
1
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
6
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
1
3
1
5
0
1
2
0
0
0
1
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
1
0
0
0
0
0
3
0
0
1
0
2
0
2
0
2
0
0
0
0
2
0
0
2
0
0
4
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
4
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
3
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
10
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
1
0
0
0
0
1
0
2
0
0
2
0
1
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
3
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
2
2
3
0
0
2
0
1
0
0
0
0
0
0
2
1
1
0
3
0
1
0
1
0
2
0
0
0
0
0
0
2
2
0
0
0
0
1
0
1
2
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
3
2
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
3
1
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
1
0
0
0
3
0
0
0
0
0
2
0
0
2
0
0
0
0
5
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
3
2
0
0
0
3
1
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
2
0
1
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
2
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
10
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
2
0
1
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
1
1
0
0
0
0
0
2
0
0
1
0
4
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
2
3
0
0
0
2
0
0
0
0
0
2
1
0
1
2
0
2
0
1
0
0
0
0
1
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
2
1
2
0
0
0
0
0
2
0
0
0
0
1
2
0
1
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
2
0
1
2
0
0
0
0
0
1
1
0
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
2
0
0
1
0
3
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
4
1
0
0
0
0
1
0
0
1
2
2
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
2
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
2
0
0
4
0
0
0
0
1
2
3
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
4
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
2
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
2
2
2
0
0
0
0
2
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
1
0
1
1
0
0
0
3
0
0
1
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
1
0
2
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
1
2
1
0
0
0
0
1
1
2
0
3
0
0
0
0
0
2
0
0
1
0
3
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
2
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
1
0
0
3
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
4
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
1
1
0
1
0
3
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
3
0
0
0
0
0
2
0
0
1
2
0
0
3
0
0
0
1
0
1
0
2
0
0
4
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
1
0
0
0
2
0
1
0
0
2
0
0
0
1
0
1
0
0
3
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
2
7
2
0
0
0
0
1
2
1
0
0
1
4
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
2
0
3
1
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
5
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
1
3
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
3
3
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
1
1
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
1
0
2
2
0
1
0
1
0
0
2
0
0
0
0
0
1
2
2
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
1
6
0
0
0
0
1
3
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
2
7
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
4
0
2
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
4
0
0
0
0
0
0
2
0
2
0
0
2
0
0
1
0
0
0
0
0
2
0
0
8
0
0
0
0
0
0
0
1
2
0
6
2
3
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
1
0
0
0
0
3
0
3
0
0
0
2
0
0
1
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
2
0
2
0
2
0
0
0
0
3
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
1
1
1
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
2
3
0
2
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
1
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
3
1
0
0
2
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
2
2
1
0
0
0
0
1
0
0
0
1
2
0
0
0
0
1
0
1
0
2
0
1
1
1
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
1
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
6
3
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
1
4
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
2
0
2
1
2
0
0
0
0
0
0
0
0
4
0
1
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
2
1
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
4
0
0
2
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
2
1
0
2
0
3
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
3
0
1
1
0
0
0
0
1
3
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
2
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
5
0
0
0
0
2
2
1
0
0
0
2
0
0
0
0
2
2
0
0
0
2
0
0
0
0
2
2
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
1
2
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
3
1
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
3
0
0
0
2
0
3
2
2
1
0
0
2
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
1
0
3
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
2
1
0
1
0
2
0
0
0
0
1
2
0
0
0
0
0
2
2
1
0
0
2
1
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
2
0
0
3
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
2
2
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
8
0
0
0
1
1
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
1
0
0
0
0
2
0
0
3
0
0
2
0
0
0
0
0
1
1
1
0
1
0
0
0
1
0
0
0
4
0
0
1
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
3
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
1
0
0
0
2
0
0
0
1
2
0
0
0
0
0
2
2
2
0
2
0
2
0
0
0
1
1
0
0
0
2
0
1
0
2
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
3
2
1
0
0
2
2
0
0
2
0
0
0
1
0
5
2
0
0
0
0
1
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
2
0
2
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
4
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
1
0
2
0
1
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
1
0
2
0
1
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
3
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
2
0
2
0
2
0
2
5
0
2
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
2
0
0
0
2
0
3
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
1
3
2
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
1
0
0
2
0
0
0
2
0
0
0
1
0
0
0
2
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
1
0
0
1
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
3
1
1
0
0
0
1
0
2
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
1
5
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
4
0
0
1
0
0
0
0
3
0
7
2
0
1
0
2
0
0
2
2
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
1
4
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
1
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
2
0
0
0
0
0
0
2
2
1
2
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
2
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
2
5
0
1
0
0
0
0
0
0
1
0
0
0
3
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
2
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
2
0
0
2
0
0
1
0
0
0
0
0
5
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
3
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
3
1
0
0
0
2
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
10
0
1
0
1
1
0
2
2
2
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
1
0
0
1
1
0
3
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
2
0
1
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
2
1
1
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
1
0
0
2
0
0
1
0
1
0
2
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
8
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
1
0
2
0
2
0
0
0
0
2
0
2
2
3
0
0
0
5
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
3
3
0
1
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
3
0
1
0
1
1
0
0
1
0
0
0
0
2
2
0
0
0
0
1
1
2
0
1
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
4
0
1
2
3
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
3
1
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
4
0
0
0
0
0
2
2
1
2
0
0
3
0
0
0
6
2
0
0
0
0
2
0
2
0
0
1
1
0
0
0
0
0
0
0
3
0
0
0
0
1
2
0
4
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
2
0
3
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
2
1
1
0
0
0
0
2
0
0
0
0
0
0
0
3
0
3
1
0
0
2
0
0
1
2
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
1
0
2
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
4
0
0
0
0
0
0
0
2
0
0
0
0
5
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
2
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
3
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
2
0
4
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
2
0
0
0
0
3
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
1
11
0
1
0
0
0
0
2
2
1
0
1
2
1
0
0
0
0
1
4
0
1
3
0
0
0
1
0
0
1
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
2
2
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
2
0
2
0
2
0
1
0
4
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
3
0
0
1
2
0
4
1
0
0
2
0
0
2
0
0
0
2
1
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
1
0
1
0
0
2
0
1
1
1
5
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
2
1
0
0
3
0
0
2
0
0
1
0
0
2
2
1
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
3
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
3
1
0
2
0
2
0
0
0
0
3
1
0
2
2
0
2
0
0
0
0
0
2
1
1
0
0
0
0
1
2
0
0
1
0
0
2
0
1
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
1
1
2
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
1
0
0
1
0
1
2
0
2
1
0
0
2
2
0
0
1
0
0
0
0
0
0
2
1
0
0
2
2
3
1
1
0
0
0
2
0
0
2
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
2
0
0
0
2
1
0
0
0
0
1
0
1
0
0
1
0
1
1
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
4
1
1
1
2
0
0
0
0
2
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
3
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
3
0
2
3
1
2
1
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
2
0
1
1
0
0
1
0
0
1
0
0
0
3
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
3
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
2
1
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
3
0
0
2
0
1
2
0
0
0
0
1
2
1
0
0
0
0
0
2
2
0
2
0
0
0
4
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
5
0
0
2
2
1
0
0
0
1
1
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
2
0
6
1
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
7
0
0
3
0
6
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
2
0
0
0
0
0
0
0
2
0
4
0
0
0
2
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
2
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
2
3
0
0
1
0
0
0
0
2
0
0
2
0
0
0
1
5
0
2
0
0
3
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
3
0
1
2
2
2
0
2
2
2
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
2
0
1
0
2
0
0
3
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
3
0
0
2
0
0
1
0
2
0
0
1
0
0
2
0
0
2
1
0
0
0
1
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
3
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
1
0
0
1
2
0
0
1
0
0
0
0
0
0
0
4
0
0
1
0
0
1
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
3
0
0
0
0
1
2
0
0
0
0
0
0
4
0
2
0
1
0
0
2
1
0
0
3
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
6
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
3
0
0
3
0
2
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
3
0
0
0
2
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
2
1
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
3
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
5
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
1
0
2
0
0
2
0
0
2
0
2
0
1
0
0
0
0
0
0
1
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
5
2
0
2
0
0
3
2
2
3
0
0
0
1
0
0
1
0
2
3
0
0
0
0
1
2
0
0
0
0
2
0
0
0
3
0
1
3
0
0
0
3
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
3
0
0
0
1
0
2
0
0
2
1
2
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
2
0
1
1
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
1
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
2
0
3
0
0
0
0
2
3
0
2
0
0
0
0
3
0
0
0
0
1
0
0
2
1
0
0
0
0
2
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
5
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
2
1
0
0
0
0
0
0
0
1
2
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
2
0
0
0
0
3
0
0
0
0
1
2
0
2
0
0
2
0
0
1
0
0
0
1
1
3
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
1
2
0
2
0
0
0
0
1
2
0
0
0
0
2
2
0
0
1
0
0
0
1
2
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
2
0
0
0
1
0
1
2
0
1
0
1
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
1
0
0
0
1
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
1
0
0
1
0
0
4
1
2
1
1
1
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
1
1
2
1
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
3
0
0
2
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
4
2
0
1
0
0
0
0
1
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
1
0
2
0
0
4
0
0
0
0
0
1
2
1
2
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
5
2
2
0
0
0
1
2
0
0
0
0
0
2
0
2
0
7
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
2
0
0
1
0
0
1
0
0
0
1
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
6
1
0
4
0
0
0
0
3
0
0
0
0
1
0
2
0
1
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
2
0
3
0
0
1
2
0
0
0
2
0
0
0
1
1
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
5
1
0
0
0
2
0
3
2
0
0
0
0
3
6
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
1
0
2
0
0
3
0
1
1
0
0
0
0
1
4
2
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
2
0
0
0
0
0
0
0
1
4
2
0
0
0
0
2
2
3
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
3
0
4
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
2
2
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
2
0
2
0
0
0
0
6
1
1
1
0
0
0
1
0
2
0
1
0
0
0
1
2
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
1
0
0
1
0
2
0
0
2
0
0
0
0
1
0
1
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
3
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
1
3
2
0
1
0
2
0
2
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
2
2
1
1
0
0
0
0
1
2
0
0
1
0
0
1
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
1
0
2
2
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
7
0
2
1
0
0
0
0
2
0
0
1
0
1
0
0
0
0
1
2
0
1
0
0
0
2
1
2
0
5
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
1
0
0
0
2
2
0
2
0
0
2
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
3
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
3
0
0
1
1
0
1
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
2
0
0
0
0
2
0
1
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
1
0
0
0
5
1
0
0
0
1
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
1
1
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
6
1
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
3
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
3
0
1
3
0
0
0
0
0
0
2
0
2
1
1
0
2
0
0
2
2
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
10
0
0
0
0
2
1
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
2
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
3
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
1
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
2
2
0
0
0
0
0
4
2
0
0
0
2
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
3
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
2
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
3
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
2
0
1
2
0
0
0
0
2
0
0
0
2
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
1
0
1
0
0
0
2
0
0
0
1
0
0
2
0
2
2
5
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
1
0
0
0
0
1
0
2
0
0
2
2
2
5
1
2
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
3
0
0
0
5
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
3
0
10
1
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
1
0
1
1
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
1
3
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
3
0
1
0
2
1
6
0
2
0
0
0
0
0
0
0
2
0
2
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
2
2
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
2
0
0
0
2
1
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
2
3
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
3
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
4
0
0
0
0
1
0
1
2
0
0
0
0
0
0
2
0
2
2
0
0
0
0
1
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
4
1
0
2
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
4
0
3
0
0
1
0
1
0
0
0
0
0
0
2
2
0
0
0
2
2
1
0
0
0
0
1
0
0
0
0
0
1
3
0
3
0
1
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
2
4
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
1
1
0
0
0
1
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
3
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
2
1
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
6
0
0
0
3
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
3
0
2
0
1
0
3
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
2
2
0
2
2
0
1
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
4
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
2
0
6
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
1
1
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
2
0
1
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
5
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
3
0
0
0
1
2
4
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
2
1
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
3
0
0
0
2
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
2
0
0
1
0
1
1
0
0
0
0
1
2
0
0
0
3
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
2
0
3
0
0
2
1
0
0
0
0
0
0
1
0
0
2
0
6
0
0
1
0
0
0
0
1
0
0
0
0
0
4
2
0
0
0
1
0
0
1
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
9
1
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
2
1
0
0
1
0
0
1
0
2
0
0
0
0
2
0
2
1
0
0
2
0
0
0
0
5
0
0
0
1
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
1
0
1
1
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
1
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
2
1
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
1
1
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
1
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
1
1
0
0
0
0
0
8
1
0
1
0
0
2
1
0
0
0
1
1
0
0
1
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
1
0
4
0
0
2
2
0
1
2
2
0
1
0
0
3
0
0
0
1
0
1
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
2
0
2
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
2
6
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
2
0
1
2
0
0
0
0
2
0
0
0
0
0
1
3
0
3
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
1
1
1
0
0
0
2
4
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
1
0
0
0
1
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
3
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
1
0
0
2
3
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
2
1
2
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
2
2
0
0
0
0
0
0
2
0
0
4
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
2
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
2
1
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
1
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
5
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
1
1
0
0
1
0
0
0
2
1
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
2
0
1
2
0
0
2
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
1
0
0
0
2
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
4
0
0
0
0
2
2
1
0
0
3
0
0
2
2
0
0
0
2
0
0
0
0
2
0
0
0
0
2
1
0
2
4
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
5
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
3
0
1
0
2
0
3
0
0
0
3
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
2
2
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
2
1
2
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
4
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
3
0
0
0
0
2
0
0
3
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
3
0
0
1
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
1
0
0
5
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
1
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
5
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
2
2
1
0
1
0
1
0
2
1
0
0
2
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
2
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
5
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
2
1
1
0
2
3
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
2
2
1
1
0
0
4
0
0
0
0
0
0
1
3
0
0
2
0
3
0
1
0
2
0
2
0
0
0
0
0
1
0
0
1
1
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
1
2
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
1
0
0
1
1
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
2
0
7
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
1
1
0
0
0
0
0
2
1
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
1
2
0
2
0
2
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
3
0
2
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
8
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
3
2
1
0
0
0
3
0
0
0
0
2
0
2
2
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
5
0
0
0
0
0
1
0
0
0
0
0
0
7
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
3
2
0
2
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
20
0
0
1
0
0
1
1
0
0
1
3
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
2
2
0
0
2
0
1
0
0
1
0
0
0
0
2
4
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
2
0
2
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
2
0
1
0
2
0
2
0
0
1
1
3
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
2
1
0
0
1
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
2
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
2
1
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
2
0
0
0
0
0
0
0
2
1
5
0
1
0
0
0
0
0
0
0
0
1
1
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
1
0
2
1
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
1
1
0
0
2
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
3
0
0
0
1
1
0
1
1
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
8
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
2
0
2
0
0
1
0
0
0
0
3
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
3
2
1
0
1
0
3
0
0
1
0
0
1
0
3
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
1
0
4
1
1
0
0
0
0
0
1
0
0
2
2
0
2
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
1
0
1
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
1
1
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
1
0
0
1
1
0
0
2
0
2
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
2
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
4
0
1
0
0
0
1
0
0
0
0
2
1
0
2
0
0
0
0
1
0
2
3
1
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
2
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
3
2
0
1
0
1
2
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
1
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
4
0
1
0
0
0
0
3
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
6
1
0
0
2
2
1
0
0
0
0
0
0
2
0
0
2
0
2
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
3
1
0
0
0
0
5
0
1
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
1
1
1
0
0
0
2
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
5
0
0
0
3
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
3
0
0
1
0
2
1
0
0
1
2
0
0
0
0
1
0
1
0
2
6
4
0
0
0
1
1
0
3
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
1
0
0
0
3
0
0
2
0
0
0
1
0
0
1
0
2
0
0
0
0
1
1
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
1
2
0
1
0
1
0
0
0
0
0
0
0
0
0
3
2
0
0
1
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
2
0
2
0
0
0
0
0
0
1
2
1
1
1
0
0
0
0
1
0
1
0
2
0
2
0
2
0
1
2
0
2
1
1
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
2
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
2
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
2
1
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
2
0
2
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
6
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
4
2
0
0
0
2
0
0
1
2
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
2
0
0
1
0
2
0
1
0
2
0
0
1
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
3
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
2
2
2
0
1
0
0
0
0
0
0
0
1
0
0
1
10
0
0
2
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
3
0
0
1
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
3
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
1
0
1
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
5
1
3
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
3
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
2
1
0
0
0
0
0
0
0
0
4
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
4
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
3
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
3
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
3
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
1
2
2
0
0
1
0
0
0
0
0
2
0
0
2
0
1
1
0
2
0
3
2
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
2
2
0
1
0
2
0
0
2
0
0
0
0
1
0
2
1
0
1
1
0
0
0
2
0
0
0
0
0
0
1
1
2
0
0
0
1
0
0
0
1
0
0
0
1
2
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
5
0
0
0
0
0
1
0
2
0
0
2
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
2
1
2
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
2
1
0
0
0
0
0
1
2
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
1
2
0
0
0
0
1
0
1
5
0
0
0
0
1
0
0
2
0
2
1
0
0
0
0
2
0
0
0
2
1
2
2
3
0
0
3
0
0
0
0
0
0
0
0
0
3
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
1
0
2
0
0
0
2
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
3
0
0
0
4
0
0
3
0
1
0
0
0
0
3
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
6
0
2
3
2
1
1
0
2
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
2
1
0
2
1
0
1
0
2
0
0
0
2
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
1
3
0
2
1
0
0
0
0
0
0
0
1
0
0
1
2
0
0
1
0
1
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
1
0
0
0
0
0
0
0
3
0
2
0
4
0
2
0
1
0
1
0
0
0
2
3
1
0
2
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
1
0
1
3
0
0
0
2
2
0
0
0
0
0
1
0
0
2
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
2
0
1
0
1
0
0
1
0
0
0
2
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
3
2
0
3
0
0
0
0
0
1
1
1
2
0
0
1
0
0
0
5
2
1
0
1
1
0
1
0
0
2
6
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
5
3
0
2
0
3
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
5
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
1
4
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
3
1
2
0
0
2
0
0
0
2
0
0
0
0
2
0
1
0
1
3
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
2
2
0
0
0
0
1
0
2
0
0
1
1
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
2
0
0
4
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
1
2
0
0
2
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
2
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
2
2
1
1
0
0
0
0
1
0
0
0
0
1
0
2
0
0
2
0
2
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
2
1
1
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
3
2
0
0
2
0
0
0
1
0
11
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
7
0
0
0
0
1
0
1
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
4
0
0
0
0
1
0
0
0
6
2
0
0
2
2
0
0
0
0
1
0
0
0
2
2
0
0
4
0
3
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
1
0
1
0
0
0
1
0
0
0
0
0
1
3
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
1
0
1
0
2
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
3
1
1
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
1
0
2
1
2
0
0
0
0
0
1
0
2
1
1
1
0
0
7
3
0
2
0
0
0
0
0
0
1
0
0
1
0
0
6
0
0
0
0
0
0
6
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
1
0
2
1
0
2
0
0
0
1
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
3
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
3
0
0
2
2
0
0
0
2
0
2
0
1
1
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
4
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
3
0
1
0
0
1
0
0
2
2
4
2
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
2
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
5
0
0
3
1
0
0
2
0
0
2
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
5
1
0
0
0
0
2
2
1
0
0
1
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
2
1
1
1
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
2
0
0
1
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
1
1
2
2
1
0
1
0
0
0
0
3
1
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
3
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
2
1
0
0
0
0
1
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
8
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
6
0
0
0
0
3
0
1
1
0
0
4
2
0
0
0
0
0
0
1
1
0
1
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
2
0
0
0
2
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
1
3
0
0
0
0
0
1
0
4
3
0
0
2
0
0
1
5
0
0
0
2
1
0
0
0
0
1
0
0
0
2
0
0
0
2
3
0
1
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
7
1
0
0
3
0
0
1
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
3
2
2
0
0
0
0
0
3
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
3
0
0
0
2
1
2
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
3
0
0
0
0
0
0
0
1
2
0
2
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
3
1
1
0
0
0
1
0
4
3
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
1
0
0
2
0
0
2
0
0
0
2
2
0
1
0
0
0
0
1
0
2
0
2
0
0
1
3
0
0
0
2
0
0
1
0
0
0
0
0
0
3
0
2
0
0
0
1
0
0
0
1
0
0
0
0
6
0
0
1
2
1
0
0
0
0
2
1
0
0
1
0
2
0
1
0
0
0
0
0
1
0
0
0
0
3
2
2
0
0
0
2
0
1
0
0
1
0
0
1
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
1
0
1
0
0
0
4
0
0
1
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
3
0
0
0
1
0
0
0
2
1
1
2
0
1
3
0
0
0
0
0
1
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
1
0
0
1
2
1
0
0
1
0
0
0
2
4
0
0
0
0
0
0
0
0
1
0
1
0
2
1
0
0
0
1
2
1
0
0
0
1
0
0
0
2
0
1
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
1
8
0
0
0
0
3
0
0
0
0
3
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
1
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
3
0
0
2
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
1
1
0
0
0
0
0
1
0
0
5
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
3
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
1
0
1
0
0
0
3
0
0
0
0
1
2
0
0
0
0
2
0
0
0
1
4
1
0
0
0
0
1
0
0
3
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
6
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
2
0
3
0
0
0
2
0
0
2
0
1
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
8
0
0
3
0
1
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
6
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
1
1
0
0
2
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
2
3
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
5
0
0
0
2
0
0
1
2
0
4
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
2
3
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
3
0
0
0
4
2
0
0
0
0
0
1
0
0
2
0
0
0
1
1
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
2
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
2
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
1
2
4
2
1
0
0
0
0
0
2
0
0
0
0
2
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
1
0
2
1
0
0
4
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
5
0
0
0
0
4
2
0
0
0
0
0
2
0
0
0
0
2
0
2
1
2
6
0
0
0
1
0
0
3
0
0
0
0
1
0
0
0
1
0
2
3
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
5
0
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
3
1
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
2
0
0
2
0
2
0
0
2
1
0
0
0
0
0
0
2
1
0
2
0
0
0
1
2
0
2
0
2
2
0
2
0
1
0
2
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
1
0
1
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
4
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
1
3
7
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
3
0
0
2
0
0
0
0
0
2
0
3
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
2
1
0
0
0
0
0
2
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
1
0
2
1
2
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
3
2
0
0
0
0
1
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
1
1
1
0
1
0
1
0
4
2
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
1
0
0
1
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
3
0
0
1
0
0
0
0
0
2
0
3
1
2
0
0
1
0
0
0
0
3
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
1
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
3
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
1
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
1
0
10
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
1
3
0
0
0
4
0
0
0
11
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
1
0
0
0
0
0
0
1
7
0
0
1
0
0
0
0
0
0
0
2
2
0
1
0
0
0
1
0
2
2
0
0
1
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
2
1
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
2
5
0
0
1
0
0
0
0
1
2
0
2
0
1
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
4
1
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
1
0
0
2
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
1
2
0
0
0
0
2
0
0
0
0
1
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
1
0
0
1
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
2
0
0
0
0
1
0
0
6
0
0
0
1
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
7
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
10
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
3
0
0
0
0
2
0
0
0
0
0
0
2
1
2
2
0
0
0
0
4
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
3
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
2
0
2
0
4
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
3
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
1
0
0
1
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
1
5
0
0
2
1
0
1
0
0
2
2
1
0
2
2
0
1
2
0
0
0
0
0
1
0
1
2
0
2
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
4
3
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
3
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
1
0
3
1
1
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
1
1
1
0
0
0
0
4
0
0
0
0
1
0
2
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
3
0
0
0
2
0
0
0
0
0
0
0
6
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
4
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
3
0
3
0
1
0
0
0
0
0
0
2
0
0
1
1
0
0
0
2
0
0
3
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
1
2
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
10
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
5
0
0
0
0
0
1
0
0
2
0
0
2
1
0
0
6
0
2
3
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
2
0
1
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
2
0
4
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
3
0
0
1
0
1
0
0
0
0
0
3
0
0
2
0
0
1
2
0
0
2
0
0
1
0
0
0
1
1
0
1
0
1
0
0
2
0
3
0
0
1
0
0
0
0
0
0
1
6
2
1
0
0
0
1
2
1
0
1
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
5
0
2
0
1
1
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
2
2
0
0
0
1
1
0
0
0
0
0
3
1
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
1
2
2
0
1
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
4
2
0
0
0
0
2
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
3
3
0
1
0
0
3
0
3
0
0
0
1
0
0
0
0
0
7
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
3
0
0
0
0
1
0
1
2
0
0
0
2
0
0
1
1
0
0
0
2
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
1
2
0
2
0
0
2
4
0
1
0
0
0
0
0
5
0
0
3
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
2
4
0
0
0
0
0
1
0
0
4
0
2
0
0
0
1
3
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
2
0
0
1
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
2
0
1
1
0
0
0
3
0
0
0
0
0
2
0
0
1
0
0
0
1
1
0
0
0
0
2
0
0
0
1
0
0
1
2
0
0
1
0
1
0
0
0
0
2
1
0
0
2
1
0
2
1
0
0
0
3
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
2
1
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
15
1
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
3
0
0
0
0
1
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
3
0
0
0
0
0
0
2
0
0
0
0
3
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
2
0
0
1
0
1
0
1
0
3
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
2
1
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
1
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
3
0
0
0
0
2
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
2
2
2
0
0
0
1
0
0
0
0
0
0
2
3
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
1
1
1
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
2
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
8
0
2
3
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
2
0
0
0
0
0
1
3
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
1
0
2
0
0
0
1
0
2
2
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
3
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
8
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
6
3
0
0
4
2
0
0
0
0
0
0
3
1
0
0
1
1
0
0
0
0
0
2
0
1
0
2
0
0
1
0
0
1
0
0
2
0
0
1
1
0
0
0
3
0
3
3
0
0
0
0
0
1
0
2
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
6
0
1
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
1
0
0
2
0
0
0
3
0
0
1
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
3
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
3
0
0
0
1
0
0
4
0
0
0
1
1
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
1
0
0
2
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
2
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
2
0
2
0
1
1
0
0
0
2
2
1
0
0
0
2
0
0
1
2
0
0
1
0
0
2
0
0
0
2
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
1
0
0
0
0
0
0
0
0
2
1
10
2
0
0
0
8
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
4
1
0
0
0
1
0
0
2
0
0
0
2
0
2
0
0
1
2
0
0
1
0
0
0
1
2
0
0
0
0
0
2
2
0
1
0
0
1
0
2
2
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
1
0
0
0
0
6
0
0
0
1
0
0
0
1
2
1
0
0
2
0
1
1
0
0
0
0
1
0
0
6
0
0
2
1
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
2
1
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
2
2
0
3
0
0
3
0
1
0
3
0
0
1
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
1
2
0
0
0
1
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
3
0
0
1
0
0
0
2
0
4
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
1
0
0
0
0
0
1
2
0
0
1
0
0
1
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
2
0
0
0
2
0
0
0
0
0
0
4
1
0
0
0
0
0
0
2
1
0
0
1
2
0
3
0
1
2
0
0
0
1
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
1
2
1
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
3
0
0
0
0
0
2
0
3
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
3
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
1
0
0
0
1
0
0
0
1
2
1
0
0
0
0
0
0
0
1
0
2
0
0
2
1
1
0
0
2
0
3
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
3
0
2
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
3
1
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
3
0
7
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
18
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
2
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
5
0
1
0
0
3
0
2
0
0
0
0
2
2
0
0
0
1
1
0
4
0
0
1
0
0
0
0
0
6
3
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
1
0
5
1
0
0
0
2
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
3
0
0
0
0
0
0
0
0
3
1
0
2
1
0
0
0
0
2
2
0
0
0
0
0
0
0
2
2
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
1
1
0
1
0
0
0
0
0
2
0
0
0
0
0
1
2
1
0
0
0
1
0
0
0
2
0
0
2
0
0
2
0
5
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
2
0
0
2
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
2
1
0
0
0
2
1
0
0
0
1
0
0
1
0
7
0
1
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
2
1
0
0
0
0
1
1
1
0
0
2
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
4
0
1
1
0
2
1
0
0
2
0
2
0
0
0
2
0
0
0
2
0
3
0
0
0
0
3
0
3
1
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
2
0
0
2
2
1
0
0
1
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
2
0
0
0
1
5
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
2
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
1
0
0
3
0
0
0
1
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
1
2
1
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
2
0
3
0
3
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
3
0
0
1
0
0
0
0
0
1
0
0
1
2
0
0
4
1
0
0
0
0
0
2
0
0
0
2
0
1
4
0
0
0
2
1
0
0
0
1
2
0
0
2
2
0
1
0
0
0
1
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
1
0
1
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
1
0
0
0
1
0
1
1
0
2
1
2
0
0
0
0
0
0
0
0
1
0
3
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
5
0
0
2
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
4
0
1
0
0
0
0
2
0
2
0
0
2
0
0
0
1
0
0
0
0
1
2
0
2
0
0
0
1
1
4
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
2
0
2
0
0
6
1
1
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
1
0
0
1
0
1
0
2
2
0
0
0
0
0
0
2
0
0
1
0
0
1
2
2
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
3
0
2
2
1
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
1
1
0
0
0
0
0
2
0
0
0
1
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
1
1
2
0
1
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
3
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
4
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
1
0
3
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
2
0
2
1
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
1
0
1
0
2
1
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
2
0
2
0
1
0
2
2
1
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
3
2
0
0
2
0
0
1
0
0
0
2
0
0
7
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
3
1
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
7
2
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
2
1
0
0
1
0
4
2
0
0
1
3
1
3
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
2
0
1
2
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
3
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
5
0
1
0
1
0
0
0
2
0
0
0
0
3
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
1
1
0
0
0
0
0
2
2
0
2
0
2
1
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
1
0
0
0
2
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
3
1
0
0
0
2
2
1
1
0
0
0
2
1
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
1
0
1
0
2
0
0
0
1
0
0
1
0
0
0
0
0
2
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
2
0
1
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
8
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
6
2
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
2
0
2
0
0
0
0
0
0
2
1
0
0
2
0
0
0
1
1
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
1
2
1
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
1
0
3
0
0
1
0
0
1
1
2
0
0
2
0
0
1
0
0
2
0
2
0
0
0
0
0
0
2
0
2
0
2
0
2
0
0
0
0
2
0
1
2
2
1
0
0
0
0
2
0
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
2
1
0
0
2
0
0
0
0
0
1
0
0
1
0
1
1
2
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
4
0
0
3
0
0
2
0
1
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
8
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
1
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
8
1
0
0
0
0
0
0
1
2
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
7
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
2
0
0
0
1
0
1
0
0
1
0
1
0
0
1
1
0
0
0
1
4
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
1
0
0
3
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
3
0
0
2
2
0
0
2
1
0
0
0
0
2
0
2
0
0
0
1
2
2
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
2
0
0
2
0
0
0
1
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
1
0
0
2
2
0
1
0
0
1
0
0
2
0
0
2
0
0
3
2
0
0
2
0
4
3
2
0
0
0
0
0
2
2
0
0
2
0
1
0
1
0
0
0
0
3
0
0
2
2
2
0
0
0
0
0
0
2
1
5
0
0
0
1
0
1
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
1
1
0
0
0
0
0
1
2
0
2
1
0
0
0
0
0
0
1
2
0
0
1
2
0
1
0
1
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
2
1
0
0
0
0
0
0
0
1
2
1
0
3
0
0
1
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
1
1
4
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
5
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
4
2
1
2
0
0
0
0
0
0
0
0
0
0
2
0
2
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
1
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
2
1
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
1
2
1
0
0
0
0
0
0
1
1
1
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
3
1
0
1
1
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
1
1
0
2
2
6
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
2
3
0
0
2
3
0
0
0
2
1
0
0
0
0
1
0
1
0
0
0
1
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
5
0
0
0
0
0
0
0
0
2
0
0
5
0
0
0
0
0
1
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
1
1
0
2
0
0
0
0
0
2
0
0
0
3
0
1
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
2
0
0
1
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
1
0
1
0
3
0
0
0
0
2
1
0
0
0
14
0
0
0
0
1
0
2
0
1
0
3
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
2
1
1
0
0
1
7
0
2
0
0
0
0
0
1
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
1
1
0
3
0
0
1
0
1
0
2
0
0
1
0
0
1
0
2
0
0
0
2
1
0
0
0
0
0
0
0
1
0
1
1
0
0
2
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
1
0
1
0
2
3
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
2
1
1
0
0
1
0
0
2
0
2
0
0
0
0
0
0
1
0
0
2
1
1
0
0
0
0
0
3
0
0
0
1
0
0
0
0
2
1
0
0
0
2
0
2
0
0
0
0
1
0
0
1
0
2
0
1
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
2
0
0
2
0
1
0
0
0
0
1
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
2
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
2
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
3
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
1
0
0
1
4
0
0
0
1
2
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
3
0
0
8
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
2
0
1
0
1
0
0
2
1
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
2
1
2
0
0
3
0
0
0
0
0
2
1
0
0
0
1
5
2
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
2
0
0
0
0
1
4
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
2
0
0
2
0
0
0
1
0
2
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
3
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
1
0
1
0
0
0
0
1
0
0
2
0
0
0
0
3
0
0
0
0
0
1
0
0
3
0
0
0
0
0
1
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
2
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
6
0
0
1
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
3
0
0
0
5
0
0
0
0
0
2
0
0
0
1
0
2
2
0
0
1
0
2
0
0
2
2
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
3
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
1
0
0
0
0
0
0
0
3
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
2
0
3
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
1
0
0
0
2
1
0
0
0
1
0
0
0
2
0
0
0
1
1
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
1
0
0
4
0
0
1
0
0
1
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
2
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
2
1
0
2
2
2
0
1
3
0
1
0
0
0
2
2
0
0
0
0
0
0
2
1
2
1
0
1
1
0
0
0
2
0
2
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
3
2
0
0
0
0
1
0
0
0
0
2
0
3
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
1
0
0
1
3
0
0
0
0
1
0
1
1
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
3
1
0
0
0
3
0
0
4
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
2
1
1
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
2
1
0
0
0
0
1
2
0
0
0
0
0
2
0
1
0
1
0
0
2
0
0
0
0
2
3
0
0
0
0
1
0
1
0
0
0
2
2
0
0
0
0
2
0
0
0
3
2
0
1
0
0
0
2
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
3
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
3
2
0
2
2
0
0
0
0
0
0
1
0
0
0
1
1
1
1
0
0
0
0
2
0
0
0
0
1
8
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
3
0
2
0
0
1
0
2
0
1
1
1
0
2
0
0
1
2
0
0
2
0
1
0
0
0
0
3
1
0
0
0
1
2
1
0
0
0
0
3
1
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
2
0
0
0
3
0
2
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
2
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
1
0
0
1
2
0
0
2
0
0
2
0
0
2
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
1
0
1
0
2
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
2
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
2
0
1
0
3
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
1
0
0
0
2
0
0
0
0
0
2
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
2
1
2
0
4
0
7
0
0
0
0
0
0
0
0
0
1
2
1
1
0
0
0
0
2
0
0
0
0
0
0
0
3
2
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
1
1
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
2
2
0
0
0
2
0
1
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
2
0
0
1
4
0
1
0
0
1
2
0
0
0
0
1
0
2
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
2
2
0
1
0
0
2
0
2
1
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
4
7
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
3
0
0
0
2
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
2
1
1
2
0
0
2
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
3
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
3
1
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
4
0
2
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
2
0
0
1
0
0
0
1
0
0
0
2
0
0
0
3
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
6
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
2
1
0
3
0
0
0
1
3
0
0
0
0
1
2
0
0
0
0
0
0
1
0
2
0
0
0
2
0
10
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
3
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
4
0
0
0
0
2
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
1
4
0
1
0
2
2
0
0
0
0
1
2
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
4
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
3
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
4
0
0
0
2
0
0
0
0
1
2
0
0
0
0
1
0
2
0
0
0
2
3
0
0
0
2
0
0
0
0
0
0
1
1
2
0
0
1
0
0
0
0
1
0
0
0
2
0
0
2
2
0
0
0
1
0
0
0
0
0
1
1
2
1
0
0
0
0
2
0
0
0
0
0
0
4
0
1
0
0
1
0
0
0
2
0
2
0
2
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
3
0
1
2
1
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
1
0
1
2
0
0
0
1
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
1
0
0
0
0
2
0
0
0
0
0
2
0
5
0
0
0
3
0
2
0
0
0
0
0
2
0
1
0
0
1
0
0
2
0
0
0
2
0
1
0
1
0
0
1
0
0
2
0
0
2
1
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
1
0
2
0
5
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
3
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
3
0
1
0
0
0
0
2
0
0
2
0
1
0
0
0
1
0
1
0
0
2
2
0
1
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
6
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
3
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
1
0
2
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
1
1
0
0
0
0
3
0
0
4
1
0
3
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
1
0
0
1
2
0
3
0
0
0
0
0
0
0
0
1
0
1
2
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
2
6
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
2
0
0
0
2
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
1
0
0
0
3
1
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
1
0
1
0
0
3
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
4
0
1
1
2
1
0
1
1
0
0
1
0
2
0
0
0
0
0
2
0
0
2
0
0
0
1
7
0
2
0
1
0
0
0
0
2
2
2
2
0
0
0
1
0
1
3
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
1
2
1
1
0
1
2
0
0
0
0
4
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
1
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
1
1
0
2
0
3
2
1
1
1
0
2
0
5
0
0
0
1
0
0
1
1
2
0
0
0
1
0
0
2
0
1
0
0
1
0
1
0
2
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
7
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
3
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
1
0
5
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
1
1
0
0
2
0
0
0
0
0
3
0
0
0
0
0
2
1
1
0
1
0
1
2
1
2
0
0
2
0
0
0
0
2
2
0
1
1
0
1
2
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
2
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
1
1
0
0
0
1
0
0
0
2
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
2
2
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
1
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
2
1
0
2
0
0
0
2
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
3
1
0
0
1
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
1
0
0
2
0
0
0
0
1
1
0
0
3
0
0
0
0
0
0
0
4
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
2
0
0
0
0
1
1
0
0
0
0
2
0
0
0
3
0
1
1
0
1
0
1
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
3
0
0
2
0
0
4
0
0
0
2
0
1
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
4
0
0
3
0
2
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
4
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
1
2
0
1
3
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
4
0
0
0
1
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
1
2
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
2
0
1
2
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
3
2
0
0
1
4
0
0
1
0
0
0
0
0
3
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
2
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
1
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
2
0
2
2
0
1
0
0
0
0
2
0
0
2
0
0
1
0
0
0
2
1
0
1
0
2
0
0
0
0
0
0
2
0
0
2
1
0
0
2
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
2
0
0
1
0
1
0
0
2
0
0
0
2
2
0
0
0
1
0
0
1
0
0
0
2
1
2
1
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
3
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
2
0
2
1
2
0
0
0
0
0
1
2
0
2
0
2
0
0
0
0
2
0
0
0
2
0
1
0
0
1
0
2
0
0
2
0
1
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
1
1
0
0
0
1
0
2
0
0
0
1
0
0
0
2
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
2
0
1
1
0
0
1
0
0
2
2
1
0
2
0
2
0
0
0
0
1
1
0
2
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
1
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
1
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
3
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
2
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
1
1
0
2
0
0
0
1
1
0
0
2
0
1
0
0
0
0
1
1
0
1
0
0
0
2
0
1
3
0
2
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
3
0
0
0
0
1
4
1
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
2
1
0
1
1
0
3
0
0
1
1
1
0
1
0
0
0
1
0
1
2
3
0
0
0
0
0
2
0
2
0
0
1
0
1
1
0
0
1
0
0
0
1
0
0
0
3
2
0
0
0
1
1
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
1
0
0
1
2
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
3
2
0
0
0
0
1
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
3
3
1
0
0
0
0
2
0
0
0
1
3
0
1
0
0
1
7
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
2
0
0
0
1
0
0
0
1
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
5
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
6
0
0
0
0
0
2
3
0
0
0
0
0
2
0
1
0
2
0
0
2
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
2
4
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
3
3
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
2
2
1
0
0
2
0
4
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
2
0
6
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
4
2
0
1
0
0
2
0
2
2
0
1
0
1
0
1
1
0
0
0
2
0
0
0
0
2
0
0
0
1
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
4
2
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
1
2
0
1
2
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
4
0
2
2
0
0
2
0
1
4
0
2
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
1
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
5
1
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
5
0
1
0
0
0
0
1
0
0
0
0
0
9
2
2
0
1
0
0
5
0
0
0
0
1
0
2
1
2
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
2
2
0
1
0
0
2
0
0
0
0
0
1
0
0
1
2
0
0
0
0
2
2
0
0
0
0
0
1
2
1
1
0
0
2
2
0
0
0
2
1
0
1
0
0
0
2
1
0
0
1
0
0
0
1
0
0
1
0
0
1
1
0
3
0
0
0
0
6
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
1
0
2
1
0
0
0
0
0
3
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
1
0
1
0
0
0
1
0
0
5
0
0
0
3
0
3
1
2
0
0
0
2
2
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
1
0
1
2
2
0
6
0
0
1
0
1
1
0
0
0
0
2
1
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
2
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
3
2
0
0
1
0
0
0
0
1
3
0
0
0
1
1
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
5
0
0
1
0
0
2
0
0
0
0
2
0
1
0
0
1
0
1
0
0
0
1
2
0
2
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
2
0
0
0
0
0
3
0
0
2
0
2
1
0
0
1
0
0
0
0
1
2
1
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
1
0
1
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
4
4
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
2
0
1
2
0
0
0
0
0
3
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
7
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
3
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
3
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
1
1
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
1
0
0
0
2
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
2
0
4
1
0
0
1
0
0
0
0
0
2
0
0
0
2
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
2
1
0
2
0
0
0
0
0
0
1
0
0
1
0
2
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
2
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
3
1
1
2
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
6
0
0
1
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
2
0
0
0
2
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
3
2
0
0
0
2
0
0
0
1
0
0
4
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
4
2
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
4
0
0
2
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
2
2
0
2
0
1
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
1
0
0
0
1
1
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
2
0
0
2
1
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
2
1
0
1
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
3
0
0
1
2
0
0
1
0
1
0
2
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
5
0
0
0
7
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
1
4
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
1
3
0
0
1
1
0
0
1
0
0
2
0
1
2
1
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
2
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
2
0
0
3
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
2
2
0
3
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
3
2
0
0
0
0
2
1
1
0
5
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
2
0
0
0
0
0
0
1
1
2
1
0
2
0
0
2
0
3
0
0
2
0
0
0
1
1
0
2
0
0
0
0
4
2
0
0
0
0
0
2
1
0
0
0
1
11
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
1
0
0
2
1
0
0
0
1
0
0
0
0
1
1
1
0
0
0
3
0
0
2
2
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
1
0
0
0
0
0
3
0
1
0
2
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
1
0
3
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
3
0
0
0
1
0
0
0
0
2
2
2
0
0
0
3
5
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
2
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
1
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
2
0
1
0
0
0
0
2
0
8
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
1
0
1
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
2
3
0
0
0
0
1
0
0
0
0
0
2
0
1
0
1
0
0
0
3
2
0
0
2
1
1
2
0
0
0
0
0
0
2
0
0
0
0
3
1
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
2
1
0
0
0
0
3
1
0
0
0
2
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
3
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
2
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
5
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
1
0
1
1
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
3
2
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
1
1
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
1
0
0
0
0
0
0
2
1
0
1
0
1
0
0
0
3
0
0
3
0
0
0
2
0
0
0
0
2
3
0
0
1
0
2
0
0
1
0
2
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
3
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
1
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
16
0
0
0
0
2
0
0
1
0
0
4
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
3
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
3
0
1
0
0
3
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
2
0
0
1
0
1
0
0
3
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
1
1
0
0
5
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
2
0
0
2
2
0
0
0
2
0
0
3
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
4
0
0
4
0
3
7
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
2
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
1
0
0
0
2
0
0
0
0
0
1
0
2
2
0
0
2
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
4
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
2
0
0
0
1
1
1
0
0
0
2
0
0
0
9
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
2
0
0
0
1
0
1
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
2
1
0
0
1
1
0
0
0
1
2
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
3
0
2
0
0
1
0
0
3
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
1
1
1
2
0
0
2
0
0
0
3
0
0
0
0
0
6
2
0
0
1
0
1
0
0
2
0
2
0
0
1
0
0
0
0
1
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
7
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
2
0
1
0
0
0
2
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
4
0
0
0
0
0
2
0
0
3
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
3
0
0
0
1
0
1
0
3
0
0
2
1
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
1
2
0
3
0
0
0
0
0
1
3
1
0
0
1
0
0
0
0
0
0
0
0
0
2
2
3
0
1
0
0
1
1
0
0
2
2
0
1
0
0
0
0
0
1
1
1
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
1
2
0
0
1
0
1
0
0
0
0
2
5
0
0
0
0
0
0
2
0
0
0
1
2
0
0
1
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
2
0
0
0
0
0
1
0
0
2
0
0
0
3
0
0
0
2
0
4
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
1
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
3
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
3
0
2
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
1
2
4
0
0
0
0
3
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
3
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
4
1
0
0
0
1
0
0
0
2
4
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
2
0
3
0
1
0
2
3
3
0
0
0
0
1
1
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
1
1
0
1
0
0
0
0
6
0
0
0
0
2
0
2
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
2
1
0
2
0
0
1
0
5
0
0
0
0
0
0
0
2
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
2
0
0
4
1
0
0
0
2
2
1
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
7
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
1
1
1
0
2
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
2
2
2
0
0
0
1
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
1
0
2
0
0
0
0
1
1
0
0
1
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
3
0
1
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
3
0
2
1
2
0
0
0
0
0
6
2
3
0
0
0
0
0
0
0
3
0
0
1
0
1
2
0
1
1
0
1
0
1
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
4
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
18
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
2
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
1
0
1
2
0
0
0
0
2
2
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
2
1
2
2
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
1
2
1
1
0
1
2
0
0
0
0
0
0
0
0
0
0
2
2
0
2
1
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
3
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
8
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
1
1
2
2
2
0
2
0
0
0
0
3
0
0
0
2
0
0
2
3
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
2
2
0
2
0
0
0
1
0
0
1
2
0
0
2
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
3
0
0
0
2
0
2
1
0
0
2
0
0
2
0
0
0
2
2
0
1
1
2
1
0
0
0
1
0
0
1
0
1
0
1
0
1
1
0
2
0
3
0
0
1
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
6
0
0
0
0
2
0
1
0
1
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
3
0
2
0
0
0
0
0
0
0
0
2
1
2
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
3
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
9
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
5
0
0
1
0
0
0
0
0
2
0
5
0
0
1
0
0
1
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
1
3
3
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
1
0
1
1
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
2
1
0
0
2
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
3
0
4
2
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
2
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
3
0
0
0
0
0
4
0
0
1
0
3
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
10
2
0
1
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
1
0
5
0
1
0
1
0
0
0
5
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
1
0
0
1
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
2
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
2
0
0
0
0
0
0
1
2
0
2
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
2
1
0
2
0
0
1
0
1
0
2
0
2
0
0
1
0
0
0
4
1
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
2
2
0
0
1
1
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
5
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
1
0
0
2
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
3
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
2
0
2
0
0
2
1
2
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
2
0
0
0
0
1
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
2
0
0
0
0
1
0
0
0
0
0
0
2
0
3
3
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
1
0
0
1
0
1
0
1
0
0
4
0
1
1
2
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
2
1
0
1
0
0
2
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
2
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
5
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
2
0
0
2
0
1
1
0
0
1
2
0
4
0
0
0
0
0
0
0
1
2
0
0
3
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
4
1
0
0
0
0
0
1
0
0
0
0
1
0
2
1
0
0
2
2
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
2
1
0
2
2
0
0
0
0
0
0
2
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
5
2
1
0
0
0
1
0
0
0
0
1
3
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
2
1
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
2
0
1
0
2
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
2
2
2
0
2
0
0
0
1
0
0
0
0
0
1
0
1
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
3
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
2
1
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
3
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
1
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
1
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
3
0
1
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
2
0
0
0
0
3
0
1
0
1
0
0
1
0
0
0
1
0
2
0
2
2
2
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
1
0
0
0
0
0
2
2
2
3
0
0
0
0
2
0
0
2
0
0
1
0
0
0
4
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
2
0
2
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
2
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
2
2
1
0
0
0
0
2
6
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
2
0
1
0
0
2
0
0
2
0
1
0
1
0
0
0
2
0
2
0
3
0
0
0
6
0
0
0
0
0
1
0
1
0
0
0
0
1
0
2
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
1
2
0
2
0
0
0
3
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
3
1
0
0
0
1
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
1
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
2
0
0
0
0
0
0
3
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
3
0
0
0
1
0
0
3
0
1
0
2
0
2
0
0
2
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
1
1
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
1
1
0
0
0
2
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
2
5
0
0
0
0
0
19
0
0
0
0
0
1
0
1
0
3
0
0
1
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
2
0
0
1
0
1
1
0
0
0
0
0
3
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
5
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
1
5
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
4
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
2
1
1
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
7
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
1
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
1
1
2
0
0
1
2
2
0
0
0
1
0
1
2
0
0
0
0
2
0
0
0
0
1
0
0
3
2
0
3
0
2
2
0
2
1
1
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
2
0
0
2
0
1
0
0
5
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
1
0
0
0
0
1
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
2
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
6
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
1
1
0
0
0
0
0
0
6
0
1
1
0
0
0
0
0
0
3
0
0
0
1
2
0
0
0
0
0
0
0
1
2
1
0
0
2
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
2
0
3
0
2
0
0
0
3
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
1
0
2
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
4
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
1
1
0
1
0
2
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
1
0
2
2
0
0
0
0
0
0
2
2
0
0
0
2
1
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
5
0
1
1
0
0
0
0
0
2
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
3
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
1
1
0
0
0
0
1
1
0
0
2
0
0
2
0
1
0
2
1
1
1
2
2
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
1
0
5
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
5
0
1
0
0
0
3
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
1
1
0
1
0
0
0
0
2
0
2
2
0
0
0
0
1
0
0
0
0
1
0
4
0
0
0
0
1
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
2
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
3
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
1
0
8
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
2
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
2
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
3
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
3
1
0
0
1
6
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
7
1
0
1
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
1
0
1
1
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
3
0
0
0
0
1
0
5
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
9
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
1
2
0
0
0
2
3
0
0
0
0
0
1
0
0
0
0
1
0
1
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
3
0
0
3
0
1
0
0
0
0
2
2
2
0
2
0
1
1
0
1
0
0
0
0
5
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
3
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
3
2
0
0
3
0
2
1
0
0
0
0
3
2
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
1
0
0
0
2
1
0
0
0
0
2
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
2
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
5
2
0
2
2
0
0
0
0
1
0
0
1
0
0
0
2
0
0
2
3
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
1
0
0
1
1
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
6
1
1
0
1
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
1
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
1
0
2
0
2
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
1
2
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
4
0
0
2
0
0
2
0
0
0
1
0
4
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
1
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
1
7
0
0
3
0
0
0
0
1
19
0
0
0
0
0
3
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
6
0
0
0
0
0
2
0
0
2
1
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
3
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
1
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
2
0
0
3
2
0
1
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
5
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
5
0
0
0
0
0
0
0
2
4
0
0
1
0
1
2
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
1
2
1
0
0
0
0
0
2
0
0
0
0
0
0
3
2
4
0
2
0
0
2
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
5
2
3
1
0
0
0
2
0
0
0
0
1
2
1
0
0
0
2
2
0
0
0
2
0
0
2
0
0
0
2
2
0
0
0
2
0
0
1
0
2
1
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
1
0
0
0
2
0
2
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
1
1
0
0
0
0
0
1
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
3
0
0
1
0
0
0
1
0
0
0
1
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
1
0
0
0
2
0
0
0
3
0
0
0
2
0
0
0
3
0
3
0
2
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
2
0
0
2
0
4
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
5
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
2
0
2
0
2
0
0
0
2
0
2
0
0
0
2
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
2
0
0
0
0
0
2
0
0
3
2
0
3
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
2
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
2
1
2
0
0
2
0
0
0
0
1
1
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
1
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
13
0
4
2
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
2
0
0
2
0
0
0
1
0
0
1
1
1
0
1
0
0
1
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
4
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
3
0
5
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
2
0
0
3
0
1
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
2
1
0
0
0
0
1
4
0
0
0
0
1
0
0
0
3
0
0
2
0
1
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
2
0
2
0
2
2
0
0
1
0
0
2
0
0
0
3
1
1
0
0
0
0
1
0
0
1
0
2
0
0
0
0
2
1
1
0
0
3
0
2
2
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
2
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
2
1
0
1
1
0
0
0
0
1
0
0
0
0
1
0
1
1
1
1
0
0
0
0
1
0
1
0
0
0
0
0
6
1
0
0
1
0
0
0
0
0
2
4
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
1
0
1
3
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
4
1
0
1
0
2
0
0
0
1
0
0
1
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
4
0
0
1
3
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
3
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
1
2
0
0
1
1
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
1
2
0
1
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
2
0
0
0
3
2
1
0
4
4
0
0
0
0
0
0
0
1
0
0
3
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
1
1
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
3
0
0
0
0
1
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
1
0
0
3
0
0
2
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
2
1
1
0
0
0
3
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
3
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
2
0
0
2
2
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
3
0
0
0
2
0
0
0
1
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
3
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
1
0
2
2
0
0
0
1
0
0
1
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
2
0
0
2
2
0
0
0
0
7
0
2
2
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
2
0
0
3
1
0
2
0
1
0
0
1
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
3
1
0
1
0
2
1
0
0
0
0
1
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
3
2
0
6
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
4
2
0
0
0
1
0
0
0
1
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
3
2
0
0
0
0
2
1
1
0
1
1
1
0
0
0
3
0
0
0
2
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
8
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
3
3
0
0
3
1
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
10
1
0
0
0
0
0
0
2
1
0
0
0
1
1
0
0
0
0
2
0
2
0
0
0
0
1
2
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
1
1
0
0
1
0
0
0
1
1
0
0
0
1
0
0
2
0
0
1
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
2
1
1
2
0
0
0
1
0
0
0
0
6
0
0
0
0
0
0
3
0
1
0
2
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
2
1
0
0
3
0
2
0
2
0
0
0
0
0
0
0
7
0
0
0
2
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
8
0
0
0
3
2
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
1
0
0
0
4
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
3
0
2
0
0
2
2
2
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
1
2
0
0
0
0
0
2
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
2
3
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
2
1
0
0
0
1
0
0
0
0
1
0
0
2
0
1
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
1
2
0
2
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
2
3
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
1
0
0
3
1
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
2
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
1
2
0
0
1
1
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
1
0
0
0
1
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
3
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
2
4
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
2
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
1
0
0
0
0
2
0
0
1
0
2
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
4
2
1
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
3
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
3
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
8
0
1
0
0
0
0
0
0
0
2
0
0
2
2
0
1
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
1
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
2
0
2
2
0
0
2
0
0
0
2
0
1
0
0
0
1
0
0
1
0
1
2
0
0
0
1
2
0
0
0
2
0
3
0
2
2
0
0
0
1
1
0
0
0
0
0
1
1
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
5
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
2
0
0
0
1
1
0
0
1
0
0
0
0
2
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
8
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
5
0
0
0
0
0
2
0
0
0
1
2
0
0
1
0
0
1
0
0
0
0
2
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
1
0
0
2
2
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
1
0
2
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
3
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
6
5
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
7
0
0
0
0
0
2
1
0
0
0
0
5
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
3
2
2
0
1
0
0
2
3
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
3
0
2
0
0
0
0
0
0
1
0
3
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
8
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
1
2
0
1
1
0
0
2
0
0
0
1
0
1
0
0
0
1
0
2
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
1
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
1
1
0
4
2
0
0
0
0
0
0
8
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
6
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
1
0
1
0
0
0
0
0
2
2
0
0
0
0
1
2
0
0
2
0
1
0
0
2
0
2
1
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
7
1
0
1
5
1
3
0
0
0
0
0
1
1
0
0
1
2
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
1
2
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
2
0
2
1
0
0
0
1
0
1
2
2
1
0
1
0
0
0
0
1
2
0
2
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
1
0
0
2
1
2
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
1
2
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
1
0
1
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
3
0
2
0
0
0
1
5
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
1
2
2
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
2
4
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
2
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
3
1
0
1
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
1
2
1
1
0
0
1
0
0
0
0
0
2
0
1
0
0
2
0
0
2
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
5
0
1
0
0
0
1
0
1
0
1
0
0
1
0
1
0
0
0
3
0
0
0
0
1
1
2
2
0
3
0
2
1
0
1
0
0
0
2
0
0
0
1
0
6
0
2
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
1
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
1
1
2
2
0
1
0
2
0
2
0
1
0
1
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
2
0
0
1
2
0
0
0
0
0
0
0
2
1
0
0
5
0
0
1
0
0
0
2
0
0
1
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
4
1
0
0
0
0
0
0
2
3
0
0
0
1
0
2
1
0
0
2
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
2
3
0
0
0
1
0
0
2
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
1
3
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
2
3
0
0
0
0
1
0
0
2
1
0
1
0
0
0
1
1
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
4
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
2
0
2
0
1
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
1
0
2
0
0
0
2
0
3
0
0
0
0
1
1
0
0
0
1
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
1
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
1
0
1
1
0
0
0
0
1
2
0
0
2
0
0
2
0
1
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
3
0
2
0
0
0
0
1
1
0
0
0
1
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
5
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
3
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
4
0
0
0
1
0
2
0
1
0
0
0
1
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
3
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
1
1
1
0
1
1
2
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
2
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
3
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
1
0
0
0
0
0
6
1
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
1
1
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
3
1
0
2
0
0
0
2
2
0
2
3
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
1
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
2
0
0
0
2
1
0
2
0
1
0
0
0
3
0
1
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
2
1
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
1
0
0
0
0
2
0
0
2
1
1
0
0
0
2
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
1
0
0
0
0
0
3
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
5
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
3
0
0
0
1
0
0
0
0
1
2
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
1
0
3
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
2
0
0
2
0
0
0
1
0
0
2
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
2
1
2
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
1
4
0
1
0
0
1
1
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
1
0
1
2
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
5
0
0
0
0
0
1
2
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
2
1
0
2
3
2
0
1
0
1
0
1
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
4
0
0
2
2
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
12
0
2
0
0
1
0
2
0
0
0
2
1
0
0
0
0
0
2
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
2
1
2
0
2
0
0
1
0
0
0
0
4
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
2
1
0
0
0
0
1
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
1
5
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
2
0
2
2
0
0
0
4
5
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
3
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
1
2
0
0
0
0
1
3
2
0
0
0
0
0
0
0
1
0
0
1
4
0
0
0
0
0
3
3
0
0
0
0
2
0
0
1
0
0
1
0
0
0
3
0
4
1
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
3
0
2
1
1
0
0
0
0
0
0
6
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
1
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
1
2
0
0
0
1
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
4
0
0
0
2
0
0
2
10
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
1
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
1
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
2
0
0
0
1
2
7
0
3
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
2
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
1
0
0
0
1
1
0
0
0
0
0
1
0
2
0
2
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
5
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
3
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
1
0
1
2
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
1
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
4
0
1
2
2
0
0
0
0
2
0
0
0
1
0
1
0
0
0
3
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
2
2
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
2
2
6
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
6
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
1
1
2
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
1
1
0
0
1
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
1
2
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
2
2
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
1
3
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
2
0
1
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
3
0
1
0
1
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
3
0
1
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
1
2
1
0
0
1
0
0
0
1
2
0
2
1
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
2
0
1
0
0
1
0
0
1
0
1
3
1
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
1
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
4
1
0
2
0
0
0
0
4
0
0
2
1
0
0
0
1
0
0
1
0
2
0
0
0
2
0
1
0
0
0
6
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
2
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
1
0
2
2
2
0
0
0
0
2
0
2
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
1
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
11
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
1
1
0
0
1
0
0
0
5
0
1
0
1
0
0
0
0
2
0
0
1
2
0
1
1
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
1
0
0
2
0
0
0
1
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
1
1
0
0
1
0
0
0
0
1
0
3
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
8
1
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
2
0
0
1
0
0
1
0
0
1
0
0
1
2
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
4
2
2
0
1
0
0
0
0
2
2
0
2
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
1
0
0
0
0
1
0
2
1
3
0
0
1
0
0
0
0
0
2
0
0
0
3
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
2
2
0
2
0
0
0
2
0
0
2
0
0
0
0
1
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
1
0
0
0
2
1
0
0
2
2
4
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
1
2
1
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
3
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
2
0
1
0
1
2
0
0
0
1
0
0
0
1
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
1
0
0
0
0
0
0
3
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
2
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
3
0
0
0
0
3
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
4
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
1
0
0
4
0
3
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
2
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
3
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
4
0
0
0
2
0
1
0
0
0
2
2
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
2
0
0
0
3
0
1
0
2
1
0
0
0
0
0
0
0
0
4
2
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
3
2
1
0
0
1
0
2
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
3
0
1
0
0
0
0
1
1
0
1
0
2
0
0
0
0
1
2
0
0
2
0
0
4
0
1
0
0
1
0
0
0
1
1
0
0
0
6
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
1
2
2
1
2
0
1
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
2
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
3
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
3
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
4
0
0
0
2
0
0
1
1
1
0
0
0
0
0
0
1
2
0
0
0
0
2
0
8
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
2
0
2
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
7
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
1
0
1
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
3
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
2
1
0
0
1
1
2
0
0
1
0
3
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
6
0
2
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
5
0
1
0
2
0
0
0
0
2
0
0
0
0
0
2
2
0
0
1
0
0
0
0
2
2
0
2
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
2
1
3
2
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
7
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
2
4
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
2
2
0
1
0
0
1
3
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
2
1
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
3
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
2
0
0
0
0
0
1
2
0
0
0
0
0
0
3
0
1
2
0
0
0
2
0
0
0
0
0
1
1
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
7
0
0
2
0
2
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
10
1
1
1
2
2
0
0
4
1
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
1
0
0
1
0
1
0
0
2
0
2
2
0
0
1
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
2
3
0
2
0
0
0
0
2
0
0
2
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
4
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
3
2
1
2
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
2
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
5
1
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
1
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
3
0
0
1
3
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
2
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
2
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
3
0
0
0
0
2
0
0
0
2
1
0
1
0
0
0
0
0
0
0
2
0
0
2
1
2
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
3
0
0
2
2
1
0
0
0
0
2
0
0
0
0
2
0
1
0
0
2
0
0
0
2
1
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
1
1
0
0
0
0
0
0
0
0
0
2
1
0
5
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
3
2
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
1
3
2
1
1
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
1
0
2
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
3
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
1
0
0
0
1
1
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
2
0
0
0
0
0
0
1
2
2
0
0
0
1
0
1
2
1
0
0
0
0
0
1
1
0
0
2
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
5
0
0
0
0
0
0
0
0
0
0
2
1
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
1
0
1
0
3
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
1
1
0
0
0
0
0
0
0
7
0
0
1
1
3
0
2
0
0
2
1
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
3
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
4
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
1
2
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
1
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
3
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
2
0
0
0
0
2
1
0
7
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
2
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
1
6
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
8
0
0
0
2
0
0
0
2
1
1
0
0
0
0
3
1
0
0
0
0
1
1
2
0
2
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
2
0
0
2
2
0
2
0
1
0
0
0
0
0
0
0
0
4
1
2
0
0
0
0
1
1
2
0
0
0
0
0
0
2
0
0
1
0
1
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
3
0
0
0
2
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
2
0
1
0
0
0
0
1
0
3
2
2
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
2
0
0
0
3
1
2
1
0
0
0
0
0
4
1
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
1
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
3
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
2
0
0
0
2
0
2
1
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
3
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
2
0
0
2
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
3
0
4
0
0
2
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
3
3
2
0
1
0
2
0
0
3
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
2
0
1
2
0
2
0
0
1
0
0
0
0
0
2
4
3
1
0
0
0
1
0
3
0
0
0
0
1
4
0
2
0
0
0
3
0
0
0
0
0
0
1
3
0
0
0
0
0
1
0
2
4
0
1
0
2
0
0
1
1
0
2
0
2
0
0
1
1
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
2
1
0
0
1
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
1
0
2
0
2
0
0
0
0
2
11
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
2
0
0
1
0
0
0
0
3
0
0
0
2
1
0
0
0
1
1
0
1
0
1
1
0
0
1
0
0
0
1
2
0
0
1
2
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
2
1
2
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
1
0
0
1
0
0
1
1
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
7
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
1
2
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
3
0
0
2
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
1
0
1
0
0
2
0
2
0
0
2
0
4
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
1
0
2
0
0
0
0
0
0
0
0
2
2
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
3
0
0
0
0
3
0
0
0
0
2
0
0
1
3
0
0
0
1
2
0
1
0
0
2
2
0
0
0
0
1
1
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
9
0
0
0
0
0
0
2
0
3
0
1
0
1
0
0
0
2
1
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
2
1
1
0
1
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
3
0
2
0
0
0
0
0
2
0
1
0
0
0
1
2
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
2
1
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
2
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
1
2
0
0
1
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
1
4
2
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
7
0
0
1
0
0
0
2
0
0
2
0
0
0
4
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
1
0
2
0
3
0
1
2
1
0
0
0
3
0
0
5
0
1
0
0
1
0
1
0
2
0
1
0
0
2
0
0
0
0
0
0
0
4
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
2
2
0
1
0
0
0
0
1
0
0
3
0
0
2
0
0
0
5
2
0
6
0
2
0
2
0
2
2
0
0
1
1
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
2
1
2
1
0
0
0
0
0
0
1
0
1
1
2
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
1
4
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
2
1
0
2
0
0
0
0
0
0
0
0
1
0
0
5
1
6
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
1
2
0
0
0
2
0
2
0
0
2
3
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
1
2
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
2
0
0
0
0
2
2
2
0
0
0
0
0
0
2
1
2
0
0
0
0
1
8
4
0
0
0
0
0
1
1
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
4
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
2
0
0
1
0
0
1
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
3
4
0
2
0
6
0
0
2
2
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
4
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
1
0
0
0
4
0
0
0
1
4
0
1
1
0
0
0
1
1
1
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
3
1
0
0
0
0
3
0
0
2
0
0
0
0
0
0
2
3
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
4
2
0
2
1
0
0
0
0
0
1
0
0
0
3
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
1
0
0
1
0
0
0
2
0
0
0
0
1
0
2
5
0
2
0
0
0
0
0
2
2
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
1
0
0
2
0
1
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
2
1
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
4
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
2
0
1
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
4
0
0
1
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
1
1
0
0
1
0
0
0
1
2
0
0
2
2
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
2
2
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
1
2
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
3
0
2
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
1
0
1
3
1
0
2
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
1
1
0
0
0
0
0
0
0
0
0
1
2
2
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
1
0
0
0
0
1
0
2
0
0
0
0
2
3
0
0
0
0
4
0
2
0
0
1
2
0
0
0
0
0
2
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
1
2
4
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
4
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
1
2
0
0
2
2
1
0
0
0
2
0
0
1
0
0
0
0
0
1
3
0
0
2
0
0
0
0
0
1
0
2
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
2
1
3
2
0
0
0
3
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
2
0
0
0
0
0
3
0
0
0
1
0
4
1
0
1
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
1
1
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
3
0
2
1
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
1
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
4
1
0
0
0
0
0
0
0
0
3
1
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
2
0
0
0
1
1
0
2
1
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
1
0
1
0
0
4
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
3
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
4
1
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
3
2
0
0
3
0
1
1
0
0
0
0
1
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
1
1
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
3
0
0
3
0
2
1
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
10
0
0
1
0
0
0
1
0
3
2
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
3
0
0
0
3
0
1
0
3
0
1
0
2
0
0
0
0
0
1
2
0
0
1
0
0
0
0
2
0
0
0
1
1
2
2
0
0
0
2
0
0
2
1
0
1
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
1
3
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
2
2
0
0
0
0
2
0
0
0
0
0
1
1
0
0
1
0
0
0
3
2
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
4
0
0
0
1
0
2
0
1
2
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
5
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
1
0
3
0
0
1
0
1
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
2
3
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
1
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
2
1
0
0
0
1
1
0
0
1
0
1
1
0
1
0
0
3
0
1
0
0
0
2
0
1
0
2
0
0
0
0
2
0
2
0
3
0
2
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
2
2
0
2
0
3
2
0
2
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
6
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
3
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
1
0
0
0
0
1
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
2
0
0
2
0
1
0
2
0
0
0
1
0
0
0
0
0
2
0
0
2
5
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
2
0
0
0
1
4
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
1
0
2
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
3
0
0
0
0
0
1
0
2
0
0
0
0
1
3
0
2
0
2
0
0
5
0
0
0
0
0
3
0
0
2
0
3
0
0
0
1
0
2
0
0
2
0
2
0
2
0
0
0
0
0
1
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
1
0
0
1
0
3
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
1
4
0
1
0
2
1
0
0
0
0
3
2
0
0
2
4
0
0
3
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
2
1
1
2
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
2
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
8
0
0
0
0
0
1
0
0
1
0
0
0
2
4
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
3
1
0
0
0
0
0
2
0
0
0
7
1
1
0
0
0
1
0
0
1
0
2
0
1
0
0
0
0
3
0
2
2
0
0
0
1
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
9
0
2
0
0
0
0
0
0
4
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
3
2
1
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
5
3
1
1
0
0
2
0
1
0
2
0
0
0
0
1
0
0
0
0
2
0
2
6
0
0
3
0
0
0
1
0
0
0
0
0
0
1
5
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
3
1
0
0
0
5
0
2
0
0
0
0
0
0
0
0
1
0
0
2
2
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
4
0
0
0
0
1
0
0
2
0
0
0
0
5
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
2
1
0
0
1
0
2
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
1
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
5
0
0
0
0
0
0
1
0
0
0
0
2
0
1
2
0
0
0
2
0
0
2
0
0
0
2
2
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
3
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
1
1
1
0
1
0
1
0
2
0
1
1
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
2
0
2
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
8
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
2
0
1
0
0
0
0
0
0
4
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
1
0
0
1
3
0
0
0
8
0
1
0
0
0
2
0
0
0
2
1
2
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
3
4
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
5
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
6
0
0
2
0
0
0
0
1
6
1
0
0
1
0
0
0
1
0
1
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
2
0
3
0
1
0
0
2
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
2
3
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
2
0
1
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
2
0
0
2
1
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
2
1
0
2
0
0
4
0
0
1
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
3
1
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
5
0
0
0
0
2
0
1
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
1
0
1
0
2
3
2
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
2
1
0
0
0
1
0
0
0
0
1
0
2
2
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
1
1
1
1
1
0
1
0
3
0
0
0
0
1
0
1
0
0
0
0
0
3
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
1
2
0
0
3
2
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
1
1
0
2
0
0
2
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
2
0
3
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
4
1
2
0
0
0
0
0
1
4
0
0
0
0
0
0
1
1
0
0
2
0
0
0
2
1
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
1
0
1
0
0
2
0
0
0
0
0
6
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
2
0
1
1
1
1
0
2
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
2
1
0
0
0
0
2
2
2
0
2
0
0
0
0
2
0
0
0
3
1
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
1
0
0
2
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
2
0
0
0
1
0
2
0
0
1
0
1
0
0
3
0
0
1
0
0
0
2
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
1
0
0
0
0
3
0
0
1
2
0
0
0
0
1
0
0
0
0
1
0
2
0
0
2
0
3
0
0
2
2
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
6
0
0
3
0
0
2
2
0
0
2
2
0
0
3
0
0
2
0
0
1
0
0
2
2
0
2
0
0
0
1
1
0
3
0
0
0
0
0
0
0
1
2
0
2
0
0
0
2
0
0
1
1
1
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
1
2
0
0
3
0
2
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
1
2
1
2
0
3
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
2
0
0
1
2
2
0
0
0
0
0
0
0
0
1
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
3
0
4
1
0
1
0
0
0
1
0
0
0
0
0
2
1
0
1
2
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
1
0
0
0
0
2
0
3
0
3
2
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
1
0
0
0
0
1
0
2
0
1
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
3
2
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
1
0
0
2
0
0
0
1
2
1
0
0
1
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
2
2
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
2
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
2
1
0
1
1
0
0
0
2
0
0
0
0
3
0
0
0
4
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
3
0
0
0
2
0
0
0
0
0
2
2
2
2
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
4
0
1
0
0
3
0
0
3
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
8
0
0
0
1
1
0
0
0
0
0
0
1
0
0
3
1
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
1
3
0
0
2
0
0
0
0
2
0
0
2
0
0
0
12
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
2
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
1
0
1
0
1
0
2
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
6
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
3
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
2
1
1
0
0
0
1
0
0
1
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
1
1
2
0
2
0
0
1
0
0
0
0
2
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
11
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
4
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
4
0
0
0
3
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
2
0
0
0
0
2
0
2
0
3
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
3
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
1
0
0
1
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
1
0
2
0
0
1
0
0
2
0
2
1
0
4
0
0
0
1
0
0
2
1
0
0
0
0
2
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
2
0
0
0
1
0
0
0
0
0
3
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
4
1
0
2
2
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
1
3
0
0
0
0
1
0
0
0
0
0
3
0
2
0
0
2
0
3
1
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
5
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
3
2
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
1
1
0
2
2
0
1
0
2
0
0
0
0
0
0
0
0
0
4
1
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
3
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
2
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
2
3
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
3
3
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
3
1
0
2
0
0
6
0
2
0
0
0
5
0
0
1
0
1
1
0
0
0
0
0
1
0
0
1
0
2
0
0
2
0
0
0
0
0
0
1
0
0
2
5
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
1
2
0
1
0
0
0
0
0
0
0
0
1
3
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
2
0
3
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
1
3
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
2
2
0
0
0
0
2
0
0
0
2
0
0
0
11
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
1
2
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
1
0
0
1
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
2
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
1
0
0
0
2
5
2
0
0
0
0
0
0
1
0
2
2
0
0
1
2
0
2
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
3
0
1
0
0
0
0
0
1
1
2
0
0
0
2
0
0
2
0
0
0
0
1
0
0
1
0
2
0
0
2
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
2
0
0
2
0
1
0
5
0
0
1
1
0
1
0
3
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
11
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
2
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
2
0
0
1
0
0
2
0
0
0
2
0
2
0
0
7
1
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
2
0
0
0
3
3
0
0
2
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
3
0
0
0
0
2
1
0
1
4
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
2
0
1
1
2
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
7
0
0
0
1
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
3
0
1
2
0
0
2
0
0
0
3
0
0
0
0
3
1
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
3
3
2
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
4
0
1
3
0
0
0
0
0
0
1
0
0
4
1
0
0
0
0
1
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
2
1
0
1
0
4
0
0
0
0
0
0
2
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
2
0
0
1
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
2
0
2
0
0
0
1
0
2
0
0
2
0
0
1
0
0
0
0
0
0
3
0
0
0
0
2
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
2
0
0
3
0
1
2
1
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
3
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
6
0
0
0
1
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
2
0
0
0
0
1
0
0
1
2
0
0
1
0
2
0
0
0
2
0
1
0
0
0
1
0
2
6
1
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
3
0
0
0
0
2
0
1
0
2
1
0
0
0
0
0
1
4
0
1
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
3
0
1
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
3
2
1
0
0
0
0
3
0
0
1
0
2
0
0
0
0
1
0
1
0
0
2
8
2
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
2
3
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
4
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
2
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
1
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
3
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
11
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
1
0
0
2
0
4
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
2
0
2
2
0
0
0
2
0
0
1
0
3
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
2
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
1
0
5
0
1
0
1
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
2
2
2
0
0
0
0
3
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
1
0
2
0
0
2
2
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
5
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
1
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
2
0
0
0
2
0
0
0
0
2
0
2
0
1
3
0
0
0
1
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
2
2
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
3
2
0
1
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
3
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
2
1
2
0
0
0
0
0
0
0
1
0
0
1
2
2
0
2
0
1
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
2
2
0
0
0
0
0
0
1
0
0
1
1
0
0
0
2
1
2
0
0
0
0
2
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
2
5
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
3
0
3
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
1
0
0
3
0
0
0
1
2
0
0
0
0
16
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
1
0
2
0
0
1
0
2
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
2
0
0
0
1
2
0
1
0
0
0
0
0
2
0
0
0
2
0
0
2
1
0
0
0
0
0
0
1
3
0
0
2
1
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
1
1
1
0
0
1
0
0
2
0
0
0
1
1
0
0
0
0
2
0
1
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
1
2
0
0
0
0
0
2
0
4
5
0
0
0
0
2
0
0
0
0
0
0
1
0
4
0
1
0
0
0
3
0
0
0
0
1
0
0
0
1
3
0
0
0
0
0
0
2
1
0
1
1
0
0
0
0
1
1
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
1
0
0
0
2
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
1
1
0
0
0
0
0
2
1
0
0
1
2
0
0
0
0
0
0
0
1
2
0
4
0
0
0
2
0
0
0
0
0
1
0
2
0
2
0
0
2
0
0
0
1
0
0
0
3
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
1
0
0
1
0
5
0
1
0
0
3
0
0
0
0
1
0
2
1
1
0
3
0
2
0
0
0
0
0
0
0
0
3
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
2
0
1
1
0
0
4
0
1
2
0
0
0
2
0
2
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
3
0
0
0
0
2
0
2
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
3
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
4
1
0
1
0
0
1
0
0
0
0
2
1
0
0
0
2
1
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
1
0
0
8
1
0
0
4
0
0
0
2
2
0
0
0
0
1
0
2
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
5
1
0
1
1
0
0
1
0
0
2
0
0
1
0
0
0
1
1
0
0
2
0
0
0
0
1
0
0
0
2
2
0
0
4
0
0
0
0
2
1
0
0
0
0
0
2
0
2
0
0
0
0
0
1
2
0
1
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
3
0
1
0
0
0
0
0
2
3
0
2
2
2
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
2
0
0
0
2
0
2
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
3
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
2
0
1
2
5
0
0
1
0
0
0
0
0
1
0
1
0
3
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
3
0
0
0
1
0
1
0
1
0
1
1
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
1
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
1
0
0
0
0
1
0
2
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
1
2
0
0
0
0
2
1
2
0
5
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
7
1
0
0
0
1
0
0
3
0
3
2
0
0
1
2
5
0
2
0
0
0
2
0
2
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
3
0
0
1
2
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
2
0
2
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
3
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
4
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
1
0
1
3
0
0
0
0
0
0
1
1
2
0
0
8
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
2
2
1
0
0
1
1
6
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
2
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
2
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
2
0
1
0
2
0
1
1
2
0
0
0
0
0
0
0
1
0
0
0
2
0
4
0
0
1
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
7
1
2
0
1
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
3
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
2
0
0
4
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
1
0
0
0
0
2
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
2
0
0
2
0
0
1
0
1
0
2
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
3
0
1
0
1
0
0
0
0
3
1
0
0
0
0
1
0
0
0
0
0
1
0
0
4
0
0
1
2
0
4
0
1
3
0
0
0
2
0
1
0
0
1
0
0
1
2
1
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
1
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
3
2
0
1
0
2
1
0
2
0
1
0
1
3
0
0
3
0
0
0
1
3
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
10
0
2
0
2
0
0
0
0
0
0
0
0
1
3
0
4
1
0
0
1
0
0
0
0
2
0
3
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
3
0
0
0
1
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
3
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
2
0
0
3
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
1
0
0
0
0
8
0
0
0
0
0
1
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
2
3
0
0
0
2
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
1
0
3
0
2
0
0
0
2
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
4
0
1
3
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
8
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
3
0
0
2
0
0
0
0
1
2
0
3
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
1
1
1
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
1
3
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
8
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
1
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
1
2
0
5
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
2
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
2
0
0
2
0
1
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
4
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
1
0
2
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
1
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
3
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
2
0
0
0
0
1
2
0
0
0
1
0
0
1
2
0
0
2
1
0
0
0
0
0
0
0
0
0
3
2
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
2
2
1
0
0
1
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
2
3
2
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
1
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
1
1
0
0
0
3
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
2
1
2
0
0
0
0
1
0
2
0
1
0
0
0
2
0
2
0
1
1
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
6
0
4
0
7
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
1
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
4
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
1
1
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
7
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
1
2
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
3
0
0
1
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
2
0
0
1
0
0
1
0
3
0
1
2
0
0
0
0
2
1
0
0
0
4
0
0
0
0
0
1
2
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
4
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
2
0
0
3
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
1
0
0
5
2
0
0
0
0
0
0
0
0
2
0
0
0
2
4
1
0
0
0
2
2
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
7
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
5
0
2
0
0
0
1
0
0
2
0
5
2
1
2
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
2
0
0
0
0
2
0
0
4
0
1
0
0
0
1
1
0
0
0
0
0
3
0
11
1
1
1
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
2
0
0
0
2
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
1
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
1
1
0
1
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
7
0
0
0
0
2
0
0
0
1
0
0
0
5
0
1
1
0
0
2
0
0
0
2
1
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
1
0
0
0
2
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
3
0
0
1
0
0
1
0
0
0
1
2
1
1
0
0
0
2
2
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
5
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
3
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
1
0
1
0
0
1
0
0
0
2
1
0
2
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
11
1
0
0
0
6
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
2
0
0
2
0
0
3
0
0
0
0
0
2
0
0
0
0
4
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
2
2
0
0
0
1
1
1
1
0
0
0
0
0
0
4
2
2
0
0
1
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
6
3
0
0
2
0
2
1
0
1
0
0
2
0
1
0
0
0
0
0
0
0
5
2
0
0
2
0
0
0
0
2
0
1
0
0
0
1
0
1
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
4
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
2
1
1
1
0
0
0
1
1
0
0
0
1
1
2
2
2
0
0
0
1
0
0
0
2
1
2
0
5
0
1
0
0
0
0
0
3
0
0
0
3
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
2
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
1
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
1
0
0
3
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
2
2
0
0
1
2
0
2
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
2
2
0
0
3
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
3
2
0
0
0
0
2
0
0
0
4
0
0
3
1
4
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
2
0
0
2
0
0
1
1
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
2
0
1
2
0
0
0
4
0
0
0
2
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
1
0
0
1
1
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
4
0
0
0
2
0
2
0
1
0
1
0
0
0
0
0
0
0
0
3
2
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
4
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
1
0
2
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
2
0
0
2
0
0
1
0
0
1
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
6
0
0
0
0
0
0
0
0
1
0
1
8
0
0
0
0
1
0
0
1
0
0
0
0
3
1
0
2
0
1
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
3
0
0
0
1
0
2
0
0
0
0
0
2
0
0
1
3
0
0
1
0
0
2
1
1
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
2
0
0
2
0
0
1
2
0
0
2
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
3
0
0
0
0
2
0
2
0
0
0
2
0
2
0
0
0
0
1
0
0
0
2
2
2
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
2
3
0
0
2
0
0
0
2
1
1
1
1
2
0
1
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
3
0
0
0
2
0
0
2
0
0
0
1
0
0
3
0
0
0
2
2
0
0
0
0
0
1
1
2
0
0
0
0
1
0
2
0
0
1
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
9
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
2
0
0
1
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
3
1
2
2
0
0
1
0
1
1
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
3
0
2
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
2
0
0
1
3
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
4
1
1
2
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
5
0
3
1
0
0
2
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
3
0
4
2
1
0
1
1
0
0
2
0
2
0
0
1
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
4
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
2
0
0
2
4
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
3
1
2
2
0
1
0
5
0
0
1
0
0
0
1
0
4
0
0
1
0
0
8
0
0
1
0
0
2
2
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
5
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
5
3
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
3
0
3
0
0
0
0
1
0
2
0
0
3
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
4
1
1
0
0
0
1
0
1
0
0
0
0
1
0
0
2
2
0
0
2
0
0
0
0
0
1
12
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
1
2
0
3
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
3
2
0
0
6
7
2
0
2
0
0
0
0
3
0
0
0
0
19
1
0
0
0
1
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
3
0
0
0
0
0
0
0
1
0
0
0
1
2
4
2
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
2
2
2
0
0
0
0
0
0
0
2
2
1
2
3
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
2
0
0
1
0
0
2
1
0
0
0
2
0
2
0
0
2
0
1
1
0
2
0
1
0
0
1
0
0
1
0
0
2
1
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
2
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
2
0
0
0
2
2
0
0
0
0
2
0
1
2
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
2
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
3
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
4
2
0
0
0
0
0
1
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
1
2
2
3
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
2
0
0
3
0
1
0
0
0
0
0
1
2
1
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
3
0
10
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
2
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
2
1
1
0
0
0
1
0
0
0
2
0
0
4
0
2
0
3
0
0
0
1
0
0
0
0
1
3
0
0
0
1
1
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
2
0
0
0
0
1
0
2
0
0
4
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
3
1
0
0
0
0
0
2
2
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
3
0
0
0
0
0
0
0
1
0
3
0
0
0
0
2
0
2
0
1
0
2
1
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
2
0
2
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
3
1
1
1
0
0
0
0
0
2
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
2
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
5
0
0
0
0
1
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
4
1
3
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
2
2
0
0
0
2
0
1
0
0
2
1
0
0
0
0
1
0
1
2
4
2
0
0
0
0
1
0
0
0
0
1
0
0
0
2
1
0
0
0
2
2
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
2
0
1
0
0
0
1
0
0
0
2
1
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
1
0
0
1
3
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
1
2
1
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
1
1
0
9
2
1
1
2
1
1
0
0
1
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
1
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
5
1
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
1
2
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
1
0
2
0
2
0
0
0
0
0
3
2
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
2
0
0
0
3
0
0
0
0
0
0
0
7
1
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
1
0
1
0
4
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
1
5
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
4
0
0
1
0
1
0
0
0
1
1
0
2
0
0
2
0
2
5
0
0
1
4
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
2
2
0
0
1
1
2
3
2
0
0
0
0
0
0
2
1
1
4
4
0
1
2
0
0
0
0
2
0
0
0
0
2
0
2
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
2
1
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
4
0
0
1
3
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
7
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
4
2
1
2
0
0
0
0
0
0
1
2
0
1
3
0
3
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
6
0
0
0
1
0
0
0
0
1
1
0
0
0
0
2
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
3
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
2
0
0
1
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
2
2
0
1
0
1
0
0
0
8
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
1
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
2
1
2
1
0
0
0
0
0
0
3
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
5
0
1
0
0
0
0
1
0
2
5
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
2
2
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
2
1
0
1
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
7
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
3
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
2
3
1
0
4
1
0
0
1
2
0
0
0
0
0
0
1
2
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
3
2
2
0
0
1
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
2
0
0
0
0
1
0
0
0
2
0
3
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
2
0
2
0
0
0
0
0
2
0
0
1
2
0
0
0
2
0
2
0
0
1
0
0
0
1
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
4
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
1
2
1
0
0
0
0
2
0
0
0
0
0
0
1
2
0
5
0
0
1
2
0
2
0
0
0
1
0
1
0
0
0
0
1
1
2
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
5
1
0
0
0
0
0
0
0
4
0
0
0
0
0
2
2
0
5
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
1
3
1
2
0
0
0
0
2
2
2
1
0
0
0
2
1
1
2
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
1
2
0
0
2
0
0
0
0
1
0
1
0
1
1
2
2
0
0
2
0
2
0
0
1
0
2
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
3
0
2
0
4
0
1
0
1
0
0
1
0
0
2
0
1
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
1
2
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
3
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
2
0
0
0
2
1
1
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
3
0
0
2
0
1
0
2
0
0
0
0
3
1
0
0
2
0
2
2
0
2
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
1
0
0
0
1
0
0
0
3
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
2
2
0
0
2
2
0
7
0
1
1
0
1
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
5
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
1
1
0
0
2
2
0
0
2
0
1
0
2
0
1
2
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
2
2
2
5
2
0
0
0
0
0
1
0
0
0
0
0
1
0
2
2
2
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
2
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
3
0
2
0
0
4
0
0
2
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
1
1
2
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
3
2
0
0
7
3
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
5
1
1
0
0
0
3
0
0
0
0
2
0
0
0
0
0
4
0
2
1
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
4
2
1
0
0
0
2
7
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
2
1
0
1
1
0
0
1
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
5
0
0
1
0
3
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
2
0
0
0
0
0
0
2
2
2
0
0
0
2
3
2
0
0
0
0
1
4
0
2
0
0
0
0
1
0
2
0
0
7
0
0
0
0
3
0
0
0
0
1
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
3
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
1
0
15
2
0
1
1
0
2
0
0
0
2
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
2
0
0
0
2
2
0
0
2
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
4
0
1
0
0
0
2
0
0
0
0
0
0
0
1
3
0
0
1
2
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
2
0
0
0
1
0
0
0
3
0
0
3
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
1
1
1
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
5
0
0
0
0
0
1
0
0
0
0
1
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
2
2
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
1
2
0
0
0
0
0
3
0
2
1
0
0
0
2
0
6
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
2
0
4
0
2
1
0
0
0
0
2
0
0
4
0
0
0
0
1
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
1
0
0
0
4
0
0
1
2
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
3
0
0
0
2
2
0
0
0
0
2
0
2
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
1
2
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
3
2
0
1
2
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
3
0
1
0
0
0
2
0
3
11
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
1
0
0
1
0
0
1
0
0
3
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
2
0
1
2
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
4
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
5
2
1
0
0
0
0
0
1
0
2
0
6
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
1
2
2
1
0
2
0
0
2
0
2
0
2
0
0
0
0
0
3
0
0
0
0
0
0
2
0
3
0
0
2
0
0
2
0
0
1
0
0
0
0
2
1
1
0
0
0
0
3
1
0
1
0
0
1
0
0
1
0
0
0
4
0
2
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
2
5
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
5
0
0
1
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
1
0
4
1
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
1
2
0
0
0
0
2
0
2
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
2
2
0
2
0
1
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
1
1
0
0
0
2
0
0
0
2
0
0
0
2
3
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
4
0
1
0
1
2
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
3
0
2
0
1
0
0
0
0
0
1
2
0
0
0
0
1
0
0
3
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
1
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
8
2
0
1
0
1
0
2
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
3
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
2
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
2
0
0
0
0
1
0
1
0
2
0
2
2
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
2
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
5
0
0
7
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
2
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
1
0
0
0
0
1
0
0
1
0
3
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
1
0
1
0
0
0
2
4
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
3
0
0
1
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
2
0
1
0
0
1
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
2
0
0
0
0
1
0
1
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
2
0
2
0
2
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
1
1
0
2
4
1
0
0
0
0
0
0
0
3
10
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
2
4
0
0
0
0
2
1
2
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
3
0
4
0
0
0
1
0
3
3
0
2
0
0
0
2
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
8
1
0
2
0
1
0
0
0
0
1
4
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
1
0
0
0
0
1
3
0
1
1
0
0
4
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
2
2
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
4
0
0
0
0
0
3
0
2
0
0
1
2
1
0
1
0
0
0
1
0
1
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
1
0
0
1
2
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
5
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
2
5
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
3
1
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
7
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
1
0
0
2
3
1
0
0
0
0
0
0
0
0
3
1
0
0
1
0
0
0
0
2
1
0
0
1
1
0
0
0
0
0
0
3
0
0
0
0
0
2
0
2
0
0
2
0
2
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
1
0
0
1
0
0
0
1
2
0
1
0
0
0
0
0
3
0
0
0
0
5
0
0
0
1
0
0
2
3
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
4
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
5
0
1
0
0
0
3
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
2
0
2
0
1
3
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
1
3
0
0
5
0
0
0
0
0
5
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
2
0
0
5
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
3
2
1
0
0
0
0
0
2
11
0
0
2
0
2
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
4
0
0
1
2
0
0
0
0
0
2
0
8
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
1
0
2
0
1
2
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
10
0
2
0
2
0
1
0
0
1
1
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
3
0
4
0
0
0
0
1
0
0
0
2
0
0
0
0
1
1
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
5
0
0
0
2
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
1
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
1
0
2
0
4
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
3
0
0
0
0
3
1
0
1
2
1
0
1
0
0
0
1
2
2
0
0
0
0
0
0
0
10
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
5
0
2
0
0
0
5
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
3
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
3
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
4
2
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
2
0
0
1
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
1
0
0
2
0
1
0
0
4
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
2
1
0
0
2
2
0
1
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
1
0
0
2
0
0
1
0
0
0
1
1
2
0
0
0
0
0
0
0
1
4
0
0
0
2
0
2
0
0
0
0
3
0
4
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
5
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
6
0
0
0
1
0
0
0
0
0
0
0
2
0
1
1
0
2
0
0
0
0
0
1
0
0
0
0
1
2
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
7
0
0
0
0
0
1
0
0
2
0
0
0
0
4
0
0
1
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
2
2
2
0
0
1
0
2
0
0
0
0
0
3
1
2
0
1
2
1
1
3
0
0
1
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
1
0
0
1
0
2
0
0
4
0
0
0
1
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
4
0
0
0
1
0
1
1
1
0
0
0
0
0
1
0
1
0
0
0
2
0
2
0
3
0
1
2
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
4
0
0
2
2
0
0
0
0
3
0
0
0
2
0
0
1
0
2
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
3
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
5
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
2
2
2
0
0
2
2
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
1
1
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
1
0
1
0
0
0
2
2
0
0
0
0
0
0
1
0
1
0
0
1
2
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
2
0
2
2
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
4
0
0
8
0
0
0
3
7
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
1
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
2
0
1
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
1
0
1
3
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
3
0
2
1
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
3
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
2
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
2
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
4
0
1
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
2
2
1
0
0
3
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
1
2
0
0
1
0
0
0
2
0
0
0
5
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
1
0
0
1
2
0
0
0
1
2
0
0
0
1
0
0
0
0
2
1
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
1
2
0
0
0
3
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
2
0
7
0
0
0
0
0
0
2
1
0
1
1
0
0
0
2
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
2
2
3
2
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
9
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
2
0
4
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
1
3
0
2
0
0
0
0
0
0
0
1
0
1
2
0
0
1
0
0
0
2
0
0
1
0
0
0
1
0
2
0
0
0
1
1
0
0
0
0
0
0
2
1
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
3
0
0
0
4
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
2
0
0
1
2
0
0
2
1
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
2
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
1
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
3
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
1
1
0
2
0
1
2
2
0
1
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
1
0
2
2
1
1
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
2
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
2
2
0
0
0
0
2
2
0
2
0
0
0
0
1
1
0
0
0
1
1
2
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
3
0
1
2
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
2
2
2
0
0
1
1
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
4
1
2
1
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
5
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
3
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
3
2
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
3
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
1
2
0
0
0
0
0
2
0
1
0
1
3
0
1
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
2
1
0
0
0
2
0
0
0
2
4
0
2
0
0
0
0
2
1
0
1
2
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
2
0
0
0
1
0
0
0
2
0
0
3
0
1
2
0
1
2
1
0
0
2
0
2
0
0
3
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
1
1
0
0
0
0
0
0
0
1
0
2
0
1
3
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
2
0
1
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
2
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
5
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
1
2
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
2
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
2
3
0
0
0
2
0
2
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
1
2
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
3
0
0
0
0
2
1
0
2
0
2
3
0
3
0
0
4
3
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
1
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
1
0
1
0
3
5
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
1
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
2
0
1
0
1
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
2
2
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
1
2
0
2
1
0
0
0
3
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
1
2
0
1
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
3
3
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
2
2
0
0
0
2
3
2
0
1
0
0
0
0
0
1
2
0
0
3
2
0
0
0
0
0
1
0
0
4
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
1
0
0
4
0
0
0
0
0
1
0
0
0
1
1
0
3
0
0
0
0
0
0
0
1
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
1
0
3
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
1
1
0
0
0
0
1
2
2
1
0
0
0
0
2
0
0
5
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
4
1
0
0
2
1
0
1
0
1
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
4
2
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
2
0
0
2
2
0
0
2
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
2
0
0
0
2
0
1
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
4
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
4
2
0
2
0
0
0
0
0
0
1
0
0
1
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
5
0
2
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
3
0
0
0
3
0
0
0
2
1
0
0
4
0
0
0
1
0
0
1
0
0
0
0
0
2
4
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
1
0
1
2
3
2
0
0
0
0
0
0
0
2
1
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
1
2
0
0
2
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
1
7
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
3
0
0
0
0
0
4
0
2
0
0
0
0
1
0
2
0
0
0
2
0
1
0
0
0
1
2
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
3
3
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
2
4
1
0
1
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
4
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
1
3
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
2
1
1
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
1
0
2
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
4
2
0
2
0
0
0
0
1
0
0
0
1
0
1
2
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
1
0
4
1
0
2
0
8
2
1
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
1
0
0
0
3
1
0
1
0
0
0
2
0
0
1
0
1
0
3
0
0
2
1
1
3
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
1
0
1
0
0
0
1
0
0
0
0
4
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
3
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
3
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
2
3
0
0
0
1
0
0
1
0
0
0
0
1
1
2
0
3
0
0
0
5
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
3
0
0
1
1
0
3
0
2
0
0
1
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
2
0
2
0
0
1
0
0
2
1
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
5
0
0
0
0
2
0
2
1
0
0
0
3
2
0
0
0
1
0
2
0
0
0
2
0
3
0
2
0
0
0
0
0
0
3
1
0
2
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
4
0
0
0
0
0
0
0
1
1
0
4
0
0
1
0
0
0
2
0
0
3
0
0
0
2
1
3
1
0
0
0
0
0
0
1
2
0
4
1
3
1
0
0
0
0
0
2
0
0
0
0
0
5
0
0
0
0
0
0
1
2
0
0
2
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
1
0
0
1
1
0
0
0
0
5
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
1
0
0
2
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
1
1
2
0
2
0
0
0
1
0
1
0
5
0
2
0
1
2
0
1
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
1
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
1
0
1
0
0
0
0
2
4
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
3
0
0
2
0
1
0
0
0
1
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
1
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
2
6
0
2
0
0
0
2
2
0
2
0
0
1
2
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
2
0
0
4
0
2
0
1
0
0
0
1
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
2
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
3
0
1
0
0
0
2
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
5
3
0
0
0
0
1
1
0
0
3
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
2
2
1
0
0
1
0
0
0
1
0
0
0
0
0
0
4
1
1
0
2
0
0
0
0
0
0
2
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
2
0
1
0
1
0
5
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
2
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
5
0
0
1
0
1
0
1
1
0
0
0
0
0
0
1
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
2
0
1
0
0
1
0
0
2
2
0
0
0
2
0
2
3
0
0
0
9
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
3
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
15
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
3
0
0
0
1
1
1
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
1
0
2
0
1
2
0
1
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
2
2
0
0
5
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
2
1
0
2
0
0
0
2
0
0
0
0
1
0
0
0
2
2
0
2
0
0
0
1
1
0
0
1
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
14
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
1
0
0
2
2
0
0
0
0
0
0
2
0
1
0
0
2
1
2
1
0
0
3
0
1
1
0
1
2
0
0
2
0
0
0
1
0
0
2
0
0
0
1
0
0
0
2
0
0
1
0
2
2
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
1
1
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
1
2
0
2
0
0
1
1
0
0
0
0
0
0
0
1
0
2
0
1
2
0
1
0
2
0
0
0
0
2
0
0
0
0
3
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
1
0
0
1
1
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
1
0
0
2
3
0
3
0
0
2
1
2
1
0
0
0
0
0
0
1
2
0
3
1
0
0
0
2
0
0
0
3
0
0
0
2
1
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
2
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
0
0
0
0
2
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
1
3
2
0
0
0
1
0
0
0
0
0
1
0
0
0
4
1
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
2
0
0
4
0
0
0
0
3
0
0
0
3
0
0
1
0
0
4
0
0
0
4
1
0
0
1
0
0
3
0
0
0
0
2
0
1
0
2
0
0
0
0
0
4
3
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
1
0
1
0
2
2
2
0
1
0
0
2
0
2
2
1
0
0
1
0
0
0
0
0
2
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
2
0
0
0
2
0
0
0
0
0
1
0
2
2
0
3
3
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
2
0
1
0
1
4
0
0
2
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
2
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
4
0
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
1
0
0
0
2
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
3
0
0
1
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
6
0
0
0
0
0
0
1
0
2
0
0
2
1
0
0
2
0
2
2
2
0
0
0
0
2
3
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
4
0
0
0
0
2
0
0
1
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
2
1
0
3
0
0
0
0
0
1
0
0
0
0
0
2
1
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
3
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
1
2
2
0
0
1
0
3
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
1
0
0
0
2
5
0
1
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
2
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
1
0
1
1
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
3
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
4
0
2
1
0
0
0
0
0
0
2
0
2
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
1
0
1
0
0
0
1
0
0
2
0
0
0
1
0
4
0
0
0
0
3
1
1
0
0
0
0
0
3
0
0
0
0
0
1
0
1
0
0
2
0
0
2
0
2
2
0
1
2
2
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
4
0
2
0
2
0
0
1
4
0
0
2
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
2
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
2
2
1
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
3
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
5
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
4
0
0
0
0
0
2
2
0
0
2
2
0
3
0
0
0
0
0
0
0
3
4
1
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
1
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
3
0
2
0
1
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
9
0
0
0
0
0
0
1
0
0
1
0
2
0
1
2
0
0
2
0
0
0
0
0
0
0
2
1
0
0
1
1
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
1
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
1
0
1
3
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
1
0
0
0
2
0
0
1
0
0
1
0
1
0
0
3
0
2
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
1
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
1
1
1
0
0
0
1
2
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
1
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
2
3
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
3
4
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
2
1
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
2
0
1
0
2
0
0
0
2
0
0
0
0
0
2
0
1
2
0
0
0
0
2
2
0
5
1
0
0
0
0
2
0
1
0
0
0
3
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
1
2
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
3
3
0
0
1
0
2
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
3
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
3
2
0
2
1
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
1
0
2
0
0
0
1
1
0
0
0
0
2
0
0
0
0
4
1
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
3
2
0
2
1
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
4
1
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
1
2
0
0
0
0
0
0
2
0
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
2
0
0
2
0
2
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
1
3
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
2
0
3
0
0
2
0
0
0
2
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
5
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
2
0
2
0
1
0
2
2
0
0
0
0
2
0
2
0
0
0
2
0
2
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
1
1
3
1
0
2
0
0
5
1
0
0
0
2
0
1
1
2
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
8
0
0
2
0
0
0
2
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
2
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
1
0
2
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
2
1
0
0
0
0
0
0
0
2
0
0
1
0
2
0
2
0
0
0
2
0
0
0
2
0
4
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
1
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
4
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
3
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
2
2
4
0
0
0
0
0
1
2
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
5
2
0
2
0
2
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
8
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
1
2
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
1
2
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
1
2
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
2
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
3
0
1
0
0
5
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
3
1
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
2
2
0
0
2
0
1
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
3
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
1
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
9
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
1
3
0
0
5
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
1
0
2
0
1
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
11
0
0
0
0
0
0
0
0
0
0
4
2
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
1
3
0
0
0
1
0
0
0
1
1
0
0
2
6
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
1
0
1
7
0
0
0
0
2
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
3
1
0
0
0
1
1
0
0
2
0
0
0
0
2
0
0
0
3
0
2
0
0
2
1
0
0
3
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
1
0
3
2
0
1
0
0
1
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
1
0
1
3
2
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
1
0
3
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
3
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
2
0
0
1
0
4
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
1
3
0
0
2
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
9
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
6
2
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
1
0
2
0
0
2
1
0
0
0
1
0
2
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
2
0
0
0
0
0
3
0
0
1
0
0
0
0
0
1
3
1
0
0
1
0
0
0
0
2
0
0
2
0
0
1
1
0
0
1
0
0
2
0
0
1
0
2
3
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
1
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
2
0
0
0
2
0
0
2
0
0
2
0
1
0
0
2
0
0
0
1
2
0
1
0
0
0
4
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
2
3
0
0
0
0
0
0
0
0
0
2
0
0
0
3
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
7
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
1
2
2
2
0
2
0
0
0
0
0
0
1
2
0
0
0
1
0
1
0
0
1
0
2
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
5
2
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
2
1
2
0
0
0
0
0
0
0
0
2
0
2
0
2
2
2
0
2
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
3
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
1
0
1
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
3
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
2
0
0
0
0
2
0
0
0
1
0
1
0
0
1
0
2
0
1
0
0
0
0
0
0
1
0
0
9
6
1
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
1
0
0
5
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
3
0
0
2
0
0
0
1
1
0
0
0
0
2
0
0
0
2
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
2
0
0
6
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
5
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
1
1
1
2
2
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
3
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
1
1
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
5
1
0
2
0
2
0
0
2
0
0
0
1
1
0
0
0
0
0
1
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
4
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
4
0
1
3
1
0
0
0
2
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
3
0
0
0
3
0
2
1
0
2
0
0
0
2
3
0
0
2
0
0
0
1
0
0
2
0
0
1
3
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
1
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
1
0
0
2
0
0
0
0
0
2
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
2
0
0
0
0
1
3
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
2
1
1
0
0
0
4
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
2
1
0
0
0
0
1
0
1
2
0
1
0
0
2
0
0
4
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
3
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
2
0
0
0
0
0
0
7
0
0
0
0
1
0
1
0
0
0
1
0
0
2
0
0
0
2
1
0
1
1
0
1
0
0
0
0
0
0
3
0
1
4
0
0
1
0
0
0
0
0
2
3
3
0
0
2
1
1
0
0
0
0
0
0
2
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
3
0
0
0
0
1
2
0
1
2
0
0
1
0
0
0
1
0
0
0
0
0
2
1
0
0
0
1
1
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
3
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
3
0
13
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
4
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
1
0
0
0
3
1
0
0
1
0
0
0
1
0
1
1
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
6
1
0
2
2
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
5
0
0
0
0
0
1
0
0
0
3
0
1
0
0
0
0
0
2
0
0
0
0
0
0
4
0
1
1
1
0
0
1
0
0
0
0
1
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
2
0
1
0
0
0
0
2
2
2
1
0
0
1
0
0
0
0
2
0
0
0
0
1
0
2
2
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
3
0
0
0
0
1
2
0
2
0
3
0
0
0
0
0
2
0
1
1
2
0
0
0
0
0
0
1
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
7
3
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
1
0
2
0
0
2
0
2
0
0
0
0
0
1
0
0
2
2
2
0
2
0
2
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
3
0
2
2
2
0
0
0
0
0
0
2
2
3
0
0
0
0
1
1
0
1
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
2
0
0
2
0
0
0
0
0
3
0
1
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
1
2
0
0
1
1
0
0
2
0
1
0
0
0
0
0
0
0
1
4
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
5
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
3
0
0
0
0
3
2
0
2
0
0
1
0
4
2
2
1
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
3
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
4
0
2
0
0
0
2
1
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
1
3
0
0
0
0
0
0
0
0
2
2
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
2
1
0
0
0
0
4
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
2
0
0
2
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
2
0
0
0
0
4
0
0
2
0
3
0
0
0
0
0
0
1
2
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
3
0
1
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
2
2
0
0
0
0
0
1
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
3
0
0
0
0
0
1
0
2
0
2
0
0
0
0
1
2
0
0
0
0
0
0
2
1
0
2
0
1
2
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
1
1
0
0
1
2
0
0
0
1
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
1
1
0
1
0
0
0
0
2
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
1
1
2
1
0
2
0
0
2
1
2
0
1
0
1
0
2
0
2
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
1
0
0
1
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
2
0
2
2
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
1
0
2
0
0
2
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
3
0
0
0
0
0
2
4
0
2
0
0
2
0
0
1
2
3
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
5
0
0
0
0
0
2
0
1
1
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
2
0
2
0
0
2
2
0
1
0
1
0
1
0
0
0
1
0
1
0
1
0
2
1
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
4
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
1
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
1
3
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
3
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
2
0
0
1
0
1
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
1
0
0
2
0
0
0
1
0
3
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
1
0
0
1
1
2
0
0
0
0
1
3
0
0
1
2
0
2
0
0
0
0
1
1
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
4
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
2
0
0
0
0
2
1
0
0
0
0
2
1
0
0
1
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
2
0
1
0
2
0
0
0
0
6
0
0
0
0
0
1
1
0
0
0
0
4
0
0
0
1
0
0
0
2
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
2
0
0
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
2
1
1
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
2
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
2
0
2
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
3
0
0
0
0
0
0
2
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
3
2
0
0
0
0
0
0
0
2
0
5
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
1
2
0
2
0
1
0
0
0
0
0
0
2
0
1
1
0
0
1
1
0
0
0
0
1
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
1
0
0
1
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
2
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
1
2
0
0
0
2
0
0
0
0
0
0
1
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
1
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
2
1
0
0
2
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
2
0
1
0
3
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
3
0
2
0
2
1
0
0
2
0
0
0
7
2
0
0
3
0
2
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
2
0
1
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
3
2
0
2
3
0
0
2
0
0
0
0
0
2
0
1
0
4
0
0
0
0
1
2
0
0
0
1
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
4
0
0
0
1
0
1
0
0
0
1
0
0
5
1
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
1
2
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
7
0
0
0
2
2
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
1
0
1
0
2
0
0
0
0
0
0
3
0
0
0
0
0
1
1
3
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
8
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
2
1
0
3
2
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
2
1
0
1
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
1
0
3
0
0
2
2
0
4
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
3
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
3
0
0
0
0
1
2
2
0
0
0
0
0
3
1
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
2
5
0
2
0
0
0
0
3
4
1
2
6
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
4
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
2
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
2
2
2
0
2
0
0
0
0
0
0
0
1
2
5
1
2
0
3
0
0
0
0
1
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
2
1
0
4
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
1
3
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
1
0
1
0
0
0
0
0
0
2
0
2
0
12
0
1
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
2
0
0
0
0
2
1
1
1
0
0
2
0
0
2
0
0
0
0
0
2
0
0
2
0
0
2
1
0
0
1
0
0
3
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
8
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
2
0
2
1
0
0
1
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
1
1
1
3
1
0
1
0
0
1
1
0
0
0
0
0
1
0
0
1
0
2
0
1
0
0
0
0
3
0
1
0
0
0
0
0
0
0
1
3
0
2
0
2
0
2
2
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
5
0
0
2
1
0
0
0
0
0
0
2
1
1
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
1
0
1
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
2
0
0
0
0
0
1
1
1
2
1
2
0
2
0
3
0
0
2
0
0
0
2
1
0
0
0
1
1
0
0
2
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
3
0
0
0
0
1
0
0
0
0
0
2
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
7
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
2
4
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
1
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
9
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
1
0
0
0
2
0
0
0
0
0
2
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
4
0
0
1
1
3
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
2
0
0
0
0
1
0
0
0
2
1
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
1
1
0
0
1
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
1
1
1
2
0
0
0
0
0
0
4
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
1
1
2
0
0
2
0
0
1
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
2
0
0
0
4
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
1
0
0
8
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
1
0
2
0
2
0
1
0
1
0
0
1
0
0
2
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
2
0
0
2
0
2
1
0
0
0
3
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
2
0
0
0
3
2
4
0
0
0
2
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
2
0
2
0
5
0
0
2
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
1
0
0
0
2
0
0
1
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
2
2
0
0
3
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
1
0
2
0
2
0
0
0
0
0
2
0
0
1
1
0
0
0
2
0
0
2
0
0
0
1
0
0
1
0
0
3
0
0
2
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
2
3
4
0
0
0
2
0
1
0
0
1
0
0
0
4
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
2
2
0
0
0
4
0
0
0
1
0
0
2
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
2
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
2
2
0
1
0
0
0
2
0
2
0
0
1
1
0
0
0
0
0
0
2
2
0
0
2
2
0
0
0
2
0
0
0
0
0
0
1
4
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
1
3
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
1
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
1
2
0
0
0
0
1
0
0
0
1
2
0
0
0
0
1
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
3
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
2
0
2
0
2
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
7
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
2
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
1
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
1
0
1
0
0
0
0
2
0
0
0
0
0
2
0
2
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
2
3
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
4
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
9
1
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
1
0
0
0
0
0
1
2
0
0
1
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
3
0
1
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
2
0
1
0
0
2
1
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
1
0
0
0
0
2
0
0
0
1
1
0
1
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
2
1
0
0
2
0
0
0
2
0
0
0
4
0
6
0
1
0
1
2
0
0
1
0
0
0
1
0
0
1
0
1
0
2
0
0
2
2
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
4
0
0
0
1
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
1
0
0
0
1
1
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
2
3
0
0
2
0
2
0
3
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
7
0
0
0
1
2
0
0
2
0
0
1
0
2
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
1
3
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
4
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
1
0
0
0
2
1
0
0
0
0
0
1
0
1
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
3
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
1
2
0
0
0
2
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
2
1
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
7
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
2
2
1
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
2
0
0
2
0
0
2
0
0
0
0
0
0
0
7
0
0
0
0
1
0
0
1
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
5
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
1
0
1
2
0
2
0
0
0
2
0
2
0
0
0
0
4
0
1
0
0
0
0
0
0
2
0
4
1
1
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
1
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
6
0
0
0
2
0
0
0
0
1
1
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
3
0
1
0
0
0
0
2
0
0
0
3
1
0
0
0
0
1
0
0
0
0
3
3
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
5
0
1
0
2
0
0
0
1
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
2
1
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
1
5
0
0
0
2
0
0
0
0
4
0
1
1
2
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
3
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
2
0
2
0
0
0
1
5
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
1
2
3
3
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
2
0
0
0
1
0
1
0
0
2
0
2
0
0
0
1
0
0
1
0
6
0
0
0
0
0
0
2
0
3
0
0
7
0
0
0
0
0
1
2
2
0
0
0
0
1
2
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
2
0
3
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
1
2
0
0
0
1
0
1
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
3
0
0
1
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
9
0
0
0
0
1
0
0
0
1
0
0
2
2
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
4
1
0
0
0
0
1
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
4
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
2
0
0
0
0
2
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
1
0
0
0
0
1
1
1
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
1
0
0
0
0
0
1
2
2
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
2
1
0
0
0
1
1
0
0
2
2
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
2
2
2
0
9
0
2
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
1
2
0
0
2
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
3
2
0
0
0
2
0
2
0
0
0
0
0
0
2
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
3
5
1
0
6
1
0
1
0
2
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
3
0
0
2
0
0
1
0
1
1
0
0
1
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
1
0
3
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
1
0
3
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
3
0
2
2
0
0
2
2
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
3
2
0
0
0
0
1
0
0
7
2
0
0
0
5
0
0
2
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
1
0
0
0
2
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
2
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
1
0
1
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
2
0
1
2
0
0
0
0
0
0
1
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
5
1
6
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
2
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
1
0
0
0
0
2
0
6
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
1
3
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
1
1
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
1
1
2
2
0
1
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
1
0
0
0
2
0
0
0
2
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
2
0
1
0
0
0
0
2
0
2
0
0
1
1
0
0
0
2
0
0
2
0
0
0
0
0
10
0
0
0
1
0
1
3
2
0
2
0
1
0
0
1
0
0
0
0
1
1
0
0
1
0
0
1
0
1
2
0
1
0
1
2
0
0
0
2
0
0
0
0
0
2
0
0
2
0
1
0
1
0
0
1
0
0
0
1
0
3
0
2
0
2
1
0
0
0
5
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
2
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
2
2
1
0
0
0
1
0
2
0
0
2
1
2
3
1
1
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
1
0
0
0
0
1
1
1
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
3
0
4
2
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
6
1
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
3
0
3
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
1
1
3
0
0
0
0
0
1
0
2
2
0
0
0
0
0
1
0
0
0
2
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
1
2
0
0
4
0
0
0
0
1
0
1
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
3
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
1
0
2
0
1
0
0
0
0
1
0
1
0
2
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
2
0
3
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
2
2
0
0
0
2
0
2
1
0
1
0
1
0
0
0
1
1
1
0
1
1
0
0
0
0
0
2
0
0
0
4
1
0
2
0
0
0
3
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
3
1
1
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
5
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
3
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
1
0
2
0
0
0
0
2
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
1
2
0
0
2
0
1
0
0
2
0
1
0
0
0
2
0
0
0
0
2
0
0
1
0
8
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
2
2
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
3
0
0
2
0
0
2
0
2
0
1
0
1
2
0
0
0
0
2
0
0
0
2
4
1
0
2
0
0
0
1
0
0
6
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
3
1
0
0
0
1
0
0
2
5
0
0
2
0
0
1
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
1
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
1
0
0
2
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
6
0
2
1
0
0
0
0
5
2
0
0
0
0
1
0
0
0
2
0
0
1
3
0
1
1
1
1
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
1
0
0
0
1
0
0
4
1
0
0
0
0
2
0
0
0
0
2
0
0
2
1
1
0
0
0
1
0
3
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
2
1
0
0
0
2
0
0
0
1
2
0
0
2
0
0
2
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
2
0
0
0
2
2
0
0
0
0
4
0
0
0
0
2
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
5
0
0
0
0
2
1
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
3
2
0
0
0
1
0
0
0
0
1
0
0
9
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
2
0
1
2
2
0
0
1
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
5
1
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
1
2
0
0
0
1
0
0
8
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
2
0
1
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
8
0
0
0
0
0
0
0
0
1
0
2
0
0
2
1
0
0
0
0
0
3
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
2
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
1
4
0
0
0
2
0
1
0
0
2
1
0
0
0
0
1
1
0
0
0
2
0
0
2
0
2
0
0
0
1
0
1
3
0
0
0
0
2
0
1
1
0
0
2
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
1
1
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
2
0
0
2
0
0
0
1
0
2
0
0
0
1
0
0
0
1
0
0
0
0
2
3
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
2
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
5
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
3
1
0
0
2
0
1
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
1
0
0
2
0
0
0
0
0
0
0
2
2
0
1
0
1
0
0
1
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
3
0
0
0
2
0
0
0
0
2
0
0
2
0
0
1
0
0
0
2
0
2
2
0
0
0
0
0
1
2
0
0
2
1
0
0
0
1
0
0
0
2
0
2
1
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
14
0
1
1
0
0
0
0
0
0
0
0
3
0
0
2
0
2
0
0
0
0
0
2
0
2
0
0
0
3
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
2
0
0
1
1
0
0
0
0
4
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
2
0
0
1
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
2
0
0
0
1
0
2
0
0
0
3
2
0
0
0
1
0
0
0
0
6
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
3
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
2
0
0
0
0
1
0
2
0
0
0
2
1
2
0
3
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
2
1
0
0
0
1
0
0
2
0
0
0
0
0
1
2
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
1
0
0
0
0
3
0
0
0
0
0
1
0
0
2
1
0
3
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
2
1
0
0
0
3
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
2
0
1
0
1
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
2
0
1
0
7
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
1
2
0
0
0
0
3
0
2
1
0
0
0
3
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
1
0
6
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
3
0
1
0
0
0
5
1
1
0
0
0
0
3
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
4
0
0
1
1
0
0
2
0
0
0
2
1
0
6
0
1
0
0
3
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
4
2
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
2
0
0
2
1
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
1
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
1
2
1
0
2
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
5
2
1
0
0
0
0
3
0
0
0
0
2
1
2
0
2
0
2
0
1
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
1
0
0
3
1
0
2
0
0
0
0
3
0
2
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
3
0
1
0
3
2
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
3
1
0
0
0
0
0
2
0
0
2
0
0
0
0
2
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
1
1
2
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
3
0
0
2
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
1
0
1
0
0
2
1
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
2
0
3
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
3
2
0
0
2
0
0
0
0
1
0
0
0
0
2
2
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
1
4
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
3
0
0
0
0
0
0
0
2
0
0
0
0
2
2
1
0
0
1
0
1
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
2
0
0
0
1
0
1
0
0
1
1
2
0
0
0
0
2
0
0
0
0
1
1
0
0
2
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
3
2
0
2
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
1
0
0
2
1
0
0
0
0
2
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
3
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
1
1
0
0
0
2
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
2
1
0
2
0
0
0
2
0
0
0
0
3
0
0
0
0
1
3
0
1
1
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
1
3
2
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
2
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
10
0
0
1
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
1
1
0
1
3
0
2
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
10
0
3
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
1
3
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
2
0
0
2
0
0
3
0
0
1
0
0
1
1
0
0
0
2
0
1
2
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
1
1
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
1
2
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
4
1
2
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
2
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
3
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
2
0
0
0
0
0
2
0
2
0
0
0
6
1
0
0
2
0
2
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
1
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
1
1
0
2
0
0
2
2
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
2
3
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
1
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
2
2
0
0
0
0
1
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
5
0
0
0
0
4
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
2
0
0
0
1
0
0
6
0
0
0
0
0
0
0
0
0
3
0
0
2
2
0
3
0
3
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
1
2
0
3
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
4
0
1
2
2
0
0
0
2
0
2
0
1
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
3
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
2
2
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
2
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
3
2
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
1
0
2
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
1
0
0
0
4
0
1
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
1
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
1
1
0
0
0
1
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
3
1
0
0
3
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
2
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
2
0
1
0
0
1
2
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
3
0
0
0
2
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
3
0
3
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
2
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
3
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
7
0
0
0
1
0
0
0
0
2
0
0
2
0
0
1
2
1
1
2
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
3
0
0
1
2
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
2
1
1
2
0
0
0
0
1
0
3
0
0
2
2
1
1
0
0
2
3
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
1
3
1
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
12
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
1
0
0
0
1
0
0
2
2
0
0
0
3
0
0
0
0
0
1
2
0
2
0
2
0
0
1
0
0
0
0
0
1
0
2
0
0
1
1
0
0
1
0
0
0
0
2
0
2
0
3
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
5
0
1
0
0
0
2
0
0
1
0
0
0
0
0
2
3
0
0
0
1
0
2
1
0
1
0
1
0
0
0
1
0
1
0
1
0
0
1
4
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
3
0
1
0
0
3
0
0
0
2
0
5
0
2
0
0
0
0
0
0
2
0
1
0
0
13
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
4
0
0
0
0
0
1
0
0
0
0
2
2
0
0
2
2
0
0
0
1
0
0
3
1
2
0
1
0
0
1
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
3
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
2
1
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
2
0
0
1
0
2
0
3
0
3
0
0
0
0
0
1
0
3
1
0
0
0
0
0
0
0
1
1
0
5
0
0
1
2
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
1
0
1
3
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
1
0
0
1
0
1
0
0
2
2
0
0
0
0
1
0
0
0
0
1
0
2
0
2
0
0
2
2
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
1
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
4
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
2
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
2
1
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
2
1
0
2
0
1
0
0
0
0
0
6
0
0
0
0
0
0
0
0
1
0
0
0
0
7
4
0
0
3
2
0
0
1
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
4
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
3
0
3
0
0
0
0
0
0
0
0
1
0
0
1
2
1
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
2
0
0
1
2
1
0
1
1
0
0
0
0
2
0
2
1
2
0
0
0
0
1
1
0
2
0
0
1
0
0
0
0
7
0
0
1
3
2
2
0
3
2
0
0
0
0
0
1
0
0
0
0
15
2
1
0
0
2
0
0
0
2
0
0
2
0
1
2
0
0
0
0
0
0
1
0
1
1
0
0
2
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
2
0
2
1
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
2
0
1
0
0
0
0
2
1
1
0
0
0
3
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
2
1
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
1
2
0
2
0
0
0
0
0
2
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
2
0
1
1
1
0
1
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
3
1
0
0
2
1
1
0
2
0
0
2
0
3
2
0
1
0
0
0
2
0
1
0
0
0
1
2
0
0
0
3
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
1
2
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
3
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
1
0
3
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
2
2
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
1
0
2
0
1
0
0
0
0
0
0
6
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
2
0
0
0
0
1
0
0
1
2
0
2
0
0
2
1
0
0
0
1
0
0
3
0
0
0
0
0
0
0
2
0
2
2
0
1
0
0
0
0
0
0
0
1
0
4
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
4
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
4
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
2
0
0
7
0
0
0
1
1
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
1
0
1
0
2
1
2
0
0
0
3
0
0
0
1
0
1
0
0
2
0
0
2
0
2
0
0
0
1
0
0
1
0
2
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
2
0
0
0
1
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
6
2
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
4
0
3
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
3
0
0
0
2
4
1
1
0
1
0
0
2
0
0
2
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
1
2
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
4
0
0
1
0
2
0
3
0
0
0
0
0
0
0
0
0
0
1
2
0
1
2
0
0
0
0
2
0
0
0
2
0
0
2
1
0
0
1
0
0
2
1
0
0
0
0
0
0
0
2
0
1
1
1
2
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
5
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
2
0
1
0
1
0
0
2
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
1
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
2
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
1
0
1
0
0
0
3
0
0
2
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
1
4
2
4
0
0
0
0
0
1
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
3
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
4
3
0
0
2
0
0
1
0
0
0
0
2
0
3
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
3
0
0
1
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
4
0
2
0
0
0
0
0
0
4
1
0
0
0
2
0
0
1
0
1
0
2
0
0
0
0
0
1
1
0
0
1
0
0
4
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
8
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
0
0
1
0
2
4
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
7
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
2
0
0
3
0
1
3
0
0
2
0
1
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
1
0
0
0
1
0
2
1
0
0
0
2
0
0
2
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
5
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
1
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
2
1
0
2
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
2
2
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
1
2
0
0
1
0
1
7
0
0
2
0
2
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
1
0
0
0
2
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
3
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
2
0
0
1
0
0
0
0
2
0
0
0
1
0
0
2
1
0
0
0
0
0
2
0
0
0
2
0
1
0
1
0
1
0
1
0
0
2
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
8
0
0
2
0
0
0
3
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
4
0
2
0
0
0
0
4
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
4
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
1
2
0
2
0
0
0
0
1
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
1
3
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
2
2
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
2
0
0
2
1
0
0
0
3
4
0
0
0
2
2
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
1
8
0
0
0
0
2
0
0
0
0
4
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
4
1
2
1
0
0
0
0
0
1
0
0
0
1
2
2
2
2
0
0
1
0
3
1
0
0
0
0
0
4
0
3
2
0
0
0
0
0
1
0
1
0
2
0
0
2
0
0
0
1
0
3
0
0
0
0
1
1
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
2
0
2
0
0
0
2
0
0
1
2
2
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
3
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
1
1
2
0
0
0
0
2
0
0
0
0
0
2
0
2
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
2
1
0
0
0
2
2
0
0
0
1
0
5
0
0
2
0
0
11
0
0
4
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
1
0
0
1
1
0
0
0
0
0
3
1
2
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
6
1
0
2
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
8
1
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
1
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
2
2
1
0
0
3
0
3
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
2
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
2
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
2
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
3
0
0
7
0
0
0
0
0
0
0
0
0
3
0
1
0
1
0
3
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
4
1
2
0
0
2
0
0
1
2
2
0
3
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
1
0
2
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
3
2
0
0
0
1
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
5
3
1
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
1
1
3
1
0
0
0
0
0
0
0
0
0
6
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
1
0
1
0
1
0
0
0
2
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
1
1
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
5
0
1
7
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
3
2
4
0
0
2
0
0
0
2
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
1
1
0
0
0
4
0
2
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
3
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
1
2
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
3
3
0
2
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
1
1
3
0
0
0
0
0
0
3
0
0
3
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
2
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
2
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
3
0
0
2
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
1
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
2
0
0
0
0
0
0
1
0
6
0
0
2
2
1
0
0
2
0
0
0
2
0
2
0
0
0
1
5
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
3
2
0
0
0
0
2
0
0
6
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
2
0
0
1
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
5
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
4
0
1
0
2
0
1
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
1
2
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
3
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
3
1
0
0
0
2
0
0
0
0
0
0
3
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
1
0
2
0
0
2
0
0
2
0
0
2
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
1
1
2
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
4
0
0
2
1
0
1
0
1
0
2
2
1
0
0
3
1
1
0
0
0
1
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
1
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
1
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
1
1
0
2
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
4
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
1
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
3
0
0
0
1
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
1
0
2
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
1
0
2
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
5
0
0
4
0
1
1
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
2
0
0
0
1
1
0
1
0
3
1
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
2
1
0
0
1
0
2
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
1
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
1
0
2
1
0
1
0
1
0
0
0
1
0
0
1
0
0
2
0
0
0
2
0
2
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
1
2
1
0
0
0
0
2
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
3
0
2
0
0
0
0
0
2
0
0
1
0
0
0
1
1
1
0
2
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
1
1
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
3
0
0
2
2
0
4
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
1
0
1
0
2
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
1
0
2
0
2
1
0
0
0
0
0
0
0
0
0
2
2
0
0
3
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
3
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
2
1
0
0
0
1
1
0
1
2
1
0
0
0
1
0
1
0
2
0
1
1
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
1
0
1
0
4
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
1
0
4
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
2
5
2
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
1
2
1
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
1
2
8
0
2
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
5
0
0
0
0
1
0
0
0
0
0
3
0
8
2
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
4
0
1
0
0
0
0
7
0
0
3
4
0
0
0
2
0
1
0
0
0
1
0
0
3
3
0
0
0
0
1
1
0
0
0
1
0
0
0
3
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
2
0
1
0
0
2
0
0
0
2
4
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
8
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
2
1
1
1
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
2
3
0
0
0
0
1
0
1
2
0
1
2
1
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
2
1
4
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
2
0
1
0
0
0
4
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
2
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
1
0
1
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
4
2
0
1
0
0
2
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
2
0
2
0
1
2
0
0
0
1
0
1
2
0
0
0
0
0
0
2
7
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
2
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
2
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
3
0
0
1
2
0
2
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
1
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
2
0
1
1
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
1
2
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
2
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
6
2
1
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
2
0
2
3
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
1
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
3
0
2
0
0
0
0
0
0
1
2
1
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
1
3
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
2
1
0
0
0
0
2
2
0
0
0
0
7
4
0
0
0
0
0
0
0
0
1
0
0
5
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
1
1
1
2
0
0
2
0
2
0
3
2
0
0
2
0
0
0
7
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
2
0
4
0
0
0
1
2
0
1
0
2
0
0
2
0
0
5
0
2
2
1
0
1
1
0
0
0
0
0
0
0
2
0
0
1
3
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
2
2
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
4
0
3
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
3
1
0
0
0
0
3
0
2
1
0
0
0
0
1
2
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
1
0
0
1
0
0
0
0
1
2
0
0
1
0
0
0
3
0
0
1
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
8
2
0
0
0
0
0
2
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
1
0
2
1
0
0
0
0
0
0
0
0
0
0
2
1
1
1
0
0
0
0
0
0
2
1
0
1
2
0
0
0
0
0
2
0
0
0
0
1
1
1
0
0
3
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
2
2
0
5
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
3
2
0
0
0
1
0
1
1
1
2
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
3
0
1
3
0
0
0
0
0
0
1
0
0
2
0
0
2
1
0
0
0
2
0
0
0
0
2
0
0
1
0
2
0
2
0
0
1
0
0
0
0
2
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
5
0
0
0
0
0
0
0
1
1
1
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
5
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
3
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
3
0
0
0
1
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
2
1
1
0
0
0
0
0
5
0
0
7
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
2
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
2
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
8
1
1
1
0
0
0
0
0
3
1
0
0
1
2
0
0
0
2
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
2
0
2
3
0
0
1
0
0
0
5
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
1
1
0
2
0
0
0
0
0
0
2
0
0
5
1
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
4
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
1
0
0
0
1
0
0
1
0
2
0
1
0
1
0
0
2
0
0
0
0
2
0
0
1
0
1
0
0
0
0
2
0
0
2
0
1
0
0
1
2
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
3
0
2
0
0
1
0
1
2
0
0
0
0
0
0
0
5
2
0
0
2
1
0
0
6
1
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
2
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
2
0
3
0
0
0
0
0
1
2
0
1
7
0
0
0
0
1
1
0
2
0
0
0
2
0
1
1
0
2
0
1
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
3
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
2
0
0
2
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
2
1
0
0
0
0
0
1
2
1
0
0
0
2
2
0
1
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
3
0
0
2
0
0
1
0
0
2
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
3
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
3
0
9
0
0
3
2
0
0
0
2
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
2
0
0
1
0
1
0
0
0
0
2
0
0
3
0
0
0
0
0
2
0
2
2
0
0
0
2
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
4
0
0
2
0
1
11
2
0
1
0
0
1
1
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
1
0
0
0
6
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
1
0
1
1
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
2
0
1
0
1
0
0
0
2
0
0
0
0
0
1
0
0
2
1
0
0
0
1
0
0
0
1
0
0
0
1
2
1
0
0
0
0
0
2
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
3
0
0
0
0
0
3
0
0
0
0
0
0
1
2
2
0
0
0
2
0
0
0
0
2
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
2
0
0
0
1
0
0
2
3
0
0
0
3
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
2
3
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
1
3
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
3
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
1
0
0
3
0
0
0
0
0
1
1
0
0
0
2
1
0
0
0
1
2
0
0
1
0
0
0
0
0
3
0
0
0
8
0
0
0
0
0
2
0
0
0
0
0
1
2
0
2
0
2
0
0
0
1
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
1
0
0
1
0
0
0
2
2
0
0
0
0
0
0
2
2
0
0
6
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
1
2
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
2
0
1
1
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
3
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
2
1
0
0
0
3
0
0
0
0
3
2
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
3
3
0
0
2
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
1
4
0
0
2
0
2
1
0
2
0
0
0
1
1
0
0
3
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
1
0
1
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
1
0
2
1
0
2
0
1
1
0
0
0
2
0
0
0
0
1
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
2
0
1
2
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
1
1
0
0
0
3
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
2
1
0
0
3
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
2
0
0
2
0
1
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
1
2
1
0
0
0
0
0
1
0
3
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
2
0
2
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
1
0
0
1
2
1
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
3
0
0
2
0
1
0
1
2
0
0
0
1
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
4
0
2
0
0
0
0
0
0
2
3
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
9
0
0
1
0
0
4
0
0
0
0
2
0
2
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
1
2
1
0
1
0
0
0
0
2
1
0
0
0
1
3
0
0
0
3
0
1
2
0
0
0
0
1
0
0
1
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
1
0
2
0
0
0
2
0
5
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
2
1
1
0
0
0
0
0
1
0
3
0
0
2
0
0
2
0
1
0
0
0
3
0
1
0
0
0
1
0
1
0
0
0
1
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
2
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
1
0
0
2
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
1
0
1
3
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
1
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
4
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
2
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
3
0
0
3
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
1
2
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
2
1
0
0
2
1
0
2
0
2
2
7
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
2
0
2
0
1
0
0
0
0
0
2
0
2
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
5
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
1
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
2
0
8
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
3
0
0
2
0
0
1
3
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
1
1
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
2
0
1
0
0
5
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
6
2
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
2
0
0
0
0
0
1
0
0
0
4
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
2
1
0
2
0
0
0
2
0
0
0
0
0
3
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
1
0
0
2
0
2
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
2
0
0
0
0
1
2
0
0
0
0
0
1
0
2
0
1
2
0
1
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
3
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
3
0
0
0
0
0
0
0
0
2
0
0
0
0
3
3
2
1
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
1
0
0
0
0
1
12
0
1
2
1
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
3
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
9
0
0
1
0
1
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
3
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
4
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
1
0
2
1
0
0
0
0
8
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
3
0
0
0
0
0
1
1
2
0
2
2
2
1
0
1
2
1
1
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
1
0
0
0
4
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
1
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
1
0
2
1
0
0
0
2
0
0
1
0
1
0
0
5
0
0
0
0
1
0
0
0
1
0
3
0
0
1
0
0
0
0
1
0
1
0
0
6
0
0
0
0
1
1
0
1
0
2
0
2
0
0
1
2
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
4
0
0
0
0
2
2
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
1
2
0
0
0
1
0
0
0
0
0
0
3
0
1
1
0
0
0
0
2
1
0
0
2
0
0
0
0
1
0
1
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
1
2
2
0
2
1
2
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
0
2
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
2
1
0
1
0
3
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
2
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
2
0
2
1
0
0
4
0
2
1
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
1
0
0
0
2
6
3
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
1
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
1
7
0
0
0
0
0
0
0
0
0
2
1
0
1
0
2
0
2
0
2
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
2
1
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
2
1
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
2
2
2
0
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
2
1
0
0
0
0
0
2
4
0
0
0
1
0
0
0
4
2
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
2
0
0
2
0
1
1
0
0
1
0
4
0
2
0
1
0
0
1
0
0
0
0
0
1
0
0
0
2
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
4
0
1
2
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
1
2
0
1
1
1
2
0
0
0
0
0
5
0
0
0
3
2
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
3
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
1
0
0
0
0
0
0
2
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
1
0
0
0
0
0
0
0
0
1
2
0
0
2
14
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
4
0
0
1
0
7
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
2
2
0
0
2
0
1
1
0
0
0
1
0
2
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
1
1
0
0
0
0
3
2
1
0
0
1
0
0
0
0
1
1
0
0
2
2
0
0
2
0
2
0
0
0
1
2
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
1
0
2
1
1
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
1
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
1
0
3
0
0
1
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
2
2
1
0
0
0
0
1
1
2
0
0
2
0
0
1
0
1
0
0
4
0
0
2
0
0
0
2
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
2
2
0
0
0
0
0
0
0
0
2
1
1
0
1
0
2
0
0
0
0
0
0
2
1
0
0
1
0
0
0
1
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
1
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
7
0
0
2
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
3
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
3
2
0
1
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
1
1
0
0
0
0
2
0
6
0
0
1
0
1
2
0
0
0
2
0
0
0
3
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
1
0
2
2
1
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
6
0
0
0
0
0
2
0
0
0
0
2
1
0
0
1
0
3
4
5
0
0
0
0
0
0
0
2
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
1
0
2
3
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
9
2
2
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
9
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
3
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
2
0
0
0
1
1
0
0
0
7
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
3
0
0
0
0
0
0
2
0
1
1
2
0
0
0
1
0
0
0
0
2
1
0
0
0
0
3
2
0
1
2
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
3
0
2
1
0
0
0
0
1
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
2
0
0
0
0
2
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
3
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
2
3
0
1
0
0
0
0
0
0
0
1
0
0
8
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
12
0
0
1
0
0
0
0
0
0
2
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
3
0
0
0
3
0
1
0
0
0
2
1
1
0
0
3
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
5
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
5
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
2
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
4
3
2
2
4
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
2
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
2
0
0
0
0
3
1
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
2
2
0
0
0
0
1
0
0
0
3
0
0
2
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
6
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
3
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
2
0
3
1
0
0
0
0
2
0
3
0
0
0
0
0
0
0
1
2
0
6
2
0
0
0
2
0
1
0
0
1
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
4
1
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
1
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
1
0
1
1
2
0
2
0
0
0
0
3
0
0
0
0
1
2
0
0
1
0
0
2
2
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
1
2
3
0
0
0
0
0
1
0
0
0
2
2
1
0
0
0
0
1
0
0
0
3
0
1
3
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
3
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
2
1
1
0
0
1
2
2
0
0
0
1
0
0
0
2
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
1
1
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
1
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
2
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
7
0
0
0
1
0
1
0
0
1
0
2
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
2
2
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
4
3
0
1
0
2
0
11
0
0
0
0
0
0
0
0
2
0
0
0
5
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
1
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
2
0
0
0
2
0
1
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
2
1
0
2
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
1
0
3
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
1
0
0
3
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
2
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
5
0
0
3
0
1
0
0
1
0
0
0
0
0
4
1
0
0
0
0
3
2
0
0
0
0
1
0
0
2
1
0
0
0
0
0
2
2
0
0
0
0
4
2
2
0
0
1
0
0
2
1
0
0
0
1
4
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
1
2
3
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
3
0
1
0
2
0
0
0
0
0
3
0
0
0
0
1
1
0
0
2
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
3
0
2
8
0
0
2
0
1
0
0
2
2
0
0
1
3
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
3
2
0
2
0
0
3
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
2
4
0
1
2
3
0
0
0
1
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
2
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
3
2
0
0
0
0
0
1
2
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
1
3
1
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
1
1
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
1
2
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
3
0
2
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
2
0
0
0
0
0
6
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
2
0
4
0
0
0
0
0
0
2
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
1
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
1
3
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
1
0
3
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
4
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
1
0
0
2
0
0
0
1
2
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
1
2
0
1
0
2
0
1
0
0
1
1
0
0
0
3
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
1
0
6
2
0
1
0
0
0
0
0
0
0
0
4
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
3
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
4
0
2
1
2
2
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
6
2
0
2
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
2
2
11
1
0
0
0
0
1
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
2
2
0
0
5
0
0
2
0
0
0
0
0
2
2
0
0
1
0
0
0
1
1
0
0
1
2
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
2
0
2
1
0
0
0
0
2
1
0
0
0
2
0
1
2
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
3
2
0
1
0
0
0
1
3
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
2
3
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
1
0
2
1
1
0
4
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
2
0
2
0
0
1
3
0
0
0
0
0
1
0
0
1
0
0
0
3
0
0
1
2
0
2
0
2
0
0
0
0
1
0
0
0
2
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
8
0
0
0
0
1
0
0
0
0
2
0
0
0
2
6
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
1
2
0
4
0
1
0
0
0
0
0
2
0
0
0
1
1
0
1
1
2
0
0
0
0
0
0
0
3
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
1
1
0
0
0
0
2
0
0
0
1
1
0
0
1
0
0
2
0
0
0
1
0
2
0
0
0
1
0
0
0
0
2
2
0
2
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
2
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
3
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
1
0
0
2
2
3
0
2
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
4
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
1
0
1
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
6
0
0
1
0
0
5
0
0
2
0
0
0
3
0
2
1
0
0
0
0
1
0
2
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
2
1
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
7
0
1
0
0
2
2
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
2
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
1
3
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
2
0
0
0
0
1
2
1
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
1
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
2
0
0
2
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
5
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
1
0
1
3
0
0
0
0
0
0
0
1
3
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
1
2
2
0
0
0
0
0
0
0
0
0
1
3
2
0
0
0
0
0
0
1
0
2
0
0
0
0
2
2
0
2
0
0
2
0
0
2
0
1
0
0
0
0
0
1
1
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
1
2
1
2
0
3
0
0
1
1
0
2
0
3
0
2
0
0
0
0
1
0
1
0
3
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
1
0
0
0
0
0
1
2
0
2
0
2
0
0
0
0
1
0
3
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
4
0
0
2
0
0
0
0
3
2
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
1
0
0
0
1
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
6
0
0
0
0
0
1
1
0
2
0
0
0
0
0
3
0
0
0
2
0
2
1
0
0
0
0
0
4
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
2
0
1
0
0
1
0
0
0
1
0
0
0
4
2
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
4
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
2
3
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
1
1
3
0
2
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
2
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
1
0
0
0
3
0
2
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
2
0
0
2
2
0
0
0
0
0
0
0
1
2
3
0
0
1
0
2
0
0
0
1
1
0
0
0
0
0
2
0
0
0
1
3
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
3
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
2
1
0
0
1
2
0
0
2
0
0
2
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
2
0
0
1
0
0
0
0
0
0
3
1
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
2
1
2
0
2
0
0
2
4
2
1
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
2
2
0
2
0
0
0
1
0
0
0
0
2
3
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
4
0
0
1
2
0
0
1
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
1
0
0
1
0
0
1
0
0
0
1
2
1
0
0
0
1
2
0
0
0
2
0
0
0
0
0
2
2
0
6
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
2
2
2
0
6
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
8
2
0
0
2
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
4
2
1
2
0
2
2
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
6
0
1
0
0
0
3
2
0
0
0
0
1
0
0
0
2
4
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
1
0
0
0
2
0
3
0
4
2
0
2
0
0
0
1
0
0
0
2
3
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
2
2
1
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
2
0
1
2
2
1
1
0
0
0
0
2
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
2
0
2
0
0
0
0
1
0
0
5
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
1
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
2
0
0
1
0
0
1
2
8
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
3
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
2
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
5
1
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
3
0
2
0
0
2
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
9
0
0
0
0
0
0
1
2
0
0
0
1
0
2
1
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
2
0
2
2
3
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
1
9
0
1
2
0
2
0
0
0
0
1
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
3
0
0
0
1
0
1
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
3
0
1
0
0
0
2
1
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
5
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
1
2
0
3
0
3
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
1
0
0
1
2
2
0
3
1
3
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
3
0
0
0
2
0
2
0
0
0
0
0
4
0
0
0
0
1
1
0
2
0
0
0
0
1
0
3
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
3
1
0
0
0
0
0
9
0
0
1
1
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
1
1
0
0
0
0
0
0
0
0
1
0
4
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
4
0
1
0
2
2
1
3
0
0
0
0
0
8
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
1
0
1
3
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
5
0
3
0
0
0
0
0
0
0
0
1
0
1
0
2
0
1
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
1
0
1
0
0
0
0
1
0
2
3
0
0
0
0
1
0
0
0
0
0
1
0
2
2
0
3
0
0
0
0
0
0
0
0
1
0
0
1
0
4
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
7
2
0
0
0
2
0
2
1
0
1
0
0
2
1
0
2
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
1
1
0
0
0
0
0
3
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
2
4
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
2
0
2
2
0
0
0
2
0
3
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
1
0
0
0
3
0
1
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
3
0
3
0
0
0
0
0
1
1
0
0
0
0
3
0
0
0
1
2
0
0
2
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
2
0
4
0
1
2
0
0
0
2
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
3
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
2
2
2
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
2
0
0
0
6
2
0
0
0
2
0
3
0
1
0
1
0
0
1
0
0
3
0
2
0
2
0
2
0
0
0
0
0
0
0
1
0
3
0
0
0
0
1
0
1
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
2
0
3
0
0
0
0
0
0
0
1
0
0
2
0
2
2
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
2
0
3
4
1
0
0
2
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
1
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
1
0
3
0
0
0
0
6
0
3
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
3
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
11
0
0
1
0
0
0
0
0
1
1
1
1
1
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
3
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
8
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
5
1
2
1
1
0
0
0
0
0
1
2
0
0
2
1
0
0
0
1
1
0
0
1
0
1
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
1
0
0
2
1
0
0
0
0
1
1
1
0
0
6
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
1
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
1
0
0
0
3
2
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
2
1
1
0
0
0
0
0
0
1
0
2
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
2
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
3
0
0
0
0
0
0
0
0
0
2
4
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
3
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
9
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
20
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
2
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
3
0
0
0
1
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
1
2
0
0
1
1
0
0
0
3
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
1
1
1
0
0
3
0
0
0
0
1
1
1
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
6
1
1
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
1
1
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
2
3
0
0
1
0
1
1
0
2
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
3
0
0
0
1
2
0
3
0
0
0
0
0
0
2
0
1
0
0
2
2
2
0
1
1
2
0
0
0
3
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
2
0
2
0
2
2
0
0
1
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
2
0
1
0
2
0
2
0
1
2
0
9
3
0
2
0
3
8
1
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
2
3
0
2
0
0
0
2
3
1
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
1
1
0
0
2
0
2
0
0
0
0
0
4
0
0
0
3
0
0
0
0
0
0
0
2
0
4
0
1
4
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
1
2
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
3
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
4
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
2
1
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
3
0
0
2
0
0
0
1
2
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
1
1
0
2
2
1
0
0
0
0
2
2
0
0
1
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
2
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
2
2
2
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
1
1
0
0
1
6
0
0
0
0
2
2
0
0
2
1
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
1
1
0
0
0
0
2
1
0
0
0
2
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
1
3
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
2
0
1
0
0
0
0
0
1
0
0
2
0
1
0
0
2
0
0
0
0
2
3
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
1
1
0
0
2
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
2
2
6
0
0
0
2
1
0
0
2
3
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
1
0
2
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
1
0
0
2
0
1
0
2
1
0
0
0
2
3
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
4
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
3
1
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
1
0
0
2
0
1
1
0
0
2
3
0
1
0
0
0
0
0
0
0
3
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
1
0
7
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
2
0
0
0
1
3
0
6
0
0
3
0
0
0
0
0
0
1
2
1
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
3
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
3
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
2
0
0
1
0
3
0
2
0
0
0
0
1
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
5
0
0
0
1
1
0
0
2
0
2
0
0
1
0
0
2
0
2
0
2
0
0
0
2
0
0
4
0
0
0
0
1
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
3
0
2
0
0
0
0
0
0
0
0
4
0
2
0
0
0
2
0
0
1
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
3
2
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
2
0
1
0
0
0
0
0
0
0
2
1
1
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
7
0
0
0
0
0
1
0
0
0
1
0
2
0
1
1
1
0
2
0
2
0
0
0
0
1
0
0
0
1
0
0
2
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
1
0
0
0
1
0
3
2
2
0
0
0
1
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
1
0
1
0
0
0
2
0
1
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
1
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
1
0
0
2
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
2
0
0
1
3
0
0
5
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
4
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
5
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
2
0
0
2
3
2
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
2
2
0
1
0
1
0
0
1
0
2
0
0
0
0
0
0
0
2
3
1
0
1
3
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
2
1
0
2
0
0
0
2
1
0
0
0
0
0
0
2
0
0
10
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
3
1
2
0
2
1
1
0
0
0
0
0
0
1
0
5
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
3
0
0
2
0
0
0
0
3
0
0
2
0
0
0
0
2
1
0
0
0
0
2
0
2
0
0
2
0
0
0
1
0
0
2
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
20
0
4
0
0
0
0
0
0
0
1
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
1
0
5
0
0
0
0
0
2
0
0
0
0
1
0
1
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
1
1
0
2
2
0
2
1
0
0
1
2
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
3
3
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
2
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
2
0
7
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
2
0
1
0
0
0
6
0
2
1
1
0
0
3
0
1
0
0
0
0
0
0
0
1
1
0
0
3
1
0
1
0
3
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
2
0
2
4
0
0
1
0
0
0
0
4
0
0
3
0
0
0
0
0
0
1
2
2
0
0
0
2
2
0
0
0
2
0
1
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
1
1
1
0
1
0
2
0
0
0
0
1
1
1
0
1
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
1
1
0
0
2
0
2
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
4
1
2
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
1
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
2
0
2
0
0
1
0
0
0
2
1
0
0
0
0
5
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
4
0
1
0
0
3
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
2
2
0
0
1
0
0
0
0
7
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
4
1
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
4
2
0
0
0
2
0
0
1
1
2
1
8
0
0
1
0
1
3
0
0
0
0
1
0
0
0
2
3
0
0
2
0
1
0
0
0
3
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
2
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
1
0
2
0
0
1
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
0
0
1
1
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
2
1
5
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
1
1
3
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
3
0
0
0
0
1
0
0
2
2
1
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
2
0
0
0
0
0
2
1
2
0
0
0
0
1
0
2
4
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
2
3
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
7
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
1
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
6
0
0
4
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
2
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
3
0
0
1
1
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
1
2
0
0
0
2
2
2
0
2
0
0
0
0
2
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
1
0
0
1
2
0
0
0
0
3
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
2
1
0
0
0
0
1
0
0
0
0
1
0
3
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
1
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
2
0
1
0
0
0
0
2
1
0
1
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
4
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
1
1
2
0
0
0
0
0
0
2
0
4
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
3
4
3
0
0
1
0
0
2
4
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
1
0
1
1
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
8
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
1
1
0
2
0
0
0
0
1
0
0
0
3
0
0
2
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
1
0
1
0
1
0
0
0
2
2
0
0
0
6
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
5
0
0
2
0
0
3
1
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
1
1
0
0
3
3
0
0
2
0
2
2
1
3
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
1
2
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
2
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
3
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
2
2
1
0
0
0
3
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
1
0
0
0
0
3
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
3
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
2
2
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
2
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
3
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
2
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
1
2
0
0
0
0
0
2
1
0
0
0
0
1
0
2
1
0
0
0
0
0
0
1
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
2
0
2
1
0
0
2
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
1
0
0
0
2
0
1
0
1
2
0
2
0
0
0
1
2
2
0
1
2
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
1
2
2
1
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
1
0
0
1
1
0
0
0
2
0
0
0
0
1
3
2
0
0
0
2
0
4
4
0
0
0
1
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
2
2
3
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
4
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
2
0
0
0
3
0
0
0
0
1
0
1
2
0
11
1
2
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
1
0
0
1
1
0
0
2
2
0
0
1
0
0
0
0
2
0
0
2
0
0
0
2
1
0
3
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
2
2
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
1
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
2
1
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
4
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
2
2
2
0
2
0
0
0
2
0
0
1
2
0
1
0
2
1
0
2
0
0
1
0
0
0
0
10
0
2
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
2
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
9
2
0
2
2
0
0
2
1
1
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
1
0
1
1
2
2
0
1
0
2
0
1
0
0
0
0
0
0
0
3
0
2
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
1
0
0
0
1
2
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
3
2
0
2
0
1
0
0
0
0
0
2
0
0
0
0
2
0
2
0
1
0
0
0
0
0
1
2
0
2
2
0
0
0
0
2
0
0
0
0
1
0
0
2
0
2
1
1
0
0
0
0
0
2
1
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
4
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
1
0
0
4
0
1
0
0
0
1
0
1
0
0
0
2
0
0
0
1
0
2
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
3
0
0
2
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
1
0
0
0
1
0
0
0
0
2
0
3
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
1
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
1
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
1
0
0
1
2
0
1
0
0
2
2
0
1
0
2
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
12
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
1
0
1
2
0
0
2
1
0
0
3
0
1
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
3
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
1
1
1
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
2
0
0
1
1
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
2
0
0
3
0
0
1
1
2
0
0
2
3
0
0
1
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
2
0
0
0
0
2
0
0
3
0
0
0
0
1
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
2
1
2
2
0
1
0
0
2
1
0
0
1
1
2
2
0
2
1
0
1
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
1
5
0
1
2
0
1
0
0
0
0
0
2
1
1
0
0
0
0
2
1
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
3
0
0
1
0
12
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
5
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
2
0
0
0
2
0
0
0
3
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
2
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
2
2
0
1
0
0
0
0
0
1
0
2
0
0
3
1
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
1
0
0
2
1
0
0
0
0
3
0
2
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
7
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
1
1
1
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
1
2
3
2
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
4
0
1
0
0
2
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
1
2
2
6
0
0
0
1
0
0
0
2
2
1
0
1
2
0
1
0
0
1
1
0
1
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
1
0
0
0
2
0
1
2
0
0
1
2
0
1
2
0
0
2
0
0
0
2
0
0
1
0
2
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
1
0
1
0
0
0
1
2
0
0
0
1
0
2
0
1
0
0
0
0
1
0
0
2
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
2
4
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
5
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
2
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
4
0
0
0
0
0
2
2
1
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
4
0
0
3
1
0
2
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
2
2
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
5
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
1
0
0
0
1
0
1
0
0
0
3
0
0
0
0
3
2
1
0
0
0
0
1
0
2
0
1
1
0
0
0
0
0
0
0
0
2
0
1
0
1
0
2
0
3
0
0
0
0
2
0
0
1
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
1
0
1
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
8
0
0
0
0
1
2
0
2
1
2
0
1
0
0
0
0
0
2
0
0
0
3
2
0
0
2
0
0
0
2
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
7
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
1
0
0
1
1
0
0
0
0
1
1
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
14
0
0
0
0
0
0
3
0
0
1
2
0
0
0
2
1
8
3
1
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
7
0
0
0
0
1
0
0
0
0
2
2
1
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
1
0
0
2
0
0
1
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
1
0
0
0
0
1
1
2
0
0
0
2
0
2
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
1
0
1
0
0
1
2
0
0
1
0
2
0
0
2
0
0
0
0
3
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
3
2
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
1
0
0
3
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
2
1
0
0
0
1
0
3
0
0
0
1
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
4
0
0
0
0
0
3
0
2
0
0
0
0
0
0
1
0
0
1
0
2
1
0
0
2
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
3
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
2
3
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
1
0
0
0
0
1
1
4
1
0
1
0
0
2
0
1
0
0
1
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
2
0
0
0
0
3
0
2
0
0
0
0
2
0
0
0
2
0
0
2
0
0
1
2
0
2
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
2
0
1
1
0
2
0
0
0
0
0
0
2
1
0
0
1
1
0
2
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
2
0
1
0
1
0
0
3
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
1
3
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
1
1
3
2
1
0
0
0
0
8
1
2
0
1
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
3
0
0
0
0
0
2
1
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
3
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
2
2
0
0
1
0
6
0
2
2
0
3
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
3
2
0
0
0
3
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
2
0
2
0
0
1
0
0
3
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
2
0
1
0
0
1
0
1
0
0
1
0
0
0
1
0
0
1
3
0
0
0
1
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
2
0
2
0
0
0
0
3
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
2
1
1
0
2
0
0
0
0
0
0
1
0
9
0
0
0
0
0
1
1
1
0
0
0
4
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
2
1
0
1
0
2
1
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
2
0
0
4
0
0
0
0
1
2
0
0
0
0
0
0
1
0
3
1
0
0
0
0
0
1
2
0
0
2
0
0
0
1
2
2
1
0
0
0
5
1
0
0
0
2
2
0
1
0
0
0
0
1
2
0
2
2
0
2
1
1
0
0
2
0
1
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
3
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
1
0
1
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
1
1
0
2
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
1
1
1
0
2
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
2
2
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
2
1
0
0
0
1
0
0
0
0
1
1
0
0
0
4
3
0
0
1
1
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
2
0
1
0
0
0
0
2
1
0
2
0
0
0
2
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
5
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
1
1
0
0
1
0
0
0
0
1
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
2
0
2
2
1
2
0
0
0
0
2
0
0
0
0
0
3
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
1
0
0
1
1
2
0
1
0
0
0
1
0
0
0
0
1
0
2
5
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
1
2
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
5
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
2
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
3
0
0
0
3
2
2
1
0
1
0
1
1
2
0
0
0
3
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
2
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
2
0
0
1
0
0
0
1
0
0
0
0
0
2
2
1
0
1
0
0
1
0
2
1
0
1
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
2
1
0
0
0
0
0
0
0
1
2
2
0
0
1
0
2
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
3
0
1
0
0
0
0
1
0
1
1
0
1
0
1
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
1
0
2
2
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
1
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
2
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
1
0
2
0
0
1
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
5
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
2
2
1
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
1
0
1
0
0
2
0
0
0
0
0
2
1
0
0
2
1
0
0
2
0
0
0
0
3
0
0
0
0
1
1
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
1
2
0
0
1
0
2
0
0
2
2
0
0
0
0
1
0
2
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
4
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
4
0
1
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
3
0
0
0
1
2
0
0
1
1
0
0
0
1
1
0
0
0
0
0
2
2
0
0
0
1
0
0
0
2
0
2
2
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
1
1
2
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
1
2
0
2
0
0
0
0
1
0
4
1
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
1
1
0
8
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
7
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
1
0
0
1
0
1
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
1
0
1
2
0
0
0
0
0
1
0
0
0
2
1
0
0
2
0
0
0
0
1
3
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
2
0
2
0
0
0
0
0
1
0
2
0
1
2
0
0
0
0
0
0
0
0
9
0
0
2
2
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
2
0
0
0
0
1
2
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
2
0
0
0
5
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
3
1
0
0
0
1
0
2
1
1
0
0
2
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
2
0
2
1
0
0
1
0
1
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
5
0
3
0
2
0
0
0
0
0
0
0
0
4
0
0
2
0
0
2
2
2
1
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
2
0
2
0
0
1
2
2
0
0
1
0
1
0
0
1
0
0
0
2
0
0
1
0
1
0
0
1
0
0
1
0
2
6
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
7
1
0
1
0
4
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
1
2
0
0
0
2
0
2
0
0
1
0
0
0
0
0
1
0
0
0
1
1
3
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
1
0
0
2
1
1
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
1
2
3
4
0
1
3
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
1
0
1
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
3
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
3
6
0
0
0
0
1
3
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
1
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
3
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
2
2
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
1
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
2
6
0
0
0
2
3
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
2
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
3
2
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
3
0
0
0
0
1
0
0
1
0
0
0
3
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
6
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
11
0
1
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
2
0
0
3
0
0
2
1
0
0
0
0
0
0
2
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
3
0
0
0
0
0
0
1
2
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
10
0
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
3
4
0
0
0
1
0
0
4
2
0
2
0
0
0
0
1
2
0
0
0
0
1
0
1
0
0
6
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
4
0
0
1
1
0
0
2
0
0
0
0
0
1
4
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
1
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
2
0
2
2
1
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
2
0
2
0
0
0
0
4
1
3
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
4
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
1
2
0
0
0
0
2
0
2
0
0
0
5
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
3
3
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
3
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
1
12
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
1
3
1
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
3
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
2
0
2
0
5
0
0
0
1
0
2
0
0
0
0
2
0
3
0
2
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
0
0
0
2
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
3
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
7
0
3
0
0
1
0
0
1
1
0
0
0
0
1
0
0
3
0
2
0
1
5
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
1
1
0
0
0
2
0
0
3
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
2
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
2
2
0
0
0
0
1
2
0
2
0
0
1
4
0
0
0
3
0
0
0
0
3
0
1
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
1
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
1
1
0
0
0
3
4
0
1
0
0
0
0
0
2
0
0
0
2
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
1
0
0
2
0
2
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
2
0
0
0
0
3
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
3
0
0
1
0
3
0
3
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
1
0
0
1
0
0
2
0
0
2
0
0
4
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
1
1
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
1
1
2
0
1
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
4
1
0
1
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
4
1
0
1
0
0
1
0
0
0
0
2
0
3
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
1
1
0
2
0
0
0
0
2
0
0
0
0
0
2
1
1
0
1
1
0
0
1
0
0
0
0
0
0
3
0
1
0
3
2
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
3
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
1
2
2
0
1
0
0
0
0
0
0
0
1
0
0
1
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
5
0
0
0
0
0
0
5
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
1
0
1
1
2
0
0
0
0
1
0
0
0
2
0
0
1
1
2
0
2
1
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
1
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
3
4
2
2
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
1
0
0
0
0
0
2
1
1
0
0
0
0
0
2
2
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
2
0
0
2
1
0
1
0
0
0
1
2
4
2
1
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
2
0
0
0
3
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
14
0
2
0
0
3
0
0
2
0
2
0
2
0
0
1
0
0
2
0
1
2
0
0
0
1
0
0
1
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
2
0
3
0
1
0
0
0
2
0
0
0
0
2
3
0
0
1
2
0
0
1
6
0
1
0
1
0
2
0
2
0
3
0
0
0
0
0
4
1
0
0
2
1
0
0
0
0
0
0
0
3
0
1
0
0
0
1
1
0
2
0
0
0
0
0
2
0
1
3
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
4
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
1
0
0
0
0
0
0
1
3
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
2
0
0
0
0
0
0
0
0
6
0
1
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
2
0
0
0
0
1
0
0
1
2
0
0
0
0
0
6
0
0
0
0
0
0
2
0
0
0
1
0
7
0
2
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
1
0
2
1
2
0
0
0
3
0
0
2
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
3
0
1
4
0
0
0
2
1
1
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
1
1
0
0
2
3
0
0
1
2
0
1
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
2
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
1
0
0
1
2
5
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
3
0
0
0
0
1
0
0
0
4
0
0
0
2
1
0
0
0
0
2
0
1
0
0
2
0
1
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
1
2
1
2
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
1
2
3
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
2
0
0
0
0
1
1
2
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
1
0
0
0
0
2
0
6
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
3
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
3
0
6
0
0
1
0
2
0
1
0
2
0
0
0
0
2
2
0
1
1
0
1
0
0
0
0
2
0
2
0
0
0
0
0
3
1
0
0
1
0
0
0
0
0
2
4
2
0
1
1
0
0
0
2
0
0
1
0
0
1
1
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
1
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
5
1
0
0
0
1
1
0
0
3
0
0
0
3
0
1
0
0
0
0
2
3
0
2
1
1
0
0
1
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
2
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
3
2
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
1
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
3
0
0
0
2
0
0
0
0
0
0
0
2
0
1
1
0
0
0
1
0
0
0
0
0
0
1
4
2
1
0
0
3
0
0
1
0
2
0
1
0
1
0
0
0
1
0
0
0
1
2
0
3
0
3
0
2
0
0
1
0
0
0
1
1
1
4
2
0
0
1
0
1
2
1
0
2
0
3
0
0
2
0
1
0
2
0
0
0
0
0
0
2
1
2
0
0
0
1
0
1
0
0
0
5
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
1
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
4
2
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
2
2
0
0
1
0
0
0
0
2
0
1
0
0
1
0
0
0
1
0
1
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
1
4
0
1
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
1
0
0
0
0
1
0
1
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
3
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
1
0
0
0
4
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
2
1
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
1
0
0
2
0
1
1
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
2
1
2
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
2
2
0
2
0
0
0
2
0
0
2
0
0
2
2
0
0
1
0
0
0
0
4
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
6
0
0
1
0
0
0
0
0
0
1
0
0
0
2
1
0
0
1
1
0
1
1
0
0
0
4
0
1
2
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
2
0
0
1
0
0
1
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
1
7
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
1
0
0
0
2
0
2
0
3
0
0
0
0
3
0
1
1
1
0
0
0
3
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
1
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
1
1
0
2
2
0
0
0
0
0
0
0
0
0
2
3
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
1
2
0
1
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
2
1
0
0
0
0
0
0
0
1
0
0
0
8
0
0
1
0
1
0
2
0
0
0
0
1
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
1
2
0
0
0
0
0
1
0
0
0
2
0
0
2
0
5
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
8
0
0
0
0
0
0
0
0
2
0
0
5
0
0
0
2
0
0
0
2
0
0
1
0
1
1
0
3
3
0
0
0
0
0
0
0
1
1
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
2
0
0
2
0
0
0
0
3
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
3
0
0
2
0
0
2
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
2
1
0
1
0
0
0
1
1
1
0
0
0
0
0
3
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
8
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
2
1
0
0
0
0
0
1
1
0
1
0
2
2
0
0
1
0
3
0
0
0
6
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
3
1
0
1
0
0
0
7
0
1
0
1
2
2
0
0
0
0
0
0
2
0
2
0
1
2
2
0
0
0
0
1
0
0
1
3
2
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
2
4
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
2
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
4
0
0
0
0
0
0
0
0
1
2
2
2
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
1
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
4
1
2
0
0
2
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
1
2
0
1
2
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
2
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
3
2
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
1
0
3
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
2
1
2
0
0
1
0
0
0
1
0
2
0
2
0
0
0
1
0
5
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
1
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
1
1
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
1
2
1
0
0
0
0
0
1
0
1
0
0
4
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
1
1
0
2
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
2
0
0
0
0
1
0
0
0
0
0
2
2
0
1
0
1
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
3
0
3
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
4
0
4
0
5
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
2
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
1
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
2
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
2
2
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
2
2
0
0
1
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
8
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
2
0
1
0
1
0
2
0
2
0
0
2
0
0
1
1
1
0
0
0
2
0
0
0
0
0
0
0
0
1
2
2
2
2
0
0
0
0
0
0
2
1
0
1
0
0
0
2
1
0
2
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
1
0
0
2
0
0
3
2
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
2
0
0
0
0
0
3
0
3
1
0
0
0
0
0
0
0
0
0
0
0
6
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
2
1
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
3
0
0
1
0
1
0
0
0
0
2
1
1
0
1
0
0
0
0
0
0
0
2
0
2
3
0
1
0
0
2
2
2
0
0
1
0
0
2
0
2
0
0
6
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
2
0
0
0
0
2
0
5
2
2
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
2
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
2
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
2
0
2
0
1
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
2
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
7
2
1
0
0
2
0
0
0
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
1
0
3
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
1
0
0
0
0
0
2
0
0
1
6
2
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
3
1
0
2
2
1
0
1
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
1
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
4
0
0
2
0
0
0
1
0
0
2
2
0
0
0
0
0
0
5
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
1
0
0
3
0
0
2
1
0
1
4
0
0
0
0
1
2
0
2
1
1
3
0
2
0
1
0
0
0
0
2
2
0
0
0
1
0
1
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
4
0
1
0
0
0
0
0
2
0
0
1
1
1
0
0
0
0
0
0
1
1
0
1
0
2
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
4
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
2
0
0
1
0
0
1
0
0
1
0
0
0
0
0
2
2
2
0
0
0
0
0
1
2
2
2
0
0
0
0
0
2
2
0
0
1
0
0
0
3
0
0
2
0
0
0
1
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
4
2
1
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
1
5
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
2
0
0
2
0
0
0
0
0
0
0
3
3
0
0
0
3
0
0
0
0
0
0
0
0
3
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
1
0
1
0
2
1
0
1
0
0
0
0
2
0
1
0
1
3
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
4
1
1
1
0
0
0
2
1
0
0
0
3
0
0
0
0
1
0
0
1
0
1
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
5
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
7
0
0
2
2
0
0
0
2
0
0
1
0
2
0
0
1
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
2
0
0
1
0
0
2
2
0
2
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
1
0
0
1
0
0
2
0
0
0
0
0
2
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
5
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
1
2
0
1
0
0
5
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
1
2
1
2
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
1
1
2
0
0
1
0
4
0
0
0
0
2
0
0
0
0
0
1
0
0
0
3
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
3
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
1
1
2
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
2
0
6
2
0
1
0
1
0
0
2
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
2
1
0
3
0
0
0
0
0
0
0
5
2
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
4
0
0
0
0
0
1
1
0
1
1
1
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
2
0
0
4
2
0
0
0
0
3
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
2
1
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
2
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
1
0
2
0
2
1
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
1
2
0
0
1
0
1
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
1
1
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
6
0
0
0
2
2
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
1
1
0
2
0
0
0
0
0
0
2
0
1
2
1
2
0
2
1
0
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
2
0
1
0
4
0
0
0
0
0
0
0
2
4
1
0
0
0
0
0
0
0
0
0
4
1
2
0
0
1
0
1
0
0
1
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
2
0
0
2
2
1
0
0
0
3
0
1
0
0
0
2
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
1
1
4
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
5
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
1
1
1
0
0
1
0
0
0
0
0
1
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
5
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
4
1
0
1
0
4
0
0
0
1
0
1
2
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
2
0
1
2
0
3
0
0
0
2
5
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
1
0
0
4
0
0
0
0
0
2
0
0
0
1
0
0
1
0
1
0
2
1
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
3
3
0
0
2
1
0
2
0
1
0
0
0
0
2
0
0
0
0
0
1
0
4
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
3
1
0
2
0
0
0
4
0
1
0
0
1
0
0
0
0
0
1
4
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
2
2
2
2
0
0
0
0
0
2
1
0
0
2
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
4
0
2
0
0
0
2
0
0
6
2
3
0
2
1
0
0
2
0
1
0
0
0
0
0
0
1
0
1
2
2
8
1
1
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
2
2
0
0
0
2
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
17
0
2
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
2
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
3
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
8
0
1
2
0
0
1
5
2
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
3
0
0
2
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
6
1
0
0
0
0
0
0
0
1
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
1
2
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
6
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
1
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
1
2
0
1
3
0
0
0
0
0
0
0
1
3
1
1
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
2
0
2
2
1
0
0
0
1
0
0
0
2
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
2
1
1
0
0
0
0
1
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
1
0
0
1
0
1
0
0
4
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
2
0
0
0
0
0
0
1
0
0
3
0
0
0
2
2
0
0
1
2
0
2
0
2
0
0
0
2
1
1
0
0
0
2
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
1
5
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
3
0
0
1
2
0
2
0
0
0
2
0
0
0
1
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
1
0
0
1
0
2
2
0
0
0
1
1
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
2
0
2
0
0
0
1
1
2
0
0
0
2
0
2
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
1
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
2
0
0
0
2
0
0
0
1
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
2
2
0
0
0
0
1
0
0
0
0
2
0
0
7
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
3
0
0
0
2
0
0
0
2
0
5
0
2
0
2
1
0
0
1
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
1
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
9
1
2
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
1
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
1
0
0
0
0
2
1
0
1
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
4
2
0
0
3
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
2
2
2
0
0
1
1
0
0
0
1
1
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
1
2
0
0
0
2
0
0
0
3
0
0
2
0
0
0
0
0
2
0
0
2
1
2
0
1
0
0
0
0
0
2
0
2
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
5
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
5
0
0
2
0
0
0
0
4
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
1
3
2
1
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
2
0
0
3
4
0
0
1
0
0
2
2
2
0
0
0
0
0
0
1
1
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
2
0
5
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
1
0
0
0
3
0
1
0
0
2
0
0
0
0
2
0
0
3
0
4
0
0
0
0
0
1
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
5
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
2
0
2
0
0
0
0
1
0
0
1
1
0
0
2
3
1
0
3
0
0
0
0
0
1
1
0
0
0
0
0
0
2
2
0
2
0
2
0
0
0
1
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
2
2
0
0
1
0
0
2
0
0
0
0
0
5
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
2
0
0
1
1
1
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7
3
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
1
2
0
2
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
3
0
0
1
0
0
0
0
0
0
2
0
0
1
1
0
5
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
1
4
1
0
0
1
1
0
0
1
1
8
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
6
0
5
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
3
0
0
0
0
1
1
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
2
1
0
0
0
0
2
0
4
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
3
0
1
0
1
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
2
3
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
3
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
3
0
0
1
1
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
2
2
0
3
0
1
4
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
1
2
0
0
0
0
4
0
1
0
3
0
0
0
0
1
1
0
1
0
0
2
0
1
3
3
0
0
1
0
0
0
0
0
0
2
2
0
0
0
2
1
0
2
1
0
0
10
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
2
1
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
2
0
2
1
0
0
1
0
0
3
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
1
0
0
0
0
1
0
0
0
1
3
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
1
0
2
0
0
2
0
0
2
1
2
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
2
0
1
1
0
0
2
0
1
1
0
0
2
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
2
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
4
0
0
2
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
1
0
0
2
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
9
0
2
2
0
0
6
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
1
0
0
1
0
0
2
0
0
2
0
0
2
0
0
0
0
3
2
0
2
0
0
1
3
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
4
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
2
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
2
0
0
1
0
0
0
2
0
0
2
0
1
1
0
1
0
0
1
2
0
0
0
0
0
0
1
0
1
1
1
0
0
3
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
2
1
0
0
0
0
2
0
3
0
0
1
0
0
2
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
2
0
0
1
1
14
1
0
0
1
0
0
3
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
2
2
1
0
0
0
3
0
0
1
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
2
0
0
0
1
2
2
0
1
1
0
0
3
0
2
0
0
1
0
0
1
2
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
1
1
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
2
2
0
0
2
0
1
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
2
0
0
1
0
0
1
0
0
0
1
0
2
4
2
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
2
1
2
0
1
0
2
0
0
0
0
0
0
1
0
0
2
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
2
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
2
2
1
0
1
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
2
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
1
0
0
6
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
2
0
2
0
3
0
2
5
0
0
1
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
4
2
2
0
1
0
0
1
0
1
1
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
1
0
0
2
0
3
2
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
3
0
1
0
0
0
2
0
2
0
2
0
0
1
0
2
2
0
0
0
1
0
0
0
4
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
1
0
2
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
1
1
0
0
0
3
0
0
0
0
0
0
0
2
0
2
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
2
2
0
0
0
0
6
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
2
1
0
0
0
1
0
0
0
2
0
0
0
1
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
3
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
2
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
4
0
0
3
1
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
3
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
1
2
2
0
0
4
1
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
3
0
1
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
2
0
1
0
0
1
0
2
3
0
0
0
2
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
2
0
2
0
1
0
0
0
0
2
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
2
0
0
0
1
0
0
1
1
0
0
3
0
1
1
1
2
2
11
0
0
0
0
2
0
1
0
0
0
2
0
0
0
2
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
1
0
2
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
6
1
0
0
0
0
0
1
0
0
1
0
0
2
1
0
0
0
4
0
1
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
1
0
0
1
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
2
1
3
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
3
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
2
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
2
0
0
0
2
0
0
1
1
0
0
0
2
0
0
0
0
0
0
1
2
3
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
3
0
0
0
0
0
1
0
2
0
0
0
4
0
0
0
5
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
1
0
0
1
1
0
0
0
0
0
0
0
1
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
1
0
4
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
1
2
0
1
0
3
0
2
0
2
1
3
0
0
2
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
1
0
0
2
2
1
0
2
1
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
3
0
0
2
0
0
2
0
0
0
0
2
0
1
0
1
1
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
2
0
0
2
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
2
0
2
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
1
1
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
8
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
1
1
8
0
0
1
1
0
4
0
0
0
1
0
0
0
0
2
0
0
2
2
0
1
0
0
0
0
0
1
0
0
0
2
0
9
0
0
0
2
0
0
0
1
0
0
0
0
0
1
1
0
3
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
1
0
0
4
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
1
0
0
0
0
0
1
0
0
0
1
0
0
3
0
2
0
0
0
0
0
0
3
0
0
2
0
1
0
3
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
1
1
1
0
0
0
2
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
2
0
1
1
0
0
0
0
1
0
0
1
1
0
0
0
0
3
0
1
0
0
1
2
0
2
0
0
0
0
0
2
2
0
0
1
1
0
0
0
1
0
0
2
0
2
0
1
0
2
0
0
2
0
0
0
0
0
0
2
1
0
1
1
2
0
0
3
0
0
1
0
0
0
0
0
0
1
0
1
1
1
2
0
3
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
2
0
0
3
1
0
0
2
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
2
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
1
0
0
0
2
0
0
1
2
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
3
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
1
2
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
3
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
2
1
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
1
0
0
0
1
0
2
0
2
0
1
0
1
2
0
2
0
0
0
0
1
4
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
3
0
0
0
0
5
0
0
2
0
2
1
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
1
0
2
0
0
0
1
2
4
0
0
0
0
9
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
3
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
1
2
0
0
4
1
0
0
0
0
0
0
2
0
0
2
0
1
1
1
0
0
2
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
2
0
0
1
0
0
0
0
2
0
0
1
1
2
0
2
2
0
1
4
0
1
2
1
0
0
1
0
2
0
0
0
2
0
0
0
0
0
3
0
1
0
0
1
0
0
0
0
0
1
2
1
2
3
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
2
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
2
1
0
0
0
0
0
0
0
0
2
1
1
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
3
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
5
0
0
2
2
2
1
0
2
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
4
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
2
2
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
2
1
1
0
2
0
0
1
1
1
0
2
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
1
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
1
0
2
2
0
2
2
0
3
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
1
1
1
0
0
0
0
0
0
0
2
0
3
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
1
1
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
2
1
3
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
3
0
0
0
2
3
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
2
0
0
1
1
3
0
0
9
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
2
1
1
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
1
0
2
0
2
0
0
2
1
2
0
0
0
0
0
0
1
0
0
0
0
0
2
3
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
1
1
1
1
3
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
1
2
0
0
2
0
0
2
2
0
0
0
0
0
0
2
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
3
0
0
0
0
0
1
0
0
0
2
0
0
0
2
5
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
4
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
4
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
3
2
2
1
0
2
1
0
0
0
0
0
3
0
0
0
2
0
1
0
0
0
0
0
0
1
0
1
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
1
3
1
0
0
0
0
0
3
0
0
0
0
4
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
4
1
0
0
0
0
2
0
2
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
11
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
3
0
1
0
1
1
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
2
0
1
4
0
0
1
0
0
2
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
1
2
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
2
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
2
1
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
1
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
2
2
1
2
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
1
3
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
2
0
0
0
0
0
2
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
2
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
5
0
0
3
0
0
0
0
1
0
5
0
0
0
1
0
3
0
0
0
0
2
0
0
2
2
0
0
0
0
0
1
0
0
2
2
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
1
2
1
0
0
0
0
1
0
0
0
1
2
1
0
0
0
0
3
2
4
0
0
0
0
0
1
7
0
0
1
3
0
0
0
0
3
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
8
0
0
0
0
0
0
0
0
6
1
0
0
0
2
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
3
0
0
0
0
2
0
0
1
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
3
0
3
0
0
0
3
0
0
0
0
0
2
1
2
0
0
3
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
8
0
5
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
1
0
0
2
1
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
2
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
1
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
2
0
2
0
0
2
0
4
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
2
2
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
2
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
1
4
0
0
2
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
2
0
0
2
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
3
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
3
4
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
1
1
2
1
0
2
0
0
0
0
0
1
0
1
0
3
0
2
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
1
0
0
0
0
1
0
0
4
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
3
0
2
0
0
2
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
10
2
0
1
2
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
5
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
2
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
1
0
0
1
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
2
1
0
0
0
0
1
0
0
0
2
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
2
2
0
0
0
2
0
0
1
0
0
0
2
1
2
1
0
1
0
0
2
1
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
2
0
1
0
0
0
0
0
0
2
6
0
0
2
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
3
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
1
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
4
3
0
0
0
0
5
0
0
0
1
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
2
0
0
0
1
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
2
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
2
0
2
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
2
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
1
0
0
2
0
0
0
0
2
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
3
1
2
0
0
0
0
1
0
2
0
0
2
5
1
0
0
0
0
0
1
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
2
0
1
0
0
0
4
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
3
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
2
0
2
0
1
0
0
1
3
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
5
0
1
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
1
1
2
0
0
0
0
0
6
0
0
0
0
2
2
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
5
0
1
0
0
0
2
0
0
3
0
0
0
0
0
0
1
0
0
1
0
2
0
2
0
0
0
0
0
2
0
0
1
0
2
0
1
2
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
1
0
2
5
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
3
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
3
0
0
0
1
0
0
0
2
0
0
0
2
0
2
0
4
0
3
0
0
0
2
0
0
0
1
1
3
0
1
0
0
0
0
0
1
0
28
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
2
0
0
0
1
0
0
0
1
0
2
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
2
0
2
2
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
1
0
1
3
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
1
0
0
0
0
1
0
0
0
2
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
2
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
1
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
3
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
2
0
0
0
0
2
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
0
1
0
1
0
2
0
0
1
0
1
1
0
0
0
0
0
0
1
0
1
0
0
4
0
0
2
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
3
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
3
1
0
0
2
2
0
2
0
0
0
0
0
4
2
0
4
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
2
1
0
0
0
0
2
2
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
7
0
0
0
0
0
0
4
0
0
1
0
0
0
4
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
4
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
2
0
2
0
0
0
1
9
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
3
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
3
2
0
0
0
0
2
0
0
0
1
0
0
2
0
0
1
0
0
0
2
0
1
0
0
1
0
0
1
1
2
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
3
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
2
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
2
1
0
0
0
0
3
0
0
0
0
2
0
0
1
4
2
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
8
2
0
1
2
0
1
0
2
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
10
0
0
0
0
2
1
0
0
1
1
0
2
0
0
0
0
1
2
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
7
2
0
2
0
2
3
2
0
0
0
0
0
0
0
12
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
4
0
0
0
1
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
10
0
0
0
0
0
3
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
2
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
2
4
0
0
0
1
0
0
0
0
2
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
8
2
0
0
2
1
0
0
1
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
1
0
0
2
0
0
2
0
4
0
0
0
0
1
0
0
0
1
1
1
0
0
0
2
0
1
0
1
2
0
0
0
0
0
0
0
3
0
1
0
0
0
1
0
0
1
0
1
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
1
1
0
0
0
1
0
0
0
1
0
3
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
2
2
2
0
1
1
0
2
2
0
0
1
0
0
2
0
0
0
0
0
3
0
0
0
0
0
2
0
9
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
1
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
2
1
0
0
1
0
2
0
0
1
1
0
0
0
0
0
0
0
10
0
0
0
0
0
0
0
0
2
0
2
0
1
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
4
0
0
1
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
2
0
0
2
0
3
2
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
4
0
0
0
1
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
2
0
0
0
2
0
0
2
0
0
1
0
1
0
0
0
2
0
2
3
0
0
1
0
0
2
3
0
0
0
1
0
0
0
1
1
2
0
0
2
0
0
2
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
2
1
0
0
0
1
2
0
0
0
3
6
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
2
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
1
0
0
1
1
2
2
0
0
1
0
0
0
0
2
2
0
0
2
0
0
3
0
0
0
0
5
0
0
0
3
0
2
0
2
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
2
0
0
0
2
1
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
1
2
2
0
1
0
2
2
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
1
3
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
3
0
2
5
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
5
0
1
0
0
0
0
1
0
7
1
0
2
1
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
2
2
3
2
0
0
1
0
0
2
3
0
0
0
0
1
0
0
2
0
2
0
1
0
1
0
0
3
1
1
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
2
0
0
0
0
1
0
0
2
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
1
0
1
0
0
1
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
1
5
0
2
0
2
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
4
2
0
1
2
2
1
0
1
0
0
0
0
0
0
0
0
1
0
0
3
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
2
0
1
0
0
1
0
0
0
0
0
3
0
1
0
0
0
0
1
0
2
0
0
0
1
0
1
0
1
0
2
0
0
0
2
4
1
0
0
0
0
0
0
1
3
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
1
0
3
0
0
0
0
1
1
0
2
0
0
2
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
2
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
4
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
1
0
2
0
1
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
3
0
0
4
2
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
1
0
1
1
1
0
0
1
3
1
1
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
1
0
0
0
1
0
3
1
0
0
0
0
1
2
0
0
0
1
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
3
0
0
0
2
0
0
2
0
0
0
0
0
0
4
2
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
7
1
2
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
7
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
1
0
1
3
0
0
0
0
0
1
0
0
0
0
0
2
1
2
0
0
0
2
0
1
0
0
0
3
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
3
1
0
0
2
1
0
0
1
0
0
0
0
6
0
0
0
0
2
2
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
2
0
1
0
2
0
10
0
0
0
3
0
0
0
2
2
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
1
2
0
1
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
3
0
0
0
0
0
2
2
0
0
0
7
2
1
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
2
2
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
2
0
0
2
0
1
0
0
0
0
2
2
2
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
2
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
2
0
0
0
1
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
2
2
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
1
3
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
2
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
1
0
0
0
0
1
0
2
1
0
0
0
1
2
0
0
1
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
2
2
1
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
4
0
1
1
2
0
0
0
0
2
0
0
2
0
1
2
1
1
3
0
0
0
0
1
0
1
0
0
0
0
0
1
0
2
0
0
0
2
0
1
3
0
0
0
0
1
1
1
1
0
0
0
1
0
0
0
0
0
0
0
3
2
0
0
0
0
1
0
1
1
2
0
0
1
0
0
0
2
1
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
2
0
0
0
2
1
1
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
3
0
1
0
0
0
2
0
2
0
1
8
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
2
0
1
5
0
0
0
0
3
0
0
0
0
0
2
2
1
1
1
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
2
2
0
2
1
0
0
0
0
0
0
0
2
0
0
3
0
2
0
0
0
4
0
0
0
0
0
2
0
1
0
0
0
0
0
3
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
2
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
2
2
0
0
0
3
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
2
0
0
1
0
2
1
2
0
0
2
0
0
0
0
2
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
4
0
1
2
0
0
0
3
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
1
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
1
0
2
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
1
1
1
0
2
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
2
0
1
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
1
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
1
0
2
0
1
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
1
0
6
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
1
0
0
2
0
0
3
0
2
0
2
2
0
0
2
1
0
0
0
1
0
0
0
0
0
2
2
0
2
2
0
0
0
2
0
0
0
0
1
0
0
0
0
5
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
1
1
0
0
0
3
0
0
0
0
2
4
0
0
0
0
1
0
0
3
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
2
1
1
2
1
0
2
0
3
2
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
3
0
0
0
1
2
0
0
1
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
3
1
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
7
0
0
1
1
3
0
0
2
2
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
1
0
3
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
3
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
2
0
0
1
0
2
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
1
0
1
2
0
0
1
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
2
0
0
1
0
2
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
2
0
0
0
0
1
1
0
4
1
0
0
0
4
0
2
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
1
0
1
0
0
2
3
1
0
1
1
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
4
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
3
1
0
1
1
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
2
1
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
3
1
0
0
1
0
2
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
2
0
2
0
0
0
5
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
1
1
0
1
0
0
0
1
0
0
1
0
0
2
0
0
0
2
0
2
0
0
1
2
0
0
0
0
2
1
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
1
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
3
1
1
0
0
0
2
0
0
0
0
0
1
6
0
0
0
0
2
0
2
0
0
1
0
2
1
0
0
0
0
0
0
1
0
0
0
2
0
0
1
2
0
1
0
0
2
0
0
2
2
4
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
3
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
2
0
0
0
1
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
6
0
0
2
0
0
3
1
0
1
0
1
0
0
0
1
1
0
1
1
0
1
0
0
0
0
0
1
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
3
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
2
0
3
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
3
0
1
0
0
1
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
2
0
0
3
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
2
0
2
0
0
0
0
0
0
1
0
0
1
0
1
2
1
1
2
1
0
2
0
0
0
0
0
0
1
0
2
0
0
0
2
0
2
3
0
2
2
2
0
0
1
2
0
0
0
3
0
5
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
3
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
2
2
2
0
1
0
0
1
0
1
0
0
0
2
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
4
0
0
0
0
0
0
0
2
0
0
4
0
0
0
0
4
2
0
0
4
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
2
0
1
1
1
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
2
2
0
1
0
2
1
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
3
0
0
0
0
0
0
0
0
1
2
2
0
0
2
0
2
1
0
0
7
0
1
1
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
2
4
0
0
0
0
0
0
3
0
2
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
2
3
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
3
0
0
0
0
0
2
0
0
1
2
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
1
1
0
0
1
0
1
1
0
0
0
0
0
4
0
3
0
0
0
2
0
1
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
2
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
1
0
0
3
3
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
2
0
1
0
0
0
3
0
1
2
0
0
0
2
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
1
0
2
0
0
2
2
2
0
2
0
1
0
0
0
1
2
0
0
3
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
1
2
0
0
0
0
0
1
2
1
0
0
1
2
0
0
0
0
0
0
3
0
0
0
0
2
2
0
0
1
2
0
0
0
1
0
0
2
0
5
2
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
2
0
0
2
0
1
2
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
1
1
0
2
2
2
0
3
0
0
0
0
0
0
0
0
3
2
0
0
1
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
1
0
2
0
2
1
0
0
0
6
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
1
0
0
2
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
2
2
0
0
3
0
0
0
0
1
0
0
1
0
0
0
0
0
4
0
0
1
0
0
0
0
0
1
0
1
2
0
1
0
0
0
0
0
0
0
4
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
7
1
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
2
0
0
1
2
0
2
0
1
0
0
0
0
2
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
3
1
0
0
2
1
0
2
0
2
0
0
0
0
0
0
0
2
0
2
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
1
0
2
0
2
0
0
0
0
10
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
1
2
3
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
4
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
2
0
1
1
2
0
0
0
0
0
0
0
4
0
2
0
2
1
1
0
1
4
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
2
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
2
2
0
0
0
1
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
1
1
2
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
1
0
0
1
0
2
2
0
1
4
0
0
0
2
2
2
0
0
0
1
0
0
2
0
1
2
0
0
0
2
0
0
0
1
0
2
5
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
3
0
2
1
0
1
0
0
0
1
0
0
0
0
1
0
1
2
1
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
4
0
0
0
3
5
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
2
0
2
1
0
0
0
2
0
0
1
0
2
0
1
0
2
0
0
0
2
0
0
0
1
0
0
1
0
0
0
1
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
2
2
0
0
2
9
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
1
0
1
0
0
2
0
0
0
0
2
0
0
0
1
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
2
0
0
0
1
0
2
1
2
0
0
1
0
0
2
1
0
0
0
2
0
1
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
3
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
8
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
2
1
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
2
1
1
0
1
0
0
5
0
2
0
0
1
0
0
0
1
0
0
0
4
0
0
2
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
9
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
3
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
1
0
0
2
0
0
0
1
0
1
3
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
3
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
3
0
1
0
0
2
4
0
0
1
0
2
1
1
0
0
2
0
1
0
0
2
2
1
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
1
1
0
0
1
1
0
0
0
0
10
0
1
4
2
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
2
2
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
1
2
0
2
0
0
0
0
1
0
4
0
0
0
0
0
1
0
0
1
0
0
0
3
2
1
0
0
1
0
0
4
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
2
0
2
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
1
0
0
0
0
0
1
2
0
0
3
0
0
0
3
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
1
0
0
0
0
0
0
1
1
1
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
1
0
10
1
0
2
1
0
0
0
3
0
0
2
0
0
0
1
0
1
1
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
1
0
3
0
0
0
1
0
0
2
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
2
1
0
0
0
0
0
1
0
0
0
1
1
0
0
2
0
1
0
0
0
0
1
0
1
0
0
2
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
2
2
0
0
0
0
2
0
0
0
0
0
0
7
0
1
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
2
0
0
1
0
1
0
1
0
0
0
1
2
0
6
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
3
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
1
0
0
1
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
1
0
0
0
2
4
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
2
1
1
2
0
1
0
0
4
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
4
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
3
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
2
0
2
0
0
0
0
0
0
0
0
0
2
1
0
4
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
1
0
0
2
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
1
2
1
0
1
0
3
0
0
0
0
0
0
2
2
0
0
0
0
2
3
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
5
6
0
0
0
2
3
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
1
2
0
0
0
0
0
2
2
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
2
0
1
0
0
3
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
6
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
10
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
3
0
2
0
0
2
1
0
1
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
3
0
0
4
0
0
0
1
0
0
1
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
1
0
2
0
0
2
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
2
1
0
0
0
0
0
2
2
0
1
0
2
0
1
0
0
0
0
0
0
0
2
1
1
0
0
0
0
2
1
0
0
0
0
0
3
0
0
1
1
0
0
0
0
0
0
0
4
1
0
0
0
3
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
1
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
1
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
2
0
0
0
0
0
0
1
1
1
0
1
0
0
2
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
6
1
0
0
0
0
2
1
0
0
0
0
0
1
0
0
1
3
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
1
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
1
0
0
0
1
0
0
0
2
1
0
0
0
0
0
2
0
3
0
1
15
0
0
0
3
0
0
0
0
0
0
0
3
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
2
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
1
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
1
0
1
2
0
0
0
0
0
0
0
0
2
2
2
0
0
0
2
0
0
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
2
0
0
0
0
0
2
4
0
2
0
0
2
0
1
1
0
2
1
1
0
1
0
0
0
0
0
2
1
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
4
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
3
4
0
2
0
0
0
0
0
2
0
1
1
0
1
1
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
3
1
2
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
9
0
0
0
0
0
0
0
4
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
2
1
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
3
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
1
0
0
0
3
0
0
2
0
0
0
0
0
6
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
2
2
0
2
0
0
1
1
0
0
1
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
3
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
1
0
7
0
0
0
0
0
0
0
0
0
1
0
0
3
5
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
2
0
1
0
2
0
1
1
0
2
0
1
0
0
0
2
0
0
9
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
1
1
0
0
0
2
0
0
2
0
0
1
2
0
2
0
0
0
0
0
0
1
1
0
4
2
0
1
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
1
0
0
2
1
0
0
0
0
0
0
1
1
0
0
0
0
0
4
0
0
0
2
2
0
0
0
0
0
0
3
0
0
0
0
0
4
0
0
1
0
2
2
0
0
0
0
0
0
1
0
0
2
1
1
0
0
0
0
0
2
0
1
0
1
0
6
2
0
0
2
1
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
7
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
3
0
0
3
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
3
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
5
0
0
2
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
1
0
0
0
1
2
3
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
3
0
2
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
2
0
2
0
1
4
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
1
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
1
2
1
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
2
0
0
0
4
1
0
1
2
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
2
1
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
1
2
0
0
1
0
0
1
0
1
0
0
0
0
3
0
0
0
1
0
2
1
0
3
0
5
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
2
1
0
0
0
0
0
2
1
3
0
2
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
4
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
4
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
1
1
1
2
0
2
0
0
2
0
0
1
0
2
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
4
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
2
2
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
2
0
0
0
0
2
0
1
1
0
0
0
0
0
1
0
0
1
3
0
0
2
0
0
0
3
1
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
4
0
0
2
2
0
0
1
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
2
0
0
0
0
0
1
0
0
0
3
1
1
0
0
0
1
0
1
0
0
1
0
0
1
0
1
0
1
9
0
0
2
0
0
0
1
0
0
3
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
1
0
3
1
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
2
0
0
0
0
1
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
2
1
0
0
2
0
2
0
0
5
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
1
0
0
0
0
1
0
1
0
4
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
3
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
3
0
0
0
0
0
2
0
0
1
0
0
3
0
0
0
0
0
0
0
6
0
3
2
0
0
0
0
1
0
1
0
0
1
0
0
2
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
1
0
0
2
0
0
1
0
0
0
1
0
0
0
0
2
0
0
1
2
2
0
0
1
0
0
1
0
0
1
0
0
0
0
0
3
3
1
1
0
0
0
1
1
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
1
0
2
0
0
1
0
2
2
0
0
1
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
4
0
0
3
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
2
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
5
0
0
1
0
0
0
0
0
4
2
0
2
1
2
2
0
0
1
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
3
0
0
1
0
0
0
0
0
0
2
0
0
2
2
0
2
0
0
1
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
4
0
2
0
0
2
1
0
0
0
1
2
0
0
0
1
2
2
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
2
0
2
2
0
0
0
2
2
1
1
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
1
0
2
2
1
0
5
1
0
0
0
4
2
0
0
2
0
0
0
1
1
1
1
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
2
0
0
3
1
0
0
2
1
0
1
0
0
0
0
1
0
0
2
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
1
2
1
0
1
0
2
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
2
0
1
0
0
0
0
2
2
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
2
0
3
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
6
3
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
1
0
1
0
2
2
2
2
0
0
1
0
0
0
0
3
0
0
1
0
4
1
3
0
0
0
0
1
2
1
0
0
3
2
0
1
2
0
0
1
2
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
1
0
3
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
1
0
0
0
1
2
0
0
0
2
0
1
2
0
0
0
1
1
3
0
3
3
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
2
1
0
2
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
3
1
1
3
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
5
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
1
0
2
0
1
2
0
0
0
0
0
2
2
0
1
1
0
3
0
0
1
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
2
0
1
0
0
0
1
1
0
0
1
0
0
4
2
1
0
0
0
0
0
0
2
1
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
5
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
1
0
0
0
2
3
0
0
6
0
5
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
6
0
0
0
0
0
0
0
1
3
0
2
0
0
0
0
0
0
0
0
2
0
0
1
3
0
2
0
0
0
0
0
2
0
0
0
2
2
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
2
1
0
2
0
3
0
1
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
2
0
1
0
0
0
1
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
1
1
1
2
1
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
1
2
0
2
0
0
1
1
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
3
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
8
0
0
2
0
2
0
2
2
0
0
1
0
0
0
0
0
2
0
0
2
1
0
0
1
0
0
2
0
0
0
5
2
0
0
0
0
2
0
0
3
0
2
0
0
0
0
0
0
0
4
0
0
1
2
2
1
0
4
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
1
3
4
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
2
0
0
0
2
3
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
5
0
2
1
0
2
0
0
0
0
1
0
1
0
1
0
2
4
0
0
0
0
2
0
0
0
0
0
0
0
2
2
4
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
2
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
3
0
0
2
0
0
0
0
0
2
1
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
4
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
3
0
0
0
0
0
1
1
0
0
2
0
0
0
1
0
2
0
0
1
0
0
0
2
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
4
0
1
1
2
1
0
1
0
0
0
1
1
1
0
0
1
0
0
0
0
4
0
0
0
0
3
0
0
0
0
0
0
2
2
1
0
0
0
0
2
0
1
1
0
0
1
0
0
0
0
0
0
0
0
2
0
2
1
0
2
0
2
0
0
0
0
1
4
0
1
0
1
2
0
0
0
4
1
3
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
4
0
0
2
2
0
2
0
0
0
0
0
0
2
1
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
2
0
0
0
0
3
1
2
0
1
0
0
0
2
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
5
0
2
2
0
1
0
0
4
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
2
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
1
0
0
0
0
1
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
2
0
0
2
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
2
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
11
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
4
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
3
1
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
1
2
0
2
0
0
0
0
0
1
2
2
2
0
0
0
0
0
0
0
0
0
6
2
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
5
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
2
2
0
0
1
2
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
4
0
0
1
1
0
0
0
0
0
1
0
0
4
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
1
0
1
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
3
0
8
0
0
0
1
1
6
0
0
0
1
1
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
4
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
2
1
0
0
1
0
0
0
0
3
0
2
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
5
1
0
0
1
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
2
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
3
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
2
1
0
0
2
2
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
2
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
1
1
0
1
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
1
0
1
0
0
0
1
1
0
2
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
1
0
2
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
10
0
0
0
0
0
2
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
2
2
1
1
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
2
0
2
1
0
0
2
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
1
2
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
2
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
2
3
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
2
0
0
1
0
1
0
0
3
0
0
0
0
0
0
0
0
0
1
2
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
2
1
1
0
0
2
0
2
1
0
0
0
0
0
0
2
0
0
0
0
1
1
0
1
1
0
0
0
1
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
3
0
0
0
2
0
3
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
5
0
1
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
2
2
0
0
0
3
0
0
0
1
0
2
1
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
4
6
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
6
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
1
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
1
2
0
1
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
1
0
0
0
1
1
0
4
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
2
0
1
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
1
2
0
1
1
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
7
0
0
0
2
0
0
0
3
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
4
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
4
0
0
0
1
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
3
2
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
4
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
3
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
1
1
1
0
0
2
0
2
0
1
0
0
0
0
2
0
2
0
0
0
0
2
0
1
1
2
0
0
0
2
2
1
1
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
2
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
3
0
0
0
1
0
0
0
0
2
0
0
2
3
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
2
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
3
0
0
1
6
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
2
0
0
0
2
0
0
3
1
0
0
1
2
0
0
6
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
4
0
1
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
2
0
3
0
0
0
0
0
0
1
0
0
1
2
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
2
0
0
1
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
1
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
1
1
1
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
9
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
2
3
2
1
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
1
0
0
2
2
2
2
0
0
1
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
1
3
0
1
2
3
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
2
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
6
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
3
0
2
1
2
0
2
0
2
2
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
3
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
2
2
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
2
0
1
0
0
1
0
2
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
4
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
2
0
0
0
0
0
0
0
0
1
2
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
3
3
0
0
0
1
3
1
1
3
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
2
0
0
6
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
1
1
0
1
0
3
0
0
0
1
2
0
0
0
1
2
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
2
2
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
3
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
4
0
0
0
0
1
0
0
0
1
0
2
0
0
1
2
1
1
1
0
0
1
0
0
0
1
0
4
0
0
0
0
0
0
0
0
3
0
0
3
0
2
1
0
0
0
0
2
1
0
1
1
1
0
0
0
0
3
0
0
1
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
1
0
0
6
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
4
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
3
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
3
1
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
1
1
0
0
2
0
2
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
2
3
1
1
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
1
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
2
2
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
2
0
2
0
0
0
5
0
0
2
0
3
0
0
0
0
0
0
0
1
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
4
0
0
2
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
9
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
1
2
0
0
0
0
0
0
0
2
0
5
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
3
0
4
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
4
0
0
0
2
4
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
2
0
3
0
0
0
0
0
1
0
0
0
1
0
1
2
0
2
1
0
0
0
2
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
2
1
1
0
0
0
0
0
0
2
0
0
1
2
0
2
0
1
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
2
0
0
0
0
2
0
0
0
3
2
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
4
0
0
0
2
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
3
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
3
4
0
0
0
2
0
0
0
1
5
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
2
0
0
6
0
0
0
2
4
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
6
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
3
0
0
0
4
0
0
0
1
0
1
0
0
0
2
0
0
3
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
10
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
2
0
0
2
1
2
0
0
0
0
2
0
0
0
2
0
0
0
2
0
1
2
0
1
0
2
0
0
0
0
0
0
2
0
6
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
4
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
1
0
2
1
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
1
1
0
0
1
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
2
1
1
0
0
2
0
1
0
0
0
3
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
2
0
2
0
4
0
0
0
0
0
1
2
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
1
0
2
0
2
0
0
5
0
1
0
1
0
2
0
0
0
0
1
0
0
0
2
2
1
0
0
0
1
0
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
2
1
0
0
1
1
0
0
0
0
0
7
0
0
3
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
2
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
2
0
0
2
0
0
0
1
1
0
0
0
2
2
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
3
2
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
8
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
2
2
1
0
2
0
0
2
0
0
0
0
1
1
0
0
3
0
3
0
0
2
1
0
0
0
0
2
0
0
1
0
1
0
0
5
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
4
0
0
0
0
2
0
0
0
1
1
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
1
0
1
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
1
2
0
0
1
1
0
0
2
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
3
2
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
4
0
0
3
0
0
2
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
4
0
2
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
2
1
1
0
3
2
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
10
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
2
3
1
0
0
0
0
0
0
0
2
2
2
0
0
3
0
0
0
0
0
0
0
1
0
0
1
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
3
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
3
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
2
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
3
1
2
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
4
0
0
2
1
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
2
2
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
3
4
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
1
1
2
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
2
3
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
3
0
2
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
2
2
2
0
0
0
3
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
2
0
0
0
1
1
0
0
0
1
0
1
0
0
0
2
0
0
1
0
0
0
2
0
0
2
2
4
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
2
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
9
2
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
1
2
1
1
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
3
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
2
4
0
0
1
0
0
0
0
0
0
1
0
1
0
2
0
0
0
2
2
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
1
0
0
2
0
2
0
1
5
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
2
0
0
0
3
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
7
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
6
0
1
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
2
0
1
0
0
4
0
1
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
4
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
1
0
1
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
2
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
8
6
0
1
1
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
2
0
0
1
1
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
6
2
2
1
0
0
0
0
0
1
0
2
0
0
2
2
0
0
0
0
2
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
2
0
2
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
9
2
0
0
2
0
5
0
0
0
0
0
0
0
0
2
3
0
0
1
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
9
0
0
0
0
2
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
1
0
0
1
0
0
0
2
0
0
0
3
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
1
0
0
3
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
1
0
0
0
0
0
2
0
0
0
2
0
1
0
0
1
2
0
0
0
0
2
0
2
2
2
0
0
2
0
0
4
0
0
0
0
0
0
0
1
0
0
2
1
1
0
1
0
2
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
2
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
8
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
2
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
11
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
1
1
0
0
1
2
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
2
0
0
0
1
4
1
0
1
1
1
0
2
0
0
0
0
0
0
0
0
1
1
1
0
0
2
0
2
0
0
0
0
0
1
0
0
2
0
2
0
1
1
0
0
0
1
0
0
0
0
0
0
3
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
3
1
0
0
0
0
0
0
2
1
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
2
1
2
0
0
0
0
0
0
1
0
1
0
3
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
2
2
0
1
2
0
0
1
0
1
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
4
1
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
1
0
0
4
0
0
0
1
1
2
0
0
1
0
0
1
0
0
0
0
2
0
0
1
0
0
0
1
0
0
2
0
1
3
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
1
0
4
0
0
0
4
0
1
0
1
0
0
3
0
0
0
0
1
0
1
4
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
2
2
1
2
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
4
2
0
0
0
2
0
2
2
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
1
1
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
6
1
0
0
0
0
0
0
0
0
0
2
0
0
0
4
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
2
0
0
0
2
1
0
5
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
5
0
1
0
0
2
0
0
0
0
3
1
0
0
0
2
0
3
0
0
0
2
0
0
0
1
1
2
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
5
1
1
0
7
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
2
0
4
1
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
4
0
0
0
0
6
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
2
1
0
0
0
1
1
1
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
2
0
0
0
0
1
2
0
0
2
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
1
2
1
2
2
1
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
2
0
1
0
0
0
1
1
0
3
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
1
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
2
0
1
0
0
4
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
1
2
0
0
1
0
2
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
3
0
0
0
4
0
1
0
1
0
0
0
0
2
0
0
2
0
0
0
2
1
0
1
0
1
0
0
0
0
0
0
3
0
0
0
5
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
1
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
1
2
0
0
2
0
0
2
0
2
0
0
0
0
1
0
0
0
1
3
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
1
1
0
2
0
0
0
0
0
2
0
0
2
1
0
0
0
2
0
0
0
0
3
0
0
0
0
0
2
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
2
1
0
0
2
0
0
1
0
2
0
0
0
0
0
2
7
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
1
0
0
5
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
4
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
2
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
4
1
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
2
1
1
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
1
0
0
2
0
0
0
3
1
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
1
2
1
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
2
4
0
0
1
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
1
0
0
2
4
0
0
0
2
1
2
0
0
4
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
2
1
0
1
1
1
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
5
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
2
0
1
1
0
0
2
0
1
0
2
0
0
0
0
0
0
1
0
4
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
5
1
2
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
2
0
0
0
0
3
0
3
0
1
0
0
0
1
4
0
2
0
0
0
0
0
2
2
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
2
0
2
0
0
2
0
0
1
0
2
0
2
0
1
0
0
2
2
1
0
0
2
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
1
3
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
2
0
1
0
0
0
0
3
1
1
0
2
0
0
0
0
0
0
0
1
0
0
2
2
0
0
1
0
1
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
3
0
0
0
2
1
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
1
0
1
1
0
0
2
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
3
0
0
1
0
2
0
2
0
0
0
0
0
2
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
2
0
2
0
0
0
2
1
1
0
0
0
0
0
3
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
2
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
2
1
0
2
1
0
2
1
0
0
1
0
2
0
0
0
0
5
0
0
0
0
1
0
0
0
2
2
1
0
2
0
0
0
1
1
0
2
2
2
0
0
0
0
0
0
3
0
2
0
0
0
7
0
0
0
2
0
2
0
2
2
1
0
1
0
2
0
0
0
0
2
1
0
0
1
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
1
0
1
0
1
2
2
1
2
0
2
0
0
0
0
0
0
0
0
0
0
3
3
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
3
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
1
0
0
2
1
0
0
0
0
0
0
0
0
2
3
2
0
1
0
0
0
0
0
0
0
0
2
2
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
5
0
0
1
0
0
0
2
0
1
0
2
0
0
0
2
0
0
2
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
2
2
0
1
0
0
0
0
3
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
1
1
0
0
1
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
2
1
0
2
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
3
0
0
0
0
0
0
0
0
3
0
3
0
0
0
0
0
0
0
2
0
0
0
1
0
1
2
1
1
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
2
1
8
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
2
0
1
0
1
0
0
1
1
0
0
2
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
3
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
2
0
0
0
2
1
0
0
0
1
0
1
2
0
2
0
0
0
3
0
0
1
0
2
0
2
0
0
0
1
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
1
0
4
0
0
0
1
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
1
2
1
0
2
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
1
1
0
0
2
0
0
1
2
2
0
0
0
2
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
1
0
0
0
2
0
2
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
1
2
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
2
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
2
2
0
0
0
0
2
0
0
0
0
1
1
0
0
2
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
1
1
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
2
0
0
0
2
2
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
8
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
2
0
2
0
1
1
0
0
0
1
0
1
0
3
0
10
0
0
0
0
1
1
0
1
0
0
2
0
1
0
0
0
0
0
0
3
1
0
0
0
0
2
0
0
0
0
1
0
0
2
0
1
1
0
2
0
0
1
0
0
0
1
2
3
1
6
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
3
0
1
0
0
2
0
0
0
1
0
0
0
2
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
7
1
0
0
0
0
0
0
2
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
3
0
0
1
0
3
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
4
0
0
0
0
0
1
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
2
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
2
0
0
2
3
0
1
0
0
0
0
1
0
0
2
0
0
0
1
0
1
2
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
2
2
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
1
2
0
0
5
0
0
2
0
0
1
0
3
1
0
0
1
1
0
2
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
2
0
0
0
0
2
1
0
0
0
2
0
0
0
0
2
0
0
2
3
0
0
0
2
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
2
6
0
0
2
0
0
0
0
0
0
2
0
2
0
1
0
0
0
1
0
0
0
0
2
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
2
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
3
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
2
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
1
0
0
0
2
0
0
0
0
0
3
1
2
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
2
8
0
0
0
2
0
0
0
2
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
6
0
0
0
0
0
0
0
3
0
0
0
0
0
2
2
0
0
0
2
1
0
2
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
3
0
2
0
0
0
0
0
0
1
1
0
0
3
0
1
0
0
0
0
0
0
1
0
0
0
3
2
0
3
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
2
1
0
1
0
0
2
0
0
1
1
1
2
0
0
0
0
0
0
0
0
1
1
2
3
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
2
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
1
0
0
0
1
0
0
2
0
0
2
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
2
0
1
0
0
2
0
2
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
1
0
0
2
0
1
0
2
0
0
1
0
0
2
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
3
1
0
0
0
1
0
0
3
0
0
0
0
3
0
0
0
1
2
0
0
0
1
0
0
2
0
0
0
0
1
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
2
0
0
1
0
1
0
0
0
0
1
0
0
6
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
2
0
0
0
0
3
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
2
1
0
2
0
2
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
2
0
4
2
0
0
1
0
0
2
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
2
0
0
1
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
3
0
0
1
0
0
0
2
0
0
0
0
2
0
0
1
0
1
2
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
8
0
0
0
0
0
0
0
1
0
0
0
0
3
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
1
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
2
0
3
2
0
0
0
5
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
1
1
0
0
0
0
1
0
0
1
2
0
0
2
0
0
2
0
0
0
4
0
0
2
0
0
0
0
2
2
1
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
2
1
0
2
1
0
0
0
2
0
1
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
2
0
1
2
2
0
0
0
0
0
0
0
1
0
0
0
5
0
2
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
2
0
0
0
2
0
0
0
1
2
0
0
0
0
2
0
2
0
1
0
1
1
0
0
2
2
0
0
0
0
0
0
2
2
2
0
0
0
0
1
0
2
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
1
3
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
2
2
0
0
0
0
0
3
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
7
1
1
2
0
0
1
0
0
0
0
1
0
0
0
4
2
0
0
0
2
0
0
1
1
0
0
0
0
7
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
2
2
0
1
5
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
4
0
0
0
0
2
1
2
2
2
0
0
1
0
0
0
0
0
0
1
2
0
0
2
1
0
0
2
0
3
0
0
0
0
0
0
2
0
0
1
0
0
0
1
2
0
3
0
0
1
0
1
2
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
1
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
2
1
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
1
1
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
1
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
3
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
6
0
0
2
1
0
3
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
1
0
0
6
1
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
2
0
0
1
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
7
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
2
1
3
0
0
0
0
2
2
3
2
0
0
0
0
0
0
0
0
1
0
2
0
0
2
1
0
0
3
0
0
0
0
0
4
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
1
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
4
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
5
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
2
0
2
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
1
0
2
2
0
0
0
1
1
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
4
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
3
0
0
1
0
2
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
5
1
0
0
1
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
1
2
0
0
0
2
0
1
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
2
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
8
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
7
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
1
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
1
2
1
2
0
2
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
2
0
0
0
0
0
0
3
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
2
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
2
0
0
2
1
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
1
0
0
2
0
0
1
2
0
2
0
0
1
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
1
2
0
0
2
0
0
3
2
2
0
0
0
0
1
3
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
1
0
0
2
0
0
1
0
1
0
2
1
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
1
2
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
8
0
0
0
1
0
0
1
1
0
0
2
0
0
2
0
0
0
2
0
0
2
0
0
1
0
0
0
1
2
1
0
0
3
2
0
0
0
0
0
1
0
1
0
0
1
0
2
0
1
0
1
2
0
3
0
0
1
0
0
0
0
0
0
0
0
9
0
0
0
1
1
0
2
2
0
2
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
2
3
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
2
0
0
0
2
1
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
7
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
2
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
3
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
9
1
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
4
1
0
2
2
0
0
0
2
0
3
0
0
1
0
1
0
0
0
0
0
0
0
0
3
0
0
0
2
0
2
0
0
3
0
0
0
0
2
0
0
2
0
3
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
5
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
2
2
0
0
1
0
0
0
0
1
7
0
0
0
2
2
0
0
1
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
4
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
1
3
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
1
2
3
3
2
2
0
0
1
0
3
3
1
1
0
2
0
1
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
2
0
5
1
0
0
0
0
2
0
0
1
0
0
1
1
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
1
0
1
0
0
2
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
6
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
2
0
0
0
0
1
0
0
1
0
0
0
0
2
1
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
1
0
0
0
1
0
3
2
0
0
0
3
0
0
0
2
2
0
1
1
0
0
0
2
0
0
1
0
0
1
1
0
0
3
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
4
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
2
1
0
0
2
0
1
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
1
0
1
0
0
2
0
1
0
0
2
0
0
0
0
2
0
2
0
0
2
0
1
2
2
0
3
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
3
1
0
0
0
2
0
2
0
1
0
0
0
1
0
0
0
1
3
1
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
2
2
0
2
0
2
0
1
2
0
2
0
0
0
0
0
0
1
1
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
1
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
12
0
0
0
1
1
1
1
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
4
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
2
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
3
0
0
0
0
1
0
2
1
2
0
0
0
0
1
2
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
2
1
2
0
0
4
1
0
1
0
0
0
0
1
2
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
1
0
0
10
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
2
1
0
1
1
0
0
0
0
0
0
1
0
1
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
1
2
0
2
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
4
1
0
0
0
0
0
3
0
1
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
7
0
2
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
2
0
0
0
0
3
0
1
0
0
0
1
0
2
0
0
2
0
0
1
1
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
3
0
0
0
3
0
0
0
4
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
2
0
1
1
0
1
0
0
2
0
0
0
0
4
0
2
0
1
0
1
2
1
2
0
0
0
0
0
1
0
0
1
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
7
3
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
2
1
0
1
0
0
0
1
0
2
2
0
2
0
2
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
1
0
3
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
3
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
2
1
0
0
0
0
0
0
3
0
0
0
0
0
1
1
0
0
2
1
1
2
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
1
1
0
0
2
0
0
1
0
2
2
0
0
1
0
0
0
0
0
4
0
0
0
1
0
4
0
0
0
1
2
0
1
0
1
0
0
2
0
0
2
0
2
1
0
2
1
0
0
0
0
0
0
1
2
0
2
0
0
0
1
0
0
1
0
0
0
0
2
2
2
2
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
2
0
2
1
0
0
1
1
0
0
0
0
0
0
2
1
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
1
0
2
0
0
0
0
3
1
4
0
0
3
1
0
0
0
0
0
2
0
3
0
0
0
0
0
0
1
0
0
0
1
2
1
0
2
0
2
1
0
0
2
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
4
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
3
0
0
0
2
4
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
4
0
0
3
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
2
0
0
1
0
0
0
0
2
0
1
2
0
0
0
0
2
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
2
0
0
3
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
3
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
3
0
1
0
0
0
1
0
2
0
1
1
0
0
1
0
0
0
2
0
0
0
2
0
2
0
0
2
0
3
0
0
6
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
1
2
4
0
2
0
2
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
5
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
2
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
2
0
1
0
0
3
0
0
0
2
0
0
0
0
0
1
0
0
7
0
2
0
0
1
4
0
0
0
3
1
0
0
0
0
0
0
1
0
0
1
0
4
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
2
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
1
2
0
0
2
0
0
1
0
2
0
0
0
2
5
0
2
1
1
0
0
0
0
2
2
0
5
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
1
2
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
3
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
1
3
0
0
0
0
0
0
2
1
0
0
0
1
6
0
0
0
0
2
0
0
0
1
3
0
1
0
2
0
0
0
1
0
0
0
0
0
3
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
4
0
1
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
1
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
2
0
0
0
1
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
1
0
2
0
1
0
0
1
0
0
0
0
0
0
3
1
0
1
0
1
0
0
0
1
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
4
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
4
0
0
0
0
0
10
0
0
0
0
0
0
0
0
3
1
1
0
0
1
2
0
2
0
0
1
2
0
0
0
0
0
0
0
1
0
0
2
0
7
1
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
1
0
0
1
0
1
6
0
2
0
0
0
0
0
0
1
0
2
3
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
5
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
3
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
1
1
1
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
3
1
1
4
2
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
2
0
0
0
1
0
0
0
7
0
1
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
1
2
2
0
0
0
0
2
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
7
2
0
0
2
0
0
0
0
0
0
0
2
0
3
0
2
0
3
1
2
0
0
0
0
3
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
1
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
3
1
1
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
3
0
0
0
0
0
3
1
0
0
0
0
0
3
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
3
3
0
0
2
0
0
1
0
0
0
0
0
2
1
0
0
0
0
2
1
0
0
0
0
7
1
0
0
0
0
0
0
1
0
3
0
0
0
1
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
3
2
2
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
3
2
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
2
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
8
0
0
5
0
0
2
0
0
0
0
0
0
2
2
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
3
0
0
5
1
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
5
0
2
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
1
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
1
0
1
1
1
2
1
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
2
0
2
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
4
0
0
0
0
1
0
0
0
1
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
2
1
0
0
0
0
1
0
1
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
3
0
2
0
0
0
0
2
0
2
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
1
0
0
0
1
0
2
0
0
2
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
3
0
0
0
2
2
1
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
5
1
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
4
0
1
3
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
3
0
1
0
2
0
0
0
2
0
1
0
0
2
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
0
0
0
5
2
0
0
0
0
0
0
0
1
2
4
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
2
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
1
2
2
2
0
0
0
6
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
3
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
1
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
3
0
0
0
0
1
0
2
1
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
2
2
2
0
0
0
0
0
2
0
0
0
0
3
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
1
1
0
3
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
2
2
0
2
2
0
3
0
0
1
0
1
0
0
1
2
0
0
3
1
1
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
1
2
0
1
1
0
0
0
1
0
0
0
0
3
0
1
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
5
1
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
2
0
0
1
0
0
0
0
2
0
0
2
0
0
4
0
0
0
0
0
0
0
1
1
0
1
0
0
0
2
1
0
0
0
0
0
1
2
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
1
2
1
2
0
1
1
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
2
0
0
1
0
0
1
0
2
0
2
0
0
0
0
0
0
2
0
5
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
3
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
3
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
3
0
0
1
0
1
0
3
0
0
0
0
0
0
0
2
0
3
0
0
0
1
0
0
2
3
0
0
0
0
0
0
0
2
1
0
2
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
2
3
0
0
0
0
0
3
1
0
0
0
3
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
2
0
0
0
0
0
2
0
0
2
0
2
0
0
0
2
0
0
2
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
3
0
0
0
2
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
3
1
1
0
0
0
0
0
1
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
2
1
0
2
0
1
2
0
0
2
0
0
0
0
0
2
1
0
0
0
0
1
0
0
4
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
4
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
1
0
0
0
0
2
3
0
2
0
0
2
2
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
1
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
1
0
0
1
1
0
0
3
0
1
2
0
0
2
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
5
0
0
0
0
1
0
1
0
2
3
0
0
0
0
3
0
2
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
1
0
0
0
3
0
0
0
1
0
0
0
2
2
0
0
0
0
1
0
5
0
0
4
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
1
1
1
1
2
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
4
0
0
0
0
1
0
0
0
0
1
2
0
2
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
4
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
4
0
1
5
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
3
0
5
2
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
2
2
0
1
0
0
0
0
0
2
0
2
2
0
0
1
4
0
2
0
0
0
2
1
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
3
1
0
0
0
0
0
0
0
0
0
0
0
1
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
3
1
0
0
2
0
0
2
0
0
0
6
1
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
1
2
0
3
1
2
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
1
1
0
1
2
0
0
1
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
1
2
0
0
2
2
2
1
0
0
0
1
1
3
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
1
0
2
1
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
2
0
1
0
0
2
0
0
0
1
0
0
1
0
1
0
0
0
1
1
1
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
3
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
1
2
2
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
3
3
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
2
2
1
0
2
0
0
0
0
0
0
0
0
2
1
2
2
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
2
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
2
0
1
0
0
0
0
0
2
0
0
0
1
0
0
1
1
0
0
0
1
0
3
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
1
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
9
0
2
0
0
0
0
2
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
5
0
0
0
0
0
0
0
1
2
2
3
0
0
0
7
0
0
0
0
0
0
2
0
3
0
0
0
1
0
0
2
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
2
0
0
2
0
0
4
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
1
2
0
1
0
0
3
1
0
0
2
1
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
2
0
2
0
0
2
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
3
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
6
0
1
0
0
0
0
1
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
3
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
1
0
0
2
4
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
2
1
0
2
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
1
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
1
0
0
0
0
1
2
0
0
0
2
0
0
0
1
0
2
0
0
0
0
1
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
4
0
2
0
0
0
0
2
2
3
0
0
0
0
2
0
1
0
0
0
0
0
0
5
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
3
1
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
3
0
0
0
0
0
2
0
0
2
2
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
1
0
0
3
2
0
0
0
3
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
4
1
0
0
2
0
4
0
0
1
0
0
0
0
0
2
0
3
0
0
1
0
1
0
2
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
1
0
3
1
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
2
0
0
0
3
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
1
0
2
1
2
0
0
0
0
2
0
0
0
2
2
0
0
0
4
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
3
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
3
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
3
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
2
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
4
0
0
0
2
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
2
1
0
1
2
0
0
0
1
0
0
0
1
2
0
0
0
0
2
0
1
0
0
1
0
2
0
5
1
5
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
5
1
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
3
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
2
0
0
0
1
0
0
1
0
0
1
1
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
1
0
0
0
2
2
2
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
2
0
0
4
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
2
0
0
1
0
1
0
1
0
0
2
0
0
0
0
0
0
0
2
2
1
2
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
5
0
0
0
4
0
0
0
1
2
0
0
1
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
4
6
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
1
0
0
0
2
2
0
0
0
0
3
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
2
0
0
1
0
0
0
0
2
0
0
0
0
0
2
2
2
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
8
2
0
1
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
1
0
1
0
0
0
2
0
0
1
0
0
0
0
1
0
1
3
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
5
0
0
0
0
0
0
1
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
3
0
0
0
1
0
0
0
0
0
3
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
2
2
0
2
0
0
1
2
1
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
1
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
3
2
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
2
1
0
0
3
0
2
0
0
0
3
0
0
0
2
0
0
0
0
1
0
0
2
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
3
1
2
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
3
0
0
0
0
0
0
1
1
1
0
0
2
0
0
0
1
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
6
0
0
1
0
2
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
7
0
2
0
2
1
2
0
0
0
0
0
0
1
0
1
1
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
1
1
0
1
2
0
0
0
0
0
3
0
0
0
2
0
0
0
0
1
0
0
2
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
2
0
1
0
1
0
0
0
0
1
2
0
0
0
0
2
1
1
0
0
2
0
1
0
1
0
0
2
1
1
3
0
0
0
0
8
0
0
0
0
2
1
2
1
0
0
0
0
0
0
0
0
0
0
12
0
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
3
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
3
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
1
0
0
2
2
0
0
0
0
0
0
6
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
1
3
3
2
0
0
0
0
2
1
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
4
1
0
0
2
0
0
0
2
0
0
0
0
1
0
3
1
1
0
1
0
0
0
0
2
1
0
0
1
0
0
0
0
4
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
8
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
2
0
1
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
3
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
4
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
6
0
1
1
1
0
0
0
0
5
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
2
3
0
0
6
0
0
1
0
0
1
0
2
0
0
0
0
2
1
0
0
0
0
0
2
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
2
3
1
1
1
0
0
2
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
2
4
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
1
0
7
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
2
0
1
0
1
0
0
0
1
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
3
0
0
0
0
0
1
0
1
1
1
0
1
0
2
1
1
0
0
1
0
0
0
0
1
0
0
3
0
0
0
0
0
2
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
1
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
2
7
2
0
1
0
0
2
1
3
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
2
2
0
0
2
0
0
0
0
0
2
0
0
1
3
0
0
0
0
1
0
2
0
0
2
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
2
3
0
0
0
2
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
1
0
2
0
0
0
0
1
0
2
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
2
0
0
2
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
2
0
0
1
4
0
1
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
1
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
2
0
2
0
0
0
0
0
3
1
0
0
5
0
0
0
0
0
0
2
3
0
2
5
0
1
1
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
2
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
1
0
2
0
0
2
3
1
1
2
0
0
0
0
2
0
3
0
0
0
0
0
3
0
3
0
0
0
0
1
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
2
0
2
4
2
1
1
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
2
0
2
2
0
1
0
2
1
0
0
0
2
1
0
0
1
0
2
0
1
2
0
1
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
3
2
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
4
0
0
9
0
0
0
0
2
0
1
0
0
0
0
0
1
2
0
2
0
0
0
1
0
0
0
0
3
2
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
1
0
0
2
0
0
0
0
0
2
4
0
0
1
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
2
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
6
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
3
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
2
0
1
0
0
0
0
2
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
1
0
2
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
2
0
0
0
4
0
1
0
0
0
1
2
0
0
0
2
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
3
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
6
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
10
0
0
0
3
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
1
0
0
2
0
0
0
2
0
0
0
0
2
0
0
2
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
3
1
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
1
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
7
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
3
0
0
0
2
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
2
0
2
0
0
0
0
0
3
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
1
1
0
0
0
0
0
1
2
0
0
2
1
0
0
1
0
3
1
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
4
0
0
0
4
2
0
0
0
3
2
0
0
0
0
0
1
0
0
4
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
1
1
1
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
3
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
2
1
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
1
0
0
0
2
1
0
0
4
0
2
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
2
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
1
0
2
0
1
0
0
0
0
3
0
0
0
0
3
0
0
2
2
0
1
0
0
0
1
0
2
2
1
0
0
1
1
0
0
3
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
2
0
0
0
0
0
6
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
14
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
3
0
0
0
0
1
2
2
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
2
0
0
7
0
0
8
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
2
0
1
0
0
0
1
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
1
0
2
2
1
0
0
2
2
0
0
0
5
0
2
4
2
1
0
3
2
0
2
0
0
0
0
0
0
1
0
0
0
0
3
0
2
2
0
0
2
0
0
0
1
1
0
0
0
2
2
1
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
2
1
0
0
2
0
1
2
0
0
0
0
1
0
0
1
0
2
0
0
2
0
0
1
3
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
1
0
1
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
3
0
0
1
3
0
0
0
0
0
0
0
0
0
2
5
1
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
3
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
3
0
2
0
0
0
2
0
0
0
3
0
0
0
1
0
0
1
2
0
2
0
0
0
0
1
2
0
0
5
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
1
1
0
2
0
0
0
2
1
0
2
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
3
1
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
1
2
3
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
3
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
1
0
1
11
2
0
2
1
3
0
0
0
0
0
0
1
0
3
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
4
1
0
0
0
0
0
0
0
1
3
0
1
0
2
0
0
0
0
0
2
0
0
0
0
1
0
1
0
2
1
0
3
0
0
0
0
0
0
0
2
1
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
3
0
0
3
1
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
3
0
0
2
0
1
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
1
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
6
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
2
2
5
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
1
0
0
0
2
1
1
0
0
0
0
2
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
2
1
2
2
0
0
1
0
0
2
0
2
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
2
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
2
0
0
3
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
1
1
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
2
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
2
0
1
0
0
0
2
0
0
0
0
0
0
1
2
0
0
2
1
0
0
3
3
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
4
0
0
0
0
0
3
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
5
1
2
1
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
2
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
2
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
1
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
2
0
1
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
8
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
1
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
7
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
2
0
0
4
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
3
0
2
1
1
2
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
3
2
0
0
0
1
0
0
0
0
1
2
0
2
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
3
2
0
0
0
3
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
3
0
0
2
2
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
1
0
0
0
1
2
0
0
2
0
0
0
0
0
0
2
0
2
0
2
0
0
0
1
0
0
0
1
0
0
1
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
1
0
3
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
1
0
0
1
0
0
2
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
4
0
0
0
0
0
0
1
1
0
0
1
1
1
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
6
0
2
0
0
2
0
0
0
0
0
2
3
0
1
0
1
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
5
0
2
0
0
0
0
3
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
3
2
0
0
2
2
1
0
0
0
2
0
0
1
0
0
1
2
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
3
0
0
1
0
1
0
0
1
2
0
3
0
2
0
0
0
0
0
0
0
2
1
0
4
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
1
2
0
0
0
0
2
0
1
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
2
0
2
0
1
0
0
0
1
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
1
0
1
2
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
1
0
1
2
0
0
2
0
0
0
0
0
2
0
0
3
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
2
2
0
0
1
0
0
3
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
1
0
0
0
1
0
0
0
0
2
1
0
0
0
2
0
0
0
0
1
0
0
2
0
0
2
2
3
0
0
1
0
2
0
0
0
1
0
2
0
0
1
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
1
2
0
0
3
0
0
0
1
0
0
0
0
1
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
1
0
0
0
6
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
4
2
0
2
0
0
0
1
0
0
0
3
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
1
1
0
0
2
0
0
0
2
1
0
1
2
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
2
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
3
3
0
0
2
0
0
0
0
0
2
0
1
0
6
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
2
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
1
2
0
0
1
0
0
0
0
2
1
0
2
0
0
0
0
1
0
4
0
0
0
0
1
0
1
0
0
0
2
0
2
2
0
0
1
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
3
3
0
0
0
0
0
0
2
1
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
3
1
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
2
0
1
1
0
0
0
1
0
1
0
1
0
0
1
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
1
1
0
0
0
0
0
0
1
0
0
1
0
3
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
2
0
0
0
3
0
0
0
0
0
0
0
2
2
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
2
2
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
3
0
0
0
2
1
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
1
3
0
1
0
1
0
0
0
1
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
3
0
1
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
2
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
2
3
0
0
2
0
1
1
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
2
0
2
0
0
2
0
0
0
0
0
3
0
0
8
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
2
0
0
1
1
1
2
1
4
0
2
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
2
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
1
2
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
6
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
2
1
0
0
1
2
0
0
0
1
1
0
1
1
1
0
2
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
1
0
0
2
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
2
0
2
2
0
3
0
0
1
0
0
2
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
1
0
0
2
0
0
2
0
2
0
0
0
0
0
1
0
3
0
2
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
2
0
2
1
0
0
1
8
9
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
2
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
2
2
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
1
0
0
0
0
3
0
0
0
0
0
1
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
2
0
0
2
0
0
0
0
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
3
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
3
0
2
1
1
3
0
0
0
0
0
2
0
1
1
2
2
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
2
0
1
2
2
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
1
0
0
0
3
0
0
0
0
0
0
1
0
0
2
0
2
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
2
2
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
1
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
2
1
4
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
2
0
0
0
3
2
0
0
1
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
2
2
3
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
2
1
0
0
0
2
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
2
1
0
2
0
0
0
2
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
2
1
0
0
1
0
3
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
1
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
1
1
0
0
0
2
0
0
3
1
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
1
0
1
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
2
0
0
0
0
1
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
1
0
0
0
0
0
5
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
2
2
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
3
0
2
0
0
0
0
0
0
2
0
0
0
1
0
1
0
1
3
0
0
2
1
0
2
0
3
0
2
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
3
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
1
4
0
1
2
0
0
1
0
1
0
0
0
2
1
0
0
0
0
1
0
0
0
1
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
6
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
5
2
0
1
0
0
2
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
2
2
0
2
2
0
0
0
0
0
3
0
0
0
0
0
2
0
0
1
1
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
2
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
2
0
1
0
3
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
2
0
3
0
0
0
0
4
0
4
0
1
2
6
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
1
0
0
0
2
0
0
2
0
5
0
0
1
0
0
0
1
0
2
1
1
2
0
1
0
0
0
1
0
0
0
0
0
0
0
1
2
0
2
1
1
0
1
0
2
0
0
0
0
0
0
0
0
2
0
4
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
2
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
2
0
1
0
0
0
0
8
2
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
2
0
0
2
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
2
0
3
0
0
0
0
1
0
0
0
0
3
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
2
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
5
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
2
0
0
0
2
2
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
1
2
0
2
2
0
1
1
0
0
2
0
0
0
1
0
0
0
0
1
0
0
2
2
1
0
1
0
0
4
1
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
5
0
0
0
1
0
0
0
0
2
1
0
1
1
0
0
4
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
1
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
1
1
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
4
0
0
0
0
1
0
0
0
0
1
3
0
0
0
0
1
0
0
2
3
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
3
2
0
0
2
5
0
1
2
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
2
0
0
0
2
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
1
1
0
0
2
1
0
0
0
0
0
0
0
1
1
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
3
3
0
3
2
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
2
0
0
0
1
2
1
0
0
0
0
1
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
4
2
1
0
0
1
0
0
1
0
0
0
2
0
0
0
0
2
3
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
3
0
0
0
2
0
1
1
1
0
0
0
0
0
1
0
0
0
2
9
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
5
0
0
0
0
0
0
1
0
1
0
0
2
0
2
0
0
0
0
1
2
0
0
0
0
1
0
0
1
0
0
0
2
0
0
2
0
0
2
0
1
0
2
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
3
0
2
2
0
0
2
0
2
0
0
0
1
0
0
0
1
0
0
0
1
3
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
2
0
2
0
0
0
0
1
0
0
0
5
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
2
2
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
6
1
0
0
0
0
5
1
1
1
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
1
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
2
0
3
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
3
2
3
0
0
1
0
0
0
2
3
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
1
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
4
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
1
3
2
0
0
0
0
0
0
7
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
2
1
0
0
0
0
5
0
1
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
5
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
2
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
7
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
5
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
2
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
2
1
1
0
0
3
2
0
2
0
0
0
0
0
1
2
0
0
0
0
1
0
2
1
3
0
0
0
1
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
0
2
0
0
3
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
4
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
1
1
2
0
0
0
0
3
1
2
2
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
3
1
2
0
0
1
0
0
0
2
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
5
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
3
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
1
0
0
0
2
1
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
5
0
0
0
6
0
0
6
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
2
0
1
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
3
0
1
0
1
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
2
0
0
0
3
0
2
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
2
0
2
0
0
2
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
1
0
2
1
2
4
0
0
0
0
0
1
0
1
2
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
2
0
3
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
3
1
0
0
0
0
0
0
2
0
0
0
1
1
2
0
0
0
0
0
2
0
0
0
0
0
1
0
1
1
3
0
2
0
0
0
0
0
1
0
0
5
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
4
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
1
0
0
0
0
0
0
0
2
1
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
4
2
0
0
3
0
0
0
0
1
0
1
0
0
0
1
0
0
2
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
5
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
3
0
0
0
0
1
0
0
0
2
2
0
0
0
2
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
1
0
0
0
0
0
0
5
0
0
1
1
2
0
2
1
0
1
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
4
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
2
2
4
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
3
0
2
0
0
4
1
0
0
1
0
0
0
0
2
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
1
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
1
2
0
2
0
0
2
0
1
1
1
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
1
0
0
0
3
0
2
0
0
2
0
1
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
1
0
2
0
0
1
3
2
0
0
0
0
0
0
2
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
3
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
2
0
0
0
0
2
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
2
1
0
2
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
1
0
2
2
0
0
5
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
2
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
1
0
1
2
0
0
1
2
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
5
1
8
0
2
0
2
0
0
0
2
1
0
2
2
0
0
0
1
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
2
1
0
0
4
0
0
0
2
1
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
1
4
0
0
0
2
0
0
2
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
1
0
1
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
1
6
0
0
2
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
1
0
4
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
7
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
8
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
5
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
1
0
2
0
12
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
4
0
0
0
0
0
0
2
0
2
0
0
2
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
3
1
0
1
0
0
6
3
0
1
1
4
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
1
0
2
1
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
1
1
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
3
2
1
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
1
0
5
0
2
0
0
0
0
3
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
1
0
1
0
0
0
3
0
0
0
2
3
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
2
5
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
2
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
3
0
3
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
2
0
0
2
0
2
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
2
2
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
6
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
3
0
3
2
0
1
0
0
0
2
0
0
0
0
2
2
1
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
3
2
0
1
0
3
1
0
0
0
3
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
2
0
0
1
0
0
1
2
1
1
0
2
0
1
0
0
0
0
0
1
0
0
0
0
1
3
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
1
0
0
2
0
0
2
0
13
0
0
0
1
0
0
0
0
6
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
1
0
0
0
0
0
0
2
2
0
0
0
1
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
4
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
2
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
2
2
0
0
0
0
1
0
1
0
2
0
0
0
2
0
0
2
0
0
2
0
0
0
0
2
0
1
0
2
2
0
0
0
0
0
0
0
0
0
2
1
4
0
2
1
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
5
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
4
0
2
1
2
2
0
1
1
0
2
0
0
2
3
0
1
1
0
0
1
0
2
0
3
0
1
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
1
1
0
0
0
1
0
8
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
2
0
0
0
0
1
2
0
2
0
0
0
0
2
0
0
0
0
0
2
2
3
0
0
2
0
1
1
0
0
0
1
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
3
1
0
0
2
1
1
0
0
2
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
1
0
0
2
2
0
0
3
0
2
1
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
2
0
0
0
0
0
3
1
0
2
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
1
0
0
2
1
0
0
0
3
0
0
0
1
2
0
0
0
0
0
0
1
2
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
4
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
5
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
1
0
0
0
0
2
0
2
1
3
0
0
0
1
0
2
0
1
2
0
0
0
1
0
1
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
5
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
11
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
1
1
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
3
0
0
3
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
2
0
2
2
0
1
0
1
1
1
0
0
0
1
3
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
4
0
4
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
2
0
0
0
0
0
1
2
0
0
5
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
4
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
2
0
1
1
0
0
0
0
10
1
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
1
0
1
0
0
3
2
0
1
0
1
0
4
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
3
0
2
0
0
0
0
0
1
2
0
0
0
0
3
0
5
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
2
2
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
2
2
0
0
3
0
0
0
0
0
4
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
4
0
0
0
0
1
0
0
1
0
1
0
3
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
1
0
2
1
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
2
2
2
0
0
0
0
0
2
0
2
1
0
0
0
1
0
3
2
2
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
2
3
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
2
1
0
0
0
0
0
2
0
0
0
0
0
2
0
2
1
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
2
2
2
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
5
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
2
2
0
2
2
3
1
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
3
0
0
0
0
1
1
0
0
1
1
0
0
0
6
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
3
0
0
0
0
2
1
2
1
0
0
5
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
5
0
0
0
1
0
0
3
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
3
3
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
2
1
4
2
4
0
0
1
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
3
0
3
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
1
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
1
0
3
0
0
0
0
0
0
0
1
0
0
0
2
12
1
1
2
0
0
0
1
0
0
0
0
0
3
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
5
1
0
0
0
0
0
2
1
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
5
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
10
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
2
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
1
0
3
0
0
3
1
0
0
0
0
0
0
1
2
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
1
1
1
0
0
1
2
0
0
1
0
0
0
0
0
0
0
1
0
2
2
0
2
0
0
2
2
9
0
2
0
1
0
0
0
1
0
0
2
0
2
0
0
2
1
0
2
0
0
0
0
4
0
0
0
2
0
0
0
6
2
0
0
2
1
0
1
2
0
0
0
0
0
0
1
0
1
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
1
0
1
1
0
2
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
3
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
6
2
0
2
0
0
0
0
0
2
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
1
0
0
2
2
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
9
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
1
3
0
2
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
1
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
2
0
0
0
1
0
0
0
0
0
2
0
1
0
2
0
1
1
0
1
0
2
0
2
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
3
0
3
0
0
1
0
0
1
2
0
0
0
0
0
1
0
0
1
0
0
1
2
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
2
2
0
0
0
1
0
1
0
1
0
1
0
0
3
2
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
3
1
0
0
0
2
0
0
0
2
1
1
0
0
1
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
1
3
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
2
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
1
1
0
0
0
0
1
0
0
1
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
2
0
1
1
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
2
3
0
0
0
0
1
0
0
0
0
2
0
0
0
2
1
0
0
3
2
0
0
1
2
0
0
0
0
0
1
0
2
0
0
0
1
1
0
2
0
3
1
0
0
0
0
0
0
0
1
0
0
1
3
1
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
2
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
4
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
3
2
2
0
2
1
0
1
0
0
0
0
0
2
0
0
1
2
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
1
1
0
0
0
4
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
2
0
1
0
0
1
1
0
0
2
0
2
0
0
0
0
3
0
0
0
1
3
2
0
2
0
1
1
4
0
0
0
1
0
0
0
0
0
0
0
6
3
0
0
0
2
0
1
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
2
0
1
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
1
3
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
2
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
2
0
1
0
0
0
2
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
2
0
2
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
2
0
1
0
0
0
0
4
0
1
0
1
0
0
0
0
2
0
0
1
1
1
0
0
0
0
0
0
1
0
1
1
2
0
0
1
0
0
0
0
3
0
0
0
0
0
0
2
1
2
0
0
0
0
0
1
0
1
2
0
2
0
1
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
3
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
2
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
4
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
2
0
0
0
0
0
2
2
2
1
0
2
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
2
2
0
1
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
4
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
3
1
0
0
0
1
0
0
1
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
3
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
2
1
0
0
1
2
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
2
2
1
0
0
0
3
0
2
3
1
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
1
1
0
1
1
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
2
2
0
0
0
1
0
0
0
1
1
0
0
0
3
0
0
1
1
0
1
0
0
0
0
1
0
2
1
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
2
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
2
0
0
2
0
0
0
0
0
0
1
0
1
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
1
0
2
1
0
2
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
4
0
0
2
0
0
0
1
0
0
0
0
0
1
1
2
3
1
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
2
0
2
0
1
0
0
0
1
0
0
0
0
0
0
4
0
0
2
0
0
0
2
0
0
0
0
2
2
1
0
2
2
0
0
2
0
0
0
0
0
0
0
0
3
0
0
4
1
3
0
0
0
0
0
0
0
2
0
0
2
1
1
1
0
0
0
0
2
0
0
0
3
0
0
0
0
0
1
0
0
2
0
1
1
1
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
2
1
2
0
2
0
0
0
1
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
3
0
0
0
2
0
0
1
0
0
0
2
0
3
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
1
1
0
0
1
0
0
0
0
2
1
0
1
0
0
0
0
4
0
2
3
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
4
0
0
1
0
2
0
1
1
0
0
0
0
2
0
0
4
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
3
0
1
0
0
0
2
0
0
2
0
0
0
0
1
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
1
0
0
0
2
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
2
0
0
1
0
0
2
1
0
0
0
0
0
1
0
1
0
0
2
0
0
1
0
0
0
0
2
2
0
0
2
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
3
3
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
3
0
1
2
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
2
0
2
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
2
0
6
0
1
0
0
1
1
2
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
2
0
0
0
4
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
3
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
1
0
1
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
2
0
4
1
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
2
1
1
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
7
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
2
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
2
0
3
0
0
0
2
0
2
1
0
0
0
0
1
1
0
0
0
0
0
1
0
4
0
0
1
1
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
4
1
0
0
3
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
2
1
0
0
0
0
2
0
2
0
0
0
0
2
3
3
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
3
3
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
1
8
2
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
2
0
1
0
3
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
1
0
1
0
0
0
1
2
0
0
0
2
1
2
0
0
0
0
0
0
3
0
1
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
3
0
0
2
0
1
0
2
0
0
0
2
0
2
1
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
2
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
2
2
0
1
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
2
0
0
0
1
1
0
0
3
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
2
1
0
0
0
0
1
0
0
2
2
0
1
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
3
0
0
0
6
0
0
1
1
0
2
0
1
1
6
2
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
1
0
2
1
0
0
0
2
0
1
0
0
0
3
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
7
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
2
2
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
1
4
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
3
0
0
1
2
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
2
2
1
2
0
0
0
0
2
0
0
6
0
0
1
1
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
3
1
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
1
0
0
2
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
2
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
2
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
1
0
0
1
0
0
0
2
4
0
3
0
0
0
1
4
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
2
0
0
3
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
2
1
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
2
0
1
2
1
0
1
1
0
0
0
1
3
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
1
0
0
0
2
1
0
0
1
0
0
0
3
2
0
0
0
1
0
0
0
0
1
0
0
0
3
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
2
1
0
0
0
6
0
1
0
0
0
0
2
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
1
0
2
0
0
0
0
2
2
0
0
2
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
1
2
0
1
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
2
0
0
1
0
0
2
0
1
1
0
0
0
2
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
3
0
2
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
1
0
2
0
1
0
2
0
0
0
1
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
1
0
0
0
1
0
1
2
0
0
0
0
2
3
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
4
4
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
1
0
1
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
2
0
3
0
2
0
2
0
2
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
1
0
0
2
3
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
1
0
0
1
0
0
0
1
2
0
3
0
0
0
1
0
0
0
2
0
0
2
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
6
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
4
2
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
1
0
2
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
4
0
0
0
0
0
1
0
0
4
0
0
0
0
0
2
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
1
0
0
0
2
1
1
2
0
1
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
2
0
1
0
1
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
10
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
5
0
0
0
5
0
1
0
1
0
2
0
1
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
5
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
5
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
3
2
0
0
0
0
0
0
0
0
0
1
0
2
0
3
0
0
1
0
0
1
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
1
0
1
0
0
0
0
1
0
0
0
2
0
0
1
0
0
1
0
1
0
0
2
0
0
0
0
0
1
0
0
0
2
2
0
0
1
0
0
3
0
0
6
1
0
0
1
0
1
0
2
0
2
0
0
0
0
2
0
0
0
2
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
4
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
1
2
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
2
2
1
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
2
1
0
2
4
1
1
0
0
0
2
2
0
0
0
0
0
5
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
5
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
3
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
2
0
0
1
2
0
0
0
0
0
2
0
1
2
0
0
0
2
4
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
2
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
1
1
0
0
0
0
0
2
0
1
0
0
0
1
3
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
4
0
0
0
3
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
3
0
8
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
3
0
0
0
0
0
0
0
0
5
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
1
0
2
1
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
2
0
0
2
0
0
0
0
0
0
1
3
0
0
1
0
0
0
0
0
1
0
0
1
0
1
2
0
2
1
0
0
0
3
1
2
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
2
0
0
0
1
0
3
0
0
1
2
0
1
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
4
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
4
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
1
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
2
2
0
0
2
0
0
1
1
0
0
0
1
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
7
0
0
2
0
2
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
2
0
2
0
1
2
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
1
0
0
0
1
2
0
0
2
2
0
0
0
0
0
1
0
2
1
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
2
1
0
0
0
0
0
0
1
0
0
1
0
9
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
1
3
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
5
0
0
0
2
3
2
0
0
11
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
2
0
0
2
0
0
0
0
2
0
0
1
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
2
0
0
0
2
0
1
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
2
0
0
0
1
0
0
0
2
0
1
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
2
2
0
1
0
2
1
0
0
0
0
1
2
0
0
1
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
1
1
0
2
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
5
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
1
0
0
0
2
8
1
0
0
0
0
2
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
2
0
1
0
0
1
0
0
0
2
2
0
0
0
0
0
0
2
0
2
0
0
0
3
0
0
0
2
0
2
0
0
0
2
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
2
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
2
2
0
2
0
1
1
0
0
1
1
3
2
0
2
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
3
0
2
1
0
0
0
0
0
0
2
0
0
2
2
2
0
0
1
0
0
2
0
0
0
0
1
0
1
5
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
4
3
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
3
0
0
0
0
0
1
0
1
0
0
1
0
2
1
1
5
0
2
0
0
0
0
1
0
0
0
1
0
2
2
1
0
0
1
0
1
0
0
0
0
0
0
1
0
2
0
0
1
0
1
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
1
0
1
1
1
0
1
2
9
0
0
0
5
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
4
1
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
2
0
3
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
3
1
0
0
2
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
1
0
0
2
0
0
0
0
2
1
3
1
0
0
0
0
0
0
0
3
0
0
0
0
2
3
0
0
1
0
0
2
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
1
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
1
1
2
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
4
1
0
1
0
0
0
0
0
4
1
1
0
0
0
0
1
4
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
5
1
0
2
0
1
0
1
0
2
0
0
0
0
1
0
0
2
1
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
3
2
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
3
0
1
1
0
0
0
0
1
0
0
0
0
3
3
1
0
2
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
2
0
0
1
2
0
0
0
0
0
0
0
1
2
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
5
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
1
5
0
0
0
0
0
0
0
2
0
1
0
1
1
0
0
0
1
1
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
2
0
1
1
0
2
0
0
0
0
1
1
1
4
4
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
2
2
0
0
0
0
2
0
0
2
0
0
0
4
0
1
1
1
0
0
0
0
0
0
0
0
2
1
2
0
1
0
0
0
2
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
4
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
1
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
2
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
2
1
0
0
0
0
0
0
0
0
0
1
1
2
0
1
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
1
2
0
0
0
1
3
0
1
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
3
1
0
0
0
0
0
0
2
0
0
0
0
6
0
0
0
0
0
2
2
4
0
0
0
2
0
1
0
2
1
0
2
2
0
0
0
4
5
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
1
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
3
2
2
0
1
1
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
5
0
0
1
0
1
0
1
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
2
1
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
1
0
0
0
0
0
0
1
2
3
0
3
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
1
2
0
1
0
0
0
0
0
1
0
0
7
0
1
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
2
1
0
0
2
1
0
2
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
1
0
1
2
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
2
3
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
2
0
0
1
0
1
0
0
2
0
1
2
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
8
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
1
0
2
1
0
0
0
0
2
2
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
2
2
0
0
2
1
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
1
0
3
0
6
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
2
1
1
0
0
1
0
0
1
0
2
0
0
0
0
0
1
0
6
0
0
0
2
0
0
2
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
2
0
4
0
1
0
2
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
1
1
0
1
0
0
0
0
0
1
3
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
1
0
1
0
0
0
2
4
0
0
0
0
2
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
2
0
3
0
0
0
0
1
0
1
0
5
0
0
2
1
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
1
0
0
0
0
1
0
1
1
0
2
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
1
1
0
0
1
0
0
0
0
2
1
0
2
0
0
0
1
1
0
0
0
0
1
0
2
0
0
1
2
0
0
1
1
5
1
0
0
0
0
2
0
0
0
1
0
0
2
10
1
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
5
2
0
0
0
0
0
0
0
4
0
0
0
0
0
0
3
0
6
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
1
2
0
1
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
3
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
2
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
1
3
0
0
0
0
0
1
2
3
0
0
2
0
2
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
2
0
0
2
5
0
0
0
0
1
0
1
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
2
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
2
0
0
1
0
2
0
0
0
1
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
1
2
1
2
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
2
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
1
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
3
1
0
0
0
0
1
2
4
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
3
0
0
0
1
0
0
0
0
0
3
1
0
0
4
1
2
0
0
0
1
0
1
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
3
0
1
0
0
0
0
0
2
1
0
0
0
0
0
1
0
2
0
0
1
0
1
1
3
0
0
1
0
0
1
0
0
0
1
0
0
4
0
2
1
0
0
0
0
0
1
2
1
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
1
2
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
1
3
0
0
1
0
0
2
0
0
1
1
2
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
1
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
8
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
1
0
3
2
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
1
1
0
3
0
0
0
0
1
0
0
0
0
2
0
0
2
2
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
8
1
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
2
2
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
2
3
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
3
0
0
1
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
2
0
2
0
0
0
0
2
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
2
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
7
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
3
0
0
0
1
0
0
3
2
0
0
0
0
1
0
1
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
2
0
3
0
0
0
0
0
1
2
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
1
0
2
1
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
3
0
0
0
2
2
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
1
0
0
0
1
1
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
2
0
2
0
0
0
0
1
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
3
0
0
0
0
2
0
4
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
3
0
0
0
1
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
3
1
0
0
2
0
2
5
0
0
0
0
0
2
0
0
0
0
2
0
0
1
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
3
0
1
0
0
0
2
2
0
1
0
5
0
2
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
3
2
1
0
0
0
2
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
1
3
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
6
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
1
1
0
0
0
0
1
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
6
0
1
0
0
1
4
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
1
0
0
1
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
3
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
3
0
0
0
0
0
0
1
0
0
2
0
2
0
0
1
0
0
0
0
2
2
4
1
1
0
0
2
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
2
1
0
0
2
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
6
1
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
1
0
0
0
0
0
0
2
3
0
2
3
3
0
0
0
0
0
0
0
0
0
0
0
2
3
2
0
0
0
0
1
0
0
2
0
0
0
0
2
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
7
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
1
0
2
0
0
0
3
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
1
2
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
8
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
3
0
1
1
0
3
0
0
0
0
0
0
1
1
0
0
0
15
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
2
1
0
2
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
2
0
2
0
1
3
0
2
0
0
2
0
0
0
1
0
2
2
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
1
0
5
0
3
0
1
0
0
1
1
1
0
0
1
1
3
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
2
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
9
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
2
1
0
0
0
2
1
0
0
0
2
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
4
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
7
0
0
0
0
0
5
1
2
0
0
0
0
0
0
1
1
1
1
0
0
2
0
7
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
1
0
0
0
1
0
0
0
0
2
0
1
1
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
1
0
2
1
0
0
2
1
0
1
0
3
0
0
0
0
0
0
2
0
0
0
0
1
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
3
0
0
0
0
2
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
2
0
0
0
0
0
0
1
2
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
5
0
2
0
0
0
1
0
2
0
1
2
3
0
0
0
2
2
0
0
0
0
1
0
6
0
0
0
0
0
0
2
0
1
0
2
0
0
1
1
2
0
0
1
0
1
0
2
2
3
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
2
1
1
0
0
0
0
0
1
3
0
1
0
3
2
3
1
0
5
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
3
1
2
0
1
0
0
0
3
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
2
0
0
1
1
0
0
0
0
0
2
2
0
1
0
0
0
0
0
4
0
0
1
3
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
2
8
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
3
2
0
6
0
0
0
0
0
2
0
3
0
2
2
0
2
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
1
1
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
1
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
3
0
0
0
2
0
1
0
1
0
0
0
0
0
3
0
0
0
3
0
1
0
1
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
1
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
2
2
2
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
1
2
0
0
1
1
0
0
0
0
6
3
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
6
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
1
0
1
0
2
0
1
1
1
1
0
2
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
1
2
0
0
1
0
0
0
1
0
1
0
1
0
0
1
0
0
5
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
4
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
3
2
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
3
0
0
0
2
0
0
1
1
1
0
0
0
2
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
3
0
0
0
2
1
0
2
1
2
0
0
0
0
1
0
0
0
1
0
1
0
2
0
0
0
0
0
1
0
0
0
0
3
2
0
0
0
0
0
2
2
1
1
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
3
1
0
0
2
0
0
3
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
7
0
0
0
0
0
0
2
2
0
0
1
1
0
0
2
0
0
0
0
0
2
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
2
1
0
0
1
0
3
1
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
3
0
1
2
0
0
1
2
2
2
0
0
0
0
0
0
0
1
0
0
0
0
3
0
1
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
1
2
0
2
0
0
0
0
6
0
0
0
0
0
0
1
0
2
0
0
0
1
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
3
1
1
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
1
2
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
2
0
0
0
0
0
0
0
0
1
3
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
5
1
0
0
2
1
0
0
0
0
1
2
0
0
0
0
0
0
0
1
3
1
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
1
2
1
0
0
4
1
0
0
0
2
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
1
0
0
3
1
0
0
1
0
0
1
3
0
1
0
0
0
3
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
3
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
5
0
2
1
0
2
2
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
3
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
3
0
1
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
2
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
2
0
0
2
0
2
0
1
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
0
1
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
3
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
1
0
1
1
0
0
1
0
2
1
0
0
0
0
0
1
0
1
2
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
2
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
3
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
1
0
1
0
1
2
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
1
1
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
1
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
3
1
0
0
0
2
0
0
2
0
2
2
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
3
0
1
0
3
4
0
2
0
0
0
0
4
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
2
0
1
0
1
0
0
0
0
2
0
0
0
0
2
0
0
1
2
0
0
0
0
2
1
0
4
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
3
0
2
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
2
1
0
1
0
0
0
0
0
0
0
2
0
1
4
1
0
2
0
2
0
0
0
0
0
0
1
0
1
0
0
5
0
0
1
0
1
0
1
1
2
0
1
0
0
1
0
0
6
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
2
2
0
0
1
0
2
0
1
0
0
2
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
1
0
1
0
0
0
0
2
0
0
3
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
5
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
4
1
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
2
1
0
2
0
0
2
1
1
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
1
2
0
0
0
0
0
0
2
0
3
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
2
7
2
0
0
0
0
0
0
0
2
0
0
0
1
2
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
1
0
0
0
1
2
1
0
0
0
1
0
1
2
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
2
1
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
1
0
2
3
0
0
0
0
0
1
0
1
0
2
0
2
0
2
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
3
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
2
0
2
0
0
0
3
1
1
0
0
0
1
0
1
0
0
0
0
0
1
0
2
0
0
0
2
0
0
1
0
3
0
0
4
2
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
6
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
2
1
1
0
0
0
0
1
0
0
2
1
0
0
2
0
0
0
1
0
0
0
5
2
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
3
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
1
0
0
2
0
0
0
1
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
2
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
1
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
1
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
1
0
1
0
0
0
5
2
1
0
0
0
0
0
0
3
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
2
0
2
0
2
0
14
2
0
0
0
0
0
2
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
6
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
4
0
0
0
1
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
1
0
0
2
0
1
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
4
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
1
0
0
0
1
1
2
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
4
0
0
1
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
1
1
0
1
0
0
0
1
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
2
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
1
0
3
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
1
0
7
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
2
0
0
1
1
0
0
0
0
0
0
2
1
2
0
0
0
0
0
3
0
2
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
2
0
1
0
0
2
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
2
0
0
2
0
2
0
0
0
0
2
0
0
5
0
7
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
3
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
1
0
12
3
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
1
2
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
1
2
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
2
0
0
0
0
2
2
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
7
0
0
0
1
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
2
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
1
0
0
3
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
6
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
3
2
0
1
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
1
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
1
0
2
0
2
1
0
0
0
0
0
0
2
0
3
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
1
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
5
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
1
2
1
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
3
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
5
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
2
0
0
0
0
0
3
0
0
0
3
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
5
0
2
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
1
2
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
2
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
2
2
0
2
0
1
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
4
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
3
0
0
0
1
2
0
8
1
0
0
0
0
2
0
0
2
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
8
0
0
0
0
0
1
0
0
0
0
0
2
0
2
6
0
0
0
1
0
3
1
2
0
1
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
1
0
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
9
1
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
3
0
0
2
0
2
3
0
1
0
0
2
0
0
0
0
0
1
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
2
0
0
3
0
0
1
0
0
1
0
0
2
0
0
0
2
0
2
0
1
0
1
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
2
3
1
0
0
0
0
0
0
0
0
0
0
0
9
0
2
0
0
0
2
0
0
0
1
0
1
1
1
2
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
3
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
4
1
0
3
2
0
1
4
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
2
0
1
0
0
2
0
0
0
0
0
0
2
0
0
4
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
1
0
2
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
3
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
4
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
1
1
1
0
1
0
2
1
0
1
0
0
0
1
0
0
0
1
0
0
0
1
2
0
0
2
0
4
3
0
0
1
0
1
1
0
6
1
0
0
1
0
0
0
0
2
2
0
0
1
0
2
0
0
1
0
0
0
0
0
0
1
1
0
0
1
2
0
2
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
2
2
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
2
2
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
7
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
3
0
0
0
0
0
0
0
0
0
1
0
0
5
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
2
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
1
2
0
0
4
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
1
2
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
4
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
4
0
3
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
2
0
2
0
0
0
0
0
0
1
2
0
0
1
0
1
0
0
0
0
1
2
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
2
1
0
0
1
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
2
2
1
0
2
0
0
0
0
1
0
1
0
0
1
2
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
1
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
4
0
0
1
0
1
1
2
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
2
2
0
0
2
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
2
1
0
0
0
0
0
2
1
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
1
0
2
0
2
5
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
3
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
2
1
0
1
4
1
0
1
0
0
2
0
1
0
1
2
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
2
2
0
0
1
0
2
0
0
1
2
0
0
0
0
0
1
0
0
3
0
1
1
1
0
0
0
0
0
1
0
0
0
2
0
2
0
0
3
0
0
1
0
0
2
0
0
0
0
0
0
2
1
0
2
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
7
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
1
0
1
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
1
0
2
0
0
0
2
0
0
2
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
1
0
2
0
2
0
0
0
0
0
0
4
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
4
0
2
0
0
0
6
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
3
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
1
1
0
0
0
1
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
4
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
2
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
4
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
7
0
2
3
0
0
5
4
0
2
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
8
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
2
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
5
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
4
1
0
2
0
0
0
0
2
0
0
0
0
0
1
1
0
0
2
0
0
3
0
0
2
0
1
2
0
4
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
1
1
0
0
0
0
0
0
2
1
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
1
0
4
1
1
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
1
2
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
3
2
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
3
0
0
0
0
0
1
1
1
1
0
0
0
1
1
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
6
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
3
1
2
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
1
2
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
1
1
0
0
0
0
2
1
0
0
0
1
0
0
1
1
0
0
0
0
0
1
1
0
0
0
1
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
5
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
1
0
2
0
0
1
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
1
3
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
2
2
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
2
0
0
2
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
3
1
3
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
2
2
0
0
2
0
1
0
1
0
0
0
0
1
1
1
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
1
0
1
3
0
0
2
2
0
0
0
0
0
2
1
2
0
3
0
0
0
4
0
1
0
0
0
2
3
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
2
2
5
0
0
4
0
2
2
2
0
0
0
5
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
2
5
0
2
0
0
2
2
1
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
1
0
2
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
1
0
2
0
1
4
0
0
0
0
2
0
0
1
0
2
2
0
0
5
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
4
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
2
0
0
3
0
1
0
0
0
0
0
1
0
2
0
2
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
2
0
1
0
1
2
0
0
0
0
1
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
1
0
0
2
0
0
0
2
2
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
1
1
1
0
0
0
9
0
0
0
0
1
1
0
0
4
0
0
1
2
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
1
0
4
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
4
0
0
0
2
2
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
1
0
2
0
0
0
3
0
0
0
0
0
3
0
0
4
0
1
0
0
0
2
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
1
0
6
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
2
0
0
0
1
1
1
1
0
0
0
0
0
2
0
0
0
0
0
1
2
1
1
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
2
2
1
0
0
0
1
1
0
0
0
2
0
0
0
3
1
7
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
1
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
1
0
0
0
0
2
1
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
1
2
1
0
1
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
3
0
2
0
0
0
0
0
0
0
2
0
2
0
0
2
0
2
0
0
0
1
1
1
1
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
2
1
0
0
1
0
1
0
0
1
0
0
0
0
1
2
1
0
2
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
4
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
3
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
3
0
0
2
4
0
1
0
2
0
0
0
1
0
0
0
1
1
5
0
0
1
0
0
3
0
0
0
2
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
2
0
0
1
0
0
0
1
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
2
2
1
0
0
0
2
0
1
1
0
0
0
0
0
0
2
0
1
0
1
2
0
1
14
0
0
0
0
0
0
2
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
2
0
0
0
2
1
2
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
2
0
2
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
5
0
0
3
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
3
1
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
2
0
0
1
0
3
0
0
1
0
0
2
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
3
0
0
2
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
5
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
2
0
2
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
2
0
0
0
0
0
3
0
0
1
0
0
0
0
0
1
0
2
1
0
0
3
2
0
0
1
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
5
1
1
0
0
0
0
0
0
1
0
0
0
0
0
2
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
2
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
5
2
0
0
0
0
2
0
0
0
1
2
0
0
2
0
2
0
0
0
1
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
2
2
0
2
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
2
2
2
3
0
1
2
0
0
0
0
0
0
2
0
0
3
0
0
0
0
3
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
3
0
0
0
0
1
1
0
2
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
2
0
1
0
1
1
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
3
0
0
0
3
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
1
0
0
0
0
1
0
2
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
3
1
0
0
0
0
0
2
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
3
1
0
0
0
1
0
1
0
0
1
1
0
0
0
7
0
0
0
0
0
0
0
3
1
0
0
0
1
0
2
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
4
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
1
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
1
0
1
1
0
2
0
0
0
0
0
5
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
4
0
0
0
0
1
0
0
2
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
1
4
1
1
0
0
0
2
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
1
0
0
1
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
8
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
1
2
0
1
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
4
1
0
0
2
0
0
2
0
0
0
1
3
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
3
1
2
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
3
0
0
1
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
1
0
0
0
1
0
0
2
0
3
0
0
0
0
1
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
2
1
0
0
0
2
1
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
2
0
1
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
8
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
3
1
0
0
3
2
0
0
4
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
2
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
3
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
3
0
0
0
0
0
1
0
3
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
1
7
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
2
2
0
0
0
0
1
0
0
0
1
0
1
0
4
0
0
0
0
2
0
1
2
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
1
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
3
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
2
0
0
1
0
0
0
0
0
1
0
2
0
0
1
0
0
1
2
1
0
0
3
1
2
2
0
0
0
0
3
1
0
1
1
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
1
1
0
0
2
0
2
0
1
1
0
1
0
2
1
0
0
0
0
0
2
0
0
2
0
2
0
2
0
1
0
1
1
0
0
0
2
8
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
2
1
0
1
0
0
2
0
0
0
2
2
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
1
1
2
0
2
0
0
2
0
0
0
1
0
4
0
0
0
1
0
0
0
0
2
0
0
0
3
0
0
0
1
0
0
0
0
1
2
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
3
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
3
0
3
0
0
2
0
0
0
0
0
1
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
1
0
0
0
0
1
0
2
0
0
2
0
1
0
1
0
0
0
1
6
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
1
2
3
0
0
0
0
0
2
0
0
0
0
4
5
1
0
2
0
0
0
0
1
0
0
2
1
0
0
0
1
1
2
0
0
0
1
0
2
0
0
0
0
0
7
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
1
0
0
0
0
2
0
1
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
4
0
0
2
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
1
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
1
0
3
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
7
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
2
1
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
1
2
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
1
3
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
2
3
0
0
0
0
1
0
0
1
4
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
2
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
9
0
2
0
0
0
2
2
1
0
0
1
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
1
2
0
0
0
3
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
1
1
0
1
2
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
3
3
2
0
0
0
0
0
2
2
0
0
1
0
2
0
0
1
0
0
1
2
0
0
0
0
0
1
0
1
2
0
0
0
0
2
0
0
0
0
1
4
0
0
0
0
2
2
0
2
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
3
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
2
2
1
0
0
0
0
0
1
0
0
2
1
0
1
0
0
1
1
1
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
1
0
2
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
1
1
0
0
0
2
0
0
2
0
2
0
1
0
0
0
0
0
0
0
2
2
3
0
0
2
0
1
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
2
1
3
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
2
0
0
0
0
0
3
5
1
0
0
0
0
0
1
2
0
1
0
0
0
1
2
2
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
6
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
1
0
1
0
0
0
0
0
0
2
1
1
0
2
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
2
2
1
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
5
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
2
0
1
0
0
1
1
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
2
2
2
0
2
0
0
1
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
2
0
1
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
1
7
1
0
0
0
0
0
0
2
0
3
0
0
1
0
2
0
0
0
1
0
2
0
0
0
2
0
1
1
0
0
0
0
1
8
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
9
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
1
2
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
8
0
0
0
0
0
1
1
0
2
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
3
0
0
2
0
0
2
0
0
0
0
0
0
0
1
1
1
0
0
0
2
1
0
0
0
0
1
0
1
0
0
0
0
6
1
0
0
0
2
0
0
0
1
0
0
2
0
0
1
2
0
2
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
1
0
4
0
0
1
0
0
3
2
0
0
0
0
0
0
2
5
0
2
0
0
0
0
0
0
0
2
0
1
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
3
1
2
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
1
1
1
1
0
0
0
0
2
3
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
1
0
1
0
0
0
0
1
0
1
1
1
0
0
0
0
0
3
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
1
2
1
0
0
0
0
0
0
0
1
1
1
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
1
0
1
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
1
0
0
0
0
2
0
1
0
0
0
1
0
2
0
0
0
0
1
2
1
0
0
0
3
0
0
1
0
0
0
0
0
2
0
0
0
3
0
0
0
0
2
0
0
2
0
0
2
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
2
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
2
3
0
0
0
0
1
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
1
0
0
0
2
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
2
0
0
0
0
1
1
0
0
0
0
1
0
2
0
0
0
0
2
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
1
2
0
2
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
2
0
1
0
1
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
6
0
0
0
0
2
1
0
0
0
0
0
2
0
3
0
1
0
0
0
0
0
0
0
0
1
0
3
2
3
0
0
0
0
1
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
2
2
1
1
0
1
0
0
0
0
1
0
0
0
0
1
1
3
0
0
0
0
0
0
3
0
0
0
4
0
0
0
2
2
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
3
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
1
1
0
1
0
2
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
1
2
0
1
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
1
0
1
1
0
1
0
0
0
2
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
4
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
2
1
0
0
0
2
1
0
8
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
2
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
4
1
1
2
1
0
0
0
2
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
1
0
0
2
0
0
2
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
1
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
1
1
2
0
2
1
2
1
0
0
0
2
0
2
0
0
0
4
0
1
0
0
1
0
3
2
2
0
5
2
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
5
1
0
0
0
1
0
1
0
0
0
0
2
2
1
0
0
1
0
2
0
0
0
0
0
0
2
0
0
2
1
2
0
0
1
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
4
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
3
0
1
0
0
9
1
0
0
1
1
2
0
0
1
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
2
1
0
0
0
0
0
2
0
2
0
2
0
1
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
2
1
2
3
0
2
0
0
2
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
4
1
0
1
0
0
2
0
0
2
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
1
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
1
1
1
0
0
0
0
0
1
2
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
1
0
1
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
5
4
0
0
0
0
0
2
2
0
0
1
0
3
0
0
0
0
0
0
0
1
2
0
1
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
4
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
3
3
0
0
0
0
2
2
0
0
0
0
0
0
2
1
2
2
2
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
3
0
0
2
0
0
0
0
1
0
1
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
1
0
0
7
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
4
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
2
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
2
0
0
3
6
0
0
0
1
0
0
2
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
2
0
0
2
2
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
1
2
1
0
0
2
0
0
1
1
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
2
1
2
0
1
0
0
0
0
2
1
0
1
1
0
0
0
1
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
1
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
5
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
2
1
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
2
3
2
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
3
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
2
2
1
0
1
0
3
0
0
0
0
2
3
0
0
0
0
0
0
1
0
3
2
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
3
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
2
0
0
1
2
0
0
0
0
0
0
0
2
0
0
2
0
1
1
0
3
1
0
0
1
1
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
3
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
1
2
0
1
3
0
0
0
0
0
1
0
2
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
1
0
0
1
1
2
0
2
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
1
2
0
1
0
0
5
1
0
0
0
0
0
0
0
5
2
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
1
0
0
0
0
0
0
0
6
0
0
2
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
3
0
0
2
1
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
5
0
1
0
1
0
0
0
1
0
0
0
1
0
0
11
2
2
1
0
0
2
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
2
0
0
0
1
0
2
0
0
1
0
0
0
2
0
2
0
0
0
2
0
1
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
3
0
0
0
0
1
0
0
0
2
0
1
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
2
0
0
1
4
0
0
3
0
0
0
0
0
0
0
1
2
0
1
0
0
1
0
6
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
2
3
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
3
2
0
2
0
2
0
0
2
0
0
0
1
0
1
1
0
0
0
0
2
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
1
0
1
2
0
0
0
1
1
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
3
0
0
2
3
1
0
0
0
1
0
3
0
1
0
1
0
0
1
2
2
0
1
0
0
0
0
0
0
2
0
0
1
0
2
2
0
4
0
0
0
2
0
1
0
1
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
1
2
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
1
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
4
0
0
0
1
0
4
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
2
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
2
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
1
2
1
1
0
1
3
0
2
0
0
2
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
2
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
2
1
0
3
0
0
0
0
3
0
0
0
0
0
1
1
0
0
5
0
0
0
0
0
0
1
0
2
2
0
2
0
1
3
0
0
0
0
0
0
0
0
0
0
2
1
0
3
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
1
0
2
0
0
0
0
2
0
4
0
2
2
0
2
0
0
1
0
1
2
0
1
1
0
7
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
1
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
2
0
0
1
0
1
0
2
0
0
0
1
0
1
0
4
0
1
0
0
2
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
1
0
4
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
8
0
0
2
2
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
2
0
1
0
0
0
3
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
1
2
0
1
5
0
1
0
3
0
0
1
1
2
0
0
0
1
0
0
3
2
1
1
0
0
0
0
0
0
1
0
0
3
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
2
2
0
0
0
0
1
3
0
0
1
0
0
0
2
0
2
0
2
0
1
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
2
0
0
0
0
2
0
2
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
2
0
0
1
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
3
0
3
2
0
0
2
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
3
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
2
0
0
0
0
0
2
0
4
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
3
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
2
0
0
0
1
0
0
2
0
0
0
1
1
2
1
0
0
2
1
0
0
0
0
0
0
6
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
2
1
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
1
1
0
0
0
2
0
0
0
1
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
2
0
1
0
0
0
0
0
0
2
0
0
3
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
1
0
1
0
0
1
0
2
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
4
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
3
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
3
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
2
0
1
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
2
0
2
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
2
0
0
1
0
1
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
8
0
0
7
0
0
0
0
0
4
1
0
5
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
2
2
0
0
0
0
0
1
0
1
1
0
2
0
0
0
0
0
0
0
1
1
0
2
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
4
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
5
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
2
2
1
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
1
0
0
0
0
1
1
0
0
0
1
4
1
1
0
1
0
2
0
0
1
0
0
0
0
0
1
0
1
0
0
1
2
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
2
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
2
1
1
1
0
0
2
0
0
2
0
0
0
0
0
0
2
4
0
0
0
0
1
1
0
0
0
0
2
1
0
0
2
0
1
0
1
0
0
0
0
1
2
0
0
0
0
0
3
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
2
0
0
0
0
0
5
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
3
0
1
0
0
2
0
0
2
1
0
0
2
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
2
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
2
0
0
3
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
2
1
1
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
1
2
0
0
0
0
2
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
3
0
0
0
0
0
4
0
1
1
0
0
0
4
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
4
0
0
1
1
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
1
0
0
0
0
2
0
2
0
0
3
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
1
0
0
2
1
0
0
0
2
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
2
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
1
2
0
0
1
0
0
1
0
2
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
1
1
2
0
0
0
0
1
0
3
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
2
1
2
0
4
1
1
1
0
0
0
1
1
0
0
2
0
0
0
0
2
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
4
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
1
0
1
2
0
0
0
0
0
1
0
0
0
1
0
1
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
1
0
0
0
0
2
1
0
0
0
1
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
2
3
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
3
0
6
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
2
4
0
0
0
0
0
0
1
1
0
1
0
0
1
0
2
0
0
5
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
2
1
0
2
0
0
0
0
2
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
1
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
3
1
0
2
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
1
1
1
1
0
1
0
0
2
1
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
2
1
1
0
1
0
0
0
0
0
0
0
0
0
0
3
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
1
1
1
0
2
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
1
4
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
2
2
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
3
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
3
0
0
2
1
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
3
1
2
0
0
1
0
0
1
2
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
1
0
0
0
0
1
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
3
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
1
1
1
0
0
1
0
0
0
1
1
2
1
2
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
1
0
0
3
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
1
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
3
0
0
0
0
0
1
0
0
1
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
1
2
0
1
0
1
0
0
0
0
0
0
1
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
8
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
5
0
0
0
2
2
0
0
2
0
1
0
0
0
0
2
2
2
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
5
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
8
1
2
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
1
0
0
0
0
2
1
0
0
0
1
1
0
2
1
0
0
0
2
0
0
0
2
0
0
0
8
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
1
0
0
0
0
1
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
2
1
0
2
1
1
0
0
2
1
1
0
0
1
2
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
2
2
0
0
2
2
0
0
1
0
2
0
2
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
1
1
1
2
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
2
0
0
1
1
2
0
0
0
0
1
0
1
1
0
0
0
1
0
1
1
1
0
0
4
0
0
0
0
3
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
2
0
1
2
0
0
0
0
0
2
0
0
0
2
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
2
0
0
0
0
1
0
0
0
1
0
0
0
2
2
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
3
0
0
0
3
0
0
0
0
0
0
0
4
2
0
0
1
0
0
1
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
1
1
2
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
2
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
2
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
1
1
0
0
0
0
4
1
0
4
0
1
2
0
0
0
2
0
0
0
1
3
0
0
0
2
0
2
0
0
0
0
1
0
1
1
0
0
0
3
0
0
0
1
0
0
2
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
6
1
1
0
2
1
4
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
8
0
0
0
1
2
0
0
1
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
4
0
0
0
0
2
0
0
0
0
0
0
3
1
0
0
0
2
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
1
5
0
1
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
2
0
0
2
2
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
3
0
0
1
1
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
1
1
1
0
0
0
0
0
0
0
0
2
1
3
0
0
0
0
2
0
0
2
0
0
0
2
1
0
0
0
0
3
0
0
0
0
0
0
2
1
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
1
0
2
2
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
8
0
1
0
2
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
2
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
3
3
0
0
0
0
0
3
1
0
0
0
2
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
2
2
4
0
2
0
0
0
1
2
0
0
0
0
0
0
0
4
0
0
0
0
2
0
1
0
2
2
0
0
0
2
1
0
0
0
2
0
2
2
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
1
0
1
0
2
4
2
2
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
1
0
0
5
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
3
0
1
0
4
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
1
1
0
0
0
1
1
0
0
0
2
1
1
1
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
3
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
4
0
0
0
0
0
2
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
4
1
0
0
0
0
1
2
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
2
2
0
3
0
0
0
0
2
0
1
0
2
0
0
0
1
1
0
0
2
0
0
2
1
0
3
0
2
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
4
0
0
2
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
5
0
0
0
0
4
0
0
0
0
0
2
0
0
0
2
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
1
0
1
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
4
0
0
0
1
0
2
0
0
0
0
0
3
0
0
0
1
0
0
3
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
1
0
0
0
0
2
0
0
2
0
2
0
0
0
0
1
2
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
1
0
0
3
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
2
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
8
0
0
0
2
0
0
2
2
0
2
0
0
2
0
2
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
2
0
4
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
1
0
1
0
1
2
0
0
0
2
2
0
1
0
0
0
2
0
0
8
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
5
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
1
0
1
0
0
0
1
0
0
0
2
2
0
2
0
0
2
0
0
2
1
0
1
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
2
0
0
1
0
0
0
2
0
1
0
0
0
0
2
0
0
1
2
1
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
2
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
3
2
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
1
2
2
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
2
0
5
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
2
0
0
0
0
1
0
0
2
2
0
0
0
0
1
0
0
0
0
0
1
1
2
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
2
0
2
3
1
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
2
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
9
0
0
0
2
0
1
0
2
1
0
0
2
0
1
0
2
2
2
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
2
2
0
0
0
1
0
0
0
3
2
0
0
0
0
0
2
0
3
0
0
0
1
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
2
2
1
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
2
2
3
0
0
0
0
0
2
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
2
0
3
0
0
0
0
0
0
0
0
0
3
0
0
1
2
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
2
1
0
0
0
0
1
0
1
0
0
2
3
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
1
0
0
2
0
1
1
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
3
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
5
0
0
0
0
2
0
0
2
0
2
0
0
1
0
1
2
2
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
2
1
0
1
0
5
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
4
0
1
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
4
0
2
1
0
4
0
0
0
1
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
3
0
0
0
0
1
0
1
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
3
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
1
1
0
0
5
1
0
0
0
0
0
3
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
2
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
1
1
2
0
0
0
0
3
0
3
0
0
0
0
0
0
0
0
0
2
1
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
3
0
0
3
0
1
0
1
0
0
2
0
0
0
1
0
1
0
0
0
1
1
0
2
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
5
0
0
0
2
0
2
1
0
0
0
0
0
1
0
1
3
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
2
0
0
0
0
1
0
4
0
0
0
1
0
2
0
6
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
1
0
0
0
0
0
2
0
0
0
0
8
1
0
0
1
0
0
2
1
0
2
2
0
4
1
0
0
1
0
0
0
3
0
2
0
0
1
0
2
0
0
0
3
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
1
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
2
0
1
0
0
2
1
0
0
0
0
1
0
0
6
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
1
2
1
0
0
0
0
3
0
0
1
1
0
0
0
2
1
0
0
0
0
5
0
0
2
0
2
0
0
2
1
0
0
0
1
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
3
1
2
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
1
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
2
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
2
8
0
0
3
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
2
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
1
0
0
0
7
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
6
0
0
0
0
0
6
2
1
1
0
4
0
0
0
1
1
0
0
3
2
0
0
0
1
0
0
0
1
0
0
0
0
0
3
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
2
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
3
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
3
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
4
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
1
0
0
0
0
0
2
0
2
5
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
4
0
0
0
0
0
1
0
4
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
5
0
0
0
0
0
0
0
0
6
2
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
3
0
1
3
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
3
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
2
2
0
1
0
0
2
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
2
1
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
4
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
2
0
0
0
1
0
3
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
3
0
0
0
1
0
1
0
0
0
0
0
0
3
1
0
0
0
0
1
0
2
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
3
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
5
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
2
0
0
0
2
1
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
4
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
1
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
1
0
0
3
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
4
1
0
2
1
1
0
0
0
2
0
4
0
4
2
0
1
0
0
2
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
1
0
3
2
2
0
4
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
3
0
0
2
1
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
3
0
2
0
0
2
0
0
0
0
1
0
0
1
0
1
1
1
2
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
2
1
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
3
2
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
3
2
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
3
0
0
0
0
2
4
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
3
1
0
2
0
0
0
0
1
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
1
1
0
0
3
1
0
1
0
0
2
8
1
2
0
0
0
0
1
1
0
0
0
0
0
0
1
1
2
1
1
0
0
0
0
0
0
0
2
0
0
2
2
1
1
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
2
0
2
0
0
1
0
0
0
2
0
0
1
4
0
0
0
0
3
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
3
0
0
0
0
0
2
1
2
0
0
2
0
2
0
0
0
1
0
2
0
1
2
0
0
2
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
1
0
2
0
1
1
1
0
0
2
0
0
0
0
0
0
1
0
0
1
7
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
15
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
3
3
2
2
1
0
0
0
0
3
2
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
1
0
1
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
1
0
2
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
2
2
2
0
0
1
0
0
2
0
0
0
2
6
0
2
0
3
0
0
0
0
0
0
2
0
3
0
1
0
0
0
1
0
0
2
0
0
2
1
1
0
0
0
2
1
1
2
0
0
3
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
1
0
2
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
3
0
0
0
0
0
1
4
0
0
0
0
1
1
0
0
1
1
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
2
2
2
1
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
2
0
0
0
0
0
6
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
2
2
0
0
2
2
0
0
0
0
0
1
0
0
0
0
1
3
0
0
0
1
2
0
0
0
0
0
2
4
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
3
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
2
0
1
1
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
3
0
0
3
0
0
0
1
9
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
6
0
0
0
0
0
0
1
2
1
0
0
2
0
2
1
0
0
0
0
1
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
2
0
0
2
0
0
0
2
0
0
3
2
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
6
2
0
0
0
0
0
0
0
1
0
0
1
3
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
7
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
6
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
1
0
0
1
1
0
0
1
0
2
4
0
0
0
1
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
2
0
1
0
0
0
0
0
2
2
0
0
0
0
3
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
1
1
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
2
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
1
0
4
0
0
0
0
2
0
0
0
0
0
1
0
1
1
0
2
0
0
0
1
2
1
2
2
2
0
0
4
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
2
0
0
0
2
0
1
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
4
0
0
0
2
0
1
1
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
1
0
2
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
2
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
3
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
1
2
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
1
2
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
1
2
0
0
2
1
0
2
6
2
1
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
1
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
6
0
0
1
0
0
0
0
0
2
0
0
0
3
0
0
1
0
0
0
2
2
0
2
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
3
0
1
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
3
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
1
6
0
0
0
0
0
0
0
0
1
1
2
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
3
0
0
0
1
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
4
0
0
0
0
2
0
0
1
1
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
1
1
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
1
0
2
1
0
0
0
0
0
0
0
2
0
0
5
2
0
0
1
1
2
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
1
0
2
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
1
3
0
2
0
0
0
2
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
2
2
0
0
2
0
0
1
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
3
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
6
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
1
0
0
1
0
2
0
0
0
0
0
1
0
0
1
3
1
0
2
0
0
0
1
1
0
0
0
1
0
0
5
7
2
0
0
0
2
0
1
0
0
0
0
0
4
1
0
0
0
0
1
1
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
1
0
6
0
1
1
1
0
0
0
0
0
2
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
5
0
2
0
0
0
1
11
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
2
0
1
0
0
0
2
0
1
2
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
2
0
2
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
3
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
3
2
0
0
0
0
0
1
1
0
0
0
1
0
2
0
0
0
0
0
2
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
2
1
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
1
1
0
0
0
0
0
0
0
2
1
1
0
0
0
2
0
1
0
0
0
0
0
4
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
1
1
0
2
0
0
1
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
2
2
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
1
0
0
0
0
0
0
0
0
0
5
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
2
2
0
0
6
1
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
2
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
2
0
0
0
0
2
0
1
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
6
0
0
0
0
0
0
1
0
0
0
0
3
0
0
1
1
0
0
0
0
0
1
0
0
0
3
0
0
2
0
0
0
2
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
2
0
0
2
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
3
2
0
0
1
0
3
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
6
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
1
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
8
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
6
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
4
5
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
5
0
0
0
2
1
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
1
0
0
1
2
0
0
0
0
2
0
0
0
0
0
2
0
2
0
2
2
1
0
2
0
0
0
3
1
0
0
0
0
0
0
1
0
2
0
0
3
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
2
0
0
0
1
0
0
0
0
2
0
1
0
0
1
0
2
0
0
0
0
4
1
1
1
0
2
0
0
0
0
0
0
0
5
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
4
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
1
2
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
2
0
0
0
0
1
0
2
1
0
1
3
0
0
0
0
0
0
2
0
1
3
0
0
0
0
0
0
0
0
0
1
0
2
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
3
0
0
1
0
1
0
0
1
0
0
3
0
0
1
0
0
0
3
0
0
4
2
0
0
0
0
0
2
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
4
0
0
1
0
1
0
0
0
1
0
0
0
0
3
2
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
2
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
1
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
2
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
4
0
2
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
2
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
2
0
0
0
0
1
2
0
0
0
0
0
5
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
6
0
0
0
2
0
1
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
4
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
2
2
1
3
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
2
0
2
1
0
0
0
12
1
0
1
0
0
0
1
0
0
1
0
0
1
0
3
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
3
0
0
0
3
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
2
2
1
0
0
0
0
1
0
0
1
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
1
0
3
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
1
0
0
2
0
0
0
0
0
0
0
2
0
0
3
0
0
3
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
2
1
1
0
0
0
0
0
3
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
2
2
0
0
0
0
0
1
0
3
0
0
0
3
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
1
2
1
0
0
2
0
2
0
0
2
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
14
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
3
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
1
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
3
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
1
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
3
2
3
1
0
0
0
2
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
3
2
0
0
0
0
0
2
0
2
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
1
0
0
2
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
4
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
1
0
2
0
0
0
0
0
1
0
0
0
3
0
0
1
0
0
4
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
2
1
0
0
0
0
0
0
3
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
1
0
0
0
0
0
0
1
1
3
0
1
0
1
0
1
0
0
0
1
1
0
0
0
0
0
1
5
0
1
2
0
0
0
2
1
2
0
1
2
0
0
0
0
1
1
0
0
0
0
1
0
2
0
0
0
0
0
1
1
3
1
0
0
0
4
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
3
0
1
0
0
2
1
0
1
0
0
0
1
0
1
1
1
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
5
0
0
0
0
2
0
0
0
0
2
0
2
0
2
0
0
0
0
1
2
0
0
2
2
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
2
2
0
0
1
1
0
0
0
0
0
0
0
0
0
2
3
0
1
0
0
0
2
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
6
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
2
0
0
1
0
0
1
4
2
0
2
0
1
0
1
0
1
0
0
1
0
0
0
2
0
0
0
1
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
3
0
2
0
0
2
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
4
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
1
0
0
2
1
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
1
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
2
1
0
0
0
0
0
0
0
0
5
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
3
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
2
2
0
1
0
0
1
0
1
0
1
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
1
0
1
0
0
1
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
1
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
3
1
0
2
0
3
2
0
0
0
1
1
0
0
4
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
2
0
0
2
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
1
0
2
0
0
0
0
0
2
0
0
1
0
0
2
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
1
0
0
0
1
2
0
2
0
0
0
2
1
0
3
0
2
0
0
0
0
0
0
0
1
0
1
0
3
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
1
0
1
1
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
2
2
0
1
0
0
1
0
0
0
1
1
2
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
2
0
0
1
2
1
0
0
0
0
0
2
1
0
0
0
2
2
1
0
0
0
2
1
0
0
0
0
2
3
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
2
2
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
1
0
1
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
1
0
2
1
0
0
4
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
2
0
1
2
0
1
0
0
0
0
3
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
2
0
0
0
0
0
0
1
1
0
2
2
2
1
0
2
0
0
0
1
1
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
1
0
0
2
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
1
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
1
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
3
0
0
2
0
1
3
0
0
1
0
0
0
3
0
0
1
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
3
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
1
0
0
2
0
1
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
3
0
1
0
0
0
9
0
3
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
4
2
1
0
0
2
0
0
0
0
2
0
0
3
2
1
2
0
1
1
3
0
0
0
0
0
1
0
2
0
2
2
0
1
2
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
2
4
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
1
0
0
5
0
0
0
4
0
3
0
0
0
0
0
2
0
1
0
0
1
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
2
1
0
0
0
0
3
1
0
0
1
2
0
1
0
1
1
4
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
6
0
2
0
0
1
2
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
3
0
2
1
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
1
1
2
0
0
1
2
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
2
2
0
0
2
0
0
0
2
0
4
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
14
2
1
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
1
8
1
0
0
0
2
1
0
1
1
0
0
0
0
3
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
3
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
2
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
1
1
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
2
1
3
0
0
0
0
0
0
0
2
2
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
3
0
0
1
0
0
0
0
2
0
0
0
1
0
1
0
2
0
2
0
5
0
0
0
0
0
0
0
0
0
0
1
1
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
2
0
2
2
0
0
1
0
0
1
0
0
3
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
2
0
3
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
2
0
0
2
0
0
0
1
1
2
0
0
0
2
2
0
0
4
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
3
0
1
0
2
0
2
0
0
1
0
0
2
1
0
0
0
0
0
6
0
0
1
0
0
0
1
0
0
2
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
2
0
0
0
2
0
1
0
7
0
1
0
0
2
0
2
2
2
0
3
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
2
0
4
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
2
0
0
0
0
1
2
0
0
0
1
0
2
0
0
0
0
1
0
0
0
1
0
0
1
0
0
3
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
1
0
2
0
0
0
0
0
0
0
2
2
0
3
1
3
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
1
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
1
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
1
1
2
2
0
1
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
6
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
3
1
2
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
6
0
0
2
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
2
0
0
5
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
6
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
5
0
3
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
3
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
1
0
1
0
0
0
1
1
0
0
1
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
5
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
4
0
0
0
0
0
0
0
2
0
0
2
2
0
2
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
1
2
1
0
1
0
0
0
0
5
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
3
0
0
0
0
0
2
0
1
0
0
0
1
0
3
1
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
1
0
1
0
0
0
0
2
0
1
0
0
0
2
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
1
0
0
0
0
0
1
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
3
1
2
0
0
0
0
2
0
0
0
0
0
3
0
0
3
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
3
0
0
0
2
1
2
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
5
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
2
2
1
1
0
2
2
1
0
0
0
1
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
7
1
0
1
0
3
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
5
3
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
1
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
2
2
1
0
0
0
1
2
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
2
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
2
0
1
0
0
2
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
1
2
3
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
1
1
0
0
0
1
2
1
1
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
1
0
2
2
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
1
2
0
0
3
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
2
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
4
0
0
1
2
0
0
0
1
2
2
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
2
0
2
0
0
0
0
2
1
0
0
0
3
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
1
0
1
0
3
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
2
1
0
0
2
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
1
4
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
3
1
2
0
1
0
0
2
0
0
0
0
0
2
0
1
0
0
1
0
2
0
0
0
0
0
0
2
2
2
0
0
0
0
5
0
3
1
0
2
0
0
2
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
1
0
2
1
0
1
0
1
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
2
0
0
4
2
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
2
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
2
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
2
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
1
1
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
1
1
0
0
0
0
0
1
2
0
2
0
0
0
0
2
1
0
0
1
1
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
5
0
0
0
0
4
0
1
0
0
0
0
0
0
2
0
0
3
0
2
1
0
1
0
0
0
0
0
2
0
0
2
0
2
2
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
1
1
3
0
0
0
2
0
1
0
4
0
0
0
0
4
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
1
0
0
0
2
0
0
0
4
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
4
1
0
2
2
0
1
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
3
2
0
3
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
2
0
0
2
0
0
2
1
0
2
0
0
0
0
0
0
1
0
1
1
0
2
0
0
0
0
0
0
0
0
2
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
4
0
0
2
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
4
0
0
3
0
0
2
0
0
2
0
0
2
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
1
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
3
0
0
1
0
1
0
0
2
1
0
0
2
0
0
0
0
2
1
0
1
0
0
0
0
1
0
0
1
2
0
1
0
2
0
1
0
0
0
0
0
0
2
1
0
0
2
0
0
0
2
1
0
1
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
2
1
0
0
1
0
0
0
2
2
2
1
0
0
2
0
8
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
2
1
0
1
0
1
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
2
2
0
3
0
0
3
0
2
0
0
0
2
0
0
0
0
1
0
5
0
0
2
0
0
0
0
3
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
8
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
3
0
0
0
0
1
0
2
0
0
1
1
0
0
1
0
0
0
1
0
1
0
1
0
2
0
0
0
1
0
0
1
0
0
1
2
1
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
1
2
1
0
0
1
3
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
3
1
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
2
2
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
5
0
0
0
0
0
0
0
0
1
0
2
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
1
2
0
2
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
1
0
1
0
0
0
0
1
0
0
2
1
0
2
0
1
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
1
2
0
0
0
0
0
0
1
3
0
2
1
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
3
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
1
0
0
0
1
0
3
1
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
2
0
0
0
0
1
0
0
0
5
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
2
0
0
0
0
0
1
0
1
0
1
0
0
2
0
2
0
3
0
0
0
0
0
1
0
0
0
1
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
2
3
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
1
0
1
0
0
0
1
0
3
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
2
0
0
0
1
4
0
0
1
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
3
0
1
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
2
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
3
0
0
2
2
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
1
0
0
2
0
1
0
0
1
0
0
0
4
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
5
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
2
0
0
0
0
1
1
3
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
1
0
1
0
0
1
2
0
0
0
0
0
1
0
0
0
1
0
1
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
3
2
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
2
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
1
0
0
2
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
3
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
1
0
0
0
1
0
0
0
3
0
1
2
1
0
2
0
0
2
0
0
0
8
2
0
0
0
2
0
0
0
2
0
3
0
0
1
0
0
0
1
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
1
0
3
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
2
2
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
3
2
0
0
0
1
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
2
0
0
1
2
1
2
0
1
0
1
0
9
0
0
0
0
1
0
0
0
0
0
0
2
1
1
0
2
1
2
0
0
0
0
1
0
2
0
0
0
0
2
2
0
0
0
1
0
2
1
0
2
0
3
0
0
0
0
0
0
1
0
2
1
1
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
2
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
5
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
8
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
2
3
0
2
0
0
0
0
2
0
1
0
0
0
0
1
0
2
1
3
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
2
1
2
0
1
0
0
0
0
0
4
0
5
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
2
0
1
0
4
2
0
0
1
0
0
2
1
1
2
4
0
0
0
2
0
0
1
8
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
2
2
0
2
0
0
1
2
0
0
0
0
1
0
0
0
0
4
1
0
0
0
0
0
0
3
0
2
0
2
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
4
0
2
0
0
0
1
0
6
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
2
1
0
0
0
0
1
2
0
2
0
0
0
0
1
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
1
2
0
2
0
1
0
0
0
0
0
1
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
4
0
0
0
1
0
0
0
2
3
0
0
0
0
0
0
2
0
1
0
2
0
4
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
1
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
1
1
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
2
0
0
1
0
0
1
0
0
2
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
2
0
2
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
1
0
0
1
3
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
2
0
2
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
6
0
0
0
0
0
0
1
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
3
0
0
0
0
0
0
0
0
1
2
2
0
1
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
3
2
0
0
3
0
0
0
0
0
0
5
0
0
2
0
0
0
2
0
0
0
0
0
0
1
3
0
0
0
1
1
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
1
2
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
1
4
0
0
1
2
2
0
0
0
0
0
0
1
1
0
1
0
0
2
0
0
1
2
0
0
0
2
0
0
1
0
2
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
4
0
0
0
4
0
0
1
1
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
2
1
0
0
1
0
1
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
3
0
0
1
2
1
0
0
0
0
2
0
0
0
0
0
3
4
0
1
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
5
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
3
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
1
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
3
0
2
0
0
0
2
0
3
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
2
2
0
0
2
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
2
2
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
2
0
6
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
2
1
1
0
0
4
0
4
2
0
0
0
2
2
0
0
1
0
1
1
4
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
1
1
2
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
1
2
2
1
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
6
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
1
0
0
2
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
2
0
0
0
3
0
1
4
2
0
0
0
0
0
0
0
0
0
0
3
1
2
0
0
0
0
0
0
2
0
0
0
1
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
3
0
0
1
0
0
0
1
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
1
2
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
5
0
2
0
0
0
2
0
0
1
1
0
0
0
3
4
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
5
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
9
0
0
2
0
0
0
0
0
0
2
0
0
3
0
2
2
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
1
0
2
2
0
0
0
3
0
0
1
0
0
0
0
1
2
0
0
0
0
2
2
0
0
1
0
1
0
0
0
1
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
1
0
0
0
8
2
0
2
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
3
2
0
2
0
0
0
0
0
3
0
0
0
1
0
0
1
1
0
2
0
1
0
1
0
2
2
0
1
0
0
0
3
3
1
0
0
0
2
1
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
6
0
0
1
1
0
0
0
0
0
0
2
0
0
2
0
2
0
0
3
0
0
0
0
0
1
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
3
1
1
0
0
0
0
0
0
6
2
2
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
1
0
0
0
6
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
4
2
0
2
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
1
1
2
0
0
1
0
0
0
0
0
0
0
0
4
0
1
0
0
3
0
0
0
2
0
0
0
5
1
0
1
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
4
0
0
2
2
2
2
2
0
0
0
0
0
0
1
2
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
1
0
0
0
0
0
2
0
2
0
1
0
1
0
1
0
0
0
2
0
0
1
0
0
0
0
0
3
0
0
1
0
0
0
0
1
0
1
0
2
1
0
1
0
0
2
3
0
0
0
1
0
0
0
3
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
4
2
2
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
2
0
2
0
1
3
1
0
0
0
5
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
2
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
7
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
6
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
2
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
2
0
0
1
0
2
0
1
0
0
2
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
1
1
0
0
0
1
2
1
0
0
2
0
2
1
1
1
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
1
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
1
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
0
4
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
5
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
2
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
1
3
5
0
0
0
0
0
0
0
0
0
2
1
0
1
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
1
0
3
0
0
0
0
0
1
0
1
0
0
0
0
0
0
3
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
2
0
2
0
3
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
2
1
0
2
3
1
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
5
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
1
1
0
1
4
0
3
1
0
2
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
3
2
1
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
1
0
1
0
2
1
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
1
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
2
0
2
0
0
0
0
0
2
0
0
2
0
1
2
0
0
0
0
0
2
2
1
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
1
0
0
2
0
0
8
2
2
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
2
1
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
1
1
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
2
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
5
0
1
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
2
0
3
8
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
3
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
8
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
1
2
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
3
0
0
1
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
6
0
0
0
2
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
1
2
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
1
0
1
1
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
5
1
1
1
0
1
1
0
0
0
1
0
0
0
2
0
3
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
3
2
3
2
0
0
0
0
1
0
0
0
0
0
0
0
0
3
4
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
2
0
1
0
2
2
1
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
3
0
0
0
2
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
5
0
0
0
2
1
1
0
0
0
0
0
2
0
0
0
1
0
0
1
3
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
2
3
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
2
0
1
2
0
0
3
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
2
5
3
0
2
1
0
0
0
0
0
0
0
0
3
0
2
0
2
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
1
2
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
1
0
7
0
0
0
0
0
0
1
0
0
0
0
3
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
5
0
0
11
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
2
2
0
1
0
0
0
1
0
0
0
3
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
4
0
1
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
2
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
2
1
0
0
1
0
2
3
1
0
0
2
0
0
0
0
0
2
4
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
3
1
1
0
0
0
1
0
0
0
0
0
9
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
1
2
0
1
2
0
1
0
2
0
0
0
0
0
0
0
0
0
4
1
0
0
2
3
2
7
0
0
2
0
0
0
2
1
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
3
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
5
0
1
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
3
0
0
2
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
1
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
7
0
0
0
0
0
0
2
0
1
0
0
0
0
0
4
1
1
1
0
0
0
0
0
0
0
0
0
1
1
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
2
0
0
2
0
5
2
0
1
0
2
0
0
1
0
1
0
0
1
0
0
1
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
3
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
3
0
0
0
0
2
0
0
0
6
1
1
0
0
0
0
1
0
0
0
1
0
0
2
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
1
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
3
0
4
0
0
0
1
2
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
2
0
0
0
1
2
2
2
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
7
0
0
0
0
0
0
3
0
0
0
2
0
4
0
2
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
1
1
2
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
7
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
1
0
0
0
2
0
2
4
1
2
1
1
1
0
2
5
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
8
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
1
1
0
2
3
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
7
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
1
0
0
2
0
0
0
2
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
3
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
2
2
0
2
4
1
3
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
2
0
0
0
0
1
1
0
0
3
0
0
2
0
0
0
0
0
1
0
0
0
0
1
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
1
2
1
0
0
0
0
4
2
0
0
2
0
4
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
3
0
0
3
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
3
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
1
6
12
0
1
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
6
0
2
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
1
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
11
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
6
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
4
0
2
0
3
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
3
0
0
0
0
0
0
0
0
0
1
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
3
0
0
1
0
4
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
2
2
0
1
0
0
0
2
0
0
0
2
0
0
0
2
4
0
0
1
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
1
0
0
4
0
2
0
0
7
2
2
0
1
2
0
1
0
0
0
0
0
0
0
3
2
0
2
0
1
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
1
1
0
0
1
0
0
2
0
0
0
1
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
2
0
11
0
2
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
2
2
0
4
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
4
0
1
3
2
0
2
0
1
0
0
0
0
2
0
1
0
1
1
0
0
2
0
0
0
0
2
1
0
0
0
1
1
0
1
1
0
0
2
2
0
2
0
0
0
0
0
0
1
0
0
0
0
3
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
4
2
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
3
2
0
0
0
2
2
2
0
0
0
0
0
1
0
0
3
1
1
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
1
1
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
1
0
1
0
0
0
2
0
1
0
0
0
0
1
0
2
0
0
0
1
0
0
0
1
0
0
2
1
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
1
0
2
0
2
0
2
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
4
0
1
2
0
0
1
0
2
2
0
0
2
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
5
2
0
0
2
3
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
0
0
0
1
0
1
2
0
0
0
1
1
1
1
0
0
0
0
0
1
1
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
5
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
1
0
2
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
1
2
4
0
0
2
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
4
0
0
0
0
1
0
0
1
0
0
2
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
3
0
0
0
2
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
2
0
0
3
1
0
1
1
0
2
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
2
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
5
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
2
0
0
2
1
0
0
1
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
3
1
3
0
2
1
0
0
0
2
2
0
0
0
1
0
0
0
1
0
0
2
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
2
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
2
1
0
0
0
0
0
0
0
2
0
0
2
3
0
0
0
0
1
0
0
0
2
0
0
2
0
2
0
0
0
0
1
0
1
0
0
2
3
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
3
0
0
2
3
3
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
2
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
2
0
2
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
3
0
0
0
0
0
0
5
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
1
2
0
2
0
2
0
0
0
0
0
2
0
2
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
3
0
2
0
2
0
0
0
0
2
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
6
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
2
0
0
3
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
1
1
1
0
0
2
0
0
0
0
0
0
1
2
1
2
2
0
0
0
0
2
1
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
5
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
2
2
8
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
1
1
1
0
1
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
1
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
1
6
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
2
1
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
2
0
0
0
2
2
0
2
0
1
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
1
2
0
2
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
2
0
0
1
0
0
2
0
0
0
1
1
0
2
0
0
2
1
3
0
0
0
2
0
0
0
0
2
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
1
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
2
0
1
0
1
0
0
0
0
2
0
0
0
0
0
6
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
2
3
0
0
0
1
0
2
5
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
2
2
0
0
0
0
0
2
6
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
5
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
1
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
3
0
0
2
0
0
2
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
3
0
2
0
1
1
0
0
3
3
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
2
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
4
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
1
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
1
1
2
2
2
0
1
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
2
1
0
2
1
0
0
0
0
0
2
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
1
0
1
0
1
0
7
0
2
0
1
0
0
0
0
0
2
1
1
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
5
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
5
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
5
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
2
0
0
1
1
1
0
0
0
0
0
2
1
1
2
1
0
0
0
0
1
0
0
0
0
0
1
2
1
0
1
3
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
4
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
2
0
0
1
2
2
0
0
0
0
0
0
0
0
1
0
0
1
2
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
2
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
6
1
0
1
0
0
0
4
0
2
0
1
3
0
0
0
0
0
0
2
2
0
0
0
0
1
3
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
2
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
2
0
1
1
0
0
0
0
0
0
1
2
0
1
1
0
0
1
1
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
1
1
4
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
5
2
0
0
0
0
0
2
0
4
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
2
0
3
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
3
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
3
0
1
0
1
0
1
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
4
2
0
0
0
1
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
3
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
1
0
0
0
3
1
1
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
1
0
0
2
1
0
0
0
0
0
0
3
0
0
6
0
0
0
2
0
0
2
2
0
0
2
1
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
2
2
1
0
3
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
2
2
7
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
3
0
1
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
2
6
0
0
0
0
0
2
0
1
2
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
3
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
3
0
0
1
0
0
0
0
0
0
4
0
4
2
0
0
0
0
1
2
1
0
2
0
1
0
0
0
2
0
2
0
1
0
0
0
2
0
0
0
0
0
5
0
2
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
1
2
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
2
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
2
0
0
0
0
0
0
0
1
1
0
0
3
0
0
0
0
0
2
2
2
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
2
0
1
0
2
0
0
0
3
0
2
0
0
0
2
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
4
1
1
0
0
0
1
0
2
1
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
2
0
0
0
0
1
0
2
0
0
1
0
0
2
2
0
0
0
1
0
0
0
0
0
2
0
1
1
2
0
4
1
0
2
0
1
0
0
0
0
2
0
0
1
1
0
0
1
2
0
0
1
0
0
0
0
3
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
6
0
0
1
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
2
2
0
0
0
1
0
2
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
6
0
0
0
0
0
4
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
1
0
1
1
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
4
0
0
0
2
1
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
6
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
4
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
7
0
0
0
1
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
1
2
0
0
3
0
0
0
0
0
0
0
14
2
2
0
0
0
1
2
0
0
0
1
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
1
1
0
0
3
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
1
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
1
2
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
3
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
3
0
2
0
1
0
0
0
0
9
0
0
0
0
0
0
2
0
0
0
0
2
2
3
0
0
0
0
1
1
0
0
0
0
0
1
4
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
7
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
2
1
0
0
0
1
2
0
0
1
4
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
2
3
2
3
0
0
0
1
0
0
0
0
0
0
0
3
0
0
3
0
0
0
0
0
1
0
0
0
0
1
2
0
0
1
7
0
0
1
0
0
0
0
0
0
2
0
2
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
2
0
2
0
0
0
0
0
1
0
0
2
4
2
2
3
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
2
0
1
0
1
0
0
1
0
0
0
0
0
0
0
10
0
0
0
0
0
0
0
0
0
0
0
2
1
2
2
1
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
4
0
0
0
0
1
0
2
0
0
1
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
6
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
3
1
0
2
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
3
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
4
1
0
0
0
0
0
1
0
0
0
3
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
1
0
4
0
3
0
0
0
0
0
5
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
4
0
0
0
0
5
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
2
0
0
0
0
0
2
2
1
0
0
0
0
0
1
0
0
0
0
0
2
0
1
2
1
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
2
3
0
0
0
1
0
3
0
0
0
0
1
0
0
0
2
0
7
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
2
0
1
1
2
2
1
0
0
5
1
0
0
2
0
0
0
2
0
2
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
1
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
2
2
0
0
2
2
1
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
2
0
3
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
2
0
2
0
1
1
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
1
2
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
4
0
0
1
2
0
0
0
1
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
2
0
0
2
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
3
0
0
0
0
0
1
0
0
0
2
2
1
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
2
0
1
1
0
4
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
2
2
0
0
0
0
0
1
0
0
0
1
0
0
1
0
2
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
1
0
2
0
1
0
0
0
0
2
2
0
0
0
2
0
1
0
0
2
0
0
1
0
0
1
0
5
0
0
1
1
1
0
0
1
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
2
7
1
0
0
0
0
2
2
0
0
4
0
2
0
1
0
1
0
2
3
3
0
0
0
2
0
3
0
0
0
1
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
1
0
3
0
0
2
0
1
2
2
0
0
4
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
1
0
1
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
2
0
1
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
5
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
1
0
0
0
4
2
1
1
3
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
11
0
2
2
0
0
0
1
1
3
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
1
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
2
1
0
1
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
2
1
3
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
2
0
2
0
0
0
2
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
1
2
4
4
0
1
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
1
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
17
0
2
0
0
1
1
0
1
1
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
3
0
3
0
0
1
0
0
1
0
0
0
0
2
0
1
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
1
1
8
0
0
0
1
0
0
0
0
0
1
2
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
3
2
0
0
2
2
0
1
0
2
1
2
0
0
0
0
1
0
0
0
0
2
1
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
5
0
2
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
1
0
0
2
2
0
1
0
0
1
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
1
0
0
0
0
0
0
3
0
1
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
2
0
0
0
0
0
2
0
1
0
0
0
1
2
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
2
1
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
2
2
0
2
0
0
0
3
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
4
3
1
2
0
0
0
0
0
0
0
2
1
3
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
1
1
1
0
0
0
0
1
0
2
0
1
0
2
0
0
0
0
1
1
2
3
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
2
4
0
0
0
0
2
0
0
1
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
5
0
0
0
0
0
2
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
1
0
3
2
2
0
0
0
0
0
2
0
0
2
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
2
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
3
1
2
0
2
0
0
0
0
2
1
0
2
0
1
0
0
2
1
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
2
0
0
2
2
3
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
2
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
2
0
0
0
0
3
0
2
0
5
0
0
0
2
0
0
1
0
0
2
0
0
1
0
0
0
2
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
2
2
0
2
5
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
3
0
0
1
3
0
0
0
0
0
0
1
2
0
1
0
0
0
0
1
3
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
8
0
0
0
2
0
0
0
0
0
0
2
1
3
0
0
0
0
0
0
3
0
1
0
0
0
0
1
2
0
1
0
0
2
0
0
1
2
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
2
2
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
2
0
2
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
6
0
0
0
2
2
0
0
2
0
3
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
1
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
4
2
0
2
0
1
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
1
1
0
0
0
0
0
2
2
0
0
3
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
2
1
0
0
0
3
0
1
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
5
2
0
0
4
0
0
0
0
2
15
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
1
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
2
1
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
1
1
4
0
1
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
1
2
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
1
0
2
0
0
0
2
0
0
0
2
0
0
2
1
0
0
1
0
0
1
0
2
1
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
3
0
0
1
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
2
2
0
0
2
0
0
0
1
0
0
2
1
0
1
0
0
0
1
0
0
0
0
2
0
1
0
2
1
0
2
0
2
0
0
3
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
2
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
2
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
2
1
0
0
0
0
0
1
0
1
0
1
0
0
0
2
0
1
0
0
0
1
2
2
0
0
2
1
0
2
0
0
0
0
0
0
0
2
1
2
0
0
0
0
1
0
0
0
0
1
1
3
0
1
0
1
0
1
0
0
0
0
0
0
8
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
3
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
5
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
1
0
0
0
0
2
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
6
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
4
2
0
0
0
0
1
1
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
2
0
0
0
1
1
0
0
1
1
0
0
0
0
1
1
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
3
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
1
1
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
4
3
1
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
13
0
0
0
0
0
1
0
0
0
0
1
1
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
3
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
4
1
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
2
2
0
2
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
4
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
4
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
6
2
2
1
0
0
0
0
0
0
5
1
1
0
0
0
0
3
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
1
0
0
0
0
0
0
0
0
2
0
1
0
1
2
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
3
1
1
0
0
0
0
1
2
2
0
2
1
3
0
2
0
0
1
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
2
2
0
0
0
0
0
0
1
0
0
2
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
3
2
0
0
2
0
0
1
0
3
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
4
2
1
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
2
6
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
4
3
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
3
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
3
6
0
2
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
4
2
0
0
0
0
0
1
3
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
3
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
1
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
6
1
0
0
0
2
2
0
0
0
0
0
0
2
1
0
1
0
0
0
0
4
0
0
0
0
2
0
0
1
2
0
0
0
2
0
0
0
1
0
1
0
0
0
2
2
0
1
0
2
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
2
0
0
0
0
2
2
0
0
1
0
2
3
0
0
3
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
2
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
4
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
4
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
3
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
5
0
2
0
0
1
5
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
3
0
3
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
2
2
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
1
2
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
1
0
0
2
2
1
0
1
0
0
2
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
2
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
2
0
1
0
0
0
1
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
2
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
3
0
2
0
0
0
0
3
0
0
0
0
0
4
0
0
1
0
0
0
2
0
0
0
0
1
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
2
0
1
3
0
2
1
0
0
0
2
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
3
0
1
0
1
0
0
0
1
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
2
1
1
2
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
3
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
4
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
3
2
0
0
0
1
0
0
2
2
2
1
0
0
0
0
0
0
0
0
2
0
5
0
0
0
0
0
3
1
1
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
3
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
4
0
2
1
1
0
0
0
0
4
0
0
1
0
1
1
2
1
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
1
0
0
2
0
0
2
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
1
5
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
3
0
2
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
5
0
0
2
0
0
0
0
0
0
1
2
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
7
0
0
2
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
4
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
1
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
3
0
1
0
1
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
3
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
1
3
2
0
1
0
2
0
1
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
1
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
2
0
0
0
0
1
0
2
2
2
0
0
0
2
3
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
1
1
0
0
0
4
0
2
0
0
0
0
0
3
0
1
0
0
0
0
0
0
2
1
2
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
8
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
1
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
3
0
0
0
1
3
2
0
0
0
2
1
4
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
2
2
2
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
3
3
1
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
3
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
3
1
0
0
1
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
3
0
0
1
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
2
0
1
0
0
3
0
0
0
0
3
1
0
0
0
1
0
0
0
5
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
1
0
0
0
0
0
2
0
2
0
1
0
4
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
3
0
0
6
2
0
0
0
0
6
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
9
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
6
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
1
1
0
1
1
0
2
0
0
0
0
1
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
1
0
0
0
0
3
0
2
1
0
0
0
0
1
2
0
2
0
2
2
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
2
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
2
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
1
0
1
0
0
0
0
3
0
0
0
0
0
1
2
0
1
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
2
2
0
8
0
6
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
2
2
1
0
1
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
4
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
2
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
2
0
0
0
0
3
4
0
0
0
0
0
2
0
0
0
3
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
1
2
0
0
0
2
0
0
0
1
1
0
0
1
2
3
0
0
0
2
0
0
1
1
0
0
0
2
1
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
3
0
0
2
0
1
0
0
0
0
0
0
0
2
0
6
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
3
13
0
2
0
0
8
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
3
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
3
0
0
1
1
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
2
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
2
1
1
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
5
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
2
2
0
0
0
2
2
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
4
2
0
1
0
7
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
2
0
1
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
2
0
0
3
2
0
0
0
0
1
0
5
0
1
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
2
5
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
2
2
0
2
0
0
0
1
0
2
2
0
0
0
0
3
0
1
0
1
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
2
1
0
1
1
0
0
2
0
0
0
1
0
2
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
1
0
0
0
2
0
0
0
0
0
2
1
0
0
0
1
0
0
0
1
0
0
0
0
0
2
1
3
0
0
0
0
0
0
0
1
0
1
0
0
0
4
0
0
1
0
0
2
3
0
0
1
0
0
0
0
0
0
1
2
1
2
0
1
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
4
2
0
0
1
0
0
2
0
0
1
0
2
4
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
1
0
1
0
0
0
0
2
1
4
1
1
0
0
0
3
1
0
0
0
0
4
0
0
2
0
2
0
3
0
0
0
1
1
0
0
7
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
2
3
0
0
0
0
0
0
0
0
0
1
1
2
1
1
0
0
0
0
0
0
0
0
2
1
2
1
0
0
0
0
1
0
0
0
0
0
0
1
13
0
0
2
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
3
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
2
0
2
2
0
0
0
0
0
0
0
2
0
2
2
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
2
0
0
0
1
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
2
0
0
1
0
0
1
0
2
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
3
0
0
0
0
2
1
3
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
1
0
2
0
1
0
4
0
0
0
0
0
3
0
0
0
0
2
0
0
1
0
0
0
1
1
0
1
2
0
3
0
0
0
0
0
0
1
0
0
0
1
5
1
1
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
2
1
0
3
0
0
0
0
0
2
0
1
2
1
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
4
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
2
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
4
3
0
1
0
1
0
1
0
0
2
3
0
0
0
0
2
1
0
1
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
1
3
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
2
0
0
0
4
0
0
0
0
0
1
0
0
2
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
1
5
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
2
2
0
2
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
2
0
0
2
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
1
3
0
2
0
1
1
0
0
0
3
0
2
2
0
1
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
3
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
3
1
0
0
2
0
0
1
0
0
0
1
1
4
0
0
1
0
1
1
2
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
1
0
2
0
0
2
0
0
0
3
0
1
2
0
0
2
1
1
0
0
0
0
0
0
0
0
0
1
0
5
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
1
3
0
0
0
0
2
0
1
0
0
0
0
3
2
2
1
0
0
1
0
0
0
0
1
2
1
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
13
0
0
0
0
0
0
0
2
3
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
2
2
0
0
1
0
0
1
2
0
0
0
1
0
0
4
0
0
0
0
3
0
2
0
1
2
1
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
2
0
1
1
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
3
1
0
0
1
0
0
0
1
0
0
0
0
0
0
2
3
1
0
0
2
4
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
5
0
0
1
0
0
1
0
0
2
1
0
0
0
1
1
0
2
0
2
0
0
1
2
2
1
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
2
0
2
1
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
2
0
0
0
0
0
0
0
0
1
2
0
0
0
4
0
0
0
0
0
0
0
0
2
6
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
2
0
2
0
1
1
0
0
0
2
2
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
9
0
0
1
0
5
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
2
2
2
2
0
0
0
1
3
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
4
0
0
0
1
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
2
0
2
1
0
1
0
0
0
0
1
0
0
2
2
1
1
0
0
5
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
1
0
0
1
0
4
0
0
2
0
4
1
0
1
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
1
0
0
4
0
0
0
0
0
1
0
1
0
1
2
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
2
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
1
0
0
2
0
1
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
2
1
0
1
1
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
2
0
0
1
0
0
0
2
1
0
0
1
0
0
0
2
0
0
0
4
0
0
2
2
0
0
0
0
0
0
1
0
2
0
0
4
0
0
2
1
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
1
3
0
0
1
0
0
1
2
3
0
1
0
0
0
0
2
0
1
2
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
2
1
0
0
1
3
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
1
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
1
2
1
1
0
0
2
0
0
0
1
0
0
0
1
0
1
0
0
0
2
0
0
0
3
0
0
0
0
0
1
0
0
0
3
2
0
0
0
1
1
0
0
0
0
0
0
0
0
2
2
0
3
3
0
1
1
0
0
0
0
0
0
1
2
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
5
0
0
1
0
5
0
0
0
0
0
0
2
2
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
2
0
3
0
0
1
0
0
0
0
5
0
0
0
1
2
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
6
5
2
0
1
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
1
0
0
0
1
1
0
2
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
4
2
1
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
3
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
1
0
2
0
1
1
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
3
0
1
0
0
1
0
0
6
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
3
3
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
3
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
1
0
0
2
0
0
1
0
0
2
1
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
1
2
0
1
0
3
1
0
0
0
0
0
0
0
0
0
1
0
4
0
0
1
2
3
0
0
0
1
0
0
0
0
5
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
3
0
3
0
0
0
0
2
0
0
0
0
0
8
0
0
3
0
0
0
4
2
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
4
0
0
0
3
0
0
0
1
1
0
3
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
2
0
0
1
1
0
2
0
1
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
1
3
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
2
4
0
1
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
3
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
2
2
1
0
0
1
1
0
1
0
0
0
0
0
2
1
1
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
5
0
1
2
1
1
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
3
0
0
1
1
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
5
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
1
0
1
0
1
0
2
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
1
2
2
0
0
1
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
4
0
2
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
4
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
4
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
4
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
2
0
0
0
0
2
0
2
2
1
0
0
0
0
0
0
0
1
1
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
0
0
1
1
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
3
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
2
1
0
1
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
1
0
0
2
1
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
1
2
0
0
0
0
0
2
0
0
3
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
3
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
2
2
0
0
0
0
0
0
2
0
0
0
0
0
4
2
0
0
3
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
1
0
0
0
0
0
0
2
1
0
2
0
0
1
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
2
0
0
0
0
1
0
1
1
0
6
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
3
0
0
0
2
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
2
0
0
0
3
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
1
0
0
0
0
0
1
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
1
1
0
0
2
2
2
0
3
0
2
0
2
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
2
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
1
0
0
0
0
2
2
0
2
0
0
0
0
0
1
0
2
2
0
3
0
0
0
0
0
0
0
0
0
1
0
1
1
0
2
3
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
2
1
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
1
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
1
0
0
1
0
4
0
0
2
0
0
0
0
0
1
2
2
0
0
1
0
0
1
0
2
0
0
0
1
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
3
2
0
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
0
0
0
3
0
0
0
0
0
1
3
0
0
0
0
0
1
1
0
0
1
0
1
2
0
2
0
0
0
2
5
0
0
1
1
0
1
0
0
2
2
0
1
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
3
0
0
3
0
0
0
1
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
1
0
0
2
0
2
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
3
1
0
0
1
3
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
1
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
1
3
1
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
1
0
2
0
0
0
1
0
0
0
1
2
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
3
2
0
0
0
4
2
0
0
2
0
0
2
2
0
0
0
0
3
0
1
0
0
0
0
2
2
0
2
5
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
1
0
1
1
0
0
2
1
0
0
0
0
0
0
0
3
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
5
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
3
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
5
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
2
0
0
0
3
0
0
0
2
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
1
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
2
3
0
0
0
2
1
2
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
1
6
1
1
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
3
0
0
1
0
0
3
1
0
0
1
0
1
0
0
0
0
1
2
0
0
0
1
0
0
1
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
6
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
3
0
0
0
0
3
0
0
0
0
0
3
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
2
0
0
0
2
0
0
1
0
2
1
0
0
1
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
2
0
3
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
2
1
0
0
1
0
0
0
0
0
3
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
2
1
0
0
2
0
0
0
0
0
0
1
7
0
1
0
0
0
1
0
0
3
0
0
0
2
0
1
1
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
1
1
0
0
0
0
0
0
0
0
0
0
2
0
5
1
0
2
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
2
4
0
0
1
2
3
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
2
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
11
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
2
2
0
0
2
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
1
5
0
0
0
0
1
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
1
2
0
0
2
0
0
2
0
0
2
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
2
0
0
2
0
1
0
0
0
2
0
2
0
0
0
1
2
2
0
0
2
0
0
0
0
0
1
0
0
0
2
0
1
0
0
2
0
0
4
0
3
0
0
0
0
0
0
0
1
0
3
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
4
2
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
2
2
0
0
2
0
0
0
0
0
0
2
1
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
3
1
1
1
0
2
0
0
0
1
0
0
0
0
0
2
0
0
1
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
1
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
1
0
0
0
1
0
0
0
1
2
1
0
2
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
3
0
0
0
1
2
0
0
0
0
2
0
1
3
2
2
0
1
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
1
2
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
1
0
0
2
2
0
0
0
1
0
2
0
0
0
0
0
0
0
4
0
1
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
3
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
3
0
1
0
0
3
0
1
0
0
0
0
0
2
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
2
3
0
2
6
0
0
3
0
2
1
0
0
5
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
2
0
0
0
1
0
3
0
1
0
0
0
1
0
0
0
0
3
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
3
1
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
8
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
2
0
0
0
0
0
0
0
0
0
2
4
0
0
2
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
2
2
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
2
0
1
0
0
0
2
2
2
2
2
0
1
0
1
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
12
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
2
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
2
0
2
0
0
1
2
0
2
0
2
0
0
1
2
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
1
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
2
2
0
2
2
0
0
0
0
0
0
0
2
1
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
3
1
1
0
0
0
1
2
1
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
3
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
2
3
0
0
1
1
0
1
1
1
1
0
0
1
0
0
0
1
0
0
0
0
1
0
1
2
0
1
0
0
0
0
0
0
1
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
1
0
0
0
2
1
1
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
4
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
1
2
1
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
4
0
2
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
1
2
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
2
2
2
0
0
0
2
0
0
0
0
2
0
0
2
1
0
0
0
1
2
0
0
0
0
0
0
1
1
0
1
0
5
0
0
0
2
0
0
0
0
0
0
2
0
1
1
0
0
1
0
0
0
2
1
0
2
0
0
0
3
0
0
0
0
0
2
0
1
1
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
1
0
2
1
0
0
0
1
0
2
1
2
0
2
0
0
0
2
0
0
0
0
0
0
0
2
1
3
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
3
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
2
0
0
0
1
2
0
2
2
1
0
0
0
0
0
1
0
0
0
0
0
7
0
0
1
1
0
1
0
0
0
0
0
0
0
2
1
1
1
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
2
0
1
1
0
1
2
0
0
1
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
4
0
0
0
0
3
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
2
2
0
2
1
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
4
2
0
0
3
0
2
0
0
0
2
2
2
3
0
0
0
2
1
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
1
2
3
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
2
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
5
0
0
0
1
2
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
2
0
0
1
0
0
2
2
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
6
0
1
0
0
0
0
0
0
0
0
0
7
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
1
0
1
0
0
2
0
0
0
2
1
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
2
0
0
0
2
1
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
2
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
1
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
2
0
2
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
3
0
0
1
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
3
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
2
0
0
0
2
0
0
2
0
1
0
0
0
1
2
6
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
1
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
2
3
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
3
0
0
0
0
3
0
0
0
2
0
0
1
0
0
0
0
0
3
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
1
0
1
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
3
2
0
2
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
2
0
0
0
2
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
3
0
2
4
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
2
2
2
2
2
0
0
0
0
0
0
0
0
0
5
0
0
0
0
2
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
5
0
0
1
0
2
0
1
0
0
0
2
0
2
0
0
5
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
3
1
0
0
4
0
0
0
0
1
0
0
1
0
0
0
0
0
1
2
0
0
0
3
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
2
0
1
2
0
0
0
2
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
2
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
2
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
2
3
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
3
0
0
1
0
3
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
4
1
3
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
3
0
1
0
0
1
0
0
0
2
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
2
2
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
2
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
2
0
1
0
0
3
0
2
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
2
0
2
0
0
0
1
0
2
0
0
0
0
3
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
2
0
0
0
2
0
2
0
1
2
0
0
0
0
0
1
0
0
2
0
0
0
2
3
0
2
1
0
2
2
0
0
2
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
3
2
0
0
0
0
2
6
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
2
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
1
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
4
0
3
0
0
1
0
0
0
2
0
2
0
0
0
0
1
0
0
4
0
0
0
2
0
0
0
0
2
4
0
2
0
0
2
2
1
0
0
1
0
1
0
0
0
0
0
0
2
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
2
2
1
0
0
2
0
1
1
5
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
1
0
0
0
3
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
3
0
0
1
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
2
1
0
3
0
0
0
1
2
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
1
2
1
0
2
1
2
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
3
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
3
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
2
0
0
1
0
0
0
3
0
0
1
0
0
0
0
0
0
1
2
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
3
0
2
1
2
0
0
0
0
1
1
1
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
1
1
2
0
1
1
0
0
0
0
0
1
0
0
0
0
0
5
0
0
0
0
0
3
1
2
0
0
0
0
0
2
0
0
1
0
0
0
0
3
1
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
4
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
3
0
1
0
2
0
0
0
1
1
0
0
0
0
2
2
0
1
0
0
2
8
0
0
0
4
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
3
1
0
0
0
1
1
1
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
1
2
0
3
0
3
0
1
0
2
0
0
0
0
0
1
0
0
1
2
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
1
0
2
0
2
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
2
0
0
0
0
1
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
3
2
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
1
0
2
0
0
0
0
1
2
0
0
3
0
10
2
0
0
2
0
0
0
1
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
2
1
0
1
0
0
0
0
2
0
1
0
0
0
2
0
1
1
2
0
1
0
1
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
1
0
5
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
1
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
3
0
0
0
1
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
1
2
0
1
2
0
2
0
0
2
0
2
0
0
0
0
1
0
1
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
2
0
1
1
0
3
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
2
0
0
0
0
0
0
0
2
0
5
0
0
0
0
0
0
0
0
1
1
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
2
3
0
0
2
1
0
0
0
0
0
0
1
0
0
1
0
1
0
1
3
0
0
0
0
0
0
0
0
3
0
0
1
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
2
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
3
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
2
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
7
0
0
0
0
0
1
0
2
1
1
0
0
2
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
3
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
2
2
2
2
0
1
0
3
0
0
0
0
0
1
0
0
2
0
2
0
2
0
1
0
2
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
2
1
0
0
1
0
0
1
0
0
1
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
8
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
4
0
0
0
0
0
5
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
2
0
2
1
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
3
2
0
3
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
1
1
5
0
1
9
3
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
3
0
0
2
0
0
0
2
1
0
0
1
0
0
6
0
3
0
0
0
1
1
1
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
1
0
1
0
2
2
0
0
0
0
0
0
2
0
0
1
0
1
0
2
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
2
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
3
2
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
1
1
0
0
2
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
5
0
0
2
0
2
0
0
0
0
0
0
0
0
4
1
2
0
0
0
1
0
0
0
2
1
0
0
0
1
0
0
1
2
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
5
2
0
0
0
0
0
0
0
0
0
0
4
0
0
0
5
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
2
3
0
2
0
3
0
0
1
0
0
1
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
1
2
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
3
1
0
0
2
0
0
0
2
0
1
2
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
3
0
1
0
2
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
2
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
2
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
7
0
1
0
0
0
1
0
2
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
1
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
1
0
0
0
0
0
1
0
1
2
3
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
2
0
3
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
4
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
3
3
1
1
0
1
0
2
0
1
0
0
1
1
0
0
0
2
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
2
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
8
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
4
2
1
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
2
0
2
0
2
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
8
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
2
1
0
0
0
0
1
0
1
0
1
0
1
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
3
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
1
0
0
0
2
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
1
10
0
2
2
0
0
0
0
2
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
3
0
0
2
0
0
1
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
1
1
3
1
4
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
1
1
0
0
1
0
2
0
0
2
0
0
3
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
3
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
2
2
0
0
2
0
3
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
1
0
0
0
1
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
1
1
0
0
1
2
1
0
0
5
0
1
0
6
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
4
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
2
0
1
1
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
2
1
1
0
0
2
0
1
0
2
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
2
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
2
2
2
0
0
1
0
0
0
1
3
0
0
0
0
0
0
1
0
2
0
4
0
0
2
1
3
0
1
3
0
1
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
3
2
1
2
0
1
0
2
0
0
0
0
0
1
0
0
0
0
2
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
1
2
1
0
0
0
0
0
1
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
11
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
2
0
0
0
0
1
0
2
3
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
3
0
0
0
1
0
0
1
0
0
1
0
0
0
0
2
2
0
0
1
1
0
1
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
1
0
1
0
0
0
0
3
0
2
0
0
0
2
0
0
0
0
1
1
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
2
1
0
0
2
0
0
0
0
1
0
0
1
0
1
1
0
0
2
0
1
0
0
0
0
0
0
0
2
5
0
3
0
0
2
0
3
3
0
0
1
0
1
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
3
0
0
1
0
0
1
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
1
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
3
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
2
0
0
2
1
1
0
2
0
2
2
0
0
0
1
0
0
2
1
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
3
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
2
0
0
0
0
1
3
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
2
0
0
0
2
0
0
2
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
1
0
1
0
1
2
0
0
0
2
2
0
1
0
0
0
0
3
4
0
1
0
2
0
1
0
2
0
5
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
11
2
0
0
0
0
0
2
0
0
0
5
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
2
0
0
2
0
0
2
1
3
2
0
5
0
0
1
0
1
0
0
1
0
0
1
0
2
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
7
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
2
0
0
1
0
0
0
0
1
0
0
1
3
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
3
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
6
0
1
0
0
1
1
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
3
0
1
2
3
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
1
0
0
0
1
2
1
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
2
0
1
0
2
0
2
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
1
2
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
3
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
5
0
1
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
6
0
2
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
3
1
1
3
0
0
0
0
3
0
0
0
1
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
1
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
2
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
1
2
4
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
3
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
2
0
0
3
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
7
1
0
0
2
0
1
3
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
1
0
0
0
0
2
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
1
0
0
4
0
2
0
2
0
0
0
0
1
0
0
1
5
0
0
0
0
1
0
0
2
0
2
0
1
1
0
1
0
2
0
0
1
6
1
0
0
0
2
0
0
0
0
0
3
4
0
0
0
0
0
0
0
0
1
2
0
1
0
2
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
2
3
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
2
1
0
0
2
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
3
0
1
0
1
0
0
0
3
1
0
0
0
0
1
0
0
1
0
3
2
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
1
3
2
0
0
0
0
0
0
0
1
1
0
0
0
0
3
2
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
3
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
2
1
0
0
0
0
1
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
3
0
0
1
0
1
0
0
0
3
0
0
0
0
1
0
2
0
0
0
0
0
0
3
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
1
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
1
1
0
0
0
0
2
2
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
1
3
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
6
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
1
0
0
1
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
7
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
6
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
1
2
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
7
0
0
0
0
0
4
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
3
0
2
0
0
4
1
4
0
0
1
3
0
0
1
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
1
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
5
2
0
1
0
1
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
2
1
2
0
0
0
2
0
1
0
1
0
2
0
0
0
0
3
0
0
1
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
2
2
2
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
2
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
3
0
1
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
2
0
0
1
0
2
0
0
1
1
2
0
0
0
1
0
1
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
3
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
1
1
0
1
0
1
0
1
1
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
4
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
2
2
3
0
0
0
0
0
0
0
0
1
0
0
0
0
5
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
2
0
0
0
2
0
0
1
3
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
2
0
0
2
2
3
0
0
0
0
2
0
0
0
0
3
0
0
2
0
2
0
0
0
1
0
0
1
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
2
0
0
0
2
0
0
0
1
2
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
7
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
2
1
1
4
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
3
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
1
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
2
0
2
2
1
1
0
0
0
0
0
0
1
1
0
2
2
1
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
2
0
0
3
0
0
0
5
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
1
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
1
0
0
2
0
0
3
0
1
2
0
0
0
0
2
0
0
0
1
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
2
0
5
0
0
0
1
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
3
0
1
0
0
0
1
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
1
0
0
2
0
0
1
0
0
2
1
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
4
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
4
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
5
2
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
2
0
0
1
0
0
0
2
0
0
1
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
5
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
2
3
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
1
2
6
0
0
0
0
0
2
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
2
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
3
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
3
1
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
2
0
0
3
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
3
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
4
0
0
2
2
3
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
1
1
1
0
0
2
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
3
1
0
0
0
0
1
0
0
1
1
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
4
1
0
0
0
1
0
0
0
0
0
0
2
1
2
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
5
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
1
0
0
1
1
0
2
0
0
0
0
1
0
0
2
2
0
1
0
0
0
2
0
2
0
2
0
0
0
0
2
2
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
1
2
0
0
1
0
0
1
0
0
0
1
2
0
2
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
1
0
1
1
0
0
0
0
0
1
0
0
2
0
1
0
0
0
2
3
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
1
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
2
3
3
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
2
0
0
1
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
2
2
0
1
0
1
0
0
0
0
0
0
3
2
0
2
3
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
3
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
2
0
1
0
0
4
0
0
0
0
2
0
2
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
4
1
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
8
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
4
1
1
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
2
0
1
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
3
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
4
0
0
0
1
1
0
0
0
0
2
0
1
1
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
3
0
0
0
1
0
1
0
2
1
0
0
0
1
1
0
0
0
0
0
0
0
2
1
2
2
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
5
0
0
8
0
0
0
0
0
0
1
0
0
2
0
0
0
2
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
1
2
0
2
0
1
0
0
2
3
0
0
0
1
1
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
1
0
0
0
1
0
1
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
3
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
2
0
0
3
0
1
0
0
0
2
0
0
0
1
0
2
0
0
2
0
2
0
0
0
0
3
0
1
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
1
0
3
0
0
0
1
0
0
2
0
1
2
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
2
2
0
0
0
1
0
0
0
3
0
0
3
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
2
0
0
2
2
1
2
1
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
3
0
1
2
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
2
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
3
0
3
0
1
0
0
0
0
2
3
1
0
0
0
2
0
0
1
0
0
5
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
1
0
2
0
0
0
2
0
2
0
1
0
2
0
2
6
0
1
0
2
2
2
0
0
0
0
0
1
0
0
1
0
0
0
0
2
1
2
1
1
0
0
1
0
1
0
0
2
2
2
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
3
1
0
2
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
3
0
2
3
0
0
3
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
2
0
1
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
6
0
0
0
0
0
0
0
3
0
0
1
0
0
1
0
0
2
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
6
0
0
0
2
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
7
0
0
0
2
0
0
0
0
1
0
0
3
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
2
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
3
0
0
2
0
0
0
2
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
4
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
2
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
2
1
0
0
0
0
4
0
0
0
2
0
0
0
0
2
0
0
2
2
0
1
0
0
0
0
0
0
4
2
0
0
0
0
0
0
0
1
1
0
3
0
0
1
0
0
0
0
0
0
0
1
0
2
1
0
0
0
2
4
1
1
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
7
1
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
2
2
0
0
0
1
3
0
0
1
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
2
0
2
1
2
1
2
0
0
1
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
1
2
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
1
2
2
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
2
0
0
3
0
0
1
1
0
1
0
0
2
0
0
1
0
1
0
0
0
0
0
0
3
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
2
0
1
0
0
1
2
0
1
0
1
2
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
2
0
1
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
3
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
1
0
0
8
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
1
0
1
1
0
0
1
0
1
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
1
0
0
1
1
0
2
3
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
9
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
1
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
2
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
2
0
0
2
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
2
2
1
0
2
0
0
0
0
2
0
2
0
0
1
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
2
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
2
0
0
2
0
0
2
2
0
0
0
0
4
0
3
0
0
1
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
2
0
1
0
0
2
2
0
0
1
0
0
0
0
0
2
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
1
2
0
0
1
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
1
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
1
2
1
1
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
4
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
3
2
2
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
2
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
1
0
0
0
0
0
0
0
1
2
0
1
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
2
0
0
1
2
0
0
1
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
1
6
1
0
0
0
0
1
0
1
0
3
0
0
0
1
0
0
1
2
0
2
3
0
1
0
1
2
0
0
0
0
2
0
0
2
0
0
0
1
0
2
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
3
0
0
1
2
2
0
2
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
2
1
0
2
0
0
0
1
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
3
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
5
0
2
0
2
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
1
0
0
0
2
0
3
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
1
3
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
3
0
0
0
0
1
0
0
2
0
1
0
0
1
2
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
1
0
0
2
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
1
2
0
1
0
3
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
1
1
2
0
0
0
0
1
0
0
0
0
0
2
0
1
0
1
2
0
0
0
1
0
2
0
0
0
1
2
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
2
4
0
2
0
4
1
0
1
0
0
2
0
0
0
0
2
1
0
0
0
0
0
2
0
0
2
0
0
1
2
0
0
1
2
0
0
1
0
0
0
3
0
2
1
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
6
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
1
3
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
1
0
2
0
0
1
0
0
3
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
1
2
2
3
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
8
0
1
2
1
0
0
0
7
0
0
1
1
0
2
0
0
0
0
2
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
5
0
1
0
0
2
0
0
0
0
2
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
2
0
0
0
0
0
4
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
3
0
1
0
0
0
1
0
0
0
0
2
0
3
1
2
3
0
0
0
0
8
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
4
0
0
1
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
3
1
2
0
0
1
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
2
0
2
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
5
0
1
1
0
0
1
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
1
8
0
0
1
0
1
0
4
2
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
4
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
1
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
1
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
1
2
0
0
0
0
0
2
0
0
0
2
2
0
0
2
0
2
0
0
0
0
0
1
0
0
0
6
0
0
2
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
4
0
0
0
0
0
1
1
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
1
0
0
0
0
0
1
0
2
0
1
0
0
0
0
3
0
0
0
1
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
2
1
0
0
2
0
1
0
0
1
0
0
0
2
0
2
1
0
1
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
1
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
4
0
0
5
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
2
0
1
0
1
0
0
0
0
0
0
3
0
2
0
0
0
0
0
1
0
0
0
0
1
3
1
2
0
0
4
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
4
0
0
0
1
0
2
0
0
0
2
1
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
5
0
6
5
0
0
2
0
0
2
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
2
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
7
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
4
0
3
0
0
2
0
2
2
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
3
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
2
0
0
0
0
2
0
0
1
0
1
0
3
0
0
0
1
2
0
0
0
0
0
1
0
0
3
1
3
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
2
0
0
0
2
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
3
0
0
1
0
1
0
2
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
1
0
1
0
0
1
3
3
0
0
0
1
0
0
0
1
0
0
2
4
0
0
2
0
0
0
0
0
0
0
0
1
1
0
4
0
0
0
0
1
1
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
3
2
0
0
0
1
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
1
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
2
0
0
0
0
0
0
2
0
1
1
2
0
1
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
3
1
1
0
0
0
0
0
2
0
0
2
0
6
2
0
0
1
2
0
2
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
2
0
0
3
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
8
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
2
1
0
0
0
0
0
0
2
1
1
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
2
0
1
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
6
1
0
1
0
2
0
0
0
0
0
3
2
4
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
1
2
0
0
1
2
0
0
1
1
0
0
2
0
1
0
0
0
0
8
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
1
0
0
0
1
1
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
2
0
3
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
5
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
2
0
2
1
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
4
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
2
2
0
0
1
1
0
0
0
0
0
2
0
0
1
1
0
2
0
0
1
0
0
2
1
0
1
0
0
1
0
0
1
0
2
1
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
1
2
0
1
52
0
0
0
2
0
2
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
3
3
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
6
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
3
1
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
5
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
2
1
0
0
1
2
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
1
0
0
0
1
0
0
0
2
0
2
0
0
1
0
0
1
3
1
5
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
2
2
0
0
0
0
0
0
2
2
0
0
0
3
2
0
2
0
0
0
0
0
0
1
0
0
0
0
2
2
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
3
1
2
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
3
1
1
0
0
1
0
0
1
1
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
2
3
0
0
0
0
0
0
0
0
0
2
1
4
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
2
0
1
1
0
0
0
2
2
0
0
0
0
4
0
0
1
2
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
2
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
5
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
3
0
1
0
0
2
0
2
0
2
2
1
0
1
0
1
0
1
2
0
1
0
0
0
0
0
1
5
0
0
0
1
0
0
0
0
0
3
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
1
0
0
0
0
2
1
0
0
1
3
0
0
0
0
0
0
0
0
1
0
3
5
0
0
0
0
2
2
0
1
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
1
0
0
0
0
1
3
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
3
0
2
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
4
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
5
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
2
0
2
2
0
1
1
0
0
0
0
1
0
4
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
1
0
3
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
2
2
1
0
0
2
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
4
1
0
3
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
2
0
2
0
0
2
0
0
0
0
4
0
0
1
3
0
0
0
0
0
0
3
1
0
2
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
2
0
0
0
1
0
2
0
0
0
2
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
2
1
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
1
0
1
1
4
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
2
2
0
2
0
0
0
0
0
2
3
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
3
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
4
2
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
2
1
0
1
0
0
1
1
1
0
2
0
2
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
5
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
2
1
0
0
2
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
1
1
2
0
0
0
4
0
0
0
1
0
0
6
0
3
0
0
0
1
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
3
2
2
0
0
2
0
0
0
1
0
0
2
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
3
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
4
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
7
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
3
1
0
1
1
0
0
0
2
2
0
0
0
0
0
3
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
3
0
0
0
0
2
2
0
0
1
0
0
0
2
0
9
0
0
0
2
0
0
0
1
0
0
1
2
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
2
0
0
0
2
0
3
2
0
0
0
0
0
0
0
0
2
1
1
1
0
0
0
2
0
0
0
0
1
0
2
0
2
0
0
0
0
0
2
0
4
2
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
2
0
0
0
1
3
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
3
2
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
4
0
0
0
2
1
0
1
1
0
0
0
2
0
0
0
1
0
0
2
0
0
1
0
0
0
1
0
2
2
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
1
0
2
0
0
0
0
2
2
0
2
0
1
2
0
3
2
1
0
0
1
2
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
2
0
0
1
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
3
2
0
0
2
0
0
0
1
0
1
0
1
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
1
1
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
2
0
1
0
0
2
1
0
0
0
0
0
1
0
1
1
0
0
2
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
3
1
2
0
0
2
2
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
2
1
0
0
0
2
2
0
0
0
1
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
1
0
0
1
2
0
2
0
0
0
0
0
0
5
0
2
2
0
2
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
1
2
0
0
0
0
2
2
1
0
0
0
1
2
0
0
0
0
5
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
2
1
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
1
2
3
0
2
0
0
1
0
0
0
1
0
1
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
2
1
1
0
0
0
2
1
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
2
0
1
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
2
0
0
0
0
0
1
0
0
1
0
0
2
1
0
0
1
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
2
0
1
1
0
0
0
0
0
1
5
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
1
2
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
1
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
2
2
2
0
1
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
4
0
2
0
0
1
1
0
1
0
0
3
2
0
0
0
0
0
0
0
0
0
0
4
0
0
1
1
2
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
4
1
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
1
1
0
1
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
1
0
1
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
1
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
1
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
5
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
2
2
1
0
1
0
0
0
0
0
0
2
0
1
0
2
1
0
0
3
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
3
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
2
0
0
5
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
2
1
0
1
1
0
0
0
2
2
0
1
3
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
1
0
0
2
0
0
1
0
1
0
0
0
1
2
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
1
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
9
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
4
1
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
4
0
3
0
0
0
0
0
0
0
1
4
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
1
3
0
0
0
0
3
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
2
0
0
1
1
0
0
1
0
0
8
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
1
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
2
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
4
2
2
0
3
0
0
0
1
0
2
1
0
0
0
0
1
1
2
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
6
0
0
0
1
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
1
0
0
2
0
2
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
6
0
0
3
0
2
2
0
0
0
0
0
0
0
3
1
0
0
0
2
0
1
0
1
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
3
0
0
2
0
0
2
0
0
0
0
4
1
0
1
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
4
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
1
1
2
1
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
1
2
0
0
0
2
0
1
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
2
0
0
2
0
0
2
0
1
0
0
0
2
0
0
0
0
0
2
2
0
1
0
0
0
2
0
0
0
2
2
9
0
0
0
0
0
2
6
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
2
0
0
2
0
0
0
2
0
1
0
0
0
0
1
0
0
4
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
6
0
0
1
0
0
2
2
2
0
0
0
0
2
1
0
0
0
0
4
0
0
0
1
0
0
2
2
0
0
0
2
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
7
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
3
0
0
1
1
1
0
0
0
0
0
2
0
0
1
2
0
0
0
0
4
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
1
0
2
2
0
0
0
2
0
0
0
0
1
1
0
0
0
0
1
2
2
0
0
0
0
2
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
1
0
0
0
2
1
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
1
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
2
1
0
0
0
1
1
0
1
0
0
2
0
2
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
2
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
2
1
2
0
1
0
0
0
3
0
1
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
3
0
2
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
1
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
3
3
3
0
2
0
3
0
1
0
0
0
0
6
0
0
0
0
0
3
0
0
0
3
0
1
0
0
0
0
0
0
1
2
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
1
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
2
1
0
2
0
0
1
0
0
0
0
4
0
0
2
0
0
0
6
3
2
0
0
0
0
0
0
1
0
1
1
2
0
4
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
3
0
0
0
0
2
0
0
1
1
5
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
1
0
2
0
0
0
1
0
0
0
0
2
3
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
6
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
2
1
2
4
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
4
2
0
1
0
0
0
0
0
1
0
0
0
0
3
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
7
1
1
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
2
1
0
0
1
0
0
0
1
0
1
0
0
0
2
0
0
0
0
1
0
0
2
1
0
1
0
1
1
1
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
1
0
0
0
0
1
0
0
0
0
3
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
4
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
1
1
0
0
0
3
0
0
4
0
0
1
0
0
1
0
0
0
2
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
6
2
0
1
0
2
0
0
0
0
1
0
0
0
1
1
1
0
0
0
3
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
2
2
0
2
2
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
2
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
3
2
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
1
0
1
0
0
3
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
1
1
0
0
0
0
0
1
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
3
0
0
0
2
3
0
0
0
0
2
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
3
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
2
2
0
2
0
0
0
0
4
2
0
0
0
0
0
0
0
0
1
0
1
3
0
3
0
0
0
0
0
0
3
4
0
0
0
0
0
2
0
3
2
0
3
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
1
4
1
0
2
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
2
2
1
3
2
0
2
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
2
0
0
2
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
1
1
2
3
2
0
0
0
1
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
7
0
1
0
0
0
1
0
1
0
1
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
1
1
1
0
1
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
2
3
0
3
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
2
0
2
0
2
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
2
0
0
0
0
2
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
2
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
2
0
0
0
0
0
2
1
0
0
0
2
0
0
1
3
1
0
0
0
1
0
0
3
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
1
1
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
7
0
0
0
1
2
0
1
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
6
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
2
0
0
0
1
0
3
0
2
0
0
1
0
2
1
2
4
0
0
1
3
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
6
0
0
2
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
1
0
0
3
0
0
2
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
1
0
0
0
1
1
0
2
0
0
0
0
0
0
1
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
3
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
2
0
1
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
2
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
3
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
2
0
0
5
0
0
0
0
0
0
0
0
4
0
0
2
0
1
0
0
5
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
1
0
0
0
0
2
0
2
0
2
0
2
0
3
0
0
0
1
0
0
2
0
2
1
0
4
0
0
0
0
0
1
0
0
2
1
0
3
0
0
0
1
0
0
0
0
2
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
5
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
2
0
0
1
0
0
0
0
2
0
2
1
0
0
0
0
2
0
0
0
1
0
0
2
0
2
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
1
2
0
1
0
0
3
3
0
1
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
2
0
0
0
11
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
4
0
0
1
7
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
1
1
0
1
0
0
3
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
4
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
2
3
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
2
2
1
0
0
2
0
0
4
0
0
0
0
3
0
0
1
0
2
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
2
1
0
0
2
2
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
2
2
1
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
2
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
7
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
3
0
3
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
1
1
0
0
0
2
0
1
0
0
0
0
0
5
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
1
2
0
0
0
0
3
0
0
0
0
0
0
0
1
0
2
0
0
0
8
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
2
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
1
0
3
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
6
0
1
0
0
0
1
0
2
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
2
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
2
5
0
0
0
0
0
0
0
0
0
2
2
2
2
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
2
0
4
0
0
1
0
2
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
1
2
0
0
1
2
0
1
1
0
0
0
1
0
1
0
0
0
1
0
0
0
1
1
2
1
0
9
0
3
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
2
0
2
0
2
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
1
0
2
1
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
2
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
2
0
0
0
2
0
0
0
1
0
0
0
7
0
1
0
0
2
0
0
0
0
0
2
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
2
2
0
0
0
0
0
0
2
0
1
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
1
0
0
2
0
0
2
0
0
0
0
2
0
2
0
1
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
2
1
0
0
1
0
0
1
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
2
2
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
3
0
0
4
0
2
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
3
0
2
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
3
0
10
0
5
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
1
2
1
0
0
1
0
0
1
2
0
0
0
3
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
3
0
0
0
0
0
2
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
1
0
0
2
0
1
0
0
0
0
0
2
0
0
1
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
4
2
2
0
0
2
0
0
1
0
0
0
2
2
5
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
1
0
1
0
0
2
3
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
3
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
3
0
0
2
0
0
2
0
0
1
0
2
1
0
0
2
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
1
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
1
0
0
0
0
0
12
0
0
0
4
0
0
2
0
1
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
3
0
0
0
0
1
0
0
0
2
1
0
0
2
2
0
0
0
2
0
0
0
0
0
4
0
1
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
2
1
0
1
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
1
2
0
0
0
0
0
6
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
1
0
1
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
5
0
1
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
4
0
6
1
1
0
0
0
0
0
2
0
1
2
0
0
0
2
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
4
0
2
0
0
1
0
2
1
0
1
0
0
1
2
0
0
2
0
0
0
0
2
4
2
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
1
1
0
0
0
2
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
3
0
0
2
0
0
4
2
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
1
4
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
5
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
2
0
6
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
2
0
0
0
0
1
0
0
1
0
0
0
0
1
0
2
2
0
0
0
1
0
0
0
0
0
0
3
1
0
0
1
2
0
2
0
2
0
0
0
0
2
0
1
0
2
0
0
0
0
2
0
3
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
1
0
0
1
1
0
2
0
1
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
1
0
0
0
0
0
2
3
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
7
1
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
1
3
0
2
0
0
0
0
0
0
0
0
0
2
3
0
4
1
7
0
0
0
0
1
2
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
2
0
2
0
2
0
0
0
2
0
2
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
3
1
0
2
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
2
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
3
0
0
1
3
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
1
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
1
0
1
0
0
0
2
0
0
1
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
1
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
3
3
0
3
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
1
1
0
0
0
3
2
2
0
4
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
2
0
2
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
2
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
5
1
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
2
0
0
0
0
0
0
6
0
0
0
0
0
0
1
0
0
2
0
0
1
2
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
2
1
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
3
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
2
0
1
0
0
0
0
3
2
0
0
0
0
0
0
6
0
2
2
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
3
0
0
2
0
0
1
1
0
2
2
3
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
1
0
0
0
1
1
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
1
1
1
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
3
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
4
0
0
0
5
1
0
1
0
0
0
0
1
0
1
0
0
0
0
3
0
1
1
0
0
0
3
0
2
0
0
0
0
0
0
2
0
0
1
1
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
1
0
0
2
0
0
0
0
0
0
1
0
2
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
3
1
0
0
0
0
0
0
1
0
0
10
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
2
0
2
0
0
2
1
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
3
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
3
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
1
2
0
0
0
0
1
0
2
0
0
4
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
5
0
0
0
0
0
2
2
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
5
2
0
0
0
0
0
0
0
0
2
0
4
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
1
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
2
0
1
1
0
1
0
1
0
0
0
2
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
12
0
0
0
0
4
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
5
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
1
1
0
0
0
1
2
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
2
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
5
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
3
0
2
2
0
0
1
0
0
0
0
0
0
0
1
1
1
2
2
3
0
2
0
2
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
2
2
1
0
2
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
2
2
0
1
0
0
0
0
0
4
1
0
0
1
2
2
0
0
0
0
0
2
0
2
4
0
0
0
1
0
0
2
0
0
0
0
1
2
0
0
2
3
0
0
2
1
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
2
2
0
0
0
0
0
1
0
0
1
0
0
4
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
1
2
1
0
2
1
0
0
1
0
0
0
0
1
2
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
1
1
1
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
2
0
0
5
1
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
3
0
1
1
0
0
0
0
2
0
0
2
0
2
0
2
2
1
0
0
0
0
1
2
0
0
1
0
0
0
0
0
3
0
0
0
5
0
1
1
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
1
0
0
0
0
2
1
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
2
1
0
0
9
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
3
0
0
0
3
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
2
0
0
1
0
0
1
0
0
0
2
0
0
2
0
0
0
1
1
2
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
2
0
0
1
0
1
0
0
0
1
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
3
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
6
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
5
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
3
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
6
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
13
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
3
0
4
1
0
0
0
0
0
0
0
4
2
0
0
0
0
0
1
0
0
3
0
0
6
0
0
0
1
0
2
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
2
0
2
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
2
0
0
0
2
0
1
2
0
3
0
1
0
0
0
0
0
2
0
0
3
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
2
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
8
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
3
2
2
2
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
1
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
12
0
0
0
2
0
2
0
0
1
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
3
0
0
2
0
0
0
0
1
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
4
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
2
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
34
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
1
0
0
0
0
2
2
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
1
2
2
0
1
2
1
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
2
0
0
1
0
1
0
0
1
2
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
3
0
0
0
1
0
0
0
1
0
0
1
1
1
2
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
6
0
2
0
0
0
0
0
2
1
0
0
0
0
4
0
0
2
2
0
0
0
0
0
1
0
1
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
2
0
0
0
2
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
2
0
0
2
2
0
2
0
2
0
0
3
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
2
0
0
0
1
0
2
1
2
0
0
2
0
0
0
1
0
2
0
0
0
1
0
1
0
1
0
0
0
0
1
4
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
1
0
0
2
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
5
1
0
0
0
1
0
0
0
0
0
0
0
1
3
0
0
0
1
1
0
0
1
2
0
2
0
0
1
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
2
1
0
1
0
0
2
2
0
0
2
1
2
0
0
1
0
1
3
0
0
0
0
1
0
0
0
0
2
1
0
1
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
9
1
0
0
0
0
0
2
0
0
0
2
0
3
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
2
0
2
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
1
0
1
4
0
0
0
0
0
0
0
2
1
0
0
0
3
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
1
2
1
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
2
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
1
0
0
1
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
1
1
2
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
3
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
1
0
2
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
2
1
0
0
0
1
0
0
0
0
1
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
3
0
0
2
1
0
0
0
3
1
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
1
1
0
0
0
1
1
0
0
2
0
2
0
1
1
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
1
0
5
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
3
2
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
3
0
0
1
0
0
3
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
4
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
2
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
2
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
1
0
1
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
3
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
1
0
0
0
2
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
3
0
2
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
1
0
2
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
2
0
0
2
0
1
0
2
0
5
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
3
2
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
1
0
1
1
0
0
0
0
0
2
1
0
0
1
0
2
0
2
2
0
0
0
0
2
0
3
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
1
0
0
0
1
0
0
1
0
0
1
0
0
3
1
0
1
4
0
1
1
0
3
0
0
0
1
1
3
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
1
2
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
2
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
1
0
3
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
4
0
0
2
0
1
2
1
0
1
0
0
1
2
0
0
0
1
0
0
2
2
0
0
3
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
3
2
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
3
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
3
1
0
0
2
0
2
0
0
1
0
0
0
2
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
2
3
0
2
0
2
0
0
0
1
0
0
0
3
0
0
0
0
1
2
2
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
2
1
0
0
3
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
1
1
0
0
1
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
3
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
2
0
0
2
0
2
0
0
0
4
0
0
0
0
1
0
0
0
0
0
3
1
0
0
0
0
2
0
2
0
0
0
1
0
0
2
0
2
0
2
0
0
0
0
1
0
0
0
0
0
4
1
0
0
0
0
0
0
2
0
0
0
0
2
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
2
0
0
0
0
0
0
0
0
3
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
2
0
0
0
0
4
0
0
0
0
2
0
1
0
0
1
0
2
0
0
0
0
2
0
0
2
0
0
3
0
0
2
2
0
0
2
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
3
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
2
0
0
2
2
0
0
0
3
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
2
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
1
3
1
0
1
0
0
0
2
0
1
2
0
0
2
3
2
0
0
1
2
1
0
2
2
0
0
1
0
0
1
0
0
0
2
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
5
1
0
0
0
0
1
0
0
0
3
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
3
0
1
2
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
3
2
0
0
2
0
1
0
0
2
2
2
2
0
1
1
2
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
3
2
0
0
1
0
2
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
2
2
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
1
0
0
0
2
0
1
0
0
2
0
0
0
1
0
0
2
1
6
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
2
1
1
0
0
0
1
1
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
3
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
2
1
0
2
0
0
1
2
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
1
2
0
0
2
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
7
0
0
0
2
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
1
0
1
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
2
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
1
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
3
1
2
2
0
1
1
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
3
0
0
0
0
2
0
1
0
0
0
0
0
1
2
4
0
0
0
2
2
0
0
0
0
2
0
3
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
3
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
3
0
0
4
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
7
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
4
1
0
0
0
1
0
0
0
0
0
0
2
2
0
0
1
0
0
1
0
0
2
0
0
1
0
2
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
4
3
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
1
0
2
0
0
1
0
0
1
0
0
0
2
1
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
1
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
3
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
1
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
3
2
0
0
1
2
0
2
0
1
1
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
2
0
0
2
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
2
1
0
0
11
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
1
0
1
0
3
1
0
0
0
1
0
2
0
0
0
0
1
0
2
0
2
0
1
1
3
2
2
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
2
4
2
0
0
0
0
0
0
0
0
0
0
2
1
0
2
1
0
0
0
2
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
2
1
0
0
0
2
3
0
2
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
3
0
1
2
0
0
1
0
0
0
0
1
3
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
3
0
2
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
1
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
8
0
0
5
0
0
1
2
0
2
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
5
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
1
0
0
0
2
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
4
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
5
1
0
0
0
4
3
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
1
0
0
0
4
0
0
0
0
0
0
1
3
2
1
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
18
1
0
1
0
0
1
0
0
0
0
0
0
0
2
2
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
1
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
1
2
0
0
0
0
2
0
4
1
0
0
0
0
0
0
1
0
0
0
1
2
1
0
0
1
0
0
0
0
1
0
1
0
0
0
2
2
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
3
1
0
0
5
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
3
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
7
0
0
0
2
0
0
4
2
0
1
2
1
0
0
2
0
0
0
2
1
1
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
3
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
1
2
2
1
0
1
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
3
2
0
0
0
2
0
0
2
0
0
0
0
2
1
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
1
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
1
4
2
0
0
2
1
2
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
2
0
0
1
2
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
2
1
0
3
0
2
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
1
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
4
0
0
2
0
0
1
0
2
0
2
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
3
1
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
2
1
0
2
0
0
4
1
0
0
0
1
0
0
0
2
0
0
0
2
0
0
1
0
1
0
0
2
2
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
2
0
4
0
1
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
1
1
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
4
0
0
2
0
1
2
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
8
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
4
3
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
5
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
5
0
0
0
0
0
0
0
0
0
0
3
0
0
3
1
0
0
1
0
0
0
0
2
2
2
0
1
2
2
1
0
0
0
1
0
0
0
0
2
2
2
0
1
2
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
2
1
0
2
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
1
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
6
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
2
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
2
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
3
0
0
0
0
0
1
3
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
1
7
0
0
0
1
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
3
0
2
0
0
1
0
3
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
6
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
2
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
2
2
1
0
0
0
0
0
0
1
0
2
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
1
0
2
0
0
0
0
1
0
0
1
0
2
0
0
0
2
2
1
2
2
2
0
1
2
0
2
0
0
2
1
0
2
0
0
0
1
2
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
4
1
0
4
0
0
0
0
0
1
0
0
1
6
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
1
2
1
2
0
1
5
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
3
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
5
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
1
1
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
2
0
3
0
0
0
0
0
1
0
0
0
0
0
1
0
0
5
2
0
0
0
1
0
0
2
0
0
1
2
0
0
0
0
1
0
0
1
4
0
1
0
2
0
1
0
0
2
0
0
0
0
0
1
1
0
1
0
0
0
1
0
2
0
2
0
0
2
0
0
2
0
0
2
1
0
0
0
0
0
2
0
2
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
1
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
1
2
0
1
2
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
1
0
0
0
2
2
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
1
1
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
2
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
1
2
0
2
2
1
2
0
0
0
0
2
0
0
1
3
2
2
1
1
2
0
2
0
3
0
2
0
0
0
0
0
0
0
0
0
3
0
2
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
1
2
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
4
0
0
6
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
4
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
1
0
1
0
2
6
1
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
1
2
1
0
0
2
0
0
0
1
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
1
2
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
3
0
1
0
0
2
5
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
2
2
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
2
0
0
1
3
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
2
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
3
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
6
0
0
2
2
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
3
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
2
1
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
3
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
3
0
0
1
0
2
0
4
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
1
1
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
2
1
2
0
2
2
2
2
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
2
0
0
1
0
0
1
1
0
3
2
0
0
0
0
0
2
0
0
2
0
0
1
0
2
0
2
2
0
4
0
0
1
0
0
0
0
0
0
0
1
0
0
2
1
0
1
0
0
0
0
0
1
0
0
0
1
0
2
0
0
1
0
0
0
1
0
3
0
3
0
0
0
0
0
1
0
2
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
2
0
1
12
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
3
0
0
0
0
1
0
1
0
1
2
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
1
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
2
0
0
1
0
0
0
0
0
0
0
2
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
2
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
5
0
0
1
1
0
0
0
1
0
1
2
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
3
0
2
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
4
0
2
0
0
1
0
3
0
0
1
0
0
1
0
2
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
2
2
0
1
1
0
2
0
0
0
3
2
0
0
1
2
0
1
0
0
0
0
0
2
0
0
0
2
2
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
6
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
5
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
2
1
3
0
2
0
0
6
0
0
0
0
0
1
2
0
0
0
3
0
1
0
0
0
0
0
0
0
6
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
1
3
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
2
0
2
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
3
1
0
0
1
0
0
2
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
1
0
0
0
2
0
2
1
0
1
0
1
0
0
1
0
0
2
2
0
0
0
2
1
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
3
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
1
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
1
2
0
0
0
0
0
2
0
0
1
0
0
0
2
1
0
0
0
0
0
3
0
0
0
0
1
0
2
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
1
0
0
0
2
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
3
0
1
0
2
0
0
2
1
1
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
2
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
2
1
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
2
0
2
0
9
2
0
0
0
1
0
3
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
1
1
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
2
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
4
2
0
1
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
2
2
0
0
0
0
0
2
2
3
1
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
2
1
1
1
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
2
0
8
0
0
0
0
0
0
0
4
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
2
0
1
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
2
0
2
0
1
5
0
2
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
1
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
2
2
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
2
0
1
1
0
0
5
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
1
0
2
0
1
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
4
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
1
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
1
2
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
1
5
0
0
0
0
0
0
0
0
0
0
1
1
1
1
2
2
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
6
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
2
3
0
0
4
0
0
0
0
1
2
0
0
2
2
0
0
1
0
1
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
4
1
0
0
0
3
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
2
0
0
2
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
2
1
1
0
0
1
1
2
0
0
0
2
0
0
0
0
0
0
0
3
2
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
5
0
0
0
0
0
0
2
3
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
6
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
1
1
0
2
1
0
0
0
0
0
1
0
1
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
4
0
0
0
0
2
1
1
0
0
0
0
0
0
2
0
4
0
0
0
0
0
2
0
1
0
0
0
0
2
2
3
2
0
0
0
0
0
0
0
2
1
2
0
1
0
0
0
0
0
2
0
1
0
0
3
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
6
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
3
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
2
0
0
0
2
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
3
0
2
0
1
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
2
0
0
1
0
0
3
2
0
3
1
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
1
2
0
2
0
0
2
0
0
0
0
0
2
1
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
1
0
0
0
0
1
2
0
1
0
1
0
0
0
0
0
2
0
0
0
3
0
0
1
0
2
0
1
0
2
0
0
1
0
0
2
0
0
2
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
5
1
0
0
0
0
2
0
1
0
0
0
1
0
0
2
0
0
1
0
0
2
1
1
0
0
0
1
0
2
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
2
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
4
0
0
0
2
1
0
2
0
0
1
0
0
2
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
2
1
2
0
0
0
0
0
3
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
2
2
0
1
0
0
0
0
2
0
0
4
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
3
2
0
0
2
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
4
2
3
0
0
0
0
0
0
3
1
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
1
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
1
0
0
0
0
1
1
1
0
2
0
1
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
3
0
1
3
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
1
2
1
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
2
1
0
2
0
3
0
2
0
0
0
0
1
0
0
1
1
2
0
3
3
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
6
2
0
0
3
0
1
0
0
0
0
1
0
2
1
2
0
1
0
2
1
0
1
1
0
0
0
0
2
0
0
1
0
0
2
0
2
0
0
0
0
0
6
0
0
0
1
2
0
0
0
0
0
0
1
0
1
1
0
0
3
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
1
0
0
0
1
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
2
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
1
0
2
3
0
0
0
2
0
0
0
0
1
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
3
2
0
0
0
2
2
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
1
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
5
0
1
0
0
2
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
1
0
1
2
0
1
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
4
2
1
0
2
0
0
1
2
0
0
0
2
0
0
0
0
0
0
1
1
2
0
0
0
3
0
0
0
1
1
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
1
3
0
2
0
0
0
0
0
3
0
2
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
4
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
2
0
0
0
2
0
0
1
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
3
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
7
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
1
3
1
0
1
0
3
1
2
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
1
0
0
3
0
1
1
0
0
0
0
0
1
1
4
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
1
0
0
0
0
0
0
1
0
2
1
3
0
0
0
0
0
2
0
0
0
0
2
1
0
0
1
1
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
2
1
0
0
0
2
0
0
0
1
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
6
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
2
0
0
3
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
3
0
2
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
1
5
2
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
2
1
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
1
1
1
0
1
0
2
1
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
4
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
8
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
2
4
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
2
0
0
2
2
1
0
0
0
0
2
0
1
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
4
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
3
0
2
0
0
0
0
1
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
1
1
2
1
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
2
1
2
0
1
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
2
1
0
0
1
0
2
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
3
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
3
0
2
1
0
1
0
0
1
1
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
2
1
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
4
1
0
0
1
0
0
1
0
0
2
2
2
2
0
0
0
0
0
0
0
0
0
0
2
0
3
0
1
0
2
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
1
0
0
0
0
0
3
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
1
3
0
2
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
2
1
0
0
0
2
0
0
1
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
1
1
3
1
0
2
0
7
2
0
0
0
1
0
1
0
0
0
0
0
3
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
1
1
0
2
1
0
0
0
0
0
1
0
0
3
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
1
0
3
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
2
0
1
1
0
0
0
0
2
1
2
0
0
0
1
0
3
0
0
2
1
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
2
0
2
0
0
4
0
0
2
0
0
3
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
1
0
0
1
0
0
0
2
2
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
4
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
2
1
0
0
1
0
0
0
0
0
0
1
0
0
5
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
3
2
4
0
0
0
0
0
2
0
1
0
0
0
0
1
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
2
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
3
1
0
0
0
0
0
2
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
3
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
2
0
9
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
2
0
0
2
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
2
1
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
5
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
4
0
1
0
1
2
0
0
0
0
4
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
4
0
1
0
0
2
1
0
0
0
0
0
0
0
1
0
1
2
1
1
0
0
0
0
0
0
0
0
2
0
0
0
1
2
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
5
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
5
2
0
0
0
1
7
3
2
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
1
1
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
2
1
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
2
2
0
1
0
0
0
0
2
2
0
0
0
2
2
0
0
1
0
0
0
0
4
0
0
0
2
1
0
0
0
0
0
2
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
2
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
1
0
0
0
1
2
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
2
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
2
0
2
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
5
0
0
0
0
0
1
0
0
0
1
0
2
0
2
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
2
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
1
0
0
0
4
1
0
0
0
2
0
1
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
3
0
3
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
2
2
0
0
0
0
3
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
1
0
0
1
2
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
2
0
2
1
3
2
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
4
0
1
0
0
1
0
0
0
0
1
0
1
0
0
3
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
2
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
3
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
1
1
0
0
0
0
0
2
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
5
0
0
2
0
1
2
2
0
1
2
1
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
3
0
0
0
0
1
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
1
2
0
0
1
0
0
0
2
1
0
0
2
0
0
4
4
0
0
1
2
0
0
1
0
0
2
0
2
0
0
1
1
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
1
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
1
1
0
2
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
2
1
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
2
2
0
1
2
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
4
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
3
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
2
1
0
1
0
0
0
4
2
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
7
1
2
0
0
1
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
6
1
1
0
2
0
2
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
2
2
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
1
1
2
0
1
1
0
0
0
0
0
9
2
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
1
1
0
1
0
0
2
1
0
0
0
2
1
1
0
0
0
0
0
1
0
1
0
1
0
0
2
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
2
1
2
0
0
0
2
0
1
0
0
0
0
1
0
3
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
4
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
1
0
0
0
0
15
0
0
0
0
2
0
2
1
0
0
0
0
5
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
1
0
3
1
0
1
3
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
1
0
1
2
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
2
1
0
0
0
0
0
5
0
0
2
0
1
1
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
3
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
2
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
3
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
4
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
1
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
3
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
1
0
2
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
2
1
0
1
0
0
0
1
0
0
0
2
0
0
0
2
0
0
2
0
1
2
0
1
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
2
0
0
2
11
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
2
2
0
4
2
1
0
0
1
0
0
2
0
0
1
0
0
1
0
4
1
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
2
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
1
0
0
0
2
2
1
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
1
0
0
0
0
2
0
0
1
0
2
0
0
0
2
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
9
0
0
1
0
1
2
0
2
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
3
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
2
3
0
1
0
0
0
1
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
5
2
2
0
1
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
2
0
1
0
0
2
0
1
0
0
0
1
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
2
1
1
0
0
0
0
0
0
2
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
1
0
0
1
0
3
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
3
0
1
0
0
0
0
0
2
0
1
2
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
3
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
2
3
2
0
0
0
0
1
2
1
0
2
2
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
1
1
0
0
2
0
1
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
7
2
1
0
2
0
0
0
0
0
1
0
0
3
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
5
0
0
0
0
0
0
1
0
0
0
0
3
0
0
2
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
2
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
2
0
0
0
1
0
0
2
1
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
2
1
0
3
1
0
0
0
0
1
0
0
1
0
1
2
1
0
0
2
0
0
1
0
1
2
0
0
0
1
0
1
0
0
0
0
2
2
0
3
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
2
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
1
0
2
0
0
0
1
0
0
2
0
0
0
0
2
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
1
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
3
0
2
0
1
0
0
0
1
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
2
1
1
0
1
0
0
0
0
0
0
5
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
2
0
1
0
0
2
3
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
2
0
2
0
1
0
5
2
0
0
1
0
0
0
0
0
2
1
0
2
0
0
2
0
0
0
0
0
2
3
2
2
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
2
1
2
0
2
2
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
3
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
2
2
0
1
0
0
1
0
1
0
0
3
0
0
0
0
0
1
2
0
1
1
0
3
0
1
0
0
1
0
0
0
3
0
1
0
0
0
2
0
0
2
0
1
1
2
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
3
0
4
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
3
0
0
0
0
0
1
0
1
3
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
6
0
0
0
1
1
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
2
0
0
3
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
1
0
0
1
8
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
1
0
2
0
0
2
0
0
0
2
0
2
2
0
2
2
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
2
0
0
1
2
1
0
0
0
1
1
2
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
3
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
6
1
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
2
3
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
1
0
1
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
4
0
0
1
0
0
0
1
0
0
1
0
1
2
0
0
2
0
0
4
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
2
2
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
1
3
1
2
0
0
0
0
0
2
0
1
1
0
0
2
2
3
0
0
1
2
0
0
0
0
0
0
3
2
1
0
0
0
0
0
0
3
0
2
0
0
0
0
0
1
2
2
0
0
0
0
1
0
0
0
0
1
2
1
2
0
0
0
2
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
2
0
0
1
2
0
0
0
0
0
0
2
0
0
1
1
0
1
0
1
1
0
0
0
2
1
0
0
0
1
3
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
2
3
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
4
0
2
0
1
0
0
0
2
0
2
0
0
0
0
0
3
0
0
1
1
0
0
0
1
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
3
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
2
1
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
1
0
0
0
0
0
0
0
0
1
0
1
3
0
2
0
0
0
0
0
0
0
2
1
4
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
1
0
2
0
0
1
0
0
0
0
0
2
0
2
2
0
0
0
0
1
1
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
5
0
0
0
0
0
0
2
0
2
1
2
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
3
2
0
0
0
3
1
2
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
2
0
3
2
2
1
0
0
1
0
2
0
0
0
2
0
1
0
0
0
0
2
1
4
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
2
0
2
0
0
1
2
0
0
1
1
0
0
3
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
3
0
1
2
2
3
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
1
0
0
0
0
2
0
4
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
5
0
0
0
2
0
0
0
2
0
0
0
1
0
0
1
1
0
0
0
0
0
3
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
2
0
0
1
4
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
2
0
0
0
2
0
1
3
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
7
0
0
0
0
0
0
0
0
4
0
1
0
3
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
1
2
2
3
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
1
0
0
0
2
0
1
0
0
0
0
2
1
0
2
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
1
0
1
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
2
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
3
0
0
1
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
5
0
0
2
1
0
2
0
1
0
0
0
0
0
2
0
0
0
2
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
4
1
2
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
2
0
1
1
0
0
1
0
5
0
0
3
2
0
0
0
0
0
0
0
0
0
8
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
2
0
0
1
0
6
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
2
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
1
0
0
2
1
1
0
0
1
0
0
2
0
1
0
0
0
0
4
1
0
0
1
0
0
0
0
0
7
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
4
1
1
1
0
2
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
3
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
2
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
5
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
3
3
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
1
2
2
1
1
0
4
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
5
0
0
1
0
0
0
0
2
2
1
2
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
2
0
0
0
1
0
1
1
0
0
0
0
4
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
4
0
0
0
2
0
0
2
1
2
0
1
1
2
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
3
0
0
0
0
0
0
0
0
0
2
0
2
2
0
2
1
0
2
0
0
0
0
0
2
1
1
0
0
0
0
0
0
2
0
3
0
1
1
1
0
0
2
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
3
2
2
0
0
1
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
6
0
1
0
0
0
1
0
0
0
0
0
1
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
2
0
1
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
1
2
1
0
0
1
0
1
0
1
0
0
0
0
0
2
0
0
2
2
0
0
2
0
2
0
0
0
0
2
0
0
0
0
3
1
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
1
0
1
0
0
0
0
0
0
0
0
4
2
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
4
0
0
1
2
2
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
2
3
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
2
3
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
3
0
1
0
0
0
0
0
0
2
2
1
0
0
0
4
0
0
0
0
0
0
0
0
0
2
0
1
0
3
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
2
0
0
0
0
8
0
0
0
0
0
1
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
4
2
0
0
0
0
0
0
0
1
0
4
0
2
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
1
2
0
1
0
4
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
1
1
0
0
0
3
0
0
1
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
7
0
0
2
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
4
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
5
0
2
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
3
2
0
2
0
0
0
1
0
2
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
3
0
0
0
1
2
0
0
0
0
2
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
1
0
3
0
2
2
0
0
1
2
0
0
0
2
0
0
0
3
0
2
0
0
2
3
0
0
0
0
0
1
1
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
2
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
1
1
0
0
1
0
0
0
2
2
0
0
0
2
0
0
0
2
0
0
0
0
0
1
1
1
0
0
1
3
2
1
0
0
0
0
0
1
0
0
0
0
0
1
0
4
0
0
0
0
1
2
0
0
2
0
2
0
0
1
0
0
0
0
0
3
1
0
0
0
0
1
2
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
3
0
0
0
1
2
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
3
0
0
2
1
0
0
0
1
0
0
0
2
0
0
0
0
5
0
0
1
0
1
0
3
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
1
0
1
2
0
4
0
1
0
0
0
0
0
0
0
0
2
1
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
4
2
1
0
0
0
2
1
0
1
0
0
3
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
3
0
2
0
0
2
0
0
0
1
0
0
0
2
0
0
0
1
2
3
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
1
0
0
2
1
2
0
1
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
1
1
2
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
5
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
6
0
0
2
0
2
0
2
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
3
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
2
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
3
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
3
0
0
0
2
0
9
0
0
0
0
4
0
0
0
3
0
0
0
2
0
0
0
0
0
0
1
0
1
4
0
1
1
0
1
1
0
0
0
2
0
1
2
0
0
1
2
1
1
0
1
1
0
0
0
2
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
9
0
0
0
1
0
0
0
0
1
2
1
0
2
4
0
1
3
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
2
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
3
0
2
0
1
0
1
0
1
0
0
0
1
0
1
1
0
1
4
0
0
0
0
1
0
0
0
1
1
1
0
0
2
0
1
1
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
1
2
2
0
0
3
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
1
1
1
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
2
3
0
0
1
0
0
0
0
0
6
0
1
0
1
0
0
0
0
2
0
0
1
0
0
0
2
1
0
0
0
1
1
3
0
0
0
2
0
0
1
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
2
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
3
1
2
0
2
0
0
0
0
3
0
0
0
0
0
0
2
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
2
2
0
0
1
3
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
3
1
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
2
0
0
2
0
1
0
0
0
0
0
2
0
0
1
0
0
2
0
0
1
0
0
0
2
0
4
0
1
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
1
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
2
4
0
0
0
1
0
2
0
2
0
0
0
2
0
0
0
4
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
1
1
0
0
2
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
2
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
3
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
3
0
0
0
0
1
2
2
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
1
2
2
0
0
0
1
0
5
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
3
0
1
0
0
0
0
0
1
0
0
0
0
5
0
1
0
2
0
0
0
2
0
0
0
0
1
0
1
0
2
1
0
0
1
0
0
0
3
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
3
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
2
0
0
0
0
0
0
0
2
0
1
1
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
4
0
0
1
0
2
1
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
4
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
2
2
0
0
0
0
2
0
0
0
3
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
3
0
0
0
1
0
0
2
1
0
0
2
2
2
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
3
1
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
3
2
1
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
2
2
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
5
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
1
0
2
2
0
0
1
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
7
0
0
0
1
0
0
1
2
1
0
2
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
1
0
0
1
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
2
0
1
0
0
2
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
3
1
2
0
0
1
2
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
2
2
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
8
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
3
0
2
0
0
2
0
3
0
0
0
1
0
0
0
0
1
1
0
0
2
2
0
1
0
0
1
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
4
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
3
0
2
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
1
1
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
2
0
2
2
0
0
2
0
0
0
0
1
1
0
0
4
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
3
0
2
2
0
0
1
0
2
0
3
0
2
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
3
1
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
5
2
0
2
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
1
2
0
0
0
0
4
0
2
0
0
0
0
0
3
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
1
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
3
0
0
1
0
0
0
1
0
0
0
3
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
1
0
2
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
1
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
1
2
0
1
2
1
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
1
0
1
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
1
0
2
0
0
0
3
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
8
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
3
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
5
0
0
0
0
1
0
1
0
1
0
1
0
2
0
1
1
0
0
1
0
2
1
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
3
2
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
3
1
0
1
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
3
3
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
9
0
0
0
0
2
0
0
1
2
1
0
1
0
0
0
1
0
0
0
0
2
0
0
1
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
2
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
8
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
1
2
2
0
7
1
0
0
0
0
0
0
0
0
6
0
0
1
0
1
0
0
0
0
3
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
3
0
4
0
0
0
0
2
0
0
1
0
0
1
0
0
1
1
0
0
1
0
0
0
3
0
1
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
2
0
0
2
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
1
0
3
0
2
0
0
0
0
7
0
2
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
3
0
2
0
0
2
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
2
2
3
0
0
0
0
0
0
0
0
0
0
2
1
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
1
1
2
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
3
0
2
1
0
0
0
0
1
1
0
0
0
3
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
2
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
1
0
2
1
0
0
0
1
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
2
0
0
0
0
0
0
0
4
0
0
3
1
2
2
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
2
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
1
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
3
0
2
0
0
0
1
0
0
0
0
2
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
2
0
0
1
0
1
1
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
5
0
0
0
0
0
0
0
0
1
0
4
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
3
0
3
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
2
0
1
1
0
1
0
1
0
2
0
0
9
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
2
1
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
5
0
0
0
0
4
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
7
2
0
1
1
2
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
2
0
0
0
0
1
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
1
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
4
2
2
1
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
7
0
4
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
2
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
5
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
1
0
2
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
1
0
0
0
2
2
0
0
2
0
0
2
0
2
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
2
0
1
0
0
0
0
1
1
0
0
1
0
0
2
1
2
0
0
0
0
0
0
2
0
0
0
0
2
1
2
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
1
1
0
0
0
4
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
2
2
0
1
0
0
2
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
3
1
0
0
0
1
0
3
0
1
1
1
2
0
0
0
0
2
0
0
2
1
2
0
1
0
0
0
0
1
0
0
0
4
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
1
0
0
0
3
0
0
0
5
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
1
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
3
0
2
1
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
3
0
1
2
0
0
0
0
2
1
0
1
0
1
1
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
2
2
0
0
0
0
1
0
2
0
2
0
0
2
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
6
0
0
0
0
0
1
5
0
0
0
0
0
3
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
3
0
1
0
0
0
0
0
0
0
2
0
4
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
4
0
1
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
1
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
4
0
0
2
0
2
0
3
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
2
1
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
2
1
0
0
0
1
0
0
0
1
0
1
1
0
3
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
2
0
1
1
2
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
2
0
0
1
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
3
0
5
0
1
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
2
0
1
0
1
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
3
0
0
0
2
1
0
1
0
0
0
1
0
0
0
0
1
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
3
3
0
0
1
1
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
1
0
0
0
1
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
1
2
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
1
0
1
0
0
2
2
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
2
0
2
2
0
0
2
2
1
0
7
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
1
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
2
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
1
0
0
0
0
0
0
6
2
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
1
3
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
2
0
0
0
0
3
1
2
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
1
0
0
1
0
0
0
0
1
0
3
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
3
1
2
0
0
0
3
0
2
0
0
0
2
0
0
3
4
0
0
1
0
0
0
0
1
0
0
0
0
0
4
0
0
2
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
1
0
0
0
0
0
5
0
0
0
0
1
0
0
0
1
2
0
1
0
0
4
0
7
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
3
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
3
0
0
0
0
0
1
0
0
0
0
2
2
1
0
0
0
0
1
1
1
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
2
2
0
0
0
2
0
0
3
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
2
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
3
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
1
5
0
0
4
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
2
0
1
0
0
1
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
1
0
1
0
0
1
2
0
0
2
0
0
1
0
0
0
1
2
2
2
0
1
1
3
0
0
0
1
0
3
0
2
0
0
1
0
0
2
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
2
2
2
0
0
3
0
0
0
0
0
2
0
0
1
3
2
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
1
2
1
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
2
0
0
2
0
0
3
5
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
7
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
1
1
0
0
1
0
3
0
0
0
2
1
0
2
0
2
0
1
1
3
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
2
0
0
1
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
10
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
2
2
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
5
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
1
3
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
3
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
1
3
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
2
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
1
0
0
2
0
0
1
0
1
0
0
3
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
2
0
1
2
2
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
1
0
2
0
0
0
1
0
2
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
2
1
2
5
0
0
0
2
2
0
0
0
0
0
0
1
3
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
3
0
2
0
1
2
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
10
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
2
0
0
2
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
6
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
2
0
2
0
0
0
0
0
0
0
2
0
0
1
2
0
3
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
1
0
0
2
1
0
1
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
1
0
0
3
0
0
0
0
0
1
6
0
0
0
1
0
0
0
0
0
3
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
1
2
0
0
0
0
0
6
2
2
2
5
1
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
1
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
2
1
0
1
0
2
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
2
0
0
5
2
1
0
2
0
1
0
0
1
0
1
0
0
0
2
2
2
0
0
0
3
0
1
0
0
0
3
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
1
0
1
2
0
2
0
0
2
1
0
0
0
2
2
3
0
0
0
2
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
2
1
2
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
1
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
5
0
0
0
2
0
0
0
0
2
2
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
7
2
1
0
2
2
2
2
0
0
1
1
0
0
0
3
0
2
0
0
0
1
0
0
2
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
3
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
4
0
0
0
0
0
0
5
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
2
1
0
2
2
8
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
4
0
1
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
3
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
2
2
0
1
0
0
1
0
0
2
0
0
2
1
0
1
2
0
0
0
0
0
0
0
3
0
1
1
1
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
1
1
1
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
2
2
0
0
0
0
0
1
0
1
0
0
2
0
1
0
0
0
0
1
0
0
0
4
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
3
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
5
0
0
0
0
2
0
2
0
3
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
3
0
0
0
0
0
0
0
0
2
1
0
0
2
0
2
3
0
0
0
0
0
2
0
0
2
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
4
0
1
0
0
2
1
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
1
0
0
0
1
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
2
0
2
1
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
2
0
3
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
1
0
1
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
1
1
0
0
2
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
1
2
0
5
0
0
0
0
2
0
0
4
2
0
0
0
0
0
0
0
0
0
0
0
0
10
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
5
1
1
2
1
1
1
0
0
0
0
0
0
1
1
0
1
1
2
2
0
0
2
0
0
0
2
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
1
0
1
0
0
0
0
1
1
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
2
0
0
0
0
2
0
0
0
1
0
2
3
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
3
0
0
0
0
1
4
0
0
1
1
1
0
2
0
3
1
2
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
1
0
0
2
0
0
2
0
0
0
0
0
0
0
4
0
0
0
1
0
0
2
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
2
1
1
6
0
0
0
1
0
0
1
0
0
0
0
0
0
0
4
3
0
0
0
0
0
2
0
0
1
0
0
0
1
0
1
0
0
3
2
0
1
0
1
0
1
0
5
0
0
0
2
0
0
0
0
1
0
0
0
0
2
2
1
3
4
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
2
0
1
0
5
1
1
2
0
4
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
2
0
0
0
2
0
0
0
1
1
2
0
0
0
0
0
1
0
2
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
2
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
3
0
1
0
0
0
3
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
6
1
2
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
6
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
1
0
0
0
1
0
0
2
2
2
1
0
1
0
2
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
1
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
3
0
0
2
0
0
3
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
1
1
1
0
0
0
4
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
1
2
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
1
0
0
0
0
1
1
0
2
1
0
0
0
2
0
0
0
2
0
0
0
1
0
0
2
1
2
0
0
0
0
0
0
1
2
3
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
2
0
0
0
0
0
2
0
1
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
5
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
1
0
2
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
3
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
3
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
1
2
0
1
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
7
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
2
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
1
0
0
0
0
1
0
0
2
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
1
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
2
1
0
1
2
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
6
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
1
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
1
0
0
2
0
0
0
0
2
6
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
1
3
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
2
1
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
2
2
2
1
0
0
0
1
0
1
4
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
1
2
2
0
0
0
0
0
0
0
2
0
0
0
0
3
0
2
0
0
1
1
0
2
0
2
0
1
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
3
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
5
0
0
4
1
8
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
3
0
0
0
0
1
0
0
0
0
0
0
1
1
1
2
0
1
0
2
2
1
0
0
0
1
4
0
0
2
0
0
0
1
0
2
0
0
0
0
2
1
1
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
2
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
1
0
2
0
2
0
0
1
0
0
0
0
0
1
0
1
0
4
0
0
1
0
0
2
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
3
0
0
4
0
0
3
2
0
0
0
0
0
0
2
1
0
1
0
1
0
2
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
1
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
6
0
1
2
1
0
0
0
0
1
0
0
0
13
0
0
1
1
0
0
0
0
2
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
1
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
7
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
1
2
0
0
0
0
1
2
0
0
0
0
0
0
2
2
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
1
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
1
0
2
2
1
0
2
10
0
0
0
0
8
1
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
1
2
0
3
1
2
1
0
0
0
0
1
1
1
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
1
0
1
0
3
1
2
0
2
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
6
0
1
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
3
0
0
0
0
0
6
0
1
0
0
0
1
0
2
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
3
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
8
0
0
0
1
0
3
0
0
0
0
0
1
0
0
0
1
0
0
0
3
0
0
2
3
0
2
0
0
0
1
1
0
2
1
0
0
0
0
0
0
6
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
3
0
1
0
0
3
0
2
0
0
2
1
2
0
2
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
1
0
0
0
0
0
0
3
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
8
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
3
2
1
1
0
0
1
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
5
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
2
1
1
1
0
0
2
0
1
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
5
1
0
3
0
0
1
0
0
0
1
0
2
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
1
0
1
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
2
0
2
0
0
1
0
0
1
2
0
0
0
1
0
0
2
0
2
0
0
0
1
1
1
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
2
0
0
2
0
2
2
1
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
3
0
2
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
4
2
0
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
2
1
0
1
1
0
2
0
1
0
0
0
3
2
0
0
0
0
0
0
2
0
0
0
3
3
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
3
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
2
0
0
2
0
0
1
1
3
2
2
2
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
1
1
0
1
2
0
0
0
0
1
0
1
0
0
0
4
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
2
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
2
1
0
0
1
0
0
0
2
1
3
0
0
2
0
2
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
2
0
1
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
1
0
1
2
0
0
2
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
2
0
1
4
2
1
0
4
0
1
0
1
2
2
0
0
0
0
0
0
0
1
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
1
1
0
0
2
0
1
1
0
1
0
0
1
0
0
0
2
0
1
0
2
0
0
0
0
0
0
1
1
0
2
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
4
0
0
1
0
0
0
0
0
2
0
0
2
2
0
2
0
0
2
1
0
0
0
1
0
2
0
0
1
0
0
1
0
0
2
0
0
0
0
3
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
1
8
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
2
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
2
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
7
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
3
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
2
1
0
0
0
0
0
3
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
3
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
1
1
2
0
0
0
0
0
1
0
1
0
2
0
0
1
0
0
0
0
1
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
5
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
1
0
2
0
0
0
10
0
0
0
2
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
2
0
0
0
0
1
4
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
2
0
9
1
0
1
0
3
4
0
0
0
0
0
0
2
0
0
1
1
0
2
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
3
4
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
2
1
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
3
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
3
1
4
0
5
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
2
1
0
1
1
0
0
1
0
3
0
1
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
1
0
1
0
0
0
2
0
0
2
0
0
0
1
0
0
0
1
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
1
2
2
0
0
1
0
0
0
0
0
1
1
1
0
0
0
2
0
0
0
0
0
0
0
0
2
2
1
2
0
0
0
0
0
0
3
3
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
0
0
0
1
0
0
2
0
0
0
0
0
3
0
0
2
2
0
1
2
0
0
0
0
0
0
2
0
2
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
2
0
0
0
2
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
1
0
2
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
1
3
2
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
1
2
0
3
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
2
1
1
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
3
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
4
0
0
2
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
1
0
1
1
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
2
0
2
0
8
0
9
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
2
0
6
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
2
1
0
0
2
2
0
0
0
0
0
0
1
1
0
0
0
0
2
1
0
0
0
0
0
5
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
1
2
0
6
1
0
0
0
0
0
0
4
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
4
0
1
0
1
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
1
6
0
2
2
1
4
0
4
0
1
0
0
0
0
0
0
0
0
0
2
5
1
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
4
0
1
0
0
2
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
5
0
0
0
1
0
0
0
0
0
3
1
0
0
1
0
0
1
0
2
0
0
0
0
0
0
1
2
2
1
1
2
0
0
0
2
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
2
0
0
1
0
0
1
0
2
0
2
0
0
1
0
0
1
0
0
0
2
0
3
0
0
0
0
2
0
0
2
0
0
2
0
2
0
0
0
0
0
1
2
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
3
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
3
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
1
1
0
0
0
2
0
0
2
0
0
1
0
0
0
0
2
1
0
0
0
0
2
0
0
0
2
1
0
0
0
0
1
2
3
0
0
0
0
1
3
0
0
0
0
0
2
0
1
2
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
4
1
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
3
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
3
1
0
2
2
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
3
0
2
1
0
1
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
4
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
1
0
0
2
2
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
7
2
3
0
2
0
0
2
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
2
0
11
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
2
0
0
3
0
0
0
0
6
0
0
0
2
0
0
0
0
1
0
0
1
0
1
2
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
1
2
6
0
0
2
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
1
1
0
1
0
0
0
0
0
2
2
0
0
0
0
0
1
2
1
1
0
3
0
3
0
2
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
2
0
3
0
0
0
2
1
0
1
3
0
0
0
0
4
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
3
0
0
0
2
0
0
0
2
4
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
2
2
2
2
2
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
1
1
0
3
2
0
0
3
0
0
2
0
2
0
1
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
2
0
0
1
0
2
0
0
0
1
0
0
6
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
2
0
0
0
4
1
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
1
0
2
0
0
0
0
0
0
1
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
2
0
1
0
0
0
3
0
1
0
0
2
0
0
0
0
0
1
1
0
2
0
1
1
0
1
1
2
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
2
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
1
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
2
2
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
3
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
6
0
0
2
0
2
0
0
1
0
2
0
3
0
1
2
1
1
0
0
2
1
2
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
3
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
1
1
0
0
1
2
1
0
2
0
0
3
0
1
0
0
0
3
0
0
0
0
0
1
0
0
1
2
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
2
0
0
5
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
3
1
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
16
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
2
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
1
0
0
1
0
0
0
0
1
0
0
0
2
1
0
2
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
2
0
0
0
2
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
4
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
11
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
2
0
2
12
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
1
2
0
3
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
2
1
0
0
0
0
2
2
1
0
2
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
1
0
2
0
0
0
1
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
1
0
0
2
1
1
0
0
0
0
3
0
0
0
0
0
0
1
0
0
1
0
3
0
0
0
2
1
3
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
3
0
2
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
1
0
0
2
2
0
0
2
0
0
6
0
0
0
0
0
0
0
0
1
2
0
2
0
0
2
0
1
0
1
3
2
0
0
1
0
2
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
3
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
5
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
3
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
2
3
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
2
0
1
0
0
0
1
1
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
2
0
1
4
1
0
2
0
0
0
0
0
0
4
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
2
3
0
0
1
1
0
0
0
0
1
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
1
0
1
0
0
1
0
0
2
2
0
1
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
4
0
0
2
2
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
1
1
2
1
0
0
2
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
1
0
0
0
1
0
0
0
0
2
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
4
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
1
2
0
2
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
2
1
0
0
0
1
0
0
2
2
0
0
0
0
0
0
12
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
1
0
2
4
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
7
2
0
0
2
0
0
2
0
2
0
0
0
0
1
0
0
1
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
2
2
0
0
1
0
0
2
4
1
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
1
3
0
4
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
2
0
0
0
0
2
0
0
1
1
0
0
1
0
0
2
4
1
0
1
0
0
0
1
1
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
5
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
3
2
2
0
2
0
3
0
0
0
0
0
1
0
2
0
0
3
0
0
1
2
1
0
1
0
0
1
0
1
0
0
5
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
1
2
0
0
0
0
0
2
0
0
0
0
2
0
0
2
1
0
4
0
0
1
0
0
0
0
1
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
3
0
0
1
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
2
0
3
1
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
1
0
0
0
2
0
2
2
1
1
1
0
0
1
0
0
0
2
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
1
1
0
0
0
3
2
0
3
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
1
2
2
1
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
2
0
0
0
0
0
2
0
0
3
0
0
0
0
2
2
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
3
1
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
6
1
0
0
2
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
2
0
2
0
0
2
0
0
1
0
0
3
1
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
2
1
2
0
0
0
1
0
0
0
0
0
0
1
1
2
4
0
3
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
3
2
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
2
1
0
0
0
0
1
1
2
1
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
2
0
0
4
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
4
0
0
2
1
0
0
0
0
0
2
0
0
0
0
2
0
0
5
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
1
2
2
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
1
0
1
2
1
0
0
0
2
0
0
3
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
11
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
2
1
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
5
0
0
1
0
3
2
0
0
1
0
0
2
0
0
0
0
0
3
0
1
1
0
2
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
2
1
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
4
0
0
0
2
1
0
0
0
1
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
3
2
0
0
0
0
2
0
0
0
0
0
5
0
0
0
1
0
0
0
0
0
2
0
0
3
2
0
0
0
0
2
1
0
0
0
0
0
1
0
2
0
2
0
1
0
1
0
0
1
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
3
0
0
0
0
0
0
0
2
1
0
0
1
1
1
2
0
0
0
0
1
0
1
1
0
0
1
0
0
2
0
0
5
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
1
1
0
0
3
0
0
0
4
0
4
0
0
1
0
0
0
0
0
0
0
2
3
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
1
2
0
2
0
0
0
0
0
0
0
2
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
1
3
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
2
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
2
0
0
0
1
0
0
1
0
2
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
4
0
2
0
0
1
2
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
7
0
0
2
0
0
0
3
0
0
0
0
0
0
1
2
2
3
2
1
2
0
2
0
1
0
0
0
0
1
2
1
0
0
3
2
1
0
0
1
0
2
0
0
1
0
1
0
0
1
0
2
0
0
0
0
0
1
0
0
3
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
5
0
2
4
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
5
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
1
2
0
0
0
1
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
3
1
0
0
0
0
5
2
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
5
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
1
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
0
2
0
2
0
0
0
2
1
6
3
3
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
2
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
1
0
2
0
1
2
2
0
0
0
0
1
0
0
1
0
0
0
0
1
1
9
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
3
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
2
0
0
1
1
0
2
0
0
0
2
2
0
0
1
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
2
0
1
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
2
0
0
0
5
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
4
0
0
0
1
0
0
2
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
2
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
1
0
0
0
0
3
2
0
0
0
0
0
0
0
5
2
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
3
0
0
0
0
0
2
0
0
0
0
0
0
1
4
0
1
3
0
1
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
1
0
0
0
0
0
2
3
0
3
1
0
0
0
2
0
0
0
2
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
1
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
2
0
1
3
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
1
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
6
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
6
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
4
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
2
0
2
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
2
1
0
0
0
1
2
2
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
2
1
0
2
2
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
2
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
1
0
6
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
3
0
0
0
1
4
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
1
1
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
1
0
0
3
1
1
0
0
2
0
0
2
0
2
0
0
0
2
0
1
0
1
0
1
0
0
0
3
0
0
2
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
2
0
1
0
0
1
0
0
0
1
0
0
2
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
1
0
0
0
0
0
0
1
0
2
1
0
1
0
1
0
0
1
1
0
0
0
0
0
2
0
1
1
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
1
0
0
0
0
4
0
0
0
0
4
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
1
1
0
1
0
0
1
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
1
1
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
2
0
2
0
0
0
0
0
0
0
3
1
0
0
0
3
0
1
0
0
0
0
0
1
2
2
0
2
1
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
1
1
0
0
0
0
0
0
0
0
2
0
2
0
0
2
1
0
0
0
2
0
1
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
2
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
1
2
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
4
0
1
0
1
1
1
0
0
0
0
0
0
0
1
0
3
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
3
0
0
0
1
0
0
0
0
0
0
5
1
0
0
0
2
3
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
2
0
0
0
0
2
2
0
1
0
1
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
2
0
0
3
0
0
0
2
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
2
0
0
0
0
1
0
0
1
2
0
0
1
0
2
2
3
1
1
0
0
1
0
2
3
0
0
0
1
1
0
1
0
0
1
2
0
2
0
0
2
0
1
0
2
0
0
1
0
0
1
0
0
1
2
1
1
1
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
2
0
0
0
0
0
4
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
1
0
1
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
4
0
0
0
0
0
2
0
1
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
1
0
0
0
5
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
2
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
3
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
2
0
0
2
2
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
3
0
0
1
1
1
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
1
0
1
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
3
0
1
0
0
0
1
0
0
0
2
0
2
9
1
0
0
2
0
0
0
0
0
10
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
2
2
0
2
0
0
1
0
0
1
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
3
0
0
0
0
0
1
1
0
1
0
0
0
0
6
0
0
1
0
0
0
0
0
1
0
0
2
1
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
2
0
1
0
2
0
2
0
2
0
3
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
2
1
3
2
0
0
0
0
3
0
1
0
2
1
0
2
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
1
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
1
2
0
1
0
0
0
2
0
0
0
0
3
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
2
0
0
5
1
2
0
0
0
0
0
0
0
3
0
19
0
0
0
2
0
2
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
2
2
2
0
2
1
0
0
0
1
0
2
0
0
1
2
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
4
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
2
1
0
0
0
2
0
0
0
0
0
2
1
0
0
0
2
0
0
0
1
1
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
1
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
4
0
2
3
0
0
0
0
0
0
0
0
1
1
0
1
1
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
1
0
0
0
3
0
0
0
0
1
4
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
1
2
1
0
0
0
0
1
2
0
0
3
0
0
1
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
1
0
1
0
0
0
0
0
2
0
0
3
0
0
0
1
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
2
1
0
0
0
0
3
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
3
2
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
1
5
1
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
1
3
1
0
0
3
0
3
0
0
3
0
0
0
4
0
0
0
0
0
10
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
1
1
0
0
0
0
0
6
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
3
0
2
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
3
0
2
0
1
0
0
4
10
0
0
0
1
0
1
0
0
0
0
0
0
0
0
4
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
2
0
1
0
0
0
0
0
1
1
0
0
0
0
2
1
0
0
0
0
0
2
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
2
0
0
0
0
0
0
3
1
0
0
1
0
2
0
0
0
0
0
1
0
0
9
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
2
2
0
2
0
0
0
3
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
2
0
0
1
0
0
0
1
0
2
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
1
0
1
0
0
2
0
2
0
0
0
0
0
2
0
0
2
1
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
3
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
3
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
6
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
1
1
0
0
0
0
1
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
2
0
2
2
0
0
3
0
1
0
1
0
15
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
1
1
0
2
2
0
0
4
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
1
2
2
1
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
10
1
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
3
0
2
2
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
1
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
2
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
4
1
2
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
1
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
1
0
0
0
0
0
2
3
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
1
0
0
1
2
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
2
1
0
0
0
1
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
3
0
0
1
4
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
1
0
1
2
2
0
3
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
2
0
2
1
0
0
0
1
0
0
2
1
0
0
0
0
2
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
2
0
0
0
0
1
0
0
1
0
0
1
0
0
0
3
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
3
0
0
0
1
0
0
0
1
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
3
2
1
1
0
1
0
0
0
1
0
1
1
1
2
2
1
1
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
5
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
2
2
4
0
0
10
0
0
2
0
0
0
0
0
0
0
0
0
0
1
3
1
0
0
0
0
0
0
0
2
3
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
3
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
3
0
0
1
0
0
2
1
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
1
1
1
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
3
1
1
0
0
0
0
0
0
0
0
2
2
0
0
3
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
1
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
2
0
1
1
1
0
0
0
0
0
3
0
0
6
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
1
0
1
0
0
2
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
2
0
0
0
0
2
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
2
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
2
2
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
2
0
1
2
1
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
3
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
4
1
0
2
0
1
0
0
1
0
2
0
3
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
8
0
0
0
3
1
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
1
3
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
2
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
1
2
3
0
0
0
2
0
1
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
4
1
0
0
0
2
0
0
0
0
0
0
1
0
0
1
2
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
2
1
0
0
0
3
0
0
2
0
0
0
0
0
1
0
2
0
0
2
0
0
1
0
0
0
2
2
0
2
0
0
2
1
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
3
0
1
0
1
0
0
0
1
1
0
1
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
2
0
0
0
0
3
0
0
0
0
0
1
2
0
1
0
1
0
2
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
4
0
0
1
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
3
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
7
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
1
2
0
2
0
2
0
1
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
1
0
0
2
0
2
0
4
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
1
1
3
0
2
0
2
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
4
0
0
0
0
2
0
2
2
4
0
0
3
0
0
0
2
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
3
1
0
0
0
1
0
0
1
2
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
2
2
0
1
0
0
2
1
0
0
0
0
0
0
0
0
1
2
2
0
2
1
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
2
0
1
2
0
0
3
0
1
2
0
3
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
1
0
0
0
0
1
2
2
2
0
1
0
2
0
0
2
0
2
0
0
0
0
2
0
0
0
0
3
1
2
1
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
3
1
0
0
4
0
0
0
2
0
2
0
3
0
0
4
2
0
0
0
0
0
0
1
2
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
3
2
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
3
2
1
0
0
0
0
1
0
0
2
0
0
1
0
0
1
2
0
0
6
1
1
0
0
0
0
6
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
1
2
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
3
0
0
2
0
0
1
0
3
0
3
0
0
1
2
2
1
0
0
1
1
0
1
0
2
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
3
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
2
1
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
2
2
2
2
1
0
0
0
0
0
0
0
0
3
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
11
0
0
2
2
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
2
1
0
17
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
2
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
1
0
1
1
3
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
2
0
0
1
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
1
1
0
0
0
0
0
0
0
3
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
1
1
1
2
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
2
0
0
2
0
0
2
0
1
0
1
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
1
0
1
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
7
0
0
0
1
0
0
0
2
0
2
0
0
1
0
0
0
2
1
0
0
0
2
0
0
0
2
2
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
2
0
1
0
0
0
2
3
0
1
2
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
3
2
2
0
0
0
0
0
0
0
0
0
0
0
5
1
1
0
1
1
2
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
2
1
0
0
0
0
2
0
1
0
0
2
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
1
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
1
0
0
6
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
1
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
2
0
2
1
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
1
0
0
0
2
0
0
0
2
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
16
0
0
0
0
1
2
0
0
0
0
0
0
1
1
0
1
2
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
2
0
0
3
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
5
1
2
0
4
0
2
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
2
0
0
0
4
0
0
0
0
3
0
0
3
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
3
4
0
0
1
1
0
3
0
1
0
0
0
0
0
1
0
2
2
0
0
0
2
0
0
0
0
1
2
0
0
1
2
0
2
2
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
1
1
0
0
0
0
1
3
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
3
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
2
0
0
0
1
2
0
1
0
0
0
3
0
3
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
2
0
0
1
2
0
2
0
2
0
0
2
0
0
1
3
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
5
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
2
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
3
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
2
0
0
0
1
2
0
0
1
0
0
2
1
0
0
0
0
0
1
0
2
0
1
0
0
0
1
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
5
0
0
1
1
1
0
1
0
0
0
3
2
0
0
3
0
0
2
1
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
1
0
0
0
1
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
2
1
6
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
2
3
1
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
12
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
2
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
2
0
0
0
0
1
2
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
1
2
0
0
1
0
1
0
2
3
3
0
0
0
1
0
0
0
0
2
2
0
3
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
1
1
2
0
0
3
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
4
0
0
0
4
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
1
0
0
5
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
7
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
2
0
3
0
0
1
3
1
1
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
3
0
1
0
0
3
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
1
0
1
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
6
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
1
0
3
0
1
0
0
0
0
1
1
1
0
2
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
2
2
1
0
0
1
0
1
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
1
0
0
0
2
0
0
1
1
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
1
2
1
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
2
2
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
3
0
0
0
0
2
2
3
1
0
0
0
2
2
0
2
0
0
1
1
2
0
1
0
0
0
0
1
0
4
0
0
0
0
1
1
0
0
1
0
1
1
0
3
0
0
0
0
0
1
0
1
1
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
5
2
3
2
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
3
0
0
1
0
1
0
3
9
4
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
1
3
1
0
0
0
0
3
0
3
0
3
0
1
0
0
2
2
1
0
0
3
0
0
0
1
0
0
0
0
0
2
1
1
3
2
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
2
2
0
0
0
0
3
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
1
4
0
0
0
1
1
0
3
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
5
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
2
0
0
0
0
0
0
1
0
0
0
2
0
3
0
0
5
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
4
0
1
1
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
1
2
2
0
0
0
0
2
0
0
2
1
2
0
4
0
0
1
0
0
1
0
0
1
2
2
1
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
1
0
0
1
1
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
3
0
0
0
2
0
0
0
1
0
1
1
2
0
0
0
0
1
4
0
0
0
0
0
1
0
0
0
0
0
1
0
0
3
2
0
2
1
0
2
0
0
0
0
1
0
1
3
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
5
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
2
0
3
1
0
0
1
1
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
2
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
2
1
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
1
4
0
0
0
0
0
0
0
1
0
0
0
0
7
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
4
0
0
2
0
1
0
0
2
0
0
0
1
3
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
4
1
0
0
0
0
0
0
0
0
4
0
2
1
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
1
0
0
0
0
1
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
3
2
2
0
0
1
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
1
1
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
4
1
1
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
1
0
0
0
0
0
0
2
2
0
2
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
1
0
2
0
0
0
0
0
1
0
2
0
0
2
1
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
3
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
5
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
2
1
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
2
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
3
0
0
1
0
1
0
0
0
0
2
2
0
2
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
1
0
0
0
0
0
1
1
0
3
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
2
0
0
0
0
3
1
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
2
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
3
1
0
1
0
0
1
0
2
0
0
0
1
3
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
5
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
3
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
1
0
2
2
0
0
0
0
6
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
7
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
2
0
1
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
1
10
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
4
0
0
3
0
3
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
7
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
8
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
2
1
0
0
1
0
0
0
0
0
0
1
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
5
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
1
0
1
2
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
2
1
0
0
0
2
0
4
0
0
2
0
1
1
0
0
8
2
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
2
0
2
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
3
2
0
0
0
2
0
3
0
3
0
0
0
0
0
0
0
0
2
0
0
1
0
1
1
1
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
3
0
0
3
0
0
2
0
1
1
0
2
0
0
0
2
0
0
2
0
1
0
2
0
0
0
3
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
1
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
4
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
1
2
0
0
3
0
2
0
0
0
1
0
1
0
1
2
0
1
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
2
1
2
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
4
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
3
0
0
0
1
10
0
0
0
0
2
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
3
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
2
0
0
2
3
0
0
1
0
0
2
0
3
0
0
1
0
0
0
2
0
0
0
1
1
0
0
2
1
1
0
0
0
1
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
8
0
0
1
2
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
1
2
1
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
2
0
1
0
0
3
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
2
2
0
2
0
0
0
2
0
0
0
1
0
0
2
0
1
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
5
3
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
2
0
0
0
1
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
5
12
1
1
3
2
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
2
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
3
0
0
0
3
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
1
0
2
0
0
2
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
1
3
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
1
8
1
0
0
2
0
0
0
2
0
0
0
0
0
1
2
0
0
0
2
0
1
0
0
0
0
0
0
1
1
1
0
0
2
0
0
2
3
1
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
5
0
0
0
3
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
4
0
1
0
3
1
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
2
0
0
1
0
0
2
1
0
2
2
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
2
0
5
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
1
1
0
0
1
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
3
0
0
4
0
0
0
2
0
0
2
0
0
2
0
0
0
1
0
0
0
0
2
1
0
2
0
0
0
2
0
0
0
0
0
2
3
2
0
0
0
0
1
2
0
0
3
0
0
0
0
0
0
2
0
1
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
4
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
1
3
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
2
0
3
0
0
0
1
0
0
0
1
0
0
0
2
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
1
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
1
1
0
0
2
1
1
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
2
2
1
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
2
3
0
0
0
1
0
0
0
0
2
0
1
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
1
0
0
1
0
0
2
2
0
0
0
1
0
0
2
2
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
2
0
1
0
2
0
0
0
2
0
10
0
0
0
0
0
0
0
0
0
0
0
1
0
3
2
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
2
0
0
0
1
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
1
0
2
0
1
0
0
0
0
0
3
0
0
2
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
1
5
0
0
0
2
0
0
1
0
0
0
1
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
1
0
2
1
0
0
1
1
2
0
2
0
0
0
11
0
2
2
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
1
2
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
2
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
6
0
0
0
1
1
0
1
0
1
0
0
2
0
0
0
0
2
0
0
0
0
2
5
0
0
0
0
0
2
0
1
1
1
1
0
2
0
0
0
0
0
1
0
3
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
6
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
2
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
2
1
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
2
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
2
0
0
0
0
1
1
0
1
1
0
0
2
0
1
0
0
0
0
0
0
0
2
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
2
0
0
1
1
0
0
2
0
1
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
5
0
0
0
0
0
0
1
0
0
1
0
0
2
0
2
1
2
0
0
1
0
0
0
1
0
0
0
0
0
6
0
0
0
2
0
0
0
1
1
0
0
0
3
1
0
0
0
0
2
1
2
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
3
0
3
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
2
1
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
2
0
3
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
1
0
1
2
0
1
4
0
0
1
0
0
0
0
1
0
0
2
0
0
1
1
0
0
4
0
0
0
0
0
0
0
0
1
1
2
0
0
0
2
2
2
0
0
0
2
0
0
1
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
2
0
0
1
3
1
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
3
0
0
1
7
0
0
0
0
0
0
0
0
0
2
2
0
2
1
0
0
0
0
2
0
0
0
1
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
2
2
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
3
2
0
0
0
0
1
2
0
0
1
0
0
1
1
0
1
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
1
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
5
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
2
1
2
3
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
2
0
0
0
0
1
1
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
1
0
0
1
0
0
0
0
3
0
0
0
2
0
2
0
2
1
0
0
0
0
0
4
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
2
1
0
0
2
0
2
2
0
2
3
0
0
0
0
0
0
1
1
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
1
1
0
1
0
1
0
2
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
2
0
1
0
1
0
0
2
0
0
0
2
0
0
3
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
1
0
3
1
1
1
0
0
2
0
0
1
2
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
3
2
0
0
0
0
0
0
1
0
1
3
0
0
0
1
1
3
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
3
1
0
0
2
0
0
0
0
0
0
2
1
0
0
0
1
0
2
0
1
2
2
0
0
2
0
0
0
0
0
1
1
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
1
0
2
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
3
0
0
0
5
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
1
0
0
4
0
2
0
0
0
0
0
0
0
2
1
1
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
2
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
1
2
0
6
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
2
2
0
1
2
0
0
0
0
2
0
1
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
2
0
1
4
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
2
0
0
0
0
3
1
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
3
1
3
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
2
0
0
0
0
1
1
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
5
0
0
2
0
1
2
0
0
2
0
3
0
2
1
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
2
0
0
2
1
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
1
2
2
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
2
0
0
2
1
1
0
0
1
1
0
0
0
2
1
0
2
2
4
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
1
0
0
2
1
2
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
3
0
1
0
2
0
1
2
0
2
0
0
2
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
1
0
3
0
0
8
0
0
1
1
1
1
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
4
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
1
3
0
0
0
0
1
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
1
2
2
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
2
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
3
0
1
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
10
0
1
0
2
0
2
1
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
2
1
0
2
0
0
0
0
2
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
2
0
1
0
2
4
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
2
0
2
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
2
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
3
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
2
2
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
2
1
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
1
0
0
3
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
5
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
2
0
1
0
5
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
2
0
1
0
1
2
0
2
1
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
3
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
5
1
0
1
1
0
0
0
2
0
0
0
1
0
1
0
2
2
0
0
0
1
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
3
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
8
1
1
2
0
0
0
2
0
0
4
0
0
2
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
3
0
2
0
0
1
0
0
5
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
2
2
0
1
1
0
0
0
1
1
2
0
1
2
2
0
1
0
0
0
0
1
2
0
0
0
2
0
1
0
5
0
0
2
0
0
0
0
0
0
1
2
0
2
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
1
0
6
0
0
2
2
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
6
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
3
0
0
1
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
1
0
1
0
0
0
0
1
0
1
1
0
3
0
0
0
2
1
0
2
0
2
0
0
0
0
2
1
1
1
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
2
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
21
0
0
2
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
8
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
2
2
0
0
4
0
0
0
0
0
1
0
1
3
0
0
0
2
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
1
0
1
0
0
0
3
0
0
0
0
3
0
2
0
1
0
0
1
0
1
1
2
0
3
0
0
0
0
0
0
0
1
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
1
0
0
1
0
1
2
2
0
0
1
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
1
1
0
1
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
2
0
1
0
1
0
0
0
4
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
2
0
0
0
2
1
0
3
0
1
2
0
0
0
0
2
2
1
0
0
0
0
2
0
0
1
0
0
2
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
2
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
5
0
0
0
0
0
0
1
0
0
0
0
0
3
2
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
3
0
0
0
0
1
0
0
2
0
2
2
0
0
0
0
0
1
2
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
4
0
0
0
7
0
0
0
0
1
0
0
0
0
0
0
0
2
1
1
0
0
0
1
1
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
3
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
4
0
0
0
0
2
0
0
0
2
5
0
0
0
0
0
0
0
2
0
0
1
2
5
1
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
1
0
2
3
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
2
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
2
3
0
0
0
0
1
0
2
0
0
2
2
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
4
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
2
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
1
0
0
1
0
0
4
1
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
2
1
0
0
0
0
6
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
2
0
0
0
2
2
3
0
2
1
0
0
0
6
4
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
5
0
3
0
0
0
0
0
0
2
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
2
0
1
1
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
6
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
2
2
0
1
0
0
2
0
0
0
2
0
0
2
2
0
0
0
2
0
2
0
3
0
0
0
0
2
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
2
0
2
0
2
0
0
0
0
2
4
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
1
2
0
3
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
2
0
0
0
0
0
2
2
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
2
0
0
2
0
2
0
0
0
2
2
0
0
0
1
0
1
3
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
1
0
0
1
0
1
2
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
2
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
3
2
1
0
0
3
0
0
0
2
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
7
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
1
0
2
1
2
0
0
0
4
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
2
2
0
0
2
1
0
0
0
0
1
0
2
2
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
1
4
0
0
0
0
0
1
4
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
2
0
0
0
1
0
1
1
1
0
2
0
0
0
2
0
2
0
0
0
2
1
0
0
0
0
1
4
1
1
2
0
0
0
0
1
0
0
0
1
0
4
0
0
1
1
0
0
1
0
0
0
0
2
0
3
0
0
0
2
0
0
0
2
0
0
0
2
1
0
0
0
1
0
4
0
1
3
0
0
1
0
0
0
0
2
0
0
1
0
0
0
1
2
0
0
0
0
0
0
1
2
1
0
0
0
1
2
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
3
0
0
1
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
1
1
2
1
0
0
0
0
3
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
1
0
2
0
0
2
0
0
1
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
3
1
1
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
1
0
0
0
1
0
0
2
0
2
6
2
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
2
0
1
0
3
0
0
0
0
1
0
0
1
2
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
2
0
2
0
0
0
2
0
7
0
0
0
0
0
1
0
0
2
9
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
4
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
3
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
3
0
0
1
2
1
0
0
0
3
0
0
0
0
0
0
0
1
2
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
2
1
0
2
0
0
2
0
0
0
0
0
1
1
3
0
0
0
0
0
1
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
2
2
0
0
0
0
0
1
0
0
2
0
0
2
0
1
0
2
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
2
0
1
0
1
0
0
1
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
3
0
1
2
0
0
3
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
5
0
0
0
0
0
0
0
1
2
0
0
3
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
1
0
1
0
1
0
0
1
0
1
0
0
1
0
1
2
0
0
2
0
2
0
0
0
0
0
0
2
0
2
2
0
0
1
0
1
0
3
1
2
0
3
0
2
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
2
0
0
2
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
6
0
0
0
0
0
0
0
0
0
0
1
0
0
6
0
2
0
0
0
0
0
1
0
0
2
1
0
1
1
5
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
3
3
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
3
0
0
0
0
0
2
2
3
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
2
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
1
1
0
1
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
1
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
2
0
1
2
0
2
1
0
0
2
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
1
0
1
1
2
0
2
0
2
0
0
1
0
2
0
0
0
2
1
0
4
0
1
1
0
2
0
0
0
1
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
2
2
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
3
0
1
0
0
0
0
0
1
2
0
7
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
1
1
0
0
1
0
0
0
0
2
0
0
0
0
2
3
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
3
0
2
1
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
2
0
3
0
0
1
2
0
1
0
0
0
2
0
0
0
1
0
1
0
0
0
0
1
2
2
0
0
0
0
0
0
0
2
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
2
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
6
1
1
0
0
0
0
4
1
0
0
0
0
0
3
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
1
0
1
0
1
0
0
5
1
0
0
2
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
1
0
0
0
0
2
0
2
1
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
2
0
0
0
2
0
2
3
1
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
3
2
1
0
0
2
0
2
0
1
2
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
2
0
0
1
1
0
0
2
0
0
2
0
0
0
0
2
2
0
0
2
0
0
1
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
1
0
1
0
0
4
1
0
0
0
0
1
0
0
2
0
2
0
1
0
1
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
4
2
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
3
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
2
0
2
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
2
0
2
0
0
1
2
1
0
0
0
0
0
0
0
0
1
0
2
0
0
2
3
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
3
0
0
1
0
0
0
0
2
2
0
0
0
0
2
0
3
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
2
5
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
2
2
1
0
1
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
1
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
2
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
1
0
0
0
0
2
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
7
0
1
0
2
2
0
0
1
0
1
2
2
0
0
0
0
0
1
0
1
1
0
0
1
4
0
0
0
0
0
0
1
0
5
0
0
0
1
1
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
2
1
0
2
0
0
3
0
0
0
1
0
0
2
0
1
0
0
0
2
0
0
2
0
2
0
0
2
1
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
3
0
4
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
1
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
2
0
2
0
0
0
2
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
3
2
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
3
0
4
0
0
0
0
1
0
2
0
0
4
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
1
0
0
0
3
0
2
0
0
1
0
0
0
0
2
0
1
0
1
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
15
0
0
0
1
0
1
2
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
1
0
0
0
3
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
2
2
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
2
0
1
0
0
1
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
7
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
2
1
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
9
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
3
0
0
1
0
0
0
1
3
0
0
0
0
0
0
1
0
0
1
0
2
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
2
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
3
0
0
2
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
3
0
2
0
3
0
0
1
0
0
1
0
0
1
0
0
1
0
2
0
0
0
0
1
0
0
0
0
3
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
2
2
2
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
2
0
1
0
1
0
0
1
4
2
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
3
2
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
2
0
0
0
0
0
1
1
0
1
0
0
1
0
0
1
1
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
2
0
0
0
9
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
2
0
0
0
0
1
8
1
0
2
1
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
1
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
2
2
1
1
0
0
0
0
0
1
2
0
1
2
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
1
3
2
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
4
0
0
2
0
0
0
0
0
0
3
1
1
0
0
1
0
0
0
0
0
2
0
0
0
1
1
0
2
0
0
0
1
1
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
1
0
2
0
2
0
0
1
0
2
0
0
1
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
2
1
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
3
1
0
0
0
0
1
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
3
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
4
1
0
0
0
0
0
0
0
4
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
3
0
0
0
0
2
0
0
0
1
0
0
1
0
0
3
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
2
0
1
0
0
0
2
0
1
6
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
1
0
0
0
1
0
0
2
1
0
0
0
0
1
0
0
0
2
2
0
2
6
0
0
0
0
4
0
0
0
0
0
0
0
1
2
1
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
1
1
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
2
0
0
0
1
0
1
0
0
0
0
1
0
1
0
1
1
0
1
2
2
0
2
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
2
1
2
0
0
0
0
0
0
0
0
2
2
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
1
0
2
1
0
0
2
0
0
2
0
0
0
1
2
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
4
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
1
1
0
3
0
0
1
0
1
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
3
2
1
0
0
2
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
1
5
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
1
1
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
5
0
4
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
1
0
5
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
3
0
0
1
0
0
0
0
4
1
1
0
0
5
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
1
0
1
0
1
0
0
0
3
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
1
1
2
3
0
0
1
0
0
0
0
0
1
0
0
1
1
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
2
0
4
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
1
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
2
1
2
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
2
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
2
1
1
0
1
1
1
0
0
0
2
1
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
1
3
0
0
2
1
0
0
0
0
0
0
0
2
3
0
0
2
0
0
1
0
2
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
2
0
1
1
0
0
0
0
1
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
2
4
0
1
1
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
7
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
2
0
0
0
0
0
1
0
0
2
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
8
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
5
0
0
0
0
0
0
1
1
0
0
0
2
1
0
0
0
2
2
0
0
0
2
0
0
0
0
0
1
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
1
0
1
7
2
2
0
1
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
3
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
1
1
2
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
3
0
0
1
2
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
2
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
3
3
0
0
0
0
2
2
0
2
1
0
2
0
2
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
1
0
1
0
0
0
2
1
2
0
0
1
1
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
2
1
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
3
2
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
2
0
0
2
0
1
0
0
0
0
1
0
4
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
2
1
0
0
2
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
3
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
3
0
0
0
0
0
0
3
0
0
0
0
4
0
1
0
0
0
0
0
3
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
2
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
1
1
0
0
0
3
0
2
0
0
1
0
1
0
0
3
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
3
0
0
0
2
0
0
1
0
2
0
0
1
1
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
2
0
0
1
0
2
0
1
0
0
0
2
0
1
0
1
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
2
1
1
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
6
0
0
1
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
1
1
0
0
0
2
0
0
1
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
6
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
8
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
3
0
0
2
0
3
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
4
2
0
1
0
0
1
2
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
2
2
1
1
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
2
0
0
0
0
1
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
1
0
2
2
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
5
1
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
1
3
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
1
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
2
2
0
2
1
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
1
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
2
0
0
0
0
2
1
0
1
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
1
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
1
0
3
0
0
0
0
1
0
0
0
0
0
3
2
2
0
0
0
0
0
0
1
2
0
4
0
0
0
1
0
2
0
0
0
3
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
2
2
0
0
0
2
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
1
3
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
0
2
1
0
0
0
0
3
0
4
2
0
0
0
1
0
0
1
1
0
0
1
0
0
1
0
1
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
4
0
0
0
0
0
0
0
0
0
3
1
0
1
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
3
2
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
4
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
3
0
1
1
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
3
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
3
0
2
0
0
0
2
3
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
2
1
3
1
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
6
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
1
0
0
0
0
2
0
1
0
0
1
0
4
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
5
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
2
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
5
0
1
0
2
3
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
3
1
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
2
0
0
1
0
0
3
0
0
0
2
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
2
0
0
2
2
0
0
0
0
0
0
1
0
2
5
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
1
0
2
2
0
3
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
1
0
0
0
0
0
0
0
3
2
2
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
3
0
0
0
0
0
2
0
2
1
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
3
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
3
0
1
0
0
0
0
0
0
2
0
4
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
3
0
1
0
4
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
6
0
1
0
0
1
0
1
0
2
3
1
0
0
2
0
0
0
1
0
1
0
2
0
1
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
4
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
1
0
1
0
3
0
0
0
0
1
0
0
1
5
0
2
2
0
0
5
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
3
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
2
0
0
1
1
1
0
2
1
0
1
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
1
0
0
0
0
1
0
0
2
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
1
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
2
2
1
0
0
0
0
0
0
2
1
0
0
0
0
2
2
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
2
0
1
0
2
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
1
1
0
3
0
2
0
0
1
0
1
0
0
1
1
0
1
0
1
0
0
0
0
4
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
2
0
0
1
0
2
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
3
2
0
0
1
0
1
0
0
0
0
0
0
0
0
3
0
0
0
1
1
0
0
0
0
0
0
0
0
5
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
3
0
0
0
1
2
0
2
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
1
0
1
2
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
2
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
3
0
0
7
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
3
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
1
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
1
3
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
1
0
1
0
0
2
0
0
2
0
2
2
0
0
0
0
0
0
0
1
1
0
0
1
0
1
1
2
0
0
0
0
3
0
0
0
0
0
0
1
0
0
2
1
1
0
4
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
2
0
0
1
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
6
0
0
0
0
2
0
0
1
0
4
3
0
3
0
7
1
1
1
0
0
0
2
0
0
0
0
1
3
0
0
0
0
0
2
1
0
0
0
5
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
2
0
0
2
1
1
0
2
2
0
0
0
0
2
0
0
0
2
0
1
0
3
0
0
0
1
2
1
1
0
1
0
1
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
1
3
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
2
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
2
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
3
2
0
3
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
3
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
1
0
1
1
0
2
0
0
0
0
0
0
0
8
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
6
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
3
0
0
0
1
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
2
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
2
1
2
0
0
1
0
0
0
0
0
4
0
1
0
1
0
1
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
1
1
1
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
2
1
1
0
0
0
0
0
0
2
0
0
0
0
4
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
2
0
0
2
0
0
2
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
1
3
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
1
3
0
0
0
0
0
0
0
0
0
1
1
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
4
0
0
0
2
2
0
0
0
0
1
2
0
2
0
0
0
0
0
0
3
0
1
2
1
0
0
0
0
2
0
0
2
0
1
0
1
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
3
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
2
4
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
2
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
14
0
2
4
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
3
0
2
0
0
1
1
0
1
0
0
0
0
2
1
0
1
3
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
3
1
2
0
0
0
1
1
1
0
0
0
0
0
3
0
0
0
0
2
2
0
0
1
2
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
2
1
0
0
5
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
2
0
0
1
0
4
0
3
1
1
0
0
0
2
2
0
0
1
1
0
0
1
2
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
3
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
2
1
1
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
1
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
3
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
6
0
0
0
0
3
1
0
2
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
2
3
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
2
3
0
0
0
4
0
1
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
1
0
0
0
0
1
2
2
0
0
3
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
2
1
0
1
0
2
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
2
0
0
0
1
2
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
2
0
0
0
0
1
0
0
2
0
0
2
2
0
1
0
0
1
2
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
2
0
1
0
0
3
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
3
2
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
3
0
2
0
2
0
0
0
2
1
2
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
1
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
2
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
2
0
0
3
0
0
2
0
1
0
0
0
0
0
0
0
2
0
1
0
0
1
0
1
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
1
2
0
0
0
2
0
0
1
0
1
1
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
2
0
2
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
2
1
1
0
2
2
2
3
0
1
0
1
0
1
0
0
0
0
0
0
3
2
1
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
3
0
0
0
1
1
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
2
0
3
0
0
0
0
5
0
0
0
0
1
0
0
1
0
2
0
0
0
2
0
0
0
1
1
0
3
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
5
0
0
1
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
5
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
2
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
6
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
5
0
2
0
0
0
1
2
0
1
1
0
0
0
2
1
0
0
1
0
2
2
0
2
0
0
0
0
0
0
0
1
0
0
2
1
2
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
3
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
1
0
0
1
0
0
0
0
1
0
3
0
0
0
1
0
0
1
3
2
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
1
2
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
5
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
2
0
1
0
0
0
0
0
1
0
0
2
0
0
1
1
0
4
0
1
0
0
2
0
1
0
0
2
0
0
0
0
1
0
0
2
0
1
1
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
3
0
0
0
2
2
0
1
0
0
0
1
0
0
0
0
1
1
2
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
5
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
2
2
0
0
0
1
0
0
0
2
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
1
0
0
1
0
2
0
0
0
0
0
0
0
0
2
4
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
6
0
0
0
0
3
0
0
0
2
0
0
2
0
0
1
1
0
0
0
3
1
0
0
1
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
2
0
1
2
0
0
0
1
0
1
0
0
0
0
0
0
1
0
2
1
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
2
5
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
1
0
3
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
3
1
0
0
0
0
0
0
0
2
0
1
2
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
6
0
0
0
0
0
0
0
0
5
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
1
0
0
1
0
0
0
3
0
0
1
0
1
0
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
2
0
0
3
0
2
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
4
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
2
0
0
0
0
1
2
2
2
0
0
0
1
3
0
0
0
0
2
0
2
4
3
2
0
1
0
2
0
0
1
3
0
0
0
0
0
1
0
0
0
0
0
5
0
0
0
1
0
2
1
3
0
2
0
0
0
2
0
0
1
0
0
2
1
1
0
1
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
1
0
0
3
0
1
0
0
1
0
0
1
0
2
0
0
0
0
2
0
2
2
2
0
0
0
0
0
0
1
0
0
3
4
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
2
0
0
0
0
0
1
1
1
0
1
0
2
0
4
0
0
3
0
1
0
0
0
1
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
8
0
1
1
0
1
0
2
0
3
2
0
0
2
0
0
0
0
0
1
5
2
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
4
0
0
0
0
0
2
0
1
0
2
0
1
2
1
2
2
0
1
0
1
1
2
2
2
1
0
4
1
0
0
0
0
1
2
0
0
0
0
2
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
2
6
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
2
3
0
1
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
4
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
2
4
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
4
0
0
0
0
0
1
1
0
2
0
1
1
2
0
0
0
0
0
1
0
0
1
4
1
0
0
0
0
0
0
0
2
4
0
0
0
0
2
0
0
0
0
0
0
2
0
1
1
1
0
0
1
0
0
0
0
2
0
6
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
3
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
3
2
0
0
4
0
2
1
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
2
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
3
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
1
0
3
3
0
3
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
2
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
1
0
0
2
0
0
0
1
0
1
2
0
1
0
0
0
0
1
1
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
1
0
0
0
0
3
0
0
1
0
0
0
0
0
2
0
0
0
2
0
1
0
5
0
1
1
0
0
1
0
0
1
1
0
0
0
0
4
0
4
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
2
2
3
0
0
0
0
0
0
0
2
0
0
1
0
0
0
21
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
1
0
0
0
1
0
1
0
0
3
0
0
0
1
0
0
3
1
0
0
4
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
2
0
0
0
0
0
1
3
0
0
0
0
2
0
1
0
0
0
0
2
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
1
3
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
2
2
2
0
1
0
1
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
2
1
0
2
1
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
22
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
2
3
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
12
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
2
0
0
0
0
1
0
0
0
0
0
0
1
2
0
2
0
0
1
0
1
1
0
1
5
1
2
1
0
0
0
0
0
1
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
1
0
0
2
0
1
8
0
0
0
1
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
1
0
0
3
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
2
0
2
0
0
3
0
0
2
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
3
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
2
0
1
0
0
2
1
1
2
2
0
0
0
0
2
1
0
0
0
1
1
0
0
0
1
0
0
2
0
0
0
0
1
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
2
0
2
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
1
0
0
1
0
0
1
0
0
0
0
2
0
1
1
2
0
0
0
1
0
0
0
0
2
0
0
2
0
3
1
0
0
1
1
0
0
2
0
0
0
0
0
0
1
2
0
0
0
3
0
0
1
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
2
0
0
1
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
7
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
2
1
1
2
0
0
1
0
1
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
2
2
0
1
2
1
1
0
0
2
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
2
0
0
0
1
0
0
0
5
0
3
2
0
0
0
0
1
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
3
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
6
0
0
0
0
3
1
1
2
0
4
0
0
0
0
3
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
2
5
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
1
1
0
1
0
0
0
1
0
2
1
0
0
0
0
0
1
0
0
0
2
2
0
1
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
7
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
3
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
3
2
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
2
1
0
0
5
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
3
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
1
2
0
0
0
2
0
1
0
3
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
1
1
0
0
4
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
3
0
0
1
2
1
1
0
0
1
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
1
0
5
0
0
0
0
3
2
0
2
0
0
0
0
0
0
0
4
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
3
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
2
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
3
1
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
2
0
0
1
2
1
0
1
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
4
0
2
0
1
2
0
0
0
0
1
0
1
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
2
0
2
2
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
3
0
2
0
0
2
0
0
2
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
1
2
0
0
0
0
1
2
0
0
3
3
0
1
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
2
1
0
0
2
0
0
0
1
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
3
0
0
6
0
0
0
1
1
1
0
0
0
0
0
0
0
2
0
1
1
2
0
0
0
1
0
0
2
2
0
0
4
3
0
0
0
0
0
1
2
0
0
1
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
1
3
2
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
3
0
1
0
0
1
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
2
0
0
0
0
0
1
2
0
0
1
0
0
1
0
1
0
0
0
1
3
0
0
0
3
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
2
0
0
0
1
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
1
0
0
0
5
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
3
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
2
0
0
5
2
0
0
0
0
0
0
0
2
1
0
2
0
1
4
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
1
0
2
1
0
1
0
0
3
1
0
1
1
1
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
5
0
0
0
0
0
0
3
0
4
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
3
0
0
3
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
3
0
0
1
0
1
0
0
1
0
2
2
0
2
0
0
3
0
0
3
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
2
1
0
1
1
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
1
2
0
0
0
0
1
1
0
1
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
3
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
3
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
2
4
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
5
0
0
2
0
1
0
0
0
0
0
1
0
0
2
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
3
0
0
0
0
1
0
0
1
0
2
0
0
0
0
1
4
0
2
0
0
0
0
2
0
0
0
0
0
2
0
5
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
1
2
0
0
0
4
6
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
3
0
1
0
0
4
0
1
1
2
0
1
0
0
0
2
0
0
0
1
0
2
1
0
1
0
0
0
0
0
0
1
0
1
0
0
7
1
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
2
2
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
2
2
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
1
0
0
0
1
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
3
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
1
0
3
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
1
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
7
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
1
1
1
0
0
0
0
0
0
0
1
1
0
5
0
0
0
0
0
0
0
2
0
3
0
0
0
0
2
0
0
0
1
0
0
2
1
0
2
2
0
2
0
0
0
0
0
2
0
7
0
0
0
0
1
0
2
2
0
0
1
2
0
0
0
0
4
0
1
0
0
0
0
0
2
0
2
0
0
3
0
0
1
0
0
0
0
2
1
0
0
0
1
3
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
2
2
1
0
4
0
0
0
3
0
0
0
0
0
4
2
0
1
1
1
0
0
0
0
0
0
1
0
0
0
2
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
1
2
0
0
2
0
0
2
0
2
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
2
0
0
2
0
2
0
2
0
0
0
0
0
0
0
1
0
1
0
1
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
4
1
0
5
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
5
0
0
1
0
1
0
0
2
0
0
0
0
7
0
0
1
1
0
1
1
0
0
2
0
1
0
0
0
2
0
1
0
0
1
0
0
0
0
0
1
2
0
0
2
0
0
1
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
1
1
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
1
0
0
8
0
0
0
3
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
4
0
0
3
2
0
4
0
0
0
1
0
2
0
1
0
0
0
1
0
0
2
2
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
4
0
0
0
1
1
2
0
2
0
0
0
0
0
0
1
0
7
2
0
0
2
0
0
0
0
1
3
0
0
0
1
2
1
0
1
0
1
2
0
0
0
0
0
0
1
0
3
0
2
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
1
0
3
2
0
0
0
1
2
0
0
0
1
0
0
0
0
0
2
0
3
0
0
0
0
0
2
0
1
1
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
1
0
2
1
0
0
0
2
0
0
0
1
0
0
0
2
1
4
0
2
0
1
0
0
0
2
1
0
0
0
1
1
2
0
0
0
0
0
0
1
0
0
0
0
0
4
1
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
7
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
2
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
3
1
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
1
0
0
1
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
1
3
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
2
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
2
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
2
1
1
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
2
0
0
2
0
0
0
1
2
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
2
0
1
0
0
3
2
0
0
0
0
0
0
0
1
0
1
0
1
1
1
3
0
0
0
0
1
0
0
2
0
0
1
0
2
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
2
2
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
3
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
5
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
2
0
1
0
0
0
2
3
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
2
0
2
0
0
0
2
1
0
0
0
1
0
0
2
0
1
1
1
0
0
0
2
0
0
0
0
0
0
0
0
1
4
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
3
2
0
2
2
2
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
2
1
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
1
5
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
2
0
1
0
2
0
1
0
0
0
0
2
3
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
1
1
0
0
2
2
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
4
0
0
0
0
2
0
2
0
0
0
1
2
2
1
0
0
0
0
0
2
0
0
0
0
2
0
2
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
2
0
0
1
1
0
1
0
1
2
0
0
1
1
0
0
0
0
0
0
0
2
0
0
1
1
1
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
2
2
0
0
2
1
0
0
1
4
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
2
0
2
0
1
0
0
0
1
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
5
0
1
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
2
1
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
1
2
1
1
0
0
0
0
2
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
2
1
0
0
0
0
0
2
0
0
3
0
0
0
0
0
1
1
1
1
2
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
6
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
2
0
1
0
0
3
0
0
0
0
0
0
3
12
1
0
0
0
1
1
0
0
2
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
2
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
4
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
2
0
0
0
0
2
2
0
0
1
4
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
2
0
2
0
0
3
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
2
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
1
0
0
0
0
0
2
0
1
0
5
0
2
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
3
1
0
2
2
1
0
2
2
2
0
0
0
0
0
1
0
0
0
2
0
4
3
2
2
0
0
0
0
0
0
2
0
0
2
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
3
0
0
2
0
0
0
0
0
7
0
0
0
1
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
2
1
2
3
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
4
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
1
0
0
3
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
3
3
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
2
0
2
2
0
1
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
1
0
0
0
1
0
0
0
1
0
2
1
0
0
0
1
0
1
0
0
0
1
1
0
1
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
1
4
3
0
0
2
2
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
3
0
2
0
0
0
0
1
0
1
0
0
0
1
0
0
2
0
0
3
0
0
3
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
2
1
0
2
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
2
1
0
0
1
2
0
0
2
0
0
2
0
1
0
0
0
0
3
0
1
0
0
0
0
3
0
0
2
0
0
1
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
1
0
0
0
1
0
0
5
0
0
0
2
0
2
0
1
0
0
2
0
1
0
1
0
1
0
0
0
0
1
0
0
3
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
2
2
2
0
4
3
0
0
0
0
3
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
2
4
0
0
1
1
0
0
1
2
0
0
0
0
0
0
0
1
0
2
0
2
1
0
2
2
0
0
0
0
2
0
0
0
0
2
0
3
0
0
1
1
0
0
0
2
0
1
0
0
0
0
0
1
0
0
6
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
3
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
4
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
7
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
1
0
0
0
0
0
0
2
7
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
1
1
3
1
0
2
0
2
0
0
0
0
0
1
1
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
3
0
0
0
0
2
1
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
1
0
0
0
0
0
1
0
0
2
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
3
1
0
0
0
3
1
2
1
1
0
0
5
4
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
2
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
2
0
0
2
0
0
2
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
1
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
1
0
3
0
2
3
0
0
0
0
0
1
0
3
1
0
0
0
0
0
0
4
2
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
2
1
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
2
1
1
0
0
2
3
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
1
1
0
0
0
0
5
1
0
0
0
0
1
2
2
0
0
0
2
0
0
0
1
0
0
0
0
0
4
0
0
0
2
0
0
1
0
2
0
0
1
1
1
0
0
2
0
2
0
0
0
0
2
2
1
7
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
1
2
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
2
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
5
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
1
0
0
0
0
0
0
0
1
2
2
0
0
0
1
0
0
0
0
2
0
0
1
0
0
2
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
2
0
2
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
2
0
0
1
0
0
1
0
2
1
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
4
0
0
0
0
0
1
0
0
0
2
1
0
0
0
1
0
5
0
3
0
2
0
2
0
0
1
0
0
0
0
2
4
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
5
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
2
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
3
0
2
2
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
1
0
0
0
0
3
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
4
2
1
0
0
0
0
2
2
0
1
2
2
0
0
0
2
0
0
2
0
0
2
0
0
1
0
2
3
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
1
0
2
4
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
1
2
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
2
2
2
0
0
1
0
1
0
0
0
0
0
1
2
2
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
3
0
0
0
0
2
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
2
0
0
0
0
2
0
6
0
0
0
2
0
1
0
3
3
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
3
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
2
1
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
2
0
0
2
0
0
2
0
1
0
1
0
0
0
0
0
0
8
2
0
2
0
1
1
5
1
2
2
0
0
2
0
2
2
0
2
0
1
0
2
2
2
0
0
0
0
0
0
0
0
0
3
4
0
1
1
0
0
0
0
0
0
0
2
0
3
0
3
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
2
0
3
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
2
0
0
2
0
0
0
2
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
2
1
0
4
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
4
0
7
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
7
0
3
0
0
0
0
0
0
1
0
6
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
3
4
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
2
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
3
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
4
1
0
0
0
1
1
2
1
0
0
0
1
0
0
3
0
0
0
0
0
0
0
2
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
2
0
0
1
1
6
0
1
1
0
1
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
6
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
1
1
0
1
2
0
0
0
1
7
0
0
2
1
1
0
0
2
1
0
1
0
2
0
1
0
0
2
0
2
2
0
0
3
0
0
1
0
4
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
8
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
1
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
3
0
1
0
1
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
2
0
2
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
2
1
0
2
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
2
0
0
0
2
2
0
1
0
0
1
1
0
0
1
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
2
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
1
4
0
2
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
3
2
0
0
2
0
3
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
2
0
2
0
0
0
0
1
0
0
1
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
3
0
0
0
0
0
1
0
0
1
1
2
0
0
0
0
0
0
1
2
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
2
0
0
0
0
0
4
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
1
1
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
3
2
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
2
0
0
2
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
2
1
2
2
0
0
0
0
0
4
1
0
1
0
0
2
4
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
3
0
4
0
4
2
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
4
1
0
0
1
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
4
2
2
0
0
1
0
1
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
2
5
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
4
0
0
0
0
0
0
0
1
1
0
0
0
3
0
0
0
0
0
1
0
0
0
0
1
0
2
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
1
1
0
0
2
0
1
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
1
1
0
0
0
2
3
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
1
0
0
1
0
0
3
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
2
3
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
1
1
1
0
0
1
0
2
1
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
11
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
2
3
0
1
0
0
0
0
3
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
3
0
0
1
0
0
0
3
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
1
1
0
0
0
2
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
1
0
0
0
3
0
0
1
2
0
1
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
2
5
0
6
1
0
0
0
0
0
4
0
1
2
2
0
0
0
0
1
1
0
1
0
0
2
0
0
0
0
0
2
1
0
1
0
0
2
0
1
0
1
1
0
2
1
2
5
0
0
0
1
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
2
0
0
0
5
1
0
2
0
0
0
0
0
0
0
1
2
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
3
0
0
0
1
2
0
1
2
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
1
0
0
2
2
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
4
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
1
4
0
1
2
2
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
3
1
0
0
0
0
0
0
0
0
0
0
0
2
4
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
1
2
0
0
2
0
0
0
1
0
0
0
0
0
2
0
1
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
3
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
2
0
0
1
1
0
0
0
0
0
1
6
0
0
1
0
0
3
0
0
2
0
0
1
0
0
0
0
0
2
2
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
5
6
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
11
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
2
0
3
0
0
0
3
0
1
1
0
0
0
1
1
1
0
0
1
5
0
2
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
3
1
3
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
2
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
2
0
0
0
1
0
0
0
1
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
2
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
3
2
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
2
0
0
0
0
3
0
0
0
0
9
0
0
0
0
0
0
1
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
1
0
0
2
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
1
0
0
0
1
0
0
1
2
2
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
1
0
0
2
2
0
4
0
0
0
0
0
3
0
1
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
2
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
2
0
1
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
1
1
5
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
3
0
1
0
0
0
1
1
0
0
0
0
0
2
1
2
2
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
3
0
2
0
1
0
2
0
0
0
0
0
1
0
1
1
2
0
0
0
0
0
0
4
1
0
0
0
1
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
2
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
1
3
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
2
2
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
2
1
0
0
0
3
1
0
0
0
0
2
0
0
0
3
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
2
0
1
2
0
0
0
0
0
0
0
3
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
3
0
0
4
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
5
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
4
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
2
2
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
2
0
0
2
2
0
1
1
0
1
1
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
3
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
2
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
1
2
0
0
2
0
0
1
0
0
0
1
1
0
2
0
0
0
1
1
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
4
3
0
0
0
0
0
0
0
1
0
1
0
4
2
0
0
0
0
2
0
0
3
0
0
2
0
0
0
0
2
0
1
0
0
0
2
0
3
0
0
1
0
0
1
0
5
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
2
0
0
2
0
1
0
1
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
3
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
1
0
0
0
1
0
0
0
1
1
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
1
2
0
0
0
9
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
2
0
1
0
0
0
9
0
0
4
0
2
0
0
0
4
2
0
0
0
0
0
1
1
0
0
0
0
0
19
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
2
0
0
0
0
2
0
0
6
0
0
0
0
0
1
0
1
1
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
2
0
1
0
1
0
2
0
0
0
0
1
0
2
0
0
0
1
2
0
0
0
2
1
1
0
0
0
2
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
1
0
1
0
0
0
0
2
0
0
0
0
2
0
0
3
9
0
0
0
2
0
0
1
1
0
1
1
0
3
0
0
0
2
0
0
0
0
1
0
0
0
2
0
1
2
1
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
2
3
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
2
0
0
1
4
1
1
0
0
0
0
0
2
0
2
0
2
0
2
0
3
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
3
2
1
0
0
0
0
0
0
0
1
2
0
30
0
0
0
0
3
2
0
0
0
1
0
0
2
0
0
0
1
2
0
0
0
0
1
0
0
0
0
3
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
1
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
1
2
1
2
1
2
0
0
0
0
0
0
0
0
3
0
1
1
0
1
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
6
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
1
0
6
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
1
0
2
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
1
2
0
2
1
0
2
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
1
1
0
1
2
0
0
0
0
0
0
2
0
0
2
2
0
1
1
0
0
0
0
0
0
0
0
0
0
2
1
0
1
1
0
0
0
1
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
3
2
0
1
1
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
2
0
2
0
2
0
1
1
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
2
2
1
0
0
0
0
1
1
1
0
0
2
0
0
0
2
0
0
1
0
0
2
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
7
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
2
0
1
0
2
2
0
1
0
0
0
1
2
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
3
3
0
1
2
0
0
0
0
0
2
1
2
1
0
1
0
0
0
0
2
1
2
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
3
2
0
2
0
0
0
5
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
1
1
0
4
0
0
0
0
2
0
0
2
0
0
0
1
0
1
2
0
0
0
0
0
1
0
2
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
2
0
3
0
0
0
0
0
2
0
2
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
2
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
2
2
1
0
0
1
0
0
0
4
1
2
0
1
2
0
0
1
0
2
0
0
0
2
0
2
0
0
0
1
0
0
2
1
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
2
0
2
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
2
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
4
1
2
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
2
0
0
0
1
0
1
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
1
0
1
4
0
0
0
0
1
2
0
1
0
3
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
3
0
1
0
0
0
3
0
0
0
2
0
0
0
0
0
1
0
3
0
0
0
1
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
1
0
5
0
0
2
2
0
2
0
0
0
0
5
0
0
1
0
2
0
0
0
0
0
0
0
0
4
0
0
1
2
1
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
2
2
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
3
2
2
0
1
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
7
0
2
2
1
2
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
2
2
3
0
0
3
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
3
0
0
2
1
0
0
0
1
0
0
1
2
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
4
0
0
0
2
1
0
0
1
2
1
0
0
1
1
1
0
0
0
0
0
1
0
2
3
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
4
0
0
0
0
0
0
2
1
0
0
2
0
0
2
3
0
0
0
3
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
4
1
1
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
1
1
0
3
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
1
4
1
1
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
1
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
1
2
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
6
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
7
2
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
4
0
0
2
0
0
2
0
5
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
1
3
0
2
6
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
3
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
2
0
1
1
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
2
1
0
1
0
0
1
0
0
1
2
0
0
0
0
2
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
1
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
2
2
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
1
0
3
0
0
0
0
1
1
0
0
0
2
0
0
0
2
0
0
0
0
2
0
2
3
0
2
0
0
0
0
0
0
0
1
0
8
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
2
0
2
1
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
2
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
1
2
0
0
0
2
2
0
0
0
1
0
0
0
1
0
0
0
2
0
0
1
0
1
0
0
0
2
1
0
0
0
0
1
0
1
0
0
2
0
0
1
2
0
0
0
0
0
0
1
0
0
5
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
1
2
3
2
0
0
0
2
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
1
0
1
1
1
1
0
0
0
1
2
0
0
1
0
0
1
2
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
2
0
0
0
0
1
0
1
0
0
0
0
5
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
2
2
0
0
0
1
0
0
1
0
1
0
0
2
0
0
0
0
0
1
1
0
4
0
0
1
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
3
0
0
0
0
1
1
0
0
0
2
0
0
0
0
2
1
0
2
0
0
2
0
0
0
0
1
0
0
2
0
0
2
1
0
2
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
2
0
3
0
2
1
0
0
0
2
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
3
0
0
4
0
0
2
0
2
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
4
0
1
0
1
0
0
1
0
2
0
1
0
2
0
1
4
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
2
2
2
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
1
0
2
2
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
3
0
1
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
3
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
2
0
0
1
0
2
0
0
2
0
0
0
2
0
0
0
3
4
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
4
0
0
2
0
0
2
1
1
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
1
0
0
0
0
2
1
0
1
0
0
1
0
1
0
0
1
0
0
0
2
0
0
0
2
0
0
1
0
1
0
0
1
0
0
0
0
1
0
2
0
0
0
5
0
0
2
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
2
0
0
1
0
0
0
0
0
0
1
0
2
0
3
0
0
0
0
0
0
2
0
0
0
2
4
0
3
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
1
1
2
0
0
0
1
0
2
0
1
0
0
0
2
0
1
2
0
1
0
0
1
2
0
0
0
2
1
0
2
0
2
1
3
2
0
0
1
0
0
1
0
1
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
1
0
0
0
2
0
0
0
0
1
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
1
2
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
3
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
2
0
1
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
2
1
1
3
2
0
0
0
0
0
3
0
0
2
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
3
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
3
0
0
2
2
1
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
2
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
2
1
0
0
0
0
3
0
3
1
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
7
2
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
2
0
0
2
0
0
0
2
0
0
7
0
0
0
0
0
2
0
0
1
1
0
0
1
0
2
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
2
0
0
0
1
3
4
2
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
3
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
2
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
2
1
1
2
1
0
0
0
0
4
0
2
0
0
1
1
0
0
0
0
0
1
0
0
0
0
3
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
1
0
1
0
0
1
2
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
2
2
1
0
0
3
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
2
0
2
0
2
2
1
0
0
2
0
0
0
1
2
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
6
0
1
0
0
0
0
2
0
2
1
0
1
1
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
2
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
2
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
3
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
2
1
0
0
2
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
4
1
0
0
0
3
0
2
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
2
0
0
0
0
0
1
0
2
4
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
3
0
0
0
1
0
3
0
0
0
2
0
1
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
5
2
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
2
1
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
3
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
1
1
0
3
0
0
0
3
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
1
3
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
1
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
2
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
3
1
0
0
2
2
0
1
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
3
0
0
0
1
0
4
2
0
0
0
1
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
1
0
2
0
0
0
2
0
0
2
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
2
1
0
3
0
0
0
1
0
0
2
0
0
3
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
1
0
2
3
2
1
0
0
1
0
0
0
1
0
0
5
2
0
0
0
0
0
0
0
2
0
0
1
3
4
0
0
3
0
0
1
1
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
2
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
2
0
1
1
0
2
1
1
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
6
0
1
1
0
0
1
0
1
0
0
0
2
0
2
0
6
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
1
1
0
0
0
2
1
0
0
4
0
0
0
0
0
0
2
1
0
4
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
2
1
0
3
0
2
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
2
0
1
1
0
1
1
0
0
0
1
0
0
0
2
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
1
0
0
0
0
4
1
0
0
0
0
0
1
0
2
0
2
0
0
0
2
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
5
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
1
0
0
0
2
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
6
3
0
1
0
3
1
2
0
0
0
2
2
0
0
0
0
0
1
0
0
1
1
0
0
0
0
2
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
1
0
0
0
1
1
0
2
0
1
0
0
0
0
0
0
0
0
2
0
2
1
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
1
1
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
2
0
0
2
1
2
0
0
0
2
1
0
0
0
0
1
0
1
1
1
0
0
2
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
1
1
4
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
3
3
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
2
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
3
0
3
2
2
0
0
2
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
2
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
2
0
0
0
0
0
1
1
0
0
0
0
2
1
0
0
0
2
2
7
2
0
0
1
0
1
0
2
0
1
0
0
0
0
2
1
0
0
0
1
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
1
4
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
2
0
1
0
0
0
0
1
1
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
2
3
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
2
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
3
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
2
0
0
0
0
0
0
1
0
0
4
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
2
0
0
0
0
1
0
0
3
0
0
0
2
0
0
1
0
2
1
0
0
0
0
2
0
0
0
1
2
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
1
3
0
0
0
2
0
1
0
0
5
0
0
1
0
0
1
0
0
0
2
2
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
3
0
0
0
0
0
0
0
1
6
1
0
0
0
0
0
3
0
1
0
0
0
1
1
0
0
0
0
0
0
2
2
1
0
0
1
0
0
0
0
2
0
0
0
0
0
1
1
0
2
1
0
0
0
0
0
0
1
0
3
0
1
0
0
2
1
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
3
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
5
0
0
0
0
1
0
3
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
2
0
1
1
0
1
1
1
2
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
2
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
1
0
2
2
0
1
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
8
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
1
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
5
0
1
3
0
0
2
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
2
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
4
1
0
0
1
0
0
4
0
0
0
2
0
0
2
4
0
0
0
0
2
1
2
2
0
1
0
1
0
1
1
2
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
1
1
1
0
1
1
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
6
0
0
0
1
1
2
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
4
3
0
0
0
2
2
0
0
0
1
0
1
2
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
2
1
0
0
0
0
0
1
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
4
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
4
0
0
0
2
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
1
0
3
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
2
0
0
1
0
2
0
0
0
0
5
0
0
0
0
0
1
1
0
1
2
2
0
1
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
3
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
2
0
0
0
1
0
0
0
5
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
4
0
1
0
0
0
1
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
2
0
2
4
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
1
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
3
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
2
0
2
1
0
9
0
0
0
0
1
0
0
0
0
0
0
2
1
2
0
1
0
1
1
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
2
0
0
1
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
2
0
4
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
3
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
1
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
2
2
2
0
2
3
0
0
0
0
0
0
5
0
0
0
0
2
0
0
0
1
0
1
0
0
2
3
0
1
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
1
1
12
0
0
0
0
0
0
4
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
6
0
0
1
0
0
0
2
0
0
2
2
1
0
1
0
2
0
1
0
0
0
0
2
0
0
1
0
0
2
1
2
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
1
1
0
0
0
0
2
2
0
0
0
0
1
0
0
4
0
2
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
2
0
0
2
1
0
0
0
2
1
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
2
0
0
0
1
0
0
1
3
6
0
0
1
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
2
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
4
0
5
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
2
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
5
0
0
0
0
0
1
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
5
1
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
1
0
2
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
4
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
1
0
1
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
1
2
0
0
3
0
3
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
5
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
2
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
1
0
0
1
0
1
16
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
2
0
0
2
2
0
0
1
0
0
2
1
0
0
0
1
0
2
0
0
1
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
1
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
3
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
1
1
1
0
0
1
2
0
0
0
0
0
1
3
1
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
4
0
3
0
2
1
0
0
0
0
0
0
0
0
5
0
2
1
1
2
0
1
0
2
0
0
0
0
1
0
0
0
1
4
0
0
1
0
0
0
2
0
1
0
0
0
8
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
3
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
2
0
1
0
1
0
0
0
0
1
0
2
0
0
2
0
2
0
0
0
4
0
0
0
0
0
0
2
0
2
2
0
0
4
0
2
2
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
2
0
0
0
0
1
0
6
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
5
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
3
0
1
0
2
0
1
1
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
0
0
0
0
2
0
2
0
0
1
1
0
2
2
1
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
2
2
0
2
0
1
0
0
0
2
2
0
2
2
0
0
0
0
1
2
0
2
0
0
0
0
2
0
0
0
0
3
1
0
0
0
0
0
1
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
3
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
2
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
2
1
0
0
2
0
0
0
3
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
7
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
3
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
1
0
0
3
0
1
0
0
0
0
0
2
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
1
0
2
3
1
0
0
2
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
5
0
1
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
2
0
9
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
2
0
0
0
2
0
0
0
1
0
0
0
2
0
1
0
0
0
1
1
0
0
1
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
3
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
1
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
2
0
0
1
0
0
0
2
0
0
0
0
2
2
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
2
2
0
2
1
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
2
0
0
0
0
2
0
1
0
0
1
2
0
0
0
0
0
2
4
0
1
0
0
1
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
2
0
0
0
0
0
0
2
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
3
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
2
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
3
0
1
0
0
0
0
0
0
2
2
0
0
2
0
0
2
2
0
0
2
1
0
0
0
0
0
0
0
1
0
1
0
0
2
1
0
0
0
0
1
0
4
1
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
1
0
2
2
1
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
1
0
0
1
0
2
3
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
2
0
0
1
2
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
1
1
0
1
1
0
3
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
1
1
0
2
0
0
1
0
0
0
2
0
2
0
1
0
1
0
0
0
2
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
4
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
1
2
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
2
0
0
2
0
0
1
0
0
2
0
0
1
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
1
2
0
0
0
0
0
1
0
0
0
3
0
0
0
2
2
0
0
0
0
0
0
0
3
2
2
0
0
0
0
4
1
0
0
0
0
2
0
0
1
1
0
0
0
0
0
2
2
0
0
0
0
1
2
0
1
0
0
1
0
0
1
0
0
0
2
0
0
1
0
0
0
0
1
0
2
1
1
0
0
1
0
0
0
1
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
2
0
2
2
0
0
0
1
0
1
0
0
0
0
2
0
0
0
2
0
0
1
1
0
0
0
0
0
1
0
4
1
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
2
2
4
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
3
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
2
0
2
2
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
1
1
1
2
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
7
0
0
0
0
0
0
0
7
0
7
0
1
0
1
1
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
2
0
2
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
5
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
1
1
0
1
0
0
0
0
0
0
0
3
1
0
0
0
2
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
9
0
1
2
0
0
0
2
0
0
2
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
3
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
6
0
2
0
0
0
1
2
1
0
1
0
2
2
1
0
1
0
1
0
0
0
0
1
0
3
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
2
2
0
2
2
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
1
3
0
0
2
0
0
0
0
0
2
3
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
2
2
0
0
0
0
0
1
0
0
2
0
0
3
0
0
4
0
0
0
0
1
1
3
0
0
0
0
1
1
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
2
0
2
0
0
1
0
0
1
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
3
1
0
0
2
2
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
3
0
2
0
0
0
1
0
2
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
4
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
2
2
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
2
0
0
1
0
2
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
1
0
0
0
0
0
1
0
1
0
0
0
1
2
0
0
0
0
0
5
1
2
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
2
0
3
0
2
0
0
1
0
0
0
0
0
1
3
0
1
0
0
0
1
0
2
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
3
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
1
1
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
3
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
2
0
2
0
0
0
1
0
0
1
0
0
0
0
1
1
0
2
0
1
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
2
0
0
3
0
2
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
5
2
6
0
0
0
0
0
0
0
0
1
4
0
0
1
0
0
0
0
0
4
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
1
0
2
3
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
1
0
0
0
1
0
2
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
2
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
2
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
2
0
0
4
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
3
2
0
0
0
2
4
2
1
0
4
1
0
0
0
0
0
1
1
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
1
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
2
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
1
2
4
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
5
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
1
0
1
1
1
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
5
0
1
0
1
0
0
0
0
4
0
0
2
0
0
1
5
0
0
0
1
0
2
2
0
1
0
2
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
3
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
2
0
0
3
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
1
2
2
0
0
0
0
1
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
3
1
2
1
2
0
1
0
0
0
1
0
1
2
0
1
0
0
0
0
0
1
0
0
0
4
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
2
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
3
0
2
1
2
0
2
0
0
1
0
0
0
1
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
1
0
0
0
2
0
2
0
0
0
1
0
1
0
0
0
0
0
0
4
1
0
0
0
0
1
0
0
0
0
1
0
0
4
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
1
2
0
0
0
2
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
1
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
4
1
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
1
0
1
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
5
0
0
1
0
2
1
1
0
0
0
1
0
0
2
1
3
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
1
0
2
0
0
0
0
0
0
2
2
0
1
0
1
0
2
3
0
3
2
0
4
0
0
0
1
2
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
2
2
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
7
1
0
1
1
1
0
0
1
0
2
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
2
1
0
3
0
1
0
0
0
0
0
0
2
3
3
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
2
0
0
4
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
5
0
0
2
0
2
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
2
1
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
2
3
0
1
0
2
1
0
0
0
0
0
1
2
0
1
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
4
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
1
0
1
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
2
0
0
0
7
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
4
0
2
2
0
2
0
2
0
1
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
1
0
1
2
0
0
0
2
0
0
0
2
0
0
2
3
1
0
0
2
0
0
0
0
0
0
1
0
0
1
0
1
0
0
2
0
0
0
0
2
0
0
0
2
0
0
7
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
1
2
0
0
0
1
1
0
2
0
0
0
0
0
0
1
2
0
0
3
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
6
0
2
0
0
1
0
0
1
0
2
0
0
1
3
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
4
1
0
0
0
0
1
0
0
0
0
0
2
1
0
2
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
2
1
3
0
0
0
0
0
0
0
1
1
0
0
0
0
1
2
0
0
0
0
2
2
0
2
0
1
0
0
0
0
2
0
0
0
0
0
2
1
0
1
0
0
3
0
0
0
2
2
1
0
1
0
3
0
0
4
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
1
2
0
0
2
0
0
1
0
1
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
1
0
1
0
2
0
2
0
1
1
0
0
4
0
2
0
0
0
2
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
10
0
0
2
0
2
2
0
0
0
2
0
0
0
3
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
2
2
0
0
2
0
0
2
0
2
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
1
3
0
0
0
0
2
0
0
0
3
0
0
2
2
0
1
3
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
1
0
2
1
1
4
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
1
0
0
1
2
2
0
1
0
2
2
0
3
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
1
2
0
0
0
0
2
0
0
1
7
0
0
0
2
0
0
0
1
2
1
0
0
0
2
3
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
1
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
1
1
1
0
0
0
3
0
2
0
0
0
2
0
2
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
3
0
0
1
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
1
1
0
0
2
0
0
1
0
3
0
2
1
2
2
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
1
0
0
0
2
0
0
2
0
0
1
3
0
2
2
0
0
0
1
0
0
3
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
3
2
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
6
1
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
2
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
2
0
2
0
1
0
0
0
0
1
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
4
0
2
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
2
0
0
1
0
0
0
2
0
0
1
0
1
2
3
1
1
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
2
0
0
0
0
0
2
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
3
2
1
0
0
0
0
0
0
1
0
1
0
5
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
1
1
0
2
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
1
0
2
0
0
1
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
3
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
3
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
2
0
2
0
4
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
4
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
4
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
2
0
0
1
0
1
0
2
0
0
0
2
0
0
0
0
2
2
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
3
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
3
0
1
0
2
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
1
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
1
1
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
1
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
2
0
1
0
0
0
0
2
0
1
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
3
0
0
0
8
0
3
0
2
0
0
0
0
0
1
1
0
0
0
0
0
2
0
2
1
0
0
1
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
1
3
0
0
0
0
1
0
3
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
6
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
4
0
0
0
0
0
0
1
2
0
2
1
0
0
6
2
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
1
0
1
1
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
1
0
2
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
4
0
0
3
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
1
1
0
2
0
1
0
0
0
1
0
0
0
0
2
1
1
0
0
1
1
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
1
0
1
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
2
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
3
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
1
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
3
3
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
2
0
1
0
0
0
0
0
1
0
17
1
0
0
0
0
0
0
0
3
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
1
2
2
0
0
1
0
0
0
0
1
2
0
1
1
0
0
0
0
0
1
0
0
0
0
2
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
3
0
1
1
0
0
0
0
1
0
0
0
0
1
3
1
0
0
1
6
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
2
0
0
2
0
0
1
0
0
0
2
0
0
0
1
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
2
1
2
0
0
0
1
0
2
0
0
1
0
1
2
0
0
7
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
1
0
0
2
0
0
0
0
0
2
0
0
6
0
0
1
0
1
0
2
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
4
0
0
0
0
0
0
0
0
0
0
1
1
2
0
2
0
0
1
0
0
2
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
1
2
0
0
0
0
0
1
0
5
1
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
2
0
0
0
0
0
3
0
1
0
2
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
1
0
0
0
0
7
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
2
0
2
0
2
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
2
1
0
0
0
1
3
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
2
1
1
0
0
0
0
1
0
0
0
2
2
0
0
5
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
3
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
1
0
0
1
2
0
2
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
1
0
0
2
0
0
0
0
2
1
0
0
0
1
1
0
1
3
1
2
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
1
2
4
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
3
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
5
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
1
0
1
1
0
0
0
0
1
1
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
1
0
0
0
0
2
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
4
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
1
2
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
2
0
0
0
0
3
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
1
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
5
2
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
1
0
0
0
0
0
5
2
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
0
2
0
2
0
0
3
2
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
2
0
0
0
1
0
1
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
1
2
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
1
2
2
0
2
8
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
1
0
0
0
0
0
1
0
0
1
0
0
0
5
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
3
4
0
0
1
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
6
0
0
0
2
1
0
0
0
0
5
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
2
1
0
2
0
6
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
1
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
4
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
1
0
0
0
1
1
0
0
0
0
0
3
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
6
0
0
0
0
1
2
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
1
2
7
0
0
0
2
0
3
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
2
3
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
3
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
2
3
0
0
0
0
0
0
2
1
0
1
0
0
0
0
2
0
1
0
0
4
0
0
2
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
3
1
0
0
0
2
2
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
3
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
3
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
3
0
3
0
0
0
0
1
0
1
3
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
2
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
4
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
1
0
1
0
3
0
0
0
2
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
1
1
0
2
0
1
0
0
2
0
0
0
0
0
2
3
2
0
0
0
2
0
2
1
0
1
2
0
0
2
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
1
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
5
0
1
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
1
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
3
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
1
3
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
2
0
2
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
1
2
0
1
0
5
0
0
1
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
2
0
0
0
2
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
1
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
3
3
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
3
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
2
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
5
0
2
6
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
1
1
0
0
0
2
0
0
0
1
5
2
0
0
0
0
0
0
1
0
0
0
0
1
7
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
1
0
1
0
6
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
2
0
0
1
2
0
0
2
0
0
0
0
0
1
0
1
2
0
0
0
0
2
0
0
1
0
0
0
2
0
8
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
4
3
1
1
0
0
0
0
0
2
0
0
0
2
0
1
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
2
2
0
0
0
0
0
0
4
2
0
0
3
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
2
0
0
1
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
1
1
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
2
1
0
0
1
0
0
2
2
0
1
2
1
2
1
2
0
7
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
2
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
3
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
1
0
0
0
1
2
0
0
0
0
0
2
0
0
1
3
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
3
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
2
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
4
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
3
0
0
0
0
1
3
0
1
1
4
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
2
1
1
1
0
0
2
3
2
2
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
1
0
0
0
0
11
0
0
0
2
2
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
2
1
0
1
0
0
5
0
0
0
1
3
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
2
3
0
3
0
0
0
2
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
3
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
2
4
2
0
0
2
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
3
0
0
0
0
2
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
2
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
5
0
0
0
1
0
0
0
0
0
0
0
0
0
10
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
3
0
1
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
2
0
1
0
0
0
3
0
0
2
1
0
0
0
1
2
0
1
0
0
0
0
0
1
0
0
0
4
0
0
0
2
0
1
0
1
0
0
0
2
3
0
2
0
0
2
0
2
0
0
0
1
0
0
1
1
0
0
1
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
2
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
1
2
1
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
2
2
1
1
0
0
0
2
0
0
0
2
0
2
1
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
1
0
0
0
1
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
4
1
6
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
3
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
1
2
2
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
2
1
0
0
3
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
3
0
0
0
0
9
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
2
1
2
0
2
0
0
0
0
2
0
0
0
0
0
0
1
1
2
0
0
0
0
1
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
2
0
0
0
2
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
1
4
1
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
2
1
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
2
0
0
0
2
1
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
1
4
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
4
0
0
3
0
0
1
0
0
0
0
1
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
3
1
0
1
1
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
2
0
3
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
2
0
0
1
1
2
1
0
2
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
4
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
1
2
0
0
0
1
0
1
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
8
0
0
0
0
0
0
3
0
1
0
0
1
1
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
3
0
2
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
5
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
1
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
3
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
2
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
2
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
2
0
0
0
0
0
0
3
0
0
0
0
0
1
2
1
0
0
0
0
5
0
2
0
0
1
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
1
0
0
0
1
0
1
2
2
12
1
0
1
1
0
0
1
0
0
0
0
2
1
0
0
0
0
3
0
0
2
0
1
0
0
2
0
0
0
2
0
1
0
0
2
1
0
0
1
0
0
1
1
0
4
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
1
0
1
0
0
2
2
1
6
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
3
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
3
0
2
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
8
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
3
1
0
3
0
0
0
0
0
2
0
0
0
0
0
4
2
1
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
1
0
0
7
0
1
2
0
1
1
1
0
1
0
1
2
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
1
0
0
3
2
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
1
0
0
2
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
1
0
0
5
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
4
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
3
2
1
0
0
1
0
0
0
0
0
2
0
1
0
1
2
0
2
1
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
2
0
0
0
2
0
0
1
0
0
0
0
0
1
2
0
2
0
0
2
0
1
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
3
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
2
1
2
0
0
2
0
2
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
1
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
2
0
0
0
3
0
1
0
1
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
2
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
1
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
1
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
1
2
1
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
3
0
0
0
0
0
1
0
0
8
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
1
1
0
0
0
0
3
0
1
0
0
0
0
0
0
0
3
0
2
0
1
0
0
0
0
0
0
0
0
4
0
2
0
0
0
2
1
0
0
0
0
0
5
0
1
0
0
0
0
2
0
0
1
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
3
0
2
0
1
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
10
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
3
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
2
0
1
0
2
0
0
0
0
0
2
2
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
1
1
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
8
1
0
5
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
1
0
1
1
1
0
0
1
1
1
1
0
0
2
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
1
1
0
0
0
0
1
2
2
3
4
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
2
2
0
0
2
2
1
0
0
0
3
0
0
2
0
0
0
0
0
0
0
4
0
0
0
0
0
2
4
2
0
1
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
1
0
1
0
12
0
1
1
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
1
1
0
1
0
0
0
2
0
0
0
0
2
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
2
7
1
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
3
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
1
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
2
0
2
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
2
0
0
0
0
0
2
1
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
1
5
0
1
2
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
3
1
1
2
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
2
0
0
1
0
0
0
1
2
1
0
0
1
0
3
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
2
0
2
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
3
0
2
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
2
4
0
0
0
0
2
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
2
2
0
3
4
0
2
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
6
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
2
0
1
1
0
0
0
0
0
2
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
3
2
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
1
2
2
0
0
0
1
2
0
0
0
0
0
1
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
9
0
1
0
0
2
0
0
0
0
2
1
0
0
1
4
0
0
3
1
3
1
0
1
1
1
0
0
0
0
1
3
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
2
2
0
0
0
0
0
3
0
0
2
0
0
0
0
0
1
0
0
0
1
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
2
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
1
2
6
4
0
0
4
0
1
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
2
0
1
0
1
0
0
0
0
0
2
1
0
0
2
3
2
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
4
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
1
0
0
1
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
6
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
6
0
1
3
2
0
1
0
0
0
0
0
2
0
0
1
3
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
2
0
4
0
0
1
0
0
2
0
0
0
0
0
0
0
1
1
1
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
4
0
0
1
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
2
0
0
0
0
0
0
0
2
1
0
4
1
2
0
4
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
2
0
0
0
2
0
1
1
0
0
1
0
0
0
0
1
3
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
2
2
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
1
0
2
5
1
0
0
1
2
0
3
1
2
0
4
0
0
2
0
0
1
0
0
3
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
1
0
0
0
6
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
3
0
1
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
1
0
2
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
5
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
1
1
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
1
0
2
0
0
1
0
0
0
1
0
0
0
2
0
0
0
1
2
0
1
0
0
0
0
0
0
0
2
0
0
1
0
2
0
2
0
0
0
0
1
0
0
1
0
0
0
1
0
0
2
3
0
0
0
0
0
2
0
0
0
0
0
2
3
2
0
0
2
0
0
2
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
1
3
0
0
0
2
2
0
0
0
3
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
1
0
1
0
0
2
0
0
0
0
0
1
0
0
0
4
0
0
0
1
0
5
0
0
0
0
3
3
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
2
0
0
0
0
0
1
0
0
0
1
0
3
0
0
0
0
1
0
0
0
0
0
2
0
1
3
2
0
0
0
0
2
1
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
4
0
0
0
1
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
2
1
1
2
0
0
0
0
2
0
1
0
0
2
2
0
0
2
1
0
0
0
0
0
2
0
0
0
2
0
2
23
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
1
0
0
2
1
0
0
0
0
0
0
1
0
0
10
0
0
2
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
2
0
0
1
3
0
1
0
0
3
0
2
0
0
2
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
2
1
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
2
0
1
1
0
0
0
0
0
0
0
0
3
0
1
1
0
3
0
0
0
0
2
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
1
2
0
0
0
0
1
1
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
1
0
0
1
2
2
0
0
0
0
0
4
2
2
0
1
0
6
0
0
0
2
0
0
2
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
3
2
3
2
0
0
0
1
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
3
0
0
0
2
0
0
0
0
0
2
0
0
6
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
2
0
0
1
0
1
0
2
0
0
1
1
1
0
0
2
1
1
0
1
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
1
0
1
2
0
2
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
3
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
1
0
3
2
0
1
2
7
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
2
0
1
1
1
1
0
1
0
1
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
1
1
3
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
2
1
0
3
0
2
0
0
5
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
5
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
1
0
0
0
2
0
2
0
2
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
5
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
1
0
1
0
0
2
0
0
2
0
0
0
0
0
0
2
0
2
0
0
3
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
3
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
4
0
0
0
2
1
0
3
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
2
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
2
2
0
0
0
0
2
1
2
0
0
2
0
0
3
0
1
0
2
0
0
3
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
2
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
2
0
0
1
0
0
1
0
1
0
0
0
1
0
0
1
2
0
1
1
0
0
0
0
2
0
0
0
0
1
0
0
1
3
1
1
1
0
0
1
0
0
0
0
0
1
0
1
0
2
1
0
0
0
1
2
2
0
0
0
0
0
0
0
9
1
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
2
0
2
0
0
0
0
2
2
0
5
2
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
1
1
1
2
0
0
1
0
0
0
0
3
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
2
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
1
1
0
1
4
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
2
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
1
0
0
0
0
0
0
2
0
2
0
2
0
0
0
2
2
1
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
2
2
4
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
2
1
2
0
2
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
3
10
0
0
0
0
0
1
0
3
0
0
1
0
0
0
2
0
2
0
3
2
0
0
3
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
3
0
2
1
0
3
2
0
0
0
2
0
0
2
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
2
1
0
0
0
0
0
2
2
0
0
0
0
0
4
0
0
0
0
2
0
2
0
3
0
0
0
0
0
1
0
1
0
2
0
0
1
0
0
0
0
0
0
0
2
1
0
0
1
0
0
2
0
0
2
0
0
0
1
3
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
2
0
0
1
2
0
0
0
1
0
1
0
2
0
2
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
2
0
0
0
0
0
0
2
0
1
3
3
2
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
3
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
2
0
0
2
0
0
3
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
1
0
0
2
0
0
0
0
2
2
0
1
2
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
1
0
11
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
1
0
1
4
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
3
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
1
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
4
0
3
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
1
1
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
2
2
0
0
0
1
0
0
0
2
2
4
0
0
1
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
2
2
1
0
0
0
1
0
0
0
0
2
0
0
2
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
2
0
3
0
0
2
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
3
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
4
1
1
0
0
0
2
0
2
3
0
0
0
2
0
0
1
2
2
0
0
0
0
2
0
0
2
0
0
0
1
4
0
2
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
2
7
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
1
2
0
0
0
0
0
2
1
0
1
0
2
0
2
3
0
0
0
2
2
2
0
0
0
0
0
0
2
1
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
3
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
3
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
2
0
0
1
0
0
1
1
0
0
0
1
0
3
0
0
0
0
1
0
0
4
0
0
0
2
0
0
0
0
1
0
4
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
3
1
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
1
0
1
1
1
0
0
1
0
0
0
3
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
2
3
3
0
2
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
7
2
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
3
0
0
0
2
0
2
0
2
0
0
0
3
0
0
0
0
1
2
0
0
0
0
0
3
0
0
0
0
2
3
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
1
0
0
0
0
4
0
0
2
0
0
0
0
0
0
4
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
2
0
0
2
1
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
3
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
1
0
4
0
0
3
0
0
2
1
0
0
1
1
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
1
2
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
1
1
0
0
6
0
0
0
0
1
1
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
7
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
2
8
3
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
6
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
4
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
3
1
2
0
0
0
1
0
3
0
0
0
0
2
2
0
0
0
0
0
4
1
0
2
4
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
2
2
0
0
1
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
6
0
0
0
0
0
0
4
0
1
0
0
0
2
0
0
0
0
3
0
2
3
0
0
0
0
6
0
3
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
2
0
0
0
0
1
0
2
0
0
1
0
0
3
1
0
0
0
0
0
0
2
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
1
0
0
0
0
3
1
1
0
0
1
1
2
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
3
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
2
1
0
0
0
0
2
0
0
3
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
3
0
1
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
5
0
1
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
1
3
0
0
0
0
1
2
2
0
0
0
0
0
0
0
2
2
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
5
0
2
0
0
2
0
1
0
0
2
0
0
0
0
0
5
3
0
0
0
2
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
2
0
0
0
0
0
1
2
0
1
2
0
1
0
0
0
0
0
0
0
0
3
2
0
0
0
10
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
2
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
1
1
0
1
2
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
1
0
1
0
0
1
0
0
4
0
0
0
3
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
0
0
1
0
4
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
1
2
0
0
0
3
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
2
6
0
0
0
0
0
0
2
0
0
2
5
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
3
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
6
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
8
2
1
0
0
2
1
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
3
3
2
3
0
0
0
4
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
2
2
0
0
0
0
0
2
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
1
0
0
0
0
0
0
1
1
2
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
5
0
1
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
1
0
0
2
0
1
0
4
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
2
1
0
0
0
2
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
2
0
2
0
0
0
0
3
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
1
0
1
0
3
0
0
0
2
0
0
0
1
0
0
1
0
0
4
1
0
0
0
0
0
1
2
0
0
0
0
2
1
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
2
0
3
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
2
0
0
1
0
0
2
0
0
2
1
2
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
3
1
0
0
0
2
2
0
0
1
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
1
0
1
1
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
2
5
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
4
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
6
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
3
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
5
1
0
0
2
0
1
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
3
0
0
0
0
5
0
0
1
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
2
1
0
0
0
0
0
1
0
2
0
0
1
0
1
0
0
0
1
0
0
0
0
0
2
1
3
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
2
0
0
0
0
0
1
0
2
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
2
1
1
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
1
0
0
0
0
2
3
0
0
0
0
0
0
0
9
2
0
0
0
0
0
0
4
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
3
0
2
0
1
2
0
0
0
0
1
0
1
2
0
2
0
0
0
0
0
2
0
0
1
0
0
0
2
1
0
0
0
0
0
2
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
2
0
2
1
0
0
0
0
0
1
1
0
0
0
0
2
0
1
0
0
1
0
2
2
0
3
2
0
0
0
1
1
0
0
2
5
0
0
0
2
0
0
0
0
0
0
1
1
1
0
0
0
0
2
2
0
0
1
2
0
0
5
0
0
0
0
2
2
0
0
0
0
0
1
1
0
0
1
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
1
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
1
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
3
1
2
0
0
0
0
0
0
0
0
2
0
2
2
0
0
2
0
0
0
0
0
0
0
4
0
0
0
3
0
0
2
1
0
0
0
0
0
0
0
1
0
4
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
1
0
1
1
1
1
1
1
2
2
1
2
0
0
0
0
1
1
2
0
0
1
4
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
4
0
2
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
2
1
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
4
0
0
2
0
0
0
0
0
2
0
5
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
4
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
2
1
2
2
0
0
0
0
3
3
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
4
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
2
1
0
1
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
3
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
5
0
0
2
2
1
1
2
0
0
1
0
0
0
0
0
0
0
2
0
1
0
1
0
2
0
0
0
0
3
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
2
2
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
2
2
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
3
1
3
0
0
0
0
0
1
0
0
0
0
1
0
0
7
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
3
0
0
0
0
0
2
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
2
2
0
0
1
1
0
0
1
0
0
3
1
1
0
0
0
2
1
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
5
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
1
2
0
0
0
1
2
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
1
1
2
0
0
0
0
0
2
0
0
0
1
1
7
7
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
1
0
6
0
0
0
0
0
0
2
0
2
1
3
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
2
0
0
1
0
2
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
2
0
0
1
1
0
2
0
0
0
0
0
1
0
16
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
1
1
3
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
1
1
0
1
4
1
0
0
0
0
2
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
2
0
0
1
1
0
0
0
0
0
0
2
2
0
0
0
0
1
1
0
0
3
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
1
0
1
0
5
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
3
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
1
0
0
3
1
0
0
0
0
0
1
0
0
0
0
1
2
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
2
1
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
1
1
0
0
1
0
2
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
5
0
1
2
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
2
1
4
0
0
0
0
1
0
0
0
2
2
0
0
0
0
9
0
5
0
2
2
0
0
2
0
0
0
0
2
3
2
2
0
0
0
0
0
0
0
0
1
2
3
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
1
0
0
0
2
1
0
0
0
1
1
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
2
0
0
0
0
3
0
0
0
0
0
5
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
3
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
2
0
0
2
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
5
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
2
3
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
2
0
1
2
0
0
2
0
0
0
0
0
0
2
0
4
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
2
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
2
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
2
1
0
1
0
0
0
0
0
1
2
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
5
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
3
0
1
1
2
0
0
0
2
0
0
2
0
1
0
0
2
0
0
1
0
0
0
0
0
4
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
2
0
1
0
0
1
1
0
2
1
0
2
0
0
1
1
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
1
1
0
0
0
0
0
1
0
1
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
4
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
3
2
2
1
0
0
0
0
0
0
1
0
0
0
0
1
0
3
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
2
1
0
0
0
0
2
0
0
0
2
0
2
2
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
4
1
0
0
0
2
0
0
1
1
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
1
0
0
1
0
0
0
0
0
3
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
4
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
5
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
2
0
1
0
0
0
0
2
0
0
2
0
0
0
2
0
0
5
0
0
0
0
0
0
0
0
1
0
1
0
1
0
2
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
4
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
2
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
7
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
3
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
2
2
0
0
0
1
0
1
0
2
2
1
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
2
0
1
0
2
0
0
2
1
9
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
3
0
0
0
0
0
2
0
0
0
2
2
0
2
0
2
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
1
0
0
1
0
0
2
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
1
0
1
0
1
0
0
0
1
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
1
0
2
0
1
1
0
0
0
0
1
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
1
5
0
0
2
0
0
3
2
0
0
0
0
0
0
2
0
0
1
0
0
1
2
0
0
0
2
0
5
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
4
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
2
0
2
0
2
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
3
0
2
0
0
0
1
0
0
2
0
0
2
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
4
1
0
1
0
0
0
0
1
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
2
1
0
0
1
2
0
0
0
0
0
0
0
2
0
2
2
0
2
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
4
1
0
3
0
1
1
0
3
0
0
2
3
1
0
0
2
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
1
0
1
0
0
2
0
1
0
0
0
2
0
2
5
0
0
1
3
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
2
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
1
1
2
0
3
0
2
0
0
0
0
2
2
0
4
2
0
0
0
4
0
0
0
0
1
0
0
0
1
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
3
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
2
1
0
0
0
2
1
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
3
1
0
2
0
0
0
6
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
1
1
1
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
4
0
0
1
0
0
0
1
0
1
1
2
0
0
0
0
0
0
0
2
0
1
0
1
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
1
0
0
0
0
0
0
2
6
0
0
0
1
0
0
0
0
0
2
0
0
6
1
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
6
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
1
2
1
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
1
4
0
0
0
0
0
0
0
2
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
4
3
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
2
1
0
0
0
3
1
0
0
0
0
0
0
1
1
3
1
0
0
2
0
0
0
2
0
0
2
3
2
0
2
0
1
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
2
2
3
6
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
2
2
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
2
0
0
0
1
0
0
2
0
0
0
0
2
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
1
0
4
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
16
1
0
0
0
0
2
1
0
0
0
0
0
1
0
2
1
0
0
0
0
1
0
0
1
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
2
1
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
1
0
0
1
1
2
0
0
0
1
2
2
0
2
1
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
2
0
3
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
1
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
1
0
1
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
2
1
0
0
1
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
1
2
0
0
0
0
3
0
0
1
0
2
0
0
2
0
0
0
0
2
2
0
0
0
4
0
0
0
0
0
0
2
0
0
0
2
0
2
0
2
0
0
0
7
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
5
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
12
0
0
0
0
0
0
0
0
0
0
1
1
4
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
2
0
1
0
0
0
3
2
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
2
0
0
2
2
1
0
0
1
0
0
1
0
1
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
1
7
0
5
0
3
0
0
0
2
2
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
1
0
0
2
0
3
0
0
0
2
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
3
0
1
2
3
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
5
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
1
2
0
0
0
4
0
1
0
9
0
0
1
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
1
0
5
0
0
0
0
1
0
0
0
2
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
1
0
3
0
2
0
0
0
0
0
0
0
0
4
0
1
0
3
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
1
0
0
0
4
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
2
0
0
1
0
0
0
1
2
0
0
0
1
0
0
0
0
0
2
0
0
0
2
1
1
2
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
3
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
1
0
1
0
0
0
0
0
0
1
0
0
0
1
1
2
0
1
0
3
0
0
5
1
0
0
0
2
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
3
0
0
0
0
0
1
3
0
1
0
0
0
1
1
0
0
0
0
0
2
2
2
0
0
0
0
0
0
1
0
0
6
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
2
2
0
0
0
2
0
0
2
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
3
0
1
0
0
0
1
2
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
2
0
1
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
13
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
1
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
1
1
0
0
0
3
0
0
0
0
1
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
8
0
0
0
0
1
2
2
0
0
0
0
0
0
0
2
2
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
2
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
2
2
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
1
2
1
0
0
1
0
0
2
0
0
0
1
1
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
10
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
13
0
0
1
1
1
0
2
0
1
0
0
4
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
6
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
1
0
0
1
0
1
0
2
1
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
2
0
1
0
2
4
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
2
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
2
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
1
0
1
0
0
0
1
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
1
0
0
0
0
1
0
2
0
0
1
0
1
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
1
1
0
0
6
0
1
0
1
1
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
3
0
0
2
0
0
0
0
1
0
0
4
1
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
2
0
0
2
1
0
0
2
0
3
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
2
2
0
0
0
0
3
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
3
1
0
0
0
0
0
2
1
0
0
2
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
3
0
1
0
2
5
1
0
0
0
1
0
0
2
0
2
0
0
1
0
0
0
5
0
1
0
2
0
2
0
0
3
0
0
0
0
1
2
0
2
0
1
0
0
0
0
0
0
1
1
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
1
0
0
2
0
3
0
0
0
0
2
0
0
0
0
0
0
8
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
1
1
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
2
1
0
0
4
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
2
1
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
2
2
0
1
0
0
1
0
0
0
0
0
0
0
2
3
0
2
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
1
1
0
2
0
0
2
2
1
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
3
0
0
0
2
0
0
0
3
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
3
2
0
1
0
4
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
1
1
1
1
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
3
0
0
0
0
0
4
0
1
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
3
3
0
1
0
1
1
0
0
0
3
0
0
1
1
0
2
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
3
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
3
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
3
0
0
0
0
0
0
0
0
0
6
0
2
0
0
0
0
0
0
1
0
0
0
2
1
0
0
2
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
2
6
0
0
4
2
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
1
0
1
0
0
0
0
2
0
2
0
0
0
1
1
2
0
3
1
0
0
0
0
0
0
0
0
0
0
1
1
0
2
2
0
0
0
0
0
2
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
1
0
2
2
0
0
1
0
2
0
0
0
0
0
0
0
8
0
0
0
0
0
0
2
1
0
0
0
1
0
2
1
0
0
0
0
0
1
0
0
2
0
1
0
0
2
1
2
0
2
0
3
0
0
0
2
1
1
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
3
1
1
0
0
0
1
1
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
1
2
0
0
0
0
0
1
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
2
0
0
0
0
0
0
0
0
5
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
5
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
2
0
2
0
2
3
2
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
3
1
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
2
2
0
0
1
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
3
1
0
0
1
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
1
0
0
0
2
0
0
1
2
0
1
0
0
0
2
0
2
0
0
0
0
0
2
1
0
0
1
9
0
0
2
0
0
2
0
0
0
0
1
0
2
0
0
0
2
1
0
0
0
0
3
1
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
2
0
0
0
0
3
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
5
1
1
1
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
4
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
4
0
0
2
0
1
0
0
0
0
0
1
1
2
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
1
1
0
0
1
5
0
0
0
0
1
2
0
0
1
0
0
1
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
1
0
0
2
0
0
1
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
1
0
0
0
2
0
0
1
1
1
0
2
0
1
0
2
1
0
1
0
3
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
4
2
0
0
0
0
0
0
0
0
0
0
0
5
0
0
2
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
3
2
0
1
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
2
1
0
1
0
0
1
1
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
1
2
0
4
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
4
0
0
0
1
1
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
1
1
0
1
0
0
1
0
1
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
1
2
0
1
0
1
2
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
9
0
3
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
3
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
9
1
0
0
0
0
0
2
0
0
0
2
0
0
0
6
0
0
0
0
1
0
0
0
0
1
1
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
2
1
0
0
0
0
0
0
0
2
0
0
1
0
3
0
0
0
2
0
0
0
0
0
0
3
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
2
4
0
0
0
0
0
0
0
0
4
0
1
2
1
2
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
1
2
0
0
0
2
2
0
0
0
1
0
0
0
2
2
2
1
0
1
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
2
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
2
0
0
1
0
1
0
0
0
1
0
2
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
6
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
3
0
0
0
0
0
0
1
2
0
1
0
2
1
1
2
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
4
0
0
3
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
3
0
0
2
0
1
1
2
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
2
2
1
0
0
0
0
0
1
0
0
0
0
1
1
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
1
0
0
0
1
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
2
1
2
1
0
1
0
0
1
0
0
0
0
0
1
1
0
2
2
0
0
1
0
0
0
1
0
2
2
2
2
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
2
0
0
0
2
4
1
1
2
3
0
0
0
2
1
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
2
2
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
2
0
2
0
2
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
3
1
0
0
0
0
0
0
0
2
0
2
1
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
1
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
3
0
0
6
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
2
1
2
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
1
3
0
0
0
0
2
0
0
0
0
2
0
1
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
1
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
1
2
0
0
0
0
0
2
0
0
3
0
0
0
0
2
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
2
0
0
1
0
0
0
0
1
2
0
1
0
0
0
0
0
0
1
0
0
0
3
0
3
3
0
1
0
0
0
0
3
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
2
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
1
2
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
3
0
0
0
0
0
0
0
0
2
2
0
0
0
1
2
0
2
0
0
0
0
0
3
1
0
0
1
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
3
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
2
0
0
0
0
0
2
2
0
1
0
0
0
1
0
1
1
2
0
2
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
1
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
3
1
2
1
0
1
0
1
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
1
1
1
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
4
0
2
0
0
2
1
0
1
0
0
0
0
0
0
3
0
0
2
2
0
2
0
0
0
0
0
0
0
2
0
2
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
2
0
1
1
0
0
1
0
0
0
0
1
2
2
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
1
0
0
0
0
0
2
1
1
0
0
0
0
2
0
3
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
13
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
2
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
4
0
0
3
1
0
2
0
0
0
1
1
2
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
1
0
0
0
3
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
2
0
1
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
3
0
2
0
0
0
0
0
0
0
1
0
0
2
0
3
0
2
0
0
0
4
0
0
0
0
0
1
0
0
0
3
0
2
0
0
0
0
2
0
0
1
0
1
0
1
0
0
0
2
0
1
3
0
0
2
0
1
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
3
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
1
3
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
3
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
1
0
2
0
1
0
0
1
0
0
0
0
0
4
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
6
0
2
2
0
0
2
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
2
0
1
0
0
2
0
0
0
1
0
0
1
0
2
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
2
0
0
1
1
7
0
0
0
0
2
0
0
2
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
2
0
2
0
0
2
3
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
2
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
2
0
0
0
4
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
4
2
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
3
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
1
0
0
2
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
3
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
1
2
0
0
2
0
0
0
0
2
0
0
0
0
0
1
4
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
1
1
1
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
4
2
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
3
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
3
2
0
0
2
0
1
0
0
3
1
0
1
0
0
1
0
2
0
0
0
0
1
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
1
1
1
0
2
0
0
0
2
0
0
0
1
1
0
2
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
3
0
2
0
0
0
0
1
0
0
1
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
5
0
3
0
1
0
2
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
3
0
1
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
3
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
2
0
0
1
0
2
0
0
0
1
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
6
0
1
1
0
0
0
0
0
0
0
0
6
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
3
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
2
1
0
2
0
0
2
0
2
0
0
0
0
0
0
1
1
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
3
0
2
0
0
2
2
0
0
0
2
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
3
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
2
0
0
0
0
3
0
4
2
0
0
0
1
0
0
0
0
0
0
0
0
5
0
1
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
2
1
2
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
3
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
3
0
0
0
1
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
3
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
5
3
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
6
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
1
0
2
0
2
2
2
2
0
0
0
0
2
0
0
1
0
0
2
2
2
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
3
0
0
1
0
2
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
4
0
2
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
2
0
0
2
0
0
0
0
0
0
1
3
0
0
0
0
1
1
0
1
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
1
0
0
1
0
0
3
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
1
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
2
0
2
2
0
2
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
4
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
4
0
0
0
0
0
1
0
0
0
3
2
0
0
0
1
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
3
1
0
0
0
3
0
0
0
0
15
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
4
0
0
0
1
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
2
0
2
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
1
2
0
2
0
1
0
1
0
2
2
1
1
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
1
0
0
1
0
0
1
2
0
1
0
0
0
0
1
0
0
1
0
1
0
4
3
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
2
0
0
2
1
0
0
0
0
0
0
1
1
1
1
0
0
2
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
2
0
0
0
0
0
2
2
0
0
2
0
1
1
0
0
0
0
0
0
1
2
0
2
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
4
0
5
0
1
0
3
0
0
0
1
0
0
0
2
2
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
2
0
1
0
0
0
2
4
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
2
0
0
3
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
3
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
1
0
2
0
0
2
0
0
0
0
0
0
3
2
1
0
0
1
0
0
2
0
0
0
0
1
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
0
0
1
2
4
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
1
2
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
3
0
2
0
0
3
0
0
0
1
0
0
0
2
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
7
2
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
2
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
3
0
0
0
1
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
5
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
2
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
8
1
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
3
0
0
1
0
0
0
0
1
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
3
0
4
2
0
0
0
0
0
1
3
0
2
0
1
1
0
2
0
0
0
0
0
0
0
4
0
0
0
2
1
0
0
1
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
3
0
1
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
5
0
0
0
0
0
2
0
1
0
0
4
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
1
2
0
0
0
7
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
3
0
2
0
0
0
4
2
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
4
1
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
4
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
9
1
2
2
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
1
1
1
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
1
0
0
5
0
0
1
1
1
0
0
0
0
5
0
0
1
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
2
0
0
0
1
0
0
0
3
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
2
0
0
0
3
2
0
0
0
0
0
0
2
1
0
0
4
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
4
0
5
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
3
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
1
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
4
0
0
0
0
0
1
0
0
0
1
0
0
3
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
1
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
2
0
0
0
0
0
8
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
3
0
0
2
0
1
2
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
1
0
0
5
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
2
0
0
0
4
0
1
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
2
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
3
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
3
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
4
0
0
0
0
0
0
1
0
4
0
0
3
0
0
2
0
2
2
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
5
0
1
2
0
0
1
0
1
0
0
1
2
2
0
0
3
0
1
0
0
2
0
1
2
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
3
0
2
0
2
0
1
0
0
2
0
0
2
0
0
2
0
2
2
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
3
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
1
0
2
0
1
0
0
2
0
0
0
0
0
1
0
1
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
2
0
0
0
2
3
1
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
1
1
3
3
1
0
2
0
0
0
0
1
1
2
2
2
2
0
2
0
0
0
0
2
2
1
2
0
0
0
0
1
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
1
0
0
0
0
0
0
2
0
0
6
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
2
0
3
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
3
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
2
1
0
0
0
2
1
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
1
2
1
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
5
0
2
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
1
0
0
0
0
0
1
0
1
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
1
0
0
0
0
0
3
0
2
0
0
0
0
1
1
0
1
0
0
0
2
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
7
4
0
0
0
0
0
0
0
2
2
4
0
2
0
0
0
0
0
0
0
0
0
2
0
1
1
0
1
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
2
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
1
0
0
0
0
0
0
1
2
0
0
0
1
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
3
0
1
0
0
1
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
1
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
7
0
0
0
0
0
0
1
9
1
0
0
0
0
1
0
0
0
0
0
0
3
1
0
2
1
0
4
0
2
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
2
1
0
2
1
0
0
1
0
1
0
0
0
0
1
0
2
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
2
0
0
0
2
0
0
4
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
1
1
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
2
0
0
1
3
0
2
0
0
0
0
0
0
0
2
0
3
0
1
0
0
0
0
0
0
1
0
2
2
2
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
1
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
3
0
2
0
0
0
1
1
0
0
3
2
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
3
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
5
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
1
1
2
0
0
0
0
2
3
0
0
0
0
2
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
2
0
0
6
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
4
3
0
0
0
0
0
0
0
0
1
2
0
0
4
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
3
0
0
2
0
1
2
0
0
0
1
0
0
2
0
2
0
2
5
0
0
4
0
0
2
0
0
1
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
2
0
2
2
0
0
2
1
0
0
0
0
0
0
0
3
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
7
0
0
1
0
0
0
0
0
0
0
0
2
1
0
2
1
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
5
0
0
0
0
0
2
0
1
0
4
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
1
0
3
0
1
0
0
2
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
3
0
2
0
0
0
0
0
2
2
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
2
2
0
1
0
1
0
0
0
0
5
1
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
2
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
1
1
0
0
0
2
0
0
0
0
0
4
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
2
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
1
4
1
0
0
0
0
0
2
0
0
2
0
2
0
0
2
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
2
0
2
0
2
1
0
2
0
0
0
0
1
0
2
1
0
2
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
3
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
1
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
1
2
0
2
0
0
3
0
0
4
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
2
0
0
2
0
0
3
0
3
0
4
1
1
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
1
0
0
0
0
1
2
0
0
0
0
1
0
0
2
0
0
0
2
0
3
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
4
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
1
0
0
2
0
0
0
0
0
0
2
0
0
0
4
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
3
0
0
1
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
1
2
0
0
6
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
2
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
2
7
0
0
3
0
1
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
1
1
0
0
0
2
0
0
1
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
5
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
2
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
2
0
1
0
0
6
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7
0
0
0
0
1
3
0
1
0
1
0
0
1
2
0
0
0
0
2
0
0
2
0
0
0
0
2
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
1
0
2
0
0
0
2
1
0
2
2
0
1
1
2
0
0
0
0
0
0
0
0
2
0
0
2
1
2
0
0
0
0
0
0
0
0
1
1
2
1
1
2
0
0
0
2
0
1
0
0
0
0
0
0
1
2
5
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
2
0
1
0
0
0
0
0
2
0
0
0
0
1
0
1
0
1
2
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
1
1
0
4
0
0
1
2
2
0
0
2
0
0
2
0
0
0
2
0
0
1
0
1
0
3
2
0
0
0
1
3
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
2
0
0
0
0
1
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
3
0
0
0
0
2
0
1
0
1
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
3
1
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
5
2
0
0
0
0
0
0
0
3
0
0
3
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
3
1
6
1
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
3
0
0
1
0
0
0
0
0
0
0
1
1
0
3
0
1
0
0
1
0
0
0
1
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
6
2
0
0
0
0
0
0
0
1
0
1
0
0
2
0
2
13
0
0
0
2
1
0
1
0
0
1
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
3
6
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
1
3
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
1
2
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
2
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
2
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
3
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
1
0
1
0
1
0
3
1
0
0
1
0
0
0
2
0
0
1
0
2
0
0
1
0
2
9
0
0
2
0
0
0
0
2
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
1
2
2
2
0
0
0
0
0
0
0
0
2
2
0
1
0
1
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
1
0
0
4
1
0
0
1
0
3
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
8
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
1
2
0
0
1
1
0
0
4
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
1
1
1
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
4
0
0
0
0
2
5
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
1
2
1
2
0
0
0
1
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
2
0
1
0
0
0
0
0
6
0
2
0
0
2
0
0
0
0
1
2
0
0
0
0
5
2
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
1
3
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
1
2
0
0
0
0
1
0
2
1
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
6
0
0
2
1
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
1
0
0
0
0
0
0
0
0
0
2
3
2
0
0
0
2
0
3
0
0
0
3
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
2
1
2
0
0
1
0
2
1
0
0
1
2
2
5
1
0
0
0
0
0
0
2
0
0
0
2
0
0
3
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
2
1
0
0
3
0
3
0
0
1
0
0
1
0
0
5
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
8
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
3
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
3
2
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
1
0
0
0
2
0
0
2
0
6
1
2
0
0
0
0
0
0
1
0
1
2
1
0
0
0
0
0
2
2
0
0
0
3
5
0
1
5
0
0
0
0
0
0
0
1
0
0
2
2
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
5
0
2
5
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
2
3
0
0
2
0
0
5
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
3
4
1
0
0
0
0
2
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
2
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
4
4
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
3
0
1
0
0
0
0
1
0
0
0
0
0
0
3
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
2
2
0
0
0
0
2
2
0
0
0
0
0
1
0
0
1
0
0
0
2
5
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
1
1
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
3
1
2
0
1
1
0
0
0
1
3
0
0
1
0
0
0
2
0
0
1
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
1
0
2
0
1
1
0
0
3
1
1
1
1
1
3
0
0
2
1
0
0
0
0
2
0
0
2
1
0
0
0
0
0
1
0
0
0
1
2
0
2
1
0
0
0
0
0
0
2
0
2
1
0
0
0
1
2
1
1
0
0
0
1
2
1
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
2
0
0
2
0
2
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
1
0
0
0
1
1
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
2
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
9
0
0
0
1
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
3
0
2
1
1
0
0
0
4
1
0
0
0
0
1
1
0
0
0
0
2
2
0
0
0
3
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
2
0
2
2
2
0
0
0
0
0
1
0
0
0
0
0
0
1
5
0
4
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
3
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
3
0
1
0
0
0
3
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
7
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
3
0
0
1
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
1
0
0
0
0
0
3
1
0
1
2
0
0
0
0
2
0
0
1
0
0
3
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
6
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
3
2
0
1
0
1
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
2
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
8
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
5
1
1
0
1
0
0
1
0
0
0
2
0
2
0
0
0
0
2
0
4
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
2
2
0
0
0
0
0
0
5
0
0
1
0
0
0
1
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
2
0
0
0
2
0
3
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
4
0
0
0
0
0
0
2
0
0
8
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
1
0
3
0
0
0
0
0
0
0
1
1
0
1
0
0
0
2
0
1
0
0
0
1
0
2
0
3
0
3
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
1
1
2
1
0
0
1
1
0
0
0
0
1
2
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
2
0
0
1
0
0
0
1
2
2
2
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
1
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
4
0
0
4
0
1
0
1
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
4
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
13
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
1
0
0
0
1
1
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
3
2
0
2
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
5
0
0
2
1
0
1
0
0
1
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
3
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
2
1
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
2
1
0
0
3
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
1
0
0
0
1
0
0
0
2
2
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
1
1
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
2
1
0
0
0
1
0
0
0
1
0
0
1
1
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
1
0
1
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
1
0
0
2
2
0
1
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
4
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
6
0
0
0
1
0
2
0
0
0
0
6
0
0
0
0
1
0
1
0
2
1
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
2
0
0
0
2
1
0
0
1
0
0
3
0
1
1
0
0
0
2
1
0
0
1
0
1
0
1
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
3
0
1
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
1
1
0
1
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
5
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
1
1
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
1
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
2
0
0
1
0
0
1
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
2
1
0
0
0
0
0
2
4
2
0
2
1
0
0
0
0
0
1
2
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
2
1
1
0
0
0
1
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
1
1
0
0
0
2
1
1
0
0
1
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
1
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
3
0
1
0
1
0
0
1
0
1
2
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
2
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
1
2
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
2
0
0
1
0
0
0
0
0
2
4
2
0
1
2
0
0
0
0
0
1
0
0
1
0
0
0
2
2
0
2
0
0
0
0
1
0
2
0
0
2
0
0
2
1
0
0
2
0
0
2
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
3
0
0
0
0
0
0
1
0
0
0
2
2
0
1
2
0
0
0
0
0
0
1
0
0
1
0
0
0
2
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
5
0
0
0
0
0
5
0
0
0
0
0
0
0
1
0
1
1
1
4
0
2
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
1
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
1
1
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
7
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
2
0
1
1
2
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
4
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
2
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
5
0
1
1
0
0
0
0
0
0
0
1
1
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
3
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
1
0
0
5
2
0
2
0
0
0
1
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
1
3
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
2
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
3
0
0
0
0
1
1
0
0
4
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
5
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
1
1
2
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
2
0
2
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
2
1
6
0
1
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
1
2
0
0
1
0
2
0
0
2
0
1
1
0
0
0
1
0
0
1
1
0
0
0
2
0
3
0
2
2
0
0
1
0
0
0
0
0
0
0
3
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
5
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
5
0
0
0
3
2
0
0
0
2
1
1
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
1
1
0
0
0
2
0
0
0
0
2
0
1
1
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
2
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
1
0
1
0
0
1
3
2
0
0
2
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
1
0
0
1
2
0
0
0
0
5
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
3
0
0
0
0
2
0
0
0
0
1
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
3
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
1
2
0
0
3
2
0
0
0
0
0
2
2
1
0
2
0
1
0
1
1
2
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
2
0
0
0
2
0
0
1
0
0
0
0
0
0
3
0
0
0
3
0
0
0
0
1
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
2
2
0
2
0
3
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
2
0
0
1
1
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
1
0
0
2
0
0
1
2
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
1
2
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
2
6
0
1
1
1
0
2
0
4
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
1
0
0
1
4
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
1
0
0
1
3
0
0
0
4
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
1
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
3
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
2
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
1
4
2
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
3
1
0
0
1
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
4
0
1
1
0
4
0
0
0
0
0
0
2
1
1
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
2
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
3
0
0
0
0
0
0
1
0
0
0
4
1
0
0
0
0
0
0
0
0
0
3
0
1
3
0
0
0
0
1
1
0
0
1
0
1
0
0
1
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
1
2
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
2
0
0
1
0
0
0
1
1
3
0
0
2
0
0
0
0
0
0
0
1
0
0
2
2
1
0
4
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
2
0
1
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
1
0
1
1
2
2
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
3
0
0
0
0
2
1
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
2
2
1
2
2
1
2
0
0
0
2
0
2
0
1
0
0
0
1
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
4
0
2
1
0
2
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
8
0
0
2
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
1
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
2
0
1
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
4
0
0
0
0
0
0
0
2
0
2
0
0
1
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
1
3
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
2
2
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
3
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
3
0
0
0
5
0
0
0
0
0
0
0
0
3
1
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
1
1
0
0
3
0
0
0
5
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
2
9
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
3
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
13
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
1
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
2
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
3
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
2
0
0
1
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
0
2
0
2
0
0
0
0
0
2
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
3
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
1
0
2
3
2
0
0
0
2
0
1
2
0
0
0
0
0
0
1
0
0
1
0
2
0
0
1
0
0
0
1
0
0
0
2
0
0
0
1
1
0
2
1
23
1
0
2
0
1
0
1
3
0
0
3
0
0
1
0
2
0
2
0
1
3
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
1
3
0
0
0
0
1
0
2
0
0
1
0
0
0
0
1
0
0
2
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
2
2
1
0
0
0
0
0
0
0
0
0
2
2
0
2
0
1
0
0
0
1
0
0
2
0
0
0
1
0
0
4
0
0
0
0
3
2
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
2
1
0
0
0
0
2
0
1
1
0
0
0
0
2
2
0
2
0
0
3
1
0
2
0
0
0
0
0
0
2
0
0
3
0
0
0
2
0
0
0
0
0
6
0
0
1
0
2
0
1
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
6
0
0
0
1
0
2
0
0
0
2
0
0
1
0
2
0
0
0
0
1
0
0
0
1
0
2
3
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
1
1
0
0
0
2
0
2
0
0
0
0
2
1
2
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
4
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
3
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
2
0
1
0
1
0
1
1
1
0
0
0
0
0
0
1
0
0
5
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
3
0
4
0
1
1
0
3
0
0
0
0
0
1
0
1
0
0
1
0
0
2
1
0
1
0
2
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
6
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
4
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
1
1
0
0
0
2
0
0
0
7
2
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
1
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
2
2
0
1
1
0
0
0
0
0
0
0
2
0
0
2
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
1
0
0
0
2
0
2
0
0
0
1
0
2
0
0
1
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
1
0
0
0
1
0
1
4
0
0
3
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
1
0
2
4
0
0
0
1
1
0
0
2
1
1
0
0
0
0
0
3
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
3
2
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
2
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
1
0
0
0
0
1
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
2
4
1
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
1
2
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
3
2
0
0
1
2
0
2
1
0
2
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
4
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
1
2
1
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
3
1
1
2
0
2
0
2
0
0
1
0
0
0
2
1
0
1
0
5
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
1
0
1
0
0
0
0
0
0
2
0
1
0
1
2
1
0
2
2
0
1
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
4
0
0
3
0
0
0
1
1
0
0
0
0
0
0
4
0
0
0
2
0
2
1
0
0
0
0
0
1
2
1
1
0
2
1
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
3
1
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
5
3
0
0
0
0
1
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
2
0
0
0
0
2
0
1
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
1
0
0
0
0
2
0
2
0
3
0
0
0
1
0
0
1
0
0
2
0
1
0
1
0
0
0
0
0
0
2
2
2
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
2
0
2
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
1
2
0
1
0
0
0
0
0
3
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
3
0
0
0
2
0
0
0
1
0
2
0
2
0
2
0
9
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
7
0
0
2
0
2
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
1
0
0
0
2
3
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
2
0
0
0
0
0
4
0
0
0
0
1
0
0
0
2
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
4
0
0
2
0
0
0
2
1
2
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
1
0
1
0
0
1
2
0
0
0
3
0
0
1
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
1
1
0
0
0
0
1
0
1
0
0
0
1
0
2
1
2
2
2
0
0
0
0
2
2
0
0
1
0
0
0
0
2
0
0
1
1
0
0
0
1
0
1
1
0
0
2
2
0
0
0
4
0
0
0
1
0
0
0
1
1
0
0
0
0
0
4
0
2
0
0
0
1
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
4
0
0
0
0
0
0
0
0
3
0
0
1
0
3
0
0
0
0
0
0
1
2
0
2
0
0
0
0
1
0
0
3
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
2
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
2
0
3
0
2
0
0
0
0
1
0
0
0
0
1
2
2
0
1
0
0
0
0
1
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
2
1
2
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
2
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
3
0
2
0
0
0
0
0
0
2
1
0
0
0
1
0
3
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
1
2
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
5
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
1
1
1
2
1
0
0
0
2
2
1
0
0
0
1
2
0
2
0
0
0
0
0
0
1
0
0
0
2
2
3
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
2
1
0
2
0
0
0
1
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
3
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
5
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
4
0
0
0
2
0
0
0
1
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
3
1
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
6
1
0
0
0
0
3
2
0
3
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
3
0
0
0
1
1
0
0
2
0
3
0
2
1
0
0
0
0
1
3
0
0
1
0
0
4
0
3
1
1
0
2
2
0
0
2
0
2
0
0
0
0
0
0
2
1
0
0
2
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
2
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
10
0
0
0
4
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
1
1
3
1
5
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
1
0
2
0
0
0
0
1
0
0
0
1
5
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
1
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
1
1
0
2
0
2
0
0
4
0
1
1
2
0
1
0
0
0
0
0
4
1
2
0
0
0
3
3
0
0
0
0
0
1
0
0
1
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
3
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
5
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
3
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
1
0
0
8
0
8
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
1
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
7
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
1
0
4
0
0
0
0
2
0
0
2
0
0
1
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
2
1
0
1
0
2
0
0
0
2
1
0
1
0
2
0
0
0
0
0
2
2
0
0
1
0
2
0
2
1
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
4
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
10
0
1
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
2
1
0
0
0
1
0
0
0
1
2
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
2
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
1
1
0
1
0
2
0
0
0
0
2
0
1
0
0
1
0
2
1
6
1
1
0
3
0
0
0
0
1
0
0
0
0
2
10
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
1
1
0
1
0
0
2
0
0
0
0
2
0
0
0
2
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
5
0
2
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
1
0
0
2
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
4
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
2
0
2
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
3
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
1
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
3
0
0
3
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
2
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
2
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
1
4
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
9
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
1
0
0
1
0
2
0
2
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
2
2
1
2
1
1
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
5
0
0
0
0
0
0
6
1
0
0
0
0
0
0
0
1
0
0
2
0
1
2
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
4
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
2
0
0
2
0
0
1
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
2
0
2
0
2
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
2
1
0
0
2
2
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
2
1
0
4
0
0
2
0
0
0
0
0
2
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
2
0
0
4
0
3
0
0
5
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
5
1
0
0
0
1
0
2
0
0
2
1
0
1
1
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
1
0
1
0
1
2
0
0
4
0
2
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
1
2
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
1
1
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
6
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
1
0
0
2
2
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
10
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
2
0
1
0
0
6
0
1
0
0
1
0
3
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
4
0
1
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
1
0
1
0
0
0
2
0
5
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
4
0
1
0
0
0
0
2
0
2
1
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
3
2
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
1
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
2
0
2
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
2
0
4
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
1
1
0
0
0
0
1
1
0
0
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
1
0
2
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
1
0
1
0
0
0
0
1
0
0
0
1
2
0
0
2
1
1
0
0
0
0
2
0
0
0
2
0
0
0
0
1
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
8
2
0
0
2
9
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
1
2
0
0
0
0
3
0
2
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
2
2
1
0
0
0
0
0
0
0
1
0
1
2
0
2
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
3
3
0
1
2
0
2
0
2
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
2
0
0
0
3
2
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
2
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
2
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
3
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
1
4
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
3
0
0
2
0
2
0
0
0
0
4
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
2
0
1
0
1
0
1
0
0
0
0
0
3
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
2
1
0
0
0
0
0
1
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
1
0
0
1
1
0
0
2
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
6
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
3
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
1
0
0
2
0
1
0
0
0
0
0
0
0
0
6
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
2
1
0
0
0
0
0
0
2
0
2
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
2
0
1
2
3
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
11
0
0
0
0
4
0
0
2
0
0
0
3
0
0
1
0
0
0
0
0
2
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
9
0
0
0
0
1
0
0
4
1
1
0
2
1
0
0
0
1
1
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
2
0
0
3
2
0
1
0
2
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
1
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
3
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
6
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
14
0
0
0
0
1
0
1
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
1
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
1
2
1
1
0
0
0
2
0
0
0
0
0
0
3
0
0
2
1
1
0
0
0
0
0
0
2
0
1
2
0
2
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
2
5
0
1
1
3
0
1
0
0
2
0
0
2
1
0
0
0
0
0
2
2
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
2
3
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
3
0
0
0
0
2
0
2
0
0
0
1
1
0
0
0
1
0
3
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
3
0
1
0
0
0
0
5
0
2
2
0
0
0
0
2
3
0
2
1
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
3
0
4
1
0
0
1
0
0
0
0
1
0
0
0
2
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
1
1
0
0
0
2
0
2
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
2
0
0
0
1
5
0
0
0
1
0
0
1
1
0
2
0
1
0
0
0
0
3
0
0
0
0
2
0
1
1
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
2
2
0
2
0
0
2
0
0
0
0
0
2
0
0
0
1
2
0
0
1
0
0
2
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
1
23
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
1
0
0
0
0
0
3
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
1
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
1
1
1
3
0
2
0
0
2
1
0
0
1
0
1
2
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
2
0
1
0
0
1
0
1
0
2
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
1
2
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
2
1
6
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
2
0
0
2
0
1
0
0
5
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
1
2
0
0
0
0
7
0
1
1
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
5
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
1
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
1
0
0
0
0
2
2
0
1
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
10
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
2
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
5
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
1
0
2
0
0
1
0
0
4
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
2
1
0
2
0
0
0
1
0
1
0
0
2
3
0
2
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
3
0
1
2
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
2
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
1
2
0
0
2
0
0
2
0
1
0
0
1
2
0
0
1
2
1
0
0
0
0
1
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
5
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
5
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
3
0
1
2
0
2
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
1
2
0
0
0
1
2
2
2
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
1
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
1
3
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
1
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
1
0
2
1
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
2
0
1
0
0
2
3
0
0
2
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
3
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
2
0
0
0
3
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
4
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
6
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
2
1
0
0
0
0
0
0
2
3
1
0
2
0
0
5
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
2
2
1
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
2
2
1
2
0
0
1
0
1
0
0
1
0
1
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
2
0
1
1
0
0
0
0
0
0
0
1
3
0
0
0
1
0
1
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
3
1
0
0
0
1
3
0
0
0
1
0
0
0
0
0
1
0
3
0
0
0
0
0
6
0
0
1
2
0
2
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
1
0
1
0
0
0
2
2
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
1
2
0
0
0
0
0
0
5
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
8
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
1
0
0
2
0
2
1
0
2
1
1
0
1
0
0
0
0
2
0
0
2
0
1
2
1
0
0
2
3
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
2
0
2
0
0
1
0
2
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
1
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
1
0
1
1
0
1
0
2
0
0
2
4
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
1
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
3
1
0
1
0
0
0
0
0
3
0
0
0
2
1
0
3
2
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
1
0
2
0
2
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
4
2
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
3
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
1
0
1
0
1
0
0
0
0
0
2
0
0
0
2
3
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
3
0
1
2
0
2
0
0
1
0
0
0
0
0
0
1
0
1
3
0
1
0
2
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
4
0
0
0
0
4
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
2
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
1
0
0
0
2
2
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
5
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
3
2
0
0
1
0
0
1
0
1
2
4
0
1
0
0
1
1
0
0
0
0
2
2
0
0
0
0
0
0
0
2
3
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
11
0
0
0
0
0
0
0
1
0
0
0
3
0
0
2
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
1
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
5
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
4
0
0
0
1
0
0
0
2
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
1
0
2
2
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
3
0
0
2
0
1
0
0
3
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
1
2
2
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
1
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
3
0
0
0
3
0
5
2
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
2
3
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
9
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
2
0
1
0
0
0
0
0
1
0
4
0
2
0
0
0
3
0
1
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
2
1
0
1
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
2
2
0
0
0
0
0
1
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
11
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
2
0
3
0
2
0
2
2
0
2
2
0
0
0
0
0
0
0
1
0
0
3
0
1
0
1
0
0
0
0
2
0
2
4
1
1
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
1
2
0
0
1
0
0
2
3
0
0
0
0
0
4
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
1
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
3
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
1
3
0
2
1
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
1
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
3
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
2
1
0
3
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
3
0
0
1
2
2
0
1
0
0
0
0
0
1
2
0
2
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
3
0
0
3
0
2
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
2
4
0
0
0
0
7
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
3
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
3
0
1
2
0
0
2
1
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
3
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
3
2
0
0
0
0
0
4
0
0
0
0
2
0
1
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
2
0
0
0
2
4
2
0
0
2
0
0
2
0
0
2
0
2
2
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
3
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
2
2
0
0
0
1
0
1
0
0
1
1
0
2
0
2
0
0
0
0
1
0
0
0
2
0
0
0
2
0
2
1
0
0
0
4
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
3
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
6
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
3
0
1
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
2
1
0
1
2
0
0
1
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
2
0
3
0
0
0
1
0
0
1
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
1
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
8
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
2
2
0
2
0
0
0
1
0
2
1
4
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
1
0
0
2
0
2
0
0
0
0
2
1
1
0
0
0
2
0
0
0
0
0
0
1
2
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
5
1
0
2
2
1
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
1
2
1
0
0
1
0
1
2
1
2
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
3
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
1
1
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
2
0
0
0
0
0
5
4
0
0
2
0
0
2
0
1
0
0
0
0
0
0
3
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
2
2
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
1
2
0
0
0
2
1
3
0
2
0
0
1
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
1
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
3
0
0
2
0
2
0
0
1
1
0
0
1
2
0
0
0
0
0
0
0
1
2
0
0
2
1
0
0
0
0
0
1
4
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
2
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
1
0
0
2
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
1
0
3
0
0
2
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
3
0
1
1
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
2
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
3
2
2
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
4
1
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
7
0
0
1
0
0
0
0
0
0
2
2
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
2
0
1
0
1
0
0
0
3
2
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
3
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
2
0
1
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
2
3
3
0
0
2
0
1
0
2
1
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
2
1
0
0
0
3
0
0
2
0
2
2
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
1
2
0
1
0
1
0
0
0
0
0
2
0
1
2
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
3
8
0
0
1
2
0
0
0
0
5
0
2
0
1
0
0
0
0
1
0
0
0
0
1
0
1
1
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
1
1
0
0
0
2
0
0
1
0
0
1
2
1
0
0
0
0
0
0
0
2
0
0
2
0
4
3
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
3
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
1
0
8
0
0
0
1
5
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
2
2
0
0
2
2
1
2
0
0
0
2
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
1
2
0
0
1
2
3
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
3
0
0
2
4
1
0
0
0
0
2
4
0
1
2
0
3
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
12
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
1
0
2
3
1
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
3
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
2
2
0
0
1
0
3
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
1
2
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
2
1
0
2
0
0
0
0
0
0
2
3
2
0
0
0
1
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
5
2
1
1
0
0
0
0
8
0
5
0
0
1
0
0
1
0
2
0
0
1
2
0
0
0
1
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
2
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
2
1
0
0
2
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
9
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
2
0
2
0
0
0
0
7
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
1
2
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
1
1
0
1
0
0
7
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
3
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
1
0
0
0
1
0
0
0
1
2
0
0
0
3
0
2
0
0
0
0
1
2
0
1
0
0
0
1
0
0
0
0
0
0
0
1
2
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
2
1
0
2
0
1
0
2
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
1
2
0
3
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
3
2
0
0
2
0
2
0
1
1
0
0
2
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
1
2
0
0
0
0
1
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
2
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
4
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
1
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
1
0
1
1
0
0
2
0
0
1
3
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
2
1
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
3
0
2
0
2
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
3
1
0
1
0
0
2
0
2
1
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
1
2
0
2
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
1
1
0
0
0
0
1
2
0
1
0
0
0
1
3
0
0
0
2
0
0
0
1
0
0
0
0
0
2
1
0
0
2
1
1
2
0
0
2
0
0
0
2
0
0
1
0
0
0
2
0
2
0
2
0
0
4
0
0
1
0
0
0
0
1
0
3
0
0
2
0
3
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
2
0
0
1
1
1
2
3
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
2
1
2
0
2
0
1
2
4
0
2
3
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
1
0
0
2
0
0
0
1
0
1
0
3
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
3
5
1
0
1
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
4
0
0
0
0
0
0
2
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
2
1
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
3
3
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
2
1
0
1
1
0
1
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
2
2
0
1
0
0
0
0
0
0
2
0
0
1
1
0
0
1
0
4
0
1
2
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
2
0
2
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
3
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
1
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
2
0
0
3
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
5
0
0
0
0
0
0
1
6
0
1
0
0
0
0
0
1
2
0
0
0
0
2
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
2
0
0
0
7
0
1
1
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
9
0
1
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
1
0
1
0
1
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
1
1
0
3
0
2
0
0
0
0
1
2
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
1
0
1
1
0
2
0
0
0
0
0
0
0
2
1
2
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
3
0
1
0
0
0
0
2
2
0
0
1
1
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
1
0
1
0
0
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
3
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
7
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
3
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
1
0
0
0
2
0
0
2
0
0
0
3
0
0
0
1
0
3
0
0
2
1
0
0
0
0
3
0
1
0
0
0
0
1
0
3
0
0
0
1
0
0
0
3
0
0
1
0
0
0
1
0
0
0
0
0
0
2
1
3
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
3
0
0
0
2
0
3
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
2
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
3
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
2
0
0
0
2
1
2
0
2
0
0
0
1
1
0
0
0
0
1
0
0
3
0
0
0
2
2
0
2
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
1
0
3
0
0
0
0
1
0
1
0
1
0
2
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
6
2
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
5
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
2
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
6
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
2
0
1
0
0
0
2
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
4
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
1
0
0
0
1
0
0
0
0
3
1
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
1
0
2
0
2
0
0
0
2
1
1
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
4
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
8
1
0
1
0
0
0
1
0
1
0
1
0
1
0
0
0
1
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
6
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
1
1
0
0
0
1
0
0
0
0
2
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
9
0
0
1
0
1
0
1
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
3
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
1
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
3
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
1
0
0
2
2
0
0
1
1
0
0
1
0
1
0
3
0
0
2
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
1
0
0
0
0
10
0
0
1
1
0
0
0
1
0
0
2
1
0
0
0
3
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
3
2
0
0
4
0
0
1
0
0
0
0
0
0
1
0
2
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
3
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
3
0
0
0
0
1
0
1
2
0
3
0
1
4
0
4
0
1
0
2
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
2
0
0
0
0
2
0
0
1
2
0
0
0
0
2
2
0
0
0
2
0
0
2
0
0
2
2
0
0
1
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
3
0
6
1
0
0
3
1
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
1
0
0
0
0
1
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
4
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
5
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
2
1
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
1
0
0
1
0
0
0
1
0
4
1
0
0
3
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
3
0
1
2
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
2
2
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
2
0
3
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
3
1
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
2
0
1
0
0
1
0
2
2
0
0
1
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
3
1
0
0
0
2
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
2
0
1
0
0
0
0
0
0
4
1
0
0
0
0
1
0
0
0
0
0
0
0
3
0
2
1
1
0
0
3
0
0
1
0
1
0
0
2
0
0
1
0
3
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
4
0
0
0
0
0
1
0
0
0
3
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
4
1
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
1
2
0
0
0
0
3
2
0
0
0
2
1
0
0
0
0
2
0
1
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
3
0
3
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
2
2
0
1
2
1
0
5
0
0
0
0
1
0
1
2
0
1
0
1
0
0
0
0
2
1
0
1
2
0
2
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
1
1
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
1
0
0
2
2
0
1
2
0
1
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
3
0
3
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
3
3
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
2
0
0
1
0
3
0
0
0
1
0
0
0
1
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
1
3
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
2
0
0
0
1
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
1
0
2
0
0
0
0
3
0
0
1
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
2
0
0
1
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
2
0
1
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
1
4
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
3
0
0
0
1
1
1
1
0
0
0
1
1
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
1
4
0
0
0
0
0
3
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
3
1
0
3
3
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
3
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
1
2
0
0
0
0
2
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
11
0
0
0
2
0
3
2
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
1
3
0
0
0
0
2
0
2
0
4
0
1
0
1
1
0
0
1
0
2
2
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
2
0
1
3
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
3
0
0
0
4
0
0
0
1
0
0
0
0
0
0
3
0
0
0
1
0
2
0
0
0
1
0
4
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
2
0
0
0
1
0
0
0
1
1
1
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
4
0
0
0
1
0
0
1
4
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
1
0
0
1
0
2
0
0
0
0
1
0
0
0
0
2
0
1
0
2
2
0
1
0
2
0
2
0
0
1
0
0
2
0
0
2
0
0
0
0
1
0
0
6
0
0
0
1
0
0
1
2
0
0
0
2
0
2
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
2
2
2
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
1
2
2
2
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
4
1
0
0
1
0
0
0
2
2
1
1
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
3
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
1
0
0
0
2
0
1
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
1
0
2
0
1
0
0
1
1
0
2
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
2
0
0
0
0
0
2
0
0
1
0
2
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
3
2
1
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
4
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
2
2
2
0
0
0
0
0
0
0
1
1
0
0
2
2
1
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
1
0
0
1
2
1
1
0
2
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
3
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
6
8
1
0
0
1
0
0
0
0
1
0
5
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
1
0
0
1
0
0
0
0
1
2
2
1
0
5
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
5
0
0
2
0
0
3
0
0
0
1
0
0
2
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
2
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
3
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
2
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
1
0
1
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
1
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
2
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
7
1
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
2
0
2
0
2
0
0
1
0
0
1
1
0
0
10
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
2
3
0
0
0
0
2
0
2
2
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
4
0
0
2
0
0
2
0
2
0
0
0
2
0
3
1
1
0
0
0
2
0
1
0
0
0
4
0
0
0
1
0
0
0
0
2
0
0
2
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
4
1
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
1
1
0
0
2
0
1
2
0
0
0
0
0
0
0
0
1
0
2
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
2
1
2
1
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
1
1
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
1
1
2
2
0
0
0
0
4
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
2
1
0
0
2
0
0
0
0
2
6
0
0
0
0
1
1
4
2
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
3
1
0
0
0
2
2
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
3
3
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
3
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
2
3
0
0
0
0
0
2
1
5
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
6
0
0
0
6
0
0
2
0
0
0
0
0
0
2
0
3
2
0
2
0
0
0
0
0
1
2
3
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
2
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
7
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
2
2
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
2
1
0
0
0
0
2
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
1
0
0
0
0
2
2
1
0
0
0
0
0
2
0
0
1
0
2
0
3
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
2
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
1
1
0
0
0
0
0
0
0
0
4
0
2
1
0
0
0
0
2
5
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
1
2
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
2
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
1
0
0
0
1
0
1
0
0
0
0
5
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
3
0
1
1
0
2
4
0
0
0
0
2
0
0
0
2
0
0
0
2
5
0
0
0
0
4
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
5
1
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
2
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
1
0
0
0
2
0
0
2
0
0
1
0
0
0
0
2
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
3
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
3
0
0
0
0
0
0
1
0
2
0
0
0
1
2
1
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
3
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
2
1
1
3
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
1
2
0
2
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
3
1
0
1
2
2
0
0
0
1
0
0
2
1
2
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
2
0
0
0
0
0
5
0
0
2
0
0
2
0
0
0
2
1
2
2
0
0
0
0
0
1
0
0
0
0
0
0
5
0
0
0
0
0
0
1
3
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
2
0
0
2
0
0
0
0
3
0
1
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
3
0
0
0
0
1
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
3
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
4
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
1
0
5
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
2
0
2
0
0
0
0
0
0
0
0
1
0
1
0
3
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
4
0
0
0
0
2
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
1
0
1
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
2
0
0
0
0
2
0
0
1
1
1
1
0
1
0
1
0
0
3
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
2
8
0
0
0
0
0
0
1
0
0
0
0
0
0
9
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
2
0
0
0
3
0
0
0
0
1
2
0
0
0
0
0
2
0
2
2
2
0
5
1
0
2
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
7
0
2
0
0
0
2
0
1
0
1
0
0
0
1
0
0
0
1
0
0
2
1
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
5
0
1
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
1
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
2
2
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
2
0
0
0
0
0
1
0
3
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
5
0
1
2
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
1
0
2
0
0
2
1
0
0
0
0
0
1
3
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
2
0
0
0
2
0
0
0
1
2
4
1
0
2
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
2
4
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
3
4
0
1
0
0
1
0
0
0
0
0
2
0
3
3
0
0
0
0
0
6
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
3
2
2
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
2
2
2
0
0
0
0
1
1
0
0
0
0
3
3
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
1
0
3
2
0
0
0
0
0
0
2
0
0
0
2
1
1
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
1
0
0
2
0
0
0
0
1
0
0
1
2
2
0
0
1
0
1
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
1
1
0
0
0
3
0
0
0
0
1
0
0
1
2
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
7
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
1
0
2
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
5
1
0
2
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
4
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
2
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
3
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
1
0
2
0
0
1
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
1
0
0
0
1
0
2
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
2
0
0
0
0
0
0
0
2
1
0
4
0
1
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
3
0
0
1
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
3
0
0
0
0
1
2
1
0
0
0
0
2
3
1
0
0
0
0
2
0
2
0
0
1
0
2
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
2
1
0
0
0
1
3
1
2
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
1
0
2
0
2
0
0
2
3
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
3
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
2
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
3
0
0
1
3
0
0
1
0
5
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
1
1
0
0
0
0
1
4
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
1
0
6
0
0
1
2
3
0
1
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
1
1
0
3
0
0
3
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
2
1
0
1
2
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
1
2
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
9
1
0
0
0
0
0
1
0
1
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
3
0
0
2
1
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
1
0
1
0
0
0
0
0
1
0
0
6
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
1
3
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
1
0
0
0
0
0
1
0
2
0
0
1
2
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
2
0
0
0
0
2
2
3
0
0
1
0
0
2
0
1
0
1
2
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
2
0
0
1
2
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
1
0
0
3
0
0
0
2
0
0
0
2
0
0
0
1
0
2
0
0
0
4
0
0
0
1
0
0
0
1
0
2
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
5
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
2
3
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
3
0
1
0
2
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
2
3
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
1
0
0
3
0
2
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
3
0
0
2
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
6
2
0
0
0
0
1
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
1
0
0
3
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
2
0
0
1
0
2
0
1
0
0
0
0
0
0
2
0
0
0
1
1
0
1
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
1
2
0
0
1
0
1
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
1
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
3
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
18
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
2
0
0
0
3
0
0
0
5
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
1
3
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
3
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
1
1
2
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
2
2
0
2
0
2
0
0
0
0
2
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
1
0
0
0
1
4
0
0
3
0
2
2
0
0
2
2
0
2
0
3
0
1
1
3
0
0
0
2
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
2
0
3
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
2
2
0
0
1
0
0
0
2
0
1
0
2
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
2
0
3
1
0
0
2
1
0
0
0
0
0
1
0
0
0
0
1
0
5
2
0
0
2
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
1
2
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
3
0
0
2
0
0
0
1
2
1
0
2
0
0
4
0
0
0
3
0
0
0
0
0
0
0
0
4
0
0
2
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
1
0
0
2
0
1
2
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
2
0
0
0
0
1
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
2
0
4
3
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
1
0
0
0
0
0
0
2
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
2
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
4
0
1
3
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
2
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
1
0
0
8
0
0
1
0
0
0
0
0
4
2
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
1
1
1
0
0
1
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
2
3
0
0
0
1
1
1
0
0
0
0
2
2
0
1
0
2
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
1
0
11
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
1
5
0
0
0
0
2
1
0
0
0
2
0
0
0
0
2
0
0
0
0
1
1
1
0
1
2
0
0
1
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
2
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
2
1
2
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
4
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
3
0
0
1
0
0
0
0
2
0
0
1
0
0
1
3
0
0
0
0
2
2
0
2
0
0
1
1
0
0
2
0
0
1
1
0
0
0
0
0
0
1
0
2
0
0
0
0
2
1
2
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
2
3
0
3
0
0
2
1
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
1
0
2
0
0
3
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
3
1
0
2
1
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
3
0
0
0
2
0
0
2
0
0
0
2
0
1
0
0
0
1
0
2
0
6
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
1
0
6
0
0
1
2
0
1
0
0
0
1
2
0
2
5
0
1
0
0
0
0
3
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
2
1
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
4
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
10
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
5
0
0
3
6
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
2
0
0
0
0
0
0
3
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
1
1
0
0
0
1
0
3
0
0
0
0
0
0
0
1
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
2
0
0
1
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
1
0
1
2
0
2
1
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
2
2
0
0
1
0
0
0
0
2
0
0
0
3
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
1
0
5
0
0
0
0
1
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
2
0
2
0
2
0
0
0
0
1
1
1
1
1
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
4
0
0
2
2
1
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
3
2
0
0
0
0
0
2
2
0
0
0
0
3
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
1
2
0
0
1
0
1
1
0
0
0
1
2
0
0
0
0
2
1
0
1
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
9
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
1
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
3
0
2
0
0
0
0
0
1
0
1
0
0
2
1
0
2
3
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
1
0
0
0
0
0
0
1
1
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
1
1
0
1
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
2
0
1
0
0
0
2
0
0
1
5
0
0
0
0
0
2
0
2
0
3
0
2
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
2
0
0
3
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
1
0
3
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
2
2
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
2
0
0
0
0
1
1
0
1
3
0
0
1
0
2
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
1
0
0
1
0
1
0
1
1
1
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
2
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
2
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
1
0
0
1
0
1
5
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
1
2
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
3
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
2
0
2
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
4
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
9
0
0
0
0
0
1
0
2
0
0
1
0
0
0
2
0
0
2
0
0
1
2
1
0
0
0
0
1
0
0
0
0
0
1
0
0
2
1
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
1
0
1
0
2
0
0
0
1
0
2
0
0
0
1
0
3
1
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
2
0
2
1
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
2
2
0
1
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
2
0
0
2
1
2
0
0
0
0
0
0
0
1
0
1
0
1
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
3
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
3
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
2
0
1
0
2
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
3
0
0
2
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
2
1
0
0
1
0
0
2
0
0
1
2
0
0
0
0
0
0
2
2
4
0
0
1
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
2
2
0
0
0
1
0
0
2
0
0
0
0
0
2
2
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
1
0
2
0
0
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
0
0
4
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
2
0
0
0
2
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
2
0
0
1
0
1
0
0
3
1
1
0
0
0
0
0
1
2
0
0
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
5
1
0
0
2
0
0
2
0
5
0
0
0
1
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
8
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
2
0
2
1
2
1
0
0
2
0
0
0
0
1
0
0
0
2
2
0
2
1
0
0
3
0
1
0
0
0
0
0
1
0
2
0
0
0
2
0
1
0
0
1
1
1
0
0
0
2
1
0
0
1
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
1
1
0
0
2
2
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
2
0
0
1
0
3
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
2
0
2
0
5
1
0
0
0
0
1
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
2
0
0
0
0
0
2
2
0
0
1
0
0
0
0
2
2
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
4
3
0
1
1
0
0
0
0
2
0
2
0
1
0
0
0
1
0
0
1
0
0
0
0
0
2
1
0
1
0
0
1
0
0
0
0
3
0
3
0
0
1
2
0
1
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
3
0
0
5
0
0
2
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
1
1
0
0
2
0
0
0
2
0
0
2
0
0
1
0
1
0
0
2
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
1
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
2
0
3
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
3
2
0
2
3
0
0
0
0
2
0
1
0
0
0
3
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
3
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
2
1
1
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
2
0
0
0
0
2
1
0
0
1
0
0
4
0
0
0
2
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
1
1
0
2
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
2
0
0
2
0
2
0
0
0
1
0
1
0
0
0
3
0
1
0
0
0
0
1
3
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
4
2
2
0
2
0
0
1
2
2
1
0
2
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
3
0
0
0
0
0
1
0
0
1
1
5
0
2
0
0
0
2
0
2
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
3
1
0
0
0
10
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
1
1
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
1
0
3
0
1
0
1
0
2
0
0
0
0
0
2
0
2
0
1
0
0
4
2
0
0
1
0
2
0
0
2
0
0
1
0
0
0
4
2
0
1
0
0
0
0
3
0
0
0
0
2
3
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
2
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
10
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
1
0
1
0
0
0
0
2
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
6
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
1
2
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
5
0
0
2
0
0
0
0
4
0
0
3
0
0
0
0
1
0
1
0
2
0
0
0
0
0
1
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
1
0
5
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
2
0
0
2
2
1
0
0
0
0
2
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
3
0
0
1
0
2
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
3
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
1
1
0
2
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
5
0
0
12
0
0
0
0
0
2
0
0
0
1
0
0
2
0
1
0
1
0
2
0
0
0
0
0
0
3
2
0
0
2
1
0
0
0
0
0
2
0
2
0
3
0
0
2
0
0
0
1
1
0
2
0
3
0
0
2
3
0
1
0
0
0
0
0
2
1
2
2
0
0
2
2
0
1
2
0
0
0
0
0
5
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
6
0
0
0
1
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
2
0
1
3
0
1
0
3
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
3
3
1
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
2
0
0
2
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
1
0
0
0
0
6
1
0
0
0
0
1
2
2
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
1
3
0
0
5
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
1
1
3
0
0
1
0
0
0
0
0
1
0
1
2
0
0
2
2
0
0
2
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
3
0
0
1
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
2
0
1
0
1
1
0
0
0
4
0
2
1
0
0
0
0
0
0
1
2
1
0
0
0
2
0
0
1
0
5
0
1
3
0
0
0
0
2
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
1
0
2
0
1
2
0
2
0
0
0
0
2
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
2
0
0
2
1
0
0
2
2
0
0
2
0
0
0
0
1
2
2
2
0
1
0
2
1
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
3
0
1
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
3
0
2
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
2
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
4
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
1
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
3
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
3
0
0
0
0
0
1
4
0
0
1
3
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
1
0
2
1
0
0
0
1
0
0
0
4
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
1
0
0
3
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
1
3
0
1
0
0
0
0
0
3
0
1
0
0
2
0
1
0
3
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
2
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
3
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
1
0
0
0
0
2
1
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
1
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
4
0
0
0
0
2
0
1
0
0
2
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
3
1
1
0
0
0
4
1
0
0
0
1
0
1
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
1
3
3
0
0
4
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
8
2
2
1
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
2
0
1
0
0
0
0
0
0
3
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
1
2
0
0
1
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
2
2
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
2
1
0
1
1
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
1
1
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
1
0
1
0
0
0
0
0
2
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
1
0
0
0
0
1
0
2
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
1
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
3
1
0
0
1
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
22
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
7
0
1
0
7
0
0
1
0
0
1
0
3
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
6
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
7
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
1
1
0
0
0
5
0
0
0
0
2
0
0
0
0
2
0
2
0
0
2
1
0
0
0
2
0
1
2
2
0
2
1
0
0
2
0
1
0
0
0
3
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
2
0
1
1
0
2
2
1
0
1
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
1
4
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
3
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
2
2
0
0
2
0
3
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
1
0
1
0
0
0
0
0
4
2
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
2
2
0
0
0
1
1
0
0
1
2
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
1
0
1
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
2
0
0
0
0
0
1
2
0
0
0
3
0
0
2
0
0
2
0
1
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
1
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
2
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
1
2
0
2
0
0
0
2
0
3
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
1
0
2
4
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
2
0
0
0
0
2
0
0
1
4
0
0
0
0
0
0
2
4
0
3
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
3
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
3
0
0
1
0
0
0
0
2
0
0
2
0
2
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
1
3
0
0
0
0
0
2
3
1
0
0
0
1
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
4
0
1
2
0
0
1
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
2
0
0
0
0
0
0
3
0
0
2
1
0
4
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
1
1
0
0
0
0
0
0
0
0
2
2
2
0
0
2
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
2
0
0
1
0
2
3
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
6
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
8
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
1
0
2
0
4
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
3
1
1
0
2
0
2
0
1
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
2
0
2
2
3
0
0
0
1
0
0
2
0
2
0
0
1
2
0
0
2
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
1
1
0
0
2
0
2
1
0
0
0
0
0
1
1
0
0
3
0
0
0
0
2
0
2
3
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
1
0
0
0
0
0
0
0
0
1
1
0
3
2
0
0
1
0
2
0
0
0
0
2
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
1
0
0
1
0
3
0
0
0
2
0
0
0
0
2
0
0
2
0
1
0
1
0
0
0
0
2
0
2
0
0
2
0
0
2
0
1
1
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
4
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
1
0
0
3
0
0
1
0
2
3
1
2
0
1
0
0
1
2
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
1
0
2
0
0
0
1
1
2
0
2
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
4
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
0
0
2
3
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
2
0
0
0
2
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
2
0
0
1
2
2
1
0
0
0
1
0
0
0
0
0
0
0
2
1
1
1
0
0
0
0
2
2
0
0
0
0
3
0
0
3
0
0
0
1
0
0
2
1
0
1
2
0
0
0
0
0
2
0
0
0
3
2
0
0
1
0
0
2
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
1
0
0
2
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
2
0
0
4
0
1
1
0
0
0
0
0
0
1
2
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
13
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
2
0
4
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
2
0
2
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
2
2
4
0
0
0
0
0
0
2
0
3
3
10
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
2
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
1
0
0
0
2
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
2
0
0
1
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
1
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
2
2
5
0
1
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
1
0
0
0
0
1
0
0
2
1
0
0
2
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
2
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
3
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
3
0
0
0
0
0
0
0
0
1
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
1
0
0
0
0
0
4
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
2
0
7
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
16
0
0
2
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
1
1
0
0
0
0
2
0
3
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
3
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
1
0
1
1
0
0
0
0
1
0
2
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
2
0
2
0
0
0
0
2
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
3
2
0
1
0
0
0
0
2
0
0
2
1
2
0
0
0
2
2
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
5
0
2
0
0
0
1
0
0
0
1
0
1
0
1
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
3
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
1
1
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
1
0
0
0
1
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
3
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
2
1
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
1
0
0
1
1
2
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
2
1
0
0
0
2
2
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
1
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
1
0
0
0
0
0
5
0
3
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
1
1
0
1
0
2
0
0
0
1
0
2
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
2
2
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
1
0
1
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
1
3
2
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
2
3
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
1
0
9
0
0
0
0
1
0
0
0
0
3
0
1
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
2
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
1
2
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
5
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
2
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
1
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
2
2
1
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
1
0
2
1
0
1
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
3
0
0
0
0
1
2
3
0
3
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
1
0
1
0
1
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
1
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
4
0
0
0
1
0
2
0
0
0
2
0
2
0
1
0
2
2
0
1
0
0
0
0
0
0
2
1
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
1
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
2
0
0
2
2
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
3
6
0
0
0
0
0
0
0
0
2
0
0
3
0
0
3
0
0
2
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
1
5
0
0
0
1
0
1
0
0
1
0
2
0
3
0
0
0
0
0
2
0
2
2
0
2
0
0
2
1
4
0
0
0
6
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
1
0
0
3
0
0
1
2
4
0
0
0
0
0
0
0
2
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
3
0
0
0
0
0
1
0
0
0
2
0
1
0
2
1
0
0
1
0
2
0
0
0
0
1
0
0
0
2
1
0
0
0
3
0
0
14
0
0
0
0
0
0
1
0
0
0
2
3
0
2
0
0
0
0
0
1
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
2
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
1
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
4
1
0
2
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
5
3
0
0
0
0
2
0
0
0
0
0
2
4
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
9
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
3
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
4
3
0
0
0
0
0
0
2
2
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
6
1
2
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
5
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
1
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
1
0
1
0
0
2
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
2
0
0
0
0
1
0
0
0
0
0
2
1
0
3
0
0
0
0
0
0
2
2
0
0
2
0
1
0
0
0
1
0
3
0
2
0
0
2
0
0
0
1
0
0
1
2
0
3
0
0
1
0
0
2
0
1
1
0
0
0
0
0
0
2
0
0
0
0
14
1
0
0
1
3
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
1
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
1
0
4
0
0
0
0
2
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
2
2
1
1
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
3
0
0
1
0
2
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
1
1
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
3
0
0
0
0
1
0
0
0
4
2
0
0
0
0
0
0
0
0
3
0
0
0
1
1
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
1
0
3
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
1
1
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
11
0
0
0
0
0
2
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
1
0
2
0
0
0
0
0
1
0
2
0
5
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
6
1
0
0
0
4
0
4
0
1
0
2
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
2
2
0
0
0
1
1
0
0
0
0
0
2
0
0
1
0
0
0
2
2
0
0
0
0
0
0
1
2
0
0
0
0
2
0
3
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
5
0
0
0
0
0
0
2
0
0
2
0
0
10
2
0
0
0
1
0
1
0
0
0
0
0
0
2
0
1
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
1
0
3
2
0
0
0
0
2
1
0
1
2
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
2
0
0
3
2
0
1
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
2
0
1
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
7
2
2
0
0
0
0
0
2
2
0
0
0
0
0
3
0
1
0
0
0
0
0
1
0
0
2
0
2
0
2
0
0
0
0
1
0
0
0
0
2
0
2
1
1
0
0
2
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
2
0
1
0
0
0
0
2
0
0
0
0
2
0
1
1
0
0
0
2
0
0
0
3
1
2
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
2
1
0
0
2
3
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
1
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
3
0
2
2
0
0
3
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
1
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
1
0
0
4
0
1
0
1
0
0
1
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
1
2
1
3
1
0
1
0
2
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
1
0
2
1
0
0
2
0
0
0
0
2
0
0
0
1
1
1
0
0
0
0
0
0
0
5
0
2
1
1
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
2
3
0
0
0
0
0
1
0
0
0
0
7
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
3
0
2
0
2
0
0
3
0
0
7
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
3
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
9
0
0
0
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
4
0
2
0
0
3
0
0
0
0
0
0
0
0
0
3
2
2
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
2
1
1
0
0
2
0
0
1
2
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
1
0
0
2
0
0
0
0
0
3
1
1
0
0
2
1
1
0
0
1
0
0
2
0
0
0
3
0
0
0
1
1
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
2
0
0
1
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
4
2
0
2
0
0
0
0
0
0
0
3
0
0
0
0
1
2
1
0
0
2
2
2
0
0
1
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
8
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
1
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
1
3
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
5
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
1
0
3
0
1
2
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
1
0
2
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
2
0
0
2
2
0
3
0
0
2
1
0
0
1
1
0
1
0
0
1
0
2
0
0
0
0
0
1
0
0
1
2
0
0
1
0
0
1
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
2
3
0
0
0
0
0
0
0
2
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
6
0
2
2
1
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
1
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
3
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
3
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
8
0
0
0
0
0
0
0
1
2
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
2
0
0
0
2
0
0
1
0
0
2
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
2
3
0
0
0
0
0
2
1
0
0
0
0
2
0
0
2
0
0
0
0
2
1
0
2
0
1
0
0
2
0
2
2
0
2
0
0
0
0
0
2
0
0
2
0
3
0
0
0
0
2
0
1
1
2
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
2
0
0
3
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
3
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
6
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
2
0
0
0
8
0
0
3
0
1
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
3
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
2
2
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
6
0
0
1
0
1
0
0
0
1
0
0
0
0
1
3
0
0
0
2
0
0
0
3
2
0
0
0
0
1
2
0
0
0
0
0
1
1
1
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
6
0
0
0
0
0
0
0
1
0
0
0
0
0
2
4
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
3
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
3
2
0
1
0
0
3
1
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
2
1
2
4
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
2
2
0
2
0
0
0
1
0
0
0
0
0
4
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
7
0
3
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
3
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
4
4
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
10
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
1
0
0
0
1
1
0
0
3
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
4
0
0
2
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
4
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
3
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
1
2
0
0
0
1
0
2
1
0
0
10
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
2
2
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
2
1
0
1
1
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
3
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
2
0
0
0
1
4
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
1
1
0
0
0
3
3
2
0
1
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
6
2
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
2
2
0
2
1
0
0
2
0
0
2
1
0
0
0
0
0
7
1
0
0
2
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
0
3
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
5
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
2
1
0
0
0
0
2
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
2
2
0
0
1
0
0
0
0
6
4
0
0
0
2
2
0
2
0
0
0
0
2
2
0
0
0
1
2
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
5
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
2
0
0
0
2
1
0
0
0
0
2
2
3
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
6
0
3
0
1
2
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
2
0
0
0
0
0
0
0
0
0
1
0
0
6
5
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
3
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
5
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
1
0
0
0
2
0
3
0
2
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
2
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
3
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
2
0
2
0
0
0
1
1
0
0
0
0
0
2
0
0
0
7
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
1
0
3
0
0
1
1
2
0
0
0
0
1
0
0
0
0
1
0
0
2
0
1
0
0
2
2
0
1
0
1
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
1
1
0
0
1
0
0
0
3
0
0
0
1
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
8
1
1
0
0
0
0
0
0
1
0
1
0
4
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
2
0
0
1
0
2
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
5
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
2
0
0
3
0
0
3
0
0
0
0
1
0
0
2
1
0
0
0
0
1
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
1
2
0
1
2
0
2
0
1
0
1
0
2
0
0
0
1
1
0
1
0
1
4
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
2
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
1
0
0
0
2
0
0
1
6
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
1
0
1
0
1
0
0
0
4
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
1
0
2
1
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
1
0
0
0
4
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
2
0
0
0
4
0
0
1
0
0
0
2
0
0
1
0
1
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
1
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
1
2
0
0
0
1
1
0
0
0
1
0
0
3
0
0
0
0
2
0
1
2
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
4
3
0
3
2
0
0
2
0
0
0
2
2
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
2
0
0
0
0
1
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
8
0
1
0
1
1
1
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
3
0
0
1
2
0
1
0
0
5
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
3
0
2
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
2
0
1
2
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
3
0
4
0
0
2
2
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
2
3
0
1
0
0
0
0
0
0
3
3
0
0
1
0
5
0
0
0
0
0
3
0
1
0
3
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
1
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
2
2
2
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
1
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
1
0
0
0
11
0
0
0
1
0
0
0
2
0
0
1
0
0
2
0
0
1
0
0
0
1
1
0
0
1
3
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
9
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
3
1
1
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
1
2
2
0
0
0
1
0
2
0
0
0
1
1
0
1
0
2
2
0
0
0
0
0
2
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
2
1
0
0
2
0
1
0
0
0
3
0
1
1
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
4
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
1
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
1
2
0
1
0
1
0
0
0
0
0
3
1
1
0
5
1
0
0
0
0
0
0
2
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
3
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
2
0
2
1
0
0
0
0
0
3
0
2
0
0
0
0
3
2
0
0
0
0
0
0
0
0
1
3
0
0
0
0
2
2
2
0
0
1
1
1
0
2
0
0
0
0
2
0
1
0
0
0
0
0
2
4
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
2
0
0
0
0
2
2
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
3
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
2
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
4
1
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
7
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
1
0
1
2
1
0
0
0
0
0
0
0
0
0
1
0
3
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
5
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
3
1
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
1
2
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
4
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
2
2
2
0
0
3
0
0
0
0
3
0
2
0
0
0
3
1
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
2
1
0
3
0
0
0
1
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
2
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
2
0
0
0
1
1
2
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
1
2
0
0
0
2
0
0
0
0
0
2
3
1
0
0
0
0
0
0
2
3
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
3
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
2
0
2
0
4
0
2
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
5
0
0
0
0
1
0
0
1
16
0
0
0
2
1
0
0
0
0
1
2
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
2
3
2
1
0
0
0
0
1
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
3
0
3
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
1
2
0
0
5
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
2
0
0
4
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
6
0
0
0
1
0
0
0
2
0
2
0
0
0
1
0
2
0
0
1
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
2
0
2
0
1
0
1
1
0
0
1
1
1
0
3
3
0
0
0
0
0
0
0
2
2
1
0
1
0
0
4
0
0
1
2
1
2
0
1
0
0
0
1
1
28
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
2
1
2
1
0
0
0
0
2
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
1
0
0
0
0
2
2
1
1
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
4
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
2
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
2
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
2
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
3
0
1
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
3
0
3
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
2
1
0
0
0
1
0
0
0
0
0
1
2
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
2
0
1
0
0
0
6
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
1
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
2
0
0
1
0
0
2
0
0
0
1
0
0
0
0
2
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
2
3
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
1
1
1
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
2
2
0
0
2
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
1
0
0
0
2
0
0
2
0
0
1
1
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
1
0
5
2
0
0
1
19
0
0
0
0
0
0
0
0
1
2
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
2
0
2
0
2
0
2
0
1
0
0
0
0
0
1
0
5
0
0
0
0
0
2
0
2
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
2
1
1
0
1
2
0
0
0
0
1
1
0
0
0
0
0
1
2
5
0
1
0
0
0
0
1
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
1
1
0
0
2
0
0
0
3
2
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
2
4
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
8
0
1
0
3
2
0
0
0
0
1
0
0
0
0
0
3
0
0
0
2
0
0
3
0
1
0
1
1
0
0
0
5
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
2
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
5
0
0
0
0
0
2
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
1
0
0
2
1
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
2
0
0
3
1
0
0
0
2
2
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
2
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
1
0
4
0
0
0
0
0
0
0
6
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
4
1
1
0
1
0
1
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
1
0
0
2
2
0
0
1
1
1
0
0
0
1
1
0
0
2
0
0
0
1
0
0
2
0
0
1
0
0
2
0
0
0
0
0
2
0
3
0
1
2
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
2
0
0
2
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
3
2
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
1
0
2
0
0
1
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
3
0
2
0
0
0
0
0
1
1
0
0
1
0
0
0
3
0
0
2
0
0
0
0
0
0
0
2
0
2
0
1
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
3
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
9
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
2
0
1
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
1
1
0
1
1
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
7
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
1
0
1
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
1
0
3
0
0
2
1
0
0
0
0
0
0
0
1
3
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
5
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
10
0
1
0
1
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
4
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
4
1
3
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
1
0
0
3
0
0
0
0
2
2
2
0
0
0
0
0
0
0
1
2
0
2
0
0
1
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
1
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
3
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
2
1
0
2
3
3
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
3
2
0
1
4
0
4
1
0
0
0
0
0
0
0
1
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
3
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
3
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
2
3
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
1
2
0
0
0
0
0
0
0
2
2
0
0
1
0
0
2
0
0
0
0
1
0
0
1
0
2
0
2
0
1
1
1
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
1
0
0
3
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
1
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
2
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
2
1
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
2
3
0
0
0
3
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
4
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
2
1
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
2
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
7
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
2
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
1
0
0
2
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
6
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
3
0
0
1
0
0
0
2
0
0
3
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
10
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
1
0
3
0
0
3
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
1
0
2
0
3
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
3
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
2
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
5
0
0
0
0
0
0
0
0
2
1
0
0
0
0
7
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
2
0
0
0
2
2
0
2
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
3
0
1
0
0
0
0
0
1
0
2
0
2
0
0
0
2
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
3
0
0
0
1
2
2
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
2
2
0
2
0
0
1
0
2
0
0
0
0
0
2
4
1
0
4
2
1
2
0
0
0
1
0
0
0
2
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
1
0
0
2
1
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
3
0
0
0
0
0
0
3
0
1
7
0
1
3
0
1
0
2
0
0
1
0
0
0
1
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
1
0
2
9
0
0
0
2
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
2
2
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
3
0
0
1
0
1
0
0
2
0
0
0
0
0
0
2
1
0
0
0
1
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
1
1
0
0
3
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
3
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
2
0
0
2
0
0
0
0
2
0
0
0
0
0
1
1
0
0
2
0
2
0
0
0
0
2
1
0
9
3
0
0
1
0
0
0
2
0
0
2
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
4
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
3
1
0
0
2
0
0
0
1
0
2
0
2
0
0
0
2
0
25
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
2
0
2
0
0
0
5
1
0
0
0
0
0
0
0
1
0
0
3
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
1
0
2
0
0
1
0
0
0
2
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
3
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
2
0
3
1
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
4
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
1
0
3
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
3
0
0
0
0
0
0
0
1
1
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
4
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
3
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
2
1
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
3
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
3
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
3
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
2
1
2
2
0
0
0
2
0
0
2
0
0
3
0
1
1
1
0
0
0
0
2
0
1
0
1
0
0
0
1
2
2
0
2
1
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
3
1
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
1
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
1
0
1
2
0
0
0
0
0
2
0
3
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
2
0
0
2
0
0
0
1
0
2
0
0
0
2
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
1
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
1
0
0
1
0
1
0
1
0
2
0
1
1
0
0
0
1
0
0
2
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
1
0
6
1
2
2
0
0
0
2
0
2
1
0
0
2
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
2
0
0
0
1
0
2
0
4
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
2
1
0
0
1
2
0
2
0
0
0
0
2
0
1
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
1
1
0
1
0
0
0
0
0
2
7
0
0
0
0
3
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
1
1
0
2
0
0
0
0
1
0
0
0
0
0
0
3
0
1
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
1
0
2
0
0
0
1
0
1
1
0
2
0
2
0
1
0
0
0
0
3
0
0
0
0
0
4
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
1
4
0
2
0
3
0
1
1
0
6
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
3
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
1
1
1
3
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
5
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
4
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
2
2
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
2
2
0
1
0
0
0
0
1
0
11
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
1
2
2
3
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
1
0
0
0
0
3
0
2
0
12
2
0
0
0
0
1
1
1
2
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
1
0
3
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
2
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
1
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
2
0
1
1
2
0
0
2
0
1
0
1
1
1
0
2
2
0
0
0
0
0
0
1
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
3
1
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
2
1
0
0
0
0
0
1
1
0
0
0
1
0
1
2
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
6
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
2
2
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
4
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
3
1
0
0
4
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
5
0
0
1
2
0
1
0
0
0
0
2
2
0
1
0
2
0
1
2
0
0
2
0
0
0
0
0
2
0
1
0
1
1
0
0
0
4
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
8
0
0
0
1
2
0
0
0
6
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
1
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
3
0
0
0
0
0
0
2
6
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
1
7
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
1
1
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
2
0
0
0
2
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
2
0
6
0
0
0
0
0
2
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
4
1
1
0
1
2
0
0
1
0
2
0
2
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
5
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
1
4
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
3
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
1
0
0
0
0
2
3
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
1
0
3
0
0
1
0
0
3
0
0
2
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
8
0
0
0
0
0
0
0
0
1
2
0
0
1
0
2
0
0
1
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
1
0
0
0
1
0
0
1
0
2
0
1
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
2
1
1
2
1
2
0
2
0
0
0
0
0
0
8
0
0
2
2
1
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
1
0
2
0
2
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
1
1
0
2
2
0
0
0
3
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
2
0
1
1
2
1
1
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
2
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
4
1
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
2
2
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
0
2
0
0
0
0
0
0
0
0
2
1
1
1
0
0
1
1
0
1
2
6
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
3
1
0
1
0
0
1
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
2
0
0
0
1
1
0
2
0
1
0
0
1
1
0
2
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
1
0
0
0
0
4
2
0
0
1
1
0
0
0
0
5
0
2
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
1
10
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
2
0
1
2
0
0
0
2
3
1
0
2
0
0
0
0
0
2
3
0
1
0
0
0
0
2
2
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
1
0
0
0
1
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
1
0
0
0
1
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
2
2
0
2
1
0
0
0
0
0
1
3
2
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
2
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
1
1
2
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
1
2
0
0
2
1
0
0
0
1
1
1
1
0
2
3
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
2
1
0
0
1
0
0
2
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
1
0
0
0
0
0
0
0
0
2
0
1
1
0
0
1
0
1
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
1
1
0
0
0
1
0
2
0
2
0
0
0
0
0
1
0
0
6
0
1
2
0
0
1
1
1
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
2
4
0
0
0
0
0
2
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
6
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
2
1
2
0
2
0
0
2
0
0
2
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
2
0
0
0
1
0
2
0
0
2
0
3
7
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
1
1
0
1
0
0
0
2
0
0
0
2
0
0
2
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
2
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
1
2
2
0
0
0
1
0
0
0
2
0
2
2
0
0
0
0
0
1
0
0
1
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
2
1
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
2
0
2
0
0
0
2
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
3
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
1
2
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
2
0
0
0
2
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
1
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
1
0
2
0
0
0
0
2
0
0
1
0
0
1
0
1
0
0
0
0
0
2
0
0
3
0
2
0
1
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
3
0
0
0
0
0
0
3
0
0
0
0
2
2
0
2
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
4
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
2
3
0
0
0
0
1
0
1
1
0
0
0
0
0
2
4
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
5
1
0
0
5
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
1
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
1
1
6
0
0
2
4
0
2
0
0
0
2
0
0
1
1
1
0
2
0
0
0
0
1
0
0
0
0
1
3
0
0
0
1
0
0
1
0
2
0
1
1
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
3
5
2
0
0
0
0
1
0
1
1
0
0
1
1
0
0
0
0
7
0
0
1
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
13
2
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
1
3
0
2
0
0
0
1
0
0
0
0
0
1
0
1
0
0
2
0
0
0
1
2
2
0
0
0
5
3
0
0
0
3
0
0
0
0
2
1
0
2
0
0
0
5
0
0
6
3
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
2
0
0
4
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
2
1
0
0
1
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
3
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
1
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
3
1
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
2
0
6
0
1
0
0
0
0
2
0
0
4
0
1
0
0
0
0
0
2
1
3
0
0
0
1
2
0
2
0
0
0
3
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
2
0
0
0
1
0
0
2
1
1
0
0
2
0
2
0
0
1
0
0
0
0
0
0
2
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
4
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
9
0
0
0
0
1
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
5
2
1
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
4
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
3
0
1
0
0
0
2
0
0
0
2
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
2
2
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
1
2
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
2
0
1
0
0
0
0
6
4
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
3
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
2
0
0
2
0
0
1
0
0
1
2
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
3
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
5
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
1
0
0
0
1
0
1
0
0
2
1
0
0
4
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
11
2
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
6
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
1
0
0
2
0
2
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
2
1
0
3
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
3
0
0
1
0
0
0
0
1
0
0
2
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
2
1
3
0
1
1
0
0
0
0
2
0
4
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
2
0
1
0
2
1
0
0
1
0
1
1
0
2
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
1
0
0
1
0
0
0
7
1
0
1
0
0
1
0
2
0
0
0
0
0
0
1
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
2
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
2
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
8
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
6
2
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
2
2
0
0
0
0
0
1
0
3
0
1
0
4
0
0
1
0
0
0
0
0
0
0
2
6
2
0
0
0
1
2
0
0
0
0
0
0
0
1
2
0
2
0
0
1
0
1
1
0
1
0
0
3
1
1
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
1
0
0
1
0
1
2
0
1
3
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
1
0
0
0
0
1
2
0
0
2
0
2
0
1
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
1
2
1
0
0
0
0
0
0
0
0
8
0
0
0
0
0
2
1
0
0
2
0
2
0
0
0
0
1
0
2
1
0
0
1
0
0
0
0
0
2
2
0
0
2
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
3
0
0
2
0
3
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
2
3
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
1
0
3
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
3
0
0
0
0
2
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
2
3
0
0
0
2
0
2
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
2
0
1
1
0
2
0
0
1
0
3
0
0
0
0
0
0
0
2
2
0
6
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
1
0
0
0
0
2
0
2
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
5
0
0
1
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
1
0
0
0
1
0
1
2
0
2
1
0
0
0
1
1
0
1
0
1
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
1
0
2
3
0
0
0
0
0
0
2
0
0
7
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
6
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
1
0
0
0
0
1
0
0
0
1
1
2
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
1
1
0
1
0
0
0
0
2
0
0
1
0
1
0
0
0
0
1
0
1
2
0
0
0
1
0
0
1
2
0
0
0
0
3
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
1
0
2
0
0
1
2
1
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
7
2
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
1
3
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
2
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
1
1
18
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
1
1
0
2
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
3
0
0
0
2
0
0
0
0
1
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
1
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
2
0
2
1
0
0
0
0
0
2
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
3
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
2
3
2
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
2
0
1
0
0
0
0
0
2
3
0
0
0
0
3
1
0
0
0
0
0
1
2
1
1
0
0
2
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
2
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
5
2
0
0
5
1
0
0
0
0
0
0
1
0
0
0
0
0
1
2
1
0
0
0
0
0
4
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
5
0
0
1
0
1
0
1
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
4
2
0
5
0
0
1
0
0
0
0
1
0
0
0
2
0
1
0
0
1
1
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
5
0
1
0
0
0
2
0
0
1
0
2
0
0
1
0
1
0
0
0
0
0
0
0
1
2
0
1
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
2
0
0
0
0
0
0
0
1
2
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
3
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
4
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
2
1
3
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
2
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
1
0
0
0
2
1
2
2
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
3
0
1
0
0
0
0
0
0
5
0
0
0
1
0
0
0
2
0
2
0
0
0
0
3
0
0
2
0
0
1
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
1
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
1
0
2
0
0
2
0
1
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
3
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
4
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
2
0
0
1
0
1
0
2
1
1
0
0
0
1
0
0
0
10
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
3
1
0
0
2
0
0
0
1
1
0
1
0
0
2
0
0
0
2
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
1
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
6
2
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
2
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
1
6
2
2
2
0
0
0
16
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
12
0
0
2
0
0
2
0
0
0
1
0
0
2
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
3
1
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
3
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
1
0
1
0
0
0
0
2
1
2
1
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
2
0
1
0
0
0
0
0
1
2
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
1
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
2
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
1
2
0
3
0
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
1
0
0
0
0
2
2
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
3
2
0
2
0
0
1
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
1
0
0
2
3
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
2
0
1
2
1
1
0
0
5
2
2
2
3
0
0
0
0
2
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
1
0
3
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
1
2
2
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
1
1
2
0
3
0
2
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
3
3
1
0
1
2
1
0
0
2
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
1
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
2
0
2
1
0
0
0
2
0
1
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
6
0
0
0
1
0
2
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
2
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
2
0
0
3
0
0
0
2
0
0
0
0
0
1
2
0
5
1
0
1
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
2
0
0
2
0
0
5
1
2
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
6
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
3
3
0
0
0
2
0
1
2
0
0
0
2
1
0
0
1
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
3
0
0
0
4
1
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
1
1
1
0
0
3
0
2
2
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
5
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
2
0
0
0
0
2
0
0
0
0
1
0
2
0
0
2
2
0
1
0
0
0
0
1
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
2
2
0
0
0
0
4
0
0
0
5
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
2
2
2
0
2
2
0
0
2
0
0
2
0
0
0
1
2
0
0
0
3
0
1
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
1
2
1
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
3
0
6
0
0
3
1
0
0
2
1
0
0
0
0
0
0
1
0
0
2
0
0
1
0
1
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
1
0
0
2
0
4
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
2
0
1
0
0
1
0
0
0
0
0
0
0
3
0
2
0
2
1
0
2
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
2
0
0
0
0
0
2
2
0
0
0
1
0
2
0
0
2
0
2
5
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
1
0
0
0
1
0
1
0
0
0
0
2
0
0
0
1
0
1
1
1
0
1
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
2
1
0
1
0
0
1
2
0
0
0
1
0
0
0
3
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
4
0
1
0
0
0
0
1
2
1
0
0
0
1
2
3
0
2
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
1
0
2
0
0
1
3
1
2
0
0
1
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
1
2
0
0
0
3
0
0
0
0
0
1
2
0
0
0
0
2
0
0
2
0
2
0
0
1
1
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
3
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
1
0
5
0
0
0
0
1
0
1
0
0
0
1
0
0
2
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
2
2
0
0
1
1
0
0
0
0
0
0
0
1
2
2
1
0
0
0
3
0
1
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
2
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
2
1
0
0
1
0
2
0
0
0
0
0
0
1
0
1
2
0
0
2
2
2
2
0
0
0
0
0
0
0
1
0
0
1
0
2
1
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
1
0
3
2
4
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
3
0
0
2
0
0
0
0
1
0
0
0
1
0
1
0
10
0
0
0
1
0
3
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
3
0
3
1
0
0
0
0
1
2
0
0
0
0
2
1
3
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
4
2
0
2
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
1
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
1
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
1
0
0
0
1
0
1
2
3
0
0
0
0
0
0
0
0
0
0
1
7
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
2
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
4
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
1
2
0
0
0
1
0
1
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
2
0
0
0
6
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
6
0
0
0
0
3
1
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
1
1
1
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
2
2
0
0
0
1
2
5
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
2
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
1
0
0
0
1
0
1
0
0
3
0
1
2
1
0
0
0
1
0
1
0
1
0
2
0
0
1
0
2
0
0
2
1
2
0
0
0
0
0
2
2
1
0
2
0
0
0
0
1
0
0
0
0
1
12
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
1
2
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
3
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
2
2
1
2
0
0
0
0
3
0
0
0
0
0
1
2
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
1
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
2
1
0
1
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
1
0
0
0
0
0
1
0
1
0
2
2
0
0
0
1
0
1
0
2
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
1
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
2
0
0
0
2
0
0
0
1
2
2
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
12
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
2
0
2
0
1
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
1
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
1
0
0
2
0
0
0
0
0
1
2
1
0
0
0
1
1
0
1
3
1
0
0
0
0
0
2
0
2
0
0
1
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
1
2
0
0
0
0
1
0
8
0
0
1
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
7
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
2
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
1
0
0
0
0
0
0
4
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
1
1
0
1
2
1
1
0
0
2
0
0
7
1
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
28
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
4
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
1
3
0
0
2
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
11
2
0
2
4
0
1
0
0
0
0
1
2
2
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
3
0
0
0
0
1
0
1
2
0
0
3
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
10
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
2
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
11
0
0
0
1
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
2
2
0
6
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
3
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
8
2
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
4
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
4
0
0
0
2
0
0
2
2
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
3
0
0
1
0
0
0
2
0
0
0
2
1
0
0
0
0
1
2
0
0
0
0
0
1
2
0
0
0
0
2
0
2
1
0
0
2
1
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
3
0
0
0
0
0
0
2
0
0
0
0
1
0
1
2
0
0
0
2
2
0
0
1
0
0
0
0
2
1
1
0
2
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
6
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
2
0
1
4
0
0
0
1
2
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
1
0
1
0
0
3
1
0
0
0
0
0
1
0
2
0
0
2
0
1
0
2
0
0
1
2
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
3
0
0
0
1
0
2
0
0
1
2
0
0
1
1
0
0
4
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
3
2
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
2
1
3
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
2
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
7
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
5
0
0
0
1
2
2
0
0
0
6
0
0
0
0
0
0
0
0
1
0
0
1
0
3
0
0
0
2
0
0
5
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
3
0
2
0
0
0
1
0
0
1
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
3
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
1
1
2
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
2
2
0
3
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
1
0
0
1
2
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
3
1
0
2
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
2
0
1
0
0
2
0
0
0
1
0
0
2
0
0
0
2
0
0
2
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
3
1
3
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
1
1
0
0
0
1
6
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
3
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
1
1
1
0
2
0
0
0
0
0
0
0
0
7
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
2
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
2
2
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
7
0
2
0
1
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
4
0
1
4
0
1
0
0
0
0
0
2
0
0
0
2
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
1
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
4
1
0
0
0
0
0
2
2
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
1
2
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
3
1
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
2
2
0
0
2
0
0
0
0
0
0
2
0
1
0
0
4
0
0
0
0
1
0
0
1
0
0
0
0
2
9
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
2
1
0
2
0
7
0
2
0
0
0
0
0
1
0
0
0
0
3
0
0
3
0
0
0
2
1
0
0
1
0
0
1
0
0
2
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
3
0
0
0
3
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
2
1
0
0
1
0
0
2
2
3
1
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
1
1
0
2
0
0
0
0
1
0
0
0
2
2
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
3
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
1
1
0
0
0
0
1
2
0
0
2
4
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
1
0
0
1
0
2
0
1
1
0
0
1
1
1
2
1
0
0
0
0
0
3
0
2
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
4
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
2
1
0
0
0
0
0
0
3
0
1
0
0
0
0
2
0
2
0
0
1
0
1
5
1
0
0
0
0
0
0
0
2
2
0
2
1
0
0
0
2
2
2
0
0
1
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
1
0
0
5
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
2
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
5
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
1
0
2
2
0
2
0
0
0
0
0
0
0
2
0
1
6
0
0
1
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
3
2
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
1
0
0
1
0
2
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
2
2
0
0
2
0
0
0
3
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
2
0
2
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
1
2
0
0
1
1
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
1
0
1
0
0
1
0
0
0
2
0
2
1
2
0
1
2
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
2
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
5
0
0
2
0
0
0
0
0
0
0
2
0
3
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
2
2
2
1
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
2
0
0
0
0
2
0
0
4
4
0
0
0
3
0
0
0
1
0
0
0
1
0
3
0
0
1
0
1
5
0
0
1
0
0
1
0
0
2
0
0
0
0
1
0
0
0
1
2
0
1
1
0
0
0
0
1
0
1
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
3
3
1
2
0
0
0
1
0
0
2
0
2
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
1
0
0
0
0
0
0
1
4
0
2
0
0
0
1
0
2
0
0
2
0
1
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
3
0
0
0
0
0
0
2
0
0
1
2
0
0
0
1
3
0
0
0
0
0
3
0
0
0
0
3
0
0
0
2
1
0
0
0
2
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
4
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
2
0
0
1
1
0
2
1
0
2
0
2
2
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
2
1
0
1
2
1
1
0
0
0
0
2
1
0
0
2
0
0
0
0
3
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
5
0
1
0
0
0
1
2
0
0
0
0
0
1
2
0
2
0
0
0
2
1
1
0
0
0
0
0
1
0
1
0
0
1
2
0
1
0
0
0
2
1
0
2
0
0
0
0
6
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
4
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
3
2
0
0
0
0
1
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
2
0
2
0
1
0
1
0
0
1
0
0
0
1
0
2
1
0
0
8
0
2
0
0
0
0
0
0
0
3
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
5
0
1
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
3
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
1
0
1
0
0
4
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
2
2
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
1
0
0
2
0
0
2
0
1
0
3
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
1
2
0
2
0
0
0
1
0
0
3
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
2
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
7
2
0
2
1
0
1
0
0
2
0
1
1
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
2
0
0
0
2
4
0
0
0
3
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
2
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
3
2
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
4
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
2
2
0
2
2
0
0
0
0
0
0
2
2
0
0
0
0
0
1
2
2
3
0
0
0
0
0
1
0
0
1
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
2
1
0
2
0
0
1
1
0
0
0
0
0
2
0
0
0
0
2
1
1
0
2
0
0
0
0
0
0
2
2
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
1
2
0
2
2
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
5
0
0
0
0
1
2
0
0
1
1
1
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
1
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
1
3
0
0
0
2
0
4
2
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
3
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
6
11
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
1
4
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
4
0
1
0
0
0
0
1
0
2
0
1
2
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
2
0
4
0
0
0
0
0
2
0
0
2
0
0
0
1
0
2
0
1
0
0
3
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
1
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
3
0
2
2
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
5
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
1
0
0
0
0
0
1
2
1
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
2
0
0
1
0
0
2
0
0
3
0
0
1
0
0
2
0
0
1
0
2
0
1
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
2
0
0
0
0
0
0
2
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
3
0
1
1
1
1
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
1
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
1
0
0
2
0
2
0
3
0
0
2
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
2
0
0
0
1
1
1
0
0
0
0
1
0
2
0
3
0
0
1
2
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
1
0
0
1
0
2
2
1
2
1
0
1
0
0
0
1
0
0
0
0
2
0
1
3
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
1
0
0
3
0
0
0
0
0
0
2
0
0
3
0
1
0
0
2
0
1
1
1
0
0
0
0
0
0
2
0
0
0
1
1
1
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
3
0
0
2
0
2
0
0
1
0
0
0
0
2
0
4
1
2
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
4
0
0
2
0
0
4
0
0
0
0
2
0
1
2
2
0
0
0
0
1
1
0
1
1
2
0
2
1
0
2
0
2
0
0
1
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
4
0
0
0
0
0
2
0
1
0
0
0
0
1
2
0
0
0
0
0
0
2
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
4
0
1
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
2
1
1
0
4
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
4
0
0
2
1
0
0
0
0
3
0
0
0
0
3
1
0
0
1
0
1
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
2
0
0
0
0
1
1
4
0
0
0
0
0
0
3
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
1
1
0
2
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
5
0
0
1
0
2
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
3
1
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
2
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
3
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
1
0
0
2
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
2
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
3
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
3
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
2
0
0
0
0
0
0
0
0
2
3
0
1
1
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
4
0
2
2
0
0
3
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
2
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
6
0
0
1
0
0
0
0
0
0
2
0
1
3
1
0
0
0
0
0
0
0
0
0
4
2
0
2
0
0
2
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
2
0
4
0
0
0
6
0
0
0
0
0
1
2
0
1
1
1
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
1
1
0
1
0
0
0
0
0
4
4
0
2
0
0
0
0
0
2
2
2
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
2
0
0
2
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
3
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
1
2
2
0
1
0
0
0
1
0
2
0
1
1
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
3
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
1
0
0
0
3
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
3
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
4
0
0
0
2
0
2
0
3
0
0
2
0
0
0
0
0
3
1
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
3
0
0
3
0
0
0
6
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
1
1
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
2
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
1
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
1
1
1
0
1
1
0
0
0
2
0
0
0
0
4
0
0
0
0
0
0
0
2
0
1
0
0
2
1
0
2
0
0
0
0
2
0
0
5
2
1
2
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
4
0
0
1
0
1
0
0
2
0
0
5
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
5
0
1
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
2
4
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
2
0
0
2
0
0
3
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
3
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
2
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
3
0
0
5
2
1
0
2
2
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
3
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
6
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
3
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
2
0
0
1
2
1
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
1
0
1
1
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
2
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
4
0
0
2
6
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
1
2
0
0
0
2
0
0
0
1
0
0
0
1
0
0
4
0
0
0
1
0
0
0
3
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
2
1
1
3
0
0
2
0
0
0
0
0
0
0
1
1
0
3
0
0
0
7
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
4
0
3
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
2
0
1
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
2
0
1
0
0
1
0
2
0
0
0
1
0
1
1
1
1
0
0
0
1
0
1
0
1
0
2
0
0
2
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
4
0
0
0
0
0
6
3
0
0
0
0
1
0
0
0
0
0
2
2
0
1
2
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
2
0
1
0
0
2
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
3
0
1
0
2
0
0
0
0
0
2
2
2
0
0
0
2
0
2
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
2
2
2
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
1
0
1
0
1
0
2
1
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
3
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
1
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
1
3
0
0
0
0
0
4
0
1
0
0
0
0
2
1
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
2
6
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
1
2
0
1
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
3
0
0
1
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
2
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
4
2
0
2
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
1
1
2
2
1
0
1
2
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
2
0
0
2
0
0
2
0
0
0
0
1
0
0
2
2
1
0
0
0
0
0
0
0
4
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
2
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
1
0
2
1
2
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
2
1
0
1
0
1
4
0
0
1
0
0
1
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
2
0
1
0
0
0
0
2
1
0
0
0
0
3
1
2
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
1
2
0
1
0
0
1
0
3
2
0
0
1
0
0
0
0
0
0
1
0
1
0
0
2
3
4
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
1
2
0
0
1
0
0
0
4
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
3
0
2
0
1
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
1
4
0
2
0
0
0
0
0
0
0
0
3
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
4
0
0
0
0
0
0
0
2
0
0
0
2
2
0
1
0
0
0
0
0
1
0
2
0
0
2
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
2
0
0
3
0
4
0
0
0
0
0
0
0
2
0
0
0
2
2
1
0
0
1
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
2
2
2
0
2
0
1
0
0
0
1
0
0
2
2
0
0
0
1
3
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
6
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
1
0
1
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
1
2
0
0
2
1
0
2
0
0
0
0
0
0
3
1
0
1
0
0
0
0
0
2
0
4
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
9
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
1
0
0
1
0
0
0
2
1
0
0
2
1
0
1
1
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
7
0
0
2
0
0
0
2
0
0
2
0
2
1
0
0
0
0
0
2
1
0
0
2
0
0
0
0
1
1
1
0
2
2
0
0
2
0
1
0
0
0
0
0
0
0
0
3
2
3
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
2
2
0
0
0
7
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
1
0
0
0
0
1
2
0
0
2
1
1
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
1
0
1
1
0
1
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
3
0
0
1
0
24
0
0
0
2
0
0
0
2
0
1
2
0
0
0
0
0
0
2
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
1
0
1
0
0
2
0
0
0
0
0
0
5
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
1
1
0
3
0
1
1
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
2
1
0
0
0
3
6
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
2
1
2
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
1
3
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
2
0
0
2
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
3
0
1
0
0
0
2
0
0
0
0
0
0
2
0
2
0
2
0
0
1
1
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
1
0
0
0
1
2
0
0
2
0
0
2
0
4
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
6
4
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
1
2
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
3
0
1
0
0
0
0
1
0
2
0
0
0
0
2
0
0
3
0
3
0
0
0
1
0
2
0
0
0
0
0
0
1
3
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
2
1
0
0
0
6
0
0
0
0
2
2
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
4
3
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
8
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
1
1
2
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
4
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
2
0
0
1
0
0
1
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
2
0
0
3
0
0
0
0
0
2
2
1
0
0
0
1
2
1
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
1
1
1
0
1
0
0
4
4
0
0
0
0
0
2
0
0
2
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
1
3
0
0
2
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
2
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
2
2
1
1
0
2
0
2
0
0
0
1
0
0
0
0
0
0
3
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
1
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
3
1
1
0
0
3
0
0
1
0
0
0
1
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
3
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
1
0
0
1
0
0
0
3
1
0
0
0
2
2
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
3
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
3
0
4
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
4
0
0
1
1
0
0
0
0
0
0
2
0
2
0
3
2
0
0
0
0
2
0
0
0
3
1
0
0
2
0
0
0
1
3
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
9
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
1
0
0
0
0
0
3
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
9
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
1
0
2
3
0
1
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
1
5
0
0
0
0
0
0
0
0
3
1
0
0
1
0
1
0
0
1
4
0
2
1
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
2
2
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
1
2
0
0
0
0
3
0
0
1
0
0
0
0
3
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
1
1
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
5
0
0
0
0
1
0
3
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
2
0
0
1
0
2
3
0
0
0
0
2
0
0
0
4
0
0
0
0
1
0
0
1
2
0
0
0
2
0
1
2
2
0
0
0
2
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
2
0
10
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
2
0
0
0
0
1
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
1
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
6
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
1
0
0
1
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
3
0
0
3
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
1
0
0
0
0
2
0
0
0
1
2
0
0
1
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
1
0
0
4
0
0
0
1
0
2
0
2
2
1
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
1
0
1
0
1
0
0
3
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
2
2
0
0
0
1
1
0
2
0
0
1
2
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
2
0
1
1
0
0
0
2
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
1
0
1
2
0
0
2
3
1
1
0
0
0
2
4
1
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
1
0
1
0
0
2
2
0
0
0
4
0
1
0
0
2
0
2
0
0
2
2
2
0
0
0
2
0
0
6
0
0
0
1
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
1
0
0
0
0
2
0
0
0
1
0
1
0
2
0
0
0
0
0
0
2
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
2
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
1
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
2
2
0
0
0
0
0
4
0
0
0
0
1
0
0
0
1
1
2
0
0
2
0
2
0
0
0
0
2
2
0
1
0
0
0
2
0
1
1
0
2
1
0
11
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
4
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
1
0
3
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
5
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
2
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
2
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
7
0
0
4
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
4
1
1
5
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
4
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
4
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
3
0
0
1
0
0
0
0
2
0
0
3
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
3
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
5
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
1
1
0
0
0
0
3
1
0
0
2
0
0
1
0
0
3
1
0
0
0
1
1
0
0
2
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
3
0
0
0
0
0
3
3
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
3
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
2
0
1
0
2
0
0
0
0
0
0
7
1
1
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
2
2
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
3
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
3
2
1
0
2
0
0
0
0
0
0
0
1
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
2
0
1
0
1
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
2
0
3
0
0
8
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
3
0
1
0
0
0
0
3
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
3
0
0
0
2
2
0
0
0
0
0
1
0
0
1
0
0
1
1
0
2
0
0
0
0
2
1
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
3
1
0
0
0
0
0
0
0
0
0
6
0
0
1
2
0
0
0
1
0
0
3
0
1
1
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
2
0
0
2
1
0
0
0
1
2
0
2
2
0
0
0
0
0
2
0
0
1
0
1
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
1
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
2
0
0
4
0
0
2
1
0
0
0
0
1
0
0
1
0
0
0
0
1
4
2
0
0
0
0
0
0
0
0
6
1
1
0
1
2
2
1
1
0
0
2
0
1
0
2
0
7
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
1
0
3
0
0
0
1
0
0
0
1
2
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
6
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
1
1
0
0
3
0
0
0
2
2
0
1
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
2
0
0
0
1
0
2
0
0
2
0
0
0
0
1
1
1
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
1
1
0
2
0
1
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
3
0
0
2
0
0
0
1
0
0
0
4
0
0
0
2
0
2
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
2
2
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
1
0
1
0
2
2
0
0
0
2
0
0
0
0
1
0
0
1
0
0
1
0
1
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
1
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
4
1
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
1
0
1
0
0
0
0
2
0
0
0
0
1
0
0
3
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
2
1
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
6
0
2
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
2
0
2
0
1
0
1
1
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
2
1
0
2
0
0
0
0
3
0
2
0
0
0
0
0
0
2
0
0
1
2
0
0
1
1
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
2
2
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
6
0
2
0
0
0
0
0
0
0
1
1
0
0
0
2
1
0
0
1
0
0
0
1
0
0
1
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
3
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
2
2
1
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
1
2
1
0
0
0
0
0
3
0
0
0
1
2
0
1
1
1
0
0
0
4
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
2
2
0
0
0
2
0
1
0
0
2
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
1
0
0
2
0
0
1
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
2
4
0
6
1
0
0
0
0
2
1
0
0
4
3
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
1
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
10
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
1
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
3
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
3
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
1
3
0
0
1
0
1
1
0
0
0
0
0
0
2
0
1
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
6
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
3
2
0
2
0
0
0
2
0
0
0
3
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
3
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
4
1
0
0
0
0
0
4
2
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
1
0
0
0
1
2
0
0
0
1
0
1
0
0
2
0
2
1
2
0
0
0
0
0
0
0
0
1
1
0
0
1
0
2
1
0
1
11
0
0
2
0
2
0
1
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
1
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
3
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
3
0
2
0
0
0
0
3
2
5
0
0
0
0
0
2
1
2
0
1
0
0
0
0
0
0
1
0
0
2
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
3
0
1
0
2
0
0
0
0
2
0
1
3
2
1
1
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
1
0
2
0
0
1
0
2
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
2
0
0
2
2
0
0
1
0
0
1
0
3
0
0
1
0
1
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
2
2
0
0
1
0
0
2
0
0
0
1
0
0
1
1
0
0
11
0
0
0
2
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
3
1
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
3
0
0
2
0
0
2
0
0
0
0
3
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
5
1
0
7
2
0
2
0
0
0
0
0
0
0
0
0
0
2
1
1
0
1
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
2
2
0
0
0
1
0
0
0
2
1
0
2
0
0
4
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
3
0
0
1
0
0
2
2
0
1
0
0
0
0
0
1
2
0
0
0
1
0
0
0
2
1
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
4
3
0
0
0
2
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
2
0
0
0
0
2
0
0
0
0
0
0
0
0
6
0
0
0
2
0
0
0
0
0
2
0
0
1
0
1
0
2
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
1
2
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
2
1
0
0
2
1
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
3
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
3
13
0
0
0
0
5
0
0
0
0
2
0
3
1
0
0
2
0
0
2
2
0
2
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
1
4
0
0
0
0
0
0
5
1
1
0
1
0
0
0
1
0
0
0
3
0
0
1
2
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
2
0
0
0
1
2
0
2
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
2
0
0
2
0
1
0
0
0
1
2
1
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
5
2
0
0
0
2
0
0
3
0
0
0
0
0
0
2
0
0
2
0
0
0
1
3
0
0
0
0
0
1
1
0
0
0
0
1
3
1
0
1
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
4
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
4
0
0
0
0
0
0
3
0
0
2
1
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
2
0
0
1
4
0
2
2
0
0
6
0
2
1
0
0
0
0
0
2
0
2
2
0
13
1
0
2
0
0
2
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
5
0
0
0
0
4
0
7
0
1
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
1
2
0
2
0
2
2
0
0
0
0
3
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
1
0
2
1
2
0
0
0
1
0
0
2
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
2
0
0
1
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
3
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
1
0
3
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
1
1
2
0
0
0
3
0
0
0
0
1
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
2
2
0
2
0
0
0
0
0
1
0
1
1
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
5
0
0
1
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
3
2
0
0
0
0
0
0
0
2
0
0
0
3
1
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
1
0
0
2
0
0
1
0
1
2
1
3
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
3
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
1
0
0
0
3
2
2
0
1
1
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
2
0
0
0
1
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
2
4
0
0
0
0
0
2
0
3
0
3
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
2
0
0
0
0
0
2
0
0
2
1
0
2
0
0
0
0
2
2
0
0
0
1
0
0
0
0
3
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
1
1
0
0
1
0
0
0
1
0
0
1
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
5
0
1
0
0
1
0
0
2
2
0
1
3
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
6
0
0
0
2
0
3
0
0
1
1
0
0
1
0
0
0
0
0
1
0
1
0
3
1
1
0
0
0
9
0
0
0
2
2
0
0
1
0
2
0
1
2
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
4
0
0
0
0
2
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
2
0
0
2
0
0
1
0
0
0
0
0
0
2
0
2
1
3
0
0
0
0
0
0
4
0
0
3
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
2
8
0
4
2
0
0
2
2
0
0
0
0
2
1
0
0
5
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
3
1
1
1
0
0
1
0
0
0
2
0
0
0
0
1
0
1
0
0
0
3
0
1
1
0
0
1
2
1
0
0
0
1
0
0
1
0
4
0
0
0
0
0
0
0
0
0
1
2
0
0
1
2
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
3
0
0
1
0
2
0
0
1
0
0
0
0
2
0
2
0
0
1
0
0
0
1
0
0
1
0
2
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
1
1
0
0
2
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
1
0
2
0
2
0
0
1
1
0
0
0
0
2
0
0
1
0
0
0
0
0
1
5
1
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
3
2
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
1
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
2
0
0
0
0
3
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
3
0
0
0
0
3
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
2
2
1
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
6
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
1
0
0
2
0
0
2
2
0
3
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
1
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
4
0
1
5
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
4
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
1
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
11
1
0
1
0
0
1
0
2
3
0
0
0
2
0
0
0
2
1
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
2
1
1
0
0
1
1
0
0
0
1
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
3
5
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
2
0
0
1
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
3
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
6
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
0
4
0
1
0
0
1
1
0
0
0
0
1
0
2
0
0
0
0
2
2
0
0
1
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
1
2
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
4
0
0
3
1
0
0
0
0
1
0
0
0
0
1
0
0
0
3
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
2
0
0
0
0
0
2
0
0
2
0
0
1
0
2
0
1
0
2
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
2
0
1
1
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
1
1
0
0
3
2
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
1
2
0
0
2
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
3
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
3
0
0
0
2
0
0
0
0
0
3
0
0
1
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
1
0
0
0
0
1
0
2
0
0
2
1
0
0
2
1
1
0
0
1
0
0
1
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
2
2
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
6
0
0
0
0
0
0
0
2
0
1
1
0
3
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
1
0
0
0
1
1
0
1
0
0
0
0
2
0
0
0
0
0
0
4
0
1
0
0
0
0
1
0
0
0
3
2
0
1
1
1
0
0
0
0
0
2
0
0
1
0
0
1
0
0
1
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
2
2
3
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
3
0
2
2
0
2
0
1
0
1
0
1
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
2
1
0
1
1
0
3
0
1
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
3
1
0
1
0
1
0
0
0
1
2
3
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
3
3
2
0
0
0
2
0
0
0
0
0
0
0
0
7
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
1
2
0
1
0
0
1
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
4
0
0
0
1
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
3
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
2
0
0
0
0
2
4
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
2
0
0
0
2
2
0
0
1
0
0
0
0
0
0
1
1
1
2
2
0
0
0
0
1
0
2
0
1
2
1
8
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
1
0
2
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
3
0
0
0
0
0
1
1
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
2
2
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
5
1
0
0
0
1
0
1
0
0
1
0
0
0
2
0
2
0
0
1
0
2
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
2
0
2
0
3
0
2
3
1
0
3
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
2
1
0
0
2
0
0
0
1
1
0
1
1
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
2
0
0
1
0
2
0
0
0
2
1
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
2
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
2
0
0
6
2
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
1
0
0
3
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
2
2
0
0
0
0
2
0
6
0
2
0
2
0
0
1
1
0
1
0
2
0
0
1
0
0
0
0
1
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
1
1
0
0
3
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
3
0
0
0
0
2
1
0
2
0
1
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
4
0
0
0
0
0
0
1
0
2
0
2
0
0
0
1
2
0
1
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
29
1
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
2
2
1
0
1
0
0
0
1
0
0
0
2
1
0
0
0
1
0
0
0
3
0
0
0
1
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
1
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
4
0
1
1
0
0
0
0
2
0
2
3
2
0
0
0
0
3
0
0
0
0
0
1
0
1
1
0
0
2
1
0
0
1
0
0
0
0
0
0
2
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
2
2
0
0
0
3
0
0
2
0
1
2
0
0
0
0
0
0
2
0
0
0
0
2
1
0
3
0
0
1
0
2
1
0
1
0
0
1
0
0
0
0
4
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
3
1
1
0
0
3
2
3
0
0
0
0
3
0
1
0
0
1
0
0
0
8
0
0
0
0
0
1
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
5
0
0
0
1
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
4
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
1
0
0
0
0
1
2
0
2
0
4
0
0
4
0
0
5
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
2
2
1
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
1
1
0
0
3
0
0
2
0
0
0
0
1
3
0
4
0
0
0
0
3
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
4
0
0
0
0
0
0
1
0
3
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
1
0
0
0
1
1
2
3
0
2
3
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
9
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
4
2
2
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
2
2
1
0
3
2
1
2
0
0
0
0
1
0
1
0
1
1
1
2
0
4
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
2
0
1
0
2
0
0
1
0
0
2
0
2
7
0
0
0
0
0
1
0
0
0
0
2
0
1
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
4
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
5
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
4
0
3
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
1
0
0
2
3
0
0
1
1
0
0
0
0
0
1
0
0
1
0
2
0
1
1
0
4
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
4
0
0
0
0
0
2
0
0
1
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
2
0
2
0
0
0
0
0
1
0
1
0
0
1
4
0
2
1
0
2
1
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
3
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
2
1
0
0
2
1
0
0
0
0
2
0
3
1
0
2
0
1
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
1
0
2
0
3
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
2
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
6
0
0
3
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
2
0
0
0
2
0
0
0
4
1
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
2
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
3
0
0
0
0
0
2
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
1
1
0
0
0
0
0
0
0
0
1
0
2
3
2
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
4
0
2
0
0
0
0
2
0
0
0
0
0
0
3
1
0
0
0
0
4
2
0
0
0
0
0
0
0
2
4
0
0
0
0
3
3
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
2
1
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
2
2
0
0
1
0
0
2
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
1
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
3
0
0
3
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
1
0
0
3
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
2
0
0
8
1
2
1
0
0
1
0
0
5
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
4
0
2
0
2
1
0
0
1
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
2
2
1
1
0
0
0
0
0
1
0
0
1
5
0
0
0
2
0
0
0
1
0
0
3
0
1
0
0
0
0
1
0
5
3
0
2
2
0
2
0
0
0
0
2
0
2
0
3
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
2
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
1
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
1
0
0
1
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
3
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
2
0
1
0
0
1
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
3
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
1
0
0
0
0
0
2
0
5
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
2
1
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
4
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
3
0
0
0
2
1
0
0
1
0
1
0
0
0
0
0
0
8
0
0
0
1
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
3
0
1
2
0
2
4
0
0
0
2
2
0
0
0
0
0
1
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
3
0
3
0
0
0
2
0
2
5
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
2
1
0
2
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
3
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
4
0
0
1
0
1
0
0
2
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
2
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
1
1
1
2
0
0
0
0
0
0
0
2
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
1
0
0
0
0
0
2
0
0
3
5
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
2
0
0
0
0
2
0
0
0
1
0
1
0
0
0
1
0
3
0
0
0
2
0
0
0
1
0
3
0
2
0
4
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
2
2
1
0
0
2
0
0
2
0
0
0
1
2
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
3
0
0
1
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
7
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
1
1
2
0
0
0
0
0
0
2
0
0
2
1
1
1
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
1
0
0
1
0
2
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
2
2
1
0
0
0
0
3
0
2
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
1
2
0
0
0
0
0
2
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
1
1
0
0
0
0
2
0
2
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
1
2
1
0
0
0
0
0
2
1
1
0
0
0
4
0
0
0
0
2
2
1
1
0
0
0
1
0
0
0
1
0
1
2
0
2
0
2
0
1
0
0
0
0
0
0
0
0
6
0
0
0
0
2
2
1
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
2
1
0
1
0
0
2
0
1
0
2
1
0
0
0
0
1
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
2
1
2
0
1
0
0
0
0
0
0
0
1
1
0
2
0
0
1
1
0
2
0
0
0
1
0
1
0
0
0
3
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
3
1
0
0
0
0
1
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
3
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
9
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
1
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
1
2
0
1
0
0
4
0
2
0
0
0
0
1
0
5
2
0
0
1
0
0
0
0
0
0
0
4
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
1
2
0
3
0
2
0
0
1
0
0
0
0
2
0
2
0
0
1
0
3
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
2
2
1
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
2
3
1
1
2
0
0
0
0
0
0
0
3
1
2
1
0
0
1
0
0
0
0
0
0
0
2
0
1
0
1
0
2
0
1
0
0
0
0
0
2
0
0
1
0
3
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
1
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
1
0
0
1
0
1
0
0
1
1
0
0
0
2
0
0
2
0
1
3
0
0
0
2
0
0
0
2
0
0
0
0
1
2
1
0
2
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
2
0
0
2
0
1
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
1
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
2
3
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
1
1
1
0
3
1
0
0
0
0
2
3
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
1
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
2
0
1
0
0
0
0
3
0
0
0
2
0
2
2
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
4
0
2
1
2
1
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
3
0
0
0
1
0
2
3
2
0
0
0
0
0
0
0
0
1
3
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
3
0
0
2
0
0
0
2
3
0
1
0
0
0
0
0
0
2
0
1
0
0
2
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
2
0
5
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
2
0
2
2
0
0
0
0
1
0
1
0
0
0
0
0
0
4
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
1
0
1
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
2
0
1
0
1
0
1
0
2
0
0
2
0
2
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
2
0
1
0
1
0
2
2
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
1
0
0
0
2
2
0
1
0
0
0
2
0
0
0
0
0
0
1
1
0
2
1
0
0
2
0
0
0
3
3
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
2
2
2
4
0
0
0
0
0
0
1
2
2
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
5
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
1
2
0
1
0
0
1
2
1
2
0
0
1
0
0
1
3
0
0
3
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
1
0
3
0
0
0
0
0
5
0
3
2
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
1
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
4
0
1
1
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
2
0
4
0
0
0
0
0
1
0
0
0
0
3
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
2
0
2
0
0
2
3
0
0
0
0
1
3
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
2
2
0
1
0
0
0
1
0
2
0
0
0
0
0
3
2
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
1
0
0
1
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
2
0
0
0
0
0
2
3
0
0
1
1
0
0
0
2
0
2
2
0
2
0
0
0
0
0
5
0
0
0
0
0
0
0
1
0
0
2
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
1
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
4
0
0
0
0
2
2
0
0
0
2
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
2
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
2
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
3
1
0
0
1
0
0
0
2
0
0
2
0
0
2
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
1
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
4
0
0
0
5
0
1
1
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
2
0
2
1
0
0
0
2
3
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
1
0
0
0
0
3
0
0
4
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
2
0
1
0
0
0
0
0
2
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
1
2
0
0
0
0
2
1
0
2
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
2
0
1
2
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
1
0
0
1
0
0
1
0
1
0
1
0
1
0
1
0
2
0
2
1
0
0
2
0
0
0
2
0
2
0
0
1
0
2
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
1
1
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
2
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
3
0
0
2
2
0
0
0
0
0
2
1
0
0
0
1
0
0
2
0
1
1
0
0
0
8
0
0
3
1
0
0
0
0
0
0
0
0
0
2
2
2
2
3
0
1
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
3
0
1
0
0
0
1
0
1
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
1
1
0
4
0
0
0
0
4
2
0
0
0
4
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
4
2
1
0
0
0
0
1
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
1
1
2
0
0
0
5
2
0
1
3
0
0
0
2
1
1
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
3
0
1
0
0
1
0
0
0
1
2
0
0
6
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
2
1
2
2
0
2
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
3
2
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
2
0
0
0
2
0
0
0
0
1
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
3
0
0
0
4
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
1
0
1
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
3
0
1
0
0
1
4
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
3
0
0
2
0
0
0
1
0
0
0
0
2
1
1
0
4
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
2
0
1
1
0
4
0
0
0
1
2
0
0
0
27
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
7
2
0
0
0
0
0
0
0
0
2
1
0
0
1
2
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
3
0
0
1
1
0
0
0
1
0
1
1
0
0
0
0
0
1
2
1
0
3
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
3
2
0
0
0
0
2
0
0
0
0
0
4
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
2
0
0
1
2
4
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
2
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
1
0
2
0
0
0
0
0
0
2
2
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
1
0
1
0
0
0
4
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
3
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
4
0
3
0
2
0
0
3
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
1
0
0
0
0
2
1
0
0
2
0
0
0
0
0
3
0
0
2
0
0
1
2
2
0
0
0
0
0
0
0
1
0
0
1
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
4
0
0
2
0
0
1
0
2
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
2
1
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
1
0
0
2
0
2
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
1
3
3
0
0
0
0
0
2
0
0
0
1
0
2
0
0
1
7
0
0
0
1
1
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
3
0
0
2
0
0
2
1
0
0
0
3
1
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
3
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
5
2
0
0
1
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
1
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
5
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
4
0
2
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
2
0
2
0
1
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
1
2
0
5
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
1
1
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
2
0
1
4
4
1
0
0
0
3
0
0
0
0
0
0
0
1
0
1
0
0
3
0
0
5
1
0
0
0
0
2
1
0
0
1
0
0
0
0
0
1
0
0
2
1
1
1
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
2
1
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
1
1
2
0
0
0
1
1
4
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
2
3
0
0
2
1
0
0
0
0
0
0
2
0
3
0
0
0
1
0
0
0
1
3
0
0
0
0
1
0
0
1
0
0
2
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
1
0
1
1
0
0
0
2
2
0
0
3
0
2
0
0
0
0
2
0
0
2
2
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
3
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
8
0
3
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
5
0
0
2
0
0
0
0
0
0
0
0
2
0
1
1
0
0
4
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
2
2
0
1
0
9
2
2
0
1
2
0
0
3
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
2
1
1
0
0
1
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
2
0
0
0
1
0
0
0
0
1
0
2
1
0
0
0
2
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
1
0
0
1
2
1
0
0
0
0
1
0
2
0
2
1
0
0
0
0
0
3
2
0
0
0
0
1
1
1
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
1
1
2
2
0
0
0
3
1
1
0
2
2
0
0
0
0
0
0
3
0
1
0
0
5
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
1
3
10
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
2
1
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
1
2
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
3
2
0
0
0
0
0
5
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
1
1
0
1
2
0
0
0
1
2
0
4
0
0
2
0
0
1
0
2
0
0
0
0
0
2
0
2
0
1
0
1
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
2
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
3
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
2
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
2
0
0
0
3
0
0
2
0
1
1
0
3
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
4
2
0
0
1
0
0
0
0
0
0
3
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
3
1
0
0
0
0
2
0
1
4
2
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
3
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
2
3
0
0
0
2
2
0
0
0
0
0
0
2
0
0
1
2
1
2
0
0
0
0
0
0
0
0
1
5
0
3
0
1
0
0
0
0
0
0
1
2
0
0
0
0
3
0
0
0
0
0
6
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
2
0
0
0
2
2
0
2
0
0
0
0
0
0
3
1
5
1
3
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
3
2
0
1
0
0
2
0
0
1
0
0
2
0
0
2
0
2
2
0
0
1
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
1
0
2
0
0
2
4
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
2
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
1
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
2
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
1
5
0
1
0
0
0
0
0
2
0
0
1
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
2
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
2
0
0
0
2
1
0
0
1
1
1
0
0
0
1
0
0
2
1
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
10
0
0
2
0
1
1
0
0
3
1
0
0
0
0
0
0
4
0
1
0
7
0
2
0
0
0
0
0
7
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
6
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
3
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
2
1
0
0
2
3
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
2
1
0
0
1
2
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
3
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
1
0
0
0
2
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
4
0
0
0
0
6
0
3
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
3
0
0
0
0
2
0
1
0
3
0
0
1
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
1
0
0
4
0
0
0
0
2
0
0
0
0
2
0
0
2
1
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
4
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
5
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
5
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
1
0
0
1
1
0
0
0
0
0
2
0
0
0
1
1
0
0
2
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
1
0
0
0
1
3
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
1
0
1
1
0
1
0
0
2
0
2
0
0
0
1
0
0
0
2
0
3
2
1
2
0
0
3
0
2
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
1
0
0
0
0
1
2
0
3
0
0
0
2
0
0
0
1
2
1
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
1
2
0
0
0
2
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
5
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
2
0
1
0
0
0
0
0
0
2
0
3
1
0
2
0
0
1
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
1
0
0
0
2
0
0
1
2
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
3
0
2
0
0
0
0
0
0
0
0
6
0
0
3
1
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
5
0
0
0
1
1
0
0
0
1
0
0
2
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
8
0
0
1
1
0
1
2
0
0
0
0
7
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
2
1
1
1
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
2
1
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
3
0
0
1
4
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
2
0
1
0
1
0
0
0
0
1
0
0
2
0
1
0
0
0
0
2
0
2
0
1
0
0
0
2
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
1
1
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
3
0
2
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
1
0
0
2
0
0
2
0
2
0
1
0
0
0
0
0
0
0
2
0
3
0
0
3
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
4
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
1
1
1
0
0
0
0
2
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
3
0
0
2
0
0
0
0
1
0
0
2
0
2
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
4
0
0
0
1
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
1
2
0
0
0
2
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
2
1
2
0
2
0
0
0
0
0
0
1
0
4
0
0
2
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
2
0
1
0
0
1
3
0
0
0
0
0
0
0
1
3
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
7
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
1
2
1
2
2
0
1
0
0
0
1
0
1
0
0
1
0
0
1
0
3
0
0
0
0
0
0
2
0
2
0
0
0
7
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
4
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
1
0
1
0
1
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
1
0
1
6
0
1
0
0
0
0
0
0
1
1
0
0
0
0
2
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
4
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
1
1
0
0
0
0
3
0
0
2
0
1
2
0
0
0
0
0
1
0
0
0
3
2
0
0
3
1
0
2
0
0
0
1
0
1
2
0
2
2
0
0
0
2
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
3
0
4
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
2
2
1
2
0
0
1
0
0
1
0
0
0
0
0
2
2
0
2
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
1
0
0
0
3
0
0
0
2
4
0
0
1
2
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
1
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
1
0
0
2
0
0
0
1
0
1
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
1
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
4
1
0
0
0
0
0
2
0
0
8
0
0
0
1
0
0
0
1
0
0
1
1
1
2
0
2
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
2
2
0
0
0
1
8
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
3
0
0
0
0
2
1
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
6
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
2
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
1
0
0
3
0
1
4
1
3
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
2
2
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
2
0
5
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
1
0
0
2
1
0
2
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
1
1
0
1
1
3
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
2
1
0
3
0
0
0
0
0
0
0
2
2
1
0
0
0
1
0
0
1
0
2
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
4
0
2
0
2
0
1
0
1
0
2
0
0
2
2
0
0
1
2
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
3
0
0
0
1
0
1
0
0
3
0
1
0
5
1
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
2
1
2
0
0
0
0
2
0
2
0
0
1
1
0
1
2
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
1
0
0
0
2
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
3
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
3
3
0
0
2
0
1
0
4
0
2
0
0
0
3
1
2
0
0
0
2
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
2
0
0
0
0
0
7
0
1
0
0
0
0
0
1
0
0
2
0
1
3
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
2
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
2
3
2
0
1
0
2
2
0
0
0
1
0
0
0
10
0
0
0
0
0
2
0
2
0
0
0
0
0
1
2
0
1
0
0
2
2
5
0
0
0
1
0
1
0
0
0
1
0
0
2
2
0
0
0
2
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
1
0
0
6
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
4
1
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
3
2
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
1
2
2
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
3
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
3
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
3
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
8
0
0
1
2
2
1
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
2
3
0
1
0
2
0
0
0
0
2
0
0
2
1
1
0
1
0
2
0
0
0
0
0
1
0
0
1
2
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
2
0
2
0
0
1
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
2
0
0
0
0
0
0
1
1
0
0
0
0
3
2
0
0
2
0
1
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
2
0
1
0
2
4
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
16
0
0
0
1
2
1
0
0
0
0
0
1
0
1
0
1
0
0
1
0
2
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
2
0
0
2
0
0
1
4
3
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
5
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
2
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
4
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
15
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
2
0
0
3
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
5
0
2
0
0
0
0
0
3
0
1
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
1
3
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
3
0
0
0
0
2
2
0
2
0
0
0
2
0
2
0
2
0
1
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
1
1
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
3
0
0
2
0
0
0
1
0
1
1
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
3
7
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
1
2
0
3
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
2
0
2
0
0
0
0
2
2
0
2
0
0
0
1
0
0
1
0
0
2
1
0
0
0
0
0
0
2
0
0
2
1
1
2
0
2
0
0
2
1
0
0
2
1
0
0
1
0
0
0
0
1
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
4
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
2
0
1
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
3
1
0
2
1
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
1
1
0
1
0
0
0
0
0
0
0
0
2
0
2
4
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
3
0
0
6
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
1
0
0
2
0
0
1
0
0
0
0
0
0
2
1
0
0
3
0
0
0
1
0
2
1
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
5
0
0
0
1
0
0
1
2
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
1
2
1
0
1
1
0
0
2
0
2
0
0
0
0
1
2
0
0
0
0
0
0
1
1
0
1
0
2
0
0
0
1
0
3
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
1
2
0
1
0
0
1
0
1
2
0
0
2
1
1
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
2
0
0
0
0
1
0
2
0
1
0
0
7
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
4
0
0
1
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
1
0
1
0
2
0
0
0
3
2
0
1
0
0
1
0
2
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
3
1
0
0
2
0
0
0
2
1
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
1
1
0
0
0
0
2
2
0
1
6
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
1
2
0
0
3
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
2
0
0
0
2
1
3
0
0
0
0
0
1
1
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
2
1
0
0
2
0
0
2
2
0
0
4
1
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
1
0
0
3
0
2
0
0
0
0
1
0
0
2
0
1
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
5
3
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
4
0
0
0
0
0
6
0
2
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
8
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
8
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
2
0
7
0
0
0
0
0
1
1
1
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
1
2
0
0
0
1
0
0
1
0
0
4
0
0
0
0
3
0
0
2
0
0
0
1
0
0
0
2
2
0
4
6
2
0
0
0
0
2
1
0
0
1
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
3
3
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
2
1
1
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
1
3
2
0
2
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
1
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
1
1
2
0
1
1
0
0
0
0
0
0
0
1
0
0
0
3
0
0
2
0
0
1
3
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
1
0
2
0
2
0
2
0
0
0
1
0
0
0
0
0
0
2
4
0
0
0
0
1
1
2
0
1
2
2
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
3
0
4
0
1
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
2
2
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
1
0
2
0
1
0
1
0
1
0
0
2
0
0
2
0
0
0
0
5
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
3
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
2
0
0
1
0
0
2
0
0
3
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
4
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
6
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
1
0
2
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
2
0
2
0
1
3
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
1
0
0
2
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
1
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
3
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
9
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
2
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
8
0
1
0
0
2
0
1
1
1
0
0
4
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
2
0
0
1
2
2
0
1
0
1
0
1
0
0
1
0
0
0
2
0
0
2
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
2
0
0
1
0
1
0
0
0
1
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
2
1
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
2
0
0
3
4
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
1
0
6
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
2
0
0
0
1
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
2
0
0
0
1
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
1
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
1
2
1
0
0
0
0
0
1
0
1
0
0
3
2
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
2
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
14
0
0
2
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
4
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
1
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
6
0
1
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
1
1
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
2
0
3
0
3
0
0
0
0
0
2
2
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
4
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
1
1
0
0
1
2
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
1
0
0
0
1
0
2
3
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
4
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
3
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
3
0
0
0
0
1
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
1
5
1
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
1
1
1
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
2
0
0
0
2
2
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
2
4
0
0
2
0
0
0
0
1
0
0
2
0
2
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
3
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
3
1
0
0
2
0
0
0
4
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
2
1
1
0
0
0
0
0
2
1
1
0
4
2
0
2
1
0
0
0
0
2
1
1
1
0
0
0
0
0
0
1
1
0
0
0
0
2
0
1
0
0
0
2
0
0
1
0
0
1
1
2
0
1
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
2
0
7
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
0
0
2
8
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
2
0
3
0
0
0
0
2
1
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
1
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
2
0
0
0
1
0
2
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
6
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
4
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
1
0
3
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
4
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
3
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
2
2
0
0
4
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
1
0
0
0
0
0
0
1
3
0
0
0
0
1
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
1
1
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
1
1
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
3
0
0
1
1
0
0
0
3
0
0
0
0
0
1
0
0
0
2
0
0
0
3
0
0
0
0
0
0
1
4
0
0
0
1
0
0
1
0
4
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
3
0
0
0
0
2
2
2
0
0
0
5
0
0
2
0
1
0
0
0
0
2
0
1
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
2
0
1
0
0
1
0
3
1
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
3
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
1
2
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
2
2
0
2
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
4
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
7
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
2
0
0
0
0
1
0
2
2
0
0
0
1
0
1
0
2
0
2
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
1
2
2
0
2
0
2
0
0
0
1
1
0
1
0
1
0
2
0
0
0
0
0
2
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
2
2
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
2
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
2
0
0
0
4
1
1
0
0
0
1
0
2
2
0
0
0
0
1
0
0
1
0
2
0
0
0
2
0
0
2
0
1
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
1
0
2
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
2
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
2
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
6
2
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
2
1
0
2
0
0
2
2
0
0
0
0
0
0
0
2
0
0
2
1
2
0
0
0
0
2
0
0
0
0
0
2
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
1
0
0
0
0
1
0
0
0
2
2
0
2
0
0
0
2
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
1
0
0
7
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
2
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
3
1
0
1
0
1
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
2
0
4
0
0
1
0
0
0
2
0
0
0
0
0
0
2
1
2
0
1
2
0
1
2
0
0
0
0
0
1
2
0
1
0
1
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
2
0
2
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
5
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
1
1
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
1
2
1
0
0
1
2
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
1
2
0
0
2
2
0
0
0
2
0
1
0
3
0
2
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
2
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
1
0
0
0
0
13
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
1
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
1
1
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
1
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
3
0
0
3
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
3
0
0
2
1
0
0
0
1
0
0
0
1
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
6
3
2
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
2
0
0
0
1
0
0
5
0
2
0
1
1
2
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
3
0
3
0
1
0
0
2
0
0
0
0
4
0
2
2
0
0
2
0
0
0
0
0
4
0
1
0
0
0
0
0
1
0
0
0
0
20
0
0
0
0
0
0
0
4
2
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
1
1
0
0
0
2
1
0
0
0
0
0
0
0
0
3
0
3
1
2
0
5
0
3
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
1
0
0
2
0
0
0
0
0
3
0
0
0
4
1
0
0
1
0
0
0
0
2
0
1
2
1
0
0
0
0
1
1
0
2
1
0
0
0
4
3
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
5
0
0
0
0
1
0
0
2
0
0
3
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
2
6
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
3
0
0
2
0
0
0
0
2
2
2
1
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
1
0
0
1
3
7
0
0
0
0
0
2
1
0
0
2
0
2
0
0
0
1
2
0
2
0
0
0
0
0
0
1
3
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
2
0
0
2
0
1
2
1
0
1
1
0
2
0
0
2
0
0
2
2
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
2
3
0
0
1
3
0
0
0
2
0
3
0
2
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
3
0
1
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
13
0
0
1
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
3
0
1
0
0
2
0
0
0
0
0
0
5
0
0
0
0
0
0
2
1
0
0
0
0
1
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
1
0
3
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
1
0
0
0
1
1
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
1
3
5
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
2
0
0
0
0
0
1
3
1
1
0
1
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
2
0
4
0
0
3
0
0
0
0
4
0
0
0
0
0
1
2
2
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
2
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
1
1
0
0
0
2
1
2
0
1
0
2
0
0
0
1
0
0
1
4
0
0
0
0
0
5
0
2
2
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
5
0
0
2
0
0
0
0
0
0
1
1
0
0
0
3
0
2
0
1
2
1
2
0
0
3
0
0
1
1
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
2
1
1
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
1
0
0
0
2
0
0
0
1
0
0
1
0
0
0
1
2
0
1
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
2
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
1
0
0
1
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
4
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
2
0
2
1
0
0
0
0
0
1
0
0
0
1
0
2
2
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
3
0
0
0
5
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
4
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
3
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
3
0
0
2
6
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
2
0
2
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
1
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
3
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
3
0
0
8
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
2
0
0
5
0
0
0
1
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
2
0
0
0
0
0
3
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
1
0
1
0
0
0
3
0
1
3
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
3
1
0
0
3
0
0
0
3
2
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
1
2
2
0
0
1
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
1
0
0
0
0
2
1
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
3
0
1
0
2
0
0
0
1
1
0
0
0
3
0
0
0
2
0
0
1
0
2
5
0
0
0
2
0
0
1
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
1
0
0
0
4
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
4
0
2
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
2
0
0
0
1
3
1
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
3
0
2
0
1
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
8
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
5
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
1
0
1
0
0
2
0
0
0
1
0
3
1
0
0
1
0
1
2
1
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
3
1
0
0
0
0
0
1
0
0
1
0
0
2
1
0
2
0
1
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
3
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
3
0
0
1
0
1
1
1
0
0
0
0
0
2
0
0
0
2
1
2
1
0
0
0
0
0
2
0
0
0
3
0
0
0
2
1
2
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
4
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
1
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
1
0
1
1
0
1
0
0
2
0
0
2
0
0
2
0
0
0
0
0
2
1
0
2
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
1
0
0
2
0
1
3
0
0
0
1
0
1
0
0
0
2
0
0
4
0
2
2
0
0
2
4
2
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
2
0
0
0
1
0
0
0
1
0
2
3
0
0
3
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
1
0
2
8
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
3
1
0
0
2
3
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
2
0
0
1
0
0
0
0
1
0
2
4
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
2
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
7
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
9
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
6
2
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
2
0
3
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
2
1
0
0
0
0
0
0
1
0
0
1
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
2
0
0
1
0
1
0
1
0
1
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
9
0
0
2
0
2
0
0
0
0
3
0
2
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
1
1
2
2
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
2
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
2
2
0
1
1
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
5
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
3
0
0
0
0
0
3
0
0
4
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
1
3
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
5
0
0
0
0
0
1
0
2
2
0
0
2
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
2
0
0
0
2
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
3
0
0
1
0
0
0
1
1
0
0
0
0
2
0
0
2
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
2
2
0
0
1
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
1
0
2
0
1
0
0
0
0
1
0
0
0
0
1
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
3
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
3
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
5
0
1
2
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
4
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
4
0
0
1
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
3
0
0
0
0
0
3
0
2
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
3
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
2
2
0
2
0
1
0
0
1
1
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
1
2
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
2
2
0
0
2
1
0
0
2
0
1
0
0
0
0
0
0
2
0
1
0
2
0
0
1
2
0
0
0
0
0
0
0
0
9
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
4
0
0
4
0
0
3
1
0
2
0
0
11
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
3
2
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
3
1
0
0
0
2
2
0
0
1
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
3
2
0
0
0
1
0
4
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
2
0
0
0
0
0
0
0
2
0
0
3
2
2
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
3
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
1
0
1
0
0
1
0
0
0
2
0
0
0
2
2
0
0
0
2
0
0
0
0
2
0
2
0
3
0
1
0
1
0
0
0
2
0
1
2
1
0
0
0
0
3
2
0
0
0
1
0
0
0
1
0
0
6
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
3
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
1
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
2
2
0
0
2
0
0
0
2
0
2
1
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
4
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
4
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
6
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
3
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
3
0
0
1
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
4
0
0
0
0
1
0
0
0
0
0
1
3
2
0
0
0
1
0
0
0
0
0
2
1
0
0
0
1
0
0
1
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
4
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
1
1
0
0
2
1
0
0
0
0
2
0
0
0
2
0
0
0
3
0
0
1
1
2
6
0
1
0
2
4
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
1
0
0
0
1
1
1
0
0
0
0
2
2
1
0
0
2
0
0
0
0
1
2
2
1
0
0
2
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
3
0
0
0
2
0
2
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
1
0
0
1
0
0
2
2
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
7
0
0
0
0
0
2
0
2
0
2
0
0
2
0
2
0
1
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
6
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
3
0
2
0
0
0
0
0
7
0
2
0
2
2
1
2
0
0
8
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
2
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
2
2
0
3
0
0
0
0
0
2
1
0
2
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
6
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
2
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
3
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
3
0
0
0
0
3
0
0
0
0
2
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
5
1
0
0
0
0
0
0
0
1
0
0
0
0
0
9
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
1
2
0
1
0
0
1
0
2
2
0
5
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
2
0
2
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
2
0
0
0
0
3
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
3
0
1
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
2
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
1
1
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
2
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
6
2
0
0
0
0
0
0
1
0
1
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
12
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
1
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
4
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
1
1
2
0
0
0
0
3
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
1
0
2
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
2
1
0
2
0
2
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
2
0
0
5
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
1
1
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
2
0
3
0
1
0
0
0
1
0
0
0
0
0
1
1
0
2
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
1
2
0
0
0
0
3
0
0
1
0
0
0
1
0
0
2
0
0
0
0
2
1
2
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
2
0
2
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
2
0
0
2
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
1
1
3
2
2
0
2
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
6
0
0
4
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
2
0
1
0
3
0
0
0
0
0
0
0
1
0
0
1
1
0
0
2
0
1
1
0
0
0
0
3
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
1
0
1
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
2
0
0
1
0
0
1
0
0
2
0
0
2
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
2
0
0
5
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
1
1
0
0
0
0
0
0
0
2
1
0
2
2
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
3
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
1
0
0
3
3
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
1
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
1
0
1
0
0
0
1
0
0
0
2
0
1
0
0
0
0
2
0
0
0
2
0
0
4
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
3
0
0
3
1
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
7
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
2
0
3
0
0
0
3
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
2
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
4
0
1
1
2
0
2
0
0
0
0
0
0
1
0
1
0
4
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
1
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
2
0
0
0
0
0
2
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
1
2
1
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
2
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
2
2
0
2
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
1
4
2
2
2
0
1
0
0
0
1
0
1
0
2
0
0
0
2
0
1
1
0
0
0
1
0
0
2
1
0
0
0
0
0
2
0
1
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
2
0
0
0
0
2
2
0
2
2
0
0
4
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
3
2
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
2
0
1
0
0
0
0
2
0
1
0
2
0
1
0
0
0
0
0
0
1
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
2
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
2
2
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
1
0
0
2
0
2
0
0
0
1
0
0
0
0
2
2
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
2
3
0
0
4
0
1
1
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
3
0
0
0
0
0
1
0
2
0
2
0
0
0
1
0
0
2
1
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
7
2
1
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
4
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
1
4
0
0
0
0
0
0
2
0
0
0
0
7
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
3
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
9
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
1
1
0
1
0
0
0
1
0
0
0
1
0
0
3
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
3
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
4
0
0
1
0
0
0
0
0
0
1
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
1
0
2
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
2
0
1
2
0
1
0
1
0
0
1
0
0
0
0
0
0
2
1
0
0
1
1
1
2
0
0
3
0
1
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
1
2
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
1
0
1
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
3
1
0
3
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
2
0
0
2
1
0
1
0
0
0
0
2
1
2
0
0
0
1
0
2
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
3
2
0
0
2
0
0
0
2
0
0
0
0
0
1
2
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
1
2
4
0
2
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
1
0
0
0
3
2
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
2
1
1
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
2
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
4
0
0
3
0
0
1
2
0
1
0
1
0
0
1
2
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
2
0
3
0
0
0
0
2
1
0
6
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
6
1
1
1
0
2
2
3
0
0
0
0
0
0
4
2
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
1
1
1
4
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
4
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
5
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
17
0
0
3
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
2
0
2
0
3
2
2
0
1
0
1
0
0
0
0
3
0
2
0
0
0
2
0
0
0
0
1
0
0
2
2
2
0
2
0
2
0
0
0
0
0
1
0
2
0
2
1
0
2
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
2
0
2
2
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
3
0
0
0
6
0
0
2
0
0
0
2
0
0
4
0
0
0
0
2
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
1
0
0
0
0
0
1
2
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
1
1
0
2
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
1
0
2
0
0
0
0
0
2
0
0
2
0
2
0
0
1
0
2
0
0
0
0
1
0
0
0
0
1
2
0
0
0
2
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
4
2
0
1
2
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
2
2
0
0
2
0
1
0
3
0
2
0
1
0
0
0
1
0
0
0
0
0
2
4
0
2
0
1
1
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
2
1
0
0
0
1
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
2
0
1
0
1
0
2
0
0
0
0
2
2
0
0
0
2
0
0
2
0
0
0
1
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
1
0
0
2
0
3
0
0
2
0
0
0
0
0
0
2
2
2
2
0
0
1
0
2
0
0
0
0
0
0
0
1
3
0
1
0
0
0
0
0
0
1
0
0
0
0
3
2
0
0
2
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
3
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
1
2
1
0
0
0
0
0
2
0
0
0
0
2
0
2
1
0
0
2
0
0
2
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
2
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
1
4
0
1
0
2
0
0
0
1
0
1
0
0
2
3
0
0
1
0
0
0
0
0
1
2
0
1
0
0
2
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
1
0
0
1
0
1
0
0
0
0
1
0
0
3
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
1
0
1
2
0
0
0
2
1
0
0
1
1
0
2
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
1
0
1
0
0
1
0
0
0
0
1
2
0
0
1
0
0
1
0
0
0
0
0
1
0
2
1
0
2
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
4
0
2
0
2
0
0
0
0
0
0
3
2
0
0
0
0
2
0
0
0
1
1
2
0
2
0
0
1
0
2
0
0
1
0
0
0
4
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
1
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
1
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
3
0
1
1
0
0
1
2
2
0
0
2
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
4
0
1
0
0
0
1
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
3
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
2
1
2
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
4
0
0
0
0
1
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
2
0
0
2
0
0
2
0
0
0
5
0
2
0
0
0
0
2
0
0
1
0
1
0
0
0
0
2
0
0
1
0
0
4
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
5
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
2
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
2
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
2
1
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
1
0
0
0
1
0
0
0
0
0
0
3
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
1
2
0
0
2
2
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
1
3
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
2
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
1
1
0
0
3
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
3
0
4
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
1
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
3
16
0
0
0
1
1
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
4
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
1
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
1
0
1
2
0
0
0
0
0
0
2
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
2
3
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
1
0
0
0
0
1
0
0
1
1
0
2
0
0
0
3
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
6
0
2
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
1
1
2
2
2
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
3
0
1
0
0
0
0
0
2
0
1
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
1
0
0
1
3
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
2
1
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
2
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
2
0
2
0
0
2
0
1
0
0
0
0
1
0
0
0
0
2
2
1
1
0
1
0
2
0
0
1
0
0
2
0
0
0
0
0
1
2
2
2
0
1
0
0
0
2
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
15
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
2
0
0
0
2
0
2
0
3
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
1
0
0
2
2
3
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
1
0
0
0
0
1
4
2
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
1
0
1
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
3
0
0
0
2
3
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
1
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
2
2
0
2
0
0
0
0
0
8
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
0
0
0
2
2
3
0
2
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
3
0
0
0
0
0
0
2
1
0
0
0
0
0
0
5
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
3
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
1
1
0
0
1
0
0
0
0
0
0
1
1
0
3
0
0
0
0
0
1
0
4
0
0
0
0
2
0
0
0
0
0
5
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
4
0
0
2
0
3
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
2
0
2
0
1
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
1
0
1
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
1
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
2
2
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
3
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
3
0
0
2
0
1
2
1
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
4
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
1
1
0
0
2
0
1
0
0
0
0
0
0
2
0
0
5
0
0
0
2
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
2
2
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
1
2
0
1
0
0
1
2
0
0
0
0
0
4
0
0
0
0
2
0
0
2
1
0
0
3
0
4
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
1
0
0
0
0
2
0
1
0
0
0
1
0
0
2
0
5
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
2
0
0
1
0
1
1
0
1
1
1
0
1
0
1
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
3
0
2
0
0
0
1
0
0
0
0
4
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
4
2
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
1
2
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
5
0
1
1
0
0
0
0
0
3
1
1
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
1
2
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
2
1
0
0
0
0
1
0
0
2
0
3
0
1
0
0
0
0
0
4
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
4
0
0
1
2
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
2
0
1
1
0
0
2
4
0
0
0
2
0
0
2
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
4
0
2
1
0
0
0
0
0
0
1
0
3
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
1
0
2
1
1
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
2
3
0
0
2
0
5
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
2
1
0
0
0
5
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
1
0
0
0
2
1
0
0
0
0
1
0
1
1
0
1
3
0
0
2
2
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
7
1
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
2
0
2
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
1
0
0
0
0
1
1
1
2
0
2
0
0
2
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
4
0
1
2
2
0
0
0
0
1
1
3
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
4
2
0
0
2
1
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
1
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
5
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
3
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
2
2
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
3
3
0
4
1
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
1
0
1
0
2
0
0
0
3
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
3
0
0
2
1
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
2
0
0
1
0
0
0
1
2
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
4
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
0
2
3
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
1
1
0
2
0
0
0
0
0
4
0
0
0
0
0
0
0
7
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
2
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
4
0
0
0
0
1
1
0
0
0
0
1
0
1
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
1
0
0
2
3
0
1
0
2
0
1
0
2
0
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
2
0
0
0
0
0
0
5
0
2
1
0
1
0
0
2
0
1
0
1
0
0
0
3
0
0
0
1
8
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
2
0
0
1
0
0
2
0
2
1
0
0
0
3
0
2
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
2
0
2
0
1
2
0
0
1
0
0
2
0
2
3
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
2
0
0
1
1
0
0
0
2
4
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
3
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
5
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
2
0
0
0
2
3
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
2
0
0
0
0
0
1
0
2
0
0
0
0
2
2
0
0
4
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
2
0
1
1
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
2
0
5
0
4
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
2
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
1
6
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
3
0
0
0
0
2
3
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
4
0
2
0
0
2
0
0
1
0
0
2
0
0
0
1
3
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
1
4
0
0
0
1
1
0
0
0
1
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
3
2
0
0
1
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
2
0
2
0
3
0
2
2
0
0
0
0
2
0
1
3
1
2
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
1
2
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
3
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
1
4
0
1
0
0
0
2
0
3
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
4
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
2
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
2
0
2
2
0
0
0
2
0
1
0
0
0
2
0
2
2
1
1
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
2
0
0
0
3
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
1
2
4
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
2
2
0
1
0
1
0
2
0
0
2
0
0
1
0
0
0
0
1
0
0
2
5
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
1
0
0
2
3
3
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
2
1
0
3
1
0
3
0
0
0
0
1
0
0
0
0
2
0
0
2
2
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
2
2
0
0
0
0
0
0
4
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
6
0
0
0
0
1
0
0
2
2
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
2
0
1
0
0
2
1
2
1
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
1
1
0
1
1
2
0
2
0
0
0
0
0
0
0
0
0
0
1
1
1
0
2
0
0
0
2
1
0
2
0
1
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
2
0
0
0
2
2
0
0
1
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
14
0
0
4
0
0
0
1
0
0
0
0
0
5
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
4
2
0
0
0
0
0
0
1
1
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
1
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
1
2
0
1
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
5
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
4
0
0
1
0
1
0
2
4
0
0
0
1
2
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
1
0
0
2
0
0
0
2
0
1
0
2
0
0
0
1
1
0
2
0
0
3
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
1
1
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
2
0
0
2
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
5
0
2
0
0
0
2
0
0
2
0
2
0
4
2
1
0
0
0
1
0
0
0
1
0
1
0
0
1
0
2
0
0
1
0
2
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
3
2
0
2
0
2
0
2
2
1
0
0
0
0
0
1
2
0
2
3
1
0
2
0
0
0
0
0
0
0
0
2
0
4
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
2
0
1
2
1
0
0
1
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
1
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
1
1
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
3
0
0
0
1
1
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
2
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
2
0
0
0
0
2
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
3
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
5
1
0
0
1
2
3
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
3
3
0
0
2
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
7
1
0
0
0
2
1
0
0
2
0
0
0
0
0
4
0
0
0
1
1
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
4
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
2
1
0
0
1
2
2
0
0
1
0
7
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
2
0
0
3
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
3
0
0
2
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
4
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
2
2
0
0
4
1
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
2
0
0
3
0
0
2
3
0
3
0
0
1
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
1
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
1
0
1
0
1
1
0
0
0
0
2
0
0
0
0
2
0
0
0
3
0
0
1
0
0
1
1
2
0
0
2
0
0
0
1
0
0
0
12
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
1
0
2
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
1
2
0
3
0
0
0
0
0
0
0
1
0
1
0
0
2
2
0
1
1
0
0
2
2
0
0
0
0
0
0
0
1
8
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
3
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
3
0
0
1
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
3
0
2
1
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
1
0
5
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
1
0
1
0
1
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
2
2
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
5
1
0
4
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
1
0
1
0
0
0
1
2
0
0
1
0
2
0
0
0
0
0
0
0
2
0
1
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
4
3
0
5
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
1
0
0
3
0
4
0
0
0
0
0
0
0
2
0
2
0
2
0
3
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
2
1
0
0
0
0
1
0
2
0
0
0
5
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
1
0
2
0
1
0
0
0
0
0
0
0
2
0
0
3
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
2
2
1
0
0
1
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
1
0
0
2
0
1
0
0
2
1
1
0
0
0
0
3
0
1
2
0
0
4
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
2
2
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
5
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
3
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
1
2
1
0
0
0
3
0
0
0
0
0
0
0
1
1
0
0
1
4
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
1
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
5
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
1
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
1
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
2
2
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
2
0
1
0
0
1
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
6
0
0
0
0
1
0
2
2
0
0
1
0
2
0
17
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
2
1
0
1
0
0
0
0
0
0
0
2
2
0
1
0
0
2
0
0
2
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
1
0
0
0
2
0
2
0
0
1
1
0
0
0
0
0
0
2
0
0
1
2
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
1
0
0
2
1
0
1
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
4
0
0
1
0
4
0
0
0
2
0
0
2
0
1
0
0
0
2
2
0
0
3
0
0
1
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
1
0
2
2
2
2
1
0
10
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
1
2
0
1
0
1
0
0
2
1
0
0
1
0
1
1
0
0
1
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
4
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
1
0
3
2
0
0
1
2
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
1
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
5
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
2
1
0
2
0
0
0
0
0
0
1
0
0
2
1
1
1
2
2
0
1
0
0
0
0
0
0
0
24
0
0
0
0
0
0
0
2
2
0
2
0
0
0
2
0
0
0
2
0
1
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
3
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
1
1
0
2
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
2
0
3
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
3
0
0
12
0
0
0
1
2
0
0
0
1
0
0
0
1
0
3
2
0
0
0
0
0
0
0
0
2
0
0
1
0
3
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
1
2
1
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
10
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
1
3
0
2
4
2
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
1
1
1
0
0
0
1
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
1
0
2
2
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
4
0
0
0
3
0
0
2
0
0
0
0
0
0
1
0
0
1
0
2
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
1
0
0
0
5
0
0
0
1
0
0
1
1
1
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
6
0
0
3
0
0
0
0
0
5
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
3
0
1
1
0
2
0
0
0
0
2
4
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
3
1
0
1
1
0
0
2
0
0
0
3
0
0
1
3
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
3
2
1
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
3
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
1
0
1
0
0
1
1
0
0
0
2
0
3
0
0
0
0
1
0
3
3
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
6
1
1
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
3
2
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
1
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
1
5
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
3
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
2
2
0
0
0
2
2
3
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
2
0
1
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
3
2
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
4
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
5
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
5
0
0
0
0
0
0
0
0
0
2
2
3
1
0
1
2
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
2
0
1
8
0
0
0
0
0
0
2
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
2
2
0
0
2
0
0
0
2
2
0
0
0
0
0
0
2
2
0
0
2
0
0
0
5
0
1
0
0
0
1
0
0
0
0
1
3
6
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
1
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
2
0
2
2
0
0
0
0
0
0
0
0
1
0
1
0
0
1
3
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
3
2
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
2
1
0
0
3
0
2
1
8
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
6
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
3
2
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
1
0
0
0
0
1
0
0
0
0
2
0
3
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
2
2
0
3
0
0
0
0
0
0
0
0
0
0
6
1
1
0
0
0
0
0
0
0
2
1
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
1
0
2
0
0
0
0
1
0
0
0
2
0
0
0
2
0
1
1
0
0
3
1
0
1
0
2
1
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
2
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
2
0
2
0
0
0
1
0
0
2
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
3
0
3
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
2
7
1
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
2
0
1
0
0
1
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
4
0
0
1
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
1
0
1
0
0
0
1
0
1
0
0
2
2
5
1
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
1
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
2
2
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
3
0
0
0
1
0
1
0
1
0
0
0
0
0
1
4
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
2
2
0
0
0
0
2
0
0
0
1
0
2
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
2
1
0
2
2
0
0
7
1
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
3
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
2
2
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
5
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
1
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
1
1
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
2
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
2
4
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
8
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
3
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
3
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
1
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
5
0
0
2
0
0
0
0
3
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
2
0
5
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
2
0
2
0
0
1
1
0
0
2
0
0
2
0
0
1
1
0
0
1
0
0
2
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
3
2
0
0
0
1
2
0
2
2
1
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
1
0
2
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
1
2
1
1
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
2
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
1
0
0
2
0
0
0
0
2
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
9
0
1
0
2
0
1
0
1
0
0
0
0
2
0
2
0
3
2
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
2
0
0
0
0
0
3
0
1
0
5
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
3
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
2
0
1
0
0
2
0
0
2
2
1
0
0
2
0
0
0
0
0
2
1
1
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
1
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
3
3
0
0
0
0
0
0
1
4
1
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
8
0
0
0
0
1
1
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
3
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
2
0
1
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
4
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
2
4
0
0
2
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
11
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
10
0
0
0
0
0
1
0
0
0
0
0
4
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
5
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
2
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
3
2
0
0
1
2
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
1
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
2
2
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
1
2
0
0
0
1
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
1
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
3
1
2
0
0
0
0
1
0
0
0
0
1
6
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
2
1
0
0
0
1
0
0
0
7
0
0
0
1
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
3
0
2
1
1
0
2
0
0
0
0
3
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
2
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
3
0
0
5
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
5
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
3
0
0
0
0
1
2
0
0
3
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
2
0
0
2
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
1
2
0
0
0
0
0
1
0
1
0
0
1
0
1
0
1
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
3
6
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
1
1
0
0
0
1
2
0
0
0
0
0
0
2
2
0
0
0
0
5
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
2
0
0
0
1
1
0
1
0
0
0
1
1
0
0
0
2
1
0
0
1
0
2
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
1
0
1
2
0
3
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
1
0
0
0
1
2
0
2
4
0
0
0
2
0
0
0
0
2
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
4
2
1
0
0
1
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
2
1
2
0
0
0
0
0
0
1
1
0
0
0
0
9
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
3
0
2
0
0
0
1
1
0
0
0
1
0
0
0
0
3
0
2
0
0
0
0
0
2
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
3
2
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
2
0
3
0
1
0
0
0
5
1
0
4
0
0
0
0
0
0
0
0
0
0
4
2
0
0
0
1
1
0
0
0
4
1
0
2
0
2
0
0
0
0
1
0
0
2
1
2
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
1
0
0
0
0
3
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
4
0
3
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
1
0
0
7
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
2
0
2
1
0
5
2
0
0
0
0
0
1
2
0
0
2
0
0
3
0
0
0
0
0
0
4
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
2
0
0
2
1
0
0
0
0
0
0
0
1
0
2
0
1
0
0
2
1
0
0
2
4
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
3
2
4
0
0
0
1
1
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
2
0
1
0
5
1
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
10
0
2
4
0
0
0
1
2
0
2
0
0
2
1
1
1
0
0
0
1
1
0
0
0
0
2
0
0
0
1
0
5
0
0
0
2
0
0
0
0
0
0
0
4
1
2
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
4
0
0
0
2
1
0
0
0
0
0
2
0
1
0
0
1
0
0
2
1
0
0
0
2
0
1
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
1
1
0
0
1
6
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
3
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
2
0
0
0
2
0
0
0
0
0
1
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
6
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
2
2
0
0
1
0
0
0
0
1
0
0
0
10
0
2
0
1
0
3
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
5
0
0
0
7
1
1
0
0
1
1
0
0
0
0
1
2
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
5
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
8
1
1
0
0
2
0
2
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
10
1
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
1
0
2
0
0
2
1
0
0
0
0
0
2
2
0
0
0
0
0
0
4
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
2
0
1
0
0
0
1
0
0
2
1
0
0
0
0
0
0
1
2
0
0
0
2
2
2
0
0
0
0
1
0
2
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
1
2
1
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
3
0
2
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
2
0
1
2
0
0
1
0
0
1
3
0
1
0
1
2
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
1
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
1
1
3
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
3
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
5
0
2
1
0
0
0
0
1
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
2
0
1
3
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
3
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
1
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
3
1
1
0
0
0
0
0
0
0
0
0
0
0
4
1
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
2
0
0
2
0
1
0
0
0
1
0
0
0
4
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
9
1
0
0
0
2
0
1
0
0
0
0
0
4
0
0
0
1
0
2
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
3
0
0
0
0
0
2
3
2
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
7
1
0
0
0
0
2
1
0
2
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
1
0
0
0
2
0
0
10
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
1
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
5
0
1
4
0
0
0
0
0
0
2
0
0
0
4
1
0
0
0
0
0
0
2
1
0
0
0
1
10
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
3
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
7
0
0
0
0
0
2
0
0
0
0
1
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
2
0
1
0
2
0
0
3
0
0
0
0
0
1
0
0
1
0
6
0
0
0
1
0
2
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
2
6
0
0
1
0
0
0
0
3
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
6
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
2
1
0
3
1
0
0
1
0
0
0
0
0
3
0
0
1
0
1
0
2
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
1
0
0
0
1
0
2
0
3
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
3
1
0
2
0
0
1
1
0
0
2
2
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
2
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
5
0
2
0
3
3
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
3
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
5
2
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
1
0
1
2
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
1
2
9
0
0
0
0
0
0
0
0
1
0
2
2
3
0
6
1
0
0
2
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
3
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
4
0
0
0
0
2
1
0
0
0
0
0
0
2
0
1
0
2
2
0
1
0
0
0
0
1
0
0
3
2
0
0
0
0
0
1
1
2
0
0
0
0
2
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
2
0
0
0
1
0
0
0
2
0
0
0
0
1
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
3
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
2
0
0
1
0
3
0
0
0
0
0
3
0
0
1
0
0
1
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
5
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
3
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
1
1
0
0
0
0
0
2
1
0
1
3
0
0
0
2
1
0
1
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
1
3
0
1
1
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
4
1
0
2
0
2
2
0
0
0
0
0
12
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
3
1
0
2
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
3
1
2
0
0
0
1
2
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
2
0
2
1
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
3
0
0
0
0
0
0
0
0
1
0
3
0
1
1
1
1
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
1
1
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
1
1
0
0
1
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
2
1
2
2
1
1
0
0
0
3
1
0
0
3
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
19
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
1
0
2
0
0
2
2
0
0
0
2
0
0
4
0
0
0
3
0
0
0
0
2
0
0
0
0
2
0
0
2
0
2
1
0
0
1
0
1
0
2
1
0
1
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
1
4
1
0
1
0
2
1
2
0
0
0
0
1
0
1
0
0
0
1
0
2
2
0
0
0
0
0
0
6
1
0
0
1
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
2
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
3
2
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
3
2
0
0
2
0
1
4
0
0
0
0
0
2
0
1
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
1
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
2
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
2
0
0
0
0
0
5
0
0
0
3
2
0
1
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
3
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
2
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
4
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
2
2
0
0
0
1
0
0
1
0
0
0
1
0
2
0
2
1
0
0
0
3
0
0
0
0
0
0
0
6
0
0
2
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
1
1
0
0
0
0
0
0
1
0
2
1
0
0
1
2
2
0
2
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
2
2
10
0
0
0
4
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
7
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
2
1
1
1
0
0
0
1
1
0
0
0
0
0
1
1
0
0
1
0
0
1
2
0
2
0
0
0
2
4
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
2
0
1
4
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
3
4
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
6
0
1
0
2
1
0
0
0
0
0
1
0
0
0
1
0
1
0
2
0
1
0
0
0
0
1
2
2
0
3
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
1
0
2
0
0
1
0
2
0
0
0
0
0
1
1
0
0
0
0
0
3
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
3
0
2
0
0
0
3
0
0
0
0
0
3
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
1
2
1
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
1
0
2
0
1
0
0
0
0
0
2
1
0
0
0
2
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
4
1
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
2
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
1
0
0
0
0
0
2
0
2
0
2
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
1
1
0
0
1
2
0
0
0
0
0
0
2
3
0
3
0
2
0
0
0
0
0
2
0
0
0
0
5
1
1
0
0
0
0
1
1
0
1
0
1
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
2
0
5
0
0
0
0
5
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
12
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
2
0
0
1
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
1
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
1
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
2
2
1
0
0
2
0
2
0
1
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
1
0
6
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
6
0
0
0
0
4
0
3
2
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
1
3
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
1
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
4
0
1
1
0
0
0
4
0
0
0
1
0
2
0
0
0
0
0
0
21
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
2
0
4
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
3
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
2
1
2
0
0
0
0
0
1
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
2
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
1
1
0
0
3
0
3
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
3
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
1
0
0
3
2
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
1
0
0
0
0
0
7
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
4
0
0
2
2
0
2
0
0
0
0
0
2
0
0
3
0
0
0
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
2
1
0
0
0
0
1
0
0
1
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
2
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
3
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
2
3
0
0
0
0
0
1
3
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
3
4
3
1
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
1
5
0
1
0
0
1
1
0
1
0
0
3
0
3
2
0
0
0
1
1
2
0
0
3
2
0
0
2
2
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
1
0
2
0
0
2
1
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
1
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
3
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
2
0
0
0
2
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
1
0
0
0
0
3
1
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
2
2
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
3
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
3
0
1
2
0
1
1
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
2
0
1
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
1
1
0
5
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
4
0
1
0
1
2
0
0
2
0
2
0
2
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
1
0
2
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
3
1
0
0
0
0
0
0
0
2
0
3
0
0
2
0
0
1
1
0
0
1
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
2
0
1
1
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
3
0
1
4
0
0
0
0
2
5
8
0
2
0
0
0
0
0
1
0
1
1
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
3
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
2
0
0
3
0
0
0
0
0
1
0
0
0
4
2
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
1
2
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
3
3
0
0
2
0
2
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
3
0
1
0
0
2
0
2
1
0
1
0
2
0
0
0
1
0
2
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
9
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
3
2
0
0
0
0
0
2
3
1
0
0
0
0
0
0
0
0
1
1
1
0
2
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
1
2
2
0
1
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
2
2
2
0
2
2
0
0
0
0
0
0
0
1
0
0
1
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
3
1
0
1
2
0
0
2
0
0
0
0
1
2
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
2
2
1
0
0
2
1
2
0
0
0
0
0
1
2
0
0
2
0
0
1
0
0
2
0
0
0
9
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
1
0
0
1
0
0
0
0
0
3
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
2
1
1
2
1
0
2
0
0
0
0
0
0
0
2
0
1
0
3
0
0
0
0
0
0
0
3
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
1
0
0
2
1
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
1
0
0
0
0
0
0
5
0
2
1
0
0
0
2
0
0
0
9
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
2
0
0
0
0
0
2
0
2
0
0
1
3
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
4
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
4
0
0
1
0
0
1
5
0
2
8
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
2
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
1
0
0
2
0
1
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
2
1
2
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
2
2
1
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
2
2
2
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
4
0
1
0
0
2
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
4
1
1
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
2
0
1
2
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
1
0
0
2
0
2
1
0
0
3
0
0
0
2
0
2
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
4
0
0
1
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
2
0
2
2
1
0
3
1
1
0
0
0
0
1
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
3
0
0
0
1
1
2
0
0
1
1
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
5
0
2
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
1
0
3
0
0
1
1
0
0
0
5
0
3
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
9
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
4
0
0
0
8
0
0
2
2
0
0
0
0
1
0
0
4
0
2
0
1
0
0
0
0
0
0
0
0
2
1
1
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
1
2
2
1
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
6
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
3
0
1
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
3
0
0
1
0
2
0
0
2
1
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
1
1
2
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
2
0
1
1
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
1
0
0
1
0
0
2
2
1
0
0
0
2
1
2
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
2
0
2
1
0
0
1
0
1
0
1
0
2
0
2
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
1
0
0
0
0
2
6
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
2
0
4
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
2
0
1
0
0
0
0
3
0
2
2
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
5
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
2
0
0
1
2
1
2
0
0
0
1
0
0
0
1
0
0
1
2
0
2
3
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
2
2
0
1
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
8
1
2
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
1
0
0
1
0
0
2
0
0
0
0
7
0
0
0
0
0
0
0
1
1
2
0
0
3
0
0
2
1
2
2
2
1
0
0
0
0
0
1
0
0
0
0
3
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
3
1
0
2
0
0
2
0
2
0
2
0
2
0
0
2
2
0
0
0
0
0
0
4
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
3
3
0
0
0
1
0
0
4
0
0
0
2
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
2
1
3
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
1
0
0
2
0
0
1
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
7
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
5
0
0
0
1
0
2
3
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
1
0
4
0
0
3
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
5
0
0
2
0
2
0
0
0
1
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
3
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
2
1
0
0
0
0
3
0
1
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
1
1
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
1
2
0
0
0
0
0
0
2
0
0
0
0
2
0
1
2
0
2
0
0
1
0
2
0
2
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
3
1
2
0
2
0
0
0
0
2
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
2
1
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
10
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
2
8
0
1
0
0
0
0
1
1
0
0
0
0
3
1
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
1
2
2
0
0
0
0
0
2
2
0
0
3
0
0
0
1
0
0
0
2
2
1
0
0
0
1
3
0
0
1
0
1
0
1
2
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
3
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
2
2
1
2
0
0
2
0
3
1
0
0
2
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
2
0
0
1
0
0
4
3
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
2
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
3
0
0
2
0
0
2
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
5
0
1
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
4
2
0
0
0
2
1
1
0
0
0
0
0
0
6
0
0
0
0
0
3
0
0
0
0
0
1
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
2
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
2
0
1
0
2
0
0
0
0
2
1
1
1
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
1
3
0
0
3
1
0
0
0
1
0
0
0
0
3
0
2
0
0
0
0
1
0
0
0
0
1
0
2
1
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
6
0
0
0
0
1
0
2
9
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
2
1
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
3
1
0
0
0
0
2
0
0
0
0
0
3
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
2
0
0
2
0
0
1
2
0
2
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
2
0
3
0
4
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
5
2
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
2
0
2
2
2
1
0
0
0
1
0
1
0
0
0
0
1
0
1
1
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
2
2
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
2
0
0
2
0
2
0
0
2
0
0
0
0
1
0
0
4
0
0
0
2
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
4
2
0
0
0
1
0
1
1
2
0
0
2
1
0
2
0
1
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
5
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
8
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
3
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
2
0
0
0
1
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
1
0
0
2
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
1
0
2
0
1
0
0
0
0
0
0
1
0
1
2
0
0
0
1
0
2
0
1
0
2
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
3
0
1
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
2
1
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
7
0
0
0
2
0
0
0
0
2
3
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
2
0
0
2
0
1
0
0
0
1
0
1
0
0
0
2
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
3
0
1
0
0
1
1
0
0
0
0
0
0
1
1
0
2
3
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
1
2
1
0
0
0
0
0
0
0
0
0
0
1
0
1
2
3
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
1
0
0
2
0
0
1
1
0
0
1
1
4
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
1
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
3
2
0
0
2
0
0
2
1
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
7
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
2
0
0
0
2
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
2
0
0
3
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
3
2
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
2
0
1
0
0
1
2
0
1
0
1
2
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
5
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
3
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
1
1
1
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
1
0
0
0
0
2
0
0
0
2
0
0
1
0
1
1
0
0
0
0
0
2
2
1
0
0
0
0
1
0
0
0
0
1
0
0
2
1
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
3
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
4
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
1
1
1
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
2
4
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
2
0
0
0
0
1
0
0
0
4
0
1
1
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
1
1
0
0
1
4
0
0
0
0
0
2
2
0
0
0
2
0
0
0
1
0
0
0
2
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
5
0
0
0
0
0
1
2
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
2
0
1
0
0
1
0
0
2
0
6
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
5
0
2
0
0
2
0
0
0
1
0
0
1
2
1
2
4
2
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
2
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
1
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
2
1
0
0
1
0
1
2
0
0
0
0
2
0
0
1
0
2
0
2
3
1
0
0
0
0
1
0
5
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
1
2
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
2
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
5
0
1
0
2
0
0
3
0
0
2
0
2
0
1
0
1
2
0
0
0
2
0
3
2
0
0
2
0
0
0
0
1
0
0
3
0
3
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
2
1
12
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
3
0
0
3
0
0
0
0
0
2
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7
0
0
2
0
0
2
0
2
0
0
0
0
0
1
2
1
0
2
6
0
2
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
1
0
0
0
2
1
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
1
0
1
0
0
2
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
1
2
0
0
0
1
0
0
1
0
0
0
3
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
3
0
0
0
0
0
0
0
0
1
3
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
3
1
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
1
0
0
0
1
2
0
1
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
2
0
0
4
0
1
0
0
1
0
0
0
0
3
2
2
0
0
0
0
0
0
0
2
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
2
0
4
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
3
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
3
0
0
1
3
0
0
1
0
1
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
3
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
16
0
0
0
1
2
0
3
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
4
0
0
2
0
1
1
0
0
2
0
0
0
0
0
0
1
0
2
2
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
2
1
0
5
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
1
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
3
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
2
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
1
1
0
0
2
0
0
0
0
0
2
0
3
3
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
2
0
0
0
3
1
0
1
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
14
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
11
3
0
0
2
0
0
0
0
2
0
1
2
0
2
1
1
0
4
0
0
0
0
0
2
0
1
2
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
2
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
3
0
0
0
1
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
3
0
0
0
1
4
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
5
0
0
0
1
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
7
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
1
0
3
0
1
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
2
1
0
0
1
0
2
0
0
5
0
0
0
0
3
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
2
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
1
4
0
0
0
0
0
4
2
1
1
0
0
0
1
0
2
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
2
0
0
0
2
2
0
0
0
4
2
1
0
1
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
2
0
4
0
0
0
0
2
0
1
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
2
0
0
0
0
0
0
0
1
2
0
0
1
0
1
0
0
2
0
0
0
0
2
1
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
3
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
1
0
2
0
2
1
0
0
0
0
2
0
1
2
0
0
3
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
11
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
4
2
2
1
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
13
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
4
0
0
2
0
2
0
0
0
2
0
0
0
0
1
5
1
4
0
0
0
2
0
2
2
2
0
0
1
1
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
1
2
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
2
2
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
1
2
0
0
2
2
4
1
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
1
0
4
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
3
0
2
2
1
2
0
0
0
0
1
0
1
1
1
2
0
0
0
0
0
1
0
5
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
1
0
2
3
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
2
0
0
0
1
0
0
2
2
1
0
2
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
5
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
2
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
2
0
1
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
1
1
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
2
0
2
1
0
0
0
0
1
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
2
1
0
0
1
0
0
0
0
0
2
0
0
0
3
2
2
3
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
2
0
1
1
0
0
1
0
3
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
1
0
7
2
1
0
0
4
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
1
1
2
0
0
0
0
0
1
1
0
0
0
7
0
3
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
3
1
0
0
0
0
2
0
2
1
0
0
0
0
0
0
2
0
0
0
1
1
0
3
0
0
0
0
0
0
0
3
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
3
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
2
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
1
1
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
3
0
2
0
0
0
0
0
0
0
2
0
1
0
1
1
2
0
0
0
2
1
1
2
0
0
0
2
0
2
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
2
0
3
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
2
0
0
2
0
0
0
2
0
2
0
0
0
5
1
1
0
0
0
0
0
0
2
0
1
4
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
1
0
0
0
0
2
0
0
0
3
0
0
0
1
0
0
0
0
0
0
2
2
1
1
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
1
0
4
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
5
0
1
0
0
0
2
0
0
0
0
0
0
0
1
1
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
1
2
0
0
0
0
0
0
2
0
0
1
0
2
0
0
2
0
0
1
0
1
0
0
2
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
3
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
5
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
1
0
0
0
2
4
0
0
0
1
0
0
0
0
2
0
0
0
0
2
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
4
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
1
0
1
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
3
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
6
0
1
1
6
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
2
3
0
0
1
0
0
2
1
0
2
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
5
0
2
2
0
1
2
0
0
0
0
0
0
0
2
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
6
0
0
0
0
0
0
0
0
0
2
0
0
3
0
1
0
1
0
0
0
0
0
2
0
2
1
0
2
1
1
2
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
1
2
0
1
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
1
2
0
0
1
0
2
0
0
1
0
0
0
0
1
1
2
0
0
0
4
0
0
0
3
0
0
0
0
5
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
8
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
3
1
0
0
0
0
0
0
1
3
0
0
1
2
2
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
2
0
0
3
0
2
0
1
0
0
0
1
1
0
0
2
0
0
0
0
0
1
0
0
1
2
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
1
1
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
4
0
2
2
0
0
0
0
0
0
0
0
0
0
1
5
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
2
1
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
9
0
0
0
1
1
0
2
0
0
0
0
2
0
0
2
0
0
2
0
0
0
3
3
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
2
0
0
1
1
0
0
1
0
0
2
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
1
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
1
0
1
3
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
2
0
0
1
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
2
1
0
0
1
2
1
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
3
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
3
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
1
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
3
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
3
1
1
1
0
0
0
1
0
0
2
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
3
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
2
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
1
0
0
0
0
0
3
0
0
0
0
0
0
1
0
2
1
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
1
2
1
7
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
3
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
1
2
0
0
0
3
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
2
0
3
0
0
0
0
0
0
0
1
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
6
1
0
2
0
2
1
0
0
1
0
1
1
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
4
1
1
0
0
0
1
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
2
1
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
2
2
2
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
1
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
2
4
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
2
3
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
3
2
0
0
6
0
2
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
3
0
0
2
1
2
0
2
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
8
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
1
0
1
2
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
3
0
2
0
0
0
2
0
2
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
3
0
2
0
0
2
0
0
0
0
0
0
2
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
1
0
1
0
0
0
1
0
0
1
2
0
0
1
2
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
1
2
0
0
3
0
0
0
0
0
1
0
0
2
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
1
0
1
2
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
3
0
4
0
1
0
0
0
1
0
0
1
0
3
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
10
2
0
0
0
2
0
0
1
2
0
1
0
0
0
0
0
1
0
0
2
0
4
0
2
3
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
2
0
0
1
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
2
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
1
1
0
2
1
0
0
0
0
0
0
1
0
0
0
2
2
0
0
2
2
2
0
1
0
0
1
0
2
0
2
0
0
2
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
1
2
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
2
0
0
0
2
2
0
1
0
0
0
0
2
1
0
1
1
0
2
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
2
0
0
0
2
1
0
0
0
0
2
0
0
0
2
0
5
0
0
1
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
2
0
2
0
0
0
0
2
1
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
3
0
0
2
1
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
1
2
0
2
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
1
0
0
1
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
3
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
5
1
2
0
0
0
1
0
0
3
0
2
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
2
1
0
1
0
1
0
0
2
1
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
1
0
0
2
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
3
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
4
0
1
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
3
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
3
2
1
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
1
0
1
1
2
0
0
0
0
0
1
0
0
2
1
0
0
0
2
0
0
4
2
2
3
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
1
0
1
0
0
0
0
0
0
0
4
1
0
0
0
1
0
1
2
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
8
0
0
0
0
1
0
3
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
4
0
0
0
0
3
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
1
1
0
0
1
1
0
0
0
0
2
0
0
0
0
7
0
0
1
1
1
0
0
0
2
0
1
0
0
0
0
0
1
0
5
0
0
0
0
0
0
0
0
0
0
1
2
3
0
0
0
0
2
1
0
0
0
0
2
0
0
2
0
2
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
1
0
0
0
2
0
3
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
2
0
2
0
0
0
2
1
0
1
0
0
0
0
0
2
0
0
19
0
0
0
1
6
0
0
0
0
0
3
2
2
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
3
0
0
0
1
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
2
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
4
0
0
0
2
0
0
0
0
0
1
5
0
1
1
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
8
0
7
0
0
1
0
0
0
4
0
0
0
0
2
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
4
0
2
5
0
0
0
0
2
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
2
0
0
0
0
0
0
8
0
1
0
0
0
0
1
2
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
2
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
1
2
0
0
1
0
0
0
3
0
0
1
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
1
0
0
2
2
0
2
0
0
0
0
0
1
0
0
0
0
1
0
1
2
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
2
0
0
0
2
2
0
0
1
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
2
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
1
2
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
2
0
1
0
1
1
6
0
1
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
2
3
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
3
0
0
1
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
2
0
2
0
0
0
0
2
0
0
1
0
1
0
1
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
1
0
0
2
0
1
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
4
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
2
1
0
1
0
0
2
0
1
2
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
3
1
1
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
3
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
1
1
5
0
0
0
1
0
1
2
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
1
3
2
0
1
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
3
0
0
0
0
1
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
1
0
0
2
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
3
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
2
2
0
0
0
0
0
0
1
0
3
0
1
2
0
0
1
1
0
0
3
2
1
2
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
3
0
3
0
2
0
0
0
1
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
3
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
1
1
0
4
0
0
0
0
2
0
2
0
0
0
0
0
3
0
0
0
2
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
1
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
2
0
0
1
0
2
0
0
2
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
3
0
0
0
0
2
0
0
0
0
0
3
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
4
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
2
9
4
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
2
0
0
0
0
1
2
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
5
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
3
0
1
0
0
1
0
1
1
0
0
2
1
0
0
2
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
2
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
2
2
0
3
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
1
2
1
0
0
0
1
2
0
1
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
3
1
0
0
2
1
0
0
0
0
0
2
0
1
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
1
3
0
0
0
0
0
2
1
0
0
0
2
0
1
6
0
0
0
0
0
0
0
0
0
0
0
1
7
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
6
0
1
0
0
0
0
2
0
2
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
1
0
0
0
1
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
3
0
0
2
0
2
0
0
0
0
0
0
0
0
3
2
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
4
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
1
0
1
1
0
0
4
0
0
0
0
1
0
1
0
0
0
0
0
2
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
3
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
2
1
1
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
1
0
0
2
2
0
0
2
0
0
2
1
0
2
0
1
2
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
4
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
2
0
1
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
4
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
3
2
0
0
0
2
0
0
3
0
0
0
0
0
2
2
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
1
0
1
1
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
3
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
2
0
1
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
4
0
0
2
0
0
0
0
0
0
0
3
2
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
3
0
0
2
3
2
0
0
5
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
3
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
2
1
0
1
2
0
1
1
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
7
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
2
0
4
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
2
3
2
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
6
0
1
0
2
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
2
2
0
0
0
0
1
0
2
0
0
0
0
0
0
2
1
0
0
0
2
5
0
0
0
4
0
2
0
0
0
0
2
2
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
1
4
2
0
0
1
1
0
1
2
0
0
0
0
1
0
0
1
0
2
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
1
0
0
2
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
2
2
0
6
2
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
2
3
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
2
1
0
1
0
0
1
0
0
2
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
1
0
0
4
0
5
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
8
0
0
0
0
1
1
0
2
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
2
0
0
0
0
0
0
1
0
0
1
2
0
0
0
2
2
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
2
2
0
0
4
0
0
0
0
0
0
1
0
1
0
0
0
3
0
0
0
0
1
0
0
0
1
0
0
1
0
0
5
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
2
0
0
0
1
0
1
0
0
1
0
0
0
2
1
0
3
0
0
0
0
0
0
2
2
0
0
2
3
0
2
0
0
2
2
1
2
0
0
0
0
0
2
0
0
1
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
2
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
1
0
0
0
2
0
2
0
2
2
1
0
0
0
1
1
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
6
0
0
3
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
2
0
1
2
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
1
0
1
1
0
0
2
2
0
2
0
0
0
0
0
0
4
0
0
1
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
4
0
0
0
0
1
7
0
0
0
0
2
6
0
0
0
0
0
0
0
8
7
0
0
0
1
2
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
1
0
2
2
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
2
0
0
2
2
0
3
1
2
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
3
2
0
1
1
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
6
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
2
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
2
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
3
0
2
0
0
2
0
0
0
0
1
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
3
0
0
0
0
0
1
0
0
0
0
4
0
0
4
2
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
5
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
2
1
2
0
1
0
1
3
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
1
1
1
3
8
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
2
0
1
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
1
0
0
0
0
0
0
10
0
1
2
2
0
0
0
0
1
1
1
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
3
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
3
3
0
2
2
0
0
0
0
0
0
0
0
0
4
0
0
2
0
2
1
1
0
0
0
0
0
1
0
0
1
0
1
0
2
0
2
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
1
0
1
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
3
0
1
0
0
0
0
0
0
0
3
0
2
1
2
0
2
0
0
0
0
1
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
9
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
1
2
0
0
0
0
1
0
0
0
0
0
0
2
0
4
0
0
0
0
0
2
0
0
2
0
0
2
1
3
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
1
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
2
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
2
0
0
1
1
2
1
0
0
3
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
2
2
0
0
0
0
0
1
0
1
0
2
0
0
0
0
2
0
0
0
0
3
2
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
3
1
0
0
1
2
0
1
1
2
0
2
0
3
0
2
0
2
0
1
0
0
4
1
1
0
0
1
0
0
0
2
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
2
0
0
1
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
2
2
0
2
1
0
0
0
1
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
1
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
3
0
3
0
0
1
1
0
0
1
0
0
0
2
0
0
8
2
2
0
0
2
0
3
0
0
1
0
2
1
0
1
0
1
2
0
0
1
2
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
2
0
1
0
1
0
1
0
0
2
1
0
2
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
3
2
0
0
1
2
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
1
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
2
1
0
0
0
0
0
0
2
0
0
0
1
3
0
1
1
0
4
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
2
2
0
0
0
0
0
0
2
0
1
1
0
2
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
1
0
0
0
1
0
2
0
0
2
0
0
3
0
0
0
2
0
0
0
2
0
0
0
3
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
3
0
0
0
0
0
0
0
6
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
2
1
0
0
0
3
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
7
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
3
1
0
1
1
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
1
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
2
2
2
1
1
0
4
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
1
0
0
0
1
0
2
1
7
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
1
1
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
1
0
0
0
0
2
1
1
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
2
3
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
3
1
2
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
1
9
0
0
2
1
1
1
0
0
1
0
0
0
0
0
1
1
1
5
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
2
4
0
0
0
0
1
1
0
0
2
0
0
0
1
0
1
0
0
0
0
0
1
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
2
0
0
1
0
0
0
1
4
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
3
0
0
0
2
0
0
0
0
2
0
0
0
0
4
0
3
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
4
0
2
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
2
0
0
0
5
0
1
2
1
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
5
0
2
0
0
0
0
0
0
0
1
0
0
2
1
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
2
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
1
0
1
0
1
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
1
0
0
0
0
1
2
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
5
2
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
1
0
0
1
0
2
0
0
2
0
2
2
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
2
0
1
0
0
3
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
5
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
3
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
1
0
0
0
2
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
2
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
2
0
0
0
0
0
0
1
0
0
0
1
2
1
1
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
3
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
4
0
0
0
1
0
1
0
0
3
7
2
0
0
2
0
0
1
0
0
0
3
1
0
1
0
0
0
0
2
0
0
0
1
0
0
2
2
0
2
0
1
0
2
0
0
0
1
0
0
0
1
0
2
0
0
0
2
1
1
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
2
2
0
9
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
2
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
6
0
0
1
1
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
2
1
1
0
0
1
0
2
0
1
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
1
0
2
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
3
2
0
0
0
0
2
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
3
2
0
0
0
0
2
0
2
2
0
0
0
0
0
1
0
0
3
2
0
0
0
0
2
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
1
2
1
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
3
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
1
2
0
0
1
1
0
0
2
0
0
2
2
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
9
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
7
2
0
0
0
3
0
3
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
4
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
1
2
0
0
0
0
0
0
3
0
0
1
0
0
0
4
0
1
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
2
1
1
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
1
0
2
1
2
0
0
0
0
0
1
0
2
0
1
0
1
2
0
0
0
4
0
1
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
6
0
2
0
1
1
0
0
2
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
2
0
3
0
0
3
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
4
0
4
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
2
2
1
0
2
0
0
0
0
1
0
0
2
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
3
1
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
1
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
9
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
3
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
8
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
3
2
2
0
0
0
1
1
0
1
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
5
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
2
2
0
0
1
1
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
3
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
2
0
3
0
1
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
2
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
3
0
0
0
2
0
1
1
0
2
0
0
0
2
0
1
6
1
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
2
0
0
0
0
2
3
1
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
4
2
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
5
0
0
0
0
2
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
3
0
1
1
0
2
0
0
0
0
0
1
0
0
0
2
1
0
0
2
0
1
0
0
2
2
0
2
0
0
0
0
0
0
4
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
2
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
2
2
0
0
0
3
0
0
0
2
0
1
1
0
0
1
0
2
1
0
0
0
0
0
0
1
0
2
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
1
0
1
0
0
2
0
0
0
0
1
2
0
0
2
0
0
3
0
0
0
3
0
0
2
0
0
0
1
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
2
1
1
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
1
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
2
2
3
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
1
0
0
0
3
0
0
0
2
0
0
1
2
0
0
0
0
0
2
3
0
0
1
2
0
2
1
1
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
2
1
1
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
1
1
0
1
0
2
2
0
0
0
2
0
0
2
0
2
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
1
0
0
0
1
2
0
2
0
1
2
0
0
0
1
1
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
0
5
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
3
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
3
3
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
1
3
2
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
1
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
1
2
0
2
0
2
1
0
1
2
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
1
0
0
0
1
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
1
2
0
0
2
1
0
0
1
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
2
2
1
0
1
0
0
1
2
0
0
1
0
2
0
0
0
2
6
0
2
0
0
0
2
2
0
0
1
0
1
0
0
2
2
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
1
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
2
1
0
0
1
2
1
1
0
0
0
2
0
0
0
0
0
0
1
0
2
0
2
2
1
2
0
3
0
0
2
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
1
1
0
0
1
3
0
0
0
1
1
2
2
4
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
4
0
0
0
2
0
0
1
0
0
0
2
0
0
1
1
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
2
1
0
0
0
0
0
2
2
0
0
0
2
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
2
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
1
0
0
2
0
1
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
5
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
6
0
3
0
3
0
0
0
0
2
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
3
0
0
0
0
0
1
2
0
2
2
1
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
3
0
1
1
0
1
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
1
1
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
2
1
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
2
2
0
0
0
2
0
0
2
0
0
0
1
0
1
0
1
0
0
0
2
0
0
2
0
0
0
0
2
1
0
0
0
0
2
0
0
1
0
1
2
0
0
0
1
1
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
4
0
0
1
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
1
2
0
2
2
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
2
0
0
0
0
0
0
1
0
0
8
0
0
1
0
0
0
7
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
2
0
2
0
2
0
1
0
0
2
2
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
4
0
0
1
0
0
2
0
0
1
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
2
0
0
0
0
0
0
0
3
0
1
0
0
1
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
3
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
7
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
3
0
2
0
1
0
0
1
3
0
1
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
4
0
0
0
0
0
0
0
0
1
2
1
1
0
2
0
0
0
0
0
0
0
1
3
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
1
2
0
0
0
0
0
0
1
1
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
2
1
2
0
0
1
0
0
0
0
0
0
4
1
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
2
1
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
2
1
0
0
0
0
1
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
1
2
0
3
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
4
3
0
0
0
2
0
0
0
0
1
0
3
2
1
0
0
0
0
1
0
0
2
4
0
0
1
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
4
1
1
0
3
0
0
0
0
0
3
0
0
0
0
0
2
0
0
2
2
0
0
1
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
1
0
2
0
1
0
0
0
0
3
0
2
0
0
5
1
2
3
0
2
0
0
0
1
0
2
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
1
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
5
5
2
3
2
0
2
0
0
0
0
0
0
1
1
2
1
0
0
1
2
0
0
0
0
0
1
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
1
1
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
3
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
4
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
1
0
3
0
1
1
0
0
12
0
1
0
0
0
0
0
2
2
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
2
1
0
0
0
0
0
3
3
0
0
0
0
3
0
0
0
2
2
1
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
3
0
1
0
0
0
3
2
1
1
2
0
0
1
0
0
2
0
2
1
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
2
0
2
1
0
0
0
0
8
0
0
0
0
2
2
0
2
2
0
0
0
0
0
0
0
0
0
2
1
2
0
0
2
0
2
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
2
2
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
2
1
0
0
0
2
2
0
0
0
0
0
0
1
0
0
3
0
0
0
1
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
4
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
2
1
0
0
1
0
0
0
0
0
2
0
0
0
1
0
3
2
1
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
2
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
2
0
1
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
5
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
4
0
0
0
1
0
0
1
1
0
1
0
0
0
2
2
2
0
0
0
0
1
0
1
0
2
0
0
1
0
3
0
0
0
0
0
0
0
1
0
2
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
2
1
0
1
0
2
0
2
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
2
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
3
0
0
0
0
4
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
2
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
2
1
1
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
2
0
1
0
0
0
3
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
2
7
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
1
0
0
0
0
0
2
0
2
0
0
2
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
1
0
0
4
0
1
0
2
1
0
0
0
0
0
0
0
0
2
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
3
0
0
1
0
1
0
0
0
3
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
3
1
1
0
0
0
0
2
0
0
1
0
6
0
0
0
2
0
0
2
0
3
0
0
0
0
2
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
2
0
0
0
1
2
0
0
0
0
2
0
2
2
0
0
0
0
1
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
4
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
2
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
1
0
1
0
4
0
0
3
0
0
0
1
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
2
1
0
0
0
0
0
0
3
2
3
3
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
3
0
2
0
0
0
0
1
0
0
0
0
1
0
0
4
0
0
0
2
0
0
3
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
2
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
4
2
0
0
1
0
0
1
0
0
0
0
0
5
0
0
0
0
1
0
2
0
3
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
1
0
3
1
2
0
0
0
0
3
2
0
0
0
0
1
2
2
1
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
3
0
0
0
0
3
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
2
2
0
1
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
2
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
2
1
0
1
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
2
4
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
4
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
6
2
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
3
0
0
0
0
1
0
0
1
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
5
0
1
0
0
0
2
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
5
1
0
1
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
7
0
3
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
2
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
2
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
3
0
1
0
0
0
0
0
0
2
0
0
3
0
2
0
1
0
0
1
0
0
0
0
1
2
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
1
0
0
5
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
5
2
0
0
0
0
0
0
0
0
1
0
2
2
2
0
0
0
0
0
2
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
2
2
0
1
0
2
0
0
0
0
2
2
1
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
1
0
1
0
1
2
0
0
0
0
0
0
0
1
0
0
1
2
0
1
0
2
1
0
0
1
2
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
1
0
0
0
0
0
2
0
0
0
0
0
2
0
2
3
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
2
2
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
2
2
0
0
0
2
0
2
1
0
2
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
2
0
1
0
0
0
5
0
0
0
0
0
0
2
3
0
0
0
0
1
4
0
2
2
0
0
0
0
0
0
0
0
0
0
1
4
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
5
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
6
0
0
5
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
4
0
0
2
2
0
2
0
0
3
2
0
0
0
0
0
0
0
3
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
1
3
2
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
2
2
2
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
6
0
0
1
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
2
0
0
0
1
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
3
1
2
0
0
0
0
1
0
0
0
0
0
0
1
4
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
2
1
0
0
0
0
0
0
2
0
2
1
0
0
1
0
0
0
1
0
0
0
0
0
9
0
0
0
0
2
0
1
0
2
2
2
2
7
0
2
0
0
2
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
2
5
0
0
0
1
0
0
0
0
1
0
2
0
0
0
2
0
0
2
0
1
1
0
0
1
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
1
1
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
2
0
0
0
1
0
3
0
2
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
3
2
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
2
1
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
5
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
2
0
0
1
1
0
0
2
0
0
0
2
0
0
1
2
0
0
1
2
0
0
0
0
1
0
0
0
0
0
3
0
0
4
0
0
5
1
0
0
0
1
2
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
1
0
2
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
1
2
0
0
2
5
0
0
1
1
0
4
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
2
0
0
2
0
0
0
0
0
0
5
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
2
2
0
0
2
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
2
0
0
4
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
1
2
0
0
1
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
4
0
0
0
0
0
2
0
5
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
3
0
0
0
1
0
0
3
2
0
0
0
0
0
0
0
0
0
0
1
1
2
2
0
1
0
0
3
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
7
2
0
2
1
0
1
0
0
1
0
0
0
0
2
0
0
1
0
2
0
1
0
0
0
1
0
1
0
0
2
2
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
1
0
0
2
0
10
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
3
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
2
0
3
0
2
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
1
2
0
0
0
2
0
0
0
3
1
0
3
0
0
0
0
2
1
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
1
0
2
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
9
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
4
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
5
0
0
0
0
0
0
0
0
0
0
2
1
0
1
1
0
1
0
0
3
0
0
2
0
0
1
0
0
0
0
5
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
4
1
0
0
0
2
0
3
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
5
0
2
1
0
0
2
0
1
0
7
0
2
2
0
0
2
0
0
0
0
0
0
4
2
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
2
0
0
2
0
1
0
0
0
1
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
3
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
4
0
2
2
0
0
4
0
0
2
0
0
0
1
2
0
2
0
0
0
1
1
0
0
1
1
1
0
0
1
0
0
0
2
1
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
2
0
0
0
2
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
2
0
0
5
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
4
0
0
3
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
1
0
0
2
0
0
0
0
1
0
2
0
1
0
0
0
2
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
1
2
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
3
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
2
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
3
0
0
0
0
3
0
0
0
0
0
2
0
0
1
0
2
0
2
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
3
0
0
2
2
0
0
0
0
3
0
1
0
0
0
1
0
1
1
0
0
0
2
1
0
0
0
0
0
3
0
0
2
0
0
0
2
0
0
3
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
2
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
1
0
0
1
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
1
0
1
0
0
3
0
0
3
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
4
0
2
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
2
2
0
2
0
0
0
1
3
0
3
6
2
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
2
1
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
3
0
1
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
1
3
1
0
0
2
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
1
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
1
0
0
1
2
1
0
0
0
1
0
5
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
3
0
0
1
1
0
0
0
1
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
2
2
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
2
2
0
0
0
2
1
2
1
0
1
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
5
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
2
2
0
0
0
3
0
0
1
0
2
1
0
0
4
0
0
0
0
1
0
2
0
0
1
2
0
0
0
0
0
0
0
3
0
3
0
0
0
0
1
0
0
1
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
1
2
0
2
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
3
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
1
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
2
1
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
2
0
2
0
2
0
0
0
0
0
0
3
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
1
1
2
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
1
2
3
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
3
0
0
6
2
0
0
1
1
2
0
0
0
2
2
0
1
0
0
0
0
1
3
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
1
0
0
0
0
0
2
0
0
1
1
0
0
0
1
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
1
1
0
1
1
0
0
0
0
1
2
1
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
3
4
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
1
0
1
0
0
0
5
0
0
2
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
7
0
2
2
0
2
0
2
0
2
0
1
1
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
1
0
2
0
0
0
0
0
0
1
1
1
0
0
0
2
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
2
0
0
2
2
0
0
2
0
1
0
0
3
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
3
0
0
0
0
1
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
3
0
0
0
0
2
0
0
0
2
0
0
2
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
2
0
2
0
0
0
0
1
0
1
1
0
1
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
3
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
2
3
0
1
0
0
2
0
1
0
0
4
0
0
0
2
0
0
0
1
2
1
2
1
0
0
0
0
0
1
0
1
0
0
0
2
3
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
2
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
4
0
0
1
0
0
0
2
0
0
0
0
3
1
1
0
0
0
2
0
0
1
2
0
0
0
0
0
1
2
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
3
1
2
1
1
0
0
0
0
0
0
0
0
1
1
5
0
1
0
0
2
1
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
2
0
0
0
2
0
0
0
2
2
0
0
0
0
0
1
3
0
1
0
0
0
0
0
0
13
0
1
0
0
1
1
0
0
0
0
1
0
0
1
2
1
0
0
0
1
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
5
0
4
0
0
0
0
1
0
0
0
2
0
2
0
1
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
15
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
2
0
1
0
0
0
2
0
0
1
0
12
0
2
0
0
0
1
0
0
0
5
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
2
0
3
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
2
4
0
0
0
4
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
2
3
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
2
0
1
0
2
0
1
0
0
4
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
1
0
2
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
5
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
5
0
0
0
0
0
0
1
0
0
0
1
2
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
4
0
0
0
1
0
1
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
2
1
0
0
1
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
1
1
0
0
0
0
0
0
2
0
1
0
0
0
1
0
2
6
0
0
3
0
0
0
1
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
1
2
0
2
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
3
0
1
0
0
2
0
1
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
7
0
0
0
0
1
0
0
2
0
1
0
3
1
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
3
1
0
1
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
4
0
0
2
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
2
0
2
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
2
0
3
2
3
1
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
3
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
2
2
4
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
2
0
2
0
6
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
4
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
4
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
1
0
0
0
0
1
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
2
0
1
0
0
5
0
0
0
1
0
0
0
0
0
1
1
2
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
2
0
0
2
0
0
0
0
1
0
0
0
0
1
0
2
0
0
3
0
0
0
0
4
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
1
0
0
0
1
1
1
0
0
2
0
0
0
1
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
4
0
0
2
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
1
1
3
0
2
2
0
0
0
2
1
0
2
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
3
0
1
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
3
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
5
1
0
0
0
0
6
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
2
0
1
0
0
0
0
0
0
0
3
0
0
0
1
3
2
1
0
0
1
0
0
2
0
2
0
0
0
0
4
2
1
4
0
1
0
0
0
0
0
1
1
0
0
0
2
2
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
2
2
1
0
2
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
2
0
2
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
3
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
1
0
1
5
0
0
7
0
3
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
1
1
1
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
1
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
4
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
4
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
1
1
2
0
1
2
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
2
0
0
0
0
0
0
3
2
1
2
0
1
1
0
0
1
0
3
0
0
0
0
0
0
1
0
6
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
1
0
1
0
0
0
0
1
5
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
3
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
3
0
0
0
2
0
0
0
1
1
0
1
0
2
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
1
0
0
0
6
0
1
0
0
0
0
2
2
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
4
0
0
1
1
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
1
0
0
2
1
0
0
0
1
2
0
1
0
1
0
0
0
0
1
0
0
0
1
3
0
0
0
0
0
0
2
1
1
0
2
1
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
1
0
0
0
0
2
0
1
2
0
0
0
1
1
0
1
0
0
1
0
0
0
0
3
0
0
0
0
0
2
0
0
2
1
0
1
0
0
2
0
0
1
1
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
1
1
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
6
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
7
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
2
0
0
0
0
1
0
1
0
0
2
0
0
2
1
0
0
0
0
0
0
5
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
1
0
1
0
2
0
0
0
0
0
4
0
1
1
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
3
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
1
0
0
0
0
1
1
1
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
2
0
0
1
2
0
0
2
0
0
0
0
1
0
0
0
1
3
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
1
0
4
1
1
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
2
2
0
0
0
1
3
0
0
0
0
0
0
0
0
11
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
5
1
0
0
2
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
2
2
0
0
1
0
0
0
0
2
0
0
0
0
1
2
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
3
0
0
0
0
0
0
0
8
0
1
0
0
2
0
0
3
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
3
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
6
0
0
0
0
0
2
0
1
0
2
0
2
1
0
0
0
0
0
2
0
0
1
0
2
0
2
1
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
5
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
1
0
0
0
0
0
1
2
0
2
0
0
1
0
2
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
4
2
6
0
0
4
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
2
0
1
0
1
1
1
0
2
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
3
2
0
0
1
0
3
2
0
3
0
1
2
0
2
1
0
0
1
1
0
0
2
1
0
0
0
1
2
0
1
0
0
2
3
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
4
1
1
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
3
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
2
0
0
0
2
0
0
0
0
0
1
0
0
1
2
0
1
0
0
0
2
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
2
0
1
0
0
0
0
0
2
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
3
1
0
0
0
2
2
0
1
0
0
0
0
0
0
0
4
0
2
0
0
2
0
2
0
0
0
0
0
3
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
2
1
0
1
2
0
0
0
1
1
0
1
0
0
0
0
0
0
2
2
0
2
0
0
1
0
2
0
0
2
1
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
1
2
3
1
0
0
0
4
2
0
0
0
2
0
1
0
6
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
1
0
2
0
0
2
2
0
0
0
4
0
0
0
0
0
0
2
0
0
0
1
0
0
2
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
2
0
0
0
2
0
2
4
0
0
0
0
3
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
4
0
0
1
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
1
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
2
3
0
0
2
1
1
0
0
1
2
0
1
0
2
1
0
0
0
2
2
0
0
0
0
2
0
0
1
0
2
2
0
0
2
1
0
0
0
1
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
1
0
0
2
2
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
1
0
3
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
2
0
0
0
0
1
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
4
0
2
0
0
1
0
1
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
2
3
1
2
0
1
0
0
0
1
0
0
0
1
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
2
0
0
1
1
0
1
0
0
2
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
1
2
0
4
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
1
0
0
4
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
2
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
2
0
0
2
0
0
3
2
1
0
1
3
0
0
0
0
0
0
1
0
0
8
0
0
0
0
0
0
3
2
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
1
0
1
0
0
0
1
0
3
0
0
5
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
5
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
4
2
0
0
1
0
0
2
0
0
0
1
1
0
0
0
2
0
0
3
1
0
2
1
2
1
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
2
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
1
0
0
2
0
1
0
0
2
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
2
2
2
0
0
0
0
2
0
0
0
1
10
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
1
0
0
1
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
3
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
1
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
1
1
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
2
1
0
0
0
0
0
2
0
0
3
0
0
2
0
3
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
6
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
5
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
1
5
0
0
1
0
0
0
0
0
0
1
0
1
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
3
0
1
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
3
0
1
1
0
0
0
0
5
0
0
0
1
0
2
0
2
3
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
2
2
0
0
0
0
0
1
0
0
2
2
0
0
0
0
2
2
0
0
1
0
0
1
3
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
2
0
1
0
0
0
1
3
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
9
0
0
2
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
3
0
0
0
0
4
0
0
0
1
0
0
1
0
0
0
0
0
2
3
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
1
1
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
1
0
1
0
2
0
1
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
1
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
3
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
2
0
0
0
0
0
2
0
0
0
0
1
1
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
11
0
0
0
0
0
0
0
3
0
0
2
0
0
0
2
0
0
2
4
0
0
0
0
0
0
0
0
1
0
0
1
0
3
2
0
2
2
0
0
0
0
0
0
0
1
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
1
1
0
0
10
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
1
0
2
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
2
0
0
0
1
0
0
0
1
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
3
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
2
2
1
1
0
0
1
0
0
0
0
1
0
0
0
0
1
2
0
0
1
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
1
0
1
2
0
2
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
9
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
1
1
0
0
0
1
0
0
0
0
0
0
3
4
0
0
1
0
0
0
1
0
0
0
0
1
0
1
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
1
0
1
0
0
2
0
0
0
1
0
0
2
0
1
0
1
2
0
0
0
0
0
3
0
2
0
2
0
1
0
0
0
0
2
0
1
0
0
0
2
0
5
0
0
0
0
0
1
0
3
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
2
1
0
0
1
0
0
3
0
0
1
0
0
0
0
0
2
2
0
0
0
4
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
1
0
0
1
0
0
0
2
0
0
0
0
2
0
0
1
0
0
2
1
1
2
0
0
3
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
1
2
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
3
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
2
0
2
0
2
0
3
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
2
2
1
0
0
0
0
3
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
2
2
0
0
4
0
0
0
0
3
0
2
0
0
0
1
0
1
0
0
0
2
2
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
2
0
0
0
1
1
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
3
4
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
3
0
1
2
2
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
1
2
0
0
1
1
1
0
0
1
1
0
0
0
7
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
5
1
0
0
0
0
0
0
1
0
0
1
1
4
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
1
0
2
1
1
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
8
0
2
0
3
0
1
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
2
0
1
2
1
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
5
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
2
0
1
0
0
0
0
2
0
2
0
1
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
1
0
1
2
0
0
0
2
0
0
0
2
0
0
0
0
2
0
1
1
0
0
0
2
1
0
0
0
0
0
1
1
1
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
4
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
1
1
2
1
0
0
0
0
0
0
0
2
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
7
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
7
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
3
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
1
0
1
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
4
2
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
2
0
1
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
1
1
1
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
1
0
1
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
2
1
0
2
0
0
0
0
6
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
3
0
0
2
2
0
0
0
0
2
0
5
0
1
0
0
4
0
0
1
0
2
0
1
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
1
0
2
0
0
0
0
0
0
4
1
0
1
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
3
0
2
0
0
1
0
2
1
0
2
0
1
1
1
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
1
2
1
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
4
1
0
0
2
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
6
0
0
0
0
0
0
0
0
0
1
5
0
2
0
0
0
0
2
0
0
0
2
1
1
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
4
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
20
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
1
2
2
0
1
6
0
0
0
0
1
3
3
1
0
1
0
2
0
1
0
0
0
0
0
0
0
0
8
0
3
3
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
3
0
0
1
0
2
0
0
1
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
5
0
1
0
1
3
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
4
0
0
0
1
0
0
1
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
7
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
6
0
0
1
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
5
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
2
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
2
1
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
3
0
0
0
0
0
0
2
0
0
3
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
2
0
1
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
2
0
3
0
1
0
0
1
0
0
0
0
0
5
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
1
0
1
2
0
4
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
3
0
0
0
2
0
0
0
2
0
1
0
1
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
3
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
2
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
4
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
3
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
1
0
0
0
0
0
0
2
0
1
1
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
3
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
2
0
2
1
0
0
1
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
3
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
6
0
0
0
0
0
2
2
0
2
0
0
0
2
1
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
7
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
2
1
0
4
3
0
0
0
0
0
0
4
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
3
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
2
1
0
1
0
0
0
1
0
1
0
0
0
0
3
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
1
0
3
2
2
2
0
0
0
0
2
0
0
0
0
0
0
0
5
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
2
0
0
1
0
2
2
5
0
0
0
0
1
2
0
0
2
2
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
2
0
0
1
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
2
0
0
2
0
1
0
0
0
0
3
2
0
0
0
1
1
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
1
0
0
0
0
2
0
3
0
1
1
0
0
0
0
0
1
0
1
2
0
0
1
0
0
2
0
0
0
0
0
0
4
1
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
3
0
0
2
0
2
0
2
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
2
0
2
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
2
1
0
0
1
0
0
0
2
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
3
0
0
0
1
1
0
2
0
0
0
0
0
0
0
2
0
0
6
0
0
0
0
0
1
0
0
1
0
2
3
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
2
1
2
1
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
2
1
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
5
5
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
5
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
2
2
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
2
0
0
0
0
0
1
2
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
1
2
1
2
0
0
0
1
0
0
0
0
2
0
0
3
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
2
2
0
0
0
0
0
0
3
0
0
1
0
1
2
1
0
0
0
0
0
0
0
0
14
0
1
1
0
0
0
0
2
0
0
1
2
2
1
3
0
0
2
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
1
1
0
0
1
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
2
2
0
0
0
4
0
1
0
0
0
2
0
3
0
1
1
0
0
0
1
0
2
0
1
0
1
0
0
1
0
1
1
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
3
0
0
3
18
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
5
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
3
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
2
0
0
0
1
3
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
2
1
0
1
0
1
0
1
0
0
0
7
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
2
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
1
1
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
3
2
0
2
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
5
0
0
1
0
0
0
2
0
0
2
2
2
4
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
2
0
0
0
0
0
1
0
1
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
1
3
0
0
0
0
1
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
3
2
0
0
1
0
1
0
0
1
2
0
1
0
0
2
0
0
0
0
0
0
0
4
2
1
0
0
0
0
0
0
0
2
0
0
0
1
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
3
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
4
0
0
0
3
1
0
0
1
2
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
1
1
0
2
0
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
3
1
0
0
2
1
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
4
0
0
0
2
1
0
0
2
0
1
1
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
1
0
0
0
2
2
5
0
1
0
0
0
0
0
0
0
1
0
0
0
2
2
1
2
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
3
0
0
0
0
0
1
1
0
0
5
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
1
2
0
0
0
0
1
2
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
0
4
0
0
2
0
0
0
2
0
1
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
7
0
0
0
0
2
5
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
3
2
0
0
0
0
0
3
0
2
2
2
1
0
0
0
0
0
3
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
3
2
0
1
0
0
0
0
2
2
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
14
0
1
0
0
0
1
0
2
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
1
0
3
1
0
1
0
0
0
0
0
0
2
0
1
2
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
4
0
0
0
0
0
3
0
0
2
2
0
0
2
2
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
1
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
2
1
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
3
0
0
2
0
0
0
2
0
3
1
1
0
0
0
2
0
0
0
0
0
0
0
0
2
2
1
0
0
2
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
2
0
0
1
0
0
0
0
1
0
1
2
0
2
0
0
4
0
0
0
2
1
0
0
0
0
0
2
3
0
2
2
0
0
0
0
0
0
0
0
0
3
5
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
1
1
0
0
2
0
0
2
0
0
0
1
0
0
0
2
0
2
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
1
2
2
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
1
1
0
0
2
0
0
0
0
0
2
0
0
2
0
0
1
1
1
1
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
10
0
0
0
0
0
0
1
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
6
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
2
2
0
1
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
1
0
1
0
0
0
0
2
2
2
0
0
0
0
1
0
1
0
0
0
0
0
3
0
0
5
0
0
0
0
0
1
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
3
0
0
2
0
2
2
0
0
5
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
1
0
0
0
0
3
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
1
1
0
0
0
1
0
2
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
4
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
3
3
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
2
0
0
0
0
0
0
0
3
0
3
0
0
0
2
1
0
0
1
0
0
0
2
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
2
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
2
2
0
3
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
3
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
3
1
0
1
0
0
1
0
0
0
0
1
0
1
0
1
4
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
2
0
0
1
0
0
0
1
0
0
0
2
3
1
0
3
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
2
0
0
2
2
2
0
2
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
1
2
0
0
1
0
0
1
0
2
1
0
0
0
1
0
0
1
0
1
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
2
1
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
1
3
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
2
2
0
3
1
0
1
0
0
5
0
0
0
2
1
0
0
0
1
0
2
0
0
0
2
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
2
0
2
1
0
0
0
0
0
0
2
0
0
1
0
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
3
1
0
0
2
1
0
1
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
1
0
0
0
2
0
0
1
0
5
0
1
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
2
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
3
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
2
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
1
1
0
0
2
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
2
0
1
0
5
0
0
0
2
0
1
0
0
1
1
0
0
0
0
2
2
0
0
0
2
0
0
1
0
2
0
1
2
0
0
0
0
0
2
0
0
0
1
2
0
2
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
1
2
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
1
3
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
1
0
0
2
1
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
1
0
0
0
1
0
0
0
0
2
3
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
2
0
6
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
1
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
2
4
0
0
0
0
0
0
2
0
1
0
0
0
3
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
1
2
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
3
1
0
0
3
2
0
2
1
0
0
0
0
0
0
1
0
0
1
0
0
6
0
0
0
0
0
0
2
0
0
2
0
1
1
0
0
0
2
0
0
0
1
2
0
1
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
1
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
6
0
2
0
1
0
0
0
0
1
2
0
0
2
0
0
0
1
0
0
1
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
3
0
1
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
1
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
3
1
0
0
1
0
0
1
0
0
0
0
1
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
3
1
0
0
3
0
0
2
3
0
2
0
0
0
0
3
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
2
1
2
2
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
2
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
2
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
1
1
0
0
0
0
0
0
0
4
2
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
7
0
2
0
0
0
0
0
1
0
2
0
0
0
2
1
3
2
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
4
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
1
0
2
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
2
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
4
2
0
0
0
0
1
5
0
1
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
5
0
0
1
2
0
1
0
0
0
3
0
1
1
0
2
0
0
2
0
0
2
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
1
0
0
1
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
3
0
1
0
1
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
2
3
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
1
0
1
1
0
3
1
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
1
1
0
0
0
1
2
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
5
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
2
0
1
0
0
0
0
2
2
0
1
0
4
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
4
0
1
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
2
2
0
0
0
3
0
0
0
2
0
0
2
0
0
0
0
0
3
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
3
1
0
0
0
0
0
2
0
0
10
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
3
0
0
0
1
0
0
0
0
1
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
1
2
0
1
0
0
0
0
1
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
3
2
0
0
0
1
2
0
1
2
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
4
1
0
2
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
1
0
1
0
0
2
0
2
0
0
0
0
1
0
1
0
2
0
3
0
0
0
4
2
0
0
0
0
2
0
0
0
2
2
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
2
1
1
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
5
0
0
2
0
0
2
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
2
2
0
0
0
0
0
2
0
0
1
0
2
3
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
2
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
4
0
1
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
2
0
2
2
0
1
0
0
1
1
0
1
0
0
3
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
1
1
0
1
0
1
0
0
0
0
0
1
2
2
0
2
0
1
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
2
0
1
3
2
2
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
3
0
0
0
0
0
0
1
2
0
0
0
1
0
0
2
1
0
1
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
1
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
2
0
0
0
2
1
1
1
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
2
0
2
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
2
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
1
0
0
0
1
0
2
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
2
2
1
0
0
0
0
1
2
0
3
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
9
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
1
0
2
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
1
0
3
0
0
0
0
2
0
1
0
3
0
0
0
1
0
0
0
1
0
1
0
0
2
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
3
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
3
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
1
2
0
0
0
0
0
0
1
1
1
2
2
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
2
0
1
0
0
0
1
0
0
0
5
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
1
0
0
0
3
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
11
2
0
0
0
2
0
0
0
1
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
2
2
1
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
1
0
0
2
2
0
2
0
0
0
0
0
1
1
2
0
0
0
2
0
0
0
0
1
0
0
1
0
0
10
0
0
0
1
1
0
0
2
0
0
0
0
1
0
0
0
0
0
1
1
4
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
1
2
0
0
2
0
0
0
2
2
0
0
0
0
0
2
1
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
2
0
0
0
2
0
0
2
0
1
3
0
2
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
3
0
0
0
0
0
0
0
0
1
0
1
2
2
0
0
0
0
0
0
2
0
3
3
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
3
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
1
0
0
0
1
0
0
0
0
0
5
0
0
0
0
3
0
0
1
0
2
0
0
0
0
1
0
0
1
1
0
2
1
0
1
0
0
0
0
3
2
0
0
0
1
1
0
2
2
0
1
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
6
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
1
0
0
0
2
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
4
1
0
2
0
1
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
1
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
3
0
0
0
0
3
0
0
0
0
0
1
0
4
0
0
1
0
0
1
1
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
5
0
1
2
0
1
0
0
0
0
3
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
4
1
0
0
0
0
1
0
0
0
2
0
3
0
0
2
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
3
0
0
0
0
0
0
0
0
0
6
0
0
1
0
0
0
2
0
2
2
0
0
1
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
7
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
3
2
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
5
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
2
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
3
3
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
5
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
1
0
1
0
0
3
1
0
0
0
0
0
2
0
0
0
0
3
0
0
1
0
3
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
1
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
1
2
0
2
0
3
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
3
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
3
5
0
0
0
0
0
0
0
0
1
0
0
0
1
11
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
1
2
0
0
0
0
1
2
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
2
0
0
2
2
3
0
3
1
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
2
1
2
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
2
2
0
0
1
0
1
0
0
1
5
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
5
0
2
0
2
0
0
0
0
0
0
0
2
0
0
3
1
0
0
0
0
0
1
0
0
1
2
0
1
0
0
0
0
0
3
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
3
0
0
1
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
2
0
0
0
2
0
0
0
1
0
1
1
1
0
2
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
2
0
0
1
2
0
0
0
2
0
1
4
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
3
1
2
2
2
0
0
0
2
0
1
2
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
2
0
2
0
0
0
3
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
1
0
0
0
1
1
0
2
0
0
0
0
0
2
0
0
0
0
2
2
2
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
2
0
0
0
2
3
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
2
1
0
2
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
2
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
4
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
4
0
2
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
2
0
0
2
0
2
0
0
0
0
1
1
0
0
0
0
0
2
1
0
0
1
0
0
1
0
0
1
0
0
1
1
0
0
6
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
7
0
0
1
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
2
0
0
0
2
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
4
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
2
0
3
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
6
0
1
0
0
1
0
1
0
0
1
1
0
0
1
0
0
0
0
2
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
2
0
2
1
1
0
0
0
0
0
0
0
0
0
1
2
0
1
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
1
0
0
4
0
2
0
0
2
0
0
0
0
0
0
1
0
3
0
0
0
0
2
0
0
5
0
2
1
2
0
0
0
3
0
0
1
0
0
5
0
0
0
0
0
0
0
0
0
0
1
0
2
4
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
3
2
1
0
4
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
2
1
2
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
1
4
1
0
0
1
2
2
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
3
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
3
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
2
0
0
0
9
2
3
0
0
0
0
2
1
0
1
0
0
7
0
0
0
0
0
10
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
3
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
4
0
2
0
1
3
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
2
0
0
2
1
2
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
2
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
1
2
3
1
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
1
0
0
1
1
0
0
0
1
0
1
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
3
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
3
0
0
0
4
0
0
6
0
0
0
0
0
1
1
0
0
0
3
0
0
2
1
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
3
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
2
0
0
0
1
0
2
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
1
1
0
0
0
0
1
0
0
1
0
1
0
0
0
3
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
1
0
1
0
0
2
0
1
0
1
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
2
1
2
0
2
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
3
1
0
0
0
2
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
6
0
0
0
0
2
1
1
1
0
0
0
3
0
0
2
0
1
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
1
2
0
2
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
3
0
1
0
0
1
0
0
2
0
2
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
3
0
0
0
1
0
2
0
0
0
0
0
0
1
0
1
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
3
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
2
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
2
0
0
2
0
0
1
0
0
1
0
0
10
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
2
0
0
0
2
0
2
0
0
0
0
2
1
3
3
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
3
5
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
8
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
2
0
0
1
2
0
0
0
0
1
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
5
0
1
0
0
0
2
0
0
0
0
2
0
3
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
3
0
0
0
0
0
0
0
0
2
0
0
4
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
1
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
1
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
4
0
0
0
3
0
0
2
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
3
0
0
0
0
0
0
0
2
1
0
1
0
0
1
0
2
0
0
0
2
0
6
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
2
0
2
1
0
2
0
0
1
1
1
1
0
0
0
0
0
0
2
0
0
0
2
2
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
1
0
0
1
0
1
4
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
1
0
0
0
2
7
0
0
2
0
0
0
0
0
1
1
4
0
0
0
0
0
0
2
0
2
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
2
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
4
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
3
1
0
3
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
2
0
1
3
0
0
0
0
1
2
0
3
0
0
0
3
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
2
2
0
0
0
0
1
0
0
3
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
6
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
3
1
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
3
2
1
2
1
1
2
1
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
3
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
2
0
2
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
1
0
0
2
0
2
0
3
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
1
0
4
0
0
1
0
0
0
1
0
0
0
0
0
3
0
3
0
2
0
0
0
0
0
0
0
0
0
1
2
0
3
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
1
0
2
2
1
2
1
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
1
2
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
3
4
0
1
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
1
0
0
0
1
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
1
0
1
1
0
0
0
0
0
0
0
1
0
0
2
9
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
2
0
0
0
0
2
0
0
1
3
2
0
1
0
0
2
2
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
2
0
0
2
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
4
0
2
0
0
0
3
0
2
1
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
4
2
0
2
0
2
0
0
1
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
1
0
0
0
0
2
0
0
5
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
2
2
0
0
3
2
2
0
0
1
0
0
0
2
2
2
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
1
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
2
2
0
1
0
0
0
0
2
0
1
0
0
0
0
2
0
1
2
2
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
5
0
0
3
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
2
0
0
0
1
0
2
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
1
0
3
2
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
1
0
1
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
7
1
0
0
2
0
0
0
0
1
0
2
0
0
2
0
0
1
0
1
0
0
0
0
1
1
2
1
0
0
1
1
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
5
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
3
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
1
5
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
3
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
2
0
2
0
0
0
0
2
0
0
0
3
0
0
2
0
0
0
0
0
0
2
2
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
1
0
0
6
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
5
3
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
3
0
2
1
0
0
2
0
1
0
0
0
0
3
0
1
0
1
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
1
1
0
2
1
2
0
0
0
0
0
2
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
1
3
2
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
4
0
0
2
0
0
1
0
0
0
0
2
2
0
1
0
2
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
3
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
2
0
1
0
1
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
1
0
0
0
0
2
0
0
2
2
0
1
0
0
0
1
0
1
0
1
0
0
2
3
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
1
0
0
3
0
4
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
4
1
2
2
0
0
2
0
1
2
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
3
0
0
0
0
0
0
2
1
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
2
1
0
0
1
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
7
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
1
1
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
2
0
1
0
0
2
2
0
2
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
1
2
1
0
0
2
2
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
2
1
0
2
0
2
0
0
1
0
0
1
0
2
2
2
4
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
6
0
0
0
0
1
0
0
0
0
1
0
0
1
2
0
0
1
0
1
0
0
0
0
0
2
3
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
1
1
0
0
1
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
2
0
0
2
0
0
0
1
0
0
2
2
0
0
0
1
0
2
1
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
1
1
0
4
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
2
1
0
0
2
2
0
0
3
0
0
0
4
0
1
0
0
0
0
1
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
2
0
0
0
2
0
1
0
0
0
0
1
2
0
2
0
1
0
0
0
0
1
1
1
0
0
2
0
1
0
1
0
0
0
4
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
1
2
0
1
0
0
0
0
0
0
2
1
0
2
0
1
1
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
3
0
0
0
1
0
1
3
1
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
6
0
0
2
0
0
3
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
1
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
2
0
1
4
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
1
0
0
2
0
0
0
0
0
0
1
1
1
0
0
0
0
3
2
2
0
2
0
0
1
0
0
0
0
1
1
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
3
3
0
2
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
3
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
4
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
2
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
1
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
3
2
0
0
0
0
2
7
0
1
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
2
0
1
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
1
2
0
2
0
0
1
0
0
1
0
0
1
0
0
0
2
2
3
0
0
0
0
0
0
0
2
0
2
4
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
2
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
4
0
1
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
1
0
1
0
0
2
0
2
0
0
0
0
0
2
0
0
0
1
0
2
0
0
1
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
2
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
1
0
0
0
0
1
0
0
0
0
0
1
0
3
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
2
0
0
0
0
1
1
1
0
1
0
0
0
0
0
2
0
0
0
0
0
5
1
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
3
2
1
0
1
0
2
2
0
0
2
2
0
0
2
0
0
0
0
1
0
1
0
0
0
3
0
0
1
2
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
2
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
1
1
2
1
0
0
1
2
0
0
0
3
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
2
0
2
0
0
3
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
5
0
0
2
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
3
2
2
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
1
2
0
0
1
0
0
1
0
1
2
0
0
2
1
0
0
0
0
1
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
3
0
2
1
2
0
0
0
0
0
0
0
0
0
9
0
0
1
0
0
1
0
2
0
2
0
0
0
0
0
0
0
2
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
9
0
0
6
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
2
0
0
2
0
1
0
0
0
1
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
3
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
2
0
2
0
2
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
2
0
0
3
0
0
2
0
0
0
1
1
0
0
0
1
0
0
0
1
2
0
1
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
2
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
1
0
2
0
0
0
0
1
0
0
2
0
1
0
2
0
1
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
1
0
0
1
0
0
0
0
3
0
0
2
2
2
0
0
0
1
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
2
0
0
5
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
1
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
1
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
1
0
0
3
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
1
1
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
2
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
3
0
0
4
2
0
0
0
2
0
0
0
6
0
0
0
2
0
0
0
0
0
0
0
0
0
2
3
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
2
2
2
0
0
0
0
2
1
0
0
0
2
0
0
2
0
2
0
0
0
1
3
0
0
0
1
0
0
0
4
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
1
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
3
2
2
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
2
4
0
0
2
0
2
0
0
0
0
1
0
0
1
2
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
1
1
0
0
0
1
3
1
0
0
1
1
0
0
3
1
0
0
0
0
0
0
0
0
0
0
2
2
1
2
2
0
0
0
2
1
1
0
3
2
0
0
0
1
0
0
0
0
0
0
2
1
1
0
0
1
0
0
0
0
0
0
0
1
0
1
3
2
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
1
3
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
1
0
2
4
0
0
0
0
0
0
0
0
0
0
2
3
1
2
0
1
2
0
2
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
3
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
4
0
0
7
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
5
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
3
0
2
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
2
1
0
2
2
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
1
3
1
0
0
1
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
1
0
0
2
2
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
1
1
4
5
2
0
4
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
2
0
1
0
0
0
1
1
0
0
0
2
0
0
3
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
2
0
1
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
3
0
0
0
2
0
0
1
0
0
0
2
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
2
2
0
1
1
0
0
0
2
0
0
1
0
2
0
0
1
2
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
2
1
2
0
0
0
0
0
0
0
0
4
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
3
1
1
0
0
2
3
0
0
0
7
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
2
0
1
0
0
0
0
3
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
2
2
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
1
0
0
2
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
3
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
3
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
3
0
0
0
1
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
1
0
0
2
0
0
0
0
1
2
0
0
1
0
0
0
0
1
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
1
2
0
0
0
1
0
2
0
3
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
2
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
6
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
1
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
2
0
0
0
2
0
4
1
0
0
0
0
1
0
0
0
2
2
0
0
2
0
0
1
1
0
0
0
2
0
0
2
0
0
1
2
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
3
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
5
0
2
0
0
1
2
3
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
2
0
0
0
0
0
1
0
0
0
0
2
1
0
0
1
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
3
1
0
2
2
0
0
1
2
1
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
2
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
3
1
0
0
0
1
1
0
1
1
0
2
1
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
2
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
1
3
4
0
0
0
0
0
2
0
1
1
2
0
1
0
0
1
2
0
3
1
1
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
1
1
2
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
3
0
1
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
9
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
4
4
0
0
2
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
1
0
0
0
3
2
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
4
1
1
1
2
0
0
0
0
2
0
0
2
0
0
0
0
2
0
3
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
5
0
1
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
2
3
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
1
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
5
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
2
0
0
0
1
0
0
0
6
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
1
0
0
1
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
2
0
0
1
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
6
1
0
0
0
1
0
0
1
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
6
0
0
0
1
0
0
0
0
0
0
2
3
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
1
0
0
0
0
3
1
0
0
1
4
0
1
0
0
3
0
1
0
2
2
0
0
0
0
0
0
0
3
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
3
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
7
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
3
0
1
2
0
0
0
0
0
1
0
0
0
1
1
0
2
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
2
0
3
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
5
0
1
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
3
0
1
0
0
0
2
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
1
2
0
0
0
4
0
0
1
0
0
1
1
0
0
2
0
0
0
0
0
1
0
1
0
0
0
2
0
0
3
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
4
0
2
0
0
0
1
0
0
0
0
1
0
0
1
2
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
1
0
2
0
0
0
0
3
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
5
1
1
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
1
0
0
0
0
3
2
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
3
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
1
1
1
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
2
1
0
0
0
0
1
0
2
1
0
2
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
1
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
2
1
0
2
0
0
0
3
0
3
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
1
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
7
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
2
0
3
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
1
0
2
2
0
2
0
0
1
0
0
0
2
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
1
1
0
0
1
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
9
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
2
0
0
1
0
0
0
0
0
1
1
0
0
0
0
2
4
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
4
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
1
2
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
3
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
1
0
2
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
3
0
0
0
0
0
0
2
2
0
1
1
0
2
0
0
1
0
0
1
0
0
2
0
2
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
2
0
2
1
0
0
0
1
0
2
0
1
2
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
3
3
0
1
0
0
2
0
0
1
1
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
1
3
0
0
1
0
3
1
2
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
2
0
0
1
0
0
0
1
6
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
1
0
0
0
1
2
2
0
1
0
0
2
0
2
0
1
0
0
1
0
0
0
2
0
0
0
3
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
3
0
2
5
0
0
0
1
0
0
0
0
0
0
2
0
1
2
0
2
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
2
0
1
1
1
0
0
0
2
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
1
0
0
0
1
0
0
2
0
0
0
1
2
0
0
0
2
0
0
0
0
0
1
1
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
3
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
1
2
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
2
0
1
1
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
4
0
2
0
0
2
0
4
1
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
2
1
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
1
2
1
2
0
0
0
2
1
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
1
0
0
0
0
1
0
3
3
0
0
0
2
0
2
0
0
0
0
0
1
0
0
8
0
0
1
0
0
1
0
0
0
0
4
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
6
1
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
1
2
0
1
1
0
4
0
0
0
0
1
1
1
0
0
0
0
0
1
9
0
1
1
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
2
4
0
0
0
2
0
1
0
1
0
2
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
3
0
0
0
0
0
2
1
0
0
0
0
0
0
1
3
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
2
0
0
1
2
0
0
0
0
0
1
2
0
1
0
0
2
1
1
0
2
0
0
0
4
1
11
0
1
0
0
0
1
1
0
1
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
1
0
1
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
3
2
0
0
0
2
0
1
1
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
4
1
2
1
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
1
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
1
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
2
0
1
0
2
1
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
1
1
0
0
2
0
0
0
0
0
0
0
3
1
0
1
0
0
0
1
0
1
1
1
2
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
1
0
1
0
0
0
1
0
0
0
0
1
3
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
2
1
0
0
0
0
0
0
5
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
2
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
3
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
2
1
0
0
0
0
2
0
2
0
0
1
7
0
1
0
0
1
0
0
1
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
1
0
0
0
0
0
2
0
0
1
1
0
0
1
2
0
0
0
1
1
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
2
0
2
0
0
0
0
0
3
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
1
2
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
5
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
3
0
0
0
0
0
1
0
2
0
1
0
0
0
1
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
4
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
2
0
0
0
0
1
0
0
0
2
0
0
1
4
0
0
0
0
0
0
0
0
0
1
3
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
3
1
0
0
0
0
0
2
3
0
1
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
3
0
0
1
2
0
0
2
1
0
0
2
0
0
0
0
0
0
3
0
0
0
1
0
4
0
0
0
0
2
0
1
2
0
0
2
2
0
0
0
0
1
0
0
0
7
0
0
3
0
0
0
0
0
0
0
3
0
1
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
3
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
2
2
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
3
2
0
1
1
0
0
0
2
2
1
0
0
2
0
0
1
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
2
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
2
0
0
1
0
2
2
0
0
1
0
0
0
1
2
0
1
0
0
1
0
0
0
2
0
0
0
2
0
0
2
0
2
0
9
0
0
2
0
0
0
0
0
0
2
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
1
0
1
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
3
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
4
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
5
0
6
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
1
0
2
3
0
0
0
0
1
0
0
2
0
0
2
1
0
2
0
0
0
1
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
4
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
3
0
3
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
2
0
0
0
0
1
0
1
1
2
0
0
0
1
0
1
0
0
0
0
1
1
2
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
1
1
1
0
1
4
0
0
0
0
1
7
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
1
0
2
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
1
1
4
1
0
2
2
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
5
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
5
1
2
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
3
2
0
0
0
0
0
0
3
2
1
1
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
1
1
1
1
0
1
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
1
2
4
0
0
1
0
2
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
2
0
1
0
0
1
0
0
1
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
4
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
3
0
1
1
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
3
0
0
3
0
0
0
0
0
0
1
2
0
0
0
0
0
3
0
0
0
0
0
0
0
2
1
0
0
0
5
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
2
1
0
0
0
0
0
2
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
7
0
2
0
0
0
0
0
0
3
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
2
0
0
0
0
0
7
0
0
0
0
1
1
1
0
0
3
0
1
2
1
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
2
0
0
0
1
3
0
0
0
0
0
2
0
3
0
0
3
0
0
0
0
4
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
4
2
0
0
1
1
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
1
0
0
0
0
3
0
1
1
0
0
1
1
0
2
0
2
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
2
0
0
0
1
0
1
0
1
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
2
0
2
1
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
3
0
3
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
6
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
3
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
2
2
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
1
0
0
0
0
2
0
0
2
3
0
1
2
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
2
0
3
0
0
0
0
0
0
2
0
0
0
1
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
5
0
0
4
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
1
0
4
0
0
0
0
0
0
1
1
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
2
8
0
0
6
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
1
2
1
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
2
0
2
0
0
0
0
3
1
0
0
1
2
2
0
1
0
3
1
0
2
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
1
1
0
0
0
0
0
2
2
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
3
2
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
1
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
3
0
0
0
1
0
1
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
2
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
4
0
2
1
2
0
0
0
2
0
0
0
0
3
0
2
0
0
0
0
1
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
1
0
0
0
1
1
0
0
1
0
0
2
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
1
0
1
0
0
1
0
0
1
0
0
0
3
0
0
0
0
2
0
0
2
0
0
0
2
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
3
0
0
0
0
0
4
0
2
0
2
0
0
0
2
0
0
2
0
0
2
2
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
5
0
0
0
2
0
0
0
2
0
0
7
0
0
0
0
0
0
0
0
0
0
1
2
1
2
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
2
0
2
0
1
3
0
1
1
0
0
0
2
2
0
0
0
1
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
3
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
2
1
0
2
0
0
0
0
0
0
0
0
2
1
1
0
0
1
1
3
0
0
1
1
1
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
10
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
3
0
0
0
0
2
0
1
1
0
3
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
5
0
0
0
0
0
0
0
0
2
2
0
1
2
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
3
0
0
0
0
0
2
0
2
1
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
3
0
0
0
0
0
1
0
0
0
0
1
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
3
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
2
0
7
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
3
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
2
2
0
0
3
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
2
0
1
0
1
0
2
0
0
0
0
0
2
3
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
4
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
2
2
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
2
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
2
0
1
0
0
1
0
0
0
2
0
0
1
4
0
0
2
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
5
0
0
0
0
0
0
0
0
1
2
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
3
0
1
0
0
2
0
0
0
0
0
1
0
9
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
2
4
0
3
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
2
0
0
0
0
0
1
1
0
1
0
0
0
0
0
2
0
2
2
1
6
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
5
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
3
0
0
0
2
2
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
6
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
3
1
2
2
2
0
0
0
0
1
1
0
0
2
0
0
2
0
0
1
0
0
2
0
0
0
0
11
0
0
0
1
0
0
0
0
3
0
0
1
0
3
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
3
0
0
2
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
2
1
0
0
0
0
2
0
1
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
1
1
0
5
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
1
0
0
3
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
1
1
1
3
0
0
2
0
1
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
3
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
4
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
3
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
2
3
0
0
1
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
3
0
1
0
0
1
3
0
0
1
0
0
2
0
0
0
4
0
0
0
2
2
0
0
0
1
0
0
0
0
2
2
0
0
3
0
0
0
0
0
0
1
2
1
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
6
2
0
0
0
0
0
0
1
2
0
0
1
1
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
1
0
0
2
6
9
0
0
1
0
0
0
2
0
0
0
0
0
2
0
2
0
2
3
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
2
2
1
0
0
0
0
0
0
0
0
2
4
3
0
0
1
0
1
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
1
2
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
1
0
1
0
2
3
0
0
0
2
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
1
0
1
0
2
0
0
0
0
0
0
0
0
2
0
2
0
1
0
1
0
0
0
0
2
0
0
0
1
0
0
2
0
0
1
0
3
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
1
3
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
2
1
2
0
0
1
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
2
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
1
0
1
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
2
0
3
0
1
3
0
0
0
1
0
1
0
0
1
0
3
0
0
0
0
0
2
0
0
2
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
1
1
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
2
0
4
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
1
1
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
1
1
0
1
0
0
0
1
1
0
0
0
2
2
0
2
0
0
0
0
1
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
1
2
4
0
0
0
0
4
2
0
5
0
0
0
0
2
0
0
0
0
1
0
0
0
1
1
0
0
0
2
1
1
0
0
0
2
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
1
1
0
0
2
0
0
5
0
0
0
2
0
0
1
0
4
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
1
1
2
0
1
2
0
0
0
2
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
5
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
3
0
0
2
3
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
5
0
2
0
1
0
0
0
0
2
0
0
0
0
0
3
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
3
0
0
0
0
0
3
0
2
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
1
0
2
0
0
0
2
1
0
0
0
2
0
2
0
0
0
0
1
2
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
8
3
2
2
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
1
2
2
0
0
0
0
0
1
0
0
0
1
2
0
0
2
0
0
0
2
1
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
7
0
2
3
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
1
0
0
2
0
0
0
2
0
0
0
0
5
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
1
0
0
0
1
1
1
1
0
1
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
3
0
0
0
0
2
3
0
0
2
0
0
0
0
1
0
2
0
2
0
0
0
2
0
0
0
2
0
2
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
1
0
1
1
0
4
1
0
2
0
3
0
1
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
1
0
2
0
0
2
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
2
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
2
0
5
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
3
2
0
1
0
0
0
0
0
0
0
2
1
0
0
2
0
0
1
0
0
1
0
2
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
1
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
8
0
2
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
1
1
0
0
3
1
0
0
0
3
1
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
1
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
2
1
0
2
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
3
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
1
0
1
0
0
2
0
0
0
2
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
1
0
0
0
2
7
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
2
2
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
1
1
0
0
0
1
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
5
0
0
0
0
1
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
5
0
0
1
0
0
0
0
0
3
0
0
1
0
0
0
0
2
2
0
2
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
2
0
0
0
0
0
0
0
2
0
1
1
0
1
0
0
0
0
0
0
2
0
0
0
2
3
0
1
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
3
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
3
3
1
0
2
1
2
0
0
1
0
0
2
3
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
2
1
0
0
1
0
0
0
3
0
0
1
0
0
0
0
1
0
1
1
2
0
0
0
0
0
2
0
0
0
2
0
1
1
2
0
0
0
0
0
0
1
0
0
0
1
3
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
2
2
1
0
0
0
0
0
0
1
0
0
0
1
1
5
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
1
3
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
1
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
1
1
0
1
2
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
2
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
6
0
0
0
0
1
0
0
0
1
1
2
0
2
0
1
0
0
0
0
0
0
2
3
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
7
0
4
0
0
0
1
0
0
0
1
1
2
0
2
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
2
0
2
0
0
1
3
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
4
1
0
1
0
3
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
1
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
4
0
3
1
2
0
0
0
0
2
0
0
1
0
2
0
0
0
0
1
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
1
0
4
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
1
2
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
1
0
0
0
0
3
0
0
0
1
3
0
0
0
0
0
0
0
0
0
3
2
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
1
1
2
0
0
0
1
0
2
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
2
0
0
0
0
0
3
2
0
0
0
0
5
2
0
0
0
4
1
3
1
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
2
0
0
2
2
2
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
2
0
1
0
2
0
10
1
1
2
1
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
1
0
0
1
0
2
1
0
0
0
0
2
0
1
0
0
0
2
0
0
0
4
2
0
0
0
0
0
2
0
0
6
0
0
1
0
0
3
0
2
0
0
0
0
0
0
1
2
0
2
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
1
2
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
2
2
2
0
2
2
0
0
1
0
0
2
0
0
3
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
3
0
2
3
0
4
0
0
0
0
0
2
0
0
0
0
1
0
1
0
3
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
2
0
2
0
0
1
0
0
0
2
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
2
0
6
0
0
2
0
0
0
0
0
2
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
4
2
0
0
0
2
0
0
2
0
2
0
1
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
11
0
0
0
0
1
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
1
0
0
0
2
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
3
0
1
0
0
3
0
0
0
1
0
3
0
1
2
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
2
2
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
7
0
1
1
0
0
0
2
1
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
1
1
3
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
2
2
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
2
0
0
0
1
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
2
2
2
0
0
9
0
0
0
1
0
0
0
0
1
0
0
2
1
3
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
3
2
4
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
3
0
1
0
2
1
0
0
0
0
0
0
1
0
0
0
0
1
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
3
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
2
0
0
1
1
0
0
0
0
0
0
0
3
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
1
1
2
3
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
1
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
4
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
3
0
0
0
1
1
1
0
0
0
0
0
2
0
0
0
1
2
1
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
1
0
0
2
6
0
0
0
0
0
2
0
1
1
0
0
3
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
2
2
6
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
1
0
1
2
0
0
0
0
0
2
0
2
0
0
2
0
0
2
0
0
1
0
4
0
0
0
0
1
0
0
1
1
0
2
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
2
0
1
0
2
0
1
0
2
0
0
0
0
1
2
0
0
0
0
1
0
3
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
1
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
3
0
2
2
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
2
0
3
0
0
1
0
0
1
2
0
0
2
1
0
0
0
0
0
2
0
1
2
1
3
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
1
2
2
0
0
3
2
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
2
0
3
0
2
0
0
0
0
4
2
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
1
0
0
0
1
0
1
0
0
2
1
0
1
0
1
1
0
1
1
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
3
0
1
2
1
0
2
0
0
0
0
0
0
2
2
1
0
0
1
0
3
4
0
2
0
0
0
4
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
6
0
1
1
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
1
0
2
2
0
0
2
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
3
0
0
0
0
1
2
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
1
0
0
2
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
5
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
3
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
2
0
1
0
0
0
0
2
1
0
0
0
0
2
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
3
0
0
0
2
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
5
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
2
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
2
0
0
0
9
2
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
2
1
0
3
3
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
3
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
3
0
1
0
2
3
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
2
1
0
0
0
3
2
0
1
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
2
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
2
0
0
0
0
0
1
0
0
1
2
0
0
7
0
8
0
0
0
0
1
0
0
0
3
0
1
0
0
0
0
0
1
1
0
2
0
0
4
0
0
0
0
0
1
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
2
0
2
0
0
4
2
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
3
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
3
0
1
0
0
0
0
0
0
0
2
4
1
0
1
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
1
0
2
0
0
0
2
0
0
0
3
0
0
0
3
0
0
1
0
0
0
2
0
0
0
0
0
1
1
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
2
2
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
1
0
2
0
0
0
2
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
1
0
3
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
1
0
0
1
0
0
4
0
0
0
0
1
0
1
3
2
2
0
0
0
1
0
0
0
1
0
0
1
2
0
0
2
0
0
2
0
0
0
0
0
2
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
3
0
2
0
0
1
0
0
0
3
0
0
0
0
1
2
0
0
0
3
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
3
0
0
1
0
0
6
0
0
5
0
3
0
0
0
2
0
1
1
0
2
0
0
1
0
0
0
2
0
0
4
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
3
0
0
2
0
0
0
2
2
0
4
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
6
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
1
0
1
2
2
0
0
0
0
0
0
0
0
2
1
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
2
3
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
1
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
1
0
0
3
4
0
2
0
0
0
2
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
2
1
1
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
1
0
0
2
0
1
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
1
1
0
0
2
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
3
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
2
2
0
2
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
2
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
2
0
0
2
2
0
0
0
0
0
2
1
2
2
0
2
1
1
0
2
0
0
2
0
0
0
3
2
0
0
2
0
0
0
1
1
0
4
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
3
0
0
2
0
2
0
2
2
0
2
0
0
1
0
0
0
2
0
2
0
0
3
1
1
0
0
0
1
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
3
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
1
0
10
0
1
0
0
0
1
0
2
0
1
2
0
2
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
1
2
3
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
1
1
0
1
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
2
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
2
0
0
0
2
0
1
1
1
0
0
1
0
0
0
0
0
0
0
1
3
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
2
2
0
1
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
4
0
0
7
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
2
0
1
0
2
0
0
0
3
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
3
2
1
0
0
1
0
0
2
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
2
0
0
0
1
2
2
0
1
0
0
0
0
0
0
0
1
0
1
0
0
2
0
1
1
0
0
1
1
0
1
0
1
0
0
0
0
0
3
0
0
2
0
2
3
1
0
0
0
0
0
5
0
0
2
0
0
0
0
2
0
4
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
3
0
1
1
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
1
0
0
2
0
1
0
2
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
1
0
1
0
0
1
0
2
0
0
0
1
2
3
1
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
3
3
0
1
0
1
2
0
0
0
0
0
5
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
2
1
1
0
0
0
1
0
0
2
2
0
0
0
0
2
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
2
1
0
0
2
1
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
1
3
0
0
0
2
3
0
0
0
0
1
2
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
4
0
0
0
0
0
0
0
0
3
2
0
0
1
0
1
0
1
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
4
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
2
2
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
1
2
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
2
0
0
3
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
1
1
0
0
0
0
0
0
0
2
2
1
3
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
3
0
3
2
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
1
0
0
2
1
2
0
0
2
2
0
1
0
1
0
0
0
2
0
1
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
3
0
0
0
1
0
2
0
0
0
2
2
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
5
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
9
2
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
1
1
0
0
0
0
0
0
2
0
0
0
2
2
1
0
1
0
1
0
0
0
0
3
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
2
0
0
2
2
0
0
1
1
0
2
0
1
0
0
1
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
5
2
0
0
0
1
1
2
0
0
1
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
2
2
1
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
4
0
2
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
1
0
0
0
0
2
0
1
1
0
1
2
0
2
0
0
0
0
0
0
0
3
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
2
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
1
0
0
0
3
0
0
1
0
0
1
1
0
2
0
0
0
0
0
2
1
0
1
0
0
0
2
0
0
2
1
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
3
2
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
3
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
3
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
3
1
0
0
0
0
1
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
3
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
2
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
2
0
2
3
1
0
2
0
1
0
0
0
0
8
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
2
0
2
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
3
0
0
1
1
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
3
1
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
4
2
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
2
0
0
0
7
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
1
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
1
1
2
0
1
1
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
5
1
0
1
0
1
0
0
1
0
1
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
3
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
2
4
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
1
2
2
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
4
0
0
0
0
2
0
2
0
1
0
0
0
0
5
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
5
2
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
2
2
0
1
0
1
3
0
0
0
0
2
0
0
2
0
0
1
0
0
2
0
2
0
2
0
1
0
0
2
0
0
0
1
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
7
1
0
0
1
2
0
0
2
0
0
0
2
0
0
0
1
2
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
1
6
0
0
0
0
0
0
0
3
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
3
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
1
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
4
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
1
2
0
1
0
0
1
0
0
0
0
1
2
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
2
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
1
0
1
2
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
2
2
0
0
1
1
1
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
2
0
0
1
0
0
2
2
0
0
1
0
0
0
2
0
1
0
3
0
0
0
1
0
0
0
0
0
1
2
0
0
1
1
0
0
1
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
2
0
0
0
0
0
0
0
3
0
1
3
2
0
0
1
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
4
1
9
0
0
2
2
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
1
0
0
2
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
2
0
6
0
0
0
2
3
0
2
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
1
1
0
0
1
1
0
0
1
0
1
0
0
0
0
6
3
0
0
0
1
2
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
1
1
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
2
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
6
3
2
0
0
2
0
1
0
0
2
1
0
2
2
0
0
0
0
1
0
0
2
7
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
1
1
0
0
0
0
0
2
0
2
0
2
0
0
0
1
0
2
2
2
3
0
0
0
0
1
0
2
1
0
2
0
0
0
0
1
0
0
0
0
1
0
0
2
0
5
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
1
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
2
0
6
1
0
0
0
2
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
1
0
1
0
0
0
0
1
0
0
5
0
2
0
0
2
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
1
1
0
0
0
1
0
0
2
2
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
2
1
0
1
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
2
1
0
1
0
0
0
3
0
2
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
3
8
0
1
1
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
1
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
3
2
0
0
0
0
0
2
0
1
0
3
0
0
0
1
0
0
0
0
2
0
0
2
0
0
2
0
1
0
0
4
0
1
0
0
0
0
2
0
3
0
0
0
1
4
0
0
0
0
1
0
1
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
1
2
0
0
0
0
0
0
1
2
0
0
0
2
0
1
1
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
2
0
0
0
2
0
1
0
0
0
1
0
2
0
3
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
2
2
0
0
0
0
1
1
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
2
1
1
3
0
0
2
0
3
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
5
1
2
1
2
5
0
0
0
0
0
1
0
2
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
7
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
2
0
0
1
0
2
4
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
5
2
0
0
1
0
0
2
5
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
1
2
1
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
5
2
0
0
2
0
0
0
1
1
2
0
0
0
0
1
0
0
0
0
0
0
2
1
1
0
1
0
0
0
0
0
0
2
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
4
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
1
4
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
2
0
0
0
3
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
2
0
3
0
4
0
1
0
0
0
1
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
1
1
0
0
0
1
0
0
0
0
0
3
4
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
2
0
0
0
2
1
0
1
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
2
0
0
0
0
0
0
0
0
2
0
0
2
0
1
1
0
1
0
0
0
0
0
1
1
2
1
2
0
0
0
1
0
0
2
1
0
1
3
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
2
0
0
0
1
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
1
0
3
0
1
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
7
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
1
0
0
2
0
2
0
2
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
2
0
0
0
5
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
2
1
0
0
0
1
0
0
0
0
1
0
0
3
2
0
0
4
0
0
0
0
2
0
0
1
0
0
0
0
0
4
0
0
0
0
0
2
0
0
1
1
1
2
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
3
3
2
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
2
0
2
1
1
2
0
0
5
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
3
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
1
0
0
1
0
1
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
3
0
0
1
0
0
0
5
0
0
2
0
0
1
0
1
0
0
1
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
1
2
0
1
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
1
0
0
0
2
0
0
1
0
2
0
0
2
0
0
0
0
0
2
0
0
4
0
1
0
3
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
5
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
4
2
0
2
0
0
1
3
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
9
0
0
1
0
0
0
0
7
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
1
3
0
0
0
0
0
0
0
1
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
2
1
1
0
0
0
1
0
0
0
0
1
0
0
0
1
5
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
2
0
1
0
0
0
2
0
0
0
1
0
0
1
2
2
0
0
0
2
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
3
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
3
0
2
0
0
0
0
0
0
4
0
2
2
3
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
3
0
1
0
2
0
2
2
0
0
0
1
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
3
0
1
0
0
0
0
0
1
0
3
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
4
1
0
1
1
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
4
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
1
0
0
2
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
3
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
5
1
2
0
0
0
3
1
1
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
2
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
3
0
2
0
0
1
0
2
0
0
2
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
2
0
0
0
0
9
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
2
1
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
4
0
0
0
1
0
0
0
0
3
0
2
0
0
0
0
2
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
2
0
0
0
2
1
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
2
2
1
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
2
1
0
0
0
1
1
0
0
0
1
2
0
0
0
0
0
1
1
1
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
5
0
1
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
3
0
1
0
0
0
1
0
0
1
0
1
0
2
0
0
1
0
0
0
1
1
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
1
3
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
1
0
0
0
1
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
2
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
3
0
0
3
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
1
0
3
2
0
0
0
0
0
0
0
1
1
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
3
0
0
2
2
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
1
2
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
3
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
1
2
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
1
0
0
0
1
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
1
1
1
0
1
0
0
0
3
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
2
1
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
2
2
0
2
0
0
1
0
2
0
0
0
2
0
2
4
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
1
4
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
3
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
1
0
2
1
1
1
0
3
0
1
2
0
1
0
0
0
0
0
0
1
0
1
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
3
2
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
3
0
0
2
2
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
3
0
2
1
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
1
0
1
1
0
0
0
2
0
0
0
1
0
1
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
1
0
1
0
1
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
4
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
2
1
0
1
0
0
0
0
2
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
2
1
0
2
0
0
0
1
1
2
0
0
2
0
0
2
1
2
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
1
0
0
2
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
1
0
0
2
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
1
2
2
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
3
0
0
0
0
0
1
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
1
1
0
2
2
0
4
1
0
0
0
0
0
0
4
0
2
0
2
0
0
7
0
0
0
0
7
3
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
1
1
0
0
2
0
0
0
0
1
2
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
3
0
0
1
0
0
1
0
4
0
0
0
0
0
1
0
1
0
2
0
2
0
3
0
4
1
0
0
0
0
0
3
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
4
0
0
0
0
2
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
1
0
1
2
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
2
0
3
0
2
0
1
2
0
2
0
0
1
1
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
5
5
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
3
0
0
0
0
0
0
1
0
2
2
0
1
1
0
0
0
2
0
0
0
2
0
0
4
0
0
2
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
4
0
0
0
1
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
1
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
2
0
1
1
6
0
1
0
2
2
0
0
0
1
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
3
0
3
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
2
1
0
0
2
1
0
0
0
2
2
0
0
0
0
1
3
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
3
1
0
1
0
1
0
0
0
0
2
1
0
0
1
0
7
0
0
0
0
0
0
1
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
2
2
0
0
0
2
0
1
5
0
1
0
2
0
1
0
0
0
0
0
0
0
1
0
0
3
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
2
0
1
0
0
4
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
2
2
0
0
2
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
3
0
1
0
2
0
0
1
0
0
1
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
1
0
2
0
5
0
0
0
0
0
0
3
1
0
0
0
1
0
3
2
0
0
0
2
0
0
2
4
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
2
0
3
2
0
1
0
0
0
0
0
0
1
2
1
0
0
1
2
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
2
2
0
2
0
1
3
2
3
0
1
0
0
2
0
0
0
0
1
2
1
0
0
2
0
1
0
0
1
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
9
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
1
0
0
0
1
0
1
0
1
0
0
0
2
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
2
1
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
2
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
1
0
0
1
1
0
0
2
0
0
0
0
2
2
0
0
0
0
1
0
0
0
3
0
0
5
0
0
0
0
0
1
0
0
1
0
0
0
0
3
1
2
1
2
0
0
0
0
2
0
0
2
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
2
0
0
0
1
1
5
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
1
0
0
0
2
1
2
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
1
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
10
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
1
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
1
0
0
3
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
1
0
0
3
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
5
0
0
3
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
2
2
0
1
1
1
0
2
1
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
1
2
2
0
2
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
5
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
2
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
1
0
1
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
2
0
2
0
0
0
5
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
4
2
0
0
0
1
0
0
2
1
0
0
0
2
0
1
1
2
0
2
2
2
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
2
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
3
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
4
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
2
0
0
2
0
0
1
0
0
0
2
3
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
5
0
0
0
2
0
0
4
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
1
0
2
0
0
1
5
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
2
0
1
1
0
1
2
0
0
0
0
0
0
1
2
0
2
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
2
2
0
1
3
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
2
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
1
1
0
0
1
0
0
0
0
2
0
3
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
1
0
1
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
3
0
0
1
0
0
0
0
0
0
1
0
4
1
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
5
0
0
0
0
0
3
0
2
0
0
0
1
1
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
2
2
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
1
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
2
1
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
2
4
0
1
0
0
0
0
0
2
0
0
0
1
2
0
2
0
0
0
1
0
2
4
0
0
1
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
1
0
0
3
1
0
0
2
0
2
0
0
3
0
1
0
1
6
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
1
0
0
0
1
2
2
0
0
2
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
1
3
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
1
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
1
0
2
1
0
0
1
0
0
2
1
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
2
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
2
0
1
0
0
0
2
1
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
2
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
1
2
0
0
0
0
1
1
0
0
0
0
2
0
0
0
1
0
1
1
0
0
0
0
0
2
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
5
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
2
0
0
0
0
0
0
1
1
0
0
2
2
0
1
0
0
1
0
1
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
1
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
7
1
0
0
2
0
6
0
1
0
1
0
1
4
2
0
1
0
1
1
1
1
0
0
0
2
0
0
3
0
2
0
0
0
1
0
0
0
3
2
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
2
0
2
0
2
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
1
0
1
0
0
0
0
1
0
0
0
1
1
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
2
0
0
0
1
2
0
0
1
0
2
0
0
0
0
0
0
3
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
10
1
0
4
2
0
0
1
0
0
1
2
0
0
0
3
0
0
0
0
6
0
2
0
1
0
0
2
0
1
2
0
2
0
0
2
1
2
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
2
1
0
0
0
0
0
0
1
0
3
0
2
0
0
0
0
2
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
1
0
0
2
0
0
1
1
1
2
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
2
0
2
1
0
2
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
2
0
0
0
1
0
0
1
3
0
0
0
0
0
1
2
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
2
0
2
0
0
2
1
0
1
1
1
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
4
2
0
0
0
0
0
1
2
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
1
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
3
0
0
0
0
0
1
2
0
0
0
0
1
2
0
3
1
1
0
0
0
0
1
2
2
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
2
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
2
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
1
1
2
0
0
1
0
0
0
2
0
2
0
5
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
1
2
0
0
1
1
0
0
0
0
4
3
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
5
0
2
0
0
0
0
0
5
0
2
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
3
0
0
2
0
1
0
0
2
0
0
0
0
2
0
1
0
0
2
1
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
1
0
0
0
1
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
1
2
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
2
1
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
2
0
1
0
2
0
0
0
0
1
1
0
0
0
6
0
0
0
1
0
0
3
0
0
4
0
0
0
0
0
1
0
3
2
0
0
0
2
1
0
0
0
0
0
1
0
0
0
2
4
0
1
0
0
0
0
0
0
0
1
0
1
0
2
0
0
1
1
2
0
0
4
0
1
2
0
0
0
0
0
0
0
2
0
0
1
3
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
3
0
0
0
1
0
2
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
4
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
3
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
1
0
0
2
0
0
0
0
2
0
1
1
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
3
0
0
0
0
1
0
0
0
4
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
3
0
0
0
0
2
0
0
0
0
2
0
0
1
1
2
0
0
0
1
0
0
0
2
0
0
1
0
0
2
0
1
0
0
0
0
2
2
2
0
0
1
3
0
0
0
0
3
1
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
4
1
0
0
0
0
0
0
0
0
0
2
1
0
0
1
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
1
1
0
3
2
2
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
1
0
0
3
0
0
2
1
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
3
0
0
0
0
2
0
0
0
2
2
0
0
0
1
0
0
3
0
0
0
0
2
0
0
0
0
0
4
0
0
1
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
5
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
1
2
2
0
0
0
2
1
0
0
0
1
0
0
0
1
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
6
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
1
0
0
0
4
0
2
1
1
0
2
0
0
0
1
2
0
0
2
0
0
0
0
0
0
1
1
0
0
2
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
1
2
3
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
2
0
0
0
1
0
0
1
0
3
2
0
0
0
0
1
0
0
0
1
0
1
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
2
0
2
1
0
0
1
0
0
0
0
1
1
0
0
3
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
2
1
0
2
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
2
0
2
2
0
0
2
1
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
8
0
0
0
0
0
0
0
0
1
4
0
0
0
1
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
3
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
2
0
2
1
0
1
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
2
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
4
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
2
2
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
2
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
3
0
0
0
0
2
0
0
0
0
0
1
0
0
0
3
0
0
3
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
1
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
2
1
0
3
0
0
3
1
0
0
0
2
2
0
0
0
1
0
0
2
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
1
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
18
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
1
0
0
0
0
2
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
2
0
5
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
3
0
0
2
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
3
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
4
0
0
0
0
2
1
0
3
0
0
1
3
0
2
0
0
0
1
1
1
0
2
1
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
1
1
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
2
2
1
0
0
1
1
0
0
0
0
0
0
3
1
0
0
0
2
0
0
0
0
3
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
1
3
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
4
0
3
0
5
0
2
0
0
0
0
0
0
0
1
2
0
2
1
0
0
0
2
0
0
0
1
2
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
3
0
0
1
0
0
0
0
2
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
1
0
0
0
1
2
0
1
0
0
0
2
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
2
0
0
0
0
0
1
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
5
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
1
0
2
0
1
0
0
0
0
0
1
0
0
1
0
3
0
0
0
0
1
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
1
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
3
0
2
2
0
0
0
1
0
0
0
0
0
0
5
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
2
0
0
0
1
0
1
0
0
0
0
0
2
2
0
2
1
0
0
0
3
0
0
0
2
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
4
0
0
0
2
0
0
2
0
1
0
0
0
0
1
0
1
1
0
0
0
3
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
5
0
0
0
2
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
3
0
0
1
0
0
1
0
0
2
0
0
0
3
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
2
2
0
0
0
3
0
2
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
1
1
2
0
0
0
1
0
1
0
0
1
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
1
0
0
1
0
2
0
0
0
2
1
0
0
1
0
0
1
0
0
0
0
1
0
0
2
0
0
0
1
3
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
3
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
2
0
2
2
0
2
0
0
1
2
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
2
2
2
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
2
0
0
4
0
0
1
0
0
0
1
0
0
0
0
1
2
1
0
0
0
0
2
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
1
1
3
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
3
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
4
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
2
0
0
0
3
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
2
0
0
0
2
0
0
2
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
3
4
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
3
0
0
0
0
3
1
0
0
1
0
1
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
2
0
1
0
0
0
1
2
0
1
0
0
0
2
0
1
0
2
0
0
3
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
7
0
0
2
2
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
2
2
0
0
0
0
2
0
0
2
4
0
2
0
0
3
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
2
0
1
0
0
0
0
0
0
0
0
2
1
0
0
1
0
1
0
2
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
3
1
0
4
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
1
2
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
3
1
0
0
0
1
0
0
0
0
0
1
1
2
0
0
0
0
0
1
0
0
1
0
0
0
2
2
0
0
6
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
1
2
1
0
1
0
0
3
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
3
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
2
0
0
1
0
0
0
3
0
1
0
1
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
3
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
3
2
1
0
1
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
3
0
0
0
0
0
0
0
1
1
10
0
0
0
2
0
0
1
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
1
3
0
1
1
0
2
2
2
1
0
1
1
2
0
0
0
2
0
0
1
2
0
0
0
0
0
0
2
0
1
1
0
0
0
2
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
2
1
0
0
0
0
0
2
3
0
0
0
4
1
0
1
1
1
2
0
0
0
0
0
1
1
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
3
0
0
2
0
0
3
0
0
0
0
0
1
0
0
0
1
2
0
0
2
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
3
1
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
1
0
1
0
2
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
5
0
1
0
0
2
2
0
0
0
0
0
1
0
0
2
2
0
1
3
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
3
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
1
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
1
0
1
0
2
0
0
2
3
2
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
4
0
0
0
1
2
0
0
0
0
0
0
2
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
7
0
0
0
0
0
1
1
1
1
0
0
2
0
0
0
0
0
0
0
1
1
2
0
1
0
3
0
0
0
0
3
0
0
0
1
0
1
0
0
3
1
2
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
1
1
3
1
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
3
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
1
0
0
0
2
0
1
0
2
0
0
0
0
0
1
0
0
0
0
4
0
1
0
0
0
5
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
8
1
4
0
0
0
2
0
0
0
3
1
0
1
0
0
0
3
0
2
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
2
0
1
0
0
2
0
0
0
2
0
0
0
0
0
2
0
2
0
2
0
1
0
0
2
0
0
1
2
2
1
1
2
0
0
1
0
2
0
0
0
0
0
1
0
0
1
1
0
2
2
0
0
0
0
0
0
0
0
2
0
0
2
1
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
5
0
0
0
0
0
1
1
0
3
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
3
0
1
1
0
0
0
0
2
0
0
3
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
1
0
1
2
0
0
0
0
0
0
0
1
0
0
0
1
0
2
2
0
0
0
2
0
0
0
1
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
1
2
0
4
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
2
1
0
0
0
1
0
0
1
0
0
2
0
0
0
0
5
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
3
0
0
0
0
0
0
2
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
1
1
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
1
2
2
4
2
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
4
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
3
0
0
0
0
1
5
0
0
0
4
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
3
0
0
0
1
2
0
0
1
1
0
2
2
0
2
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
6
2
0
0
0
1
0
0
3
0
0
0
0
1
0
0
0
1
2
0
2
1
0
0
0
1
0
0
0
1
0
1
3
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
3
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
4
2
2
0
0
0
1
1
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
9
1
0
2
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
2
0
0
1
0
3
2
0
0
2
1
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
2
0
0
0
3
0
0
2
1
1
0
0
0
1
1
0
1
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
3
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
2
0
2
2
0
0
2
4
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
1
4
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
2
0
5
5
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
3
0
0
0
4
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
3
1
0
0
0
0
1
0
1
0
0
1
0
0
1
0
2
1
0
0
3
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
2
0
2
0
0
0
1
2
0
0
0
0
0
3
1
0
1
5
0
0
1
0
0
1
2
0
0
0
0
0
0
1
3
0
0
0
1
2
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
3
0
0
0
0
0
0
0
0
0
2
2
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
1
0
1
2
0
2
3
2
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
3
0
0
1
0
0
2
0
0
0
0
1
0
5
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
2
1
1
1
0
2
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
4
0
0
4
0
0
0
0
0
0
0
1
0
0
0
3
1
0
0
1
0
0
1
0
0
2
0
0
0
5
0
0
0
0
0
0
0
2
0
0
0
6
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
1
2
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
2
2
2
0
0
0
2
2
0
0
2
0
2
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
1
0
0
2
0
1
1
0
0
0
1
0
0
0
0
4
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
3
0
0
1
0
0
0
1
2
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
2
1
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
2
0
3
0
0
0
0
4
1
0
0
0
1
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
2
7
2
1
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
1
0
3
0
0
0
0
2
0
0
0
0
0
0
3
3
1
0
8
0
0
2
0
0
0
4
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
2
2
0
0
1
0
0
0
2
0
1
0
0
0
0
1
1
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
3
0
0
3
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
7
0
2
0
0
0
0
1
1
2
0
1
3
0
0
0
0
0
0
2
0
1
1
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
1
0
2
0
0
2
7
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
3
0
0
0
2
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
16
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
2
1
0
0
0
0
1
0
2
0
0
3
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
1
1
0
0
0
0
0
4
2
2
0
1
0
2
0
0
0
0
1
3
0
1
0
0
2
0
2
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
5
0
1
5
0
1
0
2
0
4
1
0
0
0
1
1
0
0
0
0
0
0
0
3
3
1
0
1
2
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
2
1
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
2
0
1
1
0
0
0
0
0
2
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
1
0
0
4
0
0
2
1
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
2
2
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
1
0
0
1
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
5
0
0
0
2
0
3
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
2
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
5
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
3
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
6
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
2
1
2
0
2
0
0
0
0
0
0
0
0
2
3
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
3
1
0
0
0
1
0
0
2
0
0
0
0
1
2
1
0
1
0
2
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
7
0
0
1
1
1
0
2
0
1
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
2
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
1
1
0
0
1
0
0
0
1
0
0
3
0
0
0
0
0
2
3
0
0
1
5
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
1
2
1
0
2
1
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
4
0
2
0
0
0
1
2
0
0
1
4
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
1
0
0
2
3
0
2
0
0
1
2
1
0
0
0
0
0
0
0
1
0
0
1
1
1
0
1
0
2
0
0
0
0
1
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
4
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
1
0
0
2
0
0
1
2
0
1
0
0
0
0
4
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
1
0
2
1
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
9
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
1
2
0
0
2
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
3
0
0
4
1
0
0
0
2
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
2
2
0
2
2
0
0
0
0
0
4
0
0
0
0
0
15
0
0
0
0
2
0
0
0
1
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
2
0
0
2
0
0
1
0
1
0
0
0
0
2
0
0
2
0
0
1
1
2
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
1
2
1
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
5
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
3
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
2
0
0
0
0
0
0
3
0
0
0
1
1
0
0
0
0
0
0
2
2
0
0
1
0
0
1
2
0
2
0
0
1
0
0
1
1
0
0
3
0
0
0
0
0
2
2
0
1
0
0
2
1
0
0
0
0
0
1
2
0
0
1
3
2
1
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
2
0
0
1
0
1
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
2
0
0
1
2
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
6
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
3
0
3
0
0
0
0
0
0
2
1
1
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
2
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
3
1
0
0
0
0
0
1
0
2
8
0
0
0
1
0
2
0
0
0
2
2
2
0
0
0
1
0
0
0
0
0
0
0
0
5
2
2
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
1
2
0
0
0
0
1
0
1
0
0
0
4
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
7
0
0
0
0
0
0
0
0
0
0
2
0
0
3
1
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
2
6
0
0
0
0
0
2
0
0
0
1
1
0
1
0
0
0
1
1
0
1
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
5
0
0
0
0
1
0
2
2
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
2
2
0
0
0
0
0
1
2
0
1
0
0
0
1
0
1
0
1
1
0
0
0
1
1
0
0
0
1
0
0
0
0
2
5
0
2
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
4
3
2
2
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
3
0
2
0
0
1
0
0
0
0
2
0
2
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
1
0
1
0
0
0
2
0
0
0
0
0
3
0
0
1
0
1
0
0
0
1
1
0
0
3
0
0
0
0
5
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
7
0
4
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
1
0
1
4
0
1
0
2
0
0
0
0
0
2
12
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
2
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
6
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
1
0
0
0
0
1
0
3
0
0
0
0
2
2
0
1
1
0
0
2
0
1
0
0
0
1
0
0
0
1
1
0
2
0
0
0
0
0
0
1
1
0
0
2
1
0
0
0
1
0
1
1
0
5
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
3
6
0
0
0
1
2
0
0
0
1
0
0
1
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
1
0
1
0
2
0
0
0
0
0
0
0
1
0
1
0
2
5
0
0
0
0
0
3
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
2
0
2
1
2
0
0
2
0
0
0
1
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
1
1
0
0
5
0
1
0
0
0
0
2
2
0
1
0
0
0
4
1
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
3
3
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
2
0
0
1
0
0
2
0
1
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
3
0
2
0
0
1
6
0
0
0
0
0
0
1
0
1
0
0
2
0
2
0
2
2
0
1
2
0
0
1
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
3
1
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
2
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
1
1
1
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
2
0
3
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
3
0
0
2
0
0
0
0
0
1
1
2
2
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
1
1
0
0
0
0
2
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
2
0
2
5
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
3
2
1
0
1
2
2
2
0
0
0
5
1
0
0
2
0
0
3
0
2
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
2
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
1
0
1
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
5
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
1
1
2
1
2
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
3
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
1
0
0
1
2
0
0
1
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
1
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
2
0
1
0
0
1
0
0
0
2
2
0
0
0
0
2
0
0
0
2
0
0
0
8
2
0
1
0
1
2
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
1
0
0
0
3
1
1
0
0
2
0
0
0
2
0
1
0
0
0
0
1
1
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
4
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
4
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
1
2
0
0
0
0
0
1
1
1
0
0
0
0
2
0
0
0
2
0
0
1
0
1
1
0
0
0
0
2
0
0
3
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
6
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
3
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
3
1
0
2
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
1
3
0
0
1
0
0
1
3
2
0
0
3
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
2
0
0
0
0
2
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
2
0
0
0
1
2
0
0
0
1
0
0
0
0
0
2
0
0
1
1
0
1
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
1
0
1
0
0
3
0
0
0
0
2
0
0
6
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
1
0
0
2
3
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
1
4
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
1
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
2
0
1
3
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
2
0
1
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
1
0
0
2
2
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
1
1
1
0
4
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
3
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
3
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
3
0
0
0
0
2
0
0
1
2
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
1
1
2
1
0
0
0
0
0
0
1
0
3
4
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
1
0
1
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
1
1
0
0
2
2
1
1
2
0
1
0
0
0
0
0
0
1
0
0
0
0
2
2
0
1
0
0
0
0
1
0
0
0
0
2
0
0
3
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
5
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
3
0
0
0
0
3
1
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
2
1
0
0
1
1
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
3
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
2
1
0
0
5
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
2
0
1
2
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
6
0
0
1
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
1
2
0
0
1
0
0
1
0
1
0
0
2
2
0
0
2
1
0
2
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
1
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
3
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
2
0
0
0
3
2
0
1
0
0
0
2
2
1
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
1
1
0
2
0
0
0
0
2
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
2
1
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
3
1
0
0
3
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
1
2
2
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
7
0
0
1
0
0
0
0
1
4
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
2
2
0
1
2
1
1
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
2
3
0
0
2
0
0
0
1
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
1
0
0
0
2
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
5
0
1
2
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
1
1
8
2
3
0
0
0
1
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
2
2
0
2
0
0
2
0
1
1
2
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
2
1
1
0
0
0
0
0
0
3
0
0
2
2
0
0
0
0
0
1
0
0
0
1
1
0
0
2
0
0
2
0
0
0
2
0
0
0
1
2
0
1
0
1
0
0
2
0
1
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
9
2
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
2
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
1
2
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
2
0
0
0
0
0
2
3
0
2
0
2
0
0
0
0
0
0
3
2
2
2
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
2
0
2
0
0
1
0
1
0
1
0
1
0
0
3
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
1
1
0
0
0
2
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
1
2
1
1
0
1
0
1
0
0
0
0
3
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
5
1
2
0
1
0
3
0
0
0
0
3
0
2
2
0
0
0
1
0
2
0
0
1
0
0
0
0
1
0
0
0
1
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
2
0
1
0
0
3
0
0
0
4
1
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
2
0
0
0
0
2
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
2
0
1
3
0
0
0
0
0
2
0
0
0
0
0
0
1
5
0
0
0
0
4
2
0
0
0
0
1
0
4
0
0
0
0
2
0
0
0
0
0
2
0
0
2
2
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
3
2
1
0
2
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
25
0
1
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
2
3
0
3
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
2
7
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
1
1
2
0
2
0
0
0
0
0
1
0
3
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
4
0
1
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
1
0
1
0
0
0
4
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
1
0
1
1
1
0
1
0
1
0
0
2
2
3
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
10
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
2
0
0
1
2
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
2
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
4
2
0
0
0
0
0
0
0
2
0
0
0
0
2
3
0
0
0
1
2
0
0
6
0
0
0
3
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
2
5
0
2
0
0
0
2
0
2
0
0
3
0
0
0
0
0
0
0
0
1
1
0
0
0
2
2
0
2
0
0
0
0
1
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
3
0
0
2
2
0
0
6
0
2
0
0
0
0
0
0
2
0
1
2
0
1
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
4
0
2
0
0
1
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
3
2
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
1
0
0
0
2
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
3
0
0
0
0
0
1
1
0
0
0
0
1
2
2
2
2
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
3
0
0
1
1
0
2
0
0
1
0
0
0
2
0
2
0
0
0
0
0
2
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
2
0
1
1
0
2
0
0
1
0
1
0
1
1
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
1
5
1
0
0
0
0
2
0
0
1
3
0
0
2
2
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
1
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
1
0
1
0
2
1
2
0
0
0
0
1
0
0
1
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
5
0
0
2
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
1
0
0
2
0
2
0
0
1
0
0
0
0
0
2
1
0
0
0
0
1
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
3
0
0
0
1
2
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
3
0
1
2
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
2
2
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
4
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
10
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
1
2
0
0
2
0
0
1
0
0
2
2
0
2
0
3
2
1
0
0
0
1
0
0
0
0
2
1
0
3
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
3
0
0
0
0
1
0
2
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
7
0
1
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
7
1
0
1
0
0
0
1
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
2
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
4
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
8
0
2
0
0
0
0
0
1
0
0
1
0
2
0
1
0
0
0
4
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
2
2
0
0
0
0
0
1
0
0
2
0
2
0
0
1
2
2
3
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
1
2
1
1
0
0
0
0
1
0
0
0
0
2
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
5
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
1
0
1
1
2
0
0
0
0
0
0
0
0
0
0
3
0
3
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
1
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
2
0
2
4
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
2
0
0
0
1
0
0
0
2
2
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
3
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
1
1
0
0
1
0
0
0
1
2
0
0
2
3
0
0
0
0
1
0
0
7
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
4
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
1
0
0
2
1
0
1
0
0
0
2
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
9
0
0
0
0
0
0
0
0
0
0
5
0
1
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
1
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
7
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
6
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
2
0
0
1
2
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
3
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
2
1
2
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
1
2
0
0
1
0
0
0
2
2
0
0
0
2
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
1
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
1
0
0
0
0
0
0
7
0
1
0
1
0
2
0
0
2
0
0
0
0
0
1
0
1
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
2
3
0
0
0
1
0
2
0
1
0
0
0
3
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
3
0
0
0
0
0
1
0
1
1
1
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
1
1
0
2
3
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
2
0
0
0
0
2
4
0
0
0
0
0
2
0
0
0
0
0
1
0
14
2
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
2
2
0
0
2
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
2
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
2
2
2
0
0
0
0
1
1
0
0
0
0
0
0
0
4
0
0
2
0
0
0
2
0
3
0
0
0
0
0
0
0
0
1
2
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
1
2
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
2
1
0
2
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
3
0
0
0
0
0
2
0
2
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
4
0
2
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
2
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
4
3
0
0
0
0
2
0
3
0
0
0
5
2
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
2
0
1
1
0
0
0
0
0
0
0
0
1
1
0
1
1
1
0
2
0
4
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
2
0
2
0
0
0
0
1
0
0
0
2
0
1
0
3
3
1
0
1
2
0
0
2
2
2
0
0
7
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
4
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
2
0
0
1
0
1
2
1
0
0
1
1
0
0
0
0
0
0
0
0
0
2
2
2
0
3
0
0
0
0
1
0
3
0
0
0
0
0
1
0
3
2
2
3
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
2
0
0
1
0
0
0
2
0
0
1
0
0
2
0
0
0
1
0
0
0
2
0
0
2
0
0
1
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
2
0
0
1
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
13
0
2
2
0
0
0
2
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
2
7
0
0
2
0
0
0
1
3
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
1
0
0
5
2
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
1
0
7
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
2
1
0
1
1
0
0
2
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
3
2
0
1
1
2
0
0
0
1
2
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
4
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
2
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
3
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
2
2
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
1
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
3
0
2
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
2
0
2
1
0
2
0
0
0
0
0
0
0
1
0
2
0
1
1
2
6
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
1
0
2
0
0
0
0
0
1
0
1
0
0
0
0
1
0
2
0
0
0
0
1
2
0
0
3
0
0
0
0
1
0
2
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
3
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
1
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
2
1
1
4
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
1
2
5
0
1
1
0
0
0
0
0
0
0
1
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
3
0
0
0
2
0
0
0
2
1
1
0
1
1
0
0
0
1
2
1
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
3
1
2
2
0
0
0
2
0
0
0
0
5
1
1
1
0
0
3
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
3
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
1
3
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
2
1
0
1
0
0
0
2
1
2
0
0
4
0
0
0
0
0
0
0
0
1
1
2
0
2
1
0
0
0
0
0
0
1
0
1
0
1
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
2
2
0
2
0
1
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
4
0
1
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
1
1
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
1
0
1
0
1
0
0
0
0
0
1
0
0
0
2
1
1
0
0
0
1
2
0
0
0
0
0
0
3
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
3
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
4
0
0
0
0
0
0
0
3
1
0
0
0
4
2
0
0
2
1
0
0
0
2
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
1
0
0
0
3
0
0
0
0
0
1
0
0
1
1
1
0
0
1
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
2
2
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
4
3
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
2
0
1
0
1
0
1
1
0
0
3
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
3
2
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
2
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
2
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
1
6
0
0
0
0
0
0
0
1
2
0
0
2
1
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
3
0
0
0
2
3
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
1
2
1
0
2
2
2
0
0
0
0
0
0
3
5
0
1
0
2
0
0
0
0
0
0
0
0
0
3
1
2
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
3
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
1
3
0
0
0
0
2
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
2
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
1
0
1
0
2
0
1
1
0
2
0
0
0
2
1
2
5
0
0
0
0
0
0
0
2
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
1
2
1
0
1
2
0
0
0
2
2
0
0
0
0
5
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
2
2
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
6
0
1
1
2
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
2
2
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
6
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
1
2
2
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
2
1
0
1
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
2
0
0
0
0
1
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
2
3
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
2
0
1
0
0
0
1
2
2
2
0
0
0
0
1
2
0
0
0
1
2
0
2
0
0
0
2
0
0
2
0
0
0
0
1
2
1
0
1
0
1
0
3
0
0
0
0
0
0
2
0
0
1
2
0
2
0
0
0
0
1
0
1
0
2
0
0
0
1
0
0
0
1
0
3
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
1
0
0
0
4
0
0
1
0
0
0
2
3
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
4
0
0
0
0
3
0
0
0
0
0
0
0
2
0
2
0
1
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
3
0
2
2
0
1
0
1
0
0
3
0
2
2
0
0
0
0
0
3
0
0
0
1
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
3
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
4
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
1
0
1
1
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
1
0
1
2
0
0
0
2
1
4
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
1
1
1
0
0
1
0
0
1
0
0
0
0
1
0
0
8
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
4
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
2
2
0
1
2
0
0
0
0
2
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
3
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
3
0
1
0
0
1
2
0
4
0
0
0
2
0
2
0
0
0
0
0
0
1
0
1
1
0
0
0
0
3
0
0
0
3
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
8
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
5
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
4
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
7
0
1
0
0
0
0
2
0
1
0
0
0
8
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
2
0
0
2
0
1
2
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
2
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
1
2
2
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
1
3
0
0
1
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
2
1
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
5
0
2
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
5
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
1
0
0
0
1
0
1
0
2
0
0
2
3
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
5
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
1
0
0
0
0
0
2
0
0
3
0
0
2
2
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
3
0
0
2
0
0
1
1
0
1
0
1
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
2
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
2
0
1
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
1
0
0
0
2
0
1
2
1
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
5
0
0
0
0
0
0
1
2
0
0
0
3
0
0
0
0
1
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
3
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
12
2
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
3
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
3
0
0
2
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
3
0
0
0
0
0
0
0
0
0
0
5
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
3
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
3
1
0
0
0
0
0
2
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
1
2
2
0
0
0
0
0
0
4
0
0
2
2
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
1
3
0
0
0
0
0
0
0
0
9
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
2
2
0
0
2
0
0
0
0
0
2
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
1
0
0
1
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
1
0
8
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
1
0
0
0
1
0
0
1
0
2
0
0
2
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
0
2
0
0
1
1
0
0
1
0
0
0
3
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
2
0
7
0
1
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
1
0
1
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
1
0
0
2
1
0
0
0
0
2
2
0
0
0
2
0
0
0
0
2
0
1
0
0
0
1
6
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
2
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
3
0
1
0
0
0
2
0
2
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
1
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
2
1
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
5
0
0
0
0
0
2
0
1
2
0
4
0
0
0
0
2
0
0
0
0
3
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
1
0
0
0
0
1
0
0
2
3
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
10
2
0
0
0
0
0
0
0
8
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
2
0
1
0
0
0
2
0
0
0
0
0
2
0
2
2
2
0
1
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
3
0
0
0
0
2
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
1
1
0
0
0
3
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
2
1
0
2
0
0
1
0
0
0
0
2
1
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
1
1
1
0
2
1
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
1
1
0
3
3
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
3
0
2
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
3
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
1
0
2
1
0
9
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
1
0
0
0
2
0
0
2
0
1
0
0
2
0
0
0
5
2
0
0
0
0
0
0
0
1
0
0
3
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
3
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
2
1
1
1
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
1
1
2
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
1
0
4
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
4
0
2
0
0
1
2
2
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
3
0
0
0
0
1
2
2
0
0
1
0
1
1
1
0
0
0
2
1
0
0
0
2
0
0
1
0
0
0
0
2
0
0
1
0
0
2
0
2
0
7
1
0
0
1
0
0
0
5
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
3
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
2
1
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
2
0
1
0
1
1
2
0
2
2
0
0
0
1
1
1
0
2
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
5
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
1
0
0
0
0
2
0
0
2
0
0
0
0
1
0
2
1
0
0
1
0
1
0
1
1
0
0
0
0
1
0
0
0
0
2
0
0
2
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
3
0
0
0
0
0
4
0
1
0
0
0
0
2
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
13
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
2
0
2
0
0
1
1
0
3
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
3
0
1
1
1
0
0
0
0
1
1
0
2
3
0
1
0
0
2
0
0
0
2
3
2
0
0
0
2
0
2
0
0
0
0
0
3
3
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
2
0
0
2
1
0
2
0
0
1
2
1
0
0
0
2
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
1
0
5
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
12
0
0
1
0
0
0
0
0
0
1
1
1
0
2
0
0
0
0
1
5
0
1
2
2
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
3
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
1
2
0
0
0
0
0
1
1
0
0
0
0
1
0
6
0
0
2
0
2
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
3
0
0
0
0
0
0
2
0
0
4
0
0
2
0
1
0
2
2
0
0
0
0
0
2
0
0
2
0
0
2
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
1
0
2
1
0
0
1
0
0
0
0
0
1
0
4
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
4
0
2
0
1
1
2
1
4
0
0
0
2
0
0
1
0
4
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
3
0
0
0
0
6
0
0
0
0
1
0
0
0
0
1
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
2
0
2
0
0
2
2
0
0
0
0
0
2
0
0
1
1
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
1
2
1
1
4
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
1
0
0
3
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
3
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
4
0
0
0
0
2
0
0
2
2
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
7
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
1
0
0
0
1
2
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
3
0
0
2
0
1
0
1
0
1
2
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
2
0
1
1
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
6
0
1
11
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
1
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
2
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
3
0
0
0
0
6
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
1
0
0
0
2
1
0
0
0
1
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
3
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
1
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
7
0
0
0
2
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
4
0
0
2
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
5
2
0
3
3
2
0
0
1
0
0
0
3
0
0
0
1
0
0
3
0
0
0
0
0
1
0
2
0
1
1
0
1
0
0
0
1
0
0
0
1
0
2
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
2
1
0
2
0
0
1
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
9
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
2
0
1
2
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
1
0
0
2
0
2
7
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
6
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
1
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
4
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
3
0
1
2
0
1
2
0
0
0
0
0
1
0
0
0
2
0
2
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
1
0
0
0
1
0
3
0
0
2
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
2
0
0
0
1
2
1
0
0
1
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
3
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
2
2
0
1
1
2
0
2
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
5
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
2
1
0
0
0
0
0
0
0
1
0
1
0
0
1
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
4
2
1
0
2
0
0
1
3
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
1
0
0
0
2
0
0
2
3
0
1
0
1
2
0
0
0
0
1
2
2
0
0
0
0
1
2
2
0
1
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
1
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
2
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
4
0
0
0
1
0
1
0
0
2
0
0
0
1
2
0
0
2
0
0
0
0
1
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
5
0
0
0
0
0
0
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
3
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
1
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
2
0
2
9
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
2
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
2
0
0
0
0
1
0
0
0
0
1
0
0
1
2
2
0
0
1
0
1
0
0
1
1
1
1
0
1
1
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
1
0
0
2
0
0
0
3
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
3
0
0
0
0
2
2
1
2
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
1
1
0
0
0
0
0
1
1
1
0
0
0
3
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
3
3
0
0
0
0
3
0
0
0
0
0
1
0
0
1
2
0
0
0
1
0
0
2
0
1
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
3
0
2
3
0
0
0
0
0
0
0
0
8
2
0
2
0
4
0
0
1
0
0
2
3
2
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
3
2
0
0
2
0
2
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
3
0
0
1
1
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
3
0
0
0
0
1
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
6
0
0
0
0
0
0
1
1
2
0
0
0
3
0
1
0
0
2
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
9
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
2
4
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
1
1
1
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
2
4
0
0
0
2
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
6
0
0
0
0
2
0
0
0
0
0
0
3
0
1
0
0
0
2
2
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
4
1
0
0
0
0
0
0
0
1
0
1
0
0
1
3
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
1
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
1
0
0
1
0
0
0
4
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
3
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
3
0
0
0
1
0
0
0
0
0
0
0
1
1
2
1
5
0
1
0
1
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
1
0
2
4
1
1
0
0
0
0
0
0
0
3
0
2
0
0
0
1
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
1
1
0
2
0
3
0
1
2
0
0
0
0
0
1
3
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
5
0
0
0
1
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
1
1
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
3
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
2
0
1
1
2
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
5
0
1
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
3
1
0
1
3
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
3
0
0
0
0
0
0
0
1
0
1
1
0
0
0
2
0
2
0
0
1
0
0
0
1
0
2
2
2
1
0
2
4
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
1
0
1
0
1
0
0
3
0
0
0
2
0
0
0
2
0
0
1
0
0
2
0
2
2
2
1
1
2
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
3
0
0
0
0
2
2
0
1
2
0
3
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
1
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
1
0
1
0
3
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
3
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
1
2
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
2
1
0
0
1
0
0
0
0
4
0
3
0
0
0
0
1
5
0
2
0
0
1
0
1
3
0
1
0
0
0
0
1
0
1
0
0
0
2
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
2
0
2
2
0
3
1
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
4
0
3
0
0
0
1
2
2
0
0
2
0
0
0
1
0
3
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
3
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
2
3
0
0
0
0
0
0
0
0
0
1
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
1
0
1
2
0
2
3
2
0
1
0
1
1
1
2
0
2
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
5
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
3
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
5
0
0
1
0
2
2
0
0
1
0
2
0
1
0
2
3
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
4
0
0
0
0
1
0
0
0
2
1
0
1
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
3
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
2
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
5
2
1
2
0
1
0
2
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
4
0
0
0
0
0
0
0
0
0
0
2
2
1
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
3
0
2
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
2
0
0
0
1
0
1
0
1
0
1
1
0
1
0
0
1
0
3
0
0
1
0
1
0
1
0
1
4
0
0
0
0
1
0
0
1
2
0
0
0
2
0
0
2
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
2
0
0
1
1
0
0
2
0
0
0
1
0
6
2
1
0
0
0
0
1
0
1
0
0
0
2
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
3
0
0
0
1
0
1
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
1
0
0
0
1
0
1
0
0
0
2
0
0
0
1
2
0
0
2
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
1
0
0
0
0
0
3
0
0
1
0
0
2
0
0
1
0
0
2
0
2
2
0
0
2
2
0
1
1
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
1
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
7
0
2
0
0
3
0
0
0
0
0
1
4
0
0
0
2
0
3
0
0
2
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
2
0
0
1
1
0
0
0
0
2
0
0
0
0
2
0
12
0
0
0
1
0
0
1
0
2
0
0
0
1
0
0
1
4
0
5
0
2
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
5
0
0
1
0
1
1
0
0
0
1
1
0
0
0
1
0
1
0
0
1
1
2
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
7
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
3
0
0
1
0
2
1
0
1
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
2
1
0
0
3
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
3
0
1
2
0
0
0
2
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
3
0
1
3
0
2
7
1
1
0
2
2
1
0
0
0
1
0
0
0
1
0
1
1
2
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
4
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
3
0
0
1
0
0
0
2
3
0
0
2
0
0
0
1
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
1
1
1
0
0
2
0
0
0
0
3
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
3
2
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
4
0
0
3
0
0
2
1
0
0
0
5
0
0
0
0
1
1
0
3
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
5
0
0
0
0
2
0
2
0
0
1
0
3
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
2
0
1
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
2
0
1
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
2
0
0
0
0
0
3
2
0
0
2
0
2
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
2
5
0
0
0
0
1
0
0
0
2
0
0
0
4
0
0
0
0
0
2
3
0
0
0
0
1
0
0
0
3
0
0
0
0
0
2
2
1
0
1
2
1
1
0
1
0
1
0
1
1
0
0
0
0
2
2
0
2
1
1
2
1
0
0
0
0
0
0
2
2
0
0
0
0
0
8
0
0
0
0
0
2
2
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
1
0
0
0
1
2
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
3
0
0
0
0
6
1
10
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
2
0
0
1
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
2
0
0
2
1
0
0
0
2
0
1
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
4
1
0
0
0
0
1
0
1
0
0
0
1
2
0
0
1
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
8
0
0
0
0
0
0
0
1
2
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
5
0
0
0
0
3
1
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
1
0
0
0
0
2
2
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
1
0
1
2
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
6
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
2
11
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
1
1
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
1
0
0
1
2
0
1
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
2
0
3
2
0
0
0
0
0
0
0
0
3
3
1
0
0
2
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
8
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
6
1
0
3
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
3
1
0
4
0
0
0
0
0
0
0
0
2
1
1
0
0
2
2
2
1
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
1
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
1
1
0
0
0
1
0
0
0
3
3
0
0
1
0
0
2
1
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
3
1
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
1
0
0
0
0
1
0
2
2
0
2
0
0
0
3
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
3
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
1
2
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
2
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
1
0
2
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
1
0
1
0
0
3
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
1
2
0
0
1
0
0
2
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
4
0
2
2
0
2
2
2
1
0
1
0
0
1
0
3
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
1
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
6
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
2
2
0
1
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
4
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
2
0
1
0
0
2
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
1
0
3
0
0
0
0
0
1
1
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
1
0
0
0
3
0
0
2
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
2
0
2
0
0
0
1
0
2
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
1
0
1
0
1
0
2
0
2
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
5
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
1
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
3
4
0
1
0
0
0
0
1
0
0
0
0
0
1
2
0
3
0
2
1
0
2
0
0
2
2
2
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
4
0
0
0
1
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
2
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
2
1
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
5
0
1
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
2
1
0
0
0
0
1
2
0
0
0
0
0
0
0
1
1
0
3
0
0
2
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
3
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
2
0
0
7
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
3
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
2
0
2
0
0
0
0
1
1
1
1
0
2
1
2
0
0
0
2
0
0
2
0
0
1
1
0
0
1
5
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
1
0
2
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
1
0
0
0
1
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
3
0
0
0
0
1
1
0
0
0
1
0
0
0
6
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
6
1
1
0
0
1
0
0
0
0
2
0
1
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
1
0
0
0
1
0
2
5
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
4
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
3
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
2
2
1
0
0
1
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
1
1
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
2
0
4
3
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
5
0
1
3
0
2
0
6
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
2
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
4
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
2
0
0
4
0
2
0
1
0
1
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
1
2
0
1
2
0
2
3
0
1
0
0
0
1
1
0
0
0
0
2
1
0
3
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
6
0
0
0
0
0
0
0
2
0
2
0
2
0
2
2
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
3
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
3
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
2
0
1
0
1
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
3
0
0
2
0
0
2
0
0
0
0
0
0
2
2
1
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
2
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
4
0
0
0
1
0
0
2
1
0
0
1
0
0
4
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
2
2
0
1
1
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
1
1
1
2
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
7
0
1
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
2
0
0
0
0
0
2
1
3
2
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
1
0
3
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
2
1
0
0
0
2
0
1
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
10
0
0
0
0
3
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
3
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
3
0
1
2
0
0
0
2
0
1
0
2
2
0
0
0
0
0
2
0
0
2
0
1
0
1
0
1
0
2
0
2
0
1
2
0
0
1
0
0
0
0
2
0
0
2
0
0
0
5
0
0
0
0
0
0
0
2
0
0
0
2
0
1
2
0
0
2
3
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
6
0
1
0
1
0
0
0
0
1
0
0
3
2
0
0
1
0
2
0
0
0
2
0
0
0
0
2
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
5
0
0
0
0
0
0
0
0
0
0
1
0
0
3
1
1
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
3
4
0
0
1
0
0
1
2
1
0
0
0
0
0
3
1
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
2
2
0
2
0
0
1
0
1
0
2
0
2
0
0
0
0
0
0
1
0
0
0
1
4
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
2
1
1
0
0
2
1
0
0
1
0
2
2
0
0
0
0
0
2
1
3
1
0
0
0
0
1
1
1
0
0
0
0
0
4
0
1
0
1
2
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
3
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
3
2
0
0
0
1
0
0
0
0
0
1
0
1
1
6
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
3
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
2
1
0
0
0
4
2
3
0
2
4
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
3
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
2
0
2
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
2
2
2
2
0
2
2
0
2
0
2
0
3
1
2
2
0
0
0
0
4
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
4
0
1
0
3
0
2
1
2
1
0
4
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
1
2
1
0
1
0
0
2
0
0
0
0
1
0
1
2
2
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
3
0
0
0
3
0
1
0
0
0
2
0
0
4
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
2
2
0
0
0
0
3
0
0
0
1
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
1
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
1
1
0
0
1
0
1
2
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
4
0
0
0
0
0
1
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
1
0
0
2
0
1
5
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
2
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
1
2
3
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
3
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
3
0
1
0
0
0
2
0
1
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
2
1
0
1
1
0
0
0
1
3
0
1
2
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
1
0
0
0
0
2
0
3
2
0
1
0
0
0
0
0
0
1
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
1
1
0
2
0
0
1
2
0
0
0
0
0
2
0
4
0
0
3
0
2
0
0
0
1
0
7
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
1
0
0
0
2
1
0
2
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
2
0
0
0
0
1
0
0
2
0
0
0
1
2
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
3
1
2
0
1
0
0
0
0
0
1
2
0
0
0
2
5
2
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
2
0
1
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
17
0
0
1
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
1
0
3
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
1
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
4
1
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
2
1
1
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
1
0
0
1
2
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
1
0
0
0
0
0
0
0
3
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
3
0
3
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
2
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
2
0
0
1
0
1
1
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
2
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
1
0
1
2
1
1
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
2
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
2
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
1
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
4
0
0
0
1
0
0
0
0
0
1
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
2
3
0
1
1
0
0
0
2
2
3
0
0
2
0
0
0
0
1
1
0
0
0
1
0
0
0
2
0
0
0
2
0
0
5
0
1
0
0
1
2
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
2
0
1
0
0
0
3
0
0
0
3
1
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
1
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
1
1
0
1
0
1
0
2
0
1
0
1
0
0
0
1
0
2
0
1
0
0
0
1
0
0
1
1
0
2
0
2
0
1
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
2
2
2
0
0
2
2
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
2
2
5
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
1
3
0
0
0
0
0
0
0
0
0
0
2
0
2
4
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
2
0
1
0
0
0
2
0
0
0
1
0
2
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
6
0
4
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
1
0
0
0
3
0
0
0
2
0
0
1
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
2
0
3
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
4
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
1
0
1
0
2
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
2
0
5
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
4
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
1
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
5
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
3
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
1
0
0
2
1
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
2
0
0
2
0
0
3
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
2
0
2
0
0
0
1
0
2
0
0
0
2
0
1
1
0
0
0
2
0
5
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
2
1
3
0
2
0
1
2
0
0
0
0
1
0
0
1
0
0
0
0
0
2
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
3
0
3
0
0
0
0
0
3
0
1
1
0
0
0
0
1
0
0
1
2
0
0
1
0
1
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
4
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
2
1
0
1
0
1
2
0
0
0
1
4
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
4
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
3
2
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
1
0
1
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
2
2
0
2
0
0
0
0
4
2
0
2
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
3
2
0
0
0
0
0
5
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
4
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
1
0
0
1
0
0
3
2
0
2
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
3
0
2
0
0
1
0
2
1
0
0
0
0
0
2
0
0
0
0
1
5
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
2
1
2
0
0
1
2
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
1
1
3
1
0
0
1
0
0
2
0
2
0
2
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
2
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
5
3
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
1
2
1
0
0
0
0
1
0
0
0
4
1
0
0
1
0
0
2
0
0
2
0
4
0
0
0
2
0
0
0
2
1
4
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
1
0
0
0
0
2
6
1
0
0
0
0
0
2
0
0
0
2
3
0
1
0
0
5
0
0
3
0
3
0
0
2
0
0
1
0
0
0
0
0
3
2
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
4
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
2
0
1
0
0
0
2
0
0
0
0
0
0
2
2
1
2
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
2
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
3
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
9
1
0
0
0
2
0
0
2
0
0
0
0
0
1
1
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
3
0
2
0
1
1
1
0
0
0
0
1
0
0
0
0
0
2
0
4
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
2
0
2
0
0
0
0
0
1
1
0
0
1
0
0
0
2
0
0
1
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
2
2
0
1
0
2
0
0
0
1
0
0
0
1
2
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
5
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
2
1
2
3
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
5
0
0
0
0
1
0
0
3
0
2
0
0
0
0
4
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
2
2
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
4
0
0
2
0
2
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
3
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
2
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
5
0
0
0
0
6
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
4
0
1
2
2
0
0
1
0
0
2
0
0
0
0
0
0
0
2
2
0
0
1
2
0
0
0
0
0
0
2
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
2
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
5
0
0
0
0
0
1
2
2
0
1
0
0
0
1
0
0
0
0
2
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
3
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
1
1
0
0
0
0
1
2
0
0
2
2
0
0
0
0
1
0
0
2
0
0
1
1
2
0
1
0
0
3
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
5
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
4
0
0
1
2
0
2
2
0
0
1
0
0
0
2
0
0
1
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
4
0
1
0
2
0
0
3
0
0
2
0
0
0
5
0
0
1
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
3
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
1
0
0
0
0
2
0
1
0
0
0
3
1
1
2
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
1
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
2
0
0
0
0
2
0
0
0
0
2
1
0
0
1
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
1
0
1
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
2
5
1
0
0
0
0
0
0
0
0
1
3
0
0
0
0
1
1
0
0
0
0
0
0
0
2
2
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
1
0
1
0
0
0
2
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
1
4
0
3
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
3
0
2
0
0
0
0
2
4
0
1
0
2
2
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
2
4
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
1
0
0
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
17
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
2
0
0
1
0
2
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
1
1
0
0
4
2
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
1
1
2
1
0
0
0
2
0
0
0
0
2
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
2
0
1
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
4
1
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
1
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
3
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
2
0
2
0
0
1
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
1
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
1
0
3
0
1
0
0
4
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
1
0
1
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
3
0
0
3
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
1
0
0
1
3
0
0
0
0
0
2
0
2
0
0
0
0
3
0
0
2
0
2
0
0
0
2
0
0
0
0
0
2
0
3
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
2
1
0
0
0
0
2
0
1
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
1
3
0
0
2
2
2
0
2
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
1
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
3
1
0
0
0
2
0
2
0
0
0
0
0
0
1
1
2
0
0
1
2
1
0
0
0
2
3
1
2
1
3
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
4
0
0
0
0
3
1
2
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
2
0
0
0
0
0
1
1
0
2
2
0
1
0
2
0
0
4
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
2
0
0
4
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
3
0
0
0
0
2
0
3
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
8
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
6
0
0
0
0
2
0
0
0
1
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
4
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
2
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
1
1
0
0
1
0
0
0
2
0
0
0
0
3
0
0
2
0
0
0
0
1
1
0
2
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
4
0
0
0
1
0
2
0
0
1
3
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
2
0
1
1
0
0
5
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
1
2
0
2
0
0
0
0
2
0
0
2
0
4
0
0
3
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
3
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
1
1
0
0
0
0
0
5
0
4
0
0
0
0
2
0
0
0
0
2
0
7
0
3
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
3
0
0
0
2
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
3
0
0
0
0
0
0
2
2
0
0
0
3
0
0
0
0
0
0
1
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
3
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
2
1
0
0
0
1
0
2
0
5
0
1
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
1
1
3
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
8
0
2
0
0
0
0
0
1
0
1
0
1
0
0
2
1
0
0
4
0
2
0
3
0
0
1
0
0
0
0
1
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
3
0
3
0
0
1
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
2
2
2
1
0
0
0
0
0
0
1
0
0
0
2
1
0
2
1
3
0
0
0
1
0
0
0
0
0
0
0
3
1
2
1
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
2
0
1
2
0
3
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
2
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
2
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
3
0
0
0
0
1
0
0
0
0
2
1
3
0
2
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
3
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
5
2
0
0
0
1
0
1
0
1
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
2
1
4
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
1
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
1
0
0
0
2
0
0
1
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
3
1
0
3
1
0
2
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
1
0
2
0
2
3
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
2
1
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
1
1
2
0
0
1
0
2
0
0
0
0
1
0
1
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
1
2
0
0
0
2
0
0
1
0
0
0
0
0
0
2
1
0
1
5
0
1
0
0
2
2
3
0
0
0
0
0
0
0
1
11
0
0
1
0
0
0
1
0
1
0
0
4
2
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
2
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
2
3
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
5
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
1
2
0
0
2
0
0
3
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
5
0
1
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
9
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
2
5
0
1
1
3
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
3
0
2
0
0
1
1
0
0
0
0
0
0
0
3
2
1
0
0
0
2
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
3
0
0
0
1
0
0
2
0
0
0
1
1
1
0
0
1
0
0
2
13
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
1
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
3
1
1
0
0
0
1
0
0
0
0
0
2
3
0
0
1
2
0
0
2
0
3
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
2
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
1
3
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
1
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
2
0
1
0
2
0
0
0
1
2
2
0
0
0
0
1
1
0
0
1
0
0
0
0
2
0
0
0
1
1
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
2
0
1
0
0
0
5
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
2
0
2
2
0
4
0
0
0
1
3
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
6
1
0
0
0
0
0
0
0
0
0
2
4
1
0
0
0
0
0
0
0
8
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
4
1
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
2
1
0
0
0
1
0
0
2
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
7
0
0
0
0
0
2
0
0
1
1
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
3
0
0
0
0
2
0
0
7
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
5
0
1
0
0
0
0
3
1
0
0
2
0
0
2
0
0
1
3
2
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
1
2
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
2
0
2
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
2
0
1
0
3
3
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
2
0
0
0
8
2
0
3
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
5
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
2
1
1
0
0
0
2
1
1
0
0
0
0
0
0
1
2
2
0
1
1
0
1
0
1
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
2
3
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
2
1
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
3
0
0
0
0
0
0
2
1
0
0
2
0
1
2
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
3
0
0
0
0
1
0
0
0
0
2
0
0
0
1
2
0
1
0
0
1
2
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
2
0
0
2
0
0
2
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
2
0
1
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
4
2
1
0
0
0
2
2
2
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
1
0
2
0
0
1
0
0
0
0
5
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
6
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
1
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
6
0
0
0
0
0
0
0
0
0
0
2
0
1
0
3
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
7
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
2
1
0
0
1
0
0
0
0
0
1
3
0
0
0
0
0
0
1
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
2
0
0
2
0
0
0
3
1
0
0
0
1
0
2
0
0
0
0
0
7
0
0
1
0
2
0
2
0
5
0
0
0
3
0
0
1
0
3
4
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
3
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
10
0
0
0
0
0
3
0
0
0
2
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
3
0
0
2
0
0
2
2
1
0
2
1
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
1
0
0
0
0
2
0
1
0
0
0
0
0
3
1
0
0
1
0
2
2
0
3
0
0
0
2
0
0
0
0
1
0
1
2
2
1
0
0
1
0
0
2
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
3
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
3
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
5
0
3
0
0
0
1
0
0
0
0
0
0
0
2
0
4
1
0
1
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
2
0
3
0
1
0
0
0
0
0
6
3
0
0
1
0
1
1
0
0
1
0
0
0
0
0
1
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
1
0
5
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
6
0
2
1
0
0
0
1
0
1
0
0
2
1
0
0
0
1
1
0
2
1
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
1
0
0
0
2
0
2
1
0
0
1
2
0
0
0
2
3
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
1
1
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
5
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
1
2
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
1
0
0
1
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
3
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
12
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
1
2
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
2
0
1
0
0
0
0
0
1
2
0
1
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
1
1
2
0
0
0
0
4
2
2
1
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
1
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
3
2
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
2
0
0
2
0
0
0
0
1
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
1
0
0
0
0
2
0
0
0
0
1
2
0
0
0
3
2
0
0
0
0
0
1
0
0
0
0
0
0
2
1
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
1
0
1
2
1
3
1
0
0
0
0
0
1
0
0
0
2
1
0
5
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
1
1
1
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
3
0
0
0
2
2
0
1
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
1
2
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
1
0
7
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
1
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
8
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
1
0
1
0
3
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
2
2
0
0
0
0
3
0
1
1
0
0
0
0
0
2
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
1
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
3
0
2
4
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
1
0
0
1
0
0
2
4
1
0
0
2
1
0
0
1
0
3
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
3
1
0
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
2
0
4
1
0
0
1
2
1
0
0
0
3
2
1
2
0
0
2
0
0
0
0
0
0
1
0
5
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
3
2
0
0
0
0
0
0
0
0
2
2
1
2
0
0
0
0
0
0
0
1
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
5
0
0
0
2
0
0
0
0
1
0
2
2
2
2
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
3
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
3
0
0
0
0
0
2
0
2
0
1
1
0
0
0
2
0
0
0
1
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
3
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
2
0
0
1
2
0
0
4
0
0
0
0
0
0
4
0
0
2
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
3
1
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
3
0
0
1
3
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
1
0
0
1
2
0
0
1
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
5
0
2
2
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
3
1
0
0
2
0
1
2
0
0
2
0
0
0
2
0
0
0
0
0
0
2
3
0
2
0
1
0
0
0
0
0
2
3
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
3
0
1
2
0
0
0
0
0
2
2
0
0
2
1
1
0
0
0
1
4
0
2
0
0
0
0
0
0
0
2
0
3
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
1
3
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
3
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
1
0
1
0
1
0
0
0
0
0
0
0
1
3
1
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
4
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
1
0
0
3
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
1
4
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
4
1
1
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
4
0
2
0
1
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
3
2
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
3
1
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
3
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
6
1
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
3
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
1
5
0
0
0
1
0
2
1
0
0
5
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
7
1
3
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
8
0
1
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
1
0
1
0
0
2
0
0
0
0
0
0
0
3
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
1
2
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
2
2
0
0
1
1
0
2
0
0
0
0
0
2
0
0
0
2
2
0
2
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
3
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
7
0
0
0
0
0
1
1
0
4
2
0
3
0
0
0
0
0
0
0
1
1
0
0
2
0
0
1
1
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
1
2
2
2
0
0
0
0
2
1
0
1
0
0
0
0
0
0
2
2
1
0
0
0
1
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
3
1
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
1
0
0
2
0
1
0
2
0
0
0
2
1
1
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
1
2
0
0
2
1
1
0
0
0
0
1
1
0
2
0
0
1
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
2
1
0
0
0
1
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
2
0
0
0
2
4
0
0
0
0
1
1
0
0
2
2
2
0
1
0
1
1
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
1
2
0
0
1
0
0
0
2
2
0
0
1
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
3
1
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
2
0
1
3
0
0
2
0
5
0
0
0
0
0
1
0
0
0
0
3
0
0
1
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
2
0
0
2
2
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
2
0
2
0
0
2
0
0
1
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
4
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
2
1
0
0
0
1
2
0
0
0
0
2
0
0
0
0
3
2
0
0
0
0
2
0
0
1
0
5
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
4
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
1
0
2
1
1
3
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
2
0
0
0
0
1
0
3
3
0
0
0
0
0
0
0
2
0
0
1
0
2
2
0
0
5
3
0
0
0
0
2
2
0
1
0
0
1
0
0
0
0
0
2
0
1
0
0
0
1
0
0
1
4
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
5
1
0
0
0
0
0
0
0
0
1
0
0
2
0
1
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
4
0
9
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
1
0
0
1
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
2
0
0
0
2
1
0
0
1
0
0
2
1
0
0
0
0
0
0
0
2
2
0
2
0
0
0
1
0
2
0
0
2
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
1
2
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
1
2
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
2
3
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
1
0
4
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
1
2
0
6
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
2
1
0
0
0
0
0
0
3
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
3
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
2
2
0
0
1
1
2
0
0
0
1
0
2
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
3
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
2
4
0
0
0
0
0
0
5
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
1
0
0
1
0
0
2
1
1
0
0
0
1
2
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
7
0
0
0
0
1
4
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
3
2
0
3
0
0
0
0
2
0
1
0
0
2
0
3
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
1
0
3
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
3
0
0
1
1
0
1
2
1
0
0
3
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
2
0
0
1
2
0
0
4
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
6
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
1
0
2
1
0
0
0
1
0
2
0
0
1
2
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
1
2
0
0
0
0
0
0
2
2
0
0
2
1
0
0
0
1
0
0
0
2
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
2
1
0
0
3
0
0
0
0
0
0
0
1
2
0
0
2
4
0
1
0
0
0
0
2
1
0
0
3
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
1
1
0
0
0
0
0
0
4
0
0
0
0
2
1
0
0
0
3
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
2
0
0
0
0
0
0
1
0
0
2
0
1
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
4
0
2
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
3
0
0
0
0
1
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
1
0
2
2
2
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
2
1
0
0
0
0
2
2
0
1
1
2
0
2
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
2
2
0
0
4
0
0
1
0
0
0
0
2
1
0
0
0
2
0
1
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
3
0
0
0
0
0
3
2
1
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
1
0
0
0
0
2
1
0
0
0
1
0
0
0
2
2
1
4
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
2
1
0
0
0
1
2
0
1
0
0
2
0
0
2
3
0
0
0
2
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
1
1
0
5
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
3
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
3
1
0
0
0
0
0
0
0
2
3
0
0
2
0
0
1
0
1
0
0
0
1
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
1
2
0
2
2
0
0
1
0
0
0
3
0
3
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
3
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
1
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
2
0
0
0
0
2
1
0
0
0
1
0
1
0
2
0
0
0
0
1
3
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
1
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
4
0
0
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
2
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
1
0
2
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
4
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
2
0
2
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
1
1
0
0
2
1
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
5
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
2
0
2
0
2
0
0
1
0
0
1
0
2
0
4
0
1
0
0
0
4
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
3
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
3
0
0
0
2
0
3
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
2
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
2
0
0
4
2
0
0
0
0
2
0
0
0
4
0
1
0
0
1
0
0
0
0
1
0
3
2
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
3
0
1
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
4
1
2
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
3
0
0
0
0
0
0
1
2
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
1
0
3
0
0
0
0
0
2
0
0
5
1
0
0
0
0
4
0
0
0
1
0
0
3
2
2
0
1
0
1
0
0
2
2
3
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
1
1
1
0
1
1
1
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
1
0
0
0
0
0
0
3
1
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
2
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
2
0
0
5
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
3
1
1
3
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
3
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
10
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
2
1
0
0
0
0
2
0
0
0
0
1
1
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
2
1
0
1
0
2
0
0
0
1
0
0
2
0
2
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
1
0
0
2
0
0
0
2
0
0
0
0
0
3
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
6
2
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
2
1
1
2
0
2
0
0
1
4
0
0
0
1
0
0
0
0
0
2
0
4
0
0
0
0
1
2
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
12
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
2
0
2
1
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
1
0
2
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
1
0
7
1
0
0
4
0
0
1
0
3
0
2
0
3
0
0
2
3
0
0
0
1
0
0
0
2
0
0
0
1
0
2
0
0
0
0
1
0
2
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
2
2
2
1
0
0
0
0
3
0
2
0
0
0
1
0
0
4
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
1
2
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
1
0
0
0
0
0
1
1
4
1
0
0
4
0
1
1
1
0
2
0
0
0
0
0
4
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
1
0
0
5
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
4
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
4
0
0
0
0
1
0
0
0
0
1
2
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
2
0
2
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
1
4
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
3
0
0
4
0
0
1
0
0
0
0
0
3
0
0
0
0
2
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
3
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
4
0
1
0
0
0
0
0
0
1
2
0
1
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
6
0
0
2
0
0
0
0
0
2
0
3
0
2
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
2
2
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
1
0
11
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
1
0
4
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
3
0
0
0
1
0
0
0
0
0
3
2
1
0
0
0
0
1
2
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
1
0
1
0
2
0
0
0
1
5
0
2
0
2
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
1
2
0
2
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
5
0
2
0
1
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
1
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
4
1
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
3
1
1
0
0
0
0
0
0
2
3
0
0
2
0
0
1
0
0
0
0
1
0
0
2
2
1
0
0
1
0
2
0
0
0
1
0
0
1
1
0
0
1
2
0
0
0
5
0
0
0
4
0
0
0
0
1
0
0
2
0
1
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
2
2
0
0
1
0
0
2
0
0
2
1
2
0
0
3
0
0
0
0
0
0
0
0
1
0
5
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
3
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
1
0
1
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
4
0
1
2
1
0
0
0
1
2
1
2
2
0
0
3
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
2
0
2
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
1
2
0
1
2
2
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
1
2
0
1
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
5
0
0
0
0
0
1
2
0
1
0
1
0
0
0
0
2
0
0
0
1
0
0
1
0
0
2
0
0
1
0
1
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
2
0
3
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
1
1
0
0
0
1
1
3
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
3
0
0
1
0
0
0
0
0
2
0
1
0
0
0
4
2
0
1
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
2
1
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
1
0
0
0
2
1
0
0
0
1
0
2
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
2
0
0
2
1
0
2
0
0
0
0
0
2
2
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
1
0
0
0
0
0
0
0
5
5
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
3
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
2
0
0
2
1
0
0
0
0
0
0
2
1
3
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
1
0
0
0
2
0
1
0
1
1
0
0
1
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
1
0
2
1
0
0
0
0
0
0
2
0
3
2
1
0
0
0
1
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
2
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
4
1
0
1
0
1
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
4
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
1
1
1
0
0
0
0
0
0
1
1
4
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
3
2
1
1
2
0
2
1
1
0
1
1
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
2
1
2
0
0
0
1
2
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
3
1
0
0
1
1
0
0
0
0
0
4
0
0
2
9
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
1
2
2
0
0
0
0
2
0
0
0
2
1
2
0
2
2
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
6
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
2
2
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
5
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
3
2
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
3
0
0
1
0
2
0
0
1
0
2
2
0
0
0
2
0
0
0
1
0
5
0
0
1
0
0
0
1
0
0
0
6
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
5
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
3
0
1
0
0
0
0
3
0
0
0
0
2
0
0
0
0
1
0
1
4
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
3
1
2
1
0
7
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
5
2
0
0
0
0
1
2
1
0
2
0
0
1
0
0
0
2
0
0
0
0
0
5
2
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
1
5
0
0
0
1
1
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
2
2
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
1
5
0
0
2
0
0
0
0
2
0
0
0
2
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
5
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
2
0
2
2
1
0
2
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
3
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
4
0
8
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
4
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
3
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
1
0
2
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
2
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
15
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
2
0
0
1
0
2
0
0
2
2
0
0
0
0
0
2
2
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
1
1
2
0
0
0
1
2
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
1
0
0
0
0
2
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
2
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
1
2
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
1
2
0
0
0
0
0
0
0
1
0
0
1
0
2
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
1
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
3
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
1
0
2
0
0
0
0
1
0
0
0
1
2
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
3
2
0
0
1
0
0
0
2
0
0
0
3
0
1
0
0
0
0
4
2
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
1
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
2
1
0
2
2
0
0
1
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
5
1
0
0
2
3
0
0
2
0
0
1
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
1
0
2
0
0
0
0
2
2
0
1
1
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
1
2
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
3
3
0
0
0
7
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
1
1
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
3
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
3
0
0
2
2
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
5
2
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
1
1
0
0
0
1
1
2
0
1
1
1
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
2
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
1
1
0
0
0
0
2
0
0
1
1
0
1
0
0
0
0
0
7
0
1
0
0
1
0
1
0
0
0
1
0
0
2
0
0
2
0
0
1
0
0
0
0
1
1
3
0
0
0
0
0
0
0
0
2
3
2
0
0
2
1
0
2
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
1
0
0
1
2
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
2
0
2
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
3
1
0
2
0
0
2
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
1
2
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
10
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
3
4
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
7
0
4
0
0
0
0
0
0
1
1
0
1
0
0
0
6
0
0
2
0
1
0
0
0
0
0
1
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
1
0
1
1
0
0
0
0
1
0
2
2
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
3
0
1
3
0
0
0
0
0
1
0
2
2
0
2
0
0
0
0
0
1
0
2
0
1
0
3
0
0
0
0
7
2
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
2
0
2
0
0
0
0
0
0
0
4
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
2
1
2
1
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
2
0
0
2
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
1
2
0
0
0
3
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
8
0
5
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
2
3
0
0
2
0
2
2
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
3
2
0
0
2
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
1
1
0
0
0
2
0
0
0
0
2
0
0
2
2
2
0
1
0
1
0
0
1
1
2
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
2
0
0
0
1
1
0
1
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
2
1
1
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
3
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
2
1
2
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
5
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
2
1
1
1
0
0
0
1
0
3
0
2
0
0
4
0
0
2
2
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
4
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
1
7
0
0
0
0
0
3
0
0
0
0
2
1
1
0
0
0
2
0
0
0
0
0
0
2
1
0
2
0
2
1
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
1
0
2
0
3
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
2
0
2
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
3
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
3
0
2
0
0
0
1
1
0
1
0
0
0
0
0
0
0
5
0
1
0
2
0
0
2
0
0
0
0
0
1
0
5
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
3
0
0
2
0
0
1
0
0
0
1
0
2
0
8
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
5
0
1
0
2
0
0
0
0
0
0
0
0
1
2
1
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
2
0
0
7
0
2
2
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
3
0
1
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
1
2
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
6
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
2
0
0
2
0
0
2
0
0
0
1
0
0
0
1
0
0
1
2
2
0
0
0
4
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
2
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
1
0
1
2
0
1
0
0
0
0
0
1
0
1
1
0
0
0
3
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
2
4
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
5
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
2
1
0
0
0
0
3
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
1
1
0
0
2
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
3
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
4
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
3
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
5
0
0
0
1
0
0
0
0
0
7
7
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
1
0
0
0
0
3
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
2
0
0
0
2
0
2
2
0
1
0
1
2
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
1
0
1
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
2
0
0
0
2
0
0
0
1
0
0
2
2
0
2
0
0
1
0
1
0
0
1
1
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
5
2
0
0
0
2
2
1
0
0
3
0
0
0
2
0
0
3
0
1
0
0
2
2
0
1
0
0
0
0
0
0
1
2
0
0
2
1
0
2
0
0
0
0
0
0
0
0
1
2
2
0
1
0
0
0
0
2
2
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
6
0
0
1
0
0
0
2
0
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
2
1
2
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
5
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
4
0
1
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
6
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
6
0
0
0
0
0
1
1
1
0
0
0
2
1
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
8
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
2
0
0
0
0
2
2
0
0
0
1
0
0
2
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
3
0
0
0
1
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
1
0
1
0
0
0
1
5
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
1
0
2
0
0
1
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
3
0
4
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
1
0
0
2
0
3
0
0
1
0
0
3
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
5
1
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
5
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
2
0
2
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
1
1
2
0
0
0
0
2
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
1
0
0
2
1
0
0
0
3
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
2
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
5
0
0
0
0
2
1
0
1
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
1
0
1
0
0
3
0
0
0
1
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
1
4
0
0
0
0
3
0
5
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
3
0
0
1
0
0
0
1
1
2
0
0
0
0
0
0
0
1
0
3
0
1
0
0
0
4
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
2
2
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
4
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
2
3
0
1
1
0
0
0
2
0
0
2
2
0
0
6
1
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
1
0
2
1
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
2
0
0
1
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
2
0
0
0
0
0
0
0
1
1
0
0
2
0
3
0
0
0
0
0
0
2
0
5
0
0
0
0
0
7
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
1
1
0
0
1
0
0
2
0
0
0
1
0
0
3
0
1
0
0
0
0
0
0
0
0
0
9
0
0
2
0
1
0
1
1
1
0
0
0
0
0
0
1
1
1
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
3
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
2
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
1
0
0
1
2
1
3
0
0
0
0
0
0
1
0
0
0
1
2
0
1
0
1
0
1
0
4
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
2
1
2
0
0
0
2
2
1
2
0
0
0
0
3
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
1
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
1
0
0
0
2
0
2
0
1
2
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
2
0
1
1
0
2
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
2
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
2
0
0
0
0
0
0
1
0
2
0
1
1
0
1
0
2
2
1
0
0
0
0
0
0
0
0
1
0
0
1
1
10
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
1
2
0
1
2
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
1
2
0
0
0
0
0
1
0
1
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
3
1
0
0
2
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
1
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
2
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
2
0
0
1
0
1
0
0
0
0
1
0
0
0
0
2
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
1
0
0
4
2
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
2
0
0
3
0
1
0
0
0
0
0
0
0
1
0
0
1
0
3
0
1
0
0
0
0
2
1
0
0
0
1
0
0
0
3
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
1
1
0
0
0
0
0
3
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
9
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
1
2
0
0
0
0
1
2
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
3
0
1
0
2
0
0
1
1
0
0
1
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
3
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
1
0
3
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
2
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
4
0
0
0
2
1
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
1
2
0
0
1
1
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
2
0
0
1
0
1
3
0
2
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
1
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
2
0
1
4
0
2
0
2
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
2
2
0
0
2
2
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
3
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
3
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
2
3
0
0
0
2
0
0
0
0
0
1
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
1
0
0
0
0
1
2
0
0
3
2
0
0
0
0
2
0
0
0
0
2
2
1
1
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
7
0
2
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
2
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
2
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
2
2
1
0
0
3
2
0
0
0
2
0
0
0
3
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
3
1
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
1
0
0
0
0
1
1
0
3
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
2
3
3
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
6
2
0
0
1
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
4
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
1
0
1
1
2
2
0
1
2
7
1
0
1
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
3
5
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
2
2
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
2
0
0
0
0
0
1
0
0
1
0
0
0
1
0
2
0
0
0
0
0
2
0
0
1
3
0
0
0
1
2
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
2
0
0
0
2
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
2
0
0
2
2
0
1
0
0
0
0
0
2
0
2
0
0
1
1
1
0
0
0
0
2
0
0
0
0
0
0
5
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
1
0
0
1
2
0
0
1
0
0
2
0
1
0
1
0
3
2
0
0
1
2
2
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
2
0
0
0
0
3
0
0
0
1
2
0
0
4
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
2
0
0
1
0
0
0
0
0
2
0
4
0
2
3
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
3
2
0
0
0
0
0
2
0
0
1
1
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
2
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
2
0
2
0
0
0
0
1
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
2
0
2
0
0
1
1
0
0
0
1
0
1
0
2
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
2
1
2
0
0
0
1
1
1
1
0
1
2
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
4
0
0
3
2
0
0
0
0
0
0
0
1
2
0
1
0
3
0
2
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
3
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
2
1
0
3
0
0
2
0
0
4
0
0
0
0
2
2
0
1
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
2
1
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
1
0
0
1
1
0
1
2
0
0
0
1
0
0
0
0
0
0
8
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
2
2
1
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
3
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
3
0
6
0
0
0
0
0
0
0
0
0
0
2
1
1
0
1
1
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
1
2
0
0
0
0
3
0
0
0
2
0
1
0
2
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
3
1
4
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
2
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
2
0
1
1
1
1
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
6
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
5
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
2
0
1
5
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
5
0
0
2
0
0
0
0
2
1
2
3
0
1
0
0
0
0
0
1
1
0
0
0
0
0
2
3
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
2
0
0
1
0
1
0
0
0
1
0
0
2
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
2
0
0
2
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
1
3
2
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
2
2
1
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
4
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
4
0
0
0
0
0
3
0
2
0
1
0
0
0
0
0
0
3
1
0
0
2
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
1
0
2
0
0
0
0
0
5
1
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
3
2
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
1
0
2
0
1
1
0
1
0
2
1
0
0
0
1
0
1
2
0
0
0
0
2
0
0
0
0
0
0
8
5
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
2
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
2
2
3
0
0
1
0
2
0
0
1
2
0
1
0
2
0
0
3
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
1
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
5
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
2
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
2
2
0
0
0
0
2
0
3
3
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
4
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
2
2
2
1
0
0
0
1
0
0
0
0
2
1
0
0
5
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
4
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
3
0
2
0
0
1
0
1
0
1
0
2
0
0
0
1
0
2
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
2
1
0
0
1
0
2
0
3
0
0
0
0
1
0
1
1
1
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
1
1
0
1
0
2
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
2
4
1
3
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
2
0
0
2
2
2
2
0
0
0
0
7
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
2
0
1
2
3
0
0
0
0
0
0
1
0
0
0
0
0
4
0
1
0
2
0
0
1
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
1
0
1
0
0
0
3
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
1
2
0
0
0
0
0
2
0
0
1
1
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
2
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
2
0
0
0
0
2
1
0
0
0
0
2
2
2
2
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
1
5
0
0
1
0
3
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
3
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
1
0
0
0
2
0
0
0
2
0
0
1
0
0
0
6
0
0
0
1
0
0
0
0
0
0
3
0
0
1
2
1
1
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
2
2
0
0
0
0
6
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
2
0
1
1
0
0
0
2
0
0
0
1
0
2
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
2
2
2
0
1
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
3
2
0
0
0
2
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
1
0
2
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
3
1
2
2
4
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
2
2
2
0
0
0
0
1
2
2
0
0
2
2
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
2
5
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
1
0
2
0
0
1
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
2
2
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
2
0
0
0
0
1
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
3
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
3
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
1
0
1
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
1
1
0
0
0
1
0
0
2
0
0
1
0
0
2
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
2
2
1
0
1
0
1
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
3
0
0
2
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
5
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
1
0
3
0
0
0
3
0
0
0
0
0
0
2
0
2
0
1
0
2
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
5
2
0
1
0
2
0
2
0
0
0
0
0
2
0
0
0
3
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
2
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
3
0
0
0
0
0
4
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
2
0
1
0
0
0
0
0
0
0
0
0
0
5
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
1
0
0
0
0
2
3
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
5
0
0
1
2
0
1
0
0
1
0
1
1
0
1
2
0
3
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
2
0
0
0
0
1
1
0
1
5
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
1
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
1
2
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
4
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
3
0
0
0
0
0
2
0
1
0
0
1
0
2
0
0
0
0
0
0
1
2
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
2
0
1
1
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
6
0
0
0
1
0
0
0
2
1
0
0
2
0
0
0
1
0
4
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
8
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
9
0
1
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
2
0
1
1
0
0
0
1
0
0
0
0
2
2
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
2
0
2
0
0
0
0
1
0
3
1
0
0
0
0
0
0
2
0
2
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
3
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
3
1
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
6
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
2
0
0
1
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
2
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
2
0
0
1
0
2
0
1
2
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
6
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
4
1
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
1
1
2
2
1
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
4
7
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
1
0
0
2
0
0
0
9
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
1
0
0
1
2
0
0
0
1
0
0
0
0
1
0
2
0
1
2
1
0
0
2
0
0
0
0
1
1
0
0
0
1
1
0
1
0
0
1
0
1
0
0
0
1
8
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
3
2
2
0
1
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
2
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
2
2
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
2
1
0
1
1
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
3
0
0
3
4
1
0
0
4
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
5
0
3
0
0
0
0
0
0
1
0
1
1
0
0
0
0
2
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
2
0
0
1
0
0
0
2
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
1
0
1
0
4
0
0
0
2
1
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
4
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
2
0
0
0
0
1
0
0
1
0
0
0
1
2
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
4
0
0
2
0
1
0
2
2
2
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
3
1
0
0
0
0
0
0
1
0
0
0
0
7
0
2
0
2
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
2
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
2
1
0
0
2
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
2
0
2
0
0
1
0
1
0
0
0
2
0
0
1
0
1
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
2
5
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
2
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
4
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
1
0
2
0
0
1
0
1
0
0
0
2
2
2
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
1
0
0
0
0
1
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
1
0
0
0
0
2
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
4
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
3
2
1
0
0
0
0
0
2
0
2
1
1
2
1
0
1
0
0
0
0
0
0
2
0
0
1
0
0
1
1
1
1
2
0
1
0
2
2
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
1
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
4
3
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
6
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
5
0
3
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
1
0
2
0
0
0
0
2
0
0
0
2
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
1
2
0
0
2
0
0
3
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
7
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
4
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
1
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
1
1
0
6
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
2
0
0
0
1
0
0
1
2
1
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
2
0
0
0
3
2
0
0
0
0
0
0
5
0
0
0
0
0
2
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
4
0
0
0
0
0
2
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
2
0
2
2
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
1
0
1
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
2
0
3
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
4
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
2
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
1
0
1
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
3
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
4
0
0
0
0
2
2
3
0
2
0
2
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
2
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
4
1
0
1
0
0
0
0
4
0
0
2
0
0
2
0
0
0
1
1
0
0
0
0
0
0
5
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
6
0
0
0
0
1
2
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
1
0
0
0
2
0
1
1
2
0
3
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
2
4
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
3
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
5
1
0
0
0
1
0
0
0
0
1
0
3
0
0
0
0
2
3
0
2
2
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
2
2
0
1
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
3
0
0
0
1
0
0
0
0
1
2
1
2
0
0
0
0
3
0
3
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
2
1
3
1
0
0
0
0
0
1
2
1
1
0
0
1
0
0
1
0
6
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
3
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
4
0
1
0
2
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
2
0
0
1
1
1
2
0
0
2
2
0
1
0
0
2
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
5
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
4
2
0
0
0
0
1
0
0
1
0
0
0
0
2
3
2
1
1
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
1
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
1
0
0
1
0
0
2
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
3
0
0
0
1
0
5
1
1
0
0
3
0
0
2
1
1
2
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
1
0
2
1
0
2
0
1
2
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
3
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
3
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
9
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
2
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
4
0
0
2
3
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
3
0
0
0
1
1
0
2
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
1
0
0
2
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
4
0
0
0
0
1
0
3
2
0
0
0
0
1
1
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
2
2
1
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
2
3
0
0
0
0
3
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
3
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
3
0
1
0
0
0
0
0
1
0
12
0
0
0
0
0
0
3
6
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
4
2
0
0
0
0
0
0
0
0
0
0
2
1
4
0
0
0
1
5
0
0
0
0
0
0
0
3
0
1
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
1
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
3
2
0
1
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
2
0
1
0
1
2
2
2
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
1
2
2
2
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
1
2
0
0
0
0
5
0
0
1
0
0
0
0
0
6
0
2
0
1
0
1
0
5
0
0
1
0
0
0
2
1
0
0
0
1
3
2
3
0
0
0
1
0
0
1
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
2
0
3
0
0
0
0
1
0
0
1
0
2
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
1
1
1
2
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
5
0
1
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
1
0
0
0
0
0
1
0
3
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
4
1
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
3
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
1
1
0
0
0
0
0
1
0
0
1
2
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
2
0
0
0
0
0
0
1
2
1
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
1
1
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
3
0
1
0
0
2
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
3
0
1
0
0
0
0
1
2
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
1
1
1
0
0
0
1
0
0
3
0
1
0
0
0
1
4
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
1
1
0
0
0
1
2
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
2
0
0
0
0
2
3
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
3
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
4
9
0
1
0
0
0
1
0
0
0
2
2
1
0
0
0
1
0
0
0
2
0
4
0
0
2
2
1
0
0
0
1
0
0
2
2
0
1
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
2
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
2
1
0
0
0
0
1
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
2
0
2
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
7
0
0
3
2
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
1
0
0
1
0
1
5
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
4
0
0
1
1
0
1
0
0
0
0
0
1
1
3
0
0
2
0
0
0
0
5
0
0
1
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
1
0
0
1
4
2
0
0
2
0
4
2
1
1
0
2
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
14
0
0
3
0
0
0
0
0
0
3
2
1
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
2
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
1
2
0
0
3
0
0
0
2
2
0
0
0
2
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
1
2
0
2
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
1
1
1
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
4
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
0
4
2
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
2
0
0
0
0
0
1
2
0
0
1
0
0
0
0
2
0
0
2
1
0
5
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
1
0
1
5
0
1
0
0
0
0
3
0
0
0
0
2
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
3
1
0
3
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
2
4
0
0
0
0
0
1
0
0
0
0
0
0
3
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
5
0
0
0
2
0
2
0
0
0
0
2
3
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
2
0
0
0
1
2
0
2
0
0
1
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
1
2
0
1
1
2
0
1
2
0
0
0
1
0
0
2
0
0
0
2
0
0
1
0
0
0
2
0
0
0
3
0
0
1
0
2
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
1
2
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
1
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
2
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
3
0
2
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
1
1
2
0
1
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
5
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
1
0
2
2
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
4
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
3
2
1
0
0
0
0
0
2
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
2
0
0
0
0
1
1
0
3
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
2
1
0
0
0
1
0
3
0
0
0
0
0
0
0
1
3
0
0
0
1
0
0
0
2
0
0
2
2
1
0
0
1
0
0
1
0
5
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
1
2
0
0
0
1
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
3
0
0
0
2
0
0
0
0
1
0
0
1
1
0
0
0
0
1
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
2
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
3
0
1
0
0
2
1
0
2
1
0
0
1
3
2
0
0
0
0
0
0
2
1
0
2
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
2
0
0
0
2
0
0
0
0
0
1
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
2
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
2
0
0
1
0
2
0
0
0
1
0
0
0
2
0
0
2
1
0
1
2
2
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
4
0
1
0
0
0
1
2
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
25
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
2
0
0
1
2
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
2
0
1
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
1
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
2
3
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
5
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
2
2
0
1
0
0
0
2
0
0
0
2
2
1
0
0
1
0
0
0
0
0
0
0
0
0
6
0
1
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
3
0
3
1
0
3
0
3
0
0
0
0
0
3
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
2
0
1
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
4
0
0
0
0
0
1
1
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
2
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
6
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
7
0
2
0
0
1
0
0
0
2
0
0
0
3
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
6
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
2
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
1
0
1
2
0
0
0
1
0
0
0
3
0
0
0
0
1
0
1
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
2
0
0
2
2
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
3
0
0
1
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
1
1
0
0
0
3
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
2
0
0
0
1
0
0
0
1
0
2
1
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
10
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
3
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
1
1
0
0
0
0
0
0
0
0
5
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
2
1
0
0
0
0
1
0
2
0
0
0
2
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
1
0
0
4
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
2
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
2
1
1
0
0
0
0
1
0
3
2
0
0
0
0
0
1
0
0
3
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
1
0
1
2
0
3
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
1
0
2
0
0
1
2
0
0
0
0
2
0
2
0
0
2
0
0
3
0
0
0
0
1
0
0
2
0
2
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
1
0
0
0
0
0
0
5
0
0
0
0
6
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
3
1
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
5
0
1
2
2
0
0
0
0
1
0
0
0
1
0
3
0
0
1
1
0
1
2
0
1
1
1
2
0
0
0
1
0
0
0
2
0
0
0
5
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
3
0
3
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
1
0
1
1
0
1
0
0
2
0
0
0
1
0
2
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
7
0
2
10
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
3
0
2
0
0
2
0
1
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
2
0
1
0
0
0
0
0
0
2
0
0
0
1
1
2
0
0
1
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
1
1
1
0
0
0
0
2
0
0
0
3
0
2
0
0
0
0
0
7
1
2
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
1
0
0
0
3
0
0
2
0
2
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
2
0
1
0
0
2
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
2
2
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
2
1
0
0
2
0
0
0
0
1
2
0
14
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
1
0
0
0
2
1
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
6
2
0
0
0
6
0
0
2
1
0
0
0
0
3
1
0
2
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
2
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
1
0
1
0
2
0
1
0
0
0
0
1
0
2
0
0
1
1
0
0
0
0
0
0
0
1
1
0
1
0
0
3
0
0
1
0
0
0
0
2
0
2
1
0
2
0
0
6
2
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
3
2
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
3
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
3
1
0
0
1
0
2
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
2
0
0
2
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
2
0
0
1
11
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
2
0
1
0
2
2
0
0
0
1
0
0
0
5
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
1
1
0
0
1
0
0
0
0
2
0
2
0
0
0
0
2
2
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
5
0
0
0
0
0
0
1
0
1
0
2
0
1
0
2
1
0
0
3
0
2
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
4
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
1
0
1
0
0
2
0
2
0
0
1
1
2
0
0
2
0
0
0
2
0
2
0
2
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
1
0
1
0
1
2
0
0
2
0
0
2
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
2
0
0
1
1
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
4
0
0
0
1
0
0
0
0
1
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
3
0
0
1
0
3
0
2
0
0
0
0
0
0
0
1
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
2
0
0
1
2
0
2
0
1
0
0
0
0
0
3
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
1
0
0
0
0
0
0
1
0
0
3
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
2
0
1
0
2
1
0
0
1
2
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
2
2
0
0
3
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
1
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
3
2
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
1
0
1
1
0
0
1
2
6
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
5
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
2
1
0
0
1
0
0
0
2
0
0
0
0
2
2
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
1
0
0
2
0
2
1
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
2
2
0
0
2
0
1
0
0
0
0
0
0
2
1
0
0
1
2
0
0
0
0
0
0
0
0
2
4
0
9
2
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
3
0
0
1
5
2
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
1
0
0
0
3
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
2
0
5
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
3
0
1
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
3
0
0
1
3
1
0
0
0
0
0
7
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
1
1
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
3
0
2
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
3
0
2
0
0
0
1
1
1
0
0
0
0
0
0
2
0
0
2
3
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
4
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
4
0
0
0
1
1
0
2
2
0
0
2
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
1
1
0
0
0
0
0
1
0
0
1
0
1
2
2
0
0
0
1
0
2
2
0
1
2
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
5
0
2
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
1
2
1
0
0
0
1
0
2
2
0
0
0
0
2
0
0
2
0
0
0
0
0
1
1
0
0
1
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
1
0
2
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
6
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
2
1
0
0
0
0
0
0
4
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
1
1
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
1
2
0
0
0
2
0
1
0
0
0
0
2
0
1
0
1
2
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
2
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
4
1
0
0
2
2
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
3
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
4
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
2
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
2
1
0
0
0
0
2
0
3
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
1
0
1
0
1
0
1
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
2
3
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
1
2
1
1
0
1
0
0
1
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
1
1
0
0
0
0
0
1
0
2
0
0
0
0
0
2
2
2
3
0
0
0
0
0
0
0
0
0
1
7
0
0
0
1
0
0
2
1
2
0
0
0
0
0
0
0
0
1
1
0
1
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
3
0
2
1
2
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
3
2
7
2
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
5
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
1
0
2
0
0
2
0
0
1
0
0
1
1
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
3
0
1
0
0
0
1
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
1
0
0
2
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
4
1
0
1
0
1
0
1
3
0
0
0
0
0
0
0
0
2
3
1
0
0
0
0
0
4
0
0
0
0
0
0
0
5
1
0
1
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
2
0
2
0
0
2
0
0
0
0
0
1
0
1
2
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
1
1
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
6
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
5
0
0
0
1
0
2
0
0
0
0
0
1
4
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
1
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
1
1
0
0
0
2
0
0
0
1
0
1
2
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
2
0
0
1
1
0
0
1
0
6
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
6
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
2
1
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
8
1
2
0
1
0
3
0
0
1
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
2
4
1
0
1
0
0
1
0
1
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
3
2
0
0
1
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
1
1
2
0
0
1
0
0
1
0
1
2
0
0
0
0
1
0
0
0
0
0
3
3
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
2
1
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
1
0
0
2
0
0
1
0
1
0
0
0
0
2
0
0
1
2
1
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
2
5
0
0
1
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
1
0
0
0
3
3
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
5
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
2
0
0
2
0
0
0
3
2
0
0
0
0
0
0
2
4
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
5
0
2
0
0
0
2
2
0
0
0
1
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
3
0
0
2
0
0
2
0
0
0
0
0
1
2
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
5
0
0
0
0
0
0
0
0
0
0
2
0
3
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
1
0
1
0
1
0
2
0
3
0
0
0
2
0
0
1
0
2
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
1
0
0
1
0
2
0
0
0
0
0
0
3
0
1
2
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
1
0
1
0
2
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
1
2
1
2
0
1
2
1
0
0
0
0
1
0
0
2
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
3
0
0
0
0
0
3
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
2
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
5
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
2
1
2
0
0
3
0
0
1
0
0
1
0
2
0
0
1
3
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
3
1
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
14
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
1
1
5
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
1
2
0
0
0
0
0
0
0
0
0
1
1
10
0
0
0
1
0
1
0
0
3
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
2
0
2
0
0
0
2
0
1
0
0
0
2
0
0
2
4
0
1
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
6
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
4
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
4
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
1
0
0
0
5
0
0
0
1
1
1
1
2
0
0
0
0
0
3
2
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
1
1
1
0
0
0
1
2
0
0
0
0
0
2
0
0
1
2
0
1
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
2
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
2
1
0
2
0
2
0
1
0
1
0
0
0
0
0
3
0
0
0
0
2
0
1
2
0
5
0
1
6
2
0
0
1
2
5
0
0
0
0
0
1
0
0
0
1
0
2
1
0
0
2
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
1
1
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
4
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
6
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
4
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
2
0
0
1
2
0
1
0
0
0
0
0
0
1
0
0
2
0
7
0
0
0
0
0
0
2
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
3
0
0
1
2
2
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
3
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
2
0
0
3
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
2
0
2
0
0
1
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
1
0
1
1
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
4
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
1
2
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
2
0
2
0
0
1
1
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
2
0
4
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
3
2
0
0
0
0
0
2
3
0
4
0
3
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
2
1
0
2
1
0
2
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
3
2
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
4
0
0
0
0
5
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
3
0
0
0
0
2
0
0
0
0
1
2
2
0
0
2
0
2
0
0
0
2
0
1
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
3
0
2
1
0
2
1
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
2
0
2
1
0
0
0
1
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
8
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
3
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
2
2
1
0
2
1
0
0
0
0
0
2
0
0
0
0
2
1
2
0
2
0
0
0
2
0
0
0
1
1
2
0
0
0
0
5
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
3
0
2
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
2
0
2
0
0
0
3
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
1
0
0
0
0
1
8
0
2
0
0
1
0
0
0
0
0
0
0
1
1
2
0
2
1
0
1
0
1
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
3
0
0
0
0
1
0
0
5
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
1
0
0
1
0
0
0
0
2
0
0
0
2
0
0
5
0
1
0
2
0
5
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
2
1
0
0
1
0
0
1
1
0
0
0
3
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
4
1
0
1
1
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
3
3
0
0
0
0
0
0
0
0
1
0
0
0
2
3
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
2
0
0
2
0
0
0
0
1
0
0
5
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
7
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
4
0
0
0
0
1
0
1
0
0
0
2
1
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
4
0
2
3
2
5
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
1
0
0
0
2
2
0
0
0
0
2
0
0
0
0
3
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
2
1
1
0
1
0
1
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
2
0
0
0
0
0
0
0
2
2
0
1
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
4
0
0
2
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
5
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
2
0
0
1
0
2
2
0
1
0
0
0
0
0
0
1
0
0
0
2
0
3
0
0
0
0
1
0
2
0
1
0
0
1
2
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
3
1
0
0
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
1
4
0
2
0
0
2
0
1
0
1
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
2
0
0
2
2
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
2
0
0
0
2
0
3
0
2
0
2
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
1
0
0
0
0
1
1
2
0
2
7
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
2
0
5
0
0
1
0
0
0
2
0
0
8
0
0
2
2
0
3
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
1
1
5
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
2
0
2
2
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
1
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
1
0
3
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
2
2
3
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
1
0
1
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
2
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
10
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
2
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
3
0
0
0
0
1
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
2
0
0
0
0
0
0
4
1
2
0
0
0
0
2
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
3
0
0
0
0
2
0
1
0
0
2
0
4
0
1
0
1
0
1
0
0
0
0
0
0
6
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
1
2
0
0
0
0
2
0
0
2
0
3
1
0
0
1
2
0
0
2
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
2
0
0
0
1
0
0
2
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
2
0
2
0
2
0
1
0
0
2
0
0
1
0
0
1
1
1
0
0
0
0
1
0
0
3
0
6
0
0
1
0
0
1
3
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
2
2
0
2
2
2
0
3
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
5
0
0
0
5
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
4
2
0
2
0
1
1
2
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
1
0
0
0
0
1
0
0
2
1
2
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
1
1
1
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
5
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
3
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
3
0
0
2
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
7
2
0
0
2
0
0
3
0
0
0
10
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
3
0
2
0
0
0
1
0
0
3
1
2
0
0
5
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
8
0
0
0
1
0
0
2
2
1
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
4
0
0
0
1
4
0
2
1
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
3
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
1
0
2
0
0
0
0
3
2
0
0
0
0
0
2
0
1
0
0
0
0
0
3
0
0
0
0
0
1
2
1
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
4
0
0
2
1
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
2
0
0
2
0
0
1
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
2
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
2
0
2
0
0
0
2
0
2
2
2
1
4
0
1
0
8
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
4
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
2
1
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
1
0
0
0
0
0
1
2
0
0
0
3
1
0
0
0
1
0
0
1
2
0
0
0
0
0
1
2
0
0
0
0
2
1
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
2
0
0
0
0
1
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
1
1
0
1
0
0
0
0
5
0
2
2
0
4
0
0
0
0
2
0
0
1
0
0
0
7
0
0
0
2
0
0
1
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
2
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
2
0
1
0
0
0
3
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
3
0
1
2
1
0
0
0
0
0
0
3
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
3
0
1
0
0
0
0
2
0
2
4
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
1
7
0
7
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
3
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
1
0
0
2
1
0
0
0
1
0
2
1
0
0
0
0
3
2
1
0
2
0
0
1
0
1
1
0
0
0
2
0
0
1
0
0
0
3
1
0
0
0
0
2
3
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
3
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
3
1
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
1
4
0
1
0
0
0
0
0
1
2
0
1
0
1
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
1
2
1
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
1
0
3
0
1
0
3
0
4
0
0
0
3
0
0
1
0
0
0
0
0
2
1
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
1
0
1
0
0
2
0
0
0
0
0
2
0
0
1
3
2
0
0
0
0
0
0
2
2
3
0
0
1
1
0
0
0
0
0
0
1
3
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
2
0
0
1
1
3
0
4
0
1
0
1
0
0
0
2
0
0
2
0
0
1
0
2
0
4
0
0
2
0
0
1
0
0
1
0
1
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
9
1
0
0
0
0
0
1
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
4
0
2
0
0
2
1
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
1
2
0
1
0
0
3
2
0
0
1
3
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
2
0
2
0
0
0
0
2
1
1
2
1
1
0
1
0
0
0
0
1
3
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
3
1
1
0
3
0
0
2
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
1
1
0
1
0
0
2
0
0
0
3
1
0
0
0
0
2
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
4
12
1
0
0
1
0
2
0
0
0
0
2
2
0
1
18
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
1
3
0
3
1
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
2
1
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
4
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
3
0
4
0
0
0
0
0
2
0
0
0
0
0
0
0
4
2
0
0
0
0
0
2
0
0
0
2
0
2
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
5
0
0
2
1
0
0
0
1
0
0
0
0
0
0
1
0
6
0
0
3
0
3
0
0
0
0
2
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
1
0
2
0
1
0
0
0
0
1
0
0
5
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
3
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
7
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
1
0
0
0
3
0
2
1
0
0
1
2
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
3
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
4
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
2
1
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
1
0
0
2
4
0
0
0
0
0
0
0
0
2
1
0
0
2
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
1
2
1
0
0
0
0
0
0
0
1
0
2
1
0
0
2
0
0
0
0
0
1
0
1
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
4
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
12
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
11
0
0
0
0
1
2
3
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
2
6
0
0
0
0
2
0
0
0
0
0
0
3
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
3
0
0
0
1
0
0
0
0
0
2
0
0
7
0
0
1
1
0
1
0
2
0
0
1
0
0
0
1
1
1
0
0
0
0
0
1
0
1
0
2
0
0
1
0
0
0
1
2
3
0
2
0
2
0
0
0
0
0
0
2
2
0
0
0
1
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
1
0
0
3
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
2
2
0
0
0
0
4
1
0
0
1
0
0
0
1
0
0
0
5
0
0
2
5
0
0
0
0
0
2
0
0
0
0
1
0
1
0
2
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
1
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
1
1
4
0
0
1
0
2
0
1
0
0
0
1
0
0
0
1
0
1
0
2
0
0
2
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
2
2
3
0
0
1
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
1
0
0
0
0
1
1
2
0
3
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
1
2
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
1
0
2
0
1
0
1
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
2
0
0
0
0
0
0
1
0
0
9
0
2
2
2
0
0
0
0
0
4
2
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
3
0
0
0
0
0
0
0
1
0
0
0
0
3
0
2
0
1
0
0
2
0
0
0
0
2
0
1
0
0
1
0
1
0
2
0
0
0
0
0
2
1
0
0
1
3
0
0
2
2
0
0
0
0
0
0
0
1
1
2
2
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
2
0
0
2
0
0
0
0
1
2
8
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
2
2
0
0
0
2
0
2
1
2
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
4
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
1
1
2
0
0
0
0
1
3
0
1
0
2
3
0
2
0
0
2
1
1
0
0
0
0
1
1
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
1
0
1
0
2
0
0
0
1
3
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
1
2
2
0
0
0
0
2
0
0
0
0
4
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
2
2
0
0
0
0
1
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
2
0
0
2
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
1
2
0
1
1
0
2
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
7
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
2
0
2
0
1
1
1
0
0
1
0
0
2
1
3
0
0
0
0
0
0
6
0
0
0
1
0
1
2
2
1
0
2
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
8
2
2
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
4
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
5
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
1
0
4
2
2
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
1
1
0
2
3
0
0
0
0
1
0
0
0
0
0
1
0
1
2
0
4
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
2
2
2
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
1
0
3
1
0
2
0
0
0
0
2
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
2
2
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
2
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
1
1
0
2
0
0
0
2
2
0
0
0
0
0
0
2
1
0
0
1
1
0
0
0
1
0
0
0
0
2
0
0
0
0
2
1
1
0
2
0
0
2
0
1
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
3
0
0
0
0
1
0
1
0
1
0
1
0
0
0
1
0
0
1
0
1
0
1
0
0
0
2
1
0
1
3
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
1
0
4
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
1
0
2
0
1
2
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
2
0
0
0
0
3
0
2
0
3
1
0
3
2
0
0
0
2
3
1
0
0
0
0
0
0
1
2
8
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
3
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
8
0
0
0
0
0
0
0
1
2
0
0
2
2
0
0
0
0
2
1
0
0
0
2
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
2
1
1
0
2
0
2
2
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
1
0
2
2
0
1
0
0
3
0
0
0
0
1
0
3
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
1
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
3
1
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
1
0
2
0
0
0
0
0
6
0
0
0
2
0
0
0
0
0
1
0
8
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
2
0
2
0
0
1
0
0
0
2
0
0
1
1
0
0
0
0
0
0
3
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
1
0
2
0
0
4
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
2
0
0
1
0
0
1
0
0
1
0
0
0
1
2
0
0
0
0
0
1
0
0
3
0
0
3
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
3
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
1
1
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
1
2
0
0
0
0
0
0
1
0
0
0
4
0
2
2
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
3
0
0
0
2
0
1
1
0
2
0
0
0
0
3
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
2
2
0
2
0
0
1
0
2
0
2
0
0
0
0
0
4
0
1
0
0
0
0
0
1
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
2
0
0
2
1
1
0
2
0
0
0
0
1
0
0
1
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
1
0
1
2
0
0
0
1
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
1
0
0
2
5
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
1
1
0
0
0
0
0
1
0
3
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
1
0
0
0
1
0
1
0
0
2
0
0
0
0
1
0
2
0
1
1
0
2
0
2
0
0
0
0
2
0
0
0
0
0
2
2
1
0
0
2
0
0
0
0
0
2
1
1
0
1
0
0
1
0
3
0
3
0
0
0
0
0
1
1
0
2
0
1
0
0
0
2
0
2
0
0
0
0
2
0
0
0
2
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
2
1
0
0
0
0
1
0
0
1
0
0
1
0
7
0
0
0
0
0
2
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
3
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
2
0
3
0
0
0
0
0
0
0
0
0
1
0
0
4
1
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
3
0
0
1
0
0
1
0
2
0
0
0
0
2
1
0
1
3
0
2
0
0
0
0
1
2
0
0
0
2
0
0
0
5
0
1
0
1
1
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
1
3
0
1
3
4
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
1
1
0
0
0
5
0
0
3
0
0
2
5
1
0
0
0
3
0
0
0
2
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
3
2
0
0
0
2
0
0
1
2
1
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
7
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
4
1
0
0
0
1
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
1
0
0
0
0
4
0
0
0
2
0
0
0
1
0
1
0
1
0
0
3
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
3
0
2
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
2
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
1
2
0
0
0
2
0
0
0
0
4
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
2
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
9
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
1
4
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
3
1
1
0
2
0
0
0
0
2
0
0
0
1
1
0
0
0
1
0
1
1
0
0
0
5
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
9
0
3
0
0
0
1
0
1
0
1
0
0
0
0
0
3
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
4
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
8
0
1
1
2
0
0
0
0
0
1
2
0
0
1
2
1
0
2
0
2
1
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
1
0
1
0
0
2
2
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
3
1
0
0
2
0
2
1
0
0
0
1
0
1
0
0
2
3
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
3
0
0
0
1
0
0
2
0
1
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
3
0
0
2
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
2
2
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
4
0
0
0
1
0
2
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
2
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
1
1
0
0
0
0
1
0
0
0
0
2
1
0
0
1
0
0
1
2
4
0
0
0
0
1
0
0
1
2
0
0
0
0
2
0
0
0
0
0
2
1
0
3
0
0
1
0
1
0
0
0
0
0
1
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
3
1
0
2
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
4
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
1
2
0
1
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
1
0
6
0
0
5
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
3
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
2
0
3
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
3
0
0
0
0
0
0
0
1
0
0
0
0
4
5
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
3
2
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
1
0
2
0
0
0
0
0
0
0
0
1
2
2
6
0
0
0
0
0
0
0
2
0
0
0
2
0
2
3
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
1
0
0
1
1
0
0
2
1
0
3
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
1
1
0
0
5
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
3
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
3
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
7
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
3
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
2
2
0
0
1
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
2
0
1
0
1
0
0
0
0
1
0
0
0
0
1
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
1
0
3
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
2
1
0
0
3
0
0
0
0
0
0
0
0
0
4
0
2
0
3
0
1
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
2
0
0
0
0
0
1
1
0
2
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
5
0
0
2
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
1
2
2
0
0
1
2
0
0
2
1
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
1
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
2
1
0
0
1
0
0
2
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
5
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
2
2
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
1
0
7
0
0
3
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
3
0
0
0
2
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
3
0
0
0
0
0
2
3
1
2
0
2
1
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
4
0
1
0
0
1
0
2
2
0
1
0
0
0
0
0
0
3
0
0
0
1
1
0
0
0
0
0
0
0
2
3
0
0
0
0
0
2
0
1
0
0
0
0
1
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
7
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
5
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
3
1
1
0
0
0
0
0
0
0
1
0
0
4
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
2
1
0
0
6
0
1
1
0
0
1
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
2
1
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
5
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
1
0
0
0
1
0
0
0
0
8
0
0
1
0
0
2
2
0
0
0
2
2
3
0
0
0
0
0
0
1
1
0
0
0
0
9
0
0
0
0
0
0
2
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
1
0
0
1
4
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
2
2
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
2
0
0
4
2
0
0
0
2
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
3
0
2
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
2
1
0
0
3
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
4
0
0
0
2
0
0
0
0
1
0
0
2
1
0
0
0
0
5
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
2
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
3
6
2
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
5
0
0
0
0
1
0
1
0
0
1
0
0
0
1
2
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
3
0
0
0
0
0
0
2
0
0
0
0
0
2
0
3
0
0
1
1
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
2
6
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
2
0
0
1
0
0
1
0
1
4
10
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
3
0
2
3
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
1
1
0
0
0
0
0
2
0
0
3
0
0
1
0
0
0
2
0
0
2
0
0
0
2
0
0
0
2
0
0
2
0
3
0
0
0
3
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
3
3
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
1
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
1
1
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
1
1
0
0
3
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
2
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
1
0
0
3
2
2
0
0
1
3
0
4
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
2
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
3
0
0
1
0
0
2
0
0
0
1
0
2
0
2
0
0
0
0
6
0
0
1
0
1
0
2
2
0
1
0
0
0
0
0
1
0
0
0
2
0
1
2
0
0
0
0
0
2
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
1
0
1
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
1
0
1
2
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
3
0
0
0
0
2
2
1
0
2
0
0
0
0
0
3
0
0
0
0
1
1
1
0
2
0
0
0
0
0
1
0
0
1
0
4
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
1
0
1
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
4
0
0
0
2
0
0
0
1
0
0
0
1
2
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
5
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
4
1
4
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
3
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
3
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
1
1
0
0
1
0
2
15
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
2
0
2
2
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
1
5
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
1
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
3
1
1
0
0
0
0
4
0
0
0
0
3
0
0
1
0
0
3
0
2
2
0
0
0
1
2
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
1
1
0
4
1
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
5
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
3
0
2
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
1
2
0
1
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
3
0
1
0
0
0
0
0
2
0
3
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
4
0
5
0
0
0
0
0
3
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
4
0
0
1
0
0
0
0
2
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
2
0
2
0
0
0
0
2
0
2
0
0
0
3
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
2
2
1
0
0
0
0
0
0
0
2
1
0
0
0
2
1
0
0
1
6
2
0
1
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
1
0
2
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
1
2
0
0
2
0
1
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
1
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
2
3
0
0
0
1
0
0
0
0
0
0
2
0
0
0
4
0
0
0
1
2
1
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
2
0
2
0
0
2
0
0
0
0
2
0
1
11
0
1
0
3
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
1
3
6
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
1
1
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
1
0
1
1
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
2
0
0
1
0
0
2
0
0
1
2
0
0
1
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
1
0
1
0
5
1
0
0
0
0
1
0
0
0
0
0
4
0
4
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
2
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
2
1
4
0
1
0
2
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
4
1
2
0
1
0
0
0
0
2
0
0
1
0
0
1
0
1
2
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
4
0
0
0
0
1
2
0
0
0
1
1
0
0
0
0
1
0
2
0
0
0
2
1
0
0
0
1
2
0
0
3
3
0
0
1
2
0
0
3
0
0
2
0
2
1
0
0
0
0
0
2
2
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
3
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
1
1
1
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
2
0
3
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
4
0
0
0
1
1
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
2
1
0
0
1
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
3
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
2
1
1
0
3
1
0
0
0
0
0
0
2
0
0
0
1
0
2
0
2
2
0
0
0
0
1
0
6
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
3
1
0
0
0
1
0
3
0
0
1
0
0
2
2
1
2
0
0
0
1
0
0
0
2
7
1
0
0
12
0
0
2
0
0
0
0
1
1
2
0
0
10
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
3
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
3
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
1
0
0
0
1
0
0
4
1
2
0
4
0
0
0
2
1
0
1
0
1
0
2
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
1
0
2
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
4
0
0
1
1
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
2
0
3
0
1
0
0
0
0
0
0
1
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
2
0
5
0
2
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
2
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
1
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
4
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
3
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
3
0
0
2
2
0
0
0
0
0
0
4
1
0
0
0
1
3
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
2
0
1
2
0
2
4
0
1
0
0
1
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
2
1
0
0
5
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
5
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
5
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
1
0
0
1
0
1
0
1
0
2
0
0
0
0
2
2
0
0
0
1
0
2
1
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
2
2
0
0
2
0
0
0
1
0
0
8
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
1
0
0
0
1
0
3
0
0
0
0
0
0
0
4
0
1
2
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
8
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
2
0
0
2
3
0
0
0
3
0
1
0
0
0
2
0
0
0
2
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
3
3
0
0
1
0
0
0
1
0
1
0
0
0
0
5
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
1
0
0
0
0
0
3
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
3
0
0
0
0
0
2
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
7
0
0
0
0
1
0
0
3
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
1
2
0
0
0
2
0
0
0
1
0
2
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
3
0
2
0
0
1
2
1
0
0
0
0
0
0
1
0
0
1
1
0
4
1
1
0
1
0
0
1
0
0
2
0
0
1
0
2
0
0
0
0
7
0
0
1
1
1
0
3
0
3
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
1
0
2
2
2
0
1
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
4
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
6
0
0
1
0
0
1
0
0
1
0
0
4
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
4
1
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
2
1
0
0
0
1
0
0
0
0
4
2
0
0
0
1
2
0
4
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
2
1
0
0
0
1
0
0
0
1
0
1
0
0
2
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
2
0
0
0
7
2
1
0
0
0
1
0
1
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
1
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
1
2
1
2
2
0
2
1
0
2
1
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
1
0
2
0
0
3
2
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
3
0
0
0
1
2
0
0
1
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
2
0
0
1
3
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
3
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
3
1
0
0
0
0
2
0
0
0
3
0
0
0
0
3
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
5
0
0
0
0
3
0
0
0
1
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
5
0
0
3
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
2
1
0
0
1
0
0
1
0
1
0
0
0
1
0
0
2
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
3
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
2
2
0
0
1
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
2
0
3
0
0
0
0
0
0
0
0
1
0
0
4
0
1
1
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
8
0
1
0
0
0
0
0
2
0
0
0
2
0
0
3
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
2
0
0
2
0
0
0
1
0
2
0
2
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
4
0
1
2
0
0
3
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
8
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
4
0
0
0
1
1
2
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
4
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
1
1
0
0
2
0
2
2
0
0
0
1
1
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
8
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
2
1
0
5
1
0
1
0
0
1
3
4
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
2
2
0
0
1
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
2
0
0
2
0
2
0
1
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
2
2
1
1
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
2
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
1
0
1
1
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
3
0
0
0
0
3
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
10
0
0
0
1
0
0
1
3
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
2
0
1
1
0
0
0
0
0
2
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
2
0
0
0
0
0
0
0
2
0
1
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
2
0
2
0
1
0
0
0
0
3
0
0
0
0
3
0
1
0
0
0
0
1
0
0
1
0
1
2
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
1
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
3
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
3
0
0
3
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
4
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
2
0
0
0
0
0
1
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
3
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
1
0
0
1
0
1
1
0
2
0
4
0
0
0
3
0
0
0
1
0
1
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
2
1
0
0
0
0
1
0
1
0
1
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
2
0
2
1
1
1
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
3
0
2
0
0
2
0
0
0
0
0
1
0
2
1
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
4
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
1
0
2
2
5
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
1
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
2
0
1
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
1
1
2
0
0
0
1
0
2
0
0
2
0
2
0
0
0
0
0
0
2
1
3
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
2
0
2
0
0
0
2
0
0
0
0
1
0
0
1
0
2
0
0
1
0
0
0
0
3
2
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
2
0
1
1
0
1
0
0
0
0
0
0
4
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
2
0
1
1
1
0
1
0
0
0
0
0
1
0
0
1
0
1
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
1
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
6
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
3
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
3
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
3
2
0
2
0
0
0
2
0
1
2
0
3
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
2
0
0
0
0
0
0
1
1
0
2
0
0
2
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
1
2
0
0
0
0
1
0
2
5
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
2
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
2
0
1
0
0
0
0
0
0
3
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
1
1
0
2
1
0
0
0
3
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
3
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
1
0
0
0
0
0
1
0
2
1
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
1
0
0
0
2
0
1
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
4
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
2
1
1
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
2
0
3
0
1
0
1
0
0
0
0
0
0
0
1
0
3
0
2
3
0
0
0
0
0
0
0
0
0
1
3
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
5
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
2
2
0
0
0
1
0
3
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
1
1
0
0
0
0
0
0
1
0
0
0
1
0
1
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
1
0
1
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
1
1
0
4
0
0
0
2
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
1
0
0
0
0
2
3
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
1
0
0
1
5
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
2
2
0
0
0
2
0
0
0
1
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
4
0
2
0
0
0
1
0
1
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
5
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
2
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
2
1
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
3
1
0
0
0
0
1
0
0
2
1
2
0
0
0
0
0
2
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
2
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
6
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
2
0
0
1
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
2
0
0
0
0
2
1
0
2
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
3
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
5
0
0
0
0
0
1
0
0
0
0
1
0
3
0
0
0
0
1
0
1
0
0
0
2
1
1
0
0
0
2
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
1
1
1
2
1
2
0
0
0
0
0
0
0
2
2
0
0
0
3
0
0
0
0
2
2
1
1
2
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
1
2
0
1
0
1
0
0
2
0
0
2
0
1
0
1
1
0
0
0
0
5
9
0
2
0
0
0
1
2
0
0
0
0
3
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
2
3
0
0
0
1
0
1
0
1
0
0
0
0
1
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
1
0
0
0
2
0
0
1
1
1
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
1
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
2
2
2
3
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
3
2
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
2
0
1
0
0
0
0
1
0
0
0
1
0
1
0
2
0
0
0
0
2
0
0
6
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
2
0
0
2
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
4
1
7
0
0
0
0
0
0
3
0
0
0
1
1
0
0
0
0
2
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
5
0
0
1
1
2
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
2
2
1
0
0
1
1
0
2
0
0
10
2
0
0
2
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
7
3
0
0
0
2
0
2
1
0
0
0
4
0
0
0
0
1
0
0
1
0
0
1
0
3
0
0
0
1
1
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
1
0
0
0
1
1
0
2
0
0
0
2
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
1
2
1
0
0
0
4
0
1
0
1
0
6
2
0
2
0
0
0
1
4
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
2
0
1
1
0
0
1
1
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
3
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
2
0
3
0
0
0
0
0
2
0
0
0
1
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
9
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
1
0
0
0
0
2
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
6
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
4
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
2
1
0
0
0
0
2
0
1
1
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
3
1
0
0
2
0
0
0
3
0
0
2
0
1
3
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
2
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
2
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
2
0
0
0
0
0
4
0
1
0
2
0
1
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
2
1
0
0
1
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
2
0
1
0
0
0
0
4
0
0
0
0
2
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
4
0
0
0
0
3
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
3
0
0
18
0
0
0
0
0
0
0
0
1
0
4
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
1
0
4
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
1
1
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
3
0
0
0
1
2
3
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
2
0
0
0
0
0
0
1
0
1
2
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
2
1
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
1
0
2
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
3
0
0
0
1
0
2
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
2
0
4
1
2
3
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
1
0
2
0
0
2
0
0
0
2
0
0
0
2
0
1
0
0
0
2
0
0
2
0
1
0
4
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
3
0
0
0
2
0
0
1
0
0
0
1
0
2
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
4
2
0
0
2
2
3
0
0
0
0
0
0
0
0
0
2
0
4
2
0
0
0
0
1
0
2
2
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
2
0
0
1
1
0
0
0
0
0
1
0
0
4
0
1
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
5
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
1
1
0
3
0
2
0
0
0
0
2
1
0
0
0
2
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
5
0
2
1
3
0
0
0
0
1
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
8
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
3
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
1
0
5
0
0
0
0
0
0
0
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
3
0
0
0
0
1
0
0
0
3
0
0
2
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
1
0
3
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
1
1
2
1
0
0
0
0
1
2
1
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
2
0
1
1
0
0
2
0
3
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
2
0
0
0
2
0
0
2
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
5
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
1
1
2
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
5
0
1
0
0
3
1
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
3
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
2
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
3
0
0
0
0
0
0
7
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
1
1
4
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
3
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
4
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
2
3
0
2
2
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
11
2
2
2
0
1
0
1
0
0
0
0
1
6
2
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
4
0
3
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
1
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
3
1
0
0
0
0
0
0
2
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
2
2
0
0
2
0
2
0
0
11
0
0
0
0
2
3
0
2
1
0
0
0
0
1
0
0
3
0
5
0
0
1
2
0
0
0
2
3
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
5
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
1
0
2
1
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
2
0
4
0
2
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
1
1
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
3
0
1
0
0
0
2
0
0
0
0
0
1
0
0
4
0
0
0
0
0
1
1
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
4
0
0
0
0
3
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
1
1
0
0
0
0
0
9
2
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
1
1
1
2
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
3
0
0
0
0
1
2
0
0
3
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
4
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
3
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
1
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
5
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
4
1
1
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
1
1
0
0
1
1
2
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
2
0
0
0
4
0
0
0
1
2
1
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
1
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
5
0
0
0
0
0
0
1
6
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
2
0
2
0
0
0
0
2
1
0
2
3
0
1
0
0
0
1
0
1
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
2
0
0
2
0
0
0
0
1
0
0
3
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
6
0
0
1
0
0
0
0
0
1
4
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
1
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
6
0
2
0
0
0
0
1
1
0
0
0
1
0
0
1
1
0
0
2
0
2
0
0
1
6
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
1
0
0
9
0
1
0
0
0
0
0
1
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
1
0
0
2
4
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
2
0
0
1
2
0
0
2
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
1
0
2
0
0
0
1
2
2
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
3
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
2
1
0
1
8
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
3
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
3
0
0
2
0
0
0
3
1
0
2
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
2
0
0
0
0
1
0
0
2
7
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
2
1
2
0
1
0
0
1
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
2
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
1
1
2
1
0
2
0
0
1
0
0
2
0
0
0
1
2
0
2
1
0
0
0
0
1
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
2
0
2
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
2
0
2
0
0
0
4
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
2
0
0
1
1
0
1
0
0
1
0
1
2
0
0
0
0
0
2
0
2
0
0
0
0
1
2
0
1
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
3
2
0
0
1
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
2
0
1
2
0
0
1
0
0
2
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
6
0
3
0
2
0
3
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
1
0
2
0
2
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
1
2
0
0
1
0
0
0
0
0
0
2
1
0
3
0
0
4
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
2
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
2
0
0
3
0
2
1
0
0
0
0
0
0
0
0
6
0
0
0
1
3
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
2
2
2
0
0
4
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
3
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
5
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
1
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
5
0
3
0
0
0
0
0
0
3
0
1
0
0
1
0
0
0
3
3
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
3
0
2
0
0
1
0
0
0
1
4
0
0
2
1
0
1
0
0
0
0
0
1
0
1
0
0
0
2
0
0
1
0
0
2
0
2
0
1
0
0
1
0
3
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
2
2
0
1
4
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
1
0
0
0
3
0
5
0
0
2
0
0
0
0
3
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
1
1
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
1
0
0
5
0
0
0
0
0
0
2
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
1
0
0
0
1
1
0
0
2
1
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
2
2
0
0
0
2
0
0
0
1
0
0
0
2
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
1
0
4
2
0
1
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
2
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
2
0
7
3
5
0
1
0
1
0
0
0
2
0
0
0
0
2
1
0
0
0
2
3
2
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
3
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
3
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
5
0
0
0
0
0
2
1
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
3
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
7
1
0
0
3
0
0
2
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
5
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
3
0
2
0
0
0
0
0
1
2
0
0
1
0
1
0
1
1
2
1
2
0
0
0
0
4
0
0
2
3
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
2
0
1
1
0
2
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
3
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
1
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
3
1
0
0
1
2
0
0
0
0
0
0
2
0
3
0
0
1
0
0
1
0
1
0
1
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
1
2
0
0
0
0
3
0
0
0
0
0
3
1
0
2
0
0
0
0
0
2
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
2
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
1
0
2
0
1
0
1
3
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
2
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
2
2
5
0
0
5
0
1
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
3
0
0
0
3
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
2
0
1
0
2
0
0
0
3
0
0
0
0
0
0
0
1
2
1
0
0
0
1
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
6
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
5
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
1
0
0
0
0
0
2
2
0
0
4
0
0
0
0
0
0
0
0
11
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
1
1
2
0
0
0
1
0
0
0
1
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
3
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
4
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
4
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
3
0
2
0
0
0
0
0
0
0
0
1
5
0
0
0
0
2
1
4
0
0
0
0
0
0
0
0
0
0
1
0
1
1
2
0
0
0
1
2
0
6
0
1
0
0
0
3
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
1
1
0
0
0
0
0
0
2
1
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
1
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
2
0
0
3
0
1
1
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
3
0
3
2
2
0
0
0
0
0
0
0
0
0
5
0
0
0
2
0
0
0
2
1
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
1
0
1
2
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
3
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
2
1
0
0
0
0
3
0
0
0
0
2
0
0
1
0
2
0
2
0
0
0
2
2
0
0
2
2
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
1
2
0
0
2
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
2
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
3
0
0
1
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
2
2
0
3
0
0
2
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
3
0
0
0
0
0
2
0
2
0
0
2
0
0
0
4
0
1
0
0
0
1
0
0
3
1
0
0
0
1
0
0
0
0
0
2
0
0
2
3
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
1
1
3
2
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
2
0
1
0
2
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
2
1
2
0
0
3
0
1
0
0
0
2
3
1
0
1
2
0
0
0
0
0
0
0
3
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
2
0
0
0
0
2
6
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
2
2
1
0
0
0
0
0
0
12
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
9
0
1
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
4
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
1
0
0
2
2
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
4
2
0
1
10
0
1
0
0
2
0
0
1
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
5
0
0
0
0
0
0
0
0
0
0
0
3
2
0
1
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
2
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
2
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
3
0
0
1
1
0
3
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
3
0
0
1
1
0
0
2
0
0
1
0
0
0
0
1
0
2
0
1
0
0
0
0
0
2
0
0
0
2
4
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
3
2
0
1
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
2
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
2
3
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
2
0
0
0
1
4
0
0
2
0
0
1
2
1
0
2
0
1
0
3
0
0
0
0
0
0
1
0
0
1
2
1
2
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
4
0
0
1
0
3
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
3
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
2
0
0
0
0
1
0
2
1
2
0
0
0
2
0
0
0
1
0
0
1
0
1
2
1
0
0
0
0
2
0
0
0
0
0
4
4
0
0
0
0
1
0
3
0
0
0
0
0
3
0
0
0
0
2
2
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
3
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
1
0
1
0
0
0
3
1
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
1
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
1
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
3
4
0
0
0
0
0
0
0
0
2
1
1
0
1
0
0
0
0
2
0
0
0
0
0
2
1
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
1
0
0
0
2
2
0
1
0
0
1
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
2
0
0
2
0
2
0
0
1
0
0
1
0
2
1
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
2
0
0
0
0
0
0
0
4
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
2
1
2
7
0
0
2
3
0
0
0
0
0
2
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
1
2
0
1
0
0
2
2
0
0
2
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
3
0
1
0
0
1
0
0
0
2
0
0
0
0
2
3
0
0
1
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
3
0
0
2
0
6
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
3
0
2
0
2
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
3
0
0
0
1
2
0
1
2
0
0
0
1
0
0
0
0
1
0
0
0
2
1
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
1
0
1
0
0
0
0
0
0
0
2
1
0
0
2
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
5
0
1
0
2
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
3
0
1
2
0
0
0
0
0
1
0
1
0
4
2
0
0
1
0
0
0
1
0
2
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
2
0
0
0
0
3
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
1
1
1
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
4
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
8
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
2
0
2
1
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
0
1
7
0
0
0
1
0
0
0
0
0
1
0
0
3
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
2
2
1
0
0
0
1
0
0
2
0
0
0
0
6
0
0
2
0
1
0
0
0
1
2
0
0
1
0
1
2
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
2
0
2
0
0
0
1
0
0
1
0
0
2
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
2
0
0
3
2
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
3
1
1
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
19
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
2
4
0
0
1
0
0
0
0
0
0
0
0
3
0
6
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
4
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
2
0
1
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
1
0
3
0
0
0
1
2
1
0
2
3
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
1
0
0
0
0
2
0
0
0
0
3
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
7
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
3
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
3
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
5
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
1
0
2
0
1
1
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
1
0
0
1
1
0
2
0
0
0
0
0
0
0
2
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
4
0
3
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
8
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
2
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
2
0
0
0
2
2
2
0
1
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
3
0
0
3
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
2
0
2
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
8
0
1
0
2
0
0
0
0
0
1
0
0
0
2
2
0
0
0
2
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
2
0
1
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
3
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
1
0
0
0
0
0
0
2
0
0
3
1
0
0
0
0
0
1
0
0
0
0
2
0
0
1
4
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
1
0
2
0
1
0
1
0
0
1
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
2
1
0
2
0
0
0
1
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
2
2
0
1
2
0
0
0
0
0
1
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
1
0
0
0
2
3
2
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
5
1
0
2
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
2
1
0
0
0
1
0
0
0
0
0
2
0
0
0
3
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
4
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
1
2
1
2
2
1
2
0
0
0
0
0
0
0
2
0
0
0
3
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
1
0
0
0
5
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
3
0
0
0
2
0
0
3
0
0
0
0
0
3
1
0
0
0
4
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
2
0
0
0
2
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
5
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
2
2
0
0
0
0
0
0
9
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
4
0
0
0
0
0
0
2
2
0
0
3
0
0
0
3
0
0
0
1
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
2
0
0
0
2
2
0
0
3
0
0
0
0
0
1
2
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
3
5
0
0
0
0
0
0
1
1
0
2
0
0
0
0
1
0
0
0
3
0
0
2
0
0
0
0
2
0
1
0
1
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
2
1
0
0
0
1
0
0
0
0
0
2
0
0
1
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
1
2
0
0
0
1
0
0
2
0
0
0
3
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
2
0
2
0
0
1
0
1
0
0
1
0
1
0
1
2
0
0
2
0
3
0
0
6
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
1
0
2
0
0
0
1
2
0
0
3
0
0
2
1
2
0
0
2
0
0
0
1
0
2
2
0
0
0
0
2
0
0
1
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
2
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
3
0
0
1
0
3
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
6
0
2
0
1
0
2
1
2
0
0
0
0
0
5
0
1
2
1
0
0
2
0
0
0
2
0
0
1
0
1
0
0
0
0
0
2
0
0
2
0
0
0
1
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
6
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
3
1
0
0
0
2
0
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
4
3
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
6
2
0
0
0
0
2
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
2
0
0
1
0
0
2
0
0
1
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
1
1
2
0
0
1
0
0
0
1
0
0
1
4
1
0
0
0
2
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
3
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
3
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
3
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
10
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
2
0
0
0
0
2
0
0
0
2
2
2
0
0
0
0
2
0
1
0
0
0
0
2
0
0
1
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
2
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
2
2
0
0
1
0
2
0
0
1
0
2
0
0
1
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
4
3
0
0
0
1
0
0
0
3
2
0
0
0
1
0
0
3
1
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
1
2
0
0
2
0
0
0
0
0
0
4
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
1
2
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
5
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
3
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
7
0
0
2
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
2
3
0
0
1
2
0
1
0
2
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
5
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
1
5
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
6
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
2
2
1
0
0
0
0
1
2
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
3
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
6
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
4
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
2
2
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
1
0
1
2
0
1
0
0
0
0
0
0
0
3
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
1
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
2
1
0
2
0
1
0
1
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
1
1
0
0
2
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
2
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
3
0
0
0
0
1
1
0
1
0
0
0
2
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
1
0
0
1
0
0
2
1
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
3
4
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
2
1
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
4
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
6
2
0
0
0
0
0
0
2
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
2
0
2
0
0
2
0
0
0
2
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
4
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
1
0
0
2
2
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
1
0
0
0
0
0
0
1
0
2
2
0
3
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
6
0
0
0
7
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
2
3
0
2
0
0
0
1
0
1
0
2
0
0
0
1
0
0
0
2
0
0
1
1
0
0
0
2
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
1
1
1
2
0
0
0
2
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
1
2
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
2
3
2
0
0
2
0
0
0
0
2
0
0
0
1
1
0
1
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
8
1
1
1
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
1
2
0
4
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
2
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
2
0
2
0
6
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
1
0
1
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
2
0
0
0
0
1
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
1
2
0
0
2
0
0
0
1
0
0
0
0
0
0
5
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
2
0
0
0
0
0
2
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
3
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
1
0
1
0
1
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
7
1
0
2
1
1
0
6
0
1
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
2
1
3
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
1
0
0
0
0
1
0
0
2
4
0
1
1
0
0
0
3
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
9
1
0
1
0
0
2
2
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
2
0
0
0
1
0
1
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
3
0
0
1
0
0
0
0
0
2
6
0
0
2
0
0
1
1
2
2
0
0
6
0
0
0
2
0
0
0
0
0
0
0
3
5
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
1
0
1
0
2
0
1
0
0
6
0
0
1
0
0
0
0
0
1
1
0
0
0
1
1
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
1
0
0
2
0
0
1
2
0
0
0
0
0
0
2
2
1
0
1
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
3
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
1
0
0
0
0
2
0
2
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
3
0
1
0
2
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
3
1
0
0
0
0
0
0
1
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
2
1
1
0
0
0
2
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
4
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
2
0
0
0
0
1
1
1
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
3
0
1
0
0
0
0
1
4
0
0
0
0
2
0
1
2
2
0
0
0
1
0
0
0
0
0
0
0
7
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
4
1
1
0
0
2
0
0
1
0
0
0
0
0
0
6
0
0
0
3
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
2
0
1
3
4
1
2
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
3
0
2
3
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
2
0
0
0
0
1
1
0
2
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
1
0
0
0
0
7
0
0
0
0
0
0
0
1
0
0
0
0
1
3
0
1
0
1
0
0
0
1
0
0
2
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
1
0
1
0
0
2
0
0
0
4
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
2
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
4
0
0
0
0
0
1
0
0
0
2
1
0
1
0
2
2
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
2
0
0
2
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
1
0
0
0
1
2
0
2
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
2
1
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
1
0
0
0
3
0
2
0
1
1
0
0
0
0
0
1
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
1
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
1
2
0
0
3
0
0
0
0
1
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
2
0
0
0
0
0
0
1
2
0
1
0
0
1
0
0
0
0
1
0
2
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
2
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
2
1
0
1
0
0
0
2
0
0
0
1
0
2
0
0
0
0
2
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
3
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
2
0
0
3
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
2
1
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
2
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
1
3
0
0
0
0
1
0
3
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
5
1
0
0
0
1
0
0
0
2
1
4
0
1
0
3
0
0
0
0
3
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
1
2
1
0
0
0
0
0
0
2
0
1
0
0
1
0
2
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
5
0
0
0
0
0
0
2
0
0
0
3
8
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
3
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
7
1
0
1
1
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
2
0
1
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
2
0
0
2
3
0
0
0
1
1
0
0
2
1
0
2
0
1
0
3
0
0
0
0
2
1
0
0
2
0
2
0
1
0
1
0
0
0
1
0
2
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
1
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
3
0
0
0
2
0
0
0
6
2
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
2
5
1
0
0
0
1
0
2
0
0
0
2
0
0
0
0
2
0
0
1
0
0
2
2
0
0
0
0
0
0
0
2
4
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
8
1
0
0
0
0
0
0
1
2
0
1
0
1
5
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
1
0
0
0
1
0
0
0
0
1
3
0
1
0
0
0
8
2
0
0
2
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
5
0
0
0
0
0
2
0
0
0
0
1
1
0
1
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
1
2
0
0
1
0
0
2
0
0
1
3
0
0
0
2
0
0
0
0
1
1
1
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
3
2
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
3
0
2
0
0
2
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
2
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
6
0
1
0
0
1
0
0
0
0
1
0
2
0
0
1
0
2
0
0
0
3
0
2
0
0
0
2
0
0
2
0
2
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
3
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
1
1
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
4
0
0
0
0
0
0
3
0
0
0
1
0
1
0
0
1
0
0
2
2
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
2
0
6
0
0
0
0
0
0
0
2
1
0
1
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
3
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
2
2
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
2
3
0
2
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
2
0
0
2
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
2
0
0
0
1
1
1
0
0
0
0
0
0
2
0
1
0
0
0
2
2
0
0
0
0
0
0
2
1
2
0
2
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
6
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
2
0
0
1
0
0
0
0
0
0
0
0
1
0
7
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
1
0
1
1
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
2
3
0
1
1
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
3
5
0
0
0
1
0
0
0
2
0
2
0
2
0
0
0
2
0
0
0
2
0
0
0
1
2
1
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
1
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
1
0
1
2
0
0
1
0
0
0
2
2
2
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
4
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
4
0
0
6
0
0
0
0
0
0
0
1
0
1
2
1
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
7
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
2
3
0
1
0
4
3
0
0
0
0
0
2
2
0
0
0
0
0
1
0
2
0
0
0
0
2
2
1
1
0
0
0
0
0
0
0
3
0
0
0
2
3
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
3
0
1
0
0
0
1
0
0
0
0
1
0
0
0
7
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
2
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7
0
1
0
2
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
4
0
0
0
0
0
0
0
0
2
1
0
0
0
2
1
0
0
0
2
1
1
1
0
0
2
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
1
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
3
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
5
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
4
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
1
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
1
1
0
2
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
8
0
0
0
0
0
2
0
1
0
3
0
2
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
1
0
0
0
0
4
2
0
0
1
2
0
1
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
2
1
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
1
2
0
1
3
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
2
0
1
2
1
8
0
0
0
0
0
6
0
0
0
1
4
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
2
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
3
0
0
1
0
1
0
0
1
0
2
0
4
0
0
0
0
0
0
0
1
2
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
2
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
3
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
2
2
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
1
0
1
4
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
1
0
0
0
0
1
3
1
0
0
0
4
3
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
2
0
0
0
2
0
0
0
2
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
2
0
0
0
0
0
5
0
0
0
1
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
2
0
1
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
4
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
1
3
2
1
2
0
0
0
2
0
0
2
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
4
0
0
2
1
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
2
2
0
0
2
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
3
0
1
0
0
1
0
2
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
1
2
0
0
0
0
1
0
5
0
0
0
1
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
3
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
6
1
0
1
0
0
0
0
0
1
0
0
3
1
0
2
2
1
0
1
0
4
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
2
0
0
2
0
0
0
0
0
1
0
0
2
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
3
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
3
0
1
2
0
0
0
0
0
0
0
4
1
2
3
0
0
0
4
2
0
0
2
2
0
0
0
0
0
0
0
2
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
3
0
0
2
0
1
1
1
0
0
0
1
0
0
2
0
0
0
2
0
1
0
2
0
1
0
0
0
0
1
0
1
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
1
2
0
0
0
0
0
2
0
1
0
0
5
1
0
0
2
1
0
1
0
0
0
1
2
0
0
0
0
1
2
1
0
4
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
8
0
0
0
0
0
0
0
3
3
0
0
0
0
0
2
0
1
0
2
1
0
3
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
2
0
0
0
0
1
2
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
1
0
0
0
3
2
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
1
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
2
0
2
1
0
1
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
5
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
2
1
2
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
2
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
6
1
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
3
1
2
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
2
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
2
0
0
2
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
3
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
1
0
0
0
0
0
3
0
0
3
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
2
1
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
3
1
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
1
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
1
2
0
1
0
0
0
0
0
0
0
0
1
0
0
2
1
1
0
0
0
2
1
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
2
1
1
2
0
0
2
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
2
0
2
0
2
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
3
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
1
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
1
0
2
0
0
2
1
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
2
0
0
0
2
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
2
0
3
0
0
0
0
0
0
0
0
0
0
3
0
0
1
2
0
6
0
2
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
3
0
0
0
0
0
1
0
2
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
5
1
0
1
4
0
0
0
0
0
0
0
7
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
2
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
7
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
2
0
1
4
1
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
2
0
1
0
0
6
0
0
0
1
0
0
0
0
3
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
1
0
0
3
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
1
0
0
2
0
0
1
1
0
1
0
4
0
0
0
0
3
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
2
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
1
0
0
0
1
0
4
0
0
1
0
0
1
2
0
2
0
1
0
3
0
0
0
2
0
1
0
0
0
1
0
3
0
0
0
0
0
0
0
1
0
1
0
2
2
2
0
2
0
0
2
0
0
0
1
0
1
0
0
0
2
2
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
3
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
2
0
0
0
0
9
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
1
0
0
2
22
2
0
0
0
0
0
0
4
0
2
3
0
0
0
0
1
0
2
0
0
1
0
4
0
0
0
0
0
0
1
0
0
1
1
0
0
1
2
0
2
0
9
0
0
1
1
0
0
1
0
0
0
0
0
3
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
4
2
1
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
4
0
0
0
0
0
0
2
0
0
2
0
3
1
0
3
1
0
2
0
2
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
1
3
2
0
0
1
1
0
2
1
3
1
0
2
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
2
0
2
1
2
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
6
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
3
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
4
0
0
0
2
2
2
0
0
0
0
2
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
3
2
0
0
3
0
0
0
0
0
0
0
0
1
2
2
1
0
0
1
0
0
0
1
0
1
0
0
0
0
1
4
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
4
0
2
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
4
0
0
0
5
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
1
1
0
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
2
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
1
2
0
0
0
0
0
0
0
2
3
3
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
2
0
2
0
3
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
2
0
2
0
0
0
3
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
1
4
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
2
0
2
0
0
0
0
1
3
0
2
0
0
1
1
2
0
0
0
0
6
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
2
3
0
0
0
0
1
2
1
0
2
2
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
2
0
0
2
0
0
0
2
0
0
1
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
2
0
1
2
0
1
0
0
2
4
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
2
0
1
3
3
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
1
8
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
2
0
0
0
0
0
3
0
0
0
0
0
0
3
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
1
2
0
2
1
2
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
3
2
0
1
1
0
0
0
0
2
2
0
0
0
3
0
0
0
0
0
0
0
0
1
0
1
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
1
0
1
1
0
0
0
0
0
1
1
2
0
0
1
1
2
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
3
0
0
0
0
0
1
2
1
0
0
0
0
2
0
0
0
0
2
3
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
3
0
2
1
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
1
0
1
0
0
2
0
0
0
0
1
0
0
2
1
0
4
0
3
2
0
4
0
0
1
0
0
1
0
1
3
2
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
5
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
2
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
1
2
0
0
1
0
0
1
1
0
2
2
0
3
1
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
4
1
0
0
1
1
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
2
0
0
0
0
2
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
6
0
0
2
0
0
1
0
0
6
0
0
0
2
0
2
0
1
0
1
0
0
0
0
0
0
0
1
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
3
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
2
1
0
0
0
0
0
1
2
0
0
0
2
0
0
0
2
0
2
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
4
0
0
0
1
5
0
0
0
0
2
0
0
0
0
0
0
1
0
3
0
0
2
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
2
3
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
1
0
2
0
0
3
0
0
1
0
2
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
1
2
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
3
0
0
1
2
0
0
0
0
2
0
1
2
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
1
3
0
1
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
5
0
0
0
0
0
0
2
0
1
0
2
0
2
0
0
0
0
0
0
2
1
2
0
0
3
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
3
0
0
1
1
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
1
1
1
0
1
1
0
0
2
0
0
0
0
0
1
0
0
1
0
5
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
2
2
0
4
0
1
0
0
0
2
1
0
0
1
0
0
2
0
0
1
2
2
0
1
0
0
0
0
0
2
0
2
4
0
13
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
5
0
0
2
2
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
3
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
4
0
0
0
0
2
3
1
0
0
0
0
4
0
1
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
2
0
0
0
0
0
0
2
0
0
0
1
1
1
0
0
1
1
0
0
0
0
0
0
2
0
1
0
3
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
6
0
0
0
0
0
2
2
0
0
0
1
0
1
2
0
0
0
2
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
2
4
0
0
0
0
0
2
1
0
0
0
0
1
0
3
1
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
1
0
2
0
0
1
0
0
2
0
0
1
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
1
0
0
4
0
1
3
0
1
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
1
0
4
0
0
0
0
0
2
0
2
2
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
1
0
0
0
2
0
7
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
7
0
0
2
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
6
0
0
0
1
2
0
0
0
0
0
0
1
0
0
2
0
0
0
3
0
0
0
2
0
2
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
1
3
0
1
2
0
3
0
0
0
0
0
0
0
1
0
0
4
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
2
0
0
2
0
0
0
0
0
0
0
7
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
5
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
4
0
0
1
0
2
0
0
0
0
2
2
0
0
0
0
0
1
0
2
0
1
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
1
1
2
0
0
0
1
1
0
0
2
0
0
3
0
2
0
0
1
0
0
1
2
0
2
0
0
0
0
1
0
0
3
0
1
0
1
0
4
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
5
2
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
3
6
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
2
0
2
0
1
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
3
2
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
3
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
2
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
3
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
1
0
0
0
2
0
0
0
0
0
0
0
1
1
3
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
1
1
1
0
1
0
2
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
2
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
2
2
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
2
0
1
1
0
0
0
0
0
0
3
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
2
1
0
0
0
0
0
2
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
2
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
2
1
0
0
2
0
0
3
1
1
0
1
1
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
1
0
3
0
0
0
1
0
0
2
0
0
2
0
0
0
1
1
0
2
0
0
3
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
1
0
0
0
2
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
3
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
8
0
0
0
2
0
0
0
0
0
4
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
1
0
0
2
0
4
8
0
1
0
2
0
0
5
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
2
0
0
2
0
0
1
0
0
0
0
0
0
1
0
1
2
1
2
0
0
0
2
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
3
0
0
0
0
0
0
0
2
0
2
2
0
0
0
2
0
2
0
0
0
0
0
0
0
2
2
1
0
0
0
2
1
4
0
2
1
2
0
0
0
0
0
2
0
0
1
0
0
2
0
0
1
0
3
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
2
0
0
0
0
2
0
0
0
1
2
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
1
3
2
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
3
0
0
0
9
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
6
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
2
0
2
0
0
0
0
1
0
1
0
0
0
0
2
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
1
0
2
0
0
1
1
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
2
0
0
0
0
2
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
1
1
0
0
0
0
0
1
0
0
0
1
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
3
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
3
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
3
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
5
0
0
0
0
1
0
0
2
0
0
0
2
0
0
4
2
2
2
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
1
2
0
0
0
0
0
0
0
2
0
1
0
6
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
3
0
0
4
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
3
2
0
0
0
0
0
0
1
2
0
0
0
1
1
1
4
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
3
0
0
0
0
3
0
0
0
1
1
0
2
0
0
0
0
0
0
5
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
3
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
4
0
1
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
5
2
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
1
2
1
0
6
0
0
0
2
0
0
1
1
0
0
1
1
0
1
0
4
0
0
1
3
0
0
0
0
0
4
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
1
0
0
0
0
1
2
0
0
0
1
0
1
0
2
0
0
0
0
1
1
3
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
4
0
0
0
2
0
0
1
2
0
4
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
3
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
3
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
6
0
0
0
1
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
5
0
1
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
2
0
1
2
0
0
0
1
0
2
0
2
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
1
3
0
0
0
2
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
3
1
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
2
2
0
0
0
0
3
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
1
0
0
0
2
1
0
0
0
2
3
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
1
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
1
0
3
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
2
0
1
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
5
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
2
0
0
2
1
0
0
0
2
1
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
5
3
1
0
0
2
0
0
2
3
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
1
0
1
1
0
0
1
0
0
0
0
0
3
0
0
0
1
0
0
4
0
0
0
0
0
0
2
1
0
0
1
0
0
2
2
0
0
2
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
1
0
0
2
0
0
0
1
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
2
3
0
0
0
1
2
1
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
2
2
0
0
0
1
0
2
0
1
1
0
0
0
0
2
0
0
0
1
0
0
3
0
0
0
0
1
0
0
0
0
6
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
3
0
0
2
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
1
0
0
1
0
1
2
2
0
2
0
0
4
0
0
0
0
2
0
3
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
5
0
0
0
0
3
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
1
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
1
0
0
1
0
0
1
0
0
0
0
0
1
0
2
1
2
0
0
1
0
0
1
3
0
1
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
2
0
0
0
0
3
0
2
0
0
1
0
0
0
0
0
1
0
0
1
0
0
3
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
2
0
0
2
2
1
0
1
0
0
2
0
1
2
2
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
2
0
0
1
2
0
4
0
1
0
0
0
0
2
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
3
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
1
2
0
0
2
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
1
1
0
0
2
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
1
1
0
0
0
2
1
0
0
0
0
2
2
0
2
1
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
3
0
3
1
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
1
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
1
1
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
2
0
1
3
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
2
0
1
0
0
2
0
0
0
0
1
2
1
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
2
2
1
2
3
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
6
0
0
0
0
0
0
3
4
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
3
0
0
0
0
3
1
2
0
0
0
0
0
0
0
0
1
1
0
0
1
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
2
2
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
1
3
2
0
0
2
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
1
2
0
0
2
0
2
0
1
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
3
0
0
2
0
0
0
3
1
0
2
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
3
2
0
1
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
2
6
2
0
1
0
0
0
0
0
0
3
0
0
2
0
0
1
0
0
0
0
0
0
0
0
4
0
2
0
1
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
5
0
0
1
1
0
0
0
7
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
3
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
4
0
0
0
0
3
0
2
0
0
0
0
2
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
1
0
2
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
2
4
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
4
0
2
0
0
2
0
1
0
0
0
1
0
0
2
0
2
2
0
0
2
5
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
3
0
0
0
1
0
0
0
0
0
0
0
0
0
2
4
0
2
0
0
0
1
0
0
0
5
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
2
2
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
3
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
2
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
1
3
0
0
1
1
0
0
9
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
2
0
0
1
0
0
3
0
1
0
6
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
1
2
2
0
0
2
0
0
0
7
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
3
0
0
0
2
1
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
3
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
1
0
3
7
0
0
0
0
0
0
0
0
1
0
3
1
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
2
2
2
0
0
0
0
0
2
2
0
0
2
0
1
1
1
1
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
6
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
4
0
0
0
0
1
0
3
0
2
0
0
1
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
2
1
0
0
0
0
0
0
1
0
1
6
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
1
0
2
0
0
3
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
3
0
3
0
0
0
0
0
2
0
0
1
1
2
0
2
0
2
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
1
0
0
1
2
0
1
1
1
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
4
0
0
0
0
1
0
0
0
2
1
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
1
0
0
1
0
1
0
0
0
2
0
2
0
1
0
0
0
1
1
0
0
0
0
2
1
0
0
0
0
2
1
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
2
0
2
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
2
0
0
2
0
0
0
1
0
2
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
4
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
5
0
0
0
0
0
3
0
0
1
0
0
1
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
2
0
1
1
2
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
1
0
0
3
0
0
0
0
3
0
0
0
0
0
0
1
0
4
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
2
0
0
1
1
0
0
0
0
0
0
0
1
2
0
1
0
3
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
5
0
0
0
1
0
0
2
0
0
0
1
0
3
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
2
1
2
1
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
2
0
0
2
0
3
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
1
0
0
0
1
2
2
0
0
1
0
0
1
1
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
1
0
5
0
0
0
0
0
0
0
0
1
0
2
0
0
0
6
0
1
1
0
1
0
2
0
2
0
1
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
2
2
0
2
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
4
2
2
0
1
1
1
0
0
0
0
1
0
0
0
0
2
0
1
2
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
2
0
1
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
3
0
1
1
2
1
0
0
0
0
0
2
0
1
0
5
0
0
0
2
0
2
0
0
3
0
0
3
6
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
3
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
2
0
0
1
0
2
0
1
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
1
0
0
0
2
1
0
0
1
0
3
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
1
0
4
0
0
0
0
0
0
0
1
0
0
0
0
6
0
0
0
3
0
0
2
0
0
0
0
0
1
0
2
0
0
4
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
2
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
3
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
1
2
0
0
3
0
0
0
0
0
1
3
0
0
0
2
0
2
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
2
1
2
0
0
0
2
0
0
0
0
0
0
0
3
2
0
1
1
2
2
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
1
0
1
4
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
1
2
1
0
0
1
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
3
0
0
0
2
5
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
6
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
3
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
4
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
3
3
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
2
0
2
0
3
0
0
0
0
2
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
4
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
2
1
0
1
0
2
0
0
1
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
3
0
1
0
0
0
2
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
3
1
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
7
0
0
0
0
0
0
0
0
0
1
4
2
1
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
2
0
0
0
6
0
0
1
2
1
0
1
0
0
0
0
1
1
0
0
0
4
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
5
1
2
0
0
0
0
2
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
3
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
1
0
4
0
0
1
0
1
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
2
0
1
1
0
1
0
0
1
2
0
0
0
1
1
0
1
0
0
0
0
0
1
0
1
0
1
1
0
0
0
1
0
0
2
0
1
0
2
0
1
2
2
0
1
0
0
0
2
0
3
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
1
4
0
0
0
0
0
0
1
1
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
1
0
3
2
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
2
0
1
1
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
4
0
0
1
0
3
0
0
0
0
2
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
2
1
0
0
0
0
0
1
1
0
0
0
3
1
1
0
1
0
0
1
0
0
0
0
0
0
0
2
1
0
1
0
0
0
1
0
0
1
0
0
0
0
2
1
0
0
0
0
2
0
0
1
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
1
2
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
1
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
3
0
0
0
2
0
1
2
5
0
2
0
0
1
0
0
1
0
2
0
2
0
0
0
0
1
4
0
0
0
1
1
0
0
1
0
0
2
0
0
0
0
0
0
0
1
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
4
0
0
0
2
2
0
0
0
0
0
1
0
0
1
0
0
2
0
1
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
2
0
1
0
0
2
0
2
0
0
1
0
1
1
1
0
0
0
0
0
3
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
3
2
1
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
3
0
0
0
0
3
0
0
0
2
0
0
0
1
0
0
0
1
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
5
1
0
2
0
1
0
1
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
6
1
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
1
0
0
1
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
4
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
1
4
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
3
0
1
0
1
1
0
0
0
1
3
0
0
0
2
0
0
0
0
0
0
1
0
6
2
1
1
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
1
1
1
0
4
0
0
0
0
0
0
0
0
0
3
0
0
1
1
0
0
2
0
0
0
2
1
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
3
0
1
2
0
2
0
0
2
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
2
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
3
0
0
0
2
0
2
0
0
0
2
0
0
2
0
0
0
0
0
2
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
2
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
3
0
0
0
1
0
5
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
2
0
1
0
0
0
3
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
2
0
0
0
2
1
0
0
0
0
6
0
0
2
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
2
0
2
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
2
0
0
0
0
0
2
3
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
4
3
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
1
2
0
4
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
3
0
1
0
0
1
0
2
4
0
0
1
0
0
0
0
0
0
2
2
0
2
0
1
0
0
0
0
0
0
0
0
2
4
0
0
3
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
1
0
0
0
0
0
3
2
0
0
2
0
0
5
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
1
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
1
0
3
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
1
0
0
0
1
0
0
1
2
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
4
1
0
0
0
2
0
0
0
0
2
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
2
0
2
0
0
1
2
0
0
1
0
0
1
0
0
3
2
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
2
0
2
1
1
0
0
2
0
0
0
1
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
1
2
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
1
1
0
0
0
4
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
2
0
4
0
0
0
4
0
0
2
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
3
0
0
2
0
0
2
3
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
1
3
2
1
0
0
0
0
2
0
1
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
3
0
0
1
0
0
2
1
0
0
1
0
1
1
0
1
0
0
0
1
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
2
0
1
1
1
0
1
0
0
1
0
0
0
0
0
2
0
2
0
1
0
0
2
0
0
3
0
0
3
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
1
2
3
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
3
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
1
2
0
0
0
0
0
0
0
0
2
0
2
0
6
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
2
0
0
1
2
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
3
2
1
0
0
0
0
0
2
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
1
0
4
0
1
2
1
4
2
0
4
2
0
0
2
0
0
0
0
4
0
0
1
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
5
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
1
2
2
1
1
0
0
0
0
0
1
1
0
0
0
2
1
1
2
0
0
3
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
1
0
0
0
2
2
0
0
0
2
1
0
2
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
1
1
0
0
0
0
2
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
1
2
1
6
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
2
1
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
1
1
0
0
0
0
0
0
0
1
0
3
0
0
0
2
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
1
0
0
0
0
2
1
0
3
0
1
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
2
1
0
1
0
0
0
0
2
0
1
2
1
0
0
0
0
0
0
0
1
0
1
3
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
3
1
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
2
1
1
5
0
0
1
0
0
3
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
3
2
2
1
0
0
0
0
0
1
0
1
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
4
0
0
0
2
0
0
0
0
0
1
0
0
0
5
1
0
1
2
0
0
0
1
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
1
0
2
1
2
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
3
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
1
0
0
1
4
0
0
2
0
3
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
6
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
3
1
0
2
0
1
0
2
1
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
1
0
3
0
0
0
0
0
1
1
0
0
7
0
0
0
0
0
1
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
9
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
1
0
1
1
0
1
0
2
0
1
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
4
0
1
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
3
0
0
2
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
2
1
0
1
0
1
3
0
0
0
1
0
1
0
1
0
3
0
1
1
0
0
1
2
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
2
2
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
6
0
0
0
0
1
0
2
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
8
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
14
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
2
1
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
1
0
0
0
3
2
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
5
1
0
2
0
0
0
4
0
1
1
3
0
0
0
1
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
3
0
1
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
1
2
0
0
0
1
0
0
0
1
0
0
2
1
1
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
2
0
0
2
0
0
0
0
1
0
0
2
4
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
1
2
3
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
1
1
0
2
0
0
0
0
1
0
0
3
0
0
0
2
0
0
0
1
0
0
0
5
2
0
1
0
0
0
2
0
0
0
3
1
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
5
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
5
2
0
0
0
1
2
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
2
4
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
4
0
0
0
0
1
0
2
0
0
1
1
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
1
1
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
2
0
3
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
2
2
0
1
1
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
2
0
3
0
2
0
0
0
0
4
0
0
3
0
0
0
0
0
0
0
0
0
0
2
1
3
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
4
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
2
0
0
3
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
2
1
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
3
1
1
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
3
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
2
0
2
0
1
0
2
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
2
0
0
0
2
0
0
1
1
0
0
1
0
2
0
0
0
0
1
0
0
0
2
0
1
0
1
0
0
2
0
0
0
0
0
1
0
4
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
5
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
4
0
0
0
0
1
0
0
1
1
0
0
2
0
0
2
0
1
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
1
3
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
1
0
0
1
1
3
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
1
2
2
2
0
0
0
2
0
1
2
0
0
2
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
2
4
0
0
1
0
0
0
0
1
0
0
0
0
1
0
3
0
0
0
0
0
0
0
2
0
0
2
0
1
0
1
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
2
6
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
3
0
0
1
0
0
0
4
0
2
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
2
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
1
2
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
3
3
0
0
0
1
0
0
2
0
0
2
3
0
0
0
0
1
6
0
0
0
2
0
4
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
1
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
6
0
0
1
2
2
0
0
0
3
0
0
0
2
1
0
1
2
0
0
0
1
4
0
0
0
0
0
2
2
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
1
0
0
1
0
0
0
0
3
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
2
0
0
0
0
1
0
3
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
10
2
0
0
0
0
0
2
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
2
0
2
0
0
1
0
0
0
3
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
5
0
0
0
2
0
0
0
0
0
1
9
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
2
0
1
0
1
0
2
0
0
0
0
2
0
0
0
0
0
2
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
2
0
0
2
0
0
0
2
3
2
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
3
0
0
1
0
0
5
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
2
2
0
1
1
0
0
0
0
0
0
0
0
0
2
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
3
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
6
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
1
1
0
0
0
0
0
2
0
0
0
2
0
1
0
0
1
1
0
0
0
0
0
1
1
0
1
0
2
0
0
0
0
0
0
0
2
0
5
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
2
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
4
0
1
0
0
0
1
0
0
0
0
0
0
1
0
2
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
1
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
2
0
0
3
0
0
0
0
4
0
0
1
1
0
0
0
0
2
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
5
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
13
0
4
0
0
2
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
4
0
0
0
1
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
5
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
6
1
3
2
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
1
1
1
2
2
1
0
2
0
0
0
0
0
0
0
1
0
5
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
2
2
0
1
2
0
0
2
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
5
0
0
0
0
1
1
0
1
0
1
0
0
0
1
0
0
0
0
3
0
0
0
2
0
2
0
2
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
1
1
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
3
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
1
0
0
0
0
1
0
0
0
0
2
0
0
1
0
15
0
1
0
2
0
0
1
2
0
0
2
1
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
4
1
0
3
1
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
1
0
2
0
1
0
0
1
0
0
0
3
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
1
0
0
2
0
0
2
0
2
1
0
1
3
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
2
0
0
1
0
0
2
2
0
0
0
2
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
3
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
2
0
0
0
2
0
0
0
1
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
7
0
0
2
0
0
1
0
2
0
1
0
1
2
0
0
2
0
0
9
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
2
0
0
1
0
1
0
0
0
1
3
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
2
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
1
0
0
1
0
0
0
0
2
0
0
1
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
1
0
0
2
0
0
0
1
0
0
0
0
0
2
1
0
2
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
3
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
5
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
1
4
0
5
0
0
0
0
0
2
1
0
1
0
0
0
5
1
0
0
0
0
0
1
0
0
1
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
2
0
1
1
0
0
0
0
1
2
0
0
1
5
0
0
0
0
0
0
0
1
2
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
1
3
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
6
1
0
0
0
0
0
0
1
1
4
0
1
0
0
0
0
1
8
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
3
0
0
2
1
3
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
1
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
1
0
1
0
1
0
0
0
5
1
0
0
2
0
2
0
3
0
0
0
0
0
2
0
0
1
2
1
2
2
0
0
8
0
1
0
0
0
0
2
0
0
1
1
0
0
0
2
0
1
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
2
2
3
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
6
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
1
2
1
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
4
1
0
1
2
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
8
0
1
0
0
0
0
1
2
0
0
11
0
1
1
2
0
0
0
1
0
2
2
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
7
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
8
0
2
2
0
1
0
2
0
0
0
2
0
2
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
0
0
0
0
0
1
0
1
0
1
2
0
0
0
1
0
0
1
0
0
0
3
0
0
2
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
2
1
0
2
0
0
1
1
0
0
0
2
1
0
2
2
0
0
2
0
2
2
0
0
0
0
1
0
0
0
2
0
0
0
4
6
1
0
0
2
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
2
0
0
1
0
0
0
0
0
6
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
1
3
0
0
0
0
0
0
3
2
0
2
0
2
0
0
0
0
2
0
2
0
2
0
0
0
0
0
1
0
0
2
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
2
1
0
2
0
1
0
2
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
2
0
0
1
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
5
0
0
0
0
0
1
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
1
1
0
0
0
0
7
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
5
0
1
2
0
0
0
2
0
0
1
3
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
1
0
1
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
2
0
2
0
1
0
0
3
0
0
0
0
1
0
1
0
1
4
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
3
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
2
0
1
1
0
0
0
0
0
2
0
0
0
2
0
0
0
1
2
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
2
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
1
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
3
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
1
1
1
3
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
1
2
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
3
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
1
4
0
3
0
1
0
1
0
3
0
0
0
2
0
0
1
0
0
0
0
1
0
1
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
4
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
1
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
3
0
2
0
2
0
4
0
2
0
0
1
0
0
1
1
1
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
2
1
1
0
2
0
0
1
1
0
0
0
1
0
2
0
0
0
0
1
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
1
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
3
0
1
2
0
0
1
1
0
0
1
1
3
1
3
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
2
0
0
0
0
0
2
0
0
0
0
0
5
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
8
0
0
0
0
0
0
0
0
2
0
0
2
0
3
0
2
0
0
0
5
0
0
1
0
0
0
0
5
0
2
0
0
0
0
0
0
0
1
0
0
3
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
2
2
0
1
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
3
0
0
0
1
1
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
3
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
3
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
2
0
2
0
3
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
2
0
0
2
0
9
0
0
2
2
2
0
0
0
0
1
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
1
0
0
2
1
0
0
9
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
3
1
0
0
0
2
0
1
0
1
1
1
0
0
1
0
5
0
0
2
1
1
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
3
2
2
0
0
0
0
0
0
0
0
0
0
3
0
2
1
0
0
3
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
1
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
1
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
6
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
3
7
0
1
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
1
0
0
2
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
3
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
3
0
4
0
0
0
0
2
0
2
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
2
0
2
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
7
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
5
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
1
0
2
0
0
0
2
1
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
1
2
0
0
0
0
0
1
0
0
0
0
1
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
1
0
1
1
2
0
1
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
2
0
2
2
0
3
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
1
0
2
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
3
0
3
0
0
0
0
1
2
0
0
0
0
0
0
5
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
8
1
1
0
0
0
0
2
2
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
2
2
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
1
1
0
0
0
0
2
1
3
0
0
0
0
0
0
0
1
0
2
0
1
1
0
0
1
0
0
1
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
1
1
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
3
0
1
0
2
0
0
0
0
2
1
2
0
0
3
0
0
1
1
2
0
0
0
0
0
0
0
0
2
2
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
2
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
4
1
0
0
0
1
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
2
0
0
0
2
0
0
2
0
1
0
1
1
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
2
0
0
0
0
0
2
0
0
1
0
0
1
2
0
0
0
5
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
2
0
0
0
1
2
0
0
0
0
2
0
1
3
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
1
0
1
3
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
1
0
0
0
2
1
0
1
0
1
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
1
1
1
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
2
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
4
1
4
0
2
0
0
0
1
2
1
0
0
2
0
0
1
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
2
0
0
1
2
2
0
0
0
0
0
2
1
0
0
3
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
3
1
0
0
2
0
0
0
0
0
0
2
1
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
3
2
0
0
0
0
0
1
0
0
0
2
0
0
3
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
5
0
0
0
2
0
0
0
0
1
0
2
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
10
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
2
0
1
0
0
2
2
1
0
0
1
0
0
0
9
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
1
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
2
0
0
1
3
0
2
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
1
4
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
3
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
1
1
0
0
1
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
2
2
0
3
0
0
0
0
0
1
0
0
0
0
2
0
0
2
2
2
1
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
1
0
0
2
3
0
0
0
3
2
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
4
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
1
0
0
3
1
0
1
0
0
0
3
1
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
1
1
0
0
1
0
0
0
2
0
1
2
2
2
0
0
0
0
3
0
2
1
0
2
0
0
0
1
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
2
0
0
0
8
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
2
0
0
7
2
0
0
0
0
1
0
0
2
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
14
4
0
0
0
1
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
5
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
5
0
0
1
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
2
0
2
0
1
0
0
0
1
1
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
4
0
1
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
2
0
0
1
1
0
2
0
0
4
0
0
0
6
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
1
0
2
0
1
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
1
0
0
0
3
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
4
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
1
0
2
2
0
0
2
0
0
0
0
0
1
0
2
0
1
0
0
3
0
0
0
0
0
1
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
1
1
2
0
2
1
3
4
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
1
0
1
1
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
1
2
0
3
0
0
0
1
0
0
5
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
4
0
0
0
1
0
2
0
0
1
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
7
0
0
0
0
0
0
0
0
2
1
0
2
0
3
0
0
1
1
0
2
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
2
1
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
2
1
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
1
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
1
1
0
3
0
0
2
0
0
0
0
3
2
4
0
0
0
0
1
0
3
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
3
0
2
2
1
0
0
0
0
0
0
2
0
0
2
1
0
0
1
0
0
2
0
0
0
0
1
0
0
1
0
0
0
1
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
1
0
2
1
0
0
0
0
0
2
0
0
2
0
1
0
0
1
0
0
3
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
7
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
1
0
0
0
0
3
1
0
0
1
0
1
0
3
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
3
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
6
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
1
0
0
1
0
0
3
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
3
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
5
0
0
0
0
2
2
1
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
2
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
2
2
0
1
1
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
6
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
6
0
0
0
0
0
1
0
0
1
0
0
2
0
0
2
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
3
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
1
2
0
0
0
1
2
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
2
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
8
0
0
1
4
0
1
2
3
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
2
1
0
0
2
0
0
2
0
0
0
0
1
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
3
0
0
0
0
0
0
2
2
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
6
0
1
0
0
0
0
4
0
0
2
0
0
1
1
0
0
0
0
0
2
2
0
0
1
0
2
0
0
0
0
0
1
4
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
3
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
2
0
0
1
2
0
0
0
4
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
7
0
0
1
0
0
1
0
0
1
0
0
0
2
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
6
1
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
1
0
0
2
0
1
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
1
2
0
0
0
2
0
0
0
0
1
0
0
0
0
1
2
0
1
0
1
2
0
0
0
0
0
0
1
1
0
1
0
0
2
0
5
0
0
0
1
0
1
0
2
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
1
2
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
4
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
1
3
0
0
3
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
3
1
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
2
0
1
2
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
2
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
3
0
0
1
2
3
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
4
0
0
0
0
2
3
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
4
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
6
0
2
0
1
0
1
1
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
4
0
0
0
2
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
1
1
0
0
2
1
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
2
2
1
1
0
2
0
1
0
0
1
0
1
1
0
0
0
2
6
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
4
0
0
0
0
0
0
1
1
2
1
0
2
0
0
1
0
0
1
2
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
1
2
0
1
1
1
0
1
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
12
0
3
1
1
1
1
0
1
0
0
0
0
0
0
2
2
3
0
0
0
1
0
0
0
0
1
2
0
2
1
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
2
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
2
0
1
0
0
3
2
0
2
1
0
0
0
1
0
1
0
2
1
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
1
2
0
0
2
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
3
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
7
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
2
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
3
2
0
0
0
2
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
3
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
2
2
0
0
0
0
0
0
1
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
2
3
0
2
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
4
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
1
2
1
0
0
0
0
1
0
2
0
0
1
0
0
0
0
1
0
0
1
0
0
2
1
0
1
2
0
1
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
2
2
0
0
0
2
0
0
0
1
0
0
3
0
2
1
0
0
0
1
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
2
0
0
1
0
2
0
0
0
1
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
2
0
1
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
2
0
1
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
3
0
0
2
1
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
5
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
1
3
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
2
1
1
0
0
0
0
0
3
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
3
1
0
0
0
1
0
0
0
1
1
0
0
1
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
2
3
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
1
0
0
0
0
0
0
3
0
1
3
0
0
0
0
0
2
5
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
3
0
2
2
0
0
0
1
0
0
1
0
0
0
0
1
0
0
3
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
3
2
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
1
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
3
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
2
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
3
2
0
0
0
2
2
1
2
5
0
0
0
0
0
1
2
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
2
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
2
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
1
0
0
0
1
0
2
0
0
0
0
0
0
2
0
1
0
0
1
1
0
2
0
1
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
4
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
2
0
0
2
0
3
2
0
0
0
0
0
1
2
0
0
0
1
0
21
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
3
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
3
0
2
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
3
0
1
0
0
0
0
1
2
0
0
0
1
0
2
0
0
1
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
1
10
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
1
2
0
0
0
2
0
0
1
0
0
0
2
0
2
2
2
0
0
0
1
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
1
1
0
2
0
5
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
1
0
0
4
0
0
1
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
3
1
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
7
0
1
0
0
0
1
0
1
0
0
0
0
4
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
2
1
0
0
1
1
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
3
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
1
2
1
2
0
1
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
1
1
2
1
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
7
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
4
1
0
3
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
2
0
0
1
5
0
1
0
3
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
2
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
2
0
2
0
0
0
2
0
0
0
0
3
0
1
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
3
0
0
3
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
3
0
2
0
0
1
3
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
6
2
1
2
2
0
0
3
2
0
1
0
0
0
0
2
0
1
2
0
2
2
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
2
0
0
0
0
0
2
1
0
0
0
2
1
3
0
0
0
0
0
3
0
1
1
0
0
1
1
0
0
0
0
0
0
0
1
4
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
3
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
3
2
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
2
0
0
2
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
1
1
0
7
0
0
2
1
0
2
0
0
0
8
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
1
2
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
6
0
1
0
1
0
0
0
1
1
0
6
4
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
2
2
1
0
0
0
0
1
0
0
0
0
2
3
0
0
0
1
3
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
4
0
1
0
1
0
0
0
0
2
0
0
2
0
0
0
1
2
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
5
0
0
1
0
0
0
0
1
1
0
1
0
0
1
0
2
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
1
1
0
1
0
1
1
0
0
3
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
7
0
0
0
0
0
0
0
0
4
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
1
1
0
0
0
3
2
0
0
1
0
0
0
1
0
2
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
3
1
0
0
0
0
0
1
0
4
0
0
0
2
2
0
0
0
3
2
0
0
0
0
0
0
0
3
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
3
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
2
8
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
2
0
0
0
0
0
2
2
2
0
2
0
0
1
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
1
0
0
1
0
0
0
3
1
0
1
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
3
1
0
1
0
2
2
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
1
0
0
0
0
0
0
1
0
0
2
0
0
1
0
1
0
0
0
0
2
0
0
0
0
2
0
0
1
1
2
4
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
1
0
4
0
0
0
0
2
0
0
0
3
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
2
0
0
0
3
2
0
0
5
0
1
0
2
1
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
1
2
1
0
0
0
0
0
1
0
0
1
0
0
2
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
2
0
2
2
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
4
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
1
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
2
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
1
4
1
0
1
0
0
1
2
3
0
0
0
0
3
0
1
0
0
0
0
0
2
3
0
0
0
0
1
0
1
0
2
2
5
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
5
2
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
2
0
2
0
0
1
7
0
0
0
2
2
0
0
0
0
0
2
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
1
0
1
0
1
0
1
0
1
0
1
1
0
0
0
1
0
1
0
2
0
0
0
2
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
2
0
0
0
0
1
0
3
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
6
0
0
7
0
0
0
1
2
0
0
0
0
1
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
3
2
0
0
0
4
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
2
1
1
0
0
2
1
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
1
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
2
2
0
3
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
2
1
1
0
0
0
7
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
2
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
2
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
4
0
0
0
0
2
0
0
0
0
0
1
0
1
0
3
0
0
0
0
1
0
0
0
0
2
1
1
0
1
0
0
0
0
0
0
0
4
0
0
0
3
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
3
1
0
2
0
1
0
0
0
0
0
2
2
2
2
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
3
0
0
2
4
2
2
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
1
0
1
0
0
0
0
0
0
2
2
2
1
0
0
0
1
1
1
0
0
0
4
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
2
0
1
2
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
3
0
0
0
0
0
0
0
0
3
0
0
0
1
2
0
1
2
0
1
0
0
0
1
0
1
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
1
2
1
0
2
0
0
0
0
0
0
0
0
2
0
2
1
2
2
0
0
0
0
1
0
0
4
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
2
0
4
0
0
2
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
4
2
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
3
3
1
0
2
0
0
4
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
1
1
0
0
0
0
3
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
1
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
2
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
2
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
2
3
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
5
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
1
0
0
0
9
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
1
0
0
3
0
1
0
0
0
3
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
3
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
2
0
0
1
0
0
0
2
0
0
0
0
0
7
1
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
3
1
3
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
3
0
0
4
3
0
0
0
0
0
0
0
0
0
0
0
0
8
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
3
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
2
2
5
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
4
2
1
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
1
0
0
1
2
0
1
2
0
0
0
0
0
2
0
0
0
6
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
9
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
0
0
1
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
3
2
0
2
0
1
0
2
0
0
0
2
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
3
1
0
0
0
0
3
2
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
2
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
8
0
3
0
0
1
0
0
0
0
3
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
2
0
2
2
0
2
0
3
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
2
1
0
0
0
2
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
4
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
2
2
2
1
0
1
0
0
1
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
1
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
1
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
12
0
1
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
2
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
1
2
0
0
2
0
0
1
1
0
0
0
0
0
0
0
2
4
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
6
0
0
3
0
2
4
3
1
0
2
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
2
1
2
0
2
0
0
1
1
0
0
0
0
0
0
1
1
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
4
1
0
0
2
0
2
2
0
0
1
0
0
0
2
0
0
0
0
2
2
2
2
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
2
5
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
2
0
0
2
0
0
0
0
0
2
0
0
1
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
1
0
0
1
0
1
3
0
0
2
2
0
0
0
1
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
5
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
8
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
1
0
0
0
0
0
1
1
0
0
1
0
2
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
6
0
0
0
1
2
0
0
0
0
1
0
0
8
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
2
2
0
0
0
0
3
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
2
0
2
3
2
2
2
1
0
0
1
0
0
1
1
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
1
2
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
5
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
2
1
2
0
0
0
0
1
1
2
0
0
0
0
1
0
1
0
0
0
0
2
0
2
0
0
3
0
0
4
0
0
1
2
0
2
0
0
0
0
0
3
0
0
1
0
2
0
1
1
0
0
0
0
0
2
0
0
0
0
0
2
0
3
0
0
1
0
0
0
4
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
2
2
0
0
1
0
0
0
0
0
1
0
3
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
2
3
0
0
2
1
0
0
0
0
2
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
2
0
0
2
2
0
0
1
1
0
0
1
1
1
2
0
0
0
4
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
1
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
6
0
1
0
0
0
0
2
0
2
0
0
2
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
2
1
0
0
6
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
1
0
2
0
1
0
1
0
0
0
1
5
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
6
0
0
0
3
0
0
1
1
0
1
2
0
0
0
0
0
0
3
0
0
0
4
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
4
0
0
1
2
1
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
1
0
0
0
1
0
6
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
2
0
0
1
1
0
0
0
0
0
1
5
2
1
1
0
0
0
2
0
1
0
0
0
0
2
1
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
3
1
0
0
0
0
0
0
0
0
1
0
0
8
0
0
0
0
0
1
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
8
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
4
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
3
0
0
0
0
0
7
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
1
0
0
0
0
0
2
0
0
1
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
1
0
1
1
0
0
0
2
0
0
0
2
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
3
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
9
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
1
1
1
0
2
0
0
0
0
0
0
0
1
0
2
3
0
0
0
0
2
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
5
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
2
0
4
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
1
2
0
0
2
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
3
1
0
0
0
0
1
0
2
0
0
1
4
0
0
0
0
1
0
1
1
2
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
17
1
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
2
1
0
0
4
1
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
1
2
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
2
0
1
0
0
0
2
1
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
3
2
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
2
0
0
2
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
1
2
2
0
0
2
0
1
0
2
0
2
0
4
2
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
3
1
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
1
0
0
0
1
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
1
0
0
2
0
0
1
2
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
3
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
5
2
0
0
0
0
7
0
2
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
4
0
0
3
0
0
3
3
0
2
0
0
0
0
0
0
3
0
2
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
1
1
0
0
1
0
13
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
2
0
1
0
1
0
1
0
1
0
0
2
0
0
1
0
0
1
0
0
0
2
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
2
1
0
0
1
1
0
1
3
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
1
0
1
1
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
1
2
0
0
0
0
0
2
0
2
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
1
2
1
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
1
2
0
0
0
0
3
1
5
0
1
0
2
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
1
0
0
0
1
0
0
0
0
1
1
1
0
1
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
3
0
0
0
0
2
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
6
0
0
1
2
0
2
2
0
0
0
0
0
3
1
0
0
3
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
1
2
0
2
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
1
0
0
4
0
2
1
1
0
2
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
6
0
0
0
0
0
0
1
0
0
2
0
1
0
2
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
8
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
2
0
2
2
2
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
3
0
10
0
0
1
0
0
0
0
2
0
2
0
2
0
1
0
1
0
0
0
0
2
2
2
0
2
0
0
0
0
2
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
3
1
0
1
1
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
2
0
2
0
0
0
0
1
0
1
0
0
2
0
0
0
2
0
0
2
0
2
0
0
0
2
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
1
4
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
2
3
7
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
2
1
0
1
0
1
0
0
1
0
0
2
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
1
0
1
0
0
3
2
0
2
0
0
0
1
0
0
1
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
1
1
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
1
2
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
3
0
0
2
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
3
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
3
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
2
1
0
0
0
0
1
0
0
2
0
1
0
0
0
2
0
0
0
0
1
3
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
5
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
4
1
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
7
0
1
0
0
0
0
2
0
0
0
0
2
0
1
0
5
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
1
1
1
1
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
3
2
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
2
0
0
1
2
2
2
0
1
0
0
2
1
0
0
1
1
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
2
2
0
0
2
0
0
1
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
2
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
1
0
0
0
0
0
1
2
2
0
2
2
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
1
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
1
0
0
0
3
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
1
0
0
0
1
0
0
2
2
0
0
4
0
0
2
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
4
4
1
0
0
0
0
0
0
0
0
0
0
6
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
2
1
0
2
0
1
0
0
0
2
2
0
2
2
0
0
0
0
0
1
1
0
0
1
0
1
5
0
0
0
0
0
0
0
0
1
6
0
0
0
0
2
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
3
0
0
1
1
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
2
2
1
0
0
0
1
0
0
0
1
1
0
2
2
0
2
0
0
0
0
0
2
0
0
0
2
2
0
1
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
2
1
1
0
0
0
0
2
0
0
0
2
2
0
0
0
2
0
1
0
2
2
0
0
1
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
6
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
2
1
0
0
1
2
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
3
0
0
0
0
0
0
2
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
4
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
1
0
0
0
5
0
0
2
0
3
0
1
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
1
2
1
0
0
0
0
1
1
0
0
1
1
0
0
1
0
0
1
3
0
0
0
0
0
0
0
0
2
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
2
0
3
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
1
0
1
0
3
0
0
0
0
0
3
2
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
2
3
2
3
0
0
0
0
0
0
0
2
0
0
0
1
0
1
3
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
4
0
0
1
4
0
0
0
2
0
0
0
2
0
0
2
2
0
2
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
2
1
0
0
0
0
3
0
1
2
1
0
0
0
1
0
0
0
0
0
0
3
1
0
0
0
0
2
0
0
1
0
1
0
0
2
2
1
0
1
0
0
0
0
2
1
0
0
0
3
0
1
1
1
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
3
1
2
0
0
1
1
0
0
0
1
1
0
2
0
0
0
0
0
2
0
0
1
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
4
0
0
0
0
0
0
0
2
1
1
0
0
0
2
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
2
0
1
0
0
1
0
0
0
1
2
0
0
0
0
1
5
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
3
0
0
0
0
0
0
3
0
0
0
0
0
0
1
2
0
0
0
0
0
2
3
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
2
1
0
0
2
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
5
2
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
1
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
6
1
2
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
3
0
0
3
2
0
0
0
0
0
0
4
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
1
2
0
2
0
0
0
2
0
1
2
0
0
1
0
1
4
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
2
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
3
2
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
11
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
2
0
6
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
4
0
0
1
0
2
2
0
0
0
0
0
0
0
2
1
1
1
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
4
1
0
0
0
0
0
0
0
1
0
0
2
0
0
1
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
4
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
3
8
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
2
0
0
0
0
0
1
0
0
0
0
0
1
3
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
6
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
1
0
0
0
1
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
1
2
0
0
0
0
0
0
0
2
0
0
0
2
2
1
2
0
2
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
3
0
2
4
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
1
3
0
0
2
1
0
0
0
0
1
0
0
4
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
2
0
1
0
2
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
4
1
0
0
2
1
0
0
1
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
8
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
2
1
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
1
1
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
1
1
0
0
0
0
1
0
0
1
0
2
0
2
0
0
3
0
2
0
0
0
0
3
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
1
2
0
0
0
2
2
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
1
0
2
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
1
0
0
2
0
0
2
0
0
0
0
0
0
2
1
0
1
2
2
1
0
0
0
0
0
0
2
0
0
0
1
2
2
0
3
0
1
2
1
0
0
0
0
0
1
1
0
1
0
1
3
0
0
0
2
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
3
2
0
2
0
2
0
0
1
3
0
0
2
2
0
1
2
0
1
0
0
0
1
0
1
1
1
0
0
0
0
0
0
4
0
0
0
2
0
3
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
3
0
1
0
0
0
0
2
0
0
3
1
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
1
1
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
3
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
3
2
2
0
0
0
0
0
1
4
0
2
2
2
0
1
2
0
0
3
0
0
0
2
0
0
0
0
0
1
0
0
1
0
2
0
0
0
5
0
0
1
0
0
0
1
1
2
0
2
2
0
0
0
0
2
0
0
2
0
0
2
4
0
0
0
0
0
0
3
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
1
1
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
1
0
0
0
0
0
10
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
2
0
0
1
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
6
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
1
1
0
1
0
0
2
0
0
3
0
4
0
0
1
2
1
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
2
1
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
6
1
0
2
0
0
0
2
0
2
1
0
0
2
0
2
4
0
0
0
2
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
1
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
2
1
0
0
0
0
2
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
2
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
2
0
0
0
2
0
0
0
1
0
0
0
2
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
7
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
2
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
1
0
1
0
2
0
0
0
0
0
1
0
3
0
0
2
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
2
0
0
2
0
0
0
1
2
0
1
0
0
0
0
2
0
0
2
2
0
1
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
1
0
2
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
3
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
5
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
1
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
2
0
2
0
0
0
1
0
1
1
0
0
0
0
0
0
2
0
2
0
0
0
0
1
2
0
0
0
0
0
0
3
0
0
0
0
0
0
1
2
2
0
0
0
2
1
0
2
2
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
1
2
0
0
0
0
0
0
0
2
0
3
0
2
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
2
0
0
2
2
0
0
0
0
0
1
1
1
0
0
0
0
0
2
0
0
1
0
0
1
2
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
3
6
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
2
0
0
0
2
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
4
2
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
1
0
1
0
0
0
1
3
1
0
0
0
0
0
0
0
4
0
4
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
3
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
2
0
1
1
1
0
0
0
2
0
0
2
0
0
0
1
1
0
2
0
0
1
1
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
1
0
0
2
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
2
0
0
1
0
2
0
0
0
0
1
0
0
2
2
2
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
5
0
2
0
0
0
2
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
2
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
4
1
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
1
0
0
0
0
1
0
2
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
2
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
2
2
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
1
1
0
2
0
0
0
0
4
0
0
0
2
1
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
2
0
0
1
0
0
0
2
2
0
2
0
0
1
1
1
0
1
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
1
0
0
0
2
0
1
0
3
0
0
2
0
0
0
0
0
0
0
0
2
2
0
3
0
0
0
0
4
0
0
5
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
2
0
1
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
2
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
2
2
1
0
0
0
0
0
1
2
1
0
0
0
0
0
0
3
2
0
4
6
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
2
0
0
0
0
1
5
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
1
2
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
1
2
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
4
1
0
0
0
1
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
1
0
2
1
0
0
0
1
0
0
1
1
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
2
0
3
0
0
0
0
0
0
2
2
1
0
0
2
0
0
3
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
1
2
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
1
0
0
0
0
3
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
3
1
0
0
0
0
0
9
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
2
1
2
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
4
2
0
1
2
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
4
0
2
0
3
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
3
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
2
0
0
3
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
2
9
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
1
0
0
2
1
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
4
2
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
2
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
1
0
0
2
11
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
1
0
2
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
4
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
2
3
0
0
1
1
0
1
0
0
0
3
0
0
2
1
1
0
0
0
1
0
0
0
0
2
0
0
0
0
3
0
2
0
0
1
0
0
0
0
1
0
0
3
1
0
0
5
0
1
0
0
1
0
1
1
0
0
4
0
0
0
0
0
1
2
0
0
0
1
3
0
0
1
0
0
4
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
2
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
3
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
1
0
2
0
0
0
0
0
4
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
2
0
0
1
0
0
1
0
0
5
0
1
0
0
1
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
1
0
3
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
1
0
0
0
0
3
0
2
0
0
0
1
0
0
0
0
4
0
0
0
2
0
0
2
2
3
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
1
1
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
1
0
1
2
2
0
0
0
0
0
1
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
1
0
0
2
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
4
0
0
0
1
0
0
0
0
0
1
3
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
1
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
2
2
0
0
1
2
3
0
0
0
0
1
0
1
0
0
0
0
4
2
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
1
1
0
2
0
1
0
0
0
0
0
0
1
2
0
0
0
3
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
1
0
1
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
2
0
0
1
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
2
0
0
7
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
1
0
0
3
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
4
0
1
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
2
0
0
1
1
0
0
1
2
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
4
2
1
0
0
0
0
0
0
2
1
0
1
0
0
2
1
0
0
1
0
2
1
0
0
2
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
3
0
0
0
0
0
2
1
0
2
4
0
0
0
1
3
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
2
0
0
0
1
0
0
2
0
0
0
0
2
0
7
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
1
1
0
0
0
0
0
0
0
4
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
2
0
2
1
0
0
2
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
6
2
1
0
0
0
0
0
1
0
1
0
1
0
2
0
0
1
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
1
0
0
0
2
7
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
3
2
0
0
1
1
1
0
0
2
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
4
2
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
5
0
0
0
0
0
0
0
0
3
0
0
2
0
2
0
2
0
7
1
0
0
0
0
0
3
0
0
2
0
0
0
1
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
3
0
0
1
0
0
0
1
1
1
0
2
0
1
2
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
3
2
2
0
0
1
0
2
0
2
1
0
0
1
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
1
2
0
3
0
0
0
4
0
0
1
0
0
0
2
1
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
10
0
0
0
0
0
0
4
0
0
4
0
0
0
0
1
1
1
0
1
0
0
0
2
0
2
0
0
1
2
0
0
1
0
0
2
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
4
1
0
0
0
0
0
0
0
2
2
0
1
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
2
1
2
1
3
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
2
2
0
0
1
2
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
2
0
2
0
1
0
0
0
0
1
0
2
2
1
0
4
1
1
0
3
0
0
1
0
0
0
0
2
0
0
0
0
2
4
1
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
1
1
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
1
1
0
0
0
2
0
0
2
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
2
0
0
0
4
0
2
0
0
0
0
0
0
1
2
2
2
0
0
0
1
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
3
0
2
0
0
0
0
0
0
0
0
1
0
10
0
0
1
0
2
2
2
0
5
0
1
0
0
0
0
0
1
1
0
0
0
0
0
2
0
2
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
4
0
0
0
0
0
1
1
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
1
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
8
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
3
2
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
2
0
1
0
0
0
3
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
2
0
2
1
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
2
2
0
0
1
0
2
0
0
1
0
2
2
1
2
0
0
0
0
0
0
0
2
1
0
1
2
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
2
3
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
1
0
0
2
0
2
0
0
0
0
0
1
2
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
1
2
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
3
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
2
2
0
0
0
3
0
0
1
0
1
2
0
1
0
0
2
1
0
0
4
0
4
0
0
1
0
0
2
0
0
0
0
0
2
0
0
2
0
2
0
2
0
1
1
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
4
0
1
1
1
1
0
0
1
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
3
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
7
2
1
3
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
1
0
0
1
0
0
0
0
0
6
0
1
0
0
0
0
0
0
0
1
0
0
0
3
0
2
1
1
0
3
0
2
1
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
2
0
2
0
1
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
1
0
0
2
2
0
1
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
3
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
0
0
0
1
3
1
0
0
2
0
2
0
0
0
1
0
1
0
0
2
2
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
2
0
0
0
2
0
0
0
0
1
0
3
0
1
0
2
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
6
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
7
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
5
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
4
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
2
0
0
0
1
1
1
0
0
2
1
0
1
0
0
2
0
0
2
0
0
0
1
0
0
1
0
6
0
2
1
0
0
1
0
0
1
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
3
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
1
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
1
2
0
0
0
0
0
2
0
0
0
0
0
4
0
0
0
0
3
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
2
3
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
2
1
1
2
1
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
3
0
1
0
1
2
0
0
0
1
0
0
4
0
0
0
0
2
0
0
2
0
0
0
0
2
2
0
0
0
0
0
2
0
0
3
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
1
0
1
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
9
1
0
0
2
1
0
0
1
1
2
0
0
0
2
0
0
0
0
1
1
1
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
2
2
0
0
2
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
1
0
0
0
0
4
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
3
0
0
0
3
2
0
0
0
0
0
0
0
0
0
1
1
3
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
1
2
0
0
0
3
1
2
0
0
2
0
0
0
0
1
0
3
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
2
1
0
0
0
0
3
0
2
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
2
1
1
1
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
6
0
0
2
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
2
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
3
2
0
6
0
1
0
0
0
0
4
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
1
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
1
0
0
1
0
0
0
1
2
0
0
0
0
0
0
2
2
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
6
0
0
1
0
2
1
1
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
1
7
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
4
1
2
2
0
0
0
0
0
0
1
0
0
0
3
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
1
4
0
1
2
0
0
2
0
0
0
1
2
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
7
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
2
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
1
2
0
1
0
0
2
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
2
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
3
0
2
1
0
0
0
2
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
2
0
0
0
2
0
0
2
2
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
2
0
1
0
0
1
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
1
2
0
0
0
2
0
0
0
3
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
2
0
0
0
0
2
0
1
3
0
2
0
0
1
2
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
2
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
4
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
11
0
0
0
0
3
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
3
5
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
1
0
0
1
0
0
1
0
0
0
2
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
2
0
0
1
0
0
0
1
0
1
0
0
1
0
0
1
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
3
3
0
0
2
0
0
1
1
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
1
1
2
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
1
1
1
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
1
0
5
2
0
0
1
0
0
0
0
2
0
1
0
2
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
3
9
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
5
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
1
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
2
5
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
1
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
3
1
0
0
0
0
0
1
1
2
0
1
0
0
1
1
0
0
0
0
1
2
0
0
1
0
0
2
2
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
2
2
1
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
2
0
0
1
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
2
0
0
0
0
6
0
1
0
0
0
1
0
0
1
0
1
1
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
1
1
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
5
0
0
0
1
0
0
2
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
3
0
0
0
1
2
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
3
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
1
0
2
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
1
0
0
2
1
2
0
0
0
2
0
0
0
0
2
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
2
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
2
0
0
0
4
0
1
1
0
2
0
0
0
0
0
0
0
0
4
2
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
1
0
0
3
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
4
0
0
0
0
1
0
2
1
2
2
0
2
0
0
0
1
1
0
0
0
0
2
0
0
2
0
0
1
0
1
0
1
1
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
3
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
7
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
7
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
5
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
5
0
0
1
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
2
0
1
2
2
0
1
0
3
0
2
0
0
0
0
0
2
0
3
0
0
0
2
0
0
1
0
0
0
1
1
3
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
3
1
0
0
0
2
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
2
2
0
0
0
0
3
0
2
0
0
0
0
0
0
1
1
0
0
2
1
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
1
2
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
3
0
0
0
1
0
0
2
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
6
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
6
0
0
0
2
1
0
0
0
0
4
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
1
0
2
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
2
0
0
1
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
3
1
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
2
2
0
2
0
1
0
4
0
2
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
2
0
5
1
0
2
1
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
2
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
10
2
0
1
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
6
1
0
0
0
2
1
0
2
0
0
1
0
1
0
0
0
1
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
1
1
0
0
0
0
0
0
3
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
2
0
1
1
0
2
0
0
0
0
1
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
6
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
2
2
0
0
3
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
1
0
0
2
0
0
0
0
2
0
4
1
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
1
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
8
1
0
0
1
0
1
0
0
0
0
0
6
0
0
2
0
1
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
2
0
2
0
2
2
3
0
0
0
0
1
0
1
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
6
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
3
0
2
0
1
0
1
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
1
0
2
0
1
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
5
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
2
0
0
2
3
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
3
2
0
0
0
0
0
0
0
2
0
0
5
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
1
1
0
0
0
0
2
0
2
0
1
0
2
1
1
0
0
2
0
3
0
0
0
1
0
0
2
0
2
1
0
0
0
1
1
3
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
2
0
2
1
0
0
0
1
0
0
1
1
0
1
1
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
3
1
0
0
1
2
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
1
0
1
0
0
0
2
1
0
0
0
2
0
1
2
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
2
0
5
1
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
4
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
1
0
0
4
0
0
0
4
0
1
0
0
0
0
1
0
0
0
3
0
0
0
2
2
0
0
0
1
0
0
3
0
0
0
0
0
0
0
1
0
0
1
1
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
6
2
1
0
0
0
0
0
2
0
0
0
0
0
2
4
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
2
0
0
0
2
2
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
3
0
1
2
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
9
0
4
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
2
2
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
4
0
1
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
2
0
0
3
2
0
0
2
0
0
2
2
2
0
0
0
1
0
1
0
0
3
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
3
1
3
0
0
2
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
1
2
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
2
0
2
2
0
4
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
2
0
1
0
0
1
0
1
0
0
0
2
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
2
3
2
0
14
0
0
0
1
0
0
0
0
0
0
0
0
1
4
1
1
1
2
0
0
0
0
0
1
0
1
0
0
2
0
2
0
0
2
0
0
0
1
0
0
0
1
0
1
0
0
2
0
0
0
0
2
0
0
0
0
2
0
2
0
2
0
1
0
0
1
0
1
2
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
4
0
0
0
0
1
1
0
0
3
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
4
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
1
1
0
0
1
0
0
2
0
1
2
0
0
0
0
0
2
0
1
0
0
0
1
2
1
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
2
2
0
3
0
2
0
2
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
3
0
2
0
1
2
0
0
0
0
0
1
0
0
0
3
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
1
1
0
0
0
2
1
0
2
0
0
1
0
3
0
1
2
4
1
0
2
0
0
0
0
2
0
0
0
0
1
1
5
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
3
1
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
3
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
3
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
1
0
0
0
1
1
1
2
0
0
0
1
0
0
0
2
0
2
0
1
0
2
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
4
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
2
1
0
0
0
1
1
0
0
0
0
0
5
1
0
1
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
1
1
0
0
0
2
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
1
2
0
0
0
0
2
0
1
0
0
0
0
1
0
1
0
0
2
0
1
0
0
1
0
0
0
0
0
1
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
3
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
2
1
0
0
0
0
0
1
0
0
2
0
3
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
3
0
1
2
0
0
0
2
2
0
2
0
0
1
0
0
0
2
0
0
1
0
0
3
2
0
0
0
0
0
6
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
2
0
2
0
0
3
0
0
0
0
1
0
0
0
0
1
2
0
1
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
1
2
0
6
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
6
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
1
0
0
0
2
0
3
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
2
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
1
0
2
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
2
0
0
1
1
0
2
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
2
0
2
0
0
0
1
2
2
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
2
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
2
0
2
2
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
1
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
1
0
0
4
0
0
0
0
0
0
0
0
3
0
1
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
7
0
0
0
0
0
0
0
0
2
0
3
1
0
0
0
1
0
1
0
0
3
0
1
0
1
0
2
1
0
3
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
2
0
0
4
0
1
1
0
0
0
0
2
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
2
0
2
1
0
1
0
2
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
1
2
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
1
4
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
1
0
1
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
3
0
0
1
0
0
1
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
5
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
1
0
2
2
0
0
0
0
0
0
0
0
0
1
0
2
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
5
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
1
1
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
9
0
0
2
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
4
1
0
1
0
1
2
0
2
0
0
0
0
0
0
0
2
2
0
0
1
0
0
2
0
2
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
3
1
0
2
1
0
0
1
1
2
0
1
0
0
0
0
3
0
2
0
1
0
0
0
1
0
2
0
0
2
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
1
0
0
3
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
2
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
2
0
2
1
0
1
0
2
1
0
0
0
1
0
1
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
3
1
0
0
0
2
0
0
0
1
0
0
2
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
2
2
0
2
0
0
2
2
6
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
9
0
0
0
1
0
2
1
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
1
0
3
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
1
1
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
1
0
0
0
0
2
2
0
2
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
3
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
1
2
1
0
0
4
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
2
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
1
1
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
3
0
1
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
1
0
0
3
0
0
0
0
0
2
2
1
0
0
0
0
0
0
1
0
6
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
3
1
0
1
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
1
0
0
0
0
0
0
1
1
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
5
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
3
0
1
1
0
0
0
0
2
4
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
2
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
1
1
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
3
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
2
2
1
0
3
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
5
0
0
3
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
3
2
0
0
4
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
3
1
1
0
0
2
0
0
0
0
1
0
1
0
0
1
2
1
0
0
2
0
0
2
0
2
0
0
0
2
0
0
0
2
0
0
0
0
9
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
2
2
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
2
1
0
0
0
0
0
2
0
0
0
0
1
0
2
0
2
2
0
0
0
0
0
2
0
1
2
0
0
1
0
0
0
0
0
2
1
0
2
0
0
0
1
1
0
1
2
0
1
1
0
0
0
2
0
0
0
0
0
0
2
1
0
2
0
0
0
0
2
1
0
2
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
3
1
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
3
6
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
1
0
0
0
1
1
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
2
0
0
1
0
0
0
3
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
3
2
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
3
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
2
0
2
0
0
2
0
2
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
3
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
3
2
1
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
3
2
0
0
0
1
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
3
0
0
2
0
0
0
1
1
0
0
4
0
0
0
2
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
1
3
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
1
1
0
0
1
2
0
0
1
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
3
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
1
3
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
2
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
1
7
0
0
0
0
0
3
1
2
0
0
0
1
0
0
0
1
1
0
1
1
0
0
2
0
0
0
0
0
0
2
2
0
0
0
3
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
2
0
6
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
3
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
2
0
0
0
0
1
4
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
4
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
2
0
2
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
4
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
1
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
1
0
3
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
4
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
5
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
2
2
0
1
0
0
0
1
0
3
0
1
0
0
0
0
2
1
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
2
0
1
0
0
2
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
1
2
0
0
0
3
0
1
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
1
1
0
0
0
0
0
0
0
0
0
0
4
2
0
0
0
1
0
0
3
1
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
2
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
4
0
0
0
0
0
2
0
3
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
3
2
1
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
2
0
0
0
0
0
0
0
1
0
2
0
4
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
1
0
2
0
1
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
4
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
1
0
2
1
1
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
5
2
0
0
1
0
0
0
0
0
1
2
0
0
1
1
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
2
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
1
0
1
0
2
0
2
0
0
0
2
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
4
0
6
0
0
1
0
1
0
0
2
0
0
0
1
0
0
0
2
0
2
1
8
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
1
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
2
0
1
2
0
2
1
1
0
0
1
2
2
1
0
0
1
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
2
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
10
1
0
0
0
5
0
0
0
0
0
0
1
2
2
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
1
0
0
1
0
0
0
0
0
0
5
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
1
0
0
0
1
0
1
1
1
0
1
4
0
0
0
0
0
0
2
0
1
0
0
0
0
2
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
3
1
2
0
0
0
0
0
1
3
0
2
1
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
1
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
1
1
0
1
0
0
0
0
1
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
2
2
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
1
0
1
0
1
2
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
2
0
2
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
3
0
3
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
7
0
0
1
2
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
1
1
3
0
0
2
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
1
0
2
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
10
0
2
0
0
0
0
0
0
0
2
0
0
0
3
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
1
0
1
0
0
1
0
1
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
1
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
2
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
4
0
2
0
1
0
1
0
1
0
0
0
1
1
2
0
0
0
0
0
2
2
0
0
0
2
0
3
1
0
0
0
0
4
0
0
0
1
0
0
0
3
0
0
1
1
2
1
0
0
0
0
1
0
0
0
2
0
0
0
1
2
2
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
1
1
1
0
0
0
0
0
1
0
2
0
2
0
0
9
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
1
0
0
0
1
2
0
0
0
1
0
0
1
0
0
0
3
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
1
1
3
0
2
0
0
0
0
0
0
0
1
3
2
0
1
0
0
1
0
0
4
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
8
0
0
0
0
2
1
0
0
0
3
0
0
0
0
0
0
0
4
0
0
3
0
0
2
0
0
0
2
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
5
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
2
0
2
0
0
0
7
0
0
0
1
0
2
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
5
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
1
0
0
2
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
4
0
0
0
1
0
0
2
4
0
1
0
3
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
2
0
0
1
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
2
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
3
0
0
4
0
0
2
1
1
0
1
0
0
3
0
0
0
0
2
0
1
0
0
0
0
0
2
0
2
1
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
2
1
0
2
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
1
3
0
2
0
0
1
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
1
1
2
1
0
7
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
2
2
0
1
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
3
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
4
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
1
0
2
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
2
0
1
0
0
0
0
1
1
0
1
1
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
2
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
3
0
2
0
0
1
1
0
0
0
2
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
2
0
2
0
0
3
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
3
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
5
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
1
0
0
0
1
2
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
6
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
2
0
0
2
0
0
0
0
1
2
0
0
1
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
3
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
5
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
8
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
2
0
2
0
0
2
2
0
2
0
0
0
0
0
0
1
0
3
1
1
1
0
0
0
2
1
0
0
0
0
1
0
0
0
1
0
1
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
1
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
5
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
2
1
0
0
2
0
0
0
0
1
0
1
2
1
0
0
2
0
0
1
2
0
0
0
0
2
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
3
1
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
1
1
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
5
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
2
0
0
0
0
1
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
3
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
4
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
1
0
4
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
2
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
1
2
0
4
0
1
0
0
0
2
0
0
3
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
5
0
0
0
0
0
2
0
0
0
1
0
0
3
0
0
0
0
0
0
2
2
0
0
0
0
2
0
2
0
0
0
0
2
0
0
2
2
0
0
1
0
2
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
1
0
2
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
3
0
1
0
0
0
2
2
0
0
0
0
1
0
0
0
1
0
0
0
2
0
3
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
2
2
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
2
1
2
0
1
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
2
1
0
1
0
0
1
0
1
0
1
0
0
0
0
2
0
0
1
1
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
1
0
2
0
2
0
0
2
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
6
0
1
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
1
0
1
0
1
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
2
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
2
0
1
2
2
0
0
0
0
0
0
0
0
2
0
2
2
1
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
3
0
0
0
6
3
0
0
0
0
2
0
0
0
0
0
7
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
1
0
2
0
1
0
0
0
0
7
0
2
1
0
2
0
0
0
0
0
2
0
0
17
1
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
2
0
0
0
1
0
1
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
1
0
1
1
0
2
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
2
0
0
0
1
0
0
2
0
0
0
0
3
1
0
0
0
0
1
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
1
5
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
3
1
2
1
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
4
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
2
0
0
3
2
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
1
0
0
3
0
0
0
1
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
1
3
0
0
2
1
0
1
0
3
0
0
1
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
2
0
0
0
0
0
3
0
0
0
0
0
0
0
1
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
1
3
1
0
0
0
1
0
2
0
0
1
0
2
0
0
1
0
0
0
0
0
2
0
1
0
0
0
1
0
0
1
1
4
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
1
0
2
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
2
0
1
0
0
2
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
4
0
2
0
0
2
0
0
0
1
1
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
4
0
2
0
0
0
0
0
0
0
1
1
0
0
0
2
2
0
2
0
0
0
0
7
0
0
0
0
0
0
0
3
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
1
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
4
2
2
2
0
0
0
0
0
0
3
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
2
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
1
1
0
0
0
1
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
4
0
2
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
1
0
1
0
1
0
2
0
0
0
0
0
0
0
0
3
1
1
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
1
0
0
2
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
4
0
1
0
2
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
5
0
1
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
2
0
1
3
0
0
2
0
0
1
0
2
0
1
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
7
2
0
1
0
0
2
0
0
1
2
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
4
0
0
0
0
0
1
2
0
0
1
0
0
0
2
3
0
0
0
3
0
0
0
0
1
0
0
2
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
6
0
2
0
0
0
0
0
0
2
0
0
0
3
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
1
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
8
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
2
2
1
0
3
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
3
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
1
0
4
1
2
0
0
1
0
0
2
1
0
0
1
2
0
0
0
0
0
1
2
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
2
0
2
2
0
1
0
0
0
0
0
0
1
0
0
1
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
3
1
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
4
0
0
0
2
0
0
1
1
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
3
1
0
0
0
1
2
0
0
0
0
2
2
1
0
0
1
2
1
2
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
1
0
0
0
2
2
0
0
1
0
2
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
2
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
6
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
8
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
2
0
1
1
0
2
0
1
0
0
0
0
0
0
4
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
2
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
1
0
0
1
1
1
0
0
0
0
1
0
0
0
1
1
2
0
0
0
2
0
0
2
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
2
2
2
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
3
1
1
0
1
0
0
2
0
0
0
0
5
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
1
0
1
2
2
0
2
1
0
0
0
0
1
0
0
0
0
2
0
0
3
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
10
0
0
0
0
0
0
0
0
1
2
1
0
2
0
1
1
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
5
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
1
1
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
2
2
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
1
0
0
0
0
0
0
0
0
0
0
0
3
3
0
0
0
1
0
0
2
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
2
2
1
2
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
2
0
0
0
0
0
0
1
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
1
1
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
6
0
1
0
0
0
0
1
0
0
1
0
0
0
0
3
0
0
0
2
0
0
1
4
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
1
0
1
2
0
0
1
1
3
0
1
0
2
3
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
1
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
3
1
0
0
0
0
0
0
0
2
0
0
1
0
3
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
3
3
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
2
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
2
2
3
1
1
0
1
0
0
2
0
0
2
1
0
0
1
2
0
0
0
0
3
2
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
1
0
0
3
0
1
0
0
3
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
2
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
1
0
2
2
0
0
0
0
0
3
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
3
2
1
2
0
0
0
0
0
2
2
0
5
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
1
0
0
0
0
2
1
0
0
1
0
0
1
0
0
0
1
6
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
3
0
2
0
2
0
0
2
0
0
0
0
1
1
0
1
2
0
0
0
0
1
4
0
0
0
0
0
3
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
2
0
2
0
0
2
1
0
4
0
0
0
0
0
0
1
0
2
0
0
0
2
3
7
2
0
0
0
0
0
0
4
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
2
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
1
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
3
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
2
0
0
2
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
2
1
3
2
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
2
2
0
0
0
5
1
1
0
0
0
2
0
0
2
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
3
0
0
0
4
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
2
0
0
2
2
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
3
1
0
1
1
0
0
0
0
1
0
0
1
0
2
1
0
2
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
1
0
0
1
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
2
0
0
3
0
0
1
0
2
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
3
0
2
0
0
2
0
0
0
1
2
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
2
0
3
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
5
0
0
0
0
3
0
0
0
1
4
2
0
0
4
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
1
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
3
1
0
0
3
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
8
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
3
1
0
0
3
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
1
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
5
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
4
2
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
5
0
0
0
0
1
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
2
1
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
3
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
3
0
5
2
0
1
0
3
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
2
0
2
2
0
0
0
2
2
0
1
0
1
0
0
0
0
2
0
1
0
0
0
3
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
10
0
0
0
0
0
0
0
0
0
1
3
7
0
0
0
0
2
0
2
1
0
0
0
0
5
0
0
0
0
1
0
1
0
0
2
0
1
0
0
0
0
0
1
0
0
0
1
0
0
2
2
0
0
0
4
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
1
3
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
4
0
0
0
3
0
0
1
0
0
0
1
0
2
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
1
0
2
0
0
3
0
0
1
0
0
0
0
0
0
0
2
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
1
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
1
0
1
1
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
2
1
0
0
0
0
3
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
2
1
1
0
0
1
0
1
2
1
2
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
1
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
1
0
0
0
1
0
0
0
0
2
1
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
2
0
0
0
1
1
1
0
1
1
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
1
0
0
0
2
0
1
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
1
2
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
1
1
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
5
1
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
3
1
1
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
2
0
1
0
0
0
1
0
0
0
0
4
0
0
0
0
0
2
0
0
0
0
3
0
1
0
2
1
0
0
0
2
0
0
0
0
9
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
1
0
0
0
3
0
0
0
2
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
2
0
1
0
0
1
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
4
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
6
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
2
1
0
0
0
0
2
2
1
0
1
0
0
0
0
1
1
0
3
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
3
0
0
0
0
0
2
0
1
0
1
0
0
2
0
0
2
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
3
0
1
0
0
0
0
4
1
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
2
0
0
0
1
0
1
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
2
0
3
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
1
0
0
0
1
2
1
0
0
0
0
0
3
0
0
2
2
1
0
0
0
0
0
0
0
0
1
0
0
2
2
2
0
0
3
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
1
0
0
0
0
0
0
1
1
0
0
2
0
0
0
1
0
1
0
0
0
2
0
1
0
0
3
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
2
0
4
0
1
0
0
0
0
0
0
1
0
0
0
0
3
0
0
2
0
0
0
0
0
0
1
2
1
0
3
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
2
1
0
0
0
2
0
0
0
2
1
0
0
0
2
0
0
0
2
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
2
0
2
0
0
0
2
0
0
0
1
0
0
0
1
0
1
2
2
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
1
0
0
0
2
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
5
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
1
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
1
2
2
0
0
1
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
3
0
2
1
0
0
0
0
1
2
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
2
0
1
0
1
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
2
1
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
1
1
0
0
1
2
1
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
1
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
2
1
1
0
2
2
0
0
0
0
0
1
0
2
0
2
3
0
0
0
0
2
0
2
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
2
0
0
3
0
1
0
0
0
0
0
0
1
0
5
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
3
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
3
0
1
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
2
0
0
3
0
0
2
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
1
0
4
0
2
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
1
0
3
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
2
0
0
1
4
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
7
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
1
2
0
1
0
0
0
0
0
0
1
2
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
2
0
2
0
0
3
0
0
0
0
1
0
1
1
0
0
1
0
1
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
2
0
2
2
3
2
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
2
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
8
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
2
0
0
1
0
0
0
0
1
3
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
2
0
1
2
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
1
0
0
2
1
0
0
1
1
0
2
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
2
2
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
1
0
0
1
0
2
1
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
3
2
2
1
1
2
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
1
0
2
0
0
0
2
3
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
1
0
0
1
0
1
1
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
2
0
0
1
0
0
1
3
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
2
0
1
4
0
0
1
0
2
0
0
0
0
0
2
1
3
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
2
0
0
1
0
3
0
2
1
1
0
3
0
0
0
0
2
0
0
0
0
0
0
3
4
0
1
0
2
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
1
1
0
2
2
0
2
4
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
1
1
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
1
0
1
2
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
10
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
9
0
0
0
0
0
0
1
1
0
0
2
0
2
0
0
0
0
2
0
0
1
1
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
2
0
0
0
1
0
4
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
2
0
3
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
1
0
3
0
0
1
0
2
0
3
0
0
0
0
1
0
0
0
3
0
1
0
0
0
0
0
1
4
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
3
0
0
0
1
0
1
1
0
0
2
0
0
1
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
2
0
0
1
0
1
0
0
1
0
0
6
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
3
0
1
0
0
1
2
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
4
0
0
3
1
1
0
0
0
1
1
0
0
0
0
0
3
0
0
2
3
0
4
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
1
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
3
0
0
0
0
3
1
0
0
0
1
0
1
1
0
1
2
0
0
1
0
0
0
0
0
1
2
0
0
0
2
0
1
4
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
2
2
0
0
3
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
3
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
1
0
0
1
0
0
2
0
0
0
0
2
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
3
0
0
0
0
2
1
0
3
0
1
0
0
3
0
0
0
0
0
1
0
1
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
4
0
0
0
1
0
2
0
0
0
1
0
0
2
3
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
1
0
0
0
1
0
1
1
4
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
3
0
0
1
0
1
2
0
0
1
1
2
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
3
0
0
0
0
0
2
1
0
1
2
0
1
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
2
0
2
0
0
1
0
0
0
2
1
2
0
1
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
1
4
2
0
0
1
0
0
0
2
0
3
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
2
0
0
2
0
0
0
1
0
0
0
0
0
0
2
2
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
4
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
8
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
1
0
1
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
1
1
0
2
0
0
0
1
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
0
1
0
0
1
0
2
2
0
0
0
0
0
0
0
0
4
1
2
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
2
2
0
0
0
1
0
0
1
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
3
0
0
0
0
0
0
0
0
0
2
0
1
2
0
2
0
3
0
0
0
1
1
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
1
0
0
7
2
2
0
0
0
0
0
0
0
0
2
1
0
2
0
2
0
0
1
1
1
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
3
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
1
0
0
5
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
2
0
2
1
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
2
0
2
2
0
0
1
1
0
0
0
0
2
2
0
0
1
0
0
1
0
0
2
0
0
0
0
2
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
3
0
0
0
2
0
0
0
0
0
2
0
1
0
0
1
0
0
1
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
3
0
0
1
0
1
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
1
2
0
0
1
1
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
0
1
1
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
2
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
3
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
5
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
3
0
1
3
0
0
0
0
0
2
0
0
0
0
0
0
6
0
2
0
0
0
1
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
5
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
2
0
0
1
0
0
2
0
0
0
0
0
2
0
0
2
0
0
1
0
1
0
0
3
2
0
0
0
1
0
1
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
3
0
0
0
1
6
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
2
0
0
2
1
0
1
1
0
0
0
0
0
0
3
1
0
1
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
2
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
1
0
2
0
3
1
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
2
1
2
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
1
1
0
0
0
0
0
0
0
0
7
0
0
0
0
1
0
0
2
2
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
2
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
2
0
1
0
0
0
2
1
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
2
0
2
0
0
7
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
2
2
0
0
1
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
1
0
0
1
2
0
0
0
4
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
1
0
0
1
2
1
0
0
1
0
0
2
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
3
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
1
1
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
2
1
0
0
2
2
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
2
0
1
0
0
0
0
4
0
0
0
0
1
0
0
0
3
0
1
1
0
0
0
0
0
0
0
0
0
0
0
3
1
0
1
0
0
0
0
0
0
0
0
0
1
0
3
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
9
2
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
1
0
0
1
0
2
0
0
0
0
0
0
0
1
1
3
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
3
6
1
0
0
0
3
0
2
0
2
0
0
2
0
0
0
0
0
0
1
0
0
1
1
0
0
5
0
2
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
1
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
2
0
0
0
0
1
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
3
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
2
0
0
2
1
0
2
0
0
2
0
0
0
0
0
0
3
1
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
1
0
0
0
1
1
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
1
4
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
5
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
2
0
0
0
2
1
0
1
0
0
4
0
0
1
2
0
0
0
0
2
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
1
0
2
1
0
2
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
4
2
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
2
0
2
0
1
0
0
0
0
0
0
2
3
1
1
0
0
0
2
4
0
0
0
0
0
1
0
0
2
0
2
0
0
1
0
0
0
2
7
1
2
1
3
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
2
2
0
2
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
2
0
0
0
0
0
3
2
2
3
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
5
0
0
0
2
0
0
0
3
0
1
2
0
0
0
0
0
2
1
1
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
1
2
2
2
0
0
0
1
0
5
3
0
0
2
0
0
0
1
0
0
0
2
0
2
0
0
1
0
0
0
2
0
1
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
2
3
2
0
4
0
0
0
0
1
3
1
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
5
0
2
3
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
3
1
0
0
0
1
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
3
6
0
0
0
1
0
0
0
0
2
1
0
0
1
2
0
0
0
0
0
0
0
0
0
2
1
1
0
4
0
0
2
0
0
0
0
4
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
2
1
0
1
1
0
2
0
0
1
0
2
5
0
2
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
4
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
1
2
10
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
2
0
1
1
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
1
2
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
4
0
0
0
0
0
1
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
2
0
0
1
1
1
0
0
0
0
0
5
0
0
0
0
1
0
1
0
0
4
0
0
1
0
1
0
1
1
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
1
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
1
1
0
0
2
0
0
0
0
2
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
5
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
6
1
0
0
0
0
1
1
2
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
1
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
3
1
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
1
0
2
1
0
0
0
0
3
0
0
1
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
1
2
0
0
0
2
1
1
3
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
3
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
1
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
2
2
0
1
0
2
0
1
0
0
0
0
0
0
0
1
1
0
1
0
2
0
2
0
1
0
0
0
0
0
0
3
0
0
0
0
0
3
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
2
2
2
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
1
0
1
0
3
0
0
1
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
3
0
0
0
0
0
2
2
0
0
2
0
0
1
0
4
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
3
0
2
0
1
0
0
0
0
0
1
1
2
2
2
2
0
0
0
0
0
0
2
3
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
3
0
1
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
2
2
0
3
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
3
1
2
0
2
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
3
0
0
2
2
0
0
1
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
3
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
1
0
1
0
1
0
0
6
0
0
0
0
5
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
3
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
3
2
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
8
0
0
0
0
1
0
1
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
2
0
0
0
0
0
1
0
0
0
0
2
1
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
3
2
0
0
0
1
0
3
0
0
1
0
0
0
1
1
0
1
1
0
0
0
1
1
0
0
3
2
0
0
0
2
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
2
0
2
0
2
3
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
2
0
0
1
0
0
0
0
0
3
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
7
0
0
0
0
3
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
2
2
0
5
0
0
0
0
0
0
0
1
0
1
0
1
0
0
2
0
0
2
0
0
3
0
1
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
2
0
0
2
0
0
4
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
12
0
0
0
0
0
0
0
0
1
1
1
0
1
0
1
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
2
1
0
0
2
3
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
1
2
1
3
1
1
1
0
0
0
0
0
0
0
0
0
0
5
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
2
1
0
1
0
0
0
1
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
2
1
0
4
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
1
0
0
2
0
2
0
0
0
0
7
0
0
0
0
0
0
0
1
0
0
2
2
0
0
3
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
1
0
2
1
2
0
0
2
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
2
1
0
2
1
0
1
2
0
2
0
1
2
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
3
1
0
0
0
0
0
3
2
0
0
1
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
3
2
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
2
0
0
2
0
2
0
0
0
0
0
0
1
0
0
1
0
2
0
1
0
0
0
2
0
3
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
4
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
2
1
0
0
0
1
2
3
1
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
6
0
0
0
0
0
2
1
0
1
0
1
0
0
0
2
0
2
0
2
1
0
0
2
1
0
1
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
1
1
2
0
1
0
0
0
0
1
0
0
0
1
2
0
2
0
1
0
0
1
0
0
1
0
0
0
2
0
1
0
0
0
2
0
0
0
0
3
0
1
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
1
0
0
2
1
2
0
0
0
0
2
0
3
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
5
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
3
1
3
0
1
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
3
0
1
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
2
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
4
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
3
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
3
0
0
1
0
3
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
2
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
4
3
2
2
1
0
0
2
4
0
0
2
2
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
1
2
0
1
0
2
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
3
1
0
0
0
1
0
2
2
1
2
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
1
0
1
0
1
2
0
0
0
0
0
2
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
4
2
0
0
2
1
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
2
1
0
1
0
1
1
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
3
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
2
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
1
0
0
0
1
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
2
1
1
0
0
0
6
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
1
0
1
0
0
2
0
0
2
1
0
0
0
0
0
0
1
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
3
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
2
1
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
2
0
1
0
1
2
1
0
0
1
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
2
0
2
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
1
1
1
1
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
2
2
2
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
3
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
2
1
0
0
6
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
2
1
2
0
0
0
1
1
0
0
0
1
0
0
2
0
0
1
2
2
1
1
0
0
1
0
1
0
0
0
0
0
0
1
0
2
0
1
0
0
1
2
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
1
2
0
0
0
0
0
0
0
1
2
0
1
1
2
3
1
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
2
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
3
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
3
0
2
0
0
0
1
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
1
2
3
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
4
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
2
0
0
0
0
0
0
0
0
2
0
3
0
0
2
1
2
3
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
4
0
0
1
0
0
2
0
0
0
2
1
0
0
0
0
2
0
2
0
2
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
2
0
0
0
0
0
1
0
0
0
3
3
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
2
0
0
2
0
0
1
3
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
2
1
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
1
0
4
0
0
0
0
0
0
1
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
1
0
0
2
0
0
3
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
1
2
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
1
2
1
0
1
0
0
0
1
0
0
0
2
1
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
2
0
0
0
0
3
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
1
0
0
1
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
3
0
0
2
0
1
0
2
0
0
0
1
0
0
1
0
0
0
1
0
0
2
0
1
1
0
0
0
0
0
2
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
1
0
0
0
0
2
0
3
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
7
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
3
0
0
0
1
0
0
0
1
0
0
1
2
2
0
3
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
1
2
0
0
0
2
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
3
0
1
0
0
2
0
0
0
0
0
0
1
0
3
1
0
6
3
0
2
0
0
0
1
3
0
2
0
1
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
1
0
2
0
1
1
0
0
0
1
0
0
0
2
2
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
1
2
0
1
0
0
0
0
2
1
0
0
2
0
0
1
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
2
0
4
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
3
0
1
0
3
5
2
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
1
1
0
0
0
1
2
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
1
3
0
0
2
0
0
0
0
0
0
2
1
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
1
2
0
0
0
0
2
0
1
0
0
0
1
0
2
1
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
3
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
1
0
0
2
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
2
0
2
1
0
0
0
2
0
0
0
1
0
0
0
2
0
2
1
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
4
0
0
0
0
0
1
0
0
2
0
1
3
0
2
0
0
0
2
0
0
0
1
2
0
1
0
0
0
2
1
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
2
2
0
0
0
0
0
0
0
2
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
1
0
0
0
0
0
0
2
1
0
0
0
0
1
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
2
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
2
0
0
1
0
2
0
2
0
0
1
0
0
1
0
1
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
2
0
2
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
1
2
0
0
0
0
0
2
1
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
3
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
1
2
0
2
0
0
1
2
1
0
1
0
2
0
0
0
2
0
3
0
0
0
0
0
3
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
3
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
6
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
1
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
1
0
3
0
0
0
0
1
0
2
0
1
0
2
0
0
0
0
0
0
1
0
0
0
6
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
15
1
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
2
0
1
1
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
1
0
2
0
0
2
0
0
3
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
2
1
0
0
0
6
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
2
0
0
1
2
1
0
0
0
0
0
4
0
1
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
7
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
1
0
0
0
2
0
0
2
2
0
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
1
2
0
0
0
0
0
0
0
0
0
0
2
2
1
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
1
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
1
0
1
0
1
6
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
2
2
0
0
2
0
0
2
1
0
0
0
1
0
0
2
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
6
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
2
0
1
0
1
0
3
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
1
1
2
0
0
2
0
0
0
0
5
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
7
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
1
1
1
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
4
3
0
0
0
0
0
0
0
0
1
2
0
0
0
3
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
11
0
0
0
0
5
0
2
0
0
1
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
1
2
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
2
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
2
0
0
0
0
1
1
1
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
11
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
2
0
2
0
2
2
0
2
1
1
0
4
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
3
1
0
0
1
0
0
0
0
0
4
0
0
0
2
1
0
0
0
0
7
0
2
1
0
0
2
2
0
0
2
0
2
0
0
0
0
1
0
0
0
0
1
1
0
2
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
2
2
0
0
2
1
0
3
0
0
0
0
0
0
2
1
4
0
0
1
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
2
0
0
0
4
0
1
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
5
2
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
1
0
0
3
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
2
2
0
0
1
1
0
0
2
2
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
2
0
0
4
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
1
0
2
0
1
0
0
1
1
0
1
0
0
1
0
0
4
3
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
2
0
2
0
0
2
0
0
0
2
2
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
1
0
2
1
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
1
0
0
1
0
0
1
0
2
0
0
2
0
0
0
1
1
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
2
0
2
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
5
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
2
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
1
0
0
0
0
2
0
0
1
1
1
2
1
1
0
0
2
0
0
0
2
2
0
0
0
0
0
0
1
1
0
2
0
0
1
0
0
2
3
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
2
1
0
0
1
2
2
2
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
1
0
1
0
2
0
0
2
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
8
0
0
0
2
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
4
1
0
0
1
0
0
0
0
0
0
1
3
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
1
0
0
0
0
0
1
2
0
0
0
0
2
1
1
0
2
2
0
0
0
0
0
2
0
0
1
0
2
0
0
2
0
0
0
0
1
2
0
0
0
2
0
0
0
1
0
1
0
0
0
3
2
0
0
3
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
2
0
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
1
0
0
0
0
2
0
6
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
1
3
0
0
0
2
0
1
1
2
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
4
0
0
2
1
0
1
1
0
2
1
0
0
0
0
1
0
1
0
0
0
2
0
0
0
1
1
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
1
0
0
1
2
0
0
2
0
3
0
0
1
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
3
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
2
2
0
0
0
0
0
2
0
2
0
2
0
0
0
1
0
1
0
2
0
0
0
0
3
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
10
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
2
0
2
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
1
0
0
1
0
0
0
1
0
0
0
1
2
2
0
0
0
0
1
1
0
0
1
5
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
4
0
0
0
2
0
0
0
0
0
2
1
0
0
1
0
0
0
0
2
1
2
2
2
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
3
0
1
0
0
0
0
4
0
3
0
0
3
0
0
0
1
0
0
1
1
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
1
0
0
0
0
1
0
0
1
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
3
1
0
0
0
3
0
0
0
0
0
2
4
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
1
0
0
6
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
1
1
0
0
0
2
3
0
0
0
0
3
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
1
0
2
0
0
0
0
0
0
0
2
0
1
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
1
6
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
4
0
0
1
0
0
0
2
0
0
0
1
0
5
0
1
0
0
0
0
0
0
3
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
2
1
0
0
1
0
0
2
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
2
0
1
2
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
3
2
1
0
0
0
0
0
1
0
2
2
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
2
0
0
1
1
0
0
0
1
0
0
3
2
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
1
0
1
0
0
0
0
2
0
0
2
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
2
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
6
0
0
0
0
0
0
0
0
2
2
0
1
0
0
2
0
0
1
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
2
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
3
0
2
0
0
0
0
1
1
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
1
2
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
1
0
0
1
0
1
0
2
0
0
0
0
0
0
5
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
4
0
0
0
3
0
0
1
1
0
0
0
0
3
0
0
0
2
1
0
0
3
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
2
2
3
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
1
2
2
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
1
1
0
0
1
0
3
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
1
3
1
0
0
0
0
0
0
0
0
0
1
2
2
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
2
2
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
1
1
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
2
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
1
0
0
0
0
2
0
0
5
1
0
1
1
0
0
2
0
0
3
0
0
1
0
0
0
0
0
0
0
0
2
0
3
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
2
0
0
2
4
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
1
1
0
0
2
0
2
1
0
0
0
2
2
1
0
0
0
0
0
0
0
3
0
3
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
2
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
1
1
0
0
0
0
0
2
0
1
2
0
3
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
3
2
0
3
0
0
0
1
1
0
1
2
0
2
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
5
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
2
0
2
1
0
0
0
1
0
0
0
0
3
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
9
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
2
0
2
0
2
2
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
2
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
5
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
1
0
0
1
2
0
0
1
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
3
1
0
0
1
2
0
0
0
2
1
0
1
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
2
2
0
1
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
2
0
2
0
1
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
1
3
0
0
3
2
0
3
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
2
2
0
0
3
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
7
2
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
6
0
0
0
2
0
0
1
1
2
0
0
0
0
1
0
1
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
2
0
4
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
1
2
0
0
1
0
0
0
2
0
0
1
2
1
1
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
4
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
1
0
0
0
1
1
2
0
0
0
0
0
0
0
0
1
0
3
0
0
0
2
1
0
0
2
1
0
0
0
0
1
0
2
0
0
0
0
0
0
3
0
0
1
0
1
0
0
0
2
0
0
0
1
0
0
3
0
0
1
0
0
0
0
0
0
2
0
0
1
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
2
1
0
0
2
1
0
0
0
2
5
0
0
0
1
1
5
0
3
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
7
0
5
0
0
0
2
0
0
2
0
0
2
1
0
0
0
0
0
2
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
2
1
2
4
0
0
0
1
1
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
3
2
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
1
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
1
1
0
0
2
0
1
0
0
1
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
2
1
0
0
0
0
3
1
0
0
0
1
1
0
3
0
2
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
1
0
1
0
0
0
2
0
0
0
2
0
2
0
2
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
2
0
0
1
0
0
13
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
5
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
1
1
0
3
0
0
2
1
4
1
1
0
0
0
0
0
2
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
3
4
1
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
4
0
0
0
0
0
0
0
6
0
2
0
3
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
1
0
0
0
1
3
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
2
2
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
3
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
2
0
2
1
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
1
0
0
3
2
0
0
0
0
1
2
1
0
1
0
0
1
0
1
0
1
1
0
0
3
1
0
0
0
2
0
2
0
0
0
0
2
0
1
0
1
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
3
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
1
0
2
0
1
0
0
1
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
5
0
1
1
0
0
1
0
0
0
0
1
0
1
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
4
0
0
0
1
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
2
0
0
2
0
0
1
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
1
2
1
0
2
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
7
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
8
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
2
0
0
0
0
2
0
2
0
1
0
0
0
0
0
2
0
0
2
0
0
2
0
1
6
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
3
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
18
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
2
1
0
2
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
1
1
0
0
0
0
0
1
0
1
3
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
4
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
1
1
0
0
0
0
1
2
0
2
0
0
0
0
2
1
0
0
0
0
2
3
0
0
0
0
0
2
2
0
0
0
5
0
0
0
0
0
2
2
1
0
1
0
0
0
2
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
3
0
0
1
0
0
2
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
2
0
0
0
1
2
1
0
0
1
0
0
0
0
0
0
1
2
0
0
1
1
1
0
0
0
1
3
0
0
0
0
0
0
0
0
2
0
0
0
0
2
3
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
2
2
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
3
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
3
1
1
4
0
1
0
0
0
0
0
5
0
0
0
0
0
1
1
0
0
2
0
0
0
4
2
1
0
0
2
0
0
0
0
0
0
0
0
3
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
2
0
0
1
0
2
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
2
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
1
1
0
4
0
0
0
0
0
2
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
3
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
6
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
4
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
2
0
1
0
0
0
0
0
1
0
1
1
0
2
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
2
1
0
0
2
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
1
3
2
3
0
0
1
1
0
2
0
0
0
0
1
0
0
0
0
5
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
1
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
1
2
2
0
0
0
0
1
0
0
0
1
1
0
1
0
1
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
3
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
4
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
2
2
0
2
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
4
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
1
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
2
4
7
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
2
1
1
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
7
0
0
1
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
2
0
1
1
0
0
7
0
2
1
0
0
2
3
2
0
2
1
0
0
0
1
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
1
1
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
2
1
0
1
0
0
0
0
1
0
0
0
1
0
0
2
1
2
2
0
0
0
2
1
0
0
0
2
4
0
4
0
0
2
0
0
0
0
0
4
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
2
0
1
0
0
1
1
0
0
0
0
1
2
0
1
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
1
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
1
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
3
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
2
1
1
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
2
0
2
0
0
0
1
0
0
0
0
0
0
2
1
1
0
0
3
0
1
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
6
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
2
0
2
0
0
2
0
0
0
3
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
4
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
1
0
0
2
0
0
2
2
0
0
0
1
0
2
1
1
1
0
0
0
0
0
1
1
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
1
3
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
2
1
0
0
1
0
0
1
2
2
0
0
0
0
1
1
1
0
2
0
0
0
0
0
0
0
0
10
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
5
1
0
0
0
0
2
1
0
1
0
0
0
2
1
0
0
1
2
0
1
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
2
1
0
0
1
1
0
0
0
0
0
0
0
2
2
3
0
0
0
0
0
2
2
1
0
0
4
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
2
0
0
0
2
0
0
2
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
6
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
2
3
0
2
0
0
0
0
0
3
2
0
0
0
0
0
0
0
1
1
0
0
0
0
1
2
0
1
2
4
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
2
1
0
0
0
5
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
1
0
1
0
1
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
1
0
0
1
3
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
1
0
0
2
0
0
0
4
0
0
0
0
2
0
0
0
0
0
1
0
0
0
3
0
0
0
2
0
0
0
2
0
0
2
0
1
3
0
0
0
0
0
2
0
2
0
2
2
0
0
0
0
0
0
5
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
3
1
0
0
2
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
3
1
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
1
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
3
1
1
0
0
0
0
0
0
0
0
2
0
0
2
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
6
0
0
0
0
0
0
2
2
0
0
1
2
0
1
0
1
1
0
0
0
2
0
1
0
0
0
0
0
0
2
7
0
2
0
0
2
0
0
1
2
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
5
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
6
1
0
0
2
0
0
2
1
2
1
0
0
2
0
1
0
0
0
2
2
1
0
0
0
2
0
1
0
1
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
6
0
0
2
0
0
2
2
2
0
1
2
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
1
2
0
0
2
2
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
1
1
0
1
2
0
0
2
0
2
1
4
0
1
0
0
1
2
0
1
4
2
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
1
2
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
1
1
1
2
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
2
0
0
1
0
0
1
0
0
0
0
2
3
0
3
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
1
0
0
0
0
1
0
0
0
5
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
2
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
1
2
6
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
2
0
0
2
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
5
0
2
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
2
0
0
0
0
0
2
0
2
2
0
0
0
0
1
0
1
0
0
0
3
0
0
0
0
0
1
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
10
0
0
0
2
0
0
2
0
0
0
2
0
2
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
1
0
0
0
2
0
0
0
0
10
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
1
0
0
2
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
2
0
2
0
1
0
0
0
0
0
0
3
0
4
1
0
0
0
0
1
0
0
2
3
0
2
0
2
0
0
1
1
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
1
4
0
1
0
0
2
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
2
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
2
0
0
0
0
0
0
1
3
0
0
0
0
0
4
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
2
3
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
2
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
4
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
1
0
0
1
2
0
2
0
0
0
0
0
0
2
1
0
2
0
3
2
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
2
0
0
0
0
2
3
0
0
1
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
1
1
0
2
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
1
1
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
2
0
0
0
1
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
2
0
0
0
1
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
7
0
1
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
2
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
1
0
0
2
0
1
0
0
0
2
2
0
0
1
0
0
0
1
0
0
0
6
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
1
0
3
0
3
0
2
0
0
1
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
1
1
2
0
2
0
0
3
2
0
2
0
2
0
0
0
0
0
0
2
2
1
0
1
0
0
2
0
2
0
0
1
0
0
2
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
1
4
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
3
0
1
0
0
0
0
0
0
3
0
0
1
0
0
1
0
0
1
0
2
3
0
0
1
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
2
0
2
0
2
0
0
1
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
8
0
0
0
0
1
0
1
0
0
1
0
1
1
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
2
1
1
0
0
0
1
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
1
2
0
4
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
1
0
2
0
2
0
0
0
2
0
2
0
0
1
0
1
0
0
2
0
1
1
0
1
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
3
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
2
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
4
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
1
1
0
3
0
0
2
1
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
1
0
0
0
7
0
0
2
0
0
0
2
0
2
1
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
2
1
1
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
3
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
2
0
0
1
0
0
0
2
0
0
0
0
2
0
1
0
0
0
1
1
1
0
2
0
0
0
1
2
0
1
0
0
1
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
6
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
2
0
1
0
3
3
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
1
0
0
0
0
1
0
2
0
0
2
0
0
2
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
3
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
2
2
0
2
0
0
0
0
0
0
0
2
2
0
2
3
0
0
0
0
0
2
0
0
2
0
0
0
2
1
0
0
0
2
0
2
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
3
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
5
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
2
0
0
0
1
0
0
0
1
2
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
5
0
2
0
0
0
0
0
0
0
0
0
0
3
1
0
1
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
1
2
1
0
2
0
0
0
1
8
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
5
0
0
0
2
1
0
0
0
0
0
2
0
3
1
0
0
0
0
2
0
1
0
0
0
0
0
4
2
0
0
1
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
8
0
0
0
2
0
0
0
1
0
0
2
2
0
0
0
0
0
0
2
0
0
1
1
0
0
3
0
2
2
0
0
0
0
4
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
5
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
3
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
4
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
3
0
1
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
3
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
8
0
0
7
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
1
0
2
0
3
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
3
0
2
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
2
0
0
1
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
2
0
0
2
2
3
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
1
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
1
0
0
2
0
2
0
0
1
1
1
0
0
0
0
4
0
1
0
0
0
2
0
0
1
0
0
1
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
2
2
0
0
1
0
0
2
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
4
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
1
2
0
0
0
1
1
1
0
2
0
1
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
3
1
0
1
0
0
0
0
0
2
0
0
0
2
0
2
0
0
2
0
2
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
5
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
2
0
1
0
1
0
0
1
1
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
2
0
0
3
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
2
0
1
0
0
5
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
1
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
2
0
1
2
0
2
0
0
0
0
0
2
0
1
1
0
0
0
0
0
1
0
0
0
2
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
1
0
0
2
0
2
2
0
0
0
0
0
2
1
0
0
0
1
0
1
0
2
1
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
2
1
0
2
0
0
2
0
0
5
0
2
0
0
0
2
0
0
0
0
0
0
0
1
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
2
1
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
4
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
2
1
0
0
2
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
1
1
1
0
1
0
0
1
0
0
0
0
0
0
2
0
1
0
2
0
0
0
2
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
6
1
2
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
2
0
2
2
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
4
0
0
2
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
2
1
0
3
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
2
1
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
1
0
1
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
1
2
0
1
0
2
0
4
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
2
0
0
1
0
0
2
3
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
2
0
0
1
0
0
3
0
0
0
0
0
0
2
0
1
0
2
2
1
2
2
0
0
2
1
0
0
1
0
0
0
0
0
0
2
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
5
0
0
2
0
0
0
0
0
0
1
0
0
0
0
4
2
1
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
5
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
1
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
4
0
0
1
0
0
0
0
1
0
0
0
2
2
1
0
0
0
0
20
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
1
0
2
0
2
2
1
2
0
3
1
2
0
0
1
2
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
4
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
3
2
0
2
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
1
0
2
0
2
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
1
1
0
0
0
0
2
0
0
0
0
0
6
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
1
2
0
2
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
1
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
2
3
0
0
0
1
8
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
2
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
2
9
0
0
0
0
0
0
0
0
0
2
2
4
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
1
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
1
0
0
0
3
3
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
3
0
0
0
0
0
0
0
2
0
2
0
0
1
3
1
1
2
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
1
0
2
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
2
0
2
0
1
0
0
0
0
0
2
1
0
0
0
4
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
1
1
0
1
0
0
0
1
0
2
0
0
1
1
0
0
0
0
0
0
1
0
0
2
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
1
2
0
0
2
0
0
2
0
0
0
7
0
0
2
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
3
1
0
0
0
0
0
3
0
2
0
0
0
0
2
0
0
0
2
0
0
1
0
2
0
0
0
0
2
0
0
0
1
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
2
0
2
0
0
1
0
0
0
1
0
1
0
0
0
2
0
0
0
3
0
0
0
2
0
2
1
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
2
2
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
2
0
0
3
0
1
3
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
4
0
0
0
0
0
0
0
1
2
0
0
2
2
1
0
0
2
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
3
0
1
0
0
0
8
0
2
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
2
1
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
1
0
2
1
3
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
10
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
5
0
2
0
0
0
1
0
0
1
0
0
1
0
0
1
2
0
2
1
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
1
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
1
1
0
1
4
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
8
0
0
1
0
0
0
0
1
0
0
1
2
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
2
0
0
2
1
0
0
2
1
0
0
4
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
3
0
0
0
0
1
2
0
0
1
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
1
4
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
5
0
0
0
0
1
0
0
0
0
0
0
4
0
0
2
0
0
0
0
1
0
0
1
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
3
0
0
3
0
0
0
0
2
0
1
1
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
1
1
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
2
1
2
0
0
0
0
0
0
1
0
8
0
0
0
0
0
0
0
0
0
0
2
1
0
2
1
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
2
2
0
0
0
3
0
0
2
0
1
0
0
1
0
1
0
1
0
1
0
0
0
1
0
2
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
3
0
1
0
0
2
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
1
0
0
3
0
1
0
0
4
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
4
0
0
0
0
2
0
0
1
0
0
2
1
0
0
0
1
2
0
1
1
0
1
0
0
0
0
0
0
0
2
4
0
0
0
2
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
1
3
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
2
3
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
3
2
2
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
2
0
0
3
1
0
0
0
0
4
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
6
0
2
0
0
0
0
3
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
1
0
0
0
2
8
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
11
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
2
0
2
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
4
0
0
0
0
1
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
3
1
0
0
1
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
2
1
1
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
2
1
2
2
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
1
2
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
4
1
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
1
0
1
0
0
0
2
0
2
1
0
0
0
2
0
2
3
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
2
4
2
0
0
3
1
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
2
0
1
0
0
0
0
1
0
1
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
1
0
1
2
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
10
0
1
0
0
0
1
0
0
0
1
0
2
2
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
4
0
0
2
1
0
0
0
0
4
1
0
3
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
2
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
2
0
1
1
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
8
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
4
4
0
0
0
0
0
0
0
0
2
0
0
10
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
2
5
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
1
0
4
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
1
0
0
2
0
2
2
0
0
0
1
0
0
0
2
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
2
0
1
0
1
0
0
0
3
0
0
2
4
0
1
1
0
0
0
1
8
0
0
0
2
2
0
0
0
0
3
0
0
0
2
0
0
4
0
1
2
2
0
1
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
2
0
0
0
0
0
0
0
0
4
2
0
0
1
0
1
2
0
0
0
0
2
0
2
0
0
0
0
3
1
1
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
1
3
0
0
2
1
0
0
0
2
0
1
2
0
3
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
3
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
1
1
0
0
1
0
0
1
0
1
2
1
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
1
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
3
0
0
0
2
2
1
0
0
0
0
0
1
0
0
2
1
0
0
0
2
0
0
2
0
0
0
0
0
0
2
3
0
0
2
0
1
0
0
2
0
0
0
0
2
1
0
1
0
0
0
1
0
2
0
2
0
0
0
0
1
1
0
0
0
0
1
0
3
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
1
1
0
0
0
0
2
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
4
0
0
2
0
0
0
0
0
2
0
0
4
2
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
1
5
1
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
2
0
0
3
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
2
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
5
0
0
0
1
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
3
0
5
0
0
0
1
0
1
0
0
0
0
0
7
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
3
0
0
1
0
0
1
2
0
0
0
3
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
1
0
2
0
1
0
2
0
1
0
1
0
0
0
2
0
0
0
0
2
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
2
2
0
1
0
1
0
1
0
2
0
0
2
0
0
0
0
0
2
0
1
0
0
1
2
0
0
0
0
1
0
0
4
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
3
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
3
2
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
5
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
4
0
0
5
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
2
2
1
0
0
0
0
0
0
2
2
3
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
1
1
0
0
2
0
1
0
0
4
0
0
0
0
0
0
0
1
3
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
2
0
2
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
2
0
2
2
0
1
1
1
1
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
2
0
4
1
0
1
0
0
1
2
0
4
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
2
0
0
0
2
1
0
3
2
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
4
1
0
1
1
1
0
0
0
3
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
2
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
3
0
0
0
0
0
0
1
2
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
1
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
3
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
2
2
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
1
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
2
0
0
0
2
0
0
0
2
1
0
0
1
3
0
0
1
0
1
0
0
0
0
2
0
0
2
2
0
0
2
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
2
0
3
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
1
0
2
2
0
0
0
0
0
3
2
0
0
0
0
0
3
0
0
0
1
0
0
0
0
1
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
2
0
0
0
0
2
0
0
1
0
0
4
0
0
0
0
0
1
2
0
0
2
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
4
1
0
0
1
0
0
2
0
0
0
3
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
8
0
0
0
0
2
2
0
0
1
2
2
0
0
2
2
0
0
0
0
2
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
3
0
0
1
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
2
0
1
0
0
0
0
0
1
0
2
1
0
0
1
0
0
2
2
0
0
0
0
1
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
3
3
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
2
1
0
0
1
0
0
0
0
1
0
0
0
2
1
1
0
1
0
0
0
0
0
2
0
2
0
1
0
3
0
0
0
1
0
2
2
0
2
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
2
1
4
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
2
0
0
1
0
2
0
0
0
0
3
0
4
2
0
1
0
2
0
0
2
0
0
3
0
0
0
3
1
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
2
0
2
0
0
0
0
0
3
2
0
0
3
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
2
0
3
0
0
2
0
6
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
2
1
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
0
0
0
0
0
1
1
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
3
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
1
2
1
0
0
2
0
1
0
0
0
2
0
0
0
2
2
0
2
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
2
1
5
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
2
0
1
1
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
1
3
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
2
0
1
1
0
0
0
0
1
0
0
0
0
2
0
1
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
11
0
1
0
0
0
2
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
2
0
0
2
1
0
2
0
2
0
0
2
0
0
0
1
1
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
1
0
2
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
2
0
0
1
0
0
2
2
0
0
0
2
0
0
0
2
0
4
0
0
1
0
0
1
1
0
3
0
0
0
0
0
2
2
2
2
0
2
0
0
1
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
1
0
0
2
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
2
0
0
0
0
2
1
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
2
0
0
2
0
0
2
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
1
2
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
1
0
0
6
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
1
1
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
2
0
3
2
1
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
1
2
1
0
0
0
0
0
1
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
1
0
0
2
1
2
0
0
0
1
0
2
0
0
0
1
0
2
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
1
2
0
0
0
0
2
0
1
0
1
0
0
1
0
0
0
1
0
0
0
3
2
0
1
0
2
0
0
0
0
5
0
2
0
0
0
0
0
0
2
0
3
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
1
0
0
0
2
2
2
2
0
0
0
5
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
5
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
2
1
0
0
0
8
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
3
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
3
0
0
0
1
0
3
0
0
0
2
0
0
0
0
0
0
0
0
3
0
2
0
1
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
4
0
2
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
6
2
0
1
0
0
1
2
1
0
0
0
0
0
0
1
1
0
0
0
5
0
1
0
0
0
0
0
0
0
2
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
3
0
0
1
1
0
2
0
0
2
0
0
0
0
2
2
0
0
2
0
0
0
2
4
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
2
2
0
2
3
0
1
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
2
3
0
1
0
0
2
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
3
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
1
0
0
0
2
0
1
0
0
0
2
0
0
0
0
2
1
0
0
1
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
3
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
2
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
1
3
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
1
2
0
0
2
3
0
0
0
0
0
1
0
0
0
0
2
2
0
1
2
0
0
0
0
1
1
0
1
1
0
0
0
0
0
2
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
3
0
0
0
1
0
1
0
1
0
0
0
0
0
2
2
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
1
0
1
4
1
0
0
0
2
0
0
0
2
0
1
2
0
2
0
0
1
0
3
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
1
0
3
0
0
0
3
2
0
0
0
0
0
1
0
4
0
2
0
0
2
0
0
0
0
4
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
3
0
0
2
0
0
0
6
0
0
0
0
1
1
0
0
0
4
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
5
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
2
0
1
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
3
0
2
0
0
0
0
1
0
0
2
5
0
0
0
0
0
0
2
1
1
0
1
0
0
0
0
0
3
0
0
1
4
0
1
0
0
0
0
0
0
2
0
3
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
3
0
0
0
0
0
3
0
0
2
1
0
2
0
0
0
0
2
0
0
5
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
4
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
1
0
0
2
4
0
0
0
2
2
0
0
2
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
3
1
0
0
0
0
0
0
0
0
6
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
5
0
0
0
0
2
0
1
1
1
2
1
0
4
0
0
1
2
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
3
0
0
3
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
1
0
0
2
0
2
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
5
6
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
4
0
2
0
0
0
2
0
0
0
2
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
2
0
2
0
0
0
0
0
0
2
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
1
2
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
2
0
1
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
2
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
1
0
0
0
4
0
0
0
2
0
1
1
0
0
0
0
0
0
1
0
0
0
2
1
0
1
0
1
4
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
7
0
1
0
0
2
0
0
1
0
0
0
0
0
4
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
1
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
2
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
4
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
3
2
1
0
1
0
1
0
0
0
1
0
0
0
2
3
5
0
0
2
1
1
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
4
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
1
2
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
5
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
1
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
3
2
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
1
1
3
0
1
1
0
0
0
0
0
0
2
1
0
2
0
0
4
0
0
0
0
0
0
0
2
0
3
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
2
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
10
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
1
1
0
0
0
0
0
2
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
1
0
0
2
5
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
3
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
2
0
0
1
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
2
0
0
0
1
2
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
2
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
5
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
1
0
0
2
0
0
0
5
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
5
0
2
0
2
0
0
2
2
0
2
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
2
0
0
2
3
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
2
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
2
0
0
1
0
3
0
0
0
0
1
0
0
0
3
0
1
1
2
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
3
5
0
0
2
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
1
0
1
0
2
2
0
0
0
0
0
0
3
1
3
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
6
0
0
2
2
0
3
2
0
1
0
1
0
0
1
0
0
0
0
3
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
3
0
1
1
0
0
0
2
2
0
0
0
2
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
2
0
2
0
0
0
0
0
4
0
2
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
2
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
1
0
1
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
3
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
5
0
2
11
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
2
0
0
1
0
3
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
3
2
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
2
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
3
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
3
0
0
1
0
3
1
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
2
2
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
2
2
0
1
0
0
1
0
0
2
0
0
2
2
0
0
1
0
1
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
2
0
0
2
0
0
2
2
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
2
1
0
0
0
2
0
0
0
0
0
1
1
0
2
0
4
3
0
1
0
0
0
1
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
2
0
1
0
2
0
0
0
0
0
2
1
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
6
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
2
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
1
1
0
0
0
0
0
2
2
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
1
1
4
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
2
1
2
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
2
1
0
0
0
0
0
2
1
1
0
0
0
0
0
2
0
0
1
1
0
3
0
2
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
1
0
0
0
1
1
0
3
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
1
0
2
0
0
0
1
0
0
2
0
1
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
2
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
2
1
0
0
0
0
0
0
1
2
0
1
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
3
0
2
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
4
0
1
2
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
1
0
0
0
0
0
2
0
0
1
1
3
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
2
1
2
0
2
0
0
0
0
0
1
0
0
0
2
2
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
3
1
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
3
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
3
1
4
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
5
0
0
0
0
1
0
0
0
10
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
2
1
1
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
2
1
1
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
2
0
0
1
2
1
0
0
2
0
0
0
0
1
0
0
1
0
0
3
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
2
0
0
4
3
2
0
4
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
2
2
0
0
0
0
0
0
1
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
3
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
2
1
1
0
0
0
0
0
1
0
1
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
8
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
2
1
2
0
0
0
2
0
0
0
2
0
0
4
2
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
3
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
2
1
3
0
0
0
1
0
4
0
0
0
0
1
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
5
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
1
0
0
1
0
0
0
2
1
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
1
0
1
0
1
0
0
1
0
1
0
0
0
0
0
2
0
5
1
0
0
0
0
0
1
0
1
0
0
1
1
1
0
1
0
0
2
0
0
0
0
0
0
2
0
1
0
1
0
0
2
1
0
3
1
0
3
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
21
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
1
2
0
0
0
0
2
0
0
0
2
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
1
3
1
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
2
0
1
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
1
0
0
1
3
2
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
1
1
0
2
0
1
0
0
0
6
0
0
2
3
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
1
0
0
1
0
0
0
0
0
9
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
4
0
0
1
1
0
0
1
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
10
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
2
0
0
1
0
3
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
2
0
1
0
3
0
0
2
0
0
0
0
0
0
3
2
0
6
0
1
0
0
0
0
0
1
2
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
2
1
0
0
0
2
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
2
2
2
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
3
0
1
0
1
0
0
0
0
2
0
0
0
0
0
2
1
2
0
0
0
2
0
0
4
0
0
0
1
0
0
0
0
2
2
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
1
2
0
6
1
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
2
0
1
0
2
1
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
1
0
2
2
3
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
2
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
1
0
0
4
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
3
0
0
2
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
1
0
0
2
0
0
1
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
4
0
0
8
0
2
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
2
0
0
1
0
3
1
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
2
1
0
4
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
5
0
0
2
1
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
2
0
0
4
0
2
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
2
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
3
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
2
0
0
0
1
2
0
0
0
1
0
0
0
0
0
1
3
0
0
0
1
0
2
2
0
1
1
0
0
1
0
0
2
0
0
0
4
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
4
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
4
0
3
0
3
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
3
0
0
4
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
2
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
2
0
0
0
0
1
2
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
1
0
0
0
1
1
4
2
0
0
1
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
2
0
0
0
1
0
0
0
0
0
2
2
1
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
2
0
1
2
2
1
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
3
0
0
0
0
0
0
0
0
2
1
0
0
2
0
1
2
0
0
1
0
0
0
0
0
0
0
2
2
0
10
1
3
0
0
0
1
0
0
0
1
0
0
1
0
2
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
4
0
0
0
2
2
0
0
0
1
2
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
3
0
0
1
2
1
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
3
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
2
3
0
1
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
3
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
1
0
0
0
0
0
3
0
0
0
0
0
0
3
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
6
0
0
0
0
0
0
1
0
0
1
1
0
0
5
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
3
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
1
2
1
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
1
0
0
0
2
2
1
2
4
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
3
0
0
0
2
2
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
3
1
0
0
3
0
0
0
2
1
0
3
2
0
2
0
0
8
1
0
1
0
0
2
1
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
2
0
4
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
4
0
0
3
0
0
0
3
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
3
0
0
1
0
3
0
1
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
1
5
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
4
1
0
1
0
0
3
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
3
2
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
1
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
1
0
0
0
0
0
2
2
0
2
1
2
2
0
1
0
1
0
0
0
0
1
0
0
0
0
5
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
1
1
0
1
2
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
2
0
0
0
1
0
0
2
0
2
0
0
0
6
0
0
0
0
0
0
0
0
2
0
1
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
2
0
1
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
3
0
0
3
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
2
0
2
0
0
1
0
0
0
0
1
2
0
0
1
0
0
0
3
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
4
1
7
0
0
4
0
0
1
1
0
1
4
0
0
2
0
1
2
0
0
0
0
4
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
1
0
0
0
0
2
1
1
0
1
1
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
1
1
0
0
1
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
2
0
0
2
0
0
0
2
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
3
0
0
0
2
0
2
0
0
2
2
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
4
2
0
2
0
5
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
1
1
0
0
0
0
1
0
0
1
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
12
0
1
2
0
0
0
2
0
3
2
2
0
0
0
0
0
2
0
2
0
3
2
2
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
5
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
1
0
0
0
4
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
3
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
4
0
0
0
0
0
3
2
0
1
0
0
0
0
2
1
0
0
0
0
2
1
3
0
0
2
0
0
0
0
0
7
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
3
0
1
0
0
0
0
0
0
5
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
2
0
0
0
0
0
0
0
3
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
2
0
2
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
10
1
0
0
0
0
0
0
0
1
0
2
0
0
0
2
2
0
1
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
4
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
2
0
1
0
0
0
0
2
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
3
3
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
2
0
1
0
2
1
0
0
0
0
1
0
0
0
0
0
2
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
2
4
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
1
0
0
0
0
2
1
0
0
0
1
2
0
0
1
0
0
0
0
0
0
8
0
0
0
0
0
0
0
4
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
1
1
0
0
0
0
0
3
2
1
5
0
0
0
0
0
2
0
1
3
2
0
0
0
0
1
0
0
0
0
0
0
0
1
2
1
0
0
2
0
1
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
1
1
0
1
0
0
0
0
0
2
0
2
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
1
1
0
0
4
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
2
0
0
0
0
0
0
2
2
1
2
0
2
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
4
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
1
4
0
0
1
0
0
0
0
4
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
0
3
0
0
4
0
2
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
6
0
1
0
2
1
0
0
0
1
0
0
0
0
0
0
2
0
1
0
2
0
0
1
1
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
1
0
3
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
2
1
1
0
0
0
0
0
1
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
1
2
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
2
0
3
0
2
0
1
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
2
0
0
0
0
3
0
0
0
1
0
1
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
2
0
0
0
2
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
1
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
3
1
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
4
2
0
0
5
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
2
0
2
2
0
0
1
1
0
0
0
2
0
0
0
2
3
1
0
0
0
0
0
2
2
0
1
0
0
0
0
1
2
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
4
0
0
0
0
0
0
3
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
1
0
1
0
1
0
0
0
1
0
0
0
4
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
3
1
0
0
2
0
1
0
1
0
0
1
3
0
1
0
0
1
0
0
0
3
2
1
0
1
0
0
2
0
0
0
0
0
0
0
0
5
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
3
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
2
0
2
2
0
0
0
6
0
0
0
0
0
0
1
0
0
0
2
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
1
1
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
9
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
2
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
2
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
1
0
1
0
0
0
0
0
3
0
0
0
0
0
1
0
1
0
2
0
1
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
5
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
1
0
0
1
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
3
1
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
1
1
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
3
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
9
0
0
0
0
0
2
0
0
0
0
1
0
2
0
2
0
0
1
0
0
1
2
0
1
0
0
4
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
1
2
1
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
1
3
0
0
1
0
0
0
0
1
4
0
0
0
0
12
2
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
3
0
0
2
0
2
0
0
0
0
0
1
0
1
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
1
0
1
3
2
2
1
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
1
0
0
0
1
0
0
0
0
0
2
1
0
3
0
1
0
0
1
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
5
0
0
1
1
0
1
0
0
2
0
2
1
0
0
0
1
3
0
0
1
0
0
2
2
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
2
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
4
1
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
1
0
1
0
0
0
2
0
3
1
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
2
0
0
0
1
0
0
1
0
0
3
0
0
0
0
0
2
1
0
2
2
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
2
0
3
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
2
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
1
0
1
0
0
0
0
3
0
0
1
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
1
0
1
1
0
0
1
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
2
3
7
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
1
0
0
0
1
0
2
0
2
0
0
0
1
2
0
2
0
0
2
0
0
0
0
2
0
0
0
2
2
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
2
0
5
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
3
1
2
0
4
1
1
2
0
0
0
0
0
2
4
1
0
0
0
2
0
0
0
1
1
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
5
2
0
0
0
0
2
2
0
0
0
1
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
2
0
1
0
1
0
0
2
0
0
1
0
2
0
0
0
0
0
0
3
0
0
0
2
1
0
1
0
0
1
0
0
0
0
2
0
2
0
2
0
2
3
1
0
0
1
0
0
1
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
4
0
0
0
0
3
1
1
0
1
0
0
0
0
0
0
0
3
0
0
0
2
0
1
0
1
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
3
0
0
0
0
2
2
0
0
0
1
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
6
0
3
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
6
0
0
0
0
0
1
2
0
2
3
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
1
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
4
0
0
1
0
0
0
3
0
0
0
2
1
0
2
0
0
0
0
3
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
1
0
0
1
0
1
0
0
0
2
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
1
1
3
0
3
2
0
0
0
0
2
0
4
2
1
1
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
3
0
0
2
2
2
0
2
0
2
0
0
0
2
0
0
0
0
0
2
0
1
0
0
1
0
1
0
0
2
0
0
1
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
2
4
0
3
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
2
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
2
0
3
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
2
0
1
0
1
0
0
1
0
2
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
2
1
0
0
0
0
0
1
0
1
0
0
2
1
0
0
0
0
0
1
0
1
4
0
1
0
1
0
0
0
0
2
2
2
0
1
0
0
0
1
0
0
2
1
1
2
0
0
1
0
2
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
5
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
5
2
0
0
0
1
1
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
2
2
0
1
0
0
0
0
0
1
0
1
0
3
1
0
2
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
1
0
0
1
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
2
2
0
0
0
0
3
1
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
4
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
1
2
0
0
0
1
0
0
0
0
0
0
3
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
1
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
1
1
0
2
0
0
1
0
0
1
0
2
2
0
2
0
0
0
0
0
0
0
2
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
5
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
5
0
0
0
0
1
6
0
0
0
0
8
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
1
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
4
2
0
2
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
4
0
2
2
0
0
3
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
2
0
2
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
2
0
1
0
0
0
0
0
0
2
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
1
0
1
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
3
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
4
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
4
0
1
1
0
0
0
2
1
0
0
2
1
0
0
0
2
1
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
2
1
0
1
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
5
1
0
0
1
0
0
0
0
0
2
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
1
4
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
1
0
3
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
4
1
1
0
1
0
0
3
0
0
0
0
0
0
0
0
0
2
1
1
0
0
3
0
1
0
22
0
0
0
0
0
0
0
1
0
0
3
0
0
1
0
0
0
0
0
0
2
0
4
0
1
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
2
2
0
0
0
4
0
4
2
0
5
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
1
0
1
0
2
1
2
3
2
0
0
2
3
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
3
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
3
2
2
0
0
0
1
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
2
0
2
0
0
1
2
1
0
2
0
2
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
1
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
2
1
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
3
0
0
0
2
3
0
0
0
1
0
0
2
0
0
0
2
0
2
0
0
2
2
0
0
0
7
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
1
0
2
0
2
0
0
0
0
0
2
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
1
1
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
2
0
2
0
1
0
0
1
3
0
1
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
2
2
2
0
2
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
3
0
0
2
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
4
2
0
2
2
0
0
0
2
1
1
0
1
2
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
2
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
1
0
0
0
5
1
2
0
3
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
3
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
3
2
0
0
2
0
2
0
1
0
0
0
0
1
1
0
0
0
0
0
2
0
3
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
9
0
0
0
0
0
1
0
0
3
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
4
1
2
0
0
1
1
0
0
0
0
1
0
2
0
0
0
2
1
0
0
0
0
0
1
0
0
2
1
0
0
0
0
1
1
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
1
3
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
4
0
0
2
0
0
0
0
0
1
0
0
1
3
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
3
0
1
1
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
2
2
0
0
0
0
1
1
0
0
2
0
0
3
0
2
3
0
0
1
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
2
2
1
0
0
0
2
1
0
0
0
0
0
0
10
0
1
0
0
0
0
1
0
1
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
1
0
0
2
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
1
0
6
0
0
2
0
0
2
0
1
1
0
0
0
0
0
0
2
7
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
3
0
0
2
2
1
0
1
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
2
1
4
0
1
1
3
2
1
0
0
0
0
0
0
6
0
1
0
0
0
2
0
1
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
8
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
2
0
2
0
0
0
0
1
0
0
1
2
0
0
0
1
7
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
2
0
3
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
3
0
0
1
0
0
2
0
0
0
2
0
0
0
1
2
0
0
1
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
2
0
0
0
0
4
0
0
1
0
0
0
2
0
1
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
2
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
1
0
0
0
2
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
1
0
0
4
0
0
0
0
1
2
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
3
1
0
1
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
6
0
3
0
0
2
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
3
0
0
0
0
0
1
0
0
0
5
2
0
0
0
0
0
0
1
1
1
0
3
0
0
0
0
0
0
0
1
0
0
1
0
3
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
2
2
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
2
2
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
2
0
1
0
0
0
0
3
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
3
1
0
0
0
0
1
2
0
1
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
2
1
0
1
0
0
0
0
0
1
1
0
0
0
2
0
0
1
0
0
7
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
5
0
0
1
0
0
1
0
0
1
0
2
0
2
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
5
0
0
0
0
3
1
2
0
0
0
2
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
4
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
1
0
1
0
2
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
2
2
3
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
2
1
1
0
2
0
0
0
1
0
0
0
1
1
0
0
1
2
2
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
1
0
0
0
0
2
5
2
6
0
0
0
4
0
0
0
0
0
3
0
0
0
0
1
0
0
1
0
0
0
0
7
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
2
2
0
2
3
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
1
0
2
1
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
2
0
4
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
1
1
2
0
1
4
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
5
4
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
2
0
0
0
0
0
0
2
0
2
0
0
0
0
1
2
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
3
0
0
2
2
2
0
0
0
0
1
0
0
2
0
0
3
0
1
0
0
1
1
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
3
2
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
1
0
2
0
0
0
0
0
0
1
3
1
0
2
0
0
2
6
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
1
0
0
0
0
0
0
11
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
1
0
1
0
0
0
1
0
3
0
1
1
1
0
0
0
0
0
0
1
1
1
0
0
3
0
0
0
1
2
0
1
0
0
0
1
2
0
0
2
0
2
0
3
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
2
0
0
0
2
1
0
0
0
0
0
2
0
0
2
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
1
2
1
0
0
0
0
1
0
0
0
2
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
7
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
1
0
0
0
2
2
0
0
0
2
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
2
0
0
1
3
0
0
0
0
1
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
1
0
0
0
2
2
2
0
0
0
0
0
0
1
0
2
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
4
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
2
0
2
0
0
0
1
1
0
0
0
2
0
2
0
1
0
2
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
2
1
0
0
0
0
0
0
1
2
0
0
2
0
1
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
2
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
2
1
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
1
2
1
0
0
1
0
0
0
0
0
0
0
1
0
2
2
0
0
1
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
1
0
1
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
3
0
2
0
1
1
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
2
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
2
0
1
0
0
0
2
0
2
1
0
0
0
0
0
0
1
0
0
1
2
0
0
0
2
0
0
0
1
0
0
0
1
1
1
1
0
1
2
0
0
0
0
0
0
5
0
1
0
1
2
0
0
3
0
0
3
0
0
0
0
0
0
0
0
0
0
8
2
0
2
1
1
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
2
0
0
0
0
0
5
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
1
0
0
0
0
0
0
0
2
0
0
9
2
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
2
0
1
0
0
0
2
2
0
0
0
2
2
1
0
0
0
0
0
1
0
0
0
0
1
3
0
0
0
3
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
2
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
3
0
0
0
0
0
6
0
3
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
2
8
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
7
0
0
0
1
1
0
4
0
0
0
0
0
0
0
6
0
0
0
0
1
0
0
0
2
0
0
2
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
1
3
0
0
2
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
10
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
6
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
2
3
0
0
0
6
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
4
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
1
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
2
3
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
9
2
0
1
0
1
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
1
0
0
0
0
0
0
2
1
2
0
0
2
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
6
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
2
3
1
0
1
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
1
0
1
0
0
0
1
0
2
0
3
0
0
0
0
2
3
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
4
4
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
1
3
1
0
3
0
2
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
3
0
0
0
0
0
0
0
4
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
1
2
1
3
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
1
0
0
3
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
2
0
1
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
4
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
6
0
0
1
0
0
0
0
1
0
0
0
3
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
2
1
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
1
0
0
1
0
2
0
0
2
0
2
0
2
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
4
0
1
0
4
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
2
0
2
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
2
0
0
2
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
1
1
0
0
2
0
0
2
1
2
2
1
0
0
0
0
1
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
1
1
0
1
3
2
2
0
1
0
2
0
0
0
0
0
2
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
3
0
0
0
2
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
3
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
2
2
1
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
1
0
2
1
0
0
0
3
3
0
0
0
3
0
1
0
1
1
0
1
3
0
1
0
0
0
2
0
0
0
0
4
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
7
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
1
0
1
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
2
0
0
0
0
5
0
0
2
0
0
0
0
2
0
0
1
0
0
1
0
2
0
1
0
0
1
0
2
2
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
1
1
2
0
0
1
0
0
0
0
0
0
1
0
0
0
1
2
0
0
2
1
0
2
0
1
0
0
0
0
0
0
1
2
4
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
7
0
0
0
0
1
0
3
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
2
0
1
0
0
0
0
1
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
1
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
1
1
2
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
3
1
0
1
0
1
0
0
0
0
0
2
0
0
0
2
0
1
1
2
0
0
0
0
1
0
0
3
0
3
0
0
0
2
3
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
1
0
1
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
2
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
3
0
0
0
2
0
0
0
0
2
0
0
0
2
2
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
2
2
1
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
5
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
2
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
3
0
3
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
2
1
0
2
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
2
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
9
0
3
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
2
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
2
0
2
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
1
0
0
1
0
0
1
1
2
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
2
0
0
2
0
2
3
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
1
2
0
2
0
0
0
0
0
1
1
0
0
0
0
0
2
0
1
0
1
2
2
3
0
0
0
1
0
0
2
0
1
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
2
0
0
1
0
0
2
0
2
0
0
0
0
0
0
2
0
1
2
0
0
0
2
0
1
0
0
2
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
3
0
0
0
0
2
1
0
0
1
0
0
0
1
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
2
0
0
2
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
1
0
0
4
1
2
0
0
1
0
3
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
2
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
2
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
4
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
3
0
2
1
0
2
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
1
2
0
3
0
0
1
0
1
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
2
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
3
0
1
0
3
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
2
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
2
2
0
1
0
0
0
4
0
2
1
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
4
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
4
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
2
0
0
0
0
1
0
1
0
1
3
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
2
0
0
0
0
0
1
2
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
3
2
1
0
0
0
0
0
0
0
1
2
0
0
2
0
2
0
1
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
4
1
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
3
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
1
2
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
1
0
1
0
1
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
3
0
1
0
0
1
2
0
0
1
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
2
0
0
0
0
4
0
0
0
0
0
0
1
2
0
0
0
0
0
3
0
0
3
1
0
0
1
0
1
0
0
1
0
0
0
2
2
2
0
0
0
0
0
0
2
0
0
0
0
0
2
2
2
0
1
1
0
0
0
1
3
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
3
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
1
2
0
0
0
1
3
0
0
2
1
0
1
12
2
0
0
3
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
1
0
1
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
1
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
2
1
2
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
2
0
0
0
0
0
4
0
0
0
0
0
3
1
2
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
9
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
1
2
2
0
5
1
0
2
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
2
0
0
0
2
0
1
2
0
0
0
0
0
0
4
1
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
9
0
2
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
5
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
8
3
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
2
2
0
0
1
0
8
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
2
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
2
0
0
0
0
0
0
0
0
3
0
3
2
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
2
2
2
4
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
2
1
0
0
2
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
2
0
0
4
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
6
0
2
0
2
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
4
0
1
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
3
0
0
0
0
2
0
2
1
0
3
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
5
0
3
0
1
0
4
0
0
0
0
0
0
1
0
2
0
0
4
2
2
2
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
4
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
4
1
1
0
0
0
0
1
2
2
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
1
0
1
4
0
0
0
0
2
0
3
0
0
0
0
0
1
0
3
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
1
1
0
0
0
0
2
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
2
1
0
0
1
0
1
0
0
0
1
1
1
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
1
2
0
2
0
0
1
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
2
0
4
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
1
0
0
0
0
1
1
3
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
3
3
2
2
0
0
1
0
0
0
1
2
0
6
0
0
0
0
0
0
0
2
0
2
3
0
1
0
2
0
0
0
0
2
0
0
0
3
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
3
0
0
0
0
2
1
0
0
0
0
1
2
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
2
0
0
0
0
2
0
0
2
0
1
0
0
2
1
0
0
0
0
2
0
7
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
5
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
2
1
0
0
2
2
0
0
0
1
2
0
2
0
0
0
0
2
2
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
5
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
2
0
0
0
3
0
0
3
0
0
0
0
0
0
0
2
1
0
1
0
1
0
0
2
0
1
0
0
0
1
0
1
0
0
0
0
2
1
0
1
3
0
0
0
1
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
1
2
0
0
0
0
0
6
0
4
0
0
0
0
0
0
0
1
0
2
3
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
3
2
4
0
0
0
1
0
0
2
0
1
1
1
0
1
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
1
0
4
0
0
0
0
5
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
1
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
2
0
0
3
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
3
0
3
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
5
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
3
0
0
0
1
2
1
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
2
2
0
0
0
2
0
0
0
0
4
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
2
0
0
0
2
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
1
0
1
1
1
0
0
0
2
0
2
3
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
2
2
0
2
1
2
0
2
0
0
1
0
0
1
0
0
0
0
0
1
2
0
0
2
0
0
2
0
3
0
1
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
2
1
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
4
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
2
0
0
2
0
0
0
1
0
0
0
0
0
1
3
0
0
0
1
0
0
0
0
0
0
0
2
0
1
2
0
0
0
3
0
0
15
0
1
0
3
0
2
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
1
0
1
1
0
0
1
1
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
1
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
1
7
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
1
2
2
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
1
1
0
0
3
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
2
2
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
8
0
0
0
0
4
0
2
1
0
3
0
0
1
0
0
0
1
1
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
1
0
1
2
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
3
1
3
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
14
2
2
1
0
1
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
6
0
1
0
0
0
0
0
0
3
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
3
3
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
3
0
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
2
0
0
0
5
0
0
1
0
0
2
0
2
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
1
3
0
1
1
0
0
0
1
1
0
1
0
0
2
2
0
2
0
0
0
1
2
0
0
1
0
1
0
0
0
0
0
2
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
7
0
2
0
0
0
1
1
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
2
0
1
0
2
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
2
1
0
1
1
0
0
0
0
0
2
0
1
1
2
2
0
0
0
1
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
6
0
0
0
0
1
0
1
0
1
0
0
0
0
3
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
3
0
0
2
0
4
0
0
0
5
4
5
3
0
0
0
0
1
0
0
0
0
0
0
2
0
1
1
0
1
0
1
0
0
0
2
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
1
0
3
0
0
0
3
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
1
0
2
2
2
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
2
0
1
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
2
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
1
2
1
0
1
0
2
0
0
1
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
9
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
4
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
4
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
1
1
0
0
4
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
2
0
0
0
2
0
0
2
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
2
0
0
2
0
0
0
0
1
0
0
1
1
0
0
1
0
6
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
3
4
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
5
0
0
0
0
0
0
2
3
0
0
0
4
0
0
0
0
0
2
0
0
0
1
1
0
1
0
2
1
1
0
0
0
0
0
0
1
0
3
2
0
0
0
0
0
1
0
0
0
1
2
0
1
1
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
2
1
1
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
3
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
2
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
3
0
1
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
1
0
2
0
0
0
0
0
0
3
0
0
0
3
0
0
0
0
0
0
2
1
1
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
1
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
3
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
2
0
0
0
1
1
0
2
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
2
3
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
4
1
5
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
9
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
2
1
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
1
10
0
3
1
0
0
2
1
1
2
0
2
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
4
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
1
1
0
0
0
0
1
3
1
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
1
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
3
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
2
1
2
0
0
0
0
0
3
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
2
0
2
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
4
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
1
0
2
2
2
0
0
0
0
0
0
1
1
0
0
2
0
0
1
2
2
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
2
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
3
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
1
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
2
0
0
0
3
1
0
1
2
0
1
0
1
2
0
0
4
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
1
3
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
4
3
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
5
1
0
1
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
1
2
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
2
0
1
0
1
0
2
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
3
0
5
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
1
1
0
0
0
0
0
2
1
3
0
0
0
0
0
2
0
0
0
5
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
2
0
1
1
0
0
0
0
0
0
0
0
2
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
1
2
0
0
0
1
0
0
2
0
0
0
3
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
5
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
1
0
0
1
2
0
0
0
1
0
3
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
3
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
3
0
2
0
3
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
4
0
2
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
8
2
0
0
1
2
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
1
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
1
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
2
1
0
0
0
1
0
0
1
0
2
0
2
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
6
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
1
2
1
0
0
0
0
1
2
2
2
0
2
0
0
2
2
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
1
0
0
0
0
2
0
0
0
3
1
0
0
0
0
0
0
0
0
6
0
0
2
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
1
1
0
0
0
1
0
1
3
0
0
0
0
1
3
0
2
2
0
0
0
0
0
2
0
0
1
0
1
0
1
0
0
0
1
0
0
0
4
0
0
0
0
0
0
2
2
1
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
2
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
5
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
3
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
2
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
9
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
3
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
2
0
0
3
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
7
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
2
1
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
1
0
2
2
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
3
0
0
0
1
1
0
0
1
2
0
0
2
0
0
0
2
2
0
0
2
0
0
0
0
0
0
1
0
5
0
1
0
0
0
0
0
1
0
1
3
0
0
3
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
3
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
3
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
2
0
4
0
0
0
2
1
1
2
0
1
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
6
1
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
2
1
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
3
0
0
0
1
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
4
0
0
1
0
2
0
0
0
2
0
0
0
2
0
2
0
0
3
0
0
0
0
0
0
2
1
2
0
1
0
0
0
0
0
2
0
0
1
0
1
0
0
1
1
1
0
0
0
0
0
1
2
0
0
3
0
0
0
0
0
0
0
0
4
0
0
0
0
1
2
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
2
2
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
2
0
0
1
0
1
0
0
0
1
0
0
8
0
0
0
0
1
0
1
0
6
2
1
2
0
2
0
0
2
1
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
0
1
2
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
3
0
1
0
4
0
2
0
0
3
0
0
0
0
1
2
0
1
0
0
0
2
0
3
1
0
0
1
0
3
2
0
0
0
0
0
1
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
2
2
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
3
0
1
0
0
0
0
0
0
1
0
3
2
0
0
0
0
0
0
0
0
1
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
2
0
0
0
0
0
0
0
0
0
2
0
26
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
2
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
1
0
0
0
2
2
0
2
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
3
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
1
0
0
1
1
2
0
0
0
0
0
2
1
0
1
0
2
0
0
0
0
1
1
1
0
3
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
3
0
1
0
1
0
0
0
1
0
0
0
1
1
0
2
1
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
5
0
1
0
1
0
0
0
0
2
0
0
0
1
0
0
0
3
0
0
0
0
2
2
3
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
1
6
0
3
0
0
2
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
3
2
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
1
0
0
2
0
0
0
0
0
0
2
0
2
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
2
1
0
1
2
0
0
0
1
0
3
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
2
5
1
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
1
1
2
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
3
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
1
1
0
0
2
0
0
0
1
0
5
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
1
0
0
0
0
4
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
5
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
1
1
0
1
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
3
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
13
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
6
0
0
1
1
0
1
0
0
0
0
0
0
0
6
0
0
0
3
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
2
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
2
0
0
0
4
0
0
2
2
0
1
0
2
1
0
0
1
0
1
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
1
0
4
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
3
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
2
3
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
1
2
4
1
0
0
2
0
1
0
0
0
0
4
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
1
0
68
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
4
0
4
0
0
3
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
2
7
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
3
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
2
0
0
1
0
1
3
0
2
0
0
0
4
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
2
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
4
0
0
0
0
4
0
2
0
0
0
2
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
2
1
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
2
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
2
1
0
0
1
0
2
0
6
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
10
0
0
2
0
0
0
2
0
1
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
2
0
2
0
3
0
2
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
5
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
5
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
1
0
2
2
5
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
4
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
3
0
1
0
3
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
1
4
0
0
2
1
1
1
3
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
5
0
2
0
0
2
1
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
1
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
4
0
2
0
0
0
0
3
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
4
3
1
0
1
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
5
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
1
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
4
2
0
0
1
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
1
0
0
2
5
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
1
0
0
0
1
2
0
0
5
0
0
0
2
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
3
1
0
0
0
0
0
0
1
0
1
0
2
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
2
2
2
0
1
0
0
2
1
0
0
0
2
0
4
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
1
2
2
0
2
2
0
0
2
0
2
0
0
3
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
3
0
2
0
0
2
0
0
1
5
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
1
0
3
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
3
2
0
9
0
0
0
0
2
0
2
2
0
0
0
0
1
0
2
0
0
2
1
0
0
0
0
2
0
0
1
0
1
0
0
0
2
0
2
0
2
0
0
2
1
0
0
2
1
0
4
0
0
0
0
2
1
3
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
5
0
1
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
7
0
0
0
0
1
5
0
0
0
0
1
0
0
0
1
0
2
0
1
1
1
0
0
2
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
1
0
0
9
2
0
0
2
0
0
0
0
1
0
0
0
0
0
2
3
0
0
0
0
2
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
1
0
0
0
0
7
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
1
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
1
1
1
1
0
0
0
3
0
0
0
0
1
0
1
0
0
0
0
2
0
0
2
0
0
2
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
1
0
2
5
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
4
2
0
0
0
0
0
2
0
0
2
0
2
0
2
0
0
0
1
0
0
0
1
0
0
3
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
2
1
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
1
0
0
0
3
0
0
0
0
2
2
2
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
1
2
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
2
0
0
0
0
2
1
5
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
4
0
2
0
0
0
0
0
0
2
1
0
0
0
2
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
3
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
1
2
0
0
1
2
2
0
0
0
1
0
0
2
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
6
0
2
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
3
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
2
0
0
0
1
2
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
3
0
0
1
1
0
3
8
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
3
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
2
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
1
2
1
0
0
0
0
2
0
1
2
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
5
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
1
0
0
2
3
0
2
0
2
0
0
0
4
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
4
0
0
0
0
2
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
2
1
0
0
2
0
0
1
0
1
0
0
0
2
0
1
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
6
2
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
3
0
0
2
0
1
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
5
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
1
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
2
0
2
0
1
1
0
0
0
0
2
1
0
2
2
0
0
1
0
0
0
1
0
0
0
2
0
0
2
2
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
2
1
0
0
0
0
1
2
0
0
0
0
3
0
2
0
0
0
1
0
0
0
0
2
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
3
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
2
0
1
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
3
0
0
1
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
4
0
0
2
0
0
2
1
1
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
2
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
3
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
2
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
2
2
6
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
2
0
4
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
1
2
2
0
2
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
2
4
0
1
0
2
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
3
0
0
1
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
2
2
0
0
7
1
0
0
0
0
0
1
0
0
0
6
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
5
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
2
2
2
0
0
0
0
0
10
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
1
0
0
0
0
0
3
1
0
2
0
0
2
2
0
0
0
0
0
0
0
1
1
2
0
0
0
0
4
0
2
0
0
1
3
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
4
0
0
0
0
3
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
1
1
2
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
2
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
4
0
0
0
0
0
0
0
0
1
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
5
0
2
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
3
0
0
0
0
1
0
1
0
2
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
8
0
2
0
0
0
0
0
3
0
1
1
2
0
2
1
2
0
0
0
0
2
0
0
0
1
0
4
0
1
0
0
1
0
0
0
1
0
0
2
0
0
0
3
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
3
0
0
1
4
0
3
0
2
1
2
0
0
0
1
0
0
0
0
3
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
2
0
0
0
0
2
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
2
0
0
0
1
0
0
0
2
1
0
1
2
0
1
2
0
1
0
0
0
2
1
0
0
0
0
0
1
2
3
0
0
3
0
0
0
0
0
0
2
2
0
3
1
0
0
0
1
0
0
1
1
2
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
2
0
0
3
2
0
0
1
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
3
0
1
2
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
3
1
0
0
0
3
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
2
2
4
0
0
0
0
0
0
0
0
2
0
1
3
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
2
2
2
0
0
0
1
0
0
0
2
2
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
1
2
1
0
0
0
1
0
1
2
0
0
0
2
0
2
0
0
0
0
0
1
0
0
2
0
0
0
3
0
0
0
0
2
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
5
0
0
2
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
2
1
0
0
4
0
1
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
3
3
0
0
0
0
0
2
0
0
1
0
0
0
0
1
2
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
2
0
0
0
5
0
0
0
0
0
2
0
1
0
0
3
0
0
2
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
3
0
0
0
0
0
0
0
1
2
2
0
0
0
0
1
0
2
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
2
0
1
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
4
0
0
0
0
1
0
0
4
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
1
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
2
4
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
4
0
0
2
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
1
1
0
0
0
2
1
0
0
0
2
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
2
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
4
0
0
0
0
2
0
2
2
2
0
1
0
0
0
3
1
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
1
0
1
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
6
0
1
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
2
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
2
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
8
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
2
1
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
1
0
0
1
15
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
2
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
1
2
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
1
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
10
0
0
0
0
0
2
0
0
2
0
0
0
3
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
1
0
0
1
1
0
2
0
0
1
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
1
2
0
7
1
0
0
2
2
1
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
1
2
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
3
0
0
0
1
0
2
0
0
0
0
0
0
4
0
1
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
2
2
0
0
0
2
1
0
0
0
0
2
0
0
0
4
0
0
0
1
0
0
0
2
1
0
2
0
0
1
0
2
0
0
3
0
0
0
0
0
0
3
0
2
2
5
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
3
0
0
0
0
0
1
0
0
0
2
2
0
0
2
0
0
1
2
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
3
3
1
1
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
1
1
0
0
0
1
0
0
3
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
2
0
0
0
3
0
0
0
0
0
0
0
0
3
1
0
0
4
0
0
0
0
1
0
0
4
0
1
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
2
1
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
2
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
2
0
1
1
6
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
2
1
0
0
1
1
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
1
0
0
0
2
0
1
1
0
0
0
0
2
0
1
0
0
0
0
2
0
3
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
1
3
0
0
0
0
0
0
5
0
0
0
2
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
2
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
1
1
2
0
4
0
0
0
2
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
2
1
2
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
2
0
0
0
1
0
1
2
1
1
2
0
0
0
2
0
0
1
0
0
0
3
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
2
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
10
0
0
2
3
0
0
0
1
0
2
2
0
0
0
1
1
0
0
0
4
0
0
0
2
1
0
1
0
2
0
0
0
0
0
2
0
1
3
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
1
1
0
1
1
2
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
2
0
6
1
1
0
1
0
1
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
1
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
3
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
1
2
1
0
1
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
2
1
0
2
1
0
2
0
0
0
0
0
1
1
0
0
1
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
3
1
2
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
1
0
1
1
1
0
0
2
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
3
0
4
1
0
0
1
0
0
0
0
0
2
0
2
0
3
0
0
0
1
5
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
2
0
0
2
0
2
0
1
0
0
0
0
2
0
0
0
0
1
2
0
0
0
1
2
0
0
0
0
1
0
1
0
0
0
0
0
0
3
3
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
3
0
0
1
0
2
2
0
0
3
0
1
0
2
0
4
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
2
1
1
2
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
1
0
1
3
0
0
0
0
0
1
1
0
0
2
0
0
0
0
1
0
0
4
0
0
1
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
2
1
2
0
0
1
1
1
0
1
2
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
1
0
0
1
1
1
0
1
0
0
0
0
2
2
3
0
0
0
1
0
2
4
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
2
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
2
0
0
1
1
0
0
1
0
0
0
2
0
0
0
0
2
3
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
4
0
1
0
0
0
1
1
1
0
0
0
1
1
0
0
1
2
0
0
3
0
0
0
2
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
3
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
1
1
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
13
0
0
1
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
1
0
5
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
3
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
2
1
5
4
3
0
0
0
0
2
1
0
0
2
0
2
0
1
0
0
0
1
4
0
0
0
2
2
0
0
0
0
2
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
3
1
3
0
0
0
4
0
0
0
0
0
2
0
0
1
0
0
0
2
2
0
0
0
0
0
1
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
5
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
4
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
1
2
2
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
3
0
2
0
0
2
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
1
0
1
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
3
2
0
2
0
0
0
0
1
2
0
1
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
1
0
0
2
1
1
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
3
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
3
2
2
0
0
0
2
1
0
0
1
0
0
3
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
2
1
0
0
0
0
1
0
0
0
0
2
0
2
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
1
1
2
0
2
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
2
2
0
0
0
0
0
3
0
1
1
1
0
0
0
0
2
1
0
0
2
0
0
1
0
0
1
0
1
2
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
1
0
0
1
0
2
0
0
3
0
1
0
0
0
0
0
0
0
1
1
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
3
0
0
0
0
3
0
2
0
0
0
2
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
1
3
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
2
1
1
0
1
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
1
0
5
4
0
1
0
0
2
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
3
0
1
0
2
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
2
0
0
2
2
0
5
1
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
2
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
3
6
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
14
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
1
1
2
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
6
0
0
0
0
0
2
0
2
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
4
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
1
1
0
0
1
0
1
0
2
0
0
0
0
0
0
2
0
2
2
0
4
0
0
1
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
7
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
3
1
0
0
0
2
0
0
0
0
3
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
3
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
1
0
0
0
1
0
0
0
1
0
0
0
2
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
2
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
4
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
3
0
3
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
29
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
5
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
4
7
1
2
0
0
0
0
5
0
4
0
0
0
0
0
1
0
3
4
0
0
0
1
0
1
0
5
1
2
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
7
0
0
0
0
3
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
3
0
1
0
0
0
2
1
0
0
0
0
1
0
1
0
2
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
4
1
1
0
1
0
0
0
0
2
0
0
0
0
0
1
0
1
0
2
0
3
1
0
2
0
0
2
0
1
1
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
2
2
0
0
0
1
0
0
0
0
1
0
1
0
0
2
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
5
0
0
0
2
1
0
0
2
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
1
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
1
3
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
1
0
0
0
1
0
0
2
0
0
0
0
1
0
2
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
3
0
1
1
0
0
0
5
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
2
0
0
0
0
0
0
1
0
1
1
0
0
1
2
2
0
3
0
0
3
0
0
0
1
1
0
0
0
0
1
2
0
2
0
0
0
0
0
1
3
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
1
2
0
1
0
0
0
0
9
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
1
0
0
3
0
0
2
0
0
0
2
0
0
1
0
0
2
0
2
0
0
1
0
0
0
0
0
0
1
2
1
0
0
2
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
2
2
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
1
1
2
0
2
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
1
1
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
1
0
0
0
0
1
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
14
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
5
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
1
3
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
2
3
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
1
0
5
0
0
0
0
0
0
0
0
0
0
2
3
0
1
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
1
0
0
0
0
1
2
2
0
0
0
0
2
0
1
0
0
0
2
1
0
2
0
0
0
1
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
1
3
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
2
0
0
1
0
0
4
0
1
0
1
1
0
0
1
0
0
0
2
0
0
1
2
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
5
0
1
0
1
0
0
0
0
2
1
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
4
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
1
0
3
0
0
0
0
0
0
0
0
7
0
1
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
2
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
1
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
2
0
0
0
0
3
2
2
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
2
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
2
1
0
0
0
0
0
2
0
0
0
2
0
3
0
0
2
0
0
2
0
0
0
0
2
1
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
1
0
4
2
0
0
3
1
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
2
2
0
0
0
1
1
7
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
2
4
0
2
0
1
0
0
1
0
0
3
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
1
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
3
0
0
0
0
2
2
1
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
2
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
1
0
2
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
2
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
1
0
0
1
0
1
0
0
0
2
1
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
2
0
3
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
3
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
2
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
3
0
2
1
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
1
3
2
0
1
0
0
3
0
0
0
0
5
0
2
0
0
0
0
0
1
1
0
1
1
0
1
0
2
0
0
2
1
2
2
0
0
0
1
0
1
0
1
5
0
0
0
0
1
0
0
2
0
0
1
2
0
2
2
1
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
1
0
0
2
0
2
0
0
0
0
1
3
0
1
1
2
0
0
0
0
0
1
0
0
0
2
0
0
3
0
0
0
0
0
2
1
0
1
2
1
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
1
0
2
0
1
0
1
0
0
0
0
1
0
2
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
2
3
0
0
1
0
1
2
4
0
0
2
0
0
0
0
2
0
2
0
0
0
0
5
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
2
0
0
3
1
0
0
0
0
1
0
2
0
1
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
6
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
15
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
1
0
3
0
1
0
2
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
1
0
0
2
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
2
2
0
1
0
0
2
0
0
0
0
1
0
3
0
0
0
2
1
0
0
0
0
3
0
2
0
0
3
1
0
0
0
0
2
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
2
0
0
0
0
0
2
1
0
1
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
4
0
1
1
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
2
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
2
0
2
0
2
0
0
0
0
2
1
2
1
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
2
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
1
1
0
1
0
0
2
0
0
1
2
0
0
0
1
1
0
2
0
4
0
0
0
0
2
0
0
3
2
0
0
0
0
6
0
0
0
0
1
1
0
0
1
0
0
2
4
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
3
0
1
0
2
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
4
0
0
0
2
0
0
3
3
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
4
0
2
0
0
2
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
2
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
1
0
1
0
1
0
2
0
0
0
0
0
2
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
1
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
2
1
0
2
1
0
0
3
0
0
0
1
0
0
0
1
0
0
0
1
0
3
0
0
0
0
3
1
0
0
0
2
1
0
2
0
0
0
0
0
0
3
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
3
0
0
2
0
1
0
2
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
1
0
6
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
1
0
0
0
1
2
0
2
0
0
0
3
0
0
0
0
0
2
0
0
3
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
2
0
0
3
0
0
2
0
0
0
1
0
0
1
0
2
1
0
0
0
0
0
0
0
0
2
1
0
2
2
2
0
0
0
0
0
0
0
0
1
0
0
0
4
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
1
0
0
1
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
3
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
3
0
0
0
3
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
1
0
3
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
2
7
2
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
4
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
2
0
1
0
0
3
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
3
1
0
1
0
0
0
1
1
0
0
0
0
0
0
5
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
2
0
3
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
4
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
1
1
0
0
0
1
1
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
1
0
1
0
0
0
2
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
3
0
0
0
0
0
0
6
0
2
1
0
0
0
0
2
0
0
1
0
0
0
2
0
0
1
0
0
4
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
4
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
4
0
1
0
0
0
1
0
2
0
0
2
2
0
2
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
2
0
0
0
0
0
2
0
3
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
5
0
0
0
1
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
1
0
0
2
0
0
0
1
2
0
2
0
0
2
0
2
0
0
2
0
1
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
2
0
0
0
1
2
0
0
0
2
1
1
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
2
0
1
0
0
0
0
1
1
2
0
0
0
1
0
0
2
0
0
0
0
2
2
2
1
0
0
0
0
0
0
1
0
3
1
0
0
0
0
1
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
1
3
0
0
4
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
1
1
2
2
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
2
0
2
0
0
1
2
0
0
0
0
2
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
4
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
1
0
2
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
8
1
0
1
0
0
0
0
1
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
3
0
0
0
0
2
0
0
2
0
0
1
0
0
2
1
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
1
0
0
0
2
0
0
1
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
3
2
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
7
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
4
0
2
1
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
1
0
2
2
0
0
0
0
0
1
1
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
3
0
2
2
2
0
2
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
1
0
0
0
2
0
1
4
2
0
0
2
0
2
1
0
0
0
2
0
0
0
0
0
0
6
0
0
0
2
0
2
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
2
0
0
2
0
0
2
1
1
1
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
2
1
2
0
0
1
0
0
0
1
0
2
0
0
0
0
2
0
2
1
1
1
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
1
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
4
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
2
2
1
3
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
2
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
1
1
4
0
0
0
0
0
0
0
4
0
1
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
10
0
0
0
1
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
3
0
1
0
0
0
0
0
0
1
1
0
0
0
0
3
1
0
0
2
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
2
0
0
1
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
10
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
2
0
1
0
0
0
6
0
0
0
0
2
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
2
0
1
1
2
1
1
0
0
1
4
0
0
0
0
0
1
3
0
0
2
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
2
0
0
2
1
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
1
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
1
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
2
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
3
0
0
2
0
1
2
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
1
0
0
0
1
1
1
0
2
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
1
2
0
0
2
0
0
0
0
2
0
1
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
2
1
0
3
0
0
0
0
0
2
0
0
2
0
2
3
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
2
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
3
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
1
0
1
2
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
4
0
0
0
0
0
1
1
0
0
3
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
1
0
0
0
0
5
0
0
0
2
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
2
2
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
2
1
1
1
2
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
1
2
2
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
1
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
5
2
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
5
5
1
0
0
0
0
0
0
0
2
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
2
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
1
0
2
0
1
0
0
2
0
0
0
0
1
0
0
0
2
0
1
5
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
2
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
2
1
1
0
1
0
0
1
1
0
2
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
1
3
2
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
2
0
0
0
1
0
3
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
1
0
0
2
0
0
0
0
0
1
1
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
1
2
0
0
2
3
0
0
0
1
1
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
1
0
1
0
0
0
2
1
0
0
0
0
0
0
0
2
0
4
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
7
1
0
0
1
0
0
2
3
0
0
2
0
0
2
0
0
2
0
0
5
0
0
0
1
1
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
4
0
2
2
0
0
0
0
2
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
2
0
0
0
0
0
2
0
2
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
1
1
0
0
2
0
2
3
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
1
1
0
0
0
0
0
0
2
1
1
2
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
2
0
0
2
0
0
0
0
0
0
1
4
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
2
1
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
2
2
0
0
0
2
0
0
3
3
0
1
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
3
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
3
2
3
0
0
0
3
0
1
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
1
2
2
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
1
0
0
2
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
1
0
0
2
3
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
3
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
2
1
3
0
3
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
2
0
0
1
0
0
0
1
0
1
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
1
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
11
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
2
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
3
0
0
0
0
0
4
0
0
2
0
1
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
1
2
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
2
0
0
7
0
0
0
0
0
2
1
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
4
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
2
0
0
0
1
0
1
0
0
0
1
2
0
2
0
0
0
5
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
1
0
0
1
4
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
1
2
3
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
1
0
2
0
0
0
0
0
0
2
0
0
2
2
0
0
2
0
1
1
0
1
0
1
1
0
0
0
1
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
3
1
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
1
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
2
2
1
0
0
0
0
0
1
1
0
1
0
0
3
0
0
0
2
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
3
3
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
3
4
1
2
2
0
0
0
1
1
0
0
2
0
0
2
0
0
1
0
0
2
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
4
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
1
2
0
0
2
1
1
0
0
0
2
1
0
0
3
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
1
1
1
0
0
1
1
0
1
0
0
0
0
0
2
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
2
1
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
2
0
0
0
1
0
2
0
1
3
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
3
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
1
3
0
0
1
1
0
0
0
0
1
0
0
0
0
0
6
0
0
1
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
2
1
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
2
2
0
0
0
1
1
0
0
0
2
0
0
0
1
3
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
2
0
0
1
0
0
0
1
2
0
2
0
1
0
0
0
1
0
0
0
0
0
0
2
0
1
1
0
2
0
1
0
0
0
0
0
3
3
2
0
0
1
0
0
0
0
1
1
0
1
0
0
2
0
0
0
0
0
1
0
0
3
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
4
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
3
1
2
2
0
0
0
0
2
2
1
0
0
0
0
0
1
1
0
3
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
3
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
1
0
3
0
0
0
1
0
0
0
0
0
0
2
1
0
0
2
1
0
0
0
2
0
0
0
0
2
1
0
2
0
0
0
0
1
0
0
0
2
1
0
0
0
0
1
1
0
2
0
2
0
0
0
0
1
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
1
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
2
1
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
2
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
2
0
2
0
2
0
0
2
0
0
1
3
0
6
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
2
0
0
0
0
0
0
0
1
2
0
2
1
2
0
0
0
0
1
0
0
0
0
0
0
2
0
3
2
1
0
0
1
0
0
0
0
2
0
0
1
2
0
0
0
0
0
2
0
1
2
0
0
1
4
0
2
1
1
0
0
0
0
0
0
0
1
0
1
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
2
2
0
3
1
0
0
3
0
0
0
0
0
1
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
1
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
3
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
2
0
2
0
1
1
0
2
1
0
1
0
0
0
0
0
2
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
1
0
0
0
1
0
2
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
1
0
2
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
2
0
0
0
3
0
6
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
8
0
0
0
2
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
3
0
0
0
1
3
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
2
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
2
2
0
0
0
0
0
2
0
1
1
0
2
0
0
3
0
0
0
1
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
2
0
0
0
1
3
0
0
2
0
0
0
0
0
0
3
0
0
1
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
4
2
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
1
0
1
0
2
0
3
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
4
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
2
1
0
2
0
1
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
1
2
0
0
0
2
1
4
0
2
0
0
0
0
0
0
1
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
10
2
1
0
0
1
0
0
0
2
0
3
0
2
0
0
2
2
2
0
0
0
0
0
2
0
2
1
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
3
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
3
2
0
0
2
0
4
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
2
0
2
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
2
2
0
1
0
2
1
0
0
0
0
0
0
0
0
0
2
1
0
1
2
0
2
0
0
2
0
1
0
0
0
0
1
0
2
0
0
0
0
2
2
0
1
1
0
1
0
4
0
1
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
1
2
0
2
2
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
2
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
3
0
2
0
1
0
0
1
2
0
0
0
0
0
2
1
0
1
0
0
2
0
0
7
0
1
3
0
0
0
0
0
0
2
0
1
1
0
3
1
0
0
2
0
0
0
0
0
0
6
0
0
0
2
1
0
0
2
0
2
2
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
3
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
1
0
1
0
1
0
0
0
0
0
3
0
0
0
2
0
0
0
1
0
1
0
2
0
2
0
2
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
3
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
1
2
0
0
0
0
0
1
0
0
0
2
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
2
1
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
1
0
0
0
0
0
1
0
0
0
5
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
1
0
0
0
2
2
1
6
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
4
0
0
4
0
1
0
0
0
2
0
0
0
2
0
1
0
0
0
0
1
0
0
1
0
2
1
0
0
0
0
1
1
2
0
0
0
2
1
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
4
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
3
0
1
0
2
2
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
2
0
1
0
2
1
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
1
1
0
0
1
0
0
0
2
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
4
0
0
0
0
2
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
2
0
0
0
1
1
0
1
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
4
0
0
7
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
3
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
1
2
2
0
0
1
0
0
0
0
0
3
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
1
0
0
3
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
4
0
1
2
2
0
0
0
0
0
1
0
0
0
0
2
0
2
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
1
0
0
3
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
4
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
2
0
0
2
2
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
3
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
2
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
5
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
2
0
1
0
0
2
0
4
0
1
0
0
0
1
1
0
2
0
0
0
0
0
1
0
0
1
1
0
1
1
0
1
0
0
0
0
2
0
0
2
1
0
0
0
2
0
0
0
0
0
0
1
1
0
2
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
2
1
0
2
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
2
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
3
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
3
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
1
2
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
4
0
1
1
2
0
0
0
0
2
1
3
0
2
1
1
1
0
0
0
0
1
0
1
2
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
6
2
1
1
2
2
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
3
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
2
1
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
10
0
0
0
2
4
2
1
0
0
0
0
0
0
2
0
1
1
2
0
0
0
0
0
0
0
0
2
2
0
0
1
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
4
0
2
0
0
0
0
2
0
0
0
6
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
5
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
4
0
0
0
5
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
1
2
0
0
0
1
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
3
0
2
0
0
0
0
0
1
0
1
4
0
1
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
1
0
1
1
0
0
0
2
0
0
0
2
0
0
0
0
2
0
1
2
1
0
2
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
1
0
2
0
2
2
0
0
2
0
0
0
2
0
0
0
0
0
1
0
4
0
1
0
0
0
0
0
1
0
0
0
0
0
0
3
0
1
3
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
1
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
4
0
0
0
0
4
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
2
2
0
0
0
2
1
0
0
1
0
0
2
0
0
0
2
0
9
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
3
0
0
2
1
0
0
0
2
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
1
0
0
0
1
1
0
0
2
1
1
0
0
0
0
0
0
0
0
0
1
1
0
2
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
2
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
1
0
0
0
4
0
2
0
0
0
0
0
1
0
0
0
0
7
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
1
0
0
0
0
6
0
0
1
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
5
0
2
0
0
0
0
0
0
0
0
3
0
2
0
0
1
3
0
0
0
0
2
2
0
3
2
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
1
0
1
1
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
2
2
1
0
2
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
3
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
2
0
1
0
0
1
0
0
0
2
0
0
0
0
0
1
1
0
1
0
2
0
0
0
0
0
2
1
2
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
3
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
1
0
0
2
2
1
2
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
2
0
0
2
1
0
0
0
0
0
1
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
2
0
0
0
2
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
2
2
1
0
4
0
1
0
0
1
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
4
0
0
1
0
0
0
0
1
0
1
1
0
0
0
1
0
0
1
1
1
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
1
2
0
1
0
0
1
1
0
1
0
1
2
0
0
2
0
1
2
2
1
1
0
1
0
0
2
0
0
0
0
1
0
0
2
2
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
1
0
1
0
0
0
1
0
0
0
0
2
1
0
5
0
2
1
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
1
0
0
0
0
2
4
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
4
0
2
0
0
2
0
0
1
0
0
0
0
1
0
0
2
1
2
0
0
0
4
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
3
0
2
0
0
1
0
2
0
2
0
0
0
0
0
1
0
2
1
0
0
0
0
2
0
0
2
0
0
0
2
0
2
0
0
0
0
0
3
0
0
0
1
0
1
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
2
1
0
0
1
0
1
0
0
0
0
0
0
2
2
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
1
1
0
2
0
2
0
0
0
0
1
5
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
2
1
0
2
1
0
0
0
0
2
2
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
3
2
0
0
1
0
0
0
0
2
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
2
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
5
0
0
2
0
0
2
1
0
2
0
0
2
0
0
5
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
1
0
0
0
1
2
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
10
1
1
0
0
0
0
2
0
0
2
0
0
0
7
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
2
3
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
5
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
3
1
0
0
0
0
0
0
0
1
0
0
0
2
0
3
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
19
0
0
0
0
0
0
1
2
3
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
1
1
0
1
0
0
0
9
0
1
0
0
0
0
0
2
0
1
0
1
1
0
2
1
0
3
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
5
0
0
0
0
0
0
2
0
2
1
0
1
0
0
0
0
0
0
6
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
2
0
2
0
0
0
0
3
0
0
0
1
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
1
0
0
2
0
5
0
0
0
2
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
3
0
0
6
0
0
0
0
1
0
2
0
0
0
3
0
0
2
2
0
0
1
1
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
5
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
2
0
0
2
0
2
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
2
3
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
1
0
0
0
2
1
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
2
0
2
0
0
1
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
5
0
0
0
0
0
2
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
4
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
2
0
2
0
1
0
0
0
1
1
0
1
0
0
0
2
1
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
1
1
10
0
2
0
0
1
0
0
0
3
0
1
0
0
2
0
3
0
0
0
0
0
0
0
1
2
1
0
0
0
2
0
1
0
0
0
3
2
0
0
0
0
0
2
0
1
0
0
1
0
2
0
2
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
1
2
0
1
0
2
0
0
0
1
0
0
0
2
0
1
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
2
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
3
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
1
2
2
0
0
0
3
0
1
0
0
0
0
0
1
0
0
1
3
0
1
0
0
0
0
0
2
2
1
0
4
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
4
0
2
1
0
0
0
1
0
0
0
0
1
1
1
0
0
1
0
0
1
1
0
0
3
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
3
1
0
0
0
0
2
3
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
4
0
2
0
1
0
0
0
0
2
0
0
2
1
0
2
0
0
0
0
0
1
4
0
3
0
0
2
0
0
0
0
2
0
0
1
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
1
0
1
2
0
0
0
0
0
0
1
0
0
2
1
2
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
3
0
0
0
0
1
1
0
0
0
1
2
0
0
0
0
2
2
1
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
4
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
8
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
1
0
1
0
0
0
1
0
0
0
0
2
1
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
4
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
2
0
0
0
1
2
0
2
0
0
2
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
5
0
0
2
0
0
0
0
0
0
0
0
3
0
2
0
2
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
9
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
9
0
1
0
0
0
0
0
2
0
2
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
1
0
0
1
0
1
0
2
0
2
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
1
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
3
0
0
0
2
0
0
0
0
3
4
1
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
3
1
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
3
2
0
1
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
3
0
0
0
3
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
1
0
2
0
0
0
2
0
0
1
0
0
0
0
2
0
0
1
0
0
0
5
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
2
2
0
0
0
0
1
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
6
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
4
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
4
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
2
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
3
0
0
1
0
3
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
4
0
1
0
3
0
0
0
0
0
0
0
0
9
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
2
1
2
0
2
0
0
1
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
3
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
3
0
0
0
5
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
2
3
0
0
0
0
0
0
1
2
0
0
2
0
0
3
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
3
0
1
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
2
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
3
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
1
0
0
2
0
1
0
2
0
0
0
2
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
2
0
0
2
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
2
0
0
1
0
0
0
3
0
0
0
0
2
0
0
0
0
1
0
0
2
0
1
0
0
0
1
3
2
2
2
2
0
2
3
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
2
2
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
1
0
2
0
0
3
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
3
0
0
0
0
1
0
0
1
0
0
0
0
0
0
3
2
2
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
2
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
1
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
2
1
1
0
0
0
1
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
2
0
0
1
0
2
0
1
0
0
2
0
1
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
2
3
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
2
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
2
0
1
0
0
0
0
2
3
0
0
0
0
0
0
0
2
3
0
0
0
0
2
0
0
0
0
2
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
3
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
1
2
2
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
2
1
0
0
0
1
0
0
0
0
0
0
2
1
0
0
1
1
2
0
0
0
0
0
2
1
0
1
0
1
0
0
0
3
0
0
0
0
1
0
0
2
0
0
0
0
0
2
1
2
1
1
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
3
0
0
2
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
1
0
5
0
0
0
0
0
0
1
2
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
1
0
2
0
0
0
2
0
0
0
1
0
0
2
0
1
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
2
1
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
2
2
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
1
0
0
0
2
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
2
1
2
1
0
0
2
1
0
0
0
2
0
2
0
0
0
0
4
2
0
2
0
0
2
0
0
0
0
2
0
1
1
0
0
0
0
1
0
0
0
0
0
0
3
2
0
3
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
3
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
4
0
1
2
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
3
0
3
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
2
0
1
0
0
0
1
0
0
1
0
0
1
1
0
0
1
3
0
0
0
1
0
0
1
0
0
0
0
0
2
2
0
0
0
0
1
0
0
3
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
1
0
0
0
0
0
2
0
0
2
1
0
4
0
1
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
3
0
0
0
1
0
0
0
2
0
0
2
1
1
1
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
2
0
0
0
5
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
5
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
1
1
0
0
0
1
0
0
0
0
2
2
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
2
0
0
2
0
0
1
0
1
0
3
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
5
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
3
0
0
0
0
1
0
2
1
0
2
3
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
6
1
0
1
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
3
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
1
0
2
0
4
0
0
0
0
0
1
2
1
0
0
0
0
0
1
0
1
1
1
0
3
0
0
1
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
2
0
0
0
0
2
0
1
1
0
0
0
0
0
3
0
0
1
0
1
0
0
2
0
2
0
0
0
0
2
0
0
2
1
0
0
2
0
0
0
1
2
6
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
2
0
3
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
1
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
3
0
0
3
0
0
0
0
0
0
0
2
0
0
1
0
0
6
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
7
2
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
2
2
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
3
1
0
0
2
0
0
1
0
0
2
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
6
1
0
0
1
0
2
0
0
1
0
0
0
2
1
0
0
0
2
5
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
2
0
0
0
2
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
9
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
3
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
3
0
0
1
2
0
0
0
0
0
0
0
4
0
1
4
0
0
0
0
0
0
1
1
0
0
0
0
1
1
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
1
0
0
1
0
0
2
0
0
3
0
2
1
3
0
0
0
0
0
0
1
0
1
0
0
0
0
3
0
0
1
0
10
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
1
0
1
0
0
0
2
1
0
0
1
1
0
0
0
0
0
0
0
0
1
5
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
2
0
0
1
0
0
0
1
0
3
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
2
3
0
1
0
0
1
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
3
1
0
0
0
0
0
0
3
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
3
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
1
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
3
0
0
0
2
0
0
2
0
2
0
0
0
1
1
0
1
0
2
0
0
0
0
0
0
2
0
0
0
4
3
2
0
1
3
0
0
2
0
1
0
0
0
0
0
0
2
0
1
2
0
0
0
1
0
2
0
0
0
0
1
0
2
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
1
0
3
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
3
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
8
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
1
1
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
3
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
2
1
0
2
0
0
0
2
0
0
0
0
0
1
2
0
0
0
2
0
2
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
4
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
3
0
0
2
0
0
0
1
2
0
1
2
3
0
0
0
0
0
0
0
0
2
1
0
0
1
3
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
2
0
0
1
0
0
5
0
0
0
4
2
0
0
0
2
2
0
0
0
0
0
0
1
1
0
0
0
7
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
3
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
2
0
0
1
2
2
0
0
0
2
0
0
2
1
2
5
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
1
0
2
2
0
0
1
8
0
3
0
0
0
0
0
0
0
0
0
0
1
0
3
0
1
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
4
3
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
8
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
11
0
2
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
3
0
5
0
2
0
2
0
4
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
4
0
0
0
0
2
0
0
0
0
1
0
0
0
3
0
2
0
0
0
0
0
0
0
0
1
0
0
0
3
0
4
4
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
1
0
0
4
0
0
1
0
0
0
2
0
0
1
0
0
0
1
0
0
1
0
0
3
0
0
1
0
0
0
1
1
0
0
0
1
0
1
0
2
1
1
0
0
2
3
0
0
2
2
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
4
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
1
0
0
1
5
1
2
1
1
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
2
1
0
0
0
1
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
1
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
3
2
0
0
3
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
3
2
2
0
2
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
1
0
1
9
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
2
1
0
0
0
0
2
0
1
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
1
0
1
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
1
0
2
2
1
0
2
1
1
1
0
0
0
0
0
0
0
0
2
3
2
0
0
0
0
1
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
4
3
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
3
2
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
10
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
1
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
3
0
0
0
1
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
1
0
1
0
1
0
0
1
0
0
0
0
2
1
1
2
2
1
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
3
2
1
0
0
0
0
0
0
0
0
0
0
10
0
0
0
0
0
0
2
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
4
0
2
2
0
2
0
0
0
1
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
2
0
2
1
3
0
0
1
2
0
2
3
1
0
0
0
0
0
0
1
2
0
0
0
0
1
1
0
3
0
2
1
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
5
2
2
0
2
3
1
0
0
0
0
0
0
0
0
6
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
3
0
0
3
1
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
6
5
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
7
0
0
1
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
3
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
2
1
0
2
1
0
0
0
0
1
1
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
1
0
0
1
0
0
2
2
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
1
0
2
0
0
0
2
0
1
0
2
0
5
0
2
0
0
0
0
0
0
0
0
2
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
1
0
0
0
0
0
2
0
1
0
0
3
0
0
1
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
2
2
1
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
3
0
1
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
3
0
0
0
1
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
3
2
0
2
1
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
2
0
1
0
0
3
0
2
0
0
2
0
0
0
1
0
0
0
0
5
0
2
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
5
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
2
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
5
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
2
0
0
0
3
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
4
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
3
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
6
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
1
2
0
0
1
0
1
0
1
2
0
0
0
0
1
0
0
0
1
2
0
2
0
0
0
2
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
1
3
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
2
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
3
0
0
0
0
0
1
0
2
0
0
0
0
0
1
2
0
1
0
1
0
0
0
0
0
3
0
0
0
2
0
2
0
1
2
0
0
2
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
4
1
3
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
6
0
0
0
0
0
0
4
1
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
1
0
2
3
1
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
1
2
3
1
0
0
2
0
1
0
1
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
4
1
0
4
1
2
0
1
0
0
0
1
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
2
0
1
0
0
2
0
0
0
0
0
3
1
1
0
1
1
0
0
0
0
0
2
3
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
2
0
0
2
2
0
0
2
0
0
0
0
0
0
0
1
1
1
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
2
2
0
2
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
2
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
3
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
3
0
0
0
1
0
0
0
0
0
1
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
2
0
0
0
2
0
1
0
0
0
0
3
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
1
1
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
1
5
0
2
4
2
0
2
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
1
0
0
2
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
3
1
2
0
0
3
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
3
0
1
0
0
0
1
2
0
0
0
0
0
1
0
8
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
2
1
0
2
1
0
2
0
1
0
2
0
0
0
2
1
0
0
0
1
0
0
0
0
0
4
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
1
2
0
0
0
0
0
0
2
1
1
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
2
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
4
2
0
0
2
0
0
2
0
0
0
0
2
0
4
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
5
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
4
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
2
1
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
2
0
0
0
0
0
0
2
0
0
2
2
0
0
1
0
0
3
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
2
2
0
1
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
3
0
1
0
0
0
3
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
2
0
0
0
0
2
0
0
0
1
2
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
1
1
0
0
0
0
2
1
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
2
0
0
2
0
0
3
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
1
0
0
3
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
2
0
2
2
2
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
3
1
4
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
2
1
0
0
0
0
1
0
0
0
4
1
0
2
0
0
1
0
0
0
0
0
0
0
0
1
2
2
0
0
1
0
0
0
0
0
1
0
0
0
3
0
1
0
0
0
0
0
0
0
4
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
2
0
3
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
3
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
1
2
1
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
3
0
0
0
2
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
1
2
1
0
0
3
2
2
0
0
0
0
0
0
0
0
0
0
1
1
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
3
0
0
2
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
1
0
1
1
0
1
0
0
1
2
0
2
0
0
0
3
1
2
0
0
2
0
0
0
0
2
1
0
2
0
1
0
0
2
0
2
0
2
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
3
0
0
0
1
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
2
1
0
2
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
2
2
0
1
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
1
0
5
0
0
2
0
0
0
0
0
3
0
3
0
0
0
2
0
0
1
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
7
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
2
1
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
2
2
0
2
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
2
0
2
0
1
0
1
0
0
2
1
0
1
0
0
0
0
0
2
0
2
0
0
2
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
2
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
3
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
1
3
1
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
2
1
2
0
1
0
2
0
0
0
1
0
0
4
1
0
0
3
1
2
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
1
1
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
2
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
1
1
0
1
0
0
1
0
0
0
0
0
0
3
2
0
0
2
2
0
0
0
0
1
1
4
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
3
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
1
0
3
0
1
0
0
0
1
0
0
1
0
2
0
4
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
1
0
0
0
3
0
0
0
0
0
1
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
2
0
3
1
0
3
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
4
0
0
3
2
0
1
3
0
0
0
0
0
0
0
2
2
2
0
0
0
1
0
1
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
5
0
0
0
0
6
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
2
2
1
0
0
1
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
1
2
0
4
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
2
1
0
0
0
1
0
0
3
0
2
1
0
0
0
1
0
0
1
2
0
0
5
0
2
0
0
0
1
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
1
0
3
0
2
0
4
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
3
0
2
1
2
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
2
1
0
0
0
8
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
5
2
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
1
4
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
2
0
0
0
2
0
2
0
0
0
2
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
2
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
3
0
1
1
6
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
1
0
2
0
2
0
0
1
1
1
0
1
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
1
2
2
0
0
0
1
1
3
0
1
0
0
0
0
0
0
0
0
2
1
0
2
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
1
0
2
0
0
0
2
0
0
0
1
0
0
1
1
1
2
0
0
0
2
0
0
0
2
0
0
3
1
2
0
0
2
0
0
0
2
1
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
4
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
4
0
0
0
6
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
1
2
1
0
1
0
0
0
0
0
3
1
1
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
3
1
0
1
0
0
0
1
0
3
0
3
0
0
0
0
0
2
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
7
5
0
0
0
0
1
0
0
0
1
0
3
0
0
0
0
1
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
2
2
0
0
0
0
0
1
0
0
0
1
2
0
0
0
1
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
3
0
0
1
1
0
0
4
0
0
0
0
1
0
0
1
2
0
4
2
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
2
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
1
2
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
1
0
0
0
1
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
1
1
2
0
0
0
2
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
1
0
1
1
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
1
0
0
8
0
0
0
0
0
0
0
0
0
1
0
3
0
2
0
0
0
2
1
0
3
0
0
0
1
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
2
1
0
0
0
1
2
1
0
0
4
0
0
0
0
3
1
0
1
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
1
0
1
1
3
0
0
1
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
2
0
2
2
0
1
0
0
0
0
0
8
0
3
1
3
0
0
1
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
3
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
1
0
0
2
0
0
0
0
1
2
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
2
0
0
0
2
2
0
3
1
0
0
2
0
0
0
2
0
0
0
1
0
0
5
0
1
0
0
0
1
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
3
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
3
1
2
2
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
2
0
1
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
1
2
0
0
2
2
1
0
0
1
0
0
1
0
2
0
0
2
0
1
0
2
0
0
2
1
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
3
3
0
0
0
1
3
0
2
1
1
1
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
1
0
0
2
0
1
2
1
0
1
0
0
0
1
0
0
0
3
0
0
0
0
0
0
2
1
2
0
0
1
0
0
1
2
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
1
0
0
0
0
0
2
2
1
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
6
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
2
0
3
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
1
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
4
0
0
0
1
2
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
2
0
2
0
1
2
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
9
0
0
0
0
2
0
0
1
2
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
2
2
0
2
0
1
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
1
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
1
0
1
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
2
0
0
0
0
2
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
2
1
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
5
1
0
0
2
1
0
1
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
2
0
1
0
0
0
2
1
2
1
0
1
1
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
1
0
0
0
8
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
2
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
4
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
1
0
2
2
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
3
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
1
0
0
1
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
1
0
1
0
0
2
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
2
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
1
0
0
0
0
0
2
0
1
0
0
1
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
3
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
2
0
0
2
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
4
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
4
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
3
0
0
3
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
2
0
0
0
12
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
1
0
0
0
1
0
2
2
2
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
4
0
0
0
1
1
0
0
0
0
2
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
1
1
1
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
4
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
3
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
1
2
0
2
0
0
2
0
1
0
0
0
0
1
0
0
4
7
3
0
0
0
5
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
3
1
2
0
0
2
2
0
0
1
1
0
0
1
0
0
0
1
3
0
0
0
0
2
2
0
0
0
0
4
0
1
0
4
0
0
0
0
2
0
0
1
0
0
1
2
1
1
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
5
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
7
2
0
0
1
0
0
0
0
2
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
2
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
1
1
0
0
0
1
0
0
0
0
0
2
0
1
0
0
3
0
2
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
1
2
0
0
1
1
1
1
2
0
2
0
1
0
0
1
0
1
0
0
1
0
3
0
0
1
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
3
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
1
2
0
1
1
0
0
0
0
0
0
0
0
1
1
2
0
0
2
0
1
0
0
0
0
2
1
0
0
0
1
1
0
1
2
0
0
0
0
0
2
0
0
0
2
0
0
0
3
0
3
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
1
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
2
0
0
0
0
0
0
3
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
4
0
0
2
0
0
2
0
0
0
0
0
3
2
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
2
2
0
2
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
4
2
1
0
2
0
0
0
0
0
0
2
0
0
1
0
1
0
1
0
0
2
0
3
0
0
2
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
8
0
0
0
0
0
1
2
0
0
0
0
2
3
0
0
0
0
0
0
2
0
0
1
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
2
0
2
0
0
0
0
0
0
0
1
0
2
1
2
0
0
0
0
3
0
1
0
0
0
2
2
1
1
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
2
1
0
0
1
2
0
0
0
0
0
2
2
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
6
0
1
0
0
3
1
1
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
1
0
0
2
1
0
2
5
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
1
2
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
1
3
0
0
0
0
0
0
0
0
3
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
1
0
0
2
0
1
3
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
3
0
0
1
2
0
0
1
0
2
0
0
0
0
3
0
0
2
0
0
0
1
2
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
2
0
0
1
2
0
0
0
0
0
0
0
0
2
2
2
2
0
2
0
2
0
0
0
0
0
0
0
0
2
0
3
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
3
0
0
1
0
2
0
0
1
0
0
0
0
1
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
4
0
0
2
0
0
0
0
0
1
2
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
7
0
1
2
0
1
0
0
1
2
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
1
0
0
0
0
0
1
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
2
0
0
0
2
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
1
2
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
3
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
3
0
2
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
2
0
1
0
0
0
1
0
1
2
0
0
2
0
0
0
1
0
6
1
1
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
4
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
4
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
3
0
1
3
0
0
2
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
1
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
1
0
0
0
3
2
2
0
4
1
0
2
1
0
0
1
0
1
0
0
0
0
6
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
3
2
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
2
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
2
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
3
0
2
0
1
0
0
0
2
1
0
0
0
0
0
0
2
1
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
2
0
0
0
0
2
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
5
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
2
0
2
0
0
0
0
1
2
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
2
0
2
0
1
2
1
2
0
0
0
0
0
0
0
1
0
0
9
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
3
0
0
2
0
0
0
0
1
2
1
2
2
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
2
1
2
0
0
0
0
0
0
0
1
0
6
0
3
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
2
0
1
0
3
0
0
0
0
0
0
0
3
0
1
0
1
0
0
2
0
0
0
3
0
0
2
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
2
1
0
0
0
2
0
0
2
0
0
0
0
3
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
1
0
0
8
0
2
1
1
0
0
0
4
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
2
0
0
0
0
1
0
0
2
1
3
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
5
0
1
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
0
1
0
1
0
1
0
2
0
0
0
0
0
0
0
1
2
1
0
0
2
0
1
0
1
1
0
0
0
2
1
0
0
0
2
0
2
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
3
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
2
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
1
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
3
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
1
0
0
0
0
1
1
1
0
0
3
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
4
0
0
0
2
1
0
2
2
1
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
3
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
2
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
11
0
0
1
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
3
0
0
0
0
1
2
1
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
1
1
2
0
0
0
0
0
2
1
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
3
0
1
3
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
3
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
2
0
0
1
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
1
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
2
2
0
5
0
3
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
3
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
1
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
3
1
0
1
0
0
1
0
2
1
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
5
2
0
0
0
0
0
0
0
0
2
6
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
3
0
0
0
1
1
0
0
6
0
1
2
0
0
1
0
3
0
0
0
0
1
6
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
4
0
0
0
0
1
2
0
0
0
2
4
0
2
0
0
0
0
0
0
0
3
0
0
0
2
0
1
2
1
0
3
0
1
0
0
0
1
0
0
2
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
0
1
0
2
0
0
0
0
0
0
0
0
0
5
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
3
2
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
8
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
4
2
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
1
0
3
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
1
0
0
2
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
1
0
2
2
0
0
0
0
1
0
0
1
0
2
0
0
0
0
1
0
1
1
1
0
0
0
2
0
1
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
6
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
1
0
2
0
0
3
2
2
1
0
1
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
3
0
0
0
2
1
1
0
3
1
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
2
1
0
0
0
2
1
0
0
0
0
0
1
0
0
0
3
2
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
3
0
2
0
0
1
0
0
0
0
1
3
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
1
1
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
8
0
0
0
0
3
0
2
4
0
0
2
0
0
0
0
0
2
0
2
0
0
0
3
0
2
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
5
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
6
0
0
1
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
4
1
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
3
0
0
0
0
3
1
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
2
2
1
0
2
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
2
0
2
0
0
3
0
0
0
0
0
1
1
3
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
7
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
1
2
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
5
0
2
3
0
0
2
0
0
6
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
2
0
1
0
2
1
0
0
1
0
1
3
2
0
0
1
1
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
4
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7
0
4
0
2
0
0
0
0
2
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
4
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
1
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
1
2
2
2
0
0
0
0
0
0
0
0
3
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
6
0
0
0
0
0
0
0
0
0
6
0
3
0
0
0
0
1
0
1
2
0
0
0
0
0
0
1
0
1
0
0
6
0
2
0
9
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
5
2
0
0
0
0
2
1
0
0
0
0
2
0
0
0
2
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
1
0
0
2
0
0
2
0
3
0
0
0
0
0
0
2
0
0
0
1
1
0
1
0
2
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
2
5
0
1
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
2
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
3
0
0
1
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
3
0
0
3
2
0
1
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
1
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
2
0
1
0
2
0
1
0
0
0
1
1
2
0
0
2
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
2
0
0
3
0
0
2
0
3
0
0
0
0
0
0
0
2
0
0
1
2
6
0
1
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
1
0
1
0
0
2
5
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
3
0
1
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
3
0
0
1
0
2
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
2
1
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
2
2
0
0
0
0
0
9
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
4
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
1
0
0
0
0
0
3
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
5
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
2
0
0
1
0
0
1
2
0
0
0
3
0
0
0
0
0
0
0
0
3
2
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
1
2
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
4
1
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
3
0
0
0
0
2
0
3
1
9
0
0
0
0
2
0
0
0
1
2
2
0
0
0
0
0
1
0
1
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
3
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
1
0
1
0
1
2
0
1
1
0
1
0
0
1
0
1
0
0
0
3
0
0
0
0
1
0
0
3
0
0
0
2
0
0
1
0
0
0
1
0
1
1
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
2
2
0
0
0
0
3
0
0
0
2
0
2
3
0
0
0
0
0
0
0
2
1
1
2
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
2
0
2
0
0
2
1
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
4
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
2
1
0
0
1
6
2
0
0
0
0
1
3
0
2
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
1
2
0
1
0
0
0
2
0
0
0
0
0
0
7
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
1
1
0
0
3
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
4
0
1
1
0
0
0
1
0
2
0
0
1
1
0
2
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
2
0
1
2
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
1
1
0
0
0
0
0
1
1
4
0
1
0
1
0
0
0
0
1
0
0
0
0
3
1
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
5
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
2
0
3
0
2
0
0
0
0
0
0
0
0
0
0
2
0
7
0
2
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
2
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
8
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
3
0
0
0
0
2
0
0
0
0
0
0
4
2
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
3
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
3
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
1
0
1
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
1
2
2
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
3
1
0
0
2
0
3
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
4
0
0
0
1
0
1
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
1
2
3
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
17
0
5
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
2
1
1
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
7
0
0
0
0
0
0
0
1
0
0
2
2
0
2
0
0
0
3
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
3
0
0
0
2
0
2
0
0
0
3
0
0
1
2
0
1
0
0
0
0
0
0
2
2
0
4
0
0
7
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
3
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
2
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
1
0
0
0
0
0
2
1
0
1
0
0
2
0
0
2
2
0
0
0
13
1
1
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
2
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
1
2
0
2
0
0
0
0
0
0
0
0
1
5
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
3
0
0
1
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
2
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
4
1
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
3
0
2
0
0
1
1
2
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
1
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
4
3
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
1
0
0
1
0
0
2
0
0
0
0
1
1
1
0
0
2
0
0
0
0
2
0
0
1
2
0
0
1
0
0
0
0
1
1
0
0
0
2
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
1
1
0
0
3
2
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
1
1
0
1
0
0
0
1
0
0
0
4
0
0
2
0
0
1
0
2
2
0
0
0
0
0
1
0
0
2
0
0
2
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
2
1
1
0
0
1
0
0
0
0
7
1
0
0
2
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
3
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
2
0
5
1
0
2
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
2
2
1
0
0
0
0
2
13
0
0
4
1
0
0
0
2
0
0
0
0
0
0
0
3
0
0
1
0
0
1
0
0
2
2
0
2
0
0
0
0
0
3
1
0
0
0
3
0
0
0
0
0
0
1
0
0
0
1
1
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
2
1
4
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
1
0
1
0
2
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
5
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
5
2
0
0
0
1
3
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
2
4
2
2
0
0
0
0
0
0
0
0
0
0
1
6
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
2
0
2
0
0
0
2
0
0
2
1
0
0
2
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
2
4
2
0
0
1
2
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
4
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
1
0
1
0
0
0
0
2
0
0
2
3
0
1
0
0
4
0
2
1
0
0
1
0
3
1
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
1
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
1
0
1
0
2
0
1
1
0
1
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
4
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
2
1
0
0
2
0
0
0
1
2
1
0
0
0
0
1
0
0
1
4
0
0
2
1
1
1
0
1
1
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
2
5
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
3
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
3
0
3
0
1
1
0
0
0
0
0
0
1
2
2
0
0
0
1
0
1
1
0
2
0
0
0
0
0
0
0
2
1
0
0
3
0
0
0
0
0
3
0
0
0
1
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
12
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
10
3
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
2
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
1
3
0
2
0
0
0
0
2
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
2
0
2
0
0
0
2
0
0
2
0
1
0
2
2
0
0
5
0
2
0
3
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
1
0
0
0
0
0
0
0
0
8
0
0
0
2
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
2
0
3
1
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
3
1
0
0
0
0
0
1
1
0
3
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
1
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
3
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
2
0
4
0
0
0
0
0
0
3
2
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
2
0
0
2
0
0
0
0
0
0
1
0
0
1
1
0
0
3
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
1
4
0
0
0
0
0
1
2
0
0
2
0
0
0
1
0
1
0
1
1
2
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
3
0
0
0
3
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
2
1
0
1
0
0
0
1
0
0
0
0
1
0
3
0
1
0
1
0
0
1
0
0
2
0
0
0
0
1
1
0
0
0
0
1
5
0
0
2
1
0
0
1
0
1
0
0
0
0
2
0
0
0
0
1
1
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
4
1
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
2
0
1
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
1
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
1
0
2
0
0
0
0
2
0
0
0
0
1
0
0
2
0
2
0
0
0
1
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
1
0
0
0
0
0
0
0
4
2
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
5
0
0
0
0
2
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
1
3
1
0
2
0
3
0
0
0
2
0
0
0
3
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
1
3
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
2
0
0
3
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
1
0
2
4
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
3
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
2
2
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
3
1
0
2
2
0
0
1
7
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
1
0
1
2
0
2
2
0
0
0
2
0
1
0
3
0
0
0
0
0
1
0
2
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
5
0
2
0
0
0
0
1
0
1
2
1
0
2
2
0
0
0
1
0
1
0
1
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
4
0
0
0
0
1
0
1
0
0
0
1
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
1
3
6
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
1
1
2
3
0
0
0
0
0
0
1
0
0
0
0
0
2
1
2
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
1
0
0
14
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
1
0
2
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
2
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
1
0
0
1
0
0
0
0
2
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
2
0
0
2
1
0
0
0
2
2
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
2
1
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
1
3
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
1
1
0
0
2
0
0
1
1
0
2
3
0
2
0
0
1
0
0
0
2
0
0
2
1
0
0
0
15
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
1
1
1
1
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
1
0
0
2
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
4
0
3
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
3
0
0
1
0
1
0
0
1
0
0
0
0
1
0
2
0
0
0
0
1
0
1
0
0
0
0
2
0
0
2
2
5
0
2
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
4
0
0
0
1
0
2
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
5
2
0
0
0
0
0
4
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
1
0
1
2
0
0
3
0
0
0
2
1
0
0
0
1
0
0
2
0
0
1
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
3
0
2
1
0
0
5
0
0
0
2
0
1
0
0
0
1
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
6
2
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
1
2
0
0
0
0
0
0
1
0
0
4
0
0
11
0
0
1
0
2
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
5
0
0
1
0
0
0
0
0
1
0
2
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
5
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
2
0
0
2
0
0
0
0
3
1
0
1
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
8
0
0
0
0
0
1
0
2
0
6
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
2
3
0
0
3
0
1
1
1
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
5
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
1
1
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
1
0
0
0
3
0
0
1
1
2
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
1
1
1
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
1
2
0
2
0
0
0
0
0
1
0
0
3
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
2
1
1
0
0
1
0
0
3
0
0
3
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
7
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
2
0
0
2
0
0
3
0
0
0
0
0
2
0
0
1
0
2
0
1
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
3
1
1
0
0
3
0
1
0
2
0
0
1
0
0
2
0
0
1
0
0
1
0
1
0
0
2
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
1
2
0
1
0
2
2
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
1
0
2
0
0
0
0
1
2
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
3
4
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
3
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
2
0
1
0
0
1
2
0
4
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
2
1
1
0
0
1
0
0
0
0
0
0
1
2
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
1
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
1
3
0
0
0
6
1
0
0
2
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
2
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
4
0
5
3
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
1
0
0
1
0
1
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
1
0
1
0
0
1
0
0
0
0
3
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
3
0
0
0
1
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
4
2
4
0
0
0
0
2
0
0
3
0
0
0
2
3
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
2
0
2
0
0
0
2
0
0
0
1
1
0
2
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
3
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
1
0
3
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
2
1
0
0
1
2
0
3
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
2
1
1
2
1
0
0
2
2
0
0
0
2
0
1
0
0
0
0
0
0
0
2
2
3
0
0
0
1
2
0
0
0
0
0
0
2
1
0
0
0
0
6
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
3
2
0
0
2
0
2
1
0
1
0
0
1
0
0
0
0
0
0
0
0
2
4
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
3
0
0
1
0
3
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
2
0
2
0
1
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
2
2
0
2
2
0
0
0
0
1
0
0
0
1
1
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
4
2
0
0
0
0
0
0
0
1
0
0
0
0
0
5
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
4
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
2
0
0
1
0
1
0
2
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
2
0
0
0
0
2
3
0
1
0
0
2
2
0
4
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
1
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
3
0
0
5
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
2
0
3
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
1
3
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
1
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
3
2
4
4
0
8
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
2
2
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
3
0
0
0
0
0
0
0
0
0
1
10
2
0
1
0
0
0
0
1
0
0
2
0
0
0
0
2
2
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
3
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
7
0
1
2
1
0
0
2
0
0
1
1
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
3
0
1
0
0
0
1
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
2
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
2
2
1
0
0
0
4
2
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
8
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
1
0
3
1
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
7
3
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
1
2
0
0
2
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
13
1
0
0
0
0
0
4
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
5
0
0
0
0
7
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
2
0
1
0
1
0
0
3
0
2
0
2
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
8
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
1
1
0
3
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
1
2
1
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
6
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
2
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
3
0
0
1
0
2
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
12
0
1
3
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
2
0
0
1
2
0
1
0
0
2
0
0
0
0
0
1
0
0
0
2
0
6
0
0
0
0
2
1
0
3
2
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
3
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
2
0
0
0
3
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
1
0
1
2
0
1
0
0
0
0
2
1
0
1
0
0
0
3
0
6
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
2
0
2
1
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
4
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
1
0
0
0
0
1
0
0
0
4
1
2
0
0
0
1
0
4
1
0
0
1
0
2
0
0
1
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
1
0
0
7
1
0
0
0
2
0
0
0
0
0
0
0
0
2
1
1
0
1
1
0
2
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
2
0
0
0
1
0
4
0
0
2
0
0
1
0
1
1
0
0
0
0
0
2
0
0
0
1
2
0
2
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
1
2
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
6
0
3
0
0
3
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
2
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
3
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
2
0
0
0
3
1
0
1
0
0
3
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
1
0
0
1
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
2
1
0
2
2
0
0
0
0
0
0
2
0
0
3
0
2
0
0
0
0
1
2
1
1
0
0
0
0
0
0
0
1
0
0
0
3
0
0
1
1
0
0
0
0
0
0
1
0
0
3
0
1
0
0
0
2
0
0
0
0
0
3
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
2
0
0
0
2
1
0
3
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
1
1
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
1
4
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
1
0
0
2
0
2
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
2
1
2
0
1
0
1
2
1
0
0
0
2
0
0
0
0
0
0
0
0
3
7
0
1
0
2
2
0
3
0
0
1
0
0
2
0
1
1
0
0
0
1
0
0
2
0
0
0
0
2
0
1
0
0
1
0
2
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
1
0
3
0
0
3
0
0
0
2
0
0
0
3
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
2
7
2
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
1
0
2
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
5
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
1
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
1
0
0
1
0
0
0
0
0
1
2
1
0
0
0
0
0
2
0
0
3
0
2
0
0
0
0
0
0
0
1
2
0
1
1
0
1
0
0
0
0
2
4
1
0
0
2
0
0
0
0
2
2
0
1
0
0
1
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
4
0
1
0
0
2
0
1
0
3
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
4
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
1
1
0
0
0
1
0
3
0
0
1
0
2
0
1
0
0
1
1
0
1
0
1
0
0
0
1
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
2
1
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
1
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
7
0
0
0
1
0
0
0
0
0
2
4
0
2
2
0
0
2
1
0
0
0
2
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
1
3
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
8
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
1
1
0
2
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
3
0
1
0
2
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
2
0
1
1
0
2
1
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
3
0
0
0
0
1
1
2
0
0
0
1
1
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
4
0
0
0
4
0
0
2
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
1
0
0
2
0
2
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
3
0
0
1
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
6
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
1
0
0
2
2
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
9
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
2
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
2
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
2
2
0
0
0
0
0
0
1
0
0
0
1
0
0
4
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
9
0
0
0
0
3
4
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
1
0
2
1
0
2
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
2
0
0
0
0
0
2
0
2
0
0
0
5
0
0
1
1
4
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
2
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
2
3
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
3
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
2
0
0
2
0
0
0
0
0
0
6
0
0
0
1
0
1
0
1
0
1
0
3
0
0
0
6
0
0
0
0
0
0
3
0
0
0
0
0
2
7
0
0
0
0
1
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
2
1
0
0
0
1
0
0
0
0
1
3
0
0
0
0
0
2
0
0
0
0
0
3
0
0
6
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
3
0
1
0
0
0
0
2
0
2
2
0
4
0
1
0
1
0
2
0
0
0
0
0
2
2
0
0
1
2
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
2
1
0
1
0
0
1
0
3
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
3
0
0
0
1
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
3
0
0
0
0
0
2
0
4
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
1
0
0
2
0
0
1
1
2
0
1
0
0
3
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
4
1
0
0
2
0
1
0
1
0
0
2
0
0
1
0
0
1
1
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
3
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
3
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
1
2
0
3
0
0
1
0
0
1
2
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
1
0
1
0
2
0
1
0
0
0
0
0
1
0
0
1
0
5
0
0
1
0
1
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
1
1
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
5
0
0
3
0
0
0
0
1
0
0
0
0
0
0
1
0
2
1
0
7
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
1
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
2
0
0
1
0
2
0
0
0
0
3
0
0
0
1
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
1
0
1
0
1
1
0
0
0
0
0
3
1
1
0
0
0
0
0
0
3
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
4
0
0
1
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
2
2
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
4
0
1
0
0
0
0
0
0
0
1
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
1
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
2
0
0
2
0
0
0
4
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
2
1
1
0
0
0
0
3
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
2
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
1
0
1
0
3
0
2
0
0
2
0
0
1
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
3
0
0
1
0
0
1
2
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
3
0
0
0
0
0
1
0
0
1
1
0
0
0
2
0
0
2
1
0
2
3
0
0
0
0
0
1
0
0
0
2
2
0
0
1
2
0
0
0
0
1
0
0
3
0
0
0
0
0
1
2
3
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
1
2
0
0
0
0
1
0
0
0
2
2
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
3
0
0
0
2
0
0
0
0
0
1
2
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
1
5
1
0
0
0
0
0
0
0
1
1
0
0
2
0
2
2
0
0
12
0
0
1
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
3
1
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
2
0
2
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
1
4
2
0
2
0
0
2
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
2
2
0
1
0
0
0
0
3
0
3
1
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
2
0
2
2
0
4
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
2
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
2
2
2
0
0
2
1
0
0
0
2
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
2
0
2
1
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
2
0
0
2
0
0
0
0
2
2
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
1
1
2
1
0
2
0
2
0
0
0
1
2
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
1
0
1
0
1
2
1
0
1
2
0
0
0
1
2
0
0
0
0
0
6
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
1
0
2
0
1
2
0
4
0
0
0
0
0
0
3
0
1
0
0
0
0
2
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
2
0
2
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
4
2
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
14
0
0
0
0
4
3
0
0
0
0
2
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
4
0
0
0
3
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
2
0
0
0
1
2
0
0
5
0
0
0
0
0
0
1
0
3
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
3
0
0
2
0
0
2
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
3
0
8
0
2
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
1
1
0
0
0
1
0
0
2
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
2
0
0
2
0
0
1
0
0
1
2
0
0
0
0
0
3
6
0
5
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
1
0
0
0
0
2
1
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
3
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
5
1
0
0
0
0
0
3
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
1
1
1
0
0
0
1
0
0
1
0
2
0
1
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
2
2
1
1
0
0
0
0
0
0
0
0
0
1
0
2
1
0
1
1
0
2
0
0
0
0
0
0
2
0
1
4
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
3
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
2
1
0
0
0
0
0
0
3
0
1
0
0
2
1
1
0
0
2
0
1
0
0
0
1
0
0
2
0
1
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
3
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
1
0
1
0
1
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
2
2
0
3
0
1
0
1
0
2
0
0
0
0
0
0
0
4
0
2
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
3
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
1
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
1
6
0
0
0
0
0
0
0
0
0
2
5
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
6
0
0
7
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
4
1
0
0
2
0
0
0
0
1
0
0
1
0
0
1
0
0
0
2
0
0
2
0
0
0
0
3
0
1
0
0
0
1
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
3
0
2
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
1
0
2
0
1
0
0
1
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
1
0
0
0
0
1
0
1
1
1
0
0
0
1
0
1
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
1
0
1
1
0
0
3
0
1
0
1
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
4
0
1
0
1
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
3
0
0
1
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
2
0
0
1
2
0
0
0
0
0
1
0
0
3
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
2
0
2
1
1
0
0
0
0
0
0
0
0
1
3
0
1
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
2
0
0
2
4
0
2
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
2
0
2
0
2
0
2
0
0
0
0
2
0
0
1
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
1
0
1
0
0
0
0
2
0
0
0
0
2
2
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
1
2
0
0
2
2
0
2
2
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
3
0
3
1
1
0
0
0
0
1
0
0
0
0
0
0
0
4
0
2
0
2
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
1
0
4
0
1
2
0
1
1
0
0
0
0
0
0
1
1
2
2
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
7
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
1
2
2
0
0
1
2
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
2
0
2
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
2
0
1
0
0
1
0
0
3
7
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
2
2
2
1
0
0
1
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
1
0
0
1
0
0
0
3
0
0
10
0
0
0
0
4
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
13
1
1
0
0
0
0
1
0
0
0
0
0
0
2
2
1
2
0
2
0
2
0
0
0
0
0
2
0
0
5
0
0
3
0
0
1
0
1
2
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
2
2
0
2
0
2
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
4
0
2
0
1
0
0
1
0
0
0
2
0
0
2
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
2
0
0
0
1
2
0
0
0
0
2
0
2
0
0
0
0
2
1
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
6
0
0
0
1
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
7
1
0
2
0
3
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
3
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
6
1
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
5
1
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
3
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
1
0
0
0
0
2
0
2
0
0
3
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
1
1
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
4
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
1
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
7
0
0
0
0
1
0
0
0
0
2
0
0
0
0
9
0
0
2
0
0
0
1
0
0
2
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
3
0
1
0
1
0
0
0
0
0
1
0
1
0
2
0
1
0
0
2
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
3
0
0
1
0
2
0
1
0
1
1
1
0
0
0
0
0
0
1
3
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
1
2
2
2
2
0
2
0
0
0
0
0
3
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
3
1
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
1
0
0
1
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
2
0
2
0
0
2
0
0
0
1
0
3
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
3
0
1
0
2
0
1
1
0
0
0
2
0
1
0
4
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
1
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
1
0
0
0
1
0
0
0
0
5
0
0
4
2
0
7
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
2
0
0
3
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
1
0
2
0
1
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
1
3
0
0
4
0
0
0
2
2
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
3
2
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
5
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
2
0
2
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
6
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
2
0
0
0
2
0
0
0
1
0
0
0
0
3
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
2
1
0
0
0
0
1
1
2
1
1
0
0
0
0
1
0
0
0
0
3
0
0
1
0
0
0
0
0
1
0
3
1
0
0
1
2
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
2
0
1
1
0
0
0
0
2
0
0
0
0
1
0
2
2
2
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
5
0
0
0
0
0
0
3
1
0
0
2
0
0
0
0
0
0
1
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
2
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
2
7
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
1
0
0
0
2
0
3
0
0
1
0
0
1
1
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
1
1
0
4
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
2
0
3
0
2
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
3
0
2
2
2
0
0
0
0
0
0
0
1
0
1
0
2
0
0
3
1
0
2
0
0
0
0
1
0
0
0
0
2
1
0
1
0
0
2
0
3
0
0
0
0
4
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
1
1
0
2
0
0
0
0
0
2
0
0
0
3
0
1
0
0
0
0
0
0
0
2
4
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
1
0
1
0
1
0
0
0
2
0
1
1
0
8
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
2
2
2
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
1
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
2
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
1
0
3
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
1
0
1
1
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
4
2
0
0
1
0
2
0
0
0
0
0
0
0
2
1
1
1
0
0
0
0
1
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
1
0
0
3
0
1
0
0
2
2
0
0
0
0
2
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
1
0
0
0
2
0
0
1
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
2
1
0
1
2
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
4
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
1
0
1
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
2
0
1
2
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
4
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
1
0
0
2
2
0
0
2
1
1
3
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
2
0
0
2
1
0
1
0
0
0
1
0
0
3
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
1
2
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
4
0
0
2
1
0
1
0
2
0
0
2
0
3
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
6
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
2
0
2
0
0
0
1
3
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
2
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
1
0
1
1
0
0
2
0
0
0
0
2
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
4
0
0
1
2
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
4
0
0
1
0
0
0
0
0
5
0
0
0
2
5
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
3
0
0
2
0
0
2
0
0
0
0
2
2
0
0
1
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
1
0
0
2
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
2
0
1
0
0
2
0
2
3
0
1
0
0
0
0
0
0
0
5
3
0
2
0
2
0
0
0
0
0
0
1
2
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
8
0
0
0
0
2
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
2
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
1
0
0
0
0
2
0
0
1
2
0
0
0
2
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
5
0
0
0
1
0
2
0
0
0
2
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
2
1
0
2
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
2
0
0
1
0
1
1
0
0
1
0
2
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
1
1
0
0
1
2
2
0
0
0
0
0
0
0
1
2
0
2
1
0
0
0
2
0
2
0
0
0
2
1
2
2
1
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
5
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
1
0
0
3
1
0
0
2
0
1
0
1
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
2
2
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
1
0
0
1
0
1
0
1
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
2
2
1
0
0
0
0
0
0
1
0
2
0
0
1
0
2
0
0
0
1
2
0
0
2
0
0
0
4
2
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
1
0
3
0
0
2
0
2
1
0
0
0
0
0
1
0
0
0
1
2
0
0
0
1
0
0
0
2
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
5
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
1
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
2
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
1
0
0
0
1
0
0
0
6
2
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
2
2
0
3
0
0
0
2
1
0
0
1
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
1
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
2
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
1
0
0
0
0
0
4
0
1
1
0
3
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
2
0
0
0
1
2
0
0
0
0
2
0
0
0
0
2
1
0
0
0
2
0
2
1
0
0
0
1
1
0
1
0
0
1
2
2
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
4
0
1
0
2
0
0
0
0
0
1
2
0
0
0
0
0
1
1
2
1
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
3
0
0
0
0
0
0
0
0
0
1
1
0
0
4
0
0
2
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
2
0
1
0
2
0
0
0
0
1
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
2
0
0
1
0
2
0
1
0
2
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
2
2
0
0
3
0
2
0
2
0
0
0
2
0
3
0
0
0
0
1
1
0
0
0
2
2
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
5
0
0
0
0
0
2
0
0
0
0
1
2
0
0
2
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
3
2
1
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
3
1
1
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
2
2
0
2
1
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
5
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
4
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
3
0
0
3
0
0
0
0
0
0
0
0
1
3
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
2
0
0
0
1
1
0
0
0
0
1
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
5
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
3
0
2
0
0
2
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
1
0
1
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
1
1
0
0
0
0
2
1
0
0
0
0
1
1
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
1
0
2
0
0
0
0
0
2
1
1
3
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
2
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
5
0
0
0
0
0
0
3
1
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
3
0
0
0
0
0
3
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
2
0
4
2
1
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
1
3
1
1
0
0
0
0
0
0
0
4
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
6
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
3
2
0
0
0
0
7
0
0
0
0
1
3
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
4
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
5
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
2
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
10
0
0
2
0
0
0
0
1
0
0
0
1
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
4
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
2
1
0
0
0
6
0
2
2
0
1
0
0
3
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
3
0
1
0
0
0
0
0
1
0
2
2
0
0
2
0
0
0
0
0
0
3
0
0
0
0
1
0
1
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
1
0
0
0
4
0
0
2
0
1
0
2
0
0
0
0
0
0
0
3
0
0
2
1
0
0
2
1
2
0
0
1
0
0
0
0
0
2
0
0
0
2
5
0
0
0
0
0
1
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
3
0
1
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
3
0
0
0
1
0
0
0
0
2
0
0
0
0
1
1
2
0
2
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
1
2
0
0
1
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
2
2
0
1
0
0
0
0
2
0
0
0
2
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
4
0
0
1
0
3
0
0
0
2
0
0
0
5
1
1
2
0
0
0
0
0
0
2
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
3
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
4
2
0
1
0
0
0
0
0
0
3
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
1
0
0
3
4
1
0
0
0
2
7
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
2
0
3
2
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
2
8
0
0
0
0
0
0
2
0
7
2
0
0
1
2
0
2
1
3
0
0
0
0
0
0
1
1
0
0
0
0
0
3
0
0
1
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
2
1
1
0
0
0
0
1
0
0
0
2
0
1
3
0
0
0
0
1
0
0
0
0
0
1
2
5
0
0
0
1
2
3
0
0
0
0
0
2
0
0
0
0
0
0
1
3
0
0
1
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
2
0
0
0
1
0
1
1
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
1
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
3
0
0
0
2
2
0
0
0
3
2
0
0
3
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
1
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
1
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
5
0
0
3
1
0
0
0
0
0
0
1
0
5
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
2
0
0
1
3
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
3
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
2
2
0
1
0
0
0
2
0
7
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
2
0
2
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
4
5
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
7
2
0
0
0
0
0
0
2
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
3
0
2
0
0
0
0
0
0
0
0
1
0
1
0
1
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
1
1
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
4
0
0
2
4
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
2
0
0
0
0
3
1
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
3
2
0
0
0
0
0
4
0
0
0
0
0
0
2
1
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
2
0
3
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
6
2
0
2
0
0
0
1
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
1
0
3
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
1
0
0
3
4
0
0
0
2
0
0
1
0
2
2
1
0
0
0
0
2
2
0
0
0
5
0
0
0
1
1
0
1
0
0
0
0
0
1
1
0
0
2
0
0
2
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
3
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
3
0
1
0
2
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
1
3
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
3
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
1
2
1
1
0
0
0
1
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
2
1
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
1
1
0
0
2
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
1
0
0
0
3
0
7
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
3
2
0
1
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
2
0
0
1
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
4
1
0
0
0
0
0
0
0
0
0
1
0
1
4
0
2
0
1
3
0
0
0
0
0
0
0
2
0
1
1
4
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
22
0
0
0
1
0
1
2
1
0
0
0
1
3
3
0
0
0
0
0
0
0
0
0
1
0
0
3
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
2
1
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
5
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
4
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
5
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
1
1
2
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
5
2
2
2
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
1
0
0
1
4
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
2
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
4
0
0
3
1
0
0
1
2
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
2
0
0
1
0
0
1
3
0
0
3
2
0
0
1
0
0
4
0
0
0
0
0
0
0
3
0
4
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
1
0
0
2
0
2
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
4
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
1
0
0
0
0
0
0
2
2
0
1
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
2
3
0
1
2
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
3
0
1
1
0
0
0
1
0
0
0
2
2
0
0
0
0
3
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
5
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
4
0
0
0
3
0
1
0
0
0
1
0
4
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
5
0
2
0
0
3
0
0
1
0
0
1
0
0
2
0
2
0
0
0
0
6
0
0
1
2
0
0
2
0
0
1
1
1
0
7
0
0
0
0
2
0
0
0
0
1
1
0
1
0
0
4
1
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
1
0
1
0
1
0
3
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
1
0
2
0
0
0
0
0
0
0
1
2
0
1
5
2
1
0
0
2
0
0
0
1
1
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
1
5
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
2
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
3
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
11
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
3
0
0
0
0
2
0
0
0
3
1
0
0
0
0
2
1
0
0
2
1
0
0
0
0
0
1
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7
0
0
1
0
0
0
1
0
0
1
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
2
0
0
2
0
1
0
0
0
0
3
0
0
0
0
2
2
0
0
0
0
2
0
0
2
2
0
0
0
0
2
0
3
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
1
2
0
2
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
2
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
2
0
1
0
0
0
0
0
1
25
0
0
0
0
1
2
0
0
0
0
0
2
0
0
2
1
1
0
0
0
0
2
3
0
0
2
0
1
0
0
0
0
1
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
2
0
0
0
1
0
1
1
0
0
0
2
0
0
1
0
0
0
0
0
0
4
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
3
1
0
1
0
0
0
0
0
0
0
0
0
0
11
0
0
0
0
0
3
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
2
0
0
1
0
0
1
0
0
2
0
3
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
2
0
0
2
0
0
4
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
3
2
0
0
2
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
7
2
0
0
0
0
0
0
0
1
0
1
3
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
4
3
1
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
1
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
1
0
2
0
0
1
0
2
0
2
0
0
3
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
3
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
6
0
0
0
0
0
0
0
0
1
1
0
0
0
0
3
0
0
0
2
0
0
1
2
1
0
0
0
2
0
0
0
0
0
0
1
0
2
0
3
3
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
1
0
3
0
0
0
0
0
0
1
0
2
1
0
0
0
1
0
0
1
0
0
1
2
3
0
0
1
0
0
0
0
0
0
2
0
1
1
0
1
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
3
0
0
0
1
0
0
0
2
1
2
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
5
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
2
0
9
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
1
0
0
1
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
1
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
5
0
1
0
2
0
0
0
1
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
4
0
0
2
0
2
1
1
0
0
7
0
0
0
0
0
0
0
0
1
0
1
0
1
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
2
0
2
2
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
4
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
1
0
0
0
1
1
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
2
0
0
0
0
0
2
0
0
0
2
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
2
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
5
2
0
4
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
1
0
0
1
0
0
4
0
0
1
0
0
0
0
1
0
0
0
2
0
0
1
1
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
1
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
2
1
0
0
0
1
2
0
2
3
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
1
0
0
1
0
0
0
0
2
0
1
0
1
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
6
1
5
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
6
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
2
2
0
0
0
0
2
1
0
0
0
1
0
0
0
0
3
0
0
1
0
2
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
2
0
0
0
3
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
5
1
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
5
0
0
1
0
2
0
2
0
2
1
0
0
0
0
2
1
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
3
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
1
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
2
1
3
0
0
0
0
2
0
0
0
0
0
2
1
0
1
0
0
0
1
0
2
2
0
0
0
0
2
1
2
0
2
0
0
1
0
0
0
0
2
0
2
2
2
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
3
0
0
1
3
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
1
0
0
2
0
0
4
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
2
0
0
0
1
0
1
0
3
0
0
0
1
3
0
2
1
0
0
0
0
2
0
2
0
2
0
0
0
0
1
0
0
2
2
2
0
0
0
1
0
0
2
2
0
2
0
0
1
0
1
0
0
0
0
0
2
1
0
3
2
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
3
2
0
0
0
0
0
0
0
3
0
2
0
0
0
1
0
1
0
0
0
2
1
0
0
2
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
2
1
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
4
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
3
0
0
0
1
1
0
1
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
1
0
0
0
0
4
0
1
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
1
2
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
2
0
2
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
1
0
0
2
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
1
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
1
0
0
3
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
1
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
2
0
2
2
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
2
3
0
0
0
3
0
0
2
0
0
2
0
7
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
2
0
0
1
3
0
0
0
0
0
0
0
3
0
4
0
0
0
0
2
0
0
1
0
2
0
1
0
0
0
1
0
1
0
1
0
1
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
1
1
0
0
0
0
5
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
1
0
2
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
2
0
0
0
0
0
0
1
0
0
0
1
3
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
1
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
5
0
0
0
1
0
0
0
3
0
0
0
0
0
0
2
0
0
4
1
4
1
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
8
0
0
1
1
2
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
2
2
0
0
2
1
0
0
1
1
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
4
0
0
0
0
5
0
0
0
0
1
0
0
0
0
0
4
0
2
0
0
0
2
2
3
0
0
1
0
0
0
0
0
2
1
0
0
0
7
0
0
0
0
2
2
0
2
0
4
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
1
0
1
0
1
3
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
1
3
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
3
0
1
0
3
4
0
0
1
1
3
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
3
0
0
5
0
1
0
0
0
0
0
2
0
1
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
3
2
0
0
0
1
0
0
0
0
1
2
0
0
0
0
1
0
4
0
0
0
0
0
0
0
3
0
1
0
0
2
0
0
0
0
0
0
0
0
2
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
2
2
0
0
1
0
0
0
2
0
3
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
1
2
0
0
0
8
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
1
0
4
0
1
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
1
1
0
0
0
0
0
0
0
0
0
2
2
1
2
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
2
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
2
0
1
1
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
3
0
0
2
0
1
0
0
2
0
3
0
0
1
0
3
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
3
0
0
0
0
1
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
1
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
3
0
0
0
2
0
0
1
0
0
0
0
0
5
0
2
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
2
0
2
0
0
3
0
1
0
0
0
2
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
3
1
0
1
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
1
2
0
0
0
0
1
0
0
1
0
0
0
0
0
2
1
0
0
0
0
3
4
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
5
0
0
0
2
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
4
0
0
0
0
0
1
1
0
0
0
4
0
0
0
0
0
2
0
1
0
0
1
0
0
0
2
0
0
6
0
2
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
1
0
1
0
0
0
0
4
0
0
0
0
0
1
0
1
0
2
4
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
3
0
1
3
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
1
0
0
1
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
4
0
0
0
1
2
0
0
2
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
9
3
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
3
0
0
0
2
0
0
0
3
2
0
2
2
2
0
0
0
0
3
1
0
1
0
1
2
0
0
0
0
3
2
0
0
0
1
0
0
0
0
1
0
0
2
0
2
0
1
0
3
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
2
0
0
0
0
0
2
1
0
0
3
0
0
3
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
4
1
4
0
0
3
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
4
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
1
0
1
0
0
2
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
2
10
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
1
1
1
0
0
0
2
0
0
0
1
1
2
0
0
0
0
0
1
1
0
2
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
2
1
2
0
5
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
6
0
0
0
0
0
0
0
0
0
1
2
0
2
0
1
6
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
2
0
0
2
1
0
0
2
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
3
1
0
0
0
0
0
2
2
0
0
1
1
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
1
2
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
1
0
0
1
0
0
0
0
1
0
0
2
0
0
1
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
2
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
12
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
5
0
1
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
1
1
0
0
0
0
2
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
3
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
3
0
1
0
2
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
4
0
0
0
0
0
0
1
0
5
1
4
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
9
0
0
0
0
2
0
0
0
1
0
0
1
2
0
4
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
5
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
10
1
1
2
0
0
2
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
2
0
0
2
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
1
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
2
0
0
0
1
0
4
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
2
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
4
1
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
3
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
1
0
1
0
2
0
0
1
1
1
1
0
3
0
4
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
2
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
5
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
1
0
0
0
0
1
1
0
2
4
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
1
1
0
0
0
0
0
1
0
2
0
0
0
0
3
0
0
0
2
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
2
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
1
0
1
1
1
0
0
2
0
0
0
3
0
0
0
0
1
0
3
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
3
0
6
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
1
0
1
1
1
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
6
0
0
0
2
0
0
0
1
3
0
1
0
0
0
0
0
0
2
0
2
8
2
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
2
0
1
0
0
1
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
2
0
4
1
0
0
1
0
0
1
0
0
0
2
0
1
1
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
2
4
0
0
1
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
5
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
2
0
2
1
0
0
0
3
1
0
0
0
0
0
2
0
2
0
2
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
3
0
1
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
7
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
3
1
0
0
0
0
0
0
10
0
0
0
0
2
1
0
0
0
6
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
4
2
0
0
2
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
1
3
1
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
5
0
1
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
2
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
3
2
0
0
0
0
0
1
0
0
0
4
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
2
1
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
5
3
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
4
1
1
2
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
3
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
3
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
1
3
0
2
0
1
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
1
1
2
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
1
2
0
1
2
0
2
2
0
0
0
0
3
3
0
2
2
0
0
2
1
0
0
0
0
3
1
2
0
0
0
0
2
0
0
0
0
0
0
2
1
2
1
0
0
1
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
2
1
0
1
2
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
4
2
0
1
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
2
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
2
2
0
0
1
0
0
0
0
3
0
0
0
2
0
0
0
0
0
1
0
2
2
2
0
0
0
0
0
2
1
0
0
2
0
0
2
2
2
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
7
2
0
0
0
0
0
3
2
0
2
0
0
0
0
0
1
0
0
3
2
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
4
0
0
0
0
0
0
0
3
0
1
2
0
0
1
1
0
0
0
0
2
2
0
0
0
2
0
0
1
1
0
0
0
0
0
2
2
0
1
1
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
4
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
4
0
2
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
1
0
0
3
0
1
0
1
0
0
0
0
1
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
7
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
3
0
1
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
1
2
2
0
0
0
2
1
1
1
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
2
0
0
0
2
0
2
1
0
1
0
0
0
0
1
0
2
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
6
0
2
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
4
0
0
2
0
0
0
2
1
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7
0
0
1
0
0
0
0
3
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
2
1
2
0
4
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
2
0
3
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
1
0
0
0
0
2
1
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
1
0
1
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
1
2
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
4
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
5
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
2
3
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
1
3
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
2
0
1
2
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
2
1
0
0
0
1
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
5
0
0
1
0
0
0
0
0
0
3
0
0
0
5
1
0
2
1
0
0
0
0
0
0
1
1
0
2
0
0
0
1
0
1
0
2
0
1
0
1
1
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
2
1
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
7
0
0
0
0
2
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
3
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
1
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
1
0
3
0
0
1
2
0
0
0
0
0
1
0
3
0
2
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
2
3
1
1
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
3
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
1
0
2
0
0
0
0
0
1
0
1
0
0
0
2
0
0
2
0
0
0
4
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
1
5
0
5
1
0
1
0
1
0
0
0
1
0
2
0
0
3
0
2
1
1
0
2
0
0
0
0
8
0
0
0
0
0
0
0
2
0
6
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
2
0
4
0
3
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
2
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
1
2
0
2
2
0
0
4
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
2
3
0
0
1
0
0
0
0
0
2
0
1
0
1
0
4
0
6
1
2
1
0
2
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
2
2
0
1
0
0
0
0
0
1
0
0
1
2
0
0
1
0
0
1
2
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
3
3
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
4
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
3
0
0
2
0
0
0
3
2
0
0
1
2
0
0
4
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
1
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
1
1
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
3
1
1
1
0
5
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
3
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
2
0
0
1
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
1
4
3
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
3
0
0
2
0
0
0
2
1
1
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
2
2
0
1
0
0
0
0
0
1
0
0
0
4
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
1
2
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
5
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
4
2
1
0
0
0
1
0
0
0
2
0
1
0
4
0
0
0
0
0
1
0
0
0
3
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
2
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
1
0
0
1
0
0
3
0
0
0
0
0
0
2
2
2
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
3
0
1
0
2
0
0
2
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
3
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
2
0
2
1
2
0
0
2
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
2
0
0
0
0
3
0
1
2
0
1
1
0
0
2
1
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
4
0
0
0
0
0
0
4
0
0
0
1
1
0
1
1
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
2
0
0
0
2
0
0
2
1
0
0
1
0
1
0
0
0
1
0
0
0
0
3
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
3
2
0
0
3
0
0
0
0
1
0
0
1
0
0
1
1
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
2
1
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
2
1
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
2
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
2
0
1
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
1
5
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
1
0
0
2
0
1
0
0
1
2
0
0
0
0
1
0
2
2
0
0
0
0
3
0
0
2
0
0
2
0
0
1
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
2
2
0
0
1
4
2
0
0
0
1
0
1
0
3
0
1
1
0
1
0
0
0
0
1
0
5
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
10
0
0
0
1
3
0
0
0
4
2
0
0
0
0
0
2
2
0
0
0
0
0
2
3
0
0
0
1
0
4
0
0
4
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
3
0
0
0
0
0
3
0
2
0
3
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
2
0
0
0
1
9
0
0
1
2
2
2
0
0
0
0
0
1
0
0
0
0
2
0
2
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
1
0
1
0
0
0
3
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
1
0
0
1
2
3
0
0
0
0
0
0
1
2
1
2
0
2
0
0
0
0
0
2
0
0
0
0
4
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
3
1
1
0
0
2
1
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
5
2
0
0
0
0
1
0
0
1
1
0
0
0
0
2
0
0
4
0
0
1
0
2
0
5
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
2
0
0
0
3
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
1
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
1
2
1
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
5
0
2
0
0
1
0
0
0
3
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
5
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
3
1
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
1
2
0
5
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
1
4
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
1
0
2
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
3
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
1
1
0
0
0
0
1
0
0
1
0
2
1
0
0
1
0
1
0
0
1
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
2
0
0
3
2
0
0
0
0
0
0
1
4
2
1
0
0
0
0
0
3
0
0
1
0
4
0
0
1
0
0
0
1
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
2
0
1
0
0
2
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
2
0
0
0
1
0
0
0
0
1
0
0
2
0
1
1
2
0
0
0
0
0
2
0
0
0
0
1
3
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
1
0
0
3
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
2
1
0
0
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
2
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
2
1
2
0
0
0
1
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
1
0
0
0
0
2
0
0
0
1
0
1
1
2
0
0
2
0
1
0
4
0
0
0
0
1
0
2
0
0
0
1
3
0
0
0
0
0
0
0
2
2
1
0
0
0
0
1
0
0
2
0
0
0
1
0
1
2
5
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
1
2
0
2
1
2
1
0
0
10
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
8
1
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
3
0
2
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
5
0
0
0
0
0
2
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
4
0
0
0
2
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
1
0
0
0
1
3
0
0
0
1
0
0
0
0
0
0
4
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
3
2
0
0
4
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
1
1
0
7
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
3
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
2
1
2
2
0
0
0
0
1
0
3
0
1
0
2
0
0
1
1
0
0
1
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
2
0
2
0
2
0
0
0
0
1
0
0
0
0
1
2
0
0
0
1
0
1
2
0
3
2
0
0
1
0
0
0
0
0
1
2
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
4
2
1
0
0
1
0
0
2
1
0
5
0
2
0
1
0
0
1
0
0
0
0
0
2
0
2
0
1
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
4
0
1
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
2
2
0
1
0
4
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
3
0
0
0
0
2
0
0
0
0
1
0
1
0
0
1
0
1
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
2
0
3
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
1
2
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
3
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
2
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
2
0
1
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
2
0
0
0
2
0
0
0
0
2
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
4
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
4
0
0
2
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
2
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
2
0
0
1
1
2
0
1
1
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
1
2
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
5
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
3
0
0
0
2
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
1
1
2
0
0
1
0
2
0
0
0
0
0
0
0
1
1
0
0
2
0
1
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
3
0
0
0
0
2
1
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
2
2
0
0
0
2
0
1
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
2
0
2
0
0
2
0
0
3
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
1
3
1
0
3
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
2
0
2
1
0
0
2
1
0
0
0
0
0
4
2
0
2
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
5
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
1
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
2
0
1
0
1
0
0
1
2
2
0
0
1
0
0
0
0
4
0
0
0
0
0
1
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
2
2
1
0
0
2
1
0
0
0
0
0
2
0
0
0
1
0
1
1
1
0
0
0
0
0
0
2
0
0
0
1
2
2
0
0
0
0
0
1
0
2
1
0
1
0
0
0
1
0
1
0
0
1
0
5
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
1
0
0
1
0
2
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
1
0
0
0
0
2
2
0
0
0
2
1
0
1
1
0
0
0
0
0
1
2
2
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
3
0
0
2
1
0
0
1
0
2
0
1
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
2
0
1
0
3
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
1
0
0
0
0
0
0
2
0
0
0
0
1
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
2
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
3
0
1
0
0
0
1
0
2
0
1
1
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
1
0
0
1
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
2
1
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
1
0
0
2
0
0
1
2
0
4
0
0
1
1
0
0
0
0
0
1
0
0
1
0
5
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
2
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
2
0
0
1
0
0
0
0
0
3
0
0
2
1
0
0
2
7
0
1
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
5
1
0
0
0
0
0
0
0
3
2
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
1
4
0
0
0
1
1
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
4
0
1
0
2
0
3
3
0
0
1
0
1
0
0
0
0
0
0
7
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
3
2
0
0
2
0
0
0
0
0
0
0
3
2
0
0
0
1
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
5
0
0
2
1
0
0
0
0
1
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
1
0
0
3
3
3
0
0
4
0
0
2
0
0
0
0
0
0
0
2
1
2
1
0
1
0
0
0
0
0
0
0
7
0
0
0
0
1
0
0
0
0
0
2
3
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
2
1
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
1
2
2
0
0
0
0
0
0
0
0
0
3
0
1
0
1
0
0
0
2
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
9
0
0
0
6
0
0
0
2
0
1
0
0
0
0
0
1
0
0
3
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
8
2
0
0
0
2
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
3
0
1
0
0
1
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
3
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
3
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
1
2
2
0
0
2
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
1
0
1
1
0
0
2
0
5
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
2
0
2
0
0
0
1
0
0
1
1
2
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
3
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
2
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
7
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
7
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
1
0
1
0
0
2
0
0
0
4
0
2
0
3
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
1
1
2
0
0
0
2
0
0
0
0
0
0
0
0
3
3
2
1
1
0
2
2
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
4
2
0
0
2
1
0
0
0
1
0
0
0
0
0
0
2
2
1
0
2
1
0
0
0
2
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
1
0
3
2
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
2
5
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
2
0
1
5
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
7
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
1
0
0
0
1
6
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
1
0
0
1
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
2
0
0
0
0
1
0
0
0
0
0
1
3
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
6
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
1
0
1
0
2
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
2
2
0
0
0
0
0
1
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
1
1
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
2
0
0
0
0
2
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
4
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
3
3
0
1
0
0
0
0
0
0
3
0
2
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
2
0
1
0
0
0
0
2
0
0
0
2
0
0
0
1
2
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
4
0
0
0
2
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
5
0
1
2
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
3
1
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
7
0
5
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
2
0
0
1
0
0
2
0
2
0
0
0
0
5
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
3
0
2
0
0
0
0
1
1
0
0
1
0
0
0
0
0
3
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
3
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
1
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
1
2
0
0
0
3
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
3
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
1
0
0
0
0
0
0
2
0
4
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
4
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
6
0
0
0
0
0
1
0
0
0
1
0
2
1
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
1
1
2
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
4
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
2
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
2
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
2
1
2
2
0
0
0
1
0
0
0
0
0
1
0
0
3
0
0
2
4
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
3
2
0
0
1
0
1
2
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
2
0
0
1
0
3
0
0
0
2
0
0
0
2
0
0
0
0
1
2
0
0
2
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
1
3
0
0
0
2
0
0
2
1
1
5
0
4
1
0
1
0
1
2
0
2
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
3
1
0
2
1
0
0
1
0
0
0
0
0
0
0
1
0
4
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
1
1
0
0
1
0
2
1
1
0
1
1
0
1
0
3
3
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
20
0
9
0
0
0
0
2
0
0
1
0
3
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
1
1
0
1
2
2
0
0
3
0
0
0
2
1
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
1
2
2
0
0
0
0
0
2
0
1
2
0
0
0
0
0
2
1
0
1
3
0
0
1
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
2
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
1
0
0
0
0
1
0
0
0
1
1
2
0
0
1
2
0
0
1
0
0
1
0
0
0
0
0
2
1
0
0
2
1
0
0
0
1
0
0
2
0
3
1
1
0
15
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
1
0
0
2
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
1
0
2
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
2
0
1
0
0
2
0
0
0
0
0
1
3
0
0
0
0
0
3
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
2
0
0
0
0
0
0
0
0
0
0
1
5
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
1
1
0
0
1
0
4
0
0
1
0
0
1
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
3
0
4
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
1
0
0
2
2
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
1
0
1
0
0
0
0
1
0
2
1
1
0
2
0
0
2
2
0
2
0
1
0
0
0
0
0
1
2
2
0
0
0
0
0
0
1
0
0
0
3
2
1
2
1
4
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
2
0
0
3
0
0
0
0
0
1
1
0
0
1
3
0
0
0
0
0
1
2
3
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
1
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
5
0
7
0
0
1
0
0
0
0
0
0
0
0
1
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
1
1
0
0
0
1
0
2
0
1
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
3
0
0
2
2
0
1
2
0
0
0
0
0
0
0
1
0
0
1
0
1
5
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
1
0
1
0
0
0
1
1
1
2
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
14
0
0
0
1
2
2
0
1
0
0
0
0
2
4
3
0
0
1
0
0
0
0
0
0
0
0
3
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
8
2
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
2
1
1
0
0
0
0
0
0
3
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
2
0
2
0
0
0
0
2
0
2
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
1
0
1
1
2
1
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
2
0
0
0
2
0
1
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
2
2
2
0
0
0
0
0
0
0
2
0
0
0
2
4
0
0
0
2
2
7
0
0
0
0
0
0
0
2
2
0
2
0
0
2
0
0
2
0
0
1
1
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
1
0
0
0
2
0
0
3
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
1
2
0
1
0
4
1
0
0
2
2
0
0
0
2
0
2
0
0
1
3
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
2
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
5
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
3
0
0
2
1
2
0
1
0
0
0
0
0
0
0
0
2
1
2
0
1
0
0
0
0
0
0
2
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
2
0
0
0
0
1
1
0
0
1
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
4
1
0
5
0
1
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
5
0
0
1
2
0
2
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
2
0
1
0
0
0
3
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
1
2
0
4
0
1
1
4
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
9
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
1
0
2
0
1
0
0
0
1
2
0
3
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
4
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
2
1
0
0
0
0
0
4
0
3
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
6
2
0
0
1
2
0
0
1
0
3
0
0
3
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
10
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
4
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
2
2
2
0
0
3
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
1
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
5
0
0
0
0
0
1
0
0
1
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
2
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
2
0
0
1
2
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
4
0
1
0
0
0
2
0
0
0
0
0
5
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
2
1
0
0
2
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
1
2
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
5
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
2
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
1
0
1
0
0
2
0
2
0
0
0
0
0
2
1
0
0
1
0
1
2
0
0
2
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
4
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
3
0
0
0
0
2
0
0
0
0
0
1
1
0
2
3
0
0
0
0
0
2
0
1
0
2
0
0
5
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
1
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
3
0
0
0
1
0
0
1
0
0
0
0
1
2
0
0
1
0
0
0
3
0
1
1
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
4
0
2
0
2
2
1
1
2
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
3
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
1
0
1
0
0
0
0
0
0
2
0
0
0
2
2
0
0
2
0
10
6
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
7
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
2
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
2
1
2
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
7
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
3
2
0
0
1
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
1
2
0
1
1
1
0
0
0
0
4
1
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
3
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
2
0
0
0
0
2
2
0
0
2
0
1
0
2
0
2
0
0
0
0
5
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
2
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
2
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
2
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
3
1
1
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
3
1
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
1
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
1
1
0
1
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
2
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
1
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
1
3
0
0
0
0
0
1
1
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
1
2
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
4
0
3
0
0
5
0
0
0
1
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
1
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
3
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
1
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
7
0
0
4
0
0
2
1
0
0
0
0
0
0
0
0
4
0
0
0
0
3
0
0
0
0
0
0
3
0
2
1
0
0
0
0
2
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
3
1
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
1
1
2
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
3
0
0
1
0
0
0
0
2
3
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
2
3
0
0
0
0
1
0
0
0
0
1
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
1
0
0
0
2
0
0
0
0
1
2
2
0
2
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
1
4
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
2
1
0
0
1
2
0
4
0
4
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
2
2
0
0
0
0
0
1
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
1
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
13
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
4
0
0
0
0
0
0
0
1
0
0
2
0
0
1
2
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
4
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
1
2
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
3
2
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
1
0
0
0
1
0
0
0
0
0
0
1
1
2
1
3
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
2
1
0
0
0
0
0
1
0
0
0
2
0
1
3
1
0
1
0
1
0
0
2
0
0
0
3
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
1
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
2
1
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
2
2
0
0
0
1
4
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
5
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
1
0
0
0
2
1
1
0
0
0
0
0
0
0
0
8
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
1
2
0
1
2
0
0
0
0
0
0
2
2
0
2
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
1
1
0
0
0
2
0
0
0
1
0
2
0
1
1
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
2
1
1
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
7
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
2
0
0
0
1
2
0
0
1
0
0
0
0
1
0
0
2
0
2
0
2
0
2
1
0
1
0
2
0
0
2
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
1
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
5
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
3
2
2
0
0
1
0
2
2
0
1
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
2
2
0
2
0
0
0
1
0
1
2
1
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
8
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
6
0
0
1
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
1
2
0
0
0
2
0
2
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
3
0
0
0
2
0
0
0
1
0
0
0
0
1
0
3
0
2
2
0
2
0
0
3
0
0
0
3
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
4
0
2
0
0
0
0
0
0
0
2
2
0
0
2
0
3
0
0
0
0
2
1
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
3
0
2
0
0
1
1
0
0
1
0
0
1
0
1
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
2
0
0
1
0
0
1
1
0
2
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
2
0
3
2
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
6
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
1
0
0
1
1
0
0
0
0
0
0
1
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
1
0
2
0
0
0
3
0
0
6
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
1
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
2
4
0
0
0
0
0
0
3
2
0
1
1
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
2
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
2
0
0
0
1
0
2
0
12
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
1
15
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
2
0
0
0
0
0
0
7
0
0
2
0
0
0
0
0
0
1
3
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
2
2
0
1
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
3
0
0
0
0
1
0
0
0
1
0
1
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
4
3
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
1
0
2
0
0
0
0
1
1
1
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
2
2
0
1
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
3
0
0
0
1
0
2
2
0
0
1
0
4
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
4
0
0
1
0
1
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
8
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
3
0
0
0
0
2
1
0
0
0
1
0
0
0
2
0
0
0
0
0
2
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
2
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
3
0
0
0
0
0
1
0
0
2
2
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
3
2
0
0
0
0
0
1
3
0
0
1
0
1
0
0
3
0
1
0
0
0
1
2
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
1
0
1
0
0
2
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
4
2
1
0
0
0
0
0
0
2
2
3
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
2
0
2
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
17
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
3
2
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
3
0
2
0
0
0
1
0
1
0
0
1
1
0
2
0
0
0
2
0
5
0
0
0
0
0
0
0
0
1
0
0
0
0
9
0
0
0
1
0
2
0
0
1
5
0
2
1
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
2
0
1
2
0
1
0
0
0
1
0
0
1
0
2
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
1
2
1
1
0
2
0
0
1
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
1
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
6
0
0
0
0
1
0
0
2
1
0
1
0
2
1
0
2
2
0
0
1
0
0
3
0
1
1
1
1
0
0
3
0
0
0
2
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
6
1
0
1
0
2
0
0
0
0
0
0
2
0
0
4
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
2
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
2
0
0
0
0
2
0
0
1
1
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
2
3
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
1
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
2
0
2
2
0
0
0
0
2
0
0
1
0
2
0
0
0
4
0
0
1
2
0
2
0
0
0
0
0
1
0
2
0
0
2
0
0
2
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
2
1
0
0
0
2
1
0
0
0
0
0
1
0
0
1
0
1
1
0
0
2
0
0
0
4
1
1
0
0
1
0
0
1
0
1
0
1
1
0
1
0
0
0
1
0
2
0
0
1
0
0
0
0
0
2
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
2
2
2
0
0
0
2
1
0
0
0
0
1
1
0
1
1
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
4
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
2
0
0
0
0
0
1
1
0
0
2
0
0
0
2
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
11
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
7
3
2
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
4
0
1
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
4
1
0
0
0
0
0
0
0
0
0
1
5
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
1
2
0
1
1
0
0
1
1
0
0
0
0
1
2
0
1
1
0
1
2
0
0
2
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
6
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
1
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
1
2
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
1
0
0
3
0
1
0
0
0
0
0
0
0
0
8
0
0
0
0
0
0
10
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
3
0
0
1
0
0
1
1
0
1
0
0
0
0
0
1
0
0
1
1
0
0
2
0
4
0
1
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
1
0
0
0
0
2
2
0
0
0
0
2
0
1
0
1
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
6
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
5
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
5
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
2
2
0
0
0
2
0
1
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
1
2
2
1
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
1
0
0
0
0
0
0
1
0
2
0
1
0
0
13
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
5
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
2
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
3
0
0
2
0
2
0
0
1
1
0
0
0
2
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
2
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
20
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
3
0
2
1
1
1
0
2
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
6
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
5
0
0
1
3
2
0
0
0
0
1
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
2
0
5
2
0
0
1
0
2
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
1
0
0
0
0
0
2
0
2
0
3
0
0
0
0
0
0
2
0
0
1
1
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
1
1
0
0
1
0
0
3
0
0
3
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
2
0
2
0
2
1
1
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
2
0
1
0
0
0
0
2
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
1
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
3
0
0
1
5
1
0
0
0
1
2
2
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
1
0
3
1
2
4
0
0
0
0
0
2
3
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
2
1
1
0
0
2
0
0
1
0
0
1
0
0
1
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
2
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
4
1
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
3
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
4
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
2
2
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
2
1
0
0
0
0
3
0
0
0
0
4
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
2
1
0
1
0
1
0
0
2
1
0
0
2
0
0
0
0
1
1
2
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
4
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
1
0
1
3
0
0
0
0
1
0
0
0
0
0
3
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
3
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
3
5
2
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
1
0
1
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
3
1
2
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
1
0
0
0
0
3
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
2
2
0
0
0
0
4
0
0
0
0
1
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
3
0
0
0
0
4
0
1
0
0
0
0
0
3
0
0
2
1
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
7
0
1
1
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
2
0
1
2
1
0
6
0
2
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
1
2
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
2
0
0
1
2
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
1
0
0
1
2
0
0
0
0
2
0
1
0
0
0
0
1
0
7
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
5
2
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
2
2
0
0
2
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
2
0
5
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
1
0
0
1
0
2
0
1
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
3
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
1
5
0
0
0
0
0
2
1
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
2
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
1
0
1
0
1
0
0
6
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
3
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
1
0
1
2
1
3
0
0
0
0
0
3
1
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
1
1
0
9
0
0
0
1
0
0
0
0
1
0
1
0
0
4
2
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
1
2
0
0
0
1
0
1
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
3
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
1
0
0
0
4
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
2
2
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
6
0
3
0
1
0
0
1
0
0
0
0
0
2
2
0
0
1
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
1
0
0
0
2
0
0
0
0
1
0
0
3
0
0
2
0
0
1
0
0
3
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
1
2
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
2
1
1
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
3
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
2
2
0
0
1
0
2
0
0
3
3
3
0
1
3
0
4
0
0
2
0
0
0
0
3
0
1
0
0
0
1
2
0
0
1
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
5
5
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
1
0
0
1
0
2
0
0
2
3
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
3
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
3
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
2
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
7
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
4
0
0
1
1
1
0
1
1
0
1
0
1
1
0
0
0
4
1
0
0
1
0
0
0
3
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
3
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
4
0
2
0
0
0
0
0
0
2
1
0
0
0
0
1
1
2
0
0
1
0
0
0
0
0
2
2
1
3
2
0
0
0
0
0
2
3
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
2
2
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
3
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
1
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
1
0
2
0
1
0
0
0
1
1
4
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
2
3
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
3
0
0
0
4
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
4
0
0
0
0
3
0
1
1
0
0
0
0
0
0
2
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
1
0
2
0
0
0
1
0
0
1
2
0
0
1
0
0
0
0
2
0
2
0
2
0
0
0
2
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
6
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
1
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
15
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
3
0
0
1
0
0
0
1
0
0
0
2
0
3
0
1
0
0
0
0
4
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
2
0
0
0
0
1
0
1
0
0
0
10
1
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
1
0
2
4
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
4
0
2
1
0
0
0
1
0
0
4
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
3
0
0
0
0
0
0
0
0
1
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
3
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
5
3
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
1
1
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
3
0
0
3
0
0
1
0
0
0
0
0
0
2
5
1
1
0
0
0
0
2
0
0
1
0
0
4
0
1
0
0
5
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
3
2
2
0
0
0
0
0
1
0
0
0
2
1
1
0
0
0
0
0
0
1
0
3
0
1
0
0
0
0
0
0
5
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
3
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
4
0
1
0
0
0
0
0
2
0
0
3
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
2
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
5
1
2
2
0
2
1
0
0
0
0
0
0
2
2
0
0
11
0
0
2
0
0
0
0
2
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
1
2
0
3
1
0
1
0
1
2
2
0
2
1
0
0
0
3
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
1
0
0
0
2
0
0
0
0
1
1
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
2
0
0
1
3
0
0
0
1
0
0
0
2
6
0
0
0
0
8
1
0
0
0
2
0
1
5
0
0
0
2
0
2
0
1
1
0
0
0
2
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
2
0
0
0
7
1
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
3
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
1
1
1
0
0
0
0
0
1
1
0
5
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
1
0
0
0
0
1
0
1
0
0
1
2
0
1
0
0
0
0
1
0
0
3
0
0
2
0
1
1
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
2
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
3
1
0
0
0
0
0
2
0
1
0
0
7
0
0
0
0
0
1
0
5
0
0
2
0
0
8
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
1
4
0
0
0
2
2
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
1
1
0
4
0
1
0
0
0
1
0
2
0
0
1
1
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
2
2
0
0
4
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
8
0
0
0
0
0
1
1
1
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
2
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
4
1
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
1
2
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
1
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
3
1
5
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
1
1
3
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
5
2
1
2
0
4
1
0
0
0
0
0
3
0
1
0
0
2
1
0
0
0
0
3
1
2
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
5
0
1
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
2
1
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
7
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
3
0
0
0
0
0
2
0
2
0
1
0
0
2
3
0
1
0
0
0
0
0
0
0
0
1
1
1
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
1
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
1
0
0
1
0
0
0
0
0
2
0
0
3
0
0
0
0
1
0
1
4
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
3
2
2
0
10
0
0
3
0
0
2
1
0
2
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
1
0
0
0
0
0
2
0
1
6
0
1
0
0
0
0
0
0
0
0
0
5
0
0
0
0
2
4
0
2
1
0
0
0
0
0
0
5
0
0
2
0
1
1
2
1
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
3
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
1
1
2
2
0
2
0
0
0
0
1
0
2
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
5
1
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
1
1
0
0
0
0
0
4
0
0
1
0
0
0
0
2
0
1
0
1
1
0
0
0
2
0
2
0
0
1
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
1
0
2
0
2
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
1
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
5
0
1
0
1
0
9
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
2
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
3
0
0
0
0
1
0
1
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
2
1
0
0
0
2
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
1
0
0
0
0
0
2
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
2
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
8
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
1
1
0
3
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
4
0
4
4
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
1
0
1
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
5
0
0
0
0
3
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
5
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
2
0
0
0
1
0
2
2
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
2
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
4
0
0
1
0
0
1
0
0
0
0
1
0
1
2
0
1
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
1
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
2
3
0
0
0
4
0
2
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
2
0
1
0
0
0
2
0
2
0
0
3
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
2
0
3
0
1
0
0
0
0
0
0
0
0
0
0
2
0
5
0
0
0
2
0
2
1
1
0
0
0
0
2
2
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
3
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
5
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
5
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
6
1
0
0
3
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
3
0
0
0
2
0
2
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
2
0
0
2
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
3
1
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
3
0
0
3
0
0
0
0
0
3
0
1
0
0
0
1
0
0
0
0
2
1
2
0
0
0
0
0
0
2
0
0
0
4
2
0
0
0
0
1
0
0
0
0
1
1
2
0
0
0
2
0
0
1
1
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
6
2
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
1
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
2
0
0
0
0
1
0
0
0
0
1
1
2
0
0
2
2
2
0
0
1
0
0
0
1
1
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
1
2
0
0
1
0
0
0
0
2
0
0
4
1
0
0
0
0
0
0
0
3
2
2
2
0
0
1
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
4
0
0
0
0
3
2
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
2
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
1
1
0
0
0
0
0
1
19
0
0
0
0
0
0
0
2
0
0
0
5
0
0
0
1
0
0
0
0
0
1
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
7
1
1
1
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
2
2
0
0
1
0
0
0
2
3
0
0
0
5
0
2
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
1
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
3
0
1
0
0
0
0
0
0
0
0
0
2
0
0
4
0
0
2
0
0
1
0
0
1
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
6
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
3
3
1
4
0
0
0
0
0
1
3
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
4
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
2
0
1
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
2
0
0
0
1
0
0
0
2
0
3
0
0
0
0
0
3
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
1
0
0
1
2
2
0
0
1
0
2
0
2
2
0
1
0
0
1
0
0
0
0
0
0
0
3
0
1
0
0
0
1
0
0
0
0
2
1
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
3
1
0
0
0
2
0
1
3
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
3
2
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
2
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
1
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
1
0
2
0
0
0
2
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
1
0
0
0
0
0
0
0
2
0
2
0
1
1
2
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
5
0
0
0
2
1
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
2
2
0
2
0
4
0
0
0
0
0
2
0
0
0
0
2
1
1
0
0
0
0
1
0
2
0
0
0
2
1
0
0
0
0
0
2
2
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
2
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
1
1
0
2
1
0
0
0
0
2
0
0
0
0
1
0
2
0
0
1
3
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
2
0
0
1
2
0
1
0
2
0
1
0
0
0
0
0
2
0
1
0
0
0
2
0
2
0
2
0
2
0
0
0
0
0
0
0
2
2
1
0
0
0
1
0
2
2
0
2
0
0
0
0
0
1
0
1
0
0
1
0
4
0
2
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
1
2
0
1
0
2
0
0
0
0
0
0
2
1
0
4
6
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
5
0
0
0
0
0
0
2
0
0
1
3
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
2
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
4
0
1
2
0
0
1
1
2
1
0
0
0
0
0
0
0
1
2
1
2
0
0
0
0
0
0
1
0
0
0
0
6
0
0
0
7
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
2
0
2
1
0
0
0
0
0
1
0
0
0
1
1
0
0
2
0
0
0
0
0
1
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
2
1
2
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
1
1
0
0
0
1
0
2
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
3
1
0
1
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
1
0
0
0
1
1
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
4
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
2
0
0
0
0
0
0
0
0
2
2
1
0
1
1
0
0
0
0
1
0
2
1
1
3
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
1
2
0
0
0
1
1
1
0
0
0
2
0
2
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
3
0
2
0
0
0
0
0
3
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
1
0
0
0
12
0
3
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
4
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
1
0
0
0
4
0
0
0
0
0
2
1
2
2
0
1
1
0
1
0
0
0
0
0
2
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
2
0
2
0
0
0
0
1
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
4
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
3
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
1
2
1
0
1
0
0
0
0
0
3
0
0
0
0
0
0
2
1
2
2
0
0
1
1
1
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
6
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
5
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
3
0
2
1
1
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
3
2
2
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
4
0
0
0
1
0
0
3
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
3
0
0
2
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
1
1
0
0
0
0
3
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
4
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
1
0
2
2
0
3
0
0
0
0
0
2
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
1
0
0
1
1
0
1
0
0
1
2
0
1
0
0
0
2
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
1
0
2
0
2
0
2
0
0
2
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
2
0
2
0
0
2
0
2
0
0
0
0
0
0
0
4
0
1
0
1
0
0
0
0
0
1
0
0
0
0
6
0
0
0
0
0
2
0
0
4
0
0
0
0
0
7
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
3
0
2
2
1
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
1
1
0
1
0
0
2
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
1
0
0
1
0
0
0
0
2
0
0
2
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
2
2
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
3
1
0
0
0
1
0
0
0
0
1
0
1
0
2
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
1
0
3
0
0
11
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
2
0
0
0
2
0
0
0
3
0
0
1
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
2
0
1
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
1
2
0
0
0
1
0
2
0
0
1
2
0
0
3
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
1
0
0
2
2
2
0
0
0
1
3
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
2
2
0
3
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
1
0
0
0
2
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
2
8
0
0
0
0
0
1
2
0
3
0
2
0
0
2
1
1
0
0
0
1
2
0
0
2
3
0
0
0
1
0
1
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
1
0
2
0
1
1
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
2
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
5
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
4
1
0
4
3
1
0
0
1
0
0
0
0
5
2
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
2
1
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
1
0
0
0
1
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
1
2
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
2
0
2
0
0
0
0
2
0
1
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
3
0
3
0
0
0
0
1
0
1
0
2
0
0
2
0
0
0
2
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
9
3
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
8
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
1
0
3
2
0
0
0
0
1
0
2
0
0
2
0
0
0
3
1
0
0
1
0
0
0
3
1
0
0
1
0
0
0
2
0
0
0
0
0
2
2
0
1
0
3
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
7
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
2
0
0
2
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
1
1
0
0
0
1
0
3
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
2
0
0
0
1
0
0
2
2
0
1
0
2
0
0
0
1
1
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
2
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
1
0
2
2
0
0
0
0
2
3
0
1
1
0
0
2
0
0
0
0
0
2
2
0
0
1
0
2
1
0
1
0
0
2
0
0
3
2
3
0
2
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
1
3
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
1
3
0
2
1
0
1
0
0
0
2
3
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
1
0
2
0
0
5
0
0
0
0
0
0
0
2
2
0
1
1
0
1
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
1
0
0
3
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
2
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
2
1
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
1
0
0
0
1
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
1
0
1
0
0
0
3
1
0
1
0
0
3
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
1
0
1
0
2
0
1
0
1
0
0
0
2
0
0
0
0
0
2
0
0
2
2
2
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
1
0
1
0
0
1
0
0
0
0
3
0
0
2
2
0
0
3
1
0
0
0
1
0
0
0
0
1
3
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
2
0
2
0
0
0
2
2
0
0
0
0
0
0
0
1
1
0
2
0
0
0
2
2
0
0
0
2
0
0
0
4
0
0
0
0
0
0
1
0
2
0
0
2
0
0
1
1
0
0
0
1
0
0
2
0
0
2
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
2
5
0
0
2
0
0
1
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
1
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
1
0
0
0
0
2
2
0
1
0
0
2
3
0
0
0
0
0
0
0
0
1
0
0
2
1
0
2
0
0
3
0
0
0
3
1
0
0
1
0
0
2
0
0
0
1
2
2
0
0
0
2
6
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
2
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
4
0
1
1
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
2
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
2
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
1
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
1
0
1
0
1
0
1
0
0
0
4
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
5
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
2
0
0
2
1
0
0
0
2
0
0
1
0
1
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
2
0
0
1
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
1
0
0
1
1
1
0
2
0
0
3
2
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
1
2
0
3
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
2
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
2
0
1
0
0
0
1
2
0
1
0
0
0
0
0
0
0
1
0
0
2
0
1
2
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
1
2
0
0
0
3
0
0
0
0
4
0
1
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
2
0
0
0
2
0
2
2
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
2
0
0
1
4
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
2
0
1
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
3
0
0
0
0
2
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
1
7
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
1
2
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
2
0
0
3
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
2
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
1
0
2
0
0
0
1
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
1
0
0
0
3
0
1
0
0
0
0
0
0
1
1
0
3
4
0
3
0
1
0
0
0
2
0
1
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
1
3
0
0
0
1
0
0
2
0
0
0
0
2
0
0
1
3
0
1
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
1
0
1
0
0
0
2
0
1
0
0
0
1
3
0
0
0
0
1
0
0
0
2
1
0
0
0
0
2
0
0
0
0
3
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
3
1
2
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
3
1
0
0
0
1
0
0
0
2
0
0
2
0
0
0
1
0
0
0
1
1
0
2
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
4
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
5
1
0
1
0
1
2
2
0
0
0
0
0
1
1
2
0
0
1
0
0
1
0
2
1
0
0
0
2
0
0
1
1
0
2
0
1
0
0
2
0
0
0
0
0
0
0
1
0
2
0
2
1
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
5
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
3
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
4
0
2
0
0
0
2
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
1
0
2
4
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
2
0
0
0
0
0
0
2
0
0
1
2
0
0
0
3
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
1
4
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
3
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
1
0
1
2
0
0
0
2
0
0
2
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
3
1
0
1
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
1
0
0
0
0
2
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
1
1
1
0
0
2
0
0
0
0
0
0
0
3
2
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
6
0
0
1
0
0
2
0
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
3
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
2
2
0
0
0
2
1
2
0
0
1
0
0
0
0
1
0
1
0
1
3
1
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
2
0
2
1
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
2
1
3
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
5
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
10
0
1
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
1
2
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
5
0
0
0
0
0
5
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
6
0
2
0
0
0
0
1
0
0
1
0
0
0
0
1
2
2
0
1
0
0
2
2
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
2
2
0
0
0
2
3
0
0
0
0
0
0
0
0
4
1
0
0
0
0
1
1
0
0
10
0
2
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
3
1
1
0
0
0
2
0
2
0
0
1
0
1
0
2
0
0
0
2
0
0
1
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
7
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
2
2
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
3
1
2
0
0
1
0
0
0
0
0
0
2
0
0
1
0
1
0
0
2
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
3
0
1
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
1
0
0
0
0
0
5
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
2
0
0
0
0
0
0
3
0
0
0
1
0
2
2
0
0
0
0
2
0
0
0
1
1
0
0
1
4
0
2
1
1
0
0
0
0
3
0
0
3
0
0
2
0
0
0
0
0
0
0
2
0
0
2
2
0
0
3
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
3
1
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
2
4
0
1
4
3
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
1
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
1
1
0
2
0
2
0
2
0
0
0
0
0
1
1
2
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
2
0
0
1
0
0
0
2
0
2
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
1
0
2
0
2
0
0
0
0
2
1
2
0
3
0
1
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
2
0
1
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
2
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
2
0
2
0
1
0
2
1
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
3
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
1
2
0
0
1
0
1
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
2
0
1
1
0
0
0
0
3
0
2
0
0
0
1
1
0
0
7
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
1
5
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
4
2
0
1
2
0
0
3
0
0
0
0
2
4
2
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
2
0
1
2
0
4
0
0
1
2
2
0
0
2
0
0
0
4
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
1
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
6
0
0
0
3
0
3
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
1
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
1
2
2
0
0
0
1
0
0
2
0
0
1
3
0
2
1
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
2
1
6
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
1
3
0
0
0
1
0
0
0
4
0
0
0
1
0
2
0
1
0
0
0
0
3
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
1
0
1
0
0
0
1
2
0
0
0
1
2
0
2
0
1
0
0
0
0
0
0
0
0
0
5
2
0
0
0
0
0
0
0
3
0
0
0
1
0
0
1
0
1
0
2
0
0
0
0
0
2
0
0
7
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
2
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
5
0
2
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
1
1
0
0
0
0
2
0
2
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
1
0
0
0
0
1
2
3
3
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
4
0
1
2
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
6
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
1
1
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
1
0
0
2
0
2
1
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
2
2
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
5
0
0
0
0
2
0
0
0
0
0
0
2
0
2
1
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
2
2
3
0
1
0
2
0
0
0
2
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
1
2
0
0
1
0
0
0
0
0
0
3
2
0
3
1
0
0
1
0
0
1
0
0
0
0
2
2
0
0
0
0
1
0
0
4
0
0
0
0
2
0
2
0
0
0
1
6
0
0
0
0
0
1
0
0
0
0
0
3
0
0
3
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
10
0
1
0
0
2
0
2
0
0
2
0
0
0
0
1
0
0
0
4
0
3
0
3
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
1
2
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
2
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
1
2
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
6
0
0
0
0
0
1
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
1
0
1
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
1
1
0
0
0
2
0
0
0
2
1
0
0
0
3
2
0
0
0
0
1
0
2
2
0
0
0
0
2
0
2
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
2
2
0
7
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
1
0
3
1
0
0
0
0
0
0
1
0
2
3
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
1
0
0
0
2
0
1
0
0
0
0
0
12
0
3
1
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
5
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
1
0
1
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
2
0
0
2
2
2
1
1
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
6
2
0
0
0
1
0
2
2
2
1
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
2
0
0
4
0
0
1
0
0
0
1
0
0
0
1
2
0
0
0
0
1
0
2
0
4
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
1
0
0
3
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
1
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
3
1
3
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
2
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
2
1
0
1
2
2
2
0
1
0
1
0
1
2
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
3
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
2
2
0
1
0
0
0
0
2
0
2
0
0
0
1
1
0
1
1
0
1
0
4
0
0
0
1
2
0
0
1
0
0
4
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
3
2
0
1
0
0
0
1
0
0
0
2
0
0
0
0
8
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
8
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
1
0
0
0
0
7
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
3
0
1
0
0
0
0
0
2
0
0
1
0
4
0
0
0
0
0
0
0
1
5
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
4
0
0
3
0
0
1
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
1
2
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
1
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
2
0
0
2
0
1
0
0
0
0
2
2
0
0
0
2
3
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
2
2
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
3
0
0
2
0
0
0
0
0
0
0
5
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
4
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
6
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
1
4
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
1
0
1
0
4
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
1
0
0
0
1
1
0
1
0
1
1
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
1
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
2
0
0
7
0
0
0
1
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
1
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
1
0
1
0
0
1
0
0
5
0
0
2
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
2
0
1
0
0
2
2
1
0
0
0
0
1
0
2
1
0
1
0
3
0
1
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
5
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
5
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
2
0
2
0
0
7
0
0
0
1
0
0
4
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
1
0
1
0
0
0
2
0
0
0
1
0
3
0
0
2
0
0
0
0
1
0
1
0
1
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
8
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
1
0
0
3
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
2
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
3
0
0
0
0
3
0
0
3
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
4
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
2
1
0
0
3
0
0
0
1
0
0
0
0
0
0
1
1
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
1
4
0
0
0
1
1
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
4
0
0
1
0
0
0
0
3
2
5
0
0
1
0
4
0
0
3
0
1
0
0
0
0
0
2
0
0
2
2
0
2
0
0
2
0
0
2
0
0
2
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
5
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
2
5
1
0
0
2
2
1
1
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
1
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
1
2
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
1
0
0
0
3
1
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
2
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
1
0
0
0
1
0
0
0
0
6
2
0
0
0
1
2
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
2
0
1
1
0
0
0
2
0
0
1
0
2
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
3
1
0
1
3
0
0
1
0
0
0
0
1
2
2
0
0
0
2
0
0
0
2
0
0
0
2
3
0
3
0
0
0
3
0
0
1
2
0
2
1
2
0
0
1
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
2
0
0
2
2
2
2
0
2
2
0
0
0
0
2
1
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
3
0
0
2
0
0
1
0
0
0
0
0
0
0
1
1
3
0
1
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
1
0
0
3
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
4
0
0
2
0
1
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
1
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
2
0
1
0
2
3
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
2
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
5
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
1
1
2
0
3
0
0
0
0
0
0
0
0
0
1
0
0
1
3
0
0
1
0
0
0
0
0
1
0
0
0
1
0
2
2
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
1
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
2
2
0
0
0
6
2
0
0
0
0
1
1
0
2
0
1
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
5
3
0
3
0
1
0
2
0
16
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
3
0
0
0
2
0
4
1
1
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
2
0
11
2
0
0
0
2
0
0
1
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
14
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
7
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
1
0
6
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
3
0
2
2
0
1
0
1
0
1
0
0
0
1
0
2
0
0
0
0
2
0
1
1
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
2
0
1
2
2
1
1
0
7
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
1
0
1
0
0
5
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
1
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
3
0
0
0
1
1
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
1
2
0
0
2
0
0
1
0
2
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
1
3
0
5
4
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
2
2
0
2
1
0
0
0
0
0
1
1
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
1
1
1
1
0
2
0
1
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
5
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
4
1
0
1
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
3
1
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
2
0
0
0
1
1
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
3
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
2
0
1
0
0
1
0
0
1
3
0
0
2
0
0
0
0
0
0
5
0
1
1
0
0
0
0
1
0
0
2
0
0
11
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
1
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
2
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
5
2
0
0
0
2
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
1
5
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
1
0
0
4
2
0
0
0
0
1
0
2
2
0
3
0
0
3
0
0
0
1
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
2
2
0
2
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
1
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
1
0
2
0
0
0
0
0
1
0
0
0
1
2
1
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
6
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
2
0
1
0
0
1
0
2
0
0
1
0
2
0
0
0
2
0
4
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
1
0
1
1
2
0
2
2
0
2
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
1
1
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
1
0
0
0
3
2
0
4
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
4
0
0
3
1
2
2
0
1
2
2
1
0
0
2
0
0
0
0
0
0
0
0
0
2
3
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
2
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
4
1
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
3
0
3
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
4
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
2
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
3
0
3
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
4
0
2
0
0
2
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
1
0
0
2
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
1
8
2
0
0
0
1
0
0
0
0
2
1
0
0
0
2
1
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
3
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
1
0
2
1
0
1
2
0
0
0
0
0
0
0
0
3
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
6
0
2
0
0
1
0
1
2
2
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
3
0
0
0
0
0
0
1
0
0
0
7
0
0
0
0
0
1
0
0
0
0
4
0
0
1
1
0
0
2
0
0
0
1
1
1
3
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
3
0
1
0
2
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
1
2
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
1
0
0
2
0
0
3
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
3
0
0
0
0
2
1
1
0
1
0
2
0
1
1
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
1
3
0
2
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
4
2
0
0
0
0
1
6
0
0
0
0
0
0
2
3
0
2
2
0
0
0
0
1
0
0
0
3
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
1
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
1
1
0
3
0
0
2
1
0
9
0
0
0
0
0
2
1
0
4
0
0
2
0
2
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
2
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
4
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
3
0
0
0
0
2
0
0
3
0
0
0
2
0
1
0
0
2
0
0
2
0
1
2
0
0
2
0
0
1
0
0
0
1
0
1
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
1
0
5
2
0
0
4
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
2
0
0
1
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
2
0
0
1
2
0
0
1
0
1
0
0
1
0
0
0
1
0
2
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
5
1
1
0
1
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
2
0
2
2
0
2
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
2
2
0
0
0
0
0
0
5
0
3
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
3
1
0
1
2
0
2
1
0
1
0
0
0
1
1
0
0
0
0
1
2
1
0
0
0
0
1
2
2
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
5
0
0
2
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
3
0
0
1
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
1
0
2
1
0
0
1
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
2
0
2
3
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
4
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
3
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
2
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
1
2
1
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
4
2
0
0
0
0
2
1
1
0
0
0
0
2
0
0
0
0
0
1
1
0
0
3
0
0
3
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
5
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
2
0
2
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
1
0
2
0
0
2
2
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
4
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
3
0
2
0
0
1
1
0
0
0
2
0
1
0
1
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
2
0
0
2
1
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
3
0
0
0
0
0
0
0
0
1
0
5
0
0
0
0
1
1
0
2
0
1
2
0
1
0
0
0
0
1
0
0
3
0
0
0
1
0
0
0
0
0
0
1
1
0
10
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
1
2
0
0
2
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
3
1
2
0
0
0
0
0
0
0
1
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
3
0
1
0
0
0
1
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
2
0
0
2
0
1
0
1
0
0
2
0
0
0
0
1
0
0
0
0
1
2
0
0
0
2
2
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
1
0
0
0
0
2
0
1
2
2
2
0
2
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
3
0
0
0
0
1
0
0
0
0
1
0
2
0
2
2
1
1
0
0
0
0
0
0
0
0
2
3
4
2
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
2
0
1
3
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
1
0
2
0
0
0
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
1
0
6
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
5
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
1
0
0
8
0
0
0
0
0
0
1
0
0
0
0
0
3
0
1
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
4
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
0
1
8
1
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
3
3
0
0
0
0
0
1
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
2
3
0
0
0
0
0
0
3
0
1
0
3
1
0
0
3
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
3
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
1
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
5
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
4
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
2
0
0
0
0
1
2
0
0
0
1
1
3
0
2
0
1
0
2
1
2
1
0
1
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
2
0
0
0
0
2
1
1
1
1
2
0
0
0
0
0
0
0
1
1
1
0
2
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
3
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
4
1
2
0
1
0
0
0
0
0
0
0
2
0
2
2
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
4
0
0
0
1
1
0
0
3
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
1
0
0
0
0
3
2
2
0
2
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
2
1
2
0
1
0
2
1
1
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
7
0
0
3
2
0
0
0
0
0
0
2
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
3
1
0
0
0
2
0
0
0
0
0
2
0
3
0
0
0
5
0
0
0
0
0
0
0
3
0
6
0
2
0
0
2
0
0
0
0
2
2
0
0
0
0
2
1
0
0
0
0
0
2
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
1
3
0
0
0
5
0
0
1
2
0
1
0
3
0
0
0
0
0
0
0
3
5
2
0
0
0
0
0
3
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
2
2
0
2
0
1
1
1
2
0
2
0
2
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
3
0
1
0
1
0
0
2
2
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
3
1
1
1
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
3
1
0
1
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
2
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
11
0
0
1
0
3
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
3
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
1
0
1
0
2
0
0
0
0
1
1
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
2
0
0
1
0
2
3
0
0
0
0
0
1
2
0
0
1
0
2
0
0
0
0
0
2
0
2
2
0
0
0
0
2
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
1
2
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
2
1
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
1
0
2
3
0
0
0
0
0
0
0
0
0
0
1
0
4
0
2
1
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
4
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
2
1
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
4
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
1
0
2
0
2
0
0
1
0
0
0
0
3
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
1
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
2
0
1
0
0
1
0
0
5
1
5
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
1
0
0
0
0
0
1
0
2
2
1
0
0
0
0
2
3
2
1
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
3
1
0
0
0
0
2
0
6
2
0
0
0
0
0
1
1
0
0
1
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
1
0
0
2
1
0
0
0
3
0
0
0
3
0
0
0
0
0
0
0
1
1
0
1
0
0
0
3
0
0
0
0
0
3
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
1
0
2
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
3
0
0
0
0
0
0
0
1
1
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
3
0
0
0
0
0
0
0
0
0
2
0
2
0
4
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
2
1
0
0
0
0
0
0
0
1
2
1
2
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
4
0
3
0
0
0
0
2
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
8
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
3
0
0
6
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
1
1
0
2
2
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
2
2
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
1
1
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
1
4
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
6
2
0
0
0
1
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
20
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
2
1
0
0
0
1
0
0
2
1
1
1
0
0
0
0
0
1
0
0
0
0
0
2
0
4
0
0
0
1
0
0
0
0
0
2
0
1
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
3
0
0
0
0
0
0
1
0
0
0
0
1
2
1
0
0
0
1
2
4
0
0
1
0
0
0
3
0
2
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
3
0
0
0
0
0
0
1
2
0
0
0
0
2
2
0
0
1
5
0
1
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
1
0
2
0
0
0
0
2
1
2
0
1
0
0
0
0
0
0
1
1
0
0
0
0
2
0
2
0
0
0
0
0
0
1
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
2
0
0
1
0
0
0
3
2
0
0
1
0
0
0
1
0
0
0
0
0
1
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
1
0
0
2
0
0
5
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
3
0
0
0
0
1
2
1
8
0
0
0
0
0
0
0
1
4
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
1
0
0
2
0
0
1
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
2
1
0
1
0
3
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
2
0
2
5
2
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
2
2
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
4
0
2
0
0
0
2
0
0
2
0
1
3
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
1
0
1
0
3
0
3
0
0
0
0
0
0
0
0
0
0
0
6
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
2
0
2
0
0
0
1
0
0
3
6
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
4
0
0
1
2
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
2
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
5
0
0
2
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
1
0
0
0
0
5
0
1
0
3
0
0
0
0
0
1
0
0
2
1
0
0
0
2
1
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
2
1
0
0
3
0
0
0
2
0
0
0
0
2
0
0
0
1
0
2
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
2
0
2
1
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
4
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
2
1
0
1
0
0
0
2
0
0
0
0
4
0
0
2
1
0
0
2
0
0
1
0
0
1
0
4
0
1
0
0
0
1
0
1
2
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
4
0
0
0
0
2
0
0
0
0
2
2
0
0
0
5
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
2
3
0
0
0
0
2
0
0
7
0
2
0
0
0
0
0
0
1
0
3
0
3
4
0
0
1
0
0
1
0
0
0
0
1
3
0
0
2
0
0
0
0
2
0
0
0
2
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
1
2
2
0
1
0
0
0
0
0
2
2
0
2
0
0
0
0
1
0
2
3
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
4
0
0
0
0
1
1
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
5
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
4
0
1
0
0
0
0
1
0
0
0
0
0
3
0
0
1
1
2
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
5
0
0
2
0
0
0
0
0
0
0
0
0
0
5
1
0
0
0
0
0
1
0
3
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
1
0
0
1
1
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
5
0
0
1
0
0
0
2
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
1
0
2
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
1
2
0
0
0
0
0
0
0
1
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
4
0
0
1
7
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
4
4
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
5
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
6
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
2
0
2
0
0
1
0
0
3
0
0
0
0
3
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
2
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
2
0
0
1
0
5
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
2
0
0
0
2
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
8
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
3
0
0
0
2
1
0
0
0
0
2
2
0
0
0
2
0
0
2
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
1
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
2
0
0
0
0
2
4
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
13
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
3
0
0
3
0
0
0
1
0
1
0
0
2
0
0
0
2
1
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
2
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
1
1
1
3
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
2
1
0
0
0
0
2
0
0
0
0
2
3
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
2
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
2
1
3
0
2
0
0
0
0
1
1
2
0
0
2
0
0
1
0
0
0
0
0
0
2
2
0
2
0
2
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
2
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
1
1
2
0
2
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
2
0
2
0
2
0
1
2
0
0
0
0
1
0
0
0
1
0
2
2
1
1
2
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
2
3
0
0
0
0
0
0
0
4
2
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
1
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
1
0
0
0
0
2
2
0
0
0
1
0
0
0
2
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
6
0
0
1
0
2
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
3
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
2
2
0
0
0
1
1
2
1
1
0
1
0
2
0
6
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
4
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
1
0
2
0
1
0
0
1
1
0
0
0
0
0
0
0
1
1
0
2
0
0
0
3
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
4
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
3
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
1
1
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
1
2
0
0
4
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
4
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
2
0
1
1
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
3
1
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
1
1
0
1
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
1
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
2
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
2
0
0
0
0
0
2
1
0
0
0
0
0
0
2
1
3
0
0
1
0
1
0
0
12
0
0
2
0
2
0
0
0
0
0
3
0
2
0
0
0
1
2
0
0
0
0
1
0
0
0
0
1
0
2
0
0
2
0
0
2
2
0
0
0
0
2
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
2
0
0
0
0
1
0
1
3
0
2
1
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
2
2
0
3
2
0
3
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
3
0
0
1
1
0
0
2
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
4
0
0
2
0
3
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
2
4
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
2
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
1
1
0
1
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
2
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
3
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
2
0
0
1
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
2
1
3
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
2
2
0
0
2
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
1
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
3
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
2
0
0
1
1
0
0
0
2
1
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
2
2
2
2
0
4
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
3
0
2
2
1
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
5
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
3
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
2
1
0
1
1
0
0
0
0
0
0
0
0
3
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
5
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
2
0
0
1
1
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
1
1
2
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
2
0
0
2
0
0
1
0
0
0
2
0
0
0
0
1
0
3
1
1
0
2
1
0
0
0
1
2
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
3
0
0
1
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
10
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
2
1
0
0
0
1
1
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
1
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
1
0
2
0
3
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
1
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
3
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
2
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
4
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
4
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
2
0
0
2
1
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
2
0
0
0
0
1
2
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
2
0
0
2
2
0
1
0
0
2
0
0
0
0
0
0
1
0
1
3
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
1
1
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
3
0
0
0
0
1
1
2
0
1
1
3
0
1
2
0
0
0
0
3
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
3
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
7
0
0
0
0
1
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
1
0
2
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
2
0
0
1
0
0
0
2
0
2
1
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
2
2
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
2
0
0
0
0
0
1
0
0
1
2
0
0
2
3
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
1
0
3
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
1
1
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
2
0
0
1
0
0
0
0
2
0
0
0
0
0
3
0
3
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
3
0
1
0
1
0
0
0
0
1
0
1
0
0
2
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
1
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
2
0
1
1
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
2
1
1
2
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
1
0
1
1
0
2
0
0
1
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
2
0
0
1
0
2
1
0
0
0
0
0
0
0
0
6
4
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
3
0
2
2
0
3
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
1
0
0
2
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
4
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
3
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
1
2
0
0
2
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
1
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
1
1
1
2
0
0
2
0
0
1
0
0
4
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
2
0
0
1
1
0
1
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
10
0
0
0
0
3
0
2
0
0
1
0
0
0
0
2
2
0
0
0
0
1
0
1
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
1
0
3
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
2
1
1
2
0
0
0
0
0
0
2
0
1
2
0
3
2
1
0
0
2
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
2
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
4
0
0
0
0
2
0
0
2
0
0
2
9
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
1
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
1
1
0
0
0
0
0
0
2
2
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
2
0
0
0
0
2
0
0
0
2
0
1
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
1
0
0
0
2
0
5
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
1
0
1
0
0
0
1
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
4
0
1
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
5
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
2
3
0
0
0
0
0
1
2
0
0
0
0
2
1
0
0
1
0
0
1
0
3
0
0
0
0
5
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
2
1
0
0
0
0
1
0
0
0
1
0
3
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
2
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
1
1
1
8
0
0
0
0
1
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
8
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
1
0
0
0
7
2
0
0
0
0
3
0
0
2
0
3
1
2
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
2
7
0
0
0
0
0
1
0
0
2
0
2
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
2
5
0
0
0
0
0
0
2
0
0
1
1
0
0
4
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
3
0
1
0
0
0
1
0
1
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
2
2
0
1
0
0
1
0
0
0
0
2
0
1
0
2
4
0
0
0
0
1
4
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
1
1
1
1
0
0
1
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
2
0
0
1
2
0
0
0
0
0
1
2
0
0
0
0
0
0
3
2
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
1
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
3
2
0
4
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
1
1
0
0
1
0
0
2
0
2
0
0
0
1
1
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
1
0
0
0
0
1
0
0
2
0
0
0
0
3
0
0
0
0
0
0
2
0
0
1
0
0
0
2
2
0
1
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
3
0
0
1
0
0
0
2
3
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
1
0
0
0
2
1
0
0
0
1
0
0
0
1
0
0
2
1
2
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
2
0
1
0
0
2
0
0
2
2
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
1
1
3
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
2
0
0
3
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
1
0
1
3
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
7
1
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
1
0
7
2
0
0
0
3
0
0
2
0
2
2
1
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
2
0
0
2
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
3
0
0
0
1
1
0
0
0
0
1
0
1
3
0
0
0
0
0
3
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
2
0
0
1
0
2
0
0
0
0
0
1
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
2
1
0
0
1
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
1
4
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
2
0
0
0
2
6
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
2
0
0
1
2
0
0
0
0
0
1
1
0
4
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
2
1
1
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
5
0
0
0
0
1
0
0
0
1
0
0
0
0
0
11
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
2
0
1
0
0
3
1
0
0
0
0
1
0
1
0
0
1
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
2
1
0
0
3
0
0
0
0
2
0
0
2
2
6
0
2
0
0
0
0
0
1
0
0
0
1
2
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
3
0
0
0
0
0
0
2
0
2
0
0
4
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
3
0
0
0
2
0
0
0
2
0
1
0
3
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
3
0
0
2
0
2
0
2
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
1
2
0
0
0
2
2
0
2
0
1
0
0
1
2
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
5
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
2
1
0
0
1
2
0
0
2
1
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
4
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
2
0
0
1
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
5
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
2
0
3
0
0
1
0
0
2
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
1
2
0
0
1
1
0
2
0
2
2
1
0
2
1
0
0
0
0
1
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
3
1
0
0
0
1
2
0
0
1
0
2
2
2
0
0
0
4
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
3
1
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
1
0
1
2
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
5
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
3
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
6
0
0
0
1
2
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
2
2
0
0
1
0
0
0
0
0
0
0
0
2
0
2
1
0
0
2
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
2
1
1
2
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
2
2
0
0
2
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
3
0
2
0
0
0
3
0
0
0
0
0
0
0
2
2
0
1
0
0
0
2
0
0
0
2
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
2
0
0
2
2
0
2
1
1
0
0
0
0
0
2
0
2
0
0
0
0
2
2
0
0
0
1
0
0
2
1
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
3
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
1
2
1
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
2
0
0
0
2
0
0
0
0
2
2
0
0
2
0
0
0
3
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
2
0
2
0
0
0
1
0
1
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
2
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
2
0
0
0
4
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
2
0
0
2
1
0
2
1
7
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
3
0
1
0
1
2
3
0
0
0
2
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
3
0
2
1
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
1
3
0
0
0
0
0
2
0
0
0
1
0
1
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
3
0
0
0
0
2
0
0
0
0
1
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
5
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
1
0
0
2
0
1
1
1
1
0
0
0
2
0
0
0
0
0
2
1
0
1
0
0
1
0
0
2
1
2
2
1
0
1
0
0
0
0
2
0
0
2
2
0
0
1
0
0
0
1
0
0
2
2
0
0
2
0
1
1
0
0
0
1
0
0
0
0
2
1
0
1
2
2
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
5
3
2
0
1
0
0
4
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
1
2
0
1
0
1
0
0
3
0
4
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
3
0
0
2
2
0
3
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
1
1
0
0
0
0
0
3
0
0
3
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
1
0
0
0
0
0
0
0
2
1
1
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
1
0
1
1
0
0
0
0
0
0
2
0
0
4
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
1
0
0
2
0
2
0
0
0
0
1
2
0
2
0
0
2
4
1
0
0
0
0
4
0
0
0
1
0
0
0
1
0
3
2
1
0
0
0
2
1
1
1
0
0
0
1
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
1
0
2
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
1
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
2
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
3
0
0
0
0
0
0
2
0
0
1
1
6
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
1
3
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
2
0
0
0
2
0
2
4
1
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
4
0
2
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
2
1
2
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
1
2
1
0
4
0
0
0
1
0
2
0
0
3
1
0
0
0
1
0
2
0
0
1
0
0
0
2
0
0
0
0
1
0
1
0
0
1
2
0
1
2
0
0
2
0
0
0
1
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
8
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
1
0
1
0
0
0
0
0
3
0
0
0
3
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
2
1
2
0
2
1
0
3
0
2
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
1
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
3
2
1
0
0
0
2
1
3
0
0
0
2
0
2
0
0
0
0
2
0
1
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
4
2
2
2
0
0
12
0
0
0
0
2
0
1
1
0
0
0
0
4
1
1
2
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
3
0
0
0
2
0
0
1
1
0
0
0
0
2
1
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
2
0
1
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
1
0
1
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
2
0
0
2
1
0
0
0
1
0
1
0
0
0
0
2
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
1
2
0
0
0
0
1
4
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
1
24
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
2
0
0
0
2
1
0
1
0
0
0
0
0
0
0
3
2
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
2
0
0
0
7
0
0
0
0
0
0
3
0
0
1
1
0
0
0
0
2
2
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
2
1
0
0
8
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
1
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
4
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
3
0
1
0
1
0
0
1
0
4
0
1
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
1
1
4
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
1
0
2
0
1
0
0
0
0
1
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
2
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
3
0
0
1
1
0
0
0
0
1
0
2
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
4
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
2
2
0
0
5
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
3
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
2
2
0
3
0
0
0
0
5
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
2
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
3
1
0
4
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
3
2
1
0
0
2
1
1
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
2
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
8
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
3
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
1
0
0
0
5
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
2
1
2
1
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
2
2
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
1
0
0
1
0
0
0
2
0
0
0
0
2
0
1
0
0
1
0
0
2
1
2
2
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
2
1
2
1
0
0
8
0
0
1
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
1
0
2
2
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
1
3
0
0
0
0
0
0
1
2
0
0
0
0
0
5
0
1
5
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
1
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
2
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
3
0
2
0
0
0
0
0
1
0
1
2
2
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
2
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
2
1
2
0
0
2
0
0
2
1
0
1
0
0
0
0
0
0
0
2
0
2
2
0
0
2
0
0
0
0
1
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
1
0
0
0
2
0
3
0
0
2
0
0
3
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
5
0
0
0
0
1
2
2
0
2
0
0
0
0
0
0
0
0
6
0
0
0
1
0
0
0
0
0
0
0
2
0
1
3
2
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
1
2
0
0
0
2
0
1
0
1
0
0
0
0
0
2
1
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
3
0
8
0
0
0
1
0
0
0
0
0
1
0
2
0
0
1
0
1
0
0
2
0
0
3
0
0
0
2
0
0
0
0
0
3
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
2
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
4
1
0
0
0
0
0
0
0
0
0
0
2
0
2
1
2
0
0
0
2
1
0
0
0
0
0
2
2
0
0
5
1
0
0
0
0
0
0
0
0
0
2
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
1
0
0
3
2
1
0
0
2
0
2
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
1
3
2
0
0
0
0
1
0
0
2
3
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
10
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
1
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
3
3
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
2
1
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
1
0
1
0
3
0
1
1
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
3
2
0
2
0
0
0
2
0
0
0
0
0
1
2
2
0
1
0
0
0
2
0
1
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
2
0
3
0
1
1
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
1
4
0
0
0
2
1
0
0
0
0
0
1
0
0
1
2
1
2
4
2
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
4
0
0
1
0
0
0
1
0
2
0
0
1
2
0
0
0
0
0
1
0
0
0
0
1
1
0
0
2
0
0
0
2
2
1
0
1
0
0
0
0
2
3
0
4
6
0
0
0
1
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
3
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
1
0
1
1
1
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
2
1
2
1
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
2
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
2
1
0
1
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
3
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
1
4
0
0
1
0
0
3
0
0
0
0
1
0
1
0
0
2
0
1
1
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
3
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
2
2
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
1
0
1
1
0
0
2
0
0
0
1
2
0
0
0
4
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
5
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
3
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
2
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
5
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
3
0
0
0
1
0
1
1
2
0
1
0
2
3
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
2
3
0
0
0
0
1
0
0
3
3
1
0
0
0
0
0
1
0
2
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
2
0
0
0
1
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
4
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
4
0
0
2
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
1
2
2
2
0
0
5
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
3
0
0
0
3
2
0
0
1
1
3
0
0
0
2
0
0
0
0
2
0
1
2
0
0
3
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
1
0
1
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
2
1
2
0
0
0
4
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
1
0
2
0
2
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
4
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
2
0
1
1
0
0
0
3
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
2
0
0
2
0
2
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
3
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
1
0
1
0
0
0
2
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
5
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
2
0
1
0
2
4
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
1
0
0
2
2
2
0
0
1
0
0
0
0
0
2
0
0
0
1
1
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
2
0
1
0
0
0
5
2
0
2
2
0
1
2
0
0
0
0
0
1
1
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
6
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
2
0
0
1
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
8
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
1
0
0
0
2
0
0
2
0
1
2
0
0
0
5
1
0
2
0
0
1
0
0
0
0
0
9
0
0
1
0
2
0
3
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
3
0
0
1
0
0
2
0
2
3
5
1
0
0
0
0
0
0
0
1
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
3
2
4
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
1
0
1
4
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
3
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
1
0
1
0
0
0
0
1
0
0
1
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
1
0
0
3
0
1
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
0
1
0
2
1
0
0
0
6
0
1
0
0
2
4
0
0
0
2
0
0
1
0
0
0
5
1
0
0
0
1
4
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
2
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
3
0
4
0
0
0
0
0
0
1
0
0
1
2
0
1
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
6
2
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
2
1
1
0
2
0
0
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
3
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
2
0
2
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
1
0
13
2
0
0
0
0
3
0
0
0
1
3
0
0
1
0
0
2
0
0
4
0
0
0
0
0
1
0
4
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
1
0
0
0
1
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
3
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
10
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
2
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
1
1
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
1
0
0
1
0
0
0
0
2
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
1
0
0
0
1
0
1
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
2
1
2
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
4
1
0
2
2
3
0
0
0
0
0
0
2
2
1
0
0
0
0
4
0
2
0
1
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
2
1
0
1
0
2
0
2
0
0
0
1
0
0
1
0
0
1
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
4
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
1
0
2
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
3
2
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
2
3
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
1
5
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
3
0
1
0
0
0
0
0
0
10
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
4
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
1
3
1
0
0
0
2
0
0
0
0
2
1
0
4
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
2
1
2
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
2
0
2
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
2
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
1
1
0
2
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
1
0
3
0
0
2
0
0
1
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
7
0
0
0
0
2
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
2
2
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
1
1
1
0
0
0
0
0
2
0
0
3
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
3
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
3
1
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
6
1
0
0
2
0
1
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
1
4
0
0
2
0
0
0
2
0
2
0
0
2
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
2
2
2
2
1
1
3
2
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
3
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
3
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
1
5
0
0
0
1
1
0
0
0
5
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
1
1
1
0
0
0
1
0
2
0
0
0
0
0
0
2
1
1
0
0
0
1
0
0
0
0
0
0
0
0
2
1
1
1
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
4
2
0
0
0
2
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
3
0
0
0
1
0
0
0
0
2
1
1
0
1
1
0
1
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
2
0
0
0
0
0
4
1
0
1
1
1
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
2
0
6
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
1
0
0
0
1
0
3
0
0
0
3
0
0
0
0
1
0
0
0
1
1
1
1
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
3
0
0
0
1
1
0
0
1
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
5
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
6
0
0
0
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
2
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
4
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
1
0
0
1
4
1
0
0
5
1
0
0
2
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
1
0
0
0
0
3
0
0
0
0
0
3
0
0
0
0
0
2
3
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
2
1
0
2
0
0
0
1
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
1
0
0
0
0
2
2
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
2
2
1
0
0
0
3
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
3
0
0
0
0
0
0
2
0
2
4
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
2
0
0
0
0
1
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
2
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
1
2
0
0
1
3
0
0
0
0
4
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
1
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
3
0
0
0
0
0
4
0
0
0
0
0
0
4
0
0
0
5
0
0
0
0
0
0
0
0
0
0
2
0
0
0
4
1
2
0
0
0
0
1
2
0
0
1
1
0
0
0
0
0
0
0
1
2
0
0
2
0
0
2
1
0
0
1
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
1
2
1
0
1
0
0
2
0
0
0
2
0
0
2
0
1
1
0
0
2
0
0
0
4
0
2
0
0
0
1
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
2
2
0
1
0
0
0
0
1
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
5
0
0
0
2
0
0
0
0
1
2
1
1
0
2
0
0
0
0
0
0
2
0
0
1
1
2
0
0
0
0
0
0
2
0
0
0
2
0
0
1
1
0
0
0
5
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
1
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
3
0
0
0
0
2
0
0
0
0
1
0
2
0
1
0
0
0
9
0
3
3
0
2
2
2
0
1
0
0
0
0
2
1
0
0
1
1
0
0
2
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
3
0
1
2
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
3
2
0
1
1
1
1
0
1
0
0
0
3
0
0
4
0
1
0
0
0
0
0
1
0
1
0
2
0
0
0
0
2
0
0
1
0
1
0
3
1
0
0
0
0
0
0
2
0
0
0
2
0
0
2
2
0
0
0
1
0
1
1
0
0
1
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
2
2
1
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
1
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
1
0
0
2
0
0
1
1
0
0
0
0
2
0
1
2
0
0
3
1
1
0
0
0
0
0
0
2
0
0
0
0
2
1
0
1
0
0
2
0
2
0
0
0
0
0
1
1
0
0
0
0
1
0
1
2
2
2
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
3
0
5
0
1
1
0
1
2
2
2
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
2
0
2
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
3
0
0
2
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
2
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
1
2
0
0
0
1
0
2
0
0
0
1
2
2
0
0
0
9
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
1
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
5
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
2
0
0
0
0
2
0
0
1
1
0
0
3
1
2
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
1
0
0
0
3
0
0
2
1
3
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
4
0
1
0
0
0
0
0
2
2
0
0
2
0
0
1
2
0
2
1
0
6
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
1
0
2
1
0
0
0
0
0
0
1
0
2
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
3
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
24
0
0
1
0
0
3
0
0
0
2
1
0
0
2
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
2
0
0
0
0
2
2
2
0
0
2
0
1
0
1
0
2
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
2
2
3
2
0
1
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
1
0
0
0
0
0
2
1
0
0
2
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
3
3
1
0
0
3
0
0
0
0
0
5
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
1
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
5
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
1
0
1
1
0
0
1
0
0
0
1
2
0
3
2
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
2
0
0
1
3
1
2
0
1
0
2
0
1
0
0
0
1
0
1
3
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
1
1
1
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
1
0
1
0
0
0
2
1
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
3
1
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
1
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
6
0
2
0
1
5
0
2
0
0
2
0
0
0
0
0
0
0
1
1
0
1
0
2
0
1
0
0
1
1
0
0
0
2
0
2
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
2
0
1
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
5
0
1
0
0
0
1
0
0
0
2
1
0
0
0
0
1
10
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
2
0
0
3
0
0
0
0
0
1
2
0
0
1
0
0
0
2
2
1
2
0
1
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
6
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
2
0
1
0
0
0
0
1
0
0
0
1
0
3
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
1
1
0
0
1
0
0
3
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
2
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
1
1
1
0
0
2
0
0
0
0
0
1
3
0
0
2
1
0
0
3
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
2
0
0
0
3
0
0
1
0
0
2
0
2
0
0
0
0
2
0
2
0
0
2
0
0
2
1
0
1
1
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
4
0
0
1
0
0
0
0
3
0
2
0
0
0
0
1
0
3
0
0
0
0
0
0
0
1
0
1
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
2
0
8
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
4
0
1
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
4
0
1
0
0
0
0
2
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
1
1
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
1
3
0
2
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
16
1
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
2
0
2
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
6
3
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
2
0
0
0
0
2
0
1
1
0
0
1
0
0
0
0
1
0
1
3
0
0
0
0
0
0
1
0
0
0
2
2
0
1
0
0
1
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
3
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
3
0
1
2
0
0
2
1
1
0
0
2
1
0
0
0
7
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
3
0
0
0
1
2
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
3
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
3
0
0
1
0
2
2
0
0
0
0
0
0
3
0
0
0
3
2
0
1
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
3
0
0
0
2
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
2
1
0
1
6
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
2
0
2
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
1
0
0
1
2
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
1
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
4
0
0
3
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
4
0
0
2
0
0
2
1
0
0
0
2
2
0
0
0
0
0
1
1
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
2
0
2
0
0
1
0
3
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
1
0
0
0
1
1
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
1
0
0
3
0
0
2
0
2
0
0
0
1
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
3
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
4
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
1
3
0
5
0
0
0
1
2
0
0
0
0
2
0
1
1
0
3
1
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
2
0
2
2
0
0
0
2
0
2
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
5
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
2
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
2
0
5
0
0
3
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
2
8
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
2
0
1
1
0
0
2
0
0
0
0
1
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
2
0
2
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
4
0
0
0
0
0
0
0
2
0
2
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
2
0
1
0
1
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
10
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
1
2
0
0
0
0
2
0
0
0
1
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
4
0
0
0
2
0
0
1
0
0
0
2
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
1
2
0
0
0
0
0
3
0
0
0
2
0
0
3
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
1
2
1
0
1
0
0
0
2
0
0
1
0
2
2
0
2
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
2
0
2
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
2
1
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
2
0
1
0
0
0
0
1
6
0
1
0
0
0
2
0
0
1
0
2
2
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
4
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
1
0
0
4
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
3
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
21
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
2
4
0
1
2
0
1
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
1
0
2
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
1
2
2
1
1
0
2
0
0
2
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
1
9
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
2
3
0
0
0
0
0
0
0
1
1
1
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
3
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
2
1
0
1
0
0
0
7
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
1
0
0
1
1
2
0
0
0
1
0
0
2
0
2
0
0
0
0
2
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
4
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
1
0
0
0
16
0
1
0
2
0
3
0
6
1
2
0
3
0
4
0
0
1
0
2
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
4
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
1
0
1
1
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
2
0
0
3
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
1
0
0
0
1
2
0
0
0
3
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
1
1
0
0
0
0
0
1
0
2
0
1
0
2
5
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
1
2
2
0
1
5
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
1
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
2
1
0
0
0
0
0
0
1
0
0
0
1
0
0
3
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
2
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
4
2
2
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
2
0
1
5
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
3
0
3
0
4
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
2
0
0
0
3
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
2
1
2
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
6
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
2
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
2
0
0
0
1
0
0
0
1
0
2
2
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
1
0
2
0
0
0
0
1
1
2
2
0
0
3
0
0
0
0
2
1
2
0
0
0
0
1
3
0
0
2
0
2
0
1
1
0
0
2
0
0
0
0
0
3
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
4
0
0
1
0
0
2
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
2
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
4
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
2
0
0
1
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
3
0
0
0
1
0
0
2
1
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
2
0
1
3
2
1
0
0
0
2
0
1
1
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
1
0
4
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
3
2
2
0
0
0
0
4
1
1
0
1
1
2
0
0
0
1
2
0
0
2
0
0
0
0
0
2
0
0
0
0
2
1
2
1
0
0
2
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
1
0
0
2
1
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
3
2
0
1
2
0
2
0
1
0
0
2
0
0
1
0
0
0
0
0
1
2
3
0
0
0
0
0
0
0
4
1
2
0
0
0
0
1
0
6
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
2
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
9
2
0
1
0
2
1
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
1
0
0
5
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
3
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
3
0
0
2
2
1
0
1
2
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
2
4
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
1
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
3
0
2
0
0
0
0
3
0
0
0
4
4
1
1
0
0
0
0
0
1
0
0
0
3
0
0
0
0
2
0
2
0
0
0
0
1
0
1
0
1
2
4
1
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
4
0
1
0
0
1
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
1
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
2
0
0
0
2
0
2
0
1
0
0
0
0
0
0
2
0
0
1
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
4
0
1
0
1
0
0
1
0
0
6
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
5
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
2
0
0
1
0
0
0
3
0
0
0
0
0
0
1
0
2
0
0
1
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
7
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
2
2
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
2
0
2
0
0
1
2
0
1
1
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
2
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
2
0
0
0
0
3
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
1
0
0
0
1
2
0
0
2
0
0
0
0
2
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
2
0
1
2
0
1
0
0
0
1
0
2
0
0
0
0
2
4
0
0
2
1
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
2
0
1
0
0
0
1
2
0
0
3
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
3
0
0
0
1
3
0
0
0
1
2
0
0
2
0
0
1
1
2
0
0
0
0
0
0
0
0
0
1
0
4
1
0
5
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
3
0
1
0
0
0
0
0
1
0
0
5
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
3
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
9
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
1
1
0
0
0
2
2
2
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
2
0
0
6
1
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
4
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
6
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
3
0
2
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
1
0
5
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
3
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
7
0
2
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
2
0
0
1
1
0
2
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
2
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
2
0
1
3
2
0
0
0
0
0
0
0
0
1
5
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
1
0
2
0
0
1
3
0
0
2
0
1
0
0
2
0
0
0
1
0
0
1
0
1
0
1
0
0
2
2
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
3
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
1
1
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
2
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
4
0
0
0
0
1
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
2
0
0
0
2
0
0
0
0
0
2
1
0
0
0
4
1
2
3
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
1
2
1
0
0
1
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
12
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
3
0
1
1
0
2
0
0
0
0
0
0
1
1
0
1
1
0
2
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
2
2
1
2
0
3
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
3
1
0
0
0
0
0
1
0
0
0
2
0
1
0
2
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
1
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
1
0
0
2
0
1
0
0
0
0
0
2
2
0
3
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
2
2
2
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
7
0
0
0
0
2
1
0
0
0
0
0
6
0
4
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
6
0
1
0
1
2
0
0
0
0
0
0
0
4
0
0
0
1
0
0
5
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
1
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
3
0
1
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
2
0
2
0
0
0
6
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
1
1
2
1
0
0
0
0
0
2
2
0
0
1
0
0
0
1
0
12
0
0
1
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
1
0
2
0
1
0
0
2
0
0
0
2
0
0
0
4
0
5
0
0
0
0
2
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
4
2
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
1
2
3
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
6
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
7
2
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
2
2
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
2
0
0
1
2
0
1
0
0
0
0
4
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
3
2
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
1
2
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
5
0
1
0
0
0
0
0
0
0
2
2
0
4
2
1
0
0
0
0
0
3
0
0
2
0
0
0
0
0
2
2
0
1
2
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
3
0
0
1
0
0
1
0
3
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
2
3
0
0
0
0
5
0
0
0
0
0
2
0
0
0
4
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
2
2
0
4
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
2
2
1
1
0
0
2
3
0
0
0
2
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
2
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
1
1
2
0
1
0
0
4
0
1
0
2
0
0
1
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
8
0
0
0
0
1
0
2
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
1
0
1
3
0
0
0
0
0
0
0
0
0
3
0
1
1
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
2
0
0
0
1
2
0
1
0
0
3
0
0
0
2
0
0
0
2
0
0
0
0
2
1
0
2
0
7
0
0
0
0
2
0
2
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
1
2
1
1
0
2
0
0
0
0
0
1
0
9
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
3
2
0
0
0
1
1
0
0
2
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
2
0
0
0
2
1
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
3
0
1
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
4
0
0
3
0
0
0
1
0
0
0
2
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
2
0
0
2
1
0
2
1
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
5
3
0
0
0
1
0
0
0
0
0
0
2
0
5
0
0
0
0
2
0
0
0
0
2
0
0
1
2
1
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
4
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
2
2
0
2
0
1
1
1
0
0
0
0
1
3
0
0
1
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
10
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
1
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
1
0
3
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
1
6
0
0
1
2
0
0
0
0
2
2
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
2
1
0
0
0
1
0
0
0
0
1
1
0
0
5
0
0
0
0
2
4
5
0
5
0
2
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
2
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
1
0
0
0
5
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
5
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
3
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
1
0
0
0
0
2
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
4
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
2
1
1
1
2
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
4
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
3
2
0
0
0
1
0
1
0
0
0
0
0
0
1
2
0
0
0
1
3
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
1
2
2
0
0
0
4
0
0
0
0
0
4
0
0
1
2
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
5
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
1
0
0
1
0
1
0
6
0
0
0
3
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
1
0
1
2
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
2
1
3
0
0
0
0
1
2
0
8
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
3
0
0
2
0
0
0
1
0
1
0
0
0
1
0
1
3
0
0
1
4
2
0
0
0
2
1
0
0
0
1
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
3
0
0
3
3
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
1
0
5
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
7
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
1
0
0
3
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
5
0
0
0
1
5
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
1
1
0
0
2
0
0
1
0
2
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
4
0
0
1
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
7
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
4
0
1
2
1
0
0
0
0
3
0
0
2
0
0
0
1
0
3
0
1
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
2
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
2
0
1
2
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
2
3
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
2
0
1
0
0
10
0
0
0
0
0
0
0
0
2
2
2
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
4
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
2
0
0
1
1
3
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
5
0
2
0
0
2
2
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
1
5
0
1
3
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
1
0
0
1
0
0
2
0
0
0
0
1
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
1
1
0
4
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
2
0
0
4
0
0
2
1
1
1
0
0
0
0
0
6
2
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
7
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
3
2
0
0
2
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
2
2
0
1
0
0
1
0
1
0
1
2
2
0
0
0
0
0
2
0
0
0
0
0
0
1
4
0
0
0
2
0
1
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
4
0
0
0
1
0
2
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
1
1
0
0
1
0
0
2
4
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
1
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
1
1
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
2
1
1
0
0
0
0
1
0
0
4
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
2
0
0
2
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
2
2
0
1
1
0
0
0
1
0
0
2
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
1
1
0
2
1
0
2
0
0
0
3
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
4
0
1
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
1
0
2
0
0
1
0
1
1
0
4
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
3
1
1
0
0
1
0
0
0
4
0
0
1
0
0
0
0
0
1
0
0
0
2
1
0
0
1
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
3
2
0
0
2
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
2
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
1
6
0
5
1
1
0
0
2
0
0
4
0
0
0
1
1
0
0
0
4
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
3
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
2
0
0
1
0
1
0
0
2
0
0
0
0
0
4
6
1
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
1
1
0
0
1
0
0
0
0
3
0
1
2
0
0
2
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
1
2
0
0
0
0
2
0
1
0
0
2
0
0
0
0
1
1
0
0
3
0
0
0
0
0
1
2
0
1
0
0
1
0
0
0
0
1
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
4
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
1
2
2
0
0
1
1
1
1
0
0
2
0
0
1
0
0
0
1
0
0
1
0
2
0
2
0
2
0
3
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
1
1
0
0
0
0
0
1
1
0
2
0
2
0
2
0
0
0
2
2
2
0
0
2
0
1
0
2
0
0
0
0
0
5
0
0
0
0
1
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
1
0
2
2
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
2
2
0
1
0
0
1
0
0
0
1
2
1
0
0
0
0
0
1
0
0
0
2
2
0
0
1
0
0
2
2
0
0
0
0
7
6
0
0
0
3
0
0
0
0
6
1
0
0
0
0
2
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
3
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
1
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
4
1
0
0
1
0
0
2
0
0
0
0
0
0
0
2
1
0
0
3
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
1
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
2
0
0
0
5
0
0
0
0
0
0
4
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
1
9
0
2
1
0
1
2
0
0
3
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
1
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
2
1
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
2
0
2
0
0
2
0
1
0
0
0
0
0
0
1
1
1
1
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
1
1
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
5
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
2
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
3
0
0
6
0
0
2
0
1
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
2
1
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
1
2
1
0
0
0
2
0
0
4
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
1
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
5
0
4
0
0
3
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
1
0
0
1
0
0
1
0
3
4
1
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
1
1
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
3
1
0
0
0
0
2
0
1
3
0
0
2
1
0
0
7
2
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
2
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
1
1
1
1
1
0
0
0
1
0
0
0
2
0
0
2
0
1
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
3
0
0
0
0
0
1
0
0
0
0
2
1
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
6
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
1
0
1
1
1
1
0
0
0
0
0
2
0
3
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
2
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
2
0
1
0
1
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
7
0
0
2
2
0
1
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
3
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
2
1
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
3
0
0
0
0
0
2
0
2
0
0
0
0
0
1
2
0
3
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
1
4
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
1
0
1
0
0
0
0
1
2
0
0
0
0
2
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
4
2
0
2
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
1
1
1
0
0
0
0
0
0
3
0
0
2
3
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
1
0
1
0
0
0
3
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
1
3
0
0
0
0
3
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
1
0
0
0
1
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
3
0
1
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
3
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
5
0
0
0
1
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
2
3
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
5
0
0
2
0
0
0
0
0
0
0
2
0
0
4
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
6
0
1
0
0
0
0
3
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
3
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
1
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
2
0
1
0
0
0
0
0
1
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
1
0
0
2
1
2
0
2
0
3
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
2
2
2
0
0
0
0
1
0
0
2
0
1
0
5
1
1
0
2
0
1
2
0
1
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
1
0
0
0
0
1
0
1
0
0
0
2
0
2
1
0
3
0
0
0
0
2
1
0
0
0
6
2
0
0
0
0
2
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
7
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
1
0
6
0
0
0
0
2
2
21
0
0
0
0
3
3
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
1
0
1
1
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
5
0
2
0
0
0
1
0
0
0
0
1
0
0
0
1
1
1
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
2
1
0
0
0
1
0
2
0
0
1
0
0
0
2
0
0
2
0
0
0
0
1
2
2
1
0
0
0
3
0
0
0
4
0
0
0
0
0
0
1
0
0
1
2
0
2
0
0
0
0
0
1
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
3
1
0
0
0
0
0
0
4
3
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
2
0
0
2
0
0
5
0
0
0
0
0
0
2
0
0
0
4
0
0
2
2
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
2
1
0
0
3
1
0
0
2
0
1
0
0
0
0
0
0
2
0
3
0
0
0
0
2
0
0
0
0
2
0
0
1
0
1
0
2
0
0
2
0
1
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
3
2
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
2
0
5
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
1
0
1
0
0
0
0
2
0
1
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
1
0
0
2
2
0
3
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
2
0
1
2
2
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
3
0
0
0
0
0
0
0
1
2
0
0
3
1
3
0
0
0
0
0
0
1
2
0
0
0
0
1
2
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
2
0
1
1
0
0
3
0
2
0
0
0
0
1
1
0
0
1
1
0
4
2
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
2
1
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
2
1
1
1
1
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
36
1
0
0
0
0
0
0
0
3
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
2
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
3
2
0
0
0
1
0
2
2
1
0
0
0
0
1
0
2
0
0
2
1
0
0
2
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
1
2
0
0
0
1
0
0
1
1
0
2
0
0
1
0
2
1
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
3
0
1
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
4
0
1
0
2
0
2
1
1
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
1
0
0
0
0
0
3
0
0
0
1
5
0
0
0
2
0
0
0
2
0
0
0
1
0
1
0
0
0
4
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
6
1
0
0
0
0
11
0
0
0
0
0
0
0
0
1
6
0
0
0
5
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
1
0
9
0
2
2
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
6
0
0
1
0
0
0
0
0
1
0
3
0
0
0
0
0
3
0
0
2
2
1
0
0
0
0
1
2
0
0
0
1
3
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
4
0
1
2
0
2
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
4
2
4
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
2
0
1
0
0
0
0
0
0
0
3
7
0
1
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
10
0
0
2
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
3
1
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
3
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
2
0
0
0
0
0
1
2
0
1
0
0
0
0
0
1
1
0
0
0
0
0
3
0
2
0
1
1
0
0
0
0
0
2
4
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
1
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
1
0
3
1
0
0
0
0
3
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
7
0
0
0
1
1
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
2
2
0
0
0
2
0
0
0
0
1
0
0
0
3
0
2
0
0
0
0
0
0
1
0
1
0
0
1
0
0
2
0
0
0
2
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
1
1
0
0
0
0
2
1
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
1
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
1
0
0
2
1
0
0
2
0
0
0
0
0
0
3
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
1
2
3
2
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
3
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
4
0
1
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
3
1
1
6
0
2
0
0
2
0
0
0
0
0
2
0
4
0
1
6
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
3
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
1
1
0
1
0
2
1
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
3
0
0
2
0
5
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
2
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
3
0
1
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
3
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
3
0
0
1
0
2
0
2
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
1
2
0
0
0
0
0
2
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
6
0
1
1
0
0
0
0
1
0
1
0
0
0
2
0
0
1
2
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
2
3
0
0
2
0
2
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
3
1
0
2
0
2
1
0
0
0
0
0
0
0
0
0
1
2
1
2
1
0
0
0
0
0
0
0
0
1
0
0
2
2
2
2
0
0
0
0
0
0
2
0
1
0
3
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
2
0
1
2
2
0
1
1
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
4
3
0
0
0
0
0
0
0
3
0
2
1
4
0
0
0
0
8
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
1
0
0
0
1
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
3
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
2
0
1
0
0
0
0
0
0
0
0
0
2
2
1
0
1
0
0
0
0
0
0
1
0
2
2
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
2
0
2
0
3
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
5
1
0
3
0
0
0
0
0
0
2
2
2
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
1
0
1
2
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
3
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
1
4
0
0
0
0
0
2
1
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
5
1
0
0
2
0
0
0
3
0
0
1
3
0
0
0
1
0
1
2
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
2
0
2
0
0
1
1
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
3
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
5
0
1
1
0
0
0
0
0
1
0
0
2
2
0
2
0
0
0
0
0
3
0
0
3
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
1
2
0
0
2
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
3
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
2
1
0
0
1
0
0
0
2
0
0
0
0
0
1
0
4
1
0
0
0
0
0
3
2
2
0
0
0
0
0
0
2
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
2
0
0
2
0
3
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
3
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
2
0
4
0
0
0
1
2
0
0
0
0
0
1
0
1
1
0
1
0
3
0
1
0
0
0
0
2
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
3
0
2
0
3
0
0
0
0
0
2
0
2
0
0
3
0
0
2
3
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
3
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
4
1
0
0
1
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
2
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
1
0
0
2
0
0
0
2
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
3
0
3
2
2
0
0
0
1
0
2
0
0
0
0
1
0
0
2
1
1
0
0
0
0
4
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
4
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
1
0
2
1
9
1
0
0
0
1
0
0
0
0
0
0
0
0
7
2
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
5
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
5
2
1
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
1
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
2
1
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
4
0
0
0
4
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
2
2
1
2
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
3
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
3
1
1
2
2
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
2
0
0
0
0
3
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
1
0
1
0
1
0
0
0
0
1
2
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
1
0
0
2
1
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
2
0
0
4
1
0
1
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
2
0
0
0
0
0
0
0
4
0
0
2
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
3
0
0
0
0
0
0
1
0
0
1
0
0
2
1
4
1
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
2
0
2
0
2
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
7
1
0
0
3
0
0
0
4
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
3
0
0
0
0
2
2
0
0
2
0
3
0
1
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
1
2
1
0
2
2
0
2
0
1
0
0
0
0
0
2
2
0
0
0
0
1
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
2
2
0
0
2
0
0
0
2
1
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
2
0
0
0
1
0
1
2
0
0
0
0
0
0
1
0
0
2
3
0
0
0
3
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
2
0
0
0
0
1
1
0
0
0
4
0
0
0
1
0
2
2
0
2
0
0
0
0
0
0
0
1
0
0
0
1
3
3
0
0
0
0
2
3
0
1
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
2
0
4
1
0
0
0
0
0
1
1
2
0
0
2
1
1
0
0
0
2
0
0
1
0
3
0
0
0
0
4
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
1
0
3
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
3
0
0
1
0
0
0
0
0
0
0
2
3
0
0
1
0
0
1
0
1
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
5
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
4
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
1
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
3
3
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
2
2
0
0
2
1
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
3
0
0
0
2
0
0
1
1
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
2
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
7
1
0
0
2
0
0
0
0
0
0
1
0
1
0
2
0
0
0
1
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
1
2
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
4
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
5
0
1
4
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
2
0
0
0
0
3
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
2
0
0
0
3
0
0
0
1
0
2
0
0
1
0
0
0
0
3
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
1
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
5
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
1
0
7
0
0
0
0
0
2
0
0
1
0
3
2
0
0
0
0
0
0
2
0
0
1
0
0
2
0
4
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
1
1
2
1
0
1
0
0
2
1
0
1
2
3
0
2
0
1
0
1
0
1
0
0
0
2
0
0
1
0
0
2
1
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
3
2
0
0
0
0
0
0
0
0
3
2
0
0
0
0
1
0
2
0
4
0
0
0
0
0
0
0
1
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
2
1
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
1
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
13
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
1
1
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
2
0
0
2
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
2
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
5
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
3
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
3
1
0
0
2
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
2
2
0
0
2
1
0
0
2
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
2
2
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
1
1
0
1
1
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
4
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
1
0
3
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
2
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
1
0
0
0
0
2
0
0
0
0
0
3
0
0
1
3
1
0
0
1
0
0
0
0
1
1
1
3
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
2
0
0
0
0
1
0
0
0
1
1
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
4
0
0
0
0
1
0
0
0
2
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
4
0
5
0
0
0
0
1
0
2
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
1
2
0
0
0
2
0
1
2
2
0
0
0
0
1
0
0
0
2
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
2
0
0
2
0
1
0
2
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
5
0
1
1
0
0
0
0
0
0
0
1
0
2
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
3
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
3
0
2
0
0
0
2
2
0
0
0
0
1
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
1
1
0
0
1
0
0
0
0
2
0
1
1
0
2
0
2
0
2
0
0
0
0
3
1
0
0
4
0
0
0
0
0
0
0
0
1
0
2
0
1
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
6
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
4
2
1
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
2
3
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
1
0
1
0
0
0
0
2
3
1
0
0
1
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
3
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
1
0
0
1
1
0
0
1
0
0
0
2
3
1
0
0
0
0
0
0
7
0
0
0
0
1
2
2
0
0
0
0
0
0
0
1
3
2
0
2
2
1
0
2
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
1
0
0
0
0
0
2
0
0
2
0
0
2
0
0
1
0
1
1
0
1
0
0
0
1
0
0
0
2
0
0
2
0
1
0
0
0
2
0
2
0
0
0
2
1
0
2
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
1
3
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
1
0
4
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
3
0
0
0
1
1
2
0
2
0
0
0
0
0
0
1
0
0
0
1
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
2
2
2
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
2
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
2
1
0
2
0
0
0
1
0
1
0
0
0
3
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
2
1
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
3
0
1
0
0
0
1
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
2
0
1
0
0
0
1
2
0
1
0
0
2
2
4
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
2
0
1
0
0
0
0
1
2
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
1
0
1
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
7
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
3
0
0
0
2
0
6
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
2
0
0
2
6
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
2
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
3
0
0
0
0
0
0
2
1
0
0
3
1
0
0
0
0
0
0
0
0
1
0
1
0
0
2
1
0
1
0
0
0
0
0
1
0
0
0
1
2
0
0
0
5
0
2
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
2
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
2
6
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
2
0
0
0
0
0
1
0
2
0
0
3
0
0
0
0
2
0
10
0
2
0
0
1
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
3
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
5
1
0
0
0
0
0
0
0
3
1
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
4
0
1
0
2
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
1
1
2
0
1
0
0
0
1
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
2
0
0
1
0
2
0
0
0
0
0
0
2
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
2
1
1
0
0
0
2
1
1
1
1
0
0
0
1
2
0
0
1
0
0
2
0
0
0
0
6
0
0
0
0
3
0
0
1
0
2
0
2
1
6
1
1
0
1
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
2
1
0
0
1
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
1
0
0
0
0
0
0
0
3
0
0
0
0
1
0
2
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
1
0
0
0
0
0
2
0
1
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
2
1
1
2
0
2
0
1
0
0
2
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
1
0
0
0
3
0
2
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
2
1
0
1
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
3
0
0
0
2
0
0
5
0
3
1
1
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
2
1
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
1
0
2
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
2
8
1
0
0
0
1
0
0
0
1
0
0
2
1
0
0
1
0
0
2
3
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
4
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
3
0
0
0
0
0
0
0
0
1
1
0
2
0
0
2
1
0
0
0
0
6
0
0
0
0
0
6
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
4
3
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
9
0
0
0
0
0
0
1
0
3
0
0
0
0
0
1
0
0
2
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
1
10
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
2
1
4
0
0
0
0
0
2
0
0
0
0
0
0
1
0
7
0
0
0
0
0
0
0
2
0
0
0
1
1
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
1
1
2
0
0
0
0
3
1
2
0
0
0
3
0
0
0
2
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
3
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
11
0
0
0
0
0
1
0
0
0
4
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
2
2
0
0
0
0
2
0
4
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
5
0
0
0
0
3
4
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
3
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
1
0
2
0
2
0
0
3
0
0
0
2
0
2
0
0
0
0
6
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
3
0
0
0
2
1
1
2
0
0
0
0
0
0
0
0
7
0
0
1
0
1
2
2
2
0
0
1
1
0
2
0
0
0
4
1
1
1
0
0
2
0
0
0
1
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
1
2
0
1
0
0
0
0
2
0
0
0
0
0
2
1
2
0
0
0
2
0
0
12
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
3
1
0
2
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
2
1
0
0
0
0
0
1
0
1
0
0
0
0
4
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
4
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
1
4
0
0
0
4
0
0
0
0
1
0
1
3
0
0
0
2
1
0
2
0
1
0
0
0
0
0
1
0
0
0
2
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
1
0
1
0
0
0
0
0
2
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
2
0
0
0
0
1
5
0
0
0
0
0
0
2
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
3
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
2
1
2
1
3
0
0
2
0
0
2
0
0
1
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
3
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
4
1
0
0
0
0
0
0
1
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
2
4
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
1
0
0
1
2
3
2
2
0
2
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
1
0
2
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
1
4
0
3
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
1
0
0
0
0
0
3
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
5
0
0
0
3
0
0
1
0
0
2
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
1
1
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
2
4
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
1
2
0
2
1
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
4
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
3
0
0
2
2
1
0
0
2
0
0
2
0
0
3
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
12
4
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
2
1
0
0
0
2
0
0
7
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
2
0
0
1
0
0
0
2
0
1
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
1
1
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
10
0
0
0
0
0
0
0
2
2
0
0
2
0
0
1
1
0
0
0
0
0
0
0
2
1
0
1
0
0
2
0
0
0
0
4
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
1
2
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
3
0
0
0
0
0
0
3
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
2
1
0
0
4
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
3
0
1
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
4
2
0
0
1
2
2
0
0
4
0
0
0
1
2
0
0
0
0
0
0
0
0
2
2
2
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
5
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
3
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
6
3
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
2
2
0
0
0
0
1
0
1
0
0
1
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
1
0
0
0
0
2
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
1
1
5
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
3
0
0
0
0
0
0
2
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
2
1
0
0
2
0
0
0
1
1
0
2
0
0
0
1
1
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
1
1
0
0
1
3
0
1
0
0
0
0
0
0
0
0
0
1
0
2
2
2
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
7
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
2
0
0
2
2
0
0
0
0
0
0
3
0
2
0
0
2
0
0
0
1
0
0
0
1
0
0
0
1
0
1
1
0
4
0
0
0
0
4
2
0
0
0
0
2
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
2
0
0
3
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
1
0
1
0
2
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
3
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
12
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
0
0
0
3
0
0
3
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
1
0
0
0
0
0
0
0
1
0
0
2
2
5
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
3
1
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
1
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
3
3
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
2
1
0
0
0
1
2
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
1
2
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
4
0
0
0
0
0
3
2
1
0
2
0
1
0
2
1
1
0
1
0
0
2
0
0
0
0
0
1
0
0
1
3
5
0
0
0
0
3
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
2
1
1
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
10
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
2
0
4
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
2
0
2
2
0
2
0
0
0
0
0
0
0
11
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
3
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
1
1
0
1
1
0
0
1
0
0
0
1
1
1
0
1
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
7
0
2
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
3
0
0
0
6
1
0
0
1
0
0
2
0
0
0
0
1
0
3
0
0
0
1
0
3
2
0
0
0
0
0
2
0
3
2
1
0
0
0
0
0
0
5
0
0
2
0
1
1
0
0
0
0
2
0
0
0
1
2
0
0
0
0
1
0
0
0
2
0
0
2
1
0
1
0
0
0
0
0
0
0
1
2
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
2
0
1
0
0
0
2
1
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
2
0
1
0
2
0
1
0
0
2
0
0
0
0
0
0
3
1
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
1
3
0
1
0
0
0
0
2
5
0
0
0
1
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
1
1
4
2
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
3
0
0
0
0
3
0
2
1
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
5
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
2
2
0
0
2
0
0
0
0
1
0
4
2
1
0
0
0
0
1
0
1
0
2
0
5
0
0
0
0
0
3
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
3
0
0
0
0
1
0
1
2
1
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
2
0
0
0
2
1
0
0
1
0
0
1
1
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
1
0
3
0
2
0
2
1
0
0
0
0
2
0
0
0
0
0
1
6
0
0
0
2
0
1
0
0
2
0
0
0
2
0
0
3
2
3
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
2
0
2
0
0
0
0
1
0
0
0
3
1
0
1
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
1
2
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
3
0
1
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
1
2
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
2
1
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
3
0
2
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
4
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
4
0
1
0
1
0
0
0
0
1
0
2
2
0
2
0
0
1
0
0
0
0
2
0
2
0
3
0
3
0
0
0
0
2
0
0
0
0
2
1
0
1
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
4
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
3
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
7
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
3
0
3
0
1
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
1
0
1
1
0
0
1
2
1
1
0
0
0
0
0
0
0
2
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
1
1
1
2
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
2
0
0
0
0
0
3
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
3
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
5
0
0
4
0
0
0
0
1
0
0
2
0
4
0
0
0
1
0
0
0
1
0
2
0
0
0
1
0
0
0
2
0
0
0
2
0
0
1
1
1
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
4
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
3
0
2
0
0
0
0
1
0
0
0
2
0
0
4
0
0
0
0
0
1
0
1
0
0
0
3
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
1
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
1
1
0
0
0
0
0
2
0
2
1
2
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
4
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
2
1
0
2
0
0
1
0
0
0
0
2
0
1
2
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
1
0
0
0
0
5
0
0
1
0
0
0
6
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
7
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
3
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
3
0
0
0
3
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
1
1
0
0
2
0
0
0
2
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
3
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
2
0
0
2
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
1
2
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
1
1
0
3
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
2
0
2
0
0
5
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
3
0
0
0
5
2
2
0
1
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
2
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
2
0
4
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
2
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
3
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
3
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
1
1
5
3
0
3
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
3
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
3
0
0
0
4
0
0
0
0
0
3
0
2
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
1
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
2
0
2
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
3
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
2
1
2
0
0
0
0
0
2
1
3
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
1
1
0
0
2
0
0
0
0
0
0
0
0
2
1
2
2
1
0
1
1
0
0
0
2
0
1
0
0
2
0
0
1
0
2
0
0
0
2
0
2
1
1
0
1
0
0
2
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
3
0
0
0
2
0
2
0
1
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
2
2
0
0
2
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
2
0
0
0
0
2
1
0
0
0
2
3
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
1
2
0
0
0
0
0
1
1
1
2
1
0
0
0
1
0
0
0
0
1
0
2
0
0
1
0
1
0
1
0
3
0
0
0
0
1
0
0
0
0
0
0
0
2
1
4
0
0
0
2
0
0
0
0
1
2
0
0
0
2
0
1
2
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
1
6
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
1
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
2
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
3
0
0
0
2
2
2
1
0
0
0
0
0
0
2
0
0
0
0
2
2
0
1
0
0
0
0
2
0
0
0
0
4
2
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
1
3
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
3
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
4
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
3
0
0
2
2
1
0
0
0
10
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
4
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
4
1
2
0
5
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
1
28
0
0
0
2
0
4
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
1
0
0
0
3
0
0
0
5
0
0
0
2
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
5
1
0
0
2
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
4
1
1
0
0
1
1
0
0
1
0
0
2
3
0
0
3
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
2
0
0
0
0
0
0
0
2
5
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
2
0
0
0
0
1
2
1
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
1
0
1
2
1
1
1
0
0
1
0
1
3
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
2
0
0
1
2
0
0
2
0
0
0
0
0
0
0
4
0
3
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
7
0
0
0
0
0
0
0
1
0
0
0
0
0
0
6
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
2
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
1
0
3
0
0
1
1
3
9
0
0
1
0
1
0
0
2
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
2
0
0
0
3
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
3
0
0
0
0
0
0
1
1
0
0
0
4
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
2
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
2
0
0
0
0
2
0
0
0
0
0
0
1
0
3
0
0
1
1
0
2
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
1
0
0
0
2
0
0
4
0
2
0
0
0
0
0
2
0
0
0
0
0
0
3
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
2
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
3
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
1
1
0
2
0
0
2
0
0
0
2
1
0
2
0
0
0
0
0
0
1
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
3
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
3
0
1
1
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
1
3
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
2
0
12
2
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
3
0
1
0
0
0
0
0
0
0
1
0
0
5
0
2
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
2
0
0
4
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
1
0
0
0
0
3
3
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
1
2
1
2
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
1
0
0
0
0
5
2
0
2
0
4
0
2
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
2
1
1
0
3
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
6
0
0
1
0
2
0
0
0
0
0
2
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
4
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
7
0
0
0
1
0
0
2
2
0
0
1
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
1
2
1
0
0
0
0
0
1
1
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
1
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
2
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
1
2
1
0
2
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
1
0
0
1
1
0
2
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
1
1
0
0
4
0
0
0
0
0
0
0
0
1
3
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
7
0
0
1
0
2
0
1
0
0
0
0
1
2
1
0
2
0
1
2
2
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
1
0
2
1
0
0
0
0
2
0
1
0
2
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
1
0
0
2
3
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
1
2
2
2
0
0
1
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
3
0
0
0
2
1
0
4
0
1
0
0
0
0
0
3
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
2
4
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
2
0
2
0
3
2
0
1
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
7
0
0
1
0
1
2
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
2
0
0
0
0
0
2
0
0
0
11
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
7
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
1
0
4
0
0
1
2
3
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
3
0
2
0
0
2
3
0
0
0
0
0
0
0
0
1
0
2
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
1
0
1
2
0
0
2
0
0
1
0
0
1
0
2
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
3
0
0
1
0
0
3
0
0
0
0
0
0
0
1
1
0
0
0
0
1
2
2
3
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
1
0
0
1
2
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
5
0
1
0
0
0
2
0
0
0
0
3
0
1
2
1
0
2
1
0
0
0
0
1
2
2
0
0
0
0
0
0
0
2
0
0
0
0
2
1
3
0
0
0
0
0
0
0
0
4
1
0
1
1
0
3
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
6
0
2
2
0
2
1
0
1
0
1
0
0
2
2
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
3
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
1
1
0
2
1
0
1
0
2
0
0
1
0
0
0
0
2
0
0
2
0
0
0
1
3
0
1
0
0
0
0
0
1
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
6
0
1
2
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
1
13
0
2
0
0
0
2
0
0
0
0
1
0
0
0
3
2
0
0
0
0
0
2
0
0
0
1
0
0
1
1
2
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
2
0
0
1
0
0
6
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
2
0
2
2
0
0
0
0
0
1
3
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
2
0
1
1
2
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
4
0
1
0
1
1
1
1
0
1
1
0
0
1
0
0
0
2
0
0
2
2
1
0
0
0
0
1
2
0
0
0
0
0
0
3
3
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
2
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
3
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
1
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
2
0
0
2
2
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
6
0
0
0
0
0
2
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
2
1
1
0
0
2
1
0
1
2
4
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
2
0
0
1
2
0
0
0
0
1
2
0
2
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
3
2
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
2
2
0
0
0
0
1
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
2
0
0
2
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
4
1
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
2
0
0
2
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
8
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
2
0
0
1
0
0
0
2
0
2
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
1
4
0
1
1
0
0
0
10
0
0
9
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
7
1
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
2
1
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
2
0
2
1
0
3
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
5
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
3
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
1
0
0
0
3
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
3
0
1
1
0
0
0
1
0
0
0
0
0
0
2
3
2
2
2
0
0
2
0
0
0
1
0
2
0
0
2
1
0
1
0
0
0
0
1
0
0
0
0
1
3
0
0
0
0
0
1
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
2
0
2
2
0
2
0
0
1
0
0
1
0
0
0
1
0
0
0
0
3
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
10
1
1
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
1
3
0
0
2
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
4
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
5
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
1
0
2
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
5
0
0
0
0
1
0
0
0
0
0
0
1
0
3
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
3
1
0
0
1
0
0
0
0
1
0
0
0
1
0
3
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
3
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
2
1
1
0
1
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
3
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
3
0
0
0
0
2
0
1
0
0
0
0
1
0
1
0
2
2
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
2
0
3
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
3
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
4
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
2
0
0
2
2
2
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
3
1
0
0
0
0
2
0
0
0
1
0
3
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
2
0
3
0
0
0
0
0
7
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
1
0
2
0
3
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
2
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
4
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
3
0
0
0
0
0
2
1
2
0
0
0
1
0
2
0
0
1
1
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
3
0
5
2
0
0
0
0
2
2
2
0
0
0
0
0
0
1
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
2
0
2
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
5
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
3
2
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
2
4
0
0
1
0
5
0
0
0
0
2
1
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
1
1
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
1
0
0
0
0
1
1
2
2
0
0
0
0
0
1
1
0
1
0
0
1
0
1
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
2
1
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
2
0
2
1
0
0
0
0
0
2
1
2
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
3
0
2
0
0
0
2
0
0
2
0
2
2
0
2
2
0
0
0
0
2
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
1
2
3
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
1
0
2
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
2
2
0
0
0
2
2
0
0
0
4
1
0
0
0
0
0
1
0
0
7
0
1
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
5
0
1
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
5
2
0
1
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
1
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
2
0
1
0
1
0
0
2
0
0
0
0
3
0
0
3
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
1
0
2
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
1
2
0
0
0
1
0
0
0
1
1
0
0
0
0
1
1
0
2
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
1
2
3
2
0
0
5
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
2
0
0
3
1
1
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
1
1
1
0
2
2
0
3
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
8
0
0
0
2
1
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
2
2
4
0
1
2
0
0
0
0
0
5
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
2
0
0
0
0
1
1
0
3
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
3
0
0
1
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
6
0
0
0
0
1
0
3
0
1
0
1
1
0
1
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
2
0
0
0
0
0
2
0
0
1
1
1
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
2
0
2
3
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
1
0
2
0
2
0
3
1
1
0
2
0
3
0
0
0
0
0
0
0
0
0
2
0
3
1
4
1
0
0
0
3
0
0
0
0
0
0
1
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
1
2
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
5
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
5
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
1
2
0
0
2
1
2
1
0
0
2
0
1
0
0
0
0
5
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
1
1
0
0
0
0
2
3
2
0
0
2
2
0
0
0
0
1
0
0
0
0
1
0
4
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
1
1
0
0
0
0
0
2
1
1
0
0
0
1
0
5
0
3
1
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
3
2
0
0
2
0
0
0
1
4
0
0
0
0
0
2
1
0
2
0
0
2
0
0
0
1
0
1
0
0
1
0
0
2
0
1
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
5
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
2
2
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
3
0
2
0
0
0
2
2
0
0
0
9
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
3
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
3
0
0
3
0
1
0
0
0
0
0
2
0
0
0
0
2
0
1
0
1
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
1
2
0
2
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
3
0
0
0
0
1
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
1
3
2
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
10
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
1
0
0
2
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
1
0
1
0
0
2
2
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
2
0
1
2
0
0
0
0
1
0
0
0
0
2
1
2
0
0
2
1
2
0
0
2
0
0
0
0
2
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
2
3
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
3
3
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
5
2
0
0
2
0
0
2
0
0
7
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
1
2
2
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
4
0
0
0
0
0
0
0
0
0
2
1
0
1
1
0
0
2
0
0
2
1
0
0
0
0
2
0
0
2
0
0
0
0
4
0
0
0
0
1
2
1
2
0
0
0
2
0
1
0
0
0
2
0
0
0
1
0
2
0
0
0
1
0
2
0
0
1
0
0
0
2
0
0
0
1
0
2
0
3
0
5
2
0
1
1
0
4
0
2
0
2
1
0
0
0
1
0
1
1
2
0
0
0
0
1
4
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
1
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
2
1
1
2
2
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
1
0
0
2
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
4
0
0
0
5
0
0
0
0
0
0
5
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
2
1
0
0
1
0
0
0
0
0
2
0
0
1
0
1
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
2
2
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
3
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
1
0
1
2
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
2
0
0
1
2
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
5
2
1
2
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
1
0
3
1
0
0
0
4
0
0
1
0
2
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
2
3
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
3
0
0
5
0
0
4
0
0
2
0
1
0
0
1
0
0
0
0
0
0
1
0
3
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
6
2
0
1
0
0
0
0
0
2
0
3
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
4
1
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
2
0
1
0
0
0
0
1
2
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
1
0
0
0
3
0
2
0
0
0
0
0
3
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
3
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
1
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
3
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
3
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
4
0
1
0
2
0
0
0
1
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
1
1
1
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
1
2
0
0
2
0
0
0
1
2
0
0
0
0
0
0
4
0
3
1
0
0
0
0
0
1
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
2
1
0
0
0
2
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
3
0
0
0
5
0
2
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
2
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
3
0
0
0
1
0
0
1
0
0
0
1
2
1
0
0
0
0
0
0
0
2
4
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
2
1
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
2
1
0
0
0
0
6
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
1
3
0
2
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
3
2
12
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
5
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
2
0
2
0
0
2
0
1
0
0
0
0
1
0
0
2
0
0
0
0
1
0
1
0
0
2
0
0
0
1
0
0
1
0
0
0
1
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
1
0
2
0
0
0
1
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
1
1
0
0
3
0
1
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
1
0
0
1
0
0
0
2
0
2
0
2
0
0
0
1
0
0
0
1
0
0
3
0
0
1
0
0
2
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
3
2
2
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
2
3
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
2
3
2
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
2
0
0
0
0
0
1
0
0
1
0
0
1
0
3
0
0
3
3
1
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
2
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
2
0
2
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
2
2
2
0
3
0
0
0
2
0
1
0
0
2
1
0
0
2
0
1
0
1
0
0
0
0
0
2
2
2
0
0
0
0
0
0
1
2
0
0
0
2
0
0
3
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
1
0
0
3
1
0
0
2
0
0
0
0
1
0
1
0
2
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
2
0
1
0
0
1
0
1
0
3
0
1
0
0
1
0
0
1
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
1
1
0
0
2
0
2
1
0
0
0
2
2
1
0
1
0
0
0
0
3
1
1
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
4
2
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
3
5
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
2
1
0
0
1
1
0
0
2
0
1
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
2
0
0
1
0
0
0
0
0
4
0
0
1
0
0
1
1
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
1
3
0
2
1
0
0
0
0
2
0
1
0
3
0
2
1
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
5
0
0
0
1
0
1
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
3
0
0
0
0
3
0
2
11
0
1
0
0
0
0
2
1
1
1
0
0
1
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
2
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
4
1
0
0
2
0
0
0
0
0
0
5
1
0
5
0
0
0
0
0
0
0
0
0
1
0
2
2
1
0
1
0
0
1
0
4
0
0
1
0
0
0
2
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
2
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
4
1
0
1
0
1
0
10
1
0
0
0
1
0
0
2
0
0
0
5
0
2
1
1
0
0
2
2
0
0
0
0
0
0
0
0
6
0
2
2
0
0
2
1
2
0
0
0
2
0
0
2
0
2
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
1
0
0
0
0
2
2
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
9
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
2
0
7
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
1
2
0
0
0
0
0
0
3
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
1
0
2
2
0
0
0
0
7
0
0
0
0
0
1
0
0
0
1
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
2
0
0
5
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
10
0
2
0
0
0
1
0
2
0
0
2
0
0
0
0
0
2
0
2
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
3
0
0
1
0
0
0
0
0
0
0
1
0
2
0
2
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
2
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
2
1
0
0
0
0
1
5
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
1
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
1
0
5
0
0
0
3
0
0
1
0
1
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
5
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
2
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
6
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
1
0
0
2
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
2
2
1
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
2
2
0
2
2
1
0
0
0
1
0
2
0
0
1
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
4
0
0
0
0
2
4
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
1
0
1
0
0
0
0
0
1
0
1
0
0
0
3
0
0
0
0
0
0
1
0
3
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
5
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
3
2
0
0
0
0
0
2
2
0
2
0
0
2
0
0
0
0
0
0
1
0
0
2
0
2
0
3
0
1
0
0
1
0
1
3
0
0
1
2
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
1
3
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
2
2
0
2
0
1
0
2
2
0
0
0
0
0
3
0
0
0
2
0
0
0
0
2
1
2
0
0
0
0
4
0
0
0
0
6
0
0
2
0
0
2
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
1
0
0
0
0
0
0
0
2
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
1
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
1
2
0
1
0
1
0
0
0
0
1
0
1
2
1
4
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
8
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
2
1
0
0
0
2
0
0
0
4
0
0
1
0
0
0
0
2
2
2
0
0
0
0
0
1
0
0
1
1
0
3
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
4
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
2
0
0
0
0
0
1
0
1
0
0
1
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
1
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
8
0
4
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
2
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
4
2
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
2
0
0
1
0
3
2
0
0
0
0
0
0
2
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
1
0
0
1
1
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
3
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
2
1
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
1
1
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
9
2
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
2
0
0
2
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
2
0
0
1
0
3
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
2
1
1
1
0
1
0
0
0
3
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
3
4
2
2
0
0
0
0
0
1
1
0
0
0
2
0
0
0
1
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
1
0
0
2
0
0
2
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
2
0
1
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
5
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
1
0
0
2
0
1
1
2
1
0
2
0
0
0
1
0
0
1
0
0
2
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
4
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
2
0
1
2
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
10
1
0
0
0
0
1
0
0
3
0
2
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
2
0
2
0
0
0
1
0
2
0
0
0
0
0
0
1
1
1
0
2
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
1
0
0
0
0
0
0
4
0
0
0
0
5
2
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
2
1
0
0
2
0
0
1
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
1
1
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
2
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
3
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
1
3
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
4
0
0
0
0
0
0
1
1
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
3
1
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
2
0
0
0
2
2
0
0
0
2
0
1
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
8
0
0
0
0
0
1
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
5
0
0
0
1
0
0
0
0
3
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
2
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
1
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
2
0
2
3
1
0
3
0
0
0
1
0
0
1
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
3
1
0
0
2
0
0
2
1
0
1
2
0
0
0
0
0
4
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
3
0
0
1
1
0
0
1
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
3
1
0
0
0
0
2
0
1
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
3
0
2
0
0
0
1
0
1
0
0
1
1
2
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
1
8
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
1
0
2
5
1
2
0
0
0
0
2
1
2
0
0
0
0
0
2
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
3
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
1
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
3
0
1
0
1
0
0
0
1
0
0
0
5
2
1
2
0
0
3
0
0
0
1
0
0
0
0
0
2
2
0
0
0
1
1
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
2
0
0
0
0
0
3
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
4
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
2
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
1
1
1
0
0
0
0
0
1
0
6
0
0
0
2
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
1
2
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
1
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
7
0
0
0
0
1
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
5
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
4
0
2
1
0
1
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
4
0
0
1
0
1
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
4
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
2
1
0
0
0
0
1
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
5
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
1
0
1
0
0
1
1
0
2
0
2
0
0
0
0
0
0
1
0
0
2
1
0
0
0
1
0
0
0
0
1
7
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
1
2
2
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
4
0
1
0
1
0
0
7
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
1
2
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
2
2
0
1
3
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
2
1
1
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
1
4
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
2
0
0
0
0
0
0
1
0
0
0
2
1
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
6
1
0
4
0
0
5
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
2
2
0
0
1
2
0
0
2
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
1
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
1
0
0
2
0
1
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
1
0
0
0
0
0
2
0
0
1
0
0
0
0
4
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
3
2
1
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
1
0
2
0
2
2
0
0
5
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
1
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
1
0
0
0
0
0
0
3
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
1
0
0
0
6
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
2
0
0
7
0
1
0
3
0
0
1
0
2
0
0
1
1
1
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
10
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
6
0
0
0
2
0
0
0
0
1
0
0
1
2
0
0
0
0
1
2
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
2
0
0
0
1
1
0
1
1
0
3
0
0
0
0
0
0
0
3
0
0
3
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
5
0
0
0
1
2
0
2
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
3
0
0
2
5
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
2
0
1
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
2
0
0
0
1
1
2
0
2
2
0
2
0
0
2
1
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
3
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
2
1
0
0
0
0
0
0
0
1
1
1
0
0
7
1
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
1
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
2
1
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
1
0
1
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
2
0
3
2
3
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
3
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
2
0
5
1
2
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
4
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
2
1
0
1
7
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
3
1
0
0
1
5
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
2
2
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
4
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
4
0
1
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
3
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
2
0
0
0
2
0
0
0
0
2
0
4
0
4
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
1
0
0
0
0
0
8
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
3
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
3
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
1
1
0
0
0
0
4
0
0
0
2
0
0
0
0
2
2
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
4
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
8
2
1
1
0
0
0
0
1
0
0
0
0
2
0
1
0
0
1
2
0
0
0
1
0
1
1
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
3
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
2
2
0
2
3
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
1
0
0
2
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
2
1
2
0
0
0
2
1
0
0
0
2
0
4
1
0
0
0
2
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
10
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
2
0
3
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
2
0
0
0
0
1
0
0
2
1
2
0
1
0
2
0
0
0
0
0
1
0
0
0
2
0
4
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
3
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
1
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
5
0
3
0
0
2
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
1
0
2
0
1
0
2
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
2
0
2
0
0
0
2
0
0
1
0
0
0
2
0
2
0
2
0
0
0
1
0
2
0
0
0
0
0
2
0
2
2
0
0
0
1
0
0
1
0
0
2
0
2
0
0
0
1
0
2
2
2
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
2
1
0
0
0
2
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
2
2
0
3
0
0
0
0
0
2
0
2
1
0
7
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
2
0
2
1
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
4
0
0
0
2
1
1
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
4
0
0
0
0
2
0
1
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
2
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
1
0
0
0
0
1
0
0
0
2
0
4
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
3
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
1
1
0
0
1
0
0
0
3
0
0
0
1
0
0
1
0
0
1
0
3
1
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
1
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
1
1
0
0
0
0
2
1
0
1
0
0
2
0
1
0
9
0
0
0
0
0
0
0
0
1
2
0
0
4
0
2
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
1
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
2
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
4
1
1
2
2
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
1
1
0
0
0
0
1
0
0
1
0
2
0
0
1
0
0
2
0
0
2
0
0
0
2
0
0
0
0
2
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
2
2
0
0
0
0
0
1
3
0
0
0
0
0
1
0
0
2
3
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
2
0
2
1
0
1
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
2
1
1
0
2
2
0
0
0
0
0
2
0
0
0
1
2
0
0
0
2
0
1
2
0
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
1
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
2
2
0
0
0
3
0
0
0
0
0
0
0
1
0
1
2
0
0
2
0
0
0
0
0
2
0
3
0
0
2
0
0
2
0
2
0
1
0
0
0
2
1
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
4
0
4
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
3
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
1
0
0
0
2
2
0
3
0
1
0
1
2
0
0
2
0
0
2
1
2
0
0
0
0
0
0
1
0
2
0
2
1
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
2
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
1
2
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
0
4
0
0
0
0
0
0
0
3
0
0
2
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
2
0
1
1
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
2
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
6
6
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
4
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
1
0
0
3
2
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
2
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
2
0
0
0
2
0
0
0
2
0
0
0
2
0
0
2
2
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
2
0
0
2
0
4
0
4
0
0
0
0
2
1
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
1
0
0
3
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
1
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
2
0
2
0
1
0
0
2
1
1
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
3
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
1
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
2
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
11
2
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
3
1
0
0
0
0
0
4
0
0
3
2
0
0
0
0
1
0
0
0
2
1
0
0
2
0
2
2
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
1
2
0
0
0
0
1
0
1
0
1
0
0
0
3
0
0
0
0
1
0
2
1
0
0
0
2
0
0
0
1
0
0
2
0
0
2
0
2
0
0
0
2
0
0
1
2
0
0
0
0
1
0
0
3
0
2
0
0
0
2
0
3
2
0
0
0
1
0
0
1
0
0
2
0
0
0
0
1
0
1
0
0
2
0
0
2
0
0
0
0
2
2
0
2
0
0
0
1
0
2
0
0
1
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
7
1
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
1
0
0
2
0
2
4
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
2
2
2
0
0
0
0
0
0
0
0
0
3
1
2
0
0
2
0
0
0
2
0
0
1
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
2
0
0
0
0
4
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
3
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
1
0
0
0
0
0
1
2
1
0
0
0
0
2
0
0
1
0
0
0
0
1
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
1
0
2
0
0
4
0
0
1
1
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
1
4
0
1
0
0
0
7
0
0
0
0
0
0
2
0
0
1
0
2
0
2
2
0
0
3
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
1
0
0
2
0
0
0
1
1
3
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
1
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
1
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
1
2
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
1
2
0
1
0
0
2
0
2
1
0
2
2
1
0
0
0
0
2
0
0
0
2
1
0
10
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
2
0
1
0
2
0
2
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
1
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
7
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
2
0
2
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
3
0
1
2
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
3
0
3
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
4
0
1
2
1
0
0
0
2
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
5
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
1
0
0
0
1
0
2
0
0
0
0
4
2
0
1
1
0
0
1
0
1
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
2
2
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
7
0
0
0
0
0
0
0
1
1
0
0
1
1
2
0
0
0
0
2
0
0
0
1
0
3
0
2
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
4
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
2
0
6
0
0
2
0
0
2
1
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
1
2
0
1
0
0
2
2
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
2
0
1
0
2
0
0
0
0
0
1
0
0
0
0
2
0
1
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
4
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
1
0
0
0
1
0
3
2
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
2
0
0
0
0
1
0
0
0
2
0
1
0
0
2
0
0
1
0
0
0
2
0
2
1
0
3
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
3
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
1
2
2
0
2
0
4
3
2
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
2
0
0
0
0
0
6
0
0
1
1
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
2
3
0
0
1
0
0
0
0
1
1
0
0
0
0
1
2
1
1
1
0
0
0
0
2
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
4
2
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
4
0
0
3
0
2
0
0
0
2
0
2
1
0
1
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
2
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
4
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
4
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
1
1
0
4
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
1
2
0
0
0
0
0
6
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
3
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
1
1
0
0
0
0
3
1
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
1
1
0
0
0
0
3
0
0
1
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
7
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
2
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
1
0
1
1
1
0
0
0
1
3
0
0
1
1
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
2
0
0
0
0
1
0
0
0
2
0
2
8
3
0
0
0
0
1
1
0
0
2
1
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
1
1
3
0
2
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
1
1
3
0
0
1
0
0
0
0
0
1
1
2
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
1
2
0
1
0
0
0
0
0
2
0
2
0
0
2
1
0
0
1
0
2
0
0
2
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
2
1
0
0
0
1
3
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
1
0
1
1
0
0
0
0
0
0
0
0
4
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
2
0
0
0
0
0
0
1
0
0
0
3
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
2
0
0
0
1
2
0
0
0
0
0
1
1
0
0
0
0
2
1
0
0
0
1
0
2
0
0
0
0
0
2
1
0
1
2
2
0
2
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
7
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
3
0
0
0
1
1
0
0
0
0
0
3
0
1
0
1
1
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
6
2
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
7
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
3
3
0
0
2
0
2
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
2
0
0
2
1
2
0
0
2
0
0
0
0
0
0
2
1
1
0
0
2
0
0
1
2
0
0
3
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
4
1
0
0
1
2
0
0
0
0
0
0
4
0
1
0
2
0
1
0
0
0
0
0
1
0
2
0
2
1
1
0
0
0
0
1
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
1
2
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
2
3
0
0
2
2
0
2
1
1
0
0
2
1
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
3
0
2
0
2
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
5
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
2
0
2
2
2
1
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
2
0
0
1
0
0
0
2
0
0
1
0
5
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
1
2
3
0
0
0
2
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
4
1
0
0
0
0
0
0
2
1
0
0
0
2
1
1
2
0
0
0
0
6
0
2
1
0
0
1
1
0
0
0
3
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
3
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
2
0
0
1
0
2
1
0
0
0
0
4
0
1
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
3
0
6
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
1
0
1
0
0
0
0
1
1
2
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
3
0
0
0
4
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
11
0
0
0
1
1
0
0
0
0
0
0
1
2
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
3
1
1
0
0
0
0
0
2
1
0
0
2
0
1
0
0
0
0
1
0
7
0
0
0
0
0
0
0
3
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
2
1
1
2
2
3
2
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
1
1
0
0
0
2
0
0
1
0
4
0
0
2
0
0
0
0
1
2
0
1
0
0
1
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
1
3
0
0
3
0
0
3
0
0
0
3
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
3
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
1
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
1
2
0
0
3
0
0
0
1
1
0
0
0
2
0
0
1
1
0
0
1
0
0
0
0
1
0
0
2
3
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
1
0
0
0
1
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
2
2
0
2
1
0
0
0
0
0
0
0
1
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
1
0
0
0
1
0
0
0
0
1
1
0
2
0
0
2
0
2
2
0
0
1
0
0
0
0
0
4
0
1
0
0
0
0
0
0
2
0
2
0
13
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
3
0
0
2
1
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
1
0
2
0
0
2
1
0
0
0
0
3
0
0
3
0
0
0
0
4
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
3
2
0
1
0
0
2
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
1
4
0
0
3
1
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
2
2
0
3
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
2
0
0
1
0
2
0
3
0
2
2
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
1
1
1
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
2
5
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
2
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
2
1
1
0
1
0
0
0
2
2
0
0
0
1
0
0
0
0
0
2
0
0
3
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
2
0
0
0
0
1
0
0
2
1
0
0
0
0
2
0
2
0
0
0
2
2
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
2
0
2
0
0
3
0
4
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
1
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
2
1
3
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
1
0
0
0
5
0
0
0
0
0
2
0
1
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
5
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
4
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
2
0
1
1
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
1
0
1
2
0
2
2
1
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
1
2
0
1
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
4
0
0
0
0
0
0
3
0
0
0
1
2
1
0
2
5
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
1
11
0
2
0
0
0
2
3
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
1
1
0
0
2
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
2
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
5
0
0
3
0
2
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
3
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
5
0
1
2
2
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
3
0
0
0
0
2
0
0
0
2
0
0
1
0
3
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
10
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
2
0
0
7
0
0
1
0
0
0
0
0
0
1
0
2
2
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
5
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
1
1
2
0
0
0
0
0
0
0
0
1
3
3
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
1
5
1
0
0
0
0
0
0
0
0
0
1
5
0
0
0
0
1
0
0
0
0
0
0
0
0
5
0
0
1
0
0
0
3
0
0
1
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
3
0
0
0
0
0
0
1
2
1
0
0
0
0
1
2
0
2
0
2
0
0
6
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
15
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
11
0
1
0
0
2
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
2
0
0
1
0
0
0
7
1
0
0
0
0
0
0
0
0
3
0
0
0
0
2
2
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
4
4
0
2
0
2
2
0
2
0
0
0
1
0
0
0
5
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
2
1
1
1
0
0
0
0
0
0
1
1
0
1
1
1
0
0
1
0
2
2
0
0
1
0
1
0
0
0
0
1
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
1
0
0
1
0
0
0
0
0
0
2
0
1
0
2
1
0
1
1
0
2
0
3
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
1
0
0
1
0
0
0
0
0
3
2
0
2
0
0
1
2
0
1
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
5
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
3
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
2
1
0
0
1
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
2
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
2
0
5
0
0
0
1
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
1
2
6
0
0
0
2
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
2
0
0
0
2
0
4
0
0
0
1
0
0
0
0
0
0
3
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
1
1
2
2
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
2
2
0
0
1
2
0
0
0
1
0
0
1
0
5
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
2
0
0
0
2
0
1
0
0
3
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
1
1
0
0
1
2
0
0
0
2
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
4
0
0
2
3
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
2
1
0
1
2
0
0
3
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
1
2
0
1
0
0
3
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
1
0
3
0
0
0
1
0
1
0
1
1
0
1
0
2
0
2
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
2
0
1
2
0
1
1
0
4
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
2
1
1
0
0
1
0
2
0
0
1
0
0
0
0
0
1
0
0
2
1
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
1
0
2
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
8
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
1
0
1
0
0
0
0
4
0
0
0
2
0
0
1
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
3
0
0
1
1
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
3
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
1
0
0
0
1
1
0
0
0
0
2
3
1
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
4
0
0
2
0
0
1
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
2
0
1
2
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
3
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
4
1
0
0
0
1
1
3
0
0
2
2
2
0
0
0
0
1
0
0
0
0
0
0
1
0
3
0
0
0
1
0
0
6
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
1
0
6
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
3
0
1
0
2
0
2
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
4
0
0
0
3
4
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
1
0
0
2
0
2
0
2
0
0
0
1
0
0
2
1
0
0
1
5
0
2
0
0
0
0
0
0
2
0
1
0
1
0
1
1
0
1
0
0
0
1
2
2
0
1
1
2
2
0
0
2
7
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
2
1
0
0
0
0
0
0
0
0
2
0
3
1
0
0
0
1
0
0
0
1
1
0
2
0
0
0
3
1
0
1
3
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
2
5
0
0
0
0
11
0
1
0
0
0
0
0
0
1
0
0
2
1
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
10
0
0
2
0
0
0
0
0
0
0
1
0
2
2
0
2
0
1
0
1
0
0
0
0
1
0
2
1
1
0
0
2
2
0
3
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
1
0
0
0
0
1
2
0
0
0
0
3
1
4
0
0
0
0
0
3
0
0
0
0
0
1
0
0
2
0
0
0
0
0
3
0
0
0
2
1
2
0
0
0
0
1
1
0
0
1
1
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
3
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
1
0
0
4
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
3
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
3
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
1
2
0
0
0
3
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
5
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
3
0
1
0
0
0
0
1
2
1
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
3
1
2
0
0
3
1
2
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
2
1
0
4
0
2
1
0
0
0
0
0
0
4
1
2
1
0
2
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
1
1
0
3
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
1
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
1
2
1
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
1
2
1
6
0
0
0
2
0
2
0
2
0
0
0
0
0
2
0
0
1
2
0
0
0
1
0
0
2
3
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
3
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
1
0
0
0
0
0
2
0
0
1
0
3
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
1
0
0
0
2
0
1
0
2
0
0
2
1
1
0
0
3
0
0
0
0
2
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
2
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
1
0
2
0
2
0
1
3
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
1
0
1
0
0
1
0
0
1
0
1
0
1
1
0
1
0
3
2
3
0
3
0
0
1
0
0
0
0
0
1
2
2
0
0
0
5
0
0
2
0
0
2
1
0
0
2
0
1
0
0
0
2
1
0
0
0
0
2
3
0
4
0
0
0
0
1
1
1
1
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
1
2
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
1
0
1
0
2
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
1
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
3
0
1
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
6
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
2
0
0
0
3
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
2
0
2
0
0
0
2
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
2
0
0
0
0
1
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
1
3
0
2
0
0
1
1
0
0
3
1
0
0
0
1
1
0
0
0
0
0
1
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
3
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
2
1
0
2
0
0
2
0
2
0
2
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
5
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
3
0
2
2
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
1
0
0
2
0
3
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
2
2
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
3
0
0
0
0
0
1
2
0
0
1
1
0
3
3
0
0
0
1
3
0
0
0
3
0
25
2
1
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
3
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
3
0
0
0
2
0
0
3
0
0
0
0
0
0
0
2
1
0
0
2
4
0
0
0
2
1
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
3
0
3
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
4
0
0
0
2
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
3
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
3
0
0
2
0
1
0
0
0
0
1
1
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
2
1
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
1
1
0
1
0
1
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
2
0
1
2
0
0
0
0
0
0
1
2
0
0
1
1
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
1
0
1
0
1
0
0
0
0
2
0
0
1
0
1
1
2
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
11
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
1
0
0
0
0
4
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
1
0
0
0
1
2
1
0
0
0
0
2
0
2
2
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
1
2
1
1
0
3
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
1
0
0
0
0
6
0
0
0
0
0
0
0
0
1
2
1
0
0
1
2
0
0
2
0
0
2
3
2
0
0
0
0
0
2
0
0
2
1
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
2
0
3
0
2
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
2
3
0
0
0
2
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
4
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
1
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
4
0
0
2
1
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
3
1
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
4
1
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
7
0
0
1
3
0
0
0
0
0
1
1
0
1
0
2
0
0
0
0
2
1
1
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
2
2
0
1
0
3
3
0
0
0
0
1
0
1
0
2
2
1
1
1
2
0
1
2
2
0
2
2
1
2
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
1
0
2
0
0
0
7
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
4
0
1
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
1
0
3
0
0
2
0
0
0
0
2
0
1
0
0
1
0
0
1
2
0
0
1
2
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
1
0
0
2
0
0
0
1
2
0
0
0
0
1
0
2
0
0
0
7
1
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
2
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
2
0
0
1
0
0
0
0
1
0
0
1
1
1
0
1
0
0
0
2
0
0
5
1
0
0
1
0
0
0
0
0
0
1
2
0
2
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
1
2
0
2
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
1
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
3
0
0
1
1
2
2
0
0
0
0
0
5
0
6
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
1
0
0
0
0
3
2
2
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
1
3
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
3
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
7
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
5
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
1
2
0
0
0
0
0
0
2
0
2
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
4
0
3
0
0
1
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
2
1
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
3
2
0
1
0
2
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
1
2
0
0
0
0
2
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
2
0
4
0
0
0
0
0
5
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
1
0
2
0
0
0
0
1
0
2
1
0
0
0
0
2
0
2
0
2
0
2
0
3
0
0
2
1
0
0
0
0
0
0
5
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
3
2
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
1
2
1
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
2
0
1
0
2
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
3
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
1
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
5
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
4
0
2
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
2
2
0
0
0
0
0
0
0
3
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
4
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
2
3
2
0
0
0
3
2
0
0
0
2
2
0
1
0
0
0
1
0
1
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
4
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
2
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
4
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
1
1
0
0
1
0
1
0
2
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
4
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
1
0
1
1
0
2
0
0
0
0
0
0
1
4
0
2
0
0
0
2
1
2
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
3
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
1
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
5
1
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
3
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
2
1
2
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
3
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
11
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
3
1
0
0
1
0
0
0
2
0
4
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
1
1
2
0
1
3
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
2
0
1
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
2
0
0
0
3
0
0
1
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
1
0
1
0
2
0
0
0
4
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
5
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
2
0
1
0
0
1
1
2
0
0
2
0
2
0
3
0
0
0
2
0
1
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
5
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
2
1
0
1
0
1
0
0
0
0
0
0
0
0
2
1
0
0
1
2
0
0
0
0
0
1
2
0
0
2
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
2
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
4
1
3
0
0
2
2
0
0
0
1
0
2
0
0
0
0
0
0
2
0
1
1
2
2
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
1
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
4
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
3
0
1
2
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
1
0
1
0
2
0
0
0
0
0
0
2
1
0
0
0
0
2
1
3
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
2
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
3
0
2
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
7
0
0
1
0
0
0
0
0
1
2
2
0
2
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
4
0
0
0
0
0
2
0
1
0
2
1
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
1
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
2
1
3
0
1
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
1
3
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
1
0
1
0
0
0
1
1
0
0
0
0
1
0
2
6
0
0
0
3
0
0
0
0
1
0
1
2
1
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
2
1
0
0
0
0
0
1
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
3
2
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
2
0
1
2
2
2
0
2
1
0
0
2
0
0
4
0
1
2
0
1
2
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
2
4
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
2
1
2
0
0
0
0
2
0
0
2
0
2
0
0
0
0
2
2
0
1
1
2
0
5
2
0
1
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
5
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
3
2
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
1
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
1
0
0
3
1
0
1
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
5
0
0
0
0
0
1
0
0
2
0
0
0
3
0
0
0
0
0
2
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
2
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
3
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
11
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
3
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
6
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
1
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
2
0
0
1
0
3
0
0
2
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
5
1
2
0
0
0
1
0
0
0
1
0
1
4
2
0
0
0
0
1
0
0
0
0
0
3
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
1
0
0
1
2
2
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
2
1
1
0
0
0
0
0
0
0
0
1
0
1
0
2
0
2
0
0
0
0
0
0
0
0
1
2
0
0
3
0
0
3
0
1
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
2
0
1
0
0
1
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
6
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
2
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
4
0
1
2
0
0
0
0
7
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
2
1
0
0
0
0
0
0
2
0
0
1
0
0
0
3
1
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
3
2
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
3
3
0
0
0
0
0
0
1
2
0
1
0
0
0
0
2
0
0
2
0
0
0
0
2
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
1
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
2
1
0
0
0
0
2
0
0
1
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
4
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
1
1
2
0
1
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
2
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
8
0
0
0
2
1
0
1
2
0
0
0
0
3
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
3
0
2
2
0
1
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
4
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
1
1
0
0
2
0
0
2
3
0
0
1
0
0
8
2
0
0
2
0
0
0
6
0
1
0
0
0
1
2
0
1
1
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
3
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
3
0
0
0
0
0
0
3
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
1
2
0
1
0
0
0
0
0
3
0
2
0
0
1
0
1
2
0
0
0
0
0
0
1
0
0
0
4
0
0
3
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
3
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
1
2
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
5
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
6
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
1
0
0
0
0
0
0
2
0
1
0
1
0
1
0
0
1
2
0
1
2
0
0
1
0
0
2
4
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
2
0
0
2
0
2
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
1
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
4
0
1
2
0
0
0
1
0
0
4
5
0
0
2
1
0
4
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
4
3
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
3
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
1
1
2
0
0
0
1
0
0
2
0
1
0
1
1
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
3
0
1
0
1
2
0
0
0
0
2
0
0
0
1
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
2
2
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
2
0
0
0
0
3
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
2
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
2
1
0
1
0
0
1
0
0
2
0
0
0
0
2
1
1
0
0
0
0
3
0
0
0
0
0
1
0
1
0
0
0
3
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
3
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
1
2
0
0
0
0
2
0
2
0
0
0
0
0
1
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
4
2
0
0
0
2
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
2
1
2
4
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
4
0
0
1
0
1
0
2
0
0
0
0
2
0
2
1
0
3
1
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
1
0
0
2
1
0
0
2
0
1
2
2
0
0
0
0
0
0
2
1
1
0
1
0
0
0
2
1
0
0
0
0
0
1
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
1
0
0
0
0
2
0
1
0
3
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
1
1
1
0
1
2
0
0
0
0
2
0
0
2
0
0
0
1
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
1
6
2
0
0
0
2
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
7
2
0
0
0
0
0
0
0
3
0
0
4
0
0
4
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
4
0
0
0
1
0
0
2
0
0
3
0
0
0
2
0
0
0
1
0
0
0
3
0
0
1
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
2
0
1
0
1
2
0
0
0
2
1
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
3
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
7
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
1
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
2
0
0
0
0
0
0
0
2
2
2
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
2
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
3
0
0
1
2
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
2
0
2
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
3
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
2
0
0
2
0
0
2
0
0
2
0
1
0
1
0
0
3
0
3
0
0
0
0
0
0
0
0
2
2
1
0
0
1
0
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
1
0
0
0
3
0
0
2
0
0
1
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
2
0
1
2
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
4
3
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
1
0
0
0
1
0
1
0
0
0
0
2
0
1
2
0
0
0
0
1
0
1
1
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
2
1
1
2
1
0
0
0
0
1
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
3
2
4
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
3
2
0
0
1
1
2
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
2
2
0
0
0
2
0
0
0
1
0
2
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
1
0
2
0
0
2
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
1
0
0
1
4
0
0
0
0
0
1
0
0
0
0
2
0
3
2
0
0
3
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
6
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
1
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
1
2
0
2
2
3
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
2
2
2
3
2
4
0
0
0
0
0
0
0
0
2
1
0
1
2
2
1
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
3
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
3
0
0
0
0
0
2
0
1
1
4
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
3
0
3
1
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
2
0
2
0
0
0
2
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
2
9
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
1
0
0
0
7
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
3
0
0
0
0
0
2
0
2
0
0
1
0
2
0
0
2
0
2
0
0
0
0
3
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
1
1
0
4
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
4
0
0
0
2
0
2
0
0
2
0
0
0
0
2
3
0
0
0
0
2
0
1
0
2
0
1
2
3
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
3
0
0
3
0
0
1
1
1
1
0
0
0
0
0
0
1
1
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
1
0
0
0
1
0
0
0
1
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
3
0
0
1
2
0
0
2
0
0
5
0
0
2
0
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
2
0
2
0
2
0
0
1
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
3
0
0
0
2
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
3
0
0
1
0
1
1
0
3
0
0
0
1
1
1
1
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
5
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
3
0
0
0
2
0
0
0
0
2
1
0
3
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
3
1
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
1
0
1
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
2
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
3
0
4
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
4
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
1
0
0
0
1
4
0
0
0
0
0
0
0
1
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
1
0
0
0
0
2
0
0
1
0
0
0
3
2
0
0
0
0
0
0
0
2
2
0
2
0
2
1
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
5
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
3
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
2
1
2
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
4
0
0
2
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
3
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
2
2
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
12
0
2
1
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
12
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
1
2
0
0
0
0
1
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
2
1
2
0
0
1
1
0
2
0
1
0
0
0
0
0
1
0
0
3
0
0
1
2
0
0
0
0
0
0
0
0
0
1
1
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
1
0
1
2
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
6
0
0
2
0
2
0
0
0
2
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
3
1
1
0
2
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
2
0
2
0
1
0
0
0
1
0
0
0
1
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
6
0
0
0
1
0
0
0
0
0
0
0
1
1
2
0
0
0
0
2
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
3
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
4
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
12
1
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
3
0
0
1
0
1
4
0
1
1
1
1
0
3
0
0
0
0
2
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
9
2
1
0
0
3
2
0
0
2
0
1
0
2
0
0
0
0
1
6
0
0
1
0
2
3
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
8
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
1
1
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
1
1
1
0
0
0
0
0
0
5
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
1
0
1
0
1
0
2
1
0
0
1
2
0
1
0
0
2
0
1
0
2
0
0
2
3
1
2
0
0
0
0
2
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
3
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
1
0
0
0
8
0
0
0
0
2
4
0
2
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
1
0
0
1
0
2
0
0
0
0
0
0
1
1
0
0
0
2
1
0
2
0
2
0
1
2
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
1
0
1
0
1
1
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
1
0
4
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
3
0
2
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
1
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
2
1
0
0
2
0
0
0
1
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
5
1
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
4
0
1
0
0
0
0
1
0
0
0
1
2
0
0
0
2
2
0
4
2
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
2
2
0
0
3
0
2
0
0
1
3
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
2
2
0
0
0
0
0
2
0
0
1
1
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
1
0
0
2
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
4
1
0
0
2
0
0
3
1
0
0
0
0
0
0
1
0
3
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
2
0
2
0
2
0
2
0
0
0
0
1
0
0
0
0
2
0
0
1
2
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
3
0
0
0
0
0
0
2
0
2
0
0
1
2
0
0
3
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
1
2
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
3
2
0
1
0
0
0
1
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
4
0
0
1
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
1
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
5
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
4
2
2
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
2
1
1
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
1
0
6
0
0
0
0
0
2
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
3
0
1
0
0
1
0
0
2
0
0
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
10
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
5
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
1
1
0
0
1
1
0
1
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
3
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
6
0
3
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
2
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
5
0
0
1
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
2
0
0
0
1
0
0
0
3
0
1
0
0
1
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
3
0
1
0
1
0
1
0
0
1
0
2
0
1
2
0
2
0
2
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
4
0
2
5
0
0
1
3
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
7
0
0
3
0
0
1
0
0
0
0
0
0
0
2
0
5
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
3
0
0
0
0
0
0
0
1
2
2
0
0
0
1
0
0
0
0
0
3
2
0
0
1
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
2
0
0
0
1
0
1
0
1
0
0
0
0
3
0
0
0
3
0
0
1
0
0
3
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
1
0
0
1
0
0
0
0
4
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
7
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
2
2
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
3
0
2
0
0
0
1
0
0
0
0
0
0
1
4
0
0
1
0
2
0
0
0
0
0
0
6
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
2
2
0
0
3
1
0
0
1
0
2
0
0
0
0
1
1
0
0
0
0
2
5
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
4
0
0
2
0
0
0
0
0
0
0
2
0
0
4
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
2
0
5
0
0
0
0
1
2
2
0
0
0
0
0
0
1
1
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
3
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
1
1
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
5
0
0
0
0
6
2
0
2
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
3
0
0
0
2
0
0
4
0
1
0
2
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
1
2
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
4
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
1
0
2
0
0
0
0
0
0
4
0
2
1
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
2
1
0
1
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
6
1
0
0
0
0
0
0
2
1
0
1
3
0
1
0
3
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
2
0
5
0
0
2
2
0
0
0
0
5
0
0
2
1
2
0
1
2
0
0
1
0
0
2
3
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
2
0
2
0
0
0
1
0
3
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
5
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
1
0
1
0
0
1
2
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
2
6
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
3
0
0
0
0
0
2
0
2
0
0
0
1
1
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
1
2
1
0
1
2
1
0
0
0
0
7
0
3
1
0
0
0
2
0
0
1
0
0
0
0
2
0
2
0
1
0
0
1
0
3
3
1
0
0
1
1
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
1
0
2
1
0
0
0
0
2
1
0
0
2
4
0
0
0
0
3
0
0
0
0
2
0
1
4
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
2
0
0
1
0
3
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
4
0
0
0
0
0
1
0
0
1
0
0
2
0
0
1
0
0
0
0
1
3
0
0
0
0
1
0
1
0
0
1
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
3
5
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
2
0
0
0
1
0
0
1
1
0
1
2
0
3
0
0
0
0
0
0
0
0
0
1
0
1
2
0
2
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
1
0
1
0
0
1
0
2
1
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
2
1
0
0
4
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
2
0
1
1
1
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
2
0
0
1
0
0
1
0
0
0
0
0
4
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
2
2
0
0
0
0
2
0
0
2
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
1
0
0
0
0
0
0
0
3
10
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
1
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
1
1
0
0
1
0
1
0
0
2
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
1
0
0
0
2
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
2
2
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
2
0
0
1
1
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
7
2
0
2
0
3
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
2
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
2
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
1
5
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
2
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
3
0
0
0
0
0
0
0
1
0
0
1
0
0
0
11
0
3
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
3
0
1
0
1
0
2
0
0
1
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
2
2
3
0
2
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
3
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
2
0
0
0
2
0
0
2
1
1
1
0
2
1
0
0
2
0
0
0
1
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
2
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
2
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
1
2
0
21
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
1
0
0
0
0
1
2
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
1
4
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
1
0
0
0
0
3
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
1
1
0
1
2
0
0
0
0
0
1
0
0
0
0
2
0
1
3
4
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
2
2
0
0
4
1
0
0
0
0
0
0
0
0
2
3
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
1
2
2
0
0
0
4
1
0
0
0
0
1
0
1
1
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
1
0
1
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
1
2
5
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
4
0
1
0
0
0
0
1
0
0
0
0
2
2
0
0
0
2
1
0
0
0
7
1
0
3
2
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
2
0
0
2
0
0
2
0
2
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
2
1
3
1
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
2
1
8
2
3
0
0
0
0
3
0
0
0
0
0
0
3
0
2
0
1
0
0
0
0
0
0
0
6
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
3
0
0
0
0
0
1
0
0
1
3
0
2
1
0
0
0
1
2
0
0
3
0
0
0
1
2
0
0
0
0
3
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
3
0
0
0
0
2
0
0
0
2
2
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
2
1
0
0
0
1
0
0
0
0
0
1
1
0
2
0
0
1
0
0
0
0
0
2
0
0
0
1
0
1
0
4
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
2
0
2
0
0
0
2
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
2
0
5
0
0
0
1
0
1
1
2
2
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
1
2
0
0
0
0
0
3
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
7
0
0
0
0
0
0
0
3
0
0
0
0
0
4
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
2
0
0
0
0
3
0
0
0
1
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
3
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
1
2
0
0
0
0
0
0
0
0
3
0
0
2
1
0
0
0
0
0
2
0
1
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
2
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
1
0
2
0
2
0
0
0
0
1
0
0
4
0
5
0
1
1
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
2
0
1
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
2
0
0
0
0
0
2
1
0
2
0
0
0
1
3
0
0
2
0
0
0
0
1
0
1
0
1
0
1
1
0
0
2
0
1
0
0
0
0
0
0
1
2
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
1
0
3
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
1
1
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
1
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
6
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
6
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
7
3
1
0
0
2
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
1
3
0
0
0
0
3
0
3
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
4
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
3
0
2
0
0
0
1
0
0
0
1
0
1
1
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
5
0
1
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
1
0
0
0
2
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
1
0
5
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
1
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
4
0
0
0
1
0
0
1
0
2
1
1
0
0
0
0
0
0
2
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
3
0
2
0
0
0
0
0
2
0
0
0
0
2
3
1
0
0
0
2
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
2
0
0
0
2
0
2
3
0
0
0
2
0
1
0
0
0
2
0
0
10
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
2
3
1
0
0
0
0
0
3
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
2
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
2
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
3
0
0
1
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
2
0
3
0
2
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
1
2
0
2
0
1
0
2
2
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
4
0
1
1
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
3
0
2
0
0
0
2
1
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
2
0
0
0
2
0
0
1
0
0
0
0
7
1
1
1
0
0
0
0
1
0
0
0
0
2
0
0
2
0
2
0
0
1
0
0
2
0
0
0
0
1
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
2
0
1
2
0
0
1
1
0
0
2
0
2
0
0
0
0
4
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
1
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
2
0
1
0
0
0
1
2
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
4
0
0
6
0
1
0
0
0
2
1
2
1
0
3
0
0
0
1
0
1
0
0
0
0
0
1
3
0
0
0
0
5
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
2
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
3
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
2
3
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
2
8
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
2
7
0
0
1
0
2
0
0
1
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
3
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
3
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
9
0
1
0
1
0
0
5
4
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
5
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
2
1
2
0
2
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
1
0
1
2
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
2
0
6
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
6
0
0
0
0
0
2
3
0
1
0
0
3
0
0
0
0
0
4
0
0
0
0
0
0
4
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
1
2
0
2
0
0
0
0
5
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
9
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
1
0
1
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
2
1
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
3
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
2
2
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
1
0
0
0
0
0
9
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
3
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
3
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
3
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
2
0
0
0
0
0
2
0
0
0
0
0
0
4
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
1
1
0
0
0
0
0
0
0
4
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
2
1
1
0
1
0
0
0
3
0
0
1
1
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
2
0
2
0
1
1
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
2
0
0
0
2
0
0
2
2
0
0
0
0
1
0
0
1
0
0
1
0
3
0
2
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
1
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
2
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
6
0
0
0
0
1
0
0
3
0
1
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
3
2
0
0
0
1
0
1
1
0
0
1
0
2
1
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
5
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
3
0
1
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
2
0
2
0
3
0
2
1
0
0
2
2
5
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
11
0
0
0
0
1
0
1
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
5
2
0
0
0
0
2
0
0
1
1
1
0
0
1
1
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
2
3
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
4
0
2
0
0
1
0
0
0
1
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
1
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
1
0
1
0
0
1
0
2
1
0
0
0
2
1
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
4
0
0
0
0
0
0
0
1
2
3
1
0
0
0
4
3
4
0
0
0
0
1
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
1
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
2
0
2
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
8
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
2
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
2
0
0
0
0
2
0
0
1
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
4
0
0
0
0
0
1
2
2
0
0
0
0
0
1
0
3
2
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
1
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
1
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
2
2
0
2
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
1
2
0
2
0
0
0
0
3
0
0
0
2
0
0
0
0
2
2
2
0
0
2
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
2
0
1
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
3
0
4
0
1
0
0
0
1
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
1
2
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
3
0
6
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
2
0
0
0
1
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
2
0
2
0
0
5
1
1
2
0
2
0
0
2
5
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
1
0
0
2
0
2
2
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
6
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
3
1
0
2
0
1
0
6
0
0
0
1
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
6
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
1
0
1
0
2
0
0
0
0
2
0
1
0
4
3
0
1
0
0
0
1
1
0
0
2
0
2
0
0
0
3
2
1
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
4
3
2
0
0
0
0
0
0
2
0
0
0
0
1
2
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
4
0
0
2
0
0
0
0
2
1
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
2
0
0
2
0
0
3
0
2
0
0
2
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
3
0
4
0
0
0
0
0
0
5
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
2
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
3
1
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
2
2
1
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
2
1
0
0
0
0
0
1
0
1
1
0
1
2
1
0
2
0
0
0
0
2
0
0
0
4
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
2
0
0
1
0
0
1
2
0
0
0
0
0
1
0
3
0
0
0
0
2
0
1
0
2
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
2
0
0
1
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
2
1
1
0
1
0
0
0
0
0
0
0
0
1
1
0
2
0
2
0
0
0
1
1
0
0
1
0
0
1
0
0
3
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
1
2
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
2
2
0
0
0
0
0
1
1
1
0
2
1
0
0
0
3
0
2
0
0
0
0
1
1
1
0
0
0
0
3
0
0
0
1
0
0
0
0
2
1
2
2
0
1
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
2
2
2
0
0
0
0
0
1
3
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
2
0
0
1
0
0
2
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
1
2
1
2
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
5
2
1
0
1
0
0
0
0
0
1
2
0
0
0
2
2
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
4
0
1
0
2
0
4
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
2
2
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
3
2
0
0
0
2
0
0
0
0
0
0
0
0
1
1
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
2
0
0
5
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
3
1
0
0
1
0
0
1
0
0
0
2
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
1
0
4
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
3
3
3
0
1
0
0
1
0
0
0
1
2
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
3
0
0
0
0
1
1
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
2
1
0
0
1
0
0
2
0
0
2
0
0
0
0
2
3
0
0
3
0
1
2
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
1
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
2
0
3
1
0
0
0
1
0
6
2
0
0
0
0
1
0
0
0
0
1
0
3
0
0
0
0
2
2
0
0
0
0
0
0
0
1
1
0
0
0
0
4
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
2
0
0
4
0
0
1
1
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
3
1
0
0
0
4
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
5
0
1
0
1
0
0
1
0
0
0
1
2
3
0
0
3
0
0
0
2
2
0
0
0
0
1
0
1
0
0
3
0
1
0
0
0
0
0
0
1
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
6
0
2
0
0
0
2
0
0
2
0
0
0
11
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
3
0
0
0
3
0
0
4
1
0
1
0
0
1
1
2
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
1
2
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
1
1
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
3
0
4
0
0
0
1
1
2
2
1
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
3
1
0
1
0
0
0
0
0
0
0
3
0
0
1
2
0
1
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
1
0
0
0
0
2
0
2
0
1
1
1
0
0
0
0
0
0
3
2
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
2
1
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
2
2
1
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
2
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
2
0
0
3
3
0
0
0
1
0
0
0
0
1
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
8
0
0
1
1
0
0
3
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
1
0
2
0
0
2
0
0
0
1
0
1
1
0
0
0
1
1
0
1
3
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7
0
0
2
0
0
0
0
4
0
0
0
0
0
0
2
0
0
1
1
1
0
0
1
0
1
0
0
3
0
0
1
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
5
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
2
0
0
0
0
0
0
3
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
1
2
2
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
3
1
0
0
2
0
0
0
0
0
0
0
1
0
2
5
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
1
1
2
6
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
2
0
0
1
0
0
0
2
0
3
0
0
0
0
0
0
0
2
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
2
0
4
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
1
2
1
2
1
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
2
0
0
0
0
1
0
2
0
0
1
1
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
5
0
0
0
1
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
8
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
1
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
2
2
4
1
0
0
1
0
0
0
1
0
1
1
1
0
0
0
0
0
1
1
0
0
2
0
0
0
1
0
1
0
0
0
0
0
2
0
0
2
2
0
2
0
0
0
0
0
2
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
1
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
2
3
2
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
2
1
0
1
0
1
0
2
3
0
0
0
0
0
2
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
3
0
0
2
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
1
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
7
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
2
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
1
0
0
0
0
1
2
0
0
0
2
1
0
1
2
0
0
0
0
0
0
1
1
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
2
2
0
0
0
2
0
2
0
0
0
0
2
2
2
4
1
0
2
2
0
0
0
0
0
1
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
2
0
1
0
0
2
2
0
2
0
2
0
0
0
0
0
0
2
0
2
0
0
2
2
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
3
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
3
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
8
2
0
0
0
0
1
0
0
0
1
0
0
2
1
0
0
1
0
0
1
0
0
0
0
1
1
5
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
3
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
2
8
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
1
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
3
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
6
0
0
0
0
0
0
2
0
1
0
0
0
0
0
4
1
0
1
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
8
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
4
0
0
2
0
0
0
1
0
0
0
0
0
1
1
0
1
5
0
0
0
2
0
0
0
0
0
1
0
0
0
11
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
3
1
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
2
0
2
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
3
0
0
0
2
0
1
0
0
0
1
0
0
0
3
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
4
0
0
0
4
2
0
0
0
1
1
0
0
1
0
1
0
1
0
0
2
1
0
0
0
2
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
1
0
1
2
0
0
0
0
0
0
0
0
3
0
0
0
3
0
0
1
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
1
0
1
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
1
0
0
1
2
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
2
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
3
0
0
0
0
0
2
0
2
2
0
0
2
0
0
0
0
0
0
2
4
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
2
0
0
4
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
1
0
0
2
0
0
0
1
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
3
0
0
2
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
2
0
1
0
2
0
2
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
1
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
8
0
0
0
0
0
0
0
3
0
0
2
0
3
0
0
0
0
0
2
0
1
0
1
0
0
0
2
0
0
0
0
4
0
1
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
3
0
0
0
1
0
3
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
2
0
0
2
2
0
0
1
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
1
0
1
2
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
1
0
2
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
1
2
0
0
1
0
0
4
1
3
0
0
0
0
2
2
0
0
1
0
0
3
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
2
1
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
2
1
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
3
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
2
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
5
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
3
0
1
1
0
1
1
0
0
2
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
1
1
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
3
0
0
0
0
0
0
0
3
1
2
2
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
4
2
0
0
0
0
2
0
2
4
0
3
4
0
0
2
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
1
0
1
2
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
1
3
0
0
0
2
2
0
0
0
1
0
0
2
0
0
0
2
1
2
0
0
0
0
1
0
0
1
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
2
0
0
2
0
1
1
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
2
0
0
2
0
2
0
1
1
2
0
0
1
0
0
0
0
3
1
0
0
0
0
6
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
2
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
2
0
0
0
1
0
4
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
2
3
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
4
0
0
0
0
0
0
0
0
8
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
4
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
2
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
6
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
1
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
2
0
0
2
2
0
1
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
2
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
3
0
3
1
0
3
0
0
0
0
0
1
0
2
0
0
0
1
0
1
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
1
0
1
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
2
0
0
3
0
0
0
2
0
0
3
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
3
0
0
0
2
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
1
0
0
0
2
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
2
0
1
0
0
0
2
2
2
0
1
2
2
0
2
0
0
1
1
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
3
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
1
1
2
1
2
1
0
0
1
0
0
3
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
2
0
0
0
3
1
1
1
0
0
2
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
3
8
0
0
0
3
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
1
7
0
0
2
0
0
1
0
0
0
1
0
2
2
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
2
0
0
2
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
2
0
2
1
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
2
3
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
1
1
1
1
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
2
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
1
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
3
0
0
0
0
0
2
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
2
1
0
0
2
2
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
4
2
2
0
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
1
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
3
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
4
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
7
3
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
1
0
0
0
0
0
1
2
5
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
1
1
0
0
2
3
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
2
0
6
2
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
2
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
1
0
2
2
0
1
0
0
1
1
0
0
0
3
0
0
1
2
0
0
0
2
0
2
0
1
0
2
0
0
1
0
3
0
0
0
0
0
1
0
2
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
4
0
0
1
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
2
0
0
0
2
0
0
0
1
0
0
2
0
0
0
2
2
0
0
0
1
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
3
0
0
1
0
0
0
1
0
0
0
1
0
1
1
5
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
2
1
0
0
0
0
0
2
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
2
0
2
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
2
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
2
0
2
4
0
0
0
0
0
1
2
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
3
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
4
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
1
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
3
3
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
2
0
1
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
5
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
1
0
0
0
2
0
0
2
0
0
5
0
0
0
1
2
4
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
4
2
2
0
2
0
0
3
0
0
2
1
0
0
2
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
3
0
0
0
0
2
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
14
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
1
1
0
0
0
0
0
1
0
0
1
0
0
2
0
0
1
0
1
0
0
6
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
2
0
0
2
0
0
1
0
0
1
0
1
0
0
0
0
0
1
1
1
0
0
0
1
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
2
0
2
0
0
0
2
1
0
0
0
0
3
0
1
3
0
2
0
0
2
1
2
2
0
1
0
2
0
3
0
0
3
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
1
0
0
3
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
1
0
3
0
0
0
0
2
0
0
1
2
0
0
1
0
0
0
2
0
0
0
0
4
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
2
0
1
0
1
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
1
2
0
2
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
1
1
0
2
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
1
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
1
0
0
2
0
0
1
2
0
0
0
0
5
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
2
0
0
0
0
2
0
0
0
0
0
3
1
0
0
1
0
0
1
0
2
0
0
0
0
0
1
0
0
3
0
2
0
0
0
2
0
0
0
1
2
0
0
2
2
0
0
1
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
4
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
2
1
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
1
3
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
1
0
0
2
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
1
3
0
2
1
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
1
0
0
0
2
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
1
5
0
0
2
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
2
0
0
0
0
4
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
5
0
1
1
0
0
0
0
1
0
0
0
0
6
0
1
0
0
0
2
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
1
0
2
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
1
1
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
2
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
8
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
1
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
2
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
3
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
4
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
1
0
0
0
1
0
0
0
0
0
0
2
2
0
0
3
1
0
1
0
4
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
2
0
1
2
0
0
2
0
0
1
0
0
0
5
0
1
0
0
0
1
0
0
0
1
0
0
0
4
0
2
0
0
0
2
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
1
2
2
1
0
0
0
2
0
1
0
2
0
0
0
0
0
2
1
0
0
1
3
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
1
0
0
0
0
0
0
0
6
0
0
0
0
0
2
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
4
2
2
1
0
2
0
1
2
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
4
3
0
0
0
1
2
0
0
0
1
0
2
1
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
3
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
2
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
5
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
1
0
1
2
0
0
0
1
0
0
0
0
1
1
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
2
2
0
0
0
1
4
1
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
2
1
1
0
0
0
1
0
0
1
0
2
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
1
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
5
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
3
0
2
0
0
1
1
3
0
0
0
0
1
0
0
0
0
0
2
1
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
1
5
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
3
2
1
2
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
1
0
0
0
1
2
2
0
2
0
0
0
2
1
0
0
0
0
1
0
1
2
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
2
2
2
1
0
0
1
2
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
2
1
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
1
1
0
2
1
0
0
3
26
1
0
0
1
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
1
0
0
1
0
0
0
2
0
0
0
2
2
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
2
1
0
4
1
0
1
0
0
0
0
0
1
2
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
2
1
0
0
1
1
2
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
2
1
0
2
0
0
2
1
0
2
0
0
3
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
3
1
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
3
0
1
4
2
0
1
0
0
0
2
0
2
0
2
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
3
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
3
0
5
0
0
3
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
2
2
1
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
7
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
4
0
2
0
0
0
0
3
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
4
0
0
0
0
1
0
1
2
0
0
1
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
7
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
2
2
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
2
3
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
4
0
0
0
1
0
0
3
0
3
0
0
3
0
0
0
1
1
0
0
0
0
3
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
1
1
0
2
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
2
0
1
0
1
0
0
0
0
6
9
1
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
8
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
2
9
0
1
1
2
0
0
0
1
2
0
2
0
0
1
0
0
0
0
1
0
0
0
1
0
4
0
0
0
0
0
2
0
1
2
0
0
0
0
2
0
2
2
2
2
1
3
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
3
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
3
0
0
0
0
2
3
2
0
2
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
1
0
0
0
0
0
0
2
0
0
2
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
2
0
2
1
0
0
0
0
1
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
4
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
2
0
0
1
0
5
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
1
4
0
0
0
1
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
2
0
0
0
1
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
3
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
1
0
5
0
0
0
0
0
0
0
0
1
0
0
4
1
2
0
0
0
0
2
3
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
4
0
1
5
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
4
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
2
2
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
3
1
0
0
0
5
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
8
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
2
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
2
0
0
0
0
0
0
1
0
2
2
1
0
3
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
2
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
6
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
19
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
7
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
1
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
3
0
0
0
0
0
0
2
1
0
0
1
2
2
0
0
4
1
2
1
1
0
0
0
1
0
0
0
0
0
1
2
0
1
0
2
0
3
2
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
1
0
0
0
0
1
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
2
0
0
1
0
0
1
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
1
0
0
0
3
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
2
0
2
1
0
0
0
0
2
2
0
0
1
0
1
0
0
0
1
0
0
0
0
3
0
0
4
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
2
0
1
0
0
0
0
0
0
0
0
2
0
0
3
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
1
0
1
0
0
0
6
2
2
0
0
15
0
1
0
0
0
0
1
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7
3
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
8
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
2
0
0
6
0
3
2
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
8
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
5
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
2
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
4
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
1
2
0
0
2
0
0
0
2
0
6
0
0
0
0
0
2
0
1
0
0
0
0
0
3
0
0
7
0
2
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
2
0
1
1
2
2
0
0
3
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
1
3
0
2
0
2
0
0
0
1
0
0
2
0
0
0
2
3
0
0
2
0
0
0
2
0
0
0
0
1
0
3
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
1
1
1
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
2
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
1
1
0
0
1
0
0
0
1
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
1
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
6
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
2
0
0
0
0
2
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
2
2
0
0
0
0
1
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
6
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
3
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
2
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
2
0
0
0
0
1
0
0
0
0
0
2
1
4
0
3
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
3
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
2
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
4
0
0
1
0
0
0
2
0
0
0
1
0
0
0
14
0
0
1
0
0
0
2
0
0
1
0
0
0
3
0
0
0
2
0
0
0
0
2
2
2
0
0
0
2
0
1
0
0
0
0
1
0
1
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
7
0
2
0
0
0
0
1
1
0
0
0
0
0
3
4
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
8
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
4
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
3
0
0
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
1
0
3
0
1
0
0
0
0
0
0
0
1
0
4
2
0
0
0
0
0
1
0
0
0
0
0
1
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
2
2
0
0
1
2
0
0
0
0
2
0
1
0
0
0
0
1
2
2
0
0
2
0
2
1
0
0
0
0
1
0
1
1
0
0
0
0
1
3
0
0
0
0
0
1
1
2
0
0
3
0
0
0
0
2
2
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
2
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
4
1
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
6
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
2
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
7
0
1
1
0
1
0
0
1
1
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
2
1
0
1
0
0
0
0
0
0
0
0
0
2
1
1
0
5
1
0
0
0
2
8
1
0
2
1
0
2
0
2
1
0
2
1
0
0
1
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
2
0
1
0
0
0
0
0
1
0
0
2
5
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
2
2
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
2
2
0
2
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
3
1
0
0
2
0
2
0
1
0
0
0
0
0
0
1
0
1
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
3
0
0
0
2
0
2
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
4
0
0
3
4
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
1
0
1
1
0
2
0
0
0
0
4
0
0
0
1
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
3
1
2
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
1
0
0
0
3
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
5
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
2
0
0
1
0
0
0
0
0
0
0
3
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
2
0
0
0
2
0
1
1
2
0
0
0
0
0
0
1
3
2
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
2
0
0
2
2
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
3
0
2
0
0
0
0
1
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
5
0
5
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
2
0
3
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
10
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
3
0
0
4
0
1
0
0
0
3
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
2
3
2
0
0
1
0
0
5
0
2
0
0
0
0
0
0
1
0
0
0
1
2
2
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
4
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
3
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
1
4
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
2
0
0
0
1
0
2
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
2
2
2
0
0
0
0
1
2
0
2
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
1
0
3
1
0
0
0
0
0
0
0
3
1
6
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
1
1
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
3
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
2
0
0
0
1
0
4
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
1
5
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
2
0
0
2
0
0
0
0
4
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
3
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
2
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
3
0
1
0
1
1
0
2
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
2
3
0
0
0
1
1
1
0
1
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
1
5
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
2
2
2
0
0
0
0
0
3
0
0
0
0
0
8
1
0
0
0
1
0
0
1
0
0
0
2
1
0
0
0
0
0
0
2
1
0
0
0
1
2
0
3
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
3
5
0
1
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
1
0
3
0
0
0
0
1
0
0
0
3
1
0
0
0
2
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
3
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
6
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
3
0
2
3
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
2
2
0
0
0
3
0
1
1
0
0
2
0
0
0
0
0
0
0
0
1
0
3
1
0
0
0
0
0
2
0
2
0
0
0
0
3
3
0
6
1
1
0
0
3
0
0
0
0
3
0
0
1
1
0
1
0
0
3
0
0
2
0
0
0
2
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
2
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
2
0
1
6
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
2
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
3
0
0
1
6
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
5
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
1
2
0
3
0
0
1
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
2
0
0
0
0
0
1
0
1
0
1
0
2
2
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
3
1
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
2
3
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
1
1
0
6
2
0
0
0
0
0
2
2
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
1
0
2
6
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
1
2
1
0
2
0
2
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
2
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
1
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
1
1
0
0
0
1
0
0
1
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
15
0
1
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
1
0
0
0
1
0
0
0
0
2
1
2
1
0
1
0
4
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
2
0
2
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
1
2
4
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
1
0
2
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
1
0
0
3
2
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
4
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
3
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
2
2
0
5
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
3
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
2
1
0
0
1
0
0
0
2
1
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
2
0
1
1
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
2
0
0
5
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
4
2
2
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
2
0
3
0
0
0
0
1
0
2
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
1
3
3
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
2
2
0
0
2
1
0
2
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
2
1
0
1
2
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
2
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
6
2
0
0
2
1
0
0
0
1
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
2
2
0
0
0
1
2
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
6
4
0
2
0
0
0
0
0
0
0
0
0
2
4
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
8
0
0
2
0
0
0
2
0
0
0
2
0
1
0
1
2
0
0
0
0
0
3
1
1
4
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
13
0
0
1
2
0
0
0
0
0
0
0
0
4
1
1
0
1
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
4
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
2
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
10
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
2
1
1
0
3
1
0
2
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
10
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
6
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
2
0
0
1
3
0
2
0
0
1
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
5
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
2
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
1
0
0
0
2
0
1
0
2
0
0
0
0
1
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
3
0
0
0
0
1
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
1
1
0
0
0
0
0
2
1
0
0
1
0
1
1
0
0
0
0
0
0
0
1
1
0
2
0
1
0
0
0
0
0
0
0
0
1
3
0
0
0
0
1
2
0
0
0
2
1
0
0
2
0
1
0
0
1
0
0
0
0
2
0
0
1
0
0
0
3
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
4
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
1
0
0
1
0
2
0
0
0
0
0
0
2
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
5
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
3
1
0
0
1
0
0
1
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
3
0
2
0
0
1
0
3
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
2
4
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
8
0
0
1
0
0
0
2
3
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
2
1
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
2
0
0
0
2
1
0
0
0
1
0
0
0
2
0
3
0
0
0
0
9
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
1
2
0
2
2
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
1
2
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
5
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
3
0
1
0
1
2
0
0
0
0
0
0
0
3
0
2
2
3
0
0
0
0
0
0
1
0
2
1
1
1
2
0
0
0
1
1
1
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
3
0
2
0
0
5
0
0
1
0
2
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
5
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
1
0
2
0
0
0
2
0
0
0
0
0
1
0
2
1
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
1
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
1
0
0
0
0
0
0
0
3
0
2
2
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
8
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
1
3
0
2
0
0
1
0
0
2
0
0
2
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
2
1
0
1
0
4
0
0
0
0
0
2
4
0
0
0
3
0
0
0
0
2
2
1
0
0
0
0
2
1
0
0
0
2
0
2
0
0
0
2
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
2
0
0
0
1
0
0
0
1
0
2
0
0
0
0
2
0
3
0
0
0
0
0
0
1
0
1
0
2
0
3
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
4
0
2
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
2
2
0
0
0
2
2
6
0
0
0
0
0
1
0
6
0
0
2
0
0
2
0
1
3
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
1
0
15
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
6
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
3
0
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
2
0
0
3
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
1
0
1
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
9
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
1
0
0
0
2
2
0
0
0
1
0
1
0
0
4
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
3
0
0
2
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
1
2
0
1
0
0
0
0
0
0
1
0
2
0
0
1
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
2
2
0
0
0
2
0
2
0
11
0
0
2
0
0
1
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
2
0
1
0
2
1
0
0
2
0
0
0
0
0
0
0
1
3
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
2
0
4
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
1
0
0
1
1
0
0
0
0
0
2
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
12
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
2
0
0
0
3
0
0
2
1
3
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
1
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
1
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
2
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
3
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
2
0
2
0
1
0
0
0
0
1
2
1
0
0
0
1
0
0
0
0
0
0
2
0
2
0
2
1
2
1
0
1
0
0
0
0
0
0
0
2
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
1
1
2
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
9
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
2
1
2
0
0
0
0
0
4
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
3
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
2
2
0
2
0
0
1
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
2
1
0
0
2
3
2
3
0
0
0
0
0
2
1
2
0
0
3
0
0
1
0
0
0
0
1
1
1
1
8
0
0
0
0
2
1
1
0
0
0
0
0
0
0
2
2
0
0
3
2
2
0
0
0
0
1
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
3
0
5
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
1
0
1
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
1
0
0
0
1
0
0
0
2
0
9
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
1
2
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
3
0
1
0
0
0
0
0
3
0
0
0
0
0
1
0
1
0
0
1
0
0
3
0
0
1
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
3
0
0
0
2
0
0
3
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
3
0
0
5
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
2
0
0
0
2
0
2
0
2
0
0
2
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
1
0
2
0
0
0
0
1
5
0
0
0
2
0
2
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
2
2
1
0
0
2
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
1
3
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
2
5
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
2
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
1
0
1
1
0
0
0
2
0
1
0
0
1
0
0
2
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
1
0
1
3
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
3
0
0
0
1
0
5
0
2
0
1
0
0
0
0
0
1
2
1
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
7
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
1
1
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
2
2
0
2
0
0
0
0
2
0
2
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
3
0
0
2
1
0
0
0
0
1
0
0
1
0
1
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
4
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
4
0
0
0
0
1
1
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
2
0
2
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
2
1
0
0
1
0
6
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
4
0
0
3
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
1
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
5
0
1
0
1
0
0
0
0
1
3
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
1
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
2
1
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
2
1
0
0
2
0
1
2
0
0
0
3
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
2
2
1
0
0
0
0
0
1
0
0
0
2
0
2
1
0
2
2
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
2
0
0
3
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
3
3
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
4
0
0
0
1
1
0
0
2
0
2
0
3
0
0
0
1
0
0
0
0
2
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
1
0
0
1
4
2
0
0
2
1
1
0
1
1
0
1
0
1
0
0
0
0
6
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
2
0
2
2
1
0
0
1
0
0
0
1
0
0
0
0
0
1
2
0
3
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
1
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
8
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
2
3
0
0
2
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
5
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
2
1
0
0
0
0
2
4
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
7
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
8
0
0
0
0
0
0
4
0
0
4
0
0
0
1
0
0
0
0
3
0
0
0
1
0
2
3
2
0
0
3
0
2
1
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
1
1
1
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
2
4
6
1
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
1
1
0
0
0
0
0
0
0
2
0
2
2
0
0
1
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
2
2
0
0
0
1
5
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
1
0
0
2
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
4
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
2
0
1
0
2
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
7
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
3
0
1
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
5
0
0
0
0
0
0
0
0
1
0
4
0
0
1
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
3
2
1
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
3
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
5
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
2
3
0
0
0
0
0
0
0
0
1
2
2
0
0
1
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
5
0
0
0
0
0
0
1
0
7
1
0
2
1
1
0
0
1
0
1
1
2
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
2
2
0
2
2
1
0
0
0
0
2
0
0
0
1
0
0
0
2
1
0
0
0
0
0
10
1
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
2
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
2
0
6
0
0
2
2
0
0
3
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
3
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
4
2
0
0
1
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
1
2
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
3
0
0
1
0
0
4
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
5
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
1
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
2
1
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
5
0
2
3
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
2
0
0
0
0
0
2
3
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
3
1
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
1
0
0
0
0
0
3
0
0
2
2
2
0
0
0
0
1
0
0
0
0
0
1
2
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
3
0
2
0
1
1
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
6
3
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
3
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
2
1
0
2
0
0
0
1
3
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
1
0
2
0
0
2
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
2
1
0
0
0
0
1
2
0
0
0
1
1
0
4
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
2
0
2
0
0
0
0
0
0
0
1
1
0
2
0
1
0
0
0
0
1
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
1
0
0
2
2
0
1
0
0
1
0
2
0
2
2
0
0
0
0
3
0
2
2
0
0
1
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
1
0
2
0
0
2
0
0
0
0
0
0
3
2
0
0
2
0
0
0
1
0
0
2
0
0
0
1
0
2
0
2
2
0
4
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
12
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
1
1
2
0
0
0
0
2
0
0
0
2
1
3
0
1
0
0
0
2
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
1
1
0
1
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
2
2
0
0
0
1
0
0
0
0
1
0
4
0
0
1
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
1
2
2
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
1
0
1
3
0
0
0
0
0
0
0
2
1
1
0
0
0
2
0
0
2
0
1
0
0
0
2
2
2
0
1
2
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
1
1
0
0
0
0
0
2
1
2
0
0
1
0
2
1
0
2
2
0
0
0
0
1
0
2
0
1
0
2
0
1
2
6
0
2
0
3
0
0
0
0
0
2
0
0
0
0
0
1
1
0
2
2
2
1
0
0
2
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
1
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
1
1
4
0
0
0
0
0
0
0
1
0
0
2
1
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
1
1
0
0
0
0
8
0
3
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
1
0
0
0
0
0
3
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
4
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
2
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
2
1
0
0
2
2
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
0
2
0
1
1
0
0
0
0
0
5
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
2
2
0
1
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
1
0
3
0
0
1
2
1
0
0
0
0
2
0
0
1
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
2
3
0
0
0
3
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
7
2
0
0
1
3
0
3
0
0
0
0
0
2
0
2
0
0
0
1
2
0
1
0
1
1
0
1
0
3
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
3
0
2
0
4
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
3
2
0
0
5
0
0
1
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
1
0
2
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
1
0
0
0
0
0
2
0
0
0
2
9
0
0
0
0
0
3
0
0
2
0
2
0
0
0
0
1
2
0
2
1
0
0
0
2
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
3
2
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
2
3
1
0
2
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
4
0
0
0
0
0
0
0
0
0
3
0
2
0
1
2
0
0
0
0
1
0
0
2
0
0
1
2
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
7
1
0
1
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
2
2
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
4
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
2
2
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
2
0
4
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
3
0
0
1
1
0
7
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
1
0
0
0
2
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
1
3
0
0
2
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
5
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
2
0
0
1
0
0
0
0
0
0
1
0
0
2
0
1
1
0
0
0
0
0
2
0
1
0
0
0
2
1
0
0
0
0
0
13
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
1
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
2
0
0
2
0
2
1
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
5
0
0
4
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
1
2
0
0
1
2
0
0
0
0
0
1
0
2
0
0
0
0
1
0
2
0
0
0
2
1
0
0
0
2
1
0
0
0
0
0
0
0
2
0
2
0
0
3
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
6
0
0
0
0
0
0
0
0
0
2
2
0
0
1
1
0
0
0
2
0
14
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
1
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
1
4
0
2
0
0
0
0
0
0
0
0
3
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
3
6
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
3
0
0
0
2
2
2
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
2
0
0
0
0
3
0
1
1
0
2
1
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
2
1
0
0
0
3
2
0
0
0
1
2
0
0
0
1
0
0
0
1
0
0
4
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
3
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
1
3
2
2
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
1
0
0
0
0
2
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
1
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
2
2
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
4
0
1
0
0
1
0
0
2
1
0
1
0
0
0
2
1
0
0
1
0
0
0
0
0
1
0
0
1
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
4
2
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
3
1
2
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
2
0
1
0
0
2
3
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
1
0
0
2
0
1
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
1
2
1
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
2
0
0
0
2
0
0
2
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
3
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
2
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
3
0
0
0
0
0
0
3
1
0
0
0
0
0
1
0
0
0
0
2
2
0
0
1
0
2
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
1
0
2
0
0
2
3
0
0
0
0
1
0
2
1
0
2
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
2
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
3
1
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
2
1
0
0
0
1
0
1
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
2
0
2
0
3
0
8
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
3
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
3
1
1
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
1
1
0
0
1
1
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
3
0
0
0
3
2
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
4
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
1
3
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
1
4
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
5
0
3
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
2
0
0
0
1
1
3
0
0
2
1
0
0
0
0
2
0
0
1
1
2
1
0
0
0
0
2
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
1
0
0
0
2
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
2
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
2
1
0
1
1
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
1
12
0
0
2
0
0
7
0
1
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
4
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
24
0
1
0
2
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
2
0
0
0
2
2
5
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
4
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
1
0
1
0
1
0
0
2
0
2
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
1
0
0
2
0
0
0
1
0
1
1
0
4
0
0
0
0
1
2
0
0
0
3
0
2
1
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
3
0
2
1
0
0
0
1
0
0
3
1
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
3
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
2
0
2
3
0
0
0
1
2
0
0
0
0
3
0
0
1
0
2
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
2
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
3
0
0
0
0
0
2
2
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
4
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
2
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
3
0
1
0
0
2
1
0
0
0
1
0
1
0
0
0
1
0
0
0
3
0
0
0
2
0
0
0
1
0
1
0
2
0
3
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
2
0
1
2
2
0
0
0
0
0
2
1
2
2
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
6
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
2
1
0
0
0
2
0
0
0
0
0
0
0
0
1
4
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
32
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
2
0
0
0
2
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
5
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
1
1
0
1
0
5
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
1
13
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
3
0
0
4
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
1
0
2
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
3
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
2
1
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
1
2
0
1
0
0
0
0
0
0
0
0
0
3
2
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
1
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
6
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
2
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
2
0
0
1
0
2
0
0
1
1
0
0
3
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
2
0
1
1
1
0
0
0
0
0
0
2
0
8
0
0
1
0
5
5
0
2
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
1
0
1
0
2
1
0
0
0
0
0
0
4
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
2
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
2
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
2
0
1
2
0
0
0
3
1
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
1
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
3
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
2
0
0
1
0
0
2
0
1
0
2
0
0
0
0
0
0
0
3
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
3
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
1
0
1
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
6
0
0
0
2
0
0
0
0
0
1
0
0
0
1
1
2
1
0
0
0
0
0
0
0
0
2
2
3
0
0
1
0
1
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
2
0
0
1
0
0
0
2
2
0
0
2
0
0
0
0
1
0
4
2
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
1
0
4
2
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
1
1
4
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
2
0
9
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
5
0
1
0
0
0
0
0
2
0
0
7
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
1
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
2
1
0
2
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
4
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
3
0
1
2
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
3
1
0
0
0
2
1
0
0
2
0
1
0
0
2
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
6
0
0
0
0
0
0
0
0
3
0
0
4
1
1
0
2
0
1
0
0
2
0
2
2
1
0
0
0
1
0
2
0
0
1
0
0
0
0
1
0
0
0
1
1
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
2
0
0
0
0
0
0
0
1
2
0
0
1
1
2
0
0
1
0
0
1
4
2
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
2
2
0
0
2
0
0
0
1
0
0
3
0
0
0
2
0
0
0
1
0
1
0
2
1
0
2
0
1
0
0
0
0
0
0
0
2
1
0
0
1
0
1
0
0
0
0
2
0
3
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
5
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
3
0
0
1
0
0
2
0
0
0
0
0
0
0
1
2
0
1
0
2
2
2
0
2
0
0
0
4
0
0
0
0
0
0
0
3
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
2
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
1
0
0
0
0
2
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
2
1
0
2
1
0
2
0
0
0
0
1
0
0
0
2
0
0
4
1
0
5
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
3
0
1
0
1
0
0
0
0
2
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
1
0
1
0
2
0
1
0
0
0
0
2
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
2
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
6
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
2
0
0
0
1
0
2
1
1
4
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
1
0
0
1
2
0
1
0
0
2
0
0
0
0
1
0
0
0
1
2
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
11
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
2
0
0
4
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
3
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
4
0
0
1
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
1
0
3
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
3
0
2
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
3
0
2
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
13
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
1
2
0
0
1
2
0
0
3
0
0
0
1
0
0
0
0
3
0
0
0
1
1
0
0
0
0
1
1
1
0
1
0
2
0
2
2
0
0
0
0
2
0
0
2
0
0
0
2
3
0
0
0
0
1
0
1
0
0
3
1
1
1
0
0
0
0
0
0
0
0
0
0
3
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
3
0
2
0
0
0
2
0
0
2
0
1
2
0
0
0
1
0
0
0
1
1
0
2
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
1
0
0
1
1
0
0
1
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
2
0
0
0
0
1
0
0
3
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
5
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
5
1
2
0
0
2
0
0
1
2
0
1
1
0
0
0
0
0
0
2
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
1
1
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
1
0
1
0
0
4
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
1
0
1
0
2
1
0
0
0
1
1
0
1
0
0
0
2
0
2
0
0
0
0
0
0
2
2
1
0
0
1
2
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
1
0
0
1
0
0
2
2
0
0
6
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
1
0
2
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
1
2
0
0
0
1
2
0
0
2
1
2
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
3
0
0
2
0
0
2
2
2
0
0
2
1
0
0
1
0
2
5
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
1
0
0
0
0
2
0
0
3
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
1
0
2
0
0
0
3
1
0
0
2
0
1
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
1
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
1
1
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
3
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
3
0
2
0
0
0
0
0
3
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
1
0
1
0
2
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
16
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
6
0
0
0
0
2
0
0
1
0
0
2
2
0
0
0
1
0
0
0
2
2
0
1
0
0
1
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
3
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
1
1
5
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
1
0
0
4
0
0
1
0
0
3
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
4
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
1
0
0
3
0
0
0
2
1
3
1
0
0
0
2
3
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
1
1
0
0
0
0
0
1
2
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
2
3
0
0
2
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
4
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
3
0
0
0
2
0
0
0
0
1
2
0
0
1
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
6
1
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
1
1
0
1
0
0
0
0
1
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
1
0
0
1
2
0
3
1
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
3
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
2
2
0
2
0
0
0
0
0
0
1
1
0
2
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
2
0
0
1
4
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
3
0
0
0
0
0
2
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
9
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
1
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
7
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
3
2
0
0
0
0
0
0
1
0
1
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
14
2
0
1
2
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
4
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
2
1
0
1
2
2
0
0
1
2
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
2
0
7
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
3
0
0
1
1
0
3
1
0
0
0
0
0
0
6
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
4
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
2
0
1
0
1
0
0
0
0
0
0
3
2
0
1
0
0
0
0
2
0
0
2
0
0
1
0
1
0
0
3
0
2
0
0
0
0
1
0
1
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
4
0
0
2
0
0
1
0
1
0
3
1
0
0
1
0
3
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
3
0
1
0
0
1
0
0
0
0
1
2
0
2
1
2
0
0
2
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
1
1
0
0
0
1
0
0
1
0
1
0
0
0
2
0
0
0
4
4
0
0
1
0
0
2
0
0
1
2
0
0
0
0
6
0
0
0
0
0
2
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
2
0
0
0
2
0
1
0
0
1
1
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
1
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
6
1
0
0
2
1
1
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
2
0
0
0
0
4
0
0
0
0
0
0
2
0
0
2
0
0
3
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
5
0
0
0
0
0
0
1
0
0
0
0
0
3
1
0
0
2
0
0
2
0
0
0
0
0
0
2
1
0
0
0
3
0
0
2
0
0
0
0
4
0
1
2
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
1
2
1
1
0
0
0
2
2
0
4
2
0
0
1
2
0
0
2
0
0
0
4
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
1
1
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
2
0
2
0
0
1
1
0
0
0
3
0
0
0
1
0
2
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
2
0
2
1
0
1
0
1
2
0
1
0
0
0
0
2
0
2
0
0
3
0
0
0
3
0
0
0
0
0
2
0
0
2
2
0
1
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
2
0
0
2
0
0
0
1
1
0
3
1
0
0
1
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
2
0
0
1
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
2
0
0
1
2
0
2
0
0
1
1
1
2
0
2
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
2
0
2
0
0
0
0
2
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
1
2
0
2
0
0
0
0
0
0
0
0
2
0
2
1
1
0
6
0
0
0
2
0
0
0
2
2
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
3
0
0
0
4
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
1
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
2
0
0
2
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
1
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
2
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
2
0
2
0
0
2
2
1
0
5
0
1
0
0
2
1
0
0
0
0
1
0
0
0
0
2
1
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
2
4
0
0
0
0
0
0
4
0
0
0
3
0
0
0
0
0
2
1
0
1
0
1
0
0
0
5
0
1
2
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
3
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
3
0
0
3
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
1
3
0
0
0
1
0
1
0
0
4
1
0
0
0
0
0
1
0
2
0
0
0
0
3
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
4
0
2
1
0
0
0
0
1
0
1
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
2
0
0
0
1
1
0
0
0
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
6
0
2
4
0
0
4
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
2
0
0
0
1
0
0
3
0
0
0
0
0
1
0
0
3
0
0
1
0
0
0
0
0
1
0
0
0
1
0
2
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
3
1
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
2
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
2
0
0
0
1
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
3
1
0
0
3
0
1
1
0
2
1
0
3
0
2
0
3
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
3
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
2
0
1
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
2
0
1
0
0
2
0
1
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
2
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
2
0
0
0
2
0
1
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
3
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
1
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
4
0
1
0
0
2
0
2
0
0
1
2
0
2
0
0
0
0
0
0
1
0
3
0
2
0
0
0
0
1
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
3
2
2
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
1
0
2
0
0
2
0
1
0
2
0
2
0
0
2
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
1
2
0
0
0
7
0
2
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
9
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
2
0
0
3
0
2
1
2
0
0
0
2
0
4
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
2
4
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
1
0
0
2
1
1
2
0
0
3
2
0
1
2
0
0
0
2
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
2
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
3
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
1
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
1
0
0
1
8
0
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
2
3
1
0
2
0
0
0
0
0
0
0
1
0
0
2
1
0
2
0
2
0
0
0
1
0
1
2
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
5
1
1
3
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
2
1
1
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
2
0
0
0
1
0
0
2
0
1
0
0
3
2
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
2
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
8
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
3
0
0
0
0
2
0
0
0
3
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
1
2
0
4
0
1
0
0
0
2
3
0
0
0
1
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
7
4
2
0
0
0
0
0
0
2
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
3
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
1
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
1
2
0
1
0
0
3
0
2
0
2
9
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
1
0
0
0
1
0
0
2
2
0
0
1
0
0
0
15
1
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
3
0
0
0
2
3
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
2
1
2
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
2
0
2
2
1
0
1
0
2
0
1
2
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
5
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
2
0
0
0
0
0
0
0
2
0
0
1
0
2
0
2
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
2
6
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
1
0
3
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
1
0
0
2
0
0
0
0
2
0
2
1
0
1
2
0
0
0
2
3
0
0
0
3
0
0
5
0
0
0
0
3
2
0
0
1
0
0
0
5
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
2
0
0
2
0
4
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
3
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
2
2
1
0
0
2
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
2
4
0
0
3
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
1
0
0
0
1
2
2
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
2
0
0
0
1
0
0
0
0
1
0
0
2
3
0
0
0
0
0
1
0
0
0
1
3
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
3
0
1
0
0
1
1
0
0
5
0
1
0
0
0
6
0
0
0
1
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
4
0
2
0
2
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
2
1
2
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
4
1
2
0
0
0
0
0
0
0
1
0
1
0
0
2
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
3
0
1
0
0
2
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
2
0
1
1
0
2
0
0
2
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
1
0
1
0
2
0
3
1
2
0
4
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
3
0
0
1
0
0
2
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
3
0
0
0
0
0
1
0
0
2
0
2
1
0
2
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
2
4
0
0
0
4
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
2
0
0
3
0
0
0
0
0
3
0
0
8
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
4
3
0
0
7
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
2
0
0
2
0
0
3
3
1
0
0
0
2
0
1
3
0
0
0
2
0
0
0
0
2
2
2
2
0
0
0
0
0
0
0
0
0
0
1
0
4
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
2
1
0
0
1
0
0
1
1
0
2
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
1
0
0
2
1
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
3
2
0
2
1
0
2
5
3
0
0
0
0
0
0
0
3
2
1
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
2
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
1
0
2
0
4
1
0
3
3
0
0
0
0
0
3
0
3
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
1
0
2
0
0
0
0
0
0
1
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
4
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
3
2
0
2
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
1
1
2
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
5
0
0
1
0
2
1
0
0
2
0
0
1
0
0
0
0
0
3
0
0
2
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
1
1
0
0
3
0
0
0
9
0
0
2
0
0
0
0
0
3
0
2
0
1
0
0
2
2
0
0
0
1
0
0
0
1
2
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
3
0
2
2
0
3
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
1
1
1
0
0
0
0
2
0
2
0
0
0
3
5
0
0
2
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
1
0
0
0
0
1
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
1
0
0
1
0
0
0
1
2
0
0
0
0
1
0
0
0
1
0
0
2
0
1
0
0
0
1
0
0
0
0
2
0
0
2
1
1
0
0
0
2
1
0
0
2
0
0
0
0
1
0
2
0
0
0
1
0
1
1
0
0
2
2
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
7
0
3
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
3
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
8
0
0
0
0
0
0
2
2
0
0
0
0
0
1
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
5
2
1
1
0
0
2
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
2
0
0
2
1
0
0
0
3
1
0
0
0
1
0
0
0
0
3
0
0
1
2
0
0
3
0
0
0
0
0
3
1
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
4
0
0
2
0
1
1
0
1
2
0
0
0
0
0
3
1
2
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
2
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
1
0
0
0
1
2
0
0
1
0
0
1
0
0
0
2
2
0
0
0
0
0
2
3
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
1
0
0
2
0
1
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
2
0
0
1
0
3
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
2
2
0
0
0
3
0
1
0
0
1
0
2
0
0
1
0
5
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
1
0
2
0
1
0
0
0
1
1
0
0
0
0
1
0
0
7
1
1
0
0
0
0
0
2
0
0
0
0
4
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
3
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
1
2
1
0
2
0
2
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
3
2
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
2
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
2
0
2
0
0
1
6
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
5
0
0
0
0
2
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
1
6
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
2
6
0
0
1
1
0
0
0
0
1
0
0
0
0
0
2
1
1
0
0
0
0
0
1
0
0
0
0
0
0
2
3
0
1
0
1
2
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
8
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
1
0
1
0
2
0
0
0
0
0
1
0
6
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
1
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
3
1
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
1
0
0
0
1
0
0
0
0
2
2
0
0
0
0
1
1
0
4
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
4
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
3
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
3
2
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
8
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
2
3
0
0
0
1
0
0
0
2
0
1
2
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
2
0
2
2
1
2
0
0
0
0
2
2
0
0
0
1
0
0
1
2
0
0
0
0
2
0
1
1
0
0
0
0
2
0
0
0
1
2
0
0
0
0
3
2
0
0
0
1
0
0
0
0
1
0
0
2
0
0
1
1
0
0
1
0
3
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
3
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
2
2
2
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
4
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
3
2
0
2
0
0
0
2
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
1
1
0
1
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
3
1
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
2
2
0
0
0
0
1
0
0
2
0
2
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
5
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
1
0
0
0
1
1
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
1
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
1
0
2
0
0
1
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
1
0
0
0
8
0
0
0
0
0
0
0
2
0
3
0
0
0
3
0
0
0
0
5
2
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
1
0
0
2
0
2
1
0
0
5
0
2
0
0
0
0
3
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
2
0
2
0
2
0
0
1
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
1
1
0
0
0
0
2
0
1
0
0
0
0
1
0
3
0
0
0
1
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
5
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
4
0
0
2
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
5
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
1
0
4
0
0
0
2
1
0
0
0
0
0
0
9
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
1
0
0
1
0
0
0
0
0
1
0
2
0
0
2
1
0
0
0
0
1
0
1
0
0
1
2
0
3
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
2
1
0
0
0
1
1
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
2
0
0
4
0
1
0
0
0
0
0
0
0
1
0
0
0
4
1
0
2
0
0
6
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
0
2
0
1
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
1
0
0
0
0
0
0
2
2
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
13
0
2
0
0
3
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
1
0
2
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
6
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
2
1
0
1
17
1
0
0
0
0
0
0
1
0
1
0
0
0
2
2
0
0
0
0
0
1
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
1
1
2
0
0
0
5
0
2
0
0
0
0
0
0
7
0
0
1
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
3
0
0
3
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
2
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
3
0
0
2
0
2
0
1
0
0
0
0
1
0
2
0
0
0
0
1
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
4
0
2
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
5
0
0
0
1
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
2
1
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
2
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
1
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
2
2
0
0
0
0
1
0
0
0
1
1
2
0
0
0
2
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
2
2
0
0
0
2
0
1
2
0
0
0
0
0
2
1
1
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
2
1
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
1
0
0
2
0
0
0
1
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
5
0
0
1
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
9
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
2
1
0
0
1
2
1
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
1
2
0
0
1
0
0
2
0
2
0
0
11
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
2
2
0
2
0
0
0
2
6
0
0
4
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
3
2
0
0
0
0
2
0
0
0
1
1
0
0
0
2
0
2
0
0
2
0
3
0
0
0
2
0
0
0
1
0
0
0
0
0
1
1
0
1
2
0
5
0
0
0
2
0
0
0
5
6
2
0
0
0
0
3
0
0
0
0
0
1
0
3
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
4
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
2
0
0
0
0
2
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
4
0
0
0
3
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
1
0
1
0
3
0
0
0
0
0
0
2
0
2
0
1
0
0
0
1
0
0
0
3
0
0
1
2
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
3
0
0
0
0
1
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
3
1
0
0
2
0
0
0
0
0
0
0
0
2
2
0
1
0
1
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
4
1
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
4
0
3
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
2
2
2
2
2
0
2
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
4
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
6
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
1
1
0
0
0
0
0
2
0
0
3
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
2
0
3
0
0
0
0
0
1
2
0
0
1
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
1
0
1
2
0
1
1
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
3
0
0
0
3
0
0
0
2
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
5
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
1
2
3
0
2
0
0
0
1
0
2
0
0
3
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
1
0
0
1
1
3
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
2
0
1
2
2
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
2
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
1
0
1
0
0
0
1
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
2
0
1
0
2
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
2
0
0
1
0
0
3
0
2
2
0
1
1
0
0
0
0
11
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
3
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
1
2
1
0
0
3
0
0
0
0
0
0
0
5
0
0
0
0
1
1
0
0
1
3
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
3
4
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
2
2
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
9
0
0
0
0
0
1
0
0
1
0
0
0
0
3
0
0
0
3
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
4
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
1
2
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
5
0
0
0
0
0
1
0
0
3
0
0
3
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
2
0
0
0
2
2
2
0
0
0
1
0
0
2
1
1
0
0
0
1
2
1
0
0
0
0
0
0
0
3
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
2
0
10
1
0
1
1
1
2
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
3
12
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
8
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
4
0
2
2
0
0
0
0
0
0
0
0
1
1
6
0
2
0
0
0
0
0
0
1
0
0
1
0
0
6
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
2
0
2
0
0
0
0
2
2
2
0
3
0
1
0
0
1
0
0
1
0
1
0
0
0
1
0
3
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
1
0
2
0
1
0
0
0
0
0
0
0
3
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
2
0
0
0
0
2
0
3
1
0
2
5
0
0
0
0
0
0
0
0
1
1
3
0
0
0
0
4
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
1
0
3
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
2
0
3
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
8
0
0
2
0
2
0
0
1
0
2
2
1
0
2
2
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
2
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
1
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
4
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
2
0
1
0
3
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
1
0
1
1
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
0
4
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
1
0
3
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
1
0
1
1
0
1
0
1
0
3
3
0
2
0
1
0
0
2
0
0
3
0
0
0
1
1
0
0
2
0
0
5
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
2
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
3
0
0
0
0
0
2
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
2
0
0
0
0
0
1
2
0
0
2
0
0
0
4
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
2
0
1
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
5
0
0
0
0
0
4
0
0
0
1
0
0
0
0
2
3
0
3
0
0
0
0
1
4
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
1
0
1
0
1
2
0
0
1
2
2
0
0
0
1
0
0
0
0
3
0
2
0
0
0
0
0
0
1
1
0
0
0
2
0
1
0
2
0
2
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
2
0
0
0
1
1
0
0
0
0
1
0
0
0
2
0
0
2
0
0
1
0
1
0
0
0
3
0
0
0
1
0
0
0
0
1
2
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
1
0
2
0
0
2
0
0
3
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
2
5
0
4
3
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
1
0
0
0
2
1
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
3
0
0
0
0
0
0
0
2
0
1
1
0
0
1
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
1
1
0
0
0
0
2
0
3
0
2
2
0
0
0
0
2
0
0
3
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
2
0
0
0
2
0
0
2
1
0
3
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
1
1
0
0
1
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
2
0
1
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
5
3
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
3
0
2
0
0
0
1
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
5
0
0
0
1
6
2
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
2
0
3
0
0
0
0
0
2
1
0
0
0
0
1
0
1
0
0
0
2
1
4
5
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
1
2
2
0
0
0
0
1
0
0
0
0
1
2
0
1
2
0
1
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
1
2
0
0
0
0
2
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
6
0
0
1
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
2
0
0
0
0
3
0
5
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
2
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
4
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
0
4
0
2
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
2
0
0
1
0
0
1
1
0
2
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
2
0
1
0
0
0
1
0
1
0
2
0
0
2
0
0
0
3
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
4
0
1
1
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
2
1
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
1
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
1
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
3
0
4
0
0
0
0
0
1
1
0
0
1
0
1
4
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
3
0
2
1
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
3
4
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
1
0
0
4
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
4
0
0
0
0
1
3
2
3
0
0
1
0
0
1
2
0
1
0
1
0
0
0
0
4
1
1
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
2
0
0
2
0
2
1
3
2
1
0
1
2
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
1
10
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
4
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
2
0
1
1
0
0
1
0
0
0
0
10
0
0
0
2
0
0
0
0
1
0
3
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
2
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
4
0
0
0
0
2
6
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
2
0
0
1
0
0
0
0
0
2
1
0
0
1
0
0
0
2
1
0
0
0
4
2
0
0
0
0
0
0
0
2
0
0
2
1
0
0
2
2
0
3
1
1
3
1
6
0
0
0
0
2
0
2
1
0
3
0
0
0
1
0
0
0
0
0
0
1
0
2
0
1
0
1
0
0
5
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
4
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
3
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
2
2
1
2
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
1
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
4
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
4
2
0
0
0
2
0
2
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
2
0
0
0
0
4
0
2
2
0
1
1
0
0
0
0
0
2
0
2
1
1
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
6
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
3
0
1
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
1
1
0
1
1
0
0
0
0
3
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
1
2
0
0
4
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
1
1
0
2
0
0
0
1
0
0
0
0
0
0
0
3
0
1
2
0
0
0
0
1
0
0
2
0
2
1
0
1
0
2
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
2
1
0
1
2
0
0
0
4
0
0
0
1
0
0
0
0
0
5
0
0
0
0
0
0
0
0
1
0
1
3
0
0
0
0
0
1
1
2
0
1
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
5
1
1
3
1
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
7
0
0
0
0
1
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
2
0
0
1
0
0
0
2
0
1
0
0
0
3
0
0
0
0
0
3
0
0
2
0
0
0
4
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
1
0
0
1
0
1
0
3
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
1
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
3
1
2
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
1
0
3
1
0
1
0
0
1
0
2
1
2
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
4
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
2
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
1
1
2
2
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
1
0
0
0
0
0
1
0
2
2
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
2
2
0
2
0
0
0
1
1
0
0
2
0
0
0
0
3
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
3
0
0
0
2
1
0
0
2
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
3
0
0
0
1
0
0
0
2
0
0
3
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
2
0
0
1
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
5
1
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
2
0
2
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
5
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
0
0
1
3
0
1
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
1
1
3
0
2
0
0
2
0
0
2
0
0
0
0
1
0
2
0
1
0
1
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
5
0
4
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
1
0
2
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
1
2
0
0
1
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
6
0
0
0
0
0
2
0
1
0
0
2
1
0
2
0
1
0
0
1
2
0
1
0
0
5
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
2
0
2
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
1
0
0
0
0
0
0
5
0
2
0
0
1
0
0
2
0
0
0
2
1
3
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
1
2
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
1
0
5
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
1
0
0
1
0
1
0
2
0
0
2
0
1
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
5
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
5
2
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
2
2
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
5
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
2
0
0
1
2
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
2
1
0
2
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
3
0
1
0
0
0
0
0
0
0
0
0
1
4
1
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
2
1
2
0
1
2
1
3
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
2
2
0
0
3
1
0
2
0
2
0
0
2
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
2
0
0
0
2
0
0
0
3
0
3
3
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
7
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
4
0
4
2
1
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
2
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
1
2
0
0
0
1
0
1
0
0
0
1
0
2
0
2
1
1
0
0
0
0
0
4
0
0
3
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
1
0
1
0
2
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
3
1
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
1
0
1
2
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
1
0
0
0
0
0
0
2
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
3
0
0
0
0
1
0
1
0
0
1
0
0
0
2
0
2
0
0
2
5
0
0
1
0
2
1
0
2
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
2
3
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
5
0
2
0
0
0
0
3
0
0
0
0
2
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
1
1
2
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
3
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
3
0
0
1
5
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
1
1
3
0
0
0
0
1
0
0
0
4
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
1
1
2
3
2
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
2
1
0
0
2
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
4
0
2
2
0
0
0
0
1
0
0
3
0
0
0
0
8
3
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
2
4
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
2
3
0
0
0
0
1
2
0
0
0
0
0
1
0
0
1
0
0
0
1
0
2
0
1
0
2
3
0
1
3
0
0
2
0
0
0
1
1
0
0
1
0
2
3
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
2
0
0
1
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
2
2
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
3
2
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
1
0
1
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
5
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
1
0
1
0
0
3
1
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
2
1
0
3
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
5
0
0
0
2
0
8
0
0
4
0
1
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
3
0
1
0
0
0
0
0
2
8
0
0
0
0
0
2
2
1
0
0
2
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
3
0
0
1
2
2
0
0
1
2
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
1
0
0
0
6
1
0
2
0
0
3
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
2
2
1
0
0
0
0
2
0
0
12
1
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
1
2
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
3
2
2
0
1
0
0
1
0
1
0
0
0
0
0
0
0
2
0
1
2
0
2
0
0
0
0
0
0
0
0
0
1
2
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
2
0
0
1
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
1
1
0
4
0
0
3
0
0
1
1
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
1
0
0
0
0
1
0
5
0
0
2
0
0
1
0
0
1
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
3
0
1
2
2
1
4
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
3
0
0
6
0
2
0
0
1
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
2
0
0
3
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
13
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
2
4
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
1
2
1
2
0
0
0
0
0
2
1
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
2
1
0
0
1
2
2
0
0
4
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
4
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
4
0
3
2
1
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
2
0
0
3
0
2
0
0
2
0
1
0
0
0
0
0
2
0
0
0
2
0
14
0
1
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
1
0
2
0
0
0
0
0
0
4
1
0
0
0
3
2
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
1
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
5
0
0
0
0
7
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
2
1
0
1
1
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
2
0
10
0
2
0
9
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
1
0
2
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
3
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
2
0
0
0
0
0
3
0
0
0
0
1
2
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
5
2
1
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
2
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
1
0
0
0
2
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
4
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
1
0
0
0
0
0
2
0
2
0
1
0
0
0
0
1
0
2
0
1
1
0
0
0
0
1
0
1
1
1
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
2
4
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
3
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
3
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
6
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
1
0
1
0
0
0
2
1
1
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
3
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
3
0
0
1
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
2
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
1
0
2
0
0
0
0
0
0
6
3
0
1
0
0
0
2
0
3
0
0
1
0
1
0
0
0
3
0
0
0
0
0
0
0
1
0
0
1
0
2
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
3
2
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
4
0
0
0
0
0
2
0
0
0
1
0
1
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
5
0
0
1
0
1
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
2
5
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
7
1
1
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
3
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
2
3
0
2
3
0
2
0
0
1
0
1
0
0
0
0
1
3
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
3
1
0
0
0
1
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
2
0
2
0
0
0
1
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
1
0
0
0
0
2
0
2
2
0
0
1
0
0
2
1
0
1
0
0
0
0
0
2
0
0
2
0
1
0
1
0
0
0
0
3
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
5
0
0
0
1
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
1
2
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
2
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
1
0
0
0
2
0
0
0
2
2
0
1
0
2
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
2
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
1
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
1
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
4
1
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
1
0
1
0
4
0
0
0
0
1
0
2
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
4
0
0
1
0
2
0
0
1
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
2
1
0
0
0
0
2
4
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
2
0
0
1
1
0
1
0
0
0
0
0
0
0
2
2
2
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
2
0
2
0
0
1
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
2
0
2
1
2
0
4
0
0
0
2
0
0
0
3
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
1
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
2
0
2
0
0
0
3
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
3
1
1
0
0
2
0
0
2
0
2
2
7
0
0
0
0
0
0
1
1
0
0
0
2
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
2
3
0
2
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
5
0
1
1
0
0
0
0
0
2
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
2
2
0
0
2
0
2
5
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
3
0
0
1
2
0
0
1
0
0
1
1
0
1
1
1
0
2
0
2
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
3
0
0
0
0
1
0
1
5
0
0
0
1
0
0
4
0
0
0
2
4
0
1
0
0
0
0
1
1
0
0
0
0
0
0
2
3
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
5
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
4
2
0
0
3
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
3
3
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
2
0
10
0
0
0
2
0
2
0
0
0
0
0
0
0
3
0
2
0
1
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
1
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
1
0
2
3
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
3
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
1
0
0
5
1
0
0
0
0
0
1
0
0
3
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
3
0
0
0
2
0
4
2
0
2
0
0
2
0
0
11
1
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
2
1
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
5
1
2
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
2
0
0
1
0
0
1
0
2
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
2
0
0
0
0
0
0
3
0
1
0
0
0
0
3
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
2
0
1
1
0
2
0
2
3
1
2
0
0
1
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
3
0
0
0
0
0
0
1
0
0
1
0
2
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
1
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
1
2
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
1
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
2
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
2
1
0
2
0
0
0
0
0
0
4
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
3
1
0
0
1
0
0
0
0
2
0
3
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
1
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
2
2
2
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
2
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
3
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
3
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
2
0
0
2
0
0
1
1
0
1
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
2
0
0
1
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
7
2
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
1
0
0
0
2
0
3
0
0
9
0
3
0
0
0
0
1
0
0
0
2
0
0
0
0
1
1
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
3
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
4
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
2
0
2
2
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
1
0
0
3
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
1
5
0
0
0
3
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
1
0
2
0
1
0
0
1
0
0
2
0
0
0
0
5
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
3
0
1
0
2
0
0
0
1
0
0
0
0
0
1
0
0
2
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
2
0
1
0
0
1
0
0
1
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
5
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
1
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
1
0
5
2
0
0
0
0
0
0
0
0
10
0
0
2
1
0
0
0
4
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
1
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
2
4
0
1
0
0
1
0
2
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
2
0
0
0
0
0
0
3
0
0
0
1
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
1
0
3
0
0
0
2
0
0
0
2
4
0
0
0
2
2
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
3
0
0
0
2
2
0
0
0
2
0
0
0
0
2
1
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
4
0
0
1
2
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
1
0
1
2
1
0
0
2
2
0
0
0
2
1
0
0
0
1
1
0
0
0
3
0
0
0
0
3
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
3
0
2
0
2
1
2
0
0
0
1
0
2
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
3
1
0
0
0
2
4
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
2
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
3
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
1
1
0
0
0
0
1
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
5
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
3
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
2
0
1
2
0
2
0
0
0
1
0
2
1
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
3
0
0
0
0
3
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
1
1
0
0
0
1
3
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
1
0
1
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
4
1
0
1
0
0
0
0
2
0
0
0
5
0
0
0
0
0
2
1
0
1
0
1
0
0
0
0
1
0
0
7
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
3
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
3
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
1
2
0
1
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
2
0
0
0
1
1
0
3
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
3
0
1
2
0
2
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
2
0
1
0
2
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
4
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
3
0
2
1
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
2
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
2
1
0
0
0
0
0
1
0
1
0
1
3
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
10
3
0
1
0
0
1
0
0
0
2
1
0
0
0
1
2
0
0
1
2
1
0
0
0
0
0
2
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
3
0
2
1
0
0
3
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
2
2
0
2
0
4
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
2
1
0
0
1
0
2
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
2
0
0
0
5
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
2
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
1
2
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
3
0
1
0
0
1
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
3
2
0
0
2
0
4
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
1
0
3
0
0
0
0
0
2
0
0
2
0
2
1
1
0
0
0
0
2
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
2
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
2
0
0
0
0
1
0
0
2
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
3
1
0
0
1
0
0
0
0
0
0
1
3
0
1
0
0
0
0
0
0
0
2
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
6
0
0
0
0
2
0
0
1
2
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
1
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
7
2
0
2
1
0
1
0
0
1
0
2
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
15
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
1
0
0
0
1
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
1
0
2
0
0
0
1
2
0
0
0
2
0
0
1
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
2
2
0
0
4
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
3
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
3
0
1
0
0
2
0
1
0
2
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
1
2
0
0
0
0
0
0
3
0
2
0
0
2
3
2
2
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
3
0
0
0
0
1
0
0
2
2
0
4
0
1
0
0
1
1
0
2
0
0
0
2
2
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
4
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
2
1
2
1
0
2
0
0
2
4
2
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
3
0
0
0
0
2
0
0
2
4
2
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
3
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
4
0
1
0
0
0
1
1
0
0
1
0
1
2
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
3
0
0
2
1
1
0
0
1
0
0
0
0
0
0
5
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
3
0
1
0
0
2
0
0
0
0
0
0
0
1
0
2
1
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
10
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
2
0
1
0
0
0
0
0
0
3
0
0
1
2
0
0
0
0
0
0
0
2
0
0
2
2
0
2
0
0
0
1
0
4
0
0
1
0
0
0
2
0
0
0
2
0
0
1
0
0
1
0
0
2
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
3
2
1
4
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
3
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
1
2
0
0
0
0
0
2
1
0
0
2
1
1
0
1
0
0
0
3
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
1
2
1
0
0
0
2
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
2
0
1
2
0
5
0
0
0
2
1
0
0
0
3
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
4
0
0
1
0
0
1
0
0
2
0
0
0
0
0
2
0
0
2
1
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
5
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
5
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
1
0
0
1
0
6
0
0
0
0
0
1
2
0
0
2
1
1
0
0
0
1
1
2
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
3
1
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
1
2
0
0
8
0
2
0
0
0
0
2
2
2
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
3
0
0
2
0
2
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
6
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
2
0
0
0
2
2
1
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
2
0
2
0
4
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
4
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
2
0
1
0
2
0
0
0
0
1
0
0
0
1
2
1
0
2
0
0
2
0
0
1
4
0
0
2
1
0
0
0
0
2
0
2
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
7
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
1
1
2
0
0
0
3
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
3
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
1
0
2
3
1
2
0
0
2
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
1
0
0
1
0
0
2
0
4
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
6
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
3
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
2
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
1
0
0
0
2
1
0
0
2
0
6
0
0
4
0
0
0
0
0
1
0
1
0
0
0
1
2
1
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
1
4
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
3
0
0
1
0
1
2
0
2
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
2
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
1
0
1
0
0
5
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
3
0
0
0
2
0
0
0
0
0
1
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
2
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
5
2
0
0
0
1
0
0
0
2
0
0
0
0
3
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
1
0
0
0
0
0
1
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
3
1
0
2
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
2
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
1
0
0
0
0
1
1
0
5
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
2
1
0
0
2
0
0
0
0
0
1
1
0
2
1
0
0
0
2
0
0
1
0
0
0
0
0
1
1
0
2
2
0
0
0
0
0
0
1
0
0
3
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
1
0
2
3
0
0
1
2
2
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
3
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
3
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
3
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
9
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
2
3
1
0
0
2
8
2
2
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
2
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
0
0
2
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
1
2
0
2
0
0
0
0
0
0
0
0
2
1
0
2
0
1
2
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
6
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
5
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
1
2
3
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
3
2
0
0
0
1
0
0
0
0
0
0
0
0
0
5
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
1
2
0
0
3
0
0
0
1
6
0
0
0
3
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
2
1
0
1
2
2
0
1
2
2
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
1
1
1
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
1
0
1
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
3
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
4
1
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
1
0
0
1
0
0
0
2
0
1
0
0
1
2
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
4
0
1
0
0
0
0
0
0
0
5
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
1
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
1
1
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
4
3
1
0
1
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
2
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
5
0
3
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
1
0
0
3
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
2
0
2
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
3
0
0
0
0
3
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
2
5
0
2
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
1
0
2
1
0
1
0
3
0
1
0
0
0
2
9
0
1
1
0
0
0
0
0
0
1
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
2
0
0
0
3
1
0
2
0
0
0
1
2
0
0
0
0
0
1
0
0
2
2
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
1
0
1
1
1
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
2
1
0
0
1
2
3
0
0
0
1
0
0
0
2
1
2
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
3
0
1
0
0
1
0
0
0
0
1
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
1
0
0
1
2
1
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
2
0
0
0
0
0
0
0
1
1
1
0
0
0
0
2
0
0
2
2
0
0
2
3
0
0
0
0
0
0
0
2
1
1
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
13
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
4
1
0
2
0
0
2
1
0
0
0
0
0
1
2
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
5
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
5
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
4
0
0
3
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
1
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
2
1
1
0
1
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
1
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
5
0
0
2
0
1
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
2
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
2
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
2
2
0
1
0
0
1
0
0
1
0
0
0
0
0
0
2
0
2
0
4
2
0
1
0
0
1
0
3
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
2
0
0
2
1
0
0
0
0
0
0
2
0
2
0
0
1
1
0
0
0
0
2
2
0
0
0
0
2
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
3
0
0
1
0
2
0
0
1
0
4
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
4
0
0
0
0
2
0
1
1
2
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
5
0
2
1
0
1
1
0
0
0
1
2
0
0
0
0
2
0
0
2
0
0
1
0
1
2
0
0
0
0
3
0
0
2
0
0
0
0
0
3
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
2
0
1
0
0
1
0
1
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
5
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
3
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
9
1
1
3
0
1
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
2
3
1
0
0
2
1
0
1
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
1
0
0
2
1
0
0
0
0
2
0
1
0
0
1
0
0
1
0
1
0
0
2
0
0
1
0
1
0
0
2
0
0
0
0
3
0
0
2
1
0
4
0
2
0
0
3
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
2
1
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
5
1
0
0
0
0
3
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
1
0
0
0
1
0
0
2
0
2
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
2
0
0
0
0
0
0
3
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
2
0
2
0
4
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
3
0
0
2
0
1
0
2
0
0
2
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
6
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
1
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
4
0
0
3
0
0
3
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
6
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
1
2
2
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
2
1
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
2
0
0
0
2
0
0
0
4
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
4
0
0
0
2
2
1
0
0
0
0
0
0
5
2
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
4
0
3
0
5
3
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
2
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
2
0
2
0
3
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
1
0
2
1
0
0
2
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
2
1
0
1
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
1
0
0
0
2
0
3
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
1
2
0
1
2
0
0
0
0
0
0
0
0
4
1
0
0
0
2
1
0
0
1
0
1
2
2
0
0
0
2
0
1
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
4
0
0
0
0
2
1
0
0
1
0
0
0
0
0
2
0
1
0
0
3
2
1
0
0
0
0
1
0
0
0
2
2
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
3
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
2
0
2
5
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
1
0
0
0
0
2
0
2
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
3
5
0
2
0
0
1
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
2
0
0
1
0
0
0
2
0
0
0
2
2
0
2
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
4
0
0
0
3
0
0
0
0
1
0
0
0
0
2
0
0
5
0
0
0
0
2
3
0
0
0
0
0
2
0
0
0
3
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
1
1
2
0
0
0
0
0
0
1
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
1
1
0
0
2
2
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
2
0
2
0
0
0
0
2
0
0
2
0
0
0
1
0
0
1
0
1
0
0
2
0
3
2
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
3
1
3
0
1
0
0
0
0
0
0
0
1
0
0
2
2
1
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
1
4
0
2
0
2
0
1
1
2
0
4
1
0
0
1
1
1
1
0
1
6
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
3
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
3
0
0
0
0
0
2
2
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
1
0
0
1
0
1
0
2
0
0
2
0
0
0
4
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
1
0
0
0
0
0
0
1
0
0
1
0
0
4
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
3
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
2
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
11
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
3
2
0
0
0
0
2
1
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
4
2
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
3
0
0
2
2
0
0
0
2
0
1
0
2
0
0
4
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
2
0
0
3
0
0
0
8
1
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
1
0
2
0
0
0
0
0
0
4
0
0
2
0
0
0
0
1
1
0
0
2
0
2
2
0
2
1
1
0
0
0
1
0
0
0
2
0
0
0
0
3
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
3
0
1
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
2
0
0
0
0
0
1
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
2
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
2
0
0
2
0
1
0
0
0
0
3
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
6
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
3
1
0
0
1
0
9
2
0
0
0
2
0
0
0
1
0
0
0
2
2
0
0
0
0
1
2
0
1
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
5
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
1
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
1
2
0
0
1
0
0
0
0
1
0
0
0
0
0
3
0
0
1
0
0
0
0
0
1
0
2
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
3
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
2
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
2
0
2
0
0
0
0
0
2
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
2
1
0
0
0
0
1
2
0
1
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
1
0
1
0
2
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
9
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
5
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
1
2
0
2
0
0
2
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
5
0
1
2
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
3
0
0
0
0
0
0
0
1
0
1
2
0
1
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
2
0
1
0
1
0
1
0
1
0
0
0
1
0
0
0
1
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
5
0
0
0
1
0
0
1
0
1
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
2
3
0
3
0
0
1
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
4
0
0
0
2
2
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
3
1
0
2
0
0
2
0
0
0
2
0
0
1
0
2
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
5
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
4
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
1
1
0
0
2
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
4
0
0
0
1
3
0
0
0
0
2
0
6
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
1
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
2
0
1
0
1
0
0
0
1
1
3
0
2
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
2
2
0
1
0
0
0
0
0
3
0
0
0
3
0
0
0
0
2
1
0
2
0
6
0
0
0
6
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
2
0
0
1
0
1
0
2
0
1
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
6
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
1
0
1
2
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
7
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
6
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
2
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
1
2
0
1
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
3
1
2
2
0
2
1
0
0
0
0
0
4
1
0
2
0
0
2
2
1
2
0
0
0
1
0
2
0
0
2
0
2
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
3
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
2
0
2
2
0
0
2
0
1
1
0
0
1
1
0
5
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
1
0
0
0
1
0
0
2
2
0
0
2
0
0
0
0
0
1
2
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
1
4
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
2
2
0
0
1
1
0
0
0
0
0
2
0
1
0
0
0
0
1
3
0
2
2
1
0
0
0
0
3
2
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
4
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
1
0
0
0
1
0
0
9
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
1
0
0
1
0
1
0
3
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
6
0
2
0
3
0
0
0
1
0
0
0
0
1
0
1
3
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
1
2
2
0
2
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
1
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
3
0
0
0
2
0
0
0
0
2
0
0
2
0
0
1
1
0
0
0
0
1
1
2
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
2
1
0
0
2
0
0
2
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
1
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
2
0
0
0
0
3
0
0
1
0
0
0
1
2
1
0
0
2
12
0
0
0
0
2
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
1
0
0
0
0
2
0
0
3
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
2
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
2
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
1
0
0
0
2
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
19
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
2
0
0
0
0
0
1
1
0
0
0
4
0
0
0
0
0
2
2
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
4
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
2
2
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
5
2
1
1
0
0
0
0
3
0
0
0
0
1
0
2
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
3
0
0
2
4
1
0
0
0
0
0
0
0
3
0
3
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
3
0
0
0
0
2
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
2
0
0
2
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
2
1
0
1
0
1
0
1
0
0
0
7
0
1
0
0
0
0
2
0
1
1
0
0
0
0
0
2
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
1
0
1
0
0
6
0
0
0
0
2
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
5
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
2
2
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
2
1
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
3
0
2
1
0
0
0
0
0
2
10
0
1
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
1
0
0
2
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
3
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
1
0
0
0
2
1
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
2
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
2
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
4
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
5
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
3
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
3
0
0
1
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
3
0
0
0
0
1
0
3
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
7
0
0
0
0
0
0
1
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
2
3
0
0
0
1
0
0
2
0
0
0
0
0
1
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
1
1
0
0
1
0
0
0
0
0
0
3
2
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
22
1
0
2
1
0
0
0
0
0
0
3
1
0
1
0
2
0
0
0
0
0
0
1
0
0
3
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
1
2
1
0
2
0
0
5
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
3
1
0
1
0
0
0
2
2
0
0
0
2
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
3
0
2
1
0
0
3
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
4
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
6
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
1
0
0
0
0
3
0
2
2
0
0
0
2
1
0
2
0
0
1
3
6
2
0
0
0
0
1
0
2
0
0
0
2
0
0
0
5
0
0
0
0
0
0
1
1
0
0
1
2
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
1
0
1
1
0
1
0
0
0
0
2
0
0
2
0
1
2
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
3
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
2
0
0
1
0
1
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
4
0
0
0
1
0
0
0
3
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
2
0
0
1
0
0
1
0
0
1
1
0
0
0
3
2
2
0
0
2
0
0
0
0
0
0
0
0
0
5
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
1
2
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
2
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
3
0
0
0
2
0
2
0
0
0
0
0
1
0
1
2
1
0
1
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
1
2
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
1
1
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
3
0
0
0
0
1
1
2
0
1
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
6
0
1
0
0
1
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
1
0
0
1
0
0
2
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
3
0
0
0
0
6
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
3
3
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
2
0
0
1
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
1
1
0
0
0
0
0
0
1
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
1
1
0
1
1
1
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
3
0
0
0
1
0
0
0
0
1
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
3
0
0
0
1
1
0
0
0
2
0
3
0
0
0
0
0
2
0
5
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
1
0
0
0
0
0
2
3
0
7
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
3
2
0
0
0
0
1
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
7
0
1
1
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
1
0
0
0
2
1
0
5
1
0
0
3
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
1
1
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
4
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
2
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
10
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
4
0
0
0
0
0
1
2
0
0
0
0
0
2
0
1
0
1
0
1
1
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
4
1
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
2
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
1
0
0
1
0
0
0
0
0
0
0
2
0
0
2
1
1
2
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
1
1
0
0
0
0
1
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
3
1
0
1
1
3
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
2
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
2
6
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
2
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
1
1
0
0
0
1
1
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
2
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
7
1
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
1
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
2
2
0
0
7
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
3
0
0
0
0
0
0
2
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
2
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
2
0
0
0
0
3
0
1
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
4
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
2
1
0
0
2
0
0
1
0
0
0
0
0
2
0
3
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
2
1
1
0
0
0
1
0
0
1
1
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
2
0
1
0
2
2
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
2
1
0
2
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
1
1
0
2
1
2
2
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
3
0
0
0
1
0
0
0
0
0
0
1
0
2
2
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
4
0
0
0
1
0
0
0
0
1
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
4
0
0
0
0
1
0
0
0
7
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
2
0
4
2
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
1
3
2
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
1
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
6
0
0
1
0
3
1
0
0
0
3
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
1
0
0
1
0
2
0
2
0
0
3
0
0
0
0
0
0
0
1
0
0
2
1
1
2
2
0
0
0
0
0
0
1
0
0
5
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
5
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
3
2
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
2
0
7
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
1
0
0
2
0
0
0
1
2
0
4
0
0
0
0
0
0
0
0
0
5
0
2
0
3
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
3
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
2
1
2
0
0
1
0
3
0
1
0
2
1
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
2
2
0
0
0
0
3
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
3
2
0
0
0
0
0
0
3
0
4
1
2
0
0
0
3
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
1
0
1
0
0
2
2
0
3
0
0
0
0
0
0
0
0
0
1
0
1
0
2
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
2
0
2
1
1
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
1
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
3
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
1
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
3
0
0
1
0
1
0
0
0
0
0
0
0
1
2
0
0
0
3
0
0
2
0
1
1
3
0
0
1
1
0
3
0
0
0
1
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
3
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
2
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
6
0
1
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
2
2
2
0
0
0
0
4
0
0
1
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
1
3
7
0
0
2
0
0
0
0
0
0
3
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
2
3
0
0
0
0
1
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
2
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
2
2
0
1
0
0
0
0
0
0
2
3
0
0
3
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
4
0
0
2
0
1
0
0
0
3
0
0
3
0
0
0
2
0
0
0
5
2
0
3
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
2
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
3
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
1
0
0
2
0
0
0
0
1
0
0
0
0
2
0
1
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
4
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
2
2
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
2
4
0
0
0
0
0
2
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
11
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
2
0
0
1
2
0
1
2
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
5
0
2
1
1
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
1
0
3
2
0
0
0
2
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
1
0
0
0
0
1
2
0
0
0
1
0
0
1
1
2
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
1
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
15
0
0
3
2
0
2
0
0
2
0
1
0
1
2
0
2
0
0
0
0
2
2
0
0
1
2
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
2
2
1
0
0
0
1
0
1
2
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
1
2
0
0
1
0
2
0
1
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
1
0
1
0
2
0
1
1
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
4
0
1
0
0
2
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
3
0
0
1
0
0
0
0
3
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
2
0
2
0
0
2
0
1
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
1
0
1
0
0
1
0
2
6
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
2
0
0
0
0
2
0
1
0
0
2
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
1
0
0
3
2
0
2
0
0
2
0
0
0
2
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
2
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
3
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
4
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
1
0
0
2
0
2
0
1
0
0
2
1
0
1
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
3
0
0
0
0
0
1
0
5
1
0
0
0
0
0
0
1
0
0
1
2
0
5
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
1
1
0
1
0
0
2
0
2
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
5
0
0
0
0
0
2
0
0
3
0
0
0
0
0
1
0
0
0
0
3
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
1
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
1
1
0
0
0
0
2
0
0
0
0
2
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
2
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
1
0
3
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
2
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
3
2
0
0
0
0
2
0
5
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
2
0
0
0
0
0
1
0
1
0
1
0
1
0
0
1
3
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
2
3
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
3
0
2
0
0
3
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
6
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
3
0
0
2
2
0
0
8
0
0
0
0
0
1
0
1
0
0
0
0
0
0
3
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
4
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
6
0
0
1
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
1
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
3
0
2
0
0
0
0
0
0
0
4
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
2
1
1
2
0
0
0
1
0
0
0
0
0
0
2
0
0
4
0
2
0
0
0
0
0
0
1
3
0
0
0
0
5
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
3
0
0
5
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
1
2
0
4
0
0
0
0
0
2
2
2
0
1
0
0
1
0
2
0
0
1
2
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
3
0
1
1
0
0
1
0
5
0
1
0
0
0
1
1
0
1
0
0
0
0
2
1
0
2
0
2
1
0
0
0
1
0
2
1
0
0
0
2
0
0
0
0
0
0
1
0
3
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
2
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
1
0
0
2
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
2
0
2
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
2
2
2
3
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
2
0
0
2
0
0
0
1
0
0
0
2
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
3
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
1
0
0
4
3
1
2
1
2
0
0
2
3
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
3
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
2
0
0
7
0
0
0
0
0
0
2
0
0
0
0
2
0
1
2
3
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
2
0
0
0
0
1
0
1
2
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
2
0
2
2
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
2
0
0
1
0
0
3
0
4
0
3
0
2
3
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
6
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
3
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
2
0
0
2
1
0
1
0
2
0
0
2
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
2
3
0
0
4
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
3
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
1
0
1
5
1
0
0
0
0
0
1
3
0
1
0
3
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
2
2
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
1
0
2
2
0
0
0
0
0
0
0
0
0
1
3
0
0
0
3
0
0
0
1
0
0
0
0
0
5
0
0
2
2
2
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
3
0
2
0
3
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
3
0
0
0
1
1
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
6
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
1
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
1
0
0
1
2
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
7
0
0
2
1
2
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
1
0
2
2
0
0
0
0
0
0
0
1
1
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
1
0
2
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
3
0
0
0
1
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
1
2
1
0
0
3
2
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
1
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
1
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
1
2
0
0
1
0
0
0
0
1
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
3
0
0
0
0
0
2
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
2
0
2
1
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
3
2
0
0
0
2
2
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
1
0
1
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
1
0
1
0
1
0
0
0
0
1
0
0
0
1
1
2
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
2
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
3
1
0
1
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
1
4
0
2
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
2
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
2
0
0
1
2
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
3
0
0
5
0
2
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
2
4
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
2
1
0
4
0
0
2
1
0
0
2
0
0
2
0
0
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
5
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
3
1
2
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
1
0
0
1
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
2
2
0
0
1
0
1
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
2
1
0
2
1
2
0
2
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
2
1
0
0
0
2
0
0
2
3
2
0
0
0
0
1
0
0
2
0
0
0
0
2
1
0
0
2
3
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
6
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
2
0
2
0
0
2
0
1
1
2
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
2
1
0
3
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
1
0
0
1
0
0
0
0
2
1
0
0
0
0
1
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
2
1
0
3
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
4
0
0
0
0
0
0
0
0
0
0
0
5
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
2
1
0
1
0
2
0
0
0
2
1
1
0
0
1
0
1
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
3
3
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
4
2
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
3
0
0
3
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
1
2
0
0
1
1
0
0
1
0
0
1
0
2
0
0
0
0
0
0
2
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
2
3
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
2
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
3
0
0
0
2
0
0
1
0
1
1
0
0
0
0
0
0
0
0
2
3
0
0
0
1
0
0
0
0
0
1
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
3
0
2
0
0
0
0
1
0
0
5
0
0
1
2
0
0
0
1
0
3
0
0
0
2
0
0
0
0
0
0
0
1
1
2
0
0
0
0
1
0
0
0
2
1
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
2
2
0
0
0
0
2
1
0
1
1
2
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
4
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
3
2
2
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
3
0
4
3
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
1
3
3
0
0
0
0
1
1
0
0
0
0
0
0
6
2
0
0
0
0
0
1
0
2
3
0
1
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
2
1
0
0
2
1
0
2
1
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
2
3
0
0
0
3
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
2
0
0
6
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
2
0
0
0
0
1
0
2
0
2
0
2
2
2
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
2
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
2
1
0
1
0
3
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
3
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
2
0
0
1
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
4
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
3
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
3
0
0
0
3
0
0
0
0
0
10
1
0
1
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
2
0
7
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
1
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
1
1
1
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
1
1
0
0
0
1
0
0
0
0
0
0
3
0
2
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
2
0
1
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
3
0
0
0
2
0
4
0
0
0
5
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
2
0
3
0
0
3
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
2
2
2
0
0
0
0
0
1
1
1
0
0
0
0
5
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
6
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
2
1
0
0
2
0
0
1
1
0
0
11
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
3
0
1
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
4
1
1
3
1
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
1
4
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
1
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
3
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
3
0
0
0
1
0
0
0
0
1
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
7
2
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
9
0
0
0
0
0
0
0
0
0
0
1
0
2
1
1
0
0
0
0
5
0
0
0
2
0
0
0
1
0
0
0
2
2
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
2
0
0
0
1
0
2
0
0
1
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
5
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
2
1
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
5
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
2
0
2
0
0
0
2
2
0
0
0
2
0
0
0
1
0
0
0
1
0
2
2
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
2
1
0
1
0
0
3
0
1
0
1
0
0
0
0
0
0
0
2
2
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
2
0
0
3
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
5
2
2
1
1
1
0
1
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
2
1
0
0
0
0
0
1
0
2
2
0
0
0
0
1
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
1
1
0
0
0
2
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
1
0
1
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
1
0
2
2
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
1
0
0
1
0
0
3
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
2
2
0
0
4
0
0
0
0
0
0
1
0
4
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
2
0
1
1
1
0
0
1
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
1
0
2
1
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
3
0
1
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
2
0
1
0
0
0
3
0
0
3
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
1
1
0
6
0
0
0
0
0
0
0
0
0
1
1
0
0
2
1
0
2
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
3
0
0
1
0
2
5
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
3
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
3
0
0
2
1
1
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
2
0
1
0
2
0
0
0
1
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
3
4
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
2
0
0
0
5
0
2
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
2
0
1
1
1
2
0
0
2
0
0
0
0
2
1
0
0
0
2
0
0
1
0
0
0
2
0
1
1
0
2
0
0
0
0
2
0
0
1
0
0
0
5
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
1
0
0
0
0
1
0
0
2
0
1
0
3
0
0
0
0
1
0
1
2
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
3
1
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
1
0
0
1
1
0
0
0
3
0
0
7
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
1
2
0
0
0
0
0
0
2
2
0
1
0
0
2
1
0
1
0
0
2
0
0
1
0
1
0
0
0
0
3
2
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
1
1
0
1
0
0
0
0
2
0
2
1
0
0
0
0
1
2
0
0
0
1
0
1
0
0
2
0
0
3
1
1
0
0
7
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
2
2
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
2
0
0
1
4
0
4
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
1
0
1
0
2
1
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
4
0
2
1
0
3
0
0
0
2
0
4
0
2
0
0
3
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
2
1
2
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
3
0
0
0
0
0
0
0
5
0
0
0
0
0
1
0
0
2
0
2
1
0
0
0
0
0
1
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
4
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
2
0
3
1
0
0
0
2
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
2
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
1
0
12
0
0
1
0
0
2
0
0
0
0
0
4
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
6
0
2
1
0
0
0
1
2
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
1
0
2
0
0
0
2
1
0
0
0
0
0
1
2
0
1
0
1
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
2
0
0
2
0
5
0
1
0
1
0
3
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
2
0
0
0
1
0
2
0
0
2
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
2
0
0
0
2
0
1
1
1
0
1
0
1
2
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
2
3
0
2
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
5
0
0
0
0
3
0
0
0
0
1
0
0
0
0
2
0
0
0
1
1
0
0
0
1
0
2
0
0
2
0
1
1
0
0
0
2
1
0
0
1
2
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
3
0
0
0
0
3
0
0
1
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
1
1
2
0
0
0
0
2
0
0
2
2
0
0
1
0
0
0
2
2
4
0
2
1
0
0
0
0
0
1
1
0
0
0
0
2
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
4
0
2
0
0
1
2
0
0
0
0
0
0
1
0
0
1
1
2
0
0
0
0
0
1
0
2
0
0
0
0
0
1
1
0
0
0
0
1
1
1
0
0
0
2
1
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
2
1
2
0
0
3
0
0
2
0
1
0
0
0
0
0
0
2
0
1
4
0
1
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
1
0
0
0
2
2
0
1
2
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
1
2
0
4
0
1
0
0
2
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
3
0
1
0
2
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
2
0
1
0
2
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
1
0
1
0
0
0
1
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
1
2
0
0
0
0
1
2
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
1
2
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
1
0
0
0
0
2
0
5
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
1
0
3
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
3
2
0
0
0
0
3
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
1
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
1
2
0
1
0
0
0
0
2
0
0
0
0
1
2
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
4
0
0
0
2
0
0
0
2
2
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
3
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
3
0
0
0
1
1
1
0
0
0
1
1
0
0
0
0
1
2
0
6
0
1
0
0
0
1
0
0
0
0
1
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
2
1
0
0
2
0
0
0
1
3
0
0
1
0
0
0
0
0
0
0
0
1
0
1
2
0
2
1
0
2
0
0
4
1
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
2
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
2
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
3
1
0
0
0
3
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
2
2
3
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
3
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
3
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
3
0
1
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
5
0
5
0
2
0
0
0
0
2
0
3
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
3
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
4
0
0
0
0
0
5
0
0
0
0
0
0
2
0
3
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
3
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
1
0
0
1
0
0
0
0
0
2
1
0
0
0
0
2
0
1
0
0
0
1
0
0
1
0
2
0
0
0
3
1
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
9
0
2
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
2
0
0
0
0
1
0
0
1
0
0
0
0
1
5
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
3
2
0
0
0
0
0
0
0
0
0
0
3
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
1
2
0
0
0
2
0
4
0
1
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
2
0
0
0
2
1
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
2
0
3
0
0
0
0
0
1
2
0
1
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
1
3
0
0
2
0
0
4
0
0
1
11
0
1
0
0
0
1
0
0
2
0
2
0
0
0
0
2
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
2
0
3
1
2
0
0
0
0
0
0
0
0
5
0
0
2
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
2
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
4
0
0
1
0
0
0
1
0
0
0
3
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
3
0
1
0
2
2
0
0
2
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
2
1
1
1
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
4
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
3
1
0
0
0
1
0
0
0
0
0
1
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
1
2
0
0
0
0
0
2
0
0
1
1
0
0
1
0
0
0
0
1
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
3
0
0
0
1
0
1
2
0
0
0
0
0
3
0
0
1
1
2
1
0
2
0
0
0
0
2
1
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
2
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
1
1
0
0
2
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
3
2
0
0
0
0
0
2
0
0
1
0
4
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
1
0
0
0
2
2
2
0
2
2
0
1
0
0
0
0
0
1
0
0
0
0
2
1
0
0
2
0
0
0
1
0
0
0
2
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
2
5
0
0
0
0
0
2
0
0
0
0
0
0
0
1
3
0
0
2
1
2
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
3
2
1
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
5
2
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
2
0
0
0
1
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
3
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
1
0
1
0
1
1
0
0
0
1
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
1
0
2
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
1
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
7
0
2
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
1
0
0
0
0
0
0
0
1
1
0
0
1
0
2
0
2
1
0
1
0
0
0
2
2
0
0
2
0
0
0
4
0
2
0
0
0
1
0
0
0
0
0
0
2
2
1
2
1
0
3
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
7
0
1
0
0
0
1
1
0
2
0
0
0
2
1
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
4
2
1
0
0
0
0
0
0
0
3
1
2
2
1
0
0
0
0
6
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
1
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
2
0
0
5
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
7
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
1
1
0
1
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
1
0
2
0
0
0
3
0
0
0
0
0
2
0
0
2
2
0
2
2
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
1
1
1
0
1
0
2
0
0
2
0
1
1
1
2
1
0
1
1
0
0
0
0
0
2
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
1
0
0
2
1
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
1
0
2
0
0
2
0
1
3
0
0
5
0
9
0
0
0
1
0
2
0
0
4
0
0
0
0
0
2
3
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
2
0
0
1
1
0
0
0
0
3
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
4
0
1
1
0
0
0
0
0
1
0
1
0
1
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
1
4
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
1
0
0
0
1
0
0
0
0
0
2
1
0
2
2
0
0
1
0
1
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
3
0
0
3
0
2
0
0
0
0
1
2
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
2
0
0
5
1
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
2
0
0
4
1
1
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
2
0
1
2
2
4
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
4
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
5
1
0
5
0
0
0
0
0
2
0
0
0
1
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
2
2
4
0
2
0
1
4
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
1
0
1
1
0
3
0
0
0
0
0
0
0
0
0
1
2
0
1
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7
0
0
1
1
0
0
0
0
2
1
0
0
4
0
1
0
2
0
0
0
0
0
2
0
0
0
1
0
3
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
1
1
0
0
0
2
0
0
0
2
0
0
2
0
0
1
0
2
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
5
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
1
3
0
0
0
2
0
0
0
0
0
0
1
0
4
0
0
0
0
2
0
0
2
0
0
0
0
1
0
1
0
1
2
0
1
0
0
2
0
0
0
0
0
4
0
1
1
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
1
0
2
0
2
0
1
0
0
0
0
0
0
1
0
0
1
6
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
3
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
1
2
1
0
0
0
1
1
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
2
0
0
0
0
6
0
2
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
1
0
0
2
0
1
0
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
1
0
0
1
0
0
2
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
12
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
1
1
0
0
2
0
0
0
2
0
0
0
0
0
1
0
2
0
0
1
1
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
2
0
2
1
1
2
0
0
0
5
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
3
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
5
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
2
0
2
0
1
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
2
0
0
0
2
0
0
1
0
0
0
6
0
2
0
0
0
0
0
1
0
2
0
0
0
1
0
0
1
0
2
0
2
6
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
1
0
0
0
1
2
0
0
0
4
0
0
0
0
0
2
0
0
0
1
0
0
3
0
2
0
0
1
0
0
0
0
0
1
0
1
0
2
1
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
1
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
2
1
1
0
1
0
0
0
0
1
0
2
0
1
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
1
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
6
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
5
0
1
0
0
0
3
0
0
0
0
0
0
0
0
1
1
0
9
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
3
1
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
3
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
3
0
0
0
0
1
5
0
0
0
2
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
1
0
1
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
4
0
0
0
0
3
0
0
0
0
1
3
0
0
2
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
3
0
0
0
4
2
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
1
0
1
1
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
3
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
2
2
0
0
1
2
0
0
1
4
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
1
2
3
0
0
0
2
0
2
0
0
1
0
0
1
2
0
0
0
0
0
2
0
0
0
1
0
0
0
2
1
2
2
0
1
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
2
0
0
3
0
0
3
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
2
2
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
3
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
6
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
2
0
2
0
5
2
0
0
1
0
2
0
0
0
5
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
1
0
2
2
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
3
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
7
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
1
0
2
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
1
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
3
0
0
1
0
0
1
2
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
2
0
0
4
1
0
0
0
0
0
0
0
0
5
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
1
2
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
3
0
0
1
0
0
1
3
0
0
1
1
0
0
0
0
1
0
0
2
5
0
0
0
2
0
0
1
1
1
2
0
2
0
0
0
0
2
2
0
0
0
0
3
0
0
0
0
1
2
2
2
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
3
1
3
0
2
0
0
1
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
4
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
2
0
0
3
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
2
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
1
0
0
0
0
2
0
2
1
0
0
0
0
0
1
0
0
7
1
2
0
0
2
0
1
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
3
2
0
0
3
2
2
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
1
0
0
0
0
0
2
0
0
0
0
2
2
5
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
1
5
0
0
3
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
3
0
0
0
1
0
1
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
4
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
1
2
1
0
0
0
3
0
0
3
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
2
1
2
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
4
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
4
0
1
1
2
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
1
1
0
4
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
1
0
0
0
3
0
2
0
2
1
0
0
0
0
2
2
2
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
1
3
0
0
0
0
2
0
0
0
0
1
0
2
2
1
0
0
0
0
0
0
0
0
0
0
8
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
2
0
0
1
0
2
0
0
0
1
0
0
0
1
2
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
2
2
0
0
0
2
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
1
0
2
2
0
0
0
0
0
6
0
0
0
2
0
1
1
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
2
1
0
0
1
0
2
0
1
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
1
0
3
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
3
2
0
0
1
1
1
3
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
4
0
0
0
1
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
3
10
0
0
0
0
0
0
0
0
0
8
3
0
0
0
0
0
2
0
0
0
0
1
2
0
0
2
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
2
4
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
2
0
3
1
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
6
0
0
0
0
0
1
2
3
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
2
1
0
2
0
1
0
0
0
2
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
3
0
0
1
0
4
0
2
0
0
0
0
0
0
0
0
2
1
2
0
2
0
3
3
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
3
0
2
0
2
3
0
1
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
3
0
0
0
0
0
2
0
0
2
1
1
0
0
0
0
2
2
0
0
1
0
0
0
0
2
1
0
1
0
0
0
0
3
0
0
0
0
0
1
0
0
0
5
0
3
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
4
0
2
1
0
0
0
2
0
0
0
0
1
0
0
0
1
1
0
0
0
0
4
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
1
0
0
0
0
3
0
3
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
3
0
0
0
1
0
1
0
0
0
0
0
3
2
0
0
1
0
0
0
1
0
0
0
0
1
0
2
1
0
1
0
1
0
1
0
0
0
0
0
1
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
3
0
0
0
0
2
0
0
0
2
0
0
0
0
1
3
0
0
0
1
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
2
0
2
2
0
0
0
1
1
0
0
2
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
5
0
0
2
1
0
1
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
1
2
0
0
0
0
0
0
0
2
0
3
0
4
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
3
2
0
2
0
0
0
2
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
3
2
0
0
3
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
2
1
1
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
2
0
1
0
1
0
0
3
2
0
0
0
2
1
0
0
1
2
0
0
0
1
0
0
1
0
2
0
1
1
0
0
0
0
1
2
0
0
0
0
2
0
0
0
1
0
0
0
3
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
4
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
5
2
0
0
0
2
2
0
0
0
0
6
0
1
1
0
0
0
1
1
0
0
0
1
1
0
0
2
0
0
0
0
0
2
0
0
1
0
0
1
0
0
2
1
0
0
2
0
0
5
5
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
3
1
0
0
0
1
0
2
0
2
0
0
1
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
1
1
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
1
0
0
0
1
0
0
1
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
5
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
1
2
0
1
0
0
0
0
2
0
1
1
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
2
4
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
5
0
0
0
0
0
1
2
2
0
0
0
0
1
0
0
0
1
0
2
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
2
3
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
5
0
0
0
2
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
3
2
2
0
2
0
1
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
2
0
1
0
1
0
2
0
0
1
0
0
0
2
1
0
0
0
0
0
1
1
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
2
0
1
1
0
0
2
2
0
0
0
0
0
1
2
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
1
2
1
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
1
2
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
5
0
1
0
0
2
0
0
0
0
0
2
0
2
2
1
0
0
0
2
0
1
3
0
1
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
2
0
2
0
3
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
7
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
2
3
0
3
0
0
1
0
0
0
0
6
0
0
0
0
0
0
2
0
3
1
0
0
1
3
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
7
0
4
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
5
0
0
0
3
0
0
1
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
2
0
1
2
0
0
3
0
1
2
0
0
3
0
0
0
0
1
0
0
3
4
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
1
1
1
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
2
2
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
3
0
1
3
0
0
0
0
0
0
4
0
1
0
0
0
0
0
2
3
0
1
2
0
1
0
1
0
3
0
1
2
2
0
0
1
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
2
0
0
0
1
2
0
0
0
0
0
0
10
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
2
3
0
1
0
0
0
3
0
2
0
0
0
4
3
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
4
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
1
1
0
1
0
2
1
1
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
2
0
4
1
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
2
0
1
2
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
1
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
2
1
3
0
0
0
0
3
1
2
0
7
0
2
1
0
0
3
0
0
0
2
2
0
0
1
0
2
4
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
1
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
1
1
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
4
1
1
0
1
0
0
4
1
0
0
0
0
0
0
4
2
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
1
0
0
2
0
2
0
0
3
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
6
0
0
1
3
1
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
1
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
1
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
3
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
1
1
2
0
0
0
5
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
1
0
0
0
0
0
1
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
1
0
1
2
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
10
0
0
3
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
3
0
6
0
0
0
0
2
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
3
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
1
0
0
0
5
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
2
0
1
1
2
0
0
0
0
2
0
0
0
0
2
3
2
0
2
1
0
0
0
1
2
1
0
0
2
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
2
1
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
2
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
1
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
2
1
3
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
1
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
3
4
0
0
0
0
0
0
0
0
0
0
0
7
0
0
0
1
1
0
2
0
0
1
0
0
0
0
1
0
0
0
4
0
1
0
0
1
15
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
1
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
2
0
2
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
2
0
2
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
2
0
6
0
0
0
1
0
0
4
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
1
3
0
1
0
0
0
0
3
0
1
0
0
0
0
0
0
4
0
0
1
0
0
2
0
0
0
0
4
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
1
0
0
3
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
3
0
0
0
1
1
0
0
0
0
0
2
4
0
0
0
0
1
0
0
0
0
0
0
1
2
2
2
0
0
0
2
2
1
2
0
0
0
0
3
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
2
2
2
0
0
2
0
0
2
0
0
0
0
0
4
0
0
0
0
0
0
5
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
2
0
0
0
2
0
2
0
2
1
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
1
2
3
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
3
4
0
0
1
0
1
1
0
0
0
2
0
1
0
1
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
1
0
0
1
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
3
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
1
0
1
0
1
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
2
0
0
0
1
3
0
2
0
0
0
0
0
8
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
5
1
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
1
1
0
1
2
1
1
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
1
1
1
0
0
0
0
0
0
0
2
0
3
0
0
0
0
3
1
0
0
0
6
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
1
0
1
1
0
0
0
1
0
1
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
5
0
7
1
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
2
2
2
0
2
0
0
1
0
0
1
2
0
0
3
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
2
0
0
1
2
1
1
0
0
4
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
1
2
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
2
1
9
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
2
2
1
0
0
1
0
1
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
1
2
0
1
0
0
2
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
2
0
0
0
2
0
1
0
2
0
0
1
0
0
3
0
2
0
0
0
2
4
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
1
0
0
0
4
0
0
1
0
1
0
2
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
3
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
3
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
5
1
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
3
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
3
0
0
1
0
0
0
0
0
2
0
3
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
3
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
1
0
1
0
2
0
2
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
2
0
0
0
0
0
0
2
3
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
2
0
0
4
0
0
2
0
0
0
1
0
11
0
0
0
0
0
0
1
1
0
0
0
0
3
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
3
2
0
0
0
0
0
0
0
6
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
2
0
2
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
2
1
0
1
1
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
2
0
0
1
1
0
0
0
1
0
0
0
0
2
0
0
0
2
2
1
0
0
0
2
0
0
0
0
4
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
1
0
1
1
0
0
0
0
5
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
2
0
2
2
0
0
1
0
0
0
0
0
0
1
1
0
1
0
2
0
1
0
0
0
1
0
0
0
4
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
1
1
0
0
3
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
2
0
0
2
0
0
0
1
0
0
2
0
0
1
2
0
1
0
0
3
2
3
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
5
0
0
1
1
0
0
0
0
0
0
0
2
0
6
0
2
0
0
0
0
0
0
0
1
0
1
0
0
2
1
1
0
0
1
0
0
2
0
0
2
2
0
0
0
1
0
1
1
2
3
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
1
0
1
0
8
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
2
0
0
0
1
0
0
0
1
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
4
0
0
0
1
0
0
2
0
2
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
1
0
1
2
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
3
0
1
0
0
1
0
1
1
0
0
5
1
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
1
0
1
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
2
0
3
0
0
0
1
0
0
1
0
0
1
0
0
0
2
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
3
1
0
0
1
1
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
1
1
0
0
0
0
2
0
0
1
0
0
0
3
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
2
0
0
2
0
0
0
1
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
1
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
4
2
0
0
2
0
1
1
0
0
0
0
0
2
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
4
0
0
0
0
1
0
1
0
0
0
0
0
1
0
2
0
1
1
1
0
0
1
1
2
1
0
0
2
0
0
0
7
3
1
0
2
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
4
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
2
0
1
2
1
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
3
1
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
3
0
0
3
2
0
0
1
0
0
2
4
0
0
0
3
2
3
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
1
0
0
2
2
0
0
1
3
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
3
0
0
0
0
2
0
1
0
0
1
0
0
0
0
1
0
5
0
0
2
0
0
1
1
2
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
10
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
4
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
2
2
0
2
0
2
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
2
0
0
0
0
0
0
1
0
0
0
2
0
0
2
1
0
0
0
1
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
2
0
0
0
1
0
0
0
9
1
0
0
0
0
1
1
0
0
0
0
0
3
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
1
1
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
2
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
3
4
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
2
0
0
0
1
0
1
2
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
2
0
3
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
3
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
1
0
0
0
1
0
4
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
1
3
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
1
0
1
3
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
4
2
0
0
0
0
3
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
2
2
0
0
1
1
0
0
0
0
0
0
0
2
2
0
1
2
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
3
0
1
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
3
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
4
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
2
3
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
2
0
0
3
0
0
0
0
1
0
0
0
0
2
0
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
1
0
0
2
0
0
0
1
0
0
1
0
1
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
3
0
2
0
4
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
3
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
3
0
0
1
0
1
0
0
2
1
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
5
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
3
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
4
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
2
0
1
0
0
0
0
2
1
0
0
0
1
0
0
2
0
2
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
2
0
0
1
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
3
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
1
2
0
1
1
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
1
1
2
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
2
0
3
0
0
2
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
1
2
1
1
1
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
5
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
1
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
4
0
0
1
0
0
0
2
1
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
1
0
0
0
0
1
0
0
2
0
0
0
0
0
1
2
0
3
0
0
2
0
1
0
2
0
1
1
0
0
0
0
1
3
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
6
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
7
0
3
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
2
4
0
0
0
0
0
0
3
1
1
0
2
0
2
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
2
6
5
0
0
0
0
0
0
2
0
0
3
0
2
0
0
1
0
2
0
0
0
0
0
3
2
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
2
0
0
1
1
0
0
0
0
0
1
0
1
0
2
0
0
0
2
1
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
15
2
0
1
1
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
6
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
5
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
8
0
0
0
0
2
0
2
0
1
1
2
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
2
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
1
0
0
0
0
2
0
1
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
3
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
1
0
0
0
3
1
0
0
0
0
0
0
1
0
0
0
1
0
0
3
0
1
0
0
0
0
2
0
3
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
5
0
3
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
5
0
1
0
0
0
3
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
4
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
1
0
1
0
0
0
0
2
0
1
1
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
2
2
0
0
2
0
1
1
0
0
2
1
2
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
3
0
0
0
1
2
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
1
0
0
5
0
1
3
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
6
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
2
2
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
5
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
4
2
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
1
5
0
0
1
0
1
0
2
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
4
0
0
2
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
3
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
1
1
2
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
2
0
0
0
2
0
0
2
0
0
1
3
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
2
0
2
0
1
0
2
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
1
1
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
8
0
0
0
0
1
0
0
0
0
1
0
7
0
4
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
2
0
4
1
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
3
0
1
1
2
3
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
1
0
1
2
0
0
0
0
1
0
0
0
0
3
0
0
0
2
0
2
0
0
0
0
1
2
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
4
0
2
0
2
2
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
1
0
2
0
0
0
0
1
1
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
1
2
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
2
2
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
2
0
0
0
2
1
0
0
3
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
2
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
3
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
3
5
0
0
0
3
0
3
0
0
0
0
2
2
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
2
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
3
0
0
0
0
0
0
0
0
0
1
1
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
1
0
0
1
0
0
0
0
1
2
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
3
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
2
2
0
0
0
2
0
0
1
0
1
0
0
6
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
4
0
0
0
0
1
4
0
2
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
2
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
3
0
2
1
0
0
0
1
0
0
0
0
0
4
0
0
0
3
0
0
0
0
3
0
0
2
1
0
0
0
3
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
3
0
2
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
2
0
0
2
3
0
0
0
0
0
1
1
0
1
0
0
2
0
0
1
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
1
0
1
0
4
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
1
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
3
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
1
0
1
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
2
1
0
0
0
2
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
14
0
2
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
2
0
0
1
0
1
0
0
0
1
0
0
1
0
1
0
0
1
3
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
1
0
1
0
0
0
0
2
2
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
5
0
0
0
0
2
2
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
2
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
3
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
2
0
4
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
2
2
2
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
1
0
2
0
0
0
1
3
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
4
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
5
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
6
1
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
2
2
0
1
0
0
0
0
0
0
0
2
0
2
0
2
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
2
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
8
1
0
0
0
0
0
2
0
2
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
10
1
0
2
2
1
1
0
0
0
2
0
6
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
2
2
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
2
0
0
0
1
1
0
0
0
0
3
0
0
0
0
2
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
2
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
1
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
3
0
0
0
0
1
0
3
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
1
3
0
0
4
0
2
3
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
1
0
0
0
2
0
0
3
0
0
0
1
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
1
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
3
0
0
0
2
0
0
0
2
0
0
2
1
1
0
0
0
0
1
2
0
2
0
1
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
5
0
0
0
0
1
2
0
0
0
0
1
0
5
0
0
0
0
0
0
0
0
1
0
2
0
3
0
0
0
2
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
1
1
0
0
0
2
1
1
1
1
0
0
0
0
0
0
0
1
0
3
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
4
0
0
0
0
0
2
0
0
1
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
1
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
3
2
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
1
0
1
5
1
0
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
2
1
0
0
0
2
1
1
0
0
1
1
0
0
0
0
2
2
0
0
0
2
0
0
0
2
5
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
3
1
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
2
2
1
1
0
0
0
2
0
2
1
0
2
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
3
0
2
0
0
1
2
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
1
2
1
0
0
0
1
0
1
0
0
0
2
0
0
0
1
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
1
2
0
0
1
2
2
0
0
0
1
0
0
3
2
0
0
0
0
2
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
1
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
2
0
1
0
0
2
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
2
0
0
2
0
0
0
2
0
0
0
0
4
0
1
2
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
1
0
2
0
1
0
3
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
0
0
2
0
3
3
6
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
1
0
2
0
0
0
0
0
0
0
3
0
1
0
0
0
1
0
0
0
0
0
0
0
0
4
0
1
0
1
0
0
0
2
0
0
0
0
1
1
0
0
2
2
0
2
0
0
1
1
0
0
0
0
0
2
0
0
0
0
1
1
0
0
1
0
0
2
0
2
0
0
0
2
0
0
2
0
1
0
0
2
0
0
0
2
0
1
0
0
2
0
2
1
0
0
0
0
4
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
4
0
0
0
0
0
2
0
0
0
0
0
4
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
4
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
4
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
2
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
1
0
0
1
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
2
0
0
0
0
1
0
8
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
1
2
1
0
0
2
4
0
0
0
1
2
0
0
0
2
3
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
2
2
2
0
0
1
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
4
0
2
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
3
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
2
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
4
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
1
1
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
6
0
0
0
0
0
0
0
4
2
0
1
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
3
0
0
1
0
0
0
5
0
0
0
2
0
0
0
0
2
0
0
0
1
2
0
0
0
0
1
0
4
1
0
0
0
0
0
2
0
0
4
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
2
1
0
0
0
0
3
0
0
0
0
0
4
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
1
2
0
0
2
0
0
1
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
2
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
3
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
1
0
0
2
0
0
1
2
1
3
0
0
2
0
0
0
0
0
0
0
8
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
2
0
0
4
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
3
0
0
0
1
0
0
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
12
0
1
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
1
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
3
0
0
0
0
1
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
1
2
1
0
0
4
0
0
4
0
0
0
0
0
0
0
0
0
0
2
1
3
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
2
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
9
0
0
0
0
0
0
0
2
0
0
2
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
1
0
1
0
0
0
1
0
4
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
1
1
0
0
0
0
8
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
5
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
1
0
1
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
1
0
2
0
0
2
2
0
4
0
0
0
4
0
0
0
2
1
0
5
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
2
0
3
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
1
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
1
2
2
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
2
0
3
0
0
0
0
1
3
3
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
4
0
4
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
2
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
1
2
1
0
0
2
0
0
0
5
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
2
0
2
0
0
0
0
0
4
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
2
0
1
2
0
1
2
0
0
2
0
0
0
1
0
0
0
1
0
0
1
0
0
2
0
2
1
0
0
2
1
0
0
1
1
0
0
0
0
4
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
1
2
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
3
0
0
2
3
0
0
1
0
1
0
0
0
3
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
1
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
3
0
2
2
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
2
8
0
0
0
3
2
0
0
1
1
0
0
0
1
0
0
0
0
0
0
3
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
2
0
0
2
0
3
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
1
1
0
1
2
0
0
1
0
0
0
0
1
2
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
1
0
2
4
0
0
0
1
3
1
0
0
1
1
0
1
0
0
0
0
3
0
1
0
0
2
0
1
3
0
2
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
1
0
1
0
0
2
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
3
1
0
0
0
0
0
0
0
1
2
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
5
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
5
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
1
0
0
1
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
2
0
2
0
1
0
0
1
0
2
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
1
1
0
0
0
2
0
0
2
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
2
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
4
0
0
1
2
0
0
0
0
0
4
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
3
0
1
0
0
0
1
0
2
0
0
0
2
0
0
0
0
2
1
2
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
1
0
0
0
2
0
1
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
2
0
0
0
1
0
0
0
1
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
1
3
0
0
2
0
1
0
0
0
2
0
1
0
0
0
0
2
2
3
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
1
0
0
0
1
1
0
0
3
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
3
2
0
1
1
0
0
2
0
0
0
0
2
4
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
3
0
1
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
1
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
1
1
1
0
0
3
2
2
2
0
0
0
0
0
0
2
2
0
1
0
0
0
1
2
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
6
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
6
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
6
0
1
0
1
0
1
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
5
2
0
0
0
4
0
2
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
2
0
2
0
2
0
0
0
2
1
0
0
2
0
0
2
0
0
0
0
0
1
1
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
4
0
1
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
3
1
0
2
2
0
0
0
0
0
1
0
0
3
0
0
1
1
2
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
6
3
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
2
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
2
0
0
0
2
0
1
0
2
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
1
1
0
0
0
0
0
1
2
0
1
0
0
0
0
0
2
0
2
0
2
0
0
2
0
0
2
0
0
0
0
0
1
2
0
0
4
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
1
0
0
1
0
0
0
1
1
0
0
1
0
0
2
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
4
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
2
1
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
1
0
0
2
1
0
2
0
0
1
2
0
1
2
0
1
3
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
3
2
0
0
0
0
2
0
0
0
0
8
1
0
2
5
0
1
0
0
1
5
0
0
0
0
0
4
0
0
1
2
0
0
0
0
0
1
0
0
2
0
1
1
1
0
0
0
0
0
2
0
2
0
0
6
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
3
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
2
0
0
0
0
0
2
2
0
0
3
0
0
3
0
2
0
0
1
0
0
0
0
0
2
1
0
0
1
0
0
1
0
2
0
1
3
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
2
0
0
3
0
0
0
2
2
0
0
1
0
1
0
0
2
0
0
0
4
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
4
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
3
2
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
2
0
0
0
3
0
0
1
0
0
0
0
0
0
1
0
2
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
1
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
4
0
0
0
2
1
0
0
0
0
1
0
0
0
1
1
0
4
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
3
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
6
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
8
0
0
2
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
1
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
4
0
1
0
2
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
3
1
0
0
0
2
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
3
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
1
2
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
4
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
6
0
0
0
0
0
0
0
0
0
3
4
1
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
2
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
1
0
2
0
0
2
0
1
3
0
0
0
2
0
2
0
1
0
2
0
0
0
0
2
3
0
0
0
2
0
0
0
0
1
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
2
1
1
2
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
8
0
5
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
2
3
0
0
0
1
1
1
0
4
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
2
0
2
0
0
0
0
1
0
0
0
2
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
1
0
1
2
1
0
0
0
1
0
0
0
0
2
0
1
3
0
1
0
0
0
2
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
1
0
0
1
0
3
0
1
0
0
2
0
0
1
0
0
1
0
0
0
3
0
1
1
2
0
0
0
2
0
0
1
2
0
0
1
3
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
11
3
1
0
1
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
1
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
1
0
0
1
2
0
4
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
1
0
2
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
7
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
3
2
0
2
0
1
0
0
0
0
1
0
2
2
0
2
1
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
1
0
2
0
1
0
3
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
2
0
0
0
0
1
0
0
1
0
0
4
3
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
2
2
0
1
0
0
0
17
2
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
2
2
0
2
5
0
0
1
0
2
2
1
2
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
1
1
0
0
2
2
0
1
1
0
0
0
0
0
0
0
1
1
0
0
4
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
2
0
0
0
1
1
0
0
0
0
2
1
0
0
0
1
0
3
0
0
1
1
0
1
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
2
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
1
1
0
2
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
2
1
1
0
0
0
0
0
2
2
0
0
0
0
2
0
2
0
1
0
12
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
2
1
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
2
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
2
1
2
0
3
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
1
5
0
0
4
0
0
0
1
5
0
0
1
1
1
0
0
0
3
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
1
2
0
0
0
6
0
0
0
1
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
2
0
0
3
2
0
0
0
1
0
8
0
1
0
1
0
0
2
3
0
2
0
1
0
2
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
1
6
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
5
0
4
0
0
4
2
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
2
0
0
2
1
0
3
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
1
1
0
1
2
0
0
0
0
0
0
2
0
3
0
0
1
0
0
0
0
0
4
0
1
0
0
0
2
0
2
0
2
0
0
0
2
0
0
1
0
2
0
0
0
0
2
2
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
2
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
2
2
0
2
3
1
1
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
3
0
0
2
1
0
0
0
1
0
0
0
2
0
0
2
0
2
2
0
0
0
0
0
0
0
0
1
0
0
2
1
1
0
2
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
2
0
0
1
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
3
0
2
0
0
0
1
0
2
0
2
0
0
0
0
0
2
2
2
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
4
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
1
2
0
0
2
0
0
0
0
0
0
4
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
1
0
0
5
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
3
2
0
0
0
2
0
0
0
0
1
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
1
1
0
0
2
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
1
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
3
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
2
0
2
0
0
5
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
3
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
4
1
2
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
1
2
0
1
1
0
0
3
0
0
0
0
1
0
0
3
0
0
0
2
3
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
3
0
0
1
0
0
0
2
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
3
0
4
1
2
0
0
0
0
0
0
0
1
0
1
0
3
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
2
0
1
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
1
0
0
0
0
0
2
0
0
2
1
0
2
0
0
1
0
0
0
0
0
1
3
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
3
0
1
0
1
1
0
0
0
0
0
1
0
2
2
0
3
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
1
0
2
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
3
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
3
0
0
0
0
1
0
1
0
2
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
3
0
4
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
2
3
2
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
1
2
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
1
1
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
2
2
0
1
0
0
0
0
1
0
0
0
0
3
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
3
0
0
0
0
0
0
4
0
1
0
0
0
0
0
2
0
2
2
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
3
5
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
2
6
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
3
0
2
1
1
0
0
0
0
0
0
1
9
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
2
0
1
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
1
0
6
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
7
0
1
2
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
6
1
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
1
0
2
0
0
1
1
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
1
0
0
0
0
4
6
2
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
8
1
0
0
0
0
0
2
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
1
0
0
0
1
7
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
3
0
0
8
0
0
0
0
1
2
0
0
0
0
0
6
2
0
0
0
0
2
2
0
2
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
3
0
0
0
2
0
0
1
1
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
2
0
0
0
0
6
0
1
0
3
0
0
2
0
2
2
0
1
0
0
0
0
5
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
1
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
2
0
1
0
1
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
2
1
0
0
0
1
0
0
0
0
0
2
0
1
0
2
0
2
1
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
1
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
2
2
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
2
3
0
0
0
0
6
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
2
0
0
1
0
2
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
1
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
1
0
3
0
3
2
1
0
0
0
0
2
0
0
0
0
0
0
1
0
6
0
3
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
1
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
2
0
1
0
0
0
0
2
0
0
1
0
4
0
0
2
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
7
0
0
0
0
0
3
2
0
0
0
0
2
0
0
0
0
0
0
2
1
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
1
4
0
2
0
1
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
2
1
0
0
0
0
0
0
0
2
2
0
0
1
2
2
0
0
0
0
0
2
1
0
1
0
0
0
0
2
0
2
0
0
0
2
5
0
1
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
1
0
1
2
0
0
2
0
0
0
0
1
0
3
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
3
0
0
1
0
1
0
0
0
0
0
0
4
0
0
2
0
1
0
0
0
0
2
0
0
0
1
0
0
0
3
0
0
1
2
0
2
1
0
1
1
0
2
0
0
4
3
0
2
1
0
0
0
1
1
0
2
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
1
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
4
0
3
2
0
0
0
2
0
0
2
0
0
3
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
3
0
0
0
5
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
1
1
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
1
0
0
0
1
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
1
0
2
1
0
0
1
1
0
0
2
2
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
1
0
0
2
3
1
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
2
0
3
0
0
0
0
0
1
5
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
2
0
0
0
0
0
1
0
0
2
1
0
1
2
0
0
0
0
0
0
1
0
0
2
2
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
2
3
0
1
0
0
0
1
1
1
0
0
0
0
2
0
0
1
0
0
0
1
1
6
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
2
2
0
0
0
2
0
0
0
2
0
0
0
2
2
2
1
0
2
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
1
1
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
3
0
0
0
1
0
0
2
2
0
0
2
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
2
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
2
0
1
2
0
0
0
3
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
1
21
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
4
3
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
4
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
3
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
2
2
0
2
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
2
3
1
0
0
0
0
0
2
2
0
0
0
3
1
0
0
0
0
0
3
2
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
4
0
0
0
1
1
2
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
1
1
2
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
2
0
0
0
0
0
3
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
3
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
1
0
0
4
0
0
0
0
2
0
1
0
0
1
0
1
0
0
2
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
5
0
5
0
0
0
2
0
0
0
0
0
0
2
0
6
0
0
1
0
1
0
0
0
0
1
2
0
1
2
0
0
0
0
2
1
0
0
1
0
0
0
0
0
1
0
0
0
4
0
1
0
0
2
2
0
4
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
2
1
0
0
2
0
0
2
0
0
0
0
0
0
1
0
2
0
2
2
2
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
5
2
0
0
2
0
0
0
0
0
2
0
2
1
1
0
0
0
0
0
0
1
1
0
1
0
2
1
0
0
2
0
1
0
3
0
0
0
0
0
1
0
0
0
3
0
2
0
0
0
1
0
0
1
1
0
2
0
0
2
0
1
0
0
2
0
0
0
0
0
1
0
0
2
1
6
0
0
1
1
0
0
3
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
2
0
0
0
0
0
1
3
0
0
0
0
0
0
0
2
0
2
2
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
2
1
2
1
0
0
2
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
1
0
2
0
0
0
0
4
0
3
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
1
0
2
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
2
0
0
0
0
3
0
0
1
1
0
0
0
2
0
2
0
0
0
0
0
4
0
1
0
3
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
3
0
0
0
4
0
0
0
2
0
0
1
0
1
0
0
0
0
3
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
6
0
0
0
0
0
2
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
1
0
0
0
0
0
1
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
3
0
0
0
0
2
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
3
0
1
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
5
3
2
0
0
1
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
4
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
2
1
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
2
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
2
1
0
1
0
0
0
2
0
0
1
1
0
1
1
0
7
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
2
2
0
2
0
0
0
1
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
2
2
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
3
4
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
2
0
0
0
1
0
2
0
0
0
1
2
1
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
4
0
3
0
0
2
0
0
0
0
2
1
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
4
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
1
1
0
0
0
0
3
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
4
0
0
0
1
2
0
1
0
0
0
2
0
1
0
0
0
0
3
2
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
1
0
0
1
10
0
1
0
0
0
1
0
1
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
1
2
0
10
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
6
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
1
2
0
0
0
0
0
0
3
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
1
2
1
2
0
0
0
0
3
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
1
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
2
2
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
2
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
1
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
1
0
0
2
0
0
2
1
0
0
0
2
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
1
0
0
2
1
2
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
2
3
0
0
1
0
0
0
1
2
0
1
1
1
0
0
1
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
1
0
2
0
1
1
2
0
0
2
0
0
2
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
9
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
4
0
2
1
2
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
6
2
0
0
3
0
0
0
0
2
0
4
0
1
0
0
0
0
2
2
1
0
0
0
3
0
0
0
2
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
3
1
2
0
0
0
1
0
3
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
6
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
3
1
0
2
0
0
1
0
0
0
1
1
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
1
0
2
0
0
0
1
0
1
0
0
0
0
0
0
3
0
1
0
0
0
2
0
3
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
1
0
1
2
0
0
0
0
0
0
1
1
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
2
2
2
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
3
0
0
2
1
0
1
0
2
0
0
3
0
0
0
1
0
0
3
0
0
0
5
0
0
1
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
1
0
0
0
0
1
0
0
2
0
1
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
1
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
2
1
0
0
0
0
0
0
2
0
2
1
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
6
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
1
3
4
0
0
0
0
3
0
0
1
0
3
0
0
1
0
0
1
0
2
0
0
0
1
0
2
0
0
1
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
1
2
2
0
7
0
0
2
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
2
2
0
0
0
0
1
0
0
1
0
0
0
2
0
0
2
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
1
3
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
5
1
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
3
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
3
1
1
1
0
0
0
3
3
2
0
0
2
0
3
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
3
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
2
2
0
0
0
0
2
3
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
3
0
2
0
0
0
3
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
4
0
1
0
1
0
1
1
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
1
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
7
2
0
0
0
0
13
1
2
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
3
1
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
1
2
0
0
0
2
0
12
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
1
4
0
0
0
3
0
0
1
0
0
0
0
1
1
3
1
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
3
0
0
1
0
0
0
0
2
0
1
0
0
0
1
2
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
5
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
6
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
1
2
1
1
0
4
0
0
0
0
0
7
0
0
0
1
0
4
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
2
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
7
0
0
0
1
0
0
3
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
5
0
0
0
0
0
0
1
0
3
0
2
0
0
0
0
1
0
0
0
0
1
1
0
1
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
3
0
0
0
0
2
2
0
0
0
2
2
0
0
4
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
8
0
0
0
2
0
3
0
3
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
4
3
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
5
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
7
1
0
0
0
0
2
4
0
0
0
0
0
0
1
0
1
2
2
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
2
0
1
0
0
2
0
1
0
0
0
1
0
0
0
0
1
2
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
3
0
2
2
0
0
5
0
0
0
0
0
0
0
0
2
2
2
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
3
0
0
3
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
3
1
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
2
0
0
2
0
6
0
0
1
0
2
1
1
0
0
0
1
0
1
2
0
0
0
0
1
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
2
0
0
3
0
1
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
1
0
0
1
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
3
0
0
0
1
3
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
3
0
0
1
4
0
0
0
1
0
0
0
0
0
0
1
1
2
3
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
2
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
3
0
0
2
0
0
0
2
1
0
1
0
0
0
2
4
0
0
0
0
0
0
3
0
1
0
2
0
2
1
0
0
0
2
0
0
0
0
1
0
0
0
1
1
2
1
0
0
0
0
1
2
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
3
1
0
0
0
0
2
0
2
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
1
1
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
4
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
2
4
7
5
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
2
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
6
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
3
1
0
0
0
0
7
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
2
0
0
2
0
0
2
1
2
0
0
0
0
2
0
0
2
0
0
0
0
1
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
4
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
3
0
1
2
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
4
0
0
0
4
2
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
3
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
2
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
3
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
3
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
6
0
0
0
0
0
0
0
2
1
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
5
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
1
2
3
0
0
0
0
0
0
0
2
1
2
0
1
1
0
0
1
0
2
0
0
2
0
1
0
2
0
1
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
1
0
2
0
1
0
0
0
0
0
1
2
0
2
0
0
0
0
1
1
0
0
0
2
2
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
4
0
0
2
1
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
3
0
0
1
0
0
0
0
0
0
0
0
3
0
0
6
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
3
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
1
0
2
1
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
3
0
0
0
0
1
2
2
0
0
1
1
0
2
0
0
0
0
4
1
0
1
0
0
0
2
2
6
3
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
1
2
0
1
0
0
0
0
0
0
0
0
0
1
11
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
2
1
0
2
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
8
2
0
0
1
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
2
1
0
0
2
0
2
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
1
2
1
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
3
2
2
1
1
0
0
0
0
0
0
2
2
2
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
2
2
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
1
1
0
0
0
3
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
1
7
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
3
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
3
2
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
4
2
0
1
0
1
0
1
0
8
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
1
4
0
0
1
0
0
0
0
0
1
0
0
0
5
0
0
2
0
1
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
1
0
0
0
2
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
7
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
1
1
2
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
1
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
2
0
0
0
2
1
2
0
0
0
0
0
0
0
3
1
3
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
1
1
0
0
2
0
0
0
1
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
2
0
0
1
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
1
0
1
0
0
0
2
0
0
2
1
0
4
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
1
1
0
0
0
0
2
0
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
1
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
3
0
0
2
2
0
0
0
0
0
0
0
1
0
0
2
0
3
0
0
0
1
0
0
0
1
0
0
2
0
2
0
1
0
0
0
14
0
0
1
2
0
0
2
0
0
6
0
0
1
3
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
4
0
0
2
0
2
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
2
0
0
3
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
3
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
2
0
1
0
0
0
0
0
1
0
3
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
2
3
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
4
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
2
2
2
0
0
0
0
0
0
3
2
0
4
0
0
0
1
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
1
0
0
2
0
0
0
2
0
1
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
2
0
0
0
2
2
0
1
5
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
3
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
3
0
0
0
1
0
1
0
1
5
2
0
0
0
0
1
0
0
0
0
0
0
0
3
0
2
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
4
0
2
0
1
0
0
0
1
0
1
1
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
1
0
2
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
3
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
3
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
1
2
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
4
0
1
2
0
0
0
2
0
2
0
0
0
0
3
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
12
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
1
0
1
2
0
0
0
0
1
0
2
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
2
2
2
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
11
0
0
0
0
0
0
3
0
0
0
0
1
4
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
1
4
0
4
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
2
0
0
0
0
1
3
0
0
0
3
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
2
0
1
1
0
0
1
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
2
0
2
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
1
1
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
4
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
1
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
1
1
2
0
1
0
7
1
0
0
4
0
0
0
1
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
1
3
0
0
0
0
0
1
0
0
2
1
0
0
1
0
0
0
0
0
0
0
1
1
0
1
1
1
1
0
0
0
0
1
0
0
0
1
2
0
0
1
0
0
0
0
0
3
2
0
1
0
0
1
0
0
0
0
0
1
0
2
2
1
0
0
2
0
0
0
0
1
0
0
0
0
2
1
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
5
0
0
0
0
0
0
1
1
0
1
0
0
2
0
1
0
2
0
0
0
1
2
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
1
1
1
0
2
4
1
0
0
0
0
0
0
0
1
1
0
2
0
0
1
0
0
3
0
0
2
0
0
3
0
0
0
0
0
0
0
2
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
3
3
0
3
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
1
1
0
0
0
1
0
0
0
1
0
2
0
0
0
0
2
0
2
0
0
0
2
0
3
0
2
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
1
2
0
1
0
0
0
0
0
1
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
3
0
0
0
1
0
0
2
0
0
0
2
1
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
2
0
0
0
0
0
0
0
1
0
2
0
0
0
2
2
0
0
0
0
2
0
0
1
1
0
1
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
2
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
1
0
0
1
0
0
1
0
0
1
2
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
1
0
1
2
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
2
0
1
0
2
0
0
1
0
2
1
0
0
0
0
0
2
2
0
6
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
1
1
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
4
1
2
2
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
2
0
0
5
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
3
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
8
0
0
0
0
1
0
0
0
0
0
0
2
1
2
0
0
2
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
3
0
1
2
0
0
0
0
1
0
2
2
0
0
0
2
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
5
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
2
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
3
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
5
0
0
0
0
0
1
0
1
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
6
0
0
0
0
2
2
0
1
0
1
0
0
0
0
2
1
1
0
0
0
0
0
2
0
1
4
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
1
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
2
1
1
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
1
2
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
3
0
2
0
0
1
0
0
0
1
0
1
0
0
1
2
1
2
0
0
1
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
3
0
0
0
1
4
3
0
3
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
1
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
2
0
0
0
0
0
2
1
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
1
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
3
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
2
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
2
2
0
2
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
4
1
2
0
0
0
0
1
1
0
0
5
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
4
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
2
0
0
1
0
0
1
4
0
0
1
0
1
2
0
1
1
0
0
0
2
0
0
1
0
0
0
1
4
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
2
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
3
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
3
0
0
1
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
1
0
0
0
3
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
1
4
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
2
0
0
1
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
3
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
5
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
4
0
1
0
0
0
0
1
0
0
2
0
0
0
2
1
0
1
0
1
1
3
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
2
3
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
4
0
0
0
2
0
1
0
1
0
1
0
2
0
0
0
0
2
1
4
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
2
2
1
3
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
2
2
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
4
2
0
1
1
0
1
0
0
0
2
0
2
2
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
2
0
0
2
2
2
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
2
0
0
0
2
2
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
1
2
0
2
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
11
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
3
2
0
0
2
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
2
2
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
1
0
0
2
0
0
0
1
0
0
0
3
0
0
1
1
2
1
0
1
0
1
2
1
0
1
0
4
3
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
3
2
1
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
1
0
0
0
3
0
0
1
2
0
0
0
0
0
0
2
0
3
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
1
2
0
1
0
0
0
0
1
2
1
0
0
0
0
0
0
0
1
0
0
0
2
1
2
0
0
1
1
0
0
1
0
0
0
0
2
0
0
1
0
3
3
1
0
2
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
12
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
1
0
1
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
3
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
1
0
0
3
0
0
0
0
1
1
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
1
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
2
1
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
1
2
1
0
2
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
2
5
0
0
0
0
0
0
0
0
0
0
0
1
0
3
2
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
1
1
1
0
1
2
1
0
0
0
1
1
0
0
0
0
2
0
0
0
0
1
0
1
0
4
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
2
0
0
2
1
0
0
1
0
1
0
1
0
1
0
0
0
5
0
0
2
5
0
1
0
1
1
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
2
0
0
0
0
3
0
0
1
1
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
2
2
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
3
1
0
1
0
0
0
1
0
3
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
2
0
0
1
1
0
1
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
4
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
3
0
1
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
2
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
1
0
2
0
2
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
2
1
2
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
1
3
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
3
1
0
0
0
0
2
1
4
2
0
0
0
2
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
1
1
2
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
1
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
2
2
0
0
0
2
2
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
3
1
0
0
3
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
1
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
2
0
0
0
0
1
0
1
0
0
1
1
0
0
2
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
1
1
1
4
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
1
0
2
2
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
1
0
0
2
0
1
0
1
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
4
1
2
0
0
4
0
1
0
0
3
0
0
0
0
1
0
0
0
0
1
0
0
3
0
2
0
0
1
0
0
1
0
0
0
1
2
0
0
0
0
0
0
1
0
0
2
2
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
4
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
1
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
1
0
0
0
2
0
2
0
1
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
1
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
2
0
1
2
0
0
2
0
1
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
1
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
1
0
0
0
0
0
1
0
0
6
0
3
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
2
0
1
2
0
3
0
1
0
0
1
0
0
2
0
0
1
2
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
2
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
13
0
0
0
0
0
0
2
0
0
0
0
0
4
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
1
0
0
0
0
3
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
5
2
0
0
6
0
2
0
0
0
0
0
0
1
0
0
3
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
2
1
0
0
0
0
0
0
2
0
0
1
1
0
0
10
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
3
2
0
0
0
0
0
2
0
0
0
3
1
0
0
0
5
1
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
2
1
0
0
2
0
0
0
1
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
1
0
2
0
0
2
0
0
0
0
0
0
0
0
2
2
1
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
1
0
2
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
1
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
2
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
1
0
1
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
1
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
3
0
0
2
1
0
1
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
2
0
0
5
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
1
2
0
3
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
3
0
0
0
1
2
0
0
0
0
0
0
0
1
2
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
4
2
0
0
0
0
0
0
0
1
0
0
1
0
4
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
3
0
1
0
1
0
1
2
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
1
0
3
0
0
0
0
0
0
0
0
2
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
6
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
4
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
2
0
0
1
1
1
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
7
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
2
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
1
0
0
0
0
1
0
5
1
0
0
0
2
0
4
3
0
0
0
0
0
2
0
1
1
2
0
0
0
1
0
0
0
1
0
0
1
2
0
0
1
0
2
0
2
2
0
2
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
1
1
0
2
0
1
1
0
0
0
2
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
32
0
0
6
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
1
0
0
2
0
0
0
0
0
1
9
1
0
0
2
0
0
1
0
1
0
1
0
0
0
0
0
1
1
0
0
1
0
1
0
0
3
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
1
2
0
0
0
1
0
0
0
7
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
2
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
1
1
0
0
2
0
3
0
0
6
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
2
0
0
0
0
0
0
0
0
2
1
0
2
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
2
0
2
2
0
0
2
1
2
0
0
0
0
3
0
0
0
2
0
1
3
2
0
0
4
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
2
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
8
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
3
1
2
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
1
0
2
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
3
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
1
1
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
1
0
1
1
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
2
4
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
1
2
6
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
2
0
0
1
2
1
0
0
3
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
2
0
0
2
0
1
0
1
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
2
1
0
0
1
2
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
1
0
2
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
2
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
2
2
0
0
0
1
1
2
0
0
2
1
0
0
0
0
0
2
0
0
0
0
1
0
2
1
0
0
0
0
2
0
0
0
1
0
0
0
3
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
1
0
2
1
2
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
3
0
0
1
1
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
4
0
0
0
0
0
2
0
1
0
2
1
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
5
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
1
0
0
1
0
0
2
0
0
1
1
0
3
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
2
2
0
5
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
2
1
0
0
0
0
2
0
0
2
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
2
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
1
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
2
0
0
0
0
0
0
0
0
5
0
0
0
1
0
0
0
0
0
0
2
0
0
1
1
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
2
0
0
0
0
0
0
0
1
0
1
0
0
0
3
0
0
2
3
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
4
0
0
2
1
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
3
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
3
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
1
0
0
2
1
0
1
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
2
0
0
0
0
2
0
0
1
0
4
0
0
0
0
0
4
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
1
3
0
0
0
0
2
1
0
0
0
0
2
0
0
2
0
2
0
0
2
0
1
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
4
0
0
1
0
0
1
2
2
0
1
0
0
0
0
1
0
2
0
0
0
2
0
0
7
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
3
0
0
0
0
0
0
1
2
0
1
0
0
1
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
2
2
0
3
0
2
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
5
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
2
1
1
2
0
0
2
1
0
3
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
1
3
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
2
0
1
1
0
0
1
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
5
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
1
3
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
2
0
0
2
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
2
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
1
0
0
0
0
0
0
1
0
0
1
0
2
8
0
0
0
0
1
0
2
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
31
3
0
0
3
1
0
0
0
0
0
0
0
2
0
0
2
0
0
2
1
0
0
2
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
2
0
0
1
0
0
2
0
5
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
4
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
3
2
0
1
0
0
1
0
1
1
0
0
0
0
0
1
0
0
2
3
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
7
0
1
0
0
0
4
1
1
2
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
6
0
1
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
1
3
0
0
1
0
0
0
0
2
0
1
0
0
2
0
0
3
0
2
0
0
0
1
0
3
0
0
1
2
0
0
3
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
1
13
0
0
0
0
0
0
0
2
3
0
0
1
0
1
1
0
3
0
0
0
0
1
0
1
0
0
0
5
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
6
1
0
0
0
0
0
0
1
0
1
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
2
2
1
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
2
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
4
0
0
0
0
2
0
0
1
0
2
4
0
0
1
0
0
1
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
3
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
4
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
5
0
0
0
0
2
0
2
1
1
0
0
0
0
1
0
1
1
0
0
0
0
0
2
1
0
0
5
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
3
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
12
0
0
0
0
1
0
0
1
2
2
1
0
0
0
0
0
2
0
0
1
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
3
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
2
3
0
1
0
0
0
0
3
0
0
1
0
0
1
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
4
0
0
2
0
1
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
3
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
8
0
0
0
0
0
2
0
0
1
4
1
0
2
1
0
1
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
1
0
0
0
1
3
0
0
0
0
0
0
0
0
0
8
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
12
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
2
0
0
1
0
0
2
4
0
2
2
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
2
0
0
0
0
0
0
0
2
2
2
0
0
0
0
1
3
0
0
0
0
0
0
0
3
0
1
2
0
0
1
2
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
4
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
1
0
1
0
1
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
2
0
0
1
0
2
0
0
0
0
0
1
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
3
0
0
1
0
2
0
0
1
2
0
0
0
0
5
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
2
0
0
0
3
0
0
0
0
4
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
1
1
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
2
1
2
0
0
0
0
0
0
1
2
0
0
2
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
6
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
5
0
0
0
0
0
0
0
0
2
1
1
0
5
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
1
0
3
2
1
0
0
0
1
0
0
0
0
0
3
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
3
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
3
5
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
2
0
2
1
0
0
2
3
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
2
3
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
3
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
2
0
0
4
2
0
0
0
0
0
0
0
0
0
0
4
0
0
1
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
2
0
1
0
0
0
0
5
0
1
0
0
0
2
0
2
0
0
3
2
2
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
3
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
5
0
0
0
2
1
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
1
1
1
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
1
2
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
6
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
3
2
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
2
1
0
1
0
5
0
1
0
0
5
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
2
2
0
0
2
2
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
2
1
0
2
0
0
2
0
3
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
2
1
1
0
2
0
1
0
0
0
0
0
1
0
0
2
0
0
2
0
1
0
0
1
0
0
0
1
0
6
1
0
1
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
8
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
7
0
0
0
0
0
0
0
3
0
4
2
1
0
0
0
1
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
2
0
0
0
2
3
0
1
0
0
0
2
0
0
0
1
2
0
0
2
0
2
0
0
0
0
0
0
1
2
0
1
0
0
2
0
2
0
0
2
0
1
1
0
0
0
2
0
1
1
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
2
0
1
0
3
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
4
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
1
0
0
4
0
2
0
0
1
0
0
1
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
1
2
0
0
0
0
2
0
0
0
0
1
0
0
2
0
2
0
1
2
0
0
2
1
0
0
0
0
0
0
1
1
2
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
2
0
0
1
0
0
0
0
0
1
1
0
2
0
0
0
0
2
0
0
2
0
0
1
1
1
2
2
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
4
0
0
1
0
0
0
1
0
2
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
1
0
0
2
0
0
0
0
0
9
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
1
0
0
0
0
3
0
1
0
0
1
0
0
0
0
2
0
1
0
1
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
1
0
0
0
0
0
1
0
0
1
0
0
2
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
1
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
1
0
0
3
1
3
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
1
0
0
0
0
1
0
2
4
0
0
0
0
0
0
0
1
0
2
0
2
2
0
0
2
0
2
0
0
2
3
0
4
0
0
0
0
2
0
0
1
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
1
0
0
0
2
0
0
2
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
2
0
0
0
1
0
0
0
0
1
6
0
0
0
0
0
0
0
0
5
0
0
0
0
0
3
0
1
2
0
1
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
5
1
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
1
0
0
0
2
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
5
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
2
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
2
0
0
0
0
0
3
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
1
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
2
0
2
0
0
0
0
0
1
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
2
1
1
1
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
3
0
0
2
0
3
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
3
0
1
2
1
0
0
0
2
0
1
0
0
0
0
1
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
2
0
0
0
4
2
2
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
2
0
0
1
2
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
1
2
1
0
0
0
0
0
0
2
0
1
2
0
0
0
0
1
0
0
1
0
1
0
2
2
0
0
0
0
0
1
0
0
1
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
2
0
2
8
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
1
1
0
0
0
0
1
3
0
3
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
3
1
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
5
0
0
2
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
5
3
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
7
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
6
0
0
0
0
0
0
1
2
2
0
0
2
0
0
1
0
1
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
1
0
0
3
2
0
2
1
0
1
3
0
0
2
0
0
0
2
2
0
0
2
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
1
0
1
0
0
2
0
1
0
2
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
1
3
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
1
0
2
0
0
0
0
1
0
2
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
3
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
1
2
1
0
0
0
1
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
3
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
1
1
0
2
1
0
1
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
9
0
1
2
0
0
1
0
0
0
3
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
2
2
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
1
0
0
0
0
0
1
0
3
1
0
0
1
0
0
0
2
0
1
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
1
0
2
0
0
0
0
1
0
0
1
3
0
2
0
1
2
0
0
4
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
1
0
0
2
1
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
1
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
2
1
2
2
0
1
0
0
0
0
3
1
0
3
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
3
0
0
2
0
0
0
2
0
0
4
3
0
1
8
0
0
0
0
0
0
4
0
1
2
0
0
2
0
0
0
0
0
7
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
1
2
0
0
2
2
1
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
6
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
2
1
1
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
3
0
0
0
2
2
0
0
1
0
0
0
3
0
0
1
0
1
0
2
3
0
1
0
2
0
0
1
1
0
0
2
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
2
0
0
0
3
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
1
2
0
0
1
1
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
5
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
2
2
0
0
0
0
0
0
0
2
0
2
2
0
1
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
3
1
0
2
0
0
1
0
0
2
0
0
2
0
0
2
0
0
1
1
0
0
1
0
1
0
2
0
2
0
0
0
0
3
0
1
2
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
1
2
0
0
0
1
2
0
2
0
0
3
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
3
0
0
1
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
2
0
0
0
2
0
2
2
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
1
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
2
0
2
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
5
0
0
1
0
0
0
0
0
0
0
3
2
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
2
0
0
0
0
0
3
2
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
1
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
4
1
1
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
2
2
2
0
0
3
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
5
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
1
0
0
1
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
2
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
1
2
0
0
0
3
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
1
2
0
0
0
0
0
0
2
0
0
3
0
0
0
1
0
0
0
0
0
0
1
0
0
2
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
3
0
1
0
1
0
0
0
4
1
0
2
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
1
1
2
2
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
1
1
1
0
0
0
0
2
1
1
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
1
2
2
0
3
1
0
0
0
0
0
0
0
2
0
2
0
3
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
1
1
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
4
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
2
0
0
0
3
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
3
0
2
1
0
0
1
0
0
0
2
1
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
3
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
2
1
0
0
0
0
2
0
2
0
0
0
1
2
0
1
0
2
0
0
0
0
0
0
3
0
2
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
3
3
0
0
0
0
1
0
0
0
1
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
3
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
6
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
6
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
1
1
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
1
0
1
0
2
0
0
2
0
2
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
1
0
0
2
0
0
1
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
2
0
1
0
1
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
2
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
3
1
0
0
3
2
0
2
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
6
0
2
1
0
0
0
0
0
0
4
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
6
1
0
0
0
0
0
0
0
0
1
0
1
2
2
2
1
3
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
3
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
2
3
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
1
2
1
0
0
0
0
0
2
2
0
2
0
0
2
2
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
2
1
0
0
0
0
2
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
1
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
1
0
0
2
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
1
1
1
0
1
0
4
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
1
0
0
0
0
2
3
0
1
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
3
0
2
0
0
10
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
2
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
1
2
2
1
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
1
0
1
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
1
0
0
2
0
0
0
0
0
2
0
3
0
0
0
0
1
0
1
0
0
0
1
0
1
2
0
0
0
2
0
0
0
0
0
1
0
0
0
1
1
0
2
1
0
0
0
4
0
1
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
4
0
2
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
1
2
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
1
0
3
2
1
0
0
0
0
0
0
5
0
1
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
3
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
2
2
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
4
0
0
0
1
0
2
2
0
0
0
1
0
1
0
0
1
0
1
0
1
0
2
2
1
0
1
0
0
2
0
0
0
0
0
0
1
0
2
1
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
2
1
0
1
0
5
1
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
4
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
1
0
0
2
4
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
1
1
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
2
1
0
1
1
2
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
3
0
0
1
0
0
0
0
0
1
0
0
1
5
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
5
1
0
0
0
0
0
0
1
0
2
2
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
3
0
0
0
0
2
0
0
5
0
0
0
0
0
2
0
0
2
0
0
0
1
0
1
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
4
0
0
0
2
1
0
0
0
0
0
0
0
2
0
1
3
0
0
0
0
5
0
0
0
5
0
1
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
3
0
2
2
0
0
0
1
0
1
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
1
2
2
0
0
0
1
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
2
2
2
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
2
0
6
0
0
3
2
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
2
5
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
5
0
0
0
0
0
1
0
0
2
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
1
3
0
0
0
4
0
0
0
0
0
0
0
1
0
1
0
0
1
4
0
3
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
2
0
1
0
0
0
0
0
0
0
0
1
2
3
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
6
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
2
1
0
0
0
0
0
0
12
0
0
0
0
1
0
1
0
0
0
3
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
4
1
1
0
0
2
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
1
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
2
2
1
0
0
0
0
0
3
0
0
0
2
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
5
2
0
0
0
1
0
0
0
2
0
0
2
0
0
1
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
4
0
2
0
1
0
0
0
0
1
0
0
0
0
1
0
0
2
0
2
1
0
0
0
0
0
0
1
0
1
0
4
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
1
0
0
0
0
3
0
1
0
2
0
0
2
1
0
0
0
1
4
0
1
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
3
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
1
0
2
0
0
1
0
2
0
0
2
0
3
0
1
0
0
1
1
0
0
2
0
0
0
0
1
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
4
1
0
0
0
0
2
3
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
2
0
0
2
0
2
0
0
1
2
0
0
0
0
0
1
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
2
3
0
0
0
0
0
1
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
8
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
2
0
2
3
0
1
0
0
3
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
1
0
0
0
0
2
2
0
1
0
1
0
0
0
0
0
2
0
0
1
0
2
0
4
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
3
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
3
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
1
1
0
2
1
1
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
2
2
0
0
1
0
0
0
0
0
4
0
2
0
4
0
0
0
1
0
0
0
3
0
1
0
3
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
4
0
0
0
2
1
0
1
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
3
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
3
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
2
0
0
0
1
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
2
0
0
1
0
0
2
0
0
0
0
1
0
2
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
2
0
0
0
3
0
2
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
4
1
0
1
0
1
0
1
1
2
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
3
2
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
3
1
1
1
1
0
1
2
1
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
1
0
1
1
0
0
0
0
0
1
2
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
1
4
1
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
2
2
2
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
4
2
2
0
0
0
5
0
2
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
1
0
2
1
1
2
1
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
5
0
3
0
0
0
0
0
0
0
1
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
3
0
1
0
2
3
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
7
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
2
2
0
0
0
0
1
0
1
0
1
2
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
8
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
6
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
2
0
0
0
3
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
3
2
2
0
0
1
1
0
2
3
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
1
0
0
0
0
5
1
0
0
0
0
0
6
0
2
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
1
0
2
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
1
2
0
0
0
0
0
0
1
0
0
0
1
1
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
2
0
0
0
0
0
0
1
0
0
2
0
1
0
0
1
0
0
0
4
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
1
2
4
0
0
1
0
0
0
0
1
2
0
1
0
0
0
1
0
0
0
2
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
6
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
1
0
1
1
0
2
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
2
1
0
0
2
2
0
0
0
1
2
4
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
4
0
3
1
0
1
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
3
0
0
2
1
0
1
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
1
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
1
0
4
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
1
0
0
1
0
0
0
1
0
1
0
2
0
0
0
0
1
0
0
0
1
2
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
1
1
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
3
2
0
2
1
0
1
0
0
2
0
0
0
0
1
1
1
0
2
0
0
0
0
0
0
0
1
1
2
0
0
2
1
0
0
0
0
0
0
2
1
0
0
2
2
4
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
1
3
1
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
1
0
2
0
1
1
0
0
0
0
2
2
0
1
0
0
4
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
1
0
1
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
3
0
0
0
0
0
0
0
2
0
0
0
1
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
3
0
3
0
2
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
2
0
1
10
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
2
1
0
0
0
2
0
1
0
1
0
0
1
0
0
0
0
0
1
1
1
0
0
2
2
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
1
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
1
0
0
0
6
0
2
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
2
0
0
1
0
0
1
1
1
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
2
0
1
1
0
0
2
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
4
1
1
1
0
0
2
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
2
0
0
0
0
0
2
1
0
3
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
3
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
2
2
1
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
5
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
1
0
0
0
1
1
0
0
0
4
0
0
1
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
2
1
2
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
3
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
2
0
0
3
1
0
3
0
0
1
0
0
0
0
0
0
2
0
3
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
1
2
3
2
0
1
0
1
0
0
0
1
0
0
0
0
0
6
0
0
0
1
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
2
2
0
2
0
0
0
1
0
2
0
0
0
3
0
4
0
1
0
0
0
0
2
2
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
4
2
0
0
2
0
0
2
2
0
0
1
0
0
3
0
0
0
0
2
1
0
0
3
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
1
2
0
0
0
1
0
0
0
0
4
0
0
2
1
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
2
3
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
4
0
0
0
0
2
0
2
0
0
0
0
0
0
1
4
1
2
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
11
0
2
0
0
2
1
0
1
3
0
0
0
0
0
0
0
0
2
1
1
0
0
1
1
0
0
1
0
0
2
0
0
0
0
1
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
5
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
2
0
1
0
0
0
1
0
0
0
0
2
2
0
1
2
1
0
0
1
0
0
0
2
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
1
3
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
3
0
2
2
0
0
0
0
0
0
1
0
0
0
2
1
1
0
0
0
0
0
2
0
0
0
0
4
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
2
1
0
0
0
0
0
0
0
2
0
3
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
1
1
0
0
0
2
2
0
0
0
0
0
0
4
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
2
0
1
0
0
3
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
3
0
1
0
0
0
0
2
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
1
0
0
0
2
1
0
2
8
0
1
0
0
0
3
0
0
0
0
0
2
0
1
3
0
2
3
0
1
0
0
2
0
0
0
2
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
3
3
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
1
0
0
0
0
0
0
1
2
0
1
0
1
0
0
0
1
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
1
2
0
1
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
4
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
1
2
2
0
1
0
2
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
2
2
0
0
1
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
2
0
0
0
2
2
1
0
3
5
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
2
0
2
1
0
1
0
0
0
2
2
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
6
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
3
2
0
0
0
0
0
0
0
0
1
1
0
2
2
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
1
0
0
0
0
1
0
1
3
0
0
0
0
0
3
0
0
0
0
3
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
3
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
1
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
2
0
1
0
0
0
0
0
0
0
3
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
2
0
0
2
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
1
0
2
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
5
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
2
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
4
0
1
4
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
2
0
2
0
0
0
0
0
1
0
2
2
0
3
0
0
2
1
2
0
0
2
0
0
2
4
0
0
0
0
0
0
0
0
0
2
0
0
0
1
4
2
0
1
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
2
1
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
2
1
1
2
0
0
2
0
0
0
0
4
0
2
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
1
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
1
0
10
2
0
1
0
2
4
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
1
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
2
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
5
0
0
0
2
0
0
0
0
0
0
0
0
2
1
1
1
0
0
1
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
1
2
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
2
0
1
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
2
0
1
0
0
0
0
3
0
0
0
0
2
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
1
3
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
2
1
1
0
0
1
1
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
3
4
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
3
1
1
0
2
0
0
1
0
1
2
2
0
1
0
0
0
1
2
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
1
0
1
2
0
0
2
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
5
0
0
0
0
2
0
0
0
0
0
1
1
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
2
1
1
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
1
0
1
0
1
0
1
0
1
0
0
0
1
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
2
1
0
0
3
0
0
0
1
0
0
1
1
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
6
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
2
0
2
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
2
0
0
0
1
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
3
0
0
1
0
0
0
0
0
2
0
3
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
2
2
2
2
2
0
0
0
0
0
0
5
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
5
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
1
0
0
0
0
0
2
0
1
1
0
0
0
2
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
3
0
0
0
3
0
0
0
0
0
0
0
0
1
1
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
2
2
0
0
0
0
3
1
0
0
1
0
1
2
3
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
3
0
0
0
0
1
0
0
0
0
1
0
2
0
1
2
0
0
0
0
0
4
0
0
0
1
3
2
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
1
4
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
4
0
0
1
0
0
0
0
2
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
3
2
1
1
0
2
1
0
0
0
0
0
0
2
0
0
1
0
0
1
0
2
4
2
0
1
0
0
5
2
0
0
0
0
2
5
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
5
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
1
0
1
0
0
3
0
0
0
0
0
9
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
2
0
0
0
1
2
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
1
1
0
0
2
1
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
2
0
2
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
1
1
0
2
0
0
0
0
0
0
0
1
0
0
0
1
4
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
2
0
2
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
2
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
7
0
0
0
0
0
3
0
1
0
0
0
0
1
0
0
3
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
1
0
1
0
0
7
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
2
0
0
2
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
5
0
0
0
2
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
2
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
2
0
0
0
0
0
2
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
3
0
0
0
0
0
3
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
3
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
3
1
1
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
3
1
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
2
1
0
0
3
0
0
0
2
0
0
2
0
0
0
1
2
0
0
0
1
0
1
0
0
0
1
0
0
3
0
0
0
0
0
0
1
1
1
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
3
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
3
0
2
0
0
0
0
1
1
1
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
3
4
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
1
2
0
0
1
0
1
0
0
0
0
0
0
3
0
3
0
0
1
0
1
0
0
1
2
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
1
1
1
0
0
0
1
0
5
0
1
0
2
3
1
0
2
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
3
0
5
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
2
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
6
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
2
2
0
2
0
0
1
0
0
1
0
0
0
2
2
0
0
0
8
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
1
2
1
1
0
2
0
1
0
0
0
1
0
3
0
1
0
1
0
0
0
0
0
0
0
0
2
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
1
0
1
0
1
0
0
0
0
1
1
0
1
3
0
0
0
0
0
2
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
3
5
0
1
2
2
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
2
5
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
6
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
1
0
2
0
0
0
0
0
1
1
0
0
2
0
0
0
0
5
0
0
0
0
1
0
0
0
0
4
0
0
0
0
2
0
2
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
1
0
3
3
0
0
0
1
0
0
0
0
0
2
0
0
5
0
0
0
0
1
0
0
0
0
0
0
0
3
0
1
0
0
1
0
0
0
2
0
0
5
3
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
5
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
2
0
0
0
0
1
0
3
0
0
0
0
4
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
2
0
0
0
0
0
1
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
3
1
0
2
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
1
4
0
1
0
0
2
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
1
7
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
3
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
3
1
0
0
2
0
0
1
3
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
1
0
0
0
0
0
2
1
0
5
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
5
0
0
0
0
0
1
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
1
0
0
2
0
0
0
3
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
3
0
3
0
1
0
0
3
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
2
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
9
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
1
2
1
0
2
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
3
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
2
0
1
0
0
0
1
0
0
2
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
2
0
2
0
0
4
2
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
2
0
0
0
1
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
2
3
0
0
0
0
1
0
0
2
1
0
0
1
2
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
1
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
1
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
2
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
1
0
0
2
0
6
1
1
2
0
0
0
0
1
1
2
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
2
0
2
3
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
2
0
2
0
0
0
0
0
3
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
1
0
9
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
2
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
1
1
1
0
0
2
0
2
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
2
2
1
0
3
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
2
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
5
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
4
0
0
0
0
2
0
3
0
1
0
0
0
0
0
0
1
5
0
0
0
0
0
0
0
0
1
0
0
0
0
11
0
1
0
0
1
1
0
0
0
0
1
4
1
0
0
0
0
1
0
0
3
0
1
0
0
0
0
2
1
0
4
0
1
2
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
4
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
1
0
0
1
0
0
0
7
3
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
9
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
2
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
2
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
2
0
5
0
0
1
0
0
0
3
0
0
1
0
0
0
0
0
0
2
0
2
2
0
1
2
0
0
0
0
0
2
2
0
1
0
1
0
0
0
2
0
2
0
2
0
0
1
0
0
0
0
1
0
2
0
0
0
2
1
0
0
0
4
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
1
1
1
1
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
2
0
0
1
0
0
8
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
7
0
1
0
1
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
1
0
0
0
0
0
0
1
0
0
2
3
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
2
0
3
0
2
1
0
0
0
0
0
0
0
1
0
1
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
1
0
0
4
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
2
0
0
0
1
0
0
1
3
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
2
1
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
0
4
0
0
0
0
1
7
0
0
2
0
0
0
2
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
1
1
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
1
0
0
1
0
2
1
0
5
0
1
0
0
1
0
0
0
0
0
0
0
0
2
2
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
2
1
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
1
0
0
1
2
2
0
0
1
2
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
1
2
0
2
0
0
1
0
0
0
0
2
0
0
2
0
2
0
1
2
0
0
2
0
1
2
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
2
2
0
1
1
2
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
2
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
5
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
3
0
0
1
0
0
0
0
0
4
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
7
0
0
0
0
1
0
0
2
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
2
0
0
1
0
0
0
1
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
1
5
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
1
1
2
1
3
0
0
0
0
4
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
2
1
0
0
0
0
0
1
2
2
0
2
0
0
2
1
1
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
1
5
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
1
2
0
0
0
4
0
2
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
1
2
0
0
0
2
1
0
0
0
0
0
0
0
0
2
1
0
2
0
0
1
0
0
2
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
2
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
6
0
0
0
1
0
1
2
2
1
0
1
3
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
1
0
1
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
2
0
0
0
1
0
1
1
0
0
3
1
0
0
1
2
0
0
3
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
1
1
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
2
2
0
2
0
0
3
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
1
2
1
0
0
1
0
1
0
0
1
0
0
3
0
0
0
2
0
0
0
2
0
1
3
0
0
1
0
0
1
0
0
0
0
0
1
0
2
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
1
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
1
1
0
1
2
1
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
1
1
0
3
0
0
0
2
0
0
0
0
0
0
5
0
0
0
0
0
0
0
2
2
2
0
1
0
2
3
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
5
1
4
0
1
0
0
1
0
3
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
3
2
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
2
1
0
0
0
2
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
1
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
4
0
2
1
0
0
0
2
1
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
2
0
0
0
0
3
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
3
1
0
3
1
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
1
1
0
0
2
0
0
0
3
0
3
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
2
1
0
0
2
0
0
0
0
3
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
2
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
2
0
4
0
0
0
0
0
1
0
1
1
0
1
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
3
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
3
0
0
1
0
0
0
0
0
0
1
2
0
1
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
1
0
0
1
0
0
0
0
2
2
0
1
0
2
1
0
1
0
0
0
2
0
0
1
0
3
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
4
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
3
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
1
0
2
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
2
0
0
0
3
0
1
2
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
3
1
0
0
0
1
1
0
0
0
5
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
3
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
1
1
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
5
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
5
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
1
0
0
1
0
1
0
2
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
2
7
0
3
0
0
2
1
0
0
0
2
0
0
1
2
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
4
1
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
3
0
0
1
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
4
0
0
0
0
5
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
2
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
2
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
9
0
0
2
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
1
0
1
0
1
0
0
0
3
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
1
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
2
0
2
0
0
2
0
0
0
0
1
0
0
0
0
2
2
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
2
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
6
8
0
0
0
0
1
0
3
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
3
9
0
0
0
0
0
0
2
0
0
0
2
0
0
2
1
0
0
4
2
0
0
0
2
0
0
0
2
2
0
1
1
1
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
1
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
2
0
3
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
3
1
4
9
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
2
1
2
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
1
0
0
0
0
0
0
3
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
2
3
2
0
0
0
0
0
1
0
0
2
0
0
0
0
2
2
0
2
0
0
0
0
0
2
0
2
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
2
0
1
0
1
14
0
1
1
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
2
1
1
0
0
1
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
2
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
2
0
2
0
0
0
1
0
0
0
0
0
0
1
1
1
2
2
6
0
4
0
1
0
3
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
6
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
3
2
0
0
2
0
0
1
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
2
0
1
0
0
0
1
0
0
0
0
3
0
0
0
2
2
0
1
0
0
2
0
1
0
0
0
2
0
0
1
0
0
0
2
1
0
1
0
3
0
0
0
0
0
1
1
0
1
0
3
0
0
0
2
0
0
0
0
0
1
0
0
0
4
1
0
0
0
1
1
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
3
0
0
0
0
0
1
0
0
0
2
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
1
1
0
0
0
0
3
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
10
0
0
0
0
0
1
2
1
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
4
1
2
0
0
2
1
0
2
1
1
0
0
0
0
3
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
1
0
5
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
2
0
0
2
1
0
0
0
0
1
0
0
1
0
2
0
0
0
0
7
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
2
0
2
2
0
0
0
1
1
0
0
0
0
0
0
0
2
0
5
0
1
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
1
0
1
2
0
3
0
0
0
0
0
4
0
6
0
0
0
0
0
3
0
0
0
0
0
1
0
1
1
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
2
1
0
1
0
1
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
2
3
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
3
1
0
0
0
0
0
1
4
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
1
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
3
0
0
0
0
0
6
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
2
0
2
0
0
0
1
0
2
0
1
0
0
0
0
1
0
0
2
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
3
0
0
1
0
0
2
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
2
2
1
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
1
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
2
0
0
0
0
0
0
1
0
1
2
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
2
0
2
0
0
2
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
1
0
1
3
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
1
0
0
2
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
4
0
0
0
2
1
2
0
0
0
1
0
1
2
1
0
0
0
0
1
1
0
0
2
0
0
2
0
3
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
1
0
1
1
1
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
4
1
0
0
2
0
0
0
0
0
2
0
5
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
2
0
0
2
1
0
0
1
3
0
1
0
3
0
3
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
6
0
0
0
0
0
0
3
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
1
0
0
0
2
0
0
1
2
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
3
0
0
0
0
2
0
1
0
0
0
2
1
0
0
0
1
2
0
1
1
1
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
2
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
2
1
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
1
4
0
0
0
0
0
0
0
2
0
0
2
3
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
2
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
7
3
2
1
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
8
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
2
1
2
3
1
0
0
0
3
4
0
0
2
0
2
0
0
1
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
3
0
3
1
0
0
0
0
0
0
0
2
1
0
0
0
2
0
2
1
0
0
1
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
1
0
1
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
1
3
0
1
4
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
2
0
0
0
0
4
2
0
0
0
6
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
1
3
0
0
0
0
2
1
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
1
1
1
0
0
0
2
0
0
0
0
0
1
2
2
0
0
2
0
0
0
0
3
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
2
1
1
0
1
0
2
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
13
1
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
3
2
0
0
0
2
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
1
0
2
0
0
2
2
0
0
2
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
2
0
2
2
0
0
0
0
0
0
0
0
1
0
1
1
0
4
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
2
2
0
0
1
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
3
2
0
0
1
1
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
2
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
5
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
3
1
0
1
0
2
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
3
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
2
0
0
0
2
0
0
0
0
0
2
0
0
2
1
3
1
1
2
1
1
2
2
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
4
0
0
6
1
2
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
4
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
2
0
2
0
0
0
1
0
0
0
0
1
1
2
0
1
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
1
1
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
2
2
0
0
0
0
0
2
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
12
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
2
2
0
0
4
0
7
2
0
2
0
0
2
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
2
2
0
4
0
1
0
0
2
2
1
0
0
0
0
0
4
0
0
0
0
1
1
0
0
2
0
0
1
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
4
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
3
0
2
2
0
3
0
2
2
0
2
2
2
0
0
0
0
2
2
0
2
1
0
1
0
0
0
0
4
0
0
0
0
0
0
2
0
0
2
0
3
0
2
3
0
0
2
0
0
0
1
2
0
0
1
0
0
0
1
0
0
3
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
3
4
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
3
0
1
0
0
1
0
1
0
2
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
3
1
1
0
1
0
2
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
2
1
3
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
4
1
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
2
0
0
0
0
0
0
1
1
2
0
0
0
3
0
2
0
0
0
0
0
0
1
0
0
0
2
2
1
0
0
0
1
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
1
2
0
2
0
0
0
0
0
2
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
7
1
0
0
1
0
0
2
0
0
4
0
0
0
0
0
0
0
1
0
0
2
1
0
4
0
0
0
0
3
0
2
0
1
0
0
0
2
0
0
1
0
0
0
0
1
0
0
1
0
3
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
1
2
1
2
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
1
1
0
0
0
3
0
0
1
1
0
0
3
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
2
0
0
1
0
0
0
1
1
0
2
3
0
0
2
0
0
0
0
0
0
1
1
1
0
1
0
1
0
0
6
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
1
1
1
0
2
0
1
0
0
0
0
0
0
0
0
0
5
0
0
2
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
4
2
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
13
0
0
0
0
0
0
0
2
0
0
2
1
1
0
0
0
1
0
0
4
3
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
1
3
0
2
0
0
2
0
0
0
2
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
2
0
10
2
0
1
2
0
0
2
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
3
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
4
0
0
0
0
0
0
0
0
2
4
0
1
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
5
0
0
0
1
0
0
0
3
0
1
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
4
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
3
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
1
2
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
3
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
1
2
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
3
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
3
0
1
0
1
2
0
0
0
1
2
0
0
0
3
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
1
0
2
1
0
0
0
0
0
1
0
2
0
0
4
0
1
5
0
0
0
0
0
4
0
1
0
2
2
2
1
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
6
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
2
0
0
2
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
9
0
1
1
0
0
2
0
0
0
1
0
0
0
0
2
3
0
0
0
0
0
0
2
0
0
6
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
6
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
18
1
0
2
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
3
1
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
1
0
0
1
0
0
1
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
6
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
1
1
0
3
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
1
1
2
0
0
0
1
0
0
0
0
0
0
1
3
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
2
0
1
0
1
0
0
0
0
0
0
3
1
2
0
2
0
0
2
0
0
0
0
0
0
2
1
2
8
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
1
0
7
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
2
0
0
0
0
1
0
0
1
0
1
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
8
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
1
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
5
0
1
0
0
0
2
0
1
0
2
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
3
0
0
1
0
2
1
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
2
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
2
1
0
0
1
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
3
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
1
1
2
2
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
1
1
0
2
1
9
0
6
0
1
1
1
1
0
1
0
0
0
0
2
2
0
0
2
2
0
0
0
0
0
0
0
1
0
2
0
2
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
1
1
0
0
0
0
0
0
6
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
1
0
3
0
0
2
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
1
2
0
2
0
3
2
3
0
0
2
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
2
1
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
8
0
0
0
1
0
0
0
0
0
0
2
1
0
3
0
0
0
2
0
5
0
0
0
1
0
2
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
4
0
2
0
2
0
2
0
0
3
0
0
3
6
0
0
0
0
0
1
0
0
0
1
3
2
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
2
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
2
0
0
2
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
4
0
3
0
0
0
0
0
0
0
2
0
0
5
0
0
0
11
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
3
0
0
0
0
0
0
2
0
0
0
0
3
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
1
0
0
0
5
0
0
0
1
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
1
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
1
1
0
0
1
0
0
0
0
1
0
0
0
1
2
0
2
0
0
0
0
1
0
0
5
1
3
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
6
0
0
0
0
0
0
1
0
0
0
1
2
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
3
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
1
0
0
0
0
0
0
1
0
2
0
1
0
0
2
0
2
2
0
0
1
0
0
0
1
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
2
2
2
0
0
0
4
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
1
0
1
0
0
0
0
1
1
0
0
2
0
0
0
2
0
3
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
2
1
0
0
1
0
2
0
0
1
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
2
0
0
4
1
0
0
0
0
1
0
0
0
1
0
0
0
2
7
2
0
1
4
0
1
0
0
0
0
0
0
3
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
3
1
0
2
0
0
1
0
1
0
0
0
0
2
0
0
2
2
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
2
0
2
0
3
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
1
2
2
0
0
2
1
0
2
0
0
0
2
0
1
0
0
0
0
4
1
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
1
0
2
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
2
10
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
2
1
3
0
2
7
0
0
0
1
1
2
0
1
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
1
2
1
0
0
0
0
2
1
1
0
1
0
3
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
0
2
0
2
2
0
0
2
0
2
1
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
1
0
0
0
0
1
2
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
1
0
1
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
1
2
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
3
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
1
2
1
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
1
2
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
3
0
2
0
6
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
2
0
0
1
0
0
0
0
1
1
0
0
2
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
5
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
1
0
2
0
4
0
0
0
0
0
2
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
2
0
0
0
0
0
1
0
0
0
2
1
2
1
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
1
2
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
3
0
2
0
1
0
0
0
0
3
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
1
2
1
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
2
0
1
0
0
1
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
2
0
0
1
1
0
1
0
0
0
1
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
3
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
2
0
0
0
0
2
0
2
0
0
0
0
1
1
0
0
1
2
4
0
0
0
3
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
1
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
2
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
2
0
1
1
0
0
1
0
0
0
0
0
0
3
1
0
0
1
1
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
4
0
2
2
0
1
0
0
0
1
0
2
1
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
5
0
0
0
1
1
1
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
2
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
3
0
0
0
0
0
0
0
0
10
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
1
1
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
2
0
0
0
0
1
0
2
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
3
0
1
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
2
0
2
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
5
1
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
3
0
0
0
0
3
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
1
0
2
0
1
0
0
1
1
0
1
0
1
0
1
0
0
1
0
0
0
6
0
1
0
0
0
0
2
0
2
3
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
1
1
0
0
0
2
1
0
0
1
0
0
0
0
1
0
0
0
1
1
2
0
0
1
2
0
0
0
0
0
0
0
3
0
1
1
0
0
4
2
0
0
0
2
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
2
2
2
0
0
5
0
3
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
3
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
6
1
0
2
0
0
2
0
0
0
0
0
0
1
0
2
0
3
5
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
4
0
0
0
1
1
0
0
0
0
0
1
0
1
2
0
0
0
0
1
2
0
0
1
7
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
1
0
0
0
0
2
0
0
4
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
1
1
0
0
1
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
4
0
0
0
0
1
0
0
0
0
3
1
1
0
1
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
5
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
1
0
3
0
0
0
0
2
0
0
3
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
2
0
1
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
1
0
0
0
0
0
0
2
0
0
3
0
0
0
1
2
0
0
2
0
0
1
0
0
1
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
2
0
0
2
2
0
1
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
3
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
1
2
0
0
0
0
2
0
0
7
0
1
0
0
1
0
2
0
2
0
1
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
3
1
0
1
0
0
2
1
1
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
1
0
2
0
0
1
2
0
0
2
2
1
2
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
1
0
0
1
0
0
0
1
2
0
0
0
2
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
2
0
2
0
1
0
0
1
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
1
0
2
0
0
2
0
2
0
0
0
0
0
1
0
0
1
0
0
3
0
0
0
0
0
1
0
0
0
0
3
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
3
0
0
1
0
0
0
0
2
1
0
0
1
2
0
0
1
1
0
0
0
0
0
0
0
8
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
1
0
1
1
0
4
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
3
1
1
0
2
0
0
3
0
0
0
4
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
4
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
3
0
0
2
2
0
2
0
0
0
3
0
0
0
0
0
0
0
1
0
1
2
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
12
2
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
1
4
0
0
3
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
2
2
1
0
1
0
0
3
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
3
1
0
0
0
0
0
0
7
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
2
2
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
1
0
1
0
1
2
0
2
0
0
2
0
0
2
0
0
0
0
0
1
1
0
1
5
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
2
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
3
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
3
0
1
0
1
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
1
1
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
2
0
0
1
0
0
1
0
1
0
0
0
0
0
0
2
0
0
1
0
0
1
2
0
2
0
0
1
0
1
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
2
0
0
1
0
1
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
1
1
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
4
2
0
0
0
0
1
0
2
2
0
0
6
1
2
0
0
0
0
1
2
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
16
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
2
4
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
14
0
0
0
0
2
0
1
0
5
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
1
0
1
0
2
0
2
0
0
0
3
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
1
0
0
0
0
3
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
1
2
0
2
0
0
4
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
4
0
4
1
0
0
2
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
7
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
2
0
0
1
2
0
2
0
0
0
2
0
0
3
0
0
0
0
0
1
3
0
0
0
2
0
0
0
0
3
0
0
0
0
0
6
1
2
0
0
2
1
0
1
0
1
0
1
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
1
0
1
2
0
1
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
3
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
1
0
0
0
0
3
0
0
0
0
0
2
0
2
2
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
6
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
1
1
2
0
1
0
0
0
0
3
1
2
0
0
0
2
0
2
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
4
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
2
0
2
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
3
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
4
0
0
3
0
0
2
0
2
0
0
1
1
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
5
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
3
0
0
1
1
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
7
0
1
1
1
0
0
0
0
2
0
0
0
9
0
1
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
2
4
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
3
0
1
4
2
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
2
0
1
14
0
0
1
2
0
0
2
0
0
3
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
1
2
2
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
3
0
0
2
0
0
0
0
0
1
0
2
0
2
0
1
0
0
1
2
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
1
0
1
0
2
2
0
2
0
2
0
1
0
0
0
1
0
0
0
0
2
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
2
0
0
0
0
2
1
0
1
0
0
0
0
1
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
2
0
2
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
4
0
1
0
0
0
1
0
0
0
0
0
0
2
2
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
1
0
6
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
2
3
4
0
3
0
0
4
0
0
2
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
4
0
0
0
1
0
2
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
3
0
0
0
4
0
0
1
0
0
1
2
0
0
0
0
1
0
2
1
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
1
0
3
0
0
0
0
4
1
0
0
0
1
5
0
0
0
1
4
0
0
0
0
1
0
1
0
0
0
2
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
2
0
2
0
1
0
2
0
0
2
1
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
2
0
1
1
1
0
1
2
0
2
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
2
2
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
2
0
0
2
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
7
0
0
0
1
2
0
1
0
0
0
4
2
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
1
0
1
0
2
0
0
0
0
1
0
0
2
3
0
0
0
0
0
1
0
0
0
5
2
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
1
0
0
2
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
1
2
1
2
1
0
0
0
0
0
0
0
1
1
2
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
2
1
4
0
0
0
0
1
0
0
2
1
1
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
2
0
0
2
2
5
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
10
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
2
1
0
0
0
0
1
0
0
0
0
1
0
0
0
2
2
0
0
2
2
0
0
0
1
0
0
0
3
3
0
2
0
3
1
2
0
0
0
0
0
0
1
0
0
0
2
0
2
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
3
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
1
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
2
0
0
2
0
2
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
1
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
2
1
3
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
1
1
2
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
1
0
0
1
0
1
0
0
0
1
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
4
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
10
0
0
0
0
1
2
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
2
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
1
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
1
0
0
3
0
0
2
0
1
0
0
0
0
0
0
2
0
0
1
1
1
0
0
0
2
1
0
2
0
2
4
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
2
0
1
0
1
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
2
0
0
7
0
0
2
0
0
2
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
3
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
2
2
0
1
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
1
1
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
7
0
0
0
3
0
0
0
0
0
3
1
3
0
0
0
0
0
0
0
0
2
0
2
7
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
3
0
0
2
2
0
2
0
0
0
1
0
0
3
2
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
3
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
1
0
1
0
0
2
1
2
0
0
0
0
0
0
0
2
2
0
0
2
0
1
0
2
0
2
0
0
0
0
1
0
0
2
1
0
0
2
0
0
2
2
2
0
0
2
0
0
2
0
0
0
0
1
0
1
2
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
3
0
6
0
1
2
0
5
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
2
2
0
0
2
1
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
2
1
0
0
0
1
0
1
0
0
1
0
1
3
0
1
2
0
0
0
0
0
0
0
0
1
0
3
0
1
0
0
2
0
0
3
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
1
1
2
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
2
0
0
0
0
0
0
0
0
3
0
0
0
1
2
0
0
1
1
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
9
2
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
3
0
1
0
4
0
0
0
0
0
0
1
0
0
4
0
0
1
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
4
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
2
1
0
0
1
0
0
0
1
1
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
3
0
0
0
2
0
1
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
3
1
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
4
0
0
0
2
0
0
0
0
1
0
2
0
0
0
3
0
0
0
2
0
0
2
0
0
0
2
2
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
3
0
0
0
2
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
6
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
4
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
4
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
3
2
0
2
2
0
4
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
4
0
1
1
0
0
0
1
4
3
0
2
0
0
0
0
1
0
0
0
2
0
2
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
5
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
2
0
2
3
0
0
2
0
0
0
5
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
1
0
3
0
1
0
0
0
0
0
0
1
1
0
2
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
2
0
2
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
3
0
0
0
2
0
0
0
0
2
0
2
2
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
1
0
0
2
0
0
3
0
0
0
0
1
0
1
0
2
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
1
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
2
2
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
3
1
0
0
3
0
2
1
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
4
0
2
0
1
0
0
1
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
6
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
2
0
0
2
0
0
1
0
0
1
1
0
0
2
0
0
2
2
2
0
0
0
0
0
0
1
1
3
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
3
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
3
1
1
0
2
2
0
0
2
0
0
0
0
0
2
0
0
2
1
2
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
3
1
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
2
0
1
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
2
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
2
0
0
1
8
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
2
0
0
0
13
0
1
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
4
1
0
1
1
0
5
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
2
2
3
1
0
3
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
2
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
4
0
0
0
0
0
1
1
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
3
0
0
0
1
0
0
2
0
0
0
4
0
0
3
0
0
0
0
2
0
0
3
0
0
1
0
0
0
2
0
0
0
0
1
0
2
0
0
2
0
1
2
2
0
0
0
2
0
0
2
0
1
0
0
3
0
1
0
0
2
0
0
0
0
0
0
2
0
1
2
1
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
2
1
2
0
0
0
1
0
0
0
0
0
0
1
1
0
0
4
0
0
2
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
2
0
0
0
2
0
0
3
1
0
0
7
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
2
3
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
2
2
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
3
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
2
2
0
2
0
0
0
0
1
0
0
0
0
3
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
3
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
1
0
0
2
3
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
1
1
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
1
0
0
0
0
0
2
0
2
0
0
0
1
3
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
1
0
2
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
1
3
0
0
0
0
0
1
0
4
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
2
2
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
1
0
2
0
1
0
0
0
0
2
1
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
2
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
10
0
0
0
0
1
0
0
0
0
5
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
1
0
0
0
3
0
0
0
0
0
1
1
0
0
0
2
0
0
1
2
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
2
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
2
2
0
0
2
0
0
1
1
1
0
1
0
0
0
0
2
0
0
0
0
1
0
0
1
1
0
0
0
2
0
0
0
1
2
0
0
0
0
0
3
0
0
0
0
3
0
0
1
0
0
0
0
1
3
0
0
0
1
0
0
0
2
1
0
2
0
2
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
2
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
1
1
1
0
0
1
0
1
2
0
0
1
0
0
0
0
1
1
1
1
0
0
0
0
1
0
3
0
0
0
2
0
0
0
0
3
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
6
0
0
1
0
0
0
1
0
3
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
2
3
1
0
0
2
1
2
1
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
4
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
2
0
2
1
0
0
0
0
0
0
2
0
0
2
0
1
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
2
1
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
6
0
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
1
0
0
4
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
1
2
1
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
1
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
2
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
3
0
0
0
1
4
0
1
0
2
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
3
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
5
2
2
2
1
0
2
0
1
0
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
4
0
0
0
1
0
1
2
0
0
4
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
1
0
0
2
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
3
3
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
1
0
0
0
0
1
0
0
1
0
3
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
1
0
1
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
18
0
2
1
0
0
0
0
2
2
2
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
6
0
0
0
2
0
1
0
0
0
1
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
1
0
4
0
0
1
0
1
0
0
4
1
0
1
0
2
0
0
0
0
1
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
2
0
0
0
2
0
0
0
4
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
6
0
0
0
0
0
1
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
1
0
0
2
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
2
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
1
2
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
2
0
1
0
0
1
2
0
2
1
0
0
0
1
2
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
5
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
7
0
0
0
0
2
5
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
1
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
3
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
1
0
1
0
1
2
0
2
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
2
1
0
1
1
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
11
0
0
0
0
0
0
1
3
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
12
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
2
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
1
0
1
0
0
0
0
0
0
1
0
2
3
0
1
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
1
3
0
1
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
2
2
2
2
1
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
3
0
0
0
0
0
1
5
6
0
0
0
0
0
0
0
0
7
3
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
1
2
0
0
0
1
0
0
0
1
0
0
2
0
1
2
1
0
1
0
1
0
0
0
2
0
1
0
0
0
0
0
2
0
3
0
2
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
1
1
2
0
1
0
0
0
0
0
1
0
0
1
5
0
0
0
0
0
0
0
2
0
0
0
0
0
0
4
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
1
1
0
3
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
8
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
6
1
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
0
6
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
3
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
1
0
1
0
3
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
1
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
7
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
2
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
1
1
2
1
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
1
3
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
2
0
0
0
0
0
0
1
1
0
0
3
0
0
1
2
0
2
2
0
0
0
0
0
0
1
1
2
0
0
0
4
0
0
0
0
2
0
0
0
0
0
1
0
0
0
4
5
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
2
1
0
0
1
0
2
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
11
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
5
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
2
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
2
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
3
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
1
0
0
0
2
0
1
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
1
2
0
0
0
2
0
3
0
0
1
0
0
0
0
0
0
2
2
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
3
1
0
7
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
2
0
0
2
2
7
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
2
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
1
1
0
0
0
8
0
0
1
1
0
0
0
0
1
0
0
4
0
0
0
0
2
2
1
0
2
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
3
0
2
2
1
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
2
0
0
0
1
0
2
0
1
2
0
0
3
2
1
0
0
2
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
2
0
2
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
3
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
4
0
2
0
0
0
0
0
2
2
1
0
2
2
0
0
5
2
0
0
0
0
0
3
0
2
0
0
0
0
0
1
0
1
0
0
2
0
0
0
1
0
0
7
0
0
3
0
1
0
1
0
0
0
0
2
4
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
3
0
1
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
2
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
1
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
5
0
0
0
1
0
2
0
2
1
1
2
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
1
2
0
0
2
2
0
0
2
2
0
1
0
0
0
0
2
0
0
0
0
0
1
0
6
0
3
1
0
0
2
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
3
0
0
0
4
0
0
2
0
2
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
0
0
3
1
0
1
0
0
0
0
0
3
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
5
3
1
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
2
0
0
0
0
1
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
1
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
3
0
1
0
5
0
1
0
0
0
2
1
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
1
0
0
1
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
4
0
0
4
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
2
0
2
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
1
2
1
0
1
0
0
1
0
2
11
2
0
3
0
0
1
0
0
2
3
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
1
0
0
2
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
1
1
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
2
0
0
0
0
3
0
3
0
0
0
0
3
2
0
0
0
0
0
0
5
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
3
0
0
0
1
0
2
0
0
0
2
0
5
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
3
2
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
3
0
0
0
0
0
0
0
0
3
0
0
1
1
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
3
0
0
0
0
0
0
0
4
0
0
1
0
2
0
5
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
1
1
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
1
3
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
4
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
2
1
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
2
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
2
0
1
3
0
0
1
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
1
5
0
2
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
3
0
0
2
1
0
0
0
0
0
2
1
0
0
0
1
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
2
0
0
0
1
0
0
1
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
3
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
1
0
0
0
0
2
2
0
0
1
0
0
9
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
3
0
2
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
5
0
0
0
0
0
2
0
0
0
3
0
0
0
4
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
1
0
1
0
1
0
5
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
1
0
1
0
0
1
0
3
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
5
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
5
1
2
0
0
0
0
2
0
0
6
0
0
0
0
0
0
0
0
3
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
3
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
4
0
0
0
0
2
9
0
0
2
0
0
0
0
0
1
3
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
2
0
2
0
0
1
0
0
1
0
0
0
0
0
0
2
2
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
3
2
0
3
1
0
0
0
0
0
0
6
1
0
0
0
0
0
0
0
0
1
0
2
2
2
0
0
0
0
2
1
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
1
2
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
5
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
6
0
1
2
3
0
0
0
0
1
1
4
0
0
0
0
0
0
2
1
0
2
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
3
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
3
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
1
0
2
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
2
0
4
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
1
0
0
3
0
1
0
0
1
0
0
0
0
4
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
2
0
0
0
4
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
1
0
2
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
2
0
2
0
0
1
2
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
2
2
2
1
2
0
0
0
0
2
0
0
0
2
0
0
0
0
1
1
0
0
1
1
0
0
2
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
3
0
1
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
4
0
1
0
1
0
0
0
1
1
2
0
2
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
2
0
0
0
0
0
3
0
1
0
0
2
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
2
0
1
0
2
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
2
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
3
0
0
0
1
0
0
2
0
0
0
0
0
0
0
3
4
0
2
1
0
2
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
1
1
0
0
0
0
1
0
1
0
5
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
4
0
2
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
2
2
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
4
0
0
0
1
0
1
0
0
2
0
0
2
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
4
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
6
0
3
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
5
0
0
0
0
2
2
0
0
0
2
0
0
0
3
2
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
5
1
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
2
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
2
1
0
0
2
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
3
0
2
0
0
0
0
0
0
2
1
0
0
2
2
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
4
0
0
2
2
0
0
0
1
0
0
0
0
2
2
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
2
2
1
1
0
2
0
0
0
0
0
2
0
0
1
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
1
0
2
1
0
0
0
1
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
1
0
0
0
1
2
0
0
2
0
0
2
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
1
0
0
4
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
1
0
0
2
4
0
0
0
0
0
0
0
0
2
2
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
1
0
1
2
0
0
0
0
2
0
0
0
0
1
0
0
3
2
0
0
0
2
0
0
1
0
2
3
0
0
2
0
0
1
0
0
0
0
1
8
1
0
2
3
2
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
6
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
7
0
0
2
2
0
0
0
0
0
1
0
2
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
2
1
0
0
1
2
4
0
0
1
0
0
1
2
0
2
2
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
2
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
8
0
0
0
1
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
2
1
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
1
0
0
0
1
0
0
0
0
1
0
1
0
1
0
2
2
0
2
0
1
0
0
2
0
0
2
1
1
0
3
0
3
0
0
0
0
1
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
1
0
4
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
3
4
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
6
2
0
0
0
1
0
1
0
0
0
1
0
2
1
0
0
0
0
1
2
0
0
0
3
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
2
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
3
0
0
0
1
0
3
0
0
0
0
2
0
0
0
0
0
1
0
0
0
3
0
0
0
2
2
0
2
3
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
2
1
4
0
1
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
2
0
0
0
0
0
1
1
1
0
0
0
0
0
0
3
0
2
0
0
2
0
0
1
0
0
1
0
0
6
0
2
0
0
0
0
0
0
0
0
10
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
3
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
2
0
0
2
0
2
0
0
3
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
8
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
1
4
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
4
0
0
1
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
3
0
0
7
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
2
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
2
2
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
2
0
0
1
1
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
2
0
0
5
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
1
1
0
0
0
1
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
2
1
0
0
2
0
2
0
1
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
4
1
2
0
0
2
2
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
1
0
9
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
1
0
2
0
1
0
1
2
0
0
1
0
0
0
0
0
9
0
0
0
0
2
1
0
2
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
4
2
0
0
0
0
3
0
0
0
2
2
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
2
1
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
5
0
0
1
0
0
0
0
1
0
2
2
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
1
1
0
0
1
1
0
2
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
2
1
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
4
0
6
0
0
2
2
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
3
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
3
0
0
1
0
0
0
2
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
1
0
0
2
2
0
0
0
0
2
1
0
0
1
0
1
0
1
0
0
0
0
0
2
2
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
4
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
1
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
3
1
1
3
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
9
0
0
0
3
0
0
0
0
0
0
2
0
0
0
1
0
1
0
2
1
0
0
0
0
3
0
0
0
0
3
0
0
0
0
1
3
0
1
0
1
0
0
0
2
3
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
1
1
0
0
0
0
1
1
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
2
0
3
0
0
0
0
0
0
1
0
0
0
1
1
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
4
0
0
0
1
0
0
0
2
0
1
0
0
2
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
1
0
1
2
0
0
2
0
1
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
2
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
1
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
9
0
1
0
0
3
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
1
0
2
0
0
0
0
1
1
0
0
1
0
0
2
1
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
1
0
1
0
1
0
0
0
3
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
1
0
0
3
1
4
0
2
0
2
0
0
0
0
0
1
0
0
1
0
3
1
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
2
1
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
3
1
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
2
1
0
0
4
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
3
0
0
1
0
0
0
0
1
4
0
1
0
0
0
0
0
0
0
3
0
1
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
1
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
1
1
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
2
0
0
1
0
2
0
0
1
0
2
0
0
0
0
2
0
2
0
2
1
0
1
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
1
0
1
0
3
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
1
0
0
1
0
2
0
1
0
0
2
2
0
1
1
1
1
0
0
1
0
1
0
0
1
0
0
1
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
2
3
0
2
0
0
0
0
0
0
0
3
0
0
2
0
0
1
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
3
0
0
0
0
0
0
1
0
2
0
0
1
1
2
0
0
4
0
0
2
2
0
1
1
1
2
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
1
0
1
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
4
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
2
2
0
2
0
2
3
0
0
0
0
0
0
0
4
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
1
0
0
0
0
0
0
0
0
2
1
0
0
2
0
2
0
0
3
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
2
0
0
4
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
3
2
0
2
0
1
0
0
6
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
14
0
2
0
2
0
0
0
0
0
1
2
0
1
2
0
0
0
0
0
2
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
2
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
2
3
0
5
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
2
0
0
1
0
0
3
0
0
0
0
0
0
1
2
0
0
0
0
0
2
2
3
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
5
0
1
0
0
0
1
1
0
0
0
1
0
2
0
0
0
0
0
3
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
1
0
0
1
0
1
0
1
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
3
2
0
2
0
2
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
2
3
0
0
6
0
0
0
0
0
0
0
0
2
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
11
0
0
0
1
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
1
0
2
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
1
0
1
2
0
0
8
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
2
2
1
0
0
0
0
2
0
0
0
0
0
0
2
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
1
0
1
0
1
0
0
1
1
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
3
2
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
6
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
4
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
3
0
0
4
0
0
0
0
0
2
0
0
0
0
1
0
1
1
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
2
2
0
0
0
0
0
0
1
0
0
0
0
3
3
0
0
0
1
2
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
4
0
0
0
2
0
1
0
1
0
0
0
0
2
1
0
2
0
0
2
0
1
0
0
0
0
2
1
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
1
1
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
1
1
0
3
0
0
0
3
0
0
0
0
0
0
0
2
0
8
0
2
0
2
1
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
1
2
0
2
0
0
2
0
0
0
2
0
0
0
1
0
0
0
4
1
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
27
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
1
0
0
2
0
2
0
0
1
0
0
2
2
0
2
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
2
0
1
0
0
0
1
0
0
1
2
2
0
0
0
0
0
0
2
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
4
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
2
0
3
4
0
0
1
0
0
2
0
0
0
2
2
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
2
0
2
2
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
3
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
2
0
0
1
1
0
0
0
2
0
1
1
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
4
4
1
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
3
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
1
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
3
1
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
1
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
1
0
0
1
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
2
2
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
2
0
2
0
1
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
4
1
1
4
0
1
1
0
0
1
0
1
0
2
0
5
5
1
0
0
0
0
0
0
0
0
0
0
0
0
8
0
0
0
3
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
1
2
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
2
0
0
3
1
0
0
1
0
2
0
0
3
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
3
1
2
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
2
0
0
6
3
0
1
0
0
0
0
0
1
2
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
3
2
0
1
0
0
0
0
1
0
2
1
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
3
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
1
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
1
0
4
1
0
0
0
0
0
0
2
1
1
0
0
0
0
1
0
1
0
2
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
3
2
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
1
0
10
0
0
1
0
2
0
0
0
0
0
0
0
0
0
16
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
1
0
2
0
0
1
0
0
0
2
2
3
0
0
1
0
2
0
2
0
2
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
2
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
5
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
5
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
3
0
2
0
0
1
1
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
1
2
1
0
0
2
1
0
2
2
0
0
0
0
1
0
0
0
0
0
6
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
1
0
0
6
1
0
1
0
1
0
0
0
1
0
2
0
1
0
0
3
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
11
0
1
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
2
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
1
1
0
0
0
1
0
1
0
0
1
2
0
0
2
0
1
0
0
0
2
0
0
0
7
0
0
0
2
0
0
1
0
1
0
0
0
0
0
1
1
1
0
2
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
3
2
0
2
0
4
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
3
0
0
0
2
0
1
0
0
0
0
0
2
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
3
0
0
2
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
2
0
2
0
1
1
0
0
0
0
0
1
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
4
4
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
1
2
0
0
0
0
3
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
2
0
0
0
1
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
2
0
0
0
0
2
1
1
1
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
4
0
0
1
0
2
0
2
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
2
0
4
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
1
2
0
0
0
0
0
3
0
1
0
0
2
0
1
0
1
0
0
0
1
0
0
0
0
0
0
4
0
1
0
0
0
1
0
2
0
0
2
0
0
0
2
0
0
1
1
0
0
0
0
0
2
0
1
4
0
0
2
0
8
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
6
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
1
0
1
0
1
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
2
0
2
0
2
0
2
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
3
2
0
0
0
2
1
0
0
0
0
0
0
4
1
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
3
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
5
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
4
1
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
8
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
2
0
6
1
0
1
0
4
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
3
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
5
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
2
0
3
0
0
0
4
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
4
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
3
0
2
0
1
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
4
0
5
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
1
0
3
0
0
0
0
2
0
0
0
0
0
0
0
4
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
2
0
3
0
0
1
0
5
0
2
0
8
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
4
2
0
0
1
0
0
0
3
1
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
1
2
0
0
0
0
2
2
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
3
0
2
2
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
3
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
3
0
0
0
0
2
1
0
1
6
0
1
1
0
1
3
0
1
0
0
0
0
4
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
4
2
0
0
0
0
0
0
0
1
0
3
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
2
1
0
0
0
2
0
0
0
0
0
2
5
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
1
0
0
0
2
0
0
1
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
2
1
0
0
3
1
2
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
2
2
0
0
0
0
2
2
0
0
0
0
0
2
0
1
0
4
0
0
0
0
0
0
2
1
0
0
0
0
2
0
2
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
1
0
0
0
2
1
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
1
0
1
0
0
0
0
1
0
2
2
0
1
0
1
0
1
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
3
0
0
1
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
3
0
9
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
3
2
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
1
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
2
0
0
2
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
4
0
0
0
1
0
1
3
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
1
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
5
1
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
1
1
0
0
3
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
1
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
1
0
0
0
4
0
3
2
0
0
0
0
2
0
0
0
0
0
0
3
0
2
0
0
9
0
0
0
0
2
0
0
0
0
1
1
0
1
0
0
0
0
1
1
0
3
0
0
0
0
0
2
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
1
0
1
0
0
0
1
1
0
0
0
2
0
2
0
0
0
9
0
2
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
2
0
0
0
0
0
0
0
2
0
3
0
0
0
0
2
1
2
0
0
2
0
0
0
2
1
1
2
0
0
0
0
6
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
3
0
1
0
0
0
8
1
0
0
2
0
0
2
0
0
0
0
0
1
0
0
1
0
0
1
2
2
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
1
1
1
6
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
3
0
2
1
0
1
1
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
1
7
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
2
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
3
0
2
0
2
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
2
0
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
1
3
0
0
0
0
0
1
4
0
5
0
0
0
0
0
0
1
1
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
1
0
4
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
5
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
2
0
0
1
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
1
0
2
1
1
0
0
0
0
0
1
0
0
2
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
18
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
1
0
0
1
0
0
1
3
1
0
0
0
0
0
0
0
2
0
0
1
0
1
0
1
2
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
3
0
0
0
3
0
0
0
1
3
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
1
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
4
0
0
2
0
0
0
0
0
2
1
0
2
1
0
1
0
0
2
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
1
0
2
3
0
0
0
1
0
1
0
1
0
0
0
0
3
0
0
3
3
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
1
2
0
0
2
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
13
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
4
0
2
0
0
0
0
0
0
1
0
0
0
2
0
2
0
1
0
2
0
2
0
0
0
2
0
0
1
1
1
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
4
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
3
1
0
0
0
1
0
0
2
0
0
2
2
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
1
0
1
0
1
0
1
1
0
0
1
1
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
1
0
0
2
2
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
1
0
0
1
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
3
2
0
0
3
0
0
0
1
0
0
3
0
4
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
1
0
0
2
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
2
0
1
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
2
0
3
0
0
2
2
0
0
0
1
0
1
0
0
1
0
0
1
0
2
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
3
0
0
0
2
0
0
1
1
0
3
0
0
0
0
2
2
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
1
0
2
0
0
1
1
0
0
0
0
1
0
0
0
1
2
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
3
2
2
1
3
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
1
0
1
4
0
1
1
0
0
0
0
0
0
1
0
2
0
1
0
1
0
0
0
0
0
0
1
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
4
0
0
1
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
1
2
0
0
3
0
0
0
0
0
0
0
0
1
0
0
5
2
0
0
0
0
0
0
0
1
0
2
1
0
0
4
0
0
1
1
0
0
2
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
5
1
0
0
3
0
0
3
0
0
0
0
0
2
2
0
0
1
0
0
2
0
0
2
0
0
2
2
0
1
0
2
3
0
6
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
2
0
0
2
2
0
1
0
0
0
3
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
7
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
3
1
0
0
1
3
0
0
1
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
1
0
1
2
1
0
0
0
0
0
1
2
2
0
0
0
0
2
0
0
0
2
0
0
3
0
0
0
0
0
1
0
2
0
0
1
4
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
2
0
0
0
0
0
8
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
1
0
0
2
1
0
0
0
1
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
2
0
0
0
3
1
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
2
1
0
0
0
0
0
0
0
0
0
2
0
1
2
0
1
0
1
0
1
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
3
0
3
0
0
0
0
0
0
1
0
3
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
3
0
0
0
2
0
0
0
1
0
2
1
0
0
0
1
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
3
0
2
0
1
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
1
6
0
0
0
4
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
1
0
2
2
0
0
1
0
0
1
0
0
0
0
2
2
0
2
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
2
1
0
3
0
0
0
2
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
1
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
1
0
0
7
0
1
0
0
0
0
0
0
0
0
0
3
1
0
0
1
0
2
0
0
0
2
2
0
0
2
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
3
2
0
0
0
3
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
3
0
2
0
2
0
0
0
1
0
4
0
1
2
0
0
2
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
6
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
2
0
0
0
0
0
0
2
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
1
0
2
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
1
0
0
1
2
0
0
2
2
2
0
0
0
0
0
1
0
2
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
1
0
0
0
0
27
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
3
0
2
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
2
0
0
0
2
0
0
0
0
2
0
0
3
0
1
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
3
0
4
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
3
3
1
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
3
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
1
0
0
0
2
0
0
0
5
1
0
0
5
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
5
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
1
0
2
0
0
2
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
1
0
2
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
3
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
4
0
0
0
0
3
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
10
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
9
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
2
2
0
1
1
0
0
0
0
0
0
0
8
0
0
0
0
1
4
1
0
1
0
2
0
3
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
1
0
0
0
1
0
0
1
0
0
0
2
1
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
1
2
0
4
2
0
0
1
0
0
0
0
0
0
8
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
2
1
1
0
0
1
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
1
0
3
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
2
0
1
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
4
0
0
0
0
0
0
3
0
2
0
0
0
2
0
4
0
0
0
3
1
0
0
2
0
1
0
0
2
0
0
1
0
2
1
0
1
0
0
1
1
0
0
0
1
0
0
2
2
1
0
0
0
0
1
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
1
1
1
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
1
0
1
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
2
0
0
0
1
1
0
2
0
2
2
0
1
0
0
1
3
0
0
0
0
0
0
0
0
2
0
3
2
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
3
1
0
0
2
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
2
3
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
2
1
0
0
1
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
2
2
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
1
0
3
0
0
0
2
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
3
0
2
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
6
0
1
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
2
0
2
0
0
0
0
1
0
0
1
0
1
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
1
0
0
0
0
1
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
4
0
1
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
5
1
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
2
1
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
1
0
2
0
5
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
1
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
7
1
0
2
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
3
0
0
0
0
1
0
1
0
1
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
2
3
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
2
1
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
1
0
0
2
0
0
0
2
3
0
0
3
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
3
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
4
0
0
1
2
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
2
0
0
0
1
2
3
0
1
0
0
0
0
0
0
0
0
2
2
1
2
0
8
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
1
0
1
2
0
1
6
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
2
0
0
3
0
2
5
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
4
0
0
0
0
0
0
4
0
1
0
0
0
4
1
0
0
0
1
0
2
2
0
0
0
1
0
2
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
1
2
0
0
3
0
3
0
2
1
0
2
0
0
0
2
1
0
1
0
0
0
0
0
2
0
0
1
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
2
1
0
0
0
0
1
0
0
2
2
0
0
0
3
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
3
0
0
0
0
0
0
2
0
3
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
1
2
0
2
0
12
0
0
0
0
1
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
3
0
0
0
0
4
0
1
1
0
1
0
2
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
3
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
1
0
0
1
1
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
1
1
0
0
1
0
1
0
1
0
0
0
0
0
2
0
0
0
0
1
2
0
1
2
0
0
2
1
0
0
0
0
0
2
0
2
0
0
0
2
0
2
0
2
0
0
1
0
6
1
0
0
0
2
0
0
3
0
0
0
0
1
7
0
2
0
0
2
1
2
2
0
0
0
0
0
1
3
3
2
0
0
1
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
2
0
0
0
1
0
2
0
0
1
0
2
0
0
6
1
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
1
0
0
2
1
0
5
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
2
0
3
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
1
0
2
0
0
0
0
1
3
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
3
0
0
0
0
0
3
0
2
2
0
3
1
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
5
0
5
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
9
1
0
0
2
0
0
0
0
0
3
0
2
0
0
0
0
2
6
0
0
0
0
3
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
1
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
2
1
2
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
2
1
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
1
0
1
2
0
0
1
0
0
0
0
1
0
2
0
0
0
0
1
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
2
0
0
0
0
1
4
0
0
0
0
0
0
3
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
1
1
3
0
0
0
1
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
2
0
2
0
1
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
8
0
2
0
2
0
0
0
0
2
1
0
0
5
0
0
0
0
0
0
0
1
2
0
1
1
0
0
0
1
0
0
0
0
0
2
0
2
0
4
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
3
0
2
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
5
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
1
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
2
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
2
0
1
4
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
3
0
2
3
1
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
1
0
2
0
1
3
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
5
0
1
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
5
3
0
0
0
0
0
0
0
1
2
0
1
0
0
2
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
4
0
0
2
0
2
0
0
0
0
1
0
0
0
0
2
4
0
0
1
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
2
2
2
0
0
0
0
0
1
2
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
5
0
2
0
2
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
3
0
2
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
3
0
0
0
0
0
0
0
0
0
3
0
0
0
2
1
0
0
0
2
0
3
0
0
0
0
0
0
0
0
2
7
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
3
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
5
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
2
1
1
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
1
0
2
3
0
0
0
0
1
0
0
0
1
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
2
0
1
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
3
0
0
0
2
0
3
0
0
0
0
2
0
0
0
1
2
2
0
0
1
0
0
7
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
4
0
0
1
0
0
2
2
0
2
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
6
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
3
2
0
2
0
3
0
1
0
0
0
0
2
0
0
1
0
2
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
1
1
0
1
2
0
0
0
0
1
2
0
1
2
0
0
0
0
1
0
0
0
0
7
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
2
0
7
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
7
0
3
0
1
0
0
3
0
1
0
0
0
2
0
2
0
1
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
2
0
0
0
1
2
1
0
2
0
0
2
0
0
3
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
1
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
1
2
5
0
0
0
0
0
0
0
2
0
0
6
0
0
0
0
0
0
0
0
0
3
0
0
0
0
3
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
1
0
0
0
0
0
3
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
3
0
0
3
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
1
0
0
2
0
0
3
0
4
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
1
2
0
1
0
0
1
0
0
0
7
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
1
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
1
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
5
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
4
0
1
0
0
1
3
0
0
0
0
1
3
1
0
0
0
0
2
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
1
0
2
1
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
3
0
2
0
0
0
0
0
0
1
0
0
0
2
0
2
1
2
0
0
0
0
0
0
0
5
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
2
1
0
0
0
0
0
1
0
0
2
0
0
2
0
0
5
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
2
0
3
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
2
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
2
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
2
0
0
0
1
0
0
2
0
1
0
0
0
1
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
3
0
0
0
1
0
2
0
2
1
0
0
2
1
0
0
0
2
2
0
3
0
0
0
2
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
3
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
1
1
0
0
0
1
0
0
2
1
0
0
0
4
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
3
1
1
5
0
0
0
0
0
0
2
0
0
0
2
1
0
2
0
1
0
2
0
0
2
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
1
1
0
2
0
0
0
0
5
0
0
0
0
0
1
0
1
0
0
1
0
1
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
2
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
3
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
2
1
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
1
0
1
2
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
5
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
2
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
3
0
1
0
0
0
2
0
0
2
0
1
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
3
0
1
0
0
2
0
0
1
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
1
2
2
2
0
0
0
3
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
1
1
0
0
0
0
4
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
2
2
2
1
0
0
0
2
0
3
0
2
1
0
0
0
1
1
0
0
0
0
2
2
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
2
2
3
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
2
1
0
0
1
0
0
0
1
0
1
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
2
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
3
0
1
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
5
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
1
0
1
3
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
3
0
1
0
0
0
0
0
0
8
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
4
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
4
0
0
0
0
0
0
2
2
0
0
2
1
0
0
2
0
0
2
1
1
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
2
0
1
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
1
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
2
3
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
1
1
0
0
2
8
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
5
1
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
2
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
1
0
0
1
0
0
0
0
2
3
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
1
0
2
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
4
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
2
0
0
0
0
0
0
2
1
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
3
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
1
0
2
0
0
0
0
1
0
1
0
0
0
0
1
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
3
0
0
2
0
2
1
0
0
0
0
3
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
3
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
3
0
1
0
0
0
1
0
0
0
0
2
3
0
0
0
0
0
0
1
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
2
3
0
0
2
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
2
2
0
1
0
2
0
0
0
0
1
0
1
0
0
3
3
0
0
0
0
0
0
0
0
2
0
0
0
2
6
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
2
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
5
0
1
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
2
0
2
0
3
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
3
0
0
0
0
0
1
2
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
1
1
2
0
0
0
2
0
2
2
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
1
0
1
0
2
0
0
0
0
0
3
0
1
2
1
0
0
0
2
1
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
4
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
1
0
0
2
2
1
2
0
1
0
0
0
0
0
0
0
3
4
0
0
1
0
0
0
0
12
0
0
0
1
0
1
0
0
0
1
0
0
0
0
2
0
4
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
5
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
1
1
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
3
2
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
4
0
1
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
1
0
1
0
1
0
0
0
1
0
0
0
2
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
6
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
4
2
2
0
0
1
0
1
0
1
1
0
1
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
4
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
4
0
0
1
0
0
0
0
2
3
2
0
3
1
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
3
0
0
0
2
0
0
2
0
2
1
2
1
0
0
1
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
3
0
0
0
1
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
3
0
0
4
0
0
0
2
0
0
0
0
1
0
3
1
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
1
7
0
0
0
1
0
0
1
3
2
0
0
0
2
0
0
2
0
0
0
0
1
0
2
0
0
0
1
0
2
0
0
5
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
2
0
1
1
0
1
2
0
3
2
1
3
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
1
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
9
0
0
0
2
0
3
0
0
1
2
0
0
3
0
0
0
0
0
0
7
0
2
0
0
0
0
1
2
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
3
0
2
1
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
3
0
1
0
0
1
0
1
0
0
1
3
0
1
1
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
4
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
2
2
0
0
1
0
0
3
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
1
1
2
1
0
2
0
0
0
2
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
1
0
0
1
1
0
1
0
0
0
0
2
7
0
1
0
0
0
0
0
0
0
0
0
6
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
5
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
1
2
3
2
2
0
0
0
0
2
0
2
2
2
2
0
0
3
0
0
0
2
0
0
0
0
1
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
6
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
6
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
4
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
2
0
0
0
1
0
0
0
1
0
2
0
1
2
0
1
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
2
1
3
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
2
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
3
0
0
0
0
0
0
2
0
0
1
1
0
2
0
0
2
0
0
0
2
0
0
0
0
1
1
0
0
2
0
0
1
1
0
0
0
0
1
0
0
0
1
0
2
0
0
0
2
0
1
1
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
2
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
1
1
1
1
0
0
0
0
0
0
1
2
0
5
0
1
0
0
0
0
0
1
0
0
2
0
2
1
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
2
2
0
0
0
0
1
0
0
1
0
3
0
0
0
3
0
0
0
0
3
0
0
1
1
1
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
1
0
2
0
1
2
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
2
0
0
1
0
0
0
2
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
7
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
2
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
13
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
5
0
0
0
1
0
0
1
1
0
1
0
1
0
1
2
0
0
0
1
1
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
3
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
1
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
7
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
4
0
1
2
2
3
1
3
4
0
0
1
0
1
1
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
1
2
0
0
1
3
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
2
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
3
0
1
0
1
2
0
0
0
1
0
0
0
0
1
0
2
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
2
1
0
3
0
1
0
0
0
0
0
1
1
0
0
0
1
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
2
2
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
1
1
0
0
0
1
0
3
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
2
0
0
0
2
0
0
1
0
2
0
0
0
1
0
0
0
0
2
0
1
0
0
1
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
2
1
1
2
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
2
2
0
0
0
0
2
1
1
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
3
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
1
1
0
0
0
0
0
3
0
0
0
0
0
0
4
0
0
1
2
0
0
2
0
0
0
0
1
1
0
2
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
1
0
0
0
1
2
0
0
0
0
1
0
0
0
0
1
1
2
0
2
0
0
2
0
0
2
0
1
1
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
1
0
7
0
0
0
0
2
0
2
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
1
1
0
0
2
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
2
1
2
0
2
0
2
1
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
1
0
2
2
1
2
0
0
0
1
0
1
0
0
0
1
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
5
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
1
1
0
0
0
0
1
0
0
0
0
3
0
1
0
2
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
1
0
0
0
1
2
0
0
0
0
0
7
0
0
0
0
0
0
0
1
0
0
0
0
2
1
1
0
2
0
1
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
4
0
1
1
2
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
1
1
0
0
1
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
2
0
0
0
1
0
0
0
2
0
3
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
2
0
0
0
1
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
1
2
2
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
1
0
0
2
2
1
0
0
1
1
0
0
0
0
1
0
0
0
1
2
0
0
0
0
1
0
0
0
0
1
2
1
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
3
1
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
1
0
1
2
0
0
0
1
1
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
3
0
0
0
1
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
1
0
0
0
1
0
0
0
0
0
5
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
3
0
1
0
1
1
0
0
0
0
3
0
4
0
1
0
2
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
1
2
1
0
1
2
1
0
0
0
0
1
0
0
0
0
1
2
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
7
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
8
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
1
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
1
0
0
0
0
1
0
5
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
3
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
3
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
1
0
0
2
2
1
0
0
0
0
2
4
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
2
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
3
0
0
1
0
0
0
2
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
2
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
7
0
0
0
0
2
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
1
0
0
0
1
0
2
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
2
0
3
2
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
2
2
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
3
0
0
0
0
3
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
3
0
0
0
1
0
0
2
0
0
0
0
4
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
2
0
2
2
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
2
0
0
0
1
2
0
0
0
2
4
0
0
0
0
0
0
0
0
1
1
0
2
2
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
4
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
2
0
0
0
1
0
0
1
1
1
2
3
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
6
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
12
0
0
2
0
0
1
2
0
0
3
1
0
1
0
0
2
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
11
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
2
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
10
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
3
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
9
0
3
0
0
0
0
0
0
0
0
1
0
2
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
2
0
0
0
0
0
0
0
0
2
0
0
4
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
2
0
1
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
7
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
2
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
5
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
2
0
1
0
0
0
2
3
0
2
1
0
0
0
0
6
0
0
2
0
0
0
1
2
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
2
0
0
7
0
2
0
2
0
0
0
0
0
2
0
0
2
0
0
1
0
0
1
0
2
2
0
2
0
0
0
0
1
0
0
1
1
1
0
0
3
1
0
0
2
1
2
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
7
2
1
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
3
0
0
0
1
0
0
1
0
1
0
2
0
0
0
1
0
0
0
0
0
0
1
0
2
0
2
1
0
1
0
0
4
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
1
0
2
0
1
0
4
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
11
0
0
0
0
0
3
0
0
0
0
0
0
0
1
1
0
1
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
3
0
1
0
1
0
2
0
2
1
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
3
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
3
2
0
1
2
0
1
0
2
0
0
0
0
0
1
2
0
0
0
0
0
1
2
1
0
0
2
0
0
0
1
0
2
2
0
0
0
0
0
2
0
0
0
2
2
2
0
1
0
1
2
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
1
0
0
1
0
0
0
2
1
0
0
0
0
0
0
2
0
2
2
2
0
0
1
0
2
0
0
0
2
0
0
3
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
1
0
0
0
0
0
3
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
12
0
0
0
0
4
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
1
0
1
0
1
0
0
3
0
0
0
0
0
0
0
0
0
2
3
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
4
0
0
1
0
3
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
6
2
2
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
3
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
3
0
0
0
0
0
8
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
1
1
0
1
0
0
0
0
0
0
1
2
0
0
2
0
0
1
0
0
0
1
0
0
0
0
1
2
0
2
0
0
2
2
2
0
0
2
6
1
1
0
0
4
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
3
1
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
2
0
0
3
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
1
0
0
0
0
2
0
0
0
2
0
0
1
1
0
5
0
0
1
1
1
3
0
2
1
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
2
0
0
2
1
2
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
2
0
1
0
0
2
0
1
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
1
2
2
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
3
0
0
1
0
2
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
2
1
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
1
0
1
0
0
1
0
0
2
0
0
1
0
0
1
2
0
1
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
5
0
2
0
0
0
0
0
2
1
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
6
0
0
0
2
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
2
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
2
1
0
0
0
2
2
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
3
0
2
0
0
1
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
4
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
2
1
0
0
1
3
2
0
0
1
0
2
2
3
2
0
2
0
5
1
0
0
0
0
1
1
4
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
3
0
0
0
1
0
2
0
0
0
0
0
0
2
0
1
0
0
2
6
0
1
0
0
2
1
1
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
2
0
1
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
3
0
0
0
1
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
1
0
0
2
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
5
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
7
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
4
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
1
0
0
1
0
0
3
0
0
0
0
0
1
0
0
0
0
0
2
0
0
3
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
1
1
2
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
7
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
6
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
7
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
1
0
0
0
3
0
1
2
0
0
0
0
1
1
1
0
0
0
1
0
0
0
4
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
1
0
2
0
2
0
1
1
0
1
2
0
1
0
0
0
0
2
2
0
1
1
1
0
0
0
1
2
0
0
0
2
2
3
0
0
0
0
1
0
0
2
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
7
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
3
0
0
1
1
0
0
0
0
0
2
1
0
0
0
0
1
0
2
0
2
0
0
0
0
1
0
0
5
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
1
0
1
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
6
0
3
2
0
0
0
2
2
2
1
1
0
1
0
1
0
1
0
2
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
2
1
1
0
1
0
3
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
4
0
0
4
1
0
0
0
0
0
0
0
5
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
2
0
0
0
2
2
0
0
0
0
1
2
0
0
1
0
1
1
0
0
0
1
0
0
2
0
1
0
0
3
0
0
0
0
0
0
2
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
3
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
1
0
0
0
0
3
0
1
2
0
2
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
1
0
2
1
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
1
1
0
0
2
0
0
0
0
0
0
3
0
0
2
1
1
0
1
0
1
1
0
1
0
0
0
0
0
0
0
2
0
4
0
0
2
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
3
0
1
0
1
0
2
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
1
1
2
0
0
1
3
1
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
2
0
0
1
0
1
0
2
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
16
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
2
0
0
0
1
2
2
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
1
0
0
0
2
1
1
0
2
0
3
0
1
1
0
2
0
5
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
1
0
5
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
3
0
0
0
0
0
2
0
0
1
1
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
2
0
1
0
0
1
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
4
0
0
5
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
2
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
4
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
1
1
2
0
0
5
0
0
0
1
2
0
1
3
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
2
2
3
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
1
2
0
1
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
1
1
0
0
0
0
0
0
2
0
2
0
0
2
1
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
2
0
2
0
1
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
6
0
3
0
2
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
1
0
0
10
0
1
1
1
2
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
8
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
1
0
0
2
0
2
1
2
0
0
3
0
0
3
0
0
0
0
0
0
1
0
0
2
2
7
0
1
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
3
1
1
0
0
2
0
0
2
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
4
2
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
10
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
13
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
1
0
1
0
2
0
2
0
1
0
0
0
1
0
0
0
0
2
2
0
3
0
0
1
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
1
0
0
0
2
0
0
0
0
2
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
2
0
4
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
2
0
0
0
0
1
0
0
1
2
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
1
0
1
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
3
3
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
1
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
3
0
1
0
1
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
1
0
0
0
6
0
2
0
0
1
0
0
0
0
1
0
2
1
2
0
0
0
1
0
0
0
0
0
1
1
0
2
0
0
0
0
2
0
0
0
0
1
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
1
0
0
4
0
0
0
3
2
0
0
0
1
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
5
0
0
3
0
0
2
0
0
0
1
1
0
0
0
2
0
0
1
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
7
0
0
0
3
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
1
1
0
0
1
0
0
2
2
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7
0
0
2
0
0
7
0
1
1
0
0
0
2
0
1
0
0
0
1
0
2
0
1
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
3
0
1
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
1
2
2
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
4
1
0
0
1
0
2
0
2
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
1
0
0
0
0
2
1
0
2
1
2
2
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
2
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
5
0
0
1
0
0
0
0
2
1
0
0
0
0
1
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
1
2
2
0
2
1
0
1
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
4
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
1
3
0
0
1
1
0
0
2
0
3
0
0
1
0
0
0
0
0
0
0
1
2
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
1
1
0
2
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
2
0
2
4
0
0
0
0
2
0
2
0
0
1
0
0
1
0
1
0
0
5
0
0
0
4
0
0
0
0
0
0
0
3
0
0
0
0
0
2
4
0
0
2
0
0
1
0
0
0
0
0
0
0
2
1
2
0
0
2
0
0
1
0
2
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
1
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
5
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
3
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
5
0
5
0
0
1
0
0
0
2
1
0
0
0
0
1
2
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
1
2
0
1
0
0
1
0
3
0
0
2
1
0
6
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
2
2
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
1
6
0
2
0
0
0
0
0
5
0
1
0
0
0
0
0
0
2
3
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
2
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
2
0
2
0
0
2
0
0
0
1
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
3
0
2
0
0
2
1
0
0
2
0
2
0
2
0
0
0
1
0
1
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
2
0
0
0
0
0
1
2
0
0
0
2
0
2
0
0
0
0
0
4
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
3
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
5
0
0
0
0
0
2
0
2
0
2
0
0
0
3
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
2
0
3
0
2
0
0
0
0
0
0
0
0
0
1
2
2
0
4
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
1
0
1
0
0
0
1
2
0
1
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
2
0
0
0
5
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
1
2
0
4
2
1
0
0
0
0
0
1
0
0
0
1
2
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
7
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
5
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
1
0
0
2
0
0
2
0
1
0
0
2
0
0
2
0
0
0
0
3
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
3
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
1
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
3
0
2
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
5
0
0
3
0
0
1
2
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
9
0
0
2
0
1
2
0
0
2
0
0
1
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
1
1
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
1
0
2
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
3
1
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
4
0
0
0
2
0
2
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
2
0
0
1
0
0
0
1
4
0
0
1
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
2
0
2
0
1
1
0
2
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
2
4
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
1
0
0
2
1
2
0
0
2
1
2
0
5
0
0
2
0
2
0
0
0
0
4
0
2
4
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
1
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
1
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
4
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
1
0
1
2
0
0
0
3
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
7
0
0
0
0
0
0
1
2
0
2
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
1
2
0
0
1
3
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
4
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
4
0
0
0
1
0
0
5
4
0
0
0
0
2
2
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
5
0
0
0
2
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
1
3
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
1
2
0
1
0
0
1
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
5
2
0
0
0
2
0
2
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
5
2
1
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
5
0
1
0
0
0
0
0
2
1
0
1
1
0
2
0
0
0
1
0
0
2
0
0
2
0
0
1
3
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
5
0
0
0
0
0
0
3
0
0
0
0
2
0
1
0
2
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
1
0
0
0
0
0
3
2
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
4
0
1
3
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
2
2
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
2
0
1
1
0
2
0
0
0
0
0
0
0
0
0
2
4
0
0
0
2
1
1
0
0
0
0
0
0
2
0
1
0
0
2
2
0
1
0
0
3
0
0
0
0
0
0
0
0
2
2
2
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
3
0
0
1
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
1
1
2
1
0
0
1
0
2
1
0
0
0
0
0
2
2
0
0
5
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
3
0
0
0
1
0
0
0
0
1
0
0
4
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
2
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
4
0
0
0
1
0
0
0
1
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
2
0
0
1
2
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
3
0
0
0
0
0
0
0
4
0
0
1
2
0
0
0
0
0
0
0
1
0
1
0
3
0
2
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
2
0
1
0
0
2
1
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
3
0
0
1
0
0
0
1
0
1
1
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
3
0
2
0
2
0
0
0
0
0
0
2
0
0
0
2
2
2
0
1
4
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
4
0
3
0
0
0
0
0
0
0
1
0
1
1
2
0
0
0
0
1
0
0
2
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
3
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
2
1
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
5
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
2
1
0
0
0
0
1
0
0
0
0
2
1
0
2
0
2
0
0
1
2
0
0
0
0
3
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
3
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
2
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
3
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
1
2
0
2
2
0
1
0
0
0
1
2
1
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
1
1
0
1
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
4
0
4
0
0
1
0
0
0
2
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
2
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
5
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
2
0
1
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
5
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
2
1
0
0
0
0
0
0
2
0
1
2
0
0
0
0
2
0
0
0
1
2
0
0
3
0
0
0
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
1
3
0
0
3
0
0
0
4
0
0
2
2
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
2
2
0
2
1
0
3
0
0
0
0
0
0
4
0
0
1
3
0
0
3
0
0
0
0
0
2
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
2
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
0
1
2
0
0
0
2
0
0
0
2
0
0
2
0
0
0
2
1
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
1
2
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
1
0
1
3
0
2
0
0
1
0
1
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
3
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
4
0
0
1
0
0
2
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
4
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
1
0
1
2
0
0
4
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
2
0
0
0
2
3
0
1
0
0
0
2
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
2
0
0
2
2
0
0
0
0
7
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
0
2
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
1
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
2
1
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
2
0
0
1
0
0
0
1
2
1
2
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
1
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
3
0
1
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
2
0
0
0
1
0
0
1
1
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
0
0
2
0
0
2
0
2
0
1
0
1
0
1
2
0
0
1
0
1
0
0
1
1
0
0
0
2
0
1
0
3
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
1
0
0
0
0
0
1
2
1
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
2
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
1
0
2
2
0
0
1
1
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
2
1
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
2
0
0
0
1
2
0
0
1
0
0
0
1
0
1
0
0
0
0
1
2
0
2
0
0
0
1
0
0
0
0
0
0
2
1
0
1
0
2
0
0
1
0
0
1
0
1
0
1
0
0
0
4
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
1
0
0
0
1
2
0
0
0
1
0
0
0
2
1
3
1
2
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
6
2
0
1
1
0
0
0
1
1
0
0
5
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
4
1
2
0
0
0
0
0
0
0
0
2
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
2
0
0
0
1
2
0
0
1
0
1
1
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
1
2
1
0
0
3
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
1
1
0
0
0
1
0
0
3
0
1
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
4
4
0
0
0
0
0
0
4
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
2
3
0
0
0
1
2
0
0
0
0
0
0
1
0
1
0
1
2
0
5
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
2
3
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
1
1
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
2
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
1
1
0
0
1
1
2
0
0
0
2
0
0
0
7
0
3
1
0
0
0
1
0
0
0
0
0
0
0
4
2
4
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
2
2
0
0
0
0
1
0
0
0
0
2
0
0
0
4
1
0
0
0
0
0
0
0
0
0
2
5
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
5
0
0
3
1
0
0
0
0
0
1
0
2
0
1
0
0
2
4
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
2
0
1
0
0
0
1
0
1
0
0
2
0
2
0
0
0
2
0
1
0
2
0
1
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
2
0
0
0
1
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
2
0
0
0
3
0
0
1
2
1
0
0
0
0
0
0
3
0
0
0
4
0
2
1
1
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
1
1
1
1
1
0
1
1
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
1
1
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
4
0
7
1
0
0
0
0
4
0
0
0
1
1
2
2
0
0
0
0
1
0
0
0
0
1
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
3
0
0
2
3
0
1
1
0
0
0
2
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
2
1
0
0
0
0
1
0
0
0
3
1
1
2
0
0
0
0
2
1
0
0
0
0
2
0
1
1
0
0
0
0
1
0
0
1
0
0
2
1
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
2
2
4
1
0
0
0
0
0
1
0
1
3
2
0
3
2
0
2
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
1
0
1
1
0
3
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
2
7
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
1
0
1
0
0
0
0
1
0
0
0
6
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
6
0
0
0
0
0
2
0
1
0
1
0
1
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
1
0
0
3
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
2
0
0
1
2
0
2
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
2
2
0
1
0
0
2
0
2
1
1
0
0
0
1
0
1
1
0
5
1
0
0
2
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
2
2
0
0
1
10
0
0
3
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
1
1
0
0
1
0
0
0
0
0
0
0
1
1
2
1
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
3
1
2
0
0
0
1
0
1
0
0
0
0
0
0
3
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
1
0
2
1
0
0
1
0
0
0
0
0
0
2
2
2
5
0
3
0
0
2
0
0
1
0
3
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
2
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
3
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
6
0
1
0
0
2
2
0
0
0
0
0
0
5
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
3
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
3
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
3
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
3
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
8
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
2
2
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
2
0
0
0
2
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
2
0
0
0
2
0
0
0
2
0
0
4
0
2
0
0
0
0
1
0
0
1
2
0
1
0
0
2
1
0
0
1
0
0
2
0
0
0
2
0
0
1
1
2
0
0
1
0
0
1
1
0
0
1
0
2
1
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
2
0
0
1
0
0
3
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
3
0
4
0
0
2
0
0
0
0
0
0
0
0
2
0
3
0
0
1
0
0
0
1
0
0
0
0
0
0
2
2
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
5
0
2
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
7
0
1
2
0
1
1
0
2
1
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
3
2
0
1
0
1
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
2
1
0
0
3
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
3
1
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
5
3
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
5
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
2
0
4
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
2
0
2
0
0
0
2
0
2
0
0
0
0
0
1
1
0
2
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
7
1
0
0
0
2
2
0
0
0
0
0
0
0
1
2
1
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
6
0
0
2
1
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
2
0
0
1
1
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
2
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
3
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
6
0
0
0
0
0
1
2
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
3
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
3
3
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
10
0
0
0
0
1
0
0
0
0
2
0
1
1
0
0
0
0
0
0
2
0
0
0
3
0
3
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
3
0
1
0
0
0
0
2
0
0
1
0
0
0
1
0
3
0
3
0
0
3
0
1
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
1
0
1
1
1
0
1
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
4
2
0
0
0
0
0
0
0
0
0
2
1
0
0
1
2
0
0
0
0
1
1
0
0
0
0
1
0
2
0
0
1
0
1
2
0
0
0
5
1
0
0
0
0
0
1
0
3
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
5
0
0
0
0
2
2
0
0
0
3
0
4
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
4
1
2
2
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
2
2
0
0
0
0
1
6
0
0
1
0
1
0
0
2
0
1
0
2
0
1
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
2
0
1
0
0
0
0
7
0
0
1
0
3
0
0
0
2
0
0
0
0
0
1
1
0
0
2
1
0
6
0
0
0
0
2
0
1
0
2
0
0
0
2
2
2
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
1
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
2
0
4
1
0
0
0
0
0
0
0
0
0
2
2
0
0
1
2
0
0
0
1
0
2
0
0
0
1
1
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
4
0
0
2
1
4
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
3
0
5
0
2
0
0
2
1
0
1
2
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
3
0
0
1
0
0
1
2
0
0
0
4
0
0
0
0
1
0
2
3
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
4
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
3
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
4
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
2
0
0
0
1
0
2
1
0
0
1
0
1
2
1
0
2
0
2
0
0
0
0
1
1
0
0
0
0
2
1
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
2
0
2
1
0
1
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
1
0
1
1
0
0
0
0
0
3
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
2
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
3
0
0
0
0
1
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
1
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
2
1
2
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
1
0
2
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
1
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
3
2
0
0
0
1
0
0
1
1
0
0
2
1
1
1
0
0
0
0
5
0
0
1
0
0
0
0
0
0
0
0
4
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
1
0
1
12
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
3
2
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
1
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
2
0
1
0
2
0
0
1
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
2
0
1
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
3
0
0
0
4
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
3
2
0
0
4
0
1
0
0
0
0
0
0
1
0
0
1
1
0
2
0
0
0
1
2
0
3
0
2
1
0
0
1
0
0
5
0
0
2
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
1
0
2
0
1
0
0
1
0
2
0
0
0
0
0
1
0
0
0
1
0
2
1
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
3
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
1
1
0
2
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
2
3
4
0
0
0
0
0
1
0
0
0
2
0
0
3
0
0
0
0
0
2
0
3
1
0
0
0
0
1
1
0
0
0
0
0
1
2
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
2
0
0
4
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
4
1
0
0
1
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
3
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
2
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
1
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
5
5
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
3
0
0
5
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
4
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
2
0
4
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
1
1
0
0
0
0
0
0
2
2
0
0
0
0
0
6
0
0
0
0
0
0
0
11
1
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
3
0
0
2
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
1
0
0
3
0
0
0
0
0
0
0
3
0
3
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
3
1
3
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
1
0
2
2
1
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
1
0
0
1
1
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
2
8
0
3
0
2
4
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
5
2
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
1
2
0
0
0
0
1
1
3
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
2
0
0
1
0
0
4
2
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
1
0
0
2
0
2
0
0
1
0
2
0
0
0
2
2
2
2
0
0
0
8
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
2
0
2
0
0
2
0
3
2
0
0
0
1
0
0
1
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
1
0
0
8
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
2
9
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
1
0
0
0
0
0
0
0
0
4
1
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
1
2
0
2
0
0
2
0
0
1
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
3
0
1
0
0
3
0
0
0
0
2
0
0
2
3
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
1
0
0
1
2
0
0
0
0
2
0
0
2
0
0
0
1
2
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
1
2
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
3
0
0
0
1
0
3
1
0
0
1
1
0
0
0
2
0
0
2
0
0
1
6
0
0
0
0
1
0
0
0
1
0
1
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
1
2
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
1
2
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
1
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
1
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
5
0
2
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
1
1
0
7
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
2
0
0
0
2
0
1
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
2
0
1
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
2
0
1
1
0
0
0
3
0
0
0
1
4
0
0
0
1
1
1
0
0
2
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
1
0
2
0
1
2
0
0
0
0
2
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
4
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
2
0
0
0
0
1
1
0
0
1
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
1
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
2
0
0
2
2
0
0
2
2
1
0
1
2
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
4
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
2
0
2
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
2
1
2
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
1
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
2
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
3
0
0
0
2
0
0
3
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
5
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
9
1
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
3
2
3
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
1
2
0
3
0
0
0
2
2
0
0
0
1
0
0
0
1
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
5
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
1
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
2
0
2
0
0
1
0
0
0
0
1
0
1
0
0
0
2
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
2
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
1
0
0
1
0
1
1
1
0
0
0
1
0
0
0
2
2
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
1
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
2
0
0
2
1
0
2
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
4
0
1
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
5
0
1
1
0
1
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
4
0
0
0
0
0
1
1
0
0
2
0
2
0
0
0
0
0
0
0
1
1
2
0
2
0
1
0
0
1
0
0
1
0
0
0
2
0
0
0
0
2
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
1
3
0
0
2
0
2
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
6
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
2
0
1
0
0
0
3
0
4
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
1
0
0
2
1
0
2
0
0
0
0
0
0
1
0
2
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
4
0
2
0
1
2
0
1
0
0
0
0
0
4
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
5
2
2
0
0
1
0
2
0
3
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
2
0
1
2
0
0
0
0
0
0
3
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
11
0
4
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
1
0
1
0
0
2
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
5
1
0
0
0
0
0
1
2
0
0
0
1
0
1
0
0
0
0
0
0
3
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
2
0
0
0
0
1
1
0
0
1
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
4
0
1
0
0
0
0
2
0
0
7
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
4
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
1
0
0
0
0
0
1
0
0
1
0
0
2
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
2
0
1
1
0
0
1
0
1
0
2
0
2
0
1
0
0
0
0
0
6
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
2
1
0
0
3
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
2
0
0
0
0
0
2
0
2
1
1
0
0
0
0
0
0
3
0
0
1
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
2
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
1
0
3
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
3
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
2
2
1
1
0
0
0
1
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
2
1
1
0
0
1
0
0
4
0
0
0
0
0
0
1
0
0
3
1
0
0
0
2
0
0
0
4
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
8
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
3
0
0
2
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
2
0
1
1
0
0
1
0
0
1
2
0
1
0
0
0
0
1
2
2
1
1
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
2
2
0
1
0
2
0
2
0
0
0
1
0
3
0
0
0
1
1
0
0
5
0
1
1
0
0
0
0
1
0
1
2
0
0
0
0
1
2
0
0
2
3
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
3
0
2
1
0
7
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
2
1
0
2
0
0
0
0
0
0
0
11
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
2
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
4
2
0
0
0
3
0
0
0
1
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
4
3
2
0
1
0
2
0
1
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
3
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
2
2
0
0
0
2
3
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
1
0
2
0
0
2
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
4
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
4
0
0
0
0
0
1
2
1
2
2
0
1
1
0
2
0
0
3
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
2
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
4
0
0
1
0
0
0
1
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
3
1
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
3
1
0
1
0
2
0
0
0
0
0
0
0
4
3
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
3
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
2
1
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
2
1
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
1
3
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
2
3
0
2
0
0
0
0
3
0
0
0
0
0
3
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
2
0
1
2
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
2
1
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
1
3
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
3
0
3
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
3
1
2
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
1
0
1
3
0
0
1
0
1
0
0
1
0
0
0
2
1
0
0
2
1
0
0
1
0
0
0
0
0
0
3
0
2
2
2
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
2
0
1
0
0
0
0
5
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
1
0
1
0
3
0
0
5
0
0
0
0
2
0
0
2
0
2
2
0
0
0
0
0
0
0
0
1
2
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
4
0
0
0
2
5
0
2
0
0
0
0
3
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
3
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
4
0
1
0
0
1
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
1
1
2
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
2
0
1
0
0
0
0
0
2
0
2
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
1
3
0
0
1
0
0
2
2
0
0
2
0
2
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
1
0
0
0
2
0
2
0
0
0
0
1
0
1
0
1
3
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
2
0
4
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
5
0
0
0
0
0
0
0
0
0
0
5
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
4
0
0
0
0
0
1
0
1
0
0
0
2
2
0
0
0
0
4
0
0
0
0
0
0
2
0
0
0
0
1
0
3
1
0
1
0
0
0
2
0
0
0
2
0
0
4
1
0
0
2
0
0
0
0
0
0
0
0
0
1
3
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
2
2
0
2
0
2
0
0
0
0
1
4
1
0
1
0
0
0
0
1
0
1
2
2
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
3
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
1
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
3
0
0
0
0
1
1
0
1
1
0
0
0
2
0
0
2
3
0
0
3
3
0
0
0
0
1
0
1
0
0
0
0
1
0
2
0
0
0
0
3
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
4
0
1
0
0
0
2
0
0
0
0
1
0
0
2
3
0
0
5
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
1
0
1
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
6
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
1
1
0
1
1
0
1
0
0
0
1
0
1
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
3
2
2
0
0
0
0
0
1
0
0
1
7
2
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
2
0
2
1
0
0
0
0
2
2
0
0
1
0
1
2
1
0
1
0
0
1
0
1
0
2
0
1
0
1
0
0
0
0
1
4
0
0
0
0
0
2
0
2
0
0
0
5
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
1
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
3
2
0
0
2
0
1
2
0
0
0
0
0
0
2
0
0
1
0
0
4
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
3
0
0
0
2
0
0
2
3
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
1
1
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
6
0
1
0
1
2
0
0
1
0
0
0
0
0
2
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
1
0
1
0
0
3
0
0
0
0
1
0
0
0
0
2
0
6
0
0
1
0
3
0
2
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
4
0
0
0
1
0
0
1
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
2
2
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
2
0
0
0
5
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
2
1
0
4
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
1
0
1
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
2
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
5
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
2
3
0
1
1
1
2
2
4
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
1
0
2
1
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
5
0
2
1
0
0
0
3
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
1
1
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
3
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
4
2
0
0
0
0
0
0
0
2
2
2
0
0
0
2
4
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
1
0
0
2
1
0
0
2
0
0
0
1
0
0
0
0
0
3
1
0
1
1
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
5
0
0
0
0
3
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
1
1
0
0
2
0
0
1
0
1
2
2
0
0
0
0
0
5
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
3
2
2
0
0
0
0
2
0
0
0
2
0
1
0
0
1
0
0
0
0
1
0
0
1
0
2
2
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
4
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
1
0
1
0
2
0
1
0
0
0
0
1
0
0
0
0
3
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
1
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
3
1
0
2
0
0
0
0
0
0
0
3
2
0
0
0
0
0
2
0
0
0
1
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
2
4
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
2
0
0
1
2
0
0
0
2
0
0
0
0
4
0
0
0
0
0
0
0
2
1
2
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
3
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
5
2
0
0
0
1
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
4
2
0
0
0
0
6
0
0
0
0
1
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
5
1
0
0
0
0
0
5
0
0
0
0
0
0
0
2
0
0
0
1
5
1
0
0
0
1
1
0
0
0
0
2
2
0
2
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
4
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
3
2
0
0
2
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
6
2
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
2
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
1
1
0
3
2
0
0
0
0
0
4
0
1
0
2
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
3
0
0
0
2
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
2
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
1
2
0
0
0
0
2
2
0
2
0
4
0
0
0
0
1
0
0
0
0
2
1
2
0
0
0
0
0
1
0
0
2
0
0
0
3
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
4
0
2
2
0
1
0
0
0
0
1
0
0
0
0
3
0
0
0
2
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
1
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
1
0
6
3
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
5
2
0
0
1
1
0
0
1
2
0
2
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
1
0
0
2
4
0
0
6
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
3
0
0
0
0
0
0
2
0
0
2
2
0
0
0
2
2
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
2
2
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
3
2
2
0
0
1
0
0
0
2
0
0
0
0
0
0
1
1
0
2
0
2
0
0
0
1
3
0
0
0
0
2
0
2
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
1
0
0
0
1
0
2
2
0
0
1
2
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
5
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
2
0
6
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
1
1
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
2
1
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
3
0
2
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
1
0
0
2
1
0
0
0
3
0
2
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
8
0
1
0
0
0
1
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
3
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
3
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
6
0
2
0
0
1
1
0
0
0
0
0
0
1
0
0
3
2
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
1
2
0
1
1
0
0
0
0
3
0
0
0
1
2
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
1
0
1
0
1
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
2
2
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
2
0
1
0
0
1
0
0
1
0
2
0
0
0
2
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
1
2
0
1
0
0
1
11
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
6
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
5
4
0
2
0
0
0
1
0
2
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
3
1
0
3
0
0
0
4
1
3
0
0
0
0
0
1
2
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
5
0
0
0
0
0
1
0
0
0
0
0
0
0
4
1
6
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
1
2
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
3
0
0
3
0
0
0
0
1
2
4
1
0
0
0
2
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
4
4
0
2
0
0
2
2
2
0
1
0
4
2
0
2
0
2
2
0
2
0
0
0
0
0
3
0
2
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
3
2
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
6
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
2
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
1
0
0
0
0
3
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
2
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
6
0
0
1
2
0
1
0
0
0
1
1
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
2
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
1
0
2
0
4
0
0
3
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
1
0
2
0
0
2
1
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
3
0
0
0
0
0
0
0
1
0
6
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
3
0
0
2
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
3
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
1
5
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
9
0
0
0
0
0
0
0
1
2
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
1
0
2
0
2
0
1
0
0
1
0
0
0
2
2
0
0
0
3
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
2
0
1
0
1
0
0
2
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
1
2
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
3
0
2
0
4
2
5
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
2
0
1
0
0
1
2
0
0
0
0
0
0
0
4
0
2
0
0
2
3
1
0
0
2
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
2
0
4
1
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
4
0
0
0
1
0
1
0
0
2
0
1
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
3
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
2
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
7
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
1
0
0
1
0
2
3
2
0
1
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
2
2
2
2
0
0
2
0
0
2
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
4
0
0
0
1
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
7
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
3
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
1
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
2
0
0
3
0
0
0
0
0
0
0
1
0
0
1
0
0
2
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
2
0
2
2
0
1
3
0
0
0
0
0
1
0
0
1
0
0
1
2
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
3
2
1
1
0
0
0
5
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
2
1
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
3
2
0
0
1
1
0
0
0
0
6
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
2
2
0
1
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
1
0
3
0
1
0
0
0
0
1
0
2
0
3
2
0
0
0
3
5
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
2
0
2
0
0
1
0
0
0
0
1
1
0
2
0
5
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
2
1
1
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
1
1
0
0
2
0
0
2
3
3
0
0
0
2
1
0
0
2
1
0
1
0
0
0
0
0
3
0
0
2
1
0
2
0
0
1
0
0
2
0
2
0
0
0
2
0
2
2
0
0
2
0
0
0
1
4
0
0
3
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
6
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
1
0
0
0
0
0
2
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
2
1
0
2
2
2
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
1
0
1
0
1
2
0
0
0
0
1
0
0
0
2
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
2
1
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
4
2
0
0
5
0
4
1
1
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
3
1
0
0
2
0
0
1
0
2
0
2
4
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
1
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
2
1
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
1
2
0
2
3
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
2
1
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
1
1
0
2
0
2
2
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
1
0
2
1
0
1
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
3
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
1
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
3
0
2
0
1
0
4
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
6
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
2
0
1
0
0
0
0
0
0
2
2
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
2
0
2
0
1
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
2
3
4
0
0
0
0
3
0
0
0
3
0
0
2
1
0
1
0
0
0
3
9
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
2
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
3
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
5
0
0
0
1
0
0
1
0
2
3
0
0
0
0
0
0
3
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
2
1
3
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
13
1
0
0
1
0
0
0
2
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
2
0
6
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
1
0
0
2
0
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
2
0
3
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
2
0
0
2
1
0
0
0
0
0
0
2
0
0
3
0
0
0
1
0
0
0
5
0
0
1
2
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
8
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
3
3
0
0
0
0
0
0
1
3
0
1
0
0
0
0
2
1
0
0
0
0
0
2
3
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
2
0
0
3
0
0
0
0
0
0
0
0
3
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
1
2
1
0
0
0
0
0
0
1
0
3
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
7
0
0
2
0
2
0
2
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
1
2
0
3
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
2
2
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
2
0
0
2
2
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
1
1
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
3
0
0
2
0
0
0
3
0
0
3
0
0
1
0
0
0
0
0
0
0
2
6
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
9
0
1
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
1
0
2
1
0
1
1
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
1
1
0
0
1
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
1
1
0
0
0
1
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
1
0
1
0
0
3
0
0
1
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
2
0
0
1
0
2
0
1
2
0
0
0
0
0
1
2
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
2
2
0
2
0
1
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
3
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
1
0
0
1
3
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
7
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
2
0
0
0
0
4
3
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
1
3
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
1
0
0
0
0
0
0
0
1
2
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
5
0
0
0
0
2
0
1
0
0
0
2
1
0
0
0
2
1
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
4
0
0
2
0
0
0
2
0
0
1
0
7
2
0
2
0
0
0
1
0
0
0
0
0
0
1
2
0
2
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
1
2
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
6
0
2
0
0
0
0
0
0
0
1
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
1
0
1
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
7
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
2
1
0
0
2
0
2
1
0
1
1
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
2
3
0
0
0
0
0
2
0
0
0
0
1
1
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
3
2
0
0
2
2
0
0
0
0
0
1
6
0
0
1
0
0
0
0
0
0
0
0
6
0
0
0
6
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
7
0
1
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
1
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
1
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
3
1
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
2
0
1
0
2
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
2
0
2
1
1
3
2
0
0
0
0
2
1
1
0
0
0
0
1
0
2
0
0
0
0
1
0
2
0
2
0
0
0
1
3
0
0
0
0
0
0
2
0
1
0
2
1
0
0
0
1
0
0
0
0
0
3
0
0
1
0
1
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
2
0
1
2
0
0
3
0
0
0
0
0
0
0
3
0
0
0
3
0
0
0
0
0
1
1
0
0
0
0
0
2
2
1
0
0
2
0
0
0
1
2
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
2
2
0
2
0
3
2
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
5
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
2
0
0
0
2
1
0
0
2
0
0
0
0
0
0
1
2
2
1
0
0
0
0
1
0
1
0
2
0
5
0
4
0
0
0
0
0
0
1
1
0
0
0
2
0
0
5
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
3
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
1
0
2
0
0
1
1
0
0
0
2
0
0
0
0
0
0
1
0
4
1
0
1
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
2
4
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
2
0
2
2
1
0
2
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
1
2
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
8
0
0
1
0
0
0
1
1
0
3
0
0
1
0
1
1
0
1
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
3
0
0
0
1
2
2
1
0
0
0
0
6
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
1
0
0
2
0
0
0
0
1
2
2
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
2
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
2
0
0
0
0
0
2
3
2
0
0
1
0
0
0
0
1
0
0
2
0
0
0
2
0
0
1
3
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
2
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
2
2
2
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
3
0
0
6
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
1
0
0
2
1
0
0
0
4
0
0
0
1
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
2
0
0
0
0
1
2
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
1
0
1
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
3
0
0
0
0
0
2
4
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
2
2
2
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
4
1
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
2
1
0
0
0
0
0
0
1
1
2
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
2
1
0
0
1
0
0
0
0
7
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
1
2
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
4
0
0
4
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
2
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
2
0
0
0
0
2
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
7
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
4
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
6
0
0
0
0
1
2
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
5
5
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
2
1
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
1
2
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
3
0
0
0
2
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
3
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
3
0
0
2
0
0
1
0
0
2
2
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
2
2
1
1
0
0
1
0
2
0
0
1
0
0
0
0
2
0
0
2
0
2
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
2
1
2
2
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
3
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
3
0
0
0
0
0
2
1
0
1
0
1
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
6
0
0
1
0
4
0
0
0
0
0
0
3
0
2
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
6
0
0
1
3
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
2
1
1
1
0
0
0
2
0
1
0
0
0
2
0
0
2
0
3
0
0
2
0
0
1
0
2
0
0
0
1
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
2
0
0
7
0
0
2
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
1
1
2
1
2
0
0
0
0
0
0
0
2
0
5
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
2
2
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
2
2
0
1
1
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
1
3
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
1
2
1
0
0
2
0
0
0
3
0
0
0
0
0
0
0
1
0
1
0
2
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
1
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
1
0
1
2
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
1
3
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
1
2
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
7
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
2
2
0
0
0
0
1
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
2
2
0
1
0
0
1
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
3
3
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
1
0
0
0
4
1
0
0
0
0
2
0
2
0
0
0
1
0
3
6
0
2
0
0
0
0
1
0
0
2
4
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
2
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
3
0
1
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
4
0
0
1
0
0
3
0
0
0
1
1
2
1
0
0
0
0
0
1
0
1
2
0
2
3
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
4
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
1
0
2
1
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
2
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
1
0
0
2
2
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
5
0
0
2
0
0
0
0
1
0
0
1
0
1
0
2
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
2
0
0
0
0
0
1
1
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
2
0
0
4
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
2
0
1
0
2
0
2
0
0
0
1
0
4
1
0
0
1
0
1
2
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
2
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
2
0
2
1
2
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
4
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
2
1
0
5
0
0
0
0
0
0
2
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
3
0
0
2
1
0
0
2
0
0
5
0
0
2
0
2
0
0
2
0
0
1
1
1
0
0
3
1
0
3
0
0
0
0
0
0
0
1
0
0
2
1
0
1
0
0
9
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
1
0
2
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
2
2
0
0
0
1
1
4
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
3
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
2
1
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
2
0
1
1
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
2
1
1
0
2
1
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
2
0
3
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
3
4
0
0
0
0
0
1
1
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
1
0
2
2
0
2
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
2
3
0
0
2
2
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
2
0
0
2
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
4
0
0
0
2
0
0
1
0
2
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
2
0
0
2
0
0
0
1
0
0
0
2
2
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
8
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
3
0
0
0
1
0
0
1
1
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
2
2
0
0
0
0
0
2
0
0
2
0
0
2
0
0
1
1
0
0
1
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
1
0
3
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
3
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
2
2
0
2
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
5
1
3
0
0
0
1
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
2
1
1
5
0
0
0
0
0
0
1
0
0
2
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
1
6
0
0
2
0
3
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
3
2
1
1
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
6
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
1
0
2
0
0
1
0
2
0
2
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
1
0
0
3
0
0
0
0
0
0
0
1
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
1
2
1
0
0
2
0
2
0
2
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
1
0
1
0
1
0
2
1
0
0
0
0
2
0
0
0
0
2
1
0
0
3
0
0
1
0
0
0
0
2
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
2
0
0
0
1
1
0
0
0
2
1
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
6
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
5
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
2
1
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
5
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
1
1
2
0
1
2
0
0
0
2
0
1
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
5
0
0
3
2
0
0
0
0
6
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
1
0
0
0
2
0
1
0
0
0
2
1
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
3
1
0
1
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
2
2
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
1
1
3
0
0
0
2
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
6
0
1
0
0
0
0
5
0
0
0
0
1
8
1
0
2
0
0
0
0
1
0
2
0
2
0
0
0
2
1
0
0
0
2
0
0
1
1
1
0
0
0
5
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
1
0
4
0
1
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
2
0
2
0
1
0
0
1
0
0
0
2
3
1
0
0
0
0
0
1
2
0
0
0
0
1
1
3
0
0
0
1
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
2
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
3
0
0
1
0
0
1
0
0
0
0
0
2
1
1
0
0
1
0
1
0
3
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
3
0
6
2
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
2
2
0
0
2
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
2
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
2
2
4
5
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
2
0
1
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
1
0
3
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
1
2
0
1
0
0
1
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
1
0
0
0
0
0
1
0
0
2
0
0
0
1
0
2
0
0
0
1
0
2
0
0
0
2
0
1
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
6
2
0
0
0
0
1
0
0
0
0
0
1
0
0
3
0
2
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
1
2
0
0
2
0
0
0
1
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
1
0
0
1
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
2
0
0
0
1
0
0
0
1
0
2
0
0
0
1
1
0
0
0
0
0
1
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
2
0
1
1
0
0
0
1
2
1
0
0
0
0
0
2
3
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
5
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
2
2
0
0
0
1
0
0
5
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
1
0
1
0
1
0
1
0
0
0
0
0
0
3
0
0
1
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
1
0
2
0
0
0
0
0
3
2
0
0
2
1
1
0
0
2
2
1
1
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
1
2
0
0
1
0
0
0
3
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
0
1
0
5
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
2
0
0
3
0
0
0
0
1
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
5
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
2
0
1
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
1
0
3
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
2
0
2
0
1
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
2
3
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
4
0
2
0
0
1
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
5
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
1
0
2
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
1
0
2
0
2
0
3
0
0
0
0
3
0
0
1
2
0
0
3
0
1
0
0
0
0
0
0
3
0
0
0
0
0
1
0
1
0
0
0
1
0
2
0
0
0
1
2
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
2
0
0
2
0
0
2
0
2
0
0
2
1
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
9
0
0
1
2
0
0
0
1
2
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
2
0
1
0
2
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
1
1
1
0
1
0
0
1
1
2
0
0
1
0
0
0
2
0
0
1
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
2
0
0
1
0
2
0
0
0
3
0
0
2
0
0
1
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
1
0
0
1
0
0
0
0
2
3
2
2
0
0
0
1
3
0
0
0
2
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
1
1
3
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
4
0
2
0
0
0
5
0
0
3
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
1
0
0
0
0
2
0
2
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
1
1
0
0
0
0
4
0
0
3
0
0
0
2
2
0
0
0
1
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
5
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
1
0
0
0
1
0
1
1
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
2
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
2
3
0
0
0
0
0
3
0
0
0
1
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
1
15
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
4
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
2
1
0
0
5
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
7
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
2
3
0
0
0
2
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
9
0
0
0
2
0
0
2
1
0
4
3
0
1
0
0
0
0
1
0
0
0
0
0
1
2
1
2
0
0
2
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
1
3
0
0
0
0
0
0
0
0
0
1
0
0
2
4
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
3
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
2
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
3
0
0
3
0
0
0
0
0
0
1
0
1
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
9
0
0
0
2
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
7
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
1
0
1
0
0
1
0
0
0
0
0
0
1
2
1
0
0
0
0
0
2
0
2
1
0
0
2
2
1
5
0
0
0
0
2
0
0
0
0
3
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
1
0
0
2
0
0
0
1
1
0
0
2
0
6
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
6
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
2
0
0
4
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
2
0
0
1
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
3
0
2
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
1
0
0
0
3
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
4
0
2
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
2
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
1
2
0
0
0
0
0
0
1
1
0
0
0
2
1
0
0
1
1
0
0
0
2
2
1
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
1
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
1
0
0
2
0
0
3
3
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
1
1
3
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
4
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
2
1
0
0
0
0
0
0
1
2
3
2
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
1
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
1
1
1
0
0
0
0
1
0
0
2
0
0
1
0
0
0
4
2
0
0
0
0
3
0
2
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
2
1
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
2
2
7
0
0
7
0
2
2
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
2
0
3
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
3
0
0
0
0
1
2
0
0
0
0
0
3
0
0
0
0
2
0
0
0
5
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
2
3
0
0
0
2
1
0
0
0
1
3
0
0
2
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
2
0
0
0
2
1
0
2
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
3
0
0
0
0
2
0
0
0
0
0
0
2
10
1
1
1
0
2
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
2
0
3
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
4
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
1
0
0
1
1
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
1
0
0
0
0
2
1
1
0
0
0
0
0
1
0
0
1
2
0
0
2
0
0
0
2
0
1
1
1
3
1
3
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
5
1
0
1
1
2
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
2
0
0
1
1
0
0
2
0
0
0
0
1
1
0
0
0
2
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
1
0
2
0
2
0
2
0
2
1
4
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
3
2
0
0
2
0
1
0
0
0
0
2
1
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
12
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
3
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
7
1
0
0
2
0
0
0
2
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
0
0
4
0
0
1
1
0
2
0
0
0
3
2
1
0
0
0
3
0
0
1
5
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
2
0
1
2
7
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
2
0
0
0
0
7
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
3
2
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
3
0
1
1
2
0
2
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
3
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
2
1
0
0
2
0
1
0
0
0
2
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
4
0
1
0
0
0
0
0
3
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
5
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
3
0
2
1
2
2
0
0
0
0
2
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
2
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
2
0
0
0
1
3
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
4
0
2
0
0
2
0
0
0
0
1
0
1
1
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
2
1
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
4
0
0
0
2
0
0
1
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
2
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
12
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
2
0
4
0
1
0
0
0
0
0
1
1
2
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
1
0
0
1
7
1
0
1
0
0
1
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
3
1
0
0
3
0
0
1
0
1
0
0
0
0
0
0
2
1
0
2
2
0
1
0
3
0
0
1
0
1
0
1
0
0
1
0
0
0
1
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
1
0
2
0
0
0
3
0
0
5
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
5
0
0
1
3
5
0
0
2
0
0
3
0
1
0
2
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
3
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
3
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
3
0
0
2
0
2
0
0
0
1
0
1
0
0
1
2
0
1
0
1
5
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
3
0
0
0
0
3
0
0
3
1
2
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
1
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
1
0
0
0
1
0
0
0
2
2
0
0
0
0
0
1
2
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
1
0
0
0
2
0
0
1
0
0
0
1
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
2
3
0
0
3
2
0
0
0
0
0
0
0
2
0
2
0
0
1
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
11
0
0
0
0
0
0
0
0
0
3
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
2
0
1
1
2
0
2
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
6
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
1
0
0
2
0
2
1
1
0
0
0
2
0
0
3
0
1
0
0
1
3
1
0
0
0
0
0
0
0
2
2
1
1
0
0
0
2
1
0
0
0
2
1
0
1
0
0
0
0
6
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
3
3
2
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
2
0
0
4
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
1
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
1
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
2
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
7
0
1
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
1
2
0
0
0
1
0
0
0
2
2
2
1
2
0
1
0
0
1
3
3
3
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
2
1
2
0
0
1
3
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
2
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
1
5
0
2
0
0
1
0
0
0
0
1
1
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
3
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
2
0
4
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
2
0
2
1
0
0
0
0
1
2
0
2
0
0
0
3
0
0
5
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
9
0
0
1
0
0
0
0
0
0
2
1
1
0
2
3
0
0
0
0
1
0
0
0
0
1
2
0
4
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
3
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
2
0
4
0
0
0
0
0
0
0
0
1
1
0
0
1
4
3
2
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
2
1
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
1
0
2
1
0
0
0
0
0
2
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
2
1
0
1
0
0
0
2
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
2
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
4
1
0
0
0
1
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
1
2
0
4
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
1
0
0
0
3
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
1
0
1
0
1
0
0
2
5
1
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
4
0
0
0
1
0
0
0
0
1
0
2
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
6
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
4
0
1
1
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
2
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
1
2
0
2
0
4
0
0
6
0
1
0
0
2
0
0
0
0
0
2
2
0
0
3
0
1
0
0
0
2
0
1
0
0
0
0
2
1
0
0
2
0
1
0
0
0
0
1
0
0
0
1
2
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
3
3
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
3
2
0
2
0
0
0
0
4
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
3
0
1
0
0
1
0
0
3
1
0
0
0
0
0
0
1
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
2
0
2
2
0
6
0
0
0
0
1
1
2
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
3
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
3
3
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
2
0
0
1
0
1
0
0
0
1
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
1
2
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
2
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
2
0
3
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
2
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
2
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
5
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
1
0
1
1
1
0
1
2
0
0
0
0
0
1
2
0
2
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
1
0
1
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
9
0
1
0
1
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
3
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
3
1
5
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
4
0
0
0
2
1
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
4
1
2
0
1
0
0
0
2
0
0
0
0
1
2
0
7
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
1
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
2
0
0
0
1
0
0
3
1
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
3
0
0
0
0
5
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
2
0
0
1
0
0
0
2
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
1
0
0
0
0
1
1
2
3
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
2
0
5
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
2
2
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
5
0
0
1
0
2
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
2
0
0
0
1
0
0
0
0
0
0
3
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
3
0
1
0
0
0
2
0
1
0
0
0
0
0
5
0
2
0
0
0
0
1
0
1
5
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
2
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
8
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
3
0
1
2
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
4
0
0
0
1
0
0
0
0
0
0
1
0
0
2
2
0
0
2
0
1
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
3
1
2
0
0
0
2
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
5
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
5
0
2
0
0
1
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
1
1
0
0
3
1
0
0
0
0
0
1
0
0
3
0
2
4
0
4
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
4
0
0
2
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
5
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
2
0
1
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
2
0
1
0
2
0
0
0
0
1
0
0
0
0
0
1
3
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
2
0
0
0
1
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
2
0
2
0
0
1
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
3
1
0
3
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
1
2
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
1
1
0
1
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
3
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
3
2
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
4
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
3
2
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
18
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
1
2
2
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
1
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
1
0
0
1
1
2
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
2
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
1
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
2
1
0
3
0
0
0
0
0
4
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
4
0
0
0
0
1
2
0
3
0
0
0
2
0
0
1
0
0
1
1
0
0
0
0
0
2
1
0
0
0
0
0
1
2
2
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
2
0
0
0
1
1
1
1
1
0
0
2
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
1
1
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
1
0
4
1
0
0
1
3
2
0
0
0
2
0
0
0
1
0
0
0
0
1
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
3
2
1
0
0
0
0
0
0
0
0
1
0
1
1
0
1
1
1
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
1
2
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
1
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
2
0
1
3
0
2
0
1
0
2
0
0
0
3
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
2
0
0
0
2
2
0
0
0
0
0
2
0
1
3
0
0
2
1
0
1
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
1
3
0
0
0
0
0
0
1
3
0
0
3
3
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
2
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
1
0
2
0
6
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
1
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
3
0
0
4
0
1
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
1
0
0
0
2
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
2
0
2
0
0
2
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
3
1
0
0
3
0
1
0
2
3
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
3
0
0
1
2
3
0
0
0
0
2
0
0
1
0
3
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
3
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
1
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
5
0
0
0
0
1
0
0
0
0
1
1
2
0
0
0
0
0
8
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
1
0
1
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
2
8
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
4
2
1
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
2
3
0
0
0
0
0
1
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
1
0
0
15
1
2
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
12
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
5
0
0
0
0
0
0
0
1
0
1
0
4
1
0
0
0
0
2
0
0
0
0
0
7
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
2
1
0
0
0
0
0
1
1
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
2
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
2
1
0
0
0
0
2
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
3
1
0
0
1
2
0
0
5
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
1
0
0
0
0
1
0
2
1
0
0
0
2
0
1
0
0
0
1
2
0
0
2
0
0
1
0
0
1
0
1
0
0
0
1
0
2
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
2
3
0
0
2
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
1
2
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
2
0
0
1
0
0
0
0
2
0
0
1
0
3
0
0
0
0
0
5
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
3
4
0
0
0
0
0
0
0
0
2
0
0
0
0
6
0
0
0
0
1
1
0
0
0
1
0
0
2
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
1
2
2
1
0
0
2
4
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
4
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
3
1
0
0
0
2
0
0
2
1
0
0
1
2
2
1
0
2
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
1
0
0
1
1
2
0
0
0
2
0
1
0
0
3
2
0
0
0
1
0
0
0
4
1
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
2
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
10
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
2
1
0
1
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
2
0
0
0
1
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
3
0
2
1
0
0
0
5
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
2
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
2
0
0
0
0
0
2
1
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
1
0
0
2
0
0
1
0
0
0
3
0
0
0
0
0
0
3
2
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
4
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
3
0
2
0
0
0
1
1
0
3
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
4
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
3
1
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
3
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
1
2
0
0
0
0
1
2
0
1
0
0
0
1
0
0
0
0
0
0
1
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
1
1
0
1
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
2
0
2
0
0
2
0
2
0
0
1
0
0
0
4
0
0
1
0
1
0
0
1
0
0
2
0
2
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
3
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
11
1
0
3
0
1
0
0
1
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
3
0
2
0
0
1
0
0
1
0
0
2
2
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
2
0
7
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
2
0
1
0
4
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
1
4
0
0
0
0
2
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
6
0
0
0
1
0
0
3
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
1
1
1
2
0
2
0
0
0
2
0
1
0
0
5
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
3
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
18
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
3
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
1
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
2
2
2
0
1
0
3
0
1
0
2
0
0
0
4
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
1
1
0
0
2
2
0
2
2
2
0
0
1
0
0
0
0
3
0
0
0
3
2
2
1
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
1
0
1
0
4
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
1
0
1
0
0
0
2
1
0
0
1
0
0
1
0
2
1
1
0
0
0
0
0
3
0
0
0
1
1
1
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
2
0
0
0
0
0
0
2
0
0
0
0
4
0
2
0
0
0
0
1
0
0
2
2
0
0
0
0
1
0
0
2
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
4
1
0
0
1
6
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
1
1
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
2
0
0
0
0
0
0
1
0
0
0
2
2
0
2
0
0
0
0
0
0
0
2
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
1
0
0
2
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
2
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
2
2
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
2
0
11
0
0
0
0
0
0
0
0
0
3
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
1
2
1
0
0
2
0
0
0
2
0
2
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
2
0
0
0
2
0
0
0
1
0
0
0
1
2
0
1
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
4
2
0
2
1
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
4
0
3
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
3
1
1
0
0
0
5
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
2
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
1
0
0
0
3
0
0
0
0
0
0
0
1
0
3
0
0
0
1
2
2
3
0
0
0
0
0
0
1
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
1
0
2
0
2
1
2
0
0
0
0
0
1
1
0
0
0
2
0
0
0
1
0
0
0
2
0
1
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
3
0
0
0
2
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
3
1
1
1
1
0
2
0
0
0
4
2
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
4
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
3
0
2
2
0
0
3
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
1
0
1
0
1
0
2
0
2
0
0
0
0
0
0
1
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
4
2
1
0
0
0
0
0
0
0
0
0
0
2
1
2
0
2
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
1
2
0
0
0
0
0
1
3
0
0
0
0
1
0
2
0
1
0
0
1
0
2
0
0
1
0
0
0
0
5
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
3
1
0
0
0
0
0
0
0
0
0
0
0
2
3
0
2
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
1
1
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
2
0
0
1
0
0
0
5
1
2
0
0
0
2
0
0
0
3
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
1
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
2
2
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
2
0
0
0
2
0
2
0
0
0
1
0
0
3
0
0
1
0
2
1
0
1
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
2
0
2
0
0
0
2
0
0
0
0
0
3
2
0
0
1
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
1
0
0
0
0
0
9
1
0
0
0
0
0
0
2
0
0
12
0
1
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
3
0
0
4
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
1
0
2
0
0
1
1
0
0
0
3
0
0
3
2
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
2
2
0
0
2
0
0
1
1
2
0
4
0
0
1
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
2
2
0
0
0
0
0
1
2
0
0
1
1
0
0
2
1
0
2
0
0
0
2
0
0
1
1
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
4
1
1
0
1
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
1
2
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
2
0
2
0
4
1
0
0
1
0
0
0
0
7
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
3
0
1
0
0
0
2
0
2
0
0
0
2
0
3
0
0
0
3
0
0
1
0
0
0
0
0
4
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
1
1
1
0
0
0
1
2
0
0
0
4
0
0
0
1
0
2
0
0
0
2
2
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
3
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
1
0
1
0
0
0
0
10
0
2
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
3
0
3
3
1
1
3
0
0
0
2
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
3
0
2
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
1
2
0
0
0
1
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
1
0
0
0
0
4
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
1
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
3
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
2
2
0
1
0
0
0
0
4
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
2
2
0
0
2
0
2
0
1
0
0
1
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
1
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
1
0
3
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
3
2
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
1
0
0
0
0
3
0
0
0
2
3
3
0
0
0
2
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
2
0
0
0
2
0
2
0
1
0
0
4
0
1
1
0
0
0
0
2
3
0
0
1
0
0
0
1
0
0
3
2
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
3
0
0
2
0
0
0
0
0
0
2
1
0
1
1
0
0
1
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
3
0
0
0
0
0
3
0
1
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
3
0
0
1
0
0
0
0
0
0
1
2
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
1
0
1
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
1
0
1
2
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
5
0
1
2
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
3
0
2
0
0
0
0
1
0
0
0
1
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
1
0
0
0
1
0
2
0
0
2
0
3
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
1
0
0
0
1
0
2
0
0
3
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
5
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
1
0
0
2
0
0
2
3
0
0
0
7
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
3
2
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
2
0
2
0
0
1
0
0
3
0
0
0
0
4
0
0
0
2
0
2
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
1
1
0
5
1
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
1
0
2
0
0
0
0
1
1
0
1
0
2
0
1
0
4
1
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
2
1
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
2
0
3
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
1
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
2
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
5
0
0
3
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
2
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
3
2
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
2
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
3
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
5
0
0
0
0
0
0
0
0
0
0
2
4
2
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
5
2
1
0
0
3
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
1
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
1
0
0
0
3
0
0
0
0
2
0
0
2
1
0
2
8
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
1
1
0
0
3
3
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
7
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
1
0
0
0
2
2
0
0
0
0
1
1
1
0
1
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
3
2
0
2
2
0
0
1
2
0
1
4
0
0
0
0
0
0
0
5
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
2
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
2
1
0
1
4
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
3
1
3
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
1
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
2
1
0
4
0
0
1
0
1
0
0
0
1
0
2
0
1
2
5
0
0
0
8
0
0
0
0
0
3
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
3
0
1
0
0
2
0
0
0
0
0
3
3
0
0
0
0
0
0
2
2
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
1
3
2
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
3
2
0
0
5
0
0
0
0
0
0
0
0
3
0
0
4
0
0
0
2
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
1
0
0
1
0
0
2
0
2
0
0
0
0
0
1
0
2
0
0
2
0
1
2
0
1
1
0
2
1
0
0
0
0
5
0
1
4
0
0
2
0
0
0
1
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
3
0
0
0
0
4
0
0
0
2
0
1
0
0
0
0
0
0
2
4
0
0
0
0
0
0
2
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
1
0
1
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
2
0
2
7
0
5
5
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
3
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
6
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
2
0
0
0
3
0
0
1
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
1
0
3
1
0
0
0
0
0
0
1
5
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
1
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
3
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
1
0
1
0
2
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
1
2
1
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
1
0
1
0
0
0
0
3
0
1
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
1
0
0
2
2
0
0
0
0
3
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
3
0
0
0
1
0
2
0
1
0
2
10
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
3
1
0
2
0
0
0
0
4
0
0
0
0
0
1
0
3
2
0
0
0
4
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
1
2
0
0
0
0
4
0
0
0
0
3
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
3
0
2
2
1
0
0
0
0
2
0
0
0
0
1
2
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
3
0
3
1
2
2
0
0
0
2
0
1
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
3
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
1
1
0
0
0
2
0
3
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
2
0
2
0
0
0
0
0
2
0
0
1
2
0
0
0
3
2
0
0
1
3
3
0
0
0
0
1
0
0
0
0
0
0
6
0
0
0
0
0
1
0
0
0
1
1
2
1
0
0
1
0
3
0
1
0
0
0
1
2
0
0
0
2
0
2
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
3
0
0
0
0
2
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
2
0
0
1
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
2
0
2
2
0
2
0
1
0
0
3
0
0
2
0
1
0
0
0
0
2
1
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
5
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
3
2
0
0
0
1
0
2
0
1
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
1
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
4
0
0
0
3
0
0
0
0
0
2
0
0
0
4
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
4
1
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
2
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
8
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
1
2
0
0
0
2
0
2
1
2
6
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
3
0
0
1
0
1
0
0
0
0
0
7
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
3
1
2
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
3
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
5
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
2
0
2
0
0
0
2
0
0
0
0
0
0
3
0
1
0
0
2
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
2
0
0
1
1
0
2
0
0
2
1
1
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
2
2
0
0
1
0
0
2
0
1
0
0
0
0
0
2
0
1
0
4
0
0
0
1
0
0
1
0
0
0
0
0
4
1
2
0
0
0
0
3
1
0
0
0
0
1
0
2
0
1
0
0
0
0
1
0
1
0
0
0
2
0
5
0
0
1
0
1
0
0
0
1
0
0
0
2
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
1
0
0
0
3
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
2
0
0
2
0
0
0
2
0
1
2
0
0
1
0
0
0
1
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
1
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
3
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
7
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
2
1
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
1
0
0
6
0
2
0
1
0
0
2
2
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
1
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
2
2
2
1
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
3
0
2
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
1
0
0
2
1
0
0
0
0
1
0
0
0
0
1
0
0
2
3
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
8
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
1
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
2
1
0
1
0
0
0
0
1
1
0
2
0
1
0
0
0
0
1
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
4
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
4
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
2
0
3
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
1
0
2
0
0
0
2
1
2
0
2
0
0
0
0
0
0
1
1
0
0
2
1
2
0
0
1
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
1
1
0
1
0
0
0
2
0
1
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
2
0
0
0
0
0
3
0
0
0
0
2
0
0
0
1
0
1
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
1
0
0
0
0
1
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
2
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
1
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
2
0
0
2
0
0
0
0
0
1
1
0
4
0
0
2
0
4
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
3
0
2
5
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
4
0
0
0
3
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
6
2
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
2
0
0
1
0
0
0
0
2
0
0
0
1
2
0
0
0
2
1
2
0
0
2
0
0
0
5
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
6
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
2
0
0
2
0
0
0
0
1
0
0
0
5
4
1
0
0
4
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
6
0
2
1
1
0
4
1
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
1
2
0
0
1
0
4
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
1
0
5
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
1
1
0
0
0
0
0
0
0
1
0
3
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
2
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
1
1
0
0
1
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
3
0
0
0
4
0
2
2
0
0
0
0
2
0
1
0
0
0
0
1
0
1
0
0
1
7
0
0
1
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
4
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
6
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
3
2
0
0
0
2
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
1
0
2
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
1
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
3
0
0
3
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
2
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
2
2
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
5
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
5
0
0
0
1
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
3
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
3
0
2
0
1
1
2
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
1
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
2
0
0
0
0
0
1
0
2
1
3
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
6
2
1
2
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
3
3
2
1
1
0
0
2
0
0
0
1
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
2
1
5
0
0
0
4
0
0
0
3
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
7
1
0
0
2
0
0
0
0
3
1
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
1
0
3
2
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
2
0
0
0
0
0
0
3
0
0
1
0
2
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
2
0
0
1
1
1
3
0
0
0
0
2
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
2
0
0
3
0
0
0
3
0
0
0
0
0
0
3
0
0
1
2
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
3
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
3
1
0
0
2
2
0
0
0
0
0
0
0
0
3
0
0
2
2
2
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
2
2
0
0
0
1
0
0
0
0
0
1
0
0
3
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
2
0
0
0
0
1
0
1
1
2
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
1
0
4
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
3
1
0
0
3
2
2
0
0
0
0
0
0
1
2
0
0
0
3
2
0
2
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
5
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
2
3
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
2
0
0
1
0
1
0
1
0
0
2
1
2
0
0
0
0
2
1
0
1
2
0
0
2
2
1
2
0
0
0
2
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
1
0
2
0
0
0
0
1
1
0
0
0
2
2
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
6
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
7
0
0
0
5
0
0
1
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
2
0
0
1
2
0
0
0
2
0
3
2
0
0
0
0
1
0
0
0
1
0
3
0
0
1
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
3
3
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
2
0
1
2
0
0
1
0
0
2
0
0
3
0
0
0
2
0
0
0
0
0
3
0
0
0
3
0
2
0
0
0
0
2
0
0
1
2
0
0
0
2
2
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
1
0
3
0
0
1
0
0
0
0
1
0
0
0
0
1
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
1
0
0
2
0
0
0
0
4
0
0
0
0
0
0
3
1
2
0
0
0
0
1
0
1
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
1
0
1
1
0
2
0
0
0
0
1
2
0
0
0
1
2
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
1
1
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
5
1
0
0
2
1
0
1
1
0
3
0
4
0
2
0
0
0
0
0
0
0
0
2
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
3
1
1
0
0
0
2
0
0
0
0
0
1
1
0
0
0
1
0
2
0
0
0
0
1
0
1
0
0
1
0
1
2
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
3
0
0
0
4
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
1
0
2
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
3
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
2
1
0
2
0
3
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
3
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
4
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
1
2
0
5
0
1
0
0
1
0
0
4
0
2
0
0
1
0
2
0
2
1
1
0
0
5
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
4
0
0
0
0
2
1
2
0
2
0
0
2
0
0
4
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
2
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
4
4
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
5
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
1
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
1
0
2
3
0
2
0
1
0
0
0
0
1
0
3
0
0
2
0
1
0
0
2
0
5
0
0
0
0
1
1
0
1
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
2
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
1
2
0
2
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
1
0
3
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
3
1
2
1
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
2
0
0
1
0
1
4
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
3
1
0
0
1
0
0
0
1
2
0
1
0
0
0
0
0
2
4
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
1
0
1
6
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
2
1
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
10
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
5
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
1
0
0
1
2
1
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
1
0
0
0
2
1
1
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
2
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
5
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
2
1
0
0
0
2
1
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
3
0
0
1
0
0
0
0
2
1
0
2
0
0
2
0
0
0
2
0
2
2
1
0
0
0
1
0
0
1
0
0
0
0
0
3
0
1
2
0
0
1
0
0
0
1
0
2
1
1
2
0
0
0
0
1
1
0
2
0
1
2
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
5
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
1
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
1
2
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
2
1
0
0
0
0
0
3
0
2
0
1
3
1
0
0
0
0
0
0
3
5
2
0
2
0
0
0
0
1
0
2
1
0
0
0
0
0
1
1
0
1
2
0
1
0
0
0
1
3
0
1
0
0
0
1
0
2
0
0
0
3
0
0
1
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
1
1
0
0
0
0
0
3
1
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
2
1
0
0
0
1
0
1
0
0
0
2
0
0
1
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
1
0
2
0
2
0
2
1
0
1
3
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
3
2
0
0
2
0
2
2
0
0
3
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
3
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
8
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
1
0
0
2
2
1
0
0
0
8
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
5
0
0
0
3
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
1
0
0
2
0
2
0
1
2
0
0
0
0
2
0
0
0
0
0
1
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
3
0
0
0
0
0
2
7
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
2
3
0
0
1
0
2
0
0
0
1
0
2
0
0
0
0
2
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
2
1
0
0
0
3
1
0
0
0
0
0
0
0
1
1
0
0
0
4
0
0
0
0
0
3
2
0
0
4
0
0
0
1
1
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
2
2
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
2
1
1
0
0
0
0
0
1
0
0
0
0
0
4
1
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
3
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
2
0
2
5
3
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
1
1
0
0
0
0
1
0
2
0
1
1
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
4
0
2
0
0
0
2
3
2
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
1
4
2
0
0
0
0
0
0
1
1
2
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
2
0
0
0
2
4
0
0
0
0
0
4
2
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
3
0
0
0
0
1
0
1
0
1
0
0
0
2
0
2
0
0
0
0
0
6
0
2
0
1
0
1
0
0
0
0
3
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
3
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
2
2
2
0
0
1
0
0
0
0
0
4
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
1
0
0
0
0
2
4
0
3
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
3
0
2
2
0
0
0
0
2
3
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
4
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
10
0
0
0
0
0
0
1
0
0
0
1
0
0
3
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
2
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
4
0
0
0
0
0
1
2
0
0
1
0
1
1
3
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
2
0
0
2
2
1
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
2
2
2
0
1
0
0
0
0
0
0
3
0
0
0
2
0
0
0
1
7
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
1
0
1
0
0
2
0
0
0
0
1
0
0
0
0
2
2
0
1
0
1
2
1
0
2
0
1
0
0
0
0
1
0
3
0
0
0
0
1
4
0
0
1
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
4
3
1
2
1
0
0
1
0
0
1
0
0
0
0
0
3
0
2
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
2
2
0
2
0
3
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
2
0
1
0
1
0
1
2
0
2
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
2
6
1
1
0
0
1
0
1
0
0
0
2
0
0
0
0
0
1
0
0
9
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
2
1
1
2
0
0
0
0
0
1
0
0
0
0
0
1
0
3
0
0
1
0
0
0
2
0
0
0
0
0
1
1
0
0
4
1
0
2
1
0
0
0
0
0
0
2
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
2
2
0
0
0
0
0
1
0
2
0
2
0
0
0
0
1
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
3
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
1
1
0
0
0
0
1
1
0
3
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
2
2
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
0
0
2
0
2
0
1
0
0
0
2
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
5
0
0
0
0
0
0
2
0
0
3
0
0
3
0
0
0
0
0
2
0
0
0
0
1
0
1
0
4
0
0
0
0
0
2
0
0
3
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
3
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
4
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
1
2
0
0
0
0
1
0
0
0
0
2
2
0
2
0
0
2
0
0
0
0
8
1
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
2
0
2
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
2
0
0
0
0
2
0
0
5
0
0
0
3
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
1
0
2
0
0
0
1
0
4
1
0
0
2
2
0
0
0
3
0
0
0
1
0
2
0
0
0
0
3
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
3
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
2
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
3
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
1
0
0
5
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
2
0
0
0
0
1
0
2
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
1
1
0
0
1
2
1
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
4
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
1
0
0
0
1
0
0
3
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
3
0
0
0
1
0
2
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
2
0
1
0
1
0
2
0
0
0
2
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
1
1
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
1
0
0
5
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
2
0
0
0
0
1
0
0
4
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
1
0
3
0
0
0
0
0
0
1
2
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
3
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
5
0
0
0
1
1
0
2
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
1
1
0
0
0
8
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
3
0
0
3
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
3
2
1
0
0
0
0
1
1
1
0
1
0
0
0
1
2
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
4
0
0
1
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
5
0
2
0
1
0
0
0
0
0
0
1
0
0
0
1
0
3
1
0
0
0
0
2
0
2
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
7
0
0
0
0
2
4
2
0
1
0
0
1
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
2
0
0
2
0
0
3
0
0
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
2
0
0
2
2
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
2
1
0
0
1
2
0
1
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
1
0
2
0
0
1
0
5
0
2
0
0
1
0
0
0
0
1
0
2
3
0
0
0
0
3
1
0
0
0
0
0
0
9
0
2
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
5
0
0
3
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
4
0
0
0
2
0
0
3
1
1
0
0
1
2
0
0
0
0
5
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
1
1
0
1
0
0
1
0
0
0
0
1
0
2
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
9
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
4
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
9
2
0
0
2
0
0
0
2
0
0
0
11
0
0
0
1
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
6
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
2
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
1
0
0
1
0
2
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
1
1
2
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
4
0
0
1
0
1
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
2
0
3
0
0
0
2
0
0
1
0
0
0
0
0
0
0
4
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
2
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
2
0
0
2
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
1
0
2
0
0
0
0
0
2
0
0
0
2
0
2
0
2
0
0
0
0
1
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
1
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
5
0
0
0
3
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
2
0
2
0
0
2
1
0
0
0
0
0
3
0
0
0
0
1
2
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
4
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
14
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
2
1
2
0
0
0
0
0
0
1
0
4
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
2
0
2
0
0
0
0
0
1
0
0
0
3
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
3
2
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
3
3
0
0
1
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
1
0
0
0
2
0
0
0
0
1
0
2
2
0
0
1
0
0
0
0
0
0
2
3
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
1
0
0
8
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
2
3
2
0
0
0
0
1
1
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
3
0
0
0
2
0
0
1
0
1
0
0
10
0
0
6
0
0
2
0
2
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
2
0
1
1
0
0
0
0
0
5
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
2
0
0
0
0
0
1
0
0
2
0
4
0
5
2
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
2
4
0
0
2
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
2
1
2
0
0
0
0
1
0
0
0
0
1
3
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
2
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
1
0
0
4
0
0
0
0
1
0
0
0
0
0
2
0
4
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
4
0
0
2
0
0
0
0
0
2
0
0
2
1
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
1
1
0
2
0
0
1
0
0
2
0
1
6
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
5
1
0
2
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
3
2
0
0
0
2
0
0
0
1
0
0
3
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
2
2
0
3
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
2
4
1
0
2
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
1
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
3
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
2
2
0
0
0
1
1
0
0
0
1
0
0
0
3
0
0
0
1
0
1
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
4
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
2
0
2
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
2
2
1
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
4
0
0
0
0
2
0
0
3
0
0
2
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
8
0
0
0
2
0
12
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
1
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
5
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
1
2
0
0
2
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
4
0
0
0
0
0
0
1
3
2
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
3
0
2
1
0
0
1
0
0
1
0
0
0
3
0
0
2
1
4
0
0
0
1
1
2
0
2
0
2
0
0
1
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
1
0
1
0
1
0
0
0
0
0
2
0
1
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
2
2
0
3
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
1
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
2
1
0
0
3
0
1
2
0
0
0
0
1
0
1
0
5
1
2
0
1
1
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
7
0
0
0
0
2
0
2
0
2
0
0
0
2
0
1
1
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
4
0
0
0
0
0
4
0
0
0
0
1
0
0
2
0
0
0
0
1
1
0
4
0
0
0
0
2
0
0
1
0
0
0
0
0
2
6
0
0
0
0
0
1
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
3
1
3
0
1
1
0
0
1
0
2
0
0
0
2
0
1
1
2
0
0
0
0
4
0
1
0
0
0
0
0
1
2
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
5
0
1
0
0
0
0
0
1
0
1
0
0
0
0
5
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
2
0
0
1
0
0
1
0
0
0
0
3
0
0
2
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
4
1
0
1
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
4
0
0
2
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
2
1
0
0
1
0
2
3
2
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
3
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
3
0
0
0
2
0
2
1
2
0
2
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
2
1
4
0
11
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
18
2
0
0
1
0
0
1
0
0
0
0
2
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
2
2
2
1
0
9
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
4
0
0
1
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
3
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
1
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
2
0
2
2
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
1
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
4
0
2
2
1
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
2
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
1
0
1
0
0
0
0
0
0
1
0
0
0
0
2
2
3
1
0
0
0
0
0
2
2
0
0
0
1
0
1
0
1
2
4
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
4
2
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
3
4
0
0
0
0
2
0
0
0
0
0
0
0
0
5
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
1
1
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
3
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
3
0
0
1
0
1
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
2
0
2
0
0
0
0
0
5
0
0
0
2
0
0
0
0
1
0
0
0
1
0
3
0
1
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
2
0
0
0
0
1
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
1
0
0
2
0
0
2
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
2
2
0
0
1
1
1
1
2
0
0
0
0
3
0
3
1
0
0
0
0
0
0
8
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
8
0
1
0
2
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
2
0
1
3
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
3
0
0
0
0
0
0
0
1
1
2
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
3
0
1
0
1
2
0
0
0
2
0
2
0
0
0
1
1
0
0
0
1
0
0
0
2
10
0
0
0
0
0
0
2
0
1
2
2
0
0
1
0
3
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
5
0
2
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
1
1
2
1
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
1
0
0
2
0
0
2
2
0
0
1
0
0
3
0
0
1
0
2
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
2
1
0
2
0
3
0
1
0
0
0
0
0
1
5
0
0
1
2
0
0
1
0
0
0
0
0
0
0
4
2
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
5
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
3
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
18
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
2
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
1
0
0
0
0
2
2
0
0
0
3
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
2
0
1
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
12
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
2
0
0
0
0
3
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
1
1
1
1
2
1
2
1
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
1
0
2
0
0
0
1
1
2
0
1
0
2
2
0
0
1
0
0
0
0
0
0
0
0
1
0
2
1
0
1
0
3
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
1
3
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
1
3
0
1
1
0
0
0
1
0
1
0
0
0
2
0
0
1
0
0
0
2
1
0
4
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
3
0
0
0
0
2
0
0
0
0
1
5
0
0
1
2
0
0
0
0
0
0
0
0
0
3
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
2
0
0
3
0
0
0
0
2
1
0
0
5
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
4
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
1
1
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
2
0
0
0
3
0
0
0
2
2
0
0
1
0
0
0
0
2
0
1
0
0
1
4
0
0
0
0
0
0
0
0
0
3
2
0
0
0
1
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
6
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
2
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
1
1
0
1
0
0
3
2
0
0
2
1
1
9
0
0
0
0
0
0
0
5
1
0
1
2
1
0
0
3
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
1
0
2
1
0
0
3
0
0
3
0
0
0
0
4
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
1
0
0
1
1
0
0
3
2
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
2
2
0
0
0
2
4
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
2
2
0
2
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
1
0
3
2
0
0
0
0
3
2
0
0
0
1
0
0
0
2
0
0
0
1
2
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
1
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
1
0
1
2
4
6
0
0
0
0
0
0
0
0
0
1
1
0
0
2
2
0
1
0
0
0
0
0
0
0
0
4
0
1
0
0
2
0
0
0
2
0
2
0
0
0
0
0
4
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
2
2
0
4
0
0
1
1
0
0
2
1
2
1
3
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
2
1
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
3
1
0
2
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
6
0
0
0
0
3
0
2
0
0
1
0
1
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
3
0
0
1
0
0
0
0
0
2
0
0
0
3
0
1
0
3
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
7
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
1
0
4
0
2
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
3
1
0
3
0
0
3
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
1
1
0
0
2
0
0
0
1
0
1
1
0
0
1
0
2
0
0
6
2
2
7
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
2
2
2
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
2
1
0
0
0
0
0
1
1
1
0
0
0
1
0
0
1
0
0
2
0
2
0
0
0
1
1
0
0
0
1
0
0
2
0
0
1
0
0
1
2
0
0
0
1
0
0
2
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
3
2
0
0
0
2
0
0
3
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
1
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
2
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
3
1
1
0
1
0
2
2
0
2
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
2
1
1
2
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
6
0
0
0
0
0
2
1
0
0
0
2
1
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
1
2
0
1
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
1
0
0
0
1
0
0
2
0
2
0
0
0
1
0
0
2
0
0
0
2
0
0
1
2
1
0
2
0
0
0
0
2
0
1
0
0
0
0
2
0
3
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
2
0
2
0
0
2
0
0
2
2
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
2
0
0
2
1
1
1
0
0
1
0
0
1
0
2
0
0
0
3
0
0
0
1
2
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
10
0
0
2
0
0
0
1
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
4
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
2
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
4
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
2
1
0
0
1
0
3
2
0
0
2
2
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
1
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
2
1
0
2
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
2
1
0
1
0
2
0
0
0
0
1
2
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
2
2
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
3
1
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
2
2
0
3
0
2
0
0
0
0
4
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
2
1
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
2
2
0
0
1
0
2
0
3
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
1
1
0
1
0
0
0
2
0
1
1
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
1
1
0
1
0
2
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
2
0
1
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
8
2
0
0
0
0
0
1
2
0
1
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
2
0
1
0
0
2
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
1
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
4
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
6
0
0
0
1
0
0
1
0
0
0
0
0
2
3
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
1
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
1
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
1
2
0
0
0
2
0
0
1
0
0
2
0
0
0
2
0
2
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
2
0
1
0
1
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
3
0
1
0
1
0
1
1
1
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
3
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
1
0
2
2
0
0
1
0
0
0
3
0
0
1
0
3
0
0
0
2
0
1
0
0
3
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
3
0
0
1
0
1
0
1
0
2
1
1
0
0
0
1
0
0
2
0
0
2
0
1
0
0
2
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
0
2
0
2
0
1
2
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
1
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
2
2
2
0
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
2
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
2
3
0
0
0
1
0
1
0
0
0
0
0
1
2
1
0
0
0
2
0
0
1
0
1
1
0
0
0
0
0
3
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
1
0
9
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
4
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
2
0
0
1
1
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
4
0
0
0
0
0
1
0
0
0
3
0
1
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
15
0
1
4
0
0
1
0
0
0
0
1
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
2
0
0
0
1
3
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
2
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
1
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
3
0
1
0
0
0
0
0
1
0
0
0
0
2
4
1
0
0
4
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
3
2
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
1
1
0
0
1
1
0
0
1
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
3
0
1
0
0
2
0
2
1
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
3
1
0
0
2
2
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
11
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
2
5
2
0
0
2
2
1
0
2
0
0
0
0
0
0
0
0
1
0
4
0
0
2
1
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
3
0
0
2
0
0
0
1
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
2
0
1
0
0
0
0
1
1
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
6
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
1
1
0
0
2
0
0
1
0
0
0
1
0
10
0
2
0
0
0
1
2
0
1
0
1
0
1
1
0
0
0
0
0
0
2
1
0
2
1
0
0
0
0
0
0
0
0
0
1
2
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
10
0
1
0
0
0
2
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
1
0
0
1
0
0
0
2
1
0
0
0
0
1
2
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
2
0
0
1
0
0
2
0
0
0
2
3
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
4
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
3
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
1
2
0
3
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
1
0
0
0
0
0
2
2
0
2
2
0
0
2
2
0
2
0
0
0
0
1
2
1
1
0
0
0
0
0
0
2
0
1
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
6
0
3
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
21
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
1
1
3
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
2
0
0
0
0
2
0
1
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
3
2
2
0
0
0
0
1
0
0
2
0
6
0
0
0
0
1
0
0
2
1
3
0
0
1
0
0
0
0
4
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
1
2
1
0
0
0
0
1
0
2
0
0
0
0
1
0
1
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
3
0
0
0
1
3
0
0
2
0
0
0
2
0
0
0
0
2
2
0
0
4
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
3
6
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
2
0
0
0
1
0
0
0
7
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
2
5
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
2
0
1
0
1
1
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
1
0
0
0
0
0
1
0
0
3
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
3
0
0
1
0
0
0
0
0
0
3
0
0
0
0
2
2
1
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
1
0
0
2
1
0
0
2
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
1
1
2
2
2
0
1
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
3
3
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
2
3
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
1
0
0
0
1
0
0
0
5
0
3
2
0
0
0
0
0
1
0
0
0
2
0
2
0
0
1
0
1
2
0
0
0
1
0
5
1
0
2
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
1
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
3
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
3
0
0
2
0
3
0
0
0
1
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
2
0
0
2
2
3
0
0
0
2
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
5
1
0
0
0
0
2
1
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
1
2
1
0
0
2
2
1
0
0
0
3
1
2
0
0
0
0
0
0
0
2
2
2
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
3
0
2
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
2
0
1
0
0
0
0
0
1
0
0
0
3
0
0
0
0
1
0
0
0
3
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
5
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
2
0
0
0
0
1
3
0
0
2
0
2
0
1
0
0
0
0
2
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
3
0
0
2
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
1
0
0
0
0
0
1
2
0
0
1
0
1
0
2
0
2
0
0
0
1
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
1
1
2
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
3
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
2
3
1
0
0
0
2
0
2
2
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
2
3
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
1
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
4
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
2
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
3
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
2
4
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
2
2
0
2
2
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
2
1
3
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
2
1
0
0
0
0
0
1
2
0
0
1
3
1
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
5
0
1
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
5
2
1
0
0
2
1
2
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
5
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
4
0
1
0
0
0
1
2
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
1
4
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
1
0
1
0
0
0
0
1
0
2
0
0
2
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
2
2
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
4
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
1
0
0
0
1
0
0
0
2
0
0
1
0
0
2
0
1
0
0
0
2
1
0
0
0
1
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
1
3
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
1
1
3
1
0
2
1
0
5
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
1
2
0
3
2
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
1
0
0
1
0
2
1
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
1
0
2
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
2
2
0
0
0
0
2
2
0
0
0
0
0
2
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
1
0
1
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
2
2
0
0
2
0
0
0
0
0
0
2
0
3
0
0
0
0
2
0
0
1
0
1
0
1
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
3
0
0
1
3
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
1
0
0
3
1
3
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
1
0
2
0
2
2
0
0
0
0
0
1
0
1
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
3
0
0
0
0
1
0
0
0
1
0
0
2
2
2
2
0
0
0
0
0
0
0
0
4
0
3
0
2
0
0
0
0
0
4
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
1
2
2
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
1
0
2
2
0
0
0
0
2
0
0
0
0
0
0
4
0
1
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
1
0
0
2
1
2
0
0
1
0
0
0
0
0
1
0
1
0
0
3
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
2
0
0
0
2
3
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
3
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
2
0
0
0
2
1
0
2
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
1
2
1
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
2
0
5
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
3
0
0
0
0
0
0
0
0
3
0
0
0
3
2
2
0
4
0
1
0
0
2
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
3
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
6
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
2
0
0
2
0
2
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
3
2
0
0
0
0
0
2
0
2
3
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
3
0
0
0
1
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
3
2
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
1
0
2
0
0
0
1
0
0
0
1
0
0
1
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
6
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
2
1
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
2
3
1
0
0
0
0
0
0
0
0
1
0
1
0
3
0
1
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
3
0
0
0
2
1
0
0
0
1
0
0
0
0
2
0
0
0
0
3
0
0
0
0
3
0
0
0
0
0
0
0
2
1
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
3
0
0
0
1
0
0
1
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
2
1
0
0
0
1
0
0
0
1
3
0
0
2
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
3
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
5
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
1
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
1
0
0
1
2
0
0
0
0
0
0
2
0
0
0
2
1
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
3
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
1
0
0
0
0
0
0
1
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
2
1
0
0
3
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
3
0
0
0
0
0
2
0
0
0
0
2
2
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
3
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
1
1
0
0
1
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
1
2
2
0
2
1
0
0
3
0
0
0
1
0
0
0
0
6
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
2
2
0
0
0
1
2
0
2
0
0
0
0
4
0
0
1
0
0
0
0
0
0
1
0
2
0
0
2
0
0
1
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
2
1
4
0
0
0
0
0
0
0
0
0
0
0
1
0
3
4
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
2
0
1
1
3
0
0
0
0
0
1
0
8
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
3
0
3
0
0
0
1
0
0
1
1
0
0
4
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
3
0
0
2
1
4
0
0
0
0
1
0
0
1
0
2
0
5
0
0
1
2
1
0
0
1
1
0
1
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
1
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
1
0
0
0
0
0
0
5
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
2
2
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
3
2
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
3
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
1
0
0
2
1
0
0
0
1
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
3
5
0
1
0
0
3
2
0
1
2
0
0
2
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
3
0
0
1
0
0
3
0
2
0
0
0
1
0
2
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
2
0
0
2
0
0
1
0
0
0
3
0
0
0
0
1
2
0
4
0
0
0
0
1
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
1
0
0
0
0
2
0
1
0
0
3
2
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
4
2
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
2
0
5
2
0
1
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
3
0
0
2
4
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
1
1
0
0
3
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
3
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
6
0
0
0
0
1
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
4
1
1
0
0
2
2
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
9
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
3
1
2
0
0
2
0
0
0
2
0
2
0
0
0
2
0
0
0
0
3
0
0
1
0
2
0
0
0
0
2
0
0
2
0
0
1
0
0
2
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
2
0
1
1
0
0
0
1
0
1
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
2
0
1
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
2
0
0
5
0
0
0
0
1
0
1
1
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
8
0
0
0
0
0
0
5
0
0
0
1
0
2
3
0
2
0
0
0
0
3
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
4
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
4
0
0
0
0
1
0
2
0
0
1
0
1
0
0
0
0
0
0
2
0
0
3
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
3
2
4
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
4
0
0
1
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
2
2
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
2
2
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
3
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
2
2
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
1
0
0
3
0
0
2
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
3
1
0
2
0
0
2
0
0
0
0
0
4
1
0
0
2
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
1
2
0
0
2
0
0
0
0
0
3
0
0
0
0
0
1
0
0
15
0
2
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
2
0
0
10
0
2
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
1
0
0
1
0
2
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
4
0
0
0
0
2
0
2
2
1
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
6
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
3
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
2
3
0
0
0
1
3
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
5
0
0
2
0
0
1
0
0
0
0
4
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
4
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
1
4
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
4
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
3
0
1
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
3
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
3
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
6
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
5
0
1
0
0
0
0
0
0
0
1
2
0
0
3
2
1
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
1
0
1
2
2
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
4
0
0
0
2
0
0
0
0
0
4
5
0
2
0
0
0
2
0
3
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
1
0
0
0
3
0
0
1
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
2
1
0
0
0
0
0
0
2
0
0
1
0
1
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
1
0
0
1
0
2
1
0
0
4
0
2
0
0
0
0
0
0
0
0
0
1
3
1
0
0
0
1
0
0
0
2
2
0
2
1
0
0
2
1
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
4
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
3
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
1
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
6
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
4
0
3
0
1
2
0
0
0
0
0
0
0
2
0
1
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
2
0
0
0
0
0
2
1
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
2
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
4
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
3
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
8
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
7
4
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
3
0
0
0
0
2
0
0
0
0
0
0
0
5
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
3
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
2
2
0
0
1
0
1
3
0
0
0
0
0
0
1
0
0
0
0
0
3
3
0
0
2
1
0
0
0
2
0
0
0
1
0
0
0
1
0
2
0
2
0
2
0
0
1
0
0
0
1
0
0
1
0
2
0
0
0
0
0
2
0
2
1
0
0
2
0
0
0
1
1
0
0
0
0
2
0
1
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
3
0
0
0
0
1
1
0
0
0
0
0
0
4
0
0
1
0
3
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
3
0
0
0
0
0
2
0
2
2
3
1
1
0
2
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
2
0
4
0
1
0
1
0
0
0
0
0
2
1
2
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
2
0
0
0
1
2
0
0
3
1
0
0
1
0
0
0
1
1
3
1
0
0
0
0
0
0
0
0
2
0
7
0
0
0
0
0
0
0
2
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
4
0
2
0
1
2
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
1
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
2
1
0
0
0
0
1
2
0
0
0
0
0
1
0
1
1
0
3
0
0
0
2
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
1
0
1
0
0
2
0
0
1
0
0
1
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
3
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
4
0
0
2
0
0
2
0
2
0
1
3
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
1
0
1
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
2
0
4
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
4
0
4
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
2
2
0
0
0
0
1
0
0
0
1
2
2
0
0
1
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
2
0
2
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
4
2
0
0
0
3
0
0
0
0
0
2
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
6
6
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
1
0
0
0
0
0
1
1
0
1
0
0
0
2
0
0
1
0
4
0
0
0
0
0
0
1
2
0
0
1
0
0
2
2
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
1
3
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
1
0
0
0
2
1
2
0
0
0
0
0
0
0
2
2
0
3
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
3
0
0
0
0
1
1
1
0
0
0
1
2
2
0
2
0
0
1
0
0
1
6
0
0
0
2
0
0
4
2
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
2
0
1
0
1
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
3
0
0
0
0
0
1
0
1
0
3
0
0
2
1
0
0
0
1
0
0
0
0
4
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
1
0
1
2
0
0
0
0
0
3
0
0
3
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
8
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
5
1
1
0
0
0
2
1
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
3
2
1
0
2
1
0
2
0
0
1
0
0
0
1
0
0
0
0
0
1
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
2
0
2
2
2
1
0
0
1
0
0
0
2
0
0
0
0
2
1
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
2
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
1
3
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
1
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
1
3
0
0
0
4
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
7
1
2
0
2
0
0
0
0
0
0
1
2
0
1
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
2
2
0
1
0
0
1
1
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
1
1
0
0
1
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
2
0
0
1
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
5
1
0
0
0
0
0
0
0
0
0
0
0
3
3
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
2
0
0
0
7
0
2
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
1
0
1
0
0
0
0
0
2
0
1
0
0
2
0
0
1
0
0
2
0
2
2
0
1
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
3
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
3
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
2
0
6
4
0
2
0
1
2
0
0
0
0
0
0
2
0
0
0
2
1
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
3
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
3
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
3
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
2
0
0
4
0
0
2
0
0
0
0
0
0
4
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
3
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
2
0
1
0
0
0
4
0
0
0
0
2
0
1
1
0
0
2
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
2
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
3
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
2
4
0
1
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
3
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
2
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
3
1
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
2
1
1
2
0
0
1
0
0
0
0
3
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
2
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
1
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
2
0
2
1
0
3
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
2
2
2
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
3
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
4
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
1
0
0
0
1
0
2
0
0
1
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
1
0
1
0
2
0
1
0
0
0
1
0
0
0
0
1
0
1
0
2
0
0
2
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
2
0
3
1
2
0
0
0
0
0
0
0
0
1
2
0
1
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
2
0
0
0
1
0
0
0
7
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
4
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
3
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
3
0
0
0
1
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
2
3
0
0
1
0
0
0
1
2
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
4
0
0
0
0
0
0
2
3
0
0
2
0
0
3
2
2
1
0
1
0
0
2
0
1
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
2
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
1
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
2
0
1
2
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
1
1
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
2
0
0
1
0
0
0
0
0
2
2
3
1
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
2
0
2
2
0
0
0
2
0
0
3
1
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
2
3
0
0
3
0
4
0
0
2
2
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
3
0
1
1
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
2
0
2
0
0
1
0
0
0
4
0
0
0
0
1
0
3
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
4
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
4
0
0
0
0
0
6
1
0
0
0
0
0
1
0
1
0
0
0
3
2
0
0
0
0
2
0
1
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
2
2
0
0
2
0
0
0
0
1
0
0
0
0
0
1
2
2
0
0
0
0
1
0
0
0
1
0
0
2
3
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
1
0
3
0
5
1
1
0
0
4
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
2
0
2
2
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
1
0
0
1
5
1
0
0
0
2
0
0
2
3
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
3
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
3
1
0
0
0
1
2
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
2
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
4
4
0
3
0
3
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
3
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
2
0
0
1
0
0
1
0
0
0
1
2
1
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
2
0
0
4
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
4
3
0
0
0
0
0
5
0
0
0
0
0
2
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
2
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
2
2
0
4
6
4
2
0
0
0
0
0
2
0
1
0
2
2
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
1
2
2
2
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
1
0
0
3
2
0
0
3
2
2
1
0
2
0
0
0
0
0
0
0
0
0
2
1
0
2
2
1
2
0
0
2
2
0
1
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
2
1
0
0
0
0
0
2
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
3
1
0
0
0
2
1
0
0
3
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
2
0
4
0
0
0
1
0
2
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
4
2
0
0
0
2
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
1
3
0
0
1
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
3
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
2
0
0
4
0
0
0
0
0
2
0
2
0
0
0
0
0
10
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
2
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
2
0
0
0
0
1
0
0
0
3
0
0
0
0
0
1
2
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
2
2
1
0
0
4
0
1
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
2
0
0
0
2
6
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
2
2
0
0
0
0
1
0
0
2
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
1
0
1
0
0
0
0
2
0
0
0
0
1
4
0
0
0
6
0
2
0
0
0
0
0
0
0
0
0
2
0
2
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
2
1
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
3
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
2
1
0
0
1
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
1
1
0
0
1
0
1
0
0
0
0
2
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
1
0
0
1
0
0
0
1
2
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
1
0
3
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
2
2
0
0
1
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
3
0
1
0
0
1
0
5
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
5
1
0
0
2
0
0
0
4
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
2
0
0
0
1
0
0
0
0
0
2
0
2
0
0
1
0
1
2
4
0
1
0
1
1
0
0
0
0
1
0
0
2
1
1
0
1
1
0
0
0
0
0
2
2
2
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
2
1
0
6
1
1
0
2
0
1
0
0
0
1
2
1
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
2
0
5
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
4
2
1
1
0
1
2
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
7
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
1
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
2
0
2
0
0
0
0
1
2
0
0
1
0
0
8
0
0
0
0
2
0
1
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
4
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
5
0
0
0
0
0
2
1
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
1
0
0
2
0
0
5
0
2
0
0
0
0
0
3
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
3
0
0
0
2
2
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
2
0
2
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
2
1
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
3
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
2
1
0
0
2
0
1
0
1
0
0
2
0
0
0
2
1
2
1
1
9
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
3
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
3
0
2
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
5
2
0
0
0
0
2
0
0
0
0
3
0
0
2
0
0
0
2
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
4
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
1
0
1
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
1
0
1
0
0
4
0
0
0
1
1
0
0
3
2
1
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
3
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
3
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
3
0
4
0
0
2
0
0
0
0
0
1
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
1
0
1
0
0
0
4
3
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
5
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
2
0
0
0
3
0
0
0
0
0
0
0
1
1
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
1
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
1
0
3
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
2
1
0
3
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
2
2
0
0
0
0
1
4
0
4
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
1
0
0
0
0
2
1
0
3
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
1
0
1
1
2
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
1
1
0
2
0
0
0
1
0
3
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
2
2
5
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
1
0
1
0
1
0
0
0
0
0
1
0
2
0
1
0
0
3
3
0
0
1
0
0
2
0
2
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
4
1
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
4
0
2
1
0
0
1
0
0
0
0
0
0
0
0
1
0
2
4
2
1
0
0
1
2
0
1
0
2
3
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
2
0
2
0
0
0
2
0
1
0
0
0
1
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
2
3
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
2
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
6
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
1
3
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
3
1
1
0
0
2
0
2
0
0
1
0
0
0
1
0
0
1
0
0
3
0
0
2
0
0
0
0
0
2
0
0
0
0
0
3
1
0
1
0
2
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
5
0
0
0
2
2
0
0
0
4
0
0
0
0
0
0
1
0
0
3
1
0
0
0
0
1
0
0
1
0
0
0
0
0
3
0
0
1
0
4
2
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
7
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
12
0
0
1
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
3
2
1
1
0
0
2
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
1
1
0
0
1
0
0
1
0
2
0
0
2
0
0
0
0
2
2
2
0
0
1
0
1
1
0
0
0
0
0
0
2
2
0
0
2
1
0
3
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
2
1
0
0
0
1
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
1
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
2
0
0
0
2
0
0
0
1
0
0
3
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
1
3
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
4
3
0
0
1
1
0
1
0
0
2
2
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
3
0
0
1
2
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
1
0
0
0
2
2
0
0
0
0
0
1
0
2
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
3
0
0
0
0
4
0
1
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
1
0
2
1
3
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
6
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
2
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
1
0
0
3
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
10
2
0
2
2
2
0
0
2
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
4
0
0
0
0
0
2
0
0
4
0
1
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
2
2
1
1
2
0
0
4
0
1
1
3
0
1
2
0
0
0
1
1
0
2
0
0
2
4
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
6
3
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
3
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
6
1
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
1
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
3
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
5
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
1
2
2
0
0
2
0
0
1
2
0
0
1
2
0
1
0
0
0
0
2
1
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
1
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
3
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
3
0
0
0
0
2
1
0
2
2
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
3
1
0
2
0
0
0
1
0
0
0
1
0
3
1
1
0
0
0
0
0
0
0
3
0
0
3
2
1
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
2
0
0
0
0
0
1
0
0
0
2
1
0
0
2
0
1
0
0
2
0
0
0
1
0
1
0
0
1
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
2
1
0
0
0
0
2
0
0
0
0
1
1
0
1
3
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
2
2
1
3
0
1
0
2
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
4
0
0
1
1
0
1
1
0
1
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
3
2
0
0
4
0
2
1
0
0
0
0
0
1
0
0
2
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
7
0
0
2
0
1
1
1
0
0
0
0
1
0
0
1
2
0
0
2
3
0
2
0
0
6
0
0
0
0
0
0
0
0
0
3
2
2
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
1
1
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
3
0
0
0
2
0
0
0
1
0
0
0
3
0
1
5
0
0
0
0
0
0
0
0
0
1
0
2
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
3
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
6
0
0
0
1
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
4
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
3
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
3
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
1
0
0
0
0
0
0
5
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
1
2
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
1
4
1
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
1
1
0
1
1
0
4
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
1
0
2
0
0
2
1
1
0
3
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
3
3
1
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
1
3
4
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
2
2
1
0
0
0
0
0
0
1
0
0
1
0
0
1
2
0
0
0
1
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
1
2
0
3
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
2
2
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
2
1
0
0
0
1
0
3
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
4
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
2
1
0
2
2
0
2
0
0
0
0
3
0
0
0
0
1
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
13
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
2
0
4
0
0
0
0
2
0
3
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
1
0
2
2
1
0
0
0
2
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
2
0
1
0
1
0
0
0
2
0
3
1
0
0
2
2
0
0
1
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
2
0
1
0
0
0
0
2
0
0
0
1
3
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
2
1
0
2
2
0
0
0
2
0
0
0
0
2
0
0
1
2
2
0
2
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
3
1
1
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
2
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
3
2
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
2
1
0
3
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
8
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
2
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
5
0
1
0
0
0
0
0
1
4
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
4
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
2
0
2
1
2
0
0
0
0
0
0
3
2
0
0
0
1
1
2
0
0
0
1
0
1
0
0
0
0
2
1
0
1
2
3
0
7
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
1
1
1
0
1
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
2
2
1
0
1
2
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
2
1
3
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
6
2
1
0
0
0
2
0
0
0
0
0
0
1
1
0
1
1
0
2
0
0
0
1
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
1
6
0
0
0
0
0
0
3
0
0
0
0
0
0
4
0
1
0
0
1
0
3
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
2
0
0
0
4
1
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
1
0
0
3
2
0
0
0
2
0
0
2
2
0
1
0
0
0
0
0
2
0
1
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
4
2
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
2
1
0
4
0
1
0
0
0
1
0
0
0
0
0
1
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
2
8
0
0
3
0
1
0
0
0
0
0
0
0
1
0
0
4
0
0
2
0
0
0
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
3
3
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
4
2
0
0
0
0
2
1
0
0
5
0
1
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
2
0
1
2
0
3
0
0
0
0
0
0
1
1
2
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
1
0
0
5
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
2
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
1
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
3
2
0
0
0
0
1
0
0
0
0
2
1
0
0
0
1
1
2
0
2
0
0
0
0
0
0
0
0
2
0
3
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
9
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
2
1
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
3
4
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
4
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
2
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
1
2
3
0
0
0
1
0
0
1
1
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
1
0
10
2
0
0
3
0
0
2
0
3
0
0
0
0
2
1
2
0
0
3
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
3
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
7
3
0
0
1
0
0
0
0
0
2
1
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
2
0
1
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
4
3
0
0
0
2
1
0
0
0
0
1
0
2
1
0
0
0
0
1
1
0
0
2
1
0
0
0
0
2
1
0
1
0
0
1
0
0
0
1
2
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
1
0
3
4
1
0
0
0
0
3
2
0
0
0
0
2
0
0
0
0
1
1
0
1
0
1
1
2
1
3
2
0
0
0
0
0
0
0
0
0
2
2
3
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
5
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
1
0
0
0
0
2
2
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
6
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
3
0
1
1
0
0
0
0
0
2
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
1
2
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
5
0
0
0
0
0
2
0
0
0
0
0
3
0
1
2
0
2
0
0
2
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
6
0
0
4
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
2
3
0
0
0
0
0
3
0
0
1
0
0
0
0
1
1
0
0
2
0
1
0
0
0
0
2
0
1
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
1
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
3
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
5
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
2
0
2
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
4
4
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
2
0
0
0
3
0
0
0
1
0
0
0
3
1
0
0
0
2
0
0
0
0
0
1
1
1
0
2
0
1
0
0
2
0
1
1
0
0
0
0
0
0
1
0
0
5
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
1
0
1
0
2
4
0
0
2
0
3
0
0
1
0
0
1
0
1
0
0
0
1
1
0
0
0
1
4
5
0
3
0
0
3
2
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
1
2
5
0
1
1
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
9
0
0
0
0
0
2
1
1
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
1
0
4
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
3
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
1
0
0
2
0
0
2
0
0
0
0
0
3
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
3
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
2
0
0
2
1
3
1
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
5
0
0
0
0
2
1
0
0
1
2
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
3
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
1
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
1
0
2
0
6
2
1
2
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
1
5
4
1
0
0
0
1
1
0
2
2
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
1
3
0
0
0
0
1
0
0
0
0
2
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
3
0
0
0
1
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
1
1
0
0
0
3
2
0
0
3
0
2
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
2
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
1
2
1
0
0
1
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
2
1
0
0
0
0
0
2
0
0
0
2
3
0
0
1
0
0
0
0
1
0
2
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
5
0
0
0
2
0
4
2
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
1
0
1
2
1
0
0
0
1
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
6
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
2
0
0
2
0
1
1
0
2
4
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
5
0
0
0
0
0
0
0
0
0
0
3
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
1
0
0
0
7
0
0
0
0
0
0
0
0
4
0
0
0
2
1
0
1
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
5
0
1
0
0
0
3
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
1
1
0
0
0
0
2
1
1
0
0
0
0
3
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
1
0
1
0
3
1
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
1
2
1
0
6
0
0
0
0
0
0
0
0
0
0
1
0
0
0
5
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
3
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
2
1
0
1
2
0
0
0
0
0
2
0
1
0
0
1
1
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
2
0
1
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
4
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
1
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
2
1
0
0
0
1
0
5
0
0
1
2
0
3
1
3
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
1
0
1
1
3
0
0
0
0
0
0
1
2
0
0
1
0
0
0
2
1
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
4
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
1
0
2
2
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
3
1
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
3
3
0
0
0
2
0
0
1
0
8
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
3
1
0
0
1
0
0
0
0
2
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
10
0
1
2
0
0
3
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
3
0
0
7
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
1
0
0
0
1
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
1
1
1
0
0
0
2
2
0
0
0
0
2
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
1
0
0
0
0
2
1
1
0
0
3
0
0
0
0
0
0
2
0
0
0
1
0
2
0
3
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
3
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
3
0
0
0
0
3
0
0
0
0
0
0
1
3
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
1
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
1
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
4
1
0
0
0
2
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
4
2
0
0
0
0
0
2
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
2
0
2
2
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
1
1
3
0
0
2
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
3
0
0
3
0
2
0
0
3
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
2
0
0
0
0
1
0
0
0
3
0
0
1
0
2
0
0
0
0
0
1
0
0
3
0
0
0
2
0
0
4
1
0
0
0
1
4
0
0
0
1
0
1
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
1
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
2
0
0
0
0
2
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
1
0
3
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
1
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
2
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
3
0
0
0
0
0
0
0
0
2
0
0
0
4
0
0
0
1
1
0
0
0
0
0
0
2
1
0
3
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
3
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
3
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
6
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
3
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
4
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
1
2
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
2
0
0
5
0
0
0
0
0
1
0
1
0
0
0
6
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
4
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
4
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
3
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
2
1
0
0
0
0
0
0
2
1
1
0
3
0
0
0
0
0
2
0
4
1
1
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
1
0
5
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
1
0
2
1
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
2
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
4
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
1
2
0
1
0
0
0
1
1
1
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
1
1
0
2
0
0
0
3
0
0
0
0
0
0
0
0
1
0
1
0
2
0
2
1
0
0
2
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
2
0
0
2
0
0
1
0
2
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
2
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
1
3
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
1
1
0
0
0
2
1
1
0
0
1
0
0
0
0
2
0
0
0
0
2
0
3
0
1
0
3
2
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
2
0
2
0
1
0
0
3
0
0
0
0
1
0
0
0
0
1
0
0
2
1
0
1
1
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
1
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
3
1
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
5
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
4
0
0
0
0
0
1
0
0
0
0
3
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
1
0
4
2
2
1
0
0
0
2
0
0
0
1
1
0
0
0
0
2
0
0
2
0
0
3
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
1
3
0
0
1
1
2
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
3
1
0
0
0
1
0
1
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
6
2
0
0
2
2
2
0
0
0
2
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
2
0
3
0
0
1
0
0
0
0
0
3
1
0
3
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
1
2
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
1
1
0
2
1
0
4
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
2
0
0
3
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
3
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
2
1
0
0
0
1
0
2
1
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
2
2
0
0
0
0
2
4
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
1
1
0
0
1
0
0
4
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
11
3
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
2
1
0
1
0
0
0
0
0
0
0
2
1
0
3
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
6
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
1
0
0
1
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
2
0
0
6
1
1
0
0
0
3
0
0
3
4
0
0
0
0
0
0
0
0
4
0
0
0
1
2
1
0
2
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
1
0
2
0
2
1
1
0
0
2
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
2
2
2
0
0
0
4
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
8
0
0
0
0
1
0
0
0
0
1
7
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
2
0
0
0
2
0
0
1
0
0
2
1
0
0
0
3
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
1
1
0
0
0
2
0
2
0
2
1
1
0
0
1
1
0
0
0
0
3
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
1
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
1
0
1
0
2
0
0
2
0
0
0
1
0
0
0
3
0
4
0
0
1
2
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
1
3
2
0
0
3
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
1
0
1
2
2
0
0
0
0
0
2
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
2
2
2
2
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
2
0
0
1
2
1
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
8
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
1
0
0
0
0
0
3
8
2
0
2
2
0
4
0
0
1
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
7
0
0
0
1
0
0
0
0
5
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
1
0
4
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
1
2
0
0
2
0
0
3
0
0
0
0
2
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
1
0
0
0
0
0
1
1
2
0
0
0
0
0
1
0
0
0
0
1
0
6
0
0
0
0
0
0
1
0
0
3
0
0
0
1
0
0
6
0
0
2
0
1
2
0
0
0
3
0
0
1
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
1
0
2
0
2
0
1
0
0
0
2
0
0
0
0
1
0
2
1
1
2
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
5
2
0
2
0
0
1
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
2
1
1
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
3
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
1
1
1
1
3
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
1
0
2
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
3
1
1
1
0
0
0
7
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
2
2
0
2
0
0
1
5
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
3
1
0
0
4
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
2
1
0
0
0
0
0
0
1
1
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
1
2
0
0
0
0
0
0
4
0
1
0
0
0
0
2
0
0
1
0
0
0
0
1
3
0
1
0
4
1
0
0
0
2
0
0
0
0
1
2
1
0
0
0
0
0
0
0
1
2
1
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
3
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
7
1
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
1
2
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
2
0
1
2
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
5
0
2
1
0
0
1
1
3
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
1
1
0
0
2
0
0
2
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
9
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
2
1
0
0
3
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
2
3
0
1
0
0
0
0
0
1
0
0
0
2
1
0
2
0
0
2
0
0
0
0
2
1
1
2
0
0
0
2
0
0
0
0
1
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
1
2
0
0
2
0
0
0
0
0
2
0
0
1
0
0
9
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
1
2
0
2
2
0
0
0
0
0
0
0
0
2
2
0
2
3
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
2
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
4
0
0
0
0
1
3
0
0
3
0
0
0
0
0
0
0
1
0
0
0
6
0
2
0
0
0
0
0
0
0
0
0
1
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
7
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
1
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
3
0
2
0
2
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
2
0
3
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
5
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
1
0
0
8
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
3
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
1
2
0
1
0
0
0
1
1
0
0
0
2
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
6
0
0
0
0
1
0
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
2
0
2
0
0
0
3
0
0
0
1
0
1
2
0
0
4
0
0
0
1
0
0
0
0
0
1
0
2
0
0
1
1
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
2
3
0
2
0
0
0
3
0
1
0
0
0
1
0
0
2
0
1
0
0
0
2
0
0
0
1
0
0
1
0
0
0
1
2
3
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
10
0
0
0
0
2
1
0
0
0
4
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
3
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
5
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
2
2
0
1
0
2
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
2
0
6
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
1
3
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
7
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
3
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
1
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
1
3
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
1
0
0
0
0
0
0
1
1
0
0
0
0
11
0
1
1
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
2
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
3
1
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
4
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
5
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
3
0
1
1
0
2
0
0
0
0
0
2
0
1
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
2
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
2
0
0
0
1
0
2
2
0
2
0
2
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
2
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
1
0
0
0
2
2
0
2
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
3
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
2
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
1
0
0
1
0
1
1
1
1
0
0
2
0
0
1
0
1
0
0
0
0
2
3
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
2
3
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
3
1
0
1
0
0
0
0
0
0
0
2
0
3
0
2
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
1
0
1
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
3
0
0
0
2
2
1
1
0
0
0
0
0
0
1
1
0
0
0
3
0
1
0
0
0
0
0
0
2
0
6
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
3
0
0
3
0
0
0
0
0
0
1
1
1
2
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
2
0
0
2
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
3
0
2
0
0
2
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
1
3
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
4
0
0
1
0
1
0
0
1
0
0
2
0
0
0
0
0
0
2
1
1
1
0
0
0
0
2
0
0
1
0
1
0
0
0
1
2
3
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
3
0
2
0
0
0
0
0
1
2
0
0
0
2
0
0
1
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
1
0
0
1
6
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
2
2
2
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
2
0
0
0
0
6
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
2
0
0
1
0
0
1
0
0
0
0
0
1
2
0
1
0
1
0
1
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
1
2
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
1
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
1
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
2
0
0
2
0
0
0
3
0
7
0
1
0
0
2
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
3
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
9
0
0
2
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
3
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
2
1
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
2
3
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
2
1
0
0
2
0
0
0
0
0
2
2
0
0
1
2
2
0
0
0
0
3
0
0
0
2
0
0
0
2
0
0
0
0
0
1
3
0
1
0
2
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
3
0
2
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
2
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
2
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
1
1
1
0
0
1
2
0
0
0
2
1
2
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
2
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
4
0
1
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
2
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
2
0
0
0
2
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
2
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
3
0
2
0
1
0
0
0
2
0
1
0
0
0
0
0
0
4
2
0
0
1
1
0
0
0
0
0
2
0
0
0
0
3
2
0
2
0
1
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
6
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
1
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
1
1
2
0
0
0
2
1
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
2
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
1
0
0
2
0
0
0
0
0
0
0
0
1
2
0
1
0
2
0
0
0
0
1
5
7
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
5
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
1
0
0
0
0
0
2
0
0
0
1
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
2
0
2
3
0
0
1
1
0
0
0
0
0
1
0
1
0
0
6
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
6
0
1
0
2
2
0
0
0
0
1
0
0
0
0
5
0
2
0
1
1
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
2
0
1
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
5
0
4
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
4
0
0
0
1
0
0
0
0
0
2
1
2
0
0
3
0
2
1
0
2
0
0
1
0
0
0
1
0
3
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
2
0
3
0
0
0
0
0
2
0
0
1
0
0
2
2
0
0
0
0
0
0
0
2
2
0
1
0
2
1
2
2
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
2
1
0
2
0
0
4
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
2
2
0
2
0
0
0
0
1
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
3
2
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
3
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
2
2
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
2
0
0
1
2
2
1
0
0
5
0
2
1
2
0
0
2
0
0
0
0
0
0
3
0
0
0
1
1
0
0
0
0
0
0
0
3
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
6
2
2
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
3
2
0
0
1
0
2
2
0
0
0
0
0
2
9
0
0
0
0
0
0
3
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
2
2
0
4
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
2
1
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
2
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
4
0
1
1
0
0
0
1
0
0
3
0
0
1
0
0
0
0
0
2
0
2
1
2
0
0
0
0
3
1
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
1
2
2
2
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
3
0
2
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
1
0
4
0
0
0
2
0
1
2
0
4
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
2
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
4
0
0
1
0
0
0
0
4
0
0
1
1
0
0
0
0
3
1
0
0
1
1
0
0
0
0
2
2
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
2
2
2
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
1
0
0
0
0
1
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
11
0
0
0
0
2
1
0
1
0
1
0
0
1
1
0
0
0
0
0
1
8
0
0
0
2
3
2
0
0
0
0
0
1
2
0
0
0
1
1
2
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
5
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
3
0
0
0
0
0
0
0
2
0
4
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
1
0
2
1
2
0
0
0
1
0
0
0
0
1
4
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
1
5
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
2
0
2
0
2
0
0
0
0
1
0
1
0
3
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
2
0
2
0
5
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
8
0
2
0
0
0
2
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
2
0
0
2
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
4
0
2
0
1
0
0
0
0
0
2
1
1
0
2
0
1
0
2
1
0
0
0
2
2
1
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
2
1
0
1
0
1
0
0
0
0
0
2
1
2
1
0
0
0
1
0
0
1
0
0
0
2
0
1
2
4
2
2
0
2
0
6
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
1
2
2
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
3
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
1
1
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
2
0
3
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
2
1
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
2
0
3
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
3
0
0
0
2
0
1
2
2
4
0
0
0
0
0
1
1
0
0
1
0
0
0
1
2
0
0
0
0
0
1
1
2
1
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
11
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
1
1
0
1
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
2
0
2
0
0
1
3
0
0
2
0
0
0
0
1
0
0
2
2
2
0
0
0
0
0
2
0
0
0
0
1
0
2
0
2
0
0
0
0
2
2
1
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
1
1
0
0
2
1
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
6
0
0
0
0
0
0
0
5
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
2
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
1
0
1
2
2
2
0
0
3
0
1
0
0
0
0
0
0
2
1
0
1
0
5
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
3
0
1
1
4
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
2
0
0
0
0
1
1
0
2
1
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
1
0
0
1
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
2
0
0
0
0
0
0
0
1
0
0
0
2
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
7
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
3
0
0
3
1
0
0
2
0
2
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
2
1
1
1
2
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
4
0
0
0
1
0
1
2
1
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
7
0
2
0
0
0
1
1
2
1
0
0
0
2
0
1
1
0
0
3
0
2
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
2
0
1
1
2
0
0
0
2
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
2
4
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
2
3
0
0
0
0
1
0
1
0
0
2
0
0
1
1
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
11
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
2
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
2
2
0
2
0
2
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
3
7
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
4
0
2
1
0
2
2
0
1
2
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
2
1
0
0
0
0
2
0
0
0
2
0
2
0
0
1
0
2
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
5
0
0
0
0
0
0
0
2
0
0
3
0
0
2
1
0
2
0
0
0
0
0
0
1
0
0
2
1
0
4
2
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
5
0
3
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
1
4
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
2
0
1
0
0
0
4
1
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
1
0
0
0
0
1
0
2
0
0
1
0
0
0
1
2
0
0
1
2
0
0
0
1
2
0
0
1
0
0
3
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
3
0
0
1
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
1
2
0
0
0
0
0
1
2
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
4
0
0
1
2
0
0
0
0
0
0
0
2
1
0
0
0
3
0
0
1
1
2
0
0
0
2
0
0
0
1
0
1
0
1
3
0
3
0
1
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
3
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
2
0
0
0
4
0
0
1
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
2
0
0
0
0
2
1
2
0
0
1
1
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
1
3
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
5
0
1
0
1
1
0
0
0
0
0
0
2
2
4
0
0
0
1
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
1
0
0
0
3
0
0
0
0
2
0
5
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
3
0
0
0
0
5
1
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
5
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
5
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
1
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
3
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
2
0
2
0
0
0
2
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
1
0
6
3
0
0
1
5
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
5
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
1
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
2
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
3
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
5
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
3
0
1
0
0
0
0
0
1
2
1
0
0
0
2
0
0
0
0
0
1
2
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
1
0
0
1
2
2
0
0
1
1
0
0
3
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
1
1
1
0
1
0
0
1
0
0
0
2
0
0
0
0
0
3
0
0
0
0
1
0
3
0
0
0
2
1
0
2
2
0
3
0
0
1
2
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
1
1
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
2
10
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
2
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
2
0
0
1
0
2
0
1
0
0
0
3
1
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
2
6
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
8
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
2
0
2
0
0
1
1
0
0
0
0
3
0
2
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
1
1
0
0
0
0
2
2
0
1
0
4
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
1
0
2
0
0
0
0
1
0
0
0
0
1
2
0
1
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
5
1
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
7
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
1
0
2
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
1
0
1
5
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
1
3
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
1
0
0
2
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
3
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
1
2
0
1
0
3
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
2
0
0
1
2
2
2
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
2
1
0
1
0
0
0
3
0
1
2
0
0
0
4
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
5
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
2
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
2
0
1
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
1
4
0
0
0
0
1
1
0
2
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
5
1
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
3
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
3
1
0
1
1
3
0
0
0
2
0
0
0
0
0
0
0
0
1
2
1
0
1
0
0
0
1
2
2
2
0
0
2
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
3
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
3
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
1
3
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
1
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
1
1
0
3
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
4
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
6
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
2
0
1
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
1
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
1
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
3
0
2
1
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
1
1
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
1
0
0
0
0
0
2
1
0
4
0
0
0
0
0
3
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
2
0
0
0
0
2
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
5
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
2
2
0
0
1
0
0
1
1
2
2
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
2
2
0
0
0
3
2
0
4
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
4
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
2
0
0
0
0
0
1
0
0
0
1
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
2
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
2
0
0
2
0
2
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
2
0
2
2
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
3
2
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
6
2
0
0
2
1
0
0
0
0
0
0
0
1
0
0
3
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
5
0
0
0
0
0
0
2
0
0
0
0
2
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
4
0
2
0
0
2
0
0
0
2
0
0
0
2
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
5
0
3
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
1
0
0
0
0
1
5
2
0
1
0
0
0
0
1
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
3
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
7
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
2
0
0
2
1
1
0
0
2
0
0
0
3
0
0
0
0
4
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
4
0
3
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
2
1
0
1
2
0
0
0
1
0
1
0
0
1
0
1
1
0
0
0
0
6
1
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
2
1
0
1
0
0
1
0
1
2
2
4
0
0
7
0
1
0
0
0
1
2
1
0
2
0
0
0
1
2
0
0
0
0
1
2
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
5
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
6
0
0
1
0
0
0
0
1
0
1
0
0
0
0
4
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
1
0
0
1
2
0
0
1
0
0
1
0
0
1
0
0
0
1
0
2
0
0
1
1
0
1
0
0
3
2
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
3
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
5
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
1
0
2
0
0
0
2
0
0
2
0
0
1
1
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
2
0
1
2
0
2
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
2
0
6
2
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
6
2
0
1
1
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
2
0
0
0
0
0
0
2
15
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
2
0
0
4
0
0
0
0
0
1
0
1
0
0
0
4
0
0
2
0
0
0
0
4
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
2
0
0
0
0
1
0
0
2
0
0
0
1
2
1
0
0
0
3
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
4
0
1
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
1
0
3
0
1
2
0
0
0
2
1
1
0
0
2
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
2
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
2
1
0
0
1
3
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
4
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
2
2
0
1
0
2
0
0
1
2
0
0
0
0
0
0
0
1
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
4
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
2
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
3
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
4
2
0
0
0
0
2
0
1
2
1
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
18
2
0
0
0
0
0
1
5
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
1
2
2
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
1
1
0
0
1
1
0
0
0
2
0
1
0
0
0
2
0
1
0
0
0
0
9
2
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
3
0
0
1
1
0
0
2
1
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
4
0
1
0
2
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
1
0
0
0
3
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
3
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
3
0
0
0
0
2
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
3
0
1
0
1
3
0
0
0
0
0
2
3
0
0
0
0
7
0
2
3
0
0
1
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
1
0
2
0
1
2
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
1
0
2
0
0
0
2
0
0
1
3
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
2
1
4
1
2
2
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
3
1
0
2
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
2
0
0
0
0
0
2
0
2
2
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
1
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
3
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
3
0
0
2
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
2
0
0
0
0
0
0
1
0
0
1
0
0
0
1
6
0
2
1
2
0
3
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
2
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
5
0
1
1
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
4
1
0
0
0
0
0
3
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
11
2
1
0
0
0
2
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
5
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
2
1
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
1
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
3
0
0
0
0
0
2
2
0
0
0
0
0
1
1
0
0
0
0
4
0
4
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
7
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
1
2
0
0
0
0
1
3
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
3
0
0
3
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
2
5
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
1
3
0
1
5
1
0
4
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
3
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
3
0
0
1
0
0
2
0
1
2
1
1
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
3
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
2
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
3
1
0
0
1
1
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
1
0
2
0
6
1
0
0
0
0
2
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
1
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
2
0
0
2
0
0
1
0
0
0
1
0
0
2
0
2
0
0
0
0
0
1
0
0
0
1
1
2
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
2
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
2
0
3
0
0
1
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
2
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
6
0
0
0
0
0
0
0
0
4
2
0
1
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
2
0
2
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
6
1
0
0
0
2
0
4
0
2
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
1
0
0
2
1
0
0
0
0
0
4
3
3
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
4
2
0
0
0
2
6
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
2
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
6
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
4
0
1
0
0
0
0
0
2
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
1
0
0
1
0
0
0
2
0
1
1
0
3
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
2
0
0
2
0
2
0
0
0
2
0
1
0
0
0
3
1
0
2
1
0
2
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
4
0
0
1
0
0
1
0
0
2
0
0
0
0
2
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
1
0
1
0
1
0
2
0
0
1
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
1
3
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
3
0
0
4
0
2
0
0
2
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
2
1
0
0
1
0
0
2
0
0
0
1
0
0
2
1
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
4
0
0
2
5
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
3
0
0
1
0
1
0
1
0
0
0
0
0
5
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
2
2
0
0
0
0
0
0
0
0
2
2
0
1
0
0
3
0
0
1
0
0
3
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
2
0
0
1
0
2
0
0
8
0
1
0
0
0
2
1
1
1
0
0
0
1
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
1
2
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
4
0
0
0
2
0
0
3
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
1
0
0
1
4
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
5
2
2
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
5
0
1
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
4
0
0
0
2
0
2
0
0
0
1
0
2
0
2
0
0
0
0
1
0
2
2
0
0
1
0
0
0
0
2
0
0
0
0
2
1
0
0
1
1
0
1
0
0
0
0
2
1
0
2
0
0
3
1
0
2
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
2
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
2
1
0
0
8
1
1
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
2
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
1
0
2
0
2
0
1
0
1
0
0
2
0
2
3
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
1
1
2
1
0
0
0
2
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
4
0
2
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7
0
0
0
2
1
0
0
1
1
2
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
2
0
0
0
0
2
0
0
0
2
1
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
5
0
0
0
3
0
1
0
0
0
0
1
0
0
0
1
4
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
2
0
0
1
0
0
2
0
0
0
1
1
1
0
0
0
0
2
2
0
0
0
0
2
0
1
3
1
0
1
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
2
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
7
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
1
1
0
0
0
0
5
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
2
0
0
1
0
2
0
1
0
0
0
2
0
0
1
0
3
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
3
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
3
0
1
0
0
0
0
2
2
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
1
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
5
3
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
3
2
0
0
1
1
0
0
0
0
4
0
0
2
2
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
7
0
0
0
0
1
1
1
0
0
2
0
0
0
0
1
0
1
0
0
0
1
5
0
5
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
4
0
2
0
2
0
0
2
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
2
0
3
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
1
0
3
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
1
0
2
0
0
0
0
0
1
1
1
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
1
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
2
0
0
1
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
4
0
0
1
0
0
0
2
0
0
0
1
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
4
0
0
0
5
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
2
0
1
4
1
0
0
0
0
0
1
1
0
0
0
0
1
8
0
2
0
0
0
0
0
0
1
0
0
0
0
2
2
0
1
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
2
0
0
0
0
1
0
1
0
1
0
1
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
3
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
6
0
0
0
1
0
0
0
2
0
2
1
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
2
0
2
1
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
2
1
2
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
7
0
2
0
0
3
0
1
1
2
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
8
0
2
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
6
0
0
0
2
0
2
0
0
1
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
6
3
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
3
0
1
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
1
1
0
2
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
3
0
2
3
0
0
0
0
0
1
0
0
2
0
0
0
3
0
2
0
0
0
0
0
0
3
0
0
1
1
0
0
0
1
0
0
1
2
0
0
2
0
1
1
0
1
0
0
1
0
3
0
0
0
0
0
1
0
2
0
2
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
3
0
0
0
3
1
1
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
3
0
0
0
0
1
3
0
0
1
1
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
3
0
0
0
0
0
0
2
0
0
1
0
1
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
2
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
1
0
0
0
0
1
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
2
1
0
1
3
0
0
0
0
0
1
0
0
0
0
0
0
1
5
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
3
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
4
0
0
0
0
0
0
0
6
0
0
0
0
0
0
1
1
1
0
0
2
0
2
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
2
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
4
1
0
0
2
0
0
1
0
2
0
0
0
0
2
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
1
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
1
0
0
2
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
3
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
4
2
0
0
0
0
0
2
0
0
0
0
2
3
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
3
0
1
0
0
0
1
0
0
0
0
0
0
2
2
4
0
0
0
1
0
1
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
6
1
0
0
2
0
0
1
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
2
2
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
6
2
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
3
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
2
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
3
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
1
0
0
2
0
0
3
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
6
0
2
0
2
3
2
2
0
2
0
0
0
0
0
1
0
0
0
0
3
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
6
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
1
0
0
0
0
3
2
0
0
0
4
0
0
0
0
0
0
1
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
2
0
1
1
2
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
1
1
0
0
0
1
0
0
4
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
2
2
2
0
0
2
0
0
1
0
3
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
3
1
0
2
1
0
2
0
0
0
0
3
1
0
0
2
0
1
0
1
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
6
0
0
0
2
1
0
1
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
2
1
0
11
2
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
2
0
0
0
2
0
0
2
0
1
1
2
0
0
0
0
4
0
0
2
0
0
0
2
1
1
1
0
2
0
0
2
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
6
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
1
0
0
0
2
0
0
1
0
1
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
2
2
2
0
0
0
0
1
0
2
1
0
0
0
2
2
0
0
2
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
2
0
0
2
1
1
0
0
2
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
1
0
4
2
0
0
0
0
2
0
1
0
0
0
2
2
0
7
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
1
6
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
2
0
0
0
0
1
0
1
1
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
1
0
1
1
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
3
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
6
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
2
3
0
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
1
2
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
4
0
1
0
2
0
2
0
0
0
1
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
2
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
5
0
0
0
1
2
0
0
0
0
0
1
0
0
1
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
4
0
0
0
0
0
4
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
2
0
0
2
1
0
2
0
2
0
2
1
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
1
0
2
0
0
2
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
1
0
0
0
0
2
0
0
0
0
1
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
4
1
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
3
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
1
0
1
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
5
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
2
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
1
0
0
1
2
0
0
1
0
1
0
0
0
2
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
1
0
0
1
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
1
0
0
0
0
0
0
1
1
0
2
0
0
2
0
0
0
0
0
0
0
1
2
2
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
3
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
1
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
1
0
1
0
0
1
4
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
6
1
0
0
0
0
3
0
0
6
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
1
2
0
0
3
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
2
0
1
4
1
0
0
1
0
1
1
0
2
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
2
2
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
1
3
0
0
0
0
0
0
0
1
0
0
0
2
2
0
1
0
0
0
0
0
0
2
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
3
1
0
4
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
7
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
2
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
11
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
3
0
0
2
2
1
0
0
2
2
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
4
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
3
0
2
0
0
0
6
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
3
0
0
0
0
2
0
0
0
2
0
2
0
0
1
0
1
0
0
0
0
0
2
0
2
0
0
1
0
0
0
1
0
0
0
0
0
1
0
3
0
0
0
0
0
1
2
0
0
2
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
1
1
0
0
0
2
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
3
0
0
1
0
1
2
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
4
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
1
0
0
1
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
5
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
5
1
0
6
0
0
0
0
0
0
0
2
0
0
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
2
0
1
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
4
1
2
1
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
2
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
4
0
1
0
2
3
0
0
1
0
1
0
0
0
3
0
0
2
0
0
2
0
0
0
0
0
2
1
0
0
2
0
0
0
2
3
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
2
3
0
1
0
0
4
0
1
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
1
5
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
4
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
2
1
2
4
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
3
0
0
0
1
0
2
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
3
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
1
0
0
0
3
2
0
0
0
0
2
0
0
0
1
0
3
0
0
0
0
1
0
0
0
2
2
0
1
1
1
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
4
0
0
1
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
1
1
0
0
4
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
12
0
0
0
0
1
0
0
2
2
0
1
0
0
0
0
2
1
0
0
0
5
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
1
0
0
0
2
0
2
0
0
0
2
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
1
10
0
0
0
0
0
0
0
0
0
2
5
2
2
0
0
0
0
0
0
0
0
0
3
3
0
0
0
0
0
0
0
0
0
5
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
6
2
0
2
0
2
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
7
7
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
1
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
1
5
0
2
0
0
0
0
0
0
2
0
0
5
0
0
0
0
0
0
1
2
0
1
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
20
1
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
3
0
0
1
1
0
0
5
0
0
0
0
2
0
0
1
0
2
0
0
0
0
4
0
2
1
0
0
1
0
0
0
0
0
1
0
1
1
1
1
0
0
2
0
0
0
0
1
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
2
0
0
0
0
0
2
0
1
1
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
4
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
1
0
1
2
2
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
2
1
0
0
0
0
0
0
1
0
2
0
0
2
0
0
1
1
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
1
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
1
3
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
6
3
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
1
0
0
2
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
1
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
2
0
0
0
0
0
1
0
0
0
1
1
0
3
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
4
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
2
0
0
0
2
1
0
3
0
0
1
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
0
0
2
0
0
2
2
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
1
0
0
2
2
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
5
0
0
2
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
3
3
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
3
0
0
0
0
1
0
0
5
1
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
2
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
1
1
0
1
0
0
0
0
1
1
4
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
1
0
0
4
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
4
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
2
0
0
0
1
0
0
1
3
0
1
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
3
0
0
0
0
0
1
0
2
1
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
1
0
0
0
3
0
0
0
1
0
0
2
1
0
2
0
0
1
0
0
1
1
0
0
3
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
4
2
0
0
0
2
0
0
0
4
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
5
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
1
0
0
0
3
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
1
2
0
0
0
0
1
0
2
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
3
2
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
5
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
2
0
1
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
3
0
0
0
0
1
2
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
3
1
1
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
1
0
2
3
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
3
0
0
0
3
0
0
3
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
4
1
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
3
1
0
0
2
0
0
3
0
0
0
0
0
2
1
0
0
0
2
0
1
0
0
2
5
0
0
2
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
4
2
0
0
0
0
0
2
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
2
1
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
1
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
1
0
0
2
3
0
0
0
0
0
0
0
1
0
0
4
0
0
2
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
1
0
0
1
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
1
0
0
1
0
0
0
1
4
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
2
2
0
0
0
1
0
1
0
1
0
5
0
1
1
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
1
0
0
3
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
9
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
1
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
5
0
2
2
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
6
0
0
0
2
0
0
0
2
2
0
2
0
0
0
1
0
0
0
1
0
0
1
0
0
0
2
1
2
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
5
2
0
2
0
0
2
0
0
1
0
0
3
0
0
0
2
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
1
0
2
1
0
1
2
0
0
0
2
0
1
6
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
1
0
0
0
2
1
1
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
3
3
0
2
0
0
0
0
4
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
1
2
0
0
0
2
1
0
1
1
0
0
2
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
2
0
0
2
1
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
2
0
2
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
3
0
2
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
9
0
0
0
1
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
2
4
0
0
6
1
2
0
0
0
2
0
0
1
0
2
0
0
0
3
0
4
0
0
0
0
0
0
0
3
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
2
1
2
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
5
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
3
1
0
0
0
0
2
0
1
1
0
0
1
0
0
2
0
0
0
0
0
3
0
0
0
0
1
0
0
3
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
3
1
2
1
1
0
0
3
1
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
1
2
0
0
2
1
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
3
0
0
0
2
1
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
2
1
0
3
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
1
2
0
3
0
0
2
0
0
0
3
0
0
0
1
2
0
0
0
0
0
1
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
1
0
1
0
0
1
1
6
2
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
9
0
0
1
0
0
0
0
2
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
2
3
0
0
2
2
1
2
2
11
0
0
0
0
2
0
0
0
2
0
0
2
0
0
1
0
0
1
1
2
0
0
2
0
0
0
0
1
0
2
0
0
0
0
1
2
0
0
1
0
1
0
0
0
1
2
0
0
0
0
0
0
2
0
0
3
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
3
0
7
0
0
0
2
0
3
0
2
0
1
2
0
2
0
0
0
1
0
0
0
1
4
0
0
0
0
0
3
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
2
0
2
0
1
0
2
0
0
0
1
0
0
0
0
3
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
3
0
0
0
4
0
0
0
0
1
0
1
1
1
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
4
1
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
1
1
4
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
3
2
2
2
0
0
1
0
0
2
0
2
0
0
1
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
2
1
0
0
0
1
1
0
0
3
0
0
0
0
0
0
0
0
0
1
1
0
3
2
0
0
0
2
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
1
0
0
0
0
0
1
0
0
3
0
0
2
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
5
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
1
0
5
2
1
0
2
0
0
0
0
2
0
0
1
1
1
0
0
0
0
1
1
2
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
1
1
3
2
0
0
2
0
0
0
0
0
1
2
0
1
0
2
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
5
1
0
0
1
0
0
0
5
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
2
0
2
1
0
0
0
0
0
0
0
0
4
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
1
0
1
0
0
3
0
0
3
2
0
1
0
3
1
0
0
0
0
0
0
0
0
1
2
0
0
2
2
0
1
2
0
1
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
3
0
1
0
0
0
1
2
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
2
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
2
1
6
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
11
0
0
0
2
2
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
3
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
2
0
0
0
2
0
4
0
0
2
0
0
0
4
0
0
0
0
2
0
0
1
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
1
5
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
2
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
2
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
1
2
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
1
0
1
0
0
0
2
0
1
0
3
0
0
0
1
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
7
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
3
0
0
5
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
1
0
6
0
0
0
0
0
0
2
2
0
0
0
3
1
0
0
1
0
0
4
0
1
0
0
0
0
2
0
0
3
0
0
0
3
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
8
5
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
1
2
0
0
0
1
0
0
0
0
0
0
0
2
4
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
1
0
2
1
0
1
2
0
0
0
0
0
0
0
1
1
0
0
2
0
1
0
0
1
2
6
0
2
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
2
2
0
0
0
1
0
1
0
0
0
0
0
1
1
0
1
4
0
0
0
0
0
0
0
0
0
1
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
2
0
0
2
0
0
0
0
0
0
2
2
0
5
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
2
0
1
4
0
0
0
0
2
0
0
0
1
1
1
0
0
0
0
0
8
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
1
12
0
2
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
1
0
0
2
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
6
0
0
0
0
1
0
0
0
0
0
0
1
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
4
0
0
0
1
0
1
0
0
0
0
0
0
0
4
2
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
6
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
1
1
0
1
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
2
0
0
1
0
1
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
1
0
4
0
1
0
2
0
2
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
2
2
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
1
2
0
0
0
1
0
0
2
0
0
0
3
0
2
0
0
0
1
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
2
1
0
2
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
4
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
1
0
0
2
1
2
0
0
1
0
0
0
0
0
0
2
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
7
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
2
0
0
2
0
1
1
0
0
0
1
0
0
0
0
0
1
0
3
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
3
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
5
0
0
1
0
0
1
2
0
0
1
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
5
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
2
4
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
2
0
2
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
5
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
2
1
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
3
2
0
0
4
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
1
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
3
3
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
1
0
1
2
0
1
0
0
0
1
0
0
0
3
0
3
1
2
0
0
0
0
1
0
0
2
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
8
0
1
0
0
0
1
0
5
0
0
1
0
2
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
6
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
2
1
0
0
0
0
2
2
0
2
0
0
0
0
0
1
3
0
0
0
0
0
0
1
2
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
6
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
3
1
0
2
1
0
2
0
2
3
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
4
1
0
0
0
0
0
1
2
2
0
0
0
1
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
3
0
0
2
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
5
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
3
2
0
0
0
0
4
0
0
1
1
0
0
0
0
1
1
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
3
1
0
5
0
0
0
9
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
2
0
0
0
2
0
0
0
0
0
0
0
2
5
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
1
3
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
1
2
0
0
0
0
0
6
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
1
1
0
0
0
0
2
0
0
0
0
1
0
0
1
2
1
0
0
0
0
0
0
2
0
6
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
2
0
1
2
2
0
1
0
0
0
0
2
1
0
0
2
2
0
0
0
0
1
2
0
0
0
0
2
0
1
1
1
1
0
0
1
0
0
0
0
0
2
2
0
0
0
2
0
1
0
1
0
0
0
1
2
0
0
1
0
1
0
0
1
2
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
2
0
0
1
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
1
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
2
0
0
0
2
0
0
0
2
0
0
0
1
2
0
2
0
0
2
0
0
1
0
1
0
0
0
2
0
0
0
0
6
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
4
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
3
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
10
1
0
0
0
5
0
0
1
0
0
0
0
0
0
0
0
0
3
0
3
0
0
1
0
0
0
0
0
0
7
0
0
0
0
0
0
2
0
3
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
1
1
0
0
2
0
5
2
0
2
0
0
3
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
2
1
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
4
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
2
0
0
1
2
0
2
1
2
0
1
0
1
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
2
0
0
1
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
4
1
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
5
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
1
3
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
1
0
1
0
1
0
1
3
0
0
0
0
0
1
0
0
0
0
1
3
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
3
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
2
1
0
2
3
5
0
0
3
0
0
0
0
0
0
0
2
2
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
3
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
2
2
1
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
2
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
2
0
0
5
6
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
2
0
0
1
0
2
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
2
1
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
2
2
0
0
1
0
0
2
1
2
0
0
1
0
3
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
3
0
2
3
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
1
0
1
1
2
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
2
0
1
0
0
0
0
0
2
0
0
2
0
0
0
2
1
0
0
1
1
0
3
0
0
0
1
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
2
0
0
0
1
0
1
1
2
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
7
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
3
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
1
1
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
2
0
0
1
1
0
2
0
0
6
0
0
0
0
0
1
0
5
1
1
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
1
0
0
1
2
0
1
1
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
3
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
1
2
0
0
1
0
1
0
0
0
2
0
1
0
0
0
1
0
0
0
0
1
0
1
0
2
3
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
5
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
2
9
0
0
1
0
2
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
4
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
4
2
0
0
0
0
3
0
1
0
0
0
0
0
0
1
0
7
0
0
0
0
2
0
5
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
3
1
0
0
2
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
3
0
1
0
0
2
0
0
0
1
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
2
1
0
2
0
1
0
0
0
2
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
2
1
0
1
1
2
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
4
0
0
2
0
3
0
2
5
2
0
0
6
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
3
0
2
0
3
0
0
1
0
0
0
0
1
7
0
2
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
6
0
1
0
0
0
0
2
0
0
0
4
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
6
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
3
0
1
0
0
0
0
2
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
9
2
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
2
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
1
3
1
0
0
0
0
0
0
0
7
0
0
1
0
0
0
0
0
0
2
0
0
0
1
3
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
3
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
1
3
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
1
0
5
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
4
1
1
0
2
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
1
1
1
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
1
0
1
0
0
0
1
0
1
0
1
0
0
0
0
8
0
0
0
0
1
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
5
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
2
0
3
0
0
1
0
0
2
0
1
0
0
0
2
0
0
0
6
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
4
0
2
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
1
0
0
0
0
2
0
0
0
0
3
1
0
5
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
2
1
0
0
1
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
1
0
1
0
0
0
0
0
1
2
0
1
0
0
0
0
0
4
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
2
1
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
1
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
1
2
0
0
0
0
1
0
0
1
0
3
0
1
0
0
2
1
0
0
0
0
0
0
0
0
1
0
1
1
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
2
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
2
1
0
0
1
1
1
0
3
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
5
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
1
0
0
0
0
2
0
1
0
0
0
1
0
2
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
1
0
0
0
0
1
2
1
0
0
0
0
0
1
0
0
3
0
1
0
2
5
0
2
0
0
0
0
0
0
0
0
0
0
3
5
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
4
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
1
5
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
3
0
0
1
0
0
0
0
1
0
0
1
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
9
2
0
0
2
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
5
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
2
5
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
1
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
3
0
1
0
0
4
0
1
0
2
2
1
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
1
0
2
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
1
0
0
0
1
2
1
0
2
0
0
0
0
0
0
0
6
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
4
0
1
2
0
0
0
0
1
0
0
0
0
1
0
1
2
0
0
0
2
0
0
2
0
0
0
0
0
1
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
1
0
1
2
0
1
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
2
1
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
1
1
0
1
0
0
0
0
2
2
0
3
0
0
2
1
0
2
2
1
1
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
4
0
1
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
3
2
0
0
0
0
0
1
0
2
0
0
0
0
1
2
0
0
0
0
2
0
2
0
2
32
1
0
2
0
0
0
1
0
6
0
0
0
3
0
0
0
0
2
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
1
3
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
1
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
2
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
2
0
1
0
2
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
3
0
0
0
1
0
3
0
0
0
0
0
0
0
1
2
2
0
2
0
0
3
0
0
2
0
0
3
0
0
4
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
1
4
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
4
0
2
0
25
2
2
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
2
0
2
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
1
0
0
0
1
0
0
2
0
1
0
0
2
0
0
2
0
1
0
0
0
0
0
4
0
5
0
0
0
0
0
0
0
0
0
1
0
0
0
5
2
0
0
0
0
3
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
3
0
0
1
0
1
1
1
0
0
0
0
3
0
3
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
9
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
2
0
0
2
0
0
2
0
0
0
0
1
1
0
2
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
1
0
0
2
1
0
0
0
1
0
0
0
0
0
1
4
0
1
0
0
0
0
0
0
0
3
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
1
1
0
0
0
0
1
0
0
0
1
0
3
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
3
0
1
2
0
1
0
2
7
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
2
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
1
0
0
0
2
0
0
0
0
2
2
0
2
2
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
4
2
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
3
2
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
5
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
2
0
0
0
2
3
0
0
0
2
0
0
0
0
0
1
1
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
3
0
0
0
0
0
2
2
2
0
2
2
2
4
0
2
1
1
0
1
0
0
1
0
1
0
0
0
3
0
0
1
0
0
0
0
2
2
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
5
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
6
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
3
0
2
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
1
1
6
1
0
0
0
1
1
0
0
0
0
3
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
3
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
1
0
0
0
0
4
0
0
1
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
2
2
0
0
0
1
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
2
0
1
0
1
1
2
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
2
5
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
7
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
3
0
0
0
0
0
2
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
2
2
0
0
2
0
3
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
3
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
4
0
5
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
2
0
0
2
0
0
1
0
0
0
1
0
1
1
0
2
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
2
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
3
0
0
0
0
2
0
1
0
1
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
7
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
1
1
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
2
3
0
0
1
0
0
0
2
2
0
0
1
1
1
0
0
0
4
2
0
0
0
0
0
1
0
0
0
0
2
7
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
2
0
0
2
0
0
1
1
0
1
0
0
0
0
0
1
1
0
0
0
1
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
2
0
0
2
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
6
0
0
1
3
0
0
0
0
0
2
2
0
0
1
1
1
2
0
2
0
0
2
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
5
0
2
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
1
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
1
0
0
0
1
0
0
1
0
1
2
4
2
0
0
1
0
0
2
0
0
3
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
2
0
0
1
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
1
0
0
2
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
2
0
0
0
0
2
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
4
0
0
0
0
1
0
0
2
0
0
5
0
0
0
1
1
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
2
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
4
0
1
2
0
0
1
0
2
0
0
0
0
0
2
2
0
0
1
0
0
2
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
3
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
9
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
3
0
0
1
0
2
4
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
3
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
6
0
0
0
0
1
2
0
0
0
0
2
4
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
1
0
0
3
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
2
0
1
1
2
0
2
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
2
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
7
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
1
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
3
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
1
2
0
0
1
1
0
1
0
0
3
0
0
2
0
0
0
0
0
0
1
1
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
11
2
0
0
0
0
0
0
1
0
1
4
0
0
1
1
0
1
0
0
1
1
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
3
1
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
1
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
4
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
3
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
2
2
0
0
0
0
0
1
0
2
0
0
1
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
5
0
0
0
1
0
0
0
3
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
2
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
7
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
1
0
0
0
4
2
0
0
0
0
0
1
0
0
0
0
0
3
0
0
3
0
2
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
1
0
2
0
0
0
1
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
3
0
1
4
2
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
2
1
1
0
0
0
2
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
2
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
2
2
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
2
1
3
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
3
0
1
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
3
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
1
1
0
0
0
0
3
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
1
2
1
0
2
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
2
0
0
2
5
0
0
0
1
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
2
0
0
2
2
2
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
2
2
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
3
1
0
0
0
1
0
0
0
3
1
5
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
3
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
2
0
0
1
2
0
2
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
5
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
1
0
1
0
2
1
1
1
1
0
1
0
0
4
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
2
0
1
2
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
3
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
3
3
0
0
0
0
1
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
3
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
2
1
4
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
5
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
3
0
1
0
0
0
1
1
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
1
0
2
1
0
0
0
1
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
1
0
1
0
2
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
1
0
1
0
1
1
0
4
0
0
0
0
0
0
0
0
0
0
2
0
0
2
3
0
0
0
4
0
0
1
0
0
2
2
0
0
1
2
0
0
1
4
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
3
1
0
0
1
0
0
1
2
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
5
0
2
3
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
4
0
2
2
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
4
1
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
3
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
1
0
2
0
0
0
2
2
1
1
0
0
2
0
0
0
0
3
0
1
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
4
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
2
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
2
0
2
0
2
0
0
0
0
0
2
0
0
0
1
0
1
2
0
1
0
0
1
0
0
7
0
1
0
3
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
1
0
2
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
3
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
2
0
0
0
3
0
0
0
0
1
0
0
1
1
0
0
1
2
0
1
1
1
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
5
1
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
2
1
0
0
1
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
1
0
0
1
2
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
3
0
0
0
0
2
1
0
0
0
3
0
2
0
0
0
2
1
0
1
0
0
1
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
1
0
0
0
0
0
2
0
0
0
0
0
2
0
4
1
2
1
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
1
1
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
2
1
1
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
4
4
2
0
0
0
0
2
2
0
0
1
0
0
0
1
0
0
0
0
0
0
4
3
0
0
7
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
1
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7
0
0
2
1
0
0
0
1
0
0
2
0
0
2
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
3
0
1
0
0
0
0
0
2
0
2
5
2
0
0
0
0
1
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
1
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
2
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
3
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
1
0
1
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
1
0
0
1
2
0
1
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
1
0
2
1
0
0
2
4
3
3
0
0
1
0
0
6
0
2
0
0
2
0
0
0
1
0
0
0
0
0
1
0
2
0
0
2
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
2
1
0
0
2
0
0
5
0
0
0
2
1
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
5
0
0
0
1
1
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
3
0
5
0
0
0
0
0
5
0
0
1
0
2
0
0
1
0
1
0
1
0
1
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
1
0
2
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
16
0
4
0
2
0
1
2
0
0
0
0
0
0
0
0
0
5
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
2
0
1
0
2
0
1
0
1
0
4
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
4
1
0
0
0
1
0
1
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
3
0
1
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
2
0
0
1
0
0
2
0
0
0
0
0
2
3
0
0
2
1
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
2
1
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
2
0
2
0
0
0
1
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
6
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
4
1
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
3
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
2
0
2
1
2
0
0
0
0
1
0
0
2
4
0
0
0
0
0
1
1
0
0
0
2
2
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
1
0
2
0
0
1
0
0
0
0
1
1
4
0
0
1
0
0
0
9
1
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
2
3
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
1
0
1
1
0
0
0
0
4
0
0
2
0
0
1
2
0
0
2
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
2
0
1
0
0
0
0
1
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
2
1
1
1
0
0
2
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
1
0
0
3
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
1
2
0
0
2
2
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
5
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
3
3
2
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
1
0
0
1
0
0
0
2
0
0
1
1
1
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
1
0
0
2
0
6
0
0
0
2
3
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
2
2
1
0
0
0
0
0
0
2
1
0
0
4
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
2
2
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
3
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
2
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
2
0
3
0
1
0
0
5
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
5
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
2
2
0
0
0
0
0
0
0
1
0
0
2
2
0
0
2
0
0
1
0
0
0
1
3
0
1
0
0
2
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
2
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
3
0
0
0
1
0
0
0
1
0
0
6
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
8
1
0
3
0
0
0
1
0
4
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
3
1
1
5
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
3
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
2
1
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
3
0
2
0
0
0
2
2
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
4
0
2
0
2
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
4
2
0
0
0
0
1
2
2
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
3
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
1
2
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
2
0
2
0
2
2
0
0
1
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
1
0
0
1
2
1
0
0
0
0
1
0
0
0
1
0
0
2
0
2
0
2
0
0
0
0
0
3
0
0
0
0
0
0
2
0
3
1
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
3
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
2
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
1
0
0
0
0
6
2
2
0
0
0
2
5
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
3
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
4
0
1
0
0
1
1
0
0
1
0
2
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
2
0
0
2
0
0
4
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
2
2
0
0
0
2
5
3
1
0
0
0
1
0
0
0
0
2
1
0
0
0
1
4
2
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
1
0
1
0
4
0
2
1
0
1
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
1
0
0
0
2
0
0
0
3
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
1
0
0
1
0
0
1
0
2
0
2
0
0
2
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
6
0
0
1
1
0
0
3
0
0
3
1
0
0
0
0
2
1
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
1
2
0
0
0
2
2
0
0
1
2
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
3
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
2
2
0
1
5
0
0
0
1
1
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
3
0
0
3
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
2
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
3
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
1
1
1
1
1
0
0
0
0
0
1
1
0
1
2
2
0
0
2
1
0
0
0
0
3
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
1
0
2
0
0
0
0
3
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
3
0
2
6
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
2
1
0
0
1
5
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
1
0
0
0
0
1
0
0
0
2
0
1
2
0
0
0
0
0
3
0
0
2
3
0
0
3
0
0
2
1
0
0
1
0
0
0
0
2
1
0
0
1
0
0
0
0
2
1
1
1
0
1
0
1
0
0
0
0
0
2
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
2
2
0
2
0
0
0
0
2
0
0
3
0
0
0
0
2
2
0
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
4
3
0
0
0
0
0
0
0
0
0
2
3
0
0
0
1
0
2
1
0
0
0
0
1
4
0
0
1
0
0
1
2
0
0
1
2
0
2
1
2
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
2
0
2
2
0
5
0
0
4
0
0
2
0
2
0
3
0
0
2
0
1
2
3
0
0
0
0
7
0
2
0
2
0
0
2
2
0
0
0
0
0
4
0
0
0
2
0
0
0
0
1
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
4
0
0
1
2
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
2
2
2
1
2
1
0
0
0
1
2
0
0
0
3
2
0
0
0
2
0
0
5
0
2
0
0
1
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
2
0
6
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
3
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
2
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
2
0
1
0
0
1
6
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
3
0
1
0
0
0
0
0
2
1
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
3
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
5
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
3
0
0
0
0
0
2
0
0
2
0
2
2
0
2
0
0
2
2
1
0
0
1
0
0
0
0
3
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
1
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
1
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
1
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
3
1
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
6
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
2
1
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
2
0
0
0
2
2
0
0
1
0
0
0
0
0
0
4
0
0
1
0
0
0
0
2
0
2
2
0
0
2
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
3
0
0
0
1
0
2
5
0
1
0
0
2
0
0
3
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
7
0
0
0
0
1
1
0
1
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
2
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
2
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
3
0
0
2
8
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
1
0
0
1
0
0
0
1
0
0
2
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
1
0
3
2
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
4
0
6
1
0
0
0
4
0
0
1
0
0
0
0
1
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
3
0
0
0
1
0
0
2
0
2
0
0
0
2
5
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
3
0
1
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
3
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
3
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
1
0
0
2
0
1
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
1
0
0
1
0
1
0
0
0
0
1
0
2
1
2
0
0
0
0
0
1
0
0
0
0
0
0
2
3
0
1
0
0
0
0
0
0
1
0
2
0
0
5
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
2
3
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
2
5
0
0
0
1
0
3
2
2
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
2
0
0
0
0
2
0
1
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
2
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
2
2
0
0
0
0
0
1
0
1
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
1
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
1
0
3
0
0
0
0
2
0
1
0
0
1
1
0
0
0
0
0
1
0
2
1
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
3
0
2
0
2
0
0
1
0
0
2
1
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
2
2
0
2
0
1
0
0
0
0
0
1
2
0
2
0
0
0
2
0
1
1
0
0
0
0
0
2
0
0
0
0
1
0
2
0
1
0
3
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
5
1
2
1
0
1
0
0
0
2
0
0
0
0
2
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
3
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
1
0
1
0
0
1
0
1
0
0
0
2
3
0
0
0
0
0
0
0
0
3
4
3
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
1
0
3
0
2
1
1
3
0
0
1
1
0
0
0
0
0
3
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
1
0
1
1
2
0
0
1
1
0
2
0
0
1
1
0
0
0
0
0
1
0
2
0
3
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
2
0
0
1
0
3
2
16
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
2
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
2
3
3
0
2
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
2
0
0
0
0
0
0
4
3
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
3
1
1
0
0
2
2
0
3
0
1
0
0
1
0
0
0
1
2
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
1
3
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
5
1
0
0
0
4
0
1
0
0
0
1
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
3
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
3
0
2
3
0
0
0
3
2
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
5
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
2
0
0
0
1
0
1
0
4
0
0
0
1
0
0
0
2
0
0
0
2
3
1
0
0
0
0
0
0
2
2
0
1
0
0
0
0
1
0
2
0
1
0
1
0
1
1
0
1
2
2
2
0
2
0
0
0
0
1
0
1
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
3
1
0
4
1
0
0
0
2
0
0
0
0
1
0
0
3
0
0
0
4
0
0
0
0
0
0
0
0
2
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
1
1
0
1
0
0
0
1
0
3
1
2
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
1
0
0
0
2
2
0
0
0
2
0
2
0
1
0
0
0
1
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
2
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
1
0
0
0
0
0
1
0
2
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
1
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
2
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
1
2
0
0
0
0
5
0
2
0
0
2
1
0
0
1
0
0
0
2
0
1
0
0
4
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
1
0
1
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
1
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
2
0
0
0
1
0
0
0
0
1
2
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
1
4
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
2
0
0
0
0
1
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
4
0
0
0
0
0
0
0
2
2
1
0
2
0
0
0
1
0
0
1
1
0
0
3
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
1
1
0
0
0
2
1
0
0
0
1
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
1
0
0
0
6
1
0
2
2
0
0
0
2
0
0
0
0
1
0
1
0
6
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
3
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
1
1
0
1
1
3
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
3
0
1
0
2
0
1
2
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
2
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
3
2
0
2
0
1
0
1
3
0
0
0
0
0
0
0
1
0
13
0
0
0
1
0
0
2
2
0
0
1
0
0
0
0
2
0
0
4
0
0
0
1
2
0
3
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
4
1
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
8
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
4
2
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
2
0
0
2
0
0
0
2
0
0
1
0
0
2
0
0
0
3
0
0
0
1
0
0
0
0
1
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
3
2
0
0
0
0
1
2
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
2
1
0
0
0
5
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
5
0
0
0
2
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
2
0
0
0
0
0
2
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
2
0
0
0
1
0
1
0
2
0
0
0
2
1
1
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
1
0
0
0
2
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
3
0
0
1
2
0
0
1
0
1
0
0
1
0
0
3
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
3
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
2
0
1
0
1
0
0
0
0
2
3
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
1
2
0
2
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
2
1
2
2
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
2
3
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
3
0
0
2
2
3
3
0
0
2
0
2
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
5
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
1
1
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
2
1
0
0
0
0
2
0
0
0
1
0
3
0
0
0
3
2
0
0
2
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
5
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
1
0
1
0
1
0
2
1
2
0
0
2
0
0
0
2
0
0
0
0
0
5
0
3
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
2
2
0
2
0
0
2
0
2
2
2
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
1
0
2
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
6
0
0
0
1
0
1
0
2
0
0
0
5
3
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
4
0
0
2
0
0
0
1
0
0
2
2
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
4
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
2
0
0
1
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
1
1
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
4
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
2
0
0
0
2
0
0
1
0
0
3
2
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
1
0
0
1
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
2
0
1
0
2
1
0
0
3
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
1
0
0
1
0
0
1
0
2
2
0
3
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
3
0
0
0
2
0
0
2
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
2
0
0
5
0
0
0
1
0
0
2
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
2
3
0
1
0
2
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
1
0
2
0
0
4
1
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
2
0
1
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
2
0
1
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
3
0
7
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
1
0
1
0
1
0
0
0
0
0
0
3
0
0
2
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
1
2
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
1
1
0
2
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
5
0
0
0
3
0
0
1
0
0
0
3
0
0
0
0
0
0
0
1
0
2
0
1
0
3
0
0
0
0
1
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
1
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
4
2
0
0
0
1
2
0
0
1
1
0
2
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
2
0
0
2
0
0
3
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
4
1
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
3
1
2
0
2
0
0
2
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
2
0
0
0
1
2
0
2
0
0
0
6
0
0
1
0
0
3
0
2
1
0
0
0
0
0
7
0
0
2
2
0
0
0
0
0
0
0
0
0
2
1
0
0
8
3
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
1
1
3
1
0
1
0
1
0
0
2
0
2
0
0
0
0
1
3
0
0
0
1
0
2
0
0
0
0
2
0
0
0
1
0
2
1
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
3
2
0
0
2
1
0
0
0
5
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
4
0
0
0
1
0
1
1
0
0
2
0
0
2
0
0
0
1
2
0
1
0
0
0
1
0
0
0
1
1
0
2
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
3
0
2
1
1
0
0
0
0
1
0
0
0
3
0
0
0
2
0
0
0
0
1
1
0
0
0
4
0
3
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
2
1
0
0
1
2
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
2
1
0
0
0
1
0
0
0
2
3
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
5
2
0
0
2
0
2
0
0
0
1
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
2
2
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
2
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
1
5
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
2
0
1
2
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
2
0
2
0
2
0
1
2
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
1
1
2
0
2
1
0
2
0
0
0
0
3
0
2
0
0
1
0
2
0
1
0
0
0
0
3
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
5
0
1
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
3
2
0
1
0
0
0
2
0
0
0
1
0
1
0
0
0
0
2
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
1
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
1
2
0
1
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
1
1
0
2
3
2
0
0
1
0
0
0
3
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
3
2
0
0
0
0
0
0
1
0
0
0
2
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
2
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
5
0
0
0
0
0
0
2
2
1
0
0
1
0
0
1
4
0
0
0
2
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
4
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
1
0
0
0
1
2
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
5
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
3
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
8
3
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
1
4
0
0
0
1
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
1
0
3
1
0
2
4
4
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
4
1
0
0
1
0
0
1
0
1
0
2
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
1
2
0
0
0
0
1
0
0
0
2
0
0
0
2
0
2
0
2
0
0
2
0
4
5
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
1
0
0
0
0
1
2
2
0
0
0
1
0
2
0
0
0
0
2
0
0
1
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
8
0
0
0
2
0
0
1
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
1
0
3
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
11
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
3
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
1
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
1
2
3
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
4
0
0
0
1
0
2
0
0
1
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
6
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
4
2
0
0
0
1
0
0
0
0
1
0
0
3
1
0
0
7
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
2
1
0
2
0
0
0
3
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
7
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
3
0
0
0
0
0
1
0
0
0
0
1
0
0
2
3
0
1
0
0
0
0
0
1
0
3
0
0
0
0
1
3
0
0
0
2
0
2
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
1
1
1
0
0
0
0
0
2
2
0
1
2
1
0
0
0
0
0
0
1
0
0
4
0
0
1
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
1
4
0
2
0
1
0
0
0
0
4
0
1
2
0
1
0
0
1
0
1
0
0
0
0
2
0
0
0
1
1
0
0
0
0
2
1
0
0
0
1
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
1
3
0
1
0
0
0
0
0
2
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
1
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
1
2
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
5
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
3
0
0
0
2
0
1
2
0
1
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
3
0
1
1
0
0
1
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
4
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
2
0
0
2
0
0
1
2
0
2
0
0
0
0
2
0
6
0
2
1
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
6
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
1
0
1
0
0
2
1
0
0
0
1
2
0
2
0
1
0
0
12
0
0
1
2
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
4
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
1
0
0
2
2
2
0
0
0
0
1
0
0
0
2
0
0
0
1
0
3
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
2
0
0
0
0
0
0
2
0
0
0
6
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
2
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
3
0
1
1
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
3
2
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
4
0
1
0
1
0
2
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
5
0
2
2
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
1
0
1
2
0
0
0
0
0
0
0
0
1
3
1
0
0
0
0
0
1
0
2
0
0
2
1
0
1
0
1
0
0
0
0
0
1
0
1
0
14
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
3
4
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
3
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
5
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
3
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
1
0
0
2
1
1
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
2
1
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
1
0
2
1
0
0
0
3
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
2
0
0
0
0
0
1
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
8
2
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
3
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
1
2
2
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
2
0
0
0
0
1
1
0
1
0
0
2
0
0
0
0
0
1
0
1
0
0
0
4
0
1
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
2
0
2
0
1
0
0
0
0
0
10
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
1
0
0
1
1
1
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
6
0
0
0
2
0
0
3
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
3
0
0
0
0
1
0
0
1
0
0
2
0
0
2
0
1
0
0
0
0
0
2
1
2
2
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
2
0
2
0
0
0
0
3
1
0
0
0
0
0
2
0
0
3
1
0
0
1
0
1
1
0
0
2
0
0
0
0
0
1
0
1
0
5
0
0
0
0
0
0
1
2
0
0
0
6
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
1
2
0
2
0
4
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
4
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
2
0
1
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
2
0
0
0
1
0
1
0
0
0
0
0
2
0
0
1
2
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
5
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
1
0
1
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
3
0
0
0
0
1
0
0
0
0
0
0
2
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
1
0
2
1
1
0
0
1
0
0
0
0
0
2
2
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
3
2
0
1
0
0
0
2
0
0
0
1
2
0
3
0
0
0
0
0
0
0
0
0
1
1
0
9
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
2
3
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
3
2
1
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
3
0
0
2
0
2
7
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
1
1
2
0
0
2
0
0
0
1
0
0
0
3
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
1
1
0
1
0
6
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
1
0
0
0
0
0
4
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
3
0
0
0
0
0
0
0
6
7
0
1
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
7
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
1
3
0
0
1
0
0
4
0
1
3
0
0
2
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
4
0
0
0
0
1
0
2
0
0
0
0
1
1
0
2
1
1
0
0
1
0
5
0
1
0
0
0
0
1
0
2
0
0
0
0
0
1
5
0
0
0
0
6
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
1
0
0
0
1
0
0
0
1
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
1
2
0
0
1
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
2
2
3
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
3
0
0
2
0
0
0
0
2
0
2
0
1
0
0
0
2
2
0
0
0
4
0
2
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
1
4
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
2
2
0
0
0
1
0
1
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
3
1
1
0
0
2
1
0
0
1
0
4
0
0
1
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
3
1
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
2
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
1
1
1
2
0
0
0
4
0
4
0
1
5
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
4
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
1
3
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
2
1
0
0
0
2
2
0
0
0
2
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
5
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
5
0
2
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
3
0
1
0
0
1
0
1
0
2
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
3
2
0
6
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
1
1
0
0
2
2
0
0
0
0
0
2
1
0
0
1
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
2
0
0
2
1
0
0
0
0
0
0
1
2
1
2
0
4
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
2
2
1
2
0
1
0
0
0
0
0
2
0
0
0
2
0
0
2
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
4
0
1
2
0
2
1
0
0
0
3
1
0
0
0
0
0
3
0
0
0
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
6
0
0
0
1
0
0
0
3
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
1
0
3
0
0
1
0
0
0
2
2
0
0
2
0
0
0
0
0
4
1
0
0
2
0
2
2
0
0
0
0
0
3
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
3
0
1
0
0
0
0
1
0
0
1
2
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
3
0
0
0
0
3
0
0
2
0
1
0
2
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
1
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
2
0
0
0
1
0
2
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
2
1
1
0
0
0
0
0
0
3
0
0
0
0
2
3
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
1
2
0
2
1
0
0
2
2
0
3
0
0
0
0
2
0
1
1
2
1
1
0
0
1
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
1
0
0
2
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
6
0
1
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
1
0
1
0
1
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
4
2
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
3
3
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
2
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
1
1
0
1
0
1
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
3
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
3
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
1
2
3
0
0
0
2
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
3
0
0
0
1
0
5
1
0
3
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
7
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
1
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
1
1
2
0
0
0
0
0
0
0
1
0
1
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
1
2
0
1
2
0
0
0
0
2
4
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
3
0
0
2
4
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
3
0
1
0
2
1
2
1
1
4
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
1
1
0
2
5
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
2
0
1
2
0
0
0
1
2
0
0
3
0
1
0
0
2
2
1
0
3
0
0
2
1
1
0
0
0
2
0
1
1
0
0
0
1
0
1
0
0
0
3
0
0
0
3
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
1
0
0
0
0
1
6
1
0
0
0
2
0
0
0
0
3
0
1
0
2
4
0
0
1
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
7
2
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
1
0
1
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
2
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
3
2
1
0
2
0
0
0
0
2
0
0
2
0
1
1
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
2
0
2
1
0
0
0
1
0
0
0
0
2
2
0
0
0
1
0
0
1
0
1
0
0
3
0
0
1
0
0
3
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
1
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
1
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
2
1
0
0
0
0
0
0
5
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
6
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
4
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
3
1
0
0
1
0
2
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
1
0
2
0
1
0
0
0
3
0
0
5
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
3
0
2
0
0
2
0
0
0
2
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
1
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
2
0
0
0
1
1
0
0
2
0
0
2
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
9
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
2
5
0
0
2
0
0
0
0
2
0
0
1
1
0
2
0
0
0
2
0
2
0
0
1
4
0
0
3
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
3
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
1
4
0
0
1
0
0
0
0
2
1
0
0
0
1
2
0
0
0
0
0
2
0
2
0
0
0
2
2
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
1
0
0
0
1
2
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
1
0
1
0
0
0
0
1
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
9
1
2
0
1
2
2
0
0
0
1
0
3
0
2
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
1
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
2
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
5
0
0
0
0
0
3
0
0
0
2
0
1
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
3
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
2
0
0
3
0
1
0
0
0
1
0
0
0
0
2
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
2
0
0
2
0
0
0
2
0
1
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
8
1
0
0
0
2
0
0
0
1
0
0
2
4
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
1
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
2
0
0
7
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
1
0
0
2
1
0
0
2
2
0
2
0
3
0
1
1
0
0
0
0
0
0
0
2
0
2
1
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
9
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
1
0
0
0
0
1
0
0
0
0
2
1
0
0
0
1
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
3
3
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
2
0
0
1
1
0
0
1
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
15
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
5
0
0
0
5
1
0
0
0
1
2
1
2
0
4
0
0
1
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
2
0
0
0
0
1
0
4
0
0
0
0
0
2
3
0
0
1
1
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
6
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
5
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
2
1
0
2
0
4
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
6
2
0
0
0
0
0
1
1
0
1
2
1
0
0
0
0
0
0
1
4
3
2
0
2
2
1
0
1
0
0
2
0
0
0
1
0
0
0
2
0
0
0
2
3
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
2
7
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
2
0
1
0
1
0
0
0
2
0
0
0
0
0
3
1
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
3
0
2
0
4
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
2
7
0
2
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
3
2
2
0
0
0
0
0
2
2
1
0
0
0
0
1
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
1
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
3
0
0
2
2
3
0
1
0
0
1
2
1
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
8
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
1
0
1
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
1
3
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
1
0
2
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
1
0
0
1
2
0
0
1
0
0
0
2
2
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
6
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
3
4
0
0
1
2
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
2
3
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
3
1
0
3
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
2
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
1
1
0
1
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
14
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
5
1
0
0
2
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
1
1
0
0
5
0
0
0
0
0
0
5
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
3
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
2
0
0
0
0
1
0
0
0
0
0
1
1
1
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
3
0
0
4
0
0
0
2
1
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
1
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
5
1
0
0
0
0
0
0
0
2
0
0
0
0
8
2
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
1
1
2
2
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
2
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
1
2
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
2
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
1
1
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
1
1
0
0
0
0
1
7
1
0
3
0
0
0
0
0
2
5
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
1
1
0
2
0
0
0
4
0
1
0
0
0
2
1
0
0
0
0
0
0
1
2
0
1
0
1
0
0
1
0
1
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
3
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
1
0
1
0
3
0
1
0
0
1
0
2
0
1
0
0
0
2
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
2
1
0
0
0
2
1
0
0
0
0
0
0
0
2
0
2
0
0
0
1
2
0
5
0
0
1
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
5
0
0
0
0
0
0
1
0
1
0
2
2
0
1
0
0
0
4
2
2
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
2
0
3
0
0
0
0
0
1
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
1
0
3
1
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
3
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
4
0
0
0
0
0
0
2
1
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
3
4
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
1
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
2
1
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
1
1
0
0
0
6
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
2
0
0
1
2
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
5
1
0
0
0
1
0
0
0
0
0
1
0
2
0
2
0
2
1
0
0
2
0
0
3
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
2
1
0
1
0
0
0
2
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
1
1
0
0
1
0
2
1
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
3
0
0
0
0
1
0
0
0
2
0
0
0
1
1
0
0
1
0
2
0
0
0
0
1
1
0
1
1
0
0
2
0
0
0
1
0
0
0
0
3
0
0
1
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
2
1
0
0
12
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
3
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
1
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
2
0
0
0
1
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
3
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
1
1
0
0
0
4
0
0
0
0
0
0
0
0
1
2
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
2
0
2
1
0
0
0
1
0
0
0
2
1
0
0
0
6
1
2
4
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
3
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
1
0
1
1
0
4
1
0
1
0
0
0
2
2
0
0
1
2
0
0
0
0
0
0
2
0
0
1
0
0
1
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
3
1
1
0
0
0
2
0
0
0
0
2
0
0
0
1
2
0
1
0
0
0
2
3
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
2
0
0
1
0
0
2
1
2
0
0
2
0
0
1
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
2
0
3
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
2
1
0
1
0
0
0
0
0
0
2
1
0
0
1
0
2
2
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
1
3
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
1
0
0
0
0
0
2
0
0
5
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
3
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
1
0
0
0
1
0
1
0
0
0
4
2
1
0
2
0
0
0
0
0
0
0
0
5
1
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
1
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
4
1
0
0
0
0
0
0
2
2
0
0
0
0
2
3
2
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
1
2
0
0
0
0
1
0
3
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
2
0
1
0
3
0
2
2
0
0
0
1
0
2
0
1
0
0
0
0
0
2
0
2
0
0
1
0
1
0
0
1
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
2
0
1
0
0
1
0
0
0
0
0
2
6
0
0
3
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
3
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
1
0
0
0
1
0
4
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
1
0
2
1
0
0
0
0
7
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
1
0
1
2
2
2
0
0
0
0
0
0
0
0
2
4
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
5
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
1
2
0
0
0
0
1
0
0
0
3
0
1
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
1
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
2
0
1
3
0
1
0
1
0
0
2
0
2
2
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
2
0
1
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
1
0
0
1
0
0
2
1
0
0
0
0
0
0
0
1
0
8
0
0
1
2
0
0
3
2
3
0
0
0
0
0
1
0
1
2
0
0
2
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
1
3
0
6
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
4
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
3
0
0
0
0
3
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
1
7
2
0
0
0
2
1
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
2
0
2
1
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
3
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
1
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
1
2
0
0
0
0
1
0
0
0
0
2
0
0
6
0
0
2
0
0
1
0
0
0
0
0
0
4
0
0
0
1
0
1
0
3
0
0
0
0
1
1
2
0
0
0
1
1
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
1
2
0
1
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
1
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
4
3
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
4
0
0
0
3
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
2
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
8
0
1
0
0
0
2
0
0
0
2
0
0
2
0
2
0
0
0
3
0
0
1
0
0
5
1
0
0
0
0
0
5
0
2
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
1
0
0
0
2
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
2
0
0
0
2
0
1
0
0
0
1
0
2
0
0
0
2
0
2
0
8
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
3
1
2
0
1
0
0
1
0
4
1
0
0
0
0
1
1
1
1
3
0
0
0
0
0
2
0
0
0
2
0
2
1
0
2
0
2
0
0
0
0
0
0
0
0
0
4
2
0
0
1
0
0
0
0
1
0
0
1
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
1
0
0
0
2
1
0
0
0
0
1
1
1
0
0
0
1
0
2
0
0
4
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
2
2
2
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
2
1
4
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
3
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
6
6
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
1
2
2
0
0
0
0
0
0
1
0
2
1
0
0
0
2
1
0
3
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
1
2
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
3
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
4
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
7
1
0
0
0
0
0
0
0
0
1
1
2
1
1
0
0
2
0
1
2
0
2
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
3
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
2
1
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
6
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
2
1
0
1
0
4
0
0
0
1
0
0
1
0
2
1
0
2
1
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
3
2
0
0
1
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
1
2
5
0
1
2
0
0
0
2
0
0
0
1
1
0
0
0
1
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
1
0
0
5
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
9
1
0
0
0
5
2
0
1
0
0
0
1
0
1
2
0
0
0
0
0
0
2
0
2
1
0
0
0
3
0
0
0
1
0
0
2
1
0
0
2
0
1
0
0
0
2
0
1
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
1
1
9
0
0
1
0
0
0
0
0
0
1
2
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
2
4
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
5
1
0
2
0
0
2
0
6
0
0
0
0
1
1
0
1
0
2
0
0
1
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
3
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
5
0
1
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
2
0
1
2
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
2
0
0
0
0
1
0
2
0
0
3
0
0
0
0
0
0
3
2
1
0
0
0
0
3
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
1
2
0
3
0
0
1
0
0
1
1
0
0
0
0
0
0
1
2
0
0
0
1
4
0
0
1
0
0
2
0
0
2
0
1
2
1
1
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
4
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
2
0
0
3
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
1
0
0
0
0
2
9
1
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
3
0
1
0
1
0
0
0
1
2
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
3
0
1
0
1
0
1
0
0
0
2
0
0
0
2
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
2
1
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
2
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
3
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
1
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
1
0
1
0
3
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
3
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
2
1
0
0
0
0
2
0
0
0
0
2
1
0
1
2
0
0
1
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
2
2
2
0
0
0
0
0
0
1
1
2
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
2
2
1
0
0
1
0
0
0
1
1
1
0
0
0
0
0
1
1
0
0
0
1
1
1
1
0
0
1
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
2
1
2
0
0
2
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
6
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
1
0
0
0
1
0
0
1
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
1
0
0
1
0
0
0
1
2
0
1
5
0
1
1
0
1
1
0
0
2
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
3
2
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
2
1
0
0
0
2
0
0
0
2
0
0
0
0
0
3
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
2
0
0
0
2
0
0
3
0
2
0
3
0
6
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
1
1
0
0
2
1
0
2
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
1
0
0
0
0
0
0
2
1
7
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
1
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
8
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
1
2
0
0
0
3
0
0
3
0
1
0
0
0
2
0
0
0
2
0
1
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
4
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
2
0
1
1
4
0
0
1
0
0
0
0
1
0
0
3
1
1
0
0
2
0
0
1
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
8
2
0
0
0
1
0
0
0
0
2
3
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
5
2
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
1
0
3
0
0
0
0
4
2
0
0
1
0
0
0
1
2
0
0
0
0
1
0
2
0
0
0
1
6
0
1
1
0
0
0
0
0
0
2
0
1
0
0
0
2
0
2
0
0
0
0
0
0
1
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
1
2
0
1
0
2
4
0
0
1
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
1
0
1
0
1
0
0
0
0
2
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
3
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
6
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
3
0
0
0
0
3
0
1
0
0
2
0
0
0
0
0
0
0
2
0
1
2
0
0
1
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
1
1
1
0
0
0
2
1
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
3
0
0
0
1
2
0
0
0
0
0
0
0
0
1
1
0
2
1
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
1
2
2
0
0
1
4
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
1
0
2
2
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
7
0
0
0
0
0
3
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
7
0
3
1
1
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
4
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
3
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
2
2
0
0
0
0
0
5
0
1
0
2
0
2
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
7
0
0
1
0
1
0
0
0
3
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
2
0
1
0
0
0
7
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
1
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
2
0
1
0
24
0
1
0
0
0
0
0
0
1
0
0
32
0
0
2
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
2
2
0
3
3
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
2
0
0
2
1
0
0
2
0
0
0
5
1
0
1
0
0
0
0
0
0
0
0
0
3
0
0
1
0
2
0
0
0
0
2
2
0
1
0
0
0
0
2
1
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
1
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
6
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
3
0
2
1
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
3
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
1
0
0
0
3
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
6
1
0
0
0
0
0
2
1
1
2
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
2
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
1
0
0
0
2
1
4
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
3
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
2
2
2
2
1
0
0
0
0
1
0
1
2
0
4
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
5
0
0
0
0
0
7
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
5
0
0
0
2
0
0
1
4
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
4
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
2
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
1
1
0
0
0
0
2
0
0
0
1
0
0
0
0
1
6
0
0
0
2
2
1
2
2
0
0
2
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
1
0
0
0
0
0
2
0
2
0
0
0
0
1
0
3
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
3
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
1
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
1
2
2
0
0
0
0
0
2
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
1
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
3
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
1
0
0
0
1
2
3
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
4
2
0
0
0
0
0
0
0
1
0
0
1
0
0
1
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
4
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
5
0
0
0
0
0
2
0
3
0
0
2
0
0
1
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
2
0
1
1
2
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
1
0
0
2
0
0
0
2
0
1
0
1
0
0
3
0
1
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
2
1
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
2
0
0
1
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
0
1
2
2
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
5
2
1
2
0
0
0
0
0
0
1
2
0
0
1
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
1
0
0
0
3
0
2
0
1
0
0
1
1
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
1
0
3
0
0
0
3
0
0
0
0
0
0
1
0
4
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
1
0
2
1
0
0
0
0
0
0
2
0
1
0
1
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
3
0
0
0
1
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
1
0
2
1
2
0
0
0
2
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
1
2
0
1
0
0
0
0
0
0
0
0
0
0
4
1
0
0
2
0
1
0
0
1
0
2
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
3
2
0
0
0
2
0
0
0
0
0
0
6
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
2
0
0
1
1
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
1
0
0
0
2
3
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
5
1
0
0
2
0
0
1
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
6
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
1
0
0
0
5
2
0
0
0
0
0
1
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
6
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
2
2
2
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
2
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
2
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
2
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
7
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
1
0
0
0
1
2
0
2
1
0
0
0
0
0
4
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
1
0
5
0
0
0
0
0
1
2
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
1
0
4
0
3
0
0
0
0
0
0
0
1
0
0
0
1
0
1
3
1
0
1
0
0
2
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
1
1
0
0
0
8
0
0
2
0
0
0
3
0
2
0
1
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
3
1
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
1
0
2
0
0
0
2
2
0
1
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
3
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
3
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
1
0
0
1
0
0
0
0
1
0
1
0
1
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
3
2
2
0
0
0
2
0
2
0
0
0
1
0
0
3
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
1
1
2
2
0
0
2
2
2
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
6
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
1
0
0
6
0
0
2
4
0
1
0
0
0
0
0
3
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
5
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
0
2
2
0
0
0
0
0
0
2
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
1
0
1
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
1
2
0
0
1
0
0
0
0
1
0
1
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
2
1
2
0
0
4
0
1
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
3
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
11
0
0
2
0
0
0
0
0
0
0
0
1
1
0
2
4
0
2
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
4
0
0
3
1
0
2
0
3
0
0
0
0
0
3
0
0
0
2
0
6
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
9
2
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
3
0
1
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
2
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
2
9
0
2
0
0
0
0
0
1
4
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
4
1
2
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
1
1
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
3
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
2
0
0
0
1
2
2
0
2
1
1
0
0
3
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
6
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
1
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
2
2
0
0
0
1
0
0
0
0
0
1
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
3
0
0
2
0
0
2
2
0
0
0
0
0
2
0
0
2
2
0
2
1
1
1
0
2
0
1
1
0
0
0
0
0
0
0
2
0
2
2
2
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
4
0
1
0
0
2
0
0
2
1
0
2
0
0
0
0
1
0
0
1
3
0
1
0
0
0
2
2
0
2
4
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
3
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
3
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
3
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
1
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
7
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
3
2
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
1
1
0
0
2
2
0
0
0
0
0
2
1
0
0
0
2
0
0
1
1
3
0
0
0
2
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
3
1
0
1
0
0
0
1
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
1
0
2
7
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
3
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
3
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
3
0
0
1
1
0
4
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
6
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
2
1
0
0
2
0
0
0
2
0
1
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
2
3
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
2
1
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
1
2
2
0
0
2
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
1
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
1
0
3
1
0
0
0
0
3
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
1
0
2
0
0
0
0
0
1
0
0
3
1
0
0
0
0
0
0
1
0
1
0
3
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
2
0
3
0
0
1
0
2
2
0
0
1
0
0
0
1
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
5
0
0
0
0
0
0
2
0
1
0
0
0
2
0
3
0
1
0
0
1
0
0
1
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
1
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
2
0
0
0
1
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
3
3
3
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
2
0
4
0
0
0
2
2
0
0
0
0
1
0
0
1
0
3
0
0
0
1
0
0
1
2
1
0
2
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
3
0
2
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
4
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
2
0
1
1
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
1
0
2
0
3
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
2
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
4
0
3
2
0
2
0
0
1
0
1
0
0
0
2
2
0
0
0
0
0
0
0
1
1
2
2
0
3
3
0
0
0
0
0
0
1
2
0
0
4
0
0
0
0
0
1
0
1
1
0
0
2
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
2
2
1
2
2
0
0
0
0
0
1
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
2
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
2
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
3
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
1
1
1
2
0
0
0
0
2
0
0
0
0
0
0
0
3
2
0
0
2
2
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
3
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
3
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
6
1
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
3
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
2
1
1
0
5
1
0
0
2
0
0
0
0
0
2
0
0
0
0
3
0
0
0
1
1
0
0
0
0
3
0
2
0
0
0
0
0
0
0
1
2
2
0
1
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
3
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
1
0
0
0
1
0
1
2
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
3
0
0
0
0
0
0
0
1
0
1
0
2
0
0
1
0
1
0
0
1
0
0
2
0
1
0
0
0
0
1
0
1
0
0
1
4
0
0
2
0
0
0
0
0
3
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
3
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
1
6
2
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
1
0
0
2
2
0
2
1
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
3
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
2
1
0
1
1
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
6
0
0
1
0
0
0
3
0
2
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
1
0
2
0
0
0
2
0
0
0
0
2
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
2
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
3
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
3
0
0
0
2
0
2
0
0
0
2
0
2
0
0
1
1
0
0
0
1
0
0
0
1
2
0
2
1
1
0
0
0
0
1
0
2
0
0
2
2
3
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
3
2
0
0
0
1
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
2
2
0
0
0
1
0
2
0
0
0
0
3
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
2
0
0
0
0
2
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
16
0
3
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
4
0
0
0
0
1
1
2
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
3
0
0
2
0
0
0
0
0
1
7
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
3
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
1
1
0
1
2
1
1
0
1
0
2
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
1
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
1
1
0
0
1
2
0
0
0
1
1
0
0
0
0
1
0
0
0
0
3
2
2
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
2
2
0
0
0
0
0
1
0
0
2
0
1
0
2
0
0
0
2
1
0
0
2
2
0
2
0
0
0
0
0
0
0
2
3
0
1
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
4
0
2
0
0
0
1
0
2
0
0
0
1
0
6
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
2
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
3
0
2
2
0
1
1
0
0
0
0
2
0
0
2
0
0
5
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
2
1
1
0
0
0
0
1
1
0
0
0
1
1
1
0
0
1
0
0
0
0
3
2
1
0
0
0
3
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
6
0
2
0
0
0
5
0
0
0
0
0
0
1
0
2
0
0
0
0
7
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
3
1
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
3
2
0
0
0
0
0
0
0
0
0
0
0
0
4
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
3
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
2
3
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
5
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
1
2
0
0
0
5
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
3
1
1
0
0
0
0
0
0
1
2
1
0
0
1
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
2
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
2
0
4
0
0
0
1
1
0
0
0
3
0
0
2
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
3
0
2
0
0
0
2
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
2
5
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
2
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
3
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
2
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
2
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
1
0
0
0
0
5
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
1
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
2
1
1
0
0
0
0
0
0
0
2
0
0
5
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
2
0
0
0
0
2
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
2
6
2
3
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
1
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
1
0
0
1
4
0
0
0
0
0
0
2
0
0
2
2
0
3
0
1
2
0
0
0
0
0
1
2
0
0
2
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
1
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
1
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
1
1
0
0
0
1
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
3
2
0
0
0
1
0
0
0
0
0
2
0
1
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
3
0
0
0
2
2
0
0
1
2
0
0
2
0
1
0
0
0
2
1
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
11
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
3
0
0
0
0
0
0
1
2
0
1
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
3
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
3
0
0
2
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
4
0
0
0
2
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
2
0
0
1
2
0
0
2
0
3
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
4
0
0
0
0
0
1
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
1
1
4
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
2
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
1
2
0
0
1
0
0
0
1
1
7
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
2
2
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
4
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
6
0
10
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
3
1
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
1
0
2
0
2
0
4
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
3
0
0
1
0
0
0
0
0
0
0
1
0
1
0
2
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
1
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
2
1
0
2
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
2
0
1
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
2
0
0
0
0
2
6
1
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
3
2
2
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
2
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
1
0
2
0
0
0
2
0
1
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
1
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
1
2
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
5
0
1
0
0
0
1
0
0
0
3
0
1
0
0
0
0
0
2
0
2
0
0
6
5
0
0
1
2
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
2
0
2
0
0
0
1
2
2
0
0
0
5
0
0
0
2
2
0
0
0
1
0
2
0
0
0
0
0
0
1
1
0
0
0
1
0
2
0
3
2
0
2
0
0
3
1
4
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
2
0
2
1
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
2
0
0
2
1
0
0
0
0
0
0
0
2
2
0
0
0
1
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
1
0
0
0
0
2
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
2
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
1
0
1
0
0
2
0
0
0
2
1
0
0
1
0
1
0
0
1
0
1
0
2
1
0
1
0
0
1
0
0
0
2
1
0
1
3
0
0
0
0
2
0
1
0
2
0
0
0
2
2
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
1
0
0
3
0
0
0
2
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
3
0
0
0
0
2
0
0
0
2
0
0
0
1
0
2
0
4
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
2
0
0
0
3
1
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
2
0
0
0
0
0
2
1
1
0
0
0
0
0
0
1
2
0
0
1
4
0
0
0
1
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
2
0
3
0
0
0
3
0
0
1
2
0
0
0
0
0
2
0
2
1
5
0
0
1
1
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
1
2
0
2
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
11
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
4
4
0
0
2
5
0
1
0
0
2
0
0
2
0
0
0
2
0
1
0
1
0
0
0
1
2
0
0
2
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
2
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
2
0
2
0
0
1
2
0
1
0
2
0
0
0
0
0
0
0
2
0
2
1
0
2
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
4
1
2
0
0
0
0
0
0
0
4
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
2
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
1
0
0
3
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
2
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
1
0
0
2
1
2
0
0
0
0
0
2
0
2
2
0
1
0
0
1
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
3
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
2
0
2
0
0
0
2
0
2
0
0
0
0
0
2
2
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
7
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
1
4
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
2
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
3
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
4
1
0
0
0
0
0
2
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
2
0
0
0
3
0
0
0
0
5
0
0
1
3
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
3
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
2
1
0
0
0
0
0
0
0
3
0
0
0
1
0
2
0
0
1
0
0
0
2
2
0
2
0
0
0
0
0
1
1
0
0
1
0
0
1
12
0
0
0
0
0
0
0
0
3
1
0
0
1
0
0
0
0
0
0
0
1
2
1
0
0
1
0
0
0
0
0
1
0
0
2
1
2
0
2
1
0
0
0
2
0
2
0
1
1
0
0
0
0
0
1
3
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
3
0
0
2
0
1
0
1
0
1
0
1
0
0
0
0
1
0
1
3
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
5
0
0
0
0
0
2
4
0
0
0
0
0
0
1
1
0
1
0
0
5
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
3
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
1
0
2
1
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
3
3
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
2
1
0
0
3
0
0
2
0
0
0
0
1
0
0
0
2
0
0
1
6
0
2
1
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
3
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
4
0
0
0
1
2
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
7
0
0
0
5
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
7
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
3
1
0
0
2
0
0
1
2
0
0
0
5
0
0
0
1
2
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
6
1
0
3
3
0
0
0
0
0
0
0
3
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
1
2
1
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
3
0
1
0
0
0
2
1
0
0
1
3
0
0
1
0
0
1
2
0
1
0
0
0
0
0
0
0
2
0
0
0
2
2
5
0
0
1
0
14
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
3
0
2
1
0
0
0
1
5
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
3
0
0
0
0
0
1
6
0
1
0
2
2
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
2
2
0
0
0
0
1
0
0
0
4
0
2
0
2
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
7
1
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
2
0
2
1
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
3
0
1
0
1
0
1
1
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
5
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
2
0
2
2
2
0
0
11
0
0
4
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
2
0
0
2
2
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
1
0
0
0
0
3
1
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
1
2
0
0
0
0
0
0
9
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
2
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
1
0
1
0
0
0
0
0
2
2
0
0
1
0
0
0
0
1
0
3
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
4
0
0
0
1
0
1
3
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
1
0
1
0
1
0
2
2
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
3
2
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
3
2
0
2
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
2
2
0
0
0
1
1
2
0
0
2
0
0
1
1
0
0
2
0
0
0
2
0
2
0
2
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
1
0
6
0
0
0
0
0
0
2
0
0
0
2
2
0
0
2
0
0
2
0
1
0
0
1
0
0
0
2
0
0
1
0
0
0
1
0
2
0
2
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
5
0
1
0
0
0
2
0
1
1
0
1
1
0
0
1
0
0
0
0
1
0
0
1
2
0
1
0
2
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
30
0
0
0
2
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
3
0
1
1
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
1
0
2
1
0
0
2
0
0
0
2
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
1
0
0
0
0
0
0
1
0
1
1
0
1
0
0
2
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
1
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
1
0
1
0
2
0
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
2
0
0
1
2
0
0
1
0
0
0
0
0
1
0
1
1
1
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
3
0
0
0
0
1
0
0
0
2
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
6
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
11
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
2
1
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
1
4
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
7
0
1
0
1
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
2
0
0
0
0
5
0
0
0
0
0
0
0
0
1
0
0
0
3
0
2
1
0
0
0
0
2
0
0
0
0
3
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
4
0
0
0
0
0
0
0
1
0
0
1
1
0
2
0
0
0
2
0
1
3
3
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
2
0
0
1
0
0
0
0
0
7
0
3
0
0
0
2
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
1
0
0
0
1
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
2
0
0
0
0
0
0
2
0
2
0
1
2
0
0
0
0
0
1
0
0
2
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
6
0
0
0
1
7
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
5
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
7
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
2
2
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
1
1
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
4
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
3
2
0
0
0
0
2
1
0
4
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
2
1
0
0
0
0
0
2
0
0
0
0
0
1
0
1
5
2
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
3
0
0
2
1
2
2
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
2
2
0
2
2
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
3
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
2
0
1
0
2
0
1
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
1
0
2
3
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
8
2
0
0
0
1
0
0
1
0
0
1
0
1
0
0
2
0
0
0
0
2
0
0
0
3
0
0
2
2
0
1
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
3
0
0
0
0
0
6
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
1
0
1
1
1
2
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
2
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
1
7
3
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
1
0
1
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
3
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
3
1
0
0
0
2
0
0
2
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
3
0
0
2
2
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
5
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
1
1
0
0
2
1
0
0
0
0
0
0
0
0
0
3
0
2
0
0
1
0
3
1
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
1
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
1
0
0
1
0
9
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
1
0
1
0
0
0
1
0
3
0
0
0
0
2
0
1
1
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
2
2
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
3
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
1
0
1
0
0
1
0
1
2
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
2
1
0
0
0
2
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
3
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
11
2
0
0
0
0
3
0
0
1
1
0
0
0
0
0
0
0
2
1
0
0
0
0
3
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
2
2
0
0
5
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
3
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
3
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
3
0
2
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
8
0
0
0
2
0
5
0
0
0
1
0
1
1
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
2
0
0
1
1
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
2
0
2
0
0
1
0
0
0
2
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
1
2
2
1
0
0
0
4
1
0
1
2
0
0
0
0
0
1
0
2
0
2
0
0
0
2
1
0
0
0
0
0
1
2
0
0
1
0
0
0
0
4
1
2
0
0
0
5
0
0
0
0
0
0
2
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
2
2
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
3
1
0
1
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
1
1
3
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
1
0
0
0
3
0
0
0
0
0
0
1
1
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
1
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
2
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
3
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
2
1
0
0
0
0
1
0
0
2
0
2
1
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
1
1
0
0
0
0
2
0
2
1
1
0
0
0
0
0
5
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
2
0
0
3
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
3
0
0
0
2
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
2
0
0
0
1
0
0
1
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
2
2
0
3
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
3
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
2
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
1
2
2
0
1
0
0
0
0
1
0
3
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
2
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
1
0
1
3
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
3
0
1
0
0
0
0
0
2
4
0
2
2
0
1
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
3
1
1
0
2
1
0
0
0
2
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
7
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
7
0
0
0
0
2
0
0
1
1
0
0
0
1
0
0
1
1
0
1
0
2
0
1
0
2
1
0
0
0
1
0
1
0
1
0
0
0
0
0
4
0
0
0
0
0
1
1
0
4
0
2
2
0
0
2
0
1
2
1
0
0
0
5
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
1
2
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
5
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
1
0
0
0
0
0
2
4
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
2
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
2
1
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
2
4
2
0
1
0
0
2
0
2
0
1
0
0
0
0
0
2
0
0
2
1
0
0
2
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
3
0
1
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
3
0
2
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
1
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
1
1
1
0
2
0
0
0
3
0
1
0
1
1
0
0
0
0
0
3
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
1
1
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
1
0
1
0
0
0
0
0
0
0
0
3
0
0
2
0
3
0
1
0
0
0
2
0
2
0
0
2
2
0
2
0
0
2
0
7
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
1
0
0
1
0
1
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
3
0
0
0
7
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
2
0
0
1
0
2
2
0
0
3
2
0
0
1
0
0
0
0
3
0
2
0
0
0
0
0
2
1
0
0
0
0
1
1
1
2
0
0
0
0
0
0
0
0
1
1
0
3
0
0
0
0
1
2
0
0
1
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
2
0
0
0
1
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
2
0
1
2
4
0
1
0
0
0
0
2
2
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
5
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
2
2
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
2
0
0
0
1
0
0
1
0
0
3
0
3
0
0
0
0
1
0
1
0
0
0
0
2
1
0
1
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
2
2
0
0
0
0
0
1
0
1
0
0
2
0
0
0
1
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
1
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
13
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
2
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
1
0
2
0
0
0
0
0
4
3
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
3
2
0
0
1
1
0
0
2
2
4
0
3
0
1
2
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
1
1
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
2
0
2
0
0
0
0
2
0
4
2
0
0
0
0
0
2
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
3
0
0
1
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
2
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
3
0
1
0
3
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
1
0
1
0
0
0
0
0
2
0
1
0
1
0
0
2
0
0
0
0
0
0
0
3
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
4
1
0
1
0
0
0
0
0
2
0
2
2
0
0
1
1
0
0
2
0
0
0
1
5
0
0
0
1
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
5
0
0
0
2
2
1
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
1
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
6
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
4
0
2
0
1
1
0
0
4
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
2
0
4
1
0
1
2
2
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
1
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
2
0
0
0
2
0
1
0
0
0
0
0
1
0
1
1
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
3
0
0
1
2
0
1
0
0
2
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
5
2
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
6
1
1
2
0
0
0
0
1
1
0
0
0
2
0
3
0
4
0
0
2
0
2
3
0
0
0
2
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
5
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
1
0
1
0
0
0
0
0
0
2
0
0
2
1
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
5
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
1
1
0
0
0
1
0
0
0
0
1
2
1
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
3
1
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
2
0
0
1
0
2
0
2
0
3
0
0
2
0
0
0
0
0
2
1
0
0
1
0
3
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
4
3
2
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
1
0
2
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
3
2
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
2
0
0
3
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
4
2
2
0
0
1
0
0
0
0
1
0
4
0
0
2
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
3
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
2
0
0
0
1
0
1
0
0
1
0
0
1
0
2
0
2
0
0
3
0
1
0
0
0
1
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
5
0
0
1
0
1
0
0
0
0
0
1
0
1
1
0
0
2
0
0
0
0
1
0
0
0
4
1
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
1
2
4
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
1
0
0
0
1
0
0
0
2
5
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
8
3
0
2
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
3
0
0
3
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
3
2
1
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
8
0
2
0
0
3
0
0
0
0
1
0
2
0
4
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
2
2
0
0
3
0
0
0
0
0
0
3
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
6
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
3
0
0
2
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
4
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
5
0
0
0
0
0
2
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
3
0
0
0
0
0
1
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
6
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
3
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
2
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
1
0
0
0
0
2
1
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
2
0
0
1
0
1
2
0
0
0
0
1
2
1
0
0
0
2
3
2
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
1
0
0
0
1
0
0
0
0
0
2
0
1
0
0
2
0
0
2
0
0
1
0
0
2
0
0
0
0
0
1
0
1
0
1
1
0
0
0
2
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
1
0
2
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
2
0
0
0
1
0
0
3
0
0
0
2
0
0
1
2
0
3
0
0
0
0
0
0
1
0
0
3
1
0
0
3
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
3
1
0
0
0
0
0
0
2
0
1
0
1
0
1
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
3
1
0
1
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
2
0
2
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
1
0
0
0
2
0
0
3
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
1
0
2
0
0
0
0
0
0
0
1
0
0
2
1
0
1
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
3
0
1
0
0
1
0
0
4
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
1
0
2
1
1
0
0
0
2
0
2
2
3
3
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
1
0
1
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
2
0
0
0
0
0
1
2
0
0
3
2
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
1
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
1
2
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
2
0
3
0
0
0
0
1
3
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
2
1
1
0
2
0
0
0
0
1
0
0
3
0
3
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
2
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
1
0
3
0
0
0
0
0
0
0
0
2
0
2
0
1
6
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
5
1
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
6
2
0
0
0
0
0
0
0
0
1
2
0
4
4
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
3
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
3
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
2
1
1
0
0
13
0
0
1
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
4
6
2
2
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
1
7
1
0
0
0
0
4
0
0
1
0
2
0
0
0
0
0
2
1
2
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
1
0
3
0
0
0
1
0
0
0
0
1
0
0
2
0
1
0
0
3
0
0
2
0
0
2
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
8
2
2
0
0
0
0
1
0
0
3
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
1
0
0
0
1
0
0
2
0
0
2
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
1
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
4
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
3
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
3
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
1
1
2
0
0
0
0
2
2
0
0
2
0
0
0
3
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
3
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
2
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
5
0
1
0
0
2
0
0
0
6
1
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
6
2
0
0
0
2
0
0
0
1
0
0
0
2
3
0
0
0
0
2
2
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
1
2
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
3
0
0
0
0
0
1
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
2
1
2
0
0
4
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
7
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
3
1
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
2
2
0
0
0
0
1
0
0
0
0
2
1
1
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
2
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
3
2
2
0
0
13
0
2
5
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
3
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
1
2
2
1
1
0
0
4
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
3
0
1
1
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
3
2
0
0
0
1
0
1
0
0
0
1
0
2
0
0
0
0
2
0
1
0
0
1
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
2
0
0
1
0
2
2
1
2
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
3
0
0
0
0
1
0
1
2
1
0
0
3
0
1
0
1
0
0
1
0
0
0
2
2
0
0
0
0
1
0
3
0
0
1
3
0
2
0
3
0
2
0
2
0
0
1
0
0
0
0
0
6
0
0
1
1
0
3
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
1
2
0
4
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
9
0
0
0
0
0
2
0
0
1
0
0
0
0
2
6
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
2
0
0
0
3
0
0
0
1
1
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
1
0
1
4
2
2
0
0
0
0
3
0
0
0
1
1
0
0
0
0
0
1
0
3
0
0
0
3
1
0
3
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
2
0
6
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
2
2
0
0
1
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
1
0
4
0
0
0
0
2
0
4
0
0
0
0
5
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
3
0
0
1
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
4
2
10
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
2
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
6
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
2
0
0
1
0
0
0
2
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
1
0
0
2
1
0
0
1
0
1
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
1
3
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
4
0
3
2
0
0
0
0
3
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
3
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
2
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
2
0
1
0
0
0
1
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
2
0
0
0
3
0
1
0
0
0
0
1
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
9
0
0
0
0
0
2
0
0
1
0
0
1
0
1
0
0
0
2
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
1
1
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
1
0
0
0
1
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
2
1
0
0
2
1
0
3
1
0
0
0
2
0
0
1
0
1
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
2
0
0
1
0
1
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
2
0
3
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
1
0
2
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
2
0
5
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
3
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
1
0
0
0
4
0
3
1
0
0
0
0
0
5
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
3
1
0
0
0
0
1
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
1
3
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
3
0
0
2
1
0
2
0
0
2
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
8
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
3
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
12
0
0
0
1
0
0
0
0
2
2
7
1
0
0
2
2
0
3
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
3
0
0
0
0
0
0
8
2
0
0
0
0
0
0
3
0
0
0
0
6
0
0
0
0
2
1
2
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
1
3
1
0
0
0
0
0
0
1
0
0
0
3
0
2
0
1
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
2
0
0
0
2
0
1
5
0
1
1
2
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
1
0
2
0
0
2
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
1
1
0
2
2
0
0
0
0
7
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
3
0
0
0
2
0
0
2
1
0
1
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
1
0
2
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
5
0
0
5
0
1
0
1
0
0
0
1
0
0
0
0
1
0
1
0
1
3
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
1
0
2
0
0
0
0
0
0
0
0
2
0
1
7
0
0
2
0
0
0
1
4
0
0
1
0
0
0
4
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
2
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
2
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
3
1
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
1
2
0
0
0
2
0
0
0
1
0
1
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
3
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
2
0
1
2
0
0
0
0
0
0
0
0
0
3
0
1
0
0
1
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
3
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
3
3
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
3
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
2
1
0
3
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
3
0
0
1
0
1
0
0
0
2
1
0
2
0
0
0
4
0
4
0
0
0
0
0
0
0
0
0
0
3
1
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
3
2
1
2
0
1
0
1
0
0
1
0
1
0
0
0
3
1
1
0
0
0
0
0
0
1
0
0
0
2
1
0
0
1
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
2
0
0
0
0
1
0
0
0
0
3
3
0
0
2
0
0
0
2
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
2
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
3
0
0
0
0
0
0
1
0
0
1
0
3
0
0
0
5
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
2
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
2
1
2
0
0
2
2
0
2
1
10
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
2
0
0
1
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
2
0
0
1
0
0
3
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
2
0
2
0
0
0
0
0
0
2
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
1
0
2
0
0
0
0
1
0
2
0
0
0
1
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
1
2
1
1
0
0
0
7
0
2
0
2
3
0
0
1
0
1
0
0
0
1
0
0
0
0
0
4
0
0
0
2
1
0
0
0
3
0
0
0
1
0
6
0
3
3
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
3
0
0
0
0
0
5
0
0
0
0
1
1
0
2
3
1
0
1
1
0
2
2
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
2
0
1
1
0
0
0
0
0
0
0
1
1
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
5
0
0
0
0
1
0
3
1
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
2
1
0
3
0
0
0
0
0
3
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
2
1
0
0
0
3
0
0
0
0
0
0
1
0
0
1
1
0
3
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
2
0
0
1
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
6
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
3
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
2
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
2
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
3
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
2
1
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
2
0
2
1
0
3
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
2
0
0
1
0
1
0
2
0
0
2
0
0
2
0
0
1
0
1
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
2
0
4
0
2
3
0
0
0
0
0
0
0
0
0
0
3
1
0
0
3
1
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
1
2
0
2
2
1
0
1
3
0
1
0
0
0
2
2
0
4
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
2
0
2
1
1
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
2
1
0
2
0
2
2
0
0
2
0
0
1
0
0
2
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
1
1
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
1
0
1
2
0
1
0
0
0
0
1
1
2
0
0
1
0
2
0
0
0
0
2
0
2
0
0
2
0
0
2
2
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
5
0
1
1
0
0
0
2
8
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
3
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
1
1
0
0
2
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
2
2
0
0
1
1
0
0
1
0
2
0
1
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
3
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
2
2
0
0
0
0
1
1
0
0
0
0
0
0
6
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
1
0
0
0
1
1
2
1
0
1
0
0
0
0
1
0
2
0
0
0
2
1
0
1
0
1
1
2
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
3
8
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
9
0
0
0
0
0
1
1
0
0
0
0
0
0
0
3
0
1
0
1
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
3
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
2
0
1
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
1
2
0
0
2
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
1
1
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
2
0
0
1
0
2
0
5
1
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
1
2
0
2
0
0
2
2
0
3
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
1
1
1
0
1
0
0
5
1
0
2
0
1
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
6
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
4
0
0
0
0
1
0
0
2
0
0
1
0
3
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
1
0
0
2
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
4
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
2
0
0
0
2
0
0
0
0
0
2
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
3
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
2
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
5
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
1
2
1
0
1
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
4
1
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
2
0
0
0
0
2
0
2
0
0
0
0
2
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
2
3
0
0
0
0
0
0
6
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
2
0
1
1
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
1
2
0
2
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
4
0
0
0
1
2
1
2
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
1
0
0
0
0
0
2
2
0
0
0
0
0
2
0
1
0
1
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
3
0
0
0
1
2
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
1
0
1
1
0
0
0
1
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
2
2
0
0
1
2
0
2
3
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
12
1
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
1
0
0
1
0
0
0
2
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
2
1
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
1
0
2
0
0
0
0
1
0
2
0
2
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
3
1
0
0
0
0
2
3
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
2
1
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
1
2
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
2
2
0
0
0
1
1
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
3
1
1
1
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
1
0
5
1
0
1
0
0
0
2
0
0
3
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
3
0
0
0
2
0
0
2
0
1
1
0
1
0
0
0
0
2
3
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
3
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
2
0
1
0
0
0
1
0
0
1
0
1
2
0
2
1
0
1
0
1
0
0
1
1
0
0
1
0
0
1
0
0
0
1
1
0
0
0
2
1
0
1
0
1
0
0
0
2
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
1
2
2
0
4
0
0
0
0
0
3
0
0
1
1
0
5
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
5
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
1
2
0
0
1
0
1
1
0
0
1
0
0
2
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
2
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
3
0
0
0
1
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
3
0
0
0
2
0
0
0
0
2
0
1
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
2
0
0
0
2
0
0
1
3
0
1
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
3
2
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
5
0
0
0
0
1
0
0
1
0
2
0
1
0
0
1
0
0
0
0
0
3
0
1
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
3
1
0
2
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
2
0
2
0
1
0
0
4
0
0
0
0
1
0
1
1
0
2
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
2
0
4
2
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
1
2
0
0
1
0
0
0
2
0
0
2
0
0
0
2
0
0
1
2
0
0
0
0
1
0
0
1
0
0
2
2
0
0
1
0
0
0
0
0
1
0
23
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
2
3
0
0
0
0
0
0
1
0
0
0
2
0
0
1
2
7
0
0
2
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
2
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
1
3
0
0
0
0
1
0
2
0
0
0
0
0
0
1
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
4
0
1
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
3
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
3
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
1
0
0
0
3
0
0
2
0
0
2
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
1
0
0
0
0
2
3
0
3
0
2
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
3
1
0
1
5
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
1
0
0
3
0
0
2
0
0
0
0
2
1
0
2
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
2
0
0
1
2
0
0
0
0
0
0
2
0
1
0
0
2
1
0
2
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
3
1
1
0
0
0
1
0
0
0
0
0
0
1
3
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
5
1
1
0
2
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
3
0
0
0
2
2
0
0
0
0
5
0
0
0
1
2
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
3
1
1
0
0
1
2
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
1
2
0
2
0
0
0
2
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
5
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
3
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
7
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
1
0
0
0
0
0
1
0
0
1
0
0
0
2
1
0
0
4
0
0
0
0
1
2
3
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
1
0
1
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
3
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
2
0
1
1
4
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
6
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
1
0
2
0
0
0
2
0
2
2
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
2
0
0
2
2
0
0
0
0
2
5
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
1
2
0
0
0
0
5
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
1
0
0
8
2
1
0
0
0
0
3
0
2
0
0
0
1
0
2
0
0
0
0
0
2
0
0
10
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
6
1
0
0
0
0
0
1
0
1
0
0
0
1
2
0
0
0
0
0
5
1
0
0
1
3
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
1
0
0
1
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
2
2
0
1
0
1
0
0
2
1
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
2
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
8
0
1
0
0
0
0
2
1
0
4
1
0
0
1
0
0
0
0
0
0
1
2
1
0
0
3
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
1
0
2
0
0
0
3
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
2
0
2
0
0
0
2
2
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
2
0
0
0
2
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
1
0
3
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
1
1
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
1
0
1
0
0
0
2
0
2
2
0
0
1
2
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
1
3
1
0
0
2
0
0
2
0
0
0
0
0
1
0
1
1
0
0
0
1
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
5
2
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
1
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
2
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
1
1
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
4
0
2
0
5
0
0
2
1
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
1
0
0
3
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
2
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
4
0
0
0
1
0
0
0
0
1
5
0
1
2
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
2
4
0
0
2
0
0
0
4
2
0
0
0
0
0
2
0
2
0
1
0
0
0
1
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
5
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
2
0
0
0
2
3
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
3
0
4
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
3
1
2
0
0
0
0
0
0
5
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
3
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
2
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
5
0
1
0
0
1
0
0
4
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
1
0
0
0
0
5
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
6
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
2
0
0
2
1
0
0
0
0
0
1
3
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
5
0
0
3
0
0
0
0
0
0
3
1
1
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
1
0
3
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
1
0
0
0
1
0
1
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
2
2
1
2
0
2
0
0
0
0
1
0
2
0
1
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
3
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
3
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
2
2
0
0
0
0
0
2
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
4
0
0
0
0
0
0
0
4
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
1
5
0
1
2
1
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
1
2
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
3
0
0
0
1
3
2
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
1
0
0
0
2
3
0
0
0
0
1
0
2
0
0
0
2
0
0
3
5
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
1
0
3
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
2
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
1
2
0
2
0
0
0
0
0
0
8
0
0
0
0
2
0
1
0
0
0
3
0
0
0
1
0
0
3
2
0
0
2
0
0
0
0
0
1
0
0
0
2
0
2
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
3
1
0
2
0
1
1
2
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
4
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
1
1
0
1
0
0
4
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
2
1
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
6
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
1
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
1
0
1
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
2
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
9
0
0
2
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
9
0
0
0
0
0
0
3
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
1
1
0
0
0
0
0
1
0
2
1
2
0
1
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
3
2
0
2
0
0
0
4
2
0
0
0
5
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
2
1
2
0
0
0
0
4
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
2
0
0
0
1
0
2
0
3
1
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
1
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
1
2
2
0
0
2
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
1
2
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
3
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
2
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
1
0
0
0
4
1
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
4
0
1
2
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
2
0
0
2
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
2
0
0
1
0
1
2
0
0
0
2
0
2
1
1
1
0
0
0
0
6
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
2
0
1
0
0
3
0
1
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
1
0
0
0
2
0
0
0
1
0
0
0
2
0
2
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
2
0
2
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
2
0
0
0
2
0
0
3
0
1
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
3
1
1
0
0
0
0
0
0
2
0
2
0
0
0
1
1
0
0
0
0
0
2
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
1
1
1
0
0
0
0
0
1
0
0
2
0
3
0
2
0
0
0
0
0
2
0
0
0
0
2
2
2
0
1
0
0
0
0
5
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
4
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
2
0
0
0
0
0
3
0
2
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
2
0
1
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
1
0
0
3
0
2
1
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
1
1
0
0
0
3
1
0
0
1
0
0
0
0
0
0
2
0
0
1
0
2
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
4
0
0
0
1
0
3
0
1
0
2
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
2
0
2
0
1
1
0
1
3
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
3
2
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
1
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
2
0
0
1
0
0
0
0
0
1
0
1
0
4
0
1
2
0
0
0
1
0
2
0
0
0
1
3
2
0
0
0
1
0
0
1
0
2
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
4
0
2
0
0
0
1
4
0
0
0
0
0
0
1
0
0
2
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
21
0
1
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
2
0
1
0
0
1
2
0
0
2
0
2
1
1
0
0
3
0
0
0
4
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
3
2
0
0
3
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
3
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
7
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
1
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
2
1
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
2
0
1
0
0
0
0
0
6
1
0
0
0
0
2
0
3
0
2
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
2
0
2
0
0
0
1
0
0
0
0
0
0
5
0
0
0
0
0
1
0
0
0
0
0
0
4
2
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
1
0
0
0
3
0
1
0
0
1
0
0
0
0
0
0
2
0
0
1
2
0
0
1
0
0
0
0
0
0
2
0
1
1
0
0
5
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
1
0
4
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
3
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
2
4
0
0
0
0
0
0
2
0
0
2
1
0
1
0
1
2
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
1
0
0
4
0
0
0
2
0
0
0
0
0
0
1
2
0
0
3
0
3
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
2
2
0
1
2
2
0
0
1
2
0
2
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
1
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
5
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
3
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
1
1
2
0
0
0
2
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
1
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
3
1
0
0
0
2
2
0
0
2
0
0
2
0
2
0
0
0
0
0
0
3
2
2
1
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
4
0
0
4
0
0
0
0
0
4
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
2
0
1
0
2
2
0
0
1
0
0
4
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
1
5
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
1
1
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
1
0
0
2
1
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
4
0
0
2
0
0
2
0
0
3
0
0
0
1
0
2
0
0
0
0
2
2
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
2
2
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
2
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
1
1
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
2
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
2
1
0
3
2
0
0
1
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
4
0
0
0
3
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
2
1
0
3
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
1
0
3
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
2
1
1
2
0
2
0
0
0
2
1
0
0
0
2
0
0
0
0
0
1
0
3
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
2
4
2
0
1
0
0
0
0
1
0
0
0
5
0
2
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
2
1
1
2
0
0
4
0
1
0
0
0
2
7
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
1
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
3
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
2
0
2
0
0
0
0
0
2
0
2
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
2
1
2
0
0
1
1
0
0
2
0
0
0
0
2
1
3
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
2
2
2
1
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
5
1
0
0
0
0
1
0
1
0
2
0
0
0
2
0
0
0
0
0
5
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
2
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
1
2
0
0
2
2
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
1
0
0
2
0
2
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
1
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
2
0
0
3
0
0
0
0
1
1
0
2
0
2
0
0
0
0
0
0
2
0
0
5
2
0
0
1
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
1
1
0
3
1
0
1
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
1
2
1
0
0
0
0
2
0
0
1
1
2
0
2
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
1
1
0
3
0
0
3
0
0
1
0
1
0
0
2
0
0
4
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
3
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
3
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
5
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
1
0
0
0
0
1
2
1
1
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
1
1
0
0
1
0
1
0
4
0
0
0
0
2
0
1
1
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
1
0
0
1
0
0
0
0
0
1
1
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
6
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
5
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
2
1
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
1
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
1
0
2
3
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
3
0
4
0
0
0
1
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
3
0
0
0
0
4
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
2
1
0
0
0
2
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
1
1
0
1
0
4
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
2
0
0
1
1
1
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
3
0
0
2
2
0
2
0
0
0
0
1
0
0
0
2
1
1
2
0
0
3
0
0
0
0
0
0
3
1
0
4
0
0
0
0
1
0
0
2
0
0
0
1
0
0
1
0
2
0
0
1
0
1
2
0
0
0
0
1
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
4
2
0
0
1
0
1
0
2
1
0
3
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
2
0
0
1
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
2
0
1
2
0
0
1
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
1
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
2
1
1
0
0
1
0
0
0
2
2
1
3
0
3
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
3
0
1
0
0
2
0
1
2
2
3
0
13
0
0
0
0
3
0
0
0
1
0
1
0
0
0
0
0
0
1
1
2
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
1
1
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
3
1
0
2
0
0
4
0
2
0
2
0
0
1
0
2
2
0
0
0
0
1
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
1
0
0
0
2
0
2
1
0
0
1
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
2
0
2
0
1
0
0
0
0
0
0
0
4
0
0
1
1
3
0
0
0
3
2
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
3
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
2
1
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
3
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
2
0
0
0
0
1
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
2
5
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
1
0
1
2
0
0
0
0
0
0
1
2
0
0
0
1
0
1
0
0
0
1
2
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
2
1
0
0
2
0
2
2
0
0
0
0
0
1
3
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
2
0
0
2
0
1
0
0
0
1
2
0
0
0
1
1
0
0
0
0
0
2
0
2
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
3
0
1
1
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
2
0
2
0
0
0
0
0
2
2
1
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
3
0
5
2
0
5
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
1
0
1
1
0
0
4
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
4
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
3
0
3
1
0
0
0
1
1
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
3
2
2
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
1
0
0
0
11
0
0
2
0
0
0
1
0
0
0
0
1
6
0
0
0
1
0
2
0
1
0
0
1
0
1
2
0
0
0
0
2
0
2
0
0
0
0
0
1
1
3
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
1
3
0
0
0
1
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
4
2
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
5
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
3
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
1
0
1
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
1
0
2
0
1
0
0
0
0
0
2
0
0
0
1
4
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
2
0
1
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
2
1
2
2
0
0
3
2
0
0
0
0
0
3
1
0
0
0
0
1
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
1
0
1
1
0
1
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
3
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
4
0
0
0
0
0
0
1
2
2
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
6
2
0
1
2
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
1
2
0
0
2
2
0
0
0
0
1
1
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
6
0
0
0
0
0
0
1
0
0
0
2
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
2
1
1
0
0
0
1
0
0
0
0
1
2
0
1
0
0
1
1
2
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
1
0
2
2
1
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
2
0
7
0
0
0
0
0
2
3
3
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
1
2
1
0
0
2
0
0
0
1
2
0
0
0
0
0
0
2
0
2
0
0
2
0
1
0
0
0
0
1
0
0
3
0
0
0
2
3
0
1
0
0
2
0
0
0
0
0
1
0
7
0
1
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
3
4
0
0
0
0
0
0
2
0
2
0
1
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
1
2
0
0
0
0
0
0
0
2
0
0
2
3
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
2
7
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
2
7
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
1
0
2
2
2
0
0
0
1
0
0
0
1
0
0
1
0
0
2
2
0
0
0
0
0
1
1
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
1
2
0
1
0
2
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
4
0
0
0
8
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
1
1
0
3
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
1
0
0
1
2
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
2
0
2
0
2
0
0
0
3
0
0
0
0
0
0
1
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
2
0
0
0
1
2
0
0
1
0
0
1
0
0
0
2
0
0
1
2
1
2
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
1
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
1
1
1
0
2
0
0
0
0
1
0
1
0
0
2
0
2
1
0
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
1
3
0
0
1
0
0
0
1
2
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
2
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
1
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
2
0
0
0
0
1
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
4
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
2
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
6
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
3
0
1
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
2
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
1
0
0
2
1
4
1
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
1
2
0
0
0
0
1
0
2
0
2
0
2
1
0
0
0
0
3
0
3
0
0
1
0
0
2
2
0
0
0
0
1
0
2
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
2
0
0
1
0
1
0
0
0
0
2
3
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
3
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
2
0
0
3
0
2
0
0
0
2
0
0
0
0
3
2
0
0
0
0
1
0
0
2
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
3
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
3
0
0
1
0
3
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
6
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
2
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
2
0
0
2
0
1
1
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
1
1
0
0
0
2
0
1
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
3
0
0
0
0
0
2
0
0
1
2
0
10
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
2
0
0
3
1
0
1
0
2
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
2
0
2
1
0
0
2
0
0
0
0
0
0
0
2
0
0
3
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
1
1
1
2
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
1
0
0
1
0
0
0
2
0
0
0
4
0
0
0
0
1
0
0
1
2
0
1
0
3
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
1
0
0
0
0
0
0
0
1
0
2
0
1
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
2
2
0
0
0
1
1
0
1
0
0
0
1
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
2
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
1
2
0
0
2
0
2
0
2
1
0
0
3
0
0
0
0
0
2
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
2
0
2
0
0
8
0
0
0
2
2
0
0
2
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
1
0
0
2
1
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
13
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
2
0
2
0
0
0
0
0
1
0
0
0
1
1
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
2
0
0
0
1
0
0
0
1
2
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
1
3
0
0
0
0
1
0
0
0
2
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
2
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
2
1
0
0
0
2
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
2
0
1
0
0
4
1
1
0
0
0
0
3
2
0
0
0
0
0
0
2
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
3
0
0
1
0
5
1
5
0
1
0
1
0
7
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
3
1
0
0
0
0
1
0
0
1
0
0
1
2
0
1
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
3
2
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
2
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
3
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
3
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
2
0
0
0
0
2
0
6
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
1
2
3
0
1
0
0
1
0
3
0
0
1
0
0
1
1
4
2
0
2
0
0
2
0
0
0
1
0
0
0
5
0
0
0
4
0
2
0
0
2
4
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
3
0
0
2
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
2
3
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
4
0
2
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
1
1
1
0
2
0
0
0
0
8
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
5
0
3
0
0
3
0
2
0
1
0
2
1
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
3
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
2
0
0
0
1
0
2
0
2
1
0
2
0
2
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
2
1
0
0
1
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
3
0
0
0
0
1
0
1
0
2
2
0
0
0
0
0
0
5
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
1
2
2
0
0
1
0
0
0
0
0
0
0
2
1
0
1
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
4
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
1
0
0
2
0
0
3
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
1
0
1
1
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
2
0
2
0
0
0
0
10
0
1
0
1
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
1
0
0
3
0
1
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
1
4
0
0
0
1
0
0
3
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
3
2
0
0
0
2
0
6
0
1
0
1
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
1
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
3
2
0
0
0
0
0
0
1
0
0
2
0
0
1
0
2
10
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
1
0
0
2
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
1
0
1
1
0
0
2
0
1
0
1
0
0
0
0
0
0
3
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
6
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
5
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
2
0
1
0
1
2
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
3
0
7
0
0
0
0
2
1
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
1
0
5
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
2
0
0
0
0
5
0
0
2
0
0
0
0
0
5
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
2
0
0
1
0
0
2
1
0
0
0
0
0
1
6
0
1
1
0
1
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7
0
2
0
0
0
0
0
0
1
0
1
0
2
1
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
2
1
1
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
2
1
0
3
2
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
2
6
0
0
0
0
0
2
0
0
0
1
0
2
0
2
2
0
1
1
0
0
4
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
2
0
0
0
0
0
2
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
1
0
1
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
5
2
0
0
0
2
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
5
0
1
0
0
0
0
1
0
0
2
1
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
1
2
3
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
2
0
2
0
0
0
0
1
0
0
2
0
1
2
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
2
1
1
0
0
0
1
0
7
0
1
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
3
1
0
0
0
0
4
1
0
1
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
1
1
2
0
1
5
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
2
0
1
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
5
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
6
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
2
2
0
1
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
2
3
1
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
1
0
1
1
1
2
0
0
0
0
0
3
0
2
2
3
0
0
0
0
0
0
1
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
3
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
3
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
1
1
0
1
0
0
0
0
2
0
0
1
0
0
0
2
0
0
2
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
3
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
1
0
2
2
0
0
0
0
2
0
1
0
2
1
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
2
3
0
1
0
0
6
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
1
0
1
0
0
0
0
1
2
2
1
0
2
1
0
0
0
0
1
2
0
0
0
0
0
1
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
1
1
1
0
2
0
0
2
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
3
1
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
2
2
0
2
0
3
0
2
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
1
0
2
0
0
0
2
0
2
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
1
6
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
3
0
0
0
1
0
2
0
2
0
0
3
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
2
0
0
1
0
0
2
0
0
0
2
0
2
1
0
0
0
0
0
1
1
0
2
0
0
0
0
0
2
4
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
6
0
1
0
1
2
0
0
0
0
0
0
3
1
2
0
0
2
0
0
0
0
0
1
2
0
1
0
0
4
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
3
0
1
0
3
0
1
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
3
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
4
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
3
0
0
0
2
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
9
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
2
0
0
2
0
0
2
0
0
2
2
0
0
0
2
0
0
1
0
3
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
2
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
4
1
0
1
0
0
0
0
0
7
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
2
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
3
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
2
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
3
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
1
0
1
0
0
2
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
1
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
4
0
1
1
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
2
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
1
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
1
0
1
0
0
4
0
3
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
3
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
2
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
3
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
2
1
0
3
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
2
0
0
5
0
0
0
1
3
2
0
0
0
3
0
1
0
0
0
0
3
0
6
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
10
0
1
0
1
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
2
0
0
2
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
1
3
0
4
0
1
0
2
1
0
2
0
3
0
1
0
1
0
0
0
2
0
0
0
0
0
0
1
0
19
1
0
0
2
0
0
1
0
3
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
3
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
1
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
1
0
2
0
0
2
0
0
1
0
2
0
0
0
0
0
3
1
0
1
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
5
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
1
0
1
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
2
0
1
0
0
2
0
0
0
0
1
0
0
2
1
1
0
1
0
0
0
0
0
1
0
2
0
0
0
3
0
2
1
1
0
0
2
4
0
0
0
0
0
0
1
0
0
2
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
2
3
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
3
2
2
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
2
0
0
3
0
1
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
3
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
1
0
0
1
2
0
0
0
0
0
0
0
2
0
1
0
0
0
6
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
3
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
4
2
1
0
0
0
0
0
3
0
0
0
3
0
2
0
0
0
0
0
2
0
0
0
2
2
2
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
1
0
0
0
2
0
2
0
2
0
0
0
1
1
2
0
0
0
5
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
1
0
0
0
0
0
2
1
1
3
2
0
0
3
2
0
3
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
2
0
0
0
0
0
4
1
0
4
1
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
1
0
0
0
0
0
2
1
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
2
1
1
0
0
1
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
2
0
7
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
3
2
2
0
0
2
0
0
0
0
1
3
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
15
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
1
0
0
1
0
0
2
2
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
3
3
1
0
0
1
0
3
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
2
0
0
0
6
0
0
0
0
1
2
0
0
0
2
0
0
0
0
2
0
1
2
0
1
0
2
0
0
1
1
1
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
5
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
2
0
0
0
0
0
1
0
1
0
2
0
0
4
0
0
0
0
10
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
2
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
1
0
0
0
0
0
0
2
0
0
3
0
2
0
0
0
0
0
0
2
0
2
2
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
1
1
0
0
1
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
7
0
2
2
2
0
0
0
0
0
0
0
1
3
0
0
1
0
1
0
3
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
10
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
2
0
0
1
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
2
0
1
2
3
0
0
2
0
0
0
0
2
1
2
0
0
0
2
0
0
0
0
0
3
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
4
1
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
2
1
0
0
1
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
1
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
1
4
0
2
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
2
0
1
0
2
1
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
2
2
2
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
2
0
1
0
0
1
0
0
2
1
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
6
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
1
0
0
1
0
0
2
3
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
6
0
0
0
0
0
0
1
0
0
0
0
0
0
3
1
1
0
3
1
0
1
0
0
0
0
0
0
0
0
1
1
0
2
1
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
1
0
0
0
1
2
0
1
0
0
0
1
0
0
0
0
1
0
1
0
2
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
5
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
1
0
0
0
0
0
0
1
2
0
1
0
0
0
1
0
0
0
0
0
0
5
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
3
2
2
0
0
0
2
2
1
2
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
6
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
2
2
0
0
0
0
0
0
0
1
5
1
2
2
0
3
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
2
0
2
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
1
1
2
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
1
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
3
0
0
0
0
0
4
2
0
0
0
8
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
2
0
0
2
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
8
0
0
1
2
0
0
1
1
1
2
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
3
1
0
0
0
3
2
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
2
4
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
1
2
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
11
0
0
3
0
3
0
0
0
3
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
2
0
0
0
0
2
1
0
0
0
3
0
0
0
0
2
0
0
0
1
0
0
1
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
1
0
0
0
0
0
3
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
2
0
3
0
0
0
0
0
2
1
0
0
0
0
2
2
0
2
0
0
0
0
1
0
0
0
1
0
0
2
0
2
0
0
0
0
0
3
0
0
1
0
3
0
0
0
6
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
1
0
0
2
0
0
2
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
2
2
0
2
2
0
0
0
0
0
3
1
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
3
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
2
2
1
0
0
0
0
1
1
0
0
0
0
0
0
0
2
1
3
0
2
1
0
0
0
1
0
0
0
0
0
1
0
0
3
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
2
0
0
0
1
0
3
2
1
0
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
3
0
0
0
0
1
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
1
2
2
0
0
0
0
0
0
0
2
3
0
5
2
0
0
0
1
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
7
0
0
0
0
0
1
2
0
0
1
1
0
0
1
1
0
0
1
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
1
0
0
0
0
0
2
0
0
0
0
2
0
2
0
7
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
3
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
1
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
1
2
0
1
0
0
0
2
1
1
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
6
0
0
0
3
0
0
0
2
0
2
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
2
0
0
0
3
0
2
0
0
0
1
0
3
0
0
0
1
1
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
2
0
2
0
0
1
1
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
1
2
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
6
6
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
2
0
1
1
0
0
0
2
0
0
1
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
5
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
3
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
1
3
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
3
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
2
2
0
0
0
0
3
1
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
3
0
2
0
1
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
1
0
9
0
0
0
0
0
0
0
0
1
0
2
2
1
1
2
0
6
0
0
0
1
0
0
0
0
0
2
1
0
1
0
0
0
4
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
2
1
0
0
0
0
0
0
0
0
0
0
0
3
1
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
2
0
0
0
0
3
1
2
0
0
2
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
5
0
0
1
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
5
0
0
1
0
0
0
2
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
2
5
0
0
0
0
0
0
1
0
2
0
0
0
2
3
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
1
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
3
0
1
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
2
0
0
2
0
0
0
2
1
0
0
0
2
1
0
0
1
0
0
1
0
0
0
1
0
3
2
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
4
1
0
0
0
0
0
0
2
0
4
0
0
1
0
0
0
2
2
1
0
0
3
0
0
1
1
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
2
0
0
0
0
1
0
0
1
0
0
0
0
1
1
2
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
1
0
0
0
2
0
3
3
0
0
0
0
0
0
2
0
3
1
0
0
0
1
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
4
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
1
0
1
2
0
2
0
0
0
0
0
0
0
0
3
2
0
2
0
0
0
0
1
2
1
0
0
1
1
0
0
0
3
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
1
1
2
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
2
0
0
1
0
2
0
0
0
2
0
1
1
0
0
0
1
0
1
0
2
1
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
2
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
2
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
1
1
3
4
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
1
0
0
0
2
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
2
0
4
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
2
1
0
2
0
0
0
0
0
2
0
0
0
0
2
5
0
0
1
2
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
2
0
1
2
0
0
1
4
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
2
0
0
0
1
0
3
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
6
0
0
0
1
0
0
0
1
0
1
0
0
3
0
2
0
0
2
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
2
0
0
1
0
1
0
0
0
2
0
1
0
0
1
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
1
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
2
0
2
1
0
2
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
9
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
4
3
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
4
0
0
0
0
2
0
0
0
2
0
0
5
0
1
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
3
0
0
0
0
2
1
1
1
0
2
0
1
3
0
1
0
1
1
0
7
2
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
3
0
0
0
0
0
0
0
2
0
0
4
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
5
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
2
0
0
2
0
0
0
1
2
0
1
0
0
0
1
1
2
0
0
0
1
0
2
0
0
0
1
0
0
1
4
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
8
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
2
0
0
0
2
3
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
2
1
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
5
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
4
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
3
2
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
2
4
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
2
1
1
0
1
0
0
0
0
0
0
0
0
1
2
2
0
0
2
0
0
8
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
1
2
2
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
1
0
5
0
0
0
1
2
0
0
1
0
1
0
0
2
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
3
3
2
0
0
0
1
0
0
0
0
1
3
0
0
0
0
0
0
2
1
1
2
0
0
0
2
0
2
2
0
0
0
0
0
1
3
2
0
0
0
0
0
2
0
0
0
0
3
0
2
0
3
1
0
0
0
6
0
0
0
0
0
0
0
1
0
2
0
0
1
2
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
1
7
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
4
0
0
0
2
1
1
0
1
0
0
1
0
2
0
0
0
0
0
2
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
2
2
0
1
0
0
1
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
1
0
2
0
2
0
2
0
0
0
4
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
3
0
0
0
0
0
4
0
0
2
0
1
2
2
0
1
0
3
2
0
0
0
0
0
0
2
1
4
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
2
0
0
2
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
3
0
0
0
0
2
2
4
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
1
0
2
0
0
0
0
0
1
2
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
2
3
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
1
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
1
0
0
1
0
3
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
3
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
2
0
0
2
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
1
0
2
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
2
1
0
0
1
0
0
0
0
0
0
2
1
2
0
0
2
2
0
0
2
2
3
2
0
1
0
2
0
0
0
0
0
2
1
0
1
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
3
0
2
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
1
1
0
0
0
0
0
2
0
0
0
1
2
2
2
0
0
1
0
0
1
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
2
0
1
0
2
3
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
4
0
0
0
1
0
2
0
0
0
0
2
0
3
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
4
0
0
2
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
3
0
0
3
0
0
1
0
1
0
0
3
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
3
0
0
0
2
1
0
2
0
0
0
0
2
0
0
0
0
0
0
4
0
2
0
0
0
0
0
1
0
0
2
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
3
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
3
0
1
0
0
0
0
0
0
2
1
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
6
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
2
0
1
0
0
2
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
3
0
2
1
0
0
0
0
0
0
3
4
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
3
0
1
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
3
0
0
1
0
1
3
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
2
1
0
1
0
0
1
3
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
3
0
0
2
0
0
1
2
0
0
0
1
0
0
0
0
0
3
0
1
0
0
0
0
1
0
0
0
0
1
1
2
0
0
0
0
0
0
0
1
2
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
4
0
0
0
0
0
0
1
1
0
2
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
2
2
1
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
3
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
2
1
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
2
0
0
0
2
0
1
0
0
2
5
0
0
0
0
0
0
0
1
0
1
0
2
0
0
1
0
1
0
0
2
0
0
2
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
2
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
2
0
0
1
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
1
0
0
0
0
0
1
1
0
2
0
0
0
0
1
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
2
2
0
0
2
0
1
0
0
0
4
0
2
0
0
0
0
0
0
1
2
0
2
0
2
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
2
2
0
2
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
2
1
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
1
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
5
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
3
0
0
5
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
3
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
2
0
1
0
2
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
1
2
0
0
2
0
0
0
0
3
2
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
1
2
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
2
0
0
0
4
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
2
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
4
2
0
0
1
0
1
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
1
0
0
1
2
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
3
0
0
1
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
2
0
0
1
0
13
0
0
0
0
2
0
3
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
2
0
1
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
2
0
0
4
0
0
0
1
2
0
0
0
2
0
1
0
0
0
0
0
0
2
0
2
0
4
0
1
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
1
2
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
1
3
0
1
0
0
1
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
1
0
0
0
2
0
0
0
0
2
8
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
5
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
2
0
0
1
0
2
0
0
2
0
0
0
0
3
0
0
2
1
0
0
0
1
0
0
0
0
0
1
0
2
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
2
2
0
0
1
0
0
0
0
0
0
0
9
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
1
0
1
1
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
2
1
0
0
6
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
3
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
3
0
1
0
1
1
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
2
0
1
0
0
4
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
4
0
2
0
0
0
0
0
1
0
0
1
0
6
0
1
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
2
0
0
1
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
3
0
2
0
0
0
0
2
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
3
0
0
2
0
0
0
0
0
0
0
0
0
0
1
3
0
0
2
0
1
2
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
1
0
0
0
3
2
0
5
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
2
1
1
0
1
0
0
1
0
0
1
1
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
2
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
9
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
6
0
0
0
0
1
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
6
2
1
0
0
0
0
0
0
0
1
0
0
2
0
3
0
1
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
6
1
0
0
0
0
0
0
0
4
2
0
0
0
2
0
0
0
0
0
2
1
2
0
0
1
0
0
2
2
1
0
0
0
3
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
1
0
1
2
0
1
2
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
3
0
1
0
2
0
0
1
0
1
0
2
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
4
0
1
0
1
0
1
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
1
0
3
0
0
0
0
1
0
0
0
0
2
1
0
1
0
2
0
1
0
0
1
0
0
2
0
0
1
3
0
3
0
0
0
2
2
1
0
0
0
0
0
3
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
3
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
4
0
0
0
0
0
0
0
0
3
1
0
0
0
1
0
0
0
0
2
2
0
1
5
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
3
0
0
0
0
1
2
2
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
1
0
0
0
2
1
1
0
0
0
0
1
0
0
3
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
2
0
0
0
0
0
1
1
0
0
0
0
0
5
0
0
2
1
2
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
2
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
2
0
2
0
2
2
0
0
0
2
2
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
2
1
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
2
3
1
0
0
0
0
0
0
1
3
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
6
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
2
0
1
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
5
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
4
0
0
0
0
0
0
1
0
0
0
2
2
1
5
0
0
0
0
0
0
3
0
3
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
3
0
0
0
3
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
3
0
0
0
1
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
2
0
2
3
0
0
1
0
1
1
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
1
1
0
0
0
5
0
0
0
0
1
0
0
2
0
1
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
1
3
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
2
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
3
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
1
0
1
0
0
3
0
2
0
0
3
0
1
0
0
4
0
0
1
1
0
0
0
0
0
0
0
0
4
0
0
1
1
1
2
0
1
3
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
1
0
0
1
0
2
0
1
4
0
0
0
1
0
0
3
4
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
3
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
3
0
0
0
0
1
2
0
0
0
0
0
0
3
1
0
0
1
0
6
0
1
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
3
0
1
0
0
0
1
0
0
1
3
0
0
0
1
0
0
1
2
0
0
0
0
1
0
2
0
3
0
0
0
2
1
2
2
0
0
2
0
0
5
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
2
2
1
1
0
0
4
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
3
2
0
2
2
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
1
1
0
0
0
2
0
0
0
0
0
2
0
3
0
2
0
0
0
7
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
2
0
2
6
0
0
3
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
2
4
0
1
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
2
0
0
6
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
7
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
1
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
1
1
2
2
0
0
0
5
0
0
0
0
0
0
0
7
0
0
1
0
0
2
0
0
3
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
1
1
1
0
0
1
0
0
0
0
2
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
3
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
1
1
0
0
0
0
0
0
2
1
0
0
0
2
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
4
0
0
0
0
1
0
2
2
2
0
0
0
0
2
1
0
0
0
0
0
1
1
1
0
0
0
0
1
2
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
1
2
0
2
0
0
0
0
0
0
3
1
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
1
0
0
2
0
0
1
0
1
0
0
0
0
4
0
0
0
0
0
0
2
0
0
0
0
0
3
1
2
1
1
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
4
0
3
1
0
5
0
0
0
0
0
0
0
0
3
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
4
0
0
0
0
3
0
0
0
0
2
2
2
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
1
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
1
1
0
1
0
0
0
2
2
0
0
1
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
4
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
3
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
3
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
3
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
2
1
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
1
0
0
0
0
4
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
4
0
0
2
0
2
1
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
1
1
0
0
2
0
0
0
0
0
0
0
1
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
1
2
0
0
0
0
0
0
1
0
0
0
1
0
0
2
3
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
2
2
3
0
0
0
1
0
0
0
1
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
4
0
2
0
0
0
0
0
0
5
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
4
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
2
0
0
0
0
0
3
0
1
0
0
2
0
0
0
3
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
3
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
4
0
0
0
1
0
0
5
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
2
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
2
0
0
3
0
0
1
1
0
0
0
2
0
0
0
0
3
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
5
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
9
0
0
0
0
0
0
2
0
0
3
0
0
2
2
1
0
1
0
0
0
3
0
2
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
1
0
0
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
5
0
0
0
0
1
1
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
1
0
1
0
0
0
1
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
7
0
0
1
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
3
0
3
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
2
0
0
0
0
2
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
3
2
0
0
2
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
2
0
0
3
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
2
4
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
2
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
1
1
0
2
1
0
0
2
2
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
3
0
0
0
0
0
0
2
0
0
0
2
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
3
0
2
0
0
3
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
3
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
2
0
0
0
2
0
3
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
2
2
0
0
0
0
1
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
3
0
0
0
0
0
0
0
0
3
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
2
1
0
0
0
0
4
0
5
0
0
0
0
0
0
0
0
2
2
0
0
2
1
2
0
0
0
0
3
1
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
8
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
2
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
3
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
2
0
0
2
2
3
0
0
1
0
0
0
0
0
5
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
3
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
1
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
1
0
0
0
3
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
1
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
2
1
1
0
0
1
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
3
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
1
2
0
2
0
0
2
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
2
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
3
2
0
1
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
7
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
2
0
2
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
2
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
2
0
0
1
0
0
1
0
1
0
1
2
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
3
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
5
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
1
2
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
1
0
0
0
0
0
2
0
0
1
0
1
2
0
0
0
2
2
0
0
0
0
2
2
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
2
1
0
6
1
0
0
0
0
0
1
0
0
1
1
0
0
2
0
0
1
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
1
0
0
0
0
1
2
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
3
0
0
2
2
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
5
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
2
2
4
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
1
1
0
1
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
3
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
3
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
3
0
0
2
2
0
0
0
0
0
0
0
2
0
3
0
0
1
0
0
1
0
0
0
2
0
3
0
3
2
0
0
2
1
0
1
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
6
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
2
0
2
2
1
0
2
2
0
0
0
1
1
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
5
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
3
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
2
1
2
0
0
0
1
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
2
3
0
0
1
0
0
3
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
1
2
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
5
0
1
2
0
1
0
0
0
0
0
3
1
2
0
0
0
0
0
0
6
0
0
0
2
0
0
2
3
1
2
1
1
2
0
1
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
2
2
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
4
0
2
0
0
0
0
2
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
3
0
0
0
0
0
0
2
0
0
2
4
0
0
2
1
0
0
0
2
0
0
1
0
2
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
1
2
1
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
2
2
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
1
0
0
1
1
0
1
1
0
0
0
0
1
0
0
1
0
3
0
3
0
0
0
0
2
1
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
2
0
0
2
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
2
2
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
4
0
1
0
0
0
1
1
0
0
0
0
2
0
0
0
0
2
0
0
1
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
4
0
0
0
2
0
0
0
2
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
2
2
0
2
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
2
0
3
0
0
0
1
3
0
1
0
0
0
0
1
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
2
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
2
0
0
0
1
0
3
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
3
0
0
1
0
0
2
2
1
0
0
0
1
0
2
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
2
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
6
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
5
0
0
0
0
4
2
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
3
0
0
0
0
1
0
0
3
0
2
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
1
0
0
2
3
0
0
0
4
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
4
2
0
0
0
0
2
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
1
1
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
4
0
0
0
0
1
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
2
0
2
0
2
0
0
3
0
0
0
0
0
0
0
2
5
0
2
0
1
0
0
0
3
1
0
0
0
1
1
1
0
0
0
0
0
0
2
0
0
1
0
0
2
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
5
0
0
1
0
0
0
0
2
0
2
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
2
0
0
0
0
5
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
3
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
2
0
3
0
0
0
1
0
0
4
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
5
0
0
0
2
0
0
1
2
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
2
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
3
0
0
0
0
0
1
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
4
0
0
0
0
2
2
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
3
0
2
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
1
0
0
0
1
2
0
1
1
2
1
0
0
1
0
0
0
0
1
2
0
0
1
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
1
2
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
3
0
0
0
0
0
0
2
0
2
2
1
1
2
0
1
0
0
2
2
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
3
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
3
2
0
1
1
0
0
1
0
0
0
3
0
1
4
0
0
3
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
7
0
1
1
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
2
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
2
0
3
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
2
0
0
2
2
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
3
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
1
1
1
0
0
0
0
2
0
0
6
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
1
0
0
0
1
2
0
0
2
0
0
1
0
0
0
0
0
0
8
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
4
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
1
1
0
2
2
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
1
1
0
0
0
0
0
0
0
1
0
0
2
2
1
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
3
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
3
0
0
0
0
2
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
5
1
0
1
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
7
0
0
0
0
0
4
2
2
0
0
2
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
3
0
0
0
0
2
0
0
1
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
1
11
0
2
1
1
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
4
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
2
0
2
0
1
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
5
0
0
0
2
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
3
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
1
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
1
0
0
5
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
9
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
2
1
3
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
2
2
0
0
0
0
9
0
0
0
1
0
2
0
0
1
0
0
0
0
0
1
3
1
1
3
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
6
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
2
2
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
2
1
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
2
0
0
0
0
1
0
0
1
0
0
1
2
0
0
0
0
0
0
0
2
3
0
3
0
0
2
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
1
2
0
0
2
0
0
1
0
0
0
0
0
3
2
2
2
0
1
2
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
2
0
1
0
0
0
0
1
1
0
1
0
1
0
1
3
0
0
0
0
1
0
0
0
0
2
1
0
0
2
0
0
0
2
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
1
2
2
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
5
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
2
3
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
2
0
0
0
0
0
0
0
1
1
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
1
1
0
0
0
0
1
4
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
5
2
0
0
0
4
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
2
0
2
1
0
0
0
0
0
1
2
1
3
0
0
0
0
0
2
0
2
0
2
2
0
2
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
1
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
2
3
0
0
0
1
0
0
1
0
0
3
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
1
0
0
0
0
0
1
0
0
2
0
2
0
2
0
0
0
0
1
2
0
0
2
0
0
0
0
1
0
0
0
1
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
1
0
1
0
0
2
1
0
0
2
0
1
0
0
1
3
1
2
0
0
1
0
2
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
2
3
2
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
3
0
0
1
0
0
0
0
1
0
0
0
0
4
0
2
0
1
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
3
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
2
0
2
0
0
0
0
0
2
0
1
2
2
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
1
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
3
0
0
0
0
6
0
0
2
0
0
0
0
2
0
0
0
0
2
0
2
0
2
1
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
3
0
2
0
0
0
0
6
0
0
0
0
2
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
6
1
0
0
0
1
0
3
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
1
1
1
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
7
1
1
1
0
1
0
2
2
1
1
0
0
1
0
0
2
0
0
0
0
0
1
4
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
1
2
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
3
0
0
0
0
3
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
2
1
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
1
0
3
0
0
2
0
2
2
0
0
1
3
0
2
0
1
1
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
1
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
1
0
11
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
2
0
0
0
0
0
1
2
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
7
0
1
0
0
0
4
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
6
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
4
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
6
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
4
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
1
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
6
1
1
0
1
0
0
0
4
2
0
0
0
1
0
0
2
0
1
0
2
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
8
2
0
0
0
0
0
1
0
2
0
0
0
0
0
2
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
0
2
0
0
2
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
1
1
0
0
1
0
0
2
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
3
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
2
5
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
1
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
2
0
0
0
0
1
0
1
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
3
1
3
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
3
0
2
1
2
0
1
0
0
0
0
0
0
0
0
0
0
3
0
2
1
0
0
0
0
1
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
2
0
1
0
0
2
0
2
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
2
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
7
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
1
0
2
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
2
1
0
1
0
0
1
0
0
1
3
0
0
0
0
0
1
2
0
0
0
0
1
0
0
1
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
1
1
0
0
1
2
0
0
0
0
0
0
0
1
0
0
1
0
3
0
0
1
0
0
0
0
0
0
0
1
2
0
0
3
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
0
3
2
0
0
3
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
3
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
6
2
2
0
0
6
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
3
0
4
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
2
7
0
0
2
0
1
0
0
1
0
0
1
0
0
0
3
3
3
0
0
3
0
0
1
0
2
0
0
0
0
0
7
2
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
4
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
3
1
3
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
5
1
0
2
0
0
3
2
0
1
0
0
0
1
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
3
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
6
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
1
0
0
0
0
0
0
1
0
0
0
0
3
0
2
1
0
1
1
1
3
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
2
1
0
0
0
0
2
0
0
0
0
2
1
0
0
0
2
0
2
0
0
2
0
0
0
1
1
0
5
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
2
0
0
0
0
1
6
1
0
0
0
0
0
0
0
0
2
0
0
2
1
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
1
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
3
0
0
1
0
8
0
0
1
0
0
0
0
2
3
0
0
0
0
2
0
1
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
4
0
0
1
0
0
0
0
1
2
7
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
1
3
0
0
0
0
0
0
0
1
0
2
0
0
0
1
1
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
2
1
0
0
3
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
1
0
1
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
2
0
0
0
1
0
0
0
1
0
0
2
0
0
0
2
1
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
5
0
0
1
0
0
1
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
2
1
0
0
7
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
1
0
0
1
1
0
2
0
0
0
0
0
1
1
2
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
2
0
2
1
0
0
0
0
0
0
2
1
0
0
0
0
0
2
1
0
1
2
0
0
4
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
2
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
1
1
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
1
5
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
3
0
0
0
2
0
0
0
6
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
1
1
0
0
0
4
2
0
0
1
0
0
1
0
0
0
1
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
3
1
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
2
0
0
0
0
2
0
2
1
0
0
0
0
0
3
0
0
0
0
0
1
0
3
0
0
0
1
1
0
0
0
0
2
1
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
1
3
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
15
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
1
2
0
0
0
0
2
0
1
1
0
0
2
0
1
0
4
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
2
0
0
1
0
3
0
0
0
1
0
2
0
0
0
0
3
1
0
0
0
0
0
0
0
0
1
0
0
1
0
7
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
2
1
0
0
0
5
1
0
0
0
0
0
0
0
3
1
0
3
0
0
0
0
0
0
2
1
0
0
0
0
0
2
2
0
2
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
1
0
2
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
1
0
2
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
1
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
3
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
1
0
1
0
3
0
0
0
0
2
0
0
0
0
1
3
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
1
0
0
3
0
0
0
0
0
0
2
3
0
1
0
0
0
2
0
0
0
2
0
1
4
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
2
4
0
0
0
0
1
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
2
9
0
0
0
0
0
0
0
3
0
0
1
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
1
0
2
0
0
1
2
0
2
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
2
5
7
0
0
3
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
1
6
0
0
0
1
2
0
0
0
0
0
2
0
0
3
0
1
0
0
2
1
1
2
0
0
1
0
0
0
0
2
0
2
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
3
0
0
0
0
2
0
1
2
4
0
0
2
4
0
0
0
0
1
0
1
0
0
0
2
0
0
1
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
1
0
2
0
0
1
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
2
1
2
2
0
0
0
0
0
0
0
1
2
0
0
0
0
3
0
4
0
0
0
0
0
0
0
2
0
2
0
1
0
1
0
7
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
3
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
1
0
1
0
0
2
1
0
0
0
0
0
1
4
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
1
3
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
7
1
0
0
0
2
1
0
0
0
0
1
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
2
2
2
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
11
0
4
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
8
0
1
0
0
0
0
1
0
0
1
1
0
0
0
2
1
0
0
0
0
0
1
1
0
0
2
0
0
0
3
0
0
0
1
2
4
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
1
1
1
0
0
0
0
2
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
2
0
0
0
2
1
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
1
0
2
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
5
0
0
0
0
0
4
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
4
0
0
0
0
1
0
1
0
5
0
0
0
0
1
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
2
0
1
2
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
10
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
4
2
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
3
0
0
0
0
1
6
0
0
0
0
2
3
0
0
0
0
0
2
2
0
2
2
2
0
0
0
1
1
0
1
0
0
2
0
0
4
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
2
0
0
0
3
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
1
0
2
0
2
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
1
0
1
1
0
0
1
0
1
2
0
0
0
0
0
1
1
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
6
0
0
0
2
0
1
2
1
0
0
0
0
0
0
0
2
1
1
0
0
1
0
0
0
8
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
1
0
0
1
0
0
1
0
0
3
5
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
3
0
0
0
2
0
0
3
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
2
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
1
3
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
4
1
0
0
1
0
0
0
0
2
0
0
0
0
0
3
0
0
0
3
0
2
0
0
0
1
0
2
0
0
2
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
4
0
1
1
0
1
1
1
2
1
0
1
1
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
0
1
0
2
0
0
0
1
2
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
2
0
2
0
0
3
1
1
1
0
1
0
0
0
0
0
0
1
0
0
3
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
2
1
0
0
0
3
0
0
0
0
1
0
1
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
1
0
1
0
0
1
0
0
0
0
0
3
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
2
2
1
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
6
0
0
0
0
2
0
2
0
0
0
1
2
2
0
0
0
0
0
2
0
2
0
4
0
0
1
0
0
1
0
0
0
2
0
0
1
0
1
0
2
0
0
0
0
2
0
0
1
0
2
0
0
3
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
2
0
0
2
2
2
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
2
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
3
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
4
0
0
0
0
0
1
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
2
0
1
0
0
0
0
2
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
1
4
0
0
0
0
1
0
0
2
0
2
1
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
2
2
0
1
1
0
1
0
0
0
1
0
2
0
0
1
0
0
0
1
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
1
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
1
0
0
0
1
0
0
0
0
1
1
0
4
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
8
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
2
0
0
0
0
0
1
0
5
0
0
0
0
0
0
0
8
0
2
0
1
0
0
2
1
0
0
0
1
1
0
0
0
0
0
0
0
5
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
2
1
0
0
0
0
0
0
2
3
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
3
1
3
1
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
2
1
0
0
0
2
0
1
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
3
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
4
1
2
0
2
0
0
2
1
2
1
0
3
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
2
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
2
0
3
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
8
0
0
0
1
0
1
0
0
1
2
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
1
1
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
1
0
0
1
4
0
0
0
1
0
5
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
3
0
1
1
0
0
2
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
1
1
0
0
2
0
1
0
0
0
0
1
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
4
0
0
0
1
2
0
2
0
0
0
0
0
6
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
3
2
0
1
0
0
0
1
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
3
0
3
0
0
2
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
1
0
1
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
1
0
0
1
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
1
0
2
0
2
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
3
0
0
0
3
0
0
0
2
2
0
0
0
0
0
7
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
2
0
1
0
1
1
0
1
0
0
0
0
0
0
2
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
1
0
0
1
0
1
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
1
1
0
0
1
0
0
0
0
8
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
2
1
3
0
1
0
0
2
0
0
0
2
0
0
1
0
0
1
0
0
0
3
0
0
0
0
0
1
0
0
0
0
3
0
2
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
1
0
1
0
0
0
0
0
0
1
0
0
3
1
0
0
1
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
1
0
3
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
3
0
3
2
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
5
0
2
0
0
0
0
0
1
0
3
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
3
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
3
2
0
0
0
0
0
0
0
6
1
0
0
0
0
0
1
2
0
0
0
2
0
2
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
1
0
0
2
1
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
4
1
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
3
0
2
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
2
0
0
3
1
0
0
3
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
2
0
0
0
0
1
0
2
2
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
6
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
2
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
8
0
1
0
0
0
5
0
1
0
2
2
0
3
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
2
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
1
0
2
0
0
0
0
3
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
1
1
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
10
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
2
0
0
1
0
0
0
2
1
0
2
0
0
0
1
0
0
0
1
2
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
2
1
0
0
2
0
4
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
1
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
1
0
1
2
0
0
0
0
0
0
0
0
2
0
1
1
0
3
0
0
0
1
0
0
1
0
0
0
0
2
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
8
1
2
0
0
0
1
0
3
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
3
2
0
0
0
0
1
0
10
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
1
3
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
1
2
0
0
5
0
0
0
0
2
1
0
1
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
5
0
0
1
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
1
3
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
1
1
0
0
11
0
1
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
6
0
0
2
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
1
2
2
0
1
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
3
2
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
2
1
0
0
0
0
0
0
1
0
0
0
3
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
1
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
1
3
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
3
2
1
0
1
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
2
1
2
2
0
0
0
0
0
0
0
0
0
1
0
1
0
2
1
1
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
1
0
0
4
0
0
1
2
1
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
4
0
0
0
0
0
0
0
5
0
0
0
1
1
0
2
0
2
4
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
2
0
4
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
1
1
0
0
1
0
2
0
0
1
0
3
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
3
0
0
0
0
0
0
0
1
1
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
1
1
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
6
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
5
0
2
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
5
0
0
0
0
2
0
1
1
0
0
0
2
0
0
0
0
3
0
0
0
2
0
0
2
0
0
2
1
1
0
0
0
0
0
1
0
0
2
3
0
1
0
0
2
0
0
0
1
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
1
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
3
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
1
1
0
1
1
2
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
4
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
1
1
1
0
0
3
2
4
2
0
0
2
0
2
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
7
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
2
3
0
0
3
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
2
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
1
4
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
2
2
0
0
0
0
1
0
2
0
0
4
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
4
0
0
1
0
1
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
1
2
0
0
0
1
0
2
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
2
0
3
0
3
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
1
0
0
2
0
0
0
0
1
1
0
0
4
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
6
0
0
1
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
5
0
0
0
0
1
0
0
2
0
2
0
0
5
2
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
2
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
3
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
2
0
0
2
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
1
2
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
4
0
2
3
0
0
0
0
0
2
1
2
1
0
1
0
0
2
0
0
1
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
2
0
2
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
6
0
0
0
0
0
0
2
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
1
1
1
0
2
0
0
3
1
0
0
0
0
0
1
3
2
0
0
1
1
0
0
3
2
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
2
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
0
2
0
2
5
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
3
0
4
0
3
0
1
0
0
0
0
0
0
0
0
0
6
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
1
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
1
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
2
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
4
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
2
0
1
0
0
0
0
0
0
2
0
0
1
2
0
0
3
0
0
0
0
0
0
2
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
3
0
1
1
0
2
2
0
0
2
1
0
0
0
0
0
0
1
1
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
2
0
0
0
0
1
0
2
1
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
1
1
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
1
7
0
2
0
0
0
0
1
0
0
0
2
2
6
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
7
0
1
0
3
0
0
0
0
0
1
1
0
0
0
0
0
1
1
5
0
0
2
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
5
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
3
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
1
2
0
0
0
1
1
0
0
0
2
0
0
0
1
2
1
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
1
0
1
0
0
1
1
3
0
0
0
0
2
0
0
0
0
0
0
0
0
5
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
3
0
2
2
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
13
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
3
0
0
2
2
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
5
3
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
2
0
1
0
0
2
1
1
0
0
1
0
0
4
0
1
0
0
0
0
0
1
0
0
0
0
0
0
4
0
2
2
0
0
1
6
2
0
2
0
0
1
0
2
0
0
1
0
0
0
8
0
0
0
0
1
1
0
1
0
0
0
1
3
0
0
2
0
0
0
0
0
0
3
2
0
1
0
1
0
2
1
0
2
0
0
2
0
0
2
0
1
0
1
0
0
0
0
0
2
0
3
1
0
0
0
0
1
0
0
1
3
0
0
1
0
0
0
1
2
2
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
5
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
2
0
0
0
1
0
2
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
2
1
0
0
2
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
2
1
2
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
1
2
0
0
0
1
0
3
0
0
0
0
0
0
0
0
1
0
1
2
0
1
0
0
0
0
0
1
0
2
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
1
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
2
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
1
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
2
0
0
0
2
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
1
2
0
0
1
2
0
0
0
0
0
1
0
2
0
0
0
0
2
1
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
1
1
2
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
2
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
6
1
0
0
2
0
0
5
2
0
0
0
0
0
0
0
1
0
1
0
1
2
0
0
2
0
0
1
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
3
3
0
1
0
2
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
2
0
3
0
0
1
5
1
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
3
0
0
0
0
1
1
0
0
2
2
0
4
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
7
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
4
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
1
3
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
6
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
2
0
2
2
2
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
2
0
1
0
11
0
0
0
0
1
2
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
1
2
0
2
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
2
1
0
0
2
0
0
2
0
0
0
2
0
1
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
3
0
0
2
0
0
2
1
0
0
1
0
3
0
1
0
0
2
0
0
0
0
3
0
0
0
6
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
2
1
1
0
0
0
0
2
0
0
0
0
4
0
0
0
0
1
0
0
2
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
1
1
0
0
0
1
1
0
4
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
1
2
1
0
0
0
4
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
1
2
0
0
3
0
0
0
0
0
0
1
2
0
0
1
0
0
2
0
0
0
0
0
3
0
0
2
1
0
0
0
2
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
3
0
0
0
4
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
3
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
4
2
0
0
0
0
0
0
0
0
0
0
2
0
2
3
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
2
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
4
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
4
1
0
0
0
0
0
0
1
0
0
0
1
2
0
2
5
0
0
0
0
0
0
3
0
1
2
0
0
0
0
4
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
1
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
3
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
5
0
0
2
2
0
0
4
1
0
1
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
4
2
0
0
0
0
2
2
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
4
0
0
2
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
1
0
0
1
0
0
0
0
1
1
1
0
0
3
0
0
0
0
1
1
0
2
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
2
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
6
2
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
2
2
1
0
0
1
0
0
0
1
2
2
0
0
0
0
0
1
0
2
0
3
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
2
2
1
0
1
4
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
3
0
0
0
0
0
0
1
1
0
0
0
6
0
0
0
0
0
1
2
0
0
2
0
4
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
3
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
3
0
0
0
5
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
2
6
0
0
3
1
0
0
0
0
2
2
0
0
0
2
1
0
0
0
3
0
0
1
0
2
0
0
1
0
1
0
2
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
1
1
0
0
3
0
0
1
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
2
1
0
1
2
0
0
0
2
0
3
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
3
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
1
1
3
2
0
0
0
0
0
0
0
1
0
0
0
2
1
2
3
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
2
2
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
3
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
3
0
0
0
0
1
0
0
0
1
0
2
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
2
0
0
1
0
1
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
1
0
0
7
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
1
0
0
4
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
5
0
1
0
2
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
1
0
0
0
1
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
7
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
1
0
9
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
4
0
0
0
1
0
0
1
1
1
0
0
1
0
0
1
2
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
3
0
0
0
0
2
0
0
0
0
0
1
0
3
0
0
0
0
0
1
0
0
0
3
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
2
0
0
2
0
0
2
0
1
0
1
0
0
0
0
6
2
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
1
0
0
0
0
7
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
5
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
6
1
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
1
3
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
2
1
2
0
0
0
0
1
0
2
1
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
2
0
0
0
0
0
1
3
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
1
1
0
0
3
1
1
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
2
0
4
0
0
0
0
2
3
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
1
0
1
0
2
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
2
0
2
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
2
0
0
1
1
0
1
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
1
0
0
2
0
0
0
3
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
3
0
2
0
2
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
3
0
0
1
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
1
0
0
1
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
1
0
1
2
0
0
0
0
0
2
1
0
2
0
2
0
0
0
0
0
0
0
2
1
0
2
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
2
0
2
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
1
1
0
0
0
3
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
3
1
0
1
0
0
0
1
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
2
0
0
0
0
1
1
0
0
1
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
0
0
0
0
0
1
2
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
2
0
0
3
0
2
1
0
0
4
0
3
2
0
0
2
0
0
0
2
0
1
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
3
2
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
1
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
1
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
8
0
1
0
0
0
1
0
0
0
2
0
0
1
0
0
1
2
2
0
0
0
0
0
0
2
3
0
2
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
2
1
0
2
0
0
2
0
0
2
0
0
1
0
0
0
3
0
0
0
0
0
0
0
2
0
2
0
2
1
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
3
0
0
4
0
0
2
2
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
1
1
2
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
5
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
1
0
0
2
0
3
1
0
0
4
1
9
0
0
0
0
1
2
1
0
0
2
0
1
3
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
4
5
0
0
2
0
0
2
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
2
1
6
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
12
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
4
2
0
1
0
0
0
0
0
0
1
1
2
0
0
1
0
0
0
0
3
5
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
2
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
1
1
0
4
2
1
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
7
0
0
0
4
0
0
0
0
0
0
0
1
3
5
1
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
4
3
1
0
0
0
1
0
3
0
0
3
0
1
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
2
2
0
0
0
1
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
1
3
1
0
0
0
0
0
0
2
0
0
0
0
0
0
5
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
6
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
1
0
0
3
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
4
1
0
0
2
0
2
0
0
0
1
0
0
7
0
0
2
1
0
3
0
2
0
0
1
0
2
2
1
2
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
1
0
2
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
4
0
2
0
0
0
1
0
0
0
0
0
0
3
0
2
3
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
3
0
0
2
0
1
0
0
0
0
0
0
0
0
0
3
4
2
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
1
0
4
2
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
5
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
1
0
0
0
0
1
0
1
2
0
3
3
0
0
0
1
3
0
0
0
2
0
3
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
2
0
0
0
2
0
2
4
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
2
2
0
0
0
3
0
0
0
0
2
0
0
0
9
0
0
0
0
0
0
1
0
2
0
0
2
0
3
0
0
2
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
2
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
4
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
5
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
2
0
1
1
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
1
1
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
3
2
0
0
0
0
0
0
3
0
0
4
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
2
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
1
2
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
1
3
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
1
2
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
1
1
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
5
2
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
1
0
0
1
1
0
0
1
0
0
0
0
2
0
0
0
5
0
0
0
0
0
0
2
0
0
1
1
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
2
0
2
0
0
0
3
0
2
3
0
1
2
0
0
0
0
0
0
0
0
1
1
0
5
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
1
0
0
2
0
9
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
1
0
3
0
0
1
0
0
0
0
1
0
0
2
5
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
5
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
5
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
9
0
1
0
1
0
0
0
0
0
2
4
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
2
0
2
2
1
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
1
1
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
2
3
0
0
2
0
2
1
1
2
1
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
4
0
0
0
0
1
1
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
3
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
2
0
0
0
0
0
0
0
2
0
2
1
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
3
1
0
0
0
0
0
2
2
2
0
0
0
1
2
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
1
2
2
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
1
0
0
0
1
0
0
2
3
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
2
2
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
13
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
2
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
2
2
1
0
0
0
2
0
0
0
0
1
6
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
4
0
0
0
1
3
0
3
0
0
0
0
1
2
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
7
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
4
0
0
0
0
0
0
2
0
5
0
0
0
0
3
0
1
2
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
10
2
1
0
2
2
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
4
0
1
0
2
0
0
1
0
0
0
3
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
1
1
1
0
5
0
2
0
0
0
3
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
2
0
2
5
2
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
4
3
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
1
2
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
3
0
2
0
0
0
0
0
0
0
0
4
0
0
0
0
0
2
0
1
0
0
0
5
2
0
0
3
0
0
1
2
0
0
0
0
1
0
3
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
2
0
0
1
0
3
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
2
0
1
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
1
0
0
0
2
7
0
1
0
0
3
0
0
2
0
0
0
1
1
0
0
2
1
0
1
0
3
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
1
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
5
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
5
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
1
0
1
0
2
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
2
1
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
3
0
0
0
0
0
2
0
2
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
1
0
0
2
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
18
0
0
2
1
1
0
0
0
0
0
0
0
2
0
0
0
2
4
0
0
3
2
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
2
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
2
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
6
0
2
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
3
0
0
0
0
1
1
1
0
0
4
0
3
0
0
0
0
2
1
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
3
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
1
1
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
6
0
0
0
0
3
0
0
2
0
0
0
0
0
0
1
0
1
0
1
0
3
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
1
0
3
2
0
0
0
0
0
0
1
0
0
0
3
0
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
3
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
3
0
0
0
0
2
0
3
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
2
0
0
1
0
2
0
0
0
0
3
2
0
1
0
0
3
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
8
0
1
0
0
0
0
0
0
0
0
0
2
1
1
0
2
2
0
0
0
2
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
1
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
5
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
2
0
1
0
0
0
2
0
0
0
0
2
1
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
2
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
3
1
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
1
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
5
0
0
0
0
0
2
0
0
0
0
2
1
1
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
1
0
0
0
0
1
0
6
0
0
2
0
0
0
0
0
0
0
0
0
0
5
0
0
2
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
1
0
2
1
0
0
4
0
1
0
1
1
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
3
1
0
0
0
0
0
0
3
1
0
1
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
6
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
3
1
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
1
0
3
1
0
4
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
1
0
1
0
0
0
1
0
0
0
0
2
0
0
1
1
0
2
0
0
0
4
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
2
0
0
0
0
2
0
0
2
0
0
0
0
5
0
0
2
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
6
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
7
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
4
0
0
1
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
3
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
2
0
5
2
3
0
0
2
0
1
0
0
0
0
2
2
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
4
0
0
1
0
0
5
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
1
0
0
2
0
0
0
2
0
0
0
0
4
0
0
0
2
2
1
0
0
0
1
0
1
0
0
11
0
0
0
2
1
0
0
0
0
0
6
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
2
1
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
1
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
1
1
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
7
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
1
0
1
0
2
1
2
0
0
0
1
0
1
2
1
0
0
0
0
0
0
0
1
2
0
0
2
0
7
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
5
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
3
0
0
1
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
2
0
1
2
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
1
1
0
2
1
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
3
1
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
4
0
0
1
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
1
0
2
0
1
0
1
2
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
3
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
3
1
0
0
0
0
0
0
0
0
2
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
1
0
0
0
0
2
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
3
0
1
1
0
3
1
0
0
0
1
1
2
0
0
0
5
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
2
4
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
1
2
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
4
0
0
4
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
2
1
0
2
0
2
0
2
2
0
3
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
5
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
1
0
0
0
1
0
2
1
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
1
1
0
1
2
0
0
0
0
0
1
2
0
0
0
2
1
0
0
4
0
0
0
0
0
0
0
0
3
2
0
0
0
0
3
0
0
0
1
1
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
1
1
0
0
0
4
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
1
0
0
0
1
0
0
18
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
1
2
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
3
2
3
0
2
0
0
0
0
0
0
0
0
0
0
5
2
0
0
0
0
0
0
5
1
1
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
1
1
2
0
6
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
1
0
0
1
3
1
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
3
0
2
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
6
0
0
0
2
0
2
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
4
0
0
0
0
0
2
2
0
0
0
0
3
2
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
1
2
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
5
0
0
0
0
0
1
1
0
0
0
2
3
0
1
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
5
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
10
0
0
0
0
0
5
1
1
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
1
2
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
9
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
2
2
0
0
0
1
0
1
0
2
0
2
1
1
1
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
7
0
1
0
0
0
0
0
0
1
0
0
1
4
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
3
1
0
0
2
0
1
0
0
0
0
3
1
0
3
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
3
0
2
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
1
8
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
3
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
2
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
2
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
1
3
0
2
2
2
0
1
0
1
1
0
0
2
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
2
2
0
1
0
0
2
0
0
2
0
1
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
3
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
3
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
3
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
1
0
2
2
0
0
2
0
0
0
0
0
1
0
1
1
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
2
0
0
3
0
1
0
0
1
0
0
0
1
1
1
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
1
0
0
3
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
3
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
4
0
0
1
0
1
0
0
0
0
0
0
0
0
1
5
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
1
0
2
1
0
0
0
1
0
0
0
0
2
1
0
0
1
0
0
1
0
2
2
0
0
2
1
1
0
0
0
0
0
1
2
0
0
0
1
0
1
0
0
0
1
0
1
2
0
2
0
2
1
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
1
1
0
0
0
3
0
2
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
2
0
0
0
2
0
0
1
2
0
3
0
0
0
0
0
0
0
0
2
3
0
3
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
1
0
1
1
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
5
0
0
0
0
0
0
0
3
1
0
0
0
1
2
2
0
0
0
0
0
0
2
0
0
1
0
0
0
2
1
2
1
0
0
3
2
0
1
1
0
0
3
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
5
0
1
0
0
0
0
0
1
0
5
0
1
2
1
0
0
1
0
0
0
3
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
3
0
0
0
2
2
0
0
0
2
2
0
0
0
2
2
0
0
0
2
2
0
0
4
0
4
0
0
1
0
0
0
0
0
0
2
1
1
0
0
0
0
0
8
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
3
0
0
1
0
1
3
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
2
0
0
0
1
0
0
0
0
0
1
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
2
4
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
1
2
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
5
0
0
1
0
1
0
0
4
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
1
0
0
0
0
0
0
3
0
1
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
3
0
2
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
2
0
0
0
0
0
1
0
0
7
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
2
0
0
1
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
4
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
1
0
0
0
0
2
0
3
0
0
0
0
0
0
1
2
0
0
0
3
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
2
4
0
0
2
0
5
2
0
0
0
1
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
1
1
1
0
1
0
2
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
3
0
2
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
3
1
0
0
0
1
0
0
0
0
0
2
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
1
2
0
4
1
0
0
0
0
0
0
0
0
0
1
1
5
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
7
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
1
1
0
0
0
6
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
1
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
1
1
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
1
0
4
0
2
0
0
0
1
0
0
0
1
5
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
2
3
0
0
0
0
1
0
1
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
2
1
3
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
1
3
0
1
0
1
0
0
2
0
0
0
0
0
2
0
1
0
0
1
1
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
3
2
4
0
0
1
0
2
0
0
0
0
0
0
0
0
0
5
0
0
0
0
5
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
6
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
10
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
3
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
2
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
1
0
0
2
1
1
2
0
0
0
0
1
0
0
0
1
2
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
2
0
0
2
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
1
1
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
8
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
4
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
4
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
1
1
0
0
2
0
0
0
2
0
1
0
0
3
0
0
3
1
3
0
0
0
0
0
4
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
1
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
3
0
1
0
0
0
0
2
2
2
0
0
0
0
1
0
2
0
2
0
0
0
5
0
0
0
0
0
2
1
0
0
0
2
1
0
2
2
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
1
0
0
0
2
2
0
0
0
0
0
0
3
0
0
0
0
2
1
0
0
2
0
0
0
1
1
2
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
2
0
3
0
2
1
0
0
1
0
0
0
0
3
0
0
3
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
2
1
1
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
2
0
0
1
0
0
0
1
2
0
0
0
0
2
0
0
0
0
1
1
0
0
0
1
0
0
5
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
3
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
4
0
6
0
0
1
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
1
1
2
0
2
1
0
0
0
0
0
0
0
2
4
0
0
0
2
0
3
0
2
0
0
1
0
0
0
2
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
2
2
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
4
0
0
1
1
0
3
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
6
2
1
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
5
3
0
0
1
0
0
0
0
0
0
1
0
1
0
1
3
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
1
0
0
0
0
1
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
6
0
2
1
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
2
0
0
0
3
2
0
0
0
0
2
2
0
0
1
0
2
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
1
1
0
0
0
2
0
0
2
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
2
0
1
0
2
0
0
1
0
1
1
0
0
1
0
0
3
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
1
3
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
7
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
2
5
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
2
0
2
2
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
3
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
2
0
2
0
0
0
2
0
0
2
1
0
0
1
1
1
0
0
1
1
0
0
0
0
0
3
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
1
3
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
3
0
0
1
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
2
0
2
0
0
0
1
0
0
2
0
0
0
0
1
2
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
1
3
0
1
1
1
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
1
5
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
3
0
1
0
0
2
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
3
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
6
0
0
0
1
0
0
0
2
0
0
0
0
0
0
3
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
2
0
2
0
1
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
1
1
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
7
1
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
2
0
0
1
0
0
0
0
1
0
0
0
0
2
1
0
2
0
0
0
0
2
0
2
0
0
0
1
1
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
4
0
1
0
0
1
0
0
1
0
0
0
3
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
1
0
0
0
0
1
2
0
0
0
0
1
1
0
0
1
1
0
0
0
0
2
1
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
1
0
3
2
0
0
0
0
2
1
0
0
0
0
1
0
2
0
0
1
0
0
0
2
2
2
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
2
0
0
0
1
0
0
2
0
0
1
1
9
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
1
0
0
0
0
2
1
0
2
0
0
0
0
0
2
0
0
7
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
2
0
0
5
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
1
0
2
0
1
7
0
0
0
0
0
0
2
0
0
0
0
2
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
2
2
0
0
0
0
0
2
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
1
0
2
0
0
0
2
0
1
1
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
3
0
2
0
3
0
0
0
0
0
0
0
2
1
0
0
0
1
0
3
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
5
2
2
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
1
0
0
1
0
2
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
3
0
0
3
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
1
2
0
0
0
3
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
4
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
2
0
1
0
2
0
0
0
0
0
1
0
0
1
0
0
3
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
3
1
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
3
0
7
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
1
1
4
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
1
0
0
0
0
2
1
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
12
0
1
0
0
0
0
1
0
2
0
3
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
3
1
0
2
1
0
0
0
1
0
0
0
0
2
1
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
10
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
2
1
0
2
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
1
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
1
0
1
0
1
2
1
0
0
0
1
2
0
0
0
1
2
1
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
2
2
3
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
3
1
0
0
1
0
1
0
0
0
0
4
0
2
5
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
1
0
1
0
2
1
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
1
0
0
2
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
7
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
3
0
0
0
1
0
0
0
0
1
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
1
1
2
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
4
2
1
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
3
0
2
0
0
0
2
0
0
4
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
4
0
0
0
0
0
2
0
0
0
3
1
0
0
2
0
0
0
0
0
1
1
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
1
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
3
1
4
0
2
0
0
0
0
0
1
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
3
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
1
0
1
0
0
1
0
0
2
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
1
3
0
2
0
0
0
0
3
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
30
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
4
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
2
0
2
1
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
1
0
0
2
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
1
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
2
1
1
0
1
0
0
1
0
1
0
1
0
2
1
0
2
2
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
2
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
2
0
0
0
2
0
0
0
2
1
0
0
4
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
4
2
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
1
0
0
2
0
2
2
1
0
2
0
0
0
1
0
0
0
0
1
0
0
1
1
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
1
0
3
0
0
0
1
0
1
0
0
0
1
0
0
0
2
0
0
0
0
2
0
2
0
3
0
1
0
0
0
0
0
4
0
0
1
0
0
0
0
1
2
0
0
2
0
3
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
3
0
0
1
0
2
0
2
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
1
1
1
0
0
2
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
3
0
2
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
2
0
0
0
0
1
0
0
0
2
0
1
0
0
2
1
0
0
0
0
0
0
0
1
0
2
1
0
0
1
0
0
0
13
0
1
2
3
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
2
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
1
0
0
0
1
0
1
0
0
0
0
0
0
1
1
1
2
0
2
1
0
0
0
0
0
2
1
2
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
4
3
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
2
0
0
5
0
0
2
0
0
0
0
0
0
1
0
1
1
2
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
1
0
0
1
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
1
0
0
1
1
1
0
0
0
0
0
0
1
2
0
0
0
0
3
0
0
1
0
2
3
1
0
0
0
3
0
1
0
0
2
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
3
0
3
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
3
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
1
1
0
0
2
0
2
0
0
0
0
0
0
3
1
3
0
0
0
0
0
0
0
0
4
1
0
4
1
2
2
1
2
0
0
0
0
1
11
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
1
0
0
2
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
1
1
0
2
1
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
2
0
3
0
0
1
0
0
0
0
4
0
0
1
1
0
3
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
3
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
4
0
2
3
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
5
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
3
0
0
1
0
0
0
1
0
0
1
0
1
2
7
0
0
0
1
0
0
2
0
0
0
1
0
0
2
0
0
0
2
2
0
0
3
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
3
1
0
0
0
0
1
3
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
1
2
0
0
2
0
0
0
1
3
0
0
0
0
2
0
0
0
0
2
2
2
0
0
0
0
1
0
0
0
0
0
0
7
1
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
4
1
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
2
0
0
0
2
0
3
0
0
1
0
1
0
2
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
2
1
4
1
1
0
0
1
0
1
1
3
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
3
2
0
3
0
0
0
0
2
1
2
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
3
0
0
0
1
0
0
0
1
0
2
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
5
2
2
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
4
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
1
0
0
1
3
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
3
0
0
0
0
0
1
3
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
1
1
0
2
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
1
2
0
1
0
0
2
0
1
1
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
2
2
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
3
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
7
2
0
0
0
2
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
1
2
0
2
1
4
0
0
2
0
0
0
1
0
0
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
3
0
0
0
3
0
0
2
0
0
0
2
1
0
0
0
0
0
2
0
0
2
3
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
4
0
0
1
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
4
1
0
2
0
3
0
0
0
0
0
2
2
0
0
1
0
3
0
1
1
0
3
2
0
10
0
0
2
2
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
2
0
0
3
0
0
0
1
0
0
3
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
3
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
4
1
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
2
1
0
0
0
2
0
1
0
0
0
2
1
1
0
0
2
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
2
0
0
0
0
0
2
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
10
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
3
0
3
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
2
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
1
0
1
1
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
5
0
0
0
0
0
0
1
0
0
1
2
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
1
0
2
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
4
2
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
1
2
0
1
2
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
1
0
2
1
10
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
2
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
3
2
2
0
0
2
0
0
0
3
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
1
2
0
0
0
0
1
3
1
2
0
3
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
1
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
6
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
1
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
3
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
2
2
7
0
2
0
0
2
0
0
3
3
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
3
0
1
0
2
0
0
0
0
1
4
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
1
1
0
1
0
2
2
0
0
0
0
1
0
1
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
3
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
2
5
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
3
1
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
1
3
0
0
2
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
4
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
3
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
7
0
0
0
0
2
0
1
0
0
0
1
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
1
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
3
0
1
0
0
1
0
0
0
0
2
1
0
0
1
1
0
0
0
2
1
0
0
0
0
1
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
2
1
0
7
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
1
0
1
0
1
0
0
1
2
0
2
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
2
0
0
1
2
2
0
0
0
0
0
8
0
1
0
1
0
1
0
0
0
0
2
0
5
2
0
0
2
2
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
2
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
2
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
1
0
0
0
0
1
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
2
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
3
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
4
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
4
0
0
0
3
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
4
3
0
0
0
0
0
0
3
0
0
1
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
13
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
1
0
2
2
2
0
0
2
0
0
2
1
1
0
0
1
0
1
1
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
1
1
1
0
6
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
2
1
0
0
2
11
0
0
1
0
0
0
0
0
2
2
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
1
1
0
0
0
0
1
1
0
2
1
0
1
0
0
1
0
0
0
3
0
0
2
2
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
2
2
0
0
1
1
1
0
0
0
0
0
1
2
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
4
0
2
0
0
0
0
1
0
0
2
0
1
0
1
0
0
0
2
1
0
2
2
0
0
0
0
5
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
2
3
1
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
8
1
3
0
0
1
0
2
2
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
1
0
1
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
3
2
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
2
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
3
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
1
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
5
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
2
1
5
0
0
0
1
1
0
2
1
2
1
0
0
0
0
0
0
0
0
0
1
2
1
0
1
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
6
0
0
0
0
2
0
1
0
0
2
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
4
0
1
0
2
1
1
5
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
8
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
1
5
1
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
1
0
2
0
0
0
1
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
3
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
7
0
0
1
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7
0
1
0
0
0
0
2
1
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
3
0
0
0
0
0
1
1
2
0
0
0
0
1
0
0
0
9
1
0
0
0
0
1
0
0
0
10
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
1
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
2
0
3
6
0
0
0
2
0
0
2
0
0
1
0
0
2
0
0
0
0
1
2
2
2
0
7
1
0
0
1
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
3
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
2
0
0
1
2
0
0
0
3
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
1
0
0
0
6
0
1
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
1
0
1
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
5
0
1
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
5
4
0
0
0
2
0
1
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
5
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
3
0
0
3
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
9
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
2
0
1
0
0
0
0
3
2
1
0
0
0
1
0
0
0
0
1
0
3
0
0
0
1
0
0
0
0
0
1
0
0
2
0
4
0
1
0
1
0
1
0
0
4
0
0
0
0
0
1
0
11
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
3
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
2
1
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
2
0
1
0
5
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
4
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
2
0
0
0
1
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
2
1
1
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
4
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
5
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
2
0
0
1
5
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
2
0
0
3
0
0
0
1
0
0
0
2
0
0
0
0
1
1
0
0
0
1
2
1
0
0
1
3
1
1
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
1
3
0
0
0
0
1
0
1
0
0
0
2
0
0
0
1
1
1
1
0
0
0
8
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
3
0
2
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
2
0
1
1
0
0
0
0
0
2
0
0
6
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
1
1
0
1
0
0
1
2
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
8
4
0
1
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
1
0
2
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
2
0
1
0
0
0
3
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
3
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
1
0
2
0
3
1
2
0
0
0
1
0
0
0
1
2
0
0
0
1
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
1
3
0
0
0
1
1
1
0
0
0
3
1
1
10
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
1
0
1
0
0
2
0
0
1
0
0
0
0
0
0
1
4
0
0
2
0
1
0
16
0
1
2
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
2
0
2
2
5
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
2
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
5
0
0
1
1
0
3
2
2
0
1
1
0
0
0
0
0
0
1
2
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
1
0
0
2
0
0
0
2
3
1
2
2
0
6
0
0
2
1
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
2
0
2
1
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
11
0
0
2
0
1
0
0
0
3
0
0
0
1
0
1
0
0
0
0
0
2
0
0
1
2
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
2
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
4
0
1
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
2
0
0
2
0
0
0
0
0
1
1
0
0
2
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
1
0
0
0
1
0
0
2
0
2
0
0
0
0
2
2
0
1
0
0
7
0
10
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
1
1
0
0
0
2
0
0
0
2
0
0
1
0
2
0
1
0
2
0
1
1
0
0
0
2
0
0
0
2
0
0
1
0
1
0
0
0
0
1
0
0
0
1
1
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
2
0
0
1
0
0
0
0
0
3
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
1
0
2
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
6
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
8
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
1
7
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
3
1
0
0
0
0
0
0
0
0
2
0
1
3
4
0
2
2
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
2
3
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
2
0
1
0
0
2
2
0
0
0
3
0
0
0
2
0
0
2
0
1
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
1
0
1
0
5
0
0
1
0
0
0
0
2
1
1
0
0
0
0
2
0
0
0
0
1
2
0
0
0
1
0
0
0
1
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
3
0
0
0
0
0
0
0
4
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
3
0
1
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
2
0
1
1
0
0
0
0
0
6
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
1
1
0
0
2
0
0
0
0
0
2
0
0
1
0
4
3
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
2
0
1
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
2
2
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
6
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
1
0
2
0
0
0
0
2
1
0
0
3
0
0
0
0
0
0
0
2
0
0
0
1
1
0
2
0
0
1
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
4
0
0
1
0
0
0
0
2
0
0
2
0
1
0
0
10
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
3
0
0
0
0
0
0
0
5
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
2
0
3
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
3
0
0
0
0
0
4
2
0
0
1
0
1
2
0
1
2
1
0
0
0
0
0
0
0
0
2
0
0
2
0
1
1
0
1
0
0
0
2
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
1
3
0
0
3
0
0
0
2
0
0
0
1
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
2
0
1
0
1
0
1
5
0
0
1
0
2
0
1
10
0
0
0
2
0
0
7
0
0
0
0
0
0
1
0
0
2
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
1
0
0
1
1
0
2
0
0
0
1
0
2
2
0
1
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
3
0
3
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
5
0
2
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
2
0
1
0
0
0
0
0
1
0
1
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
2
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
1
0
0
0
1
0
1
0
2
0
0
1
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
3
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
2
1
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
5
1
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
5
0
1
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
2
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
5
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
2
1
3
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
4
0
0
0
0
0
0
0
2
1
0
0
0
0
2
3
2
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
1
0
0
0
0
0
0
0
1
2
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
3
0
1
0
4
0
1
1
0
2
0
0
4
4
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
1
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
4
1
0
0
0
1
2
0
1
0
1
4
0
0
0
1
0
3
0
1
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
1
0
3
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
1
7
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
1
3
1
0
0
0
0
1
0
3
0
1
0
0
0
0
1
0
0
2
0
0
1
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
3
0
0
2
1
0
0
0
2
0
0
0
2
2
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
1
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
12
0
0
1
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
2
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
4
0
1
0
1
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
7
0
0
0
0
0
0
1
1
0
2
1
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
3
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
2
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
1
2
0
0
0
0
1
0
0
2
2
0
0
2
0
1
0
0
0
5
0
0
0
0
0
0
1
0
2
1
2
0
4
1
1
0
0
0
0
0
0
0
2
0
5
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
3
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
10
0
0
2
0
1
1
0
3
1
0
0
1
0
0
2
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
2
0
1
0
0
0
0
0
2
2
3
0
0
3
1
0
0
0
0
0
0
4
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
2
1
0
0
2
0
1
1
0
0
2
0
2
1
2
2
2
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
3
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
1
0
1
0
0
0
0
0
4
1
0
8
0
0
2
0
0
0
0
0
0
0
1
4
4
0
0
0
0
0
1
0
0
3
1
0
0
0
2
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
4
0
1
0
1
1
0
0
0
1
0
1
0
0
0
2
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
11
1
1
2
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
2
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
5
0
5
0
0
0
0
0
3
2
0
0
0
0
0
0
2
2
2
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
2
1
0
0
0
0
0
0
0
0
0
0
3
5
0
0
3
0
0
0
0
2
0
0
1
0
0
0
2
0
1
0
0
1
0
2
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
2
2
0
0
2
2
0
0
0
0
0
0
0
1
0
0
1
2
0
0
2
0
0
2
1
0
1
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
3
0
1
0
0
2
0
0
1
0
2
0
0
0
1
0
1
0
0
0
2
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
1
2
0
0
1
0
0
2
1
0
0
0
4
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
2
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
1
0
0
1
0
0
3
1
14
4
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
5
1
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
2
1
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
2
1
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
1
2
0
0
1
0
2
0
3
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
1
0
0
1
1
1
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
3
0
0
2
3
0
3
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
5
0
0
0
0
1
0
1
0
1
0
1
1
0
1
0
0
0
0
1
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
3
0
3
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
5
0
0
0
2
0
2
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
3
1
1
0
0
0
0
0
1
0
3
0
0
0
2
0
0
1
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
1
0
2
1
2
0
0
1
2
0
0
0
2
0
2
0
0
2
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
2
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
3
0
0
2
0
0
0
0
0
4
4
0
0
0
0
0
0
0
0
0
0
2
0
4
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
3
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
3
0
2
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
3
0
1
0
0
1
0
0
0
4
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
1
0
0
0
0
1
0
4
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
2
0
2
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
1
0
1
0
1
0
0
0
4
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
1
0
1
0
1
0
0
1
3
3
0
0
0
0
0
3
1
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
2
0
2
1
1
3
0
0
1
0
0
0
0
0
0
8
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
1
4
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
2
1
0
0
0
0
0
1
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
2
1
0
0
0
2
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
1
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
1
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
2
2
0
1
1
5
0
1
5
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
2
0
0
4
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
2
1
1
0
0
0
0
1
0
0
0
0
0
3
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
1
0
0
2
2
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
9
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
7
0
0
2
0
0
0
3
0
0
0
3
0
2
0
3
0
1
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
5
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
2
0
0
0
2
0
1
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
6
0
1
0
0
0
0
3
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
1
0
3
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
1
0
1
2
0
0
3
0
0
2
0
1
0
0
1
0
0
3
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
2
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
5
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
1
1
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
3
0
0
0
2
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
2
0
2
0
0
0
0
6
0
0
0
1
0
0
0
1
0
0
1
0
0
3
1
0
0
0
2
0
1
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
1
0
1
1
2
0
0
0
1
2
0
2
0
0
3
0
0
0
1
0
1
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
2
0
2
2
1
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
3
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
1
0
0
1
0
2
0
0
0
0
0
3
0
1
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
3
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
4
0
0
0
0
0
2
3
0
2
1
1
10
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
3
0
0
0
1
0
2
0
2
0
0
0
0
0
0
2
0
0
2
1
2
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
1
0
0
1
0
0
3
0
0
0
0
0
1
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
2
0
0
1
1
0
1
1
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
1
0
0
0
0
0
2
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
3
0
0
0
2
2
0
0
0
0
0
1
0
1
0
1
0
0
0
1
6
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
2
0
4
1
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
5
0
2
0
0
1
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
1
3
1
1
1
0
0
0
0
0
0
0
0
4
2
0
0
0
1
0
5
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
6
9
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
1
0
4
2
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
2
0
3
2
0
1
0
2
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
1
0
1
8
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
2
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
1
2
0
1
0
0
0
0
1
2
0
4
0
0
2
0
0
0
1
0
0
1
0
2
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
1
0
0
0
0
0
0
3
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
4
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
1
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
1
0
2
0
2
0
1
0
0
0
0
0
0
0
1
6
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
2
0
0
2
0
2
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
5
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
3
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
1
1
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
3
0
0
1
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
2
4
1
1
0
0
2
0
0
1
0
0
0
0
0
0
4
0
0
0
0
1
1
0
0
0
0
1
0
0
0
3
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
4
0
0
0
0
1
0
0
0
0
0
0
3
1
0
1
0
0
0
0
0
0
0
1
2
1
0
0
3
0
0
0
0
1
0
0
0
0
0
14
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
9
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
10
1
0
0
1
0
0
0
6
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
3
8
2
0
0
0
0
1
0
0
1
0
0
0
1
3
0
4
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
1
0
0
0
0
0
2
2
2
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
6
0
1
0
0
0
0
2
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
3
0
0
4
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
5
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
1
0
2
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
3
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
2
1
1
0
0
5
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
1
0
0
0
2
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
5
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
1
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
1
0
2
0
2
0
1
0
1
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
1
0
2
0
0
1
0
0
2
2
4
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
1
0
1
1
2
0
0
1
0
0
0
0
0
1
2
0
1
2
0
3
0
0
1
0
0
1
0
0
0
0
3
0
0
1
0
2
0
2
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
1
0
1
2
0
1
1
5
0
0
0
0
1
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
4
0
2
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
2
0
0
0
1
1
0
0
0
2
0
0
0
2
1
0
2
0
0
0
0
1
0
0
0
0
1
7
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
5
1
0
0
2
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
3
0
0
2
0
1
2
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
2
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
2
2
1
2
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
3
0
2
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
2
0
2
2
0
0
0
2
1
0
0
0
1
0
3
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
3
0
0
2
0
0
1
0
0
0
3
0
2
1
0
0
0
0
2
0
0
0
0
0
6
0
0
0
0
0
2
1
0
0
0
1
0
3
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
4
0
0
0
1
0
0
0
0
4
0
2
0
0
0
0
0
2
1
0
1
0
0
1
0
0
0
2
0
1
0
1
2
0
0
0
0
0
0
0
2
1
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
1
0
0
0
1
0
1
0
2
0
0
0
0
0
1
0
0
0
0
3
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
2
0
3
2
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
4
0
2
1
0
0
2
1
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
3
0
0
1
0
0
1
0
0
0
0
2
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
3
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
3
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
2
0
1
2
0
0
1
0
0
0
0
3
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
1
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
20
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
1
1
0
1
0
0
0
0
0
0
0
0
6
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
4
0
0
2
0
0
0
0
2
0
0
1
0
1
0
0
0
1
0
1
3
0
1
0
0
0
0
0
0
0
1
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
4
0
0
0
0
3
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
1
0
1
0
0
1
0
1
1
2
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
2
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
2
0
0
0
0
4
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
5
0
2
0
0
0
0
1
3
1
0
0
0
0
0
0
0
0
1
2
2
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
2
1
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
6
0
2
0
6
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
1
2
3
1
0
1
0
0
0
3
1
0
0
1
0
0
2
1
0
0
0
0
1
0
1
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
4
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
2
1
0
0
1
0
0
0
2
2
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
1
3
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
1
3
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
1
0
0
1
0
5
0
0
1
1
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
1
0
2
1
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
1
2
1
0
0
0
0
2
0
1
0
1
2
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
10
0
0
0
0
0
0
0
2
0
1
0
0
0
1
1
2
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
8
0
0
1
0
1
0
1
2
2
0
0
0
5
1
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
1
0
0
2
2
0
0
0
0
8
0
1
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
1
2
0
0
0
0
0
0
0
0
0
2
1
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
1
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
1
1
0
1
0
0
0
2
0
0
0
0
2
2
0
1
0
0
0
0
0
3
0
0
1
1
0
0
0
3
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
3
0
2
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
1
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
2
0
0
1
1
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
6
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
3
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
1
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
1
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
3
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
4
2
0
1
0
0
0
0
1
0
0
7
0
2
2
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
3
2
0
0
1
0
0
2
0
0
0
1
0
1
0
5
2
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
7
0
1
0
0
0
0
0
1
1
1
2
0
1
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
1
0
0
3
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
4
0
0
0
0
0
2
1
1
1
3
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
2
0
3
0
0
0
0
0
1
0
0
0
0
0
0
29
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
3
0
2
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
2
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
1
0
2
2
0
0
3
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
2
1
2
0
0
2
1
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
6
0
0
1
0
0
1
2
2
0
2
0
0
0
0
0
0
0
0
1
1
2
0
3
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
2
3
0
0
0
0
0
0
0
0
3
0
2
0
1
0
1
0
0
1
4
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
1
0
0
0
1
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
3
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
13
0
0
0
0
0
0
0
2
1
2
0
2
1
0
0
0
0
0
1
0
1
0
1
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
2
2
0
1
0
2
0
0
0
2
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
3
0
2
0
0
0
0
0
1
0
2
0
0
0
0
2
0
1
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
2
0
0
0
0
3
2
0
0
0
1
0
0
0
2
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
2
0
0
0
1
0
0
0
0
2
1
1
0
1
0
0
3
1
0
0
2
0
2
0
1
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
2
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
12
0
0
0
0
0
0
1
2
0
1
0
2
0
0
1
2
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
2
0
3
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
4
1
0
0
0
1
0
0
0
0
1
2
0
2
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
1
0
0
0
2
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
1
0
0
0
6
0
0
0
6
0
2
1
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
1
0
0
2
0
0
7
2
2
0
0
0
0
0
4
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
3
0
0
1
2
2
2
0
0
0
0
0
0
0
0
1
0
2
0
1
1
0
1
0
0
2
0
0
7
0
0
0
0
0
0
0
0
0
0
0
4
2
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
3
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
1
2
0
0
2
1
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
1
0
2
0
1
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
3
2
0
0
2
0
3
0
0
0
2
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
2
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
3
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
3
0
0
0
2
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
3
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
4
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
3
0
0
2
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
1
0
0
2
1
0
0
2
1
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
2
0
2
0
2
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
2
0
0
0
4
2
0
2
2
0
0
11
0
0
0
1
0
0
0
0
0
0
9
2
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
2
1
2
0
0
0
0
1
0
1
0
4
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
2
0
1
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
4
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
1
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
3
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
3
0
0
0
2
0
0
0
0
2
5
0
0
2
0
0
0
1
2
2
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
3
1
1
0
1
0
0
0
1
0
1
1
0
1
2
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
2
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
1
1
1
2
3
0
2
0
0
0
2
0
0
0
0
3
0
0
2
0
0
0
1
0
0
0
1
0
0
2
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
2
0
1
0
1
1
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
3
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
2
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
6
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
2
0
1
0
0
3
0
0
0
0
1
2
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
1
0
0
1
2
0
0
0
2
2
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
5
0
0
0
4
0
0
0
0
0
4
0
0
0
0
0
3
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
1
0
0
2
0
1
0
2
1
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
1
0
1
0
0
0
4
0
0
0
1
0
0
0
0
0
0
1
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
4
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
18
4
0
0
0
0
0
2
0
0
0
1
0
1
0
0
1
3
0
1
0
1
2
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
3
0
0
0
1
0
2
0
1
0
1
0
0
0
2
0
2
4
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
4
0
0
4
0
0
0
0
2
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
2
0
1
2
0
0
0
3
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
1
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
2
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
16
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
1
2
3
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
6
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
2
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
2
1
0
1
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
1
3
0
0
2
1
1
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
2
0
4
0
0
1
0
1
0
0
5
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
3
0
0
4
0
0
0
2
1
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
4
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
1
0
0
0
0
0
0
0
2
0
2
0
1
0
0
1
0
0
0
0
2
0
0
0
2
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
3
0
2
0
0
1
0
0
0
2
1
1
0
0
1
1
0
0
4
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
1
0
0
0
1
0
1
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
1
0
0
1
2
0
2
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
6
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
2
3
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
7
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
3
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
3
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
3
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
1
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
3
0
0
0
2
3
0
0
0
0
0
0
3
0
0
0
0
0
0
1
4
0
1
0
2
0
0
0
0
0
0
1
0
1
0
2
0
0
0
2
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
2
0
0
1
0
0
3
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
2
0
8
0
1
0
0
0
0
0
2
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
2
0
2
1
4
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
3
0
1
2
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
1
0
0
0
0
0
0
0
3
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
1
0
3
0
0
3
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
2
1
0
2
0
0
3
0
1
1
0
0
0
0
0
0
2
0
1
0
1
1
0
3
0
0
1
0
0
1
0
0
1
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
3
0
0
0
0
0
2
1
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
2
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
2
9
3
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
1
0
0
0
1
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
3
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
1
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
9
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
1
0
1
0
0
2
0
0
6
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
1
0
0
1
0
1
0
3
5
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
1
0
0
0
0
2
0
0
3
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
3
0
0
0
1
0
2
1
0
2
0
1
0
2
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
2
7
3
2
2
2
3
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
1
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
1
1
0
0
0
0
0
3
0
0
2
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
1
3
0
0
1
0
0
1
2
1
1
0
0
0
1
0
0
0
0
2
0
0
0
0
3
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
1
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
4
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
2
0
0
0
0
4
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
1
0
1
0
0
0
1
0
0
2
0
0
2
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
3
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
2
2
0
0
0
1
3
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
1
0
0
3
1
1
0
0
0
2
0
2
0
0
1
0
0
0
2
0
1
0
0
0
2
0
1
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
4
2
0
0
0
8
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
2
4
0
0
0
0
7
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
3
2
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
2
5
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
1
0
0
0
1
1
1
0
0
0
4
3
0
0
0
1
0
0
0
0
3
1
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
2
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
3
3
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
1
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
1
2
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
1
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
2
2
0
1
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
2
2
0
0
1
2
0
0
0
0
0
0
0
1
1
2
2
2
0
5
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
4
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
2
0
0
1
0
0
0
2
3
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
3
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
4
1
0
0
0
0
1
0
1
2
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
2
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
3
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
3
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
1
1
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
3
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
3
1
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
1
0
0
1
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
2
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
10
0
0
0
1
0
2
0
0
3
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
1
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
1
3
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
2
2
0
0
1
0
0
2
2
0
1
1
1
2
0
1
0
0
0
4
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
4
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
1
4
0
0
1
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
8
0
1
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
1
0
0
1
0
0
0
0
2
1
2
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
1
0
0
0
1
0
1
0
1
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
1
0
2
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
1
5
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
2
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
2
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
3
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
2
0
4
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
5
0
0
1
1
2
0
0
0
0
0
1
0
2
0
1
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
4
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
5
0
0
1
1
0
0
0
2
2
0
0
0
0
3
2
0
0
0
0
1
0
0
0
1
0
0
1
3
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
3
0
0
0
0
1
1
0
0
0
0
5
0
1
1
0
0
0
0
1
2
0
1
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
3
0
0
3
1
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
4
0
0
2
0
0
1
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
1
1
0
1
0
0
0
0
1
0
1
0
0
2
0
1
0
0
0
3
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
4
0
0
0
0
0
2
0
2
0
0
0
0
1
1
2
0
0
0
1
0
0
2
2
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
6
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
1
0
3
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
5
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
1
0
0
0
0
0
1
0
1
2
0
0
0
0
0
1
0
0
0
2
0
1
0
1
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
7
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
2
0
2
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
1
0
0
2
1
0
1
2
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
2
0
0
0
1
0
0
0
0
1
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
18
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
2
4
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
4
0
2
4
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
3
0
1
1
0
0
0
1
0
0
0
2
0
1
0
0
6
0
1
0
0
0
0
0
1
2
0
0
0
0
0
2
1
0
1
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
1
3
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
1
0
2
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
1
2
1
3
0
0
0
2
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
2
0
1
0
2
0
3
5
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
2
1
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
3
2
0
0
0
1
0
2
0
0
0
0
0
1
0
0
1
0
1
0
1
2
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
2
2
0
0
0
0
2
0
1
0
0
0
2
0
2
0
0
2
0
0
2
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
4
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
1
0
0
0
0
1
0
0
3
0
0
0
0
1
1
1
1
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
1
0
2
0
3
0
0
0
0
0
0
1
0
0
1
0
0
1
0
4
0
0
0
0
0
0
1
0
6
2
0
0
0
1
2
0
0
2
1
0
0
0
1
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
5
0
2
0
2
0
4
0
0
0
0
4
0
0
0
3
0
2
0
0
0
0
2
1
0
0
2
0
0
2
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
2
0
0
0
0
1
0
0
0
0
0
1
2
2
0
0
0
2
2
4
0
0
0
0
1
0
2
0
0
3
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
1
2
3
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
5
0
0
0
0
6
0
0
2
0
0
0
0
1
0
2
0
1
0
2
0
0
1
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
1
2
7
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
3
0
0
1
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
5
1
0
0
0
1
3
3
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
1
0
0
2
0
0
1
5
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
1
2
1
0
0
1
0
4
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
1
3
1
0
2
0
0
2
0
0
0
2
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
3
0
2
0
0
0
0
2
1
1
2
0
0
4
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
2
1
0
0
1
0
0
0
0
0
0
1
3
0
0
2
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
5
1
3
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
1
0
0
3
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
1
1
2
0
0
0
0
10
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
1
0
1
4
1
0
1
0
0
1
0
0
0
1
1
0
0
2
2
0
0
0
0
0
0
0
0
2
1
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
7
0
2
0
0
0
2
2
2
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
3
2
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
1
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
1
0
2
0
0
0
0
0
0
1
1
0
2
2
0
0
0
0
1
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
2
1
0
0
0
0
1
0
0
8
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
4
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
1
0
0
0
2
2
0
0
2
0
1
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
3
1
1
0
3
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
1
0
2
0
0
0
0
0
3
0
0
0
1
0
0
0
0
1
0
3
3
1
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
1
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
2
1
0
2
1
0
0
0
0
0
2
0
0
1
0
1
2
0
0
1
2
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
2
1
0
0
2
0
1
1
0
0
0
0
0
1
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
1
2
1
0
0
0
0
0
1
2
0
0
1
0
2
1
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
1
2
0
0
0
0
1
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
1
2
0
2
1
0
1
0
0
0
2
0
0
1
2
0
2
2
0
2
0
3
0
0
0
0
0
3
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
4
1
0
0
0
0
1
0
2
0
0
0
1
1
0
0
0
2
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
3
0
2
3
0
2
1
0
2
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
2
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
1
3
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
11
0
4
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
5
0
0
3
2
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
2
0
1
2
0
0
1
1
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
2
0
0
5
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
4
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
3
0
0
0
0
2
0
0
0
4
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
5
0
0
0
1
0
3
0
0
0
0
2
0
2
0
2
2
0
0
0
0
0
1
1
1
0
1
0
1
2
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
6
0
0
0
0
0
0
1
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
1
2
2
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
2
0
0
2
0
1
0
1
0
2
1
0
0
2
0
0
0
0
0
0
1
1
0
2
0
1
0
0
1
0
0
1
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
2
2
1
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
1
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
3
0
1
1
0
0
0
0
0
0
0
1
0
2
4
0
0
2
0
1
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
3
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
2
1
0
0
0
1
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
8
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
1
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
3
1
0
0
0
0
0
0
3
1
1
0
0
1
0
0
0
0
2
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
2
0
0
0
0
2
1
0
0
5
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
1
0
3
2
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
1
0
1
0
0
2
0
0
1
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
7
2
0
0
0
0
0
0
0
0
1
0
0
1
3
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
2
1
2
0
0
0
0
0
0
4
0
0
0
0
3
0
1
0
0
1
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
6
1
0
0
2
0
0
0
0
1
1
0
0
0
2
0
0
0
2
0
0
0
0
9
1
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
2
0
0
0
3
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
3
0
1
0
0
0
1
0
0
0
2
1
1
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
2
0
2
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
1
0
2
1
0
2
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
1
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
2
2
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
3
0
0
3
1
0
0
0
0
4
0
0
3
0
0
0
0
2
1
1
1
0
0
0
0
0
0
0
0
0
0
0
2
2
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
1
0
0
0
0
0
2
2
0
2
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
3
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
2
0
0
1
0
1
0
0
1
0
0
0
1
0
0
3
0
0
0
0
0
0
1
4
0
0
2
3
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
2
0
1
2
0
1
0
0
1
0
0
0
2
2
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
2
0
1
0
0
0
0
0
1
0
1
0
0
3
0
0
1
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
1
0
3
2
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
1
0
0
1
0
11
1
2
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
1
2
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
2
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
3
0
5
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
1
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
6
0
0
0
0
0
1
1
0
0
1
0
0
1
1
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
1
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
1
0
0
1
0
1
0
0
3
1
5
0
0
0
2
0
0
1
0
2
2
0
0
0
0
0
0
0
2
0
2
2
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
3
0
0
0
0
0
1
0
1
1
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
4
0
0
0
0
2
0
0
0
8
0
0
0
0
0
0
0
0
2
2
2
2
0
3
4
0
0
0
0
0
6
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
6
0
0
5
2
1
0
2
0
2
2
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
3
1
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
4
0
6
0
0
8
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
2
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
4
0
0
2
0
1
0
0
3
0
0
0
0
0
0
0
0
1
0
1
0
1
0
2
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
1
1
2
0
1
0
0
2
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
7
0
0
0
0
1
0
1
0
0
1
0
0
3
2
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
3
0
2
0
0
0
3
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
6
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
5
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
4
3
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
6
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
2
0
0
1
1
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
3
0
0
0
0
0
0
0
0
1
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
1
0
0
1
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
1
1
1
0
0
1
0
0
3
0
0
0
13
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
1
0
1
1
0
0
0
0
0
1
1
1
1
0
0
2
0
1
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
2
0
0
0
1
1
2
0
2
0
0
0
2
6
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
8
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
4
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
2
0
1
0
0
1
0
0
0
3
0
0
9
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
1
2
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
1
0
1
0
1
0
0
1
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
3
0
0
0
0
0
2
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
1
2
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
3
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
1
0
0
1
4
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
3
0
0
0
1
2
0
0
0
0
1
0
0
0
2
2
0
0
0
2
2
0
1
0
0
0
0
0
11
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
5
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
2
0
0
1
1
0
0
1
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
1
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
1
0
0
2
2
0
0
1
2
0
0
1
1
1
1
1
2
0
0
0
0
2
0
1
0
2
0
1
0
0
1
0
0
3
0
0
0
0
0
4
0
0
0
0
0
2
0
0
2
5
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
2
2
0
0
1
2
0
0
0
0
0
1
0
1
1
0
0
0
1
3
0
0
0
1
1
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
1
4
0
0
3
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
2
1
0
0
2
0
2
0
0
0
1
0
1
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
1
0
0
0
0
1
0
0
2
0
0
2
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
2
1
0
0
1
0
0
1
0
0
0
2
6
0
1
0
1
0
0
1
0
0
0
0
1
0
2
3
2
1
0
1
0
0
0
0
3
0
0
0
1
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
2
0
0
0
2
3
0
0
1
0
0
0
1
0
2
0
0
1
0
0
1
0
0
4
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
1
0
1
0
2
0
0
6
1
0
0
0
3
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
1
1
0
3
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
3
0
0
2
0
0
4
0
0
0
0
0
6
0
0
1
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
2
0
7
0
1
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
1
0
2
2
0
0
0
0
1
3
1
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
1
0
0
1
0
0
0
2
1
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
2
5
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
1
0
0
2
2
2
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
1
0
0
1
0
0
5
0
1
4
0
0
0
0
0
0
0
0
0
1
2
0
1
0
2
1
3
0
0
0
0
0
0
0
1
0
0
0
1
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
4
0
1
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
3
0
1
0
0
1
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
15
0
1
0
0
0
0
0
0
1
0
0
0
0
0
7
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
7
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
3
0
0
2
0
0
1
1
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
2
0
1
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
2
2
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
2
0
1
0
0
0
1
0
0
0
1
0
0
0
4
0
1
0
0
0
0
0
0
0
2
1
1
0
0
0
1
2
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
2
1
2
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
5
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
1
2
1
2
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
1
3
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
1
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
3
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
3
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
2
1
0
2
0
1
2
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
2
0
3
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
1
6
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
1
1
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
1
1
10
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
2
3
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
2
0
1
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
2
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
2
0
0
1
2
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
1
0
0
1
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
1
0
1
0
0
2
1
0
1
0
0
2
0
0
0
0
0
3
0
0
2
0
0
0
0
0
4
0
1
0
3
0
1
0
0
0
2
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
2
0
0
0
0
0
2
0
2
0
0
2
2
2
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
4
2
0
0
0
0
1
1
0
7
2
0
2
0
0
1
0
0
0
1
3
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
5
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
3
0
4
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
4
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
1
0
0
0
0
4
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
3
0
7
0
0
4
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
2
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
3
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
6
0
1
0
0
7
0
0
0
0
0
1
0
0
1
0
0
0
7
0
0
0
0
0
2
0
0
0
2
2
2
1
0
0
0
0
1
1
0
2
0
0
0
0
3
0
1
0
3
0
1
2
0
0
2
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
3
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
4
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
1
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
2
0
4
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
4
0
1
0
0
1
0
0
0
2
0
0
0
3
0
0
0
0
4
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
3
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
8
0
0
0
0
0
1
4
0
0
0
1
2
0
0
1
2
0
0
0
0
2
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
1
0
2
2
0
0
0
0
2
0
0
0
0
1
1
0
0
2
2
1
0
0
0
0
1
0
0
0
0
3
0
0
0
1
2
2
0
3
0
0
1
1
0
2
0
0
0
0
0
1
4
2
0
0
0
1
0
4
1
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
1
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
1
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
2
2
0
0
5
0
1
0
0
0
0
0
1
0
0
0
0
1
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
2
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
4
0
2
0
0
0
1
6
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
2
1
0
1
0
0
3
0
0
1
2
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
1
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
5
0
1
0
0
0
0
1
0
2
0
2
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
1
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
1
0
2
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
3
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
3
0
0
0
0
0
2
3
0
0
2
0
2
2
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
1
1
2
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
3
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
1
4
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
2
0
0
0
0
0
1
0
0
0
2
1
0
2
0
0
0
0
0
0
0
1
0
0
1
0
2
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
2
2
0
0
1
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
6
2
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
2
1
2
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
1
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
5
1
4
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
3
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
1
2
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
3
0
0
1
0
0
0
2
0
1
0
0
2
0
0
0
0
1
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
1
1
0
0
2
2
1
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
2
0
2
3
0
0
2
0
0
2
3
0
0
2
1
0
0
1
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
1
1
0
0
2
2
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
2
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
2
0
2
1
0
0
0
0
1
1
0
0
0
0
2
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
4
1
1
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
1
0
0
0
3
0
1
0
0
7
0
2
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
1
1
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
2
0
0
1
0
5
2
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
5
0
1
0
3
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
3
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
3
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
5
0
0
0
0
0
0
0
1
0
6
0
2
1
0
1
0
0
2
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
3
0
1
0
1
1
0
2
0
0
0
0
2
0
1
0
3
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
1
2
0
0
6
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
3
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
2
1
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
4
1
0
0
0
0
0
1
4
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
1
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
1
2
2
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
1
3
0
0
1
0
0
0
1
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
3
1
1
1
5
0
0
2
0
3
0
1
0
0
0
0
1
0
0
2
0
0
0
0
2
1
0
0
0
1
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
7
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
3
2
0
0
0
0
0
2
1
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
1
1
0
0
0
0
0
4
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
2
4
0
1
0
0
2
0
0
0
0
4
0
2
0
0
0
0
0
0
0
0
3
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
1
0
0
0
1
1
0
2
3
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
1
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
5
0
2
0
0
0
0
0
0
0
2
0
1
0
0
2
0
3
0
1
0
0
0
0
1
0
0
0
0
3
0
0
0
0
1
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
2
0
1
0
0
0
2
1
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
5
0
0
1
1
0
0
1
1
0
0
1
2
1
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
2
1
3
2
0
0
2
0
4
0
1
1
1
2
1
0
0
0
0
2
6
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
2
2
0
0
2
0
1
0
3
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
6
0
0
1
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
1
3
0
3
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
5
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
2
2
0
2
1
0
1
0
1
1
0
0
1
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
2
1
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
2
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
5
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
1
0
1
0
0
0
0
2
0
0
0
0
2
0
3
0
8
1
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
7
4
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
3
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
2
0
0
2
0
1
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
2
7
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
1
0
1
0
0
6
0
0
2
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
2
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
1
1
1
1
0
0
3
0
0
2
0
0
0
0
0
1
0
1
0
0
0
5
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
3
1
0
2
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
3
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
2
2
1
0
0
3
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
3
0
2
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
2
0
0
1
1
0
3
2
1
0
2
0
1
1
0
1
0
0
1
3
0
0
1
0
0
1
2
0
0
1
0
0
1
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
3
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
2
0
11
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
3
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
1
0
2
0
0
3
0
0
0
1
0
0
0
0
0
4
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
1
0
3
0
1
5
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
2
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
2
3
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
3
0
0
0
0
0
1
0
0
0
2
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
3
1
1
2
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
10
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
5
1
0
1
0
0
0
0
2
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
3
1
1
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
1
0
2
0
3
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
2
2
1
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
3
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
1
0
0
2
0
1
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
3
8
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
9
1
0
0
0
2
0
1
2
0
0
0
0
1
3
0
2
2
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
2
0
0
1
0
0
2
0
3
0
2
0
0
2
0
1
0
0
0
0
0
0
2
2
0
0
1
1
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
2
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
5
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
1
2
1
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
1
0
0
0
0
3
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
2
0
0
2
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
3
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
3
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
1
1
0
0
1
0
1
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
4
0
0
1
0
0
1
0
2
0
0
0
1
0
0
1
1
0
0
0
1
0
3
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
1
0
0
1
2
0
1
0
1
0
2
0
0
0
0
2
0
0
2
1
2
0
0
1
0
0
0
2
0
1
0
1
0
1
0
0
1
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
1
2
0
4
0
1
0
0
0
0
1
0
1
0
0
0
0
1
2
2
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
2
0
1
2
0
0
0
0
0
2
2
0
0
0
2
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
3
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
3
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
3
3
1
0
0
0
0
0
0
1
3
0
0
2
0
2
0
0
0
1
0
0
4
0
1
0
2
1
0
0
0
1
2
2
0
0
0
0
1
0
0
0
0
3
1
0
0
0
0
1
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
2
0
1
0
0
0
0
0
2
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
6
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
1
2
0
0
3
0
0
0
1
2
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
4
2
0
1
1
2
0
0
3
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
1
1
0
0
2
0
0
0
0
1
0
0
0
0
0
3
0
0
2
0
0
0
2
0
0
2
0
0
0
0
1
0
0
2
0
1
0
8
0
0
0
2
1
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
2
1
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
4
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
1
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
6
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
1
0
1
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
1
3
0
2
0
0
0
0
0
0
0
2
2
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
3
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
3
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
4
0
0
3
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
2
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
2
1
0
2
0
1
2
0
0
0
0
0
1
0
2
0
1
1
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
2
2
0
0
0
0
1
0
0
0
0
0
1
0
3
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
2
1
2
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
1
0
1
0
0
2
2
3
0
0
1
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
2
2
2
3
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
1
2
4
0
0
0
0
0
0
2
0
1
1
2
0
0
1
2
1
9
0
0
0
0
2
0
0
0
0
0
1
0
0
0
6
1
0
2
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
2
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
3
0
0
0
0
0
4
0
5
0
0
0
1
0
0
0
2
2
0
3
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
2
3
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
1
0
0
0
0
0
6
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
2
0
0
1
0
0
0
2
0
0
1
0
1
0
0
0
0
0
2
0
0
2
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
3
0
0
1
0
1
3
0
0
0
3
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
2
1
0
1
2
0
2
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
1
2
0
0
0
1
0
0
0
0
6
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
1
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
4
0
0
0
1
0
0
2
0
0
1
0
1
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
3
0
0
0
0
1
0
2
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
2
0
0
3
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
3
0
0
2
0
3
0
1
0
0
0
0
8
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
5
0
1
2
0
0
0
1
2
2
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
4
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
2
0
6
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
2
0
1
1
0
2
0
2
0
0
0
0
1
0
3
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
3
0
2
0
2
0
4
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
1
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
2
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
1
0
1
0
0
0
0
2
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
3
1
0
0
0
0
1
0
0
1
0
0
0
0
2
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
1
0
0
0
0
2
3
0
0
0
0
0
1
0
0
1
1
0
1
2
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
2
0
3
1
0
0
2
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
6
0
2
0
0
0
1
2
0
0
0
0
2
0
3
0
0
2
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
3
0
0
3
0
0
0
0
1
0
0
0
0
0
1
2
1
2
0
0
0
0
0
0
2
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
5
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
5
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
2
0
4
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
6
2
1
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
2
0
0
0
0
4
0
0
1
0
0
0
2
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
2
0
2
0
1
0
2
1
0
0
2
0
0
2
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
3
1
1
0
0
0
0
0
2
0
0
0
1
0
1
0
0
1
0
0
2
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
8
1
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
4
1
0
0
0
0
5
0
0
0
0
2
2
0
0
2
0
2
1
0
0
0
0
2
0
0
0
0
1
0
0
3
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
6
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
3
1
0
0
1
2
0
2
0
0
0
0
1
0
1
0
0
2
2
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
1
0
0
0
0
2
2
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
2
0
0
0
1
0
2
0
0
1
0
0
1
0
0
0
0
2
0
1
0
1
0
2
0
0
0
3
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
1
0
2
0
0
0
2
0
1
0
0
2
2
5
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
3
0
0
0
3
0
0
4
0
2
0
0
9
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
1
0
0
0
0
0
0
2
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
1
0
0
1
2
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
2
0
0
2
0
1
0
0
0
0
1
0
0
0
1
0
0
1
2
0
1
0
0
0
1
0
1
1
0
0
0
0
0
3
0
0
1
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
4
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
1
2
0
2
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
5
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
1
2
0
2
0
0
1
0
2
0
3
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
2
0
1
2
1
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
1
0
2
2
0
1
1
0
11
0
0
0
0
0
1
0
0
2
0
5
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
1
0
3
0
0
0
0
1
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
2
0
0
0
3
2
0
0
0
1
0
0
2
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
1
0
0
1
0
0
1
0
0
0
0
2
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
2
0
0
5
2
0
0
2
0
1
0
0
1
0
0
0
1
0
2
0
0
3
0
1
4
0
0
3
0
0
0
0
0
0
0
0
0
1
2
3
0
0
0
0
0
1
1
0
0
0
0
0
0
4
3
0
0
0
0
0
0
0
3
0
0
0
0
3
0
2
0
0
0
2
0
2
0
1
0
0
0
2
1
0
2
4
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
2
1
0
0
0
0
3
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
3
0
0
1
0
0
2
0
0
0
0
0
1
3
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
3
0
2
0
1
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
2
1
0
0
3
0
2
0
2
0
0
0
0
0
0
0
1
4
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
1
0
2
2
4
0
2
0
0
0
0
0
0
2
2
0
2
0
0
0
0
3
2
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
3
0
0
0
2
0
2
0
0
3
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
3
0
1
0
0
0
0
0
5
1
1
0
0
0
0
0
0
0
0
0
0
2
2
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
2
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
2
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
2
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
2
0
2
0
1
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
5
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
4
1
0
0
1
2
0
0
0
0
0
1
0
2
0
1
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
3
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
5
0
0
0
0
0
0
2
1
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
1
2
1
0
2
1
0
0
1
0
0
0
1
1
1
1
0
0
0
0
2
0
0
0
4
0
0
1
1
0
0
1
0
0
0
0
0
0
4
0
0
3
1
1
1
1
0
0
0
0
1
5
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
1
0
1
0
1
0
0
1
0
0
0
0
2
3
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
1
0
0
2
1
0
2
1
0
0
0
0
3
2
2
2
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
1
0
0
1
2
0
0
0
0
1
0
0
0
0
6
2
0
0
2
2
0
0
0
1
1
1
1
0
0
0
0
0
2
2
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
7
0
0
3
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
1
2
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
10
0
0
0
2
0
0
0
3
0
0
0
1
0
2
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
2
1
1
0
0
2
0
0
0
0
1
3
2
0
0
0
0
1
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
4
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
3
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
3
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
2
0
2
0
0
0
0
0
2
0
0
0
0
0
1
1
1
0
1
2
0
0
0
1
2
0
1
2
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
2
0
0
0
4
0
0
0
0
0
1
2
1
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
5
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
1
1
0
0
0
2
0
2
1
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
2
0
0
0
0
0
0
4
0
0
1
3
0
2
0
0
0
3
1
0
0
0
1
0
1
0
1
0
1
0
0
3
0
0
0
4
0
0
2
0
0
0
0
0
2
2
0
1
3
0
2
0
0
0
1
2
2
0
2
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
3
0
1
1
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
1
2
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
4
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
6
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
3
0
0
0
0
0
0
0
0
0
0
2
2
0
1
1
0
0
2
0
1
0
0
0
0
1
1
2
0
0
0
2
0
0
0
0
0
0
0
2
0
1
2
1
2
0
4
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
1
1
0
0
2
0
0
0
0
2
0
0
2
1
0
0
0
0
1
0
0
1
1
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
2
1
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
1
1
0
2
2
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
3
0
2
0
0
0
0
0
0
0
0
0
2
0
2
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
2
7
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
1
1
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
6
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
1
0
2
0
0
1
0
0
0
0
0
0
0
1
0
3
0
0
0
1
0
0
0
1
0
0
1
2
2
1
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
6
1
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
3
1
0
1
0
3
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
4
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
1
0
0
0
0
0
0
0
0
1
2
0
0
1
2
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
2
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
1
0
0
0
0
1
1
2
0
0
0
1
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
3
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
3
0
2
1
0
2
0
1
0
0
0
0
0
1
0
0
2
1
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
1
0
2
2
2
0
0
0
1
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
3
0
3
0
0
0
0
1
0
0
1
0
0
1
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
1
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
2
2
0
2
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
7
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
2
0
0
2
2
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
3
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
3
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
3
0
0
0
0
0
1
2
1
1
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
1
0
0
0
0
1
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
3
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
6
0
0
0
0
2
0
0
1
0
0
0
2
3
0
0
0
0
0
0
0
2
0
1
1
2
0
0
0
0
0
0
1
0
2
1
2
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
3
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
2
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
7
1
0
0
1
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
1
0
2
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
3
1
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
1
3
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
3
1
0
0
0
0
0
0
0
0
2
0
1
1
1
0
0
0
0
0
0
0
1
0
2
0
4
1
0
0
4
0
0
0
0
0
0
0
3
0
0
0
0
3
0
1
4
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
5
0
0
3
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
3
1
0
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
1
0
2
2
0
0
0
2
1
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
2
0
0
0
7
0
0
2
0
0
0
0
2
2
0
0
1
0
2
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
8
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
8
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
2
0
3
0
1
0
0
0
0
0
0
1
0
0
0
0
3
0
1
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
3
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
1
0
2
1
1
0
0
0
0
2
1
0
3
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
2
0
1
0
2
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
4
1
0
0
0
0
0
0
0
3
0
0
1
5
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
3
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
2
0
2
0
1
0
0
1
0
2
4
0
2
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
3
0
5
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
1
0
3
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
2
4
0
0
0
0
0
0
3
1
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
4
1
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
1
1
0
2
0
0
0
0
0
0
2
1
1
2
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
10
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
3
0
0
0
0
0
1
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
2
1
0
0
1
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
3
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
2
2
0
0
1
0
0
0
2
0
0
0
2
2
0
0
0
0
1
0
1
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
3
0
1
0
3
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
2
2
0
0
1
0
0
0
2
0
0
0
1
0
0
3
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
1
0
1
0
0
1
1
0
3
0
0
0
0
2
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
4
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
3
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
3
0
0
0
2
0
0
3
0
2
2
0
0
0
0
0
0
2
0
1
2
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
1
0
1
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
8
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
4
0
0
0
1
0
1
2
1
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
3
0
0
0
1
2
1
1
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
2
0
0
0
0
1
1
0
0
0
2
1
0
0
0
0
4
2
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
1
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
4
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
1
1
0
0
0
2
0
2
3
0
0
0
1
0
0
0
3
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
1
0
0
0
0
2
0
0
1
0
1
0
2
0
3
1
0
0
1
0
2
0
0
0
0
1
2
1
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
3
0
4
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
1
2
0
0
0
0
0
0
0
4
0
2
0
2
0
0
0
0
1
0
0
0
1
6
0
0
0
0
0
0
4
0
0
10
3
0
0
0
2
0
0
0
2
3
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
1
0
0
2
1
0
0
1
1
1
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
4
0
0
3
0
5
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
3
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
1
2
2
0
0
1
0
0
0
0
2
0
1
1
0
0
0
0
0
0
3
0
1
0
0
0
5
0
0
1
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
3
0
0
4
0
1
0
0
1
0
3
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
2
0
0
0
0
1
2
0
1
0
0
0
0
1
1
1
2
0
0
0
0
0
1
0
0
0
2
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
4
1
0
1
1
2
0
0
0
0
2
0
3
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
6
1
0
0
0
0
0
0
0
2
0
0
0
1
1
2
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
2
1
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
1
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
7
0
2
1
0
0
1
0
0
0
4
0
0
0
5
2
0
1
2
1
0
1
2
2
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
2
1
0
0
0
0
0
3
2
0
0
1
0
0
0
0
0
2
0
0
3
0
1
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
3
0
0
1
0
0
1
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
1
1
0
0
0
2
0
0
1
2
0
0
0
1
1
0
2
0
3
0
0
0
0
1
0
1
0
2
2
0
2
0
0
2
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
4
0
1
0
3
1
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
6
0
0
2
0
1
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
2
3
1
0
0
0
1
0
0
0
2
5
0
0
0
0
2
0
0
0
0
0
0
0
1
1
2
2
0
0
0
0
1
2
0
0
4
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
4
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
1
0
0
0
1
0
1
0
1
0
3
0
0
0
0
6
0
0
0
0
1
0
2
0
3
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
3
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
2
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
1
0
0
0
1
0
0
2
0
2
0
1
0
0
0
1
2
0
0
1
0
0
2
1
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
3
1
3
0
0
0
0
0
0
0
0
0
1
0
0
0
5
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
2
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
1
2
0
3
1
0
0
2
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
3
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
1
3
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
3
0
2
0
0
0
0
0
0
0
0
4
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
4
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
2
0
1
1
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
1
0
0
0
2
2
0
1
1
0
1
1
0
0
2
0
0
2
0
0
0
1
1
0
1
0
0
2
0
0
1
0
1
0
2
2
4
1
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
5
0
1
0
0
1
1
1
0
2
0
0
1
0
0
0
0
4
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
1
1
0
0
0
2
2
0
1
0
0
1
0
0
0
0
1
2
0
0
1
0
0
5
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
3
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
7
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
3
1
0
0
1
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
7
0
4
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
3
0
0
0
1
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
2
1
0
2
0
1
0
0
0
0
0
1
0
0
0
0
2
1
0
0
1
0
0
0
0
3
2
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
2
1
0
0
3
0
0
0
0
0
2
0
2
0
0
3
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
2
0
4
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
2
2
1
0
0
1
0
1
2
0
0
0
0
0
0
0
1
0
1
1
2
0
0
2
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
1
0
0
0
1
0
1
1
3
0
0
0
1
0
0
6
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
2
0
4
1
1
0
0
2
0
3
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
5
0
0
0
2
0
0
0
5
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
1
0
5
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
3
1
0
0
0
0
0
1
4
0
0
0
0
1
2
0
0
0
0
3
0
1
1
0
3
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
3
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
2
0
0
0
3
0
1
0
2
2
1
4
0
0
0
1
1
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
1
3
0
0
0
3
3
0
1
2
0
0
0
1
0
0
1
0
0
1
1
0
0
1
1
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
2
1
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
2
3
0
0
0
2
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
1
1
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
4
0
0
1
0
0
5
0
0
0
0
0
0
0
0
0
0
1
0
1
7
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
4
0
0
0
1
3
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
3
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
3
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
1
0
0
0
2
3
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
1
0
2
0
0
0
6
0
1
0
1
0
0
0
0
3
0
2
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
1
3
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
4
0
2
0
0
1
1
0
4
2
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
3
0
0
0
2
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
2
0
0
0
0
5
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
1
2
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
6
0
0
0
2
3
0
0
1
1
0
0
1
0
0
0
0
4
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
9
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
1
0
0
1
2
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
5
0
2
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
1
0
0
0
1
2
0
2
0
1
1
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
3
2
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
2
0
0
0
0
2
0
0
0
3
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
2
0
0
0
1
0
0
10
0
0
0
0
1
2
0
0
3
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
3
0
0
1
2
2
1
0
0
1
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
1
0
0
0
3
2
0
0
0
1
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
1
0
0
2
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
5
0
1
0
0
0
0
0
0
0
0
0
2
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
1
0
0
0
0
1
2
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
4
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
2
3
2
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
4
0
0
0
0
0
0
0
1
3
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
4
0
0
0
0
0
3
1
0
0
0
2
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
4
1
1
0
0
1
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
3
0
0
0
0
2
0
6
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
1
0
2
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
1
1
2
0
5
0
1
0
1
0
0
2
0
0
1
1
3
1
2
0
2
0
0
2
0
0
0
0
0
0
3
0
0
0
0
1
3
2
0
0
0
0
1
2
0
0
0
1
0
1
0
0
1
0
0
0
0
0
2
0
2
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
8
0
0
0
0
0
2
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
3
0
2
0
0
1
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
1
0
1
2
0
0
7
2
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
2
1
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
3
0
3
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
1
0
1
0
0
0
4
0
1
0
0
0
0
3
2
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
2
0
3
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
4
0
0
2
0
0
1
1
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
2
2
1
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
3
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
5
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
1
1
0
0
0
0
0
0
0
0
0
0
2
0
4
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
1
0
2
2
0
0
1
0
1
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
1
0
0
4
1
0
0
3
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
6
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
3
2
0
0
0
0
0
1
2
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
2
0
0
4
0
2
0
1
0
5
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
5
0
0
0
3
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
4
0
2
0
0
1
0
1
5
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
3
0
0
0
0
2
1
0
0
3
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
6
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
4
3
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
2
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
1
0
0
2
0
0
0
0
0
6
2
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
5
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
1
0
4
2
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
9
1
0
0
0
0
0
0
0
0
0
2
0
2
0
1
2
0
3
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
6
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
1
3
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
4
0
2
3
0
6
0
0
0
0
0
0
0
1
2
2
0
0
1
0
2
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
15
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
5
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
1
0
2
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
1
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
3
0
2
0
2
3
0
1
0
0
0
0
0
0
3
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
2
1
0
1
0
0
2
0
0
1
0
0
0
0
2
2
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
2
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
1
0
3
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
2
2
0
0
1
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
1
0
0
6
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
3
0
2
0
0
0
0
2
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
2
2
2
2
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
3
1
1
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
2
0
0
0
0
1
0
0
0
0
0
3
1
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
1
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
2
0
1
0
0
0
0
0
1
0
1
4
0
0
0
1
0
1
1
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
3
0
0
0
0
1
0
1
2
0
2
2
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
2
0
0
2
0
2
0
2
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
3
0
0
1
0
0
0
0
2
0
0
4
1
0
0
0
0
0
0
0
0
1
2
0
2
0
0
1
0
0
0
1
2
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
1
1
0
0
0
0
0
2
0
0
3
0
2
0
1
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
3
0
0
1
0
0
0
0
1
2
0
1
1
3
0
0
0
2
0
0
0
0
0
2
0
1
0
0
1
2
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
3
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
2
2
0
2
0
2
0
0
0
0
0
0
2
1
0
0
0
2
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
1
0
2
0
2
1
0
0
0
0
0
0
0
3
0
0
3
0
2
0
0
0
0
2
0
0
4
0
0
1
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
2
0
2
1
2
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
6
1
0
0
0
0
1
0
0
1
0
0
0
0
2
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
1
0
2
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
1
2
0
0
2
0
0
2
0
1
0
1
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
2
0
1
0
1
0
1
0
0
0
0
2
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
3
0
1
0
0
0
0
0
1
5
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
1
0
1
0
0
2
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
2
2
0
0
0
0
0
0
0
0
2
0
0
0
6
0
0
0
0
0
0
0
0
3
0
2
0
0
2
1
0
0
0
0
0
0
2
1
0
0
0
2
0
1
0
0
0
0
1
0
2
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
1
1
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
3
4
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
4
3
1
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
4
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
3
2
0
0
2
1
0
1
0
0
4
1
0
0
2
0
3
2
2
0
0
1
0
0
0
0
0
2
0
0
0
0
2
6
0
0
0
0
8
0
7
0
3
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
1
0
2
0
1
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
3
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
1
0
0
2
1
0
0
0
0
1
1
0
0
0
1
0
2
2
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
0
0
0
1
7
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
1
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
2
2
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
4
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
1
3
2
0
0
0
0
0
5
0
0
0
0
4
0
1
0
0
0
0
2
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
2
1
0
1
0
0
1
0
0
1
0
2
0
5
0
0
0
0
2
0
2
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
2
3
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
2
2
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
2
0
1
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
2
2
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
2
0
0
2
0
0
0
0
0
1
1
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
1
0
0
1
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
4
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
5
0
1
0
0
0
0
0
2
0
0
0
2
1
0
0
0
1
0
0
0
0
2
1
6
6
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
5
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
1
0
0
0
2
0
0
0
0
3
0
0
8
2
0
0
0
0
1
0
2
0
2
2
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
4
2
1
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
2
0
3
0
0
1
0
0
0
0
0
0
1
1
3
0
2
0
0
0
0
0
0
1
0
1
1
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
3
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
1
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
1
1
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
1
1
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
15
1
0
0
0
0
0
0
6
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
4
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
1
2
0
1
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
2
0
2
0
0
3
0
0
0
0
0
0
0
0
4
2
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
1
0
2
0
0
0
2
0
0
0
0
2
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
1
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
11
1
3
1
4
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
3
3
0
0
2
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
2
0
0
1
0
0
1
0
0
1
0
0
2
0
0
0
0
2
0
0
0
3
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
2
0
0
2
0
2
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
2
0
0
4
6
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
6
6
0
0
0
2
0
0
0
0
0
0
1
0
1
2
0
1
0
1
2
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
1
0
0
0
1
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
2
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
6
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
1
1
0
0
3
3
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
3
0
0
2
0
0
0
0
2
0
0
0
3
2
0
0
0
0
2
0
1
0
0
1
1
0
1
0
0
1
0
3
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
5
0
0
0
1
0
0
2
1
0
0
0
0
3
0
0
0
0
0
0
2
1
0
0
2
0
4
0
6
0
0
0
0
1
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
10
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
2
3
0
1
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
3
0
0
0
1
3
0
0
0
0
1
0
1
2
0
0
1
2
0
0
1
2
3
0
0
0
0
0
0
0
2
0
2
0
0
0
2
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
2
0
1
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
4
2
0
0
0
4
0
0
1
2
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
1
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
4
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
4
0
0
0
1
0
0
0
1
0
0
3
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
3
1
3
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
1
1
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
1
0
0
2
0
0
1
2
0
0
2
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
1
0
2
0
0
0
1
0
0
2
0
0
0
1
0
1
0
0
0
2
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
1
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
2
0
0
0
0
3
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
1
0
0
0
0
4
1
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
1
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
1
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
3
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
2
0
3
0
0
0
0
1
2
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
3
1
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
1
1
0
0
0
0
8
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
3
1
2
1
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
2
0
2
2
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
2
0
0
0
2
1
0
0
0
0
1
0
0
2
1
2
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
3
0
0
1
0
1
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
1
4
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
2
0
4
0
0
2
0
1
0
2
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
2
0
0
0
1
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
32
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
3
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
3
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
1
2
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
2
2
2
2
0
1
0
1
0
0
0
0
0
0
1
0
0
2
1
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
2
4
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
1
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
2
2
0
0
0
0
0
2
4
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
5
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
1
1
0
1
0
0
0
0
3
0
2
0
0
0
1
0
0
0
0
0
0
1
1
3
4
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
2
2
2
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
6
0
0
2
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
2
3
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
2
0
1
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
10
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
1
0
3
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
1
0
2
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
4
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
1
1
0
0
0
0
0
0
0
3
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
4
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
2
1
0
0
1
0
0
1
0
0
1
2
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
2
2
1
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
4
0
0
1
2
0
0
4
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
1
0
14
2
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
4
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
1
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
1
0
2
6
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
2
0
2
0
0
0
0
4
1
0
1
0
0
0
0
0
0
0
3
1
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
6
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
2
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
1
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
3
0
1
2
0
12
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
2
0
0
2
0
1
0
1
0
0
1
0
1
3
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
4
1
1
0
0
0
0
1
0
0
2
0
0
2
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
8
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
5
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
3
0
0
0
0
0
0
0
1
0
1
3
0
3
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
2
2
0
1
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
1
1
7
1
0
0
0
0
2
1
0
0
2
1
2
0
2
0
0
0
0
0
0
0
0
1
4
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
5
0
1
0
1
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
1
0
1
0
0
2
1
1
0
1
0
0
2
2
0
2
3
2
1
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
1
0
2
0
0
0
0
2
0
0
0
3
0
0
0
3
0
0
1
1
0
0
0
2
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
2
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
3
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
2
1
0
1
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
2
0
3
3
1
4
0
0
0
5
1
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
2
0
0
2
0
0
0
1
0
0
2
0
1
0
0
0
2
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
1
0
0
0
0
2
1
2
1
0
0
0
2
0
1
3
0
0
0
0
0
0
0
3
0
1
0
0
3
0
0
0
0
2
0
1
0
1
0
0
0
0
0
3
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
1
1
2
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
2
1
3
3
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
1
4
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
1
0
1
0
0
1
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
2
7
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
9
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
2
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
5
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
3
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
1
2
0
0
0
0
0
0
1
4
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
3
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
1
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
4
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
4
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
3
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
1
0
1
1
2
0
1
0
0
1
3
0
2
1
0
0
0
0
0
1
2
2
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
2
2
0
2
0
2
3
2
0
0
0
1
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
2
1
2
0
2
0
0
0
0
0
0
0
2
0
1
0
0
3
1
0
1
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
3
1
4
0
0
1
0
1
0
0
0
0
0
0
0
0
3
0
2
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
1
0
2
2
1
0
0
0
0
0
0
0
2
0
2
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
2
0
0
0
1
0
0
2
1
0
0
0
3
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
2
0
2
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
2
2
0
1
1
1
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
1
0
5
0
0
0
0
3
0
0
0
0
0
0
2
1
0
2
2
0
0
1
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
7
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
4
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
3
0
0
0
3
0
0
0
0
0
1
1
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
2
0
1
2
3
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
2
0
3
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
2
0
0
1
0
0
0
1
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
2
1
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
2
2
2
0
2
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
3
1
0
0
2
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
5
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
1
0
5
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
8
0
2
0
3
0
1
0
0
0
0
0
0
2
0
0
0
1
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
1
0
1
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
1
1
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
9
1
0
0
0
0
0
1
0
0
0
1
0
0
2
0
2
2
0
0
0
1
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
2
0
0
0
0
1
1
0
0
0
0
1
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
1
2
0
1
1
0
0
1
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
4
0
2
0
0
0
0
1
0
0
0
1
0
2
1
0
0
0
0
0
0
1
1
0
0
0
1
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
3
0
0
1
2
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
1
2
0
0
0
0
0
0
2
0
3
0
0
0
0
2
1
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
1
0
0
0
4
0
0
0
0
1
0
2
1
0
0
0
2
1
0
6
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
4
0
1
0
0
3
0
0
1
1
0
0
0
0
1
0
1
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
5
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
23
0
0
2
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
2
1
0
0
0
0
0
0
3
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
3
1
0
0
0
0
2
2
1
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
4
0
1
1
0
1
2
0
0
1
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
2
3
0
1
0
0
3
0
0
0
0
4
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
5
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
3
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
2
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
2
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
1
0
2
1
0
0
0
3
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
6
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
3
0
1
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
4
0
0
4
0
1
1
0
2
1
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
7
0
0
0
1
2
8
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
3
0
2
0
2
0
3
0
0
0
1
0
0
1
0
0
1
0
2
0
1
0
0
1
0
0
1
3
0
0
0
0
0
0
0
5
0
2
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
2
1
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
3
0
0
0
0
1
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
4
0
2
1
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
1
2
1
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
3
0
1
2
0
2
0
1
0
2
0
0
0
3
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
2
1
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
7
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
5
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
4
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
3
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
1
3
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
5
2
0
4
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
3
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
4
1
0
0
0
4
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
2
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
1
1
0
5
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
1
0
0
2
2
2
0
3
0
0
0
0
0
0
0
0
2
1
0
1
0
0
2
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
1
0
0
0
0
2
1
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
2
0
0
0
5
0
0
0
0
0
0
0
0
0
1
1
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
1
5
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
1
0
0
0
1
2
1
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
2
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
1
0
0
0
0
1
0
0
0
0
1
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
5
0
0
0
0
0
0
0
0
2
0
1
1
2
0
1
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
1
0
0
1
0
4
8
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
2
0
1
1
0
3
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
3
0
3
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
2
1
0
0
1
0
0
2
0
0
2
0
0
0
0
2
0
0
3
0
1
0
0
0
0
0
2
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
2
0
0
0
3
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
3
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
6
0
0
0
0
0
0
0
1
0
0
1
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
4
2
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
2
1
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
2
0
0
2
0
0
1
0
1
1
0
0
0
0
0
0
1
3
2
0
0
0
0
0
3
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
2
1
0
1
0
0
0
0
1
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
2
0
0
2
0
0
0
0
0
0
2
1
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
2
0
2
0
0
0
0
0
0
0
2
1
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
4
1
1
2
0
2
0
0
0
2
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
2
0
1
0
2
2
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
4
0
1
0
0
0
0
0
0
0
1
4
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
8
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
7
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
2
1
2
0
1
2
2
2
0
1
0
0
0
0
0
0
0
0
0
0
1
3
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
2
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
4
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
2
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
3
0
4
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
3
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
2
0
0
1
0
0
0
0
1
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
3
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
3
3
0
0
0
0
3
0
0
0
0
0
1
0
0
0
4
0
0
0
1
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
3
1
0
1
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
3
0
1
0
0
2
1
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
3
1
0
0
4
0
0
0
0
0
1
1
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
1
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
2
2
0
1
1
0
0
0
1
3
0
0
0
2
0
0
0
0
0
2
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
3
0
0
2
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
4
0
0
1
0
2
0
0
0
0
1
0
0
2
0
0
0
1
0
3
0
0
0
0
4
2
1
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
1
0
3
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
3
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
2
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
3
2
0
9
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
1
0
0
0
3
0
1
0
0
0
0
3
0
0
0
0
1
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
1
0
0
0
2
2
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
2
2
0
1
0
0
0
1
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
1
3
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
1
2
0
0
1
0
0
0
0
1
2
0
1
0
0
4
0
0
0
0
0
2
0
0
0
1
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
1
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
2
2
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
1
0
0
0
0
4
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
9
0
0
0
0
0
1
1
1
0
0
0
0
2
0
0
0
0
0
4
0
0
0
0
0
0
2
1
0
0
0
0
0
0
4
0
0
2
1
1
0
0
0
0
1
1
0
2
0
0
0
0
3
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
1
0
3
1
0
3
0
0
0
0
0
0
0
2
0
0
1
0
0
2
2
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
1
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
3
0
0
0
1
2
1
0
0
0
0
0
2
0
0
1
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
1
2
1
0
0
1
0
1
1
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
1
1
0
5
2
0
0
0
0
0
2
0
0
4
1
0
0
2
2
0
0
0
0
0
0
1
2
0
0
0
1
0
0
3
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
1
0
0
0
2
0
1
0
0
2
0
0
0
0
0
1
2
2
1
0
0
0
0
6
0
0
0
0
2
0
0
0
2
2
0
0
0
1
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
4
0
2
0
0
0
1
0
1
1
4
0
0
0
1
0
0
2
1
0
4
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
2
3
1
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
2
0
0
2
0
0
3
1
0
0
1
2
0
0
1
1
0
2
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
3
0
2
1
2
0
0
0
0
0
1
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
2
0
0
0
2
3
0
3
0
0
0
0
0
3
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
1
0
0
2
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
1
0
0
1
0
0
1
2
0
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
1
0
0
2
0
0
0
1
0
1
5
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
1
1
1
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
3
1
0
0
0
9
0
0
0
1
0
0
0
3
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
2
0
0
0
0
1
0
0
1
0
0
0
2
0
2
0
0
2
1
0
0
0
2
0
0
1
0
0
0
2
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
1
1
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
1
0
2
0
1
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
3
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
2
0
0
2
1
0
0
1
0
0
1
0
3
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
8
5
0
0
0
1
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
4
0
0
0
0
1
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
9
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
4
0
1
0
0
0
1
1
1
0
0
0
0
0
1
1
1
2
0
0
0
4
1
0
2
0
1
0
2
0
0
2
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
3
0
1
0
0
0
0
2
2
0
0
0
0
0
0
2
2
0
3
0
0
0
0
1
0
1
0
0
1
2
1
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
2
2
0
0
0
1
0
2
0
0
0
3
3
0
1
4
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
5
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
5
0
0
1
0
0
0
0
1
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
1
1
0
1
0
0
2
0
0
0
4
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
2
5
0
2
0
4
0
0
0
1
0
1
0
3
0
0
2
0
0
0
0
0
2
0
0
0
1
2
2
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
3
9
2
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
5
0
3
1
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
4
1
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
1
2
2
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
2
0
0
0
1
2
0
0
0
1
0
0
0
0
1
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
1
0
2
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
1
3
0
0
0
0
0
0
0
1
0
2
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
2
0
0
0
1
0
0
0
0
0
1
0
1
2
0
2
0
2
0
3
0
0
0
0
0
1
1
0
2
4
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
2
1
0
0
1
0
0
1
2
2
2
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
1
0
2
0
0
1
1
0
0
1
1
1
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
1
1
2
0
0
2
2
0
2
0
0
0
2
0
2
1
0
0
0
0
0
0
0
3
0
0
0
0
0
1
1
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
2
0
0
0
3
0
2
0
2
0
0
2
0
0
1
2
1
0
0
0
0
0
0
1
0
0
0
3
0
2
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
2
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
1
0
1
0
0
2
0
0
0
1
1
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
1
2
0
1
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
2
1
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
13
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
2
0
1
0
2
0
0
2
0
0
2
1
0
0
0
1
0
0
0
0
0
1
0
0
0
2
4
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
1
1
0
2
0
4
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
2
1
2
2
1
0
0
1
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
5
0
0
2
0
2
0
0
0
0
0
2
0
2
0
1
0
2
0
0
0
0
0
2
1
1
0
1
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
1
0
0
0
3
1
0
2
0
1
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
4
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
3
1
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
3
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
1
0
1
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
1
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
1
1
0
1
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
5
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
1
1
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
5
1
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
9
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
3
0
1
2
1
0
0
0
0
0
0
2
0
1
0
0
0
3
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
1
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
2
0
1
1
0
0
0
0
0
1
3
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
2
0
0
0
6
2
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
2
0
0
1
1
2
0
0
0
0
0
0
0
1
0
1
0
4
2
1
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
3
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
1
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
9
0
0
2
0
0
0
1
0
0
0
0
4
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
2
0
0
2
0
0
0
0
1
2
0
1
0
1
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
1
0
2
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
5
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
2
1
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
1
0
2
0
0
3
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
3
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
3
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
2
3
1
0
0
0
0
0
0
1
0
0
0
1
1
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
2
0
0
0
0
1
0
2
0
3
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
1
0
0
0
0
0
0
1
0
2
0
0
2
1
0
0
0
3
0
0
0
2
0
0
0
2
0
0
0
2
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
2
2
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
3
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7
0
0
2
2
2
0
0
2
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
7
0
0
0
1
0
0
1
5
0
0
0
0
0
3
0
0
0
2
3
0
2
0
0
0
0
1
0
0
1
1
0
0
1
0
0
1
3
0
1
2
0
0
0
0
2
1
0
0
2
0
2
2
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
5
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
2
2
0
2
0
0
0
0
0
1
0
0
0
0
0
2
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
1
0
3
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
1
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
8
0
0
2
0
3
2
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
2
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
2
1
0
1
0
0
0
0
0
1
2
0
0
0
1
0
0
0
2
1
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
1
2
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
1
0
0
3
0
0
0
0
0
0
1
0
7
0
1
1
1
0
0
2
1
0
1
0
0
1
1
1
4
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
3
0
0
4
0
0
0
0
3
1
2
1
2
0
0
0
0
0
3
2
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
5
0
0
0
3
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
2
1
0
1
2
1
0
0
0
0
0
2
0
2
0
0
8
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
5
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
5
0
0
2
0
0
0
0
0
0
3
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
1
2
0
1
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
1
2
0
0
0
0
5
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
6
0
0
0
0
0
2
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
3
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
2
2
1
0
1
0
0
0
3
0
3
1
2
0
0
0
0
5
1
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
1
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
6
0
1
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
1
0
3
0
6
0
0
0
0
0
0
1
0
0
0
1
1
2
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
1
3
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
4
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
2
0
5
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
2
1
3
0
0
0
0
0
1
1
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
3
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
1
0
1
1
0
0
0
0
0
2
1
0
1
1
0
0
1
0
2
0
0
0
0
3
0
0
0
2
1
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
2
0
0
0
0
1
0
0
0
0
8
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
1
2
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
3
0
0
0
1
0
0
0
1
0
0
0
2
0
2
4
1
0
0
1
1
0
1
0
1
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
4
0
0
0
1
0
0
2
0
0
0
0
3
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
1
2
0
0
0
0
0
5
0
0
1
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
8
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
1
0
0
2
0
0
0
2
0
0
2
0
2
0
1
0
1
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
1
1
1
2
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
3
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
4
8
0
0
0
0
0
0
2
0
2
0
1
1
0
2
1
1
0
0
3
0
0
0
1
1
0
4
2
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
2
0
1
0
0
1
0
1
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
1
0
0
0
1
0
1
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
2
3
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
1
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
4
0
0
0
1
0
3
0
0
3
0
0
0
1
0
1
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
1
0
0
1
0
1
1
3
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
3
2
1
0
2
0
0
2
2
3
0
0
0
0
0
1
0
0
1
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
8
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
2
0
0
2
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
2
0
0
0
0
0
2
2
2
0
0
5
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
1
0
0
3
3
0
0
0
0
0
2
0
0
0
2
0
0
2
0
1
1
0
0
0
1
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
2
0
0
0
0
0
2
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
1
0
2
2
2
0
0
0
0
0
1
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
4
1
0
0
3
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
3
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
1
1
1
0
1
1
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
2
1
3
1
0
2
0
0
1
0
7
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
1
0
0
0
0
3
0
0
2
1
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
3
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
1
2
0
0
0
4
0
0
0
2
2
0
0
0
0
0
0
1
0
0
1
0
0
2
2
0
2
1
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
5
0
0
0
0
0
0
2
0
0
0
0
0
1
1
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
9
0
1
1
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
1
0
1
3
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
4
0
0
3
3
1
0
0
0
0
1
2
0
0
0
3
0
1
1
3
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
2
5
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
5
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
3
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
2
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
7
0
0
3
0
0
2
0
0
3
0
0
0
0
2
0
0
0
0
6
0
3
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
2
1
0
0
1
0
1
0
3
0
0
1
3
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
1
0
2
0
0
2
0
1
0
0
1
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
2
0
0
0
2
0
1
0
0
2
0
0
0
2
0
0
3
0
3
0
0
0
2
0
2
0
4
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
3
0
1
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
5
0
4
0
0
1
0
1
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
1
0
1
1
0
1
0
1
0
0
0
4
0
0
0
0
6
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
2
0
2
2
1
0
0
0
0
0
0
0
0
3
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
2
1
0
0
0
1
0
0
0
0
0
6
1
0
0
1
0
0
2
2
0
0
0
0
1
3
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
3
0
5
0
0
0
0
0
0
9
0
0
0
0
0
2
0
0
0
0
0
0
0
3
2
1
2
0
3
0
0
0
0
0
0
1
1
0
1
9
0
2
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
2
2
3
0
0
2
0
2
0
0
1
2
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
1
2
4
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
3
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
15
0
0
0
0
0
0
0
0
0
0
1
5
0
1
0
0
0
1
0
0
1
2
0
2
0
0
0
0
0
0
2
0
1
2
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
1
1
0
2
2
2
0
0
0
0
0
0
1
2
0
0
0
0
3
0
0
0
0
0
0
0
0
4
1
0
0
0
1
0
0
0
0
1
0
0
0
0
3
0
1
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
9
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
2
5
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
1
0
0
2
3
0
0
0
3
0
0
0
0
0
1
0
2
2
0
0
1
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
1
1
0
0
0
0
0
0
1
0
0
0
1
3
0
6
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
3
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
2
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
5
0
0
1
0
1
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
2
1
0
0
2
1
0
0
1
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
2
0
0
0
2
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
2
0
1
0
0
0
0
2
0
1
0
5
0
0
0
0
0
0
2
0
0
0
1
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
3
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
2
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
2
3
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
4
2
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
1
0
2
0
0
0
2
0
0
0
0
2
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
1
2
0
0
0
0
1
2
0
0
0
1
0
0
1
0
0
0
0
5
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
3
2
0
0
0
8
0
0
0
0
0
0
3
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
1
0
1
0
0
0
0
1
0
2
2
0
0
2
2
1
1
0
0
0
0
0
0
1
0
1
1
0
2
0
0
1
0
0
0
0
1
0
0
2
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
1
1
1
2
2
0
0
0
1
2
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
2
0
0
1
1
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
3
2
3
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
2
0
0
0
0
2
0
0
3
4
0
0
0
0
2
0
0
0
1
0
0
1
0
1
1
2
1
0
1
0
0
0
0
2
0
0
3
0
0
2
0
2
0
0
0
0
2
1
0
0
0
1
2
4
0
0
0
2
0
0
2
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
1
2
0
0
0
0
0
0
1
1
2
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
1
2
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
2
0
0
0
0
2
0
0
2
0
1
2
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
1
0
0
0
0
0
1
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
2
1
0
0
0
0
1
0
0
2
0
0
0
0
0
1
2
0
0
0
1
0
0
1
1
0
0
0
0
0
2
0
0
1
0
2
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
4
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
5
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
3
1
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
1
0
1
2
0
0
1
1
0
0
0
0
1
1
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
2
0
2
0
0
2
0
1
4
1
0
0
4
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
3
0
0
1
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
6
0
1
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
1
0
1
0
0
2
0
0
0
0
1
0
1
1
0
0
1
0
0
12
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
2
1
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
5
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
2
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
2
0
0
2
1
0
0
0
0
1
0
2
0
3
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
1
0
0
0
2
0
4
0
0
0
2
0
1
0
0
0
1
0
0
2
0
2
0
0
1
0
0
0
1
0
0
0
3
0
1
0
0
0
0
0
4
0
0
3
0
0
0
2
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
3
3
0
0
1
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
4
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
2
4
2
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
1
0
3
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
5
1
1
0
0
2
3
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
2
1
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
3
0
1
1
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
2
2
0
0
5
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
2
1
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
5
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
2
0
0
0
2
3
7
1
0
2
0
0
0
0
3
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
9
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
1
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
1
1
2
1
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
1
0
1
0
0
0
1
0
2
0
0
0
2
0
0
2
1
1
1
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
2
1
0
0
0
1
0
0
0
0
3
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
5
0
0
0
2
0
0
0
0
0
0
3
0
0
3
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
1
1
2
0
0
0
0
0
3
4
0
0
0
2
2
3
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
3
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
3
0
0
0
2
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
3
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
2
2
3
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
4
1
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
2
1
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
3
0
0
0
0
2
0
0
0
1
2
2
1
0
0
1
0
0
0
0
0
2
2
1
0
0
1
0
0
0
1
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
2
0
1
0
4
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
1
0
0
4
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
3
0
0
0
0
2
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
1
2
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
1
0
0
0
0
0
1
1
1
0
0
1
0
0
0
2
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
1
1
0
1
0
0
0
0
4
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
2
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
8
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
2
4
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
3
0
0
1
1
1
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
2
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
1
0
0
0
2
0
0
2
0
2
0
2
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
3
0
1
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
1
1
1
2
0
1
0
0
0
0
1
0
0
0
0
3
0
0
2
0
0
0
5
1
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
3
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
7
2
1
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
2
4
1
1
3
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
1
3
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
4
1
6
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
2
2
0
0
0
2
0
0
0
2
0
0
0
1
0
1
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
1
3
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
3
0
1
1
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
2
0
0
1
0
1
2
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
2
2
0
1
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
10
2
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
4
0
1
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
7
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
3
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
2
0
1
1
0
2
0
0
0
0
0
2
0
1
0
0
0
1
0
2
0
0
1
0
0
3
0
0
1
0
0
0
0
2
0
0
0
0
2
0
2
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
2
0
1
0
0
0
0
0
0
0
0
0
3
0
2
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
7
0
0
0
2
0
4
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
2
1
0
0
0
0
0
4
1
0
2
0
1
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
4
0
1
0
0
0
2
0
0
0
1
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
4
0
2
0
0
0
0
0
0
3
0
0
1
1
0
1
0
0
1
0
0
0
1
1
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
1
0
0
0
2
0
0
0
1
0
0
0
1
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
1
2
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
4
0
4
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
2
0
0
1
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
1
0
2
0
0
2
0
1
0
0
0
4
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
4
0
0
0
0
0
0
2
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
4
0
1
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
1
4
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
1
0
0
4
1
0
0
0
1
0
2
0
0
0
0
1
0
2
0
0
3
7
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
4
0
0
0
0
3
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
2
0
1
0
0
0
0
3
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
2
0
1
0
1
0
0
2
0
1
0
0
3
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
5
0
0
1
0
0
0
0
2
3
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
2
0
2
0
3
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
2
0
0
1
1
1
1
1
1
10
0
0
0
0
2
0
2
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
1
1
4
0
0
1
0
0
0
0
0
2
0
0
2
1
0
0
0
1
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
2
0
0
0
1
0
0
3
1
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
1
0
1
0
0
0
0
5
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
6
0
0
0
2
3
0
0
0
0
0
2
2
0
0
0
0
1
0
1
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
1
0
1
0
2
1
0
0
1
0
1
0
0
0
0
3
0
1
0
0
0
0
2
0
0
0
6
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
2
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
3
2
0
0
0
5
2
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
3
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
10
0
0
2
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
1
0
0
0
2
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
3
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
2
1
2
2
0
0
1
0
0
0
2
0
1
0
1
1
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
9
0
0
2
0
0
0
0
0
0
2
2
0
1
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
7
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
1
1
2
0
1
1
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
4
3
0
0
0
2
0
0
0
3
0
1
0
0
0
0
0
0
0
0
1
0
1
5
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
6
2
0
0
0
0
0
2
0
1
0
1
0
5
0
0
0
0
7
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
1
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
2
0
5
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
11
0
0
0
0
1
0
0
0
0
0
1
0
1
0
2
1
0
0
0
0
0
2
0
0
4
0
2
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
2
0
0
2
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
3
0
0
1
1
0
0
1
8
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
3
0
0
1
0
1
0
2
0
0
0
0
0
1
0
0
0
0
1
0
3
0
0
0
0
5
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
1
0
0
1
0
3
0
2
0
1
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
2
1
0
0
2
0
0
0
2
2
0
0
0
1
0
0
2
0
1
0
0
0
0
2
2
2
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
3
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
1
2
0
3
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
2
1
1
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
4
1
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
3
3
0
0
2
0
0
0
2
0
0
1
0
0
0
0
1
0
2
0
0
1
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
1
0
0
0
0
4
0
0
3
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
3
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
2
0
2
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
1
2
2
0
1
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
1
0
0
0
0
0
1
2
1
4
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
1
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
1
0
0
1
2
0
1
1
0
1
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
5
1
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
1
0
0
0
0
1
0
0
3
0
2
0
0
0
1
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
2
3
3
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
1
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
2
0
2
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
2
1
0
0
0
3
1
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
1
2
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
2
0
1
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
2
0
0
2
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
2
2
1
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
2
0
1
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
2
2
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
7
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
1
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
3
2
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
3
0
4
2
0
2
1
0
0
0
1
1
5
1
2
1
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
5
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
4
1
0
0
0
0
0
0
1
2
0
0
0
0
0
5
1
0
3
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
1
0
1
1
0
0
0
0
0
2
0
0
0
0
2
0
1
0
2
0
2
5
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
3
0
3
0
0
0
0
0
1
2
1
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
1
0
0
1
1
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
2
2
0
0
0
1
0
1
0
2
0
2
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
1
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
3
0
0
1
2
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
2
1
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
6
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
2
0
0
1
0
0
2
1
1
0
0
0
1
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
8
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
1
1
0
0
2
0
0
0
2
1
0
0
0
0
1
2
0
0
0
1
0
2
0
0
1
1
0
2
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
2
0
2
2
0
3
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
2
0
0
0
1
1
2
0
0
1
8
0
0
2
0
0
0
2
0
1
2
0
0
2
0
0
0
0
0
0
1
2
0
0
0
2
7
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
6
0
0
1
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
2
0
0
2
0
0
0
0
1
0
1
0
0
0
0
1
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
3
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
1
2
0
1
0
2
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
2
2
1
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
1
2
0
0
0
5
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
2
4
0
1
1
0
3
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
4
2
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
2
0
0
0
0
0
2
2
0
1
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
1
4
0
0
0
1
0
0
0
0
0
0
1
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
2
0
2
0
0
3
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
2
0
1
0
1
0
0
0
0
0
0
0
3
0
0
3
0
0
0
0
0
0
0
0
0
2
4
3
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
1
0
0
1
0
0
2
0
0
0
0
1
9
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
5
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
1
0
1
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
3
0
0
0
0
0
0
1
0
0
0
8
0
1
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
4
0
2
0
0
0
0
2
0
0
1
0
0
0
1
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
3
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
2
2
1
0
0
0
0
0
0
3
0
0
2
0
1
0
0
2
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
1
2
0
2
0
0
2
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
4
0
3
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
1
0
0
0
0
2
1
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
2
0
0
1
1
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
10
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
2
1
2
0
0
4
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
2
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
2
0
0
0
2
0
0
0
0
0
2
1
2
0
7
0
0
0
2
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
1
0
2
0
1
0
0
0
1
0
0
2
0
3
0
0
0
0
1
0
0
0
0
2
0
3
0
1
2
0
2
2
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
7
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
1
0
8
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
1
0
0
2
1
0
0
2
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
5
0
0
0
0
1
0
1
1
0
0
3
0
0
0
0
0
3
1
0
0
0
0
1
3
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
1
1
0
0
2
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
6
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
4
0
2
5
0
0
0
0
0
0
2
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
3
0
0
0
1
0
2
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
6
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
1
2
0
0
1
0
0
0
0
0
0
2
1
2
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
6
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
2
0
0
1
0
0
0
0
2
0
0
0
0
1
2
0
2
0
1
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
4
0
0
0
0
1
0
4
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
2
1
1
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
1
0
2
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
1
0
0
2
1
1
0
0
0
0
8
0
0
0
1
0
1
5
1
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
2
1
1
2
0
0
0
0
0
2
0
0
1
0
1
0
1
0
0
0
2
0
0
0
0
2
0
1
2
0
0
0
1
0
1
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
3
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
1
0
1
0
0
0
0
0
0
2
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
5
0
1
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
2
0
1
0
0
0
0
0
3
0
0
0
1
0
0
0
1
0
0
3
1
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
1
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
3
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
1
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
3
3
0
0
0
2
1
1
0
0
0
2
2
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
1
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
2
0
1
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
1
1
2
0
2
0
2
2
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
1
1
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
1
0
7
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
1
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
2
3
2
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
1
0
0
0
0
0
0
7
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
2
0
2
4
0
0
0
0
1
0
0
0
0
0
4
0
0
0
1
1
2
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
3
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
2
1
0
0
2
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
5
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
2
1
0
0
0
4
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
2
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
5
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
1
1
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
1
1
1
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
2
0
1
0
2
0
1
1
5
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
4
0
0
1
2
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
1
1
0
0
0
0
0
0
0
2
1
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
2
0
1
0
0
0
0
0
4
8
0
0
0
0
1
1
0
1
7
2
2
2
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
3
0
1
0
0
1
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
2
3
0
2
0
1
0
0
2
0
1
5
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
4
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
5
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
1
1
0
2
2
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
3
0
1
2
4
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
3
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
2
1
0
0
0
3
1
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
1
1
0
0
1
2
5
2
0
0
2
1
0
4
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
2
0
2
0
0
0
1
0
2
0
0
0
0
0
2
4
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
1
0
1
3
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
1
0
0
1
0
0
3
0
4
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
3
0
1
0
1
2
0
0
0
0
1
0
0
1
3
0
0
3
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
2
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
3
2
0
0
0
2
0
0
0
2
0
0
0
3
0
0
0
0
1
0
0
0
0
1
0
4
1
1
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
3
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
6
0
0
1
0
0
2
0
3
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
2
0
2
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
4
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
2
3
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
1
2
1
1
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
3
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
1
0
1
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
3
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
6
1
0
0
0
0
0
0
0
0
0
0
2
0
5
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
1
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
1
0
3
0
1
1
0
1
2
0
1
2
1
0
3
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
1
0
0
0
3
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
6
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
3
2
0
5
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
3
0
0
0
1
6
0
1
3
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
2
0
1
0
0
0
2
0
1
0
2
0
0
0
0
0
0
3
0
0
0
1
0
0
1
0
4
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
5
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
2
0
1
1
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
2
2
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
2
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
3
1
1
0
0
0
2
0
0
0
2
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
4
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
1
0
3
0
2
0
0
2
0
0
0
0
1
0
0
0
3
0
0
1
0
11
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
1
2
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
2
1
9
2
1
0
0
0
1
0
0
0
0
0
3
0
2
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
2
0
0
2
2
0
5
0
0
0
0
3
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
3
0
2
0
1
0
0
0
2
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
2
2
0
0
0
0
1
2
0
5
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
3
0
1
0
0
1
1
0
3
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
5
0
0
0
0
0
2
1
3
0
0
0
3
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
2
0
1
0
7
0
0
0
1
0
0
1
0
0
0
0
0
2
1
1
0
0
0
0
0
1
0
0
2
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
5
2
0
0
0
0
0
0
0
0
2
0
1
1
2
0
0
0
0
0
4
0
2
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
3
0
0
2
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
5
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
1
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
2
1
2
0
0
0
0
0
2
0
2
0
0
1
0
0
0
2
0
0
2
5
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
1
3
0
0
0
2
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
3
3
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
2
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
3
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
2
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
3
0
0
0
1
2
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
6
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
2
0
2
0
2
0
0
0
0
0
0
0
1
4
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
2
2
0
0
1
0
2
0
0
0
0
0
0
0
1
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
4
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
3
4
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
3
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
4
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
1
2
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
2
0
0
0
1
2
0
2
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
2
0
0
3
1
1
0
0
0
2
0
0
0
2
0
1
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
6
1
1
0
0
0
0
0
1
0
1
0
0
0
3
0
3
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
3
0
0
0
0
2
2
1
5
0
1
2
0
0
0
2
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
2
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
1
1
0
1
0
1
0
0
0
0
0
0
0
1
0
2
2
1
2
1
0
0
7
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
2
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
1
0
3
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
2
2
0
0
0
0
0
2
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
2
0
0
0
1
1
0
0
0
2
0
1
1
0
0
0
3
0
2
5
0
0
0
0
0
1
0
1
0
0
2
0
0
2
0
0
0
0
1
0
2
0
3
0
0
0
2
1
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
1
0
0
1
2
0
1
2
2
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
2
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
4
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
6
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
2
0
2
2
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
4
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
2
1
0
1
0
4
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
1
0
0
2
0
1
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
2
1
0
0
0
0
0
0
0
2
0
0
2
0
1
1
0
0
0
0
0
0
0
2
0
2
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
3
0
0
0
2
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
5
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
1
1
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
3
2
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
2
0
3
0
3
0
1
0
1
1
1
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
5
0
1
0
0
1
3
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
1
0
2
0
0
1
0
0
0
2
1
1
0
0
0
2
0
0
0
2
0
0
0
0
2
2
0
0
2
2
0
0
0
0
0
1
0
2
1
1
0
1
0
0
0
0
2
0
1
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
2
2
0
0
0
2
0
2
0
0
1
1
1
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
3
0
2
2
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
7
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
2
0
0
0
0
1
0
0
0
2
3
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
1
0
0
0
2
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
1
0
0
4
2
0
2
0
1
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
3
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
6
0
0
0
0
1
0
2
0
1
0
2
0
0
0
0
1
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
2
2
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
2
0
0
1
1
0
1
0
2
0
3
3
0
1
0
1
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
2
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
2
0
2
0
0
0
0
0
0
2
0
1
0
2
1
0
0
6
0
0
0
0
1
2
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
1
0
1
2
1
0
0
1
2
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
1
0
0
0
0
2
0
1
0
0
0
1
2
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
2
2
0
1
0
0
0
2
2
0
0
0
2
0
0
0
0
1
2
1
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
2
2
0
2
2
0
1
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
3
1
0
0
0
0
1
0
0
1
3
2
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
2
0
0
0
0
0
0
0
2
0
1
1
0
0
0
3
0
0
5
2
0
0
8
0
1
0
0
4
0
0
7
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
3
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
2
0
2
1
2
2
0
2
1
2
0
0
0
0
0
0
0
0
0
1
1
3
0
0
0
1
0
0
0
0
0
4
1
2
0
3
0
0
1
2
0
0
1
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
3
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
3
2
0
0
1
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
2
0
0
0
2
1
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
2
0
2
0
2
0
2
0
2
0
2
0
1
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
2
0
6
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
2
1
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
2
0
0
1
0
0
1
0
0
0
0
0
1
0
1
1
1
0
0
1
0
0
0
0
0
0
2
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
1
3
0
0
0
0
2
0
4
0
0
0
1
0
0
0
0
0
3
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
4
1
0
1
0
0
0
0
0
2
0
2
2
0
0
0
2
2
0
0
2
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
2
0
0
0
0
0
0
0
1
0
1
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
1
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
1
0
0
1
0
1
0
1
0
1
0
4
0
0
0
0
2
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
3
0
4
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
2
0
2
0
2
2
5
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
4
1
1
0
7
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
2
1
0
0
0
0
0
7
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
2
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
1
0
0
1
1
2
3
0
0
0
2
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
3
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
3
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
5
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
1
0
0
2
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
1
0
0
2
0
1
0
0
7
0
2
2
0
1
0
0
0
2
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
1
0
0
0
0
4
0
2
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
3
1
2
0
2
0
2
3
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
2
0
1
0
0
1
0
0
2
0
0
0
0
2
0
0
2
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
3
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
3
1
1
1
1
0
0
2
0
1
0
2
0
2
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
2
1
1
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
4
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
6
1
1
1
0
1
0
2
0
3
0
0
0
0
0
0
3
2
0
3
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
1
1
0
0
0
1
1
1
0
0
0
0
0
0
2
0
0
2
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
1
1
1
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
4
1
1
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
5
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
2
1
0
0
1
0
0
3
0
1
0
0
0
0
0
2
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
3
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
2
0
0
0
0
0
2
0
2
1
0
1
2
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
1
0
2
0
0
0
0
1
0
1
3
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
1
1
1
0
0
0
3
0
0
2
0
0
0
0
3
1
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
3
0
0
2
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
1
0
0
1
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
1
0
1
0
0
2
2
0
0
0
1
3
0
2
0
0
0
0
0
0
3
0
2
0
0
3
0
3
0
0
1
0
0
0
0
1
0
2
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
2
2
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
3
2
0
0
1
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
1
0
2
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
3
0
0
0
0
0
0
2
1
2
0
1
0
0
0
2
0
1
0
1
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
4
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
3
0
1
0
0
0
1
0
0
0
0
2
0
2
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
5
2
2
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
1
1
0
0
0
0
3
0
0
0
0
0
1
0
0
1
2
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
1
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
3
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
5
0
0
1
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
3
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
3
1
1
0
0
0
0
0
4
1
0
0
0
2
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
11
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
10
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
3
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
2
5
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
6
1
0
0
0
0
0
0
5
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
2
1
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
1
1
0
0
12
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
4
1
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
3
0
0
0
1
0
1
0
0
1
0
1
2
0
0
0
1
5
3
1
1
1
0
0
0
2
0
0
1
0
0
0
1
0
0
2
0
2
0
2
0
0
0
10
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
1
2
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
1
0
0
0
0
3
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
2
0
2
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
2
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
2
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
2
0
0
0
1
0
0
3
2
0
1
0
0
0
0
1
0
0
0
0
0
1
0
3
0
1
0
3
1
0
1
0
0
0
2
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
2
1
0
0
0
2
1
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
2
2
3
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
6
0
3
1
0
0
0
1
0
2
0
1
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
2
3
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
1
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
4
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
2
0
3
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
1
0
0
0
6
0
0
1
2
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
3
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
1
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
2
0
0
0
0
0
4
0
0
0
0
0
0
2
2
0
0
0
3
0
1
0
0
0
0
0
1
0
2
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
4
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
2
0
0
0
0
0
3
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
5
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
1
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
7
0
2
0
0
0
0
1
1
0
0
2
1
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
3
1
0
0
1
0
2
0
0
0
3
0
0
1
0
0
0
0
2
1
0
0
0
0
0
1
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
2
0
1
1
0
0
7
0
0
0
0
0
2
1
1
0
0
0
1
1
0
0
0
0
1
0
0
1
1
0
1
0
0
1
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
2
0
1
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
2
1
0
0
0
0
0
0
2
0
0
1
2
5
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
2
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
3
0
0
0
0
0
5
0
0
2
0
0
2
0
1
0
0
0
0
0
0
2
1
1
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
2
0
1
2
1
3
0
0
1
0
0
0
2
1
1
1
0
0
1
0
1
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
5
3
1
0
0
0
0
0
0
0
2
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
4
0
3
0
0
1
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
4
0
0
0
0
0
1
1
0
1
0
0
2
0
3
0
0
0
4
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
3
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
4
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
2
1
1
0
0
0
2
1
0
0
1
1
2
3
0
0
0
0
0
1
0
2
0
0
1
0
0
0
2
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
4
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
4
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
7
0
0
0
0
0
0
1
2
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
3
0
1
0
2
2
0
0
0
0
2
0
0
3
0
0
2
0
6
1
0
0
0
0
0
1
2
0
2
0
0
0
0
1
0
0
2
0
0
1
2
0
0
2
0
0
5
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
2
1
0
0
0
0
2
1
0
1
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
1
0
0
1
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
3
0
0
0
3
0
0
1
3
0
0
0
2
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
5
2
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
2
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
3
0
0
0
2
0
0
0
1
2
0
0
0
0
4
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
1
0
0
0
0
3
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
2
1
0
0
0
2
0
6
2
0
0
1
0
0
1
2
0
0
0
2
6
1
0
0
0
0
4
0
2
6
0
0
0
2
0
3
0
0
3
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
4
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
3
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
2
0
1
0
0
0
1
2
0
0
0
0
1
3
0
1
3
0
1
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
6
1
1
0
0
3
0
0
0
0
2
2
0
2
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
2
0
0
1
0
0
1
0
0
0
1
1
2
1
0
0
1
0
0
0
0
2
2
0
0
0
0
7
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
6
0
0
0
0
2
0
0
0
1
1
1
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
1
0
5
0
0
0
0
0
0
0
2
2
0
0
1
1
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
2
1
0
2
1
0
2
2
0
0
0
0
2
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
4
2
0
0
2
2
0
0
0
0
0
0
2
1
3
2
0
0
0
2
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
1
0
0
0
0
0
1
0
2
0
1
0
0
7
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
1
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
1
0
0
0
4
2
2
0
0
2
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
1
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
2
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
2
1
2
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
4
1
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
1
1
0
3
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
3
0
0
0
0
1
0
1
0
1
0
0
0
7
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
4
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
2
1
0
2
2
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
2
2
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
1
2
0
0
0
0
0
0
0
1
1
0
0
1
0
1
2
0
0
1
1
0
1
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
2
1
2
0
0
2
1
0
1
0
0
0
0
1
0
0
0
1
3
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
1
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
2
0
1
0
2
0
0
1
0
0
0
0
0
0
0
1
1
3
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
2
0
0
0
0
0
1
1
0
1
1
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
1
5
0
2
1
0
0
0
1
0
2
2
1
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
2
1
0
0
0
2
3
1
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
3
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
1
0
0
1
1
0
1
0
0
1
3
2
0
0
2
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
3
0
0
1
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
3
0
2
1
6
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
2
0
1
2
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
2
2
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
2
2
0
0
0
3
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
2
0
0
0
0
0
1
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
2
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
3
0
0
0
0
3
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
2
2
0
0
2
2
0
0
1
0
0
0
0
0
2
6
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
5
0
0
2
0
0
0
0
0
2
3
0
1
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
2
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
2
0
0
2
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
1
1
0
1
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
3
1
2
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
3
0
0
1
0
0
0
2
0
1
1
0
0
0
0
1
0
0
0
0
0
1
1
2
0
1
0
0
4
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
3
0
0
2
1
0
0
0
0
0
0
1
2
5
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
4
3
0
1
0
0
0
0
1
1
2
1
1
2
0
0
1
0
3
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
6
2
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
1
0
1
0
1
0
0
0
0
2
0
0
4
1
0
1
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
3
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
2
2
1
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
3
0
4
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
3
1
0
0
0
0
0
0
0
4
0
2
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
5
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
1
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
3
9
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
2
2
0
4
1
0
0
0
1
0
0
2
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
3
2
3
0
0
2
1
0
2
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
1
2
0
0
1
0
0
2
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
1
1
2
1
0
0
3
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
4
1
0
2
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
1
0
1
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
1
0
2
0
0
2
0
1
0
1
0
0
0
0
0
1
0
3
0
0
0
0
0
0
1
2
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
3
0
2
1
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
3
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
2
2
0
4
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
5
2
1
0
0
0
2
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
5
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
1
1
0
1
0
0
0
0
2
0
6
0
1
2
2
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
3
3
1
0
2
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
2
1
1
0
0
0
0
0
0
0
1
2
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
2
0
0
2
1
1
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
7
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
3
1
0
0
0
0
2
0
0
0
0
0
0
3
1
0
0
3
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
3
0
0
4
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
2
1
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
3
0
2
4
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
2
0
2
0
0
0
0
2
1
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
3
2
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
1
0
0
2
0
0
2
1
0
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
2
2
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
2
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
4
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
4
1
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
3
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
2
0
1
0
3
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
2
1
1
0
1
2
0
0
2
0
0
0
1
0
2
0
0
0
0
0
2
0
1
0
0
0
1
1
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
8
0
0
0
1
0
0
0
1
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
1
2
0
0
0
0
2
2
0
0
0
2
0
0
2
1
2
1
1
2
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
5
0
0
0
2
6
2
0
0
1
2
0
0
2
0
0
0
0
2
2
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
2
2
0
0
0
1
0
0
0
2
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
8
0
0
0
1
0
0
1
0
2
0
2
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
2
0
0
0
1
0
0
0
2
0
0
0
7
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
3
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
4
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
1
0
2
1
0
1
0
0
0
0
10
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
2
0
0
0
1
0
0
0
2
0
1
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
2
0
0
0
0
0
4
0
0
0
0
2
0
1
4
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
1
0
0
0
0
1
0
1
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
1
0
2
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
1
2
5
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
1
4
1
2
0
0
2
2
0
1
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
5
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
1
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
2
2
0
0
1
1
0
0
0
0
1
1
1
0
1
1
0
0
0
2
0
0
0
0
0
2
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
5
0
0
0
0
0
4
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
1
0
0
2
0
0
0
2
2
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
2
1
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
5
2
1
1
0
0
2
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
1
3
0
0
2
0
0
0
1
1
0
0
2
1
0
0
0
0
1
1
0
2
1
0
0
0
0
0
0
2
0
0
4
0
0
2
2
0
0
0
0
4
0
0
0
2
0
1
0
0
0
0
4
0
1
0
0
0
0
1
1
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
1
0
2
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
1
2
16
0
1
0
0
0
0
2
0
1
0
0
1
1
0
0
0
5
0
0
0
1
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
1
2
0
1
2
3
0
0
0
4
0
0
0
0
0
0
1
2
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
2
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
2
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
3
2
0
1
0
1
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
1
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
2
1
2
0
2
0
0
0
1
7
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
1
0
0
0
0
1
1
0
1
0
0
2
0
0
0
0
0
0
0
0
4
0
0
1
2
2
0
0
0
0
0
0
3
1
0
1
2
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
2
2
0
1
0
0
0
0
0
2
1
0
1
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
1
0
2
0
1
4
0
0
0
0
2
4
1
0
0
1
1
3
0
2
0
0
1
0
1
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
3
1
1
2
0
0
1
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
7
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
1
0
0
1
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
1
1
0
0
0
0
0
0
2
1
2
0
2
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
1
2
0
0
2
1
2
0
0
0
2
0
0
1
0
0
1
0
0
0
1
0
2
0
0
1
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
3
0
1
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
2
0
1
0
0
2
0
1
0
0
0
0
0
1
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
4
0
5
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
1
0
3
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
5
0
2
0
0
0
0
1
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
3
1
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
4
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
1
0
1
1
2
0
0
2
0
5
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
1
0
3
0
0
0
1
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
2
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
9
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
1
0
2
0
0
2
2
0
0
0
0
1
0
0
0
2
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
3
0
0
0
0
1
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
5
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
5
1
2
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
3
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
1
2
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
2
2
0
0
0
3
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
1
1
0
0
0
1
3
0
1
1
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
3
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
3
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
4
0
0
1
0
2
0
0
0
0
0
2
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
2
2
0
2
0
5
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
2
0
0
0
1
0
2
2
0
0
0
0
0
2
0
0
1
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
3
0
2
2
1
0
1
1
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
2
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
2
0
0
1
1
0
1
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
1
0
1
0
0
0
0
0
0
0
2
0
0
1
1
0
2
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
2
4
3
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
2
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
3
1
0
0
0
1
0
0
1
0
2
3
0
0
0
0
0
1
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
4
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
2
0
0
0
2
1
0
1
1
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
2
0
1
0
0
2
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
2
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
2
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
2
0
2
0
0
0
0
3
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
3
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
2
0
2
0
1
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
1
0
0
2
1
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
1
0
0
2
2
0
4
2
0
0
0
1
1
0
0
0
0
2
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
3
0
1
0
0
1
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
3
0
1
0
2
0
0
0
0
0
0
0
3
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
2
3
5
0
0
0
0
0
0
0
1
2
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
2
3
0
0
2
2
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
2
0
2
0
2
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
7
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
1
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
8
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
4
0
0
1
0
0
0
0
1
0
0
3
0
0
0
0
1
0
0
0
2
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
4
0
0
2
0
0
0
0
1
0
2
0
0
0
1
3
0
2
0
0
0
2
0
0
3
0
0
0
0
1
0
0
0
0
1
2
0
1
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
3
3
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
1
2
0
1
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
3
0
0
1
2
2
0
0
2
0
0
0
2
2
3
2
0
0
0
2
0
0
0
1
0
2
2
0
1
0
0
1
0
0
0
0
1
1
1
7
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
1
0
3
0
0
0
0
2
2
0
0
2
1
1
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
3
0
0
2
1
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
1
1
2
0
0
0
0
5
0
1
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
2
0
0
2
0
0
0
2
0
0
0
12
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
2
1
0
2
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
1
0
1
0
0
1
0
0
0
0
0
0
0
6
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
2
6
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
2
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
1
2
0
1
2
2
0
2
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
1
1
0
0
0
0
2
0
0
2
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
4
0
0
0
0
0
0
0
0
0
0
1
0
4
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
1
0
0
0
2
1
3
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
3
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
2
1
2
0
0
0
0
4
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
3
1
0
1
0
0
0
0
0
0
0
0
0
1
3
0
1
0
5
0
0
0
0
1
0
0
0
0
0
2
0
2
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
2
1
0
0
0
0
2
2
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
2
0
0
1
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
5
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
1
2
0
1
2
0
1
0
0
0
0
0
1
0
0
1
3
0
0
1
0
2
0
2
1
0
0
0
1
2
0
0
1
0
0
1
2
0
0
0
0
6
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
24
0
0
2
0
0
0
0
0
0
0
4
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
2
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
1
0
0
1
2
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
3
0
0
0
0
1
0
2
0
0
0
1
0
3
0
0
0
0
2
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
5
0
1
0
2
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
5
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
3
2
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
2
1
0
0
0
2
0
0
1
2
2
0
0
1
2
0
0
0
0
0
1
0
6
0
0
1
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
1
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
5
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
1
0
0
2
2
2
0
0
0
2
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
1
0
1
1
2
0
0
0
4
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
1
0
0
0
0
2
1
0
1
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
7
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
1
0
0
1
0
0
3
0
0
0
0
0
0
2
0
3
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
3
0
0
0
0
0
0
0
0
2
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
4
0
4
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
1
0
1
0
0
2
0
0
0
2
2
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
1
0
0
0
0
0
2
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
7
1
0
1
2
0
4
0
3
0
2
1
1
0
0
0
0
0
4
2
0
1
0
0
0
1
0
0
0
0
0
0
1
3
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
4
1
2
0
1
0
0
0
0
2
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
10
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
3
1
6
0
2
0
0
0
0
0
0
0
0
2
4
1
0
0
0
2
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
3
0
0
0
2
0
0
2
3
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
1
0
10
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
1
0
2
1
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
2
0
1
3
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
3
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
1
3
0
2
4
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
1
1
1
1
0
1
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
2
0
0
0
0
1
0
0
0
0
1
0
2
1
3
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
8
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
3
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
4
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
2
0
1
0
0
6
0
0
1
0
0
0
0
0
0
2
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
2
9
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
2
4
0
0
4
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
2
0
0
0
0
0
0
0
2
1
0
0
0
1
1
0
0
0
0
0
0
0
0
3
0
0
0
0
2
1
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
4
0
0
1
2
0
0
3
0
2
0
0
0
2
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
5
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
1
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
2
3
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
3
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
6
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
2
0
0
0
0
1
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
1
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
1
1
2
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
4
0
0
0
0
0
0
0
3
0
0
3
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
1
0
2
0
0
0
3
2
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
8
0
0
0
0
2
0
0
1
2
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
1
0
0
2
0
0
2
0
0
0
1
0
0
1
1
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
2
2
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
3
1
2
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
2
0
4
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
3
0
0
0
0
1
0
0
0
0
3
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
2
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
2
3
0
1
2
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
5
0
0
2
0
2
6
0
0
1
0
1
0
0
0
1
0
1
2
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
4
1
0
1
2
1
2
0
3
10
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
3
0
0
2
0
0
0
3
0
1
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
4
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
2
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
1
0
0
0
5
2
0
2
2
0
0
0
1
0
2
0
0
3
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
4
0
2
0
1
0
1
1
3
1
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
2
2
0
0
0
0
5
0
1
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
1
1
0
1
0
0
0
1
0
0
1
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
7
0
0
0
0
0
0
0
0
5
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
2
0
0
2
3
0
1
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
2
0
1
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
2
0
1
0
2
0
1
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
1
0
0
1
0
2
0
0
0
2
0
3
2
0
0
0
0
0
2
0
0
2
1
0
2
1
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
1
0
0
0
2
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
3
0
0
0
3
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
1
0
0
4
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
1
0
0
1
0
0
1
0
1
1
0
0
0
0
1
0
2
0
0
0
1
1
0
0
0
0
2
0
0
3
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
2
1
0
2
1
0
0
2
0
0
1
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
3
0
3
0
0
1
0
1
2
0
0
0
0
0
0
0
0
2
0
0
3
2
2
1
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
3
0
0
0
2
0
2
0
0
0
1
3
0
2
0
0
1
0
0
0
4
2
2
0
0
1
0
1
0
0
2
0
0
0
0
1
0
1
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
1
0
0
0
0
0
7
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
2
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
1
0
1
0
0
2
0
0
0
1
0
8
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
5
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
1
0
0
1
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
3
0
0
0
1
0
1
0
0
0
0
0
0
0
2
3
0
0
0
1
0
0
0
1
0
0
1
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
1
0
1
7
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
4
0
0
0
2
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
1
0
0
3
0
0
0
0
1
0
0
0
0
2
4
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
2
0
1
0
2
0
0
1
1
0
2
0
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
4
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
4
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
2
1
0
2
0
2
0
0
0
4
2
0
0
0
0
0
2
3
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
2
0
1
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
2
3
0
3
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
3
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
3
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
3
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
5
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
5
0
1
0
1
0
0
0
2
2
3
0
0
0
0
0
1
0
1
0
0
0
0
3
0
3
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
1
3
0
1
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
2
2
0
0
0
0
0
1
1
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
3
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
2
0
0
0
1
0
0
3
0
1
1
1
1
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
1
0
1
5
2
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
1
0
1
0
0
0
1
0
0
0
2
0
1
1
0
0
0
1
1
3
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
3
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
1
0
0
0
3
0
2
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
5
0
0
0
0
2
1
0
0
1
0
0
0
0
2
0
0
0
0
0
3
0
0
1
1
0
2
0
2
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
3
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
2
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
1
0
2
0
1
0
0
0
0
0
0
3
1
3
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
1
0
2
0
1
0
2
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
3
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
3
1
2
1
0
1
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
2
0
0
0
1
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
5
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
2
0
4
1
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
1
1
0
0
0
1
0
2
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
4
0
0
0
2
0
0
1
0
0
1
2
0
0
6
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
1
2
2
4
1
2
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
2
0
0
0
0
7
3
0
2
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
1
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
4
0
5
0
0
0
2
0
2
0
0
4
0
0
0
0
0
6
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
1
0
0
0
1
2
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
4
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
1
1
0
0
0
2
0
1
0
1
1
1
0
0
2
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
1
4
0
2
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
2
2
1
0
0
2
1
0
0
0
1
0
0
0
3
0
0
0
4
0
0
0
0
0
0
1
0
0
0
2
10
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
2
0
0
0
1
0
0
3
0
0
0
2
0
0
1
0
1
0
2
1
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
1
0
2
0
0
2
0
0
0
3
0
0
3
1
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
2
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
3
0
0
0
0
0
0
1
1
0
0
0
0
0
0
6
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
2
0
0
2
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
1
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
2
1
2
0
1
1
2
2
0
0
0
1
0
0
0
1
0
0
0
0
0
5
0
1
0
0
0
0
1
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
3
3
0
0
0
2
0
0
0
1
0
0
0
1
2
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
6
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
3
0
0
1
0
0
9
3
0
0
0
3
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
2
0
2
1
1
0
0
1
0
2
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
1
2
2
0
0
2
0
0
0
1
0
0
0
0
1
1
0
0
1
0
1
0
1
1
0
0
0
2
1
0
0
1
0
0
0
0
4
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
1
0
1
0
2
0
0
0
1
0
0
0
0
1
0
3
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
5
0
0
0
0
0
0
3
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
2
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
4
0
0
0
0
2
2
0
0
0
0
0
4
0
0
0
0
2
2
1
0
0
8
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
2
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
1
0
6
0
0
0
0
0
0
0
2
0
3
0
2
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
1
1
0
1
0
6
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
10
1
0
0
0
0
1
2
0
0
2
11
0
0
0
0
3
2
2
0
0
0
0
0
1
0
0
0
3
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
4
0
0
0
0
2
4
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
5
1
0
1
0
0
0
1
3
0
2
0
0
1
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
11
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
2
0
0
2
0
1
0
0
0
0
1
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
1
2
5
0
0
0
2
0
0
0
0
0
1
1
0
1
0
0
3
0
0
0
0
2
0
0
0
6
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
4
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
2
0
0
0
2
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
1
2
0
0
0
0
0
0
2
0
0
2
0
0
2
0
1
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
3
0
0
0
2
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
2
0
2
2
0
0
0
0
2
1
0
0
2
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
2
0
2
0
0
0
0
0
0
1
0
1
2
0
0
1
1
0
0
0
0
0
0
0
2
0
1
0
0
1
2
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
2
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
3
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
8
0
1
0
0
0
0
0
3
0
0
0
0
2
0
1
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
3
2
0
3
0
0
0
0
0
5
1
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
7
1
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
1
0
0
0
0
1
0
1
0
0
2
1
1
5
0
0
0
2
0
9
1
0
0
0
1
0
0
1
0
2
0
1
0
0
0
1
0
0
0
0
2
0
0
1
1
2
1
0
0
0
2
0
3
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
10
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
3
1
0
0
2
0
0
1
0
2
1
0
0
0
1
0
0
0
1
1
0
2
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
3
0
0
2
2
0
0
1
0
0
0
1
2
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
7
0
0
0
1
0
0
0
3
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
3
0
0
1
1
1
1
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
1
0
0
0
2
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
3
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
2
2
0
1
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
2
2
0
0
0
2
0
0
0
0
0
2
1
0
0
0
2
0
0
1
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
1
2
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
2
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
4
1
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
1
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
4
1
3
0
1
1
0
0
0
1
2
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
1
1
3
0
0
0
2
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
2
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
3
2
1
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
2
0
0
0
1
0
1
1
0
0
0
0
0
0
0
2
4
1
0
0
1
0
0
0
2
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
3
2
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
3
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
5
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
11
0
0
0
0
1
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
2
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
4
0
2
1
0
0
0
0
0
2
1
0
1
0
0
2
0
1
2
0
0
0
0
0
2
0
0
0
2
0
1
0
0
4
0
1
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
1
0
2
2
0
1
0
0
4
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
1
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
1
3
1
0
2
0
1
1
1
0
0
2
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
3
1
2
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
2
2
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
3
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
2
0
1
1
0
0
2
0
0
0
0
2
0
0
1
0
2
0
0
0
2
0
0
0
1
1
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
2
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
2
1
0
17
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
11
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
1
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
1
4
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
1
1
1
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
2
0
0
2
0
0
0
2
0
0
0
2
1
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
1
1
0
0
0
0
0
0
0
2
0
0
1
2
0
1
0
0
2
0
1
0
0
1
0
0
0
0
2
5
0
0
0
2
0
0
1
1
0
0
8
4
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
3
0
3
3
0
0
0
0
0
0
2
2
4
0
0
0
1
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
1
0
0
2
0
0
0
0
0
0
0
1
2
0
0
1
1
0
1
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
5
1
0
0
0
0
0
0
0
2
0
2
0
1
0
1
0
0
0
0
0
0
1
3
1
0
0
1
1
1
0
0
2
0
0
1
0
1
0
0
2
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
1
1
1
2
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
3
2
2
2
1
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
1
2
0
0
0
0
0
0
0
1
0
1
0
1
1
0
2
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
7
1
0
1
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
1
3
0
0
0
0
1
0
2
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
3
0
1
0
1
2
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
1
1
2
2
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
1
0
0
2
0
1
0
2
0
0
2
0
0
1
0
0
0
0
1
1
0
2
2
1
0
0
0
0
0
0
0
0
0
0
1
3
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
2
0
1
2
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
2
1
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
2
2
2
0
2
1
1
0
0
4
0
0
0
0
0
0
0
0
0
0
4
0
1
0
2
1
0
2
1
0
0
0
2
1
0
0
0
3
0
0
0
0
0
1
2
0
0
2
0
2
0
0
4
0
0
0
1
2
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
14
1
0
0
0
4
1
1
2
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
1
1
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
2
0
2
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
2
0
0
3
1
1
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
1
2
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
1
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
3
1
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
2
0
2
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
3
0
0
0
0
0
1
1
0
0
2
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
4
1
1
0
0
1
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
2
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
3
3
1
0
0
2
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
1
0
0
0
2
0
0
3
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
1
1
2
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
2
0
0
1
0
0
6
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
1
0
3
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
1
0
0
3
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
2
0
4
2
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
5
0
0
1
0
0
0
0
2
0
0
2
1
0
1
0
2
0
0
0
2
0
0
0
3
0
0
0
1
2
0
2
2
2
0
0
0
0
0
0
0
3
3
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
2
2
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
1
2
0
0
2
1
0
1
0
2
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
3
0
1
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
2
0
0
1
0
0
4
0
0
0
0
0
2
0
1
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
1
2
2
0
0
0
0
0
0
6
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
9
0
0
1
0
0
0
0
0
0
3
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
7
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
1
1
0
0
1
0
0
0
2
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
1
2
0
0
0
5
3
0
0
2
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
2
2
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
5
0
0
0
2
2
0
0
0
1
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
7
3
0
0
0
0
0
0
0
2
0
0
0
7
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
2
7
0
1
0
0
1
0
0
1
1
1
2
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
2
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
2
2
2
1
0
0
0
1
0
2
1
0
2
0
1
0
0
2
0
0
2
1
0
0
0
2
0
0
0
4
0
1
0
1
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
7
0
0
0
2
4
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
8
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
3
0
1
0
0
0
0
3
0
0
1
0
0
0
2
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
4
0
0
0
1
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
2
0
0
0
2
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
4
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
2
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
2
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
1
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
1
1
2
0
0
0
13
0
0
0
0
0
0
7
0
0
0
0
0
0
1
0
0
0
3
2
1
1
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
1
1
0
0
0
4
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
1
0
0
1
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
3
2
1
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
1
0
1
0
1
0
0
0
1
1
0
0
1
0
1
1
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
1
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
4
0
8
1
0
0
0
0
0
0
0
0
16
0
0
1
0
1
0
1
0
0
3
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
6
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
3
0
3
1
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
1
0
2
3
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
4
0
1
0
0
0
2
2
0
0
0
0
3
0
0
0
1
0
0
2
0
2
1
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
3
0
0
0
1
1
1
3
0
2
0
0
1
0
0
0
0
5
0
0
0
0
1
0
0
1
2
0
2
0
2
0
0
0
0
0
2
0
2
2
1
0
2
2
0
0
2
2
0
0
3
2
0
1
0
0
0
0
0
2
0
0
1
0
5
0
2
0
0
2
0
3
5
2
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
4
3
0
1
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
1
0
2
0
2
1
1
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
6
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
5
2
1
1
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
1
0
0
0
2
1
0
0
0
0
0
1
0
2
0
0
2
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
3
4
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
2
1
1
0
0
1
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
2
5
0
1
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
3
2
0
0
1
0
3
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
1
2
0
2
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
9
0
0
2
0
0
0
2
0
0
0
0
2
0
0
1
0
0
1
0
0
2
0
1
2
1
0
1
2
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
2
0
3
0
0
0
2
0
3
2
2
0
1
0
0
1
0
0
2
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
6
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
11
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
3
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
3
0
0
1
0
0
0
0
0
2
0
0
0
1
1
1
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
1
0
0
1
0
2
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
2
2
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
2
1
1
0
0
0
1
1
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
2
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
2
0
1
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
2
2
0
0
0
0
2
1
0
0
2
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
2
4
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
2
0
14
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
3
0
0
0
1
0
0
0
2
0
0
0
3
0
1
2
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
2
3
0
0
1
0
2
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
2
2
0
3
0
2
0
1
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
2
3
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
1
0
0
3
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
1
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
1
1
0
1
0
3
0
0
0
0
2
1
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
2
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
3
0
0
0
0
0
0
0
5
0
0
0
0
0
1
2
0
0
0
1
0
2
1
0
0
1
1
0
1
0
1
0
2
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
3
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
3
3
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
1
1
1
2
0
0
0
0
0
9
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
4
0
1
0
2
0
0
0
2
0
2
3
0
0
0
0
0
2
1
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
5
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
2
1
1
0
0
3
0
0
2
2
0
2
0
0
0
1
2
0
2
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
1
9
0
0
0
0
0
0
1
0
0
2
1
0
0
0
1
0
1
0
1
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
1
0
0
1
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
6
0
0
0
2
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
1
4
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
7
0
0
0
0
3
0
7
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
2
1
0
0
2
0
1
0
0
1
1
0
0
0
3
2
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
3
0
0
0
1
0
2
2
0
0
0
0
3
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
1
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
3
2
0
0
4
1
0
0
0
1
2
2
0
1
0
0
0
0
0
1
2
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
2
2
0
0
1
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
4
0
1
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
1
0
0
4
0
0
0
0
0
0
3
0
3
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
3
2
0
0
0
1
0
0
3
0
0
0
0
0
0
3
0
1
0
1
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
3
2
6
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
1
0
0
0
0
0
0
1
2
3
0
0
2
0
2
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
1
1
2
0
0
0
0
0
4
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
5
0
0
4
0
0
4
0
0
0
8
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
2
4
0
1
0
0
0
0
0
2
1
2
2
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
1
0
0
2
2
2
0
0
0
1
0
6
0
0
0
2
0
0
1
0
0
0
0
1
4
0
0
0
1
0
2
0
0
0
3
1
0
0
2
0
0
0
0
0
0
0
1
0
3
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
4
0
0
2
0
0
1
0
3
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
1
0
1
0
0
0
0
0
1
2
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
4
3
0
1
0
0
0
2
1
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
2
1
1
0
0
0
4
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
3
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
3
0
0
0
0
0
2
0
0
1
0
0
0
0
2
4
0
0
0
0
0
0
2
0
1
1
0
0
0
2
2
1
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
1
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
4
0
0
0
0
6
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
4
2
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
2
1
0
0
0
0
0
2
0
0
0
2
0
0
5
1
0
1
2
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
1
2
0
0
4
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
2
2
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
3
0
2
0
0
0
1
0
1
1
3
0
0
0
0
0
0
0
4
0
1
0
0
0
0
1
2
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
4
0
0
0
0
0
4
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
5
0
3
0
0
0
0
0
0
1
2
0
1
0
2
0
1
0
1
0
1
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
2
0
0
1
2
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
6
2
0
2
0
0
0
0
0
1
0
0
0
3
0
0
0
0
1
0
0
0
2
1
0
0
0
2
0
0
3
3
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
3
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
2
1
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
1
0
0
0
0
5
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
2
0
0
0
0
0
0
1
2
0
0
0
2
1
0
0
0
1
2
0
0
0
4
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
6
0
8
1
1
2
0
0
0
0
2
0
0
2
0
2
0
1
2
2
0
0
0
0
0
4
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
9
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
1
0
0
2
0
0
0
2
0
3
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
2
1
1
3
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
1
0
1
1
0
1
0
0
0
3
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
1
0
1
1
0
1
2
1
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
1
2
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
1
0
0
0
0
3
0
0
0
0
1
1
0
0
1
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
3
0
1
0
0
2
0
0
1
0
0
0
0
0
0
6
0
1
0
2
0
0
0
0
0
2
0
0
0
1
2
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
1
0
4
1
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
3
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
1
0
3
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
10
2
0
0
1
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
4
0
0
0
6
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
1
0
0
2
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
5
1
0
1
1
2
2
0
2
2
0
6
0
0
0
0
3
2
0
4
0
0
0
0
0
2
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
7
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
8
0
0
0
0
0
0
0
0
3
2
0
0
1
0
0
0
2
0
0
0
2
3
3
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
5
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
1
2
0
2
0
0
2
0
0
0
0
1
0
3
0
0
1
2
0
0
0
1
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
1
0
2
0
2
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
3
0
2
2
0
0
4
2
0
0
0
0
0
0
3
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
2
0
2
1
2
0
1
1
0
0
0
3
0
2
3
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
1
0
0
1
0
4
0
0
0
5
2
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
2
0
2
4
1
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
1
0
0
0
1
0
0
0
3
0
1
0
0
1
1
0
4
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
2
0
0
0
1
0
0
0
0
2
0
0
1
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
2
4
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
1
2
0
0
2
0
0
0
0
0
0
0
0
1
0
2
1
1
0
0
0
2
0
2
0
0
0
0
1
0
1
0
0
1
0
2
0
4
0
0
0
0
0
1
0
1
0
2
0
0
3
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
6
3
0
0
1
0
0
0
0
0
2
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
1
3
28
0
0
2
0
2
2
0
0
0
0
0
0
0
1
1
0
0
0
4
0
0
0
1
0
0
3
0
0
0
0
0
0
2
0
0
2
0
2
2
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
5
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
3
0
0
1
2
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
2
1
0
0
0
2
0
1
2
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
2
1
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
2
1
1
3
0
1
0
1
2
0
2
1
3
0
5
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
2
0
0
1
0
2
0
0
0
1
0
0
2
3
0
1
0
2
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
1
0
0
0
1
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
3
1
0
0
2
0
2
1
0
0
0
7
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
4
0
2
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
2
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
2
1
0
0
0
2
2
0
0
3
0
1
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
2
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
5
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
2
2
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
3
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
2
0
0
0
0
0
1
1
0
0
0
2
2
0
0
3
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
3
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
3
0
0
0
0
0
0
1
1
0
0
0
0
0
0
3
2
2
0
0
3
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
2
1
0
0
0
0
3
0
0
0
1
0
4
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
1
0
1
0
0
1
3
0
0
1
0
0
1
1
0
0
0
0
0
0
2
2
1
0
1
0
0
0
0
2
0
0
0
1
1
0
0
0
3
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
5
0
0
0
2
2
0
0
2
0
0
0
0
1
0
0
0
5
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
2
0
1
0
0
0
0
0
1
0
2
0
0
0
0
2
1
0
2
1
1
0
1
0
0
0
1
0
0
0
0
1
0
0
1
1
2
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
1
0
0
2
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
2
5
2
0
0
0
1
0
2
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
4
1
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
1
0
0
0
0
0
0
0
2
4
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
1
1
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
1
2
0
1
0
0
0
3
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
3
0
5
0
0
0
0
0
6
1
0
0
0
0
0
2
2
0
2
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
10
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
3
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
2
0
1
1
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
1
8
0
1
0
0
0
0
0
0
0
0
1
1
0
0
2
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
1
1
2
1
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
1
0
2
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
1
0
1
0
2
0
0
0
0
2
2
0
0
9
0
2
0
5
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
1
0
1
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
2
2
0
6
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
4
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
4
0
0
0
1
0
1
0
0
1
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
8
0
0
0
1
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
1
0
0
0
2
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7
0
1
4
0
0
0
2
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
5
3
0
0
0
0
0
0
0
0
0
0
0
0
1
3
1
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
3
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
5
0
0
5
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
1
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
2
0
2
2
1
0
0
0
0
0
0
1
1
0
0
0
2
0
1
1
0
1
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
1
1
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
1
1
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
3
5
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
3
1
0
2
0
1
0
2
1
1
1
0
1
1
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
1
0
0
2
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
2
3
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
2
1
0
2
0
0
0
0
1
0
0
0
1
0
2
0
0
0
4
0
2
0
0
1
0
0
0
2
0
1
1
0
0
0
0
0
0
0
1
0
4
3
0
1
2
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
1
0
0
0
2
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
1
1
0
0
0
0
0
2
0
0
7
0
1
0
1
2
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
1
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
2
2
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
3
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
1
0
3
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
3
0
0
0
0
0
0
0
0
0
1
0
1
0
0
3
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
1
2
0
0
0
0
0
0
3
4
0
0
0
0
5
2
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
2
0
1
0
0
0
0
0
0
0
3
0
0
0
1
1
0
1
0
0
1
0
0
4
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
1
4
0
0
0
0
1
3
0
0
0
0
1
1
2
3
2
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
1
0
1
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
1
0
3
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
2
2
0
2
0
0
0
0
0
0
3
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
1
0
2
0
3
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
1
0
0
4
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
2
0
0
0
5
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
3
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
1
1
4
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
3
0
0
3
0
0
2
2
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
5
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
3
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
2
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
1
0
2
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
2
0
0
2
0
1
0
0
0
2
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
2
2
0
0
2
2
0
0
0
0
1
0
0
0
2
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
3
0
0
2
0
0
0
1
0
2
0
2
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
2
0
2
1
0
0
0
0
1
0
0
1
0
0
1
2
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
2
1
0
1
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
3
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
2
0
1
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
2
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
3
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
3
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
1
2
0
0
0
0
0
1
1
2
0
0
0
1
0
0
0
1
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
2
0
2
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
8
0
1
1
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
6
0
2
2
0
0
3
0
0
3
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
7
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
3
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
3
1
0
0
1
2
3
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
4
0
0
1
1
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
4
2
1
2
2
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
1
0
0
0
0
0
2
1
2
0
0
1
5
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
4
1
0
2
1
1
0
0
0
2
0
2
0
0
7
9
0
2
0
0
0
0
1
0
0
0
1
2
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
1
1
0
0
0
1
2
0
0
1
1
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
2
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
3
0
0
0
0
2
1
2
4
0
0
2
0
0
2
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
2
0
1
0
0
3
3
1
0
0
0
0
1
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
1
0
8
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
3
0
0
0
1
0
0
0
0
0
1
0
2
0
0
2
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
3
2
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
3
0
1
0
3
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
3
0
1
0
0
0
0
2
0
1
0
2
2
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
2
0
0
0
2
0
0
0
2
0
2
1
0
4
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
3
0
1
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
3
0
0
0
2
2
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
2
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
3
0
0
0
2
0
0
0
1
0
2
2
0
0
0
2
1
0
0
0
0
0
0
0
3
0
0
0
2
1
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
2
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
1
1
0
0
0
0
1
0
1
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
1
1
2
3
4
0
0
0
0
1
0
1
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
1
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
3
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
1
0
2
0
0
0
0
0
0
0
3
0
0
0
1
0
0
2
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
2
4
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
1
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
2
2
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
1
0
0
1
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
8
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
1
1
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
2
0
1
3
0
1
0
2
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
1
0
1
1
2
0
0
0
0
0
0
3
0
0
1
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
2
1
0
0
0
0
2
2
3
0
0
0
1
0
0
0
0
0
4
1
0
0
0
0
0
0
0
5
1
0
2
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
1
0
0
0
3
0
0
0
2
2
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
1
6
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
3
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
1
0
3
0
2
1
0
0
2
0
2
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
2
0
0
0
0
0
0
2
0
0
1
0
0
2
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
2
0
0
1
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
7
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
2
0
2
1
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
4
1
1
2
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
1
0
0
0
0
2
0
1
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
2
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
3
0
0
1
0
0
0
3
0
0
0
0
0
0
0
1
0
0
1
2
1
0
0
0
0
0
0
1
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
2
2
0
0
4
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
7
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
3
0
0
2
0
0
0
0
0
0
1
0
0
7
0
2
0
0
2
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
3
3
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
3
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
1
0
0
2
1
0
0
1
0
0
2
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
1
0
3
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
2
1
5
1
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
5
0
0
0
1
0
0
0
0
0
4
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
1
2
2
0
0
0
0
3
0
2
0
0
0
0
0
0
0
3
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
9
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
1
0
0
0
0
2
0
0
0
0
0
2
0
2
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
1
0
0
3
0
0
0
2
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
3
0
0
2
0
0
2
0
2
0
0
0
0
2
0
0
0
5
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
2
0
1
2
1
0
0
1
0
0
2
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
2
0
2
2
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
1
0
0
0
3
0
0
3
1
2
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
1
1
1
0
0
1
0
0
0
0
1
0
0
0
4
0
0
1
0
0
0
0
0
0
5
0
0
2
0
0
2
0
0
0
1
2
2
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
3
0
1
0
0
0
0
0
0
0
2
0
1
4
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
1
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
2
0
2
1
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
2
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
1
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
5
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
3
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
2
2
0
0
0
2
0
1
0
0
1
0
2
1
2
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
2
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
4
0
0
0
1
0
1
1
0
0
0
1
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
2
0
2
1
11
0
1
0
0
0
0
0
0
1
0
0
2
0
3
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
2
0
0
0
3
0
3
1
0
0
0
0
1
0
3
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
1
1
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
10
0
0
2
1
0
2
1
1
0
0
2
0
2
2
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
2
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
2
0
1
0
0
5
0
0
0
0
0
0
0
0
0
0
0
1
1
2
2
0
2
1
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
2
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
1
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
1
4
0
0
1
0
2
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
1
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
2
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
5
2
3
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
6
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
6
0
0
0
1
0
2
0
0
0
0
0
0
0
3
0
0
0
1
0
1
0
0
0
1
1
0
0
0
2
0
0
1
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
7
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
5
0
0
0
0
0
0
0
0
0
0
2
1
2
0
1
0
0
0
0
0
0
5
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
1
0
0
0
0
0
1
1
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
3
0
0
4
1
0
1
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
3
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
4
0
0
0
3
0
0
0
0
1
0
0
0
2
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
2
0
0
0
3
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
2
1
4
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
2
1
4
0
0
0
0
0
0
0
0
0
0
1
0
2
1
2
0
3
0
0
0
0
0
0
5
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
2
0
1
0
0
0
0
0
1
0
4
0
1
0
2
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
4
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
1
0
2
1
0
0
0
0
0
1
0
5
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
3
3
0
2
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
3
1
0
0
0
0
0
0
0
0
1
0
0
2
2
2
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
3
0
0
0
0
2
8
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
3
2
0
0
0
0
1
1
0
2
0
0
0
4
0
2
1
2
0
0
0
0
1
0
0
0
0
0
0
0
4
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
3
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
2
0
0
0
0
2
2
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
2
0
6
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
1
1
2
2
2
0
0
0
0
1
0
3
0
0
2
1
0
0
0
2
0
0
0
0
1
0
1
2
0
1
0
0
0
1
0
0
0
2
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
2
0
3
0
1
0
0
0
0
0
1
0
2
3
0
0
2
2
0
2
3
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
1
0
0
0
2
2
0
0
0
0
1
2
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
3
0
0
0
0
3
0
0
7
0
2
0
2
0
0
2
2
2
0
2
1
0
0
0
3
1
0
0
0
2
2
0
0
1
3
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
7
2
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
2
0
0
1
0
0
0
2
2
0
0
0
0
2
3
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
4
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
2
1
0
0
2
0
0
1
0
0
0
1
1
0
1
0
1
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
8
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
1
1
0
0
0
0
0
2
0
2
0
1
0
0
3
0
0
0
1
2
1
1
4
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
2
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
1
0
1
0
2
0
0
1
0
0
2
0
3
0
0
0
0
0
0
0
1
1
0
2
2
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
2
2
1
2
0
1
1
0
0
0
0
0
1
0
2
0
0
0
3
2
4
0
0
0
0
0
0
0
2
0
0
0
4
3
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
2
0
0
1
0
1
0
2
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
2
0
2
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
1
0
0
0
2
2
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
1
0
1
1
1
0
2
0
0
1
0
0
0
0
0
0
0
7
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
1
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
2
0
0
1
1
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
2
1
0
0
1
0
1
0
0
0
3
0
0
1
0
0
0
3
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
4
2
0
0
0
0
0
0
0
6
0
1
0
0
0
0
1
0
0
2
0
0
3
0
0
0
0
1
0
0
2
0
0
3
0
4
2
0
2
0
0
0
0
0
0
0
4
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
4
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
1
0
0
3
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
1
0
1
1
0
1
4
0
1
0
1
0
0
3
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
8
0
0
0
0
0
1
1
1
0
0
0
2
2
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
2
0
2
3
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
1
3
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
1
0
0
3
0
0
0
1
0
0
0
0
1
0
2
1
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
4
0
2
0
0
1
1
0
0
1
1
0
0
0
0
2
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
4
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
4
2
3
0
0
0
0
4
0
2
0
1
0
1
2
0
0
0
0
1
0
1
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
2
0
0
1
2
0
1
0
0
0
2
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
3
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
1
0
1
2
0
1
0
0
0
1
0
0
0
0
0
1
0
0
3
0
3
1
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
2
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
4
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
2
0
0
1
0
1
1
0
1
1
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
2
1
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
3
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
3
1
2
1
0
2
0
0
0
0
3
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
1
0
1
0
2
2
0
0
0
0
0
0
1
2
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
2
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
2
2
0
2
0
0
0
0
0
0
0
0
2
2
2
0
1
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
3
1
2
0
0
0
0
0
0
0
0
2
1
0
2
0
0
2
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
2
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
1
0
0
3
0
0
0
0
0
0
1
0
1
2
0
0
0
0
3
0
1
0
0
0
3
1
0
0
0
0
0
0
0
5
1
2
0
0
1
0
0
0
0
1
0
1
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
4
2
0
0
5
0
0
0
0
0
0
0
2
2
0
1
0
1
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
0
2
0
1
0
0
0
1
0
0
0
2
1
2
0
0
0
0
0
0
0
3
0
0
1
0
0
0
2
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
4
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
2
0
5
0
2
3
1
0
1
0
0
0
0
0
0
12
0
0
0
0
0
0
1
0
0
0
0
3
0
1
0
3
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
1
1
0
0
0
2
2
0
0
1
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
7
1
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
3
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
4
0
1
0
1
1
5
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
4
0
0
2
0
2
5
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
1
0
0
0
2
1
1
0
0
0
0
2
0
0
0
0
1
0
0
1
0
2
0
0
2
0
2
0
0
0
0
0
3
2
0
0
2
0
2
0
1
1
3
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
5
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
1
1
4
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
3
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
3
0
0
1
0
0
0
1
0
0
0
0
1
0
2
0
0
2
0
2
1
2
2
2
2
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
2
1
2
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
1
0
0
1
0
0
0
1
1
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
3
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
1
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
2
0
0
0
0
2
0
0
2
0
0
1
2
0
0
0
1
0
0
3
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
6
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
3
0
1
0
0
3
0
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
1
1
0
0
1
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
3
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
2
0
2
0
0
0
0
2
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
2
1
0
0
0
2
4
0
0
0
0
0
4
0
2
0
0
0
2
0
2
0
0
0
1
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
2
0
2
0
0
0
0
1
5
1
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
5
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
2
0
1
0
1
0
0
0
0
3
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
3
0
0
0
0
2
1
1
0
0
0
0
2
0
1
0
0
0
0
1
0
2
5
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
1
0
0
0
0
0
1
2
0
2
2
0
0
0
0
2
0
0
0
2
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
1
2
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
6
0
0
1
2
0
0
1
1
0
0
0
2
0
1
0
0
1
0
0
0
0
0
1
2
0
0
0
2
1
0
0
0
3
0
0
0
0
0
0
2
0
0
0
8
2
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
1
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
1
2
0
0
2
0
0
0
1
1
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
2
2
1
0
0
2
0
3
0
2
0
1
0
0
1
0
0
1
2
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
1
2
1
0
0
0
0
0
1
0
1
0
0
0
2
0
0
10
0
0
0
0
1
0
2
0
6
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
1
2
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
5
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
3
0
2
1
0
1
0
0
2
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
1
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
5
0
0
0
0
0
0
0
1
2
0
0
0
0
7
0
0
1
0
0
1
0
0
0
2
0
1
0
3
0
0
0
1
0
0
2
2
1
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
1
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
1
2
0
0
2
0
5
0
0
1
0
0
0
1
0
0
0
1
0
2
0
0
0
0
3
2
0
1
0
0
0
3
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
2
0
3
1
0
0
0
1
0
0
1
2
1
0
0
0
5
1
1
0
3
1
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
1
1
0
0
0
0
8
0
1
0
0
0
0
0
0
0
0
0
2
1
7
0
1
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
9
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
2
2
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
2
0
0
1
0
0
0
0
2
2
1
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
1
0
0
3
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
1
0
0
0
2
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
1
1
3
0
2
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
3
1
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
3
0
1
0
4
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
1
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
2
0
2
2
0
0
1
1
2
2
0
0
0
0
0
2
1
0
1
0
1
0
0
0
0
1
0
1
0
2
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
3
0
0
2
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
3
2
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
3
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
2
1
0
0
0
3
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
3
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
1
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
2
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
3
0
0
1
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
4
1
2
0
0
1
0
1
0
1
0
0
0
3
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
2
1
1
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
2
0
1
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
3
0
0
1
0
5
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
3
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
11
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
1
3
0
0
0
0
1
0
0
1
0
9
0
0
0
2
0
3
2
0
1
0
0
2
2
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
2
0
0
5
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
10
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
5
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
1
0
1
2
0
0
1
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
3
0
0
0
2
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
2
1
0
1
0
0
0
0
0
2
0
0
0
1
1
0
0
0
1
0
0
4
0
0
1
0
1
0
2
2
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
4
2
0
1
2
0
1
0
0
3
2
2
0
0
1
1
0
0
0
2
0
0
0
0
0
1
0
0
2
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
4
0
2
5
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
3
0
0
0
0
0
0
0
2
0
4
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
2
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
3
0
1
0
0
0
0
1
0
0
0
0
3
0
0
0
0
1
5
0
1
0
0
1
0
0
2
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
2
1
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
1
0
0
1
0
0
6
0
1
0
0
0
0
4
0
2
0
0
2
0
0
0
2
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
3
1
0
2
0
2
6
0
0
2
0
1
0
0
0
1
0
2
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
2
0
1
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
2
3
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
2
2
0
2
1
0
1
0
0
0
1
2
0
0
0
3
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
6
5
2
2
0
0
2
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
5
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
3
0
0
6
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
2
0
0
2
1
0
0
1
1
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
4
0
0
2
0
0
0
1
0
0
0
3
0
0
1
0
0
0
0
0
5
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
5
1
0
2
0
0
0
0
0
0
0
0
0
0
3
0
2
4
0
0
3
0
0
5
0
0
0
3
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
1
0
4
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
2
0
0
1
0
1
0
0
2
0
1
0
0
0
0
2
0
0
0
2
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
1
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
2
0
0
0
0
0
2
0
0
0
0
2
1
3
3
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
3
0
0
2
0
2
0
2
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
2
1
0
0
1
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
4
4
0
0
0
2
15
0
0
1
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
3
0
0
0
0
4
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
3
0
1
1
1
0
0
0
0
0
0
2
0
1
0
3
0
0
1
2
1
0
0
1
0
1
1
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
3
0
1
0
2
0
2
0
0
0
1
1
0
0
0
0
0
2
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
7
0
0
0
0
1
0
0
1
1
0
0
0
2
0
0
0
0
0
5
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
1
0
0
3
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
2
0
0
1
0
0
0
0
0
7
1
0
2
3
0
1
1
2
2
0
2
0
0
0
0
0
0
0
2
3
2
0
0
1
0
1
0
0
0
0
0
1
0
0
3
1
0
0
0
2
4
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
1
4
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
5
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
1
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
2
0
0
2
1
0
0
0
0
0
1
2
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
5
2
0
0
0
4
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
1
2
0
0
0
3
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
1
2
0
0
3
1
1
0
0
0
1
0
0
0
0
2
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
3
0
3
2
0
0
2
0
1
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
4
0
0
0
0
0
1
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
3
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
2
0
0
2
0
0
2
0
0
0
0
2
2
2
1
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
1
0
1
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
4
0
2
0
0
0
1
0
1
1
0
2
0
0
5
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
3
0
0
2
2
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
1
0
2
0
0
1
0
0
0
2
2
1
0
0
0
0
0
0
1
1
0
3
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
5
2
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
2
0
0
2
1
0
1
0
0
0
0
0
0
3
0
0
0
1
0
0
3
0
0
2
0
0
7
0
4
2
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
1
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
3
1
1
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
3
0
3
0
0
0
0
1
0
2
0
3
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
3
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
2
2
0
0
0
3
0
0
0
0
1
0
0
0
0
1
1
0
0
2
3
0
0
0
0
0
0
0
2
0
0
0
4
2
0
0
5
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
6
0
0
4
0
0
0
0
0
0
0
0
0
0
2
0
0
1
3
0
0
0
0
1
1
0
0
2
0
0
0
0
4
0
0
0
0
2
1
0
0
0
0
0
4
0
2
0
0
0
0
0
3
1
1
0
0
3
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
4
0
2
1
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
5
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
3
3
1
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
5
2
0
0
0
0
0
2
2
2
2
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
5
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
3
0
4
3
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
8
2
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
6
2
4
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
2
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
1
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
1
0
0
1
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
7
0
1
0
0
0
0
0
0
1
0
2
2
1
0
0
1
0
0
1
2
0
1
3
0
2
0
1
0
0
0
1
1
0
0
0
0
0
2
1
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
4
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
2
0
0
0
4
3
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
1
0
1
0
0
0
1
3
2
0
0
0
2
0
2
0
0
2
0
0
0
0
3
0
0
0
3
0
1
0
2
2
0
2
0
2
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
4
2
1
1
1
1
0
0
0
0
0
0
0
2
0
1
0
1
1
2
0
0
1
1
0
0
0
0
0
0
0
0
2
2
1
1
2
0
0
0
0
0
1
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
1
0
1
1
0
1
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
12
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
1
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
6
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
2
1
1
2
1
0
0
2
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
1
0
3
7
0
0
0
0
1
0
0
0
0
1
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
8
7
1
0
0
1
0
0
0
0
0
2
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
2
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
1
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
2
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
1
0
1
2
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
2
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
1
0
1
2
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
3
1
0
0
1
0
0
0
2
2
2
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
1
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
2
0
1
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
2
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
3
0
0
2
0
0
1
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
2
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
3
0
3
0
0
2
0
0
0
1
0
0
2
0
6
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
3
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
3
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
3
0
0
0
7
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
3
0
1
0
0
0
0
3
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
2
0
2
0
1
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
2
0
1
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
1
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
4
0
0
5
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
2
0
1
2
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
2
0
1
3
0
0
0
0
2
0
0
0
0
0
7
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
2
0
1
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
1
0
0
4
0
0
0
0
0
0
0
1
0
3
0
0
1
0
0
4
0
0
1
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
2
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
4
3
2
0
1
1
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
7
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
2
2
0
0
0
2
0
1
0
1
0
1
1
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
2
10
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
3
0
4
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
1
3
2
0
3
0
0
0
0
0
1
1
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
2
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
1
2
1
0
0
7
0
0
0
4
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
1
0
0
2
2
0
0
6
1
0
1
0
0
0
0
1
2
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
2
3
0
1
0
0
5
1
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
6
4
1
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
3
0
2
0
0
2
0
0
1
0
1
1
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
1
0
0
0
0
0
0
3
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
3
4
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
3
0
0
0
0
1
0
0
0
2
0
0
1
1
0
2
0
0
0
0
1
3
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
1
0
0
0
3
0
0
0
2
0
0
0
0
4
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
3
2
1
0
0
0
0
0
1
2
2
0
0
0
0
2
0
0
0
0
2
0
1
3
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
3
0
1
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
2
0
0
2
0
0
0
0
5
4
2
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
2
0
0
1
2
0
0
1
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
1
0
1
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
1
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
2
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
3
0
0
0
0
0
2
0
0
0
0
0
0
1
0
3
2
0
0
0
0
0
2
0
2
0
0
2
0
2
1
1
0
1
0
0
0
0
0
0
0
2
1
0
0
1
0
0
5
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
10
0
0
0
0
0
1
3
0
0
0
0
2
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
2
2
0
1
0
3
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
3
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
2
0
1
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
2
1
0
0
0
0
0
0
1
0
0
1
0
1
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
2
4
0
0
0
2
0
0
0
0
0
0
0
3
3
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
4
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
4
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
2
0
0
1
0
0
0
0
1
0
1
4
2
0
0
1
0
5
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
3
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
2
1
0
1
0
1
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
3
0
0
1
2
0
0
0
2
3
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
5
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
3
0
0
0
0
0
4
0
1
0
0
0
1
0
0
0
2
3
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
3
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
2
0
0
0
1
0
0
0
0
1
0
2
0
0
0
2
2
0
1
0
0
2
0
1
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
2
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
2
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
8
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
4
3
0
0
0
0
0
0
2
1
0
1
0
2
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
1
0
0
0
3
1
0
2
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
3
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
2
1
0
0
2
2
0
2
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
1
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
1
1
0
0
0
0
0
0
1
0
0
0
2
0
0
3
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
4
1
0
2
0
0
0
0
0
2
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
1
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
1
2
0
0
1
1
0
1
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
2
2
0
2
1
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
3
0
0
0
3
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
2
0
0
1
0
0
4
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
1
2
0
0
0
0
1
0
0
2
0
0
0
1
0
0
2
0
0
3
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
1
0
0
2
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
2
2
1
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
1
2
0
0
0
2
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
3
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
2
0
1
1
0
0
0
0
0
0
3
0
0
0
0
2
0
1
0
0
2
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
3
0
0
2
0
0
2
0
0
1
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
2
0
0
0
0
0
0
3
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
1
4
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
1
0
1
0
0
0
0
1
2
0
2
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
6
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
1
0
0
0
1
0
1
2
0
0
1
2
0
1
0
1
3
0
0
0
0
2
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
3
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
3
2
0
2
0
0
0
0
2
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
11
0
0
0
0
2
2
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
1
1
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
1
0
0
0
0
5
0
0
0
0
1
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
2
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
3
0
0
0
0
0
0
2
0
0
0
1
0
0
2
2
1
0
0
0
0
0
0
0
1
7
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
3
0
0
0
0
1
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
4
0
1
0
0
0
0
0
1
0
2
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
3
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
8
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
3
0
1
0
2
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
1
1
0
0
2
1
1
1
3
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
1
7
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
1
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
2
2
0
2
0
0
0
0
0
0
1
1
0
2
0
2
0
0
0
4
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
2
0
0
2
2
2
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
2
0
2
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
8
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
2
6
1
3
0
0
0
0
0
0
1
0
2
0
0
1
0
2
0
0
3
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
2
1
2
0
0
2
0
1
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
1
1
1
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
1
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
4
0
0
2
0
2
0
0
0
0
0
1
1
0
0
0
0
5
1
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
2
0
1
0
1
2
0
0
1
0
4
0
1
0
0
0
0
2
0
0
2
0
0
0
1
0
0
1
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
3
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
5
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
2
2
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
1
0
0
2
1
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
5
0
0
0
1
1
0
1
0
0
0
3
0
0
2
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
3
0
0
0
2
0
1
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
4
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
10
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
2
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
5
1
0
2
0
0
2
0
0
0
2
2
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
7
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
8
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
1
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
3
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
2
0
2
3
0
0
2
0
0
0
2
0
1
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
1
0
0
0
0
0
0
4
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
3
0
1
0
1
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
1
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
2
0
4
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
3
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
2
1
0
1
0
0
2
0
0
0
3
0
0
3
1
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
2
0
0
0
0
0
0
0
1
1
2
0
0
2
0
2
0
1
0
0
0
1
0
2
0
0
0
4
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
1
1
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
1
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
1
3
0
0
0
0
0
0
0
0
1
2
0
1
0
4
0
0
0
2
0
0
0
0
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
1
0
0
0
1
2
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
2
3
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
2
0
0
0
0
0
2
0
2
0
2
1
0
0
1
1
3
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
1
0
0
0
3
0
0
2
2
2
0
0
2
0
0
0
0
0
2
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
9
0
0
1
1
0
0
0
0
2
0
0
0
0
0
2
1
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
2
2
0
0
1
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
3
0
0
1
0
0
1
0
0
0
0
3
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
1
2
0
1
0
0
0
0
1
2
0
0
1
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
3
0
0
1
2
0
2
1
0
2
0
0
0
0
4
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
2
1
3
0
0
1
0
0
2
0
0
0
0
1
2
0
2
0
1
1
0
0
0
0
0
0
0
3
0
0
0
0
3
0
0
0
2
0
0
0
2
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
3
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
2
0
1
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
1
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
2
2
0
0
5
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
1
0
2
0
0
0
2
0
1
0
0
0
1
2
0
1
1
1
11
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
4
0
0
0
0
1
1
0
0
1
0
0
1
0
0
2
1
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
3
1
0
0
0
0
0
0
0
1
4
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
3
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
2
1
2
2
0
0
1
0
0
0
0
1
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
4
0
3
0
1
2
0
0
1
2
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
2
1
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
3
1
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
2
0
0
0
0
3
0
0
0
0
0
1
0
0
3
2
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
1
2
0
0
0
0
0
1
2
0
1
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
5
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
4
2
1
0
0
2
2
0
0
0
0
0
0
4
0
0
5
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
3
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
3
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
2
0
1
2
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
2
1
0
0
0
0
2
0
1
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
1
3
2
0
0
0
0
0
5
1
0
2
0
4
0
0
0
0
0
1
0
0
4
0
0
1
0
0
0
0
0
0
0
2
0
1
0
1
4
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
1
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
1
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
4
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
6
0
2
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
7
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
1
0
1
1
0
0
0
2
2
0
0
0
0
0
1
0
0
0
1
2
0
2
0
1
0
0
0
0
0
2
2
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
1
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
3
2
0
2
1
5
0
0
0
1
0
1
0
1
2
0
0
0
0
2
1
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
6
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
1
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
3
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
1
3
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
3
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
2
0
3
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
1
2
0
0
0
3
0
0
0
0
0
0
0
0
1
0
2
0
2
2
2
0
0
0
0
0
0
0
2
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
1
0
2
0
3
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
3
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
1
0
0
2
2
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
7
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
3
2
0
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
1
0
0
1
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
1
2
0
0
0
0
8
0
0
4
0
0
0
2
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
3
0
0
0
0
0
0
0
1
0
2
0
0
0
0
3
0
2
0
1
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
1
0
0
0
0
0
3
0
0
2
0
3
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
3
1
6
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
2
0
0
1
0
2
0
2
0
0
1
0
0
0
1
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
5
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
4
10
0
0
0
2
2
0
0
0
1
1
2
0
0
0
0
0
1
0
2
1
0
0
0
3
0
0
4
0
0
0
1
0
0
0
0
2
2
0
0
1
0
0
0
1
1
2
1
0
2
0
3
0
2
0
0
0
0
0
0
1
2
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
1
0
0
3
0
0
0
0
0
0
4
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
2
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
2
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
2
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
2
2
0
0
1
1
0
0
2
0
1
0
3
2
0
0
0
0
0
1
3
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
1
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
5
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
1
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
3
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
3
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
3
0
2
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
2
0
0
0
3
0
0
2
0
0
0
2
1
2
4
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
3
0
0
0
0
0
5
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
3
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
3
2
0
0
0
0
0
1
1
1
5
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
3
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
2
0
0
0
2
0
0
0
1
2
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
1
1
0
1
0
2
0
0
0
0
0
1
0
1
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
1
0
2
0
0
2
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
2
0
5
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
1
3
0
0
0
1
0
0
0
0
2
0
0
1
0
1
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
4
0
0
6
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
1
2
0
0
0
0
0
3
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
10
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
1
0
2
0
0
0
0
2
0
2
0
3
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
2
1
0
0
2
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
2
0
0
3
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
10
0
0
0
0
0
0
1
0
0
1
1
1
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
3
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
1
0
4
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
1
2
0
1
1
0
1
0
0
0
3
0
3
0
0
0
0
0
0
2
0
1
0
1
5
0
0
1
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
4
0
0
2
0
0
1
0
0
0
0
1
1
0
0
2
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
8
1
0
0
0
2
3
0
0
2
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
5
0
0
0
0
0
0
0
0
0
1
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
2
0
0
1
0
0
0
0
0
1
0
0
0
0
2
1
2
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
2
0
0
0
0
1
1
2
1
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
2
2
0
0
0
0
3
0
0
2
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
3
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
2
0
1
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
1
2
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
2
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
6
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
1
0
1
1
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
1
0
2
0
0
0
0
0
3
1
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
3
0
2
0
2
0
0
0
0
0
3
0
0
0
0
1
2
0
3
0
2
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
3
2
0
3
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
3
2
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
7
0
0
0
2
0
1
4
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
1
0
2
0
0
0
3
0
2
4
4
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
4
1
0
2
2
2
2
0
2
1
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
3
1
0
0
0
4
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
3
1
1
0
2
1
2
0
1
0
0
2
3
0
2
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
3
1
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
1
0
1
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
4
0
0
0
1
2
0
5
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
2
0
2
0
1
0
1
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
5
0
2
0
2
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
1
1
3
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
2
3
1
0
0
0
0
0
1
0
0
6
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
3
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
3
0
0
0
1
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
2
2
0
1
0
0
0
0
0
0
0
0
2
2
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
3
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
1
2
2
0
2
0
1
0
0
0
0
0
0
0
0
0
3
1
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
3
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
4
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
1
0
0
0
1
1
0
0
1
1
0
0
0
0
2
0
0
2
2
0
2
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
2
1
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
1
0
0
4
2
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
2
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
1
0
0
1
0
0
0
2
3
0
0
0
1
0
0
1
2
0
0
0
0
0
0
3
2
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
2
1
0
0
0
5
0
1
0
0
0
0
1
0
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
0
2
2
0
1
2
0
0
0
0
1
1
0
2
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
3
0
1
0
1
2
0
1
2
0
0
8
0
2
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
1
0
0
12
0
0
0
0
2
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
2
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
2
0
0
0
0
0
2
0
4
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
8
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
2
0
0
0
0
3
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
1
7
0
1
2
0
0
0
2
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
1
0
1
0
2
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
1
2
1
0
0
2
1
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
2
0
0
2
1
1
1
0
0
0
0
2
1
0
0
1
1
2
5
1
2
0
0
0
0
0
0
0
2
2
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
1
0
1
3
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
1
0
0
1
0
0
1
0
1
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
4
8
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
1
0
0
0
0
2
0
1
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
5
0
0
0
1
2
0
0
3
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
1
0
0
0
0
0
0
1
1
1
3
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
5
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
1
0
2
0
0
0
0
1
0
2
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
2
0
0
2
0
2
7
0
1
0
0
2
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
2
2
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
2
1
0
0
0
0
2
0
1
0
1
0
0
0
2
0
1
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
3
0
0
0
0
0
1
0
5
0
0
0
2
0
0
0
2
0
0
1
0
1
0
0
0
0
2
0
0
1
0
0
2
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
3
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
2
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
1
0
2
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
3
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
1
1
0
0
1
0
2
0
0
0
0
0
0
2
1
0
0
0
1
0
1
0
0
0
3
0
2
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
1
4
0
2
0
2
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
3
0
3
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
1
0
3
0
1
0
0
2
0
0
0
1
1
0
2
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
1
0
0
1
1
3
1
0
0
0
0
3
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
5
0
2
1
0
3
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
4
0
0
0
1
0
0
0
1
1
0
0
1
0
0
7
0
0
0
0
0
0
1
0
0
3
0
0
0
0
1
1
0
2
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
2
4
0
0
3
0
0
2
0
0
0
0
1
0
2
4
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
10
0
0
1
1
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
1
1
0
1
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
1
0
4
0
0
0
0
2
0
0
3
1
3
0
2
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
1
0
2
1
0
0
0
0
2
0
0
0
3
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
1
0
0
2
3
5
3
0
1
0
0
1
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
1
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
1
0
1
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
2
1
0
0
2
2
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
1
0
1
0
0
2
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
1
1
2
0
0
2
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
2
2
0
0
2
0
0
1
0
0
0
0
1
0
1
2
1
0
0
0
1
0
0
0
0
1
0
0
0
2
1
0
0
0
3
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
2
2
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
2
2
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
2
0
0
0
0
3
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
2
0
0
4
0
0
0
0
0
2
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
1
2
1
0
1
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
2
0
2
0
1
0
0
0
0
0
0
4
0
0
2
1
0
0
1
0
0
3
2
0
2
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
2
1
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
4
0
0
0
0
2
1
0
0
1
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
1
2
0
0
1
1
2
6
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
3
6
0
4
0
0
0
0
0
1
0
0
0
1
2
0
1
8
0
0
0
0
5
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
3
0
2
2
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
1
0
1
2
0
0
3
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
2
0
0
1
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
2
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
3
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
3
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
1
4
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
2
0
0
1
0
0
1
2
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
2
1
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
2
0
0
0
2
2
0
1
0
2
0
0
3
2
0
2
0
0
0
0
1
0
0
0
0
0
1
3
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
1
0
0
0
0
7
0
0
0
0
0
0
0
0
3
1
0
0
5
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
2
0
1
0
1
0
0
0
0
0
0
2
0
0
2
0
2
1
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
4
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
2
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
2
1
0
0
0
0
0
5
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
1
0
1
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
5
0
2
2
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
1
2
3
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
1
2
0
3
2
2
1
0
4
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
2
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
7
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
2
0
1
0
1
1
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
3
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
1
1
0
2
2
0
0
1
0
2
0
1
2
0
0
0
0
1
0
0
0
1
0
1
0
0
2
0
0
1
0
3
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
2
2
0
2
0
0
0
0
0
0
0
0
3
0
1
0
0
0
2
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
3
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
1
0
2
1
0
1
3
0
0
0
5
0
0
2
0
2
0
1
0
0
2
0
2
0
0
2
3
0
0
9
0
2
0
2
0
0
1
0
0
0
0
0
0
3
0
2
0
2
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
2
2
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
2
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
2
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
3
0
2
0
1
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
4
1
0
0
1
0
0
2
6
0
1
0
0
0
0
0
0
0
1
0
0
0
1
3
3
0
0
0
0
0
0
1
3
1
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
1
0
1
1
0
0
2
1
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
4
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
1
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
12
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
5
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
1
2
2
0
0
1
0
0
1
0
0
0
1
0
2
0
0
5
0
2
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
1
0
0
0
3
0
0
0
2
2
1
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
1
1
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
4
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
7
0
0
0
0
0
0
2
1
0
1
0
4
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
4
0
0
0
1
1
0
0
0
0
2
1
5
0
0
0
0
3
0
1
1
1
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
2
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
1
1
0
0
2
0
0
1
0
0
0
0
0
0
3
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
1
2
2
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
1
0
0
0
0
0
3
2
0
0
1
0
0
0
0
0
0
3
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
1
0
2
1
1
0
0
0
0
1
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
3
0
2
0
4
0
0
0
0
0
0
0
3
0
4
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
3
0
0
1
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
3
0
2
2
0
0
1
0
2
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
2
2
0
0
1
0
0
6
1
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
3
0
0
1
1
3
1
0
0
0
0
0
0
1
0
0
4
1
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
1
0
0
1
0
0
0
0
2
1
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
1
0
1
2
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
2
1
2
1
1
0
2
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
1
0
0
0
0
2
1
0
0
1
1
0
0
0
3
3
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
3
0
1
0
0
0
1
0
0
0
0
0
0
0
0
3
0
2
2
0
0
0
0
0
0
1
0
0
5
0
0
0
0
2
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
8
0
0
2
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
3
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
4
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
2
1
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
2
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
6
0
2
0
1
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
1
2
0
0
0
2
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
2
2
1
0
1
0
0
0
2
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
2
2
0
2
1
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
1
2
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
1
1
0
2
5
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
1
1
0
1
0
1
0
1
3
2
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
1
0
0
2
0
4
1
2
0
2
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
1
0
2
0
2
0
0
0
2
0
1
2
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
2
0
2
0
1
0
0
0
0
0
2
2
0
0
0
2
0
0
2
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
2
0
1
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
1
0
4
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
2
0
2
0
2
0
0
1
0
0
0
0
0
0
1
0
2
0
0
2
1
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
2
1
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
2
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
5
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
3
3
1
0
0
0
0
1
0
0
0
0
0
10
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
1
0
1
0
4
1
2
3
0
0
0
1
0
1
1
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
2
0
2
1
0
0
3
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
19
0
0
0
0
0
6
0
0
0
0
0
0
2
0
0
0
3
1
0
0
6
0
0
0
1
2
3
1
1
1
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
4
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
5
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
3
0
0
1
0
2
0
4
0
0
0
0
0
1
1
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
2
2
1
0
2
0
2
0
1
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
2
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
5
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
2
0
0
1
0
2
0
2
0
0
0
1
3
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
5
0
2
1
0
0
0
0
2
1
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
1
1
0
2
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
3
0
0
3
0
0
2
0
2
0
0
0
1
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
3
0
1
0
0
1
0
0
0
0
0
0
0
0
1
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
1
0
1
0
0
2
0
2
2
0
0
0
0
0
0
3
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
2
0
3
0
0
1
0
2
0
2
0
0
0
0
0
2
0
0
2
0
1
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
7
0
1
1
0
0
0
1
0
1
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
3
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
2
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
4
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
2
1
0
0
1
0
0
0
1
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
3
0
0
0
0
1
1
0
0
1
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
1
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
3
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
3
1
0
0
0
0
2
0
0
2
1
0
0
0
2
0
0
0
0
0
5
0
1
2
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
1
0
0
0
2
1
0
0
0
1
1
2
0
1
0
0
0
0
10
2
0
1
0
0
1
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
1
3
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
3
0
0
1
4
0
7
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
2
0
0
3
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
1
1
2
1
2
0
2
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
2
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
3
0
0
0
1
0
0
0
0
0
0
0
1
0
5
2
0
0
2
0
0
0
0
2
0
0
0
0
0
1
1
0
2
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
2
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
2
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
5
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
5
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
4
2
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
2
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
1
0
2
0
0
0
0
0
0
1
0
0
0
0
3
0
1
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
4
2
1
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
2
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
1
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
2
0
0
0
2
0
0
0
1
0
0
0
1
0
2
1
0
9
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
1
0
0
0
1
0
1
4
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
6
0
0
0
2
0
0
0
0
0
0
0
0
4
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
2
0
0
0
0
0
1
6
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
3
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
1
4
0
0
3
0
1
0
0
0
0
0
1
0
0
0
4
1
0
0
1
0
5
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
1
1
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
1
0
2
3
0
0
0
0
1
0
0
0
1
0
0
3
3
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
2
0
2
1
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
6
0
0
0
0
0
1
0
0
0
0
1
0
0
2
3
0
0
0
1
0
5
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
3
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
5
0
2
1
1
0
3
1
0
0
0
0
0
2
0
2
0
0
0
3
2
0
0
0
0
0
2
1
0
0
0
0
0
2
2
2
2
0
0
0
0
1
1
2
0
1
0
0
1
0
0
2
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
5
0
0
1
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
2
0
3
0
0
0
2
1
0
0
0
0
1
0
0
0
0
2
1
3
0
0
0
0
0
0
0
2
0
3
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
5
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
3
0
1
0
2
0
3
0
0
2
0
0
0
0
0
2
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
1
2
2
2
0
2
2
2
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
3
0
1
0
0
1
0
2
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
6
0
0
0
2
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
6
0
0
0
1
0
1
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
2
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
2
1
0
1
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
5
0
1
2
0
1
0
0
1
0
0
0
0
1
0
0
1
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
3
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
5
0
1
0
0
0
1
0
2
2
2
0
2
2
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
2
1
1
1
0
0
3
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
2
0
1
0
2
0
3
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
1
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
3
0
1
1
0
2
0
0
0
0
3
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
4
7
0
0
0
0
0
4
2
1
0
0
0
0
0
0
1
1
1
0
0
0
2
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
4
4
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
1
0
1
2
5
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
4
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
2
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
2
2
0
1
0
1
0
2
2
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
1
2
2
15
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
3
3
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
2
0
1
0
2
1
0
0
7
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
2
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
3
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
3
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
2
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
2
5
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
4
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
4
0
2
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
3
0
0
0
0
0
2
0
1
3
1
0
0
2
0
3
1
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
3
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
1
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
3
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
2
0
0
9
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
3
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
1
0
0
2
0
0
0
5
0
0
1
0
2
0
0
0
0
0
0
0
0
0
3
0
1
0
0
2
0
2
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
3
2
0
0
2
0
0
0
1
0
1
1
1
0
0
0
0
0
1
1
0
0
0
0
2
0
0
2
0
1
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
1
10
2
0
1
0
0
0
0
0
1
0
2
0
0
5
0
0
2
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
2
3
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
3
1
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
5
0
2
0
1
3
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
2
0
2
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
2
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
3
1
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
2
0
0
0
1
0
0
4
0
2
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
1
1
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
2
0
4
0
0
2
0
0
0
0
0
0
0
2
1
1
0
0
2
0
0
0
0
2
0
0
1
1
2
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
1
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
3
2
0
0
0
0
0
2
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
1
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
8
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
2
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
2
2
0
12
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
1
0
1
0
2
1
0
1
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
2
2
2
0
2
0
0
0
0
0
2
1
0
2
1
0
0
0
0
0
0
4
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
1
0
0
0
0
0
0
3
0
1
0
0
0
0
1
2
0
0
0
0
0
1
2
0
2
3
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
1
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
1
1
0
0
0
0
3
2
1
0
2
0
0
2
0
4
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
5
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
2
1
0
1
2
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
1
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
1
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
3
0
2
0
0
0
0
0
2
0
0
1
0
0
1
0
0
7
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
10
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
1
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
1
1
2
2
0
0
0
6
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
2
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
1
0
0
0
4
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
2
2
0
0
0
0
0
1
0
0
2
4
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
1
1
1
3
1
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
4
0
0
0
3
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
1
0
0
3
2
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
2
0
0
0
0
1
0
2
0
0
0
2
2
0
0
0
2
3
0
0
0
0
0
0
0
0
4
0
1
1
1
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
1
0
0
0
0
0
0
3
2
0
0
1
0
3
1
1
2
0
2
1
0
0
1
0
0
0
0
0
0
0
2
0
2
0
2
1
1
0
0
0
1
0
0
0
0
1
0
0
0
2
0
1
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
2
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
2
0
1
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
2
3
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
1
1
3
1
0
1
0
1
1
0
2
2
2
0
0
2
1
0
0
0
2
2
0
2
0
0
0
0
0
0
1
0
0
0
0
4
0
4
0
0
0
0
0
0
0
0
5
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
3
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
1
2
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
1
0
0
2
0
0
0
0
0
4
2
3
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
2
0
0
0
0
4
1
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
7
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
3
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
2
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
5
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
4
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
4
1
1
0
0
2
0
1
0
2
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
1
2
0
0
0
0
0
3
0
0
2
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
2
0
0
1
0
0
0
0
0
0
2
2
0
1
0
1
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
1
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
1
1
0
0
0
0
0
2
2
0
1
0
1
0
0
0
3
0
0
1
0
0
5
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
1
0
0
2
0
0
0
2
2
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
3
0
2
0
0
0
0
1
0
0
0
0
1
0
3
0
3
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
3
2
0
0
0
0
0
0
0
1
0
0
0
1
0
2
2
0
1
0
0
0
1
0
0
1
0
0
0
0
2
0
1
1
1
0
0
0
0
2
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
1
2
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
1
0
4
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
8
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
4
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
1
2
0
0
0
0
2
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
1
0
0
2
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
6
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
1
0
2
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
3
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
1
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
1
0
2
1
1
1
0
0
0
0
0
0
1
0
0
1
6
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
2
0
0
0
0
0
0
1
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
8
2
0
0
0
3
0
3
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
2
0
1
1
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
1
0
0
2
1
0
0
1
0
2
0
0
3
0
0
1
0
13
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
2
3
2
0
0
0
1
1
0
0
0
1
1
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
3
0
0
0
0
0
2
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
2
1
0
1
0
0
0
0
0
1
0
1
3
0
0
0
0
0
0
3
0
0
0
1
2
0
2
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
1
3
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
2
0
0
4
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
2
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
3
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
2
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
3
0
0
0
2
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
1
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
1
0
0
0
1
0
3
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
1
4
1
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
2
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
1
1
0
0
1
1
2
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
5
0
5
0
2
0
0
1
1
0
3
1
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
2
0
0
0
0
0
1
1
0
1
0
0
1
3
2
0
2
0
2
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
4
1
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
3
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
4
0
3
0
0
1
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
1
2
0
0
1
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
1
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
6
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
2
0
0
1
2
0
0
0
0
0
1
0
0
0
3
0
0
0
0
3
1
0
0
1
0
0
0
0
0
0
0
0
3
1
2
0
0
0
1
0
1
1
1
0
3
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
4
2
2
0
2
0
2
0
0
1
2
0
0
1
0
1
0
0
0
1
2
1
0
0
2
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
6
1
0
0
0
1
0
2
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
1
1
0
2
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
4
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
3
0
0
1
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
3
0
0
0
0
0
0
1
0
0
4
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
2
0
0
1
0
2
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
7
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
3
0
0
1
0
0
0
1
0
0
0
0
0
0
2
1
0
0
2
0
0
0
2
1
0
0
0
0
0
0
2
2
0
0
2
2
0
1
0
0
2
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
2
2
0
1
1
0
0
0
1
0
0
2
0
0
0
3
0
1
1
3
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
5
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
2
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
2
0
0
1
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
1
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
1
1
8
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
3
0
0
0
0
2
0
1
0
0
3
0
0
1
0
0
7
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
7
0
0
1
3
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
5
0
1
0
0
1
0
1
0
5
0
0
5
0
0
0
0
2
0
0
0
1
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
1
0
1
0
0
0
0
2
0
0
0
0
0
2
0
6
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
2
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
4
0
0
1
0
0
0
0
1
1
3
0
0
1
2
0
0
0
3
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
2
0
1
0
1
0
0
0
0
0
2
0
2
1
0
0
0
0
0
3
0
3
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
1
0
1
0
0
0
1
3
0
0
0
0
1
0
2
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
3
0
0
0
1
0
1
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
1
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
3
2
0
1
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
1
0
3
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
2
1
2
0
0
1
0
0
1
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
2
1
0
1
0
0
0
6
0
0
1
1
4
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
1
0
4
2
0
0
0
0
0
0
0
3
0
0
1
0
7
0
0
3
1
0
0
0
0
0
3
0
0
2
0
3
0
0
0
0
3
2
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
3
1
0
0
1
1
0
0
0
0
0
2
0
0
0
3
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
2
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
1
1
0
0
2
0
0
1
0
0
0
0
0
7
0
0
0
1
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
1
2
1
0
0
1
4
0
1
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
3
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
7
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
3
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
3
0
0
3
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
2
0
1
1
0
1
2
0
1
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
1
0
2
0
0
1
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
2
0
0
6
0
2
0
0
2
0
0
2
0
1
0
0
0
0
0
0
1
2
0
2
0
1
0
0
3
1
1
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
2
0
0
1
0
7
1
0
2
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
1
0
0
0
0
3
1
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
1
0
0
1
1
0
0
0
0
2
0
1
0
0
2
1
1
2
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
12
2
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
6
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
3
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
1
0
2
0
0
0
1
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
1
3
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
1
0
5
1
0
2
0
0
0
0
0
0
6
1
0
0
6
0
0
0
0
5
0
0
0
2
2
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
1
0
2
7
0
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
1
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
2
1
1
0
0
0
3
0
1
0
2
0
0
0
0
0
0
5
0
1
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
1
0
0
0
0
0
2
1
2
2
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
1
0
0
2
4
0
2
2
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
4
0
0
1
0
0
0
0
1
1
0
0
2
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
1
0
0
0
0
0
0
5
3
0
0
0
0
0
0
0
2
1
0
1
4
0
0
0
1
0
0
0
0
1
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
2
2
0
2
1
0
0
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
1
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
1
4
0
0
2
2
0
0
1
0
2
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
3
1
2
0
0
0
0
5
0
0
2
2
0
1
2
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
3
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
3
0
1
0
0
0
0
2
0
0
2
0
0
0
1
0
2
1
0
0
1
0
2
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
3
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
3
0
2
0
1
0
0
0
2
0
0
0
0
1
0
0
0
4
2
0
1
0
0
0
0
3
0
1
6
0
0
1
0
0
1
2
0
0
0
0
3
0
2
0
0
5
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
4
0
0
0
4
5
0
0
0
0
0
2
0
1
1
0
0
0
0
0
5
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
2
1
0
0
0
1
0
0
0
2
0
1
1
2
0
0
0
2
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
2
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
1
0
0
2
0
0
0
0
1
0
3
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
3
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
2
1
0
0
0
2
4
0
0
0
0
0
0
0
0
0
2
1
1
0
2
0
0
0
2
2
1
0
1
0
0
0
0
0
0
3
6
0
0
0
0
0
0
0
0
0
0
6
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
1
0
0
2
2
1
0
1
0
1
0
1
0
0
3
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
1
0
0
1
0
1
0
0
2
0
0
0
0
0
0
1
1
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
2
0
0
3
0
2
0
0
0
0
0
2
2
1
0
1
0
2
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
4
3
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
2
1
2
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
1
0
1
0
0
0
0
1
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
3
2
0
2
0
3
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
2
3
0
2
0
0
1
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
3
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
3
0
1
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
4
0
1
2
0
1
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
1
0
4
1
1
1
0
0
0
3
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
2
0
0
0
1
0
0
2
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
2
0
0
0
1
0
0
3
1
0
2
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
5
0
2
0
0
0
0
0
2
5
3
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
3
2
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
17
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
5
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
1
3
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
4
1
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
3
0
0
2
1
0
0
7
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
3
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
3
0
0
1
0
1
0
0
3
2
0
0
0
0
6
0
0
0
0
0
0
0
1
0
1
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
2
0
0
0
0
0
2
5
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
4
0
0
1
0
0
0
0
0
2
1
2
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
1
2
0
2
0
2
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
1
2
3
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
2
2
0
1
0
0
0
0
0
12
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
4
0
0
1
0
0
0
0
1
0
3
0
2
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
3
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
6
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
2
1
1
2
2
0
0
0
0
0
1
0
6
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
2
0
0
0
2
0
2
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
5
1
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
9
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
1
0
0
3
4
0
0
2
1
1
0
0
0
0
0
0
0
1
0
0
1
0
2
2
0
0
0
1
3
2
2
0
0
0
1
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
2
0
1
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
5
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
2
3
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
6
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
1
0
0
2
2
0
0
3
0
0
0
0
2
0
0
3
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
2
2
1
0
0
1
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
2
0
1
2
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
1
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
3
2
2
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
8
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
2
2
2
0
0
0
2
0
2
0
0
1
3
1
0
0
0
0
0
0
0
2
0
1
0
1
1
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
14
3
0
0
0
0
4
0
2
0
0
2
2
0
3
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
1
1
0
6
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
2
1
2
0
0
2
3
2
2
0
0
0
0
0
0
0
0
3
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
3
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
2
0
0
0
1
0
0
0
0
0
2
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
7
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
3
0
1
0
1
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
2
1
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
1
1
0
2
1
2
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
4
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
2
0
0
3
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
1
0
2
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
3
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
3
1
0
0
1
0
0
1
0
0
2
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
3
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
1
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
10
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
7
0
0
0
2
1
0
0
0
0
0
0
0
1
1
0
0
0
2
1
0
0
1
1
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
1
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
2
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
6
2
0
1
0
0
0
0
3
1
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
1
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
2
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
2
0
2
1
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
3
0
2
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
3
1
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
3
3
0
0
2
0
0
2
0
0
1
0
2
1
0
4
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
2
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
12
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
3
0
0
0
1
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
2
0
1
1
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
2
0
1
0
3
0
0
1
1
0
0
5
2
0
2
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
3
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
1
1
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
1
1
0
2
2
0
0
0
0
4
0
0
1
1
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
5
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
1
2
2
0
0
2
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
1
0
2
1
2
3
0
0
0
0
1
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
2
1
0
0
0
1
0
0
1
0
0
0
19
0
1
0
1
2
0
3
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
1
2
0
0
1
1
1
0
0
1
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
1
0
0
0
3
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
1
0
1
2
0
0
0
2
0
0
1
0
0
0
0
1
1
2
0
1
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
5
0
0
0
1
0
0
2
0
0
0
1
0
0
2
0
0
0
1
0
0
0
2
0
1
2
0
0
0
0
0
0
0
1
3
0
0
2
0
2
0
2
2
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
2
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
3
0
0
0
0
0
1
1
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
4
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
1
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
1
2
2
1
2
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
3
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
3
3
1
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
2
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
1
0
2
2
1
1
3
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
8
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
1
0
3
0
0
0
0
0
0
1
0
0
0
2
0
1
0
2
0
0
0
1
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
3
0
0
2
0
0
1
0
1
0
1
0
1
0
2
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
2
0
2
0
0
0
3
1
0
1
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
4
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
3
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
2
1
2
0
0
0
1
0
0
0
2
0
0
0
0
0
1
1
2
3
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
2
0
3
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
3
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
1
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
2
0
2
0
0
1
0
3
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
3
0
1
0
0
0
0
0
1
0
0
0
0
2
1
1
3
0
0
1
0
7
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
1
0
2
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
2
1
0
0
0
2
0
1
0
1
0
0
0
0
2
0
0
0
7
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
5
0
0
2
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
2
0
0
1
0
0
0
1
1
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
3
2
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
2
1
1
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
1
1
2
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
1
3
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
2
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
4
0
0
1
0
2
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
2
0
0
0
2
2
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
3
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
2
0
0
0
3
0
2
0
0
0
0
2
1
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
6
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
2
4
0
1
2
0
3
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
1
0
0
0
0
0
1
0
1
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
2
3
0
0
0
0
2
0
2
0
1
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
4
0
0
2
4
0
0
0
1
0
2
0
2
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
1
0
2
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
1
0
2
2
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
2
2
0
1
0
0
0
0
0
0
0
1
1
0
1
0
2
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
5
0
2
0
1
3
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
1
1
2
3
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
3
0
1
1
2
1
1
0
0
0
0
0
1
0
0
4
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
3
0
1
1
0
0
0
0
3
0
0
1
2
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
2
0
0
1
0
1
0
0
0
0
4
0
1
1
2
0
0
0
0
0
2
2
9
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
3
0
0
0
0
2
0
1
0
2
0
0
0
2
0
0
0
0
0
3
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
2
0
0
0
0
0
1
0
1
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
2
0
0
3
0
1
0
0
2
0
0
0
0
0
0
1
0
2
0
2
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
2
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
2
1
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
1
0
0
0
1
2
0
0
0
0
0
1
0
0
0
2
2
1
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
3
9
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
2
2
0
0
0
0
0
3
2
0
0
0
0
3
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
3
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
1
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
1
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
1
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
2
0
0
1
1
0
1
0
0
1
0
0
0
1
0
0
1
1
0
1
0
0
0
0
2
1
3
0
0
0
0
1
1
1
0
2
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
3
1
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
4
1
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
8
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
1
0
5
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
2
1
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
3
0
5
0
0
0
0
0
3
1
0
0
1
1
0
0
0
3
2
0
2
4
0
0
0
0
2
2
0
1
0
0
0
3
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
3
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
3
0
0
4
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
3
5
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
2
0
0
0
2
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
2
0
0
2
0
0
0
0
0
0
5
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
1
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
7
0
0
0
0
0
0
0
0
1
0
1
3
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
1
0
4
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
1
0
1
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
2
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
3
0
0
0
0
2
2
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
1
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
1
2
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
1
0
2
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
3
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
3
2
0
0
0
0
0
0
0
0
0
5
0
0
1
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
2
1
2
0
0
0
0
2
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
1
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
2
2
0
0
0
2
0
1
0
1
0
0
0
0
0
0
3
1
0
0
2
0
0
0
4
0
0
0
1
1
1
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
3
0
0
2
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
2
1
0
1
0
0
0
0
0
2
0
3
0
0
0
1
0
0
3
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
2
0
3
0
0
0
2
0
2
0
0
0
0
3
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
3
2
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
1
1
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
6
0
0
2
2
0
0
0
0
0
0
1
2
1
0
0
1
1
0
1
0
0
2
4
0
1
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
2
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
2
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
1
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
4
0
0
2
8
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
1
1
0
1
0
2
0
0
0
2
0
2
0
0
0
2
1
0
0
0
0
0
0
0
1
2
0
0
0
5
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
2
3
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
6
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
2
0
0
0
2
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
3
0
0
1
0
0
0
0
0
2
1
0
0
1
0
0
0
0
4
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
3
0
2
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
7
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
1
2
0
2
0
0
1
0
0
0
2
0
0
2
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
1
0
1
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
6
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
1
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
2
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
3
0
0
2
1
0
0
1
0
0
0
2
2
2
1
3
0
0
0
0
2
2
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
2
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
1
2
0
2
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
2
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
1
0
0
1
0
0
2
2
0
2
0
0
1
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
1
0
0
0
1
1
0
1
0
0
1
2
0
0
0
0
0
0
2
1
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
3
2
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
2
2
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
1
2
0
1
1
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
1
1
1
0
0
0
2
0
0
0
0
2
0
0
0
0
2
1
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
7
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
4
0
0
0
0
0
0
0
2
1
0
0
0
0
4
0
0
2
0
0
0
0
2
0
0
0
4
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
3
0
1
0
3
0
0
0
0
3
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
7
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
0
2
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
5
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
6
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
2
1
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
2
0
1
3
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
1
1
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
3
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
3
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
2
0
0
1
0
0
0
3
0
0
0
1
0
0
3
0
0
0
0
3
0
2
3
0
0
2
0
2
2
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
6
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
2
1
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
3
1
2
2
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
3
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
2
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
2
0
0
2
0
0
0
1
0
2
0
0
0
2
0
1
0
0
1
0
0
2
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
2
0
2
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
1
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
1
1
0
0
1
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
3
2
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
3
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
7
0
2
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
3
10
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
4
0
1
0
0
0
0
2
0
0
1
0
1
0
0
0
2
0
0
1
0
0
0
4
0
0
0
2
0
0
1
0
1
1
1
0
0
1
0
2
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
1
3
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
2
2
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
3
5
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
2
0
0
1
5
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
2
2
0
0
3
0
1
1
0
0
0
0
1
0
2
1
1
0
0
0
0
2
0
0
0
0
0
0
4
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
1
0
0
0
1
0
2
0
1
1
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
3
0
5
0
0
2
0
2
1
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
2
2
2
0
0
0
0
1
0
0
1
2
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
1
0
1
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
1
2
0
0
0
0
5
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
2
1
0
1
0
0
0
0
1
0
0
0
3
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
4
0
0
0
2
0
0
0
1
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
2
0
1
0
0
0
0
0
0
3
0
0
0
3
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
1
0
1
0
0
0
2
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
3
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
1
0
1
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
3
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
2
0
1
1
0
0
0
1
2
2
0
0
2
0
0
1
0
0
1
1
2
0
0
1
2
1
0
0
1
2
4
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
1
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
3
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
1
0
0
0
2
0
0
0
0
2
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
2
1
0
3
0
0
0
0
0
0
0
1
0
0
0
0
2
3
0
0
0
2
0
0
0
0
0
0
0
0
3
0
2
1
0
0
0
0
0
0
1
0
2
0
0
0
1
0
1
0
1
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
1
0
1
1
1
1
0
0
2
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
2
0
0
0
1
0
9
1
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
5
0
1
0
1
0
0
0
0
5
0
2
0
0
0
0
0
0
1
3
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
2
2
1
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
1
0
2
0
0
0
0
0
1
5
1
0
0
0
1
0
2
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
1
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
1
2
0
0
1
0
0
1
0
0
0
0
0
0
1
1
4
0
0
1
0
4
1
1
0
0
1
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
4
2
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
2
1
2
0
2
0
0
0
0
0
0
0
1
2
0
0
0
4
0
0
2
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
2
0
2
0
2
0
1
1
1
0
0
0
0
2
2
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
1
0
0
2
1
0
0
0
0
2
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
1
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
4
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
5
2
0
0
0
0
0
1
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
2
1
1
1
2
0
0
0
0
0
0
2
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
1
0
0
3
2
0
0
3
0
0
0
0
0
2
0
3
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
1
0
2
1
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
1
0
2
0
2
0
0
3
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
6
0
1
3
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
3
0
0
6
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
2
2
0
4
0
0
2
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
6
0
1
2
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
5
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
4
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
2
2
0
0
0
0
0
0
2
0
1
1
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
1
2
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
4
1
2
0
1
2
0
0
0
2
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
1
0
1
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
2
0
0
1
0
0
0
0
0
2
1
0
0
1
0
2
1
0
0
0
4
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
2
0
0
0
0
0
0
3
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
1
0
0
0
4
0
0
0
0
0
2
0
1
0
0
0
2
1
0
0
3
0
0
2
0
2
2
0
2
0
0
0
1
1
0
0
0
0
0
2
1
1
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
1
3
2
0
0
4
2
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
2
0
0
0
0
0
0
1
3
1
0
0
0
0
2
0
0
0
3
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
2
0
1
0
0
5
0
0
3
0
0
0
1
0
1
0
0
0
0
0
4
2
1
0
0
0
0
0
1
0
0
2
0
0
0
0
2
3
2
0
0
1
0
3
2
1
0
0
0
0
0
0
0
0
0
4
1
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
5
0
2
0
0
3
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
5
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
5
0
0
0
0
0
3
0
0
2
2
0
0
2
0
0
0
2
0
1
2
0
1
0
0
0
0
0
0
0
2
0
1
0
1
1
1
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
6
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
1
0
0
0
0
1
0
0
6
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
1
0
0
0
0
1
1
0
0
0
1
0
0
5
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
2
0
2
0
0
0
0
2
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
3
2
0
0
1
0
1
0
0
1
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
5
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
2
0
0
2
2
0
0
0
2
1
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
1
0
0
0
0
0
2
0
1
0
2
1
0
0
0
0
0
2
0
0
0
4
0
0
1
0
1
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
1
0
4
0
1
0
0
1
1
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
5
0
6
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
3
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
3
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
2
0
3
0
1
2
0
0
0
0
2
0
1
0
0
1
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
3
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
2
10
0
0
0
0
2
0
0
0
0
0
0
2
2
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
2
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
2
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
1
1
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
12
0
0
2
0
0
0
0
4
0
2
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
1
0
0
0
0
1
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
5
1
0
0
0
0
0
0
0
1
0
2
0
0
0
3
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
2
1
2
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
3
1
0
3
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
1
0
0
0
4
0
0
0
0
1
0
2
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
7
0
0
0
0
0
0
0
2
0
0
0
0
0
2
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
3
0
0
6
0
0
1
0
0
0
0
0
1
0
3
0
1
0
0
0
2
0
0
0
0
1
0
0
1
3
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
1
0
2
3
2
0
2
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
1
0
2
0
0
2
1
1
0
0
3
0
4
0
0
0
0
0
1
0
0
2
0
1
0
3
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
4
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
8
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
4
0
0
0
1
2
2
1
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
1
3
0
0
1
3
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
2
3
2
0
0
0
2
1
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
2
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
1
0
2
2
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
4
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
4
3
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
3
2
3
0
0
0
0
0
0
1
1
1
0
0
0
1
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
3
2
0
0
0
0
0
0
0
2
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
1
0
0
0
0
0
2
1
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
3
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
9
1
2
0
0
1
1
0
1
0
0
2
0
0
0
11
0
1
11
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
1
0
0
0
0
2
0
3
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
1
1
2
2
0
0
0
0
0
0
4
0
0
3
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
2
1
1
0
0
0
0
1
2
0
0
0
0
1
1
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
1
0
2
0
2
3
1
0
1
2
0
0
0
1
0
0
1
1
0
0
0
0
3
0
0
2
0
0
0
1
0
0
1
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
2
0
1
0
2
0
0
0
0
1
1
2
1
2
0
0
4
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
8
2
0
2
1
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
9
0
0
1
0
0
0
0
0
0
0
0
0
1
1
2
0
4
0
0
0
0
0
1
0
0
1
0
0
1
2
2
3
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
2
1
0
0
0
0
2
1
0
0
0
0
1
2
0
0
0
0
0
0
2
1
0
0
0
0
2
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
1
1
0
1
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
1
0
1
0
0
1
0
2
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
1
0
0
0
2
0
0
0
0
3
0
0
0
1
0
0
0
4
0
2
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
5
0
0
2
2
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
3
0
1
0
1
0
0
2
0
0
2
1
0
0
0
0
0
0
0
1
1
0
0
1
0
2
2
0
2
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
2
1
1
0
1
1
2
0
2
0
0
0
0
0
3
1
0
0
1
6
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
4
2
3
0
3
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
2
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
1
0
0
0
0
4
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
3
1
2
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
2
6
2
0
1
0
0
2
1
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
5
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
1
1
0
0
2
0
2
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
2
0
1
0
0
1
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
4
1
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
6
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
1
2
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
2
0
0
4
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
6
0
0
0
0
0
2
0
0
1
0
0
2
0
0
2
1
0
0
0
0
3
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
1
1
0
2
0
7
0
0
1
0
1
2
0
0
1
1
0
0
0
1
0
0
0
0
3
0
0
0
2
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
2
0
0
0
0
1
0
1
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
2
0
2
0
0
0
0
3
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
1
0
0
0
2
0
0
0
0
2
1
0
2
0
0
3
0
0
1
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
1
3
0
0
0
0
1
0
1
1
0
1
0
0
0
1
0
0
1
0
0
1
0
2
2
0
0
0
2
0
0
0
0
1
0
0
0
0
1
2
2
0
0
0
1
0
0
3
0
1
0
1
2
1
0
0
0
0
1
2
0
0
0
0
0
0
1
2
0
0
4
2
0
1
0
0
0
0
1
0
0
1
0
2
0
0
2
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
5
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
2
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
2
1
0
1
0
0
1
0
1
3
1
1
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
1
0
0
1
0
0
3
1
2
0
0
0
7
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
4
1
0
0
0
1
0
0
0
0
2
0
0
0
3
1
0
0
0
2
0
0
0
1
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
1
0
4
1
0
2
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
1
1
2
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
1
0
2
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
5
0
0
0
0
0
3
1
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
6
2
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
1
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
2
1
0
2
3
0
4
0
0
0
0
1
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
1
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
1
1
0
2
1
2
3
0
0
0
0
2
0
0
0
0
0
0
1
0
2
1
0
0
0
8
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
1
1
1
0
1
0
0
0
0
0
3
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
1
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
2
0
1
0
0
2
1
0
2
0
0
0
0
2
0
2
2
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
3
0
0
1
0
0
0
0
3
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
3
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
4
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
3
0
0
0
0
0
0
0
2
0
0
5
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
2
1
1
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
2
0
0
0
2
0
0
0
0
2
0
2
0
2
0
0
0
7
2
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
2
1
0
0
0
1
2
2
0
0
2
0
0
0
0
2
0
1
3
0
0
0
1
1
0
0
2
0
0
0
0
0
0
1
4
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
1
2
0
0
2
1
1
0
1
0
3
1
0
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
7
0
0
0
0
0
2
0
0
3
0
0
1
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
3
2
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
3
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
1
0
1
1
2
0
0
0
0
0
0
2
1
0
0
1
1
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
2
0
3
0
1
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
5
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
1
0
0
3
0
1
0
2
1
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
3
0
1
2
0
1
0
2
3
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
2
2
0
1
0
0
0
0
1
0
0
2
0
0
3
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
4
0
1
4
2
0
1
0
0
2
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
2
0
1
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
1
1
0
0
0
0
1
2
1
0
0
2
0
0
0
1
2
0
0
0
2
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
1
2
0
2
0
0
0
1
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
3
0
0
0
0
0
2
0
5
0
1
0
0
0
0
5
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
3
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
2
2
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
9
0
0
1
1
0
1
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
3
0
0
0
0
0
0
3
0
0
0
1
1
0
0
3
1
0
1
0
0
0
0
0
0
1
0
1
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
0
0
0
0
1
2
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
7
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
4
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
4
1
0
0
0
0
0
0
0
3
0
0
0
0
1
1
2
0
0
0
1
0
0
0
0
1
2
1
0
0
0
0
0
3
0
0
0
2
0
0
2
1
0
0
2
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
5
0
2
0
3
0
0
0
0
2
2
0
1
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
5
0
4
2
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
1
3
0
0
0
1
1
1
0
2
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
1
0
0
0
1
6
0
0
0
0
0
0
0
0
0
2
2
0
0
1
1
0
2
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
3
0
1
1
2
0
0
2
0
1
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
4
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
3
0
3
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
2
4
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
3
0
0
0
2
0
0
0
2
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
2
2
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
3
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
1
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
1
1
5
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
1
2
2
1
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
4
0
0
0
2
1
1
0
0
1
0
0
4
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
3
0
0
0
0
1
0
7
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
4
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
1
0
2
0
0
0
0
1
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
1
0
2
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
1
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
3
3
2
2
2
0
0
1
0
7
2
2
0
0
0
0
0
0
0
0
0
1
2
0
1
3
0
0
2
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
2
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
3
2
0
0
2
0
1
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
10
0
0
0
0
2
2
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
1
0
3
0
0
2
0
0
2
0
0
0
0
1
0
0
2
0
3
0
0
1
0
2
1
0
0
0
2
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
5
0
0
0
0
0
2
4
2
0
0
3
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
6
0
0
0
0
2
0
1
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
3
2
1
0
1
2
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
2
0
2
2
0
3
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
3
0
0
0
0
1
1
0
0
0
0
0
0
0
9
0
0
0
3
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
1
0
0
0
1
0
2
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
5
0
8
2
2
0
1
1
0
0
0
0
0
3
0
0
0
0
2
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
3
0
2
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
4
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
6
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
3
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
2
0
0
2
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
4
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
2
0
3
0
0
0
0
0
3
0
0
0
0
1
0
2
0
3
0
0
0
2
0
2
0
0
2
0
0
1
0
0
0
0
5
0
0
2
0
1
1
1
0
0
0
1
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
2
0
0
0
0
1
2
0
0
2
0
2
1
1
0
2
2
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
5
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
4
1
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
4
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
4
0
0
0
0
1
0
3
0
0
0
0
0
0
0
3
1
3
0
0
1
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
1
1
2
0
0
0
0
1
1
0
5
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
1
0
0
0
0
2
2
0
0
1
1
0
2
0
2
1
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
2
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
3
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
1
2
1
0
0
0
6
0
0
0
0
2
3
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
3
0
6
0
0
0
0
1
2
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
2
1
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
1
0
0
0
3
0
1
0
2
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
8
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
1
1
0
2
2
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
1
0
1
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
4
0
0
1
0
0
0
0
2
0
0
1
0
1
0
0
2
0
0
0
0
3
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
2
1
0
1
2
0
0
0
0
1
30
0
1
2
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
2
2
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
8
0
0
2
0
0
3
0
1
1
0
0
0
0
0
6
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
5
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
3
4
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
5
0
1
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
4
1
2
0
4
0
0
0
2
2
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
1
0
0
0
0
1
1
2
0
0
0
0
0
0
3
1
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
1
0
2
0
0
0
2
1
2
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
3
0
0
6
0
0
0
2
0
0
0
0
0
1
2
0
0
0
1
0
0
0
4
0
0
0
0
1
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
4
0
0
0
0
0
0
2
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
4
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
1
3
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
3
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
1
0
0
0
2
0
0
0
2
5
0
1
0
4
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
8
1
1
0
0
1
0
0
0
0
0
2
1
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
2
0
0
0
1
4
0
2
0
0
1
0
0
0
3
1
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
4
3
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
6
3
0
0
2
0
0
1
2
0
1
0
0
0
0
0
1
2
0
0
0
0
0
3
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
5
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
1
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
6
0
0
1
0
0
0
0
0
2
2
0
0
0
1
0
0
0
1
0
0
2
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
1
2
1
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
1
0
2
0
0
0
0
2
1
0
1
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
1
2
0
1
0
1
0
0
1
0
1
0
1
0
0
0
0
1
0
1
0
1
0
0
0
3
0
0
0
0
0
3
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
4
0
0
1
1
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
3
0
0
0
0
1
0
0
0
11
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
1
0
0
1
0
0
0
0
0
0
2
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
2
0
2
0
3
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
2
1
0
0
0
0
1
0
0
0
2
4
1
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
2
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
1
2
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
3
2
1
0
0
5
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
3
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
1
0
0
2
0
0
1
0
0
0
1
0
0
0
2
1
0
0
2
0
2
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
4
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
2
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
2
2
0
1
0
0
1
0
0
0
5
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
2
0
0
0
0
1
1
0
0
2
0
0
5
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
3
0
0
0
0
0
0
6
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
4
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
1
2
0
0
0
0
0
3
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
2
1
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
1
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
9
0
0
0
1
0
0
0
0
0
0
0
0
2
0
3
0
1
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
3
0
0
0
2
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
1
0
0
0
1
12
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
4
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
3
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
3
1
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
2
0
1
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
1
0
1
3
0
0
1
6
0
0
1
1
0
1
3
1
0
0
0
0
1
0
0
0
0
0
2
1
4
0
2
0
0
1
0
0
0
0
1
0
0
4
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
3
1
0
2
0
1
1
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
2
1
1
2
1
2
0
0
0
0
0
0
0
2
0
4
1
0
0
0
2
0
0
0
0
2
2
2
0
1
1
0
0
3
0
0
0
0
1
2
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
5
2
0
0
1
0
2
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
2
0
0
0
0
4
0
0
0
2
0
2
0
1
0
0
0
1
0
1
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
3
0
0
2
0
0
0
1
0
0
0
4
1
5
0
0
3
1
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
2
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
5
0
3
2
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
1
0
0
0
3
0
0
0
0
0
0
2
4
0
0
0
1
0
0
2
1
4
0
0
1
0
2
0
2
0
0
0
0
0
2
0
3
1
0
1
2
0
0
0
0
2
2
0
0
0
0
0
0
8
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
2
1
0
1
1
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
2
0
0
0
2
0
1
3
0
0
0
0
0
2
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
2
4
0
0
0
0
0
0
0
2
2
1
2
0
0
0
1
0
1
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
8
0
0
0
0
1
0
20
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
2
0
0
3
1
0
0
0
1
0
1
0
2
0
0
0
1
0
0
1
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
1
2
2
0
0
1
0
0
2
0
0
0
1
2
0
0
0
1
0
1
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
3
0
6
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
2
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
9
0
0
0
4
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
3
0
0
1
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
4
2
0
0
2
1
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
2
0
1
2
0
0
0
0
2
2
2
0
1
0
0
2
0
1
1
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
2
1
0
0
1
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
7
1
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
3
0
0
1
0
0
0
1
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
3
0
0
0
1
2
0
1
0
1
0
0
0
0
2
0
2
2
0
0
1
1
0
0
1
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
7
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
1
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
7
0
0
0
3
0
0
0
0
2
1
0
0
2
0
0
0
0
0
3
0
1
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
1
0
0
1
1
0
3
0
2
0
1
0
0
2
0
1
0
0
0
2
2
0
0
2
0
2
2
0
3
1
0
0
2
0
1
0
0
0
0
0
0
2
1
1
0
0
2
0
1
0
2
1
0
0
0
2
0
0
0
0
0
4
0
1
0
0
1
1
0
0
0
0
2
0
3
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
3
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
4
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
5
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
1
0
0
0
2
3
0
2
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
1
1
1
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
3
0
2
0
0
0
0
0
2
0
0
6
0
1
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
4
2
2
0
0
2
0
0
3
1
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
2
0
0
3
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
3
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
8
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
2
0
1
1
0
0
1
0
1
0
2
2
0
0
0
0
0
0
2
0
2
3
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
2
0
2
0
0
0
1
0
0
0
0
0
1
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
2
0
1
0
0
0
1
0
0
0
0
0
4
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
1
0
0
2
1
0
0
0
3
0
1
0
0
0
0
0
1
0
0
0
0
0
6
2
1
0
2
0
0
0
0
0
0
3
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
1
0
2
0
0
2
0
2
1
0
0
0
3
0
0
0
0
1
2
0
0
0
2
2
2
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
3
2
0
2
0
0
0
0
2
0
0
0
0
2
0
5
0
0
0
1
0
0
0
0
2
0
2
0
2
0
0
2
1
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
10
0
0
0
2
0
4
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
3
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
1
0
2
0
0
0
2
1
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
4
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
8
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
1
0
3
0
0
0
0
0
1
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
1
0
0
0
0
0
3
2
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
2
1
4
0
0
1
0
2
0
0
0
0
0
5
1
1
0
0
0
0
1
0
0
0
2
1
0
2
0
0
0
0
0
0
0
2
1
0
0
1
1
0
0
0
0
1
0
0
1
0
0
3
2
1
0
2
0
0
0
0
0
0
0
0
5
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
3
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
9
0
0
4
0
2
0
0
0
2
3
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
2
1
0
0
0
2
0
0
0
2
0
0
0
2
1
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
2
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
7
0
0
1
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
1
0
1
1
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
7
0
0
4
2
0
2
0
0
2
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
3
0
0
0
1
0
0
3
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
1
0
0
1
0
0
1
2
1
0
1
0
1
0
0
0
6
3
0
0
0
0
2
0
1
0
1
0
3
5
0
0
0
0
2
1
0
0
0
0
0
0
0
1
1
5
0
0
1
0
0
1
0
1
0
1
0
0
0
0
2
0
2
0
1
0
2
0
1
0
0
0
0
0
0
0
0
3
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
1
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
2
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
1
1
4
1
1
3
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
3
0
0
0
0
0
1
0
4
0
3
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
5
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
1
1
2
2
0
1
1
0
0
0
2
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
2
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
1
1
0
0
0
1
3
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
2
0
5
0
0
0
0
1
3
0
0
2
1
0
0
0
0
0
0
1
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
2
0
0
0
0
1
0
2
3
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
3
0
2
0
2
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
1
1
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
2
0
3
1
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
1
0
0
1
0
0
0
0
0
2
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
1
3
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
2
1
0
0
4
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
1
0
0
2
1
1
5
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
5
1
0
0
0
0
3
1
0
5
1
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
3
0
0
0
0
0
4
0
0
0
0
0
0
0
1
2
0
2
1
0
0
0
0
0
0
1
0
0
1
0
0
11
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
2
0
0
0
2
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
4
0
3
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
3
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
2
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
3
5
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
10
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
1
0
4
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
2
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
2
2
0
1
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
1
2
3
0
1
1
0
0
0
0
2
1
2
0
0
1
0
0
1
0
0
0
2
2
2
2
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
2
0
0
0
2
0
0
1
1
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
3
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
5
0
0
0
0
1
1
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
3
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
1
10
0
0
0
2
0
1
0
1
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
2
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
3
1
0
2
0
0
0
2
0
0
0
1
0
1
0
0
2
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
1
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
3
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
4
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
1
2
1
2
1
0
0
0
0
2
0
0
0
0
2
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
3
0
0
0
1
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
3
1
0
0
1
2
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
2
0
0
2
1
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
1
2
0
0
0
0
0
1
0
1
0
1
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
2
1
2
0
1
0
0
2
0
0
0
2
3
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
2
0
1
0
3
0
0
2
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
1
0
1
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
2
0
0
0
0
4
0
0
1
2
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
11
0
12
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
4
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
1
0
0
0
0
2
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
2
1
2
0
0
0
0
0
0
2
0
2
2
0
1
0
0
0
0
1
0
3
0
2
0
0
0
0
0
1
1
2
0
2
0
0
0
3
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
8
1
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
4
0
0
1
0
0
0
1
2
0
0
0
1
0
0
2
1
1
1
1
2
0
1
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
3
0
1
3
0
0
0
0
0
0
0
6
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
2
0
2
2
2
1
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
2
2
0
1
0
1
0
0
0
0
0
1
0
0
0
3
0
0
0
4
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
3
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
3
0
0
1
1
0
0
0
0
0
2
0
0
0
0
1
1
0
0
1
0
1
0
0
2
1
0
1
0
0
0
1
1
1
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
4
1
0
0
2
2
0
0
0
0
2
1
2
0
2
3
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
2
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
3
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
0
0
0
0
0
4
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
1
0
1
0
0
0
3
8
2
1
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
2
0
0
0
0
1
0
1
0
0
1
0
2
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
0
3
0
0
0
1
2
0
0
2
1
1
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
3
0
1
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
2
0
0
1
2
3
2
0
0
0
0
1
0
3
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
1
1
0
0
1
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
1
0
0
3
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
8
0
2
0
0
0
2
0
0
0
1
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
2
1
0
0
2
3
0
2
0
2
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
1
3
0
3
0
4
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
3
0
0
2
1
0
1
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
3
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
1
0
2
0
2
0
0
2
1
0
0
1
0
0
0
0
1
0
0
3
0
4
0
0
0
0
0
0
0
1
0
0
0
0
8
4
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
3
0
0
0
0
2
4
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
1
4
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
2
0
1
0
0
2
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
1
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
1
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
4
2
0
0
0
0
0
2
1
0
0
0
0
0
2
0
2
0
0
0
0
0
3
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
1
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
3
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
1
0
0
2
0
0
0
0
2
1
0
1
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
1
0
2
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
3
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
1
0
2
0
2
0
0
0
2
0
0
0
0
2
1
0
1
0
1
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
3
3
3
0
0
0
0
0
0
2
1
2
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
3
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
8
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
3
0
0
0
0
0
1
0
3
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
2
0
0
2
1
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
5
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
3
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
1
0
4
2
7
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
3
0
0
0
0
1
0
1
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
1
2
0
0
6
0
2
1
0
0
2
0
0
0
0
3
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
1
2
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
3
1
0
0
0
2
0
0
1
1
2
0
0
2
0
0
1
2
0
0
0
0
0
0
0
2
0
2
5
2
0
0
0
0
0
1
1
0
1
3
1
0
1
0
5
0
1
0
0
1
0
0
0
2
0
0
1
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
1
0
0
0
0
2
0
0
1
0
0
2
3
0
4
0
1
0
0
1
1
1
0
0
0
0
1
0
5
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
3
0
0
3
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
1
2
0
1
2
1
0
0
0
0
0
1
0
0
0
1
0
2
2
0
0
2
0
0
1
0
0
0
0
1
0
1
0
1
0
0
3
0
2
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
1
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
1
0
2
2
0
0
0
2
0
0
0
2
0
0
0
0
0
3
0
0
0
2
0
0
0
0
2
0
1
2
2
0
0
0
1
1
0
0
0
1
0
0
0
0
0
4
0
4
0
0
0
0
0
0
0
0
0
4
0
2
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
3
5
1
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
2
0
1
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
1
1
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
1
0
0
1
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
1
0
2
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
1
2
0
0
0
0
3
0
0
0
0
2
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
1
0
1
1
1
0
2
0
0
0
6
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
5
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
1
1
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
3
0
3
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
1
1
1
1
2
0
0
1
0
2
0
0
0
0
0
0
0
2
0
1
1
0
0
1
0
0
0
0
0
0
1
0
1
0
1
2
0
0
0
1
0
2
0
1
0
0
0
1
0
0
1
0
0
0
5
0
4
0
0
1
0
0
0
3
0
2
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
5
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
1
0
0
1
2
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
2
0
1
0
0
1
1
0
2
0
1
0
0
0
0
6
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
2
0
0
0
0
0
0
0
1
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
2
0
0
0
2
0
2
3
0
0
2
2
1
0
2
0
0
2
2
0
0
0
0
0
1
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
4
1
0
0
1
1
1
1
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
1
1
0
2
0
0
0
0
0
3
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
1
0
2
1
0
0
0
1
0
1
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
2
1
2
0
1
0
0
0
0
2
0
1
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
2
0
0
2
2
0
2
0
0
7
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
2
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
1
0
2
0
3
1
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
1
0
0
3
0
2
0
1
0
0
0
0
0
2
0
0
8
0
0
0
2
0
1
0
2
2
0
0
2
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
6
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
1
2
0
0
0
0
3
0
0
2
0
0
0
0
1
0
1
0
0
4
0
1
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
3
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
5
1
0
0
0
0
0
2
0
3
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
4
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
1
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
3
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
3
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
3
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
2
5
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
3
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
5
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
3
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
1
0
0
3
0
3
0
0
2
0
1
2
0
0
1
2
0
0
0
2
1
0
0
0
0
0
2
0
0
3
0
0
0
0
0
2
0
2
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
1
2
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
1
0
1
1
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
1
2
0
2
0
0
1
0
0
0
1
0
0
0
3
0
2
0
0
2
0
0
0
0
2
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
2
0
0
0
2
0
3
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
1
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
6
0
0
3
0
0
0
0
0
0
0
0
0
0
2
1
0
1
1
1
2
2
0
0
0
0
0
0
11
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
2
3
0
0
0
2
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
4
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
4
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
2
0
0
0
2
2
0
3
0
0
0
1
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
1
1
0
0
0
0
0
0
2
3
0
6
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
1
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
3
0
3
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
2
2
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
3
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
1
3
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
1
0
1
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
2
2
0
0
0
2
2
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
1
0
0
2
3
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
2
0
0
1
1
0
0
2
0
0
0
0
1
1
0
0
5
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
2
0
5
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
4
5
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
1
2
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
7
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
1
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
4
0
2
0
0
2
0
1
0
0
2
0
0
1
0
2
1
1
0
1
2
0
2
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
3
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
2
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
3
0
0
0
1
0
0
0
0
3
0
0
0
1
0
2
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
3
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
2
1
1
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
1
2
0
1
0
0
0
0
0
0
10
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
2
0
1
0
3
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
2
3
0
0
2
1
0
0
0
1
0
1
0
1
0
0
4
1
0
0
2
0
2
0
4
0
0
0
0
2
1
1
0
3
0
0
1
0
0
0
0
0
3
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
15
3
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
11
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
4
0
0
1
0
1
0
0
1
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
1
1
0
0
3
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
2
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
3
1
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
1
0
2
3
0
0
0
0
0
0
0
0
1
0
1
0
3
0
0
0
0
0
0
4
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
1
0
0
0
0
2
1
0
1
0
0
0
3
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
4
0
0
0
1
2
0
0
0
0
0
2
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
3
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
9
0
0
2
1
2
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
1
2
0
0
0
3
0
0
1
2
0
0
0
3
0
1
0
0
0
0
0
2
0
0
2
0
1
1
0
0
0
0
0
1
0
0
1
2
0
0
0
0
2
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
5
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
1
2
1
1
0
0
0
0
0
1
1
0
2
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
6
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
2
0
1
0
0
1
1
4
0
2
0
0
2
2
0
0
0
0
0
1
0
0
0
0
1
0
0
2
2
0
2
0
1
1
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
3
2
2
1
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
1
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
15
2
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
3
0
0
0
3
2
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
5
2
0
0
0
0
0
0
0
0
0
0
0
6
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
2
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
4
2
2
0
2
0
2
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
2
0
0
3
2
0
0
0
0
0
0
1
0
0
0
0
0
3
0
1
0
1
0
0
0
3
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
2
0
2
1
1
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
1
0
0
0
3
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
1
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
1
0
0
2
1
2
0
2
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
2
0
0
2
0
2
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
3
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
6
0
0
3
3
0
0
1
0
1
2
0
1
1
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
6
1
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
3
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
4
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
7
6
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
2
0
0
0
0
0
1
1
0
0
1
3
2
0
0
3
0
1
0
0
0
2
0
2
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
1
0
0
0
0
0
0
2
0
6
0
0
0
0
0
1
0
0
0
1
0
0
3
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
2
0
1
0
0
1
3
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
3
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
2
0
0
0
4
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
1
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
2
1
1
0
0
0
2
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
9
0
1
0
0
0
0
0
0
0
3
1
0
0
0
1
0
0
0
2
2
0
0
0
0
3
0
1
0
0
0
2
0
0
0
1
0
0
1
0
1
0
0
0
0
0
2
0
1
2
0
0
0
3
2
0
0
1
4
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
3
0
0
0
0
3
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
2
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
1
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
7
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
3
0
0
1
0
0
3
0
0
0
2
4
0
0
2
2
0
0
0
0
2
0
1
0
1
0
0
2
2
0
0
0
0
8
1
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
6
0
0
0
0
0
1
2
0
0
1
0
0
1
0
0
0
3
0
0
4
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
1
2
0
0
0
0
0
0
0
3
0
0
1
1
0
0
0
1
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
2
1
0
1
2
1
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
2
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
5
1
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
2
1
0
0
0
0
0
0
0
2
2
0
0
1
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
1
3
2
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
1
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
5
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
2
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
3
0
0
1
3
0
0
0
0
0
1
1
0
0
0
1
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
1
0
2
0
0
2
0
1
0
2
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
9
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
3
0
0
0
2
0
1
0
0
0
0
2
0
0
1
0
0
5
3
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
5
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
6
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
1
1
0
0
0
0
1
0
0
1
0
2
0
0
0
1
0
0
0
0
0
3
2
0
0
1
1
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
2
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
1
2
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
6
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
1
0
0
2
0
4
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
3
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
2
2
2
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
2
2
0
0
0
0
2
1
1
0
0
2
0
0
2
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
1
3
2
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
2
2
0
0
2
0
0
0
0
0
0
3
2
0
1
0
0
0
0
0
2
0
0
4
0
0
0
0
2
0
0
0
0
0
0
0
1
1
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
2
1
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
2
0
0
0
10
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
7
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
2
4
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
3
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
1
0
2
0
0
0
0
0
2
4
0
0
1
0
0
0
0
1
0
1
1
1
0
0
0
0
1
0
0
1
0
0
0
0
5
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
4
0
0
2
1
0
0
0
1
0
0
0
0
0
3
0
0
0
1
2
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
1
1
0
1
0
2
1
5
0
0
0
3
2
0
0
0
0
0
0
2
0
0
1
0
0
5
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
1
0
2
1
2
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
2
0
1
4
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
3
0
0
0
0
3
0
0
2
0
0
0
2
0
0
0
0
0
6
0
1
4
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
1
0
2
0
0
0
0
0
2
0
0
5
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
3
0
0
2
1
0
0
1
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
3
1
0
0
0
1
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
1
0
2
0
0
0
5
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
3
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
5
2
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
1
2
0
0
1
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
2
3
0
1
0
0
0
1
0
2
0
1
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
1
2
0
0
3
0
0
0
0
1
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
4
0
1
1
0
0
1
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
1
0
3
0
0
0
0
0
0
0
1
0
2
0
1
0
0
1
0
0
1
0
0
0
0
0
2
2
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
6
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
4
0
2
0
2
2
0
1
0
2
0
0
0
1
0
0
0
0
2
0
2
0
0
0
2
0
0
0
2
0
0
0
0
1
2
0
4
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
1
10
0
0
0
0
2
0
0
0
0
0
1
0
0
1
3
0
0
2
2
0
0
0
2
2
2
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
1
2
0
4
1
0
1
0
2
0
2
1
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
1
0
1
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
4
0
1
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
3
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
4
2
0
0
2
0
0
0
2
0
0
0
0
5
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
2
0
0
2
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
3
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
1
1
0
0
2
2
0
1
0
0
2
0
0
0
2
1
0
0
3
0
0
0
0
0
0
0
0
4
2
1
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
1
1
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
5
0
2
0
0
0
1
0
0
0
0
0
2
0
1
2
2
1
0
0
0
0
0
0
0
1
1
2
0
0
0
1
0
0
1
0
2
0
0
0
2
0
0
1
0
2
0
0
4
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
2
0
2
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
5
2
0
0
2
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
3
0
0
4
0
0
0
2
0
0
0
0
3
0
0
0
0
0
1
0
0
0
1
21
2
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
4
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
3
5
0
0
0
1
0
2
0
0
0
3
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
2
0
1
5
0
0
0
1
0
0
0
3
3
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
3
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
3
2
0
0
0
1
0
0
1
0
1
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
1
0
2
0
0
0
0
0
0
1
0
0
0
0
2
3
1
2
2
0
0
0
0
0
2
0
0
1
0
1
0
1
1
1
2
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
1
1
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
1
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
2
2
0
0
2
2
0
4
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
2
1
0
1
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
2
0
2
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
2
0
1
2
0
0
0
0
0
0
0
2
3
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
3
0
1
0
0
2
2
0
3
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
2
1
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
1
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
3
2
0
0
3
0
1
0
1
0
0
0
0
0
0
2
1
1
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
1
0
1
7
2
0
0
0
0
0
3
0
0
0
1
0
2
0
2
0
0
0
0
0
2
1
2
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
3
1
0
2
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
5
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
1
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
10
2
0
0
0
1
1
0
2
0
2
7
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
5
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
3
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
1
1
0
2
0
0
0
0
0
0
1
2
0
0
1
0
0
0
1
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
1
1
2
0
0
0
0
3
2
0
0
4
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
3
0
1
0
0
0
1
0
0
0
3
2
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
3
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
3
1
1
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
2
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
7
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
7
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
2
0
0
1
0
1
0
2
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
1
0
2
0
0
0
2
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
2
2
0
0
0
0
0
1
0
4
0
0
0
0
2
0
0
0
5
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
1
0
5
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
2
0
0
0
2
0
0
0
1
0
0
0
3
0
2
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
5
0
9
0
2
2
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
7
0
0
0
0
0
2
2
0
0
3
0
1
1
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
10
2
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
3
0
0
4
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
8
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
2
2
2
0
0
2
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
2
0
1
1
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
1
0
0
0
2
0
1
0
0
0
1
0
0
0
0
4
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
3
0
3
0
1
1
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
2
1
0
2
0
0
0
0
2
0
0
1
0
0
3
0
1
0
1
0
0
0
0
0
0
0
0
6
0
0
0
0
2
0
0
0
1
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
4
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
4
0
0
0
0
2
1
0
0
0
0
0
1
0
1
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
1
0
2
0
2
0
0
0
0
0
3
0
0
0
0
0
0
3
0
0
2
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
2
0
2
2
0
0
0
1
2
0
0
0
2
0
2
0
0
1
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
3
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
5
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
1
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
4
0
0
2
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
7
1
0
1
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
1
0
0
1
2
0
0
1
2
1
0
2
0
0
0
2
1
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
3
0
0
0
0
1
2
2
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
1
2
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
1
0
3
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
2
0
0
0
1
0
0
0
0
0
1
2
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
1
0
2
0
1
0
0
0
2
0
0
0
0
0
0
3
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
1
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
1
2
1
0
1
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
2
4
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
3
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
1
1
0
0
1
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
6
0
0
1
0
0
0
0
0
0
0
2
1
1
1
3
0
0
0
2
0
0
0
5
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
1
1
0
0
0
2
1
0
0
0
0
0
0
0
9
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
2
3
3
2
0
0
1
0
0
0
2
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
6
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
4
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
1
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
1
0
1
1
2
1
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
1
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
1
0
0
0
2
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
1
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
3
0
2
0
1
2
0
0
0
1
0
1
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
1
0
4
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
0
3
0
1
0
0
0
0
4
0
0
0
0
1
0
3
0
0
0
0
3
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
4
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
2
3
0
0
1
0
0
1
1
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
6
0
0
1
0
2
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
2
2
0
0
0
2
0
0
0
2
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
1
2
1
0
1
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
1
1
3
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
1
0
0
0
0
1
0
1
0
1
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
3
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
1
2
2
0
0
2
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
4
0
0
1
6
0
0
0
0
3
0
1
1
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
3
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
1
0
0
0
1
0
0
0
0
2
3
2
0
0
0
1
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
4
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
3
1
0
0
0
0
0
0
7
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
8
0
3
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
1
2
0
1
1
0
0
0
0
0
3
0
0
0
0
2
0
0
1
0
1
2
1
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
1
0
0
0
3
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
2
0
0
0
2
0
2
2
0
0
0
0
0
2
1
0
0
0
0
1
0
0
2
0
0
0
0
3
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
3
2
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
2
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
5
1
0
1
1
2
2
0
0
0
0
2
0
0
1
1
1
2
0
1
1
0
1
0
0
0
0
0
0
0
1
1
0
2
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
3
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
2
0
0
2
0
4
5
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
4
0
0
2
2
2
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
2
0
1
2
0
1
0
0
0
0
0
0
3
0
0
1
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
3
2
1
0
0
0
0
0
0
8
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
6
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
6
2
1
0
0
8
0
0
0
8
3
0
0
0
0
1
0
0
2
2
0
0
0
0
1
0
2
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
2
0
2
0
0
0
0
0
0
0
1
2
2
1
0
3
0
0
0
2
0
0
0
0
0
0
1
0
0
0
3
0
0
0
1
1
0
1
0
0
1
0
2
2
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
1
2
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
3
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
1
3
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
2
0
2
0
1
1
1
2
2
0
1
0
0
1
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
2
4
0
4
0
1
0
0
0
0
0
1
0
1
0
2
1
2
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
1
0
6
0
0
0
0
0
1
1
0
0
3
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
1
0
1
2
0
3
1
0
0
0
0
0
3
3
0
2
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
1
3
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
3
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
1
0
1
0
0
1
0
0
2
0
0
1
2
0
0
0
0
0
0
5
0
3
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
3
0
3
0
2
0
2
0
0
2
0
0
0
8
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
1
1
1
0
5
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
3
0
2
0
0
3
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
2
2
1
0
2
0
0
2
0
0
2
0
0
0
0
0
0
1
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
3
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
3
0
0
0
0
0
0
0
3
1
1
0
0
0
0
2
0
2
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
3
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
3
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
3
0
4
0
2
1
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
3
0
0
2
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
3
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
3
0
0
0
2
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
4
0
2
5
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
5
0
0
0
2
0
0
0
2
1
1
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
1
0
1
2
0
0
0
1
0
0
0
0
0
0
1
0
2
0
6
0
0
0
2
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
1
0
0
1
0
1
0
0
1
0
0
0
1
1
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
1
2
0
0
1
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
17
1
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
1
0
2
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
1
0
1
3
0
0
0
0
0
2
0
0
0
0
0
0
1
5
0
1
2
0
0
0
2
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
2
0
0
0
0
0
0
1
0
2
1
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
5
4
0
0
0
1
0
1
3
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
6
0
0
1
0
0
0
2
1
0
0
0
0
0
0
1
0
4
0
0
2
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
6
1
0
2
0
0
0
1
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
1
0
2
3
1
0
0
0
2
0
1
0
0
0
1
0
2
2
0
0
0
1
2
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
2
0
2
0
0
2
1
0
1
0
0
0
0
0
0
1
1
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
4
0
0
0
0
0
4
2
0
0
0
1
2
0
1
0
0
1
0
0
0
0
1
0
1
1
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
3
2
0
1
1
0
2
0
0
0
0
0
0
2
0
0
1
1
0
0
2
2
1
0
0
2
2
0
2
1
0
0
0
1
0
0
0
0
1
0
3
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
9
1
2
2
0
1
0
0
0
0
0
0
2
5
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
3
2
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
4
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
2
3
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
2
0
4
0
0
2
0
0
0
0
2
0
0
1
0
0
1
3
1
0
0
0
0
1
2
2
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
1
1
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
5
2
0
0
0
0
0
2
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
1
2
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
3
0
2
0
0
0
0
3
0
0
0
0
1
1
0
1
0
2
0
0
0
3
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
2
1
0
0
1
1
1
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
1
1
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
3
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
4
0
0
1
1
0
0
0
0
0
2
0
2
1
2
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
1
3
0
0
2
0
1
1
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
3
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
4
0
1
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
1
5
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
1
0
1
0
3
0
0
0
0
3
0
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
3
0
0
1
1
2
2
0
1
0
0
0
0
5
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
2
0
0
1
1
0
0
0
0
0
0
0
0
4
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
1
3
0
0
0
0
0
1
1
0
0
2
0
2
0
0
1
0
0
0
0
0
1
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
1
0
2
0
1
0
0
0
1
0
2
5
1
0
0
0
5
0
1
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
3
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
3
0
7
0
0
0
0
0
4
3
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
2
0
1
0
0
1
0
0
0
0
0
0
1
0
3
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
1
1
1
0
2
0
0
0
3
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
2
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
2
0
0
0
0
2
0
2
0
0
1
0
0
4
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
2
0
1
0
0
0
2
2
0
13
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
4
1
1
0
0
0
0
0
0
1
0
1
0
3
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
2
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
2
0
0
1
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
3
1
0
0
0
1
0
0
0
0
0
0
0
2
3
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
7
0
0
4
0
1
1
0
2
0
0
0
0
0
2
0
3
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
9
0
2
0
0
0
3
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
1
5
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
2
1
0
0
2
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
7
2
0
1
0
2
0
2
1
0
0
0
2
3
0
0
0
0
0
1
0
0
0
2
0
0
0
7
0
1
0
0
0
0
0
0
2
0
0
1
2
0
0
1
0
0
2
0
5
0
0
0
0
0
0
1
1
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
1
0
0
0
1
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
2
0
2
1
0
0
0
0
0
0
1
2
0
0
3
0
0
0
2
0
0
0
0
2
0
0
1
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
7
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
5
0
0
2
0
3
0
0
0
0
0
2
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
1
1
21
0
2
0
0
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
2
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
4
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
3
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
3
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
3
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
3
0
0
0
2
0
0
0
2
0
0
0
0
6
0
0
0
0
0
2
0
0
2
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
1
0
5
0
1
0
0
0
0
0
1
2
0
0
0
0
0
3
0
0
0
0
0
0
7
0
0
0
0
0
1
0
0
0
0
0
1
1
0
3
1
1
0
1
2
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
5
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
1
0
4
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
3
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
4
0
0
1
0
0
4
0
0
2
0
0
3
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
1
10
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
6
0
0
2
0
0
0
1
3
0
1
0
1
0
0
1
0
0
0
0
0
2
0
0
1
5
0
2
0
2
2
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
1
2
0
2
0
2
0
0
0
0
0
1
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
3
0
0
0
1
2
0
0
0
2
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
5
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
6
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
6
1
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
1
0
0
1
0
2
1
1
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
3
0
0
2
0
0
1
0
0
0
2
0
1
0
0
0
0
0
1
0
0
3
1
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
2
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
2
0
0
0
0
0
0
1
2
0
0
1
1
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
3
2
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
1
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
2
0
3
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
2
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
2
3
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
3
1
0
0
0
0
2
0
0
1
0
0
1
0
0
0
3
0
0
1
0
1
0
0
0
2
0
0
0
9
0
1
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
2
0
0
0
0
0
1
0
0
0
2
3
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
4
0
1
2
0
0
0
1
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
2
0
0
0
0
0
1
2
0
0
0
2
0
1
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
1
1
0
0
0
2
0
0
0
0
2
0
0
0
2
1
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
1
2
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
2
2
2
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
2
0
0
1
0
2
0
1
0
0
1
0
0
0
1
0
0
0
0
7
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
3
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
5
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
2
1
0
0
0
3
0
0
1
0
0
2
0
1
2
0
0
0
0
2
0
2
0
2
0
0
3
0
1
0
0
2
0
0
0
2
1
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
1
0
3
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
2
6
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
1
3
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
1
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
5
2
0
0
3
0
0
0
0
0
0
3
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
4
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
1
0
2
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
3
1
5
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
10
0
1
0
0
0
0
0
0
0
0
2
0
0
1
5
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
2
0
0
0
0
2
1
0
2
0
0
0
1
2
0
0
0
2
0
0
0
1
0
2
2
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
6
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
3
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
3
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
1
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
7
0
0
0
0
0
0
2
0
1
1
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
3
0
0
0
0
0
3
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
5
0
0
2
0
2
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
3
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
1
0
0
2
0
2
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
2
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
7
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
3
3
1
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
1
0
4
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
4
0
0
0
0
0
1
0
0
0
0
1
0
2
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
14
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
1
0
3
0
0
0
0
0
0
1
0
0
0
0
0
2
1
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
1
2
0
1
0
0
3
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
23
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
2
0
0
0
0
1
0
0
0
3
1
0
0
0
3
0
0
0
0
0
1
0
0
3
2
0
0
0
0
0
3
2
0
0
0
1
0
0
2
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
1
0
0
1
0
0
0
0
2
2
3
0
2
0
3
0
0
0
0
3
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
1
0
6
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
2
0
1
1
3
1
0
1
0
0
0
0
2
0
0
0
0
0
7
2
1
0
0
1
0
0
1
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
2
3
0
0
0
2
2
0
1
0
1
0
0
0
0
1
3
0
3
0
2
2
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
1
0
0
0
1
0
0
0
0
4
0
0
1
0
0
3
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
3
0
8
0
0
0
1
4
0
1
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
1
1
0
0
2
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
1
0
0
0
2
0
1
1
2
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
1
0
0
3
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
2
2
0
0
0
1
0
0
2
2
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
4
0
0
0
0
0
0
1
0
1
1
0
2
0
0
0
0
0
1
0
0
0
1
2
0
0
1
0
0
5
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
2
0
3
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
1
0
2
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
4
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
2
0
0
0
0
0
0
1
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
5
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
2
1
0
1
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
3
0
0
3
0
0
0
2
0
0
0
0
2
0
0
1
2
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
2
0
2
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
5
0
0
2
0
0
1
0
2
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
1
1
0
0
1
0
0
2
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
2
0
0
0
0
0
0
0
3
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
3
0
3
1
0
2
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
1
2
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
6
0
0
0
2
0
0
1
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
4
3
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
8
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
1
0
1
2
0
2
0
3
0
0
0
0
0
0
1
0
2
0
0
2
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
2
2
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
2
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
1
0
3
0
1
0
2
0
1
0
0
0
0
1
2
1
2
0
0
0
0
0
2
0
2
0
0
0
2
1
2
0
1
0
2
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
1
1
0
0
2
0
1
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
1
2
2
1
0
1
0
2
0
2
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
3
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
2
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
2
0
2
0
0
0
0
2
3
4
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
1
0
0
1
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
1
0
2
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
2
0
0
0
0
0
0
16
0
1
0
0
0
0
0
0
0
1
0
0
0
0
7
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
2
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
1
0
0
1
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
1
2
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
7
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
2
0
2
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
2
0
0
3
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
3
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
6
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
2
3
2
0
0
0
0
2
0
1
0
0
2
0
5
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
2
3
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
1
0
1
0
2
0
0
0
0
0
3
3
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
3
0
0
0
2
0
2
0
0
2
0
1
0
2
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
4
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
1
1
0
0
0
1
0
0
2
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
6
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
3
3
1
0
0
0
1
0
0
2
0
0
0
2
0
0
0
2
4
0
1
0
0
1
3
0
2
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
2
0
1
2
0
1
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
3
2
2
3
0
0
0
0
3
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
2
0
0
0
0
0
2
2
0
0
0
0
3
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
1
0
0
0
0
1
0
2
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
5
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
1
0
0
2
0
6
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
3
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
3
0
1
0
0
1
2
0
0
1
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
2
1
0
1
0
1
0
0
0
0
0
0
0
1
0
1
2
0
0
0
1
1
0
3
0
0
0
0
0
2
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
1
2
0
0
0
0
0
0
1
2
0
0
0
2
2
3
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
2
0
1
0
1
3
0
2
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
4
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
1
2
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
1
0
0
1
0
1
0
0
0
1
0
1
0
0
3
0
0
0
0
0
1
0
1
0
0
0
0
1
0
3
0
0
0
0
0
2
0
1
2
2
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
2
5
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
1
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
6
3
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
5
2
2
0
0
3
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
5
0
2
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
1
0
0
2
0
0
1
0
2
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
2
0
3
2
0
2
0
0
1
0
0
0
1
0
0
2
1
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
1
2
0
2
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
1
0
2
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
1
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
1
1
2
0
2
2
0
1
1
1
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
1
0
2
2
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
3
1
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
4
0
2
0
0
0
2
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
2
0
1
0
0
0
0
1
3
0
0
0
0
0
10
1
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
2
0
0
0
0
1
0
0
0
0
1
2
2
3
3
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
5
0
0
3
0
0
0
2
1
0
2
0
0
1
1
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
4
3
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
2
0
0
1
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
1
2
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
1
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
4
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
7
0
0
2
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
2
0
0
0
2
1
0
0
0
2
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
10
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
2
0
2
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
2
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
3
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
20
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
1
1
2
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
2
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
1
3
0
1
1
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
3
0
0
0
0
2
2
2
0
0
1
1
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
1
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
1
0
2
0
3
1
1
0
0
0
0
0
4
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
1
1
0
3
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
1
0
0
0
2
2
1
1
0
0
3
0
0
0
0
0
0
1
0
2
0
0
0
0
0
11
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
1
1
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
4
1
1
0
0
0
0
0
2
0
0
0
0
0
2
1
0
2
0
2
1
0
0
0
3
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
1
1
0
0
0
0
1
2
2
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
3
0
2
0
0
2
0
0
0
2
4
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
1
12
0
1
0
1
1
0
0
0
0
0
3
2
3
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7
0
0
0
2
3
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
1
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
3
3
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
4
2
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
1
0
0
0
0
4
0
0
0
0
2
0
1
0
0
1
0
1
1
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
1
0
0
0
0
2
3
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
1
1
2
1
0
0
0
0
0
0
1
2
0
2
4
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
3
0
2
2
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
1
0
6
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
1
0
0
0
0
2
3
0
0
2
0
1
0
0
0
0
0
0
5
0
0
0
2
1
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
2
0
3
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
1
0
0
2
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
4
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
4
0
2
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
3
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
2
0
0
8
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
0
1
0
1
0
2
1
1
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
5
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
2
1
3
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
3
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
3
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
1
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
4
1
0
0
0
0
1
0
0
0
0
3
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
2
0
1
0
0
0
0
0
3
0
0
0
0
1
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
4
4
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
2
1
0
0
1
0
0
3
0
1
0
1
0
0
2
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
1
2
0
1
0
0
0
0
0
0
0
5
0
0
0
1
0
4
0
2
0
2
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
3
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
6
2
0
0
0
1
0
0
3
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
4
2
0
0
0
0
0
1
2
3
0
2
0
0
0
0
0
1
0
4
1
0
2
0
0
0
0
0
0
0
2
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
13
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
5
0
0
0
5
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
3
0
0
1
1
2
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
1
0
2
0
1
0
4
0
0
0
0
0
0
0
0
3
0
0
0
2
1
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
2
0
0
0
1
1
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
3
0
4
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
2
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
1
1
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
2
2
0
1
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
3
0
1
1
0
0
0
2
0
0
0
0
2
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
5
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
1
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
1
1
4
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
1
0
0
1
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
7
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
7
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
3
0
4
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
1
0
0
2
0
2
1
1
0
0
0
0
1
2
2
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
1
3
1
1
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
5
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
1
0
0
2
0
0
0
1
2
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
2
1
0
0
0
0
0
1
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
6
0
1
0
0
0
2
2
0
0
0
1
0
0
1
2
0
0
2
0
2
0
0
0
0
0
0
0
2
0
2
0
1
2
0
1
0
0
0
1
0
0
0
0
2
1
0
0
2
0
0
2
0
0
0
0
1
1
1
0
0
1
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
4
0
0
2
1
2
1
2
0
0
15
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
2
0
0
1
2
2
0
0
1
2
0
0
0
1
0
0
0
0
0
0
2
0
2
0
2
0
0
3
0
0
0
2
0
0
0
0
1
0
2
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
2
0
0
2
1
1
1
1
1
1
4
1
2
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
1
0
0
1
0
5
0
1
0
2
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
2
4
0
0
0
4
2
0
0
0
3
0
0
1
2
0
0
0
0
0
1
0
5
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
5
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
4
0
0
3
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
1
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
1
2
0
0
0
1
0
0
5
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
2
4
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
4
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
4
0
0
1
0
0
0
0
4
1
0
2
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
1
0
0
0
1
1
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
2
2
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
1
0
0
0
2
0
2
0
0
0
1
0
3
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
2
0
1
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
1
0
0
0
2
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
1
0
0
0
0
4
2
0
0
0
1
0
0
0
0
0
2
2
0
0
6
0
0
1
1
0
0
0
2
0
0
0
2
0
0
0
3
0
2
0
2
0
4
1
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
1
0
0
0
0
1
0
0
0
0
2
9
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
2
1
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
1
2
0
0
0
0
4
1
0
0
0
0
0
0
5
0
2
2
0
0
0
0
0
0
1
0
0
2
0
1
0
0
2
0
0
0
3
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
1
0
0
2
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
1
3
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
3
3
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
4
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
1
0
1
7
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
1
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
4
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
5
0
0
2
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
1
1
2
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
3
0
0
0
2
1
0
0
0
1
1
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
1
1
0
1
0
0
0
0
1
2
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
3
1
1
0
0
3
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
2
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
1
2
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
2
4
0
2
2
0
0
0
0
0
0
0
1
0
1
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
1
0
0
0
3
0
3
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
3
1
3
1
0
1
0
3
1
1
2
0
3
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
1
0
0
0
0
1
0
0
0
3
0
0
0
0
0
1
2
1
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
5
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
6
0
0
0
0
1
0
0
0
0
0
3
3
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
1
0
3
0
0
0
0
0
0
2
2
1
1
0
0
0
0
3
3
0
1
0
0
0
0
0
0
2
0
0
0
0
1
1
2
0
0
0
2
0
5
0
1
0
0
0
2
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
2
1
2
0
0
0
2
2
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
2
0
2
0
1
0
0
1
0
0
0
3
0
1
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
1
4
2
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
1
1
1
0
1
1
0
0
1
0
0
3
0
2
0
1
1
2
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
1
2
0
0
0
0
0
3
2
1
0
1
2
0
0
2
0
0
0
0
0
1
0
0
9
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
3
0
0
0
0
0
5
0
1
0
0
1
1
0
0
6
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
1
0
0
1
0
0
0
3
0
2
0
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
3
0
0
5
1
1
2
2
0
0
0
1
0
0
0
1
4
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
1
0
1
2
0
2
0
1
0
1
1
0
0
0
2
0
0
2
0
1
3
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
1
0
0
0
2
0
2
0
0
0
2
1
2
0
0
0
1
1
0
0
2
2
1
0
0
0
0
0
0
0
2
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
3
0
0
0
1
0
1
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
5
0
0
0
1
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
7
0
1
0
1
0
1
0
0
2
0
0
0
3
2
1
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
1
0
3
0
0
0
0
1
0
0
0
2
0
0
0
1
1
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
6
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
3
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
2
2
1
2
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
3
0
0
2
0
0
0
3
2
0
2
0
0
3
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
3
0
1
3
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
4
2
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
9
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
1
0
0
0
0
0
2
1
2
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
3
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
2
1
0
0
0
2
1
1
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
3
0
1
0
1
0
0
0
0
0
5
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
5
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
5
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
2
0
3
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
1
1
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
6
1
0
2
0
0
0
0
0
0
1
1
0
2
0
0
0
2
2
2
0
0
0
2
6
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
1
0
0
0
3
0
1
5
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
1
2
1
1
2
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
4
2
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
4
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
11
2
0
0
0
0
1
0
1
0
1
0
0
2
0
0
0
0
0
0
1
3
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
3
0
0
1
0
1
0
0
0
0
0
3
2
1
0
0
0
0
2
0
0
0
0
2
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
9
1
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
1
0
0
0
3
4
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
5
0
2
0
0
2
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
1
1
0
0
3
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
1
1
0
1
2
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
2
0
0
0
1
0
1
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
1
0
4
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
2
1
0
0
0
2
0
3
2
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
3
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
6
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
1
0
0
0
3
0
0
0
6
0
0
0
0
0
0
1
0
4
0
0
1
0
0
0
1
0
2
0
0
0
0
3
0
0
0
0
2
4
0
0
2
1
4
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
2
0
3
0
0
0
0
0
0
0
1
2
5
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
5
0
0
1
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
7
0
0
0
1
0
0
1
0
0
0
0
2
0
1
0
0
2
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
1
2
0
2
0
0
0
0
0
3
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
2
0
3
0
0
0
3
0
2
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
5
1
0
0
0
0
0
2
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
2
2
1
0
1
0
0
0
0
1
4
0
0
0
0
0
3
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
1
2
0
0
2
0
1
0
1
1
2
0
0
0
0
0
4
0
2
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
5
1
1
0
0
1
1
0
1
0
2
2
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
2
0
0
1
0
0
1
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
5
0
0
1
5
1
0
0
0
0
0
0
0
1
1
0
0
1
1
1
1
2
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
3
2
0
0
0
0
0
0
0
0
0
2
1
0
0
1
4
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
8
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
3
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
4
0
2
0
0
0
0
0
0
7
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
2
2
0
2
0
2
0
0
0
0
0
0
1
2
0
0
1
0
2
0
0
4
1
0
2
0
0
1
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
2
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
2
0
1
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
2
0
0
2
2
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7
1
1
0
0
0
0
0
1
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
1
0
0
2
0
0
0
0
0
0
6
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
1
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
2
1
0
6
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
2
1
0
0
1
0
0
0
0
2
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
1
0
3
2
1
2
0
0
0
1
0
0
2
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
1
5
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
3
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
2
4
0
0
1
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
4
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
2
0
1
2
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
2
2
0
0
0
2
1
1
0
0
0
0
2
3
0
0
0
0
0
0
2
3
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
1
3
2
0
1
5
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
5
0
1
0
2
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
5
0
0
1
1
0
1
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
1
2
2
0
2
0
0
1
0
3
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
2
0
2
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
2
0
0
3
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
1
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
3
0
0
1
0
0
0
0
2
0
0
0
0
2
2
0
1
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
5
0
1
2
0
1
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
2
0
1
4
0
0
2
0
0
0
0
2
1
0
0
1
0
1
1
0
0
0
0
0
7
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
2
1
0
0
0
2
0
1
0
0
0
0
0
5
1
3
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
2
1
0
0
1
2
1
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
5
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
1
2
1
0
0
0
0
6
0
0
0
0
2
0
2
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
8
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
3
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
2
0
2
0
0
2
2
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
3
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
4
2
0
0
3
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
2
1
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
1
1
0
2
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
3
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
1
2
0
0
4
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
1
0
0
2
0
0
0
1
3
0
1
0
0
2
0
0
0
6
2
0
0
0
0
2
0
3
2
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
1
2
1
0
2
2
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
2
0
0
0
5
1
0
0
0
0
2
0
1
0
0
0
0
3
0
1
0
0
2
1
0
1
0
1
0
0
0
0
0
0
1
2
0
1
0
4
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
1
0
0
1
0
1
3
0
0
0
0
2
0
0
0
1
0
1
0
2
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
2
0
0
3
1
1
0
0
0
10
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
2
0
0
0
1
0
0
2
0
1
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
3
0
2
0
0
1
0
0
0
0
0
1
0
2
0
0
1
0
2
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
1
0
0
2
0
0
0
2
1
0
1
1
0
0
2
0
0
0
0
1
2
0
2
0
2
1
0
2
2
2
0
0
0
0
0
0
0
1
0
2
1
0
0
0
2
0
0
0
2
0
1
2
2
0
0
0
0
2
0
0
2
0
0
2
0
1
0
0
1
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
3
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
1
4
1
0
2
0
0
1
1
2
1
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
1
0
0
2
0
0
0
3
0
0
2
0
0
0
0
1
0
0
0
3
0
0
0
0
4
0
0
0
2
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
3
0
1
1
0
3
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
3
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
2
0
2
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
4
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
3
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
1
0
0
2
0
0
2
1
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
3
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
6
1
0
0
0
2
4
0
1
0
1
0
0
0
0
2
0
3
0
0
0
1
1
0
0
0
2
0
3
1
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
1
0
2
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
1
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
1
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
2
1
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
1
0
0
4
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
1
2
2
0
0
1
0
1
0
0
2
1
0
0
0
1
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
1
6
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
2
2
0
0
0
0
2
0
1
0
1
1
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
2
0
0
1
1
0
0
0
6
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
1
2
0
0
5
0
1
0
1
2
0
0
0
0
0
0
0
0
0
4
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
3
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
7
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
1
0
0
3
1
0
2
1
0
0
0
0
0
0
2
0
1
0
0
2
1
0
0
0
0
0
3
0
0
0
1
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
2
0
1
0
0
0
1
0
0
0
1
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
3
2
0
2
1
0
0
1
0
0
2
1
0
0
0
0
0
1
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
2
1
0
0
0
0
0
2
1
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
4
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
6
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
3
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
1
0
0
1
0
0
1
2
1
0
0
0
2
0
0
2
0
0
0
2
1
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
1
0
0
1
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
4
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
2
0
0
2
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
4
0
2
0
1
4
0
0
0
0
2
3
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
2
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
2
0
2
0
0
0
3
0
0
0
0
2
2
0
0
3
0
0
0
4
0
2
0
0
2
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
4
0
1
0
0
0
0
0
0
1
0
0
4
1
0
2
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
1
3
0
1
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
2
1
0
0
0
0
1
0
0
1
1
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
3
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
3
0
1
0
2
0
0
0
0
2
1
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
1
2
0
1
0
2
1
0
1
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
1
0
2
0
0
1
0
0
0
0
1
1
1
2
0
0
0
0
0
0
0
0
4
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
2
1
0
0
1
0
0
2
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
3
1
7
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
2
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
1
0
0
0
0
1
0
0
0
2
0
0
2
2
5
0
0
1
1
1
0
0
0
0
0
1
0
0
0
2
5
1
0
0
0
1
1
0
0
0
0
0
2
1
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
2
0
2
0
0
2
0
0
0
0
1
0
0
3
0
0
0
0
4
0
0
0
0
2
3
0
0
1
1
0
0
0
2
0
4
0
1
1
1
0
1
0
0
0
0
0
1
0
0
0
0
1
3
0
0
0
0
2
1
0
0
1
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
2
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
3
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
2
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
5
1
0
0
1
0
0
1
1
0
0
0
3
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
1
0
0
2
0
0
2
0
0
3
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
1
7
2
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
2
1
1
2
0
0
2
0
6
0
0
0
0
0
2
3
0
1
0
0
0
0
3
2
0
0
0
0
1
6
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
2
3
0
3
0
0
3
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
3
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
2
0
2
0
0
0
1
0
0
0
0
0
3
0
2
0
1
1
0
2
0
1
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
1
0
2
0
0
0
0
0
0
4
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
2
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
3
2
0
0
1
0
0
0
2
0
0
0
0
0
1
4
0
0
10
2
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
3
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
3
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
1
0
0
2
2
3
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
1
1
0
2
0
2
0
0
0
0
1
0
0
0
0
0
1
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
2
0
1
0
1
0
0
0
0
0
0
5
1
0
0
0
0
1
1
1
0
0
0
0
7
0
0
1
0
0
3
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
10
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
2
0
0
0
0
0
1
1
0
0
0
0
6
2
1
0
0
0
0
0
0
0
0
0
5
1
0
2
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
2
0
2
0
0
1
0
2
0
0
0
0
2
1
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
2
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
1
0
1
1
0
2
1
0
0
1
0
0
0
0
1
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
1
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
2
0
1
1
0
0
0
2
1
0
0
0
1
0
1
1
0
1
0
0
0
3
0
0
0
0
3
0
0
0
0
0
4
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
3
0
4
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
3
0
0
1
1
0
0
0
2
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
3
1
2
2
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
1
0
1
1
0
0
2
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
2
1
1
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
3
0
0
0
2
2
0
0
0
0
0
0
0
0
1
1
2
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
5
0
2
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
4
0
0
0
0
1
0
0
0
0
1
0
0
3
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
2
0
0
2
0
0
2
0
2
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
1
3
0
0
0
0
0
0
0
0
0
2
0
5
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
4
2
0
0
0
1
0
2
0
0
5
2
1
0
0
0
0
0
0
0
2
0
2
2
0
2
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
1
1
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
1
1
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
2
0
1
2
0
0
1
0
0
0
0
0
0
0
1
2
1
1
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
1
5
0
0
2
0
0
0
0
0
1
0
1
1
0
0
0
0
2
0
1
0
0
0
2
0
0
0
1
0
1
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
3
1
0
0
0
0
1
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
2
1
0
2
0
0
1
0
0
2
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
3
2
0
0
0
0
0
0
3
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
6
0
0
0
2
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
2
1
9
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
1
2
0
0
0
2
0
0
0
0
1
2
0
0
2
0
0
0
2
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
7
0
0
0
0
0
0
1
0
1
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
2
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
3
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
3
2
0
0
0
0
0
5
0
0
0
1
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
4
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
1
0
1
0
2
0
2
0
0
2
0
0
0
0
5
0
0
1
0
1
0
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
4
0
0
0
2
0
1
0
1
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
2
0
1
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
1
1
1
0
0
0
1
0
0
1
0
0
2
0
0
0
1
1
0
1
2
0
0
0
0
0
1
3
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
1
0
0
1
0
35
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
1
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
5
0
0
0
0
1
0
5
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
2
0
0
5
0
0
0
2
2
0
0
0
0
0
0
2
2
0
1
2
0
0
0
1
0
0
2
0
0
0
0
0
3
1
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
1
2
0
0
0
0
2
0
0
1
0
0
3
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
2
2
2
0
0
1
0
0
0
4
0
0
0
0
1
0
1
3
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
7
2
1
2
0
2
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
2
0
1
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
1
4
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
3
1
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
2
1
0
0
2
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
1
3
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
2
2
1
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
3
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
1
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
3
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
3
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
3
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
3
1
0
0
1
0
0
0
3
0
0
1
0
0
0
1
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
1
1
0
0
0
0
4
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
2
1
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
3
0
2
0
0
0
3
0
2
0
1
0
0
5
0
0
0
0
0
0
0
0
1
0
2
1
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
2
2
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
2
0
0
2
2
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
6
1
1
0
0
0
0
0
0
0
0
1
1
0
0
1
2
0
2
0
0
0
3
0
0
0
0
0
0
0
2
6
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
1
2
1
1
0
0
0
0
2
0
0
0
0
1
8
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
2
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
4
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
2
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
2
0
0
0
0
0
0
0
3
0
0
0
0
3
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
2
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
2
1
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
2
3
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
3
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
1
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
3
2
0
0
2
0
1
0
0
0
0
2
0
0
3
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
3
0
2
1
2
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
2
0
0
0
0
1
0
0
0
0
2
0
1
1
1
0
0
0
0
0
0
2
0
1
0
0
0
1
3
0
0
2
0
0
0
0
0
3
2
2
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
5
0
1
0
3
0
3
0
0
1
0
0
0
0
0
1
2
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
1
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
1
0
1
1
0
2
2
3
0
0
0
0
0
0
3
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
3
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
2
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
2
1
0
1
0
1
0
3
0
0
0
0
0
7
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
3
0
0
2
0
0
0
0
1
0
1
1
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
5
2
2
0
0
0
0
0
0
0
0
0
3
1
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
5
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
3
2
0
0
2
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
4
0
2
0
0
0
0
0
0
0
0
0
15
0
0
1
1
1
0
0
0
0
0
0
0
2
0
0
2
0
0
1
2
0
1
3
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
5
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
2
0
0
0
0
0
0
0
0
0
0
0
0
5
0
1
0
1
3
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
2
0
2
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
1
2
0
2
0
0
0
1
1
0
0
3
0
0
0
0
0
0
1
2
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
1
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
3
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
1
1
0
0
0
1
2
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
3
0
0
3
0
2
1
0
0
0
2
0
1
1
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
2
0
0
0
3
0
0
0
2
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
3
1
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
2
2
1
0
1
0
0
0
0
1
2
3
0
0
0
0
1
0
0
0
0
2
0
0
1
1
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
3
2
4
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
3
5
0
0
0
2
0
0
6
0
6
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
2
1
0
0
0
2
0
0
1
0
0
0
0
0
5
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
1
1
3
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
4
0
2
0
0
1
2
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
1
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
2
0
0
0
0
1
0
1
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
1
4
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
1
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
1
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
1
0
1
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
1
9
0
0
1
1
0
0
0
0
0
2
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
1
2
1
0
0
0
1
0
0
0
0
3
0
1
0
0
1
1
0
1
0
0
8
0
0
1
2
0
2
0
0
0
2
0
1
2
0
2
0
1
0
0
0
3
1
4
0
0
0
0
0
3
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
1
0
0
1
0
0
1
0
0
2
2
0
1
0
0
0
0
0
0
0
2
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
3
1
0
0
1
3
0
0
0
0
0
0
0
0
2
0
0
0
0
2
4
0
0
0
2
0
1
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
2
5
0
0
0
0
0
0
0
2
0
0
1
1
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
1
6
2
3
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
4
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
3
1
0
0
0
0
2
0
0
0
0
2
0
0
1
0
2
0
2
0
0
0
3
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
2
2
2
0
0
1
0
0
0
5
0
0
3
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
7
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
4
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
1
0
0
0
1
0
0
0
1
1
2
0
0
0
7
0
8
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
8
0
0
0
1
0
0
0
0
1
0
0
2
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
7
1
1
0
0
0
0
0
0
0
2
0
3
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
5
5
0
0
0
0
2
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
7
0
0
0
0
2
0
1
0
5
0
0
0
2
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
1
2
2
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
3
0
2
0
0
0
0
0
2
0
2
1
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
1
1
0
0
2
0
0
1
0
0
0
1
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
1
1
0
0
0
0
0
0
0
1
1
0
1
2
1
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
4
0
2
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
2
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
6
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
2
0
1
0
0
1
0
0
2
0
0
0
0
2
0
0
1
1
2
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
5
2
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
2
2
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
1
3
0
0
0
2
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
2
0
2
0
2
0
2
0
0
0
0
0
0
1
1
2
0
0
2
0
0
0
0
0
0
2
0
0
0
1
2
0
0
2
0
2
1
1
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
1
0
0
0
0
3
0
0
2
0
0
2
0
1
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
6
0
0
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
1
0
2
3
0
0
1
0
2
1
2
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
1
3
0
0
2
0
1
0
1
2
0
0
0
1
0
0
2
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
1
3
0
0
2
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
3
0
0
0
1
2
0
1
0
0
0
0
1
0
1
0
1
2
1
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
2
0
0
3
2
0
0
2
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
1
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
2
3
0
2
2
0
0
0
0
1
0
0
2
0
0
0
2
1
2
2
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
2
1
1
0
1
0
2
2
0
0
2
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
2
0
2
1
0
0
0
1
2
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
2
1
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
2
0
0
0
2
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
2
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
1
0
1
1
0
1
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
4
0
0
1
0
1
0
0
0
1
0
0
1
0
2
0
0
0
0
0
1
0
2
0
1
2
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
1
1
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
3
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
3
0
0
0
1
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
2
0
2
0
0
0
0
0
0
0
1
0
0
3
0
0
0
2
2
2
0
0
2
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
1
2
0
1
0
0
0
0
0
4
0
0
2
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
10
2
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
1
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
13
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
2
2
2
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
1
0
2
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
1
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
1
0
0
0
0
1
0
0
0
2
0
0
3
0
0
2
0
0
0
0
1
0
0
1
1
2
0
1
0
1
2
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
2
1
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
2
1
1
0
1
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
2
1
15
1
3
0
1
1
0
0
0
8
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
2
0
1
0
0
2
0
0
0
0
4
2
1
1
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
3
1
0
0
0
1
0
2
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
1
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
4
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
2
1
1
1
0
0
0
0
1
0
0
1
2
0
0
0
1
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
4
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
1
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
3
0
0
0
0
1
0
0
2
1
0
0
0
0
0
3
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
2
0
1
0
0
1
0
2
1
0
0
0
1
2
0
0
0
1
2
2
2
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
1
0
1
2
0
2
0
0
0
2
0
0
0
1
2
0
0
0
0
2
0
0
0
1
2
0
4
0
1
2
0
0
0
1
2
0
0
0
0
0
0
2
0
1
0
0
2
0
1
0
1
0
0
0
2
2
0
0
0
0
0
1
0
0
1
3
0
0
0
0
0
0
0
1
0
1
3
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
1
0
1
0
0
4
0
1
0
0
0
0
0
2
0
2
0
0
2
2
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
3
0
0
0
1
0
2
0
0
0
0
0
0
1
0
1
3
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
6
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
1
0
0
1
1
2
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
2
0
0
4
0
0
1
5
2
0
2
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
3
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
2
3
1
0
2
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
1
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
2
3
0
0
0
0
5
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
8
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
1
1
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
1
0
0
0
0
2
0
1
0
4
0
0
2
0
0
0
0
0
0
1
0
0
1
2
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
2
2
1
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
2
2
1
2
0
0
0
0
1
0
1
0
4
3
0
0
0
0
0
2
0
1
0
0
0
0
0
7
1
0
4
0
0
0
0
0
2
0
0
0
2
0
4
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
1
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
2
0
0
1
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
1
0
0
2
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
3
0
1
0
0
0
0
0
1
0
1
2
0
2
0
1
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
4
2
2
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
1
0
2
0
1
1
0
0
2
1
0
0
0
2
1
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
1
3
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
3
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
4
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
1
0
0
0
1
0
3
0
0
0
0
0
1
2
0
0
0
0
0
0
2
2
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
2
0
0
0
0
2
0
0
2
0
1
0
0
1
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
2
2
0
0
1
1
0
0
1
2
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
4
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
5
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
1
2
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
3
1
0
2
1
0
0
0
1
2
0
0
1
0
5
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
2
0
3
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
2
1
0
0
0
6
0
3
0
0
0
0
0
2
4
7
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
4
0
0
0
2
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
1
1
0
3
1
0
2
2
0
0
0
2
1
2
0
0
0
0
1
1
0
0
2
0
3
0
1
0
0
0
0
0
2
0
5
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
2
0
0
0
2
0
2
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
2
0
0
2
0
1
2
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
1
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
1
0
0
2
1
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
2
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
1
0
0
0
1
0
0
0
0
1
0
1
1
0
3
0
0
0
0
2
2
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
1
0
1
3
0
0
1
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
5
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
1
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
2
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
2
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
2
0
3
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
3
0
0
0
0
3
0
1
0
0
2
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
1
0
0
0
3
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
4
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
6
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
2
1
0
0
2
0
0
0
0
1
0
2
2
2
0
0
0
1
0
0
2
0
0
2
0
2
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
6
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
5
0
0
0
0
0
5
0
0
0
0
0
3
1
0
0
0
0
0
0
5
0
2
0
0
2
0
0
0
0
5
1
0
1
5
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
3
0
0
0
8
2
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
7
0
1
2
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
1
0
0
1
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
5
0
0
4
2
0
2
2
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
3
6
0
0
1
1
0
0
0
1
0
0
0
2
0
0
0
0
0
2
2
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
5
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
1
1
0
0
0
0
0
1
0
2
0
2
0
3
0
0
0
1
0
0
0
0
3
0
2
1
4
0
0
0
0
0
0
5
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
2
0
2
4
0
0
0
0
0
0
0
0
0
2
0
10
0
6
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
3
0
2
2
0
4
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
3
0
1
0
2
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
3
0
1
2
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
5
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
6
1
0
0
0
0
0
0
0
0
1
2
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
4
0
1
0
0
2
2
0
0
1
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
3
0
2
0
0
0
0
0
0
0
0
0
1
0
3
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
1
0
0
0
0
1
3
0
1
1
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
2
7
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
3
0
1
2
0
0
2
0
0
0
0
0
0
1
0
0
0
5
0
0
2
0
0
0
1
0
0
0
0
1
0
0
2
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
1
3
0
0
0
0
0
2
0
0
0
0
1
2
2
0
0
0
0
2
0
0
0
0
2
1
2
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
2
0
4
0
0
1
0
2
0
3
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
5
0
0
0
0
2
0
0
0
0
0
0
2
3
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
3
0
0
1
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
2
0
2
0
0
0
9
0
0
0
0
0
0
0
3
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
2
0
0
2
1
0
2
0
0
2
0
0
0
0
1
0
2
0
0
2
0
0
0
2
0
0
1
2
0
0
0
0
0
1
0
2
0
0
0
0
1
0
1
0
0
0
1
0
4
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
3
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
2
0
0
0
2
0
3
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
2
1
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
2
0
0
0
1
0
0
0
2
1
0
0
2
0
0
0
0
0
2
2
0
1
0
0
0
1
0
0
0
0
0
1
0
0
3
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
9
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
9
2
0
0
0
1
0
0
1
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
2
1
4
0
0
0
0
0
0
1
0
5
0
0
0
1
3
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
2
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
1
1
0
1
0
2
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
3
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
4
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
6
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
2
4
0
1
4
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
3
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
12
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
2
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
4
0
0
0
1
0
0
0
0
0
2
0
2
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
3
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
4
0
0
0
0
0
3
0
0
0
1
0
0
2
4
0
0
0
0
0
3
2
1
2
0
0
3
0
5
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
2
0
2
0
0
1
0
0
1
2
0
0
1
0
0
0
1
0
2
0
0
2
0
0
0
0
2
1
0
0
1
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
1
1
2
1
1
0
0
0
0
2
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
8
2
3
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
6
0
2
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
3
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
1
0
2
2
0
0
0
1
0
0
1
2
0
0
0
0
1
0
5
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
5
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
2
0
1
3
0
3
0
0
1
2
0
0
1
0
0
0
2
0
0
0
0
2
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
1
0
1
0
0
0
4
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
2
0
0
8
0
0
1
0
0
0
0
0
1
2
4
0
0
2
2
0
0
2
0
0
1
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
1
0
0
2
1
0
1
0
1
0
1
0
1
2
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
1
0
1
0
2
0
0
0
0
0
0
1
1
2
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
1
0
3
0
0
0
1
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
1
2
0
0
0
0
0
2
0
0
0
0
3
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
2
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
2
0
0
0
0
0
1
0
0
1
7
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
1
4
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
1
1
0
0
0
0
5
0
0
0
3
2
1
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
1
0
0
2
0
1
0
0
0
2
0
0
0
0
0
1
1
0
3
2
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
2
0
3
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
1
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
2
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
1
3
0
0
0
0
0
0
2
3
0
0
0
0
0
4
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
3
0
6
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
1
0
2
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
1
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
4
0
0
2
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
2
2
0
0
0
2
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
1
0
2
2
2
0
0
0
1
0
2
0
0
0
2
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
2
0
2
0
0
0
1
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
8
2
0
0
1
1
1
1
3
0
0
3
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
4
0
1
3
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
1
1
0
0
2
0
0
0
0
0
2
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
4
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
4
0
1
0
0
0
0
1
1
1
1
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
2
0
0
2
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
3
0
8
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
4
0
0
2
0
0
0
0
0
0
0
0
0
6
1
0
1
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
4
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
2
0
2
0
0
1
1
2
0
0
1
0
0
0
7
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
3
0
0
0
0
1
0
0
2
1
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
6
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
3
0
0
1
0
1
0
0
1
0
2
1
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
3
0
0
1
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
3
0
0
1
0
0
0
5
1
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
1
0
0
0
8
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
8
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
4
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
1
1
1
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
10
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
5
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
2
6
1
0
0
0
0
1
0
0
0
1
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
7
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
1
1
0
0
1
0
2
0
2
0
0
1
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
1
0
1
0
1
0
0
0
0
0
0
2
0
0
2
1
0
0
0
1
0
3
0
2
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
2
0
0
0
0
2
4
0
0
0
0
1
0
1
0
0
2
0
0
0
2
0
0
0
0
2
1
0
0
0
1
0
0
0
0
3
0
2
0
0
0
0
0
0
1
0
1
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
1
2
0
1
0
0
0
1
0
0
2
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
2
0
0
2
3
2
3
0
1
0
0
0
0
2
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
1
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
7
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
2
0
0
0
0
0
0
0
3
5
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
3
0
1
0
0
1
1
1
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
1
0
0
0
2
1
0
0
0
1
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
3
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
3
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
4
0
1
1
1
3
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
1
0
0
3
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
8
3
0
0
2
1
0
4
1
0
0
2
2
0
0
0
0
0
2
0
1
0
0
0
1
4
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
8
1
2
0
0
0
0
0
0
0
5
2
0
6
1
2
1
0
1
1
0
0
0
1
4
0
0
0
0
1
0
1
0
0
1
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
1
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
3
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
3
0
2
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
7
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
3
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
3
0
0
5
2
2
0
0
9
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
1
2
0
1
0
1
0
0
4
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
3
1
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
3
0
0
0
0
2
2
0
0
2
0
0
2
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
5
1
2
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
1
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
9
0
0
1
1
0
1
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
1
0
0
2
0
1
0
0
0
0
1
0
0
0
1
0
0
0
2
2
1
2
0
0
0
0
1
0
0
0
1
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
1
2
1
0
0
0
0
0
0
0
3
0
0
0
0
3
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
1
0
0
1
0
2
0
0
2
1
0
0
0
0
0
0
1
1
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
1
2
0
1
6
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
1
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
3
1
0
0
1
0
0
0
0
0
1
1
0
0
3
0
0
1
4
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
1
2
2
1
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
2
2
3
0
0
1
2
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
4
0
0
0
2
0
1
0
1
0
0
0
2
0
1
2
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
1
0
0
0
6
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
3
3
0
0
0
1
0
0
2
0
0
3
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
2
0
4
3
2
0
0
0
0
0
0
0
0
0
0
1
1
1
2
0
0
0
0
0
2
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
3
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
1
0
1
0
0
0
0
3
0
0
2
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
1
1
0
1
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
2
0
0
2
2
0
0
0
0
0
0
2
0
2
2
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
1
0
0
5
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
1
2
2
1
0
0
0
3
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
1
3
0
2
0
0
0
0
1
0
2
0
0
1
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
10
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
1
0
6
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
3
0
0
0
0
0
1
0
3
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
3
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
7
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
1
0
1
0
0
0
1
0
2
0
3
5
1
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
1
3
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
1
0
0
0
0
1
2
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
1
2
1
2
1
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
1
1
0
0
0
1
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
1
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
2
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
3
1
2
0
2
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
2
0
4
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
1
5
0
1
0
0
2
0
0
0
0
2
1
0
2
0
0
2
0
2
0
2
0
0
0
0
1
0
0
2
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
3
3
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
1
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
1
0
1
2
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
1
0
0
1
0
0
0
1
6
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
2
0
3
0
0
0
0
0
0
0
1
0
1
1
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
3
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
6
0
0
1
2
1
2
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
1
0
2
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
2
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
3
0
6
0
2
0
1
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
2
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
4
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
1
0
0
0
0
0
0
3
0
0
2
0
0
1
2
0
0
0
0
0
0
4
0
3
0
0
0
0
0
0
3
0
2
1
0
0
3
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
1
0
2
2
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
2
0
2
0
0
2
0
1
2
0
0
1
0
0
0
3
0
0
0
0
0
0
0
3
11
2
1
2
1
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
1
1
0
2
0
0
0
3
0
0
0
0
7
2
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
1
1
0
0
1
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
1
0
0
2
1
0
0
3
0
0
0
0
2
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
3
1
2
1
0
0
0
0
9
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
3
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
3
1
0
2
0
0
0
1
0
1
0
0
0
0
0
0
1
0
2
1
0
0
0
0
2
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
4
0
1
1
0
0
0
2
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
2
1
0
0
0
0
2
4
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
3
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
8
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
2
0
1
4
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
2
1
1
0
1
1
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
7
0
1
0
0
0
0
1
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
1
0
1
0
1
4
0
2
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
2
1
0
0
2
0
3
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
3
1
4
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
2
1
0
0
0
0
1
1
1
0
3
3
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
2
2
0
0
0
0
0
1
0
0
0
0
3
0
1
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
4
0
0
0
3
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
1
0
1
0
1
0
1
0
3
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
2
0
1
0
0
5
0
0
0
0
1
0
0
3
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
2
10
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
1
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
1
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
2
0
0
0
2
2
1
0
0
0
0
2
1
0
0
0
0
1
3
0
1
2
1
0
0
0
0
1
0
1
0
3
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
1
2
0
1
0
0
0
0
2
0
4
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
2
0
2
0
0
0
0
2
0
0
1
1
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
4
0
0
0
0
0
0
3
2
0
0
1
2
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
3
0
1
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
5
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
7
1
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
3
1
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
3
0
2
1
0
1
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
2
0
1
2
1
0
2
0
1
0
1
0
3
0
0
0
2
1
2
0
0
0
0
0
0
0
2
1
0
0
1
0
0
4
0
0
0
1
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
2
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
8
0
2
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
1
0
2
0
0
4
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
8
0
0
1
1
0
0
1
0
7
0
0
4
0
0
3
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
3
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
3
0
0
2
0
1
4
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
3
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
4
0
0
2
0
4
0
0
1
4
2
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
1
0
1
0
0
5
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
1
0
0
0
0
4
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
2
5
0
0
0
0
2
0
0
0
0
1
0
1
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
3
0
0
0
2
0
0
2
0
0
0
0
0
2
3
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
5
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
2
1
1
2
1
0
0
2
0
0
6
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
1
1
2
0
0
1
0
2
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
2
0
0
0
2
0
0
1
0
0
2
4
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
2
0
0
0
0
0
2
0
5
0
2
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
7
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
3
0
1
0
3
0
0
0
0
2
0
0
0
3
2
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
1
1
1
2
0
0
0
0
2
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
2
0
0
0
0
0
0
0
0
3
1
0
2
0
0
0
1
1
0
0
0
0
1
0
0
0
0
2
2
1
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
2
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
1
0
2
0
1
0
2
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
1
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
1
2
0
0
2
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
1
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
3
2
1
0
0
0
1
0
1
2
1
2
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
1
0
2
0
1
0
2
0
0
2
0
0
0
2
0
0
1
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
1
1
0
3
6
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
2
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
6
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
2
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
1
1
1
0
2
2
0
1
0
4
0
0
0
0
0
0
2
0
0
4
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
5
4
3
0
0
0
2
2
0
0
0
3
1
0
2
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
1
0
2
2
0
0
0
3
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
3
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
1
0
0
1
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
2
3
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
4
0
0
0
1
0
5
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
1
1
2
0
1
0
0
0
0
0
1
0
0
0
0
1
1
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
1
0
0
0
0
0
1
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
1
3
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
2
0
0
1
0
0
0
0
2
3
0
0
0
0
1
0
1
0
1
0
1
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
1
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
1
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
1
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
1
3
0
1
0
0
0
0
0
0
1
0
0
0
0
0
4
2
0
0
1
0
0
1
0
0
1
1
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
3
0
0
0
1
0
0
0
2
1
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
3
1
0
0
0
0
1
0
0
0
2
2
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
4
0
0
0
0
3
0
2
3
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
2
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
2
2
0
0
4
0
0
0
0
1
0
0
4
0
0
3
0
0
0
0
2
0
4
1
0
0
0
0
0
1
2
0
2
0
1
0
0
0
2
0
2
0
1
1
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
4
1
0
0
0
0
0
2
0
1
0
0
0
2
0
0
1
0
0
3
0
0
0
0
0
0
0
1
1
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
2
0
2
2
0
0
0
0
4
1
1
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
5
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
2
0
0
0
1
0
0
0
1
0
0
3
0
0
2
0
0
1
0
0
3
4
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
2
0
3
3
1
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
1
1
0
0
0
0
0
0
0
1
0
2
0
1
1
0
0
0
0
0
2
3
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
11
2
0
0
0
0
0
0
4
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
1
0
0
0
3
0
2
0
0
0
0
1
2
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
2
1
0
0
2
0
0
0
1
0
1
4
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
1
2
1
0
0
0
0
0
3
0
0
0
1
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
1
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
8
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
1
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
4
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
1
1
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
1
1
2
0
0
1
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
3
0
1
1
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
2
4
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
1
0
0
0
0
6
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
2
3
2
2
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
1
0
1
0
0
1
1
0
0
1
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
1
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
3
0
0
0
1
2
0
0
0
0
0
3
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
3
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
1
0
0
0
0
7
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
1
0
0
2
0
0
2
0
1
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
1
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
3
1
0
2
0
0
0
0
5
6
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
3
0
1
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
1
0
0
0
0
1
2
0
0
0
2
0
0
0
3
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
2
0
1
0
0
0
2
0
0
1
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
1
0
0
0
0
1
0
1
0
2
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
7
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
2
0
1
0
0
0
1
0
0
0
0
0
0
1
1
3
0
0
0
1
2
0
0
0
0
2
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
6
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
1
0
4
1
0
1
0
1
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
2
2
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
1
0
3
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
2
0
0
0
1
0
0
1
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
2
0
0
2
2
0
0
3
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
2
0
1
1
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
2
0
1
1
0
2
2
0
0
0
0
0
2
0
4
4
0
1
0
0
0
0
0
0
1
4
1
3
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
8
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
2
2
0
1
0
8
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
2
4
1
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
10
0
0
1
2
0
0
0
0
0
1
0
1
0
0
0
1
0
0
2
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
2
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
4
0
0
0
0
2
0
0
0
2
0
1
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
3
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
2
0
0
0
0
2
0
4
0
1
0
0
0
0
3
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
5
0
0
2
1
1
3
2
0
0
1
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
9
0
0
0
0
0
0
0
0
0
2
0
0
0
5
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
1
1
3
1
0
0
0
0
0
1
0
2
0
0
1
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
2
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
1
3
0
0
2
0
0
0
0
0
1
0
0
0
0
0
4
1
0
0
0
0
0
0
2
1
0
0
0
0
0
6
0
1
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
4
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
2
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
2
0
0
0
0
4
0
0
0
0
2
2
0
2
2
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
2
0
0
0
0
0
0
4
0
0
0
1
1
2
1
0
0
2
2
2
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
6
3
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
4
0
2
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
5
0
0
0
2
13
1
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
1
2
0
0
0
0
0
0
0
2
2
2
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
2
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
2
0
0
0
0
1
2
0
0
0
0
2
3
0
1
1
0
3
0
1
0
0
0
2
0
0
0
0
0
0
0
5
1
0
0
2
2
0
0
1
0
0
0
0
0
0
1
3
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
12
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
3
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
2
3
1
0
1
0
1
1
0
0
0
0
0
2
1
0
0
0
0
3
0
0
0
0
1
0
0
3
2
0
2
0
0
0
0
1
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
1
2
0
0
4
0
0
0
1
0
3
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
2
3
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
1
1
0
0
0
1
0
0
0
0
1
0
4
1
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
1
5
0
0
0
0
0
0
2
0
8
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
5
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
1
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
2
0
1
0
0
0
0
2
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
3
0
1
0
0
0
0
0
0
0
0
0
3
0
0
2
1
0
1
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
1
2
0
0
0
0
0
0
1
2
1
1
2
0
0
0
3
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
1
1
3
2
0
1
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
3
2
0
2
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
1
0
2
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
5
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
2
2
2
0
0
0
1
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
2
2
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
2
2
2
0
2
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
3
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
1
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
3
2
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
4
1
2
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
4
0
2
2
0
0
1
0
0
0
0
0
4
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
4
0
0
0
0
0
0
2
0
0
0
0
0
0
0
11
0
1
0
0
0
1
0
0
0
0
0
1
0
0
2
2
0
0
5
0
0
0
0
2
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
5
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
2
2
2
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
1
0
2
0
0
0
0
3
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
5
2
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
2
1
2
0
0
0
0
1
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
8
0
0
1
0
0
0
4
0
0
0
0
0
2
1
2
0
0
1
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
2
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
3
1
0
2
0
0
0
2
0
1
0
0
4
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
1
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
4
1
2
0
0
1
0
0
2
0
0
2
0
0
0
0
9
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
2
1
2
0
0
0
1
0
1
2
0
0
0
1
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
1
0
3
0
0
0
2
0
0
0
0
0
1
0
0
0
4
0
5
1
0
0
2
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
5
0
0
0
1
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
5
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
2
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
1
0
2
0
0
0
1
1
0
0
2
0
1
0
0
1
1
0
0
0
0
0
0
1
1
0
3
0
0
0
0
0
0
0
0
1
0
0
0
3
0
2
0
0
0
0
4
1
0
0
1
0
0
1
0
0
2
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
3
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
3
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
3
0
0
0
0
1
1
2
0
1
0
0
0
0
4
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
4
1
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
1
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
1
0
1
3
1
0
0
3
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
5
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
2
2
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
3
0
0
1
0
0
3
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
5
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
2
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
3
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
4
2
2
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
3
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
3
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
2
0
0
0
2
2
0
1
0
0
5
0
0
1
0
0
0
0
0
0
2
0
2
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
1
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
2
2
0
1
0
0
1
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
1
4
0
7
0
0
0
0
0
0
0
2
0
0
0
5
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
2
4
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
1
0
3
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
2
2
1
1
0
1
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
4
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
2
0
0
2
2
0
0
3
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
2
2
0
2
1
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
2
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
3
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
2
0
2
0
0
0
3
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
2
3
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
4
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
2
1
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
2
0
0
3
0
0
0
1
0
0
3
0
0
0
0
3
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
3
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
3
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
1
1
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
7
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
3
0
0
1
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
2
0
0
0
1
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
8
6
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
5
0
0
0
0
0
0
4
0
0
2
0
0
0
2
0
0
0
0
1
0
1
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
9
0
2
0
0
1
0
2
0
0
2
2
1
0
0
0
2
0
0
0
0
0
0
3
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
3
0
0
2
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
1
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
2
1
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
1
0
0
0
5
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
2
1
1
0
0
3
0
2
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
3
1
0
1
0
0
0
0
1
0
5
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
1
0
1
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
1
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
6
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
5
0
1
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
2
0
4
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
1
1
4
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
1
1
0
0
0
2
0
2
0
0
0
3
0
2
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
1
0
1
0
0
2
0
0
0
3
2
1
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
3
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
2
1
0
3
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
1
0
0
0
0
0
1
2
0
1
0
0
0
0
2
1
2
2
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
1
0
0
0
0
0
0
0
1
5
0
0
5
0
0
1
1
2
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
3
1
0
3
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
8
1
2
2
0
2
1
0
2
6
1
0
0
2
2
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
1
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
3
0
6
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
1
0
0
1
3
0
0
4
0
2
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
5
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
3
0
0
2
2
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
3
0
0
0
0
0
1
0
3
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
2
0
0
0
0
0
3
0
0
0
0
1
2
2
0
0
1
0
1
1
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
2
0
3
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
2
0
1
1
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
2
1
0
1
0
0
0
3
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
2
1
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
1
1
0
0
0
0
0
0
0
1
0
1
2
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
3
0
1
1
0
0
1
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
5
0
2
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
1
0
2
2
1
0
0
2
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
2
0
1
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
2
0
0
1
1
2
0
0
1
0
4
0
0
0
0
1
0
0
0
0
1
0
1
4
0
2
0
0
3
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
4
1
2
0
2
0
7
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
6
0
0
0
0
2
0
5
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
3
2
1
0
0
1
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
2
0
0
0
2
0
0
2
0
0
0
2
4
0
0
0
2
1
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
1
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
2
1
0
2
1
0
0
0
0
0
0
0
3
3
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
3
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
2
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
4
2
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
1
0
1
0
1
0
0
0
0
0
2
0
0
0
0
2
6
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
1
0
3
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
2
0
0
2
0
0
0
4
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
1
3
0
0
0
0
6
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
4
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
5
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
1
2
11
0
0
0
0
0
0
1
0
0
0
0
0
0
3
3
0
1
2
2
0
0
0
0
3
0
0
1
0
0
0
0
6
0
2
0
1
0
0
0
0
0
1
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
2
0
0
1
0
0
0
3
0
0
0
3
0
0
0
0
0
2
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
1
2
4
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
3
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
2
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
2
0
2
1
0
0
0
3
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
3
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
3
0
2
0
2
0
2
0
0
0
2
0
0
0
0
0
0
1
1
0
0
2
0
0
1
0
0
2
1
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
2
2
0
1
0
0
1
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
3
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
3
0
0
0
0
0
1
3
0
0
0
0
2
0
0
0
4
0
0
4
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
1
1
0
0
0
0
0
0
2
1
0
2
1
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
2
0
2
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
3
0
1
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
4
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
1
1
0
2
0
1
0
3
0
0
0
7
0
0
0
3
0
0
0
0
1
0
0
0
1
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
2
0
0
2
0
0
0
0
0
0
3
0
2
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
2
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
3
1
0
0
3
0
1
0
0
4
0
0
0
0
0
0
2
1
2
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
6
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
9
0
0
0
0
1
0
1
0
0
0
2
0
0
5
2
0
0
2
2
0
0
0
8
0
0
1
1
0
0
0
0
0
3
2
1
0
0
0
2
1
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
1
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
2
0
1
1
0
0
2
0
2
0
0
3
0
0
2
2
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
3
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
10
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
14
0
0
0
1
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
2
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
3
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
7
0
0
1
0
2
1
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
2
3
2
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
1
0
0
0
0
0
3
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
1
0
0
0
0
0
2
0
0
0
1
0
3
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
1
0
0
0
6
1
0
0
0
1
0
0
0
0
2
1
0
1
1
0
1
0
0
2
1
5
2
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
2
0
3
0
0
0
0
0
0
0
2
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
1
1
0
0
0
0
0
5
0
0
0
0
0
0
0
0
2
2
0
3
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
2
3
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
1
2
1
0
1
1
0
0
2
2
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
2
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
1
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
2
0
0
1
3
0
0
0
1
2
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
3
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
1
0
0
0
2
0
0
2
2
0
0
1
0
1
1
1
0
0
0
0
0
0
1
0
1
2
0
0
0
0
1
2
0
0
0
1
0
2
0
0
0
2
1
4
0
1
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
1
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
2
0
0
0
6
0
0
0
0
4
2
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
2
1
0
3
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
6
0
0
1
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
2
0
0
0
1
1
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
1
0
2
2
2
0
0
0
0
0
0
0
0
2
1
0
0
0
1
2
0
0
0
0
4
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
2
1
0
1
0
0
1
1
0
0
0
0
0
0
3
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
0
2
2
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
2
1
0
0
1
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
4
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
2
2
0
0
0
0
0
0
0
0
0
3
0
0
1
1
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
1
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
2
0
0
0
3
0
2
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
1
0
0
1
0
0
1
0
0
0
0
1
1
0
0
1
1
0
1
0
2
0
2
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
1
2
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
3
0
0
2
0
1
0
0
4
1
0
0
3
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
2
2
0
0
5
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
6
0
2
2
2
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
2
0
0
2
0
1
0
1
0
0
0
0
1
0
3
1
2
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
1
4
2
0
0
1
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
3
0
0
1
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
2
0
5
0
0
0
0
2
8
1
0
0
0
0
0
0
3
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
2
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
1
0
0
0
0
0
2
0
0
1
0
3
2
0
0
0
0
0
1
0
2
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
2
0
0
0
2
0
0
4
0
1
3
0
0
0
0
0
0
0
3
2
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
2
1
0
1
3
0
0
2
0
3
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
17
0
2
0
2
0
2
1
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
1
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
3
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
1
0
2
2
2
0
3
0
1
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
1
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
1
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
1
0
8
0
0
0
0
3
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
4
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
3
2
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
2
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
2
0
1
0
0
0
3
0
0
1
0
1
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
4
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
3
1
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
4
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
2
1
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
2
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
9
0
0
0
1
2
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
1
2
0
1
0
0
0
4
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
2
1
0
1
2
0
1
0
0
0
0
0
1
1
1
0
0
1
0
3
0
0
0
0
0
0
3
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
1
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
5
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
3
1
0
0
0
2
0
0
0
1
3
2
3
1
2
0
2
0
2
0
1
0
0
0
0
0
0
0
2
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
5
3
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
3
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
3
0
1
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
3
2
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
5
0
0
2
2
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
1
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
5
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
2
2
0
1
27
0
4
2
0
0
0
1
1
2
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
1
1
0
0
0
1
1
0
2
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
1
0
0
0
0
1
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
2
11
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
4
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
4
1
1
2
0
3
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
2
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
3
0
0
2
2
0
0
2
0
0
0
0
0
0
0
2
0
0
1
2
0
1
0
0
1
0
0
0
0
3
0
0
0
0
1
0
3
0
1
0
1
0
0
2
0
0
0
0
2
9
0
0
0
0
1
0
0
2
0
0
0
1
0
0
2
1
0
0
1
0
0
0
0
0
0
2
0
1
2
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
2
1
0
0
0
0
0
2
0
0
0
1
0
1
2
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
3
2
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
1
2
3
0
0
0
2
0
0
0
0
0
3
1
0
2
0
0
0
0
0
2
0
0
0
0
1
0
1
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
1
0
0
4
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
4
0
1
0
4
0
0
0
0
0
2
0
0
0
0
0
0
1
0
3
0
1
0
0
0
0
2
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
1
0
0
1
1
0
0
2
0
0
2
0
0
0
1
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
1
1
0
2
1
0
0
0
1
0
0
0
0
0
0
0
9
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
2
1
1
0
0
0
2
0
0
0
0
0
1
0
5
1
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
1
2
0
2
1
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
3
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
3
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
3
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
2
1
0
1
0
0
1
0
1
0
0
3
2
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
4
0
0
3
0
0
0
1
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
2
0
0
1
0
0
0
1
0
0
0
3
2
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
1
0
2
2
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
4
0
1
0
0
3
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
3
1
0
0
2
0
0
0
0
0
0
4
0
0
2
0
0
0
1
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
2
0
0
3
0
0
0
0
0
0
0
3
0
1
0
0
0
1
0
1
2
2
0
2
0
0
2
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
4
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
7
0
0
0
0
1
0
0
0
0
0
0
0
0
9
2
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
1
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
1
0
0
1
0
2
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
2
0
1
0
0
2
0
0
2
5
0
0
0
0
0
0
0
0
2
5
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
2
0
1
0
1
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
2
0
0
0
1
2
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
7
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
2
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
1
2
2
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
2
0
0
1
2
2
0
0
2
0
0
3
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
1
0
0
0
0
1
0
0
0
0
1
0
1
0
2
2
0
0
0
3
0
0
0
7
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
4
0
0
0
0
1
0
0
0
0
0
0
0
6
0
0
0
1
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
2
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
1
7
0
0
0
2
0
1
0
0
0
4
0
0
0
0
2
0
0
2
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
2
0
0
1
0
0
0
0
0
3
2
1
0
0
2
0
0
0
0
3
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
1
0
1
2
0
0
0
0
0
0
0
1
0
0
2
0
0
3
2
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
3
0
2
0
0
1
0
2
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
2
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
1
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
3
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
5
2
2
0
0
1
0
0
0
0
1
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
2
0
2
0
0
1
0
0
0
0
0
0
0
5
0
0
1
1
0
0
0
0
0
5
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
1
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
6
0
1
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
1
2
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
1
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
2
0
2
1
0
0
0
0
0
2
1
1
0
1
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
6
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
1
0
0
0
1
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
2
2
1
5
0
1
0
0
0
0
1
0
2
0
2
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
3
0
2
0
0
0
0
0
0
0
0
7
1
2
0
2
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
1
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
1
0
1
2
0
0
1
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
2
0
3
0
2
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
2
5
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
1
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
3
0
0
0
0
0
0
0
2
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
6
0
0
2
1
0
0
2
4
0
0
2
0
0
0
0
0
0
1
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
5
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
2
1
0
2
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
2
6
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
5
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
4
1
0
2
0
0
0
0
0
1
0
0
2
2
2
0
0
0
0
0
1
0
4
0
0
1
0
0
2
0
0
0
0
0
0
0
0
3
1
2
0
5
0
0
0
1
2
2
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
3
0
0
2
1
0
1
0
0
0
1
1
0
0
2
1
0
0
0
0
2
0
0
2
0
2
1
0
1
0
0
0
2
0
0
0
2
2
0
0
0
1
2
0
3
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
1
0
1
0
1
0
1
0
1
0
0
0
0
0
2
0
1
1
0
0
0
2
2
0
0
3
1
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
1
0
0
0
3
0
1
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
2
0
1
0
0
0
0
0
1
0
0
2
0
2
1
1
0
0
0
4
1
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
1
2
0
2
0
0
0
0
0
0
2
1
1
0
0
0
0
1
0
0
0
0
2
0
0
1
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
1
1
0
0
2
0
1
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
2
0
0
0
0
1
0
0
7
0
0
0
0
4
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
7
2
0
3
1
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
1
0
1
0
0
1
0
0
1
2
0
0
1
0
2
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
5
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
2
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
1
0
0
2
2
1
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
6
1
0
0
0
1
0
0
0
1
0
0
0
0
4
2
0
2
0
1
0
0
0
3
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
2
0
0
0
3
0
2
1
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
7
0
0
4
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
4
0
0
0
1
0
0
0
0
2
0
2
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
2
3
0
5
0
0
2
0
0
0
0
1
0
0
0
3
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
1
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
2
0
3
1
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
1
2
1
1
0
0
0
0
0
0
0
1
1
0
0
7
2
0
1
0
0
0
3
2
1
0
0
0
1
0
0
1
0
0
0
1
1
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
3
0
0
0
2
2
0
0
1
0
0
0
2
0
0
1
0
0
2
0
1
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
3
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
2
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
7
0
1
1
0
0
0
0
0
1
0
0
0
0
0
3
2
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
2
0
0
0
1
4
0
1
0
2
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
2
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
6
0
0
0
0
2
0
0
0
1
1
2
0
0
2
0
0
2
0
2
2
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
3
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
3
1
0
0
1
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
2
2
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
7
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
2
1
2
0
0
0
1
0
0
1
1
0
1
2
0
0
0
0
0
0
0
2
1
2
0
0
0
1
2
0
4
1
1
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
8
2
0
0
0
1
2
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
1
2
0
4
0
0
0
0
0
0
0
0
0
5
0
0
0
2
0
0
0
0
2
0
0
0
2
0
5
1
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
3
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
2
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
2
0
2
0
0
0
0
3
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
1
0
2
0
0
2
1
0
0
0
0
2
0
0
2
0
0
2
2
0
0
1
0
0
2
0
0
2
0
2
0
0
0
2
2
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
2
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
3
1
0
0
2
0
0
0
0
0
0
2
1
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
1
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
4
1
0
0
7
0
1
2
0
0
0
0
6
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
2
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
2
0
2
0
1
0
1
0
1
0
2
1
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
2
0
0
1
0
2
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
5
0
1
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
2
0
0
2
0
0
4
0
0
0
0
0
0
2
0
0
2
0
4
0
0
0
2
0
0
0
1
0
1
0
5
0
1
2
1
0
0
4
0
0
2
0
1
0
0
0
0
0
0
0
2
0
2
2
0
0
2
0
0
2
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
4
2
0
12
0
1
2
0
0
0
0
1
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
1
0
0
4
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
1
4
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
3
3
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
1
0
2
0
1
0
3
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
1
0
0
1
0
2
1
1
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
7
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
1
0
0
2
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
6
0
0
0
0
0
0
0
0
2
0
0
4
2
0
2
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
2
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
3
0
0
0
2
4
1
0
0
2
0
1
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
3
0
1
0
0
1
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
1
3
1
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
4
1
0
0
2
0
0
2
0
0
0
0
5
0
0
0
1
0
0
0
0
3
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
1
0
0
1
4
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
3
5
0
0
2
0
0
0
0
0
2
0
0
0
0
1
2
1
0
2
0
0
0
0
2
1
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
1
0
0
2
3
4
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
5
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
3
0
0
1
0
0
2
2
1
0
0
0
0
0
0
1
0
1
1
1
0
1
2
1
0
0
0
0
2
0
0
2
0
3
0
0
0
1
0
1
1
2
0
0
5
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
2
4
0
0
0
1
2
0
4
0
0
0
0
0
3
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
2
1
0
1
2
0
1
0
2
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
1
0
0
3
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
2
0
0
0
0
3
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
2
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
2
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
5
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
5
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
2
0
1
0
0
3
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
8
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
6
0
0
0
0
0
0
2
2
0
1
1
2
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
5
0
0
0
1
0
2
2
2
0
0
0
3
2
1
0
0
2
0
0
0
0
0
0
0
5
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
1
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
1
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
2
0
0
0
0
0
0
0
1
2
1
0
0
2
0
0
0
0
3
0
0
0
0
1
0
2
1
2
0
1
1
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
1
1
4
0
1
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
3
0
0
0
1
0
2
0
1
2
0
0
0
0
0
0
1
0
2
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
3
0
2
0
0
0
3
0
0
0
0
1
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
1
1
1
0
2
0
0
0
2
0
0
0
0
0
1
0
0
4
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
1
2
0
0
0
0
3
0
0
4
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
7
0
1
0
1
3
2
2
0
0
0
3
0
0
0
0
2
0
7
0
0
1
0
0
0
0
0
6
0
2
3
0
0
0
0
0
1
2
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
2
0
1
0
0
0
3
0
0
0
0
2
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
2
0
0
0
1
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
1
0
2
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
3
0
3
0
0
0
0
0
1
0
0
2
2
0
0
0
2
0
3
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
10
0
0
0
3
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
2
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
1
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
5
0
2
2
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
1
1
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
1
4
0
0
4
0
0
0
0
2
0
3
0
0
0
0
1
0
1
0
0
0
2
2
0
2
1
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
1
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
1
0
4
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
3
0
0
0
0
0
0
0
0
0
1
2
0
0
1
2
1
0
0
0
0
0
0
1
0
1
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
3
0
0
0
0
0
1
0
0
0
0
0
1
3
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
1
2
0
2
0
0
0
0
1
0
0
0
2
1
2
0
0
0
0
0
2
0
2
0
0
0
3
1
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
4
0
2
0
0
0
0
0
0
0
0
0
2
0
0
4
1
1
1
0
0
0
2
0
0
0
1
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
2
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
2
1
0
0
1
0
0
1
0
1
2
0
0
0
0
1
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
2
1
0
2
1
1
0
0
0
2
0
0
0
0
2
0
1
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
1
0
0
0
1
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
1
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
7
1
0
1
1
1
0
0
2
1
0
0
2
0
0
0
0
0
0
0
1
2
1
0
0
0
2
1
0
0
0
0
0
0
0
2
2
3
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
3
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
5
1
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
5
0
0
0
0
0
1
0
1
0
0
0
3
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
3
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
12
0
2
0
3
2
3
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
1
0
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
4
3
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
3
2
0
6
1
6
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
1
1
0
0
0
0
1
0
5
0
0
1
0
2
0
2
0
2
0
0
0
0
0
3
2
0
0
2
0
0
1
0
0
3
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
1
0
0
0
0
0
3
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
5
0
0
0
0
0
0
2
3
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
3
0
1
0
2
3
0
0
0
0
2
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
3
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
2
0
0
0
0
2
0
0
0
0
1
0
10
0
0
0
0
0
0
7
8
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
1
0
2
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
3
4
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
2
2
2
3
2
2
0
0
0
0
0
1
0
0
1
0
2
0
0
0
3
2
0
0
0
0
0
0
0
2
0
1
0
0
7
0
0
0
6
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
2
2
0
0
0
0
0
1
1
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
1
3
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
2
0
0
0
2
0
0
1
0
1
0
0
0
0
1
4
0
1
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
1
3
0
0
2
2
0
1
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
1
11
0
0
3
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
6
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
2
0
0
0
1
0
0
0
2
0
2
4
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
1
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
3
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
3
2
0
0
0
2
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
2
2
0
0
0
0
0
0
3
0
0
0
1
0
0
1
2
3
2
0
0
2
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
5
0
2
0
0
2
2
1
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
6
0
0
2
0
4
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
5
0
2
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
2
0
0
0
1
0
0
0
1
1
0
0
1
1
7
0
0
0
0
0
2
0
2
2
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
1
0
0
3
0
3
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
4
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
4
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
3
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
1
0
1
2
0
0
0
2
0
0
0
1
0
3
1
1
0
0
0
0
0
0
0
0
1
2
1
4
2
0
0
0
0
0
0
0
0
4
0
2
0
0
0
0
1
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
3
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
2
1
1
0
0
1
3
0
0
0
0
0
0
2
0
0
1
0
3
1
0
0
0
4
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
1
0
0
0
0
2
0
1
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
4
0
0
2
0
0
0
0
0
0
0
3
1
0
0
2
0
0
2
0
4
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
6
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
1
2
0
1
0
0
0
0
0
0
0
1
0
0
1
2
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
2
1
0
0
0
2
0
0
2
1
0
0
0
1
0
0
0
0
0
1
0
0
2
2
0
0
3
0
2
3
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
2
0
3
0
0
0
2
0
0
0
0
6
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
2
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
2
0
0
0
1
2
1
0
1
0
1
0
0
1
0
0
0
2
0
2
0
0
0
2
1
0
0
1
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
1
0
0
2
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
2
0
0
1
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
2
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
1
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
8
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
3
0
2
0
1
0
0
0
0
0
3
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
1
0
2
3
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
1
1
0
0
0
0
6
0
3
0
1
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
5
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
2
0
1
2
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
2
0
0
0
2
0
0
0
2
1
2
1
0
0
1
0
0
1
6
1
0
0
0
0
7
2
2
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
11
1
0
0
0
0
0
0
0
0
0
0
4
2
3
1
0
3
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
1
0
2
0
0
0
1
0
0
1
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
1
0
0
0
1
0
0
0
0
0
2
1
0
0
7
0
0
0
0
0
0
2
0
0
0
0
2
2
1
0
0
0
1
0
1
0
0
0
0
1
4
2
0
1
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
2
1
0
2
1
2
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
4
0
0
1
0
0
0
0
1
0
1
0
0
1
2
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
1
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
1
3
0
0
0
0
0
0
1
2
1
0
0
2
0
2
0
2
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
8
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
1
0
0
0
2
0
0
0
3
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
5
0
0
0
0
1
0
0
1
0
0
0
0
0
9
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
5
0
0
0
0
0
1
0
0
0
3
0
0
0
1
1
0
0
2
0
1
0
0
2
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
9
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
5
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
2
0
4
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
1
0
2
1
0
6
0
0
0
0
0
0
0
3
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
16
2
0
0
0
0
0
0
0
3
2
0
0
2
0
0
0
2
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
3
3
0
1
0
0
4
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
2
0
7
1
0
1
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
4
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
5
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
3
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
6
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
1
3
1
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
1
3
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
1
0
7
0
0
0
0
2
2
0
0
0
0
0
0
1
0
2
1
0
0
0
3
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
2
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
2
0
0
0
2
0
1
0
0
1
0
0
0
2
0
1
2
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
2
1
2
3
0
3
0
0
0
1
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
3
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
1
6
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
2
1
2
0
0
2
0
2
0
0
0
0
0
3
0
0
0
0
0
1
0
0
1
2
0
0
2
1
0
0
3
2
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
2
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
1
2
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
2
1
0
0
0
0
1
2
2
0
0
0
0
0
0
1
0
0
0
1
3
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
5
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
1
0
0
2
2
0
0
2
0
2
0
10
0
0
0
0
0
0
0
2
0
3
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
4
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
2
2
2
2
0
2
2
0
0
0
0
1
0
2
0
0
0
1
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
4
0
2
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
3
0
0
0
3
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
3
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
2
3
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
5
0
0
0
0
0
2
2
1
0
1
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
6
0
0
2
2
0
0
0
0
0
1
0
0
0
0
1
2
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
6
0
0
2
0
0
0
2
0
0
0
0
3
0
0
1
0
2
0
1
0
0
0
0
2
2
0
0
0
2
0
1
0
0
0
1
0
0
1
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
2
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
2
0
1
0
1
0
2
2
0
0
0
1
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
3
0
0
4
1
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
4
0
3
0
0
0
2
0
0
1
0
0
1
2
0
0
3
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
2
0
0
1
2
0
0
0
1
1
0
2
3
1
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
1
2
3
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
2
0
1
0
1
0
0
2
1
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
5
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
4
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
3
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
2
0
1
0
2
0
0
3
0
0
0
0
1
2
0
0
2
1
1
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
5
1
0
0
0
0
0
0
0
0
0
2
0
3
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
3
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
3
0
1
0
0
0
2
1
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
1
0
1
2
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
2
0
0
1
3
0
0
1
1
0
0
0
3
0
1
0
0
0
0
0
2
0
0
0
0
5
0
0
0
0
0
0
0
0
0
2
0
3
1
1
1
0
2
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
3
1
0
0
0
0
0
0
0
0
2
0
0
3
1
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
1
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
4
2
0
0
1
0
2
0
0
0
0
0
2
0
0
2
0
1
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
2
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
2
0
2
0
0
0
0
1
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
1
5
0
1
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
1
2
0
1
0
1
0
0
0
0
4
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
5
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
1
0
0
1
0
3
2
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
1
1
1
0
0
0
0
3
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
2
1
0
2
0
0
0
3
2
0
0
1
0
0
0
0
0
2
0
0
4
3
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
1
0
0
0
2
0
0
0
1
2
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
1
0
0
0
0
1
0
0
1
0
1
1
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
1
0
2
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
2
0
0
0
2
0
0
0
1
0
0
0
2
1
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
1
0
0
0
2
2
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
6
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
3
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
1
0
1
0
2
0
0
0
2
0
2
1
0
0
0
0
1
3
0
1
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
6
0
0
2
0
1
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
3
0
1
1
0
1
0
0
0
0
2
0
0
0
2
0
1
1
1
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
3
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
3
2
3
0
0
1
0
1
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
2
1
0
0
0
0
2
1
0
1
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
3
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
1
1
1
3
3
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
3
0
0
4
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
2
3
1
3
3
0
2
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
2
2
1
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
4
1
0
1
0
0
1
0
0
0
0
0
0
0
0
2
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
12
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
1
0
0
2
0
1
0
0
1
2
0
3
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
2
0
2
2
0
0
0
1
0
1
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
1
3
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
1
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
1
2
2
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
2
1
2
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
2
0
1
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
3
0
3
0
1
0
0
0
0
1
0
0
2
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
1
0
0
2
0
2
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
3
0
0
4
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
2
2
0
0
2
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
2
0
2
1
0
0
0
1
0
0
3
2
2
0
0
0
7
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
1
0
0
4
0
0
0
0
1
0
1
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
3
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
3
0
2
0
0
0
0
1
0
0
1
0
0
10
0
1
3
0
4
1
2
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
1
0
2
0
2
0
0
0
1
0
6
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
2
1
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
1
0
3
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
4
1
0
1
0
2
0
1
1
0
2
0
2
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
1
1
2
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
2
0
0
0
0
1
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
2
0
0
1
0
2
0
3
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
7
1
0
1
0
0
0
0
0
0
1
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
3
0
0
1
0
1
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
2
2
0
1
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
1
1
1
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
2
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
3
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
1
2
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
1
0
2
0
1
3
0
0
0
0
0
0
0
2
0
2
0
0
0
2
3
0
2
2
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
7
0
0
0
0
2
0
0
0
0
1
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
2
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
1
0
1
2
0
0
1
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
2
2
0
3
0
1
2
0
0
0
1
1
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
9
0
0
0
0
0
1
0
0
4
2
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
3
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
1
2
0
4
0
0
2
1
2
1
0
5
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
4
0
0
2
0
2
0
6
0
0
0
0
1
0
0
3
1
0
0
1
0
0
1
2
0
0
0
0
0
2
0
0
1
0
0
1
2
2
0
0
0
0
1
0
0
2
2
2
0
0
0
0
0
2
0
0
0
3
0
0
1
0
0
0
0
2
0
0
2
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
4
0
0
0
0
1
0
1
1
1
1
0
1
0
0
0
0
0
0
0
0
4
2
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
3
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
1
0
0
0
1
0
1
0
2
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
1
5
0
0
2
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
2
0
0
2
0
0
14
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
2
0
0
0
2
0
0
3
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
3
1
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
2
0
2
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
1
1
0
0
2
0
0
1
0
0
0
1
4
0
0
0
0
0
1
4
1
1
0
0
0
0
0
0
3
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
7
0
0
3
0
4
0
0
0
0
2
0
1
0
0
0
0
0
0
0
5
0
0
0
7
0
0
0
0
0
2
2
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
2
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
4
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
2
0
2
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
6
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
3
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
6
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
1
0
0
2
0
0
0
0
2
0
0
4
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
2
1
0
0
0
0
0
0
1
0
1
0
0
1
3
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
7
1
0
0
2
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
1
0
0
1
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
2
1
0
0
0
4
1
0
0
0
0
2
0
0
2
0
0
0
0
3
0
0
0
0
1
0
1
0
0
0
2
2
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
3
0
0
0
0
6
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
2
0
0
2
0
0
2
1
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
3
0
0
0
1
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
4
2
2
1
0
0
0
0
0
0
0
1
0
0
2
1
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
3
0
0
1
1
0
6
0
2
0
0
0
0
0
1
0
0
0
1
4
0
0
0
0
0
0
1
0
1
1
0
0
0
2
0
3
5
0
1
0
2
1
2
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
1
0
2
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
3
0
0
0
0
0
2
0
1
0
0
1
1
2
3
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
1
0
1
1
0
0
0
0
0
4
1
0
0
0
1
3
0
0
0
0
2
0
1
0
0
2
0
0
1
0
0
2
0
1
0
0
0
0
0
0
6
0
0
0
2
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
1
2
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
1
0
0
0
0
0
1
0
0
1
0
4
0
0
0
2
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
3
2
0
0
0
0
0
2
0
1
0
0
0
0
0
3
0
0
0
1
1
0
0
0
1
0
3
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
3
0
2
0
0
2
0
0
1
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
4
0
0
2
0
2
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
2
5
1
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
4
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
2
2
1
0
0
0
2
0
0
0
0
2
0
0
1
1
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
2
1
0
0
2
0
0
1
0
2
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
1
0
0
2
0
0
0
1
2
2
1
0
0
0
0
0
2
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
2
0
0
1
0
0
0
0
0
0
0
1
0
2
0
1
0
0
2
1
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
1
1
0
2
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
3
0
1
0
0
0
1
0
0
2
1
2
0
0
0
0
0
0
0
0
3
2
0
0
1
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
3
1
0
0
1
0
0
0
0
0
1
0
0
1
2
2
1
0
0
0
0
2
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
2
0
0
2
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
9
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
1
0
0
0
0
0
1
0
1
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
3
0
0
0
0
0
0
0
0
3
0
0
0
2
2
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
3
0
0
0
0
0
0
2
0
0
0
0
1
0
0
6
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
1
0
0
0
0
0
1
4
0
0
0
0
0
0
0
1
0
0
0
0
4
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
2
0
2
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
1
1
0
0
0
0
0
2
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
5
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
2
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
1
0
1
0
0
3
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
5
0
0
1
0
0
0
0
0
0
0
0
2
2
2
12
3
0
0
2
0
0
0
0
1
1
0
0
0
0
0
1
1
0
4
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
1
0
6
2
2
0
2
0
0
0
0
0
0
1
2
0
0
1
1
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
3
1
0
2
0
1
0
0
1
0
0
0
0
0
0
3
1
0
0
0
1
2
1
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
5
0
0
2
0
0
2
3
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
2
0
1
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
2
1
0
1
0
0
0
1
0
0
0
0
1
2
0
0
1
2
0
0
0
1
3
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
3
0
1
0
0
0
0
2
1
0
1
2
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
1
1
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
3
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
3
0
0
0
0
3
1
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
1
0
0
1
0
0
1
0
0
2
0
2
0
0
1
0
0
0
1
0
0
1
4
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
3
3
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
2
1
1
0
0
0
0
0
0
0
1
0
0
2
2
1
2
0
1
0
0
0
0
0
1
0
3
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
2
0
0
0
3
2
0
0
0
0
0
8
0
2
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
2
0
1
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
1
0
4
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
3
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
4
2
2
3
2
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
5
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
5
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
3
1
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
1
4
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
3
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
1
2
2
0
0
0
0
3
0
1
2
0
0
0
1
0
0
2
0
0
0
0
0
0
3
0
1
2
0
0
0
0
0
1
1
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
1
0
0
1
2
2
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
1
1
0
2
1
0
0
6
0
0
0
0
0
6
1
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
13
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
3
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
3
0
0
0
0
0
0
0
0
0
0
2
11
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
4
0
1
0
0
0
4
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
2
0
0
3
0
1
0
0
0
0
0
0
1
1
4
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
2
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
1
1
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
4
1
2
0
0
0
2
4
2
2
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
3
0
1
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
3
2
0
0
0
0
0
0
0
2
2
0
3
0
0
0
1
1
0
0
1
1
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
2
2
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
2
1
0
1
0
0
0
0
0
0
0
2
0
0
1
0
1
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
2
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
2
2
0
2
0
1
0
1
0
0
5
0
0
0
1
0
0
0
0
0
1
0
0
1
2
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
2
0
0
1
0
0
0
2
0
0
0
0
1
0
2
0
2
0
2
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
3
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
5
0
1
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
1
2
0
0
1
4
0
0
0
0
0
1
0
2
0
2
0
1
2
0
0
0
2
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
1
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
1
0
2
0
0
0
0
3
0
0
0
1
0
0
1
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
1
1
0
0
1
1
0
0
0
2
1
1
0
0
0
0
0
0
2
0
3
0
0
0
7
0
5
0
0
0
0
3
1
0
0
1
0
0
2
0
0
1
0
2
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
3
0
0
0
2
2
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
2
2
1
0
0
0
1
2
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
2
1
6
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
5
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
2
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
12
0
1
1
0
1
0
2
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
2
2
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
8
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
4
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
2
1
2
0
0
0
0
2
1
0
0
0
0
1
1
1
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
5
1
0
0
0
0
0
0
2
2
0
0
2
0
0
0
2
0
0
0
4
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
2
0
1
0
0
2
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
1
3
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
1
0
0
0
0
1
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
1
0
0
0
0
8
0
0
0
0
1
0
1
0
0
7
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
1
0
0
0
0
2
0
0
0
2
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
4
0
0
3
2
0
0
1
0
1
0
0
0
0
0
6
0
0
0
0
0
0
0
0
2
0
2
0
0
2
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
2
1
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
4
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
1
3
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
4
0
0
0
0
0
1
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
3
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
3
2
0
0
1
0
0
0
0
2
2
0
0
1
0
1
1
0
1
0
4
0
2
0
0
0
1
1
0
6
0
0
2
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
7
1
0
5
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
1
0
0
1
2
0
0
2
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
3
1
0
0
0
0
3
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
2
1
0
1
0
2
0
0
0
0
1
0
0
0
0
2
0
0
2
2
0
1
0
4
0
2
2
0
0
0
2
0
1
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
1
0
0
1
0
0
0
0
0
0
1
4
0
0
0
1
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
5
0
0
0
1
2
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
3
0
0
2
0
2
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
5
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
2
0
1
0
0
2
0
0
0
2
0
0
2
0
0
0
0
1
1
0
0
2
1
0
0
0
0
0
0
2
0
0
1
0
2
0
0
3
0
0
2
0
0
0
0
0
1
0
0
0
1
1
0
0
3
0
4
0
1
0
0
0
0
2
0
1
0
2
0
1
0
0
1
0
0
2
0
0
0
0
0
4
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
4
0
2
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
1
3
2
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
6
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
1
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
2
0
0
2
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
3
0
1
2
0
0
5
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
1
0
0
2
0
0
0
1
1
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
3
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
2
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
4
0
0
1
1
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
1
1
0
2
7
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
3
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
1
0
0
0
0
0
1
0
0
3
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
3
0
0
4
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
3
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
2
0
2
1
0
0
0
0
0
2
0
0
0
0
0
3
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
3
0
2
2
4
0
0
0
0
0
0
1
0
0
0
6
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
2
2
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
2
0
3
3
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
1
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
4
0
0
4
0
0
0
0
0
0
2
0
0
0
1
0
0
2
3
0
0
0
0
1
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
1
2
0
0
1
0
0
0
0
0
0
2
0
0
1
2
0
2
0
1
0
0
0
0
0
0
0
1
7
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
3
0
0
2
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
1
0
0
2
0
0
1
1
1
1
0
0
0
0
1
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
2
2
1
0
0
0
0
0
0
2
0
0
0
0
0
7
4
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
2
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
1
1
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
2
5
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
7
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
3
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
2
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
0
2
2
0
1
0
0
0
1
1
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
1
0
0
2
2
0
0
1
7
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
2
0
2
0
0
0
0
0
0
0
0
1
0
2
1
0
1
0
1
0
1
0
0
0
2
0
0
0
2
0
1
0
0
0
0
2
0
0
0
1
1
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
2
0
1
0
0
0
0
0
1
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
2
0
0
0
1
0
1
2
0
0
0
0
0
2
6
1
1
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
3
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
1
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
1
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
4
2
0
1
0
1
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
6
2
3
0
0
1
0
0
0
1
0
0
0
0
0
0
10
0
0
0
0
0
1
0
0
2
0
1
4
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
1
0
0
6
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
1
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
2
0
0
0
1
0
0
2
1
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
8
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
1
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
1
2
0
1
0
0
0
0
0
0
2
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
1
0
1
0
0
4
0
1
0
0
0
0
0
4
0
0
2
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
3
0
0
0
2
0
1
2
0
1
2
1
1
0
0
2
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
2
1
3
2
0
0
0
0
0
0
0
0
1
0
5
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
1
0
2
1
0
1
0
7
2
0
0
0
0
0
2
1
0
0
6
1
1
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
1
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
7
0
0
0
0
4
0
1
0
0
1
1
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
2
0
1
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
1
0
2
1
0
0
2
0
0
0
0
0
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
3
0
0
0
0
0
2
0
0
0
0
1
0
0
4
0
0
0
1
1
0
0
1
3
0
0
0
1
1
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
10
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
2
0
0
1
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
1
0
0
2
0
0
0
3
0
1
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
8
0
0
1
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
3
1
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
1
1
1
3
0
1
0
0
0
3
1
0
0
1
0
1
0
0
1
2
0
0
0
2
0
0
0
0
0
1
0
1
2
0
0
2
0
0
2
1
0
1
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
3
1
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
2
1
2
0
1
0
2
0
0
0
0
0
0
0
1
7
0
0
0
2
2
0
2
0
2
2
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
3
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
3
1
0
2
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
1
0
4
2
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
1
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
5
0
2
0
0
0
0
0
0
0
5
2
0
0
0
4
0
0
1
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
3
2
0
0
3
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
6
0
1
2
0
0
0
0
0
7
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
3
3
1
0
0
0
0
0
2
29
0
0
0
0
2
0
0
0
0
0
4
0
2
2
0
0
0
2
0
0
0
0
0
0
2
2
0
2
0
0
0
1
0
1
0
0
2
3
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
4
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
3
0
0
0
0
2
0
0
2
0
0
0
3
0
0
0
0
0
1
0
0
0
2
2
0
0
2
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
4
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
6
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
2
0
0
0
0
3
0
0
1
0
1
0
0
0
0
2
0
0
0
0
4
3
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
4
0
0
0
4
0
0
0
1
3
3
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
1
0
2
0
3
1
0
0
0
0
2
0
0
2
0
0
0
0
3
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
4
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
3
1
0
0
1
0
0
0
3
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
1
3
1
0
0
0
2
0
1
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
2
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
3
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
2
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
4
1
0
0
1
0
0
0
2
1
2
2
1
3
0
0
0
2
5
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
2
1
0
2
0
0
0
0
1
0
2
0
0
2
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
2
1
0
1
1
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
3
1
0
0
0
0
1
2
0
0
0
0
0
0
4
2
0
1
0
1
0
0
0
0
0
0
3
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
1
0
0
1
0
0
3
1
0
2
1
0
1
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
4
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
2
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
1
3
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
2
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
1
2
0
1
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
6
0
0
2
5
0
1
0
0
0
2
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
9
0
2
1
0
0
1
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
3
0
0
0
1
0
3
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
1
2
0
0
0
0
2
2
0
0
0
0
1
0
1
0
0
0
1
0
1
0
1
0
3
0
1
0
3
0
0
2
0
0
0
0
0
0
9
2
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
4
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
3
0
1
0
0
2
0
0
0
1
0
0
1
1
0
2
0
0
0
1
2
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
3
0
0
4
0
0
0
0
0
2
0
0
1
0
0
0
3
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
14
0
1
0
0
0
0
2
0
0
3
0
3
2
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
2
0
0
0
1
0
1
3
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
1
0
0
2
1
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
2
0
1
1
2
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
13
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
6
2
0
0
0
1
3
2
0
1
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
5
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
1
0
3
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
2
3
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
3
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
3
0
0
4
1
0
1
0
2
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
2
0
2
0
3
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
6
0
18
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
2
0
3
0
0
0
0
0
0
4
0
0
0
0
0
0
2
0
0
0
0
0
0
1
5
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
3
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
2
0
1
0
0
1
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
5
0
0
0
4
2
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
2
3
0
1
0
0
1
0
0
0
1
2
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
1
1
0
0
2
1
0
0
0
2
0
1
0
0
0
3
0
0
0
1
1
0
1
0
0
0
0
2
0
3
1
0
1
0
0
0
0
0
0
0
0
0
0
4
0
3
0
0
0
0
0
0
0
0
0
5
2
0
0
0
0
2
2
0
0
0
0
1
2
1
0
0
0
2
0
0
0
2
0
1
0
2
0
4
1
2
0
0
0
0
0
0
0
0
0
0
0
0
4
6
1
0
0
0
0
1
0
0
0
0
0
1
2
0
0
2
3
0
0
0
0
2
0
0
0
2
0
0
3
0
1
0
0
2
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
2
0
0
2
2
1
1
2
0
1
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
1
0
2
0
0
1
0
8
2
2
3
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
1
0
3
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
2
0
0
4
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
2
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
2
0
0
0
1
3
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
1
0
0
0
5
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
3
0
2
0
0
1
0
0
0
3
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
2
0
2
0
0
1
0
0
0
0
1
1
0
2
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
2
0
2
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
1
0
1
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
6
0
0
3
0
0
0
0
0
1
0
1
1
0
0
1
1
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
2
2
0
0
0
0
1
2
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
2
1
0
0
2
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
2
2
0
0
1
1
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
2
3
4
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
2
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
2
0
2
0
0
1
0
2
0
2
0
0
0
0
0
0
3
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
1
0
0
2
0
0
0
1
1
0
0
0
0
0
2
0
2
1
1
3
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
1
2
1
2
0
0
2
1
0
0
5
1
0
0
0
1
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
1
0
0
0
0
2
1
0
1
0
0
1
2
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
3
0
3
0
0
0
0
0
0
1
0
0
1
2
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
1
3
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
1
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
8
0
0
1
0
0
0
0
3
0
0
0
1
0
0
1
0
0
0
0
0
0
5
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
2
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
3
0
1
0
3
5
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
1
5
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
3
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
6
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
2
0
5
1
2
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
4
0
2
0
0
0
0
1
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
2
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
2
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
3
1
0
3
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
1
0
0
0
1
0
2
0
0
4
0
0
0
0
1
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
2
0
3
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
3
2
0
0
1
1
0
3
0
0
0
3
1
1
1
8
0
0
2
1
1
0
0
0
0
0
0
1
2
0
0
2
0
1
0
0
2
1
0
0
0
0
0
2
0
0
0
0
2
0
2
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
3
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
4
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
2
0
0
2
0
0
0
0
0
0
0
1
0
0
1
2
0
0
3
0
0
0
0
3
0
0
0
1
4
0
2
0
0
3
0
2
0
1
0
0
6
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
3
0
0
1
0
0
6
1
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
1
0
2
2
0
0
0
1
0
0
0
0
0
3
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
2
3
0
0
0
0
0
0
0
2
3
2
0
0
0
1
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
1
0
0
0
2
2
0
0
2
0
1
0
2
0
0
0
0
2
0
0
0
0
0
1
1
3
1
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
3
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
1
0
0
0
3
0
0
0
0
3
0
0
2
0
1
0
1
2
0
3
0
0
1
0
0
0
2
0
0
0
0
0
3
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
1
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
2
4
2
0
0
1
0
0
0
3
2
0
1
0
0
0
0
0
0
2
7
3
0
1
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
2
1
0
0
2
0
0
0
5
4
1
0
1
0
0
0
0
0
0
0
4
0
0
1
0
0
0
1
0
1
2
0
0
2
0
0
0
0
0
0
0
0
1
0
1
3
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
2
0
6
1
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
2
0
2
0
2
0
2
0
0
0
0
0
0
0
0
3
0
1
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
1
2
2
2
0
1
0
0
2
0
0
0
0
1
0
1
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
3
2
1
0
0
1
1
1
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
4
0
0
0
0
0
0
2
0
2
2
0
2
0
0
0
0
0
0
0
0
1
1
0
0
5
0
0
0
0
0
0
0
0
0
0
2
0
5
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
2
0
2
0
3
2
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
3
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
3
0
0
1
0
1
3
0
0
0
6
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
5
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
3
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
1
4
0
0
0
0
1
0
0
0
0
1
0
2
0
0
2
4
0
0
0
0
1
0
1
0
3
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
1
0
0
0
0
2
3
0
0
2
0
2
0
0
0
0
1
0
0
2
0
0
0
0
1
3
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
1
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
1
0
2
2
1
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
2
2
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
2
6
2
0
0
0
0
0
0
0
1
0
1
1
0
2
0
2
0
0
0
0
3
0
0
0
2
0
3
4
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
2
0
0
0
3
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
1
0
0
0
0
7
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
3
0
0
1
0
0
0
0
2
0
0
0
0
0
6
0
3
0
0
0
0
0
2
0
0
1
0
0
0
0
0
3
0
0
0
0
2
0
2
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
1
2
0
0
0
2
0
2
0
2
0
0
1
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
1
0
1
1
0
1
0
0
0
0
1
0
0
1
0
0
2
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
2
1
2
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
3
0
1
2
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
1
0
1
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
2
0
2
0
1
0
0
0
0
0
0
1
0
0
0
1
5
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
5
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
3
0
0
1
0
0
4
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
1
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
1
0
2
0
2
2
3
0
0
1
0
1
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
3
0
0
0
0
1
0
0
1
0
0
3
2
2
0
0
0
0
2
2
1
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
2
1
0
0
0
0
3
0
0
2
0
0
0
0
0
2
0
1
0
0
3
1
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
2
0
1
2
0
0
1
0
0
1
0
0
2
0
0
4
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
2
1
1
0
0
2
0
0
0
2
0
1
0
1
0
0
0
0
0
0
2
1
0
0
4
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
2
0
0
0
2
0
0
0
0
1
2
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
1
1
0
0
2
0
0
2
0
1
2
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
2
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
5
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
4
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
2
0
0
1
0
0
5
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
1
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
1
1
0
1
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
2
2
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
3
0
1
0
0
0
1
3
0
2
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
3
2
0
1
0
0
2
2
0
0
0
0
5
1
0
0
2
0
0
0
2
0
2
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
1
1
0
0
0
0
0
1
0
3
2
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
3
2
0
1
0
1
0
0
0
1
0
0
1
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
2
0
2
1
4
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
2
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
1
0
0
1
0
3
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7
0
0
0
2
0
0
0
2
0
1
0
0
1
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
3
1
1
0
0
0
0
2
0
0
0
0
0
0
1
2
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
2
1
2
0
0
0
2
0
0
1
0
1
1
2
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
8
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
2
0
2
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
1
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
1
4
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
1
1
1
0
0
0
0
2
0
0
4
0
2
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
2
2
0
0
2
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
3
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
1
0
0
0
0
7
0
2
0
0
0
2
2
3
1
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
3
0
0
1
0
1
0
0
1
0
0
8
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
3
0
1
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
3
0
0
2
0
3
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
2
2
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
2
1
0
0
1
0
4
0
1
0
3
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
2
0
1
1
0
1
1
0
0
0
3
2
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
7
0
0
0
0
4
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
1
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
4
0
0
0
0
0
0
3
0
0
0
0
0
5
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
2
2
0
0
2
0
0
0
0
0
0
0
1
2
5
0
0
0
1
0
2
0
0
0
1
0
1
0
0
0
0
0
0
7
0
0
0
0
0
0
3
0
0
0
0
0
1
1
0
0
8
0
2
0
0
0
0
0
0
0
0
12
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
1
0
2
0
0
3
0
1
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
4
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
8
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
1
1
0
0
0
0
2
0
0
1
1
2
1
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
1
3
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
3
0
0
2
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
5
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
2
0
0
2
0
2
1
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
2
0
1
0
1
0
0
1
0
0
0
3
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
2
1
0
0
0
2
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
4
0
0
0
0
7
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
3
1
0
4
0
0
2
2
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
4
2
0
0
1
0
0
2
0
1
2
2
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
3
1
1
0
0
0
0
2
0
2
0
4
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
4
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
2
0
2
3
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
6
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
6
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
1
0
2
0
1
0
0
1
0
0
0
2
2
2
0
2
2
1
1
0
0
2
0
0
0
0
3
0
0
0
0
1
0
0
3
0
2
0
0
0
2
0
0
0
2
0
0
0
1
1
2
0
0
0
0
0
0
1
1
0
1
0
1
2
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
3
1
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
2
0
1
0
0
2
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
2
0
0
0
0
0
2
1
0
1
0
0
1
0
0
0
0
0
1
0
2
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
2
1
0
0
1
0
2
0
0
0
2
0
0
1
0
0
0
0
0
2
0
1
0
0
1
0
2
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
2
2
0
0
0
0
2
0
1
0
0
2
0
0
2
1
0
0
0
0
1
0
0
1
2
1
0
2
0
0
0
0
0
1
0
1
2
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
1
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
2
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
1
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
2
4
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
3
3
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
1
0
2
0
0
0
0
0
3
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
1
3
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
4
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
2
0
1
0
1
0
2
0
1
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
5
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
3
2
1
2
0
0
0
0
0
2
1
2
4
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
4
2
0
0
0
0
1
0
1
0
1
0
0
0
0
3
0
0
0
0
1
0
1
0
0
0
2
0
0
1
2
0
1
0
1
1
0
0
1
1
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
7
0
0
2
0
0
0
0
0
0
0
2
0
5
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
1
3
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
3
0
0
2
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
4
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
3
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
2
1
1
0
2
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
2
0
3
0
0
3
1
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
1
1
0
1
2
1
3
0
0
0
0
1
1
0
3
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
2
0
1
0
0
0
0
0
0
3
1
0
0
0
1
0
0
0
0
2
0
2
0
1
0
0
2
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
4
0
8
0
0
0
1
0
0
0
0
0
0
0
0
5
0
0
0
0
0
1
0
1
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
2
0
3
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
8
1
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
6
0
1
3
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
1
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
3
1
0
0
0
1
0
3
0
0
0
0
0
0
1
0
2
0
0
3
0
0
0
0
0
0
0
1
0
0
1
4
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
4
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
8
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
1
1
0
0
0
1
0
0
1
0
0
0
3
0
0
0
0
2
0
0
0
1
2
0
1
0
0
1
1
0
0
1
0
1
3
4
0
0
0
0
1
0
2
0
0
0
2
1
0
0
0
0
0
0
1
0
0
3
0
0
0
1
1
0
0
1
7
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
4
2
0
0
0
1
3
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
3
0
0
1
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
2
1
1
2
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
1
1
3
0
0
0
0
1
1
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
2
1
0
2
0
0
2
0
0
1
0
0
1
0
1
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
2
4
1
0
0
0
0
0
0
2
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
3
2
0
2
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
1
0
2
2
0
3
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
2
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
3
1
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
1
0
0
1
1
0
2
0
0
0
0
0
1
0
0
0
3
0
3
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
6
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
2
1
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
5
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
4
3
0
1
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
1
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
4
1
0
0
1
0
0
0
1
0
0
0
0
0
2
4
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
2
1
2
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
2
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
6
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
1
1
0
2
0
1
0
0
1
0
0
0
0
4
1
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
2
0
0
3
2
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
3
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
2
1
0
0
0
0
2
0
1
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
2
2
1
2
1
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
2
0
0
0
2
2
0
1
0
0
0
0
0
0
3
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
2
0
1
0
0
1
1
1
1
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
2
3
0
0
0
5
3
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
3
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
3
0
1
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
3
2
0
1
0
1
1
0
0
2
0
1
0
0
3
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
1
2
2
0
0
0
0
2
0
2
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
1
0
2
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
2
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
2
2
0
0
2
0
0
3
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
1
0
0
1
1
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
2
1
0
0
0
0
1
2
2
0
0
0
4
0
0
0
0
2
0
0
0
2
0
1
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
7
6
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
1
0
0
0
2
0
1
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
1
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
2
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
1
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
6
1
3
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
2
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
2
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
1
0
0
0
7
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
3
3
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
2
0
3
0
0
0
0
0
0
1
0
1
0
1
0
1
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
5
0
0
0
0
7
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
2
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
2
1
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
3
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
1
3
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
2
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
2
3
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
3
0
0
1
1
0
0
1
0
3
2
0
0
1
0
0
0
0
0
3
3
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
1
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
2
1
0
0
0
2
2
2
0
0
2
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
3
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
2
0
0
2
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
8
0
0
0
0
0
2
0
0
0
2
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
2
2
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
3
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
7
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
2
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
1
0
1
0
2
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
2
2
0
2
0
0
2
2
0
9
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
1
0
2
0
0
0
0
1
1
0
3
1
4
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
2
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
2
0
0
0
0
0
1
1
2
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
2
1
0
2
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
3
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
4
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
4
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
1
0
3
0
0
2
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
6
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
5
0
0
0
0
0
6
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
1
0
3
1
0
0
2
0
1
1
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
6
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
3
1
0
0
1
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
5
0
0
0
0
0
0
0
0
2
0
0
0
6
0
0
0
0
1
0
0
0
3
2
0
0
1
0
2
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
3
0
1
0
2
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
3
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
2
0
3
3
0
0
1
0
4
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
2
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
2
0
1
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
2
2
2
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
2
0
0
0
0
4
0
1
0
3
1
0
0
0
0
0
0
0
0
0
2
0
1
0
1
2
0
4
1
0
1
2
0
0
0
0
1
0
0
0
1
2
2
1
0
0
3
1
0
9
0
0
2
0
4
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
2
1
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
1
1
2
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
3
0
0
2
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
5
0
2
0
0
0
0
0
0
0
2
1
0
0
3
0
0
3
0
0
2
0
5
0
0
1
3
2
0
0
0
0
0
1
3
0
0
0
0
2
0
0
0
2
1
0
0
1
0
0
0
3
0
2
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
2
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
5
0
0
0
0
2
1
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
8
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
1
0
0
2
0
1
0
0
2
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
2
0
0
0
0
0
2
3
0
0
0
1
2
2
0
0
3
0
1
0
0
0
0
2
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
8
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
1
0
0
1
0
0
0
0
0
0
1
0
1
12
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
2
0
0
0
0
2
1
3
0
2
0
0
0
0
0
0
2
0
1
2
0
1
3
0
0
0
1
0
0
2
0
0
0
0
0
1
1
0
0
2
0
0
1
0
0
0
2
0
1
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
3
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
3
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
2
0
2
2
0
0
2
2
0
0
0
3
0
0
0
0
2
0
1
0
0
1
0
0
0
1
2
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
3
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
1
0
0
0
2
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
1
0
0
0
4
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
2
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
9
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
5
1
0
0
2
0
4
0
0
0
0
2
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
3
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
2
0
0
2
0
0
1
0
3
1
0
0
0
0
0
2
2
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
1
0
0
1
0
1
1
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
2
0
0
1
0
2
0
0
2
0
2
0
0
0
3
0
1
0
2
0
0
0
1
0
0
0
0
1
0
2
0
0
6
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
1
2
1
0
2
0
2
0
2
1
0
0
1
0
0
0
0
1
1
1
1
0
0
0
0
0
0
1
0
2
0
1
0
1
0
0
0
0
2
0
0
2
2
0
0
3
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
3
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
1
2
0
2
2
0
0
0
0
1
1
2
2
2
0
1
2
1
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
1
1
0
0
1
0
2
0
1
0
0
0
1
0
0
4
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
2
0
0
2
0
1
2
0
2
0
6
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
1
1
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
2
2
1
0
0
7
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
4
0
1
0
1
0
0
4
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
2
1
0
0
2
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
2
0
5
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
1
0
2
1
0
0
0
0
0
0
0
2
2
0
0
2
1
0
0
0
3
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
1
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
6
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
4
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
3
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
1
1
0
2
0
0
4
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
4
2
0
0
0
0
4
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
1
1
0
0
1
4
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
3
2
1
0
2
2
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
1
0
0
0
0
0
0
0
2
0
0
1
0
1
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
5
0
0
0
2
1
0
2
0
2
1
0
0
0
0
0
0
1
4
1
1
0
0
1
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
1
0
2
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
2
1
0
0
2
5
0
0
0
2
2
1
0
0
1
1
0
0
0
0
1
1
0
0
0
0
2
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
2
0
2
2
0
0
0
0
0
0
1
1
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
3
2
0
0
0
0
0
2
0
0
0
1
0
0
1
0
2
2
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
2
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
8
1
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
1
0
0
2
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
2
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
1
0
1
1
1
0
2
2
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
3
2
0
6
0
0
1
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
2
3
0
0
0
0
0
2
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
2
0
0
4
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
2
0
0
4
0
0
0
0
0
1
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
3
0
2
0
2
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
1
2
0
0
0
0
0
0
2
0
1
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
2
3
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
3
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
1
2
0
0
0
0
0
2
1
0
0
0
0
1
0
0
2
3
0
0
0
0
0
0
1
0
3
1
0
2
0
0
0
0
2
0
5
0
8
0
0
0
0
0
2
0
0
0
1
0
0
5
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
3
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
2
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
2
2
0
1
0
3
0
0
0
0
2
0
2
0
2
0
1
0
0
0
2
4
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
1
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
5
0
2
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
3
0
0
0
0
4
0
0
2
2
0
2
2
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
2
1
4
0
0
0
2
0
1
0
4
0
1
1
2
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
2
1
0
0
0
1
2
0
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
7
0
0
0
1
0
0
3
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
2
0
1
1
0
0
0
0
1
2
1
0
0
1
0
0
0
0
4
0
0
0
0
1
0
2
0
1
0
3
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
2
0
0
1
0
1
0
0
0
0
1
0
3
2
1
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
1
1
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
1
2
0
0
0
0
0
2
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
1
3
0
1
0
8
0
0
1
0
0
6
6
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
5
0
0
3
0
0
0
1
0
0
0
1
0
0
0
1
4
0
0
1
0
0
0
0
0
0
5
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
2
2
1
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
2
0
0
0
1
3
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
2
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
1
1
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
1
0
0
0
1
2
1
0
1
2
0
2
0
0
2
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
2
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
1
0
1
0
4
1
0
0
0
1
1
0
1
0
0
0
0
1
1
4
0
3
0
1
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
1
0
6
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
2
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
2
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
2
1
0
0
0
0
0
1
0
1
9
0
0
2
0
1
0
0
2
0
0
1
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
1
2
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
3
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
2
1
2
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
1
1
0
0
2
0
0
0
2
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
2
0
1
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
1
0
0
2
1
1
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
3
4
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
1
0
0
0
1
0
0
2
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
3
1
0
0
1
0
0
0
0
2
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
4
0
0
0
0
1
0
0
0
1
0
1
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
3
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
2
1
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
1
2
2
0
0
0
2
0
0
2
2
0
2
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
1
0
1
0
0
2
0
0
0
5
2
2
3
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
1
14
0
0
1
0
0
1
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
2
1
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
2
1
8
1
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
3
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
1
7
0
2
0
0
0
1
1
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
2
2
0
1
0
0
2
0
0
0
0
1
2
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
2
1
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
3
1
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
1
0
0
0
3
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
2
1
1
4
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
1
2
5
0
0
0
1
0
2
0
1
0
0
1
2
0
0
2
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
1
2
0
2
0
0
0
0
0
2
0
0
1
0
2
2
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
2
1
2
0
1
0
0
0
1
2
0
3
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
6
0
1
3
0
0
0
0
0
0
0
3
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
2
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
3
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
1
0
2
1
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
3
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
6
0
0
1
0
0
0
2
6
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
2
1
0
1
0
0
0
2
0
0
1
0
0
5
0
1
4
0
0
1
0
0
2
0
0
0
0
0
0
0
4
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
5
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
2
0
0
1
0
2
0
0
0
1
0
0
0
7
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
2
1
1
0
0
2
1
1
0
3
0
0
2
0
1
3
2
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
1
0
0
0
0
1
0
2
0
2
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
2
1
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
4
0
0
0
0
3
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
2
0
1
0
2
1
0
0
0
2
0
0
2
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
2
0
0
0
2
0
0
0
2
0
1
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
9
0
2
0
0
0
0
0
2
0
0
0
0
1
1
0
0
1
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
2
0
1
2
0
0
1
0
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
2
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
2
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
2
0
2
0
5
1
0
0
0
4
0
0
0
0
0
0
3
0
0
1
3
0
0
0
0
0
0
0
0
2
1
0
2
0
1
0
2
0
1
0
0
0
5
1
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
6
0
0
0
0
3
0
0
0
0
0
1
1
0
0
0
0
0
0
1
3
3
1
3
0
3
0
0
0
1
1
0
0
1
3
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
2
2
0
0
0
0
1
0
0
0
5
0
0
0
1
0
1
0
0
2
2
0
0
0
5
0
0
0
0
0
0
0
1
1
4
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
2
3
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
3
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
1
0
0
0
2
0
0
1
0
2
0
5
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
1
0
1
0
2
0
0
1
3
0
0
3
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
1
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
3
0
0
0
0
4
2
0
0
2
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
1
1
0
0
0
0
1
0
0
0
2
0
2
1
2
0
0
0
2
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
2
0
0
0
1
0
0
2
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
1
2
0
0
0
1
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
3
0
4
0
0
0
0
2
0
2
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
2
0
1
0
0
0
2
2
0
0
0
2
0
0
1
1
0
0
0
0
0
2
0
1
0
0
2
2
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
1
1
2
1
0
0
0
0
0
3
0
0
2
0
0
0
3
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
4
0
0
0
0
1
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
1
0
1
0
0
2
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
1
0
0
3
2
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
3
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
1
0
0
0
0
3
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
4
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
2
0
2
1
0
0
0
1
1
1
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
3
0
0
0
1
2
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
1
3
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
6
0
0
0
1
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
3
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
2
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
1
1
0
2
0
1
2
0
0
0
0
0
0
0
2
1
0
1
0
0
1
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
8
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
5
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
2
0
0
1
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
4
0
1
0
0
0
0
3
2
0
0
1
2
0
0
2
3
2
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
1
1
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
3
1
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
1
1
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
4
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
5
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
2
1
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
3
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
1
0
1
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
2
1
2
0
1
1
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
1
3
0
2
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
10
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
1
7
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
5
0
2
0
0
0
0
0
0
0
1
0
0
0
0
3
5
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
7
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
2
2
0
0
0
1
0
0
1
0
0
0
0
4
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
5
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
2
0
0
2
0
0
2
0
2
0
2
0
0
2
0
2
0
0
0
0
7
0
1
0
2
0
0
0
0
0
0
0
0
3
0
2
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
2
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
8
2
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
2
0
0
0
0
0
0
2
0
1
1
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
2
2
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
8
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
6
0
0
2
2
0
0
1
1
0
0
4
3
0
2
0
0
0
0
2
1
2
0
1
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
9
1
0
2
0
1
0
0
0
0
1
2
1
0
0
3
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
3
0
2
0
0
0
0
0
1
0
0
0
0
2
1
0
0
2
1
0
0
3
0
0
0
0
0
0
0
4
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
1
4
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
1
0
0
1
2
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
2
0
2
0
0
2
0
0
2
0
0
0
1
0
6
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
3
2
0
4
0
0
1
0
2
2
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
1
0
2
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
1
0
0
1
2
0
0
0
1
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
2
0
4
3
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
2
0
0
0
0
1
1
0
0
2
0
0
3
0
0
1
2
2
0
4
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
3
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
5
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
2
0
0
0
0
1
0
3
0
1
0
2
1
3
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
15
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
1
4
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
2
0
2
2
0
0
1
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
1
0
2
1
2
0
0
2
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
7
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
3
0
2
0
3
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
3
2
2
1
0
0
0
1
0
0
0
0
0
1
2
0
3
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
2
0
1
0
0
0
1
0
1
0
0
0
0
0
0
2
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
6
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
1
0
0
0
1
1
0
0
0
1
2
0
1
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
2
0
0
0
0
1
0
1
0
2
0
0
0
0
1
0
0
1
1
0
0
3
0
0
1
3
0
0
0
0
3
1
2
0
0
0
2
2
0
2
1
2
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
2
0
0
0
0
2
0
1
0
0
2
0
0
0
1
2
0
0
1
0
2
0
0
2
0
0
1
0
2
0
0
3
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
3
0
0
8
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
2
0
0
0
3
0
0
1
0
1
0
0
1
0
0
1
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
3
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
1
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
2
2
0
3
0
1
0
1
0
2
0
3
0
0
0
0
0
0
2
0
0
0
1
0
4
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
11
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
4
3
1
0
3
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
2
2
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
1
3
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
2
1
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
3
0
3
0
0
0
1
0
1
0
0
5
0
1
0
2
0
1
0
0
2
0
1
0
0
0
1
0
0
1
2
1
0
0
0
0
0
1
0
0
1
0
0
0
2
2
0
2
1
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
1
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
2
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
5
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
1
1
1
1
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
1
0
1
2
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
3
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
4
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
1
0
2
1
0
0
0
0
5
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
6
0
2
0
0
0
2
0
1
0
2
0
2
0
0
2
0
0
0
1
3
0
0
2
0
0
3
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
1
0
1
0
1
0
1
0
0
1
0
0
2
0
3
1
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
1
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
1
0
1
0
0
0
1
1
1
1
0
2
0
0
1
3
2
1
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
1
0
1
1
0
0
0
0
0
1
0
5
1
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
1
1
0
0
0
0
0
0
0
0
0
3
2
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
8
0
0
1
0
0
0
0
2
2
0
0
1
2
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
3
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
1
1
0
6
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
2
2
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
4
2
5
0
1
0
2
0
0
0
0
1
0
0
0
2
1
0
0
2
0
0
0
2
0
0
1
0
2
2
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
2
4
0
1
0
0
0
0
0
0
0
0
0
2
0
2
2
1
0
0
1
1
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
5
0
1
3
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
1
3
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
1
0
5
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
3
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
3
0
0
0
0
0
1
2
1
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
3
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
3
2
1
0
1
0
1
0
0
0
0
2
0
0
4
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
2
0
0
0
2
3
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
1
0
2
0
0
1
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
1
1
2
0
0
3
0
0
1
0
1
0
0
0
0
0
2
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
1
0
0
1
0
3
0
1
0
0
0
2
0
1
1
0
0
2
0
0
0
0
0
0
4
0
0
0
0
0
7
0
0
3
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
2
2
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
4
1
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
3
3
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
5
0
0
0
0
1
0
2
2
0
2
0
0
1
1
0
0
0
1
0
2
0
0
2
0
0
0
0
2
0
10
4
0
0
0
0
6
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
1
0
0
2
4
0
0
1
0
0
0
0
0
0
3
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
1
0
3
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
4
0
1
0
0
0
0
1
0
0
0
2
0
0
1
0
1
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
1
1
0
1
0
0
0
3
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
3
1
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
6
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
3
2
2
0
0
0
0
0
1
1
0
0
2
0
2
0
0
1
2
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
3
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
3
0
0
2
2
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
1
0
0
2
1
0
1
0
0
0
0
0
0
2
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
3
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
3
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
3
2
0
2
2
2
0
1
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
6
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
1
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
3
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
4
2
1
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
3
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
3
1
0
2
2
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
3
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
1
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
1
1
1
0
1
0
0
0
0
0
0
5
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
7
0
0
2
2
0
0
0
2
0
0
0
0
0
1
0
3
0
0
2
2
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
1
0
0
0
0
2
3
0
0
0
0
0
0
1
0
0
0
0
7
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
3
0
0
2
0
0
0
1
0
2
0
0
1
2
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
2
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
1
0
6
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
8
0
0
0
0
0
0
3
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
3
1
0
0
2
0
0
2
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
2
2
0
0
0
0
0
0
1
0
0
0
2
3
0
0
1
0
0
0
0
2
0
0
2
0
0
0
6
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
3
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
1
1
2
2
0
0
0
1
0
0
0
0
2
0
0
0
0
2
1
2
0
0
0
0
1
0
0
0
0
1
2
0
0
0
1
0
0
2
3
1
0
3
0
1
0
0
0
0
3
4
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
8
0
0
0
0
3
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
3
0
2
0
0
0
0
0
0
0
0
4
3
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
1
3
0
0
0
0
2
0
2
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
2
0
0
0
2
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
1
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
2
1
6
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
2
0
2
0
0
2
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
1
2
0
0
0
1
0
0
0
0
3
0
0
0
1
0
0
2
0
2
0
0
0
0
2
0
2
0
0
0
1
0
0
1
0
0
1
2
0
1
0
0
2
0
0
2
0
0
0
0
0
1
0
1
0
0
2
0
0
1
3
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
1
3
0
1
0
0
1
0
0
0
1
1
2
0
0
2
0
0
4
0
0
0
3
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
1
0
2
2
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
2
3
0
0
2
0
0
1
2
4
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
1
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
2
0
2
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
6
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
3
0
0
5
0
0
0
1
0
0
0
12
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
2
0
0
0
0
2
0
0
3
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
1
0
0
1
0
1
0
0
0
0
1
2
2
2
1
0
0
0
0
1
0
0
2
0
0
2
0
0
0
1
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
2
0
4
0
0
0
0
0
0
1
2
1
1
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
4
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
2
0
0
2
0
2
0
0
1
2
1
0
0
0
0
0
2
0
0
0
0
2
5
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
3
0
3
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
1
3
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
3
0
0
0
1
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
3
0
0
1
5
0
0
2
0
0
0
2
0
0
4
0
0
0
0
1
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
3
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
1
0
0
6
1
0
0
0
1
0
0
4
0
0
0
0
0
0
0
1
1
4
3
0
0
0
0
0
0
0
1
2
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
2
0
0
0
0
0
2
1
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
4
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
3
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
2
0
0
1
0
0
0
0
0
0
1
2
1
0
1
0
0
4
0
0
1
1
0
0
0
3
0
0
4
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
3
2
0
1
0
0
1
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
10
0
0
0
0
0
0
1
0
0
2
0
1
3
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
2
0
3
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
1
1
2
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
1
2
0
5
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
3
2
0
3
1
0
0
1
0
3
0
2
0
1
0
1
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
2
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
3
0
2
0
0
0
2
0
2
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
2
0
0
0
0
1
0
2
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
1
1
3
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
5
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
5
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
3
0
0
1
1
1
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
3
1
0
0
0
0
0
2
0
7
0
0
0
4
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
1
0
0
2
0
0
0
2
1
2
0
0
0
0
2
2
0
1
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
3
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
2
0
0
0
2
1
5
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
1
0
0
0
1
0
3
0
0
0
0
2
0
0
0
0
1
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
1
0
0
0
0
0
2
0
1
0
0
2
0
0
1
0
1
0
2
1
1
4
1
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
3
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
4
0
0
1
0
0
2
1
0
0
1
0
0
0
0
7
2
0
1
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
3
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
1
0
0
2
1
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
6
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
5
3
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
3
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
2
1
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
6
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
3
0
1
0
0
0
0
0
1
1
0
0
0
1
3
0
0
0
3
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
2
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
1
2
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
2
0
2
2
4
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
2
2
0
0
0
1
2
0
2
0
0
1
1
0
1
1
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
3
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
2
1
0
1
1
0
0
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
2
0
0
2
0
0
0
4
1
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
5
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
2
0
1
0
0
0
3
0
0
0
0
0
0
0
0
7
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
1
0
0
0
1
2
0
1
0
0
0
1
0
1
0
2
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
2
0
0
0
2
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
2
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
2
0
0
0
2
1
0
1
2
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
1
0
0
0
0
1
3
1
2
0
0
0
0
0
0
1
0
0
1
2
0
0
1
0
0
5
2
0
0
0
0
6
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
2
0
1
0
0
2
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
1
0
2
0
1
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
2
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
3
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
3
4
0
0
0
0
0
0
2
0
2
2
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
1
0
3
1
2
2
0
0
0
2
3
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
4
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
5
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
2
0
0
1
0
0
0
0
0
3
0
0
0
0
1
0
1
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
2
4
1
2
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
5
0
0
0
0
0
0
0
1
0
3
2
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
2
3
0
2
0
0
0
0
1
0
3
0
0
3
2
0
0
0
0
0
5
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
3
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
1
1
1
0
0
0
0
0
0
1
0
1
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
3
0
0
11
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
2
2
0
0
2
1
0
1
4
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
1
0
0
2
1
0
2
1
1
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
1
2
2
0
0
1
0
0
0
0
0
0
0
0
3
2
1
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
2
4
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
15
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
2
0
2
0
0
6
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
2
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
7
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
1
0
0
0
0
1
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
2
1
0
0
2
0
1
10
0
0
0
1
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
1
0
5
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
1
3
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
5
0
0
0
2
1
0
0
2
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
1
0
0
0
0
0
3
0
0
0
0
3
0
0
0
0
1
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
1
2
0
0
0
5
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
2
0
0
0
0
0
0
1
3
0
0
2
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
2
0
0
2
2
0
2
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
2
1
1
1
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
5
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
1
1
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
1
0
0
2
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
1
0
6
1
0
2
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
2
0
1
1
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
2
0
2
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
3
1
0
0
0
3
0
8
1
3
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
1
0
2
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
2
0
0
0
0
1
0
0
0
1
0
0
0
1
4
2
1
0
0
0
0
1
0
0
13
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
2
0
1
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
3
0
0
0
1
1
0
2
0
1
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
1
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
6
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
1
0
0
0
0
0
0
1
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
2
2
2
0
0
2
2
0
0
2
0
0
0
0
1
0
7
2
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
1
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
3
0
0
0
0
0
4
0
0
0
0
1
1
2
0
1
0
1
0
1
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
1
1
1
0
3
0
1
0
3
0
0
0
0
1
0
0
0
0
2
0
1
0
0
1
0
1
1
2
2
2
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
1
0
0
3
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
2
0
2
1
0
0
2
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
3
1
0
0
0
0
2
0
2
2
0
0
0
1
1
0
2
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
2
2
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
3
0
2
0
0
1
0
0
0
0
0
0
0
4
1
0
0
0
0
0
3
1
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
1
1
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
3
0
0
0
0
4
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
2
0
1
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
1
2
0
0
0
0
1
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
1
1
0
2
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
2
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
2
0
5
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
1
1
0
2
0
1
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
1
0
4
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
1
1
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
2
0
0
2
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
2
0
0
0
0
2
0
0
1
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
3
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
2
0
0
2
0
5
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
3
0
0
0
2
0
0
1
0
0
0
3
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
1
0
1
1
0
0
0
0
0
0
0
2
2
0
7
0
0
3
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
2
0
1
0
0
2
0
0
3
2
0
1
0
0
0
0
0
1
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
1
1
0
0
3
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
5
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
2
0
1
0
2
0
0
0
0
0
0
2
0
2
2
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
1
1
1
0
0
0
0
0
3
0
0
0
0
0
1
0
6
0
0
0
0
1
0
0
0
0
0
0
0
0
0
5
0
1
0
0
1
0
0
0
0
1
0
0
1
2
0
1
0
0
1
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
3
1
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
2
1
0
0
1
0
1
2
2
0
0
0
3
0
0
0
0
0
0
0
2
2
0
0
3
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
2
0
0
5
0
0
0
1
0
0
1
2
0
1
0
0
0
0
1
0
0
1
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
3
2
2
0
0
0
0
0
1
0
0
0
3
0
0
0
2
0
5
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
3
0
0
0
1
0
0
0
0
0
3
0
0
0
1
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
1
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
3
4
2
1
2
0
0
0
0
0
0
0
0
2
0
4
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7
0
2
0
1
0
0
0
2
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
4
0
2
0
0
2
2
1
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
7
0
0
0
1
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
4
2
0
0
2
0
0
1
0
1
0
2
0
0
0
1
0
0
2
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
3
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
2
2
2
0
0
3
0
2
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
1
1
0
0
2
1
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
1
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
4
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
1
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
2
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
3
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
1
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
4
2
1
1
3
0
0
0
0
2
0
0
3
0
2
2
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
4
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
2
5
0
0
3
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
3
1
0
0
0
0
1
1
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
1
1
0
2
0
2
0
0
0
0
0
2
0
3
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
2
0
0
0
0
0
0
0
0
0
5
0
1
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
8
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
4
0
0
0
0
0
0
4
0
0
0
0
9
0
2
0
0
0
0
6
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
3
1
0
0
3
0
0
0
1
3
0
2
0
0
0
0
0
0
2
0
0
1
3
3
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
1
0
0
0
2
1
1
0
0
0
0
1
0
4
0
1
0
0
0
0
0
1
1
0
2
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
3
0
6
0
0
0
2
2
6
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
2
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
3
0
2
2
0
6
1
0
0
0
1
0
0
0
0
4
0
0
0
0
1
0
0
1
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
2
0
4
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
5
0
1
3
1
0
2
0
0
0
0
0
0
0
1
2
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
1
0
0
0
1
0
0
2
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
2
1
0
0
1
0
0
2
0
0
0
0
4
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
4
1
0
0
0
2
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
3
4
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
1
0
0
1
0
0
0
1
1
0
0
0
2
0
1
1
0
0
0
0
0
1
0
0
0
2
2
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
4
0
2
1
0
1
0
1
0
1
0
0
0
2
1
0
0
2
2
0
0
2
2
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
4
0
0
0
2
2
0
0
0
0
0
0
0
0
2
1
0
1
1
2
0
2
1
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
5
0
0
0
0
0
0
0
5
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
25
0
0
0
0
0
0
2
0
2
0
0
10
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
2
1
0
0
0
0
1
2
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
1
5
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
1
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
2
0
1
2
0
2
0
1
2
0
0
0
0
0
2
0
0
0
0
1
0
0
3
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
1
1
0
0
0
0
1
4
0
2
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
2
0
1
0
0
0
0
1
2
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
5
0
0
0
1
0
0
0
0
0
1
0
0
0
0
3
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
3
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
1
2
1
0
0
2
1
0
0
0
0
0
2
0
0
2
0
0
0
3
0
3
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
1
3
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
1
2
1
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
2
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
1
0
1
0
0
4
2
1
4
1
1
1
2
1
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
4
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
2
0
0
1
0
0
0
1
0
0
0
1
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
1
0
1
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
6
0
0
0
0
1
0
0
0
0
0
2
3
0
1
1
0
0
0
0
0
0
3
1
0
0
1
0
0
0
0
0
5
3
0
2
5
0
0
1
0
0
0
2
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
3
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
3
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
2
3
2
0
0
2
2
2
0
0
0
1
0
0
2
0
0
0
0
0
3
0
2
3
0
2
2
0
2
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
2
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
1
0
0
0
1
0
2
0
0
0
2
0
0
1
0
0
0
2
1
0
0
0
0
0
1
0
0
0
2
1
0
0
0
4
2
0
0
2
0
0
0
0
0
3
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
1
1
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
3
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
4
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
2
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
7
0
0
1
4
2
0
0
0
0
3
0
0
0
8
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
6
0
1
0
0
1
1
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
6
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
4
0
2
0
0
1
0
2
0
0
0
2
0
0
0
0
1
1
6
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
4
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
2
0
0
5
0
0
0
0
0
0
0
2
0
0
0
0
0
1
4
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
2
0
0
1
5
2
0
0
0
0
0
0
1
0
0
3
1
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
2
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
13
0
0
0
0
0
1
2
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
2
1
2
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
1
0
1
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
1
0
0
0
0
0
0
1
1
0
0
1
0
10
2
0
0
0
0
0
0
0
4
0
1
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
2
0
1
0
1
1
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
2
0
0
7
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
6
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
3
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
8
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
2
0
1
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
1
2
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
9
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
1
0
0
0
0
1
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
2
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
2
1
0
0
0
1
0
0
0
0
0
2
1
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
2
2
2
0
0
2
0
0
0
0
3
1
0
0
0
0
0
0
7
0
0
1
1
0
0
0
0
3
3
0
0
0
0
1
0
0
0
0
0
0
1
1
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
2
0
0
1
0
0
0
3
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
2
0
3
2
0
0
0
3
0
1
0
1
0
1
0
0
0
0
0
0
2
0
0
3
0
0
0
2
0
0
3
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
2
3
2
1
0
0
1
0
0
0
0
1
0
0
4
0
1
1
0
0
0
0
2
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
4
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
1
2
0
1
0
1
0
0
0
2
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
3
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
6
2
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
2
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
2
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
7
0
0
1
1
0
0
2
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
2
1
1
0
2
0
0
0
0
4
0
0
0
0
0
1
2
0
0
1
0
0
2
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
3
0
0
0
0
0
2
1
0
0
3
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
1
0
1
0
1
1
0
0
0
0
2
0
0
0
0
1
0
0
1
0
2
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
5
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
5
0
0
0
0
4
1
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
2
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
1
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
1
2
0
0
0
0
0
0
0
1
0
0
0
1
3
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
1
0
0
0
0
0
0
0
3
2
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
4
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
1
0
2
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
3
0
0
2
1
0
0
0
0
0
0
2
0
0
1
0
0
1
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
2
1
0
2
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
3
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
5
3
0
1
0
0
0
2
0
0
2
0
0
0
1
1
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
1
1
2
0
0
0
2
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
3
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
10
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
3
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
5
0
0
0
3
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
2
3
0
0
3
0
4
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
5
0
0
0
0
0
2
0
0
0
1
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
2
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
4
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
3
0
4
0
0
0
0
1
1
0
0
0
2
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
1
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
2
0
0
0
0
0
0
2
1
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
1
0
0
0
0
0
2
3
0
0
1
0
0
0
0
2
1
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
2
1
0
0
1
0
0
0
0
0
0
0
1
0
0
2
1
1
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
2
0
2
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
5
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
2
0
3
0
0
1
1
0
0
3
1
0
1
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
1
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
1
3
0
0
0
0
2
0
2
1
0
0
0
2
0
0
0
0
1
2
0
1
4
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
5
1
0
2
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
3
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
1
0
0
0
3
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
11
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
3
0
0
0
0
0
0
0
5
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
1
2
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
1
0
1
0
0
0
0
3
0
0
2
1
0
0
0
0
52
1
3
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
1
0
3
0
0
2
0
0
3
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
3
1
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
1
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
1
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
2
2
0
0
0
0
0
0
3
0
0
1
1
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
1
0
0
1
1
2
0
0
2
0
0
2
0
1
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
1
0
0
0
0
3
0
0
0
0
0
0
1
0
2
1
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
1
1
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
2
2
0
5
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
3
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
4
0
1
2
0
2
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
1
0
1
0
2
2
0
1
0
0
0
0
0
1
0
3
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
2
2
2
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
1
0
0
0
0
0
0
2
6
0
0
0
4
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
5
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
5
0
0
2
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
5
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
1
0
0
0
2
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
7
0
0
2
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
7
0
0
0
0
2
0
0
2
1
1
1
1
1
2
0
1
3
1
2
0
2
0
0
0
0
0
0
0
2
0
0
0
3
1
2
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
7
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
7
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
2
0
0
0
0
4
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
3
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
4
2
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
2
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
2
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
1
7
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
1
1
2
0
0
7
4
2
0
1
0
0
4
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
4
0
1
0
0
0
0
0
2
0
0
0
0
0
3
1
2
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
2
0
1
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
2
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
1
0
0
0
0
0
2
2
0
0
1
0
0
1
0
0
0
1
0
0
0
0
5
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
3
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
2
0
0
0
0
0
2
2
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
1
0
1
0
0
0
2
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
2
0
0
0
0
0
1
1
2
2
0
0
1
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
7
2
2
0
1
0
0
1
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
2
0
0
2
0
2
0
0
2
0
0
2
0
2
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
1
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
2
1
0
0
1
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
3
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
2
0
0
2
0
2
0
0
1
0
0
0
0
0
0
12
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
1
0
0
2
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
1
3
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
1
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
1
2
2
0
1
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
1
2
0
0
1
0
0
0
0
0
4
0
0
0
0
0
1
0
3
0
0
0
0
1
0
1
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
2
2
0
0
0
0
0
0
0
0
0
5
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
1
0
0
2
2
0
12
0
2
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
3
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
1
1
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
5
1
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
3
0
4
0
1
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
1
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
2
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
3
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
12
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
8
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
1
1
0
4
0
0
2
0
0
2
5
0
1
0
0
0
0
0
0
1
0
1
0
2
1
0
3
0
0
0
0
0
0
2
0
0
0
4
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
3
0
0
0
0
1
0
0
0
0
1
0
3
0
0
1
0
0
0
0
0
0
0
5
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
1
0
0
0
1
0
5
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
1
3
0
0
2
0
1
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
1
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
4
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
4
0
1
0
0
2
2
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
1
2
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
2
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
4
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
9
0
1
0
0
2
0
0
0
1
0
0
0
1
1
0
0
2
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
4
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
3
0
0
1
0
2
0
3
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
1
0
0
2
2
0
0
0
0
3
0
3
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
2
2
0
0
4
0
1
0
0
0
0
1
0
0
2
1
0
0
0
2
0
2
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
1
2
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
2
0
2
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
3
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
3
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
7
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
3
0
0
0
0
0
2
0
2
2
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
2
2
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
1
7
0
0
0
0
1
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
10
0
3
2
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
1
1
3
1
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
1
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
2
1
3
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
5
1
0
2
0
0
0
0
1
0
0
0
0
0
0
2
2
0
5
0
0
0
1
0
1
0
0
0
2
1
0
4
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
1
0
3
0
0
2
3
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
2
1
3
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
2
0
1
0
0
3
0
2
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
3
0
2
0
0
0
0
0
1
0
0
0
0
2
0
1
1
0
0
0
0
0
3
0
0
4
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
2
7
2
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
8
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
1
2
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
1
1
0
0
2
0
0
0
2
0
1
0
0
0
0
1
1
0
3
0
1
2
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
2
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
1
3
0
2
0
1
2
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
1
0
0
0
0
2
1
0
0
3
0
3
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
4
0
3
0
0
0
4
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
3
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
3
3
0
0
0
0
0
1
0
0
0
5
0
0
0
2
0
0
0
0
0
0
0
2
0
2
1
0
1
0
0
0
0
0
0
0
0
2
0
2
0
3
0
0
0
2
0
0
0
1
0
0
3
0
0
0
1
2
0
0
0
1
0
2
0
0
0
0
2
0
0
2
0
0
1
0
2
2
0
2
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
2
0
0
0
0
0
3
1
2
0
0
0
0
2
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
3
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
3
0
1
0
1
0
0
0
2
0
0
2
0
0
1
0
3
0
4
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
1
2
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
3
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
1
0
0
1
1
0
1
0
0
0
1
0
2
0
0
1
1
2
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
2
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
2
2
2
0
0
0
0
0
5
0
0
0
0
0
3
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
3
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
2
1
0
0
2
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
4
2
0
0
0
0
0
6
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
2
0
3
0
0
7
0
2
8
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
2
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
2
0
0
2
0
0
2
2
0
0
0
2
0
0
0
3
0
2
2
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
2
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
1
0
2
0
0
0
0
3
0
0
0
0
0
0
2
0
0
1
2
2
0
0
1
2
0
0
0
3
0
0
0
0
0
0
0
1
0
0
3
1
0
1
0
1
0
2
0
0
0
0
0
0
1
0
1
0
0
0
1
7
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
4
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
1
0
1
0
0
0
0
0
4
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
4
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
7
0
0
0
1
0
0
0
0
2
0
0
1
0
0
3
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
2
2
0
0
1
0
0
1
0
0
0
0
0
2
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
1
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
9
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
3
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
3
0
0
0
3
0
0
1
0
1
0
0
0
2
1
1
2
0
0
5
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
3
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
5
0
0
0
0
1
1
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
2
0
2
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
3
0
0
0
0
0
1
0
2
2
3
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
2
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
1
3
1
0
6
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
3
7
0
1
0
1
2
0
1
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
3
0
0
0
2
0
0
0
7
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
3
1
0
3
2
0
2
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
1
0
0
0
7
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
1
2
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
1
0
0
3
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
5
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
1
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
3
0
0
2
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
1
2
1
1
0
0
3
2
2
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
7
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
2
3
0
0
0
1
4
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
1
0
0
0
1
0
0
0
0
3
0
0
2
2
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
7
0
2
1
0
0
2
0
0
0
1
0
1
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
2
0
2
0
1
1
2
2
0
0
0
0
0
0
0
0
0
0
0
7
0
2
2
0
0
0
4
1
0
1
0
0
1
0
0
0
3
0
0
0
1
0
0
1
3
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
3
0
0
0
4
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
2
2
0
2
2
1
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
2
0
2
0
0
1
0
0
0
2
0
0
0
3
0
0
0
0
1
0
2
2
0
0
0
1
2
0
0
0
2
0
2
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
5
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
11
0
0
0
1
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
2
0
7
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
3
0
1
0
0
0
0
0
1
2
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
1
0
0
0
1
0
0
0
1
2
0
0
2
0
0
1
2
0
1
0
0
0
3
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
3
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
4
2
0
0
3
0
0
0
3
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
1
0
0
0
0
1
3
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
2
2
0
0
1
1
2
1
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
1
0
1
0
0
3
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
2
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
2
1
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
2
0
0
2
0
2
0
1
2
0
0
0
0
0
0
2
0
0
0
2
0
3
0
0
0
0
2
5
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
6
2
0
3
0
0
0
1
0
0
0
0
1
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
3
0
0
3
0
0
4
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
3
0
0
4
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
1
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
1
0
0
5
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
4
4
0
0
0
0
3
2
0
1
0
0
0
0
2
2
1
4
1
0
0
0
13
2
0
0
0
2
0
0
1
0
0
0
0
1
0
1
2
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
2
4
0
0
0
0
0
3
1
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
5
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
1
1
3
1
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
1
4
3
2
0
3
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
2
2
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
1
1
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
4
0
1
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
2
1
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
3
2
2
0
0
2
0
2
0
2
1
0
1
0
3
4
1
0
0
0
0
0
0
0
2
0
0
4
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
1
0
0
0
1
0
0
0
3
0
0
3
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
3
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
1
0
2
0
0
2
0
0
0
0
0
1
0
1
0
1
7
1
0
0
4
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
2
0
0
3
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
2
0
0
0
0
1
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
1
0
0
0
2
0
0
2
1
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
4
0
0
2
3
2
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
1
0
0
0
1
1
1
2
1
0
0
0
1
0
5
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
1
4
0
0
0
0
2
0
2
0
0
1
1
1
0
0
0
0
1
0
0
0
2
0
1
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
3
2
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
4
0
0
2
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
1
0
0
0
0
0
0
2
0
0
1
2
0
6
0
0
1
0
0
9
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
2
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
1
0
0
2
0
2
1
0
0
0
0
2
2
0
2
1
0
2
0
0
0
1
0
0
3
3
0
1
0
0
0
0
2
4
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
1
0
3
0
5
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
3
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
3
0
0
0
0
1
0
0
7
0
1
0
0
0
1
0
0
0
3
2
0
0
1
0
0
1
0
0
0
2
0
2
0
0
0
0
3
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
2
2
0
1
1
0
0
0
0
0
2
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
4
0
1
0
0
0
0
0
0
1
0
1
0
1
1
1
0
0
0
1
0
0
2
1
2
0
2
0
2
0
1
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
2
0
0
0
2
0
0
0
0
0
0
3
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
3
0
0
0
2
0
0
2
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
4
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
1
0
1
0
0
0
0
2
0
0
2
0
0
1
0
3
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
2
0
0
1
0
0
1
1
0
0
0
0
2
0
2
0
2
2
0
4
1
1
0
1
0
3
1
1
0
0
0
2
2
0
0
0
1
0
0
1
0
0
2
0
5
0
0
0
0
1
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
5
0
0
0
1
0
0
0
0
0
0
0
0
2
2
2
0
2
1
0
0
0
0
0
1
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
1
1
0
0
0
2
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
3
4
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
3
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
2
0
1
0
0
0
0
2
4
1
0
1
1
0
0
1
0
0
2
0
2
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
2
5
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
5
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
2
0
1
1
0
2
0
0
0
0
0
0
3
0
0
0
2
0
0
2
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
3
0
0
2
2
1
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
2
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
7
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
8
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
3
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
5
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
2
1
0
0
0
1
0
3
0
0
0
2
1
0
2
0
0
3
0
0
0
0
2
0
0
0
2
0
1
0
1
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
4
1
0
0
0
0
0
0
0
0
0
4
7
0
1
0
0
0
0
3
0
0
1
0
0
0
0
1
1
0
0
1
0
2
0
0
0
0
0
0
1
2
1
0
1
0
0
0
0
0
5
1
0
0
0
0
0
2
0
0
0
1
1
0
0
0
2
0
0
0
0
0
1
0
1
2
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
1
3
0
0
0
0
0
2
0
4
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
3
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
1
1
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
2
0
2
1
2
1
1
0
0
0
0
0
2
0
1
0
0
2
0
0
3
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
4
5
0
1
0
0
0
1
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
2
4
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
3
3
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
2
2
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
3
0
1
0
0
2
0
0
0
0
1
3
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
4
2
1
0
5
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
6
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
3
2
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
3
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
4
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
3
0
0
0
0
1
0
0
2
2
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
7
2
0
1
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
3
0
0
0
0
1
2
0
0
0
1
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
2
1
0
4
0
0
0
0
0
0
1
5
1
1
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
3
0
0
0
0
0
0
3
0
0
2
0
1
1
2
0
0
2
0
0
0
0
0
2
0
0
6
0
2
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
3
1
0
0
0
0
0
0
0
3
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
3
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
6
1
0
2
0
0
0
2
0
0
0
0
0
1
0
2
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
1
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
1
2
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
2
0
2
0
0
0
1
0
0
0
2
0
1
1
0
0
6
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
4
2
0
1
0
1
0
0
0
1
0
0
1
0
0
3
1
0
0
0
0
4
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
3
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
2
3
1
0
0
0
1
0
2
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
2
2
0
2
0
1
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
2
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
6
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
3
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
2
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
2
0
2
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
2
0
2
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
2
0
0
0
1
1
0
0
4
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
3
1
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
3
1
0
0
1
0
0
1
0
1
0
0
0
0
2
1
0
0
0
1
2
0
0
2
1
0
0
0
0
0
0
0
2
1
1
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
3
0
0
1
0
3
0
0
0
4
0
0
1
0
0
1
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
3
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
4
3
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
1
2
0
1
2
0
0
1
0
0
1
0
0
0
0
1
0
0
2
0
0
2
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
3
0
2
0
2
3
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
3
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
3
0
0
0
1
0
0
0
0
0
2
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
3
0
1
0
1
0
0
0
1
0
0
1
2
0
0
6
1
0
1
0
1
0
0
1
2
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
6
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
4
0
2
0
1
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
4
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
2
2
0
3
0
0
0
0
4
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
6
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
3
1
0
0
2
0
0
0
0
0
0
0
0
0
3
0
3
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
2
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
3
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
3
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
2
0
0
3
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
3
2
0
0
0
2
0
1
0
0
3
0
0
0
0
0
2
0
0
3
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
3
2
0
3
0
0
0
0
0
1
1
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
3
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
3
1
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
1
3
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
10
2
2
0
0
5
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
2
0
4
3
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
1
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
1
2
3
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
2
0
2
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
2
4
1
0
2
0
0
0
0
2
0
0
0
0
1
0
2
0
1
0
0
0
0
0
2
0
2
0
0
0
1
0
0
2
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
1
0
4
0
0
0
1
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
1
0
0
2
0
0
2
2
0
0
1
0
0
0
2
2
2
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
1
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
2
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
6
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
3
0
0
0
0
6
0
2
0
0
1
1
1
0
7
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
2
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
1
0
1
0
2
2
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
10
1
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
1
0
1
0
0
5
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
2
3
0
0
0
0
0
6
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
2
0
0
10
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
3
0
0
1
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
2
0
1
3
0
0
0
0
0
0
0
0
3
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
1
0
0
2
0
0
0
2
0
0
1
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
3
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
3
2
0
0
1
2
0
0
2
1
0
0
1
2
0
0
0
0
0
3
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
2
0
0
1
0
1
0
2
0
1
0
0
0
0
0
0
1
0
0
0
2
4
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
3
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
7
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
2
1
0
0
0
0
0
0
2
0
1
0
1
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
2
0
0
0
0
2
2
0
2
1
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
2
0
0
0
2
2
0
0
0
2
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
1
1
4
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
2
0
2
0
0
4
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
1
0
2
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
3
1
0
3
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
18
0
0
0
0
0
0
0
5
3
0
1
0
0
0
1
0
0
0
0
1
2
1
0
0
0
0
0
0
0
2
0
0
0
0
4
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
3
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
4
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
1
0
1
2
0
0
0
2
0
0
0
2
0
0
3
1
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
4
1
0
2
0
0
0
1
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
2
0
0
3
0
0
1
3
2
0
0
0
0
0
2
2
0
0
0
2
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
1
0
0
1
0
1
0
0
2
2
0
0
0
0
5
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
1
1
2
0
0
0
1
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
4
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
3
0
0
0
0
0
1
2
0
0
0
6
0
0
2
0
0
2
0
1
0
2
0
2
0
0
0
0
0
0
0
2
0
3
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
3
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
5
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
3
0
1
1
1
2
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
2
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
5
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
5
0
2
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
1
0
0
0
3
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
3
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
3
0
2
0
1
0
0
0
0
0
0
0
2
0
0
2
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
3
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
3
3
0
1
0
0
0
2
0
3
1
0
1
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
3
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
2
0
2
0
0
3
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
2
2
2
3
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
1
1
0
4
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
2
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
1
2
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
2
2
0
0
0
2
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
1
0
0
2
0
1
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
2
0
0
1
0
0
1
3
0
2
2
0
1
0
0
0
0
0
0
3
0
0
2
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
1
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
3
0
2
0
5
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
2
0
0
2
2
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
6
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
1
0
1
2
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
2
2
0
0
2
1
0
2
2
1
0
0
0
3
0
6
0
0
0
1
0
0
0
0
1
0
1
0
2
0
0
1
0
0
4
0
2
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
2
0
0
0
0
2
3
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
2
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
2
2
0
0
0
0
3
0
0
1
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
3
1
0
0
3
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
1
1
0
0
0
0
3
3
2
0
0
2
1
1
0
0
0
0
0
1
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
8
0
0
0
2
1
0
0
1
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
1
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
4
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
1
3
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
1
1
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7
0
0
0
1
0
1
3
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
2
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
2
1
0
0
0
1
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
2
0
0
0
0
0
1
0
0
1
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
1
1
0
3
2
4
0
0
1
1
0
0
0
1
2
2
0
0
6
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
4
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
1
0
0
0
0
2
0
1
0
0
0
2
0
0
0
1
0
1
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
2
2
2
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
3
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
2
0
0
0
2
1
1
2
0
0
0
2
0
0
0
1
4
0
0
0
0
2
0
0
0
0
1
2
2
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
1
7
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
3
0
0
0
0
0
0
0
1
1
0
0
0
0
2
2
0
3
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
11
0
2
3
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
1
4
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
3
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
2
0
0
0
1
0
0
0
3
0
0
1
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
3
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
1
1
0
2
0
1
0
0
0
1
0
0
1
0
2
0
0
1
1
1
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
2
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
3
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
2
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
4
2
0
0
0
0
1
0
0
2
0
1
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
1
0
0
0
0
0
2
3
0
1
0
0
1
0
0
0
0
0
0
3
1
0
0
0
1
0
0
2
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
5
0
1
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
1
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
1
0
2
2
2
0
0
0
0
0
0
0
2
0
0
1
2
0
1
2
1
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
3
0
0
0
0
2
0
0
0
3
0
1
0
1
0
0
0
0
0
1
2
2
0
0
0
2
0
0
1
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
3
0
1
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
4
0
2
0
0
0
2
0
1
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
5
0
0
1
0
1
0
0
0
0
0
0
1
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
4
3
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
5
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
1
1
3
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
2
1
2
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
2
2
0
0
0
0
0
4
1
3
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
2
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
3
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
1
3
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
1
2
2
0
1
0
0
0
0
1
0
1
0
0
2
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
3
2
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
1
0
1
0
1
2
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
2
0
0
5
0
1
0
0
0
0
0
0
0
2
0
2
1
0
1
0
0
0
0
0
3
0
0
0
0
0
0
2
2
0
1
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
2
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
2
0
2
0
3
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
4
1
0
1
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
2
2
0
0
0
0
1
0
0
0
0
1
0
3
0
0
0
2
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
2
0
2
1
0
0
2
0
1
0
2
0
0
0
0
0
0
0
3
0
0
2
2
0
0
0
0
0
0
0
3
1
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
1
2
0
0
2
0
0
0
0
0
0
0
9
0
2
1
0
0
1
0
2
1
0
2
0
0
0
0
0
0
1
0
2
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
1
1
1
0
1
0
1
0
0
0
1
0
2
1
0
2
3
0
0
0
0
1
1
0
0
0
3
0
0
0
0
0
0
5
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
1
1
0
0
0
0
0
2
0
0
0
0
3
0
0
1
2
2
3
0
0
0
0
1
0
0
0
0
0
3
0
0
1
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
3
1
0
0
0
0
2
2
0
0
3
0
0
0
0
1
0
2
3
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
1
0
0
2
0
1
0
0
0
0
1
0
0
0
0
2
0
7
0
0
0
0
1
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
1
2
2
0
0
1
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
3
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
2
2
0
3
1
0
0
0
0
0
0
0
2
2
2
0
0
1
0
0
0
0
1
2
0
0
0
1
0
0
2
2
0
0
0
1
0
1
1
1
0
0
0
0
4
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
3
0
0
2
0
1
0
0
0
0
0
0
0
0
2
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
1
0
1
0
0
1
1
0
0
0
0
0
0
2
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
4
0
0
0
4
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
1
0
0
0
4
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
1
0
4
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
1
0
1
2
0
2
0
2
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
1
1
1
0
1
0
0
0
2
0
0
2
0
1
0
0
0
2
0
0
0
0
0
2
0
3
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
1
1
2
1
0
0
0
1
1
0
0
3
1
1
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
3
1
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
5
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
2
2
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
2
2
2
0
0
0
0
0
0
1
0
2
2
2
0
0
0
0
0
1
0
5
0
1
2
0
0
0
0
1
0
0
0
0
0
2
0
1
0
1
0
0
1
2
1
3
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
2
0
17
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
1
0
0
0
1
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
1
1
0
2
1
0
0
0
0
2
0
0
0
0
1
0
0
0
1
5
0
0
0
2
3
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
7
0
1
1
2
0
1
0
0
1
0
0
3
0
0
0
0
1
0
0
0
0
1
2
0
1
2
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
3
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
3
0
3
0
0
0
1
1
0
2
2
0
0
0
0
0
0
1
0
2
2
0
1
1
2
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
3
0
2
2
0
0
0
1
0
0
0
0
3
0
0
0
2
2
0
1
3
1
0
0
0
0
0
2
1
2
0
0
0
0
2
1
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
4
0
0
0
0
2
1
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
2
1
0
0
0
0
7
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
2
1
0
3
1
0
2
1
0
0
0
1
1
0
0
2
0
0
1
3
0
0
0
2
0
1
0
0
0
0
5
2
1
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
4
1
0
0
0
0
1
0
2
0
0
0
0
0
0
1
1
0
1
0
1
2
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
1
1
0
2
0
0
0
0
0
1
0
0
0
1
0
0
2
2
0
2
1
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
5
2
0
0
0
2
0
0
0
0
0
6
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
2
1
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
3
2
0
0
0
3
0
2
0
2
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
5
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
5
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
3
0
2
0
1
1
0
1
2
0
0
0
0
0
1
0
0
0
2
2
1
1
0
0
2
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
4
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
8
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
1
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
2
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
8
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
4
1
0
0
1
0
0
0
0
0
0
1
2
0
0
1
1
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
2
1
2
3
0
0
0
0
0
0
0
0
0
0
2
6
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
1
0
1
3
0
1
0
0
0
2
0
0
4
2
1
0
1
0
0
0
0
0
3
1
1
0
0
0
0
0
0
0
0
0
16
0
0
0
0
0
0
0
0
3
0
3
0
1
0
0
0
0
0
0
1
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
1
0
1
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
4
0
2
0
0
0
0
0
0
2
0
0
4
0
0
2
0
5
0
0
0
1
0
0
0
0
1
2
1
0
1
0
0
0
1
0
1
0
0
0
0
4
1
0
0
1
0
1
2
2
0
0
2
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
3
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
1
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
2
1
0
0
0
2
0
0
0
1
1
2
1
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
2
2
0
1
0
0
1
2
0
1
2
0
0
2
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
2
0
0
0
3
0
0
0
6
0
1
0
1
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
5
1
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
3
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
1
6
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
3
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
1
2
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
5
0
2
0
0
0
1
2
2
2
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
2
2
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
2
2
4
0
1
0
0
0
1
0
7
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
7
0
0
0
0
0
0
0
4
1
0
0
0
0
3
0
2
0
0
0
9
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
2
2
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
4
0
0
0
1
1
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
7
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
1
2
0
0
2
0
0
0
0
0
2
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
8
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
1
0
1
1
0
0
0
0
0
0
0
2
2
1
0
0
4
0
0
0
0
2
0
0
0
0
0
4
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
4
0
0
2
4
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
3
0
0
2
1
5
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
2
1
1
2
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
2
1
0
1
0
0
0
0
1
0
2
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
1
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
2
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
2
0
3
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
2
2
0
0
0
0
0
0
1
2
0
0
0
1
1
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
3
2
0
0
0
0
0
0
0
0
1
0
0
0
2
3
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
2
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
2
2
0
0
0
3
2
0
2
0
0
0
0
0
1
0
0
0
0
1
2
0
1
1
0
0
0
0
0
2
0
2
0
0
0
0
2
1
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
5
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
2
0
2
0
4
1
0
0
0
1
0
1
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
1
0
0
0
0
6
0
0
0
0
2
0
0
0
1
0
1
0
0
0
3
3
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
2
0
0
0
2
0
1
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
3
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
2
0
3
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
4
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
4
0
1
2
0
3
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
2
0
2
0
0
0
2
0
0
3
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
2
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
1
1
0
1
0
0
1
0
1
2
0
2
0
0
0
0
0
2
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
1
1
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
2
1
0
0
0
3
2
1
0
0
3
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
1
0
2
0
1
1
0
0
0
0
0
0
0
0
3
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
2
0
1
1
0
1
6
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
1
0
2
1
0
0
0
2
0
0
0
1
0
1
0
2
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
3
0
0
0
2
0
0
2
1
0
0
0
0
1
0
0
0
1
0
1
0
0
1
1
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
1
1
0
0
0
0
2
0
0
3
0
0
0
0
1
1
0
0
1
1
2
0
0
2
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
2
0
1
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
6
2
0
0
0
0
0
2
1
0
3
0
1
0
0
0
0
4
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
5
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
2
2
0
0
1
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
1
0
0
12
0
0
0
0
0
0
3
0
0
2
1
1
0
0
1
1
0
0
0
1
1
5
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
4
1
0
0
0
0
3
4
2
0
0
2
0
0
0
0
1
0
0
0
3
0
1
2
0
0
2
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
1
0
0
2
0
0
0
0
0
2
1
2
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
1
0
0
1
1
0
0
2
0
0
1
2
0
1
1
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
8
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
1
2
0
0
2
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
1
0
5
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
2
0
0
2
1
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
2
0
0
0
4
2
0
0
3
0
0
4
3
0
5
0
0
0
0
0
1
0
2
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
1
0
0
0
0
0
0
0
1
3
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
3
1
2
0
0
0
0
0
2
0
2
1
2
0
1
0
0
0
0
0
0
3
0
0
3
0
0
2
0
0
1
0
0
2
0
0
2
0
0
0
2
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
7
0
0
0
0
0
0
0
0
1
0
0
2
4
4
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
5
0
0
1
0
2
5
0
5
0
2
0
0
0
0
1
0
1
0
1
0
0
1
1
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
1
2
2
2
0
1
0
0
0
1
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
3
0
2
0
1
2
0
0
0
2
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
14
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
1
1
0
0
0
0
0
0
2
0
0
3
0
2
0
0
3
0
0
0
0
4
0
2
1
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
3
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
3
2
2
0
0
0
1
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
2
1
0
1
0
1
0
0
0
0
0
1
0
1
0
2
1
1
0
0
1
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
1
0
2
0
0
1
0
1
0
0
0
0
3
0
0
2
1
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
1
0
0
4
0
1
0
2
0
1
0
1
1
2
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
1
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
2
0
1
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
3
0
2
2
0
3
0
0
0
2
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
2
1
0
0
0
10
1
3
2
2
0
0
0
0
0
0
0
0
0
0
0
0
4
5
0
0
4
0
0
0
0
0
2
2
2
0
0
0
1
0
1
0
1
0
2
2
1
2
0
1
1
1
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
2
0
3
1
2
0
0
2
0
1
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
2
0
0
0
0
0
0
1
0
0
2
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
1
0
0
1
0
1
0
0
0
0
0
2
0
0
1
2
0
0
0
1
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
2
2
0
0
0
2
0
0
2
0
0
0
1
0
0
1
0
0
0
1
2
0
1
1
2
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
2
2
0
1
0
0
4
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
3
1
0
1
0
2
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
1
1
0
0
0
2
0
0
0
0
7
0
2
1
0
0
0
0
3
0
3
0
2
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
1
2
0
0
0
0
0
3
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
2
0
0
1
1
1
0
0
1
0
1
0
3
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
6
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
3
1
1
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
3
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
2
0
2
1
0
3
1
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
2
1
2
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
1
0
0
0
0
1
4
0
0
0
0
2
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
1
1
0
0
1
0
0
3
0
3
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
1
0
0
2
0
0
0
5
0
0
0
0
0
0
0
4
1
0
0
0
0
2
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
1
3
0
0
0
6
0
0
0
2
0
0
1
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
2
1
1
2
0
0
0
1
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
8
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
2
2
1
0
0
0
0
0
0
2
0
0
0
1
0
5
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
1
0
2
2
2
2
2
1
1
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
5
0
0
1
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
6
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
2
0
0
3
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
5
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
3
0
0
0
1
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
5
1
0
0
1
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
3
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
2
1
0
1
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
4
0
1
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
3
0
2
0
1
0
6
3
2
0
1
0
0
0
1
2
0
0
0
0
2
0
2
0
1
1
0
0
0
0
0
0
0
2
0
2
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
6
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
3
2
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
1
1
0
0
0
1
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
5
2
0
0
0
2
0
0
0
3
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
3
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
1
2
0
0
0
1
0
0
0
2
0
1
2
2
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
9
0
0
2
0
1
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
3
0
1
0
0
1
2
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
3
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
1
3
0
0
1
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
2
0
0
0
0
0
0
4
1
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
4
0
2
0
2
0
1
0
0
0
0
1
0
1
1
0
3
0
0
3
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
2
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
3
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
1
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
2
0
0
2
0
0
1
0
0
2
2
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
1
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
2
1
0
0
0
0
1
0
0
0
1
2
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
3
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
4
0
1
0
0
2
0
0
0
1
0
0
1
1
0
0
0
1
0
0
9
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
2
1
0
0
1
0
0
2
0
0
0
3
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
1
0
0
3
0
0
0
1
0
0
0
0
0
3
0
0
4
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
6
0
3
0
0
0
0
1
4
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
1
4
0
1
0
0
2
0
0
0
0
0
0
4
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
4
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
2
0
1
0
0
0
6
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
1
0
4
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
4
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
1
0
0
0
1
0
0
3
0
4
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
3
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
2
2
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
3
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
3
0
0
0
0
0
0
2
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
2
0
1
0
1
2
0
1
0
2
0
0
1
2
0
0
0
3
2
2
0
0
0
0
2
0
0
0
4
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
4
2
1
4
1
0
0
0
0
0
2
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
5
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
2
0
0
0
1
0
0
0
1
0
1
0
0
1
0
3
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
1
4
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
2
0
2
0
2
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
5
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
6
1
0
0
0
2
0
0
0
0
2
1
1
0
0
0
0
0
2
1
0
1
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
3
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
2
1
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
3
0
2
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
2
0
1
0
2
0
0
0
0
1
0
0
2
1
0
0
1
0
0
0
1
0
0
1
0
0
3
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
1
0
5
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
2
4
1
0
0
0
0
0
0
3
2
0
1
0
0
1
0
0
0
0
1
0
3
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
5
0
0
1
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
3
0
0
2
0
0
4
0
0
1
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
3
0
4
0
0
0
0
0
0
3
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
2
1
2
0
0
0
0
2
2
0
0
0
0
2
0
0
2
2
0
1
0
2
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
1
0
2
0
0
5
0
1
2
0
5
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
1
0
2
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
2
0
0
0
0
1
4
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
2
0
0
2
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
3
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
1
0
0
0
1
0
0
1
1
0
0
0
2
0
0
2
0
0
2
1
0
1
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
2
0
0
1
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
2
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
3
0
3
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
1
1
0
0
0
1
2
2
0
0
3
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
2
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
5
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
3
0
3
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
3
0
2
0
5
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
5
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
1
0
3
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
1
2
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
2
0
0
1
0
1
0
1
0
0
0
0
0
2
0
0
0
0
2
2
3
0
0
1
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
3
0
1
1
0
0
1
0
0
0
0
0
2
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
2
0
0
0
0
1
0
1
0
2
1
1
0
0
0
0
2
2
0
0
0
2
0
0
0
1
1
2
0
0
3
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
1
0
1
0
0
0
0
0
1
2
2
2
0
1
0
2
0
0
8
0
0
0
0
0
0
0
0
0
2
0
2
0
3
0
0
0
0
0
0
1
7
0
0
0
2
0
0
2
0
0
0
1
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
3
1
0
0
2
0
1
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
1
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
4
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
2
0
1
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
7
0
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
3
0
1
0
0
0
2
5
2
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
2
1
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
2
2
0
2
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
7
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
2
0
0
1
4
2
0
0
0
0
0
0
2
0
0
0
0
10
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
2
1
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
10
0
0
0
0
2
0
1
0
0
0
2
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
4
3
0
0
0
0
0
0
0
0
1
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
1
0
0
0
0
0
2
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
7
0
0
0
0
2
0
0
0
0
0
4
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
4
1
0
1
0
1
0
2
0
0
5
0
0
0
0
2
3
0
0
2
0
1
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
3
0
1
2
0
0
0
0
0
4
0
0
0
2
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
7
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
1
0
1
0
2
1
0
0
1
0
1
1
1
0
0
2
0
0
4
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
2
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
4
0
0
0
0
2
0
2
0
0
1
0
4
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
4
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
1
0
0
2
0
0
0
0
2
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
1
1
2
0
0
0
2
0
0
1
0
2
0
0
0
0
1
0
0
1
0
0
2
1
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
1
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
2
0
0
3
1
2
2
2
0
0
0
0
1
0
0
1
0
1
0
0
1
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
2
5
2
0
0
1
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
1
2
1
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
1
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
6
0
0
0
1
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
2
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
3
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
2
1
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
4
0
2
0
0
2
0
0
0
0
0
0
0
0
1
5
2
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
1
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
1
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
3
0
0
2
0
0
2
0
0
1
2
0
0
0
0
0
1
0
0
0
0
2
1
0
2
1
0
0
0
0
0
0
2
2
0
0
1
0
0
0
3
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
1
2
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
1
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
2
8
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
2
0
0
0
3
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
2
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
3
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
2
0
2
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
3
2
0
0
0
0
0
3
6
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
2
0
0
1
0
0
0
0
0
2
3
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
1
2
1
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
1
0
2
0
5
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
2
1
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
3
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
3
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
2
0
2
0
0
0
1
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
2
0
2
2
0
0
0
0
0
0
0
1
2
2
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
1
0
2
1
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
2
0
1
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
1
1
2
0
1
0
1
2
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
2
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
3
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
2
0
1
4
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
2
1
0
0
1
3
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
3
0
2
0
0
0
1
0
1
0
0
1
0
2
0
0
0
0
0
1
0
4
0
0
0
0
1
0
0
1
0
0
1
1
0
2
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
3
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
5
2
0
0
0
2
2
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
1
2
0
0
1
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
5
0
0
0
1
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
2
1
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
1
0
0
1
0
0
2
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
1
0
3
1
0
1
0
0
0
0
0
3
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
2
0
0
1
1
0
0
2
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
1
0
1
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
2
0
1
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
4
2
0
0
1
0
0
2
0
0
0
0
1
6
0
0
0
0
0
0
3
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
3
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
1
1
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
1
0
0
0
1
0
0
0
2
1
0
8
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
3
0
0
1
1
0
0
0
0
0
0
0
2
2
2
0
1
0
2
0
0
1
0
0
0
2
1
0
0
0
2
3
0
0
0
0
2
0
2
1
0
0
2
1
1
1
0
2
0
0
0
1
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
2
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
3
2
0
0
1
1
1
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
1
0
2
1
0
0
0
3
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
1
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
5
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
11
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
2
0
3
0
4
2
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
4
0
0
3
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
3
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
6
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
2
0
1
2
1
0
2
0
0
0
0
1
0
0
0
0
0
8
0
0
2
0
0
0
2
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
1
3
0
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
2
2
0
0
0
1
0
1
0
0
0
0
0
1
3
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
5
2
0
0
0
0
0
0
0
2
2
0
0
3
0
0
0
0
0
0
0
3
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
3
0
0
0
0
1
1
4
0
0
0
0
1
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
1
0
0
1
1
0
0
2
0
0
1
1
0
0
2
4
0
1
0
1
5
0
0
0
1
0
0
0
0
0
8
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
4
2
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
2
0
2
1
1
1
0
0
2
1
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
2
2
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
2
4
2
0
1
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
4
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
4
0
0
2
0
0
0
3
0
0
0
1
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
1
3
2
0
0
1
3
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
5
0
0
0
0
1
2
0
2
0
0
0
0
0
0
3
3
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
1
2
0
0
0
0
0
0
3
0
0
0
2
0
1
0
0
0
0
1
0
0
4
0
0
4
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
3
1
2
0
3
0
1
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
2
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
5
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
4
0
2
2
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
6
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
3
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
2
0
5
0
0
0
3
0
2
0
0
0
0
0
0
2
1
9
0
0
0
1
11
0
1
0
0
0
0
3
3
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
4
1
2
4
0
0
0
0
0
0
1
0
1
0
2
0
0
1
1
0
0
0
0
4
0
0
0
0
2
0
0
0
0
1
1
0
0
0
1
0
0
0
1
3
0
0
0
0
0
0
0
5
0
0
0
1
0
2
0
0
0
0
0
0
0
0
3
0
0
0
1
1
0
1
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
1
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
3
0
1
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
2
0
0
0
2
0
3
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
1
0
1
0
0
0
1
0
2
0
0
2
1
0
0
2
0
0
0
8
1
0
0
0
2
0
0
0
1
0
0
0
6
1
0
0
0
0
0
1
4
3
0
0
0
0
0
0
0
0
0
0
4
3
2
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
5
0
0
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
5
0
2
0
1
2
0
1
1
0
3
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
14
0
0
1
0
2
0
1
0
0
1
0
0
0
1
1
1
2
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
1
1
0
0
0
0
0
2
0
0
0
2
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
1
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
3
4
0
2
0
0
0
0
0
0
3
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
2
1
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
1
0
1
0
0
0
0
0
1
0
0
0
3
1
0
4
0
0
1
0
0
0
5
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
3
0
2
2
0
0
0
0
0
1
0
0
0
2
0
0
0
4
0
1
8
0
0
1
0
0
0
0
0
0
0
3
0
0
2
1
0
0
0
0
0
0
1
0
2
2
3
0
4
6
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
1
1
1
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
3
0
0
0
0
0
0
1
0
0
0
1
1
1
1
2
1
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
3
0
0
0
2
0
2
2
0
0
0
1
0
0
1
7
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
3
0
2
0
4
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
6
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
1
2
0
6
0
1
0
0
0
0
0
0
1
1
0
2
0
2
0
0
0
0
3
0
0
8
0
0
0
0
2
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
1
0
0
0
2
2
0
0
0
0
0
0
1
0
0
5
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
3
2
0
1
0
1
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
1
0
1
0
0
0
0
2
0
1
0
0
5
0
0
2
1
0
0
0
4
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
5
0
2
0
0
0
1
0
1
0
5
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
4
0
0
2
2
0
0
0
0
1
0
0
0
1
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
2
0
0
3
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
1
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
3
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
4
0
3
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
4
0
2
0
1
0
0
3
1
2
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
2
0
0
1
0
0
0
0
0
5
0
0
0
0
0
1
0
0
0
1
0
2
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
1
0
0
0
0
4
0
2
0
0
0
1
0
1
0
2
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
5
2
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
2
2
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
3
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
1
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
1
0
2
0
2
3
0
3
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
4
0
0
0
1
3
0
0
0
3
0
0
2
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
2
2
0
1
1
0
0
0
0
2
8
2
1
0
2
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
1
1
0
0
0
0
0
0
2
0
0
1
1
0
0
0
1
0
0
0
0
1
1
0
2
0
1
0
1
0
2
0
2
4
1
0
0
1
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
1
2
1
2
0
0
1
0
4
0
2
0
0
0
0
0
0
0
0
0
0
3
2
1
0
1
2
0
0
0
1
1
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
2
0
6
2
0
1
0
0
0
0
0
0
0
0
0
0
10
0
0
0
4
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
2
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
1
2
0
3
0
0
3
0
0
0
9
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
2
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
2
0
1
0
0
1
0
0
3
1
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
7
0
2
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
1
0
0
0
8
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
2
1
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
4
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
1
0
1
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
1
0
0
0
0
0
0
0
0
2
0
0
6
1
0
0
0
1
0
0
4
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
2
1
0
0
0
0
0
0
1
0
2
1
0
0
1
0
1
0
0
0
0
0
1
0
0
2
0
1
0
2
1
1
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
3
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
7
2
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
3
0
0
0
2
2
0
0
0
0
1
0
0
0
0
2
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
2
0
0
0
0
0
2
9
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
2
1
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
2
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
1
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
2
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
1
2
0
0
2
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
4
1
0
0
1
0
1
1
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
3
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
3
0
0
0
1
0
0
3
0
0
0
0
0
0
1
0
2
0
6
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
5
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
2
0
1
0
1
0
0
1
0
0
0
0
0
4
0
0
4
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
6
2
1
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
7
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
2
1
1
0
0
0
0
0
0
1
0
0
0
0
0
6
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
2
1
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
6
0
0
0
4
0
0
0
0
0
0
1
1
0
0
0
1
3
0
0
0
0
1
0
1
0
0
0
1
0
0
6
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
3
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
1
1
0
0
2
0
2
4
0
0
0
3
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
1
0
2
4
0
0
0
0
1
0
0
0
0
0
3
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
2
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
6
0
0
0
0
1
0
0
3
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
1
0
1
0
2
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
1
6
3
0
0
1
0
0
2
2
0
1
0
0
0
0
0
0
0
1
0
3
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
2
3
0
0
2
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
4
0
1
2
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
1
0
0
3
0
5
0
0
0
2
0
1
2
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
6
0
0
0
0
0
0
0
1
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
1
0
0
15
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
11
0
2
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
1
0
0
1
2
0
2
0
0
3
0
1
0
0
2
0
0
0
0
0
3
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
2
2
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
7
1
0
0
0
2
2
2
0
0
1
0
0
0
0
0
0
1
4
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
3
0
0
3
0
0
0
2
0
2
1
0
0
1
0
3
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
3
1
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
3
2
0
0
0
0
0
0
1
0
0
1
0
2
0
4
0
0
0
1
2
0
1
2
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
2
0
2
0
2
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
2
0
0
0
0
0
0
0
0
1
3
0
0
2
1
0
0
0
0
0
2
0
0
1
2
1
3
2
0
0
2
0
0
0
0
0
3
0
0
0
1
0
0
0
2
0
0
8
1
0
0
1
0
0
0
0
0
2
0
0
0
2
6
0
0
0
2
3
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
1
0
0
3
0
0
0
0
1
3
1
0
0
2
2
2
0
2
0
0
0
2
0
0
0
2
0
0
1
3
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
1
0
3
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
2
0
0
2
2
1
0
0
0
0
0
3
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
1
0
0
0
0
0
1
4
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
5
2
0
1
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
3
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
1
0
1
2
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
2
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
2
0
0
0
0
0
0
1
1
0
2
1
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
3
1
2
1
0
0
1
2
0
0
0
1
1
0
0
0
0
0
6
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
4
0
0
0
0
2
0
0
0
0
0
1
1
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
2
1
2
0
0
2
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
1
0
2
2
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
2
0
1
0
1
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
1
1
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
2
1
0
1
0
1
1
0
0
0
2
2
0
0
0
3
0
0
0
0
0
0
1
0
0
2
1
0
0
0
1
0
0
0
2
4
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
10
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
3
0
0
0
0
1
0
1
2
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
1
0
1
0
0
0
0
2
0
1
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
0
2
0
5
4
1
0
0
0
0
0
0
1
1
0
1
0
0
2
0
0
0
0
1
0
0
0
2
0
2
0
2
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
1
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
2
0
0
0
0
3
2
0
0
0
0
1
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
4
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
2
0
0
2
0
2
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
1
0
1
7
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
2
0
3
1
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
1
0
0
1
1
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
4
0
0
4
1
0
0
1
1
0
1
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
1
1
0
0
4
0
2
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
1
0
0
0
1
0
0
2
0
2
0
3
0
0
2
0
1
0
0
1
0
2
2
0
0
0
1
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
2
0
0
3
0
2
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
3
2
3
0
0
2
2
1
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
1
0
0
4
0
3
0
5
1
0
0
0
1
1
0
0
0
0
0
2
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
2
4
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
8
0
1
0
0
0
1
0
0
0
1
0
0
0
0
3
0
2
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
5
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
5
0
0
0
0
0
2
0
0
2
6
1
0
0
0
0
0
0
1
0
0
0
0
1
5
0
0
0
0
1
0
0
4
0
0
0
0
1
0
0
0
0
0
1
7
0
1
0
0
0
0
0
0
0
0
0
0
0
0
5
4
0
0
1
0
1
0
3
0
0
0
0
0
0
3
2
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
6
0
1
1
6
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
4
0
0
0
2
2
1
0
0
1
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
2
0
0
1
0
1
0
0
0
1
0
1
2
2
0
0
1
0
5
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
3
0
2
0
1
0
0
0
0
0
0
1
0
0
3
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
2
0
1
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
2
0
0
1
3
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
2
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
2
1
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
2
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
0
1
0
0
0
1
2
0
2
0
0
3
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
2
0
0
0
2
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
4
1
0
0
0
0
1
7
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
1
2
0
0
2
1
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
5
0
0
0
1
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
2
1
0
1
0
0
1
1
0
2
0
6
0
0
0
1
1
1
0
0
1
0
0
0
1
0
0
0
0
0
11
0
2
2
0
1
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
1
0
1
0
0
0
0
3
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
2
0
1
1
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
1
0
1
1
2
0
1
0
3
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
2
0
2
4
3
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
3
2
0
0
0
0
2
0
0
2
0
3
0
0
0
0
0
1
1
0
0
0
2
2
0
0
0
2
0
1
1
0
1
0
0
2
0
0
1
0
0
1
0
0
0
1
0
0
0
0
6
0
0
0
0
2
0
3
0
1
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
4
1
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
6
0
0
1
0
0
0
1
0
0
1
0
0
0
1
2
0
0
0
2
0
2
0
0
0
0
0
2
4
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
2
9
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
2
0
4
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
2
0
0
0
0
1
0
2
2
0
3
1
1
2
0
0
1
0
0
0
0
0
1
1
4
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
5
2
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
2
0
0
0
4
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
2
1
0
0
0
0
0
1
2
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
1
0
0
1
1
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
9
0
2
0
2
0
1
3
2
0
0
0
0
0
0
0
0
0
0
0
6
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
2
0
0
3
0
0
0
2
0
1
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
2
4
0
0
2
0
0
0
1
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
3
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
7
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
1
2
0
0
1
0
0
1
0
0
0
0
0
0
0
2
4
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
5
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
2
0
1
1
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
5
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
1
0
0
1
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
3
1
0
0
2
2
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
4
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
3
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
8
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
1
1
0
0
3
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
4
0
0
4
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
6
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
9
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
4
0
0
0
0
1
5
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7
0
0
5
0
0
0
0
1
1
0
0
0
3
2
0
0
0
2
0
3
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
5
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
1
0
0
0
0
3
1
0
0
0
2
0
3
1
0
0
0
0
0
0
0
0
0
2
2
1
0
3
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
1
2
3
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
2
2
0
0
3
0
2
0
2
0
2
0
2
4
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
3
0
0
1
1
1
1
0
1
0
0
2
0
0
1
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
1
1
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
2
0
1
1
0
0
0
0
8
0
0
0
1
0
1
0
0
0
0
0
0
0
1
3
0
3
0
0
2
0
0
5
0
0
0
0
0
1
0
0
0
3
0
0
3
1
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
3
0
0
0
0
0
1
0
2
0
0
0
3
0
2
0
0
1
0
0
2
2
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
3
0
1
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
1
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
1
0
3
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
1
0
0
0
1
0
2
2
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
13
0
0
0
1
0
2
0
0
0
1
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
12
0
0
0
0
0
1
0
0
2
0
3
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
1
2
0
1
0
0
0
0
2
0
0
2
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
16
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
2
2
0
2
2
2
0
0
0
0
2
0
0
0
0
2
0
0
1
3
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
2
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
8
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
1
2
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
1
0
1
0
0
0
0
0
1
0
0
2
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
3
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
6
1
2
0
0
2
0
1
0
0
0
0
0
0
0
2
2
1
1
0
2
0
2
2
3
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
2
0
0
1
0
0
0
0
2
0
9
1
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
2
0
0
0
0
0
2
0
2
2
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
3
0
0
0
0
3
0
2
1
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
1
0
0
0
0
0
2
2
2
3
0
0
0
0
0
0
0
1
0
0
4
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
3
0
0
2
0
0
0
2
1
0
0
3
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
6
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
2
1
0
0
2
1
2
0
1
0
0
1
0
0
0
0
0
2
1
0
0
0
1
0
0
1
2
0
0
3
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
4
1
2
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
4
2
1
0
0
0
0
0
0
2
0
9
0
3
0
0
0
0
0
1
0
0
2
0
0
2
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
1
5
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
4
0
0
1
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
1
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
1
3
0
0
0
2
0
0
2
0
0
2
0
0
2
1
0
0
0
0
4
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
2
0
3
0
0
0
2
0
1
0
0
5
0
1
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
3
0
0
0
0
0
1
0
0
2
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
1
1
0
2
3
2
0
3
2
3
2
0
2
0
0
1
0
2
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
8
0
0
0
0
0
1
0
0
0
3
2
1
2
0
0
3
0
1
1
0
0
1
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
4
3
6
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
2
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
2
1
0
2
2
0
0
0
1
0
2
0
0
1
0
2
0
0
2
1
2
3
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
1
1
0
2
0
0
1
2
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
4
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
1
1
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
4
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
1
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
1
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
5
0
0
0
0
0
1
0
1
0
1
1
0
0
0
2
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
3
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
2
0
1
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
1
1
3
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
2
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
3
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
5
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
3
0
0
0
1
1
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
8
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
1
0
0
2
1
0
1
0
0
2
0
0
3
0
0
0
0
0
0
0
1
0
2
2
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
5
1
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
2
0
0
1
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
2
0
1
0
0
0
0
0
2
0
0
4
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
2
1
0
0
2
0
0
3
0
1
0
0
2
2
0
0
0
2
0
1
0
0
3
3
0
0
0
0
0
1
0
0
0
0
3
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
4
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
2
0
2
0
2
0
0
0
0
0
0
1
0
0
12
0
0
2
0
2
0
0
0
1
0
0
0
0
2
2
2
0
0
0
1
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
2
1
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
3
1
0
0
0
0
1
1
0
1
0
0
0
2
0
0
0
0
0
1
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
3
0
0
0
2
1
1
0
0
0
0
3
0
0
1
0
0
0
0
0
2
0
3
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
2
4
1
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
1
0
0
0
0
1
1
0
0
2
0
0
0
1
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
0
1
2
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
3
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
1
3
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
4
2
0
0
0
1
0
0
0
0
1
0
1
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
1
0
0
0
0
0
0
0
0
1
0
3
0
1
4
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
1
9
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
6
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
1
0
0
0
0
0
0
1
3
0
3
0
1
1
0
0
2
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
2
0
2
0
0
0
0
0
2
0
1
1
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
1
0
0
1
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
2
3
0
0
2
1
0
4
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
1
0
0
0
1
1
0
0
2
0
0
1
0
2
1
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
10
1
0
0
0
4
0
0
0
0
0
1
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
3
1
0
0
0
0
0
0
0
4
2
0
0
0
2
1
1
2
2
0
0
0
2
0
2
1
0
0
0
0
0
1
0
0
0
0
0
5
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
2
0
0
1
0
0
0
1
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
2
0
2
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
7
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
2
1
1
0
0
1
3
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
7
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
2
0
2
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
1
0
0
0
0
1
0
1
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
2
0
0
1
0
0
1
0
0
0
1
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
2
0
0
2
0
1
2
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
3
0
0
0
0
0
2
0
0
3
0
0
0
0
0
1
0
0
0
3
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
3
0
0
0
1
2
0
1
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
3
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
3
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
4
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
1
2
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
2
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
2
0
2
0
1
0
1
2
1
1
0
0
0
2
0
0
0
0
0
1
0
0
1
2
7
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
3
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
1
0
3
0
0
2
0
0
0
2
0
0
0
0
0
0
1
1
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
1
1
0
2
0
1
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
7
0
0
0
4
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
2
1
0
1
0
0
2
0
0
0
0
1
0
1
0
0
0
0
2
1
0
0
0
2
1
1
0
0
0
2
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
1
0
1
7
1
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
5
0
0
1
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
1
0
1
0
0
2
2
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
6
1
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
4
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
3
1
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
2
1
0
0
0
1
1
0
1
0
1
1
0
0
2
0
0
0
0
0
0
2
4
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
3
0
1
0
1
1
0
0
0
2
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
1
1
0
3
0
2
1
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
2
0
0
2
0
3
0
0
0
1
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
5
0
2
1
0
0
0
3
0
0
0
3
0
0
2
0
1
4
0
1
0
2
0
0
0
0
3
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
2
0
1
0
0
1
0
0
0
1
1
3
0
0
2
4
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
2
1
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
5
0
1
0
0
2
1
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
5
0
0
1
0
0
2
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
1
1
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
10
0
0
0
0
0
0
3
0
10
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
1
3
0
0
1
1
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
3
0
2
2
1
2
0
0
0
2
2
0
1
0
0
0
0
0
1
2
2
0
1
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
2
1
0
2
1
0
1
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
2
2
0
0
0
0
0
0
2
0
0
2
0
2
1
0
0
0
0
0
2
1
0
2
1
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
1
0
2
0
1
0
1
1
0
0
0
0
0
1
0
0
0
4
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
1
0
1
1
0
2
1
0
0
1
1
0
0
0
2
0
1
0
0
0
5
1
0
1
0
0
0
0
0
1
1
0
0
4
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
4
0
0
0
2
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
2
0
0
1
1
0
1
0
0
0
1
2
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
1
0
2
1
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
1
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
3
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
1
8
1
0
0
0
0
1
0
1
0
2
0
2
0
2
2
0
0
0
0
0
0
2
0
0
1
0
1
0
2
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
1
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
2
0
2
0
1
1
0
1
4
0
0
0
0
0
1
2
0
0
0
0
0
1
2
1
0
0
1
1
0
2
0
0
0
2
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
2
2
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
2
2
0
3
0
1
1
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
1
2
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
1
2
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
1
1
0
2
0
0
1
0
0
0
2
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
2
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
1
0
1
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
2
0
0
0
0
1
0
1
0
2
1
0
0
0
0
0
0
0
0
3
2
1
0
1
0
1
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
2
0
0
0
1
1
0
0
0
1
0
0
2
0
0
1
0
0
2
1
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
2
4
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
1
9
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
4
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
6
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
4
3
0
0
0
2
0
3
1
0
1
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
2
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
2
0
0
0
0
0
1
0
3
0
0
1
1
0
0
0
0
2
1
0
0
0
0
0
3
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
3
0
0
1
0
1
1
0
0
0
1
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
5
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
1
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
2
1
0
0
0
0
0
0
2
2
0
0
0
1
0
0
2
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
3
1
0
2
0
0
0
3
0
0
0
4
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
4
0
2
0
0
1
3
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
2
2
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
6
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
3
3
0
0
0
0
0
0
0
1
2
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
3
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
2
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
3
0
1
1
0
0
0
1
0
1
0
0
1
0
1
1
0
0
0
2
2
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
3
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
3
2
0
0
1
3
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
1
1
3
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
9
0
2
1
2
1
2
0
0
1
0
2
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
3
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
1
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
1
1
5
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
3
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
1
0
1
0
0
0
1
0
0
0
4
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
1
1
0
3
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
1
0
1
0
0
1
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
2
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
3
5
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
4
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
2
1
1
0
0
0
0
0
0
2
0
0
0
1
1
1
1
2
0
1
0
0
2
1
0
2
1
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
1
0
0
0
1
2
0
3
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
3
0
0
1
0
3
2
0
0
1
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
4
0
0
8
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
2
1
8
0
2
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
3
2
0
0
0
0
0
0
2
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
3
0
0
1
0
1
0
1
0
0
2
0
2
0
0
0
2
1
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
5
0
0
0
2
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
2
3
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
5
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
2
0
0
0
0
0
1
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
2
1
0
1
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
4
1
2
0
0
1
0
0
0
0
0
2
1
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
2
1
0
1
0
2
1
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
2
0
0
1
1
3
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
1
2
0
0
0
3
0
0
0
0
0
0
0
1
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
2
0
0
2
4
1
0
0
0
0
0
0
0
0
1
0
2
2
0
1
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
3
0
0
0
1
1
0
0
0
2
0
0
0
1
1
0
5
0
1
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
6
2
0
0
2
0
0
1
0
0
1
3
0
1
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
1
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
4
5
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
2
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
1
1
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
2
1
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
7
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
3
1
0
2
0
0
2
0
2
1
1
0
1
2
0
2
0
0
3
0
2
2
0
0
3
0
0
0
0
0
1
0
0
4
1
0
0
1
0
0
1
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
1
0
0
0
1
0
0
1
0
2
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
3
1
0
0
0
0
1
0
0
0
0
1
0
2
4
0
0
0
3
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
2
0
1
1
0
3
0
2
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
2
0
0
0
0
1
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
2
0
0
0
1
0
0
0
1
2
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
1
5
1
0
2
2
0
1
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
1
0
4
0
0
0
0
1
1
3
1
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
3
0
0
0
0
0
0
1
2
5
1
0
2
0
3
0
0
0
0
0
0
2
0
1
0
4
0
0
0
0
3
2
0
0
0
0
1
2
0
2
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
1
4
0
0
0
4
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
7
0
0
0
2
0
1
0
0
8
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
2
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
3
11
0
1
0
1
0
0
1
0
0
0
0
2
1
1
0
3
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
2
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
1
0
0
0
2
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
2
2
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
5
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
2
0
4
0
0
0
0
0
0
4
0
2
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
1
0
0
1
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
3
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
2
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
3
0
4
0
0
0
0
1
0
1
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
2
1
2
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
2
3
3
0
0
0
0
3
0
0
1
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
3
0
2
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
4
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
2
1
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
1
0
1
0
0
1
2
0
0
1
0
0
0
0
0
0
2
5
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
2
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
2
0
0
1
0
1
0
14
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
3
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
3
1
0
2
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
4
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
1
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
7
0
0
1
0
0
0
2
0
2
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
1
1
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
2
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
1
3
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
1
6
0
0
0
0
0
0
0
0
0
0
4
4
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
3
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
1
1
2
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
2
0
1
1
0
1
0
2
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
3
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
1
2
2
0
2
0
2
0
1
1
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
4
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
5
0
4
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
3
2
1
0
2
0
0
0
2
6
0
0
2
1
0
0
1
1
0
1
0
0
1
0
1
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
4
2
0
0
0
2
0
2
2
4
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
2
0
0
0
0
0
1
3
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
1
0
0
0
2
0
1
0
0
0
0
5
0
0
0
1
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
1
2
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
3
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
5
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
2
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
1
2
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
1
2
0
0
0
1
2
0
0
0
0
1
1
0
0
0
2
0
0
0
0
1
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
9
0
1
2
0
4
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
3
5
0
0
0
0
0
2
0
1
1
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
7
0
0
0
2
0
0
0
2
4
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
3
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
2
2
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
4
1
0
0
2
0
0
3
0
0
2
0
0
0
0
2
1
0
0
0
3
0
1
0
2
0
0
0
0
0
0
0
1
0
0
1
1
3
3
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
2
0
0
2
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
1
0
0
0
1
2
0
0
0
2
0
1
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
1
0
2
2
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
2
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
1
0
0
0
0
0
0
0
1
0
2
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
3
3
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
3
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
3
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
1
1
0
0
3
1
1
0
1
2
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
2
1
0
0
0
13
0
2
0
1
0
2
0
0
0
1
1
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
3
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
2
0
0
2
1
0
3
0
0
0
0
0
0
0
0
13
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
3
0
0
0
0
0
0
0
2
0
0
1
8
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
2
2
2
3
1
0
0
0
0
0
3
0
0
0
0
0
0
2
1
0
2
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
3
0
0
0
0
3
1
0
0
2
1
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
2
0
0
1
3
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
3
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
2
0
1
1
1
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
2
0
2
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
3
1
1
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
3
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
2
1
4
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
1
1
0
0
0
1
1
1
7
0
0
1
1
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
1
0
1
0
2
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
5
0
0
0
0
2
0
0
1
0
4
0
1
0
2
0
0
0
0
0
0
0
1
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
5
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
2
3
0
0
3
1
0
0
0
0
2
0
0
0
0
1
0
1
0
1
0
0
0
2
0
2
0
0
1
0
2
0
0
2
1
4
0
0
0
0
0
0
5
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
3
0
0
0
0
0
0
0
5
3
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
1
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
4
0
0
0
5
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
2
1
0
0
0
1
1
0
0
0
0
0
3
1
1
1
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
3
0
1
2
1
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
1
0
1
0
0
0
0
0
1
2
0
2
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
3
2
0
0
0
0
1
0
2
0
0
1
2
2
0
0
1
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
6
0
0
0
2
0
3
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
5
0
0
0
1
3
1
0
0
0
0
0
0
2
0
0
1
3
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
5
0
1
5
0
0
0
0
0
1
0
0
4
0
2
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
9
3
2
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
1
0
0
2
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
2
0
0
0
0
0
2
1
0
0
0
0
1
2
0
1
1
1
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
2
1
0
0
0
1
0
2
0
3
0
1
2
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
7
0
2
2
0
0
0
0
0
0
3
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
1
0
1
2
0
0
0
0
0
0
0
0
6
0
0
1
1
2
0
0
0
0
0
6
3
0
0
0
0
2
0
1
0
0
0
2
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7
0
0
0
0
0
1
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
3
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
1
1
0
1
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
2
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
3
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
3
0
2
0
0
2
0
3
0
1
0
0
1
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
1
1
0
0
3
0
0
0
0
1
0
0
2
4
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
1
2
0
0
0
1
1
2
0
0
0
0
0
7
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
1
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
2
0
3
0
0
0
2
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
3
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
4
0
0
4
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
1
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
1
0
2
0
1
0
0
0
0
1
0
0
4
0
2
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
2
0
0
0
1
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
3
4
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
2
0
0
3
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
2
0
0
1
2
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
2
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
1
2
0
2
1
0
0
0
2
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
4
0
0
0
0
0
5
0
0
0
0
1
1
0
0
2
1
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
11
4
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
8
0
0
2
1
0
0
0
1
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
3
2
2
1
0
3
5
0
1
0
0
0
0
0
0
0
0
1
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
1
3
0
0
0
0
9
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
1
0
2
0
4
0
0
0
0
0
2
1
3
1
0
1
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
5
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
3
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
4
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
2
0
0
0
0
2
0
1
0
0
2
0
0
0
1
0
2
0
0
1
0
1
3
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
1
2
4
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
1
0
0
3
1
0
0
0
0
0
0
1
0
3
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
6
2
2
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
5
0
2
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
8
0
1
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
1
1
0
0
0
1
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
1
1
0
2
1
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
1
0
0
1
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
1
3
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
3
1
0
0
0
1
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
1
3
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
1
0
0
2
2
0
0
0
0
1
3
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
1
0
2
0
1
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
2
2
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
5
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
1
1
0
0
0
0
1
2
2
1
1
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
1
0
1
1
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
10
1
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
2
0
13
0
0
0
0
0
0
0
3
0
0
0
0
0
3
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
1
0
0
0
1
1
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
1
3
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
3
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
2
7
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
3
0
0
0
0
0
1
0
0
1
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
3
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
2
1
3
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
3
0
0
0
1
1
0
0
0
0
2
0
0
0
2
2
1
1
2
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
2
0
1
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
3
0
0
2
0
0
0
0
0
1
1
0
0
4
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
2
1
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
6
0
0
0
1
0
0
0
1
0
3
0
0
0
0
4
0
0
2
0
0
1
1
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
3
0
0
1
0
0
1
1
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
1
2
1
0
0
1
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
2
1
0
1
0
1
3
0
0
1
1
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
5
0
0
0
2
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
1
0
0
0
0
2
1
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
1
1
0
0
0
0
2
2
0
2
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
2
0
0
2
1
4
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
3
0
0
0
3
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
1
3
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
1
0
3
0
0
0
0
1
0
0
2
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
2
1
0
2
0
0
1
0
0
1
0
0
2
0
0
0
1
0
0
1
2
2
0
2
0
0
2
0
0
0
0
0
2
1
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
6
0
0
0
0
0
1
0
0
0
0
1
0
2
10
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
2
0
2
1
0
3
0
2
0
0
3
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
2
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
6
2
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
2
0
0
0
2
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
2
0
0
1
1
1
0
0
0
1
1
0
0
2
0
1
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
1
2
0
0
0
0
2
0
1
1
0
0
0
1
0
0
0
0
0
0
0
5
2
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
2
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
3
0
0
0
1
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
1
0
2
1
0
0
2
2
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
2
0
1
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
1
0
2
0
0
1
0
0
0
0
0
1
2
0
5
0
0
0
1
2
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
1
0
6
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
1
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
3
1
0
0
1
1
0
0
0
0
0
1
0
0
0
2
0
0
1
0
3
2
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
4
1
4
0
1
0
0
0
0
0
2
0
2
0
1
0
0
0
1
0
0
0
1
2
0
0
1
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
2
0
0
0
2
0
2
0
1
2
0
0
1
0
0
0
0
3
1
2
0
0
0
0
2
0
0
5
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
3
2
0
0
0
0
0
0
5
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
7
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
1
0
1
0
0
0
0
3
0
0
0
3
0
0
0
0
0
2
0
0
1
1
0
2
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
1
0
2
0
1
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
2
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
3
1
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
5
1
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
2
0
0
2
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
2
0
0
1
3
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
3
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
2
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
3
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
4
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
4
3
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
1
0
0
1
3
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
7
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
5
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
1
0
0
1
3
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
1
2
0
0
0
0
1
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
3
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
1
0
0
1
0
3
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
1
1
0
0
2
0
0
0
0
0
0
1
0
1
4
0
1
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
2
4
0
2
0
1
0
0
0
0
0
6
1
0
0
2
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
1
0
0
0
0
2
0
0
0
0
1
0
2
1
0
2
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
3
0
0
1
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
1
2
1
2
0
0
0
0
0
2
6
0
5
0
1
0
0
0
0
0
0
0
8
0
0
0
0
0
0
1
2
0
0
2
0
0
2
0
1
0
0
0
3
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
1
2
0
1
0
2
1
0
0
3
3
0
0
0
2
1
0
0
0
0
2
1
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
2
0
1
0
0
1
0
2
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
1
1
0
0
1
0
1
2
0
0
0
1
0
0
2
0
0
0
0
2
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
1
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
8
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
3
0
2
0
2
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
2
1
0
1
0
0
1
7
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
3
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
1
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
1
0
1
2
0
0
0
0
0
0
2
1
0
1
0
0
0
0
1
9
0
0
0
0
1
0
0
0
3
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
2
0
3
1
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
3
1
0
2
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
2
2
0
0
0
3
0
0
2
0
0
0
2
0
0
2
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
2
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
2
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
1
0
0
0
0
0
2
0
2
4
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
1
1
0
2
2
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
3
0
2
0
0
0
0
2
0
0
5
0
2
0
0
1
0
2
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
3
2
0
1
0
0
0
2
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
8
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
5
0
0
0
2
1
0
0
4
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
6
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
4
0
1
0
0
0
0
0
0
2
1
1
2
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
4
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
1
1
6
0
2
0
1
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
2
2
0
0
1
3
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
3
0
0
0
0
2
1
0
0
0
1
0
2
0
3
0
0
2
0
0
0
0
2
0
3
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
1
3
0
0
0
0
0
0
4
0
0
1
0
1
0
0
2
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
2
2
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
2
2
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
1
0
1
0
0
0
3
1
2
0
0
0
0
0
0
0
2
2
0
0
3
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
2
0
0
0
0
1
1
3
1
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
2
2
2
0
1
0
2
2
1
0
0
1
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
2
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
1
1
1
0
1
0
0
0
0
0
4
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
1
2
0
1
0
8
0
0
1
1
0
0
0
0
0
0
0
3
1
1
1
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
3
0
2
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
3
0
1
0
0
0
0
2
1
1
0
0
0
2
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
2
1
0
0
2
0
2
0
0
0
1
0
3
0
1
0
0
1
0
0
0
0
2
0
0
0
3
0
0
1
0
3
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
6
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
1
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
3
0
0
0
0
1
1
0
0
0
2
0
0
3
0
0
0
0
0
3
3
0
2
0
0
1
0
0
0
1
0
0
3
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
5
0
0
0
0
0
0
3
0
0
1
2
2
1
0
0
0
3
0
0
0
1
0
1
0
0
0
0
0
0
3
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
2
12
2
0
0
0
0
0
4
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
3
3
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
1
1
1
1
2
0
2
0
2
1
1
0
1
2
3
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
1
0
0
0
0
0
0
3
0
0
2
0
1
0
0
0
0
0
0
3
0
2
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
2
2
0
0
0
2
0
0
1
0
2
2
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
1
0
4
0
0
0
0
0
0
1
2
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
1
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
2
2
0
3
0
1
1
2
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
2
0
2
3
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
1
2
4
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
1
0
0
0
0
3
0
0
1
0
0
1
0
0
0
3
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
1
1
6
0
0
1
0
2
0
3
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
2
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
2
0
0
0
1
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
3
0
0
3
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
4
0
0
1
0
0
2
0
0
0
0
3
0
0
0
0
1
1
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
3
0
1
0
0
0
0
0
1
0
2
0
0
1
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
2
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
2
0
0
2
1
0
0
2
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
2
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
1
0
1
2
0
5
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
1
2
0
0
0
1
0
1
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
2
1
0
0
0
2
0
0
1
0
0
1
0
0
1
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
1
0
0
0
0
2
1
1
0
1
0
2
0
0
2
0
0
2
0
1
0
0
0
0
0
0
2
0
3
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
1
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
2
0
2
0
0
2
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
1
0
1
0
1
1
1
0
0
2
0
0
0
2
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
1
0
0
0
2
1
0
0
2
0
5
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
1
0
0
0
0
0
0
0
2
0
2
1
0
0
0
5
2
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
2
0
2
1
2
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
1
0
2
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
1
0
0
1
0
1
2
0
0
1
1
0
0
0
0
0
3
0
0
2
3
4
0
1
1
0
2
0
0
1
0
0
0
2
2
0
2
0
0
0
0
0
1
0
0
1
2
1
1
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
2
5
2
1
0
0
0
0
0
0
0
2
0
4
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
2
2
0
0
0
2
2
1
0
0
0
0
4
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
1
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
3
1
0
0
0
3
0
0
3
2
0
1
2
1
0
1
0
5
0
2
0
1
0
0
0
0
0
0
1
1
0
0
0
2
0
1
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
1
2
0
1
0
0
1
0
0
0
0
1
0
0
2
0
0
1
1
0
0
0
0
0
3
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
3
0
0
0
0
2
0
0
0
1
1
0
0
1
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
2
5
0
0
1
0
0
0
0
0
2
3
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
3
0
1
1
1
0
2
0
0
0
3
0
0
1
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
1
0
1
0
2
0
0
0
1
0
0
0
2
0
1
2
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
3
2
2
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
2
0
0
7
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
3
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
10
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
2
2
0
0
0
1
0
0
0
0
2
0
2
4
0
0
1
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
2
1
0
0
0
0
4
1
0
3
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
2
2
0
0
1
0
0
0
2
0
0
0
0
0
1
2
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
2
1
2
0
0
0
0
0
0
0
0
0
4
0
2
1
0
1
2
0
0
3
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
2
2
0
2
0
2
0
1
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
3
2
0
1
1
2
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
5
0
0
1
1
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
3
0
0
2
0
0
2
0
0
2
0
0
3
0
0
1
4
0
0
4
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
2
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
2
0
0
2
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
3
0
0
3
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
2
0
2
0
2
0
1
0
0
0
0
1
0
4
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
3
0
0
2
2
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
4
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
1
0
1
4
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
3
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
2
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
2
0
0
0
0
1
0
0
0
3
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
3
0
0
0
1
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
1
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
3
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
1
1
1
0
0
2
0
2
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
4
2
3
0
0
0
0
2
1
0
0
0
0
1
0
0
2
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
2
2
0
0
2
2
0
2
0
0
0
0
0
2
0
0
0
1
1
1
0
0
0
2
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
3
2
2
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
2
0
0
4
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
3
0
4
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
3
2
0
0
0
0
0
0
0
2
0
2
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
2
4
0
0
0
0
0
0
0
1
0
0
5
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
1
0
1
0
0
2
2
0
0
3
0
1
0
0
0
0
0
0
0
1
2
0
2
0
0
2
2
0
2
0
0
0
0
0
0
0
0
5
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
2
0
0
0
0
4
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
1
0
0
1
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
10
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
3
0
0
0
0
0
2
0
0
0
0
0
1
1
0
3
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
8
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
3
0
2
1
4
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
4
0
0
1
2
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
2
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
6
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
1
1
0
0
0
1
0
0
0
0
0
2
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
1
0
0
2
3
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
1
1
0
0
1
0
0
0
0
0
0
2
1
0
1
1
0
0
0
1
0
1
0
0
0
1
0
0
0
6
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
1
0
0
0
3
3
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
11
0
2
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
3
0
0
2
3
2
0
2
0
0
0
0
1
0
5
0
0
0
0
0
0
0
0
0
0
0
0
1
5
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
1
0
1
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
2
1
0
0
0
2
1
0
0
0
0
2
3
0
0
0
0
0
0
2
1
1
2
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
6
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
5
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
2
0
2
0
2
0
2
3
0
0
1
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
3
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
7
0
0
5
0
0
1
0
0
0
0
0
1
0
0
0
1
0
4
2
0
0
7
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
5
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
6
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
1
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
2
0
0
2
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
1
0
0
0
2
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
11
0
0
0
1
0
2
0
0
0
0
3
0
0
0
0
0
0
0
8
1
0
1
0
1
0
0
0
0
1
0
2
1
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
2
0
0
0
0
3
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
1
2
0
0
1
3
0
0
0
1
0
0
1
0
0
0
1
0
0
0
2
0
0
0
2
0
0
1
0
0
2
1
0
0
1
0
0
0
3
0
0
2
0
0
0
1
1
0
0
1
2
0
2
0
0
0
1
0
1
2
1
0
1
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
7
0
1
0
0
0
0
2
0
0
0
0
3
2
0
2
0
1
0
0
0
0
0
2
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
5
2
0
0
0
1
3
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
4
2
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
1
1
1
0
2
0
0
0
0
2
0
0
0
2
0
0
1
0
1
3
0
0
0
0
2
0
1
3
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
9
0
0
1
0
2
0
0
1
2
0
0
0
0
1
0
9
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
1
3
0
1
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
1
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
2
0
0
0
0
0
0
2
3
0
0
0
1
1
0
0
2
0
0
4
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
2
0
3
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
1
0
2
0
0
1
0
0
0
1
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
4
0
3
0
3
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
2
0
1
0
9
0
2
3
0
1
2
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
2
2
0
0
0
0
2
1
1
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
2
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
1
1
0
1
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
4
1
0
2
0
0
0
0
3
1
2
0
0
0
1
0
4
0
2
0
0
1
0
1
0
0
0
0
2
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
2
1
1
2
0
2
1
0
0
0
0
0
0
0
4
0
0
0
0
2
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
10
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
5
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
2
1
0
2
0
1
0
0
0
0
0
0
5
2
0
0
0
3
0
0
3
0
0
0
0
2
2
0
0
2
0
0
1
0
0
0
0
0
0
1
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
10
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
4
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
3
1
1
0
0
0
1
0
0
2
0
0
6
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
5
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
0
1
0
4
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
1
0
1
0
2
0
0
2
0
0
2
0
1
0
0
0
0
1
3
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
3
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
1
1
0
0
2
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
8
0
0
0
0
2
0
0
1
1
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
3
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
6
2
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
2
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
3
2
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
2
0
3
0
4
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
1
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
3
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
2
0
0
1
2
0
0
0
0
0
0
2
0
2
6
0
0
2
0
0
2
0
0
0
1
1
0
0
0
1
2
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
3
0
0
0
2
0
0
2
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
2
3
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
1
0
0
0
0
1
0
2
0
0
0
2
4
0
0
1
0
0
0
0
0
0
0
2
3
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
2
0
2
0
4
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
2
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
2
0
3
0
1
0
1
0
0
0
1
0
0
0
0
0
6
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
3
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
7
0
0
2
1
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
2
0
0
0
0
3
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
4
2
0
0
0
0
2
0
0
0
0
0
1
1
0
7
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
1
2
0
0
0
2
2
0
0
1
3
0
0
0
0
0
0
0
2
0
0
1
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
2
0
0
2
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
1
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
2
1
0
2
0
1
0
1
2
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
2
1
0
0
0
0
2
0
1
1
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
1
3
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
1
2
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
2
1
1
0
0
0
0
2
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
4
2
0
0
1
0
0
0
0
0
0
0
0
0
2
1
1
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
1
2
0
0
0
2
2
2
2
0
0
0
3
0
2
0
0
0
1
0
0
3
0
1
0
0
0
2
1
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
4
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
1
2
0
0
3
1
0
0
2
0
0
0
1
0
0
0
1
0
0
1
1
0
0
1
0
2
0
1
0
2
0
0
0
1
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
1
0
4
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
1
2
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
3
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
2
1
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
1
0
0
2
0
0
0
0
1
0
0
0
2
0
2
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
1
1
0
2
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
2
0
1
0
0
0
0
0
3
0
0
1
2
1
0
2
1
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
2
3
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
2
1
0
2
0
0
0
0
0
1
1
0
6
0
0
1
4
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
3
0
0
2
4
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
3
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
1
0
2
1
1
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
5
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
1
0
0
3
0
1
3
0
0
0
0
0
0
2
2
0
1
1
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
2
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
1
1
0
0
1
0
1
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
8
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
2
4
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
1
0
1
0
0
3
2
0
0
0
1
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
3
3
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
6
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
1
0
2
0
6
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
5
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
3
0
4
0
0
6
0
2
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
2
2
1
0
1
0
3
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
5
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
2
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
5
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
2
0
0
0
0
6
0
0
0
0
0
3
0
3
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
3
2
0
0
1
0
0
1
5
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
3
2
0
0
1
0
0
0
2
2
0
0
0
0
1
0
0
1
0
0
1
0
0
0
3
1
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
10
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
1
0
2
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
5
0
0
0
0
1
0
2
2
0
0
0
1
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
6
0
1
0
0
0
0
0
1
0
0
0
0
0
5
2
0
1
0
0
0
0
3
0
2
2
0
8
0
0
0
2
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
2
0
1
0
1
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
1
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
11
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
1
1
0
2
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
2
0
0
0
0
0
3
0
0
0
0
0
5
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
5
0
1
4
2
0
1
1
3
0
4
1
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
1
0
0
0
0
2
0
0
5
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
1
0
0
0
4
2
0
0
0
1
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
2
0
0
0
2
0
2
0
0
2
0
2
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
5
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
2
0
0
3
0
0
0
0
4
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
3
0
0
0
0
3
0
0
0
0
2
0
0
0
2
0
1
0
1
0
0
0
2
0
0
0
0
1
0
0
3
0
0
0
1
0
0
0
1
0
2
2
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
1
0
1
9
2
0
2
0
0
4
0
2
0
0
0
2
0
1
2
1
0
0
0
0
0
2
0
0
2
0
0
1
0
1
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
4
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
2
3
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
2
2
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
7
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
23
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
2
0
2
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
1
2
0
0
1
0
0
0
0
0
0
0
0
7
0
1
0
0
0
2
0
2
0
1
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
2
0
0
0
1
1
0
0
2
0
0
1
0
0
0
0
4
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
6
0
0
0
2
0
0
0
1
0
0
2
0
2
0
0
0
0
2
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
1
1
3
0
1
0
0
1
1
2
0
0
0
0
1
0
3
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
1
0
1
1
0
0
2
0
0
0
0
9
0
2
1
0
0
0
0
0
0
0
4
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
1
2
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
1
0
0
4
2
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
4
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
2
2
0
0
2
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
1
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
1
0
0
0
0
0
0
0
13
0
0
0
1
0
0
0
0
1
1
0
0
0
3
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
2
0
2
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
2
3
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
2
1
0
0
0
0
0
0
1
0
3
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
3
0
1
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
3
0
0
0
3
0
0
1
0
0
0
1
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
1
0
0
2
0
0
0
1
1
0
3
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
1
5
0
0
1
0
0
0
0
2
0
0
1
2
2
3
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
5
1
0
0
3
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7
1
0
2
0
0
0
0
0
0
1
0
0
0
0
2
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
1
0
0
0
0
2
0
0
0
2
0
2
0
1
0
0
0
1
2
0
1
1
0
0
0
0
0
0
1
0
0
0
1
1
0
1
2
0
0
0
1
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
3
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
4
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
2
0
1
2
2
1
0
0
0
0
0
3
0
0
1
0
0
0
3
1
2
0
0
0
0
0
4
0
0
0
0
0
0
1
2
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
3
0
0
2
0
2
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
3
0
0
1
0
0
0
0
0
0
0
0
2
0
3
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
2
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
1
3
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
3
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
4
0
4
0
0
2
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
2
0
1
0
0
0
0
2
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
3
2
1
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
2
0
0
1
0
0
0
2
1
0
0
2
3
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
2
0
1
0
0
0
1
0
0
2
0
5
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
3
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
1
0
0
2
0
0
2
0
0
0
0
0
1
0
2
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
3
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
1
1
2
0
0
0
2
0
1
4
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
2
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
3
3
0
3
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
1
0
1
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
2
3
0
0
2
2
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
8
0
0
5
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
2
0
0
0
1
1
0
0
0
0
0
0
14
0
1
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
5
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
2
0
0
0
2
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
2
0
1
0
1
0
0
2
1
0
2
0
1
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
1
0
6
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
1
0
1
3
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
2
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
3
0
0
0
0
0
2
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
2
0
0
0
2
0
0
0
2
0
1
3
0
2
0
0
0
0
2
0
1
0
0
1
3
0
4
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
3
0
0
0
0
2
0
0
4
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
1
0
1
0
0
2
0
0
1
0
0
11
0
2
0
0
2
3
0
0
1
0
0
0
0
0
1
0
0
0
2
1
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
3
2
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
3
0
0
0
0
2
0
0
6
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
1
0
1
0
0
0
0
2
2
2
0
0
0
1
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
1
1
1
0
0
1
0
0
0
0
2
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
2
2
0
0
0
0
1
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
2
0
0
0
1
0
0
0
3
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
8
2
2
0
1
2
0
0
0
0
0
0
1
0
0
0
1
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
4
0
0
0
3
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
1
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
2
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
3
0
0
0
1
0
0
0
1
0
1
1
0
7
0
0
0
0
0
0
0
1
2
0
0
0
2
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
4
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
1
0
1
2
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
2
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
2
2
3
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
3
0
0
0
0
0
0
0
0
4
0
2
0
0
0
2
2
0
0
1
2
0
0
0
0
0
0
0
0
0
2
1
6
0
8
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
8
0
0
2
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
1
0
1
0
0
0
4
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
1
2
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
1
0
0
1
1
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
3
1
3
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
1
0
0
3
0
0
1
1
1
0
2
10
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
1
0
0
1
1
2
0
0
3
0
1
0
2
0
0
0
1
5
0
1
0
0
0
0
0
0
2
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
2
1
0
0
2
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
5
2
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
3
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
1
3
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
2
0
0
0
1
0
0
0
0
2
0
1
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
2
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
3
0
1
0
0
0
0
1
2
0
2
0
0
1
0
0
2
0
0
3
0
0
1
0
0
3
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
3
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
1
1
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
3
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
1
2
2
1
0
2
0
2
2
2
0
2
1
1
2
2
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
2
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
1
1
0
0
2
0
0
0
4
0
2
0
0
0
0
0
0
3
0
0
1
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
1
0
1
1
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
2
1
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
2
4
0
1
0
0
0
0
0
0
0
0
0
2
0
0
3
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
1
0
0
2
0
0
0
2
2
0
3
0
0
0
0
0
2
2
0
0
0
1
1
4
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
3
1
0
0
2
0
0
0
1
0
2
1
0
0
0
0
0
1
2
1
0
0
0
0
0
0
1
1
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
1
0
2
0
1
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
2
0
1
0
2
1
0
0
0
0
2
0
2
0
0
0
1
0
0
0
1
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
1
2
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
1
0
0
0
0
0
0
2
0
0
2
0
2
3
0
0
1
2
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
1
0
0
0
4
0
2
0
0
0
0
2
1
0
0
0
0
1
0
0
0
2
0
5
0
2
0
2
0
2
0
0
0
0
0
2
0
0
0
1
0
2
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
2
0
0
1
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
4
0
0
0
0
0
0
0
1
1
0
1
3
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
4
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
4
2
0
2
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
4
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
2
2
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
1
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
1
1
0
0
0
0
0
2
0
0
1
0
0
2
1
0
0
0
1
1
1
0
0
0
0
0
0
0
2
2
0
2
0
0
1
0
0
2
1
0
0
0
3
0
0
0
1
0
0
0
0
0
2
0
0
1
1
0
0
0
1
1
0
0
0
1
0
1
0
3
0
0
0
0
0
0
0
0
1
1
1
0
1
1
1
0
0
0
2
0
2
0
0
0
0
2
1
0
2
0
0
0
0
0
1
0
0
0
1
0
2
0
0
1
1
2
0
1
4
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
9
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
1
0
0
1
0
2
0
1
0
3
1
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
6
2
1
0
0
0
0
1
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
1
5
2
0
0
0
2
1
0
0
0
1
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
3
0
0
0
2
1
0
2
0
5
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
1
0
1
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
5
0
0
0
0
5
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
4
0
0
0
1
0
0
0
0
2
0
0
1
1
0
0
2
0
0
0
2
4
0
0
1
0
0
2
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
3
0
1
3
0
0
0
2
0
0
1
0
2
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
1
0
0
0
0
2
0
0
3
0
2
2
0
0
0
2
0
1
2
0
0
0
4
0
0
0
0
1
0
0
0
0
0
1
0
1
2
0
0
0
1
0
0
0
0
2
0
1
0
1
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
2
2
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
2
0
0
4
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
3
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
2
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
3
1
0
1
0
0
1
1
0
2
1
0
0
1
0
1
0
4
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
4
3
3
1
0
2
0
6
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
2
4
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
2
0
0
0
1
0
0
0
0
3
0
0
2
1
0
0
0
1
0
5
0
0
2
1
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
3
0
0
0
1
9
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
1
0
2
0
0
0
1
0
3
0
2
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
3
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
2
2
3
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
5
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
2
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
2
0
2
0
0
0
4
0
2
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
1
1
1
0
0
0
0
0
1
1
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
7
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
2
0
0
0
0
0
2
0
0
0
1
2
2
0
0
2
1
0
0
0
0
0
3
1
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
2
0
0
0
2
2
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
3
1
0
1
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
4
0
0
0
2
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
3
1
2
0
1
0
1
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
3
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
2
0
1
0
1
0
2
0
1
2
0
4
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
1
2
2
6
0
0
0
0
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
5
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
2
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
1
2
0
1
0
0
0
3
0
7
1
0
2
0
1
0
0
4
1
3
0
0
0
0
0
0
0
2
2
4
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
1
2
0
1
0
1
0
1
0
0
2
0
0
2
0
0
1
0
0
0
1
2
1
0
0
0
0
1
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
2
0
0
2
8
0
1
0
6
0
2
0
0
1
0
1
0
0
0
0
0
2
0
0
1
0
0
1
0
0
1
0
2
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
10
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
3
2
0
0
0
0
2
0
0
0
0
0
0
3
0
4
0
0
2
0
0
0
1
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
2
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
1
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
4
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
2
0
0
0
0
0
0
1
0
1
3
0
0
3
0
3
0
0
0
0
0
0
0
1
2
0
0
2
2
4
0
0
1
1
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
6
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
4
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
1
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
3
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
2
3
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
3
1
1
1
0
0
0
0
4
0
0
0
0
0
1
0
0
0
3
0
2
0
0
0
0
0
0
0
3
0
0
0
0
2
0
1
0
2
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
1
0
1
1
4
0
2
0
0
0
1
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
1
0
9
0
0
0
1
0
2
3
0
0
2
0
2
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
2
0
0
2
0
2
0
1
0
0
0
1
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
2
0
2
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
1
0
2
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
2
0
0
0
1
0
4
2
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
2
0
7
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
6
5
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
16
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
7
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
2
1
0
0
0
0
0
0
0
0
0
0
1
0
4
2
0
0
0
0
0
0
0
0
8
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
4
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
2
0
0
2
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
1
0
0
1
0
0
2
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
1
0
0
3
0
0
0
0
2
0
0
0
7
2
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
5
1
0
0
0
0
0
0
0
0
2
2
3
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
4
0
0
2
1
0
0
0
0
0
0
0
1
0
0
1
2
0
0
2
1
1
0
2
2
2
0
0
0
0
1
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
3
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
2
1
0
0
1
0
0
1
2
0
0
4
0
0
0
1
1
0
0
0
0
2
2
2
1
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
19
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
5
2
0
1
1
1
0
0
1
0
0
0
2
0
0
0
0
0
0
1
2
2
3
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
4
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
1
1
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
1
0
2
1
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
6
0
0
0
0
0
0
3
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
1
0
1
0
4
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
4
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
1
1
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
10
1
0
0
0
0
0
0
1
0
0
0
0
0
7
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
1
0
0
4
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
1
6
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
6
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
2
0
2
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
3
0
3
3
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
2
1
1
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
3
0
1
1
1
2
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
7
0
0
0
2
0
2
2
0
1
0
0
0
0
0
1
0
0
0
2
2
1
0
0
0
0
0
2
2
0
1
0
0
0
0
0
2
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
2
0
0
0
0
0
1
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
1
0
0
0
1
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
3
2
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
3
0
0
1
2
0
0
0
1
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
2
2
2
1
0
2
2
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
3
0
1
0
0
0
2
2
1
0
0
6
0
0
0
0
0
0
0
2
0
1
1
5
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
7
0
0
0
0
1
0
0
0
0
0
1
1
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
3
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
4
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
3
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
1
0
0
0
3
0
0
2
1
2
2
0
0
0
0
1
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
3
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
1
1
1
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
2
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
2
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
2
0
3
2
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
2
0
4
2
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
1
0
0
3
1
0
0
0
2
2
1
0
0
0
0
0
1
2
0
0
0
0
1
0
0
1
0
0
3
2
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
2
0
1
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
1
0
0
0
1
0
7
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
2
0
3
1
0
0
7
0
0
0
2
0
0
0
2
2
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
3
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
3
1
2
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
2
0
0
0
1
2
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
3
0
0
0
0
2
2
0
3
0
1
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
2
0
4
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
3
3
0
0
0
1
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
6
0
3
2
1
0
0
1
0
0
0
2
0
3
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
3
1
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
3
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
1
1
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
3
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
3
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
2
0
2
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
3
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
1
1
0
1
0
0
3
1
5
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
2
0
1
2
0
0
0
1
0
0
0
3
0
0
0
0
2
2
0
1
0
0
0
0
2
0
0
2
0
0
5
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
2
0
0
0
1
1
0
0
2
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
6
0
0
0
0
0
2
0
1
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
3
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
5
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
3
0
0
0
9
0
0
0
3
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
7
0
0
0
0
1
0
0
2
1
0
3
0
0
0
0
0
1
1
2
0
0
2
0
0
1
1
0
0
1
0
0
0
0
2
0
0
2
0
0
0
1
3
0
0
0
0
0
2
1
2
1
0
0
0
0
0
0
1
1
0
0
2
4
2
0
2
0
0
1
0
1
0
0
0
1
5
1
2
1
0
2
2
0
2
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
1
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
1
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
1
2
0
2
0
0
0
2
0
0
0
1
0
4
0
0
2
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
1
2
6
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
3
0
6
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
2
2
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
4
0
0
0
0
0
3
0
0
0
0
0
2
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
1
1
0
0
0
2
0
0
2
0
2
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
7
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
2
0
1
0
0
0
2
1
0
0
0
0
0
0
2
0
1
0
0
0
2
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
1
0
1
0
0
0
0
0
0
0
4
0
2
0
0
1
0
0
0
2
0
0
0
0
3
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
3
0
0
0
1
0
0
0
0
0
1
1
0
0
9
2
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
2
0
1
0
0
0
1
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
5
0
2
2
0
0
0
1
0
0
0
1
0
0
0
4
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
2
5
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
1
0
0
1
0
1
0
0
0
0
3
1
1
0
0
0
0
0
3
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
1
2
0
0
1
0
0
4
0
0
0
0
0
3
0
0
0
2
0
2
0
4
2
0
2
0
3
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
3
0
2
0
0
0
1
0
0
1
0
0
0
1
0
0
5
0
0
0
0
1
1
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
5
5
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
1
2
0
2
1
0
0
0
0
0
2
0
2
0
7
0
2
0
1
5
0
1
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
3
0
1
0
0
0
2
0
0
1
1
0
0
0
0
1
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
0
0
0
2
0
0
0
0
0
0
0
1
1
0
1
1
2
0
0
0
0
0
1
2
3
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
5
1
0
0
2
0
0
0
1
0
3
1
0
2
0
2
1
0
0
1
0
0
2
0
0
0
0
0
0
3
0
0
1
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
1
0
2
2
2
0
0
2
0
0
0
0
1
4
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
1
3
0
0
0
0
2
0
0
0
0
0
0
1
0
1
2
0
0
0
1
1
0
0
0
2
2
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
1
2
0
0
0
0
1
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
3
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
1
0
0
2
2
0
3
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
3
1
0
0
0
0
0
0
1
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
3
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
1
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
3
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
17
0
1
0
0
0
0
0
2
0
0
0
5
2
0
2
0
1
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
6
3
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
2
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
4
0
0
0
1
0
3
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
2
0
0
6
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
3
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
2
1
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
2
0
0
1
0
7
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
2
2
0
0
2
0
1
0
1
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
8
2
1
0
0
0
0
0
0
0
3
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
12
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
2
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
1
2
2
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
1
0
1
0
1
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
1
1
0
0
0
0
0
1
5
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
1
1
0
0
0
1
0
2
0
0
2
1
0
0
0
3
0
2
0
1
0
0
0
0
0
3
0
0
1
2
2
2
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
3
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
2
0
0
0
0
0
0
1
1
1
1
2
4
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
4
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
4
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
2
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
1
1
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
2
3
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
2
3
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
1
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
3
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
2
0
4
0
0
2
2
0
0
1
1
0
1
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
1
1
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
2
0
0
0
2
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
2
1
1
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
1
2
2
0
0
0
0
0
1
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
1
0
1
1
0
0
0
0
2
0
0
0
0
0
1
2
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
14
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
3
2
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
5
0
0
1
2
0
2
1
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
5
0
0
0
1
1
0
0
1
1
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
4
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
4
2
0
2
0
2
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
2
0
1
0
0
0
2
0
0
3
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
1
0
0
2
0
4
5
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
2
2
2
0
0
0
1
0
0
0
0
0
2
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
5
0
0
0
0
0
4
8
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
1
3
0
0
0
0
0
2
0
0
0
0
0
1
2
1
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
6
0
2
0
0
0
2
0
0
1
0
1
0
0
0
0
0
1
0
0
0
2
1
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
2
0
0
2
1
1
0
0
2
3
0
0
0
0
0
0
0
0
1
0
0
2
2
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
1
0
1
1
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
1
4
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
2
1
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
3
0
2
0
5
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
6
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
5
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
1
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
3
3
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
1
0
0
0
0
0
1
0
2
0
0
2
0
0
1
0
4
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
3
0
1
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
2
0
1
0
0
0
1
1
0
3
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
1
2
0
0
1
3
0
0
0
0
0
0
1
1
1
2
0
0
0
0
0
0
4
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
5
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
1
0
3
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
2
0
2
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
1
3
0
1
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
4
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
1
1
0
0
0
0
1
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
3
0
0
1
1
2
0
2
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
1
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
3
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
5
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
1
0
0
1
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
2
1
0
1
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
3
0
0
3
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
2
4
0
0
1
0
0
2
0
0
1
2
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
2
0
0
0
1
0
0
1
2
0
2
1
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
1
0
0
0
1
0
0
0
0
0
2
2
1
0
0
1
3
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
3
2
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
1
2
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
2
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
1
0
0
0
0
0
2
3
0
0
3
0
0
0
0
0
1
0
1
0
3
0
0
0
1
0
1
0
2
0
0
0
1
2
0
3
2
2
2
0
0
1
0
0
0
0
0
2
0
0
0
1
3
0
0
0
0
0
0
0
0
1
0
1
1
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
8
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
8
0
1
4
0
0
0
0
0
0
0
0
1
0
0
0
0
6
0
0
0
1
0
7
0
0
0
2
2
0
2
0
3
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
5
0
0
0
1
0
0
0
22
2
0
0
2
0
0
0
0
0
1
0
0
0
1
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
2
1
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
1
0
0
3
1
0
0
1
4
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
3
0
0
0
1
0
0
0
0
0
1
0
1
1
2
1
1
0
0
1
0
0
0
1
0
1
0
0
0
3
0
3
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
3
3
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
1
0
0
1
2
3
0
0
0
0
0
2
0
5
1
2
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
1
0
0
0
3
0
2
1
0
0
0
0
0
0
2
1
0
0
3
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
8
1
0
0
0
0
1
0
0
1
0
1
0
1
0
1
0
0
0
2
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
1
0
1
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
7
4
0
0
0
1
0
0
3
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
1
2
0
0
0
0
0
2
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
1
0
1
0
0
0
1
2
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
2
0
0
4
0
0
0
0
0
0
0
0
0
2
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
3
0
0
2
2
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
2
1
0
2
0
0
0
1
5
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
2
0
1
0
0
0
1
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
5
0
0
3
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
1
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
7
0
1
2
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
1
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
4
0
3
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
3
0
2
0
0
0
0
0
2
0
4
0
2
0
0
1
0
0
3
0
0
0
1
0
1
0
2
0
0
0
3
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
1
2
3
0
2
2
0
2
0
0
0
0
0
2
0
0
0
1
3
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
2
0
1
0
0
0
2
0
0
2
0
0
0
0
0
4
0
0
0
0
4
0
0
0
1
0
2
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
2
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
2
0
0
0
3
0
2
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
2
0
3
1
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
21
3
0
2
0
0
0
0
0
2
2
1
0
2
0
2
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
5
2
2
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
5
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
4
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
2
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
3
2
2
0
1
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
8
0
0
2
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
1
1
0
3
0
0
1
1
0
0
0
0
0
0
0
4
0
1
0
1
0
0
0
0
0
2
1
0
0
0
0
2
2
2
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
3
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
5
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
4
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
3
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
3
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
2
1
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
1
0
0
2
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
1
0
2
1
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
1
1
0
1
0
0
0
0
0
3
0
0
0
0
1
0
0
2
0
5
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
3
0
3
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
2
0
1
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
5
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
5
0
2
0
0
1
3
0
4
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
1
0
2
1
0
0
1
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
3
1
0
1
1
0
3
3
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
4
1
0
0
0
1
1
0
3
0
2
0
1
0
4
1
0
1
0
0
0
0
0
0
1
0
1
0
0
1
1
2
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
3
0
0
2
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
7
2
0
0
2
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
4
3
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
3
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
2
0
0
2
0
1
0
0
2
0
0
0
1
0
0
1
3
0
0
2
0
0
0
2
0
0
2
0
0
2
2
0
0
0
0
0
2
2
0
0
0
2
3
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
4
0
2
0
0
0
0
0
0
0
1
0
1
0
1
1
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
1
8
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
3
0
0
0
0
0
0
5
1
0
0
0
0
0
0
0
2
2
0
0
0
0
4
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
4
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
1
2
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
2
0
0
1
0
2
0
0
0
0
2
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
1
0
0
2
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
4
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
5
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
2
0
0
0
12
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
2
0
4
2
0
0
0
0
0
1
0
0
3
2
2
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
2
0
3
1
0
0
0
0
1
1
0
5
0
0
0
1
5
0
0
0
7
0
0
0
1
0
0
2
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
1
1
1
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
1
0
1
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
1
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
4
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
2
1
0
0
1
1
0
0
1
2
0
0
0
9
0
0
0
2
0
0
1
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
4
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
2
0
5
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
3
0
1
0
2
0
2
0
0
0
0
1
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
8
0
1
0
11
0
1
0
0
0
3
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
2
0
1
0
0
0
0
0
0
0
2
0
4
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
4
0
0
3
0
2
0
0
0
0
0
2
0
0
2
0
0
3
2
0
0
0
0
1
0
0
0
4
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
7
1
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
5
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
3
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
3
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
1
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
3
2
1
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
3
0
0
0
0
2
5
10
1
1
0
0
0
1
2
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
3
2
2
0
0
0
1
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
4
0
0
0
0
1
0
0
0
2
0
2
0
0
0
1
2
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
2
0
0
3
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
2
0
0
1
0
0
1
1
2
0
0
1
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
1
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
2
0
2
0
5
0
2
0
0
3
0
0
3
1
0
0
0
1
0
2
0
0
0
1
0
0
0
2
2
2
2
2
0
0
0
0
0
0
0
2
0
2
0
1
1
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
4
0
0
1
1
0
0
0
0
2
2
1
1
0
0
1
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
10
0
0
1
0
0
1
0
1
0
1
0
2
0
0
0
2
0
0
0
0
0
0
3
3
0
0
0
0
0
1
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
2
0
0
2
0
0
0
0
0
0
3
0
2
1
1
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
2
0
1
1
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
2
1
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
4
1
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
2
5
2
2
0
0
0
0
0
2
0
2
0
0
1
0
0
0
1
1
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
1
0
0
0
0
1
0
4
0
2
0
0
1
2
0
0
0
0
0
0
0
3
0
2
0
0
3
2
0
1
0
0
0
0
2
0
1
0
2
3
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
1
0
0
1
1
0
0
0
0
1
2
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
1
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
2
0
0
11
1
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7
1
2
0
7
2
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
1
3
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
1
0
0
2
0
0
0
3
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
5
0
0
0
1
0
0
0
2
0
2
0
0
1
3
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
2
0
0
3
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
2
0
0
2
0
2
0
0
3
1
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
2
0
1
1
1
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
4
0
0
0
2
1
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
1
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
2
1
0
2
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
1
0
5
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
4
4
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
7
0
1
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
3
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
2
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
2
0
3
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
1
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
2
0
0
0
1
0
0
0
2
0
0
2
2
0
0
0
0
1
0
0
3
0
1
4
0
0
0
0
1
0
1
0
0
0
0
0
0
0
29
0
0
0
1
0
0
0
0
0
0
0
0
5
0
2
0
0
1
0
1
1
1
0
0
0
2
0
0
0
0
1
1
0
0
0
0
4
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
2
0
0
1
2
2
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
1
0
1
0
0
1
3
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
1
0
2
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
5
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
3
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
3
1
0
0
0
1
0
0
0
0
0
0
5
0
2
0
2
0
0
0
0
0
1
0
0
0
2
1
0
0
2
0
0
0
2
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
4
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
1
2
1
0
0
0
0
2
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
2
0
2
1
0
0
0
0
1
0
0
0
0
0
0
1
3
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
3
0
1
0
0
0
1
0
2
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
3
0
0
0
2
1
0
0
0
0
1
3
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
3
1
2
0
1
0
0
1
1
0
0
0
0
0
1
0
2
2
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
5
0
0
0
1
1
0
0
2
0
0
0
4
0
0
2
0
0
0
0
1
0
0
1
2
0
0
1
0
0
0
1
1
0
0
0
0
1
2
0
0
8
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
4
0
2
0
0
0
0
0
0
2
2
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
1
0
8
0
0
0
0
0
1
0
0
0
0
6
0
0
0
0
0
0
0
1
1
0
1
0
2
2
0
1
0
0
1
1
0
0
1
0
2
1
0
4
0
0
0
0
0
1
0
0
1
0
0
0
1
2
0
0
1
3
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
2
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
3
0
0
2
0
2
0
0
0
0
1
2
0
0
3
2
0
0
0
0
1
0
0
1
0
0
5
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
3
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
1
0
0
1
2
1
0
0
0
0
0
1
0
0
2
0
4
0
0
0
0
0
0
0
2
1
0
0
0
0
5
0
0
3
0
2
0
0
2
0
0
1
0
0
2
0
1
0
0
0
0
2
1
0
0
0
5
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
1
2
2
1
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
1
1
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
3
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
5
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
2
0
2
0
0
0
0
0
2
1
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
3
2
0
2
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
1
0
1
1
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
2
1
0
1
0
1
0
0
0
2
0
1
0
0
0
0
0
0
1
1
0
0
0
2
0
2
0
1
0
1
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
6
0
0
0
1
0
4
0
1
1
2
0
2
2
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
25
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
1
0
0
0
2
0
2
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
3
0
0
2
0
3
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
2
0
2
0
0
0
1
2
1
0
0
0
2
1
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
2
0
3
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
3
0
0
0
0
0
1
0
1
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
7
0
0
0
0
0
1
0
3
0
0
0
0
3
0
1
0
2
1
1
2
1
0
0
0
4
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
4
0
1
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
1
2
0
0
2
2
0
4
0
1
1
2
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
2
1
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
2
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
1
2
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
6
0
0
2
6
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
1
1
0
0
0
0
3
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
2
0
0
3
1
0
0
0
1
2
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
8
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
4
6
0
0
1
2
0
0
4
0
0
1
0
0
0
0
1
0
0
3
2
1
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
2
0
0
0
0
2
0
0
1
0
0
1
0
1
0
2
1
0
0
0
0
0
0
19
1
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
2
0
0
1
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
2
2
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
1
8
0
0
1
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
3
0
2
0
0
0
1
2
0
0
1
0
1
2
1
0
0
0
2
0
3
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
6
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
1
0
1
1
0
0
2
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
3
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
5
0
0
1
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
1
2
0
0
0
3
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
6
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
3
0
0
2
0
0
2
0
0
0
1
0
0
1
2
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
1
0
1
0
2
1
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
4
2
0
0
0
1
0
1
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
3
3
0
0
0
2
0
0
0
0
0
2
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
1
0
1
0
0
2
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
3
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
2
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
3
0
2
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
3
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
1
0
1
0
0
0
1
3
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
1
0
0
2
0
0
6
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
9
0
0
0
0
0
0
0
2
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
8
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
4
2
0
0
0
0
0
0
1
0
2
0
0
2
0
2
0
1
0
0
0
0
2
0
0
2
7
0
1
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
1
0
1
0
0
2
0
0
1
0
2
0
0
0
1
0
0
1
0
0
0
2
0
1
0
1
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
3
0
0
1
1
0
0
2
2
1
3
0
0
0
0
0
2
0
0
0
3
0
0
0
0
1
2
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
1
0
0
0
0
2
4
0
0
0
3
0
0
4
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
2
2
0
2
0
0
0
0
1
0
3
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
2
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
5
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
6
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
5
0
0
1
0
0
2
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
1
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
2
2
1
0
0
0
0
3
0
0
2
2
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
2
0
3
1
0
0
0
0
1
0
0
2
0
3
0
0
0
0
0
2
0
0
1
1
0
1
0
0
1
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
1
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
5
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
1
0
0
2
0
1
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
1
2
0
0
4
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
2
5
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
2
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
1
1
0
2
2
2
0
1
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
2
0
0
0
0
3
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
4
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
1
0
2
0
0
0
0
1
0
0
0
1
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
5
0
0
0
0
0
1
0
0
1
0
0
2
0
2
1
0
0
0
1
0
4
1
0
0
0
1
4
1
0
0
2
0
1
0
0
0
0
0
0
2
2
2
1
0
0
0
0
0
0
3
0
1
1
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
1
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
1
0
0
1
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
4
3
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
4
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
1
1
2
1
0
0
0
0
0
0
0
1
2
0
1
0
0
0
1
5
0
0
0
0
0
0
2
0
1
0
0
0
3
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
3
3
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
5
0
0
2
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
4
2
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
1
0
0
3
1
0
3
0
0
0
1
0
0
1
2
1
0
0
0
0
0
2
0
0
0
2
1
0
4
1
0
2
0
0
0
1
0
0
0
0
0
3
1
0
2
0
0
2
0
2
0
2
0
0
0
0
1
0
0
1
1
0
0
1
3
1
1
0
0
0
1
0
0
10
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
5
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
5
2
0
0
0
0
1
0
2
0
1
0
0
0
2
1
0
2
0
0
1
1
0
4
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
4
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
1
1
0
0
0
0
2
1
1
2
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
1
0
2
0
4
2
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
5
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
5
2
0
1
0
0
1
1
1
0
0
0
0
2
0
2
0
1
0
0
1
8
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
2
0
2
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
3
0
2
0
2
0
0
0
0
0
1
1
0
2
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
2
0
9
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
2
1
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
4
0
5
2
0
0
1
0
0
0
0
0
0
0
3
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
3
0
0
0
0
0
2
2
0
0
0
0
0
1
1
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
8
0
0
2
6
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
2
2
0
0
1
0
0
1
2
1
0
0
0
0
2
1
1
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
2
1
2
0
0
1
0
0
0
0
1
0
0
0
0
2
5
0
2
0
0
0
0
0
3
0
0
0
0
0
5
0
1
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
4
0
0
2
5
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
3
0
2
1
0
0
0
1
1
0
0
0
2
2
0
0
6
1
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
2
0
1
1
0
0
0
0
1
0
0
0
0
0
4
0
1
1
0
0
0
0
0
0
0
1
0
3
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
4
6
0
0
1
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
5
0
0
0
3
0
2
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
2
0
3
0
1
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
4
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
5
0
1
0
0
0
0
0
0
1
3
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
1
1
0
2
0
1
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
1
4
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
5
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
1
0
2
0
2
0
0
2
0
0
0
0
0
1
0
2
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
2
0
2
0
5
0
2
0
2
0
1
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
2
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
5
0
0
0
2
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
3
2
0
0
0
0
0
0
4
0
0
1
0
2
2
0
0
0
0
1
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
4
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
1
1
0
0
0
2
0
2
2
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
3
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
3
2
0
0
5
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
1
0
2
0
0
0
0
4
0
2
0
2
0
0
0
2
4
2
2
0
0
2
2
1
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
4
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
2
0
0
1
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
3
0
0
0
0
2
2
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
2
0
3
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
3
1
1
1
0
0
0
0
0
0
0
1
2
1
1
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
3
0
2
0
0
1
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
1
1
0
0
0
3
0
0
1
0
0
0
0
2
9
0
0
0
0
0
0
0
1
0
1
2
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
2
1
3
2
2
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
4
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
1
6
2
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
5
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
1
2
0
1
1
0
0
0
0
1
0
0
0
0
0
0
7
2
0
0
0
0
0
0
0
0
1
0
3
1
0
0
2
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
2
0
0
2
2
0
1
0
0
3
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
2
0
1
0
0
0
0
0
1
0
0
0
2
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
3
3
0
0
0
0
2
1
1
0
2
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
2
3
0
0
0
2
0
0
3
0
0
0
0
1
0
0
1
0
0
1
2
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
1
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
2
1
1
0
1
2
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
5
2
0
0
2
0
0
0
0
2
0
0
1
0
0
0
2
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
1
0
1
3
1
2
0
1
0
0
4
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
2
5
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
1
0
0
0
0
2
2
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
4
0
1
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
2
0
0
0
2
0
0
1
2
0
1
0
0
2
4
2
0
2
0
0
2
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
4
0
1
0
0
0
2
0
2
0
1
0
0
0
5
0
1
2
2
1
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
2
0
0
0
1
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
1
0
0
0
2
1
1
0
1
1
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
3
3
2
1
2
1
1
1
3
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
1
1
0
2
0
0
0
0
0
0
0
0
1
3
1
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
1
1
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
1
1
6
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
5
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
0
0
3
2
0
0
0
0
1
1
2
1
1
0
0
2
0
0
1
0
0
0
1
1
1
0
0
4
1
0
0
2
0
0
3
1
0
1
0
0
3
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
2
0
2
0
1
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
2
0
3
7
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
2
2
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
6
0
0
0
1
0
0
0
1
0
0
4
0
1
1
1
0
2
0
2
0
0
0
1
0
0
0
1
1
2
4
0
0
0
3
0
1
0
3
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
1
1
0
0
1
1
0
1
0
4
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
1
0
0
0
0
0
0
1
2
1
0
0
1
0
1
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
1
0
0
1
0
0
0
2
0
2
0
0
0
0
2
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
2
2
0
0
2
0
2
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
1
0
3
0
0
0
0
1
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
2
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
3
0
0
2
0
2
0
1
0
0
0
0
2
2
0
0
0
0
2
1
4
0
0
0
0
0
2
0
0
2
0
0
0
2
0
1
0
1
0
0
0
0
5
2
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
1
0
2
1
1
0
0
1
0
2
0
4
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
2
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
1
2
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
2
0
0
1
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
1
1
2
0
0
0
3
1
4
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
2
2
0
2
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
2
1
0
0
0
0
1
1
2
0
0
0
0
2
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
2
5
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
1
0
0
0
0
0
0
1
0
5
0
0
0
0
0
0
3
0
3
0
2
0
0
2
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
2
0
2
0
3
0
1
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
3
0
0
1
0
0
0
2
0
0
0
0
4
0
0
0
0
1
0
0
0
2
0
1
2
0
0
5
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
3
1
0
0
0
0
4
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
5
2
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
4
0
0
0
0
0
2
5
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
4
0
4
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
2
5
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
4
0
0
0
0
0
0
1
2
0
0
1
0
0
0
1
0
0
0
0
0
0
4
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
3
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
2
1
2
0
0
0
0
0
2
0
6
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
1
0
0
0
0
1
0
3
0
0
0
0
0
0
13
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
1
3
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
1
0
0
3
1
0
3
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
1
0
0
0
1
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
2
1
0
0
0
2
0
0
2
0
0
0
2
3
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
6
1
0
0
1
0
0
1
0
0
3
1
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
1
2
0
2
0
2
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
1
0
0
0
1
0
0
0
2
0
0
2
0
0
1
2
0
0
2
0
0
1
1
0
1
0
0
1
1
0
0
0
0
0
2
0
0
0
1
0
0
3
0
1
3
0
0
0
0
0
0
3
0
0
0
0
1
2
0
0
0
0
0
2
0
0
1
0
0
0
3
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
4
0
0
0
0
0
0
0
1
0
0
0
2
0
1
1
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
1
0
1
0
2
0
3
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
1
0
2
0
0
0
1
0
0
2
0
0
1
5
0
0
4
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
3
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
2
0
1
0
1
3
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
3
2
0
0
2
0
1
0
0
0
0
1
0
1
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
4
0
0
0
0
0
0
0
0
0
0
0
5
0
2
7
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
2
0
1
2
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
12
0
0
1
2
0
0
0
0
6
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
1
1
0
2
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
2
3
5
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
6
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
2
0
2
0
0
1
0
5
1
0
0
0
0
0
0
0
0
0
0
0
5
0
2
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
6
0
0
0
0
1
1
0
1
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
2
0
0
0
1
0
0
2
0
0
1
0
0
0
1
0
0
0
0
2
1
0
0
0
1
0
0
1
0
0
0
0
1
2
0
3
0
0
0
0
1
3
1
0
3
0
0
2
0
0
0
0
0
1
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
1
0
2
0
0
0
2
3
0
2
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
2
0
2
0
0
0
3
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
3
0
0
0
2
0
0
1
0
5
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
1
2
0
0
0
2
0
0
0
0
0
2
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
3
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
9
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
2
4
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
2
0
0
0
1
1
0
0
3
1
0
0
0
1
1
0
1
0
0
0
1
0
0
0
3
11
1
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
2
0
0
1
2
1
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
2
0
1
0
1
0
1
0
2
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
2
0
0
0
9
0
0
0
1
0
0
7
2
1
0
0
3
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
3
0
3
1
0
0
1
0
1
0
0
2
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
1
0
1
0
6
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
2
1
0
0
0
0
0
1
0
1
0
0
4
2
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
2
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
6
0
0
1
1
0
0
0
0
1
4
0
0
0
1
1
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
2
0
0
0
0
2
0
0
0
1
0
2
2
0
0
1
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
1
1
0
0
1
0
0
2
0
0
2
2
0
0
2
0
0
0
0
0
0
1
3
0
0
0
2
0
1
0
0
1
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
3
1
0
0
0
1
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
11
3
0
0
0
1
1
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
5
2
0
0
0
0
0
0
0
1
0
0
0
1
2
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
2
0
2
0
2
2
0
0
0
1
2
0
0
0
0
0
0
0
0
7
1
0
0
0
0
0
2
0
10
0
0
1
0
0
2
0
0
0
0
1
0
1
0
1
4
0
0
0
0
0
0
0
1
0
0
0
2
0
2
1
1
1
0
0
2
0
0
3
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
3
0
0
0
0
2
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
5
0
0
0
0
0
0
0
4
0
0
0
2
0
0
2
1
0
0
3
0
2
1
2
2
0
2
0
0
0
0
0
2
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
2
0
0
0
3
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
9
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
2
0
1
0
0
1
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
2
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
3
0
0
0
2
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
2
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
2
0
1
1
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
2
2
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
2
2
0
3
0
2
4
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
3
0
3
0
1
2
0
0
0
0
1
2
0
1
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
3
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
2
0
0
0
0
0
5
0
0
0
0
0
0
0
1
1
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
1
0
0
0
0
2
0
0
1
0
0
1
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
4
3
2
0
0
0
0
0
0
0
2
0
0
0
0
4
0
0
1
0
0
0
0
0
0
1
0
1
2
1
1
0
2
0
1
1
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
9
0
0
1
1
0
2
0
0
0
0
2
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
1
3
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
1
0
0
0
4
0
0
0
0
0
0
0
4
3
0
1
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
7
0
1
0
0
0
0
1
6
0
0
3
0
0
0
0
1
0
0
1
2
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
2
4
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
3
2
2
0
2
0
0
2
0
1
0
0
2
0
1
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
3
1
0
0
0
0
3
2
0
4
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
2
0
5
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
2
0
2
1
0
0
0
0
2
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
2
0
0
2
0
3
0
0
0
0
0
1
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
2
2
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
1
0
9
0
0
0
0
0
2
2
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
1
3
0
2
0
0
0
0
0
2
2
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
1
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
2
0
0
0
0
0
2
0
0
4
2
0
0
0
0
0
0
0
0
1
3
0
2
0
0
0
1
0
0
0
0
0
0
4
0
0
2
0
0
0
0
2
0
0
0
0
0
3
0
0
0
3
0
0
0
2
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
9
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
2
3
0
2
2
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
15
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
1
1
1
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
2
0
2
0
0
0
0
2
5
2
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
2
0
0
3
0
0
1
0
0
0
0
0
2
0
2
0
0
0
1
0
1
1
2
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
13
2
1
2
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
1
0
0
2
0
1
0
1
0
2
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
1
0
0
1
0
1
0
0
1
0
2
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
1
2
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
1
0
1
0
0
0
0
0
3
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
1
0
1
0
0
0
0
4
0
0
1
0
0
0
2
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
2
0
1
0
0
0
0
0
0
0
2
1
2
2
0
0
0
0
0
1
2
2
0
0
0
1
0
0
1
0
2
1
2
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
5
0
0
0
1
0
2
0
1
0
2
0
0
0
0
0
0
2
1
0
0
1
0
1
0
3
0
0
2
0
0
0
0
0
0
0
5
1
0
0
0
0
0
0
0
0
0
4
0
1
1
0
0
0
0
2
5
0
0
0
0
0
0
0
1
0
1
2
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
3
5
0
0
2
0
0
1
0
0
0
0
0
0
1
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
1
0
0
1
0
0
3
0
0
0
0
2
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
1
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
1
0
0
2
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
2
1
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
3
0
0
0
1
0
2
3
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
8
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
3
1
3
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
4
1
0
0
0
2
0
0
0
0
4
1
0
0
6
0
0
0
0
0
0
1
0
0
0
3
1
2
0
0
0
2
1
0
0
1
0
0
0
1
3
0
1
0
0
0
0
0
3
1
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
2
0
1
0
0
0
1
0
0
2
0
0
3
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
3
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
4
4
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
3
3
0
2
1
0
0
0
3
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
2
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
3
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
10
0
0
0
0
0
3
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
6
0
0
0
0
0
0
3
0
1
0
0
0
1
0
1
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
3
0
0
0
0
4
0
0
0
0
0
2
0
2
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
1
0
0
1
0
0
0
0
3
1
0
0
0
0
1
0
0
0
2
0
0
0
0
3
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
8
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
3
0
1
0
0
0
0
2
3
0
0
0
0
0
0
0
0
2
2
0
3
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
1
0
1
1
2
2
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
3
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
1
1
2
0
1
4
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
7
0
0
0
0
2
0
2
1
2
0
0
0
3
2
0
0
1
0
2
2
1
5
0
0
0
0
0
0
0
6
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
4
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
3
1
0
0
0
0
0
2
0
0
0
0
3
0
0
1
1
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
1
1
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
1
0
1
2
0
2
0
1
0
0
0
0
0
1
0
0
0
1
1
0
1
2
0
0
2
0
0
0
0
0
0
2
2
1
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
2
0
2
2
2
0
0
0
0
0
0
0
3
0
1
0
1
0
0
0
0
0
0
0
6
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
1
6
0
0
1
1
0
0
0
1
0
1
1
0
2
0
0
0
0
0
2
0
0
0
0
0
4
1
0
0
0
0
0
1
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
7
0
0
0
0
4
0
0
0
0
0
4
2
0
0
0
2
0
0
0
0
0
0
1
0
1
1
0
3
0
1
0
0
4
1
1
2
2
1
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
3
0
2
3
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
2
1
2
0
1
1
1
0
0
1
0
0
0
0
1
1
0
0
1
0
1
0
1
0
0
1
2
0
0
4
0
0
1
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
1
0
1
0
0
0
0
0
3
1
0
0
0
0
2
0
3
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
1
6
0
1
3
1
0
1
0
0
0
0
4
0
0
1
0
1
0
0
1
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
2
0
0
1
2
1
0
2
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
2
0
3
1
0
0
2
0
0
0
2
0
0
3
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
4
0
1
0
0
0
0
0
2
0
1
1
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
3
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
5
2
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
1
2
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
3
0
0
0
0
0
0
0
1
0
2
2
0
0
0
1
0
0
1
1
0
1
0
0
0
0
6
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
1
2
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
2
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
2
2
0
0
0
1
0
5
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
2
2
0
1
1
1
0
1
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
1
0
0
0
1
1
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
2
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
2
0
1
0
1
0
0
0
0
1
2
0
1
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
2
1
2
1
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
5
2
1
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
2
0
0
1
0
0
0
0
0
3
1
1
0
0
0
0
2
2
1
3
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
1
2
4
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
4
0
1
1
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
1
0
2
0
0
0
3
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
9
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
1
2
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
2
0
2
0
1
0
1
0
2
1
1
0
0
1
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
3
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
5
0
0
0
0
0
0
0
0
0
0
0
4
0
3
1
1
1
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
2
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
2
1
0
0
5
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
3
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
1
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
2
0
0
2
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
2
0
2
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
2
0
1
1
0
0
0
2
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
3
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
3
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
2
0
0
0
0
1
2
0
0
0
3
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
3
0
0
0
0
2
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
1
0
0
0
2
2
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
2
0
0
2
0
0
1
0
0
0
0
2
1
1
0
0
0
0
1
0
3
1
1
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
2
0
1
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
1
2
1
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
5
0
0
0
0
0
3
2
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
2
0
2
2
1
0
0
0
1
0
0
0
2
0
0
0
2
1
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
4
0
0
2
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
1
2
0
0
1
0
0
3
0
0
0
0
0
0
0
0
2
0
4
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
3
1
2
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
2
5
0
0
0
1
0
0
0
0
3
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
3
3
0
0
0
2
0
2
0
0
3
0
2
0
1
0
0
0
0
3
6
0
0
1
1
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
1
0
1
0
0
1
0
1
0
2
2
0
0
1
0
0
1
0
0
0
0
5
0
1
0
2
0
0
0
3
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
1
1
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
2
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
6
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
1
2
0
3
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
2
0
0
2
0
0
5
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
3
0
0
3
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
4
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
1
1
0
0
0
0
3
0
0
1
1
0
0
0
1
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
4
2
0
0
0
2
5
2
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
1
0
1
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
1
0
0
2
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
3
0
2
0
0
0
2
1
3
1
0
0
0
1
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
2
0
0
1
0
0
1
2
0
0
2
2
0
0
0
0
0
0
2
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
1
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
2
0
1
0
0
1
0
1
0
0
2
0
2
0
0
2
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
3
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
1
0
3
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
3
0
0
0
0
3
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
3
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
1
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
1
0
0
3
0
2
0
0
0
1
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
5
0
0
1
2
0
1
0
2
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
2
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
1
0
0
2
3
0
0
0
0
0
2
4
2
0
0
0
0
1
0
0
0
0
0
2
2
1
0
0
0
1
0
2
0
2
0
0
0
1
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
2
2
0
1
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
2
0
0
2
0
0
0
1
0
2
2
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
2
1
0
0
1
2
0
0
0
3
0
0
0
0
2
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
5
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
2
2
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
1
0
0
1
1
2
0
0
0
0
0
2
1
0
8
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
5
0
2
0
2
0
0
0
2
4
0
1
0
0
0
3
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
1
1
0
0
0
0
2
2
1
0
0
0
1
0
0
0
2
0
0
1
1
0
0
0
7
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
6
0
2
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
1
1
2
0
0
0
0
1
0
1
0
0
0
0
5
0
0
1
0
0
0
0
0
2
2
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
2
3
0
0
0
0
0
0
0
1
0
3
0
0
7
0
0
3
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
4
0
1
0
0
1
0
0
0
1
0
0
0
1
1
1
2
1
1
2
0
0
2
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
5
0
0
0
0
1
2
1
0
0
0
0
1
0
1
0
1
1
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
3
0
0
0
0
0
0
3
2
0
0
5
4
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
2
0
0
1
0
3
1
3
0
0
0
0
0
0
0
1
0
0
4
3
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
2
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
3
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
5
0
0
0
0
3
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
3
0
1
3
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
3
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
1
1
0
3
2
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
5
2
0
0
0
4
0
1
4
0
0
0
0
0
2
2
2
2
0
0
0
1
0
0
0
2
2
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
1
0
0
0
1
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
2
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
3
0
0
0
1
2
0
0
0
1
2
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
1
0
0
1
0
0
1
0
1
0
1
0
1
0
1
2
0
1
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
1
0
0
0
3
0
0
0
0
0
0
1
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
2
2
0
0
1
0
0
0
1
0
0
0
1
0
0
0
2
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
2
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
2
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
3
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
1
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
5
0
1
0
0
2
0
2
1
0
3
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
4
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
3
0
0
2
2
0
0
0
1
0
2
0
2
0
0
1
1
1
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
4
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
2
2
0
0
1
0
3
0
4
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
5
1
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
2
0
0
0
0
6
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
2
0
0
6
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
1
1
0
0
0
0
1
0
2
0
2
0
0
3
0
0
2
0
0
0
0
0
2
0
0
3
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
2
0
1
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
2
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
2
0
0
0
1
1
1
1
0
0
0
1
1
1
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
2
2
1
0
0
0
0
4
2
0
0
0
0
0
1
0
0
1
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
1
1
2
1
0
1
0
0
0
1
0
2
0
1
1
0
0
2
0
1
0
0
0
1
2
1
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
2
1
0
1
0
1
0
0
0
0
0
1
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
1
0
0
2
1
0
0
2
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
3
3
0
0
0
0
1
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
1
3
0
2
0
2
0
0
0
0
0
6
2
0
2
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
1
2
0
0
1
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
2
0
2
0
2
0
0
0
0
4
0
2
1
0
2
0
0
0
0
2
0
3
0
0
0
0
7
0
1
0
2
2
0
2
0
2
0
0
1
0
0
0
1
0
0
1
0
1
5
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
7
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
5
0
2
0
0
2
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
2
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
4
0
0
0
0
0
0
2
2
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
3
0
0
0
2
1
0
2
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
2
0
1
0
3
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
3
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
1
2
0
0
0
1
2
0
0
0
1
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
1
0
3
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
3
0
1
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
2
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
2
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
1
0
0
0
2
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
2
1
2
1
0
0
0
0
5
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
1
0
0
0
1
1
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
5
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
8
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
1
0
1
3
2
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
1
0
0
2
0
0
0
0
0
2
0
0
1
0
0
2
0
0
1
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
3
2
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
4
1
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
6
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
1
0
0
0
0
0
0
0
1
2
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
6
0
0
1
0
0
0
0
2
0
0
0
1
1
5
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
4
0
2
0
3
0
0
0
1
1
0
2
0
0
1
0
0
0
0
2
0
1
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7
0
0
2
0
0
1
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
1
2
0
0
0
2
0
0
0
4
0
1
2
0
0
2
0
0
2
4
0
0
0
0
1
0
0
1
1
0
0
2
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
5
1
2
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
7
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
5
0
0
2
0
0
0
0
2
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
3
0
1
0
4
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
2
1
1
2
0
0
1
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
1
0
0
4
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
3
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
5
0
0
0
0
0
2
1
0
0
0
0
0
1
0
1
0
3
2
0
0
0
0
0
1
0
0
2
0
2
0
3
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
1
0
0
0
0
1
3
0
0
4
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
7
0
0
2
0
0
2
0
1
0
0
0
0
4
0
0
0
0
1
0
0
0
3
0
2
2
3
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
5
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
2
0
0
0
0
0
0
0
2
0
0
0
1
1
0
1
0
0
0
0
0
1
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
1
0
0
0
0
1
6
1
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
2
0
0
1
3
0
0
1
0
1
1
2
0
1
0
0
0
0
1
1
0
0
0
1
2
0
0
0
1
0
0
0
0
0
5
0
0
0
0
1
0
3
0
2
0
0
0
0
1
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
8
0
0
2
1
0
0
0
2
0
0
0
1
0
1
2
1
0
0
0
0
0
0
2
0
1
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
1
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
1
0
0
0
0
0
1
1
1
0
2
0
0
2
1
0
0
1
0
0
0
4
0
0
0
0
0
4
3
0
2
1
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
2
1
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
2
2
2
0
0
0
3
0
0
0
0
4
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
3
2
0
0
2
0
0
0
0
1
1
0
0
1
3
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
2
0
0
2
0
0
0
0
0
1
0
0
2
0
1
1
0
0
0
6
0
4
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
3
0
2
0
0
0
0
0
0
0
1
9
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
2
2
0
0
0
2
1
0
0
0
0
0
0
1
0
4
3
2
2
0
0
1
0
0
0
0
12
0
0
0
0
1
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
3
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
3
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
2
0
2
5
1
0
3
2
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
1
2
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
3
6
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
1
0
0
3
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
2
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
5
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
2
0
2
0
0
1
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
2
0
5
0
0
0
0
0
2
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
4
0
0
0
1
0
0
0
0
2
2
1
0
0
0
0
0
1
0
0
0
0
3
0
1
0
1
0
0
2
0
0
2
0
0
0
0
0
2
2
2
0
0
7
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
2
0
1
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
4
0
0
1
0
0
0
0
0
0
0
0
0
3
3
0
0
0
1
1
0
0
0
0
0
1
1
0
0
1
0
0
0
1
2
2
1
0
0
0
1
2
1
0
2
0
2
2
3
3
0
0
0
0
0
2
0
0
1
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
1
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
5
1
3
4
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
2
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
3
4
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
2
1
0
0
0
1
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
1
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
1
0
1
3
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
1
0
0
0
0
3
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
1
0
1
2
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
1
1
0
2
0
0
1
1
7
0
0
0
0
0
0
0
0
0
4
0
0
2
0
1
2
0
0
0
0
0
0
0
4
1
3
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
1
0
0
0
0
0
1
1
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
2
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
1
1
0
0
0
4
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
2
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
2
0
0
0
0
0
0
2
5
0
0
0
0
0
0
1
0
0
0
2
0
0
1
1
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
2
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
1
7
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
3
0
0
0
0
0
0
0
0
0
4
0
5
2
1
0
0
3
0
2
0
0
0
0
0
1
1
0
0
0
2
1
0
2
0
0
0
0
0
0
2
2
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
2
1
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
1
3
0
0
0
0
0
0
3
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
1
0
0
2
0
2
0
0
0
2
0
3
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
5
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
3
0
0
1
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
1
2
0
2
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
1
0
0
2
0
1
1
0
0
0
0
0
2
0
0
1
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
3
0
1
0
0
0
0
0
2
0
0
0
1
0
0
1
0
2
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
1
0
0
0
0
0
2
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
1
0
2
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
2
2
1
1
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
2
1
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
3
1
0
0
2
3
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
5
0
0
0
2
0
0
0
0
0
0
0
3
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
2
0
0
1
0
4
1
0
0
1
0
3
0
0
0
0
0
1
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
3
2
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
1
0
0
0
0
0
0
3
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
2
0
0
0
3
1
0
0
1
0
1
3
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
3
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
2
0
1
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
2
2
2
0
0
0
1
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
3
2
3
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
1
0
0
5
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
2
1
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
2
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
9
0
1
2
0
0
0
1
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
5
2
0
0
0
0
1
0
0
0
0
0
0
2
0
7
3
0
2
1
1
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
1
0
1
1
0
0
0
3
0
0
1
0
1
0
0
0
0
2
5
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
5
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
1
0
2
2
2
0
0
3
1
0
1
0
0
0
0
0
0
2
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
2
0
1
1
0
2
0
0
0
0
0
0
2
1
0
0
0
1
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
1
2
0
0
2
0
0
2
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
1
0
0
0
2
0
2
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
7
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
4
2
0
0
2
0
1
0
1
0
0
6
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
1
0
0
3
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
3
1
0
0
1
0
0
0
1
2
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
2
0
1
0
2
2
0
1
0
0
0
2
0
2
3
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
2
2
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
1
0
0
0
0
6
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
1
0
3
0
0
3
0
0
0
1
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
3
2
0
0
1
0
0
0
2
0
0
1
0
0
1
0
1
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
5
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
4
0
0
0
1
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
1
0
0
0
2
0
7
0
0
0
0
3
0
0
0
5
2
0
0
1
3
0
0
0
2
0
0
0
2
0
0
0
0
2
1
0
0
3
0
0
1
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
7
1
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
5
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
4
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
1
0
0
0
0
0
1
2
1
1
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
2
0
0
0
2
0
0
0
0
2
0
0
3
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
5
0
1
0
2
0
0
2
0
4
0
0
0
1
0
2
0
1
0
0
0
1
1
0
0
0
0
2
0
0
1
0
0
3
0
0
0
2
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
1
2
0
0
1
2
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
7
1
1
0
0
1
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
3
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
2
0
0
0
1
0
1
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
4
1
0
0
2
1
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
3
0
1
2
0
1
0
0
0
0
0
1
0
1
0
0
0
5
0
2
1
0
2
0
2
3
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
2
0
0
1
0
0
2
0
0
0
4
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
8
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
1
2
1
0
2
0
1
0
0
1
0
0
0
2
0
1
2
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
3
2
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
1
0
1
3
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
1
0
0
1
0
0
0
0
0
2
0
0
1
3
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
1
0
4
0
0
0
0
3
0
0
0
0
3
0
2
0
3
0
2
1
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
1
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
1
0
1
0
0
1
0
1
1
2
0
1
1
1
1
0
0
0
0
0
2
0
0
0
1
0
0
2
1
0
0
0
0
0
1
0
0
2
1
0
0
2
0
0
1
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
1
1
1
2
0
0
0
0
0
2
0
0
0
0
0
2
1
2
5
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
2
0
0
1
0
0
0
2
0
0
0
3
0
0
0
0
0
0
1
0
1
0
2
2
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
1
1
0
0
2
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
2
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
1
0
0
2
0
0
0
0
0
3
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
2
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
3
0
0
0
0
1
0
0
0
1
0
1
1
0
2
0
0
0
0
0
0
3
0
2
2
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
3
0
0
0
0
0
2
0
0
3
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
4
7
0
0
0
0
2
0
1
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
2
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
1
1
0
0
0
0
0
1
0
0
2
0
2
2
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
2
0
4
0
0
0
7
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
3
0
0
0
0
0
1
3
0
0
4
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
4
1
0
0
0
0
2
0
0
0
0
0
2
1
2
0
0
0
0
2
0
1
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
1
2
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
2
0
0
2
0
0
0
0
6
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
2
0
0
0
1
0
3
0
0
0
0
0
0
2
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
5
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
1
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
3
1
1
0
0
2
0
1
0
0
2
0
0
0
0
0
2
0
0
1
2
2
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
3
2
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
1
0
0
0
0
1
0
0
2
3
0
0
0
1
0
1
0
0
1
0
0
0
2
0
1
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
4
0
0
0
0
0
2
0
1
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
2
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
4
1
1
0
0
0
0
1
2
0
0
1
0
0
2
0
2
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
1
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
1
0
0
0
1
0
1
1
0
0
2
0
1
1
1
0
2
0
0
3
0
0
0
0
2
1
2
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
10
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
7
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
1
5
0
2
1
3
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
8
0
0
4
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
1
2
2
0
0
0
0
0
0
0
2
1
3
0
0
0
1
2
0
1
1
13
0
0
0
0
1
0
1
0
1
2
0
0
0
0
1
0
1
0
1
0
0
0
3
0
0
3
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
2
0
0
0
0
0
1
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
6
0
0
2
0
0
1
0
0
0
0
0
4
2
0
0
0
0
0
0
1
0
2
0
0
1
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
1
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
2
1
0
1
1
0
0
0
2
1
1
0
2
0
0
0
0
0
2
0
4
0
0
0
0
0
1
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
3
0
2
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
14
1
0
2
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
2
0
4
3
2
0
0
0
0
0
0
14
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
3
1
3
2
1
0
1
3
0
0
3
0
0
0
0
0
0
0
0
0
3
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
1
2
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
2
0
3
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
4
0
1
0
0
0
0
0
0
0
0
0
2
4
0
0
0
2
0
2
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
3
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
2
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
2
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
2
0
2
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
3
2
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
5
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
4
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
2
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
10
2
0
5
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
2
0
2
0
0
0
0
0
0
1
2
0
2
0
0
0
0
1
1
0
0
0
1
0
0
0
0
7
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
12
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
4
0
0
0
0
0
0
0
2
0
0
0
5
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
2
1
1
0
2
6
0
0
2
1
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
3
3
0
2
0
0
0
0
0
3
0
1
0
0
0
0
0
2
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
2
2
0
2
0
0
2
2
0
0
0
1
1
0
1
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
6
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
2
0
0
0
1
0
0
2
0
0
0
1
0
4
0
0
0
1
1
2
0
2
0
0
0
0
2
0
2
0
0
0
0
2
0
1
2
0
1
0
0
0
0
0
0
2
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
3
2
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
2
0
1
2
0
1
0
0
0
1
0
0
2
0
0
0
0
1
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
2
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
4
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
6
2
1
0
0
1
0
0
4
0
0
0
0
1
0
1
2
0
3
0
1
0
1
0
1
0
0
0
0
0
0
0
0
2
3
0
0
3
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
2
2
0
0
0
2
0
2
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
4
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
1
1
0
0
3
0
0
1
1
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
4
0
5
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
1
1
0
2
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
1
0
0
1
0
2
2
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
3
0
0
0
0
2
0
0
0
1
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
2
2
1
0
2
0
0
4
0
0
0
0
0
0
0
0
2
2
2
0
0
2
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
2
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
2
0
0
0
3
0
0
1
0
0
2
0
1
0
0
0
0
0
1
6
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
2
0
2
0
0
0
0
3
2
0
0
2
0
0
0
3
0
1
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
2
1
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
10
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
3
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
3
2
0
1
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
6
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
3
0
0
1
1
1
0
0
0
0
0
0
0
2
0
0
0
2
3
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
1
0
0
1
0
0
2
0
0
0
1
0
2
2
0
0
0
2
0
1
0
2
0
0
0
0
1
0
0
3
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
3
2
0
1
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
1
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
1
4
0
0
2
0
0
0
0
0
0
0
0
6
0
1
0
0
0
3
1
1
0
0
1
0
0
1
0
0
1
3
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
5
0
1
0
2
0
0
0
0
1
2
0
2
0
0
0
0
0
0
1
1
8
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
2
0
2
1
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
7
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
3
0
0
0
1
0
1
0
0
1
0
0
1
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
4
0
1
1
0
0
0
1
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
4
0
1
2
0
0
0
0
1
0
0
2
1
0
0
0
1
1
0
2
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
2
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
7
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
2
2
0
0
0
1
1
0
0
0
0
0
3
0
0
0
0
0
1
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
3
0
0
2
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
2
1
0
0
1
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
1
0
2
0
1
0
1
0
0
0
0
2
2
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
1
0
1
1
3
0
0
1
2
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
11
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
1
0
0
0
2
1
1
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
2
1
0
12
1
2
0
1
0
0
0
0
1
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
3
0
2
0
0
1
0
1
0
1
0
0
3
0
0
0
1
1
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
2
1
0
0
0
1
0
1
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
1
0
0
2
0
2
0
0
0
0
1
1
2
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
1
0
0
0
1
0
0
1
0
6
1
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
1
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
2
0
1
0
0
0
3
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
2
0
1
1
0
0
0
3
0
2
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
2
0
1
0
0
2
1
0
0
1
0
1
0
2
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
3
1
0
0
0
0
0
0
2
2
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
1
2
0
0
0
0
0
1
0
1
0
0
0
0
2
0
2
0
0
2
0
0
0
4
0
0
0
0
2
1
2
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
3
0
0
0
1
0
1
0
0
1
0
0
0
3
2
0
2
2
1
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
1
0
0
1
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
5
0
0
0
0
0
0
2
0
3
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
2
0
1
0
3
6
1
1
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
2
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
1
2
0
0
0
0
2
0
1
0
1
0
0
1
0
1
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
4
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
1
0
0
0
0
0
2
2
0
0
0
1
0
0
1
0
0
0
1
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
1
1
0
1
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
1
0
0
2
1
0
2
3
0
0
2
0
0
0
3
0
0
0
2
0
5
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
3
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
2
2
0
0
0
0
0
1
0
0
1
0
0
2
0
4
0
0
2
0
0
0
1
2
0
0
1
0
0
0
0
0
2
0
0
3
4
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
1
0
0
0
1
3
2
0
0
0
2
0
0
0
2
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
1
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
2
0
3
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
1
2
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
1
1
5
0
0
0
0
0
1
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
1
0
4
0
1
0
0
0
0
0
1
2
0
0
0
0
0
3
0
0
0
0
2
0
2
0
0
0
0
1
0
0
7
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
2
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
1
0
2
2
1
0
0
0
2
0
2
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
1
0
0
0
2
0
0
1
0
0
0
0
5
1
0
2
0
0
0
3
0
0
0
3
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
2
1
0
1
0
2
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
3
1
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
2
1
1
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
1
1
0
0
0
2
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
2
0
0
1
0
0
1
2
1
0
0
2
5
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
3
3
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
4
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
2
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
3
0
1
0
0
0
0
1
0
0
0
6
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
4
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
5
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
1
0
2
0
4
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
2
0
0
0
1
1
0
2
0
0
3
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
3
0
0
0
2
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
1
0
0
1
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
1
0
1
0
0
1
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
5
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
2
2
2
0
0
0
1
0
2
0
2
0
0
0
0
9
2
0
0
0
0
0
0
0
0
0
1
0
5
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
1
0
5
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
2
1
0
3
0
3
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
3
0
0
2
1
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
4
1
0
2
0
3
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
2
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
5
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
1
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
1
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
3
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
2
0
3
1
0
0
0
2
0
0
1
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
1
2
2
0
0
0
4
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
2
0
0
2
0
0
2
0
0
0
2
1
0
2
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
1
2
0
0
0
0
7
1
2
0
0
2
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
1
6
0
0
1
1
0
2
1
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
2
2
2
2
0
0
0
0
0
0
0
1
2
0
0
3
1
0
2
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
1
0
2
2
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
1
0
5
0
0
2
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
6
0
1
0
0
0
0
1
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
2
0
2
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
5
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
3
2
0
1
0
0
0
0
0
0
0
0
2
0
2
2
2
1
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
3
0
1
0
0
0
1
0
0
0
0
0
1
2
0
0
1
0
0
2
0
0
0
1
0
0
0
0
2
0
2
0
0
0
1
0
1
0
2
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
1
2
2
0
0
5
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
4
1
0
0
6
0
0
1
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
3
0
0
0
0
0
0
0
0
2
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
3
2
0
0
0
0
0
0
0
1
2
0
0
1
1
0
0
0
3
0
1
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
2
0
0
0
1
5
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
3
0
1
1
0
0
0
0
0
0
0
0
0
0
0
5
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
4
0
2
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
1
2
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
3
0
1
0
0
0
2
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
1
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
2
0
0
0
0
2
3
0
2
3
2
0
0
2
0
0
0
2
1
0
0
0
0
0
2
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
1
0
0
2
7
1
0
1
1
0
0
0
2
2
0
0
0
0
2
1
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
2
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
3
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
1
0
6
0
0
0
0
0
0
0
2
1
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
1
0
0
1
0
0
0
0
0
3
0
0
1
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
2
0
0
3
0
0
0
1
1
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
2
0
0
1
2
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
2
0
0
0
2
0
1
2
0
1
0
0
0
0
0
0
0
0
0
2
2
2
1
0
0
0
1
1
3
0
0
0
0
0
0
0
0
0
0
0
2
7
0
2
0
1
0
0
0
1
0
0
0
0
1
0
0
0
2
2
0
0
1
0
0
0
2
0
2
3
1
0
2
0
2
2
0
0
3
0
1
4
2
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
1
1
1
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
1
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
2
4
0
0
0
2
0
0
0
0
2
1
0
0
1
2
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
2
1
0
0
0
0
0
0
2
0
0
0
5
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
10
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
2
0
1
0
0
0
0
1
1
0
5
0
0
0
2
0
0
0
0
1
1
0
0
0
2
0
0
2
0
0
0
0
0
8
0
0
2
0
0
1
0
3
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
1
0
1
0
0
1
2
0
0
0
0
0
0
0
8
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
10
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
3
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
4
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
1
0
0
0
2
0
0
0
1
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
3
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
1
1
0
0
0
0
2
0
2
0
3
1
1
2
0
0
1
0
0
0
0
0
3
2
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
1
0
4
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
3
0
2
1
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
3
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
3
1
0
0
0
1
0
4
0
3
1
0
2
0
1
0
0
0
0
0
1
2
2
2
0
0
0
0
1
0
6
0
0
2
1
0
0
0
0
1
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
1
1
0
0
0
2
1
0
0
0
2
0
0
0
2
0
2
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
1
0
0
2
2
2
1
1
0
0
0
1
0
0
0
0
2
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
5
0
2
0
0
0
0
1
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
8
0
1
0
2
1
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
1
0
1
1
0
0
0
0
2
2
0
1
0
0
0
2
0
0
0
2
1
2
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
2
0
0
0
5
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
1
2
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
7
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
6
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
4
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
2
0
0
3
2
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
1
1
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
3
2
2
0
0
0
1
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
3
0
0
1
0
1
1
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
1
2
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
3
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
3
0
0
0
0
0
0
2
0
0
3
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
1
0
1
1
0
1
0
0
0
0
0
0
0
2
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
1
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
4
0
0
0
0
0
0
2
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
5
2
0
0
2
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
2
0
1
9
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
2
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
6
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
2
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
3
3
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
2
5
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
3
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
2
0
1
1
0
1
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
2
0
2
0
3
1
0
3
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
2
0
0
0
5
1
0
0
1
0
0
0
2
0
5
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
3
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
1
1
0
0
0
0
1
0
0
0
4
0
0
0
3
0
0
0
0
2
1
0
0
2
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
1
1
0
1
0
0
0
0
3
0
0
0
0
3
2
0
0
0
0
2
0
3
0
1
0
0
2
0
0
0
0
1
0
2
0
0
0
0
4
2
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
3
0
2
0
0
2
0
0
0
0
2
0
0
0
1
1
2
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
1
0
3
0
0
0
0
0
0
0
2
0
3
0
1
0
2
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
3
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
1
1
2
0
3
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
3
0
2
0
0
0
0
2
1
0
2
0
0
2
0
2
0
0
0
0
3
0
0
0
0
0
0
1
2
1
0
0
0
0
1
0
0
0
2
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
6
0
2
2
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
3
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
2
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
2
0
0
5
0
2
0
0
0
0
0
0
0
0
3
0
1
2
0
0
2
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
3
2
1
1
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
1
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
3
0
0
0
0
6
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
9
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
2
1
1
0
2
5
0
0
2
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
3
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
1
0
2
2
1
1
0
0
0
0
0
0
0
0
1
1
1
2
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
2
1
1
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
2
0
0
0
1
1
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
7
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
1
0
1
2
0
0
0
0
1
2
0
0
0
0
0
0
0
1
1
0
0
0
0
1
5
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
2
1
0
0
2
0
1
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
1
0
2
0
1
0
1
0
0
1
0
0
0
1
0
0
0
3
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
2
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
4
0
0
3
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
4
2
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
2
1
0
0
0
0
0
0
2
1
0
0
1
0
0
5
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
3
1
1
0
0
0
0
0
0
0
0
1
1
0
0
1
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
3
0
0
2
0
1
0
0
1
3
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
1
1
2
0
1
0
0
0
2
1
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
2
0
3
0
2
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
2
2
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
2
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
2
0
2
1
0
1
0
0
0
1
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
1
0
0
0
1
0
0
15
0
0
2
0
0
0
0
0
2
0
3
0
2
0
0
2
0
1
3
0
0
1
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
2
1
2
1
0
0
2
0
0
1
0
0
0
3
0
0
0
0
0
0
1
1
0
2
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
3
0
0
0
0
0
1
0
2
0
0
0
3
0
1
6
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
2
0
2
1
0
0
0
0
0
0
0
1
2
0
1
0
0
0
2
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
1
1
3
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
1
2
0
1
0
1
0
2
0
1
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
1
3
0
2
1
0
0
0
1
0
2
0
1
0
0
4
1
0
0
1
0
0
0
1
0
3
0
0
0
0
0
0
2
0
0
0
0
2
1
3
0
0
0
0
0
1
0
0
0
0
0
0
2
5
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
5
1
0
0
0
3
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
5
0
2
0
0
0
0
0
0
2
1
0
1
0
0
3
0
0
2
0
2
2
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
3
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
1
1
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
1
0
0
0
0
0
3
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
1
6
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
5
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
2
0
0
1
0
0
0
0
0
0
2
0
0
1
0
3
0
0
0
0
1
0
0
1
2
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
3
0
2
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
3
1
0
2
1
2
0
0
0
1
0
4
4
0
0
1
0
0
0
2
0
0
0
2
3
0
0
0
0
1
0
0
2
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
1
1
0
1
0
0
1
0
0
0
3
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
5
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
4
2
0
0
0
0
3
1
1
0
4
0
0
0
0
0
0
0
0
0
12
0
0
0
0
2
7
0
0
2
0
0
1
1
0
1
0
0
0
1
2
0
1
0
0
0
0
2
2
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
3
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
2
0
3
2
3
0
3
2
0
0
0
0
0
1
0
0
0
0
0
0
0
3
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
2
1
0
0
0
0
0
2
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
3
1
0
1
0
0
0
0
0
0
2
2
0
0
1
1
0
1
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
1
0
0
2
1
1
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
2
0
0
0
0
0
0
8
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
1
0
1
0
0
2
0
0
3
0
0
0
0
0
0
1
0
2
0
1
1
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
5
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
1
0
0
0
3
0
0
2
2
0
0
0
1
0
0
1
1
0
0
0
0
1
0
2
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
2
3
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
1
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
2
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
5
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
2
3
4
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
2
2
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
2
0
0
1
0
0
2
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
2
2
1
1
0
0
2
0
0
0
0
1
0
0
2
0
0
1
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
2
0
0
1
2
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
8
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
1
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
1
0
0
2
0
2
0
2
1
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
4
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
1
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
3
1
0
0
0
0
0
0
1
2
0
2
0
0
0
0
3
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
2
2
0
0
0
9
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
3
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
5
0
1
2
1
0
2
0
0
8
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
1
2
0
2
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
3
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
3
0
1
0
0
2
2
1
1
0
3
2
0
0
2
0
0
0
0
1
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
2
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
1
0
1
0
0
0
0
2
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
1
0
0
0
0
0
0
1
0
0
0
0
0
2
4
1
0
2
0
0
2
0
1
2
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
5
0
2
0
0
0
0
4
2
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
3
2
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
1
2
0
3
0
0
1
0
0
0
0
0
0
2
3
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
2
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
2
0
2
0
1
3
0
1
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
5
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
1
0
1
0
0
0
5
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
2
1
1
0
0
3
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
3
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
3
0
0
1
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
3
0
0
1
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
3
0
0
0
0
0
0
1
2
0
2
0
1
1
1
0
0
2
0
1
2
0
2
0
1
0
0
2
0
2
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
3
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7
0
0
1
1
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
2
0
0
3
0
0
2
1
2
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
2
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
5
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
3
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
3
1
0
0
0
0
0
0
0
0
1
0
7
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
4
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
2
2
0
0
0
2
2
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
1
0
5
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
2
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
4
10
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
3
0
0
2
0
0
1
0
1
2
0
0
2
0
0
1
0
2
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
3
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
2
2
0
2
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
4
0
1
0
1
1
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
9
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
1
0
2
2
0
0
2
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
1
3
0
0
0
0
1
2
2
0
0
0
1
0
0
2
0
0
3
0
1
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
4
0
0
1
0
0
2
0
0
0
0
0
2
0
0
6
0
0
0
0
0
1
0
0
1
1
1
0
0
9
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
3
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
3
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
4
0
5
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
3
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
2
7
1
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
2
2
0
0
1
1
0
0
0
0
0
2
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
1
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
4
2
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
3
0
0
0
2
0
1
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
2
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
3
0
0
1
2
0
2
2
0
2
0
0
0
3
0
0
1
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
2
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
2
1
0
1
0
1
0
0
1
0
0
0
0
0
0
8
0
0
0
0
0
0
1
0
0
1
0
0
3
0
1
0
0
0
2
0
1
0
0
0
2
0
0
2
1
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
9
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
1
0
3
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
3
0
0
0
1
0
1
0
6
0
0
0
0
0
0
2
1
0
10
0
0
0
0
0
2
0
0
0
0
1
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
3
0
2
0
0
2
0
1
0
1
0
1
2
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
1
0
1
1
0
2
0
0
2
0
0
2
0
2
1
0
0
2
0
0
0
0
1
0
2
3
1
0
2
0
0
0
0
1
1
0
1
1
0
0
1
0
0
3
0
0
0
2
2
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
2
0
0
1
0
4
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
3
2
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
4
0
0
0
3
0
0
0
3
0
2
0
0
0
0
0
0
0
2
2
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
1
8
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
6
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
3
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
2
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
1
0
0
0
1
3
1
2
0
0
0
0
2
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
5
0
2
0
0
2
1
0
0
0
0
1
0
0
4
0
1
0
1
0
0
0
0
2
1
0
0
0
0
2
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
3
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
1
2
1
1
0
0
0
0
1
0
2
0
0
3
1
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
2
0
0
0
1
2
4
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
1
4
2
0
0
0
0
1
1
0
3
0
0
0
0
0
0
2
0
3
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
1
1
0
1
0
1
0
0
0
8
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
4
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
1
2
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
2
0
2
0
0
0
0
1
0
0
2
0
0
4
1
0
0
0
0
0
0
0
0
2
0
1
1
0
0
2
0
0
1
0
2
2
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
4
0
4
0
0
0
0
0
0
0
2
0
0
3
0
2
0
0
3
0
0
0
4
0
0
2
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
2
3
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
5
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
2
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
2
0
3
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
4
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
3
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
7
0
0
0
1
2
3
0
1
0
0
0
0
0
0
0
0
2
1
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
6
0
1
0
0
1
0
0
0
2
1
0
0
0
0
0
2
0
2
0
0
0
0
1
0
2
5
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
1
1
0
0
0
2
1
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
2
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
2
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
5
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
2
0
1
0
0
0
0
0
2
2
1
1
1
0
0
0
0
1
2
0
0
3
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
5
0
0
0
0
0
0
1
0
1
1
1
0
0
1
0
0
0
0
0
0
3
2
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
1
0
1
0
2
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
4
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
2
0
0
0
0
0
2
0
0
1
2
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
3
0
2
1
0
0
1
0
0
0
0
0
0
0
0
2
0
1
5
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
2
2
0
0
0
3
1
0
0
0
0
2
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
2
1
0
0
0
2
3
3
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
2
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
1
0
0
2
0
1
3
0
0
0
0
0
0
0
2
3
0
0
0
0
4
0
2
1
0
2
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
9
0
0
0
0
0
0
0
1
0
1
0
0
0
3
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
2
2
0
0
0
2
3
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
2
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
2
3
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
4
2
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
5
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
5
0
0
0
0
0
0
1
2
1
1
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
1
0
1
0
0
0
0
1
0
2
7
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
3
2
2
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
3
1
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
4
2
0
0
0
0
0
0
2
2
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
1
0
0
1
1
2
0
3
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
2
0
2
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
3
1
3
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
2
0
2
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
3
0
1
0
2
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
6
1
0
2
2
2
2
0
0
1
0
0
0
0
0
0
0
2
1
0
1
4
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
3
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
2
0
0
0
0
0
0
2
0
1
1
2
0
2
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
2
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
3
1
0
0
1
0
0
0
0
0
1
0
0
2
0
0
2
0
1
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
1
0
0
3
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
2
0
2
0
0
3
0
0
0
0
0
3
1
0
6
0
1
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
5
1
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
1
0
2
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
10
1
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
7
2
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
3
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
1
0
0
4
2
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
3
2
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
2
0
0
1
0
1
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
2
2
0
0
3
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
2
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
1
1
2
0
3
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
1
1
1
4
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
1
0
2
0
0
0
1
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
1
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
8
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
3
0
2
1
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
1
1
0
0
1
0
0
0
3
0
2
1
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
1
0
0
0
0
0
0
2
0
0
4
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
2
2
3
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
1
0
0
0
0
2
0
0
0
1
2
0
1
0
0
0
0
2
0
1
1
0
2
0
0
0
2
0
0
0
0
0
0
2
2
0
0
1
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
5
3
2
0
3
1
1
2
1
0
0
0
1
0
2
0
0
0
0
0
1
1
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
1
0
4
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
4
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
6
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
2
0
1
0
11
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
2
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
2
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
1
0
0
0
0
0
1
0
2
0
0
0
1
0
2
0
0
0
0
0
2
0
1
0
2
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
1
1
3
0
0
0
0
0
0
0
2
0
0
3
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
2
0
1
2
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
1
0
1
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
6
1
0
0
0
0
0
0
0
0
0
0
2
2
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
12
0
1
2
0
0
0
0
0
1
2
1
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
2
1
1
0
0
0
2
0
2
0
0
3
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
1
1
0
0
0
0
0
0
0
1
2
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
2
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
3
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
6
2
0
3
1
0
0
2
0
0
4
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
3
2
1
0
0
0
0
0
0
0
0
0
0
2
3
1
0
0
0
0
2
1
0
0
0
0
0
3
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
5
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
2
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
3
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
3
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
3
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
2
0
2
0
0
0
0
0
2
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
4
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
1
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
2
4
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
4
2
2
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
3
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
4
1
0
0
1
0
0
0
0
0
6
2
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
5
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
5
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
2
3
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
4
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
1
0
1
0
0
2
1
0
0
0
0
0
1
0
0
0
0
1
1
2
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
1
0
0
0
2
1
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
2
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
2
0
0
0
0
0
0
0
0
1
1
2
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
1
2
1
0
5
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
2
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
2
0
2
0
2
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
2
0
2
0
1
2
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
3
0
0
0
2
0
0
2
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
1
0
0
0
0
0
2
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
3
0
0
2
0
0
3
1
0
0
4
2
2
0
2
0
0
0
1
0
2
0
2
0
0
0
1
0
0
0
0
3
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
3
2
0
2
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
2
3
0
2
0
1
2
0
0
0
3
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
3
2
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
3
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
2
0
2
0
0
1
1
1
4
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
1
0
0
2
1
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
3
0
0
1
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
3
0
0
0
0
0
1
0
1
0
0
0
2
0
1
0
0
0
0
3
4
2
0
0
0
0
0
0
1
0
0
0
3
2
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
4
2
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
4
0
2
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
2
1
2
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
2
0
2
10
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
1
6
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
1
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
1
2
2
1
0
0
1
1
0
2
2
0
0
4
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
4
0
0
7
0
0
0
0
2
0
0
0
1
1
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
1
0
0
1
0
0
1
0
3
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
7
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
2
0
0
0
2
0
1
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
1
2
4
0
0
0
0
0
2
0
0
1
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
2
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
1
1
0
0
2
2
0
1
0
0
0
0
3
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
2
0
1
0
0
2
1
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
4
0
1
0
0
2
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
1
0
0
3
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
2
0
0
0
0
0
1
1
0
1
0
0
0
2
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
2
0
0
2
0
4
0
0
2
0
0
0
0
0
0
1
0
1
0
0
2
0
0
4
0
0
1
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
2
0
1
0
1
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
5
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
2
1
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
3
0
0
2
0
0
6
1
0
0
2
0
1
0
1
1
0
0
2
0
0
0
0
0
1
0
2
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
3
0
0
0
0
0
0
2
0
0
1
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
5
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
3
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
3
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
1
1
0
0
0
0
2
1
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
9
2
0
1
0
0
6
0
0
0
1
1
0
0
4
0
0
1
0
1
0
2
0
1
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
7
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
2
1
0
0
0
1
0
1
0
0
0
1
2
0
0
1
0
4
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
3
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
1
1
0
0
0
0
2
0
0
2
0
1
1
2
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
1
0
2
2
0
0
0
0
1
2
3
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
1
1
0
0
1
0
0
0
1
1
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
2
3
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
4
3
0
0
0
2
1
0
0
2
0
0
1
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
5
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
2
1
1
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
3
1
0
0
0
0
0
1
1
2
3
0
0
0
0
0
0
0
0
1
0
2
5
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
3
0
0
0
0
3
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
2
0
0
2
0
3
2
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
2
0
2
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
2
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
6
1
0
2
1
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
1
0
0
1
1
1
1
0
0
0
2
0
0
0
0
2
0
2
0
0
0
2
2
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
6
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
2
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
2
0
0
3
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
15
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
2
0
4
0
0
0
1
0
0
0
2
2
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
1
3
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
2
1
0
2
1
0
0
0
0
0
2
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
7
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
10
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
3
2
0
0
0
2
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
3
0
0
4
0
0
1
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
1
2
0
5
0
0
2
4
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
2
1
0
0
2
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
3
2
2
2
0
0
1
0
0
3
0
0
1
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
3
0
2
13
0
0
0
3
1
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
2
0
2
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
1
0
0
1
1
0
1
3
0
0
0
2
0
0
1
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
1
2
0
0
1
0
0
1
0
0
1
2
1
0
0
1
2
0
0
1
0
0
0
1
0
0
0
1
1
0
1
0
0
2
0
0
0
2
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
1
2
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
2
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
1
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
1
2
0
2
0
0
0
0
0
0
3
0
0
4
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
3
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
3
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
4
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
1
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
2
2
0
0
0
0
0
1
1
0
0
2
0
0
0
0
1
0
0
0
0
1
0
1
0
1
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
1
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
13
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
2
1
0
0
0
0
3
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
5
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
1
1
2
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
5
0
4
0
0
2
0
0
0
0
0
0
2
1
0
0
0
2
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
3
0
0
0
0
0
1
2
0
0
0
1
0
0
0
3
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
2
0
0
1
0
0
1
4
1
0
2
0
1
1
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
1
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
1
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
3
1
0
1
1
0
0
0
0
1
0
5
1
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
2
2
0
0
2
0
1
0
2
0
3
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
3
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
2
0
2
1
0
4
2
2
0
0
0
0
1
0
0
0
0
2
0
0
1
0
2
0
0
0
1
1
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
5
0
0
0
0
2
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
7
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
3
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
4
0
0
0
2
0
0
0
0
0
0
0
0
5
3
2
0
2
0
0
0
0
4
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
2
0
1
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
6
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
2
0
0
3
0
2
4
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
5
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
4
4
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
3
0
2
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
5
0
0
0
3
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
2
0
0
1
0
2
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
2
1
0
0
0
2
1
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
1
2
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
5
5
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
5
0
0
0
2
0
1
0
0
0
0
0
2
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
3
0
1
1
0
0
0
1
0
0
1
0
2
0
2
0
0
0
0
2
0
0
0
0
0
1
4
0
0
2
0
2
1
0
0
0
0
0
0
0
0
4
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
2
0
0
0
3
0
0
0
0
0
4
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
1
0
0
2
0
0
0
2
0
2
0
0
0
0
2
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
1
2
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
3
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
2
0
0
1
6
0
2
0
0
0
0
1
0
0
3
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
5
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
4
0
0
0
0
1
0
0
2
1
0
0
0
0
2
0
0
0
0
0
2
0
0
3
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
5
0
0
0
0
1
0
6
2
0
0
0
0
3
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
1
2
0
0
0
2
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
4
1
0
1
0
0
0
1
1
0
0
1
0
0
0
2
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
5
0
0
0
0
2
0
0
0
0
2
1
3
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
2
0
0
0
1
0
2
0
0
0
0
0
0
3
1
0
0
0
3
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
4
2
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
2
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
0
12
0
0
2
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
2
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
2
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
3
0
0
0
1
0
2
0
0
0
0
1
0
0
1
0
0
1
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
3
0
0
0
4
0
0
1
0
0
1
0
0
0
0
0
2
0
2
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
5
2
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
1
1
0
9
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
2
2
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
2
3
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
3
2
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
2
0
1
0
0
0
2
0
0
0
1
0
0
0
3
0
0
1
0
1
4
2
0
2
0
0
0
0
0
0
0
2
3
1
1
0
0
0
0
2
4
1
1
1
0
2
0
1
2
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
4
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
1
2
0
4
1
0
0
0
2
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
2
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
4
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
3
0
0
2
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
1
0
0
3
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
2
4
0
0
0
0
0
0
0
0
1
0
0
0
7
0
0
0
0
0
0
0
0
0
2
7
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
2
2
1
0
1
4
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
5
0
0
0
3
0
0
0
0
1
1
2
0
0
4
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
1
2
0
2
2
0
0
0
5
0
0
0
2
1
0
0
0
0
0
0
0
3
1
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
2
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
1
1
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
2
0
0
2
3
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
2
0
0
2
1
0
0
0
2
2
2
0
0
0
0
2
1
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
3
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
2
0
0
0
4
0
1
2
1
0
2
0
0
0
0
2
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
2
0
2
0
0
0
0
0
0
2
2
0
1
0
0
0
0
2
2
2
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
3
0
0
0
2
0
0
1
0
0
0
1
4
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
1
0
0
0
0
0
0
1
0
0
0
0
7
0
2
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
1
0
0
1
4
0
0
0
0
0
0
0
0
7
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
6
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
1
0
6
1
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
3
0
0
2
0
2
0
2
0
3
0
1
5
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
4
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
3
2
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
2
0
0
0
0
4
1
2
0
0
1
0
0
2
0
0
0
2
0
2
0
0
0
0
8
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
3
0
1
3
1
0
1
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
5
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
1
1
1
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
1
0
0
1
1
2
2
0
0
0
0
4
0
0
3
0
0
0
2
0
0
0
0
1
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
4
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
2
0
11
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
2
0
0
0
0
0
0
1
5
0
0
0
0
0
0
0
1
1
0
0
2
0
2
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
5
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
1
2
2
0
0
0
0
0
1
0
1
0
2
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
1
1
7
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
3
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
1
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
4
0
1
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
3
0
0
1
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
1
1
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
2
0
1
1
0
0
0
1
0
2
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
8
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
5
0
0
0
3
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
1
0
0
0
0
0
3
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
1
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
3
1
0
0
0
0
0
0
1
0
0
1
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
2
0
0
2
1
3
0
0
2
1
0
0
0
0
0
2
0
1
0
0
3
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
2
0
0
1
0
0
0
0
0
1
1
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
8
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
3
0
3
0
0
1
2
1
1
3
1
0
0
3
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
3
0
0
2
0
2
0
0
6
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
3
0
0
0
0
0
3
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
2
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
1
1
0
0
1
0
0
0
1
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
1
0
0
2
1
0
2
0
0
0
0
0
1
0
2
0
0
0
1
2
0
0
2
1
0
1
0
0
0
0
2
0
0
0
2
2
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
2
0
0
0
3
0
0
0
2
0
0
1
0
0
0
1
0
3
0
0
2
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
1
0
0
0
0
0
0
1
1
0
0
2
0
8
0
2
0
2
2
1
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
1
0
0
2
1
0
0
0
0
1
0
0
1
2
1
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
7
0
0
0
0
2
0
0
0
0
0
2
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
1
0
0
0
0
0
1
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
4
0
1
1
0
0
0
0
0
7
0
0
2
2
0
1
1
0
4
1
0
1
1
1
0
0
0
0
0
3
1
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
2
1
0
1
0
0
0
0
1
0
0
3
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
2
1
0
0
2
10
0
1
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
6
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
3
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
3
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
2
0
1
0
0
0
1
1
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
5
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
1
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
3
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
2
2
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
2
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
1
2
0
0
1
0
0
0
2
0
0
0
0
1
0
0
1
2
0
1
0
1
1
1
1
2
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
3
0
1
0
0
0
2
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
2
0
0
0
2
0
0
0
0
3
0
1
2
0
2
0
0
0
0
2
0
0
0
0
1
1
0
0
3
1
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
2
8
0
1
0
5
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
2
1
0
0
0
0
0
1
0
0
3
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
3
0
0
2
1
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
2
0
0
2
0
0
0
0
0
0
4
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
1
2
0
1
0
0
0
0
0
4
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
2
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
1
4
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
2
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
1
0
2
2
0
1
0
0
1
0
0
3
1
0
0
2
5
0
0
0
0
4
0
0
1
0
0
0
0
0
5
2
0
1
0
2
0
0
1
0
3
0
1
0
0
0
0
0
2
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
2
3
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
2
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
1
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
2
0
0
0
0
3
0
2
2
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
6
0
0
0
3
1
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
3
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
3
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
2
0
0
1
1
0
2
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
1
0
5
0
0
0
0
0
0
0
0
1
0
2
0
1
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
1
0
0
0
2
1
0
0
0
2
0
1
0
0
0
0
3
0
0
1
1
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
1
0
3
1
1
0
0
0
0
0
1
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
2
8
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
1
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
2
0
0
1
3
0
0
0
0
0
0
0
0
1
4
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
4
0
3
0
0
0
0
1
2
0
1
0
0
1
0
0
0
4
0
0
0
0
0
0
0
1
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
4
0
0
0
2
0
0
0
0
0
3
6
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
2
3
1
0
1
2
0
2
1
0
0
0
2
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
3
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
1
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
5
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
5
0
0
2
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
3
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
4
0
2
0
1
2
1
1
0
0
1
0
1
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
6
2
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
1
0
0
0
0
0
3
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
2
0
1
0
0
0
3
0
0
1
1
0
0
6
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
7
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
3
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
2
0
0
0
0
2
0
0
1
4
1
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
2
1
1
2
0
3
2
1
0
0
0
0
1
1
0
0
0
0
0
3
0
1
0
0
0
1
0
0
1
1
1
1
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
1
3
0
3
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
3
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
1
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
2
0
1
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
4
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
1
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
2
0
0
1
0
0
0
2
2
0
0
0
0
1
1
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
3
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
5
1
0
0
1
0
8
0
3
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
2
5
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
4
0
0
0
4
0
4
0
0
2
0
0
5
0
2
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
2
0
0
0
0
1
2
2
0
2
2
0
0
1
1
0
0
0
0
1
1
0
0
0
0
2
1
2
0
1
0
0
0
0
0
0
0
9
1
0
0
0
0
2
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
2
2
3
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
3
2
0
0
1
0
2
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
2
0
2
0
2
0
2
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
6
0
0
0
2
0
0
0
9
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
2
0
2
0
0
0
2
1
0
1
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
2
0
1
0
0
0
2
0
1
0
0
5
0
3
0
3
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
2
3
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
3
0
1
2
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
2
2
0
0
0
0
0
2
1
0
0
1
1
0
0
0
1
0
0
1
0
1
1
0
0
1
4
0
0
1
0
0
0
0
1
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
1
0
1
0
2
0
0
0
1
0
2
0
0
0
0
0
2
0
1
0
0
1
0
0
1
0
0
2
0
0
1
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
5
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
2
1
0
0
1
0
0
0
3
0
8
0
0
0
0
0
3
0
4
0
0
1
0
2
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
3
0
0
1
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
1
1
0
0
3
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
9
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
1
0
1
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
2
0
0
1
0
2
3
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
4
0
2
2
0
1
0
2
0
0
0
4
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
2
0
0
3
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
3
0
0
0
2
0
0
0
1
0
0
0
3
0
2
2
1
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
3
0
4
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
4
0
0
4
0
0
0
0
0
0
2
5
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
3
0
0
2
0
0
0
1
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
2
0
2
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
1
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
1
0
0
0
0
5
0
0
2
1
2
0
1
0
0
1
0
0
0
0
0
0
0
0
3
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
8
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
1
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
2
1
0
0
2
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
6
0
0
0
0
0
0
2
0
0
1
2
0
0
2
0
0
0
1
0
3
0
1
3
0
0
0
1
2
0
1
1
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
2
1
2
0
0
3
0
0
1
0
0
0
0
0
1
1
1
0
0
3
0
0
2
1
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
2
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
2
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
1
1
0
0
0
0
0
1
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
1
3
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
3
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
2
0
2
0
0
0
2
0
0
0
2
0
0
0
4
0
1
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
2
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
2
0
0
0
0
0
2
0
2
0
0
1
2
2
0
0
0
0
1
0
0
0
0
0
4
0
0
0
1
1
0
0
0
1
0
0
0
0
2
0
0
0
0
3
1
0
0
0
0
0
0
0
0
6
0
0
0
1
0
0
0
0
0
1
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
3
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
1
3
0
1
0
0
0
3
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
2
2
0
0
1
0
3
2
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
2
1
0
0
0
2
0
0
0
2
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
2
1
0
0
8
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
6
0
3
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
1
1
1
0
3
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
1
2
0
1
2
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
2
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
2
0
1
0
1
0
0
6
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
1
0
2
3
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
2
2
0
1
0
0
0
0
2
0
0
2
0
3
0
0
1
0
0
2
0
1
0
0
0
0
0
0
2
1
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
1
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
3
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
2
0
0
2
0
1
1
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
1
0
0
0
0
1
0
0
4
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
2
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
2
0
5
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
1
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
3
0
0
0
3
1
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
7
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
1
0
1
3
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
3
0
3
0
0
0
0
2
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
2
0
1
1
0
2
1
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
3
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
2
1
0
1
0
0
0
0
1
0
0
3
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
3
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
1
0
1
2
1
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
1
1
0
0
1
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
2
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
9
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
1
2
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
3
0
1
1
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
3
0
0
0
1
1
0
0
0
0
2
0
1
0
0
2
3
0
0
0
0
0
3
0
1
2
1
0
0
4
0
0
0
0
0
1
2
0
1
2
2
0
0
2
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
3
2
0
0
0
1
0
1
0
3
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
1
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
5
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
2
2
0
0
3
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
2
1
0
0
1
0
0
3
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
8
1
1
0
0
0
0
0
1
1
0
2
0
0
0
0
2
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
8
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
2
0
1
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
6
0
0
0
0
0
1
0
0
0
2
1
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
1
0
0
0
2
0
0
1
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
3
1
0
0
2
0
0
1
0
0
0
0
0
0
1
2
0
0
1
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
1
0
0
1
2
0
1
0
0
0
3
0
3
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
1
0
0
2
0
1
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
1
0
0
0
0
2
2
0
1
0
0
0
1
0
0
1
0
0
0
0
2
0
1
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
5
0
0
0
0
0
2
0
2
2
3
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
2
0
0
0
1
3
0
0
0
0
0
2
0
1
1
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
2
0
1
0
3
0
0
0
1
0
0
0
1
0
0
0
1
0
0
2
2
0
0
0
0
0
0
6
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
4
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
2
0
0
2
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
1
0
0
0
2
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
1
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
4
0
0
0
1
0
0
2
4
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
2
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
5
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
4
0
0
2
0
0
0
0
0
2
2
0
1
0
0
2
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
3
0
2
1
0
3
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
2
0
0
0
1
0
0
0
0
2
0
2
1
0
1
0
0
1
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
2
0
1
3
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
7
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
13
1
1
0
1
2
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
6
0
1
1
0
0
0
0
0
0
0
2
0
0
1
0
1
0
2
0
0
1
0
0
0
0
4
1
0
0
0
0
0
0
0
11
1
0
1
0
0
0
2
0
0
2
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
3
0
1
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
2
2
0
0
0
0
0
0
1
2
0
0
3
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
1
0
0
0
1
0
1
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
6
1
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
1
1
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
2
0
0
0
0
2
0
2
0
0
2
0
1
4
0
0
0
2
0
0
1
0
0
0
3
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
7
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
5
1
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
1
2
0
0
0
0
4
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
6
0
0
0
0
0
0
0
0
0
0
2
0
1
2
2
1
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
3
1
0
0
0
0
0
1
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
3
0
3
0
0
0
0
0
1
0
2
0
0
1
0
2
0
0
0
0
0
0
1
0
1
1
0
0
3
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
1
0
0
0
0
1
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
5
0
0
1
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
3
0
2
0
2
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
2
0
1
4
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
2
0
2
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
1
0
2
0
2
2
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
1
0
1
0
0
2
2
1
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
2
0
0
0
0
1
0
4
0
4
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
2
0
0
2
0
0
1
0
0
1
2
2
0
0
0
0
1
1
1
0
3
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
5
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
2
3
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
4
0
0
0
0
2
1
1
0
0
2
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
5
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
2
0
0
2
1
0
0
0
2
0
0
1
0
1
0
3
2
1
0
1
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
1
0
1
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
2
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
4
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
3
0
1
0
2
2
0
0
0
0
0
0
0
1
0
1
2
0
0
1
2
1
0
0
0
3
2
0
0
2
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
1
2
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
2
1
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
4
0
0
0
3
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
4
1
3
0
1
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
1
1
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
1
0
0
1
0
0
0
1
0
2
1
0
0
2
0
0
3
0
1
0
1
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
1
3
2
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
1
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
3
4
0
0
0
0
2
0
1
0
2
1
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
3
0
0
0
0
1
4
2
2
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
4
0
0
2
2
1
2
3
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
4
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
7
0
0
7
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
1
1
0
2
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
2
0
0
0
0
1
1
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
4
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
3
0
0
0
5
2
0
0
1
0
0
0
1
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
2
1
0
4
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
2
3
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
5
0
1
0
0
0
0
1
4
0
2
0
0
1
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
3
0
0
0
6
0
2
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
1
2
0
2
0
3
6
4
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
6
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
1
0
0
0
0
0
0
0
2
0
0
2
3
0
0
0
0
0
0
0
0
2
0
2
4
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
1
3
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
2
0
0
2
2
1
2
0
0
0
0
0
2
1
5
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
1
0
0
1
0
1
0
0
0
0
0
3
0
0
1
0
3
0
0
0
0
1
0
0
0
0
2
2
0
0
1
0
0
2
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
2
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
3
0
1
0
0
2
2
0
0
0
1
1
0
0
0
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
4
0
2
0
0
0
0
0
0
0
0
0
1
0
0
8
0
0
0
2
0
0
0
0
0
0
1
1
0
3
2
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
3
1
0
0
0
0
0
1
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
3
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
1
0
0
0
0
2
0
0
9
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
1
5
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
5
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
1
1
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
4
2
0
0
0
0
1
1
1
0
1
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
2
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
3
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
1
0
0
0
0
1
1
0
2
1
0
0
0
2
1
2
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
5
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
1
0
1
0
0
0
1
0
4
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
4
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
3
0
1
0
0
0
13
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
2
0
0
0
3
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
2
2
1
0
0
3
0
0
0
1
0
0
0
0
0
1
3
0
0
0
0
0
2
5
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
6
2
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
2
1
0
0
0
0
0
0
2
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
1
0
2
1
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
3
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
1
0
0
0
1
0
0
0
0
0
1
0
0
2
0
3
0
0
1
0
2
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
3
0
2
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
4
0
1
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
2
4
0
0
0
0
1
2
0
0
1
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
3
0
0
4
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
2
0
2
2
0
0
1
0
0
2
2
2
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
2
2
0
0
1
1
0
0
1
4
0
1
0
0
0
0
0
0
1
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
4
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
1
0
0
0
18
0
0
0
0
0
0
0
0
0
4
0
2
0
1
0
0
1
1
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
2
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
2
0
0
0
1
2
0
0
1
1
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
1
0
0
0
3
0
1
0
0
0
2
4
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
2
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
2
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
3
1
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
1
0
0
2
0
3
2
0
2
0
0
0
0
0
0
0
0
1
0
1
1
0
2
0
0
0
1
0
0
2
1
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
1
0
2
0
2
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
1
0
0
0
2
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
1
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
1
0
0
0
1
1
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
1
1
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
5
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
2
0
0
2
1
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
2
2
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
1
2
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
8
0
0
0
0
0
0
1
2
0
0
1
0
1
1
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
4
3
0
3
2
2
0
1
0
0
2
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
3
0
0
0
8
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
2
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
4
2
0
0
0
0
1
0
2
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
4
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
1
0
1
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
2
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
3
0
0
0
8
2
0
0
1
2
0
1
0
0
2
0
1
0
0
0
2
3
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
1
1
0
1
1
0
0
0
2
2
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
3
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
2
2
0
0
0
0
2
0
0
1
0
2
1
0
0
2
2
0
1
0
2
0
0
0
0
1
0
1
1
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
2
0
1
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
3
2
0
3
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
4
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
4
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
2
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
6
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
6
4
0
1
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
1
8
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
1
1
0
1
2
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
3
0
0
0
0
1
0
4
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
4
2
0
0
2
0
0
0
0
2
1
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
7
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
4
0
0
0
2
0
2
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
2
0
0
1
0
0
4
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
2
0
0
4
3
0
0
0
3
3
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
1
0
0
0
0
1
0
0
1
0
0
5
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
2
1
2
0
0
2
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
2
0
1
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
6
2
0
0
0
0
1
2
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
2
0
0
0
0
3
0
1
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
6
0
0
1
2
0
2
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
1
0
0
3
0
1
0
0
1
0
2
1
2
0
0
0
1
0
0
0
2
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
6
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
3
0
0
0
1
0
0
1
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
3
5
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
2
1
1
0
0
0
0
5
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
2
0
0
1
0
4
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
4
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
3
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
1
0
3
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
2
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
3
0
0
1
0
3
1
1
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
1
0
0
2
0
1
0
1
2
0
2
1
0
0
0
0
0
3
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
3
0
0
0
0
0
1
2
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
4
0
2
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
1
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
7
0
1
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
3
0
1
1
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
4
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
3
0
0
0
1
1
0
0
0
2
0
0
2
0
0
0
2
1
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
2
0
1
0
0
0
1
0
2
3
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
1
1
1
2
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
1
0
4
2
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
1
0
1
0
0
0
0
2
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
1
0
2
0
0
1
2
0
2
0
0
0
0
0
2
0
0
1
0
1
2
0
0
2
0
0
0
4
0
0
0
0
0
0
1
1
5
0
0
0
0
0
0
0
0
0
3
2
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
2
1
0
0
0
0
0
0
1
0
1
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
3
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
1
1
0
0
0
0
0
0
0
0
0
2
0
5
0
1
0
2
0
0
0
1
0
3
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
1
0
3
2
0
2
0
1
0
0
0
0
0
1
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
1
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
3
3
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
4
0
3
0
0
0
0
0
0
0
1
2
0
2
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
2
0
0
0
0
2
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
2
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
3
0
0
0
2
0
0
1
2
2
1
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
1
0
0
0
0
0
3
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
5
1
2
1
15
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
6
1
0
0
0
0
1
3
0
0
0
0
5
0
0
2
0
0
0
0
0
3
0
0
0
4
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
1
0
0
0
0
0
0
3
0
0
0
2
6
0
0
0
0
1
0
2
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
3
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
2
0
0
1
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
1
0
0
1
0
0
0
0
0
1
0
2
0
2
0
0
0
0
2
0
1
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
2
1
4
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
3
0
0
0
0
3
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
4
0
2
0
2
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
1
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
5
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
6
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
1
0
0
3
0
2
0
2
0
0
0
0
2
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
2
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
1
0
0
0
1
2
1
2
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
1
0
2
0
0
0
0
1
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
2
2
1
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
2
1
1
0
1
0
2
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
2
0
1
3
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
3
0
4
4
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
5
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
2
0
1
0
2
0
1
0
3
0
0
0
0
0
4
0
2
0
0
0
0
0
1
0
0
0
1
0
3
0
0
0
1
0
2
0
0
2
3
0
0
4
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
2
0
1
0
2
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
11
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
4
0
0
4
1
0
3
2
0
0
0
1
0
2
2
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
2
1
1
0
2
0
0
0
0
1
0
3
0
1
0
2
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
2
0
2
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
1
0
0
2
0
0
0
0
3
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
3
0
4
0
0
0
0
0
0
0
0
1
2
0
0
2
0
3
0
0
0
3
0
0
0
0
0
0
2
0
3
0
0
0
1
0
1
1
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
4
0
2
0
0
0
1
1
0
0
0
4
0
0
0
0
1
0
0
0
0
2
0
0
4
0
0
2
0
0
0
0
0
1
1
0
0
0
8
2
0
0
2
0
0
1
2
1
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
1
0
0
0
3
0
0
0
0
3
0
0
0
0
4
0
0
0
2
0
0
0
0
1
5
0
0
0
0
2
0
0
0
0
0
1
0
6
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
2
2
3
2
0
2
0
3
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
2
1
0
0
2
2
0
0
2
4
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
1
6
0
3
0
0
0
3
7
0
0
0
0
0
0
0
2
0
1
0
0
2
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
5
0
0
2
0
0
0
0
0
0
0
1
0
2
1
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
6
1
1
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
1
1
1
0
0
0
0
2
1
0
0
0
0
0
2
0
0
1
0
0
0
1
0
1
2
0
0
1
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
5
2
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
2
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
1
2
2
0
0
2
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
6
1
0
0
0
0
1
0
0
3
0
1
0
1
0
0
0
0
0
2
0
2
0
0
0
1
0
0
6
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
1
1
0
1
3
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
1
4
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
3
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
3
2
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
2
2
0
0
2
0
0
0
1
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
3
1
0
0
1
1
1
0
2
2
3
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
3
0
1
0
2
0
13
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
1
0
1
2
0
0
2
2
0
0
0
0
0
2
0
0
0
0
2
2
2
0
0
0
3
0
0
0
0
0
1
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
1
0
1
2
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
5
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
3
0
0
2
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
1
0
0
1
0
2
0
0
1
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
2
0
2
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
4
0
0
0
1
2
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
6
1
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
1
0
0
1
1
0
0
2
2
0
0
0
0
0
2
0
1
3
0
0
0
2
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
2
0
0
0
0
2
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
3
0
0
0
1
0
0
0
0
2
0
1
2
0
0
0
2
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
4
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
3
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
2
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
6
0
0
2
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
4
0
1
2
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
6
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
11
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
1
1
0
1
2
0
0
0
1
0
2
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
4
0
0
1
0
2
0
2
0
0
0
0
0
0
0
1
1
0
1
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
1
2
0
0
0
0
0
9
0
0
0
1
0
0
0
1
0
3
2
4
0
0
0
3
0
1
0
1
1
0
0
0
1
3
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
3
0
2
0
1
0
0
0
2
0
0
0
2
0
0
2
2
2
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
3
0
0
0
0
3
0
0
0
0
0
1
0
2
0
0
0
3
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
1
2
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
1
0
0
0
1
0
0
2
2
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
7
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
2
2
0
1
0
0
1
0
0
0
0
0
1
1
0
2
0
3
0
0
0
4
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
1
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
1
1
0
0
2
0
3
1
0
0
8
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
2
0
0
0
1
3
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
3
0
3
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
2
0
0
2
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
1
1
0
0
0
1
0
0
0
0
1
1
0
2
3
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
3
1
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
4
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
1
0
1
0
0
0
0
0
2
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
3
1
0
0
8
0
0
1
0
0
1
4
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
6
0
0
0
0
0
2
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
1
0
0
0
2
0
0
0
3
0
1
0
1
2
0
0
1
0
1
4
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
3
0
0
1
1
2
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
1
0
1
0
0
0
1
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
2
2
1
2
0
0
0
0
0
2
0
0
0
1
1
0
1
0
2
0
0
1
1
0
0
1
0
0
1
1
2
0
0
0
2
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
5
0
0
0
1
0
0
0
2
1
0
0
0
2
0
0
0
0
1
0
0
0
0
2
1
0
1
0
2
1
1
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
2
0
2
0
1
0
0
0
4
2
0
0
0
0
2
1
1
0
2
0
1
0
0
0
2
2
1
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
3
0
0
0
5
0
0
0
0
3
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
1
0
1
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
2
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
3
3
0
0
0
0
0
0
0
0
1
0
0
3
0
0
3
0
0
1
0
0
0
0
2
0
0
1
0
0
2
0
0
1
2
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
1
1
0
0
0
0
2
0
0
0
0
1
0
0
0
2
2
2
0
0
0
0
2
4
1
0
0
0
0
0
4
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
3
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
1
0
2
1
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
1
0
1
2
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
3
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
2
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
5
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
2
1
2
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
1
0
0
0
0
1
0
2
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
5
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
4
0
0
0
0
0
2
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
4
0
0
2
0
0
0
0
0
0
1
0
0
3
0
1
2
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
1
0
0
1
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
2
0
6
3
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
1
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
2
0
0
1
0
0
0
0
0
0
1
6
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
3
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
2
2
0
0
0
1
1
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
7
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
3
2
0
1
0
1
0
0
0
0
0
0
2
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
3
0
0
2
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
1
1
0
0
1
0
1
0
0
1
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
6
0
0
0
0
0
0
2
0
0
4
0
0
2
0
0
0
2
0
2
0
0
0
1
0
1
2
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
3
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
1
1
0
0
0
0
0
0
6
1
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
1
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
2
0
0
1
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
3
1
1
0
0
0
2
0
0
1
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
1
2
0
0
1
0
0
0
0
0
0
0
4
0
1
0
1
0
0
2
2
0
3
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
2
2
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
4
0
0
0
0
1
0
1
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
1
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
1
0
0
1
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
1
0
3
0
1
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
3
1
0
0
0
1
0
0
0
2
0
0
2
1
0
0
0
0
2
3
1
0
1
0
1
0
2
2
1
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
1
1
0
1
1
1
2
2
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
1
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
1
0
3
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
1
2
2
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
2
0
0
0
2
0
0
3
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
2
0
2
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
6
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
1
1
0
0
0
1
0
0
1
5
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
3
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
3
0
0
0
6
1
1
0
0
1
0
0
0
0
0
2
0
1
2
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
2
0
0
0
0
1
0
0
0
0
0
0
0
3
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
6
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
4
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
1
2
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
3
0
1
2
1
0
3
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
2
0
2
0
2
0
0
0
0
0
1
0
0
2
1
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
3
2
3
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
3
0
0
0
0
0
2
0
0
1
0
1
2
0
0
2
0
0
0
0
0
2
1
0
0
2
1
0
1
0
1
0
0
0
2
0
1
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
1
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
1
0
1
0
1
3
0
0
0
3
0
5
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
4
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
5
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
2
0
0
2
1
1
1
0
0
0
0
3
2
0
0
0
0
0
5
0
1
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
1
0
0
0
1
0
0
5
0
0
2
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
10
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
1
2
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
1
2
1
6
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
1
1
0
0
0
1
1
1
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
3
2
0
0
1
1
0
0
0
0
6
3
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
1
1
0
1
0
1
0
2
0
0
1
2
0
0
0
0
0
0
0
2
0
0
3
2
0
9
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
3
1
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
2
0
2
0
1
0
3
0
0
4
2
0
0
3
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
4
0
0
0
0
1
2
2
0
0
3
1
0
1
0
0
2
0
0
1
2
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
2
0
1
0
0
0
2
0
0
0
4
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
2
0
2
0
0
3
2
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
4
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
4
0
0
0
1
0
2
0
0
0
1
1
1
0
0
1
0
1
0
3
2
2
1
1
0
2
0
1
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
2
2
0
2
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
2
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
2
3
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
1
2
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
1
0
2
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
1
1
0
1
1
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
1
1
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
2
0
0
0
3
0
0
0
0
0
1
2
1
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
3
2
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
1
1
0
1
4
0
1
0
1
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
3
0
0
0
2
4
0
0
0
0
0
0
0
0
2
2
0
1
0
2
2
0
1
0
0
0
2
0
0
0
3
0
3
0
0
0
0
0
1
0
3
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
1
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
3
0
0
2
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
1
3
1
0
5
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
3
0
0
1
1
1
0
0
0
0
0
1
0
3
1
2
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
3
0
0
1
3
0
0
1
0
0
0
2
2
0
0
0
0
1
0
0
2
2
0
2
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
3
0
0
2
0
0
0
0
0
0
0
0
1
3
0
0
3
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
3
1
0
1
0
0
0
2
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
6
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
4
0
1
0
0
0
0
1
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
3
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
2
1
0
0
3
0
0
0
0
0
0
0
0
2
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
2
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
5
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
9
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
1
0
2
2
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
1
0
3
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
2
0
1
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
4
0
0
0
2
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
2
2
2
0
0
2
0
0
1
0
0
0
0
0
2
0
5
2
0
5
0
2
0
0
0
0
0
2
0
0
0
2
2
3
0
0
2
0
2
1
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
2
0
0
0
2
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
6
0
0
0
0
0
2
2
0
0
2
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
16
0
0
0
1
0
0
0
0
0
2
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
1
0
3
1
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
3
3
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
2
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
1
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
2
2
2
0
0
0
0
2
0
0
0
4
0
0
3
1
0
0
0
3
4
1
0
0
0
2
1
0
0
0
1
3
0
0
0
5
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
4
0
2
0
1
0
0
0
0
1
0
2
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
3
1
3
0
0
0
0
0
0
1
0
6
5
0
0
2
0
1
0
1
0
2
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
1
0
1
1
0
0
2
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
2
0
0
0
6
0
0
2
0
0
1
1
2
0
1
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
3
0
1
0
0
0
0
0
0
1
2
0
0
1
2
0
0
0
0
0
1
2
0
0
3
0
0
1
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
3
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
1
0
0
1
3
0
2
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
5
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
2
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
2
0
0
1
1
0
1
0
1
0
1
1
2
1
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
2
2
0
0
3
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
1
0
0
0
0
0
2
0
3
4
2
2
0
8
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
2
0
0
1
0
0
0
1
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
3
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
3
0
0
1
0
0
1
11
0
0
1
1
1
0
0
0
0
0
0
2
1
0
0
5
0
1
0
0
2
0
0
0
0
0
2
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
2
1
2
0
0
0
3
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
3
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
1
0
1
2
0
0
0
0
1
2
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
1
3
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
5
0
0
0
0
0
2
0
1
0
1
0
1
1
0
0
0
2
0
0
4
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
2
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
1
0
0
1
0
0
1
0
2
0
0
0
0
5
0
0
0
0
0
0
1
0
0
0
1
2
0
0
1
1
1
0
0
4
0
3
0
0
0
2
0
0
0
3
0
0
1
0
0
0
2
0
1
0
0
1
1
0
0
1
0
1
0
0
0
0
2
2
0
0
0
0
1
2
0
0
1
3
0
1
0
0
1
0
0
0
0
0
0
1
3
2
0
0
0
0
0
0
2
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
2
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
8
3
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
1
3
1
0
0
0
0
0
0
3
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
3
2
0
0
0
0
1
0
1
1
0
1
2
0
0
0
0
0
1
0
0
0
0
0
5
1
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
4
4
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
3
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
2
0
0
0
4
3
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
2
0
0
1
3
2
2
0
0
0
0
0
0
0
0
0
1
1
0
0
2
3
0
0
0
0
0
3
1
2
1
0
0
0
0
0
0
5
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
11
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
5
0
0
1
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
19
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
8
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
1
0
2
2
2
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
1
0
0
1
0
0
2
0
3
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
1
0
0
4
0
0
1
0
0
0
2
0
0
0
0
0
1
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
5
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
1
0
0
1
0
2
3
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
1
2
0
0
2
0
0
1
1
0
0
2
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
1
2
0
0
1
0
1
2
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
2
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
2
1
0
2
0
1
0
1
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
1
2
1
0
0
1
1
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
6
2
1
0
0
2
1
0
0
0
0
0
1
0
0
2
0
0
0
9
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
1
2
0
0
0
2
2
0
0
0
3
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
3
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
5
0
0
0
0
3
0
0
0
0
2
1
0
0
2
5
0
0
0
1
0
0
0
0
0
0
3
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
3
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
12
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
3
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
9
0
0
0
1
0
0
0
0
1
2
0
0
2
0
1
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
5
0
0
0
0
1
0
0
2
2
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
2
2
1
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
1
10
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
3
1
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
1
0
0
0
2
0
0
0
0
0
0
1
2
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
1
0
3
1
2
1
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
1
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
3
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
4
0
2
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
3
0
2
0
2
0
0
0
0
1
0
1
1
0
2
0
2
0
0
0
2
0
2
0
0
2
0
0
0
0
1
0
1
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
7
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
4
0
2
0
0
1
0
0
2
0
0
0
1
0
0
0
0
6
0
0
0
1
0
1
0
1
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
1
3
0
4
0
0
0
0
0
0
0
0
0
0
3
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
2
0
1
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
7
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
1
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
2
1
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
2
0
0
0
0
2
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
2
0
0
2
0
0
2
1
1
0
1
1
0
1
0
0
0
0
0
2
1
2
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
1
3
0
0
1
0
0
0
0
0
1
0
0
1
4
0
0
0
0
0
0
0
1
0
2
0
0
0
2
2
3
3
0
0
0
2
0
0
1
0
0
0
3
0
0
0
0
0
3
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
2
0
0
2
0
1
0
4
0
0
0
0
3
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
3
0
4
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
4
0
0
0
2
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
2
2
0
0
0
0
2
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
1
2
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
3
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
1
3
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
1
2
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
4
1
1
0
0
0
0
2
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
3
0
0
1
1
2
0
0
0
0
0
0
0
0
6
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
1
0
4
2
0
2
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
1
1
0
2
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
3
1
0
0
0
0
2
0
0
0
1
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
6
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
1
1
0
0
0
0
0
0
1
0
0
3
1
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
4
1
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
1
1
3
0
0
2
0
0
1
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
3
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
3
1
1
0
0
2
0
0
0
2
2
0
0
0
1
2
0
0
0
2
7
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
1
0
0
0
0
3
0
1
0
0
1
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
1
0
4
0
0
1
1
2
1
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
2
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
7
0
0
0
0
0
0
8
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
6
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
1
2
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
12
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
7
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
2
0
0
1
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
2
0
0
1
1
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
6
5
0
0
0
0
1
0
2
0
1
3
0
0
1
0
0
1
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
3
2
0
1
0
0
0
0
0
0
0
0
0
0
1
3
0
0
1
0
0
0
1
0
0
2
1
0
0
0
0
2
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
3
0
0
2
2
0
0
0
0
1
0
0
0
0
1
2
0
0
0
3
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
1
1
3
0
0
1
0
0
0
0
2
0
8
0
0
2
1
0
0
0
0
0
1
4
0
1
1
2
0
1
0
0
1
1
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
4
0
2
0
0
2
3
2
0
0
1
0
2
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
3
0
0
2
0
2
0
2
0
1
0
0
0
1
1
0
0
2
2
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
3
0
0
0
0
1
1
0
0
0
3
0
2
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
7
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
2
1
2
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
2
0
0
1
1
0
0
0
1
0
2
0
0
1
1
0
0
0
0
2
1
0
1
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
2
2
0
0
2
0
0
0
5
0
0
0
1
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
4
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
3
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
1
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
2
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
4
0
1
0
0
0
2
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
5
5
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
2
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
3
0
6
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
2
2
0
0
2
0
3
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
4
0
0
0
0
0
0
1
0
3
0
0
0
1
0
7
1
1
2
1
0
0
0
0
0
0
1
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
4
0
0
2
2
0
2
1
0
1
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
3
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
2
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
3
0
1
0
3
0
0
2
0
1
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
1
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
3
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
1
0
1
2
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
2
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
2
2
0
0
0
2
1
0
2
0
1
0
0
0
0
2
0
7
0
2
1
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
2
1
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
3
2
0
0
1
0
0
0
6
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
2
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
1
0
0
2
0
2
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
4
1
0
0
0
0
0
0
1
1
1
0
2
5
0
0
0
0
0
0
1
2
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
2
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
5
0
1
1
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
8
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
4
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
2
2
0
1
0
0
2
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
5
0
0
0
0
2
0
3
1
1
1
0
1
0
3
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
5
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
5
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
2
1
2
0
0
1
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
3
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
2
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
1
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
3
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
2
0
1
1
0
1
1
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
1
2
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
2
0
0
1
1
0
0
0
0
2
0
0
3
0
0
1
0
0
2
5
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
2
1
0
0
0
0
0
2
0
0
0
1
0
0
0
1
2
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
1
1
0
0
2
0
0
0
1
0
1
0
3
0
7
0
0
0
0
0
0
0
1
1
3
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
1
0
0
1
0
0
0
1
0
2
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
1
1
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
2
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
2
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
2
0
2
0
0
2
1
0
0
2
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
3
5
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
2
0
5
0
0
3
0
0
0
2
1
0
1
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
1
1
1
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
1
2
0
2
1
0
0
0
1
1
0
0
0
1
0
0
3
0
0
0
0
1
0
0
0
0
3
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
2
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
3
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
2
0
0
2
0
1
1
2
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
1
0
3
0
0
0
3
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
0
0
1
1
0
2
2
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
2
4
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
4
2
0
0
0
0
0
0
0
0
0
0
0
6
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
1
1
1
0
1
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
1
1
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
1
0
9
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
2
0
2
0
0
5
0
0
0
0
0
3
0
0
2
0
2
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
7
2
0
0
0
0
0
0
4
3
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
2
1
1
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
2
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
1
0
1
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
2
1
0
0
1
0
0
0
2
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
2
0
2
1
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
3
2
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
4
1
0
0
1
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
1
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
3
0
2
0
1
0
2
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
1
0
0
0
1
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
1
0
1
2
0
0
0
0
3
0
0
0
0
0
2
0
1
0
1
0
0
0
2
1
0
0
0
0
4
0
0
1
0
0
0
0
2
2
0
0
3
0
0
0
0
0
0
0
2
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
3
0
0
0
0
6
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
4
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
4
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
2
0
2
2
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
1
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
2
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
3
1
2
0
0
0
0
0
2
1
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
2
0
0
2
1
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
7
0
2
0
0
0
0
0
2
0
1
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
1
0
0
2
0
2
1
0
0
0
1
1
0
1
0
0
0
2
0
0
0
0
0
2
2
0
1
0
1
0
0
0
2
0
1
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
2
3
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
2
2
0
2
0
2
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
3
0
0
0
1
0
4
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
3
0
0
1
0
3
0
0
1
1
4
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
2
1
0
4
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
1
1
4
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
2
1
0
1
0
0
0
1
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
2
0
1
0
0
0
1
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
10
0
0
0
2
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
2
1
0
3
0
0
0
5
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
3
0
0
1
0
2
0
0
0
1
1
0
0
0
2
0
1
0
0
0
0
1
0
2
0
0
1
0
3
0
0
0
2
2
0
2
0
0
0
8
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
3
2
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
4
1
0
0
2
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
2
0
0
2
3
0
1
0
0
0
0
0
1
0
4
0
0
1
2
1
0
0
0
0
0
2
0
1
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
2
0
0
3
2
0
0
0
0
2
0
0
0
0
1
1
1
1
0
0
0
0
2
0
4
0
0
0
0
0
0
1
0
0
0
0
0
3
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
4
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
3
3
0
0
0
1
0
0
1
0
1
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
4
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
3
1
2
0
2
0
0
0
3
0
0
2
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
3
1
0
0
0
0
0
2
0
5
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
2
0
0
0
2
2
0
0
0
2
0
1
0
0
0
6
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
2
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
2
2
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
4
0
0
2
0
0
0
4
0
0
0
2
0
2
1
1
0
0
0
0
0
2
0
0
1
2
0
1
2
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
1
0
5
0
2
0
2
0
0
1
0
0
1
2
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
1
0
0
0
1
1
0
2
2
0
2
1
2
0
3
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
3
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
4
2
0
2
2
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
2
6
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
5
0
2
2
1
0
1
0
1
1
0
0
3
3
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
2
0
0
0
0
1
0
2
0
2
1
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
5
2
0
2
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
6
0
0
0
0
0
0
0
0
0
2
1
1
0
2
0
0
0
0
0
0
0
0
0
0
1
4
1
0
0
2
0
1
0
0
1
0
2
0
0
1
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
3
0
0
0
0
2
0
0
1
0
0
0
0
2
2
0
0
0
1
1
2
4
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
1
2
2
1
0
0
0
3
0
0
0
0
0
0
0
0
4
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
2
0
0
0
0
0
0
0
1
12
0
0
0
0
0
0
0
0
0
0
0
0
1
1
3
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
1
0
1
4
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
1
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
2
5
0
0
0
0
0
1
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
3
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
3
0
0
1
1
0
1
2
0
1
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
2
0
0
4
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
6
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
2
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
3
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
1
0
0
2
0
2
0
0
0
0
0
2
1
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
2
0
1
0
0
0
1
2
0
1
0
0
0
1
0
0
1
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
3
0
1
3
2
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
5
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
5
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
2
1
2
0
0
0
0
3
0
0
2
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
3
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
1
0
0
0
2
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
3
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
3
0
0
1
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
2
1
2
1
2
0
1
0
0
1
2
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
5
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
5
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
3
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
3
1
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
2
1
0
0
0
0
0
1
0
2
2
2
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
2
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
5
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
1
0
0
1
1
0
0
2
3
1
0
0
1
0
0
2
2
0
0
2
0
0
2
0
1
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
1
0
0
0
0
1
0
0
0
0
0
0
2
1
0
3
0
0
2
0
0
0
0
2
0
0
0
1
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
2
1
1
1
0
0
0
1
2
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
3
0
0
1
0
1
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
2
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
4
0
0
0
2
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
1
1
2
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
3
0
0
0
0
2
0
0
2
0
2
0
3
0
2
2
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
5
0
0
0
0
0
0
0
0
0
1
3
1
0
0
2
0
0
1
2
0
2
0
1
0
1
0
0
1
1
1
6
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
1
1
0
0
0
0
2
0
0
0
2
1
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
3
0
2
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
2
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
3
1
1
0
0
2
6
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
4
0
0
0
1
0
1
1
0
0
0
1
0
0
4
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
3
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
5
2
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
4
7
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
2
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
4
0
1
0
0
1
5
0
0
0
0
2
1
0
1
0
0
0
3
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
1
2
0
0
0
0
1
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
1
1
1
0
0
0
0
0
1
1
2
0
0
0
0
0
0
2
1
0
0
1
3
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
2
1
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
2
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
1
1
0
2
2
0
0
0
2
0
0
0
1
0
1
0
0
0
0
1
0
0
0
2
0
0
0
2
1
0
0
0
0
2
2
0
4
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
1
0
0
2
0
0
0
0
0
0
0
3
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
4
0
0
0
4
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
3
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
1
0
2
0
0
0
0
0
5
0
0
0
0
2
0
0
2
0
0
3
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
2
0
0
0
1
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
4
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
3
0
0
3
2
0
2
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
3
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
3
0
0
0
0
1
0
0
1
2
0
1
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
4
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
1
0
0
0
2
0
2
1
0
3
0
1
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
6
4
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
1
2
1
0
0
3
0
3
3
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
5
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
2
3
0
0
0
2
1
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
1
2
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
2
0
0
0
0
2
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
3
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
4
1
2
2
1
3
1
1
1
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
5
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
3
0
3
0
0
0
2
0
0
0
2
0
1
0
2
0
0
0
0
2
0
1
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
3
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
4
0
0
0
0
0
0
4
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
6
0
1
0
1
0
0
0
0
0
0
4
0
0
0
0
3
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
2
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
3
0
0
2
0
0
0
0
0
3
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
2
0
4
0
0
2
2
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
4
0
0
0
0
4
0
0
1
3
0
0
2
1
0
1
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
2
2
2
2
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
1
0
2
0
1
15
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
3
1
0
0
0
0
3
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
5
0
2
0
0
0
0
2
2
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
4
1
2
0
0
0
1
0
0
0
0
2
3
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
1
1
1
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
1
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
7
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
2
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
1
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
4
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
5
0
2
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
6
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
2
3
0
2
1
1
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
1
1
0
0
0
2
0
1
1
0
1
0
0
0
1
0
0
2
0
0
0
1
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
4
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
4
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
3
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
3
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
2
1
1
0
0
0
1
0
1
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
1
1
0
3
0
2
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
3
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
2
1
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
1
1
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
4
0
1
0
0
1
1
0
0
0
0
0
1
2
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
2
1
0
0
0
2
0
0
0
0
0
1
2
0
1
0
6
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
3
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
2
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
2
2
1
2
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
1
0
2
0
2
0
6
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
1
2
2
0
0
1
0
0
0
0
0
0
1
2
0
2
0
2
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
2
0
0
2
1
0
0
0
1
2
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
1
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
1
0
0
5
1
2
0
0
2
1
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
5
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
4
0
0
0
0
2
3
0
1
1
1
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
2
1
0
0
1
1
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
1
0
2
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
2
0
0
2
0
1
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
4
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
4
0
0
0
0
3
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
3
1
0
0
2
0
0
0
0
3
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
7
0
0
0
0
2
0
1
0
0
0
0
1
1
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
2
0
0
6
0
1
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
5
1
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
3
0
0
1
0
2
0
2
0
1
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
5
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
3
0
3
0
0
2
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
7
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
2
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
1
2
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
1
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
8
0
2
0
0
0
2
0
0
0
2
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
1
2
0
0
0
0
4
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
3
0
0
2
0
0
2
2
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
3
2
0
0
0
2
0
0
0
0
1
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
2
0
0
2
0
0
3
0
0
2
3
1
0
0
0
0
3
0
0
0
1
0
0
0
4
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
3
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
2
0
0
2
0
4
2
0
0
2
0
0
1
0
0
0
0
0
7
0
0
0
0
6
0
0
0
2
0
0
1
0
0
1
0
0
7
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
4
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
6
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
2
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
3
0
4
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
1
0
0
0
2
0
0
0
0
3
0
2
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
2
0
0
2
1
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
4
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
3
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
8
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
2
0
0
0
0
0
0
0
3
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
5
0
0
0
0
0
0
1
3
0
0
0
0
0
0
6
0
2
0
0
2
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
3
0
0
0
1
2
0
0
0
0
0
0
0
3
0
0
0
1
0
0
2
0
1
2
2
0
0
0
2
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
1
0
0
2
0
3
0
2
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
4
3
0
4
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
4
0
0
0
0
0
0
0
1
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
4
0
1
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
3
0
0
0
2
0
0
1
0
0
0
0
0
0
0
3
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
2
0
3
0
0
1
0
0
0
2
0
0
1
0
1
0
0
0
1
0
3
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
8
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
1
6
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
5
0
0
0
0
1
0
2
0
0
0
0
1
1
0
0
1
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
1
0
0
2
0
2
0
2
0
2
1
1
0
0
2
1
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
2
0
0
3
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
3
0
5
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
2
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
3
0
4
0
0
1
1
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
1
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
1
0
0
1
0
0
0
0
2
6
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
3
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
2
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
8
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
1
5
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
2
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
5
0
0
0
2
0
0
1
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
2
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
1
0
0
0
0
1
0
1
0
0
0
0
3
0
0
0
0
1
0
1
0
0
0
0
0
1
2
2
0
0
0
0
0
0
1
0
0
0
3
0
0
0
2
1
0
0
0
0
1
0
0
2
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
2
0
0
4
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
1
0
2
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
2
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
2
0
6
3
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
3
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
4
1
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
3
1
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
1
0
0
6
2
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
4
3
0
0
2
0
2
2
0
0
0
0
0
3
1
1
0
2
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
1
0
1
0
3
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
4
1
0
1
2
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
1
0
0
1
0
2
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
5
0
2
0
0
4
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
3
2
1
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
2
0
0
1
1
0
0
1
0
0
3
0
1
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
1
1
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
1
2
0
0
2
1
2
0
0
0
0
1
0
2
0
0
0
1
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
3
2
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
2
0
0
0
1
0
0
0
1
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
1
0
0
4
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
2
1
2
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
2
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
3
0
0
0
0
0
2
0
0
0
0
0
4
0
3
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
2
9
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
2
1
4
1
3
0
0
2
0
0
0
0
1
0
2
0
0
0
4
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
1
2
0
0
2
1
2
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
2
0
1
0
12
3
0
0
0
0
0
2
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
3
0
2
0
0
0
2
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
1
0
0
0
0
0
3
0
0
0
0
1
0
1
2
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
1
0
0
2
2
2
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
1
0
0
0
0
0
1
0
0
0
0
1
2
0
2
0
0
0
0
1
0
1
2
0
0
0
0
0
2
1
0
0
0
1
0
1
0
0
0
2
0
0
1
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
2
0
2
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
3
0
0
1
0
0
2
0
0
0
0
1
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
2
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
1
2
0
1
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
4
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
1
2
0
0
1
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
2
2
1
0
0
1
2
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
1
0
0
1
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
5
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
5
0
2
0
0
2
1
0
0
0
0
0
0
5
2
0
2
0
0
0
0
0
0
1
0
0
1
1
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
2
0
0
0
3
6
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
2
0
0
0
1
3
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
1
2
0
1
0
0
3
0
0
0
0
1
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
2
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
1
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
3
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
1
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
2
0
0
0
2
1
1
1
0
1
0
0
0
0
0
0
2
0
0
0
3
0
0
1
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
4
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
9
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
2
3
0
0
0
5
1
1
0
2
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
7
0
1
0
3
0
0
0
0
0
0
1
0
0
0
0
0
3
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
2
2
2
1
1
0
2
0
0
0
8
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
3
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
3
0
1
2
0
0
0
1
10
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
3
0
1
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
1
1
0
6
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
1
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
8
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
1
2
0
2
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
12
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
4
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
2
0
0
0
0
5
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
3
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
4
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
1
1
0
2
0
1
0
0
4
0
0
0
1
0
1
0
6
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
1
4
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
2
3
2
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
4
1
0
0
0
0
0
2
1
0
0
3
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
3
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
1
0
0
2
0
3
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
1
1
0
0
3
2
0
0
0
4
1
0
0
0
0
1
0
0
0
0
3
1
0
0
2
1
2
0
1
0
0
2
1
0
2
0
0
2
0
1
0
1
0
0
3
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
1
1
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
6
2
0
0
1
0
2
1
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
2
0
0
0
0
0
1
0
4
0
3
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
2
2
2
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
1
0
1
5
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
2
2
2
0
0
0
3
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
3
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
3
2
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
2
0
1
1
0
1
0
0
5
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
1
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
6
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
7
0
0
0
3
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
2
0
4
0
0
1
2
1
0
0
1
0
0
0
0
0
1
2
0
0
2
0
4
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
2
1
0
1
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
2
0
0
2
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
7
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
3
1
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
4
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
1
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
2
0
0
1
1
0
1
0
0
1
0
1
0
0
2
0
2
1
0
0
0
1
1
0
2
0
0
0
0
0
2
1
0
0
0
1
1
2
0
0
1
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
3
1
0
0
2
2
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
1
2
0
1
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
1
3
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
3
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
3
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
2
0
1
0
0
0
0
3
0
0
0
0
4
2
0
6
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
1
2
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
3
0
0
1
0
5
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
3
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
1
1
0
1
0
0
2
0
0
0
0
1
0
0
0
0
1
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
3
0
1
0
1
1
0
0
1
0
0
0
0
2
2
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
2
1
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
1
0
1
0
1
0
2
0
1
0
0
2
0
2
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
2
0
0
3
3
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
1
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
2
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
2
0
1
0
0
0
0
2
2
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
0
0
0
0
2
0
0
0
0
2
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
5
0
0
0
0
3
0
0
2
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
3
0
0
1
2
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
3
0
0
0
0
1
0
1
0
3
1
0
1
0
0
0
0
2
1
0
0
2
0
3
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
4
0
2
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
1
1
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
3
0
0
0
0
0
1
0
0
0
3
2
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
1
0
4
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
1
0
0
0
2
0
1
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
4
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
1
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
2
1
0
0
2
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
3
0
1
2
0
2
1
1
0
2
0
0
2
1
0
0
0
0
0
1
0
0
0
2
0
0
7
3
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
2
2
2
0
2
0
3
0
4
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
5
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
2
0
1
0
0
0
0
2
1
0
1
0
0
0
3
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
3
2
0
0
2
0
0
2
1
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
1
0
2
0
1
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
1
3
0
0
1
0
1
0
1
1
0
0
0
2
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
1
2
0
1
2
0
0
1
0
0
0
0
2
1
2
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
3
0
0
0
3
1
0
2
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
4
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
2
1
0
0
0
5
1
0
1
0
2
0
0
0
7
0
0
0
0
0
0
0
2
0
0
3
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
8
0
0
0
0
0
0
0
0
2
1
1
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
5
0
0
0
0
1
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
3
0
4
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
1
0
1
0
0
1
3
0
0
1
1
3
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
2
0
2
2
0
0
3
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
1
0
0
2
0
0
0
3
2
0
0
0
0
1
2
2
0
0
2
0
0
0
0
0
0
0
0
2
1
7
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
3
3
0
0
0
0
0
0
1
0
3
0
0
0
1
0
1
0
0
0
0
0
0
0
2
1
2
0
0
4
0
0
2
1
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
3
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
3
0
0
0
2
0
1
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
1
1
4
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
3
1
2
0
0
0
1
1
1
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
2
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
5
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
1
0
0
1
0
0
4
6
0
0
0
0
0
0
0
5
0
1
0
0
2
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
1
2
0
0
0
0
1
0
1
0
0
1
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
7
0
2
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
1
2
2
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
2
1
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
3
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
1
0
1
1
0
0
0
2
3
0
0
0
1
0
1
0
4
0
0
0
0
1
0
0
0
2
0
0
0
1
0
4
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
2
0
0
0
0
0
2
2
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
1
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
3
3
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
3
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
3
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
2
3
0
2
0
0
0
1
0
2
0
0
0
0
1
0
1
2
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
1
1
0
0
2
0
0
0
9
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
2
1
1
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
1
0
0
0
1
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
2
0
5
2
0
0
0
1
1
1
3
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
4
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
2
2
0
2
4
3
0
1
0
5
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
1
0
0
2
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
1
1
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
8
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
1
0
2
2
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
1
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
1
2
3
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
2
0
1
0
0
0
0
0
0
3
2
0
2
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
2
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
3
0
0
3
0
0
3
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
1
0
0
2
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
2
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
2
0
2
0
0
0
0
1
2
2
0
0
0
0
2
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
6
0
0
0
0
0
0
4
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
1
1
0
0
0
2
0
0
0
2
1
0
3
2
2
2
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
5
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
2
0
0
1
1
1
2
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
14
0
2
0
0
0
0
0
2
2
0
0
0
1
2
0
0
7
1
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
3
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
2
2
0
0
5
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
9
0
0
0
0
0
0
0
1
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
5
0
1
0
1
1
1
0
0
0
1
0
0
0
1
0
2
1
0
0
0
0
0
1
0
0
2
1
0
0
1
2
0
0
0
0
0
4
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
1
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
2
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
3
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
2
1
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
7
0
2
2
4
0
0
0
1
2
0
1
4
0
0
0
1
0
0
0
0
0
0
2
0
1
0
1
2
0
0
0
2
0
0
0
0
0
0
2
2
0
0
9
0
3
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
2
0
1
0
3
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
6
0
0
0
0
1
3
0
0
0
0
1
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
1
0
0
0
1
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
1
0
0
2
1
0
0
1
0
0
0
1
0
3
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
2
0
2
0
3
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
7
0
0
2
0
0
0
0
2
2
1
0
0
0
0
0
0
4
0
0
1
4
0
0
0
10
0
2
0
2
2
0
0
0
1
0
0
0
1
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
1
0
2
0
0
0
2
0
0
0
0
0
0
3
0
0
1
0
2
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
2
1
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
1
0
0
0
0
0
1
1
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
2
0
0
2
0
1
0
1
0
0
2
0
0
0
2
2
2
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
4
0
0
0
0
1
0
2
0
0
1
0
0
0
0
1
1
0
2
0
0
1
0
0
0
1
0
0
2
0
0
0
2
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
2
0
0
0
1
0
2
0
0
2
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
3
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
2
2
0
2
0
0
0
1
0
0
0
0
0
0
0
2
2
2
1
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
1
0
2
1
0
2
5
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
9
0
0
0
2
0
0
0
0
0
0
0
3
0
1
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
1
0
1
0
0
0
0
3
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
2
0
2
1
0
0
1
0
0
3
0
0
0
1
0
0
0
3
0
0
0
1
0
0
0
1
1
0
1
2
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
1
0
0
0
1
0
0
1
0
0
1
2
0
1
1
0
9
2
1
0
0
0
2
1
1
0
1
0
0
0
2
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
1
0
1
3
0
1
1
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
1
28
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
3
2
0
4
0
1
2
0
2
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
3
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
3
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
1
1
2
1
0
1
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
2
1
1
1
0
1
0
1
0
0
1
0
0
2
0
0
0
0
4
0
0
3
0
0
2
0
0
0
0
0
0
0
4
0
0
0
0
2
0
1
0
3
0
2
1
4
0
0
0
2
0
1
0
0
3
0
0
3
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
2
0
5
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
7
0
0
1
0
1
2
0
0
1
0
0
0
0
0
3
1
1
2
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
2
2
0
0
0
0
0
2
0
2
1
0
0
0
2
0
0
0
0
0
0
0
2
0
4
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
3
0
0
0
6
0
1
2
0
0
0
0
0
0
2
0
2
1
4
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
3
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
4
2
0
0
0
0
2
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
3
0
0
0
1
0
1
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
2
0
3
0
1
0
0
1
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
4
0
4
0
1
1
1
0
0
1
0
0
0
2
0
2
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
2
0
0
1
3
0
0
1
0
3
0
0
1
0
0
0
0
1
2
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
1
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
3
0
2
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
7
2
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
2
0
1
0
0
2
0
0
1
0
0
1
0
0
0
1
0
1
1
0
0
3
7
0
0
0
0
0
3
1
0
0
0
0
1
11
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
1
1
2
0
0
0
0
1
0
0
0
0
1
0
2
0
0
2
0
0
0
0
6
2
0
0
0
1
11
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
1
0
0
3
0
0
0
0
1
2
0
0
0
2
0
0
1
0
0
2
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
3
1
0
1
0
0
1
0
0
0
0
0
2
1
0
0
4
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
2
0
0
0
1
0
0
1
0
0
0
2
0
0
0
2
0
1
0
0
4
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
2
0
0
0
2
2
0
3
0
1
0
0
0
0
2
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
4
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
3
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
3
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
1
0
0
0
6
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
2
0
0
0
0
2
4
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
2
0
1
1
0
0
2
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
1
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
4
0
0
1
0
0
1
0
1
0
2
1
0
2
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
4
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
1
1
2
0
1
0
0
0
0
1
0
1
0
0
0
2
0
3
1
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
4
0
0
2
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
1
0
1
0
0
0
0
4
2
2
4
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
3
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
1
0
1
1
1
1
0
0
1
0
0
0
0
2
2
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
1
2
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
1
2
0
1
1
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
3
0
0
0
0
0
0
0
2
0
2
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
3
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
2
0
0
0
3
0
2
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
2
0
1
0
2
0
2
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
4
0
0
1
2
0
2
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
2
0
1
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
2
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
5
0
1
1
0
0
0
0
1
0
0
1
1
0
0
2
0
0
0
0
7
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
1
0
1
1
0
2
0
4
0
1
0
1
1
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
5
0
0
0
0
2
2
0
1
0
0
0
0
0
3
0
0
1
0
0
2
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
1
2
0
0
0
1
2
0
1
0
1
0
2
0
1
0
1
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
5
2
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
3
0
0
0
0
2
2
0
1
0
1
0
2
0
0
1
0
0
1
1
1
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
1
0
2
1
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
1
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
2
0
0
4
0
0
0
0
0
2
0
0
1
0
2
1
2
0
0
0
0
0
0
0
0
0
5
0
1
0
0
0
1
1
2
0
0
1
0
0
0
0
0
0
6
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
1
1
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
1
2
1
1
0
2
0
0
0
2
0
0
0
0
2
1
3
0
1
1
1
1
0
0
0
0
2
0
1
3
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
3
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
2
1
0
2
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
1
1
0
0
0
0
0
1
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
5
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
2
0
3
0
0
0
1
6
0
0
0
0
0
0
1
0
0
0
1
0
1
8
2
0
0
1
0
0
0
0
0
0
2
0
1
0
1
0
0
0
3
1
1
1
2
1
0
0
0
1
0
0
1
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
1
0
0
0
5
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
1
0
1
0
3
0
1
0
1
1
0
0
1
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
2
0
2
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
1
2
0
0
0
1
0
0
1
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
1
7
0
1
0
0
0
1
0
0
1
5
0
0
0
0
0
0
0
2
0
0
5
2
0
0
1
2
0
1
0
1
0
0
0
0
0
0
0
0
0
6
0
2
1
0
0
2
0
0
2
0
0
0
2
0
1
1
0
2
0
1
1
2
0
0
2
2
0
0
0
1
0
2
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
2
3
0
1
3
0
0
0
0
3
0
1
0
0
0
0
1
0
4
0
0
0
3
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
1
7
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
5
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7
0
0
1
0
0
3
2
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
5
0
0
0
0
0
1
2
0
2
0
0
1
0
0
0
0
1
1
0
0
2
0
0
0
1
0
0
0
0
1
0
0
1
0
1
2
0
1
0
0
0
0
0
2
0
0
0
0
0
3
0
2
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
5
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
2
1
2
0
0
0
4
0
0
0
2
0
1
0
0
0
2
1
0
0
0
0
0
1
1
0
0
1
1
0
0
1
1
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
8
0
1
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
5
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
7
0
0
0
0
0
1
0
0
0
1
3
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
1
2
1
0
0
0
0
2
0
2
0
1
0
0
0
0
2
0
1
3
1
0
0
1
1
3
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
2
1
0
0
1
0
0
1
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
2
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
7
1
0
1
0
0
1
0
0
1
0
1
0
0
0
4
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
5
1
0
3
0
0
0
0
0
0
0
0
2
1
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
3
2
0
0
0
0
2
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
2
0
0
3
0
0
0
0
1
3
1
1
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
2
2
1
0
2
1
0
0
1
0
0
3
0
0
0
2
0
0
0
0
0
0
0
1
5
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
2
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
3
0
2
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
2
2
0
0
0
0
1
0
0
0
0
9
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
5
0
0
0
1
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
2
0
0
2
1
0
0
3
0
0
3
3
0
0
0
1
0
0
0
1
2
0
0
3
0
0
1
0
1
0
0
2
0
0
3
0
0
4
0
0
0
0
2
1
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
10
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
1
0
0
0
0
1
1
0
2
1
0
0
0
0
0
0
1
1
0
2
1
0
0
5
0
0
0
0
0
1
0
1
0
0
0
0
1
3
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
2
1
0
0
0
0
1
0
0
1
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
2
2
0
0
0
0
2
0
4
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
2
0
1
0
0
1
0
4
0
0
0
0
0
1
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
1
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
4
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
2
0
0
0
2
0
1
0
0
0
2
0
1
1
0
0
2
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
2
0
0
0
5
0
0
2
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
2
3
0
0
1
0
2
1
0
0
0
1
1
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
1
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
2
0
0
1
0
0
0
0
1
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
4
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
2
1
1
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
1
2
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
2
0
0
2
0
1
0
2
0
0
0
0
0
0
0
2
0
0
1
0
3
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
2
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
5
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
3
1
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
1
0
0
0
1
2
0
0
0
4
2
0
0
4
0
1
0
0
0
0
0
2
0
0
1
0
0
4
2
2
0
3
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
2
0
1
0
1
0
1
0
0
0
0
1
2
0
0
2
0
0
1
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
1
1
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
1
2
0
0
0
1
2
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
3
0
0
0
1
0
0
0
3
2
0
0
0
0
2
1
0
0
0
2
0
1
5
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
2
0
2
1
0
0
0
0
0
0
0
2
2
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
1
1
1
3
0
0
0
0
0
0
0
0
2
0
7
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
3
1
0
0
0
1
2
0
0
0
0
1
0
2
2
0
0
1
0
0
0
0
0
0
2
0
0
4
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
3
0
0
0
2
1
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
3
0
0
1
0
0
0
1
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
2
0
5
0
0
0
3
0
0
2
0
0
0
0
0
0
1
0
2
0
0
1
0
0
3
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
3
0
2
0
1
0
2
2
0
0
1
0
0
0
0
3
1
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
4
0
0
0
1
0
0
0
0
3
0
2
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
1
1
0
1
2
0
1
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
1
1
2
0
1
1
0
1
2
0
1
1
0
2
1
1
0
0
2
2
4
0
0
0
0
0
0
0
3
0
0
1
0
3
0
1
0
2
1
0
1
0
0
0
0
0
0
1
0
0
0
4
0
0
2
0
0
0
0
0
0
0
3
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
1
2
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
3
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
1
0
2
0
0
2
2
1
2
0
0
0
0
1
0
0
2
1
1
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
1
2
2
0
0
0
2
0
0
2
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
1
2
1
0
0
0
0
1
0
0
0
5
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
3
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
1
1
3
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
2
1
0
2
1
1
0
0
2
0
1
0
0
1
0
1
3
1
0
0
0
1
1
3
0
0
2
2
0
0
0
0
0
0
1
1
0
0
0
1
2
0
1
0
2
0
1
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
1
5
1
1
0
0
0
0
1
0
0
0
2
1
0
0
7
0
0
0
0
0
0
0
3
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
2
3
0
9
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
2
0
1
0
0
1
0
2
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
5
0
0
0
0
0
0
0
2
1
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
1
2
2
3
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
3
0
2
0
0
0
0
0
2
1
0
0
0
1
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
2
2
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
2
2
1
0
5
0
0
1
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
4
0
0
3
3
0
0
0
0
7
1
0
0
0
0
0
0
0
1
2
2
3
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
5
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
4
2
1
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
3
0
0
3
0
0
0
0
0
0
1
0
3
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
3
0
0
0
0
1
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
1
0
0
2
0
0
0
0
2
1
0
2
0
0
0
0
0
0
1
0
0
0
0
1
2
1
0
2
0
0
0
0
3
0
0
1
0
0
0
0
0
2
0
0
0
1
0
1
1
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
1
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
4
2
0
2
2
0
1
0
2
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
2
0
0
1
0
1
1
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
2
0
1
2
2
0
0
0
0
0
0
1
1
0
2
2
0
0
4
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
1
2
4
0
1
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
2
1
0
1
3
0
1
0
0
0
0
3
1
0
0
1
2
1
0
7
0
0
2
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
3
3
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
1
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
3
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
2
0
0
1
0
0
0
0
0
3
1
0
0
0
2
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
1
0
1
0
0
1
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
3
0
1
0
0
0
1
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
2
0
0
0
0
0
0
4
1
0
1
0
0
0
2
2
0
4
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
3
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
14
0
0
0
2
3
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
1
0
0
0
0
0
0
0
0
3
0
2
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
5
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
7
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
2
1
2
5
0
0
2
1
1
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
3
1
0
0
2
2
4
0
1
3
0
0
0
2
0
2
0
0
2
2
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
1
2
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
2
2
0
0
3
0
2
0
0
1
0
1
1
0
1
1
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
1
0
1
0
3
0
0
0
0
0
0
4
0
0
0
1
0
2
0
0
0
2
0
1
3
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
5
0
0
0
3
0
0
0
0
0
2
0
0
0
2
0
4
0
1
0
0
3
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
2
2
0
0
4
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
3
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
1
0
0
0
0
0
2
0
0
1
0
0
0
1
1
0
4
1
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
2
0
0
1
2
0
0
0
0
0
1
1
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
2
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
2
1
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
2
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
3
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
3
2
0
0
0
5
0
0
0
0
0
2
3
0
0
2
1
0
0
0
2
0
0
0
0
6
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
1
0
3
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
3
0
0
0
1
0
9
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
1
0
3
0
2
0
1
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
1
5
0
0
0
0
0
0
2
2
0
0
1
0
2
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
4
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
2
1
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
1
1
1
0
0
3
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
3
0
0
0
0
0
0
2
0
0
0
0
1
0
7
0
2
0
0
0
0
0
0
0
0
1
0
0
2
1
1
0
0
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
2
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
1
2
1
0
0
1
0
0
0
0
0
2
1
0
0
8
0
0
0
0
0
0
0
0
0
0
1
0
5
0
0
0
2
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
1
0
0
0
4
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
2
2
0
2
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
1
0
0
0
0
0
1
0
0
0
3
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
1
0
0
1
1
0
0
1
0
0
0
0
0
1
0
3
0
0
0
0
1
1
0
0
0
0
0
0
0
0
3
3
1
2
0
2
4
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
3
0
0
0
0
1
4
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
3
0
1
1
0
0
2
0
2
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
6
0
1
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
6
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
3
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
3
1
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
2
0
1
0
2
0
0
0
0
0
0
1
0
6
0
1
0
3
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
1
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
1
0
0
1
0
0
0
1
0
0
0
0
1
0
2
0
1
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
1
0
1
0
2
0
0
0
1
0
2
2
1
1
0
0
0
0
7
0
0
0
0
1
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
1
2
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
3
0
0
0
12
0
3
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
3
0
1
1
0
0
1
0
0
2
1
1
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
4
4
0
0
0
1
0
1
1
0
2
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
3
1
2
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
1
0
0
1
0
0
0
1
0
2
0
0
1
0
0
2
0
0
1
0
0
2
6
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
1
0
0
2
0
2
1
0
0
0
2
1
2
0
0
0
0
2
0
0
1
0
0
1
1
1
0
0
0
3
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
2
0
0
10
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
2
1
0
2
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
5
0
1
4
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
2
2
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
1
0
0
2
2
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
2
0
0
1
0
0
0
0
2
0
2
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
5
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
1
0
0
0
2
0
0
0
0
0
2
0
1
0
0
2
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
5
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
1
0
0
0
4
1
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
1
4
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
3
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
1
0
1
0
1
0
0
0
1
0
5
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
2
0
0
2
3
1
0
0
0
1
0
1
0
2
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
3
1
0
0
0
0
0
3
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
2
0
2
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
4
0
2
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
2
0
1
2
0
0
0
12
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
2
0
4
1
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
3
4
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
2
0
2
0
1
0
1
0
0
0
0
0
2
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
5
0
0
0
0
0
1
0
1
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
1
0
9
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
2
1
0
0
0
0
0
0
8
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
1
0
1
1
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
2
3
0
0
2
1
0
5
0
0
0
1
0
0
0
2
0
0
1
0
0
0
1
0
4
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
4
0
0
0
2
3
0
0
0
0
0
0
0
2
0
1
1
2
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
3
1
2
0
0
1
0
2
0
0
0
0
0
2
0
0
7
0
3
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
2
0
0
0
0
0
1
0
5
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
4
0
0
1
0
0
0
0
2
0
0
0
0
7
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
1
3
1
2
1
0
1
2
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
2
0
0
0
1
2
1
2
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
3
0
0
0
0
1
0
0
0
1
1
0
0
0
0
2
0
4
0
0
1
0
2
1
0
0
1
2
0
0
2
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
1
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
2
0
0
0
1
0
0
1
0
0
4
2
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
1
0
2
0
0
2
0
3
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
2
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
1
1
0
1
1
2
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
1
0
0
0
2
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
3
0
0
0
2
2
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
9
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
2
0
0
0
4
0
1
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
2
0
0
0
0
0
0
3
0
1
0
0
1
0
2
1
2
0
0
4
2
0
0
2
0
0
0
2
3
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
8
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
1
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
2
0
0
0
0
0
0
0
3
0
1
0
0
2
0
0
0
0
0
0
0
0
0
3
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
1
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
3
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
2
0
0
0
0
2
0
1
0
1
1
0
0
0
0
1
3
0
1
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
3
1
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
1
2
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
1
0
0
0
0
0
0
2
0
1
2
0
1
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
3
1
0
0
0
1
0
1
0
0
2
0
2
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
1
1
0
0
0
0
0
1
1
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
2
0
2
0
1
0
0
0
0
3
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
2
0
3
0
0
0
0
0
2
0
1
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
1
2
0
0
0
0
0
0
0
0
0
2
0
0
4
2
0
0
0
0
0
0
0
0
1
2
4
2
0
0
9
0
0
4
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
2
2
1
0
0
0
2
1
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
3
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
2
2
0
2
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
3
5
0
1
0
0
2
4
0
0
1
0
1
1
0
2
0
0
3
0
0
0
0
5
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
3
0
2
0
0
0
1
1
0
0
0
0
1
0
4
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
5
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
1
0
5
0
0
0
0
0
0
0
1
0
0
1
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
1
0
1
4
0
0
0
0
0
3
2
0
0
0
0
1
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
4
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
5
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
2
0
0
0
2
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
5
0
0
0
0
0
0
8
0
1
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
1
0
0
0
30
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
6
2
1
2
0
0
0
0
2
0
0
1
1
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
2
1
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
2
2
4
0
1
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
3
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
1
0
0
1
0
0
2
0
0
0
0
0
0
2
1
2
0
0
1
0
0
0
2
3
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
1
1
2
2
0
0
0
0
0
0
0
2
2
1
0
1
2
0
1
0
0
0
1
0
0
0
2
1
0
0
0
0
3
0
1
4
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
5
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
3
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
4
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
4
0
1
2
0
0
0
1
0
1
0
0
0
0
0
0
0
2
2
0
0
1
0
1
0
0
0
0
0
0
0
5
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
7
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
1
0
0
0
0
1
0
1
0
2
0
0
0
0
1
0
1
0
1
7
2
1
1
0
0
1
0
0
0
0
1
0
0
2
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
3
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
4
0
0
2
0
0
0
0
2
2
0
1
0
0
5
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
5
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
3
0
0
0
2
0
8
0
0
0
0
1
0
0
0
0
0
1
3
0
0
0
1
2
0
2
1
0
0
0
0
0
0
0
2
0
1
0
2
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
6
1
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
4
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
10
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
2
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
4
2
3
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
3
0
0
1
0
2
1
0
0
0
2
1
2
0
1
0
1
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
2
4
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
4
0
2
0
1
0
3
0
0
0
1
2
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
2
9
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
2
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
2
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
1
0
0
1
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
3
2
0
1
0
0
1
0
0
0
0
2
1
0
0
7
0
2
0
0
0
0
0
0
1
0
2
0
3
0
0
0
1
0
0
0
0
5
0
0
0
3
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
1
3
1
2
7
1
0
0
0
0
1
0
1
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
2
0
1
0
0
2
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
2
1
0
0
0
0
0
3
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
3
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
4
0
2
1
1
0
0
0
0
0
0
3
2
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
1
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
4
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
2
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
2
0
0
0
0
3
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
3
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
7
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
1
0
0
2
0
0
0
3
2
0
0
0
0
0
0
0
0
6
1
0
0
0
0
0
2
0
0
4
1
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
3
0
0
0
1
2
1
0
0
0
2
0
0
0
0
2
2
0
0
2
0
2
0
1
1
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
8
0
0
2
0
0
2
0
0
0
2
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
5
1
0
0
4
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
5
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
1
1
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
3
3
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
3
0
2
1
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
1
0
0
0
0
2
0
2
0
0
0
2
0
0
2
0
2
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
8
0
0
0
1
0
0
0
2
0
1
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
3
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
1
2
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
1
1
0
0
0
3
0
2
0
0
0
1
0
2
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
2
0
3
0
0
1
0
0
0
0
0
0
2
0
0
1
2
1
0
0
0
2
0
0
0
1
2
1
2
0
0
0
2
0
1
0
1
1
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
6
1
0
0
0
3
2
2
2
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
2
4
0
0
0
1
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
2
0
0
2
0
0
1
0
0
0
2
1
0
0
0
2
0
0
4
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
8
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
3
1
1
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
4
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
3
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
3
0
0
0
0
0
2
0
0
0
2
0
0
1
1
0
0
0
1
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
2
0
0
0
0
1
0
2
0
0
0
3
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
4
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
1
0
0
0
0
2
0
3
0
0
0
2
1
0
0
0
1
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
3
2
0
0
2
0
0
1
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
7
0
0
5
0
3
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
2
0
1
0
3
0
1
2
0
3
0
0
2
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
4
0
2
0
0
1
0
5
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
2
4
0
0
0
0
0
2
1
0
2
0
1
0
0
0
1
0
0
0
0
0
1
3
0
2
0
0
0
0
0
0
2
0
0
3
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
4
0
1
4
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
4
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
2
0
0
0
1
1
0
3
0
0
0
1
3
2
0
0
0
1
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
5
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
2
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
2
1
0
0
0
2
1
0
0
0
0
0
1
0
1
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
2
1
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
2
2
1
2
0
5
0
2
0
0
1
0
0
2
0
0
1
1
0
0
1
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
2
3
0
0
0
0
0
1
0
0
0
0
0
0
10
0
0
1
0
0
3
0
0
1
0
0
0
0
2
0
0
0
1
0
1
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
2
2
2
0
0
0
0
1
2
0
0
0
0
1
0
4
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
5
0
2
0
0
1
0
2
0
0
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
3
2
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
2
2
3
1
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
4
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
2
1
2
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
1
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
1
0
1
1
0
0
0
3
0
0
2
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
2
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
1
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
2
1
0
2
0
2
2
0
2
1
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
2
0
0
2
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
1
0
1
0
1
0
4
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
2
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
6
0
0
0
0
1
2
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
3
2
0
1
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
2
2
0
2
0
0
0
0
0
2
1
3
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
2
2
0
0
0
0
0
0
1
0
1
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
1
3
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
1
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
3
0
1
2
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
2
0
0
0
0
4
2
0
1
0
1
0
0
0
0
0
3
0
0
0
0
2
2
0
0
1
0
0
2
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
2
5
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
1
0
0
0
2
0
0
0
0
2
2
3
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
1
1
0
1
2
0
1
0
1
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
3
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
2
2
1
0
0
0
1
0
0
0
1
0
0
0
6
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
1
0
4
0
0
0
0
12
1
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
1
0
2
0
0
1
0
1
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
2
0
0
0
0
0
0
5
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
7
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
1
0
0
0
2
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
1
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
3
0
0
1
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
5
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
3
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
3
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
10
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
8
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
2
1
0
0
0
2
0
1
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
3
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
5
2
0
0
0
0
0
2
0
0
0
0
0
4
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
2
3
1
0
0
1
0
1
2
0
0
0
3
0
0
0
4
0
3
0
0
0
0
0
2
0
0
0
1
0
0
2
0
2
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
1
1
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
1
0
3
0
0
1
0
0
0
1
2
0
0
0
0
1
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
3
1
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
2
1
0
0
0
0
0
1
1
0
0
0
0
1
0
2
2
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
3
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
3
0
0
0
1
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
1
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
1
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
3
0
2
0
0
0
0
0
0
0
2
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
1
5
0
0
0
0
2
0
0
0
0
1
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
1
0
2
0
0
1
1
0
0
1
3
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
1
0
0
2
0
1
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
3
1
0
1
0
0
0
0
0
0
2
2
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
2
2
0
2
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
2
0
0
1
0
1
0
0
1
1
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
1
0
3
0
1
0
0
0
0
0
0
2
5
0
0
0
0
1
0
0
0
5
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
6
0
0
2
3
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
2
2
0
0
0
1
0
0
1
1
1
0
1
0
2
3
5
0
1
0
0
0
0
0
0
0
2
4
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
2
0
1
0
0
0
0
0
3
0
0
0
2
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
1
0
0
0
2
1
0
1
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
1
0
1
1
0
0
0
2
0
2
1
0
0
0
0
0
2
1
0
1
0
0
0
0
2
0
0
2
3
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
1
0
0
2
0
0
0
5
0
0
0
0
12
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
2
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
2
0
2
0
0
0
0
5
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
2
2
2
0
1
3
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
2
0
1
2
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
3
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
5
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
4
1
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
5
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
1
1
1
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
2
0
0
2
1
0
0
0
5
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
8
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
1
0
0
0
0
1
0
0
4
6
0
4
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
1
7
0
0
0
0
0
0
1
0
4
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
2
0
0
2
3
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
1
4
4
0
0
1
0
0
1
0
1
0
0
0
0
1
0
3
0
0
3
1
1
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
2
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
3
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
3
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
1
0
0
5
0
0
1
0
0
0
1
0
0
0
0
4
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
1
1
0
0
0
0
0
0
4
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
3
0
0
0
2
0
0
0
1
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
1
0
2
3
0
2
0
1
0
0
1
1
0
0
0
0
0
0
1
1
1
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
2
2
0
0
2
0
1
0
0
0
0
0
0
0
2
1
0
2
0
1
1
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
2
0
2
1
0
0
0
1
0
2
0
0
1
0
0
0
0
0
1
0
0
1
0
0
2
0
0
1
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
1
0
0
2
0
0
0
0
2
0
2
0
0
0
0
2
0
1
0
1
2
0
2
0
1
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
3
2
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
2
0
2
0
1
2
3
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
1
0
0
1
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
3
1
4
0
0
1
0
2
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
3
0
1
0
0
0
2
1
2
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
1
0
2
0
0
0
0
0
0
3
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
2
0
2
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
1
1
0
0
3
0
1
1
1
3
0
0
0
0
0
2
0
2
0
1
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
3
0
1
0
0
0
0
0
0
0
0
1
2
0
2
3
0
5
0
0
1
2
0
1
0
2
0
0
0
0
0
0
1
0
0
3
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
1
0
0
2
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
2
2
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
2
0
0
0
3
0
1
1
4
1
0
0
0
0
0
0
0
1
6
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
4
0
1
2
0
0
0
0
0
0
1
0
5
1
1
0
0
0
0
4
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
3
0
1
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
4
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
3
1
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
2
1
1
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
3
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
3
0
1
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
1
0
0
0
1
2
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
2
1
0
3
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
1
2
0
0
2
3
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
2
2
0
0
0
1
0
0
2
0
1
0
0
0
0
1
0
0
0
2
3
2
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
3
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
2
1
0
0
0
0
0
1
2
1
0
0
0
2
0
0
0
0
0
5
2
0
1
5
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
1
2
3
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
1
0
0
0
1
1
0
0
0
2
1
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
1
0
0
0
1
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
4
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
3
0
0
1
0
0
0
2
0
1
3
0
0
0
0
0
0
0
0
2
0
1
0
0
2
2
0
1
1
0
0
0
2
1
0
0
0
2
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
2
1
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
2
1
0
2
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
1
0
0
0
0
3
0
0
0
0
0
0
1
1
0
2
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
1
1
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
1
0
1
3
0
0
0
0
0
2
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
3
1
0
0
0
0
2
0
0
2
0
1
2
0
0
0
0
0
4
0
0
0
3
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
1
0
2
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
11
0
2
2
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
1
5
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
1
0
1
1
0
0
2
0
0
0
2
1
0
0
0
0
0
5
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
4
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
1
0
0
0
2
2
2
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
3
1
0
0
0
0
3
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
4
2
1
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
1
2
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
7
0
2
0
0
0
1
0
2
0
0
0
2
4
0
0
1
1
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
6
0
2
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
2
2
0
1
0
0
1
0
0
0
0
4
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
3
0
0
2
0
2
0
0
0
0
0
2
0
5
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
1
0
0
0
0
2
4
1
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
3
1
1
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
1
3
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
2
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
2
1
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
3
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
1
0
0
0
0
0
3
0
0
0
0
3
2
1
1
0
0
0
0
0
2
0
1
2
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
3
0
1
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
2
0
0
0
0
0
2
0
2
0
1
1
3
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
1
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
5
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
2
0
3
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
4
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
3
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
1
0
2
0
0
0
0
1
0
0
1
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
1
0
0
7
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
1
1
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
1
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
4
0
0
0
0
0
0
0
0
1
2
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
4
0
2
0
0
0
0
0
0
0
1
0
7
0
1
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
4
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
1
0
2
0
0
1
1
0
1
1
0
0
1
0
0
0
2
0
0
1
0
5
0
0
0
0
2
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
1
0
0
0
0
1
2
4
0
3
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
3
0
0
1
0
0
0
0
1
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
4
1
0
0
0
0
0
2
1
1
4
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
1
1
5
0
2
1
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
2
0
0
0
0
0
0
1
3
0
2
1
0
1
0
0
0
0
1
0
0
0
2
0
3
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
5
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
2
1
1
0
1
0
0
0
1
0
0
0
0
0
1
0
6
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
2
0
1
1
1
0
2
0
0
0
0
3
0
0
0
2
0
1
2
0
0
0
2
2
0
0
1
1
2
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
1
1
0
1
0
0
12
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
2
1
0
0
0
1
0
0
2
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
1
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
1
0
2
1
0
2
0
0
0
0
3
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
3
0
0
0
0
1
0
1
0
0
0
2
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
1
0
2
1
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
6
1
0
0
3
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
3
2
0
1
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
1
0
1
0
0
3
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
2
0
0
2
0
0
1
0
0
0
0
1
2
0
0
0
0
0
2
0
8
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
3
0
0
0
0
0
0
0
1
0
0
1
2
2
0
0
1
0
0
0
0
0
0
3
0
0
10
0
0
0
0
0
0
0
2
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
3
6
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
11
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
1
4
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
1
0
1
1
0
1
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
3
2
0
4
0
0
3
0
0
0
1
0
0
0
0
0
1
2
0
0
0
3
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
5
0
0
1
3
1
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
4
2
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
3
1
1
0
0
0
1
3
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
1
1
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
5
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
1
2
0
0
1
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
3
2
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
4
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
2
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
4
0
0
1
0
0
0
0
1
0
1
0
0
0
2
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
3
1
0
0
0
2
2
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
3
0
1
2
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
3
1
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
2
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
2
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
4
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
6
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
3
0
2
0
1
0
1
0
0
0
0
0
0
2
0
1
1
0
1
0
1
0
0
0
0
0
3
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
3
0
0
0
0
1
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
1
0
0
0
2
0
0
2
1
0
0
0
0
2
0
0
1
2
0
4
0
1
0
0
0
0
0
2
0
0
3
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
3
0
0
0
0
1
0
2
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
3
0
0
0
1
2
0
0
4
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
5
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
1
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
2
2
1
0
0
1
0
0
3
0
0
0
2
0
0
0
0
1
0
0
2
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
1
0
1
0
0
2
3
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
2
0
0
0
0
0
1
2
0
2
2
0
0
0
0
2
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
2
1
0
0
0
0
1
3
0
0
0
0
0
4
0
0
1
0
2
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
6
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
1
5
0
0
0
3
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
4
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
4
0
0
0
0
0
0
2
0
7
0
0
0
0
0
0
2
0
2
2
0
0
0
0
1
0
0
0
0
0
5
1
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
4
2
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
4
0
0
2
2
0
0
0
0
0
0
2
2
2
0
1
0
0
0
0
0
1
4
1
0
0
2
0
1
3
2
0
1
0
0
0
0
0
1
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
4
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
5
4
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
1
0
1
0
3
0
0
0
0
0
5
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
5
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
3
0
0
0
0
0
0
1
0
0
0
1
0
3
0
0
0
6
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
1
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
3
0
1
0
0
0
0
2
1
0
2
0
0
1
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
2
0
2
0
0
0
0
1
0
0
0
1
1
0
0
2
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
2
2
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
5
0
0
0
2
0
0
0
1
5
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
3
0
0
0
1
0
6
0
0
3
0
0
0
0
1
0
0
0
2
0
1
0
0
0
3
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
1
0
2
0
1
0
0
3
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
2
2
0
3
0
0
0
1
1
0
0
0
2
2
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
4
0
3
0
1
0
0
4
0
0
0
2
2
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
3
0
0
0
1
0
2
0
2
1
7
0
0
1
0
0
0
0
0
2
0
0
2
1
0
0
1
0
0
0
0
0
2
3
0
0
0
3
0
0
1
1
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
2
3
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
2
0
2
1
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
4
0
2
0
2
0
2
0
1
0
2
0
0
1
0
0
0
1
0
0
0
4
2
1
0
0
0
2
0
2
1
0
0
0
2
0
2
1
0
0
0
0
0
2
0
0
9
2
2
0
2
0
0
0
0
0
4
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
2
0
1
0
0
0
0
0
0
0
0
1
5
0
0
0
0
0
1
4
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
3
0
0
0
0
4
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
1
0
1
2
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
1
2
0
0
4
0
2
0
0
0
6
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
3
1
2
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
3
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
3
0
0
0
2
0
0
0
2
6
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
2
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
1
0
0
0
0
0
1
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
1
0
0
1
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
3
0
0
0
1
0
2
3
1
0
0
4
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
3
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
2
1
2
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
2
0
2
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
2
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
1
1
0
3
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
6
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
3
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
5
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
1
1
0
0
0
3
0
0
1
0
0
1
0
2
0
0
0
0
0
1
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
3
1
0
0
0
1
0
0
1
0
0
3
1
0
0
2
3
0
0
0
0
0
0
0
0
3
1
0
2
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
2
2
0
0
0
0
0
2
1
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
4
0
0
1
0
0
2
2
0
0
0
0
1
2
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
4
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
2
1
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
1
2
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
2
2
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
1
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
3
0
1
3
0
0
3
0
1
0
0
3
1
4
2
0
2
0
0
0
0
1
0
2
1
0
1
0
0
0
1
0
0
1
0
0
1
0
1
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
3
0
0
0
0
1
0
3
1
4
0
3
0
0
1
0
0
0
0
0
0
0
1
3
2
0
0
0
0
0
0
1
0
3
0
2
1
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
2
0
0
0
2
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
1
0
0
0
0
3
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
3
0
1
2
0
0
0
2
0
0
0
2
0
3
0
0
3
1
0
2
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
5
1
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
2
1
0
0
3
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
5
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
1
0
1
0
0
0
1
0
0
1
0
1
0
0
0
3
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
1
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
4
1
0
0
3
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
3
2
0
0
0
0
0
0
0
2
0
0
0
1
0
1
2
0
1
0
0
0
0
0
0
2
1
0
0
0
4
0
0
0
7
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
2
2
0
0
0
1
2
4
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
3
0
1
0
0
0
0
0
0
0
1
2
3
0
1
0
0
2
0
1
0
0
0
1
0
0
0
1
0
6
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
2
0
2
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
2
0
0
0
1
2
1
0
0
0
2
0
1
0
0
0
0
2
0
0
0
2
0
1
0
0
1
0
0
1
1
0
1
0
7
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
2
0
0
2
2
2
0
0
0
0
0
1
0
0
0
2
1
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
2
1
1
0
2
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
5
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
1
2
0
0
0
0
0
0
0
0
1
0
2
0
0
1
1
0
1
0
1
0
0
0
2
2
0
3
1
0
0
0
0
2
2
3
0
1
0
0
2
0
1
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
3
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
2
0
1
0
2
0
0
0
2
4
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
3
2
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
1
0
0
2
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
3
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
6
0
2
0
0
0
0
0
1
0
2
0
1
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
1
1
0
1
1
2
1
0
0
0
0
0
0
0
2
0
6
0
0
2
9
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
3
0
0
0
0
2
0
0
0
3
0
0
0
1
2
1
0
0
0
0
0
2
0
0
1
7
0
0
0
0
0
0
0
0
0
0
4
0
2
4
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
4
1
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
3
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
4
0
0
0
0
0
1
0
0
2
2
0
1
0
0
0
0
0
0
1
0
0
0
1
4
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
5
1
0
0
0
1
0
2
0
0
4
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
1
0
2
0
0
0
0
2
0
3
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
1
0
0
3
1
0
0
0
2
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
2
0
1
5
0
0
1
0
1
1
0
6
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
1
1
3
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
2
1
0
0
1
2
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
1
2
0
1
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
1
0
2
0
4
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
2
1
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
2
0
1
0
1
1
0
2
0
0
0
0
0
0
0
1
9
0
2
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
5
0
2
0
0
1
1
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
8
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
3
0
2
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
2
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
3
1
0
0
0
3
0
0
0
3
0
0
0
2
0
0
0
0
2
2
2
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
2
0
0
0
2
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
2
0
4
0
0
2
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
2
5
0
1
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
1
0
0
1
3
0
0
0
0
1
0
1
0
0
2
0
2
1
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
12
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
2
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
2
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
1
0
3
0
0
0
1
0
0
0
0
2
2
4
1
0
0
0
4
0
0
3
2
0
0
0
1
0
0
0
2
0
12
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
7
1
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
3
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
4
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
3
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
1
0
2
0
1
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
3
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
2
0
3
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
2
3
1
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
2
0
2
2
1
0
0
0
1
0
0
0
2
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
1
0
0
1
0
0
0
0
0
1
1
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
6
0
0
1
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
2
0
2
0
0
0
0
0
0
6
2
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
1
0
0
3
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
2
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
1
1
1
0
0
5
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
1
1
0
0
0
2
0
0
1
2
0
0
0
2
1
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
3
0
0
1
1
2
0
0
0
2
1
4
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
2
0
2
0
0
2
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
6
0
2
0
1
0
1
0
0
0
0
0
0
2
1
1
1
0
0
0
0
0
1
0
2
0
1
0
0
3
3
0
3
0
0
0
0
1
0
0
4
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
4
0
0
0
2
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
1
0
2
1
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
1
1
0
1
1
0
1
0
2
0
0
2
0
0
1
0
0
1
0
2
3
7
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
3
0
1
0
0
0
0
0
0
0
2
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
1
0
0
0
2
1
0
0
3
4
1
0
0
0
1
1
3
0
0
0
0
0
0
0
0
0
2
2
0
2
1
1
0
0
0
0
0
1
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
6
0
0
2
2
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
5
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
9
0
0
0
0
0
0
1
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
8
0
0
0
0
1
0
0
1
0
0
0
0
0
3
0
0
0
0
1
3
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
1
2
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
3
2
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
2
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
3
2
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
4
2
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
4
0
5
0
0
2
0
0
0
1
0
0
0
0
0
1
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
1
1
1
1
0
0
0
0
0
0
0
2
0
2
0
0
1
2
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
2
0
4
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
1
0
2
2
0
0
3
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
1
0
4
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
2
0
0
1
0
1
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
2
1
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
1
0
1
2
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
1
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
3
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
3
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
4
0
0
0
0
3
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
3
0
1
0
0
0
0
2
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
1
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
13
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
2
0
1
0
1
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
1
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
6
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
2
0
0
0
0
3
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
7
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
1
0
2
0
0
0
3
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
4
0
0
2
0
2
0
1
0
2
0
0
2
9
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
2
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
2
2
0
1
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
2
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
2
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
1
1
1
0
0
0
1
0
0
0
0
2
2
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
2
0
2
0
3
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
6
0
0
0
1
0
0
2
0
0
2
0
0
1
1
0
1
4
2
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
1
0
1
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
1
0
0
0
0
3
0
0
3
0
2
0
0
1
1
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
3
0
3
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
3
0
0
0
2
1
0
0
0
0
0
0
0
2
1
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
4
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
1
0
1
4
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
1
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
3
0
1
0
0
0
0
0
1
2
0
0
2
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
2
0
1
1
0
0
0
0
0
0
0
2
0
0
0
2
0
3
0
0
0
0
0
1
2
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
2
0
0
0
0
0
3
0
1
0
0
0
0
1
0
0
1
0
2
0
0
3
0
0
0
0
0
1
1
1
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
3
0
1
0
0
1
0
0
0
0
0
1
1
0
2
0
0
2
2
0
0
0
0
6
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
2
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
4
1
3
0
0
0
1
0
4
0
2
0
2
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
1
1
1
0
0
2
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
3
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
3
2
2
1
1
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
8
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
2
0
1
0
0
4
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
1
2
0
0
1
0
1
0
3
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
3
0
0
0
0
0
0
1
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
3
0
2
2
0
2
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
2
0
2
0
0
2
1
1
2
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
1
2
0
0
1
0
0
0
0
2
0
1
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
5
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
1
1
0
5
0
0
0
0
3
0
0
0
0
3
0
4
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
2
0
0
2
2
1
0
0
1
1
1
0
0
2
0
0
0
0
0
2
2
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
2
1
2
0
0
0
0
0
0
3
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
4
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
1
0
1
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
4
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
3
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
3
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
2
0
0
0
0
0
0
3
0
0
0
1
0
0
0
4
0
0
0
0
0
1
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
1
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
2
4
0
2
0
0
2
0
0
0
0
0
0
0
2
1
2
1
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
1
2
2
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
1
2
5
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
1
0
1
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
1
0
7
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
3
0
0
0
0
0
0
0
2
0
0
0
7
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
3
2
0
0
0
0
2
1
1
2
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
2
0
0
3
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
1
2
0
0
0
0
0
1
1
2
0
0
0
1
1
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
1
3
0
1
3
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
10
0
0
0
0
0
0
0
0
0
0
2
2
0
2
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
3
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
3
0
0
0
0
0
0
0
0
1
6
2
1
2
5
0
0
1
0
0
0
0
0
3
0
5
0
0
1
0
0
0
2
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
1
1
0
0
0
2
1
2
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
4
0
0
0
1
0
2
2
2
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
2
0
1
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
2
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
3
0
2
1
1
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
3
0
0
0
1
2
0
0
0
5
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
4
0
0
0
0
0
0
0
2
0
0
0
1
3
0
0
0
1
2
0
0
0
8
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
1
1
0
1
2
1
0
0
0
0
4
0
0
0
0
1
4
0
0
0
0
7
1
0
0
0
2
0
0
0
0
1
0
1
1
0
1
3
0
0
0
0
0
0
0
0
0
0
3
2
2
0
0
0
37
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
2
0
0
2
0
0
0
0
0
1
0
0
3
0
1
0
0
0
0
0
0
2
2
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
2
6
0
0
0
0
0
0
0
0
1
0
1
0
0
4
0
0
0
0
0
1
0
1
0
1
2
21
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
1
0
1
0
0
0
1
1
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
2
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
1
4
0
0
1
2
0
0
2
0
0
0
0
0
2
0
0
2
1
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
1
0
0
1
4
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
1
0
0
1
8
0
1
0
0
0
1
1
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
3
0
1
0
1
0
0
0
2
2
0
0
0
0
0
0
0
1
1
0
6
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
6
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
4
0
0
2
0
0
0
3
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
1
2
0
0
1
2
0
0
0
0
1
0
0
0
0
0
2
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
1
1
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
1
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
2
0
0
2
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
2
0
0
0
3
0
2
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
1
0
0
0
2
0
2
3
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
3
0
1
1
2
1
0
0
0
2
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
5
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
2
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
3
0
1
2
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
1
0
0
2
4
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
7
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
2
0
1
2
0
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
2
1
3
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
1
5
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
1
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
9
0
0
0
0
0
0
1
0
0
1
0
0
0
0
3
2
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
2
1
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
4
0
3
0
0
0
4
0
0
1
1
0
0
0
0
0
1
1
0
0
0
3
0
1
0
0
0
0
15
1
0
0
0
3
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
5
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
2
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
3
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
3
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
2
0
0
0
0
0
6
3
0
0
0
3
0
0
0
1
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
2
3
0
0
8
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
6
2
0
0
0
0
0
0
1
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
2
5
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
2
0
0
4
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
1
0
0
2
0
0
3
0
1
0
0
1
0
0
0
0
8
0
0
0
2
1
0
0
0
2
0
0
1
0
2
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
1
2
3
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
3
0
0
2
1
0
0
0
0
1
0
2
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
3
0
0
0
2
0
2
3
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
3
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
1
1
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
4
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
3
3
2
0
0
0
0
0
0
0
1
0
1
0
0
4
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
2
0
0
0
0
0
0
1
3
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
3
0
0
0
0
0
0
6
1
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
2
0
5
0
0
0
2
4
0
0
6
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
6
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
2
0
2
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
3
0
4
0
2
2
0
0
1
0
7
5
0
2
1
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
2
0
0
0
0
1
0
0
1
0
2
1
0
0
0
0
0
0
2
2
0
5
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
3
2
0
1
0
0
1
4
1
0
0
0
0
0
0
0
0
1
0
1
0
1
3
1
0
1
2
0
0
1
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
7
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
2
0
0
2
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
1
2
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
1
1
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
2
0
0
6
0
0
2
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
2
2
0
0
2
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
1
4
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
4
0
0
0
0
0
0
0
1
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
4
0
0
1
0
1
0
0
1
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
2
1
8
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
4
0
0
0
4
0
0
0
1
0
2
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
1
1
0
0
0
0
0
0
2
1
0
2
0
1
0
1
0
2
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
3
0
0
0
2
0
2
0
0
0
0
0
1
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
5
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
5
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
7
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
1
1
2
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
2
0
1
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
1
2
0
0
2
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
1
0
0
0
0
4
0
2
1
5
0
5
0
0
0
4
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
2
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
1
1
0
0
0
0
2
2
0
2
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
1
0
1
1
0
0
1
0
1
0
0
0
0
0
2
0
0
2
0
0
0
2
2
2
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
2
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
2
0
0
5
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
2
3
2
0
0
0
0
0
0
1
0
2
0
1
3
0
1
1
0
0
0
0
0
2
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
2
2
0
0
0
1
0
0
0
0
1
2
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
3
0
0
1
0
0
0
1
0
3
0
1
0
0
0
1
0
1
0
0
2
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
3
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
2
4
0
0
1
0
0
0
0
0
3
1
0
2
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
3
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
4
0
0
0
0
0
0
0
1
0
1
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
4
1
1
0
0
0
2
0
0
6
0
1
0
2
0
0
0
0
0
0
1
0
0
0
2
2
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
1
0
2
0
1
3
0
0
3
1
0
0
3
0
0
0
0
0
1
0
2
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
9
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
1
0
0
22
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
3
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
2
1
0
1
0
0
0
0
1
0
2
0
0
1
0
2
0
0
1
0
0
0
4
0
0
0
0
0
3
0
0
2
0
0
3
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
2
2
0
0
0
1
0
0
2
0
0
4
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
1
0
4
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
2
1
0
0
2
0
0
0
0
1
1
0
0
6
0
0
1
2
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
2
2
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
1
1
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
4
1
0
0
1
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
2
0
0
0
0
1
0
2
0
1
0
0
0
0
1
0
0
0
2
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
3
0
0
0
0
0
1
0
0
0
2
0
1
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
4
0
0
0
1
2
0
1
1
0
0
0
1
5
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
1
0
0
7
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
3
0
0
2
0
0
0
0
0
0
0
0
2
0
3
0
0
2
2
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
1
2
0
2
0
0
8
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
6
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
3
1
0
4
2
0
6
0
0
1
0
0
0
0
0
0
0
3
0
2
0
1
0
0
1
0
0
0
0
2
0
0
7
0
0
0
6
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
3
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
1
0
0
0
0
3
0
0
3
1
0
0
0
0
0
2
1
0
0
9
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
2
0
0
0
2
0
0
1
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
1
0
0
1
2
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
2
0
3
1
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
4
4
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
2
7
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
4
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
3
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
14
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
1
0
3
1
0
0
0
0
0
0
1
1
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
1
2
2
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
1
2
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
5
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
3
0
0
0
0
0
0
0
0
0
0
2
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
6
0
2
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
2
0
0
2
0
0
0
1
0
0
1
0
1
2
2
0
0
0
0
0
7
0
0
0
0
0
0
2
1
0
0
0
1
2
3
2
0
1
0
2
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
2
1
0
0
2
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
2
0
1
0
0
4
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
1
4
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
2
0
0
4
2
1
2
0
2
0
2
0
1
1
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
6
3
0
0
2
0
0
0
1
3
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
3
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
2
0
0
0
0
0
2
0
2
0
1
0
4
0
0
0
0
2
1
1
0
0
0
0
0
0
0
2
0
0
1
0
4
0
0
0
2
0
0
0
1
2
0
0
3
0
1
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
4
0
0
1
0
2
0
1
0
0
1
1
2
0
0
0
0
0
0
0
0
5
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
5
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
2
0
0
0
1
0
2
2
0
0
0
0
0
0
5
0
3
0
3
0
0
0
1
2
1
1
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
1
0
1
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
2
1
0
9
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
3
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
1
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
3
0
2
0
2
0
0
1
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
5
1
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
1
2
1
0
1
0
2
0
0
1
0
0
0
2
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
1
0
2
0
0
0
0
0
2
1
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
2
4
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
3
2
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
6
1
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
1
0
1
0
0
0
2
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
1
0
1
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
3
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
2
0
0
1
1
0
3
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
3
0
2
0
2
0
0
2
0
0
3
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
3
0
1
0
4
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
3
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
8
2
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
5
1
0
0
0
0
0
3
0
0
0
1
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
4
0
0
1
2
0
0
0
0
0
0
0
0
2
0
3
0
0
2
2
0
0
0
3
0
0
0
0
0
2
0
0
1
0
0
2
0
0
1
0
0
2
0
0
0
2
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
3
0
0
0
0
0
2
1
1
1
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
1
2
0
0
2
0
0
0
0
0
0
2
0
10
1
1
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
1
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
2
0
2
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
2
2
0
0
0
0
0
0
1
3
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
2
1
1
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
3
0
0
1
3
0
0
2
0
0
1
1
0
0
0
0
0
0
1
1
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
1
0
0
1
1
1
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
1
0
0
2
0
3
0
0
0
1
0
1
0
0
0
0
0
1
1
1
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
3
0
0
0
0
2
1
0
2
0
4
0
0
2
1
0
1
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
1
0
0
2
0
0
1
0
0
0
1
0
0
0
1
0
0
1
2
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
2
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
5
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
2
1
0
0
2
0
0
2
0
0
0
0
0
4
5
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
10
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
1
0
0
0
2
0
1
2
0
0
0
0
1
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
3
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
14
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
1
0
0
0
0
0
1
2
0
0
1
0
0
0
2
2
1
1
1
2
0
1
2
1
2
0
0
1
1
0
1
0
0
0
0
0
5
0
0
0
0
1
1
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
5
0
0
0
2
5
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
2
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
3
0
1
0
0
0
1
0
2
0
0
0
0
0
1
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
2
2
0
0
0
0
2
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
3
0
0
0
0
4
0
0
0
2
0
0
0
0
3
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
1
0
2
0
0
0
0
2
1
0
0
0
0
0
3
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
2
1
0
2
0
1
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
2
0
0
1
0
3
1
2
0
2
1
0
0
0
3
0
1
0
0
0
3
0
2
0
0
0
1
0
0
0
2
1
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
5
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
2
0
0
1
0
0
2
0
1
0
0
0
1
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
2
0
0
0
0
0
1
0
3
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
1
2
0
0
0
0
0
0
2
2
2
0
0
2
0
0
3
0
1
0
0
1
1
0
0
0
0
0
0
0
2
0
0
1
1
2
1
1
0
0
0
2
1
0
0
1
0
1
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
2
0
0
3
0
0
0
2
0
0
0
0
2
0
1
0
0
2
5
0
0
0
0
0
0
0
0
6
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
1
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
3
0
0
1
0
2
0
2
1
0
0
0
0
0
0
0
0
0
1
4
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
1
0
2
0
1
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
2
1
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
2
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
1
0
0
0
1
0
2
0
0
2
1
0
1
0
0
0
2
0
0
0
0
1
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
2
2
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
2
0
0
2
0
0
0
10
3
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
1
1
6
0
0
2
0
2
0
2
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
1
0
0
0
0
0
0
1
0
0
2
0
2
1
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
5
0
1
0
3
0
0
0
2
2
0
0
2
0
0
0
0
0
2
4
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
2
2
0
1
0
0
3
0
0
0
1
0
2
0
0
0
0
0
1
1
2
0
0
6
0
0
0
3
0
2
0
0
0
0
1
0
0
0
0
2
0
1
0
0
1
2
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
1
0
0
0
1
0
3
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
0
1
3
0
0
5
0
0
0
0
0
0
0
0
0
2
0
0
0
6
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
1
6
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
2
0
0
3
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
1
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
2
0
1
0
2
0
0
0
2
0
1
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
2
2
0
5
2
0
0
0
0
1
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
4
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
2
0
1
0
1
1
1
0
0
0
0
0
3
0
0
0
1
2
0
0
0
0
0
1
0
0
2
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
7
0
0
0
0
0
0
1
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
2
1
0
0
0
0
5
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
3
2
0
0
2
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
1
0
2
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
2
0
0
0
0
9
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
4
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
5
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
2
0
2
0
0
1
3
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
3
1
4
0
0
0
0
2
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
2
0
1
0
2
1
0
0
0
0
0
0
2
0
1
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
4
0
1
0
0
4
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
3
0
0
0
1
0
1
0
0
1
1
0
4
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
1
0
0
0
2
0
5
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
2
2
3
0
0
0
1
0
0
0
0
0
0
0
0
7
0
0
0
0
0
3
1
0
2
0
1
0
1
0
0
3
1
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
2
0
0
0
0
0
0
1
0
0
4
3
3
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
1
0
0
0
0
1
2
0
0
0
2
3
0
0
0
2
1
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
2
0
0
0
2
0
0
0
1
0
1
0
2
2
1
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
2
0
1
0
0
0
0
2
1
1
0
1
1
0
1
0
0
0
0
0
0
0
0
9
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
2
2
2
0
0
2
0
0
0
0
0
2
0
0
3
0
0
2
1
2
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
1
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
3
0
0
1
0
0
2
0
7
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
1
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
1
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
6
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
2
1
0
0
2
1
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
3
1
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
1
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
8
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
1
0
1
2
0
0
1
1
0
0
1
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
3
0
1
1
0
1
0
12
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
1
0
0
0
5
2
0
0
0
0
0
0
0
0
5
0
0
0
0
1
1
0
0
2
0
1
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
4
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
9
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
6
0
0
0
2
0
0
0
0
0
0
0
1
0
0
4
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
2
0
0
0
0
0
0
0
1
0
1
2
0
1
2
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
1
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
1
1
0
0
0
1
1
6
0
0
0
0
0
0
9
0
0
1
2
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
3
0
2
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
2
2
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
6
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
5
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
1
1
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
2
0
1
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
3
0
0
2
5
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
3
0
0
0
0
0
0
0
0
1
2
5
0
1
0
0
0
0
0
0
0
1
3
0
0
0
0
0
2
0
0
3
0
0
0
0
0
1
0
0
1
0
0
1
0
0
2
0
0
0
1
0
1
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
2
0
0
2
1
0
3
2
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
3
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
1
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
3
1
0
0
2
0
0
0
0
1
5
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
2
1
0
0
0
0
1
2
0
0
0
0
0
3
0
2
0
1
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
1
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
4
1
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
2
2
1
0
0
2
0
0
0
0
0
0
0
0
2
1
0
1
3
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
3
0
0
2
0
0
0
0
3
2
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
5
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
2
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
2
0
0
0
0
2
2
1
1
2
0
0
0
0
1
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
4
0
0
0
1
0
0
0
0
0
1
0
0
0
1
4
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
3
2
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
6
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
1
0
0
3
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
6
0
1
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
5
0
0
3
0
0
0
0
2
2
0
0
7
2
0
0
0
0
0
2
0
2
0
0
0
0
0
3
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
2
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
12
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
5
0
0
1
1
0
0
3
0
3
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
1
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
1
2
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
2
0
1
0
0
2
2
0
0
0
0
1
0
6
1
0
0
0
2
0
1
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
1
0
0
0
0
1
0
0
3
0
0
0
0
4
0
0
3
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
2
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
3
0
0
1
0
0
4
2
0
0
3
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
2
1
0
0
0
1
1
2
0
3
0
0
0
0
0
1
2
0
1
0
0
0
1
0
0
3
1
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
1
1
4
0
2
0
0
0
2
2
0
0
0
0
0
0
0
2
1
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
1
1
0
2
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
1
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
2
2
0
0
0
0
0
2
2
0
3
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
1
0
1
0
1
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
10
0
1
0
2
1
0
2
1
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
2
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
3
0
0
1
0
0
0
2
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
9
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
1
0
0
2
0
0
2
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
2
0
0
0
3
0
0
0
0
0
1
0
2
0
1
0
0
0
1
0
0
2
2
0
0
1
2
0
0
0
1
0
2
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
2
1
0
1
0
0
0
1
0
0
1
0
0
0
2
0
0
0
1
0
2
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
2
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
4
4
0
0
0
0
4
1
2
0
0
0
0
0
0
1
3
1
0
1
0
1
0
0
0
0
0
0
0
0
0
2
3
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
5
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
2
0
0
1
0
0
0
0
2
7
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
1
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
4
0
0
0
2
0
0
2
0
0
0
2
0
0
2
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
4
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
1
1
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
2
0
0
0
3
0
0
0
1
0
0
0
2
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
1
0
2
1
0
0
4
0
0
2
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
3
1
0
0
0
0
0
1
3
0
0
0
0
0
1
0
0
0
1
0
1
0
2
1
0
0
0
0
0
0
0
6
1
0
0
2
0
0
2
2
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
2
0
0
0
0
0
1
0
2
3
0
0
0
2
1
0
0
0
1
1
0
0
0
2
0
0
0
1
4
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
1
1
0
2
0
1
1
1
0
1
0
1
0
0
1
2
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
2
0
3
0
0
0
0
0
0
0
0
1
2
0
0
2
3
1
0
0
1
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
1
0
0
1
0
0
1
0
0
2
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
1
0
0
0
2
0
2
0
0
0
0
3
0
0
0
0
6
0
2
0
2
0
0
0
0
0
2
0
1
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
2
0
0
0
1
3
0
0
2
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
1
2
1
0
1
0
0
2
0
0
5
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
1
1
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
4
3
1
0
2
0
0
0
0
3
1
1
1
1
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
2
3
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
1
1
2
0
0
0
0
3
0
0
0
1
0
0
0
2
1
0
2
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
5
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
2
1
0
1
1
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
1
0
0
0
0
2
1
0
0
0
0
0
0
1
0
3
1
2
0
0
0
0
0
0
4
2
1
5
3
0
3
0
0
0
0
0
1
0
0
0
0
2
0
1
2
0
2
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
2
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
1
0
0
2
1
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
3
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
2
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
3
0
0
0
0
0
0
0
0
0
0
3
1
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
3
1
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
2
2
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
4
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
1
0
3
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
3
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
1
2
0
0
0
0
0
3
0
0
1
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
3
3
0
0
2
0
0
0
0
0
0
0
0
1
0
3
0
2
0
1
1
0
0
0
1
0
0
0
1
0
0
2
3
0
7
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
3
0
0
1
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
2
0
2
0
0
0
0
0
8
0
0
0
0
0
0
0
0
4
0
0
0
4
0
1
0
0
0
0
0
0
1
1
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
1
0
1
0
3
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
7
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
2
1
0
1
0
0
2
0
0
0
0
1
0
1
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
5
0
3
0
1
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
3
1
0
0
0
0
0
0
0
0
8
1
0
0
5
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
3
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
2
2
0
1
0
2
0
0
0
0
0
1
0
0
3
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
2
2
0
2
1
0
1
0
0
2
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
2
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
1
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
2
0
0
2
1
0
0
2
5
1
0
0
0
0
0
2
0
1
0
2
0
0
2
0
0
0
0
1
0
1
0
4
0
0
2
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
2
0
0
0
0
1
2
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
7
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
1
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
7
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
1
1
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
2
0
2
0
0
0
0
1
0
1
2
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
2
1
1
0
0
2
2
0
0
1
0
0
0
0
0
2
0
1
1
3
0
1
0
0
0
0
3
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
1
0
0
0
0
0
3
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
3
0
0
2
0
0
0
0
0
0
0
1
1
0
3
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
2
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
1
2
3
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
2
2
0
0
0
0
0
0
1
0
0
0
3
1
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
2
3
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
1
2
0
0
0
1
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
3
3
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
2
0
2
1
0
0
0
2
0
0
0
1
2
0
1
1
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
3
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
2
0
1
0
0
0
0
1
0
3
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
2
0
0
2
0
0
2
0
0
0
1
0
0
1
0
0
0
2
2
1
0
2
0
0
1
2
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
5
2
0
1
0
0
0
0
0
0
3
0
3
0
0
2
1
1
0
3
0
1
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
1
0
0
0
0
2
3
0
2
2
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
2
2
1
0
0
0
1
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
3
0
2
0
0
1
0
2
2
0
0
2
0
0
0
1
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
9
0
0
2
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
2
1
0
0
0
0
5
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
6
1
0
0
0
0
0
0
0
0
2
2
2
1
0
2
1
0
0
2
0
0
0
0
2
0
2
0
0
2
0
2
0
0
0
0
0
2
1
3
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
1
0
1
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
4
0
1
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
1
1
0
0
7
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
1
0
2
0
1
0
0
0
0
3
0
0
0
0
2
1
0
0
2
0
0
4
0
0
0
0
7
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
2
0
0
0
0
1
0
0
0
1
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
2
0
2
0
0
0
2
2
2
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
5
1
2
0
1
0
0
0
0
1
1
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
1
0
0
1
0
1
0
0
2
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
5
4
0
0
0
0
0
0
0
1
2
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
2
1
2
0
0
6
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
2
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
1
1
2
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
1
0
1
2
0
3
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
2
3
0
0
2
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
1
0
1
2
1
0
0
0
2
2
0
1
1
0
0
0
0
2
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
3
1
0
0
0
0
2
0
0
0
0
1
1
0
0
2
0
0
0
3
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
1
1
4
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
1
0
1
0
0
1
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
3
0
1
0
1
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
2
1
2
0
0
0
0
1
0
0
0
1
2
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
3
2
0
0
2
0
0
3
2
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
10
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
5
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
2
1
1
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
2
5
0
1
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
3
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
1
0
0
2
0
1
0
0
0
2
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
2
0
1
1
0
1
2
3
0
5
0
0
0
0
0
3
0
0
4
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
1
2
0
1
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
1
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
1
2
2
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
1
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
1
2
0
0
2
4
2
1
0
0
0
0
0
0
0
0
0
1
0
2
1
1
0
2
1
0
0
0
1
0
0
0
0
0
0
0
3
2
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
1
0
1
1
0
2
0
0
1
0
1
2
0
4
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
4
1
0
0
1
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
2
1
0
1
0
0
0
0
1
0
1
1
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
2
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
1
0
0
0
2
1
0
0
0
0
0
0
3
0
2
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
1
0
1
0
1
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
2
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
1
0
0
0
1
2
0
0
3
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
1
0
0
2
1
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
2
0
0
0
0
2
2
0
4
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
3
0
0
0
0
0
1
0
2
1
0
2
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
3
0
1
0
0
0
0
0
0
3
3
1
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
1
0
2
0
0
0
2
0
1
0
0
0
1
0
0
2
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
7
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
1
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
3
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
3
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
1
0
2
0
0
0
1
0
0
0
10
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
1
0
1
0
0
3
0
1
3
1
0
0
0
0
0
2
3
1
2
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
4
0
1
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
3
0
1
1
0
0
0
2
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
1
2
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
2
6
0
2
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
3
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
3
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
5
0
0
0
0
0
2
0
1
0
0
0
1
2
0
0
0
1
0
1
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
3
0
1
2
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
1
0
2
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
4
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
3
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
6
3
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
2
0
0
0
2
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
3
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
3
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
4
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
1
0
0
0
1
0
1
0
0
0
0
0
14
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
2
0
0
0
0
0
4
0
0
0
0
0
0
2
0
1
2
0
2
2
1
0
0
1
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
3
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
2
1
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
1
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
2
0
0
2
1
0
0
1
0
0
0
12
0
0
7
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
6
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
3
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
2
0
0
1
0
8
0
0
2
2
0
2
2
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
5
0
0
2
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
6
0
0
1
0
0
0
0
4
0
3
1
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
1
0
2
0
0
0
0
2
2
0
0
0
1
1
0
1
0
0
0
0
0
2
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
7
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
1
1
0
0
0
2
5
0
0
0
0
2
0
0
3
0
7
0
0
1
0
0
0
0
0
2
2
0
0
0
3
0
0
0
0
3
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
3
0
0
0
0
0
0
1
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
1
1
0
0
0
0
0
2
1
1
3
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
3
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
2
2
0
2
0
0
2
0
0
0
0
0
1
0
1
0
1
0
0
0
0
2
1
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
5
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
2
0
0
0
0
0
0
2
3
2
0
0
0
0
5
0
1
0
1
0
0
1
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
1
2
0
3
0
0
0
1
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
2
0
1
0
0
0
0
2
2
0
1
0
0
1
1
2
0
0
0
1
0
0
3
2
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
3
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
3
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
1
0
1
1
1
0
0
0
0
0
0
2
0
2
1
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
3
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
2
2
0
0
0
0
0
0
0
0
0
1
1
1
0
0
2
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
1
0
2
2
0
0
1
3
0
1
5
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
1
1
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
1
0
1
0
1
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
2
0
1
0
0
3
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
3
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
1
0
2
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
2
0
0
0
0
0
6
0
1
0
0
0
0
5
0
0
0
0
0
1
0
1
0
0
0
0
1
0
2
0
0
7
0
2
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
8
0
2
0
0
0
1
0
5
2
2
0
2
0
0
0
0
0
1
0
2
2
0
3
0
2
1
1
0
1
0
0
0
0
0
0
0
0
0
3
0
0
2
0
3
4
2
0
2
0
1
0
1
1
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
1
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
3
2
0
0
0
0
3
0
0
0
0
0
0
3
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
4
1
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
6
0
0
0
1
0
0
0
0
0
0
0
5
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
2
0
1
0
0
0
0
0
0
2
1
0
0
0
1
0
0
2
0
4
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
6
0
4
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
1
1
1
0
0
0
1
0
0
0
1
2
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
6
2
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
13
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
2
1
2
0
0
0
0
1
0
2
0
1
0
0
1
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
2
1
0
0
1
1
1
1
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
2
2
0
0
0
1
0
2
1
1
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
3
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
3
0
0
2
1
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
2
0
1
0
0
3
0
0
0
0
0
3
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
1
2
0
0
0
0
2
0
1
0
1
0
1
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
2
3
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
1
0
0
0
0
0
2
0
1
0
2
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
7
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
3
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
2
0
0
0
2
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
2
0
0
0
2
0
2
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
1
0
3
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
2
0
0
0
1
3
2
0
0
0
2
2
2
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
3
1
0
1
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
3
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
5
1
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
6
1
0
1
0
0
0
1
0
0
0
2
2
0
0
0
0
1
1
4
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
1
0
1
0
0
0
0
1
3
0
0
2
0
2
0
1
1
0
0
0
0
0
0
1
1
0
0
2
0
0
0
2
0
0
0
0
1
2
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
1
1
0
4
0
0
2
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
2
0
1
2
0
0
1
2
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
2
0
2
0
0
0
0
0
0
1
2
1
0
0
0
0
3
0
0
2
0
2
0
0
0
2
0
0
1
1
3
0
0
0
0
0
2
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
1
0
0
0
0
4
0
0
0
1
0
0
0
3
0
0
0
1
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
2
0
0
0
0
0
2
1
0
0
2
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
4
3
1
0
0
2
0
0
0
2
0
0
0
0
3
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
1
1
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
1
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
3
0
0
2
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
2
3
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
3
0
2
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
4
2
0
1
0
1
1
2
1
0
2
0
0
1
0
0
0
4
0
2
0
1
0
3
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
6
0
0
0
1
0
1
0
2
0
0
0
0
0
0
2
1
1
0
2
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
1
0
1
0
1
2
0
0
0
2
0
3
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
2
1
1
0
0
0
0
2
0
1
3
1
0
0
0
0
0
0
0
2
1
2
0
9
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
1
2
2
2
0
0
0
2
0
0
0
2
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
2
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
2
0
1
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
2
2
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
1
1
0
0
0
0
0
0
2
2
4
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
9
1
0
0
0
2
0
2
0
1
0
0
4
0
2
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
4
0
0
0
0
0
2
3
0
0
0
1
1
0
0
2
0
0
0
2
0
0
0
2
2
2
0
2
0
0
1
0
0
0
0
0
0
1
4
2
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
3
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
1
0
0
0
3
0
0
1
2
0
0
0
1
0
0
3
0
1
1
0
0
0
0
0
4
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
3
0
1
0
0
2
0
0
2
0
2
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
7
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
2
1
0
0
0
1
0
0
7
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
7
0
0
0
13
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
3
0
1
2
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
2
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
2
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
1
0
0
0
0
0
1
0
7
0
0
0
0
0
0
2
0
0
0
1
0
3
4
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
1
0
2
2
0
0
1
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
2
2
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
9
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
1
0
0
2
0
1
0
3
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
2
1
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
1
1
1
0
1
1
0
2
0
0
0
1
2
0
0
0
0
1
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
3
2
1
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
1
1
0
1
0
0
1
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
1
1
0
0
2
1
2
0
1
0
1
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
1
1
1
0
0
2
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
1
0
2
0
0
0
0
1
0
1
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
3
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
2
0
3
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
5
0
2
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
4
0
2
0
0
0
0
2
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
2
0
0
0
0
0
3
0
0
0
1
0
6
0
0
0
5
0
1
0
0
1
0
0
0
1
0
0
0
0
3
0
0
0
0
0
1
0
0
2
9
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
3
0
5
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
8
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
4
0
0
0
0
2
4
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
2
0
1
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
2
1
0
0
0
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
1
0
0
2
0
0
1
0
1
0
0
0
3
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
3
1
0
0
1
0
0
1
3
0
1
0
0
2
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
3
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
2
0
0
0
0
0
2
0
0
5
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
2
0
2
0
1
0
2
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
12
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
5
0
0
0
0
1
0
1
0
0
0
0
0
0
5
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
5
0
0
1
1
0
0
5
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
2
0
2
1
0
0
0
0
1
0
0
0
0
0
1
2
2
0
0
1
0
1
0
0
0
0
0
3
0
1
0
0
1
0
1
1
0
0
2
2
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
2
1
0
0
8
0
0
0
3
1
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
2
0
1
2
0
0
0
0
3
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
2
0
0
2
0
0
0
0
1
1
0
0
0
3
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
2
0
0
2
0
2
0
0
0
1
0
0
0
0
1
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
2
0
0
0
2
3
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
4
0
0
0
0
0
2
0
0
0
3
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
2
2
0
0
0
2
1
2
0
0
0
0
1
0
1
0
2
3
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
7
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
7
0
0
0
0
0
2
0
0
0
0
2
0
1
1
0
0
0
0
0
3
0
1
0
1
0
2
1
0
1
0
2
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
4
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
1
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
4
0
0
5
0
0
0
2
1
0
0
0
0
0
3
0
0
1
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
1
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
1
4
0
3
0
3
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
1
0
0
1
1
0
0
0
0
5
0
0
0
0
0
0
0
2
1
0
1
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
1
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
7
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
3
0
0
0
2
0
0
0
0
0
1
0
2
1
0
0
0
0
0
2
0
1
0
0
0
0
0
3
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
2
1
0
4
0
2
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
3
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
2
0
1
1
1
0
0
0
0
1
0
0
6
0
0
0
0
0
0
0
1
0
0
2
1
0
2
0
1
0
0
0
2
1
0
0
0
0
2
1
0
0
0
0
0
3
0
0
3
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
1
0
0
1
0
3
1
0
0
0
0
2
0
4
2
3
1
0
0
1
0
0
2
0
1
0
0
0
0
1
0
0
0
6
1
0
1
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
1
4
0
0
0
2
0
0
1
0
0
0
0
0
1
2
0
0
0
0
2
2
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
2
0
0
0
2
0
2
2
0
2
0
2
5
2
2
0
0
1
0
0
2
2
0
0
0
0
0
2
0
0
4
0
0
0
1
0
0
0
2
2
1
1
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
8
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
6
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
3
8
0
1
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
3
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
2
0
1
1
1
0
0
0
0
0
2
0
2
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
2
0
0
3
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
7
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
3
0
0
2
0
0
0
0
0
0
0
1
0
0
1
2
0
0
2
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
1
0
0
0
0
0
0
1
6
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
1
1
0
0
2
0
0
0
0
1
0
0
2
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
1
1
0
0
0
0
0
0
0
1
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
2
0
1
2
0
0
0
0
5
2
0
0
0
0
0
0
0
3
0
1
0
2
0
1
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
6
0
2
0
0
0
0
3
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
5
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
3
0
0
2
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
2
0
1
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
9
0
0
0
0
2
2
0
1
0
5
0
0
2
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
3
2
1
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
4
0
0
0
0
0
0
4
0
2
0
0
0
0
2
1
0
2
1
0
2
0
0
0
0
4
0
0
2
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
2
0
0
1
0
0
0
2
0
0
2
0
0
0
0
2
0
2
2
0
0
0
7
2
1
0
0
0
2
0
0
1
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
1
0
0
0
2
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
2
1
2
1
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
3
1
1
2
0
0
0
1
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
3
0
0
0
0
2
2
4
0
0
0
0
0
1
0
0
0
2
0
1
1
0
0
0
5
0
3
0
1
0
2
2
1
0
1
0
0
1
0
1
0
0
0
0
0
2
0
0
2
0
0
1
0
2
0
0
0
0
5
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
4
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
2
1
0
0
3
0
2
0
0
0
1
5
0
0
0
0
0
0
1
1
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
2
0
0
0
0
0
1
0
1
0
2
0
1
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
6
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
4
0
0
1
1
0
0
1
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
2
0
0
3
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
4
5
2
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
5
1
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
3
0
0
2
0
0
4
2
0
0
3
0
0
0
5
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
1
0
0
0
0
0
0
0
0
0
4
0
2
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
4
1
0
0
0
2
0
0
2
0
0
0
4
0
1
0
3
3
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
2
2
1
0
0
7
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
6
1
0
0
0
0
0
0
2
0
3
0
2
0
1
0
2
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
1
1
0
1
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
2
4
0
0
0
0
0
2
0
0
0
3
0
3
0
1
2
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
1
1
0
0
0
2
1
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
4
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
1
2
2
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
1
0
3
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
2
0
2
0
0
0
0
0
1
2
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
4
4
0
0
2
0
2
0
2
2
2
3
0
2
0
2
1
1
2
0
1
0
15
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
1
1
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
3
1
0
0
0
1
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
6
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
2
0
0
0
0
0
0
1
0
0
3
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
3
0
2
0
1
0
4
1
0
0
1
0
0
2
0
1
0
0
0
0
2
0
0
1
1
0
0
1
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
4
0
0
0
0
0
1
0
0
2
0
0
0
1
6
2
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
2
1
0
0
1
0
0
0
0
1
0
0
0
0
2
0
1
0
0
2
0
0
1
0
0
0
0
0
0
1
0
2
1
0
1
8
0
1
0
2
0
3
0
1
1
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
2
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
2
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
1
2
0
2
0
0
0
0
6
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
1
2
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
1
1
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
5
2
2
2
0
0
2
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
2
2
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
5
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
1
1
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
5
0
0
1
0
0
1
0
0
0
2
2
0
0
2
0
0
0
0
0
7
0
0
1
0
0
0
1
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
3
2
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
1
0
0
1
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
2
2
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
5
0
0
0
4
0
0
0
2
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
1
1
0
0
0
0
3
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
7
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
5
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
2
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
1
0
0
0
0
3
1
0
4
1
1
0
2
0
2
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
2
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
4
0
0
0
0
2
2
0
4
2
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
3
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
5
0
0
0
0
1
0
0
2
0
2
0
3
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
3
0
0
0
0
0
2
5
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
2
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
4
1
0
0
0
2
0
0
0
0
0
1
1
0
1
0
0
2
2
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
3
0
1
0
1
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
3
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
2
0
0
0
2
0
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
3
1
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
2
0
1
0
0
3
2
0
0
0
0
0
0
1
6
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
8
0
0
0
0
0
0
0
1
1
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
2
0
0
0
2
0
0
1
1
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
3
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
1
1
0
0
0
0
0
0
1
0
3
2
0
0
0
0
0
0
2
0
2
2
0
2
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
1
2
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
6
3
0
1
2
0
1
0
0
0
1
0
0
0
0
0
1
0
3
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
7
1
0
0
2
2
0
0
2
0
0
0
3
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
8
0
0
0
2
1
1
0
0
0
0
0
0
0
0
2
0
0
3
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
1
0
1
0
1
0
0
2
0
0
0
0
2
2
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
8
0
0
0
0
2
0
0
0
5
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
3
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
4
2
1
0
0
1
0
0
0
0
1
1
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
2
0
2
0
0
0
0
0
0
0
0
1
2
0
0
3
0
1
2
2
1
0
3
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
1
2
2
1
3
0
0
0
3
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
3
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
2
0
3
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
2
1
1
0
0
0
4
0
0
0
0
0
2
0
0
0
9
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
2
0
4
0
1
11
1
0
0
0
0
2
0
3
0
0
0
0
0
0
1
0
0
2
1
0
1
1
0
0
0
0
0
2
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
1
0
14
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
2
0
1
0
0
0
2
2
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
2
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
4
1
1
0
0
0
0
0
3
0
0
1
0
0
0
1
1
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
1
2
4
0
0
0
0
0
2
1
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
2
3
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
2
0
0
0
2
0
0
3
1
0
0
2
0
0
0
0
1
0
1
0
0
1
0
3
0
8
0
0
0
1
2
0
0
2
0
0
0
1
0
0
0
0
0
1
2
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
1
0
1
0
0
0
0
1
0
2
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
1
2
0
2
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
4
1
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
2
3
2
0
0
3
0
0
0
0
0
0
0
0
1
0
0
7
0
6
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
1
0
1
1
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
3
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
5
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
1
0
1
1
0
0
0
0
1
2
0
2
0
1
1
0
1
0
0
2
0
0
0
0
6
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
2
0
0
2
1
1
1
0
0
2
2
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
5
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
1
1
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
1
2
0
0
0
0
2
0
1
0
0
0
6
0
0
1
0
0
0
0
1
0
0
0
0
1
6
0
1
2
1
0
0
0
0
0
0
0
1
0
3
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
1
0
3
0
0
0
1
3
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
3
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
1
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
3
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
4
0
0
2
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
7
1
0
0
0
0
3
0
2
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
3
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
3
0
0
0
0
1
0
0
0
1
2
0
0
1
0
0
0
2
0
1
3
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
2
0
1
2
0
0
0
0
1
0
2
1
0
0
0
0
0
2
1
0
0
0
7
0
2
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
4
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
2
3
0
0
0
0
2
1
0
2
9
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
3
0
0
0
0
1
2
0
0
0
0
0
1
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
18
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
2
2
0
2
3
0
0
0
0
2
0
0
0
0
2
2
3
0
0
0
2
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
4
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
4
0
0
0
1
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
5
2
0
0
2
1
1
3
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
1
1
0
0
1
2
0
0
2
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
3
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
9
0
6
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
2
2
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
9
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
6
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
2
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
6
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
6
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
4
0
2
0
0
0
1
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
3
0
0
0
1
0
0
0
2
0
2
0
1
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
1
0
3
0
0
0
0
3
0
0
1
0
0
0
2
1
0
2
1
0
0
0
0
3
2
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
3
2
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
3
2
0
0
0
2
2
0
2
1
0
0
0
2
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
4
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
2
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
1
0
0
0
1
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
7
1
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
2
0
2
0
2
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
1
0
0
0
3
1
0
0
0
0
0
0
1
0
0
0
0
4
1
0
0
0
0
1
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
2
2
2
0
0
2
0
0
3
4
0
0
0
0
0
0
7
0
0
2
0
0
2
5
1
0
0
3
0
0
0
2
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
4
2
0
0
2
0
4
0
0
2
2
1
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
2
2
2
0
0
0
0
1
0
1
0
5
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
2
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
1
1
0
0
0
2
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
1
0
0
0
0
0
0
2
2
0
0
0
4
2
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
4
1
0
1
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
2
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
1
1
1
2
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
2
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
2
0
0
0
1
0
0
0
0
0
0
0
1
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
1
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
1
1
0
1
0
0
0
0
2
1
0
0
0
2
0
1
0
3
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
2
0
2
0
2
0
0
0
1
0
0
0
1
3
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
4
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
5
0
0
0
0
2
0
0
0
2
0
1
0
0
2
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
4
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
2
0
0
0
0
2
0
0
0
3
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
8
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
3
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
4
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
1
0
0
6
0
1
0
0
0
0
3
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
3
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
7
1
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
3
0
1
1
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
3
0
0
0
0
0
0
10
2
0
0
0
2
0
0
0
2
2
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
3
0
0
0
1
0
0
0
0
0
4
0
2
0
2
1
5
1
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
1
0
1
1
1
0
1
0
0
0
2
0
3
1
0
1
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
2
2
0
0
0
0
0
3
0
1
0
0
0
1
0
2
0
0
0
0
0
1
2
3
1
0
0
7
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
1
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
1
0
0
0
3
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
1
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
3
1
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
2
0
2
0
0
2
1
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
2
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
1
0
3
0
1
0
1
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
2
0
0
0
0
4
0
0
0
0
2
2
0
1
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
5
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
2
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
1
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
2
0
0
0
4
0
1
1
0
0
2
3
0
0
2
0
0
1
0
0
1
0
0
0
1
1
0
2
1
0
0
1
2
0
0
0
1
0
2
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
1
0
0
0
1
2
0
0
0
0
2
0
0
0
3
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
1
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
2
0
0
2
0
0
0
2
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
4
0
2
0
4
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
6
0
3
0
0
0
0
0
1
1
0
0
0
0
0
0
1
2
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
7
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
5
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
7
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
2
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
2
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
1
0
0
2
0
0
0
5
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
1
0
2
3
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
2
0
0
1
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
3
0
0
0
0
0
2
1
2
0
0
1
0
0
0
0
0
0
3
0
0
1
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
3
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
2
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
2
0
1
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
2
2
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
4
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
3
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
1
0
3
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
1
0
0
0
2
0
0
2
0
0
0
0
2
0
1
0
0
0
5
0
0
4
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
3
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
1
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
1
0
0
1
1
0
0
2
2
3
0
0
1
3
1
0
1
0
0
0
2
0
0
0
4
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
4
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
3
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
2
0
2
2
1
1
0
2
0
0
0
1
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
1
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
5
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
2
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
2
0
10
0
0
0
0
4
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
2
0
1
0
2
0
2
2
1
0
0
0
0
2
0
2
0
1
0
0
1
1
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
3
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
1
0
1
0
1
0
1
1
0
1
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
4
0
0
0
0
0
0
0
0
1
1
3
0
0
0
0
2
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
14
0
1
14
0
0
1
2
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
2
0
1
2
0
0
0
0
2
0
0
0
0
0
0
3
0
1
0
0
0
0
0
2
0
0
2
0
5
0
0
0
0
1
0
0
0
1
2
0
0
0
1
0
0
3
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
2
0
1
0
0
1
0
1
0
1
0
0
0
0
1
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
5
0
3
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
2
2
1
3
4
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
2
1
0
0
0
2
0
0
0
4
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
5
1
0
0
2
0
0
0
0
0
0
0
0
2
3
0
3
0
0
0
0
0
0
1
0
0
3
1
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
3
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
4
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
3
1
0
0
0
0
0
1
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
2
1
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
3
1
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
1
0
0
0
0
2
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
2
3
0
0
0
2
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
1
2
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
1
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
2
1
0
0
0
0
2
0
0
7
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
4
1
1
0
3
0
0
1
0
0
3
0
0
0
1
2
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
1
1
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
2
1
1
0
0
0
1
0
2
0
0
0
0
0
3
0
0
0
0
0
1
0
2
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
3
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
6
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
2
0
1
2
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
3
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
1
0
2
0
0
2
0
0
1
0
0
0
3
0
0
0
0
12
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
3
0
1
0
2
1
0
0
0
0
0
1
0
0
0
1
0
0
3
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
1
0
0
1
1
0
0
0
0
1
8
0
0
0
2
0
2
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
2
1
1
0
0
0
2
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
4
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
8
2
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
1
4
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
3
1
0
0
0
0
0
0
4
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
4
0
1
0
0
1
1
0
0
0
0
1
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
2
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
1
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
3
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
2
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
3
2
0
0
0
1
0
0
0
0
0
0
0
1
0
3
1
0
0
0
0
0
0
2
0
0
0
2
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
2
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
1
0
0
0
0
0
1
2
0
0
1
0
0
1
0
0
2
0
0
0
2
0
0
0
0
9
0
1
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
5
0
0
2
0
2
0
0
0
0
2
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
1
1
0
0
0
2
1
0
1
0
1
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
1
2
0
2
2
0
1
0
0
2
2
0
3
0
0
0
0
2
0
1
0
0
0
0
0
1
1
2
2
1
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
3
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
5
0
0
0
3
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
1
0
1
0
4
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
7
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
1
2
1
0
0
2
0
5
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
3
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
3
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
3
0
0
0
0
0
0
0
2
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
1
1
2
0
0
0
0
0
1
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
2
1
0
2
1
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
4
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
4
0
0
0
0
2
0
1
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
2
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
4
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
1
1
2
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
1
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
3
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
2
1
0
0
0
2
0
0
0
0
1
0
3
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
5
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
4
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
6
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
2
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
8
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
2
3
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
1
0
2
0
0
2
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
10
0
0
0
0
0
6
1
0
2
0
0
2
0
0
2
0
2
0
0
0
0
1
0
1
1
0
2
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
5
0
0
1
0
0
0
0
2
3
0
1
0
0
0
0
0
2
0
0
0
3
0
0
1
0
0
2
0
0
0
0
1
0
0
0
1
0
7
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
3
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
1
1
1
0
0
0
0
0
0
4
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
2
0
3
0
0
0
0
0
0
0
2
3
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
3
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
1
0
0
1
0
0
0
0
2
0
0
1
1
2
0
0
3
1
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
5
1
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
1
1
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
1
0
4
0
3
0
2
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
1
0
0
0
0
0
0
0
7
0
1
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
3
1
0
0
0
0
0
0
0
0
1
1
0
4
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
3
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
2
1
0
0
0
0
0
3
0
0
0
0
2
0
0
1
4
0
0
0
1
2
0
1
0
0
1
1
0
1
0
1
2
0
0
0
0
0
0
0
4
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
2
0
3
0
0
1
4
0
0
1
0
1
1
0
0
4
0
1
0
0
0
0
0
0
0
1
1
0
0
0
2
2
0
2
0
0
0
0
13
0
0
0
2
0
0
0
0
2
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
2
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
3
0
1
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
1
1
0
0
0
0
0
1
1
0
1
0
0
1
2
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
1
2
3
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
1
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
2
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
2
3
2
1
0
0
0
0
0
7
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
6
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
3
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
2
0
1
0
0
0
0
0
0
1
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
4
1
0
3
3
0
0
0
2
0
3
1
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
6
0
0
0
0
0
2
0
0
0
1
1
0
1
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
10
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
1
0
2
2
0
0
4
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
3
0
0
0
0
0
2
2
0
0
0
2
2
2
0
0
2
0
0
2
0
0
2
0
0
2
0
2
0
0
0
0
1
0
0
2
0
0
1
0
0
0
1
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
5
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
1
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
1
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
1
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
1
0
1
1
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
2
1
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
5
2
0
0
2
4
0
3
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
1
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
3
0
0
0
0
0
0
0
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
2
0
0
0
1
0
0
0
0
4
0
0
0
0
4
2
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
1
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
4
0
1
0
2
0
1
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
5
0
1
0
1
0
1
2
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
6
0
0
2
1
1
0
0
1
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
1
0
0
2
1
0
2
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
4
3
0
0
0
0
0
0
5
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
1
0
2
0
1
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
3
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
2
2
0
2
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
1
0
0
1
3
0
0
4
0
0
0
1
0
0
0
0
1
2
0
0
0
0
1
1
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
2
3
0
0
0
0
0
1
0
0
2
0
0
0
0
0
4
0
0
0
0
0
0
0
0
8
0
0
0
2
0
0
0
1
0
3
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
3
0
2
0
1
0
1
0
0
0
0
1
0
0
3
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
2
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
1
0
0
0
2
3
0
0
1
0
0
2
0
0
2
0
1
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
3
1
0
0
0
0
0
2
2
0
0
0
1
0
0
0
1
1
1
0
0
4
1
1
0
0
3
0
0
0
1
1
0
0
1
0
0
0
0
0
0
2
0
2
0
0
1
2
0
0
0
0
0
0
2
0
2
0
4
2
1
0
0
1
2
2
3
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
2
2
0
1
0
0
1
0
2
0
1
0
0
0
2
0
2
2
2
0
3
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
2
1
0
2
0
2
0
2
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
1
0
0
0
1
0
0
2
1
5
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
4
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
3
1
0
0
0
0
0
0
4
0
0
0
4
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
3
0
1
0
3
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
3
0
0
3
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
4
1
0
0
0
0
3
0
0
0
1
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
2
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
2
2
1
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
5
0
0
0
3
0
3
0
1
0
0
0
0
0
0
2
0
0
1
0
0
1
1
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
1
1
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
2
1
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
2
0
2
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
3
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
2
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
1
1
0
0
0
0
0
7
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
4
1
0
0
2
0
1
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
1
2
0
0
0
1
0
0
0
0
0
1
0
4
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
1
1
0
0
1
1
2
0
1
2
0
0
0
1
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
2
0
1
2
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
1
0
2
3
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
2
3
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
1
1
1
0
2
0
0
0
0
0
0
0
0
0
1
3
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
1
1
2
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
2
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
2
0
0
0
1
0
0
1
1
0
4
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
3
0
0
2
0
0
0
0
0
0
0
0
2
0
2
2
1
0
1
0
0
0
0
1
1
0
0
0
0
0
4
0
1
1
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
4
0
0
0
0
3
0
0
2
0
0
0
2
0
1
0
1
0
1
0
0
0
0
0
0
2
0
1
2
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
2
1
0
1
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
2
0
0
4
0
1
1
0
1
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
1
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
3
0
0
0
2
2
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
3
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
1
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
1
0
0
1
1
0
1
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
4
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
2
3
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
4
1
0
0
1
0
2
0
2
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
1
0
2
0
1
0
0
0
1
0
1
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
2
0
0
0
1
0
1
0
0
0
2
0
0
0
2
0
0
2
1
0
0
1
4
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
3
1
0
2
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
5
2
3
1
0
0
0
0
1
0
2
0
3
0
0
3
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
1
0
0
2
0
0
2
0
1
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
1
0
0
2
2
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
2
0
0
3
0
0
0
0
0
0
3
0
0
0
0
2
0
0
1
0
0
0
0
4
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
2
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
2
2
2
0
2
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
4
0
0
3
3
0
0
0
0
0
0
3
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
1
0
0
0
0
0
1
0
3
0
0
0
1
2
0
2
0
2
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
3
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
3
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
2
0
2
0
0
2
0
2
0
0
0
0
0
0
2
2
0
0
0
0
1
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
1
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
1
0
0
0
1
0
1
0
0
0
0
0
1
2
6
0
0
0
1
0
0
1
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
1
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
2
2
0
0
0
0
0
1
0
0
0
2
3
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
3
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
1
0
0
1
2
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
7
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
4
0
0
0
0
2
1
0
0
0
0
0
1
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
4
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
1
0
1
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
1
2
0
4
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
1
1
0
0
0
0
1
0
3
0
0
0
0
1
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
5
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
2
0
0
0
0
0
0
1
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
1
4
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
5
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
1
2
0
0
0
0
1
0
2
2
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
4
1
2
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
7
0
1
0
2
0
0
0
1
0
0
1
1
0
1
1
0
3
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
1
1
0
0
0
0
2
7
0
15
2
1
0
0
2
0
0
0
0
0
2
0
0
0
1
0
1
0
2
0
1
0
0
0
1
0
0
0
4
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
2
3
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
2
1
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
2
5
0
0
0
0
2
2
1
0
0
2
2
0
1
0
2
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
1
2
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
4
0
0
0
1
0
0
1
0
0
0
0
0
0
3
1
0
2
2
0
3
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
1
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
3
0
0
0
0
0
0
2
0
0
6
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
6
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
1
0
2
2
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
3
1
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
1
2
2
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
2
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
1
2
3
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
4
4
2
0
0
0
0
1
0
0
0
0
2
1
1
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
3
0
0
4
0
0
0
0
2
0
0
0
1
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
2
0
0
2
0
3
4
0
0
0
0
0
0
0
0
6
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
6
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
1
1
0
2
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
10
0
0
2
0
1
0
1
0
0
0
1
0
0
0
0
1
2
0
1
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
2
0
1
0
1
0
0
0
2
1
0
0
2
0
0
0
0
0
1
0
4
0
0
0
1
6
0
12
0
1
1
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
4
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
2
1
2
0
1
0
7
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
3
1
0
0
0
2
0
1
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
1
0
2
0
0
0
0
0
1
0
0
2
0
1
2
0
0
1
1
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
1
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
2
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
2
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
7
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
3
0
2
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
1
0
3
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
4
0
0
0
1
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
1
0
0
0
1
0
3
2
0
0
0
1
0
0
3
2
0
0
0
0
0
0
0
5
0
0
0
0
0
2
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
3
0
0
1
0
0
0
3
0
0
2
0
0
0
0
0
0
2
0
8
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
1
0
0
0
0
1
0
4
0
1
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
3
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
4
0
0
0
0
1
2
1
2
0
0
0
1
1
0
0
0
0
0
0
0
1
4
1
0
0
3
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
5
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
2
0
0
0
1
0
0
0
1
0
2
0
1
0
0
0
0
3
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
2
0
0
2
1
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
1
0
1
0
0
0
5
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
2
0
1
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
1
0
2
0
2
3
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
8
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
3
0
1
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
4
0
0
0
0
1
0
1
1
1
3
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
1
3
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
1
0
0
0
4
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
2
4
0
0
0
1
0
0
0
0
2
1
0
1
0
0
1
0
0
0
0
0
0
0
4
3
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
2
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
5
2
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
2
2
0
2
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
2
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
2
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
2
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
9
2
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
3
0
0
0
0
0
1
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
2
1
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
4
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
3
0
1
0
2
0
0
0
0
0
0
1
0
2
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
1
0
2
0
2
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
1
1
2
1
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
4
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
4
3
0
0
0
1
0
0
0
1
1
1
0
0
0
0
1
2
0
0
0
0
0
2
0
0
7
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
2
1
0
0
0
2
0
2
0
2
1
0
0
0
1
2
0
0
0
3
2
0
1
1
0
0
1
1
0
0
0
1
0
0
0
1
0
1
0
4
0
0
0
0
2
0
2
2
0
2
0
1
0
0
0
1
0
0
0
0
0
0
3
2
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
2
0
1
1
0
0
2
0
0
0
0
0
0
10
0
1
2
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
2
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
3
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
3
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
2
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
2
2
0
1
0
0
0
0
0
8
2
0
0
3
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
4
1
3
0
0
2
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
6
1
0
0
0
2
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
3
0
2
0
0
1
0
0
1
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
4
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
2
0
0
0
0
0
0
8
0
0
0
0
0
2
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
3
0
0
0
0
0
3
0
0
0
0
0
0
0
1
2
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
1
0
0
3
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
1
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
1
5
1
1
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
2
3
1
0
0
1
3
3
0
0
1
1
0
2
0
3
2
1
0
1
0
1
0
2
3
0
0
0
0
0
1
0
0
0
1
1
0
1
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
1
1
2
0
0
0
0
0
0
0
2
0
3
0
0
1
0
3
1
0
0
0
0
0
0
0
0
0
0
0
10
0
2
0
0
0
0
0
3
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
1
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
3
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
1
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
2
2
0
0
1
0
0
0
0
0
0
2
1
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
3
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
11
0
0
1
0
0
0
0
0
0
4
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
5
1
0
0
3
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
2
0
0
2
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
1
0
0
0
2
1
1
0
0
0
0
2
0
0
2
0
0
4
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
3
0
0
1
0
0
0
0
4
1
0
0
0
3
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
3
2
0
1
0
0
3
1
1
0
2
0
1
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
2
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
3
1
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
3
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
1
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
3
0
0
1
0
0
0
0
0
2
0
3
0
0
0
0
0
3
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
2
0
0
1
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
2
0
1
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
1
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
8
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
2
0
1
0
3
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
2
1
0
0
4
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
3
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
2
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
3
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
3
0
1
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
1
1
0
1
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
2
0
0
3
0
0
0
2
0
0
2
0
0
1
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
6
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
1
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
3
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
4
0
0
0
1
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
1
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
1
1
0
1
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
2
1
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
2
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
1
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
1
2
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
2
0
0
0
1
0
0
2
0
1
0
1
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
2
3
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
2
0
1
1
1
2
1
1
2
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
2
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
3
0
1
0
0
1
0
1
0
0
0
5
0
1
0
0
0
1
0
0
1
0
2
2
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
5
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
1
2
2
0
0
0
0
1
0
7
0
0
0
1
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
2
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
6
0
0
0
1
1
0
0
7
0
0
0
2
1
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
1
1
0
0
3
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
3
0
0
0
0
2
0
1
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
3
0
0
0
1
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
5
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
1
2
1
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
1
0
1
0
2
0
2
0
1
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
1
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
3
0
0
0
3
0
2
2
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
2
0
0
0
0
2
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
2
0
0
4
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
1
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
3
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
2
0
1
2
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
3
1
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
7
1
1
3
0
1
2
3
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
3
1
2
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
2
2
0
1
0
1
0
3
0
0
2
0
1
0
0
0
1
0
0
1
1
0
0
0
0
3
1
0
0
1
0
0
0
0
0
0
0
0
1
1
2
0
2
0
0
0
0
0
0
1
4
0
0
0
0
3
0
0
1
1
4
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
5
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
1
10
0
0
0
0
1
0
0
0
1
0
1
2
2
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
7
0
0
1
0
4
0
0
0
2
0
1
0
0
0
0
2
0
0
2
2
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
2
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
2
0
0
0
0
1
0
0
0
2
0
2
0
2
0
3
0
0
0
1
0
0
1
2
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
3
0
3
0
0
0
0
0
1
2
0
0
0
2
0
0
1
0
0
0
0
0
0
1
2
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
2
0
0
2
0
1
0
1
0
0
1
2
1
1
0
0
0
0
2
0
1
0
0
0
0
0
0
1
3
0
0
0
0
0
0
4
0
2
1
0
0
0
0
0
2
0
0
0
3
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
2
1
3
0
0
0
0
1
0
2
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
3
0
1
0
0
0
2
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
1
2
2
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
2
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
1
0
2
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
4
0
0
1
1
0
0
1
0
2
0
0
0
0
1
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
3
0
2
0
0
0
1
0
0
0
0
0
1
1
0
5
0
0
0
0
2
0
1
0
0
0
0
1
0
0
2
0
2
0
0
0
3
0
0
2
0
0
0
0
0
2
2
0
2
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
3
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
2
6
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
14
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
3
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
4
0
2
0
2
0
2
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
3
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
1
0
3
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
7
0
3
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
2
0
1
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
4
0
0
0
0
0
1
0
0
6
2
2
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
1
4
0
0
0
0
1
1
2
0
2
2
0
2
0
1
0
3
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
2
2
0
1
0
0
3
0
0
0
1
2
0
0
0
1
2
0
0
3
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
14
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
2
0
0
4
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
3
0
2
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
5
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
4
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
1
1
0
0
0
1
0
3
0
0
1
3
0
0
0
0
0
2
2
0
0
0
0
2
0
1
1
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
1
0
0
1
2
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
1
0
4
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
3
0
0
1
2
0
0
0
0
0
1
0
3
0
1
0
0
2
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
1
0
2
1
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
3
0
0
1
0
0
3
0
1
0
1
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
1
2
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
3
0
1
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
4
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
1
1
1
1
0
0
2
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
1
1
3
0
0
2
1
1
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
1
2
3
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
3
2
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
10
0
0
1
0
2
0
0
3
2
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
3
0
0
2
3
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
2
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
1
1
2
1
0
0
2
1
0
2
2
2
0
0
0
3
1
0
0
1
2
1
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
2
0
0
1
0
1
0
0
0
0
1
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
1
3
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
1
0
0
1
0
6
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
6
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
5
0
0
2
0
0
3
0
1
1
0
0
3
2
2
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
3
1
3
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
7
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
10
0
2
0
2
0
2
0
0
1
0
1
0
2
3
0
2
2
2
0
0
3
0
1
0
0
0
0
0
0
0
0
1
2
1
0
0
3
0
0
0
0
7
2
0
0
1
2
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
1
0
0
0
0
0
2
0
2
0
0
3
1
1
0
0
0
0
2
0
0
1
0
0
0
1
1
0
0
0
0
2
0
0
0
1
1
0
0
2
0
0
0
4
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
5
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
3
0
0
0
1
0
0
0
4
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
1
0
1
0
4
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
1
0
2
0
2
0
0
3
0
1
0
0
4
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
9
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
4
0
0
0
0
2
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
2
2
0
0
2
2
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
5
2
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
2
1
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
3
0
1
0
0
0
0
0
0
0
9
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
2
1
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
2
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
3
0
2
0
1
0
0
0
0
0
0
1
0
2
0
0
2
0
0
1
0
0
0
4
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
1
0
2
2
0
0
0
0
1
5
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
3
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
1
0
0
1
0
1
0
0
0
1
0
0
1
2
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
4
0
1
0
0
0
2
0
0
2
0
0
1
0
1
3
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
3
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
5
1
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
4
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
2
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
1
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
3
0
1
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
5
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
2
0
0
0
0
3
0
0
1
0
2
1
1
0
0
2
0
0
0
2
2
0
0
0
0
0
0
2
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
2
2
1
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
1
7
0
0
0
0
0
1
2
4
0
1
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
3
1
0
2
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
1
0
0
0
1
7
0
2
0
0
0
0
1
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
1
1
0
0
2
0
0
0
0
1
0
0
1
0
5
0
0
2
0
0
1
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
2
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
1
2
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
2
0
0
0
3
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
1
2
5
2
1
2
1
2
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
3
0
0
1
2
0
0
1
1
0
0
2
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
2
1
0
0
4
0
0
0
0
1
2
1
1
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
2
1
7
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
3
0
0
0
0
0
2
0
0
0
1
0
10
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
3
0
0
0
0
1
0
0
0
1
0
0
4
0
1
0
0
0
0
4
0
0
3
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
2
0
2
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
2
0
2
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
1
0
0
0
0
0
1
0
5
0
0
0
0
0
0
0
2
0
0
1
0
0
3
0
1
0
0
0
0
1
1
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
2
0
2
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
1
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
4
0
1
0
0
0
6
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
1
0
2
5
2
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
2
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
1
0
1
0
0
2
1
0
1
0
2
0
0
0
0
0
0
1
0
0
8
2
2
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
3
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
3
3
0
0
0
0
0
2
0
0
0
3
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
1
1
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
3
0
0
0
5
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
2
1
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
1
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
1
0
0
1
1
0
2
0
2
0
0
0
0
2
0
0
0
0
1
1
2
0
0
0
0
0
1
0
0
1
0
0
6
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
3
1
0
0
3
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
1
0
2
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
6
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
3
2
0
0
0
2
0
0
0
0
0
0
0
3
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
2
0
2
2
0
0
0
2
1
0
0
2
1
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
3
2
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
1
0
0
0
0
1
1
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
3
0
0
0
0
1
0
0
4
2
0
0
0
2
0
0
0
0
0
0
5
0
0
1
0
0
0
1
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
3
0
0
2
1
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
1
0
0
2
2
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
3
0
0
0
0
1
3
0
0
0
0
1
0
0
1
0
2
3
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
2
1
2
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
3
1
0
1
4
0
0
0
3
0
3
3
0
0
0
0
2
0
7
0
0
1
0
0
0
0
0
0
0
0
0
0
2
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
1
0
0
2
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
3
0
0
0
3
0
0
0
0
0
2
0
1
0
0
0
3
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
2
0
1
1
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
7
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
2
1
1
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
2
0
2
1
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
1
0
0
0
0
6
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
3
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
1
1
0
0
0
2
0
2
0
0
1
0
0
0
0
3
0
0
0
0
0
2
0
2
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
1
0
0
1
0
2
1
0
3
0
0
1
0
0
0
2
3
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
10
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
2
1
0
2
3
0
2
0
2
0
0
1
3
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
4
0
0
0
0
0
0
2
0
1
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
1
0
1
0
3
0
3
0
0
0
0
0
0
2
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
3
0
0
5
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
2
3
1
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
2
1
1
0
2
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
2
0
2
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
1
0
2
0
2
0
1
0
0
0
0
0
1
3
0
0
0
1
2
0
0
0
1
1
0
1
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
3
0
4
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
2
0
0
1
0
0
0
3
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
2
4
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
2
5
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
2
0
0
2
0
0
0
2
2
1
0
2
2
0
0
0
0
3
0
1
3
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
3
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
1
0
0
0
0
4
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
3
0
0
0
1
0
0
0
2
2
0
0
1
0
0
4
0
1
0
0
0
2
0
0
0
0
3
0
0
0
0
0
6
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
2
2
0
3
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
7
0
2
0
2
0
0
0
0
0
0
0
0
4
0
0
1
2
0
1
0
0
1
0
1
0
1
0
0
0
3
0
0
0
2
0
0
0
0
4
0
4
0
2
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
3
0
0
0
0
1
0
0
0
0
1
1
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
2
0
2
1
0
0
1
0
0
2
1
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
2
0
1
2
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
3
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
3
1
0
2
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
1
2
1
0
0
1
0
0
0
0
0
0
1
2
0
0
2
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
5
0
2
1
0
0
0
0
7
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
3
0
1
2
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
3
0
0
2
0
0
0
0
0
4
0
0
0
0
0
0
3
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
2
1
0
1
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
2
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
4
0
0
1
0
2
0
0
0
2
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
3
0
0
0
0
0
0
0
0
2
0
0
1
0
4
0
1
1
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
2
1
2
2
0
0
0
0
0
4
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
6
0
0
0
0
0
0
0
1
0
1
0
0
0
2
5
0
0
4
0
0
2
0
6
0
0
3
0
0
0
1
0
0
3
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
3
0
2
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
1
0
1
0
2
1
0
0
0
0
5
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
1
0
2
0
0
0
1
1
2
0
0
0
0
2
0
2
0
0
0
0
0
0
8
3
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
1
0
0
1
0
0
0
0
1
0
0
0
2
0
0
2
2
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
1
1
1
0
1
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
4
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
2
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
1
1
0
0
1
0
1
0
0
0
3
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
4
1
2
0
1
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
3
0
0
2
0
0
1
0
0
0
0
0
6
0
0
6
1
0
1
0
0
0
0
0
0
4
1
0
1
1
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
1
0
0
0
1
0
3
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
5
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
6
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
1
0
0
2
4
1
2
0
0
3
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
5
0
0
0
0
0
2
1
0
0
2
0
2
1
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
3
0
1
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
3
0
0
0
0
0
0
0
0
1
0
2
0
2
1
0
0
0
1
0
1
2
2
0
1
0
0
3
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
2
1
2
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
3
0
0
0
0
1
0
0
0
0
1
1
2
0
1
1
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
3
1
5
0
0
0
0
1
0
0
0
0
0
1
0
2
1
1
0
2
0
0
0
0
1
0
1
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
3
0
0
1
7
0
0
1
3
0
0
0
1
0
3
0
6
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
2
1
0
0
1
0
2
0
0
0
1
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
3
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
2
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
1
2
2
0
0
0
2
0
0
0
0
0
0
2
2
0
2
0
2
1
0
2
2
2
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
2
0
0
0
1
0
1
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
19
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
3
0
2
0
0
0
0
2
0
1
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
3
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
2
1
0
0
1
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
3
0
0
1
2
0
1
2
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
1
0
0
0
3
2
0
0
0
1
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
1
0
2
0
1
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
2
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
2
0
0
0
0
0
1
2
0
1
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
2
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
1
1
1
0
0
0
0
1
1
3
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
3
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
2
1
2
0
0
0
0
1
1
0
0
0
0
0
4
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
2
0
1
0
0
0
0
2
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
1
0
0
1
0
0
1
0
0
0
0
0
2
0
0
1
1
0
1
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
2
0
0
0
0
7
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
1
0
1
0
0
0
1
4
0
0
0
0
2
2
0
2
1
0
2
0
1
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
4
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
3
2
2
0
0
0
0
1
1
1
0
2
2
0
1
1
0
0
0
0
3
0
0
0
0
2
1
0
0
1
0
3
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
5
0
1
0
0
0
2
0
0
0
1
0
0
0
1
3
2
0
0
0
0
3
1
0
0
1
0
1
0
0
0
0
4
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
3
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
7
0
0
0
0
2
1
0
3
0
0
0
2
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
2
0
0
0
3
2
0
0
0
0
0
1
0
3
2
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
7
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
3
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
3
0
2
0
0
2
0
0
0
0
7
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
2
0
0
0
1
7
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
3
0
0
1
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
2
2
1
1
0
2
0
0
0
3
0
0
0
0
0
0
5
0
2
0
1
2
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
2
0
1
0
0
5
0
0
0
0
0
0
0
3
0
0
0
0
2
2
0
0
0
2
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
1
1
2
0
0
0
2
2
0
1
0
0
0
0
0
1
1
0
0
0
0
0
2
2
0
0
0
2
9
2
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
3
0
2
0
0
2
0
0
1
0
0
3
2
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
2
1
0
0
2
3
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
2
1
0
0
0
1
0
2
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
3
0
0
0
0
0
0
2
2
0
1
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
5
1
0
3
1
2
0
0
1
1
1
1
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
4
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
6
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
1
2
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
3
0
0
0
0
0
0
0
0
1
0
0
2
2
2
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
9
0
0
1
0
0
0
2
0
0
0
3
0
0
1
0
0
4
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
1
0
1
0
0
0
0
0
0
1
2
1
2
0
0
2
0
0
1
1
1
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
4
0
0
0
0
2
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
2
1
2
1
1
2
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
1
1
2
0
0
2
1
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
2
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
3
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
2
0
3
3
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
1
0
1
0
1
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
3
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
4
0
0
2
0
5
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
7
0
0
0
0
0
0
0
1
0
2
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
5
0
0
2
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
13
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
3
0
0
1
0
0
0
0
0
2
0
0
2
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
5
1
3
0
0
0
0
0
0
0
0
1
4
0
0
3
1
0
0
2
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
2
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
1
0
0
1
0
0
2
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
3
0
0
3
1
1
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
2
1
1
0
1
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
1
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
1
3
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
3
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
1
0
0
1
1
0
2
0
0
1
0
0
1
0
2
0
0
2
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
3
2
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
4
0
3
0
1
0
0
0
0
0
2
2
2
0
0
0
1
0
1
6
0
0
0
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
2
1
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
2
1
1
0
0
0
0
0
0
1
0
0
2
0
4
2
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
3
1
0
1
0
0
1
0
2
2
0
0
0
0
0
0
0
2
2
0
4
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
9
0
0
2
0
0
0
1
0
0
0
2
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
2
1
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
2
1
1
0
0
1
0
2
2
0
1
0
0
1
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
1
0
1
0
1
0
0
0
0
0
0
1
0
1
0
1
0
2
3
0
0
2
4
0
0
0
0
0
0
0
0
0
1
0
0
0
1
3
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
3
0
1
0
0
0
0
0
0
0
0
2
0
3
0
0
3
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
1
2
0
2
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
2
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
4
0
0
2
0
0
0
2
1
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
4
0
1
3
0
0
2
0
0
0
0
0
1
2
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
1
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
1
2
0
3
0
0
0
0
0
1
0
0
0
2
2
0
2
0
0
0
0
0
2
0
0
0
2
0
0
4
2
0
0
0
8
0
1
4
0
0
0
0
0
0
0
2
0
0
0
0
3
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
2
0
3
0
4
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
2
0
0
0
8
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
2
0
2
1
0
0
0
2
0
0
1
1
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
2
2
0
0
0
0
3
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
1
1
2
0
0
0
0
3
2
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
6
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
1
0
0
0
4
0
0
0
0
2
0
3
0
0
0
0
0
0
0
2
0
0
0
0
4
0
0
0
4
0
1
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
2
2
0
0
2
2
0
0
1
0
0
0
1
0
3
1
2
1
0
0
0
1
0
0
1
1
2
0
0
0
0
0
0
3
0
2
0
0
1
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
2
0
0
0
0
0
0
2
2
1
0
1
0
0
5
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
1
1
0
0
2
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
3
1
0
0
0
0
2
1
0
0
0
0
2
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
2
0
0
2
0
0
2
0
0
2
1
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
1
1
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
1
0
2
2
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
1
0
0
0
0
1
2
0
0
0
1
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
3
0
0
0
1
0
0
0
1
0
0
6
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
4
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
2
4
1
0
0
0
0
4
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
2
4
0
0
0
1
1
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
3
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
5
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
4
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
2
0
0
3
0
0
0
0
0
0
0
1
0
3
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
1
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
2
0
0
1
0
2
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
4
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
5
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
4
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
8
0
1
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
4
2
0
0
0
1
1
0
1
2
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
5
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
1
0
0
0
0
0
2
2
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
3
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
4
0
0
0
0
2
2
0
0
0
0
0
1
2
0
0
0
0
3
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
1
3
0
0
4
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
3
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
4
0
0
0
4
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
5
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
2
0
1
0
0
1
0
2
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
4
0
0
0
1
5
0
2
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
1
0
0
0
1
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
5
0
0
0
0
0
0
0
4
0
0
0
1
0
1
0
1
3
0
0
0
0
0
0
1
0
0
1
0
3
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
3
3
0
1
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
2
3
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
3
0
0
0
1
1
0
0
2
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
6
1
4
0
0
1
0
0
0
13
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
2
0
0
3
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
10
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
7
2
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
3
0
1
1
0
0
2
2
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
3
3
2
0
2
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
3
1
0
0
0
0
0
2
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
3
5
0
2
0
2
0
0
0
0
2
0
0
2
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
2
0
0
2
2
0
0
0
2
0
1
0
0
2
0
0
1
1
0
0
0
2
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
3
2
1
0
2
1
0
1
0
0
0
0
0
0
2
0
0
0
5
0
0
0
5
0
0
3
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
3
0
1
0
1
0
0
0
0
0
0
0
10
2
0
0
0
0
0
2
0
2
0
3
0
0
0
0
1
0
1
0
1
3
0
0
0
0
0
4
0
1
2
0
0
0
2
0
0
0
0
1
2
0
0
2
0
1
0
0
1
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
3
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
2
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
2
0
1
1
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
6
0
0
0
0
2
0
1
4
0
0
0
1
0
0
1
0
0
3
0
0
0
1
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
3
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
1
0
0
0
0
1
2
0
0
0
1
2
0
0
0
0
7
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
2
0
3
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
3
0
1
2
0
0
2
1
0
0
2
0
0
0
3
0
0
0
0
2
0
0
1
0
1
1
3
0
0
0
0
0
0
0
0
0
1
1
0
10
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
3
1
1
0
0
0
0
0
9
0
0
1
0
0
0
1
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
2
0
0
1
0
3
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
15
3
2
1
0
3
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
3
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
2
5
0
0
0
2
0
1
0
0
0
0
0
1
1
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
3
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
6
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
2
1
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
1
0
2
0
3
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
1
0
0
1
3
0
1
1
0
0
0
0
0
1
1
0
3
0
0
0
0
4
0
4
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
3
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
5
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
2
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
3
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
1
0
0
3
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
3
1
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
1
0
1
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
2
0
0
0
1
2
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
2
0
0
1
1
0
2
2
0
0
0
0
0
1
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
1
0
1
0
0
2
0
0
1
0
0
2
4
0
2
2
0
0
0
0
3
0
0
0
0
0
1
2
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
4
0
1
0
4
0
0
0
2
0
2
0
1
0
0
0
3
9
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
4
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
2
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
5
0
0
2
0
0
0
2
0
1
2
0
2
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
4
0
1
2
0
0
0
0
0
2
2
0
1
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
1
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
1
1
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
2
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
6
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
1
0
0
1
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
2
1
2
2
0
0
2
0
1
0
0
0
2
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
4
0
0
0
2
0
4
2
0
0
2
0
1
0
0
0
0
0
0
0
1
1
3
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
5
0
0
0
0
0
0
2
0
0
5
0
0
0
0
0
2
2
1
0
0
0
0
2
3
0
0
0
0
0
0
0
0
2
0
2
0
2
1
0
0
0
0
0
1
3
0
0
0
0
0
0
0
2
0
1
2
0
0
2
0
1
1
0
0
0
0
2
0
0
0
0
1
1
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
2
0
0
0
4
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
2
0
0
1
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
1
0
2
0
0
0
1
0
1
0
3
0
1
2
0
0
0
0
1
0
0
0
5
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
5
0
1
0
0
2
0
0
0
0
6
0
0
1
1
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
7
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
2
0
2
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
2
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
2
1
2
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
2
4
2
0
0
0
0
3
2
0
0
0
0
0
1
0
1
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
1
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
2
3
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
2
1
1
0
0
0
0
2
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
1
0
0
3
1
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
1
0
0
1
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
3
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
1
1
0
2
1
0
0
0
1
2
0
0
0
0
0
1
0
0
0
1
2
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
2
3
0
0
0
2
3
1
0
0
0
0
0
0
0
0
0
0
1
18
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
3
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
6
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
2
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
7
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
2
2
0
2
0
0
2
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
3
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
2
0
0
2
0
1
0
0
0
5
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
5
0
0
0
3
2
4
0
0
0
0
0
0
0
3
0
1
0
0
2
0
2
1
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
2
0
0
0
1
0
0
0
3
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
1
1
0
3
0
0
0
1
0
0
0
0
1
1
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
4
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
3
1
0
1
0
0
1
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
9
3
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
2
1
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
2
1
0
1
0
0
1
0
0
1
0
0
1
0
1
3
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
5
0
0
0
0
1
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
4
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
1
2
0
0
0
2
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
2
0
1
1
0
0
2
0
1
0
0
3
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
2
0
0
0
0
1
0
0
0
2
0
0
3
0
1
0
0
0
2
0
0
0
0
0
2
1
0
0
1
0
2
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
2
0
0
0
1
1
0
0
1
0
0
1
0
2
0
0
0
4
0
1
0
0
0
0
1
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
1
0
1
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
8
0
0
0
0
0
1
0
1
0
0
0
2
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
2
0
2
0
1
0
2
0
0
0
0
0
0
0
3
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
2
0
0
0
0
0
0
0
1
1
1
0
0
2
0
0
1
2
0
3
0
0
0
2
0
0
0
0
0
2
1
1
1
3
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
1
0
0
2
0
0
0
1
0
0
0
0
4
0
0
0
1
0
2
0
0
0
0
0
1
0
0
2
0
0
2
0
0
1
0
2
0
0
0
7
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
5
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
2
0
1
0
0
0
1
0
0
2
2
2
0
0
0
0
2
0
0
0
1
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
2
3
0
0
3
0
0
0
0
2
0
2
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
3
0
0
3
0
0
0
2
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
1
0
1
0
0
0
0
0
0
4
4
1
0
4
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
1
0
0
0
0
1
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
1
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
2
0
5
0
0
2
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
4
0
0
0
1
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
1
2
0
0
0
1
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
1
0
0
0
4
0
0
0
0
0
0
4
2
0
1
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
7
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
3
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
2
6
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
1
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
3
0
0
2
1
0
0
2
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
2
0
0
0
1
0
1
1
1
0
0
1
0
0
0
0
3
0
0
2
0
0
0
1
1
0
0
1
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
1
0
1
0
0
0
0
2
1
0
0
0
3
0
2
2
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
2
0
1
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
4
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
4
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
2
0
0
0
2
0
0
0
2
1
0
1
0
0
2
10
0
0
0
1
0
1
2
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
1
2
0
0
1
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
1
0
0
1
1
0
1
0
1
0
2
0
1
1
0
0
0
0
0
0
1
3
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
1
2
0
0
1
0
1
2
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
2
1
0
0
0
1
0
0
0
0
2
0
0
0
3
0
2
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
3
3
6
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
1
0
2
0
2
1
0
0
0
0
0
0
0
12
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
2
1
2
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
2
2
3
0
4
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
5
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
1
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
1
1
2
5
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
1
0
0
2
0
3
1
0
0
0
0
1
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
2
0
4
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
2
0
0
1
0
1
0
0
0
0
0
0
3
0
1
0
0
0
1
0
0
3
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
1
0
8
0
1
0
1
1
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
1
0
2
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
3
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
2
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
2
1
0
0
4
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
2
2
0
0
0
0
0
0
2
0
0
0
3
0
1
2
2
0
0
0
0
0
0
0
1
2
0
0
0
2
3
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
3
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
5
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
1
1
0
0
0
5
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
2
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
2
0
0
1
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
2
1
0
1
0
2
1
0
0
0
0
0
0
0
2
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
1
0
0
0
5
0
0
0
0
1
0
0
1
2
0
0
2
1
0
1
0
0
0
1
3
2
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
3
0
0
0
3
0
0
0
0
0
1
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
5
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
3
2
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
3
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
2
0
1
0
0
0
0
1
2
0
1
0
0
0
2
0
2
1
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
5
1
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
2
0
1
0
1
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
2
1
2
0
0
0
0
0
0
0
0
10
2
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
2
0
2
0
1
1
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
2
0
0
0
4
1
0
0
1
2
4
6
0
0
0
1
0
0
0
1
0
0
0
2
1
0
0
1
1
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
4
0
1
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
1
1
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
1
0
0
1
0
2
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
3
2
2
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
2
2
0
2
0
0
1
0
0
0
0
0
0
2
2
0
2
0
0
0
0
3
0
0
0
0
0
0
1
0
1
0
2
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
8
1
0
1
0
0
0
2
1
0
0
4
0
0
1
0
4
0
0
0
0
0
0
0
4
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
6
1
0
0
0
0
0
4
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
1
0
11
3
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
3
0
0
3
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
3
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
3
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
1
0
2
0
0
2
0
0
0
0
2
0
1
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
1
0
0
0
0
2
0
0
0
0
0
0
1
0
2
1
0
2
1
0
0
0
0
0
2
0
0
2
3
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
1
3
0
0
0
0
0
0
0
1
1
0
1
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
1
0
0
0
0
2
0
4
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
1
2
3
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
3
1
0
0
0
0
1
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
4
2
0
2
0
1
0
0
0
0
0
3
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
3
0
3
0
0
0
0
0
0
3
0
0
0
0
2
3
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
1
2
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
1
0
0
2
3
0
0
0
0
0
5
0
0
0
3
0
0
1
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
2
0
0
2
0
0
0
3
0
0
2
1
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
2
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
2
3
1
0
1
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
2
1
1
0
0
3
0
0
1
0
4
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
2
3
0
0
2
2
0
0
2
0
2
4
3
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
2
0
0
0
2
2
0
7
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
3
0
0
0
0
1
1
0
1
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
5
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
3
0
0
1
2
0
0
1
0
0
0
1
1
1
0
0
0
1
0
0
2
0
0
2
1
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
3
1
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
2
0
0
1
0
0
2
0
0
0
0
3
0
0
1
0
0
0
0
1
0
0
1
1
2
2
0
0
0
2
0
2
0
2
0
0
0
0
0
1
1
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
2
1
0
1
0
1
0
0
0
0
0
0
1
0
0
5
0
0
0
3
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
4
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
3
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
1
8
0
1
0
0
0
0
2
4
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
1
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
2
0
0
0
1
0
1
0
2
1
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
10
0
1
1
1
1
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
3
0
0
2
0
0
0
0
0
0
5
0
0
0
2
2
1
0
1
1
0
2
1
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
5
0
0
0
2
0
0
0
0
0
0
1
2
0
1
2
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
1
1
2
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
1
0
0
1
0
1
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
16
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
4
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
3
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
1
0
0
2
0
0
0
0
2
0
3
0
0
0
2
0
2
0
0
2
0
1
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
2
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
5
1
0
0
1
0
0
2
0
0
0
0
1
0
2
0
0
0
0
1
1
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
2
0
0
0
1
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
2
4
0
0
0
2
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
1
0
1
2
0
0
2
0
0
3
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
4
0
0
2
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
2
3
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
2
2
0
0
0
0
1
0
0
1
0
1
1
0
0
0
1
1
0
1
0
0
2
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
7
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
9
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
3
0
0
2
0
0
4
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
1
0
1
0
3
0
0
0
0
0
1
0
0
0
1
0
0
2
1
1
0
0
1
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
2
1
0
2
0
0
2
0
0
0
0
0
1
2
0
0
0
0
1
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
2
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
3
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
5
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
2
1
3
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
1
0
2
0
2
0
2
0
0
0
0
0
3
0
0
0
3
1
0
2
0
0
0
0
1
0
3
0
0
0
0
0
1
2
2
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
3
0
3
0
0
0
1
0
0
0
1
4
0
1
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
1
2
0
0
0
0
0
1
0
1
0
0
0
0
3
0
0
0
0
0
0
2
0
3
3
0
0
0
2
0
0
0
0
3
2
3
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
2
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
3
0
0
0
5
3
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
1
1
0
1
0
0
2
0
2
0
0
0
4
0
0
1
0
0
0
1
0
1
0
0
0
0
0
2
2
2
0
1
0
0
0
0
1
0
1
3
2
2
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
4
0
0
0
1
0
0
0
1
2
0
7
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
3
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
1
0
1
0
0
1
0
2
0
0
0
0
0
0
0
1
2
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
7
0
1
0
1
0
0
3
0
0
0
1
0
0
4
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
1
0
1
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
1
6
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
2
0
2
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
2
0
0
2
0
0
0
1
1
0
0
0
1
0
0
1
0
1
0
1
0
0
1
0
2
0
0
0
3
2
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
3
0
0
2
0
0
3
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
1
5
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
3
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
12
1
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
2
0
0
0
2
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
3
0
2
0
2
1
0
2
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
3
0
0
2
0
0
0
3
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
2
0
0
1
0
0
0
0
2
0
1
0
0
0
0
2
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
3
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
3
0
0
1
0
0
2
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
2
0
2
2
0
0
2
0
0
2
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
1
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
3
0
0
0
0
2
2
0
0
0
3
0
2
0
1
0
1
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
4
2
0
0
0
0
0
0
2
0
2
0
0
2
0
2
0
0
0
0
1
1
0
1
0
1
0
0
2
0
0
0
0
0
1
0
0
2
2
0
2
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
2
0
0
0
6
2
0
0
0
0
3
0
0
0
0
2
0
0
0
0
3
0
2
0
1
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
3
0
1
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
1
0
1
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
1
0
4
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
1
0
0
2
1
0
0
0
0
0
0
0
2
4
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
2
0
3
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
1
0
4
0
0
0
0
1
1
0
0
0
0
0
2
1
1
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
1
0
0
0
2
0
0
0
0
1
0
0
0
2
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
2
1
1
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
1
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
2
0
0
0
0
0
0
1
3
0
0
0
0
0
0
1
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
2
0
0
0
0
2
8
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
2
1
0
0
0
2
0
2
0
0
0
0
2
0
0
0
3
2
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
7
0
0
0
2
1
0
0
0
0
3
0
0
0
0
0
2
1
3
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
2
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
3
0
3
2
5
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
10
2
1
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
1
0
1
0
0
2
2
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
15
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
1
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
1
0
2
2
0
0
2
0
0
0
0
0
1
0
0
3
0
0
0
0
4
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
1
0
0
0
0
2
2
0
0
0
0
1
3
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
2
0
2
0
2
0
0
3
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
2
0
0
2
0
0
1
0
2
0
3
0
0
2
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
2
0
0
0
0
3
0
0
0
1
0
0
2
1
0
0
0
0
1
0
1
0
0
1
0
2
0
2
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
3
0
2
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
2
0
0
0
1
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
1
12
0
0
0
0
0
1
0
2
0
2
0
0
0
2
1
0
1
0
1
2
3
0
0
2
0
1
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
3
0
5
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
7
0
2
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
2
0
1
1
0
0
1
1
0
0
0
0
2
0
3
0
0
0
0
2
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
1
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
3
0
0
0
0
2
4
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
2
0
0
2
0
0
0
3
0
0
5
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
5
0
1
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
1
0
1
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
2
0
1
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
1
0
0
2
2
0
0
0
0
0
0
0
0
3
0
0
2
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
3
0
0
0
2
0
0
3
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
6
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
3
0
0
0
0
2
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
2
1
0
0
0
1
0
0
0
0
2
0
0
1
3
0
7
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
2
1
0
5
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
1
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
1
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
8
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
1
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
1
0
0
1
2
6
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
4
0
0
0
0
0
0
0
4
0
0
0
0
5
0
2
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
1
1
0
0
1
1
0
1
3
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
2
2
2
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
1
0
2
2
0
0
0
0
1
0
0
2
0
3
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
2
0
1
2
0
1
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
2
2
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
8
0
0
2
0
1
0
0
3
0
0
1
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
3
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
2
1
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
2
0
2
1
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
8
0
0
0
2
0
1
0
0
0
2
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
4
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
3
0
1
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
2
2
0
0
0
0
1
0
1
2
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
1
0
5
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
8
0
0
2
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
3
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
2
0
3
0
0
0
0
0
1
0
2
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
2
2
0
0
1
0
0
2
0
0
0
1
0
1
3
0
1
0
0
0
2
0
0
0
2
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
4
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
5
0
2
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
1
0
4
0
0
0
0
8
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
2
0
0
1
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
1
0
0
0
2
1
1
0
1
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
2
0
0
0
0
0
2
0
1
0
1
3
1
5
0
0
0
0
0
0
1
1
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
1
0
0
0
0
0
1
5
0
0
0
0
1
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
1
2
0
0
0
0
2
2
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
2
0
0
0
1
0
2
0
1
4
0
0
1
0
0
0
2
0
0
0
1
0
2
0
1
0
0
0
0
1
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
1
0
11
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
9
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
5
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
1
2
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
2
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
4
0
0
0
1
0
1
0
0
4
1
0
4
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
3
0
2
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
3
0
3
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
2
1
0
1
0
0
0
0
0
1
0
2
0
0
8
0
0
1
0
1
0
4
1
0
0
4
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
2
2
1
2
0
0
0
1
0
3
2
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
1
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
2
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
3
2
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
2
1
2
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
1
2
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
2
2
3
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
3
1
0
0
2
0
1
0
2
0
3
0
3
0
0
1
0
0
0
1
0
2
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
5
0
2
0
0
2
0
0
0
0
0
2
2
1
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
2
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
3
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
1
1
0
2
1
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
1
0
0
1
3
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
1
0
2
0
2
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
9
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
3
0
0
0
1
2
0
0
2
0
2
0
3
0
2
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
1
3
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
5
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
1
0
1
0
0
2
5
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
5
2
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
1
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
4
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
4
1
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
1
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
2
0
0
0
0
2
0
0
0
2
0
3
2
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
1
1
0
0
0
0
1
1
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
3
1
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
1
0
0
0
0
3
0
0
0
1
1
2
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
4
2
0
2
0
0
1
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
2
2
1
3
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
2
0
0
0
2
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
5
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
3
0
0
0
1
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
1
0
2
2
0
2
6
0
0
0
0
0
0
2
4
0
2
0
0
0
1
1
1
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
3
3
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
2
0
0
0
0
2
0
2
0
0
1
1
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
2
2
0
0
0
0
0
0
0
2
2
0
1
3
0
0
1
0
0
0
0
0
2
2
0
2
0
0
0
1
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
3
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
2
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
1
3
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
1
0
1
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
19
0
0
0
0
0
0
0
2
0
0
0
0
0
5
0
0
2
0
0
0
1
0
1
0
0
0
1
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
1
4
1
1
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
3
0
0
0
2
0
0
0
0
1
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
6
0
1
0
0
3
0
6
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
1
1
0
0
0
0
3
0
2
0
0
0
0
2
0
0
1
1
0
1
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
2
1
0
3
0
0
0
1
0
0
0
0
1
2
0
0
0
0
2
1
0
0
0
0
1
0
0
2
4
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
1
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
3
2
1
0
0
0
0
0
0
0
2
1
3
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
2
0
0
1
0
0
2
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
3
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
2
1
2
0
1
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
3
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
2
2
0
0
0
0
0
0
0
2
0
1
2
6
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
2
0
0
3
0
0
0
0
0
1
1
2
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
3
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
1
0
0
2
0
0
1
3
1
0
0
0
0
2
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
6
2
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
5
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
1
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
1
0
0
0
1
2
0
3
0
0
0
0
0
4
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
3
2
0
0
7
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
2
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
1
1
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
3
0
1
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
3
5
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
4
1
0
2
3
2
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
4
1
0
0
0
0
0
0
2
0
2
2
1
2
0
1
2
0
0
0
0
0
0
0
1
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
2
0
0
2
6
0
0
2
0
0
0
1
0
0
0
2
0
2
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
2
1
0
0
0
0
0
0
0
2
1
0
0
4
1
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
5
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
10
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
3
0
2
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
1
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
3
2
0
0
0
0
1
0
1
0
0
2
0
0
1
0
0
0
1
1
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
3
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
1
0
0
0
2
1
0
1
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
2
0
0
0
0
2
0
0
2
1
4
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
1
2
0
0
2
0
0
1
2
2
0
1
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
2
0
0
3
0
0
2
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
2
3
2
1
0
0
1
1
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
1
1
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
1
0
2
0
1
2
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
2
1
0
8
0
3
0
3
0
0
0
0
0
4
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
1
2
0
0
2
0
0
1
0
0
0
0
0
3
0
1
0
4
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
2
0
3
0
0
0
0
1
0
2
1
1
0
0
1
1
0
1
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
7
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
2
0
0
0
1
0
0
0
0
4
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
1
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
2
1
0
0
0
2
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
4
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
1
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
2
0
0
0
0
0
0
3
0
3
0
1
1
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
7
2
0
1
0
0
0
1
0
0
1
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
3
0
0
0
0
0
1
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
4
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
1
1
0
0
0
1
0
4
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
1
0
0
0
0
0
0
2
0
0
3
1
0
0
0
2
1
0
0
0
0
3
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
2
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
3
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
1
2
0
0
0
1
0
0
0
1
0
0
2
0
2
1
0
1
0
0
4
0
2
0
0
0
2
1
0
2
0
0
1
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
5
0
2
0
0
0
0
1
0
0
0
3
2
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
6
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
3
0
0
0
0
0
0
4
0
0
0
2
0
0
0
1
1
2
5
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
4
0
2
1
0
0
3
0
0
0
0
2
0
0
0
2
0
1
1
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
2
2
2
1
0
0
2
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
2
0
1
0
0
0
1
4
0
0
0
1
0
0
0
0
0
2
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
10
1
0
0
0
3
0
0
2
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
4
0
2
0
0
0
0
0
0
1
0
0
0
0
2
4
0
1
2
0
2
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
2
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
1
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
3
0
0
0
0
0
1
0
0
1
0
0
0
2
0
2
0
2
0
1
0
0
0
0
0
1
0
0
4
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
1
1
2
0
0
2
0
0
0
0
0
4
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
2
1
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
1
2
2
0
1
1
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
3
0
0
1
0
0
0
0
0
7
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
1
0
0
0
0
2
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
2
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
3
1
0
0
0
0
2
2
0
1
0
0
0
2
0
0
0
0
5
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
4
1
0
0
2
2
0
0
0
0
9
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
1
1
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
2
3
0
0
1
0
0
0
0
0
2
0
0
0
0
0
8
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
2
0
0
0
2
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
1
2
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
1
0
0
0
2
0
0
0
0
1
1
0
1
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
3
0
0
3
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
1
0
3
1
1
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
2
0
0
1
0
3
1
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
2
1
0
0
4
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
2
0
0
2
0
1
0
1
2
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
3
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
3
0
0
0
0
0
0
2
1
2
0
1
0
0
4
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
1
0
1
0
0
0
1
5
0
0
0
0
1
0
1
0
0
0
3
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
1
1
2
0
0
0
0
0
0
2
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
1
2
0
2
1
0
0
0
0
1
0
1
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
2
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
2
2
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
4
0
2
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
2
2
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
2
0
1
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
1
0
0
2
0
0
1
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
1
0
2
2
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
1
0
0
0
1
0
1
1
3
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
1
0
0
0
1
1
0
0
0
0
2
0
1
2
1
2
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
1
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
4
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
4
0
0
0
0
0
0
1
0
0
2
1
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
1
3
0
0
0
0
0
0
2
2
1
1
0
0
0
0
1
0
0
0
0
0
0
0
9
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
6
0
1
1
1
2
0
0
0
5
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
1
1
0
0
2
1
2
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
2
4
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
4
1
0
1
1
1
0
1
0
0
0
0
0
0
0
11
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
2
2
8
0
0
0
0
1
1
5
0
0
2
0
0
2
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
3
1
0
1
0
1
0
2
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
5
0
2
0
2
0
0
2
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
1
0
0
1
0
0
0
0
2
0
1
0
1
0
0
1
0
0
0
0
2
0
0
2
1
4
1
0
0
0
0
0
5
1
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
3
0
0
0
1
0
2
0
5
1
0
0
1
0
0
1
0
0
0
0
0
0
2
3
0
0
3
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
2
1
0
0
0
1
0
2
0
1
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
3
0
2
2
0
0
0
0
0
2
2
0
0
1
2
0
0
1
2
0
0
2
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
4
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
5
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
1
0
2
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
2
0
1
0
2
0
0
0
0
0
0
10
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
1
0
0
0
1
2
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
1
0
1
0
0
1
0
0
0
0
0
0
0
2
1
1
0
3
0
0
5
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
2
0
0
0
2
0
5
0
0
0
0
0
0
1
0
0
1
0
0
2
2
12
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
5
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
1
2
0
1
0
0
2
2
1
1
0
0
0
0
0
1
3
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
3
0
0
0
0
4
0
0
0
2
1
0
0
3
5
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
1
0
1
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
2
2
0
0
1
0
0
0
0
0
0
7
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
3
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
1
2
0
2
2
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
2
2
0
0
0
1
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
1
0
0
0
0
2
3
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
2
0
2
1
1
2
1
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
3
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
1
0
1
0
0
1
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
6
1
0
0
2
0
0
1
0
0
0
0
1
0
4
1
0
1
2
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
2
1
1
0
0
2
4
0
0
0
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
3
0
2
0
0
0
0
0
0
0
2
0
1
0
0
2
1
2
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
2
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
1
0
0
1
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
2
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
3
0
7
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
3
0
0
0
0
0
0
0
2
0
0
2
3
1
0
1
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
2
1
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
1
0
0
0
0
0
2
1
0
0
0
0
0
1
0
3
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
1
0
0
0
0
0
1
2
0
0
3
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
1
2
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
3
0
0
0
0
0
0
1
3
2
0
0
0
0
1
2
0
1
0
0
2
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
4
3
1
1
0
0
0
0
0
0
0
0
0
0
1
1
6
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
1
1
0
0
0
4
0
0
5
0
0
0
0
2
1
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
5
0
0
0
0
0
0
5
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
4
1
0
0
0
0
1
0
0
1
0
0
0
7
0
0
2
3
2
1
0
2
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
2
2
0
0
0
1
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
1
0
2
0
0
1
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
2
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
2
0
0
2
0
1
0
0
2
0
0
0
3
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
1
2
0
0
1
2
1
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
2
0
3
0
1
0
0
1
0
0
2
0
0
0
0
0
0
3
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
4
0
1
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
1
3
0
0
2
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
3
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
1
1
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
2
0
0
0
0
1
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
1
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
2
2
0
0
1
0
0
0
0
1
0
0
0
2
0
0
2
2
0
0
0
0
0
2
0
0
1
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
1
3
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
2
0
0
0
0
0
5
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
2
1
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
1
2
1
0
1
0
0
1
0
1
1
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
1
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
4
1
1
0
0
0
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
2
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
3
0
2
0
0
2
0
0
0
0
0
1
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
2
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
1
2
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
1
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
1
2
0
0
0
0
0
0
0
0
0
6
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
1
2
0
1
0
0
0
3
0
0
0
0
0
0
0
0
7
1
0
0
0
0
0
0
0
0
3
1
0
0
3
0
0
0
0
0
0
3
0
0
0
0
0
2
0
2
0
2
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
2
0
1
0
3
1
2
0
5
0
0
0
0
0
2
2
2
0
0
0
2
0
2
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
7
0
0
0
0
0
0
0
0
0
0
2
4
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
4
0
2
1
4
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
2
0
1
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
6
0
0
2
0
1
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
1
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
4
2
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
1
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
2
0
1
0
0
1
0
0
2
2
0
0
0
1
0
0
0
1
2
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
3
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
5
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
2
0
1
0
0
2
0
0
3
0
2
1
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
10
1
0
1
0
0
0
2
0
2
5
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
3
2
0
1
2
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
3
0
0
5
0
0
0
2
0
5
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
9
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
3
2
0
0
1
2
1
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
6
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
1
0
1
0
1
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
1
2
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
2
0
0
2
1
2
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
11
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
2
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
2
0
2
0
0
0
1
2
0
0
0
2
0
1
0
1
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
1
2
0
0
0
0
0
1
0
0
0
0
0
3
0
3
0
0
0
0
0
1
0
2
2
2
0
3
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
1
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
9
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
6
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
1
0
0
1
0
0
7
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
4
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
4
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
4
1
0
0
2
0
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
2
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
4
3
0
1
0
3
0
0
0
1
0
2
0
4
0
0
1
0
1
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
1
0
0
10
1
4
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
1
2
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
2
0
0
2
1
2
0
0
0
3
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
5
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
3
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
5
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
5
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
2
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
2
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
1
0
0
0
0
0
6
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
6
1
0
1
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
2
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
1
3
2
1
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
1
2
1
1
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
1
1
0
2
0
2
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
2
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
5
0
0
2
0
0
0
0
0
0
0
2
0
0
1
2
2
8
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
1
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
5
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
3
1
0
0
0
0
1
1
0
0
3
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
4
0
1
0
2
0
1
3
0
0
0
3
0
0
0
0
1
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
2
2
0
0
0
0
2
4
2
0
0
1
0
0
1
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
2
0
2
2
0
3
0
0
2
0
3
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
2
0
0
3
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
1
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
2
1
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
3
0
0
0
0
0
0
4
0
0
5
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
2
0
1
3
0
1
0
0
0
0
2
0
0
2
0
2
0
1
5
0
2
1
0
2
0
0
1
2
0
0
1
0
2
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
2
0
0
1
0
0
0
0
0
0
1
2
0
2
0
1
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
1
0
0
0
0
0
2
2
3
0
0
0
0
0
4
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
3
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
5
2
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
3
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
2
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
1
3
0
0
0
5
0
0
0
0
0
0
2
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
1
0
2
0
0
0
0
0
0
1
0
0
1
0
1
1
2
0
0
2
2
0
0
0
4
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
4
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
3
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
2
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
5
0
1
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
4
0
0
2
0
0
0
2
0
0
0
5
1
0
0
0
0
0
4
1
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
11
0
0
0
0
0
0
6
1
1
0
0
0
0
1
0
0
0
0
0
1
0
7
0
0
0
0
0
0
1
0
0
0
0
8
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
3
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
2
0
3
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
5
0
0
0
0
0
1
0
0
1
0
0
0
1
2
2
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
2
3
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
2
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
3
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
3
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
5
1
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
2
0
0
2
0
1
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
2
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
1
0
0
0
0
1
0
0
1
2
1
1
0
0
0
2
1
0
2
2
0
0
0
0
0
0
1
0
0
5
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
12
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
2
0
2
2
3
1
0
0
1
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
1
1
0
0
0
0
0
1
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
2
2
1
2
1
0
0
0
0
0
0
1
0
0
2
2
0
0
1
3
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
4
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
2
1
0
0
0
0
1
0
1
0
0
2
2
0
0
0
1
0
1
5
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
2
3
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
2
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
3
1
2
0
2
2
0
0
0
0
0
1
2
0
0
0
0
2
0
0
2
0
0
0
3
0
2
0
0
2
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
2
0
0
0
0
0
1
0
0
2
0
2
0
0
1
1
0
0
1
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
3
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
1
0
3
0
1
0
0
0
0
0
3
0
1
1
0
0
7
1
0
0
0
0
1
3
0
2
3
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
2
2
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
2
0
0
0
4
0
3
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
3
0
1
0
0
4
0
0
0
2
0
1
0
0
0
2
0
0
2
0
0
0
0
2
1
0
0
0
0
6
0
2
0
2
0
0
2
0
0
0
3
0
0
0
2
1
0
4
0
0
0
2
0
0
1
0
2
0
3
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
1
6
0
0
2
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
2
3
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
1
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
1
0
1
1
0
1
0
1
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
4
3
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
7
0
2
0
1
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
5
0
0
3
0
0
1
0
0
3
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
2
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
1
0
7
0
2
0
0
0
0
0
1
0
0
1
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
1
2
0
0
0
0
0
2
0
0
0
1
0
0
1
2
0
0
0
0
2
0
1
0
1
0
3
0
0
1
0
1
0
0
0
2
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
5
0
0
1
0
0
0
8
0
0
0
1
0
1
2
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
1
4
0
0
5
0
0
0
0
0
0
0
1
0
2
0
0
0
2
2
0
1
3
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
3
0
2
2
0
0
0
1
0
1
0
0
0
2
0
4
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
3
0
0
0
0
0
2
0
0
0
0
0
1
1
1
1
0
0
0
3
0
1
0
1
0
0
0
0
1
0
2
2
0
0
0
0
2
0
0
2
0
0
0
0
4
0
1
0
1
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
3
1
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
4
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
1
4
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
1
0
0
0
0
3
0
0
2
0
0
0
2
6
0
0
0
2
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
4
0
1
0
0
0
2
0
0
0
0
1
2
0
0
0
3
0
1
0
1
0
0
0
0
0
0
1
0
0
7
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
3
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
2
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
4
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
1
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
2
1
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
1
1
0
0
0
2
0
0
0
1
1
0
0
1
0
0
0
1
0
1
0
2
0
0
1
0
1
2
0
0
4
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
4
1
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
8
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
2
0
2
1
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
1
0
0
2
0
2
0
0
2
1
0
1
1
0
1
0
0
2
0
0
2
2
0
0
1
0
0
2
3
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
2
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
2
3
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
6
0
0
0
3
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
2
0
2
2
0
0
0
0
0
1
1
0
0
0
2
1
0
0
5
0
0
1
0
0
2
0
1
0
3
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
6
5
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
1
0
1
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
5
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
4
0
0
0
0
0
4
1
1
0
0
1
1
1
1
0
0
0
0
1
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
2
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
2
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
12
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
7
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
4
2
0
0
0
0
2
2
0
0
2
0
0
2
0
0
0
3
0
0
0
2
0
0
1
0
0
2
0
0
2
1
0
1
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
1
0
2
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
2
1
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
2
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
0
0
1
0
0
0
0
1
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
5
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
1
0
0
1
0
0
0
0
3
1
2
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
1
0
1
1
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
2
0
1
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
1
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
3
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
1
1
0
0
0
2
1
2
0
0
1
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
1
0
2
0
0
0
0
2
0
2
0
2
3
0
1
0
0
0
2
0
1
0
1
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
2
0
0
0
2
0
2
1
0
0
2
0
0
0
1
4
0
0
0
3
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
1
1
1
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
5
0
2
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
5
4
2
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
4
0
2
0
1
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
1
0
1
0
0
2
0
1
1
2
0
0
0
0
0
2
0
12
0
0
2
1
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
1
0
1
3
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
3
0
0
0
1
0
1
0
0
2
0
1
0
0
0
0
0
9
0
0
0
0
1
0
0
0
0
5
0
0
0
1
1
0
1
2
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
2
1
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
8
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
1
2
0
1
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
2
1
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
2
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
1
0
2
1
0
0
0
2
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
3
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
1
0
2
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
3
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
5
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
1
0
1
0
4
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
2
3
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
2
4
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
1
0
1
0
0
0
0
3
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
3
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
3
0
1
2
1
0
0
0
0
0
2
0
1
0
0
0
0
0
3
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
3
0
0
0
0
0
0
0
1
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
2
0
0
1
0
2
0
0
5
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
4
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
3
0
2
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
2
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
9
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
3
0
2
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
2
0
3
0
2
0
0
1
1
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
1
0
1
0
1
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
4
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
3
0
1
0
0
0
0
1
0
3
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
1
1
2
0
0
5
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
13
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
1
1
0
0
2
1
0
2
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
1
0
9
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
3
0
0
2
0
1
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
2
0
1
1
0
0
0
0
0
0
0
2
2
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
2
0
2
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
2
4
4
0
0
0
0
2
0
0
1
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
2
1
0
0
3
0
1
0
0
1
0
0
0
0
1
3
0
2
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
1
0
1
2
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
4
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
1
2
0
0
0
0
0
2
2
1
0
0
0
1
0
0
0
0
1
0
5
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
2
0
2
0
0
1
0
0
0
2
0
0
4
0
0
2
1
0
0
0
0
0
0
1
2
1
1
4
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
9
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
1
3
2
0
2
6
0
2
0
1
0
0
0
0
0
2
0
0
2
0
2
3
0
1
0
1
0
0
0
0
0
4
2
0
0
0
0
1
1
0
2
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
2
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
2
0
0
0
0
0
3
2
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
4
0
0
2
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
2
0
0
3
1
0
0
0
0
2
0
0
0
1
1
0
3
0
0
0
1
2
0
0
0
2
0
0
0
2
0
1
2
0
0
0
0
1
0
2
6
0
0
0
0
1
1
3
0
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
1
0
2
0
0
0
1
3
0
0
0
0
3
0
0
1
0
0
0
0
2
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
9
0
0
2
1
1
0
0
2
1
0
0
0
0
0
0
0
2
2
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
3
0
0
0
0
1
0
2
1
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
2
0
1
0
0
1
5
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
2
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
3
0
3
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
3
2
4
0
0
5
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
4
0
0
1
1
0
0
0
0
0
0
0
2
0
2
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
1
2
2
0
0
2
1
0
0
0
1
0
1
1
2
0
0
1
0
0
0
0
0
2
1
0
0
2
2
1
1
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
1
0
2
0
0
2
0
0
0
1
0
0
2
0
1
0
0
0
1
1
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
1
0
5
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
2
0
0
0
0
1
0
2
1
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
30
5
0
1
1
0
0
0
1
3
0
1
2
0
0
0
2
0
2
0
0
0
1
0
0
2
1
0
0
1
0
0
0
0
0
0
2
0
0
6
2
0
0
0
0
0
0
0
1
2
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
3
0
2
1
0
1
0
0
3
3
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
2
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
1
1
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
1
0
1
0
0
0
1
1
2
3
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
4
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
1
2
0
0
1
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
2
0
0
0
2
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
6
2
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
5
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
2
13
0
0
2
0
0
0
1
0
0
0
4
0
1
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
7
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
8
0
0
0
0
1
0
0
0
0
0
0
1
0
2
3
0
0
1
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
4
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
3
0
0
2
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
1
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
1
2
0
0
3
0
0
0
1
1
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
4
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
4
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
3
1
5
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
2
0
1
0
2
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
2
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
1
1
5
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
3
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
1
3
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
3
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
2
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
2
2
2
0
2
0
2
2
0
1
0
0
1
1
0
0
1
2
3
0
0
0
1
0
0
0
1
0
3
0
3
0
0
0
2
0
2
0
1
0
0
0
1
0
1
0
0
0
0
3
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
2
3
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
3
0
2
2
0
0
0
6
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
4
1
1
1
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
1
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
4
0
1
3
0
0
0
0
0
1
0
1
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
1
0
5
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
6
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
1
0
1
0
0
0
0
2
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
2
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
4
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
4
0
0
2
2
0
0
0
0
1
1
2
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
2
0
0
3
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
1
0
2
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
3
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
2
3
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
1
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
4
2
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
1
2
0
2
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
4
0
0
5
2
1
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
1
0
1
2
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
3
0
0
0
0
0
4
2
0
0
0
0
0
2
3
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
2
0
0
3
2
0
0
0
6
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
1
0
0
0
3
2
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
4
0
0
0
3
0
0
0
1
1
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
3
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
2
0
0
0
0
3
0
1
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
1
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
5
0
0
0
0
0
3
0
0
0
0
0
2
1
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
6
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
3
0
0
1
8
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
4
2
0
0
0
0
0
4
0
2
0
0
0
1
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
1
1
1
2
0
0
2
2
1
0
0
0
0
3
2
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
3
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
1
0
0
2
0
0
2
0
7
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
3
0
0
0
2
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
3
0
2
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
1
2
0
6
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
1
0
1
3
0
2
0
0
2
0
0
0
0
0
0
3
0
0
1
2
0
0
0
0
3
2
0
0
0
2
0
0
1
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
3
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
1
1
1
2
0
0
2
1
0
0
0
0
0
0
0
2
1
0
0
0
4
2
0
0
1
0
1
2
0
3
1
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
3
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
1
2
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
2
0
2
1
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
1
0
0
3
0
0
1
0
1
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
3
0
2
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
2
0
1
0
4
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
9
0
1
0
0
0
0
0
1
0
2
0
0
1
0
0
0
1
0
1
0
0
0
4
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
1
1
2
0
0
0
0
0
2
1
0
0
11
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
1
3
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
1
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
3
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
1
1
0
1
1
0
1
0
0
0
2
0
4
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
3
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
7
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
2
0
2
0
0
0
2
0
0
0
0
0
0
1
0
2
3
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
10
0
2
0
0
0
0
0
1
0
1
0
0
2
0
0
1
0
1
0
0
0
4
0
0
1
2
0
2
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
6
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
1
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
1
0
0
1
0
0
2
1
0
0
0
2
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
2
0
0
0
0
0
5
1
0
0
0
0
0
1
0
1
0
3
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
1
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
2
5
0
0
0
0
2
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
6
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
7
0
0
0
0
0
1
1
0
0
0
0
3
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
3
1
0
2
0
0
0
1
0
0
2
0
0
0
0
0
2
3
0
0
0
0
1
0
2
0
2
0
0
2
0
0
1
0
0
0
0
2
0
1
0
3
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
1
2
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
3
0
2
0
0
0
0
5
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
2
0
6
0
0
0
1
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
1
2
0
0
1
0
1
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
1
0
2
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
3
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
6
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
3
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
2
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
4
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
2
0
1
0
0
2
5
0
0
0
0
1
0
1
0
4
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
1
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
8
1
0
0
2
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
4
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
4
0
0
0
0
1
0
0
0
0
1
0
0
2
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
1
3
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
1
2
2
0
2
0
3
0
0
0
0
0
1
3
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
2
0
0
0
0
1
0
0
0
0
2
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
2
0
1
0
0
2
1
0
0
1
0
0
1
0
1
0
0
2
0
0
0
0
0
3
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
1
0
0
1
0
0
0
1
0
0
1
1
0
0
0
1
0
0
2
0
0
2
1
0
0
0
1
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
2
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
1
0
2
1
1
0
0
0
2
0
0
1
4
0
0
9
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
2
0
0
0
0
6
1
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
1
0
0
3
1
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
1
1
1
0
0
1
1
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
9
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
3
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
9
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
6
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
3
0
1
0
2
0
1
0
0
0
0
0
0
1
0
0
0
2
0
1
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
2
1
1
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
3
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
1
0
0
0
1
0
2
2
0
0
0
2
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
6
0
1
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
2
1
1
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
4
0
1
0
0
0
0
1
0
1
1
0
0
1
0
0
1
0
0
0
0
2
0
0
2
0
1
0
2
0
0
2
0
0
1
2
0
0
0
0
0
0
0
3
2
0
0
2
4
0
1
2
0
0
2
0
0
0
0
1
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
1
1
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
3
2
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
5
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
2
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
1
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
2
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
2
2
0
0
1
0
0
0
0
2
0
0
0
1
0
0
3
2
0
0
7
0
0
1
0
2
0
2
0
1
0
0
0
0
0
0
2
0
0
8
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
1
0
0
2
0
2
0
0
0
1
1
0
1
0
0
4
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
1
9
0
2
1
0
0
0
0
0
0
2
2
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
2
0
0
0
1
2
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
1
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
2
0
2
0
0
2
0
0
0
1
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
6
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
5
0
0
1
1
0
0
0
2
0
2
1
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
1
0
3
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
3
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
3
0
1
0
7
0
0
2
0
1
0
0
0
0
3
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
3
1
0
0
2
4
1
0
0
5
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
2
0
3
0
0
1
0
0
0
0
0
0
1
0
0
2
0
1
0
0
1
1
0
2
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
1
1
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
7
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
6
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
1
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
3
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
2
2
0
2
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
3
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
4
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
1
0
2
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
5
0
3
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
1
2
0
2
0
0
0
1
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
5
2
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
1
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
4
2
0
0
0
1
2
0
2
0
1
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
3
2
0
0
0
0
3
1
0
0
0
0
0
0
0
1
1
1
1
2
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
1
2
2
1
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
2
1
0
0
0
2
0
1
0
2
0
0
0
0
0
0
3
0
6
1
0
0
0
2
0
0
0
3
0
1
1
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
4
0
0
0
0
1
0
0
0
1
0
2
1
2
0
0
0
0
0
0
1
0
1
1
3
1
0
1
0
0
0
0
0
0
0
0
0
5
0
0
0
2
2
1
0
0
0
0
2
1
0
0
0
3
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
2
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
2
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
2
0
0
2
0
4
1
0
2
2
1
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
2
0
0
2
0
1
1
0
0
2
0
0
0
1
0
0
2
1
1
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
3
1
1
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
2
0
0
1
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
7
0
0
0
0
0
1
0
0
0
0
0
2
0
3
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
6
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
4
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
2
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
3
0
0
2
0
1
0
0
0
0
0
1
0
0
2
1
0
0
2
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
2
0
0
0
0
0
1
0
0
0
5
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
5
2
0
0
0
1
3
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
2
4
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
3
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
3
3
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
2
0
2
0
0
0
0
0
0
0
1
0
0
3
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
3
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
1
0
4
0
0
3
0
0
0
0
1
0
0
1
2
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
2
0
1
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
3
2
0
0
1
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
2
7
0
0
0
1
1
1
0
1
0
1
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
4
1
2
0
2
0
0
0
0
0
2
2
3
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
2
1
2
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
7
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
1
0
0
1
0
0
4
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
2
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
1
0
0
0
0
0
0
0
3
0
0
1
2
0
2
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
4
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
5
0
0
2
0
0
0
0
2
1
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
1
2
3
1
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
1
2
4
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
1
2
1
0
0
0
0
0
0
2
0
0
0
1
0
0
4
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
2
1
0
2
0
2
0
0
0
1
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
4
0
0
2
0
0
0
1
0
0
0
0
1
1
0
2
2
0
0
1
1
0
0
0
0
0
0
0
4
2
0
3
0
0
0
0
0
2
0
0
0
1
8
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
2
0
2
2
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
8
0
0
0
0
0
0
1
0
2
1
3
0
0
0
0
0
0
0
1
1
0
2
4
0
0
0
0
0
2
1
0
0
0
0
0
1
5
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
2
0
0
0
0
2
3
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
1
3
0
0
0
0
0
0
0
0
4
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
2
1
0
0
0
0
0
3
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
1
0
0
0
1
0
0
0
0
2
0
0
2
3
0
0
0
1
2
0
0
1
0
3
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
2
0
0
2
0
2
1
0
1
0
0
0
2
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
4
0
1
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
2
3
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
1
0
1
0
2
0
0
0
2
0
0
0
1
3
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
4
0
0
7
0
1
3
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
4
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
4
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
1
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
1
0
2
0
0
0
2
0
0
0
2
2
0
0
0
0
1
0
1
5
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
1
1
2
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
1
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
2
0
0
1
0
0
0
0
0
0
0
2
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
2
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
1
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
1
3
0
3
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
2
0
0
1
0
0
0
0
6
3
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
3
7
0
0
2
0
0
0
0
1
1
1
0
0
0
0
0
0
0
4
2
0
1
1
0
0
4
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
6
5
0
0
2
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
2
1
0
0
0
0
1
0
1
0
0
2
1
0
0
1
0
2
0
3
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
1
0
0
2
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
2
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
5
0
0
2
0
0
0
0
0
0
1
0
2
1
1
1
0
0
0
0
0
0
7
0
0
1
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
2
0
0
1
0
0
0
0
0
2
2
1
0
0
0
0
2
1
0
1
0
1
1
2
0
0
0
4
1
0
3
5
0
3
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
1
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
2
0
0
0
1
1
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
5
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
5
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
2
0
1
0
2
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
1
0
0
2
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
2
0
0
0
0
1
2
2
0
0
0
3
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
2
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
2
1
1
0
0
0
1
0
0
1
0
2
0
2
0
0
0
0
0
3
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
6
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
4
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
3
0
0
0
1
0
2
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
3
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
4
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
1
1
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
2
0
0
0
0
0
1
2
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
1
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
4
0
0
0
3
1
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
2
2
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
3
0
0
1
0
0
3
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
3
0
0
2
0
1
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
1
3
1
0
0
0
0
0
3
6
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
3
0
0
0
0
0
2
2
0
0
0
0
2
3
2
0
0
0
0
0
1
2
0
0
4
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
3
0
0
1
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
2
1
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
4
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
2
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
3
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
4
0
0
0
1
1
2
2
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
4
0
0
0
0
0
2
0
0
0
2
2
1
0
0
4
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
1
1
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
1
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
1
0
1
0
0
0
2
15
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
1
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
2
2
2
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
2
0
0
1
0
1
0
0
0
1
1
2
2
0
2
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
1
1
0
3
0
0
3
2
1
2
0
1
1
3
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
2
0
0
0
0
3
0
2
0
0
0
0
1
3
2
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
1
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
3
0
0
1
2
0
0
0
0
5
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
2
0
0
2
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
4
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
4
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
1
0
0
0
0
1
2
0
2
0
0
0
0
5
1
0
0
0
0
0
1
0
0
0
0
8
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
3
0
2
1
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
2
0
0
0
1
2
1
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
2
1
0
2
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
5
0
0
2
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
5
0
0
0
1
0
0
0
2
0
2
0
0
0
3
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
1
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
1
1
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
2
1
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
1
0
2
3
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
1
0
0
0
3
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
2
0
0
0
0
0
1
0
2
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
3
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
0
2
0
0
0
1
0
0
1
0
1
3
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
3
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
1
0
1
0
0
1
2
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
1
0
0
2
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
2
0
2
0
0
2
0
0
1
0
0
2
0
0
0
0
2
1
2
0
1
1
0
0
1
0
0
0
0
0
2
0
2
0
0
2
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
2
2
0
0
1
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
3
0
0
0
0
0
3
0
0
0
0
2
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
4
1
1
0
0
0
0
1
0
0
0
4
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
3
2
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
3
0
0
2
0
0
0
0
0
0
4
0
1
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
3
0
2
0
0
0
0
2
1
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
5
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
2
1
4
0
2
1
1
1
0
1
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
2
5
0
0
0
1
2
0
0
4
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
1
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
2
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
1
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
1
1
0
0
0
0
0
0
1
0
1
0
1
0
1
2
0
1
5
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
2
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
2
2
0
1
0
2
0
3
8
2
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
2
0
0
3
0
0
0
2
1
0
1
0
0
0
5
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
2
0
0
0
0
2
3
0
0
1
0
0
0
0
0
0
0
2
2
2
0
0
1
0
0
0
1
0
0
0
0
0
5
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
3
0
0
1
0
0
0
2
0
0
0
1
0
1
0
2
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
2
0
0
2
0
5
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
3
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
2
0
1
2
4
0
2
0
0
0
0
0
0
0
0
2
0
0
0
3
1
0
0
1
0
0
2
0
1
0
1
1
0
0
0
0
0
1
0
1
0
0
3
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
1
0
0
2
0
0
3
0
0
1
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
4
0
1
4
2
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
4
0
0
0
3
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
2
2
0
0
1
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
4
0
1
0
0
0
2
0
1
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
2
0
3
0
0
0
1
0
4
0
2
0
2
0
2
2
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
2
0
0
0
0
1
1
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
7
1
2
0
0
1
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
2
0
0
1
1
1
0
1
0
0
1
2
0
2
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
1
0
1
2
0
0
0
0
0
0
1
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
2
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
7
2
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
4
2
0
1
1
0
3
0
2
1
2
0
0
2
0
1
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
2
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
1
2
0
1
0
0
0
0
2
0
4
0
3
1
0
5
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
4
0
0
4
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
2
0
3
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
2
0
0
3
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
2
0
5
2
2
0
0
0
0
0
0
0
1
0
4
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
3
0
0
0
1
0
0
4
0
1
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
4
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
5
1
0
0
2
0
2
0
3
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
1
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
3
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
4
0
0
0
0
1
0
0
1
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
3
2
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
3
0
1
0
0
0
0
0
0
3
0
0
1
2
0
5
0
0
1
1
0
0
1
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
4
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
1
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
3
0
0
0
1
1
0
0
6
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
2
0
2
1
0
1
0
0
1
0
0
1
0
0
0
0
0
1
3
0
3
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
4
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
4
0
1
1
0
1
0
0
4
2
0
1
1
0
2
0
0
0
0
0
0
0
0
0
1
1
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
2
1
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
1
0
1
1
0
0
0
1
1
0
1
0
0
0
0
0
0
2
1
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
4
2
3
0
0
0
1
0
0
0
1
0
0
2
2
0
0
1
0
0
0
0
0
0
1
0
2
0
0
3
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
1
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
3
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
2
3
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
2
1
1
0
0
1
0
2
1
0
1
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
1
2
0
4
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
5
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
1
1
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
2
1
2
0
0
0
0
0
0
5
2
0
1
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
1
1
1
0
0
1
0
0
0
1
0
0
2
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
2
0
0
2
0
2
0
1
0
0
0
0
0
0
2
2
0
0
0
0
2
0
2
0
0
0
0
0
2
0
3
0
0
0
0
2
0
2
1
1
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
4
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
3
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
8
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
2
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
1
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
1
1
2
0
0
0
1
0
1
0
0
0
0
1
0
3
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
8
1
0
0
0
7
0
4
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
2
0
1
0
0
3
2
0
0
0
5
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
1
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
3
0
0
0
1
0
0
5
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
4
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
1
5
0
0
0
0
2
0
2
0
0
0
0
0
0
1
8
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
4
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
6
0
0
1
9
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
5
0
0
1
0
0
2
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
3
0
0
0
0
0
0
2
1
1
0
0
0
0
3
0
2
0
3
0
0
0
0
0
3
0
0
3
0
0
0
2
2
0
2
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
3
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
1
1
0
1
1
0
0
0
0
2
0
0
0
0
2
2
0
0
2
3
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
1
2
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
2
1
0
0
1
0
0
2
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
4
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
3
0
0
0
1
2
0
0
0
0
3
1
0
0
4
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
4
0
0
0
0
0
2
0
0
1
3
2
0
0
0
1
1
0
2
0
0
0
0
0
2
2
3
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
1
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
3
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
1
0
2
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
4
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
2
2
0
0
0
0
0
1
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
5
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
3
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
5
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
5
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
2
1
0
0
0
0
0
5
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
1
2
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
2
1
0
1
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
1
0
1
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
1
0
0
0
4
0
3
0
0
0
0
1
0
0
0
0
0
0
0
1
0
3
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
1
0
2
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
6
1
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
4
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
2
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
2
2
0
1
1
2
7
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
1
0
2
2
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
1
1
0
0
2
0
0
1
1
0
0
0
0
0
1
1
2
0
0
4
1
0
1
1
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
1
0
0
1
0
0
3
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
2
0
1
1
0
2
2
0
0
1
0
0
1
1
0
2
0
2
1
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
3
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
2
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
1
0
2
0
0
0
0
2
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
4
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
1
0
0
0
2
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
2
0
1
2
0
0
1
2
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
1
0
1
0
0
2
0
1
0
0
2
0
0
2
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
5
3
0
0
0
1
0
1
0
0
0
1
0
0
2
0
0
0
2
3
0
2
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
3
2
2
0
2
1
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
1
2
0
0
0
0
2
0
2
0
0
0
2
0
7
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
4
0
1
0
0
0
0
2
1
0
0
0
10
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
1
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
2
3
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
2
1
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
4
0
5
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
3
3
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
2
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
2
0
0
2
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
2
0
1
1
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
2
3
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
2
2
1
0
2
0
3
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
1
0
0
6
0
2
1
0
1
0
0
0
0
0
12
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
3
9
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
9
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
4
2
0
2
2
0
0
0
0
0
1
2
1
0
0
0
1
0
1
0
0
0
0
5
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
3
5
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
4
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
1
1
0
1
1
2
0
0
0
2
0
0
0
0
0
0
1
0
1
1
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
2
1
0
1
2
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
4
1
2
0
1
0
0
0
1
0
0
0
0
0
1
0
3
0
0
1
9
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
2
0
2
0
1
5
0
0
0
2
0
0
2
0
0
2
0
0
0
1
0
3
1
0
0
1
0
0
0
0
0
0
1
1
2
4
0
0
0
0
0
0
5
0
0
0
0
0
0
2
0
0
0
0
0
0
0
5
0
0
0
0
0
2
1
0
0
1
0
0
0
3
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
3
0
2
1
0
3
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
2
1
0
13
0
2
1
0
0
0
0
0
0
2
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
1
8
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
2
0
0
1
1
1
0
0
0
2
0
0
2
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
6
0
0
0
0
1
0
0
1
1
0
2
0
2
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
3
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
2
2
0
0
0
0
0
2
0
2
0
0
0
0
1
1
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
3
0
3
2
0
0
2
0
0
0
0
1
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
4
1
1
0
3
0
0
0
2
0
0
0
2
1
0
0
0
1
0
0
0
1
0
2
2
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
1
1
0
0
0
0
0
0
1
1
0
0
0
0
2
1
0
2
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
1
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
5
0
2
1
0
0
0
0
0
0
0
2
4
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
1
3
0
0
0
1
1
2
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
5
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
6
0
0
0
0
0
3
0
0
0
0
0
1
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
3
0
0
0
0
0
1
1
0
0
0
0
0
2
0
2
2
0
1
0
0
0
9
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
1
0
0
0
0
4
0
3
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
11
0
0
0
0
0
0
0
0
1
1
0
0
0
3
2
1
0
0
0
2
1
0
1
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
4
0
1
2
0
1
2
0
0
0
4
3
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
1
6
0
0
0
2
0
0
0
3
0
1
2
1
0
0
13
0
0
0
3
0
0
0
1
2
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
3
0
5
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
4
5
0
0
0
1
0
1
0
2
0
0
2
1
0
0
1
1
0
0
0
0
0
4
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
5
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
4
0
0
0
0
0
1
1
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
3
0
0
0
0
1
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
3
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
1
3
0
3
0
0
0
2
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
2
3
0
0
2
0
0
0
0
2
0
0
0
8
0
0
0
1
0
0
2
0
8
1
2
0
0
1
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
1
2
0
2
0
0
0
1
2
1
0
3
0
0
0
0
0
2
0
0
0
2
1
0
0
5
2
0
0
0
1
2
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
8
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
1
0
2
0
0
0
1
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
1
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
4
0
0
0
3
0
0
0
0
0
0
1
0
6
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
2
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
1
0
0
0
1
0
0
0
0
0
0
0
4
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
1
1
1
0
1
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
8
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
3
1
1
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
2
0
0
0
5
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
1
0
0
0
0
2
1
1
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
1
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
2
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
6
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
1
0
2
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
1
0
1
0
6
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
5
0
1
0
1
0
0
0
1
0
4
1
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
4
1
0
0
0
0
0
0
1
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
2
0
4
1
0
0
0
0
2
0
0
0
0
0
2
2
0
1
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
1
0
2
2
1
0
3
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
4
1
0
0
2
0
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
3
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
1
0
0
1
0
0
1
0
1
0
0
0
1
2
0
2
0
0
2
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
2
0
0
0
0
0
5
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
2
6
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
4
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
1
0
0
0
0
1
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
2
1
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
2
1
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
2
0
0
0
2
0
2
1
1
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
3
0
0
0
0
2
0
0
5
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
2
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
7
0
0
0
2
0
0
2
2
0
0
0
2
4
1
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
6
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
1
2
0
0
5
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
2
0
0
4
0
2
0
0
0
0
0
2
2
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
1
1
1
0
0
0
0
1
0
0
1
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
3
2
0
0
1
0
0
1
0
0
3
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
1
0
2
1
0
1
0
1
2
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
4
0
0
2
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
2
2
0
0
0
2
0
1
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
3
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
1
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
5
2
0
0
0
0
1
2
0
0
0
2
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
3
0
1
0
0
0
1
0
0
2
4
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
3
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
7
1
0
0
2
0
0
0
0
1
0
0
0
1
0
2
1
0
1
2
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
2
2
1
0
1
0
0
0
0
0
6
0
9
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
1
1
0
2
0
2
0
0
0
0
0
2
0
0
0
0
4
0
1
0
2
0
0
0
2
0
0
0
0
0
4
0
2
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
5
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
2
0
2
0
1
0
0
0
0
0
0
0
0
2
1
0
2
0
0
1
0
0
1
2
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
9
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
6
0
0
0
0
0
0
0
0
2
0
0
1
1
1
0
2
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
1
0
0
2
0
0
0
1
0
0
1
2
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
2
0
0
3
0
0
1
0
3
0
0
0
0
2
0
1
0
1
2
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
1
0
2
0
2
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
1
2
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
2
1
0
1
0
0
2
0
1
0
0
3
0
2
4
0
0
1
1
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
1
0
2
0
0
2
1
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
2
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
2
0
2
1
0
0
1
0
0
0
0
2
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
3
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
7
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
2
0
0
3
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
5
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
2
0
1
0
8
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
6
1
0
0
0
0
0
0
0
2
0
1
0
2
0
1
0
0
0
1
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
10
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
3
2
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
1
0
0
1
0
0
3
0
0
0
0
0
0
3
1
0
0
0
0
1
0
2
0
0
0
0
4
0
0
0
0
2
0
0
0
0
1
6
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
1
0
1
1
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
2
0
0
1
0
3
0
0
0
0
0
2
0
0
0
0
0
3
0
1
0
0
0
0
2
0
0
0
0
0
1
1
0
0
2
0
2
0
2
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
1
0
0
4
2
3
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
4
0
0
0
1
0
1
0
2
2
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
3
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
2
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
2
1
3
0
0
0
2
2
2
0
1
0
3
0
0
0
0
0
0
2
0
0
0
3
0
1
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
2
0
2
0
1
0
0
1
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
2
0
1
0
2
1
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
2
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
2
14
0
0
2
1
1
0
0
0
0
3
2
0
4
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
2
2
0
0
0
1
1
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
3
3
0
0
0
3
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
1
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
1
0
1
0
0
0
0
0
0
0
2
0
0
2
1
1
0
1
0
0
0
0
0
0
2
1
0
0
2
0
0
1
0
0
1
0
2
0
0
2
2
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
4
1
0
0
1
1
0
0
2
0
1
0
0
0
1
0
0
0
2
0
0
0
0
1
0
1
0
0
1
0
0
1
1
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
3
1
2
0
0
0
0
1
2
2
0
0
0
0
2
0
0
3
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
1
0
2
0
0
0
0
0
4
0
0
0
0
1
1
2
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
2
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
1
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
3
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
1
0
0
2
0
0
2
2
0
1
2
0
0
2
0
0
0
1
1
0
1
2
2
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
2
1
0
0
0
3
0
0
0
0
0
1
0
0
1
0
0
0
0
8
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
2
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
2
0
1
0
0
3
0
0
0
1
0
0
1
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
3
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
1
0
0
0
0
0
2
1
0
2
0
5
0
0
1
0
2
0
2
0
0
0
1
0
0
3
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
1
0
2
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
1
1
0
0
0
0
4
0
0
1
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
1
10
0
1
0
0
0
0
0
4
0
1
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
2
0
3
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
2
0
2
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
5
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
1
0
2
1
0
0
0
2
0
0
2
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
3
2
0
0
1
0
0
4
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
1
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
3
0
2
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
2
2
1
0
0
0
0
0
1
0
0
1
2
0
1
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
3
0
2
4
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
2
0
0
1
0
0
1
0
0
0
0
2
0
0
3
0
0
0
0
4
0
0
0
0
0
0
2
0
1
0
0
2
0
0
2
1
0
0
0
0
0
3
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
1
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
6
1
0
0
0
0
0
0
9
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
3
2
3
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
3
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
3
7
0
0
0
0
0
3
1
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
1
0
0
0
2
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
2
0
0
0
3
0
2
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
3
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
1
0
2
0
1
0
0
2
0
2
0
0
0
0
3
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
3
0
1
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
2
0
0
0
1
0
0
1
1
2
0
0
2
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
3
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
3
0
0
0
1
0
2
1
0
2
2
1
0
0
0
0
2
0
0
0
1
0
3
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
3
1
1
2
0
0
3
0
2
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
3
0
0
1
0
2
2
0
0
2
0
1
0
0
0
0
0
0
1
0
0
8
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
4
0
0
0
0
0
1
0
0
0
3
1
2
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
1
1
1
0
0
0
1
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
1
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
3
0
5
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
1
0
0
0
5
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
2
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
2
1
1
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
2
0
1
0
1
9
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
1
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
5
0
0
0
2
1
1
0
0
4
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
2
0
0
0
0
0
0
0
5
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
3
3
0
1
0
1
0
0
0
1
2
0
0
0
0
0
1
2
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
1
0
0
5
0
0
0
0
0
3
1
0
0
0
0
0
0
2
0
1
1
2
0
1
0
0
1
1
1
0
4
0
0
0
2
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
2
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
4
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
1
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
5
1
1
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
1
0
0
3
2
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
3
0
0
0
0
0
0
1
0
0
0
2
2
2
0
0
0
2
1
1
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
1
0
3
1
0
0
0
0
0
0
1
0
7
1
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
1
2
0
1
0
1
1
0
0
0
0
0
0
2
2
0
1
2
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
5
2
0
0
0
0
1
4
0
1
0
2
0
0
0
0
0
4
0
1
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
1
0
0
0
0
0
1
2
0
4
0
0
0
0
0
0
1
1
0
1
0
0
0
2
0
1
3
3
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
1
2
0
1
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
3
0
1
0
0
0
0
0
0
0
2
0
0
0
5
0
1
0
0
0
0
5
0
0
0
0
0
0
1
0
2
1
1
0
0
0
0
0
2
0
0
4
0
0
2
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
4
0
0
0
0
2
0
0
1
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
2
3
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
2
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
1
2
0
1
3
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
2
0
0
0
0
1
0
0
0
3
0
3
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
2
1
2
1
4
0
2
0
0
0
0
3
0
1
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
2
0
3
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
2
2
2
0
0
0
0
1
0
1
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
3
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
2
0
2
0
1
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
3
0
0
0
1
0
0
1
2
0
0
1
0
0
0
0
2
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
1
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
1
0
0
0
0
2
0
0
1
4
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
2
4
0
1
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
4
1
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
2
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
2
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
3
0
0
0
0
0
1
0
0
0
1
1
2
0
0
0
0
0
1
0
1
0
0
2
0
3
2
0
0
0
0
0
2
0
3
0
0
2
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
3
0
0
1
0
0
0
2
0
1
1
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
3
0
0
0
0
0
2
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
1
0
0
3
0
0
0
0
0
2
0
0
0
0
3
0
4
0
0
0
0
2
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
3
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
1
0
0
0
0
1
3
0
0
1
1
0
0
1
0
0
0
0
0
1
5
0
0
0
1
0
1
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
1
2
0
0
0
2
0
2
0
0
2
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
1
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
3
0
2
0
2
0
0
0
1
0
3
0
0
1
1
0
0
0
0
1
0
0
0
3
1
1
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
2
0
0
2
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
3
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
3
1
0
0
0
0
0
2
0
0
4
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
4
0
7
0
0
0
0
0
0
1
1
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
3
0
2
1
0
0
0
0
3
0
0
3
1
0
0
2
0
1
0
1
2
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
3
0
0
0
0
0
3
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
6
0
0
0
0
1
0
1
0
0
0
0
1
0
1
2
0
4
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
4
0
1
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
3
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
1
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
2
0
0
0
6
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
6
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
1
7
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
1
0
0
3
0
2
1
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
2
0
0
0
0
1
2
1
0
0
3
0
0
0
0
0
0
0
0
0
3
1
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
1
1
0
2
0
1
1
0
0
0
1
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
3
1
1
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
5
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
2
3
0
0
1
0
0
0
0
1
1
0
0
1
0
4
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
2
0
0
0
0
1
2
0
0
1
0
0
2
0
0
2
0
3
0
1
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
2
0
1
2
0
0
0
0
1
0
0
0
0
2
2
8
1
0
0
0
0
0
0
2
0
0
2
0
0
0
1
2
1
0
0
4
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
5
0
0
0
0
0
0
0
0
0
0
1
0
0
0
5
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
3
0
2
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
4
0
0
0
1
0
1
0
0
0
0
3
1
2
0
0
0
0
0
0
0
0
0
2
0
1
2
2
1
1
2
0
0
0
0
0
0
0
0
5
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
3
0
0
0
0
2
2
0
0
0
0
0
1
0
1
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
1
0
2
1
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
2
2
1
0
0
0
0
0
0
1
0
2
2
0
0
0
4
0
3
0
0
0
1
0
0
0
1
0
2
5
0
0
0
2
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
2
1
0
1
0
0
0
3
0
0
1
0
2
0
0
0
0
5
0
1
0
0
0
0
2
0
1
0
1
2
0
0
0
5
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
1
0
0
0
0
1
0
0
3
2
3
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
2
1
0
0
0
0
2
1
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
3
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
3
1
0
0
0
1
0
0
0
2
3
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
9
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
1
0
0
0
3
0
2
0
2
0
0
0
2
0
0
1
0
1
0
3
0
1
1
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
1
0
0
0
0
0
1
0
0
2
1
0
0
0
1
2
0
1
1
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
5
0
0
4
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
2
0
1
0
2
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
5
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
3
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
8
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
1
0
2
0
1
0
0
0
4
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
3
5
0
0
0
0
0
2
0
0
1
0
0
5
0
3
0
0
1
2
0
1
0
0
0
2
0
0
0
3
0
0
0
2
0
0
0
0
1
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
1
0
2
0
0
0
2
0
3
0
2
0
0
2
2
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
3
0
0
1
0
0
0
0
2
1
0
3
0
3
2
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
4
1
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
4
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
6
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
2
2
0
1
0
0
0
0
4
0
0
0
0
0
0
0
2
0
4
0
0
2
0
2
0
0
2
0
2
0
0
1
2
0
3
0
0
0
0
1
1
0
2
0
2
2
3
0
1
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
2
0
1
1
0
0
0
1
0
0
0
0
3
0
0
0
0
2
2
2
0
0
0
0
0
1
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
2
1
0
0
2
0
0
2
0
1
0
0
0
5
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
1
2
2
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
1
0
3
2
2
2
2
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
2
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
2
1
0
1
0
0
0
0
2
3
2
1
1
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
6
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
1
0
0
0
1
2
2
0
1
0
0
0
0
1
0
0
1
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
4
0
1
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
1
0
0
0
0
1
0
4
1
0
0
2
0
0
2
1
0
0
1
2
0
0
0
0
0
0
1
0
2
0
2
0
0
0
2
2
1
0
0
0
2
0
2
5
1
0
0
0
1
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
1
3
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
6
1
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
5
2
0
0
1
0
0
1
3
0
0
2
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
1
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
2
0
0
2
0
0
3
0
2
0
0
1
2
0
0
3
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
2
0
0
0
0
1
0
1
1
0
0
0
2
0
0
0
2
0
0
2
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
1
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
1
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
2
0
0
0
0
1
3
0
2
0
0
4
0
0
0
2
0
1
0
0
0
1
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
5
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
3
0
2
1
0
0
2
1
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
3
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
9
0
0
0
2
0
0
0
0
1
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
3
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
1
1
0
0
2
0
0
2
0
0
0
2
0
0
2
0
0
0
1
0
1
2
2
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
2
1
0
0
0
0
0
2
1
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
5
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
1
3
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
2
5
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
2
1
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
5
2
0
2
1
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
3
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
1
0
3
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
3
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
3
0
2
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
3
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
3
3
0
1
3
0
0
2
0
2
1
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
2
0
0
8
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
3
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
2
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
6
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
3
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
2
1
0
0
0
0
0
1
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
2
1
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
3
0
0
0
1
0
0
1
2
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
2
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
7
0
0
0
0
1
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
4
0
0
0
0
0
2
0
0
0
0
1
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
1
0
0
0
0
2
2
0
1
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
2
0
0
0
1
0
0
2
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
1
0
1
0
0
0
0
2
0
1
0
0
0
0
2
1
2
0
2
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
1
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
1
1
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
1
3
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
1
0
0
2
1
2
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
2
0
1
0
0
2
0
0
0
0
0
3
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
1
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
1
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
7
0
2
0
0
1
2
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
3
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
5
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
3
0
0
1
0
0
2
0
0
3
2
0
0
0
0
0
0
0
0
1
2
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
2
2
0
0
0
1
2
1
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
12
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
1
3
3
2
1
0
0
0
0
2
0
0
3
2
0
0
1
0
0
0
0
0
0
2
0
0
4
0
0
0
3
0
2
0
0
0
3
0
0
1
0
0
2
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
1
1
1
1
3
0
0
5
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
4
0
2
0
0
4
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
3
0
2
0
0
0
0
2
0
0
3
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
7
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
8
0
0
0
0
2
0
5
2
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
2
1
0
2
2
0
0
0
1
0
0
2
0
0
1
2
0
0
2
0
0
2
0
0
3
0
1
0
3
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
5
0
0
2
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
1
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
1
0
0
2
2
1
0
0
0
0
0
2
0
0
2
2
0
0
1
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
3
2
1
0
0
2
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
5
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
1
2
2
0
1
0
0
0
1
0
0
0
0
0
1
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
1
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
2
2
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
8
0
0
0
2
2
0
2
0
0
0
0
1
0
1
1
0
0
0
1
3
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
2
0
1
0
0
2
0
0
1
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
2
1
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
1
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
9
0
0
0
0
2
0
0
0
0
0
2
0
3
0
0
0
0
0
2
0
0
2
0
0
0
3
0
0
0
0
0
0
2
0
0
0
3
3
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
3
0
0
0
0
0
0
1
0
1
1
0
1
0
0
2
0
0
0
2
0
0
0
1
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
3
3
1
0
0
0
0
0
2
2
0
0
0
0
2
1
0
1
0
3
0
0
0
0
2
0
0
0
1
0
0
2
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
1
2
2
0
0
0
0
0
0
1
2
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
5
0
2
3
0
0
0
0
2
0
1
0
0
0
0
1
2
2
0
2
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
1
0
3
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
3
1
0
3
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
3
0
0
2
0
1
1
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
7
0
0
0
0
0
1
0
2
0
2
0
3
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
1
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
3
0
1
0
1
1
0
0
0
2
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
2
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
4
3
0
0
0
0
1
0
0
0
0
3
0
0
1
1
1
3
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
2
2
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
2
0
2
1
1
0
1
2
1
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
2
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
3
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
2
5
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
2
0
1
0
0
4
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
1
2
1
0
2
0
0
1
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
1
0
0
1
0
0
0
2
0
0
0
0
5
2
0
0
1
0
1
2
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
2
3
1
0
0
0
0
0
0
0
0
0
1
0
0
3
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
2
0
0
1
2
0
1
0
0
0
2
0
1
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
3
0
0
0
2
0
1
0
1
0
0
1
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
6
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
3
0
1
1
2
0
3
0
0
0
0
3
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
4
0
1
0
0
1
1
1
0
4
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
3
0
0
0
0
0
1
0
0
0
0
0
3
0
0
1
0
1
0
1
0
0
0
0
4
0
0
0
0
0
1
0
0
0
2
0
1
2
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
1
0
2
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
6
0
0
1
5
0
1
0
0
0
0
0
2
2
0
0
7
0
0
2
0
0
0
3
1
0
0
0
0
1
0
1
0
0
2
0
2
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
1
1
0
0
0
0
0
2
2
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
2
2
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
3
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
8
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
3
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
1
0
0
2
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
5
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
5
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
3
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
3
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
2
1
0
1
0
0
0
1
2
1
0
0
0
2
0
0
0
1
0
1
0
0
3
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
2
1
2
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
3
0
1
1
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
4
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
3
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
11
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
4
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
5
0
0
0
1
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
3
1
0
1
2
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
1
1
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
3
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
3
0
0
0
1
2
1
0
0
0
0
0
9
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
3
0
0
0
0
1
0
2
0
1
0
0
3
0
1
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
2
0
2
1
0
2
0
0
3
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
1
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
2
0
0
0
2
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
6
0
0
0
1
0
0
1
0
1
0
0
0
0
0
2
0
2
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
5
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
5
0
0
1
0
0
0
0
2
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
9
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
2
6
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
1
1
0
2
0
2
0
0
1
0
0
0
0
1
2
0
2
1
2
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
4
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
6
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
1
0
1
0
0
2
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
3
0
0
0
0
0
0
0
0
13
0
0
0
0
0
0
0
5
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
1
2
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
1
1
0
2
1
0
0
2
0
1
4
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
5
1
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
3
0
0
0
3
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
5
0
1
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
1
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
3
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
6
0
2
0
0
0
1
0
0
0
2
0
1
0
0
0
0
6
0
0
0
0
0
0
2
4
1
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
1
0
1
2
0
0
0
0
0
1
1
1
0
1
1
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
3
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
2
0
0
2
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
1
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
3
0
2
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
4
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
3
1
1
0
0
0
0
0
0
2
2
1
0
1
3
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
2
2
3
0
0
0
0
0
0
0
0
0
4
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
7
1
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
1
0
0
0
0
0
1
0
2
3
0
1
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
1
0
0
1
1
0
0
0
3
0
0
0
2
4
0
0
0
2
1
2
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
9
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
2
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
2
0
4
1
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
8
0
0
1
0
0
0
3
0
3
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
1
2
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
3
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
2
0
1
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
1
0
0
1
0
0
0
0
0
0
0
1
2
0
4
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
4
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
1
3
3
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
1
1
2
1
0
0
2
2
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
1
0
0
5
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
1
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
3
1
1
0
0
6
1
0
0
1
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
7
1
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
3
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
1
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
2
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
7
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
2
3
0
1
2
2
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
1
1
0
1
0
0
0
0
1
0
1
1
1
0
0
0
0
1
1
0
2
0
1
0
0
0
0
1
3
2
0
0
0
1
1
0
0
0
0
0
0
1
1
2
2
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
2
0
0
2
0
0
0
0
0
2
5
1
0
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
2
1
0
0
0
0
1
0
2
0
0
0
0
0
0
1
3
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
1
0
0
0
0
2
0
2
1
6
0
0
1
0
0
1
0
0
0
0
0
7
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
4
1
0
1
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
2
0
0
0
2
0
2
0
0
2
0
2
1
0
7
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
2
0
0
1
0
0
2
0
0
3
1
2
3
0
0
0
1
3
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
3
0
0
0
0
0
1
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
4
0
0
2
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
2
2
3
0
0
0
2
0
3
0
1
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
1
1
1
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
3
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
2
1
2
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
3
1
0
0
1
2
0
0
6
1
0
2
0
0
0
2
3
0
0
0
1
0
0
0
0
0
0
1
1
0
2
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
2
0
0
2
2
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
1
0
0
0
2
0
0
0
0
0
1
2
0
1
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
2
9
0
0
3
0
0
2
0
0
2
0
2
1
0
0
0
0
0
0
1
0
2
0
3
1
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
2
0
2
1
2
0
0
0
0
0
0
0
0
1
0
0
0
3
1
2
0
0
2
2
0
0
2
2
0
1
0
0
7
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
2
0
1
0
1
0
0
0
0
3
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
2
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
2
0
0
0
1
0
0
2
0
0
0
0
0
0
4
0
0
0
0
0
3
3
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
3
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
1
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
3
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
4
0
0
0
0
2
0
0
2
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
4
0
0
2
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
3
0
2
0
0
2
0
1
0
0
0
0
2
0
0
1
0
1
1
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
2
0
0
1
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
6
0
0
1
0
0
0
1
3
2
5
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
1
0
2
0
0
4
1
0
0
1
0
0
0
0
5
0
0
0
0
0
7
0
2
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
4
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
1
0
1
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
3
0
2
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
2
0
1
0
0
0
1
0
0
0
2
0
0
0
2
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
1
2
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
2
0
2
0
0
1
1
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
1
1
1
0
0
2
0
0
0
5
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
9
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
1
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
2
1
0
1
0
0
0
1
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
1
0
0
2
0
0
4
0
0
1
0
0
2
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
2
2
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
4
3
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
2
0
0
2
0
0
2
2
0
0
2
5
0
1
3
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
2
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
1
0
0
1
0
2
0
2
2
0
4
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
1
2
0
0
0
0
1
0
0
2
0
0
3
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
2
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
3
0
0
2
0
0
2
0
0
1
2
0
1
2
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
3
2
0
2
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
2
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
1
1
1
0
0
0
1
2
0
0
1
0
0
1
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
1
0
0
0
0
0
0
2
0
0
0
2
2
2
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
3
0
4
0
2
0
0
5
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
2
1
0
5
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
9
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
3
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
2
0
0
0
0
0
1
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
7
0
0
0
0
0
0
1
2
0
2
1
0
0
1
2
0
0
0
0
0
4
2
0
0
0
0
0
0
0
2
0
2
2
0
1
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
2
0
0
0
0
0
2
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
2
0
7
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
2
4
0
0
0
0
2
0
1
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
3
0
0
0
3
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
2
0
0
0
0
0
3
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
2
2
0
0
0
0
0
0
1
0
0
4
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
1
1
0
3
0
1
2
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
5
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
5
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
6
2
0
0
0
1
0
1
0
1
3
1
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
1
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
2
0
0
0
0
3
0
2
0
0
0
6
2
7
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
2
2
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
4
2
0
0
0
0
0
0
0
6
1
0
0
0
0
0
0
0
8
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
9
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
3
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
3
0
0
2
0
0
0
3
1
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
2
0
0
0
0
0
2
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
2
2
0
0
1
0
0
1
0
1
1
2
0
0
0
0
0
1
1
0
0
0
2
1
1
0
2
0
0
1
1
0
3
0
0
0
0
0
0
0
1
2
2
3
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
3
2
1
0
1
0
0
3
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
8
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
1
0
1
1
0
0
0
1
0
4
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
4
0
0
0
1
0
0
2
0
0
0
1
0
0
0
1
2
0
0
2
0
0
0
0
1
0
2
1
0
0
0
2
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
1
0
3
0
2
0
0
0
0
0
3
0
0
0
0
0
5
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
3
0
1
0
0
1
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
1
1
0
4
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
1
0
0
1
6
0
0
0
3
1
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
2
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
1
0
1
0
0
0
0
3
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
2
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
2
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
2
2
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
2
2
0
2
0
0
0
1
2
1
0
2
1
0
0
0
1
0
2
0
0
2
0
2
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
2
0
0
2
1
0
0
2
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
5
0
0
0
3
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
1
0
2
2
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
2
7
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
3
0
1
0
0
1
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
5
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
4
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
1
0
2
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
2
1
0
4
0
0
0
0
1
0
0
1
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
1
0
1
0
1
0
1
0
0
0
3
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
2
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
4
0
1
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
3
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
2
0
2
1
2
0
0
2
0
0
0
0
0
1
1
0
0
0
2
0
2
0
0
0
0
0
0
0
4
0
0
0
0
1
2
0
0
2
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
4
0
0
0
0
1
0
0
0
2
0
1
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
1
0
0
0
0
1
2
0
0
0
0
1
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
2
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
1
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
2
0
1
0
0
2
0
0
0
2
0
2
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
2
0
0
0
1
2
0
0
3
4
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
1
2
0
0
1
0
0
0
0
0
2
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
6
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
1
0
0
2
1
0
1
0
0
0
0
0
0
2
0
0
1
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
4
2
1
1
0
2
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
2
0
4
0
0
1
0
0
0
0
3
0
0
0
0
0
2
0
0
0
2
2
0
0
2
0
0
0
2
0
0
2
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
3
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
3
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
3
0
0
5
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
2
2
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
3
1
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
1
2
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
4
0
2
6
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
5
1
3
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
2
2
2
0
3
0
0
1
2
0
1
0
0
0
0
2
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
8
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
2
1
1
3
0
1
0
0
0
2
0
0
1
0
1
0
0
0
0
0
2
5
0
0
0
0
2
1
0
0
2
0
0
3
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
6
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
1
0
0
1
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
3
0
0
0
0
0
0
0
2
0
0
2
1
1
0
0
0
0
0
2
0
0
1
1
0
0
1
0
0
0
0
0
2
1
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
5
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
1
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
2
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
3
0
1
0
0
0
0
2
0
0
0
2
0
4
1
1
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
1
3
0
2
0
0
2
0
0
2
0
0
0
2
0
2
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
4
1
0
1
1
0
0
1
0
0
2
0
0
0
0
0
1
0
0
2
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
5
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
1
0
1
0
0
2
0
0
0
0
0
0
2
4
0
0
0
2
0
1
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
1
0
1
2
0
0
1
0
0
3
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
1
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
5
1
0
2
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
3
0
0
1
0
0
2
0
1
2
0
2
1
1
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
1
2
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
5
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
1
0
0
1
0
3
0
0
0
1
0
0
1
0
7
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
3
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
1
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
3
0
1
0
0
0
0
0
5
0
1
2
0
0
6
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
11
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
3
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
2
2
0
0
0
4
0
0
1
1
0
0
0
0
3
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
3
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
3
1
0
0
0
0
0
2
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
2
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
2
0
2
2
0
0
1
0
0
0
1
0
3
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
1
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
1
0
0
0
2
0
0
0
0
2
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
5
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
1
1
1
0
0
0
2
0
0
1
0
2
0
0
0
0
0
2
2
2
0
0
0
0
0
5
0
0
1
0
2
0
0
0
0
0
0
1
0
0
4
0
0
5
0
0
1
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
4
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
2
2
0
0
1
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
6
1
0
0
3
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
8
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
4
0
0
0
0
0
1
5
0
0
0
0
0
0
0
2
0
2
2
0
1
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
3
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
5
0
0
0
0
2
1
0
0
1
2
0
0
0
2
0
0
1
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
1
0
1
0
0
0
1
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
2
2
2
0
0
1
0
1
0
0
3
1
0
0
2
0
0
0
0
0
0
0
3
3
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
1
2
0
0
0
2
0
2
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
2
0
0
0
1
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
2
3
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
3
1
1
0
1
1
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
1
0
2
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
1
0
2
0
0
0
0
3
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
2
0
1
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
11
0
2
0
0
1
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
2
0
1
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
8
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
3
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
2
2
0
1
0
0
0
2
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
1
0
1
0
0
0
0
0
2
1
2
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
3
1
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
7
0
2
3
1
2
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
1
0
2
0
0
2
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
2
1
1
0
2
0
1
2
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
5
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
3
0
0
1
0
0
0
0
0
1
0
3
0
3
0
0
0
0
5
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
2
0
0
0
0
1
0
2
0
0
0
0
0
2
2
0
1
1
1
0
0
0
4
0
0
2
2
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
3
2
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
3
0
0
1
0
0
0
0
0
0
2
1
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
1
0
2
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
6
0
0
0
2
2
1
0
1
0
2
1
1
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
3
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
1
0
1
1
0
0
1
0
1
0
0
2
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
3
0
0
1
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
3
0
2
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
2
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
5
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
1
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
2
4
0
0
0
0
0
0
0
0
3
0
0
7
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
2
1
0
2
0
1
0
0
0
3
0
0
0
0
0
1
0
0
0
1
2
5
0
1
0
0
0
1
0
1
0
1
0
0
1
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
2
1
0
0
0
3
0
0
0
0
1
1
1
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
5
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
1
0
0
0
0
2
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
3
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
1
1
0
0
0
1
1
0
0
0
1
0
0
0
0
2
0
0
0
0
3
0
0
0
0
2
0
0
1
1
0
0
0
0
3
0
0
2
2
0
0
0
0
0
1
1
0
0
0
0
0
4
0
0
0
3
0
0
0
2
1
0
2
4
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
2
1
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
1
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
1
0
1
2
1
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
1
0
0
2
0
1
0
0
0
0
1
0
3
0
0
1
0
0
0
0
0
0
0
0
2
2
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
1
2
0
0
0
0
0
4
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
1
0
1
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
5
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
2
2
2
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
2
1
0
0
2
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
3
1
0
0
0
2
4
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
3
5
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
3
1
0
1
0
0
0
0
2
0
0
0
0
0
1
2
0
2
2
0
0
2
0
0
6
0
1
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
3
0
0
0
0
0
0
1
1
1
0
0
0
1
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
5
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
4
0
2
1
0
0
2
0
0
0
2
2
5
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
2
1
0
1
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
2
1
0
0
0
0
1
0
1
1
2
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
2
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
2
3
5
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
1
0
1
4
5
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
5
0
0
0
0
0
3
2
0
0
2
1
1
0
0
0
4
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
4
0
0
0
1
0
4
2
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
1
0
1
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
1
3
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
1
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
3
0
0
2
0
1
0
0
3
0
2
1
0
2
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
5
0
2
0
0
0
0
2
1
0
0
0
5
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
1
1
2
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
2
1
0
5
0
0
0
0
1
1
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
2
0
2
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
2
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
4
0
0
2
0
0
0
0
0
1
0
1
1
0
3
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
2
0
1
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
1
2
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
3
0
2
1
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
6
0
0
0
0
0
0
0
0
0
0
2
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
1
1
2
7
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
1
0
0
0
2
0
0
0
0
0
1
0
4
3
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
4
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
2
1
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
3
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
2
0
1
0
0
0
0
0
0
0
2
2
0
0
2
1
0
1
0
0
0
0
0
2
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
4
3
0
0
2
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
1
0
1
0
0
0
0
0
9
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
3
0
0
1
0
1
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
4
0
1
0
3
3
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
9
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
2
3
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
2
0
0
1
0
0
4
0
0
0
0
2
0
0
1
1
0
0
0
0
1
0
1
0
0
3
0
0
1
0
0
1
2
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
3
3
0
0
0
7
1
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
1
0
0
0
4
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
2
1
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
2
0
0
0
2
0
1
0
1
0
1
0
0
0
0
0
0
0
2
0
2
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
2
0
0
2
0
0
0
1
0
2
5
0
0
0
0
1
0
0
4
0
0
0
2
3
0
0
0
1
0
0
1
0
0
0
0
0
0
0
3
0
1
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
5
0
0
0
0
0
1
0
0
0
0
0
0
2
3
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
3
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
1
4
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
4
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
3
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
2
1
2
2
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
1
3
3
0
0
0
1
2
0
1
2
0
0
0
0
0
1
0
0
2
0
0
0
0
1
5
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
1
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
11
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
6
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
3
2
0
2
0
0
0
0
1
2
0
1
0
0
2
0
0
0
0
1
0
1
0
0
1
0
0
0
4
0
2
1
0
0
0
1
1
0
0
0
2
0
0
0
0
0
2
0
0
2
1
3
0
0
2
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
2
0
0
4
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
2
0
0
3
1
0
0
0
0
0
0
3
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
6
0
0
0
0
0
0
0
1
0
0
0
0
4
0
2
0
0
0
2
0
0
0
6
0
1
0
1
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
6
0
1
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
2
0
1
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
1
2
0
2
1
0
1
0
0
0
0
0
0
1
4
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
2
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
1
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
2
0
0
0
0
2
0
0
4
0
0
0
2
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
1
3
0
0
2
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
1
0
1
1
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
2
0
2
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
1
0
1
1
0
0
2
3
0
0
0
2
1
0
0
0
1
2
0
0
2
1
0
0
0
0
2
1
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
4
1
1
0
0
5
1
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
3
0
0
1
0
0
0
0
0
1
0
0
0
3
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
3
1
1
2
1
0
0
0
2
0
0
0
0
0
1
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
1
0
4
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
3
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
1
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
6
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
4
0
2
0
2
0
3
0
1
2
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
4
2
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
3
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
8
2
0
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
1
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
5
0
0
0
3
0
0
0
0
0
0
2
0
0
2
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
2
1
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
1
0
3
0
2
0
0
0
0
1
0
2
2
0
0
1
3
0
0
0
1
2
2
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
1
0
1
0
2
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
3
0
0
0
4
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
2
0
0
0
1
0
1
2
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
2
2
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
2
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
2
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
1
0
2
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
3
0
0
0
2
0
2
1
0
0
0
0
0
1
0
2
0
4
0
0
0
0
0
0
0
0
0
0
7
0
0
4
0
1
1
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
4
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
3
1
2
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
2
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
5
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
3
0
0
1
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
1
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
7
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
2
0
0
0
0
1
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
18
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
2
0
2
2
2
0
0
2
0
1
0
0
0
1
2
1
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
2
1
0
0
2
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
2
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
2
5
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
4
0
0
1
0
0
1
0
1
0
2
0
1
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
3
0
0
0
0
0
0
0
1
2
2
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
1
0
1
0
0
2
0
0
0
1
2
0
2
0
4
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
5
0
1
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
2
2
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
2
0
2
2
1
0
3
2
4
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
4
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
3
0
3
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
2
0
3
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
2
4
0
0
0
1
0
0
1
0
0
0
2
0
0
0
3
1
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
2
0
3
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
1
0
0
1
4
0
0
0
0
0
2
0
0
3
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
1
0
0
1
0
2
0
2
0
0
0
0
0
0
1
0
10
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7
0
0
1
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
5
0
1
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
2
1
0
0
0
6
4
2
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
2
0
0
0
0
1
1
0
0
3
0
0
2
2
0
0
0
0
1
1
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
3
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
2
0
0
0
0
0
2
3
0
0
0
0
0
0
0
2
1
1
3
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
3
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
8
0
1
0
0
0
0
0
0
0
0
0
1
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
8
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
2
5
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
2
0
0
2
0
0
1
2
0
0
1
0
0
0
0
0
0
0
2
0
4
0
1
2
0
1
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
10
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
3
0
0
1
1
0
0
1
0
0
2
0
0
0
0
0
0
0
1
1
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
1
0
2
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
1
2
0
1
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
1
0
1
0
0
0
1
0
0
1
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
1
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
1
2
0
0
0
0
0
0
3
0
0
0
1
1
0
2
0
0
2
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
1
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
4
0
1
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
2
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
1
0
2
2
0
0
2
1
0
0
1
0
0
0
0
0
0
0
1
4
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
1
0
0
0
0
0
1
3
2
5
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
1
2
0
1
0
0
2
0
0
3
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
2
1
0
1
0
0
0
12
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
5
0
2
0
0
0
5
0
0
0
0
2
1
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
8
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
3
0
0
1
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
1
1
0
2
0
0
0
0
1
0
2
0
0
2
2
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
8
1
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
1
1
1
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
2
3
0
6
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
2
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
2
0
1
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
2
3
0
0
0
0
0
0
0
2
0
2
0
0
1
0
2
2
0
0
0
0
1
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
3
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
2
1
0
2
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
2
0
1
0
5
0
0
0
0
2
0
0
0
1
3
0
0
3
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
1
0
1
0
0
1
0
0
0
0
2
0
1
2
1
0
0
2
0
1
0
0
0
0
4
0
0
0
0
0
1
1
0
1
0
3
1
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
3
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
4
0
2
0
0
1
0
0
0
0
1
1
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
1
0
0
2
2
0
0
2
0
0
0
1
1
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
4
1
0
0
0
0
0
0
0
0
0
1
0
0
4
0
2
1
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
5
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
3
0
2
1
0
0
2
0
0
0
0
3
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
3
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
3
1
1
1
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
7
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
3
0
0
0
10
1
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
3
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
1
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
6
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
5
0
4
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
4
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
3
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
1
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
3
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
3
1
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
5
0
0
0
3
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
1
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
2
0
2
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
3
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
2
0
3
0
3
0
0
0
0
1
0
0
0
0
0
8
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
8
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
1
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
3
1
0
0
0
1
0
0
0
0
0
0
2
0
2
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
3
0
1
0
0
1
2
0
0
2
0
1
0
1
1
0
0
0
0
0
0
0
4
0
0
0
0
1
1
1
0
2
0
2
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
3
0
4
1
0
0
1
3
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
1
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
1
1
0
0
2
0
0
0
2
0
1
0
1
0
5
0
2
2
0
0
0
2
0
0
2
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
7
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
4
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
1
0
1
1
0
1
0
0
0
0
0
0
1
1
0
0
0
13
8
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
7
0
0
1
0
1
0
2
0
1
0
2
2
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
2
0
0
0
0
0
0
2
2
0
0
3
2
0
0
1
1
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
1
0
2
0
0
0
0
0
3
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
5
2
0
0
0
1
0
1
0
1
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
5
0
0
4
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
4
1
0
0
0
0
1
1
0
2
2
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
3
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
5
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
2
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
1
1
0
8
1
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
3
13
0
0
2
0
0
2
3
0
2
0
2
0
1
0
0
0
0
0
0
0
3
0
0
2
0
0
2
1
3
0
2
0
1
3
0
0
0
0
3
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
1
0
1
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
8
0
1
1
0
2
3
0
0
0
1
0
0
0
2
0
0
0
3
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
1
0
0
0
1
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
2
2
1
0
0
2
1
1
0
0
0
0
0
2
0
3
0
1
0
1
0
2
1
1
0
2
0
0
0
0
0
0
2
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
3
2
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
2
2
0
0
1
2
0
0
0
0
2
10
0
0
0
0
0
3
0
1
0
0
3
0
0
0
2
0
0
0
1
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
2
2
3
0
1
0
0
0
1
0
2
0
0
6
0
0
0
0
0
2
0
1
0
0
2
2
4
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
11
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
3
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
7
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
1
2
2
0
0
0
0
0
1
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
6
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
2
1
2
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
5
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
4
0
1
0
2
2
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
2
1
3
0
0
0
3
0
0
0
0
2
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
2
0
0
2
1
0
0
2
0
0
1
1
2
0
0
0
0
0
1
0
0
0
2
1
3
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
2
1
0
0
1
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
2
6
2
2
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
1
0
2
0
0
0
1
0
2
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
2
2
2
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
5
0
1
0
0
0
2
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
1
1
1
0
0
0
1
3
2
0
0
0
0
0
0
3
0
0
0
0
4
0
0
0
0
0
0
0
0
2
2
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
2
2
0
0
0
0
3
0
0
2
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
2
3
0
1
0
0
0
1
2
0
0
0
0
0
2
0
0
0
2
1
0
2
1
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
8
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
1
2
0
1
2
3
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
1
1
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
1
0
1
1
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
7
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
2
0
0
0
0
0
0
3
0
0
0
0
0
0
4
0
0
4
2
1
2
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
2
0
0
3
0
0
0
0
1
0
1
4
0
0
1
0
6
0
0
0
0
0
3
0
4
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
3
3
0
0
2
0
0
0
0
0
0
1
0
2
0
2
0
0
0
6
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
4
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
5
2
0
0
0
2
0
3
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
2
2
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
1
1
0
6
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
2
2
1
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
6
0
1
1
0
2
0
0
0
0
0
0
2
0
1
1
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
1
0
1
3
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
3
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
7
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
2
0
2
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
3
0
0
0
0
0
0
2
0
0
1
2
2
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
2
2
0
0
0
7
0
0
0
0
0
0
0
1
0
0
2
1
4
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
2
1
2
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
3
0
0
0
0
1
1
1
0
0
0
1
0
1
0
0
0
0
2
0
3
1
0
0
0
0
3
4
1
0
0
1
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
2
0
4
2
0
0
3
0
0
2
0
0
2
0
0
2
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
5
0
0
0
0
0
0
0
3
2
0
1
0
2
0
0
0
0
1
0
2
0
0
0
3
0
0
2
2
0
0
0
0
0
0
3
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
2
0
0
0
3
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
1
0
0
0
0
2
0
0
0
0
1
4
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
2
0
0
2
0
0
0
0
0
1
2
0
0
0
0
1
0
0
2
0
0
1
0
0
1
2
0
0
0
0
0
1
1
2
0
4
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
1
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
2
0
0
0
0
0
0
6
0
0
0
0
0
0
0
2
0
0
2
0
0
2
2
0
0
0
1
1
1
1
0
0
4
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
1
2
0
0
0
2
0
0
3
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
2
2
0
2
0
0
0
1
0
0
0
2
1
0
0
0
0
1
0
0
3
0
0
0
0
0
1
0
0
1
0
2
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
2
0
0
0
1
0
0
0
2
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
7
0
1
2
0
0
0
0
0
2
0
3
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
5
1
0
0
0
2
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
3
2
0
0
1
0
0
2
2
1
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
6
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
5
0
0
2
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
6
1
2
0
0
0
0
0
1
0
2
0
1
0
0
2
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
2
1
0
1
1
1
1
0
0
0
3
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
2
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
3
0
0
2
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
1
0
0
0
0
1
2
8
2
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
2
0
2
2
0
0
0
1
1
0
0
0
2
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
1
1
0
0
2
0
0
0
0
3
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
1
2
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
4
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
4
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
2
3
0
2
0
0
0
1
0
0
0
2
0
0
2
2
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
3
0
3
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
5
0
2
0
0
0
2
0
2
3
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
1
1
0
1
0
0
0
0
1
0
0
1
0
2
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
2
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
2
0
0
2
2
0
0
0
2
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
2
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
1
0
0
0
0
0
0
3
0
0
1
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
5
0
1
4
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
1
0
4
1
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
4
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
8
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
1
0
0
1
0
0
2
1
0
0
0
0
0
2
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
1
0
0
0
0
4
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
2
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
2
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
2
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
2
0
2
2
0
0
1
0
2
0
0
2
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
3
1
0
0
1
0
1
0
0
2
2
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
1
8
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
3
2
0
0
2
0
0
1
0
0
1
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
2
0
2
1
0
1
0
0
0
2
2
0
0
0
0
0
6
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
1
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
4
2
1
1
1
0
0
0
0
2
0
0
1
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
2
0
2
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
3
2
1
0
0
2
1
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
3
1
1
0
1
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
3
0
1
0
2
1
0
0
1
0
2
0
0
2
0
0
0
2
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
19
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
1
2
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
3
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
3
1
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
2
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
2
0
0
0
1
1
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
1
1
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
2
3
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
1
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
3
0
0
0
2
0
0
0
1
0
0
2
0
1
0
2
0
0
1
0
0
0
0
1
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
8
2
1
5
2
0
0
1
0
0
0
2
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
1
1
1
0
0
6
1
0
0
0
1
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
3
1
0
0
0
0
1
2
0
0
1
0
1
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
1
3
0
0
0
0
0
3
2
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
5
0
0
0
0
0
0
0
1
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
3
0
0
2
0
0
0
0
0
3
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
4
4
1
1
0
2
0
0
0
2
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
3
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
1
4
0
0
0
0
1
2
6
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
4
0
0
0
0
2
0
0
0
0
0
0
5
2
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
1
0
2
1
0
2
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
2
0
1
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
1
0
2
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
1
0
0
1
0
0
1
2
0
0
2
0
0
0
2
0
0
0
3
1
1
0
0
0
0
0
0
0
0
0
2
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
4
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
1
1
0
3
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
2
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
3
0
0
1
1
1
0
0
0
2
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
2
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
1
1
2
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
3
2
4
1
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
2
1
0
2
0
0
1
0
0
1
0
0
0
0
2
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
5
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
1
3
0
0
0
0
0
1
3
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
2
2
0
0
1
0
0
2
0
1
1
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
2
0
0
3
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
3
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
1
0
0
0
2
0
1
0
0
0
2
0
0
0
1
0
0
2
0
1
2
1
1
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
3
1
1
0
2
2
0
0
0
0
0
0
2
0
1
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
2
0
0
2
0
0
1
1
0
0
2
1
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
4
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
3
0
1
0
1
1
0
1
2
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
2
3
2
0
0
0
0
4
0
0
0
0
0
0
0
0
15
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
4
0
1
0
0
0
6
0
1
0
2
0
0
0
0
0
0
2
0
6
2
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
2
0
0
2
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
3
0
0
3
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
3
2
4
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
1
2
3
0
0
1
2
2
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
2
0
0
0
1
0
1
1
0
0
0
0
0
2
1
0
2
0
1
0
0
0
2
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
1
0
1
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
2
1
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
2
2
0
1
2
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
5
0
0
1
0
2
0
0
0
0
1
0
2
0
0
0
0
1
0
2
1
0
2
1
0
0
1
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
3
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
1
2
0
2
0
0
0
1
0
0
0
0
1
0
0
0
1
0
2
0
2
0
0
0
0
0
0
1
0
2
5
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
2
1
0
0
2
3
0
0
0
0
0
1
0
0
0
0
2
0
3
0
1
1
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
3
0
0
0
0
2
0
2
0
1
0
0
0
0
0
2
1
0
0
0
0
2
1
0
0
3
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
3
0
0
0
0
4
0
1
0
0
3
0
0
0
1
0
2
0
0
0
0
1
0
0
0
1
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
1
2
4
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
1
1
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
2
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
1
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
2
0
3
0
0
0
2
0
0
0
0
0
0
1
0
2
7
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
12
1
0
0
0
0
0
0
1
1
2
0
0
1
2
0
0
0
0
1
0
0
0
0
1
2
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
3
0
0
1
2
0
0
0
0
0
0
0
0
1
0
1
2
0
0
4
0
0
0
0
0
1
0
0
0
3
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
16
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
5
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
3
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
3
0
0
0
2
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
2
0
0
0
1
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
2
0
2
0
1
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
1
1
0
0
2
0
0
0
0
1
0
1
1
2
0
0
0
0
4
0
1
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
2
0
2
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
3
1
0
1
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
1
1
0
1
0
3
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
2
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
2
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
1
0
0
0
11
0
2
0
0
0
0
0
1
0
1
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
1
3
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
2
0
0
0
0
1
0
2
0
0
1
1
0
0
2
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
1
0
3
1
1
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
6
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
2
1
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
7
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
2
1
0
1
0
0
0
0
0
0
0
0
0
2
1
2
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
3
0
3
0
0
0
0
0
3
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
4
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
2
3
0
0
0
0
1
3
1
0
0
0
0
0
1
3
2
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
3
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
2
1
0
0
0
0
1
0
0
0
0
1
0
0
2
1
0
0
1
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
3
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
1
0
0
0
2
0
0
3
1
0
0
0
1
0
2
1
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
1
4
2
0
0
0
0
1
0
0
0
0
5
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
8
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
3
0
0
5
0
1
0
0
0
0
2
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
1
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
3
4
0
0
0
0
0
0
2
0
0
2
1
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
2
2
0
0
2
0
0
0
2
3
0
0
0
1
0
0
1
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
1
0
0
1
0
1
3
0
0
1
1
0
2
0
0
0
0
4
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
9
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
3
0
0
0
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
3
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
2
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
3
2
0
0
0
0
0
0
0
7
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
2
1
0
0
0
1
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
1
1
2
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
3
0
2
0
1
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
2
1
0
0
0
2
2
0
7
1
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
1
0
2
1
0
0
5
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
3
2
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
3
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
11
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
1
2
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
1
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
3
0
0
1
15
0
0
0
3
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
1
0
0
0
0
0
2
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
2
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
2
1
0
0
0
0
0
1
0
0
5
0
0
0
0
0
1
0
0
3
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
2
0
2
0
1
1
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
1
0
2
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
2
0
0
0
3
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
3
0
1
3
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
1
3
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
1
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
2
0
0
2
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
2
2
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
2
0
0
1
2
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
1
0
0
1
1
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
3
6
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
4
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
9
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
1
0
0
2
0
1
0
2
0
2
0
0
2
0
0
0
0
1
0
0
0
0
1
0
2
2
0
0
0
0
0
0
4
0
2
1
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
1
0
0
0
3
3
0
0
0
0
0
0
0
1
0
0
1
1
2
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
3
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
3
2
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
8
2
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
3
0
0
0
0
2
5
0
0
0
0
4
0
0
2
1
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
1
1
2
0
0
0
0
1
1
2
0
1
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
3
0
1
0
0
3
0
0
0
1
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
3
0
1
2
2
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
6
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
2
0
2
0
0
0
0
0
0
4
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
4
0
0
0
1
0
2
2
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
1
0
1
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
1
1
2
0
3
0
0
0
0
1
0
1
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
5
1
0
1
0
0
0
0
1
1
0
4
0
0
2
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
1
0
2
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
3
0
0
0
4
0
0
0
0
0
0
2
1
0
0
3
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
2
2
0
0
0
2
1
0
0
2
2
0
2
0
2
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
2
0
0
0
0
1
0
0
4
0
0
2
2
0
0
0
0
1
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
2
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
1
0
2
1
2
3
0
0
0
0
0
0
0
2
0
0
3
0
1
1
0
0
0
0
0
0
0
2
0
1
2
0
0
2
0
0
1
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
1
3
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
3
0
0
2
0
0
2
1
0
0
0
1
0
0
0
0
0
1
0
2
0
0
2
0
0
0
3
0
0
0
0
0
1
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
8
1
0
0
0
1
0
1
0
0
1
0
4
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
7
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
3
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
2
1
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
8
1
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
1
0
0
2
0
2
0
4
0
1
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
4
1
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
3
0
0
1
3
0
3
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
3
0
0
0
4
6
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
2
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
3
2
0
0
0
0
2
0
0
0
0
1
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
3
0
0
1
0
1
0
0
5
0
1
0
0
0
0
1
0
0
2
5
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
3
0
0
0
0
0
1
0
0
0
0
0
2
1
2
0
2
0
2
1
0
0
2
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
4
1
2
0
1
0
0
0
0
8
0
0
0
6
0
0
0
0
0
2
0
1
1
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
1
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
3
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
1
0
0
0
2
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
3
0
0
2
3
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
5
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
2
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
3
4
6
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
11
2
0
0
0
0
0
0
2
1
3
0
1
0
0
0
0
2
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
2
5
0
1
0
0
0
2
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
1
0
2
0
0
0
0
0
2
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
2
0
8
0
0
0
0
1
0
6
1
0
0
0
0
0
0
2
0
0
2
1
0
0
3
1
0
0
0
0
3
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
1
0
1
0
6
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
1
0
0
1
0
0
5
0
0
0
0
2
0
0
0
3
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
1
0
0
2
0
0
0
0
4
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
1
2
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
11
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
1
2
0
0
0
0
1
0
0
0
0
0
0
2
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
5
0
0
1
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
1
0
1
0
2
2
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
2
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
1
0
0
2
0
0
2
0
4
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
2
1
3
0
1
0
0
1
0
0
0
0
0
0
3
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
2
1
0
0
0
0
1
0
2
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
2
0
0
5
0
0
0
1
0
0
0
0
0
1
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
2
0
0
3
0
0
0
0
2
0
0
1
0
0
2
0
3
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
2
0
0
0
0
2
2
1
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
3
0
0
1
0
0
2
0
0
0
0
0
3
0
2
0
0
3
0
1
0
0
0
1
0
0
2
1
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
7
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
3
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
1
3
1
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
2
3
0
0
1
1
2
0
2
0
0
0
0
0
0
2
2
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
8
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
3
3
2
0
0
1
2
2
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
1
0
4
0
0
1
0
0
0
2
0
0
0
0
0
0
1
1
2
0
0
0
0
0
2
0
0
0
2
0
0
2
2
2
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
3
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
2
0
1
0
0
1
1
1
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
4
0
1
0
0
0
0
0
0
0
0
1
0
0
4
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
3
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
1
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
2
4
0
0
0
0
2
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
4
0
1
0
0
0
3
0
0
0
0
0
0
2
5
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
2
0
1
2
2
0
0
0
2
2
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
3
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
1
0
0
0
0
0
4
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
4
2
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
2
0
3
0
1
0
2
1
0
0
0
0
0
1
0
1
0
3
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
4
1
1
0
0
0
0
0
0
0
0
0
3
0
1
5
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
3
0
1
1
0
3
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
9
0
2
0
0
0
0
2
0
5
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
4
0
1
0
0
0
5
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
1
1
2
0
0
0
0
1
0
3
0
0
0
0
2
1
0
0
0
0
1
2
1
1
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
3
0
0
0
0
0
2
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
3
0
0
2
1
0
1
0
0
0
0
1
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
1
0
0
0
2
2
0
0
0
2
1
3
0
1
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
3
2
1
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
2
0
2
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
1
0
0
0
0
1
0
0
2
0
0
0
2
0
1
0
6
0
0
0
0
0
0
0
0
2
1
2
2
0
0
2
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
2
0
0
1
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
6
0
0
0
1
1
0
0
0
3
0
1
0
2
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
5
0
0
4
0
0
0
1
0
2
0
1
2
1
0
1
0
1
0
0
0
0
0
0
7
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
4
2
3
0
0
2
1
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
3
0
0
1
2
2
0
1
0
0
0
0
0
2
1
5
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
12
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
1
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
2
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
1
0
2
0
0
0
0
1
2
0
1
2
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
1
0
0
1
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
1
0
0
0
1
2
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
1
1
2
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
1
1
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
1
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
2
0
1
2
2
0
0
0
3
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
2
0
1
0
0
1
0
1
1
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
3
0
0
2
4
0
0
0
0
2
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
1
0
3
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
2
1
0
0
0
1
1
2
0
2
0
0
0
2
0
0
0
0
0
1
0
3
0
0
2
0
0
2
0
1
0
2
1
0
0
1
0
0
0
0
0
0
1
1
1
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
1
0
0
1
2
1
4
0
0
0
0
4
1
1
1
0
0
0
0
0
0
1
1
0
0
0
0
4
0
0
2
0
0
0
1
1
1
3
0
0
0
1
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
3
0
2
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
2
0
0
0
0
1
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
4
2
2
0
1
0
0
0
0
0
2
1
0
0
0
0
0
2
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
3
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
2
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
1
2
3
1
4
0
0
0
0
2
1
2
0
0
4
0
2
0
0
0
1
0
2
0
0
0
2
0
1
3
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
2
0
1
0
3
1
0
0
1
1
0
0
0
1
2
1
0
0
0
0
0
0
0
0
1
1
0
3
2
0
0
0
0
2
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
3
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
6
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
2
2
1
1
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
2
0
0
1
2
0
2
3
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
4
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
1
0
0
3
0
0
0
1
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
1
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
1
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
3
0
2
2
0
0
0
0
2
0
0
4
0
3
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
1
2
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
1
0
2
2
1
1
0
0
1
0
0
2
0
0
1
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
1
1
0
0
0
0
0
0
0
3
0
1
2
0
2
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
2
0
5
0
0
3
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
3
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
1
8
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
4
1
0
0
0
0
0
2
0
0
0
0
0
1
2
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
2
1
0
0
0
0
1
0
0
0
1
0
0
0
2
2
1
0
0
0
0
0
3
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
3
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
2
1
0
1
0
1
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
3
0
0
0
0
1
2
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
12
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
7
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
3
0
0
1
1
3
3
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
8
0
0
0
2
0
0
0
0
0
0
0
0
0
0
5
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
3
0
0
2
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
1
1
0
0
1
0
1
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
2
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
3
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
3
0
0
0
3
0
0
2
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
6
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
1
0
0
1
0
0
0
2
0
3
3
0
0
0
0
0
0
3
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
2
3
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
1
0
3
1
0
0
0
2
3
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
2
7
1
2
0
0
0
0
0
0
0
0
4
0
2
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
8
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
1
0
0
2
0
1
1
1
0
0
0
1
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
2
0
0
2
0
0
0
0
1
0
2
0
7
0
0
1
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
4
0
0
0
1
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
3
0
0
2
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
1
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
4
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
3
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
1
0
2
0
0
2
2
1
0
0
0
0
0
0
0
1
1
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
1
4
0
0
0
0
1
0
0
0
1
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
1
0
0
3
1
0
3
1
0
0
0
0
0
1
3
0
0
0
1
0
0
0
1
0
0
0
0
0
3
0
3
0
0
0
0
2
0
1
0
0
1
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
1
2
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
1
0
1
2
0
0
2
2
0
1
0
0
0
1
0
0
0
0
1
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
9
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
2
0
2
1
2
0
0
0
1
0
0
0
1
0
1
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
6
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
5
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
1
0
2
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
1
0
1
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
3
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
2
0
1
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
3
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
5
0
0
0
0
0
0
0
1
1
0
0
1
0
4
0
0
0
0
2
0
0
0
0
0
0
2
2
2
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
2
0
0
0
0
2
0
0
2
0
0
0
0
1
8
0
1
0
0
0
2
0
0
0
0
3
0
0
2
0
0
0
1
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
1
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
2
0
0
2
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
3
0
1
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
2
2
0
0
3
3
0
0
0
0
2
1
2
2
0
0
0
2
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
4
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
9
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
3
0
0
1
0
0
2
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
7
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
3
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
3
0
1
0
0
0
2
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
4
0
1
0
0
0
0
2
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
1
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
2
0
0
1
0
0
0
0
0
0
0
0
2
3
0
0
0
1
0
0
0
0
1
3
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
4
2
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
1
0
1
0
0
1
1
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
3
0
3
0
0
0
0
3
0
0
0
0
0
3
0
0
2
0
0
0
0
1
0
0
0
0
3
2
2
0
0
1
0
0
0
3
0
1
4
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
2
4
0
1
1
0
0
0
0
0
1
1
0
0
0
2
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
1
0
0
2
0
0
0
0
0
0
2
0
6
0
0
0
1
1
0
0
0
1
0
0
0
0
2
1
2
0
0
0
0
3
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
4
1
0
0
0
0
0
0
0
0
0
2
0
3
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
3
0
0
0
4
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
3
0
0
6
0
0
0
0
0
0
10
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
3
0
0
0
0
0
0
0
1
1
0
2
2
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
4
3
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
2
0
0
0
5
0
1
0
0
3
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
2
2
0
0
4
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
1
0
0
0
2
0
1
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
2
1
0
0
1
0
0
1
0
0
0
3
0
0
2
0
0
13
0
0
0
0
0
1
0
0
0
0
0
2
0
2
2
0
2
0
0
1
1
1
2
0
0
0
4
0
0
0
1
0
2
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
2
0
0
0
1
1
0
0
0
1
1
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
4
0
1
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
1
1
0
3
0
1
0
2
1
0
0
8
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
2
5
0
0
0
0
2
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
2
0
0
0
0
0
4
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
3
0
0
2
0
1
0
2
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
1
0
1
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
1
0
1
0
0
0
0
0
1
0
2
0
0
3
1
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
1
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
2
3
1
2
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
2
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
1
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
2
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
3
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
2
0
0
2
0
1
0
3
0
0
1
1
0
0
0
0
5
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
2
0
0
3
0
1
0
2
0
5
0
0
6
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
4
2
0
0
0
0
0
0
0
0
2
0
3
0
0
0
2
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
2
2
3
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
2
0
0
4
0
0
0
1
2
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
3
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
2
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
9
0
0
0
0
0
0
1
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
1
4
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
2
1
1
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
3
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
1
3
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
7
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
5
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
1
1
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
2
2
0
1
0
1
1
0
1
1
1
2
8
1
1
0
0
0
0
0
0
3
0
0
1
0
0
2
2
1
0
2
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
1
1
1
1
2
0
0
0
0
0
2
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
3
0
0
0
0
2
1
1
0
0
2
1
0
0
0
0
0
0
0
0
0
4
0
1
1
0
1
6
0
0
0
0
0
0
0
0
0
1
0
0
4
0
2
0
0
1
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
1
1
0
0
0
4
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
2
0
1
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
2
3
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
1
0
0
0
1
0
1
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
3
0
0
1
0
0
2
0
0
2
1
1
0
0
0
0
0
1
0
0
1
2
0
3
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
1
0
0
1
1
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
2
0
0
0
0
3
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
4
1
0
0
2
2
0
0
0
0
0
0
0
1
1
0
1
1
2
0
9
3
0
0
0
0
0
2
2
0
0
0
1
3
0
2
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
3
0
1
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
5
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
3
3
0
0
0
1
0
0
0
0
0
6
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
1
2
4
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
2
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
2
1
2
0
1
0
0
0
0
1
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
5
1
0
4
1
3
0
0
0
1
2
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
2
0
3
1
0
1
0
0
2
0
3
0
0
0
0
0
1
0
1
1
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
1
0
0
2
4
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
1
0
5
2
1
0
0
0
1
0
0
0
0
0
0
0
6
1
0
2
2
2
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
1
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
1
0
0
0
2
0
4
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
2
2
0
5
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
3
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
5
0
6
1
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
2
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
4
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
2
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
7
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
1
1
0
0
2
0
1
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
1
0
0
1
0
4
2
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
2
0
0
2
0
1
0
1
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
5
0
4
2
2
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
1
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
1
2
0
1
2
0
0
4
0
0
0
1
0
4
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
1
0
1
0
0
2
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
2
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
6
2
0
0
0
3
0
1
0
1
0
0
0
1
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
3
0
0
1
2
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
2
0
0
0
0
1
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
1
0
1
2
0
0
0
1
0
1
0
10
0
0
0
0
0
0
0
0
0
0
1
2
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
3
2
0
0
0
3
0
2
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
2
2
0
0
0
0
4
0
0
0
2
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
5
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
3
2
0
3
0
0
7
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
1
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
2
0
0
8
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
3
0
1
0
0
0
0
0
3
0
2
2
0
0
0
0
0
0
2
3
0
1
0
0
0
1
0
1
2
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
2
0
0
0
0
0
0
1
3
0
0
0
0
0
2
0
1
0
0
0
3
0
0
0
0
1
3
0
0
1
0
0
0
0
0
5
1
0
0
0
2
0
0
0
3
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
2
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
2
0
0
5
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
2
0
2
0
10
0
0
0
3
0
0
2
0
0
0
0
0
0
0
2
0
4
0
0
2
0
0
0
0
0
0
1
2
0
0
0
2
0
3
5
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
3
1
0
0
0
0
1
3
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
2
3
2
0
0
0
0
0
3
1
0
2
0
2
2
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
5
0
0
0
0
0
0
0
0
0
2
0
8
0
1
0
0
0
0
2
0
2
0
0
0
0
0
2
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
3
0
0
0
0
1
0
1
0
2
0
1
0
0
2
0
2
0
0
0
2
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
3
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
3
0
0
0
0
2
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
1
4
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
2
2
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
3
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
5
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
10
0
0
0
0
0
2
0
2
0
9
0
0
0
2
2
0
2
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
1
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
3
1
0
0
0
0
1
0
0
0
0
1
1
0
0
2
0
0
2
0
0
1
1
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
2
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
3
1
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
2
0
3
3
1
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
3
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
2
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
4
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
1
0
1
0
0
0
0
0
1
1
0
2
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
1
0
1
0
2
4
0
0
2
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
6
1
0
0
0
0
1
0
1
0
2
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
1
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
5
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
1
1
0
0
0
0
0
2
1
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
1
4
2
1
2
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
1
6
0
0
0
0
1
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
5
2
0
0
0
0
0
0
1
0
2
0
0
0
0
2
2
0
2
0
0
1
4
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
3
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
1
0
0
0
1
1
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
2
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
3
0
2
0
2
0
0
0
3
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
2
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
2
0
0
2
0
1
2
0
0
0
0
2
0
0
1
0
0
0
1
0
1
2
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
5
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
11
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
1
1
0
0
0
0
2
0
0
0
2
0
16
0
0
0
1
0
6
0
0
0
1
2
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
2
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
3
1
1
0
2
0
0
2
0
1
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
1
0
0
0
2
0
0
0
0
2
2
3
0
0
0
0
0
0
0
2
0
0
0
2
2
1
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
9
0
0
2
0
0
0
1
2
0
2
0
2
0
0
0
0
1
0
0
2
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
3
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
4
0
2
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
2
0
3
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
1
3
0
0
1
0
2
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
1
2
0
0
0
1
1
0
0
0
2
1
0
0
0
1
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
1
0
0
5
0
2
0
0
2
0
1
1
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
3
2
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
1
0
0
0
2
5
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
1
0
3
1
1
1
0
0
1
1
0
2
2
0
0
0
0
0
0
2
0
2
0
1
2
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
4
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
1
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
2
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
1
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
4
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
3
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
2
2
0
0
2
0
4
0
0
1
1
2
0
0
0
0
0
0
0
0
0
1
0
3
0
1
0
0
0
0
3
2
0
0
1
0
0
0
2
0
1
2
0
0
0
1
0
2
0
0
0
1
1
1
0
0
0
0
0
0
2
0
4
1
0
0
0
0
2
0
0
1
0
0
0
2
1
0
2
1
0
0
0
0
0
2
0
0
0
0
0
4
4
0
0
0
2
0
0
2
0
0
1
2
0
6
0
0
0
1
2
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
3
0
1
0
0
0
0
1
2
7
2
0
0
4
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
6
0
3
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
3
2
0
0
0
0
4
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
6
0
1
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
1
4
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
2
0
0
0
0
0
0
1
0
1
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
1
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
3
0
0
1
1
0
2
1
1
2
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
3
0
3
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
8
2
0
0
2
0
1
0
0
0
0
1
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
4
0
0
0
0
0
0
0
1
0
0
6
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
1
1
2
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
1
2
0
1
2
0
1
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
2
0
0
3
0
0
0
1
0
1
1
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
3
0
1
0
0
0
0
0
2
1
3
0
0
0
0
0
0
0
0
0
3
0
1
1
1
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
2
1
0
2
2
0
0
2
1
1
0
0
0
0
1
1
2
0
2
0
0
5
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
2
0
2
0
0
0
3
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
3
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
1
0
1
2
0
0
0
1
0
0
0
0
0
0
0
1
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
1
1
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
2
2
0
0
1
0
0
0
3
0
0
0
0
1
2
0
0
3
0
0
1
0
0
0
0
0
0
0
2
2
0
0
2
0
0
2
0
0
0
2
1
0
2
1
0
0
0
0
2
0
0
0
0
3
1
3
0
1
1
4
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
2
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
3
1
0
0
0
0
1
0
0
0
0
0
0
1
0
3
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
2
0
0
1
1
2
0
1
1
0
1
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
3
1
2
1
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
5
2
1
1
0
0
1
2
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
4
0
0
0
0
0
0
4
1
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
5
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
1
0
0
1
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
1
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
2
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
3
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
3
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
1
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
1
2
2
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
7
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
3
0
1
0
0
1
2
0
3
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
4
0
0
0
1
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
1
1
2
0
0
0
2
0
0
0
0
1
0
3
0
0
1
0
0
0
0
5
0
0
0
0
2
0
0
2
0
3
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
2
1
0
1
0
0
1
0
1
0
0
0
1
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
1
0
1
0
0
2
2
0
0
0
0
3
1
0
0
2
0
1
0
0
0
1
1
2
0
0
1
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
2
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
2
0
2
0
3
0
0
0
1
4
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
1
0
0
5
2
0
0
2
0
0
2
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
5
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
1
0
0
0
2
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
1
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
3
0
2
0
0
2
0
5
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
1
1
2
0
6
1
0
0
4
0
0
1
0
1
0
2
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
1
0
0
0
0
3
0
2
0
0
1
3
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
1
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
3
2
2
0
0
1
0
0
0
0
0
0
0
0
1
1
3
1
2
1
0
0
1
0
0
1
0
1
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
1
1
0
0
2
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
4
1
0
0
0
0
0
6
0
1
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
4
2
2
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
2
0
3
0
2
1
0
1
0
0
0
0
0
1
3
0
0
0
0
2
0
0
0
4
2
1
1
0
0
2
1
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
1
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
1
0
1
4
0
0
0
0
3
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
1
4
0
0
0
0
1
2
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
2
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
1
0
0
1
2
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
4
0
1
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
1
0
3
3
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
1
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
2
2
4
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
6
4
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
4
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
1
3
0
0
5
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
1
0
0
1
2
1
1
0
3
0
2
0
2
0
1
0
0
1
0
0
2
0
1
0
0
1
0
1
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
2
1
3
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
2
2
2
0
0
0
0
1
0
0
0
2
0
2
0
2
2
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
2
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
2
0
0
1
0
1
0
1
0
0
0
0
4
0
0
3
1
0
0
0
2
0
7
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
5
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
2
2
2
0
0
1
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
14
0
0
0
2
0
3
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
1
0
1
1
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
6
0
1
0
0
0
0
0
1
0
0
0
0
3
2
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
2
2
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
1
2
2
0
2
0
2
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
2
0
1
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
3
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
3
0
0
2
0
1
1
0
0
0
0
0
0
2
0
0
0
3
0
0
2
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
11
0
2
1
0
0
0
0
2
0
0
3
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
3
0
0
0
6
1
0
0
1
2
0
0
0
1
0
0
0
0
6
0
2
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
6
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
4
0
3
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
1
0
0
1
2
2
2
0
2
0
2
0
0
0
0
0
1
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
5
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
1
4
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
2
1
0
0
2
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
3
0
2
1
0
0
0
0
0
0
0
0
0
2
4
1
0
0
0
0
0
0
0
0
0
2
0
2
2
2
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
3
0
0
0
0
0
1
1
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
5
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
2
0
2
2
0
2
2
0
0
0
1
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
9
0
0
1
0
0
0
0
1
0
0
1
0
3
0
0
0
0
0
2
0
5
0
1
0
2
0
0
0
0
0
1
0
0
0
0
2
1
0
1
0
2
1
0
0
1
2
0
0
0
0
0
1
1
0
0
0
0
3
0
0
0
0
1
1
1
0
0
0
1
1
2
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
1
2
0
0
0
0
2
0
1
1
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
7
1
0
2
0
0
0
2
2
0
0
0
2
0
0
0
1
0
0
3
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
1
0
0
1
0
1
1
1
0
1
0
0
1
0
0
0
2
2
1
0
0
0
0
0
0
2
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
2
1
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
1
0
0
0
3
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
6
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
2
0
0
6
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
5
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
2
1
0
1
1
0
1
0
1
1
1
2
0
0
0
0
2
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
2
2
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
1
0
0
0
2
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
3
1
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
1
0
2
3
0
1
0
0
0
0
0
0
0
0
0
4
2
1
0
2
0
2
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
3
0
2
3
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
2
0
2
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
6
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
1
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
6
0
0
0
0
0
0
0
0
0
1
0
1
0
14
0
0
0
1
0
2
0
1
1
1
0
0
0
1
2
1
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
3
3
0
2
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
1
0
1
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
1
0
1
0
2
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
4
0
0
0
1
0
1
0
0
0
0
0
2
2
0
0
0
0
3
0
0
2
0
0
0
2
0
0
1
1
1
0
0
0
2
1
1
1
0
0
0
0
3
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
5
2
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
2
0
2
1
0
2
0
0
0
0
0
5
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
4
2
2
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
6
0
2
0
2
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
7
0
0
0
0
0
1
2
0
2
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
1
0
6
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
2
1
0
0
0
2
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
2
0
6
0
0
2
5
0
2
0
0
1
0
0
0
0
0
0
2
0
2
2
1
0
0
0
0
0
3
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
3
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
7
0
2
0
0
2
0
1
0
0
0
1
0
0
0
0
2
0
0
1
2
0
0
1
2
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
3
4
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
7
0
0
2
0
3
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
1
0
1
3
0
1
0
1
0
2
2
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
1
0
2
0
0
0
5
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
3
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
1
3
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
3
0
9
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
3
1
0
1
0
0
0
0
0
0
2
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
2
0
0
1
1
0
0
1
0
1
0
0
1
1
0
0
0
0
5
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
8
0
0
0
0
1
0
0
0
0
1
0
0
2
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
1
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
3
0
0
2
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
2
0
0
0
3
1
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
2
1
0
0
0
0
2
2
0
1
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
1
2
0
0
0
0
1
0
2
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
3
0
0
0
0
1
4
3
1
3
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
4
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
7
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
1
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
13
1
0
0
3
0
1
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
1
0
2
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
2
0
3
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
3
2
0
0
0
0
1
0
1
0
2
0
2
0
0
2
1
1
4
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
4
0
0
1
1
1
1
0
0
0
0
0
1
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
2
0
0
1
0
0
0
1
1
0
0
0
2
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
1
4
0
1
1
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
4
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
1
0
3
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
1
0
0
0
0
1
1
1
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
2
0
1
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
1
0
0
0
3
0
2
0
0
0
0
1
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
4
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
3
0
0
0
2
0
0
0
6
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
1
0
0
0
0
2
5
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
3
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
2
1
0
0
0
2
1
0
1
0
1
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
3
0
0
1
0
1
0
0
6
0
1
2
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
1
0
1
0
2
0
5
1
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
1
0
0
0
4
0
0
0
0
2
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
1
1
0
0
0
0
1
2
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
4
3
1
2
5
0
0
1
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
1
0
0
0
1
0
0
0
1
1
2
0
1
0
1
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
2
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
4
0
1
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
1
0
1
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
2
0
0
0
0
0
0
0
0
1
1
0
0
2
1
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
1
0
0
0
2
1
1
0
0
1
0
0
0
0
0
0
0
0
1
1
2
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
1
0
0
2
0
2
0
0
2
1
0
0
0
0
0
0
4
2
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
2
1
0
2
0
0
0
0
2
0
0
1
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
3
0
0
0
5
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
2
0
0
7
2
0
0
1
0
1
0
1
2
2
0
0
0
0
1
0
2
0
0
0
1
0
1
0
0
0
0
2
0
0
0
1
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
1
2
0
0
0
0
2
0
0
0
1
1
0
0
0
2
0
2
0
2
2
0
0
0
0
0
0
1
0
2
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
1
0
0
4
0
5
2
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
3
0
2
0
1
0
2
0
0
1
0
0
2
1
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
1
0
1
2
1
0
1
0
4
0
3
0
0
0
1
0
0
0
0
2
0
0
2
0
1
2
0
0
0
0
2
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
1
2
0
0
0
0
0
0
1
0
0
4
1
0
0
0
0
6
0
0
1
0
2
0
0
0
0
0
1
3
0
1
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
3
1
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
3
0
0
0
0
0
1
0
2
0
3
2
0
0
0
4
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
4
0
2
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
3
0
0
2
0
0
2
0
2
0
0
0
4
0
1
0
1
0
0
0
0
0
0
2
2
0
0
1
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
2
0
2
0
1
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
1
1
2
0
0
0
0
1
0
0
1
0
0
0
3
0
1
0
0
0
0
2
0
0
0
2
0
0
2
1
1
1
0
0
0
0
0
0
0
2
0
0
2
2
0
0
4
1
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
1
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
1
0
0
1
0
1
1
1
0
0
0
1
0
0
2
0
0
0
0
1
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
2
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
2
1
4
0
0
0
0
0
2
0
1
0
0
0
0
10
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
1
0
2
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
1
1
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
3
1
0
0
0
0
0
0
0
0
3
1
0
1
0
3
0
0
0
0
0
0
1
0
7
0
0
0
0
0
0
0
2
0
0
0
2
0
4
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
3
0
0
0
0
0
1
0
0
2
0
0
1
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
2
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
1
4
0
2
0
1
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
2
0
1
1
0
0
0
0
2
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
4
0
1
2
0
0
0
0
3
0
0
3
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
1
0
1
0
0
0
4
0
1
0
0
0
2
0
1
0
0
0
0
2
0
3
0
0
4
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
2
0
0
0
0
10
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
2
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
4
0
2
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
2
2
3
1
1
0
0
0
0
0
0
0
0
0
0
3
0
0
1
1
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
3
1
0
1
0
0
0
0
0
0
4
0
0
1
0
0
0
3
0
0
0
0
0
0
3
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
2
2
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
8
0
1
0
0
0
1
0
0
1
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
3
0
0
0
0
0
2
0
0
8
2
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
3
0
0
3
1
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
2
1
0
1
0
2
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
2
0
0
1
0
0
0
0
0
4
0
1
0
1
0
0
0
0
1
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
2
1
0
0
1
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
3
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
2
0
1
0
0
0
0
0
1
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
3
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
5
0
0
0
2
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
1
4
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
3
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
1
0
1
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
1
0
5
0
0
7
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
4
0
3
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
4
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
2
1
0
2
2
0
0
0
0
6
1
1
2
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
4
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
1
4
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
2
3
0
0
1
1
0
5
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
2
2
3
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
1
4
0
0
0
0
0
0
0
2
2
0
1
0
0
0
1
1
2
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
3
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
1
0
0
0
2
0
1
1
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
1
0
0
0
0
0
1
2
1
0
0
0
0
0
1
0
0
0
5
0
1
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
4
2
0
0
0
0
2
0
0
3
0
0
0
1
0
0
2
0
0
0
0
0
0
6
0
0
0
2
0
0
0
0
0
2
0
0
0
2
1
0
2
0
0
0
1
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
3
0
1
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
4
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
2
0
2
1
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
8
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
1
1
1
0
2
0
0
0
0
0
0
4
0
2
1
2
1
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
2
0
0
0
2
0
1
2
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
5
0
2
2
0
0
0
0
0
1
0
0
1
2
0
8
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
6
0
0
0
1
0
0
2
0
0
0
4
1
0
0
1
0
1
0
0
2
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
3
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
1
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
20
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
2
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
3
2
0
2
0
1
2
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
6
1
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
8
0
0
0
1
0
0
0
0
1
0
0
0
1
0
2
0
1
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
1
2
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
4
0
0
0
0
1
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
5
0
1
1
0
2
0
0
0
0
0
0
0
1
0
0
0
2
2
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
1
1
2
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
7
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
1
0
0
2
1
0
1
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
1
3
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
2
0
0
2
0
0
0
0
0
9
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
4
0
0
1
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
2
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
12
0
0
1
0
1
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
4
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
2
0
0
2
1
0
0
1
0
4
0
2
2
0
0
0
2
4
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
4
0
0
0
0
0
1
2
1
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
3
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
2
1
0
0
1
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
1
3
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
10
0
2
1
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
1
0
0
0
2
1
0
0
0
0
0
0
1
0
0
1
2
0
0
4
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
2
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
4
10
0
0
2
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
5
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
1
1
2
3
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
2
5
0
1
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
2
1
1
0
3
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
2
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
3
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
1
2
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
1
0
3
0
0
0
3
1
0
0
0
4
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
4
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
6
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
1
2
0
0
1
0
0
0
3
0
1
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
2
0
3
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
3
2
1
2
0
0
2
1
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
4
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
5
0
2
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
7
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
5
0
1
0
0
0
0
0
0
2
0
1
0
2
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
2
0
0
2
0
1
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
7
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
3
0
0
4
0
0
0
0
0
0
0
1
0
3
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
4
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
4
0
0
0
1
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
1
1
0
0
0
0
3
0
0
1
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
1
4
0
0
0
0
2
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
1
0
2
0
1
0
0
0
1
0
2
0
2
0
0
0
1
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
4
0
0
0
1
0
0
0
1
2
2
0
1
1
0
2
0
0
0
0
3
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
1
3
0
0
0
0
0
0
2
4
0
0
0
0
0
0
2
1
3
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
1
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
7
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
2
1
0
0
1
2
0
0
1
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
1
0
0
2
0
0
2
2
0
0
0
0
1
2
0
0
0
1
0
0
0
0
4
0
1
1
0
0
0
0
0
0
2
0
1
0
0
1
0
1
0
0
0
0
1
0
4
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
2
0
0
0
0
8
0
0
0
0
0
0
0
1
0
2
0
1
1
0
0
0
0
3
2
0
0
0
1
0
0
0
2
0
0
1
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
2
1
1
0
0
0
0
0
1
1
4
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
3
1
0
2
0
0
2
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
6
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
2
0
0
0
0
1
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
2
5
0
0
0
2
0
0
0
0
0
0
0
0
0
5
2
0
0
0
0
2
0
0
0
2
0
0
0
1
2
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
2
0
0
0
2
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
8
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
2
0
1
0
0
1
1
0
1
0
0
0
2
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
3
0
3
0
1
1
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
3
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
3
0
0
2
1
0
1
0
1
1
0
0
1
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
7
0
0
0
0
7
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
3
1
2
0
0
0
0
0
2
3
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
3
1
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
1
3
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
1
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
2
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
3
0
0
5
1
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
2
0
3
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
2
0
0
0
2
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
4
1
0
0
3
0
0
2
0
0
0
0
0
0
3
0
0
0
1
0
0
1
1
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
4
0
0
2
0
0
0
0
0
0
1
0
2
1
0
1
0
0
1
3
3
0
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
1
1
0
3
2
0
2
2
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
5
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
1
2
0
1
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
8
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
4
2
2
0
0
0
0
0
0
0
2
2
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
3
0
0
2
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
4
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
3
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
7
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
11
0
3
0
1
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
1
0
0
0
2
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
3
1
1
0
0
1
0
0
0
0
0
0
0
5
0
0
0
2
0
0
0
0
0
0
0
4
0
2
0
0
0
0
1
2
0
3
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
2
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
2
2
1
0
0
3
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
2
0
3
0
0
5
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
3
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
3
0
0
2
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
4
1
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
1
1
1
0
0
1
0
0
0
2
2
0
0
0
1
10
0
0
0
0
0
0
2
0
2
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
3
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
2
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
1
2
0
0
0
0
2
1
0
1
0
0
12
0
0
0
0
1
1
1
0
0
0
0
0
0
0
2
0
3
0
2
0
0
0
0
3
0
0
0
3
15
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
14
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
2
9
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
1
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
3
0
0
0
0
0
0
0
2
1
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
3
0
4
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
1
0
0
0
2
1
0
1
0
0
2
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
2
0
0
0
2
2
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
3
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
4
1
0
9
1
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
1
0
3
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
2
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
2
0
0
0
0
0
0
1
2
0
1
0
2
0
0
2
0
0
0
0
0
0
1
0
0
3
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
1
1
0
0
2
0
0
0
2
0
2
2
5
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
1
0
0
0
0
3
1
0
0
0
0
0
1
3
0
0
0
1
1
0
0
2
0
0
0
1
2
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
3
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
1
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
3
1
1
2
2
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
2
0
1
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
3
0
1
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
4
0
3
0
0
0
0
2
1
0
1
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
8
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
1
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
1
1
0
0
0
0
0
0
2
0
4
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
5
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
7
2
0
1
2
0
0
2
1
0
2
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
4
0
0
3
0
0
1
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
2
2
8
0
1
2
0
0
1
0
0
0
0
1
0
1
3
0
0
0
0
0
1
0
2
0
2
0
1
0
0
0
0
0
0
0
1
6
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
2
0
0
1
0
0
1
0
1
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
4
0
0
1
0
6
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
1
2
0
0
2
1
0
0
1
0
0
6
0
2
0
3
0
0
0
0
0
0
0
0
1
0
3
0
0
0
2
0
2
0
0
0
0
1
0
1
1
1
0
0
1
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
3
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
1
0
0
0
3
0
0
0
1
5
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
5
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
1
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
1
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
6
0
0
2
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
4
0
2
0
0
0
0
0
0
0
2
1
1
0
0
0
4
0
0
0
0
0
0
0
0
0
1
12
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
1
2
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
3
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
2
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
2
10
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
1
0
2
0
0
1
0
1
3
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
1
0
0
0
0
2
1
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
4
0
1
0
2
0
0
2
4
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
3
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
1
2
0
0
1
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
1
4
4
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
2
0
1
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
5
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
2
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
3
1
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
1
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
2
0
1
0
2
0
0
0
2
1
2
0
1
2
0
0
0
1
1
0
0
0
0
3
0
4
0
1
0
0
0
1
0
0
0
0
1
5
0
0
0
3
0
0
0
1
0
0
0
0
0
0
1
0
3
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
2
8
0
0
0
0
1
0
0
2
2
1
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
2
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
5
2
0
1
0
2
0
0
0
2
0
0
4
0
1
0
1
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
5
0
0
1
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
4
0
0
0
0
1
1
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
4
2
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
3
0
0
0
0
0
1
2
0
0
0
0
2
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
2
0
1
3
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
9
0
2
0
2
0
0
2
3
1
0
0
2
0
0
1
0
0
0
0
2
3
0
0
0
0
1
2
0
3
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
3
0
2
0
0
0
1
3
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
1
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
7
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
3
1
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
3
0
0
1
0
0
0
0
0
0
1
1
0
2
2
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
1
0
0
1
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
3
0
0
2
2
1
4
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
18
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
3
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
7
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
3
0
1
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
2
0
1
0
0
3
0
0
0
0
0
0
0
1
2
3
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
5
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
2
1
0
2
1
1
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
4
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
2
0
1
0
1
2
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
3
0
0
2
0
0
2
0
4
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
1
0
0
0
0
0
2
0
1
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
2
2
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
2
0
0
1
0
0
0
0
2
0
0
5
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
6
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
2
0
1
0
2
0
0
0
0
0
1
0
0
0
1
2
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
2
0
2
1
0
2
4
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
2
0
2
0
0
3
0
0
0
1
0
0
2
1
0
1
1
3
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
3
1
0
0
0
0
0
0
2
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
6
0
0
1
0
6
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
1
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
1
0
0
2
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
4
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
2
2
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
2
0
0
0
1
0
1
0
0
0
1
2
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
1
0
0
0
0
2
1
6
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
1
1
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
3
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
7
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
2
1
0
2
1
0
0
0
0
1
2
0
0
1
0
0
0
2
0
0
0
0
0
0
2
2
2
0
0
0
0
2
0
0
1
2
0
2
3
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
9
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
2
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
4
0
4
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
6
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
1
0
0
0
3
1
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
2
1
0
0
0
2
0
2
1
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
1
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
5
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
2
0
2
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
10
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
2
1
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
3
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
2
0
0
1
0
2
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
1
0
2
0
2
0
1
0
0
3
0
0
0
1
0
1
0
0
0
0
2
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
2
0
0
0
1
1
0
0
0
2
0
0
1
0
1
0
1
1
1
0
0
0
4
0
2
1
0
3
1
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7
1
0
0
0
1
1
0
0
0
0
1
4
1
2
0
2
0
0
1
0
0
3
0
1
2
0
0
0
2
0
0
0
0
0
2
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
2
0
3
0
1
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
4
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
3
0
0
0
0
0
2
3
0
2
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
1
2
0
0
0
0
0
0
3
0
0
0
1
1
0
1
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
1
2
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
8
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
1
0
1
0
0
1
0
1
0
0
0
1
2
0
0
0
1
0
2
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
1
0
0
0
2
2
2
0
2
1
0
3
0
0
2
0
2
3
2
0
1
0
0
0
0
0
3
0
0
0
0
0
5
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
2
0
0
3
1
0
1
1
1
0
0
0
0
1
0
0
0
0
0
3
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
9
0
0
0
4
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
4
0
2
0
0
1
0
0
3
0
0
0
0
0
0
2
0
1
0
0
1
3
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
1
1
0
2
0
0
0
0
1
0
0
2
1
0
0
0
0
0
1
0
1
0
0
0
3
0
0
1
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
2
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
2
2
1
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
3
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
1
1
0
0
0
0
0
2
0
0
1
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
8
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
1
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
1
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
3
0
1
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
2
0
0
2
1
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
10
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
4
5
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
5
0
0
0
1
1
0
0
1
0
1
0
2
1
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
3
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
2
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
1
3
0
0
1
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
2
0
1
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
1
0
0
13
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
1
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
2
4
2
0
1
0
4
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
2
0
3
0
0
0
3
0
0
0
2
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
4
0
0
0
0
0
3
2
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
4
0
0
0
2
0
1
0
0
2
0
0
0
1
1
0
0
2
0
1
0
0
0
0
0
3
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
2
0
8
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
5
1
0
0
2
0
0
1
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
1
0
0
0
3
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
4
1
2
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
5
0
0
0
0
0
1
3
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
5
0
0
0
0
0
2
4
0
2
0
0
0
0
0
1
0
0
0
0
3
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
1
0
0
2
0
1
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
5
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
3
0
1
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
2
0
0
2
2
0
0
1
0
1
0
2
3
0
0
0
1
0
0
1
0
1
0
0
0
0
2
0
1
1
1
0
1
0
2
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
1
0
0
2
1
1
4
1
0
6
1
1
0
0
1
0
2
0
1
0
0
1
0
2
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
4
0
1
0
2
0
1
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
5
2
1
2
0
0
1
2
0
7
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
1
0
0
1
0
0
0
0
0
0
0
0
1
3
0
1
0
0
0
2
0
0
1
0
0
0
1
2
1
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
1
4
0
4
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
3
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
1
0
0
0
0
3
0
0
0
0
1
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
8
0
0
0
1
1
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
3
0
0
0
2
0
2
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
2
0
0
0
1
1
2
0
0
0
0
0
0
1
0
0
2
0
2
2
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
1
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
3
0
0
0
3
0
0
3
0
0
0
0
0
0
3
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
4
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
4
0
0
0
3
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
5
2
0
1
0
1
2
2
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
1
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
1
2
0
0
0
1
0
0
1
0
0
3
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
3
0
1
0
0
0
0
3
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
2
1
0
0
0
2
1
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
2
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
7
0
3
0
2
0
0
0
2
2
0
0
0
0
0
2
2
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
1
0
0
0
3
0
1
1
0
0
0
2
0
1
0
0
0
0
0
3
0
0
0
0
0
0
1
2
1
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
3
0
0
0
4
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
3
2
3
0
0
0
0
1
2
0
1
0
2
0
0
2
0
7
0
0
0
0
0
3
0
0
0
0
0
1
1
0
0
2
1
1
1
0
0
0
4
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
2
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
2
0
2
2
1
2
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
4
2
0
1
0
2
1
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
2
2
1
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
5
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
1
1
1
2
1
0
1
0
0
0
2
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
1
0
0
0
0
0
4
0
0
0
0
4
0
0
0
2
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
2
0
1
0
0
0
2
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
4
0
2
0
1
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
1
1
8
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
2
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
5
0
1
0
0
0
2
2
0
2
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
3
0
0
0
2
3
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
2
3
0
0
0
4
0
0
0
0
1
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
1
1
0
0
0
0
0
0
1
2
0
1
1
0
2
0
0
1
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
2
0
2
0
1
0
0
0
1
0
3
0
0
2
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
2
0
1
1
0
1
0
1
0
2
2
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
1
2
0
0
0
2
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
1
0
0
0
1
0
0
0
0
2
0
2
0
4
0
2
0
0
1
0
0
2
0
0
2
0
0
0
1
1
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
1
0
3
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
3
4
0
0
1
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
2
0
0
1
1
0
0
0
0
3
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
1
2
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
3
0
0
0
0
2
0
1
0
0
0
0
2
0
2
0
1
0
2
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
1
0
0
3
0
0
2
0
3
4
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
1
0
0
0
2
0
1
0
0
1
0
1
0
0
0
0
1
0
0
4
1
1
2
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
3
0
0
0
0
0
0
4
1
0
0
0
6
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
3
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
2
0
2
0
0
0
4
0
0
0
0
0
1
0
1
0
3
1
1
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
1
2
1
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
1
0
0
2
4
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
1
2
1
0
0
0
0
0
0
0
2
0
3
0
0
0
1
0
0
1
2
0
0
0
1
0
0
0
0
1
2
0
0
2
0
2
0
1
0
0
1
0
1
1
4
3
0
0
4
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
6
0
0
0
0
0
1
0
2
0
0
0
0
3
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
1
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
1
1
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
1
3
0
0
7
0
0
3
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
7
0
1
0
1
0
0
0
0
1
2
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
2
0
0
1
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
1
0
2
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
1
0
2
0
1
0
0
0
0
0
3
2
1
0
5
2
0
0
0
0
4
0
1
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
2
0
1
0
1
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
3
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
2
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
5
2
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
4
1
1
1
1
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
3
0
0
0
3
0
0
4
0
0
0
2
0
0
1
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
7
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
3
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
3
1
3
0
0
0
0
1
0
3
0
0
1
0
0
0
1
0
0
1
0
0
0
2
3
2
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
1
1
0
2
0
3
0
0
1
0
1
1
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
3
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
2
0
5
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
2
6
0
2
0
0
0
1
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
1
2
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
2
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
1
2
0
0
3
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
3
0
0
0
6
1
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
1
0
2
0
0
0
2
0
1
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
2
0
0
2
0
0
1
0
0
0
0
0
1
0
0
1
0
3
0
0
2
2
2
6
0
0
0
0
0
1
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
5
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
3
0
3
5
0
0
0
0
2
3
0
0
0
3
0
0
1
0
1
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
5
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
2
0
1
0
0
1
0
0
4
0
2
1
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
2
0
0
0
8
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
2
1
0
2
4
1
0
0
1
0
1
0
0
1
5
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
2
0
1
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
2
1
3
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
3
0
0
0
2
0
4
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
1
3
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
2
0
2
1
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
1
0
0
0
0
0
2
1
1
1
4
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
3
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
2
1
0
0
0
3
1
0
0
0
6
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
3
0
2
0
0
1
4
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
1
3
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
2
2
2
0
0
0
0
0
1
1
0
0
0
0
4
1
0
1
0
1
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
2
0
0
0
7
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
4
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
7
0
0
0
0
0
3
0
5
0
0
0
1
0
0
1
2
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
1
0
3
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
1
0
4
0
1
0
2
0
3
1
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
4
0
0
2
0
0
0
0
4
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
3
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
2
0
2
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
2
0
0
2
0
0
1
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
3
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
4
0
0
2
0
0
1
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
2
1
0
0
3
2
21
1
0
0
0
2
2
1
0
2
0
0
0
2
2
2
0
1
1
0
0
0
0
1
0
0
0
4
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
3
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
7
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
2
1
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
3
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
1
0
2
1
2
0
0
0
1
0
0
0
0
0
2
0
0
0
3
1
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
2
1
0
0
2
0
0
0
0
2
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
4
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
2
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
2
0
1
1
0
0
0
1
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
6
2
2
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
1
1
2
0
2
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
3
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
2
0
0
2
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
1
2
0
0
0
0
0
0
1
0
2
0
2
0
0
1
2
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
2
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
1
0
0
0
0
0
0
3
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
1
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
6
0
1
0
0
0
0
2
0
2
3
0
0
1
0
0
0
4
0
0
0
0
2
0
0
0
0
3
0
2
1
0
0
2
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
3
0
1
0
3
0
4
1
0
0
0
0
0
0
0
2
2
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
2
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
2
0
0
2
0
0
1
0
0
0
3
1
1
0
0
1
0
6
0
1
0
2
1
0
0
0
4
2
0
1
0
2
9
2
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
1
0
0
1
2
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
2
2
0
0
0
3
0
0
4
2
2
0
0
0
2
0
0
0
3
0
0
0
0
0
0
2
0
0
1
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
1
1
2
0
0
0
2
1
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
1
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
6
0
0
0
1
1
1
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
2
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
8
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
1
2
0
0
0
0
0
0
0
0
2
1
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
2
0
0
0
0
2
2
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
3
0
0
0
0
2
2
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
1
1
0
0
0
0
0
2
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
4
2
0
0
0
0
1
0
0
1
1
0
2
0
0
0
0
3
0
1
0
0
1
1
0
0
2
2
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
2
1
0
0
2
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
1
0
1
2
0
2
0
0
5
0
3
1
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
4
1
0
3
1
0
0
1
0
0
0
0
0
0
0
0
0
3
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
9
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
3
0
0
0
0
0
0
0
8
0
0
0
3
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
1
1
4
5
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
3
0
0
0
0
0
0
0
0
2
2
2
0
1
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
1
2
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
2
0
0
0
0
0
3
1
0
0
0
0
0
2
0
0
0
5
0
1
0
0
0
0
0
0
1
0
0
0
0
1
5
0
0
0
0
0
3
0
3
0
1
0
0
0
0
0
2
0
2
2
0
2
0
0
0
0
0
6
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
2
0
0
0
3
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
2
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
2
1
0
1
6
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
3
0
0
1
0
0
0
0
0
0
7
0
0
0
0
0
0
5
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
2
0
0
0
0
4
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
2
0
2
0
0
5
0
0
0
0
0
0
0
0
3
0
0
2
0
2
0
0
0
0
0
0
1
1
2
0
0
0
0
0
4
0
5
2
0
2
0
0
0
0
0
0
0
0
0
0
6
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
3
0
2
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
2
0
0
2
2
1
0
0
0
0
2
0
0
0
4
0
0
1
1
0
0
3
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
2
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
5
1
0
0
2
0
1
0
1
0
0
0
2
0
0
3
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
3
0
0
6
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
6
0
2
0
0
0
0
0
1
0
0
0
2
0
0
2
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
1
0
3
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
3
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
3
0
0
0
4
0
0
2
0
0
0
3
0
0
0
2
0
2
0
0
2
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
4
0
2
2
0
2
0
0
0
0
1
0
0
0
0
0
1
2
0
2
0
0
0
1
0
0
0
0
0
2
0
1
0
2
0
3
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
3
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
5
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
4
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
1
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
3
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
2
0
0
2
0
2
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
1
0
0
0
2
0
1
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
4
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
3
0
2
0
0
2
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
2
1
0
0
0
1
0
1
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
3
0
0
3
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
1
2
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
11
0
0
0
1
0
0
0
2
0
4
2
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
5
1
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
3
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
5
0
0
0
0
2
0
1
0
1
1
0
5
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
2
1
0
0
0
2
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
3
0
0
2
0
3
0
0
1
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
1
2
0
0
0
0
0
1
0
1
1
0
0
0
2
1
0
0
0
2
2
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
1
3
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
3
1
2
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
3
0
0
0
2
0
0
0
0
0
1
0
3
0
0
0
0
4
0
0
0
0
1
0
1
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
2
0
0
0
0
2
2
0
0
0
1
0
1
0
0
2
0
0
0
5
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
2
0
0
1
1
6
0
2
3
0
0
0
0
0
3
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
4
0
0
1
0
2
3
2
1
0
0
0
0
1
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
3
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
4
0
1
0
0
4
2
0
0
0
0
2
2
2
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
2
0
2
0
0
0
2
0
0
0
2
2
0
0
0
0
3
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
1
0
0
1
2
1
0
2
3
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
5
0
1
0
0
0
2
0
0
1
2
0
0
0
2
0
1
0
0
1
0
0
0
0
2
0
1
0
1
0
0
3
0
0
0
0
0
0
0
1
0
1
1
0
2
0
0
3
0
0
0
2
0
0
0
1
0
0
2
2
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
7
0
2
0
2
2
0
0
0
0
0
0
2
2
0
9
0
4
0
0
1
0
0
0
3
0
1
1
0
0
0
2
1
0
0
0
0
2
0
0
0
0
1
5
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
1
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
5
1
1
0
3
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
2
3
0
1
2
0
0
0
0
0
6
0
0
0
0
0
0
0
0
1
0
0
0
1
9
4
0
1
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
1
0
0
0
0
0
2
0
0
0
1
1
0
3
0
6
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
5
0
1
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
1
0
0
2
0
0
0
0
1
0
0
0
0
0
1
1
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
3
3
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
3
0
2
1
0
0
0
2
0
3
0
0
0
0
0
0
2
0
3
0
2
0
0
1
0
3
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
8
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
2
0
2
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
1
1
0
1
0
1
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
2
4
1
0
0
3
1
0
1
0
0
2
0
9
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
1
0
0
0
2
2
0
1
0
0
6
3
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
3
0
2
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
2
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
2
0
0
9
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
6
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
3
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
2
3
0
0
0
1
0
0
0
0
1
2
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
8
0
2
0
0
0
0
0
2
0
0
0
1
0
1
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
2
0
0
0
0
2
0
0
2
1
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
1
3
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
7
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
1
4
0
0
2
0
0
0
0
5
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
6
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
2
1
2
0
0
0
2
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
1
3
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
1
1
0
0
0
0
2
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
5
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
2
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
2
0
1
2
1
0
1
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
1
0
0
0
2
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
7
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
1
2
0
0
0
2
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
2
1
0
1
0
1
0
2
0
0
0
1
0
0
0
2
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
6
0
0
0
0
1
1
0
0
0
0
1
1
0
2
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
2
0
4
0
2
3
2
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
4
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
4
0
0
2
0
1
2
0
0
0
0
0
0
1
0
0
1
0
0
0
5
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
2
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
1
1
0
0
0
0
1
0
0
0
3
2
0
0
2
0
0
0
0
0
0
0
0
1
3
0
1
0
0
0
0
0
0
4
0
0
1
0
0
3
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
1
0
0
0
0
0
0
0
3
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
1
0
2
1
0
0
0
2
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
3
0
0
2
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
1
0
2
0
0
0
0
0
4
0
0
3
1
0
0
3
0
1
0
0
2
1
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
1
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
2
2
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
9
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
3
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
10
4
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
2
0
16
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
3
1
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
2
0
0
1
1
0
2
2
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
2
0
0
1
1
0
1
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
3
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
2
0
2
0
2
0
1
0
0
0
0
0
1
0
0
1
4
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
1
0
3
0
2
0
1
0
2
2
0
0
0
3
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
2
1
1
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
2
0
0
0
0
1
0
1
0
2
0
1
2
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
1
1
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
6
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
5
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
1
6
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
4
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
1
0
2
0
0
2
1
0
0
0
2
0
0
1
1
0
1
0
1
1
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
2
1
0
1
2
1
0
0
0
3
0
0
0
0
0
0
0
0
4
1
1
0
0
1
0
0
0
1
1
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
1
0
0
1
1
0
0
1
0
1
0
0
2
0
2
4
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
4
3
0
0
0
7
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
3
0
0
0
0
0
2
1
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
3
0
2
0
0
0
0
0
1
2
0
0
0
0
2
0
1
1
0
1
4
7
0
6
0
0
4
0
1
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
5
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
2
0
1
0
1
0
0
1
1
0
0
0
8
1
0
0
4
0
0
3
0
0
0
0
4
1
0
0
0
2
1
0
0
0
0
0
1
3
0
0
0
8
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
2
2
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
2
0
0
0
2
2
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
1
0
4
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
3
2
1
0
0
0
0
0
0
0
0
2
0
3
0
0
2
0
0
0
2
0
4
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
6
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
4
5
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
1
0
0
3
0
0
0
7
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
1
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
2
0
3
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
2
1
0
2
1
0
2
0
2
0
3
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
5
0
0
2
2
2
1
2
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
4
0
0
0
0
4
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
1
1
2
2
0
0
0
2
0
0
0
0
0
1
2
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
1
0
3
0
2
2
0
0
0
0
0
0
0
0
0
5
0
0
3
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
2
1
1
0
0
0
0
0
0
0
2
0
0
4
0
0
2
2
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
3
0
0
0
1
0
0
0
3
1
0
1
0
1
3
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
8
0
0
2
2
3
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
1
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
5
0
1
0
0
1
0
0
0
2
0
1
0
0
0
1
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
2
0
1
3
0
1
0
0
0
3
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
2
0
0
1
0
1
1
1
0
0
1
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
3
5
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
5
0
0
0
0
0
0
1
0
0
2
1
0
1
0
0
2
0
0
1
2
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
3
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
1
0
2
1
0
0
0
2
0
1
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
3
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
1
0
1
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
2
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
1
0
2
0
0
1
0
2
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
1
0
0
0
10
1
0
0
0
2
1
0
0
0
2
0
1
0
0
1
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
1
2
0
2
0
0
0
0
3
1
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
2
1
0
1
0
0
2
3
5
0
0
3
0
2
0
0
0
0
0
2
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
2
0
1
0
6
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
9
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
6
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
1
3
0
0
0
0
0
0
0
0
0
1
0
2
1
3
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
3
0
0
0
0
0
0
0
0
0
3
1
1
0
0
1
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
4
0
0
0
2
0
2
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
2
1
0
0
0
1
0
1
1
0
2
1
0
0
0
7
0
0
0
0
2
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
10
0
2
2
0
0
2
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
3
0
0
0
1
0
1
0
0
0
0
2
0
0
0
3
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
7
5
0
0
2
0
0
1
0
0
2
0
0
0
0
1
0
1
1
2
0
1
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
1
0
0
0
3
0
1
0
0
0
0
0
0
0
0
3
0
4
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
4
0
0
0
2
2
2
2
0
1
0
1
1
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
2
0
0
4
0
3
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
5
0
0
3
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
3
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
3
2
1
1
1
0
2
1
0
0
3
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
1
0
9
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
2
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
3
1
0
0
0
0
0
4
0
1
2
2
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
2
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
2
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
3
1
0
0
0
1
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
1
0
1
1
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
1
0
2
0
0
0
3
4
0
2
0
0
1
0
0
1
2
0
2
6
1
1
2
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
1
0
1
2
0
0
2
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
5
2
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
3
4
1
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
2
0
0
1
0
1
0
0
0
0
1
2
0
1
0
0
0
0
0
0
2
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
2
1
0
0
0
2
1
2
0
0
0
0
0
1
0
2
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
3
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
2
1
1
0
2
0
0
0
0
0
2
4
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
1
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
5
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
2
2
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
4
0
0
0
0
0
2
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
7
2
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
4
0
5
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
4
0
1
0
7
2
0
0
0
2
0
0
0
2
2
1
0
0
2
0
0
0
0
2
0
4
0
0
0
0
1
0
0
0
1
0
2
1
0
0
0
0
0
2
2
2
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
3
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
2
0
0
0
1
2
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
2
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
3
1
0
0
2
0
1
1
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
1
5
0
0
0
0
0
0
0
0
2
0
2
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
5
2
1
1
1
2
0
0
0
0
1
2
0
0
2
0
3
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
2
3
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
1
0
3
2
0
0
0
3
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
3
0
0
2
2
0
0
3
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
3
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
3
1
1
1
0
0
0
0
0
3
0
0
0
0
0
0
1
1
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
5
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
9
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
1
4
0
0
0
1
0
0
0
0
0
0
0
3
2
1
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
3
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
1
0
0
3
0
0
0
0
2
0
0
2
0
0
0
1
2
0
0
0
2
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
1
0
0
0
3
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
6
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
4
2
0
0
0
0
1
0
0
1
0
2
0
2
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
3
0
1
0
2
0
0
1
1
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
3
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
4
0
0
0
0
0
0
2
0
0
0
2
1
1
3
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
2
0
0
0
2
0
1
0
0
2
1
5
0
0
0
1
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
1
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
7
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
1
4
0
0
0
0
0
0
2
0
0
0
2
5
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
2
0
0
1
0
0
0
0
0
3
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
1
2
0
2
0
2
0
0
0
0
10
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
3
0
0
2
2
0
1
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
1
0
0
0
0
1
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
2
1
0
0
1
2
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
3
0
0
2
3
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
3
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
4
0
0
0
1
0
1
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
3
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
5
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
2
0
0
0
1
3
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
3
1
0
0
1
3
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
3
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
2
0
0
4
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
3
0
2
2
0
0
0
0
0
0
1
0
1
0
1
7
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
11
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
7
0
0
0
2
0
4
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
10
0
0
0
0
0
0
0
8
1
0
1
3
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
3
2
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
1
0
0
2
2
0
1
2
4
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
3
2
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
1
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
2
1
0
2
0
0
1
0
0
0
0
0
2
1
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
2
1
3
0
0
0
0
0
1
2
1
0
0
3
3
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
2
0
0
0
1
0
0
1
2
1
0
2
0
0
0
2
1
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
2
0
2
2
0
0
0
0
0
10
0
1
0
0
0
0
0
1
0
8
4
0
2
0
0
0
0
0
0
3
0
0
0
0
4
0
0
0
0
0
1
0
0
1
0
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
1
0
0
2
1
0
0
0
0
0
0
2
1
1
0
1
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
4
2
4
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
1
1
4
1
0
0
1
0
0
3
0
0
0
0
2
1
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
1
0
1
1
0
0
0
0
0
2
0
0
0
3
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
1
0
0
1
0
0
0
0
2
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
2
0
1
0
2
0
3
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
1
3
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
1
5
2
3
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
1
0
0
0
2
4
0
1
0
0
4
0
0
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
6
0
0
0
2
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
3
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
1
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
12
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
1
3
0
0
3
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
1
0
0
2
0
0
2
0
0
1
0
2
0
0
5
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
3
0
1
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
4
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
1
0
3
0
0
0
2
1
3
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
2
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
1
5
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
4
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
2
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
3
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
1
0
0
1
2
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
3
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
2
0
0
0
0
1
0
1
0
1
0
0
0
2
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
4
1
0
0
0
1
0
2
1
6
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
19
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
3
2
0
0
2
2
0
0
0
0
1
0
1
0
0
1
0
1
4
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
2
2
0
0
3
1
0
0
0
0
0
0
2
0
1
0
0
2
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
1
0
0
3
1
0
0
0
0
1
0
1
2
0
3
0
1
0
1
0
1
0
4
0
12
2
0
0
0
0
2
0
2
2
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
3
1
0
0
0
1
0
1
0
0
0
2
0
3
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
3
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
1
2
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
2
0
0
0
2
1
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
1
0
1
2
1
1
0
0
2
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
8
0
2
0
0
1
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
7
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
3
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
1
0
0
0
0
0
2
0
0
0
2
0
2
0
2
1
0
0
1
1
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
2
1
2
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
10
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
1
0
1
0
0
0
2
0
2
3
0
0
0
2
1
0
0
0
3
1
0
0
0
1
2
2
1
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
1
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
2
0
5
0
0
1
1
0
0
0
0
1
1
0
3
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
1
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
1
0
0
0
1
0
0
0
4
1
3
1
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
1
0
2
0
0
0
1
1
0
0
1
1
1
0
0
0
0
0
7
1
0
1
0
0
0
2
0
0
0
0
0
0
0
1
2
1
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
5
0
0
2
0
4
0
0
0
2
0
0
0
0
1
2
0
1
0
0
0
0
0
2
1
0
1
2
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
1
0
1
0
0
0
1
6
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
2
0
0
0
0
1
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
4
0
0
0
0
1
0
0
0
0
2
1
5
0
0
0
0
0
0
2
1
0
1
1
1
0
0
3
0
0
0
1
0
2
0
2
2
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
1
0
0
0
0
2
0
0
0
4
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
1
0
0
1
2
0
0
0
1
1
2
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
2
0
0
0
0
4
0
0
0
0
0
2
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
5
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
5
0
0
2
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
2
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
1
0
0
0
0
1
0
1
0
0
0
2
0
0
0
3
0
1
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
2
0
0
3
0
0
9
0
0
0
2
0
0
0
0
3
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
2
1
0
0
0
2
1
0
0
0
2
0
1
0
0
0
0
0
0
1
2
0
0
0
2
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
1
0
0
4
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
1
2
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
4
0
2
0
3
1
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
3
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
3
0
0
1
0
0
2
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
2
1
5
1
0
0
1
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
2
0
0
4
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
3
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
1
0
3
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
2
1
0
2
0
2
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
3
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
5
0
0
1
0
0
0
7
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
3
2
0
5
2
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
2
3
0
1
0
0
2
0
0
0
0
4
1
0
0
0
0
5
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
6
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
7
0
0
2
0
2
1
0
0
0
0
0
5
0
3
2
4
1
0
0
0
0
0
0
2
0
1
0
0
1
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
1
0
1
0
1
0
0
0
0
2
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
1
3
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
4
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
1
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
2
0
0
0
0
1
2
2
0
3
1
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
3
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
3
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
1
2
0
0
0
2
0
0
2
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
3
0
2
0
0
0
0
0
0
11
1
0
0
0
2
0
0
0
0
2
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
1
0
1
2
0
0
0
0
0
1
0
0
0
0
2
0
1
0
1
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
4
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
2
1
0
2
0
0
0
0
0
1
0
1
0
1
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
2
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
1
2
0
2
1
0
4
1
3
0
0
0
1
0
0
1
0
1
0
1
0
0
0
1
0
1
0
1
0
0
1
2
0
0
0
2
0
1
3
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
1
2
0
0
0
0
0
0
0
3
0
0
0
3
3
0
0
2
0
0
0
1
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
3
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
1
0
0
2
2
1
1
0
0
0
3
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
1
0
1
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
5
0
0
2
0
0
1
0
0
3
0
0
0
0
0
0
0
4
0
0
0
1
3
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
2
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
5
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
2
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
4
2
0
0
0
1
0
0
0
0
0
0
1
2
0
1
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
1
0
1
0
0
0
0
1
0
1
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
5
1
0
0
0
3
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
4
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
3
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
1
1
0
1
1
0
0
2
1
0
0
0
1
1
0
3
0
0
0
5
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
3
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
5
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
1
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
1
0
0
2
0
0
2
0
0
1
2
0
1
0
0
3
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
0
1
0
1
1
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
2
0
0
0
0
7
1
2
1
0
0
0
3
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
4
0
0
0
2
0
0
4
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
1
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
3
0
0
2
0
0
0
0
0
0
0
2
0
4
1
2
0
1
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
3
0
0
0
0
2
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
3
0
1
0
0
1
4
1
0
0
0
0
1
0
1
0
3
0
2
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
1
1
0
0
0
6
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
1
0
2
0
3
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
1
1
0
0
2
2
2
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
9
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
5
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
3
1
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
3
0
1
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
4
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
4
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
2
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
13
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
1
4
0
0
0
0
0
0
0
2
0
1
2
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
1
2
0
0
0
1
0
0
1
0
0
0
0
0
0
3
0
0
0
2
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
1
0
0
4
0
0
4
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
2
0
0
0
4
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
2
4
0
0
4
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
5
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
1
1
0
0
0
0
3
0
0
0
0
0
4
0
2
3
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
10
1
0
0
0
0
0
0
0
1
1
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
1
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
2
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
3
1
0
0
0
0
0
0
0
2
0
7
4
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
2
0
1
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
4
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
1
0
1
0
2
0
0
0
0
1
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
2
0
0
0
0
0
0
5
2
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
1
1
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
2
0
2
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
1
0
3
2
1
1
0
0
0
0
0
5
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
2
0
1
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
2
3
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
2
3
0
0
0
0
2
1
2
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
1
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
4
0
1
0
0
0
0
1
0
1
5
0
0
0
2
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
1
0
0
0
1
0
6
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
2
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
1
2
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
2
1
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
2
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
2
0
3
4
1
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
2
4
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
2
1
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
5
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
2
0
6
0
0
1
0
0
0
1
0
2
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
2
0
0
1
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
5
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
4
0
2
1
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
8
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
2
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
1
0
0
2
0
0
4
0
3
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
2
2
0
6
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
2
2
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
1
0
0
1
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
3
2
0
0
1
0
0
0
0
1
0
0
5
0
2
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
2
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
5
2
0
3
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
2
1
0
2
2
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
3
0
0
7
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
1
0
0
2
0
2
0
3
0
2
1
0
1
0
0
0
0
1
0
1
2
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
3
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
3
0
0
0
0
0
1
2
2
1
2
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
3
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
2
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
4
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
2
0
0
0
0
2
0
2
3
0
0
1
0
0
0
0
2
0
3
0
0
0
0
0
3
2
1
2
1
1
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
1
1
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
1
1
1
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
3
0
0
0
2
3
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
3
1
0
2
0
0
0
0
0
0
14
0
0
1
0
0
0
1
0
0
2
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
4
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
2
2
0
0
0
0
0
2
0
0
2
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
8
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
1
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
1
0
0
1
1
0
1
0
3
0
0
0
0
0
2
0
0
0
0
3
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
2
0
2
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
3
1
0
0
2
2
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
1
0
2
0
0
0
0
1
2
0
2
0
1
0
0
0
0
0
0
1
0
1
0
2
0
1
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
2
0
1
0
0
0
1
0
0
0
5
0
1
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
2
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
6
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
2
2
0
0
3
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
2
0
7
0
1
1
0
0
0
4
0
0
0
0
2
0
0
0
0
0
0
6
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
1
2
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
4
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
6
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
3
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
2
0
2
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
1
0
0
0
0
7
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
1
1
3
0
0
0
0
1
1
0
1
0
0
3
0
0
0
1
0
5
0
0
0
0
7
0
1
0
0
0
2
2
0
0
1
0
0
0
0
0
2
0
0
0
7
0
0
0
0
2
2
0
0
0
1
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
2
0
0
0
2
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
6
0
0
1
0
0
0
0
1
0
2
0
2
0
1
1
0
2
0
0
0
0
2
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
5
0
0
0
1
1
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
3
0
0
2
2
0
2
0
0
2
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
2
0
0
1
0
0
0
4
0
0
0
0
0
0
1
1
0
0
2
0
1
0
3
1
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
1
0
1
0
0
0
2
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
4
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
3
0
1
1
0
0
0
2
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
2
1
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
3
1
0
0
3
0
2
0
0
0
0
4
0
0
2
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
3
0
0
0
0
1
2
0
2
0
2
0
1
0
0
0
0
0
0
1
0
1
2
0
3
1
0
0
0
0
0
0
0
2
2
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
3
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
4
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
5
2
0
1
0
0
0
0
0
2
2
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
5
0
0
0
4
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
3
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
1
1
1
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
3
2
0
0
0
1
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
2
2
0
0
0
0
0
2
2
1
0
1
0
0
1
0
1
2
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
2
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
6
0
0
0
0
0
3
0
0
8
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
6
2
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
1
2
0
0
0
1
1
0
1
0
0
2
0
2
0
0
1
0
0
1
1
0
0
1
5
0
1
0
0
0
0
0
0
0
0
2
0
1
3
0
0
0
1
0
0
1
0
0
4
0
0
0
1
1
0
0
0
0
0
1
4
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
2
2
0
2
0
0
0
0
0
2
0
0
0
0
1
3
0
1
0
0
2
0
0
2
0
1
1
0
0
3
0
4
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
3
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
5
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
12
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
2
1
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
1
0
0
0
1
2
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
4
0
0
0
0
1
0
0
2
0
0
0
1
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
2
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
2
2
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
4
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
2
2
1
0
0
0
0
1
0
0
0
0
0
0
1
2
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
2
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
3
0
0
0
0
1
0
1
2
0
0
0
0
0
3
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
1
0
0
3
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
1
2
0
0
0
4
0
0
0
0
0
0
0
0
2
2
0
3
1
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
5
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
2
0
4
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
5
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
2
3
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
2
2
0
2
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
2
0
2
0
0
0
0
2
4
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
2
0
1
0
0
0
0
2
0
0
4
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
2
0
0
0
4
0
0
1
0
0
0
4
0
1
0
1
3
0
1
0
3
0
2
4
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
1
1
0
3
0
2
2
0
0
0
0
0
0
0
0
2
0
4
1
0
0
1
0
0
1
0
0
1
4
0
0
2
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
6
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
4
1
2
1
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
7
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
3
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
3
0
0
0
0
3
2
0
0
0
1
0
3
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
3
0
1
0
0
0
0
0
2
0
6
0
0
0
0
0
0
1
5
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
1
0
0
1
2
0
0
0
0
0
0
0
2
2
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
1
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
3
0
2
2
0
2
2
0
0
1
0
1
0
3
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
6
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
2
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
2
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
3
0
3
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
4
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
4
1
0
0
1
2
0
0
1
0
2
0
0
2
1
0
0
1
4
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
1
2
1
0
0
1
1
0
2
2
0
0
0
0
0
4
0
0
0
0
3
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
1
0
4
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
2
0
0
0
2
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
4
1
0
1
0
2
1
1
1
0
0
0
0
0
1
5
1
1
1
1
0
0
0
0
2
0
0
0
0
1
0
4
4
0
0
0
1
0
0
0
1
0
0
8
5
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
4
0
2
0
4
0
2
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
3
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
1
0
0
0
0
0
2
1
1
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
2
0
0
1
0
0
1
0
2
1
1
0
0
2
0
0
1
0
0
0
0
0
2
0
0
1
0
1
0
3
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
2
0
0
0
2
2
0
0
0
0
0
0
1
0
0
1
1
0
2
0
0
0
3
0
0
0
0
0
0
1
3
2
0
0
0
0
0
0
2
2
1
1
0
0
1
0
0
1
2
1
0
1
2
1
0
1
0
0
0
2
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
7
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
2
2
0
0
1
1
0
0
0
0
11
2
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
4
0
0
0
0
0
0
0
2
0
1
0
2
0
0
4
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
2
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
2
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
4
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
3
1
2
0
1
0
2
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
1
2
1
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
3
0
0
0
0
5
0
0
0
1
0
2
0
0
0
2
0
2
1
0
0
0
0
0
0
0
1
0
2
0
2
2
2
0
0
0
2
0
0
0
0
0
0
1
2
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
5
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
2
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
1
0
3
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
2
2
0
0
1
0
3
0
0
1
2
0
0
0
0
4
0
1
2
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
2
0
0
1
2
1
0
2
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
1
0
0
0
0
0
0
7
1
0
4
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
2
0
2
0
0
0
1
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
3
0
0
1
0
2
1
0
0
0
2
0
0
0
2
0
0
0
2
0
0
1
0
2
0
0
1
0
0
0
1
5
1
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
3
5
1
1
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
4
0
0
0
2
2
0
0
0
0
0
1
0
2
2
1
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
1
0
1
0
2
2
0
10
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
1
0
0
0
0
1
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
1
1
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
2
2
0
0
2
0
0
0
1
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
1
2
4
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
3
2
0
0
4
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
1
0
0
0
4
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
3
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
3
0
1
4
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
1
1
2
0
0
0
1
1
0
0
2
1
1
0
0
2
0
0
0
3
0
0
1
0
0
0
2
0
2
3
0
2
0
0
2
0
1
0
0
3
0
0
0
0
1
1
0
0
1
0
0
0
0
4
0
0
0
1
0
0
0
0
1
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
1
0
2
2
0
2
0
0
0
0
0
4
1
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
1
0
0
0
0
9
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
1
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
3
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
6
0
1
0
0
0
0
0
4
0
0
0
0
0
0
3
2
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
6
0
0
5
0
2
0
0
0
2
0
1
1
0
0
2
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
4
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
1
2
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
2
4
0
0
0
1
0
3
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
5
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
1
2
0
0
0
4
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
5
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
3
0
1
0
2
0
1
0
0
0
2
0
0
3
2
2
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
6
0
1
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
6
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
2
0
2
0
0
0
0
2
0
0
0
0
2
0
0
2
1
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
1
4
0
0
0
0
0
0
0
0
0
2
0
1
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
3
3
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
3
1
0
0
0
0
0
0
0
0
0
0
1
0
1
4
2
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
10
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
5
1
0
0
0
0
2
2
0
1
1
3
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
2
0
0
0
0
0
0
0
2
0
0
2
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
6
0
2
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
8
1
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
2
0
1
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
1
0
0
0
0
2
0
1
1
0
2
0
2
0
0
0
1
5
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
3
0
0
0
0
0
0
1
2
1
0
0
1
2
1
0
0
0
0
1
0
0
0
0
2
7
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
1
2
0
0
2
0
0
2
1
0
0
0
0
1
0
2
0
2
0
0
3
0
0
0
1
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
1
2
1
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
1
1
0
1
5
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
3
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
2
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
1
4
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
5
2
0
0
1
0
0
0
0
3
0
0
5
0
1
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
1
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
4
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
2
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
5
0
0
0
0
0
4
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
1
0
0
4
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
1
1
0
8
2
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
1
1
2
0
0
0
0
0
2
0
2
0
0
0
0
4
0
1
0
0
1
0
0
1
1
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
1
0
1
2
1
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
2
1
7
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
3
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
2
1
2
0
0
2
1
0
1
1
0
2
0
0
1
0
2
0
0
0
2
0
2
0
0
1
0
3
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
9
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
1
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
5
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
2
2
0
0
0
3
0
0
2
0
1
1
0
0
0
3
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
9
2
0
0
1
1
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
3
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
4
2
2
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
1
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
5
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
2
2
0
0
0
1
0
0
1
0
0
0
1
2
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
1
0
0
0
0
1
1
2
2
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
2
0
2
0
1
0
0
2
0
0
0
5
1
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
4
1
2
0
0
0
3
0
0
0
2
0
2
0
0
1
0
0
2
0
0
0
0
4
2
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
6
0
6
2
0
0
1
18
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
4
0
0
2
0
0
0
0
0
0
0
1
0
0
8
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
1
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
3
0
0
0
0
0
4
1
0
0
0
0
2
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
3
0
0
0
1
0
0
2
0
0
1
2
0
0
0
0
0
0
2
0
0
0
2
2
0
1
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
3
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
1
0
2
0
1
0
3
0
1
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
2
0
2
1
0
0
0
0
7
2
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
2
4
0
2
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
3
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
4
0
0
0
0
0
0
3
0
1
0
0
1
0
0
0
4
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
1
2
0
0
0
1
0
2
2
0
1
0
0
2
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
1
1
2
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
2
2
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
2
2
1
0
0
0
0
2
0
0
0
0
0
3
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
3
0
0
1
0
3
2
0
0
0
0
2
0
0
0
0
0
2
0
0
2
1
1
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
3
3
0
0
0
0
0
2
0
2
0
0
1
3
1
0
2
0
0
0
0
2
3
0
0
0
0
1
0
0
0
0
1
0
1
0
2
0
0
11
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
2
0
2
0
1
0
2
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
2
1
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
3
1
1
0
1
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
1
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
2
0
2
0
0
0
1
0
1
0
0
0
2
2
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
1
1
0
3
0
0
0
0
1
0
3
0
0
0
0
0
0
1
0
2
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
3
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
3
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
4
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
4
4
0
0
0
0
2
0
0
4
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
1
0
2
0
0
0
3
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
3
0
0
0
0
1
1
0
0
0
0
1
2
2
0
0
0
0
0
1
0
0
2
4
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
1
0
1
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
2
0
1
0
3
0
0
1
0
0
4
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
1
0
2
2
0
3
0
0
0
0
0
4
0
0
0
0
0
1
0
2
0
0
7
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
1
0
3
0
2
1
0
0
0
0
2
0
0
0
2
0
0
1
1
0
0
2
0
0
0
0
1
0
1
2
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
4
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
2
1
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
6
0
1
0
0
0
3
2
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
3
2
2
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
2
0
1
0
0
1
0
1
1
4
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
2
1
0
0
2
2
0
1
0
0
0
1
0
0
0
4
0
4
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
1
2
0
2
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
1
3
0
0
0
0
3
0
2
0
0
0
1
0
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
3
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
1
1
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
1
0
1
0
0
0
0
0
0
2
1
0
2
0
0
0
1
0
0
0
2
0
2
0
0
2
0
0
1
0
1
0
0
0
0
0
0
3
1
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
1
5
0
0
1
0
1
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
1
0
4
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
1
0
0
0
0
0
1
0
0
1
0
1
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
2
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
3
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
1
0
0
0
0
6
2
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
4
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
1
0
1
0
0
0
0
0
0
0
4
2
0
0
1
3
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
2
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
2
1
0
0
3
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
1
2
0
0
0
0
0
0
0
0
3
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
3
0
0
0
0
0
2
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
4
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
3
2
0
0
0
1
3
0
0
0
1
0
0
0
0
0
0
2
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
3
0
2
2
0
2
0
0
0
0
15
0
0
0
5
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
2
3
1
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
5
0
0
0
0
0
2
0
0
0
0
2
2
2
2
0
0
0
0
0
0
0
2
1
0
1
2
0
1
0
0
1
3
0
0
0
0
1
2
3
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
3
6
1
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
2
1
0
2
0
0
0
5
1
0
3
0
1
0
0
0
1
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
3
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
4
0
0
2
0
1
4
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
5
0
0
0
0
0
1
1
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
1
0
2
2
0
0
2
0
0
0
0
0
0
0
2
2
0
3
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
3
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
1
0
3
1
0
0
0
1
0
0
1
2
0
0
2
1
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
4
0
3
0
2
0
0
2
0
2
0
1
0
2
0
0
2
0
0
0
0
3
1
1
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
2
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
3
0
0
0
2
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
3
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
1
0
0
0
8
0
1
2
0
2
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
2
1
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
1
0
0
0
2
0
0
0
1
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
2
0
0
2
0
0
0
1
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
3
0
2
0
0
0
0
1
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
4
2
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
3
0
1
0
1
1
0
1
0
0
0
3
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
13
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
2
1
2
1
0
0
0
0
0
2
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
3
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
1
1
2
0
1
0
1
0
0
0
1
0
0
1
0
0
0
1
1
2
0
2
0
0
0
1
0
0
0
1
0
0
0
0
3
0
0
4
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
1
0
0
0
1
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
2
2
0
0
0
0
1
0
0
0
0
2
0
0
1
0
1
1
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
3
0
2
0
0
0
1
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
2
0
0
0
0
0
1
0
0
1
0
0
4
0
0
0
2
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
7
2
2
2
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
4
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
3
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
3
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
1
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
3
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
2
2
0
0
4
0
0
2
1
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
1
0
0
1
2
0
0
0
0
0
0
0
0
1
4
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
2
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
18
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
4
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
1
1
0
0
0
0
1
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
1
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
2
0
0
1
1
0
0
0
0
1
1
0
0
3
0
1
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
2
0
0
2
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
1
2
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
1
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
1
2
0
1
2
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
1
0
2
0
0
0
0
0
2
0
0
1
0
0
1
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
4
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
2
0
2
2
0
0
0
2
0
1
2
0
0
0
1
2
2
3
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
4
0
0
0
0
3
0
2
0
0
1
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
2
0
0
0
0
0
0
0
1
2
0
0
0
3
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
6
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
6
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
3
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
8
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
2
0
0
0
1
0
0
1
0
1
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
2
0
1
0
0
0
0
0
1
0
0
2
0
1
0
0
2
2
0
3
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
4
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
4
1
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
2
1
0
0
3
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
3
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
9
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
4
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
2
1
0
3
0
3
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
5
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
3
0
2
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
1
2
1
1
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
2
0
1
4
1
0
0
0
1
0
0
0
4
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
2
0
1
0
1
0
0
0
1
1
0
0
1
0
0
0
1
0
1
0
0
2
1
1
1
0
0
0
2
0
0
0
0
3
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
6
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
1
0
6
0
2
3
0
2
1
0
0
1
4
0
0
0
0
1
4
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
2
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
2
1
1
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
3
1
0
0
1
0
1
0
0
0
0
2
1
2
1
0
0
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
1
0
0
0
2
1
0
0
0
0
3
0
0
0
0
3
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
14
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
1
0
2
2
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
11
0
0
0
3
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
2
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
3
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
3
0
1
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
3
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
2
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
5
0
1
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
8
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
2
0
1
0
3
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
2
1
1
0
0
0
0
2
0
2
0
0
0
4
0
0
2
0
1
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
2
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
2
1
0
1
0
1
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
3
2
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
3
0
1
0
1
2
0
0
0
1
0
0
0
1
0
0
0
0
0
3
2
0
1
0
1
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
2
3
0
1
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
3
0
0
1
0
0
0
0
2
0
0
1
0
0
0
4
0
0
0
2
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
3
2
0
1
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
8
3
0
0
7
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
2
0
0
2
0
0
0
4
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
2
2
0
0
2
0
0
0
2
0
2
0
2
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
1
2
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
8
0
2
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
9
1
1
3
0
0
2
0
0
0
0
0
1
3
0
0
0
1
0
1
0
0
2
0
0
0
2
0
0
1
2
0
0
4
3
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
3
0
0
1
2
0
0
0
0
0
1
0
0
0
3
0
0
1
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
4
1
2
2
2
2
0
1
0
0
0
0
1
0
2
0
0
0
0
2
1
0
0
1
0
0
4
0
0
3
1
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
1
0
3
2
0
0
0
1
1
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
6
0
9
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
1
2
0
3
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
7
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
3
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
3
2
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
3
3
0
0
0
0
1
0
2
0
0
0
2
0
0
3
0
0
0
0
0
0
2
0
0
2
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
2
0
3
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
5
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
2
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
5
0
3
3
0
2
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
1
2
0
0
0
1
0
0
0
3
3
2
0
1
2
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
3
0
2
1
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
2
0
0
1
2
2
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
2
2
0
0
1
0
0
1
3
0
0
0
0
0
0
0
5
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
1
0
0
0
0
0
4
0
1
0
2
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
2
0
1
0
2
3
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
2
0
0
1
0
1
0
1
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
1
0
0
0
2
0
2
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
3
0
0
2
0
1
1
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
4
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
4
2
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
4
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
11
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
1
0
1
1
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
2
1
0
3
2
0
2
0
1
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
3
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
2
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
1
0
1
1
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
3
1
0
0
1
2
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
3
2
0
0
3
0
0
0
0
0
2
0
0
0
1
1
0
0
3
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
3
0
0
2
1
0
2
1
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
1
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
1
0
3
0
4
0
0
1
0
0
2
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
12
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
1
1
0
0
1
0
0
0
1
0
0
2
2
0
0
0
2
0
0
0
0
0
4
2
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
2
0
2
0
0
0
0
3
0
0
0
0
0
2
0
0
1
3
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
3
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
1
1
0
1
4
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
8
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
5
1
0
0
0
0
0
0
9
0
1
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
1
1
0
14
1
0
0
0
5
1
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
5
0
0
0
0
2
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
3
0
1
1
1
0
1
0
0
0
0
4
0
0
0
2
0
2
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
2
3
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
5
0
2
0
0
0
6
0
0
2
0
0
0
0
2
0
4
0
0
0
2
1
0
1
0
0
2
5
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
1
0
1
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
2
0
0
5
0
1
0
2
0
0
0
0
0
0
0
0
2
4
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
3
0
0
0
0
0
0
0
0
0
0
0
2
0
5
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
6
0
1
0
0
1
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
3
0
2
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
8
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
2
2
0
1
2
1
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
1
1
0
2
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
5
0
0
0
0
0
0
0
0
2
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
5
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
4
0
0
0
0
0
2
1
0
1
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
5
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
3
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
7
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
6
0
0
2
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
1
2
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
1
0
1
0
2
1
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
2
2
0
0
2
0
0
0
2
0
5
0
0
2
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
4
0
0
0
0
0
0
0
1
0
8
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
4
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
4
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
2
0
0
1
3
0
1
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
5
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
1
0
1
1
0
1
0
0
6
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
1
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
1
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
7
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
4
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
10
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
3
0
4
0
0
1
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
5
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
2
2
0
3
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
4
0
0
0
0
0
1
0
2
0
0
0
2
0
2
0
2
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
4
0
0
0
0
0
2
0
2
0
0
0
2
0
0
8
0
1
1
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
2
0
3
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
1
0
1
0
0
1
0
2
0
0
1
0
0
0
0
2
0
0
0
0
5
0
0
1
0
2
1
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
2
0
1
1
0
0
2
0
2
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
6
1
1
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
8
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
2
2
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
3
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
3
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
2
2
0
0
3
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
1
0
1
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
2
0
0
0
0
2
0
3
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
2
1
1
2
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
4
0
0
0
1
0
0
0
0
3
2
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
1
2
0
0
0
0
1
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
1
8
0
0
0
0
1
1
0
0
0
2
0
0
0
2
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
2
5
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
1
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
8
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
1
4
1
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
2
0
2
1
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
2
2
0
0
0
1
0
0
0
1
0
0
2
0
0
0
1
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
8
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
2
0
7
0
1
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
2
1
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
2
2
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
3
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
2
0
1
0
3
0
0
0
1
2
2
0
0
0
1
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
1
3
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
3
2
2
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
1
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
2
2
2
0
0
0
1
0
0
0
0
0
1
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
2
0
1
0
0
0
0
1
0
1
2
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
1
0
0
1
0
0
1
0
0
1
0
1
0
0
2
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
2
3
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
4
1
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
1
0
0
0
0
0
1
2
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
2
2
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
1
1
0
0
0
0
1
0
0
2
1
0
1
0
0
0
4
0
2
0
0
0
0
1
0
2
0
5
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
2
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
2
0
0
1
0
3
0
0
0
0
1
2
0
0
0
0
2
0
0
1
0
1
0
1
1
0
2
0
0
0
0
0
1
0
3
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
2
0
2
0
0
2
0
2
2
0
0
0
2
0
0
2
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
1
2
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
1
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
3
0
0
1
2
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
2
0
2
0
0
3
0
0
0
0
0
2
0
0
0
2
5
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
4
1
0
0
0
0
0
0
3
0
0
1
1
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
2
1
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
2
0
1
0
1
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
4
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
7
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
1
0
0
0
0
1
5
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
1
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
3
2
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
8
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
3
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
7
1
0
0
0
0
1
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
1
0
2
1
0
0
2
2
0
0
0
3
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
1
1
0
2
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
3
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
1
0
2
0
1
0
0
0
0
2
0
0
2
0
0
0
0
1
0
1
0
0
0
1
0
1
1
0
0
0
1
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
2
0
0
1
0
1
0
0
0
1
0
0
0
0
0
2
0
2
0
0
1
2
0
0
1
0
0
0
2
0
0
1
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
1
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
4
0
2
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
1
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
1
2
4
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
3
0
0
3
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
2
0
0
1
2
0
0
1
1
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
1
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
3
3
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
3
2
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
4
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
7
0
0
1
0
0
1
0
0
0
0
0
3
6
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
2
0
0
0
2
1
0
0
0
0
0
1
2
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
1
4
0
0
0
1
2
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
2
0
0
0
0
3
0
0
1
0
0
1
2
0
0
0
0
1
0
0
2
0
2
2
0
0
1
1
0
0
1
0
2
0
1
0
0
0
0
0
0
9
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
2
1
0
0
0
2
3
0
0
0
1
0
1
0
1
0
0
0
0
9
0
0
0
3
2
0
0
0
3
0
3
5
5
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
1
1
0
0
0
0
0
1
0
0
1
0
3
0
2
3
2
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
2
0
2
3
0
0
2
1
0
1
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
1
1
0
0
0
3
2
1
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
7
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
2
0
0
0
3
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
4
0
1
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
4
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
3
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
3
0
0
1
0
0
1
0
0
3
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
4
0
5
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
1
1
0
1
0
2
0
0
0
0
1
0
0
0
2
1
1
0
0
0
2
0
0
2
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
3
2
0
1
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
2
1
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
1
1
0
0
0
0
3
0
0
0
2
0
2
0
2
2
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
1
0
2
0
0
1
1
1
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
1
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
10
0
0
3
1
0
0
2
1
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
4
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
1
2
1
0
0
2
1
3
2
3
0
0
0
1
0
3
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
2
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
2
0
0
0
2
3
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
5
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
4
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
1
0
0
1
0
0
2
0
0
2
1
1
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
4
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
3
2
4
0
2
3
0
1
1
0
2
0
1
0
0
0
1
0
0
0
0
0
1
1
0
2
0
0
0
2
0
0
0
0
1
2
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
8
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
6
0
0
1
1
1
0
0
0
0
0
1
0
3
0
1
2
0
0
0
0
0
0
2
0
6
0
0
0
0
0
0
0
0
0
1
2
0
2
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
2
2
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
1
0
3
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
6
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
3
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
1
0
0
2
3
2
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
3
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
1
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
1
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
1
2
0
4
0
0
2
1
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
5
0
1
0
0
0
1
0
0
0
2
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
2
2
1
0
0
1
0
0
0
0
2
0
0
0
1
0
0
1
0
1
0
0
0
2
2
0
0
0
0
0
0
0
1
2
0
0
3
2
0
0
0
0
2
0
1
2
0
6
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
1
0
1
2
2
0
0
2
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
7
1
0
0
0
0
3
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
3
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
2
0
0
0
4
0
2
0
1
0
0
0
0
1
0
0
2
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
1
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
1
0
1
0
0
0
0
3
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
3
4
0
2
0
0
0
0
0
2
2
0
0
3
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
1
1
0
2
2
0
0
0
0
0
0
0
1
0
0
0
2
3
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
7
0
0
0
0
1
0
0
0
1
1
1
1
0
0
1
0
0
0
0
2
0
0
0
0
1
0
1
0
0
2
0
0
2
2
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
1
0
0
0
3
0
2
0
0
2
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
3
0
0
0
2
1
0
0
0
1
0
0
4
0
2
0
1
0
1
1
0
0
0
0
0
2
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
2
0
0
2
1
0
2
1
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
2
1
0
3
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
6
0
4
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
1
0
2
1
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
1
0
0
0
0
4
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
2
8
0
2
2
0
0
7
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
1
0
0
1
2
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
1
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
2
0
0
4
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
6
0
1
0
0
0
0
2
0
0
0
1
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
2
0
1
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
2
0
0
0
2
3
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
2
0
3
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
1
0
0
3
0
0
2
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
2
2
0
0
0
0
0
0
2
0
0
1
2
0
2
0
0
0
0
0
0
1
0
1
4
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
1
1
3
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
5
2
1
0
0
0
0
0
0
0
0
1
0
1
0
2
0
1
2
2
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
1
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
1
0
2
0
0
5
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
3
0
0
0
3
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
5
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
1
1
0
0
0
0
2
0
2
0
0
0
0
0
3
3
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
3
0
0
1
0
0
2
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
2
0
2
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
3
0
0
0
0
1
0
1
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
2
1
2
0
0
0
0
0
0
1
1
1
0
0
0
0
2
0
3
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
1
0
0
2
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
1
0
0
0
0
1
0
0
0
0
1
1
2
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
3
1
0
1
0
0
0
0
0
0
1
1
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
3
1
0
1
0
0
0
0
0
0
4
0
0
0
4
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
3
0
0
0
0
0
0
3
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
2
1
0
2
0
0
0
0
0
1
1
1
0
0
0
2
0
0
0
0
1
0
0
0
0
3
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
7
3
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
1
3
0
0
0
3
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
1
0
0
2
2
1
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
1
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
3
0
0
0
2
1
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
1
4
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
2
2
0
0
1
1
0
0
0
0
0
0
0
4
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
4
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
1
0
1
0
0
5
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
1
0
2
3
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
1
0
0
2
0
0
5
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
1
0
0
0
0
0
0
1
0
1
1
0
1
0
1
0
0
0
0
0
2
2
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
5
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
2
1
0
4
0
4
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
1
2
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
1
2
1
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
5
0
3
1
0
0
0
3
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
4
0
0
0
0
1
2
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
2
1
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
2
1
0
0
0
2
2
0
1
0
0
2
3
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
1
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
1
0
0
2
0
0
1
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
1
0
0
0
0
3
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
2
0
1
0
1
0
0
2
0
0
0
1
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
2
2
2
5
0
0
1
0
0
0
1
3
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
3
0
1
1
2
0
0
0
0
4
0
0
0
0
1
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
2
5
0
0
0
0
4
0
1
0
0
2
0
0
0
0
0
0
8
0
0
2
1
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
1
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
2
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
4
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
2
2
0
1
0
0
2
0
0
1
1
0
2
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
5
0
0
2
0
2
0
0
0
0
8
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
2
0
0
0
2
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
2
0
1
2
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
2
1
1
0
0
0
0
0
0
0
0
3
0
2
0
0
2
0
0
2
1
0
0
2
0
1
0
6
0
0
1
2
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
3
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
8
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
4
0
1
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
3
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
6
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
4
5
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
2
1
0
0
2
0
3
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
1
2
0
0
1
0
1
0
0
0
0
0
0
0
3
2
0
1
0
0
0
2
0
1
0
0
1
0
0
0
2
0
0
0
0
1
2
0
2
0
0
0
4
0
1
0
0
3
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
4
0
2
0
5
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
3
1
0
0
0
1
0
0
1
0
4
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
1
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
0
0
9
0
0
0
0
0
1
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
1
0
2
0
1
0
0
2
0
0
1
0
1
2
0
0
0
2
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
7
0
0
2
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
2
5
0
0
2
1
0
0
0
1
0
2
1
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
2
2
1
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
4
0
0
0
0
2
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
3
1
4
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
1
2
0
0
0
0
0
0
4
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
3
0
0
0
2
2
0
2
0
0
0
1
0
0
0
0
0
0
0
5
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
5
0
0
0
5
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
2
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
6
0
2
0
0
0
2
0
0
2
0
0
0
1
0
0
0
1
0
0
0
1
2
0
0
0
0
2
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
2
0
1
1
0
1
1
0
2
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
1
0
0
0
0
1
2
0
1
0
0
0
3
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
1
0
0
2
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
3
0
2
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
5
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
3
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
1
2
0
0
0
1
2
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
4
0
1
0
2
0
0
1
0
0
1
0
0
0
2
0
0
4
0
2
0
1
0
0
1
0
0
1
2
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
3
2
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
12
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
2
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
1
1
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
1
3
1
0
0
1
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
1
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
3
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
7
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
5
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
4
0
0
1
0
0
1
1
0
2
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
2
0
0
0
1
0
4
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
2
0
2
0
2
2
2
0
0
3
0
0
0
0
0
0
2
0
0
0
1
2
0
1
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
2
0
4
0
0
1
0
1
0
0
5
0
2
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
9
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
1
0
0
1
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
1
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
2
0
1
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
8
0
0
0
0
1
0
0
2
0
2
0
0
0
0
2
0
0
1
0
1
1
0
2
0
0
0
0
2
0
0
0
0
0
1
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
3
1
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
1
0
3
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
2
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
4
2
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
6
0
0
0
0
0
0
2
0
1
0
0
1
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
3
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
1
0
2
2
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
5
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
1
0
0
1
0
0
0
2
0
0
0
0
0
1
0
7
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
2
0
2
0
0
1
0
1
0
1
0
0
0
2
0
0
0
0
0
5
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
3
1
0
0
1
1
0
2
2
0
0
0
1
0
2
1
0
0
3
0
0
0
1
5
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
2
0
2
0
2
0
0
3
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
2
1
3
0
2
0
0
4
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
1
0
1
1
0
0
0
0
0
0
0
2
0
1
2
2
0
0
0
0
0
0
0
1
2
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
3
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
2
1
1
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
2
3
1
0
4
0
1
0
0
0
0
0
0
1
0
4
1
0
0
0
2
5
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
1
0
0
0
0
0
2
2
4
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
7
1
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
3
0
1
1
2
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
1
1
0
2
1
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
4
2
0
0
2
0
0
1
0
0
0
1
2
0
1
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
1
0
1
1
0
0
0
0
0
1
0
3
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
1
1
0
4
5
0
0
0
0
2
1
1
0
0
4
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
2
1
0
0
0
2
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
3
0
2
0
0
1
1
0
0
0
2
0
1
0
1
2
2
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
1
0
0
0
2
0
2
0
4
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
1
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
4
2
0
0
1
0
0
1
0
0
0
1
0
0
0
2
1
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
2
0
0
1
0
0
1
0
0
4
0
2
0
0
0
0
0
1
0
0
0
0
1
2
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
2
0
2
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
2
0
1
0
0
0
2
0
3
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
2
0
0
0
0
0
0
1
0
0
0
0
0
0
5
0
0
0
0
1
0
0
1
0
0
0
0
1
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
6
0
0
0
0
2
0
0
0
0
0
0
3
0
2
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
2
2
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
6
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
1
0
0
1
1
1
3
0
0
0
0
0
0
2
0
0
0
0
3
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
4
0
1
1
0
0
1
0
0
2
1
0
0
0
0
1
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
5
0
0
0
0
0
0
2
0
2
1
0
0
0
1
0
0
1
0
0
0
3
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
1
0
0
2
4
0
0
1
1
0
0
2
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
3
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
3
1
2
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
5
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
2
0
0
0
2
0
0
2
0
0
3
0
0
0
0
1
0
0
2
0
2
8
0
1
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
5
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
3
2
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
2
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
6
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
1
0
3
0
0
0
0
1
2
5
0
3
0
0
0
2
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
5
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
1
5
2
2
0
4
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
3
2
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
3
2
0
0
3
0
1
0
0
0
0
0
0
0
0
2
0
1
0
2
1
1
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
5
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
4
0
0
4
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
1
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
5
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
30
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
3
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
3
0
0
0
13
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
3
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
2
1
2
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
2
1
1
0
0
0
0
0
1
0
0
0
0
0
1
4
0
0
0
0
0
1
0
0
0
0
0
0
0
6
0
2
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
3
0
0
0
0
2
0
2
2
0
0
1
0
0
4
0
0
2
7
0
0
0
0
0
0
2
0
1
1
1
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
3
0
2
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
2
2
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
3
2
0
3
2
2
2
1
1
0
0
0
0
0
0
3
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
7
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
2
0
1
0
2
0
1
2
0
0
1
0
1
0
0
0
0
0
1
0
0
2
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
3
0
2
0
2
0
0
0
1
4
2
0
1
0
13
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
1
1
0
5
0
0
0
1
4
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
2
1
0
0
0
0
1
2
0
0
1
0
1
0
0
0
0
1
0
0
0
2
0
0
3
1
0
0
0
0
1
0
0
0
0
0
1
2
0
0
2
3
0
0
0
0
0
0
2
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
3
0
0
1
0
0
1
0
0
0
0
0
0
2
2
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
2
2
0
1
0
0
0
0
2
0
2
0
2
0
1
0
0
2
0
0
0
1
0
1
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
5
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
2
0
0
3
0
1
0
0
1
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
3
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
4
5
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
5
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
1
0
0
0
0
4
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
3
0
2
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
4
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
1
0
2
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
3
0
1
2
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
3
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
6
0
0
1
0
0
2
0
1
1
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
11
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
2
0
3
0
0
2
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
1
0
3
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
3
1
0
0
0
0
0
3
0
0
3
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
1
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
2
1
0
0
0
0
0
0
2
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
4
0
0
0
0
5
0
0
0
1
0
0
0
0
0
0
1
14
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
3
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
1
1
0
0
0
1
0
0
0
1
2
0
1
0
0
1
1
0
2
1
0
1
2
2
2
0
0
0
0
0
4
1
1
0
0
0
2
0
1
1
0
0
0
2
0
0
2
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
2
0
0
0
0
0
3
1
0
0
0
0
1
2
0
0
0
0
0
4
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
2
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
3
7
0
0
0
3
0
0
2
0
0
0
1
0
0
0
1
1
0
4
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
8
0
0
0
0
3
0
0
2
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
4
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
3
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
1
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
1
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
3
0
1
0
0
0
3
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
2
3
0
0
0
0
0
1
1
0
0
3
0
0
1
0
2
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
6
0
0
0
0
1
0
0
0
0
0
3
1
0
0
0
0
0
0
1
0
2
0
0
2
0
1
0
0
1
2
0
3
0
0
0
0
1
0
2
6
0
0
0
0
0
0
2
0
2
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
3
0
0
0
0
3
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
2
0
0
1
1
0
0
5
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
2
0
0
0
5
0
0
0
0
2
0
3
0
0
0
3
0
2
1
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
3
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
1
0
0
2
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
3
0
0
4
0
1
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
3
2
0
1
0
0
0
2
1
1
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
2
0
1
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
1
5
0
0
0
0
0
3
3
0
2
0
0
6
0
0
0
0
0
0
1
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
1
0
0
1
1
0
0
0
0
3
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
3
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
1
1
0
1
0
2
0
0
0
0
5
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
1
0
1
1
0
0
0
0
2
1
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
1
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
3
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
7
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
3
0
1
0
0
1
1
0
0
1
0
0
2
1
0
2
0
0
0
0
2
0
0
0
1
0
0
1
0
2
0
0
0
3
2
0
0
0
1
0
0
1
0
0
0
1
0
1
1
2
0
0
2
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
8
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
1
0
1
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
3
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
2
0
1
0
0
0
0
2
0
0
1
1
0
0
0
2
0
4
0
0
0
0
0
1
5
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
4
0
0
0
0
0
0
0
0
2
1
0
1
8
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
1
2
0
0
0
0
1
1
0
0
0
2
0
0
0
1
0
0
0
2
0
1
0
0
0
0
1
0
0
1
0
0
1
0
2
0
0
0
0
0
2
0
3
5
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
1
4
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
4
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
1
0
2
0
0
2
2
0
1
0
0
1
0
4
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
4
2
0
0
3
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
1
0
0
0
0
0
1
0
1
0
2
1
0
0
0
0
4
2
0
0
0
0
0
0
3
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
3
0
1
0
0
3
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
1
3
0
0
2
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
3
0
0
0
0
0
0
1
0
0
0
1
1
1
0
6
3
2
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
1
1
2
4
0
0
1
0
0
2
1
0
4
0
0
0
1
0
19
2
0
0
0
0
1
0
1
0
0
0
0
2
1
0
0
0
0
0
0
1
3
0
1
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
3
0
0
0
2
0
7
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
1
0
0
0
0
0
2
0
1
0
0
2
0
0
0
1
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
3
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
6
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
1
0
0
2
1
0
0
0
0
2
0
0
0
1
1
0
1
2
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
2
0
4
2
0
0
0
0
2
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
1
0
1
2
2
1
1
0
0
0
0
0
1
2
0
1
0
0
0
1
0
0
0
0
0
3
3
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
1
3
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
3
2
0
0
0
0
0
0
0
0
0
0
0
6
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
1
0
1
0
2
2
1
0
0
0
0
1
0
0
0
3
0
0
1
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
1
1
2
0
0
0
0
0
0
2
7
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
8
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
5
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
3
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
2
0
2
0
1
0
0
0
0
1
0
2
1
0
1
2
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
2
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
4
1
0
6
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
1
2
2
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
20
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
3
3
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
4
0
3
0
0
0
1
1
0
0
0
1
1
2
0
2
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
6
0
1
2
2
0
0
0
2
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
12
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
5
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
1
2
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
1
3
0
0
0
1
0
0
2
1
0
0
2
0
0
0
0
3
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
2
1
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
2
1
0
0
2
0
1
1
0
1
0
0
0
0
0
0
0
0
1
2
1
0
1
0
3
0
0
1
1
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
8
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
3
1
0
0
0
3
0
1
1
2
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
3
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
5
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
9
0
1
2
0
0
0
0
0
0
0
0
2
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
6
0
2
0
1
0
2
0
0
0
0
2
1
0
2
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
2
0
2
0
0
0
1
0
0
0
0
2
3
0
0
3
1
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
2
0
2
4
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
11
0
0
0
0
0
2
0
0
0
0
0
0
4
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
2
0
2
0
0
8
0
4
0
0
0
0
1
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
1
0
1
11
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
5
0
0
0
0
0
3
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
1
2
0
1
3
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
1
2
2
2
0
0
6
0
0
0
0
0
0
0
2
2
3
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
3
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
4
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
1
1
0
0
0
1
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
7
0
0
2
0
1
0
0
1
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
2
3
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
1
1
0
0
3
0
0
0
2
0
0
0
0
2
1
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
1
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
3
0
0
2
0
0
0
1
0
2
0
2
0
0
0
3
2
0
0
0
0
1
0
1
0
0
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
2
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
3
0
2
0
1
2
0
2
0
1
0
0
0
5
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
2
1
0
0
0
0
1
0
0
0
1
2
0
1
0
0
2
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
2
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
2
0
0
0
3
0
2
2
3
0
0
0
1
2
0
3
1
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
2
2
0
0
0
1
0
0
3
0
1
1
0
0
0
3
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
3
0
1
1
0
1
1
0
0
3
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
1
3
0
1
0
0
3
2
1
0
0
0
2
1
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
2
0
1
0
2
0
0
0
2
1
2
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
6
2
0
0
0
0
0
0
0
2
1
0
0
1
1
0
1
0
1
0
1
0
0
2
0
2
0
0
0
0
0
1
1
2
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
1
1
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
5
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
2
0
0
3
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
1
2
1
1
4
2
0
2
0
0
0
0
0
6
0
5
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
2
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
2
2
1
2
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
1
0
0
0
1
1
0
0
0
1
1
0
1
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
1
0
0
0
1
0
0
3
0
0
0
0
0
3
1
0
0
0
0
0
0
4
0
1
0
3
0
0
0
1
0
1
4
0
2
1
0
5
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
2
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
6
0
3
0
0
1
4
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
1
0
0
9
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
2
0
5
0
0
2
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
2
0
1
1
0
2
0
3
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
1
0
2
1
2
0
0
0
2
1
0
0
0
0
0
0
1
3
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
3
0
0
4
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
2
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
1
4
0
2
0
0
0
5
0
0
0
0
0
2
4
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
2
1
0
0
2
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
6
0
0
0
0
0
0
1
0
0
1
0
1
2
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
2
2
0
0
0
0
0
1
0
1
0
0
0
0
6
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
4
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
1
0
2
0
0
1
2
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
1
0
0
3
0
0
1
0
0
0
0
0
2
0
2
0
0
1
2
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
3
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
1
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
5
0
0
0
1
1
0
0
2
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
14
0
2
0
0
0
3
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
1
0
0
3
0
0
0
6
1
0
0
1
0
0
0
0
2
0
0
0
0
0
1
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
9
0
1
0
0
0
0
7
0
0
0
0
0
1
0
0
2
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
1
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
4
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
5
1
0
2
0
0
0
0
0
1
1
0
0
0
2
0
2
0
0
0
0
0
4
0
1
0
2
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
3
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
1
2
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
2
0
0
1
2
1
0
0
0
0
0
0
0
1
4
1
1
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
3
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
1
1
0
0
2
0
3
0
4
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
1
3
0
3
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
8
0
3
0
0
4
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
6
0
1
1
0
0
0
0
1
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
1
0
0
0
2
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
4
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
3
2
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
1
2
1
0
0
0
2
0
0
3
0
0
0
2
0
0
1
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
3
0
2
0
0
0
0
0
0
0
1
3
0
0
0
0
1
0
0
0
0
4
0
0
0
1
1
0
2
2
1
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
1
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
2
2
0
0
0
8
1
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
3
2
0
2
3
0
0
0
1
3
0
0
0
0
0
2
1
0
0
0
1
0
1
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
2
0
0
1
0
1
0
0
0
4
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
2
0
0
1
1
0
0
0
0
0
0
2
0
0
3
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
2
0
3
0
1
0
2
2
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
1
1
0
1
0
0
0
1
0
0
2
0
0
0
0
3
2
0
0
0
0
0
1
1
0
0
2
0
0
0
0
2
1
0
0
1
0
0
2
0
1
0
0
0
0
0
0
6
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
2
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
2
0
0
0
3
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
8
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
5
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
2
0
0
0
0
0
0
7
0
0
0
1
0
1
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
3
0
0
0
1
0
0
3
0
0
0
0
5
0
0
1
0
0
0
0
0
0
1
0
1
1
0
2
2
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
5
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
3
0
0
0
2
1
0
0
0
1
0
2
0
0
0
2
0
6
1
0
0
1
0
1
3
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
4
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
2
4
0
2
2
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
3
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
2
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
2
1
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
3
2
2
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
2
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
2
2
0
2
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
4
0
0
0
0
0
4
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
1
1
2
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
2
1
0
0
2
0
2
0
0
0
0
0
2
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
4
0
0
0
0
0
0
2
0
2
1
0
0
0
2
0
0
1
0
0
1
0
2
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
3
1
0
2
2
1
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
2
2
0
0
0
0
3
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
3
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
2
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
1
0
2
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
7
3
0
0
1
0
3
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
2
0
1
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
2
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
2
8
0
0
0
0
0
0
0
2
0
0
0
0
2
0
3
0
0
1
0
0
1
2
2
1
0
0
0
0
0
5
0
0
1
0
0
2
0
0
1
9
2
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
2
4
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
1
2
0
1
0
0
0
0
1
0
2
0
0
0
1
0
0
1
0
0
2
0
2
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
1
0
0
2
0
1
0
0
3
2
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
7
2
0
2
0
0
0
0
2
0
0
0
0
2
1
0
1
1
0
3
0
0
0
2
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
1
7
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
1
1
0
0
0
0
2
0
1
6
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
1
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
5
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
12
0
2
0
2
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
2
0
1
0
1
0
0
0
0
1
0
0
0
0
2
0
4
2
0
1
2
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
1
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
2
0
0
0
0
1
1
0
0
0
0
0
0
1
1
3
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
1
0
0
0
4
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
6
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
2
0
1
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
3
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
1
0
0
1
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
2
1
0
0
0
3
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
1
0
1
1
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
2
1
0
4
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
1
0
0
0
1
0
2
0
0
2
0
0
2
0
1
1
0
0
1
0
0
0
0
0
0
2
1
1
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
5
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
5
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
2
4
1
1
1
0
0
3
0
0
0
0
0
1
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
2
0
1
0
0
1
0
9
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
8
0
0
0
0
0
2
1
0
1
0
0
0
2
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
1
6
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
3
0
0
0
0
2
0
0
0
1
0
4
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
6
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
2
0
2
2
0
3
0
0
0
2
0
0
5
0
0
0
0
4
3
0
0
0
0
0
0
5
0
1
0
0
0
1
1
0
1
1
2
0
0
0
2
1
0
2
0
0
0
0
3
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
1
0
1
0
3
0
2
0
2
0
0
0
1
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
3
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
2
0
2
0
0
0
0
1
1
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
2
2
0
1
0
1
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
3
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
2
2
0
0
0
0
0
4
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
2
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
1
1
0
0
0
0
0
3
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
11
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
2
0
1
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
3
2
0
0
1
0
1
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
1
7
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
1
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
3
0
2
0
0
0
0
0
1
0
1
2
1
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
3
0
0
0
0
1
1
0
3
0
0
13
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
14
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
9
0
0
0
0
2
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
1
2
1
0
2
2
0
0
0
0
0
0
0
0
0
4
1
0
1
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
1
6
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
2
2
1
2
0
0
0
0
0
2
1
0
0
1
1
0
2
1
0
0
2
0
0
0
0
2
2
2
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
7
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
3
3
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
1
0
2
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
5
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
4
1
2
5
0
2
1
2
0
0
0
1
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
1
0
0
0
0
1
1
0
0
0
2
4
0
2
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
1
0
0
3
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
1
1
0
0
0
0
3
0
2
0
0
1
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
3
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
4
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
1
2
0
0
0
0
1
0
0
6
2
4
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
1
0
2
0
0
1
0
0
0
1
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
3
0
1
0
0
2
0
0
0
0
0
3
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
2
0
0
2
1
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
1
0
0
2
0
0
1
2
0
0
0
1
0
0
2
0
0
0
0
2
3
0
7
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
1
0
0
0
1
0
2
1
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
4
0
0
0
0
0
0
0
1
3
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
5
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
2
0
0
1
0
2
0
1
0
0
1
0
1
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
6
0
2
0
0
0
0
0
0
2
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
1
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
2
2
0
0
0
2
0
3
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
1
2
4
0
0
0
0
0
0
0
1
0
1
0
0
0
1
2
0
0
0
0
1
0
0
1
3
0
0
0
0
2
0
0
1
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
1
2
0
0
0
0
0
1
0
0
0
0
0
3
1
0
0
0
0
0
0
0
4
0
0
0
0
0
2
0
1
2
2
0
2
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
1
0
0
0
0
0
0
2
0
0
4
0
0
0
4
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
4
0
0
0
1
2
0
0
1
0
1
0
0
0
0
2
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
1
0
1
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
1
0
1
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
3
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
7
0
0
0
0
2
2
0
0
0
0
0
4
0
1
0
0
0
2
2
0
0
0
1
1
0
0
0
1
0
1
0
0
1
0
0
0
0
1
1
0
5
0
0
0
0
0
1
0
1
2
0
0
0
1
0
0
0
1
3
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
3
0
0
1
0
0
0
0
2
0
1
1
0
0
0
2
0
0
0
0
0
2
3
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
3
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
5
0
0
0
3
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
3
1
0
2
4
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
3
0
2
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
5
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
2
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
2
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
5
0
1
0
0
0
1
0
0
0
0
0
1
0
1
1
0
2
0
0
0
0
0
0
3
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
6
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
2
0
0
1
5
0
0
1
1
0
0
0
0
4
1
0
2
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
2
0
2
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
3
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
2
0
1
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
1
0
0
0
0
1
1
1
0
0
0
1
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
2
0
3
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
1
0
0
0
0
0
0
2
1
0
0
0
2
0
0
3
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
4
0
0
2
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
13
0
0
0
2
0
1
0
0
0
1
8
0
0
1
0
1
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
2
1
0
3
1
2
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
2
0
1
0
2
0
2
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
2
0
1
0
0
2
0
1
0
0
0
0
0
2
1
0
2
0
0
0
0
1
0
0
0
0
2
0
1
1
1
1
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
3
0
2
0
0
0
0
0
0
1
2
2
2
0
0
1
0
1
0
0
0
0
0
0
0
2
0
1
0
0
3
8
6
2
0
0
0
0
0
0
0
1
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
6
2
1
2
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
6
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
2
0
2
1
0
1
0
1
1
0
0
0
0
2
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
1
0
8
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
8
0
0
3
0
1
0
0
0
2
0
2
0
7
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
1
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
1
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
1
2
0
2
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
2
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
4
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
1
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
4
2
0
0
0
0
0
0
0
0
0
8
0
0
0
3
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
2
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
1
0
0
1
1
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
1
0
1
1
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
3
2
0
0
0
0
1
1
1
0
0
0
0
2
2
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
1
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
2
1
0
0
0
0
0
0
2
0
0
2
0
0
0
4
0
0
0
0
1
0
0
1
0
0
3
1
0
1
1
0
1
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
4
0
0
2
3
2
0
0
0
1
1
0
0
1
0
0
0
0
0
2
1
0
0
0
1
0
0
0
2
0
1
2
1
0
0
0
0
0
0
2
2
0
2
1
1
1
0
0
2
2
1
1
0
1
2
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
7
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
2
0
2
0
0
0
0
0
1
2
0
0
0
0
0
5
0
0
2
1
0
0
4
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
2
2
0
0
1
0
0
0
0
1
0
1
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
1
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
5
0
1
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
2
6
1
0
0
0
0
0
0
0
1
1
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
3
0
0
1
0
1
0
0
0
2
0
0
1
0
0
0
0
2
0
0
2
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
2
0
1
0
1
0
3
0
0
0
0
0
0
1
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
3
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
3
0
1
0
6
0
2
0
1
0
0
0
0
0
1
0
1
2
0
0
1
0
0
0
0
0
0
2
3
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
5
0
0
0
2
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
4
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
3
1
0
0
0
0
0
1
0
4
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
2
0
1
1
5
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
3
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
3
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
2
0
1
0
1
0
1
0
0
0
0
2
0
1
0
0
1
2
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
7
1
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
1
0
2
0
0
0
0
1
0
1
2
0
1
0
0
1
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
2
0
0
0
1
0
3
1
0
0
2
0
0
0
1
1
0
0
2
0
0
0
4
0
3
1
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
5
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
4
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
5
0
0
1
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
1
3
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
2
0
0
0
0
0
0
8
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
3
0
0
0
0
0
0
0
0
0
1
3
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
2
1
0
0
0
1
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
1
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
1
0
0
0
2
2
4
0
0
2
1
0
0
0
0
0
2
0
0
1
2
0
0
2
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
2
4
0
0
0
3
2
0
0
0
0
2
0
1
3
0
0
0
1
3
1
0
0
0
1
0
2
0
1
0
0
1
0
0
0
0
0
3
2
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
2
0
3
0
2
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
3
0
12
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
8
0
1
7
0
0
0
0
0
0
0
0
0
0
0
6
2
0
0
0
0
5
0
0
0
1
0
0
0
2
2
0
0
1
0
0
0
0
0
2
4
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
5
0
0
2
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
2
1
4
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
1
0
1
7
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
1
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
5
0
2
2
0
0
0
0
2
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
1
0
1
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
3
1
0
2
4
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
4
0
1
0
0
2
0
2
1
0
0
0
1
3
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
2
1
0
0
0
2
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
4
1
1
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
4
1
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
8
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
1
0
0
0
1
1
0
0
4
0
0
0
0
2
0
0
0
1
1
2
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
3
0
1
0
0
0
0
1
0
0
1
2
0
0
0
0
0
1
3
1
0
0
0
0
0
2
0
3
0
0
1
0
0
0
1
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
3
1
0
0
0
0
0
0
0
4
1
0
1
0
1
0
0
0
0
0
0
2
0
2
0
1
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
3
1
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
2
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
3
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
1
0
2
1
0
0
1
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
1
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
2
0
3
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
2
0
0
2
0
0
1
0
2
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
1
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
5
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
5
0
0
0
0
0
2
1
0
0
0
0
0
1
0
2
0
0
0
2
5
0
0
1
0
0
2
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
1
0
0
1
0
0
0
1
2
0
0
3
0
0
1
0
2
0
0
0
0
0
2
0
2
0
0
2
0
4
1
0
0
4
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
9
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
1
1
0
0
0
2
1
0
2
0
0
0
0
0
2
0
0
2
4
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
7
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
1
0
2
0
0
2
5
2
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
1
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
3
1
0
0
4
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
2
0
0
0
1
2
0
0
0
3
0
0
0
0
1
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
13
0
0
0
1
2
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
4
0
0
2
0
0
0
0
0
1
1
3
2
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
2
1
0
2
0
2
0
0
1
1
3
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
4
0
0
0
4
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
2
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
1
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
6
0
2
2
0
0
0
0
0
0
0
1
1
0
1
0
0
1
2
0
0
0
2
1
0
0
0
1
0
0
0
0
0
2
0
0
0
2
5
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
5
2
0
0
0
1
1
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
1
1
0
0
0
2
1
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
1
1
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
1
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
4
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
2
2
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
5
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
4
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
2
2
2
1
0
0
0
0
0
0
0
1
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
1
0
0
0
2
0
1
1
1
0
0
0
1
1
0
0
2
5
0
0
0
0
1
3
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
2
2
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
7
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
2
1
0
1
0
4
1
0
0
2
0
0
1
0
2
0
1
0
7
0
0
3
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
1
2
6
2
1
1
3
0
0
2
3
2
1
0
0
0
2
2
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
1
0
0
0
0
0
0
0
1
1
0
2
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
2
2
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
3
0
1
0
0
3
3
0
0
0
2
0
0
2
0
1
2
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
1
2
0
2
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
1
0
0
0
1
0
2
0
2
0
0
1
0
0
2
0
0
0
2
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
4
0
0
0
1
0
0
0
0
1
2
0
0
0
0
3
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
1
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
1
0
0
2
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
1
0
2
1
0
0
4
2
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
1
2
0
7
0
0
0
0
0
0
0
0
6
0
0
1
0
0
3
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
2
0
0
2
0
3
0
0
0
1
0
0
1
0
0
0
0
4
0
0
1
2
0
3
0
0
0
0
0
1
0
0
0
0
1
0
4
1
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
3
4
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
1
0
0
0
1
0
1
0
4
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
2
0
0
0
0
0
1
0
1
0
0
0
1
0
2
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
2
0
0
1
2
0
0
0
0
0
0
0
0
1
3
0
4
0
0
1
1
0
0
0
0
2
0
0
3
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
1
0
0
0
0
0
7
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
5
1
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
2
0
0
1
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
1
1
1
0
0
2
0
3
0
0
2
0
0
2
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
3
0
0
1
0
3
1
0
0
0
0
0
0
2
2
0
0
0
0
1
2
2
1
2
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
6
0
0
0
0
2
0
0
0
0
2
15
0
0
0
0
0
1
0
0
0
0
9
1
0
0
0
0
0
0
3
0
3
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
3
0
0
0
1
1
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
3
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
2
2
2
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
2
1
1
0
2
0
1
0
0
0
0
1
0
0
0
1
4
1
0
2
1
2
1
0
0
0
2
0
0
0
0
4
0
0
0
0
0
0
2
0
2
0
0
2
7
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
3
0
1
0
1
0
2
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
2
0
9
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
3
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
3
1
0
1
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
3
0
3
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
1
0
1
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
1
0
0
0
0
0
1
0
2
1
0
0
0
0
1
2
2
0
1
0
0
0
0
0
0
0
0
4
0
0
0
2
0
2
1
0
8
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
1
0
1
0
1
1
1
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
3
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
3
0
0
0
3
0
0
0
1
0
0
0
0
2
1
3
0
1
0
0
2
0
1
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
1
1
0
0
1
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
3
1
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
3
0
0
0
0
0
2
2
0
2
0
2
0
4
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
2
0
0
0
2
0
1
1
0
0
1
2
0
1
0
1
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
3
0
0
0
2
0
0
0
0
0
0
3
2
0
0
0
0
1
0
0
0
1
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
1
0
1
2
0
2
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
2
1
0
0
4
0
2
1
0
0
2
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
4
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
2
2
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
1
0
3
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
2
0
0
0
0
0
2
2
0
0
1
1
0
0
0
0
1
0
2
2
0
1
1
0
1
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
2
3
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
2
0
0
0
1
2
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
2
1
0
2
0
1
2
1
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
2
0
4
0
0
0
2
0
0
0
0
1
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
2
1
2
0
0
0
0
0
0
0
0
2
0
6
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
5
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
3
0
2
0
0
0
1
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
3
0
3
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
2
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
2
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
2
0
1
2
0
0
0
0
0
2
0
2
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
2
0
0
0
5
0
3
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
5
0
0
0
2
0
1
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
3
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
1
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
7
0
0
0
0
0
0
0
0
0
6
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
2
0
1
0
0
1
0
2
0
0
0
0
0
5
0
1
0
0
1
0
0
0
3
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
3
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
3
1
0
0
0
0
1
2
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
3
0
0
0
0
3
0
1
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
6
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
2
1
1
0
0
0
0
2
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
2
1
1
0
0
1
2
4
0
0
1
0
0
2
1
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
3
1
0
0
1
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
3
0
0
0
0
1
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
3
1
0
0
1
0
2
2
0
0
0
0
1
0
0
5
0
0
1
0
0
1
1
0
0
0
0
0
2
0
3
2
0
0
0
0
1
0
0
0
0
1
5
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
3
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
5
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
1
0
0
0
2
1
0
1
1
0
2
0
0
3
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
5
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
1
4
0
0
1
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
1
0
2
0
3
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
2
0
0
0
0
1
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
4
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
3
0
0
0
0
0
2
1
0
3
0
2
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
1
0
0
0
0
0
2
0
2
2
2
1
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
2
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
3
0
0
0
0
2
0
0
0
3
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
2
0
3
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
5
2
0
0
0
0
0
0
1
0
0
0
0
3
2
2
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
2
0
0
2
0
0
1
2
2
2
0
0
1
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
3
0
0
0
0
0
0
0
0
1
0
3
1
0
0
0
0
0
0
0
0
1
0
0
3
0
1
0
0
0
0
0
1
2
0
0
1
1
2
0
0
1
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
1
0
1
0
0
0
0
2
2
0
1
0
1
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
1
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
3
0
0
0
2
0
0
0
1
0
0
0
3
1
0
1
0
3
4
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
2
2
0
0
0
1
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
4
0
0
0
0
2
1
0
1
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
3
0
0
0
1
0
1
0
0
0
3
1
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
6
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
17
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
10
0
0
0
4
0
2
0
2
3
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
2
1
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
3
0
0
3
0
0
0
1
0
0
1
0
1
0
1
2
0
1
0
0
2
2
0
0
0
2
0
0
0
0
2
2
0
7
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
1
0
1
0
1
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
2
0
2
0
2
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
1
0
1
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
3
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
2
0
0
0
0
11
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
1
2
1
2
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
1
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
3
0
0
0
1
0
0
0
0
1
0
2
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
4
1
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
3
0
0
0
0
0
0
0
3
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
4
0
1
1
5
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
8
1
2
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
1
0
0
0
1
0
0
5
0
2
0
0
1
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
3
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
8
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
1
0
0
0
1
1
0
0
4
1
4
0
0
0
1
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
11
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
2
3
0
2
1
0
3
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
4
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
1
0
0
0
7
1
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
1
1
0
2
0
0
0
3
0
2
0
0
0
0
0
0
2
0
0
3
0
0
0
1
0
2
0
0
0
1
2
0
1
0
0
2
0
1
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
3
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
3
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
2
0
1
1
5
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
2
5
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
3
2
6
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
3
0
0
0
2
5
0
0
0
1
0
1
1
3
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
3
2
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
1
0
1
1
0
2
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
2
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
2
1
2
0
2
4
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
10
0
2
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
3
0
1
0
1
0
0
0
0
2
0
0
0
2
0
0
3
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
2
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
5
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
10
0
0
0
2
1
0
0
0
0
0
0
1
0
0
1
2
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
3
0
0
2
0
0
1
0
2
0
5
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
3
0
1
0
0
2
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
2
0
2
0
0
2
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
8
0
0
0
0
0
0
0
1
3
2
0
1
0
0
0
0
0
2
1
2
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
2
0
2
0
1
3
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
1
1
1
0
2
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
1
3
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
5
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
3
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
2
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
2
0
0
6
2
0
0
0
0
0
2
0
0
0
0
1
3
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
4
3
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
1
0
0
2
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
3
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
1
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
4
0
2
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
4
0
0
2
0
0
0
1
2
0
0
0
0
2
0
0
0
2
0
0
5
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
4
0
0
1
2
0
0
1
0
0
0
0
0
2
0
3
0
0
0
0
1
0
2
2
0
2
0
2
0
0
1
1
0
0
3
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
1
0
0
0
0
0
1
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
2
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
3
0
0
0
0
0
0
1
0
0
0
1
3
0
0
1
0
0
0
2
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
3
0
0
4
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
2
0
0
1
0
1
2
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
4
1
0
0
0
0
0
2
0
0
4
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
1
1
0
0
2
2
1
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
3
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
1
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
1
3
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
13
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
3
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
1
1
7
0
0
1
0
0
8
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
1
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
4
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
1
0
0
0
0
1
0
0
0
1
0
2
0
0
2
0
0
0
0
2
1
0
0
0
0
0
1
0
1
1
0
2
1
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
6
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
3
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
3
1
1
2
0
0
1
0
0
2
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
2
0
0
0
2
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
2
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
3
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
2
0
0
3
0
0
0
3
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
4
1
0
1
1
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
4
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
7
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
3
3
0
0
2
0
0
0
0
0
0
0
0
2
1
1
1
0
0
0
2
4
0
0
0
0
0
2
0
0
0
0
1
0
0
7
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
4
0
3
0
0
5
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
10
0
0
2
0
0
1
2
0
0
0
0
0
3
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
7
0
1
5
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
4
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
2
0
3
0
0
0
0
1
0
0
0
0
1
2
0
0
0
5
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
4
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
2
1
2
0
13
0
1
0
3
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
6
0
0
5
1
3
10
0
1
0
0
8
0
1
0
0
2
1
0
1
1
0
0
4
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
2
0
0
0
0
3
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
2
0
2
2
0
0
0
1
0
0
1
2
0
0
0
0
0
0
3
2
0
0
0
1
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
1
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
1
0
0
0
0
1
2
0
3
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
9
0
1
0
1
2
0
0
0
1
0
0
0
2
0
1
0
1
0
0
1
1
0
0
4
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
3
0
0
2
2
0
0
0
0
0
0
0
1
0
3
0
0
2
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
3
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
1
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
1
0
2
1
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
5
0
0
0
2
0
3
1
0
0
0
1
2
0
2
1
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
1
2
0
0
0
0
2
0
0
0
3
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
2
2
2
2
0
3
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
1
0
0
2
2
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
1
0
0
0
1
0
0
2
1
0
3
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
1
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
2
0
2
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
1
0
1
1
2
0
3
1
1
0
0
2
2
2
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
3
0
3
0
0
0
0
0
0
0
1
6
1
2
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
8
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
2
0
0
0
1
0
1
2
0
1
2
0
0
1
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
2
1
0
0
0
2
2
0
2
1
3
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
3
1
1
0
0
0
2
0
0
0
0
0
1
0
2
0
1
2
1
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
2
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
3
1
0
1
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
1
0
1
0
0
0
1
0
5
0
0
0
0
0
0
0
0
0
1
0
2
0
1
1
1
0
0
2
0
0
1
0
0
0
1
4
0
0
1
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
3
0
0
0
0
0
0
2
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
4
0
0
1
2
2
1
0
0
1
0
2
4
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
2
2
3
0
0
2
1
0
1
0
0
0
0
0
0
1
0
2
0
0
3
0
0
0
0
0
0
1
0
0
0
3
0
3
0
1
0
0
1
0
0
0
1
1
0
0
0
0
1
1
0
0
2
3
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
2
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
3
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
3
0
0
0
0
1
1
0
0
0
0
1
2
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
1
1
1
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
2
0
2
0
0
0
0
1
2
0
0
1
0
0
4
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
7
0
0
0
0
0
3
0
0
1
0
1
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
8
1
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
5
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
2
0
0
3
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
1
4
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
2
0
0
3
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
3
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
1
0
0
0
8
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
2
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
2
0
1
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
2
0
0
1
0
2
0
0
2
2
0
3
0
0
0
0
1
1
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
12
1
0
1
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
4
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
2
0
0
2
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
4
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
1
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
2
3
0
1
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
1
7
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
4
0
3
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
2
0
0
2
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
2
0
0
2
0
7
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
7
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
2
1
0
0
0
4
0
0
0
2
1
1
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
8
0
1
0
1
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
1
0
0
1
0
0
0
1
0
0
0
2
0
2
0
0
0
2
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
1
0
1
2
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
1
0
0
2
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
2
0
0
0
0
2
0
1
0
2
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
2
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
3
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
2
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
6
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
6
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
1
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
6
1
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
8
0
0
0
0
0
0
1
2
0
0
3
2
3
1
0
0
0
0
0
2
0
0
0
3
1
0
0
1
0
0
0
4
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
1
0
0
2
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
3
3
2
0
0
0
3
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
3
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
1
0
1
0
1
0
0
0
0
0
1
0
1
1
0
0
1
0
3
0
0
0
3
2
1
0
0
0
2
0
0
2
1
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
6
0
2
0
0
0
0
3
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
1
1
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
1
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
3
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
1
1
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
1
1
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
4
1
4
0
0
0
0
0
1
0
0
2
0
0
3
0
0
0
0
0
2
2
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
2
0
0
0
0
0
0
1
0
3
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
1
0
5
1
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
2
1
0
0
3
0
0
0
2
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
3
2
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
4
0
1
1
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
2
0
0
1
2
0
0
0
0
0
2
0
0
0
0
1
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
1
0
0
0
1
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
1
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
2
0
0
2
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
4
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
1
0
0
0
0
0
1
1
0
0
3
1
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
1
0
0
0
1
0
3
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
1
0
0
1
2
0
0
2
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
4
0
0
1
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
2
0
4
0
1
0
0
0
0
0
0
2
2
0
0
0
2
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
6
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
1
1
0
0
0
1
0
0
0
2
1
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
1
0
2
0
0
3
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
2
1
0
0
0
1
0
0
0
1
0
0
0
1
1
3
0
2
0
0
1
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
2
0
0
0
0
0
0
1
0
1
0
0
2
0
0
1
6
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
1
2
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
3
2
0
1
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
2
0
0
0
1
0
0
2
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
4
0
2
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
3
1
0
0
2
0
0
0
4
1
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
1
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
1
2
2
0
0
3
0
0
0
1
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
1
2
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
2
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
2
1
0
0
0
0
0
0
1
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
2
1
2
0
3
0
2
0
0
0
0
1
2
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
1
0
0
2
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
1
0
0
0
1
0
3
2
2
0
1
0
2
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
6
2
0
0
0
3
0
0
0
2
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
1
0
1
2
0
3
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
1
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
1
2
0
2
2
0
0
0
0
0
0
1
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
5
1
0
0
2
3
0
2
1
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
3
0
2
4
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
6
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
2
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
1
0
0
1
0
1
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
3
0
1
1
1
0
0
0
3
1
0
0
0
0
3
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
3
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
3
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
2
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
5
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
4
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
1
0
0
2
5
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
2
0
0
0
0
2
0
0
0
7
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
1
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
3
2
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
3
1
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
24
2
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
1
5
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
5
0
3
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
12
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
13
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
1
1
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
2
0
0
2
0
0
0
1
0
0
2
0
1
0
0
0
0
3
0
0
0
0
0
1
5
1
0
0
0
2
2
0
0
1
0
4
2
2
0
0
1
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
3
2
0
0
3
0
3
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
3
0
0
1
0
0
0
0
0
3
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
1
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
3
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
2
1
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
1
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
4
0
0
1
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
7
0
0
2
1
0
0
1
2
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
2
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
1
1
0
0
0
1
0
0
12
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
1
0
0
1
0
0
0
3
0
0
0
0
0
0
3
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
2
2
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
2
2
0
0
0
0
2
0
1
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
3
0
0
2
0
0
0
0
0
0
1
1
0
0
2
3
1
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
1
0
3
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
1
0
0
4
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
1
2
0
0
0
5
1
0
0
0
0
0
0
0
3
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
6
0
0
0
0
3
0
0
0
0
1
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
2
0
3
0
0
0
0
0
3
0
0
0
0
0
0
1
1
1
2
1
0
0
0
0
0
0
0
0
6
0
0
0
0
0
2
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
1
0
1
0
0
3
0
0
2
0
0
0
0
0
2
0
2
0
2
0
1
0
2
1
0
2
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
2
0
0
1
0
0
5
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
1
1
0
0
0
0
2
0
0
0
0
0
4
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
4
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
1
0
0
1
1
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
5
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
3
1
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
2
2
1
0
0
0
0
0
0
1
0
0
2
3
0
1
0
0
1
0
0
0
0
0
0
0
0
1
2
2
0
0
1
0
0
0
0
2
2
0
0
2
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
3
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
4
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
1
2
3
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
2
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
2
0
0
3
0
0
3
0
1
0
3
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
4
0
1
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
3
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
8
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
1
0
0
3
0
1
0
0
1
0
0
0
1
2
0
0
1
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
3
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
4
1
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
8
0
0
2
1
4
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
5
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
4
2
0
2
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
5
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
1
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
2
0
0
2
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
1
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
3
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
3
0
1
2
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
1
1
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
1
2
2
0
0
0
1
0
0
0
0
2
2
2
1
0
2
0
0
0
3
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
1
1
0
0
0
0
0
0
0
0
2
1
2
0
2
0
2
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
1
0
0
2
0
0
5
0
0
1
0
0
3
1
0
0
0
0
4
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
2
0
0
0
1
1
1
0
2
0
0
0
0
2
0
0
0
0
0
0
1
1
2
0
0
0
0
2
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
2
2
1
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
1
2
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
2
2
0
0
1
1
0
1
0
1
0
4
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
8
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
1
3
0
0
0
2
0
0
0
1
1
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
3
0
0
1
2
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
2
0
0
1
2
0
2
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
3
3
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
1
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
4
3
0
0
0
0
0
0
1
1
0
0
0
3
2
0
0
0
0
1
2
0
0
1
0
0
2
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
5
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
2
0
0
0
6
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
2
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
3
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
1
0
1
2
0
0
0
0
1
0
1
0
0
3
0
0
0
0
0
1
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
8
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
1
0
0
0
0
0
0
2
2
0
0
2
1
0
0
0
1
0
1
1
0
0
1
1
0
0
0
1
0
2
0
0
0
2
2
0
0
1
4
0
0
0
0
0
0
0
0
0
2
7
0
2
0
0
0
0
0
1
0
1
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
3
0
1
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
2
0
5
0
0
1
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
3
2
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
1
1
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
1
2
0
0
0
4
0
1
1
0
1
0
0
0
0
0
0
1
0
2
0
1
1
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
7
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
1
5
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
2
0
2
0
0
0
0
0
2
0
0
1
0
1
0
0
0
5
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
1
1
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
2
0
1
1
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
2
0
1
0
3
0
0
0
0
1
0
1
0
0
3
0
0
0
0
0
9
0
1
0
0
0
0
0
1
2
0
0
0
0
0
3
1
1
0
0
0
0
1
0
0
0
1
0
0
1
1
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
3
0
1
2
0
0
0
1
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
2
4
0
0
3
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
2
1
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
1
0
1
0
0
2
0
0
1
0
0
5
3
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
3
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
3
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
3
0
0
0
0
0
0
0
1
0
0
0
2
0
3
2
0
0
0
0
0
0
2
0
2
2
0
2
0
0
2
0
0
0
0
1
0
0
4
1
0
0
0
0
0
0
0
0
0
7
4
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
1
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
4
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
3
0
0
0
0
0
0
0
0
0
0
0
4
0
3
2
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
1
2
0
1
0
0
0
0
1
0
0
0
1
0
2
0
0
0
2
0
2
2
2
2
0
3
0
0
0
0
0
0
0
1
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
8
0
0
0
1
0
0
3
0
0
0
0
0
2
5
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
3
2
0
2
0
0
1
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
3
0
0
0
0
0
1
0
3
0
0
0
0
0
0
1
0
0
0
0
0
1
0
4
0
0
0
0
0
1
2
0
0
3
0
0
0
0
3
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
2
0
0
11
2
1
2
0
1
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
1
0
0
1
3
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
5
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
1
0
0
2
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
9
2
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
6
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
3
0
1
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
8
2
0
0
0
2
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
6
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
1
0
0
0
0
2
0
0
1
0
0
0
1
0
0
1
2
2
0
0
1
0
3
0
0
4
1
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
3
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
1
2
1
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
1
0
0
1
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
1
0
0
2
0
0
0
0
0
1
3
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
1
0
0
0
0
0
0
8
1
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
2
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
3
0
1
0
0
1
0
0
0
1
0
0
2
0
0
1
0
2
0
1
0
0
0
0
0
1
2
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
1
0
2
1
3
0
2
1
1
2
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
1
0
3
1
0
0
3
0
0
1
6
0
0
0
0
0
0
0
1
0
3
1
0
0
0
2
0
0
0
2
0
2
0
2
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
2
2
0
1
0
0
0
0
2
0
2
2
0
0
4
0
0
0
0
0
0
0
0
2
2
0
2
0
1
0
2
1
1
0
0
0
0
0
0
1
0
3
0
0
0
0
0
2
0
2
0
0
3
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
2
2
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
7
0
0
2
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
3
0
1
0
0
0
2
2
4
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
4
0
2
0
0
2
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
4
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
5
0
1
0
0
0
2
0
0
2
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
1
0
0
2
0
0
1
0
0
3
0
1
0
0
0
0
0
0
1
0
0
5
1
0
2
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
3
0
0
1
2
0
0
0
0
0
1
0
0
1
2
1
0
0
0
4
2
0
1
0
1
0
1
0
2
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
3
1
0
2
0
0
2
0
0
0
0
0
4
0
1
0
1
0
0
0
0
0
0
1
0
1
0
2
3
0
0
0
1
0
0
0
0
0
4
1
2
0
0
0
3
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
2
0
1
0
2
0
0
19
0
1
0
4
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
1
0
3
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
2
0
2
0
0
2
2
0
0
0
0
0
0
0
0
2
2
0
0
0
3
0
0
0
0
2
0
0
2
0
0
0
4
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
3
2
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
2
2
0
0
1
0
1
0
0
0
0
2
1
0
0
0
3
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
3
0
0
1
0
0
1
0
0
1
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
3
0
0
0
0
6
0
1
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
2
2
0
0
6
0
0
1
0
3
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
2
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
8
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
2
0
0
0
1
0
0
1
0
0
0
0
2
0
4
0
0
0
0
2
0
1
0
2
2
0
0
2
1
1
0
0
0
0
0
0
0
0
3
0
0
2
0
2
0
0
2
2
2
0
0
2
0
1
0
3
0
1
0
0
3
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
4
1
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
1
1
0
0
0
2
0
0
0
0
8
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
3
2
0
0
0
1
0
2
1
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
1
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
3
1
2
0
2
0
1
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
2
0
1
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
4
0
0
0
0
0
1
0
1
0
3
1
3
0
0
2
1
1
2
1
1
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
2
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
10
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
2
0
1
0
1
5
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
1
0
2
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
1
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
2
3
0
2
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
3
0
0
2
1
1
6
0
0
0
0
0
3
1
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
1
0
0
4
0
2
0
0
0
0
0
0
1
0
1
0
0
3
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
5
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
2
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
2
0
4
0
0
1
0
0
0
1
3
0
0
1
0
0
1
0
0
3
0
0
0
0
0
3
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
3
0
0
0
3
0
0
0
0
2
2
1
0
0
0
3
3
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
5
0
0
0
0
2
2
0
2
0
1
0
0
0
2
1
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
4
0
1
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
4
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
1
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
1
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
1
0
3
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
10
3
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
1
1
2
0
0
0
1
0
0
0
0
1
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
1
4
2
0
0
0
0
0
2
0
0
2
0
0
1
1
0
0
2
0
0
0
0
0
0
2
4
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
1
1
1
1
2
0
3
5
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
3
0
1
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
1
2
1
0
0
2
1
0
0
0
2
0
1
0
8
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
2
0
2
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
1
1
3
0
0
1
1
2
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
3
0
0
0
0
0
0
4
0
2
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
1
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
2
0
1
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
6
0
2
0
1
0
0
0
0
1
0
0
0
0
2
1
0
2
0
0
0
0
0
0
1
0
0
2
0
1
0
0
2
0
1
1
0
0
2
0
0
3
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
3
0
1
0
0
0
0
4
3
2
1
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
2
0
1
0
0
1
1
0
1
1
2
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
1
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
2
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
2
1
2
0
2
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
2
0
0
0
2
0
0
0
2
5
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
5
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
3
0
0
0
0
0
7
0
0
0
2
0
0
0
0
0
0
1
1
2
0
1
0
2
0
0
2
0
0
0
0
4
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
7
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
1
2
0
1
3
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
3
1
0
0
0
0
0
1
1
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
3
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
3
1
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
2
0
1
1
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
1
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
3
3
0
0
0
1
0
0
0
0
0
0
0
2
4
1
2
0
1
1
0
0
0
3
0
0
1
0
0
2
0
3
0
0
0
1
0
0
0
2
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
1
0
3
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
3
0
0
0
0
0
9
10
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
4
0
0
0
0
0
0
0
0
3
1
27
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
1
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
3
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
1
0
0
1
0
0
0
0
3
0
2
0
0
0
0
0
3
1
0
2
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
2
1
0
9
0
0
0
1
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
21
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
6
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
2
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
2
0
2
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
2
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
5
0
2
0
0
0
1
1
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
3
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
3
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
1
0
1
0
1
0
2
0
0
0
0
0
2
2
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
1
0
0
2
1
2
0
2
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
1
2
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
3
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
2
1
0
0
1
1
0
3
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
2
5
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
3
0
0
0
0
2
4
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
1
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
1
0
2
0
0
3
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
1
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
2
1
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
1
0
0
2
0
1
12
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
4
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
1
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
3
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
3
0
1
0
0
1
1
1
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
10
0
0
0
0
0
0
2
5
1
0
1
0
0
0
1
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
3
0
0
2
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
6
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
8
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
3
0
0
3
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
1
5
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
4
0
0
0
0
1
3
1
2
0
0
0
0
0
1
4
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
1
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
5
0
0
4
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
2
2
2
1
0
1
0
0
2
0
0
0
2
0
0
8
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
1
0
0
0
0
0
0
0
1
3
0
0
0
0
1
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
1
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
4
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
2
0
0
1
0
4
1
0
0
0
0
0
4
2
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
1
0
0
1
2
0
0
0
1
1
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
2
4
1
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
1
0
1
0
0
0
0
0
1
0
0
0
2
0
0
2
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
1
0
0
3
0
0
0
0
0
0
0
3
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
2
0
1
0
0
0
0
0
0
1
2
0
2
0
1
5
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
1
1
0
0
3
0
0
0
0
0
1
0
0
1
0
0
2
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
1
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
1
0
0
0
1
0
0
0
3
0
1
0
2
4
2
2
0
0
2
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
2
2
2
0
0
1
0
0
0
1
0
0
5
0
0
0
1
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
4
3
0
0
0
0
0
0
2
0
0
0
5
1
2
0
0
0
1
0
3
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
12
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
3
1
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
3
0
0
0
0
0
0
0
3
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
3
0
0
0
0
2
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
3
0
0
0
0
1
5
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
3
0
0
0
2
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
2
0
0
1
0
0
0
2
0
0
2
0
0
0
0
1
0
2
0
0
0
0
4
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
1
2
2
1
0
1
0
0
1
0
0
2
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
1
0
2
0
0
0
1
0
0
1
1
4
0
0
0
0
1
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
2
0
0
0
3
0
0
2
0
0
2
0
0
0
0
2
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
1
0
0
0
1
2
0
0
0
0
0
8
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
3
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
3
2
0
0
3
0
0
0
0
0
0
5
0
3
0
0
2
0
0
0
0
2
2
2
0
0
0
0
0
4
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
4
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
1
1
5
0
0
0
0
0
2
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
3
1
0
0
2
0
1
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
2
0
3
2
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
3
0
0
1
1
1
1
0
0
2
0
0
0
0
0
0
0
0
3
1
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
2
0
2
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
4
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
5
0
0
0
1
1
2
0
0
2
5
0
2
0
0
1
0
0
2
0
0
0
2
0
0
0
2
0
1
1
0
0
0
0
0
1
1
1
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
1
0
1
0
0
0
0
2
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
3
2
0
0
0
1
0
0
0
0
0
0
2
0
2
0
2
0
1
2
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
5
0
0
0
0
0
0
0
0
2
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
2
7
0
1
0
0
0
0
0
0
5
0
0
0
2
2
2
0
0
0
0
0
2
2
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
3
0
0
0
2
0
1
0
2
0
0
1
1
1
1
0
0
0
0
1
0
0
0
0
4
2
1
0
2
0
0
2
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
5
0
1
0
0
0
0
1
0
0
0
0
0
0
1
4
1
1
0
0
0
0
2
0
2
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
1
0
0
4
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
3
0
0
0
0
1
0
1
0
0
5
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
3
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
1
1
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
4
0
2
0
2
0
1
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
1
4
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
3
0
0
0
6
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
6
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
2
1
0
0
0
2
0
0
0
0
2
0
1
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
3
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
4
0
6
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
1
2
0
1
0
2
0
0
0
2
0
2
0
0
0
0
2
0
0
0
2
1
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
1
0
3
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
1
0
0
0
2
1
2
0
0
0
2
0
0
0
0
1
0
0
1
2
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
1
0
0
0
0
0
1
0
2
3
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
3
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
4
0
1
3
2
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
1
0
1
5
0
0
0
2
0
0
2
0
0
0
0
0
3
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
1
0
6
0
0
2
0
2
2
0
0
3
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
5
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
2
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
3
0
3
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
2
0
0
1
2
2
2
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
2
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
2
0
0
0
0
3
0
0
0
0
0
2
0
0
2
2
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
2
1
0
3
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
2
2
0
0
0
1
0
1
0
0
0
4
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
2
0
0
3
1
2
2
0
0
1
1
0
0
0
4
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
2
0
1
0
0
1
0
0
1
0
2
1
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
4
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
2
1
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
5
0
0
0
1
2
1
0
0
0
0
0
0
0
0
1
0
0
0
5
0
0
0
0
1
3
0
0
0
0
0
1
0
0
1
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
2
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
3
2
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
3
0
0
0
0
0
1
0
0
0
0
0
2
1
0
1
0
0
2
1
2
1
0
0
1
0
0
0
0
1
0
0
1
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
5
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
1
2
0
0
0
0
0
0
0
3
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
2
0
2
0
1
2
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
5
0
3
0
0
2
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
5
0
0
0
0
2
0
2
4
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
3
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
1
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
1
2
0
0
1
1
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
3
1
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
3
0
2
1
1
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
3
1
3
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
1
0
0
0
0
1
2
3
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
4
0
0
1
0
0
0
0
0
2
0
0
2
0
2
0
3
4
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
2
0
0
4
0
0
0
2
0
1
0
0
0
0
1
2
0
0
0
0
0
2
12
0
0
0
0
0
0
2
0
0
0
0
3
2
0
0
0
0
0
4
1
0
2
0
0
2
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
1
1
0
1
1
0
0
0
0
2
1
0
0
2
1
0
0
0
2
2
0
0
0
0
2
0
0
0
0
6
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
3
0
0
2
0
0
1
0
0
0
2
0
0
1
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
1
2
0
0
2
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
1
0
2
0
2
0
0
2
3
0
3
0
1
0
2
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
4
0
0
2
2
0
0
0
0
0
3
0
1
1
2
3
1
0
0
0
0
0
0
0
0
1
1
1
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
6
0
0
0
0
0
2
0
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
1
1
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
2
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
6
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
2
0
0
3
2
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
2
3
0
0
0
1
0
2
0
0
1
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
1
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
2
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
5
2
3
2
1
0
2
2
0
3
0
1
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
3
0
0
0
0
1
0
1
2
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
1
1
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
5
0
1
0
0
0
0
1
0
0
0
1
0
0
6
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
11
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
2
2
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
7
1
0
0
0
1
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
2
0
0
0
1
0
1
0
0
0
2
0
3
0
1
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
2
1
0
0
0
0
0
0
2
1
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
3
0
4
0
2
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
3
2
1
0
0
2
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
3
6
8
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
2
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
6
0
0
0
0
0
0
0
0
1
1
0
0
0
1
2
0
0
0
0
0
0
3
4
1
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
2
0
0
3
0
3
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
0
1
1
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
3
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
5
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
6
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
1
0
0
0
0
4
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
2
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
2
4
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
1
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
3
2
0
0
0
0
4
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
1
0
1
2
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
2
0
0
2
0
1
1
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
2
0
0
0
2
0
1
0
0
0
1
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
5
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
4
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
11
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
3
0
0
0
1
1
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
1
0
0
3
0
0
0
2
0
2
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
1
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
2
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
2
1
2
0
0
0
2
2
0
0
2
1
2
0
0
0
2
2
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
3
2
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
1
0
1
2
2
0
0
0
2
1
0
0
0
1
0
0
2
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
3
0
3
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
1
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
1
0
0
2
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
3
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
2
0
1
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
5
0
2
0
0
0
0
0
1
0
0
0
7
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
4
0
0
0
0
0
1
0
1
0
0
2
0
0
3
0
2
0
2
0
0
0
0
0
0
0
1
3
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
6
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
7
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
2
0
0
1
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
1
1
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
1
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
2
0
3
0
1
0
0
0
1
0
0
0
3
0
0
0
3
2
0
0
0
2
0
2
1
0
1
0
0
0
2
0
0
1
0
4
0
0
0
0
0
0
1
0
0
0
0
5
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
4
0
1
0
0
0
1
0
0
0
1
2
0
1
3
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
8
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
5
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
1
0
0
0
0
4
0
0
0
0
0
3
3
0
0
0
0
0
0
0
2
1
2
1
2
8
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
5
2
0
0
0
0
0
0
2
0
1
0
0
1
0
10
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
2
0
2
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
3
2
0
0
0
0
3
0
0
0
0
2
0
0
0
0
3
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
5
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
1
0
1
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
4
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
3
0
0
0
0
0
0
0
3
4
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
3
1
0
0
1
0
0
0
0
1
2
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
1
0
0
2
0
0
2
0
0
0
0
0
0
0
2
2
0
2
0
0
3
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
2
0
2
0
2
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
3
0
0
0
1
0
2
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
1
0
0
0
1
0
0
0
0
0
5
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
3
7
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
3
1
0
2
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
2
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
2
0
0
0
3
0
0
2
1
0
0
0
2
4
0
2
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
3
0
3
1
0
0
0
0
0
0
2
2
2
0
0
0
0
7
0
0
0
0
0
0
0
0
0
0
1
2
1
2
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
4
1
0
0
2
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
2
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
1
1
1
0
0
0
1
0
0
0
0
0
2
3
1
0
0
0
0
1
0
1
1
0
0
1
1
1
1
0
0
0
1
0
0
0
1
0
0
0
1
0
2
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
2
0
1
0
2
0
0
0
1
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
8
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
3
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
1
0
0
0
0
0
1
0
0
3
4
0
2
1
0
0
0
0
6
1
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
3
0
0
0
1
0
0
0
2
2
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
1
2
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
6
0
0
0
3
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
1
0
1
2
0
0
1
2
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
1
0
2
2
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
2
0
0
0
0
2
0
2
0
1
0
0
0
2
1
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
1
0
7
0
0
1
2
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
1
0
0
0
1
1
2
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
1
0
2
0
2
1
0
0
0
0
1
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
1
1
0
0
1
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
3
0
0
0
0
3
0
2
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
1
0
1
0
0
1
2
0
0
0
3
0
1
0
2
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
2
1
0
0
0
0
3
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
8
0
1
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
1
2
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
2
2
0
0
0
0
0
0
0
0
0
4
3
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
10
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
1
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
3
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
2
0
1
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
8
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
7
0
0
0
0
0
3
1
0
0
3
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
1
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
2
0
2
0
0
2
0
1
0
0
0
1
0
4
2
1
0
2
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
1
0
0
1
6
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
1
0
0
2
0
0
2
3
0
0
0
0
0
3
2
2
1
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
5
1
2
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
5
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
3
0
0
0
0
0
1
0
0
1
1
1
2
0
0
0
3
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
3
4
0
1
0
0
0
1
0
0
1
0
0
0
2
1
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
4
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
4
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
3
0
2
0
0
1
0
3
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
6
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
3
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
1
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
1
1
0
0
0
3
0
2
1
0
0
0
2
0
1
0
3
0
0
2
1
1
0
0
0
0
0
1
0
0
0
0
1
5
0
0
0
0
0
0
2
0
0
0
3
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
6
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
3
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
1
1
1
0
0
0
0
0
0
0
0
0
7
0
0
0
2
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
1
0
0
0
0
2
2
1
1
2
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
1
1
2
0
0
0
0
0
2
0
0
0
0
0
2
1
0
3
0
0
0
8
1
2
0
1
0
0
0
2
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
2
0
3
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
6
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
2
1
0
0
0
0
0
1
0
1
0
0
2
0
1
6
0
0
0
1
1
0
10
0
0
1
0
0
1
2
0
0
0
0
0
0
3
0
2
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
3
0
1
0
0
0
0
0
1
0
0
0
1
2
0
0
1
0
0
0
2
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
2
2
3
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
3
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
1
0
0
0
2
2
0
0
0
1
1
2
1
0
0
2
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
2
0
2
0
0
0
1
1
0
0
2
2
0
0
2
3
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
2
1
0
0
0
0
0
1
2
0
0
0
1
0
0
0
2
0
3
1
0
0
0
0
0
0
0
0
0
3
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
2
1
0
0
7
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
1
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
1
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
1
0
2
0
0
0
0
0
0
0
4
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
4
0
2
2
0
1
1
0
0
0
0
2
0
1
1
2
0
0
0
6
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
1
0
0
0
3
2
0
0
0
0
1
0
0
0
1
0
0
1
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
1
0
0
0
2
0
2
1
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
2
1
0
0
3
0
0
0
0
1
0
0
0
0
0
2
0
9
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
2
0
3
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
1
1
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
3
0
0
0
1
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
4
0
0
2
0
0
0
4
0
1
0
0
0
0
0
2
0
0
0
0
2
0
4
1
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
2
2
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
2
0
0
2
0
0
0
2
2
0
2
0
0
0
0
2
0
1
0
0
1
1
2
0
0
0
0
1
5
4
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
2
1
3
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
7
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
2
0
0
0
2
0
1
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
2
1
0
2
0
1
0
1
0
1
0
0
0
0
5
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
3
0
0
0
0
0
2
0
0
0
0
0
0
1
2
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
1
3
2
0
0
0
2
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
6
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
1
0
0
0
2
0
1
1
0
0
0
0
0
0
3
1
1
4
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
3
3
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
3
0
0
2
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
2
0
0
0
0
0
1
0
2
0
1
1
0
0
0
5
0
0
0
0
0
0
0
2
1
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
4
3
0
0
0
5
0
2
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
3
0
0
0
2
0
0
0
0
0
2
1
1
0
3
0
0
0
2
0
0
2
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
2
0
0
0
0
1
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
7
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
3
0
1
0
0
0
0
0
0
1
0
1
0
0
3
2
0
0
2
0
2
0
0
0
0
0
0
0
7
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
2
3
0
0
0
0
1
0
0
4
0
0
0
0
0
2
0
0
0
1
0
0
4
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
6
0
2
0
2
2
0
1
1
0
0
0
3
0
0
0
0
2
0
0
0
1
1
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
4
0
2
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
3
1
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
1
0
3
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
3
0
0
0
4
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
1
2
2
0
2
0
3
2
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
2
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
2
1
0
3
1
0
0
1
0
0
0
1
0
2
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
2
2
0
0
0
0
0
0
2
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
2
1
0
2
3
3
0
0
0
2
2
0
0
0
0
0
3
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
3
0
0
0
1
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
3
0
2
0
0
0
0
0
1
0
0
1
3
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
3
2
0
0
0
0
0
0
0
1
2
2
0
2
0
0
0
2
1
0
0
1
1
0
2
0
1
0
0
0
0
0
0
1
1
0
0
1
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
1
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
2
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
4
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
2
0
0
0
4
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
3
0
0
2
0
1
0
0
0
0
3
1
2
0
0
1
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
1
0
1
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
2
2
1
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
2
0
0
0
1
1
0
0
1
0
0
0
0
1
1
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
2
3
0
0
2
0
1
0
0
0
2
0
0
0
0
0
2
1
0
1
0
0
2
1
0
0
0
0
0
0
0
0
1
6
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
2
0
0
1
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
4
1
1
2
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
6
0
0
0
1
0
0
5
0
0
0
0
0
0
0
0
0
4
0
0
0
1
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
6
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
6
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
3
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
2
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
3
2
0
0
0
2
0
1
1
1
1
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
4
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
1
1
0
6
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
1
2
0
2
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
2
1
0
0
0
2
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
2
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
1
0
0
1
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
8
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
2
0
1
1
0
2
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
1
0
0
2
1
0
0
0
1
0
1
0
4
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
1
0
0
0
2
2
0
0
0
2
0
0
0
1
2
2
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
5
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
6
2
0
5
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
3
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
6
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
1
0
0
1
2
2
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
4
0
2
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
1
0
0
2
0
1
0
0
3
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
2
2
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
3
0
0
0
0
0
0
0
0
1
0
3
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
2
0
0
1
0
2
0
0
0
1
0
0
1
1
0
0
0
0
0
0
2
1
0
0
0
2
6
0
1
0
0
0
2
0
3
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
2
4
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
2
3
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
1
1
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
1
0
0
0
0
0
7
2
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
3
0
1
1
0
2
0
0
1
0
0
0
5
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
2
2
0
0
0
0
0
1
1
0
0
0
0
5
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
5
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
2
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
6
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
1
2
0
1
0
0
0
0
0
1
2
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
3
2
1
0
0
1
1
1
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
1
0
2
1
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
5
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
2
1
0
0
0
1
0
3
0
0
2
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
5
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
2
0
0
0
1
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
2
0
0
0
0
0
2
1
0
4
0
3
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
2
0
1
1
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
4
0
1
0
0
6
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
1
6
0
0
1
0
0
0
1
0
2
0
0
0
0
1
1
4
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
1
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
1
0
2
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
2
0
0
0
0
2
0
0
1
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
2
0
1
0
0
2
3
2
0
2
0
1
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
5
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
3
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
1
0
0
0
0
0
2
1
3
0
5
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
1
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
3
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
3
0
0
2
0
1
0
2
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
1
0
8
0
0
1
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
4
2
2
0
0
1
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
2
0
2
0
0
0
7
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
1
0
1
0
1
3
0
0
1
0
0
1
0
0
0
0
0
3
0
1
0
0
0
1
1
0
1
2
0
0
0
2
2
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
2
1
0
0
1
0
1
0
0
2
0
1
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
5
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
5
0
2
0
0
0
0
0
0
0
1
0
2
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
2
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
4
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
1
2
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
2
1
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
3
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
1
2
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
1
3
2
1
0
0
1
1
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
1
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
3
2
2
0
0
2
0
1
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
1
3
0
0
1
3
1
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
2
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
3
1
0
0
0
2
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
2
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
7
0
0
7
0
0
0
0
0
0
5
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
4
2
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
2
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
2
1
0
0
0
2
0
1
1
0
0
1
0
0
0
3
0
0
2
1
0
0
0
0
0
0
0
1
0
1
0
0
0
3
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
3
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
3
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
1
0
1
1
0
2
2
0
1
0
0
0
0
0
0
3
0
0
1
0
0
2
2
1
0
2
0
2
0
0
0
0
0
1
2
1
0
1
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
2
2
0
2
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
6
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
2
0
0
1
0
0
0
2
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
2
0
0
0
2
2
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
5
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
1
2
2
2
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
3
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
4
0
0
1
0
0
1
1
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
5
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
1
0
2
0
0
0
1
0
0
0
0
2
0
0
0
1
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
3
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
3
1
2
0
0
0
1
1
0
0
1
1
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
1
5
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
1
0
0
0
2
0
4
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
5
0
2
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
2
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
1
0
4
1
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
2
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
1
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
4
0
3
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
3
1
0
2
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
1
0
0
1
0
6
2
0
0
0
0
0
0
0
0
0
0
2
0
0
6
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
3
0
4
0
3
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
3
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
2
0
1
0
0
0
3
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
1
0
2
0
0
2
0
2
0
0
0
1
0
3
0
1
0
1
1
0
0
0
2
0
0
0
0
0
1
0
5
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
1
0
0
5
1
0
2
1
0
1
3
0
0
2
0
2
0
0
0
0
0
0
0
0
3
0
0
1
0
0
1
0
2
0
0
0
0
2
1
0
1
0
0
0
2
0
1
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
1
0
3
0
0
3
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
1
0
33
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
1
0
2
0
0
0
0
0
0
0
1
1
0
0
0
2
1
2
0
1
0
0
0
0
0
0
3
0
5
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
4
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
3
1
0
0
2
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
1
2
2
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
1
3
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
3
0
0
2
0
0
0
1
0
0
0
2
3
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
4
0
1
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
4
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
3
3
0
0
0
0
2
0
0
0
0
1
0
0
2
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
2
0
0
2
2
0
0
0
0
5
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
1
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
5
1
2
0
0
0
0
0
2
0
1
0
3
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
2
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
1
1
1
0
1
0
2
0
0
0
0
0
2
0
0
0
0
1
6
0
0
0
0
0
0
1
0
1
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
2
0
0
0
2
1
0
0
0
1
0
0
2
0
1
1
2
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
6
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
2
1
0
1
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
2
0
1
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
6
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
3
1
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
3
1
0
0
3
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
2
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
3
1
0
2
5
0
0
1
0
1
0
0
0
0
2
2
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
3
0
0
0
0
0
1
0
0
2
0
1
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
4
1
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
1
1
0
0
0
0
2
2
0
1
0
1
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
3
0
0
0
0
0
1
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
5
0
1
0
0
0
0
1
0
0
0
0
9
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
2
1
2
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
9
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
1
1
0
0
0
1
0
2
0
0
0
2
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
5
2
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
3
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
1
0
0
0
0
0
0
0
0
0
0
1
1
0
3
0
0
0
1
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
1
0
0
0
0
2
0
2
0
3
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
1
1
1
4
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
2
0
0
0
0
0
0
2
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
2
2
0
2
0
0
0
1
0
0
0
0
1
0
4
1
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
4
1
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
1
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
3
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
1
2
0
0
3
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
2
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
2
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
1
2
0
1
0
0
0
1
3
0
0
0
1
2
0
0
0
1
0
0
2
0
0
0
0
2
0
0
3
0
0
1
0
0
2
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
2
0
1
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
2
2
0
0
1
0
0
0
2
0
2
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
3
4
0
0
0
0
0
0
1
0
1
1
0
0
4
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
2
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
3
1
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
5
1
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
7
0
0
0
0
2
0
3
0
2
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
1
0
0
0
3
1
0
1
0
1
0
0
0
0
0
1
0
3
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
5
0
0
1
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
6
0
0
0
2
0
1
0
0
2
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
1
0
0
0
1
0
1
0
0
2
0
1
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
1
2
1
0
0
4
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
1
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
7
0
0
0
0
0
0
0
3
0
0
0
6
0
0
1
0
0
0
0
2
0
0
0
0
0
5
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
3
0
0
1
0
0
1
0
5
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
1
2
1
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
7
1
0
0
0
2
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
3
2
1
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
1
0
0
1
6
0
0
3
0
2
2
0
0
0
0
0
3
0
0
1
1
2
3
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
1
1
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
1
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
2
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
1
0
10
0
3
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
8
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
3
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
2
0
0
0
4
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
1
0
0
0
0
0
1
0
2
2
0
0
0
2
1
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
3
1
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
3
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
2
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
3
1
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
6
0
0
0
1
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
1
4
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
5
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
2
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
3
0
0
0
2
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
1
0
2
0
0
0
3
0
0
4
0
0
0
4
0
0
0
3
0
0
0
0
0
2
0
0
1
0
0
1
2
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
1
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
2
2
0
2
0
0
0
0
0
0
0
1
0
1
3
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
2
2
1
1
1
0
2
1
3
3
0
1
1
0
0
0
0
0
0
2
1
4
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
2
0
2
0
0
0
0
0
1
0
3
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
7
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
7
0
0
2
1
0
3
0
3
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
2
0
1
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
3
0
2
0
0
1
0
0
1
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
2
2
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
2
6
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
4
3
2
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
6
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
5
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
1
0
0
0
2
0
1
0
2
1
2
0
0
2
1
0
0
0
0
0
2
0
0
0
1
0
1
0
0
1
2
2
0
1
0
0
1
0
2
0
0
0
2
0
0
2
0
2
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
5
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
2
0
0
0
0
0
0
2
1
0
0
0
1
0
0
2
6
0
1
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
5
0
0
0
2
1
0
2
0
0
2
5
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
2
0
2
0
0
4
0
0
0
0
1
1
0
2
2
1
0
3
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
5
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
1
1
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
4
0
0
2
0
1
2
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
2
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
1
0
0
0
2
0
0
0
5
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
3
5
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
1
2
0
0
0
0
0
0
1
0
0
2
4
0
1
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
1
0
0
1
0
0
0
1
0
0
1
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
3
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
1
0
2
1
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
3
0
0
0
0
0
3
0
0
1
1
0
2
0
0
0
0
5
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
6
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
1
1
1
2
1
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
2
0
2
2
0
0
0
1
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
3
0
0
0
0
0
0
0
2
1
1
0
0
1
1
0
0
0
0
1
1
2
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
2
0
0
1
0
0
0
2
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
1
1
2
2
0
1
1
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
12
1
0
0
0
0
0
0
0
0
0
0
0
0
0
7
0
0
0
0
0
2
0
2
3
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
2
0
4
2
0
0
0
0
0
0
0
0
0
0
0
0
4
3
3
0
1
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
2
0
0
2
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
2
1
0
3
0
1
0
0
1
0
1
1
0
0
0
0
2
0
0
0
1
0
2
1
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
1
2
8
0
1
0
2
0
1
0
1
0
0
0
0
0
0
1
0
0
3
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
4
0
0
0
0
1
0
0
0
2
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
3
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
1
0
0
2
1
0
0
0
0
0
0
1
2
0
0
0
1
1
0
0
0
2
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
3
0
0
2
1
3
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
3
3
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
1
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
3
1
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
1
0
2
2
0
1
0
0
0
0
0
2
0
0
1
1
2
0
1
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
1
0
0
11
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
2
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
2
0
0
0
0
2
1
0
2
0
0
1
0
0
0
1
0
0
0
0
2
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
1
1
2
0
0
0
2
0
1
1
1
0
0
0
0
0
1
0
0
1
0
0
3
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
1
0
1
1
0
1
2
2
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
4
3
0
0
1
0
0
0
0
0
1
1
0
0
1
3
0
0
0
0
0
0
0
0
0
0
2
4
0
0
0
2
0
0
0
0
2
1
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
2
2
0
1
0
2
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
5
2
0
1
0
2
0
0
0
3
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
6
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
2
2
0
2
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
3
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
2
0
1
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
2
1
5
1
2
0
0
0
2
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
1
1
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
4
0
0
0
0
0
0
2
0
2
0
0
0
7
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
9
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
2
0
2
0
0
0
0
0
1
1
0
0
2
0
0
2
0
0
1
0
0
0
0
0
1
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
1
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
5
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
2
0
0
0
0
0
0
4
0
0
0
2
0
0
2
0
0
0
0
1
0
3
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
3
6
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
2
1
0
0
0
0
0
0
0
1
0
2
0
0
1
1
0
0
0
0
2
0
0
1
0
0
0
1
1
0
0
3
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
3
2
0
3
1
0
1
0
0
0
0
1
0
0
3
0
0
3
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
1
0
6
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
4
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
1
0
2
0
1
0
0
0
0
0
0
0
1
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
2
0
0
0
2
1
1
0
0
0
0
1
1
0
0
1
2
0
1
1
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
3
0
0
0
1
0
0
1
0
0
0
3
0
0
0
1
0
0
0
0
0
2
1
2
0
0
0
0
1
0
0
0
1
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
1
1
0
0
4
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
2
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
4
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
1
0
0
0
3
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
7
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
2
2
1
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
1
1
3
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
1
0
3
0
0
1
0
0
0
2
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
1
0
2
0
0
1
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
3
4
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
5
2
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
2
0
0
2
0
1
0
0
0
1
2
0
0
0
0
4
2
1
0
0
0
0
0
0
0
0
0
0
0
2
3
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
4
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
3
0
0
4
3
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
4
1
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
2
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
4
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
2
0
1
3
0
0
0
3
0
0
0
2
2
2
0
0
0
1
0
0
1
0
0
0
1
0
0
3
0
0
1
0
0
2
0
0
0
7
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
3
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
2
2
1
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
1
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
3
3
0
0
0
0
1
0
0
2
1
1
0
0
0
0
0
0
2
0
0
0
2
4
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
2
2
0
0
4
0
0
0
0
0
0
0
0
0
1
1
2
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
1
0
0
1
0
0
2
3
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
2
0
1
0
1
1
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
1
0
0
0
0
2
1
0
0
0
0
1
1
1
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
2
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
0
0
1
4
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
4
0
0
1
0
1
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
5
0
0
0
3
0
0
0
0
0
2
0
2
0
4
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
5
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
10
0
1
0
8
0
0
0
0
2
1
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
1
0
0
0
2
8
0
0
0
0
0
0
3
0
0
0
0
0
2
3
0
2
0
0
0
0
0
0
0
1
6
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
2
0
0
1
0
0
0
0
0
2
4
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
2
2
0
3
0
0
0
0
1
0
0
0
0
1
0
0
0
3
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
2
2
2
0
0
0
0
1
0
0
1
2
0
1
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
1
0
2
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
8
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
2
0
0
0
2
0
1
1
1
0
0
2
0
0
2
2
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
7
0
0
0
1
0
0
2
1
0
1
1
1
1
0
2
4
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
5
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
3
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
3
0
3
0
0
0
0
1
0
2
2
1
0
0
0
0
0
10
0
0
0
0
0
0
0
0
0
0
2
1
2
0
4
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
8
0
0
0
0
3
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
2
1
0
2
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
3
0
0
0
0
1
0
1
0
0
0
0
0
0
3
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
2
0
0
0
2
0
0
1
0
2
2
4
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
1
1
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
2
2
1
0
0
1
0
4
0
0
0
0
0
0
1
2
0
0
1
0
1
0
0
2
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
3
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
1
0
0
0
0
0
0
0
1
3
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
1
0
0
1
1
0
0
0
0
0
0
0
0
3
3
0
0
2
0
0
0
1
0
0
0
4
0
0
1
0
0
0
0
0
0
0
6
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
4
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
3
2
0
4
0
0
0
0
0
0
2
0
0
0
1
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
3
1
0
2
0
0
0
0
0
0
0
4
0
0
2
0
3
0
0
0
1
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
6
4
0
0
0
0
2
0
0
0
0
0
1
1
1
0
0
0
1
1
0
0
0
0
0
1
1
0
0
1
0
0
0
2
1
0
0
4
0
0
0
1
1
0
0
0
2
1
7
0
1
2
2
1
1
1
3
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
3
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
5
2
1
0
0
0
0
1
0
1
2
3
1
0
0
0
2
0
0
0
0
1
1
0
1
0
1
0
0
0
2
0
0
0
0
1
2
0
0
0
0
1
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
5
0
0
0
0
2
0
0
0
5
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
4
2
0
0
0
0
0
0
2
5
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
3
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
4
0
0
0
0
0
0
2
0
0
1
1
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
1
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
8
1
0
2
1
2
2
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
2
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
2
0
2
2
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
7
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
2
0
2
1
0
0
1
0
2
0
0
1
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
5
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
1
1
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
2
1
0
0
2
1
0
0
1
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
5
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
2
0
2
0
0
0
0
2
0
0
1
0
2
0
0
2
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
2
0
2
0
3
1
0
2
0
0
0
2
1
0
1
0
0
0
0
0
0
2
0
0
0
3
1
0
0
2
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
5
0
0
1
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
7
0
0
1
1
0
0
0
0
1
4
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
1
0
0
0
0
0
0
1
4
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
1
0
3
0
0
0
0
1
0
2
3
2
0
1
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
3
2
0
1
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
1
0
0
0
2
1
0
5
0
0
0
0
0
0
2
2
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
2
1
1
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
1
2
0
3
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
5
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
8
2
0
0
0
3
1
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
1
0
1
0
0
0
0
0
3
0
0
1
0
0
2
0
1
0
0
4
0
1
0
0
0
2
0
0
0
0
0
6
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
3
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
7
1
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
3
1
0
0
0
0
1
3
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
6
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
2
0
0
1
1
0
1
0
3
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
1
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
2
0
0
2
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
7
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
1
2
1
0
0
0
0
0
0
1
0
0
0
0
0
2
4
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
3
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
1
0
1
0
0
0
1
3
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
4
0
6
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
1
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
3
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
1
3
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
1
0
2
0
0
0
0
0
0
2
1
0
1
2
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
2
0
0
3
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
2
2
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
2
0
0
0
1
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
1
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
5
2
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
3
1
0
0
0
0
1
0
0
0
1
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
5
0
0
0
0
0
0
1
0
0
0
3
0
2
0
0
0
1
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
7
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
4
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
4
0
0
0
1
1
0
1
0
0
0
0
0
1
0
1
2
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
3
0
0
2
0
20
0
0
1
0
0
0
0
0
3
0
0
2
0
0
1
0
0
0
0
0
0
0
0
3
0
8
0
0
0
0
0
1
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
4
1
0
0
0
2
1
0
0
0
2
0
1
2
0
0
0
0
1
2
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
3
0
0
1
3
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
1
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
5
0
0
0
0
0
1
0
0
0
0
0
1
0
0
3
1
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
1
1
0
0
0
2
0
2
0
0
0
7
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
3
0
3
1
1
0
1
0
0
0
0
4
2
1
0
0
0
0
0
0
2
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
3
2
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
4
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
3
2
0
0
1
0
0
0
0
0
1
1
0
0
3
1
0
0
0
1
0
0
0
0
1
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
3
0
0
5
0
0
1
4
2
0
0
0
2
0
0
0
0
0
1
0
3
0
0
0
0
0
0
2
1
0
2
1
2
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
7
2
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
1
0
2
0
0
0
0
0
7
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
3
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
6
2
0
0
1
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
3
0
0
1
3
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
3
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
1
3
0
0
0
2
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
1
2
0
0
1
0
0
0
6
1
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
8
0
0
0
0
0
1
0
0
0
0
2
2
0
6
0
0
0
0
0
0
0
0
0
2
2
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
5
0
1
0
0
4
0
0
0
0
0
0
2
0
0
2
1
1
0
0
1
1
0
0
0
1
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
6
0
2
0
0
0
0
0
0
0
2
2
0
3
0
0
0
1
1
2
0
2
3
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
4
2
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
4
0
0
5
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
3
0
2
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
1
1
0
1
2
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
3
0
0
0
0
2
5
0
0
0
0
0
1
1
0
1
0
1
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
2
4
0
0
0
0
0
4
2
1
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
3
0
2
0
0
2
0
0
1
0
0
0
0
1
1
0
3
0
1
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
2
0
1
1
0
0
0
3
0
0
0
0
0
0
0
1
0
2
0
0
0
1
2
1
2
0
2
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
9
0
0
0
0
1
0
1
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
3
0
0
0
1
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
2
1
0
2
0
1
0
1
0
0
3
0
0
1
0
0
0
0
1
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
3
1
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
3
0
0
0
0
0
0
1
2
0
0
0
1
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
2
2
2
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
3
1
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
3
1
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
8
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
1
2
0
0
4
0
0
0
1
0
0
0
3
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
1
0
1
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
2
0
0
2
1
3
0
0
2
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
1
5
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
2
0
4
0
0
0
0
0
0
0
3
1
1
0
1
0
0
0
1
3
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
1
0
0
1
2
0
0
0
0
1
0
2
1
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
1
5
0
0
0
2
0
0
0
1
1
0
0
0
0
0
1
0
0
3
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
3
1
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
3
0
2
2
0
2
0
0
4
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
1
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
1
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
7
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
2
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
1
2
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
7
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
6
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
2
1
0
0
0
0
0
3
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
3
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
2
0
0
0
0
0
1
0
0
0
2
2
1
2
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
4
0
2
0
1
0
0
0
0
0
1
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
4
0
2
0
0
0
0
0
0
1
0
1
0
0
2
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
8
0
0
0
3
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
7
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
7
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
2
1
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
2
0
0
0
2
0
0
1
0
0
1
0
3
0
0
0
0
0
0
2
16
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
1
0
1
3
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
3
2
0
0
0
0
0
0
1
0
2
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
3
1
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
1
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
1
0
0
0
2
0
0
0
0
0
0
0
0
3
1
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
1
0
0
0
0
0
0
2
3
1
0
0
0
2
0
0
1
0
0
0
1
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
11
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
1
0
0
0
0
0
3
0
2
0
0
0
0
0
1
0
0
2
1
2
0
0
0
0
1
2
0
0
0
1
0
2
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
6
0
0
2
0
0
0
1
0
0
1
0
0
1
0
0
2
1
2
0
4
0
2
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
1
2
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
4
0
0
0
0
0
0
1
0
2
1
1
0
0
0
0
0
0
1
0
0
0
3
1
0
0
2
0
0
1
1
0
0
0
0
0
0
2
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
1
0
2
0
0
1
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
6
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
1
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
3
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
2
1
1
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
2
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
2
0
1
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
7
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
0
0
2
1
1
0
6
1
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
1
1
0
0
0
0
3
0
1
2
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
4
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
8
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
3
0
0
1
0
3
0
0
0
1
0
0
2
1
0
0
1
3
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
3
1
0
0
2
0
0
0
1
0
0
0
0
0
1
0
3
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
2
2
2
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
4
0
3
0
0
1
0
0
0
0
1
0
0
0
2
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
4
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
1
0
3
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
4
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
3
1
2
0
1
2
0
0
2
0
0
5
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
1
0
0
1
0
0
2
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
1
0
1
2
0
1
2
1
0
0
1
2
0
2
0
1
0
0
0
2
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
3
0
0
1
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
2
0
1
1
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
5
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
1
0
2
0
4
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
2
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
1
0
0
0
2
1
0
0
1
1
1
0
0
0
0
0
0
1
2
8
1
0
0
1
0
2
1
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
2
2
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
1
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
1
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
1
0
0
0
0
0
0
0
0
0
3
1
0
0
1
1
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
2
0
0
0
2
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
2
0
5
0
0
0
0
1
0
2
1
0
0
0
1
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
4
0
0
0
0
0
2
1
0
1
0
0
0
0
0
4
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
1
0
1
0
0
1
0
0
0
0
0
0
0
2
0
7
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
1
0
3
1
0
0
1
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
3
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
4
3
2
0
0
1
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
2
0
7
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
1
0
1
1
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
2
2
2
4
2
0
0
2
0
0
0
0
3
1
2
0
0
0
0
0
0
1
0
0
1
0
0
2
1
0
1
0
0
3
0
0
0
0
3
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
2
2
0
0
0
2
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
2
0
0
0
0
0
0
0
1
2
2
1
0
0
0
0
1
0
0
0
1
0
0
2
0
2
0
2
0
0
0
0
1
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
3
0
0
0
0
3
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
7
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
1
2
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
5
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
2
0
0
0
0
0
0
11
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
3
0
0
1
0
0
0
0
1
1
0
0
2
0
0
0
3
0
0
3
0
0
0
0
1
0
2
0
0
0
0
3
0
0
0
0
0
0
1
0
0
3
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
6
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
8
0
4
0
0
2
0
0
0
1
0
0
0
0
0
3
0
1
2
0
0
0
0
0
0
0
3
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
1
2
1
0
0
1
0
0
2
0
0
0
2
1
0
0
0
0
2
0
0
6
0
0
0
0
0
0
0
4
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
3
2
2
0
0
0
0
0
1
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
2
0
0
0
0
1
1
0
0
1
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
2
0
0
0
3
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
2
1
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
2
1
0
3
0
0
0
0
0
1
0
0
2
0
1
0
1
0
0
5
0
0
1
2
2
0
0
5
2
2
0
2
0
0
2
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
3
0
0
0
0
0
0
2
1
0
1
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
1
0
0
2
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
4
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
1
0
0
2
2
0
0
0
1
0
0
1
0
0
1
0
0
0
9
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
2
3
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
1
0
0
0
0
1
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
1
2
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
4
0
0
0
3
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
1
2
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
2
3
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
2
0
0
0
0
3
0
1
0
0
0
2
0
0
2
3
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
1
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
3
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
2
0
0
0
0
0
7
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
1
4
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
2
0
0
0
0
2
1
0
0
0
2
8
1
4
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
2
0
0
2
1
0
0
0
1
7
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
3
0
0
0
0
2
0
1
1
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
2
0
2
2
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
2
0
1
3
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
4
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
4
0
0
1
0
1
0
1
0
0
0
0
0
0
3
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
1
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
2
0
1
0
2
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
5
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
4
0
0
0
1
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
8
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
2
0
0
1
2
0
1
0
0
0
0
0
1
0
0
0
0
3
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
4
0
0
0
0
0
0
0
0
3
0
0
1
1
1
0
2
0
0
0
0
1
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
1
0
0
5
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
4
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
5
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
5
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
2
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
2
0
2
0
2
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
4
2
1
1
0
0
0
0
1
0
2
1
1
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
4
0
1
0
0
2
0
0
0
0
0
0
1
0
2
0
1
2
0
0
2
2
0
0
0
2
0
0
0
0
1
0
4
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
2
0
1
0
2
3
1
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
2
0
2
1
0
9
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
5
0
1
0
0
0
12
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
3
0
0
0
2
0
0
0
1
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
4
0
2
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
5
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
8
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
1
3
0
0
1
1
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
8
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
2
0
0
0
0
2
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
4
1
0
0
0
0
0
0
0
0
6
0
0
0
1
0
0
0
0
0
0
3
0
2
2
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
3
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
2
0
0
0
0
0
2
0
1
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
1
2
0
0
1
4
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
2
2
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
2
0
0
3
2
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
7
0
0
2
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
4
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
4
1
1
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
1
1
0
3
0
0
2
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
2
0
0
0
1
1
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
3
0
0
3
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
1
1
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
3
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
1
1
0
0
0
0
0
0
0
0
4
2
0
1
0
0
0
2
0
0
2
1
2
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
1
0
0
3
0
1
0
0
0
0
0
1
0
2
2
1
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
1
1
0
2
0
3
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
2
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
2
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
1
2
0
1
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
22
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
1
1
2
0
2
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
2
3
3
0
2
0
2
0
0
0
2
0
0
0
2
0
1
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
2
2
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
2
2
2
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
1
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
2
0
2
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
1
2
0
0
0
1
1
0
0
0
0
0
3
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
1
0
1
0
4
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
2
1
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
4
0
1
0
1
0
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
4
0
0
0
0
0
0
0
3
2
2
0
0
0
0
0
0
0
0
2
1
1
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
4
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
2
2
0
1
0
0
0
0
0
0
3
0
1
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
2
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
2
0
1
2
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
1
0
1
2
5
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
2
2
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
1
0
0
2
2
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
2
1
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
4
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
2
0
0
0
2
1
0
0
2
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
1
1
0
3
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
2
0
0
1
0
1
1
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
4
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
2
3
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
1
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
2
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
1
0
0
0
1
2
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
2
2
0
0
2
0
1
2
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
3
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
4
0
0
5
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
5
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
5
0
0
0
2
1
0
2
0
0
0
1
0
0
0
0
2
0
1
0
0
2
0
1
0
0
0
2
0
0
0
0
1
0
0
0
1
3
0
0
0
0
2
0
0
1
0
4
1
0
0
0
1
3
0
0
0
0
6
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
5
1
0
2
0
1
1
0
1
2
1
2
0
0
0
0
0
1
0
3
0
1
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
5
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
3
0
0
0
1
0
0
0
0
0
0
0
0
2
0
4
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
2
1
2
1
0
2
0
3
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
2
2
0
0
0
1
0
0
1
2
2
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
10
1
0
0
2
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
3
2
1
2
2
1
0
0
0
0
0
0
0
2
0
0
2
0
0
2
3
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
1
0
5
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
1
1
1
0
0
0
5
0
0
0
2
0
2
3
0
0
0
0
1
0
0
1
1
1
0
0
0
0
2
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
6
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
1
0
2
1
1
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
1
1
0
0
0
2
0
2
0
2
0
0
0
0
0
0
1
0
5
0
0
1
0
0
3
1
0
2
1
0
0
1
0
0
0
0
0
2
1
0
0
0
1
0
0
3
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
5
0
3
0
0
2
0
0
0
1
2
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
2
2
0
1
0
0
1
1
0
0
0
0
2
3
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
1
0
0
0
0
5
0
0
0
0
0
0
0
1
2
0
0
0
0
10
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
6
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
3
1
0
0
0
0
0
0
9
0
0
0
0
2
0
0
2
0
2
0
2
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
2
3
2
0
0
0
0
0
0
0
1
2
1
2
1
0
0
1
0
4
1
0
0
0
0
0
3
0
0
0
0
2
1
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
2
0
0
0
0
3
0
0
1
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
4
0
1
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
1
0
0
6
0
0
0
0
1
1
0
0
2
3
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
3
0
0
1
0
0
0
1
2
0
0
0
1
0
0
0
1
2
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
1
2
0
0
0
1
2
1
3
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
3
2
0
0
0
5
0
2
0
0
0
0
0
2
2
0
0
0
1
0
3
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
2
1
0
0
1
0
1
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
2
4
2
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
3
2
2
0
2
0
0
1
0
0
0
0
0
0
0
7
0
1
0
1
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
1
0
0
0
0
0
2
0
3
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
9
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
3
0
1
0
0
1
0
2
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
2
2
0
2
0
3
0
0
1
4
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
2
1
1
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
1
1
0
1
1
4
0
0
0
0
0
1
1
1
0
1
0
0
1
0
0
0
0
3
1
0
0
0
2
3
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
5
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
1
1
0
0
0
2
0
2
0
0
0
1
0
0
0
1
1
0
3
0
0
0
2
2
0
0
0
0
2
0
2
0
0
1
0
0
0
1
0
1
0
2
0
0
0
0
2
0
0
2
0
5
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
2
0
1
3
2
0
0
2
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
5
2
0
1
0
2
0
3
0
0
0
2
1
1
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
1
2
4
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
2
0
0
0
0
1
0
2
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
2
0
1
0
3
6
0
0
0
0
0
2
0
2
0
0
0
0
3
0
0
0
2
0
1
0
2
0
2
2
1
0
0
5
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
1
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
2
1
3
0
0
0
0
0
0
2
0
2
0
1
1
1
0
0
0
0
0
0
0
0
1
0
1
7
2
0
0
0
0
0
0
1
0
0
0
2
1
0
0
2
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
1
0
1
0
0
0
1
1
3
0
0
0
0
0
0
1
3
0
0
2
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
3
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
2
0
0
2
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
1
0
2
0
2
0
0
1
1
2
0
1
0
2
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
0
2
0
0
1
1
0
0
2
0
0
0
0
0
2
0
1
1
2
0
1
0
2
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
2
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
3
1
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
2
0
1
1
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
1
1
0
1
4
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
1
2
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
1
1
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
3
5
0
1
0
0
1
0
0
2
2
0
0
0
4
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
2
0
0
0
0
0
1
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
2
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
1
0
3
0
0
0
0
1
0
7
2
3
1
0
0
2
1
0
0
0
0
0
0
0
0
1
2
2
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
3
2
0
0
4
0
0
0
0
1
0
1
0
0
0
8
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
10
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
6
0
0
1
1
0
2
0
0
1
0
0
0
0
0
0
0
0
1
3
2
0
0
0
0
0
0
2
2
0
1
0
0
0
1
2
0
0
0
0
0
1
0
0
3
4
0
2
1
1
0
0
2
0
0
0
3
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
3
0
0
2
0
2
1
0
1
0
0
2
0
8
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
2
3
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
2
0
0
0
0
0
1
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
3
1
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
2
0
0
0
0
0
0
0
3
1
2
2
3
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
1
0
1
0
0
0
0
2
5
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
3
0
0
0
1
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
3
0
0
0
0
0
1
0
2
0
2
2
3
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
1
0
0
1
0
3
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
8
0
2
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
4
0
0
3
1
1
0
0
0
2
2
0
2
0
0
1
0
2
0
2
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
1
0
0
0
3
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
5
2
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
3
0
0
0
0
0
1
0
0
2
0
2
0
2
3
0
2
0
1
0
0
0
0
2
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
5
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
5
1
1
0
0
3
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
2
0
1
0
1
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
1
0
1
0
0
0
0
2
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
3
2
0
0
2
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
13
0
2
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
6
0
0
1
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
4
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
2
0
2
1
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
4
1
1
0
1
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
2
1
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
2
0
1
1
3
0
0
0
1
0
0
2
0
0
0
0
2
0
1
0
1
0
0
1
0
0
1
0
3
1
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
2
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
2
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
2
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
1
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
3
0
2
0
1
0
0
1
0
1
0
0
0
0
3
0
0
0
0
3
0
0
0
1
0
0
0
0
0
2
0
0
0
2
1
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
2
0
6
1
0
0
1
0
3
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
5
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
1
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
1
0
23
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
3
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
3
3
0
1
0
1
1
0
3
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
1
0
5
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
2
0
1
0
0
0
1
1
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
0
0
1
0
1
5
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
2
0
0
1
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
1
0
0
2
1
2
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
2
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
3
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
3
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
1
0
0
0
0
2
0
0
2
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
2
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
6
1
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
7
2
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
5
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
2
0
0
0
0
0
2
2
2
2
0
0
0
0
0
0
0
1
0
1
0
0
0
4
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
5
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
2
0
0
0
3
0
2
0
3
0
0
0
0
0
0
0
0
0
6
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
2
2
2
0
0
0
1
2
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
3
0
2
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
2
0
3
0
0
0
0
1
5
0
0
0
0
0
0
1
1
1
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
1
2
1
8
0
0
2
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
2
4
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
3
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
5
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
4
3
1
0
0
3
0
1
0
0
0
0
0
1
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
9
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
3
1
1
2
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
1
0
1
0
1
0
5
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
2
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
2
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
4
2
1
0
0
1
1
2
0
0
1
1
0
0
0
7
2
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
1
0
2
0
1
0
0
1
0
1
0
0
0
0
2
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
2
0
0
0
1
1
0
0
0
0
0
0
0
6
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
2
2
0
0
2
2
2
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
4
0
0
0
0
0
2
1
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
1
2
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
4
0
0
2
0
0
1
6
0
2
0
0
0
0
0
0
0
0
0
1
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
8
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
3
0
1
0
1
0
0
0
0
0
1
0
0
0
2
0
0
1
1
2
0
2
0
0
0
1
0
0
0
0
2
0
0
0
10
2
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
1
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
4
2
0
0
0
0
0
0
0
1
0
0
2
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
2
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
4
0
1
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
5
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
1
0
1
1
2
0
2
0
0
2
1
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
2
0
0
0
3
2
0
0
1
0
0
0
1
0
0
0
0
0
0
2
1
2
0
1
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
1
0
0
0
1
2
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
3
0
0
0
0
2
0
2
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
1
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
4
5
0
0
0
0
2
1
0
0
1
0
0
2
0
0
0
0
0
2
0
1
0
2
0
8
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
1
2
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
2
0
0
1
0
0
0
0
2
0
0
2
2
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
2
0
1
1
0
0
0
2
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
7
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
2
0
0
0
1
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
3
2
0
0
0
0
0
1
0
2
0
0
2
1
0
1
0
0
0
0
0
0
1
0
1
3
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
1
0
2
2
0
2
1
0
1
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
3
3
0
0
0
0
0
0
0
0
0
0
3
0
1
1
3
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
3
1
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
3
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
3
0
0
1
2
1
0
0
1
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
10
0
0
2
0
0
1
0
2
0
0
0
0
0
0
3
0
0
0
0
2
4
0
2
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
2
7
0
0
1
0
2
0
1
0
0
3
0
0
0
0
1
0
0
0
0
0
0
6
0
0
0
0
1
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
3
0
0
0
0
0
2
1
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
2
0
0
1
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
2
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
3
0
0
0
0
4
2
0
0
3
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
4
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
3
0
0
3
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
1
2
1
0
0
1
0
2
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
1
5
0
0
0
2
0
0
0
0
2
0
0
0
2
0
1
0
0
2
1
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
3
3
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
3
0
1
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
2
1
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
3
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
1
3
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
1
0
1
0
1
0
2
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
2
1
0
0
0
2
1
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
3
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
3
2
0
0
1
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
1
0
2
2
0
2
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
3
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
9
0
2
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
8
0
0
0
0
0
2
1
3
1
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
2
0
0
5
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
2
0
0
0
0
0
0
2
0
1
0
1
0
1
0
0
2
0
0
1
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
2
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
3
0
0
0
0
0
0
0
1
2
0
0
0
5
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
2
0
0
0
1
0
2
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
4
0
2
0
0
0
0
0
0
0
1
1
0
1
0
0
0
3
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
2
2
2
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
5
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
5
0
0
0
0
0
0
0
2
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
3
0
0
0
0
2
0
0
1
0
2
0
2
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
7
1
0
0
0
0
0
0
0
1
0
0
0
6
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
2
0
0
0
2
2
1
1
0
0
2
0
0
1
4
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
1
0
0
2
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
1
0
1
0
2
1
1
0
0
0
0
0
0
2
0
3
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
1
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
8
0
0
0
0
0
1
2
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
1
0
2
0
0
0
1
0
2
0
0
0
1
0
2
0
0
2
0
0
0
2
0
0
0
0
1
0
2
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
2
2
2
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
2
0
0
0
1
0
1
1
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
2
1
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
1
1
1
2
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
5
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
1
2
0
0
0
0
0
0
1
2
0
2
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
1
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
1
0
0
2
0
2
0
0
1
0
2
2
0
0
2
1
0
0
0
1
0
1
1
1
0
0
2
1
0
0
0
1
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
5
0
1
4
0
0
0
0
5
0
0
0
1
2
0
0
2
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
2
0
0
3
0
1
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
2
6
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
1
0
0
0
1
1
2
0
0
0
0
0
0
1
0
2
0
0
3
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
1
0
0
0
2
0
0
1
3
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
5
0
0
1
0
1
2
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
3
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
2
1
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
3
0
0
0
1
0
0
2
0
1
1
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
1
5
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
2
0
0
0
0
0
0
0
1
0
1
1
2
1
0
0
0
0
2
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
3
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
3
1
1
0
1
0
0
1
0
0
0
1
0
2
0
2
0
0
0
0
6
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
3
1
0
1
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
2
4
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
2
2
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
3
0
0
0
2
0
1
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
2
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
1
0
0
1
3
0
1
0
0
0
1
0
3
1
0
0
0
2
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
4
0
0
1
0
0
0
0
2
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
2
1
2
0
0
0
0
2
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
6
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
2
1
0
3
0
0
0
0
0
1
1
1
0
0
0
0
0
0
3
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
1
0
0
0
0
3
0
1
1
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
2
0
0
1
0
0
0
0
0
0
0
2
0
3
0
0
0
1
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
2
0
0
0
0
1
0
0
2
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
2
0
0
0
0
0
1
2
0
1
0
1
1
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
2
2
0
1
0
0
0
2
0
0
0
0
0
3
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
1
0
0
0
1
0
0
5
0
0
2
0
1
0
0
2
0
0
1
0
2
0
0
3
2
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
2
0
0
0
0
0
2
2
0
0
1
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
2
0
0
0
0
0
0
1
0
0
0
3
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
1
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
1
2
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
5
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
3
0
0
0
0
0
0
1
3
2
0
1
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
1
0
1
0
2
2
0
0
1
3
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
2
2
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
3
0
1
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
4
0
0
2
0
0
0
1
2
2
2
0
0
1
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
3
0
2
0
2
1
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
2
0
4
1
1
0
0
2
1
1
1
0
0
3
2
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
2
0
0
0
1
0
0
1
0
0
0
0
1
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
1
1
2
1
1
0
0
1
0
2
0
0
0
1
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
1
0
0
0
0
0
2
0
0
0
3
2
0
4
2
0
0
0
0
0
1
0
0
0
0
0
3
7
2
0
0
0
0
1
2
2
0
0
2
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
3
0
0
0
2
0
2
0
2
0
5
1
0
0
0
0
0
1
2
0
1
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
1
0
0
0
5
1
0
0
0
3
0
0
0
1
0
0
2
0
2
2
0
0
0
2
1
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
3
0
0
0
1
0
0
0
0
0
0
1
0
1
1
2
0
0
0
0
0
1
0
1
0
2
2
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
1
0
0
0
0
1
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
2
0
2
0
1
2
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
1
2
0
0
0
0
1
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
2
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
1
0
1
0
0
3
4
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
1
0
2
0
0
0
3
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
2
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
2
2
0
0
0
1
1
1
0
0
0
2
0
1
1
1
0
0
2
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
7
2
0
0
1
0
0
0
8
1
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
1
2
0
0
2
0
0
0
0
0
1
0
0
2
5
0
0
2
0
1
0
1
2
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
2
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
3
1
0
1
0
3
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
2
2
2
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
3
0
0
0
6
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
1
0
2
0
0
0
1
2
0
2
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
3
0
2
1
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
2
2
2
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
1
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
2
0
0
3
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
7
2
0
0
1
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
1
1
0
0
0
1
0
0
0
0
2
0
0
0
0
3
0
0
0
0
2
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
2
0
0
0
0
0
0
0
1
7
0
2
0
0
0
0
0
0
0
2
1
1
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
1
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
2
0
1
0
0
2
0
3
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
4
0
1
0
0
0
1
2
0
2
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
2
0
2
0
3
0
0
5
0
0
0
1
0
3
0
0
1
3
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
2
0
0
0
0
0
2
0
1
0
1
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
3
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
2
0
0
0
0
0
0
0
2
0
0
6
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
2
1
2
0
0
2
0
0
0
3
0
0
0
1
0
0
0
0
1
0
1
3
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
2
0
4
3
5
0
0
0
0
2
1
1
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
3
0
1
0
1
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
2
1
0
2
0
0
0
2
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
3
0
0
0
0
0
0
0
1
2
0
0
0
3
0
0
0
1
0
0
0
6
0
0
0
0
2
3
0
1
0
1
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
1
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
4
0
0
0
1
2
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
1
0
1
0
2
0
0
0
0
1
1
0
1
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
1
0
0
3
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
8
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
2
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
6
0
1
0
1
0
0
1
0
0
0
2
0
2
0
0
3
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
3
0
1
4
0
0
0
0
1
7
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
3
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
1
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
1
0
0
0
2
0
1
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
6
0
0
0
0
0
1
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
4
0
0
2
0
0
0
0
2
1
2
0
0
0
4
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
2
1
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
4
0
0
1
0
3
0
0
0
1
0
6
0
0
1
0
0
1
0
0
0
0
1
3
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
2
1
0
0
0
1
1
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
2
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
5
4
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
2
0
1
3
0
0
6
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
4
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
5
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
2
1
1
0
0
2
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
6
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
1
0
1
0
3
0
0
0
0
2
5
1
2
0
0
1
3
0
2
0
0
0
1
0
0
0
0
0
0
0
4
1
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
3
0
2
0
0
0
1
0
0
0
1
0
0
0
2
0
3
0
2
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
2
0
2
0
0
3
2
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
2
0
0
0
0
0
1
1
3
0
0
0
0
0
3
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
5
0
0
2
0
6
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
3
0
0
0
1
0
1
0
0
1
0
0
0
1
0
1
1
0
0
0
2
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
2
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
3
0
0
0
3
2
0
1
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
2
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
4
1
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
1
0
1
0
0
0
0
1
2
0
0
0
2
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
2
1
3
0
0
2
1
2
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
2
0
0
3
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
4
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
1
0
2
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
4
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
2
0
0
6
0
0
0
1
0
0
3
1
1
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
7
4
0
0
0
5
0
0
0
1
0
0
0
0
0
1
2
0
1
2
0
0
0
0
0
2
0
0
0
0
2
3
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
1
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
3
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
4
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
1
2
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
3
4
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
2
1
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
1
2
0
0
0
5
0
1
2
1
0
1
0
0
1
1
1
0
0
0
2
0
0
0
2
0
3
0
0
0
2
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
2
2
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
2
0
0
0
0
0
2
1
2
0
1
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
3
0
2
0
0
0
0
1
2
1
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
1
1
0
0
3
1
0
0
0
0
0
0
0
1
0
1
0
0
1
2
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
3
1
0
0
1
0
1
0
2
0
0
2
0
0
0
0
2
0
0
0
3
0
0
2
0
2
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
2
0
0
0
0
0
2
3
1
2
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
5
0
1
0
0
0
3
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
2
1
1
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
1
0
1
1
0
0
2
3
0
0
2
2
0
0
2
0
0
0
0
2
0
2
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
3
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
3
1
1
0
0
0
0
3
1
0
0
0
1
1
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
2
0
8
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
2
0
1
0
0
2
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
6
0
3
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
1
0
0
0
2
0
0
0
1
0
0
4
0
0
1
1
0
0
0
0
0
0
3
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
7
0
2
0
0
0
0
0
2
1
2
0
0
3
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
3
0
2
0
0
0
0
1
2
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
1
0
1
1
0
0
0
1
2
0
3
0
5
0
1
0
0
0
0
1
0
0
3
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
1
0
6
2
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
3
3
1
0
0
0
0
0
0
1
1
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
4
0
0
0
1
2
0
1
0
1
1
0
0
0
4
4
2
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
2
1
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
8
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
5
0
2
0
0
0
0
0
0
0
1
0
0
0
4
0
0
1
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
1
0
0
0
0
6
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
5
0
0
1
0
0
0
0
0
0
2
2
4
0
0
0
0
0
2
0
4
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
4
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
6
2
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
2
5
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
1
2
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
7
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
4
0
2
0
0
0
0
0
0
2
0
1
0
1
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
7
0
3
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
10
0
0
1
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
2
1
0
0
2
0
2
0
0
4
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
3
0
0
2
0
1
0
0
1
0
0
1
0
0
1
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
5
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
2
0
2
0
2
0
0
0
7
0
5
0
0
1
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
3
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
5
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
3
0
0
1
0
2
0
0
20
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
1
0
0
0
0
1
0
0
0
1
0
0
0
2
0
2
0
0
0
0
3
0
2
0
0
0
0
0
0
2
1
0
0
0
0
1
2
1
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
1
0
0
1
2
3
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
6
1
0
0
24
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
8
0
0
0
0
0
0
0
0
4
1
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
2
3
3
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
1
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
7
0
2
0
0
0
0
0
3
0
0
0
0
3
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
4
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
1
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
1
0
0
0
0
2
0
1
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
3
0
0
0
1
1
0
0
1
1
0
0
0
0
0
2
2
0
0
0
14
1
0
0
0
3
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
4
1
3
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
1
1
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
2
1
2
0
0
1
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
3
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
3
0
0
0
1
0
2
0
0
0
0
0
2
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
9
0
1
0
0
0
0
3
0
0
0
3
0
0
0
2
0
0
0
0
1
0
0
0
2
0
1
6
0
0
5
2
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
2
0
0
1
0
2
0
0
1
3
0
0
0
0
0
6
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
2
2
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
2
2
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
3
0
0
1
0
0
0
3
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
2
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
2
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
6
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
3
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
3
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
2
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
5
0
0
3
1
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
2
5
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
2
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
2
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
1
1
0
0
0
4
0
0
0
2
2
0
0
0
2
0
2
0
0
0
0
0
1
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
3
0
2
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
1
2
0
0
0
0
2
1
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
4
0
0
0
0
0
0
0
0
6
0
0
2
0
0
5
1
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
2
0
1
0
4
0
0
0
2
0
0
0
0
5
0
0
1
2
0
1
0
0
5
2
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
1
0
0
0
2
1
0
0
0
2
0
2
0
0
5
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
6
0
0
0
3
0
2
1
3
1
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
2
0
0
0
1
0
0
0
1
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
1
0
0
2
10
0
1
0
1
1
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
3
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
1
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
1
2
0
0
0
4
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
3
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
2
0
0
6
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
2
1
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
7
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
1
1
0
0
0
1
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
2
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
3
2
0
0
1
0
2
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
2
0
1
0
2
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
2
3
0
0
0
1
0
0
1
0
1
0
0
0
2
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
3
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
1
0
0
0
1
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
2
0
0
0
0
2
4
0
0
0
0
0
0
1
0
2
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
4
0
0
2
0
0
1
0
0
0
0
0
0
3
0
1
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
1
0
0
0
1
0
1
2
0
0
1
0
1
2
0
0
0
2
0
0
0
2
2
0
0
0
2
0
0
0
1
2
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
5
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
4
0
1
0
2
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
1
1
2
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
1
1
2
0
0
0
0
0
3
0
0
0
1
0
0
0
0
3
0
0
0
2
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
2
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
3
2
0
0
0
0
2
2
0
1
2
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
3
0
0
0
0
0
4
0
0
0
3
1
0
1
2
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
5
1
0
0
0
0
0
0
0
0
0
0
3
2
5
0
0
0
0
0
0
2
0
0
0
2
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
4
0
0
1
1
2
1
1
0
1
0
0
0
2
0
1
0
0
0
0
3
0
0
2
0
0
0
0
0
1
0
1
0
3
2
1
0
0
0
1
0
0
1
0
0
0
0
1
1
2
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
5
0
0
0
1
0
1
0
0
0
0
0
4
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
1
0
0
3
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
3
2
0
0
3
0
0
0
2
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
1
0
1
1
0
0
0
1
0
0
1
2
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
6
0
0
0
0
0
1
1
0
2
0
0
1
2
0
0
1
0
0
0
0
1
1
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
1
1
0
0
0
0
0
2
0
3
0
2
0
0
2
0
0
2
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
1
1
0
0
0
0
6
0
0
1
0
0
0
0
0
0
1
0
1
0
3
0
0
0
2
0
6
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
4
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
1
1
0
1
0
0
1
1
0
0
0
2
0
0
2
0
1
2
0
1
0
0
0
0
0
1
3
0
1
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
3
0
0
2
0
1
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
4
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
2
0
0
1
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
7
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
2
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
4
0
1
0
4
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
1
2
0
0
0
2
0
0
0
2
2
0
0
2
1
0
0
0
2
0
0
2
2
0
0
0
0
0
9
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
2
1
4
0
1
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
5
0
0
0
0
0
0
3
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
1
0
0
0
2
0
1
1
1
1
0
0
2
0
0
1
0
0
0
0
2
0
1
2
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
2
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
3
0
0
0
1
0
0
1
0
0
1
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
5
0
0
0
0
0
0
0
0
0
3
0
0
0
3
0
2
0
0
0
0
0
3
0
2
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
3
0
2
0
0
0
1
2
0
0
0
0
0
0
2
0
0
4
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
2
0
1
1
0
0
0
2
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
3
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
1
0
1
3
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
2
0
0
0
1
1
1
0
0
2
0
0
0
0
0
2
0
0
0
1
1
1
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
8
0
1
0
0
0
0
0
0
1
0
0
6
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
3
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
1
0
1
0
1
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
1
0
3
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
3
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
3
0
0
2
2
0
2
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
1
0
3
0
1
0
0
0
0
2
0
2
0
2
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
2
0
2
1
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
2
0
1
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
1
0
0
1
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
5
2
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
2
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
3
0
0
2
0
0
0
0
0
0
4
0
0
0
1
2
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
5
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
2
0
1
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
12
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
1
3
1
0
2
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
2
0
2
0
0
2
0
0
0
0
0
0
0
4
2
0
2
0
0
0
1
0
1
2
0
0
0
0
0
1
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
2
0
1
0
0
0
0
3
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
3
1
0
0
2
0
0
0
0
0
0
0
0
0
3
2
0
3
2
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
6
0
0
0
0
0
0
0
0
0
1
0
0
0
0
5
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
2
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
3
0
4
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
1
1
3
0
2
4
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
3
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
3
0
3
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
3
5
2
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
3
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
2
6
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
1
0
0
1
0
0
2
0
0
0
0
0
1
0
5
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
8
0
1
0
1
0
0
0
0
0
0
1
2
1
0
0
0
0
1
0
2
0
0
0
0
0
3
2
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
1
0
0
0
0
2
0
0
3
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
1
0
4
0
2
0
1
3
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
5
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
7
0
0
3
0
0
2
0
0
0
2
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
3
3
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
3
0
0
0
2
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
3
0
0
0
0
5
0
2
3
1
0
0
2
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
1
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
2
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
3
2
0
0
1
0
0
0
2
0
0
1
0
0
0
2
0
0
0
1
0
0
4
2
0
0
0
0
1
0
1
0
0
1
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
8
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
2
1
0
1
2
0
1
0
1
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
3
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
1
1
0
0
0
3
0
0
0
1
0
0
1
0
0
1
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
3
0
0
2
1
0
0
0
1
5
0
0
0
1
0
2
0
0
2
0
0
1
0
1
1
0
0
1
0
0
0
0
0
2
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
1
0
3
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
2
0
0
1
3
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
3
1
0
2
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
2
1
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
1
0
0
0
2
1
0
0
3
0
1
0
0
0
0
0
1
0
0
3
0
0
0
1
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
1
0
0
0
5
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
1
0
1
3
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
1
0
1
0
0
1
0
0
0
0
4
0
0
0
3
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
2
1
0
0
2
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
3
0
2
1
0
0
0
1
0
0
2
0
1
0
0
0
1
0
2
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
2
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
1
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
3
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
1
0
0
0
3
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
3
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
1
0
0
0
3
0
0
0
0
0
0
0
0
1
1
0
0
2
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
3
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
8
0
0
0
1
0
3
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
2
0
1
0
0
0
6
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
2
0
1
1
0
0
0
3
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
2
1
1
0
0
0
1
0
0
1
0
0
0
0
3
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
2
0
0
1
2
0
3
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
4
1
1
2
3
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
2
0
0
5
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
4
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
2
0
0
0
0
2
1
1
0
0
0
0
2
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
2
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
5
1
0
2
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
6
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
3
0
2
0
0
0
0
1
0
0
0
1
1
2
7
0
0
2
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
2
0
0
5
0
0
0
0
0
0
3
0
2
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
2
0
0
0
1
0
1
1
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
3
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
2
0
0
3
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
1
4
2
2
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
3
0
1
0
0
0
0
0
0
4
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
7
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
7
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
2
2
0
0
0
1
0
1
0
1
0
0
0
4
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
3
1
1
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
2
0
0
0
0
0
1
0
1
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
4
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
1
1
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
1
1
0
0
2
2
0
1
0
0
0
2
0
0
0
3
0
1
2
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
2
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
2
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
1
0
2
2
0
0
0
0
1
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
1
0
0
2
1
0
0
7
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
1
2
0
3
3
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
2
0
0
1
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
2
3
1
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
2
0
0
1
2
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
3
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
2
0
0
3
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
2
0
1
0
0
0
1
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
2
1
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
2
1
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
1
1
0
0
0
3
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
3
0
0
0
0
0
0
2
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
3
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
11
2
0
0
0
0
1
0
0
1
1
0
0
0
0
2
0
0
2
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
3
0
2
0
5
1
0
0
4
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
2
1
0
0
0
0
0
0
1
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
5
0
1
0
0
0
0
0
0
0
3
0
0
0
1
1
0
0
0
0
0
0
1
0
1
2
0
0
1
0
5
0
2
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
1
0
1
5
0
0
2
2
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
1
1
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
1
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
2
1
1
0
0
0
2
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
2
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
4
0
0
2
0
3
0
0
1
0
0
0
0
1
2
0
0
0
1
2
2
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
2
0
3
0
1
0
2
0
0
1
1
1
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
6
2
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
3
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
3
0
0
0
0
0
2
1
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
1
0
0
0
1
0
2
0
0
1
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
1
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
4
2
0
1
0
0
1
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
2
1
0
2
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
3
1
0
0
4
0
0
0
3
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
1
0
0
0
4
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
7
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
3
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
2
1
0
0
1
0
0
0
3
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
3
0
0
0
1
2
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
2
0
9
0
0
0
1
0
0
1
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
1
0
2
0
0
4
0
0
0
0
0
2
0
0
0
1
1
1
0
2
1
0
0
0
2
1
2
3
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
2
0
0
1
1
0
3
0
0
1
0
0
1
0
1
1
0
1
0
0
0
0
2
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
1
1
2
0
0
0
0
0
0
1
1
0
0
0
1
0
0
2
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
6
0
0
2
0
0
0
2
1
1
0
1
0
0
0
0
0
2
1
4
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
3
2
0
0
0
0
0
2
0
3
0
0
0
0
1
1
0
1
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
1
2
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
1
0
3
0
0
3
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
1
2
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
4
0
0
0
1
2
0
0
3
2
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
3
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
1
0
2
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
9
0
0
0
0
0
1
0
1
0
0
0
1
2
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
5
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
3
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
1
0
4
3
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
11
0
2
0
0
2
0
0
0
0
2
6
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
3
0
2
2
0
0
0
0
0
1
0
2
0
2
1
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
1
0
0
3
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
3
0
0
0
0
1
0
5
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
1
0
0
0
0
0
0
0
5
0
0
1
0
0
0
0
0
2
2
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
1
3
0
0
0
0
0
2
0
0
0
0
0
0
2
0
3
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
4
0
1
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
1
2
0
0
2
0
0
0
0
2
0
1
1
0
0
0
2
0
0
0
3
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
1
1
1
3
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
1
2
0
2
1
0
1
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
3
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
2
2
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
1
2
0
2
0
0
0
3
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
1
0
0
2
2
0
1
1
0
0
0
0
1
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
4
0
1
0
0
0
0
0
0
1
0
1
2
0
0
1
0
1
2
0
0
1
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
3
0
0
0
0
1
0
0
2
2
5
0
1
2
0
0
0
0
0
0
0
0
1
2
5
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
3
0
0
1
0
0
2
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
2
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
6
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
1
1
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
3
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
10
0
6
2
0
2
0
0
2
0
0
2
2
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
2
2
0
2
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
4
0
0
0
0
2
0
0
0
1
0
0
2
1
0
1
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
2
2
2
1
0
0
0
1
0
0
1
0
0
2
1
1
1
0
0
0
0
0
1
0
0
1
0
0
3
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
3
0
0
1
0
0
3
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
1
1
0
1
1
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
1
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
2
1
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
1
2
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
2
0
0
0
1
0
1
0
0
2
0
0
0
0
2
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
2
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
3
1
0
2
0
0
0
2
1
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
2
1
2
0
0
1
0
0
0
1
0
5
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
2
1
0
1
0
0
0
0
2
0
3
2
0
0
0
0
0
0
0
2
0
1
0
1
1
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
4
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
1
1
1
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
1
1
0
0
1
1
0
0
0
3
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
3
0
1
0
0
2
0
0
0
0
0
1
0
3
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
1
2
0
0
2
0
0
0
0
0
1
1
0
1
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
3
0
0
0
0
0
0
1
2
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
7
1
0
0
0
0
0
0
0
1
2
0
1
0
0
0
8
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
4
0
1
0
0
0
0
3
0
0
0
3
0
0
0
0
0
0
5
0
3
0
0
0
1
0
1
0
0
0
0
0
0
0
10
0
0
0
0
1
2
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
2
0
1
0
0
0
0
1
0
0
3
0
0
1
1
0
2
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
1
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
3
0
0
7
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
8
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
2
0
1
0
0
2
0
0
1
3
0
0
0
2
0
1
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
5
0
2
0
0
2
0
0
0
0
1
0
1
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
2
0
0
0
5
0
1
3
2
3
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
2
4
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
5
0
0
0
0
0
0
0
0
1
0
0
0
2
3
0
2
0
3
0
0
0
0
0
0
3
0
0
0
1
0
0
1
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
4
0
4
0
0
0
0
0
0
0
0
8
0
3
0
0
0
0
0
0
0
2
1
1
1
0
0
4
0
1
0
0
0
0
3
2
0
1
0
0
8
0
0
1
0
0
0
0
0
1
0
3
0
0
0
0
2
0
2
0
1
0
0
2
0
0
0
0
0
1
0
0
1
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
3
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
3
0
0
0
2
0
0
2
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
9
0
0
1
1
2
0
0
0
0
0
2
1
6
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
3
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
6
0
2
0
0
0
1
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
1
1
0
0
0
0
0
0
1
0
1
1
2
2
0
1
0
0
0
0
2
0
2
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
4
1
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
2
0
3
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
2
0
0
0
0
4
2
0
1
0
2
0
0
0
0
0
0
0
0
3
0
4
2
0
0
0
0
2
0
0
1
0
0
0
2
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
2
0
1
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
3
0
0
2
1
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
6
2
1
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
2
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
1
0
0
0
1
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
3
0
2
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
1
4
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
2
1
3
0
0
0
0
0
2
0
2
0
0
0
1
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
6
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
3
0
3
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
3
1
0
3
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
3
2
2
0
0
2
1
0
0
0
0
0
2
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
5
0
0
0
0
1
2
0
0
4
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
4
0
2
1
0
0
0
0
0
0
1
0
5
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
4
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
2
2
1
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
3
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
1
0
2
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
3
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
3
1
0
1
1
1
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
6
0
0
2
0
0
0
2
0
2
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
2
0
0
0
0
0
0
2
0
2
0
2
2
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
5
0
2
0
0
0
0
1
0
0
0
0
0
2
2
2
0
0
0
2
0
0
1
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
6
0
0
0
0
0
0
0
0
0
0
1
3
2
0
0
0
0
0
0
0
0
2
0
0
1
2
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
3
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
2
2
0
1
0
0
0
0
1
0
0
0
1
0
2
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
3
1
0
0
0
0
0
0
0
0
3
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
3
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
2
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
1
1
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
3
1
2
0
2
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
2
1
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
4
0
1
0
0
0
0
2
0
0
0
0
0
0
6
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
3
0
0
0
2
0
1
0
2
1
0
1
0
0
0
0
0
2
0
0
2
0
1
1
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
1
2
2
0
0
0
0
0
1
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
2
0
0
1
0
0
1
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
4
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
4
0
0
0
2
0
0
4
0
1
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
2
0
2
0
0
0
2
0
2
5
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
3
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
3
2
0
0
1
0
0
5
0
0
0
0
0
0
2
0
5
0
0
0
0
0
0
0
0
0
0
1
1
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
1
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
2
2
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
5
3
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
3
0
0
1
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
15
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
7
0
0
0
0
0
0
0
0
5
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
8
0
0
1
0
2
0
0
0
0
0
1
0
0
1
0
0
0
2
9
2
0
3
1
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
3
0
0
0
0
0
0
0
4
0
1
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
5
0
2
1
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
2
0
0
1
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
1
0
0
2
0
4
4
0
0
0
0
2
2
0
1
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
1
0
0
3
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
2
1
0
0
0
2
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
8
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
1
0
0
0
2
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
1
0
2
0
1
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
4
1
0
3
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
4
0
0
0
1
0
0
3
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
4
0
2
1
1
0
0
0
1
0
0
0
1
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
1
0
2
0
0
2
2
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
4
0
7
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
16
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
4
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
1
3
1
1
2
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
5
1
0
1
0
0
0
0
1
0
3
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
3
0
0
0
0
0
0
1
2
0
0
0
1
2
0
0
0
0
0
0
0
1
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
2
0
0
1
0
2
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
3
1
0
0
0
0
0
0
0
0
2
1
0
1
0
2
0
1
2
0
0
0
0
1
4
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
1
2
0
0
0
1
2
0
0
0
0
0
0
0
0
5
0
1
0
2
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
3
1
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
1
7
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
2
3
0
0
2
0
0
0
0
0
0
2
0
2
0
0
2
0
1
2
0
0
3
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
10
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
1
0
0
5
1
0
2
2
0
1
0
2
2
0
0
0
0
3
0
2
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
4
0
3
0
2
0
0
0
1
0
3
1
0
0
0
0
0
2
0
0
0
0
0
1
0
3
3
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
2
0
0
0
2
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
2
0
3
2
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
2
0
1
0
2
1
0
0
0
0
0
0
2
2
0
0
0
0
2
1
0
0
1
0
2
0
0
1
2
0
1
0
0
0
4
0
0
1
0
0
0
0
0
3
0
0
1
2
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
2
1
0
0
1
1
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
1
3
0
0
1
0
0
0
0
0
0
1
0
7
0
2
1
0
0
2
0
0
0
1
2
1
0
0
0
0
0
0
0
0
2
2
3
0
0
0
1
1
0
2
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
2
0
0
3
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
5
0
1
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
1
0
0
0
0
1
2
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
5
0
0
2
2
0
0
2
1
0
0
0
1
0
0
1
0
0
2
1
1
0
0
0
0
0
0
2
0
1
2
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
6
0
1
0
0
1
0
2
5
2
1
1
0
0
0
0
0
1
0
4
1
0
0
1
0
2
0
0
1
0
0
0
0
0
0
1
0
1
1
1
2
0
0
0
1
0
1
1
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
2
1
2
0
1
0
0
0
0
0
4
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
1
0
0
0
0
3
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
1
0
0
1
0
2
0
0
1
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
2
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
1
0
0
0
0
2
0
5
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
2
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
1
1
0
3
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
2
3
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
2
0
0
0
0
2
2
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
2
0
2
0
0
0
1
0
3
0
0
1
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
1
0
0
0
2
0
0
0
0
2
1
2
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
2
0
3
1
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
2
2
0
0
1
0
0
0
0
0
1
0
7
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
3
0
0
0
0
0
0
0
0
1
0
2
0
0
2
2
1
0
0
1
0
6
0
0
0
0
0
0
0
0
0
4
0
0
5
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
1
3
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
1
0
0
0
1
0
1
0
1
0
1
0
1
0
0
0
1
0
2
1
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
1
2
0
8
0
0
0
0
0
1
0
2
0
0
3
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
2
0
0
2
0
0
0
1
0
0
2
0
0
0
2
2
2
0
0
0
4
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
1
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
3
2
0
2
0
0
0
2
0
0
0
0
5
0
3
0
0
0
0
0
0
4
0
0
1
1
1
0
0
0
0
0
2
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
2
2
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
2
4
4
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
2
0
0
1
0
0
1
0
0
2
0
0
4
1
0
0
0
0
2
0
0
0
2
2
1
2
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
2
0
0
2
0
0
4
0
1
0
1
0
1
2
0
4
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
4
0
0
3
0
2
0
0
1
1
0
0
0
0
0
2
0
1
0
2
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
1
0
0
2
1
0
0
1
0
0
0
2
0
0
0
0
1
0
0
2
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
4
0
0
0
0
7
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
2
0
0
1
0
0
0
0
0
0
3
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
1
0
4
0
1
1
1
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
2
2
0
1
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
3
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
1
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
2
2
0
0
0
2
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
2
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
2
0
0
2
0
0
0
1
0
0
0
3
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
1
0
0
1
0
6
0
0
0
2
2
1
0
0
2
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
3
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
2
0
0
0
4
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
4
0
1
0
0
3
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
3
0
0
3
0
0
0
0
2
0
6
0
1
0
0
1
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
1
6
2
0
0
2
0
0
0
0
0
0
1
2
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
1
2
0
1
0
0
3
0
1
0
0
0
2
0
0
0
1
1
1
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
7
0
2
0
3
1
1
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
1
0
1
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
3
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
2
1
0
0
0
0
1
1
0
0
4
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
3
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
5
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
2
4
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
1
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
2
0
0
4
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
1
5
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
1
1
0
2
0
2
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
2
1
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
4
1
0
0
1
0
2
0
0
3
0
0
0
0
0
0
0
1
2
0
1
2
0
0
0
0
0
1
0
1
0
0
0
0
4
0
0
0
0
0
1
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
2
0
3
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
3
0
0
3
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
3
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
1
0
0
7
0
0
0
0
0
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
1
0
0
1
1
0
1
0
0
0
2
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
2
2
1
0
0
2
0
1
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
1
1
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
5
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
1
0
0
2
2
1
0
1
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
1
0
3
0
0
0
2
0
0
2
0
0
0
0
0
5
2
0
0
0
0
1
0
0
2
0
0
1
2
1
0
0
0
2
0
0
0
0
0
0
0
4
0
0
2
0
0
0
1
0
0
3
0
1
0
1
2
2
1
0
0
0
0
4
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
2
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
3
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
3
0
0
0
0
0
0
3
0
0
0
1
0
0
2
0
0
0
1
3
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
3
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
4
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
1
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
1
0
3
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
3
2
0
0
0
2
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
1
0
0
0
2
0
0
0
1
0
2
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
1
3
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
10
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
2
2
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
1
1
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
2
0
1
1
0
1
0
0
0
1
0
0
0
1
0
2
0
1
0
0
0
3
0
3
1
0
2
0
2
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
1
0
1
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
2
0
0
0
1
3
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
1
0
0
0
0
0
1
0
0
0
5
0
1
0
0
0
0
0
0
0
3
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
1
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
3
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
1
0
0
0
0
2
0
0
2
0
1
1
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
4
1
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
5
0
0
0
1
1
0
0
0
0
1
0
1
0
0
1
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
2
0
2
0
0
1
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
5
0
0
0
3
0
0
0
1
0
1
0
2
3
0
1
1
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
1
0
1
0
0
0
2
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
2
2
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
2
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
2
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
3
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
2
2
0
0
1
0
0
1
1
0
0
1
0
1
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
3
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
3
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
2
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
1
1
0
0
1
0
0
11
0
0
0
1
0
0
0
1
0
2
4
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
3
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
3
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
2
2
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
2
0
1
1
0
0
0
2
0
2
1
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
2
0
0
0
0
3
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
2
2
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
7
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
3
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
2
4
0
0
1
0
1
0
0
0
0
0
1
0
3
1
0
2
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
1
0
0
0
1
0
1
15
0
0
0
0
0
0
2
1
0
0
0
2
0
0
2
0
2
1
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
3
0
0
2
0
0
0
1
0
1
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
2
0
2
1
0
0
0
1
0
4
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
1
0
3
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
3
2
0
0
0
1
2
1
0
0
0
0
0
2
0
2
0
2
4
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
8
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
1
0
1
0
3
0
0
0
0
0
2
0
1
0
1
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
2
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
1
8
1
0
0
0
0
0
0
1
0
1
0
0
1
2
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
4
0
1
0
0
4
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
1
0
0
0
1
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
1
2
0
1
0
1
4
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
1
0
0
0
0
0
1
0
0
0
3
0
0
0
2
0
0
0
0
0
3
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
5
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7
0
0
0
1
0
0
0
3
0
0
0
0
0
2
2
0
1
0
1
2
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
4
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
1
3
0
0
0
3
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
1
0
0
0
1
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
2
2
0
2
0
0
1
1
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
1
1
0
0
3
0
0
0
5
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
1
1
1
2
0
0
0
0
2
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
1
0
2
0
2
1
0
0
0
2
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
3
0
1
0
1
2
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
7
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
2
0
0
3
0
1
1
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
1
0
4
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
2
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
2
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
1
0
0
0
0
0
0
1
0
1
0
3
2
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
7
1
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
13
1
0
3
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
1
0
2
0
0
0
1
0
0
0
1
0
1
1
1
0
0
2
0
0
0
0
2
2
0
0
0
0
0
3
4
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
1
1
1
2
0
0
2
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
1
0
0
1
0
1
0
0
0
5
0
0
0
2
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
3
0
0
0
1
0
0
2
0
2
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
3
1
1
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
2
3
0
0
0
1
0
0
1
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
3
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
3
0
0
0
0
0
0
0
2
0
2
0
2
0
1
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
4
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
1
0
1
1
0
3
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
3
0
5
0
0
0
1
0
0
2
0
1
0
0
1
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
2
4
0
4
0
0
0
0
0
1
2
0
0
0
0
1
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
4
0
0
0
0
0
4
0
5
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
1
1
0
0
0
2
0
2
0
2
0
0
0
2
0
0
0
2
0
1
0
1
0
0
3
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
1
0
4
2
3
1
2
0
2
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
3
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
1
0
0
4
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
2
1
0
0
0
0
2
0
1
0
1
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
3
2
0
0
0
0
1
0
0
1
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
2
2
0
1
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
2
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
2
1
0
0
0
0
1
0
0
0
4
0
0
2
0
0
4
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
3
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
5
0
0
0
2
2
3
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
1
0
2
0
2
0
0
0
0
2
1
0
0
1
2
0
0
1
2
0
1
1
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
1
0
2
3
1
0
0
1
1
0
0
0
0
1
0
0
4
3
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
5
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
3
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
2
1
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
4
0
2
0
0
0
0
0
2
0
0
0
3
0
2
0
3
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
1
1
0
2
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
3
2
1
0
0
0
0
0
0
0
3
0
3
0
0
2
0
0
0
0
0
0
4
0
1
0
0
9
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
3
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
2
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
0
1
1
0
1
0
0
2
0
0
0
0
9
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
2
1
0
1
0
0
1
0
2
0
0
0
1
0
0
1
0
2
0
0
0
0
0
1
0
0
1
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
2
0
0
1
0
0
2
0
0
0
6
0
0
1
3
2
0
0
0
0
1
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
3
1
1
0
0
0
0
0
0
0
0
0
1
6
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
3
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
1
3
0
0
2
2
2
0
0
0
2
0
0
0
0
2
0
0
2
0
2
0
0
0
3
1
0
2
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
1
2
0
0
1
0
0
2
0
3
0
0
2
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
3
0
0
0
2
0
0
1
1
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
2
0
1
1
0
2
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
3
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
1
0
1
1
1
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
2
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
1
3
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
5
0
0
0
0
0
0
0
0
0
0
2
3
2
4
0
3
0
0
0
0
0
0
1
0
3
4
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
1
0
4
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
2
1
0
0
0
0
0
3
1
0
0
0
0
0
0
1
2
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
5
2
0
0
1
0
0
0
0
0
0
7
3
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
12
0
0
0
3
2
0
1
0
2
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
3
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
1
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
4
0
1
0
1
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
1
0
1
0
0
2
0
0
0
0
0
0
0
2
0
3
1
0
1
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
1
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
2
0
0
0
1
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
4
0
2
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
3
0
2
1
0
0
0
0
0
0
4
1
2
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
3
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
2
0
0
1
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
1
1
0
4
0
0
0
0
1
0
0
0
1
0
0
1
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
1
0
0
4
0
2
0
0
1
0
2
4
0
0
0
0
0
0
0
2
1
1
4
0
0
0
1
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
6
3
0
2
0
0
0
0
0
0
0
0
1
8
0
0
1
0
0
0
2
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
2
0
3
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
3
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
8
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
1
3
0
1
0
2
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
3
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
7
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
1
0
0
2
0
0
0
0
0
0
0
2
4
0
0
3
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
1
0
1
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
2
3
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
3
0
0
0
3
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
3
1
1
0
1
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
1
0
0
3
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
4
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
2
0
0
6
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
1
2
0
1
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
2
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
7
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
2
0
0
0
0
1
0
1
1
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
2
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
3
0
0
0
1
0
1
0
1
0
0
0
0
0
2
1
0
0
1
0
0
1
0
1
0
0
6
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
1
1
0
0
0
1
0
0
0
3
2
0
0
0
0
1
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
3
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
3
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
3
0
1
0
3
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
5
0
0
0
2
0
0
0
0
0
1
3
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
6
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
4
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
2
0
0
1
0
1
2
0
0
0
0
2
1
0
5
0
0
0
0
0
0
1
1
0
0
2
5
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
1
0
0
0
0
3
0
0
3
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
1
0
0
2
8
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
4
1
0
0
2
0
0
0
0
2
0
1
2
0
0
1
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
1
0
3
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
1
0
0
0
0
0
0
3
0
0
0
0
2
0
1
0
0
1
1
1
0
1
0
0
2
2
0
0
6
0
0
0
0
2
0
0
0
0
0
2
0
1
0
1
0
1
1
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
1
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
3
0
0
0
1
0
2
0
0
1
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
2
0
0
0
0
0
1
3
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
5
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
4
0
1
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
3
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
2
0
2
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
2
1
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
3
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
3
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
1
1
0
0
0
5
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
5
0
0
0
2
0
2
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
2
0
1
0
2
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
1
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
3
0
0
1
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
4
0
5
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
6
0
0
1
0
0
3
0
0
0
0
0
0
1
1
1
2
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
1
0
0
0
3
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
3
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
5
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
1
1
1
4
2
0
3
0
0
0
0
1
1
0
1
1
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
4
0
2
0
3
0
0
0
2
0
0
0
0
0
1
2
0
0
0
2
0
0
1
2
1
0
1
2
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
7
0
1
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
1
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
2
0
0
0
0
0
0
2
2
4
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
4
2
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
1
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
2
0
1
1
0
4
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
3
7
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
2
1
0
0
0
3
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
6
0
0
2
0
0
4
2
0
1
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
4
0
0
0
8
1
0
0
0
0
2
2
0
0
0
0
3
1
2
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
3
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
3
0
0
0
0
2
2
0
0
8
0
0
0
0
0
0
0
0
0
5
5
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
2
0
0
0
0
1
0
0
1
0
1
0
2
0
2
0
2
0
1
0
0
0
0
0
0
2
0
1
1
0
0
1
0
6
0
0
0
1
1
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
2
1
0
0
0
0
0
1
0
0
1
2
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
3
0
0
0
0
1
0
0
0
0
0
0
2
4
2
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
2
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
2
0
0
0
3
0
0
0
0
2
1
0
0
0
2
0
3
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
2
1
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
2
0
1
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
2
2
0
0
3
0
0
0
0
0
2
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
1
0
0
1
0
1
0
0
2
0
1
0
2
0
0
0
0
1
0
2
0
0
5
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
3
0
0
2
3
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
2
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
3
0
3
1
0
1
2
0
0
0
2
0
1
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
1
1
0
1
0
0
0
0
0
2
0
0
1
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
2
1
1
0
0
4
2
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
4
0
0
0
0
1
0
0
0
0
2
1
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
1
1
1
0
1
2
0
0
0
0
0
0
2
2
3
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
3
0
0
0
0
0
2
0
0
0
0
2
4
0
0
2
0
0
2
0
0
0
1
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
1
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
1
0
4
0
0
2
0
0
6
1
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
7
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
3
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
1
0
0
1
0
3
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
3
0
0
1
0
0
3
0
4
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
7
4
0
2
0
2
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
1
2
0
0
5
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
5
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
2
5
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
1
0
0
2
0
2
0
0
0
1
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
2
2
0
0
0
0
0
0
0
0
0
0
2
2
0
1
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
2
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
1
0
0
0
0
0
0
2
2
0
0
0
1
1
1
0
0
4
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
6
0
3
0
0
0
0
4
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
1
2
1
0
2
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
1
0
1
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
3
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
2
0
3
0
0
0
0
3
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
3
0
1
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
2
3
0
3
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
1
0
1
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
2
1
1
0
0
1
0
0
0
0
1
0
0
2
1
0
3
0
0
0
1
0
1
0
0
0
0
2
2
1
1
0
0
0
2
1
0
1
0
0
0
1
0
0
0
0
0
0
1
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
1
0
0
0
0
2
0
2
0
0
3
0
0
0
0
0
2
0
3
1
0
0
0
0
2
0
3
0
0
0
0
2
0
2
0
0
0
0
1
0
2
0
3
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
1
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
5
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
2
0
0
2
1
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
1
0
0
1
2
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
1
2
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
5
2
0
0
0
0
0
0
0
2
2
2
0
2
1
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
1
2
1
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
2
2
0
0
0
0
2
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
1
0
0
2
0
0
5
0
0
2
0
3
0
0
0
1
0
0
1
2
0
2
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
1
0
0
1
1
1
0
0
2
3
0
0
0
1
0
0
0
1
0
0
0
0
1
2
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
2
0
0
0
2
0
0
1
0
0
0
0
0
1
1
1
2
0
1
0
0
1
0
0
0
1
0
1
2
0
2
0
0
0
0
0
0
0
0
0
3
0
1
0
1
0
0
0
0
1
0
3
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
2
0
1
0
1
0
0
1
0
0
1
0
0
0
1
1
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
5
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
3
0
0
0
0
3
0
0
0
1
4
0
1
0
0
0
0
1
0
0
0
2
0
2
2
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
2
2
1
2
2
1
3
0
0
0
2
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
2
2
0
0
0
0
1
1
2
0
2
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
3
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
2
0
0
0
0
3
0
0
2
1
0
0
1
0
0
1
1
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
1
0
0
0
2
3
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
3
0
0
0
4
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
3
2
0
0
2
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
3
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
8
0
0
0
0
0
0
0
1
0
1
2
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
7
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
6
1
2
1
1
0
0
0
0
0
0
0
0
0
3
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
1
5
0
0
0
0
0
0
2
0
3
0
1
0
0
0
0
0
0
0
2
0
1
2
1
0
0
1
0
2
0
2
0
0
0
0
2
0
0
0
1
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
3
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
2
0
2
0
1
0
0
3
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
2
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
3
2
0
0
0
0
1
0
1
0
0
1
1
0
2
0
0
1
1
0
0
0
0
0
2
1
0
0
0
0
0
2
2
0
0
0
0
6
0
1
0
0
1
6
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
3
0
2
0
0
0
2
0
0
0
4
1
4
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
5
0
2
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
2
0
0
2
0
2
0
1
0
2
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
2
0
0
0
1
0
1
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
1
0
0
1
0
3
0
0
1
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
2
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
1
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
2
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
2
0
2
0
2
0
0
3
0
0
2
0
0
0
1
0
0
0
1
2
1
0
1
0
0
0
0
0
0
5
2
0
0
0
0
0
1
0
0
2
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
1
2
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
8
0
0
0
0
0
0
0
1
0
1
0
0
0
2
1
1
0
0
0
0
0
0
0
1
2
1
2
0
1
0
3
0
2
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
1
0
1
0
0
0
2
2
0
0
0
0
1
0
0
4
0
2
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
1
1
1
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
4
0
0
2
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
2
1
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
2
0
2
2
0
0
1
3
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
2
0
2
1
2
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
3
1
0
2
0
0
0
2
0
0
2
0
0
1
0
0
0
8
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
9
0
0
0
1
2
0
1
0
0
2
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
16
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
4
0
0
2
4
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
2
3
0
0
0
2
0
0
0
0
2
0
0
0
4
0
0
1
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
1
0
0
0
7
0
0
0
1
1
0
2
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
5
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
3
0
1
0
0
1
0
2
0
0
0
1
0
1
3
0
0
0
7
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
9
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
1
0
1
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
3
2
1
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
3
0
0
0
0
3
0
0
0
0
1
0
1
0
1
3
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
3
0
0
0
1
0
2
0
0
1
0
0
2
0
0
1
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
3
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
3
2
0
2
0
1
0
1
0
0
1
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
2
2
1
1
0
0
0
0
2
0
0
0
0
0
5
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
1
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
4
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
3
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
4
1
0
0
0
0
0
3
2
0
0
0
2
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
3
0
0
1
0
0
0
0
1
0
0
0
2
1
1
0
0
0
0
3
0
2
0
0
0
1
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
1
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
6
2
0
2
0
0
0
0
2
2
0
0
0
2
1
1
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
1
1
0
0
1
0
0
1
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
9
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
2
2
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
6
0
0
0
0
1
1
0
0
1
0
2
0
0
2
0
0
1
0
0
3
0
0
0
0
0
0
1
1
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
2
2
0
0
0
1
0
0
0
1
0
0
0
0
2
0
1
2
2
0
0
2
0
0
0
0
0
0
2
2
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
3
1
0
0
0
0
1
0
1
0
1
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
3
2
0
0
3
0
0
0
0
1
0
1
2
0
0
3
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
1
0
0
0
0
3
0
0
1
0
0
0
2
0
0
2
2
0
0
0
0
0
1
2
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
3
0
0
0
0
2
1
0
0
1
0
1
0
1
0
0
0
0
2
0
0
0
0
0
1
0
3
2
1
0
0
0
0
0
0
0
1
0
0
0
2
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
8
0
0
0
1
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
1
1
0
0
2
0
0
1
3
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
2
0
1
0
1
0
0
2
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
4
0
0
3
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
1
1
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
1
4
4
0
0
0
1
0
0
0
2
0
1
0
2
0
2
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
2
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
2
0
1
0
2
1
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
1
2
2
0
2
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
8
0
1
0
1
0
2
0
0
0
0
3
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
1
0
2
0
0
1
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
4
0
0
1
0
1
1
0
0
0
0
0
0
0
2
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
2
0
0
5
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
4
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
3
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
2
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
4
1
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
2
0
0
0
0
1
0
1
0
0
2
0
1
0
1
0
0
1
0
0
0
2
0
1
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
1
0
0
0
3
0
1
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
3
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
4
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
2
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
1
0
2
0
0
1
0
2
6
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
3
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
1
5
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
1
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
1
2
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
4
0
0
0
0
0
7
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
2
5
1
2
1
1
0
0
0
0
1
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
3
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
2
7
2
0
0
0
0
0
0
0
0
1
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
1
1
0
1
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
4
0
2
0
0
0
0
2
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
2
4
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
3
0
0
0
0
0
3
0
0
0
0
0
0
2
1
2
0
0
0
3
0
0
0
0
1
0
2
0
0
1
1
0
5
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
2
0
1
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
6
0
2
0
0
0
0
1
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
3
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
1
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
1
3
4
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
3
0
0
0
2
5
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
1
0
1
0
0
0
2
0
0
1
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
3
2
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
2
0
4
1
1
1
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
4
0
2
0
1
2
0
0
0
0
0
0
1
0
0
0
0
2
0
1
2
5
0
0
1
1
0
0
2
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
2
0
0
0
1
4
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
3
0
0
1
0
5
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
3
0
0
3
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
3
0
2
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
3
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
3
0
0
5
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
5
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
3
0
0
2
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
2
0
1
0
0
0
2
0
0
0
2
2
0
0
0
3
2
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
1
0
0
1
0
0
2
0
2
1
0
0
2
0
2
0
3
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
8
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
1
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
5
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
1
0
2
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
1
3
0
1
1
0
0
0
1
0
0
4
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
7
0
0
2
0
1
0
1
1
0
1
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
2
0
2
0
3
0
0
0
3
2
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
2
0
0
3
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
4
2
2
0
0
0
0
0
0
0
0
4
1
0
3
0
2
2
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
7
0
0
0
0
0
0
2
0
0
1
0
0
1
0
2
5
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
2
0
0
1
1
1
2
0
0
0
0
0
0
2
1
0
0
0
2
0
2
0
0
0
0
1
0
2
0
0
0
0
1
0
2
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
2
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
3
1
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
2
3
0
0
0
2
0
0
1
0
2
0
0
1
0
0
0
1
0
0
0
0
0
3
2
1
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
1
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
3
1
1
0
0
0
0
1
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
3
1
1
0
2
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
1
0
0
0
0
0
1
2
4
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
3
3
0
2
2
2
0
0
0
1
0
0
1
0
0
0
2
0
2
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
5
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
3
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
1
3
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
1
3
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
8
1
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
1
0
0
1
3
0
0
0
0
1
1
1
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
1
4
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
2
2
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
3
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
9
0
0
0
0
0
0
0
1
0
0
0
1
0
3
2
3
0
0
1
0
2
0
0
0
4
0
2
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
1
1
0
0
2
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
2
0
0
0
4
3
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
5
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
2
1
0
0
0
1
1
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
1
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
3
1
0
0
0
2
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
1
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
5
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
2
0
0
2
0
0
0
0
1
1
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
3
1
0
1
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
1
0
0
1
0
1
0
0
0
0
2
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
1
2
0
0
0
0
0
2
2
0
0
0
2
2
3
1
0
2
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
1
0
6
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
3
0
0
2
0
0
0
2
0
1
0
0
1
0
0
0
1
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
3
2
0
1
0
1
0
0
0
0
0
0
0
1
6
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
1
0
0
3
0
2
1
5
6
0
0
0
0
0
0
1
0
1
3
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
3
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
1
4
0
0
2
0
1
0
0
0
0
3
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
2
1
0
0
2
0
2
2
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
2
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
1
2
2
0
5
0
0
0
2
0
2
0
0
0
0
0
1
1
0
0
4
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
1
0
0
3
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
3
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
2
0
2
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
4
0
0
3
0
1
0
3
0
2
9
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
1
0
2
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
4
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
1
0
0
2
2
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
2
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
2
1
0
0
0
0
1
0
0
1
0
0
0
0
3
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
3
0
3
0
2
0
0
0
1
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
3
0
1
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
5
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
2
1
4
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
5
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
2
0
0
6
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
5
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
4
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
2
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
2
0
2
1
1
2
0
0
1
0
0
0
0
0
0
0
4
1
2
4
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
3
3
0
0
0
0
0
0
0
2
3
1
0
0
0
0
2
0
0
3
3
11
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
2
2
0
1
0
0
1
0
0
2
0
5
0
0
0
0
0
0
0
1
0
5
0
1
1
2
0
3
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
4
0
0
3
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
1
1
0
0
0
0
0
0
3
2
0
0
0
1
0
0
0
0
0
1
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
1
1
0
1
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
1
0
2
0
2
0
0
0
0
1
0
0
4
0
1
0
0
0
0
0
1
1
2
0
0
0
2
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
2
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
1
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
2
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
4
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
1
0
2
0
0
1
2
0
0
2
2
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
3
0
1
0
0
2
0
1
1
0
0
0
0
0
0
0
0
2
0
2
1
1
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
1
0
1
0
0
0
1
0
0
2
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
5
0
2
0
1
7
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
3
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
1
0
0
0
2
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
2
1
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
1
0
0
0
0
0
0
1
8
0
0
0
0
0
0
0
0
2
0
0
13
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
1
0
0
1
0
2
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
7
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
2
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
2
2
0
1
0
1
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
3
1
0
0
1
2
1
0
1
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
3
0
0
3
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
4
0
0
0
2
0
0
2
0
0
2
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
3
1
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
1
0
1
2
2
3
0
1
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
2
1
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
2
2
0
1
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
2
0
0
3
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
2
1
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
3
2
0
0
0
0
2
2
0
0
0
0
9
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
2
1
2
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
3
0
0
0
2
0
0
0
1
0
0
0
0
2
1
2
4
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
2
0
0
1
2
0
1
3
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
9
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
2
0
2
2
0
0
2
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
7
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
3
1
0
0
0
2
0
0
0
0
5
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
5
0
0
0
0
0
2
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
3
0
0
3
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
2
0
0
1
7
0
0
0
0
0
1
0
0
9
2
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
4
0
0
0
1
0
0
0
1
0
0
3
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
1
0
1
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
4
1
0
2
0
1
0
0
1
1
0
0
0
0
0
0
2
0
2
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
2
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
4
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
3
0
1
0
4
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
1
0
0
2
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
3
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
5
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
3
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
2
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
1
1
0
0
0
5
0
0
0
0
0
0
0
0
2
0
5
0
0
0
0
2
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
2
0
0
0
3
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
5
0
1
0
0
5
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
3
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
2
2
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
1
0
3
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
2
0
1
0
0
0
0
0
1
0
2
3
0
0
0
0
1
1
1
0
0
1
0
1
0
0
0
1
1
0
0
4
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
2
1
1
0
4
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
3
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
1
0
0
2
0
2
0
0
0
3
0
0
0
0
0
2
0
0
3
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
2
5
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
1
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
1
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
7
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
5
0
0
0
3
0
0
0
1
0
0
0
0
0
1
0
0
2
3
1
0
0
0
0
3
0
0
0
1
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
5
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
5
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
1
0
2
0
7
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
5
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
3
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
3
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
4
2
0
2
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
2
0
0
1
0
0
1
0
0
0
1
1
0
0
0
1
2
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
1
2
0
0
1
2
2
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
5
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
2
0
0
0
0
1
0
0
1
0
2
1
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
1
0
2
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
1
0
1
0
0
0
2
0
1
0
0
2
0
0
0
1
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
3
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
3
2
0
1
0
0
0
0
0
0
0
0
0
3
3
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
3
2
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
2
1
0
0
1
2
0
0
0
2
3
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
2
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
1
1
0
2
0
0
0
0
0
1
0
4
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
6
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
3
0
1
0
0
2
2
0
1
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
5
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
1
0
2
1
1
0
0
0
1
5
1
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
7
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
2
0
0
2
0
1
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
2
0
1
0
2
1
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
3
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
2
0
0
0
5
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
1
0
0
1
0
2
0
0
0
0
2
0
4
0
0
0
2
2
0
2
1
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
2
0
5
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
2
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
4
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
1
0
0
0
0
0
1
3
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
2
0
2
0
0
2
0
0
0
0
1
2
0
0
0
0
2
1
2
0
0
2
0
3
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
2
0
0
0
0
0
1
0
0
0
0
2
0
1
2
0
0
0
3
0
0
0
0
0
0
0
5
0
0
5
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
5
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
2
1
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
2
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
3
0
2
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
2
0
2
0
2
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
1
0
0
2
0
0
0
0
0
2
2
0
0
0
4
0
0
0
0
1
0
0
2
0
0
2
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
1
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
8
1
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
2
0
0
0
1
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
3
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
1
0
2
0
1
0
1
0
0
0
1
0
0
1
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
3
1
0
0
2
1
0
0
0
0
0
0
1
2
0
0
0
2
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
3
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
7
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
2
0
0
0
3
0
0
3
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
1
0
0
0
5
0
2
0
0
0
0
2
0
0
0
0
1
1
1
0
0
1
1
0
2
0
0
0
0
3
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
5
3
0
0
1
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
2
0
0
0
1
0
0
0
2
1
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
2
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
6
0
1
0
0
0
0
0
2
0
0
1
1
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
2
3
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
1
5
1
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
2
0
0
1
1
1
3
3
0
0
0
0
0
4
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
6
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
1
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
3
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
1
0
0
1
0
6
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
1
0
1
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
7
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
7
0
1
0
3
2
0
0
3
0
0
0
0
2
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
3
0
0
0
1
1
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
6
2
1
0
0
0
0
0
1
0
1
0
0
1
2
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
1
0
2
0
0
0
0
1
0
0
0
0
0
0
6
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
6
2
0
0
3
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
2
0
0
3
2
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
2
0
2
0
2
1
0
2
0
0
2
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
1
2
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
1
0
1
0
0
1
0
0
2
0
3
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
4
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
2
0
0
0
0
3
1
0
0
0
1
0
0
0
5
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
5
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
1
0
0
2
1
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
3
1
0
3
0
1
0
1
0
2
2
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
2
3
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
4
0
2
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
3
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
1
1
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
1
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
1
1
2
0
1
1
0
1
0
1
0
1
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
6
0
1
0
0
1
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
2
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
1
4
0
0
0
0
0
0
0
0
2
3
2
0
0
0
0
0
0
0
2
0
0
2
3
0
0
0
2
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
3
0
0
0
1
0
0
0
2
2
0
0
0
0
3
1
0
2
1
0
2
2
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
2
1
0
0
0
0
1
0
0
2
0
0
1
0
0
2
0
0
0
0
10
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
1
1
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
3
0
2
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
1
0
0
0
0
1
0
0
2
0
2
0
2
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
1
0
1
0
0
0
2
0
0
3
3
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
1
2
1
0
1
0
1
1
0
0
2
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
3
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
5
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
2
0
2
0
0
1
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
10
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
3
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
2
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
1
0
0
0
1
2
0
2
1
1
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
2
0
0
0
1
1
0
0
0
2
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
1
1
0
0
0
0
1
1
0
0
1
1
0
0
1
1
0
2
0
0
1
0
2
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
1
2
0
3
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
2
0
1
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
3
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
1
0
0
0
0
0
0
0
1
1
2
0
2
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
6
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
6
0
3
0
0
0
0
0
2
2
0
0
0
0
3
0
0
1
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
1
1
0
0
0
0
2
0
1
0
0
0
0
2
0
1
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
1
0
0
1
3
0
1
0
0
1
0
5
0
1
0
1
0
2
0
0
1
0
0
4
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
4
0
1
4
0
0
1
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
1
2
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
2
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
2
2
0
1
0
0
0
0
0
0
2
2
0
2
0
1
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
2
2
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
3
0
1
0
0
0
0
0
1
0
5
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
3
0
1
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
2
14
0
0
1
0
1
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
3
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
1
1
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
6
0
0
0
1
0
0
1
1
0
0
0
0
0
2
0
2
1
0
2
0
1
0
2
0
0
2
2
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
6
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
2
0
3
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
1
0
0
0
1
1
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
1
0
1
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
2
0
0
0
2
1
0
0
1
0
0
0
1
1
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
2
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
2
2
0
0
1
0
0
1
1
0
1
2
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
3
1
2
0
1
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
3
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
2
7
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
1
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
3
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
1
0
1
1
1
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
4
0
0
1
0
0
2
2
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
1
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
2
1
0
0
2
0
0
1
2
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
3
0
2
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
2
2
0
1
0
0
2
0
0
0
1
0
0
0
0
5
2
0
0
1
0
0
0
0
0
1
0
0
1
0
0
3
0
0
0
0
0
1
0
0
0
0
2
0
1
0
3
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
3
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
4
0
0
0
0
1
0
0
1
0
0
0
1
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
1
1
0
0
0
1
1
0
2
0
0
0
0
1
0
2
0
0
0
0
0
2
3
0
0
1
0
0
1
0
0
0
0
0
0
2
1
0
2
5
1
0
0
0
1
1
1
4
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
1
0
0
4
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
3
0
0
0
0
9
0
0
0
1
1
0
0
0
2
2
0
0
0
1
0
0
0
1
2
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
9
0
5
2
0
0
0
1
0
0
6
0
0
0
0
0
0
0
0
0
2
0
0
2
2
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
3
1
3
0
0
0
0
3
1
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
2
0
0
0
0
1
0
0
0
2
0
0
1
0
8
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
4
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
2
0
0
1
0
1
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
1
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
6
4
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
1
0
0
0
1
0
0
2
2
2
0
0
1
0
1
0
1
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
3
0
0
2
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
5
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
2
0
0
1
2
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
2
1
0
0
2
1
0
1
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
1
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
4
0
1
2
0
2
1
0
0
0
0
0
2
3
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
1
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
2
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
1
0
3
2
3
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
3
0
0
0
0
0
2
0
0
0
1
0
3
0
1
2
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
1
3
0
0
0
0
0
3
0
0
3
0
0
0
1
0
0
4
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
3
1
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
6
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
4
1
0
0
0
2
1
0
0
0
0
0
2
3
0
0
1
0
0
0
5
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
1
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
2
0
1
0
0
2
0
0
0
1
0
2
3
0
0
1
0
0
0
0
0
2
1
1
0
0
2
0
3
0
0
0
0
0
0
0
0
2
2
3
0
0
2
0
0
0
0
0
0
0
0
3
0
2
1
1
0
1
2
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
2
0
6
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
1
2
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
5
0
0
0
0
1
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
2
0
2
2
1
0
1
2
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
3
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
1
2
1
0
0
1
0
0
2
1
0
0
0
0
0
0
4
0
0
0
0
2
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
1
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
1
5
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
1
0
0
1
0
2
0
0
0
2
2
2
0
3
2
0
0
0
0
1
6
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
2
1
2
0
0
0
2
0
0
0
0
2
2
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
5
2
0
1
1
0
0
0
0
0
0
4
0
2
0
1
0
4
0
0
0
0
2
5
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
2
0
0
1
0
3
2
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
5
0
0
0
0
0
1
1
1
2
0
0
0
2
0
2
0
0
0
0
2
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
3
2
0
1
0
0
2
0
0
0
4
0
1
0
0
0
0
1
0
1
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
5
0
0
6
0
1
0
0
0
0
0
0
1
4
1
0
1
0
0
0
0
0
0
0
4
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
1
4
0
0
0
0
0
1
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
1
2
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
11
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
1
2
3
2
1
0
0
0
1
0
0
1
0
1
0
3
0
0
1
0
0
0
0
2
0
0
0
2
0
4
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
4
0
2
0
3
0
2
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
1
1
0
3
0
0
0
0
0
0
2
2
0
1
0
2
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
8
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
6
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
1
1
0
2
0
0
0
2
0
0
0
2
0
1
0
2
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
1
1
1
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
1
0
3
2
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
2
2
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
4
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
2
0
0
1
1
0
0
2
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
4
5
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
2
0
0
0
0
1
2
0
0
3
0
0
0
4
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
18
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
3
0
0
0
3
0
0
0
1
0
1
2
0
0
0
2
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
3
0
2
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
1
3
0
0
0
0
2
1
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
2
0
0
0
0
1
0
1
0
0
0
0
0
5
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
1
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
4
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
4
0
0
0
4
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
2
0
0
0
2
0
0
1
1
0
0
0
0
0
2
1
3
0
0
1
0
1
2
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
1
3
2
0
1
0
0
1
1
0
3
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
5
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
2
1
0
2
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
1
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
1
1
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
2
1
0
0
4
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
6
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
2
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
3
0
0
3
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
1
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
1
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
1
0
2
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
3
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
1
2
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
2
5
0
0
0
0
1
0
0
0
0
0
5
0
0
0
0
0
2
0
2
4
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
5
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
4
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
1
0
2
0
1
0
2
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
3
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
1
0
0
0
0
0
0
1
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
3
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
2
3
0
0
0
0
0
2
0
0
0
3
0
0
1
0
0
0
1
0
2
0
2
0
2
0
2
0
0
2
0
1
0
1
0
2
0
0
1
0
2
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
2
1
0
0
2
0
0
0
0
1
0
2
4
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
6
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
2
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
3
0
0
2
1
0
0
0
0
0
4
0
0
2
0
1
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
1
1
2
0
0
0
0
4
1
0
0
1
1
0
0
1
2
0
0
0
1
1
0
1
2
0
3
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
7
0
0
0
4
1
0
2
1
0
0
0
2
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
3
0
2
0
0
2
0
0
0
1
3
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
2
0
0
0
0
0
0
3
0
1
0
0
0
0
3
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
2
1
0
0
0
1
2
0
0
3
2
0
0
1
0
0
0
2
0
0
0
0
1
3
0
0
2
0
0
2
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
4
0
0
3
0
2
0
0
0
0
1
1
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
1
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
6
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
1
0
2
0
0
0
0
0
3
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
2
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
1
2
0
2
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
3
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
2
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
5
0
0
0
0
0
7
0
1
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
4
0
2
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
1
2
0
0
1
0
0
0
0
0
0
0
1
3
0
0
2
0
0
0
0
0
0
0
3
0
0
0
1
0
2
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
4
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
1
2
1
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
1
0
3
0
0
0
0
2
6
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
3
1
0
0
2
0
1
0
2
0
0
0
0
0
0
2
0
0
1
4
1
2
0
0
0
0
0
0
1
0
5
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
1
1
3
0
0
3
0
0
0
0
3
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
7
1
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
2
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
2
0
0
1
0
2
3
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
2
0
0
0
2
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
5
0
0
1
0
2
0
0
0
7
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
2
0
0
2
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
4
2
1
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
4
0
1
0
0
0
3
0
0
3
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
2
0
1
2
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
4
2
0
1
2
0
0
2
0
1
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
1
5
0
2
0
0
0
0
1
2
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
3
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
3
0
0
1
0
0
0
0
1
0
0
0
0
0
2
1
1
0
3
0
1
0
0
1
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
2
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
1
0
1
0
2
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
1
0
6
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
7
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
3
0
2
0
0
1
1
0
0
0
2
0
0
0
2
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
2
0
0
1
1
0
0
2
0
0
0
3
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
4
2
1
0
2
0
0
2
0
0
0
1
0
0
0
0
1
0
1
0
2
2
0
0
0
2
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
1
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
1
0
7
0
0
0
0
1
2
0
0
0
0
1
0
0
0
1
3
0
0
1
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
2
0
1
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
3
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
1
0
0
0
0
2
2
0
0
1
0
1
0
0
2
0
0
2
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
1
0
1
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
2
0
0
2
1
0
0
0
0
0
2
3
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
4
0
0
0
0
0
0
1
6
0
0
0
0
2
0
0
0
0
0
0
0
0
3
1
0
0
0
1
2
0
0
0
0
0
0
2
2
1
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
2
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
3
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
2
1
0
0
1
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
1
0
2
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
3
0
0
0
0
0
0
0
2
1
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
2
2
0
0
2
0
0
1
0
0
0
0
0
0
0
2
1
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
1
1
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
4
0
2
0
2
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
6
0
0
0
0
0
1
2
2
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
6
0
0
1
0
0
1
0
0
1
0
1
0
0
0
3
0
0
1
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
1
0
0
0
2
0
0
0
1
0
0
6
0
0
2
0
2
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
1
0
0
1
0
3
0
0
0
0
1
0
0
0
0
0
0
1
1
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
5
1
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
3
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
8
0
0
6
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
2
1
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
1
0
0
0
3
1
0
0
1
0
0
0
0
0
1
0
0
2
0
1
4
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
5
2
5
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
1
2
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
6
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
3
2
0
0
4
0
2
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
1
0
0
4
0
3
0
0
0
1
1
0
0
0
1
1
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
3
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
3
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
3
0
0
0
1
0
0
0
0
0
2
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
3
0
2
0
0
0
0
0
3
0
2
0
0
0
0
0
5
0
2
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
7
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
1
2
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
4
0
2
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
3
0
2
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
8
0
1
0
0
0
0
0
2
0
2
0
0
0
0
2
2
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
3
0
0
5
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
3
2
0
0
0
0
0
2
0
0
5
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
1
2
2
0
1
0
0
1
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
3
0
0
0
0
0
0
0
0
0
0
2
0
1
2
1
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
2
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
3
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
4
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
2
0
1
0
2
0
0
0
0
0
0
0
0
3
0
1
0
1
0
0
0
0
1
0
1
0
0
0
2
2
0
0
2
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
3
0
0
0
0
2
0
1
0
5
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
3
2
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
1
0
0
2
1
0
0
0
1
1
0
0
0
0
2
0
1
0
0
0
2
6
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
2
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
2
3
2
0
0
2
0
0
0
0
0
0
2
0
0
1
2
0
0
0
3
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
1
1
0
2
1
0
0
3
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
1
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
2
2
0
1
2
0
0
0
0
0
3
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
1
0
0
0
0
2
1
0
0
3
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
4
1
2
0
0
1
0
0
0
0
0
0
0
0
1
1
1
4
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
6
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
1
0
0
1
0
0
2
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
3
2
0
2
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
7
0
1
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
3
0
0
3
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
1
1
2
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
3
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
3
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
3
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
4
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
3
0
2
0
1
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
3
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
6
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
3
0
0
0
0
2
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
9
1
0
0
7
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
6
0
2
0
0
7
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
2
0
0
0
3
0
3
0
0
0
1
0
2
1
0
4
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
2
2
0
3
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
7
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
2
0
1
0
0
0
2
0
0
2
0
0
0
1
0
0
0
2
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
1
0
2
0
2
3
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
2
0
0
2
0
1
1
0
2
0
0
1
0
0
0
4
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
1
0
1
0
0
0
0
1
2
3
0
5
1
0
0
1
1
0
4
0
0
1
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
2
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
1
0
0
0
0
2
1
2
0
0
0
1
1
2
0
0
0
0
0
0
0
0
1
0
0
0
1
2
1
0
0
0
0
1
1
0
0
0
0
0
2
0
2
0
0
2
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
1
3
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
2
1
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
3
1
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
4
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
6
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
1
0
0
0
2
0
0
1
0
5
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
7
0
0
2
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
3
0
6
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
7
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
4
0
0
0
0
0
2
1
3
0
3
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
2
0
2
0
0
0
1
0
0
1
0
1
0
1
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
4
3
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
3
0
0
0
2
0
0
1
0
0
0
0
1
1
0
2
3
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
1
0
0
0
0
0
0
0
4
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
2
0
0
2
0
0
0
0
0
4
2
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
2
1
4
0
2
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
2
0
0
2
0
0
2
1
0
0
0
3
1
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
3
0
0
0
3
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
2
3
1
0
0
1
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
3
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
5
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
2
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
2
2
0
0
0
1
0
0
2
0
3
0
2
0
0
4
1
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
5
1
0
0
0
0
2
2
4
1
2
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
1
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
9
1
0
2
1
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
3
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
1
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
2
1
3
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
3
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
1
2
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
2
0
0
0
3
0
0
0
0
2
0
0
0
5
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
1
1
0
2
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
1
0
0
2
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
1
0
1
0
0
3
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
1
0
0
0
5
0
0
0
1
0
0
2
0
0
1
5
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
1
0
1
0
0
0
0
6
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
8
0
1
0
0
0
0
2
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
1
0
0
1
0
0
0
0
0
2
0
0
3
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
3
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
1
0
0
2
0
4
0
0
0
0
0
0
0
0
0
1
0
1
0
0
5
0
0
0
5
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
3
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
3
0
0
0
0
0
0
1
0
0
0
0
0
1
8
6
1
0
0
0
2
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
5
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
3
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
4
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
1
4
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
4
0
0
1
1
0
0
0
2
0
1
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
3
2
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
2
0
1
0
0
0
1
2
1
0
0
1
3
0
0
0
0
0
16
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
9
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
1
2
0
0
2
0
0
1
1
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
2
0
0
0
1
0
0
0
0
0
6
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
2
1
0
0
0
1
0
1
0
0
2
0
0
1
0
0
2
0
2
0
0
0
0
0
0
2
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
2
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
8
1
0
0
2
0
1
0
0
0
0
2
0
2
0
0
0
2
2
1
0
0
0
0
4
2
0
0
0
0
0
0
0
0
1
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
3
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
1
1
0
3
0
0
0
0
3
2
2
0
0
0
2
1
0
0
2
0
0
1
0
0
0
0
0
1
2
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
2
0
0
2
3
0
0
0
1
0
0
0
4
0
0
4
0
3
0
0
0
0
0
0
0
3
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
5
0
3
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
1
1
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
2
0
0
0
2
0
2
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
1
0
0
1
0
0
0
0
2
0
0
0
0
2
3
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
3
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
1
0
7
2
5
0
1
0
0
0
0
0
3
0
3
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
1
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
3
0
0
0
0
1
0
2
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
4
0
1
0
1
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
1
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
1
0
0
0
2
2
0
1
0
1
1
0
0
5
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
1
0
1
2
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
3
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
1
0
0
0
0
1
3
0
2
1
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
2
0
1
0
2
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
5
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
3
0
0
0
4
0
0
0
0
4
1
0
1
2
1
1
0
1
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
3
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
5
0
0
0
0
0
3
0
1
0
0
0
2
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
1
1
0
0
1
0
0
0
1
2
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
1
0
1
1
0
0
0
0
7
0
0
0
0
0
0
0
0
2
0
1
0
0
0
6
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
10
1
0
0
2
0
0
0
0
0
0
3
3
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
1
0
1
0
0
2
0
4
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
2
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
1
3
0
2
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
1
0
0
0
0
2
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
1
3
0
0
0
0
2
0
0
1
2
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
3
0
0
1
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
1
2
5
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
5
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
1
0
0
2
2
0
0
0
0
0
0
3
1
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
4
0
0
5
0
0
0
0
0
0
0
6
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
2
3
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
2
1
1
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
4
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
2
2
0
0
1
0
0
0
0
0
0
0
2
2
0
0
2
2
0
0
0
0
1
0
0
0
1
0
0
0
2
2
0
1
1
0
0
0
0
3
1
0
0
0
2
1
10
0
0
0
1
0
0
2
1
2
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
1
0
0
0
0
0
2
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
1
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
1
2
1
0
0
0
0
0
0
0
0
2
0
3
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
2
0
0
0
3
0
0
0
1
0
1
2
0
1
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
1
2
1
3
0
0
3
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
2
2
7
2
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
5
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
1
0
0
0
0
1
0
0
0
1
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
8
0
0
5
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
3
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
3
0
1
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
1
0
0
0
0
0
7
0
0
1
1
0
4
0
1
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
1
1
0
0
0
0
0
2
0
5
0
0
0
0
0
3
0
1
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
6
0
1
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
6
0
0
1
0
1
0
0
0
0
0
0
0
2
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
2
1
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
1
0
2
0
1
1
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
5
0
0
0
0
3
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
3
0
2
0
0
1
1
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
1
0
0
0
3
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
4
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
1
0
0
1
0
6
1
0
3
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
2
0
0
0
0
0
0
0
13
0
0
0
0
2
0
0
3
1
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
1
0
0
3
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
7
0
0
0
0
0
0
0
0
0
9
0
0
0
0
1
1
1
4
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
1
2
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
7
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
2
0
0
0
0
1
2
0
0
0
1
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
1
0
0
3
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
5
0
1
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
3
0
0
0
1
1
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
1
0
3
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
1
0
1
0
2
2
0
0
1
0
0
0
2
0
0
0
0
0
0
5
0
0
0
2
1
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
2
1
2
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
1
0
1
0
1
3
0
0
0
0
0
3
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
1
0
3
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
3
0
1
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
2
0
3
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
2
0
1
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
1
4
1
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
6
0
1
0
0
1
0
1
0
0
0
0
0
3
0
0
0
0
0
1
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
3
0
0
2
0
0
0
2
0
0
0
0
0
2
0
3
1
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
1
0
0
0
0
0
0
1
0
2
0
0
0
0
2
2
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
3
3
0
2
0
2
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
7
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
2
2
0
2
0
0
0
0
3
3
2
0
0
0
0
0
6
0
0
3
0
0
0
1
0
0
0
0
3
10
2
2
0
0
2
4
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
2
0
0
0
0
0
0
0
6
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
0
0
2
0
0
2
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
3
2
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
2
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
6
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
3
0
0
0
0
0
0
0
0
1
0
1
0
3
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
2
0
0
2
0
1
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
1
0
7
0
2
0
0
1
2
0
1
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
2
3
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
3
0
3
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
1
0
1
2
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
3
0
0
2
0
0
2
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
1
0
0
10
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
3
0
0
0
0
1
0
0
2
0
1
0
0
0
1
1
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
1
0
0
1
0
0
0
0
0
0
2
0
0
0
5
0
0
0
0
1
0
0
0
11
2
0
0
0
0
0
1
2
1
2
0
0
0
2
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
1
0
0
0
0
2
0
2
0
1
0
0
0
0
1
3
0
0
2
4
0
0
0
0
1
0
0
2
1
0
1
1
0
0
0
2
2
0
0
0
0
1
1
0
1
0
0
2
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
2
0
5
2
0
1
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
5
0
4
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
1
2
0
1
0
0
0
0
1
2
2
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
20
0
0
1
0
0
2
1
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
5
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
1
2
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
2
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
3
0
0
0
0
0
3
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
1
1
2
0
2
0
1
0
0
2
0
0
2
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
1
0
0
0
1
2
0
0
0
0
0
2
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
4
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
2
1
0
0
0
0
0
0
0
4
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
2
0
1
0
0
0
0
0
1
0
0
2
2
0
2
0
0
0
0
0
0
0
0
2
0
6
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
2
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
2
0
2
0
1
0
0
0
0
0
0
2
2
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
4
3
0
0
0
1
0
0
2
0
0
0
0
3
0
2
0
0
0
1
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
2
2
0
3
5
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
2
0
0
2
2
0
0
0
1
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
3
2
0
0
1
0
0
0
2
0
1
2
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
2
0
0
2
0
0
2
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
3
0
2
0
10
0
4
0
4
2
2
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
1
3
0
2
0
1
0
1
1
0
3
0
1
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
2
6
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
2
0
0
0
0
1
2
3
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
1
0
1
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
6
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
1
0
0
1
3
3
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
1
6
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
2
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
1
0
0
2
0
8
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
1
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
3
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
1
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
2
0
1
1
0
0
0
5
0
0
0
0
0
0
0
0
2
0
0
0
18
0
0
1
0
0
0
1
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
2
0
0
3
0
1
0
0
2
0
0
0
0
2
0
2
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
2
1
2
1
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
1
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
1
1
0
3
0
0
8
1
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
1
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
1
0
0
2
1
0
0
0
4
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
5
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
1
0
0
0
2
0
2
0
0
0
0
0
1
2
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
4
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
1
11
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
4
4
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
1
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
6
0
0
0
0
0
0
3
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
4
0
0
0
0
2
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
2
2
2
0
0
0
0
0
1
0
0
0
0
1
0
3
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
2
0
0
1
0
0
0
0
1
0
0
0
0
2
0
1
0
0
1
0
0
0
0
2
3
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
2
2
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
1
2
5
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
1
3
1
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
3
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
3
1
0
2
0
0
5
3
0
0
0
0
0
0
2
0
1
2
0
5
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
3
2
0
0
6
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
1
0
2
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
3
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
2
2
0
0
0
0
0
0
2
2
0
0
1
0
0
2
2
1
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
6
0
0
1
0
2
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
3
0
0
0
1
0
4
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
5
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
3
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
3
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
1
0
0
3
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
3
0
1
0
0
0
0
2
0
0
0
0
5
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
3
1
0
0
0
0
0
0
0
2
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
4
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
8
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
1
1
1
0
2
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
2
3
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
5
2
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
5
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
1
0
1
1
2
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
3
0
0
0
0
0
0
0
0
2
3
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
1
1
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
1
1
1
0
0
2
0
1
2
0
2
0
0
0
0
0
0
2
0
0
0
1
2
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
1
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
5
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
1
0
0
0
0
4
2
0
0
0
2
1
1
0
0
0
0
0
5
2
0
0
3
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
2
3
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
7
1
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
1
1
0
0
0
0
2
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
4
0
2
0
0
1
0
2
0
0
0
0
1
0
0
0
2
0
2
0
0
2
0
7
0
0
0
0
0
1
0
12
0
0
3
0
0
0
0
0
0
0
2
1
2
0
0
0
3
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
2
1
1
1
1
0
0
0
0
0
0
0
0
1
1
3
2
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
1
2
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
3
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
2
1
2
0
0
0
2
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
3
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
2
3
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
2
0
1
2
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
2
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
2
0
1
2
0
0
0
2
3
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
2
0
2
1
2
0
2
0
0
0
0
0
0
0
6
0
0
1
0
0
0
2
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
2
0
0
0
0
0
0
2
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
4
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
3
0
1
3
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
2
0
0
0
0
0
0
2
1
0
1
0
0
5
2
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
4
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
3
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
3
0
0
0
5
1
0
0
1
0
0
0
3
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
2
1
0
0
0
3
0
0
0
2
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
1
0
2
5
2
1
0
1
0
0
0
0
0
1
1
0
2
0
0
0
1
0
0
0
2
0
0
2
3
0
0
0
2
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
2
0
0
0
2
1
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
4
2
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
1
0
1
1
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
2
0
3
0
0
3
1
0
0
0
0
2
0
0
2
1
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
1
2
0
3
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
2
3
0
2
2
3
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
1
0
3
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
9
0
0
0
0
0
0
0
3
0
1
0
1
1
0
0
0
0
0
0
0
3
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
2
0
0
0
0
0
0
0
2
0
0
0
3
0
1
0
0
2
0
8
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
1
0
0
0
0
0
2
0
1
0
0
3
0
0
1
0
0
1
0
2
0
0
2
1
0
1
0
0
0
1
0
2
0
1
0
0
0
0
1
0
2
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
4
1
0
0
1
0
0
0
0
0
1
0
3
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
2
0
2
0
0
2
1
0
3
1
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
2
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
1
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
2
4
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
2
0
0
2
0
1
0
1
0
0
0
0
0
3
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
5
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
3
1
0
1
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
2
0
0
1
0
0
0
0
2
0
0
2
5
0
1
0
3
0
0
0
0
0
0
0
1
0
1
3
0
1
0
2
3
0
2
0
0
5
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
1
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
1
0
0
2
3
0
0
0
4
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
2
0
0
0
0
2
0
0
0
0
1
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
1
2
0
4
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
4
1
0
0
0
0
1
0
1
0
4
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
2
1
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
1
0
1
0
0
0
0
4
1
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
1
0
1
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
11
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
3
0
0
3
0
0
2
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
6
0
0
0
5
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
1
0
0
0
2
3
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
3
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
4
0
0
0
1
1
0
0
0
0
0
0
3
0
2
1
0
1
0
0
6
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
1
2
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
2
2
0
0
0
0
0
0
0
0
3
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
2
0
0
0
0
1
0
2
0
1
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
1
0
2
0
2
0
0
0
0
0
0
1
0
2
0
1
2
0
0
0
1
0
0
1
1
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
2
0
1
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
1
0
2
0
4
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
1
0
0
0
0
2
2
0
0
0
0
1
1
0
0
2
1
5
2
2
0
0
0
0
0
0
0
1
1
0
0
0
0
7
0
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
1
0
0
2
0
0
0
2
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
2
1
0
2
2
5
0
0
0
0
1
0
0
1
0
0
0
0
3
0
1
0
0
1
3
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
2
0
3
0
0
0
1
1
2
2
1
0
1
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
10
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
2
0
0
1
0
1
0
0
2
1
0
1
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
8
2
0
1
0
0
0
0
6
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
3
1
3
0
0
0
0
0
2
0
1
0
2
0
0
0
2
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
2
0
1
1
0
0
0
1
0
1
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
2
2
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
3
3
7
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
1
0
1
1
0
0
0
0
0
4
0
2
0
0
1
0
1
0
0
0
0
0
0
0
2
0
2
1
0
3
0
0
0
0
0
0
2
4
4
0
1
0
1
0
0
0
3
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
2
0
0
2
0
1
2
0
0
0
0
0
3
0
0
3
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
3
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
2
2
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
2
0
0
2
1
0
2
3
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
4
0
3
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
4
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
2
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
8
1
3
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
5
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
2
1
0
0
1
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
1
0
0
1
0
1
3
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
5
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
3
0
0
1
0
0
0
0
0
1
1
0
14
0
1
1
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
1
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
3
1
7
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
1
4
0
0
0
0
1
2
0
0
0
1
4
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
2
2
0
1
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
3
0
0
0
2
7
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
1
1
0
2
5
0
1
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
3
0
0
2
0
0
0
0
4
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
3
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
1
0
1
0
0
0
2
1
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
0
0
3
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
1
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
1
0
0
0
2
1
0
0
2
2
0
1
0
0
0
0
0
0
1
2
5
0
1
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
2
0
2
3
5
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
1
1
1
0
0
0
1
0
0
0
4
0
2
0
0
0
3
0
1
0
4
0
0
0
0
0
2
0
0
0
0
2
1
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
2
0
1
7
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
1
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
8
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
5
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
2
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
8
0
1
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
1
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
2
0
0
0
2
0
0
0
0
2
1
0
0
0
0
2
0
1
0
0
2
1
1
0
0
0
0
1
2
1
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
2
1
0
0
0
1
1
0
1
1
0
1
1
0
3
0
0
3
0
1
2
0
0
0
2
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
1
2
0
0
1
0
0
2
2
0
0
3
2
0
0
2
0
0
0
0
0
0
1
0
1
0
1
1
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
1
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
2
2
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
3
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
5
2
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
2
1
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
2
8
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
5
0
0
0
0
0
1
2
0
0
0
0
0
0
1
1
2
0
2
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
2
1
2
2
0
2
1
0
0
0
0
3
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
4
1
3
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
2
0
2
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
7
0
0
2
0
0
0
2
0
0
0
1
3
0
0
6
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
1
0
1
0
2
0
0
0
0
2
0
1
2
0
0
0
2
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
2
3
2
1
3
0
2
0
0
1
0
0
2
0
0
0
0
0
0
1
1
0
3
0
1
0
2
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
1
1
0
0
1
0
0
1
0
0
1
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
5
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
2
0
0
3
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
2
0
0
0
2
2
0
1
2
1
0
0
0
1
0
1
0
0
0
0
0
1
0
5
0
0
0
0
0
1
2
2
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
3
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
1
0
1
0
1
0
0
0
2
0
0
1
7
0
0
1
0
0
1
1
0
0
0
0
1
1
0
0
0
1
2
0
2
1
0
1
0
0
0
0
0
1
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
9
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
1
1
1
2
0
0
0
0
0
1
0
2
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
5
0
1
0
0
0
3
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
1
1
0
0
0
0
0
2
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
1
0
0
1
1
0
2
0
1
1
0
0
1
0
0
0
0
0
1
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
2
2
0
0
0
0
0
0
0
3
0
0
2
3
0
5
6
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
1
2
0
1
0
0
0
0
0
0
2
0
0
0
1
0
1
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
3
0
0
0
0
1
0
2
0
3
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
2
0
1
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
4
0
2
0
2
0
0
1
1
0
0
1
0
0
0
0
1
2
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
1
2
0
1
0
2
0
0
2
2
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
1
0
0
0
0
0
0
0
2
0
2
2
2
0
0
0
0
1
1
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
2
2
0
0
0
0
2
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
2
2
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
1
2
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
2
2
2
0
0
0
2
2
0
1
0
0
0
0
3
0
1
0
0
0
0
4
0
1
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
1
2
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
1
0
2
0
0
2
0
0
0
0
0
0
1
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
1
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
2
0
2
0
2
0
0
0
0
2
0
1
1
2
5
0
1
1
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
4
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
1
4
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
4
0
0
0
0
1
2
0
0
0
0
10
1
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
1
0
1
1
0
2
0
0
2
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
2
0
0
3
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
2
2
1
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
1
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
1
2
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
4
0
0
2
0
0
0
1
5
1
6
0
0
0
2
0
0
0
0
0
0
6
0
0
0
0
1
0
0
0
2
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
2
0
1
0
0
0
0
2
3
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
4
0
0
2
0
0
0
2
0
0
0
1
2
0
0
5
0
1
0
2
2
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
3
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
3
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
1
1
0
0
2
0
0
0
1
7
3
0
0
0
0
1
0
0
0
0
0
6
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
4
0
0
0
5
0
0
0
1
2
0
0
0
2
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
2
1
0
1
0
1
0
0
0
0
0
1
0
0
0
6
0
4
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
8
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
3
2
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
1
1
0
3
0
0
0
2
0
0
0
0
0
0
2
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
4
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
1
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
4
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
2
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
1
0
2
0
0
1
0
2
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
2
0
2
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
4
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
2
0
0
2
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
4
6
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
1
1
1
0
2
0
1
0
0
0
2
0
0
2
0
2
0
0
1
1
1
0
0
0
3
2
0
3
0
0
1
1
1
0
0
0
0
0
0
1
6
3
0
0
0
2
1
0
0
0
0
1
1
0
2
1
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
2
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
5
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
1
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
2
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
2
0
3
0
0
0
0
0
0
7
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
9
4
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
2
0
0
2
0
1
2
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
1
2
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
1
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
2
3
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
1
0
3
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
6
1
1
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
5
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
2
0
0
0
0
1
0
2
1
0
0
0
0
0
1
0
6
2
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
6
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
2
0
1
2
0
0
2
0
5
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
1
3
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
5
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
6
0
0
2
0
0
0
0
0
0
0
2
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
8
4
1
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
4
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
3
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
3
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
4
0
0
0
2
0
0
0
0
2
0
0
2
1
1
3
2
0
1
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
3
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
3
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
5
0
0
1
2
3
0
0
2
0
0
1
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
4
0
2
0
0
0
0
0
0
0
4
1
2
0
0
0
0
0
1
4
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
2
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
2
3
2
0
0
0
2
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
2
1
0
0
0
0
2
2
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
1
0
2
0
0
1
1
0
2
0
0
2
0
0
0
0
2
0
3
0
0
0
0
0
0
1
0
0
3
0
1
0
0
2
0
0
1
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
1
2
2
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
1
0
2
2
0
0
0
2
0
0
1
0
0
0
0
0
3
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
2
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
8
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
2
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
1
0
0
0
0
2
0
0
0
8
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
4
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
2
1
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
1
2
0
0
1
0
0
1
0
0
0
0
3
0
0
0
3
1
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
2
2
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
2
1
2
0
1
0
0
1
0
1
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
3
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
1
0
0
1
0
1
2
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
1
5
1
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
4
0
0
0
0
0
1
2
0
1
0
1
0
1
0
0
0
0
3
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
3
0
1
2
0
2
0
0
0
0
0
3
1
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
3
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
2
0
0
0
0
0
0
2
2
0
1
0
0
0
0
1
0
0
1
0
1
0
3
0
0
1
0
0
2
2
0
0
1
2
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
5
0
0
0
0
1
0
1
2
0
0
0
5
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
4
0
3
2
0
2
0
2
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
5
0
2
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
1
1
0
0
0
1
0
2
0
0
0
0
0
0
1
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
2
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
1
0
2
0
3
0
0
4
0
0
0
0
0
0
0
0
4
0
0
2
0
1
0
0
2
0
1
1
0
0
0
0
1
0
0
0
1
4
1
0
0
0
1
0
0
0
2
0
0
0
2
1
0
0
2
0
3
0
0
5
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
1
1
1
0
2
0
0
0
1
0
0
0
0
1
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
1
0
5
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
3
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
3
1
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
2
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
2
6
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
6
0
2
1
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
2
0
0
1
0
0
4
0
1
0
0
0
0
0
2
3
0
0
1
0
1
0
0
1
0
1
0
2
1
0
2
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
1
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
4
0
0
0
0
0
0
1
1
1
0
0
0
1
1
1
0
2
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
2
0
0
0
0
0
0
2
0
0
1
0
1
0
1
1
3
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
3
0
0
0
0
0
1
0
0
0
2
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
5
0
0
2
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
2
1
2
0
1
0
0
0
3
0
1
0
0
0
0
2
0
2
0
2
0
0
0
2
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
5
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
1
0
0
1
2
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
1
1
0
0
0
0
2
0
0
0
1
2
0
0
0
1
0
0
1
0
0
0
0
0
4
0
0
0
1
0
1
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
1
0
0
0
0
0
4
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
1
1
3
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
1
6
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
4
0
3
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
4
0
0
1
2
2
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
6
0
2
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
1
1
1
3
0
0
3
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
4
3
2
0
2
0
1
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
3
0
0
2
0
0
0
2
0
1
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
1
0
0
2
0
0
2
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
5
0
1
0
0
0
0
0
7
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
1
0
3
0
0
0
2
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
1
0
1
1
0
0
4
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
1
1
0
0
1
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
1
2
0
1
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
1
1
1
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
3
1
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
2
0
0
1
0
1
0
2
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
7
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
2
0
2
1
0
0
0
2
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
3
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
4
0
2
0
0
3
0
0
0
0
0
0
0
2
0
0
0
2
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
2
2
0
0
0
2
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
1
2
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
7
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
1
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
5
2
0
0
0
0
0
1
2
1
0
0
0
0
0
10
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
1
3
2
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
7
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
5
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
5
0
0
0
0
1
3
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
8
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
2
5
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
3
0
0
0
0
3
0
0
7
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
3
0
0
0
0
1
5
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
3
0
0
0
0
1
0
0
3
0
0
2
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
3
0
0
2
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
1
0
0
2
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
2
2
0
0
0
0
3
0
0
0
0
0
2
1
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
1
3
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
3
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
3
2
0
0
0
1
0
0
0
0
0
1
2
0
1
0
1
2
0
0
0
1
0
2
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
1
1
1
1
0
0
0
0
1
0
0
0
0
1
1
2
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
3
2
0
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
1
0
0
0
1
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
2
0
0
2
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
6
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
4
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
2
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
1
0
0
2
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
2
0
1
0
0
1
0
1
0
1
1
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
3
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
2
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
1
0
0
3
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
11
0
0
1
1
0
0
2
0
0
0
0
0
0
2
5
0
0
1
0
0
0
0
1
0
0
5
0
0
0
0
0
0
2
1
0
1
1
0
0
0
0
8
0
0
0
1
0
0
0
0
0
1
0
7
0
0
0
0
0
0
1
0
0
2
0
2
1
0
0
0
0
4
1
0
11
3
0
0
1
2
1
3
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
2
0
0
0
4
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
1
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
1
4
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
2
0
1
1
0
0
2
0
0
0
0
1
0
2
0
0
0
1
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
2
0
0
1
1
0
2
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
1
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
1
0
1
1
1
0
1
0
0
0
0
0
0
2
0
0
0
4
2
0
2
0
2
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
9
0
4
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
2
0
2
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
2
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
1
0
0
0
1
2
0
1
0
0
0
2
2
0
1
0
0
0
0
0
2
0
0
0
6
1
0
0
1
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
3
0
1
0
2
0
0
1
0
0
3
0
0
0
0
2
0
0
7
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
1
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
7
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
3
0
0
0
0
0
1
0
1
0
0
0
0
2
0
2
1
1
0
1
1
0
2
1
2
2
0
0
0
1
1
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
2
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
3
0
0
1
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
1
2
2
0
0
2
0
0
0
0
5
0
0
0
0
0
0
0
0
0
1
0
1
1
2
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
2
0
0
0
0
4
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
2
6
1
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
4
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
1
0
8
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
9
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
3
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
2
0
0
5
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
4
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
1
0
0
1
0
0
3
0
0
1
0
0
0
0
0
0
0
6
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
7
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
2
1
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
3
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
2
0
0
1
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
2
0
2
0
1
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
2
1
2
0
2
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
3
0
0
1
0
0
0
0
2
0
4
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
2
0
2
0
12
0
0
0
0
7
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
5
0
0
1
0
0
0
1
2
2
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
2
0
2
0
2
2
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
2
1
3
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
6
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
12
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
3
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
2
2
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
1
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
1
0
1
4
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
3
0
0
0
0
0
0
0
2
2
3
0
0
0
1
1
0
0
0
3
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
2
0
0
0
0
3
0
0
3
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
3
0
1
1
0
0
2
0
0
2
0
1
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
2
0
0
0
1
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
1
0
3
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
2
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
3
0
1
0
0
0
0
0
2
0
0
0
0
2
1
0
2
0
0
0
0
5
0
0
0
0
0
0
0
0
1
0
8
0
0
0
0
0
0
0
0
1
1
0
0
0
4
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
1
0
0
2
0
2
0
2
1
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
4
2
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
9
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
2
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
1
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
3
1
0
2
0
0
0
0
1
1
0
0
2
0
0
0
0
2
0
0
0
0
3
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
2
1
0
0
0
0
0
2
2
0
7
1
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
4
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
1
0
0
1
0
0
0
3
0
0
0
2
0
0
0
0
0
1
5
0
0
0
0
0
2
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
3
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
2
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
3
0
0
1
0
0
0
0
0
5
1
0
0
1
0
0
1
0
1
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
2
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
2
2
0
0
0
0
0
0
0
4
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
1
2
0
0
0
0
0
0
7
2
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
2
1
2
0
0
0
0
0
1
2
0
1
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
3
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
2
2
2
2
0
0
0
0
1
0
0
0
0
6
0
0
2
0
0
9
0
0
0
3
2
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
1
3
0
0
0
0
2
0
0
0
4
0
1
0
0
0
0
0
1
0
1
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
4
1
0
0
1
0
3
2
2
3
0
1
0
0
2
2
0
2
0
0
5
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
1
0
0
0
0
2
2
0
0
0
0
4
1
2
0
0
0
0
0
2
0
0
0
0
2
1
0
4
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
2
0
1
2
4
1
0
0
0
2
1
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
1
0
1
0
0
0
2
0
2
0
2
0
0
0
0
1
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
1
0
0
4
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
3
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
1
0
5
0
0
0
3
2
0
0
0
0
0
2
1
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
3
1
0
1
0
1
0
1
1
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
3
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
4
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
3
1
1
0
0
0
0
0
2
0
2
0
0
1
3
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
3
0
0
0
0
0
0
2
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
1
0
2
2
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
2
0
0
1
1
0
0
0
1
2
0
0
0
0
1
1
0
0
0
0
0
0
1
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
1
1
0
3
0
0
0
0
0
0
1
2
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
2
0
0
0
5
0
0
1
0
0
0
0
0
1
2
0
2
2
0
0
0
2
2
0
5
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
4
0
1
0
0
2
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
3
0
0
0
6
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
2
0
0
0
0
2
6
0
0
0
0
0
2
0
2
2
0
7
0
0
0
0
0
2
0
2
1
0
0
0
0
0
1
0
1
2
0
2
0
0
2
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
4
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
0
3
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
5
0
0
0
0
0
1
0
0
0
0
0
0
0
1
6
0
0
0
0
0
0
0
0
0
0
1
3
1
1
0
0
1
0
0
2
1
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
2
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
2
2
0
0
0
2
1
0
0
0
0
0
4
0
0
0
0
2
1
1
2
3
0
1
0
2
0
0
0
0
0
0
0
0
0
3
2
0
2
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
1
1
0
0
0
2
1
1
0
0
1
0
2
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
2
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
4
0
0
0
0
0
0
0
1
0
1
1
0
2
0
0
0
2
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
2
3
3
0
0
5
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
2
0
0
0
0
3
0
0
3
0
1
0
3
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
5
0
0
0
0
0
0
2
0
0
2
1
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
2
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
1
1
1
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
2
1
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
4
0
1
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
4
0
0
0
0
0
2
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
1
1
0
0
0
0
1
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
4
0
0
0
0
0
1
8
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
3
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
1
0
1
5
0
0
0
2
2
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
1
3
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
3
0
0
3
2
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
1
1
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
4
3
0
0
0
0
0
2
3
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
3
1
0
0
0
0
4
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
1
0
0
4
0
0
0
0
1
0
0
0
3
0
0
0
0
1
0
0
4
0
0
0
0
0
2
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
1
0
0
1
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
3
1
0
0
0
1
0
0
0
0
1
0
3
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
2
0
0
3
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
2
2
0
0
3
0
2
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
2
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
2
0
3
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
1
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
3
0
0
0
0
3
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
1
0
0
0
0
2
2
0
1
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
5
6
0
0
10
0
7
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
2
0
1
3
0
1
0
5
0
0
0
0
0
1
0
0
0
0
0
1
0
0
4
2
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
2
0
0
1
4
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
2
0
0
1
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
1
0
0
0
0
0
0
0
1
0
0
6
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
5
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
7
0
0
1
0
0
0
2
0
0
0
1
2
0
1
0
0
0
0
2
0
0
0
0
1
2
0
1
0
8
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
6
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
1
1
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
2
0
0
0
0
4
2
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
2
0
1
0
0
0
0
1
2
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
4
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
4
0
0
4
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
3
0
0
0
1
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
2
0
0
3
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
3
0
0
2
0
1
0
2
0
1
0
0
0
0
0
0
3
0
0
0
1
0
1
0
0
0
0
1
0
2
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
5
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
2
0
0
0
1
4
0
0
0
0
0
1
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
6
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
1
0
0
0
2
0
0
0
0
3
0
0
1
0
1
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
2
0
4
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
5
2
1
0
0
3
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
11
0
0
0
0
1
0
0
1
0
0
1
2
0
2
1
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
1
5
0
1
2
0
0
0
0
0
0
0
0
0
0
5
2
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
3
0
1
0
0
0
0
1
1
0
2
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
3
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
3
0
0
0
0
0
0
0
0
1
0
2
1
2
0
0
2
0
2
0
0
1
2
0
0
0
0
0
0
0
3
0
2
0
0
1
1
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
5
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
2
0
0
0
0
0
0
1
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
3
1
0
1
0
0
0
2
0
1
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
1
2
0
1
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
1
0
3
2
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
3
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
1
0
0
0
0
1
4
0
0
0
0
3
0
5
1
2
4
0
1
0
0
0
0
1
2
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
4
1
0
0
0
0
0
0
0
0
0
2
3
0
0
2
0
0
1
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
3
1
0
0
2
4
0
3
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
5
3
1
0
2
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
8
2
0
0
2
0
0
0
0
0
0
2
0
0
0
1
1
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
4
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
2
1
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
5
1
0
0
0
1
3
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
2
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
2
1
1
6
0
0
0
0
0
1
0
1
0
0
0
0
2
0
2
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
2
1
0
0
0
3
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
2
1
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
2
0
0
3
2
1
0
0
3
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
1
0
2
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
3
3
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
4
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
2
0
0
0
2
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
1
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
2
3
0
0
1
0
2
0
0
1
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
7
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
2
2
4
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
4
0
4
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
3
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
5
0
1
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
1
0
4
0
0
2
0
4
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
2
1
0
0
0
0
0
0
0
3
1
1
0
0
0
0
0
0
0
1
1
2
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
1
0
0
0
2
0
3
0
0
0
2
0
0
0
0
4
2
0
4
0
2
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
4
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
5
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
3
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
4
0
0
0
0
0
0
0
2
0
0
0
0
4
0
1
0
0
0
0
0
0
0
1
0
1
0
4
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
5
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
4
1
0
0
0
1
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
2
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
1
1
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
2
0
3
0
0
0
2
0
0
1
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
2
2
0
0
0
0
5
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
2
0
2
0
1
0
2
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
16
0
3
0
0
1
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
8
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
1
0
0
0
0
0
2
2
0
1
0
2
0
0
0
1
0
0
3
0
0
0
1
0
0
1
2
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
2
2
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
2
1
0
0
0
0
2
0
0
0
1
0
0
1
2
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
3
1
0
1
0
5
0
0
0
0
0
0
0
5
1
0
0
0
1
0
2
0
0
3
0
0
2
0
0
0
0
2
0
0
0
2
0
2
1
0
4
1
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
2
0
1
0
2
0
0
0
0
3
0
0
0
0
2
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
6
0
2
0
0
0
0
2
2
2
0
0
0
1
0
0
1
0
0
0
0
1
0
1
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
2
0
1
0
0
0
2
0
0
9
0
1
0
0
1
1
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
2
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
1
0
0
0
3
0
2
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
1
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
1
0
2
2
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
3
0
2
0
0
0
0
2
0
1
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
5
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
1
0
0
1
1
2
0
0
0
0
0
3
0
1
0
2
1
0
2
0
1
0
0
0
0
0
0
0
0
0
4
0
1
0
2
0
2
0
0
4
0
0
0
0
4
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
2
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
4
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
2
0
2
0
0
0
1
1
0
2
0
2
0
0
0
1
2
1
1
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
1
0
2
2
0
1
0
0
0
0
0
0
0
3
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
3
0
0
0
1
0
1
0
2
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
1
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
2
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
6
0
4
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
7
0
0
0
3
0
0
0
2
0
2
0
0
0
3
0
0
6
0
0
0
2
1
1
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
1
3
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
2
0
3
0
1
0
1
1
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
2
1
0
0
0
2
0
1
0
0
2
0
0
0
0
0
9
0
0
0
2
2
1
0
0
0
0
0
0
0
0
1
1
0
0
0
3
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
1
0
2
2
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
3
4
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
2
3
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
1
0
1
2
0
0
1
0
0
0
0
0
1
0
0
1
2
1
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
1
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
1
0
0
2
4
2
0
0
0
0
0
0
3
0
0
1
0
0
0
1
0
0
0
0
2
0
1
0
1
1
0
0
1
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
3
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
9
0
0
0
2
0
1
3
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
2
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
1
0
2
0
0
1
0
0
1
1
0
0
1
0
1
0
1
0
1
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
3
0
0
0
0
0
2
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
3
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
4
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
3
0
0
2
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
4
0
2
0
0
0
0
0
0
4
0
0
0
0
1
0
1
2
2
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
2
0
0
1
2
1
0
0
0
0
1
1
0
0
2
0
1
3
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
2
1
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
1
2
0
0
1
0
0
2
1
1
1
0
1
1
0
2
0
0
0
5
0
2
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
1
0
0
0
0
3
0
0
1
1
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
3
0
0
1
0
4
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
1
3
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
5
3
2
2
0
1
0
0
0
0
0
0
0
0
0
3
0
0
3
2
1
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
1
0
0
1
1
2
0
0
1
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
1
2
0
1
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
2
1
2
0
0
0
0
0
0
0
0
1
7
0
0
0
0
0
0
0
0
0
0
2
1
1
1
1
0
0
0
0
0
1
1
2
0
1
0
2
1
0
0
0
2
0
0
0
0
1
0
0
0
1
0
2
2
1
0
0
0
0
0
0
0
0
3
0
1
0
0
2
0
0
2
1
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
3
1
0
1
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
1
1
0
0
0
3
0
0
2
0
1
0
0
2
0
2
1
1
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
3
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
1
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
4
1
0
0
0
0
0
0
2
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
5
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
5
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
3
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
1
1
0
0
0
1
1
3
2
0
0
2
0
2
2
0
0
0
0
2
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
2
0
0
1
0
0
0
2
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
1
1
0
2
0
0
2
0
0
3
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
2
0
2
1
0
3
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
6
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
1
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
8
2
0
0
2
0
2
0
1
0
0
2
0
0
0
0
0
1
0
2
0
2
0
0
0
2
0
0
3
2
0
1
0
1
0
0
0
1
0
2
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
2
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
1
0
2
0
0
2
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
1
1
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
4
2
0
3
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
2
0
0
2
0
0
0
0
0
0
1
1
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
3
0
0
0
0
3
0
1
0
0
0
0
0
0
2
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
4
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
1
0
0
0
0
0
1
0
0
0
6
2
0
2
1
3
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
1
0
3
0
0
1
0
0
0
1
0
2
0
1
2
1
0
3
0
0
0
0
1
0
1
0
0
0
0
0
0
0
4
2
0
2
0
2
0
2
1
0
0
0
0
0
0
5
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
2
0
2
2
0
0
0
0
1
1
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
2
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
2
1
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
3
1
0
0
0
0
0
0
0
1
2
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
1
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
5
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
2
0
0
0
3
0
0
1
2
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
1
2
0
1
0
0
0
1
0
2
1
0
0
0
2
0
0
3
0
1
0
3
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
4
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
2
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
3
0
2
0
0
0
0
2
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
1
3
1
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
4
1
3
5
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
1
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
1
3
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
1
0
0
0
2
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
2
0
2
2
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
2
0
0
0
0
5
0
0
2
0
0
0
0
0
0
0
0
0
1
1
2
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
1
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
7
0
0
0
0
1
0
0
1
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
2
0
1
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
4
0
3
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
2
2
0
3
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
1
0
0
0
3
0
0
0
1
3
1
1
1
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
1
0
0
1
2
0
0
1
0
0
0
0
0
0
0
1
0
0
3
0
0
2
0
0
2
0
1
0
0
0
0
1
0
0
1
0
0
0
0
2
0
1
1
0
1
0
0
2
0
0
2
0
3
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
1
1
1
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
2
1
1
2
0
1
0
0
0
0
0
1
0
2
3
0
0
0
0
2
0
0
0
0
0
1
0
0
2
1
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
9
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
1
0
0
1
0
2
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
1
1
0
6
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
1
0
0
1
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
3
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
3
8
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
5
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
6
0
0
0
0
0
0
2
0
1
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
1
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
2
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
1
0
1
0
1
1
0
1
0
1
1
0
3
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
5
1
2
1
0
0
0
0
0
0
0
2
1
0
4
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
3
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
2
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
2
1
0
1
0
0
2
0
2
0
0
0
0
0
0
0
5
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
4
0
0
1
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
4
0
0
1
0
1
0
0
1
0
0
0
1
2
0
2
0
0
1
0
0
0
0
0
0
0
0
3
1
0
2
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
5
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
3
2
0
0
4
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
5
0
1
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
2
0
0
0
0
2
2
0
1
0
0
3
0
1
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
3
1
2
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
2
2
0
0
0
0
2
2
0
1
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
1
0
1
0
0
0
0
1
0
0
0
2
0
0
1
1
2
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
4
0
1
0
0
0
0
0
3
3
0
0
0
0
0
0
0
0
0
3
2
0
0
1
0
1
0
1
2
2
0
0
0
0
0
0
0
1
0
0
0
1
2
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
3
0
0
0
0
0
2
0
0
2
1
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
2
0
2
0
0
0
0
0
1
0
0
1
2
0
1
0
1
1
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
1
0
0
5
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
2
0
0
1
3
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
1
0
2
2
1
0
0
0
0
0
0
0
1
0
1
7
1
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
3
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
2
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
3
0
2
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
3
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
7
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
1
0
2
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
1
0
0
0
2
0
3
2
0
0
1
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
1
2
0
1
0
0
0
3
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
3
0
0
0
2
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
3
3
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
1
2
0
0
1
0
1
0
1
0
2
4
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
2
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
2
0
1
1
0
0
0
1
3
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
2
0
1
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
2
1
1
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
3
0
0
0
0
5
0
0
0
4
1
0
0
0
0
0
0
0
0
1
2
3
2
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
2
1
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
7
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
2
1
0
0
0
1
1
0
0
0
2
0
0
1
3
0
0
2
0
1
2
3
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
2
0
3
0
1
0
0
2
1
0
2
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
7
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
1
1
0
0
1
0
3
0
0
3
0
0
0
2
0
0
0
0
1
0
2
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
2
3
0
1
0
0
0
0
2
1
2
0
0
0
0
1
0
0
0
1
0
2
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
5
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
2
4
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
1
0
3
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
1
0
4
3
1
0
3
2
0
0
0
1
0
0
1
0
3
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
3
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
3
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
1
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
1
0
0
0
0
1
0
0
0
4
2
4
0
0
0
0
0
0
4
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
3
0
3
1
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
2
0
1
2
0
2
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
3
1
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
2
3
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
2
0
0
2
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
3
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
4
2
0
1
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
2
3
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
2
2
0
1
0
2
1
0
0
0
0
0
2
0
0
0
2
0
5
0
0
0
0
0
0
0
1
0
1
0
0
1
2
0
0
1
1
3
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
8
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
2
0
0
0
2
0
0
1
0
0
0
0
0
0
2
2
0
1
0
2
0
5
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
4
0
0
4
1
0
0
3
0
0
2
0
0
0
0
3
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
4
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
3
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
4
0
0
0
0
0
3
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
4
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
3
0
0
0
0
1
2
1
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
3
4
3
0
0
0
2
2
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
2
0
0
0
3
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
1
0
2
0
0
2
0
0
0
3
0
0
2
0
0
0
4
0
0
0
1
0
2
0
1
0
0
2
2
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
4
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
4
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
1
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
2
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
8
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
6
2
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
3
1
0
0
5
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
2
4
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
1
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
3
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
1
0
1
2
0
2
1
0
3
0
0
0
0
0
0
0
2
3
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
1
1
1
3
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
3
0
2
0
0
0
1
0
0
0
4
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
1
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
1
0
1
0
0
5
0
0
0
2
0
0
0
4
0
0
0
0
0
1
0
1
0
0
2
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
6
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
6
0
0
0
2
0
1
3
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
6
1
0
1
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
3
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
2
1
0
0
0
1
1
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
2
1
0
8
2
1
1
0
0
0
0
0
0
0
1
0
1
2
1
2
0
0
1
0
0
0
1
0
0
0
0
0
3
0
0
4
0
0
0
0
0
0
0
0
2
1
0
0
1
1
2
0
2
0
0
1
8
0
0
2
3
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
2
0
1
3
0
2
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
4
2
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
1
0
0
0
0
0
0
0
1
0
3
2
1
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
3
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
1
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
4
4
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
3
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
1
0
0
0
0
0
0
0
5
0
0
0
1
1
1
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
3
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
5
0
1
0
0
0
1
0
0
0
3
1
0
0
0
0
0
0
0
0
0
4
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
1
0
0
0
0
0
0
0
1
0
0
0
2
2
0
2
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
2
0
0
1
1
0
0
2
3
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
3
0
0
1
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
2
0
0
2
0
2
0
0
1
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
3
1
0
0
0
0
1
0
0
0
3
0
0
0
1
0
0
4
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
4
2
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
3
0
0
1
0
3
2
1
0
0
0
2
1
0
1
0
2
0
4
0
0
2
1
0
1
2
2
0
0
0
0
0
0
0
3
0
0
0
3
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
4
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
1
1
1
0
0
4
0
4
2
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
3
0
0
0
0
0
2
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
1
2
0
0
1
1
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
5
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
2
0
2
0
0
2
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
2
3
0
1
1
0
0
0
0
0
1
0
1
0
1
0
0
0
2
1
0
1
2
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
3
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
8
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
3
0
2
0
4
0
0
0
0
0
2
0
0
0
0
3
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
3
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
5
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
1
3
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
3
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
1
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
1
1
0
2
1
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
1
0
0
0
0
0
0
1
3
0
0
0
1
0
0
1
1
0
4
0
0
1
5
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
7
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
3
0
0
0
2
1
0
0
0
0
2
0
3
0
0
1
1
1
0
1
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
6
0
2
1
1
0
2
1
0
2
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
2
0
0
2
0
0
1
2
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
1
2
0
1
2
0
0
0
2
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
2
0
0
0
1
0
0
0
0
2
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
3
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
1
2
1
0
0
1
2
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
8
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
1
0
2
0
0
2
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
5
0
0
0
0
0
1
0
7
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
3
0
2
0
0
0
0
3
0
1
0
0
0
0
0
1
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
1
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
15
2
0
0
0
0
0
1
1
0
2
0
0
0
0
0
1
1
0
0
0
2
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
1
1
1
0
0
0
3
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
6
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
2
2
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
2
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
3
0
1
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
11
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
1
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
3
0
0
0
0
1
0
0
0
0
0
0
4
3
0
0
0
0
0
3
3
0
0
0
0
0
0
5
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
2
8
1
4
1
0
0
0
0
1
0
0
0
2
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
3
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
4
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
3
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
6
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
1
2
0
0
0
0
0
2
5
1
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
3
0
0
0
0
0
0
4
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
2
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
2
0
2
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
2
0
4
2
1
4
0
0
0
0
0
0
1
2
0
1
0
0
0
0
1
0
0
1
0
1
2
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
1
0
3
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
3
1
0
0
0
2
0
0
0
0
1
7
0
0
0
0
0
2
1
2
0
2
0
0
0
2
0
4
0
0
0
0
0
0
3
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
5
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
1
2
0
0
0
13
0
0
0
0
0
0
0
0
2
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
2
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
1
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
1
1
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
2
1
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
2
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
1
0
2
3
1
0
0
0
1
0
0
0
0
0
3
1
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
1
0
0
2
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
2
1
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
1
0
0
0
1
2
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
4
1
1
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
1
1
0
2
0
1
0
2
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
2
0
1
2
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
3
0
0
1
0
2
1
0
0
1
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
1
4
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
6
0
0
0
0
0
0
1
0
1
2
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
1
0
0
0
10
4
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
1
3
0
1
0
1
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
3
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
4
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
2
1
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
2
1
1
0
0
0
0
3
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
4
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
1
0
2
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
2
0
2
0
0
2
0
1
0
2
0
2
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
6
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
10
4
0
0
3
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
2
0
0
4
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
4
0
1
0
0
0
0
0
0
0
0
3
0
0
2
0
0
3
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
2
1
2
0
2
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
3
0
1
0
0
0
0
0
0
0
0
2
2
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
4
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
1
0
3
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
1
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
1
0
0
0
0
3
0
0
1
1
0
6
0
2
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
1
0
4
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
1
0
1
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
2
3
1
0
1
0
0
0
2
0
0
3
1
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
3
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
1
0
0
2
0
0
0
0
3
0
0
1
0
0
0
0
1
6
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
1
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
3
1
0
0
0
1
0
0
0
1
0
0
0
3
0
0
0
1
0
0
0
0
0
1
2
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
2
0
0
0
0
1
2
1
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
1
3
1
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
1
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
1
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
2
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
3
0
0
1
2
1
0
2
2
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
3
1
0
0
4
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
3
0
0
1
2
0
3
0
0
0
0
0
0
0
0
0
0
2
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
1
0
0
3
0
0
0
0
2
0
0
0
3
1
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
3
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
5
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
4
2
0
0
1
0
0
1
1
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
2
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
3
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
2
0
2
1
2
0
0
0
0
2
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
1
2
0
0
0
2
0
4
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
3
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
1
0
1
0
2
0
0
1
0
0
0
5
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
1
1
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
3
1
0
2
0
0
0
0
0
2
0
0
1
2
0
1
0
0
0
0
0
0
0
0
2
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
3
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
7
2
2
0
0
1
0
0
0
2
0
0
1
4
1
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
4
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
2
0
9
0
2
1
0
0
0
0
0
0
0
2
3
0
1
0
2
0
0
0
1
2
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
1
0
1
0
0
5
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
2
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
10
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
1
0
0
2
0
4
0
0
1
0
2
0
0
0
1
23
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
2
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
2
2
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
2
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
6
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
1
0
2
0
1
3
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
3
0
0
0
6
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
5
1
5
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
5
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
1
1
1
0
0
0
0
0
0
1
0
3
0
0
2
0
1
0
0
0
0
0
1
0
0
0
1
2
2
1
0
0
1
0
2
2
0
0
0
0
0
2
0
0
0
0
1
2
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
2
0
0
1
1
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
2
1
2
2
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
2
0
3
1
1
0
0
0
0
0
2
1
0
0
1
1
1
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
4
1
0
0
0
1
0
1
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
1
3
0
0
0
0
0
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
6
0
1
0
1
1
0
0
2
0
2
0
0
1
2
1
1
0
0
2
0
1
0
0
0
0
1
1
0
0
0
0
0
3
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
2
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
5
0
3
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
2
0
0
0
2
0
0
0
0
0
0
2
2
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
4
6
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
3
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
1
2
0
2
0
0
0
1
0
0
1
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
1
5
0
0
1
2
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
1
2
2
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
1
0
2
0
0
1
0
0
0
0
4
0
0
1
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
2
0
0
0
0
2
1
1
0
0
2
3
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
1
0
1
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
1
0
0
0
1
0
1
0
0
2
0
0
0
0
1
2
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
1
0
0
0
0
2
0
1
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
2
3
0
0
1
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
2
0
2
1
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
3
0
2
0
1
0
0
0
0
0
0
2
1
0
1
0
0
0
0
3
0
0
2
0
0
10
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
3
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
1
0
0
1
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
2
0
8
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
18
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
2
2
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
4
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
4
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
2
1
0
0
0
2
0
0
2
0
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
1
0
0
0
0
0
0
2
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
4
0
0
0
8
0
1
0
0
0
2
1
0
0
0
2
3
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
2
0
3
0
0
0
0
1
1
0
3
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
10
0
0
1
0
0
0
0
0
1
0
0
0
0
0
5
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
2
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
2
1
0
0
2
0
1
0
2
0
0
0
0
1
2
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
1
0
1
1
2
1
0
1
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
1
0
0
1
0
0
0
0
1
2
0
0
0
0
0
2
1
0
1
0
2
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
3
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
1
2
0
1
0
1
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
1
0
2
1
0
1
0
0
0
2
0
0
0
2
0
3
0
0
0
2
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
2
0
1
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
1
2
2
0
0
0
0
2
0
1
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
3
1
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
1
7
0
1
0
7
0
1
0
0
0
0
0
3
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
1
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
3
2
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
4
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
12
0
0
0
0
0
2
3
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
1
0
0
1
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
3
0
2
0
0
0
2
0
0
2
0
2
0
0
0
0
0
1
0
1
0
2
0
0
0
0
1
0
0
2
0
0
2
0
0
3
0
0
0
0
0
0
2
0
1
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
4
0
3
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
3
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
2
3
1
0
0
1
0
0
0
0
0
0
0
3
0
2
0
0
0
1
3
0
0
2
0
2
5
2
0
0
0
0
0
1
10
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
4
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
1
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
1
1
2
0
0
0
0
2
0
2
0
0
0
0
2
0
1
1
0
1
0
2
0
1
0
0
1
1
0
1
0
0
2
0
0
2
0
0
3
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
1
0
0
1
1
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
2
2
2
0
0
2
0
0
5
0
0
3
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
1
1
0
1
0
0
4
0
0
0
0
0
0
0
0
5
0
0
0
0
1
0
0
4
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
7
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
2
0
0
0
3
0
0
0
0
0
1
4
0
0
0
0
0
2
2
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
3
0
0
1
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
6
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
2
0
1
0
0
1
0
0
0
0
0
1
0
6
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
3
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
2
0
2
0
0
0
0
0
2
0
2
0
2
2
0
1
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
3
0
0
0
0
0
0
0
0
0
0
0
1
5
0
1
0
0
0
0
0
0
0
0
2
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
2
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
2
1
0
0
1
0
3
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
1
0
1
0
0
0
0
2
0
0
0
1
0
1
2
0
1
0
0
2
0
0
2
0
0
2
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
3
0
3
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
4
0
0
0
6
0
2
1
0
2
0
0
0
0
2
0
0
0
0
1
2
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
6
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
7
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
4
0
0
0
1
0
2
0
0
0
0
5
0
2
1
0
4
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
4
0
0
0
1
0
3
1
0
3
0
1
0
1
0
0
0
0
0
0
0
1
0
2
0
6
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
4
0
0
0
0
0
0
0
0
1
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
1
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
2
0
0
2
0
0
1
0
5
0
0
0
0
0
0
2
2
2
0
0
0
0
0
2
0
2
2
0
0
0
0
1
0
0
1
0
0
2
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
2
0
0
0
1
0
1
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
1
7
0
0
2
2
0
1
1
0
0
0
0
2
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
3
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
1
0
0
1
2
0
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
2
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
5
0
0
0
2
1
0
0
0
0
2
2
1
0
0
0
0
1
2
0
0
0
0
0
0
1
2
0
1
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
5
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
2
0
1
0
1
2
0
0
0
2
0
0
0
3
0
1
0
0
0
0
0
0
2
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
3
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
1
2
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
2
0
0
1
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
1
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
1
0
0
1
2
0
0
0
2
0
0
0
0
0
3
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
3
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
3
0
0
1
2
0
0
0
0
4
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
2
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
2
0
1
0
0
1
1
0
3
0
0
0
0
0
0
1
0
1
2
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
2
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
7
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
2
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
1
0
3
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
4
0
0
1
0
0
2
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
5
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
4
0
1
0
0
0
0
1
0
0
1
0
1
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
1
2
0
0
2
1
0
0
0
2
0
0
0
0
3
0
0
0
5
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
5
1
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
2
0
1
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
3
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
3
0
2
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
3
0
0
0
2
0
2
1
3
0
0
1
0
0
1
2
0
0
0
0
0
6
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
7
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
3
0
2
0
2
0
0
0
0
0
1
2
0
0
1
1
0
0
0
0
2
2
1
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
2
0
1
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
6
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
1
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
20
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
1
0
0
2
1
0
7
0
0
0
0
0
0
0
1
0
2
4
0
0
0
0
0
2
0
0
0
4
2
0
0
0
2
1
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
5
0
0
0
0
0
0
0
0
1
0
0
3
2
0
0
0
0
2
0
0
0
0
0
1
0
1
2
0
0
0
0
1
0
3
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
2
0
0
0
1
0
1
0
0
1
0
0
1
2
0
0
0
0
1
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
1
0
0
0
1
0
2
0
0
2
0
1
0
0
1
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
1
0
1
0
0
0
0
0
3
0
0
1
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
2
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
5
1
0
0
6
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
6
0
0
0
0
2
0
0
0
0
2
0
0
0
3
0
2
0
2
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
16
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
2
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
3
3
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
3
0
0
0
0
1
0
0
3
2
0
0
0
2
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
4
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
3
3
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
3
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
2
0
0
1
0
0
1
0
0
0
0
0
3
2
0
0
0
0
2
0
0
0
1
0
0
0
3
2
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
2
0
2
2
0
0
2
0
2
0
0
0
0
2
1
0
0
0
6
1
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
2
0
0
3
0
0
2
0
1
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
3
0
0
1
0
0
1
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
4
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
1
2
0
0
0
0
0
3
2
0
0
2
0
2
0
0
0
6
1
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
1
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
4
0
2
0
0
0
1
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
6
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
3
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
1
0
2
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
5
0
0
0
1
4
0
1
0
0
0
1
1
3
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
7
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
2
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
1
0
1
0
0
0
0
5
0
0
1
2
2
0
0
0
0
2
1
0
0
2
3
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
2
0
1
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
3
4
2
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
4
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
1
1
0
0
0
0
1
0
1
0
1
1
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
1
2
0
0
3
1
0
0
0
0
1
1
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
1
0
1
0
0
0
0
0
0
0
2
2
2
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
3
5
2
0
0
0
0
0
2
0
0
3
2
0
0
0
0
0
3
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
4
1
0
1
1
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
1
0
0
0
2
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
3
0
0
0
0
0
1
4
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
8
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
3
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
1
0
2
0
0
0
0
1
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
6
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
3
0
2
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
1
2
0
0
0
0
2
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
2
0
0
0
1
0
0
0
0
2
1
0
0
1
0
2
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
2
0
0
2
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
4
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
2
0
1
0
0
1
1
0
0
0
0
0
1
0
2
0
0
0
1
6
0
0
0
0
0
0
0
0
0
0
0
3
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
1
0
0
0
1
5
0
0
1
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
1
0
0
2
0
0
2
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
2
1
5
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
3
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
2
0
3
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
2
1
1
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
2
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
3
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
4
1
0
1
0
0
0
0
3
0
0
0
0
2
0
5
0
1
0
0
2
0
0
3
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
2
2
0
2
1
0
0
0
0
0
1
2
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
4
0
0
0
1
0
0
3
1
2
0
0
0
0
1
0
0
1
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
1
2
5
2
2
0
0
3
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
1
1
0
0
8
0
0
2
0
2
0
0
5
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
1
2
0
0
0
0
0
1
0
0
2
0
0
1
2
0
1
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
5
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
2
2
3
0
0
0
0
0
4
0
0
0
0
0
0
5
0
0
2
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
1
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
3
1
5
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
1
0
1
0
3
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
6
0
0
0
0
2
1
0
1
2
0
0
0
0
0
0
0
0
1
2
3
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
4
0
0
1
4
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
1
0
0
3
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
5
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
7
1
0
0
3
0
3
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
2
2
5
4
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
1
2
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
1
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
3
2
0
3
1
0
1
0
0
0
0
0
2
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
1
0
0
2
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
2
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
4
0
0
0
3
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
1
0
0
2
0
1
0
0
1
1
0
0
4
0
0
0
0
1
0
1
1
0
0
2
0
0
0
0
4
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
2
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
1
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
3
0
2
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
2
0
1
1
0
0
0
0
2
0
1
1
1
0
1
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
2
0
0
2
1
0
0
0
1
1
0
0
1
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
2
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
1
2
0
2
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
3
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
2
0
1
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
3
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
1
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
1
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
6
2
0
2
1
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
1
2
1
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
1
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
2
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
4
0
0
0
0
1
0
0
0
4
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
6
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
1
0
2
0
0
0
0
0
0
1
2
2
0
8
0
0
0
2
0
1
0
0
0
9
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
3
2
4
0
0
0
1
0
0
0
1
0
0
0
0
0
2
2
0
0
1
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
2
0
0
0
0
3
2
0
0
0
1
2
0
0
0
2
0
2
0
2
2
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
6
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
2
0
0
3
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
3
1
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
2
0
0
1
0
1
1
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
2
0
0
0
4
0
0
1
0
1
3
0
1
0
0
0
0
0
0
0
5
0
2
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
1
0
2
0
0
0
1
0
0
0
1
1
0
0
1
1
0
2
0
1
1
0
1
0
0
2
0
0
0
0
1
0
0
1
0
1
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
3
0
0
0
1
0
0
1
0
0
0
0
0
3
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
1
0
0
4
0
0
1
1
0
0
0
0
0
0
0
0
1
2
0
0
0
4
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
8
0
1
2
0
0
0
0
2
0
0
0
1
0
1
0
1
0
0
1
2
0
0
1
1
0
0
0
0
0
0
4
0
0
0
2
0
1
0
1
2
1
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
1
2
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
1
0
2
0
0
6
0
0
0
1
1
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
2
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
6
2
1
0
0
0
2
0
0
1
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
2
0
0
1
1
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
5
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
4
0
2
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
2
1
3
0
0
0
1
1
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
1
2
1
2
2
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
3
2
0
2
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
10
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
2
1
1
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
2
2
0
0
3
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
7
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
4
0
0
0
0
0
0
1
0
0
0
0
5
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
2
2
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
2
3
2
3
0
0
0
3
0
1
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
3
1
2
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
5
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
1
1
1
0
0
1
0
0
0
0
1
0
2
4
3
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
3
0
1
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
4
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
3
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
1
0
0
0
2
0
3
0
1
0
0
2
1
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
1
0
1
1
0
2
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
2
0
1
0
3
4
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
1
0
1
0
2
0
0
0
2
0
3
1
2
2
0
0
0
0
5
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
2
0
0
0
1
0
1
0
0
0
0
0
4
0
0
0
0
2
0
1
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
11
4
2
0
0
0
0
0
0
0
0
2
0
0
0
1
1
2
0
0
0
0
2
2
0
0
1
0
0
3
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
4
1
2
0
1
0
1
0
0
1
0
0
0
0
0
0
1
1
0
2
2
0
3
1
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
5
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
1
1
3
0
0
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
1
0
0
1
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
3
0
0
0
0
3
0
0
0
2
1
0
5
0
1
1
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
1
0
0
0
1
6
1
0
0
0
1
1
0
0
0
3
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
4
0
0
1
1
0
0
0
0
0
5
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
3
0
0
0
0
0
0
0
0
2
0
0
2
0
2
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
5
1
0
0
0
0
0
0
0
2
2
1
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
4
0
2
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
1
0
1
0
0
0
0
2
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
1
8
1
0
0
0
0
3
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
1
0
2
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
5
2
2
0
0
0
0
1
4
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
1
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
1
8
0
0
0
0
1
1
0
1
0
0
1
2
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
1
0
0
1
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
3
0
0
0
2
0
2
0
0
3
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
2
4
0
4
0
0
0
0
0
0
0
0
0
0
1
4
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
1
1
0
0
2
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
1
2
0
0
0
2
1
0
2
1
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
1
4
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
2
1
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
1
0
0
0
2
0
0
2
0
0
0
2
0
1
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
6
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
2
0
0
0
0
4
1
0
0
0
0
0
0
0
2
0
2
1
5
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
2
0
0
1
0
0
0
0
2
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
2
0
2
1
0
0
0
0
1
0
1
0
1
0
1
0
2
0
0
2
0
0
0
0
0
0
0
3
0
2
0
0
0
0
1
0
1
2
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
4
1
0
0
4
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
1
3
0
2
2
0
0
0
1
1
5
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
1
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
5
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
1
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
5
0
0
0
2
3
0
0
2
0
0
1
0
0
1
0
3
0
2
0
1
0
0
2
0
0
2
1
0
0
0
0
0
1
0
2
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
8
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
2
1
3
0
0
1
0
1
1
0
0
0
0
0
3
0
0
2
0
2
6
0
1
0
2
0
0
2
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
2
1
2
0
2
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
3
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
2
0
0
1
2
0
3
0
0
0
0
0
2
2
0
0
3
0
0
0
1
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
3
0
2
11
0
0
0
0
0
0
0
3
0
0
0
0
8
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
1
0
4
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
1
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
3
0
1
0
0
1
1
0
0
0
0
5
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
2
0
0
0
0
0
0
2
0
0
0
1
0
2
1
0
0
0
0
0
0
4
0
0
0
6
0
0
0
0
0
0
3
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
2
3
2
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
1
1
0
1
0
2
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
6
0
0
0
0
0
0
0
3
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
4
1
2
0
0
0
0
0
0
0
0
0
0
0
6
1
1
1
0
1
0
0
1
0
0
0
0
0
3
0
0
0
1
0
0
2
2
0
2
1
0
0
0
0
0
2
0
1
0
1
0
2
0
0
0
0
0
2
0
2
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
2
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
6
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
1
2
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
1
0
1
3
0
1
0
0
0
0
3
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
4
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
1
1
0
0
0
0
0
0
0
0
0
0
5
1
0
1
0
1
2
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
4
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
1
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
8
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
2
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
1
0
1
0
0
0
0
0
2
0
3
1
2
0
0
0
0
0
1
0
0
0
0
2
2
0
1
3
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
1
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
3
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
2
1
0
0
3
0
1
0
0
0
0
6
7
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
2
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
3
0
2
2
5
0
0
0
0
0
3
0
0
0
2
2
1
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
1
0
1
4
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
1
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
12
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
1
0
3
0
0
0
0
0
0
5
0
0
3
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
3
2
0
0
4
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
1
1
0
1
0
0
0
3
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
3
2
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
1
0
2
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
2
0
3
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
6
1
0
0
0
0
0
0
0
0
3
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
3
0
3
0
1
0
0
1
0
0
0
2
0
0
0
0
2
2
0
3
0
0
0
0
1
0
0
3
0
0
1
0
1
2
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
12
0
1
0
0
1
0
8
3
0
0
0
0
2
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
5
0
0
0
3
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
3
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
1
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
4
0
0
0
0
0
0
1
0
0
5
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
2
0
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
5
1
0
0
0
3
0
3
1
0
0
1
0
2
0
3
2
2
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
2
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
4
0
0
0
0
0
0
0
1
4
0
0
0
0
1
1
2
0
1
0
0
2
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
2
1
1
1
1
0
0
1
0
0
1
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
3
0
0
0
0
0
0
0
4
0
0
0
0
3
0
0
0
1
0
0
4
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
5
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
1
0
0
0
0
1
0
2
0
0
0
0
0
2
1
0
2
0
0
0
0
0
4
1
1
0
0
1
1
2
0
0
0
0
2
3
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
5
0
0
0
0
0
0
3
0
0
0
0
1
0
2
0
0
0
1
2
3
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
5
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
1
0
2
0
0
2
2
0
0
1
1
0
2
2
2
0
0
0
0
3
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
3
1
0
0
0
0
2
0
2
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
4
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
1
2
0
0
3
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
2
1
0
0
0
0
0
2
0
0
0
2
0
0
1
1
0
0
0
4
0
2
0
0
0
0
1
0
0
0
1
2
0
1
0
0
1
1
0
0
0
2
0
0
1
2
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
5
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
3
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
3
1
0
0
0
0
0
2
1
0
2
2
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
1
2
2
0
3
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
3
1
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
7
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
2
1
0
0
0
0
0
2
1
0
1
0
4
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
1
2
2
2
1
0
0
3
4
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
1
3
0
0
0
0
1
1
0
1
0
0
0
0
0
1
2
4
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
3
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
3
0
0
4
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
2
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
2
0
0
0
1
0
0
1
1
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
2
0
9
2
1
0
0
2
0
0
0
2
0
0
0
1
0
1
2
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
3
0
1
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
3
0
0
0
2
0
0
0
2
0
0
2
0
6
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
3
0
0
4
0
0
0
4
0
0
1
1
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
3
0
4
0
0
0
1
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
1
0
0
0
0
2
2
0
1
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
1
0
2
0
0
0
0
0
2
0
0
1
0
0
0
2
0
2
0
0
0
1
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
2
0
0
0
0
3
2
0
1
2
2
0
0
2
0
1
0
0
9
2
0
0
0
0
0
2
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
1
0
0
1
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
4
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
3
0
0
1
0
2
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
1
1
0
1
0
0
0
0
2
1
0
0
0
0
2
0
1
0
2
0
0
0
3
3
6
0
0
2
0
0
0
0
0
4
0
0
0
0
5
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
4
4
1
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
3
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
5
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
5
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
4
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
1
0
0
0
1
0
0
0
1
1
0
0
4
0
1
0
0
0
0
0
0
2
0
4
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
4
0
2
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
3
1
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
2
2
1
0
2
0
0
0
0
0
1
3
0
0
0
0
0
2
0
0
1
0
0
0
0
15
2
0
0
0
1
0
0
0
0
0
0
0
1
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
5
0
1
0
0
0
0
0
0
2
0
0
9
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
1
0
0
0
0
0
3
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
3
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
1
0
0
1
0
0
0
1
0
0
2
0
0
0
2
0
0
0
2
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
6
1
0
2
0
2
0
0
0
0
0
0
0
0
0
4
1
1
0
0
0
0
0
0
0
1
2
2
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
3
1
0
0
3
0
0
0
0
2
1
0
0
0
1
0
0
0
0
3
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
11
0
0
0
0
2
0
0
2
0
2
2
0
1
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
1
0
1
0
0
1
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
1
11
2
0
0
0
0
0
0
0
3
0
8
0
0
2
0
0
2
2
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
3
2
2
1
0
0
0
0
1
2
0
0
0
2
1
1
0
0
0
0
4
1
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
1
0
1
2
1
4
1
3
1
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
8
0
1
2
0
0
0
0
0
1
0
0
2
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
6
1
0
2
0
0
1
0
2
0
0
0
0
2
0
0
1
3
1
0
1
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
2
2
0
0
0
0
0
0
0
0
3
0
1
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
1
2
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
2
0
0
2
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
3
2
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
2
0
0
1
1
0
0
1
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
1
2
0
2
3
3
0
0
0
0
0
0
0
0
8
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
2
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
3
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
4
0
0
5
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
2
0
0
0
1
0
0
0
1
0
0
0
1
0
0
4
0
0
1
0
2
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
3
0
0
1
2
4
0
1
1
0
0
1
3
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
5
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
1
0
5
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
2
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
3
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
2
2
2
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
2
0
1
0
0
0
1
0
0
0
0
8
0
0
0
1
1
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
1
1
2
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
5
0
0
0
0
1
1
3
0
0
0
0
0
0
2
0
0
6
1
0
0
0
1
0
0
0
0
1
2
1
1
0
0
0
0
0
1
1
1
2
0
0
2
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
6
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
2
3
0
0
1
1
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
6
2
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
2
1
0
0
0
3
0
1
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
3
2
0
0
0
2
1
0
1
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
2
0
1
1
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
2
0
0
0
7
1
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
4
0
0
0
0
0
0
0
1
0
2
0
1
0
0
1
0
1
0
0
4
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
5
0
0
0
0
0
2
0
2
0
0
4
0
0
0
1
0
0
0
0
0
4
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
2
0
0
2
0
2
0
0
3
0
1
0
0
0
0
0
1
0
0
0
0
1
2
0
0
2
1
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
2
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
5
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
3
1
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
1
0
0
2
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
2
2
0
0
0
2
0
0
0
0
3
0
0
0
1
0
2
5
1
0
0
3
0
0
0
0
2
1
0
0
1
0
2
0
0
3
5
0
5
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
3
3
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
1
0
0
0
0
0
0
5
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
1
0
0
0
2
0
0
0
2
2
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
4
0
0
0
0
0
3
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
2
0
2
0
0
0
1
0
3
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
2
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
1
0
1
0
0
1
0
3
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
6
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
3
0
1
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
1
0
0
1
1
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
2
0
0
3
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
5
0
2
2
0
0
2
0
0
0
0
0
0
0
0
2
0
3
0
2
2
2
0
1
0
0
1
1
0
4
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
7
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
12
0
0
0
0
3
2
2
2
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
1
0
0
6
0
0
0
0
0
3
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
3
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
2
0
0
0
0
0
2
3
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
11
0
0
0
2
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
3
0
0
1
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
1
2
0
0
0
0
0
1
5
5
2
0
0
1
4
0
2
1
0
0
4
0
4
0
0
2
0
0
0
0
2
0
0
0
2
0
3
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
3
0
0
3
0
0
0
0
0
1
0
1
0
1
0
0
0
2
0
0
0
0
3
0
0
0
2
0
1
2
0
0
1
0
0
0
3
0
0
0
2
0
0
2
1
0
2
0
2
0
0
0
1
0
0
1
0
1
0
1
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
3
0
0
0
1
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
1
2
3
0
0
0
2
0
0
0
5
1
1
0
4
0
0
0
1
0
0
1
8
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
1
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
7
1
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
2
0
1
0
1
0
0
0
0
0
0
2
0
3
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
4
2
0
0
1
0
0
0
0
1
2
0
2
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
8
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
1
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
2
0
1
0
3
4
2
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
1
0
2
2
0
3
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
2
1
0
1
2
0
0
0
0
2
1
0
4
3
0
2
0
0
0
1
0
0
2
0
1
0
0
2
0
0
1
3
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
5
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
2
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
6
3
0
2
1
0
1
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
6
0
0
0
0
0
1
3
0
1
0
3
1
0
0
2
0
1
3
0
2
0
0
0
0
1
0
0
2
0
1
0
0
2
0
0
1
0
0
0
3
1
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
1
0
0
2
3
0
0
0
2
0
0
0
0
3
0
0
0
3
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
2
0
0
0
1
2
2
1
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
1
2
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
3
1
2
0
2
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
1
2
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
2
0
0
2
0
1
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
6
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
3
0
1
0
0
0
0
0
2
1
2
0
0
0
4
0
0
0
2
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
7
0
0
0
0
2
3
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
2
0
0
0
0
9
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
2
1
0
0
0
0
0
1
3
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
2
2
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
3
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
1
0
2
0
2
0
0
0
0
1
2
0
1
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
2
0
1
1
0
0
0
0
0
0
1
0
3
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
1
1
0
1
2
0
1
0
0
0
2
0
0
0
2
0
0
0
1
0
1
0
0
0
1
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
6
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
4
0
2
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
4
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
7
0
2
0
0
4
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
3
0
0
0
1
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
1
0
0
0
2
2
2
0
0
1
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
2
1
1
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
2
1
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
1
0
6
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
2
0
0
2
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
1
0
0
2
1
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
4
2
0
1
0
0
0
0
0
0
1
3
2
0
2
1
0
0
0
0
0
0
0
1
0
0
1
0
0
3
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
1
1
1
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
3
0
0
0
2
0
0
0
0
0
0
1
0
1
3
1
0
0
0
1
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
9
2
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
2
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
3
0
3
0
2
0
0
0
0
0
0
0
0
1
1
0
0
3
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
2
0
1
0
0
0
0
0
0
1
0
1
1
2
0
0
0
0
1
0
2
0
0
11
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
1
2
0
0
0
1
1
2
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
1
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
2
0
0
0
0
0
0
2
5
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
4
1
1
0
0
0
3
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
2
0
0
3
0
3
0
2
2
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
2
1
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
1
1
0
0
0
2
0
0
1
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
3
1
0
0
0
0
1
0
3
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
3
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
2
2
0
1
0
1
0
0
1
0
0
0
1
0
0
0
1
2
0
2
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
5
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
3
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
3
0
2
0
0
2
0
1
1
0
0
0
0
0
1
0
0
1
0
1
0
0
1
1
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
3
2
0
1
0
4
0
0
1
0
0
1
0
0
0
1
0
1
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
0
0
2
0
1
0
0
0
0
0
0
6
1
0
1
3
0
0
2
0
0
0
2
0
2
0
0
0
0
0
5
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
5
0
0
3
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
5
1
0
0
0
0
2
2
0
0
0
2
0
1
0
2
0
0
0
0
2
0
0
0
0
2
0
2
0
0
2
1
0
0
1
0
1
0
3
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
3
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
3
0
0
2
0
1
0
0
0
0
1
0
2
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
3
1
0
1
0
0
1
0
0
1
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
1
0
0
2
0
0
2
0
0
1
0
0
1
4
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
1
2
1
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
1
0
0
0
0
0
2
0
0
0
3
1
0
0
1
0
5
0
0
0
0
0
0
0
1
0
1
0
2
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
3
1
2
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
2
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
2
3
2
1
0
0
0
1
0
0
0
2
0
0
0
0
1
0
1
1
0
0
0
1
1
0
1
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
7
0
1
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
3
0
1
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
8
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
3
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
3
0
0
0
0
0
2
2
0
3
2
0
1
0
0
1
0
0
0
2
3
0
0
0
0
0
0
0
1
1
0
0
0
0
3
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
1
0
3
0
0
2
0
0
0
0
0
0
0
2
0
0
2
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
3
1
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
3
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
1
9
0
0
0
0
0
2
0
0
0
1
2
0
0
3
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
1
2
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
4
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
1
0
2
2
0
0
0
1
1
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
1
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
1
0
1
0
1
0
0
1
0
1
0
0
0
0
0
2
7
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
2
1
0
0
0
1
2
0
0
0
0
0
0
3
0
0
0
1
2
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
1
0
0
2
0
0
0
0
0
0
1
0
1
0
2
0
0
0
2
0
0
0
0
1
3
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
1
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
6
0
0
0
0
0
0
4
0
0
0
0
1
1
7
0
0
0
0
0
1
0
0
0
0
2
0
1
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
3
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
1
0
0
0
0
0
0
0
3
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
1
1
0
5
0
0
0
1
1
0
0
1
0
0
0
1
0
1
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
5
0
0
0
0
2
0
6
2
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
5
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
7
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
1
2
0
0
0
1
0
0
1
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
1
2
4
1
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
2
0
0
1
0
2
1
0
0
3
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
3
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
1
2
0
0
0
2
3
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
4
0
0
0
2
0
2
0
3
0
0
0
3
0
0
0
0
0
0
0
2
0
2
0
0
0
1
1
0
2
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
1
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
7
0
0
1
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
3
0
1
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
5
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
2
0
0
1
0
0
2
0
0
5
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
2
0
0
9
1
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
2
2
1
0
4
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
4
0
0
2
0
2
0
0
0
0
0
2
1
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
2
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
2
0
0
0
0
2
0
2
0
9
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
3
0
0
0
4
0
0
2
0
0
0
0
2
0
1
1
1
2
1
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
2
0
0
1
1
0
0
0
0
1
0
0
1
0
2
0
2
1
6
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
1
0
0
0
0
6
0
1
1
0
2
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
3
0
0
0
0
1
0
0
1
0
0
2
5
0
2
1
1
1
0
0
0
0
0
0
0
0
2
3
1
3
0
6
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
3
0
1
2
0
0
0
1
1
0
4
0
0
0
0
0
0
0
1
0
1
0
0
0
3
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
1
0
0
0
0
0
1
2
0
0
2
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
3
2
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
4
1
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
2
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
1
0
0
0
0
2
1
0
0
0
2
0
2
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
3
2
0
0
0
2
0
0
0
3
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
2
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
1
1
0
2
2
0
2
3
0
1
2
3
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
5
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
3
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
2
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
2
0
4
0
0
1
1
0
0
0
0
0
0
4
0
0
5
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
2
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
3
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
1
0
0
0
0
0
2
0
0
0
0
0
1
2
0
2
0
0
5
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
6
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
1
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
1
0
0
0
0
0
0
2
3
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
2
0
3
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
2
1
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
6
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
1
0
0
0
0
5
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
1
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
4
1
0
7
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
2
0
2
0
3
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
1
0
2
0
1
1
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
2
0
0
0
0
0
1
1
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
4
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
1
1
0
0
3
0
0
4
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
4
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
1
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
1
0
0
0
4
0
0
0
2
0
0
0
0
0
0
0
2
1
0
1
1
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
2
0
1
0
0
0
0
0
0
0
0
3
3
0
0
0
0
2
0
0
5
0
0
0
1
3
0
2
0
1
0
4
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
1
0
0
1
0
0
2
0
0
0
1
0
2
1
0
2
0
0
1
2
2
0
0
0
0
0
1
3
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
2
1
0
22
0
0
0
0
2
0
0
2
0
0
0
2
1
0
0
1
1
0
0
1
0
0
0
0
2
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
1
1
0
0
1
1
1
0
0
0
0
0
0
0
0
5
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
2
0
3
0
0
1
0
0
0
0
0
3
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
1
2
0
1
0
0
0
1
3
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
4
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
5
0
0
1
0
0
0
2
0
0
0
0
6
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
2
0
0
0
0
4
0
0
0
0
0
0
0
7
0
2
0
0
0
1
0
2
0
0
0
0
0
1
6
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
2
0
0
2
1
0
0
2
0
0
1
0
0
1
0
0
0
2
0
1
0
0
1
0
2
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
1
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
1
0
0
0
0
0
1
0
0
1
2
1
0
0
0
1
0
1
0
0
0
0
0
2
1
0
0
0
2
0
0
0
1
0
0
0
4
6
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
3
0
0
0
2
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
1
0
0
0
0
0
2
0
0
0
3
0
1
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
1
0
2
0
2
2
0
0
0
2
0
0
1
0
0
0
2
0
0
0
2
3
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
1
5
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
4
0
0
0
0
0
0
0
2
1
1
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
1
1
0
0
0
2
0
0
0
2
0
0
0
0
2
0
1
0
1
0
0
2
13
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
1
1
1
0
0
1
0
0
2
0
0
2
0
2
0
4
0
1
0
0
1
0
0
1
0
1
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
5
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
2
0
1
0
0
0
0
0
3
0
0
0
3
0
0
2
0
0
0
0
0
0
0
4
0
0
0
0
0
1
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
2
3
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
3
2
0
1
1
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
2
1
0
2
2
0
0
1
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
2
1
0
0
1
2
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
2
0
0
2
0
0
1
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
1
0
0
0
2
0
2
0
0
4
0
0
0
1
0
1
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
1
0
0
1
1
0
2
0
0
2
0
0
0
2
4
0
0
0
1
0
0
0
1
0
0
0
4
0
3
0
2
0
1
0
0
0
0
0
0
0
0
1
0
1
2
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
2
4
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
2
1
5
0
0
1
1
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
1
0
0
2
0
0
0
1
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
4
0
0
0
1
1
0
0
1
0
3
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
2
2
0
0
0
0
3
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
1
0
5
0
0
0
0
0
0
0
0
0
0
3
0
3
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
3
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
3
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
1
0
0
2
0
2
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
1
0
0
2
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
8
1
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
1
0
0
2
6
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
4
1
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
1
0
0
0
1
2
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
1
0
0
1
3
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
5
0
0
2
1
0
1
1
0
2
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
3
5
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
1
4
0
5
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
7
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
4
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
5
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
3
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
3
1
1
1
2
0
0
0
1
0
0
0
1
0
0
0
0
1
0
4
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
1
2
2
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
1
0
0
1
2
0
1
0
0
0
0
0
1
2
0
0
0
0
1
4
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
3
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
2
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
3
4
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
12
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
2
0
0
3
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
2
0
0
1
1
0
0
2
0
0
2
2
0
0
0
1
0
1
0
0
0
2
2
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
2
0
1
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
1
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
1
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
4
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
2
0
0
1
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
3
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
1
0
0
0
2
2
1
1
2
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
1
2
0
1
0
0
1
1
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
3
4
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
12
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
1
4
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
1
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
1
1
3
0
0
0
0
4
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
1
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
1
0
0
0
0
0
2
0
0
1
0
2
0
0
1
2
0
0
0
0
1
1
0
1
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
3
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
5
0
0
0
0
2
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
1
1
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
2
0
0
0
0
2
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
1
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
4
1
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
3
1
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
3
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
3
0
1
0
0
0
0
0
0
2
1
1
0
0
1
2
0
0
13
0
0
2
0
0
0
0
4
1
0
0
0
0
0
0
0
1
1
0
0
0
0
3
0
0
0
0
0
0
0
1
0
3
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
1
1
0
0
0
0
3
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
2
0
1
0
4
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
2
2
2
0
0
0
2
0
0
0
0
0
2
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
3
2
0
0
0
0
2
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
7
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
3
0
0
0
0
4
0
1
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
1
0
1
0
0
1
0
0
0
2
1
0
0
0
0
2
2
1
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
1
0
1
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
3
1
0
0
1
0
0
1
0
2
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
3
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
2
0
4
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
1
1
0
2
0
0
0
0
0
1
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
1
1
0
0
0
0
2
1
0
0
0
2
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
1
0
2
0
0
0
0
1
2
0
2
0
0
1
1
2
0
0
0
1
0
0
0
0
0
0
3
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
5
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
3
0
1
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
2
0
0
0
0
2
5
1
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
1
1
3
2
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
1
0
1
1
0
0
2
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
1
0
2
1
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
4
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
1
0
0
0
2
1
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
2
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
3
1
2
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
3
0
0
3
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
3
1
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
3
0
7
0
0
0
2
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
13
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
1
0
3
0
0
0
0
0
0
0
1
0
0
0
8
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
2
0
0
3
0
0
0
2
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
2
0
0
1
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
5
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
1
0
0
1
2
0
0
0
3
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
8
0
2
0
0
0
0
2
0
0
2
0
1
0
1
0
0
0
0
0
3
0
1
0
0
0
5
0
0
0
1
2
1
2
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
2
0
2
1
1
2
0
0
2
0
0
3
0
2
2
1
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
2
0
1
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
1
1
2
0
1
0
3
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
2
0
0
1
0
1
8
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
1
0
0
2
1
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
2
0
0
0
3
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
5
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
4
0
0
2
0
0
0
0
3
0
0
0
0
1
2
0
0
0
0
2
1
0
1
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
1
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
2
0
0
0
0
2
9
0
2
1
0
2
1
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
1
0
0
0
0
0
5
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
1
0
0
0
1
2
0
0
0
1
0
0
0
1
0
1
0
3
0
0
0
0
0
5
0
0
0
0
0
0
1
0
0
0
0
4
3
0
0
0
3
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
2
0
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
3
0
0
0
0
0
0
2
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
2
1
0
0
4
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
7
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
2
0
1
0
0
0
1
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
2
0
0
2
2
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
1
0
0
1
0
2
0
2
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
2
4
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
1
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
1
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
5
2
0
0
0
1
2
0
0
0
3
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
3
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
1
0
0
0
2
4
0
0
1
0
0
0
0
5
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
2
0
1
0
0
1
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
2
2
0
3
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
2
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
3
0
0
0
0
0
2
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
3
4
0
0
0
0
0
0
0
1
0
0
0
10
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
2
2
0
5
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
1
0
0
0
0
0
1
3
2
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
1
0
0
0
0
2
0
1
1
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
1
1
2
0
0
1
0
1
1
0
2
0
0
1
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
2
0
2
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
2
0
1
0
0
2
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
1
0
1
2
0
0
0
1
0
0
9
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
3
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
4
0
1
0
2
0
0
0
2
0
0
1
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
2
1
0
0
2
0
1
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
5
0
0
0
0
0
0
0
0
1
3
0
1
0
0
3
0
0
0
0
2
1
0
3
0
0
1
3
1
1
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
2
0
2
0
0
2
2
2
0
0
0
0
1
3
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
2
1
0
1
0
1
1
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
2
2
0
1
0
2
1
4
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
3
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
4
0
0
2
0
2
1
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
3
5
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
2
4
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
4
0
2
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
1
0
0
0
4
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
1
0
0
0
0
2
2
2
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
2
0
0
3
0
2
0
0
0
1
3
0
0
0
0
0
1
0
0
2
0
0
0
2
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
4
0
0
0
0
0
2
0
3
0
0
1
3
2
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
4
1
0
0
0
1
1
0
0
0
4
1
0
0
2
1
0
1
2
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
1
1
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
3
1
0
0
1
0
0
0
1
3
0
0
0
0
1
1
0
0
1
7
2
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
3
0
0
3
2
0
0
0
3
0
1
1
2
0
2
0
0
1
0
0
0
0
2
0
0
0
0
1
0
3
2
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
2
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
4
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
1
2
0
0
0
4
0
0
0
0
0
1
0
2
2
3
0
7
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
2
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
1
0
1
1
0
0
0
0
0
1
0
2
0
0
0
0
1
2
1
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
2
1
1
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
4
1
4
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
0
0
0
4
2
0
0
0
0
2
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
2
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
2
2
0
0
1
0
2
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
2
0
1
0
0
2
4
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
4
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
10
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
3
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
4
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
2
1
0
2
0
3
1
4
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
2
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
2
0
1
0
0
0
3
1
0
0
0
0
0
1
0
0
0
2
6
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
4
3
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
2
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
1
1
0
0
0
1
0
0
1
1
0
0
2
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
3
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
1
0
1
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
3
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
2
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
4
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
2
1
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
1
0
0
2
0
4
0
2
0
0
0
0
0
2
0
0
0
0
0
0
3
2
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
5
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
2
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
2
1
0
0
1
2
0
0
0
0
0
0
0
0
0
4
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
3
0
0
0
0
2
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
4
0
1
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
1
2
2
0
0
0
0
0
1
0
0
1
1
0
1
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
1
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
1
2
0
0
0
0
3
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
1
2
0
0
0
0
0
1
1
1
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
1
2
3
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
1
3
0
1
0
0
4
0
2
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
1
0
0
1
0
0
1
2
0
0
0
9
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
2
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
2
0
1
1
0
1
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
2
2
0
1
0
0
0
1
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
1
3
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
1
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
3
1
0
0
0
0
1
0
0
0
0
3
0
3
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
1
0
2
0
2
0
2
0
1
0
0
0
0
1
1
0
0
0
3
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
3
2
1
0
0
0
3
0
7
0
3
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
2
0
0
3
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
1
0
2
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
1
0
2
0
0
1
0
0
0
0
2
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
4
0
0
0
0
0
1
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
2
2
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
3
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
11
0
0
0
0
0
0
0
1
5
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
2
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
2
0
1
1
0
0
0
1
0
0
0
0
0
0
3
0
2
1
0
1
2
0
0
0
3
0
1
0
0
0
0
0
0
0
3
0
0
2
0
0
0
2
0
0
0
0
0
0
1
2
1
1
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
4
0
0
0
0
0
0
0
2
0
0
0
5
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
1
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
3
0
1
2
2
0
1
1
0
1
0
1
2
0
0
0
0
0
2
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
1
1
0
1
0
2
0
0
2
0
0
0
2
0
3
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
7
0
0
5
0
0
0
0
0
4
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
2
0
1
0
0
1
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
3
0
0
4
0
0
0
0
0
2
0
1
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
3
0
0
0
0
1
1
0
0
0
0
0
0
0
0
5
4
0
0
0
0
0
2
0
0
3
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
4
1
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
3
0
0
0
0
0
0
0
0
6
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
1
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
1
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
1
2
2
0
0
0
1
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
3
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
2
1
0
0
3
2
0
3
0
0
0
2
0
0
0
1
2
2
0
0
1
0
0
1
1
0
0
2
0
1
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
1
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
2
0
1
0
1
3
0
2
0
0
0
0
2
1
2
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
3
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
3
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
1
0
0
1
1
0
1
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
2
1
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
1
0
5
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
2
0
0
0
4
0
0
0
1
0
2
0
0
0
1
0
1
0
0
0
0
8
0
1
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
2
1
1
2
0
0
0
0
1
1
0
0
0
0
3
0
4
0
1
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
9
0
2
1
0
0
0
0
0
0
2
2
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
1
2
2
1
0
6
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
1
0
0
2
1
3
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
1
2
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
7
0
0
2
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
6
1
0
2
0
1
0
0
0
2
1
3
0
2
0
2
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
2
0
0
0
0
0
1
0
0
4
2
0
0
0
2
0
0
4
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
5
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
1
2
0
9
0
0
2
2
0
0
0
1
1
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
2
0
3
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
1
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
3
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
5
0
0
0
0
0
0
0
3
0
0
1
1
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
1
0
2
2
0
1
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
3
2
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
1
0
1
5
0
2
0
0
0
2
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
7
0
2
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
6
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
2
2
0
0
0
2
0
0
0
1
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
2
1
6
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
1
0
0
0
0
1
0
0
2
0
2
0
3
0
0
0
0
2
2
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
5
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
6
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
2
0
0
0
0
2
2
3
5
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
1
0
0
0
1
0
0
2
0
0
1
0
0
0
0
2
1
0
0
5
0
5
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
2
0
1
1
0
0
0
0
0
2
1
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
3
0
0
0
0
0
0
1
2
0
0
1
0
0
2
2
2
1
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
1
0
0
0
4
0
3
1
2
2
2
0
1
0
0
2
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
2
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
13
2
0
1
0
0
2
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
1
2
3
0
4
0
0
0
0
1
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
3
1
0
0
0
0
1
0
1
0
0
2
1
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
5
0
1
2
0
1
0
2
0
0
7
2
0
0
0
0
0
0
0
1
2
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
1
0
0
2
2
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
2
0
0
3
4
0
0
0
0
0
0
1
0
0
0
5
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
3
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
3
0
1
0
0
0
2
1
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
1
2
0
0
0
0
2
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
2
0
2
2
4
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
2
0
0
0
2
0
5
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
2
1
0
1
0
0
0
1
0
0
0
0
0
2
0
0
4
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
2
2
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
2
2
0
0
0
0
0
1
2
0
0
6
0
0
0
1
1
0
0
0
0
0
2
0
2
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
1
0
2
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
1
0
0
1
0
0
1
0
0
0
0
2
0
1
0
1
2
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
3
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
1
3
0
0
1
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
2
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
2
0
3
2
0
2
0
1
0
0
1
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
4
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
3
2
1
1
3
0
0
0
0
2
0
1
0
0
0
0
3
0
0
0
0
0
3
2
1
0
0
0
2
0
0
0
1
0
1
0
0
0
7
0
0
0
1
0
1
0
0
3
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
4
0
2
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
3
0
0
2
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
3
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
4
0
0
0
1
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
2
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
4
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
6
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
8
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
3
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
3
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
1
0
2
0
0
0
0
3
1
1
0
0
0
0
3
0
0
0
2
0
3
0
0
1
0
0
0
2
0
3
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
1
0
4
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
5
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
1
0
0
1
0
4
0
1
0
0
2
0
2
0
0
0
0
0
0
4
0
2
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
1
1
1
2
0
4
0
0
0
0
3
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
1
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
6
0
0
0
0
0
0
0
0
0
1
7
2
1
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
2
2
2
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
3
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
1
1
0
0
0
2
4
2
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
2
4
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
1
0
0
3
3
0
4
2
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
1
0
1
0
2
0
0
2
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
4
0
2
0
0
6
1
0
3
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
3
0
0
1
1
0
1
0
0
0
2
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
2
0
2
1
1
0
0
2
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
4
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
2
1
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
3
0
0
0
1
0
0
0
2
0
2
0
0
0
0
5
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
4
0
0
0
0
0
2
0
2
0
1
1
0
1
0
2
0
0
2
0
0
0
0
0
0
0
2
0
7
0
2
0
5
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
2
0
1
5
1
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
2
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
1
0
0
3
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
3
0
0
1
3
0
0
2
0
3
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
1
0
0
4
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
2
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
1
0
0
0
1
1
0
0
0
0
2
2
3
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
3
2
1
1
2
0
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
4
2
2
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
3
2
1
0
0
1
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
3
1
0
0
0
0
0
5
0
0
0
0
3
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
12
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
15
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
6
0
1
0
0
4
4
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
4
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
1
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
4
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
2
1
0
0
0
0
0
0
3
0
0
5
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
3
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
6
0
0
0
3
0
0
0
0
0
2
0
0
2
0
6
0
0
0
0
0
7
0
0
0
0
5
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
3
3
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
2
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
3
0
0
5
0
2
2
1
1
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
0
0
2
0
0
0
0
1
0
2
0
1
0
0
0
0
1
2
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
3
0
1
0
0
3
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
4
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
2
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
4
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
2
4
2
0
5
0
0
0
0
0
1
0
0
2
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
1
0
0
0
0
0
1
0
0
3
0
2
0
0
0
2
0
0
1
0
0
0
0
1
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
1
0
3
0
0
0
0
1
1
0
0
0
0
3
2
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
1
2
0
6
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
2
0
2
0
0
0
0
1
1
0
2
2
0
0
0
0
2
0
0
1
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
2
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
2
1
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
3
0
2
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
2
0
1
0
0
0
2
2
0
0
0
11
0
1
0
0
2
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
2
2
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
2
0
4
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
1
2
0
0
2
0
2
0
2
1
0
0
2
0
1
0
1
0
0
0
1
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
1
0
0
1
0
0
2
0
0
0
0
0
0
2
2
0
0
1
0
3
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
2
2
0
0
1
0
1
0
2
0
1
0
0
0
0
0
0
0
3
0
2
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
1
0
0
4
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
1
0
1
1
1
2
0
0
1
0
0
2
1
0
0
3
2
0
1
0
0
0
0
0
3
1
1
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
2
3
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
6
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
2
0
1
0
0
0
0
1
1
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
3
1
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
3
1
0
0
0
0
0
0
1
0
0
0
4
2
0
0
1
0
3
2
0
0
0
0
3
0
0
0
1
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
1
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
11
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
2
1
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
2
1
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
2
0
6
2
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
2
0
0
0
0
2
0
3
0
0
1
2
1
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
1
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
8
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
3
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
5
0
5
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
1
0
0
0
0
2
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
2
1
0
2
0
0
0
1
0
0
0
0
1
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
3
0
1
2
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
1
0
1
1
2
4
0
0
0
0
0
0
2
0
0
3
0
0
0
2
0
0
0
4
1
0
0
0
6
0
0
0
0
0
1
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
2
4
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
2
2
4
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
4
6
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
1
7
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
3
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
2
1
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
3
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
3
3
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
1
1
0
0
2
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
4
0
0
0
0
0
1
0
0
3
0
0
1
0
0
0
0
2
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
6
0
0
0
2
2
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
1
0
0
2
2
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
1
2
0
0
1
0
1
1
0
0
0
0
5
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
5
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
1
2
0
0
0
0
0
0
0
2
0
0
0
1
0
4
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
1
0
4
0
0
0
0
4
0
0
2
0
2
3
0
0
0
0
0
2
1
0
0
2
2
0
0
1
0
1
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
1
0
0
0
1
0
0
2
0
0
0
4
0
0
0
0
0
3
1
0
0
0
0
2
0
2
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
1
2
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
1
0
0
0
0
1
2
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
4
0
1
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
5
1
1
0
1
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
2
0
1
0
0
0
1
0
0
0
0
0
0
1
7
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
3
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
6
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
1
0
5
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
3
0
0
0
0
2
1
2
0
0
3
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
4
1
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
4
0
0
2
0
3
0
3
0
1
0
0
0
0
2
0
0
2
0
0
0
1
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
2
0
0
2
1
0
1
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
5
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
1
0
0
0
1
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
7
0
2
2
0
0
0
0
0
0
4
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
1
0
0
1
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
3
0
0
2
1
0
1
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
2
1
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
4
1
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
1
1
0
0
0
0
0
1
0
2
0
1
0
0
0
0
2
0
1
0
0
0
4
0
0
0
0
0
0
0
0
4
1
2
2
0
1
0
0
0
1
0
0
0
0
2
0
2
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
1
0
0
2
0
2
2
0
0
0
1
0
1
0
0
0
2
0
5
0
0
0
0
0
0
1
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
1
0
0
0
2
3
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
1
0
0
1
0
1
2
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
1
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
1
3
0
2
2
0
0
0
1
3
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
2
0
0
7
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
3
0
2
2
0
0
0
1
0
0
2
0
2
0
0
2
0
0
3
0
0
1
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
5
0
0
0
0
1
0
0
2
8
0
0
0
1
0
4
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
1
0
2
2
1
1
0
0
0
4
1
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
7
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
6
0
0
0
0
0
0
2
0
0
0
1
0
1
2
1
0
0
0
0
0
0
0
0
2
1
0
0
3
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
1
0
1
0
1
0
3
2
0
0
0
0
1
2
1
0
1
2
1
0
0
1
0
0
0
3
1
0
5
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
1
2
0
0
0
3
0
0
0
0
1
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
3
1
1
0
0
0
0
0
1
0
0
1
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
7
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
1
3
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
8
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
2
0
0
0
0
1
2
0
2
0
0
0
1
0
0
0
1
0
0
0
1
0
2
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
3
0
1
2
2
0
1
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
3
0
0
3
0
0
0
1
0
4
0
0
1
0
5
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
3
2
2
0
0
0
0
4
0
0
0
1
2
0
0
0
3
0
0
0
0
2
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
6
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
2
0
0
0
4
0
1
0
0
0
0
3
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
8
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
2
0
0
1
0
0
0
0
3
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
1
0
1
0
1
0
1
3
0
0
0
0
1
1
2
0
2
1
0
0
2
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
1
0
1
0
0
4
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
2
3
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
11
0
2
0
0
2
0
0
0
0
0
1
2
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
1
0
2
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
1
2
0
1
0
0
0
0
3
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
2
0
0
4
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
8
0
0
0
0
1
0
0
0
0
1
1
1
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
8
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
2
1
0
0
0
0
9
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
4
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
1
0
0
2
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
3
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
1
0
0
0
0
0
2
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
1
0
0
0
1
2
0
2
0
2
0
0
0
1
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
1
0
1
0
1
0
3
1
1
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
3
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
6
1
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
6
0
2
0
3
1
0
0
0
0
0
0
2
2
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
2
0
0
0
0
0
2
3
0
4
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
1
0
0
3
0
3
0
2
1
0
0
0
0
0
1
1
0
3
0
0
0
0
0
0
4
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
3
5
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
1
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
2
0
0
0
2
6
1
0
0
0
2
0
0
1
1
0
1
0
0
1
0
2
0
1
0
1
0
0
0
0
0
0
1
1
0
0
1
0
2
0
0
0
0
1
0
2
3
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
3
1
0
0
0
0
2
0
0
0
1
1
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
3
0
1
1
0
1
0
0
0
0
2
0
0
2
0
2
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
6
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
1
0
2
1
2
4
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
2
0
0
0
0
1
2
0
0
0
0
0
1
0
1
0
8
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
1
2
0
1
0
0
0
1
3
0
0
0
1
2
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
2
2
2
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
1
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
2
0
1
1
0
0
1
0
2
0
1
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
3
0
2
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
3
0
0
0
1
1
0
0
1
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
2
1
1
0
0
0
2
0
1
0
0
4
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
2
0
2
0
0
1
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
4
0
0
3
1
0
0
3
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
1
0
0
0
1
0
0
2
1
0
0
1
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
2
0
4
0
0
1
0
0
0
0
0
0
0
1
1
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
2
0
0
0
0
1
2
0
1
0
0
1
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
1
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
1
0
0
8
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
2
1
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
4
2
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
2
1
0
0
0
1
0
0
0
0
0
0
4
0
0
2
0
0
0
1
0
0
1
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
4
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
2
0
0
0
2
0
0
0
0
1
0
0
0
2
1
1
0
3
0
1
3
3
1
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
3
0
8
1
0
0
0
1
0
0
0
0
2
0
0
0
1
0
1
0
2
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
1
0
0
0
1
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
2
4
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
2
1
0
0
1
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
6
0
0
0
1
0
0
0
1
0
0
0
0
0
7
0
1
0
0
3
0
1
2
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
3
3
1
0
0
0
0
0
0
1
1
2
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
2
0
0
1
0
0
2
2
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
3
0
0
1
0
0
0
0
0
5
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
5
0
2
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
1
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
4
0
2
0
0
0
3
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
5
0
0
0
0
0
3
0
1
0
0
0
0
0
2
0
0
1
2
1
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
3
0
1
0
4
1
0
0
0
0
2
0
0
0
0
1
2
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
2
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
3
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
1
1
1
2
0
0
6
1
0
3
0
0
2
1
0
2
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
1
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
7
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
1
0
0
0
0
0
0
0
0
2
1
2
2
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
2
2
1
0
0
2
0
0
0
0
0
0
2
2
0
0
0
2
2
1
0
0
1
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
5
6
0
0
0
0
0
0
2
1
4
0
1
0
0
0
0
2
0
0
0
1
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
1
0
0
1
2
1
0
2
0
1
0
0
0
0
0
0
1
1
2
0
0
0
0
0
2
3
0
3
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
1
0
1
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
2
0
0
0
0
0
0
2
3
1
0
0
1
0
1
2
1
2
1
0
0
1
0
1
1
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
1
0
1
0
0
4
0
1
0
0
0
0
1
0
2
0
5
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
1
1
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
1
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
3
0
0
0
1
0
0
2
0
0
2
0
0
2
1
2
2
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
1
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
2
1
1
0
1
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
3
0
0
0
1
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
2
0
1
0
1
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
1
0
2
0
0
0
0
0
0
0
1
0
0
0
2
1
0
1
2
2
0
0
3
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
1
0
5
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
1
1
2
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
2
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
1
0
1
0
0
2
1
1
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
3
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
1
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
2
4
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
1
2
3
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
1
0
1
0
1
5
2
0
1
2
0
0
0
0
0
1
0
5
0
0
3
0
0
0
0
0
2
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
2
0
0
0
0
0
4
0
0
0
0
0
3
1
0
0
0
0
0
0
1
0
2
0
0
1
7
0
0
0
0
0
0
0
0
1
2
6
0
0
5
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
3
0
0
2
0
1
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
2
3
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
2
0
0
0
3
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
2
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
4
4
0
2
0
0
0
0
0
0
2
0
0
4
0
0
1
5
0
4
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
3
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
1
0
0
3
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
3
0
0
0
1
1
3
1
0
0
0
0
0
0
0
0
0
7
0
0
5
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
1
0
1
0
0
0
3
0
0
0
0
0
1
0
0
2
0
0
0
3
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
1
0
1
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
1
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
5
2
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
4
3
0
0
2
0
0
2
2
0
1
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
3
1
1
0
1
0
1
0
0
0
0
1
0
1
1
0
1
0
0
0
5
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
2
2
0
0
1
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
2
0
2
4
0
2
0
1
0
0
0
0
0
2
0
1
0
0
4
0
0
3
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
1
0
1
0
2
5
1
0
0
0
0
0
0
0
0
0
1
1
0
4
0
0
0
3
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
2
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
2
2
0
2
0
0
1
0
0
0
0
0
4
0
0
2
1
0
2
0
0
0
0
1
0
1
2
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
1
1
0
2
0
0
0
1
0
1
0
0
0
3
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
3
0
0
0
1
0
0
1
0
2
0
2
0
2
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
4
0
1
0
0
5
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
6
0
1
0
0
0
0
0
0
2
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
2
0
1
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
3
1
0
0
2
0
2
0
0
0
0
0
1
1
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
1
0
1
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
3
0
0
0
1
0
0
3
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
4
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
6
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
4
0
0
1
1
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
2
0
2
3
0
0
0
2
0
2
0
0
1
0
2
0
1
1
0
0
0
2
0
1
2
1
0
0
0
3
0
1
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
2
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
1
0
0
1
0
0
0
0
1
0
0
2
0
2
1
0
0
0
1
5
0
0
0
0
2
0
0
1
1
0
1
0
0
0
0
1
0
9
0
0
1
0
2
2
0
1
0
0
0
0
0
3
0
0
0
1
1
0
0
0
0
0
0
3
4
0
0
0
1
0
0
0
0
0
0
0
1
0
2
3
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
1
2
0
0
1
0
1
2
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
1
0
0
0
0
2
0
0
0
0
0
0
1
1
0
2
0
1
2
0
0
0
0
0
0
2
0
0
4
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
2
1
0
0
0
0
3
0
1
0
0
0
0
0
0
2
2
0
0
0
0
1
1
0
0
0
0
1
1
0
6
2
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
3
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
8
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
1
0
1
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
2
0
0
1
0
7
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
1
0
2
0
1
3
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
1
4
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
3
0
1
1
0
1
1
0
0
2
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
3
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
10
0
0
0
3
0
0
0
1
0
2
2
3
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
4
0
0
0
0
0
0
0
2
0
2
0
0
4
0
0
1
0
3
0
1
0
2
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
3
0
0
0
0
0
0
3
0
0
0
0
3
2
0
1
1
0
0
0
2
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
3
0
0
1
0
3
1
3
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
2
0
2
0
1
0
1
2
0
0
0
2
0
1
2
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
1
1
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
2
0
0
0
0
0
1
0
0
0
3
1
5
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
3
1
0
1
0
2
0
0
0
1
0
2
0
4
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
3
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
1
0
0
0
1
2
1
0
1
0
5
0
0
0
1
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
3
0
3
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
4
0
0
1
1
0
2
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
9
1
1
1
0
0
0
1
0
0
0
1
0
0
0
1
0
3
1
0
0
1
0
1
0
0
0
0
0
0
1
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
1
2
0
0
1
2
1
0
0
0
0
4
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
3
0
0
1
0
2
0
0
1
1
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
2
0
0
0
0
1
0
2
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
16
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
1
0
0
10
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
3
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
2
0
1
0
0
0
0
0
1
1
0
0
2
1
0
1
0
0
0
0
1
0
1
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
1
5
0
0
0
2
1
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
6
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
1
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
4
0
0
0
2
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
1
0
0
1
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
4
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
4
0
0
0
1
0
0
0
0
3
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
2
0
2
1
0
5
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
3
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
4
0
1
1
1
1
0
0
0
2
0
0
0
0
0
0
6
0
0
0
2
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
4
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
7
0
0
1
0
0
1
0
0
2
0
2
2
1
2
0
0
0
0
1
0
1
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
1
2
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
3
0
0
0
0
0
2
0
0
2
1
0
0
0
2
0
0
3
0
2
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
1
1
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
1
0
4
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
3
3
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
3
0
1
0
1
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
2
3
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
1
0
1
3
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
3
2
1
0
0
1
1
0
0
2
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
2
0
2
0
1
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
3
1
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
3
2
2
0
1
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
2
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
2
0
0
0
3
0
0
1
0
1
0
0
0
0
0
0
3
0
1
0
0
0
6
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
3
0
0
2
0
2
0
0
2
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
2
0
0
0
1
2
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
2
2
0
0
0
1
0
0
0
0
0
2
0
0
2
0
1
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
1
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
2
0
0
4
0
0
2
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
2
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
6
0
5
0
0
0
3
0
0
1
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
6
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
2
1
1
0
0
0
0
0
1
0
3
0
0
0
0
0
1
0
0
0
2
1
0
1
2
0
0
1
0
0
2
0
0
1
0
2
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
3
0
0
2
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
4
0
7
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
2
1
0
0
0
2
2
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
3
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
1
0
0
0
0
0
1
0
1
1
0
4
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
1
0
1
0
2
3
0
2
0
2
0
0
0
1
4
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
3
0
1
0
0
0
0
2
1
0
3
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
4
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
1
0
1
1
1
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
1
0
3
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
4
0
1
2
0
1
1
1
1
0
0
2
0
0
0
1
1
0
1
0
0
1
0
0
0
1
5
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
2
0
2
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
8
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
7
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
1
0
1
1
0
2
0
2
0
1
3
0
0
3
0
5
0
0
0
0
0
0
1
1
0
0
0
3
0
0
0
0
0
0
2
2
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
1
1
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
4
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
2
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
3
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
1
2
0
0
1
1
0
0
2
0
0
1
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
5
0
0
1
0
2
1
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
1
2
1
1
0
0
0
0
2
0
0
7
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
5
0
0
0
0
0
0
3
0
1
0
2
2
1
0
0
0
0
1
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
1
2
2
3
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
2
1
0
0
1
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
2
8
0
0
0
0
0
0
1
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
5
1
0
0
2
5
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
3
2
0
0
3
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
4
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
5
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
2
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
2
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
5
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
10
0
0
0
0
0
1
5
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
3
1
0
0
0
0
2
2
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
2
0
1
0
3
0
0
1
0
0
0
0
0
4
0
2
0
0
0
1
0
1
0
0
0
2
0
0
0
1
1
6
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
2
0
0
2
0
1
2
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
4
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
1
0
0
2
0
0
0
0
4
4
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
2
2
2
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
3
0
2
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
3
1
1
4
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
2
1
1
0
0
0
0
0
0
3
0
3
0
1
0
2
0
5
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
4
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
2
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
2
0
0
2
3
1
0
0
0
0
1
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
1
1
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
2
1
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
3
1
1
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
11
0
0
0
2
0
7
0
1
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
6
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
2
0
1
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
6
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
2
2
1
0
0
0
0
0
0
0
0
1
1
2
0
0
1
0
0
0
2
0
0
0
3
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
3
0
1
0
0
1
0
2
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
3
2
0
1
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
5
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
1
0
0
1
4
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
2
1
0
1
2
1
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
2
0
2
0
0
0
2
1
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
1
1
0
2
1
0
0
2
0
0
1
2
1
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
3
0
3
0
1
0
0
0
0
1
1
0
1
0
1
1
0
2
0
0
3
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
8
0
1
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
2
0
0
2
0
0
1
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
4
0
2
1
0
0
1
1
0
0
0
0
0
0
1
1
0
0
2
2
1
2
0
2
0
0
0
0
0
0
2
1
0
0
0
2
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
3
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
3
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
7
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
5
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
2
0
0
2
2
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
1
1
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
1
3
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
4
0
4
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
1
0
0
2
0
2
1
1
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
1
2
0
0
0
4
0
3
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
2
0
0
0
1
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
2
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
11
0
0
0
0
0
1
6
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
3
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
1
2
0
1
0
2
2
0
0
0
3
0
2
2
0
3
0
0
0
3
2
0
0
0
0
0
0
5
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
1
0
2
2
0
0
0
0
0
0
2
14
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
3
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
2
1
0
0
0
0
0
0
0
0
0
5
0
1
0
2
0
0
0
0
0
4
0
0
0
3
0
0
0
0
0
1
0
0
0
2
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
1
0
2
0
0
1
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
1
1
0
2
0
0
0
0
2
0
1
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
6
0
0
3
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
2
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
2
0
0
0
0
0
0
8
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
2
2
0
0
0
0
0
5
0
0
0
0
0
0
8
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
0
0
1
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
6
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
3
0
0
0
2
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
1
2
0
0
2
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
1
0
2
0
2
0
0
2
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
1
1
2
1
0
0
2
0
2
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
1
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
1
1
0
0
1
2
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
1
0
4
3
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
2
1
0
2
1
2
2
0
0
1
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
2
0
5
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
4
2
2
0
0
1
0
0
1
0
2
1
0
1
0
1
0
0
0
2
0
0
0
2
0
0
1
1
0
0
0
0
0
0
1
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
2
0
1
0
0
0
3
0
1
0
2
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
1
0
0
1
0
0
0
0
0
0
2
2
1
0
2
0
6
2
0
0
1
2
0
1
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
2
2
3
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
3
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
3
0
1
0
1
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
2
0
0
1
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
4
0
0
0
1
1
1
0
3
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
4
0
7
0
0
0
1
0
0
7
0
0
0
1
0
2
1
1
0
0
0
1
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
3
1
0
0
0
1
2
0
1
0
0
1
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
1
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
13
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
2
2
4
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
1
0
1
0
3
0
0
1
2
1
1
0
1
0
0
0
0
3
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
2
0
0
4
0
1
0
0
0
1
1
0
0
1
0
1
0
0
1
0
0
0
2
1
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
2
0
2
0
2
0
0
1
1
2
0
0
0
0
0
5
2
1
1
0
0
1
5
0
1
0
0
0
2
0
0
0
1
2
0
0
0
2
3
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
1
0
0
5
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
1
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
2
1
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
4
3
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
3
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
1
0
2
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
1
2
0
0
0
0
1
0
0
1
0
0
0
0
1
4
0
0
0
8
0
1
0
0
1
0
0
4
0
0
2
0
1
0
0
0
2
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
3
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
4
1
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
3
0
1
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
1
3
0
0
0
0
0
6
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
2
1
0
0
2
0
0
2
2
0
0
0
0
4
2
0
2
0
0
0
3
2
0
0
0
2
0
0
0
0
0
0
2
3
4
1
2
0
0
1
0
1
0
0
0
0
0
2
0
2
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
4
0
1
1
0
0
0
2
4
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
1
0
0
2
0
0
0
0
0
0
0
1
7
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
2
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
6
2
0
0
1
0
1
2
0
0
2
0
0
0
0
0
3
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
6
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
6
0
0
0
0
2
0
0
0
0
0
0
0
1
0
3
0
3
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
3
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
7
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
5
0
0
0
0
0
2
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
1
0
14
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
3
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
2
0
1
1
0
0
0
0
2
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
4
0
0
1
0
0
0
2
0
0
0
0
2
0
2
0
0
0
2
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
3
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
2
2
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
2
0
0
0
0
1
1
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
3
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
5
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
3
0
0
1
0
0
2
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
3
0
0
0
0
1
0
0
0
3
0
0
1
0
3
0
0
4
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
6
0
1
0
0
0
0
0
0
1
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
3
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
3
1
0
0
2
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
1
0
4
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
3
2
2
0
0
0
2
2
0
0
0
0
2
2
2
2
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
1
0
0
0
3
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
1
1
0
2
0
2
0
0
0
0
0
6
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
6
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
2
3
0
0
0
0
0
0
1
0
0
2
1
0
2
0
1
0
1
0
0
3
2
0
0
0
0
0
0
2
0
2
0
3
2
0
0
0
0
1
1
0
0
0
0
0
0
0
2
1
2
2
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
1
3
1
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
3
0
2
0
0
1
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
3
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
5
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
1
0
3
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
2
0
1
0
0
2
2
1
0
6
0
1
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
10
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
3
0
0
0
0
0
0
2
0
1
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
2
1
0
1
1
0
0
0
0
0
0
1
2
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
0
2
0
0
0
1
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
1
0
0
0
0
0
2
0
0
1
0
0
2
0
0
3
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
3
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
17
0
0
2
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
1
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
1
2
1
0
0
2
0
0
0
0
0
4
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
2
4
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
4
0
0
0
0
0
0
2
0
0
1
0
1
0
3
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
4
1
0
0
0
0
0
0
2
2
1
0
0
0
3
0
0
0
0
0
0
0
0
3
0
2
3
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
2
2
0
0
0
1
0
0
3
2
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
1
0
0
1
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
3
4
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
9
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
1
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
3
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
1
0
0
3
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
9
0
0
0
1
0
0
0
3
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
1
0
2
0
0
0
0
0
1
2
0
0
0
1
2
0
0
0
0
1
1
0
0
0
0
0
4
0
0
0
1
0
0
0
2
0
0
0
1
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
10
0
0
0
2
2
0
0
0
0
2
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
2
0
3
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
1
1
0
2
0
1
0
1
0
2
0
0
0
2
0
0
1
0
0
0
0
0
4
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
7
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
1
1
2
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
2
1
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
1
0
0
2
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
1
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
3
0
1
1
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
3
0
2
0
0
0
0
2
0
0
0
1
0
2
0
0
3
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
1
2
0
0
0
0
2
0
0
0
1
0
0
2
1
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
1
0
0
1
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
5
2
0
0
2
0
1
0
2
0
0
0
0
0
3
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
13
0
0
1
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
2
2
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
1
0
1
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
1
2
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
6
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
2
0
0
0
0
4
0
0
0
0
0
0
0
3
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
2
1
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
4
0
1
0
2
3
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
1
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
3
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
2
0
2
2
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
2
2
1
1
0
3
0
0
0
1
1
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
3
0
0
1
0
0
0
0
0
0
6
0
0
0
0
0
2
2
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
1
2
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
7
0
0
1
0
0
0
0
1
0
0
0
0
2
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
3
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
3
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
2
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
2
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
3
0
0
0
0
1
1
3
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
1
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
3
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
5
1
2
1
0
0
0
0
1
1
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
1
1
0
0
0
0
0
1
0
0
0
2
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
5
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
2
0
2
0
2
1
0
0
0
1
0
1
0
1
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
3
0
1
0
0
1
2
3
0
0
1
0
0
0
0
0
0
1
0
1
1
2
0
0
0
0
0
1
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
3
0
0
0
0
2
2
1
0
0
0
0
0
0
0
4
0
0
0
3
0
4
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
3
0
0
0
0
0
1
0
2
1
0
0
0
1
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
3
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
2
2
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
3
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
2
2
0
0
0
0
0
2
1
1
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
2
0
1
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
1
4
1
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
2
0
0
1
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
2
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
1
2
0
1
2
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
2
1
0
2
2
1
0
0
0
0
0
5
1
0
0
1
0
0
0
0
0
0
0
1
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
2
1
1
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
3
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
1
2
0
2
1
0
1
0
1
0
1
0
0
0
2
5
0
0
0
0
2
3
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
3
2
0
0
0
2
2
0
0
0
1
0
0
3
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
4
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
2
0
2
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
1
0
0
1
0
0
0
0
2
0
0
2
0
0
1
0
1
0
0
3
0
0
2
1
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
9
0
2
0
0
4
2
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
2
0
2
2
0
3
0
0
1
0
0
0
0
0
4
0
0
0
0
1
0
0
1
2
1
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
3
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
2
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
2
0
2
0
2
0
0
5
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
2
1
0
1
1
0
0
0
0
0
4
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
1
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
3
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
2
1
0
0
0
1
0
0
0
0
1
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
1
0
0
0
0
1
0
2
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
1
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
1
0
0
0
0
1
0
0
0
2
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
1
2
0
1
0
0
0
0
2
0
1
0
0
0
0
2
4
0
0
0
3
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
3
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
2
0
2
0
1
0
2
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
1
0
3
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
1
2
0
0
0
0
3
0
0
0
0
2
0
0
2
0
1
0
0
2
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
1
1
0
0
0
4
0
0
0
0
4
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
5
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
1
0
1
0
0
0
1
8
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
3
0
1
2
0
2
1
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
2
0
1
0
0
0
2
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
2
0
0
0
0
2
2
0
3
0
0
0
0
0
0
2
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
2
0
0
1
0
3
0
0
1
2
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
2
0
0
2
0
5
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
2
0
0
0
2
0
1
0
1
0
0
0
0
0
1
1
2
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
3
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
1
0
2
0
0
0
0
1
0
0
2
2
0
0
2
0
0
0
0
1
2
0
0
2
0
0
0
0
0
1
1
0
0
0
6
0
0
1
0
0
0
0
0
0
2
1
0
0
5
2
0
0
0
0
0
0
0
0
0
1
0
1
2
2
2
0
0
6
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
1
0
2
0
0
0
0
1
0
3
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
1
0
0
1
0
2
0
1
0
0
0
2
0
0
1
3
0
0
0
1
0
0
1
2
2
0
0
0
0
1
0
1
0
3
0
0
0
0
0
0
0
1
0
2
0
0
2
0
1
0
0
3
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
2
0
2
0
0
1
2
2
0
0
1
0
0
1
0
1
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
1
0
0
0
3
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
2
0
0
1
0
0
0
1
0
1
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
3
0
2
1
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
6
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
3
1
0
2
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
4
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
4
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
1
0
2
1
6
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
4
0
0
0
1
4
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
1
0
5
0
0
2
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
1
0
2
0
2
0
1
0
0
0
1
0
2
0
2
1
0
1
0
3
0
4
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
1
0
4
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
4
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
1
0
0
2
2
0
1
0
0
0
0
0
1
2
3
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
1
0
2
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
2
0
0
4
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
3
0
0
1
2
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
1
2
2
0
0
0
0
0
0
1
0
0
1
0
0
3
0
1
2
0
0
0
1
0
0
0
0
1
3
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
2
5
1
0
1
3
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
2
1
0
0
1
0
0
0
0
0
0
1
1
0
0
5
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
3
1
2
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
1
1
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
12
4
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
1
1
0
0
0
2
1
0
0
0
0
0
0
0
5
0
0
0
0
0
5
0
2
1
0
0
0
0
0
0
1
0
1
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
1
1
0
0
0
0
0
1
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
3
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
3
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
2
0
2
0
0
0
0
0
0
7
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
13
3
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
10
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
2
2
1
0
0
0
0
0
3
0
0
0
1
0
0
4
2
2
0
0
0
0
2
0
4
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
3
0
0
0
0
2
0
2
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
2
2
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
1
3
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
1
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
2
2
0
1
0
2
1
1
0
0
0
0
0
0
3
0
1
0
0
2
0
1
1
0
0
0
0
1
0
0
0
9
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
1
0
0
1
0
0
2
0
0
0
1
0
0
0
3
1
0
0
0
0
4
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
9
0
1
0
0
0
1
0
0
1
0
0
0
1
0
2
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
3
0
0
1
0
0
0
0
0
0
2
3
4
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
3
1
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
1
1
0
0
1
1
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
3
0
0
0
1
2
0
0
0
1
0
0
0
0
2
2
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
3
0
0
0
1
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
1
0
0
0
3
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
3
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
7
0
0
0
1
0
0
0
2
2
2
1
0
2
0
2
0
0
0
2
2
0
0
0
0
0
5
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
1
0
1
1
2
1
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
2
0
3
2
2
0
3
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
3
0
1
0
1
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
3
0
2
0
0
0
0
1
1
0
0
2
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
5
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
1
0
0
1
2
0
0
0
0
0
0
0
1
0
0
1
3
2
0
0
0
1
3
0
0
0
0
0
0
2
0
0
4
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
1
2
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
2
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
4
0
1
2
0
0
6
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
1
0
0
0
0
2
0
0
2
0
2
0
3
1
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
1
2
2
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
3
0
0
0
0
1
0
2
2
1
0
0
0
0
0
2
1
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
1
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
1
1
1
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
1
0
0
2
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
2
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
3
2
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
3
0
0
1
0
0
3
0
0
2
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
2
1
1
0
0
2
0
2
0
0
0
0
0
1
1
0
1
2
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
3
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
2
0
0
1
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
1
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
2
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
2
0
0
2
0
0
0
0
0
0
3
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
2
1
2
1
1
0
1
0
2
0
0
2
1
0
1
2
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
1
0
0
1
2
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
3
0
0
0
0
0
1
0
0
2
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
2
0
0
0
0
1
1
0
1
0
0
0
1
0
0
4
0
0
0
0
2
0
4
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
2
1
0
0
2
0
0
1
0
0
0
0
2
0
0
1
0
1
2
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
5
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
3
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
7
0
1
2
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
3
0
0
2
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
3
0
2
1
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
6
0
0
3
0
0
0
2
1
0
0
0
0
0
0
0
2
2
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
2
0
0
1
0
0
0
2
0
1
0
0
0
2
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
1
0
2
2
0
0
0
1
0
0
0
0
0
0
1
0
1
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
3
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
1
1
0
2
0
0
0
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
3
1
0
0
1
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
2
2
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
2
0
1
2
0
0
0
0
4
0
0
0
4
1
1
0
1
3
0
0
1
0
0
0
4
0
2
0
0
0
0
0
1
1
0
0
1
0
0
1
0
1
0
0
0
0
0
1
2
0
1
1
0
1
1
0
0
0
0
0
0
3
0
2
0
0
0
0
3
0
0
0
1
0
0
2
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
2
3
0
0
0
0
0
0
0
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
1
0
0
0
0
0
1
0
2
1
0
0
2
0
0
1
2
0
4
0
1
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
1
1
0
1
0
1
2
0
4
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
2
0
0
1
1
0
1
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
6
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
2
0
1
1
0
1
0
0
4
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
4
1
0
0
2
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
1
1
0
1
1
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
1
0
0
2
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
1
0
1
0
0
0
0
2
0
0
0
0
0
2
0
1
0
2
0
0
0
2
0
1
2
0
0
0
0
1
5
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
5
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
11
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
1
0
0
0
0
0
2
1
0
1
0
0
0
5
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
4
0
0
2
1
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
1
3
0
0
0
2
0
0
0
1
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
2
0
2
0
0
0
5
0
0
1
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
1
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
5
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
2
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
7
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
4
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
2
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
1
0
1
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
2
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
2
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
3
0
0
0
3
0
1
0
0
0
0
2
0
0
0
0
1
2
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
2
1
0
0
0
1
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
2
0
1
0
1
0
1
0
1
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
4
0
0
0
0
1
4
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
3
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
2
1
0
0
0
0
0
2
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
1
3
4
0
0
1
0
0
3
0
0
0
0
0
0
0
0
4
0
0
0
4
0
0
0
0
0
0
0
2
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
1
1
0
0
0
1
0
0
2
0
0
0
2
1
1
0
0
4
0
0
0
1
0
0
0
0
0
1
4
0
0
0
3
0
0
0
2
0
0
0
1
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
14
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
2
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
2
1
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
3
2
0
0
0
2
6
2
0
1
0
0
0
1
0
0
1
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
1
1
0
1
2
2
0
0
0
0
0
0
2
0
0
4
0
0
2
1
1
0
0
0
0
0
1
0
1
1
0
1
2
0
0
0
3
0
3
0
1
0
0
0
2
0
2
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
3
0
0
0
2
0
0
1
0
0
1
0
1
0
1
2
0
0
7
0
1
3
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
5
0
0
0
0
7
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
10
0
0
0
0
0
0
1
0
2
0
0
3
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
9
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
3
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
2
0
1
0
0
0
0
0
1
2
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
6
2
0
0
0
0
0
0
2
1
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
2
0
5
0
0
0
0
0
2
1
0
2
0
0
0
0
5
0
0
0
2
1
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
2
0
2
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
7
0
0
0
0
3
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
1
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
1
2
2
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
2
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
2
6
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
1
0
0
0
0
0
1
0
0
2
7
0
0
0
0
0
3
2
0
0
0
0
0
1
0
0
0
0
0
0
0
6
0
1
1
0
0
0
0
1
0
0
0
0
4
1
0
0
0
0
2
0
0
3
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
2
1
0
0
0
2
0
2
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
1
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
2
2
0
7
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
4
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
3
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
2
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
6
0
0
1
0
0
0
0
0
1
0
0
1
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
3
1
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
5
1
0
0
0
0
0
0
2
1
0
1
0
0
1
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
1
1
2
0
1
0
4
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
2
1
0
0
0
3
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
2
0
1
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
1
0
1
2
0
0
0
1
0
0
3
0
1
2
1
0
3
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
9
0
0
0
1
6
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
5
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
2
2
1
0
0
0
0
1
0
0
0
0
2
0
0
1
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
1
2
2
0
0
0
0
4
0
0
0
0
0
5
0
0
0
0
2
1
0
0
0
0
0
3
0
0
1
1
2
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
4
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
7
0
0
1
0
0
0
0
0
3
0
1
3
1
2
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
1
0
0
1
0
0
0
1
4
0
1
3
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
1
1
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
1
0
2
1
1
1
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
1
2
0
0
1
0
0
0
0
0
4
0
0
0
3
0
0
2
1
0
2
0
0
0
0
0
2
0
2
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
2
3
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
3
1
0
1
0
0
0
3
0
0
0
0
0
0
1
0
1
0
0
1
2
1
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
1
0
2
0
1
0
0
0
10
0
0
0
0
0
0
0
0
0
0
4
2
0
0
0
0
1
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
2
0
0
2
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
1
0
0
1
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
2
3
0
0
0
0
0
0
0
0
0
0
0
4
0
2
0
0
0
0
0
6
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
7
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
2
1
0
2
0
0
0
1
1
1
0
3
0
0
0
0
0
0
0
0
3
0
3
0
2
0
2
0
0
0
0
0
0
1
3
2
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
7
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
1
0
0
0
0
0
0
9
2
2
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
2
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
2
0
0
3
0
0
2
1
0
0
0
0
0
0
1
0
2
1
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
3
0
1
0
0
0
1
3
0
0
0
1
0
0
0
0
2
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
1
0
4
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
1
1
0
0
0
0
2
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
6
0
0
1
2
0
1
0
0
0
0
0
2
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
2
0
2
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
5
0
2
0
0
0
0
0
0
0
0
2
1
0
0
1
2
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
1
0
0
1
0
1
2
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
3
0
0
0
1
0
0
1
0
0
2
0
0
0
1
1
0
0
1
1
2
2
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
3
0
0
2
0
0
0
0
3
0
0
2
2
0
1
2
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
2
1
0
0
0
0
1
2
0
4
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
1
0
0
0
1
2
0
0
0
0
0
1
1
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
3
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
2
0
2
0
0
2
4
2
1
0
1
0
0
2
0
0
1
0
2
0
5
0
1
1
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
1
0
0
0
0
0
0
0
3
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
3
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
5
1
0
0
0
0
0
2
1
0
3
1
0
0
0
3
0
2
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
5
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
5
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
4
0
0
0
0
0
1
0
6
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
7
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
1
0
2
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
8
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
4
0
1
1
0
0
0
0
0
0
0
0
2
0
0
2
1
3
0
3
0
2
3
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
1
1
2
0
2
2
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
4
0
1
0
0
2
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
2
3
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
2
0
3
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
5
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
3
0
0
0
0
0
1
2
0
0
0
0
0
0
1
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
3
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
5
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
2
1
0
0
2
1
0
0
3
0
0
1
2
0
1
0
0
0
1
0
0
0
2
0
0
1
4
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
1
0
1
0
0
1
2
0
1
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
3
0
0
2
0
2
1
1
0
0
1
2
0
0
1
1
0
0
0
0
0
0
0
0
0
3
0
2
0
0
2
0
2
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
1
0
0
0
2
3
0
0
0
0
0
0
2
0
0
4
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
2
0
0
0
0
1
2
2
0
0
0
9
1
0
2
0
0
0
0
0
0
0
1
0
0
2
0
5
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
1
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
2
0
0
1
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
3
0
2
0
0
0
1
1
0
0
0
0
3
0
0
0
5
2
2
1
2
0
0
0
0
3
0
1
0
0
0
0
0
0
0
4
0
1
2
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
2
0
0
1
0
0
0
0
0
2
0
10
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
1
0
3
1
0
1
0
1
0
0
0
0
2
0
1
2
2
0
0
0
0
0
1
2
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
1
0
0
0
16
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
4
0
0
0
3
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
3
0
0
0
0
1
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
2
7
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
3
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
3
0
4
0
0
1
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
8
1
1
2
1
0
0
0
2
0
3
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
5
0
0
0
0
2
0
0
1
3
4
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
5
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
3
0
0
0
3
2
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
1
0
3
1
0
0
2
0
0
1
0
0
1
0
1
0
2
2
0
0
2
0
2
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
4
0
0
0
2
0
0
7
0
0
2
0
4
1
0
4
1
0
0
0
1
5
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
7
2
0
0
0
3
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
2
2
0
0
0
1
0
0
0
1
2
0
0
0
3
0
0
1
1
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
2
1
0
2
5
0
0
0
1
0
6
1
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
3
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
2
0
0
0
0
0
0
0
2
1
0
0
0
2
3
0
2
2
0
0
0
1
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
6
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
5
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
4
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
9
0
0
0
0
0
0
0
0
0
4
0
5
0
0
0
0
0
0
1
0
0
0
2
1
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
3
1
0
3
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
1
1
0
2
2
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
2
0
0
2
4
1
0
3
0
6
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
7
0
1
11
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
1
0
0
0
0
0
0
0
2
2
1
0
0
0
1
0
3
2
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
2
0
0
1
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
5
2
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
1
2
0
0
1
0
1
0
0
0
1
6
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
3
0
0
0
0
3
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
3
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
9
1
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
16
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
1
0
4
0
0
2
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
1
0
0
0
2
0
0
1
0
0
1
0
1
1
0
0
0
2
3
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
1
3
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
2
0
2
0
0
0
1
2
0
0
0
0
0
0
3
0
0
0
0
4
0
0
0
2
0
0
0
4
0
0
0
1
0
5
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
3
1
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
2
0
1
1
0
2
0
0
0
0
0
0
0
3
0
5
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
4
0
2
0
3
0
0
0
1
1
2
0
0
3
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
1
2
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
3
0
0
0
0
0
0
1
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
1
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
1
1
0
0
1
0
0
0
1
1
1
0
0
4
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
3
1
0
0
0
0
1
0
0
2
0
0
0
1
5
0
0
0
0
0
6
0
0
2
0
2
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
1
2
1
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
2
2
0
0
0
0
0
0
1
0
0
1
0
2
0
2
0
0
0
1
0
0
0
1
0
0
1
0
0
2
1
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
1
0
0
2
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
1
0
0
1
0
0
0
0
0
3
1
0
0
0
0
0
1
2
0
0
0
0
2
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
2
2
2
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
2
4
0
3
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
1
1
2
0
0
1
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
2
1
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
10
0
3
0
0
1
0
0
1
2
0
0
0
6
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
1
1
0
0
2
0
0
0
0
1
0
0
1
0
0
0
1
1
2
0
0
2
0
1
0
0
0
0
0
0
6
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
1
2
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
2
0
0
2
0
2
1
0
2
1
0
2
0
3
1
0
0
0
2
0
0
0
0
1
0
0
0
3
0
0
1
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
3
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
2
1
1
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
2
0
0
1
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
2
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
3
0
0
0
5
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
6
0
0
0
2
0
1
0
0
3
0
0
0
0
0
0
0
0
2
0
2
1
2
2
0
0
0
0
0
1
0
0
2
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
11
0
0
0
0
0
0
0
0
0
2
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
3
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
2
1
0
0
0
0
2
0
0
1
2
0
1
0
0
0
0
0
0
1
1
3
2
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
1
2
2
0
2
0
1
0
2
0
1
3
3
0
1
0
0
0
1
0
4
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
3
0
0
0
1
0
0
1
0
0
0
0
5
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
2
5
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
2
2
0
0
2
2
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
5
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
4
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
1
1
0
5
0
0
1
0
0
0
2
0
0
2
0
0
1
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
1
1
0
3
0
0
0
0
2
2
0
0
0
1
0
0
0
3
0
0
0
0
2
1
0
0
2
0
0
0
0
2
0
1
0
0
2
0
0
0
3
0
0
0
0
4
0
0
0
1
0
0
3
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
1
2
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
2
0
3
0
0
0
1
0
0
0
0
1
4
0
0
0
0
2
0
0
0
0
0
0
2
5
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
2
1
0
0
0
0
0
2
4
0
2
1
2
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
4
0
1
0
0
0
0
0
2
0
0
0
0
1
2
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
4
2
0
0
2
1
3
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
3
0
1
1
0
0
3
3
1
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
1
5
1
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
2
0
0
0
1
0
0
0
2
0
0
0
2
0
0
4
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
2
1
0
0
0
0
0
0
2
0
2
0
1
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
6
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
1
0
2
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
2
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
3
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
1
3
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
5
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
3
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
2
0
1
2
0
0
0
2
0
0
0
2
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
1
0
1
0
0
1
7
0
0
0
0
0
7
1
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
2
2
1
0
0
0
0
0
1
0
0
0
0
0
0
1
2
1
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
1
0
3
0
0
0
2
0
0
0
0
0
0
0
1
0
4
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
1
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
1
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
1
1
2
2
0
0
0
0
0
0
0
0
0
7
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
1
0
0
1
2
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
2
1
0
0
2
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
1
0
0
3
1
1
0
0
2
0
1
0
0
0
0
3
1
0
0
0
0
0
2
0
0
0
5
0
0
0
0
1
0
0
1
0
2
0
0
2
0
0
0
2
0
0
1
0
2
2
0
0
0
0
1
0
0
0
2
0
0
0
0
1
2
2
0
2
0
4
0
0
0
0
0
5
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
5
0
0
0
0
0
1
2
0
3
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
3
0
0
0
0
2
2
0
0
0
2
0
1
3
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
4
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
3
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
1
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
2
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
2
4
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
1
0
0
0
0
1
0
0
0
5
1
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
2
0
0
2
0
11
0
0
2
0
0
0
0
0
0
2
0
0
4
2
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
3
1
3
0
2
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
3
0
1
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
6
0
3
0
0
0
1
3
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
3
0
1
0
0
3
0
0
0
2
0
0
1
7
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
3
0
0
2
1
0
0
2
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
2
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
2
2
2
2
0
0
0
0
0
0
3
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
1
2
0
0
1
0
2
0
0
0
0
0
2
4
0
1
0
0
0
2
0
0
0
1
0
1
2
1
0
0
0
0
2
0
0
3
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
2
0
4
0
1
0
0
0
1
0
0
0
0
0
0
0
3
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
12
0
0
6
0
0
0
2
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
1
0
0
0
1
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
2
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
11
0
0
0
1
1
2
0
0
0
1
1
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
2
2
2
1
2
0
2
0
0
2
0
2
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
2
5
1
2
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
4
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
4
1
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
4
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
3
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
2
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
2
0
1
1
0
0
0
1
0
1
0
2
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
1
3
0
2
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
3
0
1
0
0
0
0
0
4
0
0
2
0
1
0
2
2
0
3
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
2
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
2
3
2
0
0
2
0
0
0
0
0
2
0
0
1
0
0
1
0
1
1
4
2
0
0
0
1
0
1
0
0
1
0
2
2
0
0
0
3
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
3
0
0
1
2
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
2
0
0
0
0
1
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
2
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
4
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
1
0
0
0
0
0
0
3
0
2
0
0
1
0
2
0
0
0
4
1
0
0
1
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
1
0
0
0
2
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
5
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
3
2
0
2
0
0
0
0
3
0
0
5
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
8
0
2
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
6
0
8
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
4
6
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
2
0
2
1
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
3
1
0
0
0
0
0
0
2
6
0
0
4
0
0
0
0
0
1
0
0
0
0
1
0
0
0
7
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
2
1
1
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
1
2
2
0
0
0
0
0
2
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
1
0
1
0
1
2
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
1
0
0
0
0
4
0
0
0
0
2
0
1
0
0
1
0
1
0
0
1
0
0
2
0
0
1
2
0
1
0
0
0
0
0
0
1
0
0
7
1
0
1
0
2
0
0
1
0
0
0
0
1
14
2
0
1
2
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
2
1
0
2
0
2
0
1
1
0
0
3
0
0
2
0
0
2
0
2
0
0
0
0
2
0
0
0
1
0
0
2
3
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
3
0
0
3
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
3
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
5
0
1
0
0
0
0
0
0
4
1
0
0
0
1
0
0
0
0
0
0
3
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
2
4
0
0
2
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
4
0
1
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
1
3
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
5
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
1
2
1
0
0
0
0
1
0
2
1
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
1
1
0
0
0
0
0
2
0
0
0
0
0
0
5
1
0
1
0
0
1
0
0
0
1
2
0
0
2
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
7
0
1
7
0
0
2
0
0
0
0
0
0
0
10
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
3
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
2
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
1
1
0
0
0
0
2
0
2
0
1
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
2
0
0
1
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
3
1
0
0
0
0
1
1
1
2
7
0
0
0
0
2
0
0
2
0
7
0
0
1
0
0
3
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
1
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
2
0
1
1
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
3
0
0
0
0
1
0
0
4
0
0
0
2
7
0
2
0
2
0
0
0
0
0
3
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
2
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
2
1
0
0
4
0
0
0
0
0
0
0
0
0
1
0
2
0
3
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
4
2
3
1
1
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
1
0
2
1
0
1
0
0
3
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
4
0
0
2
0
0
1
0
0
0
1
0
1
1
0
0
0
2
0
2
2
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
2
0
0
0
2
0
0
0
0
0
2
4
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
1
1
2
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
2
0
0
0
0
2
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
4
0
2
1
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
12
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
4
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
2
1
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
1
1
0
1
0
0
2
0
2
0
0
0
0
0
1
0
0
0
1
2
0
0
1
0
0
0
3
6
0
4
0
1
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
2
0
0
0
0
2
1
0
0
0
3
1
0
0
1
4
5
2
0
0
0
0
0
0
0
0
0
2
1
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
2
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
3
2
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
2
0
1
0
1
0
0
0
0
0
0
1
0
0
0
7
0
0
0
0
1
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
2
0
0
1
0
0
11
0
0
8
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
3
0
2
0
0
0
0
0
0
0
2
5
1
0
0
1
0
2
0
0
0
0
0
2
1
2
4
0
0
0
0
2
4
0
0
0
0
2
2
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
5
0
0
2
0
2
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
3
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
1
0
0
3
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
1
0
3
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
3
0
0
1
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
2
2
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
6
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
4
0
0
0
0
1
0
1
0
0
0
0
2
1
3
0
3
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
2
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
1
0
2
0
0
1
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
5
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
1
0
3
1
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
2
0
0
0
1
6
0
0
1
3
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
11
1
2
0
0
2
0
0
0
0
0
3
0
2
0
0
0
0
1
0
5
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
3
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
5
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
1
13
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
5
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
1
0
0
0
2
0
3
0
0
0
0
2
0
0
1
2
0
0
0
0
2
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
1
0
0
1
0
0
0
0
0
1
0
0
2
4
0
0
1
1
1
0
0
0
0
0
2
0
0
0
0
3
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
16
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
2
0
4
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
11
1
1
0
0
2
2
0
2
0
2
1
0
2
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
4
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
3
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
3
1
1
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
1
1
0
4
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
7
0
2
3
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
3
0
3
1
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
6
4
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
2
0
3
0
0
0
0
0
0
0
0
3
4
1
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
2
1
1
7
0
0
0
0
0
1
0
1
2
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
1
2
0
0
0
3
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
1
0
1
0
0
1
1
0
0
1
0
0
2
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
1
0
0
0
3
3
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
1
1
0
2
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
2
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
1
0
1
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
2
1
1
0
0
2
0
0
0
0
0
1
0
0
0
4
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
5
4
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
3
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
2
0
1
0
1
2
0
0
4
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
4
1
2
0
0
0
0
0
2
0
0
1
1
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
3
0
0
0
0
2
0
0
0
1
1
0
1
0
0
0
0
0
1
2
2
0
2
1
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
5
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
1
4
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
3
1
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
4
1
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
4
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
3
1
0
0
0
0
1
0
0
0
0
0
2
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
1
0
0
0
0
0
2
0
3
0
0
0
0
1
2
0
3
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
2
0
5
0
0
2
0
0
1
0
1
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
3
1
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
3
0
0
0
5
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
2
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
5
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
4
0
0
0
1
0
2
1
0
0
1
0
1
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
2
0
0
0
0
2
1
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
4
1
0
0
2
2
0
0
0
0
1
3
0
9
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7
0
0
0
2
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
5
2
1
0
0
0
2
2
0
0
0
0
1
0
0
0
2
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
6
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
5
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
2
4
0
0
2
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
3
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
2
0
2
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
1
2
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
7
0
1
0
3
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
1
2
0
0
0
1
1
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
3
0
2
0
0
0
0
2
0
1
0
3
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
2
0
0
1
4
1
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
3
0
2
0
2
0
0
2
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
1
0
0
1
3
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
2
1
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
4
0
2
1
0
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
4
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
4
0
1
2
0
0
0
0
0
0
0
0
0
1
1
0
1
0
2
0
0
3
0
0
0
0
0
6
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
1
0
0
0
2
2
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
5
2
0
0
2
2
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
3
0
0
0
0
0
3
2
0
1
0
0
2
0
2
0
0
0
3
0
0
0
1
0
0
0
0
0
0
3
0
1
0
0
11
0
1
0
0
1
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
1
0
2
0
0
3
0
0
0
0
1
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
1
0
2
0
0
0
2
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
2
3
0
0
0
0
2
0
1
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
3
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
3
0
0
0
0
2
1
0
0
0
0
1
0
1
0
2
0
0
0
2
3
0
0
1
0
0
0
2
0
0
2
0
1
3
0
0
0
0
2
1
1
0
2
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
3
0
0
0
0
0
0
0
0
1
2
2
0
0
2
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
4
0
0
0
0
1
0
1
0
0
0
0
0
0
5
0
0
3
0
0
0
1
2
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
3
1
1
1
1
2
0
1
0
0
1
2
1
0
0
0
0
0
2
1
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
1
8
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
9
11
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
4
2
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
1
0
2
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
5
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
3
3
0
0
0
0
0
2
0
0
3
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
2
2
0
0
3
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
4
0
0
1
0
1
0
5
3
0
0
1
0
1
0
0
0
0
0
0
0
0
2
1
0
10
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
3
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
3
0
0
0
3
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
5
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
1
2
0
2
0
0
1
0
0
0
0
0
0
2
0
1
1
0
2
0
0
0
0
1
0
2
0
0
1
1
0
3
0
0
1
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
8
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
5
0
0
0
0
1
0
1
0
0
0
2
1
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
5
0
0
0
1
3
4
0
2
0
6
0
0
0
1
0
2
2
0
3
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
3
0
2
2
0
1
0
0
0
0
1
0
0
2
0
0
1
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
1
4
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
4
0
1
0
0
1
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
3
0
0
0
1
0
0
0
0
0
1
1
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
1
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
6
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
5
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
4
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
2
1
0
0
0
1
2
0
0
0
1
0
1
3
0
1
0
0
0
0
2
0
0
1
0
2
1
1
0
0
0
0
1
6
3
0
0
2
0
2
0
0
0
1
0
0
1
0
1
4
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
3
0
5
0
1
0
2
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
3
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
1
2
0
0
0
2
0
0
3
0
0
0
1
0
0
4
1
0
0
0
0
0
0
1
1
1
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
1
0
0
0
2
1
5
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
3
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
3
0
6
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
6
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
2
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
3
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
4
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
7
2
0
0
1
0
0
0
0
1
0
0
0
0
0
2
1
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
1
2
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
2
0
1
0
0
0
0
0
0
0
0
1
0
0
5
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
1
0
0
0
0
0
0
0
3
1
0
0
1
0
2
0
2
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
1
0
0
1
2
1
0
0
0
2
1
1
3
0
0
2
1
0
2
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
6
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
5
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
3
0
0
2
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
2
0
1
0
0
0
3
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
6
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
1
2
0
0
0
1
1
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
1
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
1
1
0
0
0
2
0
1
2
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
1
2
1
1
1
3
1
0
1
0
1
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
2
0
2
1
2
0
0
1
0
1
0
0
2
0
0
0
2
0
0
0
0
0
5
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
1
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
2
0
1
0
2
0
0
1
0
1
0
2
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
1
0
4
1
0
1
0
0
0
0
0
3
0
0
0
2
0
1
0
1
0
0
0
0
0
0
1
1
2
0
0
0
2
0
0
0
1
0
0
2
1
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
10
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
1
0
1
0
1
7
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
1
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
6
0
0
0
0
1
3
0
0
0
0
0
0
0
2
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
2
2
1
1
1
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
2
0
0
1
0
0
1
0
0
0
0
0
1
2
2
1
0
0
0
1
2
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
6
0
1
0
2
0
0
2
0
2
0
0
0
0
2
0
0
2
0
1
0
1
0
1
0
0
2
2
0
0
0
0
0
3
1
0
0
0
2
0
1
0
0
1
0
0
2
0
0
2
0
4
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
2
0
2
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
6
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
5
0
2
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
2
0
0
2
0
1
0
0
2
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
1
0
1
0
0
0
5
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
1
6
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
16
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
1
0
0
0
0
3
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
3
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
2
2
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
4
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
1
1
0
2
0
0
0
1
1
0
2
3
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
5
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
1
0
2
2
0
0
2
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
4
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
4
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
2
2
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
5
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
3
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
5
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
1
0
3
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
4
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
2
2
1
1
0
0
0
0
2
0
1
0
1
0
0
0
0
1
0
2
0
0
0
1
0
0
1
0
1
0
1
1
1
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
3
0
0
0
0
1
0
2
0
2
0
0
1
0
0
0
0
1
1
1
1
0
0
0
1
0
4
1
0
0
0
0
0
0
0
0
0
0
0
2
1
1
1
0
0
1
0
0
0
2
0
0
2
2
1
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
3
0
0
2
5
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
2
0
0
0
0
0
1
0
3
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
12
0
0
1
2
0
0
2
2
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
4
0
0
0
2
0
0
0
1
0
0
0
0
2
2
0
0
1
0
1
0
3
0
2
0
0
0
0
0
0
0
2
3
0
2
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
1
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
1
0
0
1
0
2
0
6
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
3
0
0
0
0
0
1
2
0
2
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
3
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
1
0
1
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
2
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
3
0
0
0
0
0
0
0
2
3
1
1
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
4
2
0
1
3
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
7
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
2
3
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
4
0
0
0
3
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
2
0
0
0
0
0
2
2
1
0
0
1
1
0
0
2
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
3
0
0
2
0
1
1
0
0
0
0
1
1
0
0
0
0
0
1
0
3
0
0
2
0
1
2
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
2
1
0
0
0
0
0
0
0
0
0
1
0
2
1
4
0
3
0
1
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
2
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
2
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
1
1
0
0
0
4
1
0
0
0
0
0
0
1
0
0
1
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
2
7
0
0
7
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
7
0
0
0
0
0
0
0
0
2
0
1
0
1
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
2
0
0
3
0
0
0
1
2
0
7
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
1
0
0
1
1
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
4
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
6
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
4
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
3
0
1
0
3
0
0
0
0
0
1
0
2
0
0
4
0
0
0
0
2
0
1
0
0
0
0
1
1
0
0
0
5
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
2
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
2
0
0
1
0
0
0
1
1
0
2
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
1
0
0
0
3
0
0
0
1
0
0
0
2
0
0
0
0
0
3
0
0
0
0
2
2
6
0
0
2
1
0
0
4
0
3
1
0
2
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
2
0
1
4
0
1
0
11
0
0
0
0
0
0
0
0
0
0
3
0
0
3
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
1
1
1
0
2
2
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
1
2
0
0
2
0
3
0
0
0
1
3
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
1
3
1
0
0
0
0
2
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
8
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
2
2
0
0
3
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
3
2
8
1
1
2
0
0
0
2
0
0
0
0
0
0
10
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
1
0
0
0
3
2
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
1
1
0
0
0
0
2
0
3
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
3
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
1
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
2
0
0
0
0
1
1
0
0
1
0
0
0
0
1
1
0
0
0
0
2
0
0
0
1
1
0
3
0
0
3
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
2
1
0
2
0
1
0
0
0
0
0
0
0
4
0
0
0
2
0
3
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
1
2
0
1
2
0
0
0
0
2
1
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
2
1
1
0
0
0
0
0
0
3
0
0
0
1
1
3
1
0
0
0
0
0
0
1
2
3
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
1
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
3
1
0
0
0
0
0
0
0
2
0
2
0
0
2
2
1
0
1
1
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
2
0
0
0
0
1
1
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
2
1
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
4
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
2
0
3
0
0
0
4
3
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
4
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
10
0
1
0
0
1
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
3
0
4
0
0
0
4
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
2
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
1
1
0
0
2
0
0
0
0
0
2
1
0
3
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
3
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
3
0
0
0
0
0
0
0
2
5
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
4
3
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
2
1
0
0
2
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
3
1
0
0
0
0
0
0
0
2
0
0
2
0
1
0
1
0
0
0
2
0
1
0
0
0
0
0
2
0
0
2
0
1
2
0
0
2
0
0
0
2
0
0
0
1
0
0
2
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
2
1
0
3
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
1
0
1
0
0
2
0
1
1
0
0
1
0
0
0
1
0
0
0
0
1
0
2
0
0
0
1
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
3
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
1
0
0
1
0
2
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
2
0
0
0
1
1
0
0
0
1
0
1
5
0
1
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
2
1
0
1
0
0
1
1
0
1
2
2
0
0
0
3
0
0
0
0
0
3
0
0
3
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
1
0
0
1
0
1
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
5
0
0
0
0
0
0
1
1
0
7
0
0
0
1
0
0
1
0
0
0
1
0
6
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
4
0
1
0
1
0
1
0
0
0
1
0
3
8
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
2
0
4
3
0
0
0
2
0
1
0
2
0
0
0
6
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
2
1
0
0
0
3
0
0
0
0
1
0
2
0
2
0
1
0
1
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
3
0
0
1
1
0
2
0
0
4
2
1
0
2
0
0
0
1
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
2
0
0
0
0
0
0
0
4
0
0
0
2
3
0
0
0
0
1
0
1
1
0
1
2
0
1
0
0
0
0
0
1
1
0
0
1
0
0
2
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
1
0
30
0
1
2
0
0
0
0
0
0
2
0
0
0
2
4
0
2
0
2
0
0
0
1
0
0
0
0
3
0
0
1
0
0
1
2
0
1
0
0
2
2
1
0
0
0
0
0
0
2
0
0
3
2
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
2
1
2
0
1
0
2
2
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
2
0
0
0
0
1
0
0
1
0
2
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
1
1
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
7
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
1
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
3
0
1
0
0
2
0
0
2
0
2
0
1
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
2
0
2
0
0
0
1
0
0
2
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
1
1
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
2
0
0
0
0
0
0
2
1
0
0
0
2
1
0
0
1
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
2
4
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
2
1
0
0
2
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
4
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
6
0
0
0
0
0
0
0
0
1
1
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
3
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
8
0
0
0
0
2
0
1
0
0
1
1
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
8
0
0
0
2
0
1
0
0
3
0
1
1
0
0
1
0
0
0
0
1
0
1
0
0
0
2
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
1
2
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
1
2
0
2
0
0
0
0
1
2
2
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
2
2
0
3
1
0
0
4
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
4
0
0
0
0
0
2
0
0
0
0
2
1
1
1
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
1
0
0
9
2
0
0
0
0
1
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
3
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
1
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
1
0
2
1
0
0
0
0
3
0
4
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
3
1
0
0
0
0
3
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
3
0
1
0
0
1
0
0
0
0
2
0
4
2
0
0
0
0
0
0
1
9
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
2
0
0
1
0
2
0
0
1
2
3
0
0
0
0
0
0
0
0
2
0
0
0
1
1
2
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
3
0
0
6
0
0
1
0
0
0
1
1
0
1
0
0
0
2
1
0
2
1
0
1
3
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
2
0
0
0
0
0
0
0
3
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
5
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
3
1
0
0
0
0
0
1
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
1
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
4
0
0
0
0
0
0
8
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
4
0
2
0
0
1
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
5
0
2
0
0
0
1
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
3
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
2
0
2
0
1
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
3
0
1
1
2
0
1
0
2
0
2
0
0
0
2
0
0
0
0
5
0
0
0
0
0
0
1
1
0
3
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
1
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
1
0
1
0
0
2
0
0
1
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
2
1
0
0
2
1
0
0
1
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
1
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
2
0
0
2
0
0
0
1
0
2
3
0
0
2
0
2
0
0
0
0
0
3
0
0
2
0
2
0
2
0
0
0
0
0
5
0
0
0
1
0
2
2
2
3
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
4
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
1
0
4
0
1
0
1
0
0
0
0
0
2
0
1
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
1
1
0
0
2
0
0
0
0
0
1
2
1
0
0
1
1
0
1
0
0
0
0
1
1
0
4
0
1
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
3
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
2
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
3
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
1
2
0
3
0
0
1
0
0
0
1
0
0
1
1
2
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
3
0
0
4
0
0
0
3
0
0
0
1
0
5
1
0
0
1
0
0
0
0
0
0
0
5
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
3
0
0
0
1
2
0
0
0
2
1
0
0
3
1
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
2
0
1
0
0
2
2
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
6
0
0
0
0
0
0
0
1
0
0
6
0
0
2
0
0
1
0
2
0
2
0
0
1
0
0
0
0
0
0
5
2
3
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
5
0
0
0
0
1
1
0
0
0
2
0
0
0
0
2
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
3
2
1
0
2
0
0
1
0
1
0
1
2
0
0
0
1
0
1
0
0
0
0
0
2
0
2
0
0
1
0
1
0
0
0
0
1
0
2
0
3
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
2
0
0
3
0
1
0
0
0
0
0
2
0
3
0
0
2
0
0
0
1
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
1
0
0
0
0
5
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
1
0
3
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
1
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
2
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
3
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
3
0
4
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
5
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
1
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
2
1
0
0
0
2
2
0
0
5
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
1
0
1
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
4
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
1
0
0
3
0
1
0
0
0
1
1
0
1
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
3
0
0
0
0
0
4
0
0
0
2
1
0
0
1
1
0
0
1
0
0
0
0
2
1
0
2
1
0
0
6
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
2
0
0
1
2
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
2
0
1
0
0
0
0
0
2
0
0
0
0
0
1
3
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
1
0
0
0
0
0
1
1
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
2
0
2
4
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
1
0
0
1
3
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
1
2
0
0
1
0
0
0
0
0
0
0
1
0
0
1
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
2
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
3
2
0
0
0
1
0
0
0
0
1
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
1
2
0
0
0
0
1
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
5
0
0
0
0
0
3
0
0
2
0
0
0
2
0
2
0
0
0
0
2
0
2
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
5
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
2
1
2
0
0
0
0
0
2
0
0
1
0
2
0
0
1
0
0
2
0
0
6
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
3
0
1
0
0
0
1
0
0
0
1
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
1
0
1
2
0
1
0
0
0
0
1
0
2
1
1
0
0
2
0
0
3
2
0
0
0
0
2
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
5
0
0
0
0
7
0
0
1
2
0
0
0
1
1
0
0
2
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
1
2
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
1
0
3
0
0
0
5
0
0
7
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
7
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
4
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
1
0
1
0
0
1
0
1
0
2
0
2
0
0
3
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
6
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
3
0
1
0
0
0
0
0
0
1
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
1
0
2
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
2
2
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
2
0
0
1
1
0
0
6
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
5
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
3
4
0
1
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
1
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
2
2
1
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
4
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
1
0
0
1
0
0
0
0
1
1
1
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
3
0
0
0
1
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
2
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
1
0
0
1
1
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
4
0
1
1
0
0
0
1
2
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
2
0
3
0
1
1
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
3
0
0
1
0
1
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
3
0
0
0
1
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
3
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
5
0
0
2
0
0
0
0
1
2
1
0
0
1
0
0
0
0
1
0
0
1
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
1
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
1
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
2
0
0
4
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
1
4
0
0
0
0
0
0
2
2
3
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
2
0
1
0
4
2
0
1
0
1
0
0
0
0
0
0
3
0
2
0
0
0
2
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
4
0
0
0
4
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
2
0
0
0
0
1
0
0
2
0
0
0
1
0
1
0
2
0
0
0
2
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
4
0
0
0
3
0
1
2
2
1
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
2
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
3
0
1
0
2
1
1
0
0
0
0
0
0
3
2
1
0
0
0
0
0
0
0
3
0
0
3
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
1
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
2
0
1
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
4
0
0
0
0
0
1
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
2
0
0
0
2
1
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
4
0
2
0
0
0
0
0
1
3
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
5
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
1
2
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
3
2
0
0
2
1
1
1
0
0
0
15
0
0
2
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
1
0
0
0
0
0
0
1
3
0
1
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
5
0
0
3
0
0
0
1
0
2
0
0
9
2
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
2
2
3
0
0
1
0
0
0
1
0
1
0
3
1
1
1
0
0
0
4
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
6
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
1
2
0
0
0
2
0
2
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
2
1
0
0
1
2
0
0
2
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
3
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
3
0
0
3
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
3
0
0
1
1
0
0
0
0
0
0
0
1
0
4
2
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
1
2
0
1
0
0
1
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
12
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
3
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
1
1
0
0
0
0
3
0
0
2
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
1
3
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
1
1
3
0
0
0
0
0
0
0
0
0
1
1
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
7
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
2
0
3
0
2
0
0
2
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
6
1
0
0
0
3
6
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
2
0
0
2
1
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
3
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
4
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
1
0
2
2
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
2
2
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
3
1
1
0
0
2
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
2
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
1
2
0
0
4
0
0
1
0
0
1
0
0
0
1
0
0
2
0
0
1
1
2
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
4
0
0
2
2
0
0
0
1
0
0
5
2
2
1
2
0
2
0
2
1
6
0
0
1
1
1
0
2
1
0
0
2
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
3
0
0
1
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
2
0
1
0
1
0
0
0
1
0
3
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
1
1
1
2
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
1
0
0
2
1
0
0
0
1
0
1
1
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
2
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
2
1
0
1
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
2
1
0
0
0
1
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
4
0
1
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
1
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
10
0
0
2
0
2
0
0
0
0
0
2
0
0
2
2
2
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
2
0
7
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
6
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
1
0
1
3
2
2
0
0
0
1
0
1
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
3
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
3
1
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
2
2
0
0
0
0
1
0
0
0
0
4
0
0
0
0
1
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
3
3
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
1
2
0
0
0
0
0
0
3
0
4
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
3
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
1
0
1
2
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
3
3
0
0
0
2
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
5
0
0
2
0
0
0
0
0
0
1
3
0
4
2
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
1
0
0
1
2
0
0
3
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
1
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
1
0
0
0
0
0
3
0
0
1
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
2
0
0
0
1
2
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
5
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
2
0
2
1
0
1
0
0
0
0
2
0
0
2
0
0
0
1
0
0
1
2
0
0
9
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
7
1
1
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
5
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
3
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
8
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
2
1
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
3
0
0
0
3
0
0
0
0
2
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
2
1
0
0
1
0
4
0
0
0
1
1
1
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
2
0
0
0
0
0
2
2
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
3
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
1
0
0
1
1
0
0
0
2
0
0
0
2
0
0
0
4
0
1
0
0
0
2
0
0
0
0
0
2
0
1
1
2
0
0
0
0
1
1
0
0
0
2
5
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
1
4
2
2
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
1
0
0
0
0
0
0
1
0
4
1
0
0
1
0
1
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
2
0
0
0
0
5
0
0
2
0
0
1
0
0
0
3
0
2
0
0
0
0
0
0
2
0
0
0
2
2
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
2
0
0
0
1
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
3
0
0
0
0
0
3
0
0
4
0
2
0
0
2
0
0
0
0
1
0
0
1
0
1
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
1
2
0
0
1
0
0
2
0
0
0
1
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
2
0
0
1
3
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
1
0
0
0
0
0
4
1
1
0
0
0
4
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
3
0
1
0
0
1
0
0
0
0
0
0
6
0
0
1
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
2
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
5
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
7
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
1
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
1
1
2
0
0
0
1
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
1
2
1
1
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
3
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
3
0
0
1
0
0
0
3
0
2
0
1
1
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
2
1
3
0
0
2
0
2
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
4
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
9
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
2
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
3
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
2
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
2
0
2
2
0
0
0
0
0
0
0
0
6
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
2
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
5
0
0
0
1
0
0
0
0
0
2
0
0
0
10
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
2
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
3
2
2
1
0
0
0
0
0
2
0
0
0
0
3
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
1
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
2
0
0
2
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
1
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
3
0
0
0
1
0
4
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
3
0
0
0
0
1
0
0
0
5
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
1
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
2
0
6
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
1
0
0
4
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
1
0
1
0
0
0
0
0
1
0
0
1
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
2
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
1
0
2
2
0
0
2
0
0
1
0
2
0
0
0
0
0
3
0
0
3
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
1
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
2
2
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
1
0
0
1
2
2
0
0
0
0
1
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
2
0
1
3
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
1
0
2
0
4
2
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
1
1
0
0
1
0
1
3
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
1
0
0
0
0
0
5
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
1
0
1
0
0
0
2
2
0
0
0
1
0
0
0
2
2
0
1
0
1
0
0
0
0
1
3
1
0
2
0
3
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
1
3
2
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
3
0
0
1
0
1
0
0
0
0
3
0
0
2
0
0
0
0
0
2
0
3
0
0
0
0
0
1
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
1
0
0
0
0
0
2
3
0
0
0
1
0
0
0
0
3
0
0
1
0
1
0
0
0
4
2
0
0
0
0
0
0
2
0
0
0
0
0
5
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
1
0
0
0
0
0
1
2
0
1
0
0
0
1
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
2
1
0
0
0
9
0
1
0
3
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
2
1
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
1
1
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
3
2
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
3
2
2
1
1
0
1
0
1
0
0
4
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
3
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
2
0
1
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
2
4
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
8
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
1
2
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
5
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
8
0
0
1
4
0
0
0
0
0
0
2
0
0
0
0
0
0
0
5
0
0
0
0
0
0
1
0
0
0
0
2
0
5
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
5
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
5
0
0
2
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
2
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
11
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
1
2
0
0
0
6
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
3
0
0
2
5
1
0
0
0
2
1
0
0
0
0
1
0
2
0
0
0
4
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
2
0
1
0
0
1
2
0
0
1
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
4
0
0
0
0
0
1
0
1
0
2
11
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
1
2
0
4
0
2
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
2
0
2
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
2
1
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
1
1
0
0
0
2
0
0
1
0
0
1
2
1
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
3
0
1
2
0
0
0
0
1
1
1
0
0
0
0
0
0
0
2
0
0
0
0
4
0
1
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
8
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
7
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
5
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
8
6
0
0
2
2
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
5
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
1
3
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
6
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
6
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
2
4
2
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
1
2
0
0
0
4
0
0
2
0
0
3
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
2
0
2
4
0
0
0
0
0
0
0
0
0
0
2
0
0
3
2
0
0
2
0
2
0
0
0
2
0
0
1
0
3
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
2
1
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
1
4
0
0
0
4
2
0
0
0
0
0
0
1
0
2
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
1
0
2
0
0
0
0
0
2
14
1
3
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
1
0
0
12
4
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
3
0
2
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
3
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
1
1
0
0
8
0
0
2
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
4
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
1
1
1
0
0
2
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
3
2
0
0
0
0
0
2
0
0
2
0
1
0
0
0
1
0
0
0
1
0
0
0
1
2
0
0
0
1
0
0
0
0
5
0
3
0
4
0
1
0
0
1
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
1
0
2
0
0
0
0
0
0
1
0
0
2
1
1
0
0
0
0
0
0
1
2
0
0
0
3
2
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
1
2
0
0
0
0
0
0
2
0
0
1
0
4
0
0
0
2
2
0
0
0
1
1
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
1
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
2
0
0
3
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
3
2
3
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
7
0
1
1
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
4
2
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
1
0
0
1
0
0
0
2
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
1
1
1
0
1
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
2
0
2
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
3
0
2
1
0
0
0
0
1
0
1
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
3
0
0
6
0
1
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
1
0
0
0
2
2
1
0
1
0
0
1
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
3
2
0
0
0
0
1
0
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
2
0
2
0
2
0
1
2
1
0
0
0
0
0
1
0
0
0
0
0
1
9
1
0
0
1
2
1
0
1
1
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
6
0
0
0
0
0
0
0
8
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
5
0
1
0
1
2
1
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
7
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
3
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
1
0
2
1
0
1
0
0
0
2
0
0
0
3
0
0
0
0
1
2
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
1
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
1
2
0
1
0
0
0
0
0
1
0
1
2
0
1
2
1
0
4
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
1
0
1
0
3
0
0
0
0
0
0
0
0
2
0
5
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
3
0
1
0
0
0
0
1
4
0
0
0
2
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
2
2
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
1
0
3
2
0
0
0
0
0
1
0
1
0
0
1
3
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
4
0
0
3
0
4
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
3
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
2
0
4
2
0
1
2
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
3
0
0
0
0
2
1
0
1
0
1
1
1
1
1
0
0
0
0
0
1
0
0
4
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
1
0
0
1
0
1
0
0
1
2
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
3
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
2
2
0
2
0
0
0
3
1
0
0
0
0
1
0
2
0
1
2
0
0
0
0
0
0
4
0
2
0
0
0
3
0
0
2
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
2
0
0
0
2
0
0
1
0
0
3
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
3
1
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
13
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
1
1
0
0
0
1
0
0
4
0
0
0
0
2
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
1
2
0
0
0
1
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
6
0
3
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
2
0
2
0
1
0
5
3
2
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
4
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
5
0
1
0
0
0
0
2
0
3
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
2
0
0
0
0
0
2
1
2
1
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
1
1
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
2
3
0
0
1
0
0
1
0
0
0
2
2
0
0
1
0
0
0
3
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
3
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
2
0
1
0
0
1
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
5
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
3
2
2
0
0
0
2
0
0
0
1
0
0
2
1
0
0
2
0
5
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
0
2
9
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
4
1
2
0
2
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
2
1
1
0
0
1
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
2
0
0
1
0
1
0
2
0
0
0
0
2
0
0
0
0
4
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
2
0
0
2
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
2
1
1
3
0
0
3
0
0
0
0
0
1
3
0
0
2
1
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
1
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
3
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
1
0
4
0
0
0
0
1
0
0
0
0
1
4
0
1
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
1
1
0
2
1
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
3
0
2
3
0
0
0
0
0
0
2
3
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
4
3
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
1
0
0
0
1
4
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
1
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
2
0
0
1
0
2
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
1
1
0
0
0
2
7
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
2
0
3
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
1
1
0
0
1
3
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
2
0
1
0
0
1
0
2
0
1
0
0
0
0
0
0
0
3
0
0
2
3
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
3
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
2
0
0
4
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
2
0
1
1
1
2
0
0
1
0
1
0
0
0
0
2
0
1
0
0
0
0
1
0
2
0
0
0
1
0
0
2
0
0
0
2
1
1
1
0
0
0
0
3
0
4
0
0
0
1
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
9
1
0
1
0
0
2
3
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
3
1
0
0
0
1
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
1
3
0
0
0
1
5
0
0
2
0
0
0
1
0
0
0
0
0
0
3
1
0
1
0
0
3
0
0
1
1
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
4
0
0
0
1
0
1
0
0
0
0
0
4
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
1
1
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
1
1
2
1
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
6
0
0
0
1
0
0
0
0
0
2
0
2
0
1
0
1
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
10
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
3
1
0
0
0
0
0
0
1
2
0
1
0
0
3
1
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
1
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
2
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
2
2
0
0
0
0
0
0
0
1
0
1
1
1
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
3
2
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
1
0
0
2
2
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
7
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
2
1
0
0
0
0
0
0
2
2
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
1
0
0
0
1
2
0
0
3
2
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
2
0
0
2
0
0
1
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
1
0
4
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
2
0
3
2
3
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
2
1
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
4
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
3
1
0
0
3
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
9
0
0
1
0
0
0
0
0
0
2
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
1
0
0
2
0
0
0
2
2
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
8
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
4
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
3
2
0
0
0
0
0
2
0
0
0
1
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
1
0
0
0
2
0
0
0
0
0
2
7
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
2
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
3
0
0
1
0
2
0
0
0
0
0
0
0
0
1
5
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
1
2
0
2
0
0
3
0
0
0
2
0
2
0
1
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
1
0
3
0
0
0
2
0
0
3
0
0
3
0
0
0
0
0
0
4
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
2
3
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
1
0
0
1
0
0
3
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
4
0
1
0
3
0
1
0
1
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
2
1
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
4
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
3
1
0
0
0
0
0
0
0
0
8
0
0
2
0
0
2
1
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
1
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
8
0
0
3
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
1
1
0
0
0
0
2
0
1
0
0
0
0
1
0
0
3
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
1
2
0
0
0
7
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
1
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
3
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
2
3
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
5
0
2
2
0
1
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
2
2
0
2
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
1
0
3
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
2
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
2
0
0
1
3
2
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
1
2
0
0
0
2
2
0
0
0
0
1
1
2
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
2
0
0
0
0
2
3
2
1
0
0
0
2
0
0
0
0
2
1
0
0
1
1
0
0
3
1
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
2
0
5
1
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
3
0
1
0
0
1
0
0
2
0
0
0
3
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
3
0
0
1
0
0
0
0
0
2
0
1
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
5
1
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
1
2
2
0
0
0
0
1
0
0
0
3
0
0
1
0
0
3
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
2
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
2
2
2
0
0
3
1
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
1
0
5
0
0
0
0
0
0
1
3
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
1
0
1
0
0
0
0
0
0
1
2
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
3
2
0
0
2
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
3
0
1
1
0
3
0
0
0
0
0
1
0
2
0
2
0
0
2
2
0
1
0
2
2
0
0
0
1
0
4
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
1
2
0
0
2
1
0
0
0
5
2
0
0
1
0
2
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
2
0
0
2
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
2
0
2
1
1
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
2
2
0
0
1
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
11
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
4
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
2
0
3
0
0
3
0
0
0
0
0
0
0
0
0
0
1
2
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
1
0
1
0
0
0
2
1
0
7
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
2
0
1
2
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
3
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
1
3
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
4
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
3
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
2
1
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
3
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
1
0
0
1
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
2
3
0
0
2
0
0
0
0
1
0
1
0
10
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
3
3
1
1
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
1
0
0
0
0
0
2
0
2
0
4
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
5
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
3
0
0
0
2
0
6
2
1
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
2
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
3
4
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
2
2
7
0
2
0
2
0
0
0
1
0
0
2
0
0
2
3
1
0
0
2
0
1
0
0
0
2
0
0
0
2
0
0
1
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
3
0
2
1
2
0
0
0
0
0
0
0
0
0
1
3
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
2
0
2
0
0
0
2
0
2
1
2
0
0
0
0
3
1
0
0
2
1
0
0
5
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
8
0
0
2
2
0
0
0
0
2
0
0
0
0
1
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
6
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
2
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
2
1
0
2
2
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
1
2
0
1
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
2
1
2
2
0
1
0
0
0
0
1
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
2
0
1
0
0
3
0
0
0
2
2
0
4
2
0
0
0
0
0
0
0
0
1
1
0
3
0
0
0
0
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
2
0
1
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
2
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
3
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
2
3
0
0
4
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
4
1
0
0
0
1
0
0
0
3
1
0
3
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
2
0
0
2
2
0
0
2
0
0
0
2
0
0
1
2
0
0
2
0
0
0
2
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
2
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
1
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
2
2
4
0
1
1
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
2
4
0
1
0
1
1
0
1
0
0
0
3
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
4
0
0
2
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
5
0
0
0
2
0
1
2
1
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
4
2
1
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
1
0
0
2
0
0
3
2
0
1
0
2
0
1
0
2
0
0
0
0
1
0
0
1
0
1
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
2
1
3
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
5
2
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
2
0
0
3
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
1
1
0
2
0
0
0
2
0
0
1
0
2
3
0
0
0
0
0
0
0
3
0
0
2
0
1
2
3
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
2
1
1
0
1
0
0
0
0
1
2
0
1
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
6
0
1
0
2
0
1
0
0
1
0
0
0
0
0
1
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
1
0
15
0
1
0
0
1
0
0
3
0
0
1
0
0
0
0
2
0
0
1
0
0
0
2
2
0
2
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
2
0
0
0
1
0
0
0
1
0
3
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
1
2
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
3
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
5
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
3
0
0
1
0
0
0
1
0
0
0
0
2
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
4
0
0
0
4
2
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
3
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
2
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
2
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
6
0
0
0
10
1
0
0
0
0
0
0
0
0
0
0
1
0
0
5
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
9
1
0
0
2
1
0
0
0
0
0
0
1
0
3
1
0
0
0
0
0
1
2
1
0
0
2
0
0
0
0
0
0
1
2
1
1
0
2
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
2
2
1
0
0
2
0
0
0
0
0
0
0
1
2
5
0
0
0
0
0
0
0
1
2
0
2
2
0
0
0
0
0
0
1
0
0
0
3
7
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
7
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
1
0
3
3
0
1
0
0
0
0
0
0
2
0
0
4
0
0
0
0
0
3
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
2
2
2
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
1
3
0
0
0
0
0
1
0
0
0
0
2
0
0
0
5
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
1
0
0
0
0
0
0
1
0
4
0
0
0
1
0
0
0
2
3
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
3
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
1
0
0
3
0
0
0
2
0
0
0
1
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
4
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
2
0
5
0
1
0
0
0
1
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
1
0
4
0
0
0
0
2
1
0
0
2
0
1
1
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
2
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
4
0
0
2
0
0
1
0
2
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
4
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
2
2
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
1
0
2
2
2
0
0
2
0
0
0
0
1
1
0
2
0
1
1
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
2
2
0
0
0
1
0
0
1
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
1
0
1
0
4
1
0
0
0
0
0
1
1
2
0
4
5
0
0
0
0
1
0
0
0
0
0
1
1
1
1
0
0
2
0
0
0
0
1
0
0
2
0
3
0
0
0
0
2
0
1
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
1
1
0
2
0
0
0
0
1
0
0
0
0
0
5
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
3
0
2
2
1
0
0
2
0
1
0
0
0
0
0
5
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
2
1
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
2
0
0
1
1
0
2
0
0
0
0
0
3
0
2
0
0
8
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
2
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
1
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
2
1
0
0
0
2
0
0
2
2
0
2
0
0
1
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
2
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
3
1
0
6
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
3
0
0
1
0
0
0
2
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
3
2
0
0
0
0
2
0
0
0
0
2
0
0
3
0
0
0
0
0
2
0
0
0
0
0
1
0
3
0
0
4
0
1
0
3
0
2
1
0
2
1
0
1
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7
2
0
0
0
0
0
0
0
0
0
3
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
6
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
1
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
2
0
0
1
0
0
2
0
2
0
0
0
1
3
1
0
0
2
0
2
0
0
0
0
0
0
3
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
1
0
1
0
0
0
0
0
5
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
3
0
0
0
0
2
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
4
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
3
0
4
0
2
0
0
0
0
2
0
0
2
0
0
0
0
1
1
0
2
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
1
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
2
0
0
0
2
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
6
0
0
0
2
0
0
1
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
2
0
0
3
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
1
0
0
0
0
0
0
2
1
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
2
1
0
0
0
0
1
0
1
1
0
0
0
0
0
2
0
0
0
4
0
0
0
1
1
0
0
1
0
0
0
0
0
0
2
0
0
6
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
1
0
0
0
0
2
0
0
1
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
4
0
0
1
0
0
0
0
2
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
1
0
0
1
0
0
2
0
2
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
1
0
0
0
1
0
0
2
0
2
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
1
0
0
2
0
1
0
2
1
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
4
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
4
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
4
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
4
0
2
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
3
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
5
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
1
2
2
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
3
0
0
0
2
0
0
0
3
0
1
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
4
0
0
1
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
1
0
0
0
1
0
3
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
1
2
0
0
0
0
0
0
0
1
0
0
2
1
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
1
0
0
4
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
3
0
0
2
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
1
0
5
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
1
0
3
0
2
1
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
2
0
1
1
0
1
2
0
3
8
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
1
1
2
1
0
0
5
2
0
0
0
0
0
0
0
0
2
0
1
0
3
1
0
2
0
0
0
0
0
0
0
0
0
0
0
5
0
3
0
0
0
2
1
0
1
0
0
0
0
0
3
0
0
2
0
5
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
8
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
2
0
1
0
0
0
2
0
0
0
0
1
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
1
0
2
2
0
0
0
2
0
0
0
0
0
0
0
7
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
1
0
0
0
0
0
0
4
0
0
1
0
0
0
2
0
1
0
2
0
0
0
0
0
0
1
0
0
2
4
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
1
0
0
0
0
0
2
3
0
0
3
0
0
2
0
3
1
2
0
0
0
2
3
1
0
0
2
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
2
2
2
1
0
0
0
3
0
1
0
2
0
0
2
0
4
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
3
3
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
3
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
4
2
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
8
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
2
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
3
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
3
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
3
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
1
2
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
2
0
1
0
0
0
3
0
0
2
0
2
1
0
7
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
6
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
1
0
1
1
1
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
1
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
1
1
1
0
0
2
1
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
2
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
1
5
2
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
2
3
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
2
0
5
0
1
0
0
1
2
0
2
0
0
0
1
2
3
0
0
2
0
0
0
2
1
0
0
0
2
0
1
0
2
0
1
0
0
0
1
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
6
0
2
1
0
0
2
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
5
0
0
2
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
1
0
0
7
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
3
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
1
2
0
0
2
2
0
0
0
0
1
0
2
4
0
0
0
2
0
2
0
2
0
4
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
1
0
1
2
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
2
0
2
0
2
1
0
0
0
0
2
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
4
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
1
2
0
1
0
0
0
0
1
0
0
0
2
0
1
0
3
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
7
2
0
2
0
0
0
2
0
0
0
0
0
3
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
2
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
1
3
0
0
0
0
0
0
0
0
6
0
0
2
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
2
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
2
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
5
0
0
0
0
0
3
3
0
0
0
1
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
1
0
1
1
2
0
1
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
3
0
2
0
1
0
0
0
2
0
2
0
0
0
0
2
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
3
1
2
2
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
2
2
3
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
6
0
0
0
1
0
1
0
0
0
0
1
5
0
1
0
0
0
0
1
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
3
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
1
1
0
0
0
3
0
0
0
1
0
2
0
0
0
4
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
10
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
1
1
1
0
0
0
2
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
2
2
0
0
3
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
3
0
2
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
1
0
0
7
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
2
0
3
0
0
0
0
0
1
1
0
2
2
0
1
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
3
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
2
2
0
0
0
0
5
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
2
3
0
1
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
3
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
2
0
0
4
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
2
0
2
1
0
0
0
0
0
6
0
2
1
0
0
0
0
0
2
1
1
0
1
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
4
3
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
2
0
2
0
0
0
0
0
2
1
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
2
0
0
1
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
8
0
0
0
2
0
0
2
0
0
0
0
1
1
0
0
0
3
1
2
1
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
3
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
5
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
2
0
7
0
0
2
0
1
0
0
0
0
0
2
0
1
1
0
2
0
0
4
1
0
0
1
1
0
4
0
7
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
5
1
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
3
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
3
0
0
0
0
3
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
3
0
0
2
0
1
0
0
0
0
0
0
0
0
1
2
0
0
2
2
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
2
3
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
4
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
6
2
0
0
0
0
1
1
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
6
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
3
2
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
2
1
0
1
0
0
2
0
0
0
0
0
2
0
0
0
2
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
1
1
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
4
0
0
1
0
1
0
0
0
0
1
0
0
1
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
4
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
1
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
1
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
3
1
0
0
0
0
0
3
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
4
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
1
0
0
1
0
0
0
2
0
0
0
0
1
2
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
2
1
0
0
0
0
0
1
1
2
0
2
0
1
0
0
0
0
2
0
0
0
1
0
0
1
3
0
0
0
2
2
0
0
0
0
0
2
3
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
1
2
0
1
0
0
1
0
0
0
0
4
1
0
0
1
0
0
6
0
0
0
2
0
0
0
0
1
0
3
0
0
0
1
0
0
0
0
0
3
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
2
0
0
0
0
4
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
2
0
4
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
2
0
6
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
1
0
8
3
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
3
0
0
2
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
5
0
0
1
0
0
1
1
0
4
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
3
0
0
1
0
0
0
2
0
0
0
0
0
3
0
0
2
2
1
0
0
0
0
0
1
1
0
0
0
5
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
1
1
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
3
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
4
0
1
0
1
0
0
1
0
1
0
2
2
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
3
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
5
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
1
1
0
1
0
0
0
0
1
0
0
1
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
2
0
0
0
2
0
2
1
0
1
0
3
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
2
0
1
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
1
0
5
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
9
1
0
0
0
1
0
0
2
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
2
0
1
0
5
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
1
1
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
1
1
0
0
0
3
0
0
0
3
0
1
0
0
0
0
0
0
0
2
1
0
3
0
2
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
3
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
4
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
2
1
0
2
0
0
0
0
0
3
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
1
3
1
0
0
0
0
0
0
1
0
2
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
2
0
0
1
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
1
0
3
1
2
0
1
0
0
0
2
0
0
4
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
1
1
1
0
0
2
0
3
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
2
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
7
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
3
0
0
0
1
0
0
0
0
0
5
1
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
3
0
1
0
0
0
0
0
1
0
1
0
0
0
4
0
3
0
0
0
0
0
2
0
0
4
4
0
0
3
0
0
0
0
0
1
1
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
1
0
0
0
0
1
0
0
2
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
3
0
0
1
0
0
0
0
2
0
1
1
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
4
0
1
0
1
0
0
0
2
0
1
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
1
2
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
1
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
9
0
0
0
0
4
2
1
0
0
0
0
0
0
0
0
2
1
0
1
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
3
0
0
2
1
0
0
0
2
2
2
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
1
2
0
1
1
0
0
0
0
0
2
1
0
3
0
0
0
1
1
0
0
0
1
0
0
0
0
2
0
0
3
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
8
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
1
1
0
0
1
0
0
2
0
0
2
0
0
0
0
0
1
3
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
3
0
0
0
0
0
1
0
2
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
4
0
0
0
0
0
3
1
0
1
4
0
0
2
2
0
0
2
2
0
0
0
0
1
0
0
0
1
1
0
0
0
2
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
2
2
0
0
2
1
1
0
1
0
0
0
1
0
1
0
4
0
0
0
0
1
0
0
0
3
2
1
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
1
0
0
2
0
0
1
1
0
0
2
0
0
0
0
0
1
14
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
3
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
1
0
0
2
3
7
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
2
0
0
0
0
2
0
2
0
3
0
0
0
0
0
0
2
0
0
0
4
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
5
0
2
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
3
1
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
1
0
1
0
0
2
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
6
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
3
2
0
0
0
2
0
0
0
1
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
2
0
0
0
2
1
0
0
2
0
0
2
0
0
1
0
0
1
0
0
2
0
1
0
1
0
0
0
2
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
3
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
1
2
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
2
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
1
0
0
2
1
2
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
2
3
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
1
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
2
4
0
0
0
0
1
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
2
0
0
0
0
0
12
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
2
0
0
0
3
0
0
0
0
0
0
0
2
1
1
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
1
0
2
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
4
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
3
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
1
0
0
0
0
0
2
3
3
1
0
2
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
3
0
2
0
3
0
1
5
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
2
0
0
1
0
0
0
2
2
1
0
3
0
0
0
2
0
0
1
1
0
0
0
0
1
0
0
3
0
0
0
5
0
0
1
0
0
0
0
3
0
0
1
0
0
0
0
1
0
0
1
0
1
0
1
0
0
2
0
0
1
2
0
0
0
0
0
2
1
0
1
0
0
0
4
0
2
0
0
0
0
0
0
0
0
0
3
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
3
0
2
6
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
3
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
2
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
3
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
2
5
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
5
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
2
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
1
1
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
1
0
0
1
2
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
6
0
0
0
0
0
0
0
2
2
0
2
0
0
0
1
0
0
0
0
1
0
4
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
3
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
2
0
0
1
1
2
2
0
0
4
0
0
0
2
0
0
0
3
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
2
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
7
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
2
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
4
1
0
0
0
1
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
1
0
1
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
1
0
1
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
4
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
2
0
0
0
0
0
2
1
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
2
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
1
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
2
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
2
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
8
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
11
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
3
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
2
4
1
0
3
0
1
0
0
4
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
1
0
0
0
0
0
0
4
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
9
0
0
0
0
2
2
0
1
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
3
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
7
0
1
0
0
0
0
0
4
0
0
2
0
2
0
2
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
1
0
3
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
6
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
1
2
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
1
0
0
0
4
0
1
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
3
0
0
0
2
0
0
0
0
0
0
5
0
0
0
0
1
4
1
0
0
0
0
5
0
0
4
0
0
0
0
2
1
0
0
0
0
0
0
0
3
2
0
0
0
0
2
0
0
0
2
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
2
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
3
0
0
0
4
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
3
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
1
2
0
1
0
0
2
0
0
1
2
1
0
2
0
0
0
0
1
0
0
0
2
0
0
2
0
3
2
0
2
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
2
11
0
0
0
1
0
1
0
0
2
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
1
0
0
1
0
0
3
0
1
0
5
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
1
0
2
0
0
1
3
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
3
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
2
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
1
1
0
0
0
0
1
6
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
3
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
4
0
1
0
0
0
0
2
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
2
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
3
0
0
1
2
1
0
0
1
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
3
0
0
0
0
0
2
1
0
1
0
0
0
0
0
2
0
0
0
0
6
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
8
0
0
0
0
0
0
0
0
0
0
1
0
2
2
1
1
0
0
11
0
0
0
0
0
0
0
0
0
3
2
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
3
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
2
0
0
0
0
3
1
0
0
1
0
0
0
0
1
1
1
0
2
0
0
2
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
5
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
3
0
0
2
3
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
3
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
1
0
2
0
1
1
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
2
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
4
0
0
0
0
1
0
1
0
0
0
0
0
0
0
3
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
1
2
0
0
0
0
3
0
0
0
0
1
0
0
0
1
0
11
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
3
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
2
1
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
1
1
0
1
0
0
2
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
4
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
3
0
0
1
1
0
0
0
1
1
3
1
0
0
2
0
0
0
5
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
2
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
4
0
1
0
0
6
0
0
0
0
2
0
0
0
0
0
1
1
2
1
0
1
0
2
0
2
3
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
2
2
3
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
1
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
2
4
1
2
0
0
0
0
0
2
0
1
0
0
0
2
0
2
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
6
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
2
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
6
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
4
1
0
0
0
0
3
0
0
2
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
1
0
3
2
1
0
1
1
0
0
0
0
0
0
0
0
1
2
1
0
0
2
1
0
1
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
2
3
0
0
0
2
0
3
0
0
0
0
0
0
0
2
2
1
2
0
0
0
0
1
0
0
2
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
4
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
1
2
0
2
0
0
2
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
4
2
0
0
0
2
0
0
0
0
1
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
1
0
0
0
0
0
0
2
0
2
0
0
2
1
0
0
2
1
0
1
0
0
0
0
0
0
1
2
2
0
2
2
2
0
0
0
0
0
2
0
0
0
1
0
1
0
0
2
0
2
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
2
0
2
0
0
1
2
0
0
1
3
0
0
1
2
0
0
0
0
1
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
2
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
5
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
4
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
1
0
2
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
3
0
2
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
10
1
0
0
1
0
1
0
0
0
2
1
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
2
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
5
0
0
0
0
2
0
0
1
0
2
1
0
0
0
0
0
0
0
0
2
1
1
0
2
0
0
0
0
0
0
2
0
1
1
0
0
0
0
2
0
0
0
1
1
0
1
0
1
0
0
0
2
1
2
0
0
0
0
0
0
0
5
2
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
2
0
4
2
0
0
0
2
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
6
0
0
0
2
0
0
0
0
2
4
0
0
2
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
1
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
4
0
0
1
0
0
6
0
0
0
0
0
2
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
4
1
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
2
1
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
2
1
0
1
1
2
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
1
4
0
0
0
0
0
0
1
0
0
0
2
1
1
1
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
1
1
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
1
11
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
2
0
2
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
5
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
3
0
1
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
7
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
2
0
7
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
2
2
3
0
0
0
0
0
3
0
2
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
5
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
2
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
7
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
2
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
1
2
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
2
0
6
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
2
0
0
3
2
0
0
2
0
0
0
1
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
2
0
0
1
2
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
1
0
1
1
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
4
1
1
0
0
0
0
0
1
0
0
1
2
0
0
2
0
8
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
2
0
0
3
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
5
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
3
0
0
0
0
2
0
4
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
4
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
2
5
0
0
0
2
0
0
0
0
0
3
0
0
1
1
0
1
0
1
2
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
3
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
7
0
0
0
0
1
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
2
0
0
1
0
2
1
1
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
6
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
2
0
0
2
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
1
1
0
2
1
0
0
6
0
0
0
0
2
0
0
0
0
2
1
0
0
0
1
0
1
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
4
0
3
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
5
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
2
0
0
4
1
0
0
0
0
3
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
5
0
0
2
0
2
0
0
0
0
0
2
4
2
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
2
2
0
0
0
2
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
1
0
0
2
1
0
0
0
0
1
0
0
0
1
0
5
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
2
0
1
2
2
0
2
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
1
1
0
0
0
0
0
3
1
0
1
0
1
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
3
0
0
0
1
0
0
0
0
1
0
1
1
1
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
1
0
0
3
0
0
0
0
0
0
0
2
0
4
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
3
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
3
0
2
0
0
0
12
0
0
0
0
1
0
0
0
0
1
0
0
3
0
0
4
0
1
0
2
1
12
0
0
0
1
1
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
3
2
0
1
0
2
1
0
0
0
5
0
2
0
1
0
0
0
2
0
0
4
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
1
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
2
0
1
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
1
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
2
0
1
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
2
4
0
1
0
0
0
1
0
0
0
2
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
2
2
0
1
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
3
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
4
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
2
2
1
0
3
0
0
0
0
0
0
0
1
0
0
2
1
1
0
0
0
0
0
2
0
0
0
0
0
2
0
1
1
0
2
0
1
0
0
0
1
2
1
0
2
0
0
0
0
0
0
0
5
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
2
0
0
2
0
0
0
0
3
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
4
0
2
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
3
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
3
0
0
2
0
1
0
3
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
1
4
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
6
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
1
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
1
0
2
0
0
0
4
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
3
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
7
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
4
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
6
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
2
1
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
6
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
2
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
2
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
7
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
3
0
1
0
0
0
2
0
0
0
1
0
0
3
1
0
3
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
1
2
0
2
1
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
1
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
3
1
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
1
0
1
0
1
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
1
0
0
3
1
0
5
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
1
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
6
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
3
0
2
0
0
2
0
0
0
0
0
0
0
0
2
5
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
1
6
1
0
0
0
0
0
0
2
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
2
0
1
1
0
1
0
0
2
1
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
2
0
0
2
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
1
0
0
0
1
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
1
2
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
1
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
1
0
0
1
2
0
1
0
0
1
3
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
4
0
2
3
2
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
1
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
1
2
0
0
0
1
0
0
0
0
2
4
0
0
0
0
0
0
0
3
1
0
0
0
1
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
3
0
0
0
0
0
2
1
0
1
1
1
0
0
0
0
4
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
7
0
0
0
1
0
0
0
2
2
0
0
1
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
2
1
0
0
0
0
1
0
2
0
0
0
0
1
2
2
0
0
0
0
0
2
0
0
0
1
2
1
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
2
1
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
2
0
0
0
2
0
0
0
0
5
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
1
0
0
0
2
0
5
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
3
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
6
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
1
0
0
2
1
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
1
0
2
0
0
0
2
0
0
1
0
1
0
0
2
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
2
0
1
0
2
1
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
6
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
3
0
0
4
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
2
1
0
4
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
5
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
2
0
0
0
2
3
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
2
0
1
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
1
0
1
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
5
0
0
0
0
0
0
0
0
5
0
3
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
6
0
0
0
2
2
1
0
0
2
3
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
3
0
0
0
1
0
0
5
0
0
2
0
0
0
1
0
1
1
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
5
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
4
0
0
0
0
2
0
5
0
0
2
0
0
1
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
2
0
2
0
1
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
2
0
0
0
0
2
0
1
0
0
1
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
1
0
4
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
2
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
1
1
2
0
0
1
0
4
1
1
0
1
0
0
0
0
2
0
0
0
0
0
1
0
1
2
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
1
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
2
0
0
0
4
0
0
0
0
0
0
2
5
0
0
0
0
0
0
0
0
10
2
0
0
1
2
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
3
0
0
1
0
0
1
0
0
2
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
12
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
3
0
4
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
1
6
2
6
0
0
2
1
0
0
1
0
1
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
7
1
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
4
2
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
2
0
0
2
3
1
0
1
2
1
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
1
2
0
0
3
2
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
2
0
0
1
0
4
0
0
0
0
1
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
1
0
0
0
2
1
1
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
5
0
0
0
1
0
0
1
0
0
0
0
1
0
2
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
1
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
2
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
2
0
0
0
0
0
0
0
2
0
7
8
0
0
0
0
0
0
0
6
1
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
1
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
1
0
2
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
7
0
0
0
0
0
0
0
0
0
0
8
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
5
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
4
0
0
0
0
1
0
1
1
1
1
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
3
0
0
0
0
0
0
0
2
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
2
1
0
0
2
0
0
2
0
0
2
0
3
2
0
0
2
0
0
0
4
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
2
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
2
1
1
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
2
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
2
0
0
0
2
0
0
0
0
2
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
2
0
0
0
1
2
0
3
0
0
3
0
0
0
0
0
0
1
4
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
1
0
0
0
0
2
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
2
0
0
0
1
2
0
0
0
1
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
4
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
1
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
1
2
0
0
2
0
1
0
2
0
0
0
0
1
0
0
2
2
0
1
0
0
0
1
0
1
6
0
0
0
0
2
2
0
0
2
0
1
0
0
0
0
0
0
0
2
0
3
3
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
2
3
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
1
2
2
3
1
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
3
0
0
0
0
0
3
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
1
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
1
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
2
0
0
0
0
0
1
0
1
1
0
0
0
2
1
0
0
0
0
0
2
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
1
2
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
1
0
1
5
0
0
0
0
0
1
0
0
0
0
5
0
0
2
0
0
0
3
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
4
1
1
0
0
0
2
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
1
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
2
0
1
2
0
1
0
0
0
0
0
4
1
5
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
3
1
2
0
0
0
0
0
0
1
3
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
10
0
2
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
2
1
1
3
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
1
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
2
1
1
0
0
0
0
0
0
0
2
1
0
0
0
1
0
1
0
0
0
0
0
2
2
0
2
1
1
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
3
0
0
0
0
0
1
0
0
0
1
2
0
1
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
3
2
0
0
0
0
0
1
0
0
0
2
0
0
2
0
1
0
0
0
2
2
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
2
0
0
0
0
0
0
3
0
0
0
4
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
1
0
0
0
0
2
0
0
1
1
3
0
2
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
3
0
0
1
2
0
0
0
1
0
1
0
0
0
0
3
1
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
3
2
3
0
1
2
1
0
0
0
1
0
0
0
0
3
1
0
0
0
0
2
0
0
2
1
0
0
0
0
1
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
3
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
2
1
0
0
7
1
0
0
0
3
0
1
0
0
2
0
3
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
2
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
3
0
3
1
2
4
0
0
0
2
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
3
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
2
0
0
0
6
2
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
1
0
1
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
1
0
0
3
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
1
1
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
2
0
1
2
0
0
1
1
0
2
1
3
1
0
0
0
0
0
1
1
0
0
0
1
1
0
0
1
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
8
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
2
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
3
0
7
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
2
3
0
0
0
0
0
2
0
0
0
0
1
0
1
0
1
2
0
0
0
0
0
0
0
1
0
0
0
3
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
1
1
3
0
0
0
0
0
2
0
1
0
2
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
4
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
8
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
1
1
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
2
1
0
0
0
0
1
0
2
0
0
2
0
0
0
2
1
0
0
1
0
1
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
4
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
1
2
3
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
2
2
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
2
0
2
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
3
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
4
0
1
0
2
0
2
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
5
2
2
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
3
0
1
2
0
2
1
2
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
2
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
3
1
0
1
1
0
0
0
1
0
2
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
1
2
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
1
0
0
1
0
0
0
0
2
0
0
1
1
1
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
1
0
0
2
0
0
0
0
2
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
1
0
0
0
0
2
1
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
2
0
7
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
4
0
0
0
1
1
0
0
0
0
2
0
1
0
0
3
0
1
0
0
1
1
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
1
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
3
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
2
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
3
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
2
0
0
0
5
0
0
0
1
1
0
0
0
4
0
0
2
0
0
1
0
1
0
0
1
1
1
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
1
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
3
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
2
0
4
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
1
0
2
0
2
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
1
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
4
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
5
0
1
0
0
0
1
0
1
0
2
0
1
0
0
0
1
1
0
0
0
0
0
4
1
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
3
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
1
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
1
3
1
0
0
0
2
3
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
4
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
2
0
0
0
0
0
0
2
0
0
2
0
6
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
2
3
0
0
2
0
3
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
4
1
0
0
0
0
0
0
0
3
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
3
0
0
0
0
0
2
1
0
0
0
0
0
0
0
6
1
0
2
0
4
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
4
0
3
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
2
0
0
0
0
2
1
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
1
4
0
0
0
1
0
2
0
1
2
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
1
0
0
4
2
0
0
0
0
0
0
1
0
0
0
2
0
0
1
1
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
1
0
0
0
0
4
0
0
2
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
2
1
0
1
0
1
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
3
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
3
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
2
2
0
2
1
0
0
0
3
1
0
0
0
0
0
1
0
1
0
0
4
0
2
1
1
0
0
1
2
0
0
1
1
0
1
0
0
0
0
0
2
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
2
4
0
1
0
0
0
0
5
0
0
0
0
0
1
2
1
0
0
0
0
0
1
0
0
1
2
0
0
0
1
0
0
1
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
1
5
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
2
0
0
0
0
0
0
0
2
1
1
0
1
0
0
2
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
3
2
2
0
2
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
2
0
0
2
0
7
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
5
0
1
1
4
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
2
0
0
1
1
0
0
0
0
0
1
4
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
7
0
2
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
4
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
3
0
0
1
0
0
0
0
4
0
0
0
0
2
0
1
0
0
1
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
1
0
2
2
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
2
2
0
0
2
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
2
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
1
0
2
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
6
0
2
0
0
0
0
2
2
0
0
0
0
2
0
1
0
0
0
0
5
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
2
2
1
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
2
1
0
0
0
0
3
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
4
0
0
0
4
1
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
4
1
0
0
1
2
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
1
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
1
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
8
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
6
1
0
8
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
1
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
2
0
0
0
0
2
0
0
0
2
2
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
5
0
0
0
1
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
4
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
1
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
3
2
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
1
0
0
2
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
2
0
2
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
2
1
0
1
0
0
2
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
5
0
0
0
0
1
1
0
0
1
0
0
0
0
0
2
0
4
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
2
0
2
1
1
2
0
2
0
1
0
2
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
3
8
0
1
1
0
1
0
0
0
1
1
0
0
2
0
0
5
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
4
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
2
0
0
0
0
1
0
0
3
2
0
0
0
0
0
0
2
0
1
2
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
7
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
7
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
6
0
0
0
1
2
0
0
1
0
0
0
0
4
0
2
0
3
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
2
1
1
0
3
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
2
0
0
0
0
4
0
0
0
0
1
0
0
0
0
4
0
0
1
1
1
0
0
1
1
0
2
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
5
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
6
0
0
1
0
0
0
0
2
0
0
1
0
0
0
1
1
0
2
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
7
0
0
1
0
0
1
0
0
0
0
0
1
1
1
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
4
1
0
0
0
0
1
0
2
0
3
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
1
0
0
0
2
0
0
1
0
0
0
2
0
0
0
2
0
1
0
1
2
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
3
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
37
2
0
1
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
3
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
9
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
3
0
0
2
0
0
0
0
0
0
1
2
0
0
0
3
0
0
0
0
3
0
0
0
2
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
1
0
1
0
1
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
9
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
2
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
6
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
3
0
0
0
1
0
0
0
0
1
0
2
0
1
0
0
0
3
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
1
0
0
1
0
1
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
2
1
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
2
1
0
0
2
0
0
0
0
0
0
0
2
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
3
0
0
0
0
1
1
0
2
1
1
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
7
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
1
0
0
0
0
0
2
2
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
3
3
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
1
2
0
0
2
1
2
0
0
2
0
0
1
0
2
0
0
4
0
0
1
0
0
1
0
1
0
0
1
0
1
1
0
0
2
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
2
0
2
0
0
1
2
1
0
0
0
0
0
0
2
2
0
0
2
0
0
1
1
0
0
0
0
0
0
2
2
1
0
2
0
0
0
3
0
0
0
1
4
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
1
1
2
0
1
1
0
0
0
1
0
9
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
1
0
0
6
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
3
0
0
0
3
2
0
1
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
1
2
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
2
0
0
0
2
1
1
0
1
0
3
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
8
1
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
3
1
0
0
2
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
1
0
1
1
1
0
0
0
0
0
0
0
2
1
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
2
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
3
1
0
0
1
1
0
0
2
0
1
2
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
1
0
0
0
0
3
2
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
3
2
0
2
0
1
2
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
2
2
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
1
0
0
1
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
4
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
6
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
2
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
3
2
0
0
0
1
0
2
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
1
0
2
0
0
0
0
0
1
2
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
2
1
1
2
0
1
0
0
0
0
2
0
0
0
1
0
1
1
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
1
0
0
2
2
0
2
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
3
0
0
0
0
0
2
0
0
0
0
1
0
2
0
2
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
4
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
2
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
3
0
0
0
0
0
1
0
0
1
5
0
1
0
0
0
0
0
0
2
0
2
0
0
2
1
2
0
0
0
0
1
0
0
0
0
2
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
1
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
3
0
0
4
1
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
1
0
0
1
1
1
0
0
0
0
0
0
0
2
0
0
1
0
0
3
0
2
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
1
0
0
0
1
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
4
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
4
3
2
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
3
2
1
0
0
0
2
1
0
1
1
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
1
0
0
0
2
0
0
0
0
2
3
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
5
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
2
0
2
0
1
2
0
0
0
0
0
0
1
2
0
1
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
3
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
6
0
0
1
0
0
0
2
1
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
1
2
0
0
1
0
0
0
1
0
0
0
0
0
3
1
0
0
0
0
0
0
4
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
2
1
0
0
1
0
2
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
2
3
0
0
4
0
0
1
0
0
0
0
2
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
5
2
0
0
0
1
0
2
2
2
0
2
0
0
0
7
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
2
0
0
0
1
0
0
0
0
2
0
2
0
2
0
0
1
5
0
0
1
0
0
2
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
13
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
1
1
0
1
2
0
0
1
0
3
2
0
2
0
1
0
0
0
0
5
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
1
0
3
1
0
0
0
0
0
1
0
0
0
1
0
2
2
0
2
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
1
0
0
2
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
2
1
0
0
0
0
0
4
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
2
2
2
0
0
0
1
0
0
0
0
0
1
0
0
1
0
2
1
0
0
0
0
5
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
1
0
0
4
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
3
0
0
2
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
2
1
0
0
1
0
0
1
2
0
0
0
2
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
3
0
3
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
4
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
2
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
1
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
3
0
8
0
2
3
0
0
1
0
0
0
0
0
1
2
3
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
2
0
0
3
0
0
1
1
0
2
0
0
0
0
0
0
2
0
1
2
0
0
0
1
3
1
0
0
0
3
3
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
2
0
1
4
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
4
0
0
0
1
1
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
6
0
2
1
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
4
0
1
1
0
0
0
2
0
0
2
0
0
3
0
2
3
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
3
0
2
0
2
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
4
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
2
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
3
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
3
0
0
0
0
2
1
1
1
0
0
0
0
0
0
2
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
1
3
2
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
2
0
0
1
0
1
0
0
0
0
0
0
0
2
0
3
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
7
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
2
0
2
1
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
1
0
2
0
0
0
1
1
0
0
3
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
5
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
2
0
2
7
0
0
0
3
2
1
0
3
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
1
0
0
2
0
1
0
0
0
0
1
0
2
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
1
2
0
3
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
6
0
0
0
1
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
2
11
2
6
2
0
2
0
0
0
2
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
3
4
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
4
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
2
0
0
0
3
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
2
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
2
0
1
1
2
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
1
0
2
2
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
6
0
0
0
0
2
1
3
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
2
0
0
1
0
0
0
0
0
1
0
1
0
0
2
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
2
1
2
0
2
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
3
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
3
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
3
0
1
0
3
0
0
0
0
3
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
2
5
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
3
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
8
1
0
2
1
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
2
0
0
1
1
0
1
1
0
1
0
2
0
1
2
0
0
0
2
3
0
0
0
0
0
0
0
3
0
0
0
2
0
4
0
0
2
0
0
0
2
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
3
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
2
1
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
5
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
4
0
0
2
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
3
0
0
0
2
1
0
0
1
0
0
0
1
4
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
6
0
0
0
0
3
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
3
0
0
1
2
0
2
0
2
0
0
2
0
0
0
0
2
1
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
2
5
0
1
1
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
1
0
2
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
5
0
0
3
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
3
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
3
3
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
2
3
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
2
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
2
1
0
1
2
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
2
0
0
0
0
1
0
1
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
2
2
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
3
1
0
1
0
0
0
3
0
0
0
1
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
1
0
0
1
1
0
0
1
0
1
0
0
0
2
0
1
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
2
0
0
0
0
1
0
0
1
0
0
0
0
3
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
1
1
0
0
0
0
0
2
0
0
0
7
0
0
1
0
1
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
1
3
2
0
2
0
0
2
1
0
0
0
0
0
2
1
0
0
0
1
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
2
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
2
4
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
3
0
5
0
0
0
0
0
0
0
1
0
1
2
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
3
0
0
0
2
0
2
0
0
0
0
1
1
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
1
0
0
2
0
0
0
1
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
2
1
2
1
0
1
0
0
3
0
0
3
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
1
0
0
2
1
0
0
2
0
0
3
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
4
0
1
0
3
0
1
0
0
0
0
0
2
0
2
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
6
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
13
0
1
1
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
2
0
0
2
1
0
0
0
1
3
3
0
0
0
1
0
2
0
0
0
2
0
0
0
0
4
0
3
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
2
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
1
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
3
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
4
2
0
0
0
4
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
1
2
3
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
2
0
0
1
6
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
1
0
2
2
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
2
0
1
1
2
2
0
0
0
0
0
1
0
1
1
3
3
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
2
1
1
0
0
0
0
2
1
2
4
0
0
0
0
2
2
2
0
0
1
1
0
0
0
0
1
0
0
1
0
5
0
1
0
0
0
1
2
1
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
2
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
3
1
0
0
0
0
0
0
0
1
3
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
3
1
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
2
1
0
3
0
0
0
0
1
0
0
0
0
2
0
1
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
1
1
2
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
4
0
2
0
0
3
0
0
0
2
0
2
0
0
0
0
1
0
2
1
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
3
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
2
0
1
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
2
0
0
1
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
1
0
0
1
0
0
0
2
5
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
1
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
1
0
0
0
0
1
0
6
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
3
0
0
0
0
0
0
0
1
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
2
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
1
2
2
0
0
0
0
0
0
0
0
1
0
0
1
1
3
6
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
2
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
2
0
0
0
0
1
1
0
0
3
1
2
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
1
0
4
0
0
0
0
1
0
0
0
0
1
0
3
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
1
0
0
2
0
4
0
0
2
1
0
0
1
0
0
1
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
2
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
3
0
0
1
3
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
1
1
0
0
0
0
0
0
3
1
0
0
2
0
0
2
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
6
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
1
0
3
3
1
0
1
1
0
2
5
0
0
0
0
0
0
3
2
0
4
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
1
1
1
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
4
0
0
0
0
1
1
0
0
0
1
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
2
1
1
1
0
0
0
0
1
2
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
1
1
2
0
0
0
0
0
2
0
4
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
6
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
2
1
0
0
0
0
0
0
0
1
2
0
0
0
0
2
9
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
3
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
2
0
0
0
2
1
0
0
0
1
0
0
0
2
1
0
2
0
0
2
0
2
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
4
7
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
4
2
0
0
1
0
0
1
1
0
0
1
0
1
0
0
0
0
10
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
3
0
2
0
2
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
3
0
1
0
0
0
2
0
7
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
4
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
1
0
4
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
1
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
3
1
0
0
0
4
0
3
0
0
0
0
0
2
0
0
1
0
2
0
1
2
2
0
3
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
2
0
1
2
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
1
0
3
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
2
0
3
0
0
0
3
0
1
0
2
1
0
0
0
0
2
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
2
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
5
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
1
0
7
1
0
0
0
0
0
1
0
0
0
1
0
5
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
5
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
9
3
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
3
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
2
2
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
3
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
6
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
4
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
2
0
0
0
0
2
2
1
0
2
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
2
0
0
1
0
0
0
0
2
0
1
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
3
5
1
0
0
0
1
0
0
0
0
2
1
0
3
0
0
1
3
1
0
0
0
0
0
0
2
0
0
0
1
0
1
2
0
1
0
0
0
0
2
0
0
2
0
2
0
0
0
0
3
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
2
2
2
1
0
0
0
0
2
0
0
0
1
1
0
0
0
0
6
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
10
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
3
1
0
0
2
0
1
0
0
0
2
3
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
2
1
2
0
0
0
0
0
0
0
8
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
3
0
0
0
2
0
0
2
0
1
2
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
3
2
0
0
2
2
0
0
0
0
1
0
4
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
3
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
3
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
1
2
1
0
0
7
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
5
0
4
0
3
0
0
0
1
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
1
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
1
0
0
0
0
2
0
1
0
0
0
2
0
0
2
0
0
2
1
0
0
0
0
4
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
2
1
0
1
2
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
5
0
0
0
0
0
0
2
0
0
1
0
2
0
1
0
0
0
0
0
0
0
2
3
2
2
1
0
0
0
1
0
0
1
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
3
0
1
0
1
2
2
0
0
2
0
0
2
2
1
0
2
0
0
2
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
4
3
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
1
2
0
0
1
0
3
0
0
0
2
3
0
0
1
0
1
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
2
0
0
0
1
0
1
0
0
0
0
0
4
2
0
0
0
1
0
0
4
0
0
1
0
1
4
0
0
0
0
1
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
3
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
4
0
0
5
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
2
3
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
4
0
0
0
0
2
0
2
0
0
4
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
3
0
0
2
0
2
0
0
1
0
0
0
0
1
2
1
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
1
0
2
1
0
0
0
0
0
0
0
2
2
0
0
1
4
0
0
0
0
0
1
0
2
1
0
0
1
0
0
0
2
2
0
0
0
2
1
2
0
0
0
0
1
1
0
2
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
1
1
0
2
0
0
0
0
1
1
0
2
3
0
0
1
0
0
0
0
1
0
0
1
2
0
0
2
0
2
3
1
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
3
0
1
0
0
0
0
2
0
0
1
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
1
1
3
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
3
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
1
4
0
0
1
0
1
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
3
0
0
3
0
0
1
2
0
0
3
2
0
0
0
0
0
0
0
0
0
1
2
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
2
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
7
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
3
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
2
4
0
0
0
2
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
3
0
0
1
0
0
3
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
3
3
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
1
0
1
0
0
0
0
0
3
4
0
0
1
1
1
6
2
0
0
0
1
0
2
2
0
0
0
0
0
0
1
4
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
1
3
0
1
0
0
0
0
0
0
3
0
0
0
0
0
1
3
3
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
1
1
0
0
2
9
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
1
0
0
0
0
2
0
0
0
0
0
1
0
1
1
2
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
1
2
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
4
0
0
1
1
0
2
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
5
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
4
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
2
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
1
1
1
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
1
2
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
5
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
7
1
0
1
1
0
0
0
2
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
3
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
1
1
0
0
0
0
1
1
2
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
2
2
0
0
0
0
0
2
0
0
0
0
4
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
3
0
0
0
2
3
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
1
0
0
2
0
0
0
2
0
2
0
0
0
0
1
0
8
0
0
1
0
0
0
5
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
3
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
5
1
0
0
0
0
0
2
0
0
0
0
0
0
3
1
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
2
0
1
3
0
0
0
3
1
0
1
0
1
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
2
0
1
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
6
1
1
0
0
0
0
0
1
2
0
0
1
2
1
0
0
2
1
2
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
3
1
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
4
0
0
0
0
3
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
1
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
2
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
1
0
0
0
0
0
1
2
1
0
6
0
0
0
0
0
0
1
3
2
0
0
0
1
2
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
1
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
5
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
3
0
0
2
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
1
0
0
0
0
0
0
0
0
6
0
2
0
0
0
3
0
0
2
0
0
2
0
2
1
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
2
0
2
0
2
0
0
1
2
1
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
2
0
0
0
0
0
0
2
0
3
0
1
0
1
0
0
1
0
0
0
0
1
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
8
0
0
0
0
0
2
2
1
1
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
1
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
6
0
0
0
2
0
1
0
2
2
0
0
0
1
0
0
0
0
4
0
0
0
0
5
0
1
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
7
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
5
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
3
1
1
0
3
1
0
0
1
0
1
0
0
3
0
0
0
1
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
1
1
3
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
3
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
1
1
0
0
0
0
0
2
0
0
4
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
2
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
2
0
1
0
2
1
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
1
0
0
0
0
1
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
1
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
2
1
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
3
1
0
1
0
0
0
0
0
0
4
0
1
2
2
0
0
2
0
0
0
2
0
0
0
0
2
2
1
0
0
0
2
0
0
0
0
0
2
1
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
4
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
3
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
4
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
3
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
4
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
3
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
1
0
0
2
0
0
0
0
0
0
0
0
4
1
0
0
2
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
3
1
1
1
3
1
1
1
0
0
0
0
0
0
1
0
1
1
0
0
0
3
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
1
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
4
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
1
2
1
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
2
0
0
1
0
0
0
0
0
3
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
2
0
0
2
1
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
1
0
0
1
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
2
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
3
5
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
5
0
0
0
0
0
0
0
0
0
4
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
5
0
0
0
1
0
1
4
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
1
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
2
2
0
0
2
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
3
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
1
0
4
1
1
0
0
0
2
0
1
3
2
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
4
0
0
0
2
1
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
2
0
0
1
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
1
1
0
0
0
0
0
0
1
2
0
0
0
0
1
1
0
0
2
0
2
0
0
2
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
2
0
2
1
3
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
2
0
2
0
1
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
3
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
1
1
2
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
4
0
0
0
0
0
0
0
1
0
0
1
0
3
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
2
0
0
1
2
0
0
0
0
1
0
0
0
0
1
0
0
2
0
2
0
0
2
0
0
1
0
1
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
8
0
2
0
0
1
0
0
0
1
0
2
0
2
3
0
0
0
3
2
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
11
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
4
2
0
0
0
1
0
0
0
0
0
0
0
5
0
0
0
0
2
0
0
0
0
0
2
4
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
1
2
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
5
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
1
0
0
0
0
0
3
0
1
0
2
2
1
0
0
0
0
0
0
1
3
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
4
0
0
0
11
0
0
0
0
0
2
1
0
0
0
0
0
5
0
1
0
0
0
0
1
0
0
0
0
0
3
1
0
0
7
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
2
0
0
2
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
3
1
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
7
1
0
0
2
1
0
1
0
0
0
1
2
0
2
0
2
1
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
4
0
1
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
1
1
1
0
1
0
0
3
3
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
1
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
4
2
0
0
0
2
0
1
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
2
0
0
0
2
0
0
0
2
0
1
1
1
0
0
0
0
0
0
3
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
7
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
8
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
3
0
4
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
2
4
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
1
0
0
2
0
0
1
0
0
0
0
1
0
2
0
1
0
0
0
3
2
1
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
3
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
3
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
1
6
2
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
2
0
0
2
0
2
0
0
0
4
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
8
0
0
0
0
0
0
2
0
1
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
7
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
2
1
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
1
6
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
1
1
0
0
2
1
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
4
0
0
0
0
0
2
0
2
0
2
0
0
0
2
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
1
0
2
1
0
0
0
0
0
2
1
1
0
0
0
1
0
0
0
0
5
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
9
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
2
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
2
2
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
4
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
7
0
0
0
2
2
2
3
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
4
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
5
0
0
0
0
1
0
0
2
1
2
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
2
0
1
1
0
1
4
0
0
1
0
0
1
1
0
0
1
2
1
0
0
2
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
2
2
0
1
0
0
0
0
1
1
0
2
2
0
0
2
1
0
4
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
2
1
0
0
2
0
2
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
5
0
1
1
0
4
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
4
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
1
0
0
0
0
2
2
0
1
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
4
0
0
0
0
0
3
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
4
0
0
0
0
1
1
0
2
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
3
0
0
1
3
2
0
0
0
1
1
0
0
1
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
3
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
6
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
3
0
1
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
2
0
0
2
0
0
10
1
1
1
2
0
1
0
0
0
0
0
1
0
1
0
0
0
0
3
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
3
0
1
0
1
2
3
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
3
0
0
0
0
1
0
0
4
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
5
0
0
1
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
4
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
7
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
4
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
5
0
2
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
4
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
1
1
2
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
1
1
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
3
2
0
0
0
2
2
0
0
0
0
3
1
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
3
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
3
1
0
1
2
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
5
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
1
2
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
3
2
0
4
0
2
0
0
0
1
0
0
0
2
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
5
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
2
0
1
3
2
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
1
0
0
5
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
5
0
0
0
5
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
4
1
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
3
1
0
0
0
0
0
3
0
0
0
0
0
1
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
3
1
1
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
1
0
1
0
0
1
2
0
1
2
0
2
0
0
0
2
1
0
0
0
0
3
0
0
0
0
2
0
0
0
1
2
0
0
0
2
0
3
1
0
1
4
1
0
0
0
0
0
0
2
1
1
0
0
0
3
0
1
0
2
0
0
2
0
0
0
0
0
0
0
2
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
5
0
1
0
0
0
2
0
2
0
0
3
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
5
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
1
5
0
0
0
0
0
0
1
2
0
0
2
2
0
0
0
0
2
0
1
1
0
0
5
0
0
0
0
2
1
0
1
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
2
0
0
0
2
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
1
2
2
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
1
0
3
0
1
0
1
0
1
0
0
0
5
0
0
0
0
0
1
0
1
2
4
0
1
3
2
1
0
0
1
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
2
0
3
0
0
0
0
0
2
0
1
0
1
0
0
1
2
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
4
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
2
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
5
0
2
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
1
1
0
0
1
0
0
2
0
4
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
1
0
0
0
3
0
2
2
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
4
1
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
1
2
0
1
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
2
0
0
1
1
2
0
3
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
13
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
4
0
0
0
0
0
0
9
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
2
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
12
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
2
0
0
0
1
1
0
0
1
0
4
0
0
0
0
0
0
0
0
0
1
2
2
0
0
1
3
0
0
0
0
1
0
0
0
0
0
2
2
0
4
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
2
0
0
4
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
2
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
2
0
0
0
2
6
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
1
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
2
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
2
2
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
3
0
0
1
0
1
0
1
0
0
0
0
1
0
1
0
2
0
0
8
0
2
0
0
2
0
0
3
6
0
0
0
0
0
1
2
0
0
1
0
0
0
2
1
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
2
0
2
0
0
0
1
0
0
4
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
3
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
4
0
0
1
0
0
0
0
0
1
0
2
0
1
0
0
0
2
0
0
0
2
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
2
0
0
1
1
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
5
5
0
0
0
0
0
0
3
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
2
0
0
0
1
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
2
2
2
1
0
0
0
0
0
0
0
0
1
0
1
2
2
0
0
0
0
0
0
0
0
0
0
2
3
0
0
2
0
0
1
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
3
0
2
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
4
2
1
0
0
1
0
1
0
0
2
1
0
0
2
0
1
0
2
0
0
0
0
0
0
0
1
0
3
0
0
0
0
1
0
0
0
0
3
2
0
0
0
0
4
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
3
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
2
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
3
0
0
0
2
1
0
0
0
0
0
0
3
1
2
1
0
0
1
0
0
0
2
0
0
0
2
1
0
0
0
0
0
2
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
4
0
1
2
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
5
0
0
0
0
0
2
2
0
0
0
2
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
3
1
1
0
0
0
2
0
0
0
0
1
0
0
3
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
3
0
0
0
0
2
0
0
0
1
0
1
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
3
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
6
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
1
1
0
3
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
3
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
5
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
4
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
1
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
1
0
2
1
0
0
0
0
0
2
0
0
0
1
0
0
0
2
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
4
0
0
0
5
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
2
4
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
1
2
2
8
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
3
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
7
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
5
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
5
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
2
0
0
3
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
5
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
3
0
0
1
0
2
0
0
0
0
0
1
0
0
0
1
0
2
2
0
0
0
0
0
4
0
2
0
0
2
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
1
0
0
0
0
1
0
0
0
2
0
0
0
1
0
1
2
0
2
1
2
0
1
0
0
0
0
0
0
0
2
1
0
4
0
0
2
0
0
0
3
0
0
0
0
4
1
0
0
0
2
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
3
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
3
0
0
0
0
2
0
0
0
0
0
1
1
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
5
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
5
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
7
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
4
1
2
0
0
0
1
1
0
3
0
0
0
0
0
1
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
3
0
0
5
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
2
1
0
1
0
2
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
3
3
0
0
1
1
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
3
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
3
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
3
0
0
0
0
0
1
1
0
2
0
0
1
0
0
1
0
0
0
0
0
1
0
1
1
1
1
0
0
0
0
0
0
0
0
1
2
0
0
1
0
4
0
0
0
0
0
0
3
0
1
0
0
0
0
0
4
0
0
1
0
0
0
1
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
2
1
0
0
0
0
2
0
1
0
4
1
0
0
0
0
0
0
0
0
0
0
0
7
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
1
6
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
11
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
3
0
0
2
0
0
0
0
0
3
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
2
0
0
1
0
2
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
2
0
1
1
0
0
0
0
0
0
0
2
1
0
0
4
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
5
0
0
0
0
0
1
1
0
1
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
1
0
1
0
0
1
0
0
2
0
0
3
3
2
0
0
0
0
0
0
0
2
1
0
1
0
0
0
2
1
1
1
1
0
2
0
2
0
0
0
0
0
3
0
3
0
0
2
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
1
0
0
0
0
4
0
0
2
0
0
1
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
2
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
3
0
0
1
6
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
2
1
0
0
1
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
4
0
1
1
0
0
5
2
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
2
1
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
3
0
0
1
1
0
2
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
2
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
4
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
7
0
1
4
1
0
1
1
0
0
0
0
0
2
0
1
0
0
1
0
0
0
2
0
0
0
2
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
1
0
0
0
0
0
0
1
0
3
0
0
0
4
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
3
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
6
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
2
0
0
0
1
1
2
0
0
0
2
1
0
4
0
0
0
1
0
0
2
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
1
6
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
7
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
2
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
1
0
3
0
0
0
0
0
2
0
2
0
1
3
0
0
2
0
0
0
0
0
2
0
0
1
3
0
2
0
2
0
3
0
0
1
0
2
0
0
0
0
0
0
0
4
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
21
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
1
0
0
2
0
3
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
2
0
0
0
2
0
0
2
1
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
1
1
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
3
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
1
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
1
0
0
0
1
2
2
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
1
1
2
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
2
1
1
0
0
0
0
2
0
1
0
1
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
5
0
0
0
0
3
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
3
0
0
0
0
1
1
0
0
2
0
1
0
1
0
0
0
1
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
1
3
0
0
2
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
1
0
0
0
1
0
2
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
3
0
2
2
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
3
0
6
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
5
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
2
0
0
0
2
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
5
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
1
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
3
0
0
1
2
0
0
0
0
5
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
1
0
0
2
2
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
2
2
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
1
0
0
1
0
0
2
0
3
0
0
1
1
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
1
2
2
0
0
0
1
0
0
3
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
2
0
2
0
0
0
0
0
2
2
5
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
4
1
0
0
1
0
0
0
0
1
8
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
4
0
2
1
1
0
0
0
0
0
0
0
0
3
1
0
2
0
0
2
0
2
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
2
0
7
0
0
1
0
1
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
3
1
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
0
1
0
1
2
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
3
1
2
0
0
0
0
3
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
1
0
0
0
0
3
0
2
0
0
1
0
0
0
0
1
0
0
1
0
1
2
1
0
0
0
1
3
0
0
0
1
0
1
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
1
2
0
0
0
0
0
1
0
0
3
0
1
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
4
0
0
2
2
0
0
2
0
0
1
0
0
0
0
0
0
0
2
2
2
0
0
2
0
2
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
5
0
0
0
0
0
0
0
5
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
1
0
0
0
3
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
3
0
0
0
0
0
2
0
0
0
4
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
1
2
2
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
3
0
2
0
0
0
0
0
2
0
1
1
0
0
3
0
1
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
4
0
2
0
1
0
1
0
0
0
1
2
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
15
0
0
1
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
2
3
1
1
0
1
0
0
0
0
0
2
4
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
4
2
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
2
3
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
3
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
1
0
4
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
3
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
1
1
0
2
0
0
0
0
0
0
0
1
2
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
3
1
0
0
0
0
0
0
0
3
0
0
3
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
5
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
8
0
0
3
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
3
0
1
1
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
3
0
1
0
0
0
0
0
2
0
0
4
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
1
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
3
2
0
2
1
0
0
0
0
2
0
1
0
1
0
0
0
0
0
1
0
0
3
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
1
0
1
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
1
2
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
1
2
0
1
2
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
2
0
1
2
0
0
0
1
0
0
0
1
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
8
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
5
0
1
0
0
0
0
2
2
2
4
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
9
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
3
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
1
1
0
0
1
0
1
1
0
0
0
0
0
1
0
2
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
3
0
2
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
1
1
0
0
2
0
0
0
0
1
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
3
0
1
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
1
0
2
0
3
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
3
2
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
4
0
1
0
0
0
0
0
0
3
0
1
0
0
0
0
2
0
0
0
2
0
0
0
2
2
0
2
1
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
2
4
0
3
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
4
0
5
1
1
0
0
0
0
1
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
3
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
3
1
1
0
0
0
1
0
6
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
1
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
9
0
0
2
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
3
1
0
1
2
0
1
0
1
3
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
3
2
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
1
2
1
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
1
0
1
1
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
1
1
1
1
0
0
2
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
4
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
2
3
1
0
1
0
0
0
0
0
0
0
0
0
2
0
2
3
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
1
0
0
5
0
0
0
0
0
0
3
0
2
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
6
0
0
0
0
0
0
1
1
1
2
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
5
0
0
1
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
1
5
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
3
2
0
1
0
0
3
0
1
0
0
0
1
0
1
2
0
0
0
0
1
0
0
1
1
0
0
0
0
2
0
2
0
0
0
0
0
3
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
1
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
7
0
0
2
3
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
3
1
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
2
3
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
5
0
0
3
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
2
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
2
0
1
0
0
0
2
1
1
0
0
0
0
0
0
2
0
2
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
4
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
3
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
10
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
1
1
1
0
1
2
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
8
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
1
2
2
3
0
0
0
0
0
0
0
0
0
2
4
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
1
2
2
0
0
0
3
0
2
0
1
1
0
0
0
0
0
2
0
1
0
0
0
3
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
1
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
3
0
0
1
2
0
0
2
1
0
0
0
0
0
1
0
0
0
2
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
4
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
2
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
2
0
2
0
1
0
0
0
2
1
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
7
0
0
0
0
0
4
0
7
0
0
0
0
3
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
1
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
1
1
0
1
2
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
1
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
2
0
0
1
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
13
7
0
0
0
0
0
0
0
1
0
0
0
2
0
4
0
2
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
2
0
0
0
1
2
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
2
1
0
0
0
0
0
0
1
1
0
0
0
1
3
2
0
1
2
2
2
0
0
2
0
0
0
0
0
0
0
0
2
0
6
2
0
0
1
0
0
2
0
0
0
0
2
0
1
1
0
0
0
1
0
1
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
6
0
1
0
0
2
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
2
0
0
1
0
0
0
2
2
0
0
1
1
0
0
0
0
3
0
0
0
0
0
0
1
1
1
2
0
0
0
0
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
3
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
2
0
3
0
0
0
1
7
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
1
0
1
0
0
0
0
0
0
5
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
4
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
1
1
0
0
0
1
0
0
0
0
0
2
0
1
0
0
3
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
2
1
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
5
2
0
0
1
0
0
1
0
1
2
2
2
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
2
0
0
1
2
0
3
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
2
0
4
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
1
2
0
0
0
4
0
2
0
0
0
0
3
0
3
1
2
2
0
1
0
0
0
0
0
0
0
2
0
1
0
1
10
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
7
0
0
0
0
0
0
4
2
1
0
0
0
0
2
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
5
0
0
0
0
0
2
1
0
0
1
0
0
1
0
0
2
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
7
1
0
0
0
1
0
0
4
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
1
0
0
3
0
0
0
0
0
0
2
0
2
3
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
6
0
5
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
1
2
0
0
0
2
1
0
0
0
0
1
1
1
0
0
3
0
0
0
0
3
0
0
0
0
2
0
2
0
2
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
1
0
0
0
1
1
0
0
1
0
0
1
0
0
1
0
1
1
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
5
0
0
1
0
0
0
0
0
2
0
1
2
0
0
0
1
0
0
0
0
5
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
4
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
1
4
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
2
4
4
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
6
0
3
0
0
0
0
2
0
1
0
0
0
0
0
0
13
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
2
1
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
6
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
2
1
3
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
3
0
1
3
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
2
0
1
3
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
3
3
2
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
3
3
0
2
0
0
0
1
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
3
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
1
1
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
8
1
0
0
0
0
0
0
0
0
5
2
2
0
0
0
0
0
0
0
0
0
0
2
2
0
1
2
0
1
1
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
4
0
0
2
0
2
0
1
1
0
0
0
0
1
0
0
0
0
2
0
3
0
0
1
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
2
1
0
1
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
1
0
0
0
0
0
0
0
2
0
2
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
10
1
0
0
0
1
0
1
0
0
0
0
2
0
0
0
2
2
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
3
0
0
0
0
0
0
2
0
0
2
0
3
0
1
0
0
0
0
0
3
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
1
0
0
0
3
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
2
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
3
0
1
0
0
0
0
1
3
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
2
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
4
0
3
0
0
1
0
0
0
0
2
1
0
0
0
0
0
3
1
0
0
0
0
2
2
2
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
1
0
0
2
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
1
0
0
0
2
0
0
0
0
0
1
1
1
0
3
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
1
1
0
1
0
1
1
0
0
0
2
2
0
1
0
2
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
2
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
2
5
2
0
0
0
0
0
1
0
1
3
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
3
0
0
0
0
2
0
0
0
1
1
0
1
0
1
0
1
2
2
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
3
0
0
2
0
4
2
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
1
3
0
0
0
2
1
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
3
7
0
0
0
0
2
11
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
2
2
0
2
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
1
1
0
0
0
2
0
0
1
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
2
1
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
1
0
0
5
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
2
2
2
0
0
0
0
0
3
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
5
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
8
0
0
0
0
0
3
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
2
0
0
0
0
1
2
0
3
0
0
0
1
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
3
0
1
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
1
1
0
0
8
2
0
0
0
0
0
1
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
5
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
2
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
1
5
0
0
0
1
0
1
0
0
0
0
1
3
0
2
0
0
1
0
0
0
0
0
0
0
0
1
1
3
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
1
0
0
0
0
1
0
2
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
8
0
0
3
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
5
0
0
0
0
0
0
2
0
2
0
1
0
0
2
1
0
1
0
0
0
1
0
0
0
0
1
0
2
1
1
0
0
0
0
1
2
0
4
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
3
2
0
1
1
0
0
2
4
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
4
0
2
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
2
0
2
0
0
0
2
0
1
0
0
3
0
0
0
1
1
1
0
0
0
2
1
0
0
3
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
2
0
0
0
1
0
0
0
0
2
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
1
1
0
0
1
0
1
0
0
1
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
1
2
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
7
0
1
0
0
0
0
2
1
1
1
0
2
0
0
0
0
0
1
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
3
2
3
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
2
0
0
0
0
0
0
0
1
2
1
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
7
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
3
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
1
3
1
1
0
1
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
9
1
0
0
0
0
0
4
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
5
0
0
0
0
0
0
0
2
0
2
0
0
1
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
3
1
1
0
1
0
0
0
0
0
0
0
2
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
5
0
0
1
1
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
2
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
2
0
0
0
1
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
1
3
0
0
3
0
0
0
2
0
0
1
0
0
0
1
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
1
0
0
1
1
0
1
0
1
1
7
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
5
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
12
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
1
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
4
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
2
0
0
0
0
1
2
0
0
0
1
0
2
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
30
0
0
1
0
1
0
0
0
0
2
3
0
0
2
0
4
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
6
0
1
0
2
0
1
1
0
0
1
0
1
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
2
0
1
0
0
0
0
0
0
0
0
1
0
3
1
0
0
0
0
2
0
0
0
2
0
3
0
0
1
6
0
0
0
4
2
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
4
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
2
4
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
2
0
1
0
4
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
1
0
1
0
1
0
0
0
0
2
2
1
0
0
0
0
0
0
1
2
0
4
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
1
2
0
0
0
0
0
1
2
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
1
0
6
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
1
5
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
2
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
10
0
0
0
0
0
0
0
1
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
3
0
0
0
2
1
0
1
2
0
0
0
0
1
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
1
0
0
2
0
0
0
1
0
0
0
2
0
0
0
3
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
3
0
0
0
0
0
3
0
0
0
0
1
0
1
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
1
4
1
0
0
0
0
0
1
0
3
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
5
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
5
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
2
0
2
0
1
0
0
0
0
5
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
1
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
1
2
0
0
0
0
0
2
0
1
0
0
1
0
1
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
1
3
0
0
3
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
3
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
2
1
0
0
0
0
2
0
0
2
2
0
0
0
1
0
1
0
0
0
0
1
2
0
0
1
0
2
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
4
3
1
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
1
3
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
1
0
1
1
0
0
0
0
0
2
0
1
0
0
2
0
0
0
1
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
3
3
0
0
0
0
1
0
1
0
0
2
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
5
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
1
2
0
0
0
2
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
4
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
3
0
7
0
1
0
0
1
0
0
1
0
0
1
0
0
0
1
0
6
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
4
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
8
0
0
1
0
1
1
0
3
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
1
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
2
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
3
3
0
3
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
3
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
1
0
3
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
2
0
0
0
2
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
5
1
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
2
2
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
2
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
2
0
0
0
0
0
0
2
0
3
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
1
1
0
1
0
0
2
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
1
1
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
2
0
0
1
0
0
1
0
0
1
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
5
0
0
1
2
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
2
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
1
0
0
0
1
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
3
5
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
1
0
4
0
2
0
0
1
0
2
2
0
12
0
0
0
0
0
0
2
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
1
1
1
2
1
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
3
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
1
0
4
0
0
2
0
0
0
0
0
0
12
4
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
4
1
2
2
0
0
0
0
2
1
0
1
0
0
0
2
3
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
5
0
0
1
2
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
1
0
2
0
2
2
2
2
1
0
0
2
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
2
0
0
1
0
0
0
1
1
0
1
0
0
1
0
2
0
0
0
0
0
0
1
0
0
3
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
1
0
0
0
2
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
2
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
5
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
2
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
5
0
0
0
0
0
0
0
1
1
0
0
4
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
1
0
0
6
1
2
1
0
0
0
2
2
0
0
0
0
2
3
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
5
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
6
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
4
2
2
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
3
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
2
0
1
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
6
0
0
0
0
0
1
0
2
0
2
0
2
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
2
0
1
0
4
2
0
0
1
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
3
0
0
2
0
1
0
3
1
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
5
1
0
0
0
0
0
1
1
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
2
0
0
1
0
0
0
0
0
1
0
1
1
0
0
4
0
0
0
1
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
1
0
0
0
0
2
1
0
0
0
4
0
0
1
1
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
2
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
3
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
10
0
1
0
0
0
1
0
2
7
1
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
1
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
3
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
13
0
0
1
0
0
1
0
5
0
0
2
0
0
0
0
0
1
0
0
0
0
0
3
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
2
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
3
2
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
1
2
0
2
0
0
0
0
0
1
1
0
0
0
0
0
3
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
1
0
0
4
1
0
0
0
2
0
0
0
0
0
4
0
2
0
0
0
0
0
0
3
5
0
0
0
1
1
2
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
2
0
1
0
0
1
0
0
0
2
2
0
1
0
0
1
0
1
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
5
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
3
0
0
2
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
2
0
1
0
2
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
2
2
0
1
1
0
0
0
2
2
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
2
0
0
0
1
1
0
4
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
1
4
0
0
0
0
0
2
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
2
0
0
0
2
1
1
0
1
0
0
0
0
0
0
0
0
0
0
5
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
1
1
0
0
0
5
1
0
0
0
0
0
0
1
0
0
1
0
1
0
2
0
2
0
0
0
0
3
0
0
0
1
3
1
0
0
0
0
1
0
0
0
0
0
0
3
1
2
0
0
2
0
1
2
0
0
0
0
2
0
0
4
1
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
8
1
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
3
0
0
0
0
0
1
0
0
2
0
0
0
0
2
2
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
1
2
2
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
2
0
2
0
1
0
0
0
1
0
0
2
0
2
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
2
0
1
0
0
0
2
0
0
3
0
0
0
0
0
2
0
1
0
0
1
1
0
0
0
1
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
3
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
2
1
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
1
0
0
1
0
0
1
0
4
0
0
0
0
0
1
0
9
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
8
0
0
0
0
1
2
0
0
0
0
9
0
2
1
0
3
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
1
0
1
1
0
0
0
1
4
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
2
2
0
0
2
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
1
0
6
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
3
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
1
1
3
0
0
0
1
0
0
0
0
1
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
1
3
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
6
0
1
0
0
0
0
0
2
1
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
2
1
3
2
0
0
4
0
0
2
1
0
2
0
2
1
1
0
0
3
1
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
2
1
3
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
11
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
1
0
1
0
1
1
0
2
0
1
0
0
0
0
0
0
1
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
1
5
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
1
0
0
2
0
0
1
2
0
0
2
0
1
0
0
0
1
0
2
3
0
0
0
2
0
0
0
0
0
0
0
0
2
1
1
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
3
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
1
1
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
1
3
2
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
4
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
6
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
3
2
2
0
3
0
0
1
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
1
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
1
1
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
7
1
0
0
0
2
2
1
2
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
2
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
2
4
0
0
0
0
0
0
0
5
2
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
2
2
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
8
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
7
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
1
3
0
0
1
0
0
1
0
0
2
2
0
4
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
4
0
4
0
0
0
4
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
3
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
3
0
0
3
0
0
0
2
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
5
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
2
0
2
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
3
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
1
1
0
0
2
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
2
6
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
1
1
0
3
0
0
0
0
0
0
2
2
0
0
2
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
4
4
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
3
1
0
2
2
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
4
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
5
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
2
0
2
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
1
0
1
0
0
0
2
1
0
0
0
1
0
0
0
3
0
0
0
0
0
2
0
1
1
0
2
0
0
0
3
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
6
0
0
0
0
1
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
1
0
0
5
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
3
2
1
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
0
4
1
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
2
1
0
0
1
0
0
0
0
6
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
7
0
0
0
3
0
0
0
0
0
1
2
0
0
1
0
1
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
5
0
0
1
1
0
2
0
0
0
0
0
0
4
0
1
0
0
0
1
2
1
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
2
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
1
1
0
2
2
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
1
0
1
0
0
0
6
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
10
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
5
0
0
2
0
0
0
0
0
0
0
1
4
0
1
2
0
0
0
0
1
2
0
0
1
0
0
0
0
3
1
2
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
1
1
0
0
0
0
2
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
2
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
3
0
0
2
1
1
0
0
1
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
1
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
4
1
0
0
3
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
3
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
8
0
0
0
0
0
0
2
1
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
2
0
0
1
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
1
0
0
0
3
0
0
0
0
0
3
0
0
0
0
0
2
1
0
0
2
0
0
0
1
0
3
0
1
0
0
0
0
2
0
0
2
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
5
0
1
0
0
0
1
0
0
1
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
2
0
0
0
1
0
0
0
2
0
0
0
1
0
2
0
0
2
2
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
9
0
0
0
0
0
0
1
0
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
3
0
0
0
0
3
0
0
1
0
0
3
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
5
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
1
0
0
3
0
0
0
1
0
0
1
7
0
0
0
0
1
0
0
3
0
0
2
0
0
4
0
1
0
1
0
3
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
5
0
2
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
6
0
0
0
0
0
0
1
0
0
0
2
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
5
2
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
3
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
3
3
3
0
0
1
0
1
0
2
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
2
0
0
0
1
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
2
0
3
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
1
0
0
0
2
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
3
1
0
0
0
0
0
1
1
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
8
0
0
2
0
0
2
0
0
0
3
0
0
2
0
0
1
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
2
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
1
0
1
0
13
0
0
2
0
1
0
0
0
0
1
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
2
10
2
0
0
0
3
0
0
0
1
0
0
0
2
3
0
2
1
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
6
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
1
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
3
1
1
0
0
0
1
2
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
3
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
2
2
0
1
0
0
0
0
0
3
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
4
0
0
0
0
1
0
2
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
3
0
0
0
0
0
2
0
5
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
1
0
1
0
0
1
0
2
1
1
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
3
2
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
2
1
0
3
1
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
4
0
0
2
0
0
0
1
0
1
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
1
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
2
1
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
4
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
3
0
2
0
0
0
0
0
0
1
0
2
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
1
0
0
0
1
1
0
0
0
0
2
0
2
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
3
0
0
0
2
0
1
0
0
0
1
0
1
0
4
0
0
0
0
0
0
1
1
2
2
1
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
3
5
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
7
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
3
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
3
0
0
0
1
0
4
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
2
1
0
1
0
2
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
1
0
4
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
3
0
0
1
0
0
4
4
0
0
1
0
0
0
0
1
0
1
2
0
0
0
2
0
0
0
0
0
0
2
0
1
1
0
0
0
0
2
0
0
0
4
0
0
0
0
0
6
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
7
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
2
2
2
0
0
2
0
0
2
0
0
0
0
1
0
1
0
0
2
0
0
2
0
0
0
0
0
1
0
0
1
0
1
0
5
0
0
0
0
0
0
0
1
0
0
2
2
2
0
0
0
5
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
5
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
1
0
2
0
0
0
2
2
2
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
2
1
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
2
0
0
0
0
2
0
0
2
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
3
0
0
1
0
0
0
0
0
1
0
0
0
0
4
0
0
2
0
0
1
0
0
2
0
1
0
0
0
0
0
3
2
0
0
0
0
0
3
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
3
0
0
1
0
0
2
0
4
0
0
0
2
0
0
5
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
1
0
0
2
1
0
0
0
2
1
0
0
0
0
0
1
2
4
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
2
2
1
2
0
2
0
0
0
0
0
0
0
0
1
4
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
3
0
0
0
0
4
0
2
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
1
0
0
1
3
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
14
0
0
2
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
1
0
0
4
9
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
2
1
2
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
3
0
0
0
2
1
2
3
3
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
2
1
0
0
0
0
0
1
1
0
1
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
2
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
3
0
0
1
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
4
0
1
1
3
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
1
2
2
0
0
0
6
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
1
0
2
0
0
0
0
0
0
1
0
0
2
2
1
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
7
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
1
0
3
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
1
1
0
2
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
1
0
0
2
0
2
0
1
1
0
1
0
0
0
1
0
1
0
0
0
0
4
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
2
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
11
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
7
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
2
0
1
3
1
0
0
2
0
0
1
0
1
1
2
2
0
2
3
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
1
1
0
0
0
0
0
0
0
1
2
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
1
0
0
1
0
0
0
0
0
0
1
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
1
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
1
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
3
1
3
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
3
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
3
0
1
0
6
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
4
0
0
0
0
1
0
1
0
0
0
5
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
2
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
1
0
2
2
0
0
0
0
5
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
2
0
0
3
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
2
0
0
0
2
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
3
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
3
0
2
1
0
2
0
0
0
0
0
0
2
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
2
1
0
0
1
0
0
2
0
0
2
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
3
0
0
0
1
2
0
1
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
1
3
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
5
1
0
0
0
2
0
0
1
0
0
0
2
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
5
1
0
0
0
0
0
0
0
1
0
0
0
3
2
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
7
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
2
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
3
1
0
0
0
0
1
3
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
2
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
3
2
0
0
2
0
0
1
3
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
4
1
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
3
8
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
1
0
0
1
1
0
0
2
0
2
0
1
0
0
0
1
0
2
0
1
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
2
0
0
0
0
5
0
1
0
2
0
0
0
1
0
1
0
0
1
1
0
0
0
0
1
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
1
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
1
2
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
3
0
0
0
0
3
0
0
0
0
0
0
4
0
0
0
0
3
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
5
0
0
0
1
2
0
0
0
0
0
0
1
1
0
0
0
2
3
0
0
0
0
0
2
0
1
2
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
6
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
3
2
0
0
1
0
0
0
0
0
0
0
8
0
0
0
0
1
2
0
0
1
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
1
0
1
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
3
0
4
1
0
1
2
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
2
1
2
7
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
4
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
4
4
0
0
0
0
0
0
0
0
1
2
1
1
0
0
0
0
1
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
2
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
2
0
1
0
0
1
2
0
0
0
0
2
1
0
0
0
0
3
0
0
0
0
0
1
0
2
2
1
2
0
0
0
0
0
0
1
1
0
4
2
0
3
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
2
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
5
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
2
3
0
0
0
0
1
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
4
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
3
0
0
0
2
1
3
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
6
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
2
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
3
0
0
0
0
0
0
5
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
2
0
0
0
1
0
2
1
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
2
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
5
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
2
1
3
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
1
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
3
0
2
0
0
0
2
0
0
15
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
3
0
2
0
0
0
0
1
0
0
3
0
2
0
0
0
0
6
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
1
0
1
3
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
10
0
0
0
1
3
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
5
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
3
0
0
0
4
1
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
6
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
10
0
1
1
0
1
0
0
0
1
8
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
1
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
3
0
0
0
0
0
0
2
0
2
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7
2
0
0
0
1
0
0
2
0
0
0
2
0
0
0
2
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
1
0
0
0
0
0
0
3
0
0
1
3
0
0
0
2
0
0
3
0
0
2
2
0
0
0
0
1
0
0
0
2
0
1
3
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
4
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
1
2
1
0
0
0
0
1
0
4
0
0
0
0
2
0
2
0
0
1
0
0
2
0
3
0
0
4
0
1
0
1
0
0
0
0
0
0
0
0
5
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
2
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
1
1
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
1
0
2
0
0
1
0
0
0
3
1
0
0
2
0
0
0
0
0
2
0
1
0
2
3
1
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
2
0
3
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
2
0
1
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
1
0
1
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
4
0
0
2
1
0
2
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
1
1
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
1
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
1
0
0
0
0
0
2
0
0
1
1
2
0
0
2
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
2
0
0
0
4
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
1
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
2
0
1
0
0
0
0
1
0
0
0
0
0
3
1
0
0
0
1
2
0
1
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
4
0
0
0
1
0
2
0
0
2
3
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
4
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
7
0
0
2
0
0
3
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
5
0
4
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
4
0
2
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
6
0
0
2
0
0
0
0
0
0
1
3
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
3
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
5
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
1
0
0
0
0
4
0
0
0
0
7
1
2
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
2
0
1
0
0
0
1
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
1
4
1
0
1
0
0
0
0
0
2
0
0
0
0
2
6
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
2
1
0
0
0
0
0
0
1
0
0
4
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
1
1
1
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
6
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
4
2
3
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
3
0
0
0
0
1
2
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
2
0
0
0
0
0
0
0
3
1
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
2
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
3
0
2
0
0
2
0
0
0
0
0
0
0
1
0
3
0
0
2
0
0
0
1
0
0
2
1
6
0
0
1
1
0
2
0
1
0
0
0
0
1
1
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
2
0
2
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
1
2
0
0
1
0
0
1
1
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
4
1
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
5
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
2
0
0
0
0
0
1
0
2
0
1
0
0
0
1
0
1
0
1
0
0
0
0
5
0
1
0
1
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
4
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
3
0
2
1
2
0
0
0
2
0
1
0
0
0
2
0
2
0
0
0
0
2
0
2
1
2
0
0
0
0
2
2
0
0
0
1
0
0
0
0
1
1
2
0
0
0
0
2
0
1
0
0
0
0
0
1
0
2
0
2
0
2
1
0
0
2
0
0
0
0
2
0
0
0
0
3
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
3
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
1
0
0
2
0
1
0
7
0
1
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
3
1
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
2
0
0
1
0
0
3
0
3
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
1
0
2
0
0
0
1
1
1
0
0
10
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
1
1
0
0
2
0
2
0
0
0
2
3
0
2
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
1
0
0
0
1
0
0
0
2
0
0
0
0
2
1
0
0
0
0
2
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
1
1
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
2
0
0
8
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
4
3
1
0
2
0
0
0
0
0
1
0
1
0
0
2
0
5
0
1
2
1
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
1
2
0
0
2
1
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
5
0
0
0
2
0
0
0
6
0
0
0
1
2
0
0
1
0
0
0
8
0
2
0
2
0
0
0
0
0
0
0
2
1
0
4
0
0
0
2
2
0
0
0
0
0
0
0
2
1
0
0
0
4
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
2
0
1
0
0
0
1
0
0
0
0
2
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
1
0
0
0
0
0
4
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
2
0
5
4
0
0
1
0
1
0
2
0
0
0
0
2
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
6
0
0
0
0
0
0
6
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
3
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
1
0
0
0
0
0
0
2
0
2
1
0
2
0
1
0
0
0
1
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
2
2
2
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
6
0
1
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
2
4
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
3
1
0
0
0
0
0
1
0
0
0
0
4
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
1
3
1
0
0
1
0
0
0
0
2
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
2
0
0
0
4
0
1
0
1
0
0
1
1
1
0
0
0
0
1
1
0
0
5
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
2
1
0
0
1
2
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
1
0
1
2
2
1
0
0
0
0
8
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
5
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
1
2
2
1
0
0
2
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
2
3
0
0
0
0
0
0
1
0
0
1
0
0
3
0
2
0
0
0
0
3
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
3
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
3
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
4
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
6
0
0
1
1
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
1
2
1
0
0
4
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
2
0
2
1
0
0
0
2
0
0
0
0
0
2
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
2
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
1
0
2
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
2
0
2
0
0
0
0
0
0
1
0
0
2
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
2
3
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
2
2
0
0
1
0
2
0
0
1
0
1
2
0
1
0
1
0
0
2
0
0
0
0
1
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
3
0
0
0
0
4
2
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
1
0
2
0
0
2
1
2
0
0
0
0
0
0
0
5
0
2
0
0
4
0
0
0
0
0
0
0
2
0
3
2
2
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
2
0
1
0
0
1
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
4
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
2
1
0
0
2
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
1
0
0
2
0
0
2
0
1
0
0
0
1
1
2
0
0
0
1
0
0
0
0
3
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
5
0
0
0
2
1
1
0
1
0
0
3
0
0
1
0
0
0
0
0
2
0
1
4
0
0
0
0
0
1
1
2
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
2
0
4
1
0
0
0
0
0
0
0
0
0
1
1
0
0
3
0
0
0
0
3
0
0
0
0
5
0
0
0
0
0
0
2
0
0
4
0
0
0
3
0
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
2
2
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
1
2
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
1
1
1
0
1
0
0
2
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
2
0
1
0
1
0
0
0
0
2
1
0
0
2
0
2
2
2
2
2
0
0
0
1
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
1
0
1
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
1
1
0
6
0
0
0
0
0
1
0
0
0
11
0
0
0
0
0
1
0
0
0
1
0
2
0
2
0
1
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
1
2
0
7
0
1
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
1
0
0
0
2
1
2
1
1
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
5
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
1
0
0
2
0
0
0
0
0
0
2
1
0
0
1
0
0
0
2
0
2
3
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
1
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
1
3
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
21
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
3
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
6
0
0
1
0
0
2
0
0
2
0
1
0
0
0
1
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
1
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
1
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
2
0
1
0
0
1
0
1
1
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
2
4
0
3
0
1
3
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
7
1
0
0
2
1
0
0
0
3
1
1
4
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
3
2
0
1
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
4
3
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
2
1
1
0
0
0
3
0
0
0
0
1
0
3
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
3
0
0
1
1
0
1
0
0
4
2
1
0
1
1
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
7
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
1
5
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
1
0
0
2
0
1
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
2
0
1
0
1
0
0
2
0
5
0
0
0
0
1
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
4
0
0
0
0
0
0
3
0
0
0
0
0
4
0
2
1
0
4
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
1
0
0
1
0
1
1
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
4
0
0
0
2
1
0
0
1
0
0
0
0
0
3
0
3
0
0
0
0
0
4
0
0
1
0
0
0
3
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
7
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
2
2
0
0
0
0
1
0
1
0
0
0
2
1
0
0
0
0
0
1
1
1
2
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
1
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
5
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
2
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
6
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
1
0
13
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
3
0
0
0
0
0
2
0
1
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
1
0
0
3
0
1
0
0
3
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
1
2
0
0
2
0
2
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
4
0
1
1
1
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
4
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
3
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
4
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
1
0
0
0
0
0
3
0
1
0
0
2
0
0
0
0
0
0
0
0
6
0
3
0
2
0
0
3
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
5
0
0
0
0
1
0
0
1
0
1
4
0
0
1
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
3
1
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
1
0
0
3
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
7
0
0
0
0
0
0
1
0
3
1
0
0
0
2
3
0
1
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
3
1
0
0
2
2
0
0
0
0
2
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
1
2
0
0
0
0
0
1
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
5
0
1
0
0
0
0
1
0
2
0
0
3
0
1
0
0
1
4
3
0
2
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
5
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
2
2
0
2
0
0
4
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
7
2
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
5
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
1
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
4
1
2
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
2
0
0
0
0
0
0
1
2
0
0
0
0
0
4
0
0
0
2
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
4
9
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
1
3
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
2
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
2
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
1
0
0
1
0
0
0
1
0
0
0
1
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
1
0
0
0
2
3
0
2
2
0
1
2
0
7
0
1
0
0
0
0
6
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
5
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
3
2
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
4
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
5
1
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
2
0
2
0
0
0
0
0
1
2
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
3
1
0
0
2
0
1
0
0
0
0
2
0
2
0
1
0
0
0
1
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
2
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
5
0
0
0
1
5
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
2
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
2
2
0
0
0
5
0
1
0
2
0
2
0
0
0
0
2
0
2
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
1
0
0
0
3
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
3
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
2
1
0
1
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
1
0
0
0
1
0
0
0
2
0
0
0
0
0
9
1
0
0
2
1
0
1
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
4
2
0
0
0
0
1
2
0
0
0
1
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
1
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
2
3
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
3
0
0
2
0
0
0
0
1
0
0
0
1
2
2
1
0
1
0
0
1
2
1
0
0
0
3
2
0
0
0
0
0
1
0
0
0
1
2
1
0
0
0
0
3
0
0
0
0
1
0
0
4
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
10
0
0
0
0
1
0
0
0
4
1
0
0
0
0
0
1
0
0
3
0
0
0
2
0
0
2
0
0
1
0
0
1
0
3
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
5
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
4
0
0
0
2
1
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
1
4
0
0
0
2
1
1
0
0
0
0
3
0
0
1
2
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
1
2
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
3
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
1
4
0
1
0
0
0
2
1
0
0
2
1
0
0
1
2
4
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
2
0
2
0
0
0
1
1
0
0
0
0
1
1
0
0
0
2
0
0
0
2
0
1
1
0
0
2
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
5
0
0
0
2
1
0
0
0
0
0
2
0
2
0
0
1
0
0
2
0
2
2
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
10
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
5
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
2
0
0
0
0
2
0
2
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
6
0
0
0
0
2
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
4
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
7
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
1
2
2
0
0
2
0
7
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
2
0
2
0
1
0
0
1
1
1
0
0
0
1
0
1
0
0
0
0
0
0
8
0
0
1
0
2
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
1
2
3
2
1
0
0
1
3
0
0
0
0
0
1
0
0
0
0
1
0
2
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
1
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
5
0
0
0
0
0
0
0
0
2
0
2
0
0
0
10
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
5
0
0
0
1
0
0
0
0
0
3
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
1
0
5
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
1
0
0
1
0
1
1
0
4
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
13
0
0
0
1
0
0
0
0
2
0
0
1
1
0
0
2
1
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
3
2
0
0
0
0
2
0
0
0
0
1
0
1
0
2
2
1
3
0
0
2
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
1
0
1
3
0
1
0
0
0
0
0
2
1
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
2
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
3
0
2
2
0
0
0
0
2
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
9
3
2
2
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
1
0
0
3
0
2
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
4
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
4
0
11
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
3
2
0
1
13
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
5
1
2
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
5
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
7
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
5
0
0
0
0
1
2
0
0
1
0
6
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
3
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
3
0
0
0
0
0
1
0
0
1
2
0
2
1
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
2
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
4
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
2
2
4
0
1
0
0
0
1
0
5
0
1
0
0
0
1
2
2
0
0
0
0
0
0
0
4
5
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
1
2
0
0
0
0
0
0
0
0
3
1
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
3
0
0
0
0
0
0
0
1
0
2
1
0
0
0
1
1
0
1
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
11
2
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
4
0
1
0
0
0
1
0
1
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
1
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
3
0
2
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
2
0
0
0
3
4
2
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
2
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
3
3
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
2
0
0
1
0
0
0
0
0
0
1
2
1
0
0
0
1
0
0
2
0
1
0
1
1
2
0
0
2
0
0
0
0
3
0
2
0
0
3
0
0
2
3
0
0
0
0
1
2
1
1
2
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
3
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
2
0
0
1
10
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
6
0
4
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
2
0
0
0
2
0
0
11
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
2
1
9
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
4
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
1
0
0
2
1
1
2
0
0
0
0
4
0
1
0
2
0
1
1
1
0
0
0
0
0
0
2
0
0
1
0
1
2
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
1
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
3
0
0
0
1
0
5
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
5
0
2
0
3
1
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
3
2
2
0
1
0
2
0
3
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
7
1
0
0
2
0
0
0
0
6
0
0
1
0
0
0
0
7
0
0
0
1
0
2
0
0
0
1
0
1
1
0
0
0
3
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
1
2
1
3
1
0
1
1
2
0
0
2
0
0
0
0
0
1
0
0
1
0
2
0
0
0
1
0
2
1
0
1
1
0
0
0
1
0
0
0
0
0
2
0
1
4
0
0
0
0
0
0
1
1
2
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
1
0
0
0
6
0
0
0
0
0
0
0
0
1
0
0
0
1
1
2
0
0
0
1
0
0
0
0
0
2
0
1
2
0
0
0
0
0
1
0
0
1
3
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
1
0
0
1
0
0
0
0
0
1
4
0
0
2
0
2
0
0
2
2
0
0
1
0
2
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
1
6
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
1
0
1
0
3
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
6
0
0
6
0
4
0
2
0
3
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
3
0
0
0
0
2
0
1
2
1
0
0
3
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
5
2
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
3
0
4
2
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
3
2
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
4
0
0
2
0
0
0
0
0
0
0
1
0
0
0
8
0
1
2
0
0
1
0
0
0
1
0
2
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
1
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
2
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
1
1
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
2
0
1
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
2
3
0
1
0
1
0
0
1
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
2
0
1
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
4
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
3
2
0
0
2
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
5
1
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
6
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
2
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
2
0
1
1
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
3
4
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
3
0
2
0
0
2
0
1
0
1
0
0
0
1
0
0
2
0
0
0
0
3
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
2
2
2
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
4
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
2
0
0
0
1
2
0
0
2
0
0
0
0
0
0
6
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
18
3
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
3
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
3
0
2
0
0
0
4
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
1
5
0
0
3
0
0
0
0
0
0
2
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
3
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
4
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
1
1
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
4
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
2
0
0
0
0
0
0
3
0
2
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
3
5
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
3
0
0
2
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
3
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
3
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
2
2
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
4
0
0
1
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
3
0
0
2
0
0
0
0
0
2
0
0
2
0
8
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
1
0
0
1
0
0
3
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
2
0
0
2
0
0
0
2
3
0
0
2
0
1
2
0
1
0
0
0
2
0
1
3
1
0
2
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
3
0
2
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
1
0
0
1
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
5
0
0
0
4
0
0
0
0
1
0
0
0
0
2
2
0
2
0
1
1
2
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
3
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
1
0
2
0
0
0
0
0
0
0
0
4
1
0
0
0
2
0
0
2
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
4
1
2
0
0
0
0
0
1
0
1
2
0
0
0
2
0
0
4
0
0
0
0
0
0
0
2
1
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
6
0
2
2
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
1
2
0
1
4
15
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
2
1
4
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
2
2
0
1
1
1
0
0
0
0
0
3
1
0
1
1
2
0
0
2
0
0
0
0
3
0
0
1
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
4
0
0
0
2
0
0
0
2
2
2
0
0
0
0
0
2
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
3
2
0
2
1
3
0
0
0
0
3
1
1
2
0
0
0
0
0
0
2
2
2
1
0
2
0
0
0
0
1
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
4
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
1
4
2
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
2
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
2
1
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
2
0
1
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
4
1
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
3
5
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
3
0
1
0
0
0
1
0
3
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
3
0
0
0
1
0
0
0
1
2
1
1
0
0
5
0
4
0
0
0
0
0
4
0
2
2
2
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
1
0
1
0
0
0
2
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
2
0
0
1
0
0
4
0
0
0
0
3
0
0
0
0
0
0
0
2
5
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
4
2
1
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
1
0
2
0
0
0
0
2
1
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
2
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
2
0
2
0
0
0
1
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
1
0
0
5
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
1
0
0
0
0
0
0
0
2
0
0
0
5
0
0
0
0
0
0
0
0
1
3
1
0
0
0
0
0
2
0
0
0
0
0
3
2
14
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
2
0
0
0
2
0
0
1
1
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
1
0
0
0
4
0
0
0
3
2
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
2
3
0
1
0
0
1
5
0
1
0
1
0
0
0
0
0
0
0
0
1
2
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
2
0
1
0
0
8
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
1
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
3
0
0
0
5
1
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
5
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
3
0
3
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
2
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
2
0
0
0
0
0
4
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
3
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
5
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
3
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
5
0
1
1
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
4
3
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
1
0
3
0
3
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
2
0
1
1
1
2
0
1
0
0
0
0
1
0
0
0
0
1
2
0
1
0
1
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
3
2
0
0
1
0
2
1
1
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
3
0
0
0
4
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
1
1
2
0
0
0
0
3
1
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
1
1
0
0
0
0
0
0
0
2
0
3
0
0
1
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
4
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
1
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
5
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
1
5
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
1
0
2
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
4
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
7
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
4
2
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
2
0
0
3
0
3
2
0
0
0
1
1
0
0
0
1
0
0
1
0
2
0
0
0
0
1
0
0
0
2
0
1
0
0
1
0
2
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
3
0
1
0
1
1
0
0
0
4
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
3
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
1
0
0
1
1
0
0
0
0
0
4
2
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
1
0
0
0
2
0
6
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
3
1
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
3
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
1
0
1
0
0
2
0
0
0
1
0
2
0
0
0
0
0
6
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
3
0
2
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
17
0
0
5
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
3
1
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
1
0
1
2
0
0
0
0
0
1
1
0
0
1
5
0
0
0
1
0
0
1
0
0
0
1
0
2
0
0
0
3
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
2
0
1
0
0
0
1
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
8
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
3
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
3
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
3
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
2
0
1
0
1
0
2
6
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
2
0
0
0
7
1
0
0
0
0
2
0
0
1
2
3
2
1
0
0
0
0
1
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
2
0
1
1
0
1
0
0
0
1
3
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
3
0
1
0
0
2
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
1
1
0
1
0
0
0
2
2
2
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
2
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
2
0
0
0
0
0
0
2
0
0
5
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
1
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
1
2
2
2
0
0
0
0
0
0
3
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
1
0
0
0
0
4
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
3
0
0
0
2
0
0
0
0
0
7
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
1
0
2
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
2
0
4
0
3
0
0
0
2
2
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
1
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
3
0
0
1
0
1
0
1
0
0
0
0
0
7
0
0
0
0
0
1
0
0
0
0
1
0
3
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
2
2
0
0
2
0
0
1
1
0
1
0
0
2
2
0
0
0
0
2
0
1
0
0
2
2
0
0
0
0
0
5
2
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
1
2
0
0
0
0
0
0
5
0
3
0
0
0
1
0
0
0
2
1
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
4
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
1
4
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
1
1
1
0
1
1
3
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
1
0
3
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
3
0
0
0
0
4
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
1
0
1
1
0
0
0
1
4
0
10
0
1
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
2
1
1
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
3
1
0
0
0
0
0
0
1
0
0
0
0
0
7
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
3
0
0
0
0
0
2
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
8
0
0
0
0
0
1
0
0
0
2
3
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
2
0
2
0
0
1
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
7
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
1
0
0
2
1
2
0
0
3
1
0
2
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
3
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
7
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
1
0
0
6
0
0
5
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
3
0
0
0
1
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
3
2
0
0
1
1
2
1
0
0
0
0
1
1
0
1
1
0
0
1
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
2
0
1
0
0
2
0
0
0
0
0
0
2
0
2
1
0
0
3
0
0
0
0
0
0
0
0
1
0
0
2
0
1
2
0
2
0
0
4
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
1
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
2
0
0
4
1
0
0
0
0
0
0
0
0
1
1
0
0
1
2
1
1
0
1
1
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
1
0
1
0
0
0
0
2
4
2
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
1
0
0
1
0
0
0
0
0
5
0
0
0
3
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
3
0
0
0
4
0
0
0
0
0
1
1
1
1
0
0
0
0
2
0
5
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
2
0
0
1
0
1
3
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
3
0
0
0
0
0
0
2
0
1
0
0
3
0
0
1
0
0
2
0
0
0
0
2
0
1
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
4
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
11
0
0
0
0
0
0
0
1
1
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
2
3
4
0
0
0
2
3
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
2
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
2
0
2
0
0
0
1
0
1
0
0
0
4
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
10
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
2
2
0
1
0
0
1
0
0
0
0
0
6
0
0
0
3
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
4
0
0
0
0
6
0
1
1
0
1
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
2
0
0
0
0
6
2
0
0
0
0
2
0
0
0
1
1
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
4
0
2
0
0
0
0
0
0
5
0
1
3
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
2
3
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
10
0
0
0
0
0
0
0
0
0
0
5
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
1
0
0
0
2
0
0
0
3
0
0
0
0
1
0
0
0
0
0
2
0
1
0
2
0
0
1
0
3
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
2
2
0
1
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
8
1
4
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
1
7
0
0
1
0
0
3
0
0
2
1
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
2
0
0
2
0
0
2
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
5
0
0
1
0
0
2
3
1
0
1
0
0
0
0
0
1
2
0
0
2
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
1
0
0
0
0
1
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
1
0
0
2
2
4
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
6
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
7
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
4
1
0
0
2
2
0
0
0
1
0
0
1
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
3
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
2
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
10
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
2
0
2
0
0
0
1
0
1
0
0
0
1
0
1
6
0
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
4
0
1
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
2
0
0
5
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
3
0
2
0
0
0
0
0
0
2
2
1
0
0
0
2
0
2
2
0
0
0
0
0
0
1
1
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
3
0
0
0
0
0
1
2
0
0
0
0
1
0
0
3
1
1
0
0
0
0
0
0
1
0
1
6
0
0
1
0
0
1
1
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
3
0
2
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
2
0
0
1
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
1
0
0
0
4
0
0
0
0
0
6
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
2
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
5
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
3
2
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
1
0
2
0
0
1
0
1
1
0
0
3
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
4
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
5
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
7
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
5
0
0
1
0
0
1
0
0
2
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
4
0
0
1
1
0
0
0
0
0
0
2
0
2
0
0
0
1
0
2
0
0
0
0
0
0
3
1
0
1
0
0
1
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
1
2
0
1
2
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
1
2
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
2
2
2
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
3
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
1
4
1
0
0
1
2
0
0
0
0
2
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
2
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
2
0
0
2
0
0
1
1
1
0
0
0
0
0
0
2
0
1
1
0
2
1
0
0
0
2
0
0
0
0
0
0
3
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
3
0
6
0
1
0
3
0
1
1
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
3
0
0
0
1
0
2
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
2
0
0
2
1
0
0
0
0
2
1
0
0
0
0
3
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
4
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
6
0
0
0
2
1
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
1
1
0
1
0
0
4
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
5
0
0
0
1
1
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
4
0
1
0
0
0
0
0
0
0
0
2
1
2
0
1
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
3
2
2
0
0
2
2
0
0
3
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
2
1
2
6
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
2
0
0
0
2
1
0
1
0
1
0
0
0
0
0
0
1
0
0
2
0
0
2
1
1
0
2
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
9
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
3
2
0
2
2
1
0
0
0
0
0
0
2
1
0
0
1
3
0
0
1
0
0
0
1
8
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
1
0
2
2
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
2
2
0
1
0
0
0
2
0
0
0
1
0
2
0
1
0
4
1
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
4
0
0
2
0
1
2
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
4
1
5
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
5
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
2
1
0
0
0
2
0
2
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
1
0
0
3
2
0
0
0
0
0
1
1
0
0
0
1
2
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
7
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
1
0
0
2
1
0
0
0
2
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
3
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
3
0
1
0
0
0
1
0
2
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
1
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
6
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
1
2
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
2
0
0
3
0
1
0
0
0
0
0
2
1
0
0
0
0
0
2
1
0
2
0
0
3
3
0
0
1
1
7
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
1
1
0
0
0
0
0
1
2
1
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7
2
0
3
0
0
0
0
0
0
0
0
3
0
0
0
3
0
0
2
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
3
0
0
0
2
0
0
1
0
1
2
0
0
0
0
0
1
0
0
2
2
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
3
0
1
0
0
0
3
0
1
0
0
0
0
2
0
2
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
5
0
0
0
2
1
1
0
6
1
2
0
2
0
0
0
0
1
0
0
0
2
0
3
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
3
2
0
0
0
0
2
0
0
0
0
0
0
0
0
3
3
0
3
0
1
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
2
0
4
0
0
0
1
2
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
3
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
4
2
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
4
0
0
2
0
1
2
0
3
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
2
2
5
2
0
2
0
6
1
0
0
0
0
0
0
0
0
0
1
0
0
3
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
3
6
0
3
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
3
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
2
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
1
1
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
4
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
1
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
3
0
1
0
0
0
4
3
0
0
0
0
2
1
0
0
0
0
5
0
2
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
1
2
0
1
0
2
0
0
3
0
1
0
4
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
6
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
1
0
7
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
4
0
0
0
2
0
0
1
1
2
0
0
0
0
0
3
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
2
0
1
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
1
0
0
2
0
0
0
0
0
2
0
0
0
2
1
0
0
0
14
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
3
0
1
0
0
0
0
0
0
0
2
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
2
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
1
0
4
1
1
1
0
0
0
0
0
0
0
3
0
0
0
1
2
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
1
2
0
1
0
1
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
3
0
0
0
0
0
0
0
0
0
0
1
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
3
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
1
1
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
1
2
0
0
0
0
0
0
0
3
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
3
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
2
6
0
9
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
1
2
2
0
2
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
1
0
0
0
2
0
1
1
0
2
0
2
0
0
2
0
0
2
0
1
0
1
0
0
0
0
5
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
2
1
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
1
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
3
0
0
0
0
0
1
0
2
0
0
2
0
0
1
2
0
2
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
3
2
0
0
1
0
3
0
3
0
0
4
0
0
0
3
2
0
0
2
1
6
2
0
0
1
0
11
0
0
2
0
0
0
0
1
0
1
1
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
2
0
2
0
2
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
1
0
2
0
2
3
0
2
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
2
0
0
0
2
0
0
1
3
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
3
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
1
1
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
1
0
0
0
1
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
4
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
4
0
1
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
3
0
0
2
2
0
0
0
0
1
0
0
0
7
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
3
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
3
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
4
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
5
0
0
0
2
0
0
0
2
1
0
0
0
0
0
2
0
4
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
3
0
0
0
2
2
0
2
0
0
0
0
3
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
5
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
3
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
5
0
0
3
0
1
0
0
0
2
1
0
0
0
0
0
0
1
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
6
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
5
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
2
0
2
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
2
3
0
0
0
0
0
0
4
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
4
0
2
2
0
0
0
0
0
2
0
0
0
0
2
1
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
1
0
0
3
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
1
0
2
1
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
1
0
2
1
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
3
1
0
0
10
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
1
1
2
2
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
4
0
1
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
2
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
5
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
2
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
2
0
0
1
0
0
0
1
2
0
0
0
2
0
0
4
0
0
0
0
0
2
0
1
0
1
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
1
0
0
0
0
1
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
1
2
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
1
0
0
0
0
0
0
0
0
0
1
0
2
7
0
0
0
1
0
0
0
1
2
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
2
4
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
5
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
3
0
1
0
0
0
0
0
3
0
0
0
2
0
6
2
0
0
2
0
1
0
3
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
5
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
2
0
0
0
9
0
0
0
0
2
0
0
2
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
3
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
2
0
0
0
1
2
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
3
2
1
0
1
0
0
3
0
0
0
5
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
1
0
2
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
6
2
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
6
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
2
0
1
0
0
0
0
3
0
1
0
2
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
2
0
2
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
3
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
2
0
1
0
0
1
0
0
2
0
1
0
0
0
1
0
0
3
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
14
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
4
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
1
1
0
0
2
0
0
0
0
3
2
2
2
0
2
1
0
0
1
0
0
0
2
0
0
0
1
0
13
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
1
1
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
3
0
0
1
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
3
0
0
0
0
1
1
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
13
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
3
2
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
2
1
0
0
0
2
1
1
1
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
2
1
2
0
0
1
2
1
0
2
0
0
0
0
3
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
1
0
2
1
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
1
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
8
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
2
0
2
0
2
7
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
2
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
3
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
3
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
2
2
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
3
4
0
0
1
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
1
0
0
0
2
0
3
0
0
0
2
0
0
2
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
1
0
0
1
0
1
0
1
2
0
0
1
0
0
0
0
2
3
0
1
0
0
0
2
0
9
1
0
0
2
0
2
2
0
0
0
0
1
0
1
2
0
0
0
1
0
0
0
0
3
2
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
2
0
1
14
12
0
0
3
0
0
0
1
6
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
0
0
0
2
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7
0
2
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
6
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
4
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
1
2
2
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
6
2
0
1
0
1
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
5
0
2
0
0
0
0
1
0
0
0
2
0
9
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
1
1
1
3
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
2
2
0
0
0
1
1
0
0
0
0
0
0
0
2
2
0
0
3
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
2
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
1
0
0
0
1
0
2
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
1
1
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
1
0
2
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
2
0
3
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
1
0
0
0
5
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
2
0
0
0
2
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
3
2
0
0
0
0
1
0
0
0
0
0
0
4
3
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
1
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
6
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
1
2
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
2
0
0
0
0
1
2
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
3
0
0
0
1
0
0
1
1
0
0
0
2
0
0
0
1
0
0
1
2
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
2
0
0
1
0
2
1
0
0
0
0
0
1
1
2
0
1
0
2
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
1
1
0
0
1
4
1
0
0
0
0
0
2
4
1
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
1
0
1
0
0
0
0
0
4
0
0
0
1
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
1
0
0
1
2
0
0
1
3
0
0
0
2
0
0
4
0
0
1
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
4
0
0
0
0
1
0
0
1
0
1
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
2
3
0
0
0
0
0
2
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
3
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
4
0
0
0
0
1
0
0
1
0
0
4
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
1
3
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
1
2
0
0
0
0
3
1
1
0
1
0
0
0
0
0
0
2
2
0
2
1
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
7
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
1
0
0
0
4
0
0
1
0
1
0
2
0
0
2
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
4
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
1
1
0
1
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
1
0
0
6
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
2
1
0
0
0
0
1
0
2
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
3
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
1
3
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
1
2
0
0
0
4
0
0
2
0
0
1
0
0
2
0
0
0
0
0
1
1
0
0
1
0
0
3
0
2
0
2
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
7
4
0
0
0
1
2
0
0
0
2
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
3
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
3
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
4
0
0
1
0
0
0
1
0
1
1
0
0
0
0
4
0
0
0
0
0
0
1
0
0
1
0
1
2
2
1
0
0
0
3
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
1
2
2
6
0
0
2
0
0
0
0
0
0
0
2
0
3
1
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
5
2
1
2
0
0
0
0
2
0
3
3
0
1
0
0
2
0
0
1
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
2
0
0
1
0
0
1
0
0
3
0
0
0
1
0
2
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
1
0
0
0
0
2
9
0
1
0
0
0
0
0
2
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
2
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
5
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
1
0
0
1
0
0
0
0
3
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
5
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
1
0
0
5
0
1
0
1
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
3
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
1
0
0
0
1
6
0
0
3
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
1
0
0
0
1
0
0
0
0
2
1
0
2
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
4
1
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
4
0
1
0
0
1
1
2
1
2
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
3
3
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
2
2
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
6
0
0
0
0
0
0
0
2
3
1
1
1
0
0
0
0
0
0
0
1
0
0
2
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
13
0
0
3
3
0
1
0
0
0
0
0
0
0
1
0
0
6
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
3
0
0
0
0
2
0
0
0
2
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
1
0
1
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
2
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
7
0
1
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
2
0
0
0
2
0
0
2
2
0
0
1
0
0
1
0
0
2
1
0
0
0
0
0
0
2
2
2
1
1
4
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
3
3
0
1
0
0
0
0
2
0
0
0
0
0
0
0
3
1
0
0
0
1
0
0
0
2
0
2
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
6
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
11
0
0
0
3
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
2
2
4
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
1
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
6
1
0
0
3
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
1
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
7
0
0
2
1
2
1
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
1
0
0
0
3
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
3
0
0
0
0
1
0
1
1
0
1
2
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
1
1
0
0
0
2
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
5
0
1
0
0
0
0
0
0
0
0
0
2
2
2
4
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
3
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
2
0
0
1
0
1
0
1
0
3
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
7
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
1
0
0
0
1
0
2
1
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
2
0
3
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
3
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
1
2
1
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
2
0
2
0
0
0
0
0
0
7
0
2
1
1
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
3
0
2
1
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
3
0
0
2
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
4
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
1
1
0
0
0
0
0
3
2
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
3
0
0
2
0
1
0
0
1
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
3
0
0
0
0
1
0
3
0
1
0
0
3
1
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
2
0
0
0
7
0
0
0
0
0
2
0
0
1
0
0
2
0
4
0
1
0
1
0
0
0
0
0
0
0
1
0
0
4
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
7
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
1
0
1
1
0
0
0
0
0
0
2
0
0
3
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
3
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
2
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
2
0
0
1
0
0
0
4
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
5
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
3
2
1
0
0
0
0
0
2
1
1
0
0
2
0
0
0
0
2
1
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
1
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
2
2
0
0
1
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
1
2
0
0
0
2
0
0
0
0
2
0
2
0
2
0
0
0
0
0
3
0
0
0
0
0
2
2
2
1
0
0
0
0
0
0
2
0
0
0
1
3
0
0
0
2
0
0
0
0
2
0
0
1
2
0
3
1
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
2
2
0
0
0
2
0
0
0
1
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
3
0
4
0
1
1
0
0
0
1
0
1
2
0
0
0
0
1
1
0
2
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
5
0
0
0
1
0
1
0
0
2
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
3
3
2
0
0
2
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
2
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
4
0
0
2
0
0
0
0
0
2
1
0
0
0
6
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
2
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
1
1
2
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
2
1
2
0
1
1
0
0
0
1
0
0
2
0
0
0
3
0
2
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
3
0
1
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
4
0
2
0
0
1
0
1
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
3
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
3
1
0
2
0
0
0
2
4
0
0
1
2
1
7
0
2
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
3
1
0
2
0
0
0
1
2
0
0
0
0
2
0
5
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
6
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
5
1
0
0
2
0
0
1
0
0
0
0
0
2
2
1
2
1
0
2
0
0
0
0
1
0
1
0
0
2
2
0
0
1
1
0
0
2
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
5
0
0
6
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
2
0
0
0
1
0
0
1
1
0
1
1
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
4
1
1
0
0
0
2
0
0
0
1
6
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
3
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
4
2
0
1
0
2
0
0
1
2
0
0
0
1
0
0
0
2
0
1
0
0
1
0
0
1
1
1
0
0
2
3
0
2
0
1
0
0
1
0
1
0
0
0
1
3
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
3
0
2
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
1
1
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
1
0
0
1
0
0
1
0
0
0
3
0
0
0
0
0
0
0
1
0
2
3
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
2
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
2
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
2
0
0
0
1
1
0
3
0
0
2
2
0
0
0
2
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
1
0
1
0
0
1
1
2
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
3
1
1
0
0
2
0
0
0
0
0
2
0
1
1
0
2
0
0
3
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
2
3
0
0
0
1
0
0
0
1
0
0
0
2
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
2
0
6
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
2
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
2
2
1
2
0
2
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
1
0
1
0
1
2
0
2
1
0
0
0
0
0
1
2
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
2
1
2
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
3
3
1
0
4
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
2
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
2
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
1
0
2
1
0
0
0
0
0
2
0
2
0
1
2
3
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
3
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
5
0
2
2
0
0
2
0
0
1
1
0
3
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
2
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
2
0
0
2
0
2
0
0
0
1
0
5
1
0
2
0
0
0
1
1
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
3
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
1
0
0
0
0
1
3
0
2
0
0
0
2
0
2
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
2
0
0
0
2
0
0
1
2
0
0
0
1
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
7
5
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
4
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
1
1
0
0
0
3
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
2
2
0
0
2
0
2
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
3
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
8
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
3
2
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
1
0
2
1
0
0
1
0
0
0
1
2
0
0
1
0
1
2
1
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
1
0
0
1
2
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
1
1
0
0
0
0
0
1
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
1
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
1
0
1
1
0
1
0
0
0
0
1
6
0
0
0
1
1
0
0
0
0
1
0
2
0
0
2
2
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
2
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
3
0
1
0
0
4
0
1
0
0
0
0
0
0
0
0
1
0
0
3
0
0
2
3
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
3
0
2
0
0
0
0
0
1
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
2
0
1
0
1
2
0
1
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
6
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
1
0
0
0
1
2
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
2
0
2
0
1
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
3
1
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
3
2
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
4
0
3
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
2
0
0
2
0
2
0
0
2
0
0
1
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
3
0
1
1
0
1
1
0
0
0
0
2
2
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
2
1
0
0
2
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
3
1
0
0
0
1
0
0
0
0
0
3
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
5
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
1
0
1
0
2
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
1
0
1
4
2
0
0
0
0
0
0
0
4
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
7
0
0
0
0
0
1
0
2
0
0
2
1
0
0
0
0
0
0
1
3
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
1
0
2
0
0
1
0
0
1
0
1
2
4
0
0
0
3
0
0
0
1
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
1
1
0
0
0
1
1
2
2
1
1
0
0
0
1
2
0
1
0
0
0
1
0
2
2
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
3
0
0
4
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
2
0
0
0
0
2
2
0
1
1
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
1
3
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
1
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
1
0
0
0
2
0
0
1
2
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
5
2
0
0
0
0
0
0
0
5
0
1
0
0
0
5
3
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
5
1
0
0
0
0
0
1
3
2
2
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
1
1
0
2
3
0
1
0
1
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
1
0
6
0
0
0
0
0
2
0
3
0
0
0
0
2
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
3
0
1
0
0
0
0
0
2
0
1
2
0
0
2
0
0
2
1
0
1
0
0
0
0
0
0
1
0
0
1
2
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
1
0
5
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
3
0
0
0
2
0
0
2
0
2
1
2
1
0
0
0
0
0
0
0
0
0
0
1
3
0
1
0
0
2
0
0
2
0
0
0
1
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
2
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
4
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
2
0
0
0
0
0
0
1
0
1
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
4
0
1
0
3
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
4
0
0
1
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
2
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
3
1
0
0
0
1
0
0
0
0
0
0
0
0
5
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
4
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
6
2
0
1
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
3
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
2
1
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
2
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
3
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
1
3
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
4
0
1
0
0
0
0
0
1
2
1
1
0
0
2
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
4
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
2
0
0
2
0
1
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
4
2
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
1
2
1
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
3
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
3
1
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
3
0
0
1
0
0
0
0
2
0
0
0
1
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
2
0
2
1
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
2
0
1
0
2
0
0
1
0
0
18
0
2
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
1
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
1
10
1
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
2
0
2
1
0
2
10
0
0
0
0
0
1
0
0
2
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
4
2
0
3
0
0
1
0
2
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
2
0
2
4
0
0
0
0
3
0
0
0
0
2
0
0
2
0
0
0
2
0
1
0
1
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
3
0
0
0
0
0
0
2
0
0
0
3
0
2
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
3
3
1
0
0
0
1
0
0
0
0
1
1
0
2
0
0
1
0
0
0
0
0
0
2
0
0
8
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
1
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
1
2
0
0
0
2
7
0
0
0
0
0
1
0
0
2
2
2
1
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
3
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
1
0
0
0
2
0
0
0
0
0
0
0
6
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
7
0
0
0
0
2
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
1
0
0
0
0
2
0
0
0
0
0
0
1
1
2
0
0
0
0
1
0
0
0
2
0
2
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
6
0
0
1
0
0
1
1
0
0
0
1
1
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
1
0
0
1
0
0
0
1
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
3
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
3
0
2
0
0
0
0
1
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
3
2
0
2
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
2
0
1
1
0
1
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
1
1
0
0
0
0
2
0
0
1
1
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
2
0
0
1
1
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
2
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
2
2
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
2
0
0
11
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
3
0
0
3
0
0
0
1
0
3
0
0
3
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
5
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
1
0
1
0
0
1
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
2
0
1
0
0
2
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
1
0
0
1
0
2
0
0
0
0
0
0
10
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
2
0
2
0
0
0
1
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
1
0
2
2
2
0
5
0
0
0
1
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
12
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
2
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
3
0
0
0
0
0
0
2
1
3
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
1
0
4
0
2
0
3
0
0
0
2
1
0
0
0
0
0
0
0
9
0
0
2
1
1
0
0
0
2
2
0
0
0
6
2
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
1
0
0
1
13
0
0
1
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
5
0
2
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
1
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
9
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
2
0
0
0
0
2
1
0
0
0
1
0
0
1
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
1
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
2
2
0
0
0
0
0
1
0
1
2
0
1
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
1
0
6
0
0
0
0
3
0
0
0
0
0
1
2
0
0
2
0
0
0
0
2
0
4
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
1
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
9
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
5
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
5
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
3
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
4
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
1
2
0
0
0
6
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
3
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
1
0
0
0
1
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
3
0
0
0
0
1
0
0
1
0
0
0
0
0
0
5
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
1
0
0
4
0
6
0
0
0
2
2
1
0
1
0
0
0
4
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
2
2
2
1
3
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
2
0
0
2
2
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
2
0
1
0
0
0
3
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
2
0
1
2
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
11
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
1
0
0
1
0
4
0
0
0
1
0
0
0
0
0
3
0
0
3
0
0
1
0
2
0
0
0
0
0
5
3
1
4
2
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
0
2
0
0
1
0
2
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
4
0
1
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
5
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
2
2
6
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
1
1
1
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
3
0
0
0
0
1
6
1
0
1
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
2
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
5
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
2
1
0
0
0
1
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
2
0
0
0
1
2
1
0
0
0
0
0
0
0
2
2
1
0
0
1
0
0
0
0
0
2
0
5
0
0
0
0
0
1
0
1
0
0
2
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
1
1
0
0
0
2
0
3
0
1
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
6
1
4
1
0
0
0
2
0
0
0
3
2
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
1
1
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
3
1
0
0
0
1
0
0
0
0
0
1
3
1
0
0
0
2
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
3
0
8
0
1
0
2
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
3
0
2
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
2
0
0
0
1
1
0
2
0
0
0
0
2
3
1
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
2
2
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
1
4
2
2
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
2
0
0
4
0
0
1
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
8
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
2
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
1
0
0
2
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
3
0
2
0
0
0
0
0
1
3
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
1
0
0
1
1
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
2
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
1
0
0
5
0
0
1
1
0
0
0
0
0
1
0
3
0
1
0
2
0
0
0
0
0
0
2
0
2
0
0
0
5
0
0
0
2
0
0
0
0
0
1
1
2
1
0
1
0
0
0
2
0
0
3
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
1
0
0
0
1
1
0
0
4
0
0
0
0
5
0
2
0
1
0
0
2
0
0
1
7
0
0
1
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
5
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
1
0
2
2
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
5
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
1
2
0
0
0
0
1
3
1
1
0
0
0
0
0
0
7
0
5
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
1
6
4
0
0
0
1
0
0
2
0
1
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
2
0
0
0
1
0
4
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
1
0
1
2
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
3
3
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
4
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
2
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
4
2
0
0
0
0
0
5
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
1
0
1
1
2
0
0
1
0
0
1
0
1
0
2
0
0
0
0
1
0
0
0
0
0
1
2
0
1
0
0
1
0
0
0
0
0
0
2
2
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
2
1
0
0
0
0
1
0
0
2
0
0
0
0
3
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
2
2
3
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
5
3
0
2
1
0
0
0
3
0
0
2
3
0
0
2
0
0
0
4
0
0
0
0
0
0
2
0
0
0
0
0
3
0
3
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
1
0
0
0
1
0
0
0
0
4
0
0
0
1
0
0
0
0
0
1
0
1
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
3
1
2
0
0
0
0
2
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
2
1
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
1
9
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
2
1
0
0
2
0
0
0
1
0
2
0
0
0
3
5
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
2
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
2
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
5
0
1
0
0
0
1
0
0
2
2
1
0
0
0
0
0
0
0
1
0
1
1
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
3
0
0
0
4
0
1
0
0
0
1
2
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
1
0
0
0
3
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
2
0
0
1
0
0
2
0
0
1
0
0
1
0
0
0
0
5
0
0
0
0
7
1
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
3
2
0
0
0
0
1
1
0
0
0
0
0
3
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
3
0
0
1
0
0
0
3
0
2
0
0
0
1
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
2
0
0
0
0
3
0
3
0
0
1
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
3
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
2
0
0
2
1
1
0
0
0
0
0
0
5
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
3
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
1
0
1
1
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
3
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
3
0
0
1
1
0
0
0
0
3
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
3
0
2
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
2
3
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
2
1
0
2
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
1
0
0
1
2
0
0
0
0
1
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
5
0
0
0
1
2
0
1
1
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
6
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
1
0
0
4
0
2
0
0
2
2
0
1
0
0
0
0
0
0
0
3
0
2
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
2
1
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
1
1
2
1
1
2
2
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
1
1
2
2
0
0
0
0
0
1
0
2
1
0
0
0
3
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
1
7
5
2
5
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
2
5
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
3
0
0
1
1
1
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
1
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
8
0
0
1
0
1
0
2
0
0
0
0
0
1
0
1
2
0
0
0
0
0
2
0
0
1
0
0
2
1
0
1
1
2
2
0
0
0
0
0
0
0
0
0
4
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
11
0
0
0
0
1
1
0
0
0
0
9
0
0
2
0
0
1
0
0
2
2
1
0
0
2
0
1
0
0
0
0
0
9
0
0
0
0
0
0
0
0
0
3
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
2
2
0
2
0
0
0
2
0
2
1
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
3
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
3
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
3
0
2
2
0
0
2
0
0
1
5
0
0
1
1
0
3
0
1
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
1
0
2
0
0
0
0
0
2
2
0
2
0
0
0
0
0
4
0
5
0
0
1
0
0
8
1
0
0
2
0
0
0
0
0
1
2
0
2
0
0
0
0
1
0
0
0
0
0
0
3
0
0
1
0
0
0
0
3
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
1
0
1
1
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
8
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
3
0
2
0
0
0
2
0
0
0
1
0
2
0
2
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
1
2
0
0
0
0
0
0
2
0
0
0
3
0
1
0
0
0
0
1
0
0
2
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
1
2
0
0
0
0
3
0
0
0
0
0
0
0
2
0
2
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
4
1
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
3
0
0
2
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
4
5
0
1
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
4
1
0
2
0
0
2
0
1
3
2
2
0
1
2
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
5
0
0
0
0
2
0
0
0
2
2
0
2
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
5
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
4
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
8
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
2
1
3
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
5
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
1
1
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
2
0
0
0
1
1
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
3
0
0
0
0
1
0
0
0
0
0
0
0
1
2
1
0
2
0
0
3
0
1
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
2
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
1
1
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
2
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
7
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
1
0
0
4
0
0
0
1
0
0
0
0
0
0
2
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
3
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
1
3
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
5
0
0
0
0
0
0
0
1
0
0
1
2
0
2
0
0
0
2
0
0
3
1
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
1
2
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
1
0
2
0
0
2
0
1
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
3
1
3
0
0
0
1
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
5
0
2
0
0
0
0
0
0
1
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
1
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
1
2
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
4
0
0
0
5
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
4
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
1
1
3
0
0
2
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
3
1
2
0
2
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
2
2
0
0
1
0
1
0
0
0
0
1
3
0
0
2
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
1
3
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
1
9
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
2
0
1
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
1
0
1
0
0
2
0
1
0
3
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
2
3
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
1
0
0
2
3
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
10
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
2
0
0
2
0
0
0
0
3
1
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
2
7
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
2
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
3
2
0
0
0
0
0
1
0
2
1
0
2
1
1
0
2
0
0
0
1
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
3
0
0
0
3
0
0
2
0
0
0
0
0
1
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
2
1
0
1
0
0
0
2
0
1
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
6
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
2
0
0
1
2
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
5
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
9
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
1
0
1
1
0
0
0
0
0
2
0
1
2
0
0
0
1
0
3
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
2
0
0
4
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
2
0
0
0
0
0
5
4
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
1
2
4
0
0
0
0
0
3
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
1
0
2
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
4
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
7
0
1
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
1
0
2
0
2
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
3
0
0
0
0
0
2
1
0
2
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
6
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
1
0
0
1
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
1
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
2
0
1
2
0
0
2
0
0
0
0
2
2
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
1
0
0
0
4
0
0
0
0
0
1
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
1
0
0
0
0
0
0
1
0
0
2
2
0
2
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
2
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
3
0
0
0
0
1
0
0
0
2
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
2
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
3
0
2
0
0
0
0
0
1
1
1
0
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
1
1
1
0
2
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
3
0
0
0
2
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
2
6
0
0
1
0
0
0
2
1
0
2
0
1
0
0
0
5
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
1
1
0
0
0
1
2
1
0
0
0
0
0
3
0
0
0
0
2
0
3
3
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
2
0
2
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
6
1
1
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
2
0
0
2
2
2
1
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
4
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
3
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
3
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
9
0
0
0
2
0
1
2
0
0
0
0
0
0
1
0
0
1
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
2
2
1
2
0
0
3
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
3
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
5
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
1
0
0
0
0
0
1
0
2
0
0
0
0
4
0
0
2
0
0
0
0
0
0
0
1
0
0
3
0
1
0
0
0
1
0
0
0
0
0
2
0
1
1
0
0
0
0
0
7
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
5
1
0
1
2
0
1
1
2
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
1
0
2
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
3
2
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
5
0
1
0
0
0
1
1
0
0
0
2
0
0
1
2
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
1
2
0
0
0
1
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
6
0
0
2
0
3
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
3
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
2
0
0
0
0
0
3
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
5
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
6
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
1
3
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
5
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
2
2
0
0
0
0
0
2
0
0
0
1
2
0
2
4
0
0
0
10
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
2
0
0
0
2
2
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
1
2
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
2
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
1
0
1
0
2
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
1
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
2
0
1
0
1
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
2
0
0
2
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
1
0
1
0
0
2
1
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
9
0
1
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
3
2
0
0
0
0
1
0
1
0
0
0
0
2
0
2
0
0
1
0
0
2
0
0
0
3
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
1
3
0
0
2
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
1
3
0
0
0
0
1
0
1
0
1
0
0
0
0
5
0
1
0
0
2
1
0
1
0
1
0
0
0
4
0
0
0
2
1
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
1
2
0
0
1
0
1
1
0
0
0
0
0
0
2
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
3
0
0
2
0
2
2
1
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
4
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
7
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
3
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
3
2
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
8
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
1
1
2
0
0
0
0
0
1
0
0
0
0
0
0
7
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
1
1
0
0
0
0
3
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
3
0
4
0
0
0
1
2
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
5
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
6
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
3
2
0
1
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
1
0
1
0
0
0
1
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
2
0
0
1
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
5
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
2
0
0
0
0
2
1
0
3
1
0
1
0
0
0
0
2
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
10
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
2
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
2
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
2
0
0
2
0
3
0
0
3
0
0
0
2
0
0
0
4
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
4
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
3
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
1
0
3
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
5
2
0
0
1
2
1
0
1
0
0
0
0
2
1
0
3
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
3
1
0
0
0
0
0
0
0
3
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
1
0
1
2
0
0
0
3
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
3
0
0
0
0
0
0
1
0
0
7
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
2
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
2
1
0
2
1
0
4
0
0
0
0
0
0
3
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
1
2
2
0
0
3
0
2
0
2
0
0
0
0
0
0
0
0
1
0
1
0
3
0
0
2
0
0
2
1
0
0
2
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
2
4
0
2
0
0
0
0
0
0
0
0
2
0
0
3
0
0
1
2
3
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
2
1
0
5
0
0
0
0
0
2
0
0
1
0
1
1
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
3
3
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
1
0
0
2
1
0
2
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
4
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
1
0
2
0
0
0
2
3
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
8
0
1
0
1
1
0
0
0
0
2
0
0
0
0
2
0
1
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
4
2
0
0
0
0
4
0
3
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
8
0
0
0
0
0
3
0
1
1
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
4
2
1
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
3
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
3
1
0
1
0
0
0
0
6
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
1
0
4
0
2
0
1
2
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
5
0
0
4
2
0
0
0
0
2
3
0
1
0
0
0
0
3
0
0
2
0
1
0
0
1
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
2
0
0
2
0
0
3
2
1
0
0
1
0
0
0
3
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
1
3
0
0
0
2
3
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
2
0
4
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
1
0
2
0
0
1
0
0
0
1
0
0
2
0
0
0
0
1
2
5
0
0
2
1
0
0
0
0
1
0
0
1
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
2
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
5
0
0
1
0
0
1
0
1
0
0
2
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
7
10
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
2
3
0
2
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
3
0
0
0
0
2
1
0
0
0
2
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
2
2
1
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
1
0
1
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
2
0
0
0
0
0
3
1
0
0
2
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
4
1
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
4
0
6
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
4
0
2
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
2
0
3
1
0
1
0
1
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
4
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
7
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
2
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
3
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
4
0
1
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
3
2
0
0
0
1
0
0
0
1
0
0
1
0
0
0
2
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
1
3
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
2
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
4
0
0
1
0
0
0
0
0
3
0
0
0
1
0
0
0
0
1
0
2
2
0
1
0
0
0
0
0
1
0
0
0
3
0
2
0
0
5
1
0
0
0
1
0
0
0
1
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
2
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
5
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
2
0
1
0
0
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
1
1
0
0
0
2
0
0
0
2
0
0
1
0
0
7
0
1
0
0
0
1
0
0
0
0
3
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
1
3
0
0
0
0
1
0
0
0
0
0
0
5
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
2
0
0
0
2
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
5
1
1
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
3
1
0
2
0
0
0
1
0
0
0
1
0
0
0
1
2
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
1
0
2
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
1
1
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
1
0
1
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
3
0
0
2
0
3
0
0
0
0
0
0
2
2
2
0
2
0
1
0
2
0
0
0
0
0
1
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
0
1
2
0
0
2
0
0
2
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
3
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
1
0
0
2
0
0
0
0
1
0
3
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
1
2
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
5
2
0
0
0
0
2
0
2
0
0
0
2
0
0
3
1
0
0
0
0
0
0
1
3
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
4
2
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
7
0
2
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
5
0
0
0
1
0
1
5
0
2
0
0
0
0
1
0
0
0
2
0
0
2
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
2
0
0
1
0
0
0
2
4
1
0
0
0
0
1
1
0
3
0
0
2
1
0
7
0
1
0
0
0
0
0
1
1
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
3
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
3
0
0
4
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
1
0
5
0
1
1
0
0
0
0
0
0
2
0
0
3
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
4
0
3
0
4
0
3
0
3
0
1
2
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
3
3
0
0
0
0
0
4
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
9
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
3
0
0
1
0
1
0
2
0
3
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
1
2
4
3
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
3
0
0
1
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
4
2
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
1
0
0
0
0
2
0
0
3
1
0
0
0
2
0
0
0
0
0
1
0
2
2
3
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
2
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
2
0
2
0
0
2
1
0
0
0
4
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
4
0
4
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
4
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
4
0
1
0
0
2
0
2
2
0
1
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
9
0
0
0
0
2
1
0
0
0
0
0
0
3
4
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
5
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
2
0
0
0
0
2
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
2
0
2
0
0
0
0
8
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
4
2
0
0
0
2
0
0
2
0
0
0
2
0
0
3
0
2
2
0
0
0
0
0
0
2
1
1
3
0
0
0
0
0
0
0
0
0
0
0
1
1
3
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
1
0
0
0
2
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
4
0
1
0
0
0
0
1
0
3
1
0
0
2
0
2
0
4
0
1
0
0
0
0
0
0
1
1
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
5
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
1
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
1
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
4
0
0
0
0
0
2
2
3
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
3
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
1
0
0
2
0
0
1
1
0
0
1
0
0
0
0
0
2
2
0
1
0
0
0
0
1
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
5
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
3
0
0
0
0
0
0
2
1
0
0
1
0
0
0
2
1
0
0
0
1
3
0
0
3
1
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
1
0
2
1
0
0
0
0
0
1
0
0
2
0
0
0
0
1
2
0
2
1
0
1
1
2
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
1
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
2
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
1
0
2
0
0
2
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
3
0
2
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
1
1
0
2
1
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
10
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
6
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
3
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
2
2
1
0
0
0
0
0
0
4
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
1
0
0
2
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
1
0
0
2
2
5
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
4
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
4
0
0
0
1
3
0
0
0
0
0
0
2
4
0
0
1
0
1
1
0
0
3
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
3
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
13
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
5
0
0
2
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
3
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
1
2
0
0
0
1
0
0
0
0
0
0
2
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
1
0
1
0
0
1
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
2
0
0
2
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
8
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
3
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
1
1
0
0
2
0
0
2
0
2
0
0
0
2
0
1
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
2
1
0
0
2
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
1
1
0
0
0
3
1
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
1
1
0
0
5
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
4
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
1
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
7
0
0
0
0
0
0
6
0
1
0
0
2
1
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
3
0
0
0
0
0
0
2
0
0
1
0
1
8
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
4
0
0
0
0
0
1
0
0
1
0
0
1
0
0
3
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
1
3
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
1
0
1
0
2
0
0
1
0
1
0
2
1
0
0
0
0
0
1
0
1
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
3
0
0
0
3
0
0
0
0
0
0
0
0
0
7
2
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
5
0
1
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
2
0
1
3
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
9
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
6
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
4
0
2
0
1
0
0
0
0
1
3
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
3
2
0
0
0
0
0
2
0
0
0
4
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
1
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
5
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
3
0
4
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
3
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
1
1
0
0
0
0
0
0
0
1
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
3
2
0
6
0
0
1
1
0
0
0
2
0
0
5
4
1
0
1
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
2
0
0
0
4
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
3
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
3
0
0
0
0
1
0
0
0
0
1
2
2
0
0
1
0
1
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
1
2
0
0
0
0
0
0
0
1
0
2
0
1
1
1
0
1
0
1
1
2
0
0
1
0
0
0
0
0
0
0
0
3
0
1
0
0
0
3
0
0
0
2
0
4
0
2
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
2
2
0
2
2
0
0
0
0
1
0
0
0
2
0
1
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
4
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
2
0
2
0
0
0
1
0
2
0
0
0
2
0
0
0
1
0
0
2
1
0
0
0
2
1
0
3
0
0
0
0
0
4
0
1
0
0
0
15
0
1
0
0
1
0
1
2
0
0
0
1
0
1
0
0
0
0
1
0
0
2
0
0
4
1
1
0
0
4
0
1
1
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
3
1
2
0
0
0
0
0
6
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
3
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
3
2
0
0
1
3
0
2
0
0
2
0
0
0
1
0
0
2
2
0
1
3
0
0
0
0
1
0
3
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
3
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
2
0
0
0
0
1
1
0
0
0
3
0
1
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
1
2
0
0
0
2
0
0
0
2
0
0
0
0
3
2
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
5
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
1
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
1
0
0
0
2
0
1
0
0
0
0
0
2
0
0
2
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
1
0
0
2
2
0
0
0
1
1
1
0
2
3
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
5
0
1
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
2
0
0
0
0
0
3
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
2
0
0
3
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
2
0
2
1
0
1
0
0
0
2
1
0
1
0
0
0
0
0
5
5
0
2
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
4
0
0
1
0
1
0
0
1
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
7
1
0
0
0
2
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
1
0
0
1
0
1
0
0
1
2
3
0
2
1
0
2
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
3
0
1
1
1
0
0
3
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
3
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
3
2
0
1
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
10
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
1
2
0
0
4
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
3
1
0
1
6
0
0
0
0
0
1
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
6
0
2
0
0
1
1
0
0
1
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
5
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
3
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
1
3
0
1
3
0
0
0
2
0
0
0
2
0
0
4
4
0
0
0
2
2
0
0
0
0
0
0
1
1
0
0
2
0
0
4
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
2
0
0
1
0
3
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
3
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
1
2
0
0
0
0
1
0
0
6
0
0
0
0
0
0
0
0
1
3
0
0
0
0
1
0
0
2
0
0
0
0
0
2
4
0
0
0
0
0
2
1
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
3
0
3
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
1
1
0
1
2
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
6
0
0
0
0
0
0
0
3
2
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
3
0
0
1
0
0
0
0
1
0
0
0
7
0
2
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
1
2
0
0
1
0
0
0
4
1
1
0
0
0
0
1
0
1
0
2
0
0
2
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
5
3
0
1
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
2
1
1
0
0
0
2
0
0
0
1
1
0
0
1
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
1
1
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
5
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
1
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
1
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
2
2
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
4
0
2
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
3
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
2
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
3
1
0
0
0
0
0
1
0
1
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
4
2
0
2
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
5
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
2
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
1
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
3
0
0
3
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
7
0
0
0
1
0
0
3
0
0
1
0
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
2
0
0
1
0
0
0
2
0
0
0
0
2
3
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
2
1
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
1
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
1
0
2
0
0
5
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
2
0
0
0
2
0
0
0
0
0
0
3
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
1
0
0
0
0
0
6
1
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
1
0
3
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
3
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
1
5
0
0
0
2
0
0
0
0
0
2
2
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
1
0
0
0
0
0
0
4
1
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
2
1
0
5
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
1
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
3
0
1
0
1
0
0
0
1
0
0
0
3
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
1
5
3
1
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
4
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
2
0
1
0
0
2
0
0
0
0
0
2
2
2
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
2
1
2
0
0
0
1
0
0
3
0
0
0
2
2
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
7
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
1
1
0
0
2
0
0
1
0
0
3
2
0
1
0
0
0
0
0
2
1
0
1
0
0
1
0
0
0
0
0
0
1
2
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
3
0
1
0
1
0
0
0
3
0
0
0
0
2
0
2
0
5
0
0
1
1
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
2
0
0
1
2
0
2
0
0
0
3
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
8
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
3
3
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
2
0
0
0
1
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
3
0
1
0
0
2
2
0
0
0
4
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
5
0
0
0
2
3
0
1
0
2
1
2
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
2
2
0
0
0
1
1
9
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
1
1
0
0
1
0
0
0
1
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
2
0
1
0
0
0
0
6
1
0
0
3
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
1
0
1
0
0
2
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
2
1
0
2
0
1
1
0
0
2
2
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
1
0
3
0
0
0
0
0
1
0
0
12
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
4
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
1
1
0
3
0
2
0
0
0
0
0
0
0
2
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
1
0
0
1
0
0
2
2
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
7
0
0
0
0
0
1
0
0
0
5
0
1
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
3
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
7
0
0
0
0
0
0
0
2
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
1
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
2
2
1
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
2
2
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
1
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
5
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
5
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
5
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
1
0
1
1
3
3
0
0
1
0
1
0
0
0
8
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
1
1
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
1
2
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
3
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
3
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
2
2
0
0
2
1
2
3
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
2
0
0
0
10
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
10
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
5
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
2
1
0
1
2
0
4
0
2
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
2
0
0
2
3
1
0
0
0
0
0
2
0
7
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
2
0
0
0
1
0
1
0
3
0
0
0
0
2
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
4
0
0
2
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
3
2
0
4
2
0
1
0
0
0
0
0
0
0
0
0
0
1
7
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
2
0
0
0
0
0
3
0
5
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
2
0
0
0
0
0
1
5
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
1
0
0
1
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
4
3
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
2
0
0
0
0
0
0
0
5
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
2
0
1
2
0
0
0
0
0
0
2
0
1
0
4
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
3
0
1
0
0
0
0
1
0
3
0
0
0
2
1
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
2
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
4
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
1
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
2
0
2
0
0
0
2
5
0
0
0
2
0
0
2
3
0
0
1
1
0
0
3
1
0
4
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
6
0
0
0
0
0
0
0
0
0
0
2
4
2
0
1
1
0
1
2
1
0
4
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
2
0
2
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
2
0
0
0
0
0
0
0
0
6
1
0
2
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
19
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
5
0
1
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
1
3
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
1
0
0
0
0
0
3
0
1
11
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
12
0
0
0
0
0
0
1
0
0
0
0
2
1
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
5
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
2
7
0
2
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
3
0
1
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
3
0
0
0
0
0
1
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
1
1
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
2
2
0
0
3
0
1
0
0
0
0
0
0
1
1
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
3
2
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
2
2
0
1
0
2
15
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
1
0
0
1
1
0
0
0
5
2
2
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
1
2
0
1
0
1
4
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
2
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
2
2
0
1
2
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
3
2
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
4
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
3
0
2
0
1
0
1
2
1
2
0
0
0
0
0
0
0
0
1
0
4
1
3
1
3
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
2
0
0
0
0
1
0
0
0
0
2
0
2
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
4
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
1
0
2
0
0
0
0
0
1
1
0
0
0
0
1
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
5
0
1
0
0
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
2
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
4
0
0
0
1
0
2
0
0
0
2
0
9
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
2
0
0
1
0
0
0
2
2
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
2
1
1
0
0
0
3
0
0
1
0
2
0
1
5
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
1
3
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
3
1
0
0
0
4
0
1
0
3
1
0
1
0
0
0
1
0
0
0
0
0
0
0
2
2
0
1
1
0
0
2
0
0
0
0
3
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
3
0
0
0
0
2
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
2
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
1
0
1
2
0
0
2
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
1
2
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
3
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
6
2
0
0
0
0
0
0
3
0
6
0
0
3
0
0
0
0
0
2
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
3
0
0
0
0
0
0
1
0
3
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
2
3
1
0
0
2
0
3
0
0
0
0
0
0
7
0
0
0
1
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
5
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
5
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
4
0
0
0
0
2
0
0
0
0
0
0
1
0
0
7
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
9
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
1
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
2
0
1
0
0
2
0
0
0
2
0
0
0
1
2
0
0
0
0
2
1
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
2
2
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
1
0
0
0
1
2
0
0
2
0
0
0
2
0
0
1
0
1
0
0
0
4
0
0
2
0
0
0
1
0
0
0
1
0
0
2
0
2
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
2
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
3
1
0
1
0
0
1
0
0
0
10
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
3
2
0
1
0
0
3
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
1
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
11
0
0
0
0
0
2
0
2
0
0
1
1
0
2
0
3
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
1
1
0
0
1
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
2
7
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
1
0
0
2
0
0
1
1
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
7
1
3
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
2
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
1
5
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
3
1
0
0
2
0
2
0
1
5
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
1
0
2
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
2
0
0
0
0
3
0
0
2
2
0
0
0
6
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
3
0
0
2
0
0
0
0
0
0
0
1
0
3
0
0
4
0
0
1
2
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
5
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
2
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
4
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
6
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
3
0
0
0
1
0
0
0
0
0
0
0
0
1
3
0
0
1
0
0
0
1
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
4
0
0
0
1
0
2
0
0
1
2
2
0
3
1
0
0
0
0
0
1
0
0
1
5
2
2
0
0
0
1
4
2
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
2
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
4
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
1
2
0
1
0
0
0
0
0
0
1
2
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
2
1
0
1
2
2
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
1
1
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
2
0
1
0
0
0
3
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
7
0
0
0
0
0
0
0
4
0
2
2
0
0
2
0
0
0
1
0
2
6
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
4
0
0
2
0
0
0
1
1
0
3
0
0
1
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
1
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
4
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
3
0
0
0
0
1
0
0
0
0
8
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
2
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
2
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
2
0
0
3
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
4
0
2
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
12
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
1
2
0
0
0
8
0
0
0
0
0
0
0
1
0
0
0
2
0
0
3
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
7
0
0
0
1
0
0
1
0
0
0
1
0
1
0
3
0
0
2
0
0
1
0
0
0
6
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
1
0
0
2
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
3
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
1
0
3
0
2
0
4
0
1
0
1
0
0
1
0
0
0
2
0
2
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
2
2
0
2
0
0
5
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
4
0
0
0
5
0
1
4
0
0
0
0
0
0
1
0
0
0
2
1
0
2
1
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
3
5
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
2
1
0
1
0
0
0
0
1
0
0
2
0
1
2
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
2
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
2
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
3
0
0
1
6
0
0
0
0
0
0
0
0
0
0
0
4
2
2
2
0
2
0
0
2
0
0
0
0
2
2
1
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
1
1
0
0
0
2
0
0
0
1
0
4
0
0
1
0
4
1
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
3
1
0
0
0
1
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
7
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
11
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
3
1
0
0
4
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
2
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
2
1
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
2
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
3
2
0
1
0
0
2
0
0
1
0
0
2
1
0
0
3
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
4
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
1
0
3
0
0
0
0
0
3
1
0
0
1
0
1
0
4
0
2
2
0
0
0
1
1
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
4
0
2
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
6
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
2
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
3
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
6
0
0
0
0
0
3
0
3
0
0
0
0
0
0
0
1
0
2
7
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
2
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
6
0
1
2
0
1
0
0
0
0
1
2
0
0
0
2
0
0
0
2
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
3
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
5
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
1
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
1
0
1
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
1
0
0
0
0
0
2
3
0
0
0
2
0
0
0
0
1
0
0
2
2
0
2
0
0
0
0
2
2
0
0
7
0
0
2
0
1
1
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
1
0
0
0
0
0
0
7
0
0
3
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
1
0
1
0
1
0
0
3
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
1
0
0
0
0
0
0
1
0
0
0
1
0
0
3
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
1
0
4
1
2
0
0
3
0
0
4
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
10
4
0
0
4
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
3
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
4
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
5
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
2
0
1
0
0
0
0
0
0
0
5
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
2
0
0
1
3
0
0
0
0
0
3
0
0
0
1
1
2
0
0
0
0
0
0
0
2
0
0
4
0
2
0
1
3
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
3
0
0
0
0
0
0
4
0
4
0
0
0
1
1
1
0
2
4
0
0
1
0
0
0
4
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
2
1
0
1
0
0
0
0
0
10
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
1
0
5
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
2
0
2
0
0
0
0
0
0
2
0
2
0
0
1
1
0
1
0
0
0
0
1
0
0
0
5
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
1
2
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
1
0
2
0
3
0
1
0
0
1
0
1
0
0
0
0
0
2
0
1
0
0
1
3
0
0
0
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
1
0
1
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
2
2
1
2
2
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
2
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
3
0
0
0
6
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
2
0
0
1
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
1
2
0
1
0
1
0
0
0
3
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
1
2
0
3
0
0
0
2
0
0
0
2
5
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
2
2
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
1
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
2
4
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
1
0
1
1
0
0
1
0
0
3
1
0
0
0
4
1
0
0
0
0
0
0
2
2
2
0
0
0
0
2
0
9
0
1
0
0
1
0
2
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
2
1
0
0
0
0
2
0
0
0
0
1
2
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
1
2
2
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
3
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
5
0
0
0
0
0
1
0
3
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
1
2
1
0
1
0
0
2
0
2
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
7
0
1
2
0
3
0
2
3
0
3
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
6
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
13
1
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
2
0
0
2
2
0
1
0
0
0
0
3
2
0
4
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
2
0
0
0
0
0
0
1
0
2
0
0
2
2
1
0
2
0
0
2
0
1
0
0
8
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
2
0
4
0
0
0
0
0
1
0
1
0
1
1
0
0
0
2
2
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
1
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
2
0
0
1
1
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
9
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
5
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
3
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
3
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
1
0
2
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
1
2
0
0
1
0
0
1
0
1
0
2
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
7
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
3
3
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
7
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
5
1
2
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
1
0
0
0
2
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
5
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
1
1
0
0
0
0
1
0
0
2
3
0
0
1
0
2
0
0
0
0
2
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
3
0
0
0
0
0
2
0
0
0
1
0
4
2
1
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
3
0
0
0
2
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
3
4
0
0
0
0
0
0
0
0
0
2
0
0
1
3
0
0
0
0
1
0
0
0
1
2
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
7
0
0
0
0
2
0
0
0
0
0
2
0
1
1
0
2
1
4
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
1
0
1
0
0
0
6
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
2
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
4
0
0
0
0
0
1
0
4
0
1
2
0
0
0
0
1
0
0
2
2
0
0
0
0
1
2
0
0
0
2
0
0
2
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
2
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
7
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
9
0
2
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
6
1
2
0
1
2
0
0
0
0
4
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
2
2
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
4
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
2
1
0
1
2
1
0
0
0
2
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
3
0
1
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
3
0
1
1
2
2
0
1
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
6
2
2
2
0
0
0
0
2
0
0
0
0
1
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
1
1
0
0
0
0
0
0
0
1
0
0
2
0
2
1
0
0
0
1
1
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
4
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
6
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
2
0
3
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
1
2
0
0
2
0
2
0
0
0
0
0
0
0
2
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
2
0
0
1
6
0
0
2
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
1
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
2
1
1
3
0
0
0
1
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
3
0
1
0
1
0
0
0
1
2
0
0
2
1
0
1
1
0
0
0
0
0
0
1
0
0
3
0
0
0
1
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
1
1
0
2
0
10
0
0
2
0
0
0
0
0
3
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
6
0
0
0
2
0
0
0
0
0
0
0
0
4
3
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
5
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
4
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
1
0
0
2
0
0
3
0
3
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
5
0
0
0
0
2
2
0
3
0
0
0
2
0
1
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
2
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
1
1
0
0
0
0
0
0
2
0
2
3
1
0
1
1
0
0
0
0
0
0
2
0
0
0
2
1
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
2
0
8
0
0
0
0
0
0
1
0
0
0
6
0
1
0
0
0
0
2
0
0
0
0
2
0
3
0
0
0
0
1
0
0
7
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
3
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
1
0
0
0
3
1
0
0
0
1
1
2
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
1
0
1
0
1
1
0
0
0
3
0
0
0
0
6
2
0
2
0
0
2
1
0
1
0
0
0
3
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
5
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
6
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
3
0
2
0
0
5
1
0
0
3
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
7
0
2
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
9
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
3
0
2
1
0
0
0
0
0
0
1
0
2
0
5
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
2
0
1
0
0
0
0
0
1
0
7
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
1
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
9
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
4
1
0
0
4
1
2
6
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
0
1
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
5
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
5
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
3
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
1
0
3
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
3
0
0
0
9
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
1
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
1
3
3
0
0
0
0
0
0
0
2
1
2
2
1
0
0
0
1
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
2
0
0
0
0
0
3
0
2
0
1
0
0
2
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
3
5
0
1
0
0
1
1
4
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
1
0
0
1
0
0
2
1
1
1
0
0
0
0
2
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
0
0
4
0
0
0
0
0
0
3
3
0
0
0
0
5
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
4
1
0
1
0
0
0
0
0
0
0
0
0
4
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
8
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
1
0
0
0
0
0
1
2
0
0
1
3
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
5
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
1
5
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
2
0
1
0
2
0
0
0
0
0
0
4
4
0
0
0
1
0
3
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
2
0
1
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
4
0
0
1
0
2
0
0
2
2
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
8
1
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
1
0
1
0
1
0
1
1
0
1
0
0
0
0
1
0
0
0
3
0
0
0
0
1
2
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
1
0
0
0
0
1
0
0
0
5
1
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
2
1
0
0
1
1
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
2
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
3
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
1
2
3
1
0
1
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
2
0
0
0
0
1
1
8
1
5
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
5
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
5
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
1
7
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
2
0
0
1
1
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
8
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
1
1
0
2
0
0
0
0
0
0
5
1
0
0
0
0
2
0
2
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
2
0
2
1
0
2
5
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
1
1
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
6
0
2
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
9
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
2
0
0
3
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
2
1
0
0
2
0
0
2
0
0
1
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
1
1
0
2
22
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
6
0
0
0
0
1
0
0
0
1
0
0
0
0
1
2
0
0
0
1
3
2
0
0
0
0
2
0
2
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
2
0
0
0
3
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
1
0
0
2
0
1
1
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
5
0
1
3
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
3
0
0
1
2
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
1
1
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
1
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
2
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
2
0
0
2
1
0
0
1
0
2
1
1
0
0
0
0
0
0
2
2
0
1
1
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
1
0
3
0
0
2
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
2
2
3
0
2
0
0
0
1
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
3
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
3
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
1
0
0
2
2
0
0
0
0
0
7
0
0
0
0
1
2
0
0
1
3
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
2
0
3
0
0
0
0
1
0
1
0
3
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
2
2
0
0
0
0
0
1
1
0
1
0
0
1
0
0
2
0
3
0
0
0
2
2
1
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
1
0
2
0
0
1
2
0
2
0
0
0
0
1
1
3
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
1
3
0
0
0
0
0
0
0
4
0
0
0
1
1
0
0
0
0
0
4
0
0
0
2
1
0
0
0
0
0
1
0
5
0
0
0
0
1
0
0
0
1
0
0
0
2
1
0
0
0
3
1
0
3
0
0
0
2
0
0
0
1
0
0
3
0
0
0
0
1
0
1
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
2
0
3
0
0
4
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
1
0
0
0
0
0
3
0
0
1
3
0
0
3
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
2
0
2
1
0
0
0
0
0
0
0
0
2
1
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
4
1
0
0
1
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
3
1
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
6
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
2
0
0
1
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
5
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
3
0
0
3
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
2
1
0
0
2
0
5
0
5
1
0
0
0
0
0
0
0
2
0
6
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
3
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
1
1
3
1
0
0
1
0
0
0
0
3
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
10
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
1
9
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
2
0
1
0
2
2
0
0
0
0
0
1
2
0
0
2
0
3
0
0
0
0
0
0
0
6
0
0
0
0
5
0
2
0
2
1
1
1
0
1
0
1
0
0
0
1
0
0
0
0
0
3
2
0
0
0
0
0
0
2
0
2
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
4
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
2
0
0
1
0
0
0
0
1
2
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
6
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
1
1
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
3
0
0
1
0
0
5
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
4
0
1
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
1
0
3
0
0
0
0
1
2
1
0
0
0
0
1
0
1
0
0
0
2
0
0
2
0
0
2
0
1
1
0
0
0
0
0
1
0
0
0
2
0
0
2
0
1
0
0
1
0
1
0
0
0
1
0
0
0
2
0
0
5
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
2
0
2
0
0
0
1
0
0
0
0
2
0
0
0
2
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
5
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
3
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
4
2
0
0
0
0
0
0
0
0
0
0
1
1
4
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
1
0
0
0
1
4
2
0
0
0
2
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
4
0
0
2
0
2
1
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
2
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
1
0
0
1
0
5
0
0
7
2
0
0
0
2
2
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
2
0
0
0
0
0
1
0
0
6
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
1
1
0
3
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
3
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
1
2
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
5
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
2
0
1
2
0
0
2
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
2
2
0
1
0
0
0
2
2
0
0
1
0
0
1
3
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
2
0
0
0
1
0
2
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
3
0
0
1
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
1
0
0
2
0
0
1
1
0
0
3
0
0
0
1
0
0
0
0
0
5
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
3
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
1
1
1
10
0
0
0
0
0
1
2
4
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
2
0
0
0
0
4
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
1
0
4
0
3
1
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
3
0
0
1
0
0
3
2
1
0
0
2
4
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
3
0
0
0
5
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
1
0
4
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
4
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
4
0
1
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
3
0
0
1
1
0
2
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
8
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
4
0
0
0
0
0
0
2
1
3
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
3
0
0
2
0
0
1
2
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
20
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
3
0
0
0
0
0
0
0
3
0
0
0
0
1
1
1
0
2
0
1
0
0
0
0
0
0
3
1
0
2
0
3
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
2
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
3
0
0
1
0
0
2
3
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
3
0
0
0
0
0
0
1
3
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
1
0
0
0
0
2
0
1
0
0
0
1
0
0
2
1
0
2
0
0
0
0
0
0
1
3
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
5
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
2
0
2
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
1
0
0
0
1
1
10
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
3
0
3
1
0
2
2
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
3
0
2
1
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
5
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
3
3
0
6
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
3
0
0
3
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
3
0
0
3
1
0
0
0
0
0
2
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
1
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
4
0
0
1
0
0
0
1
0
2
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
1
0
1
0
1
0
0
1
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
5
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
7
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
3
0
0
0
1
0
1
0
0
0
2
0
0
2
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
5
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
1
1
0
2
0
0
0
1
1
0
0
0
0
1
0
3
0
0
0
0
1
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
1
2
0
0
2
0
3
1
0
0
0
0
1
2
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
2
0
2
3
0
0
0
1
2
0
0
2
0
2
0
0
0
0
0
0
0
0
1
2
4
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
4
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
5
0
0
0
1
0
0
0
1
0
0
1
0
1
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
3
0
0
0
2
0
0
1
0
0
3
2
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
5
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
2
2
0
0
0
0
0
3
0
0
0
2
0
2
0
0
0
0
1
5
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
7
0
0
0
0
0
1
0
1
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
1
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
1
0
0
0
1
0
0
1
1
0
0
2
0
0
1
0
0
0
2
0
13
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
1
0
0
4
1
0
0
0
0
0
0
1
3
0
0
0
0
0
1
3
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
2
0
0
0
2
0
0
0
2
0
1
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
8
0
2
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
5
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
4
1
0
0
0
0
0
3
0
0
0
0
1
4
0
1
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
1
0
0
0
0
2
4
2
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
3
0
3
0
0
1
0
0
0
0
0
1
2
0
0
0
0
3
0
0
0
0
2
2
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
2
2
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
5
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
3
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
3
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
3
0
0
0
0
1
0
0
1
2
0
4
0
0
0
5
0
0
3
0
2
2
0
0
0
4
0
0
0
0
0
2
0
0
0
0
2
3
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
2
2
0
0
6
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
3
4
0
0
2
0
0
2
0
0
3
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
2
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
3
2
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
3
1
1
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
1
2
1
0
0
0
0
3
0
0
2
2
1
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
2
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
1
1
0
2
0
0
1
1
2
6
0
1
4
0
0
0
1
0
0
0
2
0
0
0
2
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
1
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
2
3
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
6
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
3
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
2
0
0
0
0
1
0
0
2
0
0
0
3
1
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
2
0
0
0
0
0
0
0
1
0
1
2
0
0
4
0
2
0
0
0
0
0
0
0
1
2
1
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
1
2
0
0
0
0
0
2
3
0
3
1
1
1
0
1
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
1
0
13
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
1
0
0
0
1
0
1
0
2
0
0
0
0
0
1
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
3
3
1
1
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
10
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
1
3
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
1
0
1
0
0
0
0
0
1
0
1
1
4
0
2
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
1
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
1
1
0
0
0
1
3
0
4
0
6
0
0
0
0
0
0
0
1
0
0
0
0
2
3
0
2
0
0
0
1
1
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
1
2
0
0
2
0
1
0
4
0
1
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
2
0
0
0
0
0
0
3
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
5
0
1
0
1
0
0
0
0
1
1
0
0
2
0
0
1
0
2
0
1
1
1
0
0
0
8
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
1
0
2
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
5
0
1
2
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
5
0
2
0
1
0
1
0
0
0
1
5
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
1
0
0
1
0
0
2
0
0
0
1
0
2
1
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
5
0
1
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
3
0
1
1
1
0
1
0
0
0
1
0
0
0
0
4
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
1
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
1
1
0
2
1
2
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
2
0
2
0
2
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
1
4
0
2
0
0
1
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
5
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
3
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
3
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
4
0
1
0
0
1
0
0
1
0
0
1
2
2
0
0
0
2
2
2
0
0
0
0
1
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
5
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
1
1
0
0
0
2
0
3
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
3
0
3
1
2
0
0
0
1
0
0
0
0
0
0
1
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
1
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
2
0
0
0
2
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
7
2
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
1
0
0
0
2
0
1
1
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
1
2
3
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
3
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
1
2
0
1
2
0
0
0
1
1
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
3
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
2
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
1
0
3
0
0
2
0
0
0
0
0
3
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
4
2
0
0
1
1
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
1
2
3
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
2
2
0
0
5
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
2
0
1
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
3
0
3
2
1
3
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
4
0
0
3
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
2
1
0
0
1
2
0
0
0
0
0
2
1
0
0
0
0
2
1
0
4
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
2
0
2
0
0
2
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
3
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
2
2
0
0
2
0
1
2
1
2
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
9
1
0
2
0
0
1
1
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
2
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
8
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
3
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
3
0
0
0
0
0
6
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
1
7
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
1
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
3
3
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
6
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
3
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
7
0
0
2
0
0
0
1
0
0
1
2
0
0
0
0
0
1
3
3
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
1
3
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
5
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
5
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
1
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
1
0
1
0
0
3
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
3
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
2
2
1
1
0
1
0
0
1
0
3
2
1
1
0
0
1
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
1
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
3
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
1
2
1
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
2
1
0
0
1
2
3
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
4
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
1
2
0
2
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
1
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
3
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
4
0
1
0
0
0
0
0
11
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
3
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
3
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
2
0
1
0
0
0
0
0
0
1
1
0
1
0
2
1
0
0
0
1
0
0
0
0
0
0
0
5
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
2
0
1
1
0
0
2
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
2
0
0
0
0
1
1
1
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
3
1
0
0
1
0
0
0
0
0
2
0
0
7
0
0
1
0
0
2
0
0
0
3
0
0
0
1
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
2
0
0
0
0
0
0
1
1
0
0
0
2
1
4
0
0
0
0
2
0
0
0
0
1
0
0
6
0
4
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
2
0
0
2
0
0
0
0
3
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
2
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
3
0
0
2
2
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
2
1
0
0
0
0
0
0
0
0
5
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
2
0
0
0
0
1
2
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
1
1
0
2
0
0
0
0
0
0
0
0
1
0
2
2
0
0
1
0
0
0
0
0
2
2
0
0
0
4
3
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
7
1
0
0
3
0
0
0
2
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
1
1
0
0
0
1
0
1
2
0
1
0
0
1
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
1
0
0
0
3
0
1
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
1
0
5
0
4
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
1
0
1
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
2
0
0
0
1
0
0
0
2
0
2
0
0
2
0
3
0
0
0
5
0
3
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
2
0
0
0
1
0
0
3
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
1
0
2
0
0
4
0
0
1
0
0
0
3
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
1
2
4
0
0
0
0
0
0
1
2
3
1
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
2
1
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
2
0
1
4
0
0
1
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
3
0
1
0
0
3
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
1
0
2
1
0
3
2
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
1
3
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
0
4
0
0
0
0
0
1
0
0
0
3
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
2
0
2
2
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
2
1
1
0
2
2
0
0
1
2
0
0
0
0
1
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
1
0
1
0
0
0
0
0
1
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
4
0
1
0
2
0
0
0
0
1
1
1
1
0
0
0
1
0
0
2
0
0
2
0
0
1
2
0
0
0
2
3
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
1
0
0
3
1
0
3
0
0
3
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
2
1
0
0
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
2
2
0
2
1
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
3
1
0
0
2
0
0
0
0
0
0
0
3
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
5
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
2
0
0
2
0
0
0
3
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
2
2
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
1
0
0
0
2
0
1
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
1
3
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
2
0
2
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
3
0
0
0
0
2
0
1
1
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
1
0
2
0
0
0
2
0
0
1
0
2
3
0
1
2
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
2
0
2
0
2
0
0
0
0
0
1
0
0
0
2
1
0
1
0
2
0
0
0
0
0
2
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
3
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
4
0
0
0
0
0
0
0
3
0
0
0
0
4
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
2
2
0
7
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
2
1
0
0
0
2
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
6
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
1
0
0
0
2
0
0
0
0
0
0
0
6
0
2
0
0
0
1
0
0
0
0
0
0
1
0
2
0
2
0
0
1
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
3
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
3
5
0
1
0
0
0
0
1
0
3
0
0
0
0
0
0
2
0
10
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
8
0
0
0
0
1
3
3
0
0
0
0
0
0
4
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
1
2
1
2
4
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
2
0
0
0
0
4
1
0
0
0
3
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
5
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
1
0
0
1
0
0
1
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
7
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
10
0
0
0
3
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
2
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
8
1
0
0
0
0
0
0
2
0
0
0
2
1
0
0
1
2
1
0
0
1
0
3
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
1
0
0
1
0
1
2
0
0
0
2
1
2
0
2
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
2
5
0
0
0
0
4
1
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
3
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
2
2
0
0
2
0
1
0
0
0
1
0
0
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
2
11
0
0
0
0
0
1
3
0
1
0
2
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
1
0
0
0
0
0
2
0
3
0
0
2
0
0
0
2
0
0
0
6
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
6
0
3
1
1
1
0
1
2
0
1
0
0
0
0
0
0
2
3
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
3
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
4
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
3
1
0
0
0
0
11
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
1
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
1
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
2
0
0
0
3
0
0
0
0
0
1
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
1
0
3
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
1
0
0
0
2
0
3
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
1
6
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
2
2
0
0
3
0
0
0
2
1
3
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
3
0
0
0
0
0
1
0
1
1
3
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
3
1
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
9
0
0
0
2
0
0
1
1
0
0
0
1
0
0
0
0
2
5
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
3
0
0
4
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
1
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
6
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
4
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
6
4
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
2
0
1
0
2
0
0
0
2
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
1
1
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
1
0
0
1
0
0
2
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
2
1
0
0
0
0
0
0
0
2
0
2
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
1
0
2
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
2
0
3
4
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
4
1
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
1
1
1
0
1
0
0
1
2
0
0
0
0
0
1
1
2
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
2
3
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
4
2
0
0
6
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
2
0
2
0
0
0
0
0
1
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
2
0
0
0
2
0
0
0
2
9
2
3
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
8
0
0
0
0
0
2
3
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
3
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
4
0
0
1
0
1
0
0
0
0
1
0
1
0
1
0
0
1
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
1
0
0
1
2
1
0
0
0
1
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
1
0
2
2
0
2
2
0
1
0
3
0
2
0
0
3
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
4
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
4
2
3
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
1
0
0
0
2
0
0
0
0
3
5
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
1
0
0
1
2
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
8
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
1
2
0
0
0
0
2
1
1
0
1
1
0
0
0
1
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
3
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
5
1
0
1
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
4
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
4
0
0
0
1
1
0
0
0
0
0
1
0
0
2
0
0
0
0
1
2
1
0
0
2
0
0
0
0
2
2
0
2
0
0
0
0
2
0
0
0
0
0
0
3
2
0
0
0
0
0
0
1
2
0
0
9
0
0
0
1
1
0
0
0
0
3
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
3
2
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
5
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
2
0
5
0
0
0
2
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
5
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
3
0
3
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
4
1
0
1
0
3
2
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
2
0
4
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
1
2
0
0
0
0
5
0
0
0
0
0
3
0
0
0
2
0
1
0
0
4
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
3
0
1
0
0
1
0
0
0
0
5
0
4
1
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
3
1
0
2
0
0
2
0
0
0
1
0
0
3
1
1
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
10
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
6
2
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
2
1
2
0
0
0
0
1
0
0
0
1
2
0
0
2
0
0
0
1
0
1
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
1
2
0
0
0
0
4
0
0
0
2
0
2
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
1
0
0
0
2
0
0
0
6
3
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
7
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
1
0
0
0
0
0
0
2
0
3
3
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
5
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
1
0
0
0
2
3
1
2
0
0
1
1
1
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
1
0
1
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
1
0
1
0
0
0
10
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
2
2
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
8
0
1
0
0
0
0
2
0
0
1
0
0
0
0
1
0
2
0
0
0
1
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
2
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
4
0
0
1
2
1
4
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
5
0
0
0
0
6
1
0
0
1
0
0
0
0
0
2
0
0
3
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
1
0
1
0
0
2
0
0
3
0
6
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
2
0
0
3
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
3
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
2
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
3
2
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
2
0
5
0
0
1
0
0
0
3
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
3
0
0
0
1
0
4
3
0
0
0
0
0
0
1
0
0
0
0
3
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
1
0
2
2
1
1
0
2
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
3
1
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
2
0
0
0
3
0
2
0
2
1
0
0
1
1
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
5
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
2
0
1
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
2
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
2
2
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
2
0
0
0
0
2
2
0
0
0
3
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
2
0
1
0
0
1
2
1
3
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
3
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
7
0
0
0
2
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
5
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
1
6
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
1
0
0
3
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
4
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
1
1
0
0
1
0
2
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
2
0
0
1
0
0
0
2
0
3
2
0
1
0
0
0
2
1
0
0
1
0
0
0
0
0
0
4
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
3
3
0
0
1
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
3
1
2
0
3
0
1
2
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
1
3
2
0
1
0
3
0
0
0
0
3
0
0
2
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7
2
1
0
0
4
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
1
3
1
1
0
0
1
0
0
2
0
0
2
0
0
2
0
0
0
0
1
0
2
0
0
3
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
1
0
1
0
1
2
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
1
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
2
0
0
0
0
0
2
2
0
0
1
0
0
0
2
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
2
1
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
4
0
0
0
0
0
0
1
0
3
0
4
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
3
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
3
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
6
1
0
0
0
0
2
0
0
0
3
0
0
1
0
0
1
2
0
1
0
0
4
0
1
0
0
0
0
2
2
0
1
1
0
0
2
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
4
1
0
2
0
2
1
0
1
0
1
0
0
0
0
0
3
0
2
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
3
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
1
1
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
3
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
4
2
0
0
0
0
0
1
1
0
0
1
0
4
0
0
0
2
0
0
0
0
1
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
3
0
0
0
0
0
1
3
0
0
0
0
1
1
0
0
0
2
0
0
0
2
0
0
2
0
0
0
4
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
3
0
0
2
0
1
2
1
1
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
1
0
1
0
0
0
0
0
2
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
3
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
3
0
0
1
0
1
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
1
0
1
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
1
0
1
3
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
11
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
4
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
2
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
2
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
3
0
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
2
0
1
0
0
0
0
1
0
0
0
0
5
1
0
0
0
1
3
2
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
3
0
0
0
5
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
2
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
3
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
1
2
0
0
2
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
2
6
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
2
0
0
0
0
3
0
1
3
1
0
0
1
0
1
0
0
0
1
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
4
0
0
0
2
0
6
0
1
0
2
0
0
0
0
1
2
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
2
1
0
0
2
0
1
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
1
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
2
0
0
0
4
0
0
1
0
0
0
1
1
2
0
1
0
0
0
2
0
4
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
1
0
1
0
2
0
2
2
0
0
0
0
0
1
0
0
2
3
2
0
0
0
0
1
0
1
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
1
0
2
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
3
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
5
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
3
2
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
2
0
0
2
0
1
0
0
1
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
2
1
0
2
0
0
5
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
1
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
4
0
0
0
2
1
0
0
1
0
1
0
0
0
0
0
3
0
0
3
0
2
0
0
0
0
3
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
2
0
0
3
0
1
0
0
0
5
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
7
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
2
2
3
0
0
0
2
0
0
0
0
1
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
3
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
9
0
0
0
2
0
0
2
0
1
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
4
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
1
0
0
0
0
2
1
0
0
0
19
3
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
10
2
0
1
0
1
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
1
0
1
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
6
0
1
0
0
0
0
0
0
3
1
0
0
0
0
2
12
0
1
3
3
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
2
1
0
4
1
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
2
0
0
1
1
0
2
0
0
0
0
0
2
0
2
1
0
0
0
0
1
1
0
2
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
1
2
1
2
0
0
0
0
0
1
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
2
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
2
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
1
2
0
0
2
2
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
4
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
3
3
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
2
0
0
0
0
0
0
1
2
0
0
1
0
1
0
0
0
1
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
1
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
2
0
1
0
0
2
1
0
0
2
0
1
0
0
0
0
0
1
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
2
3
0
0
0
0
0
2
0
2
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
3
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
6
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
1
1
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
3
0
0
0
2
0
0
0
1
0
2
2
0
1
1
0
4
0
0
0
2
1
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
5
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
3
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
0
1
0
0
3
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
6
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
36
1
0
0
2
1
0
0
0
0
3
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
2
0
0
1
2
2
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
1
1
0
0
2
0
4
3
0
0
0
4
2
0
2
0
3
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
1
2
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
4
0
2
1
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
5
1
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
3
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
5
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
4
0
2
0
6
0
0
0
0
0
0
0
2
0
0
0
0
1
0
4
0
0
1
2
1
0
2
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
2
1
0
1
0
1
0
0
0
0
0
0
0
0
0
3
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
3
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
1
0
5
0
0
0
0
3
0
0
0
0
2
0
1
2
2
1
0
0
0
0
0
0
7
0
2
1
0
2
0
0
0
0
0
0
0
0
1
1
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
14
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
2
0
0
0
1
0
2
0
2
0
0
0
1
0
0
0
0
0
2
1
0
0
0
2
2
0
0
3
1
0
2
0
0
0
2
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
4
2
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
2
1
0
3
1
0
0
0
0
0
0
0
0
0
1
0
0
7
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
1
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
7
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
2
1
0
1
0
5
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
3
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
2
0
1
4
0
0
0
0
1
0
2
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
3
3
5
0
0
0
1
0
0
0
1
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
5
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
2
0
1
0
0
0
0
0
2
0
3
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
4
1
0
0
0
2
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
2
0
2
2
1
0
0
0
4
0
2
0
0
0
0
2
1
0
0
0
0
0
0
4
0
0
1
0
0
2
0
1
0
0
0
0
0
2
0
0
0
1
0
0
4
2
0
2
0
1
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
2
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
4
0
0
0
1
1
0
2
0
2
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
2
0
0
0
0
0
1
0
0
1
0
0
1
0
0
2
2
0
0
0
0
0
0
2
1
0
0
0
1
0
1
0
1
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
2
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
2
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
3
0
0
0
0
0
1
1
0
0
0
1
2
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
1
0
0
0
0
0
0
0
1
0
1
0
0
5
2
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
1
1
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
10
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
2
0
0
3
0
2
0
0
0
1
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
2
0
0
2
0
0
0
2
0
0
0
2
0
0
0
3
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
3
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
1
0
0
1
0
1
0
0
0
0
2
2
1
0
0
0
1
0
0
1
3
0
0
0
0
0
1
0
0
1
0
0
1
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
1
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
2
1
0
0
3
2
1
2
1
0
0
2
0
1
0
0
1
0
2
1
0
0
1
0
0
1
0
0
0
3
0
0
0
0
4
1
0
0
0
0
0
0
0
0
4
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
1
0
0
1
3
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
4
0
0
0
0
0
1
0
0
0
1
0
0
1
0
2
0
0
1
2
0
2
4
0
0
0
0
0
0
3
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
4
0
0
0
2
0
0
0
0
0
2
0
0
0
4
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
1
2
0
0
0
2
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
3
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
3
0
0
0
0
0
1
0
0
3
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
6
0
1
2
2
0
0
0
1
1
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
2
0
1
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
1
1
1
0
0
0
0
2
2
0
0
0
2
2
0
0
0
0
4
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
3
2
0
0
0
0
0
0
0
0
5
2
0
0
1
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
5
0
2
1
1
0
0
0
0
0
1
0
0
1
0
0
1
2
0
1
0
1
0
0
0
1
1
0
0
2
0
1
0
2
0
0
1
2
0
0
0
0
1
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
2
0
2
0
1
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
1
0
0
0
0
4
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
2
0
2
0
7
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
2
0
1
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
3
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
2
1
1
0
1
0
0
0
0
4
0
0
0
2
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
1
0
0
0
0
0
0
2
1
2
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
2
0
2
0
0
1
0
0
0
0
0
2
3
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
3
0
0
0
1
3
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
3
1
0
2
1
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
3
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
6
0
0
0
0
0
0
0
0
1
1
0
0
1
0
2
3
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
2
0
2
3
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
2
1
0
1
4
1
3
0
0
0
0
0
0
1
0
1
0
4
1
0
2
1
0
0
0
0
0
0
0
0
2
0
0
1
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
1
2
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
1
0
0
0
1
0
3
0
0
0
1
0
1
0
0
0
2
0
0
1
1
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
1
0
1
0
1
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
1
1
2
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
6
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
1
0
1
0
1
0
0
0
0
3
0
1
0
0
0
0
0
0
0
12
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
1
1
0
0
1
0
0
0
1
1
0
0
9
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
1
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
5
0
1
0
1
0
1
0
0
0
0
1
0
0
1
0
0
1
2
1
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
3
0
0
12
2
0
0
1
0
3
5
0
0
0
2
0
2
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
1
2
0
2
0
0
0
1
0
0
6
4
1
0
0
2
0
0
2
0
3
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
3
0
0
0
0
2
0
1
0
2
0
0
3
1
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
1
0
0
0
3
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
2
0
0
2
2
0
1
2
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
5
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
7
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
1
2
0
1
0
0
0
0
0
2
0
0
3
0
0
0
1
0
0
1
0
1
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
5
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
1
6
1
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
2
0
4
0
0
1
0
0
0
3
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
2
2
2
0
0
0
1
0
0
0
1
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
2
0
1
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
4
0
0
1
1
0
1
0
0
1
1
0
0
2
0
0
0
1
3
1
0
0
1
0
2
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
2
0
0
0
0
4
0
0
2
0
0
0
1
0
0
0
0
2
2
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
7
0
0
0
0
0
1
0
0
2
6
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
9
0
0
0
0
1
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
1
0
1
1
0
0
0
2
0
1
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
6
0
0
3
0
0
0
2
0
0
0
0
0
1
0
0
1
0
2
2
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
2
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
9
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
13
0
0
0
1
0
0
0
1
0
7
0
0
0
3
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
1
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
3
0
0
0
4
0
2
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
2
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
3
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
4
0
0
0
1
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
1
1
4
0
0
0
0
0
1
0
2
2
0
1
0
0
0
1
0
2
0
2
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
2
2
0
3
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
5
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
2
0
0
0
0
4
2
0
0
0
0
0
1
0
0
0
0
0
1
0
3
0
0
0
2
0
3
0
2
0
0
5
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
4
2
0
0
0
0
0
3
1
1
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
4
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
3
5
0
0
0
0
0
0
0
4
0
0
0
8
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
8
0
0
1
0
0
2
0
0
0
0
2
1
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
3
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
1
1
0
1
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
1
0
1
1
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
3
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
2
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
2
1
1
1
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
5
2
1
0
0
0
0
2
0
0
0
1
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
1
0
0
1
2
1
0
0
0
8
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
3
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
2
2
0
0
0
0
0
1
0
0
4
0
0
2
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
1
2
0
0
0
2
1
0
0
0
1
0
0
1
0
0
3
0
5
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
5
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
1
0
0
0
1
1
0
1
2
0
0
2
2
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
1
0
1
1
0
0
0
0
0
0
0
0
2
1
0
0
4
0
0
1
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
2
1
3
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
1
0
0
0
0
3
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
2
3
0
0
0
3
0
0
0
2
0
0
3
0
0
0
0
0
0
2
0
0
2
1
2
0
2
0
2
1
1
0
0
0
0
0
0
24
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
3
2
0
7
0
0
2
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
2
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
2
0
0
0
0
0
0
0
1
1
0
2
0
2
0
0
0
0
0
0
0
4
2
0
0
2
0
0
1
0
1
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
3
0
1
0
0
3
0
0
1
0
1
0
0
2
0
0
0
3
0
0
0
0
0
0
2
1
0
1
0
1
0
4
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
2
0
2
0
0
0
0
4
0
0
1
2
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
4
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
1
0
2
1
0
0
0
0
0
1
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
1
0
3
0
0
2
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
6
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
1
0
0
2
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
1
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
2
4
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
5
0
2
1
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
4
4
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
3
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
1
1
0
0
3
2
2
0
0
0
0
3
1
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
1
0
0
1
4
0
0
0
0
1
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
7
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
2
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
2
0
0
1
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
2
0
5
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
1
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
3
0
0
0
0
2
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
3
0
2
0
0
0
3
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
3
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
7
0
1
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
4
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
1
1
1
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
4
0
1
0
0
1
2
0
1
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
5
0
0
1
0
0
2
0
0
1
0
2
0
0
0
0
0
2
1
0
0
0
0
0
1
1
0
0
1
0
2
0
1
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
2
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
2
0
0
0
0
0
0
1
1
2
0
0
0
0
1
0
0
2
0
0
2
2
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
1
0
0
2
0
0
0
1
0
0
1
2
3
0
0
0
0
0
0
4
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
7
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
2
0
1
0
2
0
1
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
4
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
4
1
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
0
0
1
1
3
0
0
1
0
1
0
0
2
0
0
0
0
1
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
3
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
8
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
6
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
1
1
0
0
1
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
1
0
0
1
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
0
2
1
0
2
0
0
0
4
0
0
0
2
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
1
0
0
3
0
0
2
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
15
0
0
2
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
2
1
0
0
0
0
1
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
2
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
1
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
5
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
1
1
2
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
9
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
2
1
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
1
2
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
2
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
2
0
0
0
1
0
0
1
0
0
1
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
2
0
27
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
1
0
0
2
0
1
0
0
0
0
0
6
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
2
0
0
0
3
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
1
3
0
2
3
0
0
1
0
2
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
8
0
1
2
0
0
0
0
0
0
4
0
3
0
1
0
1
2
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
2
0
7
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
3
4
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
3
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
4
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
1
0
0
0
0
2
0
0
2
2
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
7
0
0
2
1
0
0
0
0
2
2
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
3
0
0
2
2
0
0
2
0
0
0
0
0
0
0
1
0
1
3
1
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
0
1
1
0
2
0
0
1
0
0
2
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
6
1
0
0
0
0
0
4
1
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
3
1
0
0
0
0
0
3
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
2
0
1
1
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
1
0
1
0
1
0
1
0
0
0
2
0
2
0
0
0
0
1
1
1
0
2
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
1
1
2
0
2
0
6
0
1
0
2
0
1
0
0
1
0
0
0
2
0
2
0
2
0
0
1
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
1
0
0
0
1
0
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
3
0
0
0
1
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
1
3
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
3
0
0
1
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
2
0
0
2
0
0
0
2
0
0
0
1
0
2
0
2
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
6
0
0
0
0
1
3
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
2
0
0
0
0
1
1
0
0
1
0
0
2
0
3
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
2
2
0
2
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
9
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
3
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
2
0
0
2
0
0
3
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
2
0
0
0
0
0
1
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
3
2
0
0
0
2
0
1
0
0
2
0
0
0
0
0
4
2
0
0
2
0
0
0
0
0
3
0
5
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
5
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
2
0
0
2
0
3
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
4
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
2
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
2
0
1
1
0
0
0
0
0
0
2
2
0
0
1
2
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
5
0
2
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
1
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
6
1
0
2
3
0
2
0
0
2
0
0
0
0
0
0
0
0
5
1
1
0
0
0
1
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
3
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
1
3
0
2
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
4
1
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
3
1
0
0
1
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
2
0
2
0
1
0
2
0
0
1
1
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
3
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
3
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
2
1
5
0
0
0
0
0
0
0
0
1
0
1
1
4
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
3
1
0
0
0
0
0
2
0
3
1
0
0
0
1
0
1
0
0
0
0
4
0
0
0
1
3
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
4
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
1
0
0
0
0
11
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
1
0
2
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
3
1
0
6
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
4
1
0
0
0
1
0
0
0
1
0
1
0
0
1
8
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
1
0
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
4
0
2
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
2
3
0
0
0
2
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
1
2
7
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
4
0
0
1
0
0
1
0
0
0
1
2
0
0
1
0
3
1
0
0
0
2
0
0
0
0
0
2
0
0
2
1
0
0
0
2
2
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
1
2
2
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
4
2
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
1
2
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
5
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
4
0
0
0
0
0
3
0
1
0
0
1
0
8
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
3
0
0
2
2
0
0
0
0
0
0
1
0
2
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
2
3
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
2
1
0
1
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
2
1
0
0
3
0
0
0
0
1
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
4
1
0
2
4
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
1
0
1
2
0
2
0
0
0
0
0
0
2
1
0
0
2
0
0
1
0
1
0
2
0
0
0
0
0
1
0
0
1
0
0
2
0
0
4
0
0
1
1
0
1
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
3
0
1
0
0
0
0
2
1
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
1
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
3
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
2
0
0
0
0
3
0
0
0
0
0
0
1
0
0
3
2
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
2
0
0
0
0
1
0
3
0
0
0
1
0
2
0
2
0
0
2
4
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
3
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
2
0
0
1
3
3
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
2
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
1
2
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
3
0
0
2
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
2
0
5
1
0
2
0
0
0
0
0
0
0
1
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
1
1
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
2
0
2
0
0
3
1
0
0
0
0
0
2
0
2
0
0
2
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
1
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
1
0
0
1
2
0
0
0
0
1
0
0
4
0
0
3
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
4
0
0
0
0
1
0
1
0
4
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
2
4
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
2
3
0
1
2
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
3
0
0
0
0
0
2
0
0
0
0
5
0
0
5
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
3
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
7
1
0
0
0
0
0
0
2
1
1
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
3
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
3
1
0
0
0
1
0
2
1
0
0
3
0
0
2
0
0
0
2
0
0
2
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
5
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
4
0
2
3
2
0
0
0
2
0
2
0
0
2
1
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
1
0
1
0
0
0
10
2
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
4
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
2
0
6
2
0
1
0
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
1
0
0
0
2
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
2
0
0
1
0
0
2
0
1
2
0
0
0
2
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
3
0
1
0
1
0
3
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
2
3
0
1
0
0
0
1
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
3
0
1
2
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
3
2
0
2
0
0
2
0
2
0
5
0
0
1
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
3
0
0
2
0
0
0
0
0
0
0
1
3
0
0
1
1
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
3
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
2
1
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
1
0
1
2
4
0
2
1
1
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
2
1
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
3
1
0
0
0
1
0
0
0
0
0
0
0
3
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
6
2
0
0
0
0
0
0
1
0
6
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
1
0
1
0
0
0
0
0
0
1
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
3
0
0
1
2
0
0
0
0
3
0
0
0
0
0
2
0
0
2
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
5
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
1
0
2
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
2
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
1
0
7
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
4
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
2
0
0
0
0
2
0
2
2
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
1
2
0
0
2
0
0
2
0
0
2
0
0
0
0
1
0
1
0
0
0
5
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
6
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
2
2
1
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
2
0
1
0
2
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
2
2
2
2
0
0
0
0
0
0
0
0
3
0
0
0
1
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
1
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
4
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
3
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
1
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
5
0
0
2
0
0
1
1
0
0
1
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
1
0
0
0
2
0
0
0
2
0
0
0
0
1
1
0
0
2
0
0
0
1
0
0
3
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
3
1
0
0
0
0
0
0
2
2
1
0
0
2
0
0
0
0
2
0
0
0
0
0
2
3
0
1
0
2
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
2
0
0
0
0
4
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
2
0
0
4
2
0
2
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
5
0
0
0
2
0
1
0
0
0
0
1
0
2
5
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
0
2
1
0
0
0
1
1
2
1
2
2
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
3
2
0
1
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
5
1
1
0
2
0
0
0
0
0
2
0
0
0
1
1
0
0
1
1
0
0
0
1
0
0
0
0
1
7
1
0
0
0
0
0
2
2
8
0
0
2
1
0
2
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
2
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
5
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
5
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
2
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
5
0
1
0
0
3
0
1
0
0
0
1
1
0
0
0
0
0
0
2
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
1
1
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
5
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
3
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
3
1
5
0
3
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
1
2
0
0
3
0
0
1
0
0
0
0
0
0
0
0
5
0
3
1
0
1
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
3
0
0
0
8
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
1
2
1
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
2
0
0
0
0
0
0
0
2
1
2
0
0
1
0
0
0
0
1
0
0
0
0
1
0
2
1
0
1
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
1
0
2
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
6
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
3
1
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
1
0
1
2
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
2
0
1
0
0
0
0
5
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
2
0
0
1
1
1
2
0
2
0
1
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
2
0
0
5
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
12
0
2
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
3
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
6
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
2
0
0
0
1
0
7
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
6
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
3
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
1
0
2
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
5
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
1
0
0
1
0
0
2
1
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
4
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
3
2
0
1
0
0
0
0
0
0
0
0
1
1
0
2
3
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
3
0
0
0
0
2
0
0
0
0
0
2
6
0
0
3
1
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
4
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
2
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
3
0
0
2
0
0
0
1
0
1
0
0
0
2
0
1
0
0
0
0
2
1
0
0
2
2
0
0
2
2
0
1
0
2
1
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
1
2
0
1
0
0
0
0
0
0
0
2
0
3
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
1
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
3
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
1
0
0
1
1
3
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
1
0
0
1
0
0
0
0
7
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
1
2
0
0
0
0
0
0
0
0
2
1
1
2
0
3
0
3
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
0
5
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
1
1
1
0
0
0
2
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
4
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
5
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
2
0
0
0
1
3
1
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
10
1
0
0
0
0
0
0
2
2
0
0
0
0
1
0
5
0
1
0
0
0
0
2
0
4
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
2
1
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
1
0
1
0
2
0
0
0
0
2
0
2
0
0
0
0
0
3
0
1
0
0
0
1
0
0
0
2
2
0
1
1
0
2
0
0
3
1
0
0
3
2
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
1
3
0
2
2
0
1
1
1
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
3
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
2
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
8
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
2
2
2
0
1
2
0
0
0
1
1
2
0
0
0
0
0
1
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
3
0
0
1
0
0
1
0
2
2
3
0
0
4
0
0
3
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
3
0
1
1
0
5
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
3
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
9
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
1
0
0
1
2
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
1
0
0
1
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
3
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
9
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
4
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
3
1
1
0
2
0
1
2
0
0
0
2
2
0
0
0
1
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
3
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
2
0
0
0
1
1
0
1
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
3
0
0
0
0
1
1
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
1
1
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
3
0
0
1
0
0
3
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
1
3
2
1
0
0
1
0
1
0
0
0
0
1
0
6
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
2
0
3
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
1
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
2
0
4
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
2
0
0
0
0
2
0
0
1
0
1
0
0
0
0
2
0
2
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
4
0
0
1
0
0
0
1
0
0
0
0
0
2
2
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
6
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
2
2
0
2
1
2
0
0
0
0
0
0
0
1
0
4
2
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
3
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
1
0
3
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
5
0
0
0
0
5
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
1
3
0
3
0
0
2
2
3
2
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
1
0
1
3
1
0
1
0
0
1
0
0
0
3
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
3
0
0
0
0
0
1
0
0
0
1
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
1
0
1
0
0
0
0
1
2
0
0
2
0
0
0
0
1
2
1
2
3
0
0
2
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
6
0
1
3
0
0
0
0
2
1
1
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
3
0
0
0
5
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
1
0
0
2
2
2
0
0
0
1
0
6
2
1
0
0
0
0
0
0
2
6
0
0
0
4
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
6
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
1
0
2
0
0
0
1
0
0
0
2
0
0
2
0
0
0
1
0
1
2
1
1
0
1
0
0
0
0
0
2
1
0
1
0
0
0
2
0
0
0
0
2
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
3
0
0
0
0
0
0
1
0
0
0
0
1
4
0
0
0
0
1
0
0
0
3
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
1
1
0
1
1
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
4
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
2
0
3
0
0
5
2
3
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
3
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
4
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
1
0
0
1
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
2
0
1
2
8
0
0
0
0
0
0
0
0
0
2
3
2
1
0
2
0
0
0
1
5
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
2
0
0
0
1
0
1
0
0
5
0
0
0
0
0
0
0
1
0
0
0
0
7
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
3
0
1
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
1
0
2
1
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
5
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
1
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
4
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
9
1
2
0
2
1
0
0
1
1
0
0
0
0
0
2
0
0
0
1
0
2
0
2
0
0
0
5
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
10
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
3
0
0
1
0
0
0
0
0
1
4
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
7
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
1
2
0
2
0
0
1
0
0
4
0
0
0
4
0
0
0
1
0
0
2
0
0
1
0
1
0
1
1
1
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
2
0
1
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
3
1
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
1
3
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
3
0
0
2
0
0
1
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
1
0
0
3
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
2
0
1
2
0
3
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
3
0
0
0
0
1
0
0
0
0
0
0
1
2
3
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
2
0
2
5
0
2
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
2
1
1
0
0
0
2
0
2
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
4
0
0
2
0
2
0
0
0
2
6
0
0
2
0
1
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
2
0
2
7
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
7
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
1
1
0
0
1
0
0
0
1
2
0
0
0
4
1
0
0
0
2
0
0
0
3
0
0
2
0
0
2
2
0
0
0
1
0
0
1
0
2
0
0
1
0
0
1
0
0
0
0
0
0
2
3
0
0
1
0
0
0
3
0
3
0
1
1
0
0
0
0
2
0
0
0
0
1
1
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
2
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
4
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
2
0
5
0
1
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
3
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
7
0
1
0
8
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
2
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
3
0
0
1
0
0
0
2
0
0
0
2
1
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
4
0
0
2
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
2
1
2
0
1
0
0
0
0
0
2
0
0
0
2
2
0
1
0
1
0
0
0
0
1
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
13
0
0
2
0
0
0
5
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
6
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
4
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
3
0
0
0
0
0
0
0
2
3
2
0
5
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
2
0
0
0
0
1
1
0
1
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
6
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
5
1
1
0
2
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
2
3
0
0
0
2
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
4
0
1
0
0
0
1
0
0
1
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
5
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
3
0
0
2
1
0
0
0
2
1
2
0
2
0
0
0
0
2
0
0
5
0
0
0
3
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
3
1
2
0
0
3
0
1
0
0
3
0
0
2
0
0
0
0
0
1
1
1
3
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
6
0
2
0
0
0
9
0
2
2
0
0
2
0
0
2
0
0
1
0
2
1
0
0
1
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
3
0
1
0
0
0
1
0
0
1
0
0
2
0
0
2
0
1
0
0
0
0
2
0
2
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
3
0
0
0
0
1
2
0
0
0
0
0
3
2
1
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
1
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
4
0
0
0
2
0
1
0
0
2
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
1
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
2
0
2
3
1
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
1
0
0
1
0
1
0
0
2
0
0
1
0
0
1
0
3
0
0
2
0
0
1
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
1
5
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
3
0
2
0
0
1
0
0
0
0
0
0
0
9
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
2
0
1
0
9
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
3
3
0
0
2
1
2
0
0
0
0
2
1
2
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
1
0
2
0
0
1
0
0
0
1
0
0
0
0
2
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
2
1
2
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
3
0
3
0
1
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
4
0
0
3
0
2
0
0
0
3
0
0
0
1
0
0
3
0
0
0
0
3
1
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
1
1
0
0
0
0
0
0
0
0
2
2
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
3
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
4
0
0
0
3
1
0
0
1
0
0
0
0
1
0
0
1
0
2
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
1
0
0
1
1
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
3
3
3
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
3
0
9
2
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
3
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
1
1
2
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
2
0
0
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
3
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
3
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
2
1
0
0
2
1
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
3
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
5
0
0
1
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
8
0
5
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
8
3
1
3
0
0
1
0
0
1
0
0
1
3
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
4
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
2
1
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
2
0
0
1
0
1
1
0
0
0
2
0
0
3
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
3
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
2
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
1
2
0
0
0
0
1
0
0
0
0
0
1
0
1
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
1
5
0
0
0
0
0
0
0
13
1
0
2
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
3
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
1
0
2
0
2
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
2
0
0
0
2
0
0
0
0
1
1
0
0
2
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
3
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
2
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
2
0
1
0
1
1
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
1
0
0
2
0
1
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
1
1
3
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
4
1
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
5
0
4
1
2
0
0
0
0
0
0
0
0
0
0
2
0
42
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
1
0
3
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
3
1
0
0
0
0
0
1
0
0
2
0
0
0
3
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
1
1
0
1
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
1
16
0
0
0
0
0
0
2
0
0
0
2
0
5
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
5
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
1
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
2
1
0
0
0
0
2
3
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
1
0
1
0
2
0
1
2
2
1
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
5
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
1
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
3
0
0
0
1
1
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
2
0
0
1
1
0
0
0
2
0
1
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
4
1
1
1
0
2
0
0
0
2
0
1
0
0
0
0
4
0
2
0
0
1
0
2
0
0
0
0
1
0
0
3
0
0
1
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
2
1
0
3
0
0
2
1
2
2
1
0
0
0
0
0
1
0
0
0
0
1
0
6
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
3
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
7
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
1
2
0
0
0
2
0
0
3
0
2
0
0
0
2
2
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
6
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
1
0
0
2
0
1
0
0
0
0
2
0
1
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
2
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
1
0
2
0
0
0
1
3
0
0
2
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
1
2
1
0
0
0
0
0
0
0
0
1
1
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
1
1
1
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
2
1
1
2
0
0
0
0
0
1
0
0
0
0
1
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
4
0
1
2
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
4
4
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
4
2
2
0
0
0
0
0
0
0
6
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
1
2
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
2
0
0
1
1
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
2
0
0
2
0
0
1
2
0
1
0
0
0
0
2
0
0
0
0
1
1
2
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
2
0
0
0
1
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
4
0
2
0
0
0
0
1
2
0
0
0
0
0
0
1
2
1
0
0
0
0
3
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
2
2
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
1
0
0
1
0
1
2
3
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
1
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
3
4
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
1
0
1
0
0
0
2
0
0
0
0
0
2
2
2
1
0
0
2
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
1
0
2
3
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
2
1
5
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
3
0
0
4
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
2
2
0
1
0
0
0
0
0
0
0
1
0
3
2
0
1
0
1
0
1
0
2
0
0
2
0
0
0
1
1
0
0
5
0
0
0
2
0
0
1
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
13
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
3
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
2
2
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
3
2
0
0
6
1
0
0
2
0
0
0
0
2
1
0
0
0
0
2
0
0
1
0
0
3
0
1
0
0
1
0
0
0
0
0
2
1
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
7
0
0
0
0
0
0
1
1
0
0
2
0
2
2
2
0
3
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
4
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
2
1
0
0
0
0
0
1
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
7
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
1
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
3
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
9
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
6
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
1
0
2
1
0
0
0
0
2
0
0
1
0
0
0
0
0
2
4
0
0
2
2
0
0
0
4
2
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
2
1
0
0
0
0
0
2
0
0
1
1
0
1
0
1
1
0
0
0
0
0
2
0
0
0
0
0
2
1
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
1
1
0
1
3
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
2
0
0
0
1
0
1
1
0
1
0
0
0
0
0
2
1
0
0
2
0
1
0
1
0
2
0
0
1
0
0
0
0
0
0
0
4
0
2
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
3
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
1
0
2
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
3
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
1
0
0
0
1
1
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
5
0
0
1
0
1
4
0
0
0
2
0
1
0
2
0
1
0
0
2
0
1
2
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
4
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
2
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
2
0
1
0
1
0
1
1
2
0
1
0
0
0
2
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
2
2
0
0
1
0
1
0
1
0
1
2
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
5
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
2
4
0
0
0
0
1
0
2
0
1
0
0
0
0
1
0
0
6
1
0
0
3
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
4
3
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
3
0
0
0
0
0
1
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
1
2
1
2
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
4
0
0
0
3
0
1
0
2
0
1
0
0
0
1
0
0
1
0
0
1
0
2
0
0
0
0
0
2
1
1
0
0
0
4
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
5
0
0
2
1
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
1
2
1
0
0
0
0
1
2
0
0
0
2
0
0
3
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
3
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
5
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
1
1
0
0
0
5
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
3
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
5
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
4
4
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
4
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
13
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
2
2
1
3
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
3
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
4
0
0
0
2
2
0
0
0
0
0
9
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
2
0
0
5
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
7
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
1
1
5
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
2
0
0
0
0
0
0
0
1
5
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
3
0
2
0
0
1
0
0
0
0
5
3
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
2
0
1
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
4
0
1
2
2
0
2
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
2
0
2
0
0
1
2
0
0
0
1
0
2
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
8
2
0
0
2
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
2
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
3
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
3
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
2
0
1
1
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
2
2
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
4
0
0
1
0
1
4
0
0
0
0
1
0
0
2
0
2
0
0
2
1
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
2
1
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
3
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
1
0
2
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
7
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
3
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
3
2
0
2
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
15
0
0
1
7
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
6
0
0
0
0
0
0
0
1
1
0
0
0
2
0
0
1
2
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
1
0
2
3
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
3
1
0
1
0
1
0
0
0
0
2
1
0
0
0
0
1
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
3
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
1
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
2
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
1
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
2
1
1
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
6
2
0
0
0
0
2
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
2
0
1
0
0
8
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
5
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
1
0
0
2
4
0
1
0
0
0
0
0
0
2
2
0
0
1
1
0
2
0
2
0
1
0
1
0
0
0
1
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
3
1
2
1
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
1
0
3
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
1
0
1
1
1
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
1
4
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
4
3
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
3
3
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
7
2
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
6
0
0
0
0
2
0
0
0
0
2
0
0
0
0
2
4
0
2
1
0
0
0
0
2
1
0
0
5
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
1
0
0
0
1
0
2
0
0
1
3
0
0
0
0
0
3
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
0
5
0
0
0
3
0
0
0
5
0
0
0
0
0
0
0
1
0
6
0
2
1
0
1
0
0
4
0
0
1
0
2
1
0
0
0
0
0
0
1
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
10
1
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
2
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
5
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
2
0
3
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
1
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
1
1
2
0
0
0
2
0
0
0
0
0
0
0
8
0
2
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
1
0
0
1
0
3
0
0
0
1
0
2
0
0
0
1
0
1
3
0
2
0
0
0
0
2
0
1
2
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
2
2
0
0
0
0
1
0
0
2
2
0
0
0
0
1
0
0
0
2
0
1
0
0
10
2
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
3
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
1
0
0
0
0
0
3
0
0
0
1
1
2
0
1
0
0
1
0
0
2
7
0
0
0
3
2
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
1
1
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
11
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
6
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
1
0
1
0
0
0
0
1
0
3
0
0
0
0
0
0
0
1
0
8
0
1
1
0
0
0
0
0
0
2
1
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
3
1
0
0
0
0
0
3
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
1
0
0
1
1
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
5
0
0
0
2
0
0
0
2
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
8
1
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
1
1
0
0
0
3
0
3
0
0
0
0
2
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
2
2
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
2
0
0
3
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
3
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
3
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
4
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
3
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
2
0
0
0
0
5
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
2
0
2
0
0
4
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
1
2
2
2
0
0
1
0
0
0
2
0
0
0
0
0
5
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
2
0
0
0
0
4
0
2
0
0
1
0
0
0
3
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
2
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
3
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
8
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
3
0
0
0
1
0
0
0
0
0
0
2
0
2
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
1
0
0
1
0
1
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
1
0
0
0
1
0
1
0
2
0
0
1
1
0
2
1
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
2
2
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
7
0
2
1
0
0
0
2
0
2
1
0
0
1
0
0
0
0
0
6
0
0
3
1
3
2
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
5
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
5
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
4
0
0
0
0
0
0
2
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
1
1
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
1
2
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
3
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
6
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
3
0
0
0
0
1
5
0
0
1
1
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
4
0
1
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
1
2
0
0
0
0
2
0
0
0
2
0
2
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
1
0
0
2
0
4
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
7
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
3
0
0
0
0
2
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
4
0
0
1
0
0
0
0
0
0
3
4
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
1
0
0
1
0
0
0
0
0
0
1
1
2
1
0
0
0
0
0
0
0
2
1
0
1
0
2
2
6
0
1
1
4
0
0
0
0
0
1
0
0
1
0
2
0
3
0
0
2
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
6
0
0
0
1
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
2
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
1
2
0
0
0
0
2
2
0
3
1
0
0
0
0
2
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
7
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
5
0
6
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
9
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
3
0
2
0
0
0
0
0
0
1
0
3
4
0
0
3
0
0
0
0
1
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
1
1
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
0
0
1
0
1
0
0
0
1
1
0
0
0
2
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
3
0
2
1
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
3
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
4
0
3
1
2
0
2
0
0
1
1
1
0
0
2
0
1
0
0
2
0
0
0
1
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
2
1
2
0
0
2
0
2
0
2
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
2
2
3
1
0
0
0
0
0
0
0
0
2
2
1
0
0
4
0
0
1
1
0
0
0
1
2
0
1
0
1
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
4
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
2
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
4
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
1
0
3
0
0
0
0
1
4
2
0
1
0
0
0
0
0
0
1
0
0
0
0
2
1
2
0
0
0
0
3
0
0
0
0
0
0
0
1
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
1
2
0
0
0
0
6
0
0
2
0
1
0
0
2
1
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
4
0
2
1
0
0
0
0
4
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
2
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
2
0
0
0
1
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
1
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
3
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
1
2
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
3
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
3
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
3
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
1
4
0
0
0
0
0
3
1
1
2
0
0
0
0
0
0
1
0
2
0
0
6
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
3
0
1
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
9
7
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
1
1
0
0
0
3
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
2
0
2
0
0
1
0
0
2
2
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
2
0
2
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
1
2
0
0
2
0
2
0
0
0
1
0
0
0
0
1
0
1
2
0
0
1
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
4
0
0
2
0
0
2
0
0
0
0
0
0
0
6
0
1
2
0
0
3
0
0
0
0
0
0
0
1
1
0
0
0
0
3
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
3
0
0
1
0
0
1
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
7
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
3
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
5
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
3
0
4
0
0
0
2
3
0
0
0
0
1
0
0
0
1
1
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
3
2
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
2
5
0
2
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
1
1
0
2
1
1
2
0
0
0
0
0
0
0
0
0
0
2
0
1
2
4
0
0
0
1
0
1
0
0
1
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
6
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
3
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
2
0
0
2
3
0
0
0
0
3
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
5
1
3
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
1
0
0
1
0
2
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
4
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
1
0
4
0
0
0
0
0
0
0
1
0
0
0
1
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
3
1
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
1
2
0
0
0
0
0
1
0
0
0
4
0
1
1
1
2
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
2
0
0
2
1
0
0
0
0
0
1
2
0
2
2
0
0
1
0
0
0
0
0
0
4
0
2
0
0
0
0
0
2
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
2
4
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
4
0
0
0
0
0
10
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
0
4
1
0
1
1
2
3
0
0
0
0
3
0
1
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
3
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
5
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
1
0
1
1
0
1
0
1
0
0
2
1
0
1
0
0
1
0
0
2
0
5
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
1
0
0
0
0
0
2
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
10
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
3
0
0
0
2
0
0
0
5
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
1
0
0
2
0
0
2
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
3
1
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
6
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
2
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
1
5
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
2
0
2
1
2
2
0
2
0
0
1
0
0
2
1
0
0
0
0
0
0
1
1
0
1
0
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
1
1
0
0
2
0
0
1
0
0
0
2
1
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
11
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
0
2
1
0
1
0
0
0
0
2
1
1
1
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
4
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
2
2
0
1
0
2
0
0
0
0
1
0
1
0
1
0
0
0
3
0
0
0
0
0
0
6
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
11
0
0
0
0
0
0
1
4
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
1
2
0
0
0
0
0
0
2
3
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
3
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
1
0
2
0
7
0
0
0
2
0
0
0
0
2
2
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
1
1
0
0
2
1
0
1
0
1
0
0
1
0
0
0
1
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
4
1
0
0
0
2
0
0
0
0
0
1
2
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
5
0
0
2
0
0
0
1
1
0
0
0
0
0
1
0
0
3
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
1
2
2
0
0
0
0
0
1
0
2
0
0
0
0
2
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
7
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
3
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
1
1
0
0
0
3
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
3
1
0
0
0
0
2
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
8
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
4
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
3
0
0
1
0
0
2
0
0
0
2
0
0
0
3
0
0
0
0
2
0
0
0
1
6
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
7
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
6
1
0
1
0
3
1
1
2
0
0
0
3
2
0
2
0
0
0
0
0
0
1
2
0
1
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
1
2
0
0
1
0
2
1
0
1
0
2
0
0
2
1
0
0
1
0
0
1
2
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
2
1
1
0
0
0
0
1
0
4
0
0
0
3
0
1
0
0
0
0
0
1
2
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
2
1
0
1
0
0
2
0
0
0
0
0
2
0
3
0
1
0
0
0
2
0
0
0
0
1
0
0
2
0
2
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
1
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
4
1
0
1
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
3
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
6
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
5
0
0
0
4
0
0
2
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
2
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
2
1
2
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
9
0
0
1
0
0
0
0
0
3
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
1
0
0
0
6
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
4
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
3
2
1
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
1
0
4
1
0
0
4
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
12
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
3
0
2
0
1
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
2
0
6
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
1
0
0
0
1
0
9
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
1
1
0
0
0
0
0
0
0
1
2
1
0
1
0
0
0
0
3
3
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
2
0
0
2
0
3
0
0
0
0
0
2
5
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
2
10
0
0
1
0
0
2
0
0
0
0
0
1
0
2
1
0
0
0
0
0
1
2
0
0
0
0
0
3
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
6
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
2
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
0
0
0
1
0
0
0
2
1
0
0
1
1
1
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
1
0
0
0
0
0
1
1
0
4
1
0
0
0
0
0
0
0
2
0
0
0
0
4
0
0
0
0
1
0
0
0
4
0
0
0
1
0
1
1
0
2
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
2
2
0
3
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
6
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
3
1
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
1
0
3
0
1
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
2
1
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
2
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
1
0
1
0
0
1
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
2
2
0
0
0
0
7
1
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
1
2
0
2
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
5
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
2
0
0
0
0
0
2
3
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
6
1
0
0
0
0
0
1
0
0
1
1
0
0
0
2
0
0
0
1
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
1
2
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
3
0
0
2
0
1
0
1
0
0
0
1
1
1
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
2
0
0
0
0
6
2
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
6
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
2
4
0
0
0
0
1
0
0
2
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
4
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
4
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
3
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
17
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
2
2
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
1
0
2
0
1
0
0
2
0
0
0
0
0
0
2
0
3
0
1
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
4
0
0
1
0
0
0
0
2
0
0
0
1
0
0
2
0
0
1
3
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
2
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
3
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
3
0
2
0
0
0
0
0
4
0
0
4
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
1
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
3
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
2
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
1
3
0
0
0
3
1
2
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
3
0
0
2
0
0
0
0
0
0
2
1
0
4
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
3
0
1
2
0
0
0
0
0
2
0
5
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
3
0
1
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
3
0
0
0
0
0
0
0
2
0
4
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
1
0
0
4
0
1
0
0
1
2
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
3
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
6
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
2
0
0
2
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
2
0
0
4
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
3
0
3
1
0
0
0
0
0
2
0
0
0
0
4
2
0
0
0
0
0
0
0
2
0
0
0
4
0
0
0
0
5
0
0
1
0
0
0
0
0
0
0
1
0
3
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
1
0
1
0
0
1
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
1
0
0
3
0
2
2
0
0
2
0
0
0
0
0
0
0
1
2
3
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
1
1
0
4
0
1
0
2
3
2
1
0
0
0
0
0
2
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
2
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
1
1
1
0
0
2
0
0
0
0
3
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
2
1
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
1
0
0
0
0
0
0
0
1
0
0
0
0
4
2
0
1
0
0
2
1
1
0
0
0
2
0
2
0
0
2
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
3
1
0
2
3
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
3
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
2
0
0
2
0
0
1
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
2
1
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
10
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
2
0
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
6
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
3
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
1
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
2
2
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
1
0
1
1
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
3
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
4
2
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
2
0
6
0
1
0
0
0
0
0
1
0
0
3
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
3
0
3
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
3
0
1
0
2
0
0
0
0
0
0
1
3
0
1
0
0
0
2
0
0
2
0
1
0
0
2
0
3
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
4
2
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
1
0
2
1
0
1
0
0
2
0
0
0
1
0
1
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
1
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
5
0
0
0
1
0
0
0
0
0
0
3
0
0
2
2
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
4
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
6
1
0
0
1
0
0
0
1
0
1
0
0
2
2
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
1
2
0
2
0
3
0
4
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
2
0
1
0
1
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
0
2
0
0
0
4
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
2
0
2
5
0
3
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
2
3
0
0
0
0
0
2
0
0
0
5
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
3
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
3
1
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
2
0
1
2
2
0
2
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
5
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
7
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
2
1
1
5
0
2
0
0
0
0
1
0
2
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
2
0
0
0
0
1
2
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
2
0
1
1
0
0
0
0
0
4
0
0
0
0
0
1
0
0
4
2
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
5
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
3
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
2
2
0
0
3
0
0
1
0
1
1
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
4
1
0
0
0
0
1
0
1
1
0
0
1
0
0
1
0
2
0
0
0
0
1
0
0
0
0
3
0
1
2
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
9
1
0
0
0
0
0
0
1
1
4
0
0
3
0
0
0
0
2
0
0
0
0
1
0
0
3
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
2
3
0
0
0
0
1
0
0
0
0
2
2
0
1
1
0
1
0
0
0
0
0
0
2
0
2
0
3
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
2
3
0
2
0
0
0
2
1
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
8
7
0
0
0
0
4
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
1
5
0
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
1
0
0
0
0
0
0
1
0
0
2
0
1
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
5
1
0
0
0
0
0
0
0
2
0
0
0
0
2
1
1
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
1
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
4
0
1
0
1
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
2
0
0
2
0
0
2
0
2
1
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
2
1
0
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
3
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
4
1
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
1
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
2
0
2
1
0
0
0
1
0
0
0
3
0
0
0
3
3
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
2
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
2
0
0
0
2
0
4
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
3
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
2
0
1
0
2
0
2
7
1
3
1
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
1
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
3
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
3
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
2
1
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
3
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
2
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
1
0
1
1
2
0
4
2
0
0
2
0
3
0
0
0
0
0
0
0
0
0
5
0
3
1
0
0
2
1
0
2
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
5
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
1
2
3
0
0
0
1
0
1
0
0
0
1
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
1
2
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
1
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
2
2
1
0
0
1
0
0
0
0
1
2
2
0
1
0
0
0
0
0
3
0
0
1
0
0
0
2
0
0
1
0
1
0
0
1
0
0
2
0
0
0
2
0
1
1
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
0
1
2
0
2
0
0
2
0
0
0
2
0
0
0
3
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
3
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
2
1
0
0
1
1
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
2
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
3
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
3
0
0
2
0
0
1
0
0
1
0
0
3
0
1
0
0
0
2
0
1
4
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
6
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
5
0
0
0
2
4
0
1
0
0
0
0
0
0
0
4
1
4
0
1
0
4
0
0
0
7
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
3
0
0
2
0
0
0
1
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
5
0
0
1
2
0
0
1
0
2
2
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
1
0
0
1
0
0
0
4
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
10
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
2
1
0
0
0
2
0
0
1
0
2
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
1
0
2
0
2
0
1
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
2
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
1
3
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
3
0
0
2
0
0
1
0
2
0
0
0
0
2
2
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
1
0
0
1
0
0
0
0
0
1
0
2
3
0
0
1
0
0
0
2
0
3
0
2
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
1
1
0
0
0
0
5
0
0
0
1
0
0
0
3
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7
5
1
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
4
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
5
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
1
1
0
0
3
1
0
0
0
0
0
0
1
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
2
2
0
2
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
2
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
2
0
2
1
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
5
0
0
1
1
2
0
0
0
3
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
3
0
0
0
1
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
5
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
5
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
3
1
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
2
1
0
0
1
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
4
0
1
0
2
0
1
0
1
0
0
0
0
0
1
0
0
1
2
1
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
2
0
3
0
3
1
0
2
0
1
0
0
0
0
1
5
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
2
0
0
0
0
0
4
0
0
0
0
0
0
2
0
0
0
6
1
0
0
0
1
0
0
0
3
0
0
0
3
1
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
6
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
1
1
1
0
2
0
0
1
0
0
0
15
0
0
3
2
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
2
0
1
1
0
0
5
0
0
0
1
0
0
0
1
0
1
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
4
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
1
1
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
5
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
3
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
8
0
0
1
0
0
0
2
0
3
0
0
0
0
1
0
2
0
0
2
0
0
0
1
1
0
0
0
1
0
0
3
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
5
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
1
0
0
1
0
1
0
4
0
2
3
0
1
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
1
0
0
1
0
0
0
1
4
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
3
2
2
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
2
0
0
9
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
4
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
7
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
6
1
0
0
0
0
0
1
0
7
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
2
0
2
0
0
0
1
0
0
1
4
0
0
2
0
1
0
0
1
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
5
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
2
0
2
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
3
1
0
1
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
3
0
1
0
1
0
0
0
0
2
0
0
0
3
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
2
2
1
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
5
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
1
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
9
0
0
1
1
0
3
0
2
0
0
1
0
3
0
0
5
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
2
1
0
2
0
0
0
0
0
0
1
0
0
0
3
2
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
1
3
0
0
0
0
0
0
0
0
2
1
0
4
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
2
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
1
3
0
0
0
0
0
0
0
0
0
0
1
0
0
4
2
0
0
1
2
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
5
0
1
0
2
0
2
0
1
0
2
1
0
0
0
2
0
0
6
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
1
3
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
9
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
2
2
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
1
1
1
2
0
0
1
0
1
4
0
0
0
1
0
1
0
0
0
4
2
0
0
2
1
0
0
0
0
2
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
1
0
1
0
2
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
3
2
1
0
0
0
0
0
2
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
2
0
0
0
0
0
2
0
1
0
6
0
3
1
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
1
0
0
0
1
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
2
2
0
0
4
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
3
0
0
1
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
6
0
1
2
1
0
1
0
0
0
5
0
1
0
0
0
1
1
0
1
0
1
1
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
1
0
0
0
0
0
3
1
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
1
2
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
2
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
4
0
1
0
0
2
0
0
0
0
0
0
0
2
3
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
2
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
2
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
1
2
0
0
1
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
1
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
2
0
2
3
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
1
0
0
0
0
2
8
1
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
4
0
0
0
3
0
0
0
0
2
0
4
0
0
0
2
0
0
0
2
1
0
0
0
0
0
1
0
0
2
0
0
1
1
0
0
0
1
0
0
0
0
0
2
0
0
3
0
0
1
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
4
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
1
0
0
3
0
0
0
0
0
1
0
0
0
3
0
1
0
0
0
0
0
0
1
2
0
0
0
3
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
0
2
0
0
1
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
1
2
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
2
0
1
0
0
0
0
0
3
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
2
2
1
0
2
0
0
0
1
0
0
0
2
0
1
4
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
3
0
0
0
0
0
0
0
0
2
2
5
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
4
0
1
2
0
0
0
0
0
1
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
8
0
0
0
0
0
1
1
1
1
0
2
0
0
1
1
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
2
0
2
4
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
6
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
4
0
0
0
0
0
0
0
2
0
0
1
0
9
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
1
0
0
0
0
2
2
0
0
3
0
3
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
4
0
0
0
4
0
0
0
0
0
0
0
2
0
0
0
2
0
2
3
0
0
1
0
0
0
0
0
0
0
2
2
0
0
1
5
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
5
5
0
4
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
3
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
2
1
0
0
2
0
1
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
4
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
3
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
3
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
5
0
0
0
0
0
0
4
0
1
0
2
0
0
0
0
0
0
1
0
0
2
2
1
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
2
5
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
3
0
1
0
2
1
0
0
2
3
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
5
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
3
1
1
0
0
0
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
2
0
1
0
1
1
0
0
0
0
0
1
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
1
2
1
0
0
0
0
0
1
2
1
0
0
2
0
0
2
3
3
0
0
0
2
0
0
0
0
0
2
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
2
1
2
1
4
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
2
0
0
1
0
1
2
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
1
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
3
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
3
3
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
1
0
0
0
2
0
3
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
4
1
1
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
2
0
1
0
0
0
3
0
1
0
0
0
0
0
0
1
2
0
0
0
1
2
0
1
0
1
0
4
0
7
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
1
0
0
0
2
2
0
0
1
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
2
0
0
0
2
0
0
0
1
3
0
0
1
1
6
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
1
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
8
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
2
0
2
0
0
0
1
1
1
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
3
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
3
0
0
0
0
0
0
4
0
0
2
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
3
0
0
3
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
2
0
2
0
1
0
3
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
3
0
2
1
0
0
0
0
0
4
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
1
0
2
0
0
1
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
1
2
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
4
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
3
0
0
0
1
0
0
2
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
2
0
0
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
1
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
3
0
0
0
0
0
4
0
0
1
0
5
1
0
0
0
2
3
1
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
3
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
1
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
3
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
6
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
1
0
2
0
0
2
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
4
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
4
0
0
0
0
2
2
1
2
1
0
0
0
2
1
1
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
3
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
3
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
1
0
0
0
2
0
1
2
0
0
0
1
1
0
1
1
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
1
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
1
0
1
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
4
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
5
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
2
2
2
0
1
0
1
0
0
0
0
0
2
0
2
0
1
0
0
0
0
0
2
2
2
3
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
2
0
1
0
0
0
0
0
1
0
0
0
1
2
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
1
1
1
0
0
0
0
0
0
0
3
2
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
1
0
2
3
0
2
3
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
4
1
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
2
3
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
3
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
1
0
0
1
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
3
0
5
0
2
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
6
0
0
4
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
1
0
1
6
0
6
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
3
0
1
0
0
0
0
1
2
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
1
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
3
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
1
2
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
1
1
3
0
0
0
0
0
1
3
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
4
2
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
5
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
2
2
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
10
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
1
0
1
1
0
0
2
0
2
0
0
4
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
3
0
2
0
2
1
0
1
0
7
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
3
2
2
1
0
0
0
0
0
2
1
0
0
0
0
0
0
2
0
0
0
0
9
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
3
4
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
4
0
0
0
0
1
0
1
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
1
2
0
0
0
0
0
0
3
0
1
1
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
3
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
2
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
1
3
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
1
0
0
0
7
0
0
2
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
1
1
0
1
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
2
0
0
0
1
0
0
3
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
2
2
0
0
1
3
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
4
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
2
0
1
2
0
2
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
6
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
1
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
5
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
3
0
2
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
1
0
1
0
0
0
0
0
0
0
2
0
0
2
4
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
2
0
2
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
3
1
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
2
2
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
7
0
0
1
0
2
0
2
0
2
1
1
0
0
0
3
0
4
0
1
0
2
0
0
1
0
2
0
0
0
0
3
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
6
0
0
0
0
0
0
0
0
1
0
3
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
5
1
0
1
0
0
0
0
0
2
0
0
2
0
1
0
0
0
1
0
2
0
1
0
3
0
0
1
2
2
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
2
0
1
0
1
0
0
2
0
0
0
1
0
0
0
0
1
0
4
2
0
0
6
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
1
0
0
0
0
0
2
1
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
3
0
0
2
0
0
1
1
2
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
3
0
0
0
0
0
1
2
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
2
0
0
0
0
0
0
1
0
0
3
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
3
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
0
0
0
1
2
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
4
0
0
0
2
1
0
2
2
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
2
0
3
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
3
0
2
0
0
2
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
2
0
0
0
0
0
0
0
3
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
3
0
0
0
2
3
1
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
1
2
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
4
0
0
0
0
3
0
0
0
0
1
0
0
2
2
2
1
0
1
2
0
1
2
0
0
0
0
0
0
2
3
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
1
1
0
1
0
2
0
0
0
0
5
0
0
0
0
0
0
2
1
0
0
0
3
0
0
0
0
6
0
0
1
0
0
0
2
0
2
0
2
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
2
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
2
3
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
2
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
3
1
0
0
0
0
1
2
0
0
0
0
2
1
0
0
1
0
0
0
0
3
0
0
0
0
0
0
2
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
4
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
4
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
2
0
6
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
3
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
3
0
0
3
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
2
2
0
0
0
0
1
0
0
0
0
4
1
0
1
2
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
1
2
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
3
0
0
0
0
0
0
1
0
1
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
5
0
1
0
0
2
1
1
0
0
1
0
0
0
1
0
0
1
0
3
0
2
0
2
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
2
1
0
0
1
2
0
4
0
0
0
2
0
0
0
0
0
1
1
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
5
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
5
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
6
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
1
0
0
0
1
3
0
0
1
8
0
1
1
1
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
2
0
2
1
1
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
3
1
0
0
2
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
1
0
0
0
0
0
0
4
1
3
4
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
1
1
2
2
0
0
0
0
0
0
0
0
2
1
0
0
1
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
3
2
0
1
0
0
4
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
1
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
0
0
0
0
1
1
0
2
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
3
0
0
0
0
0
0
1
2
0
0
0
1
3
0
0
2
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
1
2
0
1
0
0
2
0
0
0
0
0
0
0
1
3
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
1
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
8
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
1
0
3
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
3
0
0
2
0
6
1
0
0
1
1
0
0
0
2
1
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
2
2
1
0
0
0
2
1
2
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
6
0
0
0
1
0
0
0
1
0
0
0
4
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
1
0
0
0
1
3
0
0
0
1
0
0
0
0
0
0
0
0
0
1
6
0
0
0
0
0
0
0
0
3
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
2
6
0
0
0
1
0
0
0
0
0
1
0
1
1
0
1
0
26
2
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
7
0
0
3
0
1
0
0
0
0
0
0
2
3
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
4
12
2
0
0
0
0
0
2
1
0
0
4
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
1
0
0
1
0
3
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
9
1
0
1
0
0
0
0
0
0
4
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
1
0
2
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
1
0
1
0
0
0
0
3
2
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
1
2
0
2
0
0
0
0
0
0
1
0
0
2
0
2
1
2
0
0
0
0
2
0
1
0
2
0
0
2
1
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
1
2
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
3
0
0
3
0
0
3
0
0
4
3
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
2
0
0
2
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
0
7
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
4
0
0
4
1
1
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
1
0
0
0
0
2
0
0
0
5
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
4
0
0
0
0
0
0
0
0
0
3
1
0
0
0
3
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
1
0
3
0
0
0
10
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
9
0
0
2
0
1
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
4
0
0
0
1
1
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
3
0
0
0
0
0
0
0
0
3
12
0
2
2
0
0
0
0
0
1
2
0
2
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
3
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
5
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
2
2
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
1
0
1
1
0
0
1
0
0
0
0
0
0
4
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
5
0
0
0
0
0
0
0
0
0
2
0
1
0
1
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
4
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
3
3
1
0
0
0
0
0
0
3
2
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
2
0
0
0
0
2
0
0
0
0
0
1
0
3
1
0
2
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
2
2
2
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
2
2
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
2
0
1
0
0
1
0
0
1
1
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
1
1
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
1
2
0
0
2
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
2
0
1
0
0
2
0
3
0
0
0
0
0
0
0
0
3
0
0
5
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
2
1
0
0
1
0
0
0
1
0
0
0
2
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
1
0
0
4
0
0
0
1
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
1
0
4
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
4
0
0
0
2
0
0
0
2
0
0
0
2
0
0
1
4
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
2
0
0
0
0
2
7
1
0
2
4
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
4
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
1
1
0
0
4
0
0
0
0
0
0
0
0
2
0
1
1
5
0
2
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
4
1
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
2
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
3
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
2
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
1
0
2
0
0
2
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
3
0
0
1
0
6
0
2
0
0
0
0
0
0
0
0
2
0
2
1
0
0
1
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
3
0
1
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
3
0
0
0
1
1
1
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
4
0
2
1
2
0
3
0
0
0
0
0
0
0
2
3
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
1
0
0
3
0
1
2
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
4
0
1
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
4
0
3
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
2
2
0
3
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
3
0
0
0
2
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
5
0
0
0
0
0
1
2
1
0
0
0
2
1
0
2
2
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
3
1
0
0
0
2
0
0
0
0
0
0
1
1
0
2
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
1
0
2
0
0
5
3
2
4
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
6
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
1
0
0
0
2
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
3
0
0
2
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
3
0
2
1
1
0
0
3
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
2
3
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
3
0
0
0
0
0
0
1
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
3
0
0
0
0
0
0
0
0
0
0
3
0
2
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
3
0
0
0
2
0
0
0
1
0
1
1
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
2
1
1
0
0
2
1
0
3
0
0
0
0
2
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
2
3
0
3
1
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
2
3
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
2
0
3
2
0
0
0
1
0
2
1
0
1
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
3
1
0
0
0
0
4
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
4
3
0
0
0
0
0
0
2
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
1
2
3
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
2
1
0
0
0
0
2
2
0
0
0
1
2
0
1
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
3
0
1
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
4
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
2
0
1
1
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
1
0
0
0
0
1
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
5
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
1
2
0
2
0
0
2
2
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
2
2
2
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
3
1
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
2
0
1
0
0
2
0
1
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
8
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
1
0
1
0
2
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
8
0
0
0
1
0
1
0
0
1
3
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
1
0
2
0
1
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
0
0
0
0
2
4
1
0
0
1
0
1
0
2
0
1
0
2
2
0
0
0
0
1
0
1
3
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
1
0
3
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
2
2
1
2
0
0
0
4
0
0
1
0
2
0
3
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
2
0
0
0
0
0
0
0
0
3
0
1
1
0
0
0
0
0
0
0
0
1
2
0
2
0
0
0
1
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
5
0
1
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
2
0
3
2
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
1
0
1
2
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
1
1
2
0
2
0
0
0
0
0
0
2
0
1
2
1
0
0
0
0
0
4
2
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
2
0
1
0
0
2
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
2
0
4
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
0
2
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
1
0
3
0
0
0
0
0
0
0
0
1
0
0
0
2
2
0
1
3
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
0
0
0
2
1
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
1
1
2
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
4
0
5
1
0
0
0
0
0
1
0
2
0
0
0
2
0
1
0
1
0
0
0
0
0
3
3
0
0
0
0
1
2
0
1
0
2
0
0
0
0
0
0
1
2
4
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
3
1
0
0
0
0
0
1
0
2
1
2
0
0
0
0
0
0
1
0
0
0
1
0
3
0
0
1
3
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
5
0
2
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
2
1
0
0
0
0
0
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
3
0
0
3
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
1
0
0
3
1
1
5
0
0
0
2
0
0
1
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
2
3
2
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
1
2
0
0
0
0
1
1
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
3
1
0
3
1
0
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
3
2
0
0
4
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
5
0
1
0
1
0
0
2
2
0
0
3
1
2
0
2
1
0
2
0
0
0
2
0
0
1
0
0
1
0
0
0
0
1
3
0
0
0
4
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
1
0
3
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
5
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
4
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
1
0
0
3
2
1
0
2
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
1
1
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
3
0
0
0
2
0
0
0
0
0
0
0
5
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
2
0
0
1
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
2
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
4
0
0
0
0
0
2
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
1
0
0
2
0
0
4
0
1
2
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
2
2
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
2
1
0
0
7
0
0
3
0
0
0
0
2
0
0
0
0
5
0
0
2
0
0
0
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
3
2
0
0
0
0
2
0
0
0
1
1
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
3
0
0
1
0
0
0
0
0
0
4
0
1
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
3
1
1
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
2
0
0
1
1
0
0
0
1
1
1
0
2
0
0
0
2
0
0
0
0
4
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
1
0
1
0
1
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
1
0
0
4
0
1
1
0
0
0
1
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
9
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
1
0
2
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
1
0
1
0
0
1
3
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
1
0
2
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
3
1
0
1
0
0
0
0
0
0
2
3
0
0
0
3
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
3
4
0
0
1
0
0
0
2
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
7
0
0
3
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
4
0
0
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
0
1
2
2
1
0
0
0
2
0
0
0
0
0
0
0
1
0
1
1
1
0
2
0
0
1
0
0
0
2
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
4
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
2
0
1
0
0
0
0
4
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
4
0
0
0
1
1
0
0
0
0
0
0
0
2
6
0
0
2
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
2
0
9
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
3
0
0
2
0
4
1
1
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
1
2
3
2
0
0
5
1
0
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
6
0
0
3
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
1
23
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
1
0
0
0
1
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
3
0
0
0
1
0
0
0
0
2
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
2
0
1
0
0
1
0
3
0
0
0
0
0
2
0
0
0
0
4
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
1
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
4
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
2
0
2
0
0
0
1
0
0
2
0
0
2
0
0
0
2
0
0
1
2
0
3
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
4
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
0
1
0
0
0
0
1
0
0
1
0
1
1
1
2
1
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
14
0
0
9
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
7
0
0
0
0
3
1
0
0
2
2
0
0
0
2
2
0
0
0
0
0
0
0
6
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
0
0
1
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
7
1
0
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
2
0
2
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
2
0
2
0
1
0
2
0
0
0
2
2
1
1
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
3
1
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
1
0
2
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
2
0
3
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
5
0
7
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
3
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
1
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
1
0
0
2
0
1
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
9
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
2
0
0
0
0
0
0
0
4
0
0
2
0
0
3
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
7
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
0
3
0
0
1
0
0
0
4
0
0
0
0
0
0
3
0
3
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
2
1
2
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
5
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
3
0
1
0
0
0
0
2
0
0
0
1
0
1
0
1
0
1
3
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
2
0
1
3
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
1
0
0
4
4
2
0
3
0
0
1
2
0
0
4
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
1
5
0
3
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
1
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
8
0
0
0
1
0
0
0
0
0
0
0
0
0
3
1
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
6
0
0
0
0
0
0
0
0
0
2
0
0
1
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
1
0
1
0
2
0
0
0
0
0
4
1
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
2
2
0
0
0
1
0
1
1
0
0
1
0
0
1
0
2
0
0
0
0
2
0
14
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
1
2
0
2
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
5
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
0
3
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
2
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
2
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
2
1
0
0
1
2
0
1
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
4
2
0
2
2
0
0
0
0
0
0
1
0
1
1
0
0
2
0
0
0
0
1
1
0
0
1
0
0
2
0
2
0
0
2
0
0
0
0
0
1
1
0
0
2
0
0
3
0
1
1
0
2
0
0
0
0
0
0
3
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
4
0
1
0
1
0
2
0
2
0
0
0
0
0
0
5
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
4
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
2
0
1
0
3
0
0
0
0
0
0
0
0
2
3
1
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
1
2
11
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
2
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
1
1
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
3
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
3
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
2
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
2
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
1
0
1
2
0
2
1
7
0
0
0
1
2
0
1
0
2
0
0
0
0
1
0
0
0
4
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
2
0
2
0
4
0
0
0
0
3
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
1
4
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
14
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
3
1
0
0
0
3
0
0
0
0
1
1
3
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
2
0
0
0
0
1
0
0
0
4
0
0
0
0
2
2
0
0
0
0
4
0
0
0
0
1
0
0
2
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
2
1
0
0
0
0
2
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
3
0
0
2
3
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
2
0
0
1
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
1
0
0
1
0
0
0
2
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
0
4
0
0
0
0
1
0
2
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
3
0
2
0
0
3
0
0
2
0
3
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
1
0
0
0
4
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
3
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
0
0
0
0
1
0
0
2
2
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
1
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
2
1
0
0
1
1
2
0
0
1
0
0
0
0
1
0
0
0
1
2
0
4
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
0
0
0
2
0
0
2
1
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
1
0
0
0
5
0
0
0
0
1
0
0
0
0
1
1
0
0
0
4
0
1
5
0
0
5
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
2
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
8
0
0
0
0
0
6
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
2
0
0
2
0
1
7
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
5
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
5
2
0
0
0
0
2
0
1
0
0
1
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
1
0
1
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
4
1
0
0
1
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
6
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
2
0
0
0
1
1
0
0
0
0
0
2
2
2
1
0
1
0
0
0
1
0
3
2
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
3
1
1
0
0
1
2
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
2
1
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
3
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
2
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
5
0
0
3
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
9
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
9
0
0
0
0
0
0
0
1
2
0
0
0
1
0
0
1
2
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
3
0
0
1
0
0
2
0
0
0
2
0
0
0
5
0
0
10
0
0
1
0
0
1
0
0
3
0
0
0
1
0
1
0
0
0
5
0
2
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
2
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
2
1
0
0
0
0
1
0
0
3
0
0
0
2
4
0
0
5
0
0
0
0
0
0
0
0
0
0
3
2
1
10
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
12
0
0
0
1
0
0
1
0
0
2
0
0
2
3
2
0
0
0
0
0
0
1
0
0
0
0
2
2
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
2
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
4
0
2
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
2
0
1
1
0
0
2
0
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
2
1
0
2
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
1
1
0
2
0
4
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
2
2
0
0
0
0
0
2
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
1
0
2
0
0
0
2
0
5
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
3
0
0
0
0
0
0
3
0
4
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
1
3
1
2
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
3
0
1
0
0
0
0
0
2
0
1
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
1
1
0
1
1
3
1
0
1
0
0
1
0
0
1
0
0
0
0
3
0
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
1
0
1
0
3
2
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
2
1
2
1
0
0
0
2
0
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
2
1
0
1
3
0
0
0
0
0
0
0
0
0
0
8
0
3
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
3
0
1
0
0
0
1
1
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
2
0
1
0
0
1
0
0
0
0
2
1
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
3
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
2
0
0
1
2
0
0
3
0
0
0
1
0
0
2
1
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
8
0
0
0
1
1
0
0
0
2
2
19
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
4
3
0
1
1
0
0
0
0
0
0
0
1
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
1
0
4
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
5
2
0
2
0
8
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
1
0
1
0
0
0
1
1
1
0
0
0
0
0
2
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
1
0
0
0
0
2
0
2
0
0
0
0
1
2
2
0
0
0
0
2
0
0
0
0
0
0
7
0
0
0
0
0
0
0
0
1
1
0
0
2
0
0
1
2
1
0
0
2
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
1
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
2
0
0
0
0
0
0
0
0
1
3
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
2
0
0
0
2
0
0
2
0
2
0
0
0
1
0
1
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
3
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
4
1
0
0
0
2
0
2
0
1
0
1
3
0
0
0
0
1
0
0
0
2
0
0
2
0
1
0
1
0
2
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
1
0
0
0
0
2
0
0
2
0
0
0
0
1
0
0
2
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
3
0
2
2
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
1
0
1
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
2
0
0
1
0
0
0
0
0
0
2
1
0
1
0
0
2
3
1
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
2
1
2
0
2
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
3
0
1
1
0
0
0
0
1
0
0
0
0
1
5
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
5
0
0
2
0
0
1
1
1
1
0
0
0
0
0
0
0
0
1
2
0
1
0
0
2
0
0
1
1
1
3
0
0
4
0
0
0
0
0
0
2
1
1
0
2
0
0
1
0
0
0
5
0
0
1
0
0
1
2
0
0
0
0
1
1
1
0
0
4
0
0
0
2
0
0
0
0
0
2
0
0
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
2
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
3
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
3
0
0
1
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
6
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
2
0
2
0
1
0
2
0
1
0
0
3
1
3
1
2
1
0
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
7
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
2
0
0
0
0
0
0
0
9
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
10
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
2
1
1
0
0
1
1
0
0
2
0
0
0
0
2
2
1
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
3
1
0
1
0
0
0
3
0
3
0
1
0
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
2
0
0
1
0
0
2
0
0
0
0
2
1
1
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
6
1
0
1
0
0
0
0
0
2
0
0
1
0
3
0
1
0
0
0
0
0
1
0
0
0
3
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
2
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
0
1
0
0
1
2
0
0
2
0
1
0
2
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
2
0
0
3
0
4
0
0
0
5
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
5
0
0
0
1
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
0
3
2
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2
0
1
1
0
0
2
0
0
1
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
1
0
0
1
0
0
1
1
0
0
0
0
2
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
4
0
0
0
1
0
5
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
2
0
0
2
0
0
0
0
1
0
0
0
0
7
0
1
1
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
2
0
3
1
0
0
0
1
3
2
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
6
2
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
2
0
1
0
3
1
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
3
0
1
3
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
2
0
0
2
2
0
0
0
0
0
7
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
3
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
4
3
1
0
1
2
2
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
2
2
0
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
7
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
3
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
2
0
0
0
1
6
0
0
0
0
0
0
2
0
0
2
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
4
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
0
0
1
2
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
1
5
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
4
1
1
0
3
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
2
0
3
0
0
1
1
0
1
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
3
0
0
0
0
0
1
3
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
3
1
1
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
10
0
2
0
0
0
0
1
0
0
4
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
2
2
0
0
0
0
4
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
2
0
0
0
0
1
1
0
1
0
0
0
6
0
0
0
0
0
0
0
2
0
0
2
0
1
1
0
0
2
0
0
0
0
0
0
0
0
3
5
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
2
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
8
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
3
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
9
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
5
2
3
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
2
2
3
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
1
1
0
0
0
2
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
1
5
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
1
0
2
0
0
0
3
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
4
1
0
0
0
0
2
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
2
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
1
0
2
1
0
0
2
0
1
0
0
0
0
3
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
3
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
3
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
3
2
0
0
9
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
0
0
0
2
0
0
1
0
0
1
1
1
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
3
2
1
0
0
0
1
1
0
1
0
0
0
3
0
0
0
0
0
1
2
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
2
0
2
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
3
1
0
0
0
0
4
1
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
2
0
0
0
0
2
1
2
0
0
0
0
7
2
0
0
0
0
0
2
0
0
0
0
0
3
1
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
3
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
2
0
1
0
0
0
0
0
1
0
0
2
3
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
2
0
2
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
5
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
6
0
0
0
1
2
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
1
1
3
0
1
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
3
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
2
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
6
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
3
0
2
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
8
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
4
0
0
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
3
0
2
0
0
1
1
0
1
1
1
0
2
0
0
0
0
0
0
0
0
2
2
0
2
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
2
0
0
0
0
5
0
4
0
2
2
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
4
1
1
0
3
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
1
0
1
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
4
0
4
0
0
0
0
0
0
0
0
1
0
0
2
2
0
0
0
0
0
3
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
2
0
1
0
0
1
0
3
1
0
0
1
0
0
0
0
0
0
0
0
0
0
3
2
1
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
2
0
4
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
6
1
1
0
0
1
0
1
1
0
1
0
0
2
1
2
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
6
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
3
2
0
0
0
3
1
0
0
0
0
0
0
3
3
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
1
1
0
0
0
2
0
0
0
3
0
0
0
0
0
0
0
0
6
0
0
4
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
2
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
3
3
0
0
0
0
0
0
0
0
1
2
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
1
1
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
6
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
1
0
0
4
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
1
0
8
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
1
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
1
1
0
2
0
1
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
6
0
0
2
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
2
3
0
0
0
0
0
0
0
0
0
3
0
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
2
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
3
0
0
0
1
1
0
3
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
7
2
0
0
0
3
2
0
1
2
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
5
0
0
0
0
0
0
0
3
1
0
0
0
0
1
0
0
0
0
3
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
2
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
1
0
0
2
1
0
4
1
1
0
0
0
0
0
0
0
1
0
3
0
0
0
2
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
2
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
2
2
0
0
0
0
0
0
0
3
0
0
0
0
0
1
1
0
1
1
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
4
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
3
3
0
0
3
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
4
8
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
6
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
2
0
0
17
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
7
1
0
0
0
0
1
0
0
1
0
0
2
0
2
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
2
0
0
0
0
1
2
1
2
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
4
0
0
2
0
1
0
1
1
0
2
0
0
2
0
0
0
0
2
1
0
2
0
0
2
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
3
1
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
2
2
0
0
0
1
1
0
0
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
7
0
0
0
0
3
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
2
0
0
0
0
0
0
1
1
0
1
1
0
2
0
0
0
0
0
0
0
3
2
0
0
0
0
0
2
0
0
0
1
1
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
4
0
0
2
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
3
0
0
2
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
2
0
0
0
0
0
1
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
10
0
1
2
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
8
3
0
0
0
1
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
3
1
2
2
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
2
0
0
2
0
3
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
1
0
1
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
3
0
0
1
0
0
0
0
0
0
3
0
0
1
2
0
0
0
0
0
0
0
0
0
0
1
1
2
0
0
3
0
0
0
0
0
1
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
2
0
0
3
1
0
0
0
0
1
0
0
0
0
0
1
2
0
1
0
0
0
2
0
0
1
0
0
1
0
2
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
2
2
0
0
0
0
0
0
0
0
0
2
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7
1
0
0
1
0
0
0
0
0
2
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
3
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
8
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
2
0
1
0
5
0
0
1
0
0
0
0
5
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
2
3
0
0
2
0
0
1
0
0
1
0
0
0
0
0
3
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
3
2
0
0
0
0
0
2
1
2
0
1
0
0
0
0
2
2
1
0
1
0
0
0
1
0
0
0
1
2
0
0
5
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
1
1
2
1
2
0
0
0
2
0
0
0
0
0
2
1
2
0
1
1
0
1
0
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
2
2
0
0
0
2
0
2
2
0
2
0
0
4
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
0
2
0
0
2
2
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
1
0
2
0
0
0
2
0
0
1
0
0
1
0
0
7
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
2
0
1
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
1
0
2
0
0
1
1
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
1
0
0
0
0
0
2
3
0
0
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
7
0
2
2
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
3
0
2
1
0
3
0
0
0
0
0
1
0
0
0
0
4
0
0
0
1
0
0
0
0
0
2
2
0
1
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
2
0
0
0
0
0
2
0
0
0
2
0
2
1
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
3
1
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
2
0
0
0
0
0
1
0
2
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
2
0
3
0
0
0
0
3
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
3
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
2
0
0
1
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
0
0
0
0
3
0
0
0
1
0
1
0
2
0
0
0
0
0
2
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
3
0
0
0
0
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
2
2
2
2
0
0
0
0
2
0
4
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
3
2
0
0
0
0
0
2
1
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
2
2
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
3
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
2
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
2
0
0
0
0
0
0
2
4
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
2
1
0
0
0
0
0
2
0
0
0
2
0
5
0
0
0
2
0
0
3
0
2
5
1
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
1
0
0
0
0
0
3
2
0
0
2
0
0
2
0
1
2
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
5
1
0
2
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
2
1
1
2
0
0
0
0
2
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
0
2
0
0
3
1
0
1
0
0
2
0
0
1
0
0
4
0
0
0
2
0
0
3
1
0
0
0
0
2
0
0
2
0
0
0
0
1
3
2
0
0
1
0
0
8
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
1
2
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
2
0
1
6
0
0
3
0
0
0
0
0
0
0
0
0
0
1
3
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
2
0
0
2
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
2
0
1
0
1
0
2
2
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
3
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
2
0
1
0
0
0
2
2
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
3
0
0
0
1
0
0
0
1
0
0
0
0
4
0
1
3
1
0
0
0
0
0
0
2
0
0
0
2
1
1
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
5
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
2
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
2
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
1
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
2
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
2
0
4
2
1
0
0
0
0
3
0
0
0
0
0
0
0
2
0
0
2
0
1
2
0
0
0
1
1
2
0
3
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
2
0
1
0
0
0
0
0
0
0
0
0
0
2
4
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
11
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
3
1
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
1
0
2
0
0
0
0
0
2
4
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
2
0
2
0
2
0
1
0
2
0
0
0
0
0
0
1
2
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
0
0
0
1
0
2
0
0
0
0
0
2
0
2
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
2
0
1
0
2
0
0
0
0
1
0
0
0
2
0
0
0
1
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
1
0
0
0
6
0
0
0
0
1
0
3
0
0
1
0
0
1
1
0
0
3
0
0
1
0
0
0
0
0
2
0
0
4
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
1
4
3
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
8
0
0
0
0
0
0
2
2
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
2
0
2
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
5
0
2
2
1
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
2
3
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
2
2
0
0
1
0
5
2
0
0
1
0
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
2
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
1
0
4
0
0
2
0
0
0
2
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
1
0
2
0
0
1
0
1
2
2
0
0
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
2
3
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
2
3
1
0
0
3
1
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
2
0
0
0
2
1
0
0
0
1
0
0
0
2
0
0
1
2
0
0
0
2
0
0
1
0
0
0
0
0
15
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
3
0
0
0
0
5
0
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
2
1
0
2
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
2
0
5
0
2
0
1
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
1
4
2
2
0
0
3
0
0
1
0
2
0
0
0
0
0
0
3
0
0
2
0
1
0
2
0
0
0
0
0
0
2
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
2
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
2
1
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
2
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
1
0
0
4
0
0
3
1
0
0
0
2
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
1
0
0
0
0
5
2
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
5
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
6
1
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
3
0
0
3
1
3
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
5
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
1
0
2
0
2
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
1
0
0
7
0
0
2
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
2
0
7
1
1
0
0
0
1
0
0
2
0
1
0
0
0
0
0
0
1
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
2
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
0
2
0
0
0
0
0
2
1
0
0
2
0
2
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
1
2
0
0
0
1
0
1
2
0
0
0
0
3
0
0
0
0
0
1
0
2
0
3
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
2
1
1
1
0
0
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
3
1
0
0
0
0
0
0
0
1
1
0
1
0
0
13
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
2
7
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
3
0
0
0
0
0
2
0
0
0
0
0
2
0
4
0
0
0
0
0
0
0
0
2
0
1
0
0
2
0
1
0
2
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
3
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
2
2
0
0
0
0
0
1
0
0
0
0
0
7
0
0
0
0
0
0
0
1
0
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
1
0
0
2
0
0
0
0
0
1
0
0
2
1
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
2
1
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
2
0
0
0
0
0
2
1
0
9
0
0
0
4
0
2
0
0
0
2
0
0
0
0
2
0
0
2
0
0
0
1
3
0
2
2
2
0
0
0
0
1
4
0
2
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
2
0
0
1
0
2
2
2
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
1
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
2
0
2
0
0
0
4
0
0
0
0
0
3
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
2
0
2
0
0
0
0
0
0
0
2
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
2
0
0
0
1
0
0
1
0
2
0
0
2
0
1
0
0
1
2
1
0
1
0
1
0
0
0
3
0
0
2
8
0
0
0
0
0
0
0
0
0
0
0
0
1
0
3
0
1
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
2
0
1
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
2
3
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
1
3
1
0
0
1
0
0
0
2
0
0
4
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
1
0
0
1
2
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
2
0
0
3
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
2
3
1
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
4
1
1
1
1
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
2
0
1
0
0
1
0
3
0
0
1
0
0
0
0
0
0
0
0
0
0
9
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
5
0
0
0
0
2
0
0
0
0
4
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
2
0
1
1
1
0
0
0
0
3
0
0
0
1
0
1
0
0
7
0
1
0
0
0
0
1
0
1
0
1
0
0
0
5
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
3
2
1
0
0
0
0
0
0
0
0
2
0
1
0
0
3
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
4
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
5
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
6
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
1
0
0
3
0
2
0
2
4
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
1
1
0
0
0
2
0
1
0
1
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
1
0
1
0
0
3
0
0
0
0
0
1
0
0
0
3
0
0
0
2
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
3
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
2
1
2
0
0
1
0
0
0
1
0
2
1
0
0
1
0
0
0
0
0
2
1
2
0
0
2
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
3
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
6
0
0
2
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
2
0
2
0
1
1
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
2
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
2
2
0
2
0
0
1
0
1
0
0
0
0
1
2
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
2
2
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
0
0
2
4
0
2
1
4
0
1
2
0
0
0
0
0
3
0
0
1
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
1
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
2
0
0
4
0
1
0
0
0
0
0
1
1
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
5
2
2
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
4
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
2
0
0
1
0
0
0
1
1
0
1
0
0
2
1
3
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
3
0
0
0
0
0
2
0
2
1
0
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
2
0
0
1
0
0
1
0
0
0
2
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
2
0
0
1
0
0
1
2
0
0
0
0
0
1
2
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
2
0
0
0
1
0
1
0
0
1
0
0
0
0
0
6
0
0
0
0
2
0
0
0
2
0
0
0
3
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
3
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
2
0
4
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
2
0
0
0
1
0
0
2
2
0
0
4
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
2
0
3
0
0
0
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
7
0
1
0
0
0
0
0
2
0
0
0
0
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
1
2
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
2
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
4
0
1
0
2
0
0
2
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
41
0
5
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
2
2
0
0
1
0
0
0
0
2
1
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
2
2
0
0
2
2
1
0
0
2
3
0
0
0
0
0
0
0
2
0
0
1
1
0
0
2
0
0
0
0
0
0
0
0
0
4
1
0
2
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
2
0
2
1
0
0
0
1
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
6
2
0
1
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
0
2
2
0
2
0
0
0
0
0
0
0
0
0
0
0
3
2
0
4
0
0
0
1
1
0
0
1
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
5
0
0
0
0
1
2
0
0
0
1
0
0
0
3
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
1
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
3
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
1
1
0
0
2
0
1
0
0
0
1
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
2
2
0
0
2
1
1
0
0
0
0
0
4
0
2
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
1
2
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
6
0
0
1
0
1
0
0
0
1
0
4
0
0
0
0
0
1
4
1
0
0
1
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
1
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
2
0
0
0
0
0
1
2
2
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
2
0
0
2
0
0
0
0
0
1
1
0
0
0
3
0
0
1
0
0
0
0
0
0
1
1
0
1
2
5
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
2
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
1
2
0
3
0
0
1
0
0
0
0
0
2
2
0
0
0
2
0
0
0
2
0
0
0
3
0
1
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
2
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
4
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
1
0
2
2
3
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
1
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
5
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
2
0
0
0
1
0
0
0
1
2
0
0
0
2
0
2
0
0
2
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
2
1
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
4
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
2
1
1
0
0
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
2
0
2
0
3
0
0
0
0
0
0
0
0
1
0
2
0
0
1
2
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
1
0
0
2
2
0
0
5
0
2
2
0
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
1
0
3
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
2
0
0
0
2
1
15
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
1
0
2
2
0
0
0
0
1
0
0
0
2
1
0
0
0
0
0
0
3
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
3
0
2
0
3
2
0
0
0
0
0
4
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
2
1
0
0
0
0
0
0
0
0
0
2
0
0
7
0
0
2
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
2
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
3
0
1
2
0
0
1
0
0
0
3
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
2
1
0
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
3
0
0
0
0
1
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
2
0
1
1
1
0
1
0
0
0
1
1
0
3
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
3
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
2
0
0
1
1
0
0
0
1
0
0
0
0
1
2
0
0
0
4
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
4
1
2
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
3
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
2
2
0
1
0
1
1
1
1
1
0
0
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
2
1
1
2
2
0
0
1
0
0
2
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
0
0
0
0
0
1
0
0
0
0
0
0
1
0
2
1
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
2
0
2
1
0
2
0
1
0
1
0
0
2
0
0
0
3
2
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
2
2
2
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
1
0
0
0
4
0
2
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
5
0
0
0
0
0
0
1
1
0
0
0
0
0
1
2
2
2
0
0
0
0
0
0
1
0
0
0
6
0
0
0
0
2
0
0
2
0
1
0
0
1
0
4
0
0
0
0
1
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
1
2
0
2
2
0
0
2
0
1
0
0
0
3
0
0
0
3
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
2
0
2
0
0
0
0
2
0
0
0
0
0
2
1
0
0
0
0
0
0
0
0
0
1
1
0
2
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
2
2
3
2
0
0
0
0
0
0
0
0
0
0
1
0
0
0
4
2
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
0
1
0
0
2
0
1
0
2
2
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
6
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
1
0
2
0
4
1
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
2
0
3
1
0
0
0
0
2
0
0
1
0
0
3
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
2
0
2
0
0
0
0
0
2
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
3
0
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
1
0
0
2
1
2
2
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
3
2
1
0
0
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
0
2
0
1
0
0
1
0
0
0
0
0
3
0
0
2
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
1
0
0
0
0
1
0
0
4
2
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
2
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
2
0
0
1
1
0
0
2
0
1
1
0
0
1
0
0
0
0
0
0
0
2
1
0
0
0
0
1
0
2
0
1
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
0
0
0
0
0
0
1
0
0
2
2
1
0
0
0
2
0
0
0
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
2
1
0
0
0
2
1
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
3
0
0
1
2
2
0
1
1
0
0
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
4
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
2
2
0
1
0
1
0
0
0
0
0
2
2
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
2
0
5
0
0
0
2
0
1
0
3
3
0
1
0
0
0
0
0
2
0
0
1
0
0
0
2
0
0
0
0
0
2
0
1
2
0
0
0
0
0
0
4
0
1
0
0
0
0
0
0
0
2
2
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
1
2
0
4
0
0
2
0
3
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
1
0
0
1
0
1
0
0
2
1
0
1
0
0
0
0
0
2
0
1
0
2
0
0
0
0
0
4
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
1
0
0
0
0
5
0
0
0
0
2
0
0
1
1
0
0
1
0
0
2
2
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
2
3
2
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
6
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
1
0
0
0
0
0
0
2
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
2
0
0
0
2
0
0
0
0
0
0
5
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
2
0
2
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
1
0
1
0
0
0
0
0
6
0
0
2
0
0
1
0
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
2
0
0
0
1
1
0
0
0
0
0
0
3
0
0
0
0
0
0
0
0
1
0
0
0
3
0
2
0
0
2
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
3
0
0
0
0
0
2
2
0
1
1
0
0
0
1
0
0
0
2
0
1
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
5
0
0
0
1
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
1
0
2
0
2
0
0
3
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
2
0
1
0
0
1
0
0
3
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
3
1
3
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
2
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
2
1
2
0
0
1
0
0
0
1
0
1
0
0
0
2
0
2
0
0
2
0
0
0
0
2
0
0
2
6
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
1
2
0
0
0
0
0
0
0
3
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
1
0
2
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
2
6
0
0
0
0
1
0
0
0
1
0
0
1
1
1
3
1
0
0
0
0
0
0
2
1
0
1
0
0
0
1
0
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
4
0
0
0
0
0
0
0
0
0
0
0
4
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
2
2
0
0
0
0
2
10
0
0
1
0
1
0
1
0
0
4
0
0
2
1
0
0
0
1
2
0
0
0
0
0
0
0
0
0
0
0
3
2
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
0
2
0
0
2
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
2
0
0
0
2
0
1
0
0
0
0
0
0
0
2
0
2
0
0
3
0
0
1
1
0
0
0
0
4
1
0
0
0
0
0
3
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
1
0
2
0
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
2
0
0
0
0
1
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
2
2
0
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
2
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
7
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
1
2
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
2
1
0
2
0
2
0
0
1
0
3
0
1
0
0
0
0
3
0
0
0
0
0
1
0
4
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
6
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
4
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
2
1
0
0
1
0
0
0
0
0
0
1
0
0
0
2
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
2
2
0
0
0
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
2
0
0
0
0
0
0
3
1
0
0
0
0
0
0
1
2
0
0
0
0
0
2
0
0
1
0
0
3
0
0
0
0
2
0
1
1
0
0
0
0
0
0
3
1
2
0
0
0
0
0
0
0
7
0
0
0
0
0
2
0
0
1
0
0
0
0
1
0
0
0
2
0
0
0
0
0
1
0
0
0
2
2
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
1
1
1
0
0
0
2
0
0
0
0
0
0
1
3
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
2
0
0
0
0
0
0
0
2
0
0
1
2
1
3
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
2
0
3
0
0
2
0
0
1
0
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
4
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
2
0
1
1
0
5
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
1
0
0
1
0
0
2
1
0
0
1
0
0
0
0
0
0
1
0
1
0
2
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
2
1
2
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
2
0
0
1
0
1
0
0
0
0
2
0
1
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
0
4
0
3
0
1
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
1
2
2
2
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
5
1
0
1
0
0
0
0
0
1
0
2
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
1
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
2
0
0
3
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
2
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
2
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
2
0
0
2
0
0
0
2
0
0
1
0
0
0
0
0
0
1
0
2
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
3
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
2
0
1
1
0
0
0
0
0
3
0
0
0
1
0
2
0
0
0
0
1
0
0
1
0
0
0
2
0
0
0
1
1
0
2
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
2
4
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
2
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
3
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
1
4
0
0
2
0
0
0
2
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
4
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
1
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
1
1
1
0
0
2
0
1
0
1
1
3
0
0
2
2
0
0
0
0
3
0
2
0
0
2
0
1
0
0
0
0
1
0
0
0
2
1
1
1
0
0
0
1
0
0
2
0
0
0
1
0
0
1
0
0
0
0
0
1
2
1
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
1
2
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
5
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
2
2
0
2
0
1
0
2
1
4
0
0
0
3
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
1
0
0
0
0
0
0
1
2
2
0
0
1
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
2
0
0
2
0
0
0
1
0
8
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
2
1
7
0
0
4
0
0
0
0
1
1
0
2
1
0
0
0
0
0
0
1
0
0
2
0
1
0
2
0
0
2
0
0
0
0
0
0
1
0
0
0
0
2
2
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
2
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
0
0
0
0
0
0
0
1
0
0
6
0
0
0
0
0
0
0
4
1
0
0
0
2
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
4
1
0
0
0
0
0
0
0
0
0
0
0
0
1
2
3
2
0
0
0
2
1
1
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
2
0
0
4
0
0
0
0
0
1
0
0
0
0
0
0
1
0
4
0
1
3
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
1
0
1
0
2
1
0
4
0
0
0
0
0
0
0
0
0
0
0
1
2
0
0
1
3
0
0
2
1
0
4
2
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
1
0
0
0
0
0
0
0
0
3
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
1
2
0
0
0
0
1
2
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
2
0
0
0
0
0
1
0
0
0
0
0
0
0
3
0
0
2
1
0
0
0
0
0
2
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
3
0
0
0
2
2
0
0
0
0
1
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
2
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
2
0
0
2
0
0
2
0
4
0
1
0
2
0
0
0
0
0
1
0
2
0
0
2
0
2
0
1
2
0
0
0
2
0
0
5
1
0
0
0
0
0
0
0
0
1
0
0
0
2
0
0
0
1
0
0
0
2
10
0
0
0
2
0
2
0
0
4
0
0
0
1
0
0
2
0
0
2
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
2
0
4
0
1
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
3
0
0
0
0
3
0
0
0
0
1
0
0
3
1
0
0
0
0
0
0
0
2
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
2
1
0
0
2
0
0
3
0
0
3
1
0
0
0
1
0
0
0
0
2
0
0
0
0
0
0
0
0
0
1
0
0
2
0
2
0
0
0
0
0
0
2
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
2
2
0
0
0
0
0
0
0
0
1
0
3
0
0
0
0
2
0
2
0
1
1
2
0
0
2
0
0
0
0
0
0
0
0
0
0
2
0
2
0
0
2
0
0
0
0
0
0
0
0
0
0
0
2
1
0
0
0
0
0
1
0
0
0
3
0
2
0
0
1
0
2
0
1
0
0
0
4
0
0
0
0
0
0
0
0
0
0
0
1
0
2
0
0
0
3
0
1
0
10
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
2
0
0
0
4
0
2
0
2
1
0
1
0
2
0
0
0
1
1
2
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
2
0
0
1
0
0
1
0
0
0
0
1
3
0
2
0
0
0
0
2
0
0
1
1
1
0
0
0
0
0
0
0
0
0
2
0
0
1
0
0
1
0
0
2
2
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
2
0
3
1
0
0
1
1
0
2
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
0
0
0
0
0
2
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
2
1
0
0
1
0
0
0
0
0
3
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
2
0
0
0
0
1
0
0
0
0
0
0
0
3
0
4
0
0
0
0
0
0
0
0
0
0
0
2
0
0
0
2
0
0
0
0
0
0
0
0
2